Taxpayer Confusion over Predictable Tax Liability Changes: Evidence from the Child Tax Credit

Naomi E. Feldman, Peter Katuscak, and Laura Kawano

Figure 1: Labor Income Elasticity

credit	All Households	30-50K Households	50-70K Households
100	3.054707	4.931825	2.616922
101	3.024443	4.882939	2.590996
102	2.994773	4.835013	2.565559
103	2.965657	4.787992	2.540636
104	2.937123	4.741902	2.516174
105	2.909113	4.696667	2.492196
106	2.881631	4.65231	2.468653
107	2.854684	4.60876	2.445551
108	2.828217	4.566017	2.422895
109	2.802255	4.524084	2.400638
110	2.776746	4.48289	2.378802
111	2.751698	4.44244	2.357344
112	2.727097	4.402713	2.336269
113	2.702951	4.363713	2.315568
114	2.67921	4.325376	2.295246
115	2.655884	4.287706	2.275262
116	2.632959	4.250687	2.255624
117	2.610427	4.214302	2.236321
118	2.588294	4.178514	2.217346
119	2.566517	4.143349	2.19869
120	2.545104	4.10877	2.18036
121	2.524044	4.074765	2.162319
122	2.50333	4.041317	2.144574
123	2.482954	4.008395	2.127118
124	2.462906	3.976024	2.109944
125	2.44318	3.944154	2.093045
126	2.423767	3.912808	2.076401
127	2.404646	3.881939	2.060033
128	2.385839	3.85157	2.043921
129	2.367323	3.821656	2.028059
130	2.349092	3.792219	2.012441
131	2.33114	3.763217	1.997062
132	2.313447	3.734654	1.981916
133	2.296034	3.706522	1.966987
134	2.278881	3.678811	1.952292
135	2.261982	3.651526	1.937815
136	2.24532	3.624628	1.923551
137	2.228913	3.598123	1.909485
138	2.212733	3.572003	1.895634
139	2.196797	3.546245	1.881972
140	2.18109	3.52087	1.868516
141	2.165594	3.495856	1.85525
142	2.150328	3.471194	1.842162
143	2.135264	3.446878	1.829267
144	2.12041	3.422887	1.816542
145	2.105772	3.399241	1.804002
146	2.091325	3.375919	1.791624
147	2.077084	3.352903	1.779425
148	2.063026	3.33021	1.767381
149	2.049157	3.307811	1.755499
150	2.035483	3.28571	1.743785
151	2.021981	3.263916	1.732217
152	2.008656	3.242396	1.720802
153	1.995506	3.221158	1.709545
154	1.982527	3.200208	1.698425
155	1.969725	3.179518	1.68745
156	1.957078	3.159093	1.676615
157	1.944593	3.13893	1.665919
158	1.932265	3.119021	1.655366
159	1.920093	3.099364	1.644938
160	1.908074	3.079953	1.634641
161	1.896204	3.060784	1.624471
162	1.88448	3.041852	1.614428
163	1.872901	3.023142	1.604508
164	1.861464	3.004671	1.594709
165	1.850165	2.986424	1.585029
166	1.839002	2.968388	1.575466
167	1.827973	2.950578	1.566018
168	1.817068	2.932981	1.556682
169	1.8063	2.915583	1.547457
170	1.795659	2.898399	1.538333
171	1.785143	2.881407	1.529324
172	1.774741	2.864614	1.520419
173	1.764467	2.848024	1.511618
174	1.754312	2.831616	1.502917
175	1.744265	2.815396	1.49431
176	1.734341	2.799361	1.485807
177	1.724528	2.783507	1.477401
178	1.714819	2.767841	1.469082
179	1.705225	2.752342	1.460864
180	1.695732	2.737015	1.452736
181	1.68635	2.721849	1.444693
182	1.677065	2.706859	1.436744
183	1.667881	2.692033	1.428876
184	1.658804	2.677369	1.421099
185	1.649819	2.662863	1.413401
186	1.640937	2.648514	1.405792
187	1.632144	2.634311	1.398259
188	1.623444	2.620267	1.390811
189	1.614844	2.606364	1.383437
190	1.606327	2.592616	1.37614
191	1.5979	2.579004	1.368926
192	1.589561	2.565542	1.361781
193	1.581308	2.552213	1.354711
194	1.573147	2.539021	1.347719
195	1.565063	2.525972	1.340794
196	1.557062	2.51305	1.333939
197	1.549143	2.500259	1.327154
198	1.541303	2.487597	1.320438
199	1.533543	2.475063	1.313789
200	1.52586	2.462655	1.307212
201	1.518254	2.450371	1.300696
202	1.510724	2.438208	1.294244
203	1.503267	2.426166	1.287856
204	1.495879	2.414242	1.28153
205	1.488568	2.402434	1.275267
206	1.481328	2.390742	1.269064
207	1.474159	2.379156	1.262921
208	1.467058	2.367689	1.256838
209	1.460026	2.356332	1.250813
210	1.453055	2.345076	1.244841
211	1.446156	2.333934	1.23893
212	1.439322	2.322891	1.233075
213	1.432547	2.311959	1.227275
214	1.425841	2.301122	1.221529
215	1.419192	2.290393	1.215833
216	1.41261	2.279757	1.210194
217	1.406089	2.26922	1.204606
218	1.399622	2.25878	1.199066
219	1.39322	2.248435	1.193581
220	1.386872	2.23819	1.188146
221	1.380585	2.228033	1.182756
222	1.374351	2.217967	1.177419
223	1.368173	2.207992	1.172125
224	1.362054	2.198106	1.166883
225	1.355986	2.188303	1.161688
226	1.349971	2.178593	1.156535
227	1.344014	2.168968	1.151427
228	1.338105	2.159428	1.146368
229	1.332248	2.149966	1.14135
230	1.326441	2.140592	1.136379
231	1.320685	2.131299	1.131447
232	1.314983	2.122081	1.126559
233	1.309326	2.112948	1.121715
234	1.303718	2.103889	1.11691
235	1.298157	2.094911	1.112146
236	1.292643	2.086005	1.107422
237	1.287176	2.077174	1.102741
238	1.281755	2.068423	1.098097
239	1.27638	2.05974	1.093491
240	1.271049	2.05113	1.088924
241	1.265763	2.042591	1.084395
242	1.260521	2.034123	1.079903
243	1.255322	2.025726	1.075449
244	1.250161	2.017397	1.071031
245	1.245047	2.009136	1.066649
246	1.239974	2.000943	1.062303
247	1.234943	1.992817	1.057992
248	1.229952	1.984756	1.053716
249	1.224998	1.976755	1.049475
250	1.220087	1.968824	1.045267
251	1.215216	1.960955	1.041093
252	1.210379	1.953145	1.036952
253	1.205585	1.945401	1.032841
254	1.200824	1.937714	1.028766
255	1.196105	1.930092	1.024722
256	1.191419	1.922526	1.020711
257	1.186773	1.915022	1.01673
258	1.18216	1.907573	1.012777
259	1.177586	1.900182	1.008858
260	1.173044	1.892847	1.004967
261	1.16854	1.885573	1.001108
262	1.164067	1.878351	0.9972785
263	1.159629	1.871184	0.9934754
264	1.155227	1.864071	0.9897041
265	1.150855	1.857013	0.9859584
266	1.146517	1.850007	0.9822438
267	1.142214	1.843054	0.9785543
268	1.13794	1.83615	0.9748952
269	1.133698	1.8293	0.9712606
270	1.129487	1.822502	0.967653
271	1.125308	1.815754	0.9640749
272	1.121159	1.809052	0.9605203
273	1.117041	1.802403	0.9569919
274	1.112953	1.795802	0.953492
275	1.108895	1.789247	0.9500149
276	1.10487	1.782742	0.9465631
277	1.100867	1.776281	0.9431363
278	1.096897	1.769867	0.9397368
279	1.092955	1.763502	0.9363592
280	1.089041	1.75718	0.9330058
281	1.085155	1.750903	0.9296762
282	1.081296	1.74467	0.9263704
283	1.077466	1.738485	0.923088
284	1.073662	1.73234	0.9198287
285	1.069882	1.726239	0.9165924
286	1.066131	1.72018	0.9133788
287	1.062407	1.714164	0.9101877
288	1.058708	1.70819	0.9070187
289	1.055033	1.702254	0.9038718
290	1.051385	1.696362	0.9007466
291	1.04776	1.690511	0.897643
292	1.044163	1.6847	0.8945606
293	1.04059	1.678926	0.8914994
294	1.037039	1.673194	0.8884567
295	1.033515	1.667502	0.885437
296	1.030012	1.661845	0.8824378
297	1.026535	1.656229	0.8794588
298	1.023079	1.650648	0.8764976
299	1.019646	1.645104	0.8735585
300	1.016239	1.639601	0.8706391
301	1.012852	1.634131	0.8677369
302	1.009487	1.628698	0.8648562
303	1.006148	1.6233	0.8619924
304	1.002827	1.617942	0.8591496
305	0.9995288	1.612615	0.8563256
306	0.996252	1.607324	0.8535178
307	0.9929991	1.602067	0.8507306
308	0.9897649	1.596845	0.8479594
309	0.9865517	1.591656	0.8452062
310	0.9833593	1.586501	0.8424729
311	0.9801875	1.581376	0.8397551
312	0.9770361	1.576288	0.8370569
313	0.9739049	1.571231	0.834374
314	0.9707937	1.566208	0.8317081
315	0.9677023	1.561213	0.8290592
316	0.9646305	1.556253	0.8264292
317	0.9615782	1.551322	0.8238139
318	0.9585451	1.546424	0.8212149
319	0.9555312	1.541555	0.8186324
320	0.952536	1.536719	0.816066
321	0.9495597	1.53191	0.8135177
322	0.9465996	1.527132	0.8109832
323	0.9436601	1.522383	0.8084645
324	0.9407389	1.517666	0.8059614
325	0.9378357	1.512976	0.8034738
326	0.9349481	1.508315	0.8010015
327	0.9320805	1.503682	0.7985443
328	0.9292304	1.499078	0.7961022
329	0.9263955	1.494501	0.7936749
330	0.9235801	1.489953	0.7912624
331	0.9207795	1.485432	0.7888627
332	0.917998	1.480939	0.7864793
333	0.9152332	1.47647	0.7841103
334	0.912483	1.472031	0.7817555
335	0.9097492	1.467618	0.7794148
336	0.9070339	1.463229	0.7770863
337	0.9043326	1.458869	0.7747735
338	0.9016494	1.454535	0.7724743
339	0.8989801	1.450223	0.7701888
340	0.8963265	1.445938	0.7679151
341	0.8936906	1.44168	0.7656564
342	0.8910681	1.437444	0.763411
343	0.888461	1.433236	0.761177
344	0.8858691	1.42905	0.7589577
345	0.8832942	1.424889	0.7567497
346	0.8807323	1.420751	0.7545561
347	0.8781852	1.416638	0.7523736
348	0.8756528	1.412548	0.7502053
349	0.873135	1.408482	0.7480478
350	0.8706316	1.404439	0.7459027
351	0.8681425	1.40042	0.7437715
352	0.8656676	1.396423	0.7416508
353	0.8632068	1.392449	0.7395438
354	0.86076	1.388498	0.7374471
355	0.8583269	1.384568	0.7353622
356	0.8559076	1.380659	0.7332892
357	0.8535019	1.376775	0.7312293
358	0.8511097	1.372909	0.7291794
359	0.8487308	1.369068	0.727141
360	0.8463635	1.365246	0.725114
361	0.844011	1.361447	0.7230982
362	0.8416716	1.357667	0.7210936
363	0.8393452	1.35391	0.7191016
364	0.8370298	1.350172	0.7171191
365	0.8347289	1.346455	0.7151474
366	0.8324406	1.342758	0.7131866
367	0.8301631	1.339083	0.7112365
368	0.8278998	1.335426	0.7092971
369	0.8256487	1.331789	0.7073681
370	0.8234082	1.328172	0.7054482
371	0.8211815	1.324575	0.7035401
372	0.8189651	1.320997	0.7016423
373	0.8167623	1.317438	0.6997548
374	0.8145697	1.313896	0.6978773
375	0.8123888	1.310375	0.69601
376	0.8102212	1.306874	0.6941511
377	0.8080635	1.30339	0.6923036
378	0.8059173	1.299924	0.6904659
379	0.803784	1.296477	0.6886379
380	0.8016604	1.293047	0.6868181
381	0.799548	1.289637	0.6850094
382	0.7974483	1.286243	0.6832101
383	0.795358	1.282869	0.681419
384	0.7932787	1.279511	0.6796385
385	0.7912102	1.27617	0.6778659
386	0.7891524	1.272848	0.6761039
387	0.7871053	1.269542	0.6743498
388	0.7850689	1.266253	0.6726061
389	0.7830429	1.262981	0.6708699
390	0.7810274	1.259725	0.6691441
391	0.7790222	1.256487	0.6674258
392	0.7770272	1.253265	0.6657163
393	0.7750425	1.250059	0.6640168
394	0.7730679	1.24687	0.6623248
395	0.7711033	1.243698	0.6606413
396	0.7691487	1.240541	0.6589676
397	0.7672039	1.2374	0.6573011
398	0.765269	1.234273	0.655643
399	0.7633424	1.231164	0.6539932
400	0.7614269	1.228069	0.6523518
401	0.7595209	1.224991	0.6507198
402	0.7576245	1.221928	0.6490947
403	0.7557361	1.218879	0.6474777
404	0.7538586	1.215845	0.6458688
405	0.7519903	1.212828	0.6442678
406	0.7501298	1.209824	0.6426747
407	0.7482799	1.206835	0.6410895
408	0.7464378	1.203863	0.6395121
409	0.7446061	1.200903	0.6379424
410	0.7427819	1.197958	0.6363804
411	0.7409681	1.195027	0.6348261
412	0.7391617	1.192111	0.6332781
413	0.7373655	1.189209	0.6317389
414	0.7355766	1.18632	0.6302071
415	0.7337964	1.183446	0.6286827
416	0.7320262	1.180586	0.6271657
417	0.7302631	1.177738	0.6256548
418	0.7285085	1.174905	0.6241524
419	0.7267635	1.172086	0.6226571
420	0.7250257	1.16928	0.621169
421	0.7232962	1.166487	0.6196868
422	0.7215748	1.163707	0.6182129
423	0.7198617	1.16094	0.6167448
424	0.7181579	1.158188	0.6152848
425	0.7164609	1.155446	0.6138316
426	0.7147719	1.152718	0.6123843
427	0.7130909	1.150005	0.6109448
428	0.7114177	1.147302	0.609511
429	0.7097524	1.144612	0.6080838
430	0.7080948	1.141935	0.6066645
431	0.706445	1.139271	0.6052507
432	0.7048029	1.136619	0.6038445
433	0.7031671	1.133979	0.6024438
434	0.7015402	1.131351	0.6010495
435	0.6999207	1.128735	0.5996628
436	0.6983087	1.12613	0.5982814
437	0.6967041	1.123538	0.5969063
438	0.6951069	1.120959	0.5955375
439	0.6935158	1.118391	0.5941761
440	0.6919332	1.115835	0.5928198
441	0.6903577	1.113289	0.5914697
442	0.6887882	1.110756	0.5901257
443	0.687227	1.108233	0.5887879
444	0.6856729	1.105723	0.587456
445	0.6841246	1.103223	0.5861303
446	0.6825845	1.100735	0.5848104
447	0.6810501	1.098258	0.5834965
448	0.6795238	1.095791	0.5821885
449	0.6780031	1.093337	0.5808863
450	0.6764904	1.090893	0.57959
451	0.6749833	1.088459	0.5782993
452	0.6734829	1.086036	0.5770145
453	0.6719902	1.083624	0.5757353
454	0.6705031	1.081223	0.5744619
455	0.6690225	1.078833	0.573193
456	0.6675495	1.076452	0.5719307
457	0.6660819	1.074083	0.570674
458	0.6646208	1.071724	0.5694228
459	0.663166	1.069375	0.568176
460	0.6617187	1.067036	0.5669357
461	0.6602766	1.064707	0.5657008
462	0.6588408	1.062388	0.5644704
463	0.6574112	1.060079	0.5632461
464	0.6559878	1.057781	0.5620273
465	0.6545706	1.055493	0.5608127
466	0.6531594	1.053213	0.5596043
467	0.6517543	1.050943	0.5584002
468	0.6503553	1.048684	0.5572021
469	0.6489623	1.046434	0.5560083
470	0.6475752	1.044193	0.5548195
471	0.646194	1.041964	0.5536368
472	0.6448187	1.039742	0.5524582
473	0.6434492	1.03753	0.5512855
474	0.6420846	1.035327	0.5501168
475	0.6407267	1.033134	0.5489532
476	0.6393746	1.030949	0.5477952
477	0.6380281	1.028775	0.5466413
478	0.6366863	1.026609	0.5454923
479	0.6353512	1.024452	0.5443481
480	0.6340216	1.022303	0.5432087
481	0.6326966	1.020165	0.5420749
482	0.6313781	1.018035	0.5409449
483	0.6300641	1.015914	0.5398196
484	0.6287566	1.013801	0.538699
485	0.6274544	1.011698	0.5375831
486	0.6261567	1.009602	0.5364718
487	0.6248653	1.007516	0.535365
488	0.6235782	1.005438	0.5342628
489	0.6222965	1.003368	0.5331652
490	0.6210209	1.001307	0.5320721
491	0.6197496	0.9992546	0.5309834
492	0.6184835	0.9972101	0.5298991
493	0.6172236	0.9951739	0.5288193
494	0.6159678	0.9931472	0.527743
495	0.6147171	0.9911276	0.526672
496	0.6134723	0.9891161	0.5256053
497	0.6122317	0.9871128	0.5245429
498	0.6109961	0.9851176	0.5234839
499	0.6097655	0.9831294	0.5224301
500	0.6085399	0.9811502	0.5213805
501	0.6073191	0.979179	0.5203342
502	0.6061032	0.9772158	0.5192931
503	0.6048923	0.9752603	0.518256
504	0.6036861	0.9733117	0.5172223
505	0.6024847	0.9713718	0.5161934
506	0.6012881	0.9694386	0.5151679
507	0.6000962	0.9675142	0.5141472
508	0.5989091	0.9655963	0.5131298
509	0.5977266	0.963687	0.5121172
510	0.5965489	0.9617842	0.5111078
511	0.5953757	0.9598889	0.5101032
512	0.5942072	0.9580022	0.5091016
513	0.5930423	0.9561218	0.5081041
514	0.5918829	0.9542487	0.5071112
515	0.590728	0.952383	0.5061214
516	0.5895776	0.9505246	0.5051355
517	0.5884308	0.9486734	0.5041541
518	0.5872893	0.9468294	0.5031759
519	0.5861523	0.9449925	0.5022013
520	0.5850188	0.9431628	0.5012306
521	0.5838904	0.9413401	0.5002636
522	0.5827656	0.9395245	0.4993011
523	0.581646	0.9377149	0.4983415
524	0.5805299	0.9359132	0.4973857
525	0.5794188	0.9341184	0.4964334
526	0.5783111	0.9323295	0.4954849
527	0.5772086	0.9305484	0.4945399
528	0.5761093	0.9287732	0.4935985
529	0.5750143	0.9270056	0.4926607
530	0.5739242	0.9252439	0.4917265
531	0.5728375	0.9234897	0.4907958
532	0.5717548	0.9217413	0.4898679
533	0.570677	0.9199994	0.4889442
534	0.5696025	0.9182642	0.488024
535	0.5685321	0.9165354	0.4871072
536	0.5674656	0.9148141	0.486194
537	0.5664032	0.9130983	0.4852841
538	0.5653447	0.9113889	0.4843768
539	0.5642909	0.909686	0.4834737
540	0.5632403	0.9079893	0.482574
541	0.5621936	0.9062981	0.4816769
542	0.5611508	0.9046141	0.4807838
543	0.5601118	0.9029363	0.479894
544	0.5590767	0.9012647	0.4790069
545	0.5580454	0.8995984	0.4781237
546	0.5570179	0.8979391	0.477243
547	0.5559934	0.896286	0.4763663
548	0.5549734	0.8946381	0.4754921
549	0.5539572	0.892997	0.4746218
550	0.5529447	0.8913611	0.473754
551	0.5519358	0.8897321	0.47289
552	0.5509299	0.8881081	0.4720286
553	0.5499284	0.88649	0.4711702
554	0.5489305	0.8848788	0.4703156
555	0.5479363	0.8832724	0.4694635
556	0.5469449	0.8816719	0.4686144
557	0.5459579	0.8800772	0.4677684
558	0.5449736	0.8784882	0.4669261
559	0.5439936	0.876905	0.4660862
560	0.5430171	0.8753275	0.4652493
561	0.5420434	0.8737556	0.4644154
562	0.541074	0.8721893	0.4635845
563	0.5401073	0.8706287	0.4627572
564	0.5391439	0.8690728	0.4619322
565	0.5381848	0.8675233	0.4611101
566	0.5372283	0.8659793	0.460291
567	0.536276	0.8644399	0.4594748
568	0.5353263	0.8629069	0.4586614
569	0.53438	0.8613793	0.457851
570	0.5334377	0.8598562	0.4570433
571	0.5324981	0.8583393	0.456238
572	0.5315617	0.856827	0.455436
573	0.5306286	0.85532	0.4546369
574	0.5296988	0.8538191	0.4538406
575	0.528773	0.8523226	0.4530471
576	0.5278496	0.8508313	0.4522563
577	0.5269295	0.8493453	0.4514677
578	0.5260126	0.8478644	0.4506824
579	0.5250989	0.8463888	0.4498999
580	0.5241883	0.8449182	0.4491194
581	0.523281	0.8434528	0.4483423
582	0.5223767	0.8419924	0.4475679
583	0.5214756	0.840537	0.4467955
584	0.5205775	0.8390867	0.4460264
585	0.5196826	0.8376414	0.4452599
586	0.5187901	0.8362002	0.4444955
587	0.5179012	0.8347648	0.4437343
588	0.5170155	0.8333343	0.4429751
589	0.5161327	0.831908	0.442219
590	0.5152529	0.8304873	0.441465
591	0.5143756	0.8290706	0.4407136
592	0.5135018	0.8276595	0.4399652
593	0.512631	0.8262525	0.4392188
594	0.5117625	0.8248503	0.438475
595	0.5108976	0.8234535	0.4377342
596	0.5100356	0.8220607	0.4369954
597	0.5091758	0.8206726	0.4362591
598	0.5083196	0.8192893	0.4355258
599	0.5074657	0.8179105	0.4347944
600	0.5066152	0.8165364	0.4340655
601	0.5057669	0.8151669	0.433339
602	0.5049222	0.8138019	0.4326149
603	0.5040795	0.8124416	0.4318932
604	0.5032398	0.8110858	0.431174
605	0.5024034	0.8097345	0.4304571
606	0.5015692	0.8083877	0.4297432
607	0.5007377	0.8070446	0.429031
608	0.4999096	0.8057067	0.4283213
609	0.4990836	0.8043733	0.4276139
610	0.4982604	0.8030435	0.4269082
611	0.4974399	0.8017189	0.4262055
612	0.496622	0.8003978	0.425505
613	0.4958075	0.7990819	0.4248069
614	0.494995	0.7977695	0.424111
615	0.4941852	0.7964615	0.4234174
616	0.493378	0.7951584	0.4227261
617	0.4925734	0.7938589	0.4220365
618	0.4917715	0.7925637	0.4213496
619	0.4909722	0.7912726	0.4206651
620	0.4901755	0.7899858	0.4199822
621	0.4893813	0.7887031	0.419302
622	0.4885898	0.7874246	0.418624
623	0.4878007	0.7861502	0.4179477
624	0.4870137	0.7848799	0.4172741
625	0.4862297	0.7836137	0.4166022
626	0.4854483	0.7823517	0.4159329
627	0.4846694	0.7810937	0.4152653
628	0.483893	0.779839	0.4146003
629	0.4831185	0.778589	0.4139369
630	0.482347	0.7773431	0.4132762
631	0.4815781	0.7761004	0.4126171
632	0.4808109	0.7748624	0.4119605
633	0.4800468	0.7736276	0.4113056
634	0.4792846	0.7723975	0.4106527
635	0.4785253	0.7711706	0.4100024
636	0.4777679	0.7699475	0.4093536
637	0.4770134	0.768729	0.408707
638	0.4762613	0.7675138	0.4080623
639	0.475511	0.7663023	0.4074202
640	0.474763	0.7650946	0.4067796
641	0.474018	0.7638908	0.406141
642	0.4732748	0.7626907	0.4055044
643	0.4725344	0.7614945	0.4048698
644	0.4717958	0.7603019	0.4042372
645	0.4710595	0.7591131	0.4036065
646	0.4703255	0.757928	0.4029778
647	0.4695943	0.7567465	0.4023511
648	0.4688649	0.7555681	0.4017263
649	0.4681377	0.7543941	0.4011035
650	0.4674127	0.7532236	0.4004826
651	0.4666901	0.7520562	0.3998636
652	0.4659696	0.7508929	0.3992465
653	0.4652519	0.7497327	0.3986313
654	0.4645359	0.7485767	0.398018
655	0.463822	0.7474236	0.3974066
656	0.4631104	0.7462747	0.3967966
657	0.4624009	0.7451286	0.396189
658	0.4616936	0.7439861	0.3955832
659	0.460988	0.7428471	0.3949792
660	0.460285	0.7417122	0.3943766
661	0.4595842	0.7405801	0.3937764
662	0.4588855	0.7394515	0.3931779
663	0.4581889	0.7383263	0.3925808
664	0.4574944	0.7372046	0.391986
665	0.4568015	0.7360862	0.3913925
666	0.4561113	0.7349712	0.3908013
667	0.4554231	0.733859	0.3902114
668	0.4547369	0.7327507	0.3896237
669	0.4540524	0.7316458	0.3890373
670	0.4533704	0.7305443	0.3884532
671	0.4526899	0.7294454	0.3878704
672	0.452012	0.7283504	0.3872893
673	0.4513361	0.7272581	0.3867103
674	0.4506617	0.7261697	0.3861327
675	0.4499899	0.7250839	0.3855568
676	0.4493195	0.7240021	0.3849831
677	0.4486516	0.7229227	0.3844106
678	0.4479853	0.7218467	0.3838398
679	0.4473208	0.7207738	0.3832707
680	0.4466589	0.7197047	0.3827038
681	0.4459984	0.7186382	0.382138
682	0.4453399	0.7175748	0.381574
683	0.4446838	0.7165146	0.3810116
684	0.4440292	0.7154574	0.3804508
685	0.4433764	0.7144035	0.3798918
686	0.4427256	0.7133526	0.3793343
687	0.4420772	0.7123048	0.3787785
688	0.4414302	0.7112601	0.3782243
689	0.4407851	0.7102178	0.3776717
690	0.4401418	0.7091792	0.3771208
691	0.4395005	0.7081436	0.3765714
692	0.438861	0.7071105	0.3760237
693	0.4382233	0.7060809	0.3754775
694	0.4375876	0.7050538	0.3749325
695	0.4369536	0.7040302	0.3743895
696	0.4363215	0.703009	0.3738481
697	0.4356912	0.7019914	0.3733082
698	0.4350627	0.7009761	0.3727699
699	0.4344361	0.6999637	0.3722327
700	0.4338112	0.6989549	0.3716975
701	0.4331877	0.6979484	0.3711638
702	0.4325665	0.6969448	0.3706312
703	0.431947	0.695944	0.3701006
704	0.4313293	0.6949462	0.3695711
705	0.4307128	0.6939511	0.3690435
706	0.4300987	0.692959	0.368517
707	0.4294862	0.6919696	0.3679924
708	0.428875	0.6909831	0.3674689
709	0.4282661	0.6899994	0.3669473
710	0.4276584	0.689018	0.3664268
711	0.4270529	0.6880398	0.3659081
712	0.4264486	0.6870645	0.3653905
713	0.4258465	0.6860914	0.3648744
714	0.4252456	0.6851215	0.3643601
715	0.4246469	0.6841539	0.3638469
716	0.4240494	0.6831895	0.3633351
717	0.4234541	0.6822273	0.3628252
718	0.42286	0.6812683	0.3623162
719	0.4222675	0.6803116	0.3618087
720	0.4216771	0.6793575	0.3613027
721	0.421088	0.6784061	0.360798
722	0.4205005	0.6774578	0.3602948
723	0.4199146	0.6765116	0.3597933
724	0.4193308	0.6755682	0.3592929
725	0.4187482	0.6746273	0.3587938
726	0.4181672	0.6736891	0.3582961
727	0.4175878	0.6727535	0.3577998
728	0.41701	0.6718204	0.3573049
729	0.4164338	0.6708894	0.3568113
730	0.4158592	0.6699616	0.3563192
731	0.4152862	0.6690363	0.3558279
732	0.4147148	0.6681135	0.3553385
733	0.4141449	0.6671928	0.3548503
734	0.4135766	0.6662751	0.3543635
735	0.4130098	0.6653594	0.353878
736	0.4124446	0.6644467	0.3533939
737	0.411881	0.6635361	0.3529107
738	0.4113188	0.6626284	0.3524292
739	0.4107578	0.6617227	0.351949
740	0.4101988	0.6608195	0.3514698
741	0.4096413	0.6599193	0.3509922
742	0.4090852	0.659021	0.3505159
743	0.4085303	0.6581251	0.3500406
744	0.4079773	0.6572317	0.3495668
745	0.4074258	0.6563407	0.3490941
746	0.4068753	0.6554521	0.3486229
747	0.4063268	0.6545659	0.3481527
748	0.4057793	0.6536821	0.3476841
749	0.4052337	0.6528007	0.3472163
750	0.4046892	0.6519216	0.3467503
751	0.4041465	0.651045	0.346285
752	0.4036049	0.6501701	0.3458214
753	0.4030651	0.6492982	0.3453587
754	0.4025264	0.6484281	0.3448972
755	0.4019895	0.6475608	0.3444374
756	0.4014536	0.6466958	0.3439783
757	0.4009192	0.6458326	0.3435205
758	0.4003862	0.6449722	0.343064
759	0.399855	0.6441137	0.3426086
760	0.3993248	0.6432574	0.3421547
761	0.398796	0.6424038	0.3417018
762	0.3982686	0.6415521	0.34125
763	0.397743	0.6407026	0.3407995
764	0.3972184	0.6398553	0.3403501
765	0.3966952	0.6390103	0.3399019
766	0.3961734	0.6381676	0.3394548
767	0.3956529	0.637327	0.339009
768	0.3951338	0.6364886	0.3385643
769	0.394616	0.6356525	0.3381208
770	0.3940997	0.6348186	0.3376785
771	0.3935846	0.6339868	0.3372372
772	0.3930709	0.6331567	0.3367972
773	0.3925585	0.6323293	0.336358
774	0.3920475	0.631504	0.3359202
775	0.3915374	0.6306809	0.3354836
776	0.3910291	0.6298595	0.3350481
777	0.390522	0.6290407	0.3346138
778	0.3900163	0.6282235	0.3341802
779	0.3895115	0.6274084	0.3337481
780	0.3890083	0.626596	0.3333171
781	0.3885065	0.6257852	0.3328869
782	0.3880056	0.6249765	0.3324581
783	0.3875063	0.6241702	0.3320304
784	0.3870084	0.6233657	0.3316036
785	0.3865113	0.6225632	0.3311781
786	0.3860159	0.6217628	0.3307534
787	0.3855214	0.6209644	0.3303301
788	0.3850285	0.6201681	0.3299075
789	0.3845365	0.6193738	0.3294864
790	0.3840461	0.6185815	0.329066
791	0.3835567	0.6177913	0.3286467
792	0.3830688	0.6170027	0.3282288
793	0.3825818	0.6162165	0.3278116
794	0.382096	0.6154323	0.3273954
795	0.3816119	0.6146501	0.3269807
796	0.3811286	0.6138694	0.3265667
797	0.3806465	0.6130912	0.3261537
798	0.3801656	0.6123145	0.3257418
799	0.3796863	0.6115401	0.3253312
800	0.3792079	0.6107674	0.3249213
801	0.3787307	0.6099966	0.3245125
802	0.3782546	0.6092281	0.3241047
803	0.3777798	0.6084611	0.323698
804	0.3773061	0.6076961	0.3232922
805	0.3768337	0.606933	0.3228875
806	0.3763624	0.6061718	0.3224837
807	0.3758923	0.6054125	0.322081
808	0.3754233	0.6046551	0.3216793
809	0.3749556	0.6038997	0.3212786
810	0.374489	0.6031461	0.3208789
811	0.3740236	0.6023943	0.3204801
812	0.3735593	0.6016445	0.3200824
813	0.3730961	0.6008965	0.3196854
814	0.3726338	0.60015	0.3192896
815	0.372173	0.5994057	0.3188948
816	0.3717133	0.5986633	0.318501
817	0.3712547	0.5979223	0.3181082
818	0.3707969	0.5971835	0.317716
819	0.3703406	0.5964462	0.3173251
820	0.3698854	0.5957111	0.3169352
821	0.369431	0.5949773	0.3165459
822	0.368978	0.5942454	0.3161578
823	0.3685259	0.5935157	0.3157704
824	0.3680751	0.5927874	0.3153843
825	0.3676251	0.5920608	0.3149991
826	0.3671766	0.5913361	0.3146146
827	0.3667288	0.5906131	0.3142313
828	0.3662824	0.5898919	0.3138486
829	0.3658368	0.5891724	0.3134668
830	0.3653923	0.5884547	0.3130863
831	0.3649492	0.5877387	0.3127064
832	0.3645068	0.5870245	0.3123277
833	0.3640655	0.586312	0.3119497
834	0.3636256	0.5856012	0.3115726
835	0.3631864	0.5848918	0.3111963
836	0.3627483	0.5841845	0.3108213
837	0.3623113	0.5834789	0.3104469
838	0.3618756	0.5827745	0.3100733
839	0.3614406	0.5820723	0.3097007
840	0.3610067	0.5813714	0.309329
841	0.3605739	0.5806722	0.3089584
842	0.360142	0.579975	0.3085885
843	0.3597112	0.5792791	0.3082194
844	0.3592815	0.5785849	0.3078513
845	0.3588527	0.5778928	0.3074839
846	0.358425	0.5772018	0.3071175
847	0.3579983	0.5765126	0.306752
848	0.3575726	0.575825	0.3063873
849	0.3571476	0.575139	0.3060234
850	0.3567239	0.5744547	0.3056605
851	0.3563012	0.5737721	0.3052981
852	0.3558796	0.573091	0.3049369
853	0.3554589	0.5724115	0.3045765
854	0.3550389	0.5717333	0.304217
855	0.3546202	0.571057	0.3038583
856	0.3542025	0.5703824	0.3035002
857	0.3537858	0.5697089	0.3031432
858	0.3533698	0.5690374	0.302787
859	0.352955	0.5683672	0.3024317
860	0.3525409	0.5676989	0.3020769
861	0.3521281	0.5670317	0.3017232
862	0.3517159	0.5663666	0.3013701
863	0.351305	0.5657026	0.3010181
864	0.3508948	0.5650402	0.3006667
865	0.3504858	0.5643796	0.3003163
866	0.3500775	0.5637203	0.2999668
867	0.3496701	0.5630625	0.2996178
868	0.349264	0.5624062	0.2992696
869	0.3488585	0.5617515	0.2989224
870	0.348454	0.5610983	0.2985758
871	0.3480507	0.5604466	0.2982304
872	0.347648	0.5597964	0.2978854
873	0.3472462	0.5591477	0.2975412
874	0.3468454	0.5585002	0.2971981
875	0.3464458	0.5578545	0.2968554
876	0.3460468	0.5572103	0.2965136
877	0.3456488	0.5565676	0.2961726
878	0.3452516	0.555926	0.2958326
879	0.3448554	0.5552862	0.2954932
880	0.3444601	0.5546476	0.2951545
881	0.3440657	0.5540108	0.2948166
882	0.3436722	0.5533751	0.2944795
883	0.3432795	0.5527412	0.2941431
884	0.3428878	0.5521084	0.2938075
885	0.342497	0.5514771	0.2934727
886	0.3421071	0.5508472	0.2931386
887	0.341718	0.5502187	0.2928053
888	0.3413296	0.549592	0.2924727
889	0.3409423	0.5489664	0.2921409
890	0.3405559	0.5483422	0.2918099
891	0.3401704	0.5477195	0.2914796
892	0.3397854	0.5470981	0.2911498
893	0.3394016	0.5464778	0.290821
894	0.3390187	0.5458593	0.2904929
895	0.3386363	0.5452421	0.2901656
896	0.3382552	0.5446264	0.289839
897	0.3378748	0.5440117	0.2895129
898	0.337495	0.5433987	0.2891878
899	0.3371164	0.5427871	0.2888634
900	0.3367383	0.5421765	0.2885395

Return to Figure 1

^♣ This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to Text