Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 3e-14
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues 1,1,0,0

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Spectral parameter

$R= 5.10381155304$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.7071067811
3 0.8947388086
4 0.5000000000
5 0.4472135954
6 0.6326758789
7 1.025104012
8 0.3535533905
9 -0.1994424643
10 0.3162277660
11 -1.474671260
12 0.4473694043
13 0.3845301868
14 0.7248579989
15 0.4001393596
16 0.2500000000
17 -0.04179726381
18 -0.1410271189
19 -1.828150475
20 0.2236067977
21 0.9172003432
22 -1.042750048
23 0.7724046919
24 0.3163379394
25 0.1999999999 + 1.994842853e-13i
26 0.2719039026 - 2.781198672e-13i
27 -1.073187721 - 6.117811653e-13i
28 0.5125520063 + 1.657876702e-12i
29 -0.2907581453 + 6.907510818e-13i
30 0.2829412547 - 6.279339163e-12i
31 1.315929421 + 3.873146647e-12i
32 0.1767766936 + 1.445578546e-11i
33 -1.319445605 - 2.034799174e-11i
34 -0.02955512534 - 2.338902955e-11i
35 0.4584404440 + 6.545993549e-11i
36 -0.09972123146 + 1.859368819e-11i
37 -1.091530611 - 1.888828577e-10i
38 -1.292697572 + 1.073463993e-10i
39 0.3440540812
40 0.1581138830
41 0.1699960889
42 0.6485585824
43 1.877998262
44 -0.7373356301
45 -0.08919338158
46 0.5461725955
47 -0.6237998753
48 0.2236847021
49 0.05083823736
50 0.1414213562
51 -0.03739763400
52 0.1922650933
53 0.03138497290 - 1.004487245e-13i
54 -0.7588583154 - 1.089015787e-13i
55 -0.6594930364 + 1.905107750e-13i
56 0.3624289993 + 3.662592428e-13i
57 -1.635717177 - 2.373108790e-13i
58 -0.2055970563 - 6.971835622e-13i
59 -0.06252482078 + 3.877616779e-13i
60 0.2000696797 + 5.054801021e-13i
61 0.9697055343 - 2.322409652e-13i
62 0.9305026174
63 -0.2044492709 + 3.800707381e-13i
64 0.1250000005 + 3.330104634e-13i
65 0.1719671266 - 2.316989903e-12i
66 -0.9329889343 - 8.406217620e-13i
67 1.298033277 + 3.573440487e-12i
68 -0.02089862918 + 2.077713437e-12i
69 0.6911004527 + 1.112965015e-12i
70 0.3241663551 - 4.564439815e-12i
71 0.2747816281 - 9.751409518e-12i
72 -0.07051355828 - 3.952022713e-12i
73 -0.5109945473 + 1.954165482e-11i
74 -0.7718287080 + 3.000637759e-11i
75 0.1789477573 - 2.050079203e-11i
76 -0.9140752862 - 5.595241055e-11i
77 -1.511691325 - 9.702586419e-13i
78 0.2432829838 + 6.156033553e-11i
79 1.406992287 + 2.408921616e-11i
80 0.1118033988 + 3.237562578e-13i
81 -0.7607802391
82 0.1202053873 - 2.568822879e-13i
83 -0.5798524706
84 0.4586001716
85 -0.01869230481
86 1.327945306
87 -0.2601525964 + 2.774976959e-13i
88 -0.5213750242
89 -0.7967764141 + 1.038093719e-13i
90 -0.06306924459 + 1.551882424e-13i
91 0.3941834375 - 8.306310215e-13i
92 0.3862023456
93 1.177413121 + 1.025634502e-13i
94 -0.4410931216 + 1.296024103e-12i
95 -0.8175737468 - 4.581165206e-13i
96 0.1581689694 - 1.024919879e-12i
97 0.4448930461 + 2.579429548e-12i
98 0.03594806256 - 3.252934960e-13i
99 0.2941120582 - 3.539900131e-12i
100 0.09999999908 - 3.933858893e-12i
101 0.04694209042 + 4.688716686e-12i
102 -0.02644412713 + 8.241438779e-12i
103 0.8240518596 + 2.253947675e-12i
104 0.1359519492 - 6.574560439e-12i
105 0.4101844752 - 1.561539401e-11i
106 0.02219252288 - 6.522054286e-13i
107 -0.3812110827 + 1.186474325e-11i
108 -0.5365938736 + 2.358942516e-11i
109 -1.391071778 - 1.259146600e-12i
110 -0.4663320450 - 3.220340223e-11i
111 -0.9766342734 - 4.854674604e-12i
112 0.2562759966 + 9.600702765e-12i
113 0.4832959231 + 5.688914001e-12i
114 -1.156626971 - 4.415733749e-12i
115 0.3454287506 + 3.058291799e-11i
116 -0.1453792389 + 2.297998445e-11i
117 -0.07669164804 + 7.951174123e-13i
118 -0.04421172568 + 1.149027967e-12i
119 -0.04284654265 + 1.005988100e-12i
120 0.1414706283 + 4.692841616e-13i
121 1.174655326 - 4.049005219e-12i
122 0.6856853594 - 1.287242251e-12i
123 0.1521020964 - 6.243289669e-13i
124 0.6579647105 + 3.394436486e-12i
125 0.08944271608 + 4.432004883e-12i
126 -0.1445674679 - 3.364808320e-13i
127 0.04045737637
128 0.08838836082 - 6.629024350e-12i
129 1.680317927 - 4.340439113e-12i
130 0.1215991244 - 2.057242218e-12i
131 -0.07851639514 + 7.940175529e-12i
132 -0.6597228049 + 1.047474393e-11i
133 -1.874044385 + 6.307386883e-12i
134 0.9178481334 - 6.002067110e-12i
135 -0.4799440758 - 2.370893994e-11i
136 -0.01477764769 - 5.749102909e-12i
137 -0.5177336300 - 5.795962126e-13i
138 0.4886818025 + 2.596020255e-11i
139 -0.07254899027 + 1.905201692e-11i
140 0.2292202321 - 6.074646912e-12i
141 -0.5581376527 + 2.764906725e-12i
142 0.1942999994 - 3.714048736e-11i
143 -0.5670563165 - 2.667427118e-11i
144 -0.04986065662 - 6.853035119e-12i
145 -0.1300306059 + 3.281274973e-11i
146 -0.3613281740 + 7.458866322e-11i
147 0.04548788772 + 2.397599025e-11i
148 -0.5457654958 - 4.744427557e-11i
149 0.6980913585 - 8.474162663e-11i
150 0.1265336994 - 5.069758157e-11i
151 -0.2375254971 - 4.468740149e-12i
152 -0.6463487971 - 4.841902038e-12i
153 0.008336148203 + 4.720446283e-13i
154 -1.068927260 + 1.129504657e-11i
155 0.5885015282 + 3.533572645e-12i
156 0.1720270381
157 0.6701386253 - 7.427556039e-13i
158 0.9948936194 - 1.180705959e-11i
159 0.02808136101 - 3.883993783e-12i
160 0.07905691373 - 1.195218889e-12i
161 0.7917951503 + 3.382100246e-12i
162 -0.5379528855 + 2.123286711e-11i
163 1.493590519 + 3.056992569e-13i
164 0.08499802967 - 7.152865455e-12i
165 -0.5900738831 - 2.753040855e-12i
166 -0.4100176646 - 3.015518250e-11i
167 0.4610026293 - 9.402939341e-13i
168 0.3242794095 + 1.593650411e-11i
169 -0.8521367295 + 1.831392557e-11i
170 -0.01321746104 + 4.135863692e-11i
171 0.3646107116 - 9.778836366e-12i
172 0.9389993071 - 3.726504831e-11i
173 -1.357560333 - 4.273123492e-11i
174 -0.1839555681 - 3.898045553e-11i
175 0.2050192611 + 4.972898346e-11i
176 -0.3686678971 + 9.596535945e-11i
177 -0.05594378685 - 4.448713028e-13i
178 -0.5634068052 - 3.675743915e-11i
179 -1.001962275 - 5.005248545e-11i
180 -0.04459569130 - 6.330163727e-11i
181 0.5601013124 + 6.815058688e-11i
182 0.2787297770 - 3.557727783e-12i
183 0.8676331767 - 4.215697430e-12i
184 0.2730862940 + 2.876750207e-12i
185 -0.4881473227 + 5.496966180e-12i
186 0.8325568097 - 3.037702773e-12i
187 0.06163722423 + 8.925117690e-13i
188 -0.3118999388 + 4.553199744e-12i
189 -1.100129021 - 1.191358933e-11i
190 -0.5781119324 + 2.158895268e-12i
191 -1.243180940
192 0.1118423531 + 5.529609976e-13i
193 0.9440624355 + 2.376915570e-11i
194 0.3145868827 - 1.804694889e-11i
195 0.1538656297 - 1.501458719e-11i
196 0.02541909084 - 7.203050185e-12i
197 -1.755010097 + 8.424566521e-12i
198 0.2079686765 + 4.994547129e-11i
199 0.4396926443 - 1.829094834e-11i
200 0.07071066542 - 3.812695330e-11i
201 1.161400768 + 8.589557045e-12i
202 0.03319300518 + 1.517807793e-11i
203 -0.2980573076 - 3.658889583e-12i
204 -0.01869883370 - 2.109337384e-11i
205 0.07602426781 - 3.251641237e-11i
206 0.5826925441 + 5.440882665e-11i
207 -0.1540511599 + 5.372232617e-11i
208 0.09613258207 - 3.210032248e-11i
209 2.695920316 + 2.465201516e-12i
210 0.2900442239 - 1.211358690e-11i
211 -1.585381479 + 2.234377267e-12i
212 0.01569250504 + 5.063073953e-12i
213 0.2458577861 + 3.221629986e-12i
214 -0.2695568884 + 2.102021522e-12i
215 0.8398663613 - 7.401582659e-12i
216 -0.3794292020 + 5.036536254e-12i
217 1.348964525 - 1.226298502e-11i
218 -0.9836362363 + 2.633395282e-12i
219 -0.4572066644 - 2.145112075e-12i
220 -0.3297465036 + 2.031375132e-11i
221 -0.01607232589 + 1.592549075e-12i
222 -0.6905850997 - 1.921699529e-11i
223 0.6590370168 - 1.793883256e-12i
224 0.1812145142 - 1.933541010e-11i
225 -0.03988854520 + 3.927403864e-11i
226 0.3417419098
227 -0.7471984651 + 1.332972940e-11i
228 -0.8178585112 - 1.828762526e-11i
229 -1.030241216 - 2.510395768e-11i
230 0.2442557971 + 2.415764658e-11i
231 -1.352569193 - 3.839687465e-11i
232 -0.1027989378 + 1.628122785e-11i
233 -1.856314597 - 1.705948457e-11i
234 -0.05422921818 + 7.032998410e-11i
235 -0.2789717861 - 6.515003506e-12i
236 -0.03126240739 - 1.702376542e-12i
237 1.258890424 + 3.604482846e-12i
238 -0.03029706545 + 6.085959153e-12i
239 1.543260600 + 6.675221062e-13i
240 0.1000348267 - 7.138031291e-12i
241 0.4937530125 + 3.608018833e-12i
242 0.8306067860 - 1.025936200e-11i
243 0.3924881280 + 1.133816522e-11i
244 0.4848528106 + 6.109201985e-13i
245 0.02273552364 - 2.950565985e-12i
246 0.1075524844 - 5.306565673e-12i
247 -0.7029790055 - 1.341803486e-11i
248 0.4652512740 + 2.192213062e-11i
249 -0.5188164707 - 1.403168842e-11i
250 0.06324554168 + 1.048478578e-11i
251 1.523522158 + 1.789265595e-11i
252 -0.1022246312 + 2.051717918e-12i
253 -1.139043191 - 2.073951948e-11i
254 0.02860752383 - 2.249567231e-11i
255 -0.01672462693 + 9.189531340e-12i
256 0.06250026217 + 1.450753184e-11i
257 0.5896712588 + 1.076549991e-11i
258 1.188164252 - 2.139567406e-11i
259 -1.118932441 + 3.565788276e-11i
260 0.08598354131 + 7.405068117e-13i
261 0.05798951228 + 6.671311443e-12i
262 -0.05551947270 - 4.358592675e-13i
263 0.5783612129 - 5.090375084e-12i
264 -0.4664944671 + 2.478037058e-12i
265 0.01403580095 + 5.965545736e-13i
266 -1.325149490 + 3.822806303e-12i
267 -0.7129067204 - 7.799464493e-12i
268 0.6490166326 - 2.268468088e-12i
269 0.3768753469 + 5.345561182e-12i
270 -0.3393716870 + 1.716579737e-12i
271 0.3274745087 + 5.863775424e-12i
272 -0.01044930922 - 1.403831903e-11i
273 0.3526910744 - 5.823228383e-13i
274 -0.3660930546 - 9.695719778e-12i
275 -0.2949343219 - 3.003911546e-12i
276 0.3455502180 + 3.457380818e-11i
277 -1.023988226 + 3.015666544e-12i
278 -0.05129979631 + 4.372925382e-12i
279 -0.2624522944 - 2.269085265e-11i
280 0.1620830745 - 3.062823060e-11i
281 -0.3152082237 + 1.124244028e-11i
282 -0.3946629106 + 2.251315154e-11i
283 1.803418840 + 1.303672663e-11i
284 0.1373907607 + 1.042512608e-11i
285 -0.7315145923 - 4.087190372e-11i
286 -0.4009688889 - 2.772799030e-11i
287 0.1742625829 + 6.087940858e-11i
288 -0.03525678228 - 8.905564910e-12i
289 -0.9982529754 + 9.199331125e-12i
290 -0.09194579222 - 1.038595537e-11i
291 0.3980630936 - 6.168209873e-12i
292 -0.2554972779 - 7.847714957e-12i
293 -1.275579957 + 1.575660259e-11i
294 0.03216413665 + 1.488333269e-11i
295 -0.02796194606 - 2.318106747e-13i
296 -0.3859143560 - 1.457589298e-11i
297 1.582599090 - 2.321609230e-11i
298 0.4936251788 + 1.603629170e-11i
299 0.2970129059 - 9.921140171e-12i
300 0.08947389870 + 2.448271552e-11i
301 1.925143505 + 2.683189665e-12i
302 -0.1679558792 - 3.954577238e-12i
303 0.04200090113 - 2.198843577e-12i
304 -0.4570376185 - 8.123168723e-12i
305 0.4336655445 + 1.689821870e-11i
306 0.005894573699 - 2.089407086e-11i
307 0.9407891581 + 2.624062733e-12i
308 -0.7558456845 - 1.202238471e-11i
309 0.7373111553 + 1.791840144e-11i
310 0.4161333992 - 1.441477151e-12i
311 -1.470207179 + 9.340014263e-12i
312 0.1216413349 + 1.307300787e-11i
313 -1.240488752 - 6.050026750e-11i
314 0.4738596049 - 8.297823437e-12i
315 -0.09143283094 + 3.190844510e-11i
316 0.7034960710 + 6.698635305e-11i
317 -0.2901579602 - 1.402576783e-11i
318 0.01985646100 - 2.545285065e-11i
319 0.4287726743 + 1.210714064e-11i
320 0.05590169684 - 1.365434893e-12i
321 -0.3410842778 + 6.833947843e-12i
322 0.5598837264 - 2.712223707e-12i
323 0.07641167787 + 2.540582288e-12i
324 -0.3803901289 - 6.248221648e-12i
325 0.07690602568 - 9.262249135e-12i
326 1.056127922 + 2.227293260e-12i
327 -1.244645836 + 2.526400210e-12i
328 0.06010270331 + 1.546066175e-11i
329 -0.6394597670 - 1.881810090e-11i
330 -0.4172453308 + 2.650853136e-11i
331 -0.6889925637 - 1.103243522e-11i
332 -0.2899262489 - 1.757378166e-11i
333 0.2176975610 + 9.220897714e-12i
334 0.3259781568 + 3.720336592e-12i
335 0.5804981143 + 9.902462197e-12i
336 0.2293001070 - 1.979542335e-11i
337 -0.002025995008 + 2.092521013e-11i
338 -0.6025515372
339 0.4324236458 - 1.842118151e-12i
340 -0.009346157347 - 4.918677636e-11i
341 -1.940563307 + 1.907786803e-11i
342 0.2578187773 + 2.235653135e-11i
343 -0.9729898360 - 1.250342871e-11i
344 0.6639727795 + 4.582166430e-11i
345 0.3090695307 - 3.278737473e-11i
346 -0.9599401178 - 2.886196061e-12i
347 -0.2125172482 - 2.656378688e-11i
348 -0.1300761201 + 2.942020998e-11i
349 0.6532081988 + 1.418603767e-11i
350 0.1449715368 - 1.275670875e-11i
351 -0.4126733590 - 6.552053185e-12i
352 -0.2606876697 + 2.991578568e-11i
353 1.162309747 + 1.081966342e-11i
354 -0.03955794926 - 6.728769977e-12i
355 0.1228860586 - 6.316618783e-12i
356 -0.3983881991 + 8.464065454e-12i
357 -0.03833645822 - 1.566216013e-11i
358 -0.7084920999 + 5.424022415e-12i
359 1.140441351 + 1.449401121e-12i
360 -0.03153462711 + 4.154703529e-12i
361 2.342134165 + 7.563236368e-12i
362 0.3960514091 - 9.358217649e-12i
363 1.051009728 + 1.971830608e-12i
364 0.1970917139 - 3.759691048e-12i
365 -0.2285237035 - 1.150555503e-11i
366 0.6135092635 + 1.097585501e-11i
367 -0.3974760252 + 1.407120640e-11i
368 0.1931011816 - 9.110679633e-12i
369 -0.03390451712 - 1.562473469e-12i
370 -0.3451722701 + 1.424474927e-11i
371 0.03217285230 - 4.834540225e-12i
372 0.5887065328 - 2.230760014e-11i
373 0.7672697606 - 3.922488412e-12i
374 0.04358406134 + 5.529858256e-12i
375 0.08002787657 + 3.426664555e-11i
376 -0.2205465775 - 2.017170573e-11i
377 -0.1118052589 - 6.568790232e-12i
378 -0.7779086983 + 1.366769919e-11i
379 -1.692977936 - 3.057936946e-11i
380 -0.4087867843 + 1.437664044e-11i
381 0.03619854824 + 1.212588504e-11i
382 -0.8790617220 + 2.390482750e-12i
383 -0.8154304425 - 2.052902092e-11i
384 0.07908436645 + 2.451177898e-11i
385 -0.6760487300 - 8.916637080e-12i
386 0.6675531546 - 6.232710678e-12i
387 -0.3745525641 - 9.297406971e-12i
388 0.2224464894 - 4.903910903e-12i
389 0.3198414617 + 5.935379832e-11i
390 0.1087999799 - 8.027295567e-11i
391 -0.03228414399 + 9.011279312e-12i
392 0.01797403342 + 4.527998089e-12i
393 -0.07025165856 - 3.778865860e-12i
394 -1.240979543 + 4.834216199e-12i
395 0.6292259598 - 1.099195348e-11i
396 0.1470560522 + 1.314820356e-11i
397 -0.04206864051 + 7.130886218e-12i
398 0.3109096416 - 2.051652778e-11i
399 -1.676780243 + 1.299490924e-11i
400 0.05000000550 + 5.364196478e-12i
401 -0.008280211919 - 2.987500671e-11i
402 0.8212343428 + 6.692002218e-12i
403 0.5060146000 + 1.238464436e-11i
404 0.02347105376 - 1.359220107e-11i
405 -0.3402312560 + 2.331161677e-11i
406 -0.2107583872 - 1.289813070e-11i
407 1.609648883 + 5.162162655e-12i
408 -0.01322206704 + 7.895422019e-12i
409 0.1247539616 - 4.217721516e-11i
410 0.05375750687 + 4.870980523e-11i
411 -0.4632362782 + 6.038169024e-12i
412 0.4120258916 - 3.516988511e-11i
413 -0.06409449625 + 3.146044600e-11i
414 -0.1089299628 - 1.059982363e-12i
415 -0.2593179516 - 2.298357720e-11i
416 0.06797597228 - 8.903486165e-12i
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