Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 1e-13
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues 1,-1,0,0

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Spectral parameter

$R= 7.78033646819$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.7071067811
3 -1.173212201
4 0.4999999999
5 0.4472135955
6 0.8295863037
7 1.327754184
8 -0.3535533905
9 0.3764268706
10 -0.3162277660
11 -0.3078211997
12 -0.5866061009
13 -0.9537345451
14 -0.9388639879
15 -0.5246764470
16 0.2499999999
17 1.467194687
18 -0.2661739928
19 -1.336671565
20 0.2236067977
21 -1.557737410
22 0.2176624577
23 -0.5077420796
24 0.4147931518
25 0.2000000000
26 0.6743921643
27 0.7315836040 + 1.265479205e-13i
28 0.6638770925 - 1.076234197e-13i
29 -1.749339215 - 2.925570245e-13i
30 0.3710022733 + 4.457438301e-13i
31 -0.2185333182 + 5.377170538e-13i
32 -0.1767766944 - 1.853746102e-12i
33 0.3611395865 + 5.215098975e-13i
34 -1.037463314 + 4.162707570e-12i
35 0.5937897271 - 4.776190877e-12i
36 0.1882134361 - 5.298900654e-12i
37 -1.750211832 + 1.082210931e-11i
38 0.9451695423 + 9.960729823e-12i
39 1.118933035 - 2.855801077e-11i
40 -0.1581139551 - 1.478192165e-11i
41 -0.7400174272 + 8.996589126e-11i
42 1.101486900 - 5.632276580e-11i
43 -0.5193934418
44 -0.1539105998
45 0.1683432142
46 0.3590278676
47 0.5966829288
48 -0.2933030504
49 0.7629311756
50 -0.1414213562
51 -1.721330709
52 -0.4768672725
53 0.07426321846
54 -0.5173077274
55 -0.1376618255
56 -0.4694319938
57 1.568199390 - 1.000505341e-13i
58 1.236969621
59 -0.2960507098
60 -0.2623382236
61 -1.024122931 + 1.858279689e-13i
62 0.1545263914
63 0.4998023528 + 6.386456079e-13i
64 0.1250000000 - 4.091782789e-13i
65 -0.4265230562 - 1.737767424e-12i
66 -0.2553642495 + 1.886004079e-12i
67 1.264397158 - 4.784305783e-13i
68 0.7335973438 - 1.190789844e-12i
69 0.5956892026 + 4.157515401e-12i
70 -0.4198727396 - 1.127187456e-13i
71 -0.4469869415 - 4.766576318e-12i
72 -0.1330869979 - 5.187253111e-12i
73 -1.711616763 + 8.898619048e-12i
74 1.237586649 + 1.376212607e-12i
75 -0.2346424522 - 1.168985214e-11i
76 -0.6683357674 + 3.168216195e-11i
77 -0.4087108894 - 1.494131567e-11i
78 -0.7912051310 - 4.413899177e-11i
79 0.09774114148 + 3.814114897e-11i
80 0.1118033848 + 2.131388737e-12i
81 -1.234729650 - 1.874812481e-11i
82 0.5232713327
83 1.212371802 - 2.330176360e-13i
84 -0.7788687052 - 2.007244929e-13i
85 0.6561494113
86 0.3672666249
87 2.052346112 + 4.995880289e-13i
88 0.1088312290
89 1.366177579 + 7.558041179e-13i
90 -0.1190366285 - 1.141703639e-12i
91 -1.266325033
92 -0.2538710390 + 8.955737293e-13i
93 0.2563859551 - 3.109835602e-13i
94 -0.4219185444 + 1.701513650e-12i
95 -0.5977776982 - 3.264215696e-12i
96 0.2073965782 - 2.792518323e-13i
97 -1.266651569 - 8.322687720e-13i
98 -0.5394738073 + 6.519214150e-13i
99 -0.1158721717 + 1.336449038e-12i
100 0.1000000033 + 1.206062017e-12i
101 -0.2883410117 + 6.032953992e-12i
102 1.217164615 - 2.477931590e-12i
103 0.08863306671 + 6.026971225e-12i
104 0.3371960776 - 1.524939007e-11i
105 -0.6966413521 - 3.982859538e-12i
106 -0.05251202391 - 9.776849456e-13i
107 -0.4385215844 - 2.722941083e-12i
108 0.3657918170 + 1.824302782e-11i
109 -1.115218466 - 2.186840338e-11i
110 0.09734162197 + 2.710841535e-11i
111 2.053369846 + 7.603941554e-12i
112 0.3319385634 + 1.127094904e-11i
113 0.2934435861 - 2.043185609e-11i
114 -1.108884417 + 9.612194552e-12i
115 -0.2270691605 + 1.138184655e-11i
116 -0.8746695962 - 6.865701177e-11i
117 -0.3590113225 + 3.448822690e-11i
118 0.2093394655 - 2.331681516e-10i
119 1.948073791 + 1.235163290e-10i
120 0.1855012490 + 1.417735936e-10i
121 -0.9052461080 + 1.441239304e-12i
122 0.7241642697 + 1.600621829e-12i
123 0.8681974601 - 3.300990471e-12i
124 -0.1092666601 - 2.177111153e-12i
125 0.08944271869 - 1.280553070e-12i
126 -0.3534136309 + 3.548458381e-12i
127 -0.5653259148 + 5.577885927e-12i
128 -0.08838834576 + 7.202376102e-12i
129 0.6093587223 - 3.202842194e-12i
130 0.3015973397 - 1.685423444e-11i
131 -0.1332746468 - 7.358558596e-12i
132 0.1805697945 - 3.088696969e-12i
133 -1.774771258 + 1.436851072e-11i
134 -0.8940637996 + 1.879391654e-11i
135 0.3271741316 + 4.172846283e-12i
136 -0.5187316563 - 8.698217475e-12i
137 0.6074535668 - 1.239543121e-11i
138 -0.4212158721 - 3.692880599e-12i
139 0.1042566543 - 2.165053864e-11i
140 0.2968948768 + 3.074663938e-11i
141 -0.7000356888 + 3.484565003e-11i
142 0.3160674832 - 2.449951702e-11i
143 0.2935797053 - 1.680298756e-11i
144 0.09410671396 - 2.884616120e-11i
145 -0.7823282583 - 2.009916500e-11i
146 1.210295799 - 1.522501708e-11i
147 -0.8950801596 + 9.315291309e-11i
148 -0.8751058902 + 3.943028845e-11i
149 1.272823396 - 3.634024320e-11i
150 0.1659172972 + 1.169188676e-10i
151 0.8587657841 - 5.378031445e-11i
152 0.4725847898 - 1.614223185e-10i
153 0.5522914466 - 1.405634168e-10i
154 0.2890022586 - 6.153120397e-13i
155 -0.09773096907 + 1.775756873e-12i
156 0.5594666533 + 3.920484942e-12i
157 -0.9914326841 - 4.781381868e-12i
158 -0.06911349481 - 1.804676422e-12i
159 -0.08712673272 - 2.620663184e-13i
160 -0.07905711592 - 5.584395761e-12i
161 -0.6741566706 + 1.474716113e-12i
162 0.8730859854 - 4.143953781e-12i
163 1.057087699 - 6.781651271e-12i
164 -0.3700085361 - 4.490176085e-12i
165 0.1615063388 + 1.451213751e-11i
166 -0.8572768066 + 2.452234196e-11i
167 -0.6263576218 + 1.533808761e-11i
168 0.5507433238 + 5.674902221e-12i
169 -0.09038986337 - 1.128324342e-11i
170 -0.4639669197 - 3.833534619e-11i
171 -0.5031586366 - 4.325779785e-11i
172 -0.2596967567 + 3.645968069e-12i
173 0.5434154706 - 1.583645354e-12i
174 -1.451227893 - 2.215837702e-12i
175 0.2655508523 - 7.845027943e-12i
176 -0.07695522293 - 3.211621988e-12i
177 0.3473303932 + 2.307343643e-12i
178 -0.9660333996 + 1.248369147e-11i
179 -1.544541273 + 1.125913509e-11i
180 0.08417147285 - 3.765304044e-12i
181 0.7381324050 - 4.514593525e-12i
182 0.8954270227 - 2.067208592e-11i
183 1.201513671 + 2.677084153e-12i
184 0.1795141271 - 2.140298702e-12i
185 -0.7827184010 + 8.592535736e-12i
186 -0.1812923546 + 3.102860403e-11i
187 -0.4516336263 + 1.318946476e-12i
188 0.2983414654 + 8.768609910e-13i
189 0.9713631927 + 3.094401489e-12i
190 0.4226926652 + 3.145719655e-12i
191 1.619056595 - 3.076205989e-13i
192 -0.1466515298 + 2.143495189e-12i
193 -0.7808156085 - 7.708595093e-12i
194 0.8956579167 - 1.709110046e-12i
195 0.5004020626 + 1.177045302e-11i
196 0.3814655863 + 5.774087372e-13i
197 0.7948776077 + 3.613257764e-12i
198 0.08193398904 - 1.424809483e-11i
199 0.03168478907 - 7.980718880e-12i
200 -0.07071067504 + 7.824768674e-12i
201 -1.483406173 - 6.308586225e-12i
202 0.2038878919 - 5.778821409e-12i
203 -2.322692460 - 6.076529701e-13i
204 -0.8606653530 + 1.560963551e-11i
205 -0.3309458558 + 2.427138101e-11i
206 -0.06267304939 - 4.765880821e-12i
207 -0.1911277775 - 2.140873981e-11i
208 -0.2384336214 + 3.075325680e-11i
209 0.4114558492 - 4.794355652e-12i
210 0.4925998297 - 2.482934708e-11i
211 0.3440227188 - 2.230160953e-11i
212 0.03713158967 - 4.897686251e-11i
213 0.5244105261 + 4.603848729e-11i
214 0.3100815505 + 2.822234544e-11i
215 -0.2322797897 + 1.105844144e-11i
216 -0.2586538257 - 9.935782470e-12i
217 -0.2901585278 - 1.980162473e-11i
218 0.7885785432 + 3.173562915e-11i
219 2.008089662 - 1.152996552e-11i
220 -0.06883095937 - 1.096375765e-11i
221 -1.399314314 + 7.405627791e-11i
222 -1.451951704 + 9.847941652e-11i
223 -0.2598268055 - 7.545555094e-11i
224 -0.2347160098 - 1.310243964e-11i
225 0.07528537396 - 1.057163636e-11i
226 -0.2074959623 - 9.167855251e-12i
227 -0.7340392463 - 1.182745142e-11i
228 0.7840996797 - 7.461939473e-12i
229 -0.5345154261 + 2.290600609e-11i
230 0.1605621390 + 2.051197340e-11i
231 0.4795046209 + 4.103555052e-11i
232 0.6184847831 - 5.753343206e-12i
233 0.2506062954 - 1.890507167e-11i
234 0.2538593231 - 1.619120795e-11i
235 0.2668447231 - 3.910866206e-11i
236 -0.1480253885 + 3.357033515e-11i
237 -0.1146710601 + 1.988447541e-12i
238 -1.377496254 + 7.673482929e-13i
239 0.9133501852 - 2.653661558e-12i
240 -0.1311691466 - 4.624573394e-11i
241 1.155349582 - 5.469434099e-11i
242 0.6401056236 - 4.592969578e-12i
243 0.7170163412 + 7.453972314e-11i
244 -0.5120614774 + 1.344372256e-10i
245 0.3411932632 + 9.350225464e-11i
246 -0.6139083441 - 6.801252191e-11i
247 1.274829885 - 2.878398395e-11i
248 0.07726312995 - 1.402959091e-10i
249 -1.422369416 - 1.076683031e-10i
250 -0.06324554718 - 1.442472129e-11i
251 1.162160112 + 2.753499051e-11i
252 0.2499012741 + 1.891584380e-10i
253 0.1562937719 - 8.484119952e-12i
254 0.3997457808 + 2.231556317e-11i
255 -0.7698024757 + 3.366794486e-12i
256 0.06249999468 + 6.470151615e-12i
257 -0.1699774090 + 1.222673764e-11i
258 -0.4308817013 - 5.336736907e-12i
259 -2.323851051 + 6.327254729e-12i
260 -0.2132615383 - 2.061610096e-11i
261 -0.6584982720 + 2.207178022e-11i
262 0.09423937885 - 1.673602308e-11i
263 -0.9272202304 - 1.310428596e-11i
264 -0.1276821412 - 2.439603189e-11i
265 0.03321152029 - 3.596508916e-11i
266 1.254952773 + 1.420156907e-11i
267 -1.602816173 + 8.171112029e-12i
268 0.6321985978 + 5.916217422e-11i
269 0.6917347620 + 5.849454910e-11i
270 -0.2313471005 + 6.575603632e-11i
271 -0.8469392133 - 1.027542537e-10i
272 0.3667986833 - 3.948692273e-11i
273 1.485668030 - 1.490082197e-11i
274 -0.4295345539 - 1.284283132e-10i
275 -0.06156421555 + 4.304824499e-11i
276 0.2978446762 + 2.327142986e-11i
277 1.520882400 + 3.657303257e-12i
278 -0.07372058170 - 1.238188699e-11i
279 -0.08226181708 + 1.398647540e-11i
280 -0.2099363787 - 1.455742409e-11i
281 -1.502895657 - 1.036458142e-11i
282 0.4949999917 - 7.901164074e-13i
283 0.7787394891 + 5.996775557e-12i
284 -0.2234934804 + 7.231766034e-12i
285 0.7013200909 + 8.360879585e-12i
286 -0.2075921913 + 2.796007994e-11i
287 -0.9825612121 - 3.424261119e-11i
288 -0.06654351805 + 4.939733576e-13i
289 1.152660253 - 2.066202172e-11i
290 0.5531896281
291 1.486051084 + 3.194212842e-11i
292 -0.8558083958 + 3.235358235e-12i
293 0.2261437700 - 3.314406010e-12i
294 0.6329172458 - 1.956629295e-11i
295 -0.1323979038 + 1.313138430e-11i
296 0.6187932955 - 6.115613195e-11i
297 -0.2251969421 + 4.875539718e-11i
298 -0.9000220452 + 1.846746084e-11i
299 0.4842511722 - 2.357170141e-11i
300 -0.1173211900 + 1.710767226e-11i
301 -0.6896268337 + 1.087589868e-11i
302 -0.6072391430 + 5.571371218e-11i
303 0.3382852001 - 2.558687968e-13i
304 -0.3341678912 - 2.238113285e-13i
305 -0.4580017090 + 1.042095459e-12i
306 -0.3905290679 - 1.190013010e-11i
307 0.7109847675 - 2.776953956e-12i
308 -0.2043554388 + 2.087602870e-11i
309 -0.1039853933 - 3.934660618e-12i
310 0.06910630972 - 2.053449708e-12i
311 -0.7188914773 + 6.532471956e-12i
312 -0.3956025607 - 4.848894926e-13i
313 -0.9073646517 - 8.997472172e-12i
314 0.7010488152 - 1.498149643e-11i
315 0.2235184206 - 1.428634163e-11i
316 0.04887056724 + 2.436210340e-11i
317 -1.262234567 + 6.893019228e-12i
318 0.06160773647 - 8.178523864e-12i
319 0.5384837197 + 2.048705097e-11i
320 0.05590167793 - 7.576728083e-12i
321 0.5144788540 - 5.391167631e-12i
322 0.4767007641 - 2.114979390e-11i
323 -1.961157379 + 4.229557459e-11i
324 -0.6173648519 + 1.213464862e-11i
325 -0.1907469430 - 4.377134462e-11i
326 -0.7474736417 + 6.401747784e-12i
327 1.308387898
328 0.2616356644 - 9.524546388e-12i
329 0.7922482559 + 1.680104016e-12i
330 -0.1142023674 + 5.647671757e-12i
331 1.171055428 + 2.826007354e-12i
332 0.6061859023 + 8.155051241e-13i
333 -0.6588267588 + 8.844582039e-12i
334 0.4429014078 + 1.745995385e-11i
335 0.5654556019 - 2.630739051e-11i
336 -0.3894343527 + 1.278720604e-11i
337 0.9489947149 - 8.216477139e-12i
338 0.06391567527 - 7.882783722e-12i
339 -0.3442716074 + 9.933014101e-12i
340 0.3280747090 - 1.447590824e-11i
341 0.06726918547 + 8.108820041e-12i
342 0.3557871984 - 1.219460854e-11i
343 -0.3147691196 - 1.155660227e-11i
344 0.1836333132 - 4.075270431e-12i
345 0.2664003114 + 3.570442823e-11i
346 -0.3842528092 - 1.187013122e-11i
347 -0.1756834729 + 2.637643179e-11i
348 1.026173067 + 2.807284611e-11i
349 -1.220655798 - 4.201842010e-11i
350 -0.1877727881 + 1.718025897e-11i
351 -0.6977365598 - 3.435690332e-11i
352 0.05441562988 + 1.263910799e-11i
353 0.8523739457 - 2.188523190e-11i
354 -0.2455996071 - 9.920511660e-12i
355 -0.1998986373 + 3.581175362e-11i
356 0.6830888078 - 6.567303654e-12i
357 -2.285504078 - 3.966724548e-11i
358 1.092155575 - 1.029807993e-11i
359 0.1923568857 + 7.607380646e-11i
360 -0.05951830866 - 5.195637797e-11i
361 0.7866908854 + 7.741175910e-11i
362 -0.5219384972 + 6.742556468e-12i
363 1.062045760 - 3.019110291e-11i
364 -0.6331625025 + 1.083814696e-11i
365 -0.7654583046 - 8.576456640e-11i
366 -0.8495983513 + 4.245918554e-11i
367 0.2839532205 - 1.132277854e-11i
368 -0.1269355156 + 7.774764216e-12i
369 -0.2785624122 - 3.672606679e-11i
370 0.5534655603 + 7.256498016e-11i
371 0.09860328511 - 8.870497320e-11i
372 0.1281929723 + 2.515510144e-11i
373 -0.07590117016 + 1.277794148e-10i
374 0.3193531352 - 1.121525242e-10i
375 -0.1049353010 + 5.964355711e-11i
376 -0.2109592812 + 3.437558208e-12i
377 1.668405256 + 2.808997242e-12i
378 -0.6868575006 - 3.015024287e-12i
379 -1.530197233 - 5.851410184e-12i
380 -0.2988887971 - 3.840646875e-12i
381 0.6632472319 - 1.900480224e-12i
382 -1.144845933 + 9.962706471e-12i
383 0.4152017804 - 2.189244659e-11i
384 0.1036982157 - 1.221106020e-11i
385 -0.1827810089 + 5.446803715e-13i
386 0.5521200085 - 1.458596424e-11i
387 -0.1955136962 + 3.229311720e-11i
388 -0.6333257099 + 3.794282403e-11i
389 0.07237469912 + 4.269193181e-12i
390 -0.3538377099 - 1.809371521e-11i
391 -0.7449564316 - 4.100565541e-13i
392 -0.2697368905 - 6.075706756e-12i
393 0.1563593599 - 1.491031371e-12i
394 -0.5620632466 - 1.488972495e-11i
395 0.04371104740 + 2.066275861e-12i
396 -0.05793602517 + 2.192655142e-11i
397 -0.06158542752 - 6.238576967e-11i
398 -0.02240470324 - 5.265042812e-12i
399 2.082183478 + 1.165532185e-11i
400 0.04999992318 + 1.769137911e-11i
401 0.7113784421 - 1.175562390e-11i
402 1.048926401 - 8.498774155e-12i
403 0.2084229679 + 3.075143563e-11i
404 -0.1441706799 - 6.711098132e-11i
405 -0.5521877852 - 1.617532441e-11i
406 1.642391521 + 8.303892823e-12i
407 0.5387522937 - 1.120849152e-12i
408 0.6085823144 + 8.160704531e-13i
409 0.8927654684 - 1.347890142e-12i
410 0.2340140534 - 1.913697536e-12i
411 -0.7126719456 + 2.266012236e-12i
412 0.04431652766 + 1.921220952e-12i
413 -0.3930825643 - 1.600930271e-13i
414 0.1351477320 + 3.892547770e-12i
415 0.5421891589
416 0.1685980347 + 1.169583600e-12i
417 -0.1223151783 - 8.934915592e-13i
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