Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 5e-13
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues 1,1,0,0

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Spectral parameter

$R= 6.73532969117$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.7071067806 + 5.286557608e-13i
3 -0.6266049788
4 0.4999999997 + 2.337431837e-13i
5 0.4472135952 + 2.821587869e-13i
6 -0.4430766293 - 4.121926920e-13i
7 -1.825255500 - 4.080966868e-12i
8 0.3535533902 + 3.982766731e-13i
9 -0.6073662001 - 2.685918401e-13i
10 0.3162277653 + 6.760406046e-13i
11 -1.355624718 - 1.015860068e-12i
12 -0.3133024894
13 0.2515442705 + 1.114659998e-12i
14 -1.290650543 - 7.394489396e-13i
15 -0.2802262644 - 1.231367515e-12i
16 0.2499999985 + 1.546972510e-12i
17 0.8726715096 + 1.679536674e-12i
18 -0.4294727555 - 3.622989162e-12i
19 -0.2221097895 + 1.637757296e-12i
20 0.2236067947 + 3.183876215e-12i
21 1.143714195 - 9.547612451e-12i
22 -0.9585714361 + 4.714073330e-12i
23 -1.008662315 + 2.260141851e-11i
24 -0.2215382781 - 3.907664970e-11i
25 0.2000000232 - 2.477415785e-11i
26 0.1778685362 + 1.318972198e-10i
27 1.007183707 - 4.622269160e-11i
28 -0.9126274706 - 2.992952042e-10i
29 -0.3265086344 + 3.551686742e-10i
30 -0.1981498927 + 1.569176813e-13i
31 0.5699470549 + 1.870484361e-12i
32 0.1767766975 - 2.357161112e-12i
33 0.8494411988 - 3.354309880e-13i
34 0.6170719405 + 3.017433049e-12i
35 -0.8162790739 - 2.831510550e-12i
36 -0.3036831008 + 6.989156167e-13i
37 0.1358179814 + 6.631988302e-12i
38 -0.1570553326 - 4.943792073e-12i
39 -0.1576188835 - 9.987683225e-12i
40 0.1581138740 + 9.529089321e-12i
41 -1.381462851 + 4.664235867e-12i
42 0.8087280761 - 2.032110304e-11i
43 -0.1774540413 + 2.619964741e-11i
44 -0.6778123894 + 3.175926444e-11i
45 -0.2716223416 - 8.573251279e-11i
46 -0.7132319504 + 2.223471363e-12i
47 1.590142916 + 1.027210853e-10i
48 -0.1566511442 - 1.068155740e-10i
49 2.331557649 + 6.148760336e-12i
50 0.1414211522 + 2.166876322e-10i
51 -0.5468203130 - 9.523334707e-13i
52 0.1257721359 - 1.366018574e-13i
53 -0.5394203788 + 1.148963240e-13i
54 0.7121863912 + 8.027368779e-12i
55 -0.6062537995 - 5.619050127e-12i
56 -0.6453252545 - 1.873525688e-11i
57 0.1391750861 + 1.376161460e-11i
58 -0.2308762491 + 1.653127767e-11i
59 -1.402533145 - 1.239857084e-11i
60 -0.1401131501 + 1.834303911e-11i
61 -0.8361424645 - 1.085037774e-11i
62 0.4030134863 - 6.137549656e-11i
63 1.108598478 + 2.344222929e-11i
64 0.1249999374 + 6.642099614e-11i
65 0.1124940077 + 1.105366337e-11i
66 0.6006456800 - 5.088721833e-11i
67 -0.1647365640 - 1.574477302e-11i
68 0.4363356770 + 8.321938647e-11i
69 0.6320329583 - 1.513273578e-10i
70 -0.5771963146 - 1.663141512e-10i
71 -0.6996606741 + 1.198724147e-11i
72 -0.2147363943 + 1.564300403e-11i
73 0.4760220891 + 4.080207870e-11i
74 0.09603785995 - 4.251962648e-11i
75 -0.1253209251 - 7.494551206e-11i
76 -0.1110549092 + 1.631814803e-11i
77 2.474361520 - 4.277673016e-11i
78 -0.1114533145 - 7.758259328e-11i
79 -1.617519873 + 1.677959736e-10i
80 0.1118032529 + 1.547521865e-10i
81 -0.02373996210 - 1.445174697e-10i
82 -0.9768417186 - 3.038098677e-11i
83 -1.078679395 + 9.017498407e-11i
84 0.5718569516 + 1.504282892e-10i
85 0.3902703671 + 2.093764467e-10i
86 -0.1254790686 + 1.377654944e-10i
87 0.2045920142 - 3.048535158e-10i
88 -0.4792856520 - 6.788696115e-11i
89 0.5754130471 + 6.437109299e-12i
90 -0.1920660972 + 4.311617978e-11i
91 -0.4591326955 + 1.375578639e-10i
92 -0.5043312805 + 1.418978500e-10i
93 -0.3571316458 - 1.876974439e-11i
94 1.124401083 - 1.871958692e-10i
95 -0.09933032647 - 2.026596532e-10i
96 -0.1107689988 - 1.687853648e-10i
97 -0.4012396148 + 1.356796348e-11i
98 1.648660141 + 9.186285996e-11i
99 0.8233605737 + 6.499883819e-11i
100 0.09999996591 + 3.629251741e-11i
101 0.1218162876 - 7.280520774e-11i
102 -0.3866602027 - 1.589192440e-10i
103 -1.171581229 - 8.978072732e-11i
104 0.08893431816 + 1.251801079e-11i
105 0.5114843809 + 1.623037529e-10i
106 -0.3814280731 + 2.829010252e-10i
107 1.496524804 + 9.158014782e-11i
108 0.5035919356 - 1.101741760e-10i
109 -1.107028063 - 7.916677595e-11i
110 -0.4286861301 - 4.920664203e-11i
111 -0.08510426520 + 4.041696085e-11i
112 -0.4563139682 + 9.815692753e-11i
113 0.3712932465 + 1.266071358e-10i
114 0.09841164720 + 9.246592039e-12i
115 -0.4510873753 - 1.235266486e-10i
116 -0.1632540318 - 1.258229499e-10i
117 -0.1527793543 - 1.424986384e-10i
118 -0.9917407750 + 7.363885546e-11i
119 -1.592848776 + 3.161537859e-10i
120 -0.09907511339 + 1.772881154e-10i
121 0.8377183548 + 2.615217674e-11i
122 -0.5912417630 - 2.662555024e-10i
123 0.8656319990 - 5.327428875e-10i
124 0.2849737492 - 2.345827643e-10i
125 0.08944255603 + 1.733603619e-10i
126 0.7838969992 + 5.495790241e-10i
127 1.114984288 + 8.206733686e-10i
128 0.08838814220 + 2.178248879e-10i
129 0.1111941136 - 5.773763424e-10i
130 0.07954517285 + 1.169125841e-10i
131 -0.4642071569 + 9.708854782e-11i
132 0.4247206232 - 2.349860584e-11i
133 0.4054073385 - 2.388584888e-10i
134 -0.1164862050 - 1.564797803e-10i
135 0.4504262566 - 3.292973118e-11i
136 0.3085359841 - 1.562660372e-11i
137 0.5232457972 - 1.442566461e-10i
138 0.4469148082 - 1.257180107e-10i
139 -0.7182712090 - 5.950194957e-11i
140 -0.4081396272 + 9.431338049e-11i
141 -0.9963917165 + 1.994747840e-10i
142 -0.4947348988 + 1.058594278e-10i
143 -0.3409996048 - 2.911725869e-11i
144 -0.1518414382 - 1.189620954e-10i
145 -0.1460189276 - 2.499603543e-11i
146 0.3365984796 - 5.502981312e-12i
147 -1.460965636 + 1.410904211e-12i
148 0.06790899715 - 3.448122399e-12i
149 1.407404961 + 2.029156749e-11i
150 -0.08861532307 - 3.072165939e-12i
151 -1.272047516 - 4.301151230e-11i
152 -0.07852761723 - 5.461612468e-11i
153 -0.5300311487 - 3.310332195e-11i
154 1.749637742 + 4.110541171e-11i
155 0.2548879713 + 1.075378630e-10i
156 -0.07880952451 + 8.274052638e-11i
157 -0.4663872013 + 5.464255517e-11i
158 -1.143759168 + 1.000702322e-11i
159 0.3380035076 - 1.339603270e-11i
160 0.07905698367 - 4.485626267e-11i
161 1.841066412 - 8.008453377e-12i
162 -0.01678675422 - 3.206133928e-11i
163 0.09081795078 + 3.702158430e-11i
164 -0.6907314753 + 5.496864615e-11i
165 0.3798816436 + 9.445609820e-12i
166 -0.7627414596 + 4.676186242e-12i
167 1.509733154 - 6.923599427e-11i
168 0.4043640358 - 7.640159702e-12i
169 -0.9367254565 - 2.443792818e-11i
170 0.2759629224 + 4.254779384e-11i
171 0.1349018841 + 9.981913848e-11i
172 -0.08872702965 + 2.259319114e-11i
173 -1.174579718 - 3.749235262e-11i
174 0.1446683317 - 1.427491889e-10i
175 -0.3650510530 - 5.074894905e-11i
176 -0.3389061154 - 6.844608004e-11i
177 0.8788341259 + 1.415130098e-10i
178 0.4068783282 + 1.526465054e-10i
179 1.290516820 + 4.491719791e-11i
180 -0.1358111957 - 1.628912152e-11i
181 0.6249032983 - 6.959926383e-11i
182 -0.3246557185 - 3.454591684e-11i
183 0.5239310467 - 9.481657856e-12i
184 -0.3566160117 + 4.013682915e-11i
185 0.06073960940 + 4.371664194e-11i
186 -0.2525302292 + 8.714377309e-12i
187 -1.183015014 - 6.122029878e-11i
188 0.7950715914 - 9.037558685e-11i
189 -1.838367467 - 6.298083384e-11i
190 -0.07023732724 + 4.801803285e-11i
191 -1.544224964 + 1.425908059e-10i
192 -0.07832571908 + 1.026894396e-10i
193 -0.4385132610 + 1.124657311e-10i
194 -0.2837192020 - 4.410674785e-11i
195 -0.07048912837 - 1.950328040e-10i
196 1.165778930 - 1.087737640e-10i
197 0.6704046739 - 6.244197795e-11i
198 0.5822038156 + 7.715790271e-11i
199 -0.4309806323 + 1.051534675e-10i
200 0.07071066968 + 9.136657053e-12i
201 0.1032249875 - 2.415035354e-10i
202 0.08613726378 - 2.004437516e-10i
203 0.5959611407 - 7.197328352e-11i
204 -0.2734101976 + 4.313722816e-11i
205 -0.6178090658 + 1.051130924e-10i
206 -0.8284331512 + 6.293494524e-11i
207 0.6126273455 + 4.217163514e-11i
208 0.06288608524 - 1.836627258e-11i
209 0.3010975694 - 5.360138366e-11i
210 0.3616741770 + 5.407750316e-12i
211 1.961641592 - 2.364218708e-11i
212 -0.2697102212 + 3.405429766e-11i
213 0.4384108556 - 8.444924025e-13i
214 1.058202939 - 4.447808617e-11i
215 -0.07935983607 - 1.357988444e-11i
216 0.3560931937 + 5.990508300e-12i
217 -1.040299022 + 2.169705708e-11i
218 -0.7827871407 + 3.998556199e-11i
219 -0.2982778604 + 2.674710031e-11i
220 -0.3031269258 + 2.482270784e-11i
221 0.2195155179 + 1.898636003e-12i
222 -0.06017777518 - 1.112939625e-12i
223 0.7458005229 - 3.004584257e-11i
224 -0.3226626706 + 3.679265863e-11i
225 -0.1214731903 - 5.285767504e-11i
226 0.2625440941 - 3.981739208e-11i
227 -0.4590552820 - 3.623143062e-11i
228 0.06958763448 - 9.024379260e-11i
229 0.9476987447 + 3.946642984e-11i
230 -0.3189670417 + 1.876886671e-11i
231 -1.550447314 + 9.756668275e-11i
232 -0.1154382098 + 9.875454767e-11i
233 -1.055817956 + 4.792099314e-11i
234 -0.1080313536 - 6.232627097e-11i
235 0.7111335454 + 3.057635598e-11i
236 -0.7012665666 - 1.243373043e-11i
237 1.013545985 - 8.322459206e-11i
238 -1.126314020 + 6.312101224e-11i
239 -0.03691790714 - 1.585652595e-10i
240 -0.07005651194 - 5.766198661e-11i
241 -1.173428865 - 2.387634044e-11i
242 0.5923563554 - 9.210533605e-12i
243 -0.9923080639 + 6.752477441e-11i
244 -0.4180712058 - 3.354032233e-11i
245 1.042704230 + 5.494106286e-11i
246 0.6120938520 + 5.351299771e-11i
247 -0.05587040122 - 4.633017034e-11i
248 0.2015067066 + 8.154775590e-12i
249 0.6759058442 - 1.864975460e-11i
250 0.06324557743 - 2.557791830e-11i
251 0.4893731397 - 1.897679104e-11i
252 0.5542992360 + 1.501868788e-11i
253 1.367367610 - 7.540960748e-11i
254 0.7884134285 + 7.336969832e-11i
255 -0.2445454421 - 3.878950627e-11i
256 0.06250004755 - 5.056569005e-11i
257 -0.5001899304 + 1.554281919e-10i
258 0.07862575871 - 3.314061881e-11i
259 -0.2479026131 + 8.878934268e-11i
260 0.05624699375 + 1.621749712e-11i
261 0.1983101143 - 8.782022733e-12i
262 -0.3282438725 - 9.781209305e-11i
263 -0.4327435361 - 7.049963764e-11i
264 0.3003228638 - 5.101606523e-11i
265 -0.2412361155 - 1.223464458e-11i
266 0.2866661109 + 8.561065544e-12i
267 -0.3605565671 - 1.244329148e-10i
268 -0.08236855999 + 2.879052947e-10i
269 -0.1428860616 + 2.766768445e-12i
270 0.3184994534 - 1.407848612e-11i
271 -0.5803978701 + 3.357312486e-11i
272 0.2181679024 - 2.614947691e-11i
273 0.2876947409 + 1.160003387e-11i
274 0.3699905406 + 1.575126543e-11i
275 -0.2711248993 - 4.741909631e-11i
276 0.3160163775 + 3.219460924e-11i
277 -0.8499634456 - 8.979958607e-11i
278 -0.5078945139 + 3.366494354e-11i
279 -0.3461665838 + 6.103903867e-12i
280 -0.2885981930 - 4.498698401e-11i
281 0.1836627411 + 4.642559638e-11i
282 -0.7045552368 + 3.194294859e-11i
283 -0.5339759123 + 3.673967326e-11i
284 -0.3498303120 - 2.081638344e-11i
285 0.06224099326 + 3.402261847e-12i
286 -0.2411231558 + 3.584705763e-12i
287 2.521522545 + 1.271722813e-10i
288 -0.1073680746 - 1.220052646e-10i
289 -0.2384444018 - 3.386775261e-11i
290 -0.1032510699 + 8.455127169e-11i
291 0.2514189318 - 2.119824252e-10i
292 0.2380110323 + 3.329330301e-11i
293 1.003349013 - 1.836764228e-11i
294 -1.033058664 - 4.639934765e-11i
295 -0.6272319425 + 5.002901841e-11i
296 0.04801877615 + 1.422106065e-10i
297 -1.365363129 + 6.171074842e-11i
298 0.9951856024 + 2.615231908e-12i
299 -0.2537232117 - 1.067946289e-11i
300 -0.06266049391 - 4.275885663e-12i
301 0.3238987522 + 1.788931732e-10i
302 -0.8994731808 - 2.894456819e-10i
303 -0.07633071107 + 6.493886499e-11i
304 -0.05552749615 + 5.306651373e-11i
305 -0.3739340968 - 1.981963900e-10i
306 -0.3747885851 - 5.906139579e-11i
307 0.1191043105 - 9.343799134e-11i
308 1.237180811 - 7.570129624e-11i
309 0.7341185718 + 1.197147402e-10i
310 0.1802331771 - 9.944901432e-11i
311 1.648802391 - 1.633233277e-11i
312 -0.05572671912 + 2.354801473e-11i
313 0.1943936389 - 7.734591342e-11i
314 -0.3297854515 - 7.002322781e-11i
315 0.4957802862 + 3.690371442e-11i
316 -0.8087598610 + 4.478743884e-12i
317 0.2873360727 - 1.329736713e-10i
318 0.2390043629 + 2.137479919e-10i
319 0.4426228138 - 9.661916413e-11i
320 0.05590161645 + 8.947175568e-11i
321 -0.9377299707 + 2.210497800e-11i
322 1.301830538 + 5.172980625e-12i
323 -0.1938291317 + 2.593318633e-10i
324 -0.01186984427 - 2.163195042e-10i
325 0.05030887225 - 1.734884356e-11i
326 0.06421799836 + 1.181649512e-11i
327 0.6936693248 + 2.428096870e-11i
328 -0.4884206438 - 2.484635915e-10i
329 -2.902417378 + 9.998632708e-11i
330 0.2686169061 - 1.513392213e-11i
331 0.7146919975 - 7.886814440e-11i
332 -0.5393397579 + 1.081196602e-10i
333 -0.08249102382 - 2.440334434e-10i
334 1.067542462 + 4.515826539e-11i
335 -0.07367240505 - 3.464758114e-11i
336 0.2859284778 + 7.298485710e-11i
337 0.03260928599 + 3.729704921e-12i
338 -0.6623648960 - 4.535202953e-11i
339 -0.2326542249 - 4.961298402e-11i
340 0.1951353062 - 2.558697454e-11i
341 -0.7726342617 - 6.058463132e-11i
342 0.09539011513 - 1.242269051e-11i
343 -2.430432931 - 7.208245465e-12i
344 -0.06273955390 + 9.010874832e-11i
345 0.2826535858 + 8.730795431e-11i
346 -0.8305532640 - 4.752606103e-11i
347 -1.458716713 + 9.542112502e-11i
348 0.1022958307 + 3.473313691e-11i
349 1.835916255 - 6.797909106e-11i
350 -0.2581300971 - 1.248501700e-11i
351 0.2533512866 - 5.938849382e-12i
352 -0.2396427436 - 1.216162487e-10i
353 0.5938949150 - 7.629583013e-11i
354 0.6214297426 - 8.348446918e-11i
355 -0.3128977542 - 6.755739200e-12i
356 0.2877064652 + 6.505553020e-11i
357 0.9980868134 - 2.748774276e-11i
358 0.9125330069 + 2.319397485e-10i
359 1.483458619 + 1.413623400e-10i
360 -0.09603299647 - 3.389382744e-11i
361 -0.9506673155 + 7.809688097e-11i
362 0.4418733150 - 1.336792555e-12i
363 -0.5249184851 - 2.319971974e-11i
364 -0.2295662731 - 1.092885498e-11i
365 0.2128835821 - 1.637706831e-11i
366 0.3704752490 - 6.267426376e-11i
367 -0.2579115754 + 6.720577695e-11i
368 -0.2521655138 - 6.419582446e-11i
369 0.8390538095 + 3.285456561e-11i
370 0.04294937235 + 5.001657949e-11i
371 0.9845799952 + 2.103715858e-11i
372 -0.1785658576 + 2.718481880e-11i
373 0.7737311691 - 8.525745255e-12i
374 -0.8365180180 + 4.117619668e-11i
375 -0.05604521058 - 4.568750388e-11i
376 0.5622004396 + 1.465159583e-11i
377 -0.08213125632 - 3.800108617e-11i
378 -1.299922169 + 2.644559531e-11i
379 0.7204118106 - 4.983662331e-11i
380 -0.04966520715 - 5.449725557e-11i
381 -0.6986552368 + 5.002397001e-11i
382 -1.091931770 - 8.426315442e-11i
383 0.6114360946 + 6.432601198e-11i
384 -0.05538457512 - 2.985196791e-12i
385 1.106568088 + 7.027392774e-12i
386 -0.3100756609 + 3.665638543e-11i
387 0.1077796091 - 3.957696405e-11i
388 -0.2006198396 + 4.264542042e-11i
389 -1.182730967 + 3.123611509e-11i
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