Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 3e-12
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues 1,-1,0,0

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Spectral parameter

$R= 9.23048002425$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.7071067811
3 0.3864687242
4 0.4999999999
5 -0.4472135954 + 1.086663124e-12i
6 0.2732746556 + 1.665887596e-13i
7 -1.386243657 + 4.083123647e-13i
8 0.3535533905
9 -0.8506419251
10 -0.3162277659 + 3.460070315e-13i
11 1.241795037 - 5.591700464e-13i
12 0.1932343621
13 -0.9546036283 + 1.640556934e-13i
14 -0.9802222902 + 1.107722357e-13i
15 -0.1728340677
16 0.2499999999 - 2.005598790e-13i
17 -1.354415910
18 -0.6014946736 + 1.348839525e-13i
19 -0.2843346317 + 1.765872551e-13i
20 -0.2236067977 + 1.067148188e-13i
21 -0.5357398176 - 2.337031654e-13i
22 0.8780816917 - 3.680448381e-13i
23 -1.485073238 + 2.174274284e-13i
24 0.1366373278 + 1.652654304e-13i
25 0.1999999999 - 4.312939182e-13i
26 -0.6750066988 + 1.142160622e-12i
27 -0.7152152237 + 1.016910458e-12i
28 -0.6931218287 - 3.453437226e-12i
29 0.08751278634 - 9.136373146e-13i
30 -0.1222121410 + 3.474274461e-12i
31 1.373238440 - 1.785854159e-12i
32 0.1767766959 + 1.036632467e-11i
33 0.4799149441 + 3.723672004e-12i
34 -0.9577166788 - 6.202859879e-11i
35 0.6199470113 + 2.198742766e-11i
36 -0.4253209515 + 1.671420193e-10i
37 -0.05273340200 - 1.520112250e-10i
38 -0.2010549632 - 2.415496362e-10i
39 -0.3689244170 + 4.914545409e-10i
40 -0.1581138817 - 6.992370886e-11i
41 -0.9458496085 - 9.152398783e-10i
42 -0.3788251750 + 1.385791269e-9i
43 0.7277632560 - 2.291471656e-13i
44 0.6208975186 - 6.432245876e-13i
45 0.3804186338 + 4.811402499e-13i
46 -1.050105357 - 3.598780916e-13i
47 1.122372411 - 5.478536896e-13i
48 0.09661718123 + 2.354751907e-12i
49 0.9216714766 - 1.376130806e-12i
50 0.1414213560 - 2.430689380e-12i
51 -0.5234393885 + 5.774212201e-12i
52 -0.4773018143 - 2.062505571e-12i
53 0.7494961009 - 6.277491672e-12i
54 -0.5057335341 + 9.373178460e-12i
55 -0.5553476237 - 2.767933747e-12i
56 -0.4901111459 - 1.150761494e-11i
57 -0.1098864415 + 1.104192955e-11i
58 0.06188088495 + 4.893882989e-12i
59 -0.7114041251 - 2.393429187e-12i
60 -0.08641703405 - 5.367512058e-12i
61 -0.7730180896 - 4.867496220e-12i
62 0.9710262152 + 2.403869453e-11i
63 1.179196970 - 4.217393567e-11i
64 0.1249999983 - 1.817664190e-11i
65 0.4269117293 + 1.307685138e-10i
66 0.3393511077 - 6.222874171e-11i
67 -0.3925313478 - 1.135765411e-10i
68 -0.6772079464 + 1.390127663e-10i
69 -0.5739343671 - 7.897884701e-11i
70 0.4383687322 - 8.707772738e-11i
71 1.176356407 + 1.286258011e-10i
72 -0.3007473347 + 1.060674055e-10i
73 0.2621713423 + 3.585034654e-10i
74 -0.03728817533 - 6.765324982e-10i
75 0.07729366410 - 9.221285918e-10i
76 -0.1421671842 + 1.821088182e-9i
77 -1.721430491 + 3.067664820e-11i
78 -0.2608689773 + 6.675579990e-12i
79 1.430689038 - 3.426808583e-11i
80 -0.1118033973 + 1.825154781e-11i
81 0.5742336127 + 3.730193568e-11i
82 -0.6688166343 - 5.424450498e-11i
83 -1.191251196 - 3.644192612e-11i
84 -0.2678699011 + 9.773027442e-11i
85 0.6057132065 - 2.431193046e-11i
86 0.5146063273 - 8.453044199e-11i
87 0.03382096805 + 1.757288414e-10i
88 0.4390408394 - 8.416661759e-11i
89 -1.940876183 - 2.415308180e-10i
90 0.2689966215 + 3.444045846e-10i
91 1.323313216 - 1.087951025e-10i
92 -0.7425366441 - 3.250981555e-10i
93 0.5307137678 + 8.247317575e-10i
94 0.7936371225 - 3.266189807e-10i
95 0.1271582303 - 1.071211029e-9i
96 0.06831876342 + 1.328943024e-9i
97 0.1537709797 - 7.670289465e-11i
98 0.6517200166 - 1.799699311e-9i
99 -1.056322754 + 2.259778947e-9i
100 0.1000000826 + 1.196161852e-9i
101 1.514024463 - 3.801053352e-9i
102 -0.3701275222 + 2.984256909e-10i
103 -0.3516976978 + 3.815726277e-9i
104 -0.3375035937 - 3.191430265e-9i
105 0.2395898963 - 3.136351841e-9i
106 0.5299737799 + 5.921625220e-11i
107 -1.408520602 + 6.824076643e-11i
108 -0.3576076022 + 1.362490259e-10i
109 -1.608940856 + 2.641151198e-10i
110 -0.3926900710 - 2.902334737e-12i
111 -0.02037982841 - 2.785906293e-10i
112 -0.3465609210 - 1.241068483e-10i
113 0.3340674284 - 4.296053731e-10i
114 -0.07770148561 - 5.471271725e-10i
115 0.6641449578 + 2.592675667e-10i
116 0.04375642472 + 4.287725706e-10i
117 0.8120259004 + 5.138351776e-10i
118 -0.5030386126 + 9.015351192e-10i
119 1.877550466 + 7.349213685e-11i
120 -0.06110607993 - 2.329238589e-10i
121 0.5420548912 - 3.192306101e-10i
122 -0.5466064226 - 1.398850264e-9i
123 -0.3655412874 - 3.759028584e-11i
124 0.6866192832 + 8.504828612e-10i
125 -0.08944283202 - 1.273190515e-9i
126 0.8338181460 - 6.929143653e-10i
127 -1.327199733 - 1.325979177e-11i
128 0.08838827717 - 1.348404649e-9i
129 0.2812577667 + 4.874674039e-10i
130 0.3018725327 + 4.846284019e-9i
131 -0.3154645883 + 8.847069010e-9i
132 0.2399577137 + 3.785954384e-9i
133 0.3941570737 - 9.459318100e-11i
134 -0.2775615814 - 1.241848639e-10i
135 0.3198539912 + 2.637821887e-10i
136 -0.4788583702 - 4.427088598e-10i
137 -0.7783009497 - 9.113613545e-10i
138 -0.4058328497 + 4.177798398e-10i
139 -1.548770206 + 1.345272786e-10i
140 0.3099734379 - 9.944906986e-10i
141 0.4337619293 + 1.253264408e-9i
142 0.8318097314 + 1.951336192e-9i
143 -1.185422119 - 9.150246130e-10i
144 -0.2126604776 + 1.080520630e-10i
145 -0.03913677898 + 1.739353789e-9i
146 0.1853829697 - 1.974706896e-9i
147 0.3561969915 - 2.772352956e-9i
148 -0.02636664032 + 7.058422075e-10i
149 1.019201753 - 5.944604936e-10i
150 0.05465475617 - 2.499823698e-9i
151 -0.08149170975 + 1.320504238e-9i
152 -0.1005273036 + 2.785166253e-9i
153 1.152123000 + 8.593818117e-10i
154 -1.217234895 + 3.448233817e-9i
155 -0.6141306408 + 3.182114384e-9i
156 -0.1844622400 - 2.938530977e-10i
157 0.1024566793 + 2.759242791e-9i
158 1.011649504 - 5.583117951e-9i
159 0.2896566629 - 1.564248432e-9i
160 -0.07905772826 - 9.890811450e-9i
161 2.058673375 + 2.647425091e-10i
162 0.4060444576 - 3.133474868e-10i
163 -0.3039747931 + 7.430090075e-11i
164 -0.4729247543 + 2.653842856e-10i
165 -0.2146245598 - 9.852419952e-10i
166 -0.8423419010 - 1.421180004e-9i
167 -1.595142465 - 3.084034884e-10i
168 -0.1894126307 + 5.684706092e-11i
169 -0.08873192046 - 7.436924414e-11i
170 0.4283041182 + 2.682576789e-9i
171 0.2418672365 + 3.774518184e-9i
172 0.3638815793 - 6.856451364e-10i
173 1.293993736 - 7.434506970e-10i
174 0.02391508414 + 7.845688201e-10i
175 -0.2772490934 - 5.029306322e-9i
176 0.3104485057 - 3.382334584e-9i
177 -0.2749352109 + 3.325579205e-9i
178 -1.372406830 - 1.714735087e-9i
179 0.1579981648 + 5.634764488e-10i
180 0.1902093702 + 7.096241695e-10i
181 -1.459956494 + 3.683200948e-10i
182 0.9357237368 - 2.267129392e-10i
183 -0.2987473276 - 2.026083726e-10i
184 -0.5250526892 - 1.215436078e-10i
185 0.02358306641 - 3.696375148e-10i
186 0.3752712614 + 4.218560353e-11i
187 -1.681906939 + 2.676942178e-10i
188 0.5611861282 - 1.032826102e-9i
189 0.9914624426 - 1.884305314e-9i
190 0.08991445730 - 5.818328163e-10i
191 0.009282184404 + 5.795582119e-10i
192 0.04830865974 + 1.145297679e-9i
193 -0.3776818918 + 3.660734783e-9i
194 0.1087328042 + 4.368845082e-9i
195 0.1649880560 - 2.422724871e-11i
196 0.4608355233 - 2.920225436e-9i
197 0.3261565716 - 3.129875258e-9i
198 -0.7469334938 - 4.774943654e-9i
199 1.510520442 - 2.969718161e-9i
200 0.07071078592 + 2.076174613e-9i
201 -0.1517008608 + 2.836579318e-9i
202 1.070577213 + 1.068796367e-9i
203 -0.1213140608 - 1.151782653e-9i
204 -0.2617199224 - 2.703091743e-9i
205 0.4229969811 + 1.903204595e-9i
206 -0.2486879688 + 1.000480466e-9i
207 1.263265645 + 1.211710422e-9i
208 -0.2386508433 + 6.867968231e-10i
209 -0.3530852266 + 1.378049039e-9i
210 0.1694158933 + 1.043901525e-9i
211 -0.5918369061 + 1.239981812e-9i
212 0.3747482597 + 3.021574411e-9i
213 0.4546250371 + 1.271013248e-9i
214 -0.9959747496 - 3.738077277e-9i
215 -0.3254660117 - 5.191656326e-9i
216 -0.2528671307 - 5.105020341e-9i
217 -1.903643112 - 4.636790539e-10i
218 -1.137693054 - 7.050554000e-10i
219 0.1013209865 - 3.356042623e-10i
220 -0.2776738278 - 1.223589870e-10i
221 1.292930317 - 3.401053351e-10i
222 -0.01441064018 + 7.696507789e-10i
223 0.4013921390 + 1.578325169e-9i
224 -0.2450555402 + 3.949871682e-10i
225 -0.1701283431 + 5.564905713e-10i
226 0.2362214100 + 6.909448688e-10i
227 -1.361400981 - 1.210541514e-9i
228 -0.05494329592 - 9.301533953e-10i
229 0.2479321044 - 2.150512826e-10i
230 0.4696213057 - 1.168957427e-9i
231 -0.6652790780 - 4.151522750e-10i
232 0.03094038754 - 5.876144834e-10i
233 0.9768234393 - 1.547243850e-9i
234 0.5741890078 + 2.135840631e-10i
235 -0.5019400972 + 1.144457430e-9i
236 -0.3557019089 + 1.953959574e-9i
237 0.5529168821 + 4.176864248e-9i
238 1.327628938 + 3.867583701e-9i
239 -0.4107315247 + 8.488403716e-10i
240 -0.04320890151 - 5.062552476e-9i
241 1.220867933 - 4.213041488e-9i
242 0.3832903749 - 4.075698824e-9i
243 0.9371381253 - 6.214594366e-9i
244 -0.3865088521 + 2.623158573e-9i
245 -0.4121835360 + 6.326341734e-9i
246 -0.2584767342 - 3.296454714e-10i
247 0.2714268736 - 1.575497716e-11i
248 0.4855131775 + 9.943012165e-10i
249 -0.4603812381 + 1.244413658e-9i
250 -0.06324550635 + 6.415309690e-10i
251 -0.004313067803 - 2.079852421e-10i
252 0.5895984003 - 1.208319101e-9i
253 -1.844156679 - 1.408407484e-9i
254 -0.9384719867 - 7.519206573e-10i
255 0.2340892715 + 8.524584389e-10i
256 0.06250008462 + 1.317339075e-9i
257 0.2377175472 + 5.118402697e-10i
258 0.1988792443 - 2.061477683e-10i
259 0.07310124257 - 1.334396996e-9i
260 0.2134557229 - 2.046240272e-9i
261 -0.07444202911 + 1.153692343e-10i
262 -0.2230673560 + 2.998245194e-9i
263 -0.5845920511 + 2.103796806e-9i
264 0.1696756923 + 2.095455542e-9i
265 -0.3351848278 + 2.643664608e-10i
266 0.2787108581 - 4.167168215e-9i
267 -0.7500881999 - 3.561268515e-9i
268 -0.1962658125 - 1.819089653e-9i
269 1.611391557 + 4.011379541e-10i
270 0.2261710749 + 2.262425381e-9i
271 -0.7940855897 + 2.385292097e-9i
272 -0.3386039589 + 2.688652305e-10i
273 0.5114191469 - 4.316930915e-10i
274 -0.5503418821 - 7.738866101e-10i
275 0.2483590604 + 8.140606283e-10i
276 -0.2869671627 + 2.990170673e-10i
277 -0.03317352144 - 2.316495485e-10i
278 -1.095145880 + 4.944024114e-10i
279 -1.168134222 - 4.251636946e-10i
280 0.2191842704 - 1.335231982e-9i
281 1.134804153 - 1.635885282e-10i
282 0.3067159946 + 8.185796024e-10i
283 -0.1088701031 + 1.098215954e-10i
284 0.5881783231 + 1.792660423e-9i
285 0.04914274869 + 4.151977561e-10i
286 -0.8382200854 - 1.630331497e-9i
287 1.311177912 - 3.841161058e-10i
288 -0.1503737241 - 8.609844934e-10i
289 0.8344424161 - 5.870394329e-10i
290 -0.02767387629 + 1.334141602e-9i
291 0.05942786318 + 2.856826242e-9i
292 0.1310855558 - 1.407810413e-9i
293 -0.5170077305 - 1.973290323e-9i
294 0.2518694952 + 3.429488079e-10i
295 0.3181494060 - 2.678719952e-9i
296 -0.01864414940 - 9.853225357e-10i
297 -0.8881503587 + 5.001140032e-9i
298 0.7206845037 + 1.116694396e-10i
299 1.417656316 + 1.787956398e-10i
300 0.03864689199 + 2.259201269e-10i
301 -1.008857186 + 1.614662925e-10i
302 -0.05762343190 - 3.026314468e-10i
303 0.5851232137 + 4.858507549e-11i
304 -0.07108373032 - 1.004547180e-9i
305 0.3457042058 + 2.088227479e-10i
306 0.8146739748 + 2.618812370e-10i
307 -0.3359733215 + 6.628171749e-10i
308 -0.8607152535 - 9.809370638e-11i
309 -0.1359201995 + 1.007762166e-9i
310 -0.4342561487 - 3.746808374e-10i
311 -0.4030094383 - 2.027862122e-9i
312 -0.1304344280 + 8.420776673e-10i
313 0.2380730273 - 2.514742785e-10i
314 0.07244767159 - 6.637196569e-11i
315 -0.5273528735 + 5.715623183e-10i
316 0.7153446615 + 2.004986531e-9i
317 -1.611261619 - 1.905341223e-9i
318 0.2048182696 - 1.438447277e-10i
319 0.1086729522 + 2.392854572e-10i
320 -0.05590177803 - 1.078920141e-9i
321 -0.5443491291 + 4.705105900e-10i
322 1.455701898 - 7.266872731e-11i
323 0.3851074493 + 1.473267119e-9i
324 0.2871167091 - 1.412250638e-9i
325 -0.1909205621 + 1.943186548e-9i
326 -0.2149427377 - 1.154198136e-9i
327 -0.6218053526 - 3.698564361e-10i
328 -0.3344082783 + 4.374802052e-10i
329 -1.555881676 - 5.320274665e-10i
330 -0.1517624553 - 3.037124711e-10i
331 -0.1115184337 + 8.738938874e-11i
332 -0.5956256239 - 3.405509193e-10i
333 0.04485727410 + 5.331038127e-10i
334 -1.127935994 + 6.901012717e-10i
335 0.1755453954 + 6.347982327e-10i
336 -0.1339349425 + 9.021026513e-11i
337 1.369957916 + 5.237660120e-10i
338 -0.06274302133 - 1.098463260e-9i
339 0.1291066281 - 6.521590688e-11i
340 0.3028565578 - 6.534285504e-10i
341 1.705280606 - 1.074001658e-9i
342 0.1710258112 + 5.854319153e-10i
343 0.1085823789 - 5.136686880e-10i
344 0.2573031804 + 2.180717514e-10i
345 0.2566713180 + 9.887604737e-10i
346 0.9149918101 + 4.642563834e-10i
347 0.8421224233 - 3.663169243e-10i
348 0.01691055681 + 9.757869569e-10i
349 -1.526328251 - 1.087503900e-9i
350 -0.1960444419 + 1.926100748e-10i
351 0.6827471261 + 1.105095953e-9i
352 0.2195203904 - 4.505153536e-10i
353 1.836609357 + 1.348913884e-9i
354 -0.1944087561 - 5.892523247e-10i
355 -0.5260827821 - 2.766225503e-9i
356 -0.9704381308 - 8.470093642e-10i
357 0.7256144479 - 1.053852167e-9i
358 0.1117214329 - 1.188541242e-9i
359 0.3648285751 + 4.263901368e-9i
360 0.1344983925 + 1.383969393e-9i
361 -0.9191537314 + 1.112351513e-9i
362 -1.032345049 + 1.328492788e-9i
363 0.2094870641 - 2.861371673e-9i
364 0.6616565642 - 1.054113648e-9i
365 -0.1172465298 + 6.024008683e-10i
366 -0.2112463622 - 9.292932322e-10i
367 -0.6142450309 + 3.734312941e-12i
368 -0.3712682768 + 4.733021746e-10i
369 0.8045792469 - 4.386857407e-10i
370 0.01667579270 + 4.033570812e-10i
371 -1.038984174 + 5.731757383e-10i
372 0.2653568725 + 2.792659626e-10i
373 -1.183105995 - 6.036831051e-11i
374 -1.189287791 + 3.452095755e-10i
375 -0.03456685882 - 6.483394211e-10i
376 0.3968185187 - 7.384498487e-10i
377 -0.08354002812 - 9.568333213e-11i
378 0.7010698648 - 6.032730412e-10i
379 -0.3600955308 + 3.097340305e-10i
380 0.06357913996 - 2.028864273e-10i
381 -0.5129211468 + 5.726316049e-10i
382 0.006563443167 - 2.170253630e-10i
383 -1.460895759 + 2.953500848e-10i
384 0.03415941178 + 1.151353120e-9i
385 0.7698471313 + 2.129919240e-10i
386 -0.2670615788 + 5.113334831e-10i
387 -0.6190658570 + 9.953497566e-10i
388 0.07688542402 - 8.442683033e-10i
389 1.393167967 - 2.324243868e-9i
390 0.1166642242 + 8.414805053e-10i
391 2.011406669 - 2.181600905e-9i
392 0.3258599217 - 2.109274681e-9i
393 -0.1219172477 + 2.475272579e-9i
394 0.2306276081 - 7.328830539e-10i
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