Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 5e-14
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues 1,-1,0,0

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Spectral parameter

$R= 4.58236150313$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.7071067811
3 -1.663175459
4 0.4999999999
5 -0.4472135954
6 -1.176042645
7 -1.126006458
8 0.3535533905
9 1.766152610
10 -0.3162277660
11 -0.4387835890
12 -0.8315877299
13 0.2247263063
14 -0.7962068024
15 0.7437946773
16 0.2500000000
17 -1.129269801
18 1.248858487
19 -0.3407921390
20 -0.2236067977
21 1.872746309
22 -0.3102668512
23 -0.8395854223
24 -0.5880213230
25 0.2000000000 - 1.190927204e-13i
26 0.1589054951
27 -1.274246219
28 -0.5630032293 - 7.139292534e-13i
29 1.282349921
30 0.5259422610 + 1.673742644e-12i
31 -0.5121479281 + 3.174380776e-12i
32 0.1767766985 - 5.056765267e-12i
33 0.7297741046 - 1.058191743e-11i
34 -0.7985143417 + 4.811118216e-12i
35 0.5035653849 + 1.683993262e-11i
36 0.8830763180 + 2.860885844e-11i
37 -0.5968957530 - 5.209824012e-11i
38 -0.2409764324
39 -0.3737592778
40 -0.1581138830
41 0.4223083612
42 1.324231614
43 -0.3726852300
44 -0.2193917945
45 -0.7898474590
46 -0.5936765455
47 -1.716579951
48 -0.4157938650
49 0.2678905444
50 0.1414213562 - 1.485483371e-13i
51 1.878173820
52 0.1123631531 + 1.640425326e-13i
53 1.906683129 - 1.404839396e-13i
54 -0.9010281431 + 2.027809776e-13i
55 0.1962299865
56 -0.3981034011 - 5.191135624e-13i
57 0.5667971225
58 0.9067583251 + 1.321231273e-13i
59 0.1580893004 + 7.343998330e-13i
60 0.3718973386 - 2.904479331e-13i
61 -1.927310044 - 8.167098687e-13i
62 -0.3621432696 + 1.145824009e-12i
63 -1.988699245 - 2.298702677e-12i
64 0.1250000001 - 8.736047590e-13i
65 -0.1005006607 + 5.336007996e-12i
66 0.5160282100 + 2.748312528e-12i
67 -0.2519683285 - 6.445185201e-12i
68 -0.5646349064 - 4.121006358e-12i
69 1.396377861 + 3.515127818e-12i
70 0.3560744694 - 3.493088866e-12i
71 0.7848840494 + 1.086500183e-11i
72 0.6244292778 + 8.493473781e-12i
73 -0.9154629108 - 9.094897506e-12i
74 -0.4220690145 - 6.126635054e-12i
75 -0.3326352234 - 5.008583624e-11i
76 -0.1703963599 + 4.652089329e-11i
77 0.4940748741 + 7.131297500e-11i
78 -0.2642876191 - 7.457486455e-11i
79 -0.3025586328 + 2.291144226e-13i
80 -0.1118033988
81 0.3531424326
82 0.2986171060 - 1.588958013e-13i
83 1.683734795
84 0.9363731547 + 5.722596324e-13i
85 0.5050248078 - 4.904360000e-13i
86 -0.2635282532 - 2.848343867e-13i
87 -2.132772920 + 1.404547996e-13i
88 -0.1551334258 + 4.831797748e-13i
89 -0.003499899287 - 9.142860485e-13i
90 -0.5585064953
91 -0.2530432735 + 9.949349323e-13i
92 -0.4197927095 - 6.754086478e-13i
93 0.8517918596 + 1.751147238e-12i
94 -1.213805324 - 9.103194689e-13i
95 0.1524068847
96 -0.2940106639 - 1.002477434e-12i
97 0.5619619658 - 1.017941528e-12i
98 0.1894272059 + 5.195860623e-12i
99 -0.7749587549 - 3.005040557e-12i
100 0.1000000135 - 4.970547804e-12i
101 -0.5963275028 + 1.140546366e-12i
102 1.328069438 + 8.720297040e-12i
103 0.5486980704 - 4.719269706e-12i
104 0.07945280797 - 2.347294127e-12i
105 -0.8375175687 + 8.434035712e-12i
106 1.348228541 - 5.331145262e-13i
107 0.6094432109 + 4.019506417e-12i
108 -0.6371232785 - 1.875513929e-11i
109 -0.9316245614 + 5.115123497e-12i
110 0.1387557298 - 1.370541296e-12i
111 0.9927424384 - 2.005111723e-11i
112 -0.2815018014 + 3.629810314e-11i
113 -0.9385138110 - 5.085962397e-12i
114 0.4007890105 - 4.397582615e-11i
115 0.3754716597 + 3.270505035e-11i
116 0.6411709099 + 8.386974352e-11i
117 0.3969009512 - 2.800885321e-13i
118 0.1117860169 + 3.962108558e-13i
119 1.271565086 - 2.689511172e-13i
120 0.2629711296 + 1.320882815e-12i
121 -0.8074689643 - 4.803502418e-13i
122 -1.362814002 - 1.935053201e-12i
123 -0.7023729045 + 6.728940231e-13i
124 -0.2560739674 + 2.569684837e-12i
125 -0.08944270850 - 2.066425322e-12i
126 -1.406222723 - 1.170992005e-12i
127 -0.09627629649 + 2.277218100e-12i
128 0.08838837690 - 1.954475549e-12i
129 0.6198408494 + 2.345465674e-12i
130 -0.07106470026 - 3.586300023e-12i
131 -1.470764834 + 2.204209805e-12i
132 0.3648870189 + 5.549267580e-12i
133 0.3837340440 - 7.301651331e-12i
134 -0.1781685040 + 5.467462069e-12i
135 0.5698603726 - 1.270462664e-12i
136 -0.3992571591 - 7.181001383e-12i
137 -0.9125971493 + 6.850209133e-12i
138 0.9873885979 + 3.863686855e-12i
139 0.6556089331 - 6.082678089e-12i
140 0.2517827507 - 1.276789499e-11i
141 2.854975816 + 2.661192441e-12i
142 0.5549969814 + 2.441842682e-11i
143 -0.09860613431 + 8.627806952e-12i
144 0.4415389703 - 3.782825927e-11i
145 -0.5734840900 + 1.526059690e-11i
146 -0.6473272547 + 9.732673119e-12i
147 -0.4455514539 - 3.242455208e-11i
148 -0.2984451245 + 3.908103899e-11i
149 1.210277057 + 3.810362743e-12i
150 -0.2352100404 - 1.755774867e-11i
151 -0.5343540674 - 1.448556471e-12i
152 -0.1204882134 - 9.324100168e-13i
153 -1.994462829 - 1.573454750e-12i
154 0.3493624534 + 6.166659895e-13i
155 0.2290395543 + 1.583853257e-12i
156 -0.1868796311 + 1.237124636e-12i
157 1.144297957
158 -0.2139412712 - 2.395719888e-12i
159 -3.171148513 + 5.573293198e-12i
160 -0.07905696944 + 1.799303762e-12i
161 0.9453788002 - 6.366147144e-12i
162 0.2497096500 - 2.336883321e-12i
163 0.7137533231 - 3.138063625e-12i
164 0.2111542036 + 3.910993615e-13i
165 -0.3263652134 - 3.829480949e-12i
166 1.190580449 + 9.789076790e-12i
167 0.1923975898 + 1.615063832e-11i
168 0.6621158965 - 1.571719415e-11i
169 -0.9494979403 - 1.492968158e-11i
170 0.3571056638 + 5.937822735e-12i
171 -0.6018915733 + 5.799225374e-12i
172 -0.1863423264
173 0.4692536171 + 1.401968929e-11i
174 -1.508097497 + 4.951960490e-12i
175 -0.2252045880 - 1.892105176e-11i
176 -0.1096943278 - 1.366033130e-12i
177 -0.2629261531 - 1.878328499e-11i
178 -0.002472572793 - 6.013688899e-12i
179 1.342077593 - 3.752820397e-11i
180 -0.3949263558 + 2.724296492e-11i
181 -1.663733739 + 1.289903634e-12i
182 -0.1789286035 - 4.868765662e-12i
183 3.205454768 - 6.532472657e-12i
184 -0.2968382782 + 5.485044474e-12i
185 0.2669399079 + 1.571150959e-12i
186 0.6023077897 + 4.548122949e-12i
187 0.4955051260 + 5.649883852e-13i
188 -0.8582899860 + 2.197093361e-12i
189 1.434809440 - 5.196883025e-13i
190 0.1077679486 - 8.757447644e-12i
191 -0.01887602174 - 2.906523070e-13i
192 -0.2078971234 + 6.556713248e-12i
193 -0.3530214232 + 2.407052184e-12i
194 0.3973671284 - 1.424632999e-11i
195 0.1671500239 + 1.052052308e-12i
196 0.1339454802 + 3.140245632e-12i
197 -0.2376212552 + 5.010504182e-12i
198 -0.5479785458 + 1.245597458e-11i
199 -1.761112724 + 3.044460562e-12i
200 0.07071032661 - 1.644231535e-11i
201 0.4190684813 - 2.938080882e-11i
202 -0.4216672074 + 3.017046047e-11i
203 -1.443934080 + 2.887479105e-11i
204 0.9390870462 + 1.581349201e-12i
205 -0.1888610713 + 6.033427401e-12i
206 0.3879881288 - 1.994951669e-11i
207 -1.482835601 - 2.003031316e-11i
208 0.05618185160 - 6.158467603e-11i
209 0.1495340056 - 4.505089651e-12i
210 -0.5922143886 + 2.280055626e-12i
211 0.5840678547 + 8.658690803e-12i
212 0.9533415812 - 3.842196437e-12i
213 -1.305399749 - 2.761632184e-12i
214 0.4309414092 + 2.671337054e-12i
215 0.1666698614 + 9.693022330e-12i
216 -0.4505139379 + 3.874763360e-12i
217 0.5766819022 - 5.620387639e-12i
218 -0.6587581342 - 5.505349939e-12i
219 1.522575343 - 1.969809243e-11i
220 0.09811490496 + 1.935419228e-13i
221 -0.2537771742 + 7.448831330e-12i
222 0.7019748731 + 9.410269002e-12i
223 1.209588981 + 2.580160999e-12i
224 -0.1990510754 + 8.235850427e-12i
225 0.3532300490 + 1.566604570e-11i
226 -0.6636267630 - 2.464950213e-11i
227 -0.4695116891 - 1.814790102e-11i
228 0.2833987234 - 1.700677572e-11i
229 -0.2152661773 + 3.785363645e-11i
230 0.2655000899 + 2.193277118e-11i
231 -0.8217318268 - 1.522643943e-11i
232 0.4533789012 + 2.866724986e-11i
233 -1.357587440 + 3.998958091e-12i
234 0.2806513712 + 7.244366910e-12i
235 0.7676778251 + 4.008543397e-12i
236 0.07904469247 - 8.574437878e-12i
237 0.5032081266 - 6.673208525e-12i
238 0.8991322628 - 7.339505295e-12i
239 1.196666711 - 2.693739482e-12i
240 0.1859486844 + 2.355200225e-11i
241 0.9612512758 + 1.615315884e-12i
242 -0.5709669629 + 7.278113989e-12i
243 0.6869083905 + 6.056225966e-12i
244 -0.9636551742 - 2.808410153e-11i
245 -0.1198041224 - 1.185979418e-11i
246 -0.4966525780 - 1.356718412e-11i
247 -0.07658518634 + 1.970177220e-11i
248 -0.1810716592 + 3.039713281e-11i
249 -2.800346926 - 1.295273369e-11i
250 -0.06324635484 + 3.696539384e-13i
251 -1.934605388 + 2.467044169e-12i
252 -0.9943491830 - 1.643718269e-11i
253 0.3683952242 + 3.043319567e-12i
254 -0.06807817884 + 4.894209037e-12i
255 -0.8399433850 - 7.853224003e-12i
256 0.06250056849 + 2.096852150e-11i
257 1.203994475 - 2.242171601e-11i
258 0.4382938211 + 1.230304286e-11i
259 0.6721085178 - 6.999952131e-12i
260 -0.05025032512 - 2.288010050e-12i
261 2.264825611 - 3.851209078e-12i
262 -1.039987511 - 7.449810769e-12i
263 -0.1432458232 + 1.744966953e-12i
264 0.2580141295 + 1.089811550e-12i
265 -0.8526946889 + 9.781684154e-12i
266 0.2713410374 + 1.050404067e-11i
267 0.005821277924 - 4.429928757e-12i
268 -0.1259840555 - 1.226215812e-11i
269 0.8317476011 + 2.786663570e-12i
270 0.4029520755 - 1.416103441e-11i
271 1.532633617 + 1.444883771e-11i
272 -0.2823171390 + 3.281041775e-12i
273 0.4208557539 + 2.054466979e-13i
274 -0.6453038421 + 6.790529350e-12i
275 -0.08775653455 - 1.047785297e-11i
276 0.6981892390 + 1.208193313e-11i
277 0.002569178737 - 1.144935668e-11i
278 0.4635841727 - 1.377977269e-11i
279 -0.9045312098 + 2.201492768e-12i
280 0.1780370487 + 1.192358699e-11i
281 -1.004149218 - 1.862250744e-11i
282 2.018769717 + 1.391556121e-11i
283 -1.819362181 + 1.275769705e-11i
284 0.3924405010 + 2.479807082e-11i
285 -0.2534792212 - 1.689841818e-12i
286 -0.06972512598 + 5.105985758e-13i
287 -0.4755219401 - 1.429332950e-12i
288 0.3122146332 - 3.196822359e-12i
289 0.2752502717 - 4.854387173e-13i
290 -0.4055146427 - 4.171332220e-12i
291 -0.9346413859 - 6.654120394e-12i
292 -0.4577314011 + 3.359392913e-12i
293 1.171898735 + 3.047739316e-12i
294 -0.3150507231 + 5.855124952e-12i
295 -0.07069966347 + 1.413029948e-11i
296 -0.2110344318 - 2.653042512e-12i
297 0.5591182947 + 8.089523396e-12i
298 0.8557991657 - 7.474223912e-12i
299 -0.1886770081 - 7.291458116e-12i
300 -0.1663174588 - 8.838003683e-12i
301 0.4196460854 + 5.090259931e-12i
302 -0.3778454177 + 9.403727857e-12i
303 0.9917972700 + 4.763997609e-12i
304 -0.08519790251 - 3.589857646e-12i
305 0.8619194819 - 1.258568554e-11i
306 -1.410298272 - 9.756378960e-12i
307 -1.405709655 - 3.222125449e-11i
308 0.2470365817 + 1.392172697e-11i
309 -0.9125810560 + 5.818360007e-12i
310 0.1619551712 + 4.786529421e-11i
311 0.6224401657 + 1.711912803e-11i
312 -0.1321438146 - 3.365774281e-12i
313 -1.092452233 - 1.850089180e-11i
314 0.8091412061 - 4.170132102e-11i
315 0.8893741203 + 3.630766115e-11i
316 -0.1512795528 + 3.393005454e-12i
317 -0.4161466531 - 3.155901750e-12i
318 -2.242340670 - 3.501854533e-13i
319 -0.5626740627 - 6.663473977e-12i
320 -0.05590169230 + 5.122588634e-12i
321 -1.013611071 + 1.058924795e-11i
322 0.6684836076 + 3.299970401e-12i
323 0.3848462146 + 8.702679476e-12i
324 0.1765711994 - 1.023695166e-11i
325 0.04494527387 - 2.378378786e-12i
326 0.5047000126 - 4.972963528e-12i
327 1.549455468 - 2.305687375e-12i
328 0.1493085575 - 1.447961316e-12i
329 1.932880112 + 2.197961886e-12i
330 -0.2307748834 + 5.008271854e-12i
331 0.2656669975 - 1.800322161e-12i
332 0.8418673629 - 8.397316657e-12i
333 -1.054208875 - 5.929549573e-12i
334 0.1360458748 + 1.466434176e-12i
335 0.1126836048 + 4.188183598e-12i
336 0.4681865334 + 8.891513220e-12i
337 -0.2251618694 + 9.893037716e-12i
338 -0.6713962542 + 9.931883521e-12i
339 1.560907901 - 2.834732215e-13i
340 0.2525127297 + 4.438639355e-13i
341 0.2247222568 - 2.138639776e-11i
342 -0.4256014078 + 7.184772203e-12i
343 0.8243588374 - 8.201826101e-12i
344 -0.1317640827 - 5.421247141e-12i
345 -0.6244791114 - 1.990272469e-11i
346 0.3318118570 - 1.025516464e-11i
347 0.2459338698 + 1.208452878e-11i
348 -1.066386284 + 1.299490361e-11i
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350 -0.1592416865 - 5.028702119e-11i
351 -0.2863566256 - 5.055645009e-12i
352 -0.07756673841 + 2.883794502e-12i
353 -0.9837803877 - 5.072295009e-12i
354 -0.1859197000 + 4.948748543e-12i
355 -0.3510108371 + 7.882981932e-12i
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357 -2.114835773
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360 -0.2792532497 - 6.732727876e-13i
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362 -1.176437406 - 2.263039675e-12i
363 1.342962555 + 5.045660292e-13i
364 -0.1265216372 + 3.183919583e-12i
365 0.4094074315 + 4.280844365e-12i
366 2.266598807 + 1.803778869e-12i
367 1.172614832 - 1.680867746e-13i
368 -0.2098963586 - 2.096012937e-12i
369 0.7458610188 - 1.310341583e-13i
370 0.1887550203 - 1.544323688e-12i
371 -2.146937529 + 1.232228237e-12i
372 0.4258959333 - 8.019885367e-13i
373 -0.1948894196 - 2.578960915e-12i
374 0.3503749923 + 2.819345905e-13i
375 0.1487589329 - 2.205920014e-12i
376 -0.6069026804 + 1.248124686e-12i
377 0.2881777653 - 3.424999447e-13i
378 1.014563504 + 2.880750633e-12i
379 -0.8641474458 - 1.631000697e-12i
380 0.07620342109 - 7.573003350e-13i
381 0.1601244008 + 3.038546047e-12i
382 -0.01334731877 + 1.442630754e-12i
383 0.3251652189 + 3.846943234e-12i
384 -0.1470053325 - 3.428202510e-12i
385 -0.2209561987 - 4.203616976e-12i
386 -0.2496238220 - 1.129359137e-12i
387 -0.6582189872
388 0.2809810065 + 2.569896875e-12i
389 -0.3061193873
390 0.1181930825 + 3.982968457e-12i
391 0.9481185464 + 5.492026798e-12i
392 0.09471363205 - 1.899371521e-12i
393 2.446139793 - 1.200471583e-13i
394 -0.1680237232 - 7.211426396e-12i
395 0.1353083306 - 1.109010983e-12i
396 -0.3874794150 - 1.943713022e-12i
397 0.8230016837 + 7.719886299e-13i
398 -1.245295212 - 1.820221121e-12i
399 -0.6382173137 - 4.565700889e-12i
400 0.04999998325 + 5.520015245e-12i
401 1.775246442 - 3.500263600e-12i
402 0.2963254799 + 1.193865238e-11i
403 -0.1150930257 + 2.707678997e-12i
404 -0.2981636469 + 1.031138374e-11i
405 -0.1579302982 - 1.194605051e-12i
406 -1.021015838 - 1.590493992e-11i
407 0.2619079928 - 7.264242950e-12i
408 0.6640346973 - 5.894008659e-12i
409 -0.7070764555 + 2.013395181e-11i
410 -0.1335455147 + 8.567072873e-12i
411 1.517809334 - 1.179385733e-11i
412 0.2743489042 - 8.940171715e-12i
413 -0.1780093073 - 6.138286287e-12i
414 -1.048523516 - 2.984035762e-12i
415 -0.7529902680 + 1.523936180e-11i
416 0.03972639361 + 1.416408814e-11i
417 -1.090390935 + 1.397101514e-11i
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