Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 3e-13
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues 1,1,0,0

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Spectral parameter

$R= 9.02977428596$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.7071067811
3 -1.939086124
4 0.5000000000
5 -0.4472135955
6 1.371140948
7 0.5701321364
8 -0.3535533905
9 2.760054999
10 0.3162277660
11 0.5887892411
12 -0.9695430623
13 -0.3672062736
14 -0.4031442998
15 0.8671856778
16 0.2500000000
17 -0.6967843014
18 -1.951653606
19 -0.4901853172
20 -0.2236067977
21 -1.105535314
22 -0.4163368650
23 1.246281558
24 0.6855704740
25 0.1999999999
26 0.2596540461
27 -3.412898227
28 0.2850660682
29 1.686728680
30 -0.6131928733
31 0.2235524670
32 -0.1767766952
33 -1.141713047 - 2.177289285e-13i
34 0.4927009043 + 3.757022387e-13i
35 -0.2549708428 + 4.421063963e-13i
36 1.380027500 - 1.371109663e-12i
37 -1.466956940 + 1.209811525e-13i
38 0.3466133606 + 3.046845617e-12i
39 0.7120445892 - 3.141480251e-12i
40 0.1581138847 - 2.701195086e-12i
41 -0.5385557410 + 8.155506808e-12i
42 0.7817315102 - 3.003122591e-12i
43 0.5481270232 - 1.128563781e-11i
44 0.2943946130 + 1.855980373e-11i
45 -1.234334134 + 7.420644954e-12i
46 -0.8812541119 - 7.256167619e-11i
47 0.2408242241 + 8.940842736e-11i
48 -0.4847714149 + 1.827947951e-10i
49 -0.6749493470
50 -0.1414213562
51 1.351124770
52 -0.1836031368
53 -1.070947129
54 2.413283480
55 -0.2633145535
56 -0.2015721498
57 0.9505115473
58 -1.192697288
59 -0.4034625568
60 0.4335928389
61 -0.8424470925
62 -0.1580754653
63 1.573596053
64 0.1249999998 + 3.042005400e-13i
65 0.1642196380 + 1.246673887e-13i
66 0.8073130385 - 4.398488076e-13i
67 -0.8430325459
68 -0.3483921505 + 1.094673821e-13i
69 -2.416647277 - 7.361209127e-13i
70 0.1802916113 + 4.195241137e-13i
71 0.9657701525 + 1.396815609e-12i
72 -0.9758268019 + 3.800129033e-13i
73 -0.2071693209 - 2.021003403e-12i
74 1.037295201 - 2.679229730e-12i
75 -0.3878172247 + 3.276945531e-12i
76 -0.2450926599 + 1.498594064e-12i
77 0.3356876628 - 2.419806367e-12i
78 -0.5034915492 + 5.633565382e-12i
79 0.4878002381 - 3.253704906e-12i
80 -0.1118034012 - 8.844739523e-12i
81 3.857848604 + 5.196741158e-12i
82 0.3808164261 + 2.930484091e-12i
83 0.3751389201 + 7.117145040e-12i
84 -0.5527676350 - 4.823858273e-12i
85 0.3116114385 - 3.118321612e-12i
86 -0.3875843428 + 1.176156928e-11i
87 -3.270712211 - 5.053006054e-11i
88 -0.2081683777 + 5.266580819e-11i
89 -1.693631228 + 1.190102582e-10i
90 0.8728060050 - 1.894216205e-10i
91 -0.2093560974
92 0.6231407792
93 -0.4334874871
94 -0.1702884849 - 1.204399690e-13i
95 0.2192175385 - 2.944066518e-13i
96 0.3427852376 - 1.584883615e-13i
97 0.2821234769
98 0.4772612606
99 1.625090686 + 5.704757050e-13i
100 0.09999999960 + 4.218752669e-13i
101 -0.8752187582 + 1.236506252e-13i
102 -0.9553894855 - 2.251882547e-13i
103 -0.1102684408
104 0.1298270254 - 3.397483192e-13i
105 0.4944104228 - 1.387441154e-12i
106 0.7572739800 + 2.438954997e-13i
107 -0.2687468973 - 6.444843904e-13i
108 -1.706449114 + 2.751561684e-13i
109 -0.5596071253 - 2.475383156e-13i
110 0.1861915065 + 2.535609295e-12i
111 2.844555848 + 4.140355656e-12i
112 0.1425330346 - 5.873694243e-13i
113 0.3272848991 + 1.122079466e-12i
114 -0.6721131661 - 5.122965274e-12i
115 -0.5573540562 - 2.306254873e-12i
116 0.8433643200 - 6.301734446e-12i
117 -1.013509494 - 6.937625047e-13i
118 0.2852910993 + 3.352988232e-12i
119 -0.3972590950 - 5.343791498e-12i
120 -0.3065964239 + 9.595111071e-12i
121 -0.6533272228 + 3.867924653e-12i
122 0.5957000154 + 3.001282244e-11i
123 1.044305913 - 3.832350849e-12i
124 0.1117762295 + 2.379365787e-12i
125 -0.08944271972 + 5.495854167e-13i
126 -1.112700441 + 5.829216018e-13i
127 -1.309844585 + 3.669693277e-13i
128 -0.08838834637 - 4.483495759e-13i
129 -1.062865480 + 9.134039389e-13i
130 -0.1161208188 - 7.382691826e-13i
131 0.8393974422 - 2.948648993e-13i
132 -0.5708565236 + 2.166501473e-12i
133 -0.2794704039 - 1.757325589e-12i
134 0.5961140294 + 3.278312892e-13i
135 1.526294487 - 1.648473224e-12i
136 0.2463504584 - 3.891764699e-12i
137 1.224886306 - 1.988919961e-12i
138 1.708827677 + 2.251839279e-12i
139 -0.7692401039 + 6.300905074e-12i
140 -0.1274854249 + 6.619862553e-12i
141 -0.4669790395 + 5.857844140e-12i
142 -0.6829026222 - 3.458569116e-12i
143 -0.2162071014 - 5.629234480e-12i
144 0.6900137706 - 1.438382459e-11i
145 -0.7543279934 - 9.878214135e-13i
146 0.1464908291 + 2.136825184e-13i
147 1.308784897 - 3.359497924e-12i
148 -0.7334784743 + 1.995155097e-11i
149 -0.4554571240 - 1.222273617e-11i
150 0.2742282047 - 6.078452828e-12i
151 0.4761031241 + 1.427942819e-11i
152 0.1733067114 + 3.032776991e-12i
153 -1.923162994 - 1.203925438e-13i
154 -0.2373670281 + 9.563018561e-13i
155 -0.09997570297 - 3.250413859e-13i
156 0.3560222936 - 2.853655651e-13i
157 -0.1886062942 + 2.895332153e-12i
158 -0.3449268557 - 1.503599215e-12i
159 2.076658721 - 6.583143194e-13i
160 0.07905694001 + 1.618981873e-12i
161 0.7105451671 - 2.545400284e-12i
162 -2.727910906 - 1.935303371e-12i
163 -1.108990460 + 1.048753937e-12i
164 -0.2692778723 - 2.529308605e-13i
165 0.5105896088 - 4.885233779e-12i
166 -0.2652632928 + 3.320553507e-12i
167 0.7171072721 + 7.981914851e-12i
168 0.3908657543 + 2.373650028e-12i
169 -0.8651595544 + 3.083706265e-12i
170 -0.2203425524 + 3.733746449e-12i
171 -1.352938432 - 1.073916254e-11i
172 0.2740635212 - 1.514719514e-11i
173 1.197727507 + 9.334690359e-12i
174 2.312742757 - 2.396467505e-12i
175 0.1140264024 - 2.829392096e-12i
176 0.1471972964 + 1.555915126e-11i
177 0.7823486327 - 6.509148183e-12i
178 1.197578069 - 1.838552929e-11i
179 -1.021799855 + 6.068673174e-12i
180 -0.6171670143 + 2.572864298e-11i
181 -0.4847579827 + 2.547473408e-13i
182 0.1480370904 + 3.278175364e-11i
183 1.633577422 - 1.788204717e-11i
184 -0.4406270809 - 7.006926753e-11i
185 0.6560431263 - 5.611007272e-11i
186 0.3065219882 - 1.770621671e-11i
187 -0.4102590995 + 2.591315591e-12i
188 0.1204121420 + 2.427094875e-12i
189 -1.945802953 + 1.272774222e-12i
190 -0.1550102096 - 3.098340199e-12i
191 0.8211364202 - 7.576479805e-12i
192 -0.2423857651 + 1.636065554e-12i
193 -1.464581495 + 2.277665340e-13i
194 -0.1994914229 - 1.167080318e-12i
195 -0.3184360309 + 1.046442342e-11i
196 -0.3374746571 - 1.588691643e-12i
197 -1.620372640 - 6.894151308e-13i
198 -1.149112647 + 2.814013921e-12i
199 -0.4241711025 - 1.134143817e-11i
200 -0.07071066339 - 7.849572965e-12i
201 1.634712704 + 3.309499345e-12i
202 0.6188731386 + 6.400434833e-12i
203 0.9616582075 + 1.482829260e-11i
204 0.6755623898 + 1.309383882e-11i
205 0.2408494349 - 2.068688871e-11i
206 0.07797157213 - 2.314002973e-11i
207 3.439805634 - 1.477027884e-11i
208 -0.09180154757 + 1.080191258e-11i
209 -0.2886158154 + 2.461822274e-11i
210 -0.3496009739 + 1.773701791e-11i
211 -1.776426585 + 2.759217409e-11i
212 -0.5354735695 - 4.217234048e-11i
213 -1.872711479 - 5.314133588e-11i
214 0.1900327055 + 2.376786540e-11i
215 -0.2451298068 + 1.383175588e-11i
216 1.206641736 + 1.712100515e-12i
217 0.1274544531 - 1.802149097e-12i
218 0.3957019984 - 5.051547300e-12i
219 0.4017191666 - 1.372549537e-11i
220 -0.1316572886 - 6.433143848e-12i
221 0.2558635695 + 5.987288907e-12i
222 -2.011404746 + 1.119607242e-11i
223 1.121589524 + 9.409065730e-12i
224 -0.1007860900 + 3.541760239e-12i
225 0.5520110274 - 8.001271246e-12i
226 -0.2314253588 - 6.661740781e-12i
227 0.2759529662 - 2.067140077e-11i
228 0.4752557426 + 4.946688291e-12i
229 0.4102313048 + 2.876986828e-11i
230 0.3941088406 - 5.346676524e-12i
231 -0.6509272849 - 1.607261764e-13i
232 -0.5963486115 - 4.632191223e-12i
233 1.717747172 - 1.666649873e-11i
234 0.7166594772 - 7.433798698e-12i
235 -0.1076999279 + 1.193449615e-11i
236 -0.2017313049 + 1.458189072e-11i
237 -0.9458866711 + 4.572443227e-12i
238 0.2809046209 - 1.599185003e-12i
239 1.524943102 - 3.209331313e-12i
240 0.2167964137 + 6.129344144e-12i
241 -1.253021254 - 2.156028600e-12i
242 0.4619721136 - 4.627250807e-12i
243 -4.067802471 + 1.961771589e-12i
244 -0.4212235322 + 2.508501776e-12i
245 0.3018465341 - 7.635053818e-13i
246 -0.7384358334 - 3.291752840e-12i
247 0.1799991037 + 6.842691659e-12i
248 -0.07903773824 + 3.304211350e-12i
249 -0.7274267346 - 1.167735123e-11i
250 0.06324556768 - 6.251811822e-12i
251 -0.5428365684 + 4.882712909e-12i
252 0.7867980348 - 2.843583196e-12i
253 0.7337971650 + 5.063921273e-12i
254 0.9261999986 + 1.163377551e-11i
255 -0.6042413909 + 5.200116105e-12i
256 0.06249998616 + 5.135746435e-12i
257 -1.229004229 - 1.927814336e-11i
258 0.7515594249 - 1.494742150e-11i
259 -0.8363593228 + 1.960388336e-11i
260 0.08210978896 - 1.497074941e-11i
261 4.655463995 - 3.771799508e-12i
262 -0.5935436434 + 3.952490433e-11i
263 -1.093154715 - 2.470289751e-11i
264 0.4036565182 - 3.080443175e-12i
265 0.4789421157 - 1.844680664e-12i
266 0.1976154143 + 2.645373523e-12i
267 3.284096636 - 5.175570884e-12i
268 -0.4215162712 - 6.656624296e-13i
269 -1.425194876 + 1.166344665e-11i
270 -1.079253183 - 1.097264366e-12i
271 -0.1511003499 - 5.884159162e-12i
272 -0.1741960786 - 3.174695754e-12i
273 0.4059594930 + 2.906737951e-12i
274 -0.8661254271 - 5.877651515e-12i
275 0.1177578625 - 4.081537942e-12i
276 -1.208323639 + 1.924186589e-11i
277 -0.05736750566 + 2.831174574e-12i
278 0.5439348831 - 5.928525258e-12i
279 0.6170171267 - 1.564054403e-11i
280 0.09014582626 - 1.072520361e-11i
281 -1.581438486 + 1.131218343e-11i
282 0.3302040163 + 1.286389415e-11i
283 1.782985853 + 1.145572256e-11i
284 0.4828851000 + 1.432738186e-12i
285 -0.4250817196
286 0.1528814967 - 4.733595563e-11i
287 -0.3070479032 - 4.316000648e-12i
288 -0.4879134003 + 2.872795138e-11i
289 -0.5144917272 - 4.905296177e-12i
290 0.5333904318 + 3.696747049e-11i
291 -0.5470616806 + 9.997621203e-12i
292 -0.1035845783 - 2.895641777e-11i
293 -0.6679476777 - 7.306762724e-11i
294 -0.9254506986 + 2.070056529e-11i
295 0.1804339557 + 5.519074201e-12i
296 0.5186476034 - 3.582590507e-13i
297 -2.009477743 - 7.330232311e-12i
298 0.3220568013 + 3.487844862e-12i
299 -0.4576424024 - 2.911854153e-12i
300 -0.1939086289 + 1.513223628e-12i
301 0.3125048273 - 1.003661928e-12i
302 -0.3366557560 + 1.650975547e-13i
303 1.697124547 + 1.340615606e-11i
304 -0.1225463412 - 1.003031295e-11i
305 0.3767537947 - 5.977890811e-12i
306 1.359881596 + 2.645658924e-12i
307 -0.4028724849 + 3.409061313e-12i
308 0.1678438396 - 1.820999938e-12i
309 0.2138200193 + 1.034664373e-12i
310 0.07069352597 + 7.726228731e-12i
311 -1.675118452 - 1.628877473e-11i
312 -0.2517457998 - 6.354388330e-12i
313 0.7431270605 + 1.282077178e-11i
314 0.1333648192 + 7.800782067e-12i
315 -0.7037335761 - 1.937828482e-11i
316 0.2439001043 + 2.054503972e-11i
317 1.898523106 + 2.289983657e-11i
318 -1.468419458 - 2.863804800e-12i
319 0.9931276977 - 4.634175497e-13i
320 -0.05590170126 + 2.319793046e-12i
321 0.5211233783 - 1.897697159e-12i
322 -0.5024312980 - 1.555450424e-13i
323 0.3415534326 - 1.031466745e-12i
324 1.928924292 + 2.429595626e-12i
325 -0.07344125091 - 1.266152592e-12i
326 0.7841746655 + 1.336982647e-12i
327 1.085126404 + 5.090497019e-13i
328 0.1904082072 - 5.832642065e-13i
329 0.1373016724 - 2.179048048e-12i
330 -0.3610413660 + 2.306558344e-13i
331 -0.4151387586 + 5.769910012e-12i
332 0.1875694743 - 3.355232601e-12i
333 -4.048881827 + 1.990346031e-12i
334 -0.5070714201 - 4.297339008e-12i
335 0.3770156273 - 6.291126231e-13i
336 -0.2763838143 - 3.827716262e-12i
337 -0.8196541812 - 3.278439504e-12i
338 0.6117601529 + 1.142153463e-11i
339 -0.6346336030 + 7.751055226e-12i
340 0.1558057037 - 1.534264946e-12i
341 0.1316253010 - 1.304123308e-11i
342 0.9566719270 + 3.914457806e-12i
343 -0.9549424358 - 6.447951586e-12i
344 -0.1937921442 + 1.370784420e-12i
345 1.080757513 + 1.505564083e-11i
346 -0.8469212582 + 1.446633379e-12i
347 -1.227197120 - 9.366845983e-12i
348 -1.635356030 - 9.546446596e-12i
349 1.561167058 + 1.404262167e-12i
350 -0.08062885674 - 1.388120843e-11i
351 1.253237613 + 1.763812404e-12i
352 -0.1040841909 + 1.604022717e-11i
353 1.858252891 + 2.218064441e-11i
354 -0.5532040769 - 9.560172124e-12i
355 -0.4319055461 - 1.110468061e-11i
356 -0.8468154894 + 1.652114053e-12i
357 0.7703196746 - 1.426022588e-11i
358 0.7225216124 - 7.529825769e-12i
359 0.01421926249 + 1.705222605e-13i
360 0.4364030130
361 -0.7597183470 + 2.537847128e-12i
362 0.3427756723 - 1.931910374e-12i
363 1.266857761 - 3.726995932e-13i
364 -0.1046780491 + 2.906632248e-12i
365 0.09264894540 - 7.201893832e-12i
366 -1.155113704 - 9.026249431e-13i
367 -0.5456606765 + 8.123199419e-13i
368 0.3115703876 - 6.498105986e-13i
369 -1.486443466 + 3.441551501e-12i
370 -0.4638925182 + 2.835243924e-12i
371 -0.6105813776 + 4.130917483e-12i
372 -0.2167437395 - 1.415159670e-12i
373 0.06935378540 - 3.448650460e-12i
374 0.2900969855 - 1.316540794e-12i
375 0.1734371417 + 2.621351981e-12i
376 -0.08514424586 - 2.609406913e-12i
377 -0.6193773409 + 5.310293866e-12i
378 1.375890457 + 3.506918939e-12i
379 0.4058414397 - 1.164926233e-11i
380 0.1096087598 - 3.090147976e-12i
381 2.539901461 - 8.861579473e-12i
382 -0.5806311325 + 4.873472312e-12i
383 -0.04720813163 + 6.678535438e-12i
384 0.1713926209 + 1.639902748e-12i
385 -0.1501241147 + 1.121275896e-11i
386 1.035615501 - 3.817485776e-13i
387 1.512860709 - 1.164355666e-11i
388 0.1410617581 - 6.075137699e-12i
389 -1.463408799 + 1.798137818e-11i
390 0.2251682942 + 1.859460210e-13i
391 -0.8683894581 + 7.893438125e-12i
392 0.2386305934 + 3.362351872e-12i
393 -1.627663984 - 2.072200369e-11i
394 1.145776492 - 1.744900817e-11i
395 -0.2181508840 - 2.478254653e-11i
396 0.8125453841 + 1.421549476e-11i
397 0.2284397126 + 1.925991115e-11i
398 0.2999342373 + 1.412688094e-11i
399 0.5419171412 + 2.079949433e-11i
400 0.04999999889 + 6.099081571e-12i
401 0.8008242590 - 4.880760057e-11i
402 -1.155916446 + 5.982385944e-13i
403 -0.08208988044 + 2.886289947e-12i
404 -0.4376093786 + 6.321879379e-12i
405 -1.725282334 + 4.650462812e-13i
406 -0.6799950625 + 2.221500734e-12i
407 -0.8637284600 - 7.741109937e-12i
408 -0.4776947465 - 1.644980920e-12i
409 1.005524922 - 3.495192525e-12i
410 -0.1703062783 - 4.649632957e-12i
411 -2.375160040 + 8.140696923e-12i
412 -0.05513421524 - 4.443542947e-12i
413 -0.2300269556 + 6.711189036e-12i
414 -2.432309912 + 3.308005744e-12i
415 -0.1677672387 - 5.138391923e-12i
416 0.06491351460 - 7.205431548e-13i
417 1.491622799 + 4.224891611e-12i
418 0.2040822248 + 1.510754517e-12i
419 -1.125937509 - 1.918252254e-12i
420 0.2472051957 + 2.867609592e-12i
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