Properties

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

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Spectral parameter

$R= 12.5585779181$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.310754002
4 0.5
5 -0.447213595
6 -0.926843043
7 -1.140461797
8 -0.353553390
9 0.718076055
10 0.316227766
11 1.134668305
12 0.655377001
13 -0.139079786
14 0.806428270
15 -0.586187010
16 0.250000000
17 1.447269868
18 -0.507756447
19 -1.410888254
20 -0.223606797
21 -1.494864865
22 -0.802331653
23 1.261763309
24 -0.463421521
25 0.200000000
26 0.0983442599
27 -0.369532939
28 -0.570230898
29 0.735851137
30 0.414496810
31 1.148191440
32 -0.176776695
33 1.487271022
34 -1.023374338
35 0.510030020
36 0.359038027
37 0.999639220
38 0.997648651
39 -0.182299386
40 0.158113883
41 0.508845784
42 1.057029083
43 -0.212214728
44 0.567334152
45 -0.321133374
46 -0.892201392
47 -1.060242976
48 0.327688500
49 0.300653110
50 -0.141421356
51 1.897014772
52 -0.0695398931
53 1.625443194
54 0.261299247
55 -0.507439092
56 0.403214135
57 -1.849327425
58 -0.520325329
59 0.461218785
60 -0.293093505
61 1.287216885
62 -0.811893953
63 -0.818938308
64 0.125000000
65 0.0621983712
66 -1.051659425
67 0.525970594
68 0.723634934
69 1.653861308
70 -0.360645686
71 -0.360402637
72 -0.253878223
73 1.603784667
74 -0.706851671
75 0.262150800
76 -0.705444127
77 -1.294045854
78 0.128905132
79 1.810092326
80 -0.111803398
81 -1.202442840
82 -0.359808305
83 0.864124281
84 -0.747432432
85 -0.647238761
86 0.150058473
87 0.964519805
88 -0.401165826
89 -1.644987029
90 0.227075586
91 0.158615176
92 0.630881654
93 1.504996527
94 0.749704998
95 0.630968408
96 -0.231710760
97 -1.439380224
98 -0.212593853
99 0.814778660
100 0.100000000
101 0.391897147
102 -1.341392009
103 0.334059485
104 0.0491721299
105 0.668523891
106 -1.149361904
107 -0.497403865
108 -0.184766469
109 -1.135406159
110 0.358813623
111 1.310280612
112 -0.285115449
113 0.120061902
114 1.307671963
115 -0.564277706
116 0.367925568
117 -0.0998994339
118 -0.326130930
119 -1.650563117
120 0.207248405
121 0.287497369
122 -0.910199788
123 0.667001015
124 0.574095720
125 -0.0894427190
126 0.579076831
127 1.265709909
128 -0.0883883476
129 -0.278243082
130 -0.0439808900
131 -0.238833070
132 0.743635511
133 1.608753297
134 -0.371917373
135 0.165260154
136 -0.511687169
137 -1.095295699
138 -1.169456546
139 -0.713889442
140 0.255015010
141 -1.387476505
142 0.254843149
143 -0.149491207
144 0.179519013
145 -0.329082632
146 -1.134047014
147 0.401398489
148 0.499819610
149 1.081495225
150 -0.185368608
151 0.587797062
152 0.498824325
153 0.941407051
154 0.915028598
155 -0.513486822
156 -0.0911496932