Properties

Level 10
Symmetry odd
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

$R= 13.1075094406$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.885463898
4 0.5
5 0.447213595
6 1.333224308
7 1.370716695
8 -0.353553390
9 2.554974113
10 -0.316227766
11 -0.877469477
12 -0.942731949
13 -0.0369156551
14 -0.969243070
15 -0.843205089
16 0.250000000
17 -0.165242879
18 -1.806639521
19 1.383897945
20 0.223606797
21 -2.584436845
22 0.620464617
23 -1.452079367
24 0.666612154
25 0.200000000
26 0.0261033100
27 -2.931847555
28 0.685358347
29 0.465405180
30 0.596236036
31 -0.121934192
32 -0.176776695
33 1.654437021
34 0.116844360
35 0.613003141
36 1.277487056
37 0.420036566
38 -0.978563621
39 0.0696031350
40 -0.158113883
41 0.00879593535
42 1.827472818
43 0.662281700
44 -0.438734738
45 1.142619159
46 1.026775167
47 -0.953140607
48 -0.471365974
49 0.878864259
50 -0.141421356
51 0.311559484
52 -0.0184578275
53 0.211814199
54 2.073129287
55 -0.392416279
56 -0.484621535
57 -2.609289616
58 -0.329091159
59 0.356789888
60 -0.421602544
61 0.507811894
62 0.0862204945
63 3.502145675
64 0.125000000
65 -0.0165091828
66 -1.169863637
67 -0.839072127
68 -0.0826214397
69 2.737843227
70 -0.433458678
71 -0.869019173
72 -0.903319760
73 -1.530483872
74 -0.297010704
75 -0.377092779
76 0.691948972
77 -1.202762058
78 -0.0492168488
79 1.523376680
80 0.111803398
81 2.972918620
82 -0.00621966553
83 -0.0525383502
84 -1.292218422
85 -0.0738988623
86 -0.468303881
87 -0.877504636
88 0.310232308
89 1.084013342
90 -0.807953756
91 -0.0506008487
92 -0.726039683
93 0.229902496
94 0.673972186
95 0.618897976
96 0.333306077
97 0.735518611
98 -0.621450877
99 -2.241912037
100 0.100000000
101 1.595297277
102 -0.220305823
103 -0.906195190
104 0.0130516550
105 -1.155795293
106 -0.149775257
107 1.176724832
108 -1.465923777
109 1.789976355
110 0.277480212
111 -0.791963625
112 0.342679173
113 0.708116626
114 1.845046381
115 -0.649389634
116 0.232702590
117 -0.0943409988
118 -0.252288549
119 -0.226518023
120 0.298118018
121 -0.230052154
122 -0.359077234
123 -0.0166081503
124 -0.0609670963
125 0.0894427190
126 -2.476390955
127 0.600753175
128 -0.0883883476
129 -1.248645378
130 0.0116737551
131 0.375983751
132 0.827218510
133 1.897034892
134 0.593313591
135 -1.311162086
136 0.0584221803
137 0.764990851
138 -1.935947511
139 -1.140101374
140 0.306501570
141 1.798279552
142 0.614489350
143 0.0304216695
144 0.638743528
145 0.208135524
146 1.082215524
147 -1.647105286
148 0.210018283
149 -0.115885688
150 0.266644861
151 -0.290470104
152 -0.489281810
153 -0.419903194
154 0.850481207
155 -0.0545306287
156 0.0348015675