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

$R= 12.153525187$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.079790117
4 0.5
5 -0.447213595
6 0.763526914
7 0.513591082
8 -0.353553390
9 0.165946698
10 0.316227766
11 -1.124748807
12 -0.539895058
13 -0.117197472
14 -0.363163737
15 0.482896820
16 0.250000000
17 -1.615339626
18 -0.117342035
19 -1.365847361
20 -0.223606797
21 -0.554570575
22 0.795317508
23 -1.230979415
24 0.381763457
25 0.200000000
26 0.0828711272
27 0.900602512
28 0.256795541
29 0.332023117
30 -0.341459616
31 0.679125195
32 -0.176776695
33 1.214492646
34 1.142217603
35 -0.229684914
36 0.0829733490
37 0.936592696
38 0.965799931
39 0.126548672
40 0.158113883
41 -0.741386953
42 0.392140614
43 -0.197451909
44 -0.562374403
45 -0.0742136195
46 0.870433891
47 1.064283724
48 -0.269947529
49 -0.736224199
50 -0.141421356
51 1.744227765
52 -0.0585987360
53 -0.255223888
54 -0.636822144
55 0.503002958
56 -0.181581868
57 1.474828483
58 -0.234775797
59 -1.324714032
60 0.241448410
61 -1.006458923
62 -0.480214031
63 0.0852287443
64 0.125000000
65 0.0524123028
66 -0.858775986
67 1.905016695
68 -0.807669813
69 1.329199407
70 0.162411760
71 0.223620389
72 -0.0586710177
73 1.712842312
74 -0.662271046
75 -0.215958023
76 -0.682923680
77 -0.577660960
78 -0.0894834242
79 -1.559866937
80 -0.111803398
81 -1.138408397
82 0.524239742
83 1.290706109
84 -0.277285287
85 0.722401842
86 0.139619584
87 -0.358515274
88 0.397658754
89 1.126622159
90 0.0524769536
91 -0.0601915273
92 -0.615489707
93 -0.733312636
94 -0.752562238
95 0.610825509
96 0.190881728
97 0.492290552
98 0.520589124
99 -0.186648419
100 0.100000000
101 1.364306605
102 -1.233355280
103 -0.899368162
104 0.0414355636
105 0.248011501
106 0.180470542
107 -1.349174586
108 0.450301256
109 0.867378893
110 -0.355676802
111 -1.011326903
112 0.128397770
113 0.350215827
114 -1.042861221
115 0.550510730
116 0.166011558
117 -0.0194377898
118 0.936714275
119 -0.829616232
120 -0.170729808
121 0.265052693
122 0.711673929
123 0.800511752
124 0.339562597
125 -0.0894427190
126 -0.0602658230
127 0.613428451
128 -0.0883883476
129 0.213439841
130 -0.0370610947
131 -0.856585546
132 0.607246323
133 -0.701482373
134 -1.347050223
135 -0.402761687
136 0.571108801
137 -0.206132557
138 -0.939885914
139 1.754919789
140 -0.114842457
141 -1.150247286
142 -0.158123494
143 0.133938008
144 0.0414866745
145 -0.148485252
146 -1.211162414
147 0.793618672
148 0.468296348
149 1.908435288
150 0.152705382
151 -1.587462629
152 0.482899965
153 -0.292396011
154 0.408467982
155 -0.303714020
156 0.0632743360
157 0.724151320
158 1.102992488
159 0.280878810
160 0.0790569415