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

$R= 15.9608513054$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.596558202
4 0.5
5 -0.447213595
6 -1.128937131
7 -0.356810638
8 -0.353553390
9 1.548998094
10 0.316227766
11 -0.667905973
12 0.798279101
13 1.528741451
14 0.252303222
15 -0.714002534
16 0.250000000
17 -1.142699094
18 -1.095307056
19 -1.874128336
20 -0.223606797
21 -0.569668952
22 0.472280842
23 0.204548519
24 -0.564468565
25 0.200000000
26 -1.080983447
27 0.876507411
28 -0.178405319
29 0.658012053
30 0.504876033
31 -0.345910748
32 -0.176776695
33 -1.066350759
34 0.808010278
35 0.159570568
36 0.774499047
37 -0.390421513
38 1.325208855
39 2.440724704
40 0.158113883
41 -0.567332635
42 0.402816779
43 -1.687774357
44 -0.333952986
45 -0.692733007
46 -0.144637645
47 1.826967540
48 0.399139550
49 -0.872686168
50 -0.141421356
51 -1.824385612
52 0.764370725
53 -0.292426342
54 -0.619784334
55 0.298696631
56 0.126151611
57 -2.992154968
58 -0.465284784
59 1.063405901
60 -0.357001267
61 -1.759090918
62 0.244595836
63 -0.552698999
64 0.125000000
65 -0.683673961
66 0.754023853
67 -0.143035021
68 -0.571349547
69 0.326573616
70 -0.112833431
71 -0.736088934
72 -0.547653528
73 0.742908992
74 0.276069699
75 0.319311640
76 -0.937064168
77 0.238315956
78 -1.725852989
79 -0.0946798903
80 -0.111803398
81 -0.149602995
82 0.401164753
83 -0.906634768
84 -0.284834476
85 0.511030570
86 1.193436693
87 1.050554541
88 0.236140421
89 -0.813011291
90 0.489836207
91 -0.545471212
92 0.102274259
93 -0.552266642
94 -1.291861136
95 0.838135671
96 -0.282234282
97 0.927781866
98 0.617082307
99 -1.034585111
100 0.100000000
101 -1.388414995
102 1.290035437
103 -0.0318879982
104 -0.540491723
105 0.254763700
106 0.206776649
107 0.384983693
108 0.438253705
109 -1.423245641
110 -0.211210413
111 -0.623330632
112 -0.0892026597
113 -1.262599840
114 2.115773068
115 -0.0914768788
116 0.329006026
117 2.368017377
118 -0.751941524
119 0.407728011
120 0.252438016
121 -0.553900067
122 1.243865117
123 -0.905780414
124 -0.172955374
125 -0.0894427190
126 0.390817210
127 -1.594571391
128 -0.0883883476
129 -2.694616349
130 0.483430494
131 -0.0536940450
132 -0.533175379
133 0.668708391
134 0.101141033
135 -0.391986031
136 0.404005139
137 1.583173666
138 -0.230922418
139 -0.0594237434
140 0.0797852843
141 2.916764023
142 0.520493477
143 -1.021129058
144 0.387249523
145 -0.294271936
146 -0.525315986
147 -1.394126544
148 -0.195210756
149 0.419316281
150 -0.225787426
151 0.711274051
152 0.662604427
153 -1.769616414
154 -0.168514829
155 0.154695989
156 1.220362352
157 -1.172478628
158 0.0669487925
159 -0.450410838
160 0.0790569415
161 -0.0613688687
162 0.105785292
163 -0.882091609
164 -0.283666317
165 0.476886557
166 0.641087592
167 1.266696528
168 0.201408389
169 1.383354938
170 -0.361353181
171 -2.916577925
172 -0.843887178