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

$R= 10.1994943801$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.888171681
4 0.5
5 0.447213595
6 -0.628032218
7 -0.602337361
8 0.353553390
9 -0.211151064
10 0.316227766
11 0.758502642
12 -0.444085840
13 -0.155517678
14 -0.425916832
15 -0.397202451
16 0.250000000
17 1.279807518
18 -0.149306349
19 0.782621316
20 0.223606797
21 0.534978986
22 0.536342362
23 0.851050520
24 -0.314016109
25 0.200000000
26 -0.109967605
27 1.075710077
28 -0.301168680
29 1.908360073
30 -0.280864546
31 0.250511897
32 0.176776695
33 -0.673680567
34 0.904960574
35 -0.269373456
36 -0.105575532
37 -1.826729713
38 0.553396839
39 0.138126397
40 0.158113883
41 0.732431648
42 0.378287269
43 0.870803592
44 0.379251321
45 -0.0944296266
46 0.601783594
47 -1.261143854
48 -0.222042920
49 -0.637189703
50 0.141421356
51 -1.136688795
52 -0.0777588392
53 0.199128115
54 0.760641890
55 0.339212694
56 -0.212958416
57 -0.695102090
58 1.349414349
59 1.170153095
60 -0.198601225
61 -1.644834146
62 0.177138661
63 0.127184174
64 0.125000000
65 -0.0695496201
66 -0.476364097
67 1.347094645
68 0.639903759
69 -0.755878972
70 -0.190475798
71 -0.394700590
72 -0.0746531747
73 0.0658704952
74 -1.291692968
75 -0.177634336
76 0.391310658
77 -0.456874485
78 0.0976701126
79 1.054783887
80 0.111803398
81 -0.744264167
82 0.517907385
83 0.367418121
84 0.267489493
85 0.572347321
86 0.615751124
87 -1.694951398
88 0.268171181
89 0.839111257
90 -0.0667718293
91 0.0936740774
92 0.425525260
93 -0.222497550
94 -0.891763371
95 0.349998892
96 -0.157008054
97 -1.020490529
98 -0.450561160
99 -0.160159167
100 0.100000000
101 1.903919533
102 -0.803760355
103 -1.402680299
104 -0.0549838025
105 0.239249876
106 0.140804840
107 -0.0681904519
108 0.537855038
109 -1.102207463
110 0.239859596
111 1.622452272
112 -0.150584340
113 1.152302464
114 -0.491511401
115 0.380601363
116 0.954180036
117 0.0327946714
118 0.827423188
119 -0.770888389
120 -0.140432273
121 -0.424685529
122 -1.163073378
123 -0.650414159
124 0.125255948
125 0.0894427190
126 0.0899327925
127 -1.318671037
128 0.0883883476
129 -0.773562150
130 -0.0491790080
131 0.861359918
132 -0.336840283
133 -0.471066976
134 0.952539758
135 0.481072171
136 0.452480287
137 -0.359075815
138 -0.534487146
139 0.847745211
140 -0.134686728
141 1.135494683
142 -0.279095464
143 -0.108504362
144 -0.0527877660
145 0.853444570
146 0.0465774738
147 0.507357062
148 -0.913364856