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

$R= 10.0194866131$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.253035905
4 0.5
5 -0.447213595
6 -0.886030185
7 -0.893722119
8 0.353553390
9 0.570098980
10 -0.316227766
11 -0.329916289
12 -0.626517952
13 1.057885982
14 -0.631956971
15 0.560374692
16 0.250000000
17 -0.551080054
18 0.403120854
19 1.357396345
20 -0.223606797
21 1.119865905
22 -0.233286045
23 1.921486575
24 -0.443015092
25 0.200000000
26 0.748038351
27 0.538681413
28 -0.446861059
29 -0.477763157
30 0.396244745
31 0.00830887364
32 0.176776695
33 0.413396955
34 -0.389672443
35 0.399684682
36 0.285049490
37 1.575270024
38 0.959824160
39 -1.325569119
40 -0.158113883
41 -1.678504843
42 0.791864775
43 -1.577387670
44 -0.164958144
45 -0.254956014
46 1.358696187
47 1.324534667
48 -0.313258976
49 -0.201260772
50 0.141421356
51 0.690523094
52 0.528942991
53 -0.798869694
54 0.380905280
55 0.147543049
56 -0.315978485
57 -1.700866359
58 -0.337829568
59 -0.149275447
60 0.280187346
61 1.457638226
62 0.00587526090
63 -0.509510069
64 0.125000000
65 -0.473100993
66 0.292315790
67 0.824074740
68 -0.275540027
69 -2.407691671
70 0.282619749
71 1.343070038
72 0.201560427
73 0.352114766
74 1.113884116
75 -0.250607181
76 0.678698172
77 0.294853484
78 -0.937318913
79 0.0748920969
80 -0.111803398
81 -1.245086126
82 -1.186882157
83 0.450508575
84 0.559932952
85 0.246450492
86 -1.115381518
87 0.598654392
88 -0.116643022
89 0.472457707
90 -0.180281126
91 -0.945456114
92 0.960743287
93 -0.0104113318
94 0.936587445
95 -0.607046100
96 -0.221507546
97 0.907270884
98 -0.142312857
99 -0.188085194
100 0.100000000
101 0.576432702
102 0.488273562
103 -0.513611688
104 0.374019175
105 -0.500819258
106 -0.564886178
107 1.210993613
108 0.269340706
109 -0.293823335
110 0.104328691
111 -1.973883571
112 -0.223430529
113 0.566615367
114 -1.202694136
115 -0.859314920
116 -0.238881578
117 0.603124920
118 -0.105553681
119 0.492519645
120 0.198122372
121 -0.891174420
122 1.030705874
123 2.102939958
124 0.00415443682
125 -0.0894427190
126 -0.360278024
127 -0.353477259
128 0.0883883476
129 1.976532478
130 -0.334532920
131 0.237825972
132 0.206698477
133 -1.213447268
134 0.582708837
135 -0.240905651
136 -0.194836221
137 -0.213261393
138 -1.702495107
139 0.0741341465
140 0.199842341
141 -1.658415344
142 0.949693931
143 -0.348917792
144 0.142524745
145 0.213662179
146 0.248982738
147 0.218249860
148 0.787635012
149 -1.086363946
150 -0.177206037