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

$R= 18.8098346996$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.313428919
4 0.5
5 0.447213595
6 0.221627714
7 -1.289815369
8 0.353553390
9 -0.901762312
10 0.316227766
11 1.203781532
12 0.156714459
13 0.613609765
14 -0.912037194
15 0.140169673
16 0.250000000
17 0.545444407
18 -0.637642246
19 -1.116286135
20 0.223606797
21 -0.404265437
22 0.851202084
23 -1.669542315
24 0.110813857
25 0.200000000
26 0.433887626
27 -0.596067305
28 -0.644907684
29 0.670754659
30 0.0991149268
31 -0.849034999
32 0.176776695
33 0.377299944
34 0.385687439
35 -0.576822969
36 -0.450881156
37 0.569733210
38 -0.789333495
39 0.192323045
40 0.158113883
41 -0.784489594
42 -0.285858832
43 -1.877784896
44 0.601890766
45 -0.403280366
46 -1.180544692
47 -0.927620461
48 0.0783572297
49 0.663623688
50 0.141421356
51 0.170958051
52 0.306804882
53 1.194931416
54 -0.421483234
55 0.538347467
56 -0.456018597
57 -0.349876356
58 0.474295168
59 0.998047262
60 0.0700848369
61 -1.184417415
62 -0.600358405
63 1.163106890
64 0.125000000
65 0.274414629
66 0.266791349
67 0.705659907
68 0.272722203
69 -0.523282843
70 -0.407875432
71 -1.615610159
72 -0.318821123
73 -1.742108989
74 0.402862216
75 0.0626857838
76 -0.558143067
77 -1.552655922
78 0.135992929
79 -0.707115052
80 0.111803398
81 0.714937581
82 -0.554717911
83 -0.218719587
84 -0.202132718
85 0.243930154
86 -1.327794433
87 0.210233907
88 0.425601042
89 -1.012620023
90 -0.285162281
91 -0.791443306
92 -0.834771157
93 -0.266112122
94 -0.655926718
95 -0.499218336
96 0.0554069285
97 1.156219553
98 0.469252810
99 -1.085524818
100 0.100000000
101 -0.653348385
102 0.120885597
103 -0.524523251
104 0.216943813
105 -0.180792999
106 0.844944107
107 -0.352068110
108 -0.298033652
109 0.548146398
110 0.380669144
111 0.178570865
112 -0.322453842
113 -0.402288311
114 -0.247399944
115 -0.746642021
116 0.335377329
117 -0.553330153
118 0.705725987
119 -0.703522583
120 0.0495574634
121 0.449089976
122 -0.837509586
123 -0.245881762
124 -0.424517499
125 0.0894427190
126 0.822440769
127 0.855234443
128 0.0883883476
129 -0.588552180
130 0.194040445
131 -1.460088833
132 0.188649972
133 1.439803176
134 0.498976905
135 -0.266569403
136 0.192843719
137 -0.217108139
138 -0.370016846
139 1.271269647
140 -0.288411484
141 -0.290742522
142 -1.142408899
143 0.738656274
144 -0.225440578
145 0.299970602
146 -1.231857079
147 0.208005983
148 0.284866605
149 1.195278634
150 0.0443255428
151 -1.369683675
152 -0.394666747
153 -0.491865720
154 -1.097893531
155 -0.379699994
156 0.0961615228
157 0.997851147
158 -0.500005848
159 0.374439446
160 0.0790569415
161 2.153311487
162 0.505537211
163 1.598810065
164 -0.392244797
165 0.168733664
166 -0.154658103
167 -1.157153101
168 -0.142929416
169 -0.623983655
170 0.172484666
171 1.005814741
172 -0.938892448
173 -0.543490563
174 0.148657821
175 -0.257963073
176 0.300945383
177 0.319443103
178 -0.716030485
179 -0.104828337
180 -0.201640183
181 -0.136691000
182 -0.559634929
183 -0.370849191
184 -0.590272346
185 0.254792437
186 -0.188169686
187 0.678521509
188 -0.463810230
189 0.762099426
190 -0.353000670