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

$R= 19.7128261759$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.567894421
4 0.5
5 0.447213595
6 -1.108668777
7 1.237151573
8 -0.353553390
9 1.458292915
10 -0.316227766
11 1.953337652
12 0.783947210
13 -0.765874534
14 -0.874798267
15 0.701183701
16 0.250000000
17 0.796873771
18 -1.031168809
19 -0.646821762
20 0.223606797
21 1.939723050
22 -1.381218300
23 0.255207923
24 -0.554334388
25 0.200000000
26 0.541555076
27 0.718554905
28 0.618575786
29 1.670386896
30 -0.495811750
31 1.111261700
32 -0.176776695
33 3.062627208
34 -0.563474847
35 0.553271003
36 0.729146457
37 -0.896473668
38 0.457372054
39 -1.200810409
40 -0.158113883
41 0.536438605
42 -1.371591322
43 -1.638584864
44 0.976668826
45 0.652168418
46 -0.180459253
47 -0.848513249
48 0.391973605
49 0.530544016
50 -0.141421356
51 1.249413940
52 -0.382937267
53 -0.782186616
54 -0.508095046
55 0.873559155
56 -0.437399133
57 -1.014148232
58 -1.181141901
59 0.854848253
60 0.350591850
61 -1.257223229
62 -0.785780684
63 1.804129375
64 0.125000000
65 -0.342509504
66 -2.165604467
67 -0.421110052
68 0.398436885
69 0.400139079
70 -0.391221678
71 -0.408176556
72 -0.515584404
73 0.0200656416
74 0.633902610
75 0.313578884
76 -0.323410881
77 2.416574751
78 0.849101183
79 -0.865509441
80 0.111803398
81 -0.331674688
82 -0.379319375
83 0.812471671
84 0.969861525
85 0.356372784
86 1.158654469
87 2.618990295
88 -0.690609150
89 -0.555766521
90 -0.461152710
91 -0.947502885
92 0.127603961
93 1.742341020
94 0.599989472
95 -0.289267485
96 -0.277167194
97 -0.0662236124
98 -0.375151271
99 2.848538460
100 0.100000000
101 0.433194911
102 -0.883469069
103 1.669895880
104 0.270777538
105 0.867470519
106 0.553089460
107 -0.608572573
108 0.359277452
109 0.0794372451
110 -0.617699602
111 -1.405576063
112 0.309287893
113 -1.668157498
114 0.717111092
115 0.114132453
116 0.835193448
117 -1.116869400
118 -0.604468997
119 0.985853638
120 -0.247905875
121 2.815527975
122 0.888991070
123 0.841079108
124 0.555630850
125 0.0894427190
126 -1.275712115
127 0.399289913
128 -0.0883883476
129 -2.569128089
130 0.242190792
131 -1.243042322
132 1.531313604
133 -0.800216463
134 0.297769773
135 0.321347522
136 -0.281737423
137 1.727498771
138 -0.282941056
139 0.0939647032
140 0.276635501
141 -1.330378793
142 0.288624410
143 -1.496011038
144 0.364573228
145 0.747019729
146 -0.0141885512
147 0.831834190
148 -0.448236834
149 -0.997438842
150 -0.221733755
151 1.572694730
152 0.228686027
153 1.162064843
154 -1.708776393
155 0.496971340
156 -0.600405204
157 0.925443126
158 0.612007595
159 -1.226410427
160 -0.0790569415
161 0.315764181
162 0.234529421
163 -0.146433829
164 0.268219302
165 1.369648525
166 -0.574504228
167 -0.174839264
168 -0.685795661
169 -0.413810761
170 -0.251993612
171 -0.943627313
172 -0.819292432
173 0.624021343
174 -1.851905797
175 0.247430314
176 0.488334413
177 1.341820297
178 0.392986276
179 0.750221042
180 0.326084209
181 0.931991186
182 0.669985715
183 -1.964831161
184 -0.0902296266
185 -0.400915212
186 -1.232021150
187 1.548409932
188 -0.424256624
189 0.921683604
190 0.204543000