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

$R= 18.6257215488$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.894790618
4 0.5
5 0.447213595
6 0.632712513
7 0.999309403
8 -0.353553390
9 -0.199349749
10 -0.316227766
11 1.160800683
12 -0.447395309
13 1.775657767
14 -0.706618455
15 -0.400162529
16 0.250000000
17 1.521847866
18 0.140961559
19 1.676118854
20 0.223606797
21 -0.894172679
22 -0.820810035
23 -0.0700709448
24 0.316356256
25 0.200000000
26 -1.255579648
27 1.073166903
28 0.499654701
29 -1.399605145
30 0.282957638
31 0.580834181
32 -0.176776695
33 -1.038673561
34 -1.076108946
35 0.446904751
36 -0.0996748747
37 -0.324920446
38 -1.185195007
39 -1.588841911
40 -0.158113883
41 1.191757895
42 0.632275564
43 0.562282170
44 0.580400341
45 -0.0891519182
46 0.0495476402
47 -1.831547553
48 -0.223697654
49 -0.00138071594
50 -0.141421356
51 -1.361735193
52 0.887828883
53 0.0180051320
54 -0.758843595
55 0.519125847
56 -0.353309227
57 -1.499775425
58 0.989670289
59 -0.530169566
60 -0.200081264
61 -0.434567314
62 -0.410711788
63 -0.199212079
64 0.125000000
65 0.794098294
66 0.734453118
67 -0.632545671
68 0.760923933
69 0.0626988240
70 -0.316009380
71 1.214298543
72 0.0704807798
73 0.400421148
74 0.229753450
75 -0.178958123
76 0.838059427
77 1.159999038
78 1.123480890
79 1.342261878
80 0.111803398
81 -0.760909927
82 -0.842700089
83 0.923748589
84 -0.447086339
85 0.680591056
86 -0.397593535
87 1.252353553
88 -0.410405017
89 -0.0620965818
90 0.0630399259
91 1.774431504
92 -0.0350354724
93 -0.519724976
94 1.295099694
95 0.749583139
96 0.158178128
97 0.316505367
98 0.000976313610
99 -0.231405325
100 0.100000000
101 -0.239605539
102 0.962892189
103 -0.683194633
104 -0.627789824
105 -0.399886178
106 -0.0127315509
107 -0.791574940
108 0.536583451
109 0.706921648
110 -0.367077407
111 0.290735766
112 0.249827350
113 -0.172862675
114 1.060501373
115 -0.0313366791
116 -0.699802572
117 -0.353976931
118 0.374886495
119 1.520796888
120 0.141478819
121 0.347458267
122 0.307285494
123 -1.066373795
124 0.290417090
125 0.0894427190
126 0.140864212
127 -0.932897439
128 -0.0883883476
129 -0.503124732
130 -0.561512289
131 -0.605371527
132 -0.519336780
133 1.674961476
134 0.447277333
135 0.479934829
136 -0.538054473
137 -1.914648629
138 -0.0443347636
139 0.219797279
140 0.223452375
141 1.638853710
142 -0.858638734
143 2.061186020
144 -0.0498374373
145 -0.625922449
146 -0.283140509
147 0.00124332175
148 -0.162460223
149 1.235504821
150 0.126542502
151 0.492280869
152 -0.592597503
153 -0.303384588
154 -0.820243186
155 0.259756942
156 -0.794420955
157 0.203528486
158 -0.949122476
159 -0.0160643146
160 -0.0790569415
161 -0.0699556798
162 0.538044569
163 -0.348443320
164 0.595878947
165 -0.464508938
166 -0.653188892
167 0.0791557049
168 0.316137782
169 2.152919845
170 -0.481250551
171 -0.337961028
172 0.281141085
173 -0.101725693
174 -0.885547690
175 0.199861880
176 0.290200170
177 0.476983042
178 0.0439089140
179 -0.267279227
180 -0.0445759591
181 -0.0497325118
182 -1.254712549
183 0.396156393
184 0.0247738201
185 -0.145308840
186 0.367501055
187 1.781968462
188 -0.915773776
189 1.033637870
190 -0.530035320