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

$R= 25.8565600192$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.518897146
4 0.5
5 0.447213595
6 0.366915690
7 0.108609678
8 -0.353553390
9 -0.730745751
10 -0.316227766
11 0.574395296
12 -0.259448573
13 1.796058130
14 -0.0767986401
15 -0.232057858
16 0.250000000
17 -0.664406764
18 0.516715276
19 -1.531409774
20 0.223606797
21 -0.0563572522
22 -0.406158809
23 0.384945998
24 0.183457845
25 0.200000000
26 -1.270004883
27 0.898079031
28 0.0543048392
29 1.628380661
30 0.164089685
31 -1.055368703
32 -0.176776695
33 -0.298052079
34 0.469806528
35 0.0485717248
36 -0.365372875
37 1.880495467
38 1.082870236
39 -0.931969438
40 -0.158113883
41 1.576039088
42 0.0398505952
43 -0.0878353515
44 0.287197648
45 -0.326799435
46 -0.272197925
47 -0.656413856
48 -0.129724286
49 -0.988203937
50 -0.141421356
51 0.344758773
52 0.898029065
53 0.147142997
54 -0.635037772
55 0.256877385
56 -0.0383993200
57 0.794644161
58 -1.151439008
59 -1.190421179
60 -0.116028929
61 -0.0751225257
62 0.746258366
63 -0.0793660611
64 0.125000000
65 0.803221614
66 0.210754646
67 0.0967657359
68 -0.332203382
69 -0.199747379
70 -0.0343453960
71 0.618412620
72 0.258357638
73 -1.374468280
74 -1.329711097
75 -0.103779429
76 -0.765704887
77 0.0623848884
78 0.659001909
79 -1.302150964
80 0.111803398
81 0.264735105
82 -1.114427926
83 -0.501360513
84 -0.0281786261
85 -0.297131737
86 0.0621089727
87 -0.844962077
88 -0.203079404
89 -0.494647334
90 0.231082096
91 0.195069296
92 0.192472999
93 0.547627808
94 0.464154689
95 -0.684867271
96 0.0917289226
97 1.530320164
98 0.698765705
99 -0.419736922
100 0.100000000
101 0.262933429
102 -0.243781266
103 0.307064382
104 -0.635002441
105 -0.0252037293
106 -0.104045811
107 -1.411227120
108 0.449039515
109 0.870578070
110 -0.181639741
111 -0.975783731
112 0.0271524196
113 -1.413339718
114 -0.561898275
115 0.172153083
116 0.814190330
117 -1.312461849
118 0.841754888
119 -0.0721610050
120 0.0820448426
121 -0.670070043
122 0.0531196473
123 -0.817802184
124 -0.527684351
125 0.0894427190
126 0.0561202800
127 0.400353334
128 -0.0883883476
129 0.0455775133
130 -0.567963450
131 0.291434959
132 -0.149026039
133 -0.166325923
134 -0.0684237080
135 0.401633152
136 0.234903264
137 0.443205642
138 0.141242726
139 0.623619995
140 0.0242858624
141 0.340611276
142 -0.437283757
143 1.031647346
144 -0.182686437
145 0.728233970
146 0.971895841
147 0.512776207
148 0.940247733
149 0.141282959
150 0.0733831381
151 1.406076102
152 0.541435118
153 0.485512408
154 -0.0441127776
155 -0.471975232
156 -0.465984719
157 -0.347457481
158 0.920759776
159 -0.0763521235
160 -0.0790569415
161 0.0418088414
162 -0.187195988
163 0.189158782
164 0.788019544
165 -0.133292942
166 0.354515418
167 1.630490072
168 0.0199252976
169 2.225824467
170 0.210103866
171 1.119070894
172 -0.0439176757
173 -0.936623198
174 0.597478415
175 0.0217219357
176 0.143598824
177 0.617704454
178 0.349768484
179 -0.594749842
180 -0.163399717
181 -0.683325698
182 -0.137934822
183 0.0389776929
184 -0.136098962
185 0.840983139
186 -0.387231336
187 -0.381633075
188 -0.328206928
189 0.0975359013
190 0.484274291
191 1.790858181
192 -0.0648621432
193 -0.0368670466
194 -1.082099765
195 -0.416789403
196 -0.494101968
197 1.027442727
198 0.296798824
199 1.846440787
200 -0.0707106781
201 -0.0503510626
202 -0.185922010
203 0.176282098
204 0.172379386
205 0.704826107
206 -0.217127307
207 -0.281313876
208 0.449014532
209 -0.880461764
210 0.0178217279
211 -0.735444099
212 0.0735714985
213 -0.321059465
214 0.997888266
215 -0.0392811633
216 -0.317518886
217 -0.120402738
218 -0.615591656
219 0.719786376
220 0.128438692
221 -1.193232323
222 0.689983293