Properties

Level 10
Symmetry even
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

$R= 26.0094853283$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.715259478
4 0.5
5 0.447213595
6 1.212871609
7 0.324787323
8 -0.353553390
9 1.942115080
10 -0.316227766
11 -0.0813000890
12 -0.857629739
13 1.750081965
14 -0.229659319
15 -0.767087358
16 0.250000000
17 -0.548424402
18 -1.373282742
19 0.653595704
20 0.223606797
21 -0.557094535
22 0.0574878442
23 -0.928445127
24 0.606435804
25 0.200000000
26 -1.237494825
27 -1.615971821
28 0.162393661
29 -0.929085148
30 0.542412673
31 -0.416231061
32 -0.176776695
33 0.139450748
34 0.387794614
35 0.145249306
36 0.971057540
37 -1.211619179
38 -0.462161954
39 -3.001844680
40 -0.158113883
41 -1.527570507
42 0.393925323
43 0.168286645
44 -0.0406500445
45 0.868540267
46 0.656509845
47 1.819820864
48 -0.428814869
49 -0.894513194
50 -0.141421356
51 0.940690154
52 0.875040982
53 1.845562101
54 1.142664633
55 -0.0363585051
56 -0.114829659
57 -1.121086227
58 0.656962408
59 1.464439644
60 -0.383543679
61 -0.159519597
62 0.294319806
63 0.630774359
64 0.125000000
65 0.782660448
66 -0.0986065698
67 -1.351537036
68 -0.274212201
69 1.592524305
70 -0.102706769
71 -0.172686495
72 -0.686641371
73 0.213469197
74 0.856744138
75 -0.343051895
76 0.326797852
77 -0.0264052383
78 2.122624729
79 -0.750946391
80 0.111803398
81 0.829695904
82 1.080155464
83 1.667838707
84 -0.278547267
85 -0.245262848
86 -0.118996628
87 1.593622107
88 0.0287439221
89 -1.383913413
90 -0.614150713
91 0.568404437
92 -0.464222563
93 0.713944273
94 -1.286807673
95 0.292296884
96 0.303217902
97 -1.305764210
98 0.632516345
99 -0.157894129
100 0.100000000
101 1.537113280
102 -0.665168387
103 0.302907253
104 -0.618747412
105 -0.249140250
106 -1.305009476
107 0.823516929
108 -0.807985910
109 -0.541739174
110 0.0257093455
111 2.078241282
112 0.0811968309
113 0.173063235
114 0.792727673
115 -0.415213283
116 -0.464542574
117 3.398860576
118 -1.035515203
119 -0.178121294
120 0.271206336
121 -0.993390295
122 0.112797389
123 2.620179792
124 -0.208115530
125 0.0894427190
126 -0.446024826
127 0.0188518070
128 -0.0883883476
129 -0.288655263
130 -0.553424510
131 0.654086106
132 0.0697253742
133 0.212279599
134 0.955681003
135 -0.722684568
136 0.193897307
137 -1.342177315
138 -1.126084735
139 1.193163397
140 0.0726246534
141 -3.121464989
142 0.122107792
143 -0.142281810
144 0.485528770
145 -0.415499509
146 -0.150945517
147 1.534322233
148 -0.605809589
149 -0.579363128
150 0.242574321
151 0.0275128411
152 -0.231080977
153 -1.065103305
154 0.0186713231
155 -0.186144189
156 -1.500922340
157 -0.234494769
158 0.530999285
159 -3.165617954
160 -0.0790569415
161 -0.301547289
162 -0.586683600
163 -1.897102387
164 -0.763785253
165 0.0623642706
166 -1.179340059
167 1.906112720
168 0.196962661
169 2.062786397
170 0.173427023
171 1.269357155
172 0.0841433226
173 -0.877105530
174 -1.126860998
175 0.0649574647
176 -0.0203250222
177 -2.511892635
178 0.978574559
179 -1.429519350
180 0.434270133
181 -1.458535246
182 -0.401922632
183 0.273619873
184 0.328254922
185 -0.541852569
186 -0.504834837
187 0.0446135789
188 0.909910432
189 -0.524763743
190 -0.206685109
191 -0.150166660
192 -0.214407434
193 -0.315254849
194 0.923314727
195 -1.342465752
196 -0.447256597
197 0.604685332
198 0.111648009
199 0.566275882
200 -0.0707106781
201 2.319113656
202 -1.086903223
203 -0.301704342
204 0.470345077
205 -0.683150298
206 -0.214187773
207 -1.803986626
208 0.437520491
209 -0.0513873370
210 0.176168760
211 0.00858268967
212 0.922781050
213 0.298291891
214 -0.582314405
215 0.0752600757
216 0.571332316
217 -0.146478463
218 0.383067443
219 -0.369107244
220 -0.0181792525
221 -0.950742159
222 -1.469538503
223 -0.301620913
224 -0.0574148297
225 0.388423016
226 -0.122374187