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

$R= 22.9121308668$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.406756055
4 0.5
5 0.447213595
6 -0.994726746
7 -1.494252298
8 0.353553390
9 0.978962599
10 0.316227766
11 0.926257167
12 -0.703378027
13 -0.979676554
14 -1.056595933
15 -0.629120433
16 0.250000000
17 1.883178897
18 0.692231092
19 -1.352316745
20 0.223606797
21 2.102048470
22 0.654962724
23 0.483836290
24 -0.497363373
25 0.200000000
26 -0.692735934
27 0.0295944900
28 -0.747126149
29 0.563574327
30 -0.444855324
31 -1.208063224
32 0.176776695
33 -1.303017879
34 1.331608568
35 -0.668249943
36 0.489481299
37 0.109694221
38 -0.956232341
39 1.378165924
40 0.158113883
41 1.587978595
42 1.486372727
43 -0.0519479451
44 0.463128583
45 0.437805384
46 0.342123921
47 0.851538651
48 -0.351689013
49 1.232789932
50 0.141421356
51 -2.649173317
52 -0.489838277
53 0.361023677
54 0.0209264645
55 0.414234798
56 -0.528297966
57 1.902379770
58 0.398507228
59 -1.475065344
60 -0.314560216
61 1.497736713
62 -0.854229698
63 -1.462817115
64 0.125000000
65 -0.438124674
66 -0.921372778
67 -0.0524701997
68 0.941589448
69 -0.680639631
70 -0.472524066
71 -0.702952933
72 0.346115546
73 -0.164900948
74 0.0775655280
75 -0.281351211
76 -0.676158372
77 -1.384061901
78 0.974510471
79 -0.963847603
80 0.111803398
81 -1.020594827
82 1.122870433
83 1.346772061
84 1.051024235
85 0.842183205
86 -0.0367327442
87 -0.792811598
88 0.327481362
89 -1.622109778
90 0.309575155
91 1.463883943
92 0.241918145
93 1.699450256
94 0.602128754
95 -0.604774434
96 -0.248681686
97 -1.033850827
98 0.871714121
99 0.906771124
100 0.100000000
101 -0.787271177
102 -1.873248417
103 -0.392807947
104 -0.346367967
105 0.940064654
106 0.255282290
107 -0.463310038
108 0.0147972450
109 -1.643510533
110 0.292908234
111 -0.154313010
112 -0.373563074
113 -0.249807127
114 1.345185636
115 0.216378167
116 0.281787163
117 -0.959066706
118 -1.043028707
119 -2.813944396
120 -0.222427662
121 -0.142047658
122 1.059059786
123 -2.233898505
124 -0.604031612
125 0.0894427190
126 -1.034367901
127 -0.234112580
128 0.0883883476
129 0.0730780876
130 -0.309800928
131 -0.379522261
132 -0.651508939
133 2.020702409
134 -0.0371020340
135 0.0132350582
136 0.665804284
137 -0.614374762
138 -0.481284898
139 -0.329479626
140 -0.334124971
141 -1.197907128
142 -0.497062786
143 -0.907432508
144 0.244740649
145 0.252038101
146 -0.116602578
147 -1.734234786
148 0.0548471109
149 0.0970662188
150 -0.198945349
151 1.001787477
152 -0.478116170
153 1.843562045
154 -0.978679556
155 -0.540262298
156 0.689082962
157 -0.0548397916
158 -0.681543176
159 -0.507875071
160 0.0790569415
161 -0.722974518
162 -0.721669523
163 1.527784806
164 0.793989297
165 -0.582727310
166 0.952311657
167 -0.0300484540
168 0.743186363
169 -0.0402058099
170 0.595513455
171 -1.323885055
172 -0.0259739725
173 -1.406348572
174 -0.560602457
175 -0.298850459
176 0.231564291
177 2.074994927
178 -1.147004824
179 -1.268091649
180 0.218902692
181 -0.640495793
182 1.035122263
183 -2.106797216
184 0.171061960
185 0.0490567473
186 1.201692800
187 1.743417408
188 0.425769325
189 -0.0433725326
190 -0.427640103
191 -0.842752573
192 -0.175844506
193 1.115792832
194 -0.731042930
195 0.616334538
196 0.616394966
197 0.599402540
198 0.641184011
199 -1.240395528
200 0.0707106781
201 0.0795310950
202 -0.556684788
203 -0.826272759
204 -1.324586658
205 0.710165617
206 -0.277757163
207 0.384785777
208 -0.244919138
209 -1.288725544
210 0.664726091