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

$R= 21.5655607109$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.788068858
4 0.5
5 -0.447213595
6 -0.557248834
7 -0.675668959
8 0.353553390
9 -0.378947473
10 -0.316227766
11 0.811809684
12 -0.394034429
13 -0.0977161487
14 -0.477770102
15 0.352435107
16 0.250000000
17 -0.488166280
18 -0.267956328
19 -1.794877268
20 -0.223606797
21 0.532473665
22 0.574036132
23 -1.235382281
24 -0.278624417
25 0.200000000
26 -0.0690957513
27 1.086705562
28 -0.337834479
29 1.341179446
30 0.249209254
31 -0.785044508
32 0.176776695
33 -0.639761931
34 -0.345185687
35 0.302168344
36 -0.189473736
37 -1.022430840
38 -1.269169887
39 0.0770070538
40 -0.158113883
41 -1.068669114
42 0.376515739
43 1.208159433
44 0.405904842
45 0.169470462
46 -0.873547188
47 0.464430226
48 -0.197017214
49 -0.543471457
50 0.141421356
51 0.384708643
52 -0.0488580743
53 -0.547859032
54 0.768416872
55 -0.363052327
56 -0.238885051
57 1.414486880
58 0.948357081
59 1.352256415
60 0.176217553
61 0.312382852
62 -0.555110295
63 0.256043045
64 0.125000000
65 0.0436999902
66 -0.452380000
67 0.359368659
68 -0.244083140
69 0.973566304
70 0.213665285
71 -0.0273983392
72 -0.133978164
73 0.499460260
74 -0.722967780
75 -0.157613771
76 -0.897438634
77 -0.548514604
78 0.0544522099
79 -0.999973833
80 -0.111803398
81 -0.477451338
82 -0.755663178
83 0.274878126
84 0.266236832
85 0.218314597
86 0.854297728
87 -1.056941756
88 0.287018066
89 0.808124801
90 0.119833713
91 0.0660237685
92 -0.617691140
93 0.618669129
94 0.328401762
95 0.802693516
96 -0.139312208
97 1.253833278
98 -0.384292353
99 -0.307633228
100 0.100000000
101 1.675014210
102 0.272030090
103 0.264356014
104 -0.0345478756
105 -0.238129462
106 -0.387394837
107 1.552518265
108 0.543352781
109 0.714729225
110 -0.256716762
111 0.805745905
112 -0.168917239
113 -0.0344749057
114 1.000193265
115 0.552479751
116 0.670589723
117 0.0370292854
118 0.956189681
119 0.329838799
120 0.124604627
121 -0.340965037
122 0.220888033
123 0.842184849
124 -0.392522254
125 -0.0894427190
126 0.181049773
127 -1.482885992
128 0.0883883476
129 -0.952112828
130 0.0309005594
131 1.694657555
132 -0.319880965
133 1.212742844
134 0.254112016
135 -0.485989501
136 -0.172592843
137 1.195399234
138 0.688415336
139 0.941874519
140 0.151084172
141 -0.366002888
142 -0.0193735514
143 -0.0793269800
144 -0.0947368684
145 -0.599793682
146 0.353171736
147 0.428293225
148 -0.511215420
149 -0.487291764
150 -0.111449766
151 -0.811755261
152 -0.634584943
153 0.184989743
154 -0.387858396
155 0.351082577
156 0.0385035269
157 1.597432572
158 -0.707088278
159 0.431754104
160 -0.0790569415
161 0.834707591
162 -0.337609079
163 -0.529708105
164 -0.534334557
165 0.286110233
166 0.194368187
167 1.509962424
168 0.188257869
169 -0.990480799
170 0.154371732
171 0.680091930
172 0.604079716
173 0.0214749458
174 -0.747370683
175 -0.135133791
176 0.202952421
177 -1.065708871
178 0.571430527
179 -0.640943041
180 0.0847352311
181 -0.431052871
182 0.0466858544
183 -0.245851180
184 -0.436773594
185 0.457244972
186 0.437465137
187 -0.395934528
188 0.232215113
189 -0.736435277
190 0.567590028
191 -1.429216605
192 -0.0985086073
193 0.870065003
194 0.886594013
195 -0.0344386014
196 -0.271735728
197 1.472807891
198 -0.217529542