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

$R= 22.6900189031$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.066481935
4 0.5
5 -0.447213595
6 0.754116608
7 -1.900382421
8 0.353553390
9 0.137383717
10 -0.316227766
11 1.340281360
12 0.533240967
13 1.508165925
14 -1.343773297
15 -0.476945220
16 0.250000000
17 -0.813548005
18 0.0971449585
19 0.333503105
20 -0.223606797
21 -2.026723522
22 0.947722039
23 0.0594580065
24 0.377058304
25 0.200000000
26 1.066434353
27 -0.919964681
28 -0.950191210
29 -0.865072224
30 -0.337251199
31 0.733785347
32 0.176776695
33 1.429385859
34 -0.575265311
35 0.849876855
36 0.0686918589
37 0.614171664
38 0.235822307
39 1.608431714
40 -0.158113883
41 0.613424674
42 -1.433109946
43 -0.398361674
44 0.670140680
45 -0.0614398664
46 0.0420431596
47 -0.124390448
48 0.266620483
49 2.611453347
50 0.141421356
51 -0.867634250
52 0.754082962
53 0.763578307
54 -0.650513264
55 -0.599392046
56 -0.671886648
57 0.355675037
58 -0.611698436
59 1.761399592
60 -0.238472610
61 0.827144405
62 0.518864595
63 -0.261081602
64 0.125000000
65 -0.674472306
66 1.010728434
67 1.503636300
68 -0.406774002
69 0.0634108899
70 0.600953687
71 -0.573590661
72 0.0485724792
73 1.759691369
74 0.434284948
75 0.213296387
76 0.166751552
77 -2.547047138
78 1.137332972
79 0.835828642
80 -0.111803398
81 -1.118509431
82 0.433756747
83 0.267144691
84 -1.013361761
85 0.363829728
86 -0.281684241
87 -0.922583900
88 0.473861019
89 -0.658207329
90 -0.0434445462
91 -2.866092013
92 0.0297290032
93 0.782568817
94 -0.0879573294
95 -0.149147122
96 0.188529152
97 1.307548205
98 1.846576370
99 0.184132836
100 0.100000000
101 -1.809882379
102 -0.613510062
103 -0.389371725
104 0.533217176
105 0.906378313
106 0.539931398
107 0.897630640
108 -0.459982340
109 1.108597454
110 -0.423834180
111 0.655002985
112 -0.475095605
113 1.125517446
114 0.251500230
115 -0.0265904289
116 -0.432536112
117 0.207197444
118 1.245497596
119 1.546052328
120 -0.168625599
121 0.796354126
122 0.584879418
123 0.654206329
124 0.366892673
125 -0.0894427190
126 -0.184612571
127 1.275252832
128 0.0883883476
129 -0.424845542
130 -0.476923941
131 0.571637213
132 0.714692929
133 -0.633783425
134 1.063231424
135 0.411420713
136 -0.287632655
137 -0.586068731
138 0.0448382702
139 -1.216781053
140 0.424938427
141 -0.132659985
142 -0.405589846
143 2.021366777
144 0.0343459294
145 0.386872060
146 1.244289700
147 2.785067942
148 0.307085832
149 -1.102249574
150 0.150823321
151 -0.680254432
152 0.117911153
153 -0.111770243
154 -1.801034303
155 -0.328158783
156 0.804215857
157 -1.248011034
158 0.591020101
159 0.814347065
160 -0.0790569415
161 -0.112988872
162 -0.790905604
163 -0.416458213
164 0.306712337
165 -0.639240789
166 0.188899822
167 1.500100368
168 -0.716554973
169 1.274566897
170 0.257266468
171 0.0457936841
172 -0.199180837
173 0.764689174
174 -0.652365332
175 -0.380076484
176 0.335070340
177 1.878102573
178 -0.465422866
179 0.159238188
180 -0.0307199332
181 -0.931651066
182 -2.026633098
183 0.882446807
184 0.0210215798
185 -0.274665918
186 0.553359717
187 -1.088210257
188 -0.0621952240
189 1.751658020
190 -0.105462941
191 -0.618872995
192 0.133310241
193 -0.0322620046
194 0.924576202
195 -0.719312530
196 1.305726673
197 -1.922918545
198 0.130201577
199 -1.453374656
200 0.0707106781
201 1.582325701
202 -1.279780103
203 1.588791568
204 -0.433817125
205 -0.274331854
206 -0.275327387
207 -0.0743534878
208 0.377041481
209 0.693969359
210 0.640906251