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

$R= 21.7535258027$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.836096281
4 0.5
5 -0.447213595
6 1.298316131
7 -0.636542366
8 0.353553390
9 2.371249556
10 -0.316227766
11 -1.642432642
12 0.918048140
13 -0.484678271
14 -0.450103423
15 -0.821127219
16 0.250000000
17 -1.572479298
18 1.676726641
19 -0.456623909
20 -0.223606797
21 -1.168753071
22 -1.161375259
23 0.729907566
24 0.649158065
25 0.200000000
26 -0.342719292
27 2.517746212
28 -0.318271183
29 -1.089089111
30 -0.580624625
31 -0.272398514
32 0.176776695
33 -3.015664468
34 -1.111910775
35 0.284670400
36 1.185624778
37 -0.435955642
38 -0.322881862
39 -0.889915972
40 -0.158113883
41 -1.770567060
42 -0.826433222
43 0.906695207
44 -0.821216321
45 -1.060455040
46 0.516122589
47 0.888699581
48 0.459024070
49 -0.594813816
50 0.141421356
51 -2.887223393
52 -0.242339135
53 -0.516966976
54 1.780315420
55 0.734518207
56 -0.225051711
57 -0.838405461
58 -0.770102296
59 0.938581289
60 -0.410563609
61 -1.511355162
62 -0.192614836
63 -1.509400803
64 0.125000000
65 0.216754712
66 -2.132396795
67 0.872282149
68 -0.786239649
69 1.340180569
70 0.201292370
71 0.435065008
72 0.838363320
73 -0.915199870
74 -0.308267191
75 0.367219256
76 -0.228311954
77 1.045477960
78 -0.629265619
79 0.955750843
80 -0.111803398
81 2.251574903
82 -1.251979974
83 0.631968266
84 -0.584376535
85 0.703234120
86 0.641130329
87 -1.999672468
88 -0.580687629
89 1.310696695
90 -0.749854949
91 0.308518254
92 0.364953783
93 -0.500149899
94 0.628405500
95 0.204208420
96 0.324579032
97 0.947403732
98 -0.420596882
99 -3.894617675
100 0.100000000
101 0.673229760
102 -2.041575240
103 -1.717526605
104 -0.171359646
105 0.522682263
106 -0.365550854
107 0.332452242
108 1.258873106
109 -1.440649551
110 0.519382805
111 -0.800456534
112 -0.159135591
113 -0.837683907
114 -0.592842187
115 -0.326424587
116 -0.544544555
117 -1.149293139
118 0.663677194
119 1.000949693
120 -0.290312312
121 1.697584984
122 -1.068689483
123 -3.250931598
124 -0.136199257
125 -0.0894427190
126 -1.067307543
127 0.506311290
128 0.0883883476
129 1.664779690
130 0.153268727
131 -1.027496589
132 -1.507832234
133 0.290660474
134 0.616796622
135 -1.125970336
136 -0.555955387
137 -0.882514454
138 0.947650768
139 -0.540657508
140 0.142335200
141 1.631737995
142 0.307637417
143 0.796051527
144 0.592812389
145 0.487055457
146 -0.647144034
147 -1.092135382
148 -0.217977821
149 -0.0758626073
150 0.259663226
151 0.183267197
152 -0.161440931
153 -3.728741734
154 0.739264555
155 0.121820318
156 -0.444957986
157 -0.264886983
158 0.675817902
159 -0.949194778
160 -0.0790569415
161 -0.464621988
162 1.592103882
163 1.619757374
164 -0.885283530
165 1.348646149
166 0.446869046
167 1.542912882
168 -0.413216611
169 -0.765108213
170 0.497261615
171 -1.082681903
172 0.453347603
173 -0.649137030
174 -1.413981962
175 -0.127308473
176 -0.410608160
177 1.723293658
178 0.926802521
179 -0.405473803
180 -0.530227520
181 -0.878563976
182 0.218155349
183 -2.775288197
184 0.258061294
185 0.194965290
186 -0.353659385
187 2.581386603
188 0.444349790
189 -1.602937314
190 0.144397158
191 1.805562851
192 0.229512035
193 -0.520892563
194 0.669915603
195 0.397982521
196 -0.297406908