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

$R= 18.7767490336$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.012972205
4 0.5
5 -0.447213595
6 -0.716279515
7 0.380011810
8 0.353553390
9 0.0261126885
10 -0.316227766
11 -0.410488075
12 -0.506486102
13 0.816930550
14 0.268708928
15 0.453014942
16 0.250000000
17 0.937106464
18 0.0184644591
19 -1.674934260
20 -0.223606797
21 -0.384941401
22 -0.290258902
23 1.485155717
24 -0.358139757
25 0.200000000
26 0.577657132
27 0.986520777
28 0.190005905
29 -0.279204086
30 0.320329937
31 0.216037531
32 0.176776695
33 0.415813011
34 0.662634335
35 -0.169946448
36 0.0130563442
37 1.055872307
38 -1.184357373
39 -0.827527941
40 -0.158113883
41 -1.218740245
42 -0.272194675
43 -0.395940885
44 -0.205244037
45 -0.0116779493
46 1.050163679
47 -1.125805020
48 -0.253243051
49 -0.855591023
50 0.141421356
51 -0.949262801
52 0.408465275
53 0.580276140
54 0.697575531
55 0.183575848
56 0.134354464
57 1.696661851
58 -0.197427103
59 0.236827157
60 0.226507471
61 -0.572756503
62 0.152761603
63 0.00992313006
64 0.125000000
65 -0.365342448
66 0.294024200
67 -0.835012254
68 0.468553232
69 -1.504421462
70 -0.120170285
71 -1.417707029
72 0.00923222957
73 0.776740713
74 0.746614468
75 -0.202594441
76 -0.837467130
77 -0.155990316
78 -0.585150618
79 -0.0854009741
80 -0.111803398
81 -1.025430816
82 -0.861779492
83 -1.852610446
84 -0.192470700
85 -0.419086751
86 -0.279972484
87 0.282825979
88 -0.145129451
89 -0.855890520
90 -0.00825755716
91 0.310443257
92 0.742577858
93 -0.218840014
94 -0.796064363
95 0.749053372
96 -0.179069878
97 -0.0581099699
98 -0.604994214
99 -0.0107189463
100 0.100000000
101 -1.067209875
102 -0.671230164
103 -0.938912694
104 0.288828566
105 0.172151028
106 0.410317194
107 -0.471260262
108 0.493260388
109 0.240455181
110 0.129807727
111 -1.069569311
112 0.0950029526
113 -0.296264744
114 1.199721100
115 -0.664181828
116 -0.139602043
117 0.0213323152
118 0.167462088
119 0.356111574
120 0.160164968
121 -0.831499623
122 -0.405000007
123 1.234549845
124 0.108018765
125 -0.0894427190
126 0.00701671255
127 -0.810604810
128 0.0883883476
129 0.401077446
130 -0.258336123
131 1.044735354
132 0.207906505
133 -0.636495916
134 -0.590442827
135 -0.441185503
136 0.331317167
137 -1.946214398
138 -1.063786618
139 1.757047921
140 -0.0849732241
141 1.140405182
142 -1.002470254
143 -0.335349174
144 0.00652817213
145 0.124863863
146 0.549238625
147 0.866705672
148 0.527936153
149 1.859540131
150 -0.143255903
151 -0.0863660811
152 -0.592178686
153 0.0243934256
154 -0.110301810
155 -0.0966149211
156 -0.413763970
157 -1.099149694
158 -0.0603876079
159 -0.587689458
160 -0.0790569415
161 0.564149092
162 -0.725089083
163 0.573557788
164 -0.609370122
165 -0.185957231
166 -1.309993409
167 1.896089415
168 -0.136097337
169 -0.330227171
170 -0.296339083
171 -0.0462610404
172 -0.197970442
173 1.598739932
174 0.199988168
175 0.0760023621
176 -0.102622018
177 -0.220728398
178 -0.605205991
179 1.630804498
180 -0.00583897466