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

$R= 20.3060013567$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.577895619
4 0.5
5 -0.447213595
6 1.115740692
7 -0.193904988
8 0.353553390
9 1.489754587
10 -0.316227766
11 0.157108067
12 0.788947809
13 1.107617321
14 -0.137111532
15 -0.705656373
16 0.250000000
17 1.690776997
18 1.053415570
19 -1.244859737
20 -0.223606797
21 -0.305961832
22 0.111092180
23 -1.138872928
24 0.557870346
25 0.200000000
26 0.783203719
27 0.772781617
28 -0.0969524943
29 1.262460518
30 -0.498974406
31 1.034339426
32 0.176776695
33 0.247900132
34 1.195559880
35 0.0867169471
36 0.744877293
37 -0.134814495
38 -0.880248762
39 1.747704520
40 -0.158113883
41 0.698619399
42 -0.216347686
43 0.488973081
44 0.0785540339
45 -0.666238505
46 -0.805304770
47 1.469605080
48 0.394473904
49 -0.962400855
50 0.141421356
51 2.667869618
52 0.553808660
53 1.294662878
54 0.546439122
55 -0.0702608639
56 -0.0685557662
57 -1.964258727
58 0.892694393
59 -0.433324174
60 -0.352828186
61 0.460180489
62 0.731388422
63 -0.288870846
64 0.125000000
65 -0.495341524
66 0.175291864
67 -0.135301650
68 0.845388498
69 -1.797022605
70 0.0613181414
71 -1.655753321
72 0.526707785
73 -0.954304227
74 -0.0953282439
75 0.315579123
76 -0.622429868
77 -0.0304640381
78 1.235813717
79 1.880997193
80 -0.111803398
81 -0.270385857
82 0.493998514
83 -0.146443046
84 -0.152980916
85 -0.756138460
86 0.345756182
87 1.992030922
88 0.0555460901
89 1.639588768
90 -0.471101765
91 -0.214772524
92 -0.569436464
93 1.632079651
94 1.039167718
95 0.556718199
96 0.278935173
97 -1.052460254
98 -0.680520171
99 0.234052465
100 0.100000000
101 0.0742452814
102 1.886468698
103 1.247255588
104 0.391601859
105 0.136830291
106 0.915464900
107 1.251920049
108 0.386390808
109 -1.458988457
110 -0.0496819333
111 -0.212723202
112 -0.0484762471
113 0.122285592
114 -1.388940666
115 0.509319457
116 0.631230259
117 1.650077984
118 -0.306406462
119 -0.327850090
120 -0.249487203
121 -0.975317058
122 0.325396744
123 1.102348488
124 0.517169713
125 -0.0894427190
126 -0.204262534
127 0.0616032149
128 0.0883883476
129 0.771548481
130 -0.350259351
131 0.253216634
132 0.123950066
133 0.241384528
134 -0.0956727142
135 -0.345598445
136 0.597779940
137 -0.393473116
138 -1.270686870
139 0.559771391
140 0.0433584735
141 2.318883303
142 -1.170794401
143 0.174015996
144 0.372438646
145 -0.564589507
146 -0.674794990
147 -1.518568671
148 -0.0674072477
149 -0.329336442
150 0.223148138
151 -0.729286973
152 -0.440124381
153 2.518846550
154 -0.0215413279
155 -0.462570654
156 0.873852260
157 -1.613851812
158 1.330065871
159 2.042848280
160 -0.0790569415
161 0.220813980
162 -0.191191673
163 0.606319552
164 0.349309699
165 -0.110864309
166 -0.103550871
167 -1.712091811
168 -0.108173843
169 0.226822762
170 -0.534670632
171 -1.854672509
172 0.244486540
173 -1.794008756
174 1.408578573
175 -0.0387809977
176 0.0392770169
177 -0.683352024
178 1.159364336
179 1.356898515
180 -0.333119252
181 -0.872309979
182 -0.151867108
183 0.722613789
184 -0.402652385
185 0.0602908752
186 1.154054588
187 0.269248411
188 0.734802540
189 -0.132910952
190 0.393659213
191 -0.134500092
192 0.197236952