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

$R= 23.246400292$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.869562159
4 0.5
5 -0.447213595
6 -0.614873299
7 -0.574560882
8 0.353553390
9 -0.243861649
10 -0.316227766
11 -1.892120704
12 -0.434781079
13 -0.595741729
14 -0.406275895
15 0.388880020
16 0.250000000
17 -1.268206217
18 -0.172436226
19 0.725528405
20 -0.223606797
21 0.499616401
22 -1.337931381
23 -1.520428423
24 -0.307436649
25 0.200000000
26 -0.421253016
27 1.081615023
28 -0.287280441
29 -0.346090391
30 0.274979699
31 -0.280258543
32 0.176776695
33 1.645316566
34 -0.896757216
35 0.256951437
36 -0.121930824
37 -0.0611532146
38 0.513026055
39 0.518034464
40 -0.158113883
41 -1.855055733
42 0.353282145
43 -0.616225495
44 -0.946060352
45 0.109058245
46 -1.075105248
47 -0.500235025
48 -0.217390539
49 -0.669879792
50 0.141421356
51 1.102784137
52 -0.297870864
53 0.624614017
54 0.764817317
55 0.846182103
56 -0.203137947
57 -0.630892047
58 -0.244722862
59 -1.759158919
60 0.194440010
61 1.677460543
62 -0.198172716
63 0.140113364
64 0.125000000
65 0.266423800
66 1.163414501
67 -0.377580533
68 -0.634103108
69 1.322107024
70 0.181692104
71 -0.0429517139
72 -0.0862181131
73 0.935260934
74 -0.0432418527
75 -0.173912431
76 0.362764202
77 1.087138540
78 0.366305682
79 1.043202035
80 -0.111803398
81 -0.696669845
82 -1.311722488
83 0.560476955
84 0.249808200
85 0.567159062
86 -0.435737226
87 0.300947108
88 -0.668965690
89 -1.591915757
90 0.0771158247
91 0.342289893
92 -0.760214211
93 0.243702224
94 -0.353719579
95 -0.324466166
96 -0.153718324
97 -1.304840392
98 -0.473676544
99 0.461415676
100 0.100000000
101 -0.171853180
102 0.779786141
103 1.248188066
104 -0.210626508
105 -0.223435247
106 0.441668807
107 -1.197564705
108 0.540807511
109 1.154779675
110 0.598341103
111 0.0531765215
112 -0.143640220
113 0.0790320873
114 -0.446108044
115 0.679956262
116 -0.173045195
117 0.145278561
118 -1.243913201
119 0.728661683
120 0.137489849
121 2.580120760
122 1.186143725
123 1.613086270
124 -0.140129271
125 -0.0894427190
126 0.0990751103
127 0.959173535
128 0.0883883476
129 0.535846372
130 0.188390076
131 0.269495823
132 0.822658283
133 -0.416860244
134 -0.266989755
135 -0.483712943
136 -0.448378608
137 -0.668480065
138 0.934870842
139 0.725438695
140 0.128475718
141 0.434985436
142 -0.0303714481
143 1.127215244
144 -0.0609654124
145 0.154776328
146 0.661329348
147 0.582502031
148 -0.0305766073
149 0.332757584
150 -0.122974659
151 -0.115303453
152 0.256513027
153 0.309266870
154 0.768723034
155 0.125335430
156 0.259017232
157 -1.462181832
158 0.737655233
159 -0.543140308
160 -0.0790569415
161 0.873578331
162 -0.492619972
163 0.950780472
164 -0.927527866
165 -0.735807937
166 0.396317055
167 -0.319110813
168 0.176641072
169 -0.645090344
170 0.401042018
171 -0.176923765
172 -0.308112747
173 1.208421852
174 0.212801741
175 -0.114912176
176 -0.473030176
177 1.529688490
178 -1.125654427
179 1.345329556
180 0.0545291226
181 0.562637577
182 0.242035504
183 -1.458676223
184 -0.537552624
185 0.0273485490
186 0.172323495
187 2.399454432
188 -0.250117512
189 -0.621381505
190 -0.229432226
191 -0.675561577
192 -0.108695269
193 -0.210116454
194 -0.922661490
195 -0.231672055
196 -0.334939896
197 -0.00120559268
198 0.326270154
199 -0.297782108
200 0.0707106781
201 0.334086596
202 -0.121518549
203 0.209834808
204 0.551392068
205 0.829606144
206 0.882602246
207 0.412499463
208 -0.148935432
209 -1.329954700
210 -0.157992578