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

$R= 23.9165494096$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.534501758
4 0.5
5 0.447213595
6 1.085056599
7 -0.974357003
8 -0.353553390
9 1.354695647
10 -0.316227766
11 -1.436929830
12 -0.767250879
13 0.361387630
14 0.688974444
15 -0.686250048
16 0.250000000
17 0.604485998
18 -0.957914478
19 -1.854844001
20 0.223606797
21 1.495152535
22 1.016062827
23 -0.707643208
24 0.542528299
25 0.200000000
26 -0.255539644
27 -0.544281094
28 -0.487178501
29 0.768218719
30 0.485252063
31 1.571337894
32 -0.176776695
33 2.204971351
34 -0.427436148
35 -0.435745698
36 0.677347823
37 -1.071586438
38 1.311572771
39 -0.554549954
40 -0.158113883
41 -1.002976753
42 -1.057232496
43 -0.897527208
44 -0.718464915
45 0.605838311
46 0.500379311
47 -1.561676508
48 -0.383625439
49 -0.0506284294
50 -0.141421356
51 -0.927584827
52 0.180693815
53 -0.314155978
54 0.384864853
55 -0.642614555
56 0.344487222
57 2.846261383
58 -0.543212666
59 -1.056508451
60 -0.343125024
61 -0.910944464
62 -1.111103681
63 -1.319957191
64 0.125000000
65 0.161617461
66 -1.559150195
67 -0.682796452
68 0.302242999
69 1.085879748
70 0.308118738
71 -0.403636758
72 -0.478957239
73 -1.703095432
74 0.757726037
75 -0.306900351
76 -0.927422000
77 1.400082644
78 0.392126033
79 0.0894285913
80 0.111803398
81 -0.519495350
82 0.709211663
83 -0.648853592
84 0.747576267
85 0.270334356
86 0.634647575
87 -1.178832976
88 0.508031413
89 0.898428421
90 -0.428392378
91 -0.352120568
92 -0.353821604
93 -2.411220763
94 1.104272049
95 -0.829511455
96 0.271264149
97 -0.646882518
98 0.0357997057
99 -1.946602587
100 0.100000000
101 0.726778908
102 0.655901521
103 -1.334977858
104 -0.127769822
105 0.668652541
106 0.222141822
107 -1.154310639
108 -0.272140547
109 1.489611423
110 0.454397110
111 1.644351273
112 -0.243589250
113 -0.920632463
114 -2.012610725
115 -0.316467663
116 0.384109359
117 0.489570250
118 0.747064290
119 -0.588985166
120 0.242626031
121 1.064767337
122 0.644135008
123 1.539069591
124 0.785668947
125 0.0894427190
126 0.933350681
127 -1.205388193
128 -0.0883883476
129 1.377257080
130 -0.114280803
131 0.0197655189
132 1.102485675
133 1.807280239
134 0.482810001
135 -0.243409905
136 -0.213718074
137 -1.082147809
138 -0.767832933
139 1.020630071
140 -0.217872849
141 2.396395332
142 0.285414288
143 -0.519288688
144 0.338673911
145 0.343557855
146 1.204270329
147 0.0776893743
148 -0.535793219
149 0.338507145
150 0.217011319
151 -1.168764354
152 0.655786385
153 0.818894271
154 -0.990007931
155 0.702723669
156 -0.277274977
157 0.989362281
158 -0.0632355633
159 0.482072974
160 -0.0790569415
161 0.689495355
162 0.367338684
163 1.167385118
164 -0.501488376
165 0.986093166
166 0.458808775
167 0.816625058
168 -0.528616248
169 -0.869408450
170 -0.191155256
171 -2.512749263
172 -0.448763604
173 -1.695235861
174 0.833560791
175 -0.194871400
176 -0.359232457
177 1.621228498
178 -0.635284829
179 1.425854277
180 0.302919155
181 0.304178134
182 0.248986841
183 1.397739935
184 0.250189655
185 -0.479228023
186 1.704990552
187 -0.868464388
188 -0.780838254
189 0.529540840
190 0.586553175
191 -0.733201295
192 -0.191812719
193 -0.398716295
194 0.457415015
195 -0.248002279
196 -0.0253142147
197 -1.467903697
198 1.376455889
199 -1.547214242
200 -0.0707106781
201 1.044099635
202 -0.513910294
203 -0.737106973
204 -0.463792413
205 -0.448544840
206 0.943971896
207 -0.943327580
208 0.0903469076
209 2.737133061
210 -0.472808746
211 -0.164350120
212 -0.157077989
213 0.516788124
214 0.816220880
215 -0.401386370
216 0.192432426
217 -1.197120139
218 -1.053314339
219 3.207978136
220 -0.321307277