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

$R= 24.7649515125$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.862315620
4 0.5
5 0.447213595
6 -0.609749222
7 -1.635497425
8 -0.353553390
9 -0.256411770
10 -0.316227766
11 0.749333396
12 0.431157810
13 -1.174847408
14 1.156471319
15 0.385639269
16 0.250000000
17 -1.135408852
18 0.181310501
19 -0.849114013
20 0.223606797
21 -1.410314977
22 -0.529858725
23 -1.579316319
24 -0.304874611
25 0.200000000
26 0.830742569
27 -1.083423495
28 -0.817748712
29 1.407067685
30 -0.272688142
31 0.0736376423
32 -0.176776695
33 0.646161892
34 0.802855298
35 -0.731416683
36 -0.128205885
37 0.384217303
38 0.600414277
39 -1.013089272
40 -0.158113883
41 1.042421189
42 0.997243284
43 -1.275362146
44 0.374666698
45 -0.114670829
46 1.116745279
47 0.658272606
48 0.215578905
49 1.674851827
50 -0.141421356
51 -0.979080789
52 -0.587423704
53 1.029636058
54 0.766096100
55 0.335112082
56 0.578235659
57 -0.732204277
58 -0.994947101
59 1.290567870
60 0.192819634
61 1.386540971
62 -0.0520696762
63 0.419360789
64 0.125000000
65 -0.525407733
66 -0.456905456
67 -1.419509196
68 -0.567704426
69 -1.361869132
70 0.517189697
71 -0.877981268
72 0.0906552507
73 0.0695365834
74 -0.271682660
75 0.172463124
76 -0.424557006
77 -1.225532840
78 0.716362294
79 0.297628383
80 0.111803398
81 -0.677841234
82 -0.737103091
83 0.267154531
84 -0.705157488
85 -0.507770275
86 0.901817222
87 1.213336444
88 -0.264929362
89 0.997009681
90 0.0810845212
91 1.921459911
92 -0.789658159
93 0.0634988892
94 -0.465469023
95 -0.379735331
96 -0.152437305
97 -0.927371613
98 -1.184299084
99 -0.192137902
100 0.100000000
101 0.485534500
102 0.692314665
103 -1.854939304
104 0.415371284
105 -0.630712031
106 -0.728062639
107 1.453498827
108 -0.541711747
109 -1.089707323
110 -0.236960025
111 0.331316582
112 -0.408874356
113 -0.778658415
114 0.517746610
115 -0.706291729
116 0.703533842
117 0.301244703
118 -0.912569292
119 1.856958254
120 -0.136344071
121 -0.438499460
122 -0.980432523
123 0.898896074
124 0.0368188211
125 0.0894427190
126 -0.296532858
127 1.144950092
128 -0.0883883476
129 -1.099764700
130 0.371519371
131 1.060754424
132 0.323080946
133 1.388723783
134 1.003744578
135 -0.484521716
136 0.401427649
137 1.449567785
138 0.962986898
139 0.0430275780
140 -0.365708341
141 0.567638754
142 0.620826508
143 -0.880352401
144 -0.0641029425
145 0.629259798
146 -0.0491697896
147 1.444250889
148 0.192108651
149 0.367493268
150 -0.121949844
151 -0.449959810
152 0.300207138
153 0.291132251
154 0.866582582
155 0.0329317547
156 -0.506544636
157 -0.124343948
158 -0.210455048
159 0.887871268
160 -0.0790569415
161 2.582967566
162 0.479306133
163 -0.0930472288
164 0.521210594
165 0.288972383
166 -0.188906780
167 -0.844142510
168 0.498621642
169 0.380266186
170 0.359047804
171 0.217722633
172 -0.637681073
173 0.269004322
174 -0.857958427
175 -0.327099485
176 0.187333349
177 1.112882965
178 -0.704992306
179 1.032041926
180 -0.0573354148
181 -1.446854753
182 -1.358677333
183 1.195643217
184 0.558372639
185 0.171827201
186 -0.0449004951
187 -0.850842392
188 0.329136303
189 1.772021696
190 0.268513427
191 -0.790546416
192 0.107789452
193 0.165384961
194 0.655750756
195 -0.453067296
196 0.837425913
197 1.844322614
198 0.135862013
199 0.00885151532
200 -0.0707106781
201 -1.224146426
202 -0.343324738
203 -2.301750150
204 -0.489540394
205 0.466184928
206 1.311640161
207 0.401176387
208 -0.293711852
209 -0.627489664
210 0.445980754
211 -0.582806517
212 0.514818029
213 -0.770473033
214 -1.027778877
215 -0.570359291
216 0.383048050
217 -0.141948267
218 0.770539438
219 0.190741203
220 0.167556041
221 1.327999883
222 -0.234276202