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

$R= 30.3458704079$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.647468259
4 0.5
5 0.447213595
6 1.164935977
7 0.225871814
8 -0.353553390
9 1.714151664
10 -0.316227766
11 0.120503383
12 -0.823734129
13 -0.603816667
14 -0.159715491
15 -0.736770203
16 0.250000000
17 -0.545014711
18 -1.212088266
19 -0.798889526
20 0.223606797
21 -0.372116644
22 -0.0852087596
23 1.413986268
24 0.582467988
25 0.200000000
26 0.426962860
27 -1.176542199
28 0.112935907
29 0.295981276
30 0.520975207
31 0.357093023
32 -0.176776695
33 -0.198525499
34 0.385383598
35 0.101012946
36 0.857075832
37 -0.0153579263
38 0.564900201
39 0.994768793
40 -0.158113883
41 1.736846907
42 0.263126202
43 -1.660082438
44 0.0602516917
45 0.766591929
46 -0.999839279
47 1.771799287
48 -0.411867064
49 -0.948981923
50 -0.141421356
51 0.897894437
52 -0.301908333
53 1.245270962
54 0.831940967
55 0.0538907514
56 -0.0798577457
57 1.316145136
58 -0.209290367
59 0.783304971
60 -0.368385101
61 1.293480911
62 -0.252502898
63 0.387178546
64 0.125000000
65 -0.270035022
66 0.140378726
67 -1.668042003
68 -0.272507355
69 -2.329497496
70 -0.0714269392
71 -1.600384803
72 -0.606044133
73 -0.877953162
74 0.0108596938
75 -0.329493651
76 -0.399444763
77 0.0272183178
78 -0.703407759
79 1.305981890
80 0.111803398
81 0.224164264
82 -1.228136225
83 0.0357223716
84 -0.186058322
85 -0.243737988
86 1.173855549
87 -0.487619758
88 -0.0426043798
89 -0.584483389
90 -0.542062351
91 -0.136385166
92 0.706993134
93 -0.588299421
94 -1.252851291
95 -0.357274257
96 0.291233994
97 -0.247804529
98 0.671031553
99 0.206561075
100 0.100000000
101 0.145622934
102 -0.634907245
103 -0.944123807
104 0.213481430
105 -0.166415622
106 -0.880539541
107 0.142448780
108 -0.588271099
109 1.283723549
110 -0.0381065157
111 0.0253016961
112 0.0564679535
113 -0.802684693
114 -0.930655151
115 0.632353883
116 0.147990638
117 -1.035033345
118 -0.553880257
119 -0.123103461
120 0.260487603
121 -0.985478934
122 -0.914629124
123 -2.861400150
124 0.178546511
125 0.0894427190
126 -0.273776575
127 0.206754728
128 -0.0883883476
129 2.734933124
130 0.190943595
131 0.358130829
132 -0.0992627497
133 -0.180446626
134 1.179483811
135 -0.526165667
136 0.192691799
137 -1.385538740
138 1.647203476
139 -0.341665337
140 0.0505064731
141 -2.918983088
142 1.131642946
143 -0.0727619516
144 0.428537916
145 0.132366850
146 0.620806634
147 1.563417597
148 -0.00767896317
149 0.681215451
150 0.232987195
151 0.389791988
152 0.282450100
153 -0.934237874
154 -0.0192462571
155 0.159696855
156 0.497384396
157 -1.514416653
158 -0.923468651
159 -2.051544387
160 -0.0790569415
161 0.319379643
162 -0.158508071
163 0.764488421
164 0.868423453
165 -0.0887833024
166 -0.0252595312
167 -1.761339485
168 0.131563101
169 -0.635405425
170 0.172348784
171 -1.369417794
172 -0.830041219
173 0.00533154233
174 0.344799237
175 0.0451743628
176 0.0301258458
177 -1.290470089
178 0.413292168
179 0.913711623
180 0.383295964
181 1.699233463
182 0.0964388758
183 -2.130968729
184 -0.499919639
185 -0.00686827345
186 0.415990510
187 -0.0656763030
188 0.885899643
189 -0.265747649
190 0.252631050
191 0.807526584
192 -0.205933532
193 0.620044609
194 0.175224263
195 0.444874128
196 -0.474490961
197 -0.102744072
198 -0.146060737
199 -1.850891957
200 -0.0707106781
201 2.748050706
202 -0.102970964
203 0.0668442508
204 0.448947218
205 0.776741550
206 0.667596346
207 2.423796645
208 -0.150954166
209 -0.0962939698
210 0.117673615
211 -0.341520806
212 0.622635481
213 2.636489589
214 -0.100726498
215 -0.742411436
216 0.415970483
217 0.0806511479
218 -0.907729627
219 1.446872961
220 0.0269453757
221 0.329003841
222 -0.0178910009
223 -0.0562539596
224 -0.0399288728
225 0.342830332
226 0.567583789
227 -0.913680171
228 0.658072568
229 1.516839378
230 -0.447141719
231 -0.0479644917
232 -0.104645183
233 1.865001635
234 0.731879097
235 0.792372730
236 0.391652485
237 -2.156337823
238 0.0870472924
239 0.346943459
240 -0.184192550
241 -0.990946691
242 0.696838837
243 0.733273396
244 0.646740455
245 -0.424397618
246 2.023315449
247 0.471455999
248 -0.126251449
249 -0.500109508
250 -0.0632455532