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

$R= 29.5841732525$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.223472009
4 0.5
5 0.447213595
6 -0.865125354
7 -1.169752547
8 -0.353553390
9 0.496883758
10 -0.316227766
11 -0.419182601
12 0.611736004
13 -0.978405548
14 0.827139958
15 0.547153316
16 0.250000000
17 -0.840520471
18 -0.351349875
19 0.794005490
20 0.223606797
21 -1.431159500
22 0.296406859
23 1.088585883
24 -0.432562677
25 0.200000000
26 0.691837198
27 -0.615548638
28 -0.584876273
29 -0.793154328
30 -0.386895820
31 -1.065056177
32 -0.176776695
33 -0.512858179
34 0.594337725
35 -0.523129242
36 0.248441879
37 -1.472230182
38 -0.561446666
39 -1.197051802
40 -0.158113883
41 1.040243628
42 1.011982587
43 0.691494605
44 -0.209591300
45 0.222213172
46 -0.769746460
47 1.274865082
48 0.305868002
49 0.368321022
50 -0.141421356
51 -1.028353270
52 -0.489202774
53 -0.770408771
54 0.435258616
55 -0.187464158
56 0.413569979
57 0.971443493
58 0.560844803
59 0.359309896
60 0.273576658
61 0.180039922
62 0.753108445
63 -0.581231042
64 0.125000000
65 -0.437556263
66 0.362645496
67 0.0326924833
68 -0.420260235
69 1.331854358
70 0.369908234
71 1.639495627
72 -0.175674937
73 -0.276805387
74 1.041023945
75 0.244694401
76 0.397002745
77 0.490339915
78 0.846443447
79 1.798141253
80 0.111803398
81 -1.249990289
82 -0.735563323
83 1.517971922
84 -0.715579750
85 -0.375892182
86 -0.488960524
87 -0.970402119
88 0.148203429
89 1.444421297
90 -0.157128441
91 1.144492383
92 0.544292941
93 -1.303066421
94 -0.901465745
95 0.355090050
96 -0.216281338
97 -0.131009529
98 -0.260442292
99 -0.208285026
100 0.100000000
101 -1.837440389
102 0.727155571
103 1.296183693
104 0.345918599
105 -0.640033986
106 0.544761266
107 -1.443771470
108 -0.307774319
109 0.210262105
110 0.132557177
111 -1.801232420
112 -0.292438136
113 -1.363454436
114 -0.686914281
115 0.486830407
116 -0.396577164
117 -0.486153826
118 -0.254070464
119 0.983200963
120 -0.193447910
121 -0.824285946
122 -0.127307449
123 1.272708962
124 -0.532528088
125 0.0894427190
126 0.410992411
127 0.353060453
128 -0.0883883476
129 0.846024294
130 0.309399000
131 1.252071066
132 -0.256429089
133 -0.928789945
134 -0.0231170766
135 -0.275281719
136 0.297168862
137 0.228472672
138 -0.941763248
139 0.601619166
140 -0.261564621
141 1.559761745
142 -1.159298475
143 0.410130582
144 0.124220939
145 -0.354709398
146 0.195730966
147 0.450630462
148 -0.736115091
149 0.281909932
150 -0.173025070
151 0.241091549
152 -0.280723333
153 -0.417640971
154 -0.346722679
155 -0.476307602
156 -0.598525901
157 0.742880210
158 -1.271477873
159 -0.942573560
160 -0.0790569415
161 -1.273376104
162 0.883876609
163 -1.623873685
164 0.520121814
165 -0.229357150
166 -1.073368240
167 0.353061954
168 0.505991293
169 -0.0427225521
170 0.265795911
171 0.394528509
172 0.345747302
173 0.639227205
174 0.686177919
175 -0.233950509
176 -0.104795650
177 0.439605534
178 -1.021360094
179 0.835596236
180 0.111106586
181 -0.0423496355
182 -0.809278325
183 0.220273939
184 -0.384873230
185 -0.658401353
186 0.921407103
187 0.352329285
188 0.637432541
189 0.720037143
190 -0.251086582
191 0.731053299
192 0.152934001
193 0.982830670
194 0.0926377267
195 -0.535337840
196 0.184160511
197 1.339170449
198 0.147279754
199 1.834486888
200 -0.0707106781
201 0.0399525517
202 1.299266559
203 0.927772111
204 -0.514176635
205 0.465211093
206 -0.916540279
207 0.540940698
208 -0.244601387
209 -0.332884509
210 0.452572371
211 -0.0510963024
212 -0.385204385
213 2.005573245
214 1.020900597
215 0.309245788
216 0.217629308
217 1.246272197
218 -0.148677760
219 -0.337137350
220 -0.0937320791
221 0.822564109
222 1.273663659
223 -1.554396130
224 0.206784989
225 0.0993767517
226 0.964107877
227 -1.651874516
228 0.485721746
229 -1.305255581
230 -0.344241082
231 0.610400987
232 0.280422401
233 1.286016425
234 0.343762667
235 0.570136997
236 0.179654948
237 2.190813914
238 -0.695228068
239 1.342646350
240 0.136788329
241 -0.240593487
242 0.582858182
243 -0.842151799
244 0.0900199610
245 0.164718168
246 -0.899941138
247 -1.240424175