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

$R= 30.0454030918$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.279273748
4 0.5
5 0.447213595
6 -0.197476361
7 0.796976750
8 0.353553390
9 -0.922006173
10 0.316227766
11 1.078086981
12 -0.139636874
13 -0.805443794
14 0.563547664
15 -0.124895017
16 0.250000000
17 0.911701525
18 -0.651956817
19 -1.636093990
20 0.223606797
21 -0.222574684
22 0.762322615
23 0.314110801
24 -0.0987381807
25 0.200000000
26 -0.569534768
27 0.536765868
28 0.398488375
29 -1.890943968
30 -0.0883141136
31 -0.0788281605
32 0.176776695
33 -0.301081392
34 0.644670331
35 0.356418838
36 -0.461003086
37 -0.343904263
38 -1.156893155
39 0.224939307
40 0.158113883
41 0.668291642
42 -0.157384068
43 -0.215150621
44 0.539043490
45 -0.412333695
46 0.222109877
47 -0.784223023
48 -0.0698184371
49 -0.364828059
50 0.141421356
51 -0.254614302
52 -0.402721897
53 -1.743572528
54 0.379550785
55 0.482135155
56 0.281773832
57 0.456918101
58 -1.337099303
59 1.048191932
60 -0.0624475086
61 -0.564431630
62 -0.0557399268
63 -0.734817483
64 0.125000000
65 -0.360205415
66 -0.212896694
67 0.736783655
68 0.455850762
69 -0.0877229009
70 0.252026177
71 1.609859813
72 -0.325978408
73 -1.346796760
74 -0.243177036
75 -0.0558547497
76 -0.818046995
77 0.859210259
78 0.159056109
79 -0.638276955
80 0.111803398
81 0.772101557
82 0.472553552
83 1.021345009
84 -0.111287342
85 0.407725317
86 -0.152134463
87 0.528091010
88 0.381161307
89 0.330356079
90 -0.291563952
91 -0.641919977
92 0.157055400
93 0.0220146358
94 -0.554529417
95 -0.731683476
96 -0.0493690903
97 1.720788276
98 -0.257972394
99 -0.994002852
100 0.100000000
101 -1.247731252
102 -0.180039499
103 -1.212987828
104 -0.284767384
105 -0.0995384249
106 -1.232891958
107 -1.243073171
108 0.268382934
109 0.966061740
110 0.340921037
111 0.0960434327
112 0.199244187
113 -1.098082338
114 0.323089888
115 0.140474620
116 -0.945471984
117 0.742624150
118 0.741183623
119 0.726604919
120 -0.0441570568
121 0.162271539
122 -0.399113433
123 -0.186636312
124 -0.0394140802
125 0.0894427190
126 -0.519594425
127 -0.533844205
128 0.0883883476
129 0.0600859206
130 -0.254703691
131 -0.758120855
132 -0.150540696
133 -1.303928872
134 0.520984719
135 0.240048994
136 0.322335165
137 -1.471611678
138 -0.0620294581
139 -0.0170913439
140 0.178209419
141 0.219012903
142 1.138342790
143 -0.868338468
144 -0.230501543
145 -0.845655851
146 -0.952329122
147 0.101886899
148 -0.171952131
149 0.625676056
150 -0.0394952722
151 1.596613137
152 -0.578446577
153 -0.840594433
154 0.607553400
155 -0.0352530251
156 0.112469653
157 0.699323762
158 -0.451329963
159 0.486934038
160 0.0790569415
161 0.250339010
162 0.545958246
163 1.121420758
164 0.334145821
165 -0.134647692
166 0.722199981
167 0.278206241
168 -0.0786920343
169 -0.351260278
170 0.288305336
171 1.508488759
172 -0.107575310
173 -0.105242267
174 0.373416734
175 0.159395350
176 0.269521745
177 -0.292732481
178 0.233597024
179 -1.644163841
180 -0.206166847
181 -1.073127740
182 -0.453905969
183 0.157630743
184 0.111054938
185 -0.153798662
186 0.0155666983
187 0.982893411
188 -0.392111511
189 0.427789694
190 -0.517378347
191 0.0952381888
192 -0.0349092185
193 -0.849606942
194 1.216781059
195 0.100595916
196 -0.182414029
197 -1.150793516
198 -0.702866157
199 -0.435243073
200 0.0707106781
201 -0.205759344
202 -0.882279230
203 -1.507033436
204 -0.127307151
205 0.298869108
206 -0.857711918
207 -0.289620125
208 -0.201360948
209 -1.763869280
210 -0.0703842952
211 -0.0860079619
212 -0.871786264
213 -0.449461005
214 -0.878985468
215 -0.0962182831
216 0.189775392
217 -0.0627687572
218 0.683108808
219 0.376474617
220 0.241067577
221 -0.733690088
222 0.0679129626
223 -0.0398376537
224 0.140886916
225 -0.184401234
226 -0.776461468
227 -0.623224160
228 0.228459050
229 -0.776185158
230 0.0993305570
231 -0.237992957
232 -0.668549651
233 -1.726544166
234 0.525114572
235 -0.350715198
236 0.524095966
237 0.183359354
238 0.513787265
239 -1.049800389
240 -0.0312237543
241 -1.932779430
242 0.114743306
243 -0.785046812
244 -0.282215815
245 -0.163156068
246 -0.131971801
247 1.383895953
248 -0.0278699634
249 -0.230789153
250 0.0632455532