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

$R= 30.9231048721$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.825666908
4 0.5
5 -0.447213595
6 0.583834670
7 1.261123725
8 -0.353553390
9 -0.318274155
10 0.316227766
11 1.915184925
12 -0.412833454
13 1.580268515
14 -0.891749138
15 0.369249466
16 0.250000000
17 -0.0460505338
18 0.225053813
19 -1.616433019
20 -0.223606797
21 -1.041268128
22 -1.354240247
23 0.364596733
24 0.291917335
25 0.200000000
26 -1.117418583
27 1.088455347
28 0.630561862
29 -0.372992249
30 -0.261098802
31 0.170347076
32 -0.176776695
33 -1.581304816
34 0.0325626447
35 -0.563991675
36 -0.159137077
37 -1.236017136
38 1.142990749
39 -1.304775420
40 0.158113883
41 -1.080949647
42 0.736287754
43 -0.0888119379
44 0.957592462
45 0.142336529
46 -0.257808822
47 0.310873213
48 -0.206416727
49 0.590433051
50 -0.141421356
51 0.0380224019
52 0.790134257
53 -0.515769232
54 -0.769654156
55 -0.856496736
56 -0.445874569
57 1.334635254
58 0.263745349
59 -1.358726478
60 0.184624733
61 -0.842680564
62 -0.120453572
63 -0.401383089
64 0.125000000
65 -0.706717564
66 1.118151359
67 -1.251435933
68 -0.0230252669
69 -0.301035458
70 0.398802338
71 1.451216585
72 0.112526906
73 1.695098907
74 0.873996098
75 -0.165133381
76 -0.808216509
77 2.415285147
78 0.922615547
79 -1.491564877
80 -0.111803398
81 -0.580427406
82 0.764346826
83 -0.520191695
84 -0.520634064
85 0.0205944248
86 0.0627995235
87 0.307967357
88 -0.677120123
89 -1.215279023
90 -0.100647125
91 1.992914117
92 0.182298366
93 -0.140649943
94 -0.219820557
95 0.722890822
96 0.145958667
97 0.221469224
98 -0.417499214
99 -0.609553865
100 0.100000000
101 1.412313790
102 -0.0268858982
103 0.486257993
104 -0.558709291
105 0.465669263
106 0.364703921
107 -1.027003256
108 0.544227673
109 0.578519768
110 0.605634650
111 1.020538448
112 0.315280931
113 -1.282599010
114 -0.943729638
115 -0.163052616
116 -0.186496124
117 -0.502958627
118 0.960764706
119 -0.0580754208
120 -0.130549401
121 2.667933297
122 0.595865141
123 0.892504354
124 0.0851735380
125 -0.0894427190
126 0.283820704
127 1.319323005
128 -0.0883883476
129 0.0733290782
130 0.499724782
131 0.967951638
132 -0.790652408
133 -2.038522031
134 0.884898834
135 -0.486772029
136 0.0162813223
137 -0.274665209
138 0.212864213
139 -0.189921723
140 -0.281995837
141 -0.256677725
142 -1.026165088
143 3.026506438
144 -0.0795685389
145 0.166807205
146 -1.198615932
147 -0.487501032
148 -0.618008568
149 0.536540478
150 0.116766934
151 -1.503177214
152 0.571495374
153 0.0146566948
154 -1.707864506
155 -0.0761815283
156 -0.652387710
157 -0.0491765121
158 1.054695639
159 0.425853588
160 0.0790569415
161 0.459801592
162 0.410424154
163 0.341904501
164 -0.540474823
165 0.707181012
166 0.367831075
167 -1.665879627
168 0.368143877
169 1.497248578
170 -0.0145624574
171 0.514468857
172 -0.0444059689
173 1.261572028
174 -0.217765807
175 0.252224745
176 0.478796231
177 1.121855492
178 0.859332038
179 -0.0681695931
180 0.0711682647
181 -0.913269995
182 -1.409203087
183 0.695773493
184 -0.128904411
185 0.552763667
186 0.0994545289
187 -0.0881952523
188 0.155436606
189 1.372676898
190 -0.511161002
191 -0.591714442
192 -0.103208363
193 -1.011360928
194 -0.156602390
195 0.583513307
196 0.295216525
197 -0.223090700
198 0.431019671
199 -0.542958554
200 -0.0707106781
201 1.033271880
202 -0.998656658
203 -0.470387392
204 0.0190112009
205 0.483415378
206 -0.343836324
207 -0.116054774
208 0.395067128
209 -3.095779082
210 -0.329277894
211 -0.281170546
212 -0.257884616
213 -1.198232145
214 0.726200967
215 0.0397179060
216 -0.384827078
217 0.214899411
218 -0.409075251
219 -1.399451307
220 -0.428248368
221 -0.0728826707
222 -0.721629657
223 -0.630931277
224 -0.222937284
225 -0.0636548311
226 0.906934458
227 -1.036837230
228 0.667317627
229 -1.296959366
230 0.115295610
231 -1.992013792
232 0.131872674
233 -0.312983478
234 0.355645456
235 -0.139026727
236 -0.679363239
237 1.223234059
238 0.0410655239
239 1.595314706
240 0.0923123667
241 -0.365222366
242 -1.886513726
243 -0.584585020
244 -0.421340282
245 -0.264049687
246 -0.631095881
247 -2.512850239
248 -0.0602267863
249 0.400672610
250 0.0632455532