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

$R= 30.3643867787$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0812936100
4 0.5
5 -0.447213595
6 0.0574832629
7 0.936726973
8 -0.353553390
9 -0.993391348
10 0.316227766
11 -1.756335189
12 -0.0406468050
13 -0.945167685
14 -0.662365994
15 0.0363556076
16 0.250000000
17 0.847468088
18 0.702433759
19 0.710974750
20 -0.223606797
21 -0.0761499173
22 1.241916522
23 1.078127594
24 0.0287416314
25 0.200000000
26 0.668334479
27 0.162049979
28 0.468363486
29 -0.304557280
30 -0.0257072967
31 -0.586339068
32 -0.176776695
33 0.142778828
34 -0.599250432
35 -0.418917037
36 -0.496695674
37 0.304550345
38 -0.502735067
39 0.0768360932
40 0.158113883
41 1.035042332
42 0.0538461229
43 0.962020451
44 -0.878167594
45 0.444258116
46 -0.762351332
47 0.837479419
48 -0.0203234025
49 -0.122542577
50 -0.141421356
51 -0.0688937402
52 -0.472583842
53 -0.0377599082
54 -0.114586639
55 0.785456974
56 -0.331182997
57 -0.0577977041
58 0.215354518
59 -0.521397742
60 0.0181778038
61 -1.705560802
62 0.414604331
63 -0.930536471
64 0.125000000
65 0.422691839
66 -0.100959877
67 0.318161598
68 0.423734044
69 -0.0876448842
70 0.296219078
71 0.372372846
72 0.351216879
73 1.363615926
74 -0.215349614
75 -0.0162587220
76 0.355487375
77 -1.645206545
78 -0.0543313226
79 -1.246486037
80 -0.111803398
81 0.980217721
82 -0.731885452
83 -0.270462302
84 -0.0380749586
85 -0.378999250
86 -0.680251184
87 0.0247585608
88 0.620958261
89 1.914753647
90 -0.314137927
91 -0.885364065
92 0.539063797
93 0.0476656195
94 -0.592187376
95 -0.317957574
96 0.0143708157
97 0.816341908
98 0.0866506876
99 1.744728183
100 0.100000000
101 -1.833806637
102 0.0487152309
103 0.561469170
104 0.334167239
105 0.0340552783
106 0.0267002872
107 1.266546783
108 0.0810249895
109 -1.026219297
110 -0.555401953
111 -0.0247579970
112 0.234181743
113 1.500197379
114 0.0408691485
115 -0.482153317
116 -0.152278640
117 0.938921402
118 0.368683879
119 0.793846217
120 -0.0128536483
121 2.084713297
122 1.206013609
123 -0.0841423278
124 -0.293169534
125 -0.0894427190
126 0.657988649
127 -0.802766990
128 -0.0883883476
129 -0.0782061154
130 -0.298888265
131 -1.106616253
132 0.0713894140
133 0.665989226
134 -0.224974223
135 -0.0724709537
136 -0.299625216
137 -0.714501279
138 0.0619742919
139 0.0695728706
140 -0.209458518
141 -0.0680817254
142 -0.263307365
143 1.660031266
144 -0.248347837
145 0.136202156
146 -0.964222068
147 0.00996192816
148 0.152275172
149 -1.570177658
150 0.0114966525
151 -0.327671492
152 -0.251367533
153 -0.841867467
154 1.163336705
155 0.262218802
156 0.0384180466
157 -0.169146002
158 0.881398729
159 0.00306963611
160 0.0790569415
161 1.009911196
162 -0.693118597
163 1.825734577
164 0.517521166
165 -0.0638526330
166 0.191245728
167 0.662146954
168 0.0269230614
169 -0.106658047
170 0.267992940
171 -0.706276160
172 0.481010225
173 1.682370730
174 -0.0175069462
175 0.187345394
176 -0.439083797
177 0.0423862115
178 -1.353935288
179 1.329588397
180 0.222129058
181 -0.995563105
182 0.626046934
183 0.138651161
184 -0.381175666
185 -0.136199054
186 -0.0337046828
187 -1.488438108
188 0.418739709
189 0.151796882
190 0.224829957
191 1.154043964
192 -0.0101617012
193 0.355142374
194 -0.577240899
195 -0.0343621455
196 -0.0612712888
197 -1.320611451
198 -1.233709129
199 -1.055687305
200 -0.0707106781
201 -0.0258611346
202 1.296697108
203 -0.285280910
204 -0.0344468701
205 -0.462885003
206 -0.397018657
207 -1.071011947
208 -0.236291921
209 -1.248779042
210 -0.0240807182
211 -1.174096693
212 -0.0188799541
213 -0.0302454476
214 -0.895583819
215 -0.430228624
216 -0.0572933195
217 -0.549108021
218 0.725646624
219 -0.110930021
220 0.392728487
221 -0.800886266
222 0.0175065475
223 -1.818605611
224 -0.165591498
225 -0.198678269
226 -1.060799740
227 -0.928204431
228 -0.0288988520
229 1.222025818
230 0.340933880
231 0.138595578
232 0.107677259
233 0.895065457
234 -0.663917690
235 -0.374532182
236 -0.260698871
237 0.105244126
238 -0.561334043
239 -0.986033923
240 0.00908890191
241 -0.352721779
242 -1.474114909
243 -0.279209816
244 -0.852780401
245 0.0548027067
246 0.0594976105
247 -0.781559966
248 0.207302165
249 0.111678416
250 0.0632455532