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

$R= 23.742410121$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.994847991
4 0.5
5 0.447213595
6 0.703463761
7 -0.914970426
8 0.353553390
9 -0.0102774731
10 0.316227766
11 0.294622625
12 0.497423995
13 -1.121537570
14 -0.646981793
15 0.444909547
16 0.250000000
17 -0.114409380
18 -0.00726727094
19 0.624659166
20 0.223606797
21 -0.910256491
22 0.208329656
23 0.0188849102
24 0.351731880
25 0.200000000
26 -0.793046821
27 -1.005072515
28 -0.457485213
29 -1.030285033
30 0.314598557
31 1.085126328
32 0.176776695
33 0.293104727
34 -0.0808996487
35 -0.409187214
36 -0.00513873656
37 -1.075876546
38 0.441700732
39 -1.115759400
40 0.158113883
41 -1.025159033
42 -0.643648537
43 -1.404292714
44 0.147311312
45 -0.00459622570
46 0.0133536480
47 1.306794657
48 0.248711997
49 -0.162829118
50 0.141421356
51 -0.113819942
52 -0.560768785
53 -1.262467243
54 -0.710693591
55 0.131759243
56 -0.323490896
57 0.621440917
58 -0.728521534
59 -0.400566648
60 0.222454773
61 -0.934993361
62 0.767300185
63 0.00940358396
64 0.125000000
65 -0.501566849
66 0.207256340
67 -0.507486723
68 -0.0572046902
69 0.0187876149
70 -0.289339053
71 0.0777782182
72 -0.00363363547
73 -1.490018973
74 -0.760759601
75 0.198969598
76 0.312329583
77 -0.269570989
78 -0.788961037
79 0.102038861
80 0.111803398
81 -0.989616900
82 -0.724896904
83 1.612012498
84 -0.455128245
85 -0.0511654304
86 -0.992984901
87 -1.024976997
88 0.104164828
89 0.541683446
90 -0.00325002236
91 1.026173709
92 0.00944245510
93 1.079535748
94 0.924043363
95 0.279356071
96 0.175865940
97 0.587738658
98 -0.115137573
99 -0.00302797611
100 0.100000000
101 -0.729027066
102 -0.0804828531
103 1.812107247
104 -0.396523410
105 -0.407079078
106 -0.892699148
107 1.508605456
108 -0.502536257
109 -0.360273588
110 0.0931678546
111 -1.070333621
112 -0.228742606
113 0.129059873
114 0.439425086
115 0.00844558859
116 -0.515142516
117 0.0115265724
118 -0.283243393
119 0.104681199
120 0.157299278
121 -0.913197508
122 -0.661140146
123 -1.019877405
124 0.542563164
125 0.0894427190
126 0.00664933799
127 -1.925043363
128 0.0883883476
129 -1.397057787
130 -0.354661320
131 -1.407441586
132 0.146552363
133 -0.571544663
134 -0.358847303
135 -0.449482093
136 -0.0404498243
137 -0.314141471
138 0.0132848499
139 0.915939617
140 -0.204593607
141 1.300062039
142 0.0549975055
143 -0.330430336
144 -0.00256936828
145 -0.460757474
146 -1.053602520
147 -0.161990238
148 -0.537938273
149 -1.847864019
150 0.140692752
151 -1.529385898
152 0.220850366
153 0.00117587159
154 -0.190615474
155 0.485283246
156 -0.557879700
157 1.161787083
158 0.0721523709
159 -1.255962823
160 0.0790569415
161 -0.0172788598
162 -0.699764821
163 0.834018989
164 -0.512579516
165 0.131080418
166 1.139864969
167 0.361096364
168 -0.321824268
169 0.257846839
170 -0.0361794228
171 -0.00641998920
172 -0.702146357
173 0.484245602
174 -0.724768185
175 -0.182994085
176 0.0736556563
177 -0.398498424
178 0.383028038
179 -1.551615650
180 -0.00229811285
181 0.554765198
182 0.725614388
183 -0.930203191
184 0.00667682403
185 -0.481146618
186 0.763347048
187 -0.0335397149
188 0.653397328
189 0.919854847
190 0.197534572
191 -1.781110002
192 0.124355998
193 -0.792612218
194 0.415593991
195 -0.498982773
196 -0.0814145591
197 -0.201703302
198 -0.00214110244
199 1.577866977
200 0.0707106781
201 -0.508404117
202 -0.515499982
203 0.937168710
204 -0.0569099712
205 -0.458465057
206 1.281353322
207 0.00766953346
208 -0.280384392
209 0.192785575
210 -0.287848376
211 0.872720018
212 -0.631233621
213 0.123964415
214 1.066745148
215 -0.628018793
216 -0.355346795
217 -0.807825242
218 -0.254751897
219 -1.428229794