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

$R= 20.3173037027$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0885131702
4 0.5
5 0.447213595
6 0.0625882628
7 0.719162774
8 -0.353553390
9 -0.992165418
10 -0.316227766
11 -1.482375742
12 -0.0442565851
13 0.780145180
14 -0.508524874
15 -0.0395842931
16 0.250000000
17 0.158277450
18 0.701566895
19 -0.700316730
20 0.223606797
21 -0.0636553770
22 1.048197940
23 0.889052317
24 0.0312941314
25 0.200000000
26 -0.551645947
27 0.176332876
28 0.359581387
29 -1.305984832
30 0.0279903220
31 1.351445992
32 -0.176776695
33 0.131209776
34 -0.111919058
35 0.321619370
36 -0.496082709
37 1.448288461
38 0.495198708
39 -0.0690531231
40 -0.158113883
41 -1.263708330
42 0.0450111487
43 -1.124711981
44 -0.741187871
45 -0.443709864
46 -0.628654922
47 0.616698412
48 -0.0221282925
49 -0.482804904
50 -0.141421356
51 -0.0140096389
52 0.390072590
53 0.911767387
54 -0.124686172
55 -0.662938585
56 -0.254262437
57 0.0619872539
58 0.923470731
59 -0.777386955
60 -0.0197921465
61 -0.112669624
62 -0.955616625
63 -0.713528435
64 0.125000000
65 0.348891531
66 -0.0927793227
67 -0.642292332
68 0.0791387254
69 -0.0786928391
70 -0.227419237
71 -1.705230041
72 0.350783447
73 1.191383525
74 -1.024094592
75 -0.0177026340
76 -0.350158365
77 -1.066069451
78 0.0488279316
79 0.659860769
80 0.111803398
81 0.976557636
82 0.893576729
83 0.599333182
84 -0.0318276885
85 0.0707838278
86 0.795291469
87 0.115596857
88 0.524098970
89 0.635647291
90 0.313750253
91 0.561051372
92 0.444526158
93 -0.119620769
94 -0.436071629
95 -0.313191162
96 0.0156470657
97 0.374471013
98 0.341394621
99 1.470761949
100 0.100000000
101 0.751794542
102 0.00990631070
103 1.971432547
104 -0.275822973
105 -0.0284675500
106 -0.644716902
107 1.237632420
108 0.0881664384
109 1.371563626
110 0.468768369
111 -0.128192602
112 0.179790693
113 -1.786587859
114 -0.0438316076
115 0.397596283
116 -0.652992416
117 -0.774033066
118 0.549695587
119 0.113827251
120 0.0139951610
121 1.197437847
122 0.0796694554
123 0.111854828
124 0.675722996
125 0.0894427190
126 0.504540794
127 0.00450091062
128 -0.0883883476
129 0.0995518176
130 -0.246703567
131 0.559878567
132 0.0656048882
133 -0.503641755
134 0.454169264
135 0.0788584598
136 -0.0559595293
137 -0.393850550
138 0.0556442401
139 -0.593521064
140 0.160809685
141 -0.0545856443
142 1.205779725
143 -1.156468580
144 -0.248041354
145 -0.584054172
146 -0.842435369
147 0.0427338073
148 0.724144230
149 1.548995683
150 0.0125176525
151 -1.006638078
152 0.247599354
153 -0.157036061
154 0.753824938
155 0.604385021
156 -0.0345265615
157 -0.129125397
158 -0.466592025
159 -0.0807131496
160 -0.0790569415
161 0.639357954
162 -0.690530527
163 1.537037439
164 -0.631854165
165 0.0586787959
166 -0.423792557
167 -0.440218833
168 0.0225055743
169 -0.391276967
170 -0.0500517246
171 0.694772032
172 -0.562355990
173 0.764572205
174 -0.0817393220
175 0.143832554
176 -0.370593935
177 0.0685387805
178 -0.449470510
179 -0.260552910
180 -0.221854932
181 -0.288957861
182 -0.396723230
183 0.0108063876
184 -0.314327461
185 0.647694290
186 0.0845846570
187 -0.234746326
188 0.308349206
189 0.138927739
190 0.221459595
191 1.268377793
192 -0.0110641462