Properties

Level 10
Symmetry even
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

$R= 29.9495532252$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.337118997
4 0.5
5 -0.447213595
6 0.238379129
7 0.668379006
8 0.353553390
9 -0.886350781
10 -0.316227766
11 1.607042549
12 0.168559498
13 0.908280514
14 0.472615328
15 -0.150764199
16 0.250000000
17 -1.309308904
18 -0.626744648
19 -1.442551474
20 -0.223606797
21 0.225323260
22 1.136350684
23 -0.846796355
24 0.119189564
25 0.200000000
26 0.642251311
27 -0.635924684
28 0.334189503
29 0.0942671626
30 -0.106606387
31 -1.751210695
32 0.176776695
33 0.541764573
34 -0.925821204
35 -0.298908178
36 -0.443175390
37 0.993621816
38 -1.020037929
39 0.306198616
40 -0.158113883
41 0.767219665
42 0.159327605
43 0.653050755
44 0.803521274
45 0.396388119
46 -0.598775445
47 -1.500392345
48 0.0842797493
49 -0.553269503
50 0.141421356
51 -0.441392905
52 0.454140257
53 1.551652346
54 -0.449666656
55 -0.718691276
56 0.236307664
57 -0.486311506
58 0.0666569499
59 -0.563187636
60 -0.0753820995
61 1.666990929
62 -1.238292958
63 -0.592418255
64 0.125000000
65 -0.406195394
66 0.383085403
67 0.318120321
68 -0.654654452
69 -0.285471138
70 -0.211360000
71 -0.738333051
72 -0.313372324
73 -0.275772194
74 0.702596724
75 0.0674237995
76 -0.721275737
77 1.074113503
78 0.216515118
79 -1.352404508
80 -0.111803398
81 0.671968489
82 0.542506228
83 -1.261122922
84 0.112661630
85 0.585540742
86 0.461776617
87 0.0317792513
88 0.568175342
89 1.048001008
90 0.280288727
91 0.607075628
92 -0.423398177
93 -0.590366394
94 -1.060937601
95 0.645128631
96 0.0595947823
97 -1.844826506
98 -0.391220617
99 -1.424403419
100 0.100000000
101 -0.549069096
102 -0.312111916
103 -0.374756375
104 0.321125655
105 -0.100767625
106 1.097183895
107 -0.763088103
108 -0.317962342
109 -1.169478696
110 -0.508191475
111 0.334968790
112 0.167094751
113 0.973305022
114 -0.343874164
115 0.378698842
116 0.0471335813
117 -0.805055144
118 -0.398233797
119 -0.875114585
120 -0.0533031937
121 1.582585755
122 1.178740590
123 0.258644324
124 -0.875605347
125 -0.0894427190
126 -0.418902965
127 -0.653939336
128 0.0883883476
129 0.220155815
130 -0.287223518
131 -0.913953282
132 0.270882286
133 -0.964171121
134 0.224945036
135 0.284394164
136 -0.462910602
137 0.309357173
138 -0.201858577
139 -1.943303432
140 -0.149454089
141 -0.505810763
142 -0.522080307
143 1.459645434
144 -0.221587695
145 -0.0421575567
146 -0.195000388
147 -0.186517660
148 0.496810908
149 -0.580132127
150 0.0476758258
151 0.761231220
152 -0.510018964
153 1.160506972
154 0.759512941
155 0.783165231
156 0.153099308
157 0.497886150
158 -0.956294398
159 0.523091479
160 -0.0790569415
161 -0.565980906
162 0.475153475
163 1.325846165
164 0.383609832
165 -0.242284482
166 -0.891748570
167 0.351669751
168 0.0796638028
169 -0.175026539
170 0.414039829
171 1.278606587
172 0.326525377
173 -1.014773926
174 0.0224713241
175 0.133675801
176 0.401760637
177 -0.189861327
178 0.741048619
179 0.151661834
180 0.198194059
181 0.361279782
182 0.429267293
183 0.561974012
184 -0.299387722
185 -0.444361185
186 -0.417452080
187 -2.104116559
188 -0.750196172
189 -0.425038198
190 0.456174830
191 -1.096916034
192 0.0421398746
193 0.510773038
194 -1.304489333
195 -0.136936184
196 -0.276634751
197 -1.395056051
198 -1.007205317
199 1.140144708
200 0.0707106781
201 0.107263174
202 -0.388250481
203 0.0630302900
204 -0.220696452
205 -0.343111065
206 -0.264992774
207 0.750476296
208 0.227070128
209 -2.318260731
210 -0.0712534713
211 -0.557548794
212 0.775826173
213 -0.248677577
214 -0.539584772
215 -0.292053176
216 -0.224833328
217 -1.170804552
218 -0.826946317
219 -0.0932220126
220 -0.359345638
221 -1.189708347
222 0.236858703
223 -1.011423276
224 0.118153832
225 -0.177270156
226 0.688230581
227 -1.611412487
228 -0.243155753
229 -0.203801798
230 0.267780519
231 0.363559254
232 0.0333284749
233 -0.316195553
234 -0.569259951
235 0.670995855
236 -0.281593818
237 -0.412800138
238 -0.618799457
239 0.0178246383
240 -0.0376910497
241 -0.306546844
242 1.119057119
243 0.947078360
244 0.833495464
245 0.247429643
246 0.182889155
247 -1.122374745
248 -0.619146479
249 0.414004468