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

$R= 30.6130320107$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.851287293
4 0.5
5 0.447213595
6 -1.309057799
7 0.950982218
8 -0.353553390
9 2.427264643
10 -0.316227766
11 -0.485894316
12 0.925643646
13 -0.576910719
14 -0.672445975
15 0.827920846
16 0.250000000
17 1.147551056
18 -1.716335289
19 -1.247947462
20 0.223606797
21 1.760541297
22 0.343579165
23 -0.271997782
24 -0.654528899
25 0.200000000
26 0.407937482
27 2.642276898
28 0.475491109
29 -0.140351046
30 -0.585428445
31 1.930984909
32 -0.176776695
33 -0.899529973
34 -0.811441134
35 0.425292177
36 1.213632321
37 -1.113258573
38 0.882432113
39 -1.068027485
40 -0.158113883
41 -1.726569125
42 -1.244890689
43 1.023348734
44 -0.242947158
45 1.085505748
46 0.192331476
47 0.466606100
48 0.462821823
49 -0.0956328205
50 -0.141421356
51 2.124446690
52 -0.288455359
53 0.930533316
54 -1.868371912
55 -0.217298544
56 -0.336222987
57 -2.310309280
58 0.0992431766
59 1.232127291
60 0.413960423
61 0.0992338923
62 -1.365412523
63 2.308285514
64 0.125000000
65 -0.258002317
66 0.636063744
67 1.572495913
68 0.573775528
69 -0.503546038
70 -0.300726982
71 1.408179399
72 -0.858167644
73 1.539552230
74 0.787192686
75 0.370257458
76 -0.623973731
77 -0.462076854
78 0.755209477
79 1.215157389
80 0.111803398
81 2.464349005
82 1.220868737
83 0.673203393
84 0.880270648
85 0.513200434
86 -0.723616830
87 -0.259830108
88 0.171789582
89 -0.502258351
90 -0.767568475
91 -0.548631836
92 -0.135998891
93 3.574807826
94 -0.329940338
95 -0.558099071
96 -0.327264449
97 -0.0456907007
98 0.0676226159
99 -1.179394093
100 0.100000000
101 0.628860950
102 -1.502210661
103 -1.221295596
104 0.203968741
105 0.787338003
106 -0.657986418
107 1.414995119
108 1.321138449
109 -0.412705319
110 0.153653274
111 -2.060961452
112 0.237745554
113 -1.318385064
114 1.633635358
115 -0.121641106
116 -0.0701755232
117 -1.400314992
118 -0.871245562
119 1.091300649
120 -0.292714222
121 -0.763906713
122 -0.0701689582
123 -3.196375484
124 0.965492454
125 0.0894427190
126 -1.632204340
127 -0.104651391
128 -0.0883883476
129 1.894512509
130 0.182435188
131 0.921811297
132 -0.449764986
133 -1.186775846
134 -1.111922523
135 1.181662152
136 -0.405720567
137 0.212316457
138 0.356060818
139 1.540755404
140 0.212646088
141 0.863821945
142 -0.995733202
143 0.280317639
144 0.606816160
145 -0.0627668961
146 -1.088627822
147 -0.177043825
148 -0.556629286
149 -0.468586204
150 -0.261811559
151 0.675828871
152 0.441216056
153 2.785410107
154 0.326737677
155 0.863562704
156 -0.534013742
157 -1.737504856
158 -0.859246030
159 1.722684505
160 -0.0790569415
161 -0.258665054
162 -1.742557892
163 0.345334923
164 -0.863284562
165 -0.402282033
166 -0.476026684
167 0.846866317
168 -0.622445344
169 -0.667174026
170 -0.362887507
171 -3.029098751
172 0.511674367
173 -0.225232469
174 0.183727631
175 0.190196443
176 -0.121473579
177 2.281021570
178 0.355150286
179 -1.322507125
180 0.542752874
181 -0.428238503
182 0.387941291
183 0.183710494
184 0.0961657381
185 -0.497864369
186 -2.527770855
187 -0.557588691
188 0.233303050
189 2.512758108
190 0.394635638
191 -1.405765861
192 0.231410911
193 0.121045584
194 0.0323082043
195 -0.477636411
196 -0.0478164102
197 0.849529915
198 0.833957561
199 -0.138769047
200 -0.0707106781
201 2.911141852
202 -0.444671842
203 -0.133470727
204 1.062223345
205 -0.772145186
206 0.863586398
207 -0.660216328
208 -0.144227679
209 0.606385010
210 -0.556732041
211 -0.313236004
212 0.465266658
213 2.606962710
214 -1.000552644
215 0.457655467
216 -0.934185956
217 1.836381954
218 0.291826730
219 2.850186259
220 -0.108649272
221 -0.662157417
222 1.457319818
223 1.352880267
224 -0.168111493
225 0.485452928
226 0.932239019
227 -0.527362914
228 -1.155154640
229 -1.423163683
230 0.0860132510
231 -0.853665387
232 0.0496215883
233 0.274618436
234 0.990172226
235 0.208672592
236 0.616063645
237 2.238743259
238 -0.771666089
239 -1.157687127
240 0.206980211
241 -0.420746307
242 0.540163617
243 1.953282819
244 0.0496169461
245 -0.0427682975
246 2.260178780
247 0.706633339
248 -0.682706261
249 1.321709913
250 -0.0632455532