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

$R= 28.0277820443$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.787145372
4 0.5
5 -0.447213595
6 -1.263702611
7 0.572505163
8 -0.353553390
9 2.193888582
10 0.316227766
11 -1.527872415
12 0.893572686
13 1.288920442
14 -0.404822283
15 -0.799235707
16 0.250000000
17 1.091572597
18 -1.551313493
19 1.314293195
20 -0.223606797
21 1.023149952
22 1.080368945
23 0.895894829
24 -0.631851305
25 0.200000000
26 -0.911404385
27 2.133652454
28 0.286252581
29 -1.028786459
30 0.565144988
31 -0.356204843
32 -0.176776695
33 -2.730530116
34 -0.771858385
35 -0.256032092
36 1.096944291
37 -0.542876448
38 -0.929345631
39 2.303488203
40 0.158113883
41 0.0830274053
42 -0.723476269
43 -0.553714178
44 -0.763936207
45 -0.981136800
46 -0.633493309
47 1.490882841
48 0.446786343
49 -0.672237838
50 -0.141421356
51 1.950798916
52 0.644460221
53 -1.569033856
54 -1.508720119
55 0.683285316
56 -0.202411141
57 2.348833002
58 0.727461881
59 1.676225495
60 -0.399617853
61 -0.111050908
62 0.251874860
63 1.256012540
64 0.125000000
65 -0.576422745
66 1.930776361
67 1.327397716
68 0.545786298
69 1.601094299
70 0.181042028
71 -0.185261564
72 -0.775656746
73 -0.290165834
74 0.383871618
75 0.357429074
76 0.657146597
77 -0.874714846
78 -1.628812129
79 1.515970279
80 -0.111803398
81 1.619258528
82 -0.0587092413
83 -0.504170050
84 0.511574976
85 -0.488166106
86 0.391535050
87 -1.838590960
88 0.540184472
89 -1.056359421
90 0.693768485
91 0.737913607
92 0.447947414
93 -0.636589838
94 -1.054213367
95 -0.587769785
96 -0.315925652
97 -0.917027793
98 0.475343933
99 -3.351981846
100 0.100000000
101 1.209890083
102 -1.379423142
103 1.108554186
104 -0.455702192
105 -0.457566569
106 1.109474479
107 0.0567314851
108 1.066826227
109 0.0373609390
110 -0.483155680
111 -0.970199132
112 0.143126290
113 1.045787746
114 -1.660875744
115 -0.400656348
116 -0.514393229
117 2.827747841
118 -1.185270414
119 0.624930948
120 0.282572494
121 1.334394116
122 0.0785248503
123 0.148382043
124 -0.178102421
125 -0.0894427190
126 -0.888134984
127 1.223636918
128 -0.0883883476
129 -0.989567732
130 0.407592432
131 0.538942474
132 -1.365265058
133 0.752439641
134 -0.938611926
135 -0.954198385
136 -0.385929192
137 -1.657901552
138 -1.132144636
139 0.140605804
140 -0.128016046
141 2.664424368
142 0.130999708
143 -1.969305986
144 0.548472145
145 0.460087291
146 0.205178229
147 -1.201386728
148 -0.271438224
149 -0.927508381
150 -0.252740522
151 -0.998945142
152 -0.464672815
153 2.394788678
154 0.618516799
155 0.159299648
156 1.151744101
157 1.484543352
158 -1.071952864
159 -2.804091612
160 0.0790569415
161 0.512904503
162 -1.144988686
163 0.372001482
164 0.0415137026
165 1.221130190
166 0.356502061
167 -0.0963925806
168 -0.361738134
169 0.661315742
170 0.345185563
171 2.883413695
172 -0.276857089
173 -0.923298840
174 1.300080135
175 0.114501032
176 -0.381968103
177 2.995658286
178 0.746958910
179 0.661678016
180 -0.490568400
181 0.509109122
182 -0.521783716
183 -0.198469334
184 -0.316746654
185 0.242781728
186 0.450136991
187 -1.667790911
188 0.745441420
189 1.221532826
190 0.415616001
191 0.0274728312
192 0.223393171
193 0.530294078
194 0.648436571
195 -1.030151241
196 -0.336118919
197 -0.320195403
198 2.370209094
199 1.424693391
200 -0.0707106781
201 2.372291190
202 -0.855521482
203 -0.588950207
204 0.975399458
205 -0.0371309844
206 -0.783866182
207 1.964787602
208 0.322230110
209 -2.007659539
210 0.323548423
211 1.183571821
212 -0.784516928
213 -0.328036884
214 -0.0401152178
215 0.247628508
216 -0.754360059
217 -0.202026374
218 -0.0264181733
219 -0.527091313
220 0.341642658
221 1.416303714
222 0.686034386