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

$R= 31.0823425766$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.500875041
4 0.5
5 -0.447213595
6 0.354172138
7 0.618686474
8 0.353553390
9 -0.749124193
10 -0.316227766
11 -0.985378372
12 0.250437520
13 1.045493501
14 0.437477401
15 -0.223998128
16 0.250000000
17 -1.113318719
18 -0.529710796
19 0.236069465
20 -0.223606797
21 0.309884613
22 -0.696767729
23 1.917735913
24 0.177086069
25 0.200000000
26 0.739275544
27 -0.876092652
28 0.309343237
29 0.262601668
30 -0.158390595
31 0.236268057
32 0.176776695
33 -0.493551433
34 -0.787235216
35 -0.276685002
36 -0.374562096
37 -1.177315072
38 0.166926319
39 0.523661600
40 -0.158113883
41 0.447522045
42 0.219121511
43 -1.012728175
44 -0.492689186
45 0.335018523
46 1.356044068
47 1.102652762
48 0.125218760
49 -0.617227046
50 0.141421356
51 -0.557633559
52 0.522746750
53 -1.703735064
54 -0.619491055
55 0.440674605
56 0.218738700
57 0.118241303
58 0.185687420
59 -0.175722116
60 -0.111999064
61 1.035314736
62 0.167066745
63 -0.463473006
64 0.125000000
65 -0.467558907
66 -0.348993565
67 -0.541534799
68 -0.556659359
69 0.960546054
70 -0.195645841
71 0.544000437
72 -0.264855398
73 -1.580000404
74 -0.832487471
75 0.100175008
76 0.118034732
77 -0.609640271
78 0.370284668
79 -0.0858485469
80 -0.111803398
81 0.310311250
82 0.316445873
83 -0.792198823
84 0.154942306
85 0.497891267
86 -0.716106960
87 0.131530621
88 -0.348383864
89 -1.563645077
90 0.236893870
91 0.646832688
92 0.958867956
93 0.118340772
94 0.779693245
95 -0.105573474
96 0.0885430345
97 1.264021677
98 -0.436445429
99 0.738170778
100 0.100000000
101 -1.952343147
102 -0.394306471
103 0.288740842
104 0.369637772
105 -0.138584612
106 -1.204722617
107 -0.131256342
108 -0.438046326
109 -1.612914758
110 0.311604001
111 -0.589687735
112 0.154671618
113 -0.127347252
114 0.0836092272
115 -0.857637572
116 0.131300834
117 -0.783204475
118 -0.124254300
119 -0.688795233
120 -0.0791952976
121 -0.0290294622
122 0.732078070
123 0.224152623
124 0.118134028
125 -0.0894427190
126 -0.327724905
127 0.437944993
128 0.0883883476
129 -0.507250266
130 -0.330614074
131 0.978203575
132 -0.246775716
133 0.146052985
134 -0.382922928
135 0.391800544
136 -0.393617608
137 0.196867315
138 0.679208628
139 -0.908306622
140 -0.138342501
141 0.552291247
142 0.384666398
143 -1.030206685
144 -0.187281048
145 -0.117439036
146 -1.117229000
147 -0.309153622
148 -0.588657536
149 -0.0566606617
150 0.0708344276
151 -1.894000750
152 0.0834631598
153 0.834013987
154 -0.431080770
155 -0.105662287
156 0.261830800
157 -0.0254763830
158 -0.0607040896
159 -0.853358369
160 -0.0790569415
161 1.186477270
162 0.219423189
163 1.533765303
164 0.223761022
165 0.220722910
166 -0.560169159
167 -0.253617889
168 0.109560755
169 0.0930566646
170 0.352062291
171 -0.176845360
172 -0.506364087
173 1.381798199
174 0.0930061943
175 0.123737294
176 -0.246344593
177 -0.0880148225
178 -1.105664037
179 0.451733403
180 0.167509261
181 1.441605636
182 0.457379780
183 0.518563364
184 0.678022034
185 0.526511306
186 0.0836795630
187 1.097040246
188 0.551326381
189 -0.542026575
190 -0.0746517195
191 -0.313635396
192 0.0626093801
193 -1.514777015
194 0.893798299
195 -0.234188587
196 -0.308613523
197 0.252706083
198 0.521965563
199 -1.403637152
200 0.0707106781
201 -0.271243071
202 -1.380515079
203 0.162463081
204 -0.278816779
205 -0.200137943
206 0.204170607
207 -1.436618188
208 0.261373375
209 -0.232594334
210 -0.0979941190
211 0.409322153
212 -0.851867532
213 0.272480134
214 -0.0928122501
215 0.452905808
216 -0.309745527
217 0.146260127
218 -1.140502963
219 -0.791369085
220 0.220337302
221 -1.164088485
222 -0.416972196
223 0.141423803
224 0.109369350
225 -0.149824838
226 -0.0900481059
227 -0.623981096
228 0.0591206515
229 -1.398300629
230 -0.606441343
231 -0.304204362
232 0.0928437102
233 -1.562846896
234 -0.553809195
235 -0.493121306
236 -0.0878610582
237 -0.0455303290
238 -0.487051780
239 -0.829328865
240 -0.0559995320
241 -0.994078201
242 -0.0205269295
243 1.024435743
244 0.517657368
245 0.276032326
246 0.158499839
247 0.212353692
248 0.0835333727
249 -0.336811531
250 -0.0632455532