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

$R= 29.5701919803$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.862510342
4 0.5
5 -0.447213595
6 -0.609886912
7 -0.970934900
8 0.353553390
9 -0.256075908
10 -0.316227766
11 -0.596676327
12 -0.431255171
13 0.261226695
14 -0.686554652
15 0.385726351
16 0.250000000
17 -0.324595574
18 -0.181073011
19 1.807009602
20 -0.223606797
21 0.837441394
22 -0.421913877
23 -0.195882387
24 -0.304943456
25 0.200000000
26 0.184715167
27 1.083378462
28 -0.485467450
29 -0.879409687
30 0.272749718
31 1.704937888
32 0.176776695
33 0.514639503
34 -0.229523732
35 0.434215288
36 -0.128037954
37 -0.581293244
38 1.277748743
39 -0.225310726
40 -0.158113883
41 1.349912091
42 0.592160488
43 1.115387706
44 -0.298338163
45 0.114520627
46 -0.138509764
47 -1.181009704
48 -0.215627585
49 -0.0572854180
50 0.141421356
51 0.279967040
52 0.130613347
53 -1.850346842
54 0.766064257
55 0.266841765
56 -0.343277326
57 -1.558564471
58 -0.621836553
59 1.057044102
60 0.192863175
61 0.0142664750
62 1.205573142
63 0.248633037
64 0.125000000
65 -0.116824129
66 0.363905083
67 -0.534303173
68 -0.162297787
69 0.168950584
70 0.307036574
71 0.996075878
72 -0.0905365058
73 0.855226254
74 -0.411036395
75 -0.172502068
76 0.903504801
77 0.579333871
78 -0.159318742
79 -0.138218364
80 -0.111803398
81 -0.678349220
82 0.954531993
83 0.961889489
84 0.418720697
85 0.145163554
86 0.788698211
87 0.758499950
88 -0.210956938
89 0.252654909
90 0.0809783125
91 -0.253634115
92 -0.0979411935
93 -1.470526562
94 -0.835099970
95 -0.808119261
96 -0.152471728
97 -1.123788312
98 -0.0405069075
99 0.152794432
100 0.100000000
101 -0.403545661
102 0.197966592
103 -0.567208954
104 0.0923575839
105 -0.374515176
106 -1.308392800
107 0.776400623
108 0.541689231
109 -0.497979465
110 0.188685622
111 0.501371435
112 -0.242733725
113 0.687431912
114 -1.102071506
115 0.0876012665
116 -0.439704843
117 -0.0668938634
118 0.747443052
119 0.315161172
120 0.136374859
121 -0.643977359
122 0.0100879212
123 -1.164313140
124 0.852468944
125 -0.0894427190
126 0.175810106
127 -0.497698888
128 0.0883883476
129 -0.962033433
130 -0.0826071343
131 0.398820200
132 0.257319751
133 -1.754488689
134 -0.377809396
135 -0.484501577
136 -0.114761866
137 -0.200123607
138 0.119466104
139 -1.805781928
140 0.217107644
141 1.018633085
142 0.704332008
143 -0.155867785
144 -0.0640189772
145 0.393283968
146 0.604736283
147 0.0494092655
148 -0.290646622
149 0.861891656
150 -0.121977382
151 0.114586077
152 0.638874371
153 0.0831211061
154 0.409650908
155 -0.762471403
156 -0.112655363
157 1.138475366
158 -0.0977351427
159 1.595943290
160 -0.0790569415
161 0.190189048
162 -0.479665333
163 -1.157124065
164 0.674956045
165 -0.230153782
166 0.680158580
167 1.477710890
168 0.296080244
169 -0.931760598
170 0.102646133
171 -0.462731594
172 0.557693853
173 0.147366875
174 0.536340458
175 -0.194186980
176 -0.149169081
177 -0.911711408
178 0.178653999
179 -0.0781060870
180 0.0572603139
181 0.447569666
182 -0.179346403
183 -0.0123050720
184 -0.0692548820
185 0.259962241
186 -1.039819304
187 0.193678606
188 -0.590504852
189 -1.051890250
190 -0.571426609
191 -1.831392559
192 -0.107813792
193 -1.717732294
194 -0.794638336
195 0.100762020
196 -0.0286427090
197 0.770559998
198 0.108041979
199 -0.626645082
200 0.0707106781
201 0.460838435
202 -0.285349873
203 0.853836842
204 0.139983520
205 -0.603699040
206 -0.401077297
207 0.0501758927
208 0.0653066738
209 -1.078234485
210 -0.264822221
211 -1.500294659
212 -0.925173421
213 -0.859161923
214 0.548998146
215 -0.498816546
216 0.383032128
217 -1.655323514
218 -0.352124656
219 -0.737399260
220 0.133420882
221 -0.0852523377
222 0.354523141
223 -1.111184336
224 -0.171638663
225 -0.0512151817
226 0.486087767
227 -1.231205430
228 -0.779282235
229 1.682865272
230 0.0619434496
231 -0.494538796
232 -0.310918276
233 0.428872501
234 -0.0473011044
235 0.528163596
236 0.528522051
237 0.147767336
238 0.222852602
239 -0.623797651
240 0.0964315878
241 -1.223465898
242 -0.455360758
243 -0.335683132
244 0.00713323750
245 0.0256188177
246 -0.823293717
247 0.529959362