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

$R= 30.0339879166$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.363514183
4 0.5
5 -0.447213595
6 -0.257043344
7 -0.522733628
8 -0.353553390
9 -0.867857438
10 0.316227766
11 -0.622115707
12 0.181757091
13 -0.196432244
14 0.369628493
15 -0.162568484
16 0.250000000
17 -0.570087022
18 0.613667879
19 -0.122672188
20 -0.223606797
21 -0.190021088
22 0.439902235
23 -1.140900786
24 -0.128521672
25 0.200000000
26 0.138898571
27 -0.678992671
28 -0.261366814
29 -1.258652938
30 0.114953278
31 0.0759495394
32 -0.176776695
33 -0.226147883
34 0.403112399
35 0.233773585
36 -0.433928719
37 -0.683123838
38 0.0867423360
39 -0.0714059067
40 0.158113883
41 -1.527431065
42 0.134365199
43 -0.942029923
44 -0.311057853
45 0.388117645
46 0.806738682
47 1.024090186
48 0.0908785458
49 -0.726749553
50 -0.141421356
51 -0.207234718
52 -0.0982161220
53 -0.925602442
54 0.480120322
55 0.278218602
56 0.184814246
57 -0.0445930802
58 0.890002028
59 0.646516492
60 -0.0812842424
61 -0.00261337426
62 -0.0537044343
63 0.453658267
64 0.125000000
65 0.0878471701
66 0.159910701
67 -0.448984167
68 -0.285043511
69 -0.414733617
70 -0.165302887
71 -0.803103359
72 0.306833939
73 1.284287438
74 0.483041498
75 0.0727028366
76 -0.0613360940
77 0.325200801
78 0.0504916009
79 0.598556218
80 -0.111803398
81 0.621033972
82 1.080056864
83 -0.332227113
84 -0.0950105440
85 0.254950666
86 0.666115746
87 -0.457538195
88 0.219951117
89 -1.191684205
90 -0.274440619
91 0.102681739
92 -0.570450393
93 0.0276087348
94 -0.724141115
95 0.0548606702
96 -0.0642608360
97 0.0671857975
98 0.513889537
99 0.539907744
100 0.100000000
101 -0.175049405
102 0.146537074
103 -0.560075314
104 0.0694492859
105 0.0849800140
106 0.654499763
107 -1.785573671
108 -0.339496335
109 -0.396483311
110 -0.196730260
111 -0.248325204
112 -0.130683407
113 -1.784210117
114 0.0315320694
115 0.510226342
116 -0.629326469
117 0.170475184
118 -0.457156195
119 0.298003657
120 0.0574766390
121 -0.612972045
122 0.00184793466
123 -0.555242856
124 0.0379747697
125 -0.0894427190
126 -0.320784837
127 -0.314460671
128 -0.0883883476
129 -0.342441238
130 -0.0621173297
131 0.650689022
132 -0.113073941
133 0.0641248780
134 0.317479749
135 0.303654753
136 0.201556199
137 0.894763677
138 0.293260953
139 0.786941103
140 0.116886792
141 0.372271307
142 0.567879831
143 0.122203584
144 -0.216964359
145 0.562886706
146 -0.908128356
147 -0.264183770
148 -0.341561919
149 0.237049742
150 -0.0514086688
151 -1.967247968
152 0.0433711680
153 0.494754262
154 -0.229951691
155 -0.0339656666
156 -0.0357029533
157 -0.597811016
158 -0.423243161
159 -0.336469616
160 0.0790569415
161 0.596387207
162 -0.439137333
163 0.693783564
164 -0.763715532
165 0.101136408
166 0.234920045
167 -0.764604571
168 0.0671825999
169 -0.961414372
170 -0.180277345
171 0.106461961
172 -0.471014961
173 -1.699300055
174 0.323528360
175 -0.104546725
176 -0.155528926
177 0.235017930
178 0.842647983
179 -0.219922170
180 0.194058822
181 -0.697490963
182 -0.0726069544
183 -0.000949975551
184 0.403369341
185 0.305502268
186 -0.0195223236
187 0.354660110
188 0.512045093
189 0.354932348
190 -0.0387923519
191 1.320019329
192 0.0454392729
193 1.274249292
194 -0.0475075330
195 0.0319336923
196 -0.363374776
197 0.758012382
198 -0.381772427
199 0.900884657
200 -0.0707106781
201 -0.163210815
202 0.123778621
203 0.657937563
204 -0.103617359
205 0.683087938
206 0.396033053
207 0.990133126
208 -0.0491080610
209 0.0763241242
210 -0.0600899441
211 1.554195720
212 -0.462801221
213 -0.291930100
214 1.262591251
215 0.421288588
216 0.240060161
217 -0.0397828150
218 0.280356038
219 0.466914175
220 0.139109301
221 0.111908383
222 0.175592435
223 0.0476729911
224 0.0924071233
225 -0.173571487
226 1.261627073
227 0.537433314
228 -0.0222965401
229 1.969933240
230 -0.360784506
231 0.119405116
232 0.445001014
233 1.631784690
234 -0.120544158
235 -0.457987054
236 0.323258246
237 0.225218172
238 -0.210720407
239 -1.660712606
240 -0.0406421212
241 -1.407467294
242 0.433436690
243 0.896539474
244 -0.00130668713
245 0.325012280
246 0.392615988
247 -0.0717048264
248 -0.0268522171
249 -0.182924248
250 0.0632455532