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

$R= 27.0342235$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.375831700
4 0.5
5 -0.447213595
6 -0.972859925
7 0.875971954
8 0.353553390
9 0.892912869
10 -0.316227766
11 -0.880905238
12 -0.687915850
13 -0.124013287
14 0.619405709
15 0.615290641
16 0.250000000
17 0.0345551008
18 0.631384744
19 0.264332438
20 -0.223606797
21 -1.205189984
22 -0.622894067
23 -0.367801221
24 -0.486429962
25 0.200000000
26 -0.0876906366
27 0.147333869
28 0.437985977
29 -1.642060827
30 0.435076185
31 1.289474897
32 0.176776695
33 1.211977352
34 0.0244341461
35 -0.391746567
36 0.446456434
37 0.968802579
38 0.186911260
39 0.170621412
40 -0.158113883
41 -0.970413477
42 -0.852198010
43 -0.940419043
44 -0.440452619
45 -0.399322774
46 -0.260074737
47 1.675795046
48 -0.343957925
49 -0.232673134
50 0.141421356
51 -0.0475420032
52 -0.0620066438
53 1.443478072
54 0.104180778
55 0.393952799
56 0.309702854
57 -0.363676949
58 -1.161112346
59 1.630930612
60 0.307645320
61 0.867030667
62 0.911796444
63 0.782166631
64 0.125000000
65 0.0554604282
66 0.856997404
67 1.039737555
68 0.0172775504
69 0.506032580
70 -0.277006654
71 -0.357863194
72 0.315692372
73 -0.551858440
74 0.685046873
75 -0.275166340
76 0.132166219
77 -0.771648283
78 0.120647557
79 -0.945824272
80 -0.111803398
81 -1.095619477
82 -0.686185950
83 -0.485013255
84 -0.602594992
85 -0.0154535109
86 -0.664976682
87 2.259199341
88 -0.311447033
89 1.801407573
90 -0.282363841
91 -0.108632162
92 -0.183900610
93 -1.774100441
94 1.184966041
95 -0.118213060
96 -0.243214981
97 -1.062893719
98 -0.164524751
99 -0.786571624
100 0.100000000
101 -0.514600823
102 -0.0336172728
103 -0.582891030
104 -0.0438453183
105 0.538977346
106 1.020693133
107 -0.322891794
108 0.0736669346
109 -1.118714695
110 0.278566695
111 -1.332909300
112 0.218992988
113 -1.037816852
114 -0.257158436
115 0.164485706
116 -0.821030413
117 -0.110733060
118 1.153242095
119 0.0302692991
120 0.217538092
121 -0.224005960
122 0.613083264
123 1.335125625
124 0.644737448
125 -0.0894427190
126 0.553075329
127 -1.181300598
128 0.0883883476
129 1.293858331
130 0.0392164449
131 -0.187128271
132 0.605988676
133 0.231547803
134 0.735205476
135 -0.0658897094
136 0.0122170730
137 1.570744796
138 0.357819068
139 -0.862873006
140 -0.195873283
141 -2.305611949
142 -0.253047491
143 0.109243956
144 0.223228217
145 0.734351926
146 -0.390222845
147 0.320119073
148 0.484401289
149 0.676788608
150 -0.194571985
151 -1.589122328
152 0.0934556300
153 0.0308547007
154 -0.545637734
155 -0.576670705
156 0.0853107062
157 1.778141945
158 -0.668798757
159 -1.985982783
160 -0.0790569415
161 -0.322183560
162 -0.774719961
163 -0.484489044
164 -0.485206738
165 -0.542012749
166 -0.342956161
167 -1.020375773
168 -0.426099005
169 -0.984620707
170 -0.0109272823
171 0.236025265
172 -0.470209521
173 -0.911976244
174 1.597495174
175 0.175194390
176 -0.220226309
177 -2.243885902
178 1.273787510
179 0.464305084
180 -0.199661387
181 -1.239037110
182 -0.0768145384
183 -1.192897155
184 -0.130037368
185 -0.433261684
186 -1.254478452
187 -0.0304321571
188 0.837897523
189 0.129030358
190 -0.0835892566
191 0.218285747
192 -0.171978962
193 -0.140872359
194 -0.751579356
195 -0.0763042153
196 -0.116336567
197 1.027619060
198 -0.556190129
199 -0.488646427
200 0.0707106781
201 -1.430629650
202 -0.363877732
203 -1.438657522
204 -0.0237710016
205 0.433982100
206 -0.412166200
207 -0.327734826
208 -0.0310033219
209 -0.232215783
210 0.381114536
211 0.924492319
212 0.721739036
213 0.498728113
214 -0.228318977
215 0.420568181
216 0.0520903890
217 1.121003052
218 -0.791050747
219 0.762455594
220 0.196976399
221 -0.0145946856
222 -0.942509205
223 -1.519222976
224 0.154851427
225 0.178582573
226 -0.733847333
227 0.513083759
228 -0.181838474