Properties

Level 10
Symmetry odd
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

$R= 24.5205749989$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.307644007
4 0.5
5 0.447213595
6 0.217537163
7 1.297139421
8 0.353553390
9 -0.905355164
10 0.316227766
11 -1.265655219
12 0.153822003
13 0.314872980
14 0.917216081
15 0.137582582
16 0.250000000
17 0.868102027
18 -0.640182776
19 -1.490637935
20 0.223606797
21 0.399057169
22 -0.894953388
23 -1.151842850
24 0.108768581
25 0.200000000
26 0.222648819
27 -0.586171097
28 0.648569710
29 -1.069605235
30 0.0972855770
31 -1.488377447
32 0.176776695
33 -0.389371243
34 0.613840830
35 0.580098384
36 -0.452677582
37 0.257724389
38 -1.054040192
39 0.0968687853
40 0.158113883
41 -0.102199608
42 0.282176030
43 -1.304451381
44 -0.632827609
45 -0.404887138
46 -0.814475890
47 0.505493828
48 0.0769110017
49 0.682570679
50 0.141421356
51 0.267066386
52 0.157436490
53 1.526317168
54 -0.414485558
55 -0.566018221
56 0.458608040
57 -0.458585827
58 -0.756325115
59 -1.464822103
60 0.0687912912
61 1.660794203
62 -1.052441786
63 -1.174371874
64 0.125000000
65 0.140815477
66 -0.275327046
67 -0.113102813
68 0.434051013
69 -0.354357550
70 0.410191501
71 -0.299937068
72 -0.320091388
73 0.136383460
74 0.182238663
75 0.0615288014
76 -0.745318967
77 -1.641731279
78 0.0684965749
79 0.193122743
80 0.111803398
81 0.725023139
82 -0.0722660362
83 -1.997945182
84 0.199528584
85 0.388227028
86 -0.922386417
87 -0.329057640
88 -0.447476694
89 0.0438272464
90 -0.286298441
91 0.408434155
92 -0.575921425
93 -0.457890402
94 0.357438114
95 -0.666633550
96 0.0543842909
97 0.843933276
98 0.482650355
99 1.145867490
100 0.100000000
101 1.772614166
102 0.188844452
103 -1.493603458
104 0.111324409
105 0.178463791
106 1.079269220
107 0.649767470
108 -0.293085548
109 -0.0878281312
110 -0.400235322
111 0.0792873639
112 0.324284855
113 0.554876792
114 -0.324269148
115 -0.515119782
116 -0.534802617
117 -0.285071878
118 -1.035785642
119 1.126049361
120 0.0486427885
121 0.601883135
122 1.174358843
123 -0.0314410972
124 -0.744188723
125 0.0894427190
126 -0.830406316
127 -1.000427600
128 0.0883883476
129 -0.401306649
130 0.0995715790
131 -1.877680961
132 -0.194685621
133 -1.933565229
134 -0.0799757664
135 -0.262143684
136 0.306920415
137 -1.514023950
138 -0.250568626
139 0.241920602
140 0.290049192
141 0.155512146
142 -0.212087534
143 -0.398520639
144 -0.226338791
145 -0.478342003
146 0.0964376699
147 0.209988780
148 0.128862194
149 -0.981020480
150 0.0435074327
151 0.151886337
152 -0.527020096
153 -0.785940591
154 -1.160879320
155 -0.665622629
156 0.0484343926
157 -0.587326335
158 0.136558401
159 0.469562236
160 0.0790569415
161 -1.494100744
162 0.512668778
163 -0.323425192
164 -0.0510998043
165 -0.174132113
166 -1.412760587
167 1.130181811
168 0.141088015
169 -0.900856187
170 0.274517964
171 1.349556580
172 -0.652225690
173 0.618363267
174 -0.232678889
175 0.259427884
176 -0.316413804
177 -0.450643416
178 0.0309905431
179 -0.538653043
180 -0.202443569
181 0.157760302
182 0.288806560
183 0.510947051
184 -0.407237945
185 0.115257850
186 -0.323777408
187 -1.098801688
188 0.252746914
189 -0.760547137
190 -0.471381104
191 1.250092541
192 0.0384555008
193 -0.148469734
194 0.596750942
195 0.0433210377
196 0.341285339
197 -0.905854872
198 0.810250672
199 -1.936421164
200 0.0707106781
201 -0.0355836241
202 1.253427497
203 -1.389391567
204 0.133533193
205 -0.0457050544
206 -1.056137134
207 1.038483856
208 0.0787182450
209 1.877839677
210 0.126192957
211 0.519091274
212 0.763158584
213 -0.0669738411
214 0.459454984
215 -0.583368392
216 -0.207242779
217 -1.933256724
218 -0.0621038671
219 -0.00392489217
220 -0.283009110
221 0.153264686
222 0.0560646327