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

$R= 22.6952412757$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.354673888
4 0.5
5 -0.447213595
6 -0.957899093
7 0.417536845
8 -0.353553390
9 0.835141344
10 0.316227766
11 -0.803108677
12 0.677336944
13 -0.271753418
14 -0.295243134
15 -0.605828580
16 0.250000000
17 -0.612031607
18 -0.590534108
19 1.675355344
20 -0.223606797
21 0.565626262
22 0.567883591
23 0.354869919
24 -0.478949546
25 0.200000000
26 0.192158685
27 -0.223329715
28 0.208768422
29 0.921447962
30 0.428385497
31 -0.380378450
32 -0.176776695
33 -1.087950355
34 0.432771700
35 -0.186728153
36 0.417570672
37 -1.205116950
38 -1.184655125
39 -0.368137260
40 0.158113883
41 -0.694139569
42 -0.399958165
43 -0.549539651
44 -0.401554338
45 -0.373486563
46 -0.250930926
47 -1.252795834
48 0.338668472
49 -0.825662982
50 -0.141421356
51 -0.829103238
52 -0.135876709
53 1.438526248
54 0.157917956
55 0.359161119
56 -0.147621567
57 2.269560139
58 -0.651562102
59 1.812516507
60 -0.302914290
61 -0.717957664
62 0.268968181
63 0.348702282
64 0.125000000
65 0.121531823
66 0.769297073
67 -1.300591786
68 -0.306015803
69 0.480733013
70 0.132036743
71 -0.664555191
72 -0.295267054
73 -0.293683339
74 0.852146367
75 0.270934777
76 0.837677672
77 -0.335327463
78 0.260312353
79 -0.818699963
80 -0.111803398
81 -1.137680278
82 0.490830796
83 0.719160829
84 0.282813131
85 0.273708855
86 0.388583214
87 1.248261494
88 0.283941795
89 1.871303535
90 0.264094881
91 -0.113467065
92 0.177434959
93 -0.515288754
94 0.885860430
95 -0.749241687
96 -0.239474773
97 -1.952698868
98 0.583831893
99 -0.670709261
100 0.100000000
101 -1.153339759
102 0.586264522
103 1.410112770
104 0.0960793426
105 -0.252955754
106 -1.017191664
107 1.288505180
108 -0.111664857
109 -0.411598835
110 -0.253965262
111 -1.632540465
112 0.104384211
113 -1.177694285
114 -1.604821365
115 -0.158702652
116 0.460723981
117 -0.226952515
118 -1.281642713
119 -0.255545747
120 0.214192748
121 -0.355016451
122 0.507672733
123 -0.940332750
124 -0.190189225
125 -0.0894427190
126 -0.246569748
127 -1.167336072
128 -0.0883883476
129 -0.744447016
130 -0.0859359765
131 -0.623068447
132 -0.543975177
133 0.699522586
134 0.919657271
135 0.0998760849
136 0.216385850
137 -0.858144642
138 -0.339929573
139 0.0171565212
140 -0.0933640769
141 -1.697129798
142 0.469911482
143 0.218247546
144 0.208785336
145 -0.412084056
146 0.207665480
147 -1.118504089
148 -0.602558475
149 1.033273456
150 -0.191579818
151 -0.774798337
152 -0.592327562
153 -0.511132869
154 0.237112323
155 0.170110414
156 -0.184068630
157 -0.636625933
158 0.578908295
159 1.948733372
160 0.0790569415
161 0.148171002
162 0.804461440
163 -0.445851363
164 -0.347069784
165 0.486546190
166 -0.508523499
167 -0.823869976
168 -0.199979082
169 -0.926148904
170 -0.193541388
171 1.399153164
172 -0.274769825
173 -0.151058167
174 -0.882654167
175 0.0835073691
176 -0.200777169
177 2.455358069
178 -1.323211419
179 -1.592386266
180 -0.186743281
181 0.952528887
182 0.0802333312
183 -0.972671039
184 -0.125465463
185 0.538944684
186 0.364364172
187 0.491552112
188 -0.626397917
189 -0.0934084548
190 0.529793877
191 -0.774496934
192 0.169334236
193 0.0613603687
194 1.380766611
195 0.164635987
196 -0.412831491
197 1.753283310
198 0.474263066
199 -0.803162617
200 -0.0707106781
201 -1.764534095
202 0.815534365
203 0.384488244
204 -0.414551619
205 0.310428652
206 -0.997100302
207 0.296047533
208 -0.0679383546
209 -1.364754832
210 0.178866729