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

$R= 21.4872736484$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.307582136
4 0.5
5 -0.447213595
6 0.924600195
7 0.203253895
8 -0.353553390
9 0.709771044
10 0.316227766
11 1.808261363
12 -0.653791068
13 -0.109559113
14 -0.143722207
15 0.584768508
16 0.250000000
17 1.895512160
18 -0.501883918
19 -0.405973434
20 -0.223606797
21 -0.265771162
22 -1.278633872
23 1.777041472
24 0.462300097
25 0.200000000
26 0.0774699922
27 0.379498197
28 0.101626947
29 0.865238473
30 -0.413493778
31 0.506767976
32 -0.176776695
33 -2.364450257
34 -1.340329502
35 -0.0908979053
36 0.354885522
37 -0.338318604
38 0.287066568
39 0.143257540
40 0.158113883
41 -0.630995188
42 0.187928591
43 -0.640086307
44 0.904130681
45 -0.317419260
46 -1.256558075
47 0.570213738
48 -0.326895534
49 -0.958687854
50 -0.141421356
51 -2.478537841
52 -0.0547795568
53 1.221329663
54 -0.268345748
55 -0.808679065
56 -0.0718611038
57 0.530843611
58 -0.611815991
59 0.0358725008
60 0.292384254
61 -0.358559575
62 -0.358339072
63 0.144263729
64 0.125000000
65 0.0489963251
66 1.671918810
67 0.670081703
68 0.947756080
69 -2.323627685
70 0.0642745252
71 -1.377886183
72 -0.250941959
73 -1.628380994
74 0.239227379
75 -0.261516427
76 -0.202986717
77 0.367536165
78 -0.101298377
79 0.157713339
80 -0.111803398
81 -1.205996108
82 0.446180977
83 1.167663300
84 -0.132885581
85 -0.847698808
86 0.452609368
87 -1.131370371
88 -0.639316936
89 0.948037965
90 0.224449311
91 -0.0222683166
92 0.888520736
93 -0.662640753
94 -0.403202001
95 0.181556839
96 0.231150048
97 1.699031100
98 0.677894682
99 1.283451556
100 0.100000000
101 -0.594655507
102 1.752590915
103 0.754483848
104 0.0387349961
105 0.118856477
106 -0.863610487
107 0.380896014
108 0.189749098
109 0.799363870
110 0.571822451
111 0.442379364
112 0.0508134738
113 0.948038716
114 -0.375363117
115 -0.794717106
116 0.432619236
117 -0.0777618878
118 -0.0253656886
119 0.385270229
120 -0.206746889
121 2.269809160
122 0.253539907
123 0.825078038
124 0.253383988
125 -0.0894427190
126 -0.102009861
127 0.434009864
128 -0.0883883476
129 0.836965432
130 -0.0346456337
131 0.651950551
132 -1.182225128
133 -0.0825156646
134 -0.473819316
135 -0.169716753
136 -0.670164751
137 -1.313678053
138 1.643052893
139 0.822010506
140 -0.0454489526
141 -0.745601203
142 0.974312663
143 -0.198111436
144 0.177442761
145 -0.386946408
146 1.151439243
147 1.253563177
148 -0.169159302
149 -0.976715615
150 0.184920039
151 -1.028263552
152 0.143533284
153 1.345380337
154 -0.259887315
155 -0.226633528
156 0.0716287700
157 0.412069550
158 -0.111520171
159 -1.596988397
160 0.0790569415
161 0.361199541
162 0.852768026
163 -0.120998890
164 -0.315497594
165 1.057414301
166 -0.825662638
167 0.794696792
168 0.0939642957
169 -0.987908800
170 0.599413576
171 -0.288056982
172 -0.320043153
173 -1.679805746
174 0.799999661
175 0.0406507790
176 0.452065340
177 -0.0468313258
178 -0.670364074
179 -1.316757342
180 -0.158709630
181 1.827858026
182 0.0157460776
183 0.468470449
184 -0.628279037
185 0.151300679
186 0.468557770
187 3.426654521
188 0.285106869
189 0.0797730404
190 -0.128380072
191 -0.215674845
192 -0.163447767
193 -1.638524761
194 -1.201396412
195 -0.0640667195
196 -0.479343927
197 0.358571723
198 -0.907537299
199 0.480874784
200 -0.0707106781
201 -0.896906139
202 0.420484942
203 0.0634517067
204 -1.239268920
205 0.282189627
206 -0.533500645
207 1.469951679
208 -0.0273897784