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

$R= 22.9632098523$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.473151164
4 0.5
5 0.447213595
6 -0.334568396
7 -0.343145116
8 -0.353553390
9 -0.776127975
10 -0.316227766
11 -0.203139617
12 0.236575582
13 0.565074908
14 0.242640238
15 0.211599633
16 0.250000000
17 0.407612614
18 0.548805354
19 0.241096675
20 0.223606797
21 -0.162359511
22 0.143641401
23 0.386681515
24 -0.167284198
25 0.200000000
26 -0.399568299
27 -0.840377019
28 -0.171572558
29 0.0299853905
30 -0.149623535
31 0.371010553
32 -0.176776695
33 -0.0961157468
34 -0.288225643
35 -0.153459161
36 -0.388063987
37 -0.442136886
38 -0.170481093
39 0.267365851
40 -0.158113883
41 0.00909376977
42 0.114805511
43 -0.421943783
44 -0.101569808
45 -0.347094982
46 -0.273425121
47 -1.164956369
48 0.118287791
49 -0.882251429
50 -0.141421356
51 0.192862383
52 0.282537454
53 0.318063987
54 0.594236289
55 -0.0908467989
56 0.121320119
57 0.114075172
58 -0.0212028730
59 1.150991910
60 0.105799816
61 1.554017716
62 -0.262344078
63 0.266324524
64 0.125000000
65 0.252709181
66 0.0679640963
67 0.594082134
68 0.203806307
69 0.182958809
70 0.108512013
71 -1.469685426
72 0.274402677
73 -1.862808495
74 0.312637990
75 0.0946302329
76 0.120548337
77 0.0697063678
78 -0.189056206
79 0.631856043
80 0.111803398
81 0.378502609
82 -0.00643026627
83 1.674662143
84 -0.0811797557
85 0.182289902
86 0.298359310
87 0.0141876224
88 0.0718207007
89 -0.685319836
90 0.245433215
91 -0.193902695
92 0.193340757
93 0.175544075
94 0.823748548
95 0.107821710
96 -0.0836420992
97 0.959152124
98 0.623845968
99 0.157662340
100 0.100000000
101 0.537278992
102 -0.136374299
103 -0.920205514
104 -0.199784149
105 -0.0726093808
106 -0.224905202
107 -1.538458685
108 -0.420188509
109 -1.129261108
110 0.0642383875
111 -0.209197582
112 -0.0857862791
113 -0.329984308
114 -0.0806633281
115 0.172929230
116 0.0149926952
117 -0.438570444
118 -0.813874184
119 -0.139870277
120 -0.0748117678
121 -0.958734295
122 -1.098856465
123 0.00430272850
124 0.185505276
125 0.0894427190
126 -0.188319877
127 -0.738192722
128 -0.0883883476
129 -0.199643194
130 -0.178692375
131 -1.260283344
132 -0.0480578734
133 -0.0827311412
134 -0.420079505
135 -0.375828028
136 -0.144112821
137 -0.141818435
138 -0.129371414
139 -1.595201076
140 -0.0767295806
141 -0.551200470
142 1.039224530
143 -0.114789126
144 -0.194031993
145 0.0134098743
146 1.317204519
147 -0.417438310
148 -0.221068443
149 -1.233635298
150 -0.0669136793
151 0.923361481
152 -0.0852405469
153 -0.316359412
154 -0.0492898454
155 0.165920963
156 0.133682925
157 -0.405244675
158 -0.446789693
159 0.150492858
160 -0.0790569415
161 -0.132688234
162 -0.267641762
163 0.0561138320
164 0.00454688488
165 -0.0429842687
166 -1.184164957
167 0.220956166
168 0.0574027557
169 -0.680703775
170 -0.128898426
171 -0.187120467
172 -0.210971891
173 1.455840112
174 -0.0100321640
175 -0.0686290232
176 -0.0507849044
177 0.544630678
178 0.484594303
179 -0.0782665241
180 -0.173547491
181 0.246021215
182 0.137109910
183 0.735542282
184 -0.136712560
185 -0.197729626
186 -0.124128406
187 -0.0827434781
188 -0.582478184
189 0.288612170
190 -0.0762414629
191 -0.626999837
192 0.0591438955
193 0.358005228
194 -0.678222971
195 0.119569643
196 -0.441125714
197 -1.928405956
198 -0.111484110