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

$R= 24.3141784195$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.596250460
4 0.5
5 -0.447213595
6 -1.128719524
7 0.699720581
8 -0.353553390
9 1.548015531
10 0.316227766
11 0.264423575
12 0.798125230
13 -1.082894264
14 -0.494777168
15 -0.713864907
16 0.250000000
17 -0.166795986
18 -1.094612279
19 -1.171799301
20 -0.223606797
21 1.116929300
22 -0.186975703
23 1.316965550
24 -0.564359762
25 0.200000000
26 0.765721878
27 0.874770045
28 0.349860290
29 -1.801030376
30 0.504778717
31 0.794379222
32 -0.176776695
33 0.422086254
34 0.117942573
35 -0.312924557
36 0.774007765
37 -0.293564267
38 0.828587232
39 -1.728570468
40 0.158113883
41 0.474135267
42 -0.789788282
43 -1.574611445
44 0.132211787
45 -0.692293591
46 -0.931235271
47 -1.399877685
48 0.399062615
49 -0.510391107
50 -0.141421356
51 -0.266248170
52 -0.541447132
53 -0.169778281
54 -0.618555830
55 -0.118253818
56 -0.247388584
57 -1.870485174
58 1.273520792
59 -0.673130904
60 -0.356932453
61 0.253754580
62 -0.561710935
63 1.083178328
64 0.125000000
65 0.484285037
66 -0.298460053
67 1.876530792
68 -0.0833979934
69 2.102206866
70 0.221271076
71 0.642069648
72 -0.547306139
73 -1.834187214
74 0.207581284
75 0.319250092
76 -0.585899650
77 0.185022618
78 1.222283900
79 1.523050903
80 -0.111803398
81 -0.151663444
82 -0.335264263
83 -1.573849256
84 0.558464650
85 0.0745934329
86 1.113418431
87 -2.874895567
88 -0.0934878518
89 -0.827518465
90 0.489525493
91 -0.757723404
92 0.658482775
93 1.268028200
94 0.989863004
95 0.524044578
96 -0.282179881
97 1.432933077
98 0.360901013
99 0.409331802
100 0.100000000
101 -0.981545945
102 0.188265887
103 -0.0488129435
104 0.382860939
105 -0.499505968
106 0.120051374
107 0.872047503
108 0.437385022
109 0.591669236
110 0.0836180767
111 -0.468602097
112 0.174930145
113 0.0777925900
114 1.322632751
115 -0.588964899
116 -0.900515188
117 -1.676337141
118 0.475975426
119 -0.116710584
120 0.252389358
121 -0.930080172
122 -0.179431584
123 0.756838639
124 0.397189611
125 -0.0894427190
126 -0.765922741
127 0.683723328
128 -0.0883883476
129 -2.513474246
130 -0.342441234
131 -1.018041656
132 0.211043127
133 -0.819932087
134 -1.326907648
135 -0.391209057
136 0.0589712866
137 1.621294161
138 -1.486484731
139 0.160719755
140 -0.156462278
141 -2.234555398
142 -0.454011802
143 -0.286342769
144 0.387003882
145 0.805445270
146 1.296966217
147 -0.814712081
148 -0.146782133
149 -0.236840186
150 -0.225743904
151 -1.069934621
152 0.414293616
153 -0.258202849
154 -0.130830748
155 -0.355257188
156 -0.864285234
157 -1.749986160
158 -1.076959621
159 -0.271008578
160 0.0790569415
161 0.921508240
162 0.107242250
163 0.412922882
164 0.237067633
165 -0.188762711
166 1.112879481
167 -1.201268739
168 -0.394894141
169 0.172656987
170 -0.0527455223
171 -1.813964132
172 -0.787305722
173 0.767156737
174 2.032858150
175 0.139944116
176 0.0661058939
177 -1.074483595
178 0.585143918
179 1.340278845
180 -0.346146795
181 -1.472523289
182 0.535791357
183 0.405118296
184 -0.465617635
185 0.131285931
186 -0.896631339
187 -0.0442711720
188 -0.699938842
189 0.612032801
190 -0.370555475
191 0.117937016
192 0.199531307
193 -1.369136493
194 -1.013236696
195 0.773040214
196 -0.255195553
197 -0.00548688677
198 -0.289441293
199 -0.260599536
200 -0.0707106781
201 2.998148292
202 0.694057794
203 -1.256240123
204 -0.133124085
205 -0.212039737
206 0.0345159634
207 2.025721029
208 -0.270723566
209 -0.314095811
210 0.353204057