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

$R= 30.0062244986$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.203231380
4 0.5
5 0.447213595
6 -0.143706286
7 1.498036548
8 -0.353553390
9 -0.958697006
10 -0.316227766
11 1.074232878
12 0.101615690
13 0.712116094
14 -1.059271802
15 0.0908878361
16 0.250000000
17 -0.825611285
18 0.677901154
19 1.707059704
20 0.223606797
21 0.304448035
22 -0.759597353
23 -1.680136277
24 -0.0718531434
25 0.200000000
26 -0.503542119
27 -0.398068695
28 0.749018274
29 0.971625333
30 -0.0642674052
31 0.137774763
32 -0.176776695
33 0.218317830
34 0.583795338
35 0.669942311
36 -0.479348503
37 1.330004091
38 -1.207073492
39 0.144724336
40 -0.158113883
41 -0.167913445
42 -0.215277270
43 0.841501509
44 0.537116439
45 -0.428742335
46 1.188035755
47 -0.818702134
48 0.0508078450
49 1.244113501
50 -0.141421356
51 -0.167790120
52 0.356058047
53 -0.800027416
54 0.281477074
55 0.480411548
56 -0.529635901
57 0.346928099
58 -0.687042861
59 1.809656806
60 0.0454439180
61 1.812579329
62 -0.0974214692
63 -1.436163154
64 0.125000000
65 0.318467998
66 -0.154374018
67 -0.146496286
68 -0.412805642
69 -0.341456414
70 -0.473720751
71 -0.599149471
72 0.338950577
73 1.372686916
74 -0.940454912
75 0.0406462760
76 0.853529852
77 1.609240114
78 -0.102335559
79 -0.394319712
80 0.111803398
81 0.877796955
82 0.118732736
83 0.254412607
84 0.152224017
85 -0.369224591
86 -0.595031423
87 0.197464757
88 -0.379798676
89 -1.112913294
90 0.303166612
91 1.066775935
92 -0.840068138
93 0.0280001552
94 0.578909830
95 0.763420308
96 -0.0359265717
97 -0.756123091
98 -0.879721093
99 -1.029863844
100 0.100000000
101 -0.531285953
102 0.118645532
103 1.381611995
104 -0.251771059
105 0.136153300
106 0.565704811
107 -0.610340284
108 -0.199034347
109 -1.565597984
110 -0.339702263
111 0.270298567
112 0.374509137
113 -0.548857750
114 -0.245315211
115 -0.751379785
116 0.485812666
117 -0.682703567
118 -1.279620599
119 -1.236795880
120 -0.0321337026
121 0.153976278
122 -1.281687135
123 -0.0341252812
124 0.0688873815
125 0.0894427190
126 1.015520705
127 1.345070318
128 -0.0883883476
129 0.171019512
130 -0.225190881
131 -1.087143386
132 0.109158915
133 2.557237828
134 0.103588517
135 -0.178021732
136 0.291897669
137 -1.676897886
138 0.241446146
139 -0.319003246
140 0.334971155
141 -0.166385964
142 0.423662654
143 0.764978522
144 -0.239674251
145 0.434524058
146 -0.970636226
147 0.252842903
148 0.665002045
149 0.675159048
150 -0.0287412573
151 0.339544843
152 -0.603536746
153 0.791511065
154 -1.137904597
155 0.0616147471
156 0.0723621682
157 -1.559364194
158 0.278826142
159 -0.162590673
160 -0.0790569415
161 -2.516905559
162 -0.620696179
163 0.448795562
164 -0.0839567228
165 0.0976347019
166 -0.179896880
167 0.272851200
168 -0.107638635
169 -0.492890669
170 0.261081212
171 -1.636553050
172 0.420750754
173 -0.267464498
174 -0.139628668
175 0.299607309
176 0.268558219
177 0.367779117
178 0.786948537
179 0.860751160
180 -0.214371167
181 -0.628494923
182 -0.754324498
183 0.368372924
184 0.594017877
185 0.594795911
186 -0.0197990996
187 -0.886899306
188 -0.409351067
189 -0.596321087
190 -0.539819676
191 1.991903077
192 0.0254039225
193 0.367559505
194 0.534659765
195 0.0647226909
196 0.622056750
197 1.520849761
198 0.728223708
199 -0.703454181
200 -0.0707106781
201 -0.0297699903
202 0.375675900
203 1.455513800
204 -0.0838950604
205 -0.0750931757
206 -0.976947211
207 1.610782158
208 0.178029023
209 1.833897446
210 -0.0962749220
211 1.175195728
212 -0.400013708
213 -0.121832064
214 0.431575753
215 0.376330915
216 0.140738537
217 0.206768755
218 1.107044951
219 0.280279591
220 0.240205774
221 -0.587693184
222 -0.191129949
223 0.700083309
224 -0.264817950
225 -0.191739401
226 0.388101037
227 1.241931730
228 0.173464049
229 -0.269729767
230 0.531305741
231 0.335631901
232 -0.343521430
233 -0.816703863
234 0.482744322
235 -0.366134725
236 0.904828403
237 -0.112017558
238 0.874546754
239 0.230983532
240 0.0227219590