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

$R= 21.6168116132$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0322052048
4 0.5
5 -0.447213595
6 0.0227725187
7 -1.312980222
8 -0.353553390
9 -0.998962824
10 0.316227766
11 -0.473878824
12 -0.0161026024
13 1.288404596
14 0.928417218
15 0.0144026054
16 0.250000000
17 0.0911538448
18 0.706373387
19 0.995961563
20 -0.223606797
21 0.0422847969
22 0.335082929
23 0.286581366
24 0.0113862593
25 0.200000000
26 -0.911039626
27 0.0643770071
28 -0.656490111
29 0.268955576
30 -0.0101841799
31 0.271730125
32 -0.176776695
33 0.0152613645
34 -0.0644555018
35 0.587182605
36 -0.499481412
37 0.400090166
38 -0.704251175
39 -0.0414933338
40 0.158113883
41 -0.321292632
42 -0.0298998666
43 -1.592696437
44 -0.236939412
45 0.446749756
46 -0.202643627
47 1.659786713
48 -0.00805130120
49 0.723917063
50 -0.141421356
51 -0.00293562823
52 0.644202298
53 1.767526576
54 -0.0455214183
55 0.211925052
56 0.464208609
57 -0.0320751461
58 -0.190180312
59 -1.080771654
60 0.00720130271
61 -0.553412649
62 -0.192142214
63 1.311618431
64 0.125000000
65 -0.576192051
66 -0.0107914143
67 0.238257427
68 0.0455769224
69 -0.00922941159
70 -0.415200802
71 1.748119906
72 0.353186693
73 -1.280364185
74 -0.282906469
75 -0.00644104096
76 0.497980781
77 0.622193523
78 0.0293402177
79 1.687504105
80 -0.111803398
81 0.996889550
82 0.227188198
83 -0.563956711
84 0.0211423984
85 -0.0407652387
86 1.126206451
87 -0.00866176942
88 0.167541464
89 -0.443270447
90 -0.315899782
91 -1.691649752
92 0.143290683
93 -0.00875112433
94 -1.173646440
95 -0.445407551
96 0.00569312967
97 -0.410748497
98 -0.511886664
99 0.473387328
100 0.100000000
101 1.341028849
102 0.00207580263
103 -1.381712532
104 -0.455519813
105 -0.0189103360
106 -1.249830028
107 -0.915166015
108 0.0321885035
109 -1.232730014
110 -0.149853641
111 -0.0128849858
112 -0.328245055
113 -1.633399819
114 0.0226805533
115 -0.128163083
116 0.134477788
117 -1.287068295
118 0.764220965
119 -0.119683196
120 -0.00509208998
121 -0.775438860
122 0.391321837
123 0.0103472964
124 0.135865062
125 -0.0894427190
126 -0.927454287
127 0.784378959
128 -0.0883883476
129 0.0512931192
130 0.407429307
131 -1.190878712
132 0.00763068229
133 -1.307677840
134 -0.168473442
135 -0.0287902728
136 -0.0322277509
137 -0.628082579
138 0.00652617952
139 1.213288275
140 0.293591302
141 -0.0534537872
142 -1.236107440
143 -0.610547615
144 -0.249740706
145 -0.120280590
146 0.905354198
147 -0.0233138298
148 0.200045083
149 0.0669297044
150 0.00455450374
151 0.832471099
152 -0.352125587
153 -0.0910594174
154 -0.439957259
155 -0.121521406
156 -0.0207466669
157 1.855297626
158 -1.193245596
159 -0.0569219173
160 0.0790569415
161 -0.376279910
162 -0.704907360
163 0.334771360
164 -0.160646316
165 -0.00682508972
166 0.398777614
167 0.160527208
168 -0.0149499333
169 0.660008481
170 0.0288253767
171 -0.994951349
172 -0.796348218
173 -0.799048895
174 0.00612479589
175 -0.262596044
176 -0.118469706
177 0.0349186473
178 0.313439539
179 1.335247200
180 0.223374878
181 -0.717820214
182 1.196177011
183 0.0179115562
184 -0.101321813
185 -0.178925761
186 0.00618797936
187 -0.0434520713
188 0.829893356
189 -0.0841975193
190 0.314950700
191 -0.907491657
192 -0.00402565060
193 1.263418198
194 0.290443047
195 0.0185563830
196 0.361958531
197 -0.854437044
198 -0.334735390
199 -1.879887591
200 -0.0707106781
201 -0.000387981854
202 -0.948250593
203 -0.340699684
204 -0.00146781411
205 0.143686433
206 0.977018301
207 -0.247833825
208 0.322101149