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

$R= 29.329937903$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.853884090
4 0.5
5 -0.447213595
6 1.310894011
7 1.457893541
8 -0.353553390
9 2.436886219
10 0.316227766
11 0.621793851
12 -0.926942045
13 -0.0954809593
14 -1.030886409
15 0.829082169
16 0.250000000
17 1.920356955
18 -1.723138770
19 1.394114827
20 -0.223606797
21 -2.702765640
22 -0.439674648
23 -0.780959690
24 0.655447005
25 0.200000000
26 0.0675152338
27 -2.663820501
28 0.728946770
29 -0.537148335
30 -0.586249624
31 -1.003740157
32 -0.176776695
33 -1.152733727
34 -1.357897425
35 -0.651989812
36 1.218443109
37 -1.001721733
38 -0.985788047
39 0.177010631
40 0.158113883
41 0.423377475
42 1.911143912
43 -0.785390625
44 0.310896925
45 -1.089808648
46 0.552221893
47 0.586028670
48 -0.463471022
49 1.125453577
50 -0.141421356
51 -3.560119207
52 -0.0477404796
53 -1.456329995
54 1.883605540
55 -0.278074663
56 -0.515443204
57 -2.584527297
58 0.379821230
59 0.848619214
60 0.414541084
61 -0.226358056
62 0.709751471
63 3.552720679
64 0.125000000
65 0.0427003831
66 0.815105835
67 0.975627911
68 0.960178477
69 1.447808746
70 0.461026417
71 -1.197383409
72 -0.861569385
73 0.146803925
74 0.708324230
75 -0.370776818
76 0.697057413
77 0.906509239
78 -0.125165417
79 -0.744627593
80 -0.111803398
81 2.501528227
82 -0.299373083
83 0.748409992
84 -1.351382820
85 -0.858809738
86 0.555355037
87 0.995810753
88 -0.219837324
89 0.121419544
90 0.770611085
91 -0.139201073
92 -0.390479845
93 1.860817908
94 -0.414384846
95 -0.623467104
96 0.327723502
97 -1.243306490
98 -0.795815856
99 1.515240867
100 0.100000000
101 -0.0681603230
102 2.517384433
103 -1.086727781
104 0.0337576169
105 1.208713540
106 1.029780815
107 -1.166390897
108 -1.331910250
109 1.327290943
110 0.196628480
111 1.857075984
112 0.364473385
113 -1.144138834
114 1.827536778
115 0.349255791
116 -0.268574167
117 -0.232676233
118 -0.600064401
119 2.799676002
120 -0.293124812
121 -0.613372406
122 0.160059316
123 -0.784892765
124 -0.501870078
125 -0.0894427190
126 -2.512152884
127 -1.268066027
128 -0.0883883476
129 1.456023185
130 -0.0301937304
131 -0.243964719
132 -0.576366863
133 2.032471002
134 -0.689873111
135 1.191296744
136 -0.678948712
137 1.441281950
138 -1.023755382
139 -0.508988248
140 -0.325994906
141 -1.086429229
142 0.846677928
143 -0.0593694736
144 0.609221554
145 0.240220038
146 -0.103806051
147 -2.086460480
148 -0.500860866
149 0.105915705
150 0.262178802
151 1.465953890
152 -0.492894023
153 4.679691405
154 -0.640998830
155 0.448886244
156 0.0885053157
157 -0.0603488228
158 0.526531220
159 2.699867007
160 0.0790569415
161 -1.138556087
162 -1.768847572
163 -1.327463837
164 0.211688737
165 0.515518195
166 -0.529205780
167 -0.0342984055
168 0.955571956
169 -0.990883384
170 0.607270190
171 3.397299224
172 -0.392695312
173 -1.509665303
174 -0.704144536
175 0.291578708
176 0.155448462
177 -1.573241893
178 -0.0858565836
179 -1.080206880
180 -0.544904324
181 0.354321894
182 0.0984300233
183 0.419641303
184 0.276110946
185 0.447983578
186 -1.315796961
187 1.194066900
188 0.293014335
189 -3.883567865
190 0.440857817
191 -0.204345373
192 -0.231735511
193 -0.703388454
194 0.879150450
195 -0.0791615609
196 0.562726788
197 -1.283784049
198 -1.071437092
199 0.453184102
200 -0.0707106781
201 -1.808671441
202 0.0481966266
203 -0.783107802
204 -1.780059603
205 -0.189340162
206 0.768432583
207 -1.903096239
208 -0.0238702398
209 0.866893961
210 -0.854689540
211 -1.024492368
212 -0.728164997
213 2.219817438
214 0.824762913
215 0.351237365
216 0.941802770
217 -1.461827376
218 -0.938536426
219 -0.271869243
220 -0.139037331
221 -0.185639650
222 -1.313151022
223 0.263388904
224 -0.257721602
225 0.487377243
226 0.809028328
227 -1.011111220
228 -1.292263648
229 -0.747931128
230 -0.246961138
231 -1.678605421
232 0.189910615
233 1.017236932
234 0.164526942
235 -0.262079988
236 0.424309607
237 1.456067808
238 -1.979669886