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

$R= 28.8137386137$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.801389456
4 0.5
5 0.447213595
6 1.273774700
7 -0.842306216
8 0.353553390
9 2.245003974
10 0.316227766
11 -1.535472827
12 0.900694728
13 -1.378833450
14 -0.595600437
15 0.805605855
16 0.250000000
17 1.227497974
18 1.587457534
19 -1.259529187
20 0.223606797
21 -1.517321536
22 -1.085743248
23 -1.444873681
24 0.636887350
25 0.200000000
26 -0.974982483
27 2.242737033
28 -0.421153108
29 -1.259781133
30 0.569649363
31 -0.439046758
32 0.176776695
33 -2.765984562
34 0.867972141
35 -0.376690791
36 1.122501987
37 1.446434929
38 -0.890621629
39 -2.483816040
40 0.158113883
41 0.447833110
42 -1.072908347
43 -0.780558263
44 -0.767736413
45 1.003996299
46 -1.021679977
47 0.363179792
48 0.450347364
49 -0.290520238
50 0.141421356
51 2.211201909
52 -0.689416725
53 -0.584801076
54 1.585854564
55 -0.686684324
56 -0.297800218
57 -2.268902598
58 -0.890799782
59 0.465543482
60 0.402802927
61 -0.384177219
62 -0.310452940
63 -1.890980802
64 0.125000000
65 -0.616633065
66 -1.955846441
67 -0.674788731
68 0.613748987
69 -2.602780215
70 -0.266360613
71 0.252546951
72 0.793728767
73 -1.468477421
74 1.022783947
75 0.360277891
76 -0.629764593
77 1.293338307
78 -1.756323165
79 0.523484088
80 0.111803398
81 1.795038870
82 0.316665829
83 -1.065424216
84 -0.758660768
85 0.548953782
86 -0.551938041
87 -2.269356452
88 -0.542871624
89 -0.618295197
90 0.709932591
91 1.161399986
92 -0.722436840
93 -0.790894201
94 0.256806893
95 -0.563278576
96 0.318443675
97 -0.394523043
98 -0.205428830
99 -3.447142601
100 0.100000000
101 0.319092446
102 1.563555865
103 0.552585234
104 -0.487491241
105 -0.678566820
106 -0.413516807
107 0.479930159
108 1.121368516
109 0.136195256
110 -0.485559142
111 2.605592631
112 -0.210576554
113 0.371663521
114 -1.604356413
115 -0.646167154
116 -0.629890566
117 -3.095486576
118 0.329188953
119 -1.033929174
120 0.284824681
121 1.357676804
122 -0.271654316
123 0.806721843
124 -0.219523379
125 0.0894427190
126 -1.337125348
127 1.218067092
128 0.0883883476
129 -1.406089425
130 -0.436025421
131 -0.241837944
132 -1.382992281
133 1.060909264
134 -0.477147688
135 1.002982492
136 0.433986070
137 0.771555900
138 -1.840443540
139 0.380941556
140 -0.188345395
141 0.654228248
142 0.178577661
143 2.117161297
144 0.561250993
145 -0.563391250
146 -1.038370342
147 -0.523340093
148 0.723217464
149 1.128294935
150 0.254754940
151 -0.968225522
152 -0.445310814
153 2.755737831
154 0.914528287
155 -0.196347679
156 -1.241908020
157 0.798565519
158 0.370159148
159 -1.053454491
160 0.0790569415
161 1.217026069
162 1.269284158
163 -0.560293483
164 0.223916555
165 -1.236985901
166 -0.753368688
167 1.113690149
168 -0.536454173
169 0.901181693
170 0.388168942
171 -2.827648026
172 -0.390279131
173 -0.811782663
174 -1.604677336
175 -0.168461243
176 -0.383868206
177 0.838625247
178 -0.437200726
179 1.152896683
180 0.501998149
181 0.433020348
182 0.821233806
183 -0.692051977
184 -0.510839988
185 0.646865365
186 -0.559246652
187 -1.884789564
188 0.181589896
189 -1.889065790
190 -0.398298101
191 -1.525828023
192 0.225173682
193 0.786809010
194 -0.278969919
195 -1.110796301
196 -0.145260119
197 -0.515796564
198 -2.437497908
199 0.204874392
200 0.0707106781
201 -1.215548987
202 0.225632433
203 1.061060982
204 1.105600954
205 0.200277055
206 0.390736766
207 -3.243554992
208 -0.344708362
209 1.934319611
210 -0.479819199
211 -1.604705410
212 -0.292400538
213 0.455318606
214 0.339361870
215 -0.349076267
216 0.792927282
217 0.369809519
218 0.0963045891
219 -2.646264875
220 -0.343342162
221 -1.693921584
222 1.842432218
223 0.772396849
224 -0.148900109
225 0.449000794
226 0.262805796
227 -1.904575842
228 -1.134451299
229 0.118756867
230 -0.456909176
231 2.307255183
232 -0.445399891
233 -1.389124679
234 -2.188839549
235 0.162418940
236 0.232771741
237 0.871294504
238 -0.731098330