Properties

Level 10
Symmetry even
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

$R= 24.6001318362$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0301938360
4 0.5
5 -0.447213595
6 0.0213502662
7 -0.963531428
8 -0.353553390
9 -0.999088332
10 0.316227766
11 1.052420388
12 -0.0150969180
13 0.798236514
14 0.681319606
15 0.0135030939
16 0.250000000
17 -1.984018664
18 0.706462134
19 -0.871961819
20 -0.223606797
21 0.0290927100
22 -0.744173593
23 -0.136635967
24 0.0106751331
25 0.200000000
26 -0.564438452
27 0.0603601454
28 -0.481765714
29 -1.100256366
30 -0.00954812933
31 0.475305726
32 -0.176776695
33 -0.0317766086
34 1.402913051
35 0.430904354
36 -0.499544166
37 -0.362295770
38 0.616570115
39 -0.0241018224
40 0.158113883
41 -1.637767679
42 -0.0205716525
43 1.446181937
44 0.526210194
45 0.446805885
46 0.0966162195
47 -1.465594287
48 -0.00754845902
49 -0.0716071863
50 -0.141421356
51 0.0599051343
52 0.399118257
53 0.963963309
54 -0.0426810681
55 -0.470656705
56 0.340659803
57 0.0263278722
58 0.777998737
59 0.146752114
60 0.00675154699
61 -1.374908230
62 -0.336091902
63 0.962653007
64 0.125000000
65 -0.356982221
66 0.0224694554
67 -0.123274279
68 -0.992009332
69 0.00412556402
70 -0.304695391
71 -1.586408243
72 0.353231067
73 -1.903185957
74 0.256181795
75 -0.00603876721
76 -0.435980909
77 -1.014040120
78 0.0170425621
79 0.555692625
80 -0.111803398
81 0.997265827
82 1.158076632
83 0.0331087710
84 0.0145463550
85 0.887280120
86 -1.022605055
87 0.0332209603
88 -0.372086796
89 0.249064109
90 -0.315939471
91 -0.769125969
92 -0.0683179839
93 -0.0143513031
94 1.036331659
95 0.389953180
96 0.00533756656
97 -0.338242856
98 0.0506339270
99 -1.051460930
100 0.100000000
101 -1.054699786
102 -0.0423593267
103 0.586823786
104 -0.282219226
105 -0.0130106554
106 -0.681624993
107 -0.790657715
108 0.0301800727
109 -1.741228529
110 0.332804548
111 0.0109390991
112 -0.240882857
113 0.720751641
114 -0.0186166170
115 0.0611054625
116 -0.550128183
117 -0.797508788
118 -0.103769415
119 1.911664338
120 -0.00477406466
121 0.107588674
122 0.972206933
123 0.0494504889
124 0.237652863
125 -0.0894427190
126 -0.680698469
127 1.468473982
128 -0.0883883476
129 -0.0436657802
130 0.252424549
131 1.183958034
132 -0.0158883043
133 0.840162616
134 0.0871680788
135 -0.0269938776
136 0.701456525
137 -0.872781306
138 -0.00291721429
139 1.027693833
140 0.215452177
141 0.0442519153
142 1.121760026
143 0.840080381
144 -0.249772083
145 0.492049605
146 1.345755696
147 0.00216210316
148 -0.181147885
149 0.882272401
150 0.00427005324
151 -0.815871811
152 0.308285057
153 1.982209860
154 0.717034645
155 -0.212563182
156 -0.0120509112
157 0.652080968
158 -0.392934023
159 -0.0291057856
160 0.0790569415
161 0.131653169
162 -0.705173429
163 0.0818182487
164 -0.818883839
165 0.0142109314
166 -0.0234114364
167 1.327239612
168 -0.0102858262
169 -0.362818864
170 -0.627401790
171 0.871165918
172 0.723090968
173 1.466208764
174 -0.0234907663
175 -0.192706285
176 0.263105097
177 -0.00442997779
178 -0.176114920
179 0.0887517354
180 0.223402942
181 0.951536857
182 0.543854188
183 0.0415103097
184 0.0483081097
185 0.162023593
186 0.0101479038
187 -2.088036504
188 -0.732797143
189 -0.0581896985
190 -0.275738538
191 0.372433965
192 -0.00377422951
193 -0.465571998
194 0.239173817
195 0.0107786626
196 -0.0358035931
197 0.236831023
198 0.743495154
199 -0.898032092
200 -0.0707106781
201 0.00418861697
202 0.745785370
203 1.060316943
204 0.0299525671
205 0.732431972
206 -0.414947078
207 0.135504868
208 0.199559128
209 -0.919149250
210 0.00919992269
211 0.242496456
212 0.481981654
213 0.0611356827
214 0.559079432
215 -0.646752224
216 -0.0213405340
217 -0.484096010
218 1.231234500
219 0.0765963189
220 -0.235328352
221 -1.587643103
222 -0.00773511115