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

$R= 28.017178146$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.956122763
4 0.5
5 0.447213595
6 -0.676080889
7 -0.404454099
8 0.353553390
9 -0.0858292618
10 0.316227766
11 0.271361523
12 -0.478061381
13 0.822806278
14 -0.285992236
15 -0.427591098
16 0.250000000
17 0.0107670957
18 -0.0606904530
19 -0.643049217
20 0.223606797
21 0.386707770
22 0.191881573
23 -1.626134828
24 -0.338040444
25 0.200000000
26 0.581811899
27 1.038186074
28 -0.202227049
29 0.479805768
30 -0.302352565
31 0.553892674
32 0.176776695
33 -0.259454929
34 0.00761348643
35 -0.180877371
36 -0.0429146309
37 1.767876601
38 -0.454704462
39 -0.786703812
40 0.158113883
41 -0.0605152639
42 0.273443687
43 -1.232862842
44 0.135680761
45 -0.0383840127
46 -1.149850964
47 -0.0787738090
48 -0.239030690
49 -0.836416881
50 0.141421356
51 -0.0102946653
52 0.411403139
53 -0.646994810
54 0.734108413
55 0.121356562
56 -0.142996118
57 0.614833994
58 0.339273912
59 0.229391599
60 -0.213795549
61 0.360086543
62 0.391661265
63 0.0347139967
64 0.125000000
65 0.367970154
66 -0.183462340
67 -0.483749131
68 0.00538354788
69 1.554784525
70 -0.127899616
71 1.125481844
72 -0.0303452265
73 1.851654510
74 1.250077532
75 -0.191224552
76 -0.321524608
77 -0.109753280
78 -0.556283600
79 -1.117908447
80 0.111803398
81 -0.906804076
82 -0.0427907535
83 0.181911723
84 0.193353885
85 0.00481519161
86 -0.871765676
87 -0.458753216
88 0.0959407866
89 -0.154824547
90 -0.0271415957
91 -0.332787372
92 -0.813067414
93 -0.529589394
94 -0.0557014945
95 -0.287580352
96 -0.169020222
97 0.581859616
98 -0.591436048
99 -0.0232907592
100 0.100000000
101 1.417264069
102 -0.00727942768
103 0.254269287
104 0.290905949
105 0.172940972
106 -0.457494418
107 -0.854537318
108 0.519093037
109 -0.913537301
110 0.0858120483
111 -1.690307060
112 -0.101113524
113 -0.976608107
114 0.434753286
115 -0.727229603
116 0.239902884
117 -0.0706208555
118 0.162204355
119 -0.00435479606
120 -0.151176282
121 -0.926362923
122 0.254619636
123 0.0578600214
124 0.276946337
125 0.0894427190
126 0.0245465025
127 -1.252721460
128 0.0883883476
129 1.178768227
130 0.260194191
131 0.518447775
132 -0.129727464
133 0.260083892
134 -0.342062291
135 0.464290926
136 0.00380674321
137 -0.0369752188
138 1.099398681
139 -0.727122838
140 -0.0904386859
141 0.0753174326
142 0.795835844
143 0.223277965
144 -0.0214573154
145 0.214575662
146 1.309317461
147 0.799717219
148 0.883938300
149 -0.187682133
150 -0.135216177
151 -0.0637420864
152 -0.227352231
153 -0.000924129835
154 -0.0776072889
155 0.247708334
156 -0.393351906
157 -1.589465738
158 -0.790480643
159 0.618606460
160 0.0790569415
161 0.657696886
162 -0.641207311
163 -0.647347511
164 -0.0302576319
165 -0.116031771
166 0.128631012
167 -1.158250870
168 0.136721843
169 -0.322989856
170 0.00340485464
171 0.0551924042
172 -0.616431421
173 -0.773638735
174 -0.324387510
175 -0.0808908198
176 0.0678403808
177 -0.219326573
178 -0.109477487
179 -0.965646698
180 -0.0191920063
181 -1.181643720
182 -0.235316207
183 -0.344286990
184 -0.574925482
185 0.790618451
186 -0.374476251
187 0.00292212030
188 -0.0393869045
189 -0.419901077
190 -0.203350017
191 -1.803542041
192 -0.119515345
193 -1.408883861
194 0.411436880
195 -0.351824640
196 -0.418208440
197 -0.995572855
198 -0.0164690537
199 -1.280128249
200 0.0707106781
201 0.462542332
202 1.002157034
203 -0.194007135
204 -0.00514733267
205 -0.0270632487
206 0.179795537
207 0.139418988
208 0.205701569
209 -0.174652667
210 0.122287734
211 1.153517203
212 -0.323497405
213 -1.075903241
214 -0.604249132
215 -0.551353024
216 0.367054206
217 -0.223735255
218 -0.645968420
219 -1.771510113
220 0.0606782812
221 0.00655993120
222 -1.195227584
223 1.478000106
224 -0.0714980590
225 -0.0171658523
226 -0.690566215
227 -1.495850355
228 0.307416997
229 0.688922831
230 -0.514228983
231 0.0906274243
232 0.169636956