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

$R= 31.5872513035$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.905217539
4 0.5
5 -0.447213595
6 -1.347192241
7 -1.694297219
8 0.353553390
9 2.629853873
10 -0.316227766
11 -0.627587153
12 -0.952608769
13 -0.888615764
14 -1.198049053
15 0.852039186
16 0.250000000
17 -1.705024173
18 1.859587507
19 0.933595036
20 -0.223606797
21 3.228004779
22 -0.443771132
23 0.389155167
24 -0.673596120
25 0.200000000
26 -0.628346233
27 -3.105226186
28 -0.847148609
29 0.150273524
30 0.602482686
31 -0.669682996
32 0.176776695
33 1.195690052
34 -1.205634155
35 0.757712751
36 1.314926936
37 0.105555443
38 0.660151380
39 1.693006341
40 -0.158113883
41 0.573195318
42 2.282544069
43 -0.919532196
44 -0.313793576
45 -1.176106406
46 0.275174257
47 0.915670802
48 -0.476304384
49 1.870643067
50 0.141421356
51 3.248441960
52 -0.444307882
53 0.694519982
54 -2.195726493
55 0.280665507
56 -0.599024526
57 -1.778701637
58 0.106259427
59 -0.591451240
60 0.426019593
61 1.463641763
62 -0.473537388
63 -4.455754105
64 0.125000000
65 0.397401051
66 0.845480544
67 1.685933640
68 -0.852512086
69 -0.741425250
70 0.535783824
71 0.482482629
72 0.929793753
73 0.739425550
74 0.0746389698
75 -0.381043507
76 0.466797518
77 1.063319169
78 1.197136264
79 -0.824597580
80 -0.111803398
81 3.286277522
82 0.405310296
83 -0.467809545
84 1.614002389
85 0.762509991
86 -0.650207451
87 -0.286303754
88 -0.221885566
89 0.682312509
90 -0.831632815
91 1.505579219
92 0.194577583
93 1.275891791
94 0.647477033
95 -0.417516392
96 -0.336798060
97 -0.205056841
98 1.322744398
99 -1.650462507
100 0.100000000
101 1.151702457
102 2.296995338
103 0.593097515
104 -0.314173116
105 -1.443607623
106 0.491099789
107 -0.440194133
108 -1.552613093
109 0.325535191
110 0.198460483
111 -0.201106082
112 -0.423574304
113 -1.165198975
114 -1.257731989
115 -0.174035481
116 0.0751367620
117 -2.336929611
118 -0.418219182
119 2.888817716
120 0.301241343
121 -0.606134364
122 1.034951016
123 -1.092061775
124 -0.334841498
125 -0.0894427190
126 -3.150693942
127 0.0151510487
128 0.0883883476
129 1.751908868
130 0.281004978
131 -0.128980097
132 0.597845026
133 -1.581787473
134 1.192135109
135 1.388699367
136 -0.602817077
137 0.635456808
138 -0.524266822
139 0.136144002
140 0.378856375
141 -1.744552072
142 0.341166738
143 0.557683838
144 0.657463468
145 -0.0672043630
146 0.522852820
147 -3.563981982
148 0.0527777217
149 0.604389456
150 -0.269438448
151 1.909018986
152 0.330075690
153 -4.483964426
154 0.751880195
155 0.299491340
156 0.846503170
157 -0.431493916
158 -0.583078540
159 -1.323211652
160 -0.0790569415
161 -0.659344519
162 2.323749120
163 -1.706353809
164 0.286597659
165 -0.534728847
166 -0.330791301
167 0.855821924
168 1.141272034
169 -0.210362026
170 0.539175985
171 2.455218519
172 -0.459766098
173 -0.871539903
174 -0.202447325
175 -0.338859443
176 -0.156896788
177 1.126843254
178 0.482467802
179 -0.150315472
180 -0.588053203
181 -0.663442674
182 1.064605275
183 -2.788555952
184 0.137587128
185 -0.0472058294
186 0.902191738
187 1.070051257
188 0.457835401
189 5.261176199
190 -0.295228672
191 -0.340537798
192 -0.238152192
193 1.796639907
194 -0.144997083
195 -0.757135453
196 0.935321533
197 -0.200749921
198 -1.167053230
199 -1.899690376
200 0.0707106781
201 -3.212073141
202 0.814376617
203 -0.254608962
204 1.624220980
205 -0.256340739
206 0.419383274
207 1.023414766
208 -0.222153941
209 -0.585911207
210 -1.020784740
211 -0.707929455
212 0.347259991
213 -0.919238035
214 -0.311264256
215 0.411227299
216 -1.097863246
217 1.134647889
218 0.230188141
219 -1.408850315
220 0.140332753
221 1.515136302
222 -0.142203474
223 -0.779795472
224 -0.299512263
225 0.525970774
226 -0.823920096
227 -1.621059858
228 -0.889350818
229 -1.045985313
230 -0.123061669
231 -2.025957259
232 0.0531297139
233 0.397116519
234 -1.652458775
235 -0.409500431
236 -0.295725620
237 1.573442292
238 2.042702596
239 -0.00552374525
240 0.213009796
241 -1.295823316
242 -0.428601719
243 -3.153093305
244 0.731820881
245 -0.836577012
246 -0.772204286
247 -0.834803945
248 -0.236768694
249 0.928836736
250 -0.0632455532