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

$R= 31.4813463946$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.525618136
4 0.5
5 0.447213595
6 -1.078774930
7 -0.347132466
8 -0.353553390
9 1.327510699
10 -0.316227766
11 1.648486797
12 0.762809068
13 0.855339127
14 0.245459720
15 0.682277172
16 0.250000000
17 -0.867528302
18 -0.938691818
19 -0.763519402
20 0.223606797
21 -0.529591586
22 -1.165656193
23 -1.158669091
24 -0.539387465
25 0.200000000
26 -0.604816097
27 0.499656263
28 -0.173566233
29 -1.206075067
30 -0.482442815
31 -1.082194431
32 -0.176776695
33 2.514961356
34 0.613435145
35 -0.155242358
36 0.663755349
37 -1.561124521
38 0.539889747
39 1.304920886
40 -0.158113883
41 0.695727824
42 0.374477801
43 -0.659762279
44 0.824243398
45 0.593680833
46 0.819302771
47 -0.601635667
48 0.381404534
49 -0.879499050
50 -0.141421356
51 -1.323516912
52 0.427669563
53 -1.349016127
54 -0.353310332
55 0.737225707
56 0.122729860
57 -1.164839048
58 0.852823858
59 0.270348701
60 0.341138586
61 0.920306296
62 0.765227021
63 -0.460822063
64 0.125000000
65 0.382519286
66 -1.778346229
67 0.709571535
68 -0.433764151
69 -1.767686580
70 0.109772924
71 -1.401285381
72 -0.469345909
73 0.0812301502
74 1.103881735
75 0.305123627
76 -0.381759701
77 -0.572243287
78 -0.922718407
79 -1.684486729
80 0.111803398
81 -0.565226041
82 -0.491953862
83 1.227741815
84 -0.264795793
85 -0.387970451
86 0.466522382
87 -1.840009996
88 -0.582828096
89 -1.225879089
90 -0.419795743
91 -0.296915980
92 -0.579334545
93 -1.651015452
94 0.425420660
95 -0.341456257
96 -0.269693732
97 0.634259294
98 0.621899742
99 2.188383862
100 0.100000000
101 -0.992420822
102 0.935867784
103 -1.174451016
104 -0.302408048
105 -0.236840557
106 0.953898451
107 1.026034726
108 0.249828131
109 0.617981885
110 -0.521297297
111 -2.381679884
112 -0.0867831165
113 1.401905751
114 0.823665590
115 -0.518172570
116 -0.603037533
117 1.135471843
118 -0.191165400
119 0.301147239
120 -0.241221407
121 1.717508721
122 -0.650754822
123 1.061414987
124 -0.541097215
125 0.0894427190
126 0.325850405
127 0.846164135
128 -0.0883883476
129 -1.006545300
130 -0.270481981
131 1.443495672
132 1.257480678
133 0.265042373
134 -0.501742844
135 0.223453074
136 0.306717572
137 0.221536584
138 1.249943168
139 -0.475998875
140 -0.0776211791
141 -0.917866286
142 0.990858395
143 1.410015258
144 0.331877674
145 -0.539373167
146 -0.0574383900
147 -1.341779703
148 -0.780562260
149 -0.481880990
150 -0.215754986
151 -1.477098381
152 0.269944873
153 -1.151653104
154 0.404637108
155 -0.483972062
156 0.652460443
157 0.672406907
158 1.191111989
159 -2.058083473
160 -0.0790569415
161 0.402211659
162 0.399675166
163 -0.0346684446
164 0.347863912
165 1.124724910
166 -0.868144563
167 0.305437707
168 0.187238900
169 -0.268394974
170 0.274336537
171 -1.013580172
172 -0.329881139
173 -0.625997011
174 1.301083546
175 -0.0694264932
176 0.412121699
177 0.412448868
178 0.866827417
179 -0.889839527
180 0.296840416
181 1.634105649
182 0.209951303
183 1.404036027
184 0.409651385
185 -0.698156110
186 1.167444222
187 -1.430109082
188 -0.300817833
189 -0.173446628
190 0.241446035
191 1.080954884
192 0.190702267
193 1.491535887
194 -0.448489047
195 0.583578361
196 -0.439749525
197 -1.719753488
198 -1.547421068
199 1.005067139
200 -0.0707106781
201 1.082532075
202 0.701747493
203 0.418666139
204 -0.661758456
205 0.311138941
206 0.830462277
207 -1.538139045
208 0.213834781
209 -1.258651277
210 0.167471564
211 -0.667175005
212 -0.674508063
213 -2.137821169
214 -0.725516113
215 -0.295054661
216 -0.176655166
217 0.375694063
218 -0.436979182
219 0.123940649
220 0.368612853
221 -0.742119217
222 1.684101996
223 0.870959095
224 0.0613649301
225 0.265502139
226 -0.991297063
227 -1.029648530
228 -0.582419524
229 -1.568589329
230 0.366403338
231 -0.873417004
232 0.426411929
233 -0.680227681
234 -0.802899840
235 -0.269059650
236 0.135174350
237 -2.576460925
238 -0.212943254
239 -0.615766825
240 0.170569293
241 0.539211437
242 -1.214462063
243 -1.379606918
244 0.460153148
245 -0.393323932
246 -0.750533735
247 -0.623563939
248 0.382613510
249 1.827847610
250 -0.0632455532