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

$R= 29.9159624082$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.700375707
4 0.5
5 0.447213595
6 -1.202347193
7 -1.083873312
8 0.353553390
9 1.891277548
10 0.316227766
11 -1.717200623
12 -0.850187853
13 0.153034590
14 -0.766414169
15 -0.760431134
16 0.250000000
17 1.576585828
18 1.337335179
19 0.301521613
20 0.223606797
21 1.842991850
22 -1.214244205
23 -1.833899625
24 -0.601173596
25 0.200000000
26 0.108211796
27 -1.515506692
28 -0.541936656
29 1.003664509
30 -0.537706011
31 0.162849736
32 0.176776695
33 2.919886226
34 1.114814530
35 -0.484722881
36 0.945638774
37 -1.302256669
38 0.213207977
39 -0.260216299
40 0.158113883
41 -0.448441926
42 1.303192035
43 1.318385477
44 -0.858600311
45 0.845805032
46 -1.296762861
47 1.048449949
48 -0.425093926
49 0.174781356
50 0.141421356
51 -2.680788244
52 0.0765172951
53 0.341679497
54 -1.071625058
55 -0.767955465
56 -0.383207084
57 -0.512700026
58 0.709697980
59 0.625645838
60 -0.380215567
61 0.755946046
62 0.115152153
63 -2.049905260
64 0.125000000
65 0.0684391493
66 2.064671350
67 0.720632608
68 0.788292914
69 3.118318374
70 -0.342750836
71 -1.085752781
72 0.668667589
73 0.630388509
74 -0.920834522
75 -0.340075141
76 0.150760806
77 1.861227927
78 -0.184000710
79 0.989737894
80 0.111803398
81 0.685653216
82 -0.317096327
83 1.213600240
84 0.921495925
85 0.705070617
86 0.932239311
87 -1.706606751
88 -0.607122102
89 1.173495770
90 0.598074474
91 -0.165870108
92 -0.916949812
93 -0.276905736
94 0.741366068
95 0.134844564
96 -0.300586798
97 1.021088528
98 0.123589082
99 -3.247702985
100 0.100000000
101 -0.512819958
102 -1.895603546
103 0.568246811
104 0.0541058982
105 0.824211012
106 0.241603889
107 -1.293622231
108 -0.757753346
109 -1.090498021
110 -0.543026517
111 2.214325606
112 -0.270968328
113 0.853793652
114 -0.362533665
115 -0.820144845
116 0.501832254
117 0.289430884
118 0.442398415
119 -1.708819304
120 -0.268853005
121 1.948777981
122 0.534534575
123 0.762519758
124 0.0814248683
125 0.0894427190
126 -1.449501910
127 -1.282564126
128 0.0883883476
129 -2.241750640
130 0.0483937866
131 -1.057817640
132 1.459943113
133 -0.326811229
134 0.509564204
135 -0.677755196
136 0.557407265
137 -1.066681598
138 2.204984068
139 -0.254651891
140 -0.242361440
141 -1.782758824
142 -0.767743154
143 -0.262791094
144 0.472819387
145 0.448852414
146 0.445751990
147 -0.297193973
148 -0.651128334
149 -0.399324372
150 -0.240469438
151 -1.230062791
152 0.106603988
153 2.981761379
154 1.316086889
155 0.0728286162
156 -0.130108149
157 -0.922677660
158 0.699850377
159 -0.580983524
160 0.0790569415
161 1.987714865
162 0.484830038
163 -1.337501259
164 -0.224220963
165 1.305812817
166 0.858144959
167 -0.240739899
168 0.651596017
169 -0.976580402
170 0.498560214
171 0.570261089
172 0.659192738
173 1.463401650
174 -1.206753206
175 -0.216774662
176 -0.429300155
177 -1.063832982
178 0.829786816
179 -0.0651455202
180 0.422902516
181 0.0446599724
182 -0.117287878
183 -1.285392510
184 -0.648381430
185 -0.582386887
186 -0.195801923
187 -2.707313105
188 0.524224974
189 1.642617444
190 0.0953495061
191 1.382291365
192 -0.212546963
193 0.0157964139
194 0.722018622
195 -0.116372267
196 0.0873906784
197 0.155605053
198 -2.296472804
199 -0.195009613
200 0.0707106781
201 -1.225370601
202 -0.362618470
203 -1.087812587
204 -1.340394122
205 -0.200549326
206 0.401811173
207 -3.468420489
208 0.0382586475
209 -0.517746991
210 0.582805195
211 -0.676967564
212 0.170839748
213 1.845793503
214 -0.914729052
215 0.589599909
216 -0.535812529
217 -0.176341901
218 -0.771098545
219 -1.072228981
220 -0.383977732
221 0.241513337
222 1.565764652
223 -0.974344480
224 -0.191603542
225 0.378255509
226 0.603723281
227 0.543403873
228 -0.256350013
229 -0.951787953
230 -0.579929981
231 -3.174662438
232 0.354848990