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

$R= 28.8267168675$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.254881203
4 0.5
5 0.447213595
6 -0.180228227
7 -0.00697109774
8 -0.353553390
9 -0.935035571
10 -0.316227766
11 1.497744747
12 0.127440601
13 0.306518403
14 0.00492931048
15 0.113986339
16 0.250000000
17 1.641942050
18 0.661169993
19 -0.582506763
20 0.223606797
21 -0.00177680177
22 -1.059065467
23 -0.0448376784
24 -0.0901141138
25 0.200000000
26 -0.216741241
27 -0.493204196
28 -0.00348554887
29 -1.021008431
30 -0.0806005137
31 1.278039870
32 -0.176776695
33 0.381746984
34 -1.161028358
35 -0.00311756968
36 -0.467517785
37 0.0975119596
38 0.411894482
39 0.0781257797
40 -0.158113883
41 1.746507135
42 0.00125638858
43 -1.119625943
44 0.748872373
45 -0.418160620
46 0.0317050264
47 1.184512512
48 0.0637203009
49 -0.999951403
50 -0.141421356
51 0.418500166
52 0.153259201
53 1.057135574
54 0.348748031
55 0.669811813
56 0.00246465524
57 -0.148470025
58 0.721961985
59 -0.900153797
60 0.0569931698
61 -0.657791147
62 -0.903710659
63 0.00651822435
64 0.125000000
65 0.137079197
66 -0.269935881
67 1.523390718
68 0.820971025
69 -0.0114282814
70 0.00220445466
71 -0.0152293358
72 0.330584996
73 0.701550540
74 -0.0689513678
75 0.0509762407
76 -0.291253381
77 -0.0104409250
78 -0.0552432686
79 0.0548958592
80 0.111803398
81 0.809327092
82 -1.234967038
83 -0.803920313
84 -0.000888400885
85 0.734298807
86 0.791695096
87 -0.260235858
88 -0.529532733
89 -0.215794080
90 0.295684210
91 -0.00213676974
92 -0.0224188392
93 0.325748340
94 -0.837576829
95 -0.260504943
96 -0.0450570569
97 -1.136338751
98 0.707072418
99 -1.400444616
100 0.100000000
101 1.366633400
102 -0.295924305
103 -1.249731536
104 -0.108370620
105 -0.000794609908
106 -0.747507733
107 -0.833005890
108 -0.246602098
109 -1.565601460
110 -0.473628475
111 0.0248539656
112 -0.00174277443
113 0.919648063
114 0.104984161
115 -0.0200520193
116 -0.510504215
117 -0.286605610
118 0.636504854
119 -0.0114461384
120 -0.0403002568
121 1.243239329
122 0.465128581
123 0.445151841
124 0.639019935
125 0.0894427190
126 -0.00460908064
127 -0.704448069
128 -0.0883883476
129 -0.285371608
130 -0.0969296300
131 1.056080181
132 0.190873492
133 0.00406071159
134 -1.077199907
135 -0.220567621
136 -0.580514179
137 -0.389713743
138 0.00808101529
139 1.000543418
140 -0.00155878484
141 0.301909975
142 0.0107687666
143 0.459086328
144 -0.233758892
145 -0.456608851
146 -0.496071144
147 -0.254868817
148 0.0487559798
149 -0.943782928
150 -0.0360456455
151 -1.781594595
152 0.205947241
153 -1.535274224
154 0.00738284889
155 0.571556805
156 0.0390628898
157 -0.908568846
158 -0.0388172343
159 0.269443987
160 -0.0790569415
161 0.000312579785
162 -0.572280675
163 0.0122363662
164 0.873253567
165 0.170722441
166 0.568457505
167 1.784283305
168 0.000628194290
169 -0.906046451
170 -0.519227666
171 0.544664511
172 -0.559812971
173 1.065330641
174 0.184014540
175 -0.00139421954
176 0.374436186
177 -0.229432463
178 0.152589457
179 0.945920064
180 -0.209080310
181 0.105480204
182 0.00151092437
183 -0.167657932
184 0.0158525132
185 0.0436086740
186 -0.230338860
187 2.459211645
188 0.592256256
189 0.00343875020
190 0.184204812
191 0.830566597
192 0.0318601504
193 1.226021305
194 0.803512836
195 0.0349389108
196 -0.499975701
197 0.892667190
198 0.990263885
199 0.566291412
200 -0.0707106781
201 0.388304311
202 -0.966355745
203 0.00711464560
204 0.209250083
205 0.781061735
206 0.883693644
207 0.0419402618
208 0.0766296009
209 -0.872568193
210 0.000561874054
211 0.918594272
212 0.528567787
213 -0.00407056304
214 0.589024113
215 -0.500711943
216 0.174374015
217 -0.00946071507
218 1.107047409
219 0.177959593
220 0.334905906
221 0.502325361
222 -0.0175744076
223 -1.131022563
224 0.00123232762
225 -0.187007114
226 -0.650289382
227 1.745809163
228 -0.0742350125
229 1.672040040
230 0.0141789188
231 -0.0138352453
232 0.360980992
233 -1.032580613
234 0.202660771
235 0.529730099
236 -0.450076898
237 -0.0285601204
238 0.00809364215