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

$R= 28.3439938304$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.119514099
4 0.5
5 -0.447213595
6 0.0845092305
7 -0.743662087
8 0.353553390
9 -0.985716379
10 -0.316227766
11 -0.571398257
12 0.0597570499
13 -1.428195351
14 -0.525848504
15 -0.0534483303
16 0.250000000
17 -1.493006703
18 -0.697006736
19 0.00785586116
20 -0.223606797
21 -0.0888781050
22 -0.404039582
23 -0.506285161
24 0.0422546152
25 0.200000000
26 -1.009886617
27 -0.237321105
28 -0.371831043
29 0.584572779
30 -0.0377936768
31 0.251416374
32 0.176776695
33 -0.0682901484
34 -1.055715164
35 0.332575795
36 -0.492858189
37 -0.758970165
38 0.00555493270
39 -0.170689481
40 -0.158113883
41 0.947409235
42 -0.0628463107
43 -0.261967119
44 -0.285699128
45 0.440825766
46 -0.357997671
47 1.110544868
48 0.0298785249
49 -0.446966700
50 0.141421356
51 -0.178435352
52 -0.714097675
53 1.394648260
54 -0.167811363
55 0.255537069
56 -0.262924252
57 0.000938886182
58 0.413355376
59 0.294037717
60 -0.0267241651
61 -0.971232223
62 0.177778223
63 0.733039900
64 0.125000000
65 0.638708378
66 -0.0482884270
67 1.481717348
68 -0.746503351
69 -0.0605082154
70 0.235166600
71 -0.972286250
72 -0.348503368
73 -1.156019311
74 -0.536672950
75 0.0239028199
76 0.00392793058
77 0.424927220
78 -0.120695690
79 -1.361331396
80 -0.111803398
81 0.957353161
82 0.669919495
83 1.299792921
84 -0.0444390525
85 0.667692896
86 -0.185238726
87 0.0698646895
88 -0.202019791
89 0.246715786
90 0.311710888
91 1.062094736
92 -0.253142580
93 0.0300478016
94 0.785273807
95 -0.00351324791
96 0.0211273076
97 1.427680258
98 -0.316053184
99 0.563236621
100 0.100000000
101 -0.518114121
102 -0.126172847
103 -1.568568545
104 -0.504943308
105 0.0397474969
106 0.986165242
107 -1.255809048
108 -0.118660552
109 1.785020766
110 0.180691994
111 -0.0907076362
112 -0.185915521
113 0.948119249
114 0.000663892786
115 0.226417607
116 0.292286389
117 1.407795551
118 0.207916064
119 1.110292481
120 -0.0188968384
121 -0.673504031
122 -0.686764891
123 0.113228762
124 0.125708187
125 -0.0894427190
126 0.518337484
127 -0.0523589750
128 0.0883883476
129 -0.0313087646
130 0.451635025
131 -0.748254310
132 -0.0341450742
133 -0.00584210610
134 1.047732384
135 0.106133225
136 -0.527857582
137 -1.211247709
138 -0.0427857694
139 -0.893789611
140 0.166287897
141 0.132725770
142 -0.687510200
143 0.816068334
144 -0.246429094
145 -0.261428894
146 -0.817429094
147 -0.0534188233
148 -0.379485082
149 -1.371100186
150 0.0169018461
151 -1.328311068
152 0.00277746635
153 1.471681162
154 0.300468919
155 -0.112436820
156 -0.0853447409
157 0.0494227760
158 -0.962606661
159 0.166680131
160 -0.0790569415
161 0.376505089
162 0.676950912
163 -0.209214618
164 0.473704617
165 0.0305402828
166 0.919092389
167 -0.0634372832
168 -0.0314231553
169 1.039741981
170 0.472130174
171 -0.00774369068
172 -0.130983559
173 0.972188470
174 0.0494017957
175 -0.148732417
176 -0.142849564
177 0.0351415746
178 0.174454405
179 0.421173573
180 0.220412883
181 0.910986808
182 0.751014390
183 -0.116075426
184 -0.178998835
185 0.339421776
186 0.0212470043
187 0.853100130
188 0.555272434
189 0.176483796
190 -0.00248424142
191 0.474483784
192 0.0149392624
193 1.694600243
194 1.009522391
195 0.0763346569
196 -0.223483350
197 0.729032776
198 0.398268434
199 1.900381696
200 0.0707106781
201 0.177041047
202 -0.366362008
203 -0.434677590
204 -0.0892176761
205 -0.423694290
206 -1.109145455
207 0.499041112
208 -0.357048837
209 -0.00439976614
210 0.0281057245
211 1.591927508
212 0.697324130
213 -0.116809616
214 -0.887991093
215 0.117155257
216 -0.0839056816
217 -0.186038186
218 1.262200288
219 -0.139903350
220 0.127768534
221 2.132520671
222 -0.0641399846
223 0.364192252
224 -0.131462126
225 -0.197143275
226 0.670421550
227 0.547937864
228 0.000469443091
229 -1.162009626
230 0.160101425
231 0.0559276613
232 0.206677688
233 -0.304417175
234 0.995461781
235 -0.496650763
236 0.147018858
237 -0.284789549
238 0.785095342