Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 29.9953210933$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.730632429
4 0.5
5 -0.447213595
6 0.516635145
7 -1.592100219
8 0.353553390
9 -0.466176253
10 -0.316227766
11 -1.267127799
12 0.365316214
13 -0.372047890
14 -1.125784861
15 -0.326748755
16 0.250000000
17 -0.200072998
18 -0.329636389
19 -1.010667697
20 -0.223606797
21 -1.163240050
22 -0.895994659
23 1.392481750
24 0.258317572
25 0.200000000
26 -0.263077586
27 -1.071235917
28 -0.796050109
29 -0.734860736
30 -0.231046260
31 0.152572867
32 0.176776695
33 -0.925804662
34 -0.141472974
35 0.712008863
36 -0.233088126
37 1.135511371
38 -0.714649982
39 -0.271830254
40 -0.158113883
41 -1.251177736
42 -0.822534927
43 1.305469310
44 -0.633563899
45 0.208480358
46 0.984633288
47 -1.478656245
48 0.182658107
49 1.534783107
50 0.141421356
51 -0.146179821
52 -0.186023945
53 0.329144699
54 -0.757478181
55 0.566676779
56 -0.562892430
57 -0.738426594
58 -0.519625009
59 0.517424513
60 -0.163374377
61 1.414560924
62 0.107885309
63 0.742199315
64 0.125000000
65 0.166384874
66 -0.654642754
67 0.555496832
68 -0.100036499
69 1.017392324
70 0.503466295
71 -0.263513692
72 -0.164818194
73 0.241470306
74 0.802927790
75 0.146126485
76 -0.505333848
77 2.017394447
78 -0.192213016
79 1.013035291
80 -0.111803398
81 -0.316503447
82 -0.884716261
83 -1.596397285
84 -0.581620025
85 0.0894753652
86 0.923106201
87 -0.536913084
88 -0.447997329
89 0.328097796
90 0.147417875
91 0.592337528
92 0.696240875
93 0.111474684
94 -1.045567858
95 0.451984334
96 0.129158786
97 -0.996303214
98 1.085255543
99 0.590704890
100 0.100000000
101 1.648313562
102 -0.103364742
103 0.752168699
104 -0.131538793
105 0.520216765
106 0.232740448
107 0.904720097
108 -0.535617958
109 1.390447471
110 0.400700993
111 0.829641431
112 -0.398025054
113 -1.884548164
114 -0.522146452
115 -0.622736770
116 -0.367430368
117 0.173439891
118 0.365874382
119 0.318536265
120 -0.115523130
121 0.605612860
122 1.000245622
123 -0.914151028
124 0.0762864338
125 -0.0894427190
126 0.524814168
127 -1.086039586
128 0.0883883476
129 0.953818213
130 0.117651873
131 0.501090834
132 -0.462902331
133 1.609084262
134 0.392795577
135 0.479071266
136 -0.0707364871
137 -0.782867708
138 0.719405011
139 0.549260563
140 0.356004431
141 -1.080354204
142 -0.186332318
143 0.471432225
144 -0.116544063
145 0.328639712
146 0.170745290
147 1.121362310
148 0.567755685
149 -1.506066061
150 0.103327029
151 -1.104702813
152 -0.357324991
153 0.0932692818
154 1.426513294
155 -0.0682326607
156 -0.135915127
157 -1.294479557
158 0.716324124
159 0.240483792
160 -0.0790569415
161 -2.216970496
162 -0.223801733
163 0.584870749
164 -0.625588868
165 0.414032431
166 -1.128823346
167 -1.838375526
168 -0.411267463
169 -0.861580392
170 0.0632686375
171 0.471149298
172 0.652734655
173 1.512336361
174 -0.379654883
175 -0.318420043
176 -0.316781949
177 0.378046994
178 0.232000177
179 -0.0937683139
180 0.104240179
181 -0.528514840
182 0.418845883
183 1.033524370
184 0.492316644
185 -0.507816123
186 0.0788245056
187 0.253517999
188 -0.739328122
189 1.705513603
190 0.319601188
191 -1.539796806
192 0.0913290536
193 -0.675146789
194 -0.704492758
195 0.121566185
196 0.767391553
197 1.695141933
198 0.417691433
199 0.638810699
200 0.0707106781
201 0.405886850
202 1.165533697
203 1.169985070
204 -0.0730899106
205 0.559543694
206 0.531863588
207 -0.649188096
208 -0.0930119727
209 1.280610604
210 0.367848802
211 1.527380186
212 0.164572349
213 -0.192338389
214 0.639733715
215 -0.583823624
216 -0.378739090
217 -0.243120831
218 0.983194836
219 0.175745782
220 0.283338389
221 0.0750554021
222 0.586645082
223 1.747230986
224 -0.281446215
225 -0.0932352506
226 -1.332576786
227 -0.173669097
228 -0.369213297
229 0.809429757
230 -0.440341393
231 1.479040531
232 -0.259812504
233 0.427894692
234 0.122640523
235 0.661275175
236 0.258712256
237 0.736329053
238 0.225239153