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

$R= 27.5213532352$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.573238615
4 0.5
5 0.447213595
6 -1.112447693
7 1.166551096
8 -0.353553390
9 1.475079740
10 -0.316227766
11 0.414559159
12 0.786619307
13 -0.937307760
14 -0.824876191
15 0.703573697
16 0.250000000
17 0.945856321
18 -1.043038887
19 -0.0187727108
20 0.223606797
21 1.835263232
22 -0.293137593
23 0.908746533
24 -0.556223846
25 0.200000000
26 0.662776673
27 0.747413793
28 0.583275548
29 -0.793021317
30 -0.497501732
31 -1.809203410
32 -0.176776695
33 0.652200478
34 -0.668821418
35 0.521697510
36 0.737539870
37 1.614104018
38 0.0132743111
39 -1.474608762
40 -0.158113883
41 1.731353325
42 -1.297727076
43 -0.244262167
44 0.207279579
45 0.659675714
46 -0.642580836
47 -0.464139745
48 0.393309653
49 0.360841461
50 -0.141421356
51 1.488057689
52 -0.468653880
53 1.013905830
54 -0.528501361
55 0.185396492
56 -0.412438095
57 -0.0295339535
58 0.560750750
59 1.451164997
60 0.351786848
61 1.696225516
62 1.279300000
63 1.720755889
64 0.125000000
65 -0.419176773
66 -0.461175381
67 -1.100974961
68 0.472928160
69 1.429675137
70 -0.368895847
71 0.907815518
72 -0.521519443
73 1.475559410
74 -1.141343897
75 0.314647723
76 -0.00938635541
77 0.483604442
78 1.042705855
79 -1.276295958
80 0.111803398
81 -0.299219499
82 -1.224251676
83 0.333696682
84 0.917631616
85 0.422999806
86 0.172719435
87 -1.247611758
88 -0.146568796
89 -0.00696168089
90 -0.466461171
91 -1.093417395
92 0.454373266
93 -2.846308668
94 0.328196361
95 -0.00839541150
96 -0.278111923
97 0.545427881
98 -0.255153444
99 0.611507818
100 0.100000000
101 -0.658891861
102 -1.052215683
103 -1.084923287
104 0.331388336
105 0.820754668
106 -0.716939687
107 -0.632291485
108 0.373706896
109 1.158001801
110 -0.131095116
111 2.539370771
112 0.291637774
113 0.543278010
114 0.0208836588
115 0.406403804
116 -0.396510658
117 -1.382603687
118 -1.026128610
119 1.103389729
120 -0.248750866
121 -0.828140702
122 -1.199412565
123 2.723831908
124 -0.904601705
125 0.0894427190
126 -1.216758158
127 0.562824391
128 -0.0883883476
129 -0.384282674
130 0.296402739
131 -1.847553686
132 0.326100239
133 -0.0218993265
134 0.778506861
135 0.334253609
136 -0.334410709
137 0.214381224
138 -1.010932984
139 -1.357765892
140 0.260848755
141 -0.730202570
142 -0.641922509
143 -0.388569516
144 0.368769935
145 -0.354649914
146 -1.043378065
147 0.567689715
148 0.807052009
149 1.175044196
150 -0.222489538
151 -0.704807286
152 0.00663715556
153 1.395213498
154 -0.341959980
155 -0.809100362
156 -0.737304381
157 0.800419305
158 0.902477526
159 1.595115837
160 -0.0790569415
161 1.060099170
162 0.211580136
163 0.334152094
164 0.865676662
165 0.291672921
166 -0.235959186
167 0.184308038
168 -0.648863538
169 -0.121454488
170 -0.299106031
171 -0.0276912085
172 -0.122131083
173 1.172188870
174 0.882194734
175 0.233310219
176 0.103639789
177 2.283028165
178 0.00492265176
179 -1.680509202
180 0.329837857
181 -0.562741400
182 0.773162855
183 2.668566449
184 -0.321290418
185 0.721849261
186 2.012644161
187 0.392116424
188 -0.232069872
189 0.871902716
190 0.00593645240
191 0.0608705703
192 0.196654826
193 -1.002572894
194 -0.385675753
195 -0.659465086
196 0.180420730
197 0.582044421
198 -0.432401324
199 1.458558983
200 -0.0707106781
201 -1.731974116
202 0.465906903
203 -0.924922776
204 0.744028844
205 0.774284745
206 0.767156613
207 1.340069839
208 -0.234326940
209 -0.00659686801
210 -0.580361191
211 1.157709581
212 0.506952915
213 1.429478636
214 0.447097597
215 -0.109237362
216 -0.264250680
217 -2.100972823
218 -0.818830926
219 2.314694438
220 0.0926982462
221 -0.873446331
222 -1.795606292
223 1.700292279
224 -0.206219047
225 0.295015948
226 -0.384155565