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

$R= 31.9163478766$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.082237433
4 0.5
5 0.447213595
6 0.765257428
7 -1.009281822
8 -0.353553390
9 0.171237863
10 -0.316227766
11 1.676917849
12 -0.541118716
13 -0.593511073
14 0.713670020
15 -0.483991294
16 0.250000000
17 -1.012441677
18 -0.121083454
19 -0.00179822020
20 0.223606797
21 1.092282569
22 -1.185759982
23 0.582231036
24 0.382628714
25 0.200000000
26 0.419675705
27 0.896917408
28 -0.504640911
29 -0.406883521
30 0.342233526
31 -0.578588578
32 -0.176776695
33 -1.814823269
34 0.715904375
35 -0.451364552
36 0.0856189317
37 -0.602773619
38 0.00127153369
39 0.642319901
40 -0.158113883
41 -0.279568440
42 -0.772360411
43 1.608825334
44 0.838458924
45 0.0765799005
46 -0.411699514
47 0.544546505
48 -0.270559358
49 0.0186497969
50 -0.141421356
51 1.095702282
52 -0.296755536
53 -0.625604363
54 -0.634216381
55 0.749940460
56 0.356835010
57 0.00194610122
58 0.287710097
59 1.013272471
60 -0.241995647
61 0.872054850
62 0.409123907
63 -0.172827262
64 0.125000000
65 -0.265426221
66 1.283273840
67 0.601110247
68 -0.506220838
69 -0.630112222
70 0.319162935
71 0.950517531
72 -0.0605417272
73 -0.561200313
74 0.426225313
75 -0.216447486
76 -0.000899110099
77 -1.692482702
78 -0.454188758
79 -1.499545625
80 0.111803398
81 -1.141915457
82 0.197684740
83 -1.506787465
84 0.546141284
85 -0.452777682
86 -1.137611303
87 0.440344578
88 -0.592879991
89 1.723573369
90 -0.0541501670
91 0.599019938
92 0.291115518
93 0.626170218
94 -0.385052526
95 -0.000804188521
96 0.191314357
97 -1.734080067
98 -0.0131873978
99 0.287151829
100 0.100000000
101 1.343115695
102 -0.774778514
103 -1.323661500
104 0.209837852
105 0.488483615
106 0.442369087
107 -0.625714511
108 0.448458704
109 -1.867273856
110 -0.530287985
111 0.652344174
112 -0.252320455
113 -1.514343752
114 -0.00137610137
115 0.260381635
116 -0.203441760
117 -0.101631568
118 -0.716491835
119 1.021838980
120 0.171116763
121 1.812053472
122 -0.616635898
123 0.302559431
124 -0.289294289
125 0.0894427190
126 0.122207329
127 -1.383666896
128 -0.0883883476
129 -1.741131001
130 0.187684681
131 -1.810008159
132 -0.907411634
133 0.00181491099
134 -0.425049132
135 0.401113658
136 0.357952187
137 0.421993424
138 0.445556625
139 0.240035965
140 -0.225682276
141 -0.589328612
142 -0.672117392
143 -0.995269313
144 0.0428094658
145 -0.181963842
146 0.396828547
147 -0.0201835083
148 -0.301386809
149 0.539663359
150 0.153051485
151 0.303732344
152 0.000635766848
153 -0.173368349
154 1.196765996
155 -0.258752678
156 0.321159950
157 -0.997884676
158 1.060338880
159 0.677052461
160 -0.0790569415
161 -0.587635201
162 0.807456163
163 0.0649402911
164 -0.139784220
165 -0.811613639
166 1.065459634
167 1.802734615
168 -0.386180205
169 -0.647744603
170 0.320162169
171 -0.000307923069
172 0.804412667
173 -1.208071215
174 -0.311370637
175 -0.201856364
176 0.419229462
177 -1.096601384
178 -1.218750417
179 0.117213595
180 0.0382899502
181 0.858395076
182 -0.423571060
183 -0.943770381
184 -0.205849757
185 -0.269568557
186 -0.442769207
187 -1.697781546
188 0.272273252
189 -0.905242405
190 0.000568647156
191 1.503332253
192 -0.135279679
193 -0.889378731
194 1.226179774
195 0.287254192
196 0.00932489848
197 0.0134084376
198 -0.203047005
199 -1.206782258
200 -0.0707106781
201 -0.650542080
202 -0.949726216
203 0.410661067
204 0.547851141
205 -0.125026807
206 0.935970023
207 0.0997008065
208 -0.148377768
209 -0.00301306986
210 -0.345410076
211 0.378703876
212 -0.312802181
213 -1.028699660
214 0.442446974
215 0.719488562
216 -0.317108190
217 0.583946627
218 1.320362006
219 0.607315236
220 0.374970230
221 0.600890299
222 -0.461276989
223 -0.0978818647
224 0.178417505
225 0.0342475726
226 1.070802736
227 1.988656987
228 0.000973050612
229 -1.422782528
230 -0.184117619
231 1.831735494
232 0.143855048
233 1.408136032
234 0.0718643710
235 0.243528600
236 0.506636235
237 1.622090171
238 -0.722549272
239 -0.941634169
240 -0.120997823
241 1.582992624
242 -1.281315298
243 0.348459946
244 0.436027425
245 0.00834044275
246 -0.213941825
247 -0.00289115789
248 0.204561953
249 1.664923682
250 -0.0632455532