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

$R= 29.1014092651$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.301266970
4 0.5
5 -0.447213595
6 -0.920134699
7 -1.636531802
8 0.353553390
9 0.693295728
10 -0.316227766
11 1.466206727
12 -0.650633485
13 0.894819422
14 -1.157202735
15 0.581944280
16 0.250000000
17 0.227975011
18 0.490234111
19 -1.027244910
20 -0.223606797
21 2.129564780
22 1.036764719
23 -0.307436671
24 -0.460067349
25 0.200000000
26 0.632732881
27 0.399104138
28 -0.818265901
29 -1.828248920
30 0.411496747
31 -1.078942679
32 0.176776695
33 -1.907926386
34 0.161202676
35 0.731879271
36 0.346647864
37 -0.832903188
38 -0.726371842
39 -1.164398959
40 -0.158113883
41 -1.388677738
42 1.505829697
43 -1.655305293
44 0.733103363
45 -0.310051275
46 -0.217390555
47 0.786892128
48 -0.325316742
49 1.678236340
50 0.141421356
51 -0.296656353
52 0.447409711
53 0.961863950
54 0.282209242
55 -0.655707582
56 -0.578601367
57 1.336719872
58 -1.292767209
59 0.451290409
60 0.290972140
61 -0.104159461
62 -0.762927684
63 -1.134600508
64 0.125000000
65 -0.400175411
66 -1.349107686
67 -1.085033293
68 0.113987505
69 0.400057186
70 0.517516795
71 0.643871059
72 0.245117055
73 -1.064796091
74 -0.588951492
75 -0.260253394
76 -0.513622455
77 -2.399493938
78 -0.823354400
79 1.333920718
80 -0.111803398
81 -1.212636761
82 -0.981943445
83 0.218297051
84 1.064782390
85 -0.101953524
86 -1.170477597
87 2.379039934
88 0.518382359
89 -0.133586194
90 -0.219239359
91 -1.464400443
92 -0.153718335
93 1.403992471
94 0.556416759
95 0.459397889
96 -0.230033674
97 1.011094522
98 1.186692296
99 1.016514861
100 0.100000000
101 0.298332461
102 -0.209767718
103 -1.166356999
104 0.316366440
105 -0.952370322
106 0.680140522
107 0.856157648
108 0.199552069
109 -1.748918348
110 -0.463655278
111 1.083829408
112 -0.409132950
113 -0.386387632
114 0.945203686
115 0.137489859
116 -0.914124460
117 0.620374483
118 0.319110508
119 -0.373088357
120 0.205748373
121 1.149762168
122 -0.0736518614
123 1.807040473
124 -0.539471339
125 -0.0894427190
126 -0.802283713
127 1.295417624
128 0.0883883476
129 2.153994104
130 -0.282966747
131 -1.285903024
132 -0.953963193
133 1.681118965
134 -0.767234399
135 -0.178484796
136 0.0806013384
137 -0.784491177
138 0.282883149
139 0.448925549
140 0.365939635
141 -1.023956735
142 0.455285592
143 1.311990257
144 0.173323932
145 0.817617773
146 -0.752924536
147 -2.183833517
148 -0.416451594
149 -0.478599493
150 -0.184026939
151 0.0687760800
152 -0.363185921
153 0.158054101
154 -1.696698435
155 0.482517834
156 -0.582199479
157 -0.201925092
158 0.943224385
159 -1.251641799
160 -0.0790569415
161 0.503129886
162 -0.857463677
163 -0.233912125
164 -0.694338869
165 0.853250619
166 0.154359325
167 0.718821709
168 0.752914848
169 -0.199298258
170 -0.0720920287
171 -0.712184564
172 -0.827652646
173 0.512360276
174 1.682235270
175 -0.327306360
176 0.366551681
177 -0.587249152
178 -0.0944597041
179 1.593590781
180 -0.155025637
181 1.943933005
182 -1.035487483
183 0.135540067
184 -0.108695277
185 0.372485629
186 0.992772597
187 0.334259133
188 0.393446064
189 -0.653146593
190 0.324843363
191 -0.574823290
192 -0.162658371
193 -0.906754203
194 0.714951793
195 0.520735045
196 0.839118170
197 1.473671681
198 0.718784551
199 1.222780913
200 0.0707106781
201 1.411907934
202 0.210952906
203 2.991985587
204 -0.148328176
205 0.621035564
206 -0.824738943
207 -0.213187630
208 0.223704855
209 -1.506326495
210 -0.673427513
211 -0.540661185
212 0.480931975
213 -0.837555892
214 0.605394878
215 0.740275031
216 0.141104621
217 1.765611330
218 -1.236672023
219 1.385351971
220 -0.327853791
221 0.203019639
222 0.766383124
223 -0.394960305
224 -0.289300683
225 0.138659145
226 -0.273217315
227 1.077145489
228 0.668359936
229 -0.771090035
230 0.0972200119
231 3.124331730
232 -0.646383604
233 1.906544032
234 0.438671004
235 -0.351908857
236 0.225645204
237 -1.708883500
238 -0.263813307
239 -0.828304440
240 0.145486070