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

$R= 30.6522751725$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0555962629
4 0.5
5 0.447213595
6 0.0393124945
7 -1.617607508
8 -0.353553390
9 -0.996909055
10 -0.316227766
11 -0.00787696680
12 -0.0277981314
13 0.567999193
14 1.143821238
15 -0.0248634046
16 0.250000000
17 1.396641398
18 0.704921153
19 -0.518906068
20 0.223606797
21 0.0899329323
22 0.00556985664
23 -0.933840271
24 0.0196562472
25 0.200000000
26 -0.401636081
27 0.111020680
28 -0.808803754
29 -0.935422072
30 0.0175810820
31 -1.662009279
32 -0.176776695
33 0.000437929918
34 -0.987574603
35 -0.723416069
36 -0.498454527
37 0.725915838
38 0.366921999
39 -0.0315786324
40 -0.158113883
41 -1.004275642
42 -0.0635921863
43 0.963032369
44 -0.00393848340
45 -0.445831283
46 0.660324788
47 -0.657265897
48 -0.0138990657
49 1.616654050
50 -0.141421356
51 -0.0776480424
52 0.283999596
53 0.00104830076
54 -0.0785034763
55 -0.00352268664
56 0.571910619
57 0.0288492382
58 0.661443290
59 -1.152121944
60 -0.0124317023
61 -0.215483570
62 1.175218031
63 1.612607573
64 0.125000000
65 0.254016961
66 -0.000309663215
67 -1.683902865
68 0.698320699
69 0.0519180292
70 0.511532408
71 -1.168571590
72 0.352460576
73 -1.240422734
74 -0.513300011
75 -0.0111192525
76 -0.259453034
77 0.0127418406
78 0.0223294651
79 0.757857171
80 0.111803398
81 0.990736720
82 0.710130116
83 0.158987876
84 0.0449664661
85 0.624597021
86 -0.680966719
87 0.0520059714
88 0.00278492832
89 0.224127972
90 0.315250323
91 -0.918799759
92 -0.466920135
93 0.0924015048
94 0.464757173
95 -0.232061848
96 0.00982812363
97 0.337130226
98 -1.143147042
99 0.00785261951
100 0.100000000
101 0.508741832
102 0.0549054573
103 -1.656445969
104 -0.200818040
105 0.0402192300
106 -0.000741260577
107 0.433169097
108 0.0555103404
109 -0.454060812
110 0.00249091561
111 -0.0403582078
112 -0.404401877
113 1.095220070
114 -0.0203994919
115 -0.417626065
116 -0.467711036
117 -0.566243539
118 0.814673239
119 -2.259217613
120 0.00879054101
121 -0.999937953
122 0.152369894
123 0.0558339726
124 -0.831004639
125 0.0894427190
126 -1.140285750
127 -1.509201132
128 -0.0883883476
129 -0.0535410008
130 -0.179617116
131 1.809258408
132 0.000218964959
133 0.839386352
134 1.190699135
135 0.0496499578
136 -0.493787301
137 0.0464812617
138 -0.0367115905
139 -0.927567785
140 -0.361708034
141 0.0365415275
142 0.826304896
143 -0.00447411089
144 -0.249227263
145 -0.418333468
146 0.877111327
147 -0.0898799236
148 0.362957919
149 0.970366031
150 0.00786249890
151 1.389857491
152 0.183460999
153 -1.392324457
154 -0.00900984193
155 -0.743273145
156 -0.0157893162
157 1.472102418
158 -0.535885945
159 -5.828184360e-5
160 -0.0790569415
161 1.510587034
162 -0.700556653
163 -1.915626773
164 -0.502137821
165 0.000195848213
166 -0.112421405
167 -1.471709404
168 -0.0317960931
169 -0.677376919
170 -0.441656789
171 0.517302162
172 0.481516184
173 -1.201035921
174 -0.0367737750
175 -0.323521501
176 -0.00196924170
177 0.0640536470
178 -0.158482408
179 0.588708985
180 -0.222915641
181 -1.493356190
182 0.649689540
183 0.0119801019
184 0.330162394
185 0.324639432
186 -0.0653377306
187 -0.0110014212
188 -0.328632948
189 -0.179587898
190 0.164092506
191 1.093588493
192 -0.00694953286
193 -1.031126103
194 -0.238387069
195 -0.0141223937
196 0.808327025
197 -0.188562892
198 -0.00555264051
199 1.021662787
200 -0.0707106781
201 0.0936179887
202 -0.359734799
203 1.513144821
204 -0.0388240212
205 -0.449125720
206 1.171284177
207 0.930958141
208 0.141999798
209 0.00406890002
210 -0.0284392902
211 1.104924215
212 0.000524150381
213 0.0649444156
214 -0.306296806
215 0.430681168
216 -0.0392517381
217 2.688534987
218 0.321069479
219 0.0687674860
220 -0.00176134332
221 0.793333406
222 0.0285375624
223 1.508330207
224 0.285955309
225 -0.199381811
226 -0.774437538
227 -0.817023063
228 0.0144246191
229 1.633997981
230 0.295306222
231 0.000635742112
232 0.330721645
233 -0.574559297
234 0.400394646
235 -0.293938245
236 -0.576060972
237 -0.0430251774
238 1.597508094
239 0.172156931
240 -0.00621585115
241 1.342085782
242 0.707062907
243 -0.164417358
244 -0.107741785
245 0.722989670
246 -0.0394805806
247 -0.320275442
248 0.587609015
249 -0.120819349
250 -0.0632455532