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

$R= 26.9871409866$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.187998685
4 0.5
5 -0.447213595
6 0.132935145
7 -0.148016461
8 0.353553390
9 -0.964656494
10 -0.316227766
11 -0.604768985
12 0.0939993429
13 1.656539461
14 -0.104663443
15 -0.0840755682
16 0.250000000
17 -0.771317579
18 -0.682115148
19 0.188280638
20 -0.223606797
21 -0.0278269002
22 -0.427636250
23 -0.628837095
24 0.0664675728
25 0.200000000
26 1.171350286
27 -0.369352839
28 -0.0740082307
29 0.131987131
30 -0.0594504044
31 -0.827191843
32 0.176776695
33 -0.113695774
34 -0.545403891
35 0.0661949739
36 -0.482328247
37 0.436043906
38 0.133134516
39 0.311427241
40 -0.158113883
41 0.0900848471
42 -0.0196765898
43 0.399309702
44 -0.302384492
45 0.431407499
46 -0.444654974
47 0.758561460
48 0.0469996714
49 -0.978091127
50 0.141421356
51 -0.145006691
52 0.828269730
53 0.872975849
54 -0.261171897
55 0.270460912
56 -0.0523317218
57 0.0353965126
58 0.0933289957
59 1.677818673
60 -0.0420377841
61 -0.777410743
62 -0.584912962
63 0.142785040
64 0.125000000
65 -0.740826968
66 -0.0803950531
67 -1.713187832
68 -0.385658789
69 -0.118220547
70 0.0468069149
71 1.122108563
72 -0.341057574
73 1.579154837
74 0.308329603
75 0.0375997371
76 0.0941403191
77 0.0895157652
78 0.220212314
79 0.769530853
80 -0.111803398
81 0.895218645
82 0.0636996063
83 -0.482852838
84 -0.0139134501
85 0.344943708
86 0.282354598
87 0.0248134072
88 -0.213818125
89 0.843235013
90 0.305051168
91 -0.245195109
92 -0.314418547
93 -0.155510979
94 0.536383952
95 -0.0842016612
96 0.0332337864
97 -0.396345071
98 -0.691614868
99 0.583394328
100 0.100000000
101 0.0698715127
102 -0.102535214
103 1.526764335
104 0.585675143
105 0.0124445681
106 0.617287143
107 1.162711329
108 -0.184676419
109 1.260690243
110 0.191244745
111 0.0819756814
112 -0.0370041153
113 -1.825735096
114 0.0250291140
115 0.281224498
116 0.0659935657
117 -1.597991549
118 1.186396961
119 0.114167698
120 -0.0297252022
121 -0.634254474
122 -0.549712408
123 0.0169358329
124 -0.413595921
125 -0.0894427190
126 0.100964270
127 0.860890267
128 0.0883883476
129 0.0750696994
130 -0.523843773
131 -1.355256821
132 -0.0568478872
133 -0.0278686336
134 -1.211406734
135 0.165179611
136 -0.272701945
137 -1.140789897
138 -0.0835945509
139 0.567335971
140 0.0330974869
141 0.142608558
142 0.793450574
143 -1.001823688
144 -0.241164123
145 -0.0590264396
146 1.116631094
147 -0.183879841
148 0.218021953
149 1.097880858
150 0.0265870291
151 0.114878956
152 0.0665672580
153 0.744056525
154 0.0632972046
155 0.369931438
156 0.155713620
157 0.623817975
158 0.544140485
159 0.164118311
160 -0.0790569415
161 0.0930782324
162 0.633015175
163 0.598310262
164 0.0450424235
165 0.0508462960
166 -0.341428516
167 0.713304284
168 -0.00983829494
169 1.744123230
170 0.243912035
171 -0.181626289
172 0.199654851
173 0.462341627
174 0.0175457285
175 -0.0296032923
176 -0.151192246
177 0.315426666
178 0.596257196
179 1.397094803
180 0.215703749
181 1.939307058
182 -0.173379124
183 -0.146152766
184 -0.222327487
185 -0.195004763
186 -0.109962868
187 0.466478610
188 0.379280730
189 0.0546701706
190 -0.0595395656
191 1.786019001
192 0.0234998357
193 0.223494300
194 -0.280258287
195 -0.139274496
196 -0.489045563
197 0.308866241
198 0.412522086
199 -1.228832932
200 0.0707106781
201 -0.321998138
202 0.0494066204
203 -0.0195672418
204 -0.0725033457
205 -0.0402871683
206 1.079585415
207 0.606890499
208 0.414134865
209 -0.113878505
210 0.00879963850
211 0.406679502
212 0.436487924
213 0.214866438
214 0.822161065
215 -0.178576727
216 -0.130585948
217 0.117977409
218 0.891442620
219 0.299244186
220 0.135230456
221 -1.281324608
222 0.0579655602
223 0.173905636
224 -0.0261658609
225 -0.192931298
226 -1.290989667
227 -0.179009718
228 0.0176982563
229 -0.275838639
230 0.198855749
231 0.0408643058
232 0.0466644978