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

$R= 27.1088850091$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.347960592
4 0.5
5 0.447213595
6 0.246045294
7 0.251312302
8 -0.353553390
9 -0.878923425
10 -0.316227766
11 -0.489474086
12 -0.173980296
13 -0.654679627
14 -0.177704633
15 -0.155612707
16 0.250000000
17 -1.447171201
18 0.621492714
19 -1.819878227
20 0.223606797
21 -0.0874467776
22 0.346110445
23 -1.630616085
24 0.123022647
25 0.200000000
26 0.462928404
27 0.653791308
28 0.125656151
29 -1.473002545
30 0.110034800
31 1.127894808
32 -0.176776695
33 0.170317693
34 1.023304570
35 0.112390278
36 -0.439461712
37 -1.444416331
38 1.286848235
39 0.227802711
40 -0.158113883
41 0.411227106
42 0.0618342094
43 1.366893372
44 -0.244737043
45 -0.393066505
46 1.153019691
47 1.260231866
48 -0.0869901481
49 -0.936842126
50 -0.141421356
51 0.503558549
52 -0.327339813
53 -1.496131709
54 -0.462300267
55 -0.218899466
56 -0.0888523165
57 0.633245906
58 1.041570088
59 -0.591656235
60 -0.0778063538
61 1.418186111
62 -0.797542067
63 -0.220884269
64 0.125000000
65 -0.292781630
66 -0.120432795
67 -0.309781500
68 -0.723585600
69 0.567390139
70 -0.0794719279
71 -0.205347934
72 0.310746357
73 0.567496190
74 1.021356583
75 -0.0695921185
76 -0.909939113
77 -0.123010859
78 -0.161080841
79 -0.749282450
80 0.111803398
81 0.651429814
82 -0.290781475
83 -0.665446631
84 -0.0437233888
85 -0.647194636
86 -0.966539572
87 0.512546838
88 0.173055222
89 -1.322823200
90 0.277939991
91 -0.164529044
92 -0.815308042
93 -0.392462945
94 -0.891118498
95 -0.813874285
96 0.0615113236
97 -0.341846106
98 0.662447420
99 0.430210240
100 0.100000000
101 -0.528193883
102 -0.356069664
103 0.157081382
104 0.231464202
105 -0.0391073878
106 1.057924877
107 0.629333859
108 0.326895654
109 -0.207075778
110 0.154785296
111 0.502599962
112 0.0628280755
113 0.667009583
114 -0.447772474
115 -0.729233682
116 -0.736501272
117 0.575413261
118 0.418364136
119 -0.363691926
120 0.0550174004
121 -0.760415118
122 -1.002809016
123 -0.143090827
124 0.563947404
125 0.0894427190
126 0.156188764
127 -1.191404803
128 -0.0883883476
129 -0.475625027
130 0.207027876
131 -0.498489294
132 0.0851588465
133 -0.457357787
134 0.219048599
135 0.292384361
136 0.511652285
137 -1.004645366
138 -0.401205415
139 -0.823803884
140 0.0561951391
141 -0.438511026
142 0.145202916
143 0.320448713
144 -0.219730856
145 -0.658746764
146 -0.401280404
147 0.325984140
148 -0.722208165
149 0.670337181
150 0.0492090589
151 1.547898672
152 0.643424117
153 1.271952667
154 0.0869818129
155 0.504409892
156 0.113901355
157 0.986896293
158 0.529822701
159 0.520594914
160 -0.0790569415
161 -0.409793855
162 -0.460630439
163 0.298697046
164 0.205613553
165 0.0761683879
166 0.470541825
167 -0.409946698
168 0.0309171047
169 -0.571394565
170 0.457635716
171 1.599534254
172 0.683446686
173 1.613895420
174 -0.362425345
175 0.0502624604
176 -0.122368521
177 0.205872752
178 0.935377255
179 1.731925041
180 -0.196533252
181 1.003059881
182 0.116339603
183 -0.493470813
184 0.576509845
185 -0.645962621
186 0.277513210
187 0.708359750
188 0.630115933
189 0.164302912
190 0.575496026
191 -0.144175753
192 -0.0434950740
193 -0.811636430
194 0.241721699
195 0.101876469
196 -0.468421063
197 0.239669970
198 -0.304204578
199 0.813664812
200 -0.0707106781
201 0.107927806
202 0.373489476
203 -0.370032805
204 0.251779274
205 0.183906352
206 -0.111073310
207 1.433168440
208 -0.163669906
209 0.890709301
210 0.0276530991
211 0.540419349
212 -0.748065854
213 0.0739386021
214 -0.445006239
215 0.611293299
216 -0.231150133
217 0.282071090
218 0.146424687
219 -0.200267077
220 -0.109449733
221 0.967396789
222 -0.355391841
223 0.722061484
224 -0.0444261582
225 -0.175784685
226 -0.471646999
227 -1.756806787
228 0.316622953