Properties

Level 10
Symmetry even
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

$R= 26.8887649597$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.915110413
4 0.5
5 0.447213595
6 0.647080778
7 -1.778204906
8 -0.353553390
9 -0.162572931
10 -0.316227766
11 0.431231943
12 -0.457555206
13 -0.677231312
14 1.257380747
15 -0.409249818
16 0.250000000
17 -0.143055447
18 0.114956422
19 -1.138876176
20 0.223606797
21 1.627253826
22 -0.304927031
23 1.680612992
24 0.323540389
25 0.200000000
26 0.478874853
27 1.063882595
28 -0.889102453
29 -0.472406027
30 0.289383321
31 0.148603529
32 -0.176776695
33 -0.394624842
34 0.101155476
35 -0.795237409
36 -0.0812864659
37 0.355859929
38 0.805307067
39 0.619741426
40 -0.158113883
41 -1.656757572
42 -1.150642215
43 -1.453132969
44 0.215615971
45 -0.0727048253
46 -1.188372843
47 0.596327388
48 -0.228777603
49 2.162012688
50 -0.141421356
51 0.130911529
52 -0.338615656
53 1.107281301
54 -0.752278597
55 0.192852788
56 0.628690373
57 1.042197448
58 0.334041505
59 -0.386581753
60 -0.204624909
61 0.0521186879
62 -0.105078563
63 0.289087984
64 0.125000000
65 -0.302867050
66 0.279041901
67 1.356551003
68 -0.0715277236
69 -1.537946449
70 0.562317765
71 -0.241706260
72 0.0574782112
73 1.947254322
74 -0.251630969
75 -0.183022082
76 -0.569438088
77 -0.766818757
78 -0.438223365
79 0.682470305
80 0.111803398
81 -0.810997110
82 1.171504514
83 1.018816206
84 0.813626913
85 -0.0639763409
86 1.027520176
87 0.432303675
88 -0.152463515
89 0.621357213
90 0.0514100750
91 1.204256043
92 0.840306496
93 -0.135988636
94 -0.421667140
95 -0.509320909
96 0.161770194
97 1.144999665
98 -1.528773833
99 -0.0701066413
100 0.100000000
101 -0.347427297
102 -0.0925684302
103 0.751678141
104 0.239437426
105 0.727730034
106 -0.782966117
107 -1.672220837
108 0.531941297
109 -0.334887248
110 -0.136367514
111 -0.325651127
112 -0.444551226
113 1.016616013
114 -0.736944882
115 0.751592978
116 -0.236203013
117 0.110099480
118 0.273354579
119 0.254381898
120 0.144691660
121 -0.814039010
122 -0.0368534777
123 1.516116106
124 0.0743017645
125 0.0894427190
126 -0.204416074
127 1.858261579
128 -0.0883883476
129 1.329777112
130 0.214159345
131 -1.429874684
132 -0.197312421
133 2.025155203
134 -0.959226413
135 0.475782760
136 0.0505777384
137 0.380066897
138 1.087492363
139 -0.822092671
140 -0.397618704
141 -0.545705403
142 0.170912136
143 -0.292043774
144 -0.0406432329
145 -0.211266398
146 -1.376916736
147 -1.978480323
148 0.177929964
149 1.642842512
150 0.129416155
151 0.438780489
152 0.402653533
153 0.0232569385
154 0.542222743
155 0.0664575185
156 0.309870713
157 -0.969951138
158 -0.482579381
159 -1.013284662
160 -0.0790569415
161 -2.988474262
162 0.573461556
163 -1.717318387
164 -0.828378786
165 -0.176481594
166 -0.720411848
167 0.824192445
168 -0.575321107
169 -0.541357888
170 0.0452381045
171 0.185150368
172 -0.726566484
173 0.216857978
174 -0.305684860
175 -0.355640981
176 0.107807985
177 0.353764986
178 -0.439365899
179 0.283520006
180 -0.0363524126
181 -0.647158124
182 -0.851537614
183 -0.0476938040
184 -0.594186421
185 0.159145398
186 0.0961584873
187 -0.0616910554
188 0.298163694
189 -1.891797662
190 0.360144268
191 -1.141998782
192 -0.114388801
193 -0.452352138
194 -0.809637027
195 0.277156791
196 1.081006344
197 -1.577404131
198 0.0495728815
199 1.266801129
200 -0.0707106781
201 -1.241325300
202 0.245668197
203 0.840138636
204 0.0654557647
205 -0.740924510
206 -0.531516711
207 -0.273798284
208 -0.169307828
209 -0.491266639
210 -0.514582842
211 1.835633128
212 0.553640650
213 0.220515006
214 1.182438693
215 -0.649860820
216 -0.376139298
217 -0.258533042
218 0.236801044
219 -1.779474054
220 0.0964263940
221 0.0980754570
222 0.230270120
223 0.0212591702
224 0.314345186
225 -0.0325145863
226 -0.718856076
227 -1.147476638
228 0.521098724
229 0.0224652684
230 -0.531456492
231 0.716950153
232 0.167020752