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

$R= 25.2414671674$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.157760967
4 0.5
5 0.447213595
6 -0.818660631
7 0.671707952
8 0.353553390
9 0.340410458
10 0.316227766
11 1.860610459
12 -0.578880483
13 -1.088383077
14 0.474969248
15 -0.517766445
16 0.250000000
17 -1.247051674
18 0.240706543
19 -1.577930627
20 0.223606797
21 -0.777677249
22 1.315650273
23 -0.260886211
24 -0.409330315
25 0.200000000
26 -0.769603054
27 0.763647026
28 0.335853976
29 0.241284454
30 -0.366116164
31 1.584391473
32 0.176776695
33 -2.154142166
34 -0.881798695
35 0.300396928
36 0.170205229
37 -0.937306825
38 -1.115765446
39 1.260087444
40 0.158113883
41 -1.116361084
42 -0.549900856
43 0.526882548
44 0.930305229
45 0.152236184
46 -0.184474409
47 0.489511000
48 -0.289440241
49 -0.548808425
50 0.141421356
51 1.443787753
52 -0.544191538
53 1.866570305
54 0.539979990
55 0.832090293
56 0.237484624
57 1.826866489
58 0.170613873
59 -0.619919594
60 -0.258883222
61 -1.580906329
62 1.120333954
63 0.228656412
64 0.125000000
65 -0.486739709
66 -1.523208533
67 0.347856722
68 -0.623525837
69 0.302043872
70 0.212412705
71 -0.376585848
72 0.120353271
73 0.240761624
74 -0.662776012
75 -0.231552193
76 -0.788965313
77 1.249786843
78 0.891016376
79 -0.384208181
80 0.111803398
81 -1.224531178
82 -0.789386492
83 -0.139218817
84 -0.388838624
85 -0.557698463
86 0.372562222
87 -0.279349723
88 0.657825136
89 0.0710160615
90 0.107647238
91 -0.731075568
92 -0.130443105
93 -1.834346604
94 0.346136548
95 -0.705672029
96 -0.204665157
97 -0.739563001
98 -0.388066159
99 0.633371259
100 0.100000000
101 -0.522236814
102 1.020912111
103 1.618118719
104 -0.384801527
105 -0.347787838
106 1.319864520
107 0.740398573
108 0.381823513
109 -0.822329416
110 0.588376689
111 1.085177257
112 0.167926988
113 -1.929185849
114 1.291789683
115 -0.116671860
116 0.120642227
117 -0.370496982
118 -0.438349348
119 -0.837654527
120 -0.183058082
121 2.461871284
122 -1.117869585
123 1.292479289
124 0.792195736
125 0.0894427190
126 0.161684499
127 -0.129818353
128 0.0883883476
129 -0.610004049
130 -0.344176949
131 -1.082756527
132 -1.077071083
133 -1.059908551
134 0.245971847
135 0.341513332
136 -0.440899347
137 -0.668957984
138 0.213577270
139 -0.766179961
140 0.150198464
141 -0.566736732
142 -0.266286407
143 -2.025056939
144 0.0851026145
145 0.107905688
146 0.170244177
147 0.635388979
148 -0.468653412
149 -1.800769994
150 -0.163732126
151 -0.371611433
152 -0.557882723
153 -0.424509378
154 0.883732751
155 0.708561407
156 0.630043722
157 -0.559894073
158 -0.271676210
159 -2.161042374
160 0.0790569415
161 -0.175239220
162 -0.865874299
163 0.141771677
164 -0.558180542
165 -0.963361663
166 -0.0984425701
167 -0.103105749
168 -0.274950428
169 0.184577197
170 -0.394352365
171 -0.537141948
172 0.263441274
173 -0.785165238
174 -0.197530083
175 0.134341590
176 0.465152614
177 0.717714145
178 0.0502159386
179 0.594324246
180 0.0761180924
181 -0.680851041
182 -0.516948492
183 1.830303362
184 -0.0922372046
185 -0.419176355
186 -1.297078923
187 -2.320349110
188 0.244755500
189 0.512923387
190 -0.498985477
191 1.320703232
192 -0.144720120
193 0.316902550
194 -0.522950013
195 0.563528236
196 -0.274404212
197 -0.587255073
198 0.447861112
199 -0.402270948
200 0.0707106781
201 -0.403650168
202 -0.369277192
203 0.162013534
204 0.721893876
205 -0.499251854
206 1.144182719
207 -0.0890042914
208 -0.272095769
209 -2.932352446
210 -0.245923139
211 0.403233727
212 0.933285152
213 0.466510526
214 0.523540852
215 0.235629038
216 0.269989995
217 1.066147414
218 -0.581474706
219 -0.296858132
220 0.416045146
221 1.387082355
222 0.767336197