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

$R= 23.6178443809$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.107082633
4 0.5
5 -0.447213595
6 0.0757188565
7 -1.860505461
8 -0.353553390
9 -0.988533309
10 0.316227766
11 0.383613160
12 -0.0535413168
13 -1.561609804
14 1.315576028
15 0.0478888096
16 0.250000000
17 1.192318527
18 0.698998606
19 1.196147820
20 -0.223606797
21 0.199227824
22 -0.271255466
23 1.274990481
24 0.0378594282
25 0.200000000
26 1.104224882
27 0.212937384
28 -0.930252730
29 0.114787184
30 -0.0338625020
31 -0.261505154
32 -0.176776695
33 -0.0410783075
34 -0.843096515
35 0.832043336
36 -0.494266654
37 0.754995881
38 -0.845804235
39 0.167221290
40 0.158113883
41 -0.292881290
42 -0.140875346
43 0.757477617
44 0.191806580
45 0.442085535
46 -0.901554415
47 -1.567525051
48 -0.0267706584
49 2.461480571
50 -0.141421356
51 -0.127676608
52 -0.780804902
53 -1.515676733
54 -0.150569468
55 -0.171557020
56 0.657788014
57 -0.128086659
58 -0.0811667966
59 1.029344738
60 0.0239444048
61 0.828792800
62 0.184912067
63 1.839171620
64 0.125000000
65 0.698373135
66 0.0290467498
67 -0.303780238
68 0.596159263
69 -0.136529338
70 -0.588343485
71 -0.460341796
72 0.349499303
73 1.354839078
74 -0.533862707
75 -0.0214165267
76 0.598073910
77 -0.713714379
78 -0.118243308
79 -0.667295787
80 -0.111803398
81 0.965731413
82 0.207098346
83 -0.997208760
84 0.0996139124
85 -0.533221055
86 -0.535617559
87 -0.0122917140
88 -0.135627733
89 0.494488000
90 -0.312601680
91 2.905383570
92 0.637495240
93 0.0280026606
94 1.108407593
95 -0.534933567
96 0.0189297141
97 1.849355644
98 -1.740529603
99 -0.379214386
100 0.100000000
101 0.789558756
102 0.0902809954
103 -0.709051429
104 0.552112441
105 -0.0890973919
106 1.071745296
107 -1.463262447
108 0.106468692
109 -0.0496812123
110 0.121309132
111 -0.0808469474
112 -0.465126365
113 0.0488894775
114 0.0905709451
115 -0.570193077
116 0.0573935923
117 1.543703308
118 -0.727856644
119 -2.218315130
120 -0.0169312510
121 -0.852840943
122 -0.586045009
123 0.0313624999
124 -0.130752577
125 -0.0894427190
126 -1.300490724
127 -1.099360358
128 -0.0883883476
129 -0.0811126991
130 -0.493824379
131 1.099333842
132 -0.0205391537
133 -2.225439545
134 0.214805066
135 -0.0952284931
136 -0.421548257
137 -1.088329850
138 0.0965408213
139 -0.0362067922
140 0.416021668
141 0.167854705
142 0.325510806
143 -0.599054091
144 -0.247133327
145 -0.0513343895
146 -0.958015899
147 -0.263581837
148 0.377497940
149 -1.291082213
150 0.0151437713
151 0.498775357
152 -0.422902117
153 -1.178646710
154 0.504672277
155 0.116948660
156 0.0836106454
157 -0.517124332
158 0.471849376
159 0.162302156
160 0.0790569415
161 -2.372126773
162 -0.682875231
163 0.0910719767
164 -0.146440645
165 0.0183707776
166 0.705133076
167 1.577285363
168 -0.0704376730
169 1.438628649
170 0.377044224
171 -1.182430040
172 0.378738808
173 -0.768361988
174 0.00869155436
175 -0.372101092
176 0.0959032900
177 -0.110286867
178 -0.349655818
179 0.734522515
180 0.221042767
181 0.328093616
182 -2.054416424
183 -0.0886297434
184 -0.450777207
185 -0.337644422
186 -0.0198008712
187 0.457424986
188 -0.783762525
189 -0.396686770
190 0.378255153
191 0.680103479
192 -0.0133853292
193 -0.0259809199
194 -1.307691916
195 -0.0747836347
196 1.230740285
197 1.678730421
198 0.268145064
199 1.049579420
200 -0.0707106781
201 0.0255113481
202 -0.558302350
203 -0.213638868
204 -0.0638383041
205 0.130980494
206 0.501375073
207 -1.239582070
208 -0.390402451
209 0.514843486
210 0.0630013700
211 -0.769137400
212 -0.757838366
213 0.00790819923
214 1.034682799
215 -0.338754288
216 -0.0752847341
217 0.448900490
218 0.0351299221