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

$R= 25.759928588$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.120715401
4 0.5
5 -0.447213595
6 0.792465460
7 1.440466612
8 0.353553390
9 0.256003011
10 -0.316227766
11 1.144545430
12 0.560357700
13 1.361356913
14 1.018563709
15 -0.501199164
16 0.250000000
17 0.912915795
18 0.181021465
19 -1.121690746
20 -0.223606797
21 1.614353117
22 0.809315835
23 1.449541481
24 0.396232730
25 0.200000000
26 0.962624705
27 -0.833808883
28 0.720233306
29 0.124316968
30 -0.354401327
31 -0.764694112
32 0.176776695
33 1.282709691
34 0.645528949
35 -0.644196252
36 0.128001505
37 -0.705354750
38 -0.793155133
39 1.525693660
40 -0.158113883
41 -1.644298029
42 1.141520036
43 -1.060639040
44 0.572272715
45 -0.114488027
46 1.024980611
47 0.752390315
48 0.280178850
49 1.074944060
50 0.141421356
51 1.023118792
52 0.680678456
53 1.169473565
54 -0.589591915
55 -0.511856277
56 0.509281854
57 -1.257096095
58 0.0879053714
59 0.881948628
60 -0.250599582
61 -0.433559800
62 -0.540720392
63 0.368763790
64 0.125000000
65 -0.608817320
66 0.907012721
67 1.540086414
68 0.456457897
69 1.624523463
70 -0.455515538
71 0.492043598
72 0.0905107327
73 -1.225344157
74 -0.498761126
75 0.224143080
76 -0.560845373
77 1.648679478
78 1.078828333
79 0.359147881
80 -0.111803398
81 -1.190465469
82 -1.162694286
83 1.905781738
84 0.807176558
85 -0.408268355
86 -0.749985057
87 0.139323941
88 0.404657917
89 -0.599856980
90 -0.0809552604
91 1.960989181
92 0.724770740
93 -0.857004468
94 0.532020293
95 0.501635351
96 0.198116365
97 -0.185324290
98 0.760100234
99 0.293007076
100 0.100000000
101 1.021317600
102 0.723454236
103 -1.335371267
104 0.481312352
105 -0.721960662
106 0.826942688
107 -1.105066151
108 -0.416904441
109 -0.0588729760
110 -0.361937044
111 -0.790501932
112 0.360116653
113 -1.054949132
114 -0.888901173
115 -0.648254657
116 0.0621584842
117 0.348511469
118 0.623631855
119 1.315024723
120 -0.177200663
121 0.309984241
122 -0.306573075
123 -1.842790126
124 -0.382347056
125 -0.0894427190
126 0.260755377
127 0.784638975
128 0.0883883476
129 -1.188674507
130 -0.430498855
131 -0.712193059
132 0.641354845
133 -1.615758071
134 1.089005547
135 0.372890668
136 0.322764474
137 1.369797451
138 1.148711557
139 0.545871231
140 -0.322098126
141 0.843215419
142 0.347927364
143 1.558134846
144 0.0640007528
145 -0.0555962384
146 -0.866449163
147 1.204706368
148 -0.352677375
149 1.374475722
150 0.158493092
151 -1.411029095
152 -0.396577566
153 0.233709258
154 1.165792439
155 0.341981603
156 0.762846830
157 0.262277804
158 0.253955902
159 1.310646737
160 -0.0790569415
161 2.088016087
162 -0.841786206
163 -0.159754145
164 -0.822149014
165 -0.573645213
166 1.347591190
167 0.829594532
168 0.570760018
169 0.853293341
170 -0.288689322
171 -0.287155237
172 -0.530319520
173 1.630125331
174 0.0985169036
175 0.288093322
176 0.286136357
177 0.988418799
178 -0.424162938
179 -1.272254264
180 -0.0572440136
181 0.101381316
182 1.386628748
183 -0.485904758
184 0.512490305
185 0.315444233
186 -0.605993671
187 1.044887625
188 0.376195157
189 -1.201034574
190 0.354709758
191 -1.285015705
192 0.140089425
193 0.571619490
194 -0.131044062
195 -0.682310947
196 0.537472030
197 -0.442143891
198 0.207187291
199 0.204881963
200 0.0707106781
201 1.725812274
202 0.722180601
203 0.178982155
204 0.511559396
205 0.735352433
206 -0.944250078
207 0.371636069
208 0.340339228
209 -1.283402470
210 -0.510503280
211 0.00181980515
212 0.584736782
213 0.542213021
214 -0.781399769
215 0.474332198
216 -0.294795957
217 -1.083251440
218 -0.0416294806
219 -1.482534944
220 -0.255928138
221 1.308920508
222 -0.558969276