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

$R= 23.9699254626$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.867591225
4 0.5
5 0.447213595
6 0.613479638
7 -0.746073291
8 -0.353553390
9 -0.247285465
10 -0.316227766
11 0.627046933
12 -0.433795612
13 -0.309226096
14 0.527553483
15 -0.387998591
16 0.250000000
17 0.940237465
18 0.174857229
19 0.422782211
20 0.223606797
21 0.647286640
22 -0.443389138
23 -1.631658077
24 0.306739819
25 0.200000000
26 0.218655869
27 1.082133925
28 -0.373036645
29 -1.213950832
30 0.274356434
31 -1.192982253
32 -0.176776695
33 -0.544020416
34 -0.664848287
35 -0.333654119
36 -0.123642732
37 1.012364577
38 -0.298952168
39 0.268281848
40 -0.158113883
41 0.532449102
42 -0.457700773
43 0.393535990
44 0.313523466
45 -0.110589422
46 1.153756490
47 1.546563649
48 -0.216897806
49 -0.443374643
50 -0.141421356
51 -0.815741774
52 -0.154613048
53 0.542698376
54 -0.765184236
55 0.280423913
56 0.263776741
57 -0.366802136
58 0.858392865
59 0.849838735
60 -0.193999295
61 -0.820362758
62 0.843565840
63 0.184493081
64 0.125000000
65 -0.138290114
66 0.384680525
67 1.574249603
68 0.470118732
69 1.415612230
70 0.235929090
71 0.440629694
72 0.0874286149
73 -0.148278747
74 -0.715849857
75 -0.173518245
76 0.211391105
77 -0.467822969
78 -0.189703914
79 -0.208677963
80 0.111803398
81 -0.691564432
82 -0.376498371
83 -0.178905326
84 0.323643320
85 0.420486977
86 -0.278271967
87 1.053213090
88 -0.221694569
89 0.677831363
90 0.0781985304
91 0.230705331
92 -0.815829038
93 1.035020934
94 -1.093585643
95 0.189073952
96 0.153369909
97 1.274361949
98 0.313513217
99 -0.155059593
100 0.100000000
101 -0.469036374
102 0.576816540
103 1.719861100
104 0.109327934
105 0.289475386
106 -0.383745702
107 -0.500370408
108 0.541066962
109 1.608027269
110 -0.198289650
111 -0.878318623
112 -0.186518322
113 -0.927413883
114 0.259368278
115 -0.729699675
116 -0.606975416
117 0.0764671196
118 -0.600926733
119 -0.701486060
120 0.137178217
121 -0.606812143
122 0.580084069
123 -0.461948169
124 -0.596491126
125 0.0894427190
126 -0.130456309
127 -0.733585774
128 -0.0883883476
129 -0.341428372
130 0.0977858777
131 -0.750489619
132 -0.272010208
133 -0.315426516
134 -1.113162570
135 0.483945003
136 -0.332424143
137 -0.503391166
138 -1.000989007
139 0.229541434
140 -0.166827059
141 -1.341785057
142 -0.311572245
143 -0.193899269
144 -0.0618213664
145 -0.542895316
146 0.104848907
147 0.384667967
148 0.506182288
149 -1.148894347
150 0.122695927
151 -1.316810419
152 -0.149476084
153 -0.232507071
154 0.330800793
155 -0.533517882
156 0.134140924
157 -0.487882384
158 0.147557603
159 -0.470840326
160 -0.0790569415
161 1.217337193
162 0.489009899
163 1.021622066
164 0.266224551
165 -0.243293326
166 0.126505169
167 -1.900935026
168 -0.228850386
169 -0.904381723
170 -0.297329193
171 -0.104548337
172 0.196767995
173 -1.024389407
174 -0.744734118
175 -0.149214658
176 0.156761733
177 -0.737318489
178 -0.479299153
179 1.391993788
180 -0.0552947111
181 1.216697723
182 -0.163133304
183 0.711730456
184 0.576878245
185 0.452743202
186 -0.731870321
187 0.589578245
188 0.773281824
189 -0.807149573
190 -0.133695474
191 -0.111690459
192 -0.108448903
193 0.172672054
194 -0.901109976
195 0.119979289
196 -0.221687321
197 1.146021723
198 0.109643689
199 -1.812613766
200 -0.0707106781
201 -1.368225821
202 0.331658800
203 0.906645639
204 -0.407870887
205 0.238118477
206 -1.216125446
207 0.408177055
208 -0.0773065241
209 0.271223274
210 -0.204690008
211 1.379114201
212 0.271349188
213 -0.371115407
214 0.353815309
215 0.175994645
216 -0.382592118
217 0.853937800
218 -1.137046986
219 0.205258145
220 0.140211956