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

$R= 25.5713135417$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.794687081
4 0.5
5 -0.447213595
6 -0.561928624
7 1.798162437
8 -0.353553390
9 -0.368472442
10 0.316227766
11 -1.750067741
12 0.397343540
13 0.408821741
14 -1.271492853
15 -0.355394866
16 0.250000000
17 -1.595469287
18 0.260549362
19 -0.187359204
20 -0.223606797
21 1.428976459
22 1.237484767
23 0.330802981
24 -0.280964312
25 0.200000000
26 -0.289080625
27 -1.087507371
28 0.899081218
29 -0.427080532
30 0.251302120
31 -0.0885148128
32 -0.176776695
33 -1.390756226
34 1.128167152
35 -0.804162688
36 -0.184236221
37 1.140031364
38 0.132482963
39 0.324885356
40 0.158113883
41 -0.477125032
42 -1.010438944
43 1.267645163
44 -0.875033870
45 0.164785885
46 -0.233913031
47 1.005658074
48 0.198671770
49 2.233388151
50 -0.141421356
51 -1.267898831
52 0.204410870
53 0.558482576
54 0.768983836
55 0.782654087
56 -0.635746426
57 -0.148891939
58 0.301991540
59 0.729012038
60 -0.177697433
61 1.361132855
62 0.0625894244
63 -0.662573305
64 0.125000000
65 -0.182830640
66 0.983413158
67 -1.122628176
68 -0.797734643
69 0.262884855
70 0.568628890
71 1.042750880
72 0.130274681
73 -0.461254738
74 -0.806123908
75 0.158937416
76 -0.0936796020
77 -3.146906076
78 -0.229728638
79 -1.119180268
80 -0.111803398
81 -0.495755616
82 0.337378346
83 -0.102349480
84 0.714488229
85 0.713515556
86 -0.896360491
87 -0.339395381
88 0.618742383
89 0.0563024824
90 -0.116521217
91 0.735127898
92 0.165401490
93 -0.0703415783
94 -0.711107644
95 0.0837895833
96 -0.140482156
97 1.294550013
98 -1.579243906
99 0.644851735
100 0.100000000
101 1.510635352
102 0.896539861
103 -1.316099618
104 -0.144540312
105 -0.639057700
106 -0.394906816
107 -0.985092510
108 -0.543753685
109 0.782154485
110 -0.553420012
111 0.905968197
112 0.449540609
113 -1.697772464
114 0.105282499
115 -0.147939590
116 -0.213540266
117 -0.150639545
118 -0.515489356
119 -2.868912943
120 0.125651060
121 2.062737101
122 -0.962466272
123 -0.379165099
124 -0.0442574064
125 -0.0894427190
126 0.468510077
127 0.843679659
128 -0.0883883476
129 1.007381235
130 0.129280785
131 -0.313986967
132 -0.695378113
133 -0.336902282
134 0.793817996
135 0.486348081
136 0.564083576
137 1.787680783
138 -0.185887664
139 0.143106750
140 -0.402081344
141 0.799183479
142 -0.737336218
143 -0.715465739
144 -0.0921181106
145 0.190996220
146 0.326156353
147 1.774844701
148 0.570015682
149 0.104892234
150 -0.112385724
151 1.564073361
152 0.0662414818
153 0.587886428
154 2.225198626
155 0.0395850277
156 0.162442678
157 -1.890424548
158 0.791379956
159 0.443818732
160 0.0790569415
161 0.594837303
162 0.350552158
163 1.602057015
164 -0.238562516
165 0.621965092
166 0.0723720120
167 0.207760283
168 -0.505219472
169 -0.832865131
170 -0.504531688
171 0.0690365357
172 0.633822581
173 -0.156439676
174 0.239988775
175 0.359632487
176 -0.437516935
177 0.579335490
178 -0.0398118671
179 0.941822955
180 0.0823929429
181 1.342669757
182 -0.519813922
183 1.081651553
184 -0.116956515
185 -0.509837525
186 0.0497390070
187 2.792191140
188 0.502829037
189 -1.955513513
190 -0.0592481825
191 -0.803516419
192 0.0993358851
193 0.138082154
194 -0.915385093
195 -0.145293148
196 1.116694075
197 0.453702451
198 -0.455979035
199 0.781893563
200 -0.0707106781
201 -0.890886555
202 -1.068180501
203 -0.769784220
204 -0.633949415
205 0.213376801
206 0.930622965
207 -0.115951554
208 0.102205435
209 0.332413373
210 0.451882033
211 1.168409833
212 0.279241288
213 0.834857623
214 0.696565594
215 -0.566908151
216 0.384491918
217 -0.158975608
218 -0.553066740
219 -0.381013817
220 0.391327043
221 -0.658846509
222 -0.640616255