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

$R= 27.7811733014$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.888933340
4 0.5
5 -0.447213595
6 1.335677574
7 1.425814481
8 0.353553390
9 2.568069165
10 -0.316227766
11 -0.547098872
12 0.944466670
13 0.196599775
14 1.008203088
15 -0.844756670
16 0.250000000
17 -1.081535606
18 1.815899121
19 0.126888675
20 -0.223606797
21 2.693268511
22 -0.386857322
23 -0.219799897
24 0.667838787
25 0.200000000
26 0.139017034
27 2.961978127
28 0.712907240
29 1.441137589
30 -0.597333170
31 1.500924758
32 0.176776695
33 -1.033433300
34 -0.764761161
35 -0.637643620
36 1.284034582
37 1.347272785
38 0.0897238431
39 0.371363871
40 -0.158113883
41 -1.506010654
42 1.904428428
43 -0.0135926709
44 -0.273549436
45 -1.148475445
46 -0.155421997
47 -1.335198916
48 0.472233335
49 1.032946935
50 0.141421356
51 -2.042948666
52 0.0982998879
53 1.286683829
54 2.094434819
55 0.244670053
56 0.504101544
57 0.239684250
58 1.019038161
59 -0.164983574
60 -0.422378335
61 1.775098679
62 1.061314074
63 3.661590205
64 0.125000000
65 -0.0879220926
66 -0.730747694
67 -0.199123675
68 -0.540767803
69 -0.415187354
70 -0.450882128
71 0.371573233
72 0.907949560
73 -1.219932980
74 0.952665722
75 0.377786668
76 0.0634443379
77 -0.780061495
78 0.262593911
79 0.660592310
80 -0.111803398
81 3.026910074
82 -1.064910346
83 -1.072189899
84 1.346634255
85 0.483677427
86 -0.00961146982
87 2.722212840
88 -0.193428661
89 -1.908060420
90 -0.812094775
91 0.280314807
92 -0.109899948
93 2.835146818
94 -0.944128208
95 -0.0567463409
96 0.333919393
97 0.454552645
98 0.730403782
99 -1.404987744
100 0.100000000
101 -0.598466689
102 -1.444582855
103 1.547057635
104 0.0695085173
105 -1.204466294
106 0.909822860
107 -0.0991633122
108 1.480989063
109 -1.178396402
110 0.173007854
111 2.544908483
112 0.356453620
113 0.911535744
114 0.169482358
115 0.0982975023
116 0.720568794
117 0.504881822
118 -0.116661004
119 -1.542069129
120 -0.298666585
121 -0.700682823
122 1.255184313
123 -2.844753736
124 0.750462379
125 -0.0894427190
126 2.589135264
127 -0.868701401
128 0.0883883476
129 -0.0256756495
130 -0.0621703079
131 0.497730000
132 -0.516716650
133 0.180919711
134 -0.140801701
135 -1.324636888
136 -0.382380580
137 -0.334157117
138 -0.293581793
139 0.130801624
140 -0.318821810
141 -2.522101750
142 0.262741952
143 -0.107559517
144 0.642017291
145 -0.644496322
146 -0.862622883
147 1.951167904
148 0.673636392
149 -0.633430394
150 0.267135514
151 1.387941803
152 0.0448619215
153 -2.777458238
154 -0.551586772
155 -0.671233957
156 0.185681935
157 0.503986685
158 0.467109302
159 2.430459989
160 -0.0790569415
161 -0.313393851
162 2.140348639
163 -0.161749497
164 -0.753005327
165 0.462165422
166 -0.758152748
167 1.457227012
168 0.952214214
169 -0.961348560
170 0.342011588
171 0.325858672
172 -0.00679633548
173 0.819182699
174 1.924895159
175 0.285162896
176 -0.136774718
177 -0.311642950
178 -1.349202462
179 0.357965528
180 -0.574237722
181 -0.632228707
182 0.198212501
183 3.353042548
184 -0.0777109989
185 -0.602518706
186 2.004751541
187 0.591705454
188 -0.667599458
189 4.223220037
190 -0.0401257224
191 -1.044232956
192 0.236116667
193 0.311596804
194 0.321417257
195 -0.166078972
196 0.516473467
197 -0.526073452
198 -0.993476361
199 -0.292623532
200 0.0707106781
201 -0.376230961
202 -0.423179854
203 2.054978918
204 -1.021474333
205 0.673508439
206 1.093934944
207 -0.564085164
208 0.0491499439
209 -0.0705939401
210 -0.851686284
211 0.909063512
212 0.643341914
213 0.701550453
214 -0.0701190505
215 0.00607882725
216 1.047217409
217 2.144135897
218 -0.833252087
219 -2.297503915
220 0.122335026
221 -0.203742847
222 1.799522046
223 -0.452804129
224 0.252050772
225 0.513613833
226 0.644553105
227 -0.522147582
228 0.119842125