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

$R= 30.6967542171$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.307781802
4 0.5
5 -0.447213595
6 -0.924741380
7 -1.177173122
8 -0.353553390
9 0.710293242
10 0.316227766
11 -0.291955603
12 0.653890901
13 1.467967388
14 0.832387097
15 -0.584857801
16 0.250000000
17 -1.905828943
18 -0.502253168
19 0.968552669
20 -0.223606797
21 -1.539485587
22 0.206443786
23 0.0114167379
24 -0.462370690
25 0.200000000
26 -1.038009694
27 -0.378873225
28 -0.588586561
29 1.045050201
30 0.413556917
31 1.378443877
32 -0.176776695
33 -0.381814225
34 1.347624570
35 0.526447824
36 0.355146621
37 -0.951315924
38 -0.684870160
39 1.919781037
40 0.158113883
41 1.445830164
42 1.088580698
43 0.465524978
44 -0.145977801
45 -0.317652794
46 -0.00807285279
47 -0.326708461
48 0.326945450
49 0.385736559
50 -0.141421356
51 -2.492408411
52 0.733983694
53 0.531952324
54 0.267903826
55 0.130566515
56 0.416193548
57 1.266655555
58 -0.738962084
59 1.164156238
60 -0.292428900
61 -0.192220469
62 -0.974707013
63 -0.836138113
64 0.125000000
65 -0.656494973
66 0.269983427
67 -0.376875357
68 -0.952914471
69 0.0149306020
70 -0.372254826
71 0.256393691
72 -0.251126584
73 -1.427793791
74 0.672681941
75 0.261556360
76 0.484276334
77 0.343682289
78 -1.357490189
79 -0.921773135
80 -0.111803398
81 -1.205776752
82 -1.022356313
83 -1.913776487
84 -0.769742793
85 0.852312614
86 -0.329175868
87 1.366697636
88 0.103221893
89 -0.719612387
90 0.224614445
91 -1.728051753
92 0.00570836895
93 1.802703819
94 0.231017768
95 -0.433149921
96 -0.231185345
97 -0.506115795
98 -0.272756937
99 -0.207374092
100 0.100000000
101 1.946869890
102 1.762398889
103 -1.365397523
104 -0.519004847
105 0.688478884
106 -0.376147096
107 0.0559102967
108 -0.189436612
109 0.772933803
110 -0.0923244681
111 -1.244113654
112 -0.294293280
113 1.749455985
114 -0.895660732
115 -0.00510572040
116 0.522525100
117 1.042687316
118 -0.823182770
119 2.243490608
120 0.206778458
121 -0.914761925
122 0.135920397
123 1.890830378
124 0.689221938
125 -0.0894427190
126 0.591238930
127 -0.0308280495
128 -0.0883883476
129 0.608805095
130 0.464212047
131 -0.687235758
132 -0.190907112
133 -1.140154170
134 0.266491121
135 0.169437257
136 0.673812285
137 -0.777262961
138 -0.0105575299
139 -0.708073651
140 0.263223912
141 -0.427263381
142 -0.181297718
143 -0.428581304
144 0.177573310
145 -0.467360658
146 1.009602671
147 0.504459252
148 -0.475657962
149 0.195189726
150 -0.184948276
151 0.0382030125
152 -0.342435080
153 -1.353697419
154 -0.243020077
155 -0.616458842
156 0.959890518
157 -1.647125260
158 0.651792034
159 0.695677569
160 0.0790569415
161 -0.0134394806
162 0.852612918
163 -1.179293056
164 0.722915082
165 0.170752512
166 1.353244331
167 1.546126689
168 0.544290349
169 1.154928256
170 -0.602676029
171 0.687956418
172 0.232762489
173 -0.820239987
174 -0.966401166
175 -0.235434624
176 -0.0729889008
177 1.522462309
178 0.508842799
179 0.756863451
180 -0.158826397
181 -1.653310505
182 1.221917113
183 -0.251382344
184 -0.00403642639
185 0.425441414
186 -1.274704095
187 0.556417601
188 -0.163354230
189 0.445999713
190 0.306283246
191 0.195936128
192 0.163472725
193 -0.387242059
194 0.357877910
195 -0.858552180
196 0.192868279
197 -0.727529588
198 0.146635626
199 0.926472056
200 -0.0707106781
201 -0.492873215
202 -1.376644901
203 -1.230210534
204 -1.246204205
205 -0.646594906
206 0.965481848
207 0.00811628479
208 0.366991847
209 -0.282760683
210 -0.486828088
211 -0.527939801
212 0.265976162
213 0.335388392
214 -0.0395345499
215 -0.208189099
216 0.133951913
217 -1.622853748
218 -0.546546733
219 -1.867346711
220 0.0652832575
221 -2.797709416
222 0.879721201
223 -1.431157735
224 0.208096774
225 0.142058648
226 -1.237052190
227 0.730356845
228 0.633327777
229 0.488000020
230 0.00361028952
231 0.451671602
232 -0.369481042
233 1.225165345
234 -0.737291271
235 0.146108465
236 0.582078119
237 -1.211575745
238 -1.586387422
239 -0.423445831
240 -0.146214450
241 -0.737942157
242 0.646834360
243 -1.217968554
244 -0.0961102349
245 -0.172506633
246 -1.337018982
247 1.419231126
248 -0.487353506
249 -2.476861521
250 0.0632455532