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

$R= 28.1553130021$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.984265533
4 0.5
5 -0.447213595
6 0.695980833
7 -0.423643941
8 -0.353553390
9 -0.0312213590
10 0.316227766
11 -1.197746094
12 -0.492132766
13 -0.709079391
14 0.299561503
15 0.440176928
16 0.250000000
17 1.563536677
18 0.0220768346
19 -0.734980319
20 -0.223606797
21 0.416978129
22 0.846934385
23 -0.327877780
24 0.347990416
25 0.200000000
26 0.501394846
27 1.014995641
28 -0.211821970
29 -1.840298811
30 -0.311252090
31 0.399986391
32 -0.176776695
33 1.178900198
34 -1.105587387
35 0.189459330
36 -0.0156106795
37 -0.225064218
38 0.519709567
39 0.697922405
40 0.158113883
41 0.148445777
42 -0.294848063
43 0.437242374
44 -0.598873047
45 0.0139626162
46 0.231844601
47 -1.128181141
48 -0.246066383
49 -0.820525811
50 -0.141421356
51 -1.538935262
52 -0.354539695
53 1.562774496
54 -0.717710300
55 0.535648337
56 0.149780751
57 0.723415796
58 1.301287768
59 0.796642033
60 0.220088464
61 0.804162646
62 -0.282833090
63 0.0132267395
64 0.125000000
65 0.317109944
66 -0.833608324
67 -1.061500998
68 0.781768338
69 0.322718798
70 -0.133967977
71 1.491836912
72 0.0110384173
73 -0.116718806
74 0.159144435
75 -0.196853106
76 -0.367490159
77 0.507417875
78 -0.493505665
79 1.497239745
80 -0.111803398
81 -0.967803867
82 -0.104967015
83 0.271218184
84 0.208489064
85 -0.699234859
86 -0.309177047
87 1.811342691
88 0.423467192
89 -0.145492922
90 -0.00987306061
91 0.300397188
92 -0.163938890
93 -0.393692819
94 0.797744535
95 0.328693191
96 0.173995208
97 0.583148276
98 0.580199365
99 0.0373952608
100 0.100000000
101 1.020612733
102 1.088191559
103 0.965427581
104 0.250697423
105 -0.186478288
106 -1.105048443
107 -0.998762885
108 0.507497820
109 1.622905190
110 -0.378760571
111 0.221522953
112 -0.105910985
113 -0.480775703
114 -0.511532215
115 0.146631401
116 -0.920149405
117 0.0221384222
118 -0.563310984
119 -0.662382840
120 -0.155626045
121 0.434595706
122 -0.568628860
123 -0.146110062
124 0.199993195
125 -0.0894427190
126 -0.00935271724
127 1.454575655
128 -0.0883883476
129 -0.430362598
130 -0.224230591
131 0.944460553
132 0.589450099
133 0.311369959
134 0.750594554
135 -0.453919850
136 -0.552793693
137 -0.949618727
138 -0.228196650
139 0.814311786
140 0.0947296650
141 1.110429813
142 -1.054887997
143 0.849297071
144 -0.00780533975
145 0.823006648
146 0.0825326597
147 0.807615275
148 -0.112532109
149 1.326867505
150 0.139196166
151 1.618703099
152 0.259854783
153 -0.0488157376
154 -0.358798620
155 -0.178879352
156 0.348961202
157 -1.719024048
158 -1.058708377
159 -1.538185069
160 0.0790569415
161 0.138903441
162 0.684340677
163 -0.585185232
164 0.0742228885
165 -0.527220196
166 -0.191780217
167 0.0372026651
168 -0.147424031
169 -0.497206430
170 0.494433710
171 0.0229471079
172 0.218621187
173 0.196150290
174 -1.280812700
175 -0.0847287882
176 -0.299436523
177 -0.784107453
178 0.102879032
179 -0.476220998
180 0.00698130810
181 -1.524919826
182 -0.212412888
183 -0.791509399
184 0.115922300
185 0.100651778
186 0.278382862
187 -1.872721361
188 -0.564090570
189 -0.429996890
190 -0.232421184
191 0.293711148
192 -0.123033191
193 -0.122448230
194 -0.412348100
195 -0.312120388
196 -0.410262905
197 -1.673751291
198 -0.0264424424
199 -0.248252146
200 -0.0707106781
201 1.044763783
202 -0.721682185
203 0.779631959
204 -0.769467631
205 -0.0663869697
206 -0.682660389
207 0.0103279562
208 -0.177269847
209 0.880228471
210 0.131860062
211 -0.674445015
212 0.781387248
213 -1.468699639
214 0.706232009
215 -0.195540734
216 -0.358855150
217 -0.169129076
218 -1.147567265
219 0.114493269
220 0.267824168
221 -1.108770763
222 -0.156640382
223 -1.441723082
224 0.0748903758
225 -0.00624427180
226 0.339959760
227 1.553520132
228 0.361707898
229 -1.093666578
230 -0.103684058
231 -0.496362553
232 0.650643884
233 -0.276822167
234 -0.0156542284
235 0.504537944
236 0.398321016
237 -1.511440554
238 0.468375397
239 -0.0535420428
240 0.110044232