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

$R= 28.1082072398$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.210630706
4 0.5
5 0.447213595
6 0.856045182
7 1.931135780
8 -0.353553390
9 0.465626708
10 -0.316227766
11 -0.107920935
12 -0.605315353
13 0.249271772
14 -1.365519205
15 -0.541410511
16 0.250000000
17 -0.363848668
18 -0.329247803
19 0.567650880
20 0.223606797
21 -2.337892275
22 0.0763116250
23 1.370926499
24 0.428022591
25 0.200000000
26 -0.176261761
27 0.646928715
28 0.965567890
29 0.934026322
30 0.382835043
31 1.169981413
32 -0.176776695
33 0.130652397
34 0.257279861
35 0.863630175
36 0.232813354
37 0.861168602
38 -0.401389786
39 -0.301776062
40 -0.158113883
41 -1.352654812
42 1.653139481
43 0.741941013
44 -0.0539604675
45 0.208234594
46 -0.969391424
47 1.720816090
48 -0.302657676
49 2.729285403
50 -0.141421356
51 0.440486371
52 0.124635886
53 -0.423778064
54 -0.457447681
55 -0.0482637094
56 -0.682759602
57 -0.687215586
58 -0.660456346
59 -1.297818265
60 -0.270705255
61 -0.751875663
62 -0.827301791
63 0.899188397
64 0.125000000
65 0.111477725
66 -0.0923851965
67 0.693389792
68 -0.181924334
69 -1.659685716
70 -0.610678753
71 1.674291975
72 -0.164623901
73 -1.140557321
74 -0.608938158
75 -0.242126141
76 0.283825440
77 -0.208409979
78 0.213387900
79 0.480225564
80 0.111803398
81 -1.248818476
82 0.956471390
83 1.103789939
84 -1.168946137
85 -0.162718071
86 -0.524631522
87 -1.130760946
88 0.0381558125
89 0.550455717
90 -0.147244093
91 0.481377639
92 0.685463249
93 -1.416415426
94 -1.216800726
95 0.253861191
96 0.214011295
97 -0.401295693
98 -1.929896216
99 -0.0502508697
100 0.100000000
101 0.0482336134
102 -0.311470900
103 -0.787012033
104 -0.0881308805
105 -1.045537210
106 0.299656343
107 -0.946905070
108 0.323464357
109 1.715165887
110 0.0341275962
111 -1.042557153
112 0.482783945
113 -0.256691076
114 0.485934801
115 0.613096968
116 0.467013161
117 0.116067595
118 0.917696096
119 -0.702641183
120 0.191417521
121 -0.988353071
122 0.531656380
123 1.637565452
124 0.584990706
125 0.0894427190
126 -0.635822213
127 -1.066535367
128 -0.0883883476
129 -0.898216574
130 -0.0788266559
131 -1.546999432
132 0.0653261989
133 1.096210925
134 -0.490300624
135 0.289315316
136 0.128639930
137 -0.892766913
138 1.173575025
139 1.000128866
140 0.431815087
141 -2.083272800
142 -1.183903209
143 -0.0269016441
144 0.116406677
145 0.417709269
146 0.806495816
147 -3.304156720
148 0.430584301
149 -1.575317620
150 0.171209036
151 -0.498814803
152 -0.200694893
153 -0.169417655
154 0.147368109
155 0.523231594
156 -0.150888031
157 1.608697922
158 -0.339570753
159 0.513038690
160 -0.0790569415
161 2.647445204
162 0.883048013
163 0.368851279
164 -0.676327406
165 0.0584295286
166 -0.780497351
167 -1.342234982
168 0.826569740
169 -0.937863611
170 0.115059051
171 0.264313211
172 0.370970506
173 1.246121749
174 0.799568733
175 0.386227156
176 -0.0269802337
177 1.571178959
178 -0.389230970
179 0.680254093
180 0.104117297
181 0.0682075612
182 -0.340385393
183 0.910241271
184 -0.484695712
185 0.385126306
186 1.001556952
187 0.0392665139
188 0.860408045
189 1.249308570
190 -0.179506969
191 1.399592203
192 -0.151328838
193 0.517167231
194 0.283758905
195 -0.134958358
196 1.364642701
197 -1.572599097
198 0.0355327307
199 0.779436016
200 -0.0707106781
201 -0.839346998
202 -0.0341063151
203 1.803780705
204 0.220243185
205 -0.604925622
206 0.556501545
207 0.637857574
208 0.0623179432
209 -0.0614335637
210 0.739306451
211 -0.320858312
212 -0.211889032
213 -2.026696124
214 0.669562996
215 0.331806108
216 -0.228723840
217 2.258763904
218 -1.212805429
219 1.391806646
220 -0.0241318547
221 -0.0777052355
222 0.737199233
223 1.244050446
224 -0.341379801
225 0.0931253417
226 0.181508000
227 0.421447830
228 -0.343607793