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

$R= 31.9875849983$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.072200765
4 0.5
5 -0.447213595
6 0.758160432
7 -0.181080411
8 0.353553390
9 0.149614481
10 -0.316227766
11 -1.728992675
12 0.536100382
13 -0.145308459
14 -0.128043186
15 -0.479502759
16 0.250000000
17 -0.196406340
18 0.105793414
19 0.456782629
20 -0.223606797
21 -0.194154555
22 -1.222582445
23 -1.320479047
24 0.379080216
25 0.200000000
26 -0.102748596
27 -0.911784003
28 -0.0905402055
29 1.502252390
30 -0.339059652
31 0.271183048
32 0.176776695
33 -1.853827270
34 -0.138880255
35 0.0809816217
36 0.0748072409
37 1.875246568
38 0.322994094
39 -0.155799841
40 -0.158113883
41 1.071639721
42 -0.137288002
43 0.606860290
44 -0.864496337
45 -0.0669096303
46 -0.933719689
47 0.690982965
48 0.268050191
49 -0.967209884
50 0.141421356
51 -0.210587029
52 -0.0726542296
53 0.504557627
54 -0.644728651
55 0.773229031
56 -0.0640215932
57 0.489762684
58 1.062252852
59 -0.541190958
60 -0.239751379
61 0.0153690225
62 0.191755372
63 -0.0270922518
64 0.125000000
65 0.0649839185
66 -1.310853834
67 -0.354533685
68 -0.0982031704
69 -1.415818646
70 0.0572626538
71 1.792708780
72 0.0528967073
73 1.393938036
74 1.325999565
75 0.214440153
76 0.228391314
77 0.313086704
78 -0.110167124
79 0.823550262
80 -0.111803398
81 -1.127229988
82 0.757763714
83 1.459145905
84 -0.0970772776
85 0.0878355858
86 0.429115026
87 1.610716162
88 -0.611291222
89 0.245439998
90 -0.0473122533
91 0.0263125155
92 -0.660239523
93 0.290762672
94 0.488598740
95 -0.204279401
96 0.189540108
97 0.0757798782
98 -0.683920668
99 -0.258682343
100 0.100000000
101 0.802297703
102 -0.148907516
103 -0.394451862
104 -0.0513742984
105 0.0868285567
106 0.356776119
107 -1.154907528
108 -0.455892001
109 -0.871177668
110 0.546755491
111 2.010640806
112 -0.0452701027
113 0.571735057
114 0.346314515
115 0.590536182
116 0.751126195
117 -0.0217402498
118 -0.382679796
119 0.0355653409
120 -0.169529826
121 1.989415672
122 0.0108675400
123 1.149012930
124 0.135591524
125 -0.0894427190
126 -0.0191571150
127 0.977029263
128 0.0883883476
129 0.650676067
130 0.0459505694
131 -0.805603344
132 -0.926913635
133 -0.0827143862
134 -0.250693172
135 0.407762202
136 -0.0694401277
137 -0.456012880
138 -1.001134965
139 -0.762764024
140 0.0404908108
141 0.740872464
142 1.267636535
143 0.251237262
144 0.0374036204
145 -0.671827692
146 0.985663038
147 -1.037043178
148 0.937623284
149 0.576940046
150 0.151632086
151 -0.0654726911
152 0.161497047
153 -0.0293852325
154 0.221385731
155 -0.121276746
156 -0.0778999206
157 -0.824383587
158 0.582337975
159 0.540987073
160 -0.0790569415
161 0.239112888
162 -0.797071968
163 1.233852746
164 0.535819860
165 0.829056759
166 1.031771964
167 0.967702321
168 -0.0686440013
169 -0.978885448
170 0.0621091384
171 0.0683412978
172 0.303430145
173 -1.718326671
174 1.138948321
175 -0.0362160822
176 -0.432248168
177 -0.580265339
178 0.173552287
179 -1.185314650
180 -0.0334548151
181 -1.460612032
182 0.0186057581
183 0.0164787103
184 -0.466859844
185 -0.838635760
186 0.205600257
187 0.339585123
188 0.345491482
189 0.165106241
190 -0.144447350
191 -1.277510079
192 0.134025095
193 0.171472248
194 0.0535844657
195 0.0696758072
196 -0.483604942
197 -1.098041993
198 -0.182916039
199 1.207974504
200 0.0707106781
201 -0.380131288
202 0.567310146
203 -0.272026080
204 -0.105293514
205 -0.479251853
206 -0.278919586
207 -0.197565172
208 -0.0363271148
209 -0.789773059
210 0.0613970613
211 0.405843278
212 0.252278813
213 1.922146115
214 -0.816642944
215 -0.271396172
216 -0.322364325
217 -0.0490926601
218 -0.616015637
219 1.494653523
220 0.386614515
221 0.0284248752
222 1.421737749
223 0.742336704
224 -0.0320107966
225 0.0299228963
226 0.404277736
227 1.366752014
228 0.244881342
229 1.587048405
230 0.417572139
231 0.335577875
232 0.531126426
233 -1.212348402
234 -0.0153726780
235 -0.309016976
236 -0.270595479
237 0.880211694
238 0.0251484937
239 0.372754430
240 -0.119875689
241 -0.567530974
242 1.406729312
243 -0.288011203
244 0.00768451128
245 0.432549410
246 0.812474834
247 -0.0936948485
248 0.0958776862
249 1.546074642
250 -0.0632455532