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

$R= 27.5885331611$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.442613702
4 0.5
5 0.447213595
6 0.312975150
7 0.541428788
8 0.353553390
9 -0.804093110
10 0.316227766
11 -1.723360595
12 0.221306851
13 -0.628866795
14 0.382847967
15 0.197942865
16 0.250000000
17 1.083695568
18 -0.568579690
19 1.559808355
20 0.223606797
21 0.239643800
22 -1.218599963
23 0.608110313
24 0.156487575
25 0.200000000
26 -0.444675975
27 -0.798516331
28 0.270714394
29 -0.862352624
30 0.139966742
31 -0.0646168878
32 0.176776695
33 -0.762783014
34 0.766288485
35 0.242134315
36 -0.402046555
37 -1.970960678
38 1.102951065
39 -0.278345060
40 0.158113883
41 -1.386450906
42 0.169453756
43 0.780765836
44 -0.861680297
45 -0.359601370
46 0.429998926
47 0.0784175534
48 0.110653425
49 -0.706854867
50 0.141421356
51 0.479658508
52 -0.314433397
53 -0.0840226086
54 -0.564636313
55 -0.770710288
56 0.191423983
57 0.690392551
58 -0.609775388
59 -0.854548951
60 0.0989714327
61 -1.065590746
62 -0.0456910395
63 -0.435359158
64 0.125000000
65 -0.281237780
66 -0.539369042
67 1.558208927
68 0.541847784
69 0.269157957
70 0.171214816
71 1.574239292
72 -0.284289845
73 -0.0214304567
74 -1.393679661
75 0.0885227405
76 0.779904177
77 -0.933077038
78 -0.196819680
79 -1.283299561
80 0.111803398
81 0.450658839
82 -0.980368838
83 -1.188707634
84 0.119821900
85 0.484643391
86 0.552084817
87 -0.381689088
88 -0.609299981
89 -0.889071738
90 -0.254276567
91 -0.340486586
92 0.304055156
93 -0.0286003200
94 0.0554495837
95 0.697567502
96 0.0782437876
97 -1.444892299
98 -0.499821870
99 1.385742381
100 0.100000000
101 0.0574698009
102 0.339169783
103 0.438037766
104 -0.222337987
105 0.107171965
106 -0.0594129563
107 -1.734739772
108 -0.399258165
109 -0.786666245
110 -0.544974471
111 -0.872374203
112 0.135357197
113 -1.214857884
114 0.488181255
115 0.271955199
116 -0.431176312
117 0.505667457
118 -0.604257358
119 0.586743978
120 0.0699833712
121 1.969971743
122 -0.753486442
123 -0.613662169
124 -0.0323084439
125 0.0894427190
126 -0.307845412
127 0.108492997
128 0.0883883476
129 0.345577658
130 -0.198865141
131 0.110346122
132 -0.381391507
133 0.844525147
134 1.101820099
135 -0.357107359
136 0.383144242
137 1.164268891
138 0.190323416
139 -0.611415877
140 0.121067157
141 0.0347086836
142 1.113155279
143 1.083764254
144 -0.201023277
145 -0.385655817
146 -0.0151536212
147 -0.312863650
148 -0.985480339
149 1.355138557
150 0.0625950301
151 0.0759176342
152 0.551475532
153 -0.871392137
154 -0.659785101
155 -0.0288975507
156 -0.139172530
157 -1.228536724
158 -0.907429822
159 -0.0371895548
160 0.0790569415
161 0.329248434
162 0.318663921
163 -0.0500960719
164 -0.693225453
165 -0.341126934
166 -0.840543228
167 -0.741048666
168 0.0847268782
169 -0.604526596
170 0.342694628
171 -1.254231214
172 0.390382918
173 -0.253496449
174 -0.269894942
175 0.108285757
176 -0.430840148
177 -0.378234964
178 -0.628668655
179 0.465914093
180 -0.179800685
181 -1.103909000
182 -0.240760374
183 -0.471643181
184 0.214999463
185 -0.881440411
186 -0.0202234802
187 -1.867598312
188 0.0392087767
189 -0.432339581
190 0.493254711
191 -0.565186732
192 0.0553267128
193 -1.488899829
194 -1.021693143
195 -0.124479695
196 -0.353427433
197 0.272247587
198 0.979867834
199 0.849118960
200 0.0707106781
201 0.689656469
202 0.0406372859
203 -0.467120793
204 0.239829254
205 -0.620039695
206 0.309739474
207 -0.488480859
208 -0.157216698
209 -2.688159881
210 0.0757820237
211 1.277554377
212 -0.0420113043
213 0.697389069
214 -1.226646256
215 0.349169097
216 -0.282318156
217 -0.0351922724
218 -0.556257036
219 -0.00685468201
220 -0.385355144
221 -0.680311252
222 -0.616861715
223 -0.666331375
224 0.0957119919
225 -0.160818622
226 -0.859034247
227 1.864684742
228 0.345196275