Properties

Level 10
Symmetry even
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

$R= 24.5253828384$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.938990145
4 0.5
5 -0.447213595
6 -0.663966299
7 1.646675024
8 0.353553390
9 -0.118297506
10 -0.316227766
11 -0.130279289
12 -0.469495072
13 0.0324898754
14 1.164375075
15 0.419929159
16 0.250000000
17 -1.159908551
18 -0.0836489689
19 -0.486099357
20 -0.223606797
21 -1.546211620
22 -0.0921213693
23 0.327812621
24 -0.331983149
25 0.200000000
26 0.0229738112
27 1.050070338
28 0.823337512
29 0.460311486
30 0.296934756
31 -1.569126204
32 0.176776695
33 0.122330969
34 -0.820179202
35 -0.736415458
36 -0.0591487532
37 1.317333551
38 -0.343724152
39 -0.0305076729
40 -0.158113883
41 0.290083230
42 -1.093336722
43 -0.0539846265
44 -0.0651396449
45 0.0529042531
46 0.231798527
47 1.625124715
48 -0.234747536
49 1.711538635
50 0.141421356
51 1.089142699
52 0.0162449377
53 -1.012786028
54 0.742511856
55 0.0582626696
56 0.582187537
57 0.456442506
58 0.325489373
59 -0.247766395
60 0.209964579
61 -1.534065436
62 -1.109539779
63 -0.194797549
64 0.125000000
65 -0.0145299140
66 0.0865010580
67 0.717611680
68 -0.579954275
69 -0.307812821
70 -0.520724364
71 1.094730914
72 -0.0418244844
73 -1.063066367
74 0.931495487
75 -0.187798029
76 -0.243049678
77 -0.214527652
78 -0.0215721823
79 -0.897492112
80 -0.111803398
81 -0.867708193
82 0.205119819
83 -0.874191770
84 -0.773105810
85 0.518726873
86 -0.0381728955
87 -0.432227949
88 -0.0460606846
89 -1.728378174
90 0.0374089561
91 0.0535002664
92 0.163906310
93 1.473394043
94 1.149136706
95 0.217390241
96 -0.165991574
97 -1.650984766
98 1.210240575
99 0.0154117151
100 0.100000000
101 -1.336034438
102 0.770140188
103 0.636719888
104 0.0114869056
105 0.691486858
106 -0.716147868
107 1.043881858
108 0.525035169
109 1.327390306
110 0.0411979288
111 -1.236963223
112 0.411668756
113 1.413509156
114 0.322753591
115 -0.146602261
116 0.230155743
117 -0.00384347118
118 -0.175197298
119 -1.909992442
120 0.148467378
121 -0.983027306
122 -1.084748073
123 -0.272385294
124 -0.784563102
125 -0.0894427190
126 -0.137742668
127 0.963661755
128 0.0883883476
129 0.0506910326
130 -0.0102742007
131 -0.545594439
132 0.0611654847
133 -0.800447672
134 0.507428085
135 -0.469605731
136 -0.410089601
137 -1.831747583
138 -0.217656533
139 -0.147924531
140 -0.368207729
141 -1.525976084
142 0.774091652
143 -0.00423276396
144 -0.0295743766
145 -0.205857554
146 -0.751701437
147 -1.607117903
148 0.658666775
149 -1.528935474
150 -0.132793259
151 -0.457197599
152 -0.171862076
153 0.137214249
154 -0.151693958
155 0.701734571
156 -0.0152538364
157 -0.459408306
158 -0.634622758
159 0.950996110
160 -0.0790569415
161 0.539801008
162 -0.613562347
163 -1.301127039
164 0.145041615
165 -0.0547080726
166 -0.618146928
167 1.593598304
168 -0.546668361
169 -0.998947147
170 0.366795290
171 0.0575023357
172 -0.0269923132
173 -1.468509991
174 -0.305631314
175 0.329335004
176 -0.0325698224
177 0.232650721
178 -1.222147927
179 0.0357574485
180 0.0264521265
181 -1.217373710
182 0.0378304012
183 1.440466909
184 0.115899263
185 -0.589129473
186 1.041846919
187 0.151061024
188 0.812562357
189 1.729035220
190 0.153718114
191 -1.595906721
192 -0.117373768
193 -1.578186333
194 -1.167422523
195 0.0136434460
196 0.855769317
197 1.028811680
198 0.0108977282
199 -0.168934416
200 0.0707106781
201 -0.673642435
202 -0.944719011
203 0.755856536
204 0.544571349
205 -0.129729164
206 0.450228951
207 -0.0306430531
208 0.00812246886
209 0.0732649786
210 0.488955046
211 -0.908982256
212 -0.506393014
213 -1.035940059
214 0.738135941
215 0.0241426589
216 0.371255928
217 -2.565131828
218 0.938606686
219 1.162151298
220 0.0291313348
221 -0.0690350758
222 -0.874665083