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

$R= 28.9384997445$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.245179729
4 0.5
5 -0.447213595
6 -0.173368249
7 1.621165915
8 0.353553390
9 -0.939886900
10 -0.316227766
11 -1.524664975
12 -0.122589864
13 1.385833868
14 1.146337412
15 0.109647708
16 0.250000000
17 1.293952423
18 -0.664600400
19 -1.448697307
20 -0.223606797
21 -0.397477020
22 -1.078100942
23 -0.599475561
24 -0.0866841245
25 0.200000000
26 0.979932525
27 0.475620945
28 0.810582957
29 0.0812691804
30 0.0775326380
31 0.792761654
32 0.176776695
33 0.373816945
34 0.914962533
35 -0.725007438
36 -0.469943450
37 0.467485815
38 -1.024383689
39 -0.339778372
40 -0.158113883
41 -0.628116275
42 -0.281058696
43 1.681183952
44 -0.762332487
45 0.420330200
46 -0.423893234
47 -0.177228041
48 -0.0612949323
49 1.628178926
50 0.141421356
51 -0.317250904
52 0.692916934
53 -1.879094649
54 0.336314795
55 0.681850905
56 0.573168706
57 0.355191213
58 0.0574659886
59 -0.606457893
60 0.0548238541
61 0.196092033
62 0.560567141
63 -1.523712607
64 0.125000000
65 -0.619763747
66 0.264328497
67 0.972653055
68 0.646976211
69 0.146979255
70 -0.512657675
71 -0.319938787
72 -0.332300200
73 0.815677076
74 0.330562390
75 -0.0490359458
76 -0.724348653
77 -2.471734890
78 -0.240259591
79 -0.802895561
80 -0.111803398
81 0.823274285
82 -0.444145277
83 1.409704964
84 -0.198738510
85 -0.578673115
86 1.188776573
87 -0.0199255556
88 -0.539050471
89 -0.171287655
90 0.297218334
91 2.246666632
92 -0.299737780
93 -0.194369087
94 -0.125319149
95 0.647877131
96 -0.0433420622
97 -0.210178850
98 1.151296360
99 1.433012637
100 0.100000000
101 0.869446298
102 -0.224330266
103 -0.885463640
104 0.489966262
105 0.177757127
106 -1.328720569
107 -0.845316350
108 0.237810472
109 -0.782027042
110 0.482141399
111 -0.114618045
112 0.405291478
113 0.835317886
114 0.251158115
115 0.268093621
116 0.0406345902
117 -1.302527099
118 -0.428830489
119 2.097711565
120 0.0387663190
121 1.324603286
122 0.138658006
123 0.154001378
124 0.396380827
125 -0.0894427190
126 -1.077427517
127 1.555957824
128 0.0883883476
129 -0.412192226
130 -0.438239148
131 1.856516617
132 0.186908472
133 -2.348578696
134 0.687769571
135 -0.212704152
136 0.457481266
137 -0.0834505402
138 0.103930028
139 1.404803904
140 -0.362503719
141 0.0434527218
142 -0.226230886
143 -2.112932360
144 -0.234971725
145 -0.0363446824
146 0.576770792
147 -0.399196468
148 0.233742907
149 -0.658869463
150 -0.0346736498
151 0.915348511
152 -0.512191844
153 -1.216168928
154 -1.747780502
155 -0.354533789
156 -0.169889186
157 0.565775104
158 -0.567732895
159 0.460715910
160 -0.0790569415
161 -0.971849353
162 0.582142830
163 0.615519030
164 -0.314058137
165 -0.167176020
166 0.996811939
167 -1.057367041
168 -0.140529348
169 0.920535505
170 -0.409183684
171 1.361611371
172 0.840591976
173 -0.707591994
174 -0.0140894955
175 0.324233183
176 -0.381166243
177 0.148691771
178 -0.121118662
179 1.481967112
180 0.210165100
181 0.483660088
182 1.588633210
183 -0.0480784784
184 -0.211946617
185 -0.209066012
186 -0.137439700
187 -1.972846445
188 -0.0886140206
189 0.771055870
190 0.458118313
191 1.908578494
192 -0.0306474661
193 1.177371552
194 -0.148618890
195 0.151953507
196 0.814089463
197 1.918793812
198 1.013292953
199 0.356090632
200 0.0707106781
201 -0.238467360
202 0.614791373
203 0.131658583
204 -0.158625452
205 0.280902137
206 -0.626117344
207 0.563906452
208 0.346458467
209 2.208746863
210 0.125693270
211 -0.921308141
212 -0.939547324
213 0.0783840681
214 -0.597728923
215 -0.751848320
216 0.168157397
217 1.285441143
218 -0.552976624
219 -0.201338926
220 0.340925452
221 1.789876539
222 -0.0810471973
223 0.772446754
224 0.286584353
225 -0.187977380
226 0.590658941
227 0.604223648
228 0.177595606
229 0.494892685
230 0.189570817
231 0.598612699
232 0.0287329943
233 -0.278550589
234 -0.921025744
235 0.0792587895
236 -0.303228946
237 0.251655461
238 1.483306072