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

$R= 27.6452063226$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.828141789
4 0.5
5 -0.447213595
6 -0.585584675
7 1.190939245
8 0.353553390
9 -0.314181176
10 -0.316227766
11 1.500172510
12 -0.414070894
13 -0.342006043
14 0.842121216
15 0.370356267
16 0.250000000
17 0.694324681
18 -0.222159640
19 -0.353942081
20 -0.223606797
21 -0.986266557
22 1.060782155
23 1.477201852
24 -0.292792337
25 0.200000000
26 -0.241834792
27 1.088328351
28 0.595469622
29 -0.526441867
30 0.261881428
31 0.0346665954
32 0.176776695
33 -1.242355547
34 0.490961690
35 -0.532604221
36 -0.157090588
37 -1.274735873
38 -0.250274845
39 0.283229497
40 -0.158113883
41 1.549835655
42 -0.697395771
43 -0.481774005
44 0.750086255
45 0.140506093
46 1.044539447
47 0.295748608
48 -0.207035447
49 0.418336286
50 0.141421356
51 -0.574999284
52 -0.171003021
53 -0.787621663
54 0.769564357
55 -0.670897542
56 0.421060608
57 0.293114228
58 -0.372250614
59 -1.824015219
60 0.185178133
61 1.088164782
62 0.0245129846
63 -0.374170693
64 0.125000000
65 0.152949752
66 -0.878478032
67 -1.210686261
68 0.347162340
69 -1.223332585
70 -0.376608057
71 -0.927452579
72 -0.111079820
73 0.182713435
74 -0.901374380
75 -0.165628357
76 -0.176971040
77 1.786614318
78 0.200273498
79 1.446165810
80 -0.111803398
81 -0.587109011
82 1.095899301
83 0.412109572
84 -0.493133278
85 -0.310511437
86 -0.340665666
87 0.435968510
88 0.530391077
89 1.304005098
90 0.0993528116
91 -0.407308419
92 0.738600926
93 -0.0287088563
94 0.209125846
95 0.158287710
96 -0.146396168
97 -0.777137769
98 0.295808424
99 -0.471325964
100 0.100000000
101 -0.609375061
102 -0.406585892
103 0.629014234
104 -0.120917396
105 0.441071813
106 -0.556932619
107 1.245143529
108 0.544164175
109 1.865137557
110 -0.474396201
111 1.055662047
112 0.297734811
113 0.315795938
114 0.207263058
115 -0.660624751
116 -0.263220933
117 0.107451861
118 -1.289773530
119 0.826898512
120 0.130940714
121 1.250517562
122 0.769448696
123 -1.283483673
124 0.0173332977
125 -0.0894427190
126 -0.264578634
127 -1.533350415
128 0.0883883476
129 0.398977186
130 0.108151807
131 0.743432596
132 -0.621177773
133 -0.421523515
134 -0.856084465
135 -0.486715235
136 0.245480845
137 1.779045531
138 -0.865026767
139 -1.534597704
140 -0.266302110
141 -0.244921781
142 -0.655808007
143 -0.513068066
144 -0.0785452941
145 0.235431960
146 0.129197909
147 -0.346441763
148 -0.637367936
149 -0.189261285
150 -0.117116935
151 1.384156188
152 -0.125137422
153 -0.218143746
154 1.263327099
155 -0.0155033727
156 0.141614748
157 -0.945789259
158 1.022593651
159 0.652262422
160 -0.0790569415
161 1.759257631
162 -0.415148763
163 -0.696032173
164 0.774917827
165 0.555598291
166 0.291405473
167 1.182409905
168 -0.348697885
169 -0.883031789
170 -0.219564742
171 0.111201932
172 -0.240887002
173 1.557368550
174 0.308276290
175 0.238187849
176 0.375043127
177 1.510543336
178 0.922070847
179 0.838382430
180 0.0702530468
181 -0.331664181
182 -0.288010545
183 -0.901152818
184 0.522269723
185 0.570079213
186 -0.0203002270
187 1.041604765
188 0.147874304
189 1.296128768
190 0.111926313
191 0.753524391
192 -0.103517723
193 1.343275720
194 -0.549519386
195 -0.126664081
196 0.209168143
197 1.769964204
198 -0.333277785
199 -0.750080957
200 0.0707106781
201 1.002590515
202 -0.430893238
203 -0.626949912
204 -0.287499642
205 -0.693107576
206 0.444780230
207 -0.464039374
208 -0.0855015109
209 -0.531020094
210 0.311884870
211 1.351313569
212 -0.393810831
213 0.766930082
214 0.880449433
215 0.215455885
216 0.384782178
217 0.0426119627
218 1.318851414
219 -0.149366573
220 -0.335448771
221 -0.232283779
222 0.746465792
223 0.689354896
224 0.210530304
225 -0.0628362353
226 0.223301449
227 -0.673046795
228 0.146557114
229 0.191698509
230 -0.467132241
231 -1.387731994
232 -0.186125307
233 0.113834977
234 0.0759799397
235 -0.132262798
236 -0.912007609
237 -1.385738252
238 0.584705545