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

$R= 26.7760271783$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.334892346
4 0.5
5 0.447213595
6 -0.236804649
7 1.017133204
8 -0.353553390
9 -0.887847116
10 -0.316227766
11 -1.314089431
12 0.167446173
13 0.451924766
14 -0.719221786
15 0.149768410
16 0.250000000
17 1.706749338
18 0.627802716
19 0.0628373862
20 0.223606797
21 0.340630125
22 0.929201547
23 -1.401645571
24 -0.118402324
25 0.200000000
26 -0.319559067
27 -0.632225550
28 0.508566602
29 0.490113637
30 -0.105902258
31 0.137761104
32 -0.176776695
33 -0.440078493
34 -1.206854031
35 0.454875797
36 -0.443923558
37 0.835132145
38 -0.0444327419
39 0.151346145
40 -0.158113883
41 -0.371555800
42 -0.240861871
43 -1.339934434
44 -0.657044715
45 -0.397057301
46 0.991113088
47 0.303594667
48 0.0837230866
49 0.0345599560
50 -0.141421356
51 0.571577291
52 0.225962383
53 -1.627055048
54 0.447050974
55 -0.587678659
56 -0.359610893
57 0.0210437597
58 -0.346562676
59 1.010234070
60 0.0748842052
61 -1.226527875
62 -0.0974118113
63 -0.903058782
64 0.125000000
65 0.202106899
66 0.311182486
67 -1.013188746
68 0.853374669
69 -0.469400374
70 -0.321645761
71 1.851024254
72 0.313901358
73 -1.066237727
74 -0.590527603
75 0.0669784693
76 0.0314186931
77 -1.336603994
78 -0.107017885
79 1.233758358
80 0.111803398
81 0.676119617
82 0.262729626
83 0.512048633
84 0.170315062
85 0.763281508
86 0.947476724
87 0.164135306
88 0.464600773
89 0.829254449
90 0.280761910
91 0.459667686
92 -0.700822785
93 0.0461351396
94 -0.214673848
95 0.0281017334
96 -0.0592011623
97 0.784337664
98 -0.0244375792
99 1.166710511
100 0.100000000
101 -1.880758576
102 -0.404166178
103 -1.284014580
104 -0.159779533
105 0.152334423
106 1.150501658
107 0.566566847
108 -0.316112775
109 -0.956880214
110 0.415551565
111 0.279679363
112 0.254283301
113 -0.744023499
114 -0.0148801852
115 -0.626834955
116 0.245056818
117 -0.401240100
118 -0.714343361
119 1.735991424
120 -0.0529511293
121 0.726831033
122 0.867286178
123 -0.124431193
124 0.0688805523
125 0.0894427190
126 0.638558988
127 1.400242952
128 -0.0883883476
129 -0.448733787
130 -0.142911159
131 1.528572849
132 -0.220039246
133 0.0639139921
134 0.716432633
135 -0.282739861
136 -0.603427015
137 0.391582336
138 0.331916187
139 -0.949504840
140 0.227437898
141 0.101671528
142 -1.308871802
143 -0.593869561
144 -0.221961779
145 0.219185481
146 0.753943927
147 0.0115738665
148 0.417566072
149 -0.502881064
150 -0.0473609298
151 -0.423649337
152 -0.0222163709
153 -1.515332496
154 0.945121748
155 0.0616086389
156 0.0756730728
157 0.000281285279
158 -0.872398901
159 -0.544888312
160 -0.0790569415
161 -1.425660269
162 -0.478088766
163 -1.652685948
164 -0.185777900
165 -0.196809085
166 -0.362073060
167 -0.631127852
168 -0.120430935
169 -0.795763999
170 -0.539721530
171 -0.0557897313
172 -0.669967217
173 1.177220900
174 -0.116061187
175 0.203426640
176 -0.328522357
177 0.338319980
178 -0.586371444
179 -0.678197971
180 -0.198528650
181 0.163830647
182 -0.325034137
183 -0.410753669
184 0.495556544
185 0.373482449
186 -0.0326224701
187 -2.242793302
188 0.151797333
189 -0.643042642
190 -0.0198709262
191 -0.635798951
192 0.0418615433
193 0.131002858
194 -0.554610481
195 0.0676840539
196 0.0172799780
197 -0.313321086
198 -0.824988914
199 -1.512720539
200 -0.0707106781
201 -0.339296802
202 1.329897142
203 0.498889187
204 0.285788645
205 -0.166164805
206 0.907935417
207 1.244099635
208 0.112981191
209 -0.0835548386
210 -0.107716703
211 -1.451015539
212 -0.813527524
213 0.621094482
214 -0.400623259
215 -0.599236896
216 0.223525487
217 0.131785902
218 0.676616488
219 -0.366128689
220 -0.293839329
221 0.767980432
222 -0.197763174
223 -1.580786888
224 -0.179805446
225 -0.177569423
226 0.526104062