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

$R= 22.5374419869$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.725143114
4 0.5
5 -0.447213595
6 -1.219860394
7 1.767650773
8 0.353553390
9 1.976118765
10 -0.316227766
11 0.856304491
12 -0.862571557
13 1.577969622
14 1.249917848
15 0.771507454
16 0.250000000
17 0.866003956
18 1.397326979
19 0.597896769
20 -0.223606797
21 -3.049450560
22 0.605498712
23 -0.210893852
24 -0.609930197
25 0.200000000
26 1.115793020
27 -1.683944567
28 0.883825386
29 0.393556591
30 0.545538153
31 1.349810619
32 0.176776695
33 -1.477247797
34 0.612357270
35 -0.790517457
36 0.988059382
37 -1.200143133
38 0.422776860
39 -2.722223429
40 -0.158113883
41 -0.774236885
42 -2.156287170
43 0.237204880
44 0.428152245
45 -0.883747178
46 -0.149124473
47 -0.695481852
48 -0.431285778
49 2.124589256
50 0.141421356
51 -1.493980762
52 0.788984811
53 1.234603461
54 -1.190728622
55 -0.382951010
56 0.624958924
57 -1.031457495
58 0.278286534
59 -1.027911287
60 0.385753727
61 0.243581416
62 0.954460242
63 3.493087863
64 0.125000000
65 -0.705689468
66 -1.044571934
67 -0.287435881
68 0.433001978
69 0.363822078
70 -0.558980255
71 1.270778921
72 0.698663489
73 1.267644200
74 -0.848629347
75 -0.345028622
76 0.298948384
77 1.513647296
78 -1.924902646
79 0.280217711
80 -0.111803398
81 0.928926609
82 -0.547468152
83 -1.121584023
84 -1.524725280
85 -0.387288743
86 0.167729179
87 -0.678941444
88 0.302749356
89 -0.0524520801
90 -0.624903622
91 2.789299223
92 -0.105446926
93 -2.328616496
94 -0.491779934
95 -0.267387564
96 -0.304965098
97 -1.016542959
98 1.502311470
99 1.692159374
100 0.100000000
101 0.996520446
102 -1.056403928
103 -0.165343763
104 0.557896510
105 1.363755749
106 0.872996479
107 0.455540746
108 -0.841972283
109 -1.440539523
110 -0.270787256
111 2.070418662
112 0.441912693
113 0.0680180106
114 -0.729350589
115 0.0943145982
116 0.196778295
117 3.118255382
118 -0.726843041
119 1.530792561
120 0.272769076
121 -0.266742616
122 0.172238071
123 1.335669430
124 0.674905309
125 -0.0894427190
126 2.469986115
127 -0.997323501
128 0.0883883476
129 -0.409212375
130 -0.498997808
131 -1.897185486
132 -0.738623898
133 1.056872690
134 -0.203247860
135 0.753082904
136 0.306178635
137 0.355350575
138 0.257261058
139 1.113844047
140 -0.395258728
141 1.199805722
142 0.898576393
143 1.351222429
144 0.494029691
145 -0.176003858
146 0.896359810
147 -3.665220570
148 -0.600071566
149 -0.241700889
150 -0.243972078
151 1.456304950
152 0.211388430
153 1.711326005
154 1.070310267
155 -0.603653660
156 -1.361111714
157 0.508107544
158 0.198143844
159 -2.129869933
160 -0.0790569415
161 -0.372788709
162 0.656850305
163 0.657325057
164 -0.387118442
165 0.660645298
166 -0.793079668
167 0.841023384
168 -1.078143585
169 1.489956374
170 -0.273854496
171 1.181479433
172 0.118602440
173 -1.600124456
174 -0.480084099
175 0.353530154
176 0.214076122
177 1.773202475
178 -0.0370892215
179 -1.010779041
180 -0.441873589
181 0.763111716
182 1.972332395
183 -0.420333159
184 -0.0745622367
185 0.536720325
186 -1.646580515
187 0.743113340
188 -0.347740926
189 -2.978660991
190 -0.189071559
191 0.0705297566
192 -0.215642889
193 -0.445658548
194 -0.718804420
195 1.217415327
196 1.062294628
197 0.101619188
198 1.196537368
199 -0.953758151
200 0.0707106781
201 0.498933143
202 0.704646365
203 0.769917509
204 -0.746990381
205 0.346249261
206 -0.116915696
207 -0.442474283
208 0.394492405
209 0.566509965
210 0.964320938