Properties

Label 3751.1.t.d.3657.1
Level 37513751
Weight 11
Character 3751.3657
Analytic conductor 1.8721.872
Analytic rank 00
Dimension 88
Projective image D6D_{6}
CM discriminant -31
Inner twists 1616

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3751,1,Mod(2138,3751)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3751, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([2, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3751.2138");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 3751=11231 3751 = 11^{2} \cdot 31
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3751.t (of order 1010, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.871992862391.87199286239
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ10)\Q(\zeta_{10})
Coefficient field: 8.0.324000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+3x6+9x4+27x2+81 x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D6D_{6}
Projective field: Galois closure of 6.0.1279091.1

Embedding invariants

Embedding label 3657.1
Root 1.401261.01807i-1.40126 - 1.01807i of defining polynomial
Character χ\chi == 3751.3657
Dual form 3751.1.t.d.2913.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5352331.64728i)q2+(1.61803+1.17557i)q4+(0.309017+0.951057i)q5+(1.401261.01807i)q7+(1.40126+1.01807i)q8+(0.309017+0.951057i)q9+1.73205q10+(2.427051.76336i)q14+(0.3090170.951057i)q16+(1.401261.01807i)q18+(1.401261.01807i)q19+(0.6180341.90211i)q20+(1.07047+3.29456i)q28+(0.3090170.951057i)q31+(0.535233+1.64728i)q35+(1.618031.17557i)q36+(0.927051+2.85317i)q38+(1.40126+1.01807i)q40+(1.40126+1.01807i)q411.00000q45+(1.61803+1.17557i)q47+(0.6180341.90211i)q49+3.00000q56+(0.8090170.587785i)q59+(1.40126+1.01807i)q62+(1.40126+1.01807i)q63+(0.3090170.951057i)q64+2.00000q67+(2.427051.76336i)q70+(0.3090170.951057i)q71+(0.535233+1.64728i)q72+3.46410q76+(0.809017+0.587785i)q80+(0.809017+0.587785i)q81+(0.9270512.85317i)q82+(0.535233+1.64728i)q90+(1.070473.29456i)q94+(1.401261.01807i)q95+(0.309017+0.951057i)q973.46410q98+O(q100)q+(-0.535233 - 1.64728i) q^{2} +(-1.61803 + 1.17557i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(1.40126 - 1.01807i) q^{7} +(1.40126 + 1.01807i) q^{8} +(0.309017 + 0.951057i) q^{9} +1.73205 q^{10} +(-2.42705 - 1.76336i) q^{14} +(0.309017 - 0.951057i) q^{16} +(1.40126 - 1.01807i) q^{18} +(-1.40126 - 1.01807i) q^{19} +(-0.618034 - 1.90211i) q^{20} +(-1.07047 + 3.29456i) q^{28} +(-0.309017 - 0.951057i) q^{31} +(0.535233 + 1.64728i) q^{35} +(-1.61803 - 1.17557i) q^{36} +(-0.927051 + 2.85317i) q^{38} +(-1.40126 + 1.01807i) q^{40} +(1.40126 + 1.01807i) q^{41} -1.00000 q^{45} +(1.61803 + 1.17557i) q^{47} +(0.618034 - 1.90211i) q^{49} +3.00000 q^{56} +(0.809017 - 0.587785i) q^{59} +(-1.40126 + 1.01807i) q^{62} +(1.40126 + 1.01807i) q^{63} +(-0.309017 - 0.951057i) q^{64} +2.00000 q^{67} +(2.42705 - 1.76336i) q^{70} +(0.309017 - 0.951057i) q^{71} +(-0.535233 + 1.64728i) q^{72} +3.46410 q^{76} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.927051 - 2.85317i) q^{82} +(0.535233 + 1.64728i) q^{90} +(1.07047 - 3.29456i) q^{94} +(1.40126 - 1.01807i) q^{95} +(0.309017 + 0.951057i) q^{97} -3.46410 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q4q4+2q52q96q142q16+4q20+2q314q36+6q388q45+4q474q49+24q56+2q59+2q64+16q67+6q702q71+2q80+2q97+O(q100) 8 q - 4 q^{4} + 2 q^{5} - 2 q^{9} - 6 q^{14} - 2 q^{16} + 4 q^{20} + 2 q^{31} - 4 q^{36} + 6 q^{38} - 8 q^{45} + 4 q^{47} - 4 q^{49} + 24 q^{56} + 2 q^{59} + 2 q^{64} + 16 q^{67} + 6 q^{70} - 2 q^{71} + 2 q^{80}+ \cdots - 2 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3751Z)×\left(\mathbb{Z}/3751\mathbb{Z}\right)^\times.

nn 24212421 25432543
χ(n)\chi(n) 1-1 e(25)e\left(\frac{2}{5}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.535233 1.64728i −0.535233 1.64728i −0.743145 0.669131i 0.766667π-0.766667\pi
0.207912 0.978148i 0.433333π-0.433333\pi
33 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
44 −1.61803 + 1.17557i −1.61803 + 1.17557i
55 −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i 0.266667π0.266667\pi
−0.978148 + 0.207912i 0.933333π0.933333\pi
66 0 0
77 1.40126 1.01807i 1.40126 1.01807i 0.406737 0.913545i 0.366667π-0.366667\pi
0.994522 0.104528i 0.0333333π-0.0333333\pi
88 1.40126 + 1.01807i 1.40126 + 1.01807i
99 0.309017 + 0.951057i 0.309017 + 0.951057i
1010 1.73205 1.73205
1111 0 0
1212 0 0
1313 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
1414 −2.42705 1.76336i −2.42705 1.76336i
1515 0 0
1616 0.309017 0.951057i 0.309017 0.951057i
1717 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
1818 1.40126 1.01807i 1.40126 1.01807i
1919 −1.40126 1.01807i −1.40126 1.01807i −0.994522 0.104528i 0.966667π-0.966667\pi
−0.406737 0.913545i 0.633333π-0.633333\pi
2020 −0.618034 1.90211i −0.618034 1.90211i
2121 0 0
2222 0 0
2323 0 0 1.00000 00
−1.00000 π\pi
2424 0 0
2525 0 0
2626 0 0
2727 0 0
2828 −1.07047 + 3.29456i −1.07047 + 3.29456i
2929 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
3030 0 0
3131 −0.309017 0.951057i −0.309017 0.951057i
3232 0 0
3333 0 0
3434 0 0
3535 0.535233 + 1.64728i 0.535233 + 1.64728i
3636 −1.61803 1.17557i −1.61803 1.17557i
3737 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
3838 −0.927051 + 2.85317i −0.927051 + 2.85317i
3939 0 0
4040 −1.40126 + 1.01807i −1.40126 + 1.01807i
4141 1.40126 + 1.01807i 1.40126 + 1.01807i 0.994522 + 0.104528i 0.0333333π0.0333333\pi
0.406737 + 0.913545i 0.366667π0.366667\pi
4242 0 0
4343 0 0 1.00000 00
−1.00000 π\pi
4444 0 0
4545 −1.00000 −1.00000
4646 0 0
4747 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i 0.200000π0.200000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
4848 0 0
4949 0.618034 1.90211i 0.618034 1.90211i
5050 0 0
5151 0 0
5252 0 0
5353 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
5454 0 0
5555 0 0
5656 3.00000 3.00000
5757 0 0
5858 0 0
5959 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i 0.533333π-0.533333\pi
0.913545 + 0.406737i 0.133333π0.133333\pi
6060 0 0
6161 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
6262 −1.40126 + 1.01807i −1.40126 + 1.01807i
6363 1.40126 + 1.01807i 1.40126 + 1.01807i
6464 −0.309017 0.951057i −0.309017 0.951057i
6565 0 0
6666 0 0
6767 2.00000 2.00000 1.00000 00
1.00000 00
6868 0 0
6969 0 0
7070 2.42705 1.76336i 2.42705 1.76336i
7171 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i 0.733333π-0.733333\pi
0.978148 0.207912i 0.0666667π-0.0666667\pi
7272 −0.535233 + 1.64728i −0.535233 + 1.64728i
7373 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
7474 0 0
7575 0 0
7676 3.46410 3.46410
7777 0 0
7878 0 0
7979 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
8080 0.809017 + 0.587785i 0.809017 + 0.587785i
8181 −0.809017 + 0.587785i −0.809017 + 0.587785i
8282 0.927051 2.85317i 0.927051 2.85317i
8383 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 0 0 1.00000 00
−1.00000 π\pi
9090 0.535233 + 1.64728i 0.535233 + 1.64728i
9191 0 0
9292 0 0
9393 0 0
9494 1.07047 3.29456i 1.07047 3.29456i
9595 1.40126 1.01807i 1.40126 1.01807i
9696 0 0
9797 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i 0.0666667π0.0666667\pi
−0.669131 + 0.743145i 0.733333π0.733333\pi
9898 −3.46410 −3.46410
9999 0 0
100100 0 0
101101 0.535233 + 1.64728i 0.535233 + 1.64728i 0.743145 + 0.669131i 0.233333π0.233333\pi
−0.207912 + 0.978148i 0.566667π0.566667\pi
102102 0 0
103103 −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i 0.866667π-0.866667\pi
0.104528 + 0.994522i 0.466667π0.466667\pi
104104 0 0
105105 0 0
106106 0 0
107107 −1.40126 1.01807i −1.40126 1.01807i −0.994522 0.104528i 0.966667π-0.966667\pi
−0.406737 0.913545i 0.633333π-0.633333\pi
108108 0 0
109109 1.73205 1.73205 0.866025 0.500000i 0.166667π-0.166667\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
110110 0 0
111111 0 0
112112 −0.535233 1.64728i −0.535233 1.64728i
113113 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i 0.133333π-0.133333\pi
−0.104528 + 0.994522i 0.533333π0.533333\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 −1.40126 1.01807i −1.40126 1.01807i
119119 0 0
120120 0 0
121121 0 0
122122 0 0
123123 0 0
124124 1.61803 + 1.17557i 1.61803 + 1.17557i
125125 −0.809017 + 0.587785i −0.809017 + 0.587785i
126126 0.927051 2.85317i 0.927051 2.85317i
127127 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
128128 −1.40126 + 1.01807i −1.40126 + 1.01807i
129129 0 0
130130 0 0
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 0 0
133133 −3.00000 −3.00000
134134 −1.07047 3.29456i −1.07047 3.29456i
135135 0 0
136136 0 0
137137 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
138138 0 0
139139 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
140140 −2.80252 2.03615i −2.80252 2.03615i
141141 0 0
142142 −1.73205 −1.73205
143143 0 0
144144 1.00000 1.00000
145145 0 0
146146 0 0
147147 0 0
148148 0 0
149149 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
150150 0 0
151151 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
152152 −0.927051 2.85317i −0.927051 2.85317i
153153 0 0
154154 0 0
155155 1.00000 1.00000
156156 0 0
157157 −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i 0.466667π-0.466667\pi
−0.913545 + 0.406737i 0.866667π0.866667\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 1.40126 + 1.01807i 1.40126 + 1.01807i
163163 −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i 0.933333π-0.933333\pi
0.669131 0.743145i 0.266667π-0.266667\pi
164164 −3.46410 −3.46410
165165 0 0
166166 0 0
167167 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
168168 0 0
169169 −0.809017 + 0.587785i −0.809017 + 0.587785i
170170 0 0
171171 0.535233 1.64728i 0.535233 1.64728i
172172 0 0
173173 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
180180 1.61803 1.17557i 1.61803 1.17557i
181181 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 −4.00000 −4.00000
189189 0 0
190190 −2.42705 1.76336i −2.42705 1.76336i
191191 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i 0.533333π-0.533333\pi
0.913545 + 0.406737i 0.133333π0.133333\pi
192192 0 0
193193 0.535233 1.64728i 0.535233 1.64728i −0.207912 0.978148i 0.566667π-0.566667\pi
0.743145 0.669131i 0.233333π-0.233333\pi
194194 1.40126 1.01807i 1.40126 1.01807i
195195 0 0
196196 1.23607 + 3.80423i 1.23607 + 3.80423i
197197 0 0 1.00000 00
−1.00000 π\pi
198198 0 0
199199 0 0 1.00000 00
−1.00000 π\pi
200200 0 0
201201 0 0
202202 2.42705 1.76336i 2.42705 1.76336i
203203 0 0
204204 0 0
205205 −1.40126 + 1.01807i −1.40126 + 1.01807i
206206 1.40126 + 1.01807i 1.40126 + 1.01807i
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 −0.535233 1.64728i −0.535233 1.64728i −0.743145 0.669131i 0.766667π-0.766667\pi
0.207912 0.978148i 0.433333π-0.433333\pi
212212 0 0
213213 0 0
214214 −0.927051 + 2.85317i −0.927051 + 2.85317i
215215 0 0
216216 0 0
217217 −1.40126 1.01807i −1.40126 1.01807i
218218 −0.927051 2.85317i −0.927051 2.85317i
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
224224 0 0
225225 0 0
226226 0.535233 1.64728i 0.535233 1.64728i
227227 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
228228 0 0
229229 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
230230 0 0
231231 0 0
232232 0 0
233233 0.535233 + 1.64728i 0.535233 + 1.64728i 0.743145 + 0.669131i 0.233333π0.233333\pi
−0.207912 + 0.978148i 0.566667π0.566667\pi
234234 0 0
235235 −1.61803 + 1.17557i −1.61803 + 1.17557i
236236 −0.618034 + 1.90211i −0.618034 + 1.90211i
237237 0 0
238238 0 0
239239 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
240240 0 0
241241 0 0 1.00000 00
−1.00000 π\pi
242242 0 0
243243 0 0
244244 0 0
245245 1.61803 + 1.17557i 1.61803 + 1.17557i
246246 0 0
247247 0 0
248248 0.535233 1.64728i 0.535233 1.64728i
249249 0 0
250250 1.40126 + 1.01807i 1.40126 + 1.01807i
251251 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
252252 −3.46410 −3.46410
253253 0 0
254254 0 0
255255 0 0
256256 1.61803 + 1.17557i 1.61803 + 1.17557i
257257 −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i 0.866667π-0.866667\pi
0.104528 + 0.994522i 0.466667π0.466667\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 0 0 1.00000 00
−1.00000 π\pi
264264 0 0
265265 0 0
266266 1.60570 + 4.94183i 1.60570 + 4.94183i
267267 0 0
268268 −3.23607 + 2.35114i −3.23607 + 2.35114i
269269 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
270270 0 0
271271 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
278278 0 0
279279 0.809017 0.587785i 0.809017 0.587785i
280280 −0.927051 + 2.85317i −0.927051 + 2.85317i
281281 0.535233 1.64728i 0.535233 1.64728i −0.207912 0.978148i 0.566667π-0.566667\pi
0.743145 0.669131i 0.233333π-0.233333\pi
282282 0 0
283283 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
284284 0.618034 + 1.90211i 0.618034 + 1.90211i
285285 0 0
286286 0 0
287287 3.00000 3.00000
288288 0 0
289289 −0.809017 0.587785i −0.809017 0.587785i
290290 0 0
291291 0 0
292292 0 0
293293 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
294294 0 0
295295 0.309017 + 0.951057i 0.309017 + 0.951057i
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 −1.40126 + 1.01807i −1.40126 + 1.01807i
305305 0 0
306306 0 0
307307 −1.73205 −1.73205 −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
308308 0 0
309309 0 0
310310 −0.535233 1.64728i −0.535233 1.64728i
311311 −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i 0.466667π-0.466667\pi
−0.913545 + 0.406737i 0.866667π0.866667\pi
312312 0 0
313313 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
314314 −0.535233 + 1.64728i −0.535233 + 1.64728i
315315 −1.40126 + 1.01807i −1.40126 + 1.01807i
316316 0 0
317317 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i 0.0666667π0.0666667\pi
−0.669131 + 0.743145i 0.733333π0.733333\pi
318318 0 0
319319 0 0
320320 1.00000 1.00000
321321 0 0
322322 0 0
323323 0 0
324324 0.618034 1.90211i 0.618034 1.90211i
325325 0 0
326326 −1.40126 + 1.01807i −1.40126 + 1.01807i
327327 0 0
328328 0.927051 + 2.85317i 0.927051 + 2.85317i
329329 3.46410 3.46410
330330 0 0
331331 0 0 1.00000 00
−1.00000 π\pi
332332 0 0
333333 0 0
334334 0 0
335335 −0.618034 + 1.90211i −0.618034 + 1.90211i
336336 0 0
337337 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
338338 1.40126 + 1.01807i 1.40126 + 1.01807i
339339 0 0
340340 0 0
341341 0 0
342342 −3.00000 −3.00000
343343 −0.535233 1.64728i −0.535233 1.64728i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
348348 0 0
349349 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
350350 0 0
351351 0 0
352352 0 0
353353 0 0 1.00000 00
−1.00000 π\pi
354354 0 0
355355 0.809017 + 0.587785i 0.809017 + 0.587785i
356356 0 0
357357 0 0
358358 0 0
359359 −1.40126 + 1.01807i −1.40126 + 1.01807i −0.406737 + 0.913545i 0.633333π0.633333\pi
−0.994522 + 0.104528i 0.966667π0.966667\pi
360360 −1.40126 1.01807i −1.40126 1.01807i
361361 0.618034 + 1.90211i 0.618034 + 1.90211i
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
368368 0 0
369369 −0.535233 + 1.64728i −0.535233 + 1.64728i
370370 0 0
371371 0 0
372372 0 0
373373 −1.73205 −1.73205 −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
374374 0 0
375375 0 0
376376 1.07047 + 3.29456i 1.07047 + 3.29456i
377377 0 0
378378 0 0
379379 −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i 0.600000π0.600000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
380380 −1.07047 + 3.29456i −1.07047 + 3.29456i
381381 0 0
382382 −1.40126 1.01807i −1.40126 1.01807i
383383 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
384384 0 0
385385 0 0
386386 −3.00000 −3.00000
387387 0 0
388388 −1.61803 1.17557i −1.61803 1.17557i
389389 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
390390 0 0
391391 0 0
392392 2.80252 2.03615i 2.80252 2.03615i
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
398398 0 0
399399 0 0
400400 0 0
401401 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
402402 0 0
403403 0 0
404404 −2.80252 2.03615i −2.80252 2.03615i
405405 −0.309017 0.951057i −0.309017 0.951057i
406406 0 0
407407 0 0
408408 0 0
409409 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
410410 2.42705 + 1.76336i 2.42705 + 1.76336i
411411 0 0
412412 0.618034 1.90211i 0.618034 1.90211i
413413 0.535233 1.64728i 0.535233 1.64728i
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
420420 0 0
421421 −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i 0.466667π-0.466667\pi
−0.913545 + 0.406737i 0.866667π0.866667\pi
422422 −2.42705 + 1.76336i −2.42705 + 1.76336i
423423 −0.618034 + 1.90211i −0.618034 + 1.90211i
424424 0 0
425425 0 0
426426 0 0
427427 0 0
428428 3.46410 3.46410
429429 0 0
430430 0 0
431431 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
432432 0 0
433433 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
434434 −0.927051 + 2.85317i −0.927051 + 2.85317i
435435 0 0
436436 −2.80252 + 2.03615i −2.80252 + 2.03615i
437437 0 0
438438 0 0
439439 1.73205 1.73205 0.866025 0.500000i 0.166667π-0.166667\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
440440 0 0
441441 2.00000 2.00000
442442 0 0
443443 −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i 0.466667π-0.466667\pi
−0.913545 + 0.406737i 0.866667π0.866667\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 −1.40126 1.01807i −1.40126 1.01807i
449449 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
450450 0 0
451451 0 0
452452 −2.00000 −2.00000
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 1.00000 00
−1.00000 π\pi
462462 0 0
463463 0 0 1.00000 00
−1.00000 π\pi
464464 0 0
465465 0 0
466466 2.42705 1.76336i 2.42705 1.76336i
467467 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i 0.733333π-0.733333\pi
0.978148 0.207912i 0.0666667π-0.0666667\pi
468468 0 0
469469 2.80252 2.03615i 2.80252 2.03615i
470470 2.80252 + 2.03615i 2.80252 + 2.03615i
471471 0 0
472472 1.73205 1.73205
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 −0.535233 + 1.64728i −0.535233 + 1.64728i 0.207912 + 0.978148i 0.433333π0.433333\pi
−0.743145 + 0.669131i 0.766667π0.766667\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0 0
485485 −1.00000 −1.00000
486486 0 0
487487 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
488488 0 0
489489 0 0
490490 1.07047 3.29456i 1.07047 3.29456i
491491 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 −1.00000 −1.00000
497497 −0.535233 1.64728i −0.535233 1.64728i
498498 0 0
499499 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
500500 0.618034 1.90211i 0.618034 1.90211i
501501 0 0
502502 0 0
503503 −1.40126 1.01807i −1.40126 1.01807i −0.994522 0.104528i 0.966667π-0.966667\pi
−0.406737 0.913545i 0.633333π-0.633333\pi
504504 0.927051 + 2.85317i 0.927051 + 2.85317i
505505 −1.73205 −1.73205
506506 0 0
507507 0 0
508508 0 0
509509 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
510510 0 0
511511 0 0
512512 0.535233 1.64728i 0.535233 1.64728i
513513 0 0
514514 1.40126 + 1.01807i 1.40126 + 1.01807i
515515 −0.309017 0.951057i −0.309017 0.951057i
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i 0.200000π-0.200000\pi
0.809017 0.587785i 0.200000π-0.200000\pi
522522 0 0
523523 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 1.00000 1.00000
530530 0 0
531531 0.809017 + 0.587785i 0.809017 + 0.587785i
532532 4.85410 3.52671i 4.85410 3.52671i
533533 0 0
534534 0 0
535535 1.40126 1.01807i 1.40126 1.01807i
536536 2.80252 + 2.03615i 2.80252 + 2.03615i
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 −0.535233 1.64728i −0.535233 1.64728i −0.743145 0.669131i 0.766667π-0.766667\pi
0.207912 0.978148i 0.433333π-0.433333\pi
542542 0 0
543543 0 0
544544 0 0
545545 −0.535233 + 1.64728i −0.535233 + 1.64728i
546546 0 0
547547 1.40126 + 1.01807i 1.40126 + 1.01807i 0.994522 + 0.104528i 0.0333333π0.0333333\pi
0.406737 + 0.913545i 0.366667π0.366667\pi
548548 0 0
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
558558 −1.40126 1.01807i −1.40126 1.01807i
559559 0 0
560560 1.73205 1.73205
561561 0 0
562562 −3.00000 −3.00000
563563 0.535233 + 1.64728i 0.535233 + 1.64728i 0.743145 + 0.669131i 0.233333π0.233333\pi
−0.207912 + 0.978148i 0.566667π0.566667\pi
564564 0 0
565565 −0.809017 + 0.587785i −0.809017 + 0.587785i
566566 0 0
567567 −0.535233 + 1.64728i −0.535233 + 1.64728i
568568 1.40126 1.01807i 1.40126 1.01807i
569569 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
570570 0 0
571571 0 0 1.00000 00
−1.00000 π\pi
572572 0 0
573573 0 0
574574 −1.60570 4.94183i −1.60570 4.94183i
575575 0 0
576576 0.809017 0.587785i 0.809017 0.587785i
577577 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i 0.400000π-0.400000\pi
0.309017 0.951057i 0.400000π-0.400000\pi
578578 −0.535233 + 1.64728i −0.535233 + 1.64728i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
588588 0 0
589589 −0.535233 + 1.64728i −0.535233 + 1.64728i
590590 1.40126 1.01807i 1.40126 1.01807i
591591 0 0
592592 0 0
593593 −1.73205 −1.73205 −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i 0.733333π-0.733333\pi
0.978148 0.207912i 0.0666667π-0.0666667\pi
600600 0 0
601601 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
602602 0 0
603603 0.618034 + 1.90211i 0.618034 + 1.90211i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
614614 0.927051 + 2.85317i 0.927051 + 2.85317i
615615 0 0
616616 0 0
617617 −2.00000 −2.00000 −1.00000 π\pi
−1.00000 π\pi
618618 0 0
619619 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
620620 −1.61803 + 1.17557i −1.61803 + 1.17557i
621621 0 0
622622 −0.535233 + 1.64728i −0.535233 + 1.64728i
623623 0 0
624624 0 0
625625 −0.309017 0.951057i −0.309017 0.951057i
626626 0 0
627627 0 0
628628 2.00000 2.00000
629629 0 0
630630 2.42705 + 1.76336i 2.42705 + 1.76336i
631631 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
632632 0 0
633633 0 0
634634 1.40126 1.01807i 1.40126 1.01807i
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 1.00000 1.00000
640640 −0.535233 1.64728i −0.535233 1.64728i
641641 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
642642 0 0
643643 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
648648 −1.73205 −1.73205
649649 0 0
650650 0 0
651651 0 0
652652 1.61803 + 1.17557i 1.61803 + 1.17557i
653653 −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i 0.800000π0.800000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
654654 0 0
655655 0 0
656656 1.40126 1.01807i 1.40126 1.01807i
657657 0 0
658658 −1.85410 5.70634i −1.85410 5.70634i
659659 −1.73205 −1.73205 −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
660660 0 0
661661 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
662662 0 0
663663 0 0
664664 0 0
665665 0.927051 2.85317i 0.927051 2.85317i
666666 0 0
667667 0 0
668668 0 0
669669 0 0
670670 3.46410 3.46410
671671 0 0
672672 0 0
673673 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
674674 0 0
675675 0 0
676676 0.618034 1.90211i 0.618034 1.90211i
677677 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
678678 0 0
679679 1.40126 + 1.01807i 1.40126 + 1.01807i
680680 0 0
681681 0 0
682682 0 0
683683 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
684684 1.07047 + 3.29456i 1.07047 + 3.29456i
685685 0 0
686686 −2.42705 + 1.76336i −2.42705 + 1.76336i
687687 0 0
688688 0 0
689689 0 0
690690 0 0
691691 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i 0.0666667π0.0666667\pi
−0.669131 + 0.743145i 0.733333π0.733333\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 0 0
701701 1.40126 + 1.01807i 1.40126 + 1.01807i 0.994522 + 0.104528i 0.0333333π0.0333333\pi
0.406737 + 0.913545i 0.366667π0.366667\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 0 0
707707 2.42705 + 1.76336i 2.42705 + 1.76336i
708708 0 0
709709 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
710710 0.535233 1.64728i 0.535233 1.64728i
711711 0 0
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 2.42705 + 1.76336i 2.42705 + 1.76336i
719719 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
720720 −0.309017 + 0.951057i −0.309017 + 0.951057i
721721 −0.535233 + 1.64728i −0.535233 + 1.64728i
722722 2.80252 2.03615i 2.80252 2.03615i
723723 0 0
724724 0 0
725725 0 0
726726 0 0
727727 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
728728 0 0
729729 −0.809017 0.587785i −0.809017 0.587785i
730730 0 0
731731 0 0
732732 0 0
733733 −1.40126 + 1.01807i −1.40126 + 1.01807i −0.406737 + 0.913545i 0.633333π0.633333\pi
−0.994522 + 0.104528i 0.966667π0.966667\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 3.00000 3.00000
739739 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
744744 0 0
745745 0 0
746746 0.927051 + 2.85317i 0.927051 + 2.85317i
747747 0 0
748748 0 0
749749 −3.00000 −3.00000
750750 0 0
751751 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i 0.133333π-0.133333\pi
−0.104528 + 0.994522i 0.533333π0.533333\pi
752752 1.61803 1.17557i 1.61803 1.17557i
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
758758 3.46410 3.46410
759759 0 0
760760 3.00000 3.00000
761761 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
762762 0 0
763763 2.42705 1.76336i 2.42705 1.76336i
764764 −0.618034 + 1.90211i −0.618034 + 1.90211i
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 −1.73205 −1.73205 −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
770770 0 0
771771 0 0
772772 1.07047 + 3.29456i 1.07047 + 3.29456i
773773 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
774774 0 0
775775 0 0
776776 −0.535233 + 1.64728i −0.535233 + 1.64728i
777777 0 0
778778 0 0
779779 −0.927051 2.85317i −0.927051 2.85317i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −1.61803 1.17557i −1.61803 1.17557i
785785 0.809017 0.587785i 0.809017 0.587785i
786786 0 0
787787 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
788788 0 0
789789 0 0
790790 0 0
791791 1.73205 1.73205
792792 0 0
793793 0 0
794794 −0.535233 1.64728i −0.535233 1.64728i
795795 0 0
796796 0 0
797797 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 −0.927051 + 2.85317i −0.927051 + 2.85317i
809809 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
810810 −1.40126 + 1.01807i −1.40126 + 1.01807i
811811 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
812812 0 0
813813 0 0
814814 0 0
815815 1.00000 1.00000
816816 0 0
817817 0 0
818818 0 0
819819 0 0
820820 1.07047 3.29456i 1.07047 3.29456i
821821 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
822822 0 0
823823 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
824824 −1.73205 −1.73205
825825 0 0
826826 −3.00000 −3.00000
827827 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
828828 0 0
829829 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0.535233 + 1.64728i 0.535233 + 1.64728i
839839 −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i 0.800000π-0.800000\pi
−0.809017 0.587785i 0.800000π-0.800000\pi
840840 0 0
841841 0.309017 0.951057i 0.309017 0.951057i
842842 −0.535233 + 1.64728i −0.535233 + 1.64728i
843843 0 0
844844 2.80252 + 2.03615i 2.80252 + 2.03615i
845845 −0.309017 0.951057i −0.309017 0.951057i
846846 3.46410 3.46410
847847 0 0
848848 0 0
849849 0 0
850850 0 0
851851 0 0
852852 0 0
853853 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
854854 0 0
855855 1.40126 + 1.01807i 1.40126 + 1.01807i
856856 −0.927051 2.85317i −0.927051 2.85317i
857857 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
858858 0 0
859859 0 0 1.00000 00
−1.00000 π\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
864864 0 0
865865 0 0
866866 0 0
867867 0 0
868868 3.46410 3.46410
869869 0 0
870870 0 0
871871 0 0
872872 2.42705 + 1.76336i 2.42705 + 1.76336i
873873 −0.809017 + 0.587785i −0.809017 + 0.587785i
874874 0 0
875875 −0.535233 + 1.64728i −0.535233 + 1.64728i
876876 0 0
877877 −1.40126 1.01807i −1.40126 1.01807i −0.994522 0.104528i 0.966667π-0.966667\pi
−0.406737 0.913545i 0.633333π-0.633333\pi
878878 −0.927051 2.85317i −0.927051 2.85317i
879879 0 0
880880 0 0
881881 0 0 1.00000 00
−1.00000 π\pi
882882 −1.07047 3.29456i −1.07047 3.29456i
883883 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
884884 0 0
885885 0 0
886886 −0.535233 + 1.64728i −0.535233 + 1.64728i
887887 −1.40126 + 1.01807i −1.40126 + 1.01807i −0.406737 + 0.913545i 0.633333π0.633333\pi
−0.994522 + 0.104528i 0.966667π0.966667\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 −1.07047 3.29456i −1.07047 3.29456i
894894 0 0
895895 0 0
896896 −0.927051 + 2.85317i −0.927051 + 2.85317i
897897 0 0
898898 0 0
899899 0 0
900900 0 0
901901 0 0
902902 0 0
903903 0 0
904904 0.535233 + 1.64728i 0.535233 + 1.64728i
905905 0 0
906906 0 0
907907 −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i 0.266667π0.266667\pi
−0.978148 + 0.207912i 0.933333π0.933333\pi
908908 0 0
909909 −1.40126 + 1.01807i −1.40126 + 1.01807i
910910 0 0
911911 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 −0.809017 0.587785i −0.809017 0.587785i
928928 0 0
929929 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
930930 0 0
931931 −2.80252 + 2.03615i −2.80252 + 2.03615i
932932 −2.80252 2.03615i −2.80252 2.03615i
933933 0 0
934934 −1.73205 −1.73205
935935 0 0
936936 0 0
937937 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
938938 −4.85410 3.52671i −4.85410 3.52671i
939939 0 0
940940 1.23607 3.80423i 1.23607 3.80423i
941941 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
942942 0 0
943943 0 0
944944 −0.309017 0.951057i −0.309017 0.951057i
945945 0 0
946946 0 0
947947 0 0 1.00000 00
−1.00000 π\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
954954 0 0
955955 0.309017 + 0.951057i 0.309017 + 0.951057i
956956 0 0
957957 0 0
958958 3.00000 3.00000
959959 0 0
960960 0 0
961961 −0.809017 + 0.587785i −0.809017 + 0.587785i
962962 0 0
963963 0.535233 1.64728i 0.535233 1.64728i
964964 0 0
965965 1.40126 + 1.01807i 1.40126 + 1.01807i
966966 0 0
967967 0 0 1.00000 00
−1.00000 π\pi
968968 0 0
969969 0 0
970970 0.535233 + 1.64728i 0.535233 + 1.64728i
971971 −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i 0.800000π-0.800000\pi
−0.809017 0.587785i 0.800000π-0.800000\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i 0.0666667π0.0666667\pi
−0.669131 + 0.743145i 0.733333π0.733333\pi
978978 0 0
979979 0 0
980980 −4.00000 −4.00000
981981 0.535233 + 1.64728i 0.535233 + 1.64728i
982982 0 0
983983 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 1.00000 00
−1.00000 π\pi
992992 0 0
993993 0 0
994994 −2.42705 + 1.76336i −2.42705 + 1.76336i
995995 0 0
996996 0 0
997997 1.40126 1.01807i 1.40126 1.01807i 0.406737 0.913545i 0.366667π-0.366667\pi
0.994522 0.104528i 0.0333333π-0.0333333\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3751.1.t.d.3657.1 8
11.2 odd 10 inner 3751.1.t.d.2913.2 8
11.3 even 5 3751.1.d.c.1332.1 2
11.4 even 5 inner 3751.1.t.d.2665.2 8
11.5 even 5 inner 3751.1.t.d.2138.2 8
11.6 odd 10 inner 3751.1.t.d.2138.1 8
11.7 odd 10 inner 3751.1.t.d.2665.1 8
11.8 odd 10 3751.1.d.c.1332.2 yes 2
11.9 even 5 inner 3751.1.t.d.2913.1 8
11.10 odd 2 inner 3751.1.t.d.3657.2 8
31.30 odd 2 CM 3751.1.t.d.3657.1 8
341.30 even 10 3751.1.d.c.1332.2 yes 2
341.61 even 10 inner 3751.1.t.d.2138.1 8
341.92 odd 10 inner 3751.1.t.d.2665.2 8
341.123 even 10 inner 3751.1.t.d.2913.2 8
341.185 odd 10 inner 3751.1.t.d.2913.1 8
341.216 even 10 inner 3751.1.t.d.2665.1 8
341.247 odd 10 inner 3751.1.t.d.2138.2 8
341.278 odd 10 3751.1.d.c.1332.1 2
341.340 even 2 inner 3751.1.t.d.3657.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3751.1.d.c.1332.1 2 11.3 even 5
3751.1.d.c.1332.1 2 341.278 odd 10
3751.1.d.c.1332.2 yes 2 11.8 odd 10
3751.1.d.c.1332.2 yes 2 341.30 even 10
3751.1.t.d.2138.1 8 11.6 odd 10 inner
3751.1.t.d.2138.1 8 341.61 even 10 inner
3751.1.t.d.2138.2 8 11.5 even 5 inner
3751.1.t.d.2138.2 8 341.247 odd 10 inner
3751.1.t.d.2665.1 8 11.7 odd 10 inner
3751.1.t.d.2665.1 8 341.216 even 10 inner
3751.1.t.d.2665.2 8 11.4 even 5 inner
3751.1.t.d.2665.2 8 341.92 odd 10 inner
3751.1.t.d.2913.1 8 11.9 even 5 inner
3751.1.t.d.2913.1 8 341.185 odd 10 inner
3751.1.t.d.2913.2 8 11.2 odd 10 inner
3751.1.t.d.2913.2 8 341.123 even 10 inner
3751.1.t.d.3657.1 8 1.1 even 1 trivial
3751.1.t.d.3657.1 8 31.30 odd 2 CM
3751.1.t.d.3657.2 8 11.10 odd 2 inner
3751.1.t.d.3657.2 8 341.340 even 2 inner