Properties

Label 3192.1.eb.a.341.6
Level 31923192
Weight 11
Character 3192.341
Analytic conductor 1.5931.593
Analytic rank 00
Dimension 1212
Projective image D18D_{18}
CM discriminant -152
Inner twists 88

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3192,1,Mod(341,3192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3192, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 5, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3192.341");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 3192=233719 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3192.eb (of order 66, degree 22, 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: 1.593015520321.59301552032
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ36)\Q(\zeta_{36})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12x6+1 x^{12} - x^{6} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D18D_{18}
Projective field: Galois closure of Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)

Embedding invariants

Embedding label 341.6
Root 0.984808+0.173648i-0.984808 + 0.173648i of defining polynomial
Character χ\chi == 3192.341
Dual form 3192.1.eb.a.2621.6

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+(0.866025+0.500000i)q2+(0.9848080.173648i)q3+(0.500000+0.866025i)q4+(0.939693+0.342020i)q6+(0.7660440.642788i)q7+1.00000iq8+(0.9396930.342020i)q9+(0.642788+0.766044i)q12+1.53209iq13+(0.9848080.173648i)q14+(0.500000+0.866025i)q16+(0.1736480.300767i)q17+(0.984808+0.173648i)q18+(0.8660250.500000i)q19+(0.6427880.766044i)q21+(1.705740.984808i)q23+(0.173648+0.984808i)q24+(0.5000000.866025i)q25+(0.766044+1.32683i)q26+(0.8660250.500000i)q27+(0.939693+0.342020i)q28+1.87939iq29+(0.866025+0.500000i)q320.347296iq34+(0.766044+0.642788i)q36+(0.8660251.50000i)q37+(0.5000000.866025i)q38+(0.266044+1.50881i)q39+(0.9396930.342020i)q42+(0.9848081.70574i)q46+(0.500000+0.866025i)q47+(0.342020+0.939693i)q48+(0.1736480.984808i)q491.00000iq50+(0.2232380.266044i)q51+(1.32683+0.766044i)q52+(0.3007670.173648i)q53+1.00000q54+(0.642788+0.766044i)q56+(0.9396930.342020i)q57+(0.939693+1.62760i)q58+(0.9848081.70574i)q59+(0.5000000.866025i)q631.00000q64+(0.342020+0.592396i)q67+(0.1736480.300767i)q68+(1.850830.673648i)q69+(0.342020+0.939693i)q72+(1.11334+0.642788i)q73+(1.500000.866025i)q74+(0.6427880.766044i)q751.00000iq76+(0.524005+1.43969i)q78+(0.7660440.642788i)q81+(0.984808+0.173648i)q84+(0.326352+1.85083i)q87+(0.984808+1.17365i)q911.96962iq92+(0.866025+0.500000i)q94+(0.766044+0.642788i)q96+(0.6427880.766044i)q98+O(q100)q+(0.866025 + 0.500000i) q^{2} +(0.984808 - 0.173648i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.939693 + 0.342020i) q^{6} +(0.766044 - 0.642788i) q^{7} +1.00000i q^{8} +(0.939693 - 0.342020i) q^{9} +(0.642788 + 0.766044i) q^{12} +1.53209i q^{13} +(0.984808 - 0.173648i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.173648 - 0.300767i) q^{17} +(0.984808 + 0.173648i) q^{18} +(-0.866025 - 0.500000i) q^{19} +(0.642788 - 0.766044i) q^{21} +(-1.70574 - 0.984808i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.766044 + 1.32683i) q^{26} +(0.866025 - 0.500000i) q^{27} +(0.939693 + 0.342020i) q^{28} +1.87939i q^{29} +(-0.866025 + 0.500000i) q^{32} -0.347296i q^{34} +(0.766044 + 0.642788i) q^{36} +(0.866025 - 1.50000i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(0.266044 + 1.50881i) q^{39} +(0.939693 - 0.342020i) q^{42} +(-0.984808 - 1.70574i) q^{46} +(-0.500000 + 0.866025i) q^{47} +(-0.342020 + 0.939693i) q^{48} +(0.173648 - 0.984808i) q^{49} -1.00000i q^{50} +(-0.223238 - 0.266044i) q^{51} +(-1.32683 + 0.766044i) q^{52} +(0.300767 - 0.173648i) q^{53} +1.00000 q^{54} +(0.642788 + 0.766044i) q^{56} +(-0.939693 - 0.342020i) q^{57} +(-0.939693 + 1.62760i) q^{58} +(-0.984808 - 1.70574i) q^{59} +(0.500000 - 0.866025i) q^{63} -1.00000 q^{64} +(0.342020 + 0.592396i) q^{67} +(0.173648 - 0.300767i) q^{68} +(-1.85083 - 0.673648i) q^{69} +(0.342020 + 0.939693i) q^{72} +(-1.11334 + 0.642788i) q^{73} +(1.50000 - 0.866025i) q^{74} +(-0.642788 - 0.766044i) q^{75} -1.00000i q^{76} +(-0.524005 + 1.43969i) q^{78} +(0.766044 - 0.642788i) q^{81} +(0.984808 + 0.173648i) q^{84} +(0.326352 + 1.85083i) q^{87} +(0.984808 + 1.17365i) q^{91} -1.96962i q^{92} +(-0.866025 + 0.500000i) q^{94} +(-0.766044 + 0.642788i) q^{96} +(0.642788 - 0.766044i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+6q46q166q256q386q396q47+12q54+6q6312q64+18q74+6q87+O(q100) 12 q + 6 q^{4} - 6 q^{16} - 6 q^{25} - 6 q^{38} - 6 q^{39} - 6 q^{47} + 12 q^{54} + 6 q^{63} - 12 q^{64} + 18 q^{74} + 6 q^{87}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3192Z)×\left(\mathbb{Z}/3192\mathbb{Z}\right)^\times.

nn 799799 913913 10091009 15971597 21292129
χ(n)\chi(n) 11 e(56)e\left(\frac{5}{6}\right) 1-1 1-1 1-1

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 0.866025 + 0.500000i 0.866025 + 0.500000i
33 0.984808 0.173648i 0.984808 0.173648i
44 0.500000 + 0.866025i 0.500000 + 0.866025i
55 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
66 0.939693 + 0.342020i 0.939693 + 0.342020i
77 0.766044 0.642788i 0.766044 0.642788i
88 1.00000i 1.00000i
99 0.939693 0.342020i 0.939693 0.342020i
1010 0 0
1111 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
1212 0.642788 + 0.766044i 0.642788 + 0.766044i
1313 1.53209i 1.53209i 0.642788 + 0.766044i 0.277778π0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
1414 0.984808 0.173648i 0.984808 0.173648i
1515 0 0
1616 −0.500000 + 0.866025i −0.500000 + 0.866025i
1717 −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
1818 0.984808 + 0.173648i 0.984808 + 0.173648i
1919 −0.866025 0.500000i −0.866025 0.500000i
2020 0 0
2121 0.642788 0.766044i 0.642788 0.766044i
2222 0 0
2323 −1.70574 0.984808i −1.70574 0.984808i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.766044 0.642788i 0.777778π-0.777778\pi
2424 0.173648 + 0.984808i 0.173648 + 0.984808i
2525 −0.500000 0.866025i −0.500000 0.866025i
2626 −0.766044 + 1.32683i −0.766044 + 1.32683i
2727 0.866025 0.500000i 0.866025 0.500000i
2828 0.939693 + 0.342020i 0.939693 + 0.342020i
2929 1.87939i 1.87939i 0.342020 + 0.939693i 0.388889π0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
3030 0 0
3131 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
3232 −0.866025 + 0.500000i −0.866025 + 0.500000i
3333 0 0
3434 0.347296i 0.347296i
3535 0 0
3636 0.766044 + 0.642788i 0.766044 + 0.642788i
3737 0.866025 1.50000i 0.866025 1.50000i 1.00000i 0.5π-0.5\pi
0.866025 0.500000i 0.166667π-0.166667\pi
3838 −0.500000 0.866025i −0.500000 0.866025i
3939 0.266044 + 1.50881i 0.266044 + 1.50881i
4040 0 0
4141 0 0 1.00000 00
−1.00000 π\pi
4242 0.939693 0.342020i 0.939693 0.342020i
4343 0 0 1.00000 00
−1.00000 π\pi
4444 0 0
4545 0 0
4646 −0.984808 1.70574i −0.984808 1.70574i
4747 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
4848 −0.342020 + 0.939693i −0.342020 + 0.939693i
4949 0.173648 0.984808i 0.173648 0.984808i
5050 1.00000i 1.00000i
5151 −0.223238 0.266044i −0.223238 0.266044i
5252 −1.32683 + 0.766044i −1.32683 + 0.766044i
5353 0.300767 0.173648i 0.300767 0.173648i −0.342020 0.939693i 0.611111π-0.611111\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
5454 1.00000 1.00000
5555 0 0
5656 0.642788 + 0.766044i 0.642788 + 0.766044i
5757 −0.939693 0.342020i −0.939693 0.342020i
5858 −0.939693 + 1.62760i −0.939693 + 1.62760i
5959 −0.984808 1.70574i −0.984808 1.70574i −0.642788 0.766044i 0.722222π-0.722222\pi
−0.342020 0.939693i 0.611111π-0.611111\pi
6060 0 0
6161 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
6262 0 0
6363 0.500000 0.866025i 0.500000 0.866025i
6464 −1.00000 −1.00000
6565 0 0
6666 0 0
6767 0.342020 + 0.592396i 0.342020 + 0.592396i 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
6868 0.173648 0.300767i 0.173648 0.300767i
6969 −1.85083 0.673648i −1.85083 0.673648i
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0.342020 + 0.939693i 0.342020 + 0.939693i
7373 −1.11334 + 0.642788i −1.11334 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
7474 1.50000 0.866025i 1.50000 0.866025i
7575 −0.642788 0.766044i −0.642788 0.766044i
7676 1.00000i 1.00000i
7777 0 0
7878 −0.524005 + 1.43969i −0.524005 + 1.43969i
7979 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
8080 0 0
8181 0.766044 0.642788i 0.766044 0.642788i
8282 0 0
8383 0 0 1.00000 00
−1.00000 π\pi
8484 0.984808 + 0.173648i 0.984808 + 0.173648i
8585 0 0
8686 0 0
8787 0.326352 + 1.85083i 0.326352 + 1.85083i
8888 0 0
8989 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
9090 0 0
9191 0.984808 + 1.17365i 0.984808 + 1.17365i
9292 1.96962i 1.96962i
9393 0 0
9494 −0.866025 + 0.500000i −0.866025 + 0.500000i
9595 0 0
9696 −0.766044 + 0.642788i −0.766044 + 0.642788i
9797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9898 0.642788 0.766044i 0.642788 0.766044i
9999 0 0
100100 0.500000 0.866025i 0.500000 0.866025i
101101 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
102102 −0.0603074 0.342020i −0.0603074 0.342020i
103103 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
104104 −1.53209 −1.53209
105105 0 0
106106 0.347296 0.347296
107107 1.32683 + 0.766044i 1.32683 + 0.766044i 0.984808 0.173648i 0.0555556π-0.0555556\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
108108 0.866025 + 0.500000i 0.866025 + 0.500000i
109109 0.642788 + 1.11334i 0.642788 + 1.11334i 0.984808 + 0.173648i 0.0555556π0.0555556\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
110110 0 0
111111 0.592396 1.62760i 0.592396 1.62760i
112112 0.173648 + 0.984808i 0.173648 + 0.984808i
113113 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
114114 −0.642788 0.766044i −0.642788 0.766044i
115115 0 0
116116 −1.62760 + 0.939693i −1.62760 + 0.939693i
117117 0.524005 + 1.43969i 0.524005 + 1.43969i
118118 1.96962i 1.96962i
119119 −0.326352 0.118782i −0.326352 0.118782i
120120 0 0
121121 0.500000 0.866025i 0.500000 0.866025i
122122 0 0
123123 0 0
124124 0 0
125125 0 0
126126 0.866025 0.500000i 0.866025 0.500000i
127127 0 0 1.00000 00
−1.00000 π\pi
128128 −0.866025 0.500000i −0.866025 0.500000i
129129 0 0
130130 0 0
131131 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
132132 0 0
133133 −0.984808 + 0.173648i −0.984808 + 0.173648i
134134 0.684040i 0.684040i
135135 0 0
136136 0.300767 0.173648i 0.300767 0.173648i
137137 0.592396 0.342020i 0.592396 0.342020i −0.173648 0.984808i 0.555556π-0.555556\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
138138 −1.26604 1.50881i −1.26604 1.50881i
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 0 0
141141 −0.342020 + 0.939693i −0.342020 + 0.939693i
142142 0 0
143143 0 0
144144 −0.173648 + 0.984808i −0.173648 + 0.984808i
145145 0 0
146146 −1.28558 −1.28558
147147 1.00000i 1.00000i
148148 1.73205 1.73205
149149 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
150150 −0.173648 0.984808i −0.173648 0.984808i
151151 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
152152 0.500000 0.866025i 0.500000 0.866025i
153153 −0.266044 0.223238i −0.266044 0.223238i
154154 0 0
155155 0 0
156156 −1.17365 + 0.984808i −1.17365 + 0.984808i
157157 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
158158 0 0
159159 0.266044 0.223238i 0.266044 0.223238i
160160 0 0
161161 −1.93969 + 0.342020i −1.93969 + 0.342020i
162162 0.984808 0.173648i 0.984808 0.173648i
163163 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 1.00000 00
−1.00000 π\pi
168168 0.766044 + 0.642788i 0.766044 + 0.642788i
169169 −1.34730 −1.34730
170170 0 0
171171 −0.984808 0.173648i −0.984808 0.173648i
172172 0 0
173173 −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i 0.5π0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
174174 −0.642788 + 1.76604i −0.642788 + 1.76604i
175175 −0.939693 0.342020i −0.939693 0.342020i
176176 0 0
177177 −1.26604 1.50881i −1.26604 1.50881i
178178 0 0
179179 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
180180 0 0
181181 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
182182 0.266044 + 1.50881i 0.266044 + 1.50881i
183183 0 0
184184 0.984808 1.70574i 0.984808 1.70574i
185185 0 0
186186 0 0
187187 0 0
188188 −1.00000 −1.00000
189189 0.342020 0.939693i 0.342020 0.939693i
190190 0 0
191191 −0.592396 0.342020i −0.592396 0.342020i 0.173648 0.984808i 0.444444π-0.444444\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
192192 −0.984808 + 0.173648i −0.984808 + 0.173648i
193193 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
194194 0 0
195195 0 0
196196 0.939693 0.342020i 0.939693 0.342020i
197197 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
198198 0 0
199199 −1.70574 + 0.984808i −1.70574 + 0.984808i −0.766044 + 0.642788i 0.777778π0.777778\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
200200 0.866025 0.500000i 0.866025 0.500000i
201201 0.439693 + 0.524005i 0.439693 + 0.524005i
202202 0 0
203203 1.20805 + 1.43969i 1.20805 + 1.43969i
204204 0.118782 0.326352i 0.118782 0.326352i
205205 0 0
206206 0 0
207207 −1.93969 0.342020i −1.93969 0.342020i
208208 −1.32683 0.766044i −1.32683 0.766044i
209209 0 0
210210 0 0
211211 −1.28558 −1.28558 −0.642788 0.766044i 0.722222π-0.722222\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
212212 0.300767 + 0.173648i 0.300767 + 0.173648i
213213 0 0
214214 0.766044 + 1.32683i 0.766044 + 1.32683i
215215 0 0
216216 0.500000 + 0.866025i 0.500000 + 0.866025i
217217 0 0
218218 1.28558i 1.28558i
219219 −0.984808 + 0.826352i −0.984808 + 0.826352i
220220 0 0
221221 0.460802 0.266044i 0.460802 0.266044i
222222 1.32683 1.11334i 1.32683 1.11334i
223223 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
224224 −0.342020 + 0.939693i −0.342020 + 0.939693i
225225 −0.766044 0.642788i −0.766044 0.642788i
226226 0 0
227227 −0.642788 1.11334i −0.642788 1.11334i −0.984808 0.173648i 0.944444π-0.944444\pi
0.342020 0.939693i 0.388889π-0.388889\pi
228228 −0.173648 0.984808i −0.173648 0.984808i
229229 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
230230 0 0
231231 0 0
232232 −1.87939 −1.87939
233233 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 00
0.500000 + 0.866025i 0.333333π0.333333\pi
234234 −0.266044 + 1.50881i −0.266044 + 1.50881i
235235 0 0
236236 0.984808 1.70574i 0.984808 1.70574i
237237 0 0
238238 −0.223238 0.266044i −0.223238 0.266044i
239239 1.28558i 1.28558i −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 0.642788i 0.222222π-0.222222\pi
240240 0 0
241241 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
242242 0.866025 0.500000i 0.866025 0.500000i
243243 0.642788 0.766044i 0.642788 0.766044i
244244 0 0
245245 0 0
246246 0 0
247247 0.766044 1.32683i 0.766044 1.32683i
248248 0 0
249249 0 0
250250 0 0
251251 0 0 1.00000 00
−1.00000 π\pi
252252 1.00000 1.00000
253253 0 0
254254 0 0
255255 0 0
256256 −0.500000 0.866025i −0.500000 0.866025i
257257 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
258258 0 0
259259 −0.300767 1.70574i −0.300767 1.70574i
260260 0 0
261261 0.642788 + 1.76604i 0.642788 + 1.76604i
262262 0 0
263263 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
1.00000 00
264264 0 0
265265 0 0
266266 −0.939693 0.342020i −0.939693 0.342020i
267267 0 0
268268 −0.342020 + 0.592396i −0.342020 + 0.592396i
269269 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
270270 0 0
271271 1.11334 + 0.642788i 1.11334 + 0.642788i 0.939693 0.342020i 0.111111π-0.111111\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
272272 0.347296 0.347296
273273 1.17365 + 0.984808i 1.17365 + 0.984808i
274274 0.684040 0.684040
275275 0 0
276276 −0.342020 1.93969i −0.342020 1.93969i
277277 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
278278 0 0
279279 0 0
280280 0 0
281281 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
282282 −0.766044 + 0.642788i −0.766044 + 0.642788i
283283 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 −0.642788 + 0.766044i −0.642788 + 0.766044i
289289 0.439693 0.761570i 0.439693 0.761570i
290290 0 0
291291 0 0
292292 −1.11334 0.642788i −1.11334 0.642788i
293293 −1.96962 −1.96962 −0.984808 0.173648i 0.944444π-0.944444\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
294294 0.500000 0.866025i 0.500000 0.866025i
295295 0 0
296296 1.50000 + 0.866025i 1.50000 + 0.866025i
297297 0 0
298298 0 0
299299 1.50881 2.61334i 1.50881 2.61334i
300300 0.342020 0.939693i 0.342020 0.939693i
301301 0 0
302302 0 0
303303 0 0
304304 0.866025 0.500000i 0.866025 0.500000i
305305 0 0
306306 −0.118782 0.326352i −0.118782 0.326352i
307307 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
308308 0 0
309309 0 0
310310 0 0
311311 −0.939693 1.62760i −0.939693 1.62760i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.173648 0.984808i 0.555556π-0.555556\pi
312312 −1.50881 + 0.266044i −1.50881 + 0.266044i
313313 −0.592396 0.342020i −0.592396 0.342020i 0.173648 0.984808i 0.444444π-0.444444\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
314314 0 0
315315 0 0
316316 0 0
317317 −1.32683 0.766044i −1.32683 0.766044i −0.342020 0.939693i 0.611111π-0.611111\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
318318 0.342020 0.0603074i 0.342020 0.0603074i
319319 0 0
320320 0 0
321321 1.43969 + 0.524005i 1.43969 + 0.524005i
322322 −1.85083 0.673648i −1.85083 0.673648i
323323 0.347296i 0.347296i
324324 0.939693 + 0.342020i 0.939693 + 0.342020i
325325 1.32683 0.766044i 1.32683 0.766044i
326326 0 0
327327 0.826352 + 0.984808i 0.826352 + 0.984808i
328328 0 0
329329 0.173648 + 0.984808i 0.173648 + 0.984808i
330330 0 0
331331 −0.642788 + 1.11334i −0.642788 + 1.11334i 0.342020 + 0.939693i 0.388889π0.388889\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
332332 0 0
333333 0.300767 1.70574i 0.300767 1.70574i
334334 0 0
335335 0 0
336336 0.342020 + 0.939693i 0.342020 + 0.939693i
337337 0 0 1.00000 00
−1.00000 π\pi
338338 −1.16679 0.673648i −1.16679 0.673648i
339339 0 0
340340 0 0
341341 0 0
342342 −0.766044 0.642788i −0.766044 0.642788i
343343 −0.500000 0.866025i −0.500000 0.866025i
344344 0 0
345345 0 0
346346 −1.50000 + 0.866025i −1.50000 + 0.866025i
347347 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
348348 −1.43969 + 1.20805i −1.43969 + 1.20805i
349349 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
350350 −0.642788 0.766044i −0.642788 0.766044i
351351 0.766044 + 1.32683i 0.766044 + 1.32683i
352352 0 0
353353 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
354354 −0.342020 1.93969i −0.342020 1.93969i
355355 0 0
356356 0 0
357357 −0.342020 0.0603074i −0.342020 0.0603074i
358358 1.00000 1.00000
359359 1.11334 + 0.642788i 1.11334 + 0.642788i 0.939693 0.342020i 0.111111π-0.111111\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
360360 0 0
361361 0.500000 + 0.866025i 0.500000 + 0.866025i
362362 −0.500000 + 0.866025i −0.500000 + 0.866025i
363363 0.342020 0.939693i 0.342020 0.939693i
364364 −0.524005 + 1.43969i −0.524005 + 1.43969i
365365 0 0
366366 0 0
367367 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
1.00000 00
368368 1.70574 0.984808i 1.70574 0.984808i
369369 0 0
370370 0 0
371371 0.118782 0.326352i 0.118782 0.326352i
372372 0 0
373373 −0.984808 + 1.70574i −0.984808 + 1.70574i −0.342020 + 0.939693i 0.611111π0.611111\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
374374 0 0
375375 0 0
376376 −0.866025 0.500000i −0.866025 0.500000i
377377 −2.87939 −2.87939
378378 0.766044 0.642788i 0.766044 0.642788i
379379 1.96962 1.96962 0.984808 0.173648i 0.0555556π-0.0555556\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
380380 0 0
381381 0 0
382382 −0.342020 0.592396i −0.342020 0.592396i
383383 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
384384 −0.939693 0.342020i −0.939693 0.342020i
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
390390 0 0
391391 0.684040i 0.684040i
392392 0.984808 + 0.173648i 0.984808 + 0.173648i
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
398398 −1.96962 −1.96962
399399 −0.939693 + 0.342020i −0.939693 + 0.342020i
400400 1.00000 1.00000
401401 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
402402 0.118782 + 0.673648i 0.118782 + 0.673648i
403403 0 0
404404 0 0
405405 0 0
406406 0.326352 + 1.85083i 0.326352 + 1.85083i
407407 0 0
408408 0.266044 0.223238i 0.266044 0.223238i
409409 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
410410 0 0
411411 0.524005 0.439693i 0.524005 0.439693i
412412 0 0
413413 −1.85083 0.673648i −1.85083 0.673648i
414414 −1.50881 1.26604i −1.50881 1.26604i
415415 0 0
416416 −0.766044 1.32683i −0.766044 1.32683i
417417 0 0
418418 0 0
419419 0 0 1.00000 00
−1.00000 π\pi
420420 0 0
421421 0.684040 0.684040 0.342020 0.939693i 0.388889π-0.388889\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
422422 −1.11334 0.642788i −1.11334 0.642788i
423423 −0.173648 + 0.984808i −0.173648 + 0.984808i
424424 0.173648 + 0.300767i 0.173648 + 0.300767i
425425 −0.173648 + 0.300767i −0.173648 + 0.300767i
426426 0 0
427427 0 0
428428 1.53209i 1.53209i
429429 0 0
430430 0 0
431431 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
432432 1.00000i 1.00000i
433433 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
434434 0 0
435435 0 0
436436 −0.642788 + 1.11334i −0.642788 + 1.11334i
437437 0.984808 + 1.70574i 0.984808 + 1.70574i
438438 −1.26604 + 0.223238i −1.26604 + 0.223238i
439439 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
440440 0 0
441441 −0.173648 0.984808i −0.173648 0.984808i
442442 0.532089 0.532089
443443 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
444444 1.70574 0.300767i 1.70574 0.300767i
445445 0 0
446446 0 0
447447 0 0
448448 −0.766044 + 0.642788i −0.766044 + 0.642788i
449449 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
450450 −0.342020 0.939693i −0.342020 0.939693i
451451 0 0
452452 0 0
453453 0 0
454454 1.28558i 1.28558i
455455 0 0
456456 0.342020 0.939693i 0.342020 0.939693i
457457 0.173648 0.300767i 0.173648 0.300767i −0.766044 0.642788i 0.777778π-0.777778\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
458458 0 0
459459 −0.300767 0.173648i −0.300767 0.173648i
460460 0 0
461461 0 0 1.00000 00
−1.00000 π\pi
462462 0 0
463463 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
464464 −1.62760 0.939693i −1.62760 0.939693i
465465 0 0
466466 0.866025 + 1.50000i 0.866025 + 1.50000i
467467 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
468468 −0.984808 + 1.17365i −0.984808 + 1.17365i
469469 0.642788 + 0.233956i 0.642788 + 0.233956i
470470 0 0
471471 0 0
472472 1.70574 0.984808i 1.70574 0.984808i
473473 0 0
474474 0 0
475475 1.00000i 1.00000i
476476 −0.0603074 0.342020i −0.0603074 0.342020i
477477 0.223238 0.266044i 0.223238 0.266044i
478478 0.642788 1.11334i 0.642788 1.11334i
479479 −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
480480 0 0
481481 2.29813 + 1.32683i 2.29813 + 1.32683i
482482 0 0
483483 −1.85083 + 0.673648i −1.85083 + 0.673648i
484484 1.00000 1.00000
485485 0 0
486486 0.939693 0.342020i 0.939693 0.342020i
487487 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
488488 0 0
489489 0 0
490490 0 0
491491 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
492492 0 0
493493 0.565258 0.326352i 0.565258 0.326352i
494494 1.32683 0.766044i 1.32683 0.766044i
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
500500 0 0
501501 0 0
502502 0 0
503503 1.87939 1.87939 0.939693 0.342020i 0.111111π-0.111111\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
504504 0.866025 + 0.500000i 0.866025 + 0.500000i
505505 0 0
506506 0 0
507507 −1.32683 + 0.233956i −1.32683 + 0.233956i
508508 0 0
509509 0.866025 1.50000i 0.866025 1.50000i 1.00000i 0.5π-0.5\pi
0.866025 0.500000i 0.166667π-0.166667\pi
510510 0 0
511511 −0.439693 + 1.20805i −0.439693 + 1.20805i
512512 1.00000i 1.00000i
513513 −1.00000 −1.00000
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 0.592396 1.62760i 0.592396 1.62760i
519519 −0.592396 + 1.62760i −0.592396 + 1.62760i
520520 0 0
521521 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
522522 −0.326352 + 1.85083i −0.326352 + 1.85083i
523523 0.300767 + 0.173648i 0.300767 + 0.173648i 0.642788 0.766044i 0.277778π-0.277778\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
524524 0 0
525525 −0.984808 0.173648i −0.984808 0.173648i
526526 1.73205 1.73205
527527 0 0
528528 0 0
529529 1.43969 + 2.49362i 1.43969 + 2.49362i
530530 0 0
531531 −1.50881 1.26604i −1.50881 1.26604i
532532 −0.642788 0.766044i −0.642788 0.766044i
533533 0 0
534534 0 0
535535 0 0
536536 −0.592396 + 0.342020i −0.592396 + 0.342020i
537537 0.766044 0.642788i 0.766044 0.642788i
538538 0 0
539539 0 0
540540 0 0
541541 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
542542 0.642788 + 1.11334i 0.642788 + 1.11334i
543543 0.173648 + 0.984808i 0.173648 + 0.984808i
544544 0.300767 + 0.173648i 0.300767 + 0.173648i
545545 0 0
546546 0.524005 + 1.43969i 0.524005 + 1.43969i
547547 −1.73205 −1.73205 −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
548548 0.592396 + 0.342020i 0.592396 + 0.342020i
549549 0 0
550550 0 0
551551 0.939693 1.62760i 0.939693 1.62760i
552552 0.673648 1.85083i 0.673648 1.85083i
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
564564 −0.984808 + 0.173648i −0.984808 + 0.173648i
565565 0 0
566566 0 0
567567 0.173648 0.984808i 0.173648 0.984808i
568568 0 0
569569 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
570570 0 0
571571 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
572572 0 0
573573 −0.642788 0.233956i −0.642788 0.233956i
574574 0 0
575575 1.96962i 1.96962i
576576 −0.939693 + 0.342020i −0.939693 + 0.342020i
577577 −0.592396 + 0.342020i −0.592396 + 0.342020i −0.766044 0.642788i 0.777778π-0.777778\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
578578 0.761570 0.439693i 0.761570 0.439693i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 −0.642788 1.11334i −0.642788 1.11334i
585585 0 0
586586 −1.70574 0.984808i −1.70574 0.984808i
587587 0 0 1.00000 00
−1.00000 π\pi
588588 0.866025 0.500000i 0.866025 0.500000i
589589 0 0
590590 0 0
591591 0 0
592592 0.866025 + 1.50000i 0.866025 + 1.50000i
593593 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 0.866025i 0.333333π-0.333333\pi
594594 0 0
595595 0 0
596596 0 0
597597 −1.50881 + 1.26604i −1.50881 + 1.26604i
598598 2.61334 1.50881i 2.61334 1.50881i
599599 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
600600 0.766044 0.642788i 0.766044 0.642788i
601601 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
602602 0 0
603603 0.524005 + 0.439693i 0.524005 + 0.439693i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
608608 1.00000 1.00000
609609 1.43969 + 1.20805i 1.43969 + 1.20805i
610610 0 0
611611 −1.32683 0.766044i −1.32683 0.766044i
612612 0.0603074 0.342020i 0.0603074 0.342020i
613613 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
614614 −0.500000 + 0.866025i −0.500000 + 0.866025i
615615 0 0
616616 0 0
617617 1.73205i 1.73205i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
618618 0 0
619619 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
620620 0 0
621621 −1.96962 −1.96962
622622 1.87939i 1.87939i
623623 0 0
624624 −1.43969 0.524005i −1.43969 0.524005i
625625 −0.500000 + 0.866025i −0.500000 + 0.866025i
626626 −0.342020 0.592396i −0.342020 0.592396i
627627 0 0
628628 0 0
629629 −0.601535 −0.601535
630630 0 0
631631 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
632632 0 0
633633 −1.26604 + 0.223238i −1.26604 + 0.223238i
634634 −0.766044 1.32683i −0.766044 1.32683i
635635 0 0
636636 0.326352 + 0.118782i 0.326352 + 0.118782i
637637 1.50881 + 0.266044i 1.50881 + 0.266044i
638638 0 0
639639 0 0
640640 0 0
641641 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
642642 0.984808 + 1.17365i 0.984808 + 1.17365i
643643 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
644644 −1.26604 1.50881i −1.26604 1.50881i
645645 0 0
646646 −0.173648 + 0.300767i −0.173648 + 0.300767i
647647 0.766044 + 1.32683i 0.766044 + 1.32683i 0.939693 + 0.342020i 0.111111π0.111111\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
648648 0.642788 + 0.766044i 0.642788 + 0.766044i
649649 0 0
650650 1.53209 1.53209
651651 0 0
652652 0 0
653653 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
654654 0.223238 + 1.26604i 0.223238 + 1.26604i
655655 0 0
656656 0 0
657657 −0.826352 + 0.984808i −0.826352 + 0.984808i
658658 −0.342020 + 0.939693i −0.342020 + 0.939693i
659659 1.53209i 1.53209i 0.642788 + 0.766044i 0.277778π0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
660660 0 0
661661 −1.62760 + 0.939693i −1.62760 + 0.939693i −0.642788 + 0.766044i 0.722222π0.722222\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
662662 −1.11334 + 0.642788i −1.11334 + 0.642788i
663663 0.407604 0.342020i 0.407604 0.342020i
664664 0 0
665665 0 0
666666 1.11334 1.32683i 1.11334 1.32683i
667667 1.85083 3.20574i 1.85083 3.20574i
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 −0.173648 + 0.984808i −0.173648 + 0.984808i
673673 0 0 1.00000 00
−1.00000 π\pi
674674 0 0
675675 −0.866025 0.500000i −0.866025 0.500000i
676676 −0.673648 1.16679i −0.673648 1.16679i
677677 0.342020 0.592396i 0.342020 0.592396i −0.642788 0.766044i 0.722222π-0.722222\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
678678 0 0
679679 0 0
680680 0 0
681681 −0.826352 0.984808i −0.826352 0.984808i
682682 0 0
683683 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
684684 −0.342020 0.939693i −0.342020 0.939693i
685685 0 0
686686 1.00000i 1.00000i
687687 0 0
688688 0 0
689689 0.266044 + 0.460802i 0.266044 + 0.460802i
690690 0 0
691691 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
692692 −1.73205 −1.73205
693693 0 0
694694 0 0
695695 0 0
696696 −1.85083 + 0.326352i −1.85083 + 0.326352i
697697 0 0
698698 0 0
699699 1.62760 + 0.592396i 1.62760 + 0.592396i
700700 −0.173648 0.984808i −0.173648 0.984808i
701701 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
702702 1.53209i 1.53209i
703703 −1.50000 + 0.866025i −1.50000 + 0.866025i
704704 0 0
705705 0 0
706706 1.87939i 1.87939i
707707 0 0
708708 0.673648 1.85083i 0.673648 1.85083i
709709 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
710710 0 0
711711 0 0
712712 0 0
713713 0 0
714714 −0.266044 0.223238i −0.266044 0.223238i
715715 0 0
716716 0.866025 + 0.500000i 0.866025 + 0.500000i
717717 −0.223238 1.26604i −0.223238 1.26604i
718718 0.642788 + 1.11334i 0.642788 + 1.11334i
719719 0.766044 1.32683i 0.766044 1.32683i −0.173648 0.984808i 0.555556π-0.555556\pi
0.939693 0.342020i 0.111111π-0.111111\pi
720720 0 0
721721 0 0
722722 1.00000i 1.00000i
723723 0 0
724724 −0.866025 + 0.500000i −0.866025 + 0.500000i
725725 1.62760 0.939693i 1.62760 0.939693i
726726 0.766044 0.642788i 0.766044 0.642788i
727727 0.684040i 0.684040i −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 0.342020i 0.111111π-0.111111\pi
728728 −1.17365 + 0.984808i −1.17365 + 0.984808i
729729 0.500000 0.866025i 0.500000 0.866025i
730730 0 0
731731 0 0
732732 0 0
733733 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
734734 1.73205 1.73205
735735 0 0
736736 1.96962 1.96962
737737 0 0
738738 0 0
739739 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
740740 0 0
741741 0.524005 1.43969i 0.524005 1.43969i
742742 0.266044 0.223238i 0.266044 0.223238i
743743 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
744744 0 0
745745 0 0
746746 −1.70574 + 0.984808i −1.70574 + 0.984808i
747747 0 0
748748 0 0
749749 1.50881 0.266044i 1.50881 0.266044i
750750 0 0
751751 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
752752 −0.500000 0.866025i −0.500000 0.866025i
753753 0 0
754754 −2.49362 1.43969i −2.49362 1.43969i
755755 0 0
756756 0.984808 0.173648i 0.984808 0.173648i
757757 0 0 1.00000 00
−1.00000 π\pi
758758 1.70574 + 0.984808i 1.70574 + 0.984808i
759759 0 0
760760 0 0
761761 −0.939693 + 1.62760i −0.939693 + 1.62760i −0.173648 + 0.984808i 0.555556π0.555556\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
762762 0 0
763763 1.20805 + 0.439693i 1.20805 + 0.439693i
764764 0.684040i 0.684040i
765765 0 0
766766 0 0
767767 2.61334 1.50881i 2.61334 1.50881i
768768 −0.642788 0.766044i −0.642788 0.766044i
769769 1.96962i 1.96962i 0.173648 + 0.984808i 0.444444π0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
770770 0 0
771771 0 0
772772 0 0
773773 0.642788 + 1.11334i 0.642788 + 1.11334i 0.984808 + 0.173648i 0.0555556π0.0555556\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
774774 0 0
775775 0 0
776776 0 0
777777 −0.592396 1.62760i −0.592396 1.62760i
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 −0.342020 + 0.592396i −0.342020 + 0.592396i
783783 0.939693 + 1.62760i 0.939693 + 1.62760i
784784 0.766044 + 0.642788i 0.766044 + 0.642788i
785785 0 0
786786 0 0
787787 0.300767 0.173648i 0.300767 0.173648i −0.342020 0.939693i 0.611111π-0.611111\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
788788 0 0
789789 1.32683 1.11334i 1.32683 1.11334i
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 −1.70574 0.984808i −1.70574 0.984808i
797797 −0.684040 −0.684040 −0.342020 0.939693i 0.611111π-0.611111\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
798798 −0.984808 0.173648i −0.984808 0.173648i
799799 0.347296 0.347296
800800 0.866025 + 0.500000i 0.866025 + 0.500000i
801801 0 0
802802 0 0
803803 0 0
804804 −0.233956 + 0.642788i −0.233956 + 0.642788i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 −1.70574 + 0.984808i −1.70574 + 0.984808i −0.766044 + 0.642788i 0.777778π0.777778\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
810810 0 0
811811 0.347296i 0.347296i 0.984808 + 0.173648i 0.0555556π0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
812812 −0.642788 + 1.76604i −0.642788 + 1.76604i
813813 1.20805 + 0.439693i 1.20805 + 0.439693i
814814 0 0
815815 0 0
816816 0.342020 0.0603074i 0.342020 0.0603074i
817817 0 0
818818 0 0
819819 1.32683 + 0.766044i 1.32683 + 0.766044i
820820 0 0
821821 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
822822 0.673648 0.118782i 0.673648 0.118782i
823823 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
824824 0 0
825825 0 0
826826 −1.26604 1.50881i −1.26604 1.50881i
827827 1.87939i 1.87939i −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 0.939693i 0.388889π-0.388889\pi
828828 −0.673648 1.85083i −0.673648 1.85083i
829829 1.62760 0.939693i 1.62760 0.939693i 0.642788 0.766044i 0.277778π-0.277778\pi
0.984808 0.173648i 0.0555556π-0.0555556\pi
830830 0 0
831831 0 0
832832 1.53209i 1.53209i
833833 −0.326352 + 0.118782i −0.326352 + 0.118782i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 1.00000 00
−1.00000 π\pi
840840 0 0
841841 −2.53209 −2.53209
842842 0.592396 + 0.342020i 0.592396 + 0.342020i
843843 0 0
844844 −0.642788 1.11334i −0.642788 1.11334i
845845 0 0
846846 −0.642788 + 0.766044i −0.642788 + 0.766044i
847847 −0.173648 0.984808i −0.173648 0.984808i
848848 0.347296i 0.347296i
849849 0 0
850850 −0.300767 + 0.173648i −0.300767 + 0.173648i
851851 −2.95442 + 1.70574i −2.95442 + 1.70574i
852852 0 0
853853 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
854854 0 0
855855 0 0
856856 −0.766044 + 1.32683i −0.766044 + 1.32683i
857857 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
858858 0 0
859859 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
864864 −0.500000 + 0.866025i −0.500000 + 0.866025i
865865 0 0
866866 0 0
867867 0.300767 0.826352i 0.300767 0.826352i
868868 0 0
869869 0 0
870870 0 0
871871 −0.907604 + 0.524005i −0.907604 + 0.524005i
872872 −1.11334 + 0.642788i −1.11334 + 0.642788i
873873 0 0
874874 1.96962i 1.96962i
875875 0 0
876876 −1.20805 0.439693i −1.20805 0.439693i
877877 0.642788 1.11334i 0.642788 1.11334i −0.342020 0.939693i 0.611111π-0.611111\pi
0.984808 0.173648i 0.0555556π-0.0555556\pi
878878 0 0
879879 −1.93969 + 0.342020i −1.93969 + 0.342020i
880880 0 0
881881 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
882882 0.342020 0.939693i 0.342020 0.939693i
883883 0 0 1.00000 00
−1.00000 π\pi
884884 0.460802 + 0.266044i 0.460802 + 0.266044i
885885 0 0
886886 0 0
887887 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
888888 1.62760 + 0.592396i 1.62760 + 0.592396i
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 0.866025 0.500000i 0.866025 0.500000i
894894 0 0
895895 0 0
896896 −0.984808 + 0.173648i −0.984808 + 0.173648i
897897 1.03209 2.83564i 1.03209 2.83564i
898898 0 0
899899 0 0
900900 0.173648 0.984808i 0.173648 0.984808i
901901 −0.104455 0.0603074i −0.104455 0.0603074i
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 0.984808 + 1.70574i 0.984808 + 1.70574i 0.642788 + 0.766044i 0.277778π0.277778\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
908908 0.642788 1.11334i 0.642788 1.11334i
909909 0 0
910910 0 0
911911 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
912912 0.766044 0.642788i 0.766044 0.642788i
913913 0 0
914914 0.300767 0.173648i 0.300767 0.173648i
915915 0 0
916916 0 0
917917 0 0
918918 −0.173648 0.300767i −0.173648 0.300767i
919919 0.173648 0.300767i 0.173648 0.300767i −0.766044 0.642788i 0.777778π-0.777778\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
920920 0 0
921921 0.173648 + 0.984808i 0.173648 + 0.984808i
922922 0 0
923923 0 0
924924 0 0
925925 −1.73205 −1.73205
926926 −0.866025 0.500000i −0.866025 0.500000i
927927 0 0
928928 −0.939693 1.62760i −0.939693 1.62760i
929929 0.766044 1.32683i 0.766044 1.32683i −0.173648 0.984808i 0.555556π-0.555556\pi
0.939693 0.342020i 0.111111π-0.111111\pi
930930 0 0
931931 −0.642788 + 0.766044i −0.642788 + 0.766044i
932932 1.73205i 1.73205i
933933 −1.20805 1.43969i −1.20805 1.43969i
934934 0 0
935935 0 0
936936 −1.43969 + 0.524005i −1.43969 + 0.524005i
937937 1.28558i 1.28558i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
938938 0.439693 + 0.524005i 0.439693 + 0.524005i
939939 −0.642788 0.233956i −0.642788 0.233956i
940940 0 0
941941 0.342020 + 0.592396i 0.342020 + 0.592396i 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
942942 0 0
943943 0 0
944944 1.96962 1.96962
945945 0 0
946946 0 0
947947 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
948948 0 0
949949 −0.984808 1.70574i −0.984808 1.70574i
950950 −0.500000 + 0.866025i −0.500000 + 0.866025i
951951 −1.43969 0.524005i −1.43969 0.524005i
952952 0.118782 0.326352i 0.118782 0.326352i
953953 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
954954 0.326352 0.118782i 0.326352 0.118782i
955955 0 0
956956 1.11334 0.642788i 1.11334 0.642788i
957957 0 0
958958 2.00000i 2.00000i
959959 0.233956 0.642788i 0.233956 0.642788i
960960 0 0
961961 0.500000 0.866025i 0.500000 0.866025i
962962 1.32683 + 2.29813i 1.32683 + 2.29813i
963963 1.50881 + 0.266044i 1.50881 + 0.266044i
964964 0 0
965965 0 0
966966 −1.93969 0.342020i −1.93969 0.342020i
967967 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
968968 0.866025 + 0.500000i 0.866025 + 0.500000i
969969 0.0603074 + 0.342020i 0.0603074 + 0.342020i
970970 0 0
971971 −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i 0.5π0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
972972 0.984808 + 0.173648i 0.984808 + 0.173648i
973973 0 0
974974 0 0
975975 1.17365 0.984808i 1.17365 0.984808i
976976 0 0
977977 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
978978 0 0
979979 0 0
980980 0 0
981981 0.984808 + 0.826352i 0.984808 + 0.826352i
982982 0 0
983983 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
984984 0 0
985985 0 0
986986 0.652704 0.652704
987987 0.342020 + 0.939693i 0.342020 + 0.939693i
988988 1.53209 1.53209
989989 0 0
990990 0 0
991991 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
992992 0 0
993993 −0.439693 + 1.20805i −0.439693 + 1.20805i
994994 0 0
995995 0 0
996996 0 0
997997 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
998998 0 0
999999 1.73205i 1.73205i
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 3192.1.eb.a.341.6 yes 12
3.2 odd 2 3192.1.eb.b.341.3 yes 12
7.3 odd 6 3192.1.eb.b.2621.3 yes 12
8.5 even 2 inner 3192.1.eb.a.341.1 12
19.18 odd 2 inner 3192.1.eb.a.341.1 12
21.17 even 6 inner 3192.1.eb.a.2621.6 yes 12
24.5 odd 2 3192.1.eb.b.341.4 yes 12
56.45 odd 6 3192.1.eb.b.2621.4 yes 12
57.56 even 2 3192.1.eb.b.341.4 yes 12
133.94 even 6 3192.1.eb.b.2621.4 yes 12
152.37 odd 2 CM 3192.1.eb.a.341.6 yes 12
168.101 even 6 inner 3192.1.eb.a.2621.1 yes 12
399.227 odd 6 inner 3192.1.eb.a.2621.1 yes 12
456.341 even 2 3192.1.eb.b.341.3 yes 12
1064.493 even 6 3192.1.eb.b.2621.3 yes 12
3192.2621 odd 6 inner 3192.1.eb.a.2621.6 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3192.1.eb.a.341.1 12 8.5 even 2 inner
3192.1.eb.a.341.1 12 19.18 odd 2 inner
3192.1.eb.a.341.6 yes 12 1.1 even 1 trivial
3192.1.eb.a.341.6 yes 12 152.37 odd 2 CM
3192.1.eb.a.2621.1 yes 12 168.101 even 6 inner
3192.1.eb.a.2621.1 yes 12 399.227 odd 6 inner
3192.1.eb.a.2621.6 yes 12 21.17 even 6 inner
3192.1.eb.a.2621.6 yes 12 3192.2621 odd 6 inner
3192.1.eb.b.341.3 yes 12 3.2 odd 2
3192.1.eb.b.341.3 yes 12 456.341 even 2
3192.1.eb.b.341.4 yes 12 24.5 odd 2
3192.1.eb.b.341.4 yes 12 57.56 even 2
3192.1.eb.b.2621.3 yes 12 7.3 odd 6
3192.1.eb.b.2621.3 yes 12 1064.493 even 6
3192.1.eb.b.2621.4 yes 12 56.45 odd 6
3192.1.eb.b.2621.4 yes 12 133.94 even 6