LMFDB - Embedded newform 2565.1.dy.d.2374.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2565,1,Mod(94,2565)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2565, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8, 9, 9])) N = Newforms(chi, 1, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2565.94"); S:= CuspForms(chi, 1); N := Newforms(S);

Level:	$ N $	$=$	$ 2565 = 3^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2565.dy (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.28010175740$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{72})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{12} + 1 $ x^24 - x^12 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{36}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{36} - \cdots)$

Embedding invariants

Embedding label			2374.3
Root			$0.996195 + 0.0871557i$ of defining polynomial
Character	$\chi$	$=$	2565.2374
Dual form			2565.1.dy.d.94.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0302689 - 0.171663i) q^{2} +(-0.0871557 - 0.996195i) q^{3} +(0.911141 + 0.331628i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 - 0.0151922i) q^{6} +(0.171663 - 0.297330i) q^{8} +(-0.984808 + 0.173648i) q^{9} +(0.0871557 + 0.150958i) q^{10} +(0.984808 + 0.826352i) q^{11} +(0.250955 - 0.936577i) q^{12} +(-0.199201 - 1.12973i) q^{13} +(0.707107 + 0.707107i) q^{15} +(0.696924 + 0.584789i) q^{16} +0.174311i q^{18} +(0.500000 - 0.866025i) q^{19} +(-0.911141 + 0.331628i) q^{20} +(0.171663 - 0.144043i) q^{22} +(-0.311160 - 0.145096i) q^{24} +(0.173648 - 0.984808i) q^{25} -0.199962 q^{26} +(0.258819 + 0.965926i) q^{27} +(0.142788 - 0.0999810i) q^{30} +(0.384485 - 0.322621i) q^{32} +(0.737376 - 1.05308i) q^{33} +(-0.954885 - 0.168372i) q^{36} +(0.996195 + 1.72546i) q^{37} +(-0.133530 - 0.112045i) q^{38} +(-1.10806 + 0.296905i) q^{39} +(0.0596180 + 0.338111i) q^{40} +(0.623257 + 1.07951i) q^{44} +(0.642788 - 0.766044i) q^{45} +(0.521822 - 0.745240i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-0.163799 - 0.0596180i) q^{50} +(0.193148 - 1.09540i) q^{52} +1.81262 q^{53} +(0.173648 - 0.0151922i) q^{54} -1.28558 q^{55} +(-0.906308 - 0.422618i) q^{57} +(0.409777 + 0.878770i) q^{60} +(0.411141 + 0.712116i) q^{64} +(0.878770 + 0.737376i) q^{65} +(-0.158456 - 0.158456i) q^{66} +(-0.335463 - 1.90250i) q^{67} +(-0.117425 + 0.322621i) q^{72} +(0.326352 - 0.118782i) q^{74} +(-0.996195 - 0.0871557i) q^{75} +(0.742769 - 0.623257i) q^{76} +(0.0174278 + 0.199201i) q^{78} -0.909770 q^{80} +(0.939693 - 0.342020i) q^{81} +(0.414754 - 0.150958i) q^{88} +(-0.112045 - 0.133530i) q^{90} +(0.173648 + 0.984808i) q^{95} +(-0.354904 - 0.354904i) q^{96} +(-0.396534 - 0.332731i) q^{97} +(-0.0871557 - 0.150958i) q^{98} +(-1.11334 - 0.642788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{16} + 12 q^{19} + 12 q^{24} - 12 q^{30} - 24 q^{36} + 12 q^{44} - 12 q^{64} + 24 q^{66} + 12 q^{74} - 24 q^{80} - 12 q^{96}+O(q^{100}) $ 24 * q + 12 * q^16 + 12 * q^19 + 12 * q^24 - 12 * q^30 - 24 * q^36 + 12 * q^44 - 12 * q^64 + 24 * q^66 + 12 * q^74 - 24 * q^80 - 12 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2565\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0302689	−	0.171663i	0.0302689	−	0.171663i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	0.0302689	−	0.171663i	0.0302689	−	0.171663i	0.996195	+	0.0871557i	$0.0277778\pi$
$3$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$3$	−0.0871557	−	0.996195i	−0.0871557	−	0.996195i
$4$	0.911141	+	0.331628i	0.911141	+	0.331628i
$5$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$5$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$6$	−0.173648	−	0.0151922i	−0.173648	−	0.0151922i
$7$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$7$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$8$	0.171663	−	0.297330i	0.171663	−	0.297330i
$9$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$10$	0.0871557	+	0.150958i	0.0871557	+	0.150958i
$11$	0.984808	+	0.826352i	0.984808	+	0.826352i	0.984808	−	0.173648i	$-0.0555556\pi$
$11$	0.984808	+	0.826352i	0.984808	+	0.826352i			1.00000i	$0.5\pi$
$12$	0.250955	−	0.936577i	0.250955	−	0.936577i
$13$	−0.199201	−	1.12973i	−0.199201	−	1.12973i	−0.906308	−	0.422618i	$-0.861111\pi$
$13$	−0.199201	−	1.12973i	−0.199201	−	1.12973i	0.707107	−	0.707107i	$-0.250000\pi$
$14$		0			0
$15$	0.707107	+	0.707107i	0.707107	+	0.707107i
$16$	0.696924	+	0.584789i	0.696924	+	0.584789i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$			0.174311i			0.174311i
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i
$20$	−0.911141	+	0.331628i	−0.911141	+	0.331628i
$21$		0			0
$22$	0.171663	−	0.144043i	0.171663	−	0.144043i
$23$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$23$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$24$	−0.311160	−	0.145096i	−0.311160	−	0.145096i
$25$	0.173648	−	0.984808i	0.173648	−	0.984808i
$26$	−0.199962			−0.199962
$27$	0.258819	+	0.965926i	0.258819	+	0.965926i
$28$		0			0
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$	0.142788	−	0.0999810i	0.142788	−	0.0999810i
$31$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$31$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$32$	0.384485	−	0.322621i	0.384485	−	0.322621i
$33$	0.737376	−	1.05308i	0.737376	−	1.05308i
$34$		0			0
$35$		0			0
$36$	−0.954885	−	0.168372i	−0.954885	−	0.168372i
$37$	0.996195	+	1.72546i	0.996195	+	1.72546i	0.573576	+	0.819152i	$0.305556\pi$
$37$	0.996195	+	1.72546i	0.996195	+	1.72546i	0.422618	+	0.906308i	$0.361111\pi$
$38$	−0.133530	−	0.112045i	−0.133530	−	0.112045i
$39$	−1.10806	+	0.296905i	−1.10806	+	0.296905i
$40$	0.0596180	+	0.338111i	0.0596180	+	0.338111i
$41$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$41$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$42$		0			0
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$	0.623257	+	1.07951i	0.623257	+	1.07951i
$45$	0.642788	−	0.766044i	0.642788	−	0.766044i
$46$		0			0
$47$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$47$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$48$	0.521822	−	0.745240i	0.521822	−	0.745240i
$49$	0.766044	−	0.642788i	0.766044	−	0.642788i
$50$	−0.163799	−	0.0596180i	−0.163799	−	0.0596180i
$51$		0			0
$52$	0.193148	−	1.09540i	0.193148	−	1.09540i
$53$	1.81262			1.81262			0.906308	−	0.422618i	$-0.138889\pi$
$53$	1.81262			1.81262			0.906308	+	0.422618i	$0.138889\pi$
$54$	0.173648	−	0.0151922i	0.173648	−	0.0151922i
$55$	−1.28558			−1.28558
$56$		0			0
$57$	−0.906308	−	0.422618i	−0.906308	−	0.422618i
$58$		0			0
$59$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$59$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$60$	0.409777	+	0.878770i	0.409777	+	0.878770i
$61$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$61$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$62$		0			0
$63$		0			0
$64$	0.411141	+	0.712116i	0.411141	+	0.712116i
$65$	0.878770	+	0.737376i	0.878770	+	0.737376i
$66$	−0.158456	−	0.158456i	−0.158456	−	0.158456i
$67$	−0.335463	−	1.90250i	−0.335463	−	1.90250i	−0.422618	−	0.906308i	$-0.638889\pi$
$67$	−0.335463	−	1.90250i	−0.335463	−	1.90250i	0.0871557	−	0.996195i	$-0.472222\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$	−0.117425	+	0.322621i	−0.117425	+	0.322621i
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$	0.326352	−	0.118782i	0.326352	−	0.118782i
$75$	−0.996195	−	0.0871557i	−0.996195	−	0.0871557i
$76$	0.742769	−	0.623257i	0.742769	−	0.623257i
$77$		0			0
$78$	0.0174278	+	0.199201i	0.0174278	+	0.199201i
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$	−0.909770			−0.909770
$81$	0.939693	−	0.342020i	0.939693	−	0.342020i
$82$		0			0
$83$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$83$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.414754	−	0.150958i	0.414754	−	0.150958i
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$	−0.112045	−	0.133530i	−0.112045	−	0.133530i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.173648	+	0.984808i	0.173648	+	0.984808i
$96$	−0.354904	−	0.354904i	−0.354904	−	0.354904i
$97$	−0.396534	−	0.332731i	−0.396534	−	0.332731i	0.422618	−	0.906308i	$-0.361111\pi$
$97$	−0.396534	−	0.332731i	−0.396534	−	0.332731i	−0.819152	+	0.573576i	$0.805556\pi$
$98$	−0.0871557	−	0.150958i	−0.0871557	−	0.150958i
$99$	−1.11334	−	0.642788i	−1.11334	−	0.642788i
$100$	0.484808	−	0.839712i	0.484808	−	0.839712i
$101$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.984808	−	0.173648i	$-0.944444\pi$
$101$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.642788	+	0.766044i	$0.722222\pi$
$102$		0			0
$103$	0.133530	−	0.112045i	0.133530	−	0.112045i	−0.573576	−	0.819152i	$-0.694444\pi$
$103$	0.133530	−	0.112045i	0.133530	−	0.112045i	0.707107	+	0.707107i	$0.250000\pi$
$104$	−0.370096	−	0.134704i	−0.370096	−	0.134704i
$105$		0			0
$106$	0.0548658	−	0.311160i	0.0548658	−	0.311160i
$107$	−0.845237			−0.845237			−0.422618	−	0.906308i	$-0.638889\pi$
$107$	−0.845237			−0.845237			−0.422618	+	0.906308i	$0.638889\pi$
$108$	−0.0845076	+	0.965926i	−0.0845076	+	0.965926i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	−0.0389129	+	0.220686i	−0.0389129	+	0.220686i
$111$	1.63207	−	1.14279i	1.63207	−	1.14279i
$112$		0			0
$113$	−1.47988	+	1.24177i	−1.47988	+	1.24177i	−0.573576	+	0.819152i	$0.694444\pi$
$113$	−1.47988	+	1.24177i	−1.47988	+	1.24177i	−0.906308	+	0.422618i	$0.861111\pi$
$114$	−0.0999810	+	0.142788i	−0.0999810	+	0.142788i
$115$		0			0
$116$		0			0
$117$	0.392349	+	1.07797i	0.392349	+	1.07797i
$118$		0			0
$119$		0			0
$120$	0.331628	−	0.0888595i	0.331628	−	0.0888595i
$121$	0.113341	+	0.642788i	0.113341	+	0.642788i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.500000	+	0.866025i	0.500000	+	0.866025i
$126$		0			0
$127$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$127$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$128$	0.606330	−	0.220686i	0.606330	−	0.220686i
$129$		0			0
$130$	0.153180	−	0.128533i	0.153180	−	0.128533i
$131$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$131$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$132$	1.02108	−	0.714971i	1.02108	−	0.714971i
$133$		0			0
$134$	−0.336744			−0.336744
$135$	−0.819152	−	0.573576i	−0.819152	−	0.573576i
$136$		0			0
$137$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$137$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$138$		0			0
$139$	−1.62760	−	0.592396i	−1.62760	−	0.592396i	−0.642788	−	0.766044i	$-0.722222\pi$
$139$	−1.62760	−	0.592396i	−1.62760	−	0.592396i	−0.984808	+	0.173648i	$0.944444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.737376	−	1.27717i	0.737376	−	1.27717i
$144$	−0.787884	−	0.454885i	−0.787884	−	0.454885i
$145$		0			0
$146$		0			0
$147$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$148$	0.335463	+	1.90250i	0.335463	+	1.90250i
$149$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	−0.984808	−	0.173648i	$-0.944444\pi$
$149$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	0.866025	−	0.500000i	$-0.166667\pi$
$150$	−0.0451151	+	0.168372i	−0.0451151	+	0.168372i
$151$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$151$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$152$	−0.171663	−	0.297330i	−0.171663	−	0.297330i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−1.10806	−	0.0969431i	−1.10806	−	0.0969431i
$157$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$157$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$158$		0			0
$159$	−0.157980	−	1.80572i	−0.157980	−	1.80572i
$160$	−0.0871557	+	0.494285i	−0.0871557	+	0.494285i
$161$		0			0
$162$	−0.0302689	−	0.171663i	−0.0302689	−	0.171663i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$	0.112045	+	1.28068i	0.112045	+	1.28068i
$166$		0			0
$167$	−1.25501	+	1.05308i	−1.25501	+	1.05308i	−0.258819	+	0.965926i	$0.583333\pi$
$167$	−1.25501	+	1.05308i	−1.25501	+	1.05308i	−0.996195	+	0.0871557i	$0.972222\pi$
$168$		0			0
$169$	−0.296905	+	0.108065i	−0.296905	+	0.108065i
$170$		0			0
$171$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$172$		0			0
$173$	−0.878770	−	0.737376i	−0.878770	−	0.737376i	0.0871557	−	0.996195i	$-0.472222\pi$
$173$	−0.878770	−	0.737376i	−0.878770	−	0.737376i	−0.965926	+	0.258819i	$0.916667\pi$
$174$		0			0
$175$		0			0
$176$	0.203095	+	1.15181i	0.203095	+	1.15181i
$177$		0			0
$178$		0			0
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	0.839712	−	0.484808i	0.839712	−	0.484808i
$181$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$181$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.87223	−	0.681437i	−1.87223	−	0.681437i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.174311			0.174311
$191$	0.326352	−	1.85083i	0.326352	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$191$	0.326352	−	1.85083i	0.326352	−	1.85083i	0.500000	−	0.866025i	$-0.333333\pi$
$192$	0.673573	−	0.471641i	0.673573	−	0.471641i
$193$	−1.70330	−	0.619951i	−1.70330	−	0.619951i	−0.707107	−	0.707107i	$-0.750000\pi$
$193$	−1.70330	−	0.619951i	−1.70330	−	0.619951i	−0.996195	+	0.0871557i	$0.972222\pi$
$194$	−0.0691204	+	0.0579989i	−0.0691204	+	0.0579989i
$195$	0.657980	−	0.939693i	0.657980	−	0.939693i
$196$	0.911141	−	0.331628i	0.911141	−	0.331628i
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$	−0.144043	+	0.171663i	−0.144043	+	0.171663i
$199$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$199$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$200$	−0.263003	−	0.220686i	−0.263003	−	0.220686i
$201$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$202$	0.0524272	+	0.297330i	0.0524272	+	0.297330i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.0151922	−	0.0263137i	−0.0151922	−	0.0263137i
$207$		0			0
$208$	0.521822	−	0.903823i	0.521822	−	0.903823i
$209$	1.20805	−	0.439693i	1.20805	−	0.439693i
$210$		0			0
$211$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$211$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$212$	1.65155	+	0.601114i	1.65155	+	0.601114i
$213$		0			0
$214$	−0.0255844	+	0.145096i	−0.0255844	+	0.145096i
$215$		0			0
$216$	0.331628	+	0.0888595i	0.331628	+	0.0888595i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−1.17134	−	0.426333i	−1.17134	−	0.426333i
$221$		0			0
$222$	−0.146774	−	0.314757i	−0.146774	−	0.314757i
$223$	1.53950	−	0.560333i	1.53950	−	0.560333i	0.573576	−	0.819152i	$-0.305556\pi$
$223$	1.53950	−	0.560333i	1.53950	−	0.560333i	0.965926	+	0.258819i	$0.0833333\pi$
$224$		0			0
$225$			1.00000i			1.00000i
$226$	0.168372	+	0.291629i	0.168372	+	0.291629i
$227$	1.08335	+	0.909039i	1.08335	+	0.909039i	0.996195	−	0.0871557i	$-0.0277778\pi$
$227$	1.08335	+	0.909039i	1.08335	+	0.909039i	0.0871557	+	0.996195i	$0.472222\pi$
$228$	−0.685622	−	0.685622i	−0.685622	−	0.685622i
$229$	0.342020	+	1.93969i	0.342020	+	1.93969i	0.342020	+	0.939693i	$0.388889\pi$
$229$	0.342020	+	1.93969i	0.342020	+	1.93969i			1.00000i	$0.500000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$	0.196924	−	0.0347230i	0.196924	−	0.0347230i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$239$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$240$	0.0792917	+	0.906308i	0.0792917	+	0.906308i
$241$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$241$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$242$	0.113774			0.113774
$243$	−0.422618	−	0.906308i	−0.422618	−	0.906308i
$244$		0			0
$245$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$246$		0			0
$247$	−1.07797	−	0.392349i	−1.07797	−	0.392349i
$248$		0			0
$249$		0			0
$250$	0.163799	−	0.0596180i	0.163799	−	0.0596180i
$251$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$251$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$252$		0			0
$253$		0			0
$254$	0.257961	+	0.216455i	0.257961	+	0.216455i
$255$		0			0
$256$	0.123257	+	0.699024i	0.123257	+	0.699024i
$257$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	−0.819152	−	0.573576i	$-0.805556\pi$
$257$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	0.573576	−	0.819152i	$-0.305556\pi$
$258$		0			0
$259$		0			0
$260$	0.556149	+	0.963278i	0.556149	+	0.963278i
$261$		0			0
$262$	−0.0302689	+	0.0524272i	−0.0302689	+	0.0524272i
$263$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$263$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$264$	−0.186532	−	0.400019i	−0.186532	−	0.400019i
$265$	−1.38854	+	1.16513i	−1.38854	+	1.16513i
$266$		0			0
$267$		0			0
$268$	0.325270	−	1.84470i	0.325270	−	1.84470i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−0.123257	+	0.123257i	−0.123257	+	0.123257i
$271$	−1.73205			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$271$	−1.73205			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.984808	−	0.826352i	0.984808	−	0.826352i
$276$		0			0
$277$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$277$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$278$	−0.150958	+	0.261467i	−0.150958	+	0.261467i
$279$		0			0
$280$		0			0
$281$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$281$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$282$		0			0
$283$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$283$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$284$		0			0
$285$	0.965926	−	0.258819i	0.965926	−	0.258819i
$286$	−0.196924	−	0.165239i	−0.196924	−	0.165239i
$287$		0			0
$288$	−0.322621	+	0.384485i	−0.322621	+	0.384485i
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$		0			0
$291$	−0.296905	+	0.424024i	−0.296905	+	0.424024i
$292$		0			0
$293$	−1.81535	−	0.660732i	−1.81535	−	0.660732i	−0.996195	−	0.0871557i	$-0.972222\pi$
$293$	−1.81535	−	0.660732i	−1.81535	−	0.660732i	−0.819152	−	0.573576i	$-0.805556\pi$
$294$	−0.142788	+	0.0999810i	−0.142788	+	0.0999810i
$295$		0			0
$296$	0.684040			0.684040
$297$	−0.543308	+	1.16513i	−0.543308	+	1.16513i
$298$	−0.119236			−0.119236
$299$		0			0
$300$	−0.878770	−	0.409777i	−0.878770	−	0.409777i
$301$		0			0
$302$		0			0
$303$	0.731996	+	1.56977i	0.731996	+	1.56977i
$304$	0.854904	−	0.311160i	0.854904	−	0.311160i
$305$		0			0
$306$		0			0
$307$	0.906308	+	1.56977i	0.906308	+	1.56977i	0.819152	+	0.573576i	$0.194444\pi$
$307$	0.906308	+	1.56977i	0.906308	+	1.56977i	0.0871557	+	0.996195i	$0.472222\pi$
$308$		0			0
$309$	−0.123257	−	0.123257i	−0.123257	−	0.123257i
$310$		0			0
$311$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$311$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$312$	−0.101935	+	0.380428i	−0.101935	+	0.380428i
$313$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$313$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.906308	−	0.422618i	$-0.861111\pi$
$317$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.422618	+	0.906308i	$0.638889\pi$
$318$	−0.314757	−	0.0275377i	−0.314757	−	0.0275377i
$319$		0			0
$320$	−0.772691	−	0.281237i	−0.772691	−	0.281237i
$321$	0.0736672	+	0.842020i	0.0736672	+	0.842020i
$322$		0			0
$323$		0			0
$324$	0.969616			0.969616
$325$	−1.14715			−1.14715
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	0.223238	+	0.0195308i	0.223238	+	0.0195308i
$331$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$331$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$332$		0			0
$333$	−1.28068	−	1.52626i	−1.28068	−	1.52626i
$334$	0.142788	+	0.247315i	0.142788	+	0.247315i
$335$	1.47988	+	1.24177i	1.47988	+	1.24177i
$336$		0			0
$337$	0.245576	+	1.39273i	0.245576	+	1.39273i	0.819152	+	0.573576i	$0.194444\pi$
$337$	0.245576	+	1.39273i	0.245576	+	1.39273i	−0.573576	+	0.819152i	$0.694444\pi$
$338$	0.00956374	+	0.0542387i	0.00956374	+	0.0542387i
$339$	1.36603	+	1.36603i	1.36603	+	1.36603i
$340$		0			0
$341$		0			0
$342$	0.150958	+	0.0871557i	0.150958	+	0.0871557i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.153180	+	0.128533i	−0.153180	+	0.128533i
$347$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$347$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$348$		0			0
$349$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$349$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$350$		0			0
$351$	1.03967	−	0.484808i	1.03967	−	0.484808i
$352$	0.645243			0.645243
$353$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$353$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.642788	−	1.11334i	0.642788	−	1.11334i	−0.342020	−	0.939693i	$-0.611111\pi$
$359$	0.642788	−	1.11334i	0.642788	−	1.11334i	0.984808	−	0.173648i	$-0.0555556\pi$
$360$	−0.117425	−	0.322621i	−0.117425	−	0.322621i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	0.630463	−	0.168932i	0.630463	−	0.168932i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$367$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$368$		0			0
$369$		0			0
$370$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$371$		0			0
$372$		0			0
$373$	−1.25501	+	1.05308i	−1.25501	+	1.05308i	−0.258819	+	0.965926i	$0.583333\pi$
$373$	−1.25501	+	1.05308i	−1.25501	+	1.05308i	−0.996195	+	0.0871557i	$0.972222\pi$
$374$		0			0
$375$	0.819152	−	0.573576i	0.819152	−	0.573576i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−0.168372	+	0.954885i	−0.168372	+	0.954885i
$381$	1.75085	+	0.816436i	1.75085	+	0.816436i
$382$	−0.307842	−	0.112045i	−0.307842	−	0.112045i
$383$	1.52626	−	1.28068i	1.52626	−	1.28068i	0.707107	−	0.707107i	$-0.250000\pi$
$383$	1.52626	−	1.28068i	1.52626	−	1.28068i	0.819152	−	0.573576i	$-0.194444\pi$
$384$	−0.272691	−	0.584789i	−0.272691	−	0.584789i
$385$		0			0
$386$	−0.157980	+	0.273629i	−0.157980	+	0.273629i
$387$		0			0
$388$	−0.250955	−	0.434667i	−0.250955	−	0.434667i
$389$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$389$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$390$	−0.141394	−	0.141394i	−0.141394	−	0.141394i
$391$		0			0
$392$	−0.0596180	−	0.338111i	−0.0596180	−	0.338111i
$393$	−0.0898869	+	0.335463i	−0.0898869	+	0.335463i
$394$		0			0
$395$		0			0
$396$	−0.801244	−	0.954885i	−0.801244	−	0.954885i
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	0.250955	−	0.0913401i	0.250955	−	0.0913401i
$399$		0			0
$400$	0.696924	−	0.584789i	0.696924	−	0.584789i
$401$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$401$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$402$	0.0293492	+	0.335463i	0.0293492	+	0.335463i
$403$		0			0
$404$	−1.67942			−1.67942
$405$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$406$		0			0
$407$	−0.444777	+	2.52245i	−0.444777	+	2.52245i
$408$		0			0
$409$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$409$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$410$		0			0
$411$		0			0
$412$	0.158822	−	0.0578066i	0.158822	−	0.0578066i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.441063	−	0.370096i	−0.441063	−	0.370096i
$417$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$418$	−0.0389129	−	0.220686i	−0.0389129	−	0.220686i
$419$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$419$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$420$		0			0
$421$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$421$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$422$		0			0
$423$		0			0
$424$	0.311160	−	0.538944i	0.311160	−	0.538944i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.770129	−	0.280304i	−0.770129	−	0.280304i
$429$	−1.33658	−	0.623257i	−1.33658	−	0.623257i
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	−0.384485	+	0.824531i	−0.384485	+	0.824531i
$433$	0.517638			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$433$	0.517638			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$	−0.220686	+	0.382240i	−0.220686	+	0.382240i
$441$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$442$		0			0
$443$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$443$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$444$	1.86603	−	0.500000i	1.86603	−	0.500000i
$445$		0			0
$446$	−0.0495896	−	0.281237i	−0.0495896	−	0.281237i
$447$	−0.660732	+	0.177043i	−0.660732	+	0.177043i
$448$		0			0
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	0.171663	+	0.0302689i	0.171663	+	0.0302689i
$451$		0			0
$452$	−1.76019	+	0.640656i	−1.76019	+	0.640656i
$453$		0			0
$454$	0.188840	−	0.158456i	0.188840	−	0.158456i
$455$		0			0
$456$	−0.281237	+	0.196924i	−0.281237	+	0.196924i
$457$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$457$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$458$	0.343327			0.343327
$459$		0			0
$460$		0			0
$461$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$461$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$463$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$			1.11230i			1.11230i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$476$		0			0
$477$	−1.78508	+	0.314757i	−1.78508	+	0.314757i
$478$	0.163799	−	0.283709i	0.163799	−	0.283709i
$479$	0.642788	−	0.233956i	0.642788	−	0.233956i		−	1.00000i	$-0.5\pi$
$479$	0.642788	−	0.233956i	0.642788	−	0.233956i	0.642788	+	0.766044i	$0.277778\pi$
$480$	0.500000	+	0.0437443i	0.500000	+	0.0437443i
$481$	1.75085	−	1.46914i	1.75085	−	1.46914i
$482$		0			0
$483$		0			0
$484$	−0.109897	+	0.623257i	−0.109897	+	0.623257i
$485$	0.517638			0.517638
$486$	−0.168372	+	0.0451151i	−0.168372	+	0.0451151i
$487$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$487$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$488$		0			0
$489$		0			0
$490$	0.163799	+	0.0596180i	0.163799	+	0.0596180i
$491$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$491$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$	−0.0999810	+	0.173172i	−0.0999810	+	0.173172i
$495$	1.26604	−	0.223238i	1.26604	−	0.223238i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.118782	+	0.673648i	0.118782	+	0.673648i	0.984808	+	0.173648i	$0.0555556\pi$
$499$	0.118782	+	0.673648i	0.118782	+	0.673648i	−0.866025	+	0.500000i	$0.833333\pi$
$500$	0.168372	+	0.954885i	0.168372	+	0.954885i
$501$	1.15846	+	1.15846i	1.15846	+	1.15846i
$502$	−0.0463746	−	0.0389129i	−0.0463746	−	0.0389129i
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$		0			0
$505$	0.866025	−	1.50000i	0.866025	−	1.50000i
$506$		0			0
$507$	0.133530	+	0.286357i	0.133530	+	0.286357i
$508$	−1.43492	+	1.20404i	−1.43492	+	1.20404i
$509$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$509$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$510$		0			0
$511$		0			0
$512$	0.768971			0.768971
$513$	0.965926	+	0.258819i	0.965926	+	0.258819i
$514$	−0.246514			−0.246514
$515$	−0.0302689	+	0.171663i	−0.0302689	+	0.171663i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.657980	+	0.939693i	−0.657980	+	0.939693i
$520$	0.370096	−	0.134704i	0.370096	−	0.134704i
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$	−0.906308	−	1.56977i	−0.906308	−	1.56977i	−0.819152	−	0.573576i	$-0.805556\pi$
$523$	−0.906308	−	1.56977i	−0.906308	−	1.56977i	−0.0871557	−	0.996195i	$-0.527778\pi$
$524$	−0.257961	−	0.216455i	−0.257961	−	0.216455i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.12973	−	0.302709i	1.12973	−	0.302709i
$529$	0.766044	+	0.642788i	0.766044	+	0.642788i
$530$	0.157980	+	0.273629i	0.157980	+	0.273629i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.647489	−	0.543308i	0.647489	−	0.543308i
$536$	−0.623257	−	0.226847i	−0.623257	−	0.226847i
$537$		0			0
$538$		0			0
$539$	1.28558			1.28558
$540$	−0.556149	−	0.794263i	−0.556149	−	0.794263i
$541$	0.684040			0.684040			0.342020	−	0.939693i	$-0.388889\pi$
$541$	0.684040			0.684040			0.342020	+	0.939693i	$0.388889\pi$
$542$	−0.0524272	+	0.297330i	−0.0524272	+	0.297330i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.794263	+	0.289088i	−0.794263	+	0.289088i	−0.707107	−	0.707107i	$-0.750000\pi$
$547$	−0.794263	+	0.289088i	−0.794263	+	0.289088i	−0.0871557	+	0.996195i	$0.527778\pi$
$548$		0			0
$549$		0			0
$550$	−0.112045	−	0.194068i	−0.112045	−	0.194068i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.515668	+	1.92450i	−0.515668	+	1.92450i
$556$	−1.28651	−	1.07951i	−1.28651	−	1.07951i
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.794263	−	0.289088i	−0.794263	−	0.289088i	−0.0871557	−	0.996195i	$-0.527778\pi$
$563$	−0.794263	−	0.289088i	−0.794263	−	0.289088i	−0.707107	+	0.707107i	$0.750000\pi$
$564$		0			0
$565$	0.335463	−	1.90250i	0.335463	−	1.90250i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$569$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$570$	−0.0151922	−	0.173648i	−0.0151922	−	0.173648i
$571$	−1.85083	−	0.673648i	−1.85083	−	0.673648i	−0.984808	−	0.173648i	$-0.944444\pi$
$571$	−1.85083	−	0.673648i	−1.85083	−	0.673648i	−0.866025	−	0.500000i	$-0.833333\pi$
$572$	1.09540	−	0.919149i	1.09540	−	0.919149i
$573$	−1.87223	−	0.163799i	−1.87223	−	0.163799i
$574$		0			0
$575$		0			0
$576$	−0.528552	−	0.629904i	−0.528552	−	0.629904i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	0.133530	+	0.112045i	0.133530	+	0.112045i
$579$	−0.469139	+	1.75085i	−0.469139	+	1.75085i
$580$		0			0
$581$		0			0
$582$	0.0638024	+	0.0638024i	0.0638024	+	0.0638024i
$583$	1.78508	+	1.49786i	1.78508	+	1.49786i
$584$		0			0
$585$	−0.993464	−	0.573576i	−0.993464	−	0.573576i
$586$	−0.168372	+	0.291629i	−0.168372	+	0.291629i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	−0.409777	−	0.878770i	−0.409777	−	0.878770i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.314757	+	1.78508i	−0.314757	+	1.78508i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	0.183564	+	0.128533i	0.183564	+	0.128533i
$595$		0			0
$596$	0.115173	−	0.653180i	0.115173	−	0.653180i
$597$	1.25501	−	0.878770i	1.25501	−	0.878770i
$598$		0			0
$599$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$599$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$600$	−0.196924	+	0.281237i	−0.196924	+	0.281237i
$601$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$601$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$602$		0			0
$603$	0.660732	+	1.81535i	0.660732	+	1.81535i
$604$		0			0
$605$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$606$	0.291629	−	0.0781417i	0.291629	−	0.0781417i
$607$	−0.146774	−	0.832395i	−0.146774	−	0.832395i	−0.965926	−	0.258819i	$-0.916667\pi$
$607$	−0.146774	−	0.832395i	−0.146774	−	0.832395i	0.819152	−	0.573576i	$-0.194444\pi$
$608$	−0.0871557	−	0.494285i	−0.0871557	−	0.494285i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$	0.296905	−	0.108065i	0.296905	−	0.108065i
$615$		0			0
$616$		0			0
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$	−0.0248895	+	0.0174278i	−0.0248895	+	0.0174278i
$619$	0.223238	−	1.26604i	0.223238	−	1.26604i	−0.642788	−	0.766044i	$-0.722222\pi$
$619$	0.223238	−	1.26604i	0.223238	−	1.26604i	0.866025	−	0.500000i	$-0.166667\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−0.945864	−	0.441063i	−0.945864	−	0.441063i
$625$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$626$		0			0
$627$	−0.543308	−	1.16513i	−0.543308	−	1.16513i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.642788	−	1.11334i	−0.642788	−	1.11334i	−0.984808	−	0.173648i	$-0.944444\pi$
$631$	−0.642788	−	1.11334i	−0.642788	−	1.11334i	0.342020	−	0.939693i	$-0.388889\pi$
$632$		0			0
$633$		0			0
$634$	0.0428066	+	0.242769i	0.0428066	+	0.242769i
$635$	−0.335463	−	1.90250i	−0.335463	−	1.90250i
$636$	0.454885	−	1.69765i	0.454885	−	1.69765i
$637$	−0.878770	−	0.737376i	−0.878770	−	0.737376i
$638$		0			0
$639$		0			0
$640$	−0.322621	+	0.558797i	−0.322621	+	0.558797i
$641$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$641$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$642$	0.146774	+	0.0128410i	0.146774	+	0.0128410i
$643$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$643$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	0.0596180	−	0.338111i	0.0596180	−	0.338111i
$649$		0			0
$650$	−0.0347230	+	0.196924i	−0.0347230	+	0.196924i
$651$		0			0
$652$		0			0
$653$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$653$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$654$		0			0
$655$	0.326352	−	0.118782i	0.326352	−	0.118782i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$	−0.322621	+	1.20404i	−0.322621	+	1.20404i
$661$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$661$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.300767	+	0.173648i	−0.300767	+	0.173648i
$667$		0			0
$668$	−1.49273	+	0.543308i	−1.49273	+	0.543308i
$669$	−0.692377	−	1.48481i	−0.692377	−	1.48481i
$670$	0.257961	−	0.216455i	0.257961	−	0.216455i
$671$		0			0
$672$		0			0
$673$	0.0302689	−	0.171663i	0.0302689	−	0.171663i	−0.965926	−	0.258819i	$-0.916667\pi$
$673$	0.0302689	−	0.171663i	0.0302689	−	0.171663i	0.996195	+	0.0871557i	$0.0277778\pi$
$674$	0.246514			0.246514
$675$	0.996195	−	0.0871557i	0.996195	−	0.0871557i
$676$	−0.306359			−0.306359
$677$	−0.345975	+	1.96212i	−0.345975	+	1.96212i	−0.0871557	+	0.996195i	$0.527778\pi$
$677$	−0.345975	+	1.96212i	−0.345975	+	1.96212i	−0.258819	+	0.965926i	$0.583333\pi$
$678$	0.275844	−	0.193148i	0.275844	−	0.193148i
$679$		0			0
$680$		0			0
$681$	0.811160	−	1.15846i	0.811160	−	1.15846i
$682$		0			0
$683$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$683$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$684$	−0.623257	+	0.742769i	−0.623257	+	0.742769i
$685$		0			0
$686$		0			0
$687$	1.90250	−	0.509774i	1.90250	−	0.509774i
$688$		0			0
$689$	−0.361075	−	2.04776i	−0.361075	−	2.04776i
$690$		0			0
$691$	−0.524005	−	0.439693i	−0.524005	−	0.439693i	0.342020	−	0.939693i	$-0.388889\pi$
$691$	−0.524005	−	0.439693i	−0.524005	−	0.439693i	−0.866025	+	0.500000i	$0.833333\pi$
$692$	−0.556149	−	0.963278i	−0.556149	−	0.963278i
$693$		0			0
$694$		0			0
$695$	1.62760	−	0.592396i	1.62760	−	0.592396i
$696$		0			0
$697$		0			0
$698$	0.250955	+	0.0913401i	0.250955	+	0.0913401i
$699$		0			0
$700$		0			0
$701$	−1.96962			−1.96962			−0.984808	−	0.173648i	$-0.944444\pi$
$701$	−1.96962			−1.96962			−0.984808	+	0.173648i	$0.944444\pi$
$702$	−0.0517540	−	0.193148i	−0.0517540	−	0.193148i
$703$	1.99239			1.99239
$704$	−0.183564	+	1.04104i	−0.183564	+	1.04104i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$709$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	0.256088	+	1.45235i	0.256088	+	1.45235i
$716$		0			0
$717$	0.486421	−	1.81535i	0.486421	−	1.81535i
$718$	−0.171663	−	0.144043i	−0.171663	−	0.144043i
$719$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$719$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$720$	0.895948	−	0.157980i	0.895948	−	0.157980i
$721$		0			0
$722$	−0.163799	+	0.0596180i	−0.163799	+	0.0596180i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.00991603	−	0.113341i	−0.00991603	−	0.113341i
$727$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$727$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$728$		0			0
$729$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$733$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$734$		0			0
$735$	0.996195	+	0.0871557i	0.996195	+	0.0871557i
$736$		0			0
$737$	1.24177	−	2.15081i	1.24177	−	2.15081i
$738$		0			0
$739$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$739$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$740$	−1.47988	−	1.24177i	−1.47988	−	1.24177i
$741$	−0.296905	+	1.10806i	−0.296905	+	1.10806i
$742$		0			0
$743$	−0.0302689	−	0.171663i	−0.0302689	−	0.171663i	0.965926	−	0.258819i	$-0.0833333\pi$
$743$	−0.0302689	−	0.171663i	−0.0302689	−	0.171663i	−0.996195	+	0.0871557i	$0.972222\pi$
$744$		0			0
$745$	0.524005	+	0.439693i	0.524005	+	0.439693i
$746$	0.142788	+	0.247315i	0.142788	+	0.247315i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−0.0736672	−	0.157980i	−0.0736672	−	0.157980i
$751$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$751$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$752$		0			0
$753$	−0.314757	−	0.146774i	−0.314757	−	0.146774i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	0.322621	+	0.117425i	0.322621	+	0.117425i
$761$	0.524005	−	0.439693i	0.524005	−	0.439693i	−0.342020	−	0.939693i	$-0.611111\pi$
$761$	0.524005	−	0.439693i	0.524005	−	0.439693i	0.866025	+	0.500000i	$0.166667\pi$
$762$	0.193148	−	0.275844i	0.193148	−	0.275844i
$763$		0			0
$764$	0.911141	−	1.57814i	0.911141	−	1.57814i
$765$		0			0
$766$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$767$		0			0
$768$	0.685622	−	0.183712i	0.685622	−	0.183712i
$769$	0.300767	+	1.70574i	0.300767	+	1.70574i	0.642788	+	0.766044i	$0.277778\pi$
$769$	0.300767	+	1.70574i	0.300767	+	1.70574i	−0.342020	+	0.939693i	$0.611111\pi$
$770$		0			0
$771$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$772$	−1.34635	−	1.12973i	−1.34635	−	1.12973i
$773$	0.422618	+	0.731996i	0.422618	+	0.731996i	0.996195	−	0.0871557i	$-0.0277778\pi$
$773$	0.422618	+	0.731996i	0.422618	+	0.731996i	−0.573576	+	0.819152i	$0.694444\pi$
$774$		0			0
$775$		0			0
$776$	−0.167001	+	0.0607835i	−0.167001	+	0.0607835i
$777$		0			0
$778$	−0.250955	+	0.210576i	−0.250955	+	0.210576i
$779$		0			0
$780$	0.911141	−	0.637987i	0.911141	−	0.637987i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.909770			0.909770
$785$		0			0
$786$	0.0548658	+	0.0255844i	0.0548658	+	0.0255844i
$787$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.906308	−	0.422618i	$-0.138889\pi$
$787$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.422618	+	0.906308i	$0.361111\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.382240	+	0.220686i	−0.382240	+	0.220686i
$793$		0			0
$794$		0			0
$795$	1.28171	+	1.28171i	1.28171	+	1.28171i
$796$	0.257961	+	1.46297i	0.257961	+	1.46297i
$797$	0.146774	+	0.832395i	0.146774	+	0.832395i	0.965926	+	0.258819i	$0.0833333\pi$
$797$	0.146774	+	0.832395i	0.146774	+	0.832395i	−0.819152	+	0.573576i	$0.805556\pi$
$798$		0			0
$799$		0			0
$800$	−0.250955	−	0.434667i	−0.250955	−	0.434667i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−1.86603	−	0.163256i	−1.86603	−	0.163256i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.103261	+	0.585625i	−0.103261	+	0.585625i
$809$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$809$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$810$	0.133530	+	0.112045i	0.133530	+	0.112045i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	0.150958	+	1.72546i	0.150958	+	1.72546i
$814$	0.419550	+	0.152704i	0.419550	+	0.152704i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$821$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$822$		0			0
$823$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$823$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$824$	−0.0103921	−	0.0589366i	−0.0103921	−	0.0589366i
$825$	−0.909039	−	0.909039i	−0.909039	−	0.909039i
$826$		0			0
$827$	−0.965926	−	1.67303i	−0.965926	−	1.67303i	−0.707107	−	0.707107i	$-0.750000\pi$
$827$	−0.965926	−	1.67303i	−0.965926	−	1.67303i	−0.258819	−	0.965926i	$-0.583333\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$	0.722596	−	0.606330i	0.722596	−	0.606330i
$833$		0			0
$834$	0.273629	+	0.127595i	0.273629	+	0.127595i
$835$	0.284489	−	1.61341i	0.284489	−	1.61341i
$836$	1.24651			1.24651
$837$		0			0
$838$	−0.174311			−0.174311
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$		0			0
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.157980	−	0.273629i	0.157980	−	0.273629i
$846$		0			0
$847$		0			0
$848$	1.26326	+	1.06000i	1.26326	+	1.06000i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$853$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$854$		0			0
$855$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$856$	−0.145096	+	0.251314i	−0.145096	+	0.251314i
$857$	0.163799	−	0.0596180i	0.163799	−	0.0596180i	−0.258819	−	0.965926i	$-0.583333\pi$
$857$	0.163799	−	0.0596180i	0.163799	−	0.0596180i	0.422618	+	0.906308i	$0.361111\pi$
$858$	−0.147447	+	0.210576i	−0.147447	+	0.210576i
$859$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.845237			0.845237			0.422618	−	0.906308i	$-0.361111\pi$
$863$	0.845237			0.845237			0.422618	+	0.906308i	$0.361111\pi$
$864$	0.411141	+	0.287884i	0.411141	+	0.287884i
$865$	1.14715			1.14715
$866$	0.0156683	−	0.0888595i	0.0156683	−	0.0888595i
$867$	0.906308	+	0.422618i	0.906308	+	0.422618i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−2.08248	+	0.757961i	−2.08248	+	0.757961i
$872$		0			0
$873$	0.448288	+	0.258819i	0.448288	+	0.258819i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	−0.819152	−	0.573576i	$-0.805556\pi$
$877$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	0.573576	−	0.819152i	$-0.305556\pi$
$878$		0			0
$879$	−0.500000	+	1.86603i	−0.500000	+	1.86603i
$880$	−0.895948	−	0.751790i	−0.895948	−	0.751790i
$881$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.642788	−	0.766044i	$-0.722222\pi$
$881$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.342020	−	0.939693i	$-0.611111\pi$
$882$	0.112045	+	0.133530i	0.112045	+	0.133530i
$883$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$883$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.81535	+	0.660732i	1.81535	+	0.660732i	0.996195	+	0.0871557i	$0.0277778\pi$
$887$	1.81535	+	0.660732i	1.81535	+	0.660732i	0.819152	+	0.573576i	$0.194444\pi$
$888$	−0.0596180	−	0.681437i	−0.0596180	−	0.681437i
$889$		0			0
$890$		0			0
$891$	1.20805	+	0.439693i	1.20805	+	0.439693i
$892$	1.58853			1.58853
$893$		0			0
$894$	0.0103921	+	0.118782i	0.0103921	+	0.118782i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.331628	+	0.911141i	−0.331628	+	0.911141i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.115173	+	0.653180i	0.115173	+	0.653180i
$905$		0			0
$906$		0			0
$907$	−0.647489	−	0.543308i	−0.647489	−	0.543308i	0.258819	−	0.965926i	$-0.416667\pi$
$907$	−0.647489	−	0.543308i	−0.647489	−	0.543308i	−0.906308	+	0.422618i	$0.861111\pi$
$908$	0.685622	+	1.18753i	0.685622	+	1.18753i
$909$	1.50000	−	0.866025i	1.50000	−	0.866025i
$910$		0			0
$911$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$911$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$912$	−0.384485	−	0.824531i	−0.384485	−	0.824531i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.331628	+	1.88076i	−0.331628	+	1.88076i
$917$		0			0
$918$		0			0
$919$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$919$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$920$		0			0
$921$	1.48481	−	1.03967i	1.48481	−	1.03967i
$922$	0.163799	+	0.0596180i	0.163799	+	0.0596180i
$923$		0			0
$924$		0			0
$925$	1.87223	−	0.681437i	1.87223	−	0.681437i
$926$		0			0
$927$	−0.112045	+	0.133530i	−0.112045	+	0.133530i
$928$		0			0
$929$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$929$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$930$		0			0
$931$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.387865	+	0.0683910i	0.387865	+	0.0683910i
$937$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$937$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$941$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$947$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$948$		0			0
$949$		0			0
$950$	−0.133530	+	0.112045i	−0.133530	+	0.112045i
$951$	0.597672	+	1.28171i	0.597672	+	1.28171i
$952$		0			0
$953$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$953$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$954$			0.315960i			0.315960i
$955$	0.939693	+	1.62760i	0.939693	+	1.62760i
$956$	1.39595	+	1.17134i	1.39595	+	1.17134i
$957$		0			0
$958$	−0.0207051	−	0.117425i	−0.0207051	−	0.117425i
$959$		0			0
$960$	−0.212822	+	0.794263i	−0.212822	+	0.794263i
$961$	0.766044	+	0.642788i	0.766044	+	0.642788i
$962$	−0.199201	−	0.345026i	−0.199201	−	0.345026i
$963$	0.832395	−	0.146774i	0.832395	−	0.146774i
$964$		0			0
$965$	1.70330	−	0.619951i	1.70330	−	0.619951i
$966$		0			0
$967$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$967$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$968$	0.210576	+	0.0766435i	0.210576	+	0.0766435i
$969$		0			0
$970$	0.0156683	−	0.0888595i	0.0156683	−	0.0888595i
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	−0.0845076	−	0.965926i	−0.0845076	−	0.965926i
$973$		0			0
$974$	0.0428066	−	0.242769i	0.0428066	−	0.242769i
$975$	0.0999810	+	1.14279i	0.0999810	+	1.14279i
$976$		0			0
$977$	1.25501	−	1.05308i	1.25501	−	1.05308i	0.258819	−	0.965926i	$-0.416667\pi$
$977$	1.25501	−	1.05308i	1.25501	−	1.05308i	0.996195	−	0.0871557i	$-0.0277778\pi$
$978$		0			0
$979$		0			0
$980$	−0.484808	+	0.839712i	−0.484808	+	0.839712i
$981$		0			0
$982$	0.133530	+	0.231281i	0.133530	+	0.231281i
$983$	1.25501	+	1.05308i	1.25501	+	1.05308i	0.996195	+	0.0871557i	$0.0277778\pi$
$983$	1.25501	+	1.05308i	1.25501	+	1.05308i	0.258819	+	0.965926i	$0.416667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.852069	−	0.714971i	−0.852069	−	0.714971i
$989$		0			0
$990$		−	0.224091i		−	0.224091i
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$996$		0			0
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$	0.119236			0.119236
$999$	−1.40883	+	1.40883i	−1.40883	+	1.40883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2565.1.dy.d.2374.3	yes	24
5.4	even	2	inner	2565.1.dy.d.2374.2	yes	24
19.18	odd	2	inner	2565.1.dy.d.2374.2	yes	24
27.13	even	9	inner	2565.1.dy.d.94.3	yes	24
95.94	odd	2	CM	2565.1.dy.d.2374.3	yes	24
135.94	even	18	inner	2565.1.dy.d.94.2	✓	24
513.94	odd	18	inner	2565.1.dy.d.94.2	✓	24
2565.94	odd	18	inner	2565.1.dy.d.94.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2565.1.dy.d.94.2	✓	24	135.94	even	18	inner
2565.1.dy.d.94.2	✓	24	513.94	odd	18	inner
2565.1.dy.d.94.3	yes	24	27.13	even	9	inner
2565.1.dy.d.94.3	yes	24	2565.94	odd	18	inner
2565.1.dy.d.2374.2	yes	24	5.4	even	2	inner
2565.1.dy.d.2374.2	yes	24	19.18	odd	2	inner
2565.1.dy.d.2374.3	yes	24	1.1	even	1	trivial
2565.1.dy.d.2374.3	yes	24	95.94	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2565 = 3^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2565.dy (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0302689 - 0.171663i) q^{2} +(-0.0871557 - 0.996195i) q^{3} +(0.911141 + 0.331628i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 - 0.0151922i) q^{6} +(0.171663 - 0.297330i) q^{8} +(-0.984808 + 0.173648i) q^{9} +(0.0871557 + 0.150958i) q^{10} +(0.984808 + 0.826352i) q^{11} +(0.250955 - 0.936577i) q^{12} +(-0.199201 - 1.12973i) q^{13} +(0.707107 + 0.707107i) q^{15} +(0.696924 + 0.584789i) q^{16} +0.174311i q^{18} +(0.500000 - 0.866025i) q^{19} +(-0.911141 + 0.331628i) q^{20} +(0.171663 - 0.144043i) q^{22} +(-0.311160 - 0.145096i) q^{24} +(0.173648 - 0.984808i) q^{25} -0.199962 q^{26} +(0.258819 + 0.965926i) q^{27} +(0.142788 - 0.0999810i) q^{30} +(0.384485 - 0.322621i) q^{32} +(0.737376 - 1.05308i) q^{33} +(-0.954885 - 0.168372i) q^{36} +(0.996195 + 1.72546i) q^{37} +(-0.133530 - 0.112045i) q^{38} +(-1.10806 + 0.296905i) q^{39} +(0.0596180 + 0.338111i) q^{40} +(0.623257 + 1.07951i) q^{44} +(0.642788 - 0.766044i) q^{45} +(0.521822 - 0.745240i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-0.163799 - 0.0596180i) q^{50} +(0.193148 - 1.09540i) q^{52} +1.81262 q^{53} +(0.173648 - 0.0151922i) q^{54} -1.28558 q^{55} +(-0.906308 - 0.422618i) q^{57} +(0.409777 + 0.878770i) q^{60} +(0.411141 + 0.712116i) q^{64} +(0.878770 + 0.737376i) q^{65} +(-0.158456 - 0.158456i) q^{66} +(-0.335463 - 1.90250i) q^{67} +(-0.117425 + 0.322621i) q^{72} +(0.326352 - 0.118782i) q^{74} +(-0.996195 - 0.0871557i) q^{75} +(0.742769 - 0.623257i) q^{76} +(0.0174278 + 0.199201i) q^{78} -0.909770 q^{80} +(0.939693 - 0.342020i) q^{81} +(0.414754 - 0.150958i) q^{88} +(-0.112045 - 0.133530i) q^{90} +(0.173648 + 0.984808i) q^{95} +(-0.354904 - 0.354904i) q^{96} +(-0.396534 - 0.332731i) q^{97} +(-0.0871557 - 0.150958i) q^{98} +(-1.11334 - 0.642788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{16} + 12 q^{19} + 12 q^{24} - 12 q^{30} - 24 q^{36} + 12 q^{44} - 12 q^{64} + 24 q^{66} + 12 q^{74} - 24 q^{80} - 12 q^{96}+O(q^{100}) \) 24 * q + 12 * q^16 + 12 * q^19 + 12 * q^24 - 12 * q^30 - 24 * q^36 + 12 * q^44 - 12 * q^64 + 24 * q^66 + 12 * q^74 - 24 * q^80 - 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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