LMFDB - Embedded newform 560.2.t.a.43.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (of order $4$, degree $2$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.18
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07328 + 0.920909i) q^{2} -1.27333i q^{3} +(0.303853 - 1.97678i) q^{4} +(-1.92329 + 1.14059i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.49432 + 2.40146i) q^{8} +1.37862 q^{9} +O(q^{10})$	\(q+(-1.07328 + 0.920909i) q^{2} -1.27333i q^{3} +(0.303853 - 1.97678i) q^{4} +(-1.92329 + 1.14059i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.49432 + 2.40146i) q^{8} +1.37862 q^{9} +(1.01385 - 2.99535i) q^{10} +(3.26300 - 3.26300i) q^{11} +(-2.51710 - 0.386906i) q^{12} -6.72886 q^{13} +(-0.107741 + 1.41010i) q^{14} +(1.45235 + 2.44899i) q^{15} +(-3.81535 - 1.20130i) q^{16} +(1.71563 - 1.71563i) q^{17} +(-1.47965 + 1.26959i) q^{18} +(-2.30052 + 2.30052i) q^{19} +(1.67030 + 4.14851i) q^{20} +(-0.900382 - 0.900382i) q^{21} +(-0.497180 + 6.50703i) q^{22} +(1.87556 + 1.87556i) q^{23} +(3.05786 - 1.90277i) q^{24} +(2.39811 - 4.38738i) q^{25} +(7.22194 - 6.19666i) q^{26} -5.57545i q^{27} +(-1.18294 - 1.61265i) q^{28} +(-2.00799 - 2.00799i) q^{29} +(-3.81408 - 1.29097i) q^{30} -6.13492i q^{31} +(5.20122 - 2.22425i) q^{32} +(-4.15488 - 4.15488i) q^{33} +(-0.261409 + 3.42128i) q^{34} +(-0.553455 + 2.16649i) q^{35} +(0.418899 - 2.72524i) q^{36} -2.72024 q^{37} +(0.350529 - 4.58767i) q^{38} +8.56807i q^{39} +(-5.61309 - 2.91431i) q^{40} -10.0998i q^{41} +(1.79553 + 0.137191i) q^{42} -1.44198 q^{43} +(-5.45877 - 7.44171i) q^{44} +(-2.65150 + 1.57244i) q^{45} +(-3.74022 - 0.285778i) q^{46} +(-7.89571 - 7.89571i) q^{47} +(-1.52966 + 4.85821i) q^{48} -1.00000i q^{49} +(1.46653 + 6.91732i) q^{50} +(-2.18456 - 2.18456i) q^{51} +(-2.04458 + 13.3015i) q^{52} -10.4902i q^{53} +(5.13448 + 5.98400i) q^{54} +(-2.55396 + 9.99744i) q^{55} +(2.75473 + 0.641445i) q^{56} +(2.92933 + 2.92933i) q^{57} +(4.00431 + 0.305956i) q^{58} +(2.38194 + 2.38194i) q^{59} +(5.28243 - 2.12685i) q^{60} +(4.82900 - 4.82900i) q^{61} +(5.64970 + 6.58447i) q^{62} +(0.974834 - 0.974834i) q^{63} +(-3.53402 + 7.17710i) q^{64} +(12.9416 - 7.67486i) q^{65} +(8.28561 + 0.633076i) q^{66} +0.335471 q^{67} +(-2.87013 - 3.91272i) q^{68} +(2.38821 - 2.38821i) q^{69} +(-1.40113 - 2.83493i) q^{70} +1.00678 q^{71} +(2.06010 + 3.31071i) q^{72} +(-8.26933 + 8.26933i) q^{73} +(2.91957 - 2.50509i) q^{74} +(-5.58659 - 3.05359i) q^{75} +(3.84861 + 5.24665i) q^{76} -4.61457i q^{77} +(-7.89042 - 9.19593i) q^{78} -1.97499 q^{79} +(8.70822 - 2.04129i) q^{80} -2.96353 q^{81} +(9.30099 + 10.8399i) q^{82} +1.82753i q^{83} +(-2.05344 + 1.50628i) q^{84} +(-1.34283 + 5.25648i) q^{85} +(1.54765 - 1.32793i) q^{86} +(-2.55684 + 2.55684i) q^{87} +(12.7119 + 2.96000i) q^{88} +6.29659 q^{89} +(1.39772 - 4.12946i) q^{90} +(-4.75802 + 4.75802i) q^{91} +(4.27747 - 3.13768i) q^{92} -7.81179 q^{93} +(15.7455 + 1.20306i) q^{94} +(1.80063 - 7.04853i) q^{95} +(-2.83222 - 6.62288i) q^{96} +(-1.69671 + 1.69671i) q^{97} +(0.920909 + 1.07328i) q^{98} +(4.49844 - 4.49844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.07328	+	0.920909i	−0.758922	+	0.651181i
$2$	−1.07328	+	0.920909i	−0.758922	+	0.651181i
$3$		−	1.27333i		−	0.735159i	−0.929992	−	0.367580i	$-0.880187\pi$
$3$		−	1.27333i		−	0.735159i	0.929992	−	0.367580i	$-0.119813\pi$
$4$	0.303853	−	1.97678i	0.151926	−	0.988392i
$5$	−1.92329	+	1.14059i	−0.860123	+	0.510087i
$5$	−1.92329	+	1.14059i	−0.860123	+	0.510087i
$6$	1.17262	+	1.36664i	0.478722	+	0.557929i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	1.49432	+	2.40146i	0.528322	+	0.849044i
$9$	1.37862			0.459541
$10$	1.01385	−	2.99535i	0.320607	−	0.947212i
$11$	3.26300	−	3.26300i	0.983830	−	0.983830i	−0.0160411	−	0.999871i	$-0.505106\pi$
$11$	3.26300	−	3.26300i	0.983830	−	0.983830i	0.999871	+	0.0160411i	$0.00510626\pi$
$12$	−2.51710	−	0.386906i	−0.726625	−	0.111690i
$13$	−6.72886			−1.86625			−0.933124	−	0.359554i	$-0.882929\pi$
$13$	−6.72886			−1.86625			−0.933124	+	0.359554i	$0.882929\pi$
$14$	−0.107741	+	1.41010i	−0.0287951	+	0.376866i
$15$	1.45235	+	2.44899i	0.374995	+	0.632327i
$16$	−3.81535	−	1.20130i	−0.953837	−	0.300326i
$17$	1.71563	−	1.71563i	0.416101	−	0.416101i	−0.467757	−	0.883857i	$-0.654938\pi$
$17$	1.71563	−	1.71563i	0.416101	−	0.416101i	0.883857	+	0.467757i	$0.154938\pi$
$18$	−1.47965	+	1.26959i	−0.348756	+	0.299244i
$19$	−2.30052	+	2.30052i	−0.527776	+	0.527776i	−0.919909	−	0.392133i	$-0.871737\pi$
$19$	−2.30052	+	2.30052i	−0.527776	+	0.527776i	0.392133	+	0.919909i	$0.371737\pi$
$20$	1.67030	+	4.14851i	0.373491	+	0.927634i
$21$	−0.900382	−	0.900382i	−0.196480	−	0.196480i
$22$	−0.497180	+	6.50703i	−0.105999	+	1.38730i
$23$	1.87556	+	1.87556i	0.391082	+	0.391082i	0.875073	−	0.483991i	$-0.160813\pi$
$23$	1.87556	+	1.87556i	0.391082	+	0.391082i	−0.483991	+	0.875073i	$0.660813\pi$
$24$	3.05786	−	1.90277i	0.624183	−	0.388400i
$25$	2.39811	−	4.38738i	0.479622	−	0.877475i
$26$	7.22194	−	6.19666i	1.41634	−	1.21527i
$27$		−	5.57545i		−	1.07299i
$28$	−1.18294	−	1.61265i	−0.223555	−	0.304763i
$29$	−2.00799	−	2.00799i	−0.372874	−	0.372874i	0.495649	−	0.868523i	$-0.334930\pi$
$29$	−2.00799	−	2.00799i	−0.372874	−	0.372874i	−0.868523	+	0.495649i	$0.834930\pi$
$30$	−3.81408	−	1.29097i	−0.696352	−	0.235697i
$31$		−	6.13492i		−	1.10186i	−0.834550	−	0.550932i	$-0.814272\pi$
$31$		−	6.13492i		−	1.10186i	0.834550	−	0.550932i	$-0.185728\pi$
$32$	5.20122	−	2.22425i	0.919454	−	0.393196i
$33$	−4.15488	−	4.15488i	−0.723272	−	0.723272i
$34$	−0.261409	+	3.42128i	−0.0448313	+	0.586745i
$35$	−0.553455	+	2.16649i	−0.0935509	+	0.366204i
$36$	0.418899	−	2.72524i	0.0698165	−	0.454207i
$37$	−2.72024			−0.447204			−0.223602	−	0.974681i	$-0.571782\pi$
$37$	−2.72024			−0.447204			−0.223602	+	0.974681i	$0.571782\pi$
$38$	0.350529	−	4.58767i	0.0568633	−	0.744219i
$39$			8.56807i			1.37199i
$40$	−5.61309	−	2.91431i	−0.887508	−	0.460792i
$41$		−	10.0998i		−	1.57732i	−0.614828	−	0.788661i	$-0.710775\pi$
$41$		−	10.0998i		−	1.57732i	0.614828	−	0.788661i	$-0.289225\pi$
$42$	1.79553	+	0.137191i	0.277056	+	0.0211690i
$43$	−1.44198			−0.219900			−0.109950	−	0.993937i	$-0.535069\pi$
$43$	−1.44198			−0.219900			−0.109950	+	0.993937i	$0.535069\pi$
$44$	−5.45877	−	7.44171i	−0.822940	−	1.12188i
$45$	−2.65150	+	1.57244i	−0.395262	+	0.234406i
$46$	−3.74022	−	0.285778i	−0.551466	−	0.0421357i
$47$	−7.89571	−	7.89571i	−1.15171	−	1.15171i	−0.986210	−	0.165498i	$-0.947077\pi$
$47$	−7.89571	−	7.89571i	−1.15171	−	1.15171i	−0.165498	−	0.986210i	$-0.552923\pi$
$48$	−1.52966	+	4.85821i	−0.220787	+	0.701222i
$49$		−	1.00000i		−	0.142857i
$50$	1.46653	+	6.91732i	0.207399	+	0.978256i
$51$	−2.18456	−	2.18456i	−0.305900	−	0.305900i
$52$	−2.04458	+	13.3015i	−0.283533	+	1.84459i
$53$		−	10.4902i		−	1.44094i	−0.693485	−	0.720471i	$-0.743926\pi$
$53$		−	10.4902i		−	1.44094i	0.693485	−	0.720471i	$-0.256074\pi$
$54$	5.13448	+	5.98400i	0.698714	+	0.814320i
$55$	−2.55396	+	9.99744i	−0.344375	+	1.34805i
$56$	2.75473	+	0.641445i	0.368117	+	0.0857168i
$57$	2.92933	+	2.92933i	0.387999	+	0.387999i
$58$	4.00431	+	0.305956i	0.525791	+	0.0401740i
$59$	2.38194	+	2.38194i	0.310102	+	0.310102i	0.844949	−	0.534847i	$-0.179631\pi$
$59$	2.38194	+	2.38194i	0.310102	+	0.310102i	−0.534847	+	0.844949i	$0.679631\pi$
$60$	5.28243	−	2.12685i	0.681959	−	0.274575i
$61$	4.82900	−	4.82900i	0.618291	−	0.618291i	−0.326802	−	0.945093i	$-0.605971\pi$
$61$	4.82900	−	4.82900i	0.618291	−	0.618291i	0.945093	+	0.326802i	$0.105971\pi$
$62$	5.64970	+	6.58447i	0.717513	+	0.836229i
$63$	0.974834	−	0.974834i	0.122818	−	0.122818i
$64$	−3.53402	+	7.17710i	−0.441753	+	0.897137i
$65$	12.9416	−	7.67486i	1.60520	−	0.951950i
$66$	8.28561	+	0.633076i	1.01989	+	0.0779263i
$67$	0.335471			0.0409844			0.0204922	−	0.999790i	$-0.493477\pi$
$67$	0.335471			0.0409844			0.0204922	+	0.999790i	$0.493477\pi$
$68$	−2.87013	−	3.91272i	−0.348054	−	0.474487i
$69$	2.38821	−	2.38821i	0.287507	−	0.287507i
$70$	−1.40113	−	2.83493i	−0.167467	−	0.338839i
$71$	1.00678			0.119483			0.0597416	−	0.998214i	$-0.480972\pi$
$71$	1.00678			0.119483			0.0597416	+	0.998214i	$0.480972\pi$
$72$	2.06010	+	3.31071i	0.242786	+	0.390171i
$73$	−8.26933	+	8.26933i	−0.967852	+	0.967852i	−0.999499	−	0.0316470i	$-0.989925\pi$
$73$	−8.26933	+	8.26933i	−0.967852	+	0.967852i	0.0316470	+	0.999499i	$0.489925\pi$
$74$	2.91957	−	2.50509i	0.339393	−	0.291211i
$75$	−5.58659	−	3.05359i	−0.645084	−	0.352599i
$76$	3.84861	+	5.24665i	0.441466	+	0.601832i
$77$		−	4.61457i		−	0.525879i
$78$	−7.89042	−	9.19593i	−0.893414	−	1.04123i
$79$	−1.97499			−0.222204			−0.111102	−	0.993809i	$-0.535438\pi$
$79$	−1.97499			−0.222204			−0.111102	+	0.993809i	$0.535438\pi$
$80$	8.70822	−	2.04129i	0.973609	−	0.228223i
$81$	−2.96353			−0.329281
$82$	9.30099	+	10.8399i	1.02712	+	1.19707i
$83$			1.82753i			0.200597i	0.994957	+	0.100299i	$0.0319798\pi$
$83$			1.82753i			0.200597i	−0.994957	+	0.100299i	$0.968020\pi$
$84$	−2.05344	+	1.50628i	−0.224049	+	0.164348i
$85$	−1.34283	+	5.25648i	−0.145650	+	0.570145i
$86$	1.54765	−	1.32793i	0.166887	−	0.143195i
$87$	−2.55684	+	2.55684i	−0.274122	+	0.274122i
$88$	12.7119	+	2.96000i	1.35509	+	0.315537i
$89$	6.29659			0.667437			0.333719	−	0.942673i	$-0.391696\pi$
$89$	6.29659			0.667437			0.333719	+	0.942673i	$0.391696\pi$
$90$	1.39772	−	4.12946i	0.147332	−	0.435283i
$91$	−4.75802	+	4.75802i	−0.498776	+	0.498776i
$92$	4.27747	−	3.13768i	0.445957	−	0.327126i
$93$	−7.81179			−0.810045
$94$	15.7455	+	1.20306i	1.62403	+	0.124087i
$95$	1.80063	−	7.04853i	0.184740	−	0.723164i
$96$	−2.83222	−	6.62288i	−0.289062	−	0.675945i
$97$	−1.69671	+	1.69671i	−0.172274	+	0.172274i	−0.787978	−	0.615704i	$-0.788872\pi$
$97$	−1.69671	+	1.69671i	−0.172274	+	0.172274i	0.615704	+	0.787978i	$0.288872\pi$
$98$	0.920909	+	1.07328i	0.0930259	+	0.108417i
$99$	4.49844	−	4.49844i	0.452110	−	0.452110i
$100$	−7.94422	−	6.07366i	−0.794422	−	0.607366i
$101$	12.8706	+	12.8706i	1.28067	+	1.28067i	0.940287	+	0.340384i	$0.110557\pi$
$101$	12.8706	+	12.8706i	1.28067	+	1.28067i	0.340384	+	0.940287i	$0.389443\pi$
$102$	4.35643	+	0.332861i	0.431351	+	0.0329581i
$103$	7.23217	+	7.23217i	0.712607	+	0.712607i	0.967080	−	0.254473i	$-0.0819019\pi$
$103$	7.23217	+	7.23217i	0.712607	+	0.712607i	−0.254473	+	0.967080i	$0.581902\pi$
$104$	−10.0551	−	16.1591i	−0.985980	−	1.58453i
$105$	2.75867	+	0.704732i	0.269218	+	0.0687748i
$106$	9.66053	+	11.2589i	0.938314	+	1.09356i
$107$			17.6332i			1.70466i	0.523003	+	0.852331i	$0.324812\pi$
$107$			17.6332i			1.70466i	−0.523003	+	0.852331i	$0.675188\pi$
$108$	−11.0214	−	1.69412i	−1.06054	−	0.163016i
$109$	−10.7301	−	10.7301i	−1.02775	−	1.02775i	−0.999604	−	0.0281500i	$-0.991038\pi$
$109$	−10.7301	−	10.7301i	−1.02775	−	1.02775i	−0.0281500	−	0.999604i	$-0.508962\pi$
$110$	−6.46562	−	13.0820i	−0.616473	−	1.24732i
$111$			3.46377i			0.328766i
$112$	−3.54731	+	1.84841i	−0.335189	+	0.174658i
$113$	6.09130	+	6.09130i	0.573021	+	0.573021i	0.932971	−	0.359950i	$-0.117206\pi$
$113$	6.09130	+	6.09130i	0.573021	+	0.573021i	−0.359950	+	0.932971i	$0.617206\pi$
$114$	−5.84163	−	0.446340i	−0.547119	−	0.0418036i
$115$	−5.74650	−	1.46801i	−0.535864	−	0.136892i
$116$	−4.57949	+	3.35923i	−0.425195	+	0.311896i
$117$	−9.27656			−0.857618
$118$	−4.75003	−	0.362934i	−0.437276	−	0.0334108i
$119$		−	2.42626i		−	0.222415i
$120$	−3.71088	+	7.14734i	−0.338756	+	0.652460i
$121$		−	10.2943i		−	0.935844i
$122$	−0.735792	+	9.62994i	−0.0666155	+	0.871854i
$123$	−12.8604			−1.15958
$124$	−12.1274	−	1.86411i	−1.08907	−	0.167402i
$125$	0.391928	+	11.1735i	0.0350551	+	0.999385i
$126$	−0.148535	+	1.94400i	−0.0132325	+	0.173185i
$127$	10.3424	+	10.3424i	0.917740	+	0.917740i	0.996865	−	0.0791248i	$-0.0252125\pi$
$127$	10.3424	+	10.3424i	0.917740	+	0.917740i	−0.0791248	+	0.996865i	$0.525213\pi$
$128$	−2.81646	−	10.9575i	−0.248943	−	0.968518i
$129$			1.83612i			0.161662i
$130$	−6.82204	+	20.1553i	−0.598333	+	1.76773i
$131$	6.55920	+	6.55920i	0.573080	+	0.573080i	0.932988	−	0.359908i	$-0.117192\pi$
$131$	6.55920	+	6.55920i	0.573080	+	0.573080i	−0.359908	+	0.932988i	$0.617192\pi$
$132$	−9.47577	+	6.95083i	−0.824760	+	0.604992i
$133$			3.25343i			0.282108i
$134$	−0.360054	+	0.308939i	−0.0311039	+	0.0266882i
$135$	6.35930	+	10.7232i	0.547321	+	0.922907i
$136$	6.68370	+	1.55632i	0.573123	+	0.133453i
$137$	−9.09364	−	9.09364i	−0.776922	−	0.776922i	0.202384	−	0.979306i	$-0.435131\pi$
$137$	−9.09364	−	9.09364i	−0.776922	−	0.776922i	−0.979306	+	0.202384i	$0.935131\pi$
$138$	−0.363891	+	4.76255i	−0.0309764	+	0.405415i
$139$	−3.37410	−	3.37410i	−0.286187	−	0.286187i	0.549383	−	0.835571i	$-0.314863\pi$
$139$	−3.37410	−	3.37410i	−0.286187	−	0.286187i	−0.835571	+	0.549383i	$0.814863\pi$
$140$	4.11452	+	1.75236i	0.347740	+	0.148101i
$141$	−10.0539	+	10.0539i	−0.846689	+	0.846689i
$142$	−1.08056	+	0.927156i	−0.0906785	+	0.0778052i
$143$	−21.9562	+	21.9562i	−1.83607	+	1.83607i
$144$	−5.25993	−	1.65614i	−0.438327	−	0.138012i
$145$	6.15224	+	1.57166i	0.510916	+	0.130519i
$146$	1.25999	−	16.4906i	0.104278	−	1.36477i
$147$	−1.27333			−0.105023
$148$	−0.826552	+	5.37732i	−0.0679421	+	0.442013i
$149$	8.73456	−	8.73456i	0.715563	−	0.715563i	−0.252130	−	0.967693i	$-0.581131\pi$
$149$	8.73456	−	8.73456i	0.715563	−	0.715563i	0.967693	+	0.252130i	$0.0811311\pi$
$150$	8.80805	−	1.86739i	0.719174	−	0.152471i
$151$	2.84338			0.231391			0.115695	−	0.993285i	$-0.463090\pi$
$151$	2.84338			0.231391			0.115695	+	0.993285i	$0.463090\pi$
$152$	−8.96232	−	2.08690i	−0.726940	−	0.169270i
$153$	2.36520	−	2.36520i	0.191215	−	0.191215i
$154$	4.24960	+	4.95272i	0.342443	+	0.399102i
$155$	6.99742	+	11.7992i	0.562046	+	0.947738i
$156$	16.9372	+	2.60343i	1.35606	+	0.208442i
$157$		−	5.81437i		−	0.464037i	−0.972711	−	0.232018i	$-0.925467\pi$
$157$		−	5.81437i		−	0.464037i	0.972711	−	0.232018i	$-0.0745330\pi$
$158$	2.11971	−	1.81879i	0.168635	−	0.144695i
$159$	−13.3575			−1.05932
$160$	−7.46651	+	10.2104i	−0.590279	+	0.807199i
$161$	2.65244			0.209042
$162$	3.18069	−	2.72914i	0.249899	−	0.214421i
$163$		−	4.09873i		−	0.321037i	−0.987033	−	0.160519i	$-0.948683\pi$
$163$		−	4.09873i		−	0.321037i	0.987033	−	0.160519i	$-0.0513167\pi$
$164$	−19.9651	−	3.06885i	−1.55901	−	0.239637i
$165$	12.7301	+	3.25204i	0.991034	+	0.253171i
$166$	−1.68299	−	1.96145i	−0.130625	−	0.152238i
$167$	8.80222	−	8.80222i	0.681136	−	0.681136i	−0.279120	−	0.960256i	$-0.590043\pi$
$167$	8.80222	−	8.80222i	0.681136	−	0.681136i	0.960256	+	0.279120i	$0.0900428\pi$
$168$	0.816774	−	3.50769i	0.0630154	−	0.270624i
$169$	32.2775			2.48288
$170$	−3.39951	−	6.87829i	−0.260731	−	0.527541i
$171$	−3.17155	+	3.17155i	−0.242535	+	0.242535i
$172$	−0.438150	+	2.85049i	−0.0334087	+	0.217348i
$173$	−10.4031			−0.790934			−0.395467	−	0.918480i	$-0.629417\pi$
$173$	−10.4031			−0.790934			−0.395467	+	0.918480i	$0.629417\pi$
$174$	0.389584	−	5.09882i	0.0295343	−	0.386540i
$175$	−1.40662	−	4.79806i	−0.106331	−	0.362699i
$176$	−16.3693	+	8.52961i	−1.23388	+	0.642944i
$177$	3.03300	−	3.03300i	0.227974	−	0.227974i
$178$	−6.75799	+	5.79859i	−0.506533	+	0.434622i
$179$	−5.56325	+	5.56325i	−0.415817	+	0.415817i	−0.883759	−	0.467942i	$-0.844996\pi$
$179$	−5.56325	+	5.56325i	−0.415817	+	0.415817i	0.467942	+	0.883759i	$0.344996\pi$
$180$	2.30272	+	5.71923i	0.171634	+	0.426286i
$181$	−2.09167	−	2.09167i	−0.155473	−	0.155473i	0.625084	−	0.780557i	$-0.285065\pi$
$181$	−2.09167	−	2.09167i	−0.155473	−	0.155473i	−0.780557	+	0.625084i	$0.785065\pi$
$182$	0.724976	−	9.48838i	0.0537388	−	0.703326i
$183$	−6.14893	−	6.14893i	−0.454542	−	0.454542i
$184$	−1.70140	+	7.30677i	−0.125429	+	0.538662i
$185$	5.23181	−	3.10267i	0.384650	−	0.228113i
$186$	8.38423	−	7.19395i	0.614761	−	0.527486i
$187$		−	11.1962i		−	0.818745i
$188$	−18.0073	+	13.2090i	−1.31331	+	0.963364i
$189$	−3.94244	−	3.94244i	−0.286770	−	0.286770i
$190$	4.55848	+	9.22324i	0.330707	+	0.669124i
$191$			17.3158i			1.25293i	0.779450	+	0.626464i	$0.215499\pi$
$191$			17.3158i			1.25293i	−0.779450	+	0.626464i	$0.784501\pi$
$192$	9.13883	+	4.49998i	0.659538	+	0.324758i
$193$	−15.7700	−	15.7700i	−1.13515	−	1.13515i	−0.989308	−	0.145842i	$-0.953411\pi$
$193$	−15.7700	−	15.7700i	−1.13515	−	1.13515i	−0.145842	−	0.989308i	$-0.546589\pi$
$194$	0.258526	−	3.38355i	0.0185611	−	0.242925i
$195$	−9.77266	−	16.4789i	−0.699834	−	1.18008i
$196$	−1.97678	−	0.303853i	−0.141199	−	0.0217038i
$197$	8.59144			0.612115			0.306057	−	0.952013i	$-0.400990\pi$
$197$	8.59144			0.612115			0.306057	+	0.952013i	$0.400990\pi$
$198$	−0.685424	+	8.97074i	−0.0487110	+	0.637523i
$199$			9.65879i			0.684693i	0.939574	+	0.342347i	$0.111222\pi$
$199$			9.65879i			0.684693i	−0.939574	+	0.342347i	$0.888778\pi$
$200$	14.1196	−	0.797174i	0.998410	−	0.0563687i
$201$		−	0.427167i		−	0.0301300i
$202$	−25.6663	−	1.96108i	−1.80588	−	0.137981i
$203$	−2.83973			−0.199310
$204$	−4.98220	+	3.65463i	−0.348824	+	0.255875i
$205$	11.5197	+	19.4249i	0.804572	+	1.35669i
$206$	−14.4223	−	1.10196i	−1.00485	−	0.0767773i
$207$	2.58569	+	2.58569i	0.179718	+	0.179718i
$208$	25.6729	+	8.08340i	1.78010	+	0.560483i
$209$			15.0132i			1.03848i
$210$	−3.60981	+	1.78411i	−0.249101	+	0.123115i
$211$	−14.9227	−	14.9227i	−1.02732	−	1.02732i	−0.999616	−	0.0277041i	$-0.991180\pi$
$211$	−14.9227	−	14.9227i	−1.02732	−	1.02732i	−0.0277041	−	0.999616i	$-0.508820\pi$
$212$	−20.7369	−	3.18748i	−1.42422	−	0.218917i
$213$		−	1.28197i		−	0.0878392i
$214$	−16.2385	−	18.9253i	−1.11004	−	1.29371i
$215$	2.77335	−	1.64471i	0.189141	−	0.112168i
$216$	13.3892	−	8.33149i	0.911020	−	0.566886i
$217$	−4.33804	−	4.33804i	−0.294485	−	0.294485i
$218$	21.3978	+	1.63493i	1.44924	+	0.110732i
$219$	10.5296	+	10.5296i	0.711525	+	0.711525i
$220$	18.9867	+	8.08637i	1.28009	+	0.545183i
$221$	−11.5442	+	11.5442i	−0.776548	+	0.776548i
$222$	−3.18981	−	3.71758i	−0.214086	−	0.249508i
$223$	20.6951	−	20.6951i	1.38585	−	1.38585i	0.552011	−	0.833837i	$-0.313860\pi$
$223$	20.6951	−	20.6951i	1.38585	−	1.38585i	0.833837	−	0.552011i	$-0.186140\pi$
$224$	2.10503	−	5.25060i	0.140648	−	0.350821i
$225$	3.30609	−	6.04854i	0.220406	−	0.403236i
$226$	−12.1472	−	0.928127i	−0.808019	−	0.0617381i
$227$	21.7765			1.44536			0.722680	−	0.691183i	$-0.242910\pi$
$227$	21.7765			1.44536			0.722680	+	0.691183i	$0.242910\pi$
$228$	6.68074	−	4.90057i	0.442443	−	0.324548i
$229$	−5.84434	+	5.84434i	−0.386205	+	0.386205i	−0.873331	−	0.487127i	$-0.838045\pi$
$229$	−5.84434	+	5.84434i	−0.386205	+	0.386205i	0.487127	+	0.873331i	$0.338045\pi$
$230$	7.51950	−	3.71642i	0.495821	−	0.245054i
$231$	−5.87589			−0.386605
$232$	1.82153	−	7.82268i	0.119589	−	0.513584i
$233$	12.7385	−	12.7385i	0.834525	−	0.834525i	−0.153607	−	0.988132i	$-0.549089\pi$
$233$	12.7385	−	12.7385i	0.834525	−	0.834525i	0.988132	+	0.153607i	$0.0490891\pi$
$234$	9.95633	−	8.54287i	0.650866	−	0.558465i
$235$	24.1915	+	6.18000i	1.57808	+	0.403139i
$236$	5.43233	−	3.98482i	0.353615	−	0.259389i
$237$			2.51482i			0.163355i
$238$	2.23437	+	2.60406i	0.144833	+	0.168796i
$239$	1.16635			0.0754448			0.0377224	−	0.999288i	$-0.487990\pi$
$239$	1.16635			0.0754448			0.0377224	+	0.999288i	$0.487990\pi$
$240$	−2.59924	−	11.0885i	−0.167780	−	0.715757i
$241$	−17.6599			−1.13757			−0.568787	−	0.822485i	$-0.692587\pi$
$241$	−17.6599			−1.13757			−0.568787	+	0.822485i	$0.692587\pi$
$242$	9.48010	+	11.0486i	0.609404	+	0.710233i
$243$		−	12.9528i		−	0.830921i
$244$	−8.07859	−	11.0132i	−0.517179	−	0.705048i
$245$	1.14059	+	1.92329i	0.0728696	+	0.122875i
$246$	13.8028	−	11.8433i	0.880033	−	0.755098i
$247$	15.4799	−	15.4799i	0.984961	−	0.984961i
$248$	14.7328	−	9.16752i	0.935531	−	0.582138i
$249$	2.32705			0.147471
$250$	−10.7104	−	11.6313i	−0.677385	−	0.735629i
$251$	6.40087	−	6.40087i	0.404020	−	0.404020i	−0.475627	−	0.879647i	$-0.657779\pi$
$251$	6.40087	−	6.40087i	0.404020	−	0.404020i	0.879647	+	0.475627i	$0.157779\pi$
$252$	−1.63083	−	2.22324i	−0.102733	−	0.140051i
$253$	12.2399			0.769516
$254$	−20.6247	−	1.57586i	−1.29411	−	0.0988786i
$255$	6.69325	+	1.70987i	0.419148	+	0.107076i
$256$	13.1137	+	9.16678i	0.819609	+	0.572923i
$257$	3.75800	−	3.75800i	0.234418	−	0.234418i	−0.580116	−	0.814534i	$-0.696993\pi$
$257$	3.75800	−	3.75800i	0.234418	−	0.234418i	0.814534	+	0.580116i	$0.196993\pi$
$258$	−1.69090	−	1.97067i	−0.105271	−	0.122689i
$259$	−1.92350	+	1.92350i	−0.119520	+	0.119520i
$260$	−11.2392	−	27.9147i	−0.697026	−	1.73120i
$261$	−2.76826	−	2.76826i	−0.171351	−	0.171351i
$262$	−13.0803	−	0.999421i	−0.808102	−	0.0617444i
$263$	14.3792	+	14.3792i	0.886662	+	0.886662i	0.994201	−	0.107538i	$-0.0342969\pi$
$263$	14.3792	+	14.3792i	0.886662	+	0.886662i	−0.107538	+	0.994201i	$0.534297\pi$
$264$	3.76906	−	16.1865i	0.231970	−	0.996210i
$265$	11.9650	+	20.1758i	0.735006	+	1.23939i
$266$	−2.99611	−	3.49183i	−0.183703	−	0.214098i
$267$		−	8.01765i		−	0.490672i
$268$	0.101934	−	0.663154i	0.00622661	−	0.0405086i
$269$	10.2388	+	10.2388i	0.624269	+	0.624269i	0.946620	−	0.322351i	$-0.104473\pi$
$269$	10.2388	+	10.2388i	0.624269	+	0.624269i	−0.322351	+	0.946620i	$0.604473\pi$
$270$	−16.7004	−	5.65266i	−1.01635	−	0.344010i
$271$			12.8071i			0.777975i	0.921243	+	0.388987i	$0.127175\pi$
$271$			12.8071i			0.777975i	−0.921243	+	0.388987i	$0.872825\pi$
$272$	−8.60670	+	4.48472i	−0.521858	+	0.271926i
$273$	6.05854	+	6.05854i	0.366680	+	0.366680i
$274$	18.1344	+	1.38559i	1.09554	+	0.0837066i
$275$	−6.49097	−	22.1410i	−0.391420	−	1.33515i
$276$	−3.99532	−	5.44665i	−0.240490	−	0.327850i
$277$	12.1869			0.732237			0.366119	−	0.930568i	$-0.380686\pi$
$277$	12.1869			0.732237			0.366119	+	0.930568i	$0.380686\pi$
$278$	6.72859	+	0.514109i	0.403554	+	0.0308342i
$279$		−	8.45774i		−	0.506352i
$280$	−6.02978	+	1.90833i	−0.360348	+	0.114045i
$281$		−	2.33852i		−	0.139504i	−0.997564	−	0.0697522i	$-0.977779\pi$
$281$		−	2.33852i		−	0.139504i	0.997564	−	0.0697522i	$-0.0222209\pi$
$282$	1.53190	−	20.0493i	0.0912234	−	1.19392i
$283$	−13.1189			−0.779837			−0.389919	−	0.920849i	$-0.627497\pi$
$283$	−13.1189			−0.779837			−0.389919	+	0.920849i	$0.627497\pi$
$284$	0.305914	−	1.99019i	0.0181527	−	0.118096i
$285$	−8.97512	−	2.29280i	−0.531640	−	0.135813i
$286$	3.34546	−	43.7848i	0.197821	−	2.58905i
$287$	−7.14163	−	7.14163i	−0.421557	−	0.421557i
$288$	7.17052	−	3.06641i	0.422527	−	0.180690i
$289$			11.1132i			0.653720i
$290$	−8.05042	+	3.97883i	−0.472737	+	0.233645i
$291$	2.16047	+	2.16047i	0.126649	+	0.126649i
$292$	13.8340	+	18.8593i	0.809575	+	1.10366i
$293$			14.3419i			0.837862i	0.908018	+	0.418931i	$0.137595\pi$
$293$			14.3419i			0.837862i	−0.908018	+	0.418931i	$0.862405\pi$
$294$	1.36664	−	1.17262i	0.0797041	−	0.0683888i
$295$	−7.29798	−	1.86435i	−0.424905	−	0.108547i
$296$	−4.06490	−	6.53254i	−0.236268	−	0.379696i
$297$	−18.1927	−	18.1927i	−1.05564	−	1.05564i
$298$	−1.33088	+	17.4184i	−0.0770957	+	1.00902i
$299$	−12.6204	−	12.6204i	−0.729856	−	0.729856i
$300$	−7.73379	+	10.1156i	−0.446511	+	0.584027i
$301$	−1.01964	+	1.01964i	−0.0587708	+	0.0587708i
$302$	−3.05174	+	2.61849i	−0.175608	+	0.150677i
$303$	16.3885	−	16.3885i	0.941497	−	0.941497i
$304$	11.5409	−	6.01366i	0.661917	−	0.344907i
$305$	−3.77968	+	14.7955i	−0.216424	+	0.847188i
$306$	−0.360384	+	4.71666i	−0.0206018	+	0.269633i
$307$	14.7843			0.843785			0.421892	−	0.906646i	$-0.361366\pi$
$307$	14.7843			0.843785			0.421892	+	0.906646i	$0.361366\pi$
$308$	−9.12201	−	1.40215i	−0.519775	−	0.0798950i
$309$	9.20896	−	9.20896i	0.523880	−	0.523880i
$310$	−18.3762	−	6.21988i	−1.04370	−	0.353265i
$311$	19.2681			1.09259			0.546297	−	0.837592i	$-0.316037\pi$
$311$	19.2681			1.09259			0.546297	+	0.837592i	$0.316037\pi$
$312$	−20.5759	+	12.8034i	−1.16488	+	0.724852i
$313$	−12.7097	+	12.7097i	−0.718392	+	0.718392i	−0.968276	−	0.249884i	$-0.919608\pi$
$313$	−12.7097	+	12.7097i	−0.718392	+	0.718392i	0.249884	+	0.968276i	$0.419608\pi$
$314$	5.35450	+	6.24043i	0.302172	+	0.352168i
$315$	−0.763005	+	2.98678i	−0.0429905	+	0.168286i
$316$	−0.600107	+	3.90413i	−0.0337586	+	0.219624i
$317$		−	32.4711i		−	1.82376i	−0.410461	−	0.911878i	$-0.634632\pi$
$317$		−	32.4711i		−	1.82376i	0.410461	−	0.911878i	$-0.365368\pi$
$318$	14.3364	−	12.3011i	0.803943	−	0.689810i
$319$	−13.1041			−0.733690
$320$	−1.38917	−	17.8345i	−0.0776567	−	0.996980i
$321$	22.4529			1.25320
$322$	−2.84681	+	2.44266i	−0.158647	+	0.136124i
$323$			7.89368i			0.439216i
$324$	−0.900477	+	5.85825i	−0.0500265	+	0.325458i
$325$	−16.1365	+	29.5220i	−0.895094	+	1.63759i
$326$	3.77456	+	4.39908i	0.209053	+	0.243642i
$327$	−13.6629	+	13.6629i	−0.755563	+	0.755563i
$328$	24.2542	−	15.0923i	1.33922	−	0.833333i
$329$	−11.1662			−0.615614
$330$	−16.6577	+	8.23289i	−0.916978	+	0.453206i
$331$	−1.37082	+	1.37082i	−0.0753471	+	0.0753471i	−0.743776	−	0.668429i	$-0.766967\pi$
$331$	−1.37082	+	1.37082i	−0.0753471	+	0.0753471i	0.668429	+	0.743776i	$0.266967\pi$
$332$	3.61263	+	0.555300i	0.198269	+	0.0304760i
$333$	−3.75018			−0.205509
$334$	−1.34119	+	17.5533i	−0.0733865	+	0.960472i
$335$	−0.645210	+	0.382635i	−0.0352516	+	0.0209056i
$336$	2.35364	+	4.51690i	0.128402	+	0.246417i
$337$	−22.1999	+	22.1999i	−1.20930	+	1.20930i	−0.238051	+	0.971253i	$0.576509\pi$
$337$	−22.1999	+	22.1999i	−1.20930	+	1.20930i	−0.971253	+	0.238051i	$0.923491\pi$
$338$	−34.6427	+	29.7246i	−1.88432	+	1.61681i
$339$	7.75625	−	7.75625i	0.421262	−	0.421262i
$340$	9.98290	+	4.25167i	0.541399	+	0.230579i
$341$	−20.0182	−	20.0182i	−1.08405	−	1.08405i
$342$	0.483247	−	6.32467i	0.0261310	−	0.341999i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−2.15478	−	3.46286i	−0.116178	−	0.186705i
$345$	−1.86926	+	7.31721i	−0.100638	+	0.393945i
$346$	11.1654	−	9.58032i	0.600258	−	0.515041i
$347$			11.8380i			0.635496i	0.948175	+	0.317748i	$0.102927\pi$
$347$			11.8380i			0.635496i	−0.948175	+	0.317748i	$0.897073\pi$
$348$	4.27741	+	5.83122i	0.229293	+	0.312586i
$349$	−12.3500	−	12.3500i	−0.661079	−	0.661079i	0.294556	−	0.955634i	$-0.404828\pi$
$349$	−12.3500	−	12.3500i	−0.661079	−	0.661079i	−0.955634	+	0.294556i	$0.904828\pi$
$350$	5.92828	+	3.85429i	0.316880	+	0.206020i
$351$			37.5164i			2.00248i
$352$	9.71382	−	24.2293i	0.517749	−	1.29143i
$353$	−11.0354	−	11.0354i	−0.587357	−	0.587357i	0.349558	−	0.936915i	$-0.386332\pi$
$353$	−11.0354	−	11.0354i	−0.587357	−	0.587357i	−0.936915	+	0.349558i	$0.886332\pi$
$354$	−0.462136	+	6.04837i	−0.0245623	+	0.321467i
$355$	−1.93634	+	1.14833i	−0.102770	+	0.0609468i
$356$	1.91324	−	12.4470i	0.101401	−	0.659689i
$357$	−3.08944			−0.163511
$358$	0.847668	−	11.0942i	0.0448007	−	0.586345i
$359$			31.1792i			1.64557i	0.568350	+	0.822787i	$0.307582\pi$
$359$			31.1792i			1.64557i	−0.568350	+	0.822787i	$0.692418\pi$
$360$	−7.73834	−	4.01773i	−0.407846	−	0.211753i
$361$			8.41520i			0.442905i
$362$	4.17119	+	0.318707i	0.219233	+	0.0167509i
$363$	−13.1080			−0.687994
$364$	7.95984	+	10.8513i	0.417209	+	0.568763i
$365$	6.47243	−	25.3363i	0.338783	−	1.32616i
$366$	12.2621	+	0.936908i	0.640951	+	0.0489730i
$367$	−2.21993	−	2.21993i	−0.115880	−	0.115880i	0.646789	−	0.762669i	$-0.276111\pi$
$367$	−2.21993	−	2.21993i	−0.115880	−	0.115880i	−0.762669	+	0.646789i	$0.776111\pi$
$368$	−4.90280	−	9.40904i	−0.255576	−	0.490480i
$369$		−	13.9238i		−	0.724844i
$370$	−2.75791	+	8.14805i	−0.143377	+	0.423597i
$371$	−7.41770	−	7.41770i	−0.385108	−	0.385108i
$372$	−2.37364	+	15.4422i	−0.123067	+	0.800642i
$373$			5.66635i			0.293393i	0.989182	+	0.146696i	$0.0468640\pi$
$373$			5.66635i			0.293393i	−0.989182	+	0.146696i	$0.953136\pi$
$374$	10.3107	+	12.0166i	0.533151	+	0.621364i
$375$	14.2275	−	0.499054i	0.734707	−	0.0257711i
$376$	7.16253	−	30.7600i	0.369379	−	1.58632i
$377$	13.5115	+	13.5115i	0.695876	+	0.695876i
$378$	7.86195	+	0.600706i	0.404375	+	0.0308970i
$379$	−20.0154	−	20.0154i	−1.02812	−	1.02812i	−0.999593	−	0.0285302i	$-0.990917\pi$
$379$	−20.0154	−	20.0154i	−1.02812	−	1.02812i	−0.0285302	−	0.999593i	$-0.509083\pi$
$380$	−13.3863	−	5.70116i	−0.686702	−	0.292463i
$381$	13.1693	−	13.1693i	0.674685	−	0.674685i
$382$	−15.9463	−	18.5847i	−0.815884	−	0.950876i
$383$	19.2607	−	19.2607i	0.984175	−	0.984175i	−0.0157017	−	0.999877i	$-0.504998\pi$
$383$	19.2607	−	19.2607i	0.984175	−	0.984175i	0.999877	+	0.0157017i	$0.00499822\pi$
$384$	−13.9526	+	3.58630i	−0.712015	+	0.183012i
$385$	5.26333	+	8.87517i	0.268244	+	0.452321i
$386$	31.4484	+	2.40286i	1.60068	+	0.122303i
$387$	−1.98795			−0.101053
$388$	2.83847	+	3.86957i	0.144102	+	0.196448i
$389$	−2.61826	+	2.61826i	−0.132751	+	0.132751i	−0.770360	−	0.637609i	$-0.779924\pi$
$389$	−2.61826	+	2.61826i	−0.132751	+	0.132751i	0.637609	+	0.770360i	$0.279924\pi$
$390$	25.6644	+	8.68673i	1.29957	+	0.439870i
$391$	6.43553			0.325459
$392$	2.40146	−	1.49432i	0.121292	−	0.0754745i
$393$	8.35205	−	8.35205i	0.421305	−	0.421305i
$394$	−9.22100	+	7.91193i	−0.464547	+	0.398597i
$395$	3.79848	−	2.25265i	0.191123	−	0.113343i
$396$	−7.52558	−	10.2593i	−0.378175	−	0.515550i
$397$			14.3337i			0.719386i	0.933071	+	0.359693i	$0.117119\pi$
$397$			14.3337i			0.719386i	−0.933071	+	0.359693i	$0.882881\pi$
$398$	−8.89487	−	10.3666i	−0.445859	−	0.519629i
$399$	4.14270			0.207394
$400$	−14.4202	+	13.8585i	−0.721009	+	0.692925i
$401$	−28.4153			−1.41899			−0.709496	−	0.704710i	$-0.751077\pi$
$401$	−28.4153			−1.41899			−0.709496	+	0.704710i	$0.751077\pi$
$402$	0.393382	+	0.458469i	0.0196201	+	0.0228663i
$403$			41.2810i			2.05635i
$404$	29.3531	−	21.5316i	1.46037	−	1.07124i
$405$	5.69973	−	3.38017i	0.283222	−	0.167962i
$406$	3.04782	−	2.61513i	0.151261	−	0.129787i
$407$	−8.87612	+	8.87612i	−0.439973	+	0.439973i
$408$	1.98171	−	8.51058i	0.0981092	−	0.421337i
$409$	8.75887			0.433098			0.216549	−	0.976272i	$-0.430520\pi$
$409$	8.75887			0.433098			0.216549	+	0.976272i	$0.430520\pi$
$410$	−30.2524	−	10.2397i	−1.49406	−	0.505701i
$411$	−11.5792	+	11.5792i	−0.571161	+	0.571161i
$412$	16.4940	−	12.0989i	0.812599	−	0.596071i
$413$	3.36857			0.165756
$414$	−5.15636	−	0.393980i	−0.253421	−	0.0193631i
$415$	−2.08446	−	3.51487i	−0.102322	−	0.172538i
$416$	−34.9983	+	14.9667i	−1.71593	+	0.733802i
$417$	−4.29635	+	4.29635i	−0.210393	+	0.210393i
$418$	−13.8258	−	16.1133i	−0.676241	−	0.788129i
$419$	5.51336	−	5.51336i	0.269345	−	0.269345i	−0.559491	−	0.828836i	$-0.689003\pi$
$419$	5.51336	−	5.51336i	0.269345	−	0.269345i	0.828836	+	0.559491i	$0.189003\pi$
$420$	2.23133	−	5.23915i	0.108878	−	0.255644i
$421$	8.93086	+	8.93086i	0.435263	+	0.435263i	0.890414	−	0.455151i	$-0.150415\pi$
$421$	8.93086	+	8.93086i	0.435263	+	0.435263i	−0.455151	+	0.890414i	$0.650415\pi$
$422$	29.7586	+	2.27376i	1.44863	+	0.110685i
$423$	−10.8852	−	10.8852i	−0.529257	−	0.529257i
$424$	25.1918	−	15.6757i	1.22342	−	0.761281i
$425$	−3.41284	−	11.6414i	−0.165547	−	0.564689i
$426$	1.18058	+	1.37591i	0.0571992	+	0.0666631i
$427$		−	6.82924i		−	0.330490i
$428$	34.8569	+	5.35789i	1.68487	+	0.258983i
$429$	27.9576	+	27.9576i	1.34981	+	1.34981i
$430$	−1.46195	+	4.31924i	−0.0705016	+	0.208292i
$431$			36.9828i			1.78140i	0.454591	+	0.890700i	$0.349785\pi$
$431$			36.9828i			1.78140i	−0.454591	+	0.890700i	$0.650215\pi$
$432$	−6.69780	+	21.2723i	−0.322248	+	1.02346i
$433$	3.28725	+	3.28725i	0.157975	+	0.157975i	0.781669	−	0.623694i	$-0.214369\pi$
$433$	3.28725	+	3.28725i	0.157975	+	0.157975i	−0.623694	+	0.781669i	$0.714369\pi$
$434$	8.65087	+	0.660984i	0.415255	+	0.0317283i
$435$	2.00125	−	7.83385i	0.0959524	−	0.375604i
$436$	−24.4714	+	17.9507i	−1.17197	+	0.859680i
$437$	−8.62954			−0.412807
$438$	−20.9980	−	1.60439i	−1.00332	−	0.0766607i
$439$			14.5348i			0.693709i	0.937919	+	0.346855i	$0.112750\pi$
$439$			14.5348i			0.693709i	−0.937919	+	0.346855i	$0.887250\pi$
$440$	−27.8249	+	8.80613i	−1.32650	+	0.419816i
$441$		−	1.37862i		−	0.0656487i
$442$	1.75898	−	23.0213i	0.0836663	−	1.09501i
$443$	−6.21102			−0.295094			−0.147547	−	0.989055i	$-0.547138\pi$
$443$	−6.21102			−0.295094			−0.147547	+	0.989055i	$0.547138\pi$
$444$	6.84711	+	1.05248i	0.324950	+	0.0499483i
$445$	−12.1102	+	7.18183i	−0.574078	+	0.340451i
$446$	−3.15330	+	41.2700i	−0.149313	+	1.95419i
$447$	−11.1220	−	11.1220i	−0.526053	−	0.526053i
$448$	2.57604	+	7.57390i	0.121707	+	0.357833i
$449$			12.9545i			0.611362i	0.952134	+	0.305681i	$0.0988841\pi$
$449$			12.9545i			0.611362i	−0.952134	+	0.305681i	$0.901116\pi$
$450$	2.02180	+	9.53637i	0.0953085	+	0.449549i
$451$	−32.9556	−	32.9556i	−1.55182	−	1.55182i
$452$	13.8920	−	10.1903i	0.653426	−	0.479312i
$453$		−	3.62057i		−	0.170109i
$454$	−23.3723	+	20.0542i	−1.09692	+	0.941191i
$455$	3.72412	−	14.5780i	0.174589	−	0.683428i
$456$	−2.65731	+	11.4120i	−0.124440	+	0.534417i
$457$	13.8025	+	13.8025i	0.645656	+	0.645656i	0.951940	−	0.306285i	$-0.0990859\pi$
$457$	13.8025	+	13.8025i	0.645656	+	0.645656i	−0.306285	+	0.951940i	$0.599086\pi$
$458$	0.890498	−	11.6547i	0.0416102	−	0.544589i
$459$	−9.56539	−	9.56539i	−0.446474	−	0.446474i
$460$	−4.64802	+	10.9135i	−0.216715	+	0.508846i
$461$	−4.74064	+	4.74064i	−0.220793	+	0.220793i	−0.808833	−	0.588039i	$-0.799900\pi$
$461$	−4.74064	+	4.74064i	−0.220793	+	0.220793i	0.588039	+	0.808833i	$0.299900\pi$
$462$	6.30646	−	5.41116i	0.293403	−	0.251750i
$463$	17.8769	−	17.8769i	0.830810	−	0.830810i	−0.156818	−	0.987628i	$-0.550124\pi$
$463$	17.8769	−	17.8769i	0.830810	−	0.830810i	0.987628	+	0.156818i	$0.0501236\pi$
$464$	5.24897	+	10.0734i	0.243677	+	0.467645i
$465$	15.0244	−	8.91005i	0.696738	−	0.413194i
$466$	−1.94095	+	25.4029i	−0.0899128	+	1.17677i
$467$	22.4914			1.04078			0.520389	−	0.853929i	$-0.325787\pi$
$467$	22.4914			1.04078			0.520389	+	0.853929i	$0.325787\pi$
$468$	−2.81871	+	18.3377i	−0.130295	+	0.847663i
$469$	0.237214	−	0.237214i	0.0109535	−	0.0109535i
$470$	−31.6555	+	15.6454i	−1.46016	+	0.721666i
$471$	−7.40362			−0.341141
$472$	−2.16075	+	9.27950i	−0.0994567	+	0.427124i
$473$	−4.70518	+	4.70518i	−0.216344	+	0.216344i
$474$	−2.31592	−	2.69910i	−0.106374	−	0.123974i
$475$	4.57635	+	15.6102i	0.209977	+	0.716243i
$476$	−4.79620	−	0.737227i	−0.219833	−	0.0337908i
$477$		−	14.4621i		−	0.662172i
$478$	−1.25182	+	1.07410i	−0.0572568	+	0.0491282i
$479$	−21.3461			−0.975327			−0.487664	−	0.873032i	$-0.662151\pi$
$479$	−21.3461			−0.975327			−0.487664	+	0.873032i	$0.662151\pi$
$480$	13.0012	+	9.50735i	0.593420	+	0.433949i
$481$	18.3041			0.834594
$482$	18.9540	−	16.2631i	0.863330	−	0.740766i
$483$		−	3.37744i		−	0.153679i
$484$	−20.3496	−	3.12795i	−0.924980	−	0.142179i
$485$	1.32802	−	5.19851i	0.0603021	−	0.236052i
$486$	11.9283	+	13.9019i	0.541080	+	0.630605i
$487$	29.4655	−	29.4655i	1.33521	−	1.33521i	0.434570	−	0.900638i	$-0.356900\pi$
$487$	29.4655	−	29.4655i	1.33521	−	1.33521i	0.900638	−	0.434570i	$-0.143100\pi$
$488$	18.8127	+	4.38059i	0.851612	+	0.198300i
$489$	−5.21905			−0.236013
$490$	−2.99535	−	1.01385i	−0.135316	−	0.0458010i
$491$	17.4275	−	17.4275i	0.786493	−	0.786493i	−0.194425	−	0.980917i	$-0.562284\pi$
$491$	17.4275	−	17.4275i	0.786493	−	0.786493i	0.980917	+	0.194425i	$0.0622840\pi$
$492$	−3.90767	+	25.4222i	−0.176171	+	1.14612i
$493$	−6.88992			−0.310306
$494$	−2.35866	+	30.8698i	−0.106121	+	1.38890i
$495$	−3.52094	+	13.7827i	−0.158255	+	0.619486i
$496$	−7.36989	+	23.4068i	−0.330918	+	1.05100i
$497$	0.711903	−	0.711903i	0.0319332	−	0.0319332i
$498$	−2.49757	+	2.14300i	−0.111919	+	0.0960302i
$499$	23.6289	−	23.6289i	1.05778	−	1.05778i	0.0595504	−	0.998225i	$-0.481033\pi$
$499$	23.6289	−	23.6289i	1.05778	−	1.05778i	0.998225	−	0.0595504i	$-0.0189667\pi$
$500$	22.2066	+	2.62033i	0.993110	+	0.117185i
$501$	−11.2082	−	11.2082i	−0.500743	−	0.500743i
$502$	−0.975297	+	12.7645i	−0.0435296	+	0.569709i
$503$	−18.0619	−	18.0619i	−0.805339	−	0.805339i	0.178585	−	0.983924i	$-0.442848\pi$
$503$	−18.0619	−	18.0619i	−0.805339	−	0.805339i	−0.983924	+	0.178585i	$0.942848\pi$
$504$	3.79774	+	0.884312i	0.169165	+	0.0393904i
$505$	−39.4339	−	10.0738i	−1.75479	−	0.448280i
$506$	−13.1368	+	11.2718i	−0.584003	+	0.501094i
$507$		−	41.1000i		−	1.82532i
$508$	23.5873	−	17.3021i	1.04652	−	0.767658i
$509$	−23.4364	−	23.4364i	−1.03880	−	1.03880i	−0.999216	−	0.0395817i	$-0.987397\pi$
$509$	−23.4364	−	23.4364i	−1.03880	−	1.03880i	−0.0395817	−	0.999216i	$-0.512603\pi$
$510$	−8.75835	+	4.32871i	−0.387826	+	0.191679i
$511$			11.6946i			0.517339i
$512$	−22.5165	+	2.23806i	−0.995096	+	0.0989093i
$513$	12.8264	+	12.8264i	0.566301	+	0.566301i
$514$	−0.572604	+	7.49416i	−0.0252565	+	0.330553i
$515$	−22.1585	−	5.66064i	−0.976421	−	0.249438i
$516$	3.62962	+	0.557911i	0.159785	+	0.0245607i
$517$	−51.5274			−2.26617
$518$	0.293082	−	3.83581i	0.0128773	−	0.168536i
$519$			13.2466i			0.581462i
$520$	37.7697	+	19.6099i	1.65631	+	0.859953i
$521$		−	13.3876i		−	0.586520i	−0.956033	−	0.293260i	$-0.905260\pi$
$521$		−	13.3876i		−	0.586520i	0.956033	−	0.293260i	$-0.0947402\pi$
$522$	5.52043	+	0.421798i	0.241623	+	0.0184616i
$523$	29.1077			1.27279			0.636396	−	0.771363i	$-0.280425\pi$
$523$	29.1077			1.27279			0.636396	+	0.771363i	$0.280425\pi$
$524$	14.9592	−	10.9731i	0.653494	−	0.479362i
$525$	−6.10953	+	1.79110i	−0.266642	+	0.0781700i
$526$	−28.6749	−	2.19096i	−1.25029	−	0.0955302i
$527$	−10.5252	−	10.5252i	−0.458486	−	0.458486i
$528$	10.8610	+	20.8436i	0.472666	+	0.907100i
$529$		−	15.9645i		−	0.694110i
$530$	−31.4218	−	10.6355i	−1.36488	−	0.461976i
$531$	3.28379	+	3.28379i	0.142505	+	0.142505i
$532$	6.43132	+	0.988564i	0.278833	+	0.0428597i
$533$			67.9600i			2.94368i
$534$	7.38353	+	8.60518i	0.319517	+	0.372382i
$535$	−20.1122	−	33.9137i	−0.869526	−	1.46622i
$536$	0.501301	+	0.805621i	0.0216529	+	0.0347975i
$537$	7.08387	+	7.08387i	0.305692	+	0.305692i
$538$	−20.4180	−	1.56008i	−0.880285	−	0.0672596i
$539$	−3.26300	−	3.26300i	−0.140547	−	0.140547i
$540$	23.1298	−	9.31267i	0.995347	−	0.400754i
$541$	−32.3520	+	32.3520i	−1.39092	+	1.39092i	−0.567653	+	0.823268i	$0.692148\pi$
$541$	−32.3520	+	32.3520i	−1.39092	+	1.39092i	−0.823268	+	0.567653i	$0.807852\pi$
$542$	−11.7942	−	13.7456i	−0.506603	−	0.590423i
$543$	−2.66340	+	2.66340i	−0.114297	+	0.114297i
$544$	5.10736	−	12.7393i	0.218976	−	0.546195i
$545$	32.8757	+	8.39845i	1.40824	+	0.359750i
$546$	−12.0819	−	0.923136i	−0.517056	−	0.0395066i
$547$	13.0529			0.558103			0.279052	−	0.960276i	$-0.409980\pi$
$547$	13.0529			0.558103			0.279052	+	0.960276i	$0.409980\pi$
$548$	−20.7393	+	15.2130i	−0.885938	+	0.649868i
$549$	6.65738	−	6.65738i	0.284130	−	0.284130i
$550$	27.3565	+	17.7859i	1.16648	+	0.758392i
$551$	9.23884			0.393588
$552$	9.30395	+	2.16645i	0.396003	+	0.0922101i
$553$	−1.39653	+	1.39653i	−0.0593865	+	0.0593865i
$554$	−13.0799	+	11.2230i	−0.555711	+	0.476819i
$555$	−3.95074	−	6.66184i	−0.167699	−	0.282779i
$556$	−7.69510	+	5.64464i	−0.326345	+	0.239386i
$557$			4.90851i			0.207980i	0.994578	+	0.103990i	$0.0331610\pi$
$557$			4.90851i			0.207980i	−0.994578	+	0.103990i	$0.966839\pi$
$558$	7.78881	+	9.07751i	0.329727	+	0.384282i
$559$	9.70289			0.410388
$560$	4.71423	−	7.60105i	0.199213	−	0.321203i
$561$	−14.2565			−0.601908
$562$	2.15356	+	2.50988i	0.0908426	+	0.105873i
$563$		−	31.3073i		−	1.31945i	−0.751508	−	0.659724i	$-0.770673\pi$
$563$		−	31.3073i		−	1.31945i	0.751508	−	0.659724i	$-0.229327\pi$
$564$	16.8194	+	22.9292i	0.708226	+	0.965495i
$565$	−18.6630	−	4.76768i	−0.785159	−	0.200578i
$566$	14.0802	−	12.0813i	0.591836	−	0.507815i
$567$	−2.09553	+	2.09553i	−0.0880040	+	0.0880040i
$568$	1.50446	+	2.41775i	0.0631256	+	0.101447i
$569$	−3.62849			−0.152114			−0.0760572	−	0.997103i	$-0.524233\pi$
$569$	−3.62849			−0.152114			−0.0760572	+	0.997103i	$0.524233\pi$
$570$	11.7443	−	5.80446i	0.491913	−	0.243122i
$571$	10.5531	−	10.5531i	0.441634	−	0.441634i	−0.450927	−	0.892561i	$-0.648906\pi$
$571$	10.5531	−	10.5531i	0.441634	−	0.441634i	0.892561	+	0.450927i	$0.148906\pi$
$572$	36.7312	+	50.0742i	1.53581	+	2.09371i
$573$	22.0488			0.921102
$574$	14.2417	+	1.08817i	0.594439	+	0.0454191i
$575$	12.7266	−	3.73099i	0.530736	−	0.155593i
$576$	−4.87208	+	9.89451i	−0.203003	+	0.412271i
$577$	14.2057	−	14.2057i	0.591393	−	0.591393i	−0.346615	−	0.938008i	$-0.612669\pi$
$577$	14.2057	−	14.2057i	0.591393	−	0.591393i	0.938008	+	0.346615i	$0.112669\pi$
$578$	−10.2343	−	11.9276i	−0.425690	−	0.496123i
$579$	−20.0805	+	20.0805i	−0.834516	+	0.834516i
$580$	4.97621	−	11.6841i	0.206626	−	0.485156i
$581$	1.29226	+	1.29226i	0.0536119	+	0.0536119i
$582$	−4.30839	−	0.329190i	−0.178588	−	0.0136453i
$583$	−34.2295	−	34.2295i	−1.41764	−	1.41764i
$584$	−32.2155	−	7.50145i	−1.33309	−	0.310412i
$585$	17.8415	−	10.5807i	0.737657	−	0.437460i
$586$	−13.2076	−	15.3928i	−0.545600	−	0.635872i
$587$			44.9515i			1.85535i	0.373392	+	0.927674i	$0.378195\pi$
$587$			44.9515i			1.85535i	−0.373392	+	0.927674i	$0.621805\pi$
$588$	−0.386906	+	2.51710i	−0.0159557	+	0.103804i
$589$	14.1135	+	14.1135i	0.581537	+	0.581537i
$590$	9.54966	−	4.71981i	0.393153	−	0.194311i
$591$		−	10.9398i		−	0.450002i
$592$	10.3786	+	3.26783i	0.426560	+	0.134307i
$593$	12.4054	+	12.4054i	0.509428	+	0.509428i	0.914351	−	0.404923i	$-0.132702\pi$
$593$	12.4054	+	12.4054i	0.509428	+	0.509428i	−0.404923	+	0.914351i	$0.632702\pi$
$594$	36.2796	+	2.77200i	1.48857	+	0.113737i
$595$	2.76737	+	4.66641i	0.113451	+	0.191304i
$596$	−14.6123	−	19.9204i	−0.598544	−	0.815970i
$597$	12.2989			0.503359
$598$	25.1674	+	1.92296i	1.02917	+	0.0786356i
$599$		−	1.06248i		−	0.0434119i	−0.999764	−	0.0217059i	$-0.993090\pi$
$599$		−	1.06248i		−	0.0434119i	0.999764	−	0.0217059i	$-0.00690976\pi$
$600$	−1.01507	−	17.9790i	−0.0414400	−	0.733990i
$601$			12.1915i			0.497302i	0.968593	+	0.248651i	$0.0799873\pi$
$601$			12.1915i			0.497302i	−0.968593	+	0.248651i	$0.920013\pi$
$602$	0.155361	−	2.03334i	0.00633205	−	0.0828729i
$603$	0.462489			0.0188340
$604$	0.863969	−	5.62074i	0.0351544	−	0.228705i
$605$	11.7416	+	19.7989i	0.477362	+	0.804941i
$606$	−2.49711	+	32.6818i	−0.101438	+	1.32761i
$607$	6.15215	+	6.15215i	0.249708	+	0.249708i	0.820851	−	0.571143i	$-0.193500\pi$
$607$	6.15215	+	6.15215i	0.249708	+	0.249708i	−0.571143	+	0.820851i	$0.693500\pi$
$608$	−6.84857	+	17.0825i	−0.277746	+	0.692785i
$609$			3.61592i			0.146524i
$610$	−9.56867	−	19.3604i	−0.387424	−	0.783881i
$611$	53.1291	+	53.1291i	2.14937	+	2.14937i
$612$	−3.95682	−	5.39417i	−0.159945	−	0.218046i
$613$		−	13.5179i		−	0.545982i	−0.962017	−	0.272991i	$-0.911987\pi$
$613$		−	13.5179i		−	0.545982i	0.962017	−	0.272991i	$-0.0880129\pi$
$614$	−15.8677	+	13.6150i	−0.640367	+	0.549456i
$615$	24.7343	−	14.6684i	0.997383	−	0.591488i
$616$	11.0817	−	6.89564i	0.446495	−	0.277833i
$617$	−2.52264	−	2.52264i	−0.101558	−	0.101558i	0.654502	−	0.756060i	$-0.272878\pi$
$617$	−2.52264	−	2.52264i	−0.101558	−	0.101558i	−0.756060	+	0.654502i	$0.772878\pi$
$618$	−1.40316	+	18.3644i	−0.0564435	+	0.738724i
$619$	21.6100	+	21.6100i	0.868577	+	0.868577i	0.992315	−	0.123738i	$-0.0394881\pi$
$619$	21.6100	+	21.6100i	0.868577	+	0.868577i	−0.123738	+	0.992315i	$0.539488\pi$
$620$	25.4507	−	10.2472i	1.02213	−	0.411536i
$621$	10.4571	−	10.4571i	0.419629	−	0.419629i
$622$	−20.6800	+	17.7442i	−0.829194	+	0.711476i
$623$	4.45236	−	4.45236i	0.178380	−	0.178380i
$624$	10.2929	−	32.6902i	0.412044	−	1.30865i
$625$	−13.4981	−	21.0428i	−0.539925	−	0.841713i
$626$	1.93656	−	25.3454i	0.0774006	−	1.01301i
$627$	19.1168			0.763451
$628$	−11.4937	−	1.76671i	−0.458650	−	0.0704995i
$629$	−4.66691	+	4.66691i	−0.186082	+	0.186082i
$630$	−1.93163	−	3.90830i	−0.0769581	−	0.155710i
$631$	−26.0445			−1.03681			−0.518407	−	0.855134i	$-0.673475\pi$
$631$	−26.0445			−1.03681			−0.518407	+	0.855134i	$0.673475\pi$
$632$	−2.95127	−	4.74286i	−0.117395	−	0.188661i
$633$	−19.0016	+	19.0016i	−0.755244	+	0.755244i
$634$	29.9029	+	34.8505i	1.18760	+	1.38409i
$635$	−31.6879	−	8.09503i	−1.25750	−	0.321242i
$636$	−4.05873	+	26.4050i	−0.160939	+	1.04702i
$637$			6.72886i			0.266607i
$638$	14.0644	−	12.0677i	0.556814	−	0.477765i
$639$	1.38797			0.0549074
$640$	17.9149	+	17.8621i	0.708150	+	0.706062i
$641$	−40.6458			−1.60541			−0.802707	−	0.596373i	$-0.796608\pi$
$641$	−40.6458			−1.60541			−0.802707	+	0.596373i	$0.796608\pi$
$642$	−24.0982	+	20.6771i	−0.951080	+	0.816059i
$643$			2.60900i			0.102889i	0.998676	+	0.0514445i	$0.0163825\pi$
$643$			2.60900i			0.102889i	−0.998676	+	0.0514445i	$0.983617\pi$
$644$	0.805953	−	5.24331i	0.0317590	−	0.206615i
$645$	−2.09426	−	3.53140i	−0.0824615	−	0.139049i
$646$	−7.26936	−	8.47211i	−0.286009	−	0.333331i
$647$	−0.747727	+	0.747727i	−0.0293962	+	0.0293962i	−0.721652	−	0.692256i	$-0.756617\pi$
$647$	−0.747727	+	0.747727i	−0.0293962	+	0.0293962i	0.692256	+	0.721652i	$0.256617\pi$
$648$	−4.42846	−	7.11679i	−0.173966	−	0.279574i
$649$	15.5445			0.610175
$650$	−9.86810	−	46.5456i	−0.387059	−	1.82567i
$651$	−5.52377	+	5.52377i	−0.216494	+	0.216494i
$652$	−8.10230	−	1.24541i	−0.317311	−	0.0487741i
$653$	35.8180			1.40167			0.700834	−	0.713325i	$-0.252811\pi$
$653$	35.8180			1.40167			0.700834	+	0.713325i	$0.252811\pi$
$654$	2.08181	−	27.2465i	0.0814053	−	1.06542i
$655$	−20.0966	−	5.13391i	−0.785240	−	0.200598i
$656$	−12.1329	+	38.5342i	−0.473710	+	1.50451i
$657$	−11.4003	+	11.4003i	−0.444768	+	0.444768i
$658$	11.9845	−	10.2831i	0.467203	−	0.400876i
$659$	−9.84609	+	9.84609i	−0.383549	+	0.383549i	−0.872379	−	0.488830i	$-0.837424\pi$
$659$	−9.84609	+	9.84609i	−0.383549	+	0.383549i	0.488830	+	0.872379i	$0.337424\pi$
$660$	10.2966	−	24.1764i	0.400796	−	0.941067i
$661$	17.8149	+	17.8149i	0.692918	+	0.692918i	0.962873	−	0.269955i	$-0.0870089\pi$
$661$	17.8149	+	17.8149i	0.692918	+	0.692918i	−0.269955	+	0.962873i	$0.587009\pi$
$662$	0.208871	−	2.73367i	0.00811800	−	0.106247i
$663$	14.6996	+	14.6996i	0.570886	+	0.570886i
$664$	−4.38873	+	2.73091i	−0.170316	+	0.105980i
$665$	−3.71083	−	6.25730i	−0.143900	−	0.242648i
$666$	4.02499	−	3.45358i	0.155965	−	0.133823i
$667$		−	7.53221i		−	0.291648i
$668$	−14.7255	−	20.0747i	−0.569747	−	0.776712i
$669$	−26.3518	−	26.3518i	−1.01882	−	1.01882i
$670$	0.340117	−	1.00485i	0.0131399	−	0.0388209i
$671$		−	31.5140i		−	1.21659i
$672$	−6.68577	−	2.68041i	−0.257909	−	0.103399i
$673$	−21.5505	−	21.5505i	−0.830709	−	0.830709i	0.156905	−	0.987614i	$-0.449849\pi$
$673$	−21.5505	−	21.5505i	−0.830709	−	0.830709i	−0.987614	+	0.156905i	$0.949849\pi$
$674$	3.38258	−	44.2707i	0.130292	−	1.70524i
$675$	−24.4616	−	13.3705i	−0.941526	−	0.514632i
$676$	9.80761	−	63.8056i	0.377216	−	2.45406i
$677$	−12.4739			−0.479411			−0.239706	−	0.970846i	$-0.577051\pi$
$677$	−12.4739			−0.479411			−0.239706	+	0.970846i	$0.577051\pi$
$678$	−1.18181	+	15.4674i	−0.0453873	+	0.594022i
$679$			2.39950i			0.0920845i
$680$	−14.6298	+	4.63011i	−0.561029	+	0.177557i
$681$		−	27.7288i		−	1.06257i
$682$	39.9201	+	3.05016i	1.52862	+	0.116797i
$683$	−3.46419			−0.132553			−0.0662767	−	0.997801i	$-0.521112\pi$
$683$	−3.46419			−0.132553			−0.0662767	+	0.997801i	$0.521112\pi$
$684$	5.30579	+	7.23316i	0.202872	+	0.276567i
$685$	27.8618	+	7.11762i	1.06455	+	0.271950i
$686$	1.41010	+	0.107741i	0.0538380	+	0.00411358i
$687$	7.44179	+	7.44179i	0.283922	+	0.283922i
$688$	5.50166	+	1.73226i	0.209749	+	0.0660417i
$689$			70.5872i			2.68916i
$690$	−4.73224	−	9.57482i	−0.180153	−	0.364507i
$691$	0.942094	+	0.942094i	0.0358389	+	0.0358389i	0.724799	−	0.688960i	$-0.241933\pi$
$691$	0.942094	+	0.942094i	0.0358389	+	0.0358389i	−0.688960	+	0.724799i	$0.741933\pi$
$692$	−3.16102	+	20.5647i	−0.120164	+	0.781753i
$693$		−	6.36176i		−	0.241663i
$694$	−10.9017	−	12.7054i	−0.413823	−	0.482292i
$695$	10.3378	+	2.64092i	0.392137	+	0.100176i
$696$	−9.96088	−	2.31941i	−0.377566	−	0.0879171i
$697$	−17.3275	−	17.3275i	−0.656325	−	0.656325i
$698$	24.6281	+	1.88176i	0.932189	+	0.0712255i
$699$	−16.2203	−	16.2203i	−0.613508	−	0.613508i
$700$	−9.91214	+	1.32268i	−0.374644	+	0.0499928i
$701$	22.3178	−	22.3178i	0.842932	−	0.842932i	−0.146307	−	0.989239i	$-0.546739\pi$
$701$	22.3178	−	22.3178i	0.842932	−	0.842932i	0.989239	+	0.146307i	$0.0467388\pi$
$702$	−34.5492	−	40.2655i	−1.30397	−	1.51972i
$703$	6.25796	−	6.25796i	0.236023	−	0.236023i
$704$	11.8873	+	34.9503i	0.448021	+	1.31724i
$705$	7.86920	−	30.8039i	0.296371	−	1.16014i
$706$	22.0067	+	1.68146i	0.828234	+	0.0632826i
$707$	18.2017			0.684547
$708$	−5.07400	−	6.91717i	−0.190693	−	0.259963i
$709$	28.7102	−	28.7102i	1.07823	−	1.07823i	0.0815667	−	0.996668i	$-0.474008\pi$
$709$	28.7102	−	28.7102i	1.07823	−	1.07823i	0.996668	−	0.0815667i	$-0.0259924\pi$
$710$	1.02073	−	3.01567i	0.0383072	−	0.113176i
$711$	−2.72277			−0.102112
$712$	9.40911	+	15.1210i	0.352621	+	0.566684i
$713$	11.5064	−	11.5064i	0.430919	−	0.430919i
$714$	3.31583	−	2.84509i	0.124092	−	0.106475i
$715$	17.1852	−	67.2713i	0.642690	−	2.51580i
$716$	9.30693	+	12.6878i	0.347816	+	0.474164i
$717$		−	1.48515i		−	0.0554640i
$718$	−28.7132	−	33.4639i	−1.07157	−	1.24886i
$719$	−23.9587			−0.893508			−0.446754	−	0.894657i	$-0.647420\pi$
$719$	−23.9587			−0.893508			−0.446754	+	0.894657i	$0.647420\pi$
$720$	12.0054	−	2.81417i	0.447413	−	0.104878i
$721$	10.2278			0.380905
$722$	−7.74963	−	9.03185i	−0.288412	−	0.336131i
$723$			22.4869i			0.836297i
$724$	−4.77035	+	3.49923i	−0.177289	+	0.130048i
$725$	−13.6252	+	3.99442i	−0.506027	+	0.148349i
$726$	14.0686	−	12.0713i	0.522134	−	0.448009i
$727$	−25.9889	+	25.9889i	−0.963875	+	0.963875i	−0.999370	−	0.0354953i	$-0.988699\pi$
$727$	−25.9889	+	25.9889i	−0.963875	+	0.963875i	0.0354953	+	0.999370i	$0.488699\pi$
$728$	−18.5362	−	4.31619i	−0.686997	−	0.159969i
$729$	−25.3838			−0.940140
$730$	16.3857	+	33.1534i	0.606461	+	1.22706i
$731$	−2.47390	+	2.47390i	−0.0915006	+	0.0915006i
$732$	−14.0235	+	10.2867i	−0.518323	+	0.380209i
$733$	21.8954			0.808724			0.404362	−	0.914599i	$-0.367494\pi$
$733$	21.8954			0.808724			0.404362	+	0.914599i	$0.367494\pi$
$734$	4.42696	+	0.338250i	0.163402	+	0.0124850i
$735$	2.44899	−	1.45235i	0.0903324	−	0.0535708i
$736$	13.9269	+	5.58348i	0.513354	+	0.205810i
$737$	1.09464	−	1.09464i	0.0403216	−	0.0403216i
$738$	12.8226	+	14.9441i	0.472005	+	0.550101i
$739$	−17.8596	+	17.8596i	−0.656974	+	0.656974i	−0.954663	−	0.297689i	$-0.903784\pi$
$739$	−17.8596	+	17.8596i	−0.656974	+	0.656974i	0.297689	+	0.954663i	$0.403784\pi$
$740$	−4.54361	−	11.2849i	−0.167026	−	0.414842i
$741$	−19.7110	−	19.7110i	−0.724103	−	0.724103i
$742$	14.7923	+	1.13023i	0.543042	+	0.0414921i
$743$	−23.5083	−	23.5083i	−0.862434	−	0.862434i	0.129186	−	0.991620i	$-0.458764\pi$
$743$	−23.5083	−	23.5083i	−0.862434	−	0.862434i	−0.991620	+	0.129186i	$0.958764\pi$
$744$	−11.6733	−	18.7597i	−0.427964	−	0.687764i
$745$	−6.83657	+	26.7617i	−0.250472	+	0.980472i
$746$	−5.21819	−	6.08157i	−0.191052	−	0.222662i
$747$			2.51947i			0.0921827i
$748$	−22.1324	−	3.40199i	−0.809241	−	0.124389i
$749$	12.4685	+	12.4685i	0.455590	+	0.455590i
$750$	−14.8105	+	13.6379i	−0.540804	+	0.497986i
$751$		−	36.4196i		−	1.32897i	−0.747302	−	0.664484i	$-0.768651\pi$
$751$		−	36.4196i		−	1.32897i	0.747302	−	0.664484i	$-0.231349\pi$
$752$	20.6397	+	39.6100i	0.752654	+	1.44443i
$753$	−8.15044	−	8.15044i	−0.297019	−	0.297019i
$754$	−26.9444	−	2.05873i	−0.981257	−	0.0749746i
$755$	−5.46865	+	3.24313i	−0.199024	+	0.118029i
$756$	−8.99126	+	6.59542i	−0.327009	+	0.239873i
$757$	23.6762			0.860527			0.430264	−	0.902703i	$-0.358421\pi$
$757$	23.6762			0.860527			0.430264	+	0.902703i	$0.358421\pi$
$758$	39.9145	+	3.04974i	1.44976	+	0.110771i
$759$		−	15.5855i		−	0.565717i
$760$	19.6175	−	6.20862i	0.711600	−	0.225210i
$761$			24.9638i			0.904937i	0.891780	+	0.452469i	$0.149457\pi$
$761$			24.9638i			0.904937i	−0.891780	+	0.452469i	$0.850543\pi$
$762$	−2.00660	+	26.2621i	−0.0726915	+	0.951375i
$763$	−15.1746			−0.549357
$764$	34.2296	+	5.26146i	1.23838	+	0.190353i
$765$	−1.85125	+	7.24671i	−0.0669322	+	0.262005i
$766$	−2.93474	+	38.4094i	−0.106036	+	1.38779i
$767$	−16.0277	−	16.0277i	−0.578727	−	0.578727i
$768$	11.6724	−	16.6982i	0.421190	−	0.602543i
$769$		−	14.0070i		−	0.505106i	−0.967583	−	0.252553i	$-0.918730\pi$
$769$		−	14.0070i		−	0.505106i	0.967583	−	0.252553i	$-0.0812702\pi$
$770$	−13.8223	−	4.67848i	−0.498119	−	0.168601i
$771$	−4.78519	−	4.78519i	−0.172334	−	0.172334i
$772$	−35.9657	+	26.3821i	−1.29443	+	0.949514i
$773$			4.28623i			0.154165i	0.997025	+	0.0770825i	$0.0245605\pi$
$773$			4.28623i			0.154165i	−0.997025	+	0.0770825i	$0.975440\pi$
$774$	2.13362	−	1.83072i	0.0766915	−	0.0658039i
$775$	−26.9162	−	14.7122i	−0.966858	−	0.528478i
$776$	−6.60999	−	1.53915i	−0.237285	−	0.0552523i
$777$	2.44925	+	2.44925i	0.0878664	+	0.0878664i
$778$	0.398943	−	5.22130i	0.0143028	−	0.187193i
$779$	23.2348	+	23.2348i	0.832473	+	0.832473i
$780$	−35.5447	+	14.3113i	−1.27270	+	0.512425i
$781$	3.28513	−	3.28513i	0.117551	−	0.117551i
$782$	−6.90711	+	5.92654i	−0.246998	+	0.211933i
$783$	−11.1954	+	11.1954i	−0.400092	+	0.400092i
$784$	−1.20130	+	3.81535i	−0.0429037	+	0.136262i
$785$	6.63181	+	11.1827i	0.236699	+	0.399129i
$786$	−1.27260	+	16.6555i	−0.0453920	+	0.594084i
$787$	−5.64585			−0.201253			−0.100626	−	0.994924i	$-0.532085\pi$
$787$	−5.64585			−0.201253			−0.100626	+	0.994924i	$0.532085\pi$
$788$	2.61053	−	16.9834i	0.0929964	−	0.605009i
$789$	18.3096	−	18.3096i	0.651838	−	0.651838i
$790$	−2.00234	+	5.91578i	−0.0712401	+	0.210474i
$791$	8.61440			0.306293
$792$	17.5249	+	4.08072i	0.622722	+	0.145002i
$793$	−32.4937	+	32.4937i	−1.15388	+	1.15388i
$794$	−13.2000	−	15.3840i	−0.468450	−	0.545958i
$795$	25.6905	−	15.2355i	0.911146	−	0.540346i
$796$	19.0933	+	2.93485i	0.676745	+	0.104023i
$797$		−	20.8995i		−	0.740298i	−0.928972	−	0.370149i	$-0.879307\pi$
$797$		−	20.8995i		−	0.740298i	0.928972	−	0.370149i	$-0.120693\pi$
$798$	−4.44627	+	3.81505i	−0.157396	+	0.135051i
$799$	−27.0922			−0.958453
$800$	2.71446	−	28.1537i	0.0959705	−	0.995384i
$801$	8.68063			0.306715
$802$	30.4975	−	26.1679i	1.07690	−	0.924020i
$803$			53.9656i			1.90440i
$804$	−0.844416	−	0.129796i	−0.0297803	−	0.00457755i
$805$	−5.10143	+	3.02535i	−0.179802	+	0.106630i
$806$	−38.0160	−	44.3060i	−1.33906	−	1.56061i
$807$	13.0374	−	13.0374i	0.458937	−	0.458937i
$808$	−11.6754	+	50.1409i	−0.410740	+	1.76395i
$809$	21.1336			0.743018			0.371509	−	0.928429i	$-0.378841\pi$
$809$	21.1336			0.743018			0.371509	+	0.928429i	$0.378841\pi$
$810$	−3.00457	+	8.87680i	−0.105570	+	0.311899i
$811$	−30.2074	+	30.2074i	−1.06072	+	1.06072i	−0.0626906	+	0.998033i	$0.519968\pi$
$811$	−30.2074	+	30.2074i	−1.06072	+	1.06072i	−0.998033	+	0.0626906i	$0.980032\pi$
$812$	−0.862859	+	5.61352i	−0.0302804	+	0.196996i
$813$	16.3077			0.571935
$814$	1.35245	−	17.7006i	0.0474033	−	0.620407i
$815$	4.67497	+	7.88306i	0.163757	+	0.276131i
$816$	5.71055	+	10.9592i	0.199909	+	0.383649i
$817$	3.31731	−	3.31731i	0.116058	−	0.116058i
$818$	−9.40071	+	8.06612i	−0.328688	+	0.282025i
$819$	−6.55952	+	6.55952i	−0.229208	+	0.229208i
$820$	41.8990	−	16.8697i	1.46318	−	0.589115i
$821$	4.12000	+	4.12000i	0.143789	+	0.143789i	0.775337	−	0.631548i	$-0.217580\pi$
$821$	4.12000	+	4.12000i	0.143789	+	0.143789i	−0.631548	+	0.775337i	$0.717580\pi$
$822$	1.76432	−	23.0912i	0.0615377	−	0.805396i
$823$	−0.141649	−	0.141649i	−0.00493757	−	0.00493757i	0.704634	−	0.709571i	$-0.251111\pi$
$823$	−0.141649	−	0.141649i	−0.00493757	−	0.00493757i	−0.709571	+	0.704634i	$0.751111\pi$
$824$	−6.56060	+	28.1749i	−0.228549	+	0.981521i
$825$	−28.1929	+	8.26516i	−0.981550	+	0.287756i
$826$	−3.61541	+	3.10215i	−0.125796	+	0.107937i
$827$			27.5589i			0.958316i	0.877729	+	0.479158i	$0.159058\pi$
$827$			27.5589i			0.958316i	−0.877729	+	0.479158i	$0.840942\pi$
$828$	5.89703	−	4.32568i	0.204936	−	0.150328i
$829$	−7.35288	−	7.35288i	−0.255376	−	0.255376i	0.567794	−	0.823170i	$-0.307797\pi$
$829$	−7.35288	−	7.35288i	−0.255376	−	0.255376i	−0.823170	+	0.567794i	$0.807797\pi$
$830$	5.47408	+	1.85284i	0.190008	+	0.0643129i
$831$		−	15.5179i		−	0.538311i
$832$	23.7799	−	48.2936i	0.824420	−	1.67428i
$833$	−1.71563	−	1.71563i	−0.0594430	−	0.0594430i
$834$	0.654632	−	8.56773i	0.0226681	−	0.296676i
$835$	−6.88952	+	26.9690i	−0.238422	+	0.933299i
$836$	29.6778	+	4.56180i	1.02643	+	0.157773i
$837$	−34.2049			−1.18229
$838$	−0.840067	+	10.9947i	−0.0290196	+	0.379805i
$839$		−	21.1319i		−	0.729554i	−0.931095	−	0.364777i	$-0.881145\pi$
$839$		−	21.1319i		−	0.729554i	0.931095	−	0.364777i	$-0.118855\pi$
$840$	2.42994	+	7.67792i	0.0838409	+	0.264913i
$841$		−	20.9360i		−	0.721930i
$842$	−17.8098	−	1.36079i	−0.613766	−	0.0468959i
$843$	−2.97772			−0.102558
$844$	−34.0332	+	24.9646i	−1.17147	+	0.859318i
$845$	−62.0791	+	36.8154i	−2.13559	+	1.26649i
$846$	21.7072	+	1.65857i	0.746308	+	0.0570229i
$847$	−7.27916	−	7.27916i	−0.250115	−	0.250115i
$848$	−12.6019	+	40.0238i	−0.432752	+	1.37442i
$849$			16.7047i			0.573304i
$850$	14.3836	+	9.35151i	0.493352	+	0.320754i
$851$	−5.10197	−	5.10197i	−0.174893	−	0.174893i
$852$	−2.53418	−	0.389530i	−0.0868195	−	0.0133451i
$853$		−	9.88276i		−	0.338379i	−0.985584	−	0.169190i	$-0.945885\pi$
$853$		−	9.88276i		−	0.338379i	0.985584	−	0.169190i	$-0.0541150\pi$
$854$	6.28911	+	7.32968i	0.215209	+	0.250816i
$855$	2.48238	−	9.71726i	0.0848957	−	0.332323i
$856$	−42.3453	+	26.3496i	−1.44733	+	0.900610i
$857$	−29.1583	−	29.1583i	−0.996029	−	0.996029i	0.00396326	−	0.999992i	$-0.498738\pi$
$857$	−29.1583	−	29.1583i	−0.996029	−	0.996029i	−0.999992	+	0.00396326i	$0.998738\pi$
$858$	−55.7527	−	4.25988i	−1.90336	−	0.145430i
$859$	34.0990	+	34.0990i	1.16344	+	1.16344i	0.983717	+	0.179726i	$0.0575210\pi$
$859$	34.0990	+	34.0990i	1.16344	+	1.16344i	0.179726	+	0.983717i	$0.442479\pi$
$860$	−2.40854	−	5.98207i	−0.0821307	−	0.203987i
$861$	−9.09367	+	9.09367i	−0.309912	+	0.309912i
$862$	−34.0578	−	39.6929i	−1.16001	−	1.35194i
$863$	28.0672	−	28.0672i	0.955418	−	0.955418i	−0.0436294	−	0.999048i	$-0.513892\pi$
$863$	28.0672	−	28.0672i	0.955418	−	0.955418i	0.999048	+	0.0436294i	$0.0138921\pi$
$864$	−12.4012	−	28.9991i	−0.421898	−	0.986570i
$865$	20.0082	−	11.8657i	0.680300	−	0.403445i
$866$	−6.55539	−	0.500876i	−0.222761	−	0.0170205i
$867$	14.1509			0.480588
$868$	−9.89349	+	7.25724i	−0.335807	+	0.246327i
$869$	−6.44439	+	6.44439i	−0.218611	+	0.218611i
$870$	5.06637	+	10.2509i	0.171766	+	0.347537i
$871$	−2.25734			−0.0764870
$872$	9.73368	−	41.8020i	0.329624	−	1.41559i
$873$	−2.33912	+	2.33912i	−0.0791672	+	0.0791672i
$874$	9.26190	−	7.94702i	0.313288	−	0.268812i
$875$	8.17797	+	7.62370i	0.276466	+	0.257728i
$876$	24.0142	−	17.6153i	0.811365	−	0.595166i
$877$		−	28.8331i		−	0.973623i	−0.873507	−	0.486811i	$-0.838160\pi$
$877$		−	28.8331i		−	0.973623i	0.873507	−	0.486811i	$-0.161840\pi$
$878$	−13.3852	−	15.5999i	−0.451730	−	0.526471i
$879$	18.2620			0.615962
$880$	21.7542	−	35.0756i	0.733333	−	1.18240i
$881$	41.1147			1.38519			0.692595	−	0.721327i	$-0.256468\pi$
$881$	41.1147			1.38519			0.692595	+	0.721327i	$0.256468\pi$
$882$	1.26959	+	1.47965i	0.0427492	+	0.0498223i
$883$		−	23.0096i		−	0.774336i	−0.922009	−	0.387168i	$-0.873453\pi$
$883$		−	23.0096i		−	0.774336i	0.922009	−	0.387168i	$-0.126547\pi$
$884$	19.3127	+	26.3281i	0.649555	+	0.885511i
$885$	−2.37394	+	9.29275i	−0.0797991	+	0.312373i
$886$	6.66615	−	5.71978i	0.223954	−	0.192160i
$887$	−12.1772	+	12.1772i	−0.408869	+	0.408869i	−0.881344	−	0.472475i	$-0.843361\pi$
$887$	−12.1772	+	12.1772i	−0.408869	+	0.408869i	0.472475	+	0.881344i	$0.343361\pi$
$888$	−8.31809	+	5.17597i	−0.279137	+	0.173694i
$889$	14.6264			0.490553
$890$	6.38379	−	18.8605i	0.213985	−	0.632205i
$891$	−9.66998	+	9.66998i	−0.323956	+	0.323956i
$892$	−34.6215	−	47.1981i	−1.15921	−	1.58031i
$893$	36.3285			1.21569
$894$	22.1794	+	1.69465i	0.741789	+	0.0566776i
$895$	4.35437	−	17.0451i	0.145551	−	0.569756i
$896$	−9.73969	−	5.75660i	−0.325380	−	0.192315i
$897$	−16.0699	+	16.0699i	−0.536560	+	0.536560i
$898$	−11.9299	−	13.9038i	−0.398107	−	0.463976i
$899$	−12.3188	+	12.3188i	−0.410856	+	0.410856i
$900$	−10.9521	−	8.37329i	−0.365070	−	0.279110i
$901$	−17.9973	−	17.9973i	−0.599577	−	0.599577i
$902$	65.7196	+	5.02142i	2.18822	+	0.167195i
$903$	1.29834	+	1.29834i	0.0432059	+	0.0432059i
$904$	−5.52566	+	23.7303i	−0.183781	+	0.789260i
$905$	6.40864	+	1.63716i	0.213031	+	0.0544210i
$906$	3.33421	+	3.88588i	0.110772	+	0.129100i
$907$			13.1204i			0.435657i	0.975987	+	0.217829i	$0.0698974\pi$
$907$			13.1204i			0.435657i	−0.975987	+	0.217829i	$0.930103\pi$
$908$	6.61686	−	43.0475i	0.219588	−	1.42858i
$909$	17.7437	+	17.7437i	0.588521	+	0.588521i
$910$	9.42801	+	19.0758i	0.312536	+	0.632358i
$911$			31.5760i			1.04616i	0.852284	+	0.523079i	$0.175217\pi$
$911$			31.5760i			1.04616i	−0.852284	+	0.523079i	$0.824783\pi$
$912$	−7.65740	−	14.6954i	−0.253562	−	0.486614i
$913$	5.96321	+	5.96321i	0.197354	+	0.197354i
$914$	−27.5248	−	2.10308i	−0.910441	−	0.0695638i
$915$	18.8396	+	4.81279i	0.622818	+	0.159106i
$916$	9.77717	+	13.3288i	0.323047	+	0.440396i
$917$	9.27611			0.306324
$918$	19.0752	+	1.45747i	0.629574	+	0.0481037i
$919$		−	2.70772i		−	0.0893194i	−0.999002	−	0.0446597i	$-0.985780\pi$
$919$		−	2.70772i		−	0.0893194i	0.999002	−	0.0446597i	$-0.0142204\pi$
$920$	−5.06174	−	15.9937i	−0.166881	−	0.527295i
$921$		−	18.8253i		−	0.620316i
$922$	0.722328	−	9.45372i	0.0237886	−	0.311342i
$923$	−6.77450			−0.222985
$924$	−1.78541	+	11.6154i	−0.0587355	+	0.382117i
$925$	−6.52342	+	11.9347i	−0.214489	+	0.392410i
$926$	−2.72389	+	35.6499i	−0.0895126	+	1.17153i
$927$	9.97044	+	9.97044i	0.327472	+	0.327472i
$928$	−14.9103	−	5.97771i	−0.489454	−	0.196228i
$929$		−	19.6925i		−	0.646091i	−0.946383	−	0.323045i	$-0.895293\pi$
$929$		−	19.6925i		−	0.646091i	0.946383	−	0.323045i	$-0.104707\pi$
$930$	−7.91998	+	23.3990i	−0.259706	+	0.767284i
$931$	2.30052	+	2.30052i	0.0753965	+	0.0753965i
$932$	−21.3106	−	29.0518i	−0.698051	−	0.951624i
$933$		−	24.5347i		−	0.803230i
$934$	−24.1396	+	20.7126i	−0.789870	+	0.677735i
$935$	12.7702	+	21.5335i	0.417631	+	0.704221i
$936$	−13.8621	−	22.2773i	−0.453098	−	0.728156i
$937$	9.98966	+	9.98966i	0.326348	+	0.326348i	0.851196	−	0.524848i	$-0.175878\pi$
$937$	9.98966	+	9.98966i	0.326348	+	0.326348i	−0.524848	+	0.851196i	$0.675878\pi$
$938$	−0.0361441	+	0.473049i	−0.00118015	+	0.0154456i
$939$	16.1836	+	16.1836i	0.528133	+	0.528133i
$940$	19.5672	−	45.9436i	0.638212	−	1.49852i
$941$	19.9907	−	19.9907i	0.651679	−	0.651679i	−0.301718	−	0.953397i	$-0.597560\pi$
$941$	19.9907	−	19.9907i	0.651679	−	0.651679i	0.953397	+	0.301718i	$0.0975601\pi$
$942$	7.94615	−	6.81806i	0.258899	−	0.222145i
$943$	18.9428	−	18.9428i	0.616862	−	0.616862i
$944$	−6.22649	−	11.9493i	−0.202655	−	0.388918i
$945$	12.0792	+	3.08576i	0.392935	+	0.100380i
$946$	0.716925	−	9.38301i	0.0233092	−	0.305068i
$947$	−32.0465			−1.04137			−0.520686	−	0.853748i	$-0.674324\pi$
$947$	−32.0465			−1.04137			−0.520686	+	0.853748i	$0.674324\pi$
$948$	4.97126	+	0.764136i	0.161459	+	0.0248180i
$949$	55.6431	−	55.6431i	1.80625	−	1.80625i
$950$	−19.2872	−	12.5396i	−0.625760	−	0.406840i
$951$	−41.3465			−1.34075
$952$	5.82657	−	3.62561i	0.188840	−	0.117507i
$953$	−19.6279	+	19.6279i	−0.635810	+	0.635810i	−0.949519	−	0.313710i	$-0.898428\pi$
$953$	−19.6279	+	19.6279i	−0.635810	+	0.635810i	0.313710	+	0.949519i	$0.398428\pi$
$954$	13.3182	+	15.5218i	0.431194	+	0.502537i
$955$	−19.7502	−	33.3034i	−0.639103	−	1.07767i
$956$	0.354398	−	2.30562i	0.0114621	−	0.0745691i
$957$			16.6859i			0.539379i
$958$	22.9103	−	19.6578i	0.740198	−	0.635115i
$959$	−12.8603			−0.415282
$960$	−22.7093	+	1.76887i	−0.732939	+	0.0570900i
$961$	−6.63719			−0.214103
$962$	−19.6454	+	16.8564i	−0.633392	+	0.543472i
$963$			24.3095i			0.783362i
$964$	−5.36601	+	34.9098i	−0.172827	+	1.12437i
$965$	48.3174	+	12.3432i	1.55539	+	0.397343i
$966$	3.11032	+	3.62494i	0.100073	+	0.116630i
$967$	−17.3151	+	17.3151i	−0.556815	+	0.556815i	−0.928399	−	0.371584i	$-0.878815\pi$
$967$	−17.3151	+	17.3151i	−0.556815	+	0.556815i	0.371584	+	0.928399i	$0.378815\pi$
$968$	24.7213	−	15.3829i	0.794573	−	0.494427i
$969$	10.0513			0.322894
$970$	3.36202	+	6.80243i	0.107948	+	0.218413i
$971$	−4.02234	+	4.02234i	−0.129083	+	0.129083i	−0.768697	−	0.639614i	$-0.779094\pi$
$971$	−4.02234	+	4.02234i	−0.129083	+	0.129083i	0.639614	+	0.768697i	$0.279094\pi$
$972$	−25.6048	−	3.93574i	−0.821276	−	0.126239i
$973$	−4.77170			−0.152974
$974$	−4.48963	+	58.7597i	−0.143857	+	1.88278i
$975$	37.5914	+	20.5472i	1.20389	+	0.658037i
$976$	−24.2254	+	12.6232i	−0.775437	+	0.404060i
$977$	−12.6876	+	12.6876i	−0.405913	+	0.405913i	−0.880311	−	0.474398i	$-0.842666\pi$
$977$	−12.6876	+	12.6876i	−0.405913	+	0.405913i	0.474398	+	0.880311i	$0.342666\pi$
$978$	5.60149	−	4.80627i	0.179116	−	0.153687i
$979$	20.5457	−	20.5457i	0.656645	−	0.656645i
$980$	4.14851	−	1.67030i	0.132519	−	0.0533558i
$981$	−14.7927	−	14.7927i	−0.472295	−	0.472295i
$982$	−2.65542	+	34.7537i	−0.0847378	+	1.10904i
$983$	−16.9846	−	16.9846i	−0.541726	−	0.541726i	0.382309	−	0.924035i	$-0.375129\pi$
$983$	−16.9846	−	16.9846i	−0.541726	−	0.541726i	−0.924035	+	0.382309i	$0.875129\pi$
$984$	−19.2175	−	30.8837i	−0.612633	−	0.984537i
$985$	−16.5239	+	9.79931i	−0.526494	+	0.312232i
$986$	7.39480	−	6.34499i	0.235499	−	0.202066i
$987$			14.2183i			0.452574i
$988$	−25.8968	−	35.3040i	−0.823886	−	1.12317i
$989$	−2.70453	−	2.70453i	−0.0859989	−	0.0859989i
$990$	−8.91366	−	18.0351i	−0.283295	−	0.573194i
$991$		−	23.8194i		−	0.756648i	−0.925673	−	0.378324i	$-0.876501\pi$
$991$		−	23.8194i		−	0.756648i	0.925673	−	0.378324i	$-0.123499\pi$
$992$	−13.6456	−	31.9090i	−0.433249	−	1.01311i
$993$	1.74551	+	1.74551i	0.0553921	+	0.0553921i
$994$	−0.108472	+	1.41967i	−0.00344053	+	0.0450292i
$995$	−11.0167	−	18.5767i	−0.349253	−	0.588920i
$996$	0.707081	−	4.60008i	0.0224047	−	0.145759i
$997$	24.7382			0.783465			0.391733	−	0.920079i	$-0.371876\pi$
$997$	24.7382			0.783465			0.391733	+	0.920079i	$0.371876\pi$
$998$	−3.60032	+	47.1205i	−0.113966	+	1.49157i
$999$			15.1665i			0.479848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.18	✓	144
5.2	odd	4		560.2.bl.a.267.20	yes	144
16.3	odd	4		560.2.bl.a.323.20	yes	144
80.67	even	4	inner	560.2.t.a.547.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.18	✓	144	1.1	even	1	trivial
560.2.t.a.547.18	yes	144	80.67	even	4	inner
560.2.bl.a.267.20	yes	144	5.2	odd	4
560.2.bl.a.323.20	yes	144	16.3	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07328 + 0.920909i) q^{2} -1.27333i q^{3} +(0.303853 - 1.97678i) q^{4} +(-1.92329 + 1.14059i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.49432 + 2.40146i) q^{8} +1.37862 q^{9} +O(q^{10})\)	\(q+(-1.07328 + 0.920909i) q^{2} -1.27333i q^{3} +(0.303853 - 1.97678i) q^{4} +(-1.92329 + 1.14059i) q^{5} +(1.17262 + 1.36664i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.49432 + 2.40146i) q^{8} +1.37862 q^{9} +(1.01385 - 2.99535i) q^{10} +(3.26300 - 3.26300i) q^{11} +(-2.51710 - 0.386906i) q^{12} -6.72886 q^{13} +(-0.107741 + 1.41010i) q^{14} +(1.45235 + 2.44899i) q^{15} +(-3.81535 - 1.20130i) q^{16} +(1.71563 - 1.71563i) q^{17} +(-1.47965 + 1.26959i) q^{18} +(-2.30052 + 2.30052i) q^{19} +(1.67030 + 4.14851i) q^{20} +(-0.900382 - 0.900382i) q^{21} +(-0.497180 + 6.50703i) q^{22} +(1.87556 + 1.87556i) q^{23} +(3.05786 - 1.90277i) q^{24} +(2.39811 - 4.38738i) q^{25} +(7.22194 - 6.19666i) q^{26} -5.57545i q^{27} +(-1.18294 - 1.61265i) q^{28} +(-2.00799 - 2.00799i) q^{29} +(-3.81408 - 1.29097i) q^{30} -6.13492i q^{31} +(5.20122 - 2.22425i) q^{32} +(-4.15488 - 4.15488i) q^{33} +(-0.261409 + 3.42128i) q^{34} +(-0.553455 + 2.16649i) q^{35} +(0.418899 - 2.72524i) q^{36} -2.72024 q^{37} +(0.350529 - 4.58767i) q^{38} +8.56807i q^{39} +(-5.61309 - 2.91431i) q^{40} -10.0998i q^{41} +(1.79553 + 0.137191i) q^{42} -1.44198 q^{43} +(-5.45877 - 7.44171i) q^{44} +(-2.65150 + 1.57244i) q^{45} +(-3.74022 - 0.285778i) q^{46} +(-7.89571 - 7.89571i) q^{47} +(-1.52966 + 4.85821i) q^{48} -1.00000i q^{49} +(1.46653 + 6.91732i) q^{50} +(-2.18456 - 2.18456i) q^{51} +(-2.04458 + 13.3015i) q^{52} -10.4902i q^{53} +(5.13448 + 5.98400i) q^{54} +(-2.55396 + 9.99744i) q^{55} +(2.75473 + 0.641445i) q^{56} +(2.92933 + 2.92933i) q^{57} +(4.00431 + 0.305956i) q^{58} +(2.38194 + 2.38194i) q^{59} +(5.28243 - 2.12685i) q^{60} +(4.82900 - 4.82900i) q^{61} +(5.64970 + 6.58447i) q^{62} +(0.974834 - 0.974834i) q^{63} +(-3.53402 + 7.17710i) q^{64} +(12.9416 - 7.67486i) q^{65} +(8.28561 + 0.633076i) q^{66} +0.335471 q^{67} +(-2.87013 - 3.91272i) q^{68} +(2.38821 - 2.38821i) q^{69} +(-1.40113 - 2.83493i) q^{70} +1.00678 q^{71} +(2.06010 + 3.31071i) q^{72} +(-8.26933 + 8.26933i) q^{73} +(2.91957 - 2.50509i) q^{74} +(-5.58659 - 3.05359i) q^{75} +(3.84861 + 5.24665i) q^{76} -4.61457i q^{77} +(-7.89042 - 9.19593i) q^{78} -1.97499 q^{79} +(8.70822 - 2.04129i) q^{80} -2.96353 q^{81} +(9.30099 + 10.8399i) q^{82} +1.82753i q^{83} +(-2.05344 + 1.50628i) q^{84} +(-1.34283 + 5.25648i) q^{85} +(1.54765 - 1.32793i) q^{86} +(-2.55684 + 2.55684i) q^{87} +(12.7119 + 2.96000i) q^{88} +6.29659 q^{89} +(1.39772 - 4.12946i) q^{90} +(-4.75802 + 4.75802i) q^{91} +(4.27747 - 3.13768i) q^{92} -7.81179 q^{93} +(15.7455 + 1.20306i) q^{94} +(1.80063 - 7.04853i) q^{95} +(-2.83222 - 6.62288i) q^{96} +(-1.69671 + 1.69671i) q^{97} +(0.920909 + 1.07328i) q^{98} +(4.49844 - 4.49844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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