LMFDB - Embedded newform 672.2.bo.a.125.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (of order $8$, degree $4$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.19
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21868 + 0.717517i) q^{2} +(-1.53560 - 0.801206i) q^{3} +(0.970338 - 1.74884i) q^{4} +(-1.29133 - 3.11756i) q^{5} +(2.44628 - 0.125409i) q^{6} +(-1.18607 + 2.36500i) q^{7} +(0.0722962 + 2.82750i) q^{8} +(1.71614 + 2.46067i) q^{9} +O(q^{10})$	\(q+(-1.21868 + 0.717517i) q^{2} +(-1.53560 - 0.801206i) q^{3} +(0.970338 - 1.74884i) q^{4} +(-1.29133 - 3.11756i) q^{5} +(2.44628 - 0.125409i) q^{6} +(-1.18607 + 2.36500i) q^{7} +(0.0722962 + 2.82750i) q^{8} +(1.71614 + 2.46067i) q^{9} +(3.81062 + 2.87274i) q^{10} +(1.06867 + 2.57999i) q^{11} +(-2.89123 + 1.90808i) q^{12} +(-3.41537 - 1.41469i) q^{13} +(-0.251488 - 3.73320i) q^{14} +(-0.514833 + 5.82195i) q^{15} +(-2.11689 - 3.39393i) q^{16} +4.01050i q^{17} +(-3.85698 - 1.76739i) q^{18} +(6.86210 + 2.84237i) q^{19} +(-6.70514 - 0.766747i) q^{20} +(3.71619 - 2.68140i) q^{21} +(-3.15355 - 2.37738i) q^{22} +(-0.124984 + 0.124984i) q^{23} +(2.15440 - 4.39984i) q^{24} +(-4.51609 + 4.51609i) q^{25} +(5.17729 - 0.726535i) q^{26} +(-0.663800 - 5.15358i) q^{27} +(2.98511 + 4.36911i) q^{28} +(2.77924 - 6.70969i) q^{29} +(-3.54993 - 7.46447i) q^{30} -3.06699i q^{31} +(5.01500 + 2.61720i) q^{32} +(0.426059 - 4.81806i) q^{33} +(-2.87761 - 4.88750i) q^{34} +(8.90465 + 0.643650i) q^{35} +(5.96854 - 0.613573i) q^{36} +(-1.96953 - 4.75487i) q^{37} +(-10.4021 + 1.45974i) q^{38} +(4.11118 + 4.90881i) q^{39} +(8.72155 - 3.87664i) q^{40} +(1.26117 + 1.26117i) q^{41} +(-2.60487 + 5.93419i) q^{42} +(6.70616 - 2.77778i) q^{43} +(5.54896 + 0.634535i) q^{44} +(5.45516 - 8.52770i) q^{45} +(0.0626366 - 0.241993i) q^{46} -9.12869i q^{47} +(0.531452 + 6.90779i) q^{48} +(-4.18645 - 5.61013i) q^{49} +(2.26327 - 8.74402i) q^{50} +(3.21324 - 6.15853i) q^{51} +(-5.78813 + 4.60020i) q^{52} +(5.24438 + 12.6611i) q^{53} +(4.50674 + 5.80425i) q^{54} +(6.66326 - 6.66326i) q^{55} +(-6.77279 - 3.18265i) q^{56} +(-8.26011 - 9.86270i) q^{57} +(1.42732 + 10.1711i) q^{58} +(3.47911 + 8.39931i) q^{59} +(9.68210 + 6.54962i) q^{60} +(0.178041 - 0.429829i) q^{61} +(2.20062 + 3.73766i) q^{62} +(-7.85494 + 1.14013i) q^{63} +(-7.98955 + 0.408835i) q^{64} +12.4744i q^{65} +(2.93781 + 6.17735i) q^{66} +(-2.56695 - 1.06327i) q^{67} +(7.01373 + 3.89155i) q^{68} +(0.292063 - 0.0917874i) q^{69} +(-11.3137 + 5.60484i) q^{70} +(10.5260 + 10.5260i) q^{71} +(-6.83347 + 5.03028i) q^{72} +(-1.46250 + 1.46250i) q^{73} +(5.81192 + 4.38147i) q^{74} +(10.5532 - 3.31659i) q^{75} +(11.6294 - 9.24265i) q^{76} +(-7.36920 - 0.532664i) q^{77} +(-8.53235 - 3.03241i) q^{78} +1.85387i q^{79} +(-7.84718 + 10.9822i) q^{80} +(-3.10975 + 8.44568i) q^{81} +(-2.44187 - 0.632047i) q^{82} +(2.04061 - 4.92648i) q^{83} +(-1.08339 - 9.10089i) q^{84} +(12.5030 - 5.17890i) q^{85} +(-6.17952 + 8.19700i) q^{86} +(-9.64365 + 8.07665i) q^{87} +(-7.21767 + 3.20818i) q^{88} +(6.54657 - 6.54657i) q^{89} +(-0.529297 + 14.3067i) q^{90} +(7.39663 - 6.39941i) q^{91} +(0.0973002 + 0.339853i) q^{92} +(-2.45729 + 4.70967i) q^{93} +(6.54999 + 11.1249i) q^{94} -25.0634i q^{95} +(-5.60413 - 8.03703i) q^{96} -0.138925i q^{97} +(9.12729 + 3.83308i) q^{98} +(-4.51451 + 7.05725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.21868	+	0.717517i	−0.861733	+	0.507361i
$2$	−1.21868	+	0.717517i	−0.861733	+	0.507361i
$3$	−1.53560	−	0.801206i	−0.886579	−	0.462577i
$3$	−1.53560	−	0.801206i	−0.886579	−	0.462577i
$4$	0.970338	−	1.74884i	0.485169	−	0.874420i
$5$	−1.29133	−	3.11756i	−0.577503	−	1.39421i	−0.895047	−	0.445971i	$-0.852858\pi$
$5$	−1.29133	−	3.11756i	−0.577503	−	1.39421i	0.317545	−	0.948243i	$-0.397142\pi$
$6$	2.44628	−	0.125409i	0.998689	−	0.0511982i
$7$	−1.18607	+	2.36500i	−0.448294	+	0.893886i
$7$	−1.18607	+	2.36500i	−0.448294	+	0.893886i
$8$	0.0722962	+	2.82750i	0.0255606	+	0.999673i
$9$	1.71614	+	2.46067i	0.572046	+	0.820222i
$10$	3.81062	+	2.87274i	1.20502	+	0.908439i
$11$	1.06867	+	2.57999i	0.322215	+	0.777896i	0.999125	+	0.0418302i	$0.0133188\pi$
$11$	1.06867	+	2.57999i	0.322215	+	0.777896i	−0.676909	+	0.736066i	$0.736681\pi$
$12$	−2.89123	+	1.90808i	−0.834627	+	0.550815i
$13$	−3.41537	−	1.41469i	−0.947252	−	0.392365i	−0.145055	−	0.989424i	$-0.546336\pi$
$13$	−3.41537	−	1.41469i	−0.947252	−	0.392365i	−0.802197	+	0.597059i	$0.796336\pi$
$14$	−0.251488	−	3.73320i	−0.0672131	−	0.997739i
$15$	−0.514833	+	5.82195i	−0.132929	+	1.50322i
$16$	−2.11689	−	3.39393i	−0.529222	−	0.848483i
$17$			4.01050i			0.972690i	0.873767	+	0.486345i	$0.161670\pi$
$17$			4.01050i			0.972690i	−0.873767	+	0.486345i	$0.838330\pi$
$18$	−3.85698	−	1.76739i	−0.909100	−	0.416579i
$19$	6.86210	+	2.84237i	1.57427	+	0.652085i	0.987493	−	0.157662i	$-0.0503956\pi$
$19$	6.86210	+	2.84237i	1.57427	+	0.652085i	0.586779	+	0.809747i	$0.300396\pi$
$20$	−6.70514	−	0.766747i	−1.49932	−	0.171450i
$21$	3.71619	−	2.68140i	0.810939	−	0.585130i
$22$	−3.15355	−	2.37738i	−0.672338	−	0.506860i
$23$	−0.124984	+	0.124984i	−0.0260609	+	0.0260609i	−0.720017	−	0.693956i	$-0.755866\pi$
$23$	−0.124984	+	0.124984i	−0.0260609	+	0.0260609i	0.693956	+	0.720017i	$0.255866\pi$
$24$	2.15440	−	4.39984i	0.439764	−	0.898113i
$25$	−4.51609	+	4.51609i	−0.903218	+	0.903218i
$26$	5.17729	−	0.726535i	1.01535	−	0.142485i
$27$	−0.663800	−	5.15358i	−0.127748	−	0.991807i
$28$	2.98511	+	4.36911i	0.564134	+	0.825683i
$29$	2.77924	−	6.70969i	0.516092	−	1.24596i	−0.424193	−	0.905572i	$-0.639442\pi$
$29$	2.77924	−	6.70969i	0.516092	−	1.24596i	0.940286	−	0.340386i	$-0.110558\pi$
$30$	−3.54993	−	7.46447i	−0.648126	−	1.36282i
$31$		−	3.06699i		−	0.550847i	−0.961323	−	0.275424i	$-0.911182\pi$
$31$		−	3.06699i		−	0.550847i	0.961323	−	0.275424i	$-0.0888181\pi$
$32$	5.01500	+	2.61720i	0.886536	+	0.462660i
$33$	0.426059	−	4.81806i	0.0741674	−	0.838716i
$34$	−2.87761	−	4.88750i	−0.493505	−	0.838200i
$35$	8.90465	+	0.643650i	1.50516	+	0.108797i
$36$	5.96854	−	0.613573i	0.994757	−	0.102262i
$37$	−1.96953	−	4.75487i	−0.323789	−	0.781696i	−0.999027	−	0.0440964i	$-0.985959\pi$
$37$	−1.96953	−	4.75487i	−0.323789	−	0.781696i	0.675238	−	0.737600i	$-0.264041\pi$
$38$	−10.4021	+	1.45974i	−1.68745	+	0.236801i
$39$	4.11118	+	4.90881i	0.658316	+	0.786039i
$40$	8.72155	−	3.87664i	1.37900	−	0.612951i
$41$	1.26117	+	1.26117i	0.196962	+	0.196962i	0.798696	−	0.601734i	$-0.205523\pi$
$41$	1.26117	+	1.26117i	0.196962	+	0.196962i	−0.601734	+	0.798696i	$0.705523\pi$
$42$	−2.60487	+	5.93419i	−0.401941	+	0.915666i
$43$	6.70616	−	2.77778i	1.02268	−	0.423608i	0.192615	−	0.981274i	$-0.438303\pi$
$43$	6.70616	−	2.77778i	1.02268	−	0.423608i	0.830065	+	0.557667i	$0.188303\pi$
$44$	5.54896	+	0.634535i	0.836537	+	0.0956597i
$45$	5.45516	−	8.52770i	0.813207	−	1.27123i
$46$	0.0626366	−	0.241993i	0.00923527	−	0.0356799i
$47$		−	9.12869i		−	1.33156i	−0.746150	−	0.665778i	$-0.768100\pi$
$47$		−	9.12869i		−	1.33156i	0.746150	−	0.665778i	$-0.231900\pi$
$48$	0.531452	+	6.90779i	0.0767085	+	0.997054i
$49$	−4.18645	−	5.61013i	−0.598065	−	0.801448i
$50$	2.26327	−	8.74402i	0.320075	−	1.23659i
$51$	3.21324	−	6.15853i	0.449944	−	0.862367i
$52$	−5.78813	+	4.60020i	−0.802669	+	0.637934i
$53$	5.24438	+	12.6611i	0.720371	+	1.73913i	0.672291	+	0.740287i	$0.265310\pi$
$53$	5.24438	+	12.6611i	0.720371	+	1.73913i	0.0480798	+	0.998843i	$0.484690\pi$
$54$	4.50674	+	5.80425i	0.613289	+	0.789858i
$55$	6.66326	−	6.66326i	0.898474	−	0.898474i
$56$	−6.77279	−	3.18265i	−0.905053	−	0.425299i
$57$	−8.26011	−	9.86270i	−1.09408	−	1.30635i
$58$	1.42732	+	10.1711i	0.187416	+	1.33553i
$59$	3.47911	+	8.39931i	0.452941	+	1.09350i	0.971199	+	0.238272i	$0.0765809\pi$
$59$	3.47911	+	8.39931i	0.452941	+	1.09350i	−0.518257	+	0.855225i	$0.673419\pi$
$60$	9.68210	+	6.54962i	1.24995	+	0.845552i
$61$	0.178041	−	0.429829i	0.0227958	−	0.0550340i	−0.912072	−	0.410031i	$-0.865518\pi$
$61$	0.178041	−	0.429829i	0.0227958	−	0.0550340i	0.934868	+	0.354997i	$0.115518\pi$
$62$	2.20062	+	3.73766i	0.279479	+	0.474684i
$63$	−7.85494	+	1.14013i	−0.989630	+	0.143643i
$64$	−7.98955	+	0.408835i	−0.998693	+	0.0511044i
$65$			12.4744i			1.54726i
$66$	2.93781	+	6.17735i	0.361620	+	0.760379i
$67$	−2.56695	−	1.06327i	−0.313603	−	0.129899i	0.220330	−	0.975425i	$-0.429287\pi$
$67$	−2.56695	−	1.06327i	−0.313603	−	0.129899i	−0.533933	+	0.845527i	$0.679287\pi$
$68$	7.01373	+	3.89155i	0.850540	+	0.471919i
$69$	0.292063	−	0.0917874i	0.0351603	−	0.0110499i
$70$	−11.3137	+	5.60484i	−1.35225	+	0.669906i
$71$	10.5260	+	10.5260i	1.24920	+	1.24920i	0.956073	+	0.293128i	$0.0946963\pi$
$71$	10.5260	+	10.5260i	1.24920	+	1.24920i	0.293128	+	0.956073i	$0.405304\pi$
$72$	−6.83347	+	5.03028i	−0.805332	+	0.592824i
$73$	−1.46250	+	1.46250i	−0.171173	+	0.171173i	−0.787494	−	0.616322i	$-0.788622\pi$
$73$	−1.46250	+	1.46250i	−0.171173	+	0.171173i	0.616322	+	0.787494i	$0.288622\pi$
$74$	5.81192	+	4.38147i	0.675622	+	0.509336i
$75$	10.5532	−	3.31659i	1.21858	−	0.382967i
$76$	11.6294	−	9.24265i	1.33398	−	1.06020i
$77$	−7.36920	−	0.532664i	−0.839798	−	0.0607027i
$78$	−8.53235	−	3.03241i	−0.966098	−	0.343353i
$79$			1.85387i			0.208577i	0.994547	+	0.104288i	$0.0332565\pi$
$79$			1.85387i			0.208577i	−0.994547	+	0.104288i	$0.966743\pi$
$80$	−7.84718	+	10.9822i	−0.877341	+	1.22785i
$81$	−3.10975	+	8.44568i	−0.345528	+	0.938409i
$82$	−2.44187	−	0.632047i	−0.269660	−	0.0697979i
$83$	2.04061	−	4.92648i	0.223986	−	0.540751i	−0.771438	−	0.636305i	$-0.780462\pi$
$83$	2.04061	−	4.92648i	0.223986	−	0.540751i	0.995424	+	0.0955535i	$0.0304621\pi$
$84$	−1.08339	−	9.10089i	−0.118207	−	0.992989i
$85$	12.5030	−	5.17890i	1.35614	−	0.561731i
$86$	−6.17952	+	8.19700i	−0.666355	+	0.883905i
$87$	−9.64365	+	8.07665i	−1.03391	+	0.865908i
$88$	−7.21767	+	3.20818i	−0.769406	+	0.341993i
$89$	6.54657	−	6.54657i	0.693935	−	0.693935i	−0.269160	−	0.963095i	$-0.586746\pi$
$89$	6.54657	−	6.54657i	0.693935	−	0.693935i	0.963095	+	0.269160i	$0.0867461\pi$
$90$	−0.529297	+	14.3067i	−0.0557928	+	1.50806i
$91$	7.39663	−	6.39941i	0.775377	−	0.670841i
$92$	0.0973002	+	0.339853i	0.0101442	+	0.0354322i
$93$	−2.45729	+	4.70967i	−0.254809	+	0.488370i
$94$	6.54999	+	11.1249i	0.675580	+	1.14745i
$95$		−	25.0634i		−	2.57145i
$96$	−5.60413	−	8.03703i	−0.571969	−	0.820275i
$97$		−	0.138925i		−	0.0141057i	−0.999975	−	0.00705286i	$-0.997755\pi$
$97$		−	0.138925i		−	0.0141057i	0.999975	−	0.00705286i	$-0.00224501\pi$
$98$	9.12729	+	3.83308i	0.921996	+	0.387200i
$99$	−4.51451	+	7.05725i	−0.453726	+	0.709280i
$100$	3.51579	+	12.2801i	0.351579	+	1.22801i
$101$	−0.935221	−	2.25782i	−0.0930580	−	0.224662i	0.870496	−	0.492175i	$-0.163798\pi$
$101$	−0.935221	−	2.25782i	−0.0930580	−	0.224662i	−0.963554	+	0.267513i	$0.913798\pi$
$102$	0.502955	+	9.81081i	0.0498000	+	0.971415i
$103$	11.1586	+	11.1586i	1.09949	+	1.09949i	0.994471	+	0.105015i	$0.0334890\pi$
$103$	11.1586	+	11.1586i	1.09949	+	1.09949i	0.105015	+	0.994471i	$0.466511\pi$
$104$	3.75313	−	9.75924i	0.368024	−	0.956972i
$105$	−13.1583	−	8.12285i	−1.28412	−	0.792709i
$106$	−15.4757	−	11.6668i	−1.50314	−	1.13318i
$107$	−3.49875	−	8.44672i	−0.338237	−	0.816576i	−0.997885	−	0.0650014i	$-0.979295\pi$
$107$	−3.49875	−	8.44672i	−0.338237	−	0.816576i	0.659648	−	0.751574i	$-0.270705\pi$
$108$	−9.65690	−	3.83983i	−0.929235	−	0.369488i
$109$	4.14298	−	10.0020i	0.396826	−	0.958023i	−0.591588	−	0.806240i	$-0.701499\pi$
$109$	4.14298	−	10.0020i	0.396826	−	0.958023i	0.988414	−	0.151782i	$-0.0485012\pi$
$110$	−3.33935	+	12.9014i	−0.318394	+	1.23010i
$111$	−0.785219	+	8.87959i	−0.0745297	+	0.842813i
$112$	10.5374	−	0.980980i	0.995695	−	0.0926939i
$113$	10.4612			0.984110			0.492055	−	0.870564i	$-0.336246\pi$
$113$	10.4612			0.984110			0.492055	+	0.870564i	$0.336246\pi$
$114$	17.1430	+	6.09266i	1.60559	+	0.570630i
$115$	0.551040	+	0.228248i	0.0513848	+	0.0212843i
$116$	−9.03737	−	11.3711i	−0.839098	−	1.05578i
$117$	−2.38016	−	10.8319i	−0.220045	−	1.00141i
$118$	−10.2665	−	7.73971i	−0.945112	−	0.712498i
$119$	−9.48485	−	4.75676i	−0.869474	−	0.436051i
$120$	−16.4988	−	1.03479i	−1.50613	−	0.0944627i
$121$	2.26387	−	2.26387i	0.205807	−	0.205807i
$122$	0.0914356	+	0.651570i	0.00827819	+	0.0589904i
$123$	−0.926198	−	2.94712i	−0.0835124	−	0.265732i
$124$	−5.36367	−	2.97602i	−0.481672	−	0.267254i
$125$	4.32317	+	1.79071i	0.386676	+	0.160166i
$126$	8.75456	−	7.02550i	0.779918	−	0.625882i
$127$	10.3963			0.922519			0.461259	−	0.887265i	$-0.347398\pi$
$127$	10.3963			0.922519			0.461259	+	0.887265i	$0.347398\pi$
$128$	9.44332	−	6.23087i	0.834679	−	0.550737i
$129$	−12.5236	−	1.10745i	−1.10264	−	0.0975058i
$130$	−8.95063	−	15.2023i	−0.785022	−	1.33333i
$131$	2.48721	+	1.03024i	0.217309	+	0.0900123i	0.488682	−	0.872462i	$-0.337478\pi$
$131$	2.48721	+	1.03024i	0.217309	+	0.0900123i	−0.271373	+	0.962474i	$0.587478\pi$
$132$	−8.01259	−	5.42025i	−0.697407	−	0.471773i
$133$	−14.8612	+	12.8576i	−1.28863	+	1.11489i
$134$	3.89119	−	0.546056i	0.336148	−	0.0471720i
$135$	−15.2094	+	8.72443i	−1.30902	+	0.750879i
$136$	−11.3397	+	0.289944i	−0.972373	+	0.0248625i
$137$	0.0735543	−	0.0735543i	0.00628417	−	0.00628417i	−0.703958	−	0.710242i	$-0.748586\pi$
$137$	0.0735543	−	0.0735543i	0.00628417	−	0.00628417i	0.710242	+	0.703958i	$0.248586\pi$
$138$	−0.290071	+	0.321419i	−0.0246925	+	0.0273610i
$139$	−1.31182	−	3.16702i	−0.111267	−	0.268623i	0.858431	−	0.512929i	$-0.171440\pi$
$139$	−1.31182	−	3.16702i	−0.111267	−	0.268623i	−0.969698	+	0.244306i	$0.921440\pi$
$140$	9.76616	−	14.9482i	0.825391	−	1.26336i
$141$	−7.31396	+	14.0180i	−0.615947	+	1.18053i
$142$	−20.3803	−	5.27517i	−1.71028	−	0.442682i
$143$		−	10.3234i		−	0.863290i
$144$	4.71847	−	11.0334i	0.393206	−	0.919451i
$145$	−24.5068			−2.03518
$146$	0.732943	−	2.83168i	0.0606588	−	0.234352i
$147$	1.93384	+	11.9691i	0.159501	+	0.987198i
$148$	−10.2266	−	1.16944i	−0.840624	−	0.0961270i
$149$	2.30720	+	5.57009i	0.189014	+	0.456319i	0.989770	−	0.142671i	$-0.0455690\pi$
$149$	2.30720	+	5.57009i	0.189014	+	0.456319i	−0.800757	+	0.598990i	$0.795569\pi$
$150$	−10.4812	+	11.6140i	−0.855790	+	0.948276i
$151$	14.0678	+	14.0678i	1.14482	+	1.14482i	0.987557	+	0.157261i	$0.0502662\pi$
$151$	14.0678	+	14.0678i	1.14482	+	1.14482i	0.157261	+	0.987557i	$0.449734\pi$
$152$	−7.54071	+	19.6081i	−0.611633	+	1.59043i
$153$	−9.86851	+	6.88258i	−0.797822	+	0.556423i
$154$	9.36285	−	4.63838i	0.754480	−	0.373771i
$155$	−9.56152	+	3.96051i	−0.767999	+	0.318116i
$156$	12.5740	−	2.42659i	1.00672	−	0.194283i
$157$	−5.96845	+	14.4091i	−0.476334	+	1.14997i	0.484982	+	0.874524i	$0.338826\pi$
$157$	−5.96845	+	14.4091i	−0.476334	+	1.14997i	−0.961316	+	0.275448i	$0.911174\pi$
$158$	−1.33019	−	2.25927i	−0.105824	−	0.179738i
$159$	2.09084	−	23.6442i	0.165815	−	1.87510i
$160$	1.68322	−	19.0142i	0.133070	−	1.50321i
$161$	−0.147347	−	0.443827i	−0.0116125	−	0.0349785i
$162$	−2.27015	−	12.5238i	−0.178360	−	0.983965i
$163$	7.17106	+	2.97035i	0.561681	+	0.232656i	0.645415	−	0.763832i	$-0.276685\pi$
$163$	7.17106	+	2.97035i	0.561681	+	0.232656i	−0.0837339	+	0.996488i	$0.526685\pi$
$164$	3.42935	−	0.981826i	0.267787	−	0.0766677i
$165$	−15.5708	+	4.89346i	−1.21218	+	0.380955i
$166$	1.04799	+	7.46795i	0.0813396	+	0.579625i
$167$	−8.65519	+	8.65519i	−0.669759	+	0.669759i	−0.957660	−	0.287901i	$-0.907043\pi$
$167$	−8.65519	+	8.65519i	−0.669759	+	0.669759i	0.287901	+	0.957660i	$0.407043\pi$
$168$	7.85035	+	10.3137i	0.605667	+	0.795718i
$169$	0.470993	+	0.470993i	0.0362302	+	0.0362302i
$170$	−11.5211	+	15.2825i	−0.883630	+	1.17211i
$171$	4.78217	+	21.7632i	0.365701	+	1.66428i
$172$	1.64934	−	14.4234i	0.125761	−	1.09977i
$173$	5.41202	−	13.0658i	0.411468	−	0.993372i	−0.573276	−	0.819363i	$-0.694328\pi$
$173$	5.41202	−	13.0658i	0.411468	−	0.993372i	0.984744	−	0.174010i	$-0.0556724\pi$
$174$	5.95734	−	16.7623i	0.451625	−	1.27075i
$175$	−5.32413	−	16.0370i	−0.402467	−	1.21228i
$176$	6.49407	−	9.08854i	0.489509	−	0.685074i
$177$	1.38706	−	15.6855i	0.104258	−	1.17899i
$178$	−3.28087	+	12.6754i	−0.245911	+	0.950063i
$179$	−4.47582	−	1.85394i	−0.334538	−	0.138570i	0.209090	−	0.977896i	$-0.432950\pi$
$179$	−4.47582	−	1.85394i	−0.334538	−	0.138570i	−0.543628	+	0.839326i	$0.682950\pi$
$180$	−9.62024	−	17.8150i	−0.717050	−	1.32785i
$181$	−2.19189	−	5.29170i	−0.162922	−	0.393329i	0.821244	−	0.570577i	$-0.193280\pi$
$181$	−2.19189	−	5.29170i	−0.162922	−	0.393329i	−0.984166	+	0.177248i	$0.943280\pi$
$182$	−4.42240	+	13.1060i	−0.327810	+	0.971482i
$183$	−0.617782	+	0.517398i	−0.0456678	+	0.0382472i
$184$	−0.362428	−	0.344356i	−0.0267185	−	0.0253863i
$185$	−12.2803	+	12.2803i	−0.902863	+	0.902863i
$186$	−0.384629	−	7.50270i	−0.0282024	−	0.550125i
$187$	−10.3471	+	4.28589i	−0.756652	+	0.313416i
$188$	−15.9646	−	8.85791i	−1.16434	−	0.646030i
$189$	12.9755	+	4.54264i	0.943831	+	0.330429i
$190$	17.9834	+	30.5442i	1.30466	+	2.21591i
$191$		−	3.30666i		−	0.239261i	−0.992818	−	0.119631i	$-0.961829\pi$
$191$		−	3.30666i		−	0.239261i	0.992818	−	0.119631i	$-0.0381711\pi$
$192$	12.5963	+	5.77347i	0.909061	+	0.416664i
$193$	9.69346			0.697750			0.348875	−	0.937169i	$-0.386564\pi$
$193$	9.69346			0.697750			0.348875	+	0.937169i	$0.386564\pi$
$194$	0.0996813	+	0.169305i	0.00715670	+	0.0121554i
$195$	9.99460	−	19.1558i	0.715729	−	1.37177i
$196$	−13.8735	+	1.87771i	−0.990965	+	0.134122i
$197$	24.6676	−	10.2176i	1.75749	−	0.727977i	0.760598	−	0.649223i	$-0.224906\pi$
$197$	24.6676	−	10.2176i	1.75749	−	0.727977i	0.996894	−	0.0787535i	$-0.0250940\pi$
$198$	0.438029	−	11.8397i	0.0311294	−	0.841413i
$199$	10.9340	+	10.9340i	0.775093	+	0.775093i	0.978992	−	0.203899i	$-0.0653613\pi$
$199$	10.9340	+	10.9340i	0.775093	+	0.775093i	−0.203899	+	0.978992i	$0.565361\pi$
$200$	−13.0958	−	12.4428i	−0.926010	−	0.879836i
$201$	3.08992	+	3.68941i	0.217946	+	0.260231i
$202$	2.75976	+	2.08052i	0.194176	+	0.146385i
$203$	12.5720	+	14.5311i	0.882383	+	1.01988i
$204$	−7.65236	−	11.5953i	−0.535772	−	0.811834i
$205$	2.30318	−	5.56037i	0.160861	−	0.388353i
$206$	−21.6051	−	5.59220i	−1.50530	−	0.389627i
$207$	−0.522033	−	0.0930540i	−0.0362838	−	0.00646770i
$208$	2.42858	+	14.5863i	0.168392	+	1.01138i
$209$			20.7417i			1.43473i
$210$	21.8640	+	0.457820i	1.50876	+	0.0315926i
$211$	−9.02924	+	21.7985i	−0.621598	+	1.50067i	0.228228	+	0.973608i	$0.426707\pi$
$211$	−9.02924	+	21.7985i	−0.621598	+	1.50067i	−0.849826	+	0.527063i	$0.823293\pi$
$212$	27.2310	+	3.11392i	1.87023	+	0.213865i
$213$	−7.73020	−	24.5971i	−0.529665	−	1.68537i
$214$	10.3245	+	7.78340i	0.705769	+	0.532062i
$215$	−17.3198	−	17.3198i	−1.18120	−	1.18120i
$216$	14.5238	−	2.24948i	0.988217	−	0.153058i
$217$	7.25343	+	3.63768i	0.492395	+	0.246942i
$218$	2.12769	+	15.1619i	0.144105	+	1.02689i
$219$	3.41758	−	1.07405i	0.230939	−	0.0725776i
$220$	−5.18737	−	18.1186i	−0.349732	−	1.22156i
$221$	5.67363	−	13.6973i	0.381649	−	0.921383i
$222$	−5.41433	−	11.3847i	−0.363386	−	0.764094i
$223$			17.2016i			1.15191i	0.817483	+	0.575953i	$0.195369\pi$
$223$			17.2016i			1.15191i	−0.817483	+	0.575953i	$0.804631\pi$
$224$	−12.1378	+	8.75629i	−0.810994	+	0.585054i
$225$	−18.8628	−	3.36236i	−1.25752	−	0.224157i
$226$	−12.7488	+	7.50612i	−0.848041	+	0.499299i
$227$	7.07673	+	2.93128i	0.469699	+	0.194556i	0.604963	−	0.796254i	$-0.293188\pi$
$227$	7.07673	+	2.93128i	0.469699	+	0.194556i	−0.135263	+	0.990810i	$0.543188\pi$
$228$	−25.2634	+	4.87546i	−1.67311	+	0.322885i
$229$	10.1648	−	4.21040i	0.671709	−	0.278231i	−0.0206475	−	0.999787i	$-0.506573\pi$
$229$	10.1648	−	4.21040i	0.671709	−	0.278231i	0.692356	+	0.721556i	$0.256573\pi$
$230$	−0.835311	+	0.117220i	−0.0550788	+	0.00772927i
$231$	10.8894	+	6.72221i	0.716468	+	0.442289i
$232$	19.1726	+	7.37323i	1.25874	+	0.484076i
$233$	8.50611	−	8.50611i	0.557254	−	0.557254i	−0.371271	−	0.928525i	$-0.621078\pi$
$233$	8.50611	−	8.50611i	0.557254	−	0.557254i	0.928525	+	0.371271i	$0.121078\pi$
$234$	10.6727	+	11.4927i	0.697696	+	0.751304i
$235$	−28.4592	+	11.7882i	−1.85647	+	0.768977i
$236$	18.0650	+	2.06576i	1.17593	+	0.134470i
$237$	1.48533	−	2.84681i	0.0964828	−	0.184920i
$238$	14.9720	−	1.00860i	0.970491	−	0.0653775i
$239$	−26.6206			−1.72194			−0.860971	−	0.508653i	$-0.830143\pi$
$239$	−26.6206			−1.72194			−0.860971	+	0.508653i	$0.830143\pi$
$240$	20.8492	−	10.5771i	1.34581	−	0.682749i
$241$	−4.77107			−0.307331			−0.153666	−	0.988123i	$-0.549108\pi$
$241$	−4.77107			−0.307331			−0.153666	+	0.988123i	$0.549108\pi$
$242$	−1.13456	+	4.38329i	−0.0729321	+	0.281769i
$243$	11.5421	−	10.4776i	0.740423	−	0.672141i
$244$	−0.578943	−	0.728446i	−0.0370630	−	0.0466339i
$245$	−12.0838	+	20.2961i	−0.772006	+	1.29667i
$246$	3.24334	+	2.92701i	0.206788	+	0.186620i
$247$	−19.4155	−	19.4155i	−1.23538	−	1.23538i
$248$	8.67192	−	0.221732i	0.550667	−	0.0140800i
$249$	−7.08069	+	5.93015i	−0.448721	+	0.375808i
$250$	−6.55340	+	0.919647i	−0.414474	+	0.0581636i
$251$	7.29815	+	17.6193i	0.460655	+	1.11212i	0.968129	+	0.250452i	$0.0805794\pi$
$251$	7.29815	+	17.6193i	0.460655	+	1.11212i	−0.507474	+	0.861667i	$0.669421\pi$
$252$	−5.62804	+	14.8434i	−0.354533	+	0.935043i
$253$	−0.456023	−	0.188891i	−0.0286699	−	0.0118755i
$254$	−12.6697	+	7.45949i	−0.794965	+	0.468050i
$255$	−23.3490	−	2.06474i	−1.46217	−	0.129299i
$256$	−7.03757	+	14.3692i	−0.439848	+	0.898072i
$257$	−23.4325			−1.46168			−0.730841	−	0.682548i	$-0.760872\pi$
$257$	−23.4325			−1.46168			−0.730841	+	0.682548i	$0.760872\pi$
$258$	16.0568	−	7.63624i	0.999650	−	0.475412i
$259$	13.5813	+	0.981690i	0.843900	+	0.0609992i
$260$	21.8158	+	12.1044i	1.35296	+	0.750685i
$261$	21.2799	−	4.67595i	1.31719	−	0.289434i
$262$	−3.77032	+	0.529094i	−0.232931	+	0.0326875i
$263$	0.475707	+	0.475707i	0.0293334	+	0.0293334i	0.721621	−	0.692288i	$-0.243397\pi$
$263$	0.475707	+	0.475707i	0.0293334	+	0.0293334i	−0.692288	+	0.721621i	$0.743397\pi$
$264$	13.6539	+	0.856356i	0.840338	+	0.0527051i
$265$	32.6993	−	32.6993i	2.00870	−	2.00870i
$266$	8.88540	−	26.3324i	0.544799	−	1.61454i
$267$	−15.2981	+	4.80777i	−0.936227	+	0.294230i
$268$	−4.35029	+	3.45746i	−0.265736	+	0.211198i
$269$	2.44497	−	5.90269i	0.149073	−	0.359893i	−0.831649	−	0.555301i	$-0.812603\pi$
$269$	2.44497	−	5.90269i	0.149073	−	0.359893i	0.980722	+	0.195408i	$0.0626030\pi$
$270$	12.2754	−	21.5452i	0.747056	−	1.31120i
$271$	−7.63081			−0.463539			−0.231769	−	0.972771i	$-0.574451\pi$
$271$	−7.63081			−0.463539			−0.231769	+	0.972771i	$0.574451\pi$
$272$	13.6114	−	8.48979i	0.825312	−	0.514769i
$273$	−16.4855	+	3.90072i	−0.997749	+	0.236082i
$274$	−0.0368623	+	0.142415i	−0.00222693	+	0.00860362i
$275$	−16.4777	−	6.82527i	−0.993641	−	0.411579i
$276$	0.122878	−	0.599836i	0.00739641	−	0.0361059i
$277$	2.55346	−	1.05768i	0.153423	−	0.0635497i	−0.304651	−	0.952464i	$-0.598540\pi$
$277$	2.55346	−	1.05768i	0.153423	−	0.0635497i	0.458073	+	0.888914i	$0.348540\pi$
$278$	3.87107	+	2.91831i	0.232171	+	0.175029i
$279$	7.54683	−	5.26337i	0.451817	−	0.315110i
$280$	−1.17615	+	25.2244i	−0.0702885	+	1.50745i
$281$	−7.26490	−	7.26490i	−0.433388	−	0.433388i	0.456391	−	0.889779i	$-0.349142\pi$
$281$	−7.26490	−	7.26490i	−0.433388	−	0.433388i	−0.889779	+	0.456391i	$0.849142\pi$
$282$	−1.14482	−	22.3313i	−0.0681732	−	1.32981i
$283$	−28.3895	+	11.7593i	−1.68758	+	0.699019i	−0.999642	−	0.0267489i	$-0.991485\pi$
$283$	−28.3895	+	11.7593i	−1.68758	+	0.699019i	−0.687939	+	0.725768i	$0.741485\pi$
$284$	28.6220	−	8.19448i	1.69840	−	0.486253i
$285$	−20.0810	+	38.4874i	−1.18949	+	2.27980i
$286$	7.40725	+	12.5809i	0.438000	+	0.743926i
$287$	−4.47852	+	1.48683i	−0.264359	+	0.0877647i
$288$	2.16638	+	16.8317i	0.127655	+	0.991819i
$289$	0.915850			0.0538736
$290$	29.8658	−	17.5840i	1.75378	−	1.03257i
$291$	−0.111308	+	0.213334i	−0.00652498	+	0.0125058i
$292$	1.13856	+	3.97680i	0.0666291	+	0.232724i
$293$	0.0790494	+	0.190842i	0.00461812	+	0.0111491i	0.926172	−	0.377102i	$-0.123079\pi$
$293$	0.0790494	+	0.190842i	0.00461812	+	0.0111491i	−0.921554	+	0.388251i	$0.873079\pi$
$294$	−10.9448	−	13.1989i	−0.638313	−	0.769777i
$295$	21.6926	−	21.6926i	1.26299	−	1.26299i
$296$	13.3020	−	5.91262i	0.773165	−	0.343664i
$297$	12.5868	−	7.22006i	0.730360	−	0.418950i
$298$	−6.80837	−	5.13267i	−0.394398	−	0.297327i
$299$	0.603679	−	0.250052i	0.0349117	−	0.0144609i
$300$	4.44001	−	21.6741i	0.256344	−	1.25136i
$301$	−1.38455	+	19.1547i	−0.0798042	+	1.10406i
$302$	−27.2379	−	7.05017i	−1.56736	−	0.405692i
$303$	−0.372856	+	4.21642i	−0.0214200	+	0.242227i
$304$	−4.87946	−	29.3065i	−0.279856	−	1.68084i
$305$	−1.56993			−0.0898939
$306$	7.08814	−	15.4684i	0.405202	−	0.884272i
$307$	19.1503	+	7.93232i	1.09297	+	0.452721i	0.855040	−	0.518562i	$-0.173532\pi$
$307$	19.1503	+	7.93232i	1.09297	+	0.452721i	0.237926	+	0.971283i	$0.423532\pi$
$308$	−8.08216	+	12.3707i	−0.460524	+	0.704885i
$309$	−8.19478	−	26.0754i	−0.466185	−	1.48338i
$310$	8.81065	−	11.6871i	0.500411	−	0.663784i
$311$	−0.203016	−	0.203016i	−0.0115120	−	0.0115120i	0.701327	−	0.712839i	$-0.252591\pi$
$311$	−0.203016	−	0.203016i	−0.0115120	−	0.0115120i	−0.712839	+	0.701327i	$0.752591\pi$
$312$	−13.5825	+	11.9793i	−0.768956	+	0.678192i
$313$	7.96846	+	7.96846i	0.450404	+	0.450404i	0.895489	−	0.445085i	$-0.146826\pi$
$313$	7.96846	+	7.96846i	0.450404	+	0.450404i	−0.445085	+	0.895489i	$0.646826\pi$
$314$	−3.06518	−	21.8425i	−0.172978	−	1.23264i
$315$	13.6978	+	23.0159i	0.771783	+	1.29680i
$316$	3.24213	+	1.79888i	0.182384	+	0.101195i
$317$	−7.71066	+	18.6152i	−0.433074	+	1.04553i	0.545217	+	0.838295i	$0.316447\pi$
$317$	−7.71066	+	18.6152i	−0.433074	+	1.04553i	−0.978291	+	0.207238i	$0.933553\pi$
$318$	14.4170	+	30.3148i	0.808467	+	1.69997i
$319$	20.2810			1.13552
$320$	11.5917	+	24.3799i	0.647998	+	1.36288i
$321$	−1.39489	+	15.7740i	−0.0778552	+	0.880419i
$322$	0.498021	+	0.435157i	0.0277536	+	0.0242504i
$323$	−11.3994	+	27.5205i	−0.634277	+	1.53128i
$324$	11.7526	+	13.6336i	0.652924	+	0.757423i
$325$	21.8130	−	9.03523i	1.20997	−	0.501184i
$326$	−10.8705	+	1.52547i	−0.602060	+	0.0844878i
$327$	−14.3757	+	12.0398i	−0.794977	+	0.665801i
$328$	−3.47479	+	3.65715i	−0.191863	+	0.201932i
$329$	21.5893	+	10.8273i	1.19026	+	0.596929i
$330$	15.4646	−	17.1358i	0.851296	−	0.943296i
$331$	13.3120	−	5.51399i	0.731691	−	0.303076i	0.0144443	−	0.999896i	$-0.495402\pi$
$331$	13.3120	−	5.51399i	0.731691	−	0.303076i	0.717247	+	0.696819i	$0.245402\pi$
$332$	−6.63554	−	8.34906i	−0.364173	−	0.458214i
$333$	8.32016	−	13.0064i	0.455942	−	0.712745i
$334$	4.33762	−	16.7581i	0.237344	−	0.916964i
$335$			9.37565i			0.512247i
$336$	−16.9673	−	6.93627i	−0.925640	−	0.378405i
$337$		−	12.4035i		−	0.675664i	−0.941206	−	0.337832i	$-0.890306\pi$
$337$		−	12.4035i		−	0.675664i	0.941206	−	0.337832i	$-0.109694\pi$
$338$	−0.911932	−	0.236042i	−0.0496026	−	0.0128390i
$339$	−16.0643	−	8.38161i	−0.872492	−	0.455226i
$340$	3.07504	−	26.8910i	0.166768	−	1.45837i
$341$	7.91280	−	3.27759i	0.428502	−	0.177491i
$342$	−21.4434	−	23.0910i	−1.15953	−	1.24862i
$343$	18.2334	−	3.24692i	0.984512	−	0.175317i
$344$	8.33902	+	18.7609i	0.449610	+	1.01152i
$345$	−0.663304	−	0.791995i	−0.0357111	−	0.0426396i
$346$	2.77942	+	19.8061i	0.149423	+	1.06479i
$347$	8.50581	−	3.52322i	0.456616	−	0.189137i	−0.142507	−	0.989794i	$-0.545516\pi$
$347$	8.50581	−	3.52322i	0.456616	−	0.189137i	0.599123	+	0.800657i	$0.295516\pi$
$348$	4.76717	+	24.7023i	0.255547	+	1.32418i
$349$	9.86656	−	23.8200i	0.528145	−	1.27505i	−0.404592	−	0.914497i	$-0.632587\pi$
$349$	9.86656	−	23.8200i	0.528145	−	1.27505i	0.932737	−	0.360557i	$-0.117413\pi$
$350$	17.9952	+	15.7237i	0.961883	+	0.840467i
$351$	−5.02360	+	18.5404i	−0.268140	+	0.989615i
$352$	−1.39298	+	15.7356i	−0.0742461	+	0.838709i
$353$	34.6593			1.84473			0.922363	−	0.386323i	$-0.126255\pi$
$353$	34.6593			1.84473			0.922363	+	0.386323i	$0.126255\pi$
$354$	9.56421	+	20.1107i	0.508332	+	1.06887i
$355$	19.2228	−	46.4078i	1.02024	−	2.46307i
$356$	−5.09652	−	17.8013i	−0.270115	−	0.943467i
$357$	10.7538	+	14.9038i	0.569151	+	0.788793i
$358$	6.78481	−	0.952120i	0.358588	−	0.0503211i
$359$	−5.28967	−	5.28967i	−0.279178	−	0.279178i	0.553603	−	0.832781i	$-0.313253\pi$
$359$	−5.28967	−	5.28967i	−0.279178	−	0.279178i	−0.832781	+	0.553603i	$0.813253\pi$
$360$	24.5065	+	14.8080i	1.29161	+	0.780448i
$361$	25.5742	+	25.5742i	1.34601	+	1.34601i
$362$	6.46810	+	4.87614i	0.339956	+	0.256284i
$363$	−5.29023	+	1.66257i	−0.277665	+	0.0872625i
$364$	−4.01433	−	19.1451i	−0.210408	−	1.00348i
$365$	6.44800	+	2.67085i	0.337504	+	0.139799i
$366$	0.381633	−	1.07381i	0.0199483	−	0.0561289i
$367$	−21.9357			−1.14504			−0.572518	−	0.819892i	$-0.694033\pi$
$367$	−21.9357			−1.14504			−0.572518	+	0.819892i	$0.694033\pi$
$368$	0.688763	+	0.159610i	0.0359043	+	0.00832025i
$369$	−0.938979	+	5.26767i	−0.0488813	+	0.274224i
$370$	6.15435	−	23.7770i	0.319950	−	1.23611i
$371$	−36.1636	−	2.61400i	−1.87752	−	0.135712i
$372$	5.85206	+	8.86738i	0.303415	+	0.459752i
$373$	−25.9553	+	10.7510i	−1.34391	+	0.556667i	−0.934592	−	0.355723i	$-0.884235\pi$
$373$	−25.9553	+	10.7510i	−1.34391	+	0.556667i	−0.409322	+	0.912390i	$0.634235\pi$
$374$	9.53451	−	12.6473i	0.493018	−	0.653977i
$375$	−5.20392	−	6.21357i	−0.268729	−	0.320867i
$376$	25.8114	−	0.659969i	1.33112	−	0.0340353i
$377$	−18.9843	+	18.9843i	−0.977740	+	0.977740i
$378$	−19.0724	+	3.77416i	−0.980977	+	0.194122i
$379$	−2.83185	−	6.83668i	−0.145462	−	0.351177i	0.834309	−	0.551297i	$-0.185867\pi$
$379$	−2.83185	−	6.83668i	−0.145462	−	0.351177i	−0.979771	+	0.200120i	$0.935867\pi$
$380$	−43.8320	−	24.3200i	−2.24853	−	1.24759i
$381$	−15.9645	−	8.32955i	−0.817886	−	0.426736i
$382$	2.37258	+	4.02974i	0.121392	+	0.206180i
$383$	−17.4260			−0.890428			−0.445214	−	0.895424i	$-0.646872\pi$
$383$	−17.4260			−0.890428			−0.445214	+	0.895424i	$0.646872\pi$
$384$	−19.4934	+	2.00209i	−0.994767	+	0.102169i
$385$	7.85549	+	23.6618i	0.400353	+	1.20591i
$386$	−11.8132	+	6.95522i	−0.601275	+	0.354012i
$387$	18.3439	+	11.7346i	0.932472	+	0.596501i
$388$	−0.242958	−	0.134804i	−0.0123343	−	0.00684366i
$389$	−15.2114	+	6.30076i	−0.771248	+	0.319461i	−0.733378	−	0.679821i	$-0.762057\pi$
$389$	−15.2114	+	6.30076i	−0.771248	+	0.319461i	−0.0378702	+	0.999283i	$0.512057\pi$
$390$	1.56441	+	30.5160i	0.0792172	+	1.54524i
$391$	−0.501248	−	0.501248i	−0.0253492	−	0.0253492i
$392$	15.5600	−	12.2428i	0.785899	−	0.618355i
$393$	−2.99393	−	3.57480i	−0.151024	−	0.180325i
$394$	−22.7304	+	30.1514i	−1.14514	+	1.51901i
$395$	5.77956	−	2.39397i	0.290801	−	0.120454i
$396$	7.96140	+	14.7431i	0.400075	+	0.740868i
$397$	−2.12362	−	0.879631i	−0.106581	−	0.0441474i	0.328756	−	0.944415i	$-0.393371\pi$
$397$	−2.12362	−	0.879631i	−0.106581	−	0.0441474i	−0.435337	+	0.900268i	$0.643371\pi$
$398$	−21.1704	−	5.47968i	−1.06118	−	0.274671i
$399$	33.1224	−	7.83726i	1.65819	−	0.392354i
$400$	24.8874	+	5.76726i	1.24437	+	0.288363i
$401$	−23.0755			−1.15234			−0.576168	−	0.817331i	$-0.695453\pi$
$401$	−23.0755			−1.15234			−0.576168	+	0.817331i	$0.695453\pi$
$402$	−6.41282	−	2.27912i	−0.319842	−	0.113672i
$403$	−4.33884	+	10.4749i	−0.216133	+	0.521792i
$404$	−4.85605	−	0.555299i	−0.241598	−	0.0276272i
$405$	30.3456	−	1.21138i	1.50789	−	0.0601939i
$406$	−25.7475	−	8.68805i	−1.27783	−	0.431181i
$407$	10.1628	−	10.1628i	0.503749	−	0.503749i
$408$	17.6456	+	8.64021i	0.873586	+	0.427754i
$409$	19.2449	+	19.2449i	0.951597	+	0.951597i	0.998881	−	0.0472847i	$-0.0150568\pi$
$409$	19.2449	+	19.2449i	0.951597	+	0.951597i	−0.0472847	+	0.998881i	$0.515057\pi$
$410$	1.18283	+	8.42886i	0.0584160	+	0.416272i
$411$	−0.171882	+	0.0540178i	−0.00847832	+	0.00266450i
$412$	30.3421	−	8.68697i	1.49485	−	0.427976i
$413$	−23.9908	−	1.73412i	−1.18051	−	0.0853304i
$414$	0.702956	−	0.261165i	0.0345484	−	0.0128355i
$415$	−17.9937			−0.883276
$416$	−13.4256	−	16.0334i	−0.658242	−	0.786101i
$417$	−0.523000	+	5.91431i	−0.0256114	+	0.289625i
$418$	−14.8825	−	25.2774i	−0.727928	−	1.23636i
$419$	−4.29767	−	1.78015i	−0.209955	−	0.0869662i	0.275227	−	0.961379i	$-0.411247\pi$
$419$	−4.29767	−	1.78015i	−0.209955	−	0.0869662i	−0.485182	+	0.874413i	$0.661247\pi$
$420$	−26.9735	+	15.1298i	−1.31617	+	0.738260i
$421$	−7.90498	−	19.0843i	−0.385265	−	0.930112i	−0.990928	−	0.134391i	$-0.957092\pi$
$421$	−7.90498	−	19.0843i	−0.385265	−	0.930112i	0.605663	−	0.795721i	$-0.292908\pi$
$422$	−4.63710	−	33.0439i	−0.225730	−	1.60855i
$423$	22.4626	−	15.6661i	1.09217	−	0.761711i
$424$	−35.4200	+	15.7439i	−1.72015	+	0.764589i
$425$	−18.1118	−	18.1118i	−0.878551	−	0.878551i
$426$	27.0695	+	24.4294i	1.31152	+	1.18361i
$427$	0.805376	+	0.930877i	0.0389749	+	0.0450483i
$428$	−18.1669	−	2.07743i	−0.878132	−	0.100416i
$429$	−8.27121	+	15.8527i	−0.399338	+	0.765375i
$430$	33.5344	+	8.67995i	1.61717	+	0.418584i
$431$	14.9228			0.718808			0.359404	−	0.933182i	$-0.382980\pi$
$431$	14.9228			0.718808			0.359404	+	0.933182i	$0.382980\pi$
$432$	−16.0857	+	13.1624i	−0.773924	+	0.633278i
$433$	−31.1053			−1.49482			−0.747412	−	0.664361i	$-0.768704\pi$
$433$	−31.1053			−1.49482			−0.747412	+	0.664361i	$0.768704\pi$
$434$	−11.4497	+	0.771312i	−0.549602	+	0.0370242i
$435$	37.6326	+	19.6350i	1.80435	+	0.941425i
$436$	−13.4719	−	16.9508i	−0.645187	−	0.811796i
$437$	−1.21290	+	0.502400i	−0.0580209	+	0.0240331i
$438$	−3.39427	+	3.76109i	−0.162184	+	0.179712i
$439$	3.25920	−	3.25920i	0.155553	−	0.155553i	−0.625040	−	0.780593i	$-0.714917\pi$
$439$	3.25920	−	3.25920i	0.155553	−	0.155553i	0.780593	+	0.625040i	$0.214917\pi$
$440$	19.3221	+	18.3587i	0.921146	+	0.875215i
$441$	6.62014	−	19.9292i	0.315245	−	0.949010i
$442$	2.91377	+	20.7635i	0.138594	+	0.987621i
$443$	9.32226	−	3.86141i	0.442914	−	0.183461i	−0.150070	−	0.988675i	$-0.547950\pi$
$443$	9.32226	−	3.86141i	0.442914	−	0.183461i	0.592984	+	0.805214i	$0.297950\pi$
$444$	14.7671	+	9.98942i	0.700813	+	0.474077i
$445$	−28.8631	−	11.9555i	−1.36824	−	0.566745i
$446$	−12.3425	−	20.9632i	−0.584432	−	0.992636i
$447$	0.919843	−	10.4020i	0.0435071	−	0.491996i
$448$	8.50930	−	19.3802i	0.402027	−	0.915628i
$449$			5.63604i			0.265981i	0.991117	+	0.132990i	$0.0424580\pi$
$449$			5.63604i			0.265981i	−0.991117	+	0.132990i	$0.957542\pi$
$450$	25.4002	−	9.43677i	1.19738	−	0.444854i
$451$	−1.90604	+	4.60159i	−0.0897519	+	0.216680i
$452$	10.1509	−	18.2950i	0.477460	−	0.860526i
$453$	−10.3313	−	32.8736i	−0.485406	−	1.54454i
$454$	−10.7275	+	1.50540i	−0.503466	+	0.0706520i
$455$	−29.5021	−	14.7956i	−1.38308	−	0.693630i
$456$	27.2896	−	24.0685i	1.27795	−	1.12711i
$457$	24.1185	+	24.1185i	1.12822	+	1.12822i	0.990467	+	0.137751i	$0.0439874\pi$
$457$	24.1185	+	24.1185i	1.12822	+	1.12822i	0.137751	+	0.990467i	$0.456013\pi$
$458$	−9.36655	+	12.4245i	−0.437670	+	0.580560i
$459$	20.6685	−	2.66217i	0.964721	−	0.124260i
$460$	0.933865	−	0.742204i	0.0435417	−	0.0346054i
$461$	6.05240	−	14.6118i	0.281888	−	0.680538i	−0.717991	−	0.696052i	$-0.754938\pi$
$461$	6.05240	−	14.6118i	0.281888	−	0.680538i	0.999880	+	0.0155136i	$0.00493834\pi$
$462$	−18.0939	−	0.378877i	−0.841804	−	0.0176270i
$463$		−	29.0495i		−	1.35005i	−0.737797	−	0.675023i	$-0.764134\pi$
$463$		−	29.0495i		−	1.35005i	0.737797	−	0.675023i	$-0.235866\pi$
$464$	−28.6556	+	4.77108i	−1.33030	+	0.221492i
$465$	17.8559	+	1.57899i	0.828045	+	0.0732238i
$466$	−4.26290	+	16.4695i	−0.197475	+	0.762933i
$467$	−1.37255	+	3.31363i	−0.0635141	+	0.153337i	−0.952450	−	0.304695i	$-0.901445\pi$
$467$	−1.37255	+	3.31363i	−0.0635141	+	0.153337i	0.888936	+	0.458032i	$0.151445\pi$
$468$	−21.2528	−	6.34807i	−0.982410	−	0.293440i
$469$	5.55922	−	4.80973i	0.256701	−	0.222093i
$470$	26.2243	−	34.7859i	1.20964	−	1.60456i
$471$	20.7098	−	17.3447i	0.954258	−	0.799200i
$472$	−23.4975	+	10.4444i	−1.08156	+	0.480743i
$473$	14.3333	+	14.3333i	0.659046	+	0.659046i
$474$	0.232493	+	4.53509i	0.0106788	+	0.208303i
$475$	−43.8262	+	18.1534i	−2.01089	+	0.832936i
$476$	−17.5223	+	11.9718i	−0.803134	+	0.548727i
$477$	−22.1545	+	34.6328i	−1.01439	+	1.58573i
$478$	32.4419	−	19.1007i	1.48386	−	0.873647i
$479$	10.5484			0.481971			0.240985	−	0.970529i	$-0.422529\pi$
$479$	10.5484			0.481971			0.240985	+	0.970529i	$0.422529\pi$
$480$	−17.8191	+	27.8497i	−0.813327	+	1.27116i
$481$			19.0259i			0.867507i
$482$	5.81438	−	3.42332i	0.264838	−	0.155928i
$483$	−0.129331	+	0.799596i	−0.00588478	+	0.0363829i
$484$	−1.76243	−	6.15587i	−0.0801105	−	0.279812i
$485$	−0.433108	+	0.179399i	−0.0196664	+	0.00814609i
$486$	−6.54814	+	21.0505i	−0.297030	+	0.954868i
$487$	6.94506	−	6.94506i	0.314711	−	0.314711i	−0.532021	−	0.846731i	$-0.678567\pi$
$487$	6.94506	−	6.94506i	0.314711	−	0.314711i	0.846731	+	0.532021i	$0.178567\pi$
$488$	1.22822	+	0.472337i	0.0555987	+	0.0213817i
$489$	−8.63202	−	10.3068i	−0.390353	−	0.466088i
$490$	0.163458	−	33.4047i	0.00738428	−	1.50907i
$491$	−10.8321	−	26.1509i	−0.488844	−	1.18017i	−0.955302	−	0.295631i	$-0.904470\pi$
$491$	−10.8321	−	26.1509i	−0.488844	−	1.18017i	0.466458	−	0.884543i	$-0.345530\pi$
$492$	−6.05276	−	1.23993i	−0.272880	−	0.0559002i
$493$	26.9092	+	11.1462i	1.21193	+	0.501998i
$494$	37.5921	+	9.73023i	1.69135	+	0.437784i
$495$	27.8311	+	4.96099i	1.25092	+	0.222980i
$496$	−10.4092	+	6.49247i	−0.467385	+	0.291521i
$497$	−37.3785	+	12.4093i	−1.67665	+	0.556634i
$498$	4.37408	−	12.3074i	0.196007	−	0.551510i
$499$	11.2787	−	27.2291i	0.504903	−	1.21894i	−0.441881	−	0.897074i	$-0.645689\pi$
$499$	11.2787	−	27.2291i	0.504903	−	1.21894i	0.946784	−	0.321870i	$-0.104311\pi$
$500$	7.32661	−	5.82293i	0.327656	−	0.260409i
$501$	20.2255	−	6.35632i	0.903609	−	0.283980i
$502$	−21.5362	−	16.2356i	−0.961208	−	0.724632i
$503$	17.7934	+	17.7934i	0.793367	+	0.793367i	0.982040	−	0.188673i	$-0.0604187\pi$
$503$	17.7934	+	17.7934i	0.793367	+	0.793367i	−0.188673	+	0.982040i	$0.560419\pi$
$504$	−3.79161	−	22.1274i	−0.168892	−	0.985635i
$505$	−5.83121	+	5.83121i	−0.259485	+	0.259485i
$506$	0.691277	−	0.0970077i	0.0307310	−	0.00431252i
$507$	−0.345894	−	1.10062i	−0.0153617	−	0.0488802i
$508$	10.0879	−	18.1814i	0.447578	−	0.806669i
$509$	26.7840	+	11.0943i	1.18718	+	0.491746i	0.886836	−	0.462085i	$-0.152898\pi$
$509$	26.7840	+	11.0943i	1.18718	+	0.491746i	0.300344	+	0.953831i	$0.402898\pi$
$510$	29.9363	−	14.2370i	1.32560	−	0.630426i
$511$	−1.72418	−	5.19345i	−0.0762731	−	0.229744i
$512$	−1.73360	−	22.5609i	−0.0766149	−	0.997061i
$513$	10.0933	−	37.2511i	0.445632	−	1.64468i
$514$	28.5567	−	16.8133i	1.25958	−	0.741601i
$515$	20.3780	−	49.1969i	0.897963	−	2.16787i
$516$	−14.0888	+	20.8271i	−0.620227	+	0.916862i
$517$	23.5519	−	9.75553i	1.03581	−	0.429048i
$518$	−17.2556	+	8.54845i	−0.758166	+	0.375597i
$519$	−18.7791	+	15.7277i	−0.824310	+	0.690368i
$520$	−35.2715	+	0.901855i	−1.54676	+	0.0395490i
$521$	3.80906	+	3.80906i	0.166878	+	0.166878i	0.785606	−	0.618728i	$-0.212352\pi$
$521$	3.80906	+	3.80906i	0.166878	+	0.166878i	−0.618728	+	0.785606i	$0.712352\pi$
$522$	−22.5782	+	20.9671i	−0.988219	+	0.917706i
$523$	7.34247	+	17.7263i	0.321064	+	0.775117i	0.999193	+	0.0401737i	$0.0127911\pi$
$523$	7.34247	+	17.7263i	0.321064	+	0.775117i	−0.678129	+	0.734943i	$0.737209\pi$
$524$	4.21516	−	3.35006i	0.184140	−	0.146348i
$525$	−4.67318	+	28.8921i	−0.203954	+	1.26096i
$526$	−0.921061	−	0.238405i	−0.0401602	−	0.0103949i
$527$	12.3002			0.535804
$528$	−17.2541	+	8.75327i	−0.750888	+	0.380937i
$529$			22.9688i			0.998642i
$530$	−16.3875	+	63.3122i	−0.711829	+	2.75011i
$531$	−14.6973	+	22.9753i	−0.637807	+	0.997042i
$532$	8.06551	+	38.4660i	0.349684	+	1.66771i
$533$	−2.52320	−	6.09154i	−0.109292	−	0.263854i
$534$	15.1937	−	16.8357i	0.657497	−	0.728554i
$535$	−21.8151	+	21.8151i	−0.943149	+	0.943149i
$536$	2.82081	−	7.33493i	0.121840	−	0.316821i
$537$	5.38768	+	6.43297i	0.232495	+	0.277603i
$538$	1.25565	+	8.94777i	0.0541350	+	0.385766i
$539$	10.0002	−	16.7964i	0.430738	−	0.723471i
$540$	0.499385	+	35.0645i	0.0214901	+	1.50893i
$541$	−30.5458	−	12.6525i	−1.31327	−	0.543973i	−0.387432	−	0.921898i	$-0.626638\pi$
$541$	−30.5458	−	12.6525i	−1.31327	−	0.543973i	−0.925836	+	0.377925i	$0.876638\pi$
$542$	9.29948	−	5.47524i	0.399447	−	0.235182i
$543$	−0.873871	+	9.88210i	−0.0375014	+	0.424082i
$544$	−10.4963	+	20.1127i	−0.450025	+	0.862325i
$545$	−36.5320			−1.56486
$546$	17.2917	−	16.5823i	0.740014	−	0.709659i
$547$	−22.0585	−	9.13694i	−0.943155	−	0.390667i	−0.142501	−	0.989795i	$-0.545514\pi$
$547$	−22.0585	−	9.13694i	−0.943155	−	0.390667i	−0.800654	+	0.599127i	$0.795514\pi$
$548$	−0.0572622	−	0.200007i	−0.00244612	−	0.00854389i
$549$	1.36321	−	0.299546i	0.0581804	−	0.0127843i
$550$	24.9782	−	3.50522i	1.06507	−	0.149463i
$551$	38.1429	−	38.1429i	1.62494	−	1.62494i
$552$	0.280644	+	0.819173i	0.0119450	+	0.0348663i
$553$	−4.38441	−	2.19883i	−0.186444	−	0.0935038i
$554$	−2.35294	+	3.12112i	−0.0999667	+	0.132604i
$555$	28.6966	−	9.01855i	1.21810	−	0.382816i
$556$	−6.81152	−	0.778911i	−0.288873	−	0.0330332i
$557$	−7.08405	−	2.93431i	−0.300161	−	0.124331i	0.227520	−	0.973773i	$-0.426938\pi$
$557$	−7.08405	−	2.93431i	−0.300161	−	0.124331i	−0.527681	+	0.849443i	$0.676938\pi$
$558$	−5.42058	+	11.8293i	−0.229471	+	0.500775i
$559$	−26.8337			−1.13494
$560$	−16.6656	−	31.5843i	−0.704251	−	1.33468i
$561$	19.3228	+	1.70871i	0.815811	+	0.0721419i
$562$	14.0662	+	3.64086i	0.593349	+	0.153581i
$563$	2.89294	−	6.98417i	0.121923	−	0.294348i	−0.851120	−	0.524970i	$-0.824076\pi$
$563$	2.89294	−	6.98417i	0.121923	−	0.294348i	0.973043	+	0.230623i	$0.0740764\pi$
$564$	17.4183	+	26.3932i	0.733441	+	1.11135i
$565$	−13.5090	−	32.6135i	−0.568326	−	1.37206i
$566$	26.1601	−	34.7008i	1.09959	−	1.45858i
$567$	−16.2856	−	17.3718i	−0.683932	−	0.729545i
$568$	−29.0012	+	30.5232i	−1.21686	+	1.28072i
$569$	3.50091	+	3.50091i	0.146766	+	0.146766i	0.776672	−	0.629906i	$-0.216906\pi$
$569$	3.50091	+	3.50091i	0.146766	+	0.146766i	−0.629906	+	0.776672i	$0.716906\pi$
$570$	−3.14319	−	61.3121i	−0.131654	−	2.56808i
$571$	−5.60391	−	13.5290i	−0.234516	−	0.566172i	0.762182	−	0.647362i	$-0.224128\pi$
$571$	−5.60391	−	13.5290i	−0.234516	−	0.566172i	−0.996699	+	0.0811901i	$0.974128\pi$
$572$	−18.0541	−	10.0172i	−0.754878	−	0.418842i
$573$	−2.64932	+	5.07771i	−0.110677	+	0.212124i
$574$	4.39103	−	5.02537i	0.183278	−	0.209755i
$575$		−	1.12888i		−	0.0470774i
$576$	−14.7172	−	18.9580i	−0.613215	−	0.789916i
$577$		−	37.6177i		−	1.56605i	−0.621992	−	0.783023i	$-0.713677\pi$
$577$		−	37.6177i		−	1.56605i	0.621992	−	0.783023i	$-0.286323\pi$
$578$	−1.11612	+	0.657138i	−0.0464246	+	0.0273334i
$579$	−14.8853	−	7.76646i	−0.618611	−	0.322763i
$580$	−23.7799	+	42.8584i	−0.987405	+	1.77960i
$581$	9.23080	+	10.6692i	0.382958	+	0.442634i
$582$	−0.0174225	−	0.339850i	−0.000722188	−	0.0140872i
$583$	−27.0609	+	27.0609i	−1.12075	+	1.12075i
$584$	−4.24095	−	4.02949i	−0.175492	−	0.166741i
$585$	−30.6954	+	21.4079i	−1.26910	+	0.885106i
$586$	−0.233268	−	0.175855i	−0.00963621	−	0.00726451i
$587$	11.1425	−	4.61537i	0.459899	−	0.190497i	−0.140691	−	0.990054i	$-0.544932\pi$
$587$	11.1425	−	4.61537i	0.459899	−	0.190497i	0.600590	+	0.799557i	$0.294932\pi$
$588$	22.8086	+	8.23213i	0.940611	+	0.339487i
$589$	8.71753	−	21.0460i	0.359199	−	0.867184i
$590$	−10.8714	+	42.0011i	−0.447570	+	1.72916i
$591$	−46.0660	−	4.07360i	−1.89490	−	0.167565i
$592$	−11.9684	+	16.7500i	−0.491900	+	0.688421i
$593$		−	20.4535i		−	0.839924i	−0.907542	−	0.419962i	$-0.862043\pi$
$593$		−	20.4535i		−	0.839924i	0.907542	−	0.419962i	$-0.137957\pi$
$594$	−10.1587	+	17.8302i	−0.416817	+	0.731580i
$595$	−2.58136	+	35.7121i	−0.105826	+	1.46405i
$596$	11.9800	+	1.36993i	0.490718	+	0.0561146i
$597$	−8.02989	−	25.5507i	−0.328642	−	1.04572i
$598$	−0.556272	+	0.737882i	−0.0227477	+	0.0301743i
$599$	−26.4205	+	26.4205i	−1.07951	+	1.07951i	−0.0829580	+	0.996553i	$0.526437\pi$
$599$	−26.4205	+	26.4205i	−1.07951	+	1.07951i	−0.996553	+	0.0829580i	$0.973563\pi$
$600$	10.1406	+	29.5995i	0.413989	+	1.20839i
$601$	27.2402	+	27.2402i	1.11115	+	1.11115i	0.992995	+	0.118154i	$0.0376975\pi$
$601$	27.2402	+	27.2402i	1.11115	+	1.11115i	0.118154	+	0.992995i	$0.462302\pi$
$602$	−12.0565	−	24.3368i	−0.491387	−	0.991895i
$603$	−1.78890	−	8.14112i	−0.0728496	−	0.331532i
$604$	38.2527	−	10.9518i	1.55648	−	0.445622i
$605$	−9.98117	−	4.13434i	−0.405792	−	0.168085i
$606$	−2.57096	−	5.40598i	−0.104438	−	0.219603i
$607$		−	23.9677i		−	0.972820i	−0.873731	−	0.486410i	$-0.838306\pi$
$607$		−	23.9677i		−	0.972820i	0.873731	−	0.486410i	$-0.161694\pi$
$608$	26.9744	+	32.2140i	1.09396	+	1.30645i
$609$	−7.66319	−	32.3867i	−0.310528	−	1.31238i
$610$	1.91323	−	1.12645i	0.0774646	−	0.0456087i
$611$	−12.9143	+	31.1778i	−0.522456	+	1.26132i
$612$	2.46074	+	23.9369i	0.0994694	+	0.967591i
$613$	−10.8240	−	26.1316i	−0.437179	−	1.05544i	−0.976919	−	0.213612i	$-0.931477\pi$
$613$	−10.8240	−	26.1316i	−0.437179	−	1.05544i	0.539740	−	0.841832i	$-0.318523\pi$
$614$	−29.0296	+	4.07376i	−1.17154	+	0.164403i
$615$	−7.99177	+	6.69319i	−0.322259	+	0.269895i
$616$	0.973344	−	20.8749i	0.0392172	−	0.841075i
$617$	−2.39178	+	2.39178i	−0.0962896	+	0.0962896i	−0.753611	−	0.657321i	$-0.771690\pi$
$617$	−2.39178	+	2.39178i	−0.0962896	+	0.0962896i	0.657321	+	0.753611i	$0.271690\pi$
$618$	28.6963	+	25.8975i	1.15434	+	1.04175i
$619$	−12.0605	−	29.1165i	−0.484751	−	1.17029i	−0.957328	−	0.289003i	$-0.906676\pi$
$619$	−12.0605	−	29.1165i	−0.484751	−	1.17029i	0.472578	−	0.881289i	$-0.343324\pi$
$620$	−2.35160	+	20.5646i	−0.0944427	+	0.825894i
$621$	0.727078	+	0.561150i	0.0291766	+	0.0225182i
$622$	0.393078	+	0.101743i	0.0157610	+	0.00407953i
$623$	7.71792	+	23.2474i	0.309212	+	0.931386i
$624$	7.95729	−	24.3445i	0.318546	−	0.974559i
$625$			16.1434i			0.645738i
$626$	−15.4285	−	3.99346i	−0.616646	−	0.159611i
$627$	16.6184	−	31.8509i	0.663674	−	1.27200i
$628$	19.4078	+	24.4196i	0.774456	+	0.974447i
$629$	19.0694	−	7.89882i	0.760348	−	0.314947i
$630$	−33.2075	−	18.2206i	−1.32302	−	0.725925i
$631$	8.53097	+	8.53097i	0.339613	+	0.339613i	0.856221	−	0.516609i	$-0.172806\pi$
$631$	8.53097	+	8.53097i	0.339613	+	0.339613i	−0.516609	+	0.856221i	$0.672806\pi$
$632$	−5.24183	+	0.134028i	−0.208509	+	0.00533135i
$633$	31.3304	−	26.2395i	1.24527	−	1.04293i
$634$	−3.95992	−	28.2184i	−0.157269	−	1.12070i
$635$	−13.4250	−	32.4109i	−0.532757	−	1.28619i
$636$	−39.3210	−	26.5994i	−1.55918	−	1.05473i
$637$	6.36166	+	25.0832i	0.252058	+	0.993833i
$638$	−24.7160	+	14.5520i	−0.978514	+	0.576118i
$639$	−7.83687	+	43.9648i	−0.310022	+	1.73922i
$640$	−31.6196	−	21.3939i	−1.24987	−	0.845670i
$641$		−	6.52247i		−	0.257622i	−0.991669	−	0.128811i	$-0.958884\pi$
$641$		−	6.52247i		−	0.257622i	0.991669	−	0.128811i	$-0.0411161\pi$
$642$	−9.61821	−	20.2243i	−0.379600	−	0.798188i
$643$	−8.81032	+	21.2700i	−0.347445	+	0.838807i	0.649475	+	0.760383i	$0.274989\pi$
$643$	−8.81032	+	21.2700i	−0.347445	+	0.838807i	−0.996920	+	0.0784237i	$0.975011\pi$
$644$	−0.919159	−	0.172976i	−0.0362199	−	0.00681623i
$645$	12.7196	+	40.4730i	0.500832	+	1.59362i
$646$	−5.85430	−	41.7177i	−0.230334	−	1.64136i
$647$	−5.98654	+	5.98654i	−0.235355	+	0.235355i	−0.814924	−	0.579568i	$-0.803221\pi$
$647$	−5.98654	+	5.98654i	−0.235355	+	0.235355i	0.579568	+	0.814924i	$0.303221\pi$
$648$	−24.1050	−	8.18223i	−0.946934	−	0.321428i
$649$	−17.9521	+	17.9521i	−0.704682	+	0.704682i
$650$	−20.1000	+	26.6622i	−0.788387	+	1.04578i
$651$	−8.22384	−	11.3975i	−0.322318	−	0.446704i
$652$	12.1530	−	9.65880i	0.475949	−	0.378268i
$653$	5.39949	+	2.23654i	0.211298	+	0.0875227i	0.485822	−	0.874058i	$-0.338520\pi$
$653$	5.39949	+	2.23654i	0.211298	+	0.0875227i	−0.274524	+	0.961580i	$0.588520\pi$
$654$	8.88054	−	24.9874i	0.347257	−	0.977083i
$655$		−	9.08441i		−	0.354957i
$656$	1.61058	−	6.95010i	0.0628824	−	0.271356i
$657$	−6.10857	−	1.08887i	−0.238318	−	0.0424810i
$658$	−34.0792	+	2.29576i	−1.32854	+	0.0894980i
$659$	−1.59797	−	0.661902i	−0.0622482	−	0.0257840i	0.351342	−	0.936247i	$-0.385725\pi$
$659$	−1.59797	−	0.661902i	−0.0622482	−	0.0257840i	−0.413590	+	0.910463i	$0.635725\pi$
$660$	−6.55102	+	31.9791i	−0.254998	+	1.24478i
$661$	−2.39080	−	5.77190i	−0.0929913	−	0.224501i	0.870539	−	0.492099i	$-0.163770\pi$
$661$	−2.39080	−	5.77190i	−0.0929913	−	0.224501i	−0.963531	+	0.267598i	$0.913770\pi$
$662$	−12.2666	+	16.2713i	−0.476753	+	0.632403i
$663$	−19.6868	+	16.4879i	−0.764573	+	0.640337i
$664$	14.0772	+	5.41368i	0.546300	+	0.210091i
$665$	59.2750	+	29.7271i	2.29859	+	1.15277i
$666$	−0.807279	+	21.8204i	−0.0312814	+	0.845523i
$667$	0.491242	+	1.18596i	0.0190210	+	0.0459206i
$668$	6.73809	+	23.5350i	0.260705	+	0.910597i
$669$	13.7820	−	26.4148i	0.532845	−	1.02126i
$670$	−6.72719	−	11.4259i	−0.259894	−	0.441420i
$671$	1.29922			0.0501559
$672$	25.6545	−	3.72124i	0.989643	−	0.143550i
$673$	27.6222			1.06476			0.532378	−	0.846506i	$-0.321298\pi$
$673$	27.6222			1.06476			0.532378	+	0.846506i	$0.321298\pi$
$674$	8.89976	+	15.1159i	0.342806	+	0.582243i
$675$	26.2718	+	20.2762i	1.01120	+	0.780433i
$676$	1.28071	−	0.366669i	0.0492582	−	0.0141027i
$677$	−1.97941	−	4.77873i	−0.0760751	−	0.183661i	0.881267	−	0.472619i	$-0.156691\pi$
$677$	−1.97941	−	4.77873i	−0.0760751	−	0.183661i	−0.957342	+	0.288958i	$0.906691\pi$
$678$	25.5911	−	1.31194i	0.982820	−	0.0503847i
$679$	0.328558	+	0.164776i	0.0126089	+	0.00632351i
$680$	15.5473	+	34.9778i	0.596211	+	1.34134i
$681$	−8.51847	−	10.1712i	−0.326429	−	0.389761i
$682$	−7.29141	+	9.67189i	−0.279202	+	0.370356i
$683$	13.4634	+	32.5035i	0.515163	+	1.24371i	0.940844	+	0.338840i	$0.110035\pi$
$683$	13.4634	+	32.5035i	0.515163	+	1.24371i	−0.425681	+	0.904873i	$0.639965\pi$
$684$	42.7007	+	12.7544i	1.63270	+	0.487678i
$685$	−0.324293	−	0.134327i	−0.0123906	−	0.00513235i
$686$	−19.8909	+	17.0397i	−0.759438	+	0.650580i
$687$	−18.9825	−	1.67861i	−0.724226	−	0.0640430i
$688$	−23.6238	−	16.8800i	−0.900649	−	0.643544i
$689$		−	50.6613i		−	1.93004i
$690$	1.37662	+	0.489253i	0.0524071	+	0.0186255i
$691$	−35.1989	−	14.5799i	−1.33903	−	0.554644i	−0.405812	−	0.913957i	$-0.633011\pi$
$691$	−35.1989	−	14.5799i	−1.33903	−	0.554644i	−0.933217	+	0.359313i	$0.883011\pi$
$692$	−17.5985	−	22.1430i	−0.668993	−	0.841750i
$693$	−11.3358	−	19.0473i	−0.430613	−	0.723545i
$694$	−7.83785	+	10.3967i	−0.297521	+	0.394655i
$695$	−8.17936	+	8.17936i	−0.310261	+	0.310261i
$696$	−23.5340	−	26.6835i	−0.892052	−	1.01144i
$697$	−5.05794	+	5.05794i	−0.191583	+	0.191583i
$698$	5.06711	+	36.1082i	0.191793	+	1.36672i
$699$	−19.8771	+	6.24683i	−0.751822	+	0.236277i
$700$	−33.2123	−	6.25023i	−1.25531	−	0.236236i
$701$	−5.47144	+	13.2092i	−0.206653	+	0.498905i	−0.992892	−	0.119017i	$-0.962026\pi$
$701$	−5.47144	+	13.2092i	−0.206653	+	0.498905i	0.786239	+	0.617923i	$0.212026\pi$
$702$	−7.18094	−	26.1993i	−0.271027	−	0.988828i
$703$		−	38.2265i		−	1.44174i
$704$	−9.59296	−	20.1760i	−0.361548	−	0.760413i
$705$	53.1467	+	4.69975i	2.00162	+	0.177003i
$706$	−42.2384	+	24.8686i	−1.58966	+	0.935943i
$707$	6.44899	+	0.466149i	0.242539	+	0.0175314i
$708$	−26.0854	−	17.6459i	−0.980351	−	0.663175i
$709$	−3.00659	−	7.25855i	−0.112915	−	0.272600i	0.857313	−	0.514796i	$-0.172132\pi$
$709$	−3.00659	−	7.25855i	−0.112915	−	0.272600i	−0.970227	+	0.242196i	$0.922132\pi$
$710$	9.87212	+	70.3487i	0.370494	+	2.64014i
$711$	−4.56176	+	3.18150i	−0.171079	+	0.119316i
$712$	18.9837	+	18.0372i	0.711446	+	0.675971i
$713$	0.383324	+	0.383324i	0.0143556	+	0.0143556i
$714$	−23.7991	−	10.4469i	−0.890659	−	0.390964i
$715$	−32.1840	+	13.3310i	−1.20361	+	0.498552i
$716$	−7.58531	+	6.02854i	−0.283476	+	0.225297i
$717$	40.8786	+	21.3286i	1.52664	+	0.796531i
$718$	10.2418	+	2.65096i	0.382221	+	0.0989330i
$719$		−	6.46068i		−	0.240943i	−0.992717	−	0.120471i	$-0.961559\pi$
$719$		−	6.46068i		−	0.240943i	0.992717	−	0.120471i	$-0.0384406\pi$
$720$	−40.4904	−	0.462270i	−1.50899	−	0.0172278i
$721$	−39.6249	+	13.1551i	−1.47571	+	0.489922i
$722$	−49.5166	−	12.8167i	−1.84282	−	0.476989i
$723$	7.32645	+	3.82261i	0.272474	+	0.142164i
$724$	−11.3812	−	1.30147i	−0.422980	−	0.0483686i
$725$	17.7502	+	42.8529i	0.659227	+	1.59152i
$726$	5.25415	−	5.82197i	0.195000	−	0.216074i
$727$	−4.03399	+	4.03399i	−0.149612	+	0.149612i	−0.777945	−	0.628332i	$-0.783738\pi$
$727$	−4.03399	+	4.03399i	−0.149612	+	0.149612i	0.628332	+	0.777945i	$0.283738\pi$
$728$	18.6291	+	20.4513i	0.690441	+	0.757977i
$729$	−26.1187	+	6.84189i	−0.967361	+	0.253403i
$730$	−9.77440	+	1.37165i	−0.361767	+	0.0507672i
$731$	11.1403	+	26.8951i	0.412039	+	0.994750i
$732$	0.305390	+	1.58245i	0.0112875	+	0.0584892i
$733$	−13.7845	+	33.2786i	−0.509141	+	1.22917i	0.435238	+	0.900315i	$0.356664\pi$
$733$	−13.7845	+	33.2786i	−0.509141	+	1.22917i	−0.944379	+	0.328859i	$0.893336\pi$
$734$	26.7325	−	15.7393i	0.986716	−	0.580947i
$735$	34.8172	−	21.4850i	1.28425	−	0.792487i
$736$	−0.953902	+	0.299687i	−0.0351613	+	0.0110466i
$737$		−	7.75899i		−	0.285806i
$738$	−2.63533	−	7.09331i	−0.0970079	−	0.261108i
$739$	−30.8458	−	12.7767i	−1.13468	−	0.470000i	−0.265311	−	0.964163i	$-0.585475\pi$
$739$	−30.8458	−	12.7767i	−1.13468	−	0.470000i	−0.869369	+	0.494163i	$0.835475\pi$
$740$	9.56022	+	33.3922i	0.351441	+	1.22752i
$741$	14.2586	+	45.3703i	0.523804	+	1.66672i
$742$	45.9473	−	22.7624i	1.68678	−	0.835635i
$743$	−19.8887	−	19.8887i	−0.729644	−	0.729644i	0.240904	−	0.970549i	$-0.422556\pi$
$743$	−19.8887	−	19.8887i	−0.729644	−	0.729644i	−0.970549	+	0.240904i	$0.922556\pi$
$744$	−13.4943	−	6.60751i	−0.494723	−	0.242243i
$745$	14.3857	−	14.3857i	0.527051	−	0.527051i
$746$	23.9170	−	31.7254i	0.875664	−	1.16155i
$747$	15.6244	−	3.43324i	0.571666	−	0.125616i
$748$	−2.54481	+	22.2541i	−0.0930473	+	0.813692i
$749$	24.1263	+	1.74391i	0.881555	+	0.0637210i
$750$	10.8002	+	3.83842i	0.394369	+	0.140159i
$751$			15.1060i			0.551227i	0.961269	+	0.275613i	$0.0888809\pi$
$751$			15.1060i			0.551227i	−0.961269	+	0.275613i	$0.911119\pi$
$752$	−30.9822	+	19.3244i	−1.12980	+	0.704688i
$753$	2.90965	−	32.9035i	0.106033	−	1.19907i
$754$	9.51412	−	36.7572i	0.346484	−	1.33862i
$755$	25.6909	−	62.0232i	0.934986	−	2.25726i
$756$	20.5350	−	18.2842i	0.746851	−	0.664991i
$757$	−35.0877	+	14.5338i	−1.27529	+	0.528240i	−0.914567	−	0.404434i	$-0.867468\pi$
$757$	−35.0877	+	14.5338i	−1.27529	+	0.528240i	−0.360718	+	0.932675i	$0.617468\pi$
$758$	8.35653	+	6.29979i	0.303523	+	0.228819i
$759$	0.548929	+	0.655430i	0.0199248	+	0.0237906i
$760$	70.8669	−	1.81199i	2.57061	−	0.0657278i
$761$	−20.4410	+	20.4410i	−0.740986	+	0.740986i	−0.972768	−	0.231782i	$-0.925544\pi$
$761$	−20.4410	+	20.4410i	−0.740986	+	0.740986i	0.231782	+	0.972768i	$0.425544\pi$
$762$	25.4321	−	1.30379i	0.921309	−	0.0472313i
$763$	18.7410	+	21.6613i	0.678468	+	0.784193i
$764$	−5.78282	−	3.20858i	−0.209215	−	0.116082i
$765$	34.2004	+	21.8779i	1.23652	+	0.790999i
$766$	21.2367	−	12.5035i	0.767312	−	0.451769i
$767$		−	33.6086i		−	1.21354i
$768$	22.3196	−	16.4267i	0.805388	−	0.592748i
$769$		−	10.2645i		−	0.370147i	−0.982725	−	0.185074i	$-0.940748\pi$
$769$		−	10.2645i		−	0.370147i	0.982725	−	0.185074i	$-0.0592524\pi$
$770$	−26.5510	−	23.1995i	−0.956832	−	0.836053i
$771$	35.9830	+	18.7743i	1.29590	+	0.676140i
$772$	9.40593	−	16.9523i	0.338527	−	0.610127i
$773$	0.309945	+	0.748273i	0.0111479	+	0.0269135i	0.929355	−	0.369186i	$-0.120363\pi$
$773$	0.309945	+	0.748273i	0.0111479	+	0.0269135i	−0.918208	+	0.396100i	$0.870363\pi$
$774$	−30.7750	−	1.13857i	−1.10618	−	0.0409249i
$775$	13.8508	+	13.8508i	0.497535	+	0.497535i
$776$	0.392812	−	0.0100438i	0.0141011	−	0.000360550i
$777$	−20.0689	−	12.3889i	−0.719968	−	0.444449i
$778$	14.0168	−	18.5930i	0.502528	−	0.666592i
$779$	5.06956	+	12.2390i	0.181636	+	0.438508i
$780$	−23.8022	−	36.0665i	−0.852257	−	1.29139i
$781$	−15.9081	+	38.4056i	−0.569238	+	1.37426i
$782$	0.970513	+	0.251205i	0.0347055	+	0.00898305i
$783$	−36.4238	−	9.86916i	−1.30168	−	0.352695i
$784$	−10.1782	+	26.0846i	−0.363506	+	0.931592i
$785$	52.6285			1.87839
$786$	6.21362	+	2.20833i	0.221632	+	0.0787684i
$787$	−16.1743	−	6.69961i	−0.576551	−	0.238815i	0.0753017	−	0.997161i	$-0.476008\pi$
$787$	−16.1743	−	6.69961i	−0.576551	−	0.238815i	−0.651853	+	0.758346i	$0.726008\pi$
$788$	6.06686	−	53.0542i	0.216123	−	1.88998i
$789$	−0.349357	−	1.11164i	−0.0124374	−	0.0395753i
$790$	−5.32569	+	7.06440i	−0.189479	+	0.251340i
$791$	−12.4078	+	24.7408i	−0.441171	+	0.879683i
$792$	−20.2808	−	12.2546i	−0.720646	−	0.435448i
$793$	−1.21615	+	1.21615i	−0.0431868	+	0.0431868i
$794$	3.21915	−	0.451747i	0.114243	−	0.0160319i
$795$	−76.4120	+	24.0142i	−2.71005	+	0.851696i
$796$	29.7316	−	8.51217i	1.05381	−	0.301706i
$797$	43.7235	+	18.1109i	1.54877	+	0.641519i	0.983092	−	0.183110i	$-0.0586166\pi$
$797$	43.7235	+	18.1109i	1.54877	+	0.641519i	0.565673	+	0.824630i	$0.308617\pi$
$798$	−34.7421	+	33.3170i	−1.22986	+	1.17941i
$799$	36.6106			1.29519
$800$	−34.4677	+	10.8287i	−1.21862	+	0.382852i
$801$	27.3437	+	4.87411i	0.966144	+	0.172218i
$802$	28.1216	−	16.5571i	0.993007	−	0.584651i
$803$	−5.33616	−	2.21031i	−0.188309	−	0.0780001i
$804$	9.45045	−	1.82380i	0.333292	−	0.0643203i
$805$	−1.19338	+	1.03249i	−0.0420612	+	0.0363905i
$806$	−2.22828	−	15.8787i	−0.0784877	−	0.559303i
$807$	−8.48377	+	7.10524i	−0.298643	+	0.250116i
$808$	6.31639	−	2.80757i	0.222210	−	0.0987700i
$809$	31.2075	−	31.2075i	1.09720	−	1.09720i	0.102461	−	0.994737i	$-0.467328\pi$
$809$	31.2075	−	31.2075i	1.09720	−	1.09720i	0.994737	−	0.102461i	$-0.0326718\pi$
$810$	−36.1123	+	23.2498i	−1.26886	+	0.816914i
$811$	−4.45136	−	10.7465i	−0.156308	−	0.377362i	0.826253	−	0.563299i	$-0.190468\pi$
$811$	−4.45136	−	10.7465i	−0.156308	−	0.377362i	−0.982562	+	0.185937i	$0.940468\pi$
$812$	37.6117	−	7.88638i	1.31991	−	0.276758i
$813$	11.7179	+	6.11385i	0.410964	+	0.214422i
$814$	−5.09314	+	19.6770i	−0.178515	+	0.689680i
$815$		−	26.1919i		−	0.917463i
$816$	−27.7037	+	2.13139i	−0.969824	+	0.0746136i
$817$	53.9138			1.88620
$818$	−37.2617	−	9.64471i	−1.30283	−	0.337219i
$819$	28.4404	+	7.21835i	0.993789	+	0.252230i
$820$	−7.48934	−	9.42334i	−0.261539	−	0.329077i
$821$	−14.1700	−	34.2094i	−0.494537	−	1.19392i	−0.952388	−	0.304888i	$-0.901381\pi$
$821$	−14.1700	−	34.2094i	−0.494537	−	1.19392i	0.457851	−	0.889029i	$-0.348619\pi$
$822$	0.170710	−	0.189159i	0.00595419	−	0.00659766i
$823$	−9.69324	−	9.69324i	−0.337885	−	0.337885i	0.517686	−	0.855571i	$-0.326794\pi$
$823$	−9.69324	−	9.69324i	−0.337885	−	0.337885i	−0.855571	+	0.517686i	$0.826794\pi$
$824$	−30.7441	+	32.3576i	−1.07102	+	1.12723i
$825$	19.8347	+	23.6829i	0.690554	+	0.824533i
$826$	30.4813	−	15.1005i	1.06058	−	0.525414i
$827$	−7.61831	+	3.15561i	−0.264914	+	0.109731i	−0.511187	−	0.859469i	$-0.670794\pi$
$827$	−7.61831	+	3.15561i	−0.264914	+	0.109731i	0.246273	+	0.969201i	$0.420794\pi$
$828$	−0.669285	+	0.822658i	−0.0232593	+	0.0285893i
$829$	7.48548	−	18.0716i	0.259982	−	0.627651i	−0.738955	−	0.673755i	$-0.764680\pi$
$829$	7.48548	−	18.0716i	0.259982	−	0.627651i	0.998937	+	0.0461036i	$0.0146804\pi$
$830$	21.9285	−	12.9108i	0.761148	−	0.448140i
$831$	−4.76851	−	0.421678i	−0.165418	−	0.0146278i
$832$	27.8656	+	9.90642i	0.966066	+	0.343443i
$833$	22.4995	−	16.7898i	0.779561	−	0.581732i
$834$	−3.60625	−	7.58289i	−0.124874	−	0.262574i
$835$	38.1598	+	15.8063i	1.32058	+	0.547000i
$836$	36.2739	+	20.1265i	1.25456	+	0.696088i
$837$	−15.8060	+	2.03587i	−0.546334	+	0.0703699i
$838$	6.51476	−	0.914224i	0.225049	−	0.0315813i
$839$	−5.66161	+	5.66161i	−0.195460	+	0.195460i	−0.798051	−	0.602590i	$-0.794135\pi$
$839$	−5.66161	+	5.66161i	−0.195460	+	0.195460i	0.602590	+	0.798051i	$0.294135\pi$
$840$	22.0161	−	37.7923i	0.759627	−	1.30396i
$841$	−16.7896	−	16.7896i	−0.578952	−	0.578952i
$842$	23.3269	+	17.5856i	0.803899	+	0.606040i
$843$	5.33530	+	16.9767i	0.183757	+	0.584708i
$844$	29.3607	+	36.9426i	1.01064	+	1.27162i
$845$	0.860138	−	2.07656i	0.0295896	−	0.0714357i
$846$	−16.1340	+	35.2092i	−0.554698	+	1.21052i
$847$	2.66894	+	8.03918i	0.0917058	+	0.276230i
$848$	31.8690	−	44.6011i	1.09439	−	1.53161i
$849$	53.0166	+	4.68824i	1.81952	+	0.160900i
$850$	35.0679	+	9.07687i	1.20282	+	0.311334i
$851$	0.840442	+	0.348122i	0.0288100	+	0.0119335i
$852$	−50.5174	−	10.3486i	−1.73070	−	0.354539i
$853$	2.64950	+	6.39646i	0.0907172	+	0.219011i	0.962725	−	0.270480i	$-0.0871826\pi$
$853$	2.64950	+	6.39646i	0.0907172	+	0.219011i	−0.872008	+	0.489491i	$0.837183\pi$
$854$	−1.64941	−	0.556566i	−0.0564417	−	0.0190453i
$855$	61.6727	−	43.0123i	2.10916	−	1.47099i
$856$	23.6302	−	10.5034i	0.807663	−	0.358998i
$857$	25.1016	−	25.1016i	0.857454	−	0.857454i	−0.133584	−	0.991038i	$-0.542649\pi$
$857$	25.1016	−	25.1016i	0.857454	−	0.857454i	0.991038	+	0.133584i	$0.0426486\pi$
$858$	−1.29466	−	25.2540i	−0.0441989	−	0.862158i
$859$	37.4258	−	15.5023i	1.27695	−	0.528931i	0.361881	−	0.932224i	$-0.382135\pi$
$859$	37.4258	−	15.5023i	1.27695	−	0.528931i	0.915071	+	0.403293i	$0.132135\pi$
$860$	−47.0956	+	13.4835i	−1.60595	+	0.459784i
$861$	8.06847	+	1.30504i	0.274973	+	0.0444757i
$862$	−18.1861	+	10.7074i	−0.619421	+	0.364695i
$863$			37.5866i			1.27946i	0.768598	+	0.639731i	$0.220954\pi$
$863$			37.5866i			1.27946i	−0.768598	+	0.639731i	$0.779046\pi$
$864$	10.1590	−	27.5825i	0.345616	−	0.938376i
$865$	−47.7220			−1.62260
$866$	37.9072	−	22.3186i	1.28814	−	0.758415i
$867$	−1.40638	−	0.733785i	−0.0477632	−	0.0249206i
$868$	13.4000	−	9.15531i	0.454826	−	0.310752i
$869$	−4.78297	+	1.98117i	−0.162251	+	0.0672067i
$870$	−59.9504	+	3.07338i	−2.03251	+	0.104197i
$871$	7.26289	+	7.26289i	0.246094	+	0.246094i
$872$	28.5803	+	10.9912i	0.967853	+	0.372209i
$873$	0.341849	−	0.238415i	0.0115698	−	0.00806912i
$874$	1.11765	−	1.48254i	0.0378051	−	0.0501477i
$875$	−9.36264	+	8.10037i	−0.316515	+	0.273842i
$876$	1.43786	−	7.01899i	0.0485809	−	0.237150i
$877$	8.63326	−	20.8425i	0.291524	−	0.703802i	−0.708474	−	0.705737i	$-0.750616\pi$
$877$	8.63326	−	20.8425i	0.291524	−	0.703802i	0.999998	+	0.00193515i	$0.000615976\pi$
$878$	−1.63337	+	6.31043i	−0.0551236	+	0.212967i
$879$	0.0315156	−	0.356392i	0.00106300	−	0.0120208i
$880$	−36.7201	−	8.50930i	−1.23783	−	0.286848i
$881$			24.3382i			0.819973i	0.912092	+	0.409987i	$0.134467\pi$
$881$			24.3382i			0.819973i	−0.912092	+	0.409987i	$0.865533\pi$
$882$	6.23176	+	29.0373i	0.209834	+	0.977737i
$883$	16.4796	−	39.7853i	0.554583	−	1.33888i	−0.359420	−	0.933176i	$-0.617025\pi$
$883$	16.4796	−	39.7853i	0.554583	−	1.33888i	0.914003	−	0.405707i	$-0.132975\pi$
$884$	−18.4491	−	23.2133i	−0.620512	−	0.780749i
$885$	−50.6915	+	15.9309i	−1.70398	+	0.535513i
$886$	−8.59018	+	11.3947i	−0.288593	+	0.382812i
$887$	26.9471	+	26.9471i	0.904794	+	0.904794i	0.995846	−	0.0910522i	$-0.0290230\pi$
$887$	26.9471	+	26.9471i	0.904794	+	0.904794i	−0.0910522	+	0.995846i	$0.529023\pi$
$888$	−25.1638	−	1.57825i	−0.844443	−	0.0529625i
$889$	−12.3307	+	24.5872i	−0.413560	+	0.824627i
$890$	43.7531	−	6.13992i	1.46661	−	0.205811i
$891$	−25.1131	+	1.00250i	−0.841319	+	0.0335849i
$892$	30.0829	+	16.6914i	1.00725	+	0.558869i
$893$	25.9471	−	62.6419i	0.868288	−	2.09623i
$894$	6.34260	+	13.3366i	0.212128	+	0.446044i
$895$			16.3477i			0.546443i
$896$	3.53554	+	29.7237i	0.118114	+	0.993000i
$897$	−1.12735	−	0.0996914i	−0.0376412	−	0.00332860i
$898$	−4.04395	−	6.86850i	−0.134948	−	0.229205i
$899$	−20.5785	−	8.52391i	−0.686332	−	0.284288i
$900$	−24.1835	+	29.7254i	−0.806118	+	0.990848i
$901$	−50.7772	+	21.0326i	−1.69163	+	0.700698i
$902$	−0.978874	−	6.97545i	−0.0325929	−	0.232257i
$903$	17.4730	−	28.3047i	0.581465	−	0.941921i
$904$	0.756308	+	29.5792i	0.0251544	+	0.983789i
$905$	−13.6667	+	13.6667i	−0.454297	+	0.454297i
$906$	36.1779	+	32.6494i	1.20193	+	1.08470i
$907$	4.77607	−	1.97831i	0.158587	−	0.0656887i	−0.301978	−	0.953315i	$-0.597647\pi$
$907$	4.77607	−	1.97831i	0.158587	−	0.0656887i	0.460565	+	0.887626i	$0.347647\pi$
$908$	11.9932	−	9.53175i	0.398007	−	0.316322i
$909$	3.95078	−	6.17600i	0.131039	−	0.204845i
$910$	46.5696	−	3.13718i	1.54377	−	0.103996i
$911$	−15.8597			−0.525457			−0.262728	−	0.964870i	$-0.584622\pi$
$911$	−15.8597			−0.525457			−0.262728	+	0.964870i	$0.584622\pi$
$912$	−15.9876	+	48.9125i	−0.529404	+	1.61965i
$913$	14.8910			0.492820
$914$	−46.6981	−	12.0872i	−1.54464	−	0.399809i
$915$	2.41078	+	1.25784i	0.0796980	+	0.0415828i
$916$	2.49998	−	21.8621i	0.0826016	−	0.722345i
$917$	−5.38653	+	4.66032i	−0.177879	+	0.153897i
$918$	−23.2780	+	18.0743i	−0.768288	+	0.596541i
$919$	23.1453	+	23.1453i	0.763492	+	0.763492i	0.976952	−	0.213460i	$-0.0684732\pi$
$919$	23.1453	+	23.1453i	0.763492	+	0.763492i	−0.213460	+	0.976952i	$0.568473\pi$
$920$	−0.605535	+	1.57457i	−0.0199639	+	0.0519120i
$921$	−23.0518	−	27.5242i	−0.759583	−	0.906954i
$922$	3.10830	+	22.1497i	0.102366	+	0.729462i
$923$	−21.0590	−	50.8410i	−0.693166	−	1.67345i
$924$	22.3224	−	12.5210i	0.734354	−	0.411909i
$925$	30.3680	+	12.5788i	0.998494	+	0.413590i
$926$	20.8435	+	35.4019i	0.684961	+	1.16338i
$927$	−8.30786	+	46.6071i	−0.272866	+	1.53078i
$928$	31.4985	−	26.3753i	1.03399	−	0.865811i
$929$	−36.8548			−1.20917			−0.604584	−	0.796541i	$-0.706661\pi$
$929$	−36.8548			−1.20917			−0.604584	+	0.796541i	$0.706661\pi$
$930$	−22.8934	+	10.8876i	−0.750705	+	0.357019i
$931$	−12.7817	−	50.3967i	−0.418905	−	1.65169i
$932$	−6.62203	−	23.1296i	−0.216912	−	0.757636i
$933$	0.149094	+	0.474409i	0.00488111	+	0.0155315i
$934$	−0.704894	−	5.02307i	−0.0230648	−	0.164360i
$935$	26.7231	+	26.7231i	0.873937	+	0.873937i
$936$	30.4551	−	7.51300i	0.995456	−	0.245570i
$937$	−3.35236	+	3.35236i	−0.109517	+	0.109517i	−0.759742	−	0.650225i	$-0.774675\pi$
$937$	−3.35236	+	3.35236i	−0.109517	+	0.109517i	0.650225	+	0.759742i	$0.274675\pi$
$938$	−3.32382	+	9.85033i	−0.108527	+	0.321625i
$939$	−5.85199	−	18.6207i	−0.190972	−	0.607665i
$940$	−6.99939	+	61.2092i	−0.228295	+	1.99642i
$941$	−18.9433	+	45.7331i	−0.617533	+	1.49086i	0.237026	+	0.971503i	$0.423827\pi$
$941$	−18.9433	+	45.7331i	−0.617533	+	1.49086i	−0.854559	+	0.519354i	$0.826173\pi$
$942$	−12.7934	+	35.9972i	−0.416833	+	1.17285i
$943$	−0.315252			−0.0102660
$944$	21.1418	−	29.5882i	0.688107	−	0.963015i
$945$	−2.59380	−	46.3180i	−0.0843764	−	1.50673i
$946$	−27.7520	−	7.18325i	−0.902296	−	0.233548i
$947$	29.3594	+	12.1611i	0.954054	+	0.395182i	0.804753	−	0.593610i	$-0.202298\pi$
$947$	29.3594	+	12.1611i	0.954054	+	0.395182i	0.149301	+	0.988792i	$0.452298\pi$
$948$	−3.53734	−	5.35998i	−0.114887	−	0.174084i
$949$	7.06396	−	2.92599i	0.229306	−	0.0949816i
$950$	40.3846	−	53.5692i	1.31025	−	1.73801i
$951$	26.7551	−	22.4076i	0.867593	−	0.726618i
$952$	12.7640	−	27.1623i	0.413685	−	0.880336i
$953$	−17.8143	−	17.8143i	−0.577062	−	0.577062i	0.357030	−	0.934093i	$-0.383789\pi$
$953$	−17.8143	−	17.8143i	−0.577062	−	0.577062i	−0.934093	+	0.357030i	$0.883789\pi$
$954$	2.14958	−	58.1024i	0.0695954	−	1.88113i
$955$	−10.3087	+	4.27000i	−0.333582	+	0.138174i
$956$	−25.8310	+	46.5552i	−0.835433	+	1.50570i
$957$	−31.1435	−	16.2493i	−1.00673	−	0.525264i
$958$	−12.8551	+	7.56869i	−0.415331	+	0.244533i
$959$	0.0867150	+	0.261197i	0.00280017	+	0.00843448i
$960$	1.73306	−	46.7252i	0.0559343	−	1.50805i
$961$	21.5936			0.696567
$962$	−13.6514	−	23.1864i	−0.440140	−	0.747560i
$963$	14.7802	−	23.1050i	0.476286	−	0.744548i
$964$	−4.62955	+	8.34384i	−0.149108	+	0.268737i
$965$	−12.5175	−	30.2199i	−0.402953	−	0.972814i
$966$	−0.416111	−	1.06724i	−0.0133881	−	0.0343380i
$967$	1.96297	−	1.96297i	0.0631248	−	0.0631248i	−0.674840	−	0.737964i	$-0.735787\pi$
$967$	1.96297	−	1.96297i	0.0631248	−	0.0631248i	0.737964	+	0.674840i	$0.235787\pi$
$968$	6.56478	+	6.23744i	0.211000	+	0.200479i
$969$	39.5544	−	33.1272i	1.27067	−	1.06420i
$970$	0.399096	−	0.529391i	0.0128142	−	0.0169977i
$971$	−43.4630	+	18.0029i	−1.39479	+	0.577742i	−0.948395	−	0.317093i	$-0.897293\pi$
$971$	−43.4630	+	18.0029i	−1.39479	+	0.577742i	−0.446398	+	0.894835i	$0.647293\pi$
$972$	−7.12401	−	30.3521i	−0.228503	−	0.973543i
$973$	9.04591	+	0.653861i	0.289999	+	0.0209618i
$974$	−3.48057	+	13.4470i	−0.111525	+	0.430869i
$975$	−40.7351	−	3.60219i	−1.30457	−	0.115362i
$976$	−1.83571	+	0.305641i	−0.0587595	+	0.00978332i
$977$	0.0130975			0.000419027			0.000209514	−	1.00000i	$-0.499933\pi$
$977$	0.0130975			0.000419027			0.000209514		1.00000i	$0.499933\pi$
$978$	17.9149	+	6.36698i	0.572856	+	0.203594i
$979$	23.8862	+	9.89399i	0.763406	+	0.316213i
$980$	23.7692	+	40.8267i	0.759280	+	1.30416i
$981$	31.7216	−	6.97039i	1.01279	−	0.222547i
$982$	31.9645	+	24.0973i	1.02003	+	0.768975i
$983$	−35.5168	−	35.5168i	−1.13281	−	1.13281i	−0.989708	−	0.143100i	$-0.954293\pi$
$983$	−35.5168	−	35.5168i	−1.13281	−	1.13281i	−0.143100	−	0.989708i	$-0.545707\pi$
$984$	8.26602	−	2.83189i	0.263511	−	0.0902774i
$985$	−63.7082	−	63.7082i	−2.02991	−	2.02991i
$986$	−40.7912	+	5.72428i	−1.29906	+	0.182298i
$987$	−24.4777	−	33.9239i	−0.779134	−	1.07981i
$988$	−52.7942	+	15.1150i	−1.67961	+	0.480873i
$989$	−0.490983	+	1.18534i	−0.0156124	+	0.0376916i
$990$	−37.4767	+	13.9235i	−1.19109	+	0.442517i
$991$	−9.31437			−0.295881			−0.147940	−	0.988996i	$-0.547264\pi$
$991$	−9.31437			−0.295881			−0.147940	+	0.988996i	$0.547264\pi$
$992$	8.02692	−	15.3810i	0.254855	−	0.488346i
$993$	−24.8597	−	2.19833i	−0.788898	−	0.0697620i
$994$	36.6483	−	41.9426i	1.16241	−	1.33034i
$995$	19.9680	−	48.2070i	0.633028	−	1.52826i
$996$	3.50022	+	18.1373i	0.110909	+	0.574701i
$997$	40.2060	−	16.6539i	1.27334	−	0.527433i	0.359360	−	0.933199i	$-0.382995\pi$
$997$	40.2060	−	16.6539i	1.27334	−	0.527433i	0.913977	+	0.405766i	$0.132995\pi$
$998$	5.79233	+	41.2761i	0.183353	+	1.30657i
$999$	−23.1972	+	13.3064i	−0.733928	+	0.420997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.19	✓	496
3.2	odd	2	inner	672.2.bo.a.125.106	yes	496
7.6	odd	2	inner	672.2.bo.a.125.20	yes	496
21.20	even	2	inner	672.2.bo.a.125.105	yes	496
32.21	even	8	inner	672.2.bo.a.629.105	yes	496
96.53	odd	8	inner	672.2.bo.a.629.20	yes	496
224.181	odd	8	inner	672.2.bo.a.629.106	yes	496
672.629	even	8	inner	672.2.bo.a.629.19	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.19	✓	496	1.1	even	1	trivial
672.2.bo.a.125.20	yes	496	7.6	odd	2	inner
672.2.bo.a.125.105	yes	496	21.20	even	2	inner
672.2.bo.a.125.106	yes	496	3.2	odd	2	inner
672.2.bo.a.629.19	yes	496	672.629	even	8	inner
672.2.bo.a.629.20	yes	496	96.53	odd	8	inner
672.2.bo.a.629.105	yes	496	32.21	even	8	inner
672.2.bo.a.629.106	yes	496	224.181	odd	8	inner

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21868 + 0.717517i) q^{2} +(-1.53560 - 0.801206i) q^{3} +(0.970338 - 1.74884i) q^{4} +(-1.29133 - 3.11756i) q^{5} +(2.44628 - 0.125409i) q^{6} +(-1.18607 + 2.36500i) q^{7} +(0.0722962 + 2.82750i) q^{8} +(1.71614 + 2.46067i) q^{9} +O(q^{10})\)	\(q+(-1.21868 + 0.717517i) q^{2} +(-1.53560 - 0.801206i) q^{3} +(0.970338 - 1.74884i) q^{4} +(-1.29133 - 3.11756i) q^{5} +(2.44628 - 0.125409i) q^{6} +(-1.18607 + 2.36500i) q^{7} +(0.0722962 + 2.82750i) q^{8} +(1.71614 + 2.46067i) q^{9} +(3.81062 + 2.87274i) q^{10} +(1.06867 + 2.57999i) q^{11} +(-2.89123 + 1.90808i) q^{12} +(-3.41537 - 1.41469i) q^{13} +(-0.251488 - 3.73320i) q^{14} +(-0.514833 + 5.82195i) q^{15} +(-2.11689 - 3.39393i) q^{16} +4.01050i q^{17} +(-3.85698 - 1.76739i) q^{18} +(6.86210 + 2.84237i) q^{19} +(-6.70514 - 0.766747i) q^{20} +(3.71619 - 2.68140i) q^{21} +(-3.15355 - 2.37738i) q^{22} +(-0.124984 + 0.124984i) q^{23} +(2.15440 - 4.39984i) q^{24} +(-4.51609 + 4.51609i) q^{25} +(5.17729 - 0.726535i) q^{26} +(-0.663800 - 5.15358i) q^{27} +(2.98511 + 4.36911i) q^{28} +(2.77924 - 6.70969i) q^{29} +(-3.54993 - 7.46447i) q^{30} -3.06699i q^{31} +(5.01500 + 2.61720i) q^{32} +(0.426059 - 4.81806i) q^{33} +(-2.87761 - 4.88750i) q^{34} +(8.90465 + 0.643650i) q^{35} +(5.96854 - 0.613573i) q^{36} +(-1.96953 - 4.75487i) q^{37} +(-10.4021 + 1.45974i) q^{38} +(4.11118 + 4.90881i) q^{39} +(8.72155 - 3.87664i) q^{40} +(1.26117 + 1.26117i) q^{41} +(-2.60487 + 5.93419i) q^{42} +(6.70616 - 2.77778i) q^{43} +(5.54896 + 0.634535i) q^{44} +(5.45516 - 8.52770i) q^{45} +(0.0626366 - 0.241993i) q^{46} -9.12869i q^{47} +(0.531452 + 6.90779i) q^{48} +(-4.18645 - 5.61013i) q^{49} +(2.26327 - 8.74402i) q^{50} +(3.21324 - 6.15853i) q^{51} +(-5.78813 + 4.60020i) q^{52} +(5.24438 + 12.6611i) q^{53} +(4.50674 + 5.80425i) q^{54} +(6.66326 - 6.66326i) q^{55} +(-6.77279 - 3.18265i) q^{56} +(-8.26011 - 9.86270i) q^{57} +(1.42732 + 10.1711i) q^{58} +(3.47911 + 8.39931i) q^{59} +(9.68210 + 6.54962i) q^{60} +(0.178041 - 0.429829i) q^{61} +(2.20062 + 3.73766i) q^{62} +(-7.85494 + 1.14013i) q^{63} +(-7.98955 + 0.408835i) q^{64} +12.4744i q^{65} +(2.93781 + 6.17735i) q^{66} +(-2.56695 - 1.06327i) q^{67} +(7.01373 + 3.89155i) q^{68} +(0.292063 - 0.0917874i) q^{69} +(-11.3137 + 5.60484i) q^{70} +(10.5260 + 10.5260i) q^{71} +(-6.83347 + 5.03028i) q^{72} +(-1.46250 + 1.46250i) q^{73} +(5.81192 + 4.38147i) q^{74} +(10.5532 - 3.31659i) q^{75} +(11.6294 - 9.24265i) q^{76} +(-7.36920 - 0.532664i) q^{77} +(-8.53235 - 3.03241i) q^{78} +1.85387i q^{79} +(-7.84718 + 10.9822i) q^{80} +(-3.10975 + 8.44568i) q^{81} +(-2.44187 - 0.632047i) q^{82} +(2.04061 - 4.92648i) q^{83} +(-1.08339 - 9.10089i) q^{84} +(12.5030 - 5.17890i) q^{85} +(-6.17952 + 8.19700i) q^{86} +(-9.64365 + 8.07665i) q^{87} +(-7.21767 + 3.20818i) q^{88} +(6.54657 - 6.54657i) q^{89} +(-0.529297 + 14.3067i) q^{90} +(7.39663 - 6.39941i) q^{91} +(0.0973002 + 0.339853i) q^{92} +(-2.45729 + 4.70967i) q^{93} +(6.54999 + 11.1249i) q^{94} -25.0634i q^{95} +(-5.60413 - 8.03703i) q^{96} -0.138925i q^{97} +(9.12729 + 3.83308i) q^{98} +(-4.51451 + 7.05725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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