LMFDB - Embedded newform 966.2.l.c.47.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.9
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.185627 + 1.72208i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.97297 - 3.41729i) q^{5} +(0.700280 - 1.58417i) q^{6} +(1.45851 + 2.20743i) q^{7} -1.00000i q^{8} +(-2.93109 + 0.639328i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.185627 + 1.72208i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.97297 - 3.41729i) q^{5} +(0.700280 - 1.58417i) q^{6} +(1.45851 + 2.20743i) q^{7} -1.00000i q^{8} +(-2.93109 + 0.639328i) q^{9} +(-3.41729 + 1.97297i) q^{10} +(3.65793 - 2.11191i) q^{11} +(-1.39855 + 1.02180i) q^{12} -4.40215i q^{13} +(-0.159393 - 2.64095i) q^{14} +(6.25106 + 2.76326i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.19885 + 3.80852i) q^{17} +(2.85806 + 0.911868i) q^{18} +(-1.64871 - 0.951881i) q^{19} +3.94594 q^{20} +(-3.53062 + 2.92142i) q^{21} -4.22382 q^{22} +(0.866025 + 0.500000i) q^{23} +(1.72208 - 0.185627i) q^{24} +(-5.28524 - 9.15430i) q^{25} +(-2.20108 + 3.81238i) q^{26} +(-1.64506 - 4.92887i) q^{27} +(-1.18243 + 2.36682i) q^{28} -4.49568i q^{29} +(-4.03195 - 5.51859i) q^{30} +(6.13213 - 3.54039i) q^{31} +(0.866025 - 0.500000i) q^{32} +(4.31588 + 5.90721i) q^{33} -4.39770i q^{34} +(10.4210 - 0.628955i) q^{35} +(-2.01922 - 2.21873i) q^{36} +(-2.06920 + 3.58397i) q^{37} +(0.951881 + 1.64871i) q^{38} +(7.58084 - 0.817159i) q^{39} +(-3.41729 - 1.97297i) q^{40} -3.65400 q^{41} +(4.51832 - 0.764717i) q^{42} -10.6333 q^{43} +(3.65793 + 2.11191i) q^{44} +(-3.59818 + 11.2777i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(2.87648 - 4.98221i) q^{47} +(-1.58417 - 0.700280i) q^{48} +(-2.74549 + 6.43912i) q^{49} +10.5705i q^{50} +(-6.15040 + 4.49355i) q^{51} +(3.81238 - 2.20108i) q^{52} +(3.65112 - 2.10798i) q^{53} +(-1.03977 + 5.09106i) q^{54} -16.6669i q^{55} +(2.20743 - 1.45851i) q^{56} +(1.33317 - 3.01589i) q^{57} +(-2.24784 + 3.89338i) q^{58} +(7.12712 + 12.3445i) q^{59} +(0.732474 + 6.79521i) q^{60} +(3.67300 + 2.12061i) q^{61} -7.08078 q^{62} +(-5.68629 - 5.53770i) q^{63} -1.00000 q^{64} +(-15.0434 - 8.68532i) q^{65} +(-0.784055 - 7.27373i) q^{66} +(6.03398 + 10.4512i) q^{67} +(-2.19885 + 3.80852i) q^{68} +(-0.700280 + 1.58417i) q^{69} +(-9.33935 - 4.66582i) q^{70} -3.03021i q^{71} +(0.639328 + 2.93109i) q^{72} +(-3.46049 + 1.99791i) q^{73} +(3.58397 - 2.06920i) q^{74} +(14.7833 - 10.8009i) q^{75} -1.90376i q^{76} +(9.99702 + 4.99439i) q^{77} +(-6.97378 - 3.08274i) q^{78} +(7.65531 - 13.2594i) q^{79} +(1.97297 + 3.41729i) q^{80} +(8.18252 - 3.74785i) q^{81} +(3.16445 + 1.82700i) q^{82} +10.1200 q^{83} +(-4.29534 - 1.59689i) q^{84} +17.3531 q^{85} +(9.20870 + 5.31665i) q^{86} +(7.74190 - 0.834521i) q^{87} +(-2.11191 - 3.65793i) q^{88} +(4.83530 - 8.37498i) q^{89} +(8.75498 - 7.96771i) q^{90} +(9.71744 - 6.42059i) q^{91} +1.00000i q^{92} +(7.23510 + 9.90280i) q^{93} +(-4.98221 + 2.87648i) q^{94} +(-6.50570 + 3.75607i) q^{95} +(1.02180 + 1.39855i) q^{96} +15.1375i q^{97} +(5.59723 - 4.20370i) q^{98} +(-9.37151 + 8.52880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.185627	+	1.72208i	0.107172	+	0.994241i
$3$	0.185627	+	1.72208i	0.107172	+	0.994241i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.97297	−	3.41729i	0.882340	−	1.52826i	0.0336072	−	0.999435i	$-0.489300\pi$
$5$	1.97297	−	3.41729i	0.882340	−	1.52826i	0.848733	−	0.528822i	$-0.177366\pi$
$6$	0.700280	−	1.58417i	0.285888	−	0.646736i
$7$	1.45851	+	2.20743i	0.551265	+	0.834330i
$7$	1.45851	+	2.20743i	0.551265	+	0.834330i
$8$		−	1.00000i		−	0.353553i
$9$	−2.93109	+	0.639328i	−0.977028	+	0.213109i
$10$	−3.41729	+	1.97297i	−1.08064	+	0.623908i
$11$	3.65793	−	2.11191i	1.10291	−	0.636764i	0.165925	−	0.986138i	$-0.446939\pi$
$11$	3.65793	−	2.11191i	1.10291	−	0.636764i	0.936983	+	0.349374i	$0.113606\pi$
$12$	−1.39855	+	1.02180i	−0.403726	+	0.294967i
$13$		−	4.40215i		−	1.22094i	−0.792040	−	0.610469i	$-0.790981\pi$
$13$		−	4.40215i		−	1.22094i	0.792040	−	0.610469i	$-0.209019\pi$
$14$	−0.159393	−	2.64095i	−0.0425995	−	0.705822i
$15$	6.25106	+	2.76326i	1.61402	+	0.713472i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.19885	+	3.80852i	0.533300	+	0.923703i	0.999244	+	0.0388882i	$0.0123816\pi$
$17$	2.19885	+	3.80852i	0.533300	+	0.923703i	−0.465944	+	0.884814i	$0.654285\pi$
$18$	2.85806	+	0.911868i	0.673651	+	0.214929i
$19$	−1.64871	−	0.951881i	−0.378239	−	0.218376i	0.298813	−	0.954312i	$-0.403409\pi$
$19$	−1.64871	−	0.951881i	−0.378239	−	0.218376i	−0.677052	+	0.735935i	$0.736743\pi$
$20$	3.94594			0.882340
$21$	−3.53062	+	2.92142i	−0.770445	+	0.637507i
$22$	−4.22382			−0.900521
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	1.72208	−	0.185627i	0.351517	−	0.0378910i
$25$	−5.28524	−	9.15430i	−1.05705	−	1.83086i
$26$	−2.20108	+	3.81238i	−0.431667	+	0.747669i
$27$	−1.64506	−	4.92887i	−0.316592	−	0.948562i
$28$	−1.18243	+	2.36682i	−0.223459	+	0.447287i
$29$		−	4.49568i		−	0.834827i	−0.908717	−	0.417414i	$-0.862937\pi$
$29$		−	4.49568i		−	0.834827i	0.908717	−	0.417414i	$-0.137063\pi$
$30$	−4.03195	−	5.51859i	−0.736129	−	1.00755i
$31$	6.13213	−	3.54039i	1.10136	−	0.635873i	0.164785	−	0.986330i	$-0.447307\pi$
$31$	6.13213	−	3.54039i	1.10136	−	0.635873i	0.936579	+	0.350457i	$0.113974\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	4.31588	+	5.90721i	0.751297	+	1.02831i
$34$		−	4.39770i		−	0.754200i
$35$	10.4210	−	0.628955i	1.76147	−	0.106313i
$36$	−2.01922	−	2.21873i	−0.336536	−	0.369788i
$37$	−2.06920	+	3.58397i	−0.340175	+	0.589201i	−0.984465	−	0.175581i	$-0.943820\pi$
$37$	−2.06920	+	3.58397i	−0.340175	+	0.589201i	0.644290	+	0.764781i	$0.277153\pi$
$38$	0.951881	+	1.64871i	0.154415	+	0.267455i
$39$	7.58084	−	0.817159i	1.21391	−	0.130850i
$40$	−3.41729	−	1.97297i	−0.540321	−	0.311954i
$41$	−3.65400			−0.570658			−0.285329	−	0.958430i	$-0.592103\pi$
$41$	−3.65400			−0.570658			−0.285329	+	0.958430i	$0.592103\pi$
$42$	4.51832	−	0.764717i	0.697192	−	0.117998i
$43$	−10.6333			−1.62156			−0.810781	−	0.585350i	$-0.800957\pi$
$43$	−10.6333			−1.62156			−0.810781	+	0.585350i	$0.800957\pi$
$44$	3.65793	+	2.11191i	0.551454	+	0.318382i
$45$	−3.59818	+	11.2777i	−0.536385	+	1.68119i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	2.87648	−	4.98221i	0.419578	−	0.726731i	−0.576319	−	0.817225i	$-0.695511\pi$
$47$	2.87648	−	4.98221i	0.419578	−	0.726731i	0.995897	+	0.0904944i	$0.0288447\pi$
$48$	−1.58417	−	0.700280i	−0.228656	−	0.101077i
$49$	−2.74549	+	6.43912i	−0.392213	+	0.919874i
$50$			10.5705i			1.49489i
$51$	−6.15040	+	4.49355i	−0.861228	+	0.629223i
$52$	3.81238	−	2.20108i	0.528682	−	0.305234i
$53$	3.65112	−	2.10798i	0.501520	−	0.289553i	−0.227821	−	0.973703i	$-0.573160\pi$
$53$	3.65112	−	2.10798i	0.501520	−	0.289553i	0.729341	+	0.684150i	$0.239827\pi$
$54$	−1.03977	+	5.09106i	−0.141495	+	0.692805i
$55$		−	16.6669i		−	2.24737i
$56$	2.20743	−	1.45851i	0.294980	−	0.194902i
$57$	1.33317	−	3.01589i	0.176582	−	0.399464i
$58$	−2.24784	+	3.89338i	−0.295156	+	0.511225i
$59$	7.12712	+	12.3445i	0.927872	+	1.60712i	0.786875	+	0.617112i	$0.211697\pi$
$59$	7.12712	+	12.3445i	0.927872	+	1.60712i	0.140997	+	0.990010i	$0.454969\pi$
$60$	0.732474	+	6.79521i	0.0945620	+	0.877258i
$61$	3.67300	+	2.12061i	0.470280	+	0.271516i	0.716357	−	0.697734i	$-0.245808\pi$
$61$	3.67300	+	2.12061i	0.470280	+	0.271516i	−0.246077	+	0.969250i	$0.579142\pi$
$62$	−7.08078			−0.899260
$63$	−5.68629	−	5.53770i	−0.716405	−	0.697684i
$64$	−1.00000			−0.125000
$65$	−15.0434	−	8.68532i	−1.86591	−	1.07728i
$66$	−0.784055	−	7.27373i	−0.0965105	−	0.895334i
$67$	6.03398	+	10.4512i	0.737168	+	1.27681i	0.953765	+	0.300552i	$0.0971709\pi$
$67$	6.03398	+	10.4512i	0.737168	+	1.27681i	−0.216597	+	0.976261i	$0.569496\pi$
$68$	−2.19885	+	3.80852i	−0.266650	+	0.461851i
$69$	−0.700280	+	1.58417i	−0.0843038	+	0.190712i
$70$	−9.33935	−	4.66582i	−1.11627	−	0.557672i
$71$		−	3.03021i		−	0.359620i	−0.983701	−	0.179810i	$-0.942452\pi$
$71$		−	3.03021i		−	0.359620i	0.983701	−	0.179810i	$-0.0575483\pi$
$72$	0.639328	+	2.93109i	0.0753455	+	0.345432i
$73$	−3.46049	+	1.99791i	−0.405020	+	0.233838i	−0.688648	−	0.725096i	$-0.741795\pi$
$73$	−3.46049	+	1.99791i	−0.405020	+	0.233838i	0.283628	+	0.958934i	$0.408462\pi$
$74$	3.58397	−	2.06920i	0.416628	−	0.240540i
$75$	14.7833	−	10.8009i	1.70703	−	1.24718i
$76$		−	1.90376i		−	0.218376i
$77$	9.99702	+	4.99439i	1.13927	+	0.569163i
$78$	−6.97378	−	3.08274i	−0.789625	−	0.349051i
$79$	7.65531	−	13.2594i	0.861289	−	1.49180i	−0.00939605	−	0.999956i	$-0.502991\pi$
$79$	7.65531	−	13.2594i	0.861289	−	1.49180i	0.870685	−	0.491841i	$-0.163676\pi$
$80$	1.97297	+	3.41729i	0.220585	+	0.382064i
$81$	8.18252	−	3.74785i	0.909169	−	0.416428i
$82$	3.16445	+	1.82700i	0.349455	+	0.201758i
$83$	10.1200			1.11081			0.555405	−	0.831580i	$-0.312563\pi$
$83$	10.1200			1.11081			0.555405	+	0.831580i	$0.312563\pi$
$84$	−4.29534	−	1.59689i	−0.468660	−	0.174236i
$85$	17.3531			1.88221
$86$	9.20870	+	5.31665i	0.993000	+	0.573309i
$87$	7.74190	−	0.834521i	0.830019	−	0.0894700i
$88$	−2.11191	−	3.65793i	−0.225130	−	0.389937i
$89$	4.83530	−	8.37498i	0.512540	−	0.887746i	−0.487354	−	0.873205i	$-0.662038\pi$
$89$	4.83530	−	8.37498i	0.512540	−	0.887746i	0.999894	−	0.0145415i	$-0.00462888\pi$
$90$	8.75498	−	7.96771i	0.922856	−	0.839871i
$91$	9.71744	−	6.42059i	1.01866	−	0.673061i
$92$			1.00000i			0.104257i
$93$	7.23510	+	9.90280i	0.750245	+	1.02687i
$94$	−4.98221	+	2.87648i	−0.513876	+	0.296686i
$95$	−6.50570	+	3.75607i	−0.667471	+	0.385364i
$96$	1.02180	+	1.39855i	0.104287	+	0.142739i
$97$			15.1375i			1.53698i	0.639862	+	0.768490i	$0.278991\pi$
$97$			15.1375i			1.53698i	−0.639862	+	0.768490i	$0.721009\pi$
$98$	5.59723	−	4.20370i	0.565405	−	0.424637i
$99$	−9.37151	+	8.52880i	−0.941872	+	0.857177i
$100$	5.28524	−	9.15430i	0.528524	−	0.915430i
$101$	−4.50036	−	7.79485i	−0.447802	−	0.775616i	0.550440	−	0.834874i	$-0.314460\pi$
$101$	−4.50036	−	7.79485i	−0.447802	−	0.775616i	−0.998243	+	0.0592582i	$0.981126\pi$
$102$	7.57318	−	0.816333i	0.749856	−	0.0808290i
$103$	−11.9795	−	6.91639i	−1.18038	−	0.681492i	−0.224276	−	0.974526i	$-0.572002\pi$
$103$	−11.9795	−	6.91639i	−1.18038	−	0.681492i	−0.956102	+	0.293034i	$0.905335\pi$
$104$	−4.40215			−0.431667
$105$	3.01753	+	17.8290i	0.294481	+	1.73994i
$106$	−4.21595			−0.409490
$107$	7.12901	+	4.11593i	0.689187	+	0.397902i	0.803307	−	0.595565i	$-0.203072\pi$
$107$	7.12901	+	4.11593i	0.689187	+	0.397902i	−0.114120	+	0.993467i	$0.536405\pi$
$108$	3.44600	−	3.88910i	0.331591	−	0.374229i
$109$	7.15057	+	12.3852i	0.684901	+	1.18628i	0.973468	+	0.228823i	$0.0734878\pi$
$109$	7.15057	+	12.3852i	0.684901	+	1.18628i	−0.288567	+	0.957460i	$0.593179\pi$
$110$	−8.33347	+	14.4340i	−0.794565	+	1.37623i
$111$	−6.55596	−	2.89804i	−0.622264	−	0.275070i
$112$	−2.64095	+	0.159393i	−0.249546	+	0.0150612i
$113$			3.40461i			0.320279i	0.987094	+	0.160139i	$0.0511943\pi$
$113$			3.40461i			0.320279i	−0.987094	+	0.160139i	$0.948806\pi$
$114$	−2.66250	+	1.94525i	−0.249366	+	0.182190i
$115$	3.41729	−	1.97297i	0.318664	−	0.183981i
$116$	3.89338	−	2.24784i	0.361491	−	0.208707i
$117$	2.81442	+	12.9031i	0.260193	+	1.19289i
$118$		−	14.2542i		−	1.31221i
$119$	−5.20000	+	10.4086i	−0.476683	+	0.954153i
$120$	2.76326	−	6.25106i	0.252250	−	0.570641i
$121$	3.42031	−	5.92415i	0.310937	−	0.538559i
$122$	−2.12061	−	3.67300i	−0.191991	−	0.332538i
$123$	−0.678281	−	6.29245i	−0.0611585	−	0.567372i
$124$	6.13213	+	3.54039i	0.550682	+	0.317936i
$125$	−21.9808			−1.96602
$126$	2.15562	+	7.63893i	0.192038	+	0.680530i
$127$	7.19411			0.638374			0.319187	−	0.947692i	$-0.396590\pi$
$127$	7.19411			0.638374			0.319187	+	0.947692i	$0.396590\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.97383	−	18.3113i	−0.173786	−	1.61222i
$130$	8.68532	+	15.0434i	0.761753	+	1.31940i
$131$	1.03238	−	1.78814i	0.0901998	−	0.156231i	−0.817395	−	0.576077i	$-0.804583\pi$
$131$	1.03238	−	1.78814i	0.0901998	−	0.156231i	0.907595	+	0.419847i	$0.137916\pi$
$132$	−2.95785	+	6.69126i	−0.257448	+	0.582399i
$133$	−0.303446	−	5.02773i	−0.0263121	−	0.435960i
$134$		−	12.0680i		−	1.04251i
$135$	−20.0890	−	4.10289i	−1.72899	−	0.353120i
$136$	3.80852	−	2.19885i	0.326578	−	0.188550i
$137$	−6.09412	+	3.51844i	−0.520656	+	0.300601i	−0.737203	−	0.675671i	$-0.763854\pi$
$137$	−6.09412	+	3.51844i	−0.520656	+	0.300601i	0.216547	+	0.976272i	$0.430521\pi$
$138$	1.39855	−	1.02180i	0.119052	−	0.0869810i
$139$			5.70531i			0.483918i	0.970287	+	0.241959i	$0.0777899\pi$
$139$			5.70531i			0.483918i	−0.970287	+	0.241959i	$0.922210\pi$
$140$	5.75520	+	8.71039i	0.486403	+	0.736163i
$141$	9.11370	+	4.02868i	0.767512	+	0.339276i
$142$	−1.51511	+	2.62424i	−0.127145	+	0.220221i
$143$	−9.29694	−	16.1028i	−0.777449	−	1.34658i
$144$	0.911868	−	2.85806i	0.0759890	−	0.238172i
$145$	−15.3630	−	8.86986i	−1.27583	−	0.736601i
$146$	3.99583			0.330697
$147$	−11.5983	−	3.53267i	−0.956611	−	0.291369i
$148$	−4.13841			−0.340175
$149$	−4.95665	−	2.86172i	−0.406064	−	0.234441i	0.283033	−	0.959110i	$-0.408659\pi$
$149$	−4.95665	−	2.86172i	−0.406064	−	0.234441i	−0.689097	+	0.724669i	$0.741993\pi$
$150$	−18.2031	+	1.96217i	−1.48628	+	0.160210i
$151$	−0.696649	−	1.20663i	−0.0566925	−	0.0981943i	0.836286	−	0.548293i	$-0.184722\pi$
$151$	−0.696649	−	1.20663i	−0.0566925	−	0.0981943i	−0.892979	+	0.450099i	$0.851389\pi$
$152$	−0.951881	+	1.64871i	−0.0772077	+	0.133728i
$153$	−8.87992	−	9.75732i	−0.717899	−	0.788833i
$154$	−6.16048	−	9.32378i	−0.496426	−	0.751331i
$155$		−	27.9403i		−	2.24422i
$156$	4.49810	+	6.15662i	0.360136	+	0.492924i
$157$	−11.4182	+	6.59230i	−0.911271	+	0.526123i	−0.880840	−	0.473414i	$-0.843021\pi$
$157$	−11.4182	+	6.59230i	−0.911271	+	0.526123i	−0.0304315	+	0.999537i	$0.509688\pi$
$158$	−13.2594	+	7.65531i	−1.05486	+	0.609023i
$159$	4.30784	+	5.89621i	0.341634	+	0.467600i
$160$		−	3.94594i		−	0.311954i
$161$	0.159393	+	2.64095i	0.0125619	+	0.208136i
$162$	−8.96019	−	0.845528i	−0.703979	−	0.0664310i
$163$	0.743800	−	1.28830i	0.0582589	−	0.100907i	−0.835425	−	0.549604i	$-0.814778\pi$
$163$	0.743800	−	1.28830i	0.0582589	−	0.100907i	0.893684	+	0.448697i	$0.148112\pi$
$164$	−1.82700	−	3.16445i	−0.142665	−	0.247102i
$165$	28.7017	−	3.09384i	2.23443	−	0.240855i
$166$	−8.76415	−	5.05998i	−0.680230	−	0.392731i
$167$	6.63358			0.513322			0.256661	−	0.966502i	$-0.417378\pi$
$167$	6.63358			0.513322			0.256661	+	0.966502i	$0.417378\pi$
$168$	2.92142	+	3.53062i	0.225393	+	0.272393i
$169$	−6.37895			−0.490689
$170$	−15.0282	−	8.67655i	−1.15261	−	0.665461i
$171$	5.44106	+	1.73598i	0.416088	+	0.132754i
$172$	−5.31665	−	9.20870i	−0.405390	−	0.702157i
$173$	−5.39613	+	9.34637i	−0.410260	+	0.710591i	−0.994918	−	0.100689i	$-0.967895\pi$
$173$	−5.39613	+	9.34637i	−0.410260	+	0.710591i	0.584658	+	0.811280i	$0.301229\pi$
$174$	−7.12195	−	3.14824i	−0.539913	−	0.238667i
$175$	12.4989	−	25.0184i	0.944827	−	1.89122i
$176$			4.22382i			0.318382i
$177$	−19.9352	+	14.5649i	−1.49842	+	1.09477i
$178$	−8.37498	+	4.83530i	−0.627731	+	0.362421i
$179$	−17.1978	+	9.92914i	−1.28542	+	0.742139i	−0.977834	−	0.209381i	$-0.932855\pi$
$179$	−17.1978	+	9.92914i	−1.28542	+	0.742139i	−0.307588	+	0.951520i	$0.599522\pi$
$180$	−11.5659	+	2.52275i	−0.862071	+	0.188035i
$181$			6.20202i			0.460992i	0.973073	+	0.230496i	$0.0740349\pi$
$181$			6.20202i			0.460992i	−0.973073	+	0.230496i	$0.925965\pi$
$182$	−11.6258	+	0.701671i	−0.861765	+	0.0520113i
$183$	−2.97004	+	6.71883i	−0.219552	+	0.496670i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	8.16496	+	14.1421i	0.600300	+	1.03975i
$186$	−1.31438	−	12.1936i	−0.0963753	−	0.894080i
$187$	16.0865	+	9.28755i	1.17636	+	0.679173i
$188$	5.75296			0.419578
$189$	8.48080	−	10.8202i	0.616888	−	0.787051i
$190$	7.51214			0.544988
$191$	−3.68179	−	2.12569i	−0.266405	−	0.153809i	0.360848	−	0.932625i	$-0.382487\pi$
$191$	−3.68179	−	2.12569i	−0.266405	−	0.153809i	−0.627253	+	0.778816i	$0.715821\pi$
$192$	−0.185627	−	1.72208i	−0.0133965	−	0.124280i
$193$	−2.79559	−	4.84211i	−0.201231	−	0.348542i	0.747694	−	0.664043i	$-0.231161\pi$
$193$	−2.79559	−	4.84211i	−0.201231	−	0.348542i	−0.948925	+	0.315501i	$0.897828\pi$
$194$	7.56874	−	13.1094i	0.543404	−	0.941204i
$195$	12.1643	−	27.5181i	0.871105	−	1.97061i
$196$	−6.94919	+	0.841895i	−0.496371	+	0.0601354i
$197$			1.45726i			0.103825i	0.998652	+	0.0519127i	$0.0165317\pi$
$197$			1.45726i			0.103825i	−0.998652	+	0.0519127i	$0.983468\pi$
$198$	12.3804	−	2.70040i	0.879834	−	0.191909i
$199$	−17.4052	+	10.0489i	−1.23382	+	0.712348i	−0.967825	−	0.251626i	$-0.919035\pi$
$199$	−17.4052	+	10.0489i	−1.23382	+	0.712348i	−0.265998	+	0.963974i	$0.585701\pi$
$200$	−9.15430	+	5.28524i	−0.647306	+	0.373723i
$201$	−16.8776	+	12.3310i	−1.19046	+	0.869761i
$202$			9.00071i			0.633288i
$203$	9.92390	−	6.55700i	0.696521	−	0.460211i
$204$	−6.96673	−	3.07962i	−0.487769	−	0.215617i
$205$	−7.20923	+	12.4868i	−0.503514	+	0.872113i
$206$	6.91639	+	11.9795i	0.481887	+	0.834653i
$207$	−2.85806	−	0.911868i	−0.198649	−	0.0633792i
$208$	3.81238	+	2.20108i	0.264341	+	0.152617i
$209$	−8.04114			−0.556217
$210$	6.30126	−	16.9492i	0.434828	−	1.16960i
$211$	−28.5864			−1.96797			−0.983984	−	0.178259i	$-0.942954\pi$
$211$	−28.5864			−1.96797			−0.983984	+	0.178259i	$0.942954\pi$
$212$	3.65112	+	2.10798i	0.250760	+	0.144776i
$213$	5.21825	−	0.562489i	0.357549	−	0.0385411i
$214$	−4.11593	−	7.12901i	−0.281359	−	0.487329i
$215$	−20.9792	+	36.3370i	−1.43077	+	2.47816i
$216$	−4.92887	+	1.64506i	−0.335367	+	0.111932i
$217$	16.7589	+	8.37256i	1.13767	+	0.568366i
$218$		−	14.3011i		−	0.968596i
$219$	−4.08292	−	5.58835i	−0.275898	−	0.377626i
$220$	14.4340	−	8.33347i	0.973140	−	0.561842i
$221$	16.7657	−	9.67968i	1.12778	−	0.651126i
$222$	4.22861	+	5.78776i	0.283806	+	0.388449i
$223$			7.22918i			0.484102i	0.970264	+	0.242051i	$0.0778201\pi$
$223$			7.22918i			0.484102i	−0.970264	+	0.242051i	$0.922180\pi$
$224$	2.36682	+	1.18243i	0.158140	+	0.0790047i
$225$	21.3441	+	23.4530i	1.42294	+	1.56353i
$226$	1.70230	−	2.94848i	0.113236	−	0.196130i
$227$	3.03276	+	5.25290i	0.201292	+	0.348647i	0.948945	−	0.315442i	$-0.102153\pi$
$227$	3.03276	+	5.25290i	0.201292	+	0.348647i	−0.747653	+	0.664089i	$0.768819\pi$
$228$	3.27842	−	0.353390i	0.217119	−	0.0234038i
$229$	2.34054	+	1.35131i	0.154667	+	0.0892973i	0.575336	−	0.817917i	$-0.304871\pi$
$229$	2.34054	+	1.35131i	0.154667	+	0.0892973i	−0.420669	+	0.907214i	$0.638205\pi$
$230$	−3.94594			−0.260188
$231$	−6.74499	+	18.1427i	−0.443788	+	1.19370i
$232$	−4.49568			−0.295156
$233$	−7.92945	−	4.57807i	−0.519476	−	0.299920i	0.217244	−	0.976117i	$-0.430293\pi$
$233$	−7.92945	−	4.57807i	−0.519476	−	0.299920i	−0.736720	+	0.676198i	$0.763626\pi$
$234$	4.01419	−	12.5816i	0.262415	−	0.822486i
$235$	−11.3504	−	19.6595i	−0.740421	−	1.28245i
$236$	−7.12712	+	12.3445i	−0.463936	+	0.803561i
$237$	24.2547	+	10.7217i	1.57551	+	0.696450i
$238$	9.70762	−	6.41410i	0.629252	−	0.415764i
$239$		−	16.9188i		−	1.09438i	−0.837007	−	0.547192i	$-0.815697\pi$
$239$		−	16.9188i		−	1.09438i	0.837007	−	0.547192i	$-0.184303\pi$
$240$	−5.51859	+	4.03195i	−0.356223	+	0.260261i
$241$	−19.4840	+	11.2491i	−1.25507	+	0.724618i	−0.972113	−	0.234514i	$-0.924650\pi$
$241$	−19.4840	+	11.2491i	−1.25507	+	0.724618i	−0.282962	+	0.959131i	$0.591317\pi$
$242$	−5.92415	+	3.42031i	−0.380819	+	0.219866i
$243$	7.97297	+	13.3952i	0.511466	+	0.859303i
$244$			4.24122i			0.271516i
$245$	16.5875	+	22.0863i	1.05974	+	1.41104i
$246$	−2.55882	+	5.78857i	−0.163144	+	0.369065i
$247$	−4.19033	+	7.25786i	−0.266624	+	0.461806i
$248$	−3.54039	−	6.13213i	−0.224815	−	0.389391i
$249$	1.87854	+	17.4273i	0.119048	+	1.10441i
$250$	19.0359	+	10.9904i	1.20394	+	0.695093i
$251$	−16.7337			−1.05622			−0.528110	−	0.849176i	$-0.677099\pi$
$251$	−16.7337			−1.05622			−0.528110	+	0.849176i	$0.677099\pi$
$252$	1.95264	−	7.69332i	0.123005	−	0.484634i
$253$	4.22382			0.265549
$254$	−6.23028	−	3.59705i	−0.390922	−	0.225699i
$255$	3.22120	+	29.8833i	0.201720	+	1.87137i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.46013	+	5.99312i	−0.215837	+	0.373840i	−0.953531	−	0.301295i	$-0.902581\pi$
$257$	−3.46013	+	5.99312i	−0.215837	+	0.373840i	0.737694	+	0.675135i	$0.235915\pi$
$258$	−7.44628	+	16.8450i	−0.463585	+	1.04872i
$259$	−10.9293	+	0.659632i	−0.679115	+	0.0409876i
$260$		−	17.3706i		−	1.07728i
$261$	2.87421	+	13.1772i	0.177909	+	0.815650i
$262$	−1.78814	+	1.03238i	−0.110472	+	0.0637809i
$263$	12.0164	−	6.93767i	0.740963	−	0.427795i	−0.0814565	−	0.996677i	$-0.525957\pi$
$263$	12.0164	−	6.93767i	0.740963	−	0.427795i	0.822419	+	0.568882i	$0.192624\pi$
$264$	5.90721	−	4.31588i	0.363563	−	0.265624i
$265$		−	16.6359i		−	1.02194i
$266$	−2.25107	+	4.50587i	−0.138022	+	0.276272i
$267$	15.3199	+	6.77212i	0.937563	+	0.414447i
$268$	−6.03398	+	10.4512i	−0.368584	+	0.638407i
$269$	−4.87272	−	8.43979i	−0.297095	−	0.514583i	0.678375	−	0.734716i	$-0.262684\pi$
$269$	−4.87272	−	8.43979i	−0.297095	−	0.514583i	−0.975470	+	0.220132i	$0.929351\pi$
$270$	15.3462	+	13.5977i	0.933938	+	0.827531i
$271$	8.55412	+	4.93872i	0.519626	+	0.300006i	0.736782	−	0.676131i	$-0.236345\pi$
$271$	8.55412	+	4.93872i	0.519626	+	0.300006i	−0.217156	+	0.976137i	$0.569678\pi$
$272$	−4.39770			−0.266650
$273$	12.8606	+	15.5423i	0.778356	+	0.940665i
$274$	7.03688			0.425114
$275$	−38.6661	−	22.3239i	−2.33165	−	1.34618i
$276$	−1.72208	+	0.185627i	−0.103657	+	0.0111734i
$277$	−3.17678	−	5.50234i	−0.190874	−	0.330604i	0.754666	−	0.656109i	$-0.227799\pi$
$277$	−3.17678	−	5.50234i	−0.190874	−	0.330604i	−0.945540	+	0.325505i	$0.894466\pi$
$278$	2.85265	−	4.94094i	0.171091	−	0.296338i
$279$	−15.7103	+	14.2976i	−0.940553	+	0.855976i
$280$	−0.628955	−	10.4210i	−0.0375872	−	0.622775i
$281$		−	18.4309i		−	1.09949i	−0.835332	−	0.549746i	$-0.814724\pi$
$281$		−	18.4309i		−	1.09949i	0.835332	−	0.549746i	$-0.185276\pi$
$282$	−5.87835	−	8.04579i	−0.350051	−	0.479120i
$283$	−13.5932	+	7.84804i	−0.808032	+	0.466517i	−0.846272	−	0.532751i	$-0.821158\pi$
$283$	−13.5932	+	7.84804i	−0.808032	+	0.466517i	0.0382402	+	0.999269i	$0.487825\pi$
$284$	2.62424	−	1.51511i	0.155720	−	0.0899050i
$285$	−7.67587	−	10.5061i	−0.454679	−	0.622326i
$286$			18.5939i			1.09948i
$287$	−5.32939	−	8.06594i	−0.314584	−	0.476117i
$288$	−2.21873	+	2.01922i	−0.130740	+	0.118983i
$289$	−1.16990	+	2.02633i	−0.0688177	+	0.119196i
$290$	8.86986	+	15.3630i	0.520856	+	0.902149i
$291$	−26.0679	+	2.80993i	−1.52813	+	0.164721i
$292$	−3.46049	−	1.99791i	−0.202510	−	0.116919i
$293$	16.3071			0.952674			0.476337	−	0.879263i	$-0.341964\pi$
$293$	16.3071			0.952674			0.476337	+	0.879263i	$0.341964\pi$
$294$	8.27808	+	8.85852i	0.482787	+	0.516640i
$295$	56.2464			3.27479
$296$	3.58397	+	2.06920i	0.208314	+	0.120270i
$297$	−16.4268	−	14.5553i	−0.953182	−	0.844582i
$298$	2.86172	+	4.95665i	0.165775	+	0.287131i
$299$	2.20108	−	3.81238i	0.127292	−	0.220475i
$300$	16.7455	+	7.40229i	0.966800	+	0.427371i
$301$	−15.5088	−	23.4722i	−0.893911	−	1.35292i
$302$			1.39330i			0.0801753i
$303$	12.5879	−	9.19689i	0.723157	−	0.528347i
$304$	1.64871	−	0.951881i	0.0945598	−	0.0545941i
$305$	14.4935	−	8.36780i	0.829893	−	0.479139i
$306$	2.81157	+	12.8900i	0.160727	+	0.736875i
$307$			18.7643i			1.07093i	0.844556	+	0.535467i	$0.179864\pi$
$307$			18.7643i			1.07093i	−0.844556	+	0.535467i	$0.820136\pi$
$308$	0.673246	+	11.1549i	0.0383617	+	0.635608i
$309$	9.68681	−	21.9135i	0.551063	−	1.24662i
$310$	−13.9702	+	24.1970i	−0.793452	+	1.37430i
$311$	13.0236	+	22.5576i	0.738503	+	1.27912i	0.953169	+	0.302437i	$0.0978001\pi$
$311$	13.0236	+	22.5576i	0.738503	+	1.27912i	−0.214667	+	0.976687i	$0.568867\pi$
$312$	−0.817159	−	7.58084i	−0.0462625	−	0.429180i
$313$	−14.6376	−	8.45101i	−0.827365	−	0.477679i	0.0255849	−	0.999673i	$-0.491855\pi$
$313$	−14.6376	−	8.45101i	−0.827365	−	0.477679i	−0.852949	+	0.521994i	$0.825189\pi$
$314$	13.1846			0.744050
$315$	−30.1428	+	8.50597i	−1.69835	+	0.479257i
$316$	15.3106			0.861289
$317$	−0.579456	−	0.334549i	−0.0325455	−	0.0187901i	0.483639	−	0.875268i	$-0.339315\pi$
$317$	−0.579456	−	0.334549i	−0.0325455	−	0.0187901i	−0.516184	+	0.856477i	$0.672648\pi$
$318$	−0.782596	−	7.26019i	−0.0438858	−	0.407131i
$319$	−9.49447	−	16.4449i	−0.531588	−	0.920738i
$320$	−1.97297	+	3.41729i	−0.110292	+	0.191032i
$321$	−5.76461	+	13.0407i	−0.321749	+	0.727862i
$322$	1.18243	−	2.36682i	0.0658945	−	0.131898i
$323$		−	8.37218i		−	0.465841i
$324$	7.33699	+	5.21235i	0.407611	+	0.289575i
$325$	−40.2986	+	23.2664i	−2.23537	+	1.29059i
$326$	−1.28830	+	0.743800i	−0.0713523	+	0.0411953i
$327$	−20.0008	+	14.6128i	−1.10605	+	0.808092i
$328$			3.65400i			0.201758i
$329$	15.1933	−	0.916981i	0.837632	−	0.0505548i
$330$	−26.4033	−	11.6715i	−1.45346	−	0.642496i
$331$	−13.6544	+	23.6501i	−0.750512	+	1.29992i	0.197063	+	0.980391i	$0.436860\pi$
$331$	−13.6544	+	23.6501i	−0.750512	+	1.29992i	−0.947575	+	0.319534i	$0.896474\pi$
$332$	5.05998	+	8.76415i	0.277703	+	0.480995i
$333$	3.77369	−	11.8278i	0.206797	−	0.648160i
$334$	−5.74485	−	3.31679i	−0.314344	−	0.181487i
$335$	47.6195			2.60173
$336$	−0.764717	−	4.51832i	−0.0417188	−	0.246495i
$337$	16.6598			0.907517			0.453758	−	0.891125i	$-0.350083\pi$
$337$	16.6598			0.907517			0.453758	+	0.891125i	$0.350083\pi$
$338$	5.52434	+	3.18948i	0.300484	+	0.173485i
$339$	−5.86299	+	0.631988i	−0.318434	+	0.0343249i
$340$	8.67655	+	15.0282i	0.470552	+	0.815020i
$341$	14.9539	−	25.9010i	0.809802	−	1.40262i
$342$	−3.84411	−	4.22393i	−0.207866	−	0.228404i
$343$	−18.2182	+	3.33105i	−0.983692	+	0.179860i
$344$			10.6333i			0.573309i
$345$	4.03195	+	5.51859i	0.217073	+	0.297111i
$346$	9.34637	−	5.39613i	0.502464	−	0.290098i
$347$	2.75433	−	1.59021i	0.147860	−	0.0853671i	−0.424245	−	0.905548i	$-0.639460\pi$
$347$	2.75433	−	1.59021i	0.147860	−	0.0853671i	0.572105	+	0.820180i	$0.306127\pi$
$348$	4.59367	+	6.28742i	0.246246	+	0.337041i
$349$			4.44215i			0.237783i	0.992907	+	0.118891i	$0.0379340\pi$
$349$			4.44215i			0.237783i	−0.992907	+	0.118891i	$0.962066\pi$
$350$	−23.3336	+	15.4171i	−1.24723	+	0.824081i
$351$	−21.6977	+	7.24180i	−1.15813	+	0.386539i
$352$	2.11191	−	3.65793i	0.112565	−	0.194968i
$353$	−18.1183	−	31.3818i	−0.964341	−	1.67029i	−0.711376	−	0.702811i	$-0.751928\pi$
$353$	−18.1183	−	31.3818i	−0.964341	−	1.67029i	−0.252964	−	0.967476i	$-0.581406\pi$
$354$	24.5469	−	2.64597i	1.30465	−	0.140632i
$355$	−10.3551	−	5.97852i	−0.549592	−	0.317307i
$356$	9.67059			0.512540
$357$	−18.8896	−	7.02267i	−0.999745	−	0.371679i
$358$	19.8583			1.04954
$359$	−28.1832	−	16.2716i	−1.48745	−	0.858780i	−0.487553	−	0.873094i	$-0.662110\pi$
$359$	−28.1832	−	16.2716i	−1.48745	−	0.858780i	−0.999898	+	0.0143137i	$0.995444\pi$
$360$	11.2777	+	3.59818i	0.594389	+	0.189641i
$361$	−7.68785	−	13.3157i	−0.404623	−	0.700828i
$362$	3.10101	−	5.37110i	0.162985	−	0.282299i
$363$	10.8367	+	4.79035i	0.568781	+	0.251428i
$364$	10.4191	+	5.20526i	0.546110	+	0.272830i
$365$			15.7673i			0.825299i
$366$	5.93154	−	4.33366i	0.310047	−	0.226524i
$367$	31.5699	−	18.2269i	1.64794	−	0.951436i	0.670045	−	0.742321i	$-0.266275\pi$
$367$	31.5699	−	18.2269i	1.64794	−	0.951436i	0.977891	−	0.209115i	$-0.0670584\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	10.7102	−	2.33610i	0.557549	−	0.121613i
$370$		−	16.3299i		−	0.848953i
$371$	9.97842	+	4.98509i	0.518054	+	0.258813i
$372$	−4.95852	+	11.2172i	−0.257088	+	0.581584i
$373$	−13.0901	+	22.6728i	−0.677782	+	1.17395i	0.297865	+	0.954608i	$0.403725\pi$
$373$	−13.0901	+	22.6728i	−0.677782	+	1.17395i	−0.975647	+	0.219345i	$0.929608\pi$
$374$	−9.28755	−	16.0865i	−0.480248	−	0.831813i
$375$	−4.08023	−	37.8525i	−0.210702	−	1.95470i
$376$	−4.98221	−	2.87648i	−0.256938	−	0.148343i
$377$	−19.7907			−1.01927
$378$	−12.7547	+	5.13014i	−0.656030	+	0.263866i
$379$	26.9998			1.38688			0.693442	−	0.720512i	$-0.256093\pi$
$379$	26.9998			1.38688			0.693442	+	0.720512i	$0.256093\pi$
$380$	−6.50570	−	3.75607i	−0.333735	−	0.192682i
$381$	1.33542	+	12.3888i	0.0684157	+	0.634697i
$382$	2.12569	+	3.68179i	0.108760	+	0.188377i
$383$	−18.8101	+	32.5800i	−0.961150	+	1.66476i	−0.241529	+	0.970394i	$0.577649\pi$
$383$	−18.8101	+	32.5800i	−0.961150	+	1.66476i	−0.719621	+	0.694367i	$0.755685\pi$
$384$	−0.700280	+	1.58417i	−0.0357360	+	0.0808421i
$385$	36.7911	−	24.3089i	1.87505	−	1.23890i
$386$			5.59118i			0.284584i
$387$	31.1671	−	6.79816i	1.58431	−	0.345570i
$388$	−13.1094	+	7.56874i	−0.665531	+	0.384245i
$389$	25.4261	−	14.6798i	1.28916	−	0.744294i	0.310652	−	0.950524i	$-0.399453\pi$
$389$	25.4261	−	14.6798i	1.28916	−	0.744294i	0.978504	+	0.206229i	$0.0661193\pi$
$390$	−24.2937	+	17.7492i	−1.23016	+	0.898768i
$391$			4.39770i			0.222401i
$392$	6.43912	+	2.74549i	0.325225	+	0.138668i
$393$	3.27095	+	1.44591i	0.164998	+	0.0729367i
$394$	0.728629	−	1.26202i	0.0367078	−	0.0635798i
$395$	−30.2074	−	52.3208i	−1.51990	−	2.63254i
$396$	−12.0719	−	3.85156i	−0.606636	−	0.193548i
$397$	12.1921	+	7.03912i	0.611905	+	0.353284i	0.773711	−	0.633539i	$-0.218398\pi$
$397$	12.1921	+	7.03912i	0.611905	+	0.353284i	−0.161806	+	0.986823i	$0.551732\pi$
$398$	20.0978			1.00741
$399$	8.60180	−	1.45584i	0.430629	−	0.0728832i
$400$	10.5705			0.528524
$401$	−14.7318	−	8.50543i	−0.735672	−	0.424741i	0.0848213	−	0.996396i	$-0.472968\pi$
$401$	−14.7318	−	8.50543i	−0.735672	−	0.424741i	−0.820494	+	0.571656i	$0.806301\pi$
$402$	20.7819	−	2.24014i	1.03651	−	0.111728i
$403$	−15.5853	−	26.9946i	−0.776361	−	1.34470i
$404$	4.50036	−	7.79485i	0.223901	−	0.387808i
$405$	3.33641	−	35.3564i	0.165787	−	1.75687i
$406$	−11.8729	+	0.716579i	−0.589240	+	0.0355632i
$407$			17.4799i			0.866445i
$408$	4.49355	+	6.15040i	0.222464	+	0.304490i
$409$	−7.78474	+	4.49452i	−0.384931	+	0.222240i	−0.679961	−	0.733248i	$-0.738003\pi$
$409$	−7.78474	+	4.49452i	−0.384931	+	0.222240i	0.295031	+	0.955488i	$0.404670\pi$
$410$	12.4868	−	7.20923i	0.616677	−	0.356038i
$411$	−7.19026	−	9.84141i	−0.354669	−	0.485441i
$412$		−	13.8328i		−	0.681492i
$413$	−16.8547	+	33.7373i	−0.829366	+	1.66010i
$414$	2.01922	+	2.21873i	0.0992391	+	0.109045i
$415$	19.9664	−	34.5828i	0.980112	−	1.69760i
$416$	−2.20108	−	3.81238i	−0.107917	−	0.186917i
$417$	−9.82497	+	1.05906i	−0.481131	+	0.0518624i
$418$	6.96383	+	4.02057i	0.340612	+	0.196652i
$419$	10.8623			0.530658			0.265329	−	0.964158i	$-0.414519\pi$
$419$	10.8623			0.530658			0.265329	+	0.964158i	$0.414519\pi$
$420$	−13.9316	+	11.5278i	−0.679794	+	0.562498i
$421$	−3.62117			−0.176485			−0.0882424	−	0.996099i	$-0.528125\pi$
$421$	−3.62117			−0.176485			−0.0882424	+	0.996099i	$0.528125\pi$
$422$	24.7565	+	14.2932i	1.20513	+	0.695782i
$423$	−5.24595	+	16.4423i	−0.255067	+	0.799452i
$424$	−2.10798	−	3.65112i	−0.102372	−	0.177314i
$425$	23.2429	−	40.2579i	1.12745	−	1.95279i
$426$	−4.80038	−	2.12200i	−0.232579	−	0.102811i
$427$	0.676019	+	11.2008i	0.0327149	+	0.542046i
$428$			8.23187i			0.397902i
$429$	26.0044	−	18.9991i	1.25551	−	0.917287i
$430$	36.3370	−	20.9792i	1.75233	−	1.01171i
$431$	−3.57964	+	2.06670i	−0.172425	+	0.0995496i	−0.583729	−	0.811949i	$-0.698407\pi$
$431$	−3.57964	+	2.06670i	−0.172425	+	0.0995496i	0.411304	+	0.911498i	$0.365074\pi$
$432$	5.09106	+	1.03977i	0.244944	+	0.0500261i
$433$			24.9503i			1.19904i	0.800362	+	0.599518i	$0.204641\pi$
$433$			24.9503i			1.19904i	−0.800362	+	0.599518i	$0.795359\pi$
$434$	−10.3274	−	15.6303i	−0.495731	−	0.750279i
$435$	12.4228	−	28.1028i	0.595626	−	1.34743i
$436$	−7.15057	+	12.3852i	−0.342450	+	0.593142i
$437$	−0.951881	−	1.64871i	−0.0455346	−	0.0788683i
$438$	0.741734	+	6.88112i	0.0354414	+	0.328792i
$439$	−19.6009	−	11.3166i	−0.935499	−	0.540111i	−0.0469524	−	0.998897i	$-0.514951\pi$
$439$	−19.6009	−	11.3166i	−0.935499	−	0.540111i	−0.888547	+	0.458787i	$0.848284\pi$
$440$	−16.6669			−0.794565
$441$	3.93056	−	20.6289i	0.187170	−	0.982328i
$442$	−19.3594			−0.920831
$443$	1.81833	+	1.04981i	0.0863915	+	0.0498782i	0.542573	−	0.840008i	$-0.317450\pi$
$443$	1.81833	+	1.04981i	0.0863915	+	0.0498782i	−0.456182	+	0.889887i	$0.650783\pi$
$444$	−0.768201	−	7.12665i	−0.0364572	−	0.338216i
$445$	−19.0798	−	33.0472i	−0.904470	−	1.56659i
$446$	3.61459	−	6.26065i	0.171156	−	0.296451i
$447$	4.00801	−	9.06693i	0.189572	−	0.428851i
$448$	−1.45851	−	2.20743i	−0.0689082	−	0.104291i
$449$		−	27.0596i		−	1.27702i	−0.769613	−	0.638511i	$-0.779551\pi$
$449$		−	27.0596i		−	1.27702i	0.769613	−	0.638511i	$-0.220449\pi$
$450$	−6.75800	−	30.9829i	−0.318575	−	1.46055i
$451$	−13.3661	+	7.71690i	−0.629383	+	0.363375i
$452$	−2.94848	+	1.70230i	−0.138685	+	0.0800697i
$453$	1.94859	−	1.42367i	0.0915529	−	0.0668897i
$454$		−	6.06553i		−	0.284669i
$455$	−2.76876	−	45.8749i	−0.129801	−	2.15065i
$456$	−3.01589	−	1.33317i	−0.141232	−	0.0624312i
$457$	16.2362	−	28.1219i	0.759496	−	1.31549i	−0.183612	−	0.982999i	$-0.558779\pi$
$457$	16.2362	−	28.1219i	0.759496	−	1.31549i	0.943108	−	0.332487i	$-0.107888\pi$
$458$	−1.35131	−	2.34054i	−0.0631427	−	0.109366i
$459$	15.1545	−	17.1031i	0.707351	−	0.798305i
$460$	3.41729	+	1.97297i	0.159332	+	0.0919903i
$461$	−16.1636			−0.752814			−0.376407	−	0.926454i	$-0.622840\pi$
$461$	−16.1636			−0.752814			−0.376407	+	0.926454i	$0.622840\pi$
$462$	14.9127	−	12.3396i	0.693801	−	0.574088i
$463$	−5.69669			−0.264748			−0.132374	−	0.991200i	$-0.542260\pi$
$463$	−5.69669			−0.264748			−0.132374	+	0.991200i	$0.542260\pi$
$464$	3.89338	+	2.24784i	0.180745	+	0.104353i
$465$	48.1154	−	5.18649i	2.23130	−	0.240518i
$466$	4.57807	+	7.92945i	0.212075	+	0.367325i
$467$	−11.8710	+	20.5612i	−0.549326	+	0.951460i	0.448995	+	0.893534i	$0.351782\pi$
$467$	−11.8710	+	20.5612i	−0.549326	+	0.951460i	−0.998321	+	0.0579258i	$0.981551\pi$
$468$	−9.76719	+	8.88890i	−0.451489	+	0.410890i
$469$	−14.2696	+	28.5627i	−0.658908	+	1.31890i
$470$			22.7009i			1.04711i
$471$	−13.4720	−	18.4393i	−0.620755	−	0.849637i
$472$	12.3445	−	7.12712i	0.568203	−	0.328052i
$473$	−38.8959	+	22.4565i	−1.78843	+	1.03255i
$474$	−15.6443	−	21.4126i	−0.718567	−	0.983514i
$475$			20.1237i			0.923337i
$476$	−11.6141	+	0.700962i	−0.532331	+	0.0321285i
$477$	−9.35407	+	8.51293i	−0.428293	+	0.389780i
$478$	−8.45939	+	14.6521i	−0.386923	+	0.670171i
$479$	4.34917	+	7.53299i	0.198719	+	0.344191i	0.948113	−	0.317933i	$-0.102989\pi$
$479$	4.34917	+	7.53299i	0.198719	+	0.344191i	−0.749394	+	0.662124i	$0.769655\pi$
$480$	6.79521	−	0.732474i	0.310158	−	0.0334327i
$481$	15.7772	+	9.10896i	0.719377	+	0.415333i
$482$	22.4982			1.02476
$483$	−4.51832	+	0.764717i	−0.205591	+	0.0347959i
$484$	6.84062			0.310937
$485$	51.7291	+	29.8658i	2.34890	+	1.35614i
$486$	−0.207192	−	15.5871i	−0.00939841	−	0.707044i
$487$	9.99684	+	17.3150i	0.453000	+	0.784619i	0.998571	−	0.0534458i	$-0.0170204\pi$
$487$	9.99684	+	17.3150i	0.453000	+	0.784619i	−0.545571	+	0.838065i	$0.683687\pi$
$488$	2.12061	−	3.67300i	0.0959955	−	0.166269i
$489$	2.35662	+	1.04174i	0.106570	+	0.0471089i
$490$	−3.32207	−	27.4211i	−0.150076	−	1.23876i
$491$			0.211264i			0.00953422i	0.999989	+	0.00476711i	$0.00151742\pi$
$491$			0.211264i			0.00953422i	−0.999989	+	0.00476711i	$0.998483\pi$
$492$	5.11028	−	3.73364i	0.230389	−	0.168325i
$493$	17.1219	−	9.88534i	0.771132	−	0.445213i
$494$	7.25786	−	4.19033i	0.326546	−	0.188532i
$495$	10.6556	+	48.8522i	0.478935	+	2.19574i
$496$			7.08078i			0.317936i
$497$	6.68898	−	4.41960i	0.300042	−	0.198246i
$498$	7.08681	−	16.0318i	0.317567	−	0.718402i
$499$	1.82865	−	3.16732i	0.0818617	−	0.141789i	−0.822188	−	0.569216i	$-0.807247\pi$
$499$	1.82865	−	3.16732i	0.0818617	−	0.141789i	0.904050	+	0.427428i	$0.140580\pi$
$500$	−10.9904	−	19.0359i	−0.491505	−	0.851311i
$501$	1.23137	+	11.4235i	0.0550136	+	0.510365i
$502$	14.4918	+	8.36683i	0.646800	+	0.373430i
$503$	−14.5422			−0.648406			−0.324203	−	0.945988i	$-0.605096\pi$
$503$	−14.5422			−0.648406			−0.324203	+	0.945988i	$0.605096\pi$
$504$	−5.53770	+	5.68629i	−0.246669	+	0.253288i
$505$	−35.5163			−1.58045
$506$	−3.65793	−	2.11191i	−0.162615	−	0.0938858i
$507$	−1.18411	−	10.9850i	−0.0525880	−	0.487863i
$508$	3.59705	+	6.23028i	0.159593	+	0.276424i
$509$	−14.0615	+	24.3552i	−0.623263	+	1.07952i	0.365611	+	0.930768i	$0.380860\pi$
$509$	−14.0615	+	24.3552i	−0.623263	+	1.07952i	−0.988874	+	0.148756i	$0.952473\pi$
$510$	12.1520	−	27.4903i	0.538100	−	1.21729i
$511$	−9.45742	−	4.72481i	−0.418371	−	0.209013i
$512$			1.00000i			0.0441942i
$513$	−1.97948	+	9.69216i	−0.0873962	+	0.427919i
$514$	5.99312	−	3.46013i	0.264345	−	0.152620i
$515$	−47.2706	+	27.2917i	−2.08299	+	1.20261i
$516$	14.8712	−	10.8650i	0.654666	−	0.478307i
$517$		−	24.2995i		−	1.06869i
$518$	9.79488	+	4.89340i	0.430362	+	0.215004i
$519$	−17.0968	−	7.55760i	−0.750467	−	0.331742i
$520$	−8.68532	+	15.0434i	−0.380877	+	0.659698i
$521$	4.16034	+	7.20593i	0.182268	+	0.315697i	0.942653	−	0.333776i	$-0.108323\pi$
$521$	4.16034	+	7.20593i	0.182268	+	0.315697i	−0.760385	+	0.649473i	$0.774990\pi$
$522$	4.09947	−	12.8489i	0.179429	−	0.562382i
$523$	7.05397	+	4.07261i	0.308449	+	0.178083i	0.646232	−	0.763141i	$-0.276344\pi$
$523$	7.05397	+	4.07261i	0.308449	+	0.178083i	−0.337783	+	0.941224i	$0.609677\pi$
$524$	2.06477			0.0901998
$525$	45.4037	+	16.8799i	1.98158	+	0.736701i
$526$	−13.8753			−0.604994
$527$	26.9673	+	15.5696i	1.17471	+	0.678222i
$528$	−7.27373	+	0.784055i	−0.316548	+	0.0341216i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−8.31796	+	14.4071i	−0.361309	+	0.625806i
$531$	−28.7824	−	31.6263i	−1.24905	−	1.37247i
$532$	4.20242	−	2.77666i	0.182198	−	0.120383i
$533$			16.0854i			0.696738i
$534$	−9.88137	−	13.5248i	−0.427609	−	0.585275i
$535$	28.1307	−	16.2412i	1.21619	−	0.702170i
$536$	10.4512	−	6.03398i	0.451422	−	0.260628i
$537$	−20.2911	−	27.7727i	−0.875625	−	1.19848i
$538$			9.74544i			0.420156i
$539$	3.55601	+	29.3521i	0.153168	+	1.26428i
$540$	−6.49131	−	19.4491i	−0.279342	−	0.836954i
$541$	4.27728	−	7.40846i	0.183895	−	0.318515i	−0.759309	−	0.650730i	$-0.774463\pi$
$541$	4.27728	−	7.40846i	0.183895	−	0.318515i	0.943203	+	0.332216i	$0.107796\pi$
$542$	−4.93872	−	8.55412i	−0.212136	−	0.367431i
$543$	−10.6803	+	1.15126i	−0.458337	+	0.0494054i
$544$	3.80852	+	2.19885i	0.163289	+	0.0942750i
$545$	56.4315			2.41726
$546$	−3.36640	−	19.8903i	−0.144069	−	0.851228i
$547$	24.8905			1.06424			0.532121	−	0.846668i	$-0.321395\pi$
$547$	24.8905			1.06424			0.532121	+	0.846668i	$0.321395\pi$
$548$	−6.09412	−	3.51844i	−0.260328	−	0.150300i
$549$	−12.1216	−	3.86743i	−0.517339	−	0.165058i
$550$	22.3239	+	38.6661i	0.951893	+	1.64873i
$551$	−4.27935	+	7.41206i	−0.182307	+	0.315764i
$552$	1.58417	+	0.700280i	0.0674269	+	0.0298059i
$553$	40.4345	−	2.44040i	1.71945	−	0.103776i
$554$			6.35356i			0.269937i
$555$	−22.8382	+	16.6858i	−0.969427	+	0.708275i
$556$	−4.94094	+	2.85265i	−0.209543	+	0.120979i
$557$	−24.6759	+	14.2466i	−1.04555	+	0.603649i	−0.921400	−	0.388615i	$-0.872954\pi$
$557$	−24.6759	+	14.2466i	−1.04555	+	0.603649i	−0.124150	+	0.992263i	$0.539620\pi$
$558$	20.7544	−	4.52694i	0.878602	−	0.191641i
$559$			46.8094i			1.97983i
$560$	−4.66582	+	9.33935i	−0.197167	+	0.394659i
$561$	−13.0078	+	29.4262i	−0.549188	+	1.24237i
$562$	−9.21543	+	15.9616i	−0.388729	+	0.673299i
$563$	18.6929	+	32.3771i	0.787812	+	1.36453i	0.927305	+	0.374307i	$0.122120\pi$
$563$	18.6929	+	32.3771i	0.787812	+	1.36453i	−0.139493	+	0.990223i	$0.544547\pi$
$564$	1.06791	+	9.90704i	0.0449670	+	0.417162i
$565$	11.6345	+	6.71720i	0.489468	+	0.282595i
$566$	15.6961			0.659755
$567$	20.2074	+	12.5961i	0.848631	+	0.528985i
$568$	−3.03021			−0.127145
$569$	3.96158	+	2.28722i	0.166078	+	0.0958853i	0.580735	−	0.814092i	$-0.302765\pi$
$569$	3.96158	+	2.28722i	0.166078	+	0.0958853i	−0.414657	+	0.909978i	$0.636098\pi$
$570$	1.39446	+	12.9365i	0.0584073	+	0.541849i
$571$	0.639897	+	1.10833i	0.0267788	+	0.0463823i	0.879104	−	0.476630i	$-0.158142\pi$
$571$	0.639897	+	1.10833i	0.0267788	+	0.0463823i	−0.852325	+	0.523012i	$0.824808\pi$
$572$	9.29694	−	16.1028i	0.388725	−	0.673291i
$573$	2.97715	−	6.73491i	0.124372	−	0.281355i
$574$	0.582420	+	9.65000i	0.0243098	+	0.402783i
$575$		−	10.5705i		−	0.440819i
$576$	2.93109	−	0.639328i	0.122129	−	0.0266387i
$577$	−19.8503	+	11.4606i	−0.826380	+	0.477110i	−0.852611	−	0.522545i	$-0.824982\pi$
$577$	−19.8503	+	11.4606i	−0.826380	+	0.477110i	0.0262319	+	0.999656i	$0.491649\pi$
$578$	2.02633	−	1.16990i	0.0842841	−	0.0486614i
$579$	7.81953	−	5.71304i	0.324969	−	0.237426i
$580$		−	17.7397i		−	0.736601i
$581$	14.7601	+	22.3391i	0.612351	+	0.926783i
$582$	23.9804	+	10.6005i	0.994020	+	0.439404i
$583$	8.90371	−	15.4217i	0.368754	−	0.638700i
$584$	1.99791	+	3.46049i	0.0826743	+	0.143196i
$585$	49.6463	+	15.8397i	2.05262	+	0.654893i
$586$	−14.1224	−	8.15357i	−0.583391	−	0.336821i
$587$	25.2253			1.04116			0.520580	−	0.853813i	$-0.325716\pi$
$587$	25.2253			1.04116			0.520580	+	0.853813i	$0.325716\pi$
$588$	−2.73976	−	11.8107i	−0.112986	−	0.487067i
$589$	−13.4801			−0.555438
$590$	−48.7109	−	28.1232i	−2.00539	−	1.15781i
$591$	−2.50951	+	0.270507i	−0.103227	+	0.0111272i
$592$	−2.06920	−	3.58397i	−0.0850438	−	0.147300i
$593$	−2.91383	+	5.04691i	−0.119657	+	0.207252i	−0.919632	−	0.392782i	$-0.871513\pi$
$593$	−2.91383	+	5.04691i	−0.119657	+	0.207252i	0.799975	+	0.600033i	$0.204846\pi$
$594$	6.94843	+	20.8186i	0.285097	+	0.854199i
$595$	25.3097	+	38.3057i	1.03760	+	1.57038i
$596$		−	5.72344i		−	0.234441i
$597$	−20.5358	−	28.1077i	−0.840476	−	1.15037i
$598$	−3.81238	+	2.20108i	−0.155900	+	0.0900087i
$599$	25.6272	−	14.7959i	1.04710	−	0.604544i	0.125264	−	0.992123i	$-0.460022\pi$
$599$	25.6272	−	14.7959i	1.04710	−	0.604544i	0.921836	+	0.387580i	$0.126689\pi$
$600$	−10.8009	−	14.7833i	−0.440943	−	0.603526i
$601$			24.9708i			1.01858i	0.860595	+	0.509290i	$0.170092\pi$
$601$			24.9708i			1.01858i	−0.860595	+	0.509290i	$0.829908\pi$
$602$	1.69487	+	28.0819i	0.0690777	+	1.14453i
$603$	−24.3678	−	26.7756i	−0.992335	−	1.09039i
$604$	0.696649	−	1.20663i	0.0283463	−	0.0490972i
$605$	−13.4964	−	23.3764i	−0.548705	−	0.950384i
$606$	−15.4999	+	1.67078i	−0.629641	+	0.0678707i
$607$	−28.3776	−	16.3838i	−1.15181	−	0.664999i	−0.202483	−	0.979286i	$-0.564901\pi$
$607$	−28.3776	−	16.3838i	−1.15181	−	0.664999i	−0.949328	+	0.314287i	$0.898235\pi$
$608$	−1.90376			−0.0772077
$609$	13.1338	+	15.8725i	0.532208	+	0.643188i
$610$	−16.7356			−0.677605
$611$	−21.9325	−	12.6627i	−0.887293	−	0.512279i
$612$	4.01013	−	12.5689i	0.162100	−	0.508067i
$613$	−12.2108	−	21.1498i	−0.493190	−	0.854231i	0.506779	−	0.862076i	$-0.330836\pi$
$613$	−12.2108	−	21.1498i	−0.493190	−	0.854231i	−0.999969	+	0.00784537i	$0.997503\pi$
$614$	9.38214	−	16.2503i	0.378632	−	0.655811i
$615$	−22.8414	−	10.0970i	−0.921052	−	0.407149i
$616$	4.99439	−	9.99702i	0.201230	−	0.402791i
$617$			28.1827i			1.13459i	0.823514	+	0.567296i	$0.192010\pi$
$617$			28.1827i			1.13459i	−0.823514	+	0.567296i	$0.807990\pi$
$618$	−19.3458	+	14.1343i	−0.778201	+	0.568563i
$619$	37.7681	−	21.8054i	1.51803	−	0.876433i	0.518252	−	0.855228i	$-0.326583\pi$
$619$	37.7681	−	21.8054i	1.51803	−	0.876433i	0.999775	−	0.0212050i	$-0.00675026\pi$
$620$	24.1970	−	13.9702i	0.971777	−	0.561056i
$621$	1.03977	−	5.09106i	0.0417246	−	0.204297i
$622$		−	26.0473i		−	1.04440i
$623$	25.5395	−	1.54142i	1.02322	−	0.0617558i
$624$	−3.08274	+	6.97378i	−0.123408	+	0.279175i
$625$	−16.9412	+	29.3431i	−0.677650	+	1.17372i
$626$	8.45101	+	14.6376i	0.337770	+	0.585035i
$627$	−1.49265	−	13.8474i	−0.0596108	−	0.553014i
$628$	−11.4182	−	6.59230i	−0.455636	−	0.263061i
$629$	−18.1995			−0.725662
$630$	30.3574	+	7.70501i	1.20947	+	0.306975i
$631$	−24.8004			−0.987289			−0.493644	−	0.869664i	$-0.664336\pi$
$631$	−24.8004			−0.987289			−0.493644	+	0.869664i	$0.664336\pi$
$632$	−13.2594	−	7.65531i	−0.527430	−	0.304512i
$633$	−5.30641	−	49.2279i	−0.210911	−	1.95663i
$634$	0.334549	+	0.579456i	0.0132866	+	0.0230131i
$635$	14.1938	−	24.5843i	0.563263	−	0.975599i
$636$	−2.95235	+	6.67881i	−0.117068	+	0.264832i
$637$	28.3460	+	12.0861i	1.12311	+	0.478868i
$638$			18.9889i			0.751779i
$639$	1.93730	+	8.88181i	0.0766383	+	0.351359i
$640$	3.41729	−	1.97297i	0.135080	−	0.0779886i
$641$	−19.3357	+	11.1635i	−0.763716	+	0.440931i	−0.830628	−	0.556827i	$-0.812018\pi$
$641$	−19.3357	+	11.1635i	−0.763716	+	0.440931i	0.0669126	+	0.997759i	$0.478685\pi$
$642$	11.5127	−	8.41128i	0.454368	−	0.331967i
$643$		−	46.2731i		−	1.82483i	−0.409265	−	0.912416i	$-0.634215\pi$
$643$		−	46.2731i		−	1.82483i	0.409265	−	0.912416i	$-0.365785\pi$
$644$	−2.20743	+	1.45851i	−0.0869849	+	0.0574734i
$645$	−66.4694	−	29.3826i	−2.61723	−	1.15694i
$646$	−4.18609	+	7.25052i	−0.164700	+	0.285268i
$647$	0.0209456	+	0.0362789i	0.000823458	+	0.00142627i	0.866437	−	0.499287i	$-0.166405\pi$
$647$	0.0209456	+	0.0362789i	0.000823458	+	0.00142627i	−0.865613	+	0.500713i	$0.833071\pi$
$648$	−3.74785	−	8.18252i	−0.147229	−	0.321440i
$649$	52.1411	+	30.1037i	2.04672	+	1.18167i
$650$	46.5328			1.82517
$651$	−11.3073	+	30.4143i	−0.443166	+	1.19203i
$652$	1.48760			0.0582589
$653$	41.3097	+	23.8502i	1.61657	+	0.933329i	0.987798	+	0.155743i	$0.0497771\pi$
$653$	41.3097	+	23.8502i	1.61657	+	0.933329i	0.628776	+	0.777586i	$0.283556\pi$
$654$	24.6277	−	2.65468i	0.963017	−	0.103806i
$655$	−4.07373	−	7.05590i	−0.159174	−	0.275697i
$656$	1.82700	−	3.16445i	0.0713323	−	0.123551i
$657$	8.86567	−	8.06844i	0.345883	−	0.314780i
$658$	−13.6162	−	6.80250i	−0.530817	−	0.265189i
$659$		−	34.3309i		−	1.33734i	−0.743559	−	0.668670i	$-0.766864\pi$
$659$		−	34.3309i		−	1.33734i	0.743559	−	0.668670i	$-0.233136\pi$
$660$	17.0302	+	23.3095i	0.662900	+	0.907321i
$661$	−9.08092	+	5.24287i	−0.353207	+	0.203924i	−0.666097	−	0.745865i	$-0.732036\pi$
$661$	−9.08092	+	5.24287i	−0.353207	+	0.203924i	0.312890	+	0.949789i	$0.398703\pi$
$662$	23.6501	−	13.6544i	0.919186	−	0.530692i
$663$	19.7813	+	27.0750i	0.768243	+	1.05151i
$664$		−	10.1200i		−	0.392731i
$665$	−17.7799	−	8.88261i	−0.689475	−	0.344453i
$666$	−9.18201	+	8.35634i	−0.355796	+	0.323802i
$667$	2.24784	−	3.89338i	0.0870368	−	0.150752i
$668$	3.31679	+	5.74485i	0.128330	+	0.222275i
$669$	−12.4492	+	1.34193i	−0.481314	+	0.0518821i
$670$	−41.2397	−	23.8098i	−1.59323	−	0.919851i
$671$	17.9141			0.691567
$672$	−1.59689	+	4.29534i	−0.0616016	+	0.165696i
$673$	48.4423			1.86731			0.933656	−	0.358170i	$-0.116599\pi$
$673$	48.4423			1.86731			0.933656	+	0.358170i	$0.116599\pi$
$674$	−14.4278	−	8.32989i	−0.555738	−	0.320856i
$675$	−36.4258	+	41.1096i	−1.40203	+	1.58231i
$676$	−3.18948	−	5.52434i	−0.122672	−	0.212475i
$677$	−2.01964	+	3.49812i	−0.0776211	+	0.134444i	−0.902223	−	0.431270i	$-0.858066\pi$
$677$	−2.01964	+	3.49812i	−0.0776211	+	0.134444i	0.824602	+	0.565713i	$0.191399\pi$
$678$	5.39349	+	2.38418i	0.207136	+	0.0915638i
$679$	−33.4149	+	22.0782i	−1.28235	+	0.847283i
$680$		−	17.3531i		−	0.665461i
$681$	−8.48292	+	6.19773i	−0.325066	+	0.237497i
$682$	−25.9010	+	14.9539i	−0.991800	+	0.572616i
$683$	19.6888	−	11.3673i	0.753371	−	0.434959i	−0.0735396	−	0.997292i	$-0.523430\pi$
$683$	19.6888	−	11.3673i	0.753371	−	0.434959i	0.826911	+	0.562333i	$0.190096\pi$
$684$	1.21713	+	5.58009i	0.0465380	+	0.213360i
$685$			27.7671i			1.06093i
$686$	17.4430	+	6.22434i	0.665976	+	0.237647i
$687$	−1.89259	+	4.28143i	−0.0722070	+	0.163347i
$688$	5.31665	−	9.20870i	0.202695	−	0.351078i
$689$	−9.27964	−	16.0728i	−0.353526	−	0.612325i
$690$	−0.732474	−	6.79521i	−0.0278848	−	0.258689i
$691$	35.8455	+	20.6954i	1.36363	+	0.787290i	0.990105	−	0.140331i	$-0.0448168\pi$
$691$	35.8455	+	20.6954i	1.36363	+	0.787290i	0.373522	+	0.927621i	$0.378150\pi$
$692$	−10.7923			−0.410260
$693$	−32.4952	−	8.24760i	−1.23439	−	0.313300i
$694$	−3.18043			−0.120727
$695$	19.4967	+	11.2564i	0.739551	+	0.426980i
$696$	−0.834521	−	7.74190i	−0.0316324	−	0.293456i
$697$	−8.03460	−	13.9163i	−0.304332	−	0.527118i
$698$	2.22107	−	3.84701i	0.0840689	−	0.145612i
$699$	6.41186	−	14.5049i	0.242519	−	0.548627i
$700$	27.9160	−	1.68486i	1.05513	−	0.0636816i
$701$			29.5368i			1.11559i	0.829979	+	0.557794i	$0.188352\pi$
$701$			29.5368i			1.11559i	−0.829979	+	0.557794i	$0.811648\pi$
$702$	22.4116	+	4.57724i	0.845872	+	0.172757i
$703$	6.82302	−	3.93927i	0.257335	−	0.148572i
$704$	−3.65793	+	2.11191i	−0.137863	+	0.0795955i
$705$	31.7482	−	23.1956i	1.19571	−	0.873599i
$706$			36.2366i			1.36378i
$707$	10.6428	−	21.3031i	0.400262	−	0.801185i
$708$	−22.5812	−	9.98196i	−0.848654	−	0.375145i
$709$	−4.19632	+	7.26824i	−0.157596	+	0.272965i	−0.934001	−	0.357270i	$-0.883708\pi$
$709$	−4.19632	+	7.26824i	−0.157596	+	0.272965i	0.776405	+	0.630234i	$0.217041\pi$
$710$	5.97852	+	10.3551i	0.224370	+	0.388620i
$711$	−13.9613	+	43.7586i	−0.523588	+	1.64108i
$712$	−8.37498	−	4.83530i	−0.313866	−	0.181210i
$713$	7.08078			0.265177
$714$	12.8476	+	15.5266i	0.480808	+	0.581069i
$715$	−73.3704			−2.74390
$716$	−17.1978	−	9.92914i	−0.642711	−	0.371069i
$717$	29.1354	−	3.14058i	1.08808	−	0.117287i
$718$	16.2716	+	28.1832i	0.607249	+	1.05179i
$719$	5.48624	−	9.50244i	0.204602	−	0.354381i	−0.745404	−	0.666613i	$-0.767743\pi$
$719$	5.48624	−	9.50244i	0.204602	−	0.354381i	0.950006	+	0.312232i	$0.101077\pi$
$720$	−7.96771	−	8.75498i	−0.296939	−	0.326279i
$721$	−2.20484	−	36.5316i	−0.0821127	−	1.36051i
$722$			15.3757i			0.572224i
$723$	−22.9885	−	31.4648i	−0.854953	−	1.17019i
$724$	−5.37110	+	3.10101i	−0.199616	+	0.115248i
$725$	−41.1548	+	23.7607i	−1.52845	+	0.882452i
$726$	−6.98971	−	9.56693i	−0.259413	−	0.355062i
$727$			5.92737i			0.219834i	0.993941	+	0.109917i	$0.0350585\pi$
$727$			5.92737i			0.219834i	−0.993941	+	0.109917i	$0.964941\pi$
$728$	−6.42059	−	9.71744i	−0.237963	−	0.360152i
$729$	−21.5876	+	16.2166i	−0.799539	+	0.600614i
$730$	7.88366	−	13.6549i	0.291787	−	0.505390i
$731$	−23.3810	−	40.4971i	−0.864779	−	1.49784i
$732$	−7.30370	+	0.787285i	−0.269952	+	0.0290989i
$733$	39.3249	+	22.7042i	1.45250	+	0.838600i	0.998623	−	0.0524646i	$-0.0167077\pi$
$733$	39.3249	+	22.7042i	1.45250	+	0.838600i	0.453876	+	0.891065i	$0.350041\pi$
$734$	−36.4538			−1.34553
$735$	−34.9552	+	32.6648i	−1.28934	+	1.20486i
$736$	1.00000			0.0368605
$737$	44.1438	+	25.4864i	1.62606	+	0.938805i
$738$	−10.4433	−	3.33196i	−0.384424	−	0.122651i
$739$	−7.36063	−	12.7490i	−0.270765	−	0.468979i	0.698293	−	0.715812i	$-0.253943\pi$
$739$	−7.36063	−	12.7490i	−0.270765	−	0.468979i	−0.969058	+	0.246833i	$0.920610\pi$
$740$	−8.16496	+	14.1421i	−0.300150	+	0.519875i
$741$	−13.2764	−	5.86880i	−0.487721	−	0.215596i
$742$	−6.14902	−	9.30642i	−0.225737	−	0.341650i
$743$		−	42.2846i		−	1.55127i	−0.631180	−	0.775637i	$-0.717429\pi$
$743$		−	42.2846i		−	1.55127i	0.631180	−	0.775637i	$-0.282571\pi$
$744$	9.90280	−	7.23510i	0.363054	−	0.265252i
$745$	−19.5586	+	11.2922i	−0.716573	+	0.413714i
$746$	22.6728	−	13.0901i	0.830110	−	0.479264i
$747$	−29.6625	+	6.46998i	−1.08529	+	0.236724i
$748$			18.5751i			0.679173i
$749$	1.31210	+	21.7399i	0.0479431	+	0.794359i
$750$	−15.3927	+	34.8214i	−0.562061	+	1.27150i
$751$	−4.94135	+	8.55866i	−0.180312	+	0.312310i	−0.941987	−	0.335650i	$-0.891044\pi$
$751$	−4.94135	+	8.55866i	−0.180312	+	0.312310i	0.761675	+	0.647960i	$0.224378\pi$
$752$	2.87648	+	4.98221i	0.104895	+	0.181683i
$753$	−3.10622	−	28.8166i	−0.113197	−	1.05014i
$754$	17.1392	+	9.89534i	0.624174	+	0.360367i
$755$	−5.49788			−0.200088
$756$	13.6109	+	1.93451i	0.495025	+	0.0703573i
$757$	−12.3001			−0.447053			−0.223527	−	0.974698i	$-0.571757\pi$
$757$	−12.3001			−0.447053			−0.223527	+	0.974698i	$0.571757\pi$
$758$	−23.3825	−	13.4999i	−0.849290	−	0.490338i
$759$	0.784055	+	7.27373i	0.0284594	+	0.264020i
$760$	3.75607	+	6.50570i	0.136247	+	0.235987i
$761$	2.21651	−	3.83910i	0.0803483	−	0.139167i	−0.823051	−	0.567967i	$-0.807730\pi$
$761$	2.21651	−	3.83910i	0.0803483	−	0.139167i	0.903400	+	0.428800i	$0.141063\pi$
$762$	5.03789	−	11.3967i	0.182503	−	0.412860i
$763$	−16.9102	+	33.8483i	−0.612189	+	1.22539i
$764$		−	4.25137i		−	0.153809i
$765$	−50.8634	+	11.0943i	−1.83897	+	0.401116i
$766$	32.5800	−	18.8101i	1.17716	−	0.679636i
$767$	54.3426	−	31.3747i	1.96220	−	1.13287i
$768$	1.39855	−	1.02180i	0.0504657	−	0.0368709i
$769$			16.2983i			0.587733i	0.955846	+	0.293867i	$0.0949422\pi$
$769$			16.2983i			0.587733i	−0.955846	+	0.293867i	$0.905058\pi$
$770$	−44.0165	+	2.65659i	−1.58624	+	0.0957368i
$771$	−10.9629	−	4.84611i	−0.394819	−	0.174529i
$772$	2.79559	−	4.84211i	0.100616	−	0.174271i
$773$	19.8210	+	34.3310i	0.712913	+	1.23480i	0.963759	+	0.266775i	$0.0859580\pi$
$773$	19.8210	+	34.3310i	0.712913	+	1.23480i	−0.250846	+	0.968027i	$0.580709\pi$
$774$	−30.3906	−	9.69616i	−1.09237	−	0.348521i
$775$	−64.8195	−	37.4236i	−2.32839	−	1.34429i
$776$	15.1375			0.543404
$777$	−3.16471	−	18.6987i	−0.113533	−	0.670810i
$778$	−29.3596			−1.05259
$779$	6.02436	+	3.47817i	0.215845	+	0.124618i
$780$	29.9136	−	3.22446i	1.07108	−	0.115454i
$781$	−6.39953	−	11.0843i	−0.228993	−	0.396628i
$782$	2.19885	−	3.80852i	0.0786308	−	0.136193i
$783$	−22.1586	+	7.39566i	−0.791885	+	0.264299i
$784$	−4.20370	−	5.59723i	−0.150132	−	0.199901i
$785$			52.0257i			1.85688i
$786$	−2.10977	−	2.88767i	−0.0752530	−	0.103000i
$787$	−2.11493	+	1.22105i	−0.0753889	+	0.0435258i	−0.537221	−	0.843442i	$-0.680526\pi$
$787$	−2.11493	+	1.22105i	−0.0753889	+	0.0435258i	0.461832	+	0.886968i	$0.347192\pi$
$788$	−1.26202	+	0.728629i	−0.0449577	+	0.0259563i
$789$	14.1778	+	19.4053i	0.504742	+	0.690848i
$790$			60.4148i			2.14946i
$791$	−7.51543	+	4.96566i	−0.267218	+	0.176559i
$792$	8.52880	+	9.37151i	0.303058	+	0.333002i
$793$	9.33525	−	16.1691i	0.331504	−	0.574182i
$794$	−7.03912	−	12.1921i	−0.249809	−	0.432682i
$795$	28.6483	−	3.08808i	1.01605	−	0.109523i
$796$	−17.4052	−	10.0489i	−0.616911	−	0.356174i
$797$	−41.7265			−1.47803			−0.739014	−	0.673690i	$-0.764708\pi$
$797$	−41.7265			−1.47803			−0.739014	+	0.673690i	$0.764708\pi$
$798$	−8.17730	−	3.04011i	−0.289473	−	0.107619i
$799$	25.2998			0.895044
$800$	−9.15430	−	5.28524i	−0.323653	−	0.186861i
$801$	−8.81831	+	27.6391i	−0.311580	+	0.976580i
$802$	8.50543	+	14.7318i	0.300337	+	0.520199i
$803$	−8.43882	+	14.6165i	−0.297800	+	0.515804i
$804$	−19.1178	−	8.45095i	−0.674231	−	0.298042i
$805$	9.33935	+	4.66582i	0.329169	+	0.164449i
$806$			31.1707i			1.09794i
$807$	13.6295	−	9.95784i	0.479779	−	0.350533i
$808$	−7.79485	+	4.50036i	−0.274222	+	0.158322i
$809$	−37.9864	+	21.9315i	−1.33553	+	0.771069i	−0.986141	−	0.165908i	$-0.946945\pi$
$809$	−37.9864	+	21.9315i	−1.33553	+	0.771069i	−0.349390	+	0.936977i	$0.613611\pi$
$810$	−20.5676	+	28.9514i	−0.722673	+	1.01725i
$811$		−	0.990892i		−	0.0347949i	−0.999849	−	0.0173975i	$-0.994462\pi$
$811$		−	0.990892i		−	0.0347949i	0.999849	−	0.0173975i	$-0.00553806\pi$
$812$	10.6405	+	5.31585i	0.373408	+	0.186550i
$813$	−6.91698	+	15.6476i	−0.242589	+	0.548785i
$814$	8.73994	−	15.1380i	0.306335	−	0.530587i
$815$	−2.93499	−	5.08356i	−0.102808	−	0.178069i
$816$	−0.816333	−	7.57318i	−0.0285774	−	0.265114i
$817$	17.5312	+	10.1216i	0.613338	+	0.354111i
$818$	8.98905			0.314295
$819$	−24.3778	+	25.0319i	−0.851829	+	0.874686i
$820$	−14.4185			−0.503514
$821$	−32.6498	−	18.8504i	−1.13949	−	0.657883i	−0.193183	−	0.981163i	$-0.561881\pi$
$821$	−32.6498	−	18.8504i	−1.13949	−	0.657883i	−0.946303	+	0.323280i	$0.895214\pi$
$822$	1.30624	+	12.1180i	0.0455602	+	0.422665i
$823$	−0.314181	−	0.544177i	−0.0109517	−	0.0189688i	0.860498	−	0.509454i	$-0.170153\pi$
$823$	−0.314181	−	0.544177i	−0.0109517	−	0.0189688i	−0.871449	+	0.490486i	$0.836819\pi$
$824$	−6.91639	+	11.9795i	−0.240944	+	0.417327i
$825$	31.2659	−	70.7298i	1.08854	−	2.46249i
$826$	31.4652	−	20.7900i	1.09482	−	0.723376i
$827$			0.192457i			0.00669237i	0.999994	+	0.00334619i	$0.00106513\pi$
$827$			0.192457i			0.00669237i	−0.999994	+	0.00334619i	$0.998935\pi$
$828$	−0.639328	−	2.93109i	−0.0222182	−	0.101862i
$829$	−33.1756	+	19.1539i	−1.15224	+	0.665244i	−0.949431	−	0.313975i	$-0.898339\pi$
$829$	−33.1756	+	19.1539i	−1.15224	+	0.665244i	−0.202805	+	0.979219i	$0.565006\pi$
$830$	−34.5828	+	19.9664i	−1.20039	+	0.693044i
$831$	8.88575	−	6.49203i	0.308243	−	0.225206i
$832$			4.40215i			0.152617i
$833$	−30.5605	+	3.70241i	−1.05886	+	0.128281i
$834$	9.03820	+	3.99531i	0.312967	+	0.138346i
$835$	13.0879	−	22.6688i	0.452924	−	0.784488i
$836$	−4.02057	−	6.96383i	−0.139054	−	0.240849i
$837$	−27.5378	−	24.4003i	−0.951847	−	0.843399i
$838$	−9.40703	−	5.43115i	−0.324961	−	0.187616i
$839$	30.0004			1.03573			0.517864	−	0.855463i	$-0.326727\pi$
$839$	30.0004			1.03573			0.517864	+	0.855463i	$0.326727\pi$
$840$	17.8290	−	3.01753i	0.615160	−	0.104115i
$841$	8.78884			0.303063
$842$	3.13602	+	1.81058i	0.108074	+	0.0623968i
$843$	31.7393	−	3.42127i	1.09316	−	0.117835i
$844$	−14.2932	−	24.7565i	−0.491992	−	0.852155i
$845$	−12.5855	+	21.7987i	−0.432954	+	0.749899i
$846$	12.7643	−	11.6165i	0.438845	−	0.399383i
$847$	18.0657	−	1.09035i	0.620745	−	0.0374647i
$848$			4.21595i			0.144776i
$849$	−16.0382	−	21.9517i	−0.550429	−	0.753380i
$850$	−40.2579	+	23.2429i	−1.38083	+	0.797225i
$851$	−3.58397	+	2.06920i	−0.122857	+	0.0709314i
$852$	3.09626	+	4.23789i	0.106076	+	0.145188i
$853$			10.8430i			0.371256i	0.982620	+	0.185628i	$0.0594320\pi$
$853$			10.8430i			0.371256i	−0.982620	+	0.185628i	$0.940568\pi$
$854$	5.01496	−	10.0382i	0.171608	−	0.343500i
$855$	16.6674	−	15.1686i	0.570013	−	0.518756i
$856$	4.11593	−	7.12901i	0.140680	−	0.243664i
$857$	−12.7662	−	22.1117i	−0.436086	−	0.755323i	0.561298	−	0.827614i	$-0.310302\pi$
$857$	−12.7662	−	22.1117i	−0.436086	−	0.755323i	−0.997384	+	0.0722911i	$0.976969\pi$
$858$	−32.0201	+	3.45153i	−1.09315	+	0.117833i
$859$	−7.97347	−	4.60349i	−0.272051	−	0.157069i	0.357768	−	0.933810i	$-0.383538\pi$
$859$	−7.97347	−	4.60349i	−0.272051	−	0.157069i	−0.629820	+	0.776742i	$0.716871\pi$
$860$	−41.9584			−1.43077
$861$	12.9009	−	10.6749i	0.439660	−	0.363799i
$862$	4.13341			0.140784
$863$	38.3431	+	22.1374i	1.30521	+	0.753566i	0.981293	−	0.192518i	$-0.0616655\pi$
$863$	38.3431	+	22.1374i	1.30521	+	0.753566i	0.323921	+	0.946084i	$0.394999\pi$
$864$	−3.88910	−	3.44600i	−0.132310	−	0.117235i
$865$	21.2928	+	36.8802i	0.723977	+	1.25397i
$866$	12.4752	−	21.6076i	0.423923	−	0.734256i
$867$	−3.70665	−	1.63851i	−0.125885	−	0.0556469i
$868$	1.12862	+	18.6999i	0.0383080	+	0.634718i
$869$		−	64.6692i		−	2.19375i
$870$	−24.8098	+	18.1264i	−0.841132	+	0.614541i
$871$	46.0076	−	26.5625i	1.55891	−	0.900037i
$872$	12.3852	−	7.15057i	0.419414	−	0.242149i
$873$	−9.67782	−	44.3693i	−0.327544	−	1.50167i
$874$			1.90376i			0.0643957i
$875$	−32.0592	−	48.5210i	−1.08380	−	1.64031i
$876$	2.79820	−	6.33009i	0.0945423	−	0.213874i
$877$	8.77547	−	15.1996i	0.296326	−	0.513252i	−0.678966	−	0.734170i	$-0.737572\pi$
$877$	8.77547	−	15.1996i	0.296326	−	0.513252i	0.975293	+	0.220917i	$0.0709050\pi$
$878$	11.3166	+	19.6009i	0.381916	+	0.661498i
$879$	3.02705	+	28.0821i	0.102100	+	0.947187i
$880$	14.4340	+	8.33347i	0.486570	+	0.280921i
$881$	−17.0227			−0.573511			−0.286755	−	0.958004i	$-0.592577\pi$
$881$	−17.0227			−0.573511			−0.286755	+	0.958004i	$0.592577\pi$
$882$	−13.7184	+	15.8999i	−0.461923	+	0.535376i
$883$	30.9468			1.04144			0.520722	−	0.853727i	$-0.325663\pi$
$883$	30.9468			1.04144			0.520722	+	0.853727i	$0.325663\pi$
$884$	16.7657	+	9.67968i	0.563892	+	0.325563i
$885$	10.4409	+	96.8606i	0.350966	+	3.25593i
$886$	−1.04981	−	1.81833i	−0.0352692	−	0.0610880i
$887$	18.1920	−	31.5094i	0.610827	−	1.05798i	−0.380275	−	0.924874i	$-0.624171\pi$
$887$	18.1920	−	31.5094i	0.610827	−	1.05798i	0.991101	−	0.133109i	$-0.0424961\pi$
$888$	−2.89804	+	6.55596i	−0.0972520	+	0.220004i
$889$	10.4927	+	15.8805i	0.351913	+	0.532614i
$890$			38.1596i			1.27911i
$891$	22.0160	−	30.9901i	0.737563	−	1.03821i
$892$	−6.26065	+	3.61459i	−0.209622	+	0.121025i
$893$	−9.48495	+	5.47614i	−0.317402	+	0.183252i
$894$	−8.00450	+	5.84819i	−0.267711	+	0.195593i
$895$			78.3596i			2.61927i
$896$	0.159393	+	2.64095i	0.00532494	+	0.0882278i
$897$	6.97378	+	3.08274i	0.232848	+	0.102930i
$898$	−13.5298	+	23.4343i	−0.451495	+	0.782013i
$899$	−15.9165	−	27.5681i	−0.530844	−	0.919448i
$900$	−9.63888	+	30.2110i	−0.321296	+	1.00703i
$901$	16.0566	+	9.27026i	0.534922	+	0.308837i
$902$	15.4338			0.513889
$903$	37.5421	−	31.0644i	1.24932	−	1.03376i
$904$	3.40461			0.113236
$905$	21.1941	+	12.2364i	0.704515	+	0.406752i
$906$	−2.39937	+	0.258634i	−0.0797136	+	0.00859254i
$907$	18.0948	+	31.3411i	0.600828	+	1.04066i	0.992696	+	0.120643i	$0.0384955\pi$
$907$	18.0948	+	31.3411i	0.600828	+	1.04066i	−0.391868	+	0.920021i	$0.628171\pi$
$908$	−3.03276	+	5.25290i	−0.100646	+	0.174324i
$909$	18.1744	+	19.9702i	0.602806	+	0.662368i
$910$	−20.5397	+	41.1132i	−0.680883	+	1.36289i
$911$			32.1799i			1.06617i	0.846062	+	0.533084i	$0.178967\pi$
$911$			32.1799i			1.06617i	−0.846062	+	0.533084i	$0.821033\pi$
$912$	1.94525	+	2.66250i	0.0644138	+	0.0881642i
$913$	37.0181	−	21.3724i	1.22512	−	0.707324i
$914$	−28.1219	+	16.2362i	−0.930189	+	0.537045i
$915$	17.1004	+	23.4055i	0.565321	+	0.773763i
$916$			2.70263i			0.0892973i
$917$	5.45294	−	0.329109i	0.180072	−	0.0108681i
$918$	−21.6757	+	7.23448i	−0.715405	+	0.238774i
$919$	18.9578	−	32.8358i	0.625359	−	1.08315i	−0.363113	−	0.931745i	$-0.618286\pi$
$919$	18.9578	−	32.8358i	0.625359	−	1.08315i	0.988471	−	0.151408i	$-0.0483807\pi$
$920$	−1.97297	−	3.41729i	−0.0650470	−	0.112665i
$921$	−32.3135	+	3.48316i	−1.06477	+	0.114774i
$922$	13.9981	+	8.08180i	0.461002	+	0.266160i
$923$	−13.3395			−0.439074
$924$	−19.0845	+	3.23003i	−0.627836	+	0.106260i
$925$	43.7449			1.43832
$926$	4.93348	+	2.84835i	0.162124	+	0.0936024i
$927$	39.5349	+	12.6137i	1.29850	+	0.414287i
$928$	−2.24784	−	3.89338i	−0.0737890	−	0.127806i
$929$	0.140005	−	0.242495i	0.00459341	−	0.00795602i	−0.863720	−	0.503973i	$-0.831871\pi$
$929$	0.140005	−	0.242495i	0.00459341	−	0.00795602i	0.868313	+	0.496017i	$0.165205\pi$
$930$	−44.2624	−	19.5661i	−1.45142	−	0.641596i
$931$	10.6558	−	8.00284i	0.349229	−	0.262282i
$932$		−	9.15615i		−	0.299920i
$933$	−36.4283	+	26.6150i	−1.19261	+	0.871335i
$934$	20.5612	−	11.8710i	0.672784	−	0.388432i
$935$	63.4764	−	36.6481i	2.07590	−	1.19852i
$936$	12.9031	−	2.81442i	0.421751	−	0.0919922i
$937$			25.1759i			0.822461i	0.911531	+	0.411231i	$0.134901\pi$
$937$			25.1759i			0.822461i	−0.911531	+	0.411231i	$0.865099\pi$
$938$	26.6392	−	17.6013i	0.869800	−	0.574702i
$939$	11.8361	−	26.7757i	0.386258	−	0.873793i
$940$	11.3504	−	19.6595i	0.370210	−	0.641223i
$941$	−27.8765	−	48.2835i	−0.908748	−	1.57400i	−0.815805	−	0.578327i	$-0.803706\pi$
$941$	−27.8765	−	48.2835i	−0.908748	−	1.57400i	−0.0929428	−	0.995671i	$-0.529627\pi$
$942$	2.44742	+	22.7049i	0.0797412	+	0.739765i
$943$	−3.16445	−	1.82700i	−0.103049	−	0.0594952i
$944$	−14.2542			−0.463936
$945$	−20.2432	−	50.3292i	−0.658513	−	1.63721i
$946$	44.9131			1.46025
$947$	26.2822	+	15.1740i	0.854057	+	0.493090i	0.862018	−	0.506878i	$-0.169201\pi$
$947$	26.2822	+	15.1740i	0.854057	+	0.493090i	−0.00796071	+	0.999968i	$0.502534\pi$
$948$	2.84206	+	26.3660i	0.0923060	+	0.856329i
$949$	8.79513	+	15.2336i	0.285502	+	0.494504i
$950$	10.0618	−	17.4276i	0.326449	−	0.565426i
$951$	0.468556	−	1.05997i	0.0151940	−	0.0343718i
$952$	10.4086	+	5.20000i	0.337344	+	0.168533i
$953$		−	20.3030i		−	0.657678i	−0.944386	−	0.328839i	$-0.893343\pi$
$953$		−	20.3030i		−	0.657678i	0.944386	−	0.328839i	$-0.106657\pi$
$954$	12.3573	−	2.69538i	0.400083	−	0.0872660i
$955$	−14.5282	+	8.38783i	−0.470120	+	0.271424i
$956$	14.6521	−	8.45939i	0.473882	−	0.273596i
$957$	26.5569	−	19.4028i	0.858463	−	0.627204i
$958$		−	8.69835i		−	0.281031i
$959$	−16.6551	−	8.32066i	−0.537820	−	0.268688i
$960$	−6.25106	−	2.76326i	−0.201752	−	0.0891840i
$961$	9.56870	−	16.5735i	0.308668	−	0.534628i
$962$	−9.10896	−	15.7772i	−0.293685	−	0.508677i
$963$	−23.5272	−	7.50638i	−0.758152	−	0.241890i
$964$	−19.4840	−	11.2491i	−0.627537	−	0.362309i
$965$	−22.0625			−0.710217
$966$	4.29534	+	1.59689i	0.138200	+	0.0513792i
$967$	−10.4675			−0.336613			−0.168306	−	0.985735i	$-0.553830\pi$
$967$	−10.4675			−0.336613			−0.168306	+	0.985735i	$0.553830\pi$
$968$	−5.92415	−	3.42031i	−0.190409	−	0.109933i
$969$	14.4175	−	1.55410i	0.463158	−	0.0499250i
$970$	−29.8658	−	51.7291i	−0.958934	−	1.66092i
$971$	18.4763	−	32.0020i	0.592934	−	1.02699i	−0.400901	−	0.916122i	$-0.631303\pi$
$971$	18.4763	−	32.0020i	0.592934	−	1.02699i	0.993835	−	0.110871i	$-0.0353639\pi$
$972$	−7.61411	+	13.6024i	−0.244223	+	0.436297i
$973$	−12.5941	+	8.32125i	−0.403747	+	0.266767i
$974$		−	19.9937i		−	0.640639i
$975$	−47.5470	−	65.0784i	−1.52272	−	2.08418i
$976$	−3.67300	+	2.12061i	−0.117570	+	0.0678790i
$977$	−8.68257	+	5.01289i	−0.277780	+	0.160376i	−0.632418	−	0.774627i	$-0.717937\pi$
$977$	−8.68257	+	5.01289i	−0.277780	+	0.160376i	0.354638	+	0.935004i	$0.384604\pi$
$978$	−1.52002	−	2.08048i	−0.0486050	−	0.0665264i
$979$		−	40.8468i		−	1.30547i
$980$	−10.8336	+	25.4084i	−0.346065	+	0.811642i
$981$	−28.8771	−	31.7304i	−0.921975	−	1.01307i
$982$	0.105632	−	0.182960i	0.00337086	−	0.00583849i
$983$	−13.0563	−	22.6142i	−0.416431	−	0.721280i	0.579146	−	0.815224i	$-0.303386\pi$
$983$	−13.0563	−	22.6142i	−0.416431	−	0.721280i	−0.995578	+	0.0939433i	$0.970053\pi$
$984$	−6.29245	+	0.678281i	−0.200596	+	0.0216228i
$985$	4.97987	+	2.87513i	0.158672	+	0.0916092i
$986$	−19.7707			−0.629627
$987$	4.39939	+	25.9937i	0.140034	+	0.827390i
$988$	−8.38065			−0.266624
$989$	−9.20870	−	5.31665i	−0.292820	−	0.169060i
$990$	15.1981	−	47.6351i	0.483026	−	1.51394i
$991$	−3.74980	−	6.49484i	−0.119116	−	0.206315i	0.800301	−	0.599598i	$-0.204673\pi$
$991$	−3.74980	−	6.49484i	−0.119116	−	0.206315i	−0.919418	+	0.393283i	$0.871339\pi$
$992$	3.54039	−	6.13213i	0.112407	−	0.194695i
$993$	−43.2618	−	19.1238i	−1.37287	−	0.606874i
$994$	−8.00262	+	0.482994i	−0.253828	+	0.0153196i
$995$			79.3048i			2.51413i
$996$	−14.1533	+	10.3405i	−0.448463	+	0.327652i
$997$	−39.3105	+	22.6960i	−1.24498	+	0.718788i	−0.970103	−	0.242692i	$-0.921970\pi$
$997$	−39.3105	+	22.6960i	−1.24498	+	0.718788i	−0.274874	+	0.961480i	$0.588636\pi$
$998$	−3.16732	+	1.82865i	−0.100260	+	0.0578850i
$999$	21.0689	+	4.30301i	0.666590	+	0.136141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.9	✓	56
3.2	odd	2	inner	966.2.l.c.47.19	yes	56
7.3	odd	6	inner	966.2.l.c.185.19	yes	56
21.17	even	6	inner	966.2.l.c.185.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.9	✓	56	1.1	even	1	trivial
966.2.l.c.47.19	yes	56	3.2	odd	2	inner
966.2.l.c.185.9	yes	56	21.17	even	6	inner
966.2.l.c.185.19	yes	56	7.3	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.185627 + 1.72208i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.97297 - 3.41729i) q^{5} +(0.700280 - 1.58417i) q^{6} +(1.45851 + 2.20743i) q^{7} -1.00000i q^{8} +(-2.93109 + 0.639328i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.185627 + 1.72208i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.97297 - 3.41729i) q^{5} +(0.700280 - 1.58417i) q^{6} +(1.45851 + 2.20743i) q^{7} -1.00000i q^{8} +(-2.93109 + 0.639328i) q^{9} +(-3.41729 + 1.97297i) q^{10} +(3.65793 - 2.11191i) q^{11} +(-1.39855 + 1.02180i) q^{12} -4.40215i q^{13} +(-0.159393 - 2.64095i) q^{14} +(6.25106 + 2.76326i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.19885 + 3.80852i) q^{17} +(2.85806 + 0.911868i) q^{18} +(-1.64871 - 0.951881i) q^{19} +3.94594 q^{20} +(-3.53062 + 2.92142i) q^{21} -4.22382 q^{22} +(0.866025 + 0.500000i) q^{23} +(1.72208 - 0.185627i) q^{24} +(-5.28524 - 9.15430i) q^{25} +(-2.20108 + 3.81238i) q^{26} +(-1.64506 - 4.92887i) q^{27} +(-1.18243 + 2.36682i) q^{28} -4.49568i q^{29} +(-4.03195 - 5.51859i) q^{30} +(6.13213 - 3.54039i) q^{31} +(0.866025 - 0.500000i) q^{32} +(4.31588 + 5.90721i) q^{33} -4.39770i q^{34} +(10.4210 - 0.628955i) q^{35} +(-2.01922 - 2.21873i) q^{36} +(-2.06920 + 3.58397i) q^{37} +(0.951881 + 1.64871i) q^{38} +(7.58084 - 0.817159i) q^{39} +(-3.41729 - 1.97297i) q^{40} -3.65400 q^{41} +(4.51832 - 0.764717i) q^{42} -10.6333 q^{43} +(3.65793 + 2.11191i) q^{44} +(-3.59818 + 11.2777i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(2.87648 - 4.98221i) q^{47} +(-1.58417 - 0.700280i) q^{48} +(-2.74549 + 6.43912i) q^{49} +10.5705i q^{50} +(-6.15040 + 4.49355i) q^{51} +(3.81238 - 2.20108i) q^{52} +(3.65112 - 2.10798i) q^{53} +(-1.03977 + 5.09106i) q^{54} -16.6669i q^{55} +(2.20743 - 1.45851i) q^{56} +(1.33317 - 3.01589i) q^{57} +(-2.24784 + 3.89338i) q^{58} +(7.12712 + 12.3445i) q^{59} +(0.732474 + 6.79521i) q^{60} +(3.67300 + 2.12061i) q^{61} -7.08078 q^{62} +(-5.68629 - 5.53770i) q^{63} -1.00000 q^{64} +(-15.0434 - 8.68532i) q^{65} +(-0.784055 - 7.27373i) q^{66} +(6.03398 + 10.4512i) q^{67} +(-2.19885 + 3.80852i) q^{68} +(-0.700280 + 1.58417i) q^{69} +(-9.33935 - 4.66582i) q^{70} -3.03021i q^{71} +(0.639328 + 2.93109i) q^{72} +(-3.46049 + 1.99791i) q^{73} +(3.58397 - 2.06920i) q^{74} +(14.7833 - 10.8009i) q^{75} -1.90376i q^{76} +(9.99702 + 4.99439i) q^{77} +(-6.97378 - 3.08274i) q^{78} +(7.65531 - 13.2594i) q^{79} +(1.97297 + 3.41729i) q^{80} +(8.18252 - 3.74785i) q^{81} +(3.16445 + 1.82700i) q^{82} +10.1200 q^{83} +(-4.29534 - 1.59689i) q^{84} +17.3531 q^{85} +(9.20870 + 5.31665i) q^{86} +(7.74190 - 0.834521i) q^{87} +(-2.11191 - 3.65793i) q^{88} +(4.83530 - 8.37498i) q^{89} +(8.75498 - 7.96771i) q^{90} +(9.71744 - 6.42059i) q^{91} +1.00000i q^{92} +(7.23510 + 9.90280i) q^{93} +(-4.98221 + 2.87648i) q^{94} +(-6.50570 + 3.75607i) q^{95} +(1.02180 + 1.39855i) q^{96} +15.1375i q^{97} +(5.59723 - 4.20370i) q^{98} +(-9.37151 + 8.52880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Introduction

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