LMFDB - Embedded newform 731.2.j.a.135.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(135,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.135");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.j (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			135.5
Character	$\chi$	$=$	731.135
Dual form			731.2.j.a.509.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51145 q^{2} +(-1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(1.18626 + 0.684888i) q^{5} +(4.42321 + 2.55374i) q^{6} +(3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 + 0.983681i) q^{9} +O(q^{10})$	\(q-2.51145 q^{2} +(-1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(1.18626 + 0.684888i) q^{5} +(4.42321 + 2.55374i) q^{6} +(3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 + 0.983681i) q^{9} +(-2.97923 - 1.72006i) q^{10} -5.71903i q^{11} +(-7.58623 - 4.37991i) q^{12} +(-0.967741 - 1.67618i) q^{13} +(-9.65264 + 5.57296i) q^{14} +(-1.39284 - 2.41247i) q^{15} +5.93872 q^{16} +(2.78875 + 3.03692i) q^{17} +(-1.42632 - 2.47046i) q^{18} +(3.28388 - 5.68786i) q^{19} +(5.10967 + 2.95007i) q^{20} -9.02556 q^{21} +14.3631i q^{22} +(3.56220 + 2.05664i) q^{23} +(10.2060 + 5.89244i) q^{24} +(-1.56186 - 2.70522i) q^{25} +(2.43043 + 4.20963i) q^{26} +3.79107i q^{27} +(16.5552 - 9.55815i) q^{28} +(-1.60279 + 0.925373i) q^{29} +(3.49805 + 6.05880i) q^{30} +(7.10692 + 4.10318i) q^{31} -3.32510 q^{32} +(-5.81534 + 10.0725i) q^{33} +(-7.00381 - 7.62706i) q^{34} +6.07912 q^{35} +(2.44628 + 4.23708i) q^{36} +(-0.467527 - 0.269927i) q^{37} +(-8.24731 + 14.2848i) q^{38} +3.93615i q^{39} +(-6.87420 - 3.96882i) q^{40} +3.51693i q^{41} +22.6672 q^{42} +(4.98908 - 4.25548i) q^{43} -24.6340i q^{44} +1.55587i q^{45} +(-8.94629 - 5.16514i) q^{46} -10.7488 q^{47} +(-10.4594 - 6.03873i) q^{48} +(6.34810 - 10.9952i) q^{49} +(3.92253 + 6.79401i) q^{50} +(-1.82355 - 8.18439i) q^{51} +(-4.16842 - 7.21992i) q^{52} +(-2.08650 + 3.61392i) q^{53} -9.52108i q^{54} +(3.91689 - 6.78426i) q^{55} +(-22.2723 + 12.8589i) q^{56} +(-11.5673 + 6.67837i) q^{57} +(4.02533 - 2.32403i) q^{58} -6.09785 q^{59} +(-5.99949 - 10.3914i) q^{60} +(-1.58893 + 0.917368i) q^{61} +(-17.8487 - 10.3049i) q^{62} +(4.36561 + 2.52049i) q^{63} -3.52664 q^{64} -2.65118i q^{65} +(14.6049 - 25.2965i) q^{66} +(-7.10904 + 12.3132i) q^{67} +(12.0122 + 13.0811i) q^{68} +(-4.18255 - 7.24438i) q^{69} -15.2674 q^{70} +(4.83502 - 2.79150i) q^{71} +(-3.29106 - 5.70028i) q^{72} +(5.46456 - 3.15496i) q^{73} +(1.17417 + 0.677908i) q^{74} +6.35264i q^{75} +(14.1449 - 24.4997i) q^{76} +(-12.6906 - 21.9808i) q^{77} -9.88544i q^{78} +(11.6828 - 6.74508i) q^{79} +(7.04487 + 4.06736i) q^{80} +(5.55870 - 9.62795i) q^{81} -8.83259i q^{82} +(-4.69845 + 8.13795i) q^{83} -38.8765 q^{84} +(1.22824 + 5.51255i) q^{85} +(-12.5298 + 10.6874i) q^{86} +3.76383 q^{87} +33.1409i q^{88} +(8.13518 - 14.0905i) q^{89} -3.90748i q^{90} +(-7.43894 - 4.29487i) q^{91} +(15.3437 + 8.85871i) q^{92} +(-8.34456 - 14.4532i) q^{93} +26.9951 q^{94} +(7.79108 - 4.49818i) q^{95} +(5.85622 + 3.38109i) q^{96} +18.8175i q^{97} +(-15.9429 + 27.6140i) q^{98} +(5.62570 - 3.24800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9}+O(q^{10}) $ 128 * q - 4 * q^2 + 116 * q^4 - 12 * q^8 + 70 * q^9	$ 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9} + 4 q^{13} - 12 q^{15} + 76 q^{16} + 2 q^{17} - 16 q^{18} - 2 q^{19} - 20 q^{21} + 60 q^{25} - 2 q^{26} - 28 q^{30} - 48 q^{32} + 22 q^{33} - 18 q^{34} - 112 q^{35} + 36 q^{36} - 40 q^{38} + 36 q^{42} + 10 q^{43} + 36 q^{47} + 52 q^{49} + 16 q^{50} + 10 q^{51} + 10 q^{52} + 24 q^{55} - 12 q^{59} - 78 q^{60} + 36 q^{64} + 14 q^{66} + 10 q^{67} - q^{68} - 64 q^{70} - 68 q^{72} - 22 q^{76} - 28 q^{77} - 20 q^{81} - 6 q^{83} + 32 q^{84} + 6 q^{85} - 58 q^{86} + 32 q^{87} + 36 q^{89} + 6 q^{93} + 132 q^{94} - 48 q^{98}+O(q^{100}) $ 128 * q - 4 * q^2 + 116 * q^4 - 12 * q^8 + 70 * q^9 + 4 * q^13 - 12 * q^15 + 76 * q^16 + 2 * q^17 - 16 * q^18 - 2 * q^19 - 20 * q^21 + 60 * q^25 - 2 * q^26 - 28 * q^30 - 48 * q^32 + 22 * q^33 - 18 * q^34 - 112 * q^35 + 36 * q^36 - 40 * q^38 + 36 * q^42 + 10 * q^43 + 36 * q^47 + 52 * q^49 + 16 * q^50 + 10 * q^51 + 10 * q^52 + 24 * q^55 - 12 * q^59 - 78 * q^60 + 36 * q^64 + 14 * q^66 + 10 * q^67 - q^68 - 64 * q^70 - 68 * q^72 - 22 * q^76 - 28 * q^77 - 20 * q^81 - 6 * q^83 + 32 * q^84 + 6 * q^85 - 58 * q^86 + 32 * q^87 + 36 * q^89 + 6 * q^93 + 132 * q^94 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.51145			−1.77586			−0.887931	−	0.459976i	$-0.847858\pi$
$2$	−2.51145			−1.77586			−0.887931	+	0.459976i	$0.847858\pi$
$3$	−1.76122	−	1.01684i	−1.01684	−	0.587073i	−0.103653	−	0.994614i	$-0.533053\pi$
$3$	−1.76122	−	1.01684i	−1.01684	−	0.587073i	−0.913187	+	0.407540i	$0.866387\pi$
$4$	4.30737			2.15369
$5$	1.18626	+	0.684888i	0.530512	+	0.306291i	0.741225	−	0.671257i	$-0.234245\pi$
$5$	1.18626	+	0.684888i	0.530512	+	0.306291i	−0.210713	+	0.977548i	$0.567579\pi$
$6$	4.42321	+	2.55374i	1.80577	+	1.04256i
$7$	3.84346	−	2.21902i	1.45269	−	0.838711i	0.454056	−	0.890973i	$-0.349976\pi$
$7$	3.84346	−	2.21902i	1.45269	−	0.838711i	0.998633	+	0.0522621i	$0.0166431\pi$
$8$	−5.79485			−2.04879
$9$	0.567928	+	0.983681i	0.189309	+	0.327894i
$10$	−2.97923	−	1.72006i	−0.942116	−	0.543931i
$11$		−	5.71903i		−	1.72435i	−0.506608	−	0.862176i	$-0.669101\pi$
$11$		−	5.71903i		−	1.72435i	0.506608	−	0.862176i	$-0.330899\pi$
$12$	−7.58623	−	4.37991i	−2.18996	−	1.26437i
$13$	−0.967741	−	1.67618i	−0.268403	−	0.464888i	0.700047	−	0.714097i	$-0.253163\pi$
$13$	−0.967741	−	1.67618i	−0.268403	−	0.464888i	−0.968450	+	0.249210i	$0.919829\pi$
$14$	−9.65264	+	5.57296i	−2.57978	+	1.48944i
$15$	−1.39284	−	2.41247i	−0.359630	−	0.622898i
$16$	5.93872			1.48468
$17$	2.78875	+	3.03692i	0.676372	+	0.736560i
$17$	2.78875	+	3.03692i	0.676372	+	0.736560i
$18$	−1.42632	−	2.47046i	−0.336187	−	0.582294i
$19$	3.28388	−	5.68786i	0.753375	−	1.30488i	−0.192803	−	0.981237i	$-0.561758\pi$
$19$	3.28388	−	5.68786i	0.753375	−	1.30488i	0.946178	−	0.323646i	$-0.104909\pi$
$20$	5.10967	+	2.95007i	1.14256	+	0.659655i
$21$	−9.02556			−1.96954
$22$			14.3631i			3.06221i
$23$	3.56220	+	2.05664i	0.742771	+	0.428839i	0.823076	−	0.567932i	$-0.192256\pi$
$23$	3.56220	+	2.05664i	0.742771	+	0.428839i	−0.0803052	+	0.996770i	$0.525590\pi$
$24$	10.2060	+	5.89244i	2.08329	+	1.20279i
$25$	−1.56186	−	2.70522i	−0.312372	−	0.541043i
$26$	2.43043	+	4.20963i	0.476647	+	0.825577i
$27$			3.79107i			0.729592i
$28$	16.5552	−	9.55815i	3.12864	−	1.80632i
$29$	−1.60279	+	0.925373i	−0.297631	+	0.171837i	−0.641378	−	0.767225i	$-0.721637\pi$
$29$	−1.60279	+	0.925373i	−0.297631	+	0.171837i	0.343747	+	0.939062i	$0.388304\pi$
$30$	3.49805	+	6.05880i	0.638654	+	1.10618i
$31$	7.10692	+	4.10318i	1.27644	+	0.736953i	0.976192	−	0.216908i	$-0.0695971\pi$
$31$	7.10692	+	4.10318i	1.27644	+	0.736953i	0.300248	+	0.953861i	$0.402930\pi$
$32$	−3.32510			−0.587800
$33$	−5.81534	+	10.0725i	−1.01232	+	1.75339i
$34$	−7.00381	−	7.62706i	−1.20114	−	1.30803i
$35$	6.07912			1.02756
$36$	2.44628	+	4.23708i	0.407713	+	0.706180i
$37$	−0.467527	−	0.269927i	−0.0768610	−	0.0443757i	0.461077	−	0.887360i	$-0.347463\pi$
$37$	−0.467527	−	0.269927i	−0.0768610	−	0.0443757i	−0.537938	+	0.842984i	$0.680797\pi$
$38$	−8.24731	+	14.2848i	−1.33789	+	2.31729i
$39$			3.93615i			0.630289i
$40$	−6.87420	−	3.96882i	−1.08691	−	0.627526i
$41$			3.51693i			0.549253i	0.961551	+	0.274626i	$0.0885541\pi$
$41$			3.51693i			0.549253i	−0.961551	+	0.274626i	$0.911446\pi$
$42$	22.6672			3.49763
$43$	4.98908	−	4.25548i	0.760827	−	0.648955i
$43$	4.98908	−	4.25548i	0.760827	−	0.648955i
$44$		−	24.6340i		−	3.71372i
$45$			1.55587i			0.231935i
$46$	−8.94629	−	5.16514i	−1.31906	−	0.761559i
$47$	−10.7488			−1.56788			−0.783939	−	0.620838i	$-0.786793\pi$
$47$	−10.7488			−1.56788			−0.783939	+	0.620838i	$0.786793\pi$
$48$	−10.4594	−	6.03873i	−1.50968	−	0.871616i
$49$	6.34810	−	10.9952i	0.906872	−	1.57075i
$50$	3.92253	+	6.79401i	0.554729	+	0.960819i
$51$	−1.82355	−	8.18439i	−0.255348	−	1.14604i
$52$	−4.16842	−	7.21992i	−0.578056	−	1.00122i
$53$	−2.08650	+	3.61392i	−0.286603	+	0.496411i	−0.972997	−	0.230819i	$-0.925859\pi$
$53$	−2.08650	+	3.61392i	−0.286603	+	0.496411i	0.686394	+	0.727230i	$0.259193\pi$
$54$		−	9.52108i		−	1.29566i
$55$	3.91689	−	6.78426i	0.528154	−	0.914789i
$56$	−22.2723	+	12.8589i	−2.97626	+	1.71834i
$57$	−11.5673	+	6.67837i	−1.53212	+	0.884572i
$58$	4.02533	−	2.32403i	0.528552	−	0.305160i
$59$	−6.09785			−0.793872			−0.396936	−	0.917846i	$-0.629927\pi$
$59$	−6.09785			−0.793872			−0.396936	+	0.917846i	$0.629927\pi$
$60$	−5.99949	−	10.3914i	−0.774531	−	1.34153i
$61$	−1.58893	+	0.917368i	−0.203441	+	0.117457i	−0.598260	−	0.801302i	$-0.704141\pi$
$61$	−1.58893	+	0.917368i	−0.203441	+	0.117457i	0.394818	+	0.918759i	$0.370808\pi$
$62$	−17.8487	−	10.3049i	−2.26678	−	1.30873i
$63$	4.36561	+	2.52049i	0.550016	+	0.317552i
$64$	−3.52664			−0.440830
$65$		−	2.65118i		−	0.328838i
$66$	14.6049	−	25.2965i	1.79774	−	3.11378i
$67$	−7.10904	+	12.3132i	−0.868508	+	1.50430i	−0.00498622	+	0.999988i	$0.501587\pi$
$67$	−7.10904	+	12.3132i	−0.868508	+	1.50430i	−0.863522	+	0.504312i	$0.831746\pi$
$68$	12.0122	+	13.0811i	1.45669	+	1.58632i
$69$	−4.18255	−	7.24438i	−0.503519	−	0.872121i
$70$	−15.2674			−1.82480
$71$	4.83502	−	2.79150i	0.573811	−	0.331290i	−0.184859	−	0.982765i	$-0.559183\pi$
$71$	4.83502	−	2.79150i	0.573811	−	0.331290i	0.758670	+	0.651475i	$0.225849\pi$
$72$	−3.29106	−	5.70028i	−0.387855	−	0.671785i
$73$	5.46456	−	3.15496i	0.639578	−	0.369261i	−0.144874	−	0.989450i	$-0.546278\pi$
$73$	5.46456	−	3.15496i	0.639578	−	0.369261i	0.784452	+	0.620190i	$0.212944\pi$
$74$	1.17417	+	0.677908i	0.136495	+	0.0788052i
$75$			6.35264i			0.733540i
$76$	14.1449	−	24.4997i	1.62253	−	2.81031i
$77$	−12.6906	−	21.9808i	−1.44623	−	2.50495i
$78$		−	9.88544i		−	1.11931i
$79$	11.6828	−	6.74508i	1.31442	−	0.758880i	0.331595	−	0.943422i	$-0.392413\pi$
$79$	11.6828	−	6.74508i	1.31442	−	0.758880i	0.982825	+	0.184541i	$0.0590800\pi$
$80$	7.04487	+	4.06736i	0.787641	+	0.454744i
$81$	5.55870	−	9.62795i	0.617633	−	1.06977i
$82$		−	8.83259i		−	0.975397i
$83$	−4.69845	+	8.13795i	−0.515722	+	0.893257i	0.484112	+	0.875006i	$0.339143\pi$
$83$	−4.69845	+	8.13795i	−0.515722	+	0.893257i	−0.999833	+	0.0182503i	$0.994190\pi$
$84$	−38.8765			−4.24177
$85$	1.22824	+	5.51255i	0.133221	+	0.597920i
$86$	−12.5298	+	10.6874i	−1.35112	+	1.15245i
$87$	3.76383			0.403525
$88$			33.1409i			3.53284i
$89$	8.13518	−	14.0905i	0.862327	−	1.49359i	−0.00734982	−	0.999973i	$-0.502340\pi$
$89$	8.13518	−	14.0905i	0.862327	−	1.49359i	0.869677	−	0.493621i	$-0.164327\pi$
$90$		−	3.90748i		−	0.411885i
$91$	−7.43894	−	4.29487i	−0.779813	−	0.450225i
$92$	15.3437	+	8.85871i	1.59970	+	0.923585i
$93$	−8.34456	−	14.4532i	−0.865291	−	1.49873i
$94$	26.9951			2.78434
$95$	7.79108	−	4.49818i	0.799348	−	0.461504i
$96$	5.85622	+	3.38109i	0.597698	+	0.345081i
$97$			18.8175i			1.91063i	0.295585	+	0.955316i	$0.404485\pi$
$97$			18.8175i			1.91063i	−0.295585	+	0.955316i	$0.595515\pi$
$98$	−15.9429	+	27.6140i	−1.61048	+	2.78943i
$99$	5.62570	−	3.24800i	0.565404	−	0.326436i
$100$	−6.72751	−	11.6524i	−0.672751	−	1.16524i
$101$	−0.223258	−	0.386694i	−0.0222150	−	0.0384775i	0.854704	−	0.519115i	$-0.173739\pi$
$101$	−0.223258	−	0.386694i	−0.0222150	−	0.0384775i	−0.876919	+	0.480638i	$0.840405\pi$
$102$	4.57974	+	20.5547i	0.453462	+	2.03522i
$103$	−1.22446	−	2.12083i	−0.120650	−	0.208971i	0.799374	−	0.600833i	$-0.205164\pi$
$103$	−1.22446	−	2.12083i	−0.120650	−	0.208971i	−0.920024	+	0.391862i	$0.871831\pi$
$104$	5.60792	+	9.71319i	0.549901	+	0.952457i
$105$	−10.7067	−	6.18149i	−1.04486	−	0.603252i
$106$	5.24014	−	9.07619i	0.508967	−	0.881557i
$107$		−	4.76103i		−	0.460266i	−0.973159	−	0.230133i	$-0.926084\pi$
$107$		−	4.76103i		−	0.460266i	0.973159	−	0.230133i	$-0.0739161\pi$
$108$			16.3296i			1.57131i
$109$	−9.19461	−	5.30851i	−0.880684	−	0.508463i	−0.00980034	−	0.999952i	$-0.503120\pi$
$109$	−9.19461	−	5.30851i	−0.880684	−	0.508463i	−0.870884	+	0.491489i	$0.836453\pi$
$110$	−9.83708	+	17.0383i	−0.937928	+	1.62454i
$111$	0.548945	+	0.950801i	0.0521036	+	0.0902460i
$112$	22.8252	−	13.1781i	2.15678	−	1.24522i
$113$		−	10.9962i		−	1.03443i	−0.855854	−	0.517217i	$-0.826968\pi$
$113$		−	10.9962i		−	1.03443i	0.855854	−	0.517217i	$-0.173032\pi$
$114$	29.0506	−	16.7724i	2.72084	−	1.57088i
$115$	2.81713	+	4.87942i	0.262699	+	0.455008i
$116$	−6.90383	+	3.98593i	−0.641004	+	0.370084i
$117$	1.09921	−	1.90390i	0.101622	−	0.176015i
$118$	15.3144			1.40981
$119$	17.4574	+	5.48395i	1.60032	+	0.502713i
$120$	8.07132	+	13.9799i	0.736807	+	1.27619i
$121$	−21.7073			−1.97339
$122$	3.99051	−	2.30392i	0.361284	−	0.208587i
$123$	3.57616	−	6.19409i	0.322451	−	0.558502i
$124$	30.6122	+	17.6739i	2.74905	+	1.58717i
$125$		−	11.1277i		−	0.995289i
$126$	−10.9640	−	6.33008i	−0.976752	−	0.563928i
$127$	−4.14740			−0.368022			−0.184011	−	0.982924i	$-0.558908\pi$
$127$	−4.14740			−0.368022			−0.184011	+	0.982924i	$0.558908\pi$
$128$	15.5072			1.37065
$129$	−13.1140	+	2.42174i	−1.15462	+	0.213222i
$130$			6.65829i			0.583971i
$131$			5.10448i			0.445981i	0.974821	+	0.222990i	$0.0715819\pi$
$131$			5.10448i			0.445981i	−0.974821	+	0.222990i	$0.928418\pi$
$132$	−25.0489	+	43.3859i	−2.18022	+	3.77626i
$133$		−	29.1480i		−	2.52745i
$134$	17.8540	−	30.9240i	1.54235	−	2.67143i
$135$	−2.59646	+	4.49720i	−0.223468	+	0.387057i
$136$	−16.1604	−	17.5985i	−1.38574	−	1.50906i
$137$	−8.15290			−0.696549			−0.348275	−	0.937393i	$-0.613232\pi$
$137$	−8.15290			−0.696549			−0.348275	+	0.937393i	$0.613232\pi$
$138$	10.5042	+	18.1939i	0.894181	+	1.54877i
$139$	−11.7337	−	6.77447i	−0.995242	−	0.574603i	−0.0884048	−	0.996085i	$-0.528177\pi$
$139$	−11.7337	−	6.77447i	−0.995242	−	0.574603i	−0.906837	+	0.421482i	$0.861510\pi$
$140$	26.1850			2.21304
$141$	18.9310	+	10.9298i	1.59428	+	0.920459i
$142$	−12.1429	+	7.01071i	−1.01901	+	0.588325i
$143$	−9.58611	+	5.53454i	−0.801630	+	0.462822i
$144$	3.37277	+	5.84181i	0.281064	+	0.486817i
$145$	−2.53511			−0.210529
$146$	−13.7240	+	7.92353i	−1.13580	+	0.655756i
$147$	−22.3608	+	12.9100i	−1.84429	+	1.06480i
$148$	−2.01381	−	1.16268i	−0.165535	−	0.0955714i
$149$	0.586861	−	1.01647i	0.0480775	−	0.0832727i	−0.840985	−	0.541058i	$-0.818024\pi$
$149$	0.586861	−	1.01647i	0.0480775	−	0.0832727i	0.889063	+	0.457785i	$0.151357\pi$
$150$		−	15.9543i		−	1.30267i
$151$	4.37075			0.355687			0.177843	−	0.984059i	$-0.443088\pi$
$151$	4.37075			0.355687			0.177843	+	0.984059i	$0.443088\pi$
$152$	−19.0296	+	32.9603i	−1.54351	+	2.67343i
$153$	−1.40354	+	4.46799i	−0.113470	+	0.361216i
$154$	31.8719	+	55.2038i	2.56831	+	4.44845i
$155$	5.62044	+	9.73488i	0.451444	+	0.781924i
$156$			16.9545i			1.35744i
$157$	4.38370	+	7.59279i	0.349857	+	0.605971i	0.986224	−	0.165416i	$-0.0528967\pi$
$157$	4.38370	+	7.59279i	0.349857	+	0.605971i	−0.636367	+	0.771387i	$0.719563\pi$
$158$	−29.3408	+	16.9399i	−2.33423	+	1.34767i
$159$	7.34957	−	4.24328i	0.582859	−	0.336514i
$160$	−3.94443	−	2.27732i	−0.311835	−	0.180038i
$161$	18.2549			1.43869
$162$	−13.9604	+	24.1801i	−1.09683	+	1.89977i
$163$	3.58760	−	2.07130i	0.281003	−	0.162237i	−0.352875	−	0.935671i	$-0.614796\pi$
$163$	3.58760	−	2.07130i	0.281003	−	0.162237i	0.633877	+	0.773434i	$0.281462\pi$
$164$			15.1487i			1.18292i
$165$	−13.7970	+	7.96571i	−1.07410	+	0.620130i
$166$	11.7999	−	20.4381i	0.915851	−	1.58630i
$167$	2.80154	+	1.61747i	0.216790	+	0.125164i	0.604463	−	0.796633i	$-0.293388\pi$
$167$	2.80154	+	1.61747i	0.216790	+	0.125164i	−0.387673	+	0.921797i	$0.626721\pi$
$168$	52.3018			4.03517
$169$	4.62696	−	8.01412i	0.355920	−	0.616471i
$170$	−3.08466	−	13.8445i	−0.236583	−	1.06182i
$171$	7.46004			0.570484
$172$	21.4898	−	18.3300i	1.63858	−	1.39765i
$173$			7.13873i			0.542748i	0.962474	+	0.271374i	$0.0874780\pi$
$173$			7.13873i			0.542748i	−0.962474	+	0.271374i	$0.912522\pi$
$174$	−9.45266			−0.716604
$175$	−12.0059	−	6.93159i	−0.907558	−	0.523979i
$176$		−	33.9637i		−	2.56011i
$177$	10.7396	+	6.20054i	0.807241	+	0.466061i
$178$	−20.4311	+	35.3877i	−1.53137	+	2.65242i
$179$	2.57082	+	4.45279i	0.192152	+	0.332817i	0.945963	−	0.324274i	$-0.105120\pi$
$179$	2.57082	+	4.45279i	0.192152	+	0.332817i	−0.753811	+	0.657091i	$0.771787\pi$
$180$			6.70171i			0.499516i
$181$	−11.0474	+	6.37822i	−0.821147	+	0.474089i	−0.850812	−	0.525470i	$-0.823889\pi$
$181$	−11.0474	+	6.37822i	−0.821147	+	0.474089i	0.0296649	+	0.999560i	$0.490556\pi$
$182$	18.6825	+	10.7864i	1.38484	+	0.799538i
$183$	3.73127			0.275823
$184$	−20.6424	−	11.9179i	−1.52178	−	0.878600i
$185$	−0.369739	−	0.640407i	−0.0271838	−	0.0470837i
$186$	20.9569	+	36.2985i	1.53664	+	2.66153i
$187$	17.3682	−	15.9490i	1.27009	−	1.16630i
$188$	−46.2992			−3.37672
$189$	8.41247	+	14.5708i	0.611917	+	1.05987i
$190$	−19.5669	+	11.2970i	−1.41953	+	0.819567i
$191$	2.78150	−	4.81770i	0.201262	−	0.348597i	−0.747673	−	0.664067i	$-0.768829\pi$
$191$	2.78150	−	4.81770i	0.201262	−	0.348597i	0.948935	+	0.315470i	$0.102162\pi$
$192$	6.21118	+	3.58603i	0.448254	+	0.258799i
$193$			0.578350i			0.0416306i	0.999783	+	0.0208153i	$0.00662619\pi$
$193$			0.578350i			0.0416306i	−0.999783	+	0.0208153i	$0.993374\pi$
$194$		−	47.2593i		−	3.39302i
$195$	−2.69582	+	4.66930i	−0.193052	+	0.334376i
$196$	27.3437	−	47.3606i	1.95312	−	3.38290i
$197$	5.49896	−	3.17483i	0.391785	−	0.226197i	−0.291148	−	0.956678i	$-0.594037\pi$
$197$	5.49896	−	3.17483i	0.391785	−	0.226197i	0.682933	+	0.730481i	$0.260704\pi$
$198$	−14.1287	+	8.15718i	−1.00408	+	0.579706i
$199$			10.0023i			0.709042i	0.935048	+	0.354521i	$0.115356\pi$
$199$			10.0023i			0.709042i	−0.935048	+	0.354521i	$0.884644\pi$
$200$	9.05074	+	15.6763i	0.639984	+	1.10848i
$201$	25.0412	−	14.4575i	1.76627	−	1.01975i
$202$	0.560701	+	0.971163i	0.0394508	+	0.0683308i
$203$	−4.10684	+	7.11326i	−0.288244	+	0.499253i
$204$	−7.85470	−	35.2532i	−0.549939	−	2.46822i
$205$	−2.40870	+	4.17200i	−0.168231	+	0.291385i
$206$	3.07517	+	5.32635i	0.214257	+	0.371104i
$207$			4.67209i			0.324733i
$208$	−5.74715	−	9.95435i	−0.398493	−	0.690210i
$209$	−32.5290	−	18.7806i	−2.25008	−	1.29908i
$210$	26.8892	+	15.5245i	1.85553	+	1.07129i
$211$		−	13.1262i		−	0.903642i	−0.892109	−	0.451821i	$-0.850775\pi$
$211$		−	13.1262i		−	0.903642i	0.892109	−	0.451821i	$-0.149225\pi$
$212$	−8.98734	+	15.5665i	−0.617253	+	1.06911i
$213$	−11.3540			−0.777966
$214$			11.9571i			0.817369i
$215$	8.83287	−	1.63115i	0.602397	−	0.111244i
$216$		−	21.9687i		−	1.49478i
$217$	36.4202			2.47236
$218$	23.0918	+	13.3321i	1.56397	+	0.902961i
$219$	−12.8324			−0.867132
$220$	16.8715	−	29.2223i	1.13748	−	1.97017i
$221$	2.39162	−	7.61339i	0.160878	−	0.512132i
$222$	−1.37865	−	2.38789i	−0.0925288	−	0.160265i
$223$	−13.2886			−0.889872			−0.444936	−	0.895562i	$-0.646774\pi$
$223$	−13.2886			−0.889872			−0.444936	+	0.895562i	$0.646774\pi$
$224$	−12.7799	+	7.37846i	−0.853890	+	0.492994i
$225$	1.77405	−	3.07274i	0.118270	−	0.204849i
$226$			27.6163i			1.83701i
$227$	−3.39154	−	1.95811i	−0.225105	−	0.129964i	0.383207	−	0.923662i	$-0.374820\pi$
$227$	−3.39154	−	1.95811i	−0.225105	−	0.129964i	−0.608312	+	0.793698i	$0.708153\pi$
$228$	−49.8246	+	28.7662i	−3.29971	+	1.90509i
$229$	2.79328	+	4.83811i	0.184585	+	0.319711i	0.943437	−	0.331553i	$-0.107572\pi$
$229$	2.79328	+	4.83811i	0.184585	+	0.319711i	−0.758851	+	0.651264i	$0.774239\pi$
$230$	−7.07508	−	12.2544i	−0.466517	−	0.808031i
$231$			51.6174i			3.39618i
$232$	9.28795	−	5.36240i	0.609784	−	0.352059i
$233$	9.70656	−	5.60409i	0.635898	−	0.367136i	−0.147135	−	0.989116i	$-0.547005\pi$
$233$	9.70656	−	5.60409i	0.635898	−	0.367136i	0.783033	+	0.621981i	$0.213672\pi$
$234$	−2.76062	+	4.78154i	−0.180467	+	0.312579i
$235$	−12.7509	−	7.36174i	−0.831778	−	0.480227i
$236$	−26.2657			−1.70975
$237$	−27.4347			−1.78207
$238$	−43.8434	−	13.7727i	−2.84195	−	0.892749i
$239$	−13.4872	+	23.3605i	−0.872413	+	1.51106i	−0.0129202	+	0.999917i	$0.504113\pi$
$239$	−13.4872	+	23.3605i	−0.872413	+	1.51106i	−0.859493	+	0.511148i	$0.829221\pi$
$240$	−8.27171	−	14.3270i	−0.533936	−	0.924805i
$241$	−5.97009	+	3.44683i	−0.384567	+	0.222030i	−0.679804	−	0.733394i	$-0.737935\pi$
$241$	−5.97009	+	3.44683i	−0.384567	+	0.222030i	0.295236	+	0.955424i	$0.404602\pi$
$242$	54.5168			3.50447
$243$	−9.73068	+	5.61801i	−0.624223	+	0.360396i
$244$	−6.84411	+	3.95145i	−0.438149	+	0.252965i
$245$	15.0610	−	8.69547i	0.962212	−	0.555533i
$246$	−8.98134	+	15.5561i	−0.572629	+	0.991823i
$247$	−12.7118			−0.808832
$248$	−41.1835	−	23.7773i	−2.61516	−	1.50986i
$249$	16.5500	−	9.55515i	1.04881	−	0.605533i
$250$			27.9466i			1.76750i
$251$	−12.1298	−	21.0095i	−0.765629	−	1.32611i	−0.939913	−	0.341413i	$-0.889094\pi$
$251$	−12.1298	−	21.0095i	−0.765629	−	1.32611i	0.174284	−	0.984695i	$-0.444239\pi$
$252$	18.8043	+	10.8567i	1.18456	+	0.683907i
$253$	11.7620	−	20.3723i	0.739469	−	1.28080i
$254$	10.4160			0.653556
$255$	3.44219	−	10.9577i	0.215558	−	0.686200i
$256$	−31.8922			−1.99326
$257$	1.53014			0.0954475			0.0477237	−	0.998861i	$-0.484803\pi$
$257$	1.53014			0.0954475			0.0477237	+	0.998861i	$0.484803\pi$
$258$	32.9351	−	6.08208i	2.05045	−	0.378654i
$259$	−2.39589			−0.148874
$260$		−	11.4196i		−	0.708214i
$261$	−1.82054	−	1.05109i	−0.112689	−	0.0650609i
$262$		−	12.8196i		−	0.792001i
$263$	6.75217	−	11.6951i	0.416357	−	0.721151i	−0.579213	−	0.815176i	$-0.696640\pi$
$263$	6.75217	−	11.6951i	0.416357	−	0.721151i	0.995570	+	0.0940254i	$0.0299735\pi$
$264$	33.6990	−	58.3684i	2.07403	−	3.59233i
$265$	−4.95026	+	2.85804i	−0.304092	+	0.175568i
$266$			73.2038i			4.48841i
$267$	−28.6557	+	16.5444i	−1.75370	+	1.01250i
$268$	−30.6213	+	53.0377i	−1.87049	+	3.23979i
$269$		−	9.71634i		−	0.592416i	−0.955124	−	0.296208i	$-0.904278\pi$
$269$		−	9.71634i		−	0.592416i	0.955124	−	0.296208i	$-0.0957221\pi$
$270$	6.52087	−	11.2945i	0.396848	−	0.687360i
$271$	14.0264	+	24.2944i	0.852042	+	1.47578i	0.879363	+	0.476153i	$0.157969\pi$
$271$	14.0264	+	24.2944i	0.852042	+	1.47578i	−0.0273211	+	0.999627i	$0.508698\pi$
$272$	16.5616	+	18.0354i	1.00420	+	1.09356i
$273$	8.73440	+	15.1284i	0.528630	+	0.915614i
$274$	20.4756			1.23698
$275$	−15.4712	+	8.93231i	−0.932950	+	0.538639i
$276$	−18.0158	−	31.2043i	−1.08442	−	1.87828i
$277$	19.5223	+	11.2712i	1.17298	+	0.677222i	0.954381	−	0.298593i	$-0.0965172\pi$
$277$	19.5223	+	11.2712i	1.17298	+	0.677222i	0.218601	+	0.975814i	$0.429851\pi$
$278$	29.4687	+	17.0137i	1.76741	+	1.02042i
$279$			9.32125i			0.558049i
$280$	−35.2276			−2.10525
$281$	−7.71795	+	13.3679i	−0.460414	+	0.797461i	−0.998981	−	0.0451218i	$-0.985632\pi$
$281$	−7.71795	+	13.3679i	−0.460414	+	0.797461i	0.538567	+	0.842582i	$0.318966\pi$
$282$	−47.5444	−	27.4497i	−2.83123	−	1.63461i
$283$	25.7997	−	14.8955i	1.53364	−	0.885445i	0.534446	−	0.845203i	$-0.320520\pi$
$283$	25.7997	−	14.8955i	1.53364	−	0.885445i	0.999190	−	0.0402423i	$-0.0128130\pi$
$284$	20.8262	−	12.0240i	1.23581	−	0.713495i
$285$	−18.2957			−1.08375
$286$	24.0750	−	13.8997i	1.42359	−	0.821907i
$287$	7.80414	+	13.5172i	0.460664	+	0.797894i
$288$	−1.88842	−	3.27083i	−0.111276	−	0.192736i
$289$	−1.44572	+	16.9384i	−0.0850421	+	0.996377i
$290$	6.36679			0.373871
$291$	19.1344	−	33.1418i	1.12168	−	1.94281i
$292$	23.5379	−	13.5896i	1.37745	−	0.795272i
$293$	−14.1121			−0.824440			−0.412220	−	0.911084i	$-0.635247\pi$
$293$	−14.1121			−0.824440			−0.412220	+	0.911084i	$0.635247\pi$
$294$	56.1580	−	32.4228i	3.27520	−	1.89094i
$295$	−7.23363	−	4.17634i	−0.421158	−	0.243156i
$296$	2.70925	+	1.56419i	0.157472	+	0.0909165i
$297$	21.6813			1.25807
$298$	−1.47387	+	2.55282i	−0.0853791	+	0.147881i
$299$		−	7.96117i		−	0.460407i
$300$			27.3632i			1.57982i
$301$	9.73229	−	27.4266i	0.560960	−	1.58084i
$302$	−10.9769			−0.631650
$303$			0.908071i			0.0521673i
$304$	19.5021	−	33.7786i	1.11852	−	1.93734i
$305$	−2.51318			−0.143904
$306$	3.52493	−	11.2211i	0.201507	−	0.641470i
$307$	8.07909	−	13.9934i	0.461098	−	0.798646i	−0.537918	−	0.842997i	$-0.680789\pi$
$307$	8.07909	−	13.9934i	0.461098	−	0.798646i	0.999016	+	0.0443517i	$0.0141222\pi$
$308$	−54.6634	−	94.6797i	−3.11473	−	5.39488i
$309$			4.98032i			0.283320i
$310$	−14.1154	−	24.4487i	−0.801703	−	1.38859i
$311$	15.8950	+	9.17695i	0.901320	+	0.520377i	0.877628	−	0.479342i	$-0.159125\pi$
$311$	15.8950	+	9.17695i	0.901320	+	0.520377i	0.0236918	+	0.999719i	$0.492458\pi$
$312$		−	22.8094i		−	1.29133i
$313$	−2.33614	−	1.34877i	−0.132046	−	0.0762370i	0.432522	−	0.901624i	$-0.357624\pi$
$313$	−2.33614	−	1.34877i	−0.132046	−	0.0762370i	−0.564568	+	0.825387i	$0.690957\pi$
$314$	−11.0094	−	19.0689i	−0.621298	−	1.07612i
$315$	3.45250	+	5.97991i	0.194527	+	0.336930i
$316$	50.3223	−	29.0536i	2.83085	−	1.63439i
$317$		−	14.9707i		−	0.840835i	−0.907331	−	0.420418i	$-0.861884\pi$
$317$		−	14.9707i		−	0.840835i	0.907331	−	0.420418i	$-0.138116\pi$
$318$	−18.4581	+	10.6568i	−1.03508	+	0.597602i
$319$	5.29224	+	9.16642i	0.296308	+	0.513221i
$320$	−4.18351	−	2.41535i	−0.233865	−	0.135022i
$321$	−4.84121	+	8.38521i	−0.270210	+	0.468017i
$322$	−45.8462			−2.55491
$323$	26.4315	−	5.88914i	1.47069	−	0.327681i
$324$	23.9434	−	41.4712i	1.33019	−	2.30395i
$325$	−3.02295	+	5.23590i	−0.167683	+	0.290435i
$326$	−9.01007	+	5.20197i	−0.499022	+	0.288110i
$327$	10.7958	+	18.6989i	0.597010	+	1.03405i
$328$		−	20.3801i		−	1.12530i
$329$	−41.3127	+	23.8519i	−2.27764	+	1.31500i
$330$	34.6505	−	20.0055i	1.90745	−	1.10126i
$331$	2.62803	+	4.55188i	0.144449	+	0.250194i	0.929167	−	0.369659i	$-0.120526\pi$
$331$	2.62803	+	4.55188i	0.144449	+	0.250194i	−0.784718	+	0.619853i	$0.787192\pi$
$332$	−20.2380	+	35.0532i	−1.11070	+	1.92380i
$333$		−	0.613196i		−	0.0336030i
$334$	−7.03593	−	4.06219i	−0.384989	−	0.222273i
$335$	−16.8663	+	9.73779i	−0.921507	+	0.532032i
$336$	−53.6003			−2.92414
$337$	−19.8729	+	11.4736i	−1.08255	+	0.625008i	−0.931582	−	0.363531i	$-0.881571\pi$
$337$	−19.8729	+	11.4736i	−1.08255	+	0.625008i	−0.150964	+	0.988539i	$0.548238\pi$
$338$	−11.6204	+	20.1271i	−0.632064	+	1.09477i
$339$	−11.1814	+	19.3667i	−0.607288	+	1.05185i
$340$	5.29049	+	23.7446i	0.286917	+	1.28773i
$341$	23.4662	−	40.6447i	1.27077	−	2.20103i
$342$	−18.7355			−1.01310
$343$		−	25.2800i		−	1.36499i
$344$	−28.9110	+	24.6599i	−1.55877	+	1.32957i
$345$		−	11.4583i		−	0.616894i
$346$		−	17.9286i		−	0.963846i
$347$	−12.0411	−	6.95194i	−0.646401	−	0.373200i	0.140675	−	0.990056i	$-0.455073\pi$
$347$	−12.0411	−	6.95194i	−0.646401	−	0.373200i	−0.787076	+	0.616856i	$0.788406\pi$
$348$	16.2122			0.869066
$349$	−14.8500	+	25.7210i	−0.794905	+	1.37682i	0.127995	+	0.991775i	$0.459146\pi$
$349$	−14.8500	+	25.7210i	−0.794905	+	1.37682i	−0.922900	+	0.385041i	$0.874187\pi$
$350$	30.1521	+	17.4083i	1.61170	+	0.930514i
$351$	6.35451	−	3.66878i	0.339178	−	0.195825i
$352$			19.0163i			1.01357i
$353$	2.32936	+	4.03456i	0.123979	+	0.214738i	0.921333	−	0.388773i	$-0.127101\pi$
$353$	2.32936	+	4.03456i	0.123979	+	0.214738i	−0.797354	+	0.603511i	$0.793768\pi$
$354$	−26.9721	−	15.5723i	−1.43355	−	0.827660i
$355$	7.64745			0.405885
$356$	35.0413	−	60.6932i	1.85718	−	3.21673i
$357$	−25.1700	−	27.4099i	−1.33214	−	1.45068i
$358$	−6.45649	−	11.1830i	−0.341236	−	0.591038i
$359$	1.62902	+	2.82155i	0.0859766	+	0.148916i	0.905807	−	0.423691i	$-0.139266\pi$
$359$	1.62902	+	2.82155i	0.0859766	+	0.148916i	−0.819830	+	0.572606i	$0.805932\pi$
$360$		−	9.01603i		−	0.475186i
$361$	−12.0678	−	20.9020i	−0.635147	−	1.10011i
$362$	27.7450	−	16.0186i	1.45824	−	0.841918i
$363$	38.2313	+	22.0729i	2.00662	+	1.15853i
$364$	−32.0423	−	18.4996i	−1.67947	−	0.969644i
$365$	8.64318			0.452405
$366$	−9.37088			−0.489824
$367$	20.2158	+	11.6716i	1.05526	+	0.609253i	0.924117	−	0.382111i	$-0.124803\pi$
$367$	20.2158	+	11.6716i	1.05526	+	0.609253i	0.131141	+	0.991364i	$0.458136\pi$
$368$	21.1549	+	12.2138i	1.10278	+	0.636689i
$369$	−3.45954	+	1.99737i	−0.180096	+	0.103979i
$370$	0.928581	+	1.60835i	0.0482746	+	0.0836141i
$371$			18.5199i			0.961508i
$372$	−35.9431	−	62.2554i	−1.86357	−	3.22779i
$373$	−1.92466	−	3.33361i	−0.0996550	−	0.172608i	0.811887	−	0.583815i	$-0.198441\pi$
$373$	−1.92466	−	3.33361i	−0.0996550	−	0.172608i	−0.911542	+	0.411207i	$0.865107\pi$
$374$	−43.6194	+	40.0550i	−2.25550	+	2.07119i
$375$	−11.3151	+	19.5983i	−0.584307	+	1.01205i
$376$	62.2879			3.21225
$377$	3.10218	+	1.79104i	0.159770	+	0.0922434i
$378$	−21.1275	−	36.5939i	−1.08668	−	1.88219i
$379$		−	0.0120364i		−	0.000618270i	−1.00000		0.000309135i	$-0.999902\pi$
$379$		−	0.0120364i		−	0.000618270i	1.00000		0.000309135i	$-9.84007e-5\pi$
$380$	33.5591	−	19.3754i	1.72155	−	0.993935i
$381$	7.30447	+	4.21724i	0.374220	+	0.216056i
$382$	−6.98560	+	12.0994i	−0.357414	+	0.619060i
$383$	34.3781			1.75664			0.878320	−	0.478073i	$-0.158665\pi$
$383$	34.3781			1.75664			0.878320	+	0.478073i	$0.158665\pi$
$384$	−27.3115	−	15.7683i	−1.39373	−	0.804673i
$385$		−	34.7667i		−	1.77187i
$386$		−	1.45250i		−	0.0739302i
$387$	7.01947	+	2.49085i	0.356820	+	0.126617i
$388$			81.0542i			4.11490i
$389$	22.0169			1.11630			0.558150	−	0.829740i	$-0.311512\pi$
$389$	22.0169			1.11630			0.558150	+	0.829740i	$0.311512\pi$
$390$	6.77042	−	11.7267i	0.342833	−	0.593805i
$391$	3.68826	+	16.5536i	0.186524	+	0.837150i
$392$	−36.7863	+	63.7158i	−1.85799	+	3.21813i
$393$	5.19044	−	8.99011i	0.261823	−	0.453491i
$394$	−13.8104	+	7.97341i	−0.695756	+	0.401695i
$395$	18.4785			0.929753
$396$	24.2320	−	13.9903i	1.21770	−	0.703042i
$397$	−17.7075	−	10.2234i	−0.888715	−	0.513100i	−0.0151930	−	0.999885i	$-0.504836\pi$
$397$	−17.7075	−	10.2234i	−0.888715	−	0.513100i	−0.873522	+	0.486785i	$0.838170\pi$
$398$		−	25.1202i		−	1.25916i
$399$	−29.6389	+	51.3361i	−1.48380	+	2.57002i
$400$	−9.27544	−	16.0655i	−0.463772	−	0.803277i
$401$	1.42805	−	0.824485i	0.0713134	−	0.0411728i	−0.463919	−	0.885877i	$-0.653557\pi$
$401$	1.42805	−	0.824485i	0.0713134	−	0.0411728i	0.535233	+	0.844705i	$0.320224\pi$
$402$	−62.8896	+	36.3093i	−3.13665	+	1.81094i
$403$		−	15.8833i		−	0.791202i
$404$	−0.961656	−	1.66564i	−0.0478442	−	0.0828686i
$405$	13.1881	−	7.61417i	0.655323	−	0.378351i
$406$	10.3141	−	17.8646i	0.511881	−	0.886605i
$407$	−1.54372	+	2.67380i	−0.0765194	+	0.132535i
$408$	10.5672	+	47.4273i	0.523153	+	2.34800i
$409$	−30.2220			−1.49438			−0.747191	−	0.664609i	$-0.768598\pi$
$409$	−30.2220			−1.49438			−0.747191	+	0.664609i	$0.768598\pi$
$410$	6.04933	−	10.4778i	0.298755	−	0.517459i
$411$	14.3590	+	8.29020i	0.708280	+	0.408925i
$412$	−5.27421	−	9.13519i	−0.259841	−	0.450059i
$413$	−23.4368	+	13.5312i	−1.15325	+	0.665829i
$414$		−	11.7337i		−	0.576681i
$415$	−11.1472	+	6.43582i	−0.547193	+	0.315922i
$416$	3.21783	+	5.57345i	0.157767	+	0.273261i
$417$	13.7771	+	23.8627i	0.674668	+	1.16856i
$418$	81.6950	+	47.1666i	3.99583	+	2.30699i
$419$			4.37648i			0.213805i	0.994270	+	0.106902i	$0.0340933\pi$
$419$			4.37648i			0.213805i	−0.994270	+	0.106902i	$0.965907\pi$
$420$	−46.1176	−	26.6260i	−2.25031	−	1.29922i
$421$	4.11951	+	7.13520i	0.200773	+	0.347749i	0.948778	−	0.315945i	$-0.102321\pi$
$421$	4.11951	+	7.13520i	0.200773	+	0.347749i	−0.748005	+	0.663693i	$0.768988\pi$
$422$			32.9657i			1.60474i
$423$	−6.10457	−	10.5734i	−0.296814	−	0.514097i
$424$	12.0910	−	20.9422i	0.587189	−	1.01704i
$425$	3.85988	−	12.2874i	0.187232	−	0.596027i
$426$	28.5151			1.38156
$427$	−4.07132	+	7.05173i	−0.197025	+	0.341257i
$428$		−	20.5075i		−	0.991269i
$429$	22.5110			1.08684
$430$	−22.1833	+	4.09655i	−1.06977	+	0.197553i
$431$			15.6456i			0.753621i	0.926290	+	0.376810i	$0.122979\pi$
$431$			15.6456i			0.753621i	−0.926290	+	0.376810i	$0.877021\pi$
$432$			22.5141i			1.08321i
$433$	−14.9478	+	25.8904i	−0.718347	+	1.24421i	0.243307	+	0.969949i	$0.421768\pi$
$433$	−14.9478	+	25.8904i	−0.718347	+	1.24421i	−0.961654	+	0.274265i	$0.911566\pi$
$434$	−91.4674			−4.39058
$435$	4.46488	+	2.57780i	0.214074	+	0.123596i
$436$	−39.6046	−	22.8658i	−1.89672	−	1.09507i
$437$	23.3957	−	13.5075i	1.11917	−	0.646153i
$438$	32.2279			1.53991
$439$	−8.11746	+	4.68662i	−0.387425	+	0.223680i	−0.681044	−	0.732242i	$-0.738474\pi$
$439$	−8.11746	+	4.68662i	−0.387425	+	0.223680i	0.293619	+	0.955923i	$0.405140\pi$
$440$	−22.6978	+	39.3138i	−1.08208	+	1.87421i
$441$	14.4211			0.686718
$442$	−6.00642	+	19.1206i	−0.285696	+	0.909476i
$443$	0.638830	+	1.10649i	0.0303517	+	0.0525707i	0.880802	−	0.473484i	$-0.157004\pi$
$443$	0.638830	+	1.10649i	0.0303517	+	0.0525707i	−0.850451	+	0.526055i	$0.823671\pi$
$444$	2.36451	+	4.09545i	0.112215	+	0.194362i
$445$	19.3009	−	11.1434i	0.914949	−	0.528246i
$446$	33.3737			1.58029
$447$	−2.06718	+	1.19349i	−0.0977743	+	0.0564500i
$448$	−13.5545	+	7.82568i	−0.640389	+	0.369729i
$449$	18.8811	+	10.9010i	0.891057	+	0.514452i	0.874288	−	0.485408i	$-0.161329\pi$
$449$	18.8811	+	10.9010i	0.891057	+	0.514452i	0.0167686	+	0.999859i	$0.494662\pi$
$450$	−4.45543	+	7.71703i	−0.210031	+	0.363784i
$451$	20.1134			0.947105
$452$		−	47.3647i		−	2.22785i
$453$	−7.69785	−	4.44436i	−0.361676	−	0.208814i
$454$	8.51768	+	4.91769i	0.399755	+	0.230798i
$455$	−5.88301	−	10.1897i	−0.275800	−	0.477699i
$456$	67.0307	−	38.7002i	3.13900	−	1.81230i
$457$	−27.1570			−1.27035			−0.635175	−	0.772368i	$-0.719072\pi$
$457$	−27.1570			−1.27035			−0.635175	+	0.772368i	$0.719072\pi$
$458$	−7.01519	−	12.1507i	−0.327798	−	0.567763i
$459$	−11.5132	+	10.5724i	−0.537389	+	0.493476i
$460$	12.1344	+	21.0175i	0.565771	+	0.979945i
$461$	−0.901498	+	1.56144i	−0.0419869	+	0.0727235i	−0.886255	−	0.463197i	$-0.846702\pi$
$461$	−0.901498	+	1.56144i	−0.0419869	+	0.0727235i	0.844268	+	0.535921i	$0.180035\pi$
$462$		−	129.635i		−	6.03115i
$463$	−14.8320	+	25.6897i	−0.689301	+	1.19390i	0.282764	+	0.959190i	$0.408749\pi$
$463$	−14.8320	+	25.6897i	−0.689301	+	1.19390i	−0.972064	+	0.234714i	$0.924585\pi$
$464$	−9.51855	+	5.49553i	−0.441887	+	0.255124i
$465$		−	22.8603i		−	1.06012i
$466$	−24.3775	+	14.0744i	−1.12927	+	0.651983i
$467$	−10.2978	+	17.8363i	−0.476524	+	0.825363i	−0.999638	−	0.0268992i	$-0.991437\pi$
$467$	−10.2978	+	17.8363i	−0.476524	+	0.825363i	0.523114	+	0.852262i	$0.324770\pi$
$468$	4.73473	−	8.20079i	0.218863	−	0.379082i
$469$			63.1004i			2.91371i
$470$	32.0233	+	18.4886i	1.47712	+	0.852817i
$471$		−	17.8301i		−	0.821567i
$472$	35.3361			1.62648
$473$	−24.3372	−	28.5327i	−1.11903	−	1.31193i
$474$	68.9008			3.16472
$475$	−20.5158			−0.941332
$476$	75.1957	+	23.6214i	3.44659	+	1.08269i
$477$	−4.73993			−0.217027
$478$	33.8724	−	58.6687i	1.54929	−	2.68344i
$479$	19.3025	+	11.1443i	0.881952	+	0.509195i	0.871302	−	0.490748i	$-0.163276\pi$
$479$	19.3025	+	11.1443i	0.881952	+	0.509195i	0.0106505	+	0.999943i	$0.496610\pi$
$480$	4.63134	+	8.02171i	0.211391	+	0.366139i
$481$			1.04488i			0.0476423i
$482$	14.9936	−	8.65654i	0.682939	−	0.394295i
$483$	−32.1509	−	18.5623i	−1.46291	−	0.844614i
$484$	−93.5015			−4.25007
$485$	−12.8879	+	22.3225i	−0.585210	+	1.01361i
$486$	24.4381	−	14.1093i	1.10853	−	0.640013i
$487$	−19.8836	+	11.4798i	−0.901010	+	0.520198i	−0.877528	−	0.479526i	$-0.840809\pi$
$487$	−19.8836	+	11.4798i	−0.901010	+	0.520198i	−0.0234821	+	0.999724i	$0.507475\pi$
$488$	9.20760	−	5.31601i	0.416808	−	0.240644i
$489$	−8.42473			−0.380980
$490$	−37.8249	+	21.8382i	−1.70876	+	0.986551i
$491$	−3.40750	−	5.90197i	−0.153778	−	0.266352i	0.778835	−	0.627229i	$-0.215811\pi$
$491$	−3.40750	−	5.90197i	−0.153778	−	0.266352i	−0.932614	+	0.360877i	$0.882478\pi$
$492$	15.4039	−	26.6803i	0.694459	−	1.20284i
$493$	−7.28007	−	2.28691i	−0.327878	−	0.102997i
$494$	31.9250			1.43637
$495$	8.89806			0.399938
$496$	42.2060	+	24.3677i	1.89511	+	1.09414i
$497$	12.3888	−	21.4580i	0.555713	−	0.962523i
$498$	−41.5645	+	23.9973i	−1.86255	+	1.07534i
$499$	5.83929	−	3.37132i	0.261403	−	0.150921i	−0.363572	−	0.931566i	$-0.618443\pi$
$499$	5.83929	−	3.37132i	0.261403	−	0.150921i	0.624974	+	0.780645i	$0.285109\pi$
$500$		−	47.9310i		−	2.14354i
$501$	−3.28942	−	5.69744i	−0.146960	−	0.254543i
$502$	30.4635	+	52.7643i	1.35965	+	2.35499i
$503$	13.2162	−	7.63037i	0.589281	−	0.340221i	−0.175532	−	0.984474i	$-0.556165\pi$
$503$	13.2162	−	7.63037i	0.589281	−	0.340221i	0.764813	+	0.644252i	$0.222831\pi$
$504$	−25.2981	−	14.6059i	−1.12687	−	0.650597i
$505$		−	0.611627i		−	0.0272170i
$506$	−29.5396	+	51.1641i	−1.31320	+	2.27452i
$507$	−16.2982	+	9.40975i	−0.723827	+	0.417902i
$508$	−17.8644			−0.792604
$509$	−5.14392	−	8.90953i	−0.228000	−	0.394908i	0.729215	−	0.684285i	$-0.239885\pi$
$509$	−5.14392	−	8.90953i	−0.228000	−	0.394908i	−0.957215	+	0.289376i	$0.906552\pi$
$510$	−8.64488	+	27.5198i	−0.382802	+	1.21860i
$511$	14.0019	−	24.2519i	0.619406	−	1.07284i
$512$	49.0812			2.16910
$513$	21.5631	+	12.4494i	0.952033	+	0.549656i
$514$	−3.84287			−0.169502
$515$		−	3.35447i		−	0.147816i
$516$	−56.4869	+	10.4313i	−2.48670	+	0.459214i
$517$			61.4729i			2.70358i
$518$	6.01716			0.264379
$519$	7.25895	−	12.5729i	0.318633	−	0.551888i
$520$			15.3632i			0.673719i
$521$	18.6103	+	10.7447i	0.815334	+	0.470733i	0.848805	−	0.528707i	$-0.177323\pi$
$521$	18.6103	+	10.7447i	0.815334	+	0.470733i	−0.0334709	+	0.999440i	$0.510656\pi$
$522$	4.57220	+	2.63976i	0.200120	+	0.115539i
$523$	14.3812	+	24.9090i	0.628846	+	1.08919i	0.987784	+	0.155832i	$0.0498058\pi$
$523$	14.3812	+	24.9090i	0.628846	+	1.08919i	−0.358937	+	0.933362i	$0.616861\pi$
$524$			21.9869i			0.960503i
$525$	14.0966	+	24.4161i	0.615228	+	1.06561i
$526$	−16.9577	+	29.3716i	−0.739392	+	1.28066i
$527$	7.35842	+	33.0259i	0.320538	+	1.43863i
$528$	−34.5357	+	59.8176i	−1.50297	+	2.60323i
$529$	−3.04048	−	5.26626i	−0.132195	−	0.228968i
$530$	12.4323	−	7.17781i	0.540026	−	0.311784i
$531$	−3.46314	−	5.99833i	−0.150287	−	0.260306i
$532$		−	125.551i		−	5.44335i
$533$	5.89500	−	3.40348i	0.255341	−	0.147421i
$534$	71.9672	−	41.5503i	3.11433	−	1.79806i
$535$	3.26077	−	5.64782i	0.140975	−	0.244176i
$536$	41.1958	−	71.3533i	1.77939	−	3.08199i
$537$		−	10.4565i		−	0.451230i
$538$			24.4021i			1.05205i
$539$	−62.8821	−	36.3050i	−2.70852	−	1.56377i
$540$	−11.1839	+	19.3711i	−0.481279	+	0.833600i
$541$	−4.91450	+	2.83739i	−0.211291	+	0.121989i	−0.601911	−	0.798563i	$-0.705594\pi$
$541$	−4.91450	+	2.83739i	−0.211291	+	0.121989i	0.390620	+	0.920552i	$0.372261\pi$
$542$	−35.2265	−	61.0141i	−1.51311	−	2.62078i
$543$	25.9425			1.11330
$544$	−9.27287	−	10.0980i	−0.397571	−	0.432950i
$545$	−7.27147	−	12.5946i	−0.311476	−	0.539491i
$546$	−21.9360	−	37.9943i	−0.938774	−	1.62600i
$547$	−23.2117	−	13.4013i	−0.992460	−	0.572997i	−0.0864512	−	0.996256i	$-0.527553\pi$
$547$	−23.2117	−	13.4013i	−0.992460	−	0.572997i	−0.906009	+	0.423259i	$0.860886\pi$
$548$	−35.1176			−1.50015
$549$	−1.80479	−	1.04200i	−0.0770267	−	0.0444714i
$550$	38.8552	−	22.4330i	1.65679	−	0.956548i
$551$			12.1553i			0.517832i
$552$	24.2372	+	41.9801i	1.03161	+	1.78679i
$553$	29.9349	−	51.8488i	1.27296	−	2.20484i
$554$	−49.0293	−	28.3071i	−2.08305	−	1.20265i
$555$			1.50386i			0.0638354i
$556$	−50.5416	−	29.1802i	−2.14344	−	1.23752i
$557$	−4.61019			−0.195340			−0.0976699	−	0.995219i	$-0.531139\pi$
$557$	−4.61019			−0.195340			−0.0976699	+	0.995219i	$0.531139\pi$
$558$		−	23.4098i		−	0.991018i
$559$	−11.9611	−	4.24437i	−0.505899	−	0.179518i
$560$	36.1022			1.52560
$561$	−46.8068	+	10.4289i	−1.97618	+	0.440309i
$562$	19.3832	−	33.5727i	0.817632	−	1.41618i
$563$	22.1779			0.934688			0.467344	−	0.884076i	$-0.345211\pi$
$563$	22.1779			0.934688			0.467344	+	0.884076i	$0.345211\pi$
$564$	81.5431	+	47.0789i	3.43358	+	1.98238i
$565$	7.53115	−	13.0443i	0.316838	−	0.548779i
$566$	−64.7947	+	37.4093i	−2.72353	+	1.57243i
$567$		−	49.3395i		−	2.07206i
$568$	−28.0182	+	16.1763i	−1.17562	+	0.678744i
$569$	−20.3358	+	35.2226i	−0.852519	+	1.47661i	0.0264086	+	0.999651i	$0.491593\pi$
$569$	−20.3358	+	35.2226i	−0.852519	+	1.47661i	−0.878928	+	0.476955i	$0.841740\pi$
$570$	45.9488			1.92458
$571$	39.4525	+	22.7779i	1.65103	+	0.953225i	0.976648	+	0.214846i	$0.0689249\pi$
$571$	39.4525	+	22.7779i	1.65103	+	0.953225i	0.674386	+	0.738379i	$0.264408\pi$
$572$	−41.2909	+	23.8393i	−1.72646	+	0.996773i
$573$	−9.79767	+	5.65669i	−0.409303	+	0.236311i
$574$	−19.5997	−	33.9477i	−0.818076	−	1.41695i
$575$		−	12.8487i		−	0.535828i
$576$	−2.00288	−	3.46909i	−0.0834532	−	0.144545i
$577$	−8.81635	−	15.2704i	−0.367030	−	0.635714i	0.622070	−	0.782962i	$-0.286292\pi$
$577$	−8.81635	−	15.2704i	−0.367030	−	0.635714i	−0.989100	+	0.147248i	$0.952959\pi$
$578$	3.63084	−	42.5400i	0.151023	−	1.76943i
$579$	0.588090	−	1.01860i	0.0244402	−	0.0423316i
$580$	−10.9196			−0.453414
$581$			41.7038i			1.73017i
$582$	−48.0552	+	83.2340i	−1.99195	+	3.45016i
$583$	20.6681	+	11.9328i	0.855987	+	0.494204i
$584$	−31.6663	+	18.2825i	−1.31036	+	0.756537i
$585$	2.60791	−	1.50568i	0.107824	−	0.0622521i
$586$	35.4419			1.46409
$587$	−15.6017	−	27.0230i	−0.643953	−	1.11536i	−0.984542	−	0.175147i	$-0.943960\pi$
$587$	−15.6017	−	27.0230i	−0.643953	−	1.11536i	0.340590	−	0.940212i	$-0.389373\pi$
$588$	−96.3163	+	55.6083i	−3.97202	+	2.29325i
$589$	46.6766	−	26.9487i	1.92328	−	1.11040i
$590$	18.1669	+	10.4887i	0.747919	+	0.431811i
$591$	−12.9132			−0.531177
$592$	−2.77651	−	1.60302i	−0.114114	−	0.0658838i
$593$	−11.3200	−	19.6068i	−0.464855	−	0.805153i	0.534340	−	0.845270i	$-0.320560\pi$
$593$	−11.3200	−	19.6068i	−0.464855	−	0.805153i	−0.999195	+	0.0401168i	$0.987227\pi$
$594$	−54.4514			−2.23417
$595$	16.9532	+	18.4618i	0.695012	+	0.756859i
$596$	2.52783	−	4.37833i	0.103544	−	0.179343i
$597$	10.1707	−	17.6162i	0.416259	−	0.720982i
$598$			19.9941i			0.817619i
$599$	0.0513591	−	0.0889565i	0.00209848	−	0.00363467i	−0.864974	−	0.501816i	$-0.832665\pi$
$599$	0.0513591	−	0.0889565i	0.00209848	−	0.00363467i	0.867073	+	0.498182i	$0.165999\pi$
$600$		−	36.8126i		−	1.50287i
$601$		−	16.2904i		−	0.664500i	−0.943191	−	0.332250i	$-0.892192\pi$
$601$		−	16.2904i		−	0.664500i	0.943191	−	0.332250i	$-0.107808\pi$
$602$	−24.4422	+	68.8805i	−0.996188	+	2.80736i
$603$	−16.1497			−0.657667
$604$	18.8265			0.766038
$605$	−25.7505	−	14.8671i	−1.04691	−	0.604432i
$606$		−	2.28057i		−	0.0926420i
$607$	31.4586	+	18.1626i	1.27686	+	0.737198i	0.976271	−	0.216554i	$-0.0694819\pi$
$607$	31.4586	+	18.1626i	1.27686	+	0.737198i	0.300594	+	0.953752i	$0.402815\pi$
$608$	−10.9192	+	18.9127i	−0.442833	+	0.767010i
$609$	14.4661	−	8.35201i	0.586196	−	0.338440i
$610$	6.31171			0.255554
$611$	10.4021	+	18.0169i	0.420823	+	0.728887i
$612$	−6.04559	+	19.2453i	−0.244378	+	0.777946i
$613$	28.5802			1.15434			0.577171	−	0.816623i	$-0.304156\pi$
$613$	28.5802			1.15434			0.577171	+	0.816623i	$0.304156\pi$
$614$	−20.2902	+	35.1437i	−0.818847	+	1.41828i
$615$	8.48451	−	4.89853i	0.342128	−	0.197528i
$616$	73.5404	+	127.376i	2.96303	+	5.13211i
$617$	6.79067	−	3.92060i	0.273382	−	0.157837i	−0.357042	−	0.934089i	$-0.616215\pi$
$617$	6.79067	−	3.92060i	0.273382	−	0.157837i	0.630424	+	0.776251i	$0.282881\pi$
$618$		−	12.5078i		−	0.503138i
$619$	31.9910	−	18.4700i	1.28583	−	0.742372i	0.307919	−	0.951413i	$-0.400367\pi$
$619$	31.9910	−	18.4700i	1.28583	−	0.742372i	0.977907	+	0.209041i	$0.0670341\pi$
$620$	24.2093	+	41.9318i	0.972270	+	1.68402i
$621$	−7.79687	+	13.5046i	−0.312877	+	0.541920i
$622$	−39.9194	−	23.0474i	−1.60062	−	0.924119i
$623$		−	72.2085i		−	2.89297i
$624$			23.3757i			0.935778i
$625$	−0.188091	+	0.325782i	−0.00752362	+	0.0130313i
$626$	5.86710	+	3.38737i	0.234496	+	0.135386i
$627$	38.1938	+	66.1536i	1.52531	+	2.64192i
$628$	18.8822	+	32.7050i	0.753483	+	1.30507i
$629$	−0.484072	−	2.17260i	−0.0193012	−	0.0866272i
$630$	−8.67078	−	15.0182i	−0.345452	−	0.598341i
$631$	−3.32085	−	5.75188i	−0.132201	−	0.228979i	0.792324	−	0.610101i	$-0.208871\pi$
$631$	−3.32085	−	5.75188i	−0.132201	−	0.228979i	−0.924525	+	0.381122i	$0.875538\pi$
$632$	−67.7002	+	39.0867i	−2.69297	+	1.55479i
$633$	−13.3472	+	23.1180i	−0.530504	+	0.918859i
$634$			37.5980i			1.49321i
$635$	−4.91989	−	2.84050i	−0.195240	−	0.112722i
$636$	31.6573	−	18.2774i	1.25530	−	0.724745i
$637$	−24.5733			−0.973629
$638$	−13.2912	−	23.0210i	−0.526203	−	0.911410i
$639$	5.49189	+	3.17074i	0.217256	+	0.125433i
$640$	18.3955	+	10.6207i	0.727147	+	0.419819i
$641$		−	25.1134i		−	0.991919i	−0.868346	−	0.495960i	$-0.834816\pi$
$641$		−	25.1134i		−	0.991919i	0.868346	−	0.495960i	$-0.165184\pi$
$642$	12.1584	−	21.0590i	0.479855	−	0.831134i
$643$			3.42114i			0.134916i	0.997722	+	0.0674582i	$0.0214889\pi$
$643$			3.42114i			0.134916i	−0.997722	+	0.0674582i	$0.978511\pi$
$644$	78.6306			3.09848
$645$	−17.2152	−	6.10880i	−0.677849	−	0.240534i
$646$	−66.3813	+	14.7903i	−2.61174	+	0.581916i
$647$	−13.7238			−0.539537			−0.269769	−	0.962925i	$-0.586947\pi$
$647$	−13.7238			−0.539537			−0.269769	+	0.962925i	$0.586947\pi$
$648$	−32.2118	+	55.7925i	−1.26540	+	2.19174i
$649$			34.8738i			1.36892i
$650$	7.59198	−	13.1497i	0.297782	−	0.515773i
$651$	−64.1439	−	37.0335i	−2.51400	−	1.45146i
$652$	15.4531	−	8.92187i	0.605192	−	0.349408i
$653$		−	20.9825i		−	0.821110i	−0.911836	−	0.410555i	$-0.865335\pi$
$653$		−	20.9825i		−	0.821110i	0.911836	−	0.410555i	$-0.134665\pi$
$654$	−27.1131	−	46.9613i	−1.06021	−	1.83633i
$655$	−3.49600	+	6.05525i	−0.136600	+	0.236598i
$656$			20.8861i			0.815465i
$657$	6.20695	+	3.58359i	0.242156	+	0.139809i
$658$	103.755	−	59.9028i	4.04478	−	2.33525i
$659$	−7.21480	−	12.4964i	−0.281049	−	0.486790i	0.690595	−	0.723242i	$-0.257349\pi$
$659$	−7.21480	−	12.4964i	−0.281049	−	0.486790i	−0.971643	+	0.236452i	$0.924016\pi$
$660$	−59.4289	+	34.3113i	−2.31327	+	1.33557i
$661$	37.9604			1.47649			0.738245	−	0.674533i	$-0.235655\pi$
$661$	37.9604			1.47649			0.738245	+	0.674533i	$0.235655\pi$
$662$	−6.60016	−	11.4318i	−0.256522	−	0.444310i
$663$	−11.9538	+	10.9770i	−0.464246	+	0.426310i
$664$	27.2268	−	47.1582i	1.05661	−	1.83009i
$665$	19.9631	−	34.5771i	0.774137	−	1.34084i
$666$			1.54001i			0.0596742i
$667$	−7.61263			−0.294762
$668$	12.0673	+	6.96705i	0.466897	+	0.269563i
$669$	23.4042	+	13.5124i	0.904857	+	0.522420i
$670$	42.3590	−	24.4560i	1.63647	−	0.944816i
$671$	5.24646	+	9.08713i	0.202537	+	0.350805i
$672$	30.0108			1.15769
$673$	−15.4260	+	8.90621i	−0.594629	+	0.343309i	−0.766926	−	0.641736i	$-0.778215\pi$
$673$	−15.4260	+	8.90621i	−0.594629	+	0.343309i	0.172297	+	0.985045i	$0.444881\pi$
$674$	49.9098	−	28.8154i	1.92245	−	1.10993i
$675$	10.2557	−	5.92112i	0.394741	−	0.227904i
$676$	19.9300	−	34.5198i	0.766539	−	1.32769i
$677$			16.4685i			0.632936i	0.948603	+	0.316468i	$0.102497\pi$
$677$			16.4685i			0.632936i	−0.948603	+	0.316468i	$0.897503\pi$
$678$	28.0814	−	48.6384i	1.07846	−	1.86795i
$679$	41.7565	+	72.3244i	1.60247	+	2.77556i
$680$	−7.11747	−	31.9444i	−0.272943	−	1.22501i
$681$	3.98217	+	6.89731i	0.152597	+	0.264306i
$682$	−58.9342	+	102.077i	−2.25671	+	3.90873i
$683$	−9.20879	−	5.31670i	−0.352365	−	0.203438i	0.313362	−	0.949634i	$-0.398545\pi$
$683$	−9.20879	−	5.31670i	−0.352365	−	0.203438i	−0.665726	+	0.746196i	$0.731878\pi$
$684$	32.1332			1.22864
$685$	−9.67146	−	5.58382i	−0.369528	−	0.213347i
$686$			63.4894i			2.42404i
$687$		−	11.3613i		−	0.433460i
$688$	29.6287	−	25.2721i	1.12959	−	0.963491i
$689$	8.07677			0.307700
$690$			28.7769i			1.09552i
$691$	−8.97676	−	5.18273i	−0.341492	−	0.197160i	0.319440	−	0.947607i	$-0.396505\pi$
$691$	−8.97676	−	5.18273i	−0.341492	−	0.197160i	−0.660932	+	0.750446i	$0.729839\pi$
$692$			30.7492i			1.16891i
$693$	14.4148	−	24.9671i	0.547571	−	0.948421i
$694$	30.2407	+	17.4594i	1.14792	+	0.662752i
$695$	−9.27950	−	16.0726i	−0.351992	−	0.609667i
$696$	−21.8108			−0.826737
$697$	−10.6806	+	9.80785i	−0.404558	+	0.371499i
$698$	37.2951	−	64.5971i	1.41164	−	2.44503i
$699$	−22.7938			−0.862142
$700$	−51.7138	−	29.8569i	−1.95460	−	1.12849i
$701$	10.6373	+	18.4243i	0.401765	+	0.695877i	0.993939	−	0.109933i	$-0.0350636\pi$
$701$	10.6373	+	18.4243i	0.401765	+	0.695877i	−0.592174	+	0.805810i	$0.701730\pi$
$702$	−15.9590	+	9.21394i	−0.602334	+	0.347758i
$703$	−3.07061	+	1.77282i	−0.115810	+	0.0668631i
$704$			20.1690i			0.760146i
$705$	14.9714	+	25.9313i	0.563857	+	0.976629i
$706$	−5.85006	−	10.1326i	−0.220170	−	0.381345i
$707$	−1.71617	−	0.990828i	−0.0645430	−	0.0372639i
$708$	46.2597	+	26.7080i	1.73854	+	1.00375i
$709$			45.3238i			1.70217i	0.525027	+	0.851086i	$0.324055\pi$
$709$			45.3238i			1.70217i	−0.525027	+	0.851086i	$0.675945\pi$
$710$	−19.2062			−0.720795
$711$	13.2700	+	7.66144i	0.497664	+	0.287326i
$712$	−47.1421	+	81.6526i	−1.76673	+	3.06006i
$713$	16.8775	+	29.2327i	0.632068	+	1.09477i
$714$	63.2133	+	68.8384i	2.36570	+	2.57621i
$715$	−15.1622			−0.567032
$716$	11.0735	+	19.1798i	0.413836	+	0.716785i
$717$	47.5078	−	27.4286i	1.77421	−	1.02434i
$718$	−4.09121	−	7.08618i	−0.152683	−	0.264454i
$719$	20.7953	+	12.0062i	0.775534	+	0.447755i	0.834845	−	0.550485i	$-0.185557\pi$
$719$	20.7953	+	12.0062i	0.775534	+	0.447755i	−0.0593112	+	0.998240i	$0.518890\pi$
$720$			9.23987i			0.344350i
$721$	−9.41231	−	5.43420i	−0.350533	−	0.202380i
$722$	30.3077	+	52.4944i	1.12793	+	1.95364i
$723$	14.0195			0.521391
$724$	−47.5853	+	27.4734i	−1.76849	+	1.02104i
$725$	5.00667	+	2.89060i	0.185943	+	0.107354i
$726$	−96.0160	−	55.4349i	−3.56349	−	2.05738i
$727$	25.2064			0.934853			0.467426	−	0.884032i	$-0.345181\pi$
$727$	25.2064			0.934853			0.467426	+	0.884032i	$0.345181\pi$
$728$	43.1075	+	24.8882i	1.59767	+	0.922416i
$729$	−10.5017			−0.388953
$730$	−21.7069			−0.803409
$731$	26.8368	+	3.28392i	0.992596	+	0.121460i
$732$	16.0720			0.594037
$733$	17.5659			0.648813			0.324406	−	0.945918i	$-0.394835\pi$
$733$	17.5659			0.648813			0.324406	+	0.945918i	$0.394835\pi$
$734$	−50.7710	−	29.3126i	−1.87399	−	1.08195i
$735$	−35.3676			−1.30455
$736$	−11.8447	−	6.83852i	−0.436600	−	0.252071i
$737$	70.4197	+	40.6568i	2.59394	+	1.49761i
$738$	8.68845	−	5.01628i	0.319826	−	0.184652i
$739$	31.7737			1.16882			0.584408	−	0.811460i	$-0.301327\pi$
$739$	31.7737			1.16882			0.584408	+	0.811460i	$0.301327\pi$
$740$	−1.59260	−	2.75847i	−0.0585453	−	0.101403i
$741$	22.3883	+	12.9259i	0.822453	+	0.474844i
$742$		−	46.5119i		−	1.70751i
$743$	5.91820	+	3.41688i	0.217118	+	0.125353i	0.604615	−	0.796518i	$-0.293327\pi$
$743$	5.91820	+	3.41688i	0.217118	+	0.125353i	−0.387497	+	0.921871i	$0.626660\pi$
$744$	48.3555	+	83.7542i	1.77280	+	3.07058i
$745$	1.39234	−	0.803867i	0.0510114	−	0.0294514i
$746$	4.83368	+	8.37218i	0.176974	+	0.306527i
$747$	−10.6735			−0.390524
$748$	74.8114	−	68.6982i	2.73538	−	2.51185i
$749$	−10.5648	−	18.2988i	−0.386030	−	0.668624i
$750$	28.4172	−	49.2200i	1.03765	−	1.79726i
$751$	−24.3491	−	14.0579i	−0.888510	−	0.512982i	−0.0150554	−	0.999887i	$-0.504792\pi$
$751$	−24.3491	−	14.0579i	−0.888510	−	0.512982i	−0.873455	+	0.486905i	$0.838126\pi$
$752$	−63.8343			−2.32780
$753$			49.3365i			1.79792i
$754$	−7.79096	−	4.49811i	−0.283730	−	0.163812i
$755$	5.18485	+	2.99347i	0.188696	+	0.108944i
$756$	36.2356	+	62.7620i	1.31788	+	2.28263i
$757$	−20.6236	−	35.7212i	−0.749579	−	1.29831i	−0.948025	−	0.318197i	$-0.896923\pi$
$757$	−20.6236	−	35.7212i	−0.749579	−	1.29831i	0.198446	−	0.980112i	$-0.436411\pi$
$758$			0.0302289i			0.00109796i
$759$	−41.4308	+	23.9201i	−1.50384	+	0.868245i
$760$	−45.1482	+	26.0663i	−1.63770	+	0.945524i
$761$	−26.9871	−	46.7431i	−0.978282	−	1.69443i	−0.668648	−	0.743579i	$-0.733127\pi$
$761$	−26.9871	−	46.7431i	−0.978282	−	1.69443i	−0.309635	−	0.950856i	$-0.600207\pi$
$762$	−18.3448	−	10.5914i	−0.664562	−	0.383685i
$763$	−47.1188			−1.70581
$764$	11.9810	−	20.7516i	0.433456	−	0.750768i
$765$	−4.72504	+	4.33893i	−0.170834	+	0.156874i
$766$	−86.3389			−3.11955
$767$	5.90114	+	10.2211i	0.213078	+	0.369061i
$768$	56.1691	+	32.4292i	2.02683	+	1.17019i
$769$	−6.70884	+	11.6201i	−0.241927	+	0.419030i	−0.961263	−	0.275632i	$-0.911113\pi$
$769$	−6.70884	+	11.6201i	−0.241927	+	0.419030i	0.719336	+	0.694662i	$0.244446\pi$
$770$			87.3147i			3.14660i
$771$	−2.69491	−	1.55591i	−0.0970548	−	0.0560346i
$772$			2.49117i			0.0896592i
$773$	−24.1643			−0.869128			−0.434564	−	0.900641i	$-0.643097\pi$
$773$	−24.1643			−0.869128			−0.434564	+	0.900641i	$0.643097\pi$
$774$	−17.6290	−	6.25564i	−0.633663	−	0.224854i
$775$		−	25.6343i		−	0.920813i
$776$		−	109.045i		−	3.91448i
$777$	4.21969	+	2.43624i	0.151381	+	0.0873996i
$778$	−55.2942			−1.98239
$779$	20.0038	+	11.5492i	0.716711	+	0.413793i
$780$	−11.6119	+	20.1124i	−0.415773	+	0.720140i
$781$	−15.9647	−	27.6516i	−0.571261	−	0.989453i
$782$	−9.26288	−	41.5734i	−0.331240	−	1.48666i
$783$	−3.50816	−	6.07630i	−0.125371	−	0.217149i
$784$	37.6996	−	65.2977i	1.34642	−	2.33206i
$785$			12.0094i			0.428633i
$786$	−13.0355	+	22.5782i	−0.464962	+	0.805338i
$787$	0.936636	−	0.540767i	0.0333875	−	0.0192763i	−0.483213	−	0.875503i	$-0.660530\pi$
$787$	0.936636	−	0.540767i	0.0333875	−	0.0192763i	0.516601	+	0.856226i	$0.327197\pi$
$788$	23.6861	−	13.6752i	0.843782	−	0.487158i
$789$	−23.7841	+	13.7318i	−0.846736	+	0.488863i
$790$	−46.4078			−1.65111
$791$	−24.4007	−	42.2633i	−0.867591	−	1.50271i
$792$	−32.6001	+	18.8217i	−1.15839	+	0.668799i
$793$	3.07534	+	1.77555i	0.109209	+	0.0630516i
$794$	44.4715	+	25.6756i	1.57824	+	0.911195i
$795$	11.6247			0.412284
$796$			43.0835i			1.52705i
$797$	−2.35135	+	4.07266i	−0.0832892	+	0.144261i	−0.904661	−	0.426132i	$-0.859876\pi$
$797$	−2.35135	+	4.07266i	−0.0832892	+	0.144261i	0.821372	+	0.570393i	$0.193209\pi$
$798$	74.4365	−	128.928i	2.63503	−	4.56400i
$799$	−29.9758	−	32.6433i	−1.06047	−	1.15484i
$800$	5.19333	+	8.99511i	0.183612	+	0.318025i
$801$	18.4808			0.652987
$802$	−3.58647	+	2.07065i	−0.126643	+	0.0731172i
$803$	−18.0433	−	31.2520i	−0.636736	−	1.10286i
$804$	107.862	−	62.2740i	3.80399	−	2.19623i
$805$	21.6550	+	12.5025i	0.763240	+	0.440657i
$806$			39.8900i			1.40507i
$807$	−9.87996	+	17.1126i	−0.347791	+	0.602392i
$808$	1.29375	+	2.24084i	0.0455139	+	0.0788323i
$809$			10.9139i			0.383713i	0.981423	+	0.191857i	$0.0614509\pi$
$809$			10.9139i			0.383713i	−0.981423	+	0.191857i	$0.938549\pi$
$810$	−33.1213	+	19.1226i	−1.16376	+	0.671899i
$811$	−1.01339	−	0.585080i	−0.0355849	−	0.0205449i	0.482102	−	0.876115i	$-0.339873\pi$
$811$	−1.01339	−	0.585080i	−0.0355849	−	0.0205449i	−0.517687	+	0.855570i	$0.673207\pi$
$812$	−17.6897	+	30.6395i	−0.620787	+	1.07523i
$813$		−	57.0503i		−	2.00084i
$814$	3.87697	−	6.71512i	0.135888	−	0.235365i
$815$	5.67444			0.198767
$816$	−10.8295	−	48.6048i	−0.379110	−	1.70151i
$817$	−7.82101	−	42.3516i	−0.273623	−	1.48170i
$818$	75.9010			2.65382
$819$		−	9.75672i		−	0.340927i
$820$	−10.3752	+	17.9703i	−0.362317	+	0.627552i
$821$		−	43.2389i		−	1.50905i	−0.656272	−	0.754524i	$-0.727868\pi$
$821$		−	43.2389i		−	1.50905i	0.656272	−	0.754524i	$-0.272132\pi$
$822$	−36.0620	−	20.8204i	−1.25781	−	0.726195i
$823$	−1.20177	−	0.693840i	−0.0418909	−	0.0241857i	0.478908	−	0.877865i	$-0.341033\pi$
$823$	−1.20177	−	0.693840i	−0.0418909	−	0.0241857i	−0.520799	+	0.853679i	$0.674366\pi$
$824$	7.09556	+	12.2899i	0.247186	+	0.428138i
$825$	36.3309			1.26488
$826$	58.8603	−	33.9830i	2.04801	−	1.18242i
$827$	1.72267	+	0.994583i	0.0599030	+	0.0345850i	0.529652	−	0.848215i	$-0.322322\pi$
$827$	1.72267	+	0.994583i	0.0599030	+	0.0345850i	−0.469749	+	0.882800i	$0.655656\pi$
$828$			20.1245i			0.699373i
$829$	8.47665	−	14.6820i	0.294406	−	0.509927i	−0.680440	−	0.732804i	$-0.738211\pi$
$829$	8.47665	−	14.6820i	0.294406	−	0.509927i	0.974847	+	0.222877i	$0.0715448\pi$
$830$	27.9955	−	16.1632i	0.971739	−	0.561034i
$831$	−22.9220	−	39.7021i	−0.795157	−	1.37725i
$832$	3.41287	+	5.91127i	0.118320	+	0.204936i
$833$	51.0949	−	11.3843i	1.77033	−	0.394444i
$834$	−34.6005	−	59.9298i	−1.19812	−	2.07520i
$835$	2.21557	+	3.83748i	0.0766730	+	0.132802i
$836$	−140.115	−	80.8952i	−4.84597	−	2.79782i
$837$	−15.5555	+	26.9428i	−0.537675	+	0.931281i
$838$		−	10.9913i		−	0.379688i
$839$			12.4160i			0.428648i	0.976763	+	0.214324i	$0.0687549\pi$
$839$			12.4160i			0.428648i	−0.976763	+	0.214324i	$0.931245\pi$
$840$	62.0435	+	35.8208i	2.14070	+	1.23594i
$841$	−12.7874	+	22.1484i	−0.440944	+	0.763737i
$842$	−10.3459	−	17.9197i	−0.356545	−	0.617554i
$843$	27.1860	−	15.6958i	0.936335	−	0.540593i
$844$		−	56.5393i		−	1.94616i
$845$	10.9775	−	6.33789i	0.377639	−	0.218030i
$846$	15.3313	+	26.5546i	0.527101	+	0.912966i
$847$	−83.4311	+	48.1690i	−2.86673	+	1.65511i
$848$	−12.3911	+	21.4621i	−0.425514	+	0.737012i
$849$	−60.5853			−2.07928
$850$	−9.69389	+	30.8592i	−0.332498	+	1.05846i
$851$	−1.11028	−	1.92307i	−0.0380600	−	0.0659219i
$852$	−48.9061			−1.67549
$853$	−24.8955	+	14.3734i	−0.852404	+	0.492136i	−0.861461	−	0.507823i	$-0.830450\pi$
$853$	−24.8955	+	14.3734i	−0.852404	+	0.492136i	0.00905718	+	0.999959i	$0.497117\pi$
$854$	10.2249	−	17.7100i	0.349889	−	0.606025i
$855$	8.84955	+	5.10929i	0.302648	+	0.174734i
$856$			27.5895i			0.942988i
$857$	16.0963	+	9.29320i	0.549839	+	0.317450i	0.749057	−	0.662505i	$-0.230507\pi$
$857$	16.0963	+	9.29320i	0.549839	+	0.317450i	−0.199218	+	0.979955i	$0.563840\pi$
$858$	−56.5352			−1.93008
$859$	36.4400			1.24332			0.621659	−	0.783288i	$-0.286459\pi$
$859$	36.4400			1.24332			0.621659	+	0.783288i	$0.286459\pi$
$860$	38.0465	−	7.02598i	1.29737	−	0.239584i
$861$		−	31.7423i		−	1.08177i
$862$		−	39.2930i		−	1.33833i
$863$	24.2347	−	41.9758i	0.824960	−	1.42887i	−0.0769892	−	0.997032i	$-0.524531\pi$
$863$	24.2347	−	41.9758i	0.824960	−	1.42887i	0.901950	−	0.431841i	$-0.142136\pi$
$864$		−	12.6057i		−	0.428854i
$865$	−4.88923	+	8.46840i	−0.166239	+	0.287934i
$866$	37.5407	−	65.0225i	1.27569	−	2.20955i
$867$	19.7699	−	28.3622i	0.671420	−	0.963231i
$868$	156.875			5.32470
$869$	−38.5753	−	66.8144i	−1.30858	−	2.26652i
$870$	−11.2133	−	6.47401i	−0.380167	−	0.219489i
$871$	27.5188			0.932440
$872$	53.2814	+	30.7620i	1.80434	+	1.04173i
$873$	−18.5105	+	10.6870i	−0.626484	+	0.361701i
$874$	−58.7572	+	33.9235i	−1.98749	+	1.14748i
$875$	−24.6925	−	42.7687i	−0.834759	−	1.44585i
$876$	−55.2739			−1.86753
$877$	−25.3430	+	14.6318i	−0.855772	+	0.494080i	−0.862594	−	0.505896i	$-0.831162\pi$
$877$	−25.3430	+	14.6318i	−0.855772	+	0.494080i	0.00682189	+	0.999977i	$0.497829\pi$
$878$	20.3866	−	11.7702i	0.688014	−	0.397225i
$879$	24.8546	+	14.3498i	0.838324	+	0.484007i
$880$	23.2613	−	40.2898i	0.784140	−	1.35817i
$881$		−	52.8264i		−	1.77977i	−0.456187	−	0.889884i	$-0.650785\pi$
$881$		−	52.8264i		−	1.77977i	0.456187	−	0.889884i	$-0.349215\pi$
$882$	−36.2178			−1.21952
$883$	−8.43591	+	14.6114i	−0.283891	+	0.491713i	−0.972340	−	0.233572i	$-0.924959\pi$
$883$	−8.43591	+	14.6114i	−0.283891	+	0.491713i	0.688449	+	0.725285i	$0.258292\pi$
$884$	10.3016	−	32.7937i	0.346480	−	1.10297i
$885$	8.49334	+	14.7109i	0.285501	+	0.494501i
$886$	−1.60439	−	2.77888i	−0.0539005	−	0.0933584i
$887$			48.0721i			1.61410i	0.590480	+	0.807052i	$0.298938\pi$
$887$			48.0721i			1.61410i	−0.590480	+	0.807052i	$0.701062\pi$
$888$	−3.18106	−	5.50975i	−0.106749	−	0.184895i
$889$	−15.9403	+	9.20316i	−0.534622	+	0.308664i
$890$	−48.4732	+	27.9860i	−1.62482	+	0.938092i
$891$	−55.0625	−	31.7904i	−1.84466	−	1.06502i
$892$	−57.2390			−1.91650
$893$	−35.2979	+	61.1378i	−1.18120	+	2.04590i
$894$	5.19162	−	2.99738i	0.173634	−	0.100247i
$895$			7.04290i			0.235418i
$896$	59.6011	−	34.4107i	1.99113	−	1.14958i
$897$	−8.09524	+	14.0214i	−0.270292	+	0.468160i
$898$	−47.4190	−	27.3774i	−1.58239	−	0.913595i
$899$	−15.1879			−0.506545
$900$	7.64148	−	13.2354i	0.254716	−	0.441181i
$901$	−16.7939	+	3.74182i	−0.559487	+	0.124658i
$902$	−50.5139			−1.68193
$903$	−45.0292	+	38.4081i	−1.49848	+	1.27814i
$904$			63.7212i			2.11934i
$905$	−17.4735			−0.580837
$906$	19.3328	+	11.1618i	0.642288	+	0.370825i
$907$		−	39.7575i		−	1.32013i	−0.751211	−	0.660063i	$-0.770530\pi$
$907$		−	39.7575i		−	1.32013i	0.751211	−	0.660063i	$-0.229470\pi$
$908$	−14.6086	−	8.43430i	−0.484805	−	0.279902i
$909$	0.253589	−	0.439229i	0.00841102	−	0.0145683i
$910$	14.7749	+	25.5908i	0.489783	+	0.848328i
$911$		−	9.10274i		−	0.301587i	−0.988565	−	0.150794i	$-0.951817\pi$
$911$		−	9.10274i		−	0.301587i	0.988565	−	0.150794i	$-0.0481829\pi$
$912$	−68.6949	+	39.6610i	−2.27471	+	1.31331i
$913$	46.5412	+	26.8706i	1.54029	+	0.889287i
$914$	68.2033			2.25597
$915$	4.42625	+	2.55550i	0.146327	+	0.0844822i
$916$	12.0317	+	20.8395i	0.397539	+	0.688558i
$917$	11.3270	+	19.6189i	0.374049	+	0.647872i
$918$	28.9147	−	26.5519i	0.954328	−	0.876345i
$919$	46.8822			1.54650			0.773251	−	0.634100i	$-0.218629\pi$
$919$	46.8822			1.54650			0.773251	+	0.634100i	$0.218629\pi$
$920$	−16.3249	−	28.2755i	−0.538215	−	0.932215i
$921$	−28.4581	+	16.4303i	−0.937727	+	0.541397i
$922$	2.26407	−	3.92148i	0.0745630	−	0.129147i
$923$	−9.35809	−	5.40290i	−0.308025	−	0.177839i
$924$			222.336i			7.31431i
$925$			1.68635i			0.0554468i
$926$	37.2498	−	64.5185i	1.22410	−	2.12021i
$927$	1.39081	−	2.40895i	0.0456802	−	0.0791205i
$928$	5.32944	−	3.07695i	0.174947	−	0.101006i
$929$	−45.7157	+	26.3940i	−1.49988	+	0.865958i	−1.00000		0.000134320i	$-0.999957\pi$
$929$	−45.7157	+	26.3940i	−1.49988	+	0.865958i	−0.499884	+	0.866093i	$0.666624\pi$
$930$			57.4126i			1.88263i
$931$	−41.6929	−	72.2142i	−1.36643	−	2.36672i
$932$	41.8098	−	24.1389i	1.36953	−	0.790696i
$933$	−18.6630	−	32.3253i	−0.610999	−	1.05828i
$934$	25.8623	−	44.7948i	0.846240	−	1.46573i
$935$	31.5265	−	7.02434i	1.03103	−	0.229721i
$936$	−6.36979	+	11.0328i	−0.208203	+	0.360618i
$937$	12.1415	+	21.0297i	0.396645	+	0.687009i	0.993310	−	0.115481i	$-0.0368410\pi$
$937$	12.1415	+	21.0297i	0.396645	+	0.687009i	−0.596665	+	0.802491i	$0.703508\pi$
$938$		−	158.474i		−	5.17434i
$939$	2.74297	+	4.75096i	0.0895134	+	0.155042i
$940$	−54.9229	−	31.7098i	−1.79139	−	1.03426i
$941$	11.7112	+	6.76145i	0.381774	+	0.220417i	0.678590	−	0.734518i	$-0.262591\pi$
$941$	11.7112	+	6.76145i	0.381774	+	0.220417i	−0.296816	+	0.954935i	$0.595925\pi$
$942$			44.7794i			1.45899i
$943$	−7.23306	+	12.5280i	−0.235541	+	0.407969i
$944$	−36.2134			−1.17865
$945$			23.0464i			0.749699i
$946$	61.1217	+	71.6584i	1.98724	+	2.32981i
$947$		−	33.5617i		−	1.09061i	−0.838238	−	0.545304i	$-0.816414\pi$
$947$		−	33.5617i		−	1.09061i	0.838238	−	0.545304i	$-0.183586\pi$
$948$	−118.171			−3.83803
$949$	−10.5766	−	6.10638i	−0.343329	−	0.198221i
$950$	51.5245			1.67168
$951$	−15.2228	+	26.3666i	−0.493632	+	0.854995i
$952$	−101.163	−	31.7787i	−3.27872	−	1.02995i
$953$	9.75277	+	16.8923i	0.315923	+	0.547195i	0.979633	−	0.200795i	$-0.0643525\pi$
$953$	9.75277	+	16.8923i	0.315923	+	0.547195i	−0.663710	+	0.747990i	$0.731019\pi$
$954$	11.9041			0.385409
$955$	6.59917	−	3.81003i	0.213544	−	0.123290i
$956$	−58.0943	+	100.622i	−1.87891	+	3.25436i
$957$		−	21.5254i		−	0.695819i
$958$	−48.4771	−	27.9883i	−1.56623	−	0.904261i
$959$	−31.3353	+	18.0915i	−1.01187	+	0.584204i
$960$	4.91205	+	8.50792i	0.158536	+	0.274592i
$961$	18.1722	+	31.4752i	0.586200	+	1.01533i
$962$		−	2.62416i		−	0.0846062i
$963$	4.68333	−	2.70392i	0.150918	−	0.0871327i
$964$	−25.7154	+	14.8468i	−0.828238	+	0.478183i
$965$	−0.396105	+	0.686074i	−0.0127511	+	0.0220855i
$966$	80.7452	+	46.6183i	2.59794	+	1.49992i
$967$	16.0624			0.516532			0.258266	−	0.966074i	$-0.416849\pi$
$967$	16.0624			0.516532			0.258266	+	0.966074i	$0.416849\pi$
$968$	125.791			4.04307
$969$	−52.5399	−	16.5045i	−1.68783	−	0.530202i
$970$	32.3673	−	56.0618i	1.03925	−	1.80004i
$971$	21.9395	+	38.0003i	0.704071	+	1.21949i	0.967026	+	0.254678i	$0.0819696\pi$
$971$	21.9395	+	38.0003i	0.704071	+	1.21949i	−0.262955	+	0.964808i	$0.584697\pi$
$972$	−41.9137	+	24.1989i	−1.34438	+	0.776179i
$973$	−60.1308			−1.92770
$974$	49.9365	−	28.8309i	1.60007	−	0.923800i
$975$	10.6481	−	6.14771i	0.341014	−	0.196884i
$976$	−9.43620	+	5.44799i	−0.302045	+	0.174386i
$977$	3.21030	−	5.56040i	0.102707	−	0.177893i	−0.810092	−	0.586302i	$-0.800583\pi$
$977$	3.21030	−	5.56040i	0.102707	−	0.177893i	0.912799	+	0.408409i	$0.133916\pi$
$978$	21.1583			0.676567
$979$	−80.5842	−	46.5253i	−2.57548	−	1.48696i
$980$	64.8734	−	37.4547i	2.07230	−	1.19645i
$981$		−	12.0594i		−	0.385028i
$982$	8.55777	+	14.8225i	0.273089	+	0.473005i
$983$	3.55603	+	2.05307i	0.113420	+	0.0654828i	0.555637	−	0.831425i	$-0.312475\pi$
$983$	3.55603	+	2.05307i	0.113420	+	0.0654828i	−0.442217	+	0.896908i	$0.645808\pi$
$984$	−20.7233	+	35.8938i	−0.660635	+	1.14425i
$985$	8.69760			0.277129
$986$	18.2835	+	5.74346i	0.582266	+	0.182909i
$987$	97.0142			3.08800
$988$	−54.7545			−1.74197
$989$	26.5241	−	4.89816i	0.843417	−	0.155752i
$990$	−22.3470			−0.710235
$991$		−	61.9572i		−	1.96814i	−0.177794	−	0.984068i	$-0.556896\pi$
$991$		−	61.9572i		−	1.96814i	0.177794	−	0.984068i	$-0.443104\pi$
$992$	−23.6312	−	13.6435i	−0.750291	−	0.433181i
$993$		−	10.6891i		−	0.339210i
$994$	−31.1138	+	53.8907i	−0.986870	+	1.70931i
$995$	−6.85043	+	11.8653i	−0.217173	+	0.376155i
$996$	71.2870	−	41.1576i	2.25882	−	1.30413i
$997$			13.1965i			0.417936i	0.977922	+	0.208968i	$0.0670104\pi$
$997$			13.1965i			0.417936i	−0.977922	+	0.208968i	$0.932990\pi$
$998$	−14.6651	+	8.46689i	−0.464215	+	0.268015i
$999$	1.02331	−	1.77243i	0.0323762	−	0.0560772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.j.a.135.5	✓	128
17.16	even	2	inner	731.2.j.a.135.6	yes	128
43.36	even	3	inner	731.2.j.a.509.6	yes	128
731.509	even	6	inner	731.2.j.a.509.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.j.a.135.5	✓	128	1.1	even	1	trivial
731.2.j.a.135.6	yes	128	17.16	even	2	inner
731.2.j.a.509.5	yes	128	731.509	even	6	inner
731.2.j.a.509.6	yes	128	43.36	even	3	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.51145 q^{2} +(-1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(1.18626 + 0.684888i) q^{5} +(4.42321 + 2.55374i) q^{6} +(3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 + 0.983681i) q^{9} +O(q^{10})\)	\(q-2.51145 q^{2} +(-1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(1.18626 + 0.684888i) q^{5} +(4.42321 + 2.55374i) q^{6} +(3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 + 0.983681i) q^{9} +(-2.97923 - 1.72006i) q^{10} -5.71903i q^{11} +(-7.58623 - 4.37991i) q^{12} +(-0.967741 - 1.67618i) q^{13} +(-9.65264 + 5.57296i) q^{14} +(-1.39284 - 2.41247i) q^{15} +5.93872 q^{16} +(2.78875 + 3.03692i) q^{17} +(-1.42632 - 2.47046i) q^{18} +(3.28388 - 5.68786i) q^{19} +(5.10967 + 2.95007i) q^{20} -9.02556 q^{21} +14.3631i q^{22} +(3.56220 + 2.05664i) q^{23} +(10.2060 + 5.89244i) q^{24} +(-1.56186 - 2.70522i) q^{25} +(2.43043 + 4.20963i) q^{26} +3.79107i q^{27} +(16.5552 - 9.55815i) q^{28} +(-1.60279 + 0.925373i) q^{29} +(3.49805 + 6.05880i) q^{30} +(7.10692 + 4.10318i) q^{31} -3.32510 q^{32} +(-5.81534 + 10.0725i) q^{33} +(-7.00381 - 7.62706i) q^{34} +6.07912 q^{35} +(2.44628 + 4.23708i) q^{36} +(-0.467527 - 0.269927i) q^{37} +(-8.24731 + 14.2848i) q^{38} +3.93615i q^{39} +(-6.87420 - 3.96882i) q^{40} +3.51693i q^{41} +22.6672 q^{42} +(4.98908 - 4.25548i) q^{43} -24.6340i q^{44} +1.55587i q^{45} +(-8.94629 - 5.16514i) q^{46} -10.7488 q^{47} +(-10.4594 - 6.03873i) q^{48} +(6.34810 - 10.9952i) q^{49} +(3.92253 + 6.79401i) q^{50} +(-1.82355 - 8.18439i) q^{51} +(-4.16842 - 7.21992i) q^{52} +(-2.08650 + 3.61392i) q^{53} -9.52108i q^{54} +(3.91689 - 6.78426i) q^{55} +(-22.2723 + 12.8589i) q^{56} +(-11.5673 + 6.67837i) q^{57} +(4.02533 - 2.32403i) q^{58} -6.09785 q^{59} +(-5.99949 - 10.3914i) q^{60} +(-1.58893 + 0.917368i) q^{61} +(-17.8487 - 10.3049i) q^{62} +(4.36561 + 2.52049i) q^{63} -3.52664 q^{64} -2.65118i q^{65} +(14.6049 - 25.2965i) q^{66} +(-7.10904 + 12.3132i) q^{67} +(12.0122 + 13.0811i) q^{68} +(-4.18255 - 7.24438i) q^{69} -15.2674 q^{70} +(4.83502 - 2.79150i) q^{71} +(-3.29106 - 5.70028i) q^{72} +(5.46456 - 3.15496i) q^{73} +(1.17417 + 0.677908i) q^{74} +6.35264i q^{75} +(14.1449 - 24.4997i) q^{76} +(-12.6906 - 21.9808i) q^{77} -9.88544i q^{78} +(11.6828 - 6.74508i) q^{79} +(7.04487 + 4.06736i) q^{80} +(5.55870 - 9.62795i) q^{81} -8.83259i q^{82} +(-4.69845 + 8.13795i) q^{83} -38.8765 q^{84} +(1.22824 + 5.51255i) q^{85} +(-12.5298 + 10.6874i) q^{86} +3.76383 q^{87} +33.1409i q^{88} +(8.13518 - 14.0905i) q^{89} -3.90748i q^{90} +(-7.43894 - 4.29487i) q^{91} +(15.3437 + 8.85871i) q^{92} +(-8.34456 - 14.4532i) q^{93} +26.9951 q^{94} +(7.79108 - 4.49818i) q^{95} +(5.85622 + 3.38109i) q^{96} +18.8175i q^{97} +(-15.9429 + 27.6140i) q^{98} +(5.62570 - 3.24800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9}+O(q^{10}) \) 128 * q - 4 * q^2 + 116 * q^4 - 12 * q^8 + 70 * q^9	\( 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9} + 4 q^{13} - 12 q^{15} + 76 q^{16} + 2 q^{17} - 16 q^{18} - 2 q^{19} - 20 q^{21} + 60 q^{25} - 2 q^{26} - 28 q^{30} - 48 q^{32} + 22 q^{33} - 18 q^{34} - 112 q^{35} + 36 q^{36} - 40 q^{38} + 36 q^{42} + 10 q^{43} + 36 q^{47} + 52 q^{49} + 16 q^{50} + 10 q^{51} + 10 q^{52} + 24 q^{55} - 12 q^{59} - 78 q^{60} + 36 q^{64} + 14 q^{66} + 10 q^{67} - q^{68} - 64 q^{70} - 68 q^{72} - 22 q^{76} - 28 q^{77} - 20 q^{81} - 6 q^{83} + 32 q^{84} + 6 q^{85} - 58 q^{86} + 32 q^{87} + 36 q^{89} + 6 q^{93} + 132 q^{94} - 48 q^{98}+O(q^{100}) \) 128 * q - 4 * q^2 + 116 * q^4 - 12 * q^8 + 70 * q^9 + 4 * q^13 - 12 * q^15 + 76 * q^16 + 2 * q^17 - 16 * q^18 - 2 * q^19 - 20 * q^21 + 60 * q^25 - 2 * q^26 - 28 * q^30 - 48 * q^32 + 22 * q^33 - 18 * q^34 - 112 * q^35 + 36 * q^36 - 40 * q^38 + 36 * q^42 + 10 * q^43 + 36 * q^47 + 52 * q^49 + 16 * q^50 + 10 * q^51 + 10 * q^52 + 24 * q^55 - 12 * q^59 - 78 * q^60 + 36 * q^64 + 14 * q^66 + 10 * q^67 - q^68 - 64 * q^70 - 68 * q^72 - 22 * q^76 - 28 * q^77 - 20 * q^81 - 6 * q^83 + 32 * q^84 + 6 * q^85 - 58 * q^86 + 32 * q^87 + 36 * q^89 + 6 * q^93 + 132 * q^94 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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