LMFDB - Embedded newform 240.2.t.b.59.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(59,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("240.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			59.9
Character	$\chi$	$=$	240.59
Dual form			240.2.t.b.179.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03022 + 0.968834i) q^{2} +(-1.72231 - 0.183389i) q^{3} +(0.122722 - 1.99623i) q^{4} +(-2.23605 - 0.00763900i) q^{5} +(1.95204 - 1.47971i) q^{6} -1.25117i q^{7} +(1.80759 + 2.17546i) q^{8} +(2.93274 + 0.631707i) q^{9} +O(q^{10})$	\(q+(-1.03022 + 0.968834i) q^{2} +(-1.72231 - 0.183389i) q^{3} +(0.122722 - 1.99623i) q^{4} +(-2.23605 - 0.00763900i) q^{5} +(1.95204 - 1.47971i) q^{6} -1.25117i q^{7} +(1.80759 + 2.17546i) q^{8} +(2.93274 + 0.631707i) q^{9} +(2.31104 - 2.15850i) q^{10} +(0.583641 + 0.583641i) q^{11} +(-0.577452 + 3.41563i) q^{12} +(4.72397 + 4.72397i) q^{13} +(1.21218 + 1.28899i) q^{14} +(3.84979 + 0.423225i) q^{15} +(-3.96988 - 0.489962i) q^{16} -0.341889 q^{17} +(-3.63339 + 2.19054i) q^{18} +(-1.20217 - 1.20217i) q^{19} +(-0.289662 + 4.46275i) q^{20} +(-0.229451 + 2.15491i) q^{21} +(-1.16673 - 0.0358296i) q^{22} +7.68785 q^{23} +(-2.71428 - 4.07832i) q^{24} +(4.99988 + 0.0341625i) q^{25} +(-9.44349 - 0.290004i) q^{26} +(-4.93525 - 1.62583i) q^{27} +(-2.49763 - 0.153546i) q^{28} +(4.28058 + 4.28058i) q^{29} +(-4.37618 + 3.29379i) q^{30} +1.36594i q^{31} +(4.56456 - 3.34138i) q^{32} +(-0.898180 - 1.11225i) q^{33} +(0.352222 - 0.331234i) q^{34} +(-0.00955770 + 2.79769i) q^{35} +(1.62094 - 5.77690i) q^{36} +(-4.63227 + 4.63227i) q^{37} +(2.40320 + 0.0738009i) q^{38} +(-7.26984 - 9.00249i) q^{39} +(-4.02524 - 4.87826i) q^{40} +5.52847 q^{41} +(-1.85136 - 2.44234i) q^{42} +(-1.47233 - 1.47233i) q^{43} +(1.23671 - 1.09346i) q^{44} +(-6.55294 - 1.43493i) q^{45} +(-7.92020 + 7.44825i) q^{46} -7.73797i q^{47} +(6.74753 + 1.57190i) q^{48} +5.43457 q^{49} +(-5.18410 + 4.80886i) q^{50} +(0.588841 + 0.0626987i) q^{51} +(10.0099 - 8.85040i) q^{52} +(2.84096 + 2.84096i) q^{53} +(6.65957 - 3.10647i) q^{54} +(-1.30059 - 1.30951i) q^{55} +(2.72187 - 2.26160i) q^{56} +(1.85005 + 2.29098i) q^{57} +(-8.55712 - 0.262784i) q^{58} +(-5.90216 - 5.90216i) q^{59} +(1.31731 - 7.63313i) q^{60} +(6.34507 - 6.34507i) q^{61} +(-1.32337 - 1.40722i) q^{62} +(0.790374 - 3.66936i) q^{63} +(-1.46527 + 7.86467i) q^{64} +(-10.5270 - 10.5991i) q^{65} +(2.00291 + 0.275676i) q^{66} +(3.78069 - 3.78069i) q^{67} +(-0.0419572 + 0.682490i) q^{68} +(-13.2409 - 1.40987i) q^{69} +(-2.70065 - 2.89150i) q^{70} +11.0919i q^{71} +(3.92692 + 7.52192i) q^{72} -7.08099 q^{73} +(0.284374 - 9.26017i) q^{74} +(-8.60511 - 0.975762i) q^{75} +(-2.54734 + 2.25227i) q^{76} +(0.730234 - 0.730234i) q^{77} +(16.2115 + 2.23131i) q^{78} +12.5003i q^{79} +(8.87312 + 1.12591i) q^{80} +(8.20189 + 3.70526i) q^{81} +(-5.69556 + 5.35617i) q^{82} +(7.33041 + 7.33041i) q^{83} +(4.27354 + 0.722492i) q^{84} +(0.764483 + 0.00261169i) q^{85} +(2.94327 + 0.0903859i) q^{86} +(-6.58749 - 8.15751i) q^{87} +(-0.214708 + 2.32467i) q^{88} -9.31805 q^{89} +(8.14120 - 4.87040i) q^{90} +(5.91049 - 5.91049i) q^{91} +(0.943467 - 15.3467i) q^{92} +(0.250498 - 2.35258i) q^{93} +(7.49681 + 7.97184i) q^{94} +(2.67893 + 2.69730i) q^{95} +(-8.47437 + 4.91782i) q^{96} -0.0541765i q^{97} +(-5.59882 + 5.26520i) q^{98} +(1.34298 + 2.08036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) $ 80 * q - 8 * q^4 - 4 * q^6	$ 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) $ 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.03022	+	0.968834i	−0.728478	+	0.685069i
$2$	−1.03022	+	0.968834i	−0.728478	+	0.685069i
$3$	−1.72231	−	0.183389i	−0.994379	−	0.105880i
$3$	−1.72231	−	0.183389i	−0.994379	−	0.105880i
$4$	0.122722	−	1.99623i	0.0613609	−	0.998116i
$5$	−2.23605	−	0.00763900i	−0.999994	−	0.00341627i
$5$	−2.23605	−	0.00763900i	−0.999994	−	0.00341627i
$6$	1.95204	−	1.47971i	0.796918	−	0.604087i
$7$		−	1.25117i		−	0.472898i	−0.971644	−	0.236449i	$-0.924016\pi$
$7$		−	1.25117i		−	0.472898i	0.971644	−	0.236449i	$-0.0759836\pi$
$8$	1.80759	+	2.17546i	0.639078	+	0.769142i
$9$	2.93274	+	0.631707i	0.977579	+	0.210569i
$10$	2.31104	−	2.15850i	0.730814	−	0.682576i
$11$	0.583641	+	0.583641i	0.175974	+	0.175974i	0.789598	−	0.613624i	$-0.210289\pi$
$11$	0.583641	+	0.583641i	0.175974	+	0.175974i	−0.613624	+	0.789598i	$0.710289\pi$
$12$	−0.577452	+	3.41563i	−0.166696	+	0.986008i
$13$	4.72397	+	4.72397i	1.31019	+	1.31019i	0.921270	+	0.388923i	$0.127153\pi$
$13$	4.72397	+	4.72397i	1.31019	+	1.31019i	0.388923	+	0.921270i	$0.372847\pi$
$14$	1.21218	+	1.28899i	0.323968	+	0.344496i
$15$	3.84979	+	0.423225i	0.994011	+	0.109276i
$16$	−3.96988	−	0.489962i	−0.992470	−	0.122491i
$17$	−0.341889			−0.0829203			−0.0414601	−	0.999140i	$-0.513201\pi$
$17$	−0.341889			−0.0829203			−0.0414601	+	0.999140i	$0.513201\pi$
$18$	−3.63339	+	2.19054i	−0.856399	+	0.516314i
$19$	−1.20217	−	1.20217i	−0.275796	−	0.275796i	0.555632	−	0.831428i	$-0.312476\pi$
$19$	−1.20217	−	1.20217i	−0.275796	−	0.275796i	−0.831428	+	0.555632i	$0.812476\pi$
$20$	−0.289662	+	4.46275i	−0.0647704	+	0.997900i
$21$	−0.229451	+	2.15491i	−0.0500703	+	0.470240i
$22$	−1.16673	−	0.0358296i	−0.248748	−	0.00763890i
$23$	7.68785			1.60303			0.801514	−	0.597977i	$-0.204028\pi$
$23$	7.68785			1.60303			0.801514	+	0.597977i	$0.204028\pi$
$24$	−2.71428	−	4.07832i	−0.554049	−	0.832484i
$25$	4.99988	+	0.0341625i	0.999977	+	0.00683249i
$26$	−9.44349	−	0.290004i	−1.85202	−	0.0568744i
$27$	−4.93525	−	1.62583i	−0.949789	−	0.312891i
$28$	−2.49763	−	0.153546i	−0.472007	−	0.0290175i
$29$	4.28058	+	4.28058i	0.794883	+	0.794883i	0.982284	−	0.187400i	$-0.0600062\pi$
$29$	4.28058	+	4.28058i	0.794883	+	0.794883i	−0.187400	+	0.982284i	$0.560006\pi$
$30$	−4.37618	+	3.29379i	−0.798977	+	0.601361i
$31$			1.36594i			0.245330i	0.992448	+	0.122665i	$0.0391441\pi$
$31$			1.36594i			0.245330i	−0.992448	+	0.122665i	$0.960856\pi$
$32$	4.56456	−	3.34138i	0.806907	−	0.590679i
$33$	−0.898180	−	1.11225i	−0.156353	−	0.193617i
$34$	0.352222	−	0.331234i	0.0604056	−	0.0568061i
$35$	−0.00955770	+	2.79769i	−0.00161555	+	0.472895i
$36$	1.62094	−	5.77690i	0.270157	−	0.962816i
$37$	−4.63227	+	4.63227i	−0.761540	+	0.761540i	−0.976601	−	0.215061i	$-0.931005\pi$
$37$	−4.63227	+	4.63227i	−0.761540	+	0.761540i	0.215061	+	0.976601i	$0.431005\pi$
$38$	2.40320	+	0.0738009i	0.389851	+	0.0119721i
$39$	−7.26984	−	9.00249i	−1.16411	−	1.44155i
$40$	−4.02524	−	4.87826i	−0.636447	−	0.771321i
$41$	5.52847			0.863402			0.431701	−	0.902017i	$-0.357914\pi$
$41$	5.52847			0.863402			0.431701	+	0.902017i	$0.357914\pi$
$42$	−1.85136	−	2.44234i	−0.285672	−	0.376861i
$43$	−1.47233	−	1.47233i	−0.224528	−	0.224528i	0.585874	−	0.810402i	$-0.300751\pi$
$43$	−1.47233	−	1.47233i	−0.224528	−	0.224528i	−0.810402	+	0.585874i	$0.800751\pi$
$44$	1.23671	−	1.09346i	0.186441	−	0.164845i
$45$	−6.55294	−	1.43493i	−0.976854	−	0.213907i
$46$	−7.92020	+	7.44825i	−1.16777	+	1.09818i
$47$		−	7.73797i		−	1.12870i	−0.825536	−	0.564350i	$-0.809127\pi$
$47$		−	7.73797i		−	1.12870i	0.825536	−	0.564350i	$-0.190873\pi$
$48$	6.74753	+	1.57190i	0.973922	+	0.226884i
$49$	5.43457			0.776367
$50$	−5.18410	+	4.80886i	−0.733142	+	0.680076i
$51$	0.588841	+	0.0626987i	0.0824542	+	0.00877957i
$52$	10.0099	−	8.85040i	1.38812	−	1.22733i
$53$	2.84096	+	2.84096i	0.390235	+	0.390235i	0.874771	−	0.484536i	$-0.161012\pi$
$53$	2.84096	+	2.84096i	0.390235	+	0.390235i	−0.484536	+	0.874771i	$0.661012\pi$
$54$	6.65957	−	3.10647i	0.906253	−	0.422737i
$55$	−1.30059	−	1.30951i	−0.175372	−	0.176574i
$56$	2.72187	−	2.26160i	0.363726	−	0.302219i
$57$	1.85005	+	2.29098i	0.245045	+	0.303447i
$58$	−8.55712	−	0.262784i	−1.12361	−	0.0345052i
$59$	−5.90216	−	5.90216i	−0.768396	−	0.768396i	0.209428	−	0.977824i	$-0.432840\pi$
$59$	−5.90216	−	5.90216i	−0.768396	−	0.768396i	−0.977824	+	0.209428i	$0.932840\pi$
$60$	1.31731	−	7.63313i	0.170064	−	0.985433i
$61$	6.34507	−	6.34507i	0.812402	−	0.812402i	−0.172591	−	0.984994i	$-0.555214\pi$
$61$	6.34507	−	6.34507i	0.812402	−	0.812402i	0.984994	+	0.172591i	$0.0552140\pi$
$62$	−1.32337	−	1.40722i	−0.168068	−	0.178718i
$63$	0.790374	−	3.66936i	0.0995777	−	0.462295i
$64$	−1.46527	+	7.86467i	−0.183159	+	0.983083i
$65$	−10.5270	−	10.5991i	−1.30571	−	1.31466i
$66$	2.00291	+	0.275676i	0.246541	+	0.0339333i
$67$	3.78069	−	3.78069i	0.461884	−	0.461884i	−0.437388	−	0.899273i	$-0.644096\pi$
$67$	3.78069	−	3.78069i	0.461884	−	0.461884i	0.899273	+	0.437388i	$0.144096\pi$
$68$	−0.0419572	+	0.682490i	−0.00508806	+	0.0827640i
$69$	−13.2409	−	1.40987i	−1.59402	−	0.169728i
$70$	−2.70065	−	2.89150i	−0.322789	−	0.345601i
$71$			11.0919i			1.31637i	0.752855	+	0.658186i	$0.228676\pi$
$71$			11.0919i			1.31637i	−0.752855	+	0.658186i	$0.771324\pi$
$72$	3.92692	+	7.52192i	0.462792	+	0.886467i
$73$	−7.08099			−0.828767			−0.414383	−	0.910102i	$-0.636003\pi$
$73$	−7.08099			−0.828767			−0.414383	+	0.910102i	$0.636003\pi$
$74$	0.284374	−	9.26017i	0.0330578	−	1.07647i
$75$	−8.60511	−	0.975762i	−0.993632	−	0.112671i
$76$	−2.54734	+	2.25227i	−0.292200	+	0.258353i
$77$	0.730234	−	0.730234i	0.0832179	−	0.0832179i
$78$	16.2115	+	2.23131i	1.83559	+	0.252646i
$79$			12.5003i			1.40639i	0.710996	+	0.703196i	$0.248244\pi$
$79$			12.5003i			1.40639i	−0.710996	+	0.703196i	$0.751756\pi$
$80$	8.87312	+	1.12591i	0.992045	+	0.125880i
$81$	8.20189	+	3.70526i	0.911321	+	0.411696i
$82$	−5.69556	+	5.35617i	−0.628969	+	0.591490i
$83$	7.33041	+	7.33041i	0.804617	+	0.804617i	0.983813	−	0.179197i	$-0.0573498\pi$
$83$	7.33041	+	7.33041i	0.804617	+	0.804617i	−0.179197	+	0.983813i	$0.557350\pi$
$84$	4.27354	+	0.722492i	0.466282	+	0.0788303i
$85$	0.764483	+	0.00261169i	0.0829198	+	0.000283278i
$86$	2.94327	+	0.0903859i	0.317381	+	0.00974656i
$87$	−6.58749	−	8.15751i	−0.706253	−	0.874577i
$88$	−0.214708	+	2.32467i	−0.0228879	+	0.247811i
$89$	−9.31805			−0.987711			−0.493856	−	0.869544i	$-0.664413\pi$
$89$	−9.31805			−0.987711			−0.493856	+	0.869544i	$0.664413\pi$
$90$	8.14120	−	4.87040i	0.858158	−	0.513385i
$91$	5.91049	−	5.91049i	0.619588	−	0.619588i
$92$	0.943467	−	15.3467i	0.0983632	−	1.60001i
$93$	0.250498	−	2.35258i	0.0259755	−	0.243951i
$94$	7.49681	+	7.97184i	0.773237	+	0.822233i
$95$	2.67893	+	2.69730i	0.274852	+	0.276737i
$96$	−8.47437	+	4.91782i	−0.864912	+	0.501923i
$97$		−	0.0541765i		−	0.00550079i	−0.999996	−	0.00275040i	$-0.999125\pi$
$97$		−	0.0541765i		−	0.00550079i	0.999996	−	0.00275040i	$-0.000875480\pi$
$98$	−5.59882	+	5.26520i	−0.565567	+	0.531865i
$99$	1.34298	+	2.08036i	0.134974	+	0.209084i
$100$	0.681791	−	9.97673i	0.0681791	−	0.997673i
$101$	−4.24025	+	4.24025i	−0.421921	+	0.421921i	−0.885865	−	0.463944i	$-0.846434\pi$
$101$	−4.24025	+	4.24025i	−0.421921	+	0.421921i	0.463944	+	0.885865i	$0.346434\pi$
$102$	−0.667382	+	0.505895i	−0.0660807	+	0.0500911i
$103$			17.3562i			1.71015i	0.518502	+	0.855076i	$0.326490\pi$
$103$			17.3562i			1.71015i	−0.518502	+	0.855076i	$0.673510\pi$
$104$	−1.73784	+	18.8158i	−0.170409	+	1.84504i
$105$	0.529526	−	4.81675i	0.0516765	−	0.470066i
$106$	−5.67924	−	0.174406i	−0.551616	−	0.0169398i
$107$	−5.36404	+	5.36404i	−0.518561	+	0.518561i	−0.917136	−	0.398575i	$-0.869505\pi$
$107$	−5.36404	+	5.36404i	−0.518561	+	0.518561i	0.398575	+	0.917136i	$0.369505\pi$
$108$	−3.85120	+	9.65237i	−0.370581	+	0.928800i
$109$	1.76004	−	1.76004i	0.168581	−	0.168581i	−0.617774	−	0.786356i	$-0.711965\pi$
$109$	1.76004	−	1.76004i	0.168581	−	0.168581i	0.786356	+	0.617774i	$0.211965\pi$
$110$	2.60860	+	0.0890297i	0.248720	+	0.00848864i
$111$	8.82773	−	7.12871i	0.837891	−	0.676628i
$112$	−0.613027	+	4.96700i	−0.0579256	+	0.469337i
$113$	−9.11992			−0.857930			−0.428965	−	0.903321i	$-0.641122\pi$
$113$	−9.11992			−0.857930			−0.428965	+	0.903321i	$0.641122\pi$
$114$	−4.12554	−	0.567829i	−0.386392	−	0.0531821i
$115$	−17.1905	−	0.0587275i	−1.60302	−	0.00547637i
$116$	9.07034	−	8.01970i	0.842160	−	0.744611i
$117$	10.8700	+	16.8383i	1.00493	+	1.55670i
$118$	11.7988	+	0.362333i	1.08616	+	0.0333554i
$119$			0.427762i			0.0392128i
$120$	6.03812	+	9.14009i	0.551202	+	0.834372i
$121$		−	10.3187i		−	0.938066i
$122$	−0.389522	+	12.6842i	−0.0352657	+	1.14837i
$123$	−9.52176	−	1.01386i	−0.858548	−	0.0914167i
$124$	2.72673	+	0.167631i	0.244868	+	0.0150537i
$125$	−11.1798	−	0.114583i	−0.999947	−	0.0102486i
$126$	2.74073	+	4.54600i	0.244164	+	0.404990i
$127$	2.72023			0.241381			0.120690	−	0.992690i	$-0.461489\pi$
$127$	2.72023			0.241381			0.120690	+	0.992690i	$0.461489\pi$
$128$	−6.11000	−	9.52197i	−0.540053	−	0.841631i
$129$	2.26580	+	2.80582i	0.199493	+	0.247039i
$130$	21.1139	+	0.720603i	1.85181	+	0.0632011i
$131$	−2.78476	+	2.78476i	−0.243306	+	0.243306i	−0.818216	−	0.574911i	$-0.805037\pi$
$131$	−2.78476	+	2.78476i	−0.243306	+	0.243306i	0.574911	+	0.818216i	$0.305037\pi$
$132$	−2.33053	+	1.65648i	−0.202846	+	0.144178i
$133$	−1.50412	+	1.50412i	−0.130423	+	0.130423i
$134$	−0.232096	+	7.55781i	−0.0200500	+	0.652895i
$135$	11.0231	+	3.67315i	0.948715	+	0.316134i
$136$	−0.617994	−	0.743767i	−0.0529925	−	0.0637775i
$137$		−	5.33434i		−	0.455744i	−0.973691	−	0.227872i	$-0.926823\pi$
$137$		−	5.33434i		−	0.455744i	0.973691	−	0.227872i	$-0.0731767\pi$
$138$	15.0070	−	11.3758i	1.27748	−	0.968368i
$139$	9.28039	−	9.28039i	0.787153	−	0.787153i	−0.193874	−	0.981026i	$-0.562105\pi$
$139$	9.28039	−	9.28039i	0.787153	−	0.787153i	0.981026	+	0.193874i	$0.0621053\pi$
$140$	5.58366	+	0.362417i	0.471905	+	0.0306298i
$141$	−1.41906	+	13.3272i	−0.119506	+	1.12235i
$142$	−10.7463	−	11.4272i	−0.901806	−	0.958948i
$143$			5.51420i			0.461121i
$144$	−11.3331	−	3.94473i	−0.944425	−	0.328728i
$145$	−9.53891	−	9.60431i	−0.792163	−	0.797594i
$146$	7.29500	−	6.86030i	0.603739	−	0.567763i
$147$	−9.36004	−	0.996640i	−0.772003	−	0.0822015i
$148$	8.67860	+	9.81556i	0.713376	+	0.806834i
$149$	14.3276	−	14.3276i	1.17376	−	1.17376i	0.192456	−	0.981306i	$-0.438355\pi$
$149$	14.3276	−	14.3276i	1.17376	−	1.17376i	0.981306	−	0.192456i	$-0.0616454\pi$
$150$	9.81054	−	7.33167i	0.801027	−	0.598628i
$151$	18.2876			1.48822			0.744111	−	0.668056i	$-0.232873\pi$
$151$	18.2876			1.48822			0.744111	+	0.668056i	$0.232873\pi$
$152$	0.442249	−	4.78829i	0.0358711	−	0.388382i
$153$	−1.00267	−	0.215974i	−0.0810611	−	0.0174604i
$154$	−0.0448290	+	1.45978i	−0.00361242	+	0.117632i
$155$	0.0104344	−	3.05432i	0.000838113	−	0.245329i
$156$	−18.8632	+	13.4075i	−1.51027	+	1.07346i
$157$	8.46556	+	8.46556i	0.675625	+	0.675625i	0.959007	−	0.283382i	$-0.0914565\pi$
$157$	8.46556	+	8.46556i	0.675625	+	0.675625i	−0.283382	+	0.959007i	$0.591456\pi$
$158$	−12.1107	−	12.8781i	−0.963475	−	1.02453i
$159$	−4.37202	−	5.41402i	−0.346724	−	0.429360i
$160$	−10.2321	+	7.43665i	−0.808920	+	0.587918i
$161$		−	9.61881i		−	0.758069i
$162$	−12.0396	+	4.12902i	−0.945918	+	0.324407i
$163$	12.3909	−	12.3909i	0.970530	−	0.970530i	−0.0290482	−	0.999578i	$-0.509248\pi$
$163$	12.3909	−	12.3909i	0.970530	−	0.970530i	0.999578	+	0.0290482i	$0.00924764\pi$
$164$	0.678464	−	11.0361i	0.0529791	−	0.861775i
$165$	1.99988	+	2.49391i	0.155691	+	0.194150i
$166$	−14.6539	−	0.450012i	−1.13736	−	0.0349277i
$167$	−9.52085			−0.736746			−0.368373	−	0.929678i	$-0.620085\pi$
$167$	−9.52085			−0.736746			−0.368373	+	0.929678i	$0.620085\pi$
$168$	−5.10268	+	3.39602i	−0.393680	+	0.262009i
$169$			31.6318i			2.43321i
$170$	−0.790119	+	0.737966i	−0.0605993	+	0.0565994i
$171$	−2.76622	−	4.28506i	−0.211538	−	0.327687i
$172$	−3.11979	+	2.75842i	−0.237882	+	0.210327i
$173$	5.08390	−	5.08390i	0.386522	−	0.386522i	−0.486923	−	0.873445i	$-0.661881\pi$
$173$	5.08390	−	5.08390i	0.386522	−	0.386522i	0.873445	+	0.486923i	$0.161881\pi$
$174$	14.6899	+	2.02188i	1.11364	+	0.153278i
$175$	0.0427431	−	6.25571i	0.00323107	−	0.472887i
$176$	−2.03102	−	2.60295i	−0.153094	−	0.196204i
$177$	9.08299	+	11.2478i	0.682720	+	0.845435i
$178$	9.59968	−	9.02764i	0.719526	−	0.676650i
$179$	−6.00054	+	6.00054i	−0.448502	+	0.448502i	−0.894856	−	0.446354i	$-0.852722\pi$
$179$	−6.00054	+	6.00054i	−0.448502	+	0.448502i	0.446354	+	0.894856i	$0.352722\pi$
$180$	−3.66865	+	12.9051i	−0.273445	+	0.961888i
$181$	−4.20035	−	4.20035i	−0.312210	−	0.312210i	0.533555	−	0.845765i	$-0.320856\pi$
$181$	−4.20035	−	4.20035i	−0.312210	−	0.312210i	−0.845765	+	0.533555i	$0.820856\pi$
$182$	−0.362844	+	11.8154i	−0.0268958	+	0.875817i
$183$	−12.0918	+	9.76459i	−0.893853	+	0.721819i
$184$	13.8964	+	16.7246i	1.02446	+	1.23296i
$185$	10.3934	−	10.3226i	0.764137	−	0.758934i
$186$	2.02119	+	2.66637i	0.148201	+	0.195508i
$187$	−0.199540	−	0.199540i	−0.0145918	−	0.0145918i
$188$	−15.4468	−	0.949618i	−1.12657	−	0.0692580i
$189$	−2.03419	+	6.17484i	−0.147966	+	0.449153i
$190$	−5.37313	−	0.183381i	−0.389808	−	0.0133038i
$191$	7.96465			0.576302			0.288151	−	0.957585i	$-0.406960\pi$
$191$	7.96465			0.576302			0.288151	+	0.957585i	$0.406960\pi$
$192$	3.96595	−	13.2767i	0.286218	−	0.958165i
$193$		−	26.5230i		−	1.90917i	−0.297940	−	0.954584i	$-0.596300\pi$
$193$		−	26.5230i		−	1.90917i	0.297940	−	0.954584i	$-0.403700\pi$
$194$	0.0524881	+	0.0558140i	0.00376842	+	0.00400721i
$195$	16.1870	+	20.1856i	1.15917	+	1.44552i
$196$	0.666940	−	10.8487i	0.0476386	−	0.774904i
$197$	0.435336	+	0.435336i	0.0310164	+	0.0310164i	0.722445	−	0.691428i	$-0.243018\pi$
$197$	0.435336	+	0.435336i	0.0310164	+	0.0310164i	−0.691428	+	0.722445i	$0.743018\pi$
$198$	−3.39908	−	0.842111i	−0.241562	−	0.0598463i
$199$	−15.2579			−1.08161			−0.540803	−	0.841150i	$-0.681879\pi$
$199$	−15.2579			−1.08161			−0.540803	+	0.841150i	$0.681879\pi$
$200$	8.96340	+	10.9388i	0.633808	+	0.773490i
$201$	−7.20487	+	5.81820i	−0.508192	+	0.410384i
$202$	0.260308	−	8.47651i	0.0183152	−	0.596405i
$203$	5.35573	−	5.35573i	0.375899	−	0.375899i
$204$	0.197425	−	1.16777i	0.0138225	−	0.0817601i
$205$	−12.3620	−	0.0422320i	−0.863397	−	0.00294961i
$206$	−16.8152	−	17.8807i	−1.17157	−	1.24581i
$207$	22.5464	+	4.85647i	1.56709	+	0.337548i
$208$	−16.4390	−	21.0682i	−1.13984	−	1.46081i
$209$		−	1.40327i		−	0.0970661i
$210$	4.12110	+	5.47535i	0.284383	+	0.377835i
$211$	−2.75868	−	2.75868i	−0.189915	−	0.189915i	0.605744	−	0.795659i	$-0.292875\pi$
$211$	−2.75868	−	2.75868i	−0.189915	−	0.189915i	−0.795659	+	0.605744i	$0.792875\pi$
$212$	6.01985	−	5.32256i	0.413445	−	0.365555i
$213$	2.03414	−	19.1038i	0.139377	−	1.30897i
$214$	0.329297	−	10.7230i	0.0225103	−	0.733011i
$215$	3.28096	+	3.30345i	0.223759	+	0.225294i
$216$	−5.38395	−	13.6753i	−0.366332	−	0.930484i
$217$	1.70902			0.116016
$218$	−0.108049	+	3.51842i	−0.00731798	+	0.238298i
$219$	12.1957	+	1.29857i	0.824108	+	0.0877496i
$220$	−2.77370	+	2.43558i	−0.187003	+	0.164207i
$221$	−1.61507	−	1.61507i	−0.108642	−	0.108642i
$222$	−2.18799	+	15.8968i	−0.146849	+	1.06692i
$223$	−14.5166			−0.972107			−0.486053	−	0.873929i	$-0.661564\pi$
$223$	−14.5166			−0.972107			−0.486053	+	0.873929i	$0.661564\pi$
$224$	−4.18064	−	5.71104i	−0.279331	−	0.381585i
$225$	14.6418	+	3.25865i	0.976117	+	0.217243i
$226$	9.39556	−	8.83569i	0.624983	−	0.587741i
$227$	−8.61554	−	8.61554i	−0.571833	−	0.571833i	0.360807	−	0.932640i	$-0.382501\pi$
$227$	−8.61554	−	8.61554i	−0.571833	−	0.571833i	−0.932640	+	0.360807i	$0.882501\pi$
$228$	4.80036	−	3.41197i	0.317911	−	0.225963i
$229$	−4.81569	−	4.81569i	−0.318230	−	0.318230i	0.529857	−	0.848087i	$-0.322246\pi$
$229$	−4.81569	−	4.81569i	−0.318230	−	0.318230i	−0.848087	+	0.529857i	$0.822246\pi$
$230$	17.7669	−	16.5942i	1.17152	−	1.09419i
$231$	−1.39161	+	1.12378i	−0.0915613	+	0.0739391i
$232$	−1.57472	+	17.0497i	−0.103386	+	1.11937i
$233$			1.07868i			0.0706670i	0.999376	+	0.0353335i	$0.0112493\pi$
$233$			1.07868i			0.0706670i	−0.999376	+	0.0353335i	$0.988751\pi$
$234$	−27.5121	−	6.81602i	−1.79852	−	0.445577i
$235$	−0.0591104	+	17.3025i	−0.00385594	+	1.12869i
$236$	−12.5064	+	11.0578i	−0.814098	+	0.719799i
$237$	2.29241	−	21.5294i	0.148908	−	1.39849i
$238$	−0.414430	−	0.440690i	−0.0268635	−	0.0285657i
$239$	−1.38032			−0.0892853			−0.0446427	−	0.999003i	$-0.514215\pi$
$239$	−1.38032			−0.0892853			−0.0446427	+	0.999003i	$0.514215\pi$
$240$	−15.0758	−	3.56640i	−0.973141	−	0.230210i
$241$	−15.0538			−0.969702			−0.484851	−	0.874597i	$-0.661126\pi$
$241$	−15.0538			−0.969702			−0.484851	+	0.874597i	$0.661126\pi$
$242$	9.99713	+	10.6306i	0.642640	+	0.683361i
$243$	−13.4467	−	7.88576i	−0.862609	−	0.505872i
$244$	−11.8875	−	13.4449i	−0.761022	−	0.860721i
$245$	−12.1520	−	0.0415147i	−0.776363	−	0.00265228i
$246$	10.7918	−	8.18050i	0.688060	−	0.521570i
$247$		−	11.3580i		−	0.722693i
$248$	−2.97155	+	2.46905i	−0.188694	+	0.156785i
$249$	−11.2810	−	13.9696i	−0.714901	−	0.885286i
$250$	11.6287	−	10.7133i	0.735461	−	0.677567i
$251$	1.19752	+	1.19752i	0.0755871	+	0.0755871i	0.743890	−	0.668303i	$-0.232979\pi$
$251$	1.19752	+	1.19752i	0.0755871	+	0.0755871i	−0.668303	+	0.743890i	$0.732979\pi$
$252$	−7.22789	−	2.02808i	−0.455314	−	0.127757i
$253$	4.48694	+	4.48694i	0.282092	+	0.282092i
$254$	−2.80244	+	2.63545i	−0.175841	+	0.165363i
$255$	−1.31620	−	0.144696i	−0.0824237	−	0.00906121i
$256$	15.5199	+	3.89018i	0.969992	+	0.243136i
$257$	23.7676			1.48258			0.741292	−	0.671183i	$-0.234213\pi$
$257$	23.7676			1.48258			0.741292	+	0.671183i	$0.234213\pi$
$258$	−5.05266	−	0.695436i	−0.314565	−	0.0432959i
$259$	5.79576	+	5.79576i	0.360131	+	0.360131i
$260$	−22.4502	+	19.7135i	−1.39230	+	1.22258i
$261$	9.84974	+	15.2579i	0.609683	+	0.944439i
$262$	0.170956	−	5.56689i	0.0105617	−	0.343924i
$263$	11.6796			0.720194			0.360097	−	0.932915i	$-0.382744\pi$
$263$	11.6796			0.720194			0.360097	+	0.932915i	$0.382744\pi$
$264$	0.796113	−	3.96444i	0.0489974	−	0.243994i
$265$	−6.33083	−	6.37424i	−0.388900	−	0.391566i
$266$	0.0923375	−	3.00682i	0.00566157	−	0.184360i
$267$	16.0486	+	1.70883i	0.982159	+	0.104579i
$268$	−7.08315	−	8.01110i	−0.432672	−	0.489356i
$269$	−10.9610	−	10.9610i	−0.668306	−	0.668306i	0.289018	−	0.957324i	$-0.406671\pi$
$269$	−10.9610	−	10.9610i	−0.668306	−	0.668306i	−0.957324	+	0.289018i	$0.906671\pi$
$270$	−14.9149	+	6.89536i	−0.907691	+	0.419638i
$271$			18.6788i			1.13466i	0.823492	+	0.567328i	$0.192023\pi$
$271$			18.6788i			1.13466i	−0.823492	+	0.567328i	$0.807977\pi$
$272$	1.35726	+	0.167513i	0.0822959	+	0.0101570i
$273$	−11.2636	+	9.09581i	−0.681707	+	0.550504i
$274$	5.16809	+	5.49557i	0.312216	+	0.331999i
$275$	2.89820	+	2.93807i	0.174768	+	0.177173i
$276$	−4.43937	+	26.2589i	−0.267218	+	1.58060i
$277$	−6.27183	+	6.27183i	−0.376838	+	0.376838i	−0.869960	−	0.493122i	$-0.835856\pi$
$277$	−6.27183	+	6.27183i	−0.376838	+	0.376838i	0.493122	+	0.869960i	$0.335856\pi$
$278$	−0.569722	+	18.5520i	−0.0341696	+	1.11268i
$279$	−0.862874	+	4.00594i	−0.0516589	+	0.239830i
$280$	−6.10354	+	5.03627i	−0.364756	+	0.300974i
$281$	13.5108			0.805984			0.402992	−	0.915204i	$-0.367970\pi$
$281$	13.5108			0.805984			0.402992	+	0.915204i	$0.367970\pi$
$282$	−11.4499	−	15.1049i	−0.681833	−	0.899481i
$283$	4.13591	+	4.13591i	0.245854	+	0.245854i	0.819267	−	0.573412i	$-0.194381\pi$
$283$	4.13591	+	4.13591i	0.245854	+	0.245854i	−0.573412	+	0.819267i	$0.694381\pi$
$284$	22.1421	+	1.36122i	1.31389	+	0.0807738i
$285$	−4.11931	−	5.13688i	−0.244007	−	0.304282i
$286$	−5.34235	−	5.68086i	−0.315900	−	0.335916i
$287$		−	6.91706i		−	0.408301i
$288$	15.4974	−	6.91593i	0.913194	−	0.407525i
$289$	−16.8831			−0.993124
$290$	19.1322	+	0.652967i	1.12348	+	0.0383436i
$291$	−0.00993538	+	0.0933091i	−0.000582422	+	0.00546987i
$292$	−0.868992	+	14.1353i	−0.0508539	+	0.827205i
$293$	−6.09497	−	6.09497i	−0.356072	−	0.356072i	0.506291	−	0.862363i	$-0.331016\pi$
$293$	−6.09497	−	6.09497i	−0.356072	−	0.356072i	−0.862363	+	0.506291i	$0.831016\pi$
$294$	10.6085	−	8.04156i	0.618701	−	0.468994i
$295$	13.1525	+	13.2427i	0.765767	+	0.771017i
$296$	−18.4505	−	1.70410i	−1.07242	−	0.0990489i
$297$	−1.93151	−	3.82931i	−0.112078	−	0.222199i
$298$	−0.879568	+	28.6417i	−0.0509520	+	1.65917i
$299$	36.3172	+	36.3172i	2.10028	+	2.10028i
$300$	−3.00388	+	17.0580i	−0.173429	+	0.984846i
$301$	−1.84213	+	1.84213i	−0.106179	+	0.106179i
$302$	−18.8403	+	17.7176i	−1.08414	+	1.01953i
$303$	8.08067	−	6.52544i	0.464222	−	0.374877i
$304$	4.18344	+	5.36148i	0.239937	+	0.307502i
$305$	−14.2364	+	14.1394i	−0.815173	+	0.809622i
$306$	1.24222	−	0.748920i	0.0710129	−	0.0428129i
$307$	9.71578	−	9.71578i	0.554509	−	0.554509i	−0.373230	−	0.927739i	$-0.621750\pi$
$307$	9.71578	−	9.71578i	0.554509	−	0.554509i	0.927739	+	0.373230i	$0.121750\pi$
$308$	−1.36810	−	1.54733i	−0.0779548	−	0.0881675i
$309$	3.18293	−	29.8928i	0.181070	−	1.70054i
$310$	2.94838	+	3.15674i	0.167456	+	0.179291i
$311$		−	3.55506i		−	0.201589i	−0.994907	−	0.100795i	$-0.967862\pi$
$311$		−	3.55506i		−	0.201589i	0.994907	−	0.100795i	$-0.0321385\pi$
$312$	6.44371	−	32.0880i	0.364803	−	1.81663i
$313$	−8.23163			−0.465279			−0.232640	−	0.972563i	$-0.574736\pi$
$313$	−8.23163			−0.465279			−0.232640	+	0.972563i	$0.574736\pi$
$314$	−16.9231	−	0.519699i	−0.955028	−	0.0293283i
$315$	−1.79535	+	8.19884i	−0.101156	+	0.461952i
$316$	24.9535	+	1.53406i	1.40374	+	0.0862975i
$317$	−0.843941	+	0.843941i	−0.0474004	+	0.0474004i	−0.730410	−	0.683009i	$-0.760671\pi$
$317$	−0.843941	+	0.843941i	−0.0474004	+	0.0474004i	0.683009	+	0.730410i	$0.260671\pi$
$318$	9.74945	+	1.34189i	0.546722	+	0.0752495i
$319$			4.99664i			0.279758i
$320$	3.33650	−	17.5746i	0.186516	−	0.982452i
$321$	10.2223	−	8.25486i	0.570551	−	0.460741i
$322$	9.31903	+	9.90953i	0.519329	+	0.552236i
$323$	0.411008	+	0.411008i	0.0228691	+	0.0228691i
$324$	8.40311	−	15.9182i	0.466839	−	0.884342i
$325$	23.4579	+	23.7807i	1.30121	+	1.31911i
$326$	−0.760675	+	24.7701i	−0.0421299	+	1.37189i
$327$	−3.35412	+	2.70857i	−0.185483	+	0.149784i
$328$	9.99318	+	12.0270i	0.551781	+	0.664078i
$329$	−9.68152			−0.533760
$330$	−4.47651	−	0.631726i	−0.246424	−	0.0347754i
$331$	−20.0190	+	20.0190i	−1.10035	+	1.10035i	−0.105976	+	0.994369i	$0.533797\pi$
$331$	−20.0190	+	20.0190i	−1.10035	+	1.10035i	−0.994369	+	0.105976i	$0.966203\pi$
$332$	15.5328	−	13.7336i	0.852472	−	0.753728i
$333$	−16.5115	+	10.6590i	−0.904822	+	0.584109i
$334$	9.80861	−	9.22412i	0.536703	−	0.504722i
$335$	−8.48270	+	8.42494i	−0.463460	+	0.460304i
$336$	1.96672	−	8.44231i	0.107293	−	0.460566i
$337$			15.2778i			0.832234i	0.909311	+	0.416117i	$0.136609\pi$
$337$			15.2778i			0.832234i	−0.909311	+	0.416117i	$0.863391\pi$
$338$	−30.6459	−	32.5878i	−1.66692	−	1.77254i
$339$	15.7074	+	1.67249i	0.853108	+	0.0908374i
$340$	0.0990323	−	1.52576i	0.00537078	−	0.0827462i
$341$	−0.797218	+	0.797218i	−0.0431718	+	0.0431718i
$342$	7.00134	+	1.73456i	0.378589	+	0.0937942i
$343$		−	15.5578i		−	0.840041i
$344$	0.541634	−	5.86435i	0.0292030	−	0.316184i
$345$	29.5966	+	3.25369i	1.59343	+	0.175173i
$346$	−0.312100	+	10.1630i	−0.0167786	+	0.546367i
$347$	−13.9362	+	13.9362i	−0.748133	+	0.748133i	−0.974128	−	0.225996i	$-0.927437\pi$
$347$	−13.9362	+	13.9362i	−0.748133	+	0.748133i	0.225996	+	0.974128i	$0.427437\pi$
$348$	−17.0927	+	12.1491i	−0.916265	+	0.651258i
$349$	14.7635	−	14.7635i	0.790270	−	0.790270i	−0.191268	−	0.981538i	$-0.561260\pi$
$349$	14.7635	−	14.7635i	0.790270	−	0.790270i	0.981538	+	0.191268i	$0.0612599\pi$
$350$	6.01671	+	6.48619i	0.321607	+	0.346701i
$351$	−15.6336	−	30.9943i	−0.834459	−	1.65436i
$352$	4.61423	+	0.713894i	0.245939	+	0.0380507i
$353$	22.2619			1.18488			0.592442	−	0.805613i	$-0.298164\pi$
$353$	22.2619			1.18488			0.592442	+	0.805613i	$0.298164\pi$
$354$	−20.2547	−	2.78781i	−1.07653	−	0.148171i
$355$	0.0847314	−	24.8022i	0.00449708	−	1.31636i
$356$	−1.14353	+	18.6010i	−0.0606069	+	0.985850i
$357$	0.0784468	−	0.736740i	0.00415184	−	0.0389924i
$358$	0.368372	−	11.9954i	0.0194691	−	0.633978i
$359$		−	31.1204i		−	1.64247i	−0.570588	−	0.821236i	$-0.693285\pi$
$359$		−	31.1204i		−	1.64247i	0.570588	−	0.821236i	$-0.306715\pi$
$360$	−8.72335	−	16.8494i	−0.459761	−	0.888043i
$361$		−	16.1096i		−	0.847873i
$362$	8.39674	+	0.257859i	0.441323	+	0.0135528i
$363$	−1.89234	+	17.7721i	−0.0993221	+	0.932793i
$364$	−11.0734	−	12.5241i	−0.580402	−	0.656439i
$365$	15.8335	+	0.0540917i	0.828762	+	0.00283129i
$366$	2.99701	−	21.7747i	0.156656	−	1.13818i
$367$	−26.0999			−1.36241			−0.681203	−	0.732095i	$-0.738543\pi$
$367$	−26.0999			−1.36241			−0.681203	+	0.732095i	$0.738543\pi$
$368$	−30.5198	−	3.76676i	−1.59096	−	0.196356i
$369$	16.2135	+	3.49237i	0.844043	+	0.181806i
$370$	−0.706614	+	20.7041i	−0.0367351	+	1.07635i
$371$	3.55452	−	3.55452i	0.184542	−	0.184542i
$372$	−4.66555	−	0.788765i	−0.241897	−	0.0408956i
$373$	18.1875	−	18.1875i	0.941712	−	0.941712i	−0.0566806	−	0.998392i	$-0.518052\pi$
$373$	18.1875	−	18.1875i	0.941712	−	0.941712i	0.998392	+	0.0566806i	$0.0180517\pi$
$374$	0.398893	+	0.0122498i	0.0206263	+	0.000633420i
$375$	19.2340	+	2.24759i	0.993242	+	0.116065i
$376$	16.8337	−	13.9870i	0.868130	−	0.721327i
$377$			40.4426i			2.08290i
$378$	−3.88672	−	8.33226i	−0.199911	−	0.428565i
$379$	15.4007	−	15.4007i	0.791083	−	0.791083i	−0.190587	−	0.981670i	$-0.561039\pi$
$379$	15.4007	−	15.4007i	0.791083	−	0.791083i	0.981670	+	0.190587i	$0.0610392\pi$
$380$	5.71319	−	5.01675i	0.293080	−	0.257354i
$381$	−4.68508	−	0.498859i	−0.240024	−	0.0255573i
$382$	−8.20537	+	7.71642i	−0.419823	+	0.394806i
$383$			13.2437i			0.676720i	0.941017	+	0.338360i	$0.109872\pi$
$383$			13.2437i			0.676720i	−0.941017	+	0.338360i	$0.890128\pi$
$384$	8.77712	+	17.5203i	0.447906	+	0.894081i
$385$	−1.63842	+	1.62727i	−0.0835018	+	0.0829332i
$386$	25.6964	+	27.3246i	1.30791	+	1.39079i
$387$	−3.38787	−	5.24803i	−0.172215	−	0.266772i
$388$	−0.108149	−	0.00664864i	−0.00549043	−	0.000337534i
$389$	−0.366020	+	0.366020i	−0.0185579	+	0.0185579i	−0.716325	−	0.697767i	$-0.754177\pi$
$389$	−0.366020	+	0.366020i	−0.0185579	+	0.0185579i	0.697767	+	0.716325i	$0.254177\pi$
$390$	−36.2327	−	5.11317i	−1.83471	−	0.258915i
$391$	−2.62839			−0.132923
$392$	9.82345	+	11.8227i	0.496159	+	0.597137i
$393$	5.30693	−	4.28554i	0.267699	−	0.216177i
$394$	−0.870262	−	0.0267252i	−0.0438431	−	0.00134640i
$395$	0.0954897	−	27.9513i	0.00480461	−	1.40638i
$396$	4.31768	−	2.42558i	0.216972	−	0.121890i
$397$	−10.1900	−	10.1900i	−0.511422	−	0.511422i	0.403540	−	0.914962i	$-0.367780\pi$
$397$	−10.1900	−	10.1900i	−0.511422	−	0.511422i	−0.914962	+	0.403540i	$0.867780\pi$
$398$	15.7191	−	14.7824i	0.787926	−	0.740974i
$399$	2.86640	−	2.31472i	0.143500	−	0.115881i
$400$	−19.8322	−	2.58537i	−0.991610	−	0.129269i
$401$			22.9515i			1.14615i	0.819505	+	0.573073i	$0.194249\pi$
$401$			22.9515i			1.14615i	−0.819505	+	0.573073i	$0.805751\pi$
$402$	1.78576	−	12.9744i	0.0890657	−	0.647103i
$403$	−6.45266	+	6.45266i	−0.321430	+	0.321430i
$404$	7.94416	+	8.98490i	0.395236	+	0.447015i
$405$	−18.3116	−	8.34782i	−0.909910	−	0.414807i
$406$	−0.328788	+	10.7064i	−0.0163175	+	0.531351i
$407$	−5.40716			−0.268023
$408$	0.927981	+	1.39433i	0.0459419	+	0.0690298i
$409$			14.3821i			0.711150i	0.934648	+	0.355575i	$0.115715\pi$
$409$			14.3821i			0.711150i	−0.934648	+	0.355575i	$0.884285\pi$
$410$	12.7765	−	11.9332i	0.630986	−	0.589337i
$411$	−0.978259	+	9.18742i	−0.0482540	+	0.453182i
$412$	34.6469	+	2.12998i	1.70693	+	0.104937i
$413$	−7.38462	+	7.38462i	−0.363373	+	0.363373i
$414$	−27.9330	+	16.8405i	−1.37283	+	0.827666i
$415$	−16.3352	−	16.4472i	−0.801863	−	0.807361i
$416$	37.3474	+	5.77823i	1.83111	+	0.283301i
$417$	−17.6857	+	14.2818i	−0.866071	+	0.699384i
$418$	1.35953	+	1.44568i	0.0664970	+	0.0707105i
$419$	−7.06947	+	7.06947i	−0.345366	+	0.345366i	−0.858380	−	0.513014i	$-0.828529\pi$
$419$	−7.06947	+	7.06947i	−0.345366	+	0.345366i	0.513014	+	0.858380i	$0.328529\pi$
$420$	−9.55035	−	1.64818i	−0.466009	−	0.0804228i
$421$	7.39193	+	7.39193i	0.360260	+	0.360260i	0.863909	−	0.503648i	$-0.168009\pi$
$421$	7.39193	+	7.39193i	0.360260	+	0.360260i	−0.503648	+	0.863909i	$0.668009\pi$
$422$	5.51475	+	0.169355i	0.268454	+	0.00824405i
$423$	4.88813	−	22.6934i	0.237669	−	1.10339i
$424$	−1.04512	+	11.3157i	−0.0507555	+	0.549537i
$425$	−1.70941	−	0.0116798i	−0.0829183	−	0.000566552i
$426$	16.4128	+	21.6520i	0.795203	+	1.04904i
$427$	−7.93876	−	7.93876i	−0.384184	−	0.384184i
$428$	10.0496	+	11.3661i	0.485765	+	0.549403i
$429$	1.01124	−	9.49719i	0.0488233	−	0.458529i
$430$	−6.58062	−	0.224591i	−0.317345	−	0.0108308i
$431$	−21.1125			−1.01695			−0.508476	−	0.861076i	$-0.669791\pi$
$431$	−21.1125			−1.01695			−0.508476	+	0.861076i	$0.669791\pi$
$432$	18.7957	+	8.87243i	0.904311	+	0.426875i
$433$			18.9380i			0.910101i	0.890466	+	0.455050i	$0.150379\pi$
$433$			18.9380i			0.910101i	−0.890466	+	0.455050i	$0.849621\pi$
$434$	−1.76068	+	1.65576i	−0.0845152	+	0.0794791i
$435$	14.6677	+	18.2910i	0.703261	+	0.876985i
$436$	−3.29745	−	3.72944i	−0.157919	−	0.178608i
$437$	−9.24208	−	9.24208i	−0.442109	−	0.442109i
$438$	−13.8224	+	10.4778i	−0.660459	+	0.500647i
$439$	−14.2211			−0.678734			−0.339367	−	0.940654i	$-0.610213\pi$
$439$	−14.2211			−0.678734			−0.339367	+	0.940654i	$0.610213\pi$
$440$	0.497856	−	5.19645i	0.0237344	−	0.247731i
$441$	15.9382	+	3.43306i	0.758960	+	0.163479i
$442$	3.22863	+	0.0991491i	0.153570	+	0.00471604i
$443$	15.3749	−	15.3749i	0.730485	−	0.730485i	−0.240230	−	0.970716i	$-0.577223\pi$
$443$	15.3749	−	15.3749i	0.730485	−	0.730485i	0.970716	+	0.240230i	$0.0772230\pi$
$444$	−13.1472	−	18.4970i	−0.623939	−	0.877830i
$445$	20.8357	+	0.0711806i	0.987705	+	0.00337428i
$446$	14.9554	−	14.0642i	0.708158	−	0.665960i
$447$	−27.3041	+	22.0491i	−1.29144	+	1.04289i
$448$	9.84004	+	1.83330i	0.464898	+	0.0866154i
$449$			13.5965i			0.641660i	0.947137	+	0.320830i	$0.103962\pi$
$449$			13.5965i			0.641660i	−0.947137	+	0.320830i	$0.896038\pi$
$450$	−18.2414	+	10.8283i	−0.859907	+	0.510451i
$451$	3.22664	+	3.22664i	0.151937	+	0.151937i
$452$	−1.11921	+	18.2055i	−0.0526434	+	0.856313i
$453$	−31.4970	−	3.35374i	−1.47986	−	0.157572i
$454$	17.2230	+	0.528906i	0.808313	+	0.0248228i
$455$	−13.2613	+	13.1710i	−0.621701	+	0.617468i
$456$	−1.63981	+	8.16584i	−0.0767912	+	0.382400i
$457$	−22.2602			−1.04129			−0.520645	−	0.853774i	$-0.674308\pi$
$457$	−22.2602			−1.04129			−0.520645	+	0.853774i	$0.674308\pi$
$458$	9.62684	+	0.295634i	0.449833	+	0.0138141i
$459$	1.68731	+	0.555854i	0.0787568	+	0.0259450i
$460$	−2.22688	+	34.3089i	−0.103829	+	1.59966i
$461$	−13.1839	−	13.1839i	−0.614035	−	0.614035i	0.329960	−	0.943995i	$-0.392965\pi$
$461$	−13.1839	−	13.1839i	−0.614035	−	0.614035i	−0.943995	+	0.329960i	$0.892965\pi$
$462$	0.344917	−	2.50598i	0.0160470	−	0.116589i
$463$	−7.19683			−0.334465			−0.167233	−	0.985917i	$-0.553483\pi$
$463$	−7.19683			−0.334465			−0.167233	+	0.985917i	$0.553483\pi$
$464$	−14.8961	−	19.0907i	−0.691532	−	0.886263i
$465$	−0.578099	+	5.25858i	−0.0268087	+	0.243861i
$466$	−1.04507	−	1.11129i	−0.0484118	−	0.0514794i
$467$	2.53743	+	2.53743i	0.117418	+	0.117418i	0.763375	−	0.645956i	$-0.223541\pi$
$467$	2.53743	+	2.53743i	0.117418	+	0.117418i	−0.645956	+	0.763375i	$0.723541\pi$
$468$	34.9472	−	19.6326i	1.61543	−	0.907517i
$469$	−4.73029	−	4.73029i	−0.218424	−	0.218424i
$470$	−16.7024	−	17.8827i	−0.770423	−	0.824869i
$471$	−13.0279	−	16.1328i	−0.600292	−	0.743362i
$472$	2.17127	−	23.5086i	0.0999406	−	1.08207i
$473$		−	1.71862i		−	0.0790223i
$474$	18.4967	+	24.4011i	0.849583	+	1.12078i
$475$	−5.96963	−	6.05177i	−0.273905	−	0.277674i
$476$	0.853911	+	0.0524957i	0.0391390	+	0.00240614i
$477$	6.53713	+	10.1264i	0.299314	+	0.463657i
$478$	1.42204	−	1.33730i	0.0650424	−	0.0611666i
$479$	−33.0502			−1.51010			−0.755051	−	0.655666i	$-0.772388\pi$
$479$	−33.0502			−1.51010			−0.755051	+	0.655666i	$0.772388\pi$
$480$	18.9867	−	10.9318i	0.866622	−	0.498966i
$481$	−43.7654			−1.99553
$482$	15.5088	−	14.5846i	0.706407	−	0.664313i
$483$	−1.76398	+	16.5666i	−0.0802641	+	0.753808i
$484$	−20.5986	−	1.26633i	−0.936298	−	0.0575606i
$485$	−0.000413855		0.121142i	−1.87922e−5		0.00550076i
$486$	21.4931	−	4.90355i	0.974949	−	0.222430i
$487$		−	7.60399i		−	0.344570i	−0.985047	−	0.172285i	$-0.944885\pi$
$487$		−	7.60399i		−	0.344570i	0.985047	−	0.172285i	$-0.0551150\pi$
$488$	25.2727	+	2.33420i	1.14404	+	0.105664i
$489$	−23.6134	+	19.0687i	−1.06783	+	0.862315i
$490$	12.5595	−	11.7305i	0.567380	−	0.529930i
$491$	−24.9759	−	24.9759i	−1.12715	−	1.12715i	−0.990639	−	0.136509i	$-0.956412\pi$
$491$	−24.9759	−	24.9759i	−1.12715	−	1.12715i	−0.136509	−	0.990639i	$-0.543588\pi$
$492$	−3.19243	+	18.8832i	−0.143926	+	0.851321i
$493$	−1.46348	−	1.46348i	−0.0659119	−	0.0659119i
$494$	11.0040	+	11.7013i	0.495094	+	0.526466i
$495$	−2.98707	−	4.66205i	−0.134259	−	0.209543i
$496$	0.669259	−	5.42262i	0.0300506	−	0.243483i
$497$	13.8779			0.622510
$498$	25.1561	+	3.46243i	1.12727	+	0.155155i
$499$	−11.5540	−	11.5540i	−0.517230	−	0.517230i	0.399502	−	0.916732i	$-0.369183\pi$
$499$	−11.5540	−	11.5540i	−0.517230	−	0.517230i	−0.916732	+	0.399502i	$0.869183\pi$
$500$	−1.60073	+	22.3033i	−0.0715870	+	0.997434i
$501$	16.3979	+	1.74602i	0.732604	+	0.0780064i
$502$	−2.39392	−	0.0735159i	−0.106846	−	0.00328117i
$503$	−1.08877			−0.0485460			−0.0242730	−	0.999705i	$-0.507727\pi$
$503$	−1.08877			−0.0485460			−0.0242730	+	0.999705i	$0.507727\pi$
$504$	9.41121	−	4.91325i	0.419209	−	0.218853i
$505$	9.51383	−	9.44905i	0.423360	−	0.420477i
$506$	−8.96966	−	0.275453i	−0.398750	−	0.0122454i
$507$	5.80092	−	54.4799i	0.257628	−	2.41954i
$508$	0.333831	−	5.43020i	0.0148114	−	0.240926i
$509$	19.8749	+	19.8749i	0.880941	+	0.880941i	0.993630	−	0.112690i	$-0.0359466\pi$
$509$	19.8749	+	19.8749i	0.880941	+	0.880941i	−0.112690	+	0.993630i	$0.535947\pi$
$510$	1.49617	−	1.12611i	0.0662514	−	0.0498650i
$511$			8.85953i			0.391922i
$512$	−19.7579	+	11.0284i	−0.873183	+	0.487392i
$513$	3.97848	+	7.88751i	0.175654	+	0.348242i
$514$	−24.4860	+	23.0269i	−1.08003	+	1.01567i
$515$	0.132584	−	38.8093i	0.00584234	−	1.71014i
$516$	5.87913	−	4.17873i	0.258814	−	0.183958i
$517$	4.51620	−	4.51620i	0.198622	−	0.198622i
$518$	−11.5861	−	0.355801i	−0.509062	−	0.0156330i
$519$	−9.68841	+	7.82375i	−0.425274	+	0.343425i
$520$	4.02963	−	42.0599i	0.176711	−	1.84445i
$521$	−31.6135			−1.38501			−0.692506	−	0.721412i	$-0.743493\pi$
$521$	−31.6135			−1.38501			−0.692506	+	0.721412i	$0.743493\pi$
$522$	−24.9298	−	6.17627i	−1.09115	−	0.270328i
$523$	5.47824	+	5.47824i	0.239547	+	0.239547i	0.816662	−	0.577116i	$-0.195822\pi$
$523$	5.47824	+	5.47824i	0.239547	+	0.239547i	−0.577116	+	0.816662i	$0.695822\pi$
$524$	5.21727	+	5.90077i	0.227918	+	0.257776i
$525$	−1.22084	+	10.7665i	−0.0532820	+	0.469887i
$526$	−12.0326	+	11.3156i	−0.524646	+	0.493383i
$527$		−	0.467000i		−	0.0203428i
$528$	3.02071	+	4.85556i	0.131459	+	0.211311i
$529$	36.1030			1.56970
$530$	12.6977	+	0.433365i	0.551555	+	0.0188242i
$531$	−13.5811	−	21.0379i	−0.589368	−	0.912969i
$532$	2.81798	+	3.18715i	0.122175	+	0.138181i
$533$	26.1163	+	26.1163i	1.13122	+	1.13122i
$534$	−18.1892	+	13.7880i	−0.787125	+	0.596664i
$535$	12.0353	−	11.9533i	0.520330	−	0.516787i
$536$	15.0587	+	1.39082i	0.650435	+	0.0600745i
$537$	11.4353	−	9.23439i	0.493468	−	0.398493i
$538$	21.9117	+	0.672896i	0.944682	+	0.0290106i
$539$	3.17184	+	3.17184i	0.136621	+	0.136621i
$540$	8.68522	−	21.5538i	0.373752	−	0.927529i
$541$	6.32141	−	6.32141i	0.271779	−	0.271779i	−0.558037	−	0.829816i	$-0.688445\pi$
$541$	6.32141	−	6.32141i	0.271779	−	0.271779i	0.829816	+	0.558037i	$0.188445\pi$
$542$	−18.0966	−	19.2433i	−0.777317	−	0.826571i
$543$	6.46403	+	8.00463i	0.277398	+	0.343511i
$544$	−1.56057	+	1.14238i	−0.0669090	+	0.0489792i
$545$	−3.94899	+	3.92210i	−0.169156	+	0.168004i
$546$	2.79175	−	20.2833i	0.119476	−	0.868046i
$547$	4.29122	−	4.29122i	0.183479	−	0.183479i	−0.609391	−	0.792870i	$-0.708586\pi$
$547$	4.29122	−	4.29122i	0.183479	−	0.183479i	0.792870	+	0.609391i	$0.208586\pi$
$548$	−10.6486	−	0.654640i	−0.454885	−	0.0279648i
$549$	22.6166	−	14.6002i	0.965254	−	0.623121i
$550$	−5.83230	−	0.219002i	−0.248690	−	0.00933829i
$551$		−	10.2919i		−	0.438451i
$552$	−20.8669	−	31.3535i	−0.888156	−	1.33449i
$553$	15.6400			0.665080
$554$	0.385027	−	12.5377i	0.0163582	−	0.532678i
$555$	−19.7937	+	15.8728i	−0.840198	+	0.673761i
$556$	−17.3869	−	19.6647i	−0.737369	−	0.833970i
$557$	−23.0729	+	23.0729i	−0.977630	+	0.977630i	−0.999755	−	0.0221251i	$-0.992957\pi$
$557$	−23.0729	+	23.0729i	−0.977630	+	0.977630i	0.0221251	+	0.999755i	$0.492957\pi$
$558$	−2.99214	−	4.96300i	−0.126667	−	0.210100i
$559$		−	13.9105i		−	0.588350i
$560$	1.40870	−	11.1018i	0.0595286	−	0.469136i
$561$	0.307078	+	0.380265i	0.0129648	+	0.0160548i
$562$	−13.9191	+	13.0897i	−0.587142	+	0.552155i
$563$	1.29935	+	1.29935i	0.0547609	+	0.0547609i	0.733957	−	0.679196i	$-0.237671\pi$
$563$	1.29935	+	1.29935i	0.0547609	+	0.0547609i	−0.679196	+	0.733957i	$0.737671\pi$
$564$	26.4301	+	4.46831i	1.11291	+	0.188150i
$565$	20.3926	+	0.0696671i	0.857925	+	0.00293092i
$566$	−8.26793	−	0.253903i	−0.347527	−	0.0106723i
$567$	4.63592	−	10.2620i	0.194690	−	0.430962i
$568$	−24.1301	+	20.0496i	−1.01248	+	0.841264i
$569$	−8.89968			−0.373094			−0.186547	−	0.982446i	$-0.559730\pi$
$569$	−8.89968			−0.373094			−0.186547	+	0.982446i	$0.559730\pi$
$570$	9.22059	+	1.30121i	0.386208	+	0.0545018i
$571$	−29.8462	+	29.8462i	−1.24903	+	1.24903i	−0.292876	+	0.956150i	$0.594612\pi$
$571$	−29.8462	+	29.8462i	−1.24903	+	1.24903i	−0.956150	+	0.292876i	$0.905388\pi$
$572$	11.0076	+	0.676713i	0.460252	+	0.0282948i
$573$	−13.7176	−	1.46063i	−0.573062	−	0.0610186i
$574$	6.70148	+	7.12612i	0.279714	+	0.297438i
$575$	38.4383	+	0.262636i	1.60299	+	0.0109527i
$576$	−9.26541	+	22.1394i	−0.386059	+	0.922474i
$577$		−	29.0417i		−	1.20902i	−0.796597	−	0.604510i	$-0.793369\pi$
$577$		−	29.0417i		−	1.20902i	0.796597	−	0.604510i	$-0.206631\pi$
$578$	17.3934	−	16.3569i	0.723469	−	0.680359i
$579$	−4.86403	+	45.6810i	−0.202142	+	1.89844i
$580$	−20.3430	+	17.8632i	−0.844699	+	0.741729i
$581$	9.17159	−	9.17159i	0.380502	−	0.380502i
$582$	−0.0801653	−	0.105755i	−0.00332296	−	0.00438368i
$583$			3.31620i			0.137343i
$584$	−12.7995	−	15.4044i	−0.529647	−	0.637439i
$585$	−24.1773	−	37.7345i	−0.999607	−	1.56013i
$586$	12.1842	+	0.374169i	0.503325	+	0.0154568i
$587$	−2.93878	+	2.93878i	−0.121296	+	0.121296i	−0.765149	−	0.643853i	$-0.777335\pi$
$587$	−2.93878	+	2.93878i	−0.121296	+	0.121296i	0.643853	+	0.765149i	$0.277335\pi$
$588$	−3.13821	+	18.5625i	−0.129417	+	0.765505i
$589$	1.64209	−	1.64209i	0.0676611	−	0.0676611i
$590$	−26.3799	−	0.900327i	−1.08604	−	0.0370659i
$591$	−0.669950	−	0.829621i	−0.0275580	−	0.0341261i
$592$	20.6592	−	16.1199i	0.849087	−	0.662524i
$593$	2.27542			0.0934402			0.0467201	−	0.998908i	$-0.485123\pi$
$593$	2.27542			0.0934402			0.0467201	+	0.998908i	$0.485123\pi$
$594$	5.69986	+	2.07374i	0.233868	+	0.0850864i
$595$	0.00326767	−	0.956499i	0.000133962	−	0.0392126i
$596$	−26.8429	−	30.3595i	−1.09953	−	1.24357i
$597$	26.2789	+	2.79813i	1.07553	+	0.114520i
$598$	−72.6001	−	2.22950i	−2.96884	−	0.0911712i
$599$		−	4.85563i		−	0.198396i	−0.995068	−	0.0991978i	$-0.968372\pi$
$599$		−	4.85563i		−	0.198396i	0.995068	−	0.0991978i	$-0.0316277\pi$
$600$	−13.4317	−	20.4839i	−0.548348	−	0.836250i
$601$		−	13.1968i		−	0.538309i	−0.963097	−	0.269155i	$-0.913256\pi$
$601$		−	13.1968i		−	0.538309i	0.963097	−	0.269155i	$-0.0867443\pi$
$602$	0.113088	−	3.68253i	0.00460913	−	0.150089i
$603$	13.4760	−	8.69947i	0.548787	−	0.354270i
$604$	2.24428	−	36.5062i	0.0913186	−	1.48542i
$605$	−0.0788248	+	23.0732i	−0.00320468	+	0.938061i
$606$	−2.00283	+	14.5515i	−0.0813595	+	0.591114i
$607$	30.6617			1.24452			0.622260	−	0.782810i	$-0.286215\pi$
$607$	30.6617			1.24452			0.622260	+	0.782810i	$0.286215\pi$
$608$	−9.50426	−	1.47046i	−0.385449	−	0.0596350i
$609$	−10.2064	+	8.24208i	−0.413586	+	0.333986i
$610$	0.967888	−	28.3595i	0.0391886	−	1.14824i
$611$	36.5539	−	36.5539i	1.47881	−	1.47881i
$612$	−0.554183	+	1.97506i	−0.0224015	+	0.0798370i
$613$	−27.6734	+	27.6734i	−1.11772	+	1.11772i	−0.125641	+	0.992076i	$0.540099\pi$
$613$	−27.6734	+	27.6734i	−1.11772	+	1.11772i	−0.992076	+	0.125641i	$0.959901\pi$
$614$	−0.596450	+	19.4224i	−0.0240708	+	0.783824i
$615$	21.2834	+	2.33978i	0.858231	+	0.0943492i
$616$	2.90856	+	0.268636i	0.117189	+	0.0108237i
$617$		−	36.0938i		−	1.45308i	−0.687123	−	0.726541i	$-0.741127\pi$
$617$		−	36.0938i		−	1.45308i	0.687123	−	0.726541i	$-0.258873\pi$
$618$	25.6820	+	33.8800i	1.03308	+	1.36285i
$619$	5.13765	−	5.13765i	0.206499	−	0.206499i	−0.596278	−	0.802778i	$-0.703355\pi$
$619$	5.13765	−	5.13765i	0.206499	−	0.206499i	0.802778	+	0.596278i	$0.203355\pi$
$620$	−6.09584	−	0.395661i	−0.244815	−	0.0158901i
$621$	−37.9414	−	12.4991i	−1.52254	−	0.501573i
$622$	3.44427	+	3.66251i	0.138103	+	0.146853i
$623$			11.6585i			0.467087i
$624$	24.4495	+	39.3007i	0.978763	+	1.57329i
$625$	24.9977	+	0.341617i	0.999907	+	0.0136647i
$626$	8.48042	−	7.97508i	0.338946	−	0.318748i
$627$	−0.257344	+	2.41687i	−0.0102773	+	0.0965205i
$628$	17.9381	−	15.8603i	0.715809	−	0.632895i
$629$	1.58372	−	1.58372i	0.0631471	−	0.0631471i
$630$	−6.09371	−	10.1860i	−0.242779	−	0.405821i
$631$	2.56482			0.102104			0.0510520	−	0.998696i	$-0.483743\pi$
$631$	2.56482			0.102104			0.0510520	+	0.998696i	$0.483743\pi$
$632$	−27.1939	+	22.5953i	−1.08171	+	0.898794i
$633$	4.24540	+	5.25722i	0.168739	+	0.208956i
$634$	0.0518094	−	1.68709i	0.00205761	−	0.0670027i
$635$	−6.08257	−	0.0207798i	−0.241380	−	0.000824622i
$636$	−11.3442	+	8.06315i	−0.449826	+	0.319725i
$637$	25.6727	+	25.6727i	1.01719	+	1.01719i
$638$	−4.84091	−	5.14766i	−0.191654	−	0.203798i
$639$	−7.00686	+	32.5298i	−0.277187	+	1.28686i
$640$	13.5896	+	21.3383i	0.537175	+	0.843471i
$641$		−	5.23757i		−	0.206872i	−0.994636	−	0.103436i	$-0.967016\pi$
$641$		−	5.23757i		−	0.206872i	0.994636	−	0.103436i	$-0.0329836\pi$
$642$	−2.53364	+	18.4080i	−0.0999947	+	0.726507i
$643$	−12.7843	+	12.7843i	−0.504163	+	0.504163i	−0.912729	−	0.408566i	$-0.866029\pi$
$643$	−12.7843	+	12.7843i	−0.504163	+	0.504163i	0.408566	+	0.912729i	$0.366029\pi$
$644$	−19.2014	−	1.18044i	−0.756640	−	0.0465158i
$645$	−5.04502	−	6.29127i	−0.198648	−	0.247719i
$646$	−0.821629	−	0.0252317i	−0.0323265	−	0.000992728i
$647$	0.683654			0.0268772			0.0134386	−	0.999910i	$-0.495722\pi$
$647$	0.683654			0.0268772			0.0134386	+	0.999910i	$0.495722\pi$
$648$	6.76497	+	24.5405i	0.265753	+	0.964041i
$649$		−	6.88949i		−	0.270436i
$650$	−47.2064	−	1.77260i	−1.85159	−	0.0695270i
$651$	−2.94348	−	0.313416i	−0.115364	−	0.0122837i
$652$	−23.2145	−	26.2557i	−0.909148	−	1.02825i
$653$	24.3535	−	24.3535i	0.953025	−	0.953025i	−0.0459199	−	0.998945i	$-0.514622\pi$
$653$	24.3535	−	24.3535i	0.953025	−	0.953025i	0.998945	+	0.0459199i	$0.0146219\pi$
$654$	0.831334	−	6.04002i	0.0325077	−	0.236183i
$655$	6.24815	−	6.20560i	0.244135	−	0.242473i
$656$	−21.9473	−	2.70874i	−0.856900	−	0.105759i
$657$	−20.7667	−	4.47311i	−0.810185	−	0.174513i
$658$	9.97414	−	9.37979i	0.388832	−	0.365662i
$659$	15.9467	−	15.9467i	0.621196	−	0.621196i	−0.324641	−	0.945837i	$-0.605244\pi$
$659$	15.9467	−	15.9467i	0.621196	−	0.621196i	0.945837	+	0.324641i	$0.105244\pi$
$660$	5.22384	−	3.68617i	0.203338	−	0.143484i
$661$	−21.2739	−	21.2739i	−0.827461	−	0.827461i	0.159704	−	0.987165i	$-0.448946\pi$
$661$	−21.2739	−	21.2739i	−0.827461	−	0.827461i	−0.987165	+	0.159704i	$0.948946\pi$
$662$	1.22896	−	40.0192i	0.0477651	−	1.55539i
$663$	2.48548	+	3.07785i	0.0965280	+	0.119534i
$664$	−2.69668	+	29.1974i	−0.104652	+	1.13308i
$665$	3.37478	−	3.35180i	0.130868	−	0.129977i
$666$	6.68371	−	26.9780i	0.258988	−	1.04538i
$667$	32.9084	+	32.9084i	1.27422	+	1.27422i
$668$	−1.16842	+	19.0058i	−0.0452074	+	0.735357i
$669$	25.0022	+	2.66219i	0.966642	+	0.102926i
$670$	0.576713	−	16.8979i	0.0222804	−	0.652823i
$671$	7.40648			0.285924
$672$	6.15304	+	10.6029i	0.237359	+	0.409015i
$673$			24.8030i			0.956084i	0.878337	+	0.478042i	$0.158653\pi$
$673$			24.8030i			0.956084i	−0.878337	+	0.478042i	$0.841347\pi$
$674$	−14.8016	−	15.7395i	−0.570137	−	0.606264i
$675$	−24.6201	−	8.29756i	−0.947629	−	0.319373i
$676$	63.1443	+	3.88191i	2.42863	+	0.149304i
$677$	−31.5804	−	31.5804i	−1.21373	−	1.21373i	−0.969790	−	0.243942i	$-0.921560\pi$
$677$	−31.5804	−	31.5804i	−1.21373	−	1.21373i	−0.243942	−	0.969790i	$-0.578440\pi$
$678$	−17.8025	+	13.4948i	−0.683700	+	0.518265i
$679$	−0.0677841			−0.00260132
$680$	1.37619	+	1.66782i	0.0527743	+	0.0639581i
$681$	13.2587	+	16.4187i	0.508073	+	0.629164i
$682$	0.0489411	−	1.59369i	0.00187405	−	0.0610254i
$683$	14.7887	−	14.7887i	0.565873	−	0.565873i	−0.365097	−	0.930970i	$-0.618964\pi$
$683$	14.7887	−	14.7887i	0.565873	−	0.565873i	0.930970	+	0.365097i	$0.118964\pi$
$684$	−8.89344	+	4.99615i	−0.340049	+	0.191033i
$685$	−0.0407491	+	11.9279i	−0.00155694	+	0.455741i
$686$	15.0729	+	16.0280i	0.575486	+	0.611951i
$687$	7.41099	+	9.17728i	0.282747	+	0.350135i
$688$	5.12358	+	6.56634i	0.195334	+	0.250340i
$689$			26.8412i			1.02257i
$690$	−33.6434	+	25.3222i	−1.28078	+	0.963998i
$691$	32.9798	+	32.9798i	1.25461	+	1.25461i	0.953630	+	0.300981i	$0.0973142\pi$
$691$	32.9798	+	32.9798i	1.25461	+	1.25461i	0.300981	+	0.953630i	$0.402686\pi$
$692$	−9.52474	−	10.7726i	−0.362076	−	0.409511i
$693$	2.60288	−	1.68029i	0.0988752	−	0.0638290i
$694$	0.855539	−	27.8592i	0.0324758	−	1.05752i
$695$	−20.8224	+	20.6806i	−0.789837	+	0.784459i
$696$	5.83890	−	29.0762i	0.221323	−	1.10213i
$697$	−1.89012			−0.0715935
$698$	−0.906327	+	29.5130i	−0.0343050	+	1.11708i
$699$	0.197819	−	1.85783i	0.00748220	−	0.0702698i
$700$	−12.4826	−	0.853037i	−0.471798	−	0.0322418i
$701$	18.9950	+	18.9950i	0.717431	+	0.717431i	0.968078	−	0.250648i	$-0.0806436\pi$
$701$	18.9950	+	18.9950i	0.717431	+	0.717431i	−0.250648	+	0.968078i	$0.580644\pi$
$702$	46.1345	+	16.7847i	1.74123	+	0.633499i
$703$	11.1375			0.420060
$704$	−5.44533	+	3.73495i	−0.205229	+	0.140766i
$705$	3.27490	−	29.7896i	0.123340	−	1.12194i
$706$	−22.9348	+	21.5681i	−0.863162	+	0.811727i
$707$	5.30528	+	5.30528i	0.199526	+	0.199526i
$708$	23.5678	−	16.7514i	0.885734	−	0.629556i
$709$	−4.09108	−	4.09108i	−0.153644	−	0.153644i	0.626099	−	0.779743i	$-0.284650\pi$
$709$	−4.09108	−	4.09108i	−0.153644	−	0.153644i	−0.779743	+	0.626099i	$0.784650\pi$
$710$	23.9419	+	25.6339i	0.898524	+	0.962024i
$711$	−7.89652	+	36.6600i	−0.296143	+	1.37486i
$712$	−16.8432	−	20.2711i	−0.631225	−	0.759690i
$713$			10.5011i			0.393271i
$714$	0.632961	+	0.835009i	0.0236880	+	0.0312494i
$715$	0.0421230	−	12.3301i	0.00157531	−	0.461118i
$716$	11.2421	+	12.7149i	0.420136	+	0.475177i
$717$	2.37734	+	0.253135i	0.0887834	+	0.00945350i
$718$	30.1505	+	32.0610i	1.12521	+	1.19651i
$719$	30.4753			1.13654			0.568268	−	0.822844i	$-0.307614\pi$
$719$	30.4753			1.13654			0.568268	+	0.822844i	$0.307614\pi$
$720$	25.3113	+	8.90721i	0.943296	+	0.331952i
$721$	21.7155			0.808728
$722$	15.6075	+	16.5965i	0.580852	+	0.617657i
$723$	25.9274	+	2.76070i	0.964251	+	0.102672i
$724$	−8.90035	+	7.86940i	−0.330779	+	0.292464i
$725$	21.2562	+	21.5486i	0.789434	+	0.800296i
$726$	−15.2687	−	20.1426i	−0.566674	−	0.747562i
$727$			50.8749i			1.88684i	0.331593	+	0.943422i	$0.392414\pi$
$727$			50.8749i			1.88684i	−0.331593	+	0.943422i	$0.607586\pi$
$728$	23.5418	+	2.17433i	0.872516	+	0.0805860i
$729$	21.7134	+	16.0478i	0.804198	+	0.594361i
$730$	−16.3644	+	15.2843i	−0.605675	+	0.565697i
$731$	0.503373	+	0.503373i	0.0186179	+	0.0186179i
$732$	18.0084	+	25.3364i	0.665611	+	0.936460i
$733$	−21.0616	−	21.0616i	−0.777929	−	0.777929i	0.201550	−	0.979478i	$-0.435402\pi$
$733$	−21.0616	−	21.0616i	−0.777929	−	0.777929i	−0.979478	+	0.201550i	$0.935402\pi$
$734$	26.8888	−	25.2865i	0.992483	−	0.933342i
$735$	20.9220	+	2.30004i	0.771718	+	0.0848384i
$736$	35.0916	−	25.6880i	1.29349	−	0.946874i
$737$	4.41313			0.162560
$738$	−20.0871	+	12.1103i	−0.739416	+	0.445786i
$739$	−5.61355	−	5.61355i	−0.206498	−	0.206498i	0.596279	−	0.802777i	$-0.296645\pi$
$739$	−5.61355	−	5.61355i	−0.206498	−	0.206498i	−0.802777	+	0.596279i	$0.796645\pi$
$740$	−19.3308	−	22.0144i	−0.710616	−	0.809266i
$741$	−2.08293	+	19.5621i	−0.0765184	+	0.718630i
$742$	−0.218212	+	7.10569i	−0.00801080	+	0.260858i
$743$	−32.9702			−1.20956			−0.604779	−	0.796393i	$-0.706738\pi$
$743$	−32.9702			−1.20956			−0.604779	+	0.796393i	$0.706738\pi$
$744$	5.57074	−	3.70754i	0.204233	−	0.135925i
$745$	−32.1467	+	31.9278i	−1.17776	+	1.16975i
$746$	−1.11653	+	36.3578i	−0.0408789	+	1.33115i
$747$	16.8675	+	26.1288i	0.617149	+	0.956004i
$748$	−0.422817	+	0.373841i	−0.0154597	+	0.0136690i
$749$	6.71133	+	6.71133i	0.245227	+	0.245227i
$750$	−21.9929	+	16.3191i	−0.803067	+	0.595888i
$751$			8.53556i			0.311467i	0.987799	+	0.155734i	$0.0497741\pi$
$751$			8.53556i			0.311467i	−0.987799	+	0.155734i	$0.950226\pi$
$752$	−3.79131	+	30.7188i	−0.138255	+	1.12020i
$753$	−1.84290	−	2.28213i	−0.0671591	−	0.0831654i
$754$	−39.1822	−	41.6650i	−1.42693	−	1.51735i
$755$	−40.8920	−	0.139699i	−1.48821	−	0.00508416i
$756$	12.0768	+	4.81850i	0.439228	+	0.175247i
$757$	8.88889	−	8.88889i	0.323072	−	0.323072i	−0.526872	−	0.849944i	$-0.676635\pi$
$757$	8.88889	−	8.88889i	0.323072	−	0.323072i	0.849944	+	0.526872i	$0.176635\pi$
$758$	−0.945449	+	30.7870i	−0.0343403	+	1.11823i
$759$	−6.90507	−	8.55078i	−0.250638	−	0.310374i
$760$	−1.02547	+	10.7035i	−0.0371977	+	0.388257i
$761$	14.4998			0.525618			0.262809	−	0.964848i	$-0.415351\pi$
$761$	14.4998			0.525618			0.262809	+	0.964848i	$0.415351\pi$
$762$	5.31000	−	4.02513i	0.192361	−	0.145815i
$763$	−2.20211	−	2.20211i	−0.0797218	−	0.0797218i
$764$	0.977436	−	15.8993i	0.0353624	−	0.575216i
$765$	2.24038	+	0.490589i	0.0810010	+	0.0177373i
$766$	−12.8309	−	13.6440i	−0.463600	−	0.492976i
$767$		−	55.7633i		−	2.01350i
$768$	−26.0167	−	9.54629i	−0.938797	−	0.344472i
$769$	4.50749			0.162544			0.0812721	−	0.996692i	$-0.474102\pi$
$769$	4.50749			0.162544			0.0812721	+	0.996692i	$0.474102\pi$
$770$	0.111391	−	3.26381i	0.00401426	−	0.117619i
$771$	−40.9353	−	4.35872i	−1.47425	−	0.156976i
$772$	−52.9461	−	3.25495i	−1.90557	−	0.117148i
$773$	16.0793	+	16.0793i	0.578332	+	0.578332i	0.934444	−	0.356111i	$-0.115898\pi$
$773$	16.0793	+	16.0793i	0.578332	+	0.578332i	−0.356111	+	0.934444i	$0.615898\pi$
$774$	8.57473	+	2.12436i	0.308212	+	0.0763586i
$775$	−0.0466639	+	6.82954i	−0.00167622	+	0.245324i
$776$	0.117859	−	0.0979287i	0.00423089	−	0.00351544i
$777$	−8.91924	−	11.0450i	−0.319976	−	0.396237i
$778$	0.0224699	−	0.731695i	0.000805585	−	0.0262325i
$779$	−6.64614	−	6.64614i	−0.238123	−	0.238123i
$780$	42.2816	−	29.8358i	1.51392	−	1.06829i
$781$	−6.47371	+	6.47371i	−0.231648	+	0.231648i
$782$	2.70783	−	2.54647i	0.0968319	−	0.0910618i
$783$	−14.1662	−	28.0852i	−0.506259	−	1.00368i
$784$	−21.5746	−	2.66273i	−0.770521	−	0.0950977i
$785$	−18.8648	−	18.9941i	−0.673313	−	0.677929i
$786$	−1.31535	+	9.55659i	−0.0469169	+	0.340872i
$787$	1.42475	−	1.42475i	0.0507867	−	0.0507867i	−0.681257	−	0.732044i	$-0.738567\pi$
$787$	1.42475	−	1.42475i	0.0507867	−	0.0507867i	0.732044	+	0.681257i	$0.238567\pi$
$788$	0.922456	−	0.815606i	0.0328611	−	0.0290548i
$789$	−20.1159	−	2.14191i	−0.716146	−	0.0762539i
$790$	26.9818	+	28.8886i	0.959970	+	1.02781i
$791$			11.4106i			0.405714i
$792$	−2.09819	+	6.68201i	−0.0745560	+	0.237435i
$793$	59.9478			2.12881
$794$	20.3704	+	0.625563i	0.722919	+	0.0222004i
$795$	9.73472	+	12.1394i	0.345255	+	0.430542i
$796$	−1.87248	+	30.4583i	−0.0663683	+	1.07957i
$797$	14.2806	−	14.2806i	0.505846	−	0.505846i	−0.407403	−	0.913248i	$-0.633566\pi$
$797$	14.2806	−	14.2806i	0.505846	−	0.505846i	0.913248	+	0.407403i	$0.133566\pi$
$798$	−0.710451	+	5.16175i	−0.0251497	+	0.182724i
$799$			2.64553i			0.0935920i
$800$	22.9364	−	16.5506i	0.810924	−	0.585152i
$801$	−27.3274	−	5.88628i	−0.965566	−	0.207981i
$802$	−22.2362	−	23.6452i	−0.785189	−	0.834942i
$803$	−4.13275	−	4.13275i	−0.145842	−	0.145842i
$804$	10.7303	+	15.0966i	0.378427	+	0.532416i
$805$	−0.0734781	+	21.5082i	−0.00258976	+	0.758064i
$806$	0.396128	−	12.8992i	0.0139530	−	0.454356i
$807$	16.8682	+	20.8885i	0.593790	+	0.735310i
$808$	−16.8891	−	1.55989i	−0.594158	−	0.0548767i
$809$	−8.24807			−0.289987			−0.144993	−	0.989433i	$-0.546316\pi$
$809$	−8.24807			−0.289987			−0.144993	+	0.989433i	$0.546316\pi$
$810$	26.9527	−	9.14075i	0.947020	−	0.321173i
$811$	33.9396	−	33.9396i	1.19178	−	1.19178i	0.215215	−	0.976567i	$-0.430955\pi$
$811$	33.9396	−	33.9396i	1.19178	−	1.19178i	0.976567	−	0.215215i	$-0.0690453\pi$
$812$	−10.0340	−	11.3485i	−0.352125	−	0.398256i
$813$	3.42548	−	32.1707i	0.120137	−	1.12828i
$814$	5.57058	−	5.23864i	0.195249	−	0.183614i
$815$	−27.8014	+	27.6121i	−0.973840	+	0.967209i
$816$	−2.30691	−	0.537416i	−0.0807579	−	0.0188133i
$817$			3.53997i			0.123848i
$818$	−13.9339	−	14.8168i	−0.487187	−	0.518057i
$819$	21.0676	−	13.6002i	0.736162	−	0.475230i
$820$	−1.60139	+	24.6721i	−0.0559228	+	0.861589i
$821$	−11.1525	+	11.1525i	−0.389226	+	0.389226i	−0.874411	−	0.485185i	$-0.838752\pi$
$821$	−11.1525	+	11.1525i	−0.389226	+	0.389226i	0.485185	+	0.874411i	$0.338752\pi$
$822$	−7.89325	−	10.4129i	−0.275309	−	0.363190i
$823$		−	14.5445i		−	0.506989i	−0.967337	−	0.253495i	$-0.918420\pi$
$823$		−	14.5445i		−	0.506989i	0.967337	−	0.253495i	$-0.0815801\pi$
$824$	−37.7576	+	31.3727i	−1.31535	+	1.09292i
$825$	−4.45280	−	5.59179i	−0.155027	−	0.194681i
$826$	0.453340	−	14.7623i	0.0157737	−	0.513645i
$827$	−25.2445	+	25.2445i	−0.877836	+	0.877836i	−0.993310	−	0.115474i	$-0.963161\pi$
$827$	−25.2445	+	25.2445i	−0.877836	+	0.877836i	0.115474	+	0.993310i	$0.463161\pi$
$828$	12.4616	−	44.4119i	0.433070	−	1.54342i
$829$	−3.82527	+	3.82527i	−0.132857	+	0.132857i	−0.770408	−	0.637551i	$-0.779948\pi$
$829$	−3.82527	+	3.82527i	−0.132857	+	0.132857i	0.637551	+	0.770408i	$0.279948\pi$
$830$	32.7635	+	1.11819i	1.13724	+	0.0388131i
$831$	11.9522	−	9.65188i	0.414619	−	0.334820i
$832$	−44.0743	+	30.2306i	−1.52800	+	1.04806i
$833$	−1.85802			−0.0643766
$834$	4.38348	−	31.8480i	0.151787	−	1.10280i
$835$	21.2891	+	0.0727298i	0.736741	+	0.00251692i
$836$	−2.80125	−	0.172212i	−0.0968832	−	0.00595606i
$837$	2.22079	−	6.74125i	0.0767616	−	0.233012i
$838$	0.433994	−	14.1323i	0.0149921	−	0.488192i
$839$		−	39.6246i		−	1.36799i	−0.729485	−	0.683997i	$-0.760240\pi$
$839$		−	39.6246i		−	1.36799i	0.729485	−	0.683997i	$-0.239760\pi$
$840$	11.4358	−	7.55471i	0.394573	−	0.260662i
$841$			7.64669i			0.263679i
$842$	−14.7769	−	0.453789i	−0.509245	−	0.0156386i
$843$	−23.2698	−	2.47772i	−0.801453	−	0.0853373i
$844$	−5.84550	+	5.16841i	−0.201211	+	0.177904i
$845$	0.241635	−	70.7304i	0.00831250	−	2.43320i
$846$	16.9503	+	28.1151i	0.582763	+	0.966617i
$847$	−12.9105			−0.443610
$848$	−9.88629	−	12.6702i	−0.339497	−	0.435097i
$849$	−6.36486	−	7.88182i	−0.218442	−	0.270503i
$850$	1.77239	−	1.64410i	0.0607923	−	0.0563921i
$851$	−35.6122	+	35.6122i	−1.22077	+	1.22077i
$852$	−37.8860	−	6.40507i	−1.29795	−	0.219434i
$853$	−6.10287	+	6.10287i	−0.208958	+	0.208958i	−0.803825	−	0.594866i	$-0.797205\pi$
$853$	−6.10287	+	6.10287i	−0.208958	+	0.208958i	0.594866	+	0.803825i	$0.297205\pi$
$854$	15.8700	+	0.487359i	0.543062	+	0.0166771i
$855$	6.15269	+	9.60276i	0.210418	+	0.328407i
$856$	−21.3652	−	1.97330i	−0.730248	−	0.0674461i
$857$			20.1732i			0.689103i	0.938767	+	0.344551i	$0.111969\pi$
$857$			20.1732i			0.689103i	−0.938767	+	0.344551i	$0.888031\pi$
$858$	8.15940	+	10.7640i	0.278557	+	0.367476i
$859$	18.0207	−	18.0207i	0.614858	−	0.614858i	−0.329350	−	0.944208i	$-0.606830\pi$
$859$	18.0207	−	18.0207i	0.614858	−	0.614858i	0.944208	+	0.329350i	$0.106830\pi$
$860$	6.99710	−	6.14414i	0.238599	−	0.209514i
$861$	−1.26851	+	11.9134i	−0.0432308	+	0.406006i
$862$	21.7506	−	20.4545i	0.740828	−	0.696683i
$863$		−	35.6266i		−	1.21275i	−0.795181	−	0.606373i	$-0.792624\pi$
$863$		−	35.6266i		−	1.21275i	0.795181	−	0.606373i	$-0.207376\pi$
$864$	−27.9597	+	9.06936i	−0.951209	+	0.308546i
$865$	−11.4067	+	11.3291i	−0.387840	+	0.385199i
$866$	−18.3477	−	19.5103i	−0.623482	−	0.662988i
$867$	29.0780	+	3.09618i	0.987542	+	0.105152i
$868$	0.209735	−	3.41161i	0.00711886	−	0.115798i
$869$	−7.29568	+	7.29568i	−0.247489	+	0.247489i
$870$	−32.8319	−	4.63325i	−1.11311	−	0.157082i
$871$	35.7197			1.21032
$872$	7.01033	+	0.647477i	0.237400	+	0.0219263i
$873$	0.0342237	−	0.158886i	0.00115830	−	0.00537746i
$874$	18.4755	+	0.567370i	0.624942	+	0.0191916i
$875$	−0.143363	+	13.9878i	−0.00484656	+	0.472873i
$876$	4.08893	−	24.1861i	0.138152	−	0.817171i
$877$	−16.8587	−	16.8587i	−0.569279	−	0.569279i	0.362647	−	0.931926i	$-0.381873\pi$
$877$	−16.8587	−	16.8587i	−0.569279	−	0.569279i	−0.931926	+	0.362647i	$0.881873\pi$
$878$	14.6509	−	13.7778i	0.494443	−	0.464980i
$879$	9.37971	+	11.6152i	0.316370	+	0.391771i
$880$	4.52159	+	5.83584i	0.152423	+	0.196726i
$881$		−	47.5327i		−	1.60142i	−0.599055	−	0.800708i	$-0.704457\pi$
$881$		−	47.5327i		−	1.60142i	0.599055	−	0.800708i	$-0.295543\pi$
$882$	−19.7459	+	11.9046i	−0.664880	+	0.400849i
$883$	−19.1982	+	19.1982i	−0.646069	+	0.646069i	−0.952041	−	0.305971i	$-0.901019\pi$
$883$	−19.1982	+	19.1982i	−0.646069	+	0.646069i	0.305971	+	0.952041i	$0.401019\pi$
$884$	−3.42227	+	3.02586i	−0.115103	+	0.101771i
$885$	−20.2242	−	25.2200i	−0.679827	−	0.847762i
$886$	−0.943865	+	30.7354i	−0.0317098	+	1.03258i
$887$	44.2588			1.48607			0.743033	−	0.669255i	$-0.233387\pi$
$887$	44.2588			1.48607			0.743033	+	0.669255i	$0.233387\pi$
$888$	31.4651	+	6.31862i	1.05590	+	0.212039i
$889$		−	3.40347i		−	0.114149i
$890$	−21.5344	+	20.1130i	−0.721834	+	0.674188i
$891$	2.62442	+	6.94950i	0.0879213	+	0.232817i
$892$	−1.78151	+	28.9786i	−0.0596493	+	0.970275i
$893$	−9.30234	+	9.30234i	−0.311291	+	0.311291i
$894$	6.76746	−	49.1687i	0.226338	−	1.64445i
$895$	13.4634	−	13.3717i	0.450031	−	0.446967i
$896$	−11.9136	+	7.64466i	−0.398006	+	0.255390i
$897$	−55.8894	−	69.2098i	−1.86609	−	2.31085i
$898$	−13.1728	−	14.0075i	−0.439581	−	0.467435i
$899$	−5.84701	+	5.84701i	−0.195009	+	0.195009i
$900$	8.30188	−	28.8284i	0.276729	−	0.960948i
$901$	−0.971292	−	0.971292i	−0.0323584	−	0.0323584i
$902$	−6.45024	−	0.198083i	−0.214769	−	0.00659544i
$903$	3.51056	−	2.83491i	0.116824	−	0.0943398i
$904$	−16.4850	−	19.8400i	−0.548284	−	0.659870i
$905$	9.36013	+	9.42430i	0.311141	+	0.313274i
$906$	35.6981	−	27.0602i	1.18599	−	0.899016i
$907$	−34.3925	−	34.3925i	−1.14199	−	1.14199i	−0.988087	−	0.153899i	$-0.950817\pi$
$907$	−34.3925	−	34.3925i	−1.14199	−	1.14199i	−0.153899	−	0.988087i	$-0.549183\pi$
$908$	−18.2559	+	16.1413i	−0.605844	+	0.535667i
$909$	−15.1141	+	9.75695i	−0.501305	+	0.323618i
$910$	0.901598	−	26.4171i	0.0298877	−	0.875720i
$911$	32.3613			1.07218			0.536088	−	0.844162i	$-0.319901\pi$
$911$	32.3613			1.07218			0.536088	+	0.844162i	$0.319901\pi$
$912$	−6.22197	−	10.0013i	−0.206030	−	0.331178i
$913$			8.55665i			0.283184i
$914$	22.9330	−	21.5665i	0.758556	−	0.713355i
$915$	27.1126	−	21.7418i	0.896313	−	0.718761i
$916$	−10.2042	+	9.02224i	−0.337157	+	0.298103i
$917$	3.48421	+	3.48421i	0.115059	+	0.115059i
$918$	−2.27683	+	1.06207i	−0.0751467	+	0.0350534i
$919$	−32.3460			−1.06700			−0.533498	−	0.845801i	$-0.679123\pi$
$919$	−32.3460			−1.06700			−0.533498	+	0.845801i	$0.679123\pi$
$920$	−30.9455	−	37.5033i	−1.02024	−	1.23645i
$921$	−18.5154	+	14.9519i	−0.610103	+	0.492680i
$922$	26.3554	+	0.809357i	0.867968	+	0.0266548i
$923$	−52.3980	+	52.3980i	−1.72470	+	1.72470i
$924$	2.07254	+	2.91589i	0.0681815	+	0.0959257i
$925$	−23.3190	+	23.0025i	−0.766725	+	0.756319i
$926$	7.41435	−	6.97253i	0.243651	−	0.229132i
$927$	−10.9640	+	50.9010i	−0.360105	+	1.67181i
$928$	33.8420	+	5.23589i	1.11092	+	0.171876i
$929$		−	22.5066i		−	0.738418i	−0.929346	−	0.369209i	$-0.879629\pi$
$929$		−	22.5066i		−	0.738418i	0.929346	−	0.369209i	$-0.120371\pi$
$930$	−4.49912	−	5.97760i	−0.147532	−	0.196013i
$931$	−6.53326	−	6.53326i	−0.214119	−	0.214119i
$932$	2.15330	+	0.132378i	0.0705338	+	0.00433619i
$933$	−0.651960	+	6.12294i	−0.0213442	+	0.200456i
$934$	−5.07248	−	0.155773i	−0.165977	−	0.00509704i
$935$	0.444659	+	0.447708i	0.0145419	+	0.0146416i
$936$	−16.9827	+	54.0840i	−0.555096	+	1.76779i
$937$	43.9221			1.43487			0.717437	−	0.696624i	$-0.245315\pi$
$937$	43.9221			1.43487			0.717437	+	0.696624i	$0.245315\pi$
$938$	9.45611	+	0.290391i	0.308753	+	0.00948162i
$939$	14.1775	+	1.50959i	0.462664	+	0.0492636i
$940$	34.5326	+	2.24140i	1.12633	+	0.0731063i
$941$	−4.35025	−	4.35025i	−0.141814	−	0.141814i	0.632636	−	0.774450i	$-0.281973\pi$
$941$	−4.35025	−	4.35025i	−0.141814	−	0.141814i	−0.774450	+	0.632636i	$0.781973\pi$
$942$	29.0517	+	3.99860i	0.946554	+	0.130281i
$943$	42.5020			1.38406
$944$	20.5390	+	26.3227i	0.668489	+	0.856731i
$945$	4.59573	−	13.7917i	0.149499	−	0.448645i
$946$	1.66506	+	1.77056i	0.0541357	+	0.0575660i
$947$	21.6140	+	21.6140i	0.702360	+	0.702360i	0.964917	−	0.262557i	$-0.0845657\pi$
$947$	21.6140	+	21.6140i	0.702360	+	0.702360i	−0.262557	+	0.964917i	$0.584566\pi$
$948$	−42.6964	−	7.21832i	−1.38671	−	0.234440i
$949$	−33.4504	−	33.4504i	−1.08584	−	1.08584i
$950$	12.0132	+	0.451095i	0.389760	+	0.0146355i
$951$	1.60830	−	1.29876i	0.0521527	−	0.0421152i
$952$	−0.930579	+	0.773216i	−0.0301602	+	0.0250601i
$953$		−	22.6159i		−	0.732600i	−0.930497	−	0.366300i	$-0.880624\pi$
$953$		−	22.6159i		−	0.732600i	0.930497	−	0.366300i	$-0.119376\pi$
$954$	−16.5455	−	4.09910i	−0.535681	−	0.132713i
$955$	−17.8094	−	0.0608420i	−0.576298	−	0.00196880i
$956$	−0.169395	+	2.75543i	−0.00547863	+	0.0891171i
$957$	0.916329	−	8.60579i	0.0296207	−	0.278186i
$958$	34.0491	−	32.0201i	1.10008	−	1.03452i
$959$	−6.67417			−0.215520
$960$	−8.96950	+	29.6572i	−0.289489	+	0.957181i
$961$	29.1342			0.939813
$962$	45.0881	−	42.4014i	1.45370	−	1.36708i
$963$	−19.1198	+	12.3428i	−0.616127	+	0.397742i
$964$	−1.84743	+	30.0509i	−0.0595018	+	0.967874i
$965$	−0.202609	+	59.3069i	−0.00652223	+	1.90916i
$966$	−14.2330	−	18.7763i	−0.457940	−	0.604119i
$967$			5.32971i			0.171392i	0.996321	+	0.0856960i	$0.0273114\pi$
$967$			5.32971i			0.171392i	−0.996321	+	0.0856960i	$0.972689\pi$
$968$	22.4480	−	18.6520i	0.721506	−	0.599497i
$969$	−0.632511	−	0.783259i	−0.0203192	−	0.0251619i
$970$	−0.116940	−	0.125204i	−0.00375471	−	0.00402006i
$971$	28.3978	+	28.3978i	0.911329	+	0.911329i	0.996377	−	0.0850483i	$-0.0271045\pi$
$971$	28.3978	+	28.3978i	0.911329	+	0.911329i	−0.0850483	+	0.996377i	$0.527104\pi$
$972$	−17.3920	+	25.8750i	−0.557849	+	0.829942i
$973$	−11.6114	−	11.6114i	−0.372243	−	0.372243i
$974$	7.36700	+	7.83381i	0.236054	+	0.251012i
$975$	−36.0408	−	45.2597i	−1.15423	−	1.44947i
$976$	−28.2980	+	22.0803i	−0.905796	+	0.706773i
$977$	20.7758			0.664677			0.332339	−	0.943160i	$-0.392162\pi$
$977$	20.7758			0.664677			0.332339	+	0.943160i	$0.392162\pi$
$978$	5.85269	−	42.5224i	0.187148	−	1.35972i
$979$	−5.43839	−	5.43839i	−0.173812	−	0.173812i
$980$	−1.57419	+	24.2531i	−0.0502856	+	0.774737i
$981$	6.27357	−	4.04991i	0.200300	−	0.129304i
$982$	49.9283	+	1.53327i	1.59328	+	0.0489285i
$983$	4.06051			0.129510			0.0647551	−	0.997901i	$-0.479373\pi$
$983$	4.06051			0.129510			0.0647551	+	0.997901i	$0.479373\pi$
$984$	−15.0058	−	22.5469i	−0.478367	−	0.718768i
$985$	−0.970110	−	0.976761i	−0.0309103	−	0.0311222i
$986$	2.92559	+	0.0898430i	0.0931696	+	0.00286118i
$987$	16.6746	+	1.77548i	0.530759	+	0.0565143i
$988$	−22.6732	−	1.39387i	−0.721331	−	0.0443451i
$989$	−11.3190	−	11.3190i	−0.359924	−	0.359924i
$990$	7.59410	+	1.90897i	0.241356	+	0.0606712i
$991$			23.1547i			0.735534i	0.929918	+	0.367767i	$0.119878\pi$
$991$			23.1547i			0.735534i	−0.929918	+	0.367767i	$0.880122\pi$
$992$	4.56413	+	6.23491i	0.144911	+	0.197959i
$993$	38.1503	−	30.8078i	1.21066	−	0.977656i
$994$	−14.2974	+	13.4454i	−0.453485	+	0.426462i
$995$	34.1175	+	0.116555i	1.08160	+	0.00369505i
$996$	−29.2709	+	20.8050i	−0.927485	+	0.659232i
$997$	12.9630	−	12.9630i	0.410542	−	0.410542i	−0.471385	−	0.881927i	$-0.656246\pi$
$997$	12.9630	−	12.9630i	0.410542	−	0.410542i	0.881927	+	0.471385i	$0.156246\pi$
$998$	23.0972	+	0.709300i	0.731129	+	0.0224525i
$999$	30.3927	−	15.3301i	0.961581	−	0.485023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.t.b.59.9	✓	80
3.2	odd	2	inner	240.2.t.b.59.31	yes	80
4.3	odd	2		960.2.t.b.719.40		80
5.4	even	2	inner	240.2.t.b.59.32	yes	80
12.11	even	2		960.2.t.b.719.20		80
15.14	odd	2	inner	240.2.t.b.59.10	yes	80
16.3	odd	4	inner	240.2.t.b.179.10	yes	80
16.13	even	4		960.2.t.b.239.21		80
20.19	odd	2		960.2.t.b.719.1		80
48.29	odd	4		960.2.t.b.239.1		80
48.35	even	4	inner	240.2.t.b.179.32	yes	80
60.59	even	2		960.2.t.b.719.21		80
80.19	odd	4	inner	240.2.t.b.179.31	yes	80
80.29	even	4		960.2.t.b.239.20		80
240.29	odd	4		960.2.t.b.239.40		80
240.179	even	4	inner	240.2.t.b.179.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.t.b.59.9	✓	80	1.1	even	1	trivial
240.2.t.b.59.10	yes	80	15.14	odd	2	inner
240.2.t.b.59.31	yes	80	3.2	odd	2	inner
240.2.t.b.59.32	yes	80	5.4	even	2	inner
240.2.t.b.179.9	yes	80	240.179	even	4	inner
240.2.t.b.179.10	yes	80	16.3	odd	4	inner
240.2.t.b.179.31	yes	80	80.19	odd	4	inner
240.2.t.b.179.32	yes	80	48.35	even	4	inner
960.2.t.b.239.1		80	48.29	odd	4
960.2.t.b.239.20		80	80.29	even	4
960.2.t.b.239.21		80	16.13	even	4
960.2.t.b.239.40		80	240.29	odd	4
960.2.t.b.719.1		80	20.19	odd	2
960.2.t.b.719.20		80	12.11	even	2
960.2.t.b.719.21		80	60.59	even	2
960.2.t.b.719.40		80	4.3	odd	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03022 + 0.968834i) q^{2} +(-1.72231 - 0.183389i) q^{3} +(0.122722 - 1.99623i) q^{4} +(-2.23605 - 0.00763900i) q^{5} +(1.95204 - 1.47971i) q^{6} -1.25117i q^{7} +(1.80759 + 2.17546i) q^{8} +(2.93274 + 0.631707i) q^{9} +O(q^{10})\)	\(q+(-1.03022 + 0.968834i) q^{2} +(-1.72231 - 0.183389i) q^{3} +(0.122722 - 1.99623i) q^{4} +(-2.23605 - 0.00763900i) q^{5} +(1.95204 - 1.47971i) q^{6} -1.25117i q^{7} +(1.80759 + 2.17546i) q^{8} +(2.93274 + 0.631707i) q^{9} +(2.31104 - 2.15850i) q^{10} +(0.583641 + 0.583641i) q^{11} +(-0.577452 + 3.41563i) q^{12} +(4.72397 + 4.72397i) q^{13} +(1.21218 + 1.28899i) q^{14} +(3.84979 + 0.423225i) q^{15} +(-3.96988 - 0.489962i) q^{16} -0.341889 q^{17} +(-3.63339 + 2.19054i) q^{18} +(-1.20217 - 1.20217i) q^{19} +(-0.289662 + 4.46275i) q^{20} +(-0.229451 + 2.15491i) q^{21} +(-1.16673 - 0.0358296i) q^{22} +7.68785 q^{23} +(-2.71428 - 4.07832i) q^{24} +(4.99988 + 0.0341625i) q^{25} +(-9.44349 - 0.290004i) q^{26} +(-4.93525 - 1.62583i) q^{27} +(-2.49763 - 0.153546i) q^{28} +(4.28058 + 4.28058i) q^{29} +(-4.37618 + 3.29379i) q^{30} +1.36594i q^{31} +(4.56456 - 3.34138i) q^{32} +(-0.898180 - 1.11225i) q^{33} +(0.352222 - 0.331234i) q^{34} +(-0.00955770 + 2.79769i) q^{35} +(1.62094 - 5.77690i) q^{36} +(-4.63227 + 4.63227i) q^{37} +(2.40320 + 0.0738009i) q^{38} +(-7.26984 - 9.00249i) q^{39} +(-4.02524 - 4.87826i) q^{40} +5.52847 q^{41} +(-1.85136 - 2.44234i) q^{42} +(-1.47233 - 1.47233i) q^{43} +(1.23671 - 1.09346i) q^{44} +(-6.55294 - 1.43493i) q^{45} +(-7.92020 + 7.44825i) q^{46} -7.73797i q^{47} +(6.74753 + 1.57190i) q^{48} +5.43457 q^{49} +(-5.18410 + 4.80886i) q^{50} +(0.588841 + 0.0626987i) q^{51} +(10.0099 - 8.85040i) q^{52} +(2.84096 + 2.84096i) q^{53} +(6.65957 - 3.10647i) q^{54} +(-1.30059 - 1.30951i) q^{55} +(2.72187 - 2.26160i) q^{56} +(1.85005 + 2.29098i) q^{57} +(-8.55712 - 0.262784i) q^{58} +(-5.90216 - 5.90216i) q^{59} +(1.31731 - 7.63313i) q^{60} +(6.34507 - 6.34507i) q^{61} +(-1.32337 - 1.40722i) q^{62} +(0.790374 - 3.66936i) q^{63} +(-1.46527 + 7.86467i) q^{64} +(-10.5270 - 10.5991i) q^{65} +(2.00291 + 0.275676i) q^{66} +(3.78069 - 3.78069i) q^{67} +(-0.0419572 + 0.682490i) q^{68} +(-13.2409 - 1.40987i) q^{69} +(-2.70065 - 2.89150i) q^{70} +11.0919i q^{71} +(3.92692 + 7.52192i) q^{72} -7.08099 q^{73} +(0.284374 - 9.26017i) q^{74} +(-8.60511 - 0.975762i) q^{75} +(-2.54734 + 2.25227i) q^{76} +(0.730234 - 0.730234i) q^{77} +(16.2115 + 2.23131i) q^{78} +12.5003i q^{79} +(8.87312 + 1.12591i) q^{80} +(8.20189 + 3.70526i) q^{81} +(-5.69556 + 5.35617i) q^{82} +(7.33041 + 7.33041i) q^{83} +(4.27354 + 0.722492i) q^{84} +(0.764483 + 0.00261169i) q^{85} +(2.94327 + 0.0903859i) q^{86} +(-6.58749 - 8.15751i) q^{87} +(-0.214708 + 2.32467i) q^{88} -9.31805 q^{89} +(8.14120 - 4.87040i) q^{90} +(5.91049 - 5.91049i) q^{91} +(0.943467 - 15.3467i) q^{92} +(0.250498 - 2.35258i) q^{93} +(7.49681 + 7.97184i) q^{94} +(2.67893 + 2.69730i) q^{95} +(-8.47437 + 4.91782i) q^{96} -0.0541765i q^{97} +(-5.59882 + 5.26520i) q^{98} +(1.34298 + 2.08036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) \) 80 * q - 8 * q^4 - 4 * q^6	\( 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) \) 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more