LMFDB - Embedded newform 650.2.l.b.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 43 x^{18} - 132 x^{17} + 291 x^{16} - 480 x^{15} + 624 x^{14} - 653 x^{13} + \cdots + 31 $ x^20 - 9x^19 + 43x^18 - 132x^17 + 291x^16 - 480x^15 + 624x^14 - 653x^13 + 552x^12 - 246x^11 - 32x^10 + 229x^9 - 103x^8 + 657x^7 - 46x^6 - 270x^5 + 1406x^4 + 588x^3 + 548x^2 + 126*x + 31
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			131.2
Root			$0.704508 + 1.87902i$ of defining polynomial
Character	$\chi$	$=$	650.131
Dual form			650.2.l.b.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.47354 + 1.07059i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.58287 + 1.57940i) q^{5} +(1.47354 + 1.07059i) q^{6} +2.37656 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.0981028 - 0.301929i) q^{9} +(1.01296 - 1.99347i) q^{10} +(0.545866 + 1.68000i) q^{11} +(0.562841 - 1.73225i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.734398 - 2.26025i) q^{14} +(-4.02331 - 0.632700i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.73745 - 1.26233i) q^{17} -0.317467 q^{18} +(-1.87664 - 1.36346i) q^{19} +(-2.20892 - 0.347372i) q^{20} +(-3.50195 + 2.54432i) q^{21} +(1.42910 - 1.03830i) q^{22} +(0.00699235 + 0.0215202i) q^{23} -1.82139 q^{24} +(0.0109859 + 4.99999i) q^{25} +1.00000 q^{26} +(-1.50984 - 4.64681i) q^{27} +(-1.92268 + 1.39691i) q^{28} +(-1.40191 + 1.01855i) q^{29} +(0.641538 + 4.02191i) q^{30} +(6.29427 + 4.57306i) q^{31} -1.00000 q^{32} +(-2.60294 - 1.89115i) q^{33} +(-0.663647 + 2.04249i) q^{34} +(3.76180 + 3.75354i) q^{35} +(0.0981028 + 0.301929i) q^{36} +(-2.40896 + 7.41402i) q^{37} +(-0.716813 + 2.20613i) q^{38} +(-0.562841 - 1.73225i) q^{39} +(0.352224 + 2.20815i) q^{40} +(-3.92009 + 12.0648i) q^{41} +(3.50195 + 2.54432i) q^{42} +3.00250 q^{43} +(-1.42910 - 1.03830i) q^{44} +(0.632152 - 0.322973i) q^{45} +(0.0183062 - 0.0133002i) q^{46} +(5.30120 - 3.85155i) q^{47} +(0.562841 + 1.73225i) q^{48} -1.35195 q^{49} +(4.75188 - 1.55553i) q^{50} +3.91163 q^{51} +(-0.309017 - 0.951057i) q^{52} +(2.55981 - 1.85981i) q^{53} +(-3.95281 + 2.87188i) q^{54} +(-1.78936 + 3.52137i) q^{55} +(1.92268 + 1.39691i) q^{56} +4.22500 q^{57} +(1.40191 + 1.01855i) q^{58} +(-2.21570 + 6.81923i) q^{59} +(3.62682 - 1.85298i) q^{60} +(2.69420 + 8.29189i) q^{61} +(2.40420 - 7.39936i) q^{62} +(0.233148 - 0.717554i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.99123 + 1.01734i) q^{65} +(-0.994235 + 3.05994i) q^{66} +(-4.76139 - 3.45935i) q^{67} +2.14761 q^{68} +(-0.0333428 - 0.0242250i) q^{69} +(2.40737 - 4.73759i) q^{70} +(-6.84272 + 4.97153i) q^{71} +(0.256837 - 0.186603i) q^{72} +(-3.34722 - 10.3017i) q^{73} +7.79556 q^{74} +(-5.36911 - 7.35590i) q^{75} +2.31966 q^{76} +(1.29728 + 3.99263i) q^{77} +(-1.47354 + 1.07059i) q^{78} +(7.13073 - 5.18078i) q^{79} +(1.99123 - 1.01734i) q^{80} +(7.97013 + 5.79064i) q^{81} +12.6857 q^{82} +(-0.0452762 - 0.0328951i) q^{83} +(1.33763 - 4.11679i) q^{84} +(-0.756439 - 4.74224i) q^{85} +(-0.927822 - 2.85554i) q^{86} +(0.975325 - 3.00174i) q^{87} +(-0.545866 + 1.68000i) q^{88} +(-2.77568 - 8.54267i) q^{89} +(-0.502511 - 0.501408i) q^{90} +(-0.734398 + 2.26025i) q^{91} +(-0.0183062 - 0.0133002i) q^{92} -14.1707 q^{93} +(-5.30120 - 3.85155i) q^{94} +(-0.817039 - 5.12216i) q^{95} +(1.47354 - 1.07059i) q^{96} +(6.00416 - 4.36228i) q^{97} +(0.417776 + 1.28578i) q^{98} +0.560793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - 4 q^{3} - 5 q^{4} - 10 q^{5} + 4 q^{6} + 8 q^{7} + 5 q^{8} - 7 q^{9} + 10 q^{10} + q^{12} + 5 q^{13} + 2 q^{14} + 5 q^{15} - 5 q^{16} + 2 q^{18} - 4 q^{19} + 5 q^{20} + 3 q^{21} - 5 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) $ 20 * q + 5 * q^2 - 4 * q^3 - 5 * q^4 - 10 * q^5 + 4 * q^6 + 8 * q^7 + 5 * q^8 - 7 * q^9 + 10 * q^10 + q^12 + 5 * q^13 + 2 * q^14 + 5 * q^15 - 5 * q^16 + 2 * q^18 - 4 * q^19 + 5 * q^20 + 3 * q^21 - 5 * q^22 - 17 * q^23 - 6 * q^24 + 20 * q^26 - 19 * q^27 - 2 * q^28 + 9 * q^29 + 10 * q^30 - 2 * q^31 - 20 * q^32 - 3 * q^33 - 5 * q^34 + 30 * q^35 - 7 * q^36 - 19 * q^37 - q^38 - q^39 - 5 * q^40 + 33 * q^41 - 3 * q^42 + 2 * q^43 + 5 * q^44 + 35 * q^45 + 2 * q^46 - 13 * q^47 + q^48 - 4 * q^49 + 15 * q^50 + 12 * q^51 + 5 * q^52 - 7 * q^53 - 16 * q^54 + 35 * q^55 + 2 * q^56 - 18 * q^57 - 9 * q^58 + 11 * q^59 + 20 * q^60 - 18 * q^61 - 13 * q^62 + 44 * q^63 - 5 * q^64 - 10 * q^65 + 8 * q^66 - 27 * q^67 - 10 * q^68 - 8 * q^69 + 20 * q^70 - 7 * q^71 - 8 * q^72 - 30 * q^73 - 16 * q^74 - 60 * q^75 + 6 * q^76 + q^77 - 4 * q^78 - q^79 + 10 * q^80 + 28 * q^81 + 52 * q^82 - 6 * q^83 + 18 * q^84 + 25 * q^85 - 7 * q^86 - 37 * q^87 + 29 * q^89 - 20 * q^90 + 2 * q^91 - 2 * q^92 + 8 * q^93 + 13 * q^94 - 20 * q^95 + 4 * q^96 - 15 * q^97 - 11 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−1.47354	+	1.07059i	−0.850747	+	0.618104i	−0.925352	−	0.379109i	$-0.876230\pi$
$3$	−1.47354	+	1.07059i	−0.850747	+	0.618104i	0.0746050	+	0.997213i	$0.476230\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.58287	+	1.57940i	0.707883	+	0.706330i
$5$	1.58287	+	1.57940i	0.707883	+	0.706330i
$6$	1.47354	+	1.07059i	0.601569	+	0.437065i
$7$	2.37656			0.898256			0.449128	−	0.893467i	$-0.351735\pi$
$7$	2.37656			0.898256			0.449128	+	0.893467i	$0.351735\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.0981028	−	0.301929i	0.0327009	−	0.100643i
$10$	1.01296	−	1.99347i	0.320327	−	0.630389i
$11$	0.545866	+	1.68000i	0.164585	+	0.506540i	0.999005	−	0.0445883i	$-0.0141976\pi$
$11$	0.545866	+	1.68000i	0.164585	+	0.506540i	−0.834421	+	0.551128i	$0.814198\pi$
$12$	0.562841	−	1.73225i	0.162478	−	0.500056i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−0.734398	−	2.26025i	−0.196276	−	0.604076i
$15$	−4.02331	−	0.632700i	−1.03881	−	0.163362i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.73745	−	1.26233i	−0.421393	−	0.306160i	0.356805	−	0.934179i	$-0.383866\pi$
$17$	−1.73745	−	1.26233i	−0.421393	−	0.306160i	−0.778198	+	0.628019i	$0.783866\pi$
$18$	−0.317467			−0.0748278
$19$	−1.87664	−	1.36346i	−0.430531	−	0.312799i	0.351330	−	0.936252i	$-0.385730\pi$
$19$	−1.87664	−	1.36346i	−0.430531	−	0.312799i	−0.781861	+	0.623452i	$0.785730\pi$
$20$	−2.20892	−	0.347372i	−0.493930	−	0.0776747i
$21$	−3.50195	+	2.54432i	−0.764189	+	0.555216i
$22$	1.42910	−	1.03830i	0.304684	−	0.221366i
$23$	0.00699235	+	0.0215202i	0.00145801	+	0.00448728i	0.951783	−	0.306772i	$-0.0992491\pi$
$23$	0.00699235	+	0.0215202i	0.00145801	+	0.00448728i	−0.950325	+	0.311260i	$0.899249\pi$
$24$	−1.82139			−0.371790
$25$	0.0109859	+	4.99999i	0.00219717	+	0.999998i
$26$	1.00000			0.196116
$27$	−1.50984	−	4.64681i	−0.290569	−	0.894278i
$28$	−1.92268	+	1.39691i	−0.363352	+	0.263991i
$29$	−1.40191	+	1.01855i	−0.260329	+	0.189140i	−0.710292	−	0.703907i	$-0.751437\pi$
$29$	−1.40191	+	1.01855i	−0.260329	+	0.189140i	0.449963	+	0.893047i	$0.351437\pi$
$30$	0.641538	+	4.02191i	0.117128	+	0.734297i
$31$	6.29427	+	4.57306i	1.13048	+	0.821345i	0.985765	−	0.168128i	$-0.0537721\pi$
$31$	6.29427	+	4.57306i	1.13048	+	0.821345i	0.144719	+	0.989473i	$0.453772\pi$
$32$	−1.00000			−0.176777
$33$	−2.60294	−	1.89115i	−0.453114	−	0.329207i
$34$	−0.663647	+	2.04249i	−0.113814	+	0.350285i
$35$	3.76180	+	3.75354i	0.635860	+	0.634465i
$36$	0.0981028	+	0.301929i	0.0163505	+	0.0503216i
$37$	−2.40896	+	7.41402i	−0.396031	+	1.21886i	0.532125	+	0.846666i	$0.321394\pi$
$37$	−2.40896	+	7.41402i	−0.396031	+	1.21886i	−0.928156	+	0.372191i	$0.878606\pi$
$38$	−0.716813	+	2.20613i	−0.116282	+	0.357881i
$39$	−0.562841	−	1.73225i	−0.0901267	−	0.277381i
$40$	0.352224	+	2.20815i	0.0556915	+	0.349140i
$41$	−3.92009	+	12.0648i	−0.612216	+	1.88421i	−0.175914	+	0.984406i	$0.556288\pi$
$41$	−3.92009	+	12.0648i	−0.612216	+	1.88421i	−0.436302	+	0.899800i	$0.643712\pi$
$42$	3.50195	+	2.54432i	0.540363	+	0.392597i
$43$	3.00250			0.457876			0.228938	−	0.973441i	$-0.426475\pi$
$43$	3.00250			0.457876			0.228938	+	0.973441i	$0.426475\pi$
$44$	−1.42910	−	1.03830i	−0.215444	−	0.156529i
$45$	0.632152	−	0.322973i	0.0942357	−	0.0481460i
$46$	0.0183062	−	0.0133002i	0.00269910	−	0.00196101i
$47$	5.30120	−	3.85155i	0.773260	−	0.561806i	−0.129689	−	0.991555i	$-0.541398\pi$
$47$	5.30120	−	3.85155i	0.773260	−	0.561806i	0.902949	+	0.429748i	$0.141398\pi$
$48$	0.562841	+	1.73225i	0.0812391	+	0.250028i
$49$	−1.35195			−0.193136
$50$	4.75188	−	1.55553i	0.672017	−	0.219985i
$51$	3.91163			0.547738
$52$	−0.309017	−	0.951057i	−0.0428529	−	0.131888i
$53$	2.55981	−	1.85981i	0.351617	−	0.255465i	−0.397930	−	0.917416i	$-0.630271\pi$
$53$	2.55981	−	1.85981i	0.351617	−	0.255465i	0.749547	+	0.661951i	$0.230271\pi$
$54$	−3.95281	+	2.87188i	−0.537909	+	0.390814i
$55$	−1.78936	+	3.52137i	−0.241277	+	0.474822i
$56$	1.92268	+	1.39691i	0.256929	+	0.186670i
$57$	4.22500			0.559615
$58$	1.40191	+	1.01855i	0.184080	+	0.133742i
$59$	−2.21570	+	6.81923i	−0.288460	+	0.887788i	0.696881	+	0.717187i	$0.254571\pi$
$59$	−2.21570	+	6.81923i	−0.288460	+	0.887788i	−0.985340	+	0.170601i	$0.945429\pi$
$60$	3.62682	−	1.85298i	0.468220	−	0.239218i
$61$	2.69420	+	8.29189i	0.344957	+	1.06167i	0.961607	+	0.274431i	$0.0884894\pi$
$61$	2.69420	+	8.29189i	0.344957	+	1.06167i	−0.616650	+	0.787237i	$0.711511\pi$
$62$	2.40420	−	7.39936i	0.305333	−	0.939719i
$63$	0.233148	−	0.717554i	0.0293738	−	0.0904033i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.99123	+	1.01734i	−0.246982	+	0.126186i
$66$	−0.994235	+	3.05994i	−0.122382	+	0.376653i
$67$	−4.76139	−	3.45935i	−0.581697	−	0.422627i	0.257639	−	0.966241i	$-0.417056\pi$
$67$	−4.76139	−	3.45935i	−0.581697	−	0.422627i	−0.839335	+	0.543614i	$0.817056\pi$
$68$	2.14761			0.260435
$69$	−0.0333428	−	0.0242250i	−0.00401400	−	0.00291634i
$70$	2.40737	−	4.73759i	0.287736	−	0.566251i
$71$	−6.84272	+	4.97153i	−0.812081	+	0.590011i	−0.914433	−	0.404737i	$-0.867363\pi$
$71$	−6.84272	+	4.97153i	−0.812081	+	0.590011i	0.102352	+	0.994748i	$0.467363\pi$
$72$	0.256837	−	0.186603i	0.0302685	−	0.0219913i
$73$	−3.34722	−	10.3017i	−0.391762	−	1.20572i	−0.931454	−	0.363858i	$-0.881459\pi$
$73$	−3.34722	−	10.3017i	−0.391762	−	1.20572i	0.539692	−	0.841862i	$-0.318541\pi$
$74$	7.79556			0.906215
$75$	−5.36911	−	7.35590i	−0.619972	−	0.849387i
$76$	2.31966			0.266083
$77$	1.29728	+	3.99263i	0.147839	+	0.455002i
$78$	−1.47354	+	1.07059i	−0.166845	+	0.121220i
$79$	7.13073	−	5.18078i	0.802270	−	0.582883i	−0.109309	−	0.994008i	$-0.534864\pi$
$79$	7.13073	−	5.18078i	0.802270	−	0.582883i	0.911579	+	0.411124i	$0.134864\pi$
$80$	1.99123	−	1.01734i	0.222627	−	0.113742i
$81$	7.97013	+	5.79064i	0.885569	+	0.643404i
$82$	12.6857			1.40090
$83$	−0.0452762	−	0.0328951i	−0.00496971	−	0.00361070i	0.585298	−	0.810819i	$-0.300978\pi$
$83$	−0.0452762	−	0.0328951i	−0.00496971	−	0.00361070i	−0.590267	+	0.807208i	$0.700978\pi$
$84$	1.33763	−	4.11679i	0.145947	−	0.449179i
$85$	−0.756439	−	4.74224i	−0.0820473	−	0.514368i
$86$	−0.927822	−	2.85554i	−0.100050	−	0.307921i
$87$	0.975325	−	3.00174i	0.104566	−	0.321820i
$88$	−0.545866	+	1.68000i	−0.0581895	+	0.179089i
$89$	−2.77568	−	8.54267i	−0.294222	−	0.905522i	−0.983482	−	0.181008i	$-0.942064\pi$
$89$	−2.77568	−	8.54267i	−0.294222	−	0.905522i	0.689260	−	0.724514i	$-0.257936\pi$
$90$	−0.502511	−	0.501408i	−0.0529693	−	0.0528531i
$91$	−0.734398	+	2.26025i	−0.0769858	+	0.236938i
$92$	−0.0183062	−	0.0133002i	−0.00190856	−	0.00138665i
$93$	−14.1707			−1.46943
$94$	−5.30120	−	3.85155i	−0.546777	−	0.397257i
$95$	−0.817039	−	5.12216i	−0.0838265	−	0.525522i
$96$	1.47354	−	1.07059i	0.150392	−	0.109266i
$97$	6.00416	−	4.36228i	0.609630	−	0.442922i	−0.239654	−	0.970858i	$-0.577034\pi$
$97$	6.00416	−	4.36228i	0.609630	−	0.442922i	0.849284	+	0.527936i	$0.177034\pi$
$98$	0.417776	+	1.28578i	0.0422017	+	0.129884i
$99$	0.560793			0.0563618
$100$	−2.94781	−	4.03862i	−0.294781	−	0.403862i
$101$	−5.75530			−0.572674			−0.286337	−	0.958129i	$-0.592438\pi$
$101$	−5.75530			−0.572674			−0.286337	+	0.958129i	$0.592438\pi$
$102$	−1.20876	−	3.72018i	−0.119685	−	0.368353i
$103$	11.0631	−	8.03780i	1.09008	−	0.791988i	0.110666	−	0.993858i	$-0.464702\pi$
$103$	11.0631	−	8.03780i	1.09008	−	0.791988i	0.979412	+	0.201870i	$0.0647017\pi$
$104$	−0.809017	+	0.587785i	−0.0793306	+	0.0576371i
$105$	−9.56165	−	1.50365i	−0.933121	−	0.146741i
$106$	−2.55981	−	1.85981i	−0.248631	−	0.180641i
$107$	−3.25018			−0.314207			−0.157103	−	0.987582i	$-0.550216\pi$
$107$	−3.25018			−0.314207			−0.157103	+	0.987582i	$0.550216\pi$
$108$	3.95281	+	2.87188i	0.380359	+	0.276347i
$109$	−3.08958	+	9.50874i	−0.295928	+	0.910772i	0.686981	+	0.726676i	$0.258936\pi$
$109$	−3.08958	+	9.50874i	−0.295928	+	0.910772i	−0.982908	+	0.184096i	$0.941064\pi$
$110$	3.90197	+	0.613618i	0.372038	+	0.0585062i
$111$	−4.38766	−	13.5038i	−0.416458	−	1.28173i
$112$	0.734398	−	2.26025i	0.0693941	−	0.213573i
$113$	−1.96720	+	6.05441i	−0.185058	+	0.569551i	−0.999949	−	0.0100630i	$-0.996797\pi$
$113$	−1.96720	+	6.05441i	−0.185058	+	0.569551i	0.814891	+	0.579614i	$0.196797\pi$
$114$	−1.30560	−	4.01822i	−0.122280	−	0.376341i
$115$	−0.0229211	+	0.0451076i	−0.00213740	+	0.00420630i
$116$	0.535483	−	1.64805i	0.0497184	−	0.153017i
$117$	0.256837	+	0.186603i	0.0237445	+	0.0172514i
$118$	7.17016			0.660067
$119$	−4.12916	−	3.00001i	−0.378519	−	0.275010i
$120$	−2.88304	−	2.87671i	−0.263184	−	0.262606i
$121$	6.37475	−	4.63153i	0.579523	−	0.421048i
$122$	7.05351	−	5.12467i	0.638594	−	0.463966i
$123$	−7.14002	−	21.9747i	−0.643794	−	1.98140i
$124$	−7.78015			−0.698678
$125$	−7.87960	+	7.93171i	−0.704772	+	0.709433i
$126$	−0.754481			−0.0672145
$127$	−2.80749	−	8.64057i	−0.249125	−	0.766727i	−0.994931	−	0.100564i	$-0.967935\pi$
$127$	−2.80749	−	8.64057i	−0.249125	−	0.766727i	0.745806	−	0.666163i	$-0.232065\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−4.42429	+	3.21443i	−0.389537	+	0.283015i
$130$	1.58287	+	1.57940i	0.138827	+	0.138523i
$131$	−3.19970	−	2.32472i	−0.279559	−	0.203112i	0.439166	−	0.898406i	$-0.355274\pi$
$131$	−3.19970	−	2.32472i	−0.279559	−	0.203112i	−0.718725	+	0.695294i	$0.755274\pi$
$132$	3.21741			0.280040
$133$	−4.45996	−	3.24035i	−0.386727	−	0.280974i
$134$	−1.81869	+	5.59735i	−0.157111	+	0.483538i
$135$	4.94928	−	9.73996i	0.425967	−	0.838282i
$136$	−0.663647	−	2.04249i	−0.0569072	−	0.175142i
$137$	−0.191468	+	0.589278i	−0.0163582	+	0.0503455i	−0.958902	−	0.283736i	$-0.908426\pi$
$137$	−0.191468	+	0.589278i	−0.0163582	+	0.0503455i	0.942544	+	0.334081i	$0.108426\pi$
$138$	−0.0127358	+	0.0391968i	−0.00108414	+	0.00333665i
$139$	1.05738	+	3.25429i	0.0896861	+	0.276026i	0.985832	−	0.167733i	$-0.0536447\pi$
$139$	1.05738	+	3.25429i	0.0896861	+	0.276026i	−0.896146	+	0.443759i	$0.853645\pi$
$140$	−5.24964	−	0.825550i	−0.443675	−	0.0697717i
$141$	−3.68810	+	11.3508i	−0.310594	+	0.955910i
$142$	6.84272	+	4.97153i	0.574228	+	0.417201i
$143$	−1.76646			−0.147719
$144$	−0.256837	−	0.186603i	−0.0214030	−	0.0155502i
$145$	−3.82775	−	0.601946i	−0.317877	−	0.0499889i
$146$	−8.76313	+	6.36679i	−0.725242	+	0.526919i
$147$	1.99215	−	1.44738i	0.164310	−	0.119378i
$148$	−2.40896	−	7.41402i	−0.198015	−	0.609429i
$149$	10.5637			0.865412			0.432706	−	0.901535i	$-0.357559\pi$
$149$	10.5637			0.865412			0.432706	+	0.901535i	$0.357559\pi$
$150$	−5.33673	+	7.37943i	−0.435743	+	0.602528i
$151$	11.9026			0.968618			0.484309	−	0.874897i	$-0.339071\pi$
$151$	11.9026			0.968618			0.484309	+	0.874897i	$0.339071\pi$
$152$	−0.716813	−	2.20613i	−0.0581412	−	0.178940i
$153$	−0.551584	+	0.400749i	−0.0445929	+	0.0323986i
$154$	3.39633	−	2.46758i	0.273684	−	0.198843i
$155$	2.74036	+	17.1797i	0.220111	+	1.37991i
$156$	1.47354	+	1.07059i	0.117977	+	0.0857156i
$157$	−6.82434			−0.544642			−0.272321	−	0.962206i	$-0.587791\pi$
$157$	−6.82434			−0.544642			−0.272321	+	0.962206i	$0.587791\pi$
$158$	−7.13073	−	5.18078i	−0.567291	−	0.412161i
$159$	−1.78089	+	5.48100i	−0.141233	+	0.434672i
$160$	−1.58287	−	1.57940i	−0.125137	−	0.124863i
$161$	0.0166178	+	0.0511442i	0.00130966	+	0.00403073i
$162$	3.04432	−	9.36944i	0.239184	−	0.736133i
$163$	5.62828	−	17.3221i	0.440841	−	1.35677i	−0.446139	−	0.894963i	$-0.647201\pi$
$163$	5.62828	−	17.3221i	0.440841	−	1.35677i	0.886981	−	0.461807i	$-0.152799\pi$
$164$	−3.92009	−	12.0648i	−0.306108	−	0.942103i
$165$	−1.13325	−	7.10454i	−0.0882235	−	0.553088i
$166$	−0.0172940	+	0.0532253i	−0.00134227	+	0.00413109i
$167$	15.1537	+	11.0098i	1.17263	+	0.851964i	0.991321	−	0.131463i	$-0.0419675\pi$
$167$	15.1537	+	11.0098i	1.17263	+	0.851964i	0.181306	+	0.983427i	$0.441967\pi$
$168$	−4.32865			−0.333963
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−4.27639	+	2.18485i	−0.327984	+	0.167570i
$171$	−0.595773	+	0.432854i	−0.0455599	+	0.0331012i
$172$	−2.42907	+	1.76482i	−0.185215	+	0.134566i
$173$	4.33124	+	13.3302i	0.329298	+	1.01348i	0.969463	+	0.245238i	$0.0788661\pi$
$173$	4.33124	+	13.3302i	0.329298	+	1.01348i	−0.640165	+	0.768238i	$0.721134\pi$
$174$	−3.15622			−0.239272
$175$	0.0261086	+	11.8828i	0.00197362	+	0.898254i
$176$	1.76646			0.133152
$177$	−4.03566	−	12.4205i	−0.303339	−	0.933581i
$178$	−7.26683	+	5.27966i	−0.544672	+	0.395727i
$179$	−4.58848	+	3.33373i	−0.342959	+	0.249174i	−0.745909	−	0.666047i	$-0.767985\pi$
$179$	−4.58848	+	3.33373i	−0.342959	+	0.249174i	0.402950	+	0.915222i	$0.367985\pi$
$180$	−0.321583	+	0.632860i	−0.0239694	+	0.0471706i
$181$	15.3471	+	11.1503i	1.14074	+	0.828794i	0.987222	−	0.159352i	$-0.0509404\pi$
$181$	15.3471	+	11.1503i	1.14074	+	0.828794i	0.153516	+	0.988146i	$0.450940\pi$
$182$	2.37656			0.176163
$183$	−12.8472	−	9.33403i	−0.949692	−	0.689992i
$184$	−0.00699235	+	0.0215202i	−0.000515483	+	0.00158649i
$185$	−15.5228	+	7.93075i	−1.14126	+	0.583080i
$186$	4.37898	+	13.4771i	0.321083	+	0.988191i
$187$	1.17230	−	3.60798i	0.0857274	−	0.263842i
$188$	−2.02488	+	6.23194i	−0.147680	+	0.454511i
$189$	−3.58823	−	11.0434i	−0.261005	−	0.803291i
$190$	−4.61898	+	2.35988i	−0.335096	+	0.171204i
$191$	3.04772	−	9.37993i	0.220525	−	0.678708i	−0.778190	−	0.628029i	$-0.783862\pi$
$191$	3.04772	−	9.37993i	0.220525	−	0.678708i	0.998715	−	0.0506782i	$-0.0161383\pi$
$192$	−1.47354	−	1.07059i	−0.106343	−	0.0772630i
$193$	17.3405			1.24819			0.624097	−	0.781347i	$-0.285467\pi$
$193$	17.3405			1.24819			0.624097	+	0.781347i	$0.285467\pi$
$194$	−6.00416	−	4.36228i	−0.431074	−	0.313193i
$195$	1.84500	−	3.63088i	0.132124	−	0.260013i
$196$	1.09375	−	0.794657i	0.0781251	−	0.0567612i
$197$	−8.60546	+	6.25223i	−0.613114	+	0.445453i	−0.850509	−	0.525960i	$-0.823706\pi$
$197$	−8.60546	+	6.25223i	−0.613114	+	0.445453i	0.237396	+	0.971413i	$0.423706\pi$
$198$	−0.173295	−	0.533346i	−0.0123155	−	0.0379033i
$199$	5.64579			0.400220			0.200110	−	0.979773i	$-0.435870\pi$
$199$	5.64579			0.400220			0.200110	+	0.979773i	$0.435870\pi$
$200$	−2.93003	+	4.05153i	−0.207185	+	0.286487i
$201$	10.7196			0.756104
$202$	1.77849	+	5.47362i	0.125134	+	0.385122i
$203$	−3.33173	+	2.42065i	−0.233842	+	0.169896i
$204$	−3.16458	+	2.29920i	−0.221565	+	0.160976i
$205$	−25.2602	+	12.9057i	−1.76425	+	0.901372i
$206$	−11.0631	−	8.03780i	−0.770802	−	0.560020i
$207$	0.00718357			0.000499292
$208$	0.809017	+	0.587785i	0.0560952	+	0.0407556i
$209$	1.26622	−	3.89703i	0.0875864	−	0.269563i
$210$	1.52466	+	9.55832i	0.105211	+	0.659587i
$211$	−8.24588	−	25.3782i	−0.567670	−	1.74711i	−0.659882	−	0.751369i	$-0.729394\pi$
$211$	−8.24588	−	25.3782i	−0.567670	−	1.74711i	0.0922124	−	0.995739i	$-0.470606\pi$
$212$	−0.977761	+	3.00924i	−0.0671529	+	0.206675i
$213$	4.76054	−	14.6515i	0.326187	−	1.00390i
$214$	1.00436	+	3.09111i	0.0686567	+	0.211304i
$215$	4.75257	+	4.74214i	0.324123	+	0.323411i
$216$	1.50984	−	4.64681i	0.102732	−	0.316175i
$217$	14.9587	+	10.8682i	1.01546	+	0.737778i
$218$	9.99808			0.677155
$219$	15.9611	+	11.5964i	1.07855	+	0.783613i
$220$	−0.622190	−	3.90061i	−0.0419480	−	0.262979i
$221$	1.73745	−	1.26233i	0.116874	−	0.0849136i
$222$	−11.4870	+	8.34583i	−0.770960	+	0.560135i
$223$	1.81140	+	5.57491i	0.121300	+	0.373324i	0.993209	−	0.116345i	$-0.0371178\pi$
$223$	1.81140	+	5.57491i	0.121300	+	0.373324i	−0.871909	+	0.489668i	$0.837118\pi$
$224$	−2.37656			−0.158791
$225$	1.51072	+	0.487196i	0.100715	+	0.0324797i
$226$	6.36599			0.423459
$227$	−5.40028	−	16.6204i	−0.358429	−	1.10313i	−0.953994	−	0.299825i	$-0.903072\pi$
$227$	−5.40028	−	16.6204i	−0.358429	−	1.10313i	0.595565	−	0.803307i	$-0.296928\pi$
$228$	−3.41810	+	2.48340i	−0.226369	+	0.164467i
$229$	7.61135	−	5.52997i	0.502972	−	0.365431i	−0.307179	−	0.951652i	$-0.599385\pi$
$229$	7.61135	−	5.52997i	0.502972	−	0.365431i	0.810151	+	0.586221i	$0.199385\pi$
$230$	0.0499829	+	0.00786023i	0.00329577	+	0.000518288i
$231$	−6.18605	−	4.49443i	−0.407013	−	0.295712i
$232$	−1.73286			−0.113768
$233$	−20.2388	−	14.7043i	−1.32589	−	0.963313i	−0.999839	−	0.0179591i	$-0.994283\pi$
$233$	−20.2388	−	14.7043i	−1.32589	−	0.963313i	−0.326047	−	0.945353i	$-0.605717\pi$
$234$	0.0981028	−	0.301929i	0.00641318	−	0.0197377i
$235$	14.4743	+	2.27620i	0.944198	+	0.148483i
$236$	−2.21570	−	6.81923i	−0.144230	−	0.443894i
$237$	−4.96092	+	15.2681i	−0.322246	+	0.991773i
$238$	−1.57720	+	4.85412i	−0.102235	+	0.314646i
$239$	1.87103	+	5.75844i	0.121027	+	0.372483i	0.993156	−	0.116793i	$-0.0372613\pi$
$239$	1.87103	+	5.75844i	0.121027	+	0.372483i	−0.872129	+	0.489275i	$0.837261\pi$
$240$	−1.84500	+	3.63088i	−0.119095	+	0.234372i
$241$	8.28344	−	25.4938i	0.533583	−	1.64220i	−0.213107	−	0.977029i	$-0.568358\pi$
$241$	8.28344	−	25.4938i	0.533583	−	1.64220i	0.746690	−	0.665172i	$-0.231642\pi$
$242$	−6.37475	−	4.63153i	−0.409784	−	0.297726i
$243$	−3.28583			−0.210786
$244$	−7.05351	−	5.12467i	−0.451554	−	0.328073i
$245$	−2.13997	−	2.13527i	−0.136718	−	0.136418i
$246$	−18.6928	+	13.5811i	−1.19181	+	0.865901i
$247$	1.87664	−	1.36346i	0.119408	−	0.0867549i
$248$	2.40420	+	7.39936i	0.152667	+	0.469860i
$249$	0.101933			0.00645975
$250$	9.97843	+	5.04291i	0.631091	+	0.318942i
$251$	22.8332			1.44122			0.720611	−	0.693340i	$-0.243861\pi$
$251$	22.8332			1.44122			0.720611	+	0.693340i	$0.243861\pi$
$252$	0.233148	+	0.717554i	0.0146869	+	0.0452017i
$253$	−0.0323372	+	0.0234943i	−0.00203302	+	0.00147708i
$254$	−7.35011	+	5.34017i	−0.461187	+	0.335072i
$255$	6.19162	+	6.17803i	0.387735	+	0.386884i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−4.79768			−0.299271			−0.149636	−	0.988741i	$-0.547810\pi$
$257$	−4.79768			−0.299271			−0.149636	+	0.988741i	$0.547810\pi$
$258$	4.42429	+	3.21443i	0.275444	+	0.200122i
$259$	−5.72504	+	17.6199i	−0.355737	+	1.09485i
$260$	1.01296	−	1.99347i	0.0628214	−	0.123629i
$261$	0.169998	+	0.523202i	0.0105226	+	0.0323854i
$262$	−1.22218	+	3.76148i	−0.0755064	+	0.232385i
$263$	5.62095	−	17.2995i	0.346603	−	1.06673i	−0.614118	−	0.789215i	$-0.710488\pi$
$263$	5.62095	−	17.2995i	0.346603	−	1.06673i	0.960720	−	0.277519i	$-0.0895121\pi$
$264$	−0.994235	−	3.05994i	−0.0611910	−	0.188326i
$265$	6.98925	+	1.09912i	0.429346	+	0.0675184i
$266$	−1.70355	+	5.24299i	−0.104451	+	0.321469i
$267$	13.2357	+	9.61633i	0.810015	+	0.588510i
$268$	5.88540			0.359508
$269$	−10.1363	−	7.36443i	−0.618019	−	0.449017i	0.234210	−	0.972186i	$-0.424750\pi$
$269$	−10.1363	−	7.36443i	−0.618019	−	0.449017i	−0.852229	+	0.523169i	$0.824750\pi$
$270$	−10.7927	−	1.69724i	−0.656820	−	0.103291i
$271$	16.5696	−	12.0385i	1.00653	−	0.731290i	0.0430546	−	0.999073i	$-0.486291\pi$
$271$	16.5696	−	12.0385i	1.00653	−	0.731290i	0.963479	+	0.267783i	$0.0862911\pi$
$272$	−1.73745	+	1.26233i	−0.105348	+	0.0765401i
$273$	−1.33763	−	4.11679i	−0.0809568	−	0.249160i
$274$	0.619604			0.0374316
$275$	−8.39399	+	2.74778i	−0.506177	+	0.165697i
$276$	0.0412140			0.00248079
$277$	1.38222	+	4.25405i	0.0830498	+	0.255601i	0.983956	−	0.178414i	$-0.0570966\pi$
$277$	1.38222	+	4.25405i	0.0830498	+	0.255601i	−0.900906	+	0.434015i	$0.857097\pi$
$278$	2.76827	−	2.01126i	0.166030	−	0.120628i
$279$	1.99823	−	1.45180i	0.119631	−	0.0869168i
$280$	0.837083	+	5.24781i	0.0500253	+	0.313617i
$281$	17.6536	+	12.8261i	1.05313	+	0.765142i	0.972805	−	0.231627i	$-0.0744048\pi$
$281$	17.6536	+	12.8261i	1.05313	+	0.765142i	0.0803231	+	0.996769i	$0.474405\pi$
$282$	11.9349			0.710715
$283$	0.590755	+	0.429209i	0.0351167	+	0.0255138i	0.605205	−	0.796070i	$-0.293091\pi$
$283$	0.590755	+	0.429209i	0.0351167	+	0.0255138i	−0.570088	+	0.821583i	$0.693091\pi$
$284$	2.61369	−	8.04410i	0.155094	−	0.477329i
$285$	6.68765	+	6.67298i	0.396142	+	0.395273i
$286$	0.545866	+	1.68000i	0.0322777	+	0.0993406i
$287$	−9.31634	+	28.6728i	−0.549926	+	1.69250i
$288$	−0.0981028	+	0.301929i	−0.00578077	+	0.0177914i
$289$	−3.82804	−	11.7815i	−0.225179	−	0.693029i
$290$	0.610355	+	3.82642i	0.0358413	+	0.224695i
$291$	−4.17715	+	12.8560i	−0.244869	+	0.753629i
$292$	8.76313	+	6.36679i	0.512823	+	0.372588i
$293$	16.7217			0.976893			0.488446	−	0.872594i	$-0.337564\pi$
$293$	16.7217			0.976893			0.488446	+	0.872594i	$0.337564\pi$
$294$	−1.99215	−	1.44738i	−0.116185	−	0.0844130i
$295$	−14.2775	+	7.29450i	−0.831267	+	0.424702i
$296$	−6.30674	+	4.58212i	−0.366572	+	0.266330i
$297$	6.98248	−	5.07307i	0.405164	−	0.294369i
$298$	−3.26436	−	10.0467i	−0.189099	−	0.581988i
$299$	−0.0226277			−0.00130860
$300$	8.66739	+	2.79517i	0.500412	+	0.161379i
$301$	7.13562			0.411290
$302$	−3.67810	−	11.3200i	−0.211651	−	0.651394i
$303$	8.48065	−	6.16155i	0.487201	−	0.353972i
$304$	−1.87664	+	1.36346i	−0.107633	+	0.0781998i
$305$	−8.83164	+	17.3802i	−0.505698	+	0.995190i
$306$	0.551584	+	0.400749i	0.0315319	+	0.0229093i
$307$	23.1903			1.32354			0.661771	−	0.749706i	$-0.269805\pi$
$307$	23.1903			1.32354			0.661771	+	0.749706i	$0.269805\pi$
$308$	−3.39633	−	2.46758i	−0.193524	−	0.140603i
$309$	−7.69669	+	23.6880i	−0.437850	+	1.34756i
$310$	15.4921	−	7.91507i	0.879892	−	0.449546i
$311$	−3.99602	−	12.2985i	−0.226594	−	0.697383i	−0.998126	−	0.0611933i	$-0.980509\pi$
$311$	−3.99602	−	12.2985i	−0.226594	−	0.697383i	0.771532	−	0.636190i	$-0.219491\pi$
$312$	0.562841	−	1.73225i	0.0318646	−	0.0980691i
$313$	6.74905	−	20.7714i	0.381479	−	1.17407i	−0.557524	−	0.830161i	$-0.688249\pi$
$313$	6.74905	−	20.7714i	0.381479	−	1.17407i	0.939003	−	0.343910i	$-0.111751\pi$
$314$	2.10884	+	6.49033i	0.119009	+	0.366271i
$315$	1.50235	−	0.767565i	0.0846478	−	0.0432474i
$316$	−2.72370	+	8.38268i	−0.153220	+	0.471563i
$317$	1.95894	+	1.42325i	0.110025	+	0.0799379i	0.641437	−	0.767175i	$-0.278338\pi$
$317$	1.95894	+	1.42325i	0.110025	+	0.0799379i	−0.531412	+	0.847113i	$0.678338\pi$
$318$	5.76307			0.323177
$319$	−2.47642	−	1.79923i	−0.138653	−	0.100737i
$320$	−1.01296	+	1.99347i	−0.0566264	+	0.111438i
$321$	4.78926	−	3.47960i	0.267310	−	0.194212i
$322$	0.0435059	−	0.0316089i	0.00242449	−	0.00176149i
$323$	1.53943	+	4.73789i	0.0856563	+	0.263623i
$324$	−9.85162			−0.547312
$325$	−4.75867	−	1.53463i	−0.263963	−	0.0851261i
$326$	−18.2135			−1.00875
$327$	−5.62733	−	17.3191i	−0.311192	−	0.957750i
$328$	−10.2629	+	7.45646i	−0.566676	+	0.411714i
$329$	12.5986	−	9.15345i	0.694586	−	0.504646i
$330$	−6.40663	+	3.27321i	−0.352673	+	0.180184i
$331$	12.6220	+	9.17039i	0.693766	+	0.504050i	0.877896	−	0.478852i	$-0.158947\pi$
$331$	12.6220	+	9.17039i	0.693766	+	0.504050i	−0.184130	+	0.982902i	$0.558947\pi$
$332$	0.0559644			0.00307145
$333$	2.00218	+	1.45467i	0.109719	+	0.0797156i
$334$	5.78819	−	17.8142i	0.316716	−	0.974751i
$335$	−2.07298	−	12.9959i	−0.113259	−	0.710040i
$336$	1.33763	+	4.11679i	0.0729735	+	0.224589i
$337$	−7.29318	+	22.4461i	−0.397285	+	1.22272i	0.529883	+	0.848071i	$0.322236\pi$
$337$	−7.29318	+	22.4461i	−0.397285	+	1.22272i	−0.927168	+	0.374646i	$0.877764\pi$
$338$	−0.309017	+	0.951057i	−0.0168083	+	0.0517307i
$339$	−3.58304	−	11.0275i	−0.194604	−	0.598929i
$340$	3.39939	+	3.39193i	0.184358	+	0.183953i
$341$	−4.24692	+	13.0707i	−0.229983	+	0.707816i
$342$	0.595773	+	0.432854i	0.0322157	+	0.0234061i
$343$	−19.8489			−1.07174
$344$	2.42907	+	1.76482i	0.130967	+	0.0951528i
$345$	−0.0145166	−	0.0910067i	−0.000781545	−	0.00489964i
$346$	11.3393	−	8.23851i	0.609607	−	0.442905i
$347$	−21.9482	+	15.9463i	−1.17824	+	0.856041i	−0.991972	−	0.126458i	$-0.959639\pi$
$347$	−21.9482	+	15.9463i	−1.17824	+	0.856041i	−0.186267	+	0.982499i	$0.559639\pi$
$348$	0.975325	+	3.00174i	0.0522829	+	0.160910i
$349$	32.2855			1.72820			0.864101	−	0.503319i	$-0.167888\pi$
$349$	32.2855			1.72820			0.864101	+	0.503319i	$0.167888\pi$
$350$	11.2931	−	3.69681i	0.603643	−	0.197603i
$351$	4.88594			0.260792
$352$	−0.545866	−	1.68000i	−0.0290947	−	0.0895444i
$353$	14.9842	−	10.8866i	0.797526	−	0.579437i	−0.112661	−	0.993633i	$-0.535937\pi$
$353$	14.9842	−	10.8866i	0.797526	−	0.579437i	0.910187	+	0.414197i	$0.135937\pi$
$354$	−10.5655	+	7.67628i	−0.561550	+	0.407990i
$355$	−18.6832	−	2.93809i	−0.991601	−	0.155938i
$356$	7.26683	+	5.27966i	0.385141	+	0.279822i
$357$	9.29624			0.492009
$358$	4.58848	+	3.33373i	0.242509	+	0.176193i
$359$	−8.84426	+	27.2198i	−0.466782	+	1.43661i	0.389945	+	0.920838i	$0.372494\pi$
$359$	−8.84426	+	27.2198i	−0.466782	+	1.43661i	−0.856727	+	0.515770i	$0.827506\pi$
$360$	0.701261	+	0.110279i	0.0369597	+	0.00581222i
$361$	−4.20856	−	12.9526i	−0.221503	−	0.681717i
$362$	5.86205	−	18.0415i	0.308103	−	0.948243i
$363$	−4.43497	+	13.6494i	−0.232776	+	0.716410i
$364$	−0.734398	−	2.26025i	−0.0384929	−	0.118469i
$365$	10.9723	−	21.5929i	0.574314	−	1.13022i
$366$	−4.90719	+	15.1028i	−0.256503	+	0.789435i
$367$	16.7385	+	12.1612i	0.873740	+	0.634810i	0.931588	−	0.363516i	$-0.118424\pi$
$367$	16.7385	+	12.1612i	0.873740	+	0.634810i	−0.0578476	+	0.998325i	$0.518424\pi$
$368$	0.0226277			0.00117955
$369$	3.25815	+	2.36718i	0.169612	+	0.123231i
$370$	12.3394	+	12.3123i	0.641495	+	0.640087i
$371$	6.08355	−	4.41996i	0.315842	−	0.229473i
$372$	11.4643	−	8.32932i	0.594398	−	0.431855i
$373$	9.50176	+	29.2434i	0.491983	+	1.51417i	0.821607	+	0.570055i	$0.193078\pi$
$373$	9.50176	+	29.2434i	0.491983	+	1.51417i	−0.329624	+	0.944112i	$0.606922\pi$
$374$	−3.79366			−0.196165
$375$	3.11929	−	20.1235i	0.161080	−	1.03917i
$376$	6.55265			0.337927
$377$	−0.535483	−	1.64805i	−0.0275788	−	0.0848788i
$378$	−9.39410	+	6.82521i	−0.483180	+	0.351051i
$379$	−16.8106	+	12.2136i	−0.863503	+	0.627371i	−0.928836	−	0.370492i	$-0.879189\pi$
$379$	−16.8106	+	12.2136i	−0.863503	+	0.627371i	0.0653329	+	0.997864i	$0.479189\pi$
$380$	3.67173	+	3.66367i	0.188356	+	0.187942i
$381$	13.3874	+	9.72653i	0.685859	+	0.498305i
$382$	−9.86264			−0.504616
$383$	−2.77830	−	2.01855i	−0.141964	−	0.103143i	0.514536	−	0.857469i	$-0.327964\pi$
$383$	−2.77830	−	2.01855i	−0.141964	−	0.103143i	−0.656501	+	0.754325i	$0.727964\pi$
$384$	−0.562841	+	1.73225i	−0.0287224	+	0.0883983i
$385$	−4.25253	+	8.36877i	−0.216729	+	0.426512i
$386$	−5.35850	−	16.4918i	−0.272741	−	0.839409i
$387$	0.294553	−	0.906542i	0.0149730	−	0.0460821i
$388$	−2.29339	+	7.05831i	−0.116429	+	0.358332i
$389$	−6.13494	−	18.8814i	−0.311054	−	0.957325i	−0.977348	−	0.211636i	$-0.932121\pi$
$389$	−6.13494	−	18.8814i	−0.311054	−	0.957325i	0.666295	−	0.745688i	$-0.267879\pi$
$390$	−4.02331	−	0.632700i	−0.203728	−	0.0320380i
$391$	0.0150168	−	0.0462170i	0.000759433	−	0.00233729i
$392$	−1.09375	−	0.794657i	−0.0552428	−	0.0401362i
$393$	7.20369			0.363378
$394$	8.60546	+	6.25223i	0.433537	+	0.314983i
$395$	19.4696	+	3.06176i	0.979621	+	0.154054i
$396$	−0.453691	+	0.329626i	−0.0227988	+	0.0165643i
$397$	−3.67030	+	2.66663i	−0.184207	+	0.133834i	−0.676067	−	0.736840i	$-0.736317\pi$
$397$	−3.67030	+	2.66663i	−0.184207	+	0.133834i	0.491860	+	0.870674i	$0.336317\pi$
$398$	−1.74465	−	5.36947i	−0.0874512	−	0.269147i
$399$	10.0410			0.502678
$400$	4.75867	+	1.53463i	0.237933	+	0.0767317i
$401$	−27.1355			−1.35508			−0.677542	−	0.735484i	$-0.736955\pi$
$401$	−27.1355			−1.35508			−0.677542	+	0.735484i	$0.736955\pi$
$402$	−3.31255	−	10.1950i	−0.165215	−	0.508479i
$403$	−6.29427	+	4.57306i	−0.313540	+	0.227800i
$404$	4.65614	−	3.38288i	0.231652	−	0.168305i
$405$	3.46998	+	21.7539i	0.172425	+	1.08096i
$406$	3.33173	+	2.42065i	0.165351	+	0.120135i
$407$	−13.7705			−0.682580
$408$	3.16458	+	2.29920i	0.156670	+	0.113827i
$409$	−0.980100	+	3.01644i	−0.0484628	+	0.149153i	−0.972359	−	0.233489i	$-0.924986\pi$
$409$	−0.980100	+	3.01644i	−0.0484628	+	0.149153i	0.923897	+	0.382642i	$0.124986\pi$
$410$	20.0799	+	20.0358i	0.991673	+	0.989497i
$411$	−0.348739	−	1.07331i	−0.0172020	−	0.0529423i
$412$	−4.22572	+	13.0054i	−0.208186	+	0.640732i
$413$	−5.26575	+	16.2063i	−0.259111	+	0.797461i
$414$	−0.00221984	−	0.00683198i	−0.000109099	−	0.000335773i
$415$	−0.0197120	−	0.123578i	−0.000967625	−	0.00606621i
$416$	0.309017	−	0.951057i	0.0151508	−	0.0466294i
$417$	−5.04210	−	3.66330i	−0.246913	−	0.179393i
$418$	−4.09758			−0.200419
$419$	−10.0584	−	7.30789i	−0.491387	−	0.357014i	0.314330	−	0.949314i	$-0.398220\pi$
$419$	−10.0584	−	7.30789i	−0.491387	−	0.357014i	−0.805717	+	0.592300i	$0.798220\pi$
$420$	8.61936	−	4.40372i	0.420582	−	0.214879i
$421$	8.54794	−	6.21044i	0.416601	−	0.302678i	−0.359668	−	0.933080i	$-0.617110\pi$
$421$	8.54794	−	6.21044i	0.416601	−	0.302678i	0.776269	+	0.630402i	$0.217110\pi$
$422$	−21.5880	+	15.6846i	−1.05089	+	0.763514i
$423$	−0.642833	−	1.97844i	−0.0312556	−	0.0961949i
$424$	3.16410			0.153662
$425$	6.29255	−	8.70110i	0.305234	−	0.422065i
$426$	−15.4054			−0.746396
$427$	6.40293	+	19.7062i	0.309860	+	0.953650i
$428$	2.62945	−	1.91041i	0.127099	−	0.0923431i
$429$	2.60294	−	1.89115i	0.125671	−	0.0913055i
$430$	3.04142	−	5.98537i	0.146670	−	0.288640i
$431$	−22.2619	−	16.1742i	−1.07232	−	0.779084i	−0.0959900	−	0.995382i	$-0.530602\pi$
$431$	−22.2619	−	16.1742i	−1.07232	−	0.779084i	−0.976327	+	0.216298i	$0.930602\pi$
$432$	−4.88594			−0.235075
$433$	10.8368	+	7.87341i	0.520784	+	0.378372i	0.816899	−	0.576781i	$-0.195691\pi$
$433$	10.8368	+	7.87341i	0.520784	+	0.378372i	−0.296115	+	0.955152i	$0.595691\pi$
$434$	5.71372	−	17.5850i	0.274268	−	0.844109i
$435$	6.28477	−	3.21095i	0.301332	−	0.153953i
$436$	−3.08958	−	9.50874i	−0.147964	−	0.455386i
$437$	0.0162199	−	0.0499196i	0.000775901	−	0.00238798i
$438$	6.09660	−	18.7634i	0.291307	−	0.896550i
$439$	6.47832	+	19.9382i	0.309193	+	0.951599i	0.978079	+	0.208234i	$0.0667715\pi$
$439$	6.47832	+	19.9382i	0.309193	+	0.951599i	−0.668886	+	0.743365i	$0.733228\pi$
$440$	−3.51743	+	1.79709i	−0.167687	+	0.0856730i
$441$	−0.132630	+	0.408194i	−0.00631573	+	0.0194378i
$442$	−1.73745	−	1.26233i	−0.0826421	−	0.0600430i
$443$	13.0873			0.621798			0.310899	−	0.950443i	$-0.399370\pi$
$443$	13.0873			0.621798			0.310899	+	0.950443i	$0.399370\pi$
$444$	11.4870	+	8.34583i	0.545151	+	0.396075i
$445$	9.09875	−	17.9059i	0.431322	−	0.848821i
$446$	4.74230	−	3.44548i	0.224554	−	0.163148i
$447$	−15.5660	+	11.3094i	−0.736246	+	0.534914i
$448$	0.734398	+	2.26025i	0.0346971	+	0.106787i
$449$	−31.7619			−1.49894			−0.749468	−	0.662041i	$-0.769691\pi$
$449$	−31.7619			−1.49894			−0.749468	+	0.662041i	$0.769691\pi$
$450$	−0.00348765	−	1.58733i	−0.000164409	−	0.0748276i
$451$	−22.4087			−1.05519
$452$	−1.96720	−	6.05441i	−0.0925292	−	0.284776i
$453$	−17.5389	+	12.7427i	−0.824049	+	0.598706i
$454$	−14.1381	+	10.2719i	−0.663535	+	0.482086i
$455$	−4.73229	+	2.41778i	−0.221853	+	0.113347i
$456$	3.41810	+	2.48340i	0.160067	+	0.116296i
$457$	−5.32914			−0.249287			−0.124643	−	0.992202i	$-0.539779\pi$
$457$	−5.32914			−0.249287			−0.124643	+	0.992202i	$0.539779\pi$
$458$	−7.61135	−	5.52997i	−0.355655	−	0.258399i
$459$	−3.24254	+	9.97951i	−0.151349	+	0.465804i
$460$	−0.00797003	−	0.0499655i	−0.000371605	−	0.00232965i
$461$	2.59274	+	7.97962i	0.120756	+	0.371648i	0.993104	−	0.117237i	$-0.0374037\pi$
$461$	2.59274	+	7.97962i	0.120756	+	0.371648i	−0.872348	+	0.488885i	$0.837404\pi$
$462$	−2.36286	+	7.27214i	−0.109930	+	0.338331i
$463$	5.57148	−	17.1472i	0.258929	−	0.796900i	−0.734102	−	0.679040i	$-0.762396\pi$
$463$	5.57148	−	17.1472i	0.258929	−	0.796900i	0.993030	−	0.117860i	$-0.0376036\pi$
$464$	0.535483	+	1.64805i	0.0248592	+	0.0765087i
$465$	−22.4304	−	22.3812i	−1.04019	−	1.03790i
$466$	−7.73052	+	23.7921i	−0.358110	+	1.10215i
$467$	−0.988546	−	0.718221i	−0.0457444	−	0.0332353i	0.564678	−	0.825311i	$-0.309000\pi$
$467$	−0.988546	−	0.718221i	−0.0457444	−	0.0332353i	−0.610423	+	0.792076i	$0.709000\pi$
$468$	−0.317467			−0.0146749
$469$	−11.3157	−	8.22137i	−0.522513	−	0.379628i
$470$	−2.30800	−	14.4692i	−0.106460	−	0.667417i
$471$	10.0559	−	7.30605i	0.463352	−	0.336645i
$472$	−5.80078	+	4.21451i	−0.267003	+	0.193989i
$473$	1.63896	+	5.04420i	0.0753594	+	0.231933i
$474$	16.0539			0.737379
$475$	6.79667	−	9.39817i	0.311853	−	0.431217i
$476$	5.10392			0.233938
$477$	−0.310407	−	0.955336i	−0.0142126	−	0.0437418i
$478$	4.89843	−	3.55891i	0.224049	−	0.162781i
$479$	22.5228	−	16.3638i	1.02909	−	0.747680i	0.0609661	−	0.998140i	$-0.480582\pi$
$479$	22.5228	−	16.3638i	1.02909	−	0.747680i	0.968127	+	0.250460i	$0.0805818\pi$
$480$	4.02331	+	0.632700i	0.183638	+	0.0288787i
$481$	−6.30674	−	4.58212i	−0.287563	−	0.208926i
$482$	−26.8058			−1.22097
$483$	−0.0792412	−	0.0575721i	−0.00360560	−	0.00261962i
$484$	−2.43494	+	7.49397i	−0.110679	+	0.340635i
$485$	16.3936	+	2.57804i	0.744396	+	0.117063i
$486$	1.01538	+	3.12501i	0.0460584	+	0.141753i
$487$	7.24705	−	22.3041i	0.328395	−	1.01070i	−0.641490	−	0.767132i	$-0.721683\pi$
$487$	7.24705	−	22.3041i	0.328395	−	1.01070i	0.969885	−	0.243565i	$-0.0783168\pi$
$488$	−2.69420	+	8.29189i	−0.121961	+	0.375356i
$489$	10.2513	+	31.5503i	0.463580	+	1.42675i
$490$	−1.36948	+	2.69507i	−0.0618667	+	0.121751i
$491$	−7.97498	+	24.5445i	−0.359906	+	1.10768i	0.593204	+	0.805052i	$0.297863\pi$
$491$	−7.97498	+	24.5445i	−0.359906	+	1.10768i	−0.953110	+	0.302624i	$0.902137\pi$
$492$	18.6928	+	13.5811i	0.842738	+	0.612285i
$493$	3.72150			0.167608
$494$	−1.87664	−	1.36346i	−0.0844341	−	0.0613450i
$495$	0.887666	+	0.885717i	0.0398976	+	0.0398100i
$496$	6.29427	−	4.57306i	0.282621	−	0.205336i
$497$	−16.2621	+	11.8151i	−0.729457	+	0.529981i
$498$	−0.0314991	−	0.0969442i	−0.00141151	−	0.00434417i
$499$	−40.2044			−1.79980			−0.899898	−	0.436101i	$-0.856359\pi$
$499$	−40.2044			−1.79980			−0.899898	+	0.436101i	$0.856359\pi$
$500$	1.71259	−	11.0484i	0.0765892	−	0.494099i
$501$	−34.1165			−1.52421
$502$	−7.05586	−	21.7157i	−0.314919	−	0.969220i
$503$	−24.4184	+	17.7410i	−1.08876	+	0.791032i	−0.979190	−	0.202947i	$-0.934948\pi$
$503$	−24.4184	+	17.7410i	−1.08876	+	0.791032i	−0.109572	+	0.993979i	$0.534948\pi$
$504$	0.610388	−	0.443473i	0.0271888	−	0.0197539i
$505$	−9.10993	−	9.08993i	−0.405386	−	0.404497i
$506$	0.0323372	+	0.0234943i	0.00143756	+	0.00104445i
$507$	1.82139			0.0808908
$508$	7.35011	+	5.34017i	0.326108	+	0.236932i
$509$	6.83169	−	21.0258i	0.302809	−	0.931951i	−0.677677	−	0.735360i	$-0.737013\pi$
$509$	6.83169	−	21.0258i	0.302809	−	0.931951i	0.980486	−	0.196591i	$-0.0629870\pi$
$510$	3.96234	−	7.79770i	0.175455	−	0.345288i
$511$	−7.95487	−	24.4826i	−0.351903	−	1.08305i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−3.50231	+	10.7790i	−0.154631	+	0.475904i
$514$	1.48256	+	4.56287i	0.0653931	+	0.201259i
$515$	30.2064	+	4.75021i	1.33105	+	0.209319i
$516$	1.68993	−	5.20106i	0.0743949	−	0.228964i
$517$	9.36436	+	6.80361i	0.411844	+	0.299222i
$518$	18.5266			0.814014
$519$	−20.6534	−	15.0056i	−0.906583	−	0.658671i
$520$	−2.20892	−	0.347372i	−0.0968676	−	0.0152333i
$521$	−15.0417	+	10.9284i	−0.658988	+	0.478783i	−0.866321	−	0.499488i	$-0.833522\pi$
$521$	−15.0417	+	10.9284i	−0.658988	+	0.478783i	0.207333	+	0.978270i	$0.433522\pi$
$522$	0.445062	−	0.323356i	0.0194798	−	0.0141529i
$523$	6.96686	+	21.4418i	0.304639	+	0.937583i	0.979812	+	0.199923i	$0.0640693\pi$
$523$	6.96686	+	21.4418i	0.304639	+	0.937583i	−0.675172	+	0.737660i	$0.735931\pi$
$524$	3.95505			0.172777
$525$	−12.7600	−	17.4818i	−0.556893	−	0.762967i
$526$	−18.1898			−0.793112
$527$	−5.16327	−	15.8909i	−0.224916	−	0.692219i
$528$	−2.60294	+	1.89115i	−0.113279	+	0.0823017i
$529$	18.6070	−	13.5188i	0.808999	−	0.587772i
$530$	−1.11447	−	6.98682i	−0.0484096	−	0.303488i
$531$	1.84156	+	1.33797i	0.0799169	+	0.0580630i
$532$	5.51281			0.239011
$533$	−10.2629	−	7.45646i	−0.444537	−	0.322975i
$534$	5.05561	−	15.5596i	0.218777	−	0.673328i
$535$	−5.14463	−	5.13334i	−0.222422	−	0.221934i
$536$	−1.81869	−	5.59735i	−0.0785555	−	0.241769i
$537$	3.19225	−	9.82474i	0.137756	−	0.423969i
$538$	−3.87171	+	11.9159i	−0.166921	+	0.513731i
$539$	−0.737984	−	2.27128i	−0.0317872	−	0.0978310i
$540$	1.72095	+	10.7889i	0.0740578	+	0.464281i
$541$	0.757929	−	2.33267i	0.0325859	−	0.100289i	−0.933441	−	0.358732i	$-0.883209\pi$
$541$	0.757929	−	2.33267i	0.0325859	−	0.100289i	0.966027	+	0.258443i	$0.0832093\pi$
$542$	−16.5696	−	12.0385i	−0.711727	−	0.517100i
$543$	−34.5518			−1.48276
$544$	1.73745	+	1.26233i	0.0744925	+	0.0541220i
$545$	−19.9085	+	10.1715i	−0.852787	+	0.435698i
$546$	−3.50195	+	2.54432i	−0.149870	+	0.108887i
$547$	−29.9531	+	21.7622i	−1.28070	+	0.930485i	−0.999574	−	0.0291854i	$-0.990709\pi$
$547$	−29.9531	+	21.7622i	−1.28070	+	0.930485i	−0.281128	+	0.959670i	$0.590709\pi$
$548$	−0.191468	−	0.589278i	−0.00817911	−	0.0251727i
$549$	2.76788			0.118130
$550$	5.20718	+	7.13405i	0.222035	+	0.304197i
$551$	4.01964			0.171242
$552$	−0.0127358	−	0.0391968i	−0.000542072	−	0.00166833i
$553$	16.9466	−	12.3125i	0.720644	−	0.523579i
$554$	3.61871	−	2.62915i	0.153744	−	0.111702i
$555$	14.3828	−	28.3047i	0.610518	−	1.20147i
$556$	−2.76827	−	2.01126i	−0.117401	−	0.0852966i
$557$	−4.20360			−0.178112			−0.0890561	−	0.996027i	$-0.528385\pi$
$557$	−4.20360			−0.178112			−0.0890561	+	0.996027i	$0.528385\pi$
$558$	−1.99823	−	1.45180i	−0.0845917	−	0.0614594i
$559$	−0.927822	+	2.85554i	−0.0392427	+	0.120777i
$560$	4.73229	−	2.41778i	0.199976	−	0.102170i
$561$	2.13523	+	6.57155i	0.0901493	+	0.277451i
$562$	6.74309	−	20.7531i	0.284440	−	0.875417i
$563$	9.73037	−	29.9470i	0.410086	−	1.26212i	−0.506487	−	0.862248i	$-0.669056\pi$
$563$	9.73037	−	29.9470i	0.410086	−	1.26212i	0.916573	−	0.399868i	$-0.130944\pi$
$564$	−3.68810	−	11.3508i	−0.155297	−	0.477955i
$565$	−12.6762	+	6.47639i	−0.533291	+	0.272464i
$566$	0.225648	−	0.694474i	0.00948471	−	0.0291909i
$567$	18.9415	+	13.7618i	0.795468	+	0.577941i
$568$	−8.45806			−0.354892
$569$	26.3337	+	19.1326i	1.10397	+	0.802079i	0.981703	−	0.190418i	$-0.0609844\pi$
$569$	26.3337	+	19.1326i	1.10397	+	0.802079i	0.122264	+	0.992498i	$0.460984\pi$
$570$	4.27978	−	8.42240i	0.179260	−	0.352775i
$571$	15.4922	−	11.2557i	0.648328	−	0.471038i	−0.214373	−	0.976752i	$-0.568771\pi$
$571$	15.4922	−	11.2557i	0.648328	−	0.471038i	0.862701	+	0.505714i	$0.168771\pi$
$572$	1.42910	−	1.03830i	0.0597535	−	0.0434134i
$573$	5.55110	+	17.0845i	0.231900	+	0.713716i
$574$	30.1483			1.25837
$575$	−0.107524	+	0.0351981i	−0.00448407	+	0.00146786i
$576$	0.317467			0.0132278
$577$	−10.6060	−	32.6418i	−0.441532	−	1.35890i	−0.886242	−	0.463222i	$-0.846693\pi$
$577$	−10.6060	−	32.6418i	−0.441532	−	1.35890i	0.444710	−	0.895675i	$-0.353307\pi$
$578$	−10.0219	+	7.28136i	−0.416857	+	0.302865i
$579$	−25.5518	+	18.5645i	−1.06190	+	0.771514i
$580$	3.45053	−	1.76291i	0.143276	−	0.0732009i
$581$	−0.107602	−	0.0781772i	−0.00446407	−	0.00324334i
$582$	13.5176			0.560320
$583$	4.52180	+	3.28528i	0.187274	+	0.136062i
$584$	3.34722	−	10.3017i	0.138509	−	0.426287i
$585$	0.111820	+	0.701017i	0.00462318	+	0.0289835i
$586$	−5.16729	−	15.9033i	−0.213459	−	0.656959i
$587$	8.25799	−	25.4155i	0.340844	−	1.04901i	−0.622928	−	0.782279i	$-0.714057\pi$
$587$	8.25799	−	25.4155i	0.340844	−	1.04901i	0.963771	−	0.266730i	$-0.0859430\pi$
$588$	−0.760934	+	2.34191i	−0.0313804	+	0.0965789i
$589$	−5.57691	−	17.1640i	−0.229793	−	0.707229i
$590$	11.3495	+	11.3246i	0.467250	+	0.466225i
$591$	5.98690	−	18.4258i	0.246268	−	0.757936i
$592$	6.30674	+	4.58212i	0.259205	+	0.188324i
$593$	43.8372			1.80018			0.900088	−	0.435708i	$-0.143502\pi$
$593$	43.8372			1.80018			0.900088	+	0.435708i	$0.143502\pi$
$594$	−6.98248	−	5.07307i	−0.286495	−	0.208150i
$595$	−1.79772	−	11.2702i	−0.0736995	−	0.462035i
$596$	−8.54621	+	6.20918i	−0.350066	+	0.254338i
$597$	−8.31929	+	6.04432i	−0.340486	+	0.247377i
$598$	0.00699235	+	0.0215202i	0.000285939	+	0.000880028i
$599$	11.8321			0.483448			0.241724	−	0.970345i	$-0.422287\pi$
$599$	11.8321			0.483448			0.241724	+	0.970345i	$0.422287\pi$
$600$	−0.0200095	−	9.10694i	−0.000816886	−	0.371789i
$601$	8.49841			0.346657			0.173329	−	0.984864i	$-0.444548\pi$
$601$	8.49841			0.346657			0.173329	+	0.984864i	$0.444548\pi$
$602$	−2.20503	−	6.78637i	−0.0898702	−	0.276592i
$603$	−1.51159	+	1.09823i	−0.0615566	+	0.0447235i
$604$	−9.62939	+	6.99616i	−0.391814	+	0.284670i
$605$	17.4055	+	2.73716i	0.707633	+	0.111281i
$606$	−8.48065	−	6.16155i	−0.344503	−	0.250296i
$607$	−27.3586			−1.11045			−0.555225	−	0.831700i	$-0.687368\pi$
$607$	−27.3586			−1.11045			−0.555225	+	0.831700i	$0.687368\pi$
$608$	1.87664	+	1.36346i	0.0761079	+	0.0552956i
$609$	2.31792	−	7.13382i	0.0939268	−	0.289077i
$610$	19.2587	+	3.02860i	0.779763	+	0.122624i
$611$	2.02488	+	6.23194i	0.0819179	+	0.252117i
$612$	0.210686	−	0.648426i	0.00851649	−	0.0262111i
$613$	−6.01139	+	18.5012i	−0.242798	+	0.747255i	0.753193	+	0.657799i	$0.228513\pi$
$613$	−6.01139	+	18.5012i	−0.242798	+	0.747255i	−0.995991	+	0.0894551i	$0.971487\pi$
$614$	−7.16621	−	22.0553i	−0.289205	−	0.890080i
$615$	23.4051	−	46.0602i	0.943787	−	1.85733i
$616$	−1.29728	+	3.99263i	−0.0522691	+	0.160868i
$617$	16.6818	+	12.1200i	0.671584	+	0.487935i	0.870555	−	0.492071i	$-0.163760\pi$
$617$	16.6818	+	12.1200i	0.671584	+	0.487935i	−0.198971	+	0.980005i	$0.563760\pi$
$618$	24.9070			1.00191
$619$	17.1141	+	12.4341i	0.687872	+	0.499768i	0.875960	−	0.482384i	$-0.160229\pi$
$619$	17.1141	+	12.4341i	0.687872	+	0.499768i	−0.188088	+	0.982152i	$0.560229\pi$
$620$	−12.3150	−	12.2880i	−0.494582	−	0.493497i
$621$	0.0894431	−	0.0649842i	0.00358923	−	0.00260773i
$622$	−10.4617	+	7.60088i	−0.419477	+	0.304768i
$623$	−6.59658	−	20.3022i	−0.264287	−	0.813390i
$624$	−1.82139			−0.0729140
$625$	−24.9998	+	0.109858i	−0.999990	+	0.00439433i
$626$	−21.8404			−0.872917
$627$	2.30629	+	7.09802i	0.0921042	+	0.283467i
$628$	5.52101	−	4.01125i	0.220312	−	0.160066i
$629$	13.5444	−	9.84058i	0.540050	−	0.392370i
$630$	−1.19425	−	1.19163i	−0.0475800	−	0.0474756i
$631$	−27.5474	−	20.0144i	−1.09664	−	0.796759i	−0.116136	−	0.993233i	$-0.537051\pi$
$631$	−27.5474	−	20.0144i	−1.09664	−	0.796759i	−0.980509	+	0.196474i	$0.937051\pi$
$632$	8.81407			0.350605
$633$	39.3202	+	28.5678i	1.56284	+	1.13547i
$634$	0.748249	−	2.30287i	0.0297168	−	0.0914588i
$635$	9.20302	−	18.1111i	0.365211	−	0.718717i
$636$	−1.78089	−	5.48100i	−0.0706167	−	0.217336i
$637$	0.417776	−	1.28578i	0.0165529	−	0.0509445i
$638$	−0.945909	+	2.91121i	−0.0374489	+	0.115256i
$639$	0.829760	+	2.55374i	0.0328248	+	0.101024i
$640$	2.20892	+	0.347372i	0.0873153	+	0.0137311i
$641$	−1.09444	+	3.36833i	−0.0432277	+	0.133041i	−0.970341	−	0.241740i	$-0.922282\pi$
$641$	−1.09444	+	3.36833i	−0.0432277	+	0.133041i	0.927113	+	0.374781i	$0.122282\pi$
$642$	−4.78926	−	3.47960i	−0.189017	−	0.137329i
$643$	−17.3271			−0.683313			−0.341657	−	0.939825i	$-0.610988\pi$
$643$	−17.3271			−0.683313			−0.341657	+	0.939825i	$0.610988\pi$
$644$	−0.0435059	−	0.0316089i	−0.00171437	−	0.00124556i
$645$	−12.0800	−	1.89968i	−0.475648	−	0.0747997i
$646$	4.03029	−	2.92818i	0.158570	−	0.115208i
$647$	−5.73147	+	4.16416i	−0.225327	+	0.163710i	−0.694722	−	0.719279i	$-0.744472\pi$
$647$	−5.73147	+	4.16416i	−0.225327	+	0.163710i	0.469394	+	0.882989i	$0.344472\pi$
$648$	3.04432	+	9.36944i	0.119592	+	0.368067i
$649$	−12.6658			−0.497176
$650$	0.0109859	+	4.99999i	0.000430901	+	0.196116i
$651$	−33.6775			−1.31993
$652$	5.62828	+	17.3221i	0.220421	+	0.678385i
$653$	1.26005	−	0.915483i	0.0493097	−	0.0358256i	−0.562857	−	0.826554i	$-0.690298\pi$
$653$	1.26005	−	0.915483i	0.0493097	−	0.0358256i	0.612167	+	0.790728i	$0.290298\pi$
$654$	−14.7325	+	10.7038i	−0.576088	+	0.418552i
$655$	−1.39306	−	8.73335i	−0.0544315	−	0.341240i
$656$	10.2629	+	7.45646i	0.400700	+	0.291126i
$657$	−3.43875			−0.134159
$658$	−12.5986	−	9.15345i	−0.491146	−	0.356839i
$659$	4.85627	−	14.9460i	0.189173	−	0.582215i	−0.810822	−	0.585293i	$-0.800980\pi$
$659$	4.85627	−	14.9460i	0.189173	−	0.582215i	0.999995	+	0.00307741i	$0.000979572\pi$
$660$	5.09276	+	5.08159i	0.198236	+	0.197800i
$661$	−13.0011	−	40.0133i	−0.505684	−	1.55634i	−0.799617	−	0.600510i	$-0.794964\pi$
$661$	−13.0011	−	40.0133i	−0.505684	−	1.55634i	0.293933	−	0.955826i	$-0.405036\pi$
$662$	4.82116	−	14.8380i	0.187380	−	0.576695i
$663$	−1.20876	+	3.72018i	−0.0469444	+	0.144480i
$664$	−0.0172940	−	0.0532253i	−0.000671136	−	0.00206554i
$665$	−1.94174	−	12.1731i	−0.0752976	−	0.472054i
$666$	0.764767	−	2.35371i	0.0296341	−	0.0912044i
$667$	−0.0317221	−	0.0230475i	−0.00122829	−	0.000892401i
$668$	−18.7310			−0.724724
$669$	−8.63759	−	6.27557i	−0.333948	−	0.242628i
$670$	−11.7192	+	5.98747i	−0.452753	+	0.231316i
$671$	−12.4597	+	9.05252i	−0.481002	+	0.349469i
$672$	3.50195	−	2.54432i	0.135091	−	0.0981492i
$673$	12.2075	+	37.5707i	0.470563	+	1.44824i	0.851850	+	0.523786i	$0.175481\pi$
$673$	12.2075	+	37.5707i	0.470563	+	1.44824i	−0.381287	+	0.924457i	$0.624519\pi$
$674$	23.6012			0.909085
$675$	23.2174	−	7.60023i	0.893638	−	0.292533i
$676$	1.00000			0.0384615
$677$	3.26323	+	10.0432i	0.125416	+	0.385991i	0.993977	−	0.109592i	$-0.0349544\pi$
$677$	3.26323	+	10.0432i	0.125416	+	0.385991i	−0.868561	+	0.495583i	$0.834954\pi$
$678$	−9.38052	+	6.81534i	−0.360257	+	0.261742i
$679$	14.2693	−	10.3672i	0.547604	−	0.397858i
$680$	2.17545	−	4.28118i	0.0834246	−	0.164176i
$681$	25.7511	+	18.7092i	0.986783	+	0.716940i
$682$	13.7433			0.526258
$683$	25.3803	+	18.4399i	0.971150	+	0.705581i	0.955713	−	0.294299i	$-0.0950863\pi$
$683$	25.3803	+	18.4399i	0.971150	+	0.705581i	0.0154363	+	0.999881i	$0.495086\pi$
$684$	0.227565	−	0.700373i	0.00870116	−	0.0267794i
$685$	−1.23378	+	0.630349i	−0.0471402	+	0.0240844i
$686$	6.13366	+	18.8775i	0.234184	+	0.720745i
$687$	−5.29529	+	16.2972i	−0.202028	+	0.621778i
$688$	0.927822	−	2.85554i	0.0353729	−	0.108867i
$689$	0.977761	+	3.00924i	0.0372497	+	0.114643i
$690$	−0.0820667	+	0.0419287i	−0.00312422	+	0.00159620i
$691$	−5.97365	+	18.3850i	−0.227248	+	0.699398i	0.770807	+	0.637068i	$0.219853\pi$
$691$	−5.97365	+	18.3850i	−0.227248	+	0.699398i	−0.998056	+	0.0623298i	$0.980147\pi$
$692$	−11.3393	−	8.23851i	−0.431057	−	0.313181i
$693$	1.33276			0.0506274
$694$	21.9482	+	15.9463i	0.833141	+	0.605312i
$695$	−3.46613	+	6.82117i	−0.131478	+	0.258742i
$696$	2.55343	−	1.85518i	0.0967876	−	0.0703203i
$697$	22.0407	−	16.0135i	0.834853	−	0.606556i
$698$	−9.97676	−	30.7053i	−0.377626	−	1.16221i
$699$	45.5648			1.72342
$700$	−7.00565	−	9.59803i	−0.264789	−	0.362771i
$701$	22.9605			0.867205			0.433603	−	0.901104i	$-0.357242\pi$
$701$	22.9605			0.867205			0.433603	+	0.901104i	$0.357242\pi$
$702$	−1.50984	−	4.64681i	−0.0569852	−	0.175382i
$703$	14.6295	−	10.6289i	0.551761	−	0.400878i
$704$	−1.42910	+	1.03830i	−0.0538611	+	0.0391323i
$705$	−23.7653	+	12.1419i	−0.895052	+	0.457291i
$706$	−14.9842	−	10.8866i	−0.563936	−	0.409724i
$707$	−13.6778			−0.514408
$708$	10.5655	+	7.67628i	0.397076	+	0.288492i
$709$	7.30584	−	22.4851i	0.274377	−	0.844445i	−0.715007	−	0.699117i	$-0.753576\pi$
$709$	7.30584	−	22.4851i	0.274377	−	0.844445i	0.989384	−	0.145327i	$-0.0464235\pi$
$710$	2.97913	+	18.6767i	0.111805	+	0.700924i
$711$	−0.864686	−	2.66123i	−0.0324282	−	0.0998039i
$712$	2.77568	−	8.54267i	0.104023	−	0.320150i
$713$	−0.0544015	+	0.167431i	−0.00203735	+	0.00627033i
$714$	−2.87270	−	8.84125i	−0.107508	−	0.330875i
$715$	−2.79608	−	2.78995i	−0.104568	−	0.104338i
$716$	1.75264	−	5.39408i	0.0654994	−	0.201586i
$717$	−8.92195	−	6.48218i	−0.333196	−	0.242081i
$718$	28.6206			1.06811
$719$	5.00628	+	3.63728i	0.186703	+	0.135648i	0.677211	−	0.735789i	$-0.263189\pi$
$719$	5.00628	+	3.63728i	0.186703	+	0.135648i	−0.490508	+	0.871437i	$0.663189\pi$
$720$	−0.111820	−	0.701017i	−0.00416727	−	0.0261253i
$721$	26.2921	−	19.1023i	0.979169	−	0.711408i
$722$	−11.0182	+	8.00516i	−0.410053	+	0.297921i
$723$	15.0874	+	46.4342i	0.561106	+	1.72691i
$724$	−18.9700			−0.705015
$725$	−5.10814	−	6.99836i	−0.189711	−	0.259913i
$726$	14.3519			0.532648
$727$	−11.3440	−	34.9134i	−0.420727	−	1.29487i	−0.907027	−	0.421073i	$-0.861653\pi$
$727$	−11.3440	−	34.9134i	−0.420727	−	1.29487i	0.486299	−	0.873792i	$-0.338347\pi$
$728$	−1.92268	+	1.39691i	−0.0712592	+	0.0517729i
$729$	−19.0686	+	13.8541i	−0.706244	+	0.513116i
$730$	−23.9267	−	3.76267i	−0.885565	−	0.139263i
$731$	−5.21668	−	3.79014i	−0.192946	−	0.140184i
$732$	15.8800			0.586942
$733$	−32.4243	−	23.5576i	−1.19762	−	0.870121i	−0.203570	−	0.979060i	$-0.565255\pi$
$733$	−32.4243	−	23.5576i	−1.19762	−	0.870121i	−0.994048	+	0.108939i	$0.965255\pi$
$734$	6.39352	−	19.6772i	0.235989	−	0.726300i
$735$	5.43932	+	0.855379i	0.200632	+	0.0315511i
$736$	−0.00699235	−	0.0215202i	−0.000257742	−	0.000793247i
$737$	3.21264	−	9.88749i	0.118339	−	0.364211i
$738$	1.24450	−	3.83018i	0.0458107	−	0.140991i
$739$	9.23378	+	28.4186i	0.339670	+	1.04540i	0.964376	+	0.264536i	$0.0852190\pi$
$739$	9.23378	+	28.4186i	0.339670	+	1.04540i	−0.624706	+	0.780860i	$0.714781\pi$
$740$	7.89662	−	15.5402i	0.290286	−	0.571268i
$741$	−1.30560	+	4.01822i	−0.0479623	+	0.147613i
$742$	−6.08355	−	4.41996i	−0.223334	−	0.162262i
$743$	−10.3758			−0.380653			−0.190326	−	0.981721i	$-0.560955\pi$
$743$	−10.3758			−0.380653			−0.190326	+	0.981721i	$0.560955\pi$
$744$	−11.4643	−	8.32932i	−0.420303	−	0.305368i
$745$	16.7210	+	16.6843i	0.612610	+	0.611266i
$746$	24.8759	−	18.0734i	0.910773	−	0.661715i
$747$	−0.0143737	+	0.0104431i	−0.000525907	+	0.000382094i
$748$	1.17230	+	3.60798i	0.0428637	+	0.131921i
$749$	−7.72426			−0.282238
$750$	−20.1025	+	3.25187i	−0.734038	+	0.118741i
$751$	−4.98603			−0.181943			−0.0909715	−	0.995853i	$-0.528997\pi$
$751$	−4.98603			−0.181943			−0.0909715	+	0.995853i	$0.528997\pi$
$752$	−2.02488	−	6.23194i	−0.0738398	−	0.227255i
$753$	−33.6456	+	24.4450i	−1.22611	+	0.890825i
$754$	−1.40191	+	1.01855i	−0.0510547	+	0.0370934i
$755$	18.8403	+	18.7989i	0.685668	+	0.684164i
$756$	9.39410	+	6.82521i	0.341660	+	0.248231i
$757$	−46.5561			−1.69211			−0.846054	−	0.533096i	$-0.821028\pi$
$757$	−46.5561			−1.69211			−0.846054	+	0.533096i	$0.821028\pi$
$758$	16.8106	+	12.2136i	0.610589	+	0.443619i
$759$	0.0224973	−	0.0692395i	0.000816600	−	0.00251324i
$760$	2.34973	−	4.62416i	0.0852337	−	0.167736i
$761$	−11.7819	−	36.2610i	−0.427094	−	1.31446i	−0.900975	−	0.433871i	$-0.857147\pi$
$761$	−11.7819	−	36.2610i	−0.427094	−	1.31446i	0.473881	−	0.880589i	$-0.342853\pi$
$762$	5.11354	−	15.7379i	0.185244	−	0.570123i
$763$	−7.34257	+	22.5981i	−0.265819	+	0.818106i
$764$	3.04772	+	9.37993i	0.110263	+	0.339354i
$765$	−1.50603	−	0.236836i	−0.0544507	−	0.00856283i
$766$	−1.06121	+	3.26608i	−0.0383432	+	0.118008i
$767$	−5.80078	−	4.21451i	−0.209454	−	0.152177i
$768$	1.82139			0.0657238
$769$	−2.69017	−	1.95452i	−0.0970098	−	0.0704818i	0.538223	−	0.842803i	$-0.319096\pi$
$769$	−2.69017	−	1.95452i	−0.0970098	−	0.0704818i	−0.635233	+	0.772321i	$0.719096\pi$
$770$	9.27327	+	1.45830i	0.334186	+	0.0525535i
$771$	7.06956	−	5.13634i	0.254604	−	0.184981i
$772$	−14.0287	+	10.1925i	−0.504905	+	0.366835i
$773$	−6.54749	−	20.1511i	−0.235497	−	0.724784i	−0.997055	−	0.0766881i	$-0.975565\pi$
$773$	−6.54749	−	20.1511i	−0.235497	−	0.724784i	0.761558	−	0.648096i	$-0.224435\pi$
$774$	−0.953194			−0.0342619
$775$	−22.7961	+	31.5215i	−0.818859	+	1.13229i
$776$	7.42155			0.266418
$777$	−10.4275	−	32.0927i	−0.374086	−	1.15132i
$778$	−16.0615	+	11.6693i	−0.575832	+	0.418366i
$779$	23.8065	−	17.2964i	0.852956	−	0.619709i
$780$	0.641538	+	4.02191i	0.0229707	+	0.144008i
$781$	−12.0874	−	8.78200i	−0.432520	−	0.314245i
$782$	−0.0485954			−0.00173777
$783$	6.84967	+	4.97657i	0.244787	+	0.177848i
$784$	−0.417776	+	1.28578i	−0.0149206	+	0.0459208i
$785$	−10.8021	−	10.7784i	−0.385543	−	0.384697i
$786$	−2.22606	−	6.85112i	−0.0794011	−	0.244371i
$787$	1.37967	−	4.24618i	0.0491798	−	0.151360i	−0.923451	−	0.383717i	$-0.874644\pi$
$787$	1.37967	−	4.24618i	0.0491798	−	0.151360i	0.972631	+	0.232357i	$0.0746438\pi$
$788$	3.28699	−	10.1163i	0.117094	−	0.360379i
$789$	10.2380	+	31.5092i	0.364481	+	1.12176i
$790$	−3.10453	−	19.4628i	−0.110454	−	0.692456i
$791$	−4.67517	+	14.3887i	−0.166230	+	0.511603i
$792$	0.453691	+	0.329626i	0.0161212	+	0.0117128i
$793$	−8.71861			−0.309607
$794$	3.67030	+	2.66663i	0.130254	+	0.0946351i
$795$	−11.4756	+	5.86301i	−0.406998	+	0.207940i
$796$	−4.56754	+	3.31851i	−0.161892	+	0.117622i
$797$	−25.1640	+	18.2827i	−0.891354	+	0.647607i	−0.936231	−	0.351386i	$-0.885711\pi$
$797$	−25.1640	+	18.2827i	−0.891354	+	0.647607i	0.0448766	+	0.998993i	$0.485711\pi$
$798$	−3.10284	−	9.54954i	−0.109839	−	0.338050i
$799$	−14.0725			−0.497850
$800$	−0.0109859	−	4.99999i	−0.000388409	−	0.176776i
$801$	−2.85159			−0.100756
$802$	8.38534	+	25.8074i	0.296097	+	0.911291i
$803$	15.4797	−	11.2467i	0.546267	−	0.396886i
$804$	−8.67236	+	6.30084i	−0.305851	+	0.222213i
$805$	−0.0544734	+	0.107201i	−0.00191993	+	0.00377834i
$806$	6.29427	+	4.57306i	0.221706	+	0.161079i
$807$	22.8204			0.803317
$808$	−4.65614	−	3.38288i	−0.163802	−	0.119009i
$809$	−6.09462	+	18.7573i	−0.214275	+	0.659472i	0.784929	+	0.619586i	$0.212700\pi$
$809$	−6.09462	+	18.7573i	−0.214275	+	0.659472i	−0.999204	+	0.0398861i	$0.987300\pi$
$810$	19.6169	−	10.0225i	0.689267	−	0.352153i
$811$	12.5172	+	38.5241i	0.439540	+	1.35276i	0.888362	+	0.459143i	$0.151844\pi$
$811$	12.5172	+	38.5241i	0.439540	+	1.35276i	−0.448823	+	0.893621i	$0.648156\pi$
$812$	1.27261	−	3.91669i	0.0446598	−	0.137449i
$813$	−11.5277	+	35.4785i	−0.404293	+	1.24428i
$814$	4.25533	+	13.0966i	0.149149	+	0.459034i
$815$	36.2674	−	18.5294i	1.27039	−	0.649055i
$816$	1.20876	−	3.72018i	0.0423151	−	0.130232i
$817$	−5.63461	−	4.09378i	−0.197130	−	0.143223i
$818$	3.17167			0.110895
$819$	0.610388	+	0.443473i	0.0213287	+	0.0154962i
$820$	12.8501	−	25.2885i	0.448747	−	0.883112i
$821$	12.7465	−	9.26088i	0.444856	−	0.323207i	−0.342705	−	0.939443i	$-0.611343\pi$
$821$	12.7465	−	9.26088i	0.444856	−	0.323207i	0.787562	+	0.616236i	$0.211343\pi$
$822$	−0.913009	+	0.663340i	−0.0318449	+	0.0231366i
$823$	0.845444	+	2.60201i	0.0294703	+	0.0907003i	0.964710	−	0.263315i	$-0.0848160\pi$
$823$	0.845444	+	2.60201i	0.0294703	+	0.0907003i	−0.935239	+	0.354016i	$0.884816\pi$
$824$	13.6747			0.476382
$825$	9.42712	−	13.0355i	0.328210	−	0.453836i
$826$	17.0403			0.592909
$827$	3.28487	+	10.1098i	0.114226	+	0.351552i	0.991785	−	0.127917i	$-0.0408293\pi$
$827$	3.28487	+	10.1098i	0.114226	+	0.351552i	−0.877559	+	0.479469i	$0.840829\pi$
$828$	−0.00581163	+	0.00422240i	−0.000201968	+	0.000146738i
$829$	36.2058	−	26.3050i	1.25748	−	0.913612i	0.258848	−	0.965918i	$-0.416657\pi$
$829$	36.2058	−	26.3050i	1.25748	−	0.913612i	0.998631	+	0.0523063i	$0.0166572\pi$
$830$	−0.111438	+	0.0569350i	−0.00386808	+	0.00197624i
$831$	−6.59109	−	4.78870i	−0.228642	−	0.166118i
$832$	−1.00000			−0.0346688
$833$	2.34895	+	1.70661i	0.0813862	+	0.0591305i
$834$	−1.92591	+	5.92734i	−0.0666888	+	0.205247i
$835$	6.59751	+	41.3609i	0.228316	+	1.43135i
$836$	1.26622	+	3.89703i	0.0437932	+	0.134782i
$837$	11.7468	−	36.1528i	0.406028	−	1.24962i
$838$	−3.84198	+	11.8244i	−0.132719	+	0.408467i
$839$	16.3106	+	50.1988i	0.563104	+	1.73305i	0.673520	+	0.739169i	$0.264782\pi$
$839$	16.3106	+	50.1988i	0.563104	+	1.73305i	−0.110416	+	0.993885i	$0.535218\pi$
$840$	−6.85171	−	6.83667i	−0.236407	−	0.235888i
$841$	−8.03358	+	24.7248i	−0.277020	+	0.852579i
$842$	−8.54794	−	6.21044i	−0.294581	−	0.214026i
$843$	−39.7448			−1.36888
$844$	21.5880	+	15.6846i	0.743090	+	0.539886i
$845$	−0.352224	−	2.20815i	−0.0121169	−	0.0759628i
$846$	−1.68296	+	1.22274i	−0.0578614	+	0.0420387i
$847$	15.1500	−	11.0071i	0.520560	−	0.378209i
$848$	−0.977761	−	3.00924i	−0.0335765	−	0.103338i
$849$	−1.33000			−0.0456456
$850$	−10.2197	−	3.29579i	−0.350534	−	0.113045i
$851$	−0.176396			−0.00604677
$852$	4.76054	+	14.6515i	0.163094	+	0.501950i
$853$	−16.1481	+	11.7323i	−0.552899	+	0.401705i	−0.828853	−	0.559466i	$-0.811006\pi$
$853$	−16.1481	+	11.7323i	−0.552899	+	0.401705i	0.275954	+	0.961171i	$0.411006\pi$
$854$	16.7631	−	12.1791i	0.573621	−	0.416760i
$855$	−1.62668	−	0.255810i	−0.0556314	−	0.00874851i
$856$	−2.62945	−	1.91041i	−0.0898728	−	0.0652964i
$857$	10.6381			0.363392			0.181696	−	0.983355i	$-0.441841\pi$
$857$	10.6381			0.363392			0.181696	+	0.983355i	$0.441841\pi$
$858$	−2.60294	−	1.89115i	−0.0888630	−	0.0645627i
$859$	−4.04606	+	12.4525i	−0.138050	+	0.424874i	−0.996052	−	0.0887723i	$-0.971706\pi$
$859$	−4.04606	+	12.4525i	−0.138050	+	0.424874i	0.858002	+	0.513646i	$0.171706\pi$
$860$	−6.63227	−	1.04298i	−0.226159	−	0.0355654i
$861$	−16.9687	−	52.2243i	−0.578292	−	1.77980i
$862$	−8.50328	+	26.1704i	−0.289623	+	0.891368i
$863$	−1.23293	+	3.79457i	−0.0419695	+	0.129169i	−0.969846	−	0.243719i	$-0.921632\pi$
$863$	−1.23293	+	3.79457i	−0.0419695	+	0.129169i	0.927876	+	0.372888i	$0.121632\pi$
$864$	1.50984	+	4.64681i	0.0513658	+	0.158088i
$865$	−14.1979	+	27.9408i	−0.482743	+	0.950016i
$866$	4.13929	−	12.7394i	0.140659	−	0.432904i
$867$	18.2539	+	13.2622i	0.619934	+	0.450408i
$868$	−18.4900			−0.627592
$869$	12.5962	+	9.15164i	0.427295	+	0.310448i
$870$	−4.99590	−	4.98493i	−0.169377	−	0.169005i
$871$	4.76139	−	3.45935i	0.161334	−	0.117216i
$872$	−8.08862	+	5.87672i	−0.273915	+	0.199011i
$873$	−0.728075	−	2.24079i	−0.0246416	−	0.0758391i
$874$	−0.0524886			−0.00177545
$875$	−18.7264	+	18.8502i	−0.633066	+	0.637253i
$876$	−19.7290			−0.666581
$877$	1.40621	+	4.32788i	0.0474844	+	0.146142i	0.971987	−	0.235033i	$-0.0755197\pi$
$877$	1.40621	+	4.32788i	0.0474844	+	0.146142i	−0.924503	+	0.381175i	$0.875520\pi$
$878$	16.9605	−	12.3225i	0.572388	−	0.415864i
$879$	−24.6401	+	17.9020i	−0.831088	+	0.603821i
$880$	2.79608	+	2.78995i	0.0942560	+	0.0940491i
$881$	29.5546	+	21.4727i	0.995719	+	0.723432i	0.961166	−	0.275970i	$-0.0889992\pi$
$881$	29.5546	+	21.4727i	0.995719	+	0.723432i	0.0345532	+	0.999403i	$0.488999\pi$
$882$	0.429201			0.0144519
$883$	−37.2615	−	27.0721i	−1.25395	−	0.911048i	−0.255505	−	0.966808i	$-0.582242\pi$
$883$	−37.2615	−	27.0721i	−1.25395	−	0.911048i	−0.998444	+	0.0557601i	$0.982242\pi$
$884$	−0.663647	+	2.04249i	−0.0223209	+	0.0686965i
$885$	13.2290	−	26.0340i	0.444687	−	0.875123i
$886$	−4.04421	−	12.4468i	−0.135868	−	0.418158i
$887$	2.35415	−	7.24532i	0.0790446	−	0.243274i	−0.903724	−	0.428116i	$-0.859177\pi$
$887$	2.35415	−	7.24532i	0.0790446	−	0.243274i	0.982768	+	0.184842i	$0.0591774\pi$
$888$	4.38766	−	13.5038i	0.147240	−	0.453159i
$889$	−6.67218	−	20.5349i	−0.223778	−	0.688717i
$890$	−19.8412	−	3.12020i	−0.665078	−	0.104589i
$891$	−5.37766	+	16.5507i	−0.180158	+	0.554471i
$892$	−4.74230	−	3.44548i	−0.158784	−	0.115363i
$893$	−15.1999			−0.508645
$894$	15.5660	+	11.3094i	0.520605	+	0.378241i
$895$	−12.5283	−	1.97018i	−0.418774	−	0.0658558i
$896$	1.92268	−	1.39691i	0.0642322	−	0.0466674i
$897$	0.0333428	−	0.0242250i	0.00111328	−	0.000808848i
$898$	9.81496	+	30.2073i	0.327529	+	1.00803i
$899$	−13.4819			−0.449647
$900$	−1.50857	+	0.493830i	−0.0502855	+	0.0164610i
$901$	−6.79524			−0.226382
$902$	6.92468	+	21.3120i	0.230567	+	0.709611i
$903$	−10.5146	+	7.63930i	−0.349904	+	0.254220i
$904$	−5.15019	+	3.74183i	−0.171293	+	0.124452i
$905$	6.68169	+	41.8887i	0.222107	+	1.39243i
$906$	17.5389	+	12.7427i	0.582690	+	0.423349i
$907$	2.40767			0.0799454			0.0399727	−	0.999201i	$-0.487273\pi$
$907$	2.40767			0.0799454			0.0399727	+	0.999201i	$0.487273\pi$
$908$	14.1381	+	10.2719i	0.469190	+	0.340887i
$909$	−0.564612	+	1.73770i	−0.0187270	+	0.0576357i
$910$	3.76180	+	3.75354i	0.124702	+	0.124429i
$911$	4.72527	+	14.5429i	0.156555	+	0.481827i	0.998315	−	0.0580247i	$-0.0184802\pi$
$911$	4.72527	+	14.5429i	0.156555	+	0.481827i	−0.841760	+	0.539852i	$0.818480\pi$
$912$	1.30560	−	4.01822i	0.0432327	−	0.133056i
$913$	0.0305491	−	0.0940204i	0.00101103	−	0.00311162i
$914$	1.64679	+	5.06831i	0.0544711	+	0.167645i
$915$	−5.59332	−	35.0655i	−0.184910	−	1.15923i
$916$	−2.90728	+	8.94768i	−0.0960592	+	0.295640i
$917$	−7.60429	−	5.52484i	−0.251116	−	0.182446i
$918$	10.4931			0.346323
$919$	−9.35532	−	6.79704i	−0.308603	−	0.224213i	0.422694	−	0.906273i	$-0.361085\pi$
$919$	−9.35532	−	6.79704i	−0.308603	−	0.224213i	−0.731297	+	0.682059i	$0.761085\pi$
$920$	−0.0450571	+	0.0230201i	−0.00148549	+	0.000758951i
$921$	−34.1718	+	24.8273i	−1.12600	+	0.818087i
$922$	6.78787	−	4.93168i	0.223547	−	0.162416i
$923$	−2.61369	−	8.04410i	−0.0860305	−	0.264775i
$924$	7.64638			0.251548
$925$	−37.0965	−	11.9633i	−1.21972	−	0.393352i
$926$	−18.0297			−0.592492
$927$	−1.34153	−	4.12880i	−0.0440616	−	0.135608i
$928$	1.40191	−	1.01855i	0.0460201	−	0.0334355i
$929$	6.10850	−	4.43809i	0.200414	−	0.145609i	−0.483052	−	0.875592i	$-0.660472\pi$
$929$	6.10850	−	4.43809i	0.200414	−	0.145609i	0.683466	+	0.729983i	$0.260472\pi$
$930$	−14.3544	+	28.2488i	−0.470699	+	0.926314i
$931$	2.53713	+	1.84333i	0.0831510	+	0.0604128i
$932$	25.0165			0.819443
$933$	19.0549	+	13.8442i	0.623829	+	0.453238i
$934$	−0.377591	+	1.16211i	−0.0123552	+	0.0380252i
$935$	7.55406	−	3.85945i	0.247044	−	0.126217i
$936$	0.0981028	+	0.301929i	0.00320659	+	0.00986887i
$937$	−14.4371	+	44.4327i	−0.471639	+	1.45155i	0.378799	+	0.925479i	$0.376337\pi$
$937$	−14.4371	+	44.4327i	−0.471639	+	1.45155i	−0.850438	+	0.526075i	$0.823663\pi$
$938$	−4.32223	+	13.3025i	−0.141126	+	0.434341i
$939$	12.2927	+	37.8329i	0.401156	+	1.23463i
$940$	−13.0479	+	6.66628i	−0.425574	+	0.217430i
$941$	−16.6527	+	51.2517i	−0.542862	+	1.67076i	0.183157	+	0.983084i	$0.441368\pi$
$941$	−16.6527	+	51.2517i	−0.542862	+	1.67076i	−0.726019	+	0.687674i	$0.758632\pi$
$942$	−10.0559	−	7.30605i	−0.327640	−	0.238044i
$943$	−0.287048			−0.00934758
$944$	5.80078	+	4.21451i	0.188799	+	0.137171i
$945$	11.7623	−	23.1476i	0.382627	−	0.752992i
$946$	4.29085	−	3.11749i	0.139508	−	0.101358i
$947$	−10.7571	+	7.81549i	−0.349559	+	0.253969i	−0.748684	−	0.662927i	$-0.769314\pi$
$947$	−10.7571	+	7.81549i	−0.349559	+	0.253969i	0.399125	+	0.916896i	$0.369314\pi$
$948$	−4.96092	−	15.2681i	−0.161123	−	0.495886i
$949$	10.8318			0.351616
$950$	−11.0385	−	3.55982i	−0.358135	−	0.115496i
$951$	−4.41029			−0.143013
$952$	−1.57720	−	4.85412i	−0.0511173	−	0.157323i
$953$	5.86484	−	4.26106i	0.189981	−	0.138029i	−0.488729	−	0.872436i	$-0.662539\pi$
$953$	5.86484	−	4.26106i	0.189981	−	0.138029i	0.678710	+	0.734406i	$0.262539\pi$
$954$	−0.812657	+	0.590430i	−0.0263107	+	0.0191159i
$955$	19.6388	−	10.0337i	0.635498	−	0.324682i
$956$	−4.89843	−	3.55891i	−0.158426	−	0.115104i
$957$	5.57533			0.180225
$958$	−22.5228	−	16.3638i	−0.727679	−	0.528690i
$959$	−0.455036	+	1.40046i	−0.0146939	+	0.0452231i
$960$	−0.641538	−	4.02191i	−0.0207056	−	0.129807i
$961$	9.12548	+	28.0853i	0.294370	+	0.905979i
$962$	−2.40896	+	7.41402i	−0.0776680	+	0.239038i
$963$	−0.318852	+	0.981325i	−0.0102749	+	0.0316228i
$964$	8.28344	+	25.4938i	0.266792	+	0.821100i
$965$	27.4478	+	27.3876i	0.883576	+	0.881637i
$966$	−0.0302675	+	0.0931536i	−0.000973839	+	0.00299717i
$967$	44.3916	+	32.2524i	1.42754	+	1.03717i	0.990469	+	0.137738i	$0.0439832\pi$
$967$	44.3916	+	32.2524i	1.42754	+	1.03717i	0.437068	+	0.899428i	$0.356017\pi$
$968$	7.87962			0.253261
$969$	−7.34073	−	5.33335i	−0.235818	−	0.171332i
$970$	−2.61405	−	16.3879i	−0.0839321	−	0.526184i
$971$	−50.0261	+	36.3461i	−1.60542	+	1.16640i	−0.729442	+	0.684043i	$0.760220\pi$
$971$	−50.0261	+	36.3461i	−1.60542	+	1.16640i	−0.875973	+	0.482360i	$0.839780\pi$
$972$	2.65829	−	1.93136i	0.0852646	−	0.0619484i
$973$	2.51294	+	7.73403i	0.0805611	+	0.247942i
$974$	−23.4519			−0.751449
$975$	8.65503	−	2.83323i	0.277183	−	0.0907359i
$976$	8.71861			0.279076
$977$	−9.76304	−	30.0475i	−0.312347	−	0.961306i	−0.976833	−	0.214005i	$-0.931349\pi$
$977$	−9.76304	−	30.0475i	−0.312347	−	0.961306i	0.664485	−	0.747301i	$-0.268651\pi$
$978$	26.8383	−	19.4992i	0.858194	−	0.623514i
$979$	12.8366	−	9.32631i	0.410258	−	0.298070i
$980$	2.98635	+	0.469630i	0.0953956	+	0.0150018i
$981$	2.56787	+	1.86567i	0.0819859	+	0.0595662i
$982$	25.8076			0.823553
$983$	−34.8837	−	25.3445i	−1.11262	−	0.808364i	−0.129543	−	0.991574i	$-0.541351\pi$
$983$	−34.8837	−	25.3445i	−1.11262	−	0.808364i	−0.983074	+	0.183210i	$0.941351\pi$
$984$	7.14002	−	21.9747i	0.227616	−	0.700529i
$985$	−23.4961	−	3.69497i	−0.748649	−	0.117731i
$986$	−1.15001	−	3.53936i	−0.0366237	−	0.112716i
$987$	−8.76500	+	26.9759i	−0.278993	+	0.858652i
$988$	−0.716813	+	2.20613i	−0.0228049	+	0.0701862i
$989$	0.0209945	+	0.0646144i	0.000667586	+	0.00205462i
$990$	0.568064	−	1.11792i	0.0180542	−	0.0355299i
$991$	0.733851	−	2.25856i	0.0233115	−	0.0717455i	−0.938724	−	0.344670i	$-0.887991\pi$
$991$	0.733851	−	2.25856i	0.0233115	−	0.0717455i	0.962036	+	0.272924i	$0.0879909\pi$
$992$	−6.29427	−	4.57306i	−0.199843	−	0.145195i
$993$	−28.4166			−0.901774
$994$	16.2621	+	11.8151i	0.515804	+	0.374753i
$995$	8.93659	+	8.91697i	0.283309	+	0.282687i
$996$	−0.0824656	+	0.0599148i	−0.00261302	+	0.00189847i
$997$	−29.7948	+	21.6472i	−0.943611	+	0.685573i	−0.949287	−	0.314411i	$-0.898193\pi$
$997$	−29.7948	+	21.6472i	−0.943611	+	0.685573i	0.00567637	+	0.999984i	$0.498193\pi$
$998$	12.4238	+	38.2366i	0.393270	+	1.21036i
$999$	38.0887			1.20507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.b.131.2	✓	20
25.21	even	5	inner	650.2.l.b.521.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.b.131.2	✓	20	1.1	even	1	trivial
650.2.l.b.521.2	yes	20	25.21	even	5	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.47354 + 1.07059i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.58287 + 1.57940i) q^{5} +(1.47354 + 1.07059i) q^{6} +2.37656 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.0981028 - 0.301929i) q^{9} +(1.01296 - 1.99347i) q^{10} +(0.545866 + 1.68000i) q^{11} +(0.562841 - 1.73225i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.734398 - 2.26025i) q^{14} +(-4.02331 - 0.632700i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.73745 - 1.26233i) q^{17} -0.317467 q^{18} +(-1.87664 - 1.36346i) q^{19} +(-2.20892 - 0.347372i) q^{20} +(-3.50195 + 2.54432i) q^{21} +(1.42910 - 1.03830i) q^{22} +(0.00699235 + 0.0215202i) q^{23} -1.82139 q^{24} +(0.0109859 + 4.99999i) q^{25} +1.00000 q^{26} +(-1.50984 - 4.64681i) q^{27} +(-1.92268 + 1.39691i) q^{28} +(-1.40191 + 1.01855i) q^{29} +(0.641538 + 4.02191i) q^{30} +(6.29427 + 4.57306i) q^{31} -1.00000 q^{32} +(-2.60294 - 1.89115i) q^{33} +(-0.663647 + 2.04249i) q^{34} +(3.76180 + 3.75354i) q^{35} +(0.0981028 + 0.301929i) q^{36} +(-2.40896 + 7.41402i) q^{37} +(-0.716813 + 2.20613i) q^{38} +(-0.562841 - 1.73225i) q^{39} +(0.352224 + 2.20815i) q^{40} +(-3.92009 + 12.0648i) q^{41} +(3.50195 + 2.54432i) q^{42} +3.00250 q^{43} +(-1.42910 - 1.03830i) q^{44} +(0.632152 - 0.322973i) q^{45} +(0.0183062 - 0.0133002i) q^{46} +(5.30120 - 3.85155i) q^{47} +(0.562841 + 1.73225i) q^{48} -1.35195 q^{49} +(4.75188 - 1.55553i) q^{50} +3.91163 q^{51} +(-0.309017 - 0.951057i) q^{52} +(2.55981 - 1.85981i) q^{53} +(-3.95281 + 2.87188i) q^{54} +(-1.78936 + 3.52137i) q^{55} +(1.92268 + 1.39691i) q^{56} +4.22500 q^{57} +(1.40191 + 1.01855i) q^{58} +(-2.21570 + 6.81923i) q^{59} +(3.62682 - 1.85298i) q^{60} +(2.69420 + 8.29189i) q^{61} +(2.40420 - 7.39936i) q^{62} +(0.233148 - 0.717554i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.99123 + 1.01734i) q^{65} +(-0.994235 + 3.05994i) q^{66} +(-4.76139 - 3.45935i) q^{67} +2.14761 q^{68} +(-0.0333428 - 0.0242250i) q^{69} +(2.40737 - 4.73759i) q^{70} +(-6.84272 + 4.97153i) q^{71} +(0.256837 - 0.186603i) q^{72} +(-3.34722 - 10.3017i) q^{73} +7.79556 q^{74} +(-5.36911 - 7.35590i) q^{75} +2.31966 q^{76} +(1.29728 + 3.99263i) q^{77} +(-1.47354 + 1.07059i) q^{78} +(7.13073 - 5.18078i) q^{79} +(1.99123 - 1.01734i) q^{80} +(7.97013 + 5.79064i) q^{81} +12.6857 q^{82} +(-0.0452762 - 0.0328951i) q^{83} +(1.33763 - 4.11679i) q^{84} +(-0.756439 - 4.74224i) q^{85} +(-0.927822 - 2.85554i) q^{86} +(0.975325 - 3.00174i) q^{87} +(-0.545866 + 1.68000i) q^{88} +(-2.77568 - 8.54267i) q^{89} +(-0.502511 - 0.501408i) q^{90} +(-0.734398 + 2.26025i) q^{91} +(-0.0183062 - 0.0133002i) q^{92} -14.1707 q^{93} +(-5.30120 - 3.85155i) q^{94} +(-0.817039 - 5.12216i) q^{95} +(1.47354 - 1.07059i) q^{96} +(6.00416 - 4.36228i) q^{97} +(0.417776 + 1.28578i) q^{98} +0.560793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - 4 q^{3} - 5 q^{4} - 10 q^{5} + 4 q^{6} + 8 q^{7} + 5 q^{8} - 7 q^{9} + 10 q^{10} + q^{12} + 5 q^{13} + 2 q^{14} + 5 q^{15} - 5 q^{16} + 2 q^{18} - 4 q^{19} + 5 q^{20} + 3 q^{21} - 5 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - 4 * q^3 - 5 * q^4 - 10 * q^5 + 4 * q^6 + 8 * q^7 + 5 * q^8 - 7 * q^9 + 10 * q^10 + q^12 + 5 * q^13 + 2 * q^14 + 5 * q^15 - 5 * q^16 + 2 * q^18 - 4 * q^19 + 5 * q^20 + 3 * q^21 - 5 * q^22 - 17 * q^23 - 6 * q^24 + 20 * q^26 - 19 * q^27 - 2 * q^28 + 9 * q^29 + 10 * q^30 - 2 * q^31 - 20 * q^32 - 3 * q^33 - 5 * q^34 + 30 * q^35 - 7 * q^36 - 19 * q^37 - q^38 - q^39 - 5 * q^40 + 33 * q^41 - 3 * q^42 + 2 * q^43 + 5 * q^44 + 35 * q^45 + 2 * q^46 - 13 * q^47 + q^48 - 4 * q^49 + 15 * q^50 + 12 * q^51 + 5 * q^52 - 7 * q^53 - 16 * q^54 + 35 * q^55 + 2 * q^56 - 18 * q^57 - 9 * q^58 + 11 * q^59 + 20 * q^60 - 18 * q^61 - 13 * q^62 + 44 * q^63 - 5 * q^64 - 10 * q^65 + 8 * q^66 - 27 * q^67 - 10 * q^68 - 8 * q^69 + 20 * q^70 - 7 * q^71 - 8 * q^72 - 30 * q^73 - 16 * q^74 - 60 * q^75 + 6 * q^76 + q^77 - 4 * q^78 - q^79 + 10 * q^80 + 28 * q^81 + 52 * q^82 - 6 * q^83 + 18 * q^84 + 25 * q^85 - 7 * q^86 - 37 * q^87 + 29 * q^89 - 20 * q^90 + 2 * q^91 - 2 * q^92 + 8 * q^93 + 13 * q^94 - 20 * q^95 + 4 * q^96 - 15 * q^97 - 11 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more