LMFDB - Embedded newform 100.9.j.b.11.48

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.48
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.48

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.95273 - 15.5041i) q^{2} +(142.345 + 46.2507i) q^{3} +(-224.752 + 122.567i) q^{4} +(-200.398 + 592.001i) q^{5} +(154.422 - 2389.74i) q^{6} +4177.48i q^{7} +(2788.67 + 3000.09i) q^{8} +(12815.0 + 9310.66i) q^{9} +(9970.54 + 766.963i) q^{10} +(-16299.6 - 22434.5i) q^{11} +(-37661.1 + 7051.83i) q^{12} +(6703.03 + 4870.04i) q^{13} +(64767.9 - 16512.4i) q^{14} +(-55906.2 + 74999.9i) q^{15} +(35490.8 - 55094.2i) q^{16} +(-6077.97 - 18706.1i) q^{17} +(93698.7 - 235487. i) q^{18} +(-6561.74 + 2132.04i) q^{19} +(-27519.8 - 157616. i) q^{20} +(-193211. + 594643. i) q^{21} +(-283398. + 341388. i) q^{22} +(91274.5 + 125629. i) q^{23} +(258196. + 556026. i) q^{24} +(-310306. - 237272. i) q^{25} +(49010.1 - 123174. i) q^{26} +(816332. + 1.12359e6i) q^{27} +(-512020. - 938896. i) q^{28} +(-331171. + 1.01924e6i) q^{29} +(1.38379e6 + 570318. i) q^{30} +(-485219. + 157657. i) q^{31} +(-994469. - 332479. i) q^{32} +(-1.28256e6 - 3.94731e6i) q^{33} +(-265996. + 168173. i) q^{34} +(-2.47307e6 - 837158. i) q^{35} +(-4.02138e6 - 521893. i) q^{36} +(-1.35566e6 - 984945. i) q^{37} +(58992.0 + 93306.2i) q^{38} +(728901. + 1.00325e6i) q^{39} +(-2.33490e6 + 1.04968e6i) q^{40} +(-738039. - 536217. i) q^{41} +(9.98310e6 + 645096. i) q^{42} -1.05209e6i q^{43} +(6.41310e6 + 3.04441e6i) q^{44} +(-8.08003e6 + 5.72067e6i) q^{45} +(1.58697e6 - 1.91170e6i) q^{46} +(3.21895e6 + 1.04590e6i) q^{47} +(7.60008e6 - 6.20091e6i) q^{48} -1.16865e7 q^{49} +(-2.45212e6 + 5.74888e6i) q^{50} -2.94383e6i q^{51} +(-2.10342e6 - 272981. i) q^{52} +(-1.93443e6 + 5.95357e6i) q^{53} +(1.41934e7 - 1.70977e7i) q^{54} +(1.65477e7 - 5.15357e6i) q^{55} +(-1.25328e7 + 1.16496e7i) q^{56} -1.03264e6 q^{57} +(1.71114e7 + 1.10572e6i) q^{58} +(-3.25429e6 + 4.47915e6i) q^{59} +(3.37252e6 - 2.37086e7i) q^{60} +(-1.18607e6 + 861728. i) q^{61} +(4.36227e6 + 6.89969e6i) q^{62} +(-3.88951e7 + 5.35345e7i) q^{63} +(-1.22391e6 + 1.67325e7i) q^{64} +(-4.22634e6 + 2.99226e6i) q^{65} +(-5.61298e7 + 3.54875e7i) q^{66} +(2.33934e7 - 7.60097e6i) q^{67} +(3.65878e6 + 3.45927e6i) q^{68} +(7.18206e6 + 2.21041e7i) q^{69} +(-3.20397e6 + 4.16517e7i) q^{70} +(1.58541e7 + 5.15130e6i) q^{71} +(7.80396e6 + 6.44106e7i) q^{72} +(-1.46316e7 + 1.06305e7i) q^{73} +(-9.91209e6 + 2.49115e7i) q^{74} +(-3.31966e7 - 4.81264e7i) q^{75} +(1.21345e6 - 1.28343e6i) q^{76} +(9.37197e7 - 6.80913e7i) q^{77} +(1.26732e7 - 1.52665e7i) q^{78} +(-2.04259e7 - 6.63678e6i) q^{79} +(2.55036e7 + 3.20514e7i) q^{80} +(3.21188e7 + 9.88515e7i) q^{81} +(-5.39627e6 + 1.35621e7i) q^{82} +(3.95465e7 - 1.28494e7i) q^{83} +(-2.94589e7 - 1.57328e8i) q^{84} +(1.22920e7 + 150494. i) q^{85} +(-1.63117e7 + 4.15864e6i) q^{86} +(-9.42811e7 + 1.29767e8i) q^{87} +(2.18514e7 - 1.11463e8i) q^{88} +(7.58380e6 - 5.50995e6i) q^{89} +(1.20632e8 + 1.02661e8i) q^{90} +(-2.03445e7 + 2.80018e7i) q^{91} +(-3.59120e7 - 1.70480e7i) q^{92} -7.63603e7 q^{93} +(3.49207e6 - 5.40410e7i) q^{94} +(52790.4 - 4.31181e6i) q^{95} +(-1.26180e8 - 9.33217e7i) q^{96} +(-1.66217e7 + 5.11563e7i) q^{97} +(4.61936e7 + 1.81188e8i) q^{98} -4.39259e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−3.95273	−	15.5041i	−0.247046	−	0.969004i
$2$	−3.95273	−	15.5041i	−0.247046	−	0.969004i
$3$	142.345	+	46.2507i	1.75735	+	0.570996i	0.996920	−	0.0784278i	$-0.0249900\pi$
$3$	142.345	+	46.2507i	1.75735	+	0.570996i	0.760426	+	0.649424i	$0.224990\pi$
$4$	−224.752	+	122.567i	−0.877937	+	0.478776i
$5$	−200.398	+	592.001i	−0.320637	+	0.947202i
$5$	−200.398	+	592.001i	−0.320637	+	0.947202i
$6$	154.422	−	2389.74i	0.119153	−	1.84394i
$7$			4177.48i			1.73989i	0.493148	+	0.869945i	$0.335846\pi$
$7$			4177.48i			1.73989i	−0.493148	+	0.869945i	$0.664154\pi$
$8$	2788.67	+	3000.09i	0.680826	+	0.732445i
$9$	12815.0	+	9310.66i	1.95321	+	1.41909i
$10$	9970.54	+	766.963i	0.997054	+	0.0766963i
$11$	−16299.6	−	22434.5i	−1.11329	−	1.53231i	−0.816483	−	0.577369i	$-0.804079\pi$
$11$	−16299.6	−	22434.5i	−1.11329	−	1.53231i	−0.296804	−	0.954939i	$-0.595921\pi$
$12$	−37661.1	+	7051.83i	−1.81622	+	0.340077i
$13$	6703.03	+	4870.04i	0.234692	+	0.170514i	0.698915	−	0.715205i	$-0.253666\pi$
$13$	6703.03	+	4870.04i	0.234692	+	0.170514i	−0.464223	+	0.885718i	$0.653666\pi$
$14$	64767.9	−	16512.4i	1.68596	−	0.429832i
$15$	−55906.2	+	74999.9i	−1.10432	+	1.48148i
$16$	35490.8	−	55094.2i	0.541547	−	0.840671i
$17$	−6077.97	−	18706.1i	−0.0727718	−	0.223969i	0.908055	−	0.418852i	$-0.137567\pi$
$17$	−6077.97	−	18706.1i	−0.0727718	−	0.223969i	−0.980826	+	0.194883i	$0.937567\pi$
$18$	93698.7	−	235487.i	0.892573	−	2.24325i
$19$	−6561.74	+	2132.04i	−0.0503506	+	0.0163599i	−0.334084	−	0.942543i	$-0.608427\pi$
$19$	−6561.74	+	2132.04i	−0.0503506	+	0.0163599i	0.283733	+	0.958903i	$0.408427\pi$
$20$	−27519.8	−	157616.i	−0.171999	−	0.985097i
$21$	−193211.	+	594643.i	−0.993471	+	3.05759i
$22$	−283398.	+	341388.i	−1.20978	+	1.45733i
$23$	91274.5	+	125629.i	0.326166	+	0.448929i	0.940337	−	0.340244i	$-0.110510\pi$
$23$	91274.5	+	125629.i	0.326166	+	0.448929i	−0.614171	+	0.789173i	$0.710510\pi$
$24$	258196.	+	556026.i	0.778225	+	1.67591i
$25$	−310306.	−	237272.i	−0.794384	−	0.607416i
$26$	49010.1	−	123174.i	0.107249	−	0.269542i
$27$	816332.	+	1.12359e6i	1.53607	+	2.11422i
$28$	−512020.	−	938896.i	−0.833018	−	1.52751i
$29$	−331171.	+	1.01924e6i	−0.468231	+	1.44107i	0.386642	+	0.922230i	$0.373635\pi$
$29$	−331171.	+	1.01924e6i	−0.468231	+	1.44107i	−0.854873	+	0.518837i	$0.826365\pi$
$30$	1.38379e6	+	570318.i	1.70838	+	0.704096i
$31$	−485219.	+	157657.i	−0.525401	+	0.170713i	−0.559695	−	0.828699i	$-0.689082\pi$
$31$	−485219.	+	157657.i	−0.525401	+	0.170713i	0.0342940	+	0.999412i	$0.489082\pi$
$32$	−994469.	−	332479.i	−0.948400	−	0.317077i
$33$	−1.28256e6	−	3.94731e6i	−1.08149	−	3.32848i
$34$	−265996.	+	168173.i	−0.199048	+	0.125847i
$35$	−2.47307e6	−	837158.i	−1.64803	−	0.557873i
$36$	−4.02138e6	−	521893.i	−2.39422	−	0.310721i
$37$	−1.35566e6	−	984945.i	−0.723343	−	0.525539i	0.164108	−	0.986442i	$-0.447526\pi$
$37$	−1.35566e6	−	984945.i	−0.723343	−	0.525539i	−0.887450	+	0.460903i	$0.847526\pi$
$38$	58992.0	+	93306.2i	0.0282917	+	0.0447483i
$39$	728901.	+	1.00325e6i	0.315072	+	0.433660i
$40$	−2.33490e6	+	1.04968e6i	−0.912071	+	0.410031i
$41$	−738039.	−	536217.i	−0.261183	−	0.189760i	0.449486	−	0.893288i	$-0.351607\pi$
$41$	−738039.	−	536217.i	−0.261183	−	0.189760i	−0.710668	+	0.703527i	$0.751607\pi$
$42$	9.98310e6	+	645096.i	3.20825	+	0.207313i
$43$		−	1.05209e6i		−	0.307738i	−0.988091	−	0.153869i	$-0.950827\pi$
$43$		−	1.05209e6i		−	0.307738i	0.988091	−	0.153869i	$-0.0491733\pi$
$44$	6.41310e6	+	3.04441e6i	1.71103	+	0.812254i
$45$	−8.08003e6	+	5.72067e6i	−1.97044	+	1.39507i
$46$	1.58697e6	−	1.91170e6i	0.354436	−	0.426962i
$47$	3.21895e6	+	1.04590e6i	0.659664	+	0.214338i	0.619671	−	0.784862i	$-0.287266\pi$
$47$	3.21895e6	+	1.04590e6i	0.659664	+	0.214338i	0.0399937	+	0.999200i	$0.487266\pi$
$48$	7.60008e6	−	6.20091e6i	1.43170	−	1.16813i
$49$	−1.16865e7			−2.02722
$50$	−2.45212e6	+	5.74888e6i	−0.392339	+	0.919821i
$51$		−	2.94383e6i		−	0.435143i
$52$	−2.10342e6	−	272981.i	−0.287682	−	0.0373353i
$53$	−1.93443e6	+	5.95357e6i	−0.245160	+	0.754525i	0.750450	+	0.660927i	$0.229837\pi$
$53$	−1.93443e6	+	5.95357e6i	−0.245160	+	0.754525i	−0.995610	+	0.0935981i	$0.970163\pi$
$54$	1.41934e7	−	1.70977e7i	1.66921	−	2.01077i
$55$	1.65477e7	−	5.15357e6i	1.80837	−	0.563193i
$56$	−1.25328e7	+	1.16496e7i	−1.27437	+	1.18456i
$57$	−1.03264e6			−0.0978249
$58$	1.71114e7	+	1.10572e6i	1.51207	+	0.0977085i
$59$	−3.25429e6	+	4.47915e6i	−0.268565	+	0.369647i	−0.921904	−	0.387417i	$-0.873367\pi$
$59$	−3.25429e6	+	4.47915e6i	−0.268565	+	0.369647i	0.653340	+	0.757065i	$0.273367\pi$
$60$	3.37252e6	−	2.37086e7i	0.260225	−	1.82937i
$61$	−1.18607e6	+	861728.i	−0.0856623	+	0.0622373i	−0.629792	−	0.776764i	$-0.716860\pi$
$61$	−1.18607e6	+	861728.i	−0.0856623	+	0.0622373i	0.544130	+	0.839001i	$0.316860\pi$
$62$	4.36227e6	+	6.89969e6i	0.295220	+	0.466942i
$63$	−3.88951e7	+	5.35345e7i	−2.46906	+	3.39837i
$64$	−1.22391e6	+	1.67325e7i	−0.0729506	+	0.997336i
$65$	−4.22634e6	+	2.99226e6i	−0.236762	+	0.167628i
$66$	−5.61298e7	+	3.54875e7i	−2.95813	+	1.87025i
$67$	2.33934e7	−	7.60097e6i	1.16090	−	0.377198i	0.335659	−	0.941984i	$-0.391041\pi$
$67$	2.33934e7	−	7.60097e6i	1.16090	−	0.377198i	0.825238	+	0.564785i	$0.191041\pi$
$68$	3.65878e6	+	3.45927e6i	0.171120	+	0.161789i
$69$	7.18206e6	+	2.21041e7i	0.316849	+	0.975162i
$70$	−3.20397e6	+	4.16517e7i	−0.133443	+	1.73477i
$71$	1.58541e7	+	5.15130e6i	0.623889	+	0.202714i	0.603866	−	0.797086i	$-0.293626\pi$
$71$	1.58541e7	+	5.15130e6i	0.623889	+	0.202714i	0.0200229	+	0.999800i	$0.493626\pi$
$72$	7.80396e6	+	6.44106e7i	0.290392	+	2.39677i
$73$	−1.46316e7	+	1.06305e7i	−0.515229	+	0.374335i	−0.814803	−	0.579737i	$-0.803155\pi$
$73$	−1.46316e7	+	1.06305e7i	−0.515229	+	0.374335i	0.299575	+	0.954073i	$0.403155\pi$
$74$	−9.91209e6	+	2.49115e7i	−0.330551	+	0.830754i
$75$	−3.31966e7	−	4.81264e7i	−1.04918	−	1.52103i
$76$	1.21345e6	−	1.28343e6i	0.0363719	−	0.0384696i
$77$	9.37197e7	−	6.80913e7i	2.66605	−	1.93700i
$78$	1.26732e7	−	1.52665e7i	0.342381	−	0.412440i
$79$	−2.04259e7	−	6.63678e6i	−0.524413	−	0.170392i	0.0348343	−	0.999393i	$-0.488910\pi$
$79$	−2.04259e7	−	6.63678e6i	−0.524413	−	0.170392i	−0.559247	+	0.829001i	$0.688910\pi$
$80$	2.55036e7	+	3.20514e7i	0.622645	+	0.782504i
$81$	3.21188e7	+	9.88515e7i	0.746138	+	2.29638i
$82$	−5.39627e6	+	1.35621e7i	−0.119354	+	0.299966i
$83$	3.95465e7	−	1.28494e7i	0.833289	−	0.270752i	0.138859	−	0.990312i	$-0.455656\pi$
$83$	3.95465e7	−	1.28494e7i	0.833289	−	0.270752i	0.694430	+	0.719560i	$0.255656\pi$
$84$	−2.94589e7	−	1.57328e8i	−0.591696	−	3.16002i
$85$	1.22920e7	+	150494.i	0.235477	+	0.00288299i
$86$	−1.63117e7	+	4.15864e6i	−0.298199	+	0.0760252i
$87$	−9.42811e7	+	1.29767e8i	−1.64569	+	2.26510i
$88$	2.18514e7	−	1.11463e8i	0.364376	−	1.85866i
$89$	7.58380e6	−	5.50995e6i	0.120872	−	0.0878189i	−0.525707	−	0.850666i	$-0.676199\pi$
$89$	7.58380e6	−	5.50995e6i	0.120872	−	0.0878189i	0.646579	+	0.762847i	$0.276199\pi$
$90$	1.20632e8	+	1.02661e8i	1.83862	+	1.56472i
$91$	−2.03445e7	+	2.80018e7i	−0.296675	+	0.408338i
$92$	−3.59120e7	−	1.70480e7i	−0.501289	−	0.237971i
$93$	−7.63603e7			−1.02079
$94$	3.49207e6	−	5.40410e7i	0.0447271	−	0.692168i
$95$	52790.4	−	4.31181e6i	0.000648128	−	0.0529378i
$96$	−1.26180e8	−	9.33217e7i	−1.48562	−	1.09875i
$97$	−1.66217e7	+	5.11563e7i	−0.187754	+	0.577846i	−0.999985	−	0.00548913i	$-0.998253\pi$
$97$	−1.66217e7	+	5.11563e7i	−0.187754	+	0.577846i	0.812231	+	0.583336i	$0.198253\pi$
$98$	4.61936e7	+	1.81188e8i	0.500816	+	1.96438i
$99$		−	4.39259e8i		−	4.57278i
$100$	9.88235e7	+	1.52941e7i	0.988235	+	0.152941i
$101$	1.35620e8			1.30328			0.651639	−	0.758529i	$-0.274082\pi$
$101$	1.35620e8			1.30328			0.651639	+	0.758529i	$0.274082\pi$
$102$	−4.56413e7	+	1.16362e7i	−0.421655	+	0.107500i
$103$	6.12296e7	+	1.98947e7i	0.544017	+	0.176762i	0.568117	−	0.822948i	$-0.307672\pi$
$103$	6.12296e7	+	1.98947e7i	0.544017	+	0.176762i	−0.0241003	+	0.999710i	$0.507672\pi$
$104$	4.08194e6	+	3.36906e7i	0.0348926	+	0.287989i
$105$	−3.13310e8	−	2.33547e8i	−2.57761	−	1.92139i
$106$	9.99508e7	+	6.45870e6i	0.791704	+	0.0511590i
$107$			6.35959e7i			0.485170i	0.970130	+	0.242585i	$0.0779953\pi$
$107$			6.35959e7i			0.485170i	−0.970130	+	0.242585i	$0.922005\pi$
$108$	−3.21186e8	−	1.52473e8i	−2.36082	−	1.12072i
$109$	−1.08419e8	−	7.87707e7i	−0.768065	−	0.558032i	0.133309	−	0.991075i	$-0.457440\pi$
$109$	−1.08419e8	−	7.87707e7i	−0.768065	−	0.558032i	−0.901373	+	0.433043i	$0.857440\pi$
$110$	−1.45310e8	−	2.36186e8i	−0.992485	−	1.61318i
$111$	−1.47417e8	−	2.02902e8i	−0.971082	−	1.33658i
$112$	2.30155e8	+	1.48262e8i	1.46268	+	0.942232i
$113$	1.88520e8	+	1.36967e8i	1.15623	+	0.840047i	0.989296	−	0.145921i	$-0.0466147\pi$
$113$	1.88520e8	+	1.36967e8i	1.15623	+	0.840047i	0.166930	+	0.985969i	$0.446615\pi$
$114$	4.08174e6	+	1.60101e7i	0.0241672	+	0.0947927i
$115$	−9.26635e7	+	2.88589e7i	−0.529807	+	0.165002i
$116$	−5.04935e7	−	2.69667e8i	−0.278871	−	1.48934i
$117$	4.05562e7	+	1.24819e8i	0.216428	+	0.666098i
$118$	8.23084e7	+	3.27499e7i	0.424537	+	0.168920i
$119$	7.81442e7	−	2.53906e7i	0.389681	−	0.126615i
$120$	−3.80910e8	+	4.14259e7i	−1.83695	+	0.199778i
$121$	−1.71389e8	+	5.27481e8i	−0.799543	+	2.46074i
$122$	1.80485e7	+	1.49827e7i	0.0814707	+	0.0676316i
$123$	−8.02558e7	−	1.10463e8i	−0.350636	−	0.482609i
$124$	8.97303e7	−	9.49054e7i	0.379536	−	0.401425i
$125$	2.02650e8	−	1.36153e8i	0.830055	−	0.557682i
$126$	9.83743e8	+	3.91424e8i	3.90301	+	1.55298i
$127$	−7.00679e7	−	9.64402e7i	−0.269342	−	0.370718i	0.652825	−	0.757508i	$-0.273584\pi$
$127$	−7.00679e7	−	9.64402e7i	−0.269342	−	0.370718i	−0.922168	+	0.386791i	$0.873584\pi$
$128$	2.64260e8	−	4.71636e7i	0.984444	−	0.175698i
$129$	4.86601e7	−	1.49760e8i	0.175717	−	0.540802i
$130$	6.30977e7	+	5.36979e7i	0.220923	+	0.188011i
$131$	−2.10770e8	+	6.84834e7i	−0.715689	+	0.232541i	−0.644153	−	0.764897i	$-0.722790\pi$
$131$	−2.10770e8	+	6.84834e7i	−0.715689	+	0.232541i	−0.0715358	+	0.997438i	$0.522790\pi$
$132$	7.72067e8	+	7.29967e8i	2.54307	+	2.40440i
$133$	−8.90654e6	−	2.74115e7i	−0.0284644	−	0.0876045i
$134$	−2.10314e8	−	3.32648e8i	−0.652301	−	1.03173i
$135$	−8.28755e8	+	2.58106e8i	−2.49512	+	0.777074i
$136$	3.91706e7	−	7.03995e7i	0.114500	−	0.205785i
$137$	−1.18051e8	−	8.57693e7i	−0.335111	−	0.243472i	0.407485	−	0.913212i	$-0.366406\pi$
$137$	−1.18051e8	−	8.57693e7i	−0.335111	−	0.243472i	−0.742596	+	0.669739i	$0.766406\pi$
$138$	3.14315e8	−	1.98723e8i	0.866660	−	0.547938i
$139$	3.68673e8	+	5.07434e8i	0.987601	+	1.35932i	0.932632	+	0.360829i	$0.117506\pi$
$139$	3.68673e8	+	5.07434e8i	0.987601	+	1.35932i	0.0549692	+	0.998488i	$0.482494\pi$
$140$	6.58435e8	−	1.14963e8i	1.71396	−	0.299259i
$141$	4.09828e8	+	2.97758e8i	1.03687	+	0.753332i
$142$	1.71992e7	−	2.66164e8i	0.0423015	−	0.654631i
$143$		−	2.29759e8i		−	0.549451i
$144$	9.67779e8	−	3.75591e8i	2.25074	−	0.873504i
$145$	−5.37025e8	−	4.00307e8i	−1.21485	−	0.905569i
$146$	2.22650e8	+	1.84830e8i	0.490017	+	0.406781i
$147$	−1.66352e9	−	5.40510e8i	−3.56253	−	1.15753i
$148$	4.25409e8	+	5.52094e7i	0.886665	+	0.115071i
$149$	−3.65442e8			−0.741436			−0.370718	−	0.928746i	$-0.620888\pi$
$149$	−3.65442e8			−0.741436			−0.370718	+	0.928746i	$0.620888\pi$
$150$	−6.14937e8	+	7.04912e8i	−1.21469	+	1.39242i
$151$			5.48144e8i			1.05435i	0.849755	+	0.527177i	$0.176750\pi$
$151$			5.48144e8i			1.05435i	−0.849755	+	0.527177i	$0.823250\pi$
$152$	−2.46948e7	−	1.37403e7i	−0.0462627	−	0.0257408i
$153$	9.62766e7	−	2.96309e8i	0.175693	−	0.540728i
$154$	−1.42614e9	−	1.18389e9i	−2.53559	−	2.10488i
$155$	3.90368e6	−	3.18845e8i	0.00676312	−	0.552398i
$156$	−2.86786e8	−	1.36142e8i	−0.484239	−	0.229877i
$157$	−4.70404e8			−0.774234			−0.387117	−	0.922031i	$-0.626529\pi$
$157$	−4.70404e8			−0.774234			−0.387117	+	0.922031i	$0.626529\pi$
$158$	−2.21590e7	+	3.42918e8i	−0.0355567	+	0.550253i
$159$	−5.50714e8	+	7.57992e8i	−0.861663	+	1.18598i
$160$	3.96118e8	−	5.22099e8i	0.604428	−	0.796660i
$161$	−5.24811e8	+	3.81297e8i	−0.781087	+	0.567493i
$162$	1.40564e9	−	8.88705e8i	2.04087	−	1.29032i
$163$	8.09765e8	−	1.11455e9i	1.14712	−	1.57887i	0.396648	−	0.917971i	$-0.370173\pi$
$163$	8.09765e8	−	1.11455e9i	1.14712	−	1.57887i	0.750471	−	0.660903i	$-0.229827\pi$
$164$	2.31598e8	+	3.00567e7i	0.320155	+	0.0415495i
$165$	2.59384e9	+	3.17569e7i	3.49951	+	0.0428452i
$166$	−3.55535e8	−	5.62341e8i	−0.468220	−	0.740572i
$167$	9.76292e8	−	3.17216e8i	1.25520	−	0.407840i	0.395420	−	0.918500i	$-0.370599\pi$
$167$	9.76292e8	−	3.17216e8i	1.25520	−	0.407840i	0.859782	+	0.510660i	$0.170599\pi$
$168$	−2.32279e9	+	1.07861e9i	−2.91590	+	1.35403i
$169$	−2.30861e8	−	7.10518e8i	−0.283012	−	0.871020i
$170$	−4.62538e7	−	1.91171e8i	−0.0553799	−	0.228890i
$171$	−1.03940e8	−	3.37720e7i	−0.121562	−	0.0394977i
$172$	1.28952e8	+	2.36460e8i	0.147337	+	0.270174i
$173$	9.58230e7	−	6.96195e7i	0.106976	−	0.0777225i	−0.533011	−	0.846108i	$-0.678940\pi$
$173$	9.58230e7	−	6.96195e7i	0.106976	−	0.0777225i	0.639987	+	0.768386i	$0.278940\pi$
$174$	2.38458e9	+	9.48807e8i	2.60145	+	1.03510i
$175$	9.91198e8	−	1.29630e9i	1.05684	−	1.38214i
$176$	−1.81450e9	+	1.01796e8i	−1.89106	+	0.106092i
$177$	−6.70396e8	+	4.87071e8i	−0.683028	+	0.496249i
$178$	−1.15403e8	−	9.58004e7i	−0.114958	−	0.0954305i
$179$	1.72920e9	+	5.61853e8i	1.68436	+	0.547281i	0.985749	−	0.168223i	$-0.0538029\pi$
$179$	1.72920e9	+	5.61853e8i	1.68436	+	0.547281i	0.698609	+	0.715504i	$0.253803\pi$
$180$	1.11484e9	−	2.27607e9i	1.06199	−	2.16819i
$181$	9.27130e7	+	2.85341e8i	0.0863826	+	0.265858i	0.984912	−	0.173054i	$-0.0553637\pi$
$181$	9.27130e7	+	2.85341e8i	0.0863826	+	0.265858i	−0.898530	+	0.438913i	$0.855364\pi$
$182$	5.14557e8	+	2.04739e8i	0.468973	+	0.186601i
$183$	−2.08686e8	+	6.78063e7i	−0.186076	+	0.0604596i
$184$	−1.22363e8	+	6.24168e8i	−0.106753	+	0.544541i
$185$	8.54761e8	−	6.05172e8i	0.729722	−	0.516644i
$186$	3.01831e8	+	1.18389e9i	0.252181	+	0.989148i
$187$	−3.20593e8	+	4.41259e8i	−0.262173	+	0.360850i
$188$	−8.51658e8	+	1.59468e8i	−0.681764	+	0.127656i
$189$	−4.69375e9	+	3.41021e9i	−3.67852	+	2.67260i
$190$	−6.70593e7	+	1.62250e7i	−0.0514570	+	0.0124500i
$191$	−4.82523e8	+	6.64137e8i	−0.362564	+	0.499027i	−0.950861	−	0.309618i	$-0.899799\pi$
$191$	−4.82523e8	+	6.64137e8i	−0.362564	+	0.499027i	0.588297	+	0.808645i	$0.299799\pi$
$192$	−9.48108e8	+	2.32518e9i	−0.697674	+	1.71101i
$193$	5.46979e7			0.0394223			0.0197111	−	0.999806i	$-0.493725\pi$
$193$	5.46979e7			0.0394223			0.0197111	+	0.999806i	$0.493725\pi$
$194$	8.58832e8	+	5.54967e7i	0.606319	+	0.0391796i
$195$	−7.39993e8	+	2.30462e8i	−0.511787	+	0.159390i
$196$	2.62657e9	−	1.43238e9i	1.77977	−	0.970584i
$197$	6.22981e7	−	1.91734e8i	0.0413628	−	0.127302i	−0.928243	−	0.371975i	$-0.878681\pi$
$197$	6.22981e7	−	1.91734e8i	0.0413628	−	0.127302i	0.969606	+	0.244673i	$0.0786807\pi$
$198$	−6.81030e9	+	1.73627e9i	−4.43104	+	1.12968i
$199$		−	1.32211e9i		−	0.843052i	−0.906816	−	0.421526i	$-0.861495\pi$
$199$		−	1.32211e9i		−	0.843052i	0.906816	−	0.421526i	$-0.138505\pi$
$200$	−1.53502e8	−	1.59262e9i	−0.0959389	−	0.995387i
$201$	3.68148e9			2.25548
$202$	−5.36068e8	−	2.10265e9i	−0.321969	−	1.26288i
$203$	−4.25785e9	−	1.38346e9i	−2.50730	−	0.814671i
$204$	3.60815e8	+	6.61631e8i	0.208336	+	0.382028i
$205$	4.65343e8	−	3.29464e8i	0.263486	−	0.186549i
$206$	6.64246e7	−	1.02795e9i	0.0368859	−	0.570823i
$207$			2.45976e9i			1.33971i
$208$	5.06207e8	−	1.96457e8i	0.270442	−	0.104957i
$209$	1.54785e8	+	1.12458e8i	0.0811230	+	0.0589393i
$210$	−2.38249e9	+	5.78073e9i	−1.22505	+	2.97239i
$211$	4.80191e8	+	6.60926e8i	0.242261	+	0.333444i	0.912782	−	0.408447i	$-0.133929\pi$
$211$	4.80191e8	+	6.60926e8i	0.242261	+	0.333444i	−0.670521	+	0.741890i	$0.733929\pi$
$212$	−2.94942e8	−	1.57517e9i	−0.146014	−	0.779803i
$213$	2.01850e9	+	1.46652e9i	0.980640	+	0.712477i
$214$	9.85994e8	−	2.51377e8i	0.470131	−	0.119859i
$215$	6.22841e8	+	2.10838e8i	0.291490	+	0.0986720i
$216$	−1.09438e9	+	5.58238e9i	−0.502753	+	2.56451i
$217$	−6.58609e8	−	2.02699e9i	−0.297022	−	0.914140i
$218$	−7.92717e8	+	1.99229e9i	−0.350988	+	0.882117i
$219$	−2.57440e9	+	8.36473e8i	−1.11918	+	0.363643i
$220$	−3.08747e9	+	3.18647e9i	−1.31799	+	1.36025i
$221$	5.03585e7	−	1.54987e8i	0.0211107	−	0.0649722i
$222$	−2.56311e9	+	3.08758e9i	−1.05525	+	1.27118i
$223$	4.38932e8	+	6.04138e8i	0.177491	+	0.244296i	0.888488	−	0.458899i	$-0.151756\pi$
$223$	4.38932e8	+	6.04138e8i	0.177491	+	0.244296i	−0.710997	+	0.703195i	$0.751756\pi$
$224$	1.38892e9	−	4.15437e9i	0.551679	−	1.65011i
$225$	−1.76742e9	−	5.92980e9i	−0.689621	−	2.31372i
$226$	1.37839e9	−	3.46421e9i	0.528369	−	1.32792i
$227$	−1.13066e9	−	1.55623e9i	−0.425824	−	0.586097i	0.541164	−	0.840917i	$-0.317984\pi$
$227$	−1.13066e9	−	1.55623e9i	−0.425824	−	0.586097i	−0.966988	+	0.254820i	$0.917984\pi$
$228$	2.32088e8	−	1.26567e8i	0.0858841	−	0.0468362i
$229$	−9.85356e8	+	3.03261e9i	−0.358304	+	1.10275i	0.595765	+	0.803158i	$0.296849\pi$
$229$	−9.85356e8	+	3.03261e9i	−0.358304	+	1.10275i	−0.954069	+	0.299587i	$0.903151\pi$
$230$	8.13704e8	+	1.32259e9i	0.290774	+	0.472622i
$231$	1.64898e10	−	5.35786e9i	5.79119	−	1.88167i
$232$	−3.98134e9	+	1.84877e9i	−1.37429	+	0.638163i
$233$	1.54091e9	+	4.74243e9i	0.522822	+	1.60908i	0.768584	+	0.639749i	$0.220962\pi$
$233$	1.54091e9	+	4.74243e9i	0.522822	+	1.60908i	−0.245762	+	0.969330i	$0.579038\pi$
$234$	1.77490e9	−	1.12216e9i	0.591984	−	0.374277i
$235$	−1.26425e9	+	1.69603e9i	−0.414534	+	0.556111i
$236$	1.82414e8	−	1.40557e9i	0.0588043	−	0.453109i
$237$	−2.60057e9	−	1.88943e9i	−0.824282	−	0.598876i
$238$	−7.02540e8	−	1.11119e9i	−0.218959	−	0.346323i
$239$	2.72877e9	+	3.75583e9i	0.836325	+	1.15110i	0.986712	+	0.162476i	$0.0519480\pi$
$239$	2.72877e9	+	3.75583e9i	0.836325	+	1.15110i	−0.150387	+	0.988627i	$0.548052\pi$
$240$	2.14791e9	+	5.74191e9i	0.647396	+	1.73066i
$241$	−7.33588e7	−	5.32983e7i	−0.0217462	−	0.0157996i	0.576859	−	0.816844i	$-0.304278\pi$
$241$	−7.33588e7	−	5.32983e7i	−0.0217462	−	0.0157996i	−0.598605	+	0.801044i	$0.704278\pi$
$242$	8.85556e9	+	5.72236e8i	2.58199	+	0.166845i
$243$			6.44444e9i			1.84825i
$244$	1.60952e8	−	3.39047e8i	0.0454084	−	0.0956535i
$245$	2.34196e9	−	6.91843e9i	0.650001	−	1.92019i
$246$	−1.39539e9	+	1.68092e9i	−0.381027	+	0.458994i
$247$	−5.43667e7	−	1.76648e7i	−0.0146065	−	0.00474593i
$248$	−1.82610e9	−	1.01605e9i	−0.482745	−	0.268601i
$249$	6.22355e9			1.61898
$250$	−2.91194e9	−	2.60372e9i	−0.745457	−	0.666553i
$251$			3.44105e9i			0.866953i	0.901165	+	0.433476i	$0.142713\pi$
$251$			3.44105e9i			0.866953i	−0.901165	+	0.433476i	$0.857287\pi$
$252$	2.18019e9	−	1.67992e10i	0.540621	−	4.16569i
$253$	1.33068e9	−	4.09540e9i	0.324781	−	0.999572i
$254$	−1.21826e9	+	1.46754e9i	−0.292687	+	0.352578i
$255$	1.74275e9	+	5.89938e8i	0.412168	+	0.139523i
$256$	−1.77577e9	−	3.91067e9i	−0.413455	−	0.910525i
$257$	−2.80618e9			−0.643254			−0.321627	−	0.946866i	$-0.604230\pi$
$257$	−2.80618e9			−0.643254			−0.321627	+	0.946866i	$0.604230\pi$
$258$	−2.51423e9	−	1.62467e8i	−0.567449	−	0.0366679i
$259$	4.11459e9	−	5.66324e9i	0.914381	−	1.25854i
$260$	5.83127e8	−	1.19052e9i	0.127606	−	0.260522i
$261$	−1.37338e10	+	9.97816e9i	−2.95956	+	2.15025i
$262$	1.89489e9	+	2.99710e9i	0.402141	+	0.636057i
$263$	−2.83877e9	+	3.90723e9i	−0.593345	+	0.816669i	−0.995079	−	0.0990875i	$-0.968408\pi$
$263$	−2.83877e9	+	3.90723e9i	−0.593345	+	0.816669i	0.401734	+	0.915756i	$0.368408\pi$
$264$	8.26568e9	−	1.48555e10i	1.70162	−	3.05825i
$265$	−3.13686e9	−	2.33827e9i	−0.636081	−	0.474145i
$266$	−3.89785e8	+	2.46438e8i	−0.0778571	+	0.0492245i
$267$	1.33436e9	−	4.33558e8i	0.262559	−	0.0853105i
$268$	−4.32608e9	+	4.57558e9i	−0.838601	+	0.886966i
$269$	−1.90085e8	−	5.85022e8i	−0.0363027	−	0.111728i	0.931263	−	0.364348i	$-0.118708\pi$
$269$	−1.90085e8	−	5.85022e8i	−0.0363027	−	0.111728i	−0.967566	+	0.252619i	$0.918708\pi$
$270$	7.27753e9	+	1.18289e10i	1.36940	+	2.22581i
$271$	−6.42967e9	−	2.08913e9i	−1.19210	−	0.387336i	−0.355249	−	0.934772i	$-0.615604\pi$
$271$	−6.42967e9	−	2.08913e9i	−1.19210	−	0.387336i	−0.836848	+	0.547436i	$0.815604\pi$
$272$	−1.24631e9	−	3.29033e8i	−0.227693	−	0.0601123i
$273$	−4.19104e9	+	3.04497e9i	−0.754520	+	0.548191i
$274$	−8.63148e8	+	2.16930e9i	−0.153138	+	0.384873i
$275$	−2.65203e8	+	1.08290e10i	−0.0463712	+	1.89347i
$276$	−4.32341e9	−	4.08766e9i	−0.745058	−	0.704431i
$277$	−2.37772e9	+	1.72751e9i	−0.403869	+	0.293428i	−0.771115	−	0.636696i	$-0.780301\pi$
$277$	−2.37772e9	+	1.72751e9i	−0.403869	+	0.293428i	0.367246	+	0.930124i	$0.380301\pi$
$278$	6.41003e9	−	7.72167e9i	1.07320	−	1.29280i
$279$	−7.68598e9	−	2.49733e9i	−1.26848	−	0.412153i
$280$	−4.38502e9	−	9.75400e9i	−0.713410	−	1.58690i
$281$	1.80996e9	+	5.57049e9i	0.290298	+	0.893445i	0.984760	+	0.173916i	$0.0556422\pi$
$281$	1.80996e9	+	5.57049e9i	0.290298	+	0.893445i	−0.694462	+	0.719529i	$0.744358\pi$
$282$	2.99651e9	−	7.53095e9i	0.473827	−	1.19084i
$283$	6.65017e9	−	2.16077e9i	1.03678	−	0.336870i	0.259313	−	0.965793i	$-0.416504\pi$
$283$	6.65017e9	−	2.16077e9i	1.03678	−	0.336870i	0.777468	+	0.628923i	$0.216504\pi$
$284$	−4.19461e9	+	7.85417e8i	−0.644790	+	0.120733i
$285$	2.06939e8	−	6.11324e8i	0.0313663	−	0.0926599i
$286$	−3.56220e9	+	9.08176e8i	−0.532420	+	0.135739i
$287$	2.24003e9	−	3.08314e9i	0.330162	−	0.454429i
$288$	−9.64855e9	−	1.35199e10i	−1.40246	−	1.96518i
$289$	5.33053e9	−	3.87286e9i	0.764151	−	0.555188i
$290$	−4.08367e9	+	9.90838e9i	−0.577377	+	1.40091i
$291$	−4.73203e9	+	6.51308e9i	−0.659896	+	0.908270i
$292$	1.98553e9	−	4.18256e9i	0.273115	−	0.575322i
$293$	1.02824e10			1.39516			0.697579	−	0.716508i	$-0.254261\pi$
$293$	1.02824e10			1.39516			0.697579	+	0.716508i	$0.254261\pi$
$294$	−1.80466e9	+	2.79278e10i	−0.241549	+	3.73807i
$295$	−1.99951e9	−	2.82416e9i	−0.264019	−	0.372907i
$296$	−8.25556e8	−	6.81379e9i	−0.107542	−	0.887610i
$297$	1.19012e10	−	3.66280e10i	1.52955	−	4.70747i
$298$	1.44449e9	+	5.66584e9i	0.183168	+	0.718454i
$299$			1.28660e9i			0.160976i
$300$	1.33597e10	+	6.74770e9i	1.64934	+	0.833049i
$301$	4.39510e9			0.535430
$302$	8.49845e9	−	2.16666e9i	1.02167	−	0.260474i
$303$	1.93048e10	+	6.27250e9i	2.29031	+	0.744167i
$304$	−1.15418e8	+	4.37181e8i	−0.0135139	+	0.0511879i
$305$	−2.72459e8	−	8.74842e8i	−0.0314848	−	0.101095i
$306$	−4.97454e9	−	3.21449e8i	−0.567372	−	0.0366629i
$307$			3.08353e9i			0.347132i	0.984822	+	0.173566i	$0.0555290\pi$
$307$			3.08353e9i			0.347132i	−0.984822	+	0.173566i	$0.944471\pi$
$308$	−1.27179e10	+	2.67906e10i	−1.41323	+	2.97700i
$309$	7.79558e9	+	5.66382e9i	0.855095	+	0.621263i
$310$	−4.95882e9	+	1.19978e9i	−0.536947	+	0.129914i
$311$	−4.70271e9	−	6.47273e9i	−0.502698	−	0.691904i	0.479969	−	0.877286i	$-0.340648\pi$
$311$	−4.70271e9	−	6.47273e9i	−0.502698	−	0.691904i	−0.982667	+	0.185381i	$0.940648\pi$
$312$	−9.77171e8	+	4.98449e9i	−0.103122	+	0.526020i
$313$	−8.49245e9	−	6.17013e9i	−0.884822	−	0.642861i	0.0497010	−	0.998764i	$-0.484173\pi$
$313$	−8.49245e9	−	6.17013e9i	−0.884822	−	0.642861i	−0.934523	+	0.355904i	$0.884173\pi$
$314$	1.85938e9	+	7.29317e9i	0.191271	+	0.750236i
$315$	−2.38980e10	−	3.37541e10i	−2.42727	−	3.42835i
$316$	5.40421e9	−	1.01191e9i	0.541981	−	0.101483i
$317$	5.01238e9	+	1.54265e10i	0.496372	+	1.52768i	0.814808	+	0.579731i	$0.196842\pi$
$317$	5.01238e9	+	1.54265e10i	0.496372	+	1.52768i	−0.318436	+	0.947944i	$0.603158\pi$
$318$	1.39288e10	+	5.54216e9i	1.36209	+	0.541964i
$319$	2.82641e10	−	9.18357e9i	2.72943	−	0.886847i
$320$	−9.66040e9	−	4.07772e9i	−0.921288	−	0.388882i
$321$	−2.94135e9	+	9.05255e9i	−0.277030	+	0.852611i
$322$	7.98609e9	+	6.62953e9i	0.742866	+	0.616679i
$323$	7.97642e7	+	1.09786e8i	0.00732821	+	0.0100864i
$324$	−1.93347e10	−	1.82804e10i	−1.75451	−	1.65884i
$325$	−9.24470e8	−	3.10164e9i	−0.0828627	−	0.278009i
$326$	−2.04808e10	−	8.14915e9i	−1.81333	−	0.721509i
$327$	−1.17896e10	−	1.62271e10i	−1.03112	−	1.41922i
$328$	−4.49444e8	−	3.70952e9i	−0.0388311	−	0.320496i
$329$	−4.36923e9	+	1.34471e10i	−0.372925	+	1.14774i
$330$	−9.76037e9	−	4.03405e10i	−0.823021	−	3.40162i
$331$	1.13910e10	−	3.70116e9i	0.948964	−	0.308337i	0.206670	−	0.978411i	$-0.433737\pi$
$331$	1.13910e10	−	3.70116e9i	0.948964	−	0.308337i	0.742295	+	0.670074i	$0.233737\pi$
$332$	−7.31324e9	+	7.73502e9i	−0.601946	+	0.636662i
$333$	−8.20233e9	−	2.52442e10i	−0.667053	−	2.05298i
$334$	−8.77716e9	−	1.38826e10i	−0.705291	−	1.11554i
$335$	−1.88204e8	+	1.53721e10i	−0.0149434	+	1.22055i
$336$	2.59042e10	+	3.17492e10i	2.03242	+	2.49101i
$337$	1.16312e10	+	8.45054e9i	0.901787	+	0.655186i	0.938924	−	0.344124i	$-0.111824\pi$
$337$	1.16312e10	+	8.45054e9i	0.901787	+	0.655186i	−0.0371375	+	0.999310i	$0.511824\pi$
$338$	−1.01034e10	+	6.38777e9i	−0.774105	+	0.489421i
$339$	2.05000e10	+	2.82158e10i	1.55223	+	2.13645i
$340$	−2.78110e9	+	1.47277e9i	−0.208114	+	0.110210i
$341$	1.14459e10	+	8.31590e9i	0.846507	+	0.615024i
$342$	−1.12758e8	+	1.74498e9i	−0.00824222	+	0.127551i
$343$		−	2.47378e10i		−	1.78725i
$344$	3.15638e9	−	2.93394e9i	0.225401	−	0.209516i
$345$	−1.45249e10	−	1.77832e8i	−1.02527	−	0.0125526i
$346$	−1.45815e9	−	1.21046e9i	−0.101741	−	0.0844590i
$347$	−1.19116e10	−	3.87032e9i	−0.821586	−	0.266949i	−0.132089	−	0.991238i	$-0.542168\pi$
$347$	−1.19116e10	−	3.87032e9i	−0.821586	−	0.266949i	−0.689497	+	0.724289i	$0.742168\pi$
$348$	5.28476e9	−	4.07211e10i	0.360337	−	2.77653i
$349$	1.60783e10			1.08377			0.541886	−	0.840452i	$-0.317711\pi$
$349$	1.60783e10			1.08377			0.541886	+	0.840452i	$0.317711\pi$
$350$	−2.40158e10	−	1.02437e10i	−1.60039	−	0.682628i
$351$			1.15070e10i			0.758112i
$352$	8.75048e9	+	2.77297e10i	0.569982	+	1.80624i
$353$	−6.31546e9	+	1.94370e10i	−0.406730	+	1.25179i	0.512713	+	0.858560i	$0.328641\pi$
$353$	−6.31546e9	+	1.94370e10i	−0.406730	+	1.25179i	−0.919442	+	0.393225i	$0.871359\pi$
$354$	1.02015e10	+	8.46861e9i	0.649606	+	0.539261i
$355$	−6.22670e9	+	8.35332e9i	−0.392053	+	0.525952i
$356$	−1.02914e9	+	2.16789e9i	−0.0640727	+	0.134970i
$357$	1.22978e10			0.757101
$358$	1.87592e9	−	2.90305e10i	0.114204	−	1.76735i
$359$	1.49687e10	−	2.06026e10i	0.901167	−	1.24035i	−0.0689268	−	0.997622i	$-0.521957\pi$
$359$	1.49687e10	−	2.06026e10i	0.901167	−	1.24035i	0.970094	−	0.242729i	$-0.0780425\pi$
$360$	−3.96950e10	−	8.28780e9i	−2.36334	−	0.493434i
$361$	−1.37015e10	+	9.95471e9i	−0.806749	+	0.586138i
$362$	4.05748e9	−	2.56531e9i	0.236277	−	0.149384i
$363$	−4.87928e10	+	6.71575e10i	−2.81015	+	3.86784i
$364$	1.14037e9	−	8.78700e9i	0.0649594	−	0.500536i
$365$	−3.36111e9	−	1.07922e10i	−0.189370	−	0.608051i
$366$	1.87615e9	+	2.96746e9i	0.104555	+	0.165372i
$367$	−2.08854e10	+	6.78607e9i	−1.15127	+	0.374071i	−0.821622	−	0.570032i	$-0.806931\pi$
$367$	−2.08854e10	+	6.78607e9i	−1.15127	+	0.374071i	−0.329650	+	0.944103i	$0.606931\pi$
$368$	1.01608e10	−	5.70037e8i	0.554035	−	0.0310822i
$369$	−4.46546e9	−	1.37433e10i	−0.240858	−	0.741284i
$370$	−1.27613e10	−	1.08602e10i	−0.680905	−	0.579469i
$371$	−2.48709e10	−	8.08104e9i	−1.31279	−	0.426552i
$372$	1.71621e10	−	9.35923e9i	0.896188	−	0.488729i
$373$	2.41862e10	−	1.75723e10i	1.24949	−	0.907808i	0.251299	−	0.967910i	$-0.419142\pi$
$373$	2.41862e10	−	1.75723e10i	1.24949	−	0.907808i	0.998192	+	0.0601012i	$0.0191423\pi$
$374$	8.10852e9	+	3.22632e9i	0.414434	+	0.164900i
$375$	3.51434e10	−	1.00080e10i	1.77713	−	0.506082i
$376$	5.83878e9	+	1.25738e10i	0.292126	+	0.629095i
$377$	−7.18359e9	+	5.21918e9i	−0.355612	+	0.258367i
$378$	7.14252e10	+	5.92926e10i	3.49852	+	2.90424i
$379$	−2.01187e10	−	6.53696e9i	−0.975087	−	0.316825i	−0.222219	−	0.974997i	$-0.571330\pi$
$379$	−2.01187e10	−	6.53696e9i	−0.975087	−	0.316825i	−0.752868	+	0.658172i	$0.771330\pi$
$380$	5.16620e8	+	9.75559e8i	0.0247763	+	0.0467863i
$381$	−5.51339e9	−	1.69685e10i	−0.261649	−	0.805273i
$382$	1.22041e10	+	4.85592e9i	0.573129	+	0.228044i
$383$	2.76479e10	−	8.98336e9i	1.28489	−	0.417488i	0.414593	−	0.910007i	$-0.363924\pi$
$383$	2.76479e10	−	8.98336e9i	1.28489	−	0.417488i	0.870302	+	0.492519i	$0.163924\pi$
$384$	3.97974e10	+	5.50870e9i	1.83033	+	0.253352i
$385$	2.15289e10	+	6.91276e10i	0.979895	+	3.14636i
$386$	−2.16206e8	−	8.48040e8i	−0.00973910	−	0.0382003i
$387$	9.79569e9	−	1.34826e10i	0.436708	−	0.601077i
$388$	−2.53431e9	−	1.35347e10i	−0.111823	−	0.597205i
$389$	−2.53293e9	+	1.84028e9i	−0.110618	+	0.0803686i	−0.641719	−	0.766940i	$-0.721778\pi$
$389$	−2.53293e9	+	1.84028e9i	−0.110618	+	0.0803686i	0.531101	+	0.847308i	$0.321778\pi$
$390$	6.49809e9	+	1.05619e10i	0.280884	+	0.456547i
$391$	1.79525e9	−	2.47096e9i	0.0768102	−	0.105720i
$392$	−3.25898e10	−	3.50606e10i	−1.38018	−	1.48483i
$393$	−3.31695e10			−1.39049
$394$	−3.21890e9	−	2.08002e8i	−0.133574	−	0.00863141i
$395$	8.02230e9	−	1.07622e10i	0.329542	−	0.442091i
$396$	5.38386e10	+	9.87243e10i	2.18934	+	4.01461i
$397$	8.74466e9	−	2.69133e10i	0.352031	−	1.08344i	−0.605680	−	0.795708i	$-0.707099\pi$
$397$	8.74466e9	−	2.69133e10i	0.352031	−	1.08344i	0.957711	−	0.287732i	$-0.0929012\pi$
$398$	−2.04980e10	+	5.22593e9i	−0.816921	+	0.208272i
$399$		−	4.31383e9i		−	0.170205i
$400$	−2.40853e10	+	8.67510e9i	−0.940833	+	0.338871i
$401$	4.77052e9			0.184497			0.0922483	−	0.995736i	$-0.470595\pi$
$401$	4.77052e9			0.184497			0.0922483	+	0.995736i	$0.470595\pi$
$402$	−1.45519e10	−	5.70779e10i	−0.557205	−	2.18557i
$403$	−4.02024e9	−	1.30625e9i	−0.152416	−	0.0495230i
$404$	−3.04808e10	+	1.66224e10i	−1.14420	+	0.623978i
$405$	−6.49568e10	−	7.95279e8i	−2.41437	−	0.0295596i
$406$	−4.61911e9	+	7.14824e10i	−0.170002	+	2.63084i
$407$			4.64678e10i			1.69346i
$408$	8.83176e9	−	8.20935e9i	0.318718	−	0.296257i
$409$	−9.21280e9	−	6.69349e9i	−0.329229	−	0.239199i	0.410874	−	0.911692i	$-0.365224\pi$
$409$	−9.21280e9	−	6.69349e9i	−0.329229	−	0.239199i	−0.740104	+	0.672493i	$0.765224\pi$
$410$	−6.94740e9	−	5.91243e9i	−0.245859	−	0.209233i
$411$	−1.28371e10	−	1.76688e10i	−0.449884	−	0.619213i
$412$	−1.61999e10	+	3.03334e9i	−0.562242	+	0.105277i
$413$	−1.87115e10	−	1.35947e10i	−0.643146	−	0.467273i
$414$	3.81363e10	−	9.72276e9i	1.29819	−	0.330970i
$415$	−3.18159e8	+	2.59866e10i	−0.0107263	+	0.876107i
$416$	−5.04677e9	−	7.07172e9i	−0.168516	−	0.236130i
$417$	2.90095e10	+	8.92821e10i	0.959393	+	2.95271i
$418$	1.13173e9	−	2.84432e9i	0.0370714	−	0.0931693i
$419$	−5.51361e10	+	1.79148e10i	−1.78887	+	0.581240i	−0.999467	−	0.0326305i	$-0.989612\pi$
$419$	−5.51361e10	+	1.79148e10i	−1.78887	+	0.581240i	−0.789406	+	0.613871i	$0.789612\pi$
$420$	9.90421e10	+	1.40886e10i	3.18290	+	0.452764i
$421$	−4.96727e9	+	1.52877e10i	−0.158121	+	0.486646i	−0.998464	−	0.0554092i	$-0.982354\pi$
$421$	−4.96727e9	+	1.52877e10i	−0.158121	+	0.486646i	0.840343	+	0.542055i	$0.182354\pi$
$422$	8.34897e9	−	1.00574e10i	0.263259	−	0.317128i
$423$	3.15129e10	+	4.33738e10i	0.984299	+	1.35477i
$424$	−2.32557e10	+	1.07990e10i	−0.719560	+	0.334135i
$425$	−2.55239e9	+	7.24675e9i	−0.0782334	+	0.222120i
$426$	1.47585e10	−	3.70917e10i	0.448130	−	1.12626i
$427$	−3.59985e9	−	4.95477e9i	−0.108286	−	0.149043i
$428$	−7.79474e9	−	1.42933e10i	−0.232288	−	0.425948i
$429$	1.06265e10	−	3.27051e10i	0.313734	−	0.965575i
$430$	8.06917e8	−	1.04899e10i	0.0236023	−	0.306831i
$431$	3.50418e10	−	1.13858e10i	1.01549	−	0.329954i	0.246454	−	0.969154i	$-0.420735\pi$
$431$	3.50418e10	−	1.13858e10i	1.01549	−	0.329954i	0.769040	+	0.639200i	$0.220735\pi$
$432$	9.08753e10	−	5.09824e9i	2.60922	−	0.146381i
$433$	4.76523e8	+	1.46659e9i	0.0135560	+	0.0417211i	0.957606	−	0.288082i	$-0.0930176\pi$
$433$	4.76523e8	+	1.46659e9i	0.0135560	+	0.0417211i	−0.944050	+	0.329803i	$0.893018\pi$
$434$	−2.88233e10	+	1.82233e10i	−0.812428	+	0.513650i
$435$	−5.79284e10	−	8.18196e10i	−1.61784	−	2.28507i
$436$	3.40220e10	+	4.41535e9i	0.941485	+	0.122185i
$437$	−8.66765e8	−	6.29741e8i	−0.0237671	−	0.0172678i
$438$	2.31446e10	+	3.66073e10i	0.628860	+	0.994652i
$439$	−2.37359e10	−	3.26696e10i	−0.639068	−	0.879601i	0.359498	−	0.933146i	$-0.382948\pi$
$439$	−2.37359e10	−	3.26696e10i	−0.639068	−	0.879601i	−0.998565	+	0.0535449i	$0.982948\pi$
$440$	6.16071e10	+	3.52730e10i	1.64369	+	0.941091i
$441$	−1.49763e11	−	1.08809e11i	−3.95959	−	2.87681i
$442$	−2.60199e9	−	1.68137e8i	−0.0681736	−	0.00440530i
$443$			2.19693e10i			0.570430i	0.958464	+	0.285215i	$0.0920649\pi$
$443$			2.19693e10i			0.570430i	−0.958464	+	0.285215i	$0.907935\pi$
$444$	5.80014e10	+	2.75342e10i	1.49247	+	0.708502i
$445$	1.74212e9	+	5.59381e9i	0.0444261	+	0.142649i
$446$	7.63161e9	−	9.19322e9i	0.192875	−	0.232342i
$447$	−5.20189e10	−	1.69020e10i	−1.30296	−	0.423357i
$448$	−6.98997e10	−	5.11285e9i	−1.73525	−	0.126926i
$449$	9.37514e9			0.230671			0.115335	−	0.993327i	$-0.463206\pi$
$449$	9.37514e9			0.230671			0.115335	+	0.993327i	$0.463206\pi$
$450$	−8.49498e10	+	5.08411e10i	−2.07163	+	1.23984i
$451$			2.52977e10i			0.611470i
$452$	−5.91578e10	−	7.67747e9i	−1.41729	−	0.183935i
$453$	−2.53520e10	+	7.80255e10i	−0.602033	+	1.85287i
$454$	−1.96586e10	+	2.36812e10i	−0.462732	+	0.557418i
$455$	−1.25001e10	−	1.76555e10i	−0.291654	−	0.411939i
$456$	−2.87969e9	−	3.09801e9i	−0.0666018	−	0.0716513i
$457$	4.80200e10			1.10092			0.550462	−	0.834860i	$-0.314452\pi$
$457$	4.80200e10			1.10092			0.550462	+	0.834860i	$0.314452\pi$
$458$	5.09127e10	+	3.28992e9i	1.15708	+	0.0747693i
$459$	1.60562e10	−	2.20995e10i	0.361737	−	0.497888i
$460$	1.72892e10	−	1.78436e10i	0.386138	−	0.398520i
$461$	2.05201e10	−	1.49087e10i	0.454335	−	0.330094i	−0.336970	−	0.941515i	$-0.609402\pi$
$461$	2.05201e10	−	1.49087e10i	0.454335	−	0.330094i	0.791305	+	0.611422i	$0.209402\pi$
$462$	−1.48248e11	−	2.34481e11i	−3.25403	−	5.14682i
$463$	−2.48921e10	+	3.42610e10i	−0.541674	+	0.745550i	−0.988853	−	0.148894i	$-0.952429\pi$
$463$	−2.48921e10	+	3.42610e10i	−0.541674	+	0.745550i	0.447179	+	0.894444i	$0.352429\pi$
$464$	4.44007e10	+	5.44192e10i	0.957894	+	1.17403i
$465$	1.53025e10	−	4.52054e10i	0.327302	−	0.966893i
$466$	6.74362e10	−	4.26359e10i	1.43004	−	0.904132i
$467$	3.73762e10	−	1.21443e10i	0.785827	−	0.255331i	0.111501	−	0.993764i	$-0.464434\pi$
$467$	3.73762e10	−	1.21443e10i	0.785827	−	0.255331i	0.674326	+	0.738434i	$0.264434\pi$
$468$	−2.44138e10	−	2.30825e10i	−0.508923	−	0.481171i
$469$	3.17529e10	+	9.77253e10i	0.656284	+	2.01983i
$470$	3.12925e10	+	1.28970e10i	0.641282	+	0.264300i
$471$	−6.69596e10	−	2.17565e10i	−1.36060	−	0.442085i
$472$	−2.25130e10	+	2.72767e9i	−0.453592	+	0.0549570i
$473$	−2.36032e10	+	1.71487e10i	−0.471549	+	0.342600i
$474$	−1.90144e10	+	4.77878e10i	−0.376678	+	0.946682i
$475$	2.54202e9	+	8.95331e8i	0.0499350	+	0.0175877i
$476$	−1.44510e10	+	1.52845e10i	−0.281495	+	0.297730i
$477$	−8.02214e10	+	5.82843e10i	−1.54959	+	1.12584i
$478$	4.74445e10	−	5.71528e10i	0.908813	−	1.09478i
$479$	4.28525e10	+	1.39236e10i	0.814018	+	0.264490i	0.686298	−	0.727320i	$-0.259234\pi$
$479$	4.28525e10	+	1.39236e10i	0.814018	+	0.264490i	0.127719	+	0.991810i	$0.459234\pi$
$480$	8.05329e10	−	5.59975e10i	1.51708	−	1.05488i
$481$	−4.29032e9	−	1.32042e10i	−0.0801510	−	0.246679i
$482$	−5.36373e8	+	1.34803e9i	−0.00993753	+	0.0249754i
$483$	−9.23395e10	+	3.00029e10i	−1.69668	+	0.551283i
$484$	−2.61316e10	−	1.39559e11i	−0.476196	−	2.54318i
$485$	−2.69537e10	−	2.00917e10i	−0.487137	−	0.363120i
$486$	9.99150e10	−	2.54731e10i	1.79096	−	0.456601i
$487$	2.01888e10	−	2.77875e10i	0.358918	−	0.494008i	−0.590929	−	0.806724i	$-0.701239\pi$
$487$	2.01888e10	−	2.77875e10i	0.358918	−	0.494008i	0.949847	+	0.312715i	$0.101239\pi$
$488$	−5.89281e9	−	1.15524e9i	−0.103907	−	0.0203701i
$489$	1.66815e11	−	1.21198e11i	2.91742	−	2.11963i
$490$	−1.16521e11	−	8.96313e9i	−2.02125	−	0.155480i
$491$	4.21344e10	−	5.79930e10i	0.724955	−	0.997815i	−0.274390	−	0.961619i	$-0.588476\pi$
$491$	4.21344e10	−	5.79930e10i	0.724955	−	0.997815i	0.999345	−	0.0361962i	$-0.0115241\pi$
$492$	3.15767e10	+	1.49900e10i	0.538898	+	0.255824i
$493$	2.10788e10			0.356828
$494$	−5.89794e7	+	9.12728e8i	−0.000990359	+	0.0153262i
$495$	2.60042e11	+	8.80267e10i	4.33134	+	1.46620i
$496$	−8.53481e9	+	3.23281e10i	−0.141016	+	0.534139i
$497$	−2.15194e10	+	6.62300e10i	−0.352700	+	1.08550i
$498$	−2.46000e10	−	9.64902e10i	−0.399961	−	1.56879i
$499$		−	6.51936e10i		−	1.05149i	−0.850644	−	0.525743i	$-0.823788\pi$
$499$		−	6.51936e10i		−	1.05149i	0.850644	−	0.525743i	$-0.176212\pi$
$500$	−2.88582e10	+	5.54388e10i	−0.461731	+	0.887020i
$501$	1.53642e11			2.43870
$502$	5.33502e10	−	1.36015e10i	0.840081	−	0.214177i
$503$	−9.87585e10	−	3.20886e10i	−1.54278	−	0.501278i	−0.590635	−	0.806939i	$-0.701123\pi$
$503$	−9.87585e10	−	3.20886e10i	−1.54278	−	0.501278i	−0.952140	+	0.305661i	$0.901123\pi$
$504$	−2.69074e11	+	3.26009e10i	−4.17013	+	0.505251i
$505$	−2.71779e10	+	8.02870e10i	−0.417879	+	1.23447i
$506$	−6.87551e10	−	4.44288e9i	−1.04883	−	0.0677739i
$507$		−	1.11816e11i		−	1.69228i
$508$	2.75683e10	+	1.30871e10i	0.413956	+	0.196512i
$509$	−4.45338e10	−	3.23557e10i	−0.663466	−	0.482036i	0.204366	−	0.978895i	$-0.434487\pi$
$509$	−4.45338e10	−	3.23557e10i	−0.663466	−	0.482036i	−0.867832	+	0.496858i	$0.834487\pi$
$510$	2.25781e9	−	2.93516e10i	0.0333738	−	0.433861i
$511$	−4.44085e10	−	6.11231e10i	−0.651303	−	0.896441i
$512$	−5.36122e10	+	4.29895e10i	−0.780160	+	0.625580i
$513$	−7.75209e9	−	5.63222e9i	−0.111931	−	0.0813224i
$514$	1.10921e10	+	4.35072e10i	0.158913	+	0.623316i
$515$	−2.40480e10	+	3.22611e10i	−0.341861	+	0.458618i
$516$	7.41919e9	+	3.96230e10i	0.104654	+	0.558919i
$517$	−2.90034e10	−	8.92634e10i	−0.405964	−	1.24943i
$518$	−1.04067e11	−	4.14075e10i	−1.44542	−	0.575122i
$519$	1.68599e10	−	5.47811e9i	0.232373	−	0.0755025i
$520$	−2.07629e10	−	4.33502e9i	−0.283972	−	0.0592895i
$521$	3.25274e10	−	1.00109e11i	0.441467	−	1.35870i	−0.444845	−	0.895608i	$-0.646741\pi$
$521$	3.25274e10	−	1.00109e11i	0.441467	−	1.35870i	0.886312	−	0.463088i	$-0.153259\pi$
$522$	2.08988e11	+	1.73488e11i	2.81474	+	2.33662i
$523$	−2.34047e10	−	3.22138e10i	−0.312821	−	0.430562i	0.623437	−	0.781873i	$-0.285736\pi$
$523$	−2.34047e10	−	3.22138e10i	−0.312821	−	0.430562i	−0.936259	+	0.351312i	$0.885736\pi$
$524$	3.89772e10	−	4.12252e10i	0.516994	−	0.546812i
$525$	2.01047e11	−	1.38678e11i	2.64643	−	1.82545i
$526$	7.17988e10	+	2.85682e10i	0.937939	+	0.373199i
$527$	5.89830e9	+	8.11831e9i	0.0764688	+	0.105250i
$528$	−2.62993e11	−	6.94317e10i	−3.38383	−	0.893351i
$529$	1.67479e10	−	5.15448e10i	0.213864	−	0.658206i
$530$	−2.38535e10	+	5.78767e10i	−0.302307	+	0.733500i
$531$	−8.34077e10	+	2.71008e10i	−1.04913	+	0.340882i
$532$	5.36150e9	+	5.06914e9i	0.0669329	+	0.0632831i
$533$	−2.33571e9	−	7.18856e9i	−0.0289407	−	0.0890703i
$534$	−1.19963e10	−	1.89742e10i	−0.147530	−	0.233345i
$535$	−3.76488e10	−	1.27445e10i	−0.459554	−	0.155563i
$536$	8.80399e10	+	4.89857e10i	1.06665	+	0.593486i
$537$	2.20158e11	+	1.59954e11i	2.64750	+	1.92352i
$538$	−8.31886e9	+	5.25953e9i	−0.0992967	+	0.0627794i
$539$	1.90486e11	+	2.62181e11i	2.25688	+	3.10632i
$540$	1.54629e11	−	1.59588e11i	1.81851	−	1.87683i
$541$	7.15879e10	+	5.20116e10i	0.835700	+	0.607172i	0.921166	−	0.389170i	$-0.127238\pi$
$541$	7.15879e10	+	5.20116e10i	0.835700	+	0.607172i	−0.0854662	+	0.996341i	$0.527238\pi$
$542$	−6.97520e9	+	1.07944e11i	−0.0808276	+	1.25084i
$543$			4.49050e10i			0.516529i
$544$	−1.75022e8	+	2.06234e10i	−0.00199846	+	0.235486i
$545$	6.83593e10	−	4.83985e10i	0.774839	−	0.548587i
$546$	6.37754e10	+	5.29422e10i	0.717600	+	0.595705i
$547$	1.33752e10	+	4.34588e9i	0.149401	+	0.0485432i	0.382763	−	0.923847i	$-0.374973\pi$
$547$	1.33752e10	+	4.34588e9i	0.149401	+	0.0485432i	−0.233362	+	0.972390i	$0.574973\pi$
$548$	3.70447e10	+	4.80765e9i	0.410775	+	0.0533102i
$549$	−2.32227e10			−0.255637
$550$	1.68942e11	−	3.86924e10i	1.84623	−	0.422839i
$551$		−	7.39405e9i		−	0.0802188i
$552$	−4.62861e10	+	8.31879e10i	−0.498533	+	0.895991i
$553$	2.77250e10	−	8.53288e10i	0.296463	−	0.912421i
$554$	3.61819e10	+	3.00359e10i	0.384107	+	0.318861i
$555$	1.49661e11	−	4.66099e10i	1.57738	−	0.491254i
$556$	−1.45054e11	−	6.88598e10i	−1.51786	−	0.720554i
$557$	−7.41647e10			−0.770507			−0.385253	−	0.922811i	$-0.625886\pi$
$557$	−7.41647e10			−0.770507			−0.385253	+	0.922811i	$0.625886\pi$
$558$	−8.33811e9	+	1.29035e11i	−0.0860064	+	1.33098i
$559$	5.12374e9	−	7.05222e9i	0.0524734	−	0.0722235i
$560$	−1.33894e11	+	1.06541e11i	−1.36147	+	1.08333i
$561$	−6.60434e10	+	4.79833e10i	−0.666773	+	0.484439i
$562$	7.92109e10	−	5.00804e10i	0.794035	−	0.502022i
$563$	2.00952e10	−	2.76587e10i	0.200013	−	0.275295i	−0.697215	−	0.716863i	$-0.745578\pi$
$563$	2.00952e10	−	2.76587e10i	0.200013	−	0.275295i	0.897228	+	0.441568i	$0.145578\pi$
$564$	−1.28605e11	−	1.66903e10i	−1.27099	−	0.164948i
$565$	−1.18864e11	+	8.41558e10i	−1.16642	+	0.825829i
$566$	−5.97870e10	−	9.45636e10i	−0.582561	−	0.921422i
$567$	−4.12950e11	+	1.34176e11i	−3.99545	+	1.29820i
$568$	2.87573e10	+	6.19290e10i	0.276284	+	0.594977i
$569$	3.01798e10	+	9.28839e10i	0.287917	+	0.886118i	0.985509	+	0.169622i	$0.0542548\pi$
$569$	3.01798e10	+	9.28839e10i	0.287917	+	0.886118i	−0.697592	+	0.716495i	$0.745745\pi$
$570$	−1.02960e10	−	7.91996e8i	−0.0975367	−	0.00750281i
$571$	−2.20736e10	−	7.17213e9i	−0.207648	−	0.0674690i	0.203346	−	0.979107i	$-0.434818\pi$
$571$	−2.20736e10	−	7.17213e9i	−0.207648	−	0.0674690i	−0.410994	+	0.911638i	$0.634818\pi$
$572$	2.81608e10	+	5.16388e10i	0.263064	+	0.482383i
$573$	−9.94016e10	+	7.22195e10i	−0.922093	+	0.669940i
$574$	−5.66555e10	−	2.25428e10i	−0.521909	−	0.207664i
$575$	1.48508e9	−	6.06402e10i	0.0135856	−	0.554740i
$576$	−1.71475e11	+	2.03032e11i	−1.55780	+	1.84448i
$577$	−2.17915e10	+	1.58324e10i	−0.196600	+	0.142838i	−0.681730	−	0.731604i	$-0.738772\pi$
$577$	−2.17915e10	+	1.58324e10i	−0.196600	+	0.142838i	0.485130	+	0.874442i	$0.338772\pi$
$578$	−8.11152e10	−	6.73365e10i	−0.726759	−	0.603308i
$579$	7.78598e9	+	2.52982e9i	0.0692786	+	0.0225100i
$580$	1.69762e11	+	2.41484e10i	1.50013	+	0.213391i
$581$	5.36782e10	+	1.65205e11i	0.471079	+	1.44983i
$582$	1.19684e11	+	4.76213e10i	1.04314	+	0.415058i
$583$	1.65096e11	−	5.36429e10i	1.42910	−	0.464342i
$584$	−7.26950e10	−	1.42513e10i	−0.624961	−	0.122519i
$585$	−8.20206e10	−	1.00419e9i	−0.700325	−	0.00857421i
$586$	−4.06435e10	−	1.59419e11i	−0.344667	−	1.35191i
$587$	4.43177e10	−	6.09981e10i	0.373272	−	0.513765i	−0.580515	−	0.814250i	$-0.697149\pi$
$587$	4.43177e10	−	6.09981e10i	0.373272	−	0.513765i	0.953786	+	0.300485i	$0.0971486\pi$
$588$	4.40127e11	−	8.24113e10i	3.68187	−	0.689410i
$589$	2.84775e9	−	2.06901e9i	0.0236614	−	0.0171910i
$590$	−3.58824e10	+	4.21636e10i	−0.296124	+	0.347961i
$591$	1.77356e10	−	2.44110e10i	0.145377	−	0.200095i
$592$	−1.02378e11	+	3.97325e10i	−0.833529	+	0.323489i
$593$	−6.40487e10			−0.517955			−0.258977	−	0.965883i	$-0.583385\pi$
$593$	−6.40487e10			−0.517955			−0.258977	+	0.965883i	$0.583385\pi$
$594$	−6.14926e11	−	3.97358e10i	−4.93943	−	0.319180i
$595$	−6.28685e8	+	5.13497e10i	−0.00501609	+	0.409704i
$596$	8.21338e10	−	4.47910e10i	0.650934	−	0.354982i
$597$	6.11484e10	−	1.88196e11i	0.481380	−	1.48154i
$598$	1.99476e10	−	5.08559e9i	0.155986	−	0.0397683i
$599$		−	1.89501e10i		−	0.147199i	−0.997288	−	0.0735993i	$-0.976551\pi$
$599$		−	1.89501e10i		−	0.147199i	0.997288	−	0.0735993i	$-0.0234486\pi$
$600$	5.18095e10	−	2.33801e11i	0.399765	−	1.80402i
$601$	−1.26049e11			−0.966143			−0.483071	−	0.875581i	$-0.660479\pi$
$601$	−1.26049e11			−0.966143			−0.483071	+	0.875581i	$0.660479\pi$
$602$	−1.73726e10	−	6.81419e10i	−0.132276	−	0.518834i
$603$	3.70557e11	+	1.20401e11i	2.80276	+	0.910671i
$604$	−6.71842e10	−	1.23196e11i	−0.504800	−	0.925657i
$605$	−2.77924e11	−	2.07169e11i	−2.07445	−	1.54633i
$606$	2.09427e10	−	3.24096e11i	0.155290	−	2.40316i
$607$			2.27494e11i			1.67577i	0.545847	+	0.837885i	$0.316208\pi$
$607$			2.27494e11i			1.67577i	−0.545847	+	0.837885i	$0.683792\pi$
$608$	7.23431e9	+	6.13943e7i	0.0529398	+	0.000449276i
$609$	−5.42098e11	−	3.93857e11i	−3.94102	−	2.86332i
$610$	−1.24866e10	+	7.68223e9i	−0.0901833	+	0.0554840i
$611$	1.64832e10	+	2.26871e10i	0.118270	+	0.162785i
$612$	1.46793e10	+	7.83963e10i	0.104640	+	0.558843i
$613$	9.43931e10	+	6.85806e10i	0.668495	+	0.485690i	0.869521	−	0.493896i	$-0.164428\pi$
$613$	9.43931e10	+	6.85806e10i	0.668495	+	0.485690i	−0.201026	+	0.979586i	$0.564428\pi$
$614$	4.78072e10	−	1.21884e10i	0.336372	−	0.0857574i
$615$	8.14772e10	−	2.53751e10i	0.569555	−	0.177381i
$616$	4.65633e11	+	9.12839e10i	3.23386	+	0.633974i
$617$	−4.10742e10	−	1.26413e11i	−0.283418	−	0.872272i	−0.986868	−	0.161527i	$-0.948358\pi$
$617$	−4.10742e10	−	1.26413e11i	−0.283418	−	0.872272i	0.703450	−	0.710745i	$-0.251642\pi$
$618$	5.69984e10	−	1.43251e11i	0.390759	−	0.982071i
$619$	2.77836e11	−	9.02745e10i	1.89246	−	0.614897i	0.915135	−	0.403148i	$-0.132084\pi$
$619$	2.77836e11	−	9.02745e10i	1.89246	−	0.614897i	0.977324	−	0.211750i	$-0.0679162\pi$
$620$	3.82024e10	+	7.21394e10i	0.258537	+	0.488209i
$621$	−6.66441e10	+	2.05109e11i	−0.448121	+	1.37917i
$622$	−8.17651e10	+	9.84961e10i	−0.546269	+	0.658048i
$623$	2.30177e10	+	3.16812e10i	0.152795	+	0.210305i
$624$	8.11423e10	−	4.55221e9i	0.535191	−	0.0300250i
$625$	3.99920e10	+	1.47254e11i	0.262092	+	0.965043i
$626$	−6.20937e10	+	1.56056e11i	−0.404343	+	1.01621i
$627$	1.68316e10	+	2.31668e10i	0.108907	+	0.149898i
$628$	1.05724e11	−	5.76558e10i	0.679728	−	0.370685i
$629$	−1.01848e10	+	3.13456e10i	−0.0650653	+	0.200250i
$630$	−4.28864e11	+	5.03937e11i	−2.72243	+	3.19900i
$631$	−1.42326e11	+	4.62446e10i	−0.897775	+	0.291705i	−0.721318	−	0.692604i	$-0.756464\pi$
$631$	−1.42326e11	+	4.62446e10i	−0.897775	+	0.291705i	−0.176457	+	0.984308i	$0.556464\pi$
$632$	−3.70501e10	−	7.97874e10i	−0.232231	−	0.500111i
$633$	3.77845e10	+	1.16289e11i	0.235341	+	0.724307i
$634$	2.19361e11	−	1.38689e11i	1.35770	−	0.858392i
$635$	7.11342e10	−	2.21539e10i	0.437506	−	0.136256i
$636$	3.08693e10	−	2.37859e11i	0.188668	−	1.45376i
$637$	−7.83351e10	−	5.69138e10i	−0.475772	−	0.345668i
$638$	−2.54103e11	−	4.01908e11i	−1.53365	−	2.42574i
$639$	1.55208e11	+	2.13626e11i	0.930918	+	1.28130i
$640$	−2.50363e10	+	1.65894e11i	−0.149228	+	0.988803i
$641$	7.05448e10	+	5.12538e10i	0.417862	+	0.303594i	0.776777	−	0.629776i	$-0.216853\pi$
$641$	7.05448e10	+	5.12538e10i	0.417862	+	0.303594i	−0.358915	+	0.933370i	$0.616853\pi$
$642$	1.51978e11	+	9.82062e9i	0.894623	+	0.0578095i
$643$			2.37741e11i			1.39079i	0.718630	+	0.695393i	$0.244770\pi$
$643$			2.37741e11i			1.39079i	−0.718630	+	0.695393i	$0.755230\pi$
$644$	7.12178e10	−	1.50022e11i	0.414043	−	0.872188i
$645$	7.89069e10	+	5.88185e10i	0.455907	+	0.339841i
$646$	1.38684e9	−	1.67062e9i	0.00796337	−	0.00959286i
$647$	1.48204e11	+	4.81545e10i	0.845754	+	0.274802i	0.699666	−	0.714470i	$-0.253332\pi$
$647$	1.48204e11	+	4.81545e10i	0.845754	+	0.274802i	0.146087	+	0.989272i	$0.453332\pi$
$648$	−2.06995e11	+	3.72023e11i	−1.17398	+	2.10994i
$649$	1.53531e11			0.865403
$650$	−4.44339e10	+	2.65930e10i	−0.248921	+	0.148975i
$651$		−	3.18993e11i		−	1.77606i
$652$	−4.53900e10	+	3.49746e11i	−0.251171	+	1.93537i
$653$	8.98224e10	−	2.76445e11i	0.494006	−	1.52039i	−0.324495	−	0.945887i	$-0.605194\pi$
$653$	8.98224e10	−	2.76445e11i	0.494006	−	1.52039i	0.818501	−	0.574506i	$-0.194806\pi$
$654$	−2.04984e11	+	2.46929e11i	−1.12049	+	1.34977i
$655$	1.69569e9	−	1.38500e11i	0.00921256	−	0.752463i
$656$	−5.57361e10	+	2.16309e10i	−0.300968	+	0.116805i
$657$	−2.86481e11			−1.53757
$658$	2.25755e11	+	1.45880e10i	1.20430	+	0.0778203i
$659$	−4.92677e10	+	6.78112e10i	−0.261229	+	0.359550i	−0.919404	−	0.393314i	$-0.871328\pi$
$659$	−4.92677e10	+	6.78112e10i	−0.261229	+	0.359550i	0.658176	+	0.752865i	$0.271328\pi$
$660$	−5.86862e11	+	3.10781e11i	−3.09286	+	1.63787i
$661$	−2.70169e9	+	1.96290e9i	−0.0141524	+	0.0102823i	−0.594839	−	0.803845i	$-0.702784\pi$
$661$	−2.70169e9	+	1.96290e9i	−0.0141524	+	0.0102823i	0.580687	+	0.814127i	$0.302784\pi$
$662$	−1.02409e11	−	1.61977e11i	−0.533217	−	0.843377i
$663$	1.43366e10	−	1.97326e10i	0.0741978	−	0.102124i
$664$	1.48832e11	+	8.28105e10i	0.765636	+	0.426003i
$665$	1.80125e10	+	2.20531e8i	0.0921059	+	0.00112767i
$666$	−3.58966e11	+	2.26953e11i	−1.82455	+	1.15356i
$667$	−1.58273e11	+	5.14261e10i	−0.799657	+	0.259824i
$668$	−1.80543e11	+	1.90956e11i	−0.906724	+	0.959019i
$669$	3.45380e10	+	1.06297e11i	0.172422	+	0.530660i
$670$	2.39074e11	−	5.78439e10i	1.18641	−	0.287051i
$671$	3.86649e10	+	1.25630e10i	0.190733	+	0.0619730i
$672$	3.89849e11	−	5.27116e11i	1.91170	−	2.58481i
$673$	7.53028e10	−	5.47107e10i	0.367072	−	0.266693i	−0.388924	−	0.921270i	$-0.627153\pi$
$673$	7.53028e10	−	5.47107e10i	0.367072	−	0.266693i	0.755996	+	0.654577i	$0.227153\pi$
$674$	8.50428e10	−	2.13733e11i	0.412096	−	1.03570i
$675$	1.32821e10	−	5.42348e11i	0.0639813	−	2.61254i
$676$	1.38972e11	+	1.31394e11i	0.665490	+	0.629202i
$677$	−2.95490e11	+	2.14686e11i	−1.40666	+	1.02200i	−0.412861	+	0.910794i	$0.635470\pi$
$677$	−2.95490e11	+	2.14686e11i	−1.40666	+	1.02200i	−0.993798	+	0.111203i	$0.964530\pi$
$678$	3.56429e11	−	4.29362e11i	1.68676	−	2.03191i
$679$	−2.13704e11	−	6.94368e10i	−1.00539	−	0.326671i
$680$	3.38269e10	+	3.72969e10i	0.158207	+	0.174437i
$681$	−8.89679e10	−	2.73815e11i	−0.413661	−	1.27312i
$682$	8.36879e10	−	2.10328e11i	0.386834	−	0.972208i
$683$	−3.49253e11	+	1.13479e11i	−1.60494	+	0.521475i	−0.968321	−	0.249707i	$-0.919666\pi$
$683$	−3.49253e11	+	1.13479e11i	−1.60494	+	0.521475i	−0.636614	+	0.771183i	$0.719666\pi$
$684$	2.74999e10	−	5.14921e9i	0.125634	−	0.0235243i
$685$	7.44328e10	−	5.26986e10i	0.338067	−	0.239352i
$686$	−3.83537e11	+	9.77819e10i	−1.73185	+	0.441532i
$687$	−2.80521e11	+	3.86104e11i	−1.25933	+	1.73331i
$688$	−5.79643e10	−	3.73396e10i	−0.258706	−	0.166654i
$689$	−4.19607e10	+	3.04862e10i	−0.186194	+	0.135278i
$690$	5.46560e10	+	2.25899e11i	0.241125	+	0.996591i
$691$	1.63544e11	−	2.25099e11i	0.717336	−	0.987329i	−0.282272	−	0.959334i	$-0.591088\pi$
$691$	1.63544e11	−	2.25099e11i	0.717336	−	0.987329i	0.999608	−	0.0279943i	$-0.00891202\pi$
$692$	−1.30034e10	+	2.73918e10i	−0.0567063	+	0.119453i
$693$	1.83500e12			7.95613
$694$	−1.29223e10	+	1.99977e11i	−0.0557059	+	0.862068i
$695$	−3.74283e11	+	1.16566e11i	−1.60421	+	0.499611i
$696$	−6.52231e11	+	7.90240e10i	−2.77949	+	0.336761i
$697$	−5.54474e9	+	1.70649e10i	−0.0234936	+	0.0723059i
$698$	−6.35530e10	−	2.49278e11i	−0.267741	−	1.05018i
$699$			7.46330e11i			3.12624i
$700$	−6.38907e10	+	4.12833e11i	−0.266100	+	1.71942i
$701$	9.35193e9			0.0387284			0.0193642	−	0.999812i	$-0.493836\pi$
$701$	9.35193e9			0.0387284			0.0193642	+	0.999812i	$0.493836\pi$
$702$	1.78405e11	−	4.54840e10i	0.734614	−	0.187288i
$703$	1.09954e10	+	3.57263e9i	0.0450185	+	0.0146274i
$704$	3.95335e11	−	2.45276e11i	1.60944	−	0.998538i
$705$	−2.58402e11	+	1.82949e11i	−1.04602	+	0.740582i
$706$	3.26315e11	+	2.10861e10i	1.31347	+	0.0848746i
$707$			5.66548e11i			2.26756i
$708$	9.09741e10	−	1.91639e11i	0.362063	−	0.762693i
$709$	−8.33825e9	−	6.05809e9i	−0.0329982	−	0.0239746i	0.571164	−	0.820836i	$-0.306492\pi$
$709$	−8.33825e9	−	6.05809e9i	−0.0329982	−	0.0239746i	−0.604162	+	0.796861i	$0.706492\pi$
$710$	1.54123e11	+	6.35208e10i	0.606504	+	0.249967i
$711$	−1.99966e11	−	2.75229e11i	−0.782487	−	1.07700i
$712$	3.76791e10	+	7.38670e9i	0.146616	+	0.0287429i
$713$	−6.40944e10	−	4.65673e10i	−0.248006	−	0.180187i
$714$	−4.86098e10	−	1.90665e11i	−0.187038	−	0.733634i
$715$	1.36018e11	+	4.60433e10i	0.520441	+	0.176174i
$716$	−4.57506e11	+	8.56655e10i	−1.74078	+	0.325952i
$717$	2.14717e11	+	6.60831e11i	0.812438	+	2.50043i
$718$	−3.78591e11	−	1.50639e11i	−1.42453	−	0.566812i
$719$	−2.86255e10	+	9.30099e9i	−0.107112	+	0.0348028i	−0.362083	−	0.932146i	$-0.617934\pi$
$719$	−2.86255e10	+	9.30099e9i	−0.107112	+	0.0348028i	0.254971	+	0.966949i	$0.417934\pi$
$720$	2.84092e10	+	6.48194e11i	0.105713	+	2.41199i
$721$	−8.31096e10	+	2.55785e11i	−0.307546	+	0.946530i
$722$	2.08497e11	+	1.73080e11i	0.767274	+	0.636941i
$723$	−7.97718e9	−	1.09796e10i	−0.0291942	−	0.0401823i
$724$	−5.58108e10	−	5.27675e10i	−0.203125	−	0.192049i
$725$	3.44601e11	−	2.37699e11i	1.24728	−	0.860350i
$726$	1.23408e12	+	4.91031e11i	4.44218	+	1.76751i
$727$	−2.80332e11	−	3.85844e11i	−1.00354	−	1.38126i	−0.923127	−	0.384494i	$-0.874376\pi$
$727$	−2.80332e11	−	3.85844e11i	−1.00354	−	1.38126i	−0.0804136	−	0.996762i	$-0.525624\pi$
$728$	−1.40742e11	+	1.70522e10i	−0.501069	+	0.0607093i
$729$	−8.73285e10	+	2.68770e11i	−0.309205	+	0.951634i
$730$	−1.54038e11	+	9.47697e10i	−0.542421	+	0.333717i
$731$	−1.96805e10	+	6.39460e9i	−0.0689236	+	0.0223946i
$732$	3.85918e10	−	4.08176e10i	0.134416	−	0.142168i
$733$	−2.89538e9	−	8.91107e9i	−0.0100297	−	0.0308684i	0.945916	−	0.324410i	$-0.105166\pi$
$733$	−2.89538e9	−	8.91107e9i	−0.0100297	−	0.0308684i	−0.955946	+	0.293542i	$0.905166\pi$
$734$	1.87766e11	+	2.96985e11i	0.646893	+	1.02317i
$735$	6.53348e11	−	8.76488e11i	2.23870	−	3.00328i
$736$	−4.90008e10	−	1.55281e11i	−0.166991	−	0.529183i
$737$	−5.51827e11	−	4.00926e11i	−1.87039	−	1.35892i
$738$	−1.95426e11	+	1.23556e11i	−0.658804	+	0.416523i
$739$	−1.45070e11	−	1.99671e11i	−0.486406	−	0.669481i	0.493314	−	0.869851i	$-0.335785\pi$
$739$	−1.45070e11	−	1.99671e11i	−0.486406	−	0.669481i	−0.979720	+	0.200371i	$0.935785\pi$
$740$	−1.17935e11	+	2.40779e11i	−0.393293	+	0.802955i
$741$	−6.92182e9	−	5.02899e9i	−0.0229587	−	0.0166805i
$742$	−2.69811e10	+	4.17542e11i	−0.0890110	+	1.37748i
$743$		−	2.71805e11i		−	0.891873i	−0.895065	−	0.445936i	$-0.852871\pi$
$743$		−	2.71805e11i		−	0.891873i	0.895065	−	0.445936i	$-0.147129\pi$
$744$	−2.12943e11	−	2.29088e11i	−0.694980	−	0.747671i
$745$	7.32339e10	−	2.16342e11i	0.237732	−	0.702289i
$746$	−3.68044e11	−	3.05526e11i	−1.18835	−	0.986492i
$747$	6.26426e11	+	2.03538e11i	2.01181	+	0.653677i
$748$	1.79703e10	−	1.38468e11i	0.0574049	−	0.442326i
$749$	−2.65670e11			−0.844142
$750$	−2.94077e11	−	5.05307e11i	−0.929427	−	1.59702i
$751$		−	5.27376e11i		−	1.65791i	−0.559316	−	0.828954i	$-0.688936\pi$
$751$		−	5.27376e11i		−	1.65791i	0.559316	−	0.828954i	$-0.311064\pi$
$752$	1.71866e11	−	1.40226e11i	0.537427	−	0.438486i
$753$	−1.59151e11	+	4.89816e11i	−0.495027	+	1.52354i
$754$	1.09313e11	+	9.07447e10i	0.338211	+	0.280761i
$755$	−3.24502e11	−	1.09847e11i	−0.998687	−	0.338065i
$756$	6.36951e11	−	1.34175e12i	1.94993	−	4.10756i
$757$	1.90025e11			0.578664			0.289332	−	0.957229i	$-0.406567\pi$
$757$	1.90025e11			0.578664			0.289332	+	0.957229i	$0.406567\pi$
$758$	−2.18257e10	+	3.37761e11i	−0.0661137	+	1.02313i
$759$	3.78830e11	−	5.21415e11i	1.14150	−	1.57115i
$760$	1.30831e10	−	1.18658e10i	0.0392153	−	0.0355667i
$761$	−7.76208e10	+	5.63948e10i	−0.231441	+	0.168151i	−0.697461	−	0.716622i	$-0.745687\pi$
$761$	−7.76208e10	+	5.63948e10i	−0.231441	+	0.168151i	0.466021	+	0.884774i	$0.345687\pi$
$762$	−2.41287e11	+	1.52552e11i	−0.715673	+	0.452478i
$763$	3.29063e11	−	4.52916e11i	0.970914	−	1.33635i
$764$	2.70470e10	−	2.08407e11i	0.0793863	−	0.611701i
$765$	1.56122e11	+	1.16376e11i	0.455845	+	0.339794i
$766$	−2.48563e11	−	3.93146e11i	−0.721975	−	1.14193i
$767$	−4.36273e10	+	1.41754e10i	−0.126060	+	0.0409593i
$768$	−7.19011e10	−	6.38796e11i	−0.206676	−	1.83619i
$769$	−5.21507e10	−	1.60503e11i	−0.149126	−	0.458964i	0.848392	−	0.529368i	$-0.177571\pi$
$769$	−5.21507e10	−	1.60503e11i	−0.149126	−	0.458964i	−0.997519	+	0.0704045i	$0.977571\pi$
$770$	9.86660e11	−	6.07028e11i	2.80676	−	1.72682i
$771$	−3.99446e11	−	1.29788e11i	−1.13042	−	0.367296i
$772$	−1.22935e10	+	6.70415e9i	−0.0346103	+	0.0188745i
$773$	4.30289e11	−	3.12623e11i	1.20515	−	0.875595i	0.210371	−	0.977622i	$-0.432533\pi$
$773$	4.30289e11	−	3.12623e11i	1.20515	−	0.875595i	0.994782	+	0.102027i	$0.0325327\pi$
$774$	−2.47755e11	−	9.85798e10i	−0.690332	−	0.274678i
$775$	1.87974e11	+	6.62068e10i	0.521064	+	0.183525i
$776$	−1.99826e11	+	9.27912e10i	−0.551068	+	0.255894i
$777$	8.47620e11	−	6.15832e11i	2.32550	−	1.68958i
$778$	3.85439e10	+	3.19966e10i	0.105205	+	0.0873345i
$779$	5.98606e9	+	1.94499e9i	0.0162552	+	0.00528162i
$780$	1.38068e11	−	1.42495e11i	0.373005	−	0.384966i
$781$	−1.42849e11	−	4.39643e11i	−0.383948	−	1.18167i
$782$	−4.54060e10	−	1.80667e10i	−0.121419	−	0.0483117i
$783$	−1.41555e12	+	4.59939e11i	−3.76598	+	1.22364i
$784$	−4.14764e11	+	6.43859e11i	−1.09783	+	1.70422i
$785$	9.42680e10	−	2.78480e11i	0.248248	−	0.733356i
$786$	1.31110e11	+	5.14262e11i	0.343515	+	1.34739i
$787$	1.79376e11	−	2.46890e11i	0.467590	−	0.643582i	−0.508471	−	0.861079i	$-0.669789\pi$
$787$	1.79376e11	−	2.46890e11i	0.467590	−	0.643582i	0.976061	+	0.217497i	$0.0697892\pi$
$788$	9.49857e9	+	5.07282e10i	0.0246350	+	0.131566i
$789$	−5.84797e11	+	4.24880e11i	−1.50903	+	1.09637i
$790$	−1.98567e11	−	8.18383e10i	−0.509800	−	0.210111i
$791$	−5.72179e11	+	7.87536e11i	−1.46159	+	2.01171i
$792$	1.31782e12	−	1.22495e12i	3.34931	−	3.11327i
$793$	−1.21469e10			−0.0307165
$794$	−4.51831e11	−	2.91968e10i	−1.13683	−	0.0734603i
$795$	−3.38370e11	−	4.77923e11i	−0.847079	−	1.19644i
$796$	1.62046e11	+	2.97146e11i	0.403634	+	0.740147i
$797$	−1.62981e11	+	5.01603e11i	−0.403927	+	1.24316i	0.517861	+	0.855465i	$0.326728\pi$
$797$	−1.62981e11	+	5.01603e11i	−0.403927	+	1.24316i	−0.921788	+	0.387694i	$0.873272\pi$
$798$	−6.68818e10	+	1.70514e10i	−0.164929	+	0.0420483i
$799$		−	6.65709e10i		−	0.163342i
$800$	2.29702e11	+	3.39130e11i	0.560796	+	0.827954i
$801$	1.48488e11			0.360712
$802$	−1.88566e10	−	7.39625e10i	−0.0455791	−	0.178778i
$803$	4.76979e11	+	1.54980e11i	1.14719	+	0.372746i
$804$	−8.27419e11	+	4.51227e11i	−1.98017	+	1.07987i
$805$	−1.20557e11	−	3.87100e11i	−0.287085	−	0.921806i
$806$	−4.36133e9	+	6.74932e10i	−0.0103343	+	0.159926i
$807$		−	9.20666e10i		−	0.217074i
$808$	3.78198e11	+	4.06871e11i	0.887306	+	0.954579i
$809$	−3.15188e11	−	2.28997e11i	−0.735826	−	0.534609i	0.155575	−	0.987824i	$-0.450277\pi$
$809$	−3.15188e11	−	2.28997e11i	−0.735826	−	0.534609i	−0.891401	+	0.453215i	$0.850277\pi$
$810$	2.44427e11	+	1.01024e12i	0.567817	+	2.34684i
$811$	−6.15323e10	−	8.46920e10i	−0.142239	−	0.195776i	0.731953	−	0.681355i	$-0.238609\pi$
$811$	−6.15323e10	−	8.46920e10i	−0.142239	−	0.195776i	−0.874193	+	0.485579i	$0.838609\pi$
$812$	1.12653e12	−	2.10936e11i	2.59130	−	0.485206i
$813$	−8.18608e11	−	5.94753e11i	−1.87376	−	1.36137i
$814$	7.20440e11	−	1.83675e11i	1.64097	−	0.418362i
$815$	4.97537e11	+	7.02735e11i	1.12770	+	1.59280i
$816$	−1.62188e11	−	1.04479e11i	−0.365812	−	0.235650i
$817$	2.24310e9	+	6.90356e9i	0.00503456	+	0.0154948i
$818$	−6.73606e10	+	1.69293e11i	−0.150450	+	0.378118i
$819$	−5.21430e11	+	1.69423e11i	−1.15894	+	0.376562i
$820$	−6.42054e10	+	1.31083e11i	−0.142009	+	0.289929i
$821$	−2.00413e11	+	6.16807e11i	−0.441116	+	1.35762i	0.445571	+	0.895247i	$0.353001\pi$
$821$	−2.00413e11	+	6.16807e11i	−0.441116	+	1.35762i	−0.886687	+	0.462370i	$0.846999\pi$
$822$	−2.23196e11	+	2.68868e11i	−0.488877	+	0.588913i
$823$	−2.62743e11	−	3.61635e11i	−0.572707	−	0.788263i	0.420165	−	0.907448i	$-0.361972\pi$
$823$	−2.62743e11	−	3.61635e11i	−0.572707	−	0.788263i	−0.992872	+	0.119184i	$0.961972\pi$
$824$	1.11063e11	+	2.39174e11i	0.240913	+	0.518806i
$825$	−5.38600e11	+	1.52919e12i	−1.16265	+	3.30100i
$826$	−1.36812e11	+	3.43841e11i	−0.293903	+	0.738649i
$827$	−4.57942e11	−	6.30302e11i	−0.979012	−	1.34749i	−0.937360	−	0.348362i	$-0.886738\pi$
$827$	−4.57942e11	−	6.30302e11i	−0.979012	−	1.34749i	−0.0416518	−	0.999132i	$-0.513262\pi$
$828$	−3.01485e11	−	5.52835e11i	−0.641422	−	1.17618i
$829$	2.48238e11	−	7.63999e11i	0.525595	−	1.61761i	−0.237542	−	0.971377i	$-0.576342\pi$
$829$	2.48238e11	−	7.63999e11i	0.525595	−	1.61761i	0.763137	−	0.646237i	$-0.223658\pi$
$830$	4.04155e11	−	9.77852e10i	0.851601	−	0.206044i
$831$	−4.18355e11	+	1.35932e11i	−0.877284	+	0.285047i
$832$	−8.96919e10	+	1.06198e11i	−0.187180	+	0.221627i
$833$	7.10303e10	+	2.18609e11i	0.147524	+	0.454033i
$834$	1.26957e12	−	8.02674e11i	2.62417	−	1.65911i
$835$	−7.85445e9	+	6.41536e11i	−0.0161573	+	1.31970i
$836$	−4.85719e10	−	6.30364e9i	−0.0994397	−	0.0129052i
$837$	−5.73241e11	−	4.16484e11i	−1.16798	−	0.848588i
$838$	4.95690e11	+	7.84021e11i	1.00516	+	1.58983i
$839$	5.28821e11	+	7.27860e11i	1.06724	+	1.46893i	0.872842	+	0.488002i	$0.162274\pi$
$839$	5.28821e11	+	7.27860e11i	1.06724	+	1.46893i	0.194395	+	0.980923i	$0.437726\pi$
$840$	−1.73056e11	−	1.59124e12i	−0.347592	−	3.19609i
$841$	−5.24467e11	−	3.81048e11i	−1.04842	−	0.761720i
$842$	2.56655e11	+	1.65848e10i	0.510625	+	0.0329960i
$843$			8.76643e11i			1.73585i
$844$	−1.88931e11	−	8.96889e10i	−0.372335	−	0.176754i
$845$	4.66892e11	+	5.71625e9i	0.915776	+	0.0112120i
$846$	5.47908e11	−	6.60023e11i	1.06961	−	1.28848i
$847$	−2.20354e12	−	7.15974e11i	−4.28142	−	1.39112i
$848$	2.59353e11	+	3.17873e11i	0.501542	+	0.614710i
$849$	1.04656e12			2.01433
$850$	1.22443e11	+	1.09280e10i	0.234562	+	0.0209347i
$851$		−	2.60210e11i		−	0.496142i
$852$	−6.33408e11	−	8.22034e10i	−1.20206	−	0.156003i
$853$	−2.89061e11	+	8.89639e11i	−0.546001	+	1.68042i	0.172596	+	0.984993i	$0.444785\pi$
$853$	−2.89061e11	+	8.89639e11i	−0.546001	+	1.68042i	−0.718597	+	0.695427i	$0.755215\pi$
$854$	−6.25898e10	+	7.53971e10i	−0.117672	+	0.141750i
$855$	4.08223e10	−	5.47645e10i	0.0763895	−	0.102479i
$856$	−1.90794e11	+	1.77348e11i	−0.355360	+	0.330316i
$857$	−9.30729e11			−1.72544			−0.862720	−	0.505682i	$-0.831241\pi$
$857$	−9.30729e11			−1.72544			−0.862720	+	0.505682i	$0.831241\pi$
$858$	−5.49065e11	−	3.54800e10i	−1.01315	−	0.0654687i
$859$	−5.30435e11	+	7.30081e11i	−0.974225	+	1.34091i	−0.0343414	+	0.999410i	$0.510933\pi$
$859$	−5.30435e11	+	7.30081e11i	−0.974225	+	1.34091i	−0.939883	+	0.341495i	$0.889067\pi$
$860$	−1.65826e11	+	2.89534e10i	−0.303151	+	0.0529305i
$861$	4.61455e11	−	3.35267e11i	0.839686	−	0.610068i
$862$	−3.15037e11	−	4.98286e11i	−0.570600	−	0.902504i
$863$	−1.21846e11	+	1.67707e11i	−0.219669	+	0.302349i	−0.904602	−	0.426258i	$-0.859832\pi$
$863$	−1.21846e11	+	1.67707e11i	−0.219669	+	0.302349i	0.684933	+	0.728606i	$0.259832\pi$
$864$	−4.38249e11	−	1.38878e12i	−0.786441	−	2.49218i
$865$	2.20121e10	+	7.06790e10i	0.0393185	+	0.126248i
$866$	2.08545e10	−	1.31851e10i	0.0370790	−	0.0234429i
$867$	9.37897e11	−	3.04741e11i	1.65989	−	0.539330i
$868$	3.96465e11	+	3.74846e11i	0.698436	+	0.660351i
$869$	1.84042e11	+	5.66423e11i	0.322729	+	0.993257i
$870$	−1.03956e12	+	1.22154e12i	−1.81457	+	2.13221i
$871$	1.93824e11	+	6.29771e10i	0.336770	+	0.109423i
$872$	−6.60236e10	−	5.44931e11i	−0.114191	−	0.942488i
$873$	−6.89307e11	+	5.00811e11i	−1.18674	+	0.862217i
$874$	−6.33746e9	+	1.59276e10i	−0.0108610	+	0.0272963i
$875$	5.68776e11	+	8.46566e11i	0.970306	+	1.44420i
$876$	4.76077e11	−	5.03535e11i	0.808465	−	0.855092i
$877$	−5.23182e11	+	3.80114e11i	−0.884412	+	0.642563i	−0.934415	−	0.356186i	$-0.884077\pi$
$877$	−5.23182e11	+	3.80114e11i	−0.884412	+	0.642563i	0.0500029	+	0.998749i	$0.484077\pi$
$878$	−4.12690e11	+	4.97136e11i	−0.694458	+	0.836560i
$879$	1.46365e12	+	4.75567e11i	2.45177	+	0.796630i
$880$	3.03359e11	−	1.09459e12i	0.505855	−	1.82524i
$881$	1.59667e11	+	4.91403e11i	0.265039	+	0.815707i	0.991684	+	0.128694i	$0.0410785\pi$
$881$	1.59667e11	+	4.91403e11i	0.265039	+	0.815707i	−0.726645	+	0.687013i	$0.758922\pi$
$882$	−1.09501e12	+	2.75203e12i	−1.80944	+	4.54756i
$883$	4.51167e11	−	1.46593e11i	0.742154	−	0.241141i	0.0865525	−	0.996247i	$-0.472415\pi$
$883$	4.51167e11	−	1.46593e11i	0.742154	−	0.241141i	0.655602	+	0.755107i	$0.272415\pi$
$884$	7.67814e9	+	4.10060e10i	0.0125732	+	0.0671488i
$885$	−1.54001e11	−	4.94484e11i	−0.251044	−	0.806081i
$886$	3.40614e11	−	8.68388e10i	0.552748	−	0.140922i
$887$	−2.63682e11	+	3.62927e11i	−0.425977	+	0.586306i	−0.967024	−	0.254686i	$-0.918028\pi$
$887$	−2.63682e11	+	3.62927e11i	−0.425977	+	0.586306i	0.541047	+	0.840992i	$0.318028\pi$
$888$	1.97629e11	−	1.00809e12i	0.317833	−	1.62124i
$889$	4.02877e11	−	2.92707e11i	0.645008	−	0.468626i
$890$	7.98406e10	−	4.91208e10i	0.127252	−	0.0782898i
$891$	1.69416e12	−	2.33181e12i	2.68809	−	3.69984i
$892$	−1.72698e11	−	8.19826e10i	−0.272789	−	0.129498i
$893$	−2.33518e10			−0.0367210
$894$	−5.64324e10	+	8.73312e11i	−0.0883443	+	1.36716i
$895$	−6.79147e11	+	9.11097e11i	−1.05845	+	1.41995i
$896$	1.97025e11	+	1.10394e12i	0.305695	+	1.71283i
$897$	−5.95063e10	+	1.83142e11i	−0.0919164	+	0.282890i
$898$	−3.70574e10	−	1.45353e11i	−0.0569862	−	0.223521i
$899$		−	5.46766e11i		−	0.837072i
$900$	1.12403e12	+	1.11611e12i	1.71320	+	1.70112i
$901$	1.23125e11			0.186831
$902$	3.92217e11	−	9.99950e10i	0.592516	−	0.151061i
$903$	6.25620e11	+	2.03276e11i	0.940936	+	0.305728i
$904$	1.14803e11	+	9.47533e11i	0.171901	+	1.41880i
$905$	−1.87502e11	−	2.29562e9i	−0.279519	−	0.00342221i
$906$	1.30992e12	+	8.46457e10i	1.94416	+	0.125630i
$907$		−	6.99899e11i		−	1.03420i	−0.855924	−	0.517102i	$-0.827011\pi$
$907$		−	6.99899e11i		−	1.03420i	0.855924	−	0.517102i	$-0.172989\pi$
$908$	4.44861e11	+	2.11183e11i	0.654456	+	0.310681i
$909$	1.73797e12	+	1.26271e12i	2.54558	+	1.84947i
$910$	−2.24322e11	+	2.63589e11i	−0.327119	+	0.384381i
$911$	−1.19633e11	−	1.64660e11i	−0.173691	−	0.239065i	0.713292	−	0.700867i	$-0.247203\pi$
$911$	−1.19633e11	−	1.64660e11i	−0.173691	−	0.239065i	−0.886983	+	0.461802i	$0.847203\pi$
$912$	−3.66492e10	+	5.68924e10i	−0.0529767	+	0.0822385i
$913$	−9.32865e11	−	6.77766e11i	−1.34257	−	0.975431i
$914$	−1.89810e11	−	7.44505e11i	−0.271978	−	1.06680i
$915$	1.67892e9	−	1.37131e11i	0.00239522	−	0.195637i
$916$	−1.50237e11	−	8.02357e11i	−0.213400	−	1.13969i
$917$	−2.86088e11	−	8.80488e11i	−0.404597	−	1.24522i
$918$	−4.06098e11	−	1.61583e11i	−0.571821	−	0.227523i
$919$	3.57170e11	−	1.16052e11i	0.500741	−	0.162701i	−0.0477462	−	0.998859i	$-0.515204\pi$
$919$	3.57170e11	−	1.16052e11i	0.500741	−	0.162701i	0.548487	+	0.836159i	$0.315204\pi$
$920$	−3.44987e11	−	1.97521e11i	−0.481561	−	0.275717i
$921$	−1.42615e11	+	4.38925e11i	−0.198211	+	0.610031i
$922$	−3.12257e11	−	2.59215e11i	−0.432104	−	0.358704i
$923$	8.11833e10	+	1.11739e11i	0.111856	+	0.153957i
$924$	−3.04942e12	+	3.22529e12i	−4.18340	+	4.42467i
$925$	1.86970e11	+	6.27295e11i	0.255391	+	0.856850i
$926$	6.29577e11	+	2.50504e11i	0.856259	+	0.340699i
$927$	5.99426e11	+	8.25038e11i	0.811739	+	1.11726i
$928$	6.68215e11	−	9.03495e11i	0.900999	−	1.21824i
$929$	2.16624e11	−	6.66701e11i	0.290833	−	0.895093i	−0.693756	−	0.720210i	$-0.744045\pi$
$929$	2.16624e11	−	6.66701e11i	0.290833	−	0.895093i	0.984589	−	0.174883i	$-0.0559547\pi$
$930$	−7.61354e11	−	5.85655e10i	−1.01778	−	0.0782907i
$931$	7.66839e10	−	2.49161e10i	0.102072	−	0.0331651i
$932$	−9.27587e11	−	8.77006e11i	−1.22939	−	1.16236i
$933$	−3.70040e11	−	1.13886e12i	−0.488339	−	1.50295i
$934$	−3.36023e11	−	5.31479e11i	−0.441552	−	0.698391i
$935$	−1.96979e11	−	2.78219e11i	−0.257736	−	0.364033i
$936$	−2.61372e11	+	4.69752e11i	−0.340530	+	0.612019i
$937$	8.03701e11	+	5.83923e11i	1.04264	+	0.757526i	0.970800	−	0.239890i	$-0.0771115\pi$
$937$	8.03701e11	+	5.83923e11i	1.04264	+	0.757526i	0.0718445	+	0.997416i	$0.477111\pi$
$938$	1.38963e12	−	8.78580e11i	1.79509	−	1.13493i
$939$	−9.23486e11	−	1.27107e12i	−1.18787	−	1.63496i
$940$	7.62652e10	−	5.36140e11i	0.0976821	−	0.686699i
$941$	5.21754e11	+	3.79076e11i	0.665437	+	0.483469i	0.868495	−	0.495698i	$-0.165088\pi$
$941$	5.21754e11	+	3.79076e11i	0.665437	+	0.483469i	−0.203057	+	0.979167i	$0.565088\pi$
$942$	−7.26409e10	+	1.12414e12i	−0.0922524	+	1.42764i
$943$		−	1.41662e11i		−	0.179146i
$944$	1.31278e11	+	3.38261e11i	0.165312	+	0.425956i
$945$	−1.07823e12	−	3.46211e12i	−1.35202	−	4.34123i
$946$	3.59172e11	+	2.98161e11i	0.448475	+	0.372295i
$947$	−3.11794e11	−	1.01308e11i	−0.387675	−	0.125963i	0.108693	−	0.994075i	$-0.465333\pi$
$947$	−3.11794e11	−	1.01308e11i	−0.387675	−	0.125963i	−0.496368	+	0.868112i	$0.665333\pi$
$948$	8.16064e11	+	1.05908e11i	1.01039	+	0.131129i
$949$	−1.49847e11			−0.184749
$950$	3.83335e9	−	4.29507e10i	0.00470635	−	0.0527321i
$951$			2.42772e12i			2.96808i
$952$	2.94092e11	+	1.63634e11i	0.358044	+	0.199217i
$953$	−2.46515e11	+	7.58696e11i	−0.298863	+	0.919806i	0.683033	+	0.730387i	$0.260660\pi$
$953$	−2.46515e11	+	7.58696e11i	−0.298863	+	0.919806i	−0.981896	+	0.189419i	$0.939340\pi$
$954$	1.22074e12	+	1.01338e12i	1.47377	+	1.22342i
$955$	−2.96473e11	−	4.18746e11i	−0.356428	−	0.503428i
$956$	−1.07364e12	−	5.09673e11i	−1.28536	−	0.610183i
$957$	4.44800e12			5.30295
$958$	4.64883e10	−	7.19424e11i	0.0551927	−	0.854127i
$959$	3.58300e11	−	4.93157e11i	0.423615	−	0.583057i
$960$	−1.18651e12	−	1.02724e12i	−1.39697	−	1.20945i
$961$	−4.79422e11	+	3.48320e11i	−0.562114	+	0.408399i
$962$	−1.87761e11	+	1.18710e11i	−0.219232	+	0.138608i
$963$	−5.92119e11	+	8.14982e11i	−0.688500	+	0.947639i
$964$	2.30201e10	+	2.98754e9i	0.0266563	+	0.00345944i
$965$	−1.09614e10	+	3.23813e10i	−0.0126402	+	0.0373409i
$966$	8.30160e11	+	1.31304e12i	0.953352	+	1.50789i
$967$	1.07764e12	−	3.50148e11i	1.23245	−	0.400447i	0.380849	−	0.924637i	$-0.375632\pi$
$967$	1.07764e12	−	3.50148e11i	1.23245	−	0.400447i	0.851601	+	0.524190i	$0.175632\pi$
$968$	−2.06044e12	+	9.56786e11i	−2.34671	+	1.08972i
$969$	6.27636e9	+	1.93166e10i	0.00711889	+	0.0219097i
$970$	−2.04962e11	+	4.97308e11i	−0.231519	+	0.561744i
$971$	−2.55397e11	−	8.29835e10i	−0.287302	−	0.0933501i	0.161821	−	0.986820i	$-0.448263\pi$
$971$	−2.55397e11	−	8.29835e10i	−0.287302	−	0.0933501i	−0.449123	+	0.893470i	$0.648263\pi$
$972$	−7.89874e11	−	1.44840e12i	−0.884897	−	1.62265i
$973$	−2.11980e12	+	1.54012e12i	−2.36506	+	1.71832i
$974$	−5.10621e11	−	2.03172e11i	−0.567365	−	0.225750i
$975$	1.18596e10	−	4.84261e11i	0.0131235	−	0.535872i
$976$	5.38175e9	+	9.59288e10i	0.00593095	+	0.105718i
$977$	5.12071e11	−	3.72041e11i	0.562020	−	0.408332i	−0.270177	−	0.962811i	$-0.587082\pi$
$977$	5.12071e11	−	3.72041e11i	0.562020	−	0.408332i	0.832198	+	0.554479i	$0.187082\pi$
$978$	−2.53843e12	−	2.10724e12i	−2.77466	−	2.30334i
$979$	−2.47226e11	−	8.03287e10i	−0.269131	−	0.0874460i
$980$	3.21611e11	+	1.84198e12i	0.348679	+	1.99701i
$981$	−6.55979e11	−	2.01890e12i	−0.708295	−	2.17991i
$982$	−1.06567e12	−	4.24024e11i	−1.14598	−	0.455978i
$983$	9.82435e11	−	3.19212e11i	1.05218	−	0.341874i	0.268656	−	0.963236i	$-0.413421\pi$
$983$	9.82435e11	−	3.19212e11i	1.05218	−	0.341874i	0.783523	+	0.621363i	$0.213421\pi$
$984$	1.07592e11	−	5.48819e11i	0.114762	−	0.585394i
$985$	1.01022e11	+	7.53036e10i	0.107318	+	0.0799965i
$986$	−8.33189e10	−	3.26807e11i	−0.0881527	−	0.345768i
$987$	−1.24388e12	+	1.71205e12i	−1.31071	+	1.80404i
$988$	1.43841e10	−	2.69335e9i	0.0150958	−	0.00282660i
$989$	1.32173e11	−	9.60294e10i	0.138152	−	0.100373i
$990$	3.36896e11	−	4.37965e12i	0.350715	−	4.55931i
$991$	−1.12395e12	+	1.54699e12i	−1.16534	+	1.60395i	−0.476176	+	0.879350i	$0.657977\pi$
$991$	−1.12395e12	+	1.54699e12i	−1.16534	+	1.60395i	−0.689165	+	0.724604i	$0.742023\pi$
$992$	5.34953e11	+	4.53990e9i	0.552420	+	0.00468813i
$993$	1.79263e12			1.84372
$994$	1.11190e12	+	7.18494e10i	1.13899	+	0.0735999i
$995$	7.82690e11	+	2.64948e11i	0.798541	+	0.270314i
$996$	−1.39875e12	+	7.62800e11i	−1.42136	+	0.775127i
$997$	−3.27723e11	+	1.00863e12i	−0.331686	+	1.02082i	0.636646	+	0.771156i	$0.280321\pi$
$997$	−3.27723e11	+	1.00863e12i	−0.331686	+	1.02082i	−0.968332	+	0.249667i	$0.919679\pi$
$998$	−1.01077e12	+	2.57693e11i	−1.01889	+	0.259765i
$999$		−	2.32724e12i		−	2.33658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.48	✓	464
4.3	odd	2	inner	100.9.j.b.11.95	yes	464
25.16	even	5	inner	100.9.j.b.91.95	yes	464
100.91	odd	10	inner	100.9.j.b.91.48	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.48	✓	464	1.1	even	1	trivial
100.9.j.b.11.95	yes	464	4.3	odd	2	inner
100.9.j.b.91.48	yes	464	100.91	odd	10	inner
100.9.j.b.91.95	yes	464	25.16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.95273 - 15.5041i) q^{2} +(142.345 + 46.2507i) q^{3} +(-224.752 + 122.567i) q^{4} +(-200.398 + 592.001i) q^{5} +(154.422 - 2389.74i) q^{6} +4177.48i q^{7} +(2788.67 + 3000.09i) q^{8} +(12815.0 + 9310.66i) q^{9} +(9970.54 + 766.963i) q^{10} +(-16299.6 - 22434.5i) q^{11} +(-37661.1 + 7051.83i) q^{12} +(6703.03 + 4870.04i) q^{13} +(64767.9 - 16512.4i) q^{14} +(-55906.2 + 74999.9i) q^{15} +(35490.8 - 55094.2i) q^{16} +(-6077.97 - 18706.1i) q^{17} +(93698.7 - 235487. i) q^{18} +(-6561.74 + 2132.04i) q^{19} +(-27519.8 - 157616. i) q^{20} +(-193211. + 594643. i) q^{21} +(-283398. + 341388. i) q^{22} +(91274.5 + 125629. i) q^{23} +(258196. + 556026. i) q^{24} +(-310306. - 237272. i) q^{25} +(49010.1 - 123174. i) q^{26} +(816332. + 1.12359e6i) q^{27} +(-512020. - 938896. i) q^{28} +(-331171. + 1.01924e6i) q^{29} +(1.38379e6 + 570318. i) q^{30} +(-485219. + 157657. i) q^{31} +(-994469. - 332479. i) q^{32} +(-1.28256e6 - 3.94731e6i) q^{33} +(-265996. + 168173. i) q^{34} +(-2.47307e6 - 837158. i) q^{35} +(-4.02138e6 - 521893. i) q^{36} +(-1.35566e6 - 984945. i) q^{37} +(58992.0 + 93306.2i) q^{38} +(728901. + 1.00325e6i) q^{39} +(-2.33490e6 + 1.04968e6i) q^{40} +(-738039. - 536217. i) q^{41} +(9.98310e6 + 645096. i) q^{42} -1.05209e6i q^{43} +(6.41310e6 + 3.04441e6i) q^{44} +(-8.08003e6 + 5.72067e6i) q^{45} +(1.58697e6 - 1.91170e6i) q^{46} +(3.21895e6 + 1.04590e6i) q^{47} +(7.60008e6 - 6.20091e6i) q^{48} -1.16865e7 q^{49} +(-2.45212e6 + 5.74888e6i) q^{50} -2.94383e6i q^{51} +(-2.10342e6 - 272981. i) q^{52} +(-1.93443e6 + 5.95357e6i) q^{53} +(1.41934e7 - 1.70977e7i) q^{54} +(1.65477e7 - 5.15357e6i) q^{55} +(-1.25328e7 + 1.16496e7i) q^{56} -1.03264e6 q^{57} +(1.71114e7 + 1.10572e6i) q^{58} +(-3.25429e6 + 4.47915e6i) q^{59} +(3.37252e6 - 2.37086e7i) q^{60} +(-1.18607e6 + 861728. i) q^{61} +(4.36227e6 + 6.89969e6i) q^{62} +(-3.88951e7 + 5.35345e7i) q^{63} +(-1.22391e6 + 1.67325e7i) q^{64} +(-4.22634e6 + 2.99226e6i) q^{65} +(-5.61298e7 + 3.54875e7i) q^{66} +(2.33934e7 - 7.60097e6i) q^{67} +(3.65878e6 + 3.45927e6i) q^{68} +(7.18206e6 + 2.21041e7i) q^{69} +(-3.20397e6 + 4.16517e7i) q^{70} +(1.58541e7 + 5.15130e6i) q^{71} +(7.80396e6 + 6.44106e7i) q^{72} +(-1.46316e7 + 1.06305e7i) q^{73} +(-9.91209e6 + 2.49115e7i) q^{74} +(-3.31966e7 - 4.81264e7i) q^{75} +(1.21345e6 - 1.28343e6i) q^{76} +(9.37197e7 - 6.80913e7i) q^{77} +(1.26732e7 - 1.52665e7i) q^{78} +(-2.04259e7 - 6.63678e6i) q^{79} +(2.55036e7 + 3.20514e7i) q^{80} +(3.21188e7 + 9.88515e7i) q^{81} +(-5.39627e6 + 1.35621e7i) q^{82} +(3.95465e7 - 1.28494e7i) q^{83} +(-2.94589e7 - 1.57328e8i) q^{84} +(1.22920e7 + 150494. i) q^{85} +(-1.63117e7 + 4.15864e6i) q^{86} +(-9.42811e7 + 1.29767e8i) q^{87} +(2.18514e7 - 1.11463e8i) q^{88} +(7.58380e6 - 5.50995e6i) q^{89} +(1.20632e8 + 1.02661e8i) q^{90} +(-2.03445e7 + 2.80018e7i) q^{91} +(-3.59120e7 - 1.70480e7i) q^{92} -7.63603e7 q^{93} +(3.49207e6 - 5.40410e7i) q^{94} +(52790.4 - 4.31181e6i) q^{95} +(-1.26180e8 - 9.33217e7i) q^{96} +(-1.66217e7 + 5.11563e7i) q^{97} +(4.61936e7 + 1.81188e8i) q^{98} -4.39259e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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