LMFDB - Embedded newform 43.7.h.a.18.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [43,7,Mod(3,43)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("43.3"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(43, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.h (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$252$
Relative dimension:	$21$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			18.5
Character	$\chi$	$=$	43.18
Dual form			43.7.h.a.12.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.41348 + 9.16469i) q^{2} +(-13.5449 + 19.8667i) q^{3} +(-24.6094 - 30.8593i) q^{4} +(24.4163 + 26.3145i) q^{5} +(-122.292 - 211.817i) q^{6} +(-444.560 - 256.667i) q^{7} +(-243.260 + 55.5224i) q^{8} +(55.1109 + 140.420i) q^{9} +(-348.925 + 107.629i) q^{10} +(738.948 - 926.611i) q^{11} +(946.406 - 70.9233i) q^{12} +(-1123.48 - 346.547i) q^{13} +(4314.33 - 2941.46i) q^{14} +(-853.500 + 128.644i) q^{15} +(1126.89 - 4937.22i) q^{16} +(6252.95 + 5801.89i) q^{17} +(-1530.14 - 114.668i) q^{18} +(709.179 + 278.332i) q^{19} +(211.175 - 1401.05i) q^{20} +(11120.7 - 5355.42i) q^{21} +(5230.77 + 10861.8i) q^{22} +(-6700.25 - 1009.90i) q^{23} +(2191.88 - 5584.82i) q^{24} +(1071.36 - 14296.3i) q^{25} +(8134.44 - 8766.84i) q^{26} +(-20625.3 - 4707.60i) q^{27} +(3019.82 + 20035.2i) q^{28} +(-21123.3 - 30982.2i) q^{29} +(2587.92 - 8389.83i) q^{30} +(1914.17 + 25542.8i) q^{31} +(27789.6 + 22161.4i) q^{32} +(8399.76 + 27231.4i) q^{33} +(-80769.9 + 31699.8i) q^{34} +(-4100.44 - 17965.2i) q^{35} +(2977.02 - 5156.35i) q^{36} +(-30122.7 + 17391.4i) q^{37} +(-5680.78 + 5271.00i) q^{38} +(22102.1 - 17625.9i) q^{39} +(-7400.54 - 5045.60i) q^{40} +(-809.744 - 389.952i) q^{41} +125553. i q^{42} +(-43324.4 - 66666.0i) q^{43} -46779.6 q^{44} +(-2349.49 + 4878.76i) q^{45} +(38826.9 - 56948.6i) q^{46} +(-107554. - 134868. i) q^{47} +(82822.9 + 89261.9i) q^{48} +(72931.0 + 126320. i) q^{49} +(126293. + 72915.2i) q^{50} +(-199960. + 45639.6i) q^{51} +(16954.0 + 43198.0i) q^{52} +(-9769.56 + 3013.51i) q^{53} +(134173. - 168248. i) q^{54} +(42425.7 - 3179.36i) q^{55} +(122394. + 37753.6i) q^{56} +(-15135.3 + 10319.1i) q^{57} +(377170. - 56849.2i) q^{58} +(-2552.02 + 11181.1i) q^{59} +(24974.0 + 23172.5i) q^{60} +(-87130.3 - 6529.51i) q^{61} +(-242540. - 95190.1i) q^{62} +(11541.1 - 76570.3i) q^{63} +(-33740.3 + 16248.5i) q^{64} +(-18311.9 - 38025.1i) q^{65} +(-286639. - 43203.9i) q^{66} +(-1930.25 + 4918.19i) q^{67} +(25160.4 - 335743. i) q^{68} +(110818. - 119433. i) q^{69} +(182743. + 41709.9i) q^{70} +(-104153. - 691008. i) q^{71} +(-21202.7 - 31098.7i) q^{72} +(-91428.2 + 296403. i) q^{73} +(-26440.4 - 352822. i) q^{74} +(269510. + 214927. i) q^{75} +(-8863.37 - 28734.4i) q^{76} +(-566337. + 222271. i) q^{77} +(63988.3 + 280351. i) q^{78} +(-294153. + 509487. i) q^{79} +(157435. - 90895.1i) q^{80} +(292281. - 271197. i) q^{81} +(7147.58 - 5700.01i) q^{82} +(151985. + 103622. i) q^{83} +(-438937. - 211381. i) q^{84} +306204. i q^{85} +(802185. - 102825. i) q^{86} +901629. q^{87} +(-128308. + 266435. i) q^{88} +(-419429. + 615189. i) q^{89} +(-34342.9 - 43064.6i) q^{90} +(410505. + 442419. i) q^{91} +(133725. + 231618. i) q^{92} +(-533380. - 307947. i) q^{93} +(1.71072e6 - 390460. i) q^{94} +(9991.34 + 25457.5i) q^{95} +(-816683. + 251913. i) q^{96} +(-643405. + 806804. i) q^{97} +(-1.47957e6 + 110878. i) q^{98} +(170839. + 52696.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9} + 967 q^{10} + 4090 q^{11} - 484 q^{12} + 1527 q^{13} + 7812 q^{14} - 8923 q^{15} - 13760 q^{16} - 3655 q^{17}+ \cdots + 18452884 q^{99}+O(q^{100}) $ 252 * q - 14 * q^2 - 11 * q^3 + 1180 * q^4 - 11 * q^5 - 118 * q^6 + 126 * q^7 - 2254 * q^8 - 8178 * q^9 + 967 * q^10 + 4090 * q^11 - 484 * q^12 + 1527 * q^13 + 7812 * q^14 - 8923 * q^15 - 13760 * q^16 - 3655 * q^17 + 5596 * q^18 + 38605 * q^19 + 26085 * q^20 + 24873 * q^21 - 25214 * q^22 + 27991 * q^23 - 20480 * q^24 - 24146 * q^25 - 34923 * q^26 - 14 * q^27 - 77634 * q^28 - 112735 * q^29 + 375072 * q^30 + 290647 * q^31 - 344064 * q^32 - 152174 * q^33 - 198311 * q^34 - 182471 * q^35 - 930891 * q^36 + 282762 * q^37 + 487342 * q^38 + 857290 * q^39 + 745459 * q^40 + 27674 * q^41 + 148802 * q^43 - 1255832 * q^44 - 191310 * q^45 - 1344785 * q^46 + 69166 * q^47 - 871241 * q^48 + 1786604 * q^49 + 837705 * q^50 - 182756 * q^51 + 2906416 * q^52 + 7779 * q^53 + 487154 * q^54 - 529592 * q^55 - 2464007 * q^56 - 767855 * q^57 - 1523780 * q^58 + 1531338 * q^59 - 1858647 * q^60 + 646957 * q^61 - 448559 * q^62 - 2007847 * q^63 + 3937366 * q^64 - 1473542 * q^65 + 1513319 * q^66 - 575523 * q^67 + 2717157 * q^68 + 967041 * q^69 + 4624473 * q^70 - 2149319 * q^71 - 9986371 * q^72 - 514565 * q^73 - 882972 * q^74 - 6655138 * q^75 + 1152658 * q^76 - 341803 * q^77 + 6322388 * q^78 - 2476742 * q^79 + 10750038 * q^80 + 4308941 * q^81 + 5079172 * q^82 + 2318609 * q^83 + 5578407 * q^84 + 585292 * q^86 - 1990710 * q^87 - 2864890 * q^88 - 4561993 * q^89 - 17681545 * q^90 - 4648506 * q^91 - 1991714 * q^92 - 8868294 * q^93 - 10200218 * q^94 + 10091737 * q^95 + 6250318 * q^96 - 1676750 * q^97 + 7512700 * q^98 + 18452884 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{29}{42}\right)$

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 $

$2$	−4.41348	+	9.16469i	−0.551686	+	1.14559i	0.419609	+	0.907705i	$0.362167\pi$
$2$	−4.41348	+	9.16469i	−0.551686	+	1.14559i	−0.971294	+	0.237882i	$0.923547\pi$
$3$	−13.5449	+	19.8667i	−0.501664	+	0.735805i	−0.990641	−	0.136491i	$-0.956418\pi$
$3$	−13.5449	+	19.8667i	−0.501664	+	0.735805i	0.488978	+	0.872296i	$0.337370\pi$
$4$	−24.6094	−	30.8593i	−0.384522	−	0.482176i
$5$	24.4163	+	26.3145i	0.195330	+	0.210516i	0.823121	−	0.567866i	$-0.192231\pi$
$5$	24.4163	+	26.3145i	0.195330	+	0.210516i	−0.627790	+	0.778382i	$0.716041\pi$
$6$	−122.292	−	211.817i	−0.566168	−	0.980632i
$7$	−444.560	−	256.667i	−1.29609	−	0.748299i	−0.316365	−	0.948637i	$-0.602463\pi$
$7$	−444.560	−	256.667i	−1.29609	−	0.748299i	−0.979727	+	0.200338i	$0.935796\pi$
$8$	−243.260	+	55.5224i	−0.475116	+	0.108442i
$9$	55.1109	+	140.420i	0.0755980	+	0.192621i
$10$	−348.925	+	107.629i	−0.348925	+	0.107629i
$11$	738.948	−	926.611i	0.555182	−	0.696177i	−0.422477	−	0.906374i	$-0.638839\pi$
$11$	738.948	−	926.611i	0.555182	−	0.696177i	0.977659	+	0.210197i	$0.0674106\pi$
$12$	946.406	−	70.9233i	0.547688	−	0.0410436i
$13$	−1123.48	−	346.547i	−0.511368	−	0.157736i	0.0283236	−	0.999599i	$-0.490983\pi$
$13$	−1123.48	−	346.547i	−0.511368	−	0.157736i	−0.539692	+	0.841863i	$0.681459\pi$
$14$	4314.33	−	2941.46i	1.57228	−	1.07196i
$15$	−853.500	+	128.644i	−0.252889	+	0.0381168i
$16$	1126.89	−	4937.22i	0.275119	−	1.20538i
$17$	6252.95	+	5801.89i	1.27274	+	1.18093i	0.973989	+	0.226594i	$0.0727589\pi$
$17$	6252.95	+	5801.89i	1.27274	+	1.18093i	0.298746	+	0.954333i	$0.403432\pi$
$18$	−1530.14	−	114.668i	−0.262370	−	0.0196619i
$19$	709.179	+	278.332i	0.103394	+	0.0405791i	0.416474	−	0.909148i	$-0.363266\pi$
$19$	709.179	+	278.332i	0.103394	+	0.0405791i	−0.313080	+	0.949727i	$0.601361\pi$
$20$	211.175	−	1401.05i	0.0263968	−	0.175132i
$21$	11120.7	−	5355.42i	1.20080	−	0.578277i
$22$	5230.77	+	10861.8i	0.491245	+	1.02008i
$23$	−6700.25	−	1009.90i	−0.550691	−	0.0830033i	−0.132198	−	0.991223i	$-0.542203\pi$
$23$	−6700.25	−	1009.90i	−0.550691	−	0.0830033i	−0.418493	+	0.908220i	$0.637442\pi$
$24$	2191.88	−	5584.82i	0.158556	−	0.403994i
$25$	1071.36	−	14296.3i	0.0685670	−	0.914964i
$26$	8134.44	−	8766.84i	0.462815	−	0.498796i
$27$	−20625.3	−	4707.60i	−1.04788	−	0.239171i
$28$	3019.82	+	20035.2i	0.137565	+	0.912682i
$29$	−21123.3	−	30982.2i	−0.866100	−	1.27034i	−0.961475	−	0.274894i	$-0.911357\pi$
$29$	−21123.3	−	30982.2i	−0.866100	−	1.27034i	0.0953745	−	0.995441i	$-0.469595\pi$
$30$	2587.92	−	8389.83i	0.0958489	−	0.310735i
$31$	1914.17	+	25542.8i	0.0642533	+	0.857401i	0.932477	+	0.361229i	$0.117643\pi$
$31$	1914.17	+	25542.8i	0.0642533	+	0.857401i	−0.868224	+	0.496172i	$0.834738\pi$
$32$	27789.6	+	22161.4i	0.848070	+	0.676314i
$33$	8399.76	+	27231.4i	0.233736	+	0.757753i
$34$	−80769.9	+	31699.8i	−2.05500	+	0.806529i
$35$	−4100.44	−	17965.2i	−0.0956371	−	0.419013i
$36$	2977.02	−	5156.35i	0.0638079	−	0.110518i
$37$	−30122.7	+	17391.4i	−0.594688	+	0.343343i	−0.766949	−	0.641708i	$-0.778226\pi$
$37$	−30122.7	+	17391.4i	−0.594688	+	0.343343i	0.172261	+	0.985051i	$0.444893\pi$
$38$	−5680.78	+	5271.00i	−0.103528	+	0.0960598i
$39$	22102.1	−	17625.9i	0.372598	−	0.297137i
$40$	−7400.54	−	5045.60i	−0.115633	−	0.0788375i
$41$	−809.744	−	389.952i	−0.0117489	−	0.00565796i	0.428000	−	0.903779i	$-0.359218\pi$
$41$	−809.744	−	389.952i	−0.0117489	−	0.00565796i	−0.439749	+	0.898121i	$0.644933\pi$
$42$			125553.i			1.69465i
$43$	−43324.4	−	66666.0i	−0.544913	−	0.838493i
$43$	−43324.4	−	66666.0i	−0.544913	−	0.838493i
$44$	−46779.6			−0.549160
$45$	−2349.49	+	4878.76i	−0.0257831	+	0.0535392i
$46$	38826.9	−	56948.6i	0.398896	−	0.585072i
$47$	−107554.	−	134868.i	−1.03594	−	1.29902i	−0.953164	−	0.302454i	$-0.902194\pi$
$47$	−107554.	−	134868.i	−1.03594	−	1.29902i	−0.0827717	−	0.996569i	$-0.526377\pi$
$48$	82822.9	+	89261.9i	0.748905	+	0.807128i
$49$	72931.0	+	126320.i	0.619903	+	1.07370i
$50$	126293.	+	72915.2i	1.01034	+	0.583322i
$51$	−199960.	+	45639.6i	−1.50742	+	0.344058i
$52$	16954.0	+	43198.0i	0.120576	+	0.307223i
$53$	−9769.56	+	3013.51i	−0.0656217	+	0.0202416i	−0.327392	−	0.944889i	$-0.606170\pi$
$53$	−9769.56	+	3013.51i	−0.0656217	+	0.0202416i	0.261771	+	0.965130i	$0.415694\pi$
$54$	134173.	−	168248.i	0.852089	−	1.06849i
$55$	42425.7	−	3179.36i	0.255000	−	0.0191096i
$56$	122394.	+	37753.6i	0.696942	+	0.214978i
$57$	−15135.3	+	10319.1i	−0.0817273	+	0.0557207i
$58$	377170.	−	56849.2i	1.93309	−	0.291367i
$59$	−2552.02	+	11181.1i	−0.0124259	+	0.0544414i	−0.980761	−	0.195213i	$-0.937460\pi$
$59$	−2552.02	+	11181.1i	−0.0124259	+	0.0544414i	0.968335	+	0.249655i	$0.0803172\pi$
$60$	24974.0	+	23172.5i	0.115620	+	0.107280i
$61$	−87130.3	−	6529.51i	−0.383866	−	0.0287668i	−0.118600	−	0.992942i	$-0.537841\pi$
$61$	−87130.3	−	6529.51i	−0.383866	−	0.0287668i	−0.265266	+	0.964175i	$0.585460\pi$
$62$	−242540.	−	95190.1i	−1.01767	−	0.399408i
$63$	11541.1	−	76570.3i	0.0461558	−	0.306224i
$64$	−33740.3	+	16248.5i	−0.128709	+	0.0619829i
$65$	−18311.9	−	38025.1i	−0.0666797	−	0.138462i
$66$	−286639.	−	43203.9i	−0.997020	−	0.150277i
$67$	−1930.25	+	4918.19i	−0.00641784	+	0.0163524i	−0.934047	−	0.357151i	$-0.883748\pi$
$67$	−1930.25	+	4918.19i	−0.00641784	+	0.0163524i	0.927629	+	0.373503i	$0.121843\pi$
$68$	25160.4	−	335743.i	0.0800187	−	1.06778i
$69$	110818.	−	119433.i	0.337336	−	0.363561i
$70$	182743.	+	41709.9i	0.532778	+	0.121603i
$71$	−104153.	−	691008.i	−0.291002	−	1.93067i	−0.359779	−	0.933037i	$-0.617148\pi$
$71$	−104153.	−	691008.i	−0.291002	−	1.93067i	0.0687777	−	0.997632i	$-0.478090\pi$
$72$	−21202.7	−	31098.7i	−0.0568060	−	0.0833191i
$73$	−91428.2	+	296403.i	−0.235024	+	0.761928i	0.758836	+	0.651282i	$0.225768\pi$
$73$	−91428.2	+	296403.i	−0.235024	+	0.761928i	−0.993860	+	0.110647i	$0.964708\pi$
$74$	−26440.4	−	352822.i	−0.0652488	−	0.870684i
$75$	269510.	+	214927.i	0.638837	+	0.509456i
$76$	−8863.37	−	28734.4i	−0.0201910	−	0.0654577i
$77$	−566337.	+	222271.i	−1.24052	+	0.486867i
$78$	63988.3	+	280351.i	0.134839	+	0.590770i
$79$	−294153.	+	509487.i	−0.596611	+	1.03336i	0.396706	+	0.917946i	$0.370153\pi$
$79$	−294153.	+	509487.i	−0.596611	+	1.03336i	−0.993317	+	0.115415i	$0.963180\pi$
$80$	157435.	−	90895.1i	0.307490	−	0.177529i
$81$	292281.	−	271197.i	0.549978	−	0.510305i
$82$	7147.58	−	5700.01i	0.0129634	−	0.0103379i
$83$	151985.	+	103622.i	0.265807	+	0.181224i	0.688888	−	0.724868i	$-0.258099\pi$
$83$	151985.	+	103622.i	0.265807	+	0.181224i	−0.423081	+	0.906092i	$0.639052\pi$
$84$	−438937.	−	211381.i	−0.740568	−	0.356639i
$85$			306204.i			0.498602i
$86$	802185.	−	102825.i	1.26119	−	0.161661i
$87$	901629.			1.36921
$88$	−128308.	+	266435.i	−0.188281	+	0.390970i
$89$	−419429.	+	615189.i	−0.594960	+	0.872647i	−0.999116	−	0.0420437i	$-0.986613\pi$
$89$	−419429.	+	615189.i	−0.594960	+	0.872647i	0.404155	+	0.914690i	$0.367566\pi$
$90$	−34342.9	−	43064.6i	−0.0471096	−	0.0590736i
$91$	410505.	+	442419.i	0.544747	+	0.587097i
$92$	133725.	+	231618.i	0.171731	+	0.297446i
$93$	−533380.	−	307947.i	−0.663114	−	0.382849i
$94$	1.71072e6	−	390460.i	2.05965	−	0.470103i
$95$	9991.34	+	25457.5i	0.0116534	+	0.0296924i
$96$	−816683.	+	251913.i	−0.923081	+	0.284733i
$97$	−643405.	+	806804.i	−0.704968	+	0.884002i	−0.997384	−	0.0722897i	$-0.976969\pi$
$97$	−643405.	+	806804.i	−0.704968	+	0.884002i	0.292416	+	0.956291i	$0.405541\pi$
$98$	−1.47957e6	+	110878.i	−1.57201	+	0.117806i
$99$	170839.	+	52696.9i	0.176069	+	0.0543100i
$100$	−467539.	+	318763.i	−0.467539	+	0.318763i
$101$	201938.	−	30437.3i	0.195999	−	0.0295421i	−0.0503088	−	0.998734i	$-0.516021\pi$
$101$	201938.	−	30437.3i	0.195999	−	0.0295421i	0.246308	+	0.969192i	$0.420782\pi$
$102$	464248.	−	2.03401e6i	0.437472	−	1.91669i
$103$	1751.70	+	1625.34i	0.00160306	+	0.00148742i	0.680974	−	0.732308i	$-0.261557\pi$
$103$	1751.70	+	1625.34i	0.00160306	+	0.00148742i	−0.679371	+	0.733795i	$0.737747\pi$
$104$	292537.	+	21922.6i	0.260065	+	0.0194892i
$105$	412450.	+	161875.i	0.356290	+	0.139833i
$106$	15499.9	−	102835.i	0.0130140	−	0.0863424i
$107$	−2.03028e6	+	977729.i	−1.65731	+	0.798118i	−0.658341	+	0.752720i	$0.728742\pi$
$107$	−2.03028e6	+	977729.i	−1.65731	+	0.798118i	−0.998969	+	0.0453986i	$0.985544\pi$
$108$	362305.	+	752334.i	0.287609	+	0.597227i
$109$	38076.5	+	5739.12i	0.0294021	+	0.00443165i	0.163727	−	0.986506i	$-0.447648\pi$
$109$	38076.5	+	5739.12i	0.0294021	+	0.00443165i	−0.134325	+	0.990937i	$0.542887\pi$
$110$	−158107.	+	402850.i	−0.118788	+	0.302667i
$111$	62500.0	−	834005.i	0.0456995	−	0.609817i
$112$	−1.76819e6	+	1.90565e6i	−1.25856	+	1.35641i
$113$	−1.44464e6	−	329731.i	−1.00121	−	0.228520i	−0.309660	−	0.950847i	$-0.600215\pi$
$113$	−1.44464e6	−	329731.i	−1.00121	−	0.228520i	−0.691551	+	0.722327i	$0.743072\pi$
$114$	−27771.8	−	184254.i	−0.0187452	−	0.124366i
$115$	−137020.	−	200972.i	−0.0900930	−	0.132142i
$116$	−436255.	+	1.41430e6i	−0.279490	+	0.906085i
$117$	−13253.6	−	176857.i	−0.00827518	−	0.110425i
$118$	−91208.3	−	72736.2i	−0.0555122	−	0.0442695i
$119$	−1.29066e6	−	4.18421e6i	−0.765897	−	2.48298i
$120$	200479.	−	78682.3i	0.116018	−	0.0455337i
$121$	81644.9	+	357709.i	0.0460864	+	0.201918i
$122$	444389.	−	769704.i	0.244728	−	0.423882i
$123$	18715.0	−	10805.1i	0.0100571	−	0.00580649i
$124$	741126.	−	687665.i	0.388711	−	0.360671i
$125$	840883.	−	670582.i	0.430532	−	0.343338i
$126$	650807.	+	443713.i	0.325342	+	0.221815i
$127$	2.24941e6	+	1.08326e6i	1.09814	+	0.528837i	0.893073	−	0.449911i	$-0.148544\pi$
$127$	2.24941e6	+	1.08326e6i	1.09814	+	0.528837i	0.205068	+	0.978748i	$0.434259\pi$
$128$			1.89390e6i			0.903081i
$129$	1.91126e6	+	42271.0i	0.890330	+	0.0196913i
$130$	429308.			0.195406
$131$	1.14712e6	−	2.38202e6i	0.510264	−	1.05957i	−0.473614	−	0.880732i	$-0.657051\pi$
$131$	1.14712e6	−	2.38202e6i	0.510264	−	1.05957i	0.983878	−	0.178841i	$-0.0572348\pi$
$132$	633626.	−	929359.i	0.275493	−	0.404075i
$133$	−243834.	−	305758.i	−0.103643	−	0.129964i
$134$	−36554.6	−	39396.5i	−0.0151924	−	0.0163736i
$135$	−379716.	−	657687.i	−0.154333	−	0.267312i
$136$	−1.84322e6	−	1.06419e6i	−0.732760	−	0.423059i
$137$	1.15120e6	−	262753.i	0.447701	−	0.102185i	0.00727436	−	0.999974i	$-0.497684\pi$
$137$	1.15120e6	−	262753.i	0.447701	−	0.102185i	0.440426	+	0.897789i	$0.354827\pi$
$138$	605476.	+	1.54273e6i	0.230388	+	0.587019i
$139$	3.17695e6	−	979958.i	1.18295	−	0.364891i	0.359969	−	0.932964i	$-0.382787\pi$
$139$	3.17695e6	−	979958.i	1.18295	−	0.364891i	0.822978	+	0.568073i	$0.192311\pi$
$140$	−453483.	+	568650.i	−0.165264	+	0.207234i
$141$	4.13620e6	−	309966.i	1.47552	−	0.110575i
$142$	6.79255e6	+	2.09522e6i	2.37229	+	0.731755i
$143$	−1.15130e6	+	784946.i	−0.393715	+	0.268430i
$144$	755390.	−	113857.i	0.252979	−	0.0381304i
$145$	299528.	−	1.31232e6i	0.0982503	−	0.430463i
$146$	−2.31293e6	−	2.14608e6i	−0.743196	−	0.689585i
$147$	−3.49741e6	−	262095.i	−1.10102	−	0.0825100i
$148$	1.27799e6	+	501573.i	0.394223	+	0.154721i
$149$	−777734.	+	5.15993e6i	−0.235111	+	1.55986i	0.490308	+	0.871549i	$0.336884\pi$
$149$	−777734.	+	5.15993e6i	−0.235111	+	1.55986i	−0.725419	+	0.688308i	$0.758354\pi$
$150$	−3.15921e6	+	1.52140e6i	−0.936063	+	0.450784i
$151$	−1.69134e6	−	3.51211e6i	−0.491248	−	1.02009i	−0.988322	−	0.152379i	$-0.951306\pi$
$151$	−1.69134e6	−	3.51211e6i	−0.491248	−	1.02009i	0.497074	−	0.867708i	$-0.334408\pi$
$152$	−187968.	−	28331.7i	−0.0535246	−	0.00806754i
$153$	−470098.	+	1.19779e6i	−0.131254	+	0.334431i
$154$	462474.	−	6.17129e6i	0.126627	−	1.68972i
$155$	−625410.	+	674031.i	−0.167946	+	0.181003i
$156$	−1.08784e6	−	248293.i	−0.286545	−	0.0654019i
$157$	53631.8	+	355824.i	0.0138587	+	0.0919467i	0.994691	−	0.102908i	$-0.0328147\pi$
$157$	53631.8	+	355824.i	0.0138587	+	0.0919467i	−0.980832	+	0.194854i	$0.937577\pi$
$158$	−3.37106e6	−	4.94443e6i	−0.854663	−	1.25356i
$159$	72459.3	−	234907.i	0.0180261	−	0.0584393i
$160$	95350.8	+	1.27237e6i	0.0232790	+	0.310637i
$161$	2.71945e6	+	2.16869e6i	0.651635	+	0.519661i
$162$	1.19546e6	+	3.87559e6i	0.281184	+	0.911575i
$163$	−3.65273e6	+	1.43359e6i	−0.843441	+	0.331026i	−0.747419	−	0.664353i	$-0.768707\pi$
$163$	−3.65273e6	+	1.43359e6i	−0.843441	+	0.331026i	−0.0960223	+	0.995379i	$0.530612\pi$
$164$	7893.71	+	34584.6i	0.00178957	+	0.00784063i
$165$	−511488.	+	885924.i	−0.113863	+	0.197217i
$166$	−1.62044e6	+	935563.i	−0.354250	+	0.204526i
$167$	2.82768e6	−	2.62370e6i	0.607128	−	0.563333i	−0.315547	−	0.948910i	$-0.602188\pi$
$167$	2.82768e6	−	2.62370e6i	0.607128	−	0.563333i	0.922676	+	0.385577i	$0.125998\pi$
$168$	−2.40786e6	+	1.92020e6i	−0.507812	+	0.404967i
$169$	−2.84599e6	−	1.94036e6i	−0.589622	−	0.401997i
$170$	−2.80626e6	−	1.35143e6i	−0.571192	−	0.275071i
$171$			114922.i			0.0229835i
$172$	−991075.	+	2.97757e6i	−0.194770	+	0.585163i
$173$	786949.			0.151988			0.0759938	−	0.997108i	$-0.475787\pi$
$173$	786949.			0.151988			0.0759938	+	0.997108i	$0.475787\pi$
$174$	−3.97933e6	+	8.26316e6i	−0.755374	+	1.56855i
$175$	−4.14567e6	+	6.08058e6i	−0.773536	+	1.13457i
$176$	−3.74217e6	−	4.69254e6i	−0.686414	−	0.860736i
$177$	−187566.	−	202148.i	−0.0338247	−	0.0364543i
$178$	−3.78688e6	−	6.55906e6i	−0.671462	−	1.16301i
$179$	6.95535e6	+	4.01567e6i	1.21272	+	0.700163i	0.963351	−	0.268246i	$-0.0864438\pi$
$179$	6.95535e6	+	4.01567e6i	1.21272	+	0.700163i	0.249368	+	0.968409i	$0.419777\pi$
$180$	208374.	−	47560.1i	0.0357295	−	0.00815502i
$181$	155390.	+	395927.i	0.0262051	+	0.0667696i	0.943377	−	0.331721i	$-0.107629\pi$
$181$	155390.	+	395927.i	0.0262051	+	0.0667696i	−0.917172	+	0.398491i	$0.869534\pi$
$182$	−5.86640e6	+	1.80954e6i	−0.973100	+	0.300161i
$183$	1.30989e6	−	1.64255e6i	0.213738	−	0.268019i
$184$	1.68597e6	−	126346.i	0.270643	−	0.0202819i
$185$	−1.19313e6	−	368032.i	−0.188440	−	0.0581260i
$186$	5.17631e6	−	3.52915e6i	0.804417	−	0.548442i
$187$	9.99670e6	−	1.50676e6i	1.52873	−	0.230420i
$188$	−1.51510e6	+	6.63807e6i	−0.228017	+	0.999007i
$189$	7.96091e6	+	7.38665e6i	1.17917	+	1.09411i
$190$	−277407.	−	20788.8i	−0.0404443	−	0.00303088i
$191$	−9.00803e6	−	3.53539e6i	−1.29280	−	0.507385i	−0.383502	−	0.923540i	$-0.625282\pi$
$191$	−9.00803e6	−	3.53539e6i	−1.29280	−	0.507385i	−0.909293	+	0.416155i	$0.863377\pi$
$192$	134205.	−	890393.i	0.0189612	−	0.125799i
$193$	6.49122e6	−	3.12601e6i	0.902930	−	0.434828i	0.0759838	−	0.997109i	$-0.475790\pi$
$193$	6.49122e6	−	3.12601e6i	0.902930	−	0.434828i	0.826946	+	0.562281i	$0.190076\pi$
$194$	−4.55446e6	−	9.45743e6i	−0.623780	−	1.29529i
$195$	1.00347e6	+	151248.i	0.135332	+	0.0203980i
$196$	2.10336e6	−	5.35927e6i	0.279347	−	0.711766i
$197$	−189039.	+	2.52255e6i	−0.0247259	+	0.329944i	0.971100	+	0.238673i	$0.0767123\pi$
$197$	−189039.	+	2.52255e6i	−0.0247259	+	0.329944i	−0.995826	+	0.0912718i	$0.970907\pi$
$198$	−1.23695e6	+	1.33311e6i	−0.159351	+	0.171740i
$199$	−1.86254e6	−	425112.i	−0.236345	−	0.0539442i	0.102708	−	0.994712i	$-0.467249\pi$
$199$	−1.86254e6	−	425112.i	−0.236345	−	0.0539442i	−0.339053	+	0.940767i	$0.610106\pi$
$200$	533147.	+	3.53720e6i	0.0666433	+	0.442150i
$201$	−71563.4	−	104964.i	−0.00881258	−	0.0129257i
$202$	−612303.	+	1.98504e6i	−0.0742869	+	0.240832i
$203$	1.43847e6	+	1.91951e7i	0.171955	+	2.29457i
$204$	6.32932e6	+	5.04746e6i	0.745532	+	0.594542i
$205$	−9509.54	−	30829.2i	−0.00110382	−	0.00357849i
$206$	−22626.9	+	8880.40i	−0.00258835	+	0.00101585i
$207$	−227447.	−	996508.i	−0.0256430	−	0.112349i
$208$	−2.97701e6	+	5.15633e6i	−0.330819	+	0.572995i
$209$	781952.	−	451460.i	0.0856528	−	0.0494517i
$210$	−3.30387e6	+	3.06555e6i	−0.356751	+	0.331017i
$211$	959862.	−	765464.i	0.102179	−	0.0814850i	−0.571068	−	0.820903i	$-0.693471\pi$
$211$	959862.	−	765464.i	0.102179	−	0.0814850i	0.673247	+	0.739418i	$0.264899\pi$
$212$	333418.	+	227321.i	0.0349930	+	0.0238579i
$213$	1.51388e7	+	7.29047e6i	1.56658	+	0.754426i
$214$		−	2.29221e7i		−	2.33890i
$215$	696462.	−	2.76780e6i	0.0700780	−	0.278496i
$216$	5.27869e6			0.523799
$217$	5.70503e6	−	1.18466e7i	0.558314	−	1.15935i
$218$	−220647.	+	323630.i	−0.0212975	+	0.0312378i
$219$	−4.65017e6	−	5.83113e6i	−0.442728	−	0.555163i
$220$	−1.14218e6	−	1.23098e6i	−0.107268	−	0.115607i
$221$	−5.01442e6	−	8.68522e6i	−0.464562	−	0.804645i
$222$	7.36756e6	+	4.25366e6i	0.673387	+	0.388780i
$223$	−1.88210e7	+	4.29577e6i	−1.69718	+	0.387370i	−0.958142	−	0.286293i	$-0.907577\pi$
$223$	−1.88210e7	+	4.29577e6i	−1.69718	+	0.387370i	−0.739038	+	0.673664i	$0.764720\pi$
$224$	−6.66602e6	−	1.69847e7i	−0.593093	−	1.51118i
$225$	2.06654e6	−	637442.i	0.181424	−	0.0559620i
$226$	9.39780e6	−	1.17845e7i	0.814143	−	1.02090i
$227$	−1.34313e7	+	1.00654e6i	−1.14826	+	0.0860501i	−0.635231	−	0.772322i	$-0.719095\pi$
$227$	−1.34313e7	+	1.00654e6i	−1.14826	+	0.0860501i	−0.513028	+	0.858372i	$0.671476\pi$
$228$	690912.	+	213118.i	0.0582932	+	0.0179811i
$229$	−1.14983e7	+	7.83940e6i	−0.957473	+	0.652794i	−0.937860	−	0.347014i	$-0.887196\pi$
$229$	−1.14983e7	+	7.83940e6i	−0.957473	+	0.652794i	−0.0196129	+	0.999808i	$0.506243\pi$
$230$	2.44658e6	−	368763.i	0.201083	−	0.0303084i
$231$	3.25519e6	−	1.42619e7i	0.264083	−	1.15702i
$232$	6.85865e6	+	6.36390e6i	0.549256	+	0.509635i
$233$	6.78118e6	+	508179.i	0.536090	+	0.0401744i	0.340025	−	0.940417i	$-0.389565\pi$
$233$	6.78118e6	+	508179.i	0.536090	+	0.0401744i	0.196065	+	0.980591i	$0.437184\pi$
$234$	1.67934e6	+	659092.i	0.131066	+	0.0514397i
$235$	922926.	−	6.12321e6i	0.0711153	−	0.471819i
$236$	407845.	−	196408.i	0.0310284	−	0.0149425i
$237$	−6.13758e6	−	1.27448e7i	−0.461054	−	0.957389i
$238$	4.40433e7	+	6.63846e6i	3.26700	+	0.492421i
$239$	−2.57988e6	+	6.57342e6i	−0.188976	+	0.481502i	−0.993690	−	0.112160i	$-0.964223\pi$
$239$	−2.57988e6	+	6.57342e6i	−0.188976	+	0.481502i	0.804715	+	0.593662i	$0.202318\pi$
$240$	−326653.	+	4.35888e6i	−0.0236294	+	0.315313i
$241$	−1.54764e7	+	1.66795e7i	−1.10565	+	1.19161i	−0.125762	+	0.992060i	$0.540137\pi$
$241$	−1.54764e7	+	1.66795e7i	−1.10565	+	1.19161i	−0.979888	+	0.199547i	$0.936053\pi$
$242$	−3.63864e6	−	830495.i	−0.256739	−	0.0585991i
$243$	−869731.	−	5.77029e6i	−0.0606130	−	0.402141i
$244$	1.94273e6	+	2.84946e6i	0.133734	+	0.196152i
$245$	−1.54335e6	+	5.00341e6i	−0.104946	+	0.340226i
$246$	16427.2	+	219205.i	0.00110346	+	0.0147247i
$247$	−700291.	−	558463.i	−0.0464716	−	0.0370599i
$248$	−1.88384e6	−	6.10726e6i	−0.123506	−	0.400397i
$249$	−4.11725e6	+	1.61590e6i	−0.266691	+	0.104669i
$250$	2.43445e6	+	1.06660e7i	0.155805	+	0.682626i
$251$	9.15792e6	−	1.58620e7i	0.579129	−	1.00308i	−0.416450	−	0.909159i	$-0.636726\pi$
$251$	9.15792e6	−	1.58620e7i	0.579129	−	1.00308i	0.995579	−	0.0939229i	$-0.0299407\pi$
$252$	−2.64692e6	+	1.52820e6i	−0.165402	+	0.0954947i
$253$	−5.88692e6	+	5.46227e6i	−0.363519	+	0.337296i
$254$	−1.98555e7	+	1.58342e7i	−1.21166	+	0.966264i
$255$	−6.08327e6	−	4.14750e6i	−0.366874	−	0.250130i
$256$	−1.95164e7	−	9.39859e6i	−1.16327	−	0.560199i
$257$			2.23069e6i			0.131414i	0.997839	+	0.0657068i	$0.0209302\pi$
$257$			2.23069e6i			0.131414i	−0.997839	+	0.0657068i	$0.979070\pi$
$258$	−8.82273e6	+	1.73296e7i	−0.513740	+	1.00909i
$259$	1.78551e7			1.02769
$260$	−722780.	+	1.50087e6i	−0.0411231	+	0.0853930i
$261$	3.18641e6	−	4.67360e6i	0.179217	−	0.262863i
$262$	1.67677e7	+	2.10260e7i	0.932328	+	1.16910i
$263$	3.44278e6	+	3.71043e6i	0.189253	+	0.203966i	0.820550	−	0.571575i	$-0.193668\pi$
$263$	3.44278e6	+	3.71043e6i	0.189253	+	0.203966i	−0.631297	+	0.775541i	$0.717477\pi$
$264$	−3.55527e6	−	6.15791e6i	−0.193224	−	0.334674i
$265$	−317835.	−	183502.i	−0.0170791	−	0.00986062i
$266$	3.87834e6	−	885205.i	0.206063	−	0.0470326i
$267$	−6.54067e6	−	1.66654e7i	−0.343628	−	0.875550i
$268$	199274.	−	61467.9i	0.0103525	−	0.00319333i
$269$	1.41895e7	−	1.77930e7i	0.728970	−	0.914099i	−0.269838	−	0.962906i	$-0.586970\pi$
$269$	1.41895e7	−	1.77930e7i	0.728970	−	0.914099i	0.998808	+	0.0488063i	$0.0155417\pi$
$270$	7.70338e6	−	577288.i	0.391372	−	0.0293293i
$271$	−2.11288e7	−	6.51738e6i	−1.06162	−	0.327465i	−0.285711	−	0.958316i	$-0.592230\pi$
$271$	−2.11288e7	−	6.51738e6i	−1.06162	−	0.327465i	−0.775904	+	0.630851i	$0.782706\pi$
$272$	3.56916e7	−	2.43341e7i	1.77361	−	1.20923i
$273$	−1.43497e7	+	2.16287e6i	−0.705269	+	0.106302i
$274$	−2.67274e6	+	1.17100e7i	−0.129928	+	0.569254i
$275$	−1.24554e7	−	1.15570e7i	−0.598909	−	0.555706i
$276$	−6.41278e6	−	480572.i	−0.305014	−	0.0228576i
$277$	−8.24868e6	−	3.23737e6i	−0.388101	−	0.152318i	0.163264	−	0.986582i	$-0.447798\pi$
$277$	−8.24868e6	−	3.23737e6i	−0.388101	−	0.152318i	−0.551365	+	0.834264i	$0.685893\pi$
$278$	−5.04038e6	+	3.34408e7i	−0.234601	+	1.55647i
$279$	−3.48124e6	+	1.67648e6i	−0.160296	+	0.0771943i
$280$	1.99494e6	+	4.14254e6i	0.0908775	+	0.188709i
$281$	3.46523e7	+	5.22299e6i	1.56175	+	0.235397i	0.872314	−	0.488946i	$-0.162618\pi$
$281$	3.46523e7	+	5.22299e6i	1.56175	+	0.235397i	0.689440	+	0.724342i	$0.257857\pi$
$282$	−1.54143e7	+	3.92751e7i	−0.687349	+	1.75134i
$283$	−2.10261e6	+	2.80574e7i	−0.0927682	+	1.23791i	0.735481	+	0.677546i	$0.236956\pi$
$283$	−2.10261e6	+	2.80574e7i	−0.0927682	+	1.23791i	−0.828249	+	0.560360i	$0.810663\pi$
$284$	−1.87609e7	+	2.02194e7i	−0.819026	+	0.882700i
$285$	−641090.	−	146325.i	−0.0276939	−	0.00632096i
$286$	−2.11253e6	−	1.40157e7i	−0.0903034	−	0.599124i
$287$	259892.	+	381191.i	0.0109938	+	0.0161249i
$288$	−1.58041e6	+	5.12356e6i	−0.0661595	+	0.214484i
$289$	3.63366e6	+	4.84878e7i	0.150540	+	2.00881i
$290$	1.07050e7	+	8.53699e6i	0.438929	+	0.350034i
$291$	−7.31371e6	−	2.37105e7i	−0.296796	−	0.962190i
$292$	1.13968e7	−	4.47290e6i	0.457755	−	0.179656i
$293$	−3.37796e6	−	1.47998e7i	−0.134293	−	0.588374i	−0.996629	−	0.0820388i	$-0.973857\pi$
$293$	−3.37796e6	−	1.47998e7i	−0.134293	−	0.588374i	0.862337	−	0.506336i	$-0.169000\pi$
$294$	1.78378e7	−	3.08960e7i	0.701939	−	1.21579i
$295$	−356537.	+	205846.i	−0.0138879	+	0.00801821i
$296$	6.36203e6	−	5.90310e6i	0.245313	−	0.227617i
$297$	−1.96032e7	+	1.56330e7i	−0.748268	+	0.596723i
$298$	−4.38566e7	−	2.99010e7i	−1.65724	−	1.12989i
$299$	7.17760e6	+	3.45655e6i	0.268513	+	0.129309i
$300$		−	1.36061e7i		−	0.503929i
$301$	2.14934e6	+	4.07569e7i	0.0788142	+	1.49452i
$302$	3.96522e7			1.43961
$303$	−2.13055e6	+	4.42413e6i	−0.0765885	+	0.159038i
$304$	2.17335e6	−	3.18773e6i	0.0773588	−	0.113465i
$305$	−1.95558e6	−	2.45222e6i	−0.0689248	−	0.0864289i
$306$	−8.90260e6	−	9.59472e6i	−0.310708	−	0.334864i
$307$	−2.45801e7	−	4.25739e7i	−0.849509	−	1.47139i	−0.881647	−	0.471909i	$-0.843565\pi$
$307$	−2.45801e7	−	4.25739e7i	−0.849509	−	1.47139i	0.0321385	−	0.999483i	$-0.489768\pi$
$308$	2.07963e7	+	1.20068e7i	0.711762	+	0.410936i
$309$	−56016.9	+	12785.5i	−0.00189864	+	0.000433353i
$310$	−3.41706e6	−	8.70652e6i	−0.114701	−	0.292253i
$311$	−3.08865e7	+	9.52722e6i	−1.02680	+	0.316727i	−0.762001	−	0.647575i	$-0.775783\pi$
$311$	−3.08865e7	+	9.52722e6i	−1.02680	+	0.316727i	−0.264803	+	0.964303i	$0.585307\pi$
$312$	−4.39793e6	+	5.51482e6i	−0.144805	+	0.181580i
$313$	2.79018e7	−	2.09095e6i	0.909913	−	0.0681885i	0.388457	−	0.921467i	$-0.373008\pi$
$313$	2.79018e7	−	2.09095e6i	0.909913	−	0.0681885i	0.521456	+	0.853278i	$0.325389\pi$
$314$	−3.49772e6	−	1.07890e6i	−0.112979	−	0.0348493i
$315$	2.29670e6	−	1.56586e6i	0.0734806	−	0.0500982i
$316$	2.29613e7	−	3.46086e6i	0.727672	−	0.109679i
$317$	6.26064e6	−	2.74296e7i	0.196535	−	0.861078i	−0.776444	−	0.630186i	$-0.782979\pi$
$317$	6.26064e6	−	2.74296e7i	0.196535	−	0.861078i	0.972979	−	0.230892i	$-0.0741643\pi$
$318$	1.83305e6	+	1.70083e6i	0.0570025	+	0.0528906i
$319$	−4.43175e7	−	3.32114e6i	−1.36522	−	0.102309i
$320$	−1.25138e6	−	491131.i	−0.0381891	−	0.0149881i
$321$	8.07562e6	−	5.35782e7i	0.244152	−	1.61984i
$322$	−3.18777e7	+	1.53515e7i	−0.954814	+	0.459814i
$323$	2.81961e6	+	5.85498e6i	0.0836722	+	0.173747i
$324$	−1.55618e7	−	2.34556e6i	−0.457536	−	0.0689624i
$325$	−6.15798e6	+	1.56903e7i	−0.179386	+	0.457068i
$326$	2.98284e6	−	3.98033e7i	0.0860950	−	1.14886i
$327$	−629761.	+	678721.i	−0.0180108	+	0.0194110i
$328$	218629.	+	49900.6i	0.00619564	+	0.00141411i
$329$	1.31979e7	+	8.75625e7i	0.370611	+	2.45884i
$330$	−5.86178e6	−	8.59765e6i	−0.163113	−	0.239242i
$331$	3.59803e6	−	1.16645e7i	0.0992157	−	0.321650i	−0.892334	−	0.451375i	$-0.850934\pi$
$331$	3.59803e6	−	1.16645e7i	0.0992157	−	0.321650i	0.991550	+	0.129726i	$0.0414097\pi$
$332$	−542579.	−	7.24021e6i	−0.0148268	−	0.197850i
$333$	−4.10219e6	−	3.27139e6i	−0.111092	−	0.0885930i
$334$	1.15655e7	+	3.74945e7i	0.310403	+	1.00630i
$335$	−176549.	+	69290.5i	−0.00469604	+	0.00184306i
$336$	−1.39092e7	−	6.09401e7i	−0.366677	−	1.60652i
$337$	−1.50386e7	+	2.60476e7i	−0.392932	+	0.680578i	−0.992835	−	0.119495i	$-0.961872\pi$
$337$	−1.50386e7	+	2.60476e7i	−0.392932	+	0.680578i	0.599903	+	0.800073i	$0.295206\pi$
$338$	3.03436e7	−	1.75189e7i	0.785809	−	0.453687i
$339$	2.61183e7	−	2.42342e7i	0.670417	−	0.622056i
$340$	9.44922e6	−	7.53550e6i	0.240414	−	0.191724i
$341$	2.50827e7	+	1.71011e7i	0.632575	+	0.431282i
$342$	−1.05323e6	−	507208.i	−0.0263296	−	0.0126797i
$343$		−	1.44827e7i		−	0.358894i
$344$	1.42405e7	+	1.38117e7i	0.349825	+	0.339290i
$345$	5.84858e6			0.142427
$346$	−3.47319e6	+	7.21214e6i	−0.0838493	+	0.174115i
$347$	1.34034e7	−	1.96592e7i	0.320795	−	0.470520i	−0.631640	−	0.775262i	$-0.717618\pi$
$347$	1.34034e7	−	1.96592e7i	0.320795	−	0.470520i	0.952435	+	0.304742i	$0.0985702\pi$
$348$	−2.21886e7	−	2.78236e7i	−0.526492	−	0.660200i
$349$	5.38707e7	+	5.80588e7i	1.26729	+	1.36582i	0.900108	+	0.435667i	$0.143487\pi$
$349$	5.38707e7	+	5.80588e7i	1.26729	+	1.36582i	0.367183	+	0.930149i	$0.380322\pi$
$350$	−3.74298e7	−	6.48303e7i	−0.872998	−	1.51208i
$351$	2.15407e7	+	1.24365e7i	0.498125	+	0.287592i
$352$	4.10701e7	−	9.37398e6i	0.941668	−	0.214930i
$353$	−2.79031e7	−	7.10959e7i	−0.634348	−	1.61629i	−0.779154	−	0.626833i	$-0.784351\pi$
$353$	−2.79031e7	−	7.10959e7i	−0.634348	−	1.61629i	0.144805	−	0.989460i	$-0.453744\pi$
$354$	2.68044e6	−	826806.i	0.0604222	−	0.0186378i
$355$	1.56405e7	−	1.96126e7i	0.349595	−	0.438379i
$356$	2.93062e7	−	2.19619e6i	0.649545	−	0.0486767i
$357$	1.00608e8	+	3.10336e7i	2.21121	+	0.682068i
$358$	−6.74998e7	+	4.60206e7i	−1.47114	+	1.00300i
$359$	4.56033e7	−	6.87360e6i	0.985629	−	0.148560i	0.363601	−	0.931555i	$-0.381547\pi$
$359$	4.56033e7	−	6.87360e6i	0.985629	−	0.148560i	0.622028	+	0.782995i	$0.286309\pi$
$360$	300654.	−	1.31725e6i	0.00644407	−	0.0282333i
$361$	−3.40616e7	−	3.16046e7i	−0.724008	−	0.671781i
$362$	−4.31436e6	−	323316.i	−0.0909474	−	0.00681556i
$363$	−8.21239e6	−	3.22313e6i	−0.171692	−	0.0673841i
$364$	3.55043e6	−	2.35556e7i	0.0736168	−	0.488416i
$365$	−1.00320e7	+	4.83117e6i	−0.206305	+	0.0993514i
$366$	9.27231e6	+	1.92541e7i	0.189123	+	0.392718i
$367$	6.14141e7	+	9.25669e6i	1.24242	+	0.187265i	0.737171	−	0.675706i	$-0.236161\pi$
$367$	6.14141e7	+	9.25669e6i	1.24242	+	0.187265i	0.505253	+	0.862971i	$0.331399\pi$
$368$	−1.25365e7	+	3.19426e7i	−0.251556	+	0.640954i
$369$	10131.5	−	135195.i	0.000201648	−	0.00269080i
$370$	8.63876e6	−	9.31037e6i	0.170548	−	0.183807i
$371$	5.11662e6	+	1.16784e6i	0.100199	+	0.0228697i
$372$	3.62316e6	+	2.40381e7i	0.0703816	+	0.466951i
$373$	1.65984e7	+	2.43454e7i	0.319845	+	0.469126i	0.952166	−	0.305580i	$-0.0988502\pi$
$373$	1.65984e7	+	2.43454e7i	0.319845	+	0.469126i	−0.632322	+	0.774706i	$0.717898\pi$
$374$	−3.03113e7	+	9.82668e7i	−0.579415	+	1.87842i
$375$	1.93259e6	+	2.57886e7i	0.0366476	+	0.489028i
$376$	3.36517e7	+	2.68364e7i	0.633059	+	0.504847i
$377$	1.29948e7	+	4.21280e7i	0.242518	+	0.786225i
$378$	−1.02832e8	+	4.03585e7i	−1.90393	+	0.747239i
$379$	−1.70657e7	−	7.47698e7i	−0.313478	−	1.37344i	−0.848766	−	0.528768i	$-0.822654\pi$
$379$	−1.70657e7	−	7.47698e7i	−0.313478	−	1.37344i	0.535288	−	0.844669i	$-0.320203\pi$
$380$	539719.	−	934821.i	0.00983597	−	0.0170364i
$381$	−5.19890e7	+	3.00158e7i	−0.940018	+	0.542720i
$382$	7.21576e7	−	6.69525e7i	1.29447	−	1.20109i
$383$	−4.02048e7	+	3.20623e7i	−0.715619	+	0.570687i	−0.912173	−	0.409806i	$-0.865596\pi$
$383$	−4.02048e7	+	3.20623e7i	−0.715619	+	0.570687i	0.196554	+	0.980493i	$0.437025\pi$
$384$	−3.76256e7	−	2.56527e7i	−0.664491	−	0.453043i
$385$	−1.96768e7	−	9.47583e6i	−0.344803	−	0.166049i
$386$			7.32866e7i			1.27427i
$387$	6.97362e6	−	9.75765e6i	0.120317	−	0.168350i
$388$	4.07312e7			0.697320
$389$	3.11022e7	−	6.45844e7i	0.528375	−	1.09718i	−0.450510	−	0.892772i	$-0.648758\pi$
$389$	3.11022e7	−	6.45844e7i	0.528375	−	1.09718i	0.978885	−	0.204411i	$-0.0655280\pi$
$390$	−5.81493e6	+	8.52894e6i	−0.0980282	+	0.143781i
$391$	−3.60370e7	−	4.51890e7i	−0.602863	−	0.755966i
$392$	−2.47548e7	−	2.66793e7i	−0.410961	−	0.442910i
$393$	3.17853e7	+	5.50537e7i	0.523659	+	0.907004i
$394$	−2.22841e7	−	1.28657e7i	−0.364339	−	0.210351i
$395$	−2.05890e7	+	4.69931e6i	−0.334075	+	0.0762505i
$396$	−2.57807e6	−	6.56881e6i	−0.0415154	−	0.105779i
$397$	−7.18052e7	+	2.21490e7i	−1.14758	+	0.353983i	−0.809492	−	0.587131i	$-0.800257\pi$
$397$	−7.18052e7	+	2.21490e7i	−1.14758	+	0.353983i	−0.338091	+	0.941113i	$0.609781\pi$
$398$	1.21163e7	−	1.51934e7i	0.192186	−	0.240993i
$399$	9.37712e6	−	702718.i	0.147622	−	0.0110627i
$400$	−6.93767e7	−	2.13999e7i	−1.08401	−	0.334373i
$401$	−7.02464e7	+	4.78932e7i	−1.08941	+	0.742746i	−0.968274	−	0.249890i	$-0.919606\pi$
$401$	−7.02464e7	+	4.78932e7i	−1.08941	+	0.742746i	−0.121135	+	0.992636i	$0.538653\pi$
$402$	1.27781e6	−	192599.i	0.0196693	−	0.00296466i
$403$	6.70125e6	−	2.93601e7i	0.102386	−	0.448583i
$404$	−5.90886e6	−	5.48262e6i	−0.0896107	−	0.0831466i
$405$	1.42728e7	+	1.06960e6i	0.214855	+	0.0161011i
$406$	−1.82266e8	−	7.15341e7i	−2.72350	−	1.06889i
$407$	−6.14409e6	+	4.07634e7i	−0.0911327	+	0.604626i
$408$	4.61082e7	−	2.22046e7i	0.678888	−	0.326935i
$409$	−4.19736e7	−	8.71591e7i	−0.613488	−	1.27392i	−0.943946	−	0.330101i	$-0.892917\pi$
$409$	−4.19736e7	−	8.71591e7i	−0.613488	−	1.27392i	0.330457	−	0.943821i	$-0.392797\pi$
$410$	324510.	+	48912.0i	0.00470844	+	0.000709683i
$411$	−1.03728e7	+	2.64295e7i	−0.149407	+	0.380683i
$412$	7048.45	−	94055.0i	0.000100786	−	0.00134490i
$413$	4.00435e6	−	4.31566e6i	0.0568436	−	0.0612628i
$414$	1.01365e7	+	2.31360e6i	0.142853	+	0.0326052i
$415$	984157.	+	6.52946e6i	0.0137696	+	0.0913551i
$416$	−2.35410e7	−	3.45282e7i	−0.326997	−	0.479617i
$417$	−2.35629e7	+	7.63890e7i	−0.324953	+	1.05347i
$418$	686362.	+	9.15887e6i	0.00939776	+	0.125404i
$419$	8.12661e7	+	6.48075e7i	1.10476	+	0.881015i	0.993619	−	0.112790i	$-0.0359786\pi$
$419$	8.12661e7	+	6.48075e7i	1.10476	+	0.881015i	0.111139	+	0.993805i	$0.464550\pi$
$420$	−5.15483e6	−	1.67116e7i	−0.0695771	−	0.225564i
$421$	−1.22123e8	+	4.79298e7i	−1.63663	+	0.642332i	−0.992462	−	0.122549i	$-0.960893\pi$
$421$	−1.22123e8	+	4.79298e7i	−1.63663	+	0.642332i	−0.644172	+	0.764881i	$0.722798\pi$
$422$	2.77891e6	+	1.21752e7i	0.0369775	+	0.162009i
$423$	1.30109e7	−	2.25355e7i	0.171904	−	0.297746i
$424$	2.20922e6	−	1.27550e6i	0.0289829	−	0.0167333i
$425$	8.96448e7	−	8.31782e7i	1.16777	−	1.08353i
$426$	−1.33630e8	+	1.06566e8i	−1.72852	+	1.37845i
$427$	3.70587e7	+	2.52662e7i	0.475999	+	0.324531i
$428$	8.01360e7	+	3.85914e7i	1.02211	+	0.492221i
$429$		−	3.35047e7i		−	0.424359i
$430$	2.22922e7	+	1.85985e7i	0.280380	+	0.233923i
$431$	8.95369e6			0.111833			0.0559165	−	0.998435i	$-0.482192\pi$
$431$	8.95369e6			0.111833			0.0559165	+	0.998435i	$0.482192\pi$
$432$	−4.64849e7	+	9.65270e7i	−0.576582	+	1.19728i
$433$	5.20850e7	−	7.63946e7i	0.641577	−	0.941021i	−0.358395	−	0.933570i	$-0.616676\pi$
$433$	5.20850e7	−	7.63946e7i	0.641577	−	0.941021i	0.999972	−	0.00745077i	$-0.00237168\pi$
$434$	8.33916e7	+	1.04570e8i	1.02012	+	1.27919i
$435$	2.20144e7	+	2.37259e7i	0.267448	+	0.288241i
$436$	−759938.	−	1.31625e6i	−0.00916893	−	0.0158810i
$437$	−4.47059e6	−	2.58110e6i	−0.0535699	−	0.0309286i
$438$	7.39640e7	−	1.68818e7i	0.880234	−	0.200908i
$439$	2.72488e7	+	6.94288e7i	0.322072	+	0.820627i	0.996601	+	0.0823785i	$0.0262516\pi$
$439$	2.72488e7	+	6.94288e7i	0.322072	+	0.820627i	−0.674529	+	0.738249i	$0.735653\pi$
$440$	−1.01439e7	+	3.12898e6i	−0.119082	+	0.0367321i
$441$	−1.37186e7	+	1.72026e7i	−0.159954	+	0.200576i
$442$	1.01728e8	−	7.62350e6i	1.17808	−	0.0882851i
$443$	6.06746e7	+	1.87156e7i	0.697904	+	0.215275i	0.623351	−	0.781942i	$-0.285771\pi$
$443$	6.06746e7	+	1.87156e7i	0.697904	+	0.215275i	0.0745532	+	0.997217i	$0.476247\pi$
$444$	−2.72749e7	+	1.85957e7i	−0.311612	+	0.212453i
$445$	−2.64293e7	+	3.98357e6i	−0.299920	+	0.0452056i
$446$	4.36967e7	−	1.91448e8i	0.492543	−	2.15797i
$447$	−9.19766e7	−	8.53418e7i	−1.02980	−	0.955519i
$448$	1.91700e7	+	1.43659e6i	0.213200	+	0.0159772i
$449$	1.35114e8	+	5.30283e7i	1.49266	+	0.585826i	0.964679	−	0.263430i	$-0.0848537\pi$
$449$	1.35114e8	+	5.30283e7i	1.49266	+	0.585826i	0.527982	+	0.849256i	$0.322949\pi$
$450$	−3.27866e6	+	2.17525e7i	−0.0359798	+	0.238711i
$451$	−959692.	+	462163.i	−0.0104617	+	0.00503809i
$452$	2.53766e7	+	5.26952e7i	0.274801	+	0.570631i
$453$	9.26833e7	+	1.39698e7i	0.997027	+	0.150278i
$454$	5.00541e7	−	1.27536e8i	0.534900	−	1.36290i
$455$	−1.61903e6	+	2.16045e7i	−0.0171878	+	0.229356i
$456$	3.10887e6	−	3.35057e6i	0.0327875	−	0.0353365i
$457$	1.71320e8	+	3.91026e7i	1.79498	+	0.409692i	0.984401	−	0.175941i	$-0.0562967\pi$
$457$	1.71320e8	+	3.91026e7i	1.79498	+	0.409692i	0.810577	+	0.585633i	$0.199154\pi$
$458$	−2.10982e7	−	1.39977e8i	−0.219608	−	1.45701i
$459$	−1.01656e8	−	1.49102e8i	−1.05123	−	1.54187i
$460$	−2.82985e6	+	9.17415e6i	−0.0290730	+	0.0942523i
$461$	−1.11864e7	−	1.49272e8i	−0.114179	−	1.52362i	−0.700568	−	0.713586i	$-0.747070\pi$
$461$	−1.11864e7	−	1.49272e8i	−0.114179	−	1.52362i	0.586388	−	0.810030i	$-0.300549\pi$
$462$	1.16339e8	+	9.27774e7i	1.17978	+	0.940842i
$463$	−3.46131e7	−	1.12213e8i	−0.348737	−	1.13058i	−0.944802	−	0.327641i	$-0.893746\pi$
$463$	−3.46131e7	−	1.12213e8i	−0.348737	−	1.13058i	0.596066	−	0.802936i	$-0.296730\pi$
$464$	−1.76770e8	+	6.93770e7i	−1.76951	+	0.694483i
$465$	−4.91969e6	−	2.15545e7i	−0.0489304	−	0.214378i
$466$	−3.45859e7	+	5.99046e7i	−0.341776	+	0.591974i
$467$	1.27454e8	−	7.35857e7i	1.25142	−	0.722509i	0.280030	−	0.959991i	$-0.409656\pi$
$467$	1.27454e8	−	7.35857e7i	1.25142	−	0.722509i	0.971392	+	0.237483i	$0.0763223\pi$
$468$	−5.13152e6	+	4.76136e6i	−0.0500621	+	0.0464508i
$469$	2.12045e6	−	1.69100e6i	0.0205546	−	0.0163917i
$470$	5.20440e7	+	3.54830e7i	0.501277	+	0.341765i
$471$	−7.79550e6	−	3.75411e6i	−0.0746073	−	0.0359290i
$472$		−	2.86161e6i		−	0.0272135i
$473$	−9.37880e7	−	9.11784e6i	−0.886265	−	0.0861605i
$474$	1.43890e8			1.35113
$475$	4.73891e6	−	9.84045e6i	0.0442179	−	0.0918193i
$476$	−9.73593e7	+	1.42800e8i	−0.902727	+	1.32406i
$477$	−961568.	−	1.20577e6i	−0.00885982	−	0.0111099i
$478$	−4.88572e7	−	5.26555e7i	−0.447347	−	0.482126i
$479$	7.31269e7	+	1.26660e8i	0.665382	+	1.15247i	0.979182	+	0.202986i	$0.0650644\pi$
$479$	7.31269e7	+	1.26660e8i	0.665382	+	1.15247i	−0.313800	+	0.949489i	$0.601602\pi$
$480$	−2.65693e7	−	1.53398e7i	−0.240246	−	0.138706i
$481$	3.98691e7	−	9.09986e6i	0.358262	−	0.0817710i
$482$	−8.45583e7	−	2.15451e8i	−0.755119	−	1.92401i
$483$	−7.99196e7	+	2.46519e7i	−0.709271	+	0.218781i
$484$	9.02942e6	−	1.13225e7i	0.0796386	−	0.0998636i
$485$	−3.69402e7	+	2.76829e6i	−0.323798	+	0.0242653i
$486$	5.67214e7	+	1.74962e7i	0.494127	+	0.152418i
$487$	−1.29190e8	+	8.80803e7i	−1.11852	+	0.762591i	−0.973918	−	0.226899i	$-0.927141\pi$
$487$	−1.29190e8	+	8.80803e7i	−1.11852	+	0.762591i	−0.144598	+	0.989491i	$0.546189\pi$
$488$	2.15578e7	−	3.24932e6i	0.185500	−	0.0279597i
$489$	2.09951e7	−	9.19857e7i	0.179553	−	0.786672i
$490$	−3.90432e7	−	3.62268e7i	−0.331862	−	0.307923i
$491$	−1.63526e8	−	1.22546e7i	−1.38147	−	0.103527i	−0.636837	−	0.770999i	$-0.719757\pi$
$491$	−1.63526e8	−	1.22546e7i	−1.38147	−	0.103527i	−0.744635	+	0.667472i	$0.767376\pi$
$492$	−794003.	−	311623.i	−0.00666694	−	0.00261658i
$493$	4.76724e7	−	3.16285e8i	0.397856	−	2.63960i
$494$	8.20887e6	−	3.95318e6i	0.0680930	−	0.0327919i
$495$	2.78456e6	+	5.78221e6i	0.0229584	+	0.0476736i
$496$	1.28268e8	+	1.93332e7i	1.05117	+	0.158438i
$497$	−1.31057e8	+	3.33927e8i	−1.06755	+	2.72008i
$498$	3.36217e6	−	4.48650e7i	0.0272227	−	0.363262i
$499$	−1.38106e8	+	1.48843e8i	−1.11151	+	1.19792i	−0.133127	+	0.991099i	$0.542502\pi$
$499$	−1.38106e8	+	1.48843e8i	−1.11151	+	1.19792i	−0.978379	+	0.206820i	$0.933689\pi$
$500$	−4.13873e7	−	9.44638e6i	−0.331098	−	0.0755711i
$501$	1.38237e7	+	9.17145e7i	0.109929	+	0.729332i
$502$	1.04952e8	+	1.53936e8i	0.829620	+	1.21683i
$503$	−9.12581e6	+	2.95851e7i	−0.0717080	+	0.232472i	−0.984331	−	0.176331i	$-0.943577\pi$
$503$	−9.12581e6	+	2.95851e7i	−0.0717080	+	0.232472i	0.912623	+	0.408802i	$0.134053\pi$
$504$	1.44388e6	+	1.92673e7i	0.0112782	+	0.150497i
$505$	5.73152e6	+	4.57074e6i	0.0445037	+	0.0354905i
$506$	−2.40782e7	−	7.80595e7i	−0.185854	−	0.602524i
$507$	7.70975e7	−	3.02585e7i	0.591584	−	0.232179i
$508$	−2.19282e7	−	9.60737e7i	−0.167268	−	0.732847i
$509$	4.50671e7	−	7.80586e7i	0.341749	−	0.591926i	−0.643009	−	0.765859i	$-0.722314\pi$
$509$	4.50671e7	−	7.80586e7i	0.341749	−	0.591926i	0.984758	+	0.173933i	$0.0556476\pi$
$510$	6.48590e7	−	3.74464e7i	0.488945	−	0.282292i
$511$	1.16722e8	−	1.08302e8i	0.874763	−	0.811661i
$512$	7.75050e7	−	6.18082e7i	0.577457	−	0.460507i
$513$	−1.33168e7	−	9.07923e6i	−0.0986387	−	0.0672507i
$514$	−2.04436e7	−	9.84512e6i	−0.150546	−	0.0724990i
$515$			85780.0i			0.000628007i
$516$	−4.57306e7	−	6.00204e7i	−0.332857	−	0.436868i
$517$	−2.04447e8			−1.47948
$518$	−7.88033e7	+	1.63637e8i	−0.566964	+	1.17731i
$519$	−1.06592e7	+	1.56341e7i	−0.0762466	+	0.111833i
$520$	6.56579e6	+	8.23324e6i	0.0466957	+	0.0585546i
$521$	−4.99880e7	−	5.38742e7i	−0.353470	−	0.380950i	0.531138	−	0.847285i	$-0.321764\pi$
$521$	−4.99880e7	−	5.38742e7i	−0.353470	−	0.380950i	−0.884608	+	0.466335i	$0.845574\pi$
$522$	2.87690e7	+	4.98293e7i	0.202261	+	0.350327i
$523$	6.90774e7	+	3.98819e7i	0.482871	+	0.278786i	0.721612	−	0.692298i	$-0.243401\pi$
$523$	6.90774e7	+	3.98819e7i	0.482871	+	0.278786i	−0.238741	+	0.971083i	$0.576735\pi$
$524$	−1.01737e8	+	2.32209e7i	−0.707109	+	0.161393i
$525$	−6.46485e7	−	1.64722e8i	−0.446767	−	1.13834i
$526$	−4.91997e7	+	1.51761e7i	−0.338069	+	0.104280i
$527$	−1.36228e8	+	1.70824e8i	−0.930750	+	1.16712i
$528$	1.43913e8	−	1.07848e7i	0.977682	−	0.0732672i
$529$	−9.75856e7	−	3.01012e7i	−0.659202	−	0.203337i
$530$	3.08450e6	−	2.10298e6i	0.0207185	−	0.0141256i
$531$	−1.71070e6	+	257847.i	−0.0114259	+	0.00172218i
$532$	−3.43485e6	+	1.50491e7i	−0.0228125	+	0.0999481i
$533$	774591.	+	718716.i	0.00511553	+	0.00474652i
$534$	1.81600e8	+	1.36090e7i	1.19259	+	0.0893725i
$535$	−7.53002e7	−	2.95532e7i	−0.491739	−	0.192993i
$536$	196481.	−	1.30357e6i	0.00127593	−	0.00846525i
$537$	−1.73988e8	+	8.37882e7i	−1.12356	+	0.541078i
$538$	1.00443e8	+	2.08572e8i	0.645018	+	1.33939i
$539$	1.70942e8	+	2.57653e7i	1.09165	+	0.164539i
$540$	−1.09511e7	+	2.79031e7i	−0.0695470	+	0.177203i
$541$	−3.13854e6	+	4.18809e7i	−0.0198215	+	0.264499i	0.978485	+	0.206320i	$0.0661487\pi$
$541$	−3.13854e6	+	4.18809e7i	−0.0198215	+	0.264499i	−0.998306	+	0.0581796i	$0.981470\pi$
$542$	1.52981e8	−	1.64875e8i	0.960817	−	1.03551i
$543$	−9.97051e6	−	2.27570e6i	−0.0622756	−	0.0142140i
$544$	4.51886e7	+	2.99806e8i	0.280693	+	1.86228i
$545$	778666.	+	1.14209e6i	0.00481018	+	0.00705524i
$546$	4.35101e7	−	1.41056e8i	0.267308	−	0.866592i
$547$	1.87171e7	+	2.49763e8i	0.114361	+	1.52604i	0.699222	+	0.714905i	$0.253530\pi$
$547$	1.87171e7	+	2.49763e8i	0.114361	+	1.52604i	−0.584861	+	0.811133i	$0.698851\pi$
$548$	−3.64387e7	−	2.90589e7i	−0.221422	−	0.176578i
$549$	−3.88495e6	−	1.25947e7i	−0.0234784	−	0.0761152i
$550$	1.60888e8	−	6.31438e7i	0.967020	−	0.379527i
$551$	−6.35686e6	−	2.78512e7i	−0.0380004	−	0.166491i
$552$	−2.03263e7	+	3.52061e7i	−0.120848	+	0.209315i
$553$	2.61537e8	−	1.50998e8i	1.54653	−	0.892887i
$554$	6.60749e7	−	6.13085e7i	0.388604	−	0.360572i
$555$	2.34724e7	−	1.87186e7i	0.137303	−	0.109495i
$556$	−1.08424e8	−	7.39220e7i	−0.630811	−	0.430080i
$557$	8.89453e7	+	4.28338e7i	0.514704	+	0.247868i	0.673159	−	0.739498i	$-0.264937\pi$
$557$	8.89453e7	+	4.28338e7i	0.514704	+	0.247868i	−0.158455	+	0.987366i	$0.550651\pi$
$558$		−	3.93036e7i		−	0.226220i
$559$	2.55711e7	+	8.99116e7i	0.146391	+	0.514731i
$560$	−9.33189e7			−0.531381
$561$	−1.05470e8	+	2.19011e8i	−0.597366	+	1.24044i
$562$	−2.00804e8	+	2.94526e8i	−1.13126	+	1.65926i
$563$	3.87717e7	+	4.86181e7i	0.217265	+	0.272441i	0.878505	−	0.477732i	$-0.158541\pi$
$563$	3.87717e7	+	4.86181e7i	0.217265	+	0.272441i	−0.661241	+	0.750174i	$0.729970\pi$
$564$	−1.11355e8	−	1.20012e8i	−0.620687	−	0.668941i
$565$	−2.65961e7	−	4.60659e7i	−0.147460	−	0.255408i
$566$	−2.47857e8	−	1.43101e8i	−1.36695	−	0.789209i
$567$	−1.99543e8	+	4.55445e7i	−1.09468	+	0.249854i
$568$	6.37025e7	+	1.62311e8i	0.347626	+	0.885736i
$569$	−3.78001e7	+	1.16598e7i	−0.205190	+	0.0632926i	−0.395646	−	0.918403i	$-0.629479\pi$
$569$	−3.78001e7	+	1.16598e7i	−0.205190	+	0.0632926i	0.190457	+	0.981696i	$0.439003\pi$
$570$	4.17046e6	−	5.22959e6i	0.0225195	−	0.0282386i
$571$	1.67546e8	−	1.25558e7i	0.899963	−	0.0674429i	0.383292	−	0.923627i	$-0.374790\pi$
$571$	1.67546e8	−	1.25558e7i	0.899963	−	0.0674429i	0.516671	+	0.856184i	$0.327171\pi$
$572$	5.25558e7	+	1.62113e7i	0.280823	+	0.0866224i
$573$	1.92250e8	−	1.31074e8i	1.02188	−	0.696709i
$574$	−4.64053e6	+	699447.i	−0.0245376	+	0.00369844i
$575$	−2.16162e7	+	9.47069e7i	−0.113704	+	0.498171i
$576$	−4.14107e6	−	3.84235e6i	−0.0216693	−	0.0201062i
$577$	−4.07354e6	−	305270.i	−0.0212053	−	0.00158912i	0.0641232	−	0.997942i	$-0.479575\pi$
$577$	−4.07354e6	−	305270.i	−0.0212053	−	0.00158912i	−0.0853285	+	0.996353i	$0.527194\pi$
$578$	−4.60413e8	−	1.80699e8i	−2.38432	−	0.935775i
$579$	−2.58194e7	+	1.71301e8i	−0.133018	+	0.882518i
$580$	−4.78684e7	+	2.30522e7i	−0.245338	+	0.118149i
$581$	−4.09702e7	−	8.50754e7i	−0.208900	−	0.433786i
$582$	2.49578e8	+	3.76178e7i	1.26601	+	0.190820i
$583$	−4.42684e6	+	1.12794e7i	−0.0223403	+	0.0569221i
$584$	5.78378e6	−	7.71792e7i	0.0290384	−	0.387491i
$585$	4.33031e6	−	4.66696e6i	0.0216297	−	0.0233113i
$586$	1.50544e8	+	3.43608e7i	0.748121	+	0.170754i
$587$	−8.70442e6	−	5.77501e7i	−0.0430354	−	0.285521i	0.956953	−	0.290241i	$-0.0937356\pi$
$587$	−8.70442e6	−	5.77501e7i	−0.0430354	−	0.285521i	−0.999989	+	0.00472030i	$0.998497\pi$
$588$	7.79813e7	+	1.14378e8i	0.383582	+	0.562612i
$589$	−5.75191e6	+	1.86472e7i	−0.0281492	+	0.0912574i
$590$	−312952.	−	4.17605e6i	−0.00152378	−	0.0203334i
$591$	−4.75543e7	−	3.79233e7i	−0.230371	−	0.183714i
$592$	5.19201e7	+	1.68321e8i	0.250248	+	0.811283i
$593$	8.30160e7	−	3.25814e7i	0.398105	−	0.156245i	−0.157838	−	0.987465i	$-0.550452\pi$
$593$	8.30160e7	−	3.25814e7i	0.398105	−	0.156245i	0.555943	+	0.831220i	$0.312357\pi$
$594$	−5.67534e7	−	2.48653e8i	−0.270790	−	1.18641i
$595$	7.85923e7	−	1.36126e8i	0.373103	−	0.646234i
$596$	1.78371e8	−	1.02983e8i	0.842531	−	0.486435i
$597$	3.36735e7	−	3.12445e7i	0.158258	−	0.146842i
$598$	−6.33564e7	+	5.05251e7i	−0.296270	+	0.236267i
$599$	−1.35186e8	−	9.21680e7i	−0.628999	−	0.428844i	0.206415	−	0.978464i	$-0.433820\pi$
$599$	−1.35186e8	−	9.21680e7i	−0.628999	−	0.428844i	−0.835415	+	0.549620i	$0.814773\pi$
$600$	−7.74940e7	−	3.73191e7i	−0.358769	−	0.172774i
$601$			4.89898e7i			0.225674i	0.993614	+	0.112837i	$0.0359938\pi$
$601$			4.89898e7i			0.225674i	−0.993614	+	0.112837i	$0.964006\pi$
$602$	−3.83011e8	−	1.60182e8i	−1.75558	−	0.734217i
$603$	−796992.			−0.00363498
$604$	−6.67582e7	+	1.38625e8i	−0.302966	+	0.629115i
$605$	−7.41948e6	+	1.08824e7i	−0.0335048	+	0.0491425i
$606$	−3.11426e7	−	3.90516e7i	−0.139939	−	0.175477i
$607$	−7.50361e6	−	8.08697e6i	−0.0335509	−	0.0361593i	0.716053	−	0.698045i	$-0.245947\pi$
$607$	−7.50361e6	−	8.08697e6i	−0.0335509	−	0.0361593i	−0.749604	+	0.661886i	$0.769756\pi$
$608$	1.35395e7	+	2.34512e7i	0.0602411	+	0.104341i
$609$	−4.00828e8	−	2.31418e8i	−1.77462	−	1.02458i
$610$	3.11047e7	−	7.09945e6i	0.137037	−	0.0312777i
$611$	7.40961e7	+	1.88794e8i	0.324842	+	0.827683i
$612$	4.85317e7	−	1.49701e7i	0.211725	−	0.0653084i
$613$	8.28003e7	−	1.03828e8i	0.359460	−	0.450748i	−0.568913	−	0.822397i	$-0.692636\pi$
$613$	8.28003e7	−	1.03828e8i	0.359460	−	0.450748i	0.928373	+	0.371649i	$0.121207\pi$
$614$	4.98661e8	−	3.73695e7i	2.15427	−	0.161440i
$615$	741281.	+	228655.i	0.00318682	+	0.000983004i
$616$	1.25426e8	−	8.55138e7i	0.536592	−	0.365843i
$617$	−2.11711e7	+	3.19104e6i	−0.0901340	+	0.0135855i	−0.193954	−	0.981011i	$-0.562131\pi$
$617$	−2.11711e7	+	3.19104e6i	−0.0901340	+	0.0135855i	0.103820	+	0.994596i	$0.466893\pi$
$618$	130055.	−	569807.i	0.000551011	−	0.00241414i
$619$	−9.29671e7	−	8.62609e7i	−0.391974	−	0.363699i	0.459426	−	0.888216i	$-0.348055\pi$
$619$	−9.29671e7	−	8.62609e7i	−0.391974	−	0.363699i	−0.851400	+	0.524517i	$0.824246\pi$
$620$	3.61911e7	+	2.71215e6i	0.151854	+	0.0113799i
$621$	1.33441e8	+	5.23717e7i	0.557204	+	0.218686i
$622$	4.90030e7	−	3.25114e8i	0.203635	−	1.35103i
$623$	3.44359e8	−	1.65835e8i	1.42412	−	0.685822i
$624$	−6.21162e7	−	1.28986e8i	−0.255653	−	0.530869i
$625$	−1.83327e8	−	2.76321e7i	−0.750907	−	0.113181i
$626$	−1.03981e8	+	2.64940e8i	−0.423870	+	1.08000i
$627$	−1.62243e6	+	2.16498e7i	−0.00658209	+	0.0878318i
$628$	9.66061e6	−	1.04117e7i	0.0390055	−	0.0420379i
$629$	−2.89259e8	−	6.60214e7i	−1.16234	−	0.265297i
$630$	4.21421e6	+	2.79595e7i	0.0168537	+	0.111817i
$631$	2.56268e7	+	3.75877e7i	0.102002	+	0.149609i	0.873846	−	0.486202i	$-0.161618\pi$
$631$	2.56268e7	+	3.75877e7i	0.102002	+	0.149609i	−0.771845	+	0.635811i	$0.780666\pi$
$632$	4.32675e7	−	1.40270e8i	0.171400	−	0.555665i
$633$	2.20603e6	+	2.94375e7i	0.00869763	+	0.116062i
$634$	2.23753e8	+	1.78437e8i	0.878014	+	0.700192i
$635$	2.64169e7	+	8.56414e7i	0.103172	+	0.334474i
$636$	−9.03224e6	+	3.54489e6i	−0.0351095	+	0.0137795i
$637$	−3.81604e7	−	1.67192e8i	−0.147637	−	0.646839i
$638$	2.26032e8	−	3.91499e8i	0.870377	−	1.50754i
$639$	9.12916e7	−	5.27072e7i	0.349887	−	0.202008i
$640$	−4.98369e7	+	4.62419e7i	−0.190113	+	0.176399i
$641$	−1.45818e8	+	1.16286e8i	−0.553652	+	0.441523i	−0.859925	−	0.510421i	$-0.829490\pi$
$641$	−1.45818e8	+	1.16286e8i	−0.553652	+	0.441523i	0.306272	+	0.951944i	$0.400918\pi$
$642$	4.55386e8	+	3.10477e8i	1.72098	+	1.17334i
$643$	3.89418e8	+	1.87534e8i	1.46481	+	0.705418i	0.985096	−	0.172005i	$-0.0550244\pi$
$643$	3.89418e8	+	1.87534e8i	1.46481	+	0.705418i	0.479719	+	0.877422i	$0.340739\pi$
$644$		−	1.37291e8i		−	0.514024i
$645$	4.55536e7	+	5.13260e7i	0.169763	+	0.191275i
$646$	−6.61034e7			−0.245203
$647$	1.12798e8	−	2.34227e8i	0.416474	−	0.864818i	−0.582185	−	0.813056i	$-0.697802\pi$
$647$	1.12798e8	−	2.34227e8i	0.416474	−	0.864818i	0.998659	−	0.0517616i	$-0.0164836\pi$
$648$	−5.60426e7	+	8.21994e7i	−0.205965	+	0.302095i
$649$	8.47475e6	+	1.06270e7i	0.0310022	+	0.0388756i
$650$	−1.16618e8	−	1.25685e8i	−0.424646	−	0.457660i
$651$	1.58080e8	+	2.73802e8i	0.572971	+	0.992415i
$652$	1.34131e8	+	7.74407e7i	0.483935	+	0.279400i
$653$	−3.02166e8	+	6.89674e7i	−1.08519	+	0.247688i	−0.727469	−	0.686141i	$-0.759303\pi$
$653$	−3.02166e8	+	6.89674e7i	−1.08519	+	0.247688i	−0.357721	+	0.933828i	$0.616446\pi$
$654$	−3.44083e6	−	8.76709e6i	−0.0123007	−	0.0313417i
$655$	9.06899e7	−	2.79741e7i	0.322727	−	0.0995481i
$656$	−2.83777e6	+	3.55845e6i	−0.0100523	+	0.0126052i
$657$	−4.66597e7	+	3.49666e6i	−0.164530	+	0.0123298i
$658$	−8.60733e8	−	2.65501e8i	−3.02128	−	0.931941i
$659$	−3.00650e8	+	2.04980e8i	−1.05052	+	0.716234i	−0.960096	−	0.279669i	$-0.909775\pi$
$659$	−3.00650e8	+	2.04980e8i	−1.05052	+	0.716234i	−0.0904261	+	0.995903i	$0.528823\pi$
$660$	3.99264e7	−	6.01794e6i	0.138876	−	0.0209322i
$661$	−2.45858e7	+	1.07718e8i	−0.0851296	+	0.372977i	−0.999490	−	0.0319233i	$-0.989837\pi$
$661$	−2.45858e7	+	1.07718e8i	−0.0851296	+	0.372977i	0.914361	+	0.404901i	$0.132694\pi$
$662$	9.10219e7	+	8.44560e7i	0.313742	+	0.291110i
$663$	2.40467e8	+	1.80205e7i	0.825116	+	0.0618339i
$664$	−4.27251e7	−	1.67684e7i	−0.145941	−	0.0572778i
$665$	2.09235e6	−	1.38818e7i	0.00711491	−	0.0472043i
$666$	4.80863e7	−	2.31571e7i	0.162779	−	0.0783902i
$667$	1.10243e8	+	2.28921e8i	0.371511	+	0.771451i
$668$	−1.50553e8	−	2.26922e7i	−0.505080	−	0.0761286i
$669$	1.69586e8	−	4.32098e8i	0.566384	−	1.44312i
$670$	144171.	−	1.92383e6i	0.000479352	−	0.00639650i
$671$	−7.04350e7	+	7.59109e7i	−0.233142	+	0.251268i
$672$	4.27722e8	+	9.76248e7i	1.40946	+	0.321701i
$673$	−2.55471e7	−	1.69494e8i	−0.0838101	−	0.556044i	−0.990847	−	0.134992i	$-0.956899\pi$
$673$	−2.55471e7	−	1.69494e8i	−0.0838101	−	0.556044i	0.907037	−	0.421052i	$-0.138339\pi$
$674$	−1.72346e8	−	2.52785e8i	−0.562886	−	0.825602i
$675$	−8.93985e7	+	2.89823e8i	−0.290682	+	0.942369i
$676$	1.01601e7	+	1.35577e8i	0.0328894	+	0.438879i
$677$	2.07657e8	+	1.65601e8i	0.669237	+	0.533699i	0.898117	−	0.439756i	$-0.144935\pi$
$677$	2.07657e8	+	1.65601e8i	0.669237	+	0.533699i	−0.228880	+	0.973455i	$0.573506\pi$
$678$	1.06827e8	+	3.46323e8i	0.342760	+	1.11120i
$679$	4.93112e8	−	1.93532e8i	1.57520	−	0.618221i
$680$	−1.70012e7	−	7.44870e7i	−0.0540695	−	0.236894i
$681$	1.61929e8	−	2.80469e8i	0.512723	−	0.888063i
$682$	−2.67429e8	+	1.54400e8i	−0.843054	+	0.486737i
$683$	−7.05303e7	+	6.54425e7i	−0.221367	+	0.205399i	−0.783058	−	0.621948i	$-0.786341\pi$
$683$	−7.05303e7	+	6.54425e7i	−0.221367	+	0.205399i	0.561691	+	0.827347i	$0.310151\pi$
$684$	3.54642e6	−	2.82817e6i	0.0110821	−	0.00883767i
$685$	3.50221e7	+	2.38777e7i	0.108961	+	0.0742883i
$686$	1.32729e8	+	6.39190e7i	0.411144	+	0.197996i
$687$		−	3.34617e8i		−	1.03200i
$688$	−3.77967e8	+	1.38777e8i	−1.16062	+	0.426140i
$689$	1.20202e7			0.0367497
$690$	−2.58126e7	+	5.36005e7i	−0.0785751	+	0.163163i
$691$	8.49709e7	−	1.24629e8i	0.257535	−	0.377734i	−0.675595	−	0.737273i	$-0.736113\pi$
$691$	8.49709e7	−	1.24629e8i	0.257535	−	0.377734i	0.933130	+	0.359538i	$0.117066\pi$
$692$	−1.93664e7	−	2.42847e7i	−0.0584426	−	0.0732847i
$693$	−6.24227e7	−	6.72756e7i	−0.187561	−	0.202143i
$694$	1.21015e8	+	2.09604e8i	0.362044	+	0.627078i
$695$	1.03356e8	+	5.96728e7i	0.307881	+	0.177755i
$696$	−2.19330e8	+	5.00606e7i	−0.650534	+	0.148480i
$697$	−2.80083e6	−	7.13640e6i	−0.00827157	−	0.0210756i
$698$	−7.69849e8	+	2.37467e8i	−2.26381	+	0.698292i
$699$	−1.01946e8	+	1.27837e8i	−0.298497	+	0.374303i
$700$	2.89665e8	−	2.17074e7i	0.844503	−	0.0632868i
$701$	−4.69681e8	−	1.44877e8i	−1.36348	−	0.420578i	−0.475199	−	0.879878i	$-0.657624\pi$
$701$	−4.69681e8	−	1.44877e8i	−1.36348	−	0.420578i	−0.888281	+	0.459300i	$0.848100\pi$
$702$	−2.09046e8	+	1.42525e8i	−0.604270	+	0.411984i
$703$	−2.62030e7	+	3.94947e6i	−0.0754197	+	0.0113677i
$704$	−9.87629e6	+	4.32709e7i	−0.0283058	+	0.124016i
$705$	1.09147e8	+	1.01274e8i	0.311491	+	0.289022i
$706$	7.74722e8	+	5.80574e7i	2.20157	+	0.164984i
$707$	−9.75859e7	−	3.82996e7i	−0.276140	−	0.108377i
$708$	−1.62224e6	+	1.07629e7i	−0.00457105	+	0.0303270i
$709$	1.09206e8	−	5.25908e7i	0.306413	−	0.147561i	−0.274358	−	0.961628i	$-0.588465\pi$
$709$	1.09206e8	−	5.25908e7i	0.306413	−	0.147561i	0.580771	+	0.814067i	$0.302751\pi$
$710$	1.10714e8	+	2.29900e8i	0.309334	+	0.642339i
$711$	−8.77534e7	−	1.32267e7i	−0.244149	−	0.0367996i
$712$	6.78733e7	−	1.72938e8i	0.188044	−	0.479127i
$713$	1.29703e7	−	1.73077e8i	0.0357834	−	0.477496i
$714$	−7.28447e8	+	7.85080e8i	−2.00126	+	2.15685i
$715$	−4.87660e7	−	1.11305e7i	−0.133413	−	0.0304507i
$716$	−4.72466e7	−	3.13460e8i	−0.128716	−	0.853972i
$717$	−9.56483e7	−	1.40290e8i	−0.259489	−	0.380601i
$718$	−1.38275e8	+	4.48277e8i	−0.373569	+	1.21108i
$719$	1.97229e7	+	2.63184e8i	0.0530621	+	0.708065i	0.958774	+	0.284171i	$0.0917182\pi$
$719$	1.97229e7	+	2.63184e8i	0.0530621	+	0.708065i	−0.905712	+	0.423894i	$0.860663\pi$
$720$	2.14399e7	+	1.70978e7i	0.0574414	+	0.0458080i
$721$	−361565.	−	1.17217e6i	−0.000964674	−	0.00312740i
$722$	4.39976e8	−	1.72678e8i	1.16901	−	0.458802i
$723$	−1.21742e8	−	5.33388e8i	−0.322127	−	1.41133i
$724$	8.39395e6	−	1.45387e7i	0.0221182	−	0.0383099i
$725$	−4.65562e8	+	2.68792e8i	−1.22170	+	0.705347i
$726$	6.57843e7	−	6.10389e7i	0.171914	−	0.159513i
$727$	−1.54713e8	+	1.23380e8i	−0.402646	+	0.321100i	−0.803787	−	0.594917i	$-0.797185\pi$
$727$	−1.54713e8	+	1.23380e8i	−0.402646	+	0.321100i	0.401141	+	0.916016i	$0.368614\pi$
$728$	−1.24423e8	−	8.48305e7i	−0.322484	−	0.219866i
$729$	3.88298e8	+	1.86994e8i	1.00226	+	0.482665i
$730$		−	1.13263e8i		−	0.291151i
$731$	1.15884e8	−	6.68223e8i	0.296668	−	1.71068i
$732$	−8.29237e7			−0.211420
$733$	5.82370e7	−	1.20930e8i	0.147872	−	0.307060i	−0.813855	−	0.581068i	$-0.802635\pi$
$733$	5.82370e7	−	1.20930e8i	0.147872	−	0.307060i	0.961728	+	0.274008i	$0.0883494\pi$
$734$	−3.55885e8	+	5.21987e8i	−0.899957	+	1.31999i
$735$	−7.84969e7	−	9.84321e7i	−0.197693	−	0.247899i
$736$	−1.63816e8	−	1.76552e8i	−0.410888	−	0.442832i
$737$	3.13090e6	+	5.42288e6i	0.00782108	+	0.0135465i
$738$	1.19431e6	+	689533.i	0.00297130	+	0.00171548i
$739$	−3.15155e8	+	7.19321e7i	−0.780892	+	0.178234i	−0.594343	−	0.804212i	$-0.702588\pi$
$739$	−3.15155e8	+	7.19321e7i	−0.780892	+	0.178234i	−0.186550	+	0.982446i	$0.559731\pi$
$740$	1.80051e7	+	4.58762e7i	0.0444324	+	0.113212i
$741$	2.05802e7	−	6.34816e6i	0.0505819	−	0.0156025i
$742$	−3.32850e7	+	4.17381e7i	−0.0814773	+	0.102169i
$743$	−7.74782e7	+	5.80619e6i	−0.188892	+	0.0141555i	−0.168840	−	0.985643i	$-0.554002\pi$
$743$	−7.74782e7	+	5.80619e6i	−0.188892	+	0.0141555i	−0.0200517	+	0.999799i	$0.506383\pi$
$744$	1.46848e8	+	4.52965e7i	0.356573	+	0.109988i
$745$	−1.54770e8	+	1.05521e8i	−0.374299	+	0.255193i
$746$	−2.96375e8	+	4.46713e7i	−0.713879	+	0.107600i
$747$	−6.17455e6	+	2.70525e7i	−0.0148130	+	0.0649000i
$748$	−2.92511e8	−	2.71410e8i	−0.698935	−	0.648517i
$749$	1.15353e9	+	8.64451e7i	2.74526	+	0.205729i
$750$	−2.44874e8	−	9.61059e7i	−0.580442	−	0.227807i
$751$	−5.09014e7	+	3.37709e8i	−0.120174	+	0.797301i	0.844824	+	0.535044i	$0.179705\pi$
$751$	−5.09014e7	+	3.37709e8i	−0.120174	+	0.797301i	−0.964998	+	0.262257i	$0.915533\pi$
$752$	−7.87077e8	+	3.79036e8i	−1.85082	+	0.891306i
$753$	1.91083e8	+	3.96787e8i	0.447545	+	0.929336i
$754$	−4.43442e8	−	6.68382e7i	−1.03448	−	0.155923i
$755$	5.11231e7	−	1.30260e8i	0.118789	−	0.302670i
$756$	3.20329e7	−	4.27449e8i	0.0741362	−	0.989279i
$757$	2.71586e8	−	2.92700e8i	0.626066	−	0.674739i	−0.337772	−	0.941228i	$-0.609673\pi$
$757$	2.71586e8	−	2.92700e8i	0.626066	−	0.674739i	0.963838	+	0.266489i	$0.0858637\pi$
$758$	7.60562e8	+	1.73593e8i	1.74633	+	0.398589i
$759$	−2.87796e7	−	1.90940e8i	−0.0658201	−	0.436688i
$760$	−3.84395e6	−	5.63804e6i	−0.00875664	−	0.0128436i
$761$	2.03677e7	−	6.60305e7i	0.0462156	−	0.149827i	−0.929524	−	0.368762i	$-0.879782\pi$
$761$	2.03677e7	−	6.60305e7i	0.0462156	−	0.149827i	0.975740	+	0.218934i	$0.0702581\pi$
$762$	−4.56336e7	−	6.08938e8i	−0.103138	−	1.37628i
$763$	−1.54543e7	−	1.23244e7i	−0.0347916	−	0.0277454i
$764$	1.12583e8	+	3.64985e8i	0.252460	+	0.818456i
$765$	−4.29972e7	+	1.68752e7i	−0.0960409	+	0.0376933i
$766$	−1.16398e8	−	5.09971e8i	−0.258975	−	1.13464i
$767$	6.74191e6	−	1.16773e7i	0.0149416	−	0.0258796i
$768$	4.51067e8	−	2.60424e8i	0.995766	−	0.574906i
$769$	−3.08823e8	+	2.86546e8i	−0.679096	+	0.630109i	−0.942354	−	0.334616i	$-0.891393\pi$
$769$	−3.08823e8	+	2.86546e8i	−0.679096	+	0.630109i	0.263258	+	0.964725i	$0.415203\pi$
$770$	1.73686e8	−	1.38510e8i	0.380446	−	0.303396i
$771$	−4.43166e7	−	3.02145e7i	−0.0966948	−	0.0659254i
$772$	−2.56211e8	−	1.23385e8i	−0.556861	−	0.268170i
$773$			5.96777e8i			1.29203i	0.763324	+	0.646016i	$0.223566\pi$
$773$			5.96777e8i			1.29203i	−0.763324	+	0.646016i	$0.776434\pi$
$774$	5.86480e7	+	1.06976e8i	0.126482	+	0.230709i
$775$	3.67219e8			0.788896
$776$	1.11719e8	−	2.31986e8i	0.239079	−	0.496452i
$777$	−2.41846e8	+	3.54723e8i	−0.515556	+	0.756182i
$778$	4.54627e8	+	5.70085e8i	0.965421	+	1.21060i
$779$	−465717.	−	501924.i	−0.000985167	−	0.00106176i
$780$	−2.00274e7	−	3.46884e7i	−0.0422027	−	0.0730972i
$781$	−7.17259e8	−	4.14110e8i	−1.50565	−	0.869285i
$782$	5.73192e8	−	1.30827e8i	1.19862	−	0.273576i
$783$	2.89824e8	+	7.38459e8i	0.603738	+	1.53830i
$784$	7.05856e8	−	2.17728e8i	1.46476	−	0.451820i
$785$	−8.05383e6	+	1.00992e7i	−0.0166492	+	0.0208774i
$786$	−6.44835e8	+	4.83237e7i	−1.32795	+	0.0995158i
$787$	−4.65649e8	−	1.43634e8i	−0.955289	−	0.294668i	−0.222354	−	0.974966i	$-0.571374\pi$
$787$	−4.65649e8	−	1.43634e8i	−0.955289	−	0.294668i	−0.732935	+	0.680298i	$0.761850\pi$
$788$	8.24961e7	−	5.62449e7i	0.168599	−	0.114949i
$789$	−1.20346e8	+	1.81393e7i	−0.245020	+	0.0369309i
$790$	4.78016e7	−	2.09432e8i	0.0969529	−	0.424778i
$791$	5.57600e8	+	5.17377e8i	1.12666	+	1.04539i
$792$	−4.44841e7	−	3.33362e6i	−0.0895425	−	0.00671029i
$793$	9.56260e7	+	3.75304e7i	0.191759	+	0.0752600i
$794$	1.13923e8	−	7.55827e8i	0.227587	−	1.50994i
$795$	7.95065e6	−	3.82883e6i	0.0158234	−	0.00762017i
$796$	3.27174e7	+	6.79384e7i	0.0648693	+	0.134703i
$797$	5.03430e8	+	7.58798e7i	0.994406	+	0.149883i	0.626034	−	0.779796i	$-0.284677\pi$
$797$	5.03430e8	+	7.58798e7i	0.994406	+	0.149883i	0.368372	+	0.929678i	$0.379915\pi$
$798$	−3.49456e7	+	8.90399e7i	−0.0687676	+	0.175217i
$799$	1.09962e8	−	1.46734e9i	0.215577	−	2.87668i
$800$	3.46599e8	−	3.73545e8i	0.676952	−	0.729581i
$801$	−1.09500e8	−	2.49927e7i	−0.213067	−	0.0486313i
$802$	−1.28895e8	−	8.55163e8i	−0.249869	−	1.65777i
$803$	2.07090e8	+	3.03745e8i	0.399956	+	0.586627i
$804$	−1.47798e6	+	4.79151e6i	−0.00284382	+	0.00921942i
$805$	9.33092e6	+	1.24512e8i	0.0178870	+	0.238685i
$806$	2.39501e8	+	1.90995e8i	0.457406	+	0.364769i
$807$	1.61295e8	+	5.22904e8i	0.306901	+	0.994950i
$808$	−4.74335e7	+	1.86163e7i	−0.0899189	+	0.0352906i
$809$	1.22828e8	+	5.38144e8i	0.231981	+	1.01637i	0.947994	+	0.318287i	$0.103108\pi$
$809$	1.22828e8	+	5.38144e8i	0.231981	+	1.01637i	−0.716014	+	0.698086i	$0.754035\pi$
$810$	−7.27954e7	+	1.26085e8i	−0.136977	+	0.237252i
$811$	3.34938e8	−	1.93376e8i	0.627916	−	0.362527i	−0.152029	−	0.988376i	$-0.548581\pi$
$811$	3.34938e8	−	1.93376e8i	0.627916	−	0.362527i	0.779944	+	0.625849i	$0.215247\pi$
$812$	5.56946e8	−	5.16771e8i	1.04027	−	0.965228i
$813$	4.15667e8	−	3.31483e8i	0.773524	−	0.616865i
$814$	−3.46467e8	−	2.36217e8i	−0.642375	−	0.437964i
$815$	−1.26910e8	−	6.11168e7i	−0.234436	−	0.112898i
$816$			1.03868e9i			1.91166i
$817$	−1.21695e7	−	5.93367e7i	−0.0223154	−	0.108807i
$818$	9.84036e8			1.79784
$819$	−3.95014e7	+	8.20254e7i	−0.0719052	+	0.149313i
$820$	−717341.	+	1.05215e6i	−0.00130102	+	0.00190825i
$821$	−4.79891e8	−	6.01764e8i	−0.867188	−	1.08742i	−0.995413	−	0.0956741i	$-0.969499\pi$
$821$	−4.79891e8	−	6.01764e8i	−0.867188	−	1.08742i	0.128225	−	0.991745i	$-0.459072\pi$
$822$	−1.96438e8	−	2.11710e8i	−0.353680	−	0.381176i
$823$	−1.00092e8	−	1.73364e8i	−0.179555	−	0.310999i	0.762173	−	0.647373i	$-0.224133\pi$
$823$	−1.00092e8	−	1.73364e8i	−0.179555	−	0.310999i	−0.941728	+	0.336375i	$0.890799\pi$
$824$	−516361.	−	298121.i	−0.000922937	−	0.000532858i
$825$	3.98307e8	−	9.09110e7i	0.709343	−	0.161903i
$826$	2.18786e7	+	5.57457e7i	0.0388221	+	0.0989171i
$827$	−3.17705e7	+	9.79989e6i	−0.0561703	+	0.0173263i	−0.322713	−	0.946497i	$-0.604595\pi$
$827$	−3.17705e7	+	9.79989e6i	−0.0561703	+	0.0173263i	0.266543	+	0.963823i	$0.414119\pi$
$828$	−2.51542e7	+	3.15423e7i	−0.0443118	+	0.0555652i
$829$	6.26099e8	−	4.69196e7i	1.09895	−	0.0823551i	0.487115	−	0.873338i	$-0.338049\pi$
$829$	6.26099e8	−	4.69196e7i	1.09895	−	0.0823551i	0.611838	+	0.790983i	$0.290430\pi$
$830$	−6.41841e7	−	1.97982e7i	−0.112252	−	0.0346251i
$831$	1.76044e8	−	1.20024e8i	0.306773	−	0.209154i
$832$	4.35372e7	−	6.56218e6i	0.0755946	−	0.0113941i
$833$	−2.76862e8	+	1.21301e9i	−0.478992	+	2.09860i
$834$	−5.96087e8	−	5.53088e8i	−1.02757	−	0.953446i
$835$	1.38083e8	+	1.03479e7i	0.237181	+	0.0177743i
$836$	−3.31751e7	−	1.30203e7i	−0.0567798	−	0.0222844i
$837$	8.07650e7	−	5.35841e8i	0.137736	−	0.913817i
$838$	−9.52608e8	+	4.58752e8i	−1.61876	+	0.779553i
$839$	2.25803e8	+	4.68884e8i	0.382334	+	0.793925i	0.999972	+	0.00746258i	$0.00237544\pi$
$839$	2.25803e8	+	4.68884e8i	0.382334	+	0.793925i	−0.617638	+	0.786463i	$0.711910\pi$
$840$	−1.09320e8	−	1.64774e7i	−0.184443	−	0.0278003i
$841$	−2.96390e8	+	7.55189e8i	−0.498282	+	1.26960i
$842$	9.97266e7	−	1.33076e9i	0.167061	−	2.22927i
$843$	−5.73126e8	+	6.17683e8i	−0.956681	+	1.03106i
$844$	−4.72433e7	−	1.07830e7i	−0.0785802	−	0.0179354i
$845$	−1.84288e7	−	1.22267e8i	−0.0305441	−	0.202647i
$846$	1.49108e8	+	2.18701e8i	0.246257	+	0.361193i
$847$	5.55161e7	−	1.79979e8i	0.0913626	−	0.296190i
$848$	3.86916e6	+	5.16304e7i	0.00634497	+	0.0846677i
$849$	−5.28929e8	−	4.21807e8i	−0.864319	−	0.689272i
$850$	3.66657e8	+	1.18867e9i	0.597040	+	1.93555i
$851$	2.19393e8	−	8.61056e7i	0.355988	−	0.139715i
$852$	−1.47579e8	−	6.46587e8i	−0.238620	−	1.04546i
$853$	3.98951e8	−	6.91004e8i	0.642795	−	1.11335i	−0.342011	−	0.939696i	$-0.611108\pi$
$853$	3.98951e8	−	6.91004e8i	0.642795	−	1.11335i	0.984806	−	0.173658i	$-0.0555588\pi$
$854$	−3.95115e8	+	2.28120e8i	−0.634380	+	0.366260i
$855$	−3.02412e6	+	2.80598e6i	−0.00483839	+	0.00448937i
$856$	4.39598e8	−	3.50568e8i	0.700865	−	0.558921i
$857$	8.04180e7	+	5.48281e7i	0.127765	+	0.0871085i	0.625516	−	0.780211i	$-0.284888\pi$
$857$	8.04180e7	+	5.48281e7i	0.127765	+	0.0871085i	−0.497751	+	0.867320i	$0.665841\pi$
$858$	3.07060e8	+	1.47872e8i	0.486140	+	0.234113i
$859$			4.52627e8i			0.714104i	0.934085	+	0.357052i	$0.116218\pi$
$859$			4.52627e8i			0.714104i	−0.934085	+	0.357052i	$0.883782\pi$
$860$	−1.02552e8	+	4.66216e7i	−0.161231	+	0.0732980i
$861$	−1.10932e7			−0.0173800
$862$	−3.95170e7	+	8.20578e7i	−0.0616967	+	0.128114i
$863$	−5.26132e8	+	7.71694e8i	−0.818582	+	1.20064i	0.158412	+	0.987373i	$0.449363\pi$
$863$	−5.26132e8	+	7.71694e8i	−0.818582	+	1.20064i	−0.976994	+	0.213267i	$0.931590\pi$
$864$	−4.68842e8	−	5.87910e8i	−0.726918	−	0.911527i
$865$	1.92144e7	+	2.07082e7i	0.0296878	+	0.0319958i
$866$	4.70257e8	+	8.14510e8i	0.724072	+	1.25413i
$867$	−1.01251e9	−	5.84574e8i	−1.55361	−	0.896979i
$868$	−5.05975e8	+	1.15486e8i	−0.773696	+	0.176591i
$869$	2.54733e8	+	6.49050e8i	0.388174	+	0.989051i
$870$	−3.14601e8	+	9.70416e7i	−0.477752	+	0.147367i
$871$	3.87297e6	−	4.85655e6i	0.00586124	−	0.00734977i
$872$	−9.58113e6	+	718007.i	−0.0144500	+	0.00108288i
$873$	−1.48750e8	−	4.58834e7i	−0.223571	−	0.0689625i
$874$	4.33859e7	−	2.95800e7i	0.0649851	−	0.0443061i
$875$	−5.45938e8	+	8.22870e7i	−0.814928	+	0.122831i
$876$	−6.55063e7	+	2.87002e8i	−0.0974475	+	0.426946i
$877$	−7.19523e8	−	6.67619e8i	−1.06671	−	0.989761i	−0.0667403	−	0.997770i	$-0.521260\pi$
$877$	−7.19523e8	−	6.67619e8i	−1.06671	−	0.989761i	−0.999968	+	0.00800977i	$0.997450\pi$
$878$	−7.56555e8	−	5.66960e7i	−1.11778	−	0.0837662i
$879$	3.39778e8	+	1.33353e8i	0.500299	+	0.196353i
$880$	3.21118e7	−	2.13048e8i	0.0471212	−	0.312629i
$881$	−2.81689e8	+	1.35654e8i	−0.411948	+	0.198384i	−0.628367	−	0.777917i	$-0.716276\pi$
$881$	−2.81689e8	+	1.35654e8i	−0.411948	+	0.198384i	0.216419	+	0.976301i	$0.430562\pi$
$882$	−9.71098e7	−	2.01651e8i	−0.141533	−	0.293896i
$883$	−4.54698e8	−	6.85347e7i	−0.660452	−	0.0995471i	−0.189740	−	0.981834i	$-0.560765\pi$
$883$	−4.54698e8	−	6.85347e7i	−0.660452	−	0.0995471i	−0.470711	+	0.882287i	$0.656003\pi$
$884$	−1.44618e8	+	3.68480e8i	−0.209346	+	0.533405i
$885$	739759.	−	9.87139e6i	0.00106724	−	0.0142413i
$886$	−4.39310e8	+	4.73463e8i	−0.631640	+	0.680746i
$887$	−4.29976e8	−	9.81392e7i	−0.616131	−	0.140628i	−0.0969459	−	0.995290i	$-0.530907\pi$
$887$	−4.29976e8	−	9.81392e7i	−0.616131	−	0.140628i	−0.519185	+	0.854662i	$0.673765\pi$
$888$	3.11022e7	+	2.06350e8i	0.0444173	+	0.294690i
$889$	−7.21962e8	−	1.05892e9i	−1.02756	−	1.50716i
$890$	8.01370e7	−	2.59798e8i	0.113674	−	0.368523i
$891$	−3.53139e7	−	4.71231e8i	−0.0499244	−	0.666194i
$892$	5.95738e8	+	4.75085e8i	0.839385	+	0.669387i
$893$	−3.87368e7	−	1.25582e8i	−0.0543963	−	0.176348i
$894$	1.18807e9	−	4.66283e8i	1.66276	−	0.652584i
$895$	6.41534e7	+	2.81074e8i	0.0894850	+	0.392060i
$896$	4.86100e8	−	8.41950e8i	0.675774	−	1.17048i
$897$	−1.65890e8	+	9.57768e7i	−0.229850	+	0.132704i
$898$	−1.08231e9	+	1.00424e9i	−1.49459	+	1.38678i
$899$	7.50940e8	−	5.98855e8i	1.03354	−	0.824218i
$900$	−7.05273e7	−	4.80847e7i	−0.0967452	−	0.0659598i
$901$	−7.85727e7	−	3.78386e7i	−0.107423	−	0.0517322i
$902$		−	1.08350e7i		−	0.0147642i
$903$	−8.38820e8	−	5.09349e8i	−1.13921	−	0.691755i
$904$	3.69731e8			0.500473
$905$	−6.62457e6	+	1.37561e7i	−0.00893741	+	0.0185587i
$906$	−5.37085e8	+	7.87759e8i	−0.722202	+	1.05928i
$907$	−5.24712e6	−	6.57968e6i	−0.00703233	−	0.00881826i	0.778303	−	0.627889i	$-0.216081\pi$
$907$	−5.24712e6	−	6.57968e6i	−0.00703233	−	0.00881826i	−0.785335	+	0.619071i	$0.787509\pi$
$908$	3.61597e8	+	3.89709e8i	0.483023	+	0.520575i
$909$	1.54030e7	+	2.66788e7i	0.0205076	+	0.0355202i
$910$	−1.90853e8	−	1.10189e8i	−0.253265	−	0.146222i
$911$	8.74732e8	−	1.99652e8i	1.15696	−	0.264070i	0.399366	−	0.916791i	$-0.369230\pi$
$911$	8.74732e8	−	1.99652e8i	1.15696	−	0.264070i	0.757598	+	0.652722i	$0.226373\pi$
$912$	3.38918e7	+	8.63550e7i	0.0446797	+	0.113842i
$913$	2.08326e8	−	6.42600e7i	0.273735	−	0.0844361i
$914$	−1.11448e9	+	1.39751e9i	−1.45960	+	1.83028i
$915$	7.52056e7	−	5.63588e6i	0.0981719	−	0.00735697i
$916$	5.24884e8	+	1.61905e8i	0.682931	+	0.210656i
$917$	−1.12135e9	+	7.64521e8i	−1.45423	+	0.991475i
$918$	1.81514e9	−	2.73588e8i	2.34629	−	0.353646i
$919$	6.22682e7	−	2.72815e8i	0.0802268	−	0.351497i	−0.918843	−	0.394624i	$-0.870875\pi$
$919$	6.22682e7	−	2.72815e8i	0.0802268	−	0.351497i	0.999070	+	0.0431272i	$0.0137321\pi$
$920$	4.44899e7	+	4.12806e7i	0.0571344	+	0.0530130i
$921$	1.17874e9	+	8.83343e7i	1.50883	+	0.113071i
$922$	1.41740e9	+	5.56290e8i	1.80843	+	0.709755i
$923$	−1.22453e8	+	8.12425e8i	−0.155728	+	1.03318i
$924$	−5.20220e8	+	2.50525e8i	−0.659434	+	0.317566i
$925$	2.16360e8	+	4.49276e8i	0.273371	+	0.567660i
$926$	1.18116e9	+	1.78032e8i	1.48757	+	0.224215i
$927$	−131693.	+	335549.i	−0.000165320	+	0.000421227i
$928$	9.96027e7	−	1.32911e9i	0.124631	−	1.66309i
$929$	−3.92395e7	+	4.22901e7i	−0.0489414	+	0.0527463i	−0.757048	−	0.653359i	$-0.773359\pi$
$929$	−3.92395e7	+	4.22901e7i	−0.0489414	+	0.0527463i	0.708107	+	0.706106i	$0.249550\pi$
$930$	2.19254e8	+	5.00433e7i	0.272583	+	0.0622152i
$931$	1.65622e7	+	1.09883e8i	0.0205243	+	0.136170i
$932$	−1.51199e8	−	2.21768e8i	−0.186767	−	0.273937i
$933$	2.29080e8	−	7.42660e8i	0.282061	−	0.914418i
$934$	1.11874e8	+	1.49285e9i	0.137305	+	1.83221i
$935$	2.83732e8	+	2.26269e8i	0.347115	+	0.276815i
$936$	1.30436e7	+	4.22864e7i	0.0159064	+	0.0515671i
$937$	−1.09770e9	+	4.30817e8i	−1.33434	+	0.523690i	−0.921947	−	0.387316i	$-0.873402\pi$
$937$	−1.09770e9	+	4.30817e8i	−1.33434	+	0.523690i	−0.412394	+	0.911006i	$0.635307\pi$
$938$	6.13894e6	+	2.68964e7i	0.00743849	+	0.0325901i
$939$	−3.36388e8	+	5.82640e8i	−0.406297	+	0.703726i
$940$	−2.11670e8	+	1.22208e8i	−0.254845	+	0.147135i
$941$	4.49952e8	−	4.17495e8i	0.540005	−	0.501051i	−0.362352	−	0.932041i	$-0.618026\pi$
$941$	4.49952e8	−	4.17495e8i	0.540005	−	0.501051i	0.902357	+	0.430990i	$0.141836\pi$
$942$	6.88106e7	−	5.48746e7i	0.0823195	−	0.0656476i
$943$	5.03167e6	+	3.43054e6i	0.00600036	+	0.00409098i
$944$	5.23279e7	+	2.51998e7i	0.0622038	+	0.0299558i
$945$			3.89842e8i			0.461948i
$946$	4.97494e8	−	8.19297e8i	0.587644	−	0.967760i
$947$	−9.25997e8			−1.09033			−0.545167	−	0.838327i	$-0.683534\pi$
$947$	−9.25997e8			−1.09033			−0.545167	+	0.838327i	$0.683534\pi$
$948$	−2.42253e8	+	5.03044e8i	−0.284344	+	0.590447i
$949$	2.05435e8	−	3.01318e8i	0.240367	−	0.352554i
$950$	6.92696e7	+	8.68613e7i	0.0807927	+	0.101311i
$951$	4.60138e8	+	4.95911e8i	0.534991	+	0.576583i
$952$	5.46282e8	+	9.46188e8i	0.633149	+	1.09665i
$953$	−3.13479e8	−	1.80987e8i	−0.362185	−	0.209107i	0.307854	−	0.951434i	$-0.400389\pi$
$953$	−3.13479e8	−	1.80987e8i	−0.362185	−	0.209107i	−0.670039	+	0.742326i	$0.733723\pi$
$954$	1.52944e7	−	3.49084e6i	0.0176151	−	0.00402054i
$955$	−1.26911e8	−	3.23363e8i	−0.145709	−	0.371262i
$956$	2.66340e8	−	8.21551e7i	0.304834	−	0.0940288i
$957$	6.66257e8	−	8.35460e8i	0.760162	−	0.953212i
$958$	−1.48354e9	+	1.11176e8i	−1.68734	+	0.126449i
$959$	−5.79215e8	−	1.78664e8i	−0.656726	−	0.202573i
$960$	2.67070e7	−	1.82085e7i	0.0301864	−	0.0205808i
$961$	2.28819e8	−	3.44889e7i	0.257823	−	0.0388605i
$962$	−9.25642e7	+	4.05550e8i	−0.103972	+	0.455532i
$963$	−2.49183e8	−	2.31208e8i	−0.279023	−	0.258896i
$964$	8.95583e8	+	6.71147e7i	0.999712	+	0.0749180i
$965$	2.40751e8	+	9.44876e7i	0.267908	+	0.105146i
$966$	1.26797e8	−	8.41240e8i	0.140662	−	0.933230i
$967$	1.38596e9	−	6.67444e8i	1.53275	−	0.738134i	0.538243	−	0.842790i	$-0.319088\pi$
$967$	1.38596e9	−	6.67444e8i	1.53275	−	0.738134i	0.994509	+	0.104655i	$0.0333739\pi$
$968$	−3.97218e7	−	8.24831e7i	−0.0437928	−	0.0909367i
$969$	−1.54511e8	−	2.32887e7i	−0.169819	−	0.0255962i
$970$	1.37665e8	−	3.50763e8i	0.150837	−	0.384325i
$971$	1.31543e8	−	1.75532e9i	0.143685	−	1.91734i	−0.202685	−	0.979244i	$-0.564967\pi$
$971$	1.31543e8	−	1.75532e9i	0.143685	−	1.91734i	0.346370	−	0.938098i	$-0.387414\pi$
$972$	−1.56663e8	+	1.68843e8i	−0.170596	+	0.183858i
$973$	−1.66386e9	−	3.79766e8i	−1.80626	−	0.412266i
$974$	−2.37051e8	−	1.57273e9i	−0.256545	−	1.70207i
$975$	−2.28305e8	−	3.34863e8i	−0.246322	−	0.361287i
$976$	−1.30424e8	+	4.22823e8i	−0.140284	+	0.454789i
$977$	−9.29505e7	−	1.24034e9i	−0.0996709	−	1.33002i	−0.792924	−	0.609321i	$-0.791442\pi$
$977$	−9.29505e7	−	1.24034e9i	−0.0996709	−	1.33002i	0.693253	−	0.720694i	$-0.256177\pi$
$978$	7.50359e8	+	5.98392e8i	0.802145	+	0.639689i
$979$	2.60105e8	+	8.43240e8i	0.277205	+	0.898676i
$980$	1.92382e8	−	7.55046e7i	0.204403	−	0.0802223i
$981$	1.29255e6	+	5.66301e6i	0.00136911	+	0.00599847i
$982$	8.34028e8	−	1.44458e9i	0.880737	−	1.52548i
$983$	5.40509e7	−	3.12063e7i	0.0569039	−	0.0328535i	−0.471278	−	0.881985i	$-0.656207\pi$
$983$	5.40509e7	−	3.12063e7i	0.0569039	−	0.0328535i	0.528182	+	0.849131i	$0.322874\pi$
$984$	−3.95267e6	+	3.66754e6i	−0.00414864	+	0.00384937i
$985$	−7.09952e7	+	5.66168e7i	−0.0742883	+	0.0592429i
$986$	2.68826e9	+	1.83282e9i	2.80440	+	1.91201i
$987$	−1.91835e9	−	9.23827e8i	−1.99515	−	0.960814i
$988$			3.53539e7i			0.0366578i
$989$	2.22958e8	+	4.90433e8i	0.230481	+	0.506980i
$990$	−6.52818e7			−0.0672801
$991$	−7.64767e8	+	1.58805e9i	−0.785793	+	1.63172i	−0.0106392	+	0.999943i	$0.503387\pi$
$991$	−7.64767e8	+	1.58805e9i	−0.785793	+	1.63172i	−0.775154	+	0.631773i	$0.782328\pi$
$992$	−5.12872e8	+	7.52245e8i	−0.525381	+	0.770592i
$993$	1.83001e8	+	2.29476e8i	0.186899	+	0.234363i
$994$	−2.48192e9	−	2.67487e9i	−2.52714	−	2.72360i
$995$	−3.42897e7	−	5.93914e7i	−0.0348092	−	0.0602913i
$996$	1.51189e8	+	8.72888e7i	0.153017	+	0.0883447i
$997$	2.86878e8	−	6.54781e7i	0.289476	−	0.0660709i	−0.0753173	−	0.997160i	$-0.523997\pi$
$997$	2.86878e8	−	6.54781e7i	0.289476	−	0.0660709i	0.364793	+	0.931089i	$0.381140\pi$
$998$	−7.54572e8	−	1.92262e9i	−0.759118	−	1.93420i
$999$	7.03163e8	−	2.16897e8i	0.705277	−	0.217549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.h.a.18.5	yes	252
43.12	odd	42	inner	43.7.h.a.12.5	✓	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.h.a.12.5	✓	252	43.12	odd	42	inner
43.7.h.a.18.5	yes	252	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.h (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.41348 + 9.16469i) q^{2} +(-13.5449 + 19.8667i) q^{3} +(-24.6094 - 30.8593i) q^{4} +(24.4163 + 26.3145i) q^{5} +(-122.292 - 211.817i) q^{6} +(-444.560 - 256.667i) q^{7} +(-243.260 + 55.5224i) q^{8} +(55.1109 + 140.420i) q^{9} +(-348.925 + 107.629i) q^{10} +(738.948 - 926.611i) q^{11} +(946.406 - 70.9233i) q^{12} +(-1123.48 - 346.547i) q^{13} +(4314.33 - 2941.46i) q^{14} +(-853.500 + 128.644i) q^{15} +(1126.89 - 4937.22i) q^{16} +(6252.95 + 5801.89i) q^{17} +(-1530.14 - 114.668i) q^{18} +(709.179 + 278.332i) q^{19} +(211.175 - 1401.05i) q^{20} +(11120.7 - 5355.42i) q^{21} +(5230.77 + 10861.8i) q^{22} +(-6700.25 - 1009.90i) q^{23} +(2191.88 - 5584.82i) q^{24} +(1071.36 - 14296.3i) q^{25} +(8134.44 - 8766.84i) q^{26} +(-20625.3 - 4707.60i) q^{27} +(3019.82 + 20035.2i) q^{28} +(-21123.3 - 30982.2i) q^{29} +(2587.92 - 8389.83i) q^{30} +(1914.17 + 25542.8i) q^{31} +(27789.6 + 22161.4i) q^{32} +(8399.76 + 27231.4i) q^{33} +(-80769.9 + 31699.8i) q^{34} +(-4100.44 - 17965.2i) q^{35} +(2977.02 - 5156.35i) q^{36} +(-30122.7 + 17391.4i) q^{37} +(-5680.78 + 5271.00i) q^{38} +(22102.1 - 17625.9i) q^{39} +(-7400.54 - 5045.60i) q^{40} +(-809.744 - 389.952i) q^{41} +125553. i q^{42} +(-43324.4 - 66666.0i) q^{43} -46779.6 q^{44} +(-2349.49 + 4878.76i) q^{45} +(38826.9 - 56948.6i) q^{46} +(-107554. - 134868. i) q^{47} +(82822.9 + 89261.9i) q^{48} +(72931.0 + 126320. i) q^{49} +(126293. + 72915.2i) q^{50} +(-199960. + 45639.6i) q^{51} +(16954.0 + 43198.0i) q^{52} +(-9769.56 + 3013.51i) q^{53} +(134173. - 168248. i) q^{54} +(42425.7 - 3179.36i) q^{55} +(122394. + 37753.6i) q^{56} +(-15135.3 + 10319.1i) q^{57} +(377170. - 56849.2i) q^{58} +(-2552.02 + 11181.1i) q^{59} +(24974.0 + 23172.5i) q^{60} +(-87130.3 - 6529.51i) q^{61} +(-242540. - 95190.1i) q^{62} +(11541.1 - 76570.3i) q^{63} +(-33740.3 + 16248.5i) q^{64} +(-18311.9 - 38025.1i) q^{65} +(-286639. - 43203.9i) q^{66} +(-1930.25 + 4918.19i) q^{67} +(25160.4 - 335743. i) q^{68} +(110818. - 119433. i) q^{69} +(182743. + 41709.9i) q^{70} +(-104153. - 691008. i) q^{71} +(-21202.7 - 31098.7i) q^{72} +(-91428.2 + 296403. i) q^{73} +(-26440.4 - 352822. i) q^{74} +(269510. + 214927. i) q^{75} +(-8863.37 - 28734.4i) q^{76} +(-566337. + 222271. i) q^{77} +(63988.3 + 280351. i) q^{78} +(-294153. + 509487. i) q^{79} +(157435. - 90895.1i) q^{80} +(292281. - 271197. i) q^{81} +(7147.58 - 5700.01i) q^{82} +(151985. + 103622. i) q^{83} +(-438937. - 211381. i) q^{84} +306204. i q^{85} +(802185. - 102825. i) q^{86} +901629. q^{87} +(-128308. + 266435. i) q^{88} +(-419429. + 615189. i) q^{89} +(-34342.9 - 43064.6i) q^{90} +(410505. + 442419. i) q^{91} +(133725. + 231618. i) q^{92} +(-533380. - 307947. i) q^{93} +(1.71072e6 - 390460. i) q^{94} +(9991.34 + 25457.5i) q^{95} +(-816683. + 251913. i) q^{96} +(-643405. + 806804. i) q^{97} +(-1.47957e6 + 110878. i) q^{98} +(170839. + 52696.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9} + 967 q^{10} + 4090 q^{11} - 484 q^{12} + 1527 q^{13} + 7812 q^{14} - 8923 q^{15} - 13760 q^{16} - 3655 q^{17}+ \cdots + 18452884 q^{99}+O(q^{100}) \) 252 * q - 14 * q^2 - 11 * q^3 + 1180 * q^4 - 11 * q^5 - 118 * q^6 + 126 * q^7 - 2254 * q^8 - 8178 * q^9 + 967 * q^10 + 4090 * q^11 - 484 * q^12 + 1527 * q^13 + 7812 * q^14 - 8923 * q^15 - 13760 * q^16 - 3655 * q^17 + 5596 * q^18 + 38605 * q^19 + 26085 * q^20 + 24873 * q^21 - 25214 * q^22 + 27991 * q^23 - 20480 * q^24 - 24146 * q^25 - 34923 * q^26 - 14 * q^27 - 77634 * q^28 - 112735 * q^29 + 375072 * q^30 + 290647 * q^31 - 344064 * q^32 - 152174 * q^33 - 198311 * q^34 - 182471 * q^35 - 930891 * q^36 + 282762 * q^37 + 487342 * q^38 + 857290 * q^39 + 745459 * q^40 + 27674 * q^41 + 148802 * q^43 - 1255832 * q^44 - 191310 * q^45 - 1344785 * q^46 + 69166 * q^47 - 871241 * q^48 + 1786604 * q^49 + 837705 * q^50 - 182756 * q^51 + 2906416 * q^52 + 7779 * q^53 + 487154 * q^54 - 529592 * q^55 - 2464007 * q^56 - 767855 * q^57 - 1523780 * q^58 + 1531338 * q^59 - 1858647 * q^60 + 646957 * q^61 - 448559 * q^62 - 2007847 * q^63 + 3937366 * q^64 - 1473542 * q^65 + 1513319 * q^66 - 575523 * q^67 + 2717157 * q^68 + 967041 * q^69 + 4624473 * q^70 - 2149319 * q^71 - 9986371 * q^72 - 514565 * q^73 - 882972 * q^74 - 6655138 * q^75 + 1152658 * q^76 - 341803 * q^77 + 6322388 * q^78 - 2476742 * q^79 + 10750038 * q^80 + 4308941 * q^81 + 5079172 * q^82 + 2318609 * q^83 + 5578407 * q^84 + 585292 * q^86 - 1990710 * q^87 - 2864890 * q^88 - 4561993 * q^89 - 17681545 * q^90 - 4648506 * q^91 - 1991714 * q^92 - 8868294 * q^93 - 10200218 * q^94 + 10091737 * q^95 + 6250318 * q^96 - 1676750 * q^97 + 7512700 * q^98 + 18452884 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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