LMFDB - Embedded newform 38.8.e.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	38.23
Dual form			38.8.e.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.51754 - 2.73616i) q^{2} +(-7.18109 - 40.7260i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-24.6197 + 20.6584i) q^{5} +(-57.4487 + 325.808i) q^{6} +(764.198 - 1323.63i) q^{7} +(-256.000 - 443.405i) q^{8} +(448.070 - 163.084i) q^{9} +O(q^{10})$	\(q+(-7.51754 - 2.73616i) q^{2} +(-7.18109 - 40.7260i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-24.6197 + 20.6584i) q^{5} +(-57.4487 + 325.808i) q^{6} +(764.198 - 1323.63i) q^{7} +(-256.000 - 443.405i) q^{8} +(448.070 - 163.084i) q^{9} +(241.604 - 87.9368i) q^{10} +(-523.733 - 907.132i) q^{11} +(1323.34 - 2292.08i) q^{12} +(-1069.14 + 6063.39i) q^{13} +(-9366.55 + 7859.47i) q^{14} +(1018.13 + 854.312i) q^{15} +(711.263 + 4033.77i) q^{16} +(-32284.3 - 11750.5i) q^{17} -3814.61 q^{18} +(-16217.2 - 25117.2i) q^{19} -2056.88 q^{20} +(-59393.9 - 21617.6i) q^{21} +(1455.12 + 8252.42i) q^{22} +(4865.64 + 4082.75i) q^{23} +(-16219.7 + 13610.0i) q^{24} +(-13386.9 + 75920.9i) q^{25} +(24627.7 - 42656.5i) q^{26} +(-55080.3 - 95401.8i) q^{27} +(91918.2 - 33455.5i) q^{28} +(-63919.0 + 23264.6i) q^{29} +(-5316.30 - 9208.09i) q^{30} +(-18170.9 + 31473.0i) q^{31} +(5690.10 - 32270.2i) q^{32} +(-33182.9 + 27843.7i) q^{33} +(210547. + 176670. i) q^{34} +(8529.73 + 48374.5i) q^{35} +(28676.5 + 10437.4i) q^{36} +96004.7 q^{37} +(53188.4 + 233193. i) q^{38} +254615. q^{39} +(15462.7 + 5627.96i) q^{40} +(-51287.7 - 290867. i) q^{41} +(387347. + 325023. i) q^{42} +(712452. - 597818. i) q^{43} +(11641.0 - 66019.4i) q^{44} +(-7662.30 + 13271.5i) q^{45} +(-25406.6 - 44005.4i) q^{46} +(-492235. + 179159. i) q^{47} +(159172. - 57933.8i) q^{48} +(-756226. - 1.30982e6i) q^{49} +(308368. - 534110. i) q^{50} +(-246715. + 1.39919e6i) q^{51} +(-301855. + 253286. i) q^{52} +(1.22004e6 + 1.02373e6i) q^{53} +(153033. + 867896. i) q^{54} +(31634.1 + 11513.9i) q^{55} -782539. q^{56} +(-906467. + 840829. i) q^{57} +544169. q^{58} +(-772060. - 281007. i) q^{59} +(14770.6 + 83768.5i) q^{60} +(-2.05541e6 - 1.72470e6i) q^{61} +(222716. - 186881. i) q^{62} +(126551. - 717708. i) q^{63} +(-131072. + 227023. i) q^{64} +(-98938.0 - 171366. i) q^{65} +(325639. - 118523. i) q^{66} +(2.88147e6 - 1.04877e6i) q^{67} +(-1.09940e6 - 1.90421e6i) q^{68} +(131334. - 227476. i) q^{69} +(68237.8 - 386996. i) q^{70} +(-3.38742e6 + 2.84238e6i) q^{71} +(-187018. - 156927. i) q^{72} +(281250. + 1.59505e6i) q^{73} +(-721720. - 262684. i) q^{74} +3.18809e6 q^{75} +(238206. - 1.89857e6i) q^{76} -1.60094e6 q^{77} +(-1.91408e6 - 696668. i) q^{78} +(-305656. - 1.73346e6i) q^{79} +(-100842. - 84616.8i) q^{80} +(-2.69095e6 + 2.25798e6i) q^{81} +(-410301. + 2.32693e6i) q^{82} +(1.22884e6 - 2.12842e6i) q^{83} +(-2.02258e6 - 3.50321e6i) q^{84} +(1.03758e6 - 377647. i) q^{85} +(-6.99162e6 + 2.54474e6i) q^{86} +(1.40648e6 + 2.43610e6i) q^{87} +(-268151. + 464452. i) q^{88} +(267580. - 1.51752e6i) q^{89} +(93914.7 - 78803.8i) q^{90} +(7.20865e6 + 6.04878e6i) q^{91} +(70588.8 + 400329. i) q^{92} +(1.41225e6 + 514018. i) q^{93} +4.19060e6 q^{94} +(918144. + 283358. i) q^{95} -1.35510e6 q^{96} +(1.07881e7 + 3.92654e6i) q^{97} +(2.10108e6 + 1.19158e7i) q^{98} +(-382608. - 321046. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) $ 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−7.51754	−	2.73616i	−0.664463	−	0.241845i
$2$	−7.51754	−	2.73616i	−0.664463	−	0.241845i
$3$	−7.18109	−	40.7260i	−0.153556	−	0.870858i	−0.960094	−	0.279676i	$-0.909773\pi$
$3$	−7.18109	−	40.7260i	−0.153556	−	0.870858i	0.806539	−	0.591181i	$-0.201338\pi$
$4$	49.0268	+	41.1384i	0.383022	+	0.321394i
$5$	−24.6197	+	20.6584i	−0.0880822	+	0.0739097i	−0.685766	−	0.727823i	$-0.740532\pi$
$5$	−24.6197	+	20.6584i	−0.0880822	+	0.0739097i	0.597683	+	0.801732i	$0.296088\pi$
$6$	−57.4487	+	325.808i	−0.108580	+	0.615789i
$7$	764.198	−	1323.63i	0.842098	−	1.45856i	−0.0460192	−	0.998941i	$-0.514654\pi$
$7$	764.198	−	1323.63i	0.842098	−	1.45856i	0.888118	−	0.459616i	$-0.152013\pi$
$8$	−256.000	−	443.405i	−0.176777	−	0.306186i
$9$	448.070	−	163.084i	0.204879	−	0.0745698i
$10$	241.604	−	87.9368i	0.0764020	−	0.0278081i
$11$	−523.733	−	907.132i	−0.118641	−	0.205493i	0.800588	−	0.599215i	$-0.204521\pi$
$11$	−523.733	−	907.132i	−0.118641	−	0.205493i	−0.919229	+	0.393722i	$0.871187\pi$
$12$	1323.34	−	2292.08i	0.221073	−	0.382910i
$13$	−1069.14	+	6063.39i	−0.134969	+	0.765445i	0.839913	+	0.542721i	$0.182606\pi$
$13$	−1069.14	+	6063.39i	−0.134969	+	0.765445i	−0.974882	+	0.222724i	$0.928505\pi$
$14$	−9366.55	+	7859.47i	−0.912288	+	0.765500i
$15$	1018.13	+	854.312i	0.0778904	+	0.0653578i
$16$	711.263	+	4033.77i	0.0434120	+	0.246202i
$17$	−32284.3	−	11750.5i	−1.59375	−	0.580077i	−0.615613	−	0.788049i	$-0.711091\pi$
$17$	−32284.3	−	11750.5i	−1.59375	−	0.580077i	−0.978135	+	0.207972i	$0.933314\pi$
$18$	−3814.61			−0.154169
$19$	−16217.2	−	25117.2i	−0.542422	−	0.840106i
$19$	−16217.2	−	25117.2i	−0.542422	−	0.840106i
$20$	−2056.88			−0.0574916
$21$	−59393.9	−	21617.6i	−1.39950	−	0.509378i
$22$	1455.12	+	8252.42i	0.0291354	+	0.165235i
$23$	4865.64	+	4082.75i	0.0833858	+	0.0699690i	0.683528	−	0.729924i	$-0.260445\pi$
$23$	4865.64	+	4082.75i	0.0833858	+	0.0699690i	−0.600142	+	0.799894i	$0.704889\pi$
$24$	−16219.7	+	13610.0i	−0.239500	+	0.200964i
$25$	−13386.9	+	75920.9i	−0.171352	+	0.971787i
$26$	24627.7	−	42656.5i	0.274800	−	0.475968i
$27$	−55080.3	−	95401.8i	−0.538546	−	0.932789i
$28$	91918.2	−	33455.5i	0.791314	−	0.288015i
$29$	−63919.0	+	23264.6i	−0.486672	+	0.177134i	−0.573690	−	0.819073i	$-0.694489\pi$
$29$	−63919.0	+	23264.6i	−0.486672	+	0.177134i	0.0870177	+	0.996207i	$0.472266\pi$
$30$	−5316.30	−	9208.09i	−0.0359488	−	0.0622652i
$31$	−18170.9	+	31473.0i	−0.109550	+	0.189746i	−0.915588	−	0.402118i	$-0.868274\pi$
$31$	−18170.9	+	31473.0i	−0.109550	+	0.189746i	0.806038	+	0.591863i	$0.201608\pi$
$32$	5690.10	−	32270.2i	0.0306970	−	0.174091i
$33$	−33182.9	+	27843.7i	−0.160737	+	0.134874i
$34$	210547.	+	176670.i	0.918698	+	0.770879i
$35$	8529.73	+	48374.5i	0.0336277	+	0.190712i
$36$	28676.5	+	10437.4i	0.102439	+	0.0372849i
$37$	96004.7			0.311592			0.155796	−	0.987789i	$-0.450206\pi$
$37$	96004.7			0.311592			0.155796	+	0.987789i	$0.450206\pi$
$38$	53188.4	+	233193.i	0.157244	+	0.689401i
$39$	254615.			0.687319
$40$	15462.7	+	5627.96i	0.0382010	+	0.0139040i
$41$	−51287.7	−	290867.i	−0.116217	−	0.659099i	−0.986140	−	0.165913i	$-0.946943\pi$
$41$	−51287.7	−	290867.i	−0.116217	−	0.659099i	0.869924	−	0.493187i	$-0.164168\pi$
$42$	387347.	+	325023.i	0.806729	+	0.676926i
$43$	712452.	−	597818.i	1.36652	−	1.14665i	0.392613	−	0.919704i	$-0.371571\pi$
$43$	712452.	−	597818.i	1.36652	−	1.14665i	0.973908	−	0.226943i	$-0.0728732\pi$
$44$	11641.0	−	66019.4i	0.0206018	−	0.116839i
$45$	−7662.30	+	13271.5i	−0.0125347	+	0.0217108i
$46$	−25406.6	−	44005.4i	−0.0384852	−	0.0666583i
$47$	−492235.	+	179159.i	−0.691560	+	0.251707i	−0.663803	−	0.747908i	$-0.731059\pi$
$47$	−492235.	+	179159.i	−0.691560	+	0.251707i	−0.0277569	+	0.999615i	$0.508836\pi$
$48$	159172.	−	57933.8i	0.207741	−	0.0756114i
$49$	−756226.	−	1.30982e6i	−0.918259	−	1.59047i
$50$	308368.	−	534110.i	0.348879	−	0.604276i
$51$	−246715.	+	1.39919e6i	−0.260435	+	1.47700i
$52$	−301855.	+	253286.i	−0.297705	+	0.249804i
$53$	1.22004e6	+	1.02373e6i	1.12566	+	0.944543i	0.998877	−	0.0473867i	$-0.0150893\pi$
$53$	1.22004e6	+	1.02373e6i	1.12566	+	0.944543i	0.126786	+	0.991930i	$0.459534\pi$
$54$	153033.	+	867896.i	0.132254	+	0.750048i
$55$	31634.1	+	11513.9i	0.0256381	+	0.00933150i
$56$	−782539.			−0.595453
$57$	−906467.	+	840829.i	−0.648321	+	0.601375i
$58$	544169.			0.366215
$59$	−772060.	−	281007.i	−0.489406	−	0.178129i	0.0855171	−	0.996337i	$-0.472746\pi$
$59$	−772060.	−	281007.i	−0.489406	−	0.178129i	−0.574923	+	0.818208i	$0.694968\pi$
$60$	14770.6	+	83768.5i	0.00882816	+	0.0500670i
$61$	−2.05541e6	−	1.72470e6i	−1.15943	−	0.972878i	−0.159533	−	0.987193i	$-0.550999\pi$
$61$	−2.05541e6	−	1.72470e6i	−1.15943	−	0.972878i	−0.999898	+	0.0143150i	$0.995443\pi$
$62$	222716.	−	186881.i	0.118681	−	0.0995849i
$63$	126551.	−	717708.i	0.0637639	−	0.361623i
$64$	−131072.	+	227023.i	−0.0625000	+	0.108253i
$65$	−98938.0	−	171366.i	−0.0446855	−	0.0773975i
$66$	325639.	−	118523.i	0.139422	−	0.0507456i
$67$	2.88147e6	−	1.04877e6i	1.17045	−	0.426009i	0.317630	−	0.948215i	$-0.397113\pi$
$67$	2.88147e6	−	1.04877e6i	1.17045	−	0.426009i	0.852819	+	0.522206i	$0.174891\pi$
$68$	−1.09940e6	−	1.90421e6i	−0.424008	−	0.734403i
$69$	131334.	−	227476.i	0.0481287	−	0.0833613i
$70$	68237.8	−	386996.i	0.0237784	−	0.134854i
$71$	−3.38742e6	+	2.84238e6i	−1.12322	+	0.942493i	−0.998763	−	0.0497323i	$-0.984163\pi$
$71$	−3.38742e6	+	2.84238e6i	−1.12322	+	0.942493i	−0.124457	+	0.992225i	$0.539719\pi$
$72$	−187018.	−	156927.i	−0.0590501	−	0.0495489i
$73$	281250.	+	1.59505e6i	0.0846179	+	0.479892i	0.997438	+	0.0715310i	$0.0227885\pi$
$73$	281250.	+	1.59505e6i	0.0846179	+	0.479892i	−0.912820	+	0.408361i	$0.866100\pi$
$74$	−721720.	−	262684.i	−0.207042	−	0.0753570i
$75$	3.18809e6			0.872601
$76$	238206.	−	1.89857e6i	0.0622452	−	0.496110i
$77$	−1.60094e6			−0.399630
$78$	−1.91408e6	−	696668.i	−0.456698	−	0.166224i
$79$	−305656.	−	1.73346e6i	−0.0697489	−	0.395566i	−0.999617	−	0.0276727i	$-0.991190\pi$
$79$	−305656.	−	1.73346e6i	−0.0697489	−	0.395566i	0.929868	−	0.367893i	$-0.119921\pi$
$80$	−100842.	−	84616.8i	−0.0220205	−	0.0184774i
$81$	−2.69095e6	+	2.25798e6i	−0.562611	+	0.472087i
$82$	−410301.	+	2.32693e6i	−0.0821778	+	0.466053i
$83$	1.22884e6	−	2.12842e6i	0.235898	−	0.408587i	−0.723636	−	0.690182i	$-0.757530\pi$
$83$	1.22884e6	−	2.12842e6i	0.235898	−	0.408587i	0.959533	+	0.281596i	$0.0908637\pi$
$84$	−2.02258e6	−	3.50321e6i	−0.372330	−	0.644895i
$85$	1.03758e6	−	377647.i	0.183254	−	0.0666990i
$86$	−6.99162e6	+	2.54474e6i	−1.18531	+	0.431419i
$87$	1.40648e6	+	2.43610e6i	0.228990	+	0.396622i
$88$	−268151.	+	464452.i	−0.0419460	+	0.0726526i
$89$	267580.	−	1.51752e6i	0.0402335	−	0.228176i	−0.958060	−	0.286567i	$-0.907486\pi$
$89$	267580.	−	1.51752e6i	0.0402335	−	0.228176i	0.998294	+	0.0583912i	$0.0185971\pi$
$90$	93914.7	−	78803.8i	0.0135795	−	0.0113946i
$91$	7.20865e6	+	6.04878e6i	1.00279	+	0.841439i
$92$	70588.8	+	400329.i	0.00945102	+	0.0535994i
$93$	1.41225e6	+	514018.i	0.182063	+	0.0662656i
$94$	4.19060e6			0.520390
$95$	918144.	+	283358.i	0.109870	+	0.0339081i
$96$	−1.35510e6			−0.156322
$97$	1.07881e7	+	3.92654e6i	1.20017	+	0.436827i	0.863284	−	0.504718i	$-0.168403\pi$
$97$	1.07881e7	+	3.92654e6i	1.20017	+	0.436827i	0.336888	+	0.941545i	$0.390626\pi$
$98$	2.10108e6	+	1.19158e7i	0.225502	+	1.27889i
$99$	−382608.	−	321046.i	−0.0396306	−	0.0332541i
$100$	−3.77958e6	+	3.17145e6i	−0.377958	+	0.317145i
$101$	2.60012e6	−	1.47460e7i	0.251113	−	1.42413i	−0.554743	−	0.832022i	$-0.687183\pi$
$101$	2.60012e6	−	1.47460e7i	0.251113	−	1.42413i	0.805856	−	0.592111i	$-0.201705\pi$
$102$	5.68310e6	−	9.84341e6i	0.530255	−	0.918428i
$103$	5.10620e6	+	8.84419e6i	0.460434	+	0.797495i	0.998983	−	0.0450995i	$-0.0143605\pi$
$103$	5.10620e6	+	8.84419e6i	0.460434	+	0.797495i	−0.538549	+	0.842594i	$0.681027\pi$
$104$	2.96224e6	−	1.07817e6i	0.258228	−	0.0939873i
$105$	1.90885e6	−	694763.i	0.160919	−	0.0585699i
$106$	−6.37059e6	−	1.10342e7i	−0.519529	−	0.899850i
$107$	−2.25111e6	+	3.89904e6i	−0.177645	+	0.307691i	−0.941074	−	0.338202i	$-0.890181\pi$
$107$	−2.25111e6	+	3.89904e6i	−0.177645	+	0.307691i	0.763428	+	0.645893i	$0.223515\pi$
$108$	1.22427e6	−	6.94316e6i	0.0935175	−	0.530364i
$109$	7.54719e6	−	6.33284e6i	0.558203	−	0.468388i	−0.319504	−	0.947585i	$-0.603516\pi$
$109$	7.54719e6	−	6.33284e6i	0.558203	−	0.468388i	0.877708	+	0.479197i	$0.159072\pi$
$110$	−206307.	−	173112.i	−0.0147788	−	0.0124009i
$111$	−689419.	−	3.90989e6i	−0.0478468	−	0.271353i
$112$	5.88277e6	+	2.14115e6i	0.395657	+	0.144007i
$113$	9.53443e6			0.621613			0.310807	−	0.950473i	$-0.399401\pi$
$113$	9.53443e6			0.621613			0.310807	+	0.950473i	$0.399401\pi$
$114$	9.11505e6	−	3.84073e6i	0.576225	−	0.242799i
$115$	−204134.			−0.0125162
$116$	−4.09081e6	−	1.48893e6i	−0.243336	−	0.0885671i
$117$	509794.	+	2.89119e6i	0.0294269	+	0.166888i
$118$	5.03511e6	+	4.22496e6i	0.282112	+	0.236720i
$119$	−4.02249e7	+	3.37527e7i	−2.18817	+	1.83609i
$120$	118165.	−	670148.i	0.00624245	−	0.0354027i
$121$	9.19499e6	−	1.59262e7i	0.471849	−	0.817266i
$122$	1.07326e7	+	1.85894e7i	0.535113	+	0.926843i
$123$	−1.14775e7	+	4.17748e6i	−0.556136	+	0.202417i
$124$	−2.18561e6	+	795497.i	−0.102943	+	0.0374682i
$125$	−2.49424e6	−	4.32015e6i	−0.114223	−	0.197840i
$126$	−2.91512e6	+	5.04913e6i	−0.129825	+	0.224864i
$127$	658443.	−	3.73421e6i	0.0285236	−	0.161766i	−0.967219	−	0.253944i	$-0.918272\pi$
$127$	658443.	−	3.73421e6i	0.0285236	−	0.161766i	0.995742	+	0.0921787i	$0.0293831\pi$
$128$	1.60651e6	−	1.34802e6i	0.0677094	−	0.0568149i
$129$	−2.94629e7	−	2.47223e7i	−1.20840	−	1.01397i
$130$	274887.	+	1.55896e6i	0.0109737	+	0.0622348i
$131$	1.08664e7	+	3.95506e6i	0.422316	+	0.153711i	0.544431	−	0.838805i	$-0.316745\pi$
$131$	1.08664e7	+	3.95506e6i	0.422316	+	0.153711i	−0.122115	+	0.992516i	$0.538968\pi$
$132$	−2.77230e6			−0.104913
$133$	−4.56390e7	+	2.27098e6i	−1.68212	+	0.0837016i
$134$	−2.45312e7			−0.880748
$135$	3.32691e6	+	1.21090e6i	0.116378	+	0.0423583i
$136$	3.05454e6	+	1.73231e7i	0.104126	+	0.590528i
$137$	−4.11960e7	−	3.45676e7i	−1.36878	−	1.14854i	−0.973161	−	0.230127i	$-0.926086\pi$
$137$	−4.11960e7	−	3.45676e7i	−1.36878	−	1.14854i	−0.395618	−	0.918415i	$-0.629470\pi$
$138$	−1.60972e6	+	1.35071e6i	−0.0521402	+	0.0437509i
$139$	4.44731e6	−	2.52220e7i	0.140458	−	0.796575i	−0.830445	−	0.557101i	$-0.811914\pi$
$139$	4.44731e6	−	2.52220e7i	0.140458	−	0.796575i	0.970903	−	0.239475i	$-0.0769752\pi$
$140$	−1.57186e6	+	2.72255e6i	−0.0484135	+	0.0838547i
$141$	1.08312e7	+	1.87602e7i	0.325394	+	0.563599i
$142$	3.32423e7	−	1.20992e7i	0.974275	−	0.354607i
$143$	6.06024e6	−	2.20575e6i	0.173306	−	0.0630783i
$144$	976541.	+	1.69142e6i	0.0272535	+	0.0472044i
$145$	1.09306e6	−	1.89323e6i	0.0297752	−	0.0515722i
$146$	2.25000e6	−	1.27604e7i	0.0598339	−	0.339335i
$147$	−4.79132e7	+	4.02040e7i	−1.24407	+	1.04390i
$148$	4.70681e6	+	3.94948e6i	0.119347	+	0.100144i
$149$	−128488.	−	728690.i	−0.00318207	−	0.0180464i	0.983175	−	0.182664i	$-0.0584721\pi$
$149$	−128488.	−	728690.i	−0.00318207	−	0.0180464i	−0.986357	+	0.164618i	$0.947361\pi$
$150$	−2.39666e7	−	8.72312e6i	−0.579811	−	0.211034i
$151$	4.12346e7			0.974636			0.487318	−	0.873225i	$-0.337975\pi$
$151$	4.12346e7			0.974636			0.487318	+	0.873225i	$0.337975\pi$
$152$	−6.98551e6	+	1.36208e7i	−0.161341	+	0.314593i
$153$	−1.63819e7			−0.369782
$154$	1.20352e7	+	4.38044e6i	0.265540	+	0.0966485i
$155$	−202818.	−	1.15024e6i	−0.00437467	−	0.0248100i
$156$	1.24830e7	+	1.04745e7i	0.263258	+	0.220900i
$157$	3.81960e7	−	3.20503e7i	0.787716	−	0.660972i	−0.157463	−	0.987525i	$-0.550332\pi$
$157$	3.81960e7	−	3.20503e7i	0.787716	−	0.660972i	0.945179	+	0.326553i	$0.105887\pi$
$158$	−2.44524e6	+	1.38677e7i	−0.0493199	+	0.279707i
$159$	3.29314e7	−	5.70388e7i	0.649711	−	1.12533i
$160$	526561.	+	912031.i	0.0101632	+	0.0176031i
$161$	9.12237e6	−	3.32027e6i	0.172273	−	0.0627022i
$162$	2.64075e7	−	9.61155e6i	0.488006	−	0.177620i
$163$	−8.13987e6	−	1.40987e7i	−0.147218	−	0.254989i	0.782980	−	0.622047i	$-0.213699\pi$
$163$	−8.13987e6	−	1.40987e7i	−0.147218	−	0.254989i	−0.930198	+	0.367058i	$0.880365\pi$
$164$	9.45133e6	−	1.63702e7i	0.167317	−	0.289801i
$165$	241746.	−	1.37101e6i	0.00418953	−	0.0237600i
$166$	−1.50616e7	+	1.26382e7i	−0.255560	+	0.214440i
$167$	7.87938e7	+	6.61159e7i	1.30914	+	1.09850i	0.988488	+	0.151296i	$0.0483447\pi$
$167$	7.87938e7	+	6.61159e7i	1.30914	+	1.09850i	0.320647	+	0.947199i	$0.396100\pi$
$168$	5.61948e6	+	3.18697e7i	0.0914353	+	0.518555i
$169$	2.33427e7	+	8.49603e6i	0.372003	+	0.135398i
$170$	−8.83332e6			−0.137896
$171$	−1.13627e7	−	8.60952e6i	−0.173777	−	0.131672i
$172$	5.95226e7			0.891933
$173$	−7.96198e7	−	2.89793e7i	−1.16912	−	0.425526i	−0.316774	−	0.948501i	$-0.602600\pi$
$173$	−7.96198e7	−	2.89793e7i	−1.16912	−	0.425526i	−0.852348	+	0.522975i	$0.824822\pi$
$174$	−3.90773e6	−	2.21618e7i	−0.0562344	−	0.318921i
$175$	9.02609e7	+	7.57379e7i	1.27311	+	1.06827i
$176$	3.28665e6	−	2.75783e6i	0.0454422	−	0.0381306i
$177$	−5.90005e6	+	3.34608e7i	−0.0799741	+	0.453556i
$178$	−6.16372e6	+	1.06759e7i	−0.0819168	+	0.141884i
$179$	2.41413e7	+	4.18139e7i	0.314612	+	0.544923i	0.979355	−	0.202149i	$-0.0647924\pi$
$179$	2.41413e7	+	4.18139e7i	0.314612	+	0.544923i	−0.664743	+	0.747072i	$0.731459\pi$
$180$	−921627.	+	335445.i	−0.0117788	+	0.00428714i
$181$	1.01270e8	−	3.68594e7i	1.26942	−	0.462033i	0.382504	−	0.923954i	$-0.375062\pi$
$181$	1.01270e8	−	3.68594e7i	1.26942	−	0.462033i	0.886921	+	0.461921i	$0.152840\pi$
$182$	−3.76409e7	−	6.51960e7i	−0.462818	−	0.801624i
$183$	−5.54798e7	+	9.60939e7i	−0.669201	+	1.15909i
$184$	564711.	−	3.20263e6i	0.00668288	−	0.0379005i
$185$	−2.36361e6	+	1.98330e6i	−0.0274457	+	0.0230297i
$186$	−9.21024e6	−	7.72831e6i	−0.104948	−	0.0880621i
$187$	6.24907e6	+	3.54402e7i	0.0698827	+	0.396324i
$188$	−3.15030e7	−	1.14662e7i	−0.345780	−	0.125854i
$189$	−1.68369e8			−1.81403
$190$	−6.12687e6	−	4.64235e6i	−0.0648039	−	0.0491021i
$191$	8.23644e7			0.855309			0.427654	−	0.903942i	$-0.359340\pi$
$191$	8.23644e7			0.855309			0.427654	+	0.903942i	$0.359340\pi$
$192$	1.01870e7	+	3.70776e6i	0.103870	+	0.0378057i
$193$	4.63006e6	+	2.62584e7i	0.0463592	+	0.262916i	0.999174	−	0.0406361i	$-0.0129384\pi$
$193$	4.63006e6	+	2.62584e7i	0.0463592	+	0.262916i	−0.952815	+	0.303552i	$0.901827\pi$
$194$	−7.03563e7	−	5.90359e7i	−0.691826	−	0.580511i
$195$	−6.26855e6	+	5.25994e6i	−0.0605405	+	0.0507995i
$196$	1.68086e7	−	9.53263e7i	0.159454	−	0.904309i
$197$	8.60620e7	−	1.49064e8i	0.802010	−	1.38912i	−0.116281	−	0.993216i	$-0.537097\pi$
$197$	8.60620e7	−	1.49064e8i	0.802010	−	1.38912i	0.918291	−	0.395906i	$-0.129569\pi$
$198$	1.99784e6	+	3.46036e6i	0.0182908	+	0.0316806i
$199$	9.19335e7	−	3.34610e7i	0.826966	−	0.300991i	0.106353	−	0.994328i	$-0.466083\pi$
$199$	9.19335e7	−	3.34610e7i	0.826966	−	0.300991i	0.720613	+	0.693337i	$0.243860\pi$
$200$	3.70908e7	−	1.34999e7i	0.327839	−	0.119324i
$201$	−6.34043e7	−	1.09819e8i	−0.550722	−	0.953879i
$202$	−5.98941e7	+	1.03740e8i	−0.511275	+	0.885553i
$203$	−1.80530e7	+	1.02384e8i	−0.151466	+	0.859004i
$204$	−6.96561e7	+	5.84484e7i	−0.574452	+	0.482022i
$205$	7.27153e6	+	6.10154e6i	0.0589505	+	0.0494653i
$206$	−1.41869e7	−	8.04580e7i	−0.113071	−	0.641259i
$207$	2.84598e6	+	1.03585e6i	0.0223016	+	0.00811711i
$208$	−2.52188e7			−0.194313
$209$	−1.42912e7	+	2.78658e7i	−0.108282	+	0.211135i
$210$	−1.62508e7			−0.121090
$211$	−2.31536e8	−	8.42723e7i	−1.69680	−	0.617584i	−0.701345	−	0.712822i	$-0.747417\pi$
$211$	−2.31536e8	−	8.42723e7i	−1.69680	−	0.617584i	−0.995455	+	0.0952379i	$0.969639\pi$
$212$	1.76999e7	+	1.00381e8i	0.127584	+	0.723562i
$213$	1.40084e8	+	1.17545e8i	0.993254	+	0.833439i
$214$	2.75912e7	−	2.31518e7i	0.192452	−	0.161487i
$215$	−5.19040e6	+	2.94362e7i	−0.0356178	+	0.201998i
$216$	−2.82011e7	+	4.88457e7i	−0.190405	+	0.329791i
$217$	2.77724e7	+	4.81031e7i	0.184503	+	0.319569i
$218$	−7.40640e7	+	2.69571e7i	−0.484183	+	0.176228i
$219$	6.29402e7	−	2.29084e7i	0.404924	−	0.147380i
$220$	1.07726e6	+	1.86586e6i	0.00682087	+	0.0118141i
$221$	1.05764e8	−	1.83189e8i	0.659123	−	1.14163i
$222$	−5.51535e6	+	3.12791e7i	−0.0338328	+	0.191875i
$223$	9.76570e7	−	8.19440e7i	0.589707	−	0.494823i	−0.298411	−	0.954437i	$-0.596457\pi$
$223$	9.76570e7	−	8.19440e7i	0.589707	−	0.494823i	0.888119	+	0.459614i	$0.152012\pi$
$224$	−3.83654e7	−	3.21924e7i	−0.228072	−	0.191375i
$225$	6.38323e6	+	3.62011e7i	0.0373595	+	0.211877i
$226$	−7.16755e7	−	2.60877e7i	−0.413039	−	0.150334i
$227$	−2.09447e8			−1.18846			−0.594228	−	0.804297i	$-0.702542\pi$
$227$	−2.09447e8			−1.18846			−0.594228	+	0.804297i	$0.702542\pi$
$228$	−7.90316e7	+	3.93259e6i	−0.441600	+	0.0219739i
$229$	−3.11275e8			−1.71285			−0.856426	−	0.516270i	$-0.827320\pi$
$229$	−3.11275e8			−1.71285			−0.856426	+	0.516270i	$0.827320\pi$
$230$	1.53458e6	+	558543.i	0.00831655	+	0.00302698i
$231$	1.14965e7	+	6.52000e7i	0.0613655	+	0.348021i
$232$	2.66789e7	+	2.23862e7i	0.140268	+	0.117699i
$233$	−1.58213e7	+	1.32756e7i	−0.0819400	+	0.0687559i	−0.682838	−	0.730570i	$-0.739254\pi$
$233$	−1.58213e7	+	1.32756e7i	−0.0819400	+	0.0687559i	0.600898	+	0.799326i	$0.294810\pi$
$234$	4.07835e6	−	2.31295e7i	0.0208079	−	0.118008i
$235$	8.41755e6	−	1.45796e7i	0.0423105	−	0.0732839i
$236$	−2.62915e7	−	4.55382e7i	−0.130204	−	0.225519i
$237$	−6.84019e7	+	2.48962e7i	−0.333771	+	0.121483i
$238$	3.94745e8	−	1.43675e8i	1.89800	−	0.690817i
$239$	1.55708e8	+	2.69694e8i	0.737765	+	1.27785i	0.953500	+	0.301394i	$0.0974520\pi$
$239$	1.55708e8	+	2.69694e8i	0.737765	+	1.27785i	−0.215735	+	0.976452i	$0.569215\pi$
$240$	−2.72194e6	+	4.71454e6i	−0.0127098	+	0.0220141i
$241$	−7.65983e6	+	4.34411e7i	−0.0352500	+	0.199913i	−0.997347	−	0.0727950i	$-0.976808\pi$
$241$	−7.65983e6	+	4.34411e7i	−0.0352500	+	0.199913i	0.962097	+	0.272708i	$0.0879192\pi$
$242$	−1.12700e8	+	9.45668e7i	−0.511177	+	0.428929i
$243$	−7.32740e7	−	6.14842e7i	−0.327588	−	0.274879i
$244$	−2.98192e7	−	1.69113e8i	−0.131411	−	0.745268i
$245$	4.56769e7	+	1.66250e7i	0.198434	+	0.0722239i
$246$	9.77131e7			0.418485
$247$	1.69634e8	−	7.14772e7i	0.716265	−	0.301806i
$248$	1.86070e7			0.0774633
$249$	−9.55065e7	−	3.47615e7i	−0.392044	−	0.142692i
$250$	6.92993e6	+	3.93016e7i	0.0280504	+	0.159082i
$251$	−1.64416e8	−	1.37962e8i	−0.656276	−	0.550681i	0.252692	−	0.967547i	$-0.418684\pi$
$251$	−1.64416e8	−	1.37962e8i	−0.656276	−	0.550681i	−0.908968	+	0.416866i	$0.863129\pi$
$252$	3.57298e7	−	2.99808e7i	0.140646	−	0.118016i
$253$	1.15530e6	−	6.55205e6i	0.00448512	−	0.0254364i
$254$	−1.51673e7	+	2.62705e7i	−0.0580751	+	0.100589i
$255$	−2.28310e7	−	3.95444e7i	−0.0862251	−	0.149346i
$256$	−1.57654e7	+	5.73815e6i	−0.0587308	+	0.0213763i
$257$	1.29859e8	−	4.72650e7i	0.477208	−	0.173689i	−0.0922068	−	0.995740i	$-0.529392\pi$
$257$	1.29859e8	−	4.72650e7i	0.477208	−	0.173689i	0.569415	+	0.822050i	$0.307170\pi$
$258$	1.53844e8	+	2.66466e8i	0.557716	+	0.965992i
$259$	7.33666e7	−	1.27075e8i	0.262391	−	0.454475i
$260$	2.19909e6	−	1.24717e7i	0.00775955	−	0.0440066i
$261$	−2.48461e7	+	2.08483e7i	−0.0865000	+	0.0725822i
$262$	−7.08673e7	−	5.94647e7i	−0.243440	−	0.204270i
$263$	−5.84444e7	−	3.31455e8i	−0.198106	−	1.12352i	−0.907925	−	0.419132i	$-0.862334\pi$
$263$	−5.84444e7	−	3.31455e8i	−0.198106	−	1.12352i	0.709819	−	0.704384i	$-0.248777\pi$
$264$	2.08409e7	+	7.58546e6i	0.0697111	+	0.0253728i
$265$	−5.11857e7			−0.168962
$266$	3.49307e8	+	1.07804e8i	1.13795	+	0.351194i
$267$	−6.37240e7			−0.204887
$268$	1.84414e8	+	6.71213e7i	0.585225	+	0.213004i
$269$	6.71456e7	+	3.80802e8i	0.210322	+	1.19280i	0.888842	+	0.458214i	$0.151511\pi$
$269$	6.71456e7	+	3.80802e8i	0.210322	+	1.19280i	−0.678520	+	0.734582i	$0.737378\pi$
$270$	−2.16970e7	−	1.82059e7i	−0.0670851	−	0.0562911i
$271$	−3.76108e8	+	3.15592e8i	−1.14794	+	0.963237i	−0.999669	−	0.0257094i	$-0.991816\pi$
$271$	−3.76108e8	+	3.15592e8i	−1.14794	+	0.963237i	−0.148272	+	0.988947i	$0.547371\pi$
$272$	2.44363e7	−	1.38585e8i	0.0736282	−	0.417566i
$273$	1.94576e8	−	3.37016e8i	0.578790	−	1.00249i
$274$	2.15110e8	+	3.72582e8i	0.631734	+	1.09420i
$275$	7.58815e7	−	2.76186e7i	0.220025	−	0.0800824i
$276$	1.57969e7	−	5.74960e6i	0.0452262	−	0.0164610i
$277$	1.97040e8	+	3.41284e8i	0.557026	+	0.964798i	0.997743	+	0.0671515i	$0.0213911\pi$
$277$	1.97040e8	+	3.41284e8i	0.557026	+	0.964798i	−0.440716	+	0.897646i	$0.645276\pi$
$278$	−1.02444e8	+	1.77438e8i	−0.285977	+	0.495326i
$279$	−3.00911e6	+	1.70655e7i	−0.00829512	+	0.0470440i
$280$	1.92659e7	−	1.61660e7i	0.0524488	−	0.0440098i
$281$	−1.34433e8	−	1.12803e8i	−0.361438	−	0.303282i	0.443926	−	0.896064i	$-0.353585\pi$
$281$	−1.34433e8	−	1.12803e8i	−0.361438	−	0.303282i	−0.805363	+	0.592781i	$0.798030\pi$
$282$	−3.00931e7	−	1.70666e8i	−0.0799088	−	0.453186i
$283$	3.19094e8	+	1.16141e8i	0.836886	+	0.304601i	0.724682	−	0.689084i	$-0.241987\pi$
$283$	3.19094e8	+	1.16141e8i	0.836886	+	0.304601i	0.112204	+	0.993685i	$0.464209\pi$
$284$	−2.83005e8			−0.733129
$285$	4.94678e6	−	3.94271e7i	0.0126580	−	0.100888i
$286$	−5.15934e7			−0.130411
$287$	−4.24194e8	−	1.54394e8i	−1.05920	−	0.385517i
$288$	−2.71319e6	−	1.53873e7i	−0.00669278	−	0.0379567i
$289$	5.89861e8	+	4.94952e8i	1.43750	+	1.20620i
$290$	−1.33973e7	+	1.12417e7i	−0.0322570	+	0.0270668i
$291$	8.24421e7	−	4.67553e8i	0.196121	−	1.11226i
$292$	−5.18289e7	+	8.97703e7i	−0.121824	+	0.211005i
$293$	2.54565e8	+	4.40919e8i	0.591237	+	1.02405i	0.994066	+	0.108777i	$0.0346936\pi$
$293$	2.54565e8	+	4.40919e8i	0.591237	+	1.02405i	−0.402829	+	0.915275i	$0.631973\pi$
$294$	4.70194e8	−	1.71137e8i	1.07910	−	0.392760i
$295$	2.48131e7	−	9.03121e6i	0.0562734	−	0.0204818i
$296$	−2.45772e7	−	4.25690e7i	−0.0550823	−	0.0954053i
$297$	−5.76947e7	+	9.99302e7i	−0.127788	+	0.221335i
$298$	−1.02790e6	+	5.82952e6i	−0.00225006	+	0.0127607i
$299$	−2.99574e7	+	2.51372e7i	−0.0648119	+	0.0543836i
$300$	1.56302e8	+	1.31153e8i	0.334225	+	0.280448i
$301$	−2.46836e8	−	1.39987e9i	−0.521705	−	2.95874i
$302$	−3.09983e8	−	1.12825e8i	−0.647610	−	0.235711i
$303$	−6.19219e8			−1.27878
$304$	8.97825e7	−	8.32813e7i	0.183288	−	0.170016i
$305$	8.62331e7			0.174030
$306$	1.23152e8	+	4.48236e7i	0.245706	+	0.0894297i
$307$	3.03652e7	+	1.72209e8i	0.0598951	+	0.339682i	0.999999	−	0.00120532i	$-0.000383666\pi$
$307$	3.03652e7	+	1.72209e8i	0.0598951	+	0.339682i	−0.940104	+	0.340887i	$0.889273\pi$
$308$	−7.84892e7	−	6.58603e7i	−0.153067	−	0.128439i
$309$	3.23520e8	−	2.71466e8i	0.623802	−	0.523432i
$310$	−1.62254e6	+	9.20190e6i	−0.00309336	+	0.0175433i
$311$	2.18383e8	−	3.78251e8i	0.411678	−	0.713047i	−0.583395	−	0.812188i	$-0.698276\pi$
$311$	2.18383e8	−	3.78251e8i	0.411678	−	0.713047i	0.995073	+	0.0991412i	$0.0316096\pi$
$312$	−6.51815e7	−	1.12898e8i	−0.121502	−	0.210448i
$313$	−5.12546e8	+	1.86552e8i	−0.944774	+	0.343870i	−0.768049	−	0.640391i	$-0.778772\pi$
$313$	−5.12546e8	+	1.86552e8i	−0.944774	+	0.343870i	−0.176725	+	0.984260i	$0.556550\pi$
$314$	−3.74835e8	+	1.36429e8i	−0.683260	+	0.248686i
$315$	1.17110e7	+	2.02841e7i	0.0211110	+	0.0365653i
$316$	5.63264e7	−	9.75602e7i	0.100417	−	0.173927i
$317$	7.51389e6	−	4.26134e7i	0.0132482	−	0.0751344i	−0.977467	−	0.211089i	$-0.932299\pi$
$317$	7.51389e6	−	4.26134e7i	0.0132482	−	0.0751344i	0.990715	+	0.135955i	$0.0434101\pi$
$318$	−4.03631e8	+	3.38686e8i	−0.703864	+	0.590612i
$319$	5.45805e7	+	4.57985e7i	0.0941392	+	0.0789922i
$320$	−1.46298e6	−	8.29699e6i	−0.00249583	−	0.0141545i
$321$	1.74958e8	+	6.36794e7i	0.295233	+	0.107456i
$322$	−7.76626e7			−0.129633
$323$	2.28419e8	+	1.00145e9i	0.377158	+	1.65356i
$324$	−2.24818e8			−0.367218
$325$	−4.46026e8	−	1.62340e8i	−0.720723	−	0.262322i
$326$	2.26156e7	+	1.28259e8i	0.0361531	+	0.205035i
$327$	−3.12108e8	−	2.61890e8i	−0.493615	−	0.414192i
$328$	−1.15842e8	+	9.72031e7i	−0.181263	+	0.152097i
$329$	−1.39025e8	+	7.88449e8i	−0.215232	+	1.22064i
$330$	−5.56864e6	+	9.64517e6i	−0.00853003	+	0.0147744i
$331$	−4.35198e8	−	7.53785e8i	−0.659612	−	1.14248i	−0.980716	−	0.195438i	$-0.937387\pi$
$331$	−4.35198e8	−	7.53785e8i	−0.659612	−	1.14248i	0.321104	−	0.947044i	$-0.395946\pi$
$332$	1.47806e8	−	5.37971e7i	0.221671	−	0.0806817i
$333$	4.30169e7	−	1.56569e7i	0.0638387	−	0.0232354i
$334$	−4.11432e8	−	7.12621e8i	−0.604207	−	1.04652i
$335$	−4.92751e7	+	8.53470e7i	−0.0716095	+	0.124031i
$336$	4.49558e7	−	2.54957e8i	0.0646545	−	0.366674i
$337$	−9.34019e8	+	7.83735e8i	−1.32939	+	1.11549i	−0.345165	+	0.938542i	$0.612177\pi$
$337$	−9.34019e8	+	7.83735e8i	−1.32939	+	1.11549i	−0.984221	+	0.176945i	$0.943378\pi$
$338$	−1.52233e8	−	1.27739e8i	−0.214437	−	0.179934i
$339$	−6.84676e7	−	3.88299e8i	−0.0954523	−	0.541337i
$340$	6.64049e7	+	2.41694e7i	0.0916270	+	0.0333495i
$341$	3.80669e7			0.0519884
$342$	6.18622e7	+	9.58125e7i	0.0836246	+	0.129518i
$343$	−1.05293e9			−1.40886
$344$	−4.47464e8	−	1.62863e8i	−0.592657	−	0.215709i
$345$	1.46590e6	+	8.31355e6i	0.00192193	+	0.0108998i
$346$	5.19254e8	+	4.35705e8i	0.673927	+	0.565492i
$347$	4.61851e8	−	3.87539e8i	0.593401	−	0.497923i	−0.295916	−	0.955214i	$-0.595625\pi$
$347$	4.61851e8	−	3.87539e8i	0.593401	−	0.497923i	0.889317	+	0.457291i	$0.151180\pi$
$348$	−3.12618e7	+	1.77295e8i	−0.0397637	+	0.225511i
$349$	−2.63972e8	+	4.57213e8i	−0.332406	+	0.575744i	−0.982983	−	0.183696i	$-0.941194\pi$
$349$	−2.63972e8	+	4.57213e8i	−0.332406	+	0.575744i	0.650577	+	0.759440i	$0.274527\pi$
$350$	−4.71309e8	−	8.16331e8i	−0.587581	−	1.01772i
$351$	6.37347e8	−	2.31975e8i	0.786685	−	0.286330i
$352$	−3.22534e7	+	1.17393e7i	−0.0394164	+	0.0143464i
$353$	5.21137e8	+	9.02636e8i	0.630580	+	1.09220i	0.987433	+	0.158037i	$0.0505164\pi$
$353$	5.21137e8	+	9.02636e8i	0.630580	+	1.09220i	−0.356853	+	0.934161i	$0.616150\pi$
$354$	1.35908e8	−	2.35400e8i	0.162830	−	0.282030i
$355$	2.46782e7	−	1.39957e8i	0.0292762	−	0.166034i
$356$	7.55469e7	−	6.33914e7i	0.0887446	−	0.0744655i
$357$	1.66347e9	+	1.39582e9i	1.93498	+	1.62364i
$358$	−6.70734e7	−	3.80392e8i	−0.0772609	−	0.438169i
$359$	1.29264e9	+	4.70483e8i	1.47451	+	0.536678i	0.949321	−	0.314308i	$-0.101773\pi$
$359$	1.29264e9	+	4.70483e8i	1.47451	+	0.536678i	0.525188	+	0.850986i	$0.323995\pi$
$360$	7.84620e6			0.00886341
$361$	−3.67879e8	+	8.14661e8i	−0.411557	+	0.911384i
$362$	−8.62156e8			−0.955226
$363$	−7.14640e8	−	2.60108e8i	−0.784177	−	0.285417i
$364$	1.04580e8	+	5.93105e8i	0.113657	+	0.644580i
$365$	−3.98754e7	−	3.34594e7i	−0.0429220	−	0.0360159i
$366$	6.80000e8	−	5.70588e8i	0.724979	−	0.608330i
$367$	1.42716e8	−	8.09382e8i	0.150710	−	0.854717i	−0.811894	−	0.583804i	$-0.801563\pi$
$367$	1.42716e8	−	8.09382e8i	0.150710	−	0.854717i	0.962604	−	0.270913i	$-0.0873254\pi$
$368$	−1.30082e7	+	2.25308e7i	−0.0136066	+	0.0235673i
$369$	−7.04163e7	−	1.21965e8i	−0.0729593	−	0.126369i
$370$	2.31952e7	−	8.44235e6i	0.0238063	−	0.00866478i
$371$	2.28740e9	−	8.32545e8i	2.32559	−	0.846445i
$372$	4.80925e7	+	8.32986e7i	0.0484369	+	0.0838952i
$373$	3.99780e8	−	6.92439e8i	0.398878	−	0.690877i	−0.594710	−	0.803940i	$-0.702733\pi$
$373$	3.99780e8	−	6.92439e8i	0.398878	−	0.690877i	0.993588	+	0.113064i	$0.0360664\pi$
$374$	4.99925e7	−	2.83522e8i	0.0494145	−	0.280244i
$375$	−1.58031e8	+	1.32604e8i	−0.154751	+	0.129851i
$376$	2.05452e8	+	1.72395e8i	0.199321	+	0.167250i
$377$	−7.27241e7	−	4.12439e8i	−0.0699010	−	0.396428i
$378$	1.26572e9	+	4.60685e8i	1.20536	+	0.438715i
$379$	1.31842e9			1.24399			0.621994	−	0.783022i	$-0.286323\pi$
$379$	1.31842e9			1.24399			0.621994	+	0.783022i	$0.286323\pi$
$380$	3.33568e7	+	5.16631e7i	0.0311847	+	0.0482990i
$381$	−1.56808e8			−0.145255
$382$	−6.19178e8	−	2.25362e8i	−0.568321	−	0.206852i
$383$	−1.72083e8	−	9.75929e8i	−0.156510	−	0.887611i	−0.957393	−	0.288790i	$-0.906747\pi$
$383$	−1.72083e8	−	9.75929e8i	−0.156510	−	0.887611i	0.800883	−	0.598821i	$-0.204364\pi$
$384$	−6.64361e7	−	5.57465e7i	−0.0598749	−	0.0502410i
$385$	3.94148e7	−	3.30729e7i	0.0352003	−	0.0295366i
$386$	3.70405e7	−	2.10067e8i	0.0327809	−	0.185910i
$387$	2.21734e8	−	3.84054e8i	0.194466	−	0.336825i
$388$	3.67374e8	+	6.36311e8i	0.319299	+	0.553042i
$389$	2.02105e8	−	7.35604e7i	0.174082	−	0.0633607i	−0.253509	−	0.967333i	$-0.581585\pi$
$389$	2.02105e8	−	7.35604e7i	0.174082	−	0.0633607i	0.427591	+	0.903972i	$0.359362\pi$
$390$	6.15161e7	−	2.23900e7i	0.0525125	−	0.0191130i
$391$	−1.09109e8	−	1.88982e8i	−0.0923086	−	0.159883i
$392$	−3.87188e8	+	6.70629e8i	−0.324654	+	0.562316i
$393$	8.30409e7	−	4.70948e8i	0.0690110	−	0.391381i
$394$	−1.05484e9	+	8.85114e8i	−0.868858	+	0.729058i
$395$	4.33356e7	+	3.63629e7i	0.0353798	+	0.0296872i
$396$	−5.55074e6	−	3.14798e7i	−0.00449177	−	0.0254741i
$397$	−7.96086e8	−	2.89752e8i	−0.638548	−	0.232412i	0.00239979	−	0.999997i	$-0.499236\pi$
$397$	−7.96086e8	−	2.89752e8i	−0.638548	−	0.232412i	−0.640947	+	0.767585i	$0.721458\pi$
$398$	−7.82668e8			−0.622282
$399$	4.20226e8	+	1.84239e9i	0.331191	+	1.45203i
$400$	−3.15769e8			−0.246695
$401$	1.34523e9	+	4.89622e8i	1.04181	+	0.379189i	0.805567	−	0.592504i	$-0.201861\pi$
$401$	1.34523e9	+	4.89622e8i	1.04181	+	0.379189i	0.236246	+	0.971693i	$0.424083\pi$
$402$	1.76161e8	+	9.99057e8i	0.135244	+	0.767006i
$403$	−1.71406e8	−	1.43826e8i	−0.130454	−	0.109464i
$404$	7.34104e8	−	6.15987e8i	0.553889	−	0.464768i
$405$	1.96043e7	−	1.11181e8i	0.0146642	−	0.0831648i
$406$	4.15853e8	−	7.20278e8i	0.308389	−	0.534145i
$407$	−5.02809e7	−	8.70890e7i	−0.0369677	−	0.0640299i
$408$	6.83567e8	−	2.48798e8i	0.498276	−	0.181358i
$409$	−7.55440e8	+	2.74958e8i	−0.545969	+	0.198717i	−0.600255	−	0.799809i	$-0.704934\pi$
$409$	−7.55440e8	+	2.74958e8i	−0.545969	+	0.198717i	0.0542855	+	0.998525i	$0.482712\pi$
$410$	−3.79692e7	−	6.57646e7i	−0.0272075	−	0.0471247i
$411$	−1.11197e9	+	1.92598e9i	−0.790033	+	1.36838i
$412$	−1.13495e8	+	6.43664e8i	−0.0799535	+	0.453439i
$413$	−9.61956e8	+	8.07177e8i	−0.671939	+	0.563824i
$414$	−1.85605e7	−	1.55741e7i	−0.0128555	−	0.0107870i
$415$	1.37160e7	+	7.77871e7i	0.00942015	+	0.0534243i
$416$	1.89583e8	+	6.90027e7i	0.129114	+	0.0469936i
$417$	−1.05913e9			−0.715272
$418$	1.83680e8	−	1.70380e8i	0.123011	−	0.114104i
$419$	−1.79790e9			−1.19403			−0.597016	−	0.802230i	$-0.703647\pi$
$419$	−1.79790e9			−1.19403			−0.597016	+	0.802230i	$0.703647\pi$
$420$	1.22166e8	+	4.44648e7i	0.0804597	+	0.0292849i
$421$	−2.89880e7	−	1.64399e8i	−0.0189335	−	0.107377i	0.973876	−	0.227079i	$-0.0729174\pi$
$421$	−2.89880e7	−	1.64399e8i	−0.0189335	−	0.107377i	−0.992810	+	0.119701i	$0.961806\pi$
$422$	1.51000e9	+	1.26704e9i	0.978101	+	0.820724i
$423$	−1.91338e8	+	1.60551e8i	−0.122916	+	0.103139i
$424$	1.41599e8	−	8.03048e8i	0.0902152	−	0.511636i
$425$	1.32430e9	−	2.29375e9i	0.836804	−	1.44939i
$426$	−7.31467e8	−	1.26694e9i	−0.458418	−	0.794002i
$427$	−3.85360e9	+	1.40260e9i	−2.39535	+	0.871837i
$428$	−2.70765e8	+	9.85505e7i	−0.166932	+	0.0607583i
$429$	−1.33350e8	−	2.30970e8i	−0.0815443	−	0.141239i
$430$	1.19561e8	−	2.07086e8i	0.0725189	−	0.125606i
$431$	5.75277e8	−	3.26256e9i	0.346104	−	1.96285i	0.0915063	−	0.995804i	$-0.470832\pi$
$431$	5.75277e8	−	3.26256e9i	0.346104	−	1.96285i	0.254597	−	0.967047i	$-0.418057\pi$
$432$	3.45653e8	−	2.90037e8i	0.206275	−	0.173085i
$433$	2.17754e9	+	1.82717e9i	1.28902	+	1.08161i	0.991933	+	0.126760i	$0.0404578\pi$
$433$	2.17754e9	+	1.82717e9i	1.28902	+	1.08161i	0.297082	+	0.954852i	$0.403987\pi$
$434$	−7.71619e7	−	4.37607e8i	−0.0453095	−	0.256963i
$435$	−8.49530e7	−	3.09204e7i	−0.0494842	−	0.0180108i
$436$	6.30538e8			0.364341
$437$	2.36406e7	−	1.88422e8i	0.0135511	−	0.108006i
$438$	−5.35837e8			−0.304700
$439$	−2.90129e9	−	1.05598e9i	−1.63669	−	0.595705i	−0.650232	−	0.759736i	$-0.725328\pi$
$439$	−2.90129e9	−	1.05598e9i	−1.63669	−	0.595705i	−0.986455	+	0.164031i	$0.947550\pi$
$440$	−2.99302e6	−	1.69742e7i	−0.00167504	−	0.00949962i
$441$	−5.52454e8	−	4.63564e8i	−0.306733	−	0.257380i
$442$	−1.29632e9	+	1.08774e9i	−0.714061	+	0.599168i
$443$	4.91093e8	−	2.78513e9i	0.268380	−	1.52206i	−0.490853	−	0.871242i	$-0.663315\pi$
$443$	4.91093e8	−	2.78513e9i	0.268380	−	1.52206i	0.759233	−	0.650819i	$-0.225574\pi$
$444$	1.27047e8	−	2.20051e8i	0.0688846	−	0.119312i
$445$	2.47618e7	+	4.28887e7i	0.0133205	+	0.0230719i
$446$	−9.58352e8	+	3.48812e8i	−0.511509	+	0.186174i
$447$	−2.87539e7	+	1.04656e7i	−0.0152272	+	0.00554225i
$448$	2.00330e8	+	3.46982e8i	0.105262	+	0.182320i
$449$	−4.85522e8	+	8.40948e8i	−0.253132	+	0.438437i	−0.964386	−	0.264498i	$-0.914794\pi$
$449$	−4.85522e8	+	8.40948e8i	−0.253132	+	0.438437i	0.711255	+	0.702934i	$0.248127\pi$
$450$	5.10658e7	−	2.89609e8i	0.0264172	−	0.149819i
$451$	−2.36994e8	+	1.98861e8i	−0.121652	+	0.102078i
$452$	4.67443e8	+	3.92231e8i	0.238092	+	0.199783i
$453$	−2.96109e8	−	1.67932e9i	−0.149661	−	0.848769i
$454$	1.57452e9	+	5.73080e8i	0.789685	+	0.287422i
$455$	−3.02433e8			−0.150518
$456$	6.04883e8	+	1.86680e8i	0.298741	+	0.0921977i
$457$	−3.79489e9			−1.85991			−0.929957	−	0.367667i	$-0.880157\pi$
$457$	−3.79489e9			−1.85991			−0.929957	+	0.367667i	$0.880157\pi$
$458$	2.34002e9	+	8.51698e8i	1.13813	+	0.414244i
$459$	6.57205e8	+	3.72720e9i	0.317217	+	1.79903i
$460$	−1.00080e7	−	8.39774e6i	−0.00479398	−	0.00402263i
$461$	1.15080e9	−	9.65633e8i	0.547073	−	0.459049i	−0.326876	−	0.945067i	$-0.605996\pi$
$461$	1.15080e9	−	9.65633e8i	0.547073	−	0.459049i	0.873948	+	0.486019i	$0.161551\pi$
$462$	9.19721e7	−	5.21600e8i	0.0433920	−	0.246088i
$463$	−1.10758e9	+	1.91839e9i	−0.518612	+	0.898262i	0.481154	+	0.876636i	$0.340218\pi$
$463$	−1.10758e9	+	1.91839e9i	−0.518612	+	0.898262i	−0.999766	+	0.0216260i	$0.993116\pi$
$464$	−1.39307e8	−	2.41287e8i	−0.0647382	−	0.112130i
$465$	−4.53881e7	+	1.65199e7i	−0.0209342	+	0.00761943i
$466$	1.55261e8	−	5.65106e7i	0.0710744	−	0.0258690i
$467$	1.58017e9	+	2.73693e9i	0.717950	+	1.24353i	0.961811	+	0.273716i	$0.0882527\pi$
$467$	1.58017e9	+	2.73693e9i	0.717950	+	1.24353i	−0.243861	+	0.969810i	$0.578414\pi$
$468$	−9.39452e7	+	1.62718e8i	−0.0423657	+	0.0733795i
$469$	8.13832e8	−	4.61547e9i	0.364275	−	2.06591i
$470$	−1.03171e8	+	8.65711e7i	−0.0458371	+	0.0384619i
$471$	−1.57957e9	−	1.32541e9i	−0.696571	−	0.584492i
$472$	7.30475e7	+	4.14273e8i	0.0319749	+	0.181338i
$473$	−9.15435e8	−	3.33191e8i	−0.397753	−	0.144770i
$474$	5.82334e8			0.251159
$475$	2.12402e9	−	8.94980e8i	0.909350	−	0.383165i
$476$	−3.36063e9			−1.42822
$477$	7.13618e8	+	2.59736e8i	0.301059	+	0.109577i
$478$	−4.32614e8	−	2.45348e9i	−0.181177	−	1.02751i
$479$	1.82429e9	+	1.53076e9i	0.758438	+	0.636405i	0.937720	−	0.347393i	$-0.112933\pi$
$479$	1.82429e9	+	1.53076e9i	0.758438	+	0.636405i	−0.179282	+	0.983798i	$0.557377\pi$
$480$	3.33621e7	−	2.79941e7i	0.0137692	−	0.0115537i
$481$	−1.02642e8	+	5.82114e8i	−0.0420552	+	0.238507i
$482$	1.76445e8	−	3.05611e8i	0.0717702	−	0.124310i
$483$	−2.00730e8	−	3.47674e8i	−0.0810582	−	0.140397i
$484$	1.10598e9	−	4.02544e8i	0.443393	−	0.161382i
$485$	−3.46716e8	+	1.26194e8i	−0.138000	+	0.0502277i
$486$	3.82610e8	+	6.62700e8i	0.151192	+	0.261872i
$487$	2.34686e8	−	4.06487e8i	0.0920736	−	0.159476i	−0.816310	−	0.577614i	$-0.803984\pi$
$487$	2.34686e8	−	4.06487e8i	0.0920736	−	0.159476i	0.908383	+	0.418138i	$0.137317\pi$
$488$	−2.38553e8	+	1.35290e9i	−0.0929214	+	0.526984i
$489$	−5.15729e8	+	4.32748e8i	−0.199453	+	0.167361i
$490$	−2.97889e8	−	2.49959e8i	−0.114385	−	0.0959802i
$491$	−1.31522e8	−	7.45900e8i	−0.0501434	−	0.284378i	0.949417	−	0.314017i	$-0.101675\pi$
$491$	−1.31522e8	−	7.45900e8i	−0.0501434	−	0.284378i	−0.999561	+	0.0296399i	$0.990564\pi$
$492$	−7.34562e8	−	2.67359e8i	−0.278068	−	0.101208i
$493$	2.33695e9			0.878384
$494$	−1.47080e9	+	7.31868e7i	−0.548922	+	0.0273142i
$495$	1.60520e7			0.00594855
$496$	−1.39879e8	−	5.09118e7i	−0.0514715	−	0.0187341i
$497$	1.17360e9	+	6.65583e9i	0.428819	+	2.43195i
$498$	6.22861e8	+	5.22642e8i	0.225989	+	0.189628i
$499$	−1.20381e9	+	1.01012e9i	−0.433717	+	0.363932i	−0.833352	−	0.552742i	$-0.813581\pi$
$499$	−1.20381e9	+	1.01012e9i	−0.433717	+	0.363932i	0.399635	+	0.916674i	$0.369137\pi$
$500$	5.54394e7	−	3.14413e8i	0.0198346	−	0.112488i
$501$	2.12681e9	−	3.68374e9i	0.755608	−	1.30875i
$502$	8.58521e8	+	1.48700e9i	0.302892	+	0.524624i
$503$	2.80890e9	−	1.02236e9i	0.984120	−	0.358190i	0.200679	−	0.979657i	$-0.435685\pi$
$503$	2.80890e9	−	1.02236e9i	0.984120	−	0.358190i	0.783441	+	0.621467i	$0.213463\pi$
$504$	−3.50632e8	+	1.27620e8i	−0.121996	+	0.0444029i
$505$	2.40615e8	+	4.16758e8i	0.0831387	+	0.144000i
$506$	−2.66125e7	+	4.60942e7i	−0.00913186	+	0.0158168i
$507$	1.78384e8	−	1.01166e9i	0.0607893	−	0.344753i
$508$	1.85901e8	−	1.55989e8i	0.0629156	−	0.0527925i
$509$	−2.29254e9	−	1.92367e9i	−0.770556	−	0.646573i	0.170295	−	0.985393i	$-0.445528\pi$
$509$	−2.29254e9	−	1.92367e9i	−0.770556	−	0.646573i	−0.940851	+	0.338820i	$0.889972\pi$
$510$	6.34329e7	+	3.59746e8i	0.0211748	+	0.120088i
$511$	2.32618e9	+	8.46662e8i	0.771207	+	0.280696i
$512$	1.34218e8			0.0441942
$513$	−1.50298e9	+	2.93061e9i	−0.491523	+	0.958401i
$514$	−1.10555e9			−0.359093
$515$	−3.08420e8	−	1.12256e8i	−0.0994987	−	0.0362145i
$516$	−4.27437e8	−	2.42412e9i	−0.136961	−	0.776747i
$517$	4.20320e8	+	3.52691e8i	0.133771	+	0.112248i
$518$	−8.99234e8	+	7.54547e8i	−0.284262	+	0.238524i
$519$	−6.08451e8	+	3.45070e9i	−0.191047	+	1.08348i
$520$	−5.06563e7	+	8.77392e7i	−0.0157987	+	0.0273642i
$521$	1.33086e9	+	2.30511e9i	0.412287	+	0.714101i	0.995139	−	0.0984765i	$-0.0313969\pi$
$521$	1.33086e9	+	2.30511e9i	0.412287	+	0.714101i	−0.582853	+	0.812578i	$0.698064\pi$
$522$	2.43826e8	−	8.87454e7i	0.0750297	−	0.0273086i
$523$	3.00365e9	−	1.09324e9i	0.918106	−	0.334163i	0.160621	−	0.987016i	$-0.448650\pi$
$523$	3.00365e9	−	1.09324e9i	0.918106	−	0.334163i	0.757485	+	0.652853i	$0.226428\pi$
$524$	3.70043e8	+	6.40933e8i	0.112355	+	0.194604i
$525$	2.43633e9	−	4.21985e9i	0.734816	−	1.27274i
$526$	−4.67556e8	+	2.65164e9i	−0.140082	+	0.794446i
$527$	9.56458e8	−	8.02563e8i	0.284661	−	0.238859i
$528$	−1.35917e8	−	1.14048e8i	−0.0401842	−	0.0337185i
$529$	−5.84236e8	−	3.31337e9i	−0.171591	−	0.973139i
$530$	3.84791e8	+	1.40052e8i	0.112269	+	0.0408625i
$531$	−3.91765e8			−0.113552
$532$	−2.33096e9	−	1.76618e9i	−0.671189	−	0.508562i
$533$	1.81847e9			0.520190
$534$	4.79048e8	+	1.74359e8i	0.136140	+	0.0495507i
$535$	−2.51262e7	−	1.42498e8i	−0.00709395	−	0.0402318i
$536$	−1.20269e9	−	1.00917e9i	−0.337346	−	0.283067i
$537$	1.52955e9	−	1.28345e9i	0.426240	−	0.357658i
$538$	5.37165e8	−	3.04641e9i	0.148720	−	0.843434i
$539$	−7.92121e8	+	1.37199e9i	−0.217887	+	0.377391i
$540$	1.13294e8	+	1.96230e8i	0.0309619	+	0.0536275i
$541$	−1.68145e9	+	6.11996e8i	−0.456554	+	0.166172i	−0.560052	−	0.828457i	$-0.689219\pi$
$541$	−1.68145e9	+	6.11996e8i	−0.456554	+	0.166172i	0.103498	+	0.994630i	$0.466997\pi$
$542$	3.69092e9	−	1.34338e9i	0.995719	−	0.362412i
$543$	−2.22836e9	−	3.85964e9i	−0.597292	−	1.03454i
$544$	−5.62892e8	+	9.74957e8i	−0.149909	+	0.259651i
$545$	−5.49833e7	+	3.11826e8i	−0.0145493	+	0.0825133i
$546$	−2.38487e9	+	2.00114e9i	−0.627032	+	0.526143i
$547$	4.29962e9	+	3.60781e9i	1.12324	+	0.942513i	0.998764	−	0.0497086i	$-0.0158293\pi$
$547$	4.29962e9	+	3.60781e9i	1.12324	+	0.942513i	0.124480	+	0.992222i	$0.460274\pi$
$548$	−5.97656e8	−	3.38948e9i	−0.155138	−	0.879834i
$549$	−1.20224e9	−	4.37580e8i	−0.310090	−	0.112864i
$550$	−6.46011e8			−0.165566
$551$	1.62093e9	+	1.22818e9i	0.412793	+	0.312775i
$552$	−1.34486e8			−0.0340321
$553$	−2.52804e9	−	9.20131e8i	−0.635691	−	0.231372i
$554$	−5.47451e8	−	3.10475e9i	−0.136792	−	0.775786i
$555$	9.77453e7	+	8.20180e7i	0.0242700	+	0.0203650i
$556$	1.25563e9	−	1.05360e9i	0.309813	−	0.259964i
$557$	−4.22161e8	+	2.39419e9i	−0.103511	+	0.587038i	0.888294	+	0.459275i	$0.151891\pi$
$557$	−4.22161e8	+	2.39419e9i	−0.103511	+	0.587038i	−0.991805	+	0.127763i	$0.959220\pi$
$558$	6.93150e7	−	1.20057e8i	0.0168891	−	0.0292528i
$559$	2.86310e9	+	4.95903e9i	0.693258	+	1.20076i
$560$	−1.89065e8	+	6.88140e7i	−0.0454938	+	0.0165584i
$561$	1.39846e9	−	5.08999e8i	0.334411	−	0.121716i
$562$	7.01958e8	+	1.21583e9i	0.166815	+	0.288932i
$563$	−2.97495e9	+	5.15276e9i	−0.702587	+	1.21692i	0.264969	+	0.964257i	$0.414638\pi$
$563$	−2.97495e9	+	5.15276e9i	−0.702587	+	1.21692i	−0.967555	+	0.252659i	$0.918695\pi$
$564$	−2.40745e8	+	1.36533e9i	−0.0565041	+	0.320451i
$565$	−2.34735e8	+	1.96966e8i	−0.0547530	+	0.0459433i
$566$	−2.08102e9	−	1.74619e9i	−0.482413	−	0.404793i
$567$	9.32305e8	+	5.28736e9i	0.214792	+	1.21814i
$568$	2.12750e9	+	7.74348e8i	0.487137	+	0.177303i
$569$	−6.48902e9			−1.47668			−0.738339	−	0.674429i	$-0.764390\pi$
$569$	−6.48902e9			−1.47668			−0.738339	+	0.674429i	$0.764390\pi$
$570$	−1.45067e8	+	2.82860e8i	−0.0328099	+	0.0639749i
$571$	8.19100e9			1.84124			0.920621	−	0.390458i	$-0.127683\pi$
$571$	8.19100e9			1.84124			0.920621	+	0.390458i	$0.127683\pi$
$572$	3.87856e8	+	1.41168e8i	0.0866531	+	0.0315391i
$573$	−5.91466e8	−	3.35437e9i	−0.131338	−	0.744852i
$574$	2.76645e9	+	2.32133e9i	0.610564	+	0.512324i
$575$	−3.75102e8	+	3.14748e8i	−0.0822834	+	0.0690440i
$576$	−2.17055e7	+	1.23098e8i	−0.00473251	+	0.0268394i
$577$	−1.82895e9	+	3.16783e9i	−0.396357	+	0.686510i	−0.993273	−	0.115793i	$-0.963059\pi$
$577$	−1.82895e9	+	3.16783e9i	−0.396357	+	0.686510i	0.596917	+	0.802303i	$0.296392\pi$
$578$	−3.08004e9	−	5.33478e9i	−0.663450	−	1.14913i
$579$	1.03615e9	−	3.77127e8i	0.221844	−	0.0807445i
$580$	1.31474e8	−	4.78525e7i	0.0279795	−	0.0101837i
$581$	−1.87816e9	−	3.25307e9i	−0.397298	−	0.688140i
$582$	−1.89906e9	+	3.28927e9i	−0.399308	+	0.691623i
$583$	2.89688e8	−	1.64290e9i	0.0605467	−	0.343377i
$584$	6.35252e8	−	5.33040e8i	0.131978	−	0.110743i
$585$	−7.22782e7	−	6.06486e7i	−0.0149266	−	0.0125249i
$586$	−7.07275e8	−	4.01116e9i	−0.145193	−	0.823433i
$587$	−3.63986e9	−	1.32480e9i	−0.742764	−	0.270344i	−0.0572066	−	0.998362i	$-0.518219\pi$
$587$	−3.63986e9	−	1.32480e9i	−0.742764	−	0.270344i	−0.685558	+	0.728018i	$0.740442\pi$
$588$	−4.00296e9			−0.812009
$589$	1.08519e9	−	5.39989e7i	0.218829	−	0.0108888i
$590$	−2.11244e8			−0.0423450
$591$	−6.68879e9	−	2.43452e9i	−1.33288	−	0.485129i
$592$	6.82846e7	+	3.87261e8i	0.0135269	+	0.0767146i
$593$	−5.24849e9	−	4.40401e9i	−1.03358	−	0.867274i	−0.0423050	−	0.999105i	$-0.513470\pi$
$593$	−5.24849e9	−	4.40401e9i	−1.03358	−	0.867274i	−0.991272	+	0.131830i	$0.957915\pi$
$594$	7.07148e8	−	5.93367e8i	0.138439	−	0.116164i
$595$	2.93049e8	−	1.66196e9i	0.0570336	−	0.323454i
$596$	2.36778e7	−	4.10111e7i	0.00458120	−	0.00793487i
$597$	−2.02292e9	−	3.50379e9i	−0.389106	−	0.673951i
$598$	2.93985e8	−	1.07002e8i	0.0562175	−	0.0204615i
$599$	−8.10298e9	+	2.94924e9i	−1.54046	+	0.560682i	−0.966156	−	0.257958i	$-0.916950\pi$
$599$	−8.10298e9	+	2.94924e9i	−1.54046	+	0.560682i	−0.574306	+	0.818641i	$0.694728\pi$
$600$	−8.16150e8	−	1.41361e9i	−0.154255	−	0.267178i
$601$	3.36322e9	−	5.82528e9i	0.631968	−	1.09460i	−0.355181	−	0.934798i	$-0.615581\pi$
$601$	3.36322e9	−	5.82528e9i	0.631968	−	1.09460i	0.987149	−	0.159803i	$-0.0510860\pi$
$602$	−1.97469e9	+	1.11990e10i	−0.368901	+	2.09214i
$603$	1.12006e9	−	9.39845e8i	0.208033	−	0.174560i
$604$	2.02160e9	+	1.69633e9i	0.373307	+	0.313242i
$605$	1.02632e8	+	5.82052e8i	0.0188424	+	0.106861i
$606$	4.65500e9	+	1.69428e9i	0.849700	+	0.309266i
$607$	−1.83225e9			−0.332524			−0.166262	−	0.986082i	$-0.553170\pi$
$607$	−1.83225e9			−0.332524			−0.166262	+	0.986082i	$0.553170\pi$
$608$	−9.02815e8	+	3.80411e8i	−0.162906	+	0.0686421i
$609$	4.29932e9			0.771328
$610$	−6.48261e8	−	2.35948e8i	−0.115637	−	0.0420883i
$611$	−5.60042e8	−	3.17616e9i	−0.0993291	−	0.563323i
$612$	−8.03155e8	−	6.73927e8i	−0.141635	−	0.118846i
$613$	−1.23757e9	+	1.03845e9i	−0.217000	+	0.182084i	−0.744807	−	0.667280i	$-0.767459\pi$
$613$	−1.23757e9	+	1.03845e9i	−0.217000	+	0.182084i	0.527808	+	0.849364i	$0.323014\pi$
$614$	2.42921e8	−	1.37767e9i	0.0423522	−	0.240191i
$615$	1.96274e8	−	3.39956e8i	0.0340251	−	0.0589332i
$616$	4.09841e8	+	7.09866e8i	0.0706453	+	0.122361i
$617$	3.25290e9	−	1.18396e9i	0.557536	−	0.202927i	−0.0478555	−	0.998854i	$-0.515239\pi$
$617$	3.25290e9	−	1.18396e9i	0.557536	−	0.202927i	0.605392	+	0.795928i	$0.293016\pi$
$618$	−3.17485e9	+	1.15555e9i	−0.541083	+	0.196938i
$619$	1.16446e9	+	2.01691e9i	0.197337	+	0.341798i	0.947664	−	0.319269i	$-0.103437\pi$
$619$	1.16446e9	+	2.01691e9i	0.197337	+	0.341798i	−0.750327	+	0.661067i	$0.770104\pi$
$620$	3.73754e7	−	6.47361e7i	0.00629818	−	0.0109088i
$621$	1.21502e8	−	6.89070e8i	0.0203592	−	0.115463i
$622$	−2.67666e9	+	2.24598e9i	−0.445991	+	0.374231i
$623$	−1.80415e9	−	1.51386e9i	−0.298927	−	0.250829i
$624$	1.81098e8	+	1.02706e9i	0.0298379	+	0.169219i
$625$	−5.50894e9	−	2.00509e9i	−0.902586	−	0.328514i
$626$	4.36352e9			0.710931
$627$	1.23749e9	+	3.81916e8i	0.200496	+	0.0618772i
$628$	3.19113e9			0.514145
$629$	−3.09944e9	−	1.12810e9i	−0.496599	−	0.180747i
$630$	−3.25376e7	−	1.84530e8i	−0.00518434	−	0.0294019i
$631$	7.93613e8	+	6.65920e8i	0.125749	+	0.105516i	0.703494	−	0.710702i	$-0.251622\pi$
$631$	7.93613e8	+	6.65920e8i	0.125749	+	0.105516i	−0.577744	+	0.816218i	$0.696067\pi$
$632$	−6.90376e8	+	5.79295e8i	−0.108787	+	0.0912830i
$633$	−1.76939e9	+	1.00347e10i	−0.277275	+	1.57250i
$634$	−1.73083e8	+	2.99789e8i	−0.0269738	+	0.0467200i
$635$	6.09322e7	+	1.05538e8i	0.00944363	+	0.0163568i
$636$	3.96101e9	−	1.44169e9i	0.610528	−	0.222214i
$637$	8.75047e9	−	3.18491e9i	1.34135	−	0.488213i
$638$	−2.84999e8	−	4.93633e8i	−0.0434482	−	0.0752544i
$639$	−1.05425e9	+	1.82602e9i	−0.159842	+	0.276855i
$640$	−1.17039e7	+	6.63759e7i	−0.00176482	+	0.0100088i
$641$	−3.36194e9	+	2.82101e9i	−0.504182	+	0.423059i	−0.859076	−	0.511847i	$-0.828961\pi$
$641$	−3.36194e9	+	2.82101e9i	−0.504182	+	0.423059i	0.354894	+	0.934906i	$0.384517\pi$
$642$	−1.14102e9	−	9.57425e8i	−0.170184	−	0.142801i
$643$	−2.68601e8	−	1.52331e9i	−0.0398445	−	0.225969i	0.958383	−	0.285486i	$-0.0921551\pi$
$643$	−2.68601e8	−	1.52331e9i	−0.0398445	−	0.225969i	−0.998227	+	0.0595169i	$0.981044\pi$
$644$	5.83831e8	+	2.12497e8i	0.0861365	+	0.0313511i
$645$	1.23609e9			0.181381
$646$	1.02298e9	−	8.15344e9i	0.149298	−	1.18995i
$647$	1.12625e10			1.63483			0.817413	−	0.576052i	$-0.195408\pi$
$647$	1.12625e10			1.63483			0.817413	+	0.576052i	$0.195408\pi$
$648$	1.69008e9	+	6.15139e8i	0.244003	+	0.0888098i
$649$	1.49443e8	+	8.47533e8i	0.0214595	+	0.121703i
$650$	2.90883e9	+	2.44080e9i	0.415452	+	0.348606i
$651$	1.75961e9	−	1.47649e9i	0.249967	−	0.209748i
$652$	1.80925e8	−	1.02607e9i	0.0255641	−	0.144981i
$653$	−3.50673e8	+	6.07384e8i	−0.0492840	+	0.0853625i	−0.889615	−	0.456711i	$-0.849027\pi$
$653$	−3.50673e8	+	6.07384e8i	−0.0492840	+	0.0853625i	0.840331	+	0.542074i	$0.182361\pi$
$654$	1.62971e9	+	2.82275e9i	0.227819	+	0.394593i
$655$	−3.49234e8	+	1.27111e8i	−0.0485593	+	0.0176741i
$656$	1.13681e9	−	4.13766e8i	0.157226	−	0.0572257i
$657$	3.86147e8	+	6.68826e8i	0.0531219	+	0.0920099i
$658$	3.20245e9	−	5.54681e9i	0.438219	−	0.759018i
$659$	−1.05970e9	+	6.00988e9i	−0.144240	+	0.818026i	0.823734	+	0.566976i	$0.191887\pi$
$659$	−1.05970e9	+	6.00988e9i	−0.144240	+	0.818026i	−0.967974	+	0.251050i	$0.919224\pi$
$660$	6.82532e7	−	5.72713e7i	0.00924101	−	0.00775413i
$661$	−3.81551e9	−	3.20160e9i	−0.513864	−	0.431183i	0.348623	−	0.937263i	$-0.386649\pi$
$661$	−3.81551e9	−	3.20160e9i	−0.513864	−	0.431183i	−0.862486	+	0.506080i	$0.831094\pi$
$662$	1.20914e9	+	6.85738e9i	0.161985	+	0.918661i
$663$	−8.22006e9	−	2.99186e9i	−1.09541	−	0.398698i
$664$	−1.25834e9			−0.166805
$665$	1.07671e9	−	9.98740e8i	0.141978	−	0.131697i
$666$	−3.66221e8			−0.0480378
$667$	−4.05990e8	−	1.47768e8i	−0.0529755	−	0.0192815i
$668$	1.14311e9	+	6.48291e9i	0.148378	+	0.841496i
$669$	−4.03853e9	−	3.38873e9i	−0.521473	−	0.437568i
$670$	6.03951e8	−	5.06775e8i	0.0775782	−	0.0650959i
$671$	−4.88040e8	+	2.76781e9i	−0.0623629	+	0.353678i
$672$	−1.03556e9	+	1.79365e9i	−0.131639	+	0.228005i
$673$	4.69818e9	+	8.13749e9i	0.594124	+	1.02905i	0.993670	+	0.112340i	$0.0358346\pi$
$673$	4.69818e9	+	8.13749e9i	0.594124	+	1.02905i	−0.399545	+	0.916713i	$0.630832\pi$
$674$	9.16595e9	−	3.33613e9i	1.15310	−	0.419695i
$675$	7.98035e9	−	2.90461e9i	0.998754	−	0.363517i
$676$	7.94904e8	+	1.37681e9i	0.0989694	+	0.171420i
$677$	5.12755e9	−	8.88117e9i	0.635111	−	1.10004i	−0.351381	−	0.936233i	$-0.614288\pi$
$677$	5.12755e9	−	8.88117e9i	0.635111	−	1.10004i	0.986492	−	0.163811i	$-0.0523788\pi$
$678$	−5.47741e8	+	3.10639e9i	−0.0674949	+	0.382783i
$679$	1.34415e10	−	1.12788e10i	1.64780	−	1.38267i
$680$	−4.33070e8	−	3.63389e8i	−0.0528174	−	0.0443190i
$681$	1.50406e9	+	8.52992e9i	0.182494	+	1.03498i
$682$	−2.86169e8	−	1.04157e8i	−0.0345444	−	0.0125731i
$683$	−3.98583e9			−0.478682			−0.239341	−	0.970936i	$-0.576931\pi$
$683$	−3.98583e9			−0.478682			−0.239341	+	0.970936i	$0.576931\pi$
$684$	−2.02893e8	−	8.89539e8i	−0.0242421	−	0.106284i
$685$	1.72834e9			0.205453
$686$	7.91541e9	+	2.88097e9i	0.936136	+	0.340726i
$687$	2.23529e9	+	1.26770e10i	0.263018	+	1.49165i
$688$	2.91820e9	+	2.44866e9i	0.341630	+	0.286662i
$689$	−7.51170e9	+	6.30306e9i	−0.874925	+	0.734149i
$690$	1.17272e7	−	6.65084e7i	0.00135901	−	0.00770734i
$691$	4.37268e9	−	7.57370e9i	0.504167	−	0.873242i	−0.495822	−	0.868424i	$-0.665133\pi$
$691$	4.37268e9	−	7.57370e9i	0.504167	−	0.873242i	0.999988	−	0.00481798i	$-0.00153362\pi$
$692$	−2.71135e9	−	4.69620e9i	−0.311039	−	0.538735i
$693$	−7.17335e8	+	2.61089e8i	−0.0818758	+	0.0298004i
$694$	−4.53235e9	+	1.64964e9i	−0.514713	+	0.187340i
$695$	4.11554e8	+	7.12832e8i	0.0465028	+	0.0805453i
$696$	7.20118e8	−	1.24728e9i	0.0809602	−	0.140227i
$697$	−1.76205e9	+	9.99308e9i	−0.197108	+	1.11785i
$698$	3.23543e9	−	2.71485e9i	0.360112	−	0.302170i
$699$	6.54278e8	+	5.49004e8i	0.0724589	+	0.0608003i
$700$	1.30947e9	+	7.42638e9i	0.144296	+	0.818341i
$701$	−1.56815e9	−	5.70758e8i	−0.171939	−	0.0625805i	0.254617	−	0.967042i	$-0.418051\pi$
$701$	−1.56815e9	−	5.70758e8i	−0.171939	−	0.0625805i	−0.426555	+	0.904462i	$0.640273\pi$
$702$	−5.42600e9			−0.591971
$703$	−1.55692e9	−	2.41137e9i	−0.169015	−	0.261771i
$704$	2.74587e8			0.0296603
$705$	−6.54216e8	−	2.38115e8i	−0.0703169	−	0.0255932i
$706$	−1.44791e9	−	8.21152e9i	−0.154855	−	0.878227i
$707$	−1.75313e10	−	1.47105e10i	−1.86572	−	1.56552i
$708$	−1.66579e9	+	1.39776e9i	−0.176402	+	0.148019i
$709$	1.17443e9	−	6.66055e9i	0.123756	−	0.701856i	−0.858283	−	0.513177i	$-0.828468\pi$
$709$	1.17443e9	−	6.66055e9i	0.123756	−	0.701856i	0.982039	−	0.188679i	$-0.0604205\pi$
$710$	−5.68465e8	+	9.84610e8i	−0.0596073	+	0.103243i
$711$	−4.19655e8	−	7.26864e8i	−0.0437874	−	0.0758419i
$712$	−7.41376e8	+	2.69839e8i	−0.0769766	+	0.0280172i
$713$	−2.16909e8	+	7.89486e7i	−0.0224112	+	0.00815701i
$714$	−8.68602e9	−	1.50446e10i	−0.893053	−	1.54681i
$715$	−1.03634e8	+	1.79500e8i	−0.0106031	+	0.0183651i
$716$	−5.36587e8	+	3.04314e9i	−0.0546317	+	0.309832i
$717$	9.86540e9	−	8.27805e9i	0.999534	−	0.838709i
$718$	−8.43017e9	−	7.07375e9i	−0.849964	−	0.713205i
$719$	−1.28256e9	−	7.27378e9i	−0.128685	−	0.729808i	−0.979051	−	0.203616i	$-0.934730\pi$
$719$	−1.28256e9	−	7.27378e9i	−0.128685	−	0.729808i	0.850366	−	0.526192i	$-0.176381\pi$
$720$	−5.89841e7	−	2.14685e7i	−0.00588941	−	0.00214357i
$721$	1.56086e10			1.55092
$722$	4.99459e9	−	5.11767e9i	0.493878	−	0.506048i
$723$	1.82419e9			0.179508
$724$	6.48130e9	+	2.35900e9i	0.634712	+	0.231016i
$725$	−9.10592e8	−	5.16423e9i	−0.0887444	−	0.503294i
$726$	4.66064e9	+	3.91074e9i	0.452030	+	0.379298i
$727$	−8.36419e9	+	7.01839e9i	−0.807334	+	0.677434i	−0.949970	−	0.312341i	$-0.898887\pi$
$727$	−8.36419e9	+	7.01839e9i	−0.807334	+	0.677434i	0.142636	+	0.989775i	$0.454442\pi$
$728$	8.36643e8	−	4.74484e9i	0.0803675	−	0.455787i
$729$	−5.81905e9	+	1.00789e10i	−0.556296	+	0.963532i
$730$	2.08215e8	+	3.60638e8i	0.0198099	+	0.0343117i
$731$	−3.00257e10	+	1.09284e10i	−2.84303	+	1.03478i
$732$	−6.67315e9	+	2.42883e9i	−0.628843	+	0.228880i
$733$	7.22003e9	+	1.25055e10i	0.677134	+	1.17283i	0.975840	+	0.218486i	$0.0701117\pi$
$733$	7.22003e9	+	1.25055e10i	0.677134	+	1.17283i	−0.298706	+	0.954345i	$0.596555\pi$
$734$	−3.28747e9	+	5.69407e9i	−0.306850	+	0.531480i
$735$	3.49061e8	−	1.97962e9i	0.0324261	−	0.183898i
$736$	1.59437e8	−	1.33784e8i	0.0147407	−	0.0123689i
$737$	−2.46050e9	−	2.06460e9i	−0.226405	−	0.189977i
$738$	1.95643e8	+	1.10954e9i	0.0179170	+	0.101613i
$739$	−1.58905e9	−	5.78368e8i	−0.144838	−	0.0527168i	0.268584	−	0.963256i	$-0.413444\pi$
$739$	−1.58905e9	−	5.78368e8i	−0.144838	−	0.0527168i	−0.413422	+	0.910540i	$0.635667\pi$
$740$	−1.97470e8			−0.0179139
$741$	−4.12914e9	−	6.39523e9i	−0.372817	−	0.577421i
$742$	−1.94736e10			−1.74998
$743$	1.73114e10	+	6.30084e9i	1.54836	+	0.563556i	0.968032	−	0.250827i	$-0.0807027\pi$
$743$	1.73114e10	+	6.30084e9i	1.54836	+	0.563556i	0.580327	+	0.814384i	$0.302925\pi$
$744$	−1.33619e8	−	7.57789e8i	−0.0118949	−	0.0674595i
$745$	1.82169e7	+	1.52858e7i	0.00161409	+	0.00135438i
$746$	−4.89998e9	+	4.11158e9i	−0.432124	+	0.362595i
$747$	2.03497e8	−	1.15409e9i	0.0178622	−	0.101302i
$748$	−1.15158e9	+	1.99460e9i	−0.100610	+	0.174261i
$749$	3.44059e9	+	5.95928e9i	0.299190	+	0.518212i
$750$	1.55083e9	−	5.64456e8i	0.134230	−	0.0488558i
$751$	−1.25732e10	+	4.57629e9i	−1.08320	+	0.394252i	−0.821097	−	0.570789i	$-0.806637\pi$
$751$	−1.25732e10	+	4.57629e9i	−1.08320	+	0.394252i	−0.262101	+	0.965041i	$0.584415\pi$
$752$	−1.07279e9	−	1.85813e9i	−0.0919928	−	0.159336i
$753$	−4.43793e9	+	7.68673e9i	−0.378790	+	0.656083i
$754$	−5.81793e8	+	3.29951e9i	−0.0494275	+	0.280317i
$755$	−1.01518e9	+	8.51841e8i	−0.0858481	+	0.0720351i
$756$	−8.25460e9	−	6.92643e9i	−0.694816	−	0.583020i
$757$	2.17229e9	+	1.23196e10i	0.182004	+	1.03220i	0.929744	+	0.368206i	$0.120028\pi$
$757$	2.17229e9	+	1.23196e10i	0.182004	+	1.03220i	−0.747740	+	0.663992i	$0.768861\pi$
$758$	−9.91126e9	−	3.60740e9i	−0.826584	−	0.300852i
$759$	−2.75135e8			−0.0228402
$760$	−1.09402e8	−	4.79649e8i	−0.00904021	−	0.0396348i
$761$	1.93378e10			1.59060			0.795299	−	0.606218i	$-0.207314\pi$
$761$	1.93378e10			1.59060			0.795299	+	0.606218i	$0.207314\pi$
$762$	1.17881e9	+	4.29052e8i	0.0965164	+	0.0351291i
$763$	−2.61479e9	−	1.48292e10i	−0.213109	−	1.20860i
$764$	4.03807e9	+	3.38834e9i	0.327602	+	0.274891i
$765$	4.03319e8	−	3.38425e8i	0.0325712	−	0.0273305i
$766$	−1.37666e9	+	7.80743e9i	−0.110669	+	0.627636i
$767$	2.52930e9	−	4.38087e9i	0.202402	−	0.350571i
$768$	3.46905e8	+	6.00856e8i	0.0276341	+	0.0478637i
$769$	−1.11131e10	+	4.04485e9i	−0.881241	+	0.320745i	−0.742710	−	0.669613i	$-0.766460\pi$
$769$	−1.11131e10	+	4.04485e9i	−0.881241	+	0.320745i	−0.138531	+	0.990358i	$0.544238\pi$
$770$	−3.86795e8	+	1.40782e8i	−0.0305326	+	0.0111129i
$771$	−2.85745e9	−	4.94924e9i	−0.224537	−	0.388909i
$772$	−8.53230e8	+	1.47784e9i	−0.0667430	+	0.115602i
$773$	4.10205e9	−	2.32639e10i	0.319428	−	1.81157i	−0.226815	−	0.973938i	$-0.572831\pi$
$773$	4.10205e9	−	2.32639e10i	0.319428	−	1.81157i	0.546242	−	0.837627i	$-0.316058\pi$
$774$	−2.71773e9	+	2.28045e9i	−0.210675	+	0.176777i
$775$	−2.14620e9	−	1.80088e9i	−0.165621	−	0.138972i
$776$	−1.02070e9	−	5.78869e9i	−0.0784121	−	0.444697i
$777$	−5.70210e9	−	2.07539e9i	−0.436075	−	0.158718i
$778$	−1.72061e9			−0.130995
$779$	−6.47403e9	+	6.00524e9i	−0.490675	+	0.455145i
$780$	−5.23713e8			−0.0395150
$781$	4.35252e9	+	1.58419e9i	0.326935	+	0.118995i
$782$	3.03145e8	+	1.71922e9i	0.0226687	+	0.128561i
$783$	5.74016e9	+	4.81656e9i	0.427324	+	0.358568i
$784$	4.74565e9	−	3.98207e9i	0.351714	−	0.295123i
$785$	−2.78268e8	+	1.57814e9i	−0.0205315	+	0.116440i
$786$	−1.91285e9	+	3.31316e9i	−0.140509	+	0.243368i
$787$	−1.92948e8	−	3.34196e8i	−0.0141101	−	0.0244393i	0.858884	−	0.512170i	$-0.171158\pi$
$787$	−1.92948e8	−	3.34196e8i	−0.0141101	−	0.0244393i	−0.872994	+	0.487731i	$0.837825\pi$
$788$	1.03516e10	−	3.76767e9i	0.753643	−	0.274304i
$789$	−1.30791e10	+	4.76042e9i	−0.948002	+	0.345045i
$790$	−2.26283e8	−	3.91933e8i	−0.0163289	−	0.0282824i
$791$	7.28619e9	−	1.26201e10i	0.523459	−	0.906658i
$792$	−4.44059e7	+	2.51838e8i	−0.00317616	+	0.0180129i
$793$	1.26550e10	−	1.06188e10i	0.901171	−	0.756172i
$794$	5.19180e9	+	4.35644e9i	0.368084	+	0.308859i
$795$	3.67569e8	+	2.08459e9i	0.0259450	+	0.147142i
$796$	5.88374e9	+	2.14151e9i	0.413483	+	0.150496i
$797$	2.24561e10			1.57119			0.785596	−	0.618739i	$-0.212356\pi$
$797$	2.24561e10			1.57119			0.785596	+	0.618739i	$0.212356\pi$
$798$	1.88200e9	−	1.50000e10i	0.131102	−	1.04492i
$799$	1.79966e10			1.24818
$800$	2.37381e9	+	8.63996e8i	0.163920	+	0.0596618i
$801$	−1.27589e8	−	7.23593e8i	−0.00877202	−	0.0497486i
$802$	−8.77310e9	−	7.36151e9i	−0.600541	−	0.503914i
$803$	1.29962e9	−	1.09051e9i	0.0885751	−	0.0743234i
$804$	1.40929e9	−	7.99245e9i	0.0956319	−	0.542355i
$805$	−1.55999e8	+	2.70198e8i	−0.0105399	+	0.0182556i
$806$	8.95017e8	+	1.55021e9i	0.0602086	+	0.104284i
$807$	1.50263e10	−	5.46914e9i	1.00646	−	0.366321i
$808$	−7.20410e9	+	2.62208e9i	−0.480441	+	0.174866i
$809$	7.19287e9	+	1.24584e10i	0.477620	+	0.827262i	0.999671	−	0.0256525i	$-0.00816634\pi$
$809$	7.19287e9	+	1.24584e10i	0.477620	+	0.827262i	−0.522051	+	0.852914i	$0.674833\pi$
$810$	−4.51586e8	+	7.82170e8i	−0.0298568	+	0.0517135i
$811$	−2.45758e8	+	1.39376e9i	−0.0161784	+	0.0917521i	−0.991828	−	0.127584i	$-0.959278\pi$
$811$	−2.45758e8	+	1.39376e9i	−0.0161784	+	0.0917521i	0.975649	+	0.219336i	$0.0703890\pi$
$812$	−5.09699e9	+	4.27688e9i	−0.334093	+	0.280337i
$813$	1.55537e10	+	1.30511e10i	1.01512	+	0.851783i
$814$	1.39699e8	+	7.92272e8i	0.00907836	+	0.0514860i
$815$	4.91657e8	+	1.78949e8i	0.0318134	+	0.0115791i
$816$	−5.81949e9			−0.374947
$817$	−2.65695e10	−	8.19991e9i	−1.70454	−	0.526056i
$818$	6.43138e9			0.410835
$819$	4.21644e9	+	1.53466e9i	0.268196	+	0.0976154i
$820$	1.05493e8	+	5.98278e8i	0.00668149	+	0.0378926i
$821$	−5.35573e9	−	4.49399e9i	−0.337767	−	0.283421i	0.458088	−	0.888907i	$-0.348534\pi$
$821$	−5.35573e9	−	4.49399e9i	−0.337767	−	0.283421i	−0.795856	+	0.605486i	$0.792979\pi$
$822$	1.36290e10	−	1.14361e10i	0.855882	−	0.718170i
$823$	−3.99653e9	+	2.26655e10i	−0.249910	+	1.41731i	0.558897	+	0.829237i	$0.311225\pi$
$823$	−3.99653e9	+	2.26655e10i	−0.249910	+	1.41731i	−0.808807	+	0.588074i	$0.799886\pi$
$824$	2.61437e9	−	4.52823e9i	0.162788	−	0.281957i
$825$	−1.66971e9	−	2.89202e9i	−0.103526	−	0.179313i
$826$	9.44011e9	−	3.43592e9i	0.582837	−	0.212135i
$827$	3.74684e8	−	1.36374e8i	0.0230354	−	0.00838420i	−0.330477	−	0.943814i	$-0.607210\pi$
$827$	3.74684e8	−	1.36374e8i	0.0230354	−	0.00838420i	0.353512	+	0.935430i	$0.384987\pi$
$828$	9.69161e7	+	1.67864e8i	0.00593321	+	0.0102766i
$829$	−8.08470e9	+	1.40031e10i	−0.492860	+	0.853658i	−0.999966	−	0.00822539i	$-0.997382\pi$
$829$	−8.08470e9	+	1.40031e10i	−0.492860	+	0.853658i	0.507106	+	0.861883i	$0.330715\pi$
$830$	1.09728e8	−	6.22297e8i	0.00666105	−	0.0377767i
$831$	1.24841e10	−	1.04754e10i	0.754667	−	0.633241i
$832$	−1.23640e9	−	1.03746e9i	−0.0744263	−	0.0624511i
$833$	9.02312e9	+	5.11726e10i	0.540878	+	3.06747i
$834$	7.96202e9	+	2.89794e9i	0.475272	+	0.172985i
$835$	−3.30573e9			−0.196501
$836$	−1.84701e9	+	7.78258e8i	−0.109332	+	0.0460682i
$837$	4.00344e9			0.235990
$838$	1.35158e10	+	4.91934e9i	0.793390	+	0.288770i
$839$	−4.45667e9	−	2.52750e10i	−0.260522	−	1.47749i	−0.781491	−	0.623917i	$-0.785541\pi$
$839$	−4.45667e9	−	2.52750e10i	−0.260522	−	1.47749i	0.520969	−	0.853575i	$-0.325571\pi$
$840$	−7.96726e8	−	6.68533e8i	−0.0463801	−	0.0389175i
$841$	−9.66978e9	+	8.11391e9i	−0.560571	+	0.470375i
$842$	−2.31904e8	+	1.31519e9i	−0.0133880	+	0.0759271i
$843$	−3.62862e9	+	6.28495e9i	−0.208615	+	0.361331i
$844$	−7.88466e9	−	1.36566e10i	−0.451424	−	0.781889i
$845$	−7.50204e8	+	2.73052e8i	−0.0427741	+	0.0155685i
$846$	1.87768e9	−	6.83421e8i	0.106617	−	0.0388054i
$847$	−1.40536e10	−	2.43415e10i	−0.794686	−	1.37644i
$848$	−3.26174e9	+	5.64951e9i	−0.183681	+	0.318145i
$849$	2.43850e9	−	1.38294e10i	0.136756	−	0.775581i
$850$	−1.62315e10	+	1.36198e10i	−0.906552	+	0.760687i
$851$	4.67124e8	+	3.91964e8i	0.0259824	+	0.0218018i
$852$	2.03229e9	+	1.15257e10i	0.112576	+	0.638451i
$853$	−3.11947e8	−	1.13539e8i	−0.0172091	−	0.00626361i	0.333401	−	0.942785i	$-0.391804\pi$
$853$	−3.11947e8	−	1.13539e8i	−0.0172091	−	0.00626361i	−0.350610	+	0.936521i	$0.614026\pi$
$854$	3.28073e10			1.80247
$855$	4.57604e8	−	2.27702e7i	0.0250385	−	0.00124591i
$856$	2.30514e9			0.125614
$857$	−3.07127e10	−	1.11785e10i	−1.66680	−	0.606667i	−0.675395	−	0.737456i	$-0.736027\pi$
$857$	−3.07127e10	−	1.11785e10i	−1.66680	−	0.606667i	−0.991410	+	0.130789i	$0.958249\pi$
$858$	3.70497e8	+	2.10119e9i	0.0200253	+	0.113569i
$859$	−3.41747e9	−	2.86760e9i	−0.183962	−	0.154363i	0.546156	−	0.837684i	$-0.316091\pi$
$859$	−3.41747e9	−	2.86760e9i	−0.183962	−	0.154363i	−0.730118	+	0.683321i	$0.760535\pi$
$860$	−1.46543e9	+	1.22964e9i	−0.0785634	+	0.0659225i
$861$	−3.24167e9	+	1.83844e10i	−0.173084	+	0.981611i
$862$	−1.32515e10	+	2.29523e10i	−0.704679	+	1.22054i
$863$	8.29352e9	+	1.43648e10i	0.439239	+	0.760785i	0.997631	−	0.0687927i	$-0.0219147\pi$
$863$	8.29352e9	+	1.43648e10i	0.439239	+	0.760785i	−0.558392	+	0.829577i	$0.688581\pi$
$864$	−3.39205e9	+	1.23460e9i	−0.178922	+	0.0651223i
$865$	2.55888e9	−	9.31357e8i	0.134429	−	0.0489283i
$866$	−1.13703e10	−	1.96939e10i	−0.594921	−	1.03043i
$867$	1.59216e10	−	2.75770e10i	0.829696	−	1.43708i
$868$	−6.17295e8	+	3.50086e9i	−0.0320386	+	0.181700i
$869$	−1.41239e9	+	1.18514e9i	−0.0730108	+	0.0612633i
$870$	5.54035e8	+	4.64890e8i	0.0285246	+	0.0239350i
$871$	3.27841e9	+	1.85928e10i	0.168112	+	0.953412i
$872$	−4.74009e9	−	1.72525e9i	−0.242091	−	0.0881140i
$873$	5.47418e9			0.278464
$874$	−6.93273e8	+	1.35179e9i	−0.0351248	+	0.0684885i
$875$	−7.62438e9			−0.384748
$876$	4.02817e9	+	1.46614e9i	0.202462	+	0.0736902i
$877$	−1.69663e9	−	9.62210e9i	−0.0849356	−	0.481694i	−0.997370	−	0.0724718i	$-0.976911\pi$
$877$	−1.69663e9	−	9.62210e9i	−0.0849356	−	0.481694i	0.912435	−	0.409222i	$-0.134200\pi$
$878$	1.89212e10	+	1.58768e10i	0.943450	+	0.791648i
$879$	1.61288e10	−	1.35337e10i	0.801016	−	0.672132i
$880$	−2.39441e7	+	1.35794e8i	−0.00118443	+	0.00671724i
$881$	−5.37482e9	+	9.30945e9i	−0.264818	+	0.458679i	−0.967516	−	0.252810i	$-0.918645\pi$
$881$	−5.37482e9	+	9.30945e9i	−0.264818	+	0.458679i	0.702698	+	0.711488i	$0.251979\pi$
$882$	2.88471e9	+	4.99646e9i	0.141567	+	0.245201i
$883$	−5.52438e9	+	2.01071e9i	−0.270035	+	0.0982849i	−0.473489	−	0.880800i	$-0.657006\pi$
$883$	−5.52438e9	+	2.01071e9i	−0.270035	+	0.0982849i	0.203454	+	0.979085i	$0.434783\pi$
$884$	1.27214e10	−	4.63021e9i	0.619373	−	0.225433i
$885$	−5.45990e8	−	9.45682e8i	−0.0264779	−	0.0458610i
$886$	−1.13124e10	+	1.95936e10i	−0.546431	+	0.946447i
$887$	4.77344e9	−	2.70715e10i	0.229667	−	1.30251i	−0.623891	−	0.781511i	$-0.714449\pi$
$887$	4.77344e9	−	2.70715e10i	0.229667	−	1.30251i	0.853559	−	0.520997i	$-0.174440\pi$
$888$	−1.55717e9	+	1.30662e9i	−0.0746262	+	0.0626188i
$889$	−4.43954e9	−	3.72521e9i	−0.211925	−	0.177826i
$890$	−6.87974e7	−	3.90170e8i	−0.00327120	−	0.0185519i
$891$	3.45762e9	+	1.25847e9i	0.163759	+	0.0596035i
$892$	8.15886e9			0.384904
$893$	1.24826e10	+	9.45813e9i	0.586578	+	0.444452i
$894$	2.44794e8			0.0114583
$895$	−1.45816e9	−	5.30727e8i	−0.0679868	−	0.0247452i
$896$	−5.56591e8	−	3.15658e9i	−0.0258498	−	0.146602i
$897$	1.23887e9	+	1.03953e9i	0.0573126	+	0.0480910i
$898$	5.95090e9	−	4.99340e9i	0.274230	−	0.230106i
$899$	4.29261e8	−	2.43446e9i	0.0197043	−	0.111749i
$900$	−1.17631e9	+	2.03742e9i	−0.0537863	+	0.0931605i
$901$	−2.73587e10	−	4.73866e10i	−1.24611	−	2.15833i
$902$	2.32573e9	−	8.46495e8i	0.105520	−	0.0384062i
$903$	−5.52387e10	+	2.01053e10i	−2.49653	+	0.908662i
$904$	−2.44081e9	−	4.22761e9i	−0.109887	−	0.190329i
$905$	−1.73179e9	+	2.99955e9i	−0.0776650	+	0.134520i
$906$	−2.36888e9	+	1.34346e10i	−0.105826	+	0.600171i
$907$	1.81004e10	−	1.51881e10i	0.805496	−	0.675891i	−0.144032	−	0.989573i	$-0.546007\pi$
$907$	1.81004e10	−	1.51881e10i	0.805496	−	0.675891i	0.949528	+	0.313682i	$0.101562\pi$
$908$	−1.02685e10	−	8.61630e9i	−0.455205	−	0.381962i
$909$	−1.23981e9	−	7.03130e9i	−0.0547496	−	0.310500i
$910$	2.27355e9	+	8.27505e8i	0.100014	+	0.0364021i
$911$	1.17064e10			0.512990			0.256495	−	0.966546i	$-0.417432\pi$
$911$	1.17064e10			0.512990			0.256495	+	0.966546i	$0.417432\pi$
$912$	−4.03645e9	−	3.05843e9i	−0.176205	−	0.133511i
$913$	−2.57435e9			−0.111949
$914$	2.85283e10	+	1.03834e10i	1.23584	+	0.449811i
$915$	−6.19248e8	−	3.51193e9i	−0.0267233	−	0.151556i
$916$	−1.52608e10	−	1.28053e10i	−0.656060	−	0.550500i
$917$	1.35392e10	−	1.13607e10i	0.579828	−	0.486533i
$918$	5.25764e9	−	2.98176e10i	0.224306	−	1.27211i
$919$	−3.66805e8	+	6.35325e8i	−0.0155894	+	0.0270017i	−0.873715	−	0.486438i	$-0.838296\pi$
$919$	−3.66805e8	+	6.35325e8i	−0.0155894	+	0.0270017i	0.858125	+	0.513440i	$0.171629\pi$
$920$	5.22582e7	+	9.05139e7i	0.00221257	+	0.00383229i
$921$	6.79534e9	−	2.47330e9i	0.286617	−	0.104320i
$922$	−1.12933e10	+	4.11042e9i	−0.474528	+	0.172714i
$923$	−1.36128e10	−	2.35781e10i	−0.569827	−	0.986969i
$924$	−2.11859e9	+	3.66950e9i	−0.0883475	+	0.153022i
$925$	−1.28521e9	+	7.28877e9i	−0.0533921	+	0.302801i
$926$	1.35753e10	−	1.13910e10i	0.561838	−	0.471438i
$927$	3.73028e9	+	3.13008e9i	0.153802	+	0.129055i
$928$	3.87047e8	+	2.19505e9i	0.0158981	+	0.0901628i
$929$	1.10736e10	+	4.03048e9i	0.453143	+	0.164931i	0.558501	−	0.829504i	$-0.311377\pi$
$929$	1.10736e10	+	4.03048e9i	0.453143	+	0.164931i	−0.105358	+	0.994434i	$0.533599\pi$
$930$	3.86408e8			0.0157527
$931$	−2.06352e10	+	4.02359e10i	−0.838081	+	1.63414i
$932$	−1.32181e9			−0.0534826
$933$	−1.69729e10	−	6.17761e9i	−0.684178	−	0.249020i
$934$	−4.39029e9	−	2.48986e10i	−0.176311	−	0.999909i
$935$	−8.85988e8	−	7.43433e8i	−0.0354476	−	0.0297441i
$936$	1.15146e9	−	9.66189e8i	0.0458969	−	0.0385120i
$937$	−1.97511e9	+	1.12014e10i	−0.0784336	+	0.444819i	0.920148	+	0.391571i	$0.128068\pi$
$937$	−1.97511e9	+	1.12014e10i	−0.0784336	+	0.444819i	−0.998581	+	0.0532476i	$0.983043\pi$
$938$	−1.87467e10	+	3.24702e10i	−0.741677	+	1.28462i
$939$	1.12781e10	+	1.95343e10i	0.444537	+	0.769961i
$940$	1.01247e9	−	3.68508e8i	0.0397588	−	0.0144710i
$941$	−1.50823e10	+	5.48950e9i	−0.590069	+	0.214768i	−0.619760	−	0.784791i	$-0.712770\pi$
$941$	−1.50823e10	+	5.48950e9i	−0.590069	+	0.214768i	0.0296905	+	0.999559i	$0.490548\pi$
$942$	8.24792e9	+	1.42858e10i	0.321489	+	0.556835i
$943$	9.37991e8	−	1.62465e9i	0.0364257	−	0.0630911i
$944$	5.84380e8	−	3.31419e9i	0.0226096	−	0.128226i
$945$	4.14520e9	−	3.47823e9i	0.159784	−	0.134075i
$946$	5.97016e9	+	5.00956e9i	0.229280	+	0.192389i
$947$	−1.95744e9	−	1.11012e10i	−0.0748970	−	0.424762i	−0.999083	−	0.0428189i	$-0.986366\pi$
$947$	−1.95744e9	−	1.11012e10i	−0.0748970	−	0.424762i	0.924186	−	0.381943i	$-0.124745\pi$
$948$	−4.37772e9	−	1.59336e9i	−0.166886	−	0.0607414i
$949$	−9.97209e9			−0.378752
$950$	−1.84162e10	+	9.16385e8i	−0.696896	+	0.0346773i
$951$	−1.78943e9			−0.0674657
$952$	2.52637e10	+	9.19523e9i	0.949002	+	0.345409i
$953$	−2.66659e9	−	1.51230e10i	−0.0998003	−	0.565996i	−0.993170	−	0.116674i	$-0.962777\pi$
$953$	−2.66659e9	−	1.51230e10i	−0.0998003	−	0.565996i	0.893370	−	0.449322i	$-0.148334\pi$
$954$	−4.65398e9	−	3.90515e9i	−0.173542	−	0.145619i
$955$	−2.02779e9	+	1.70152e9i	−0.0753375	+	0.0632156i
$956$	−3.46091e9	+	1.96278e10i	−0.128112	+	0.726556i
$957$	1.47324e9	−	2.55173e9i	0.0543353	−	0.0941115i
$958$	−9.52578e9	−	1.64991e10i	−0.350043	−	0.606292i
$959$	−7.72366e10	+	2.81118e10i	−2.82786	+	1.02926i
$960$	−3.27397e8	+	1.19163e8i	−0.0119433	+	0.00434702i
$961$	1.30959e10	+	2.26828e10i	0.475998	+	0.824452i
$962$	2.36438e9	−	4.09522e9i	0.0856257	−	0.148308i
$963$	−3.72785e8	+	2.11417e9i	−0.0134513	+	0.0762864i
$964$	−2.16263e9	+	1.81466e9i	−0.0777523	+	0.0652419i
$965$	−6.56447e8	−	5.50824e8i	−0.0235155	−	0.0197318i
$966$	5.57702e8	+	3.16288e9i	0.0199059	+	0.112892i
$967$	−4.50784e9	−	1.64072e9i	−0.160316	−	0.0583502i	0.260616	−	0.965443i	$-0.416074\pi$
$967$	−4.50784e9	−	1.64072e9i	−0.160316	−	0.0583502i	−0.420931	+	0.907092i	$0.638297\pi$
$968$	−9.41567e9			−0.333647
$969$	3.91448e10	−	1.64941e10i	1.38210	−	0.582365i
$970$	2.95174e9			0.103843
$971$	1.95948e10	+	7.13193e9i	0.686869	+	0.250000i	0.661794	−	0.749686i	$-0.269795\pi$
$971$	1.95948e10	+	7.13193e9i	0.686869	+	0.250000i	0.0250752	+	0.999686i	$0.492017\pi$
$972$	−1.06303e9	−	6.02875e9i	−0.0371291	−	0.210570i
$973$	−2.99859e10	−	2.51612e10i	−1.04357	−	0.875660i
$974$	−2.87647e9	+	2.41365e9i	−0.0997479	+	0.0836985i
$975$	−3.40851e9	+	1.93306e10i	−0.117774	+	0.667928i
$976$	5.49509e9	−	9.51778e9i	0.189191	−	0.327689i
$977$	−5.37476e9	−	9.30936e9i	−0.184386	−	0.319366i	0.758983	−	0.651110i	$-0.225696\pi$
$977$	−5.37476e9	−	9.30936e9i	−0.184386	−	0.319366i	−0.943370	+	0.331744i	$0.892363\pi$
$978$	5.06108e9	−	1.84208e9i	0.173004	−	0.0629685i
$979$	−1.51673e9	+	5.52045e8i	−0.0516618	+	0.0188033i
$980$	1.55547e9	+	2.69415e9i	0.0527921	+	0.0914387i
$981$	2.34888e9	−	4.06839e9i	0.0794365	−	0.137588i
$982$	−1.05218e9	+	5.96720e9i	−0.0354568	+	0.201085i
$983$	4.41816e9	−	3.70727e9i	0.148356	−	0.124485i	−0.565589	−	0.824687i	$-0.691351\pi$
$983$	4.41816e9	−	3.70727e9i	0.148356	−	0.124485i	0.713945	+	0.700202i	$0.246907\pi$
$984$	4.79057e9	+	4.01976e9i	0.160289	+	0.134499i
$985$	9.60596e8	+	5.44781e9i	0.0320268	+	0.181633i
$986$	−1.75681e10	−	6.39426e9i	−0.583654	−	0.212433i
$987$	3.31087e10			1.09606
$988$	1.12571e10	+	3.47417e9i	0.371344	+	0.114605i
$989$	5.90728e9			0.194178
$990$	−1.20672e8	−	4.39209e7i	−0.00395259	−	0.00143863i
$991$	6.46822e9	+	3.66831e10i	0.211119	+	1.19731i	0.887516	+	0.460777i	$0.152429\pi$
$991$	6.46822e9	+	3.66831e10i	0.211119	+	1.19731i	−0.676397	+	0.736537i	$0.736460\pi$
$992$	9.12244e8	+	7.65463e8i	0.0296702	+	0.0248962i
$993$	−2.75734e10	+	2.31369e10i	−0.893652	+	0.749863i
$994$	9.38882e9	−	5.32466e10i	0.303220	−	1.71965i
$995$	−1.57212e9	+	2.72300e9i	−0.0505948	+	0.0876328i
$996$	−3.25235e9	−	5.63323e9i	−0.104301	−	0.180655i
$997$	4.15794e10	−	1.51337e10i	1.32875	−	0.483627i	0.422501	−	0.906362i	$-0.361152\pi$
$997$	4.15794e10	−	1.51337e10i	1.32875	−	0.483627i	0.906253	+	0.422735i	$0.138930\pi$
$998$	1.18136e10	−	4.29978e9i	0.376204	−	0.136927i
$999$	−5.28797e9	−	9.15903e9i	−0.167807	−	0.290650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.23.2	yes	30
19.5	even	9	inner	38.8.e.a.5.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.5.2	✓	30	19.5	even	9	inner
38.8.e.a.23.2	yes	30	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.51754 - 2.73616i) q^{2} +(-7.18109 - 40.7260i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-24.6197 + 20.6584i) q^{5} +(-57.4487 + 325.808i) q^{6} +(764.198 - 1323.63i) q^{7} +(-256.000 - 443.405i) q^{8} +(448.070 - 163.084i) q^{9} +O(q^{10})\)	\(q+(-7.51754 - 2.73616i) q^{2} +(-7.18109 - 40.7260i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-24.6197 + 20.6584i) q^{5} +(-57.4487 + 325.808i) q^{6} +(764.198 - 1323.63i) q^{7} +(-256.000 - 443.405i) q^{8} +(448.070 - 163.084i) q^{9} +(241.604 - 87.9368i) q^{10} +(-523.733 - 907.132i) q^{11} +(1323.34 - 2292.08i) q^{12} +(-1069.14 + 6063.39i) q^{13} +(-9366.55 + 7859.47i) q^{14} +(1018.13 + 854.312i) q^{15} +(711.263 + 4033.77i) q^{16} +(-32284.3 - 11750.5i) q^{17} -3814.61 q^{18} +(-16217.2 - 25117.2i) q^{19} -2056.88 q^{20} +(-59393.9 - 21617.6i) q^{21} +(1455.12 + 8252.42i) q^{22} +(4865.64 + 4082.75i) q^{23} +(-16219.7 + 13610.0i) q^{24} +(-13386.9 + 75920.9i) q^{25} +(24627.7 - 42656.5i) q^{26} +(-55080.3 - 95401.8i) q^{27} +(91918.2 - 33455.5i) q^{28} +(-63919.0 + 23264.6i) q^{29} +(-5316.30 - 9208.09i) q^{30} +(-18170.9 + 31473.0i) q^{31} +(5690.10 - 32270.2i) q^{32} +(-33182.9 + 27843.7i) q^{33} +(210547. + 176670. i) q^{34} +(8529.73 + 48374.5i) q^{35} +(28676.5 + 10437.4i) q^{36} +96004.7 q^{37} +(53188.4 + 233193. i) q^{38} +254615. q^{39} +(15462.7 + 5627.96i) q^{40} +(-51287.7 - 290867. i) q^{41} +(387347. + 325023. i) q^{42} +(712452. - 597818. i) q^{43} +(11641.0 - 66019.4i) q^{44} +(-7662.30 + 13271.5i) q^{45} +(-25406.6 - 44005.4i) q^{46} +(-492235. + 179159. i) q^{47} +(159172. - 57933.8i) q^{48} +(-756226. - 1.30982e6i) q^{49} +(308368. - 534110. i) q^{50} +(-246715. + 1.39919e6i) q^{51} +(-301855. + 253286. i) q^{52} +(1.22004e6 + 1.02373e6i) q^{53} +(153033. + 867896. i) q^{54} +(31634.1 + 11513.9i) q^{55} -782539. q^{56} +(-906467. + 840829. i) q^{57} +544169. q^{58} +(-772060. - 281007. i) q^{59} +(14770.6 + 83768.5i) q^{60} +(-2.05541e6 - 1.72470e6i) q^{61} +(222716. - 186881. i) q^{62} +(126551. - 717708. i) q^{63} +(-131072. + 227023. i) q^{64} +(-98938.0 - 171366. i) q^{65} +(325639. - 118523. i) q^{66} +(2.88147e6 - 1.04877e6i) q^{67} +(-1.09940e6 - 1.90421e6i) q^{68} +(131334. - 227476. i) q^{69} +(68237.8 - 386996. i) q^{70} +(-3.38742e6 + 2.84238e6i) q^{71} +(-187018. - 156927. i) q^{72} +(281250. + 1.59505e6i) q^{73} +(-721720. - 262684. i) q^{74} +3.18809e6 q^{75} +(238206. - 1.89857e6i) q^{76} -1.60094e6 q^{77} +(-1.91408e6 - 696668. i) q^{78} +(-305656. - 1.73346e6i) q^{79} +(-100842. - 84616.8i) q^{80} +(-2.69095e6 + 2.25798e6i) q^{81} +(-410301. + 2.32693e6i) q^{82} +(1.22884e6 - 2.12842e6i) q^{83} +(-2.02258e6 - 3.50321e6i) q^{84} +(1.03758e6 - 377647. i) q^{85} +(-6.99162e6 + 2.54474e6i) q^{86} +(1.40648e6 + 2.43610e6i) q^{87} +(-268151. + 464452. i) q^{88} +(267580. - 1.51752e6i) q^{89} +(93914.7 - 78803.8i) q^{90} +(7.20865e6 + 6.04878e6i) q^{91} +(70588.8 + 400329. i) q^{92} +(1.41225e6 + 514018. i) q^{93} +4.19060e6 q^{94} +(918144. + 283358. i) q^{95} -1.35510e6 q^{96} +(1.07881e7 + 3.92654e6i) q^{97} +(2.10108e6 + 1.19158e7i) q^{98} +(-382608. - 321046. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

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