LMFDB - Embedded newform 38.8.e.a.17.4

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			17.4
Character	$\chi$	$=$	38.17
Dual form			38.8.e.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38919 - 7.87846i) q^{2} +(28.3430 + 23.7826i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-54.5194 + 19.8434i) q^{5} +(226.744 - 190.261i) q^{6} +(-356.201 - 616.958i) q^{7} +(-256.000 + 443.405i) q^{8} +(-142.054 - 805.630i) q^{9} +O(q^{10})$	\(q+(1.38919 - 7.87846i) q^{2} +(28.3430 + 23.7826i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-54.5194 + 19.8434i) q^{5} +(226.744 - 190.261i) q^{6} +(-356.201 - 616.958i) q^{7} +(-256.000 + 443.405i) q^{8} +(-142.054 - 805.630i) q^{9} +(80.5982 + 457.095i) q^{10} +(3641.45 - 6307.17i) q^{11} +(-1183.97 - 2050.70i) q^{12} +(3073.79 - 2579.22i) q^{13} +(-5355.51 + 1949.25i) q^{14} +(-2017.18 - 734.192i) q^{15} +(3137.72 + 2632.86i) q^{16} +(320.112 - 1815.45i) q^{17} -6544.46 q^{18} +(-17260.6 - 24412.0i) q^{19} +3713.17 q^{20} +(4577.07 - 25957.9i) q^{21} +(-44632.2 - 37450.8i) q^{22} +(-43309.0 - 15763.2i) q^{23} +(-17801.2 + 6479.09i) q^{24} +(-57268.6 + 48054.1i) q^{25} +(-16050.2 - 27799.8i) q^{26} +(55592.4 - 96288.9i) q^{27} +(7917.27 + 44901.1i) q^{28} +(-14366.1 - 81474.4i) q^{29} +(-8586.53 + 14872.3i) q^{30} +(137821. + 238713. i) q^{31} +(25101.7 - 21062.9i) q^{32} +(253211. - 92161.2i) q^{33} +(-13858.2 - 5043.98i) q^{34} +(31662.4 + 26567.9i) q^{35} +(-9091.47 + 51560.3i) q^{36} +169842. q^{37} +(-216307. + 102074. i) q^{38} +148461. q^{39} +(5158.29 - 29254.1i) q^{40} +(354627. + 297567. i) q^{41} +(-198150. - 72120.6i) q^{42} +(-251443. + 91517.7i) q^{43} +(-357057. + 299607. i) q^{44} +(23731.2 + 41103.6i) q^{45} +(-184354. + 319311. i) q^{46} +(26312.5 + 149226. i) q^{47} +(26316.2 + 149246. i) q^{48} +(158013. - 273687. i) q^{49} +(299035. + 517945. i) q^{50} +(52249.0 - 43842.1i) q^{51} +(-241316. + 87831.9i) q^{52} +(480452. + 174870. i) q^{53} +(-681380. - 571746. i) q^{54} +(-73373.5 + 416122. i) q^{55} +364750. q^{56} +(91363.8 - 1.10241e6i) q^{57} -661850. q^{58} +(-141598. + 803043. i) q^{59} +(105243. + 88309.1i) q^{60} +(458131. + 166746. i) q^{61} +(2.07215e6 - 754201. i) q^{62} +(-446440. + 374608. i) q^{63} +(-131072. - 227023. i) q^{64} +(-116401. + 201612. i) q^{65} +(-374332. - 2.12294e6i) q^{66} +(-609882. - 3.45881e6i) q^{67} +(-58990.4 + 102174. i) q^{68} +(-852619. - 1.47678e6i) q^{69} +(253300. - 212544. i) q^{70} +(487438. - 177413. i) q^{71} +(393586. + 143254. i) q^{72} +(-3.21047e6 - 2.69390e6i) q^{73} +(235942. - 1.33809e6i) q^{74} -2.76602e6 q^{75} +(503696. + 1.84597e6i) q^{76} -5.18835e6 q^{77} +(206240. - 1.16965e6i) q^{78} +(3.78932e6 + 3.17962e6i) q^{79} +(-223312. - 81278.7i) q^{80} +(2.18446e6 - 795080. i) q^{81} +(2.83701e6 - 2.38054e6i) q^{82} +(1.89078e6 + 3.27493e6i) q^{83} +(-843466. + 1.46093e6i) q^{84} +(18572.4 + 105329. i) q^{85} +(371718. + 2.10812e6i) q^{86} +(1.53050e6 - 2.65090e6i) q^{87} +(1.86442e6 + 3.22927e6i) q^{88} +(-5.43816e6 + 4.56316e6i) q^{89} +(356800. - 129865. i) q^{90} +(-2.68616e6 - 977681. i) q^{91} +(2.25957e6 + 1.89601e6i) q^{92} +(-1.77096e6 + 1.00436e7i) q^{93} +1.21222e6 q^{94} +(1.42545e6 + 988417. i) q^{95} +1.21239e6 q^{96} +(-1.44635e6 + 8.20264e6i) q^{97} +(-1.93672e6 - 1.62510e6i) q^{98} +(-5.59853e6 - 2.03770e6i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$3$	28.3430	+	23.7826i	0.606069	+	0.508552i	0.893390	−	0.449282i	$-0.148320\pi$
$3$	28.3430	+	23.7826i	0.606069	+	0.508552i	−0.287321	+	0.957834i	$0.592765\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	−54.5194	+	19.8434i	−0.195055	+	0.0709941i	−0.437700	−	0.899121i	$-0.644207\pi$
$5$	−54.5194	+	19.8434i	−0.195055	+	0.0709941i	0.242646	+	0.970115i	$0.421985\pi$
$6$	226.744	−	190.261i	0.428556	−	0.359601i
$7$	−356.201	−	616.958i	−0.392511	−	0.679849i	0.600269	−	0.799798i	$-0.295060\pi$
$7$	−356.201	−	616.958i	−0.392511	−	0.679849i	−0.992780	+	0.119949i	$0.961727\pi$
$8$	−256.000	+	443.405i	−0.176777	+	0.306186i
$9$	−142.054	−	805.630i	−0.0649539	−	0.368372i
$10$	80.5982	+	457.095i	0.0254874	+	0.144546i
$11$	3641.45	−	6307.17i	0.824897	−	1.42876i	−0.0771018	−	0.997023i	$-0.524567\pi$
$11$	3641.45	−	6307.17i	0.824897	−	1.42876i	0.901998	−	0.431740i	$-0.142100\pi$
$12$	−1183.97	−	2050.70i	−0.197792	−	0.342585i
$13$	3073.79	−	2579.22i	0.388037	−	0.325601i	−0.427811	−	0.903868i	$-0.640715\pi$
$13$	3073.79	−	2579.22i	0.388037	−	0.325601i	0.815848	+	0.578267i	$0.196271\pi$
$14$	−5355.51	+	1949.25i	−0.521618	+	0.189854i
$15$	−2017.18	−	734.192i	−0.154321	−	0.0561682i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	320.112	−	1815.45i	0.0158027	−	0.0896214i	−0.975886	−	0.218279i	$-0.929956\pi$
$17$	320.112	−	1815.45i	0.0158027	−	0.0896214i	0.991689	+	0.128658i	$0.0410668\pi$
$18$	−6544.46			−0.264497
$19$	−17260.6	−	24412.0i	−0.577321	−	0.816517i
$19$	−17260.6	−	24412.0i	−0.577321	−	0.816517i
$20$	3713.17			0.103786
$21$	4577.07	−	25957.9i	0.107850	−	0.611648i
$22$	−44632.2	−	37450.8i	−0.893652	−	0.749863i
$23$	−43309.0	−	15763.2i	−0.742217	−	0.270145i	−0.0568903	−	0.998380i	$-0.518119\pi$
$23$	−43309.0	−	15763.2i	−0.742217	−	0.270145i	−0.685327	+	0.728235i	$0.740341\pi$
$24$	−17801.2	+	6479.09i	−0.262851	+	0.0956698i
$25$	−57268.6	+	48054.1i	−0.733038	+	0.615092i
$26$	−16050.2	−	27799.8i	−0.179091	−	0.310195i
$27$	55592.4	−	96288.9i	0.543553	−	0.941462i
$28$	7917.27	+	44901.1i	0.0681588	+	0.386548i
$29$	−14366.1	−	81474.4i	−0.109382	−	0.620338i	−0.989379	−	0.145358i	$-0.953567\pi$
$29$	−14366.1	−	81474.4i	−0.109382	−	0.620338i	0.879997	−	0.474980i	$-0.157545\pi$
$30$	−8586.53	+	14872.3i	−0.0580622	+	0.100567i
$31$	137821.	+	238713.i	0.830901	+	1.43916i	0.897324	+	0.441372i	$0.145508\pi$
$31$	137821.	+	238713.i	0.830901	+	1.43916i	−0.0664230	+	0.997792i	$0.521159\pi$
$32$	25101.7	−	21062.9i	0.135419	−	0.113630i
$33$	253211.	−	92161.2i	1.22654	−	0.446426i
$34$	−13858.2	−	5043.98i	−0.0604688	−	0.0220088i
$35$	31662.4	+	26567.9i	0.124826	+	0.104742i
$36$	−9091.47	+	51560.3i	−0.0324770	+	0.184186i
$37$	169842.			0.551238			0.275619	−	0.961267i	$-0.411117\pi$
$37$	169842.			0.551238			0.275619	+	0.961267i	$0.411117\pi$
$38$	−216307.	+	102074.i	−0.639481	+	0.301768i
$39$	148461.			0.400762
$40$	5158.29	−	29254.1i	0.0127437	−	0.0722731i
$41$	354627.	+	297567.i	0.803578	+	0.674282i	0.949066	−	0.315078i	$-0.102031\pi$
$41$	354627.	+	297567.i	0.803578	+	0.674282i	−0.145488	+	0.989360i	$0.546475\pi$
$42$	−198150.	−	72120.6i	−0.412687	−	0.150206i
$43$	−251443.	+	91517.7i	−0.482280	+	0.175536i	−0.571707	−	0.820458i	$-0.693719\pi$
$43$	−251443.	+	91517.7i	−0.482280	+	0.175536i	0.0894268	+	0.995993i	$0.471496\pi$
$44$	−357057.	+	299607.i	−0.631907	+	0.530233i
$45$	23731.2	+	41103.6i	0.0388218	+	0.0672413i
$46$	−184354.	+	319311.i	−0.279255	+	0.483683i
$47$	26312.5	+	149226.i	0.0369674	+	0.209653i	0.997697	−	0.0678353i	$-0.0216092\pi$
$47$	26312.5	+	149226.i	0.0369674	+	0.209653i	−0.960729	+	0.277488i	$0.910498\pi$
$48$	26316.2	+	149246.i	0.0343462	+	0.194787i
$49$	158013.	−	273687.i	0.191870	−	0.332329i
$50$	299035.	+	517945.i	0.338320	+	0.585987i
$51$	52249.0	−	43842.1i	0.0551547	−	0.0462803i
$52$	−241316.	+	87831.9i	−0.237999	+	0.0866244i
$53$	480452.	+	174870.i	0.443287	+	0.161343i	0.554013	−	0.832508i	$-0.313096\pi$
$53$	480452.	+	174870.i	0.443287	+	0.161343i	−0.110727	+	0.993851i	$0.535318\pi$
$54$	−681380.	−	571746.i	−0.588859	−	0.494111i
$55$	−73373.5	+	416122.i	−0.0594662	+	0.337249i
$56$	364750.			0.277547
$57$	91363.8	−	1.10241e6i	0.0653450	−	0.788464i
$58$	−661850.			−0.445412
$59$	−141598.	+	803043.i	−0.0897585	+	0.509046i	0.906470	+	0.422271i	$0.138767\pi$
$59$	−141598.	+	803043.i	−0.0897585	+	0.509046i	−0.996228	+	0.0867744i	$0.972344\pi$
$60$	105243.	+	88309.1i	0.0629017	+	0.0527808i
$61$	458131.	+	166746.i	0.258425	+	0.0940592i	0.467984	−	0.883737i	$-0.344980\pi$
$61$	458131.	+	166746.i	0.258425	+	0.0940592i	−0.209559	+	0.977796i	$0.567203\pi$
$62$	2.07215e6	−	754201.i	1.10421	−	0.401898i
$63$	−446440.	+	374608.i	−0.224942	+	0.188749i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−116401.	+	201612.i	−0.0525726	+	0.0910583i
$66$	−374332.	−	2.12294e6i	−0.160270	−	0.908938i
$67$	−609882.	−	3.45881e6i	−0.247733	−	1.40496i	−0.814058	−	0.580783i	$-0.802746\pi$
$67$	−609882.	−	3.45881e6i	−0.247733	−	1.40496i	0.566325	−	0.824182i	$-0.308365\pi$
$68$	−58990.4	+	102174.i	−0.0227510	+	0.0394059i
$69$	−852619.	−	1.47678e6i	−0.312452	−	0.541183i
$70$	253300.	−	212544.i	0.0882655	−	0.0740636i
$71$	487438.	−	177413.i	0.161628	−	0.0588276i	−0.259939	−	0.965625i	$-0.583703\pi$
$71$	487438.	−	177413.i	0.161628	−	0.0588276i	0.421567	+	0.906797i	$0.361480\pi$
$72$	393586.	+	143254.i	0.124273	+	0.0452316i
$73$	−3.21047e6	−	2.69390e6i	−0.965913	−	0.810497i	0.0159919	−	0.999872i	$-0.494909\pi$
$73$	−3.21047e6	−	2.69390e6i	−0.965913	−	0.810497i	−0.981905	+	0.189375i	$0.939354\pi$
$74$	235942.	−	1.33809e6i	0.0676853	−	0.383862i
$75$	−2.76602e6			−0.757078
$76$	503696.	+	1.84597e6i	0.131620	+	0.482365i
$77$	−5.18835e6			−1.29512
$78$	206240.	−	1.16965e6i	0.0492087	−	0.279077i
$79$	3.78932e6	+	3.17962e6i	0.864702	+	0.725571i	0.962976	−	0.269588i	$-0.0868876\pi$
$79$	3.78932e6	+	3.17962e6i	0.864702	+	0.725571i	−0.0982737	+	0.995159i	$0.531332\pi$
$80$	−223312.	−	81278.7i	−0.0487636	−	0.0177485i
$81$	2.18446e6	−	795080.i	0.456717	−	0.166231i
$82$	2.83701e6	−	2.38054e6i	0.568215	−	0.476789i
$83$	1.89078e6	+	3.27493e6i	0.362968	+	0.628680i	0.988448	−	0.151561i	$-0.0484300\pi$
$83$	1.89078e6	+	3.27493e6i	0.362968	+	0.628680i	−0.625480	+	0.780241i	$0.715097\pi$
$84$	−843466.	+	1.46093e6i	−0.155271	+	0.268937i
$85$	18572.4	+	105329.i	0.00328021	+	0.0186030i
$86$	371718.	+	2.10812e6i	0.0630186	+	0.357397i
$87$	1.53050e6	−	2.65090e6i	0.249181	−	0.431594i
$88$	1.86442e6	+	3.22927e6i	0.291645	+	0.505144i
$89$	−5.43816e6	+	4.56316e6i	−0.817686	+	0.686120i	−0.952429	−	0.304760i	$-0.901424\pi$
$89$	−5.43816e6	+	4.56316e6i	−0.817686	+	0.686120i	0.134743	+	0.990881i	$0.456979\pi$
$90$	356800.	−	129865.i	0.0515913	−	0.0187777i
$91$	−2.68616e6	−	977681.i	−0.373669	−	0.136004i
$92$	2.25957e6	+	1.89601e6i	0.302531	+	0.253853i
$93$	−1.77096e6	+	1.00436e7i	−0.228306	+	1.29479i
$94$	1.21222e6			0.150534
$95$	1.42545e6	+	988417.i	0.170577	+	0.118279i
$96$	1.21239e6			0.139860
$97$	−1.44635e6	+	8.20264e6i	−0.160906	+	0.912541i	0.792281	+	0.610157i	$0.208894\pi$
$97$	−1.44635e6	+	8.20264e6i	−0.160906	+	0.912541i	−0.953186	+	0.302384i	$0.902217\pi$
$98$	−1.93672e6	−	1.62510e6i	−0.207863	−	0.174417i
$99$	−5.59853e6	−	2.03770e6i	−0.579897	−	0.211065i
$100$	4.49602e6	−	1.63642e6i	0.449602	−	0.163642i
$101$	6.62505e6	−	5.55907e6i	0.639829	−	0.536881i	−0.264137	−	0.964485i	$-0.585087\pi$
$101$	6.62505e6	−	5.55907e6i	0.639829	−	0.536881i	0.903966	+	0.427605i	$0.140643\pi$
$102$	−272825.	−	472547.i	−0.0254556	−	0.0440904i
$103$	9.13431e6	−	1.58211e7i	0.823655	−	1.42661i	−0.0792880	−	0.996852i	$-0.525265\pi$
$103$	9.13431e6	−	1.58211e7i	0.823655	−	1.42661i	0.902943	−	0.429760i	$-0.141402\pi$
$104$	356747.	+	2.02321e6i	0.0310988	+	0.176370i
$105$	265554.	+	1.50603e6i	0.0223867	+	0.126961i
$106$	2.04515e6	−	3.54230e6i	0.166784	−	0.288878i
$107$	1.05430e7	+	1.82609e7i	0.831992	+	1.44105i	0.896456	+	0.443133i	$0.146133\pi$
$107$	1.05430e7	+	1.82609e7i	0.831992	+	1.44105i	−0.0644639	+	0.997920i	$0.520534\pi$
$108$	−5.45104e6	+	4.57397e6i	−0.416386	+	0.349389i
$109$	−1.05922e7	+	3.85526e6i	−0.783421	+	0.285142i	−0.702598	−	0.711587i	$-0.747977\pi$
$109$	−1.05922e7	+	3.85526e6i	−0.783421	+	0.285142i	−0.0808225	+	0.996729i	$0.525755\pi$
$110$	3.17647e6	+	1.15614e6i	0.227547	+	0.0828202i
$111$	4.81384e6	+	4.03929e6i	0.334088	+	0.280333i
$112$	506705.	−	2.87367e6i	0.0340794	−	0.193274i
$113$	1.34252e6			0.0875275			0.0437638	−	0.999042i	$-0.486065\pi$
$113$	1.34252e6			0.0875275			0.0437638	+	0.999042i	$0.486065\pi$
$114$	−8.55839e6	−	2.25126e6i	−0.541034	−	0.142318i
$115$	2.67398e6			0.163952
$116$	−919433.	+	5.21436e6i	−0.0546911	+	0.310169i
$117$	−2.51454e6	−	2.10995e6i	−0.145147	−	0.121793i
$118$	6.13004e6	+	2.23115e6i	0.343460	+	0.125009i
$119$	−1.23408e6	+	449168.i	−0.0671318	+	0.0244340i
$120$	841941.	−	706473.i	0.0444782	−	0.0373217i
$121$	−1.67767e7	−	2.90581e7i	−0.860909	−	1.49114i
$122$	1.95013e6	−	3.37773e6i	0.0972309	−	0.168409i
$123$	2.97427e6	+	1.68679e7i	0.144116	+	0.817323i
$124$	−3.06334e6	−	1.73731e7i	−0.144285	−	0.818278i
$125$	4.43503e6	−	7.68171e6i	0.203101	−	0.351781i
$126$	2.33114e6	+	4.03766e6i	0.103818	+	0.179818i
$127$	2.74960e7	−	2.30719e7i	1.19112	−	0.999470i	0.191283	−	0.981535i	$-0.438735\pi$
$127$	2.74960e7	−	2.30719e7i	1.19112	−	0.999470i	0.999839	−	0.0179356i	$-0.00570938\pi$
$128$	−1.97068e6	+	717268.i	−0.0830579	+	0.0302306i
$129$	−9.30319e6	−	3.38608e6i	−0.381564	−	0.138878i
$130$	1.42669e6	+	1.19714e6i	0.0569545	+	0.0477905i
$131$	−1.71725e6	+	9.73900e6i	−0.0667396	+	0.378499i	0.933083	+	0.359661i	$0.117108\pi$
$131$	−1.71725e6	+	9.73900e6i	−0.0667396	+	0.378499i	−0.999823	+	0.0188378i	$0.994003\pi$
$132$	−1.72455e7			−0.652631
$133$	−8.91293e6	+	1.93446e7i	−0.328503	+	0.712983i
$134$	−2.80974e7			−1.00879
$135$	−1.12016e6	+	6.35276e6i	−0.0391844	+	0.222226i
$136$	723029.	+	606693.i	0.0246473	+	0.0206815i
$137$	−2.55917e7	−	9.31461e6i	−0.850309	−	0.309487i	−0.120143	−	0.992757i	$-0.538335\pi$
$137$	−2.55917e7	−	9.31461e6i	−0.850309	−	0.309487i	−0.730167	+	0.683269i	$0.760558\pi$
$138$	−1.28192e7	+	4.66581e6i	−0.415226	+	0.151130i
$139$	4.04495e7	−	3.39412e7i	1.27750	−	1.07195i	0.283919	−	0.958848i	$-0.408365\pi$
$139$	4.04495e7	−	3.39412e7i	1.27750	−	1.07195i	0.993583	−	0.113104i	$-0.0360792\pi$
$140$	−1.32264e6	−	2.29087e6i	−0.0407373	−	0.0705591i
$141$	−2.80320e6	+	4.85529e6i	−0.0842146	+	0.145864i
$142$	−720599.	−	4.08672e6i	−0.0211196	−	0.119775i
$143$	−5.07452e6	−	2.87790e7i	−0.145117	−	0.823000i
$144$	1.67538e6	−	2.90185e6i	0.0467569	−	0.0809853i
$145$	2.39997e6	+	4.15686e6i	0.0653758	+	0.113234i
$146$	−2.56837e7	+	2.15512e7i	−0.683004	+	0.573108i
$147$	1.09876e7	−	3.99915e6i	0.285293	−	0.103838i
$148$	−1.02143e7	−	3.71772e6i	−0.258997	−	0.0942672i
$149$	−3.78685e7	−	3.17755e7i	−0.937835	−	0.786937i	0.0393724	−	0.999225i	$-0.487464\pi$
$149$	−3.78685e7	−	3.17755e7i	−0.937835	−	0.786937i	−0.977207	+	0.212288i	$0.931909\pi$
$150$	−3.84251e6	+	2.17920e7i	−0.0929600	+	0.527202i
$151$	3.13992e7			0.742164			0.371082	−	0.928600i	$-0.378987\pi$
$151$	3.13992e7			0.742164			0.371082	+	0.928600i	$0.378987\pi$
$152$	1.52431e7	−	1.40396e6i	0.352063	−	0.0324267i
$153$	−1.50805e6			−0.0340405
$154$	−7.20758e6	+	4.08762e7i	−0.159025	+	0.901878i
$155$	−1.22508e7	−	1.02796e7i	−0.264243	−	0.221726i
$156$	−8.92851e6	−	3.24971e6i	−0.188297	−	0.0685344i
$157$	5.02665e7	−	1.82955e7i	1.03664	−	0.377308i	0.233037	−	0.972468i	$-0.425134\pi$
$157$	5.02665e7	−	1.82955e7i	1.03664	−	0.377308i	0.803607	+	0.595160i	$0.202911\pi$
$158$	3.03146e7	−	2.54369e7i	0.611437	−	0.513056i
$159$	9.45860e6	+	1.63828e7i	0.186611	+	0.323219i
$160$	−950573.	+	1.64644e6i	−0.0183470	+	0.0317780i
$161$	5.70148e6	+	3.23347e7i	0.107671	+	0.610631i
$162$	−3.22938e6	−	1.83147e7i	−0.0596783	−	0.338453i
$163$	6.53206e6	−	1.13139e7i	0.118139	−	0.204623i	−0.800891	−	0.598810i	$-0.795640\pi$
$163$	6.53206e6	−	1.13139e7i	0.118139	−	0.204623i	0.919030	+	0.394187i	$0.128974\pi$
$164$	−1.48138e7	−	2.56583e7i	−0.262249	−	0.454229i
$165$	−1.19761e7	+	1.00491e7i	−0.207550	+	0.174155i
$166$	2.84281e7	−	1.03470e7i	0.482358	−	0.175564i
$167$	7.04015e7	+	2.56241e7i	1.16970	+	0.425736i	0.852553	−	0.522641i	$-0.175053\pi$
$167$	7.04015e7	+	2.56241e7i	1.16970	+	0.425736i	0.317146	+	0.948377i	$0.397275\pi$
$168$	1.03381e7	+	8.67471e6i	0.168213	+	0.141147i
$169$	−8.10033e6	+	4.59393e7i	−0.129092	+	0.732117i
$170$	855632.			0.0133572
$171$	−1.72151e7	+	1.73735e7i	−0.263283	+	0.265705i
$172$	1.71251e7			0.256616
$173$	−9.36723e6	+	5.31242e7i	−0.137547	+	0.780065i	0.835506	+	0.549482i	$0.185175\pi$
$173$	−9.36723e6	+	5.31242e7i	−0.137547	+	0.780065i	−0.973052	+	0.230584i	$0.925936\pi$
$174$	−1.87589e7	−	1.57405e7i	−0.269950	−	0.226515i
$175$	5.00465e7	+	1.82154e7i	0.705896	+	0.256925i
$176$	2.80317e7	−	1.02027e7i	0.387575	−	0.141066i
$177$	−2.31118e7	+	1.93931e7i	−0.313276	+	0.262870i
$178$	2.83960e7	+	4.91834e7i	0.377388	+	0.653655i
$179$	−5.14012e7	+	8.90296e7i	−0.669866	+	1.16024i	0.308075	+	0.951362i	$0.400315\pi$
$179$	−5.14012e7	+	8.90296e7i	−0.669866	+	1.16024i	−0.977941	+	0.208880i	$0.933018\pi$
$180$	−527472.	−	2.99144e6i	−0.00674133	−	0.0382320i
$181$	−9.31235e6	−	5.28130e7i	−0.116730	−	0.662011i	−0.985879	−	0.167460i	$-0.946443\pi$
$181$	−9.31235e6	−	5.28130e7i	−0.116730	−	0.662011i	0.869148	−	0.494551i	$-0.164668\pi$
$182$	−1.14342e7	+	1.98046e7i	−0.140590	+	0.243510i
$183$	9.01917e6	+	1.56217e7i	0.108790	+	0.188429i
$184$	1.80766e7	−	1.51681e7i	0.213921	−	0.179501i
$185$	−9.25968e6	+	3.37025e6i	−0.107521	+	0.0391346i
$186$	7.66679e7	+	2.79048e7i	0.873612	+	0.317969i
$187$	−1.02847e7	−	8.62985e6i	−0.115012	−	0.0965067i
$188$	1.68400e6	−	9.55043e6i	0.0184837	−	0.104826i
$189$	−7.92083e7			−0.853403
$190$	9.76743e6	−	9.85729e6i	0.103310	−	0.104261i
$191$	−6.12259e7			−0.635796			−0.317898	−	0.948125i	$-0.602977\pi$
$191$	−6.12259e7			−0.635796			−0.317898	+	0.948125i	$0.602977\pi$
$192$	1.68423e6	−	9.55177e6i	0.0171731	−	0.0973934i
$193$	−3.51754e7	−	2.95156e7i	−0.352199	−	0.295530i	0.449473	−	0.893294i	$-0.351612\pi$
$193$	−3.51754e7	−	2.95156e7i	−0.352199	−	0.295530i	−0.801672	+	0.597764i	$0.796056\pi$
$194$	6.26149e7	+	2.27900e7i	0.615704	+	0.224098i
$195$	−8.09402e6	+	2.94598e6i	−0.0781705	+	0.0284517i
$196$	−1.54938e7	+	1.30008e7i	−0.146981	+	0.123332i
$197$	−3.23034e7	−	5.59511e7i	−0.301034	−	0.521407i	0.675336	−	0.737510i	$-0.263999\pi$
$197$	−3.23034e7	−	5.59511e7i	−0.301034	−	0.521407i	−0.976371	+	0.216103i	$0.930665\pi$
$198$	−2.38313e7	+	4.12770e7i	−0.218182	+	0.377903i
$199$	2.73939e7	+	1.55359e8i	0.246416	+	1.39749i	0.817181	+	0.576381i	$0.195535\pi$
$199$	2.73939e7	+	1.55359e8i	0.246416	+	1.39749i	−0.570766	+	0.821113i	$0.693354\pi$
$200$	−6.64665e6	−	3.76950e7i	−0.0587487	−	0.333180i
$201$	6.49738e7	−	1.12538e8i	0.564355	−	0.977491i
$202$	−3.45935e7	−	5.99178e7i	−0.295301	−	0.511477i
$203$	−4.51491e7	+	3.78846e7i	−0.378802	+	0.317853i
$204$	−4.10195e6	+	1.49299e6i	−0.0338286	+	0.0123126i
$205$	−2.52388e7	−	9.18617e6i	−0.204612	−	0.0744725i
$206$	−1.11957e8	−	9.39427e7i	−0.892307	−	0.748734i
$207$	−6.54707e6	+	3.71303e7i	−0.0513040	+	0.290959i
$208$	1.64354e7			0.126636
$209$	−2.16824e8	+	1.99705e7i	−1.64284	+	0.151313i
$210$	1.22341e7			0.0911602
$211$	2.88058e7	−	1.63366e8i	0.211102	−	1.19722i	−0.676443	−	0.736495i	$-0.736479\pi$
$211$	2.88058e7	−	1.63366e8i	0.211102	−	1.19722i	0.887544	−	0.460722i	$-0.152410\pi$
$212$	−2.50668e7	−	2.10335e7i	−0.180685	−	0.151613i
$213$	1.80348e7	+	6.56414e6i	0.127874	+	0.0465425i
$214$	1.58514e8	−	5.76945e7i	1.10566	−	0.402426i
$215$	1.18925e7	−	9.97898e6i	0.0816090	−	0.0684781i
$216$	2.84633e7	+	4.92999e7i	0.192175	+	0.332857i
$217$	9.81839e7	−	1.70060e8i	0.652276	−	1.12978i
$218$	1.56589e7	+	8.88062e7i	0.102368	+	0.580558i
$219$	−2.69263e7	−	1.52707e8i	−0.173230	−	0.982434i
$220$	1.35213e7	−	2.34196e7i	0.0856130	−	0.148286i
$221$	−3.69847e6	−	6.40594e6i	−0.0230488	−	0.0399218i
$222$	3.85107e7	−	3.23143e7i	0.236236	−	0.198226i
$223$	4.96214e7	−	1.80607e7i	0.299642	−	0.109061i	−0.187824	−	0.982203i	$-0.560144\pi$
$223$	4.96214e7	−	1.80607e7i	0.299642	−	0.109061i	0.487466	+	0.873142i	$0.337921\pi$
$224$	−2.19362e7	−	7.98411e6i	−0.130405	−	0.0474634i
$225$	4.68491e7	+	3.93110e7i	0.274197	+	0.230078i
$226$	1.86500e6	−	1.05770e7i	0.0107473	−	0.0609510i
$227$	1.30276e8			0.739220			0.369610	−	0.929187i	$-0.379491\pi$
$227$	1.30276e8			0.739220			0.369610	+	0.929187i	$0.379491\pi$
$228$	−2.96257e7	+	6.42995e7i	−0.165537	+	0.359282i
$229$	1.88520e8			1.03737			0.518685	−	0.854965i	$-0.326422\pi$
$229$	1.88520e8			1.03737			0.518685	+	0.854965i	$0.326422\pi$
$230$	3.71465e6	−	2.10668e7i	0.0201313	−	0.114170i
$231$	−1.47054e8	−	1.23393e8i	−0.784935	−	0.658638i
$232$	3.98039e7	+	1.44874e7i	0.209275	+	0.0761699i
$233$	−2.36272e8	+	8.59960e7i	−1.22368	+	0.445382i	−0.871428	−	0.490524i	$-0.836805\pi$
$233$	−2.36272e8	+	8.59960e7i	−1.22368	+	0.445382i	−0.352249	+	0.935906i	$0.614583\pi$
$234$	−2.01163e7	+	1.68796e7i	−0.102634	+	0.0861205i
$235$	−4.39569e6	−	7.61356e6i	−0.0220948	−	0.0382693i
$236$	2.60938e7	−	4.51958e7i	0.129225	−	0.223824i
$237$	3.17812e7	+	1.80240e8i	0.155078	+	0.879492i
$238$	1.82439e6	+	1.03466e7i	0.00877198	+	0.0497484i
$239$	8.00356e7	−	1.38626e8i	0.379219	−	0.656827i	−0.611730	−	0.791067i	$-0.709526\pi$
$239$	8.00356e7	−	1.38626e8i	0.379219	−	0.656827i	0.990949	+	0.134240i	$0.0428593\pi$
$240$	−4.39630e6	−	7.61462e6i	−0.0205281	−	0.0355557i
$241$	8.58712e7	−	7.20545e7i	0.395173	−	0.331590i	−0.423451	−	0.905919i	$-0.639181\pi$
$241$	8.58712e7	−	7.20545e7i	0.395173	−	0.331590i	0.818624	+	0.574329i	$0.194737\pi$
$242$	−2.52239e8	+	9.18074e7i	−1.14408	+	0.416413i
$243$	−1.47673e8	−	5.37487e7i	−0.660207	−	0.240296i
$244$	−2.39022e7	−	2.00563e7i	−0.105335	−	0.0883867i
$245$	−3.18390e6	+	1.80568e7i	−0.0138318	+	0.0784439i
$246$	1.37025e8			0.586850
$247$	−1.16019e8	−	3.05185e7i	−0.489881	−	0.128862i
$248$	−1.41129e8			−0.587536
$249$	−2.42960e7	+	1.37789e8i	−0.0997326	+	0.565612i
$250$	−5.43589e7	−	4.56126e7i	−0.220030	−	0.184627i
$251$	3.35506e8	+	1.22114e8i	1.33919	+	0.487426i	0.909558	−	0.415578i	$-0.136421\pi$
$251$	3.35506e8	+	1.22114e8i	1.33919	+	0.487426i	0.429633	+	0.903004i	$0.358643\pi$
$252$	3.50489e7	−	1.27568e7i	0.137966	−	0.0502156i
$253$	−2.57129e8	+	2.15757e8i	−0.998226	+	0.837611i
$254$	−1.43574e8	−	2.48677e8i	−0.549740	−	0.952178i
$255$	−1.97861e6	+	3.42705e6i	−0.00747255	+	0.0129428i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	1.68069e7	+	9.53165e7i	0.0617619	+	0.350269i	0.999991	+	0.00425439i	$0.00135422\pi$
$257$	1.68069e7	+	9.53165e7i	0.0617619	+	0.350269i	−0.938229	+	0.346015i	$0.887535\pi$
$258$	−3.96010e7	+	6.85909e7i	−0.143561	+	0.248655i
$259$	−6.04979e7	−	1.04785e8i	−0.216367	−	0.374758i
$260$	1.14135e7	−	9.57708e6i	0.0402729	−	0.0337930i
$261$	−6.35974e7	+	2.31476e7i	−0.221410	+	0.0805868i
$262$	7.43428e7	+	2.70586e7i	0.255378	+	0.0929501i
$263$	3.66287e8	+	3.07352e8i	1.24159	+	1.04181i	0.997398	+	0.0720869i	$0.0229659\pi$
$263$	3.66287e8	+	3.07352e8i	1.24159	+	1.04181i	0.244188	+	0.969728i	$0.421479\pi$
$264$	−2.39572e7	+	1.35868e8i	−0.0801351	+	0.454469i
$265$	−2.96640e7			−0.0979195
$266$	1.40024e8	+	9.70934e7i	0.456160	+	0.316304i
$267$	−2.62658e8			−0.844502
$268$	−3.90325e7	+	2.21364e8i	−0.123867	+	0.702482i
$269$	1.01892e8	+	8.54973e7i	0.319158	+	0.267805i	0.788265	−	0.615336i	$-0.210980\pi$
$269$	1.01892e8	+	8.54973e7i	0.319158	+	0.267805i	−0.469107	+	0.883141i	$0.655424\pi$
$270$	4.84938e7	+	1.76503e7i	0.149939	+	0.0545732i
$271$	3.75297e8	−	1.36597e8i	1.14547	−	0.416916i	0.301582	−	0.953440i	$-0.402485\pi$
$271$	3.75297e8	−	1.36597e8i	1.14547	−	0.416916i	0.843885	+	0.536524i	$0.180263\pi$
$272$	5.78423e6	−	4.85355e6i	0.0174283	−	0.0146241i
$273$	−5.28820e7	−	9.15944e7i	−0.157304	−	0.272458i
$274$	−1.08936e8	+	1.88683e8i	−0.319924	+	0.554124i
$275$	9.45446e7	+	5.36189e8i	0.274140	+	1.55473i
$276$	1.89511e7	+	1.07477e8i	0.0542567	+	0.307705i
$277$	1.77971e8	−	3.08255e8i	0.503119	−	0.871427i	−0.496875	−	0.867822i	$-0.665519\pi$
$277$	1.77971e8	−	3.08255e8i	0.503119	−	0.871427i	0.999994	−	0.00360479i	$-0.00114744\pi$
$278$	−2.11212e8	−	3.65831e8i	−0.589607	−	1.02123i
$279$	1.72736e8	−	1.44943e8i	0.476177	−	0.399560i
$280$	−1.98859e7	+	7.23789e6i	−0.0541369	+	0.0197042i
$281$	5.25565e8	+	1.91290e8i	1.41304	+	0.514304i	0.932020	−	0.362406i	$-0.118045\pi$
$281$	5.25565e8	+	1.91290e8i	1.41304	+	0.514304i	0.481019	+	0.876710i	$0.340267\pi$
$282$	3.43580e7	+	2.88298e7i	0.0912339	+	0.0765543i
$283$	−6.61420e7	+	3.75110e8i	−0.173470	+	0.983799i	0.766425	+	0.642334i	$0.222034\pi$
$283$	−6.61420e7	+	3.75110e8i	−0.173470	+	0.983799i	−0.939895	+	0.341464i	$0.889077\pi$
$284$	−3.31981e7			−0.0860002
$285$	1.68945e7	+	6.19158e7i	0.0432304	+	0.158433i
$286$	−2.33784e8			−0.590926
$287$	5.72681e7	−	3.24784e8i	0.142997	−	0.810975i
$288$	−2.05347e7	−	1.72306e7i	−0.0506541	−	0.0425038i
$289$	3.82399e8	+	1.39182e8i	0.931910	+	0.339188i
$290$	3.60837e7	−	1.31334e7i	0.0868796	−	0.0316216i
$291$	−2.36074e8	+	1.98090e8i	−0.561595	+	0.471234i
$292$	1.34111e8	+	2.32287e8i	0.315227	+	0.545990i
$293$	1.95859e8	−	3.39238e8i	0.454891	−	0.787894i	−0.543791	−	0.839221i	$-0.683012\pi$
$293$	1.95859e8	−	3.39238e8i	0.454891	−	0.787894i	0.998682	+	0.0513265i	$0.0163449\pi$
$294$	−1.62434e7	−	9.21208e7i	−0.0372787	−	0.211418i
$295$	−8.21529e6	−	4.65912e7i	−0.0186314	−	0.105664i
$296$	−4.34795e7	+	7.53088e7i	−0.0974460	+	0.168781i
$297$	−4.04873e8	−	7.01261e8i	−0.896751	−	1.55322i
$298$	−3.02948e8	+	2.54204e8i	−0.663149	+	0.556448i
$299$	−1.73780e8	+	6.32506e7i	−0.375967	+	0.136841i
$300$	1.66349e8	+	6.05462e7i	0.355710	+	0.129468i
$301$	1.46027e8	+	1.22531e8i	0.308638	+	0.258978i
$302$	4.36194e7	−	2.47378e8i	0.0911286	−	0.516816i
$303$	3.19983e8			0.660813
$304$	1.01144e7	−	1.22043e8i	0.0206483	−	0.249146i
$305$	−2.82858e7			−0.0570847
$306$	−2.09496e6	+	1.18811e7i	−0.00417976	+	0.0237046i
$307$	−7.46698e8	−	6.26554e8i	−1.47286	−	1.23587i	−0.913431	−	0.406994i	$-0.866577\pi$
$307$	−7.46698e8	−	6.26554e8i	−1.47286	−	1.23587i	−0.559426	−	0.828880i	$-0.688979\pi$
$308$	3.12029e8	+	1.13569e8i	0.608509	+	0.221479i
$309$	6.35161e8	−	2.31180e8i	1.22470	−	0.445754i
$310$	−9.80064e7	+	8.22372e7i	−0.186848	+	0.156784i
$311$	−3.68475e8	−	6.38217e8i	−0.694619	−	1.20311i	−0.970309	−	0.241868i	$-0.922240\pi$
$311$	−3.68475e8	−	6.38217e8i	−0.694619	−	1.20311i	0.275690	−	0.961246i	$-0.411094\pi$
$312$	−3.80061e7	+	6.58284e7i	−0.0708454	+	0.122708i
$313$	−7.84133e7	−	4.44704e8i	−0.144539	−	0.819721i	−0.967736	−	0.251965i	$-0.918923\pi$
$313$	−7.84133e7	−	4.44704e8i	−0.144539	−	0.819721i	0.823197	−	0.567755i	$-0.192188\pi$
$314$	−7.43110e7	−	4.21439e8i	−0.135456	−	0.768211i
$315$	1.69061e7	−	2.92823e7i	0.0304760	−	0.0527859i
$316$	−1.58291e8	−	2.74169e8i	−0.282197	−	0.488780i
$317$	−6.34748e8	+	5.32617e8i	−1.11916	+	0.939091i	−0.998562	−	0.0536102i	$-0.982927\pi$
$317$	−6.34748e8	+	5.32617e8i	−1.11916	+	0.939091i	−0.120603	+	0.992701i	$0.538483\pi$
$318$	1.42211e8	−	5.17605e7i	0.247992	−	0.0902617i
$319$	−5.66186e8	−	2.06075e8i	−0.976545	−	0.355433i
$320$	1.16509e7	+	9.77626e6i	0.0198762	+	0.0166781i
$321$	−1.35474e8	+	7.68310e8i	−0.228606	+	1.29649i
$322$	2.62668e8			0.438442
$323$	−4.98439e7	+	2.35211e7i	−0.0823007	+	0.0388372i
$324$	−1.48778e8			−0.243014
$325$	−5.20899e7	+	2.95416e8i	−0.0841708	+	0.477357i
$326$	−8.00616e7	−	6.71797e7i	−0.127986	−	0.107393i
$327$	−3.91905e8	−	1.42642e8i	−0.619817	−	0.225595i
$328$	−2.22727e8	+	8.10661e7i	−0.348510	+	0.126847i
$329$	8.26934e7	−	6.93880e7i	0.128022	−	0.107423i
$330$	6.25348e7	+	1.08313e8i	0.0957906	+	0.165914i
$331$	−2.83631e8	+	4.91263e8i	−0.429888	+	0.744588i	−0.996863	−	0.0791472i	$-0.974780\pi$
$331$	−2.83631e8	+	4.91263e8i	−0.429888	+	0.744588i	0.566975	+	0.823735i	$0.308114\pi$
$332$	−4.20264e7	−	2.38344e8i	−0.0630288	−	0.357454i
$333$	−2.41268e7	−	1.36830e8i	−0.0358051	−	0.203061i
$334$	2.99679e8	−	5.19059e8i	0.440092	−	0.762262i
$335$	1.01885e8	+	1.76470e8i	0.148066	+	0.256457i
$336$	8.27049e7	−	6.93977e7i	0.118944	−	0.0998062i
$337$	−2.93803e8	+	1.06935e8i	−0.418168	+	0.152201i	−0.542531	−	0.840036i	$-0.682534\pi$
$337$	−2.93803e8	+	1.06935e8i	−0.418168	+	0.152201i	0.124362	+	0.992237i	$0.460311\pi$
$338$	3.50678e8	+	1.27636e8i	0.493969	+	0.179790i
$339$	3.80510e7	+	3.19285e7i	0.0530477	+	0.0445123i
$340$	1.18863e6	−	6.74106e6i	0.00164010	−	0.00930148i
$341$	2.00747e9			2.74163
$342$	1.12961e8	+	1.59763e8i	0.152700	+	0.215966i
$343$	−8.11831e8			−1.08627
$344$	2.37900e7	−	1.34920e8i	0.0315093	−	0.178698i
$345$	7.57887e7	+	6.35943e7i	0.0993660	+	0.0833779i
$346$	4.05524e8	+	1.47599e8i	0.526321	+	0.191565i
$347$	−6.58536e8	+	2.39687e8i	−0.846109	+	0.307958i	−0.728453	−	0.685096i	$-0.759760\pi$
$347$	−6.58536e8	+	2.39687e8i	−0.846109	+	0.307958i	−0.117656	+	0.993054i	$0.537538\pi$
$348$	−1.50071e8	+	1.25924e8i	−0.190884	+	0.160170i
$349$	−4.36676e8	−	7.56345e8i	−0.549883	−	0.952425i	−0.998282	−	0.0585917i	$-0.981339\pi$
$349$	−4.36676e8	−	7.56345e8i	−0.549883	−	0.952425i	0.448399	−	0.893833i	$-0.351994\pi$
$350$	2.13033e8	−	3.68985e8i	0.265589	−	0.460013i
$351$	−7.74705e7	−	4.39357e8i	−0.0956227	−	0.542304i
$352$	−4.14404e7	−	2.35020e8i	−0.0506436	−	0.287214i
$353$	1.50084e8	−	2.59953e8i	0.181603	−	0.314545i	−0.760824	−	0.648959i	$-0.775205\pi$
$353$	1.50084e8	−	2.59953e8i	0.181603	−	0.314545i	0.942426	+	0.334413i	$0.108538\pi$
$354$	1.20681e8	+	2.09026e8i	0.144587	+	0.250432i
$355$	−2.30544e7	+	1.93449e7i	−0.0273498	+	0.0229492i
$356$	4.26937e8	−	1.55392e8i	0.501520	−	0.182538i
$357$	−4.56599e7	−	1.66188e7i	−0.0531124	−	0.0193314i
$358$	6.30010e8	+	5.28641e8i	0.725700	+	0.608934i
$359$	−2.74211e8	+	1.55513e9i	−0.312791	+	1.77393i	0.271556	+	0.962423i	$0.412462\pi$
$359$	−2.74211e8	+	1.55513e9i	−0.312791	+	1.77393i	−0.584348	+	0.811504i	$0.698649\pi$
$360$	−2.43007e7			−0.0274512
$361$	−2.98017e8	+	8.42729e8i	−0.333400	+	0.942785i
$362$	−4.29021e8			−0.475334
$363$	2.15575e8	−	1.22259e9i	0.236551	−	1.34155i
$364$	1.40146e8	+	1.17596e8i	0.152309	+	0.127802i
$365$	2.28489e8	+	8.31632e7i	0.245946	+	0.0895171i
$366$	1.35604e8	−	4.93558e7i	0.144573	−	0.0526204i
$367$	−1.44933e9	+	1.21613e9i	−1.53051	+	1.28425i	−0.736071	+	0.676904i	$0.763321\pi$
$367$	−1.44933e9	+	1.21613e9i	−1.53051	+	1.28425i	−0.794438	+	0.607345i	$0.792235\pi$
$368$	−9.43893e7	−	1.63487e8i	−0.0987314	−	0.171008i
$369$	1.89353e8	−	3.27969e8i	0.196191	−	0.339813i
$370$	1.36890e7	+	7.76340e7i	0.0140496	+	0.0796793i
$371$	−6.32499e7	−	3.58708e8i	−0.0643059	−	0.364697i
$372$	3.26353e8	−	5.65260e8i	0.328691	−	0.569309i
$373$	−1.87525e8	−	3.24802e8i	−0.187102	−	0.324070i	0.757181	−	0.653205i	$-0.226576\pi$
$373$	−1.87525e8	−	3.24802e8i	−0.187102	−	0.324070i	−0.944283	+	0.329135i	$0.893243\pi$
$374$	−8.22772e7	+	6.90388e7i	−0.0813259	+	0.0682405i
$375$	3.08394e8	−	1.12246e8i	0.301992	−	0.109916i
$376$	−7.29033e7	−	2.65346e7i	−0.0707278	−	0.0257428i
$377$	−2.54299e8	−	2.13382e8i	−0.244427	−	0.205099i
$378$	−1.10035e8	+	6.24039e8i	−0.104787	+	0.594279i
$379$	1.07864e9			1.01775			0.508873	−	0.860842i	$-0.330062\pi$
$379$	1.07864e9			1.01775			0.508873	+	0.860842i	$0.330062\pi$
$380$	−6.40915e7	−	9.06459e7i	−0.0599181	−	0.0847433i
$381$	1.32803e9			1.23019
$382$	−8.50541e7	+	4.82366e8i	−0.0780681	+	0.442746i
$383$	7.85651e8	+	6.59239e8i	0.714552	+	0.599580i	0.925872	−	0.377836i	$-0.123332\pi$
$383$	7.85651e8	+	6.59239e8i	0.714552	+	0.599580i	−0.211320	+	0.977417i	$0.567776\pi$
$384$	−7.29136e7	−	2.65384e7i	−0.0657126	−	0.0239174i
$385$	2.82866e8	−	1.02955e8i	0.252620	−	0.0919461i
$386$	−2.81403e8	+	2.36125e8i	−0.249042	+	0.208971i
$387$	1.09448e8	+	1.89569e8i	0.0959885	+	0.166257i
$388$	2.66534e8	−	4.61650e8i	0.231655	−	0.401238i
$389$	1.74202e8	+	9.87951e8i	0.150048	+	0.850965i	0.963174	+	0.268878i	$0.0866527\pi$
$389$	1.74202e8	+	9.87951e8i	0.150048	+	0.850965i	−0.813126	+	0.582087i	$0.802236\pi$
$390$	1.19657e7	+	6.78609e7i	0.0102144	+	0.0579287i
$391$	−4.24810e7	+	7.35792e7i	−0.0359398	+	0.0622496i
$392$	8.09028e7	+	1.40128e8i	0.0678363	+	0.117496i
$393$	−2.80291e8	+	2.35192e8i	−0.232935	+	0.195456i
$394$	−4.85684e8	+	1.76774e8i	−0.400052	+	0.145607i
$395$	−2.69686e8	−	9.81577e7i	−0.220175	−	0.0801373i
$396$	2.92094e8	+	2.45096e8i	0.236368	+	0.198336i
$397$	−2.05597e8	+	1.16600e9i	−0.164911	+	0.935255i	0.784246	+	0.620451i	$0.213050\pi$
$397$	−2.05597e8	+	1.16600e9i	−0.164911	+	0.935255i	−0.949156	+	0.314805i	$0.898061\pi$
$398$	1.26204e9			1.00342
$399$	−7.12686e8	+	3.36312e8i	−0.561685	+	0.265056i
$400$	−3.06212e8			−0.239228
$401$	1.18690e8	−	6.73126e8i	0.0919200	−	0.521304i	−0.903728	−	0.428108i	$-0.859180\pi$
$401$	1.18690e8	−	6.73126e8i	0.0919200	−	0.521304i	0.995648	−	0.0931964i	$-0.0297085\pi$
$402$	−7.96365e8	−	6.68230e8i	−0.611394	−	0.513020i
$403$	1.03933e9	+	3.78284e8i	0.791014	+	0.287905i
$404$	−5.20117e8	+	1.89307e8i	−0.392433	+	0.142834i
$405$	−1.03319e8	+	8.66945e7i	−0.0772833	+	0.0648484i
$406$	2.35752e8	+	4.08334e8i	0.174829	+	0.302813i
$407$	6.18470e8	−	1.07122e9i	0.454714	−	0.787588i
$408$	6.06407e6	+	3.43911e7i	0.00442032	+	0.0250689i
$409$	−7.81158e7	−	4.43017e8i	−0.0564556	−	0.320176i	0.943481	−	0.331426i	$-0.107530\pi$
$409$	−7.81158e7	−	4.43017e8i	−0.0564556	−	0.320176i	−0.999937	+	0.0112506i	$0.996419\pi$
$410$	−1.07434e8	+	1.86082e8i	−0.0769838	+	0.133340i
$411$	−5.03820e8	−	8.72642e8i	−0.357956	−	0.619998i
$412$	−8.95652e8	+	7.51542e8i	−0.630956	+	0.529435i
$413$	5.45881e8	−	1.98685e8i	0.381305	−	0.138784i
$414$	2.83434e8	+	1.03162e8i	0.196314	+	0.0714525i
$415$	−1.68070e8	−	1.41028e8i	−0.115431	−	0.0968582i
$416$	2.28318e7	−	1.29486e8i	0.0155494	−	0.0881851i
$417$	1.95367e9			1.31940
$418$	−1.43872e8	+	1.73598e9i	−0.0963515	+	1.16259i
$419$	−1.68220e9			−1.11719			−0.558595	−	0.829440i	$-0.688659\pi$
$419$	−1.68220e9			−1.11719			−0.558595	+	0.829440i	$0.688659\pi$
$420$	1.69955e7	−	9.63861e7i	0.0111934	−	0.0634807i
$421$	5.73138e8	+	4.80920e8i	0.374345	+	0.314113i	0.810478	−	0.585770i	$-0.199208\pi$
$421$	5.73138e8	+	4.80920e8i	0.374345	+	0.314113i	−0.436133	+	0.899882i	$0.643652\pi$
$422$	−1.24706e9	−	4.53891e8i	−0.807779	−	0.294007i
$423$	1.16483e8	−	4.23962e7i	0.0748290	−	0.0272355i
$424$	−2.00534e8	+	1.68268e8i	−0.127764	+	0.107207i
$425$	6.89072e7	+	1.19351e8i	0.0435415	+	0.0754161i
$426$	7.67691e7	−	1.32968e8i	0.0481119	−	0.0833323i
$427$	−6.03114e7	−	3.42043e8i	−0.0374888	−	0.212610i
$428$	−2.34338e8	−	1.32900e9i	−0.144474	−	0.819352i
$429$	5.40614e8	−	9.36370e8i	0.330587	−	0.572594i
$430$	−6.20982e7	−	1.07557e8i	−0.0376651	−	0.0652379i
$431$	−1.42997e9	+	1.19988e9i	−0.860311	+	0.721886i	−0.962035	−	0.272926i	$-0.912008\pi$
$431$	−1.42997e9	+	1.19988e9i	−0.860311	+	0.721886i	0.101724	+	0.994813i	$0.467564\pi$
$432$	4.27948e8	−	1.55760e8i	0.255387	−	0.0929531i
$433$	−2.48289e9	−	9.03697e8i	−1.46977	−	0.534952i	−0.521731	−	0.853110i	$-0.674714\pi$
$433$	−2.48289e9	−	9.03697e8i	−1.46977	−	0.534952i	−0.948038	+	0.318157i	$0.896936\pi$
$434$	−1.20341e9	−	1.00978e9i	−0.706643	−	0.592944i
$435$	−3.08388e7	+	1.74896e8i	−0.0179633	+	0.101875i
$436$	7.21410e8			0.416850
$437$	3.62728e8	+	1.32934e9i	0.207920	+	0.761994i
$438$	−1.24050e9			−0.705403
$439$	−1.98389e8	+	1.12512e9i	−0.111916	+	0.634707i	0.876315	+	0.481739i	$0.159995\pi$
$439$	−1.98389e8	+	1.12512e9i	−0.111916	+	0.634707i	−0.988231	+	0.152969i	$0.951117\pi$
$440$	−1.65727e8	−	1.39061e8i	−0.0927489	−	0.0778256i
$441$	−2.42937e8	−	8.84218e7i	−0.134883	−	0.0490935i
$442$	−5.56068e7	+	2.02392e7i	−0.0306302	+	0.0111485i
$443$	1.95820e9	−	1.64313e9i	1.07015	−	0.897961i	0.0750828	−	0.997177i	$-0.476078\pi$
$443$	1.95820e9	−	1.64313e9i	1.07015	−	0.897961i	0.995066	+	0.0992159i	$0.0316334\pi$
$444$	−2.01089e8	−	3.48296e8i	−0.109030	−	0.188846i
$445$	2.05936e8	−	3.56692e8i	0.110783	−	0.191882i
$446$	−7.33573e7	−	4.16030e8i	−0.0391536	−	0.222051i
$447$	−3.17605e8	−	1.80123e9i	−0.168194	−	0.953876i
$448$	−9.33759e7	+	1.61732e8i	−0.0490639	+	0.0849811i
$449$	−1.63063e9	−	2.82433e9i	−0.850145	−	1.47249i	−0.881077	−	0.472973i	$-0.843181\pi$
$449$	−1.63063e9	−	2.82433e9i	−0.850145	−	1.47249i	0.0309320	−	0.999521i	$-0.490152\pi$
$450$	3.74792e8	−	3.14488e8i	0.193886	−	0.162690i
$451$	3.16816e9	−	1.15312e9i	1.62626	−	0.591909i
$452$	−8.07393e7	−	2.93867e7i	−0.0411245	−	0.0149681i
$453$	8.89950e8	+	7.46757e8i	0.449802	+	0.377429i
$454$	1.80978e8	−	1.02637e9i	0.0907672	−	0.514767i
$455$	1.65848e8			0.0825412
$456$	4.65426e8	+	3.22729e8i	0.229865	+	0.159390i
$457$	−3.54056e9			−1.73526			−0.867631	−	0.497209i	$-0.834358\pi$
$457$	−3.54056e9			−1.73526			−0.867631	+	0.497209i	$0.834358\pi$
$458$	2.61890e8	−	1.48525e9i	0.127376	−	0.722387i
$459$	−1.57011e8	−	1.31748e8i	−0.0757856	−	0.0635917i
$460$	−1.60814e8	−	5.85315e7i	−0.0770320	−	0.0280374i
$461$	2.18041e9	−	7.93604e8i	1.03654	−	0.377268i	0.232970	−	0.972484i	$-0.425156\pi$
$461$	2.18041e9	−	7.93604e8i	1.03654	−	0.377268i	0.803566	+	0.595215i	$0.202933\pi$
$462$	−1.17643e9	+	9.87140e8i	−0.555033	+	0.465728i
$463$	−1.12541e9	−	1.94927e9i	−0.526960	−	0.912721i	−0.999506	−	0.0314155i	$-0.989998\pi$
$463$	−1.12541e9	−	1.94927e9i	−0.526960	−	0.912721i	0.472547	−	0.881306i	$-0.343335\pi$
$464$	1.69434e8	−	2.93468e8i	0.0787384	−	0.136379i
$465$	−1.02748e8	−	5.82713e8i	−0.0473902	−	0.268763i
$466$	3.49291e8	+	1.98093e9i	0.159896	+	0.906812i
$467$	−3.31017e8	+	5.73338e8i	−0.150398	+	0.260496i	−0.931374	−	0.364065i	$-0.881389\pi$
$467$	−3.31017e8	+	5.73338e8i	−0.150398	+	0.260496i	0.780976	+	0.624561i	$0.214722\pi$
$468$	1.05040e8	+	1.81935e8i	0.0473690	+	0.0820455i
$469$	−1.91670e9	+	1.60830e9i	−0.857926	+	0.719886i
$470$	−6.60895e7	+	2.40546e7i	−0.0293623	+	0.0106870i
$471$	1.85982e9	+	6.76920e8i	0.820159	+	0.298513i
$472$	−3.19824e8	−	2.68364e8i	−0.139996	−	0.117470i
$473$	−3.38398e8	+	1.91915e9i	−0.147033	+	0.833863i
$474$	1.46416e9			0.631489
$475$	2.16158e9	+	5.68599e8i	0.925432	+	0.243432i
$476$	8.40498e7			0.0357201
$477$	7.26304e7	−	4.11908e8i	0.0306411	−	0.173774i
$478$	−9.80973e8	−	8.23134e8i	−0.410827	−	0.344725i
$479$	2.56814e9	+	9.34727e8i	1.06769	+	0.388607i	0.815312	−	0.579022i	$-0.196566\pi$
$479$	2.56814e9	+	9.34727e8i	1.06769	+	0.388607i	0.252377	+	0.967629i	$0.418788\pi$
$480$	−6.60988e7	+	2.40580e7i	−0.0272803	+	0.00992922i
$481$	5.22059e8	−	4.38059e8i	0.213900	−	0.179484i
$482$	−4.48387e8	−	7.76630e8i	−0.182385	−	0.315900i
$483$	−6.07408e8	+	1.05206e9i	−0.245282	+	0.424841i
$484$	3.72895e8	+	2.11479e9i	0.149495	+	0.847830i
$485$	−8.39146e7	−	4.75903e8i	−0.0333996	−	0.189419i
$486$	−6.28603e8	+	1.08877e9i	−0.248399	+	0.430239i
$487$	−1.35390e9	−	2.34502e9i	−0.531171	−	0.920014i	−0.999338	−	0.0363747i	$-0.988419\pi$
$487$	−1.35390e9	−	2.34502e9i	−0.531171	−	0.920014i	0.468168	−	0.883640i	$-0.344914\pi$
$488$	−1.91218e8	+	1.60451e8i	−0.0744832	+	0.0624988i
$489$	4.54212e8	−	1.65320e8i	0.175662	−	0.0639357i
$490$	1.37837e8	+	5.01684e7i	0.0529271	+	0.0192639i
$491$	2.08473e9	+	1.74930e9i	0.794813	+	0.666927i	0.946932	−	0.321435i	$-0.104165\pi$
$491$	2.08473e9	+	1.74930e9i	0.794813	+	0.666927i	−0.152119	+	0.988362i	$0.548610\pi$
$492$	1.90353e8	−	1.07955e9i	0.0720580	−	0.408661i
$493$	−1.52511e8			−0.0573241
$494$	−4.01611e8	+	8.71657e8i	−0.149886	+	0.325313i
$495$	3.45663e8			0.128096
$496$	−1.96054e8	+	1.11188e9i	−0.0721423	+	0.409139i
$497$	−2.83082e8	−	2.37534e8i	−0.103434	−	0.0867918i
$498$	1.05182e9	+	3.82830e8i	0.381626	+	0.138900i
$499$	2.56929e9	−	9.35145e8i	0.925681	−	0.336920i	0.165185	−	0.986263i	$-0.447178\pi$
$499$	2.56929e9	−	9.35145e8i	0.925681	−	0.336920i	0.760496	+	0.649342i	$0.224956\pi$
$500$	−4.34871e8	+	3.64901e8i	−0.155584	+	0.130551i
$501$	1.38599e9	+	2.40060e9i	0.492410	+	0.852879i
$502$	1.42815e9	−	2.47363e9i	0.503862	−	0.872715i
$503$	−1.86327e8	−	1.05671e9i	−0.0652811	−	0.370227i	−0.999894	−	0.0145609i	$-0.995365\pi$
$503$	−1.86327e8	−	1.05671e9i	−0.0652811	−	0.370227i	0.934613	−	0.355667i	$-0.115746\pi$
$504$	−5.18143e7	−	2.93853e8i	−0.0180278	−	0.102241i
$505$	−2.50882e8	+	4.34541e8i	−0.0866863	+	0.150145i
$506$	1.34263e9	+	2.32550e9i	0.460712	+	0.797977i
$507$	−1.32215e9	+	1.10941e9i	−0.450559	+	0.378064i
$508$	−2.15865e9	+	7.85683e8i	−0.730564	+	0.265904i
$509$	−4.80624e9	−	1.74933e9i	−1.61545	−	0.587976i	−0.632943	−	0.774199i	$-0.718153\pi$
$509$	−4.80624e9	−	1.74933e9i	−1.61545	−	0.587976i	−0.982508	+	0.186223i	$0.940375\pi$
$510$	2.42512e7	+	2.03492e7i	0.00809539	+	0.00679284i
$511$	−5.18453e8	+	2.94029e9i	−0.171884	+	0.974804i
$512$	1.34218e8			0.0441942
$513$	−3.31016e9	+	3.04881e8i	−1.08252	+	0.0997057i
$514$	7.74295e8			0.251499
$515$	−1.84052e8	+	1.04381e9i	−0.0593767	+	0.336742i
$516$	4.85378e8	+	4.07280e8i	0.155527	+	0.130503i
$517$	1.03701e9	+	3.77439e8i	0.330038	+	0.120124i
$518$	−9.09590e8	+	3.31064e8i	−0.287536	+	0.104654i
$519$	−1.52893e9	+	1.28292e9i	−0.480067	+	0.402824i
$520$	−5.95972e7	−	1.03225e8i	−0.0185872	−	0.0321940i
$521$	−1.47074e9	+	2.54740e9i	−0.455622	+	0.789160i	−0.998724	−	0.0505065i	$-0.983916\pi$
$521$	−1.47074e9	+	2.54740e9i	−0.455622	+	0.789160i	0.543102	+	0.839667i	$0.317250\pi$
$522$	9.40187e7	+	5.33206e8i	0.0289313	+	0.164077i
$523$	2.37183e8	+	1.34513e9i	0.0724983	+	0.411159i	0.999361	+	0.0357568i	$0.0113842\pi$
$523$	2.37183e8	+	1.34513e9i	0.0724983	+	0.411159i	−0.926862	+	0.375402i	$0.877505\pi$
$524$	3.16456e8	−	5.48117e8i	0.0960845	−	0.166423i
$525$	9.85259e8	+	1.70652e9i	0.297162	+	0.514699i
$526$	2.93030e9	−	2.45881e9i	0.877934	−	0.736674i
$527$	4.77488e8	−	1.73792e8i	0.142110	−	0.0517239i
$528$	1.03715e9	+	3.77492e8i	0.306636	+	0.111606i
$529$	−9.81054e8	−	8.23202e8i	−0.288136	−	0.241775i
$530$	−4.12088e7	+	2.33707e8i	−0.0120233	+	0.0681876i
$531$	6.67070e8			0.193348
$532$	9.59466e8	−	9.68294e8i	0.276273	−	0.278815i
$533$	1.85754e9			0.531365
$534$	−3.64880e8	+	2.06934e9i	−0.103695	+	0.588081i
$535$	−9.37156e8	−	7.86367e8i	−0.264590	−	0.222017i
$536$	1.68979e9	+	6.15032e8i	0.473974	+	0.172513i
$537$	−3.57423e9	+	1.30091e9i	−0.996029	+	0.362525i
$538$	8.15133e8	−	6.83978e8i	0.225679	−	0.189367i
$539$	−1.15079e9	−	1.99323e9i	−0.316546	−	0.548274i
$540$	2.06424e8	−	3.57537e8i	0.0564134	−	0.0977109i
$541$	8.04608e8	+	4.56316e9i	0.218471	+	1.23901i	0.874781	+	0.484519i	$0.161005\pi$
$541$	8.04608e8	+	4.56316e9i	0.218471	+	1.23901i	−0.656310	+	0.754492i	$0.727884\pi$
$542$	−5.54817e8	−	3.14652e9i	−0.149676	−	0.848854i
$543$	9.92091e8	−	1.71835e9i	0.265921	−	0.460588i
$544$	−3.02031e7	−	5.23133e7i	−0.00804369	−	0.0139321i
$545$	5.00981e8	−	4.20373e8i	0.132566	−	0.111236i
$546$	−7.95086e8	+	2.89387e8i	−0.209045	+	0.0760861i
$547$	1.72799e9	+	6.28937e8i	0.451425	+	0.164305i	0.557720	−	0.830029i	$-0.311676\pi$
$547$	1.72799e9	+	6.28937e8i	0.451425	+	0.164305i	−0.106294	+	0.994335i	$0.533899\pi$
$548$	1.33520e9	+	1.12037e9i	0.346589	+	0.290823i
$549$	6.92561e7	−	3.92771e8i	0.0178630	−	0.101306i
$550$	4.35569e9			1.11632
$551$	−1.74098e9	+	1.75700e9i	−0.443368	+	0.447447i
$552$	8.73082e8			0.220937
$553$	6.11931e8	−	3.47043e9i	0.153874	−	0.872662i
$554$	−2.18134e9	−	1.83036e9i	−0.545054	−	0.457354i
$555$	−3.42601e8	−	1.24697e8i	−0.0850674	−	0.0309620i
$556$	−3.17560e9	+	1.15582e9i	−0.783544	+	0.285187i
$557$	4.53585e8	−	3.80603e8i	0.111216	−	0.0933210i	−0.585484	−	0.810684i	$-0.699095\pi$
$557$	4.53585e8	−	3.80603e8i	0.111216	−	0.0933210i	0.696700	+	0.717363i	$0.254651\pi$
$558$	−9.01965e8	−	1.56225e9i	−0.219771	−	0.380654i
$559$	−5.36839e8	+	9.29832e8i	−0.129988	+	0.225145i
$560$	2.93982e7	+	1.66725e8i	0.00707396	+	0.0401184i
$561$	−8.62578e7	−	4.89192e8i	−0.0206266	−	0.116979i
$562$	2.23718e9	−	3.87491e9i	0.531647	−	0.920840i
$563$	−1.00122e9	−	1.73417e9i	−0.236456	−	0.409554i	0.723239	−	0.690598i	$-0.242653\pi$
$563$	−1.00122e9	−	1.73417e9i	−0.236456	−	0.409554i	−0.959695	+	0.281044i	$0.909319\pi$
$564$	2.74864e8	−	2.30638e8i	0.0645121	−	0.0541321i
$565$	−7.31931e7	+	2.66401e7i	−0.0170726	+	0.00621393i
$566$	2.86341e9	+	1.04219e9i	0.663782	+	0.241597i
$567$	−1.26864e9	−	1.06451e9i	−0.292279	−	0.245251i
$568$	−4.61184e7	+	2.61550e8i	−0.0105598	+	0.0598875i
$569$	−3.70253e9			−0.842569			−0.421285	−	0.906928i	$-0.638421\pi$
$569$	−3.70253e9			−0.842569			−0.421285	+	0.906928i	$0.638421\pi$
$570$	5.11271e8	−	4.70905e7i	0.115635	−	0.0106505i
$571$	3.45950e9			0.777655			0.388827	−	0.921311i	$-0.372880\pi$
$571$	3.45950e9			0.777655			0.388827	+	0.921311i	$0.372880\pi$
$572$	−3.24769e8	+	1.84186e9i	−0.0725585	+	0.411500i
$573$	−1.73533e9	−	1.45611e9i	−0.385337	−	0.323336i
$574$	−2.47924e9	−	9.02369e8i	−0.547176	−	0.199156i
$575$	3.23773e9	−	1.17844e9i	0.710238	−	0.258505i
$576$	−1.64277e8	+	1.37845e8i	−0.0358178	+	0.0300547i
$577$	−1.91958e9	−	3.32480e9i	−0.415997	−	0.720527i	0.579536	−	0.814947i	$-0.303234\pi$
$577$	−1.91958e9	−	3.32480e9i	−0.415997	−	0.720527i	−0.995533	+	0.0944193i	$0.969901\pi$
$578$	1.62776e9	−	2.81937e9i	0.350625	−	0.607301i
$579$	−2.95017e8	−	1.67313e9i	−0.0631644	−	0.358223i
$580$	−5.33440e7	−	3.02529e8i	−0.0113524	−	0.0643826i
$581$	1.34700e9	−	2.33307e9i	0.284938	−	0.493527i
$582$	1.23269e9	+	2.13509e9i	0.259194	+	0.448936i
$583$	2.85248e9	−	2.39351e9i	0.596187	−	0.500260i
$584$	2.01637e9	−	7.33898e8i	0.418914	−	0.152472i
$585$	1.78960e8	+	6.51361e7i	0.0369581	+	0.0134517i
$586$	−2.40059e9	−	2.01433e9i	−0.492806	−	0.413514i
$587$	−9.60934e8	+	5.44973e9i	−0.196092	+	1.11209i	0.714763	+	0.699367i	$0.246535\pi$
$587$	−9.60934e8	+	5.44973e9i	−0.196092	+	1.11209i	−0.910855	+	0.412727i	$0.864576\pi$
$588$	−7.48335e8			−0.151801
$589$	3.44858e9	−	7.48481e9i	0.695404	−	1.50930i
$590$	−3.78480e8			−0.0758683
$591$	4.15088e8	−	2.35408e9i	0.0827150	−	0.469100i
$592$	5.32916e8	+	4.47170e8i	0.105568	+	0.0885822i
$593$	−5.78875e9	−	2.10693e9i	−1.13997	−	0.414915i	−0.298068	−	0.954545i	$-0.596342\pi$
$593$	−5.78875e9	−	2.10693e9i	−1.13997	−	0.414915i	−0.841903	+	0.539629i	$0.818564\pi$
$594$	−6.08731e9	+	2.21560e9i	−1.19172	+	0.433749i
$595$	5.83682e7	−	4.89767e7i	0.0113597	−	0.00953192i
$596$	1.58188e9	+	2.73990e9i	0.306064	+	0.530119i
$597$	−2.91841e9	+	5.05484e9i	−0.561354	+	0.972293i
$598$	2.56905e8	+	1.45698e9i	0.0491269	+	0.278612i
$599$	1.22465e9	+	6.94532e9i	0.232818	+	1.32038i	0.847160	+	0.531338i	$0.178310\pi$
$599$	1.22465e9	+	6.94532e9i	0.232818	+	1.32038i	−0.614342	+	0.789040i	$0.710578\pi$
$600$	7.08101e8	−	1.22647e9i	0.133834	−	0.231807i
$601$	−9.41837e8	−	1.63131e9i	−0.176976	−	0.306532i	0.763867	−	0.645374i	$-0.223298\pi$
$601$	−9.41837e8	−	1.63131e9i	−0.176976	−	0.306532i	−0.940843	+	0.338842i	$0.889965\pi$
$602$	1.16821e9	−	9.80248e8i	0.218240	−	0.183125i
$603$	−2.69989e9	+	9.82679e8i	−0.501459	+	0.182516i
$604$	−1.88836e9	−	6.87307e8i	−0.348703	−	0.126917i
$605$	1.49127e9	+	1.25132e9i	0.273786	+	0.229734i
$606$	4.44516e8	−	2.52098e9i	0.0811397	−	0.460166i
$607$	−5.09136e9			−0.924002			−0.462001	−	0.886879i	$-0.652868\pi$
$607$	−5.09136e9			−0.924002			−0.462001	+	0.886879i	$0.652868\pi$
$608$	−9.47457e8	−	2.49226e8i	−0.170961	−	0.0449708i
$609$	−2.18066e9			−0.391225
$610$	−3.92943e7	+	2.22849e8i	−0.00700931	+	0.0397517i
$611$	4.65764e8	+	3.90823e8i	0.0826079	+	0.0693163i
$612$	9.06946e7	+	3.30101e7i	0.0159938	+	0.00582127i
$613$	9.59606e9	−	3.49268e9i	1.68260	−	0.612417i	0.688939	−	0.724819i	$-0.258077\pi$
$613$	9.59606e9	−	3.49268e9i	1.68260	−	0.612417i	0.993663	+	0.112402i	$0.0358544\pi$
$614$	−5.97358e9	+	5.01243e9i	−1.04147	+	0.873895i
$615$	−4.96873e8	−	8.60609e8i	−0.0861356	−	0.149191i
$616$	1.32822e9	−	2.30054e9i	0.228948	−	0.396549i
$617$	−2.44285e8	−	1.38541e9i	−0.0418695	−	0.237454i	0.956690	−	0.291109i	$-0.0940241\pi$
$617$	−2.44285e8	−	1.38541e9i	−0.0418695	−	0.237454i	−0.998560	+	0.0536547i	$0.982913\pi$
$618$	−9.38984e8	−	5.32524e9i	−0.160029	−	0.907570i
$619$	−2.51174e8	+	4.35047e8i	−0.0425656	+	0.0737257i	−0.886523	−	0.462684i	$-0.846886\pi$
$619$	−2.51174e8	+	4.35047e8i	−0.0425656	+	0.0737257i	0.843958	+	0.536410i	$0.180220\pi$
$620$	5.11753e8	+	8.86383e8i	0.0862362	+	0.149366i
$621$	−3.92547e9	+	3.29386e9i	−0.657766	+	0.551931i
$622$	−5.54005e9	+	2.01641e9i	−0.923097	+	0.335980i
$623$	4.75235e9	+	1.72971e9i	0.787409	+	0.286593i
$624$	4.65829e8	+	3.90877e8i	0.0767504	+	0.0644013i
$625$	9.24835e8	−	5.24500e9i	0.151525	−	0.859340i
$626$	−3.61251e9			−0.588572
$627$	−6.62040e9	−	4.59062e9i	−1.07262	−	0.743764i
$628$	−3.42352e9			−0.551587
$629$	5.43684e7	−	3.08339e8i	0.00871103	−	0.0494027i
$630$	−2.07214e8	−	1.73873e8i	−0.0330162	−	0.0277038i
$631$	7.96339e9	+	2.89844e9i	1.26181	+	0.459262i	0.884377	−	0.466773i	$-0.154584\pi$
$631$	7.96339e9	+	2.89844e9i	1.26181	+	0.459262i	0.377436	+	0.926036i	$0.376806\pi$
$632$	−2.37992e9	+	8.66221e8i	−0.375019	+	0.136496i
$633$	4.70172e9	−	3.94521e9i	0.736790	−	0.618240i
$634$	3.31442e9	+	5.74074e9i	0.516529	+	0.894655i
$635$	−1.04124e9	+	1.80348e9i	−0.161377	+	0.279514i
$636$	−2.10236e8	−	1.19231e9i	−0.0324046	−	0.183776i
$637$	−2.20198e8	−	1.24881e9i	−0.0337541	−	0.191429i
$638$	−2.41009e9	+	4.17440e9i	−0.367419	+	0.636388i
$639$	−2.12172e8	−	3.67492e8i	−0.0321688	−	0.0557180i
$640$	9.32071e7	−	7.82101e7i	0.0140546	−	0.0117932i
$641$	−1.00103e10	+	3.64345e9i	−1.50122	+	0.546398i	−0.956375	−	0.292141i	$-0.905632\pi$
$641$	−1.00103e10	+	3.64345e9i	−1.50122	+	0.546398i	−0.544842	+	0.838539i	$0.683410\pi$
$642$	5.86490e9	+	2.13465e9i	0.874759	+	0.318386i
$643$	−2.61802e9	−	2.19678e9i	−0.388360	−	0.325873i	0.427614	−	0.903962i	$-0.359354\pi$
$643$	−2.61802e9	−	2.19678e9i	−0.388360	−	0.325873i	−0.815974	+	0.578089i	$0.803799\pi$
$644$	3.64895e8	−	2.06942e9i	0.0538353	−	0.305315i
$645$	5.74396e8			0.0842854
$646$	1.16067e8	+	4.25368e8i	0.0169393	+	0.0620800i
$647$	7.59069e9			1.10183			0.550917	−	0.834560i	$-0.314278\pi$
$647$	7.59069e9			1.10183			0.550917	+	0.834560i	$0.314278\pi$
$648$	−2.06680e8	+	1.17214e9i	−0.0298392	+	0.169226i
$649$	4.54931e9	+	3.81732e9i	0.653264	+	0.548154i
$650$	2.25506e9	+	8.20776e8i	0.322079	+	0.117227i
$651$	6.82730e9	−	2.48493e9i	0.969874	−	0.353005i
$652$	−6.40493e8	+	5.37437e8i	−0.0904998	+	0.0759384i
$653$	5.34590e9	+	9.25937e9i	0.751319	+	1.30132i	0.947184	+	0.320692i	$0.103915\pi$
$653$	5.34590e9	+	9.25937e9i	0.751319	+	1.30132i	−0.195864	+	0.980631i	$0.562751\pi$
$654$	−1.66822e9	+	2.88945e9i	−0.233202	+	0.403918i
$655$	−9.96319e7	−	5.65041e8i	−0.0138533	−	0.0785661i
$656$	3.29267e8	+	1.86736e9i	0.0455391	+	0.258265i
$657$	−1.71423e9	+	2.96913e9i	−0.235825	+	0.408460i
$658$	−4.31794e8	−	7.47889e8i	−0.0590862	−	0.102340i
$659$	8.04240e9	−	6.74837e9i	1.09468	−	0.918544i	0.0976224	−	0.995224i	$-0.468876\pi$
$659$	8.04240e9	−	6.74837e9i	1.09468	−	0.918544i	0.997056	+	0.0766795i	$0.0244318\pi$
$660$	9.40216e8	−	3.42211e8i	0.127299	−	0.0463329i
$661$	9.03326e9	+	3.28784e9i	1.21658	+	0.442798i	0.868980	−	0.494847i	$-0.164776\pi$
$661$	9.03326e9	+	3.28784e9i	1.21658	+	0.442798i	0.347596	+	0.937644i	$0.386998\pi$
$662$	3.47638e9	+	2.91703e9i	0.465719	+	0.390785i
$663$	4.75242e7	−	2.69523e8i	0.00633312	−	0.0359169i
$664$	−1.93616e9			−0.256657
$665$	1.02064e8	−	1.23152e9i	0.0134585	−	0.162392i
$666$	−1.11152e9			−0.145801
$667$	−6.62114e8	+	3.75503e9i	−0.0863957	+	0.489975i
$668$	−3.67308e9	−	3.08208e9i	−0.476774	−	0.400061i
$669$	1.83595e9	+	6.68232e8i	0.237067	+	0.0862852i
$670$	1.53185e9	−	5.57549e8i	0.196768	−	0.0716178i
$671$	2.71995e9	−	2.28231e9i	0.347562	−	0.291640i
$672$	−4.31855e8	−	7.47994e8i	−0.0548966	−	0.0950836i
$673$	−5.38866e9	+	9.33344e9i	−0.681441	+	1.18029i	0.293100	+	0.956082i	$0.405313\pi$
$673$	−5.38866e9	+	9.33344e9i	−0.681441	+	1.18029i	−0.974541	+	0.224209i	$0.928020\pi$
$674$	4.34340e8	+	2.46327e9i	0.0546412	+	0.309886i
$675$	1.44337e9	+	8.18577e9i	0.180641	+	1.02446i
$676$	1.49273e9	−	2.58549e9i	0.185853	−	0.321907i
$677$	−1.31949e9	−	2.28542e9i	−0.163435	−	0.283078i	0.772663	−	0.634816i	$-0.218924\pi$
$677$	−1.31949e9	−	2.28542e9i	−0.163435	−	0.283078i	−0.936099	+	0.351738i	$0.885591\pi$
$678$	3.04408e8	−	2.55428e8i	0.0375104	−	0.0314750i
$679$	5.57587e9	−	2.02945e9i	0.683548	−	0.248791i
$680$	−5.14580e7	−	1.87292e7i	−0.00627584	−	0.00228422i
$681$	3.69242e9	+	3.09831e9i	0.448019	+	0.375932i
$682$	2.78875e9	−	1.58158e10i	0.336639	−	1.90917i
$683$	−1.39719e10			−1.67797			−0.838984	−	0.544156i	$-0.816850\pi$
$683$	−1.39719e10			−1.67797			−0.838984	+	0.544156i	$0.816850\pi$
$684$	1.41561e9	−	6.68020e8i	0.169141	−	0.0798166i
$685$	1.58008e9			0.187829
$686$	−1.12778e9	+	6.39598e9i	−0.133380	+	0.756437i
$687$	5.34324e9	+	4.48351e9i	0.628718	+	0.527557i
$688$	−1.02991e9	−	3.74857e8i	−0.120570	−	0.0438839i
$689$	1.92784e9	−	7.01676e8i	0.224545	−	0.0817277i
$690$	6.06310e8	−	5.08754e8i	0.0702623	−	0.0589571i
$691$	−4.97542e8	−	8.61768e8i	−0.0573662	−	0.0993612i	0.835916	−	0.548857i	$-0.184937\pi$
$691$	−4.97542e8	−	8.61768e8i	−0.0573662	−	0.0993612i	−0.893282	+	0.449496i	$0.851604\pi$
$692$	1.72620e9	−	2.98986e9i	0.198025	−	0.342989i
$693$	7.37027e8	+	4.17989e9i	0.0841234	+	0.477088i
$694$	9.73540e8	+	5.52122e9i	0.110559	+	0.627013i
$695$	−1.53177e9	+	2.65311e9i	−0.173080	+	0.299784i
$696$	7.83614e8	+	1.35726e9i	0.0880988	+	0.152592i
$697$	6.53737e8	−	5.48551e8i	0.0731288	−	0.0613623i
$698$	−6.56546e9	+	2.38963e9i	−0.730754	+	0.265973i
$699$	−8.74188e9	−	3.18179e9i	−0.968133	−	0.352372i
$700$	−2.61109e9	−	2.19096e9i	−0.287726	−	0.241431i
$701$	−8.08202e8	+	4.58354e9i	−0.0886149	+	0.502560i	0.907903	+	0.419180i	$0.137683\pi$
$701$	−8.08202e8	+	4.58354e9i	−0.0886149	+	0.502560i	−0.996518	+	0.0833797i	$0.973429\pi$
$702$	−3.56908e9			−0.389382
$703$	−2.93157e9	−	4.14618e9i	−0.318241	−	0.450095i
$704$	−1.90917e9			−0.206224
$705$	5.64832e7	−	3.20332e8i	0.00607097	−	0.0344302i
$706$	−1.83953e9	−	1.54355e9i	−0.196739	−	0.165084i
$707$	−5.78956e9	−	2.10723e9i	−0.616138	−	0.224256i
$708$	1.81445e9	−	6.60407e8i	0.192145	−	0.0699351i
$709$	4.81767e9	−	4.04251e9i	0.507663	−	0.425980i	−0.352643	−	0.935758i	$-0.614717\pi$
$709$	4.81767e9	−	4.04251e9i	0.507663	−	0.425980i	0.860306	+	0.509778i	$0.170273\pi$
$710$	1.20381e8	+	2.08507e8i	0.0126228	+	0.0218633i
$711$	2.02331e9	−	3.50447e9i	0.211114	−	0.365661i
$712$	−6.31158e8	−	3.57947e9i	−0.0655327	−	0.371654i
$713$	−2.20601e9	−	1.25109e10i	−0.227927	−	1.29264i
$714$	−1.94361e8	+	3.36643e8i	−0.0199832	+	0.0346120i
$715$	8.47734e8	+	1.46832e9i	0.0867338	+	0.150227i
$716$	5.04008e9	−	4.22913e9i	0.513147	−	0.430582i
$717$	5.56534e9	−	2.02562e9i	0.563864	−	0.205230i
$718$	1.18711e10	+	4.32072e9i	1.19689	+	0.435633i
$719$	−6.40692e9	−	5.37604e9i	−0.642833	−	0.539401i	0.262054	−	0.965053i	$-0.415600\pi$
$719$	−6.40692e9	−	5.37604e9i	−0.642833	−	0.539401i	−0.904887	+	0.425653i	$0.860045\pi$
$720$	−3.37582e7	+	1.91452e8i	−0.00337067	+	0.0191160i
$721$	−1.30146e10			−1.29317
$722$	6.22541e9	+	3.51862e9i	0.615585	+	0.347930i
$723$	4.14750e9			0.408133
$724$	−5.95990e8	+	3.38003e9i	−0.0583652	+	0.331006i
$725$	4.73791e9	+	3.97558e9i	0.461746	+	0.387451i
$726$	−9.33263e9	−	3.39680e9i	−0.905161	−	0.329452i
$727$	−7.96244e9	+	2.89809e9i	−0.768556	+	0.279732i	−0.696393	−	0.717661i	$-0.745213\pi$
$727$	−7.96244e9	+	2.89809e9i	−0.768556	+	0.279732i	−0.0721640	+	0.997393i	$0.522990\pi$
$728$	1.12116e9	−	9.40769e8i	0.107698	−	0.0903698i
$729$	−5.44924e9	−	9.43836e9i	−0.520942	−	0.902298i
$730$	9.72611e8	−	1.68461e9i	0.0925357	−	0.160277i
$731$	8.56555e7	+	4.85777e8i	0.00811044	+	0.0459966i
$732$	−2.00469e8	−	1.13691e9i	−0.0188911	−	0.107137i
$733$	−8.43431e9	+	1.46086e10i	−0.791016	+	1.37008i	0.134322	+	0.990938i	$0.457114\pi$
$733$	−8.43431e9	+	1.46086e10i	−0.791016	+	1.37008i	−0.925338	+	0.379143i	$0.876219\pi$
$734$	7.56786e9	+	1.31079e10i	0.706378	+	1.22348i
$735$	−5.19679e8	+	4.36063e8i	−0.0482758	+	0.0405082i
$736$	−1.41915e9	+	5.16529e8i	−0.131207	+	0.0477553i
$737$	−2.40362e10	−	8.74846e9i	−2.21172	−	0.804999i
$738$	−2.32084e9	−	1.94742e9i	−0.212544	−	0.178345i
$739$	3.11152e7	−	1.76463e8i	0.00283607	−	0.0160842i	−0.983357	−	0.181684i	$-0.941845\pi$
$739$	3.11152e7	−	1.76463e8i	0.00283607	−	0.0160842i	0.986193	+	0.165600i	$0.0529562\pi$
$740$	6.30653e8			0.0572110
$741$	−2.56253e9	−	3.62423e9i	−0.231369	−	0.327229i
$742$	−2.91393e9			−0.261858
$743$	9.69491e8	−	5.49826e9i	0.0867127	−	0.491772i	−0.910261	−	0.414035i	$-0.864119\pi$
$743$	9.69491e8	−	5.49826e9i	0.0867127	−	0.491772i	0.996974	−	0.0777377i	$-0.0247697\pi$
$744$	−4.00002e9	−	3.35641e9i	−0.356087	−	0.298793i
$745$	2.69510e9	+	9.80938e8i	0.238797	+	0.0869149i
$746$	−2.81945e9	+	1.02620e9i	−0.248644	+	0.0904991i
$747$	2.36979e9	−	1.98849e9i	0.208012	−	0.174543i
$748$	4.29621e8	+	7.44125e8i	0.0375344	+	0.0650116i
$749$	7.51082e9	−	1.30091e10i	0.653132	−	1.13126i
$750$	−4.55911e8	−	2.58560e9i	−0.0394607	−	0.223793i
$751$	3.65296e8	+	2.07169e9i	0.0314706	+	0.178479i	0.996491	−	0.0836945i	$-0.0266720\pi$
$751$	3.65296e8	+	2.07169e9i	0.0314706	+	0.178479i	−0.965021	+	0.262173i	$0.915561\pi$
$752$	−3.10328e8	+	5.37505e8i	−0.0266109	+	0.0460914i
$753$	6.60507e9	+	1.14403e10i	0.563761	+	0.976462i
$754$	−2.03439e9	+	1.70706e9i	−0.172836	+	0.145027i
$755$	−1.71187e9	+	6.23069e8i	−0.144762	+	0.0526892i
$756$	4.76361e9	+	1.73381e9i	0.400968	+	0.145940i
$757$	4.88553e9	+	4.09944e9i	0.409332	+	0.343470i	0.824088	−	0.566462i	$-0.191688\pi$
$757$	4.88553e9	+	4.09944e9i	0.409332	+	0.343470i	−0.414755	+	0.909933i	$0.636133\pi$
$758$	1.49843e9	−	8.49802e9i	0.124967	−	0.708721i
$759$	−1.24191e10			−1.03096
$760$	−8.03185e8	+	3.79019e8i	−0.0663694	+	0.0313194i
$761$	1.79822e10			1.47910			0.739549	−	0.673103i	$-0.235039\pi$
$761$	1.79822e10			1.47910			0.739549	+	0.673103i	$0.235039\pi$
$762$	1.84488e9	−	1.04628e10i	0.151052	−	0.856657i
$763$	6.15150e9	+	5.16172e9i	0.501355	+	0.420687i
$764$	3.68214e9	+	1.34019e9i	0.298727	+	0.108728i
$765$	8.22180e7	−	2.99249e7i	0.00663975	−	0.00241667i
$766$	6.28521e9	−	5.27392e9i	0.505265	−	0.423967i
$767$	1.63598e9	+	2.83360e9i	0.130916	+	0.226754i
$768$	−3.10372e8	+	5.37580e8i	−0.0247240	+	0.0428232i
$769$	−5.60386e8	−	3.17811e9i	−0.0444370	−	0.252015i	0.954495	−	0.298228i	$-0.0963957\pi$
$769$	−5.60386e8	−	3.17811e9i	−0.0444370	−	0.252015i	−0.998932	+	0.0462134i	$0.985285\pi$
$770$	−4.18172e8	−	2.37157e9i	−0.0330093	−	0.187205i
$771$	−1.79052e9	+	3.10127e9i	−0.140698	+	0.243697i
$772$	1.46938e9	+	2.54504e9i	0.114941	+	0.199083i
$773$	1.18884e10	−	9.97559e9i	0.925757	−	0.776802i	−0.0492940	−	0.998784i	$-0.515697\pi$
$773$	1.18884e10	−	9.97559e9i	0.925757	−	0.776802i	0.975051	+	0.221982i	$0.0712527\pi$
$774$	1.64556e9	−	5.98934e8i	0.127562	−	0.0464286i
$775$	−1.93639e10	−	7.04790e9i	−1.49430	−	0.543881i
$776$	−3.26683e9	−	2.74119e9i	−0.250963	−	0.210583i
$777$	7.77379e8	−	4.40873e9i	0.0594510	−	0.337163i
$778$	8.02553e9			0.611006
$779$	1.14314e9	−	1.37933e10i	0.0866399	−	1.04541i
$780$	5.51262e8			0.0415937
$781$	6.56006e8	−	3.72039e9i	0.0492753	−	0.279454i
$782$	5.20677e8	+	4.36900e8i	0.0389354	+	0.0326707i
$783$	−8.64373e9	−	3.14606e9i	−0.643480	−	0.234207i
$784$	1.21638e9	−	4.42726e8i	0.0901495	−	0.0328117i
$785$	−2.37745e9	+	1.99492e9i	−0.175416	+	0.147191i
$786$	1.46358e9	+	2.53499e9i	0.107507	+	0.186207i
$787$	−2.65515e9	+	4.59885e9i	−0.194168	+	0.336308i	−0.946627	−	0.322330i	$-0.895534\pi$
$787$	−2.65515e9	+	4.59885e9i	−0.194168	+	0.336308i	0.752460	+	0.658638i	$0.228867\pi$
$788$	7.18006e8	+	4.07201e9i	0.0522741	+	0.296461i
$789$	3.07207e9	+	1.74226e10i	0.222670	+	1.26282i
$790$	−1.14798e9	+	1.98835e9i	−0.0828396	+	0.143482i
$791$	−4.78205e8	−	8.28276e8i	−0.0343555	−	0.0595055i
$792$	2.33675e9	−	1.96076e9i	0.167137	−	0.140245i
$793$	1.83827e9	−	6.69077e8i	0.130904	−	0.0476453i
$794$	8.90064e9	+	3.23957e9i	0.631029	+	0.229676i
$795$	−8.40768e8	−	7.05488e8i	−0.0593460	−	0.0497972i
$796$	1.75321e9	−	9.94296e9i	0.123208	−	0.698747i
$797$	−1.44802e10			−1.01314			−0.506571	−	0.862198i	$-0.669087\pi$
$797$	−1.44802e10			−1.01314			−0.506571	+	0.862198i	$0.669087\pi$
$798$	1.65957e9	+	6.08207e9i	0.115607	+	0.423683i
$799$	2.79334e8			0.0193736
$800$	−4.25386e8	+	2.41248e9i	−0.0293743	+	0.166590i
$801$	4.44873e9	+	3.73293e9i	0.305860	+	0.256647i
$802$	−5.13831e9	−	1.87019e9i	−0.351731	−	0.128020i
$803$	−2.86816e10	+	1.04393e10i	−1.95479	+	0.711484i
$804$	−6.37092e9	+	5.34584e9i	−0.432321	+	0.362760i
$805$	−9.52474e8	−	1.64973e9i	−0.0643528	−	0.111462i
$806$	4.42411e9	−	7.66278e9i	0.297614	−	0.515482i
$807$	8.54570e8	+	4.84651e9i	0.0572387	+	0.324617i
$808$	7.68909e8	+	4.36070e9i	0.0512785	+	0.290815i
$809$	9.38024e9	−	1.62471e10i	0.622865	−	1.07883i	−0.366084	−	0.930582i	$-0.619302\pi$
$809$	9.38024e9	−	1.62471e10i	0.622865	−	1.07883i	0.988950	−	0.148253i	$-0.0473649\pi$
$810$	5.39491e8	+	9.34426e8i	0.0356687	+	0.0617799i
$811$	−1.34528e9	+	1.12883e9i	−0.0885607	+	0.0743113i	−0.685993	−	0.727608i	$-0.740632\pi$
$811$	−1.34528e9	+	1.12883e9i	−0.0885607	+	0.0743113i	0.597432	+	0.801919i	$0.296188\pi$
$812$	3.54455e9	−	1.29011e9i	0.232335	−	0.0845630i
$813$	1.38857e10	+	5.05398e9i	0.906255	+	0.329850i
$814$	−7.58041e9	−	6.36072e9i	−0.492615	−	0.413353i
$815$	−1.31618e8	+	7.46444e8i	−0.00851656	+	0.0482998i
$816$	2.79373e8			0.0179998
$817$	6.57418e9	+	4.55857e9i	0.421759	+	0.292450i
$818$	−3.59881e9			−0.229891
$819$	−4.06069e8	+	2.30293e9i	−0.0258289	+	0.146483i
$820$	1.31679e9	+	1.10492e9i	0.0834004	+	0.0699813i
$821$	−2.23135e10	−	8.12143e9i	−1.40723	−	0.512191i	−0.476916	−	0.878949i	$-0.658245\pi$
$821$	−2.23135e10	−	8.12143e9i	−1.40723	−	0.512191i	−0.930316	+	0.366758i	$0.880468\pi$
$822$	−7.57498e9	+	2.75707e9i	−0.475697	+	0.173139i
$823$	1.95147e10	−	1.63748e10i	1.22029	−	1.02394i	0.221477	−	0.975165i	$-0.428912\pi$
$823$	1.95147e10	−	1.63748e10i	1.22029	−	1.02394i	0.998810	−	0.0487770i	$-0.0155324\pi$
$824$	4.67677e9	+	8.10039e9i	0.291206	+	0.504384i
$825$	−1.00723e10	+	1.74458e10i	−0.624511	+	1.08169i
$826$	−8.06998e8	−	4.57671e9i	−0.0498244	−	0.282568i
$827$	2.41240e9	+	1.36814e10i	0.148313	+	0.841127i	0.964647	+	0.263546i	$0.0848921\pi$
$827$	2.41240e9	+	1.36814e10i	0.148313	+	0.841127i	−0.816333	+	0.577581i	$0.803997\pi$
$828$	1.20650e9	−	2.08972e9i	0.0738619	−	0.127933i
$829$	1.17201e10	+	2.02997e10i	0.714478	+	1.23751i	0.963161	+	0.268927i	$0.0866690\pi$
$829$	1.17201e10	+	2.02997e10i	0.714478	+	1.23751i	−0.248683	+	0.968585i	$0.579998\pi$
$830$	−1.34456e9	+	1.12822e9i	−0.0816221	+	0.0684891i
$831$	1.23754e10	−	4.50426e9i	0.748091	−	0.272283i
$832$	−9.88431e8	−	3.59759e8i	−0.0594997	−	0.0216561i
$833$	−4.46282e8	−	3.74475e8i	−0.0267517	−	0.0224474i
$834$	2.71402e9	−	1.53919e10i	0.162006	−	0.918782i
$835$	−4.34672e9			−0.258380
$836$	1.34770e10	+	3.54509e9i	0.797758	+	0.209848i
$837$	3.06472e10			1.80656
$838$	−2.33688e9	+	1.32531e10i	−0.137177	+	0.777972i
$839$	2.01406e9	+	1.69000e9i	0.117735	+	0.0987913i	0.699754	−	0.714384i	$-0.253293\pi$
$839$	2.01406e9	+	1.69000e9i	0.117735	+	0.0987913i	−0.582019	+	0.813175i	$0.697737\pi$
$840$	−7.35764e8	−	2.67796e8i	−0.0428313	−	0.0155893i
$841$	9.77789e9	−	3.55886e9i	0.566838	−	0.206312i
$842$	4.58511e9	−	3.84736e9i	0.264702	−	0.222111i
$843$	1.03467e10	+	1.79211e10i	0.594849	+	1.03031i
$844$	−5.30836e9	+	9.19435e9i	−0.303922	+	0.526408i
$845$	−4.69968e8	−	2.66532e9i	−0.0267960	−	0.151968i
$846$	−1.72201e8	−	9.76601e8i	−0.00977777	−	0.0554525i
$847$	−1.19517e10	+	2.07010e10i	−0.675832	+	1.17058i
$848$	1.04711e9	+	1.81366e9i	0.0589670	+	0.102134i
$849$	−1.07958e10	+	9.05873e9i	−0.605448	+	0.508031i
$850$	1.03602e9	−	3.77082e8i	0.0578634	−	0.0210606i
$851$	−7.35569e9	−	2.67725e9i	−0.409138	−	0.148914i
$852$	−9.40936e8	−	7.89539e8i	−0.0521221	−	0.0437356i
$853$	−3.48259e9	+	1.97508e10i	−0.192124	+	1.08959i	0.724332	+	0.689452i	$0.242148\pi$
$853$	−3.48259e9	+	1.97508e10i	−0.192124	+	1.08959i	−0.916455	+	0.400137i	$0.868963\pi$
$854$	−2.77855e9			−0.152657
$855$	5.93806e8	−	1.28880e9i	0.0324910	−	0.0705185i
$856$	−1.07960e10			−0.588307
$857$	−1.85310e8	+	1.05095e9i	−0.0100570	+	0.0570358i	−0.989423	−	0.145057i	$-0.953663\pi$
$857$	−1.85310e8	+	1.05095e9i	−0.0100570	+	0.0570358i	0.979366	+	0.202093i	$0.0647744\pi$
$858$	−6.62614e9	−	5.55999e9i	−0.358142	−	0.300517i
$859$	−1.13052e10	−	4.11474e9i	−0.608556	−	0.221496i	0.0193153	−	0.999813i	$-0.493851\pi$
$859$	−1.13052e10	−	4.11474e9i	−0.608556	−	0.221496i	−0.627871	+	0.778317i	$0.716074\pi$
$860$	−9.33651e8	+	3.39821e8i	−0.0500541	+	0.0182182i
$861$	9.34736e9	−	7.84337e9i	0.499089	−	0.418785i
$862$	7.46675e9	+	1.29328e10i	0.397060	+	0.687728i
$863$	−9.06445e9	+	1.57001e10i	−0.480069	+	0.831504i	−0.999739	−	0.0228631i	$-0.992722\pi$
$863$	−9.06445e9	+	1.57001e10i	−0.480069	+	0.831504i	0.519669	+	0.854367i	$0.326055\pi$
$864$	−6.32653e8	−	3.58795e9i	−0.0333709	−	0.189256i
$865$	−5.43471e8	−	3.08218e9i	−0.0285509	−	0.161920i
$866$	−1.05689e10	+	1.83059e10i	−0.552991	+	0.957809i
$867$	7.52824e9	+	1.30393e10i	0.392307	+	0.679496i
$868$	−9.62730e9	+	8.07826e9i	−0.499672	+	0.419275i
$869$	3.38530e10	−	1.23215e10i	1.74996	−	0.636933i
$870$	1.33507e9	+	4.85925e8i	0.0687363	+	0.0250180i
$871$	−1.07957e10	−	9.05866e9i	−0.553588	−	0.464516i
$872$	1.00217e9	−	5.68360e9i	0.0511840	−	0.290279i
$873$	6.81375e9			0.346606
$874$	1.09771e10	−	1.01104e9i	0.556155	−	0.0512245i
$875$	−6.31905e9			−0.318878
$876$	−1.72328e9	+	9.77323e9i	−0.0866149	+	0.491217i
$877$	9.46605e9	+	7.94296e9i	0.473882	+	0.397634i	0.848208	−	0.529663i	$-0.177682\pi$
$877$	9.46605e9	+	7.94296e9i	0.473882	+	0.397634i	−0.374326	+	0.927297i	$0.622126\pi$
$878$	8.58863e9	+	3.12600e9i	0.428246	+	0.155869i
$879$	1.36192e10	−	4.95699e9i	0.676381	−	0.246182i
$880$	−1.32582e9	+	1.11249e9i	−0.0655834	+	0.0550310i
$881$	−9.70923e9	−	1.68169e10i	−0.478376	−	0.828571i	0.521317	−	0.853363i	$-0.325441\pi$
$881$	−9.70923e9	−	1.68169e10i	−0.478376	−	0.828571i	−0.999693	+	0.0247920i	$0.992108\pi$
$882$	−1.03411e9	+	1.79113e9i	−0.0507490	+	0.0878999i
$883$	−5.84351e9	−	3.31402e10i	−0.285635	−	1.61992i	−0.703009	−	0.711181i	$-0.748161\pi$
$883$	−5.84351e9	−	3.31402e10i	−0.285635	−	1.61992i	0.417374	−	0.908735i	$-0.362950\pi$
$884$	8.22058e7	+	4.66212e8i	0.00400239	+	0.0226987i
$885$	8.75216e8	−	1.51592e9i	0.0424437	−	0.0735147i
$886$	−1.02250e10	−	1.77102e10i	−0.493907	−	0.855472i
$887$	−3.12148e9	+	2.61923e9i	−0.150185	+	0.126021i	−0.714785	−	0.699345i	$-0.753475\pi$
$887$	−3.12148e9	+	2.61923e9i	−0.150185	+	0.126021i	0.564599	+	0.825365i	$0.309031\pi$
$888$	−3.02338e9	+	1.10042e9i	−0.144893	+	0.0527368i
$889$	−2.40285e10	−	8.74565e9i	−1.14702	−	0.417480i
$890$	−2.52410e9	−	2.11797e9i	−0.120017	−	0.100706i
$891$	2.93990e9	−	1.66730e10i	0.139239	−	0.789664i
$892$	−3.37958e9			−0.159436
$893$	3.18872e9	−	3.21806e9i	0.149843	−	0.151222i
$894$	−1.46321e10			−0.684897
$895$	1.03571e9	−	5.87382e9i	0.0482902	−	0.273867i
$896$	1.14448e9	+	9.60334e8i	0.0531534	+	0.0446010i
$897$	−6.42971e9	−	2.34022e9i	−0.297453	−	0.108264i
$898$	−2.45166e10	+	8.92333e9i	−1.12978	+	0.411206i
$899$	1.74690e10	−	1.46583e10i	0.801882	−	0.672858i
$900$	−1.95703e9	−	3.38967e9i	−0.0894845	−	0.154992i
$901$	4.71266e8	−	8.16256e8i	0.0214649	−	0.0371783i
$902$	−4.68362e9	−	2.65621e10i	−0.212500	−	1.20515i
$903$	1.22473e9	+	6.94580e9i	0.0553521	+	0.313917i
$904$	−3.43684e8	+	5.95278e8i	−0.0154728	+	0.0267997i
$905$	1.55569e9	+	2.69454e9i	0.0697677	+	0.120841i
$906$	7.11960e9	−	5.97405e9i	0.318058	−	0.266883i
$907$	−4.13663e9	+	1.50561e9i	−0.184086	+	0.0670018i	−0.432418	−	0.901673i	$-0.642340\pi$
$907$	−4.13663e9	+	1.50561e9i	−0.184086	+	0.0670018i	0.248332	+	0.968675i	$0.420117\pi$
$908$	−7.83484e9	−	2.85165e9i	−0.347320	−	0.126414i
$909$	−5.41967e9	−	4.54764e9i	−0.239331	−	0.200823i
$910$	2.30394e8	−	1.30663e9i	0.0101351	−	0.0574788i
$911$	2.13506e10			0.935612			0.467806	−	0.883831i	$-0.345045\pi$
$911$	2.13506e10			0.935612			0.467806	+	0.883831i	$0.345045\pi$
$912$	3.18917e9	−	3.21851e9i	0.139218	−	0.140499i
$913$	2.75408e10			1.19765
$914$	−4.91849e9	+	2.78942e10i	−0.213069	+	1.20837i
$915$	−8.01707e8	−	6.72712e8i	−0.0345973	−	0.0290306i
$916$	−1.13377e10	−	4.12657e9i	−0.487405	−	0.177401i
$917$	6.62024e9	−	2.40957e9i	0.283518	−	0.103192i
$918$	−1.25609e9	+	1.05399e9i	−0.0535885	+	0.0449661i
$919$	9.90030e9	+	1.71478e10i	0.420769	+	0.728794i	0.996015	−	0.0891869i	$-0.0284269\pi$
$919$	9.90030e9	+	1.71478e10i	0.420769	+	0.728794i	−0.575246	+	0.817981i	$0.695094\pi$
$920$	−6.84539e8	+	1.18566e9i	−0.0289828	+	0.0501997i
$921$	−6.26259e9	−	3.55169e10i	−0.264147	−	1.49805i
$922$	−3.22339e9	−	1.82807e10i	−0.135442	−	0.768131i
$923$	1.04070e9	−	1.80254e9i	0.0435630	−	0.0754534i
$924$	6.14287e9	+	1.06398e10i	0.256165	+	0.443691i
$925$	−9.72661e9	+	8.16160e9i	−0.404078	+	0.339062i
$926$	−1.69206e10	+	6.15861e9i	−0.700291	+	0.254885i
$927$	−1.40435e10	−	5.11142e9i	−0.579024	−	0.210747i
$928$	−2.07670e9	−	1.74256e9i	−0.0853013	−	0.0715763i
$929$	6.66755e9	−	3.78136e10i	0.272842	−	1.54736i	−0.472892	−	0.881121i	$-0.656790\pi$
$929$	6.66755e9	−	3.78136e10i	0.272842	−	1.54736i	0.745734	−	0.666244i	$-0.232099\pi$
$930$	−4.73362e9			−0.192976
$931$	−9.40864e9	+	8.66580e8i	−0.382123	+	0.0351953i
$932$	1.60919e10			0.651105
$933$	4.73479e9	−	2.68523e10i	0.190860	−	1.08242i
$934$	4.05718e9	+	3.40438e9i	0.162933	+	0.136717i
$935$	7.31959e8	+	2.66411e8i	0.0292851	+	0.0106589i
$936$	1.57928e9	−	5.74813e8i	0.0629499	−	0.0229119i
$937$	−1.56307e10	+	1.31157e10i	−0.620712	+	0.520839i	−0.898027	−	0.439940i	$-0.855000\pi$
$937$	−1.56307e10	+	1.31157e10i	−0.620712	+	0.520839i	0.277315	+	0.960779i	$0.410555\pi$
$938$	1.00083e10	+	1.73349e10i	0.395960	+	0.685822i
$939$	8.35376e9	−	1.44691e10i	0.329270	−	0.570313i
$940$	9.77028e7	+	5.54100e8i	0.00383672	+	0.0217591i
$941$	2.33470e9	+	1.32407e10i	0.0913412	+	0.518022i	0.995807	+	0.0914761i	$0.0291585\pi$
$941$	2.33470e9	+	1.32407e10i	0.0913412	+	0.518022i	−0.904466	+	0.426546i	$0.859730\pi$
$942$	7.91672e9	−	1.37122e10i	0.308580	−	0.534476i
$943$	−1.06679e10	−	1.84774e10i	−0.414276	−	0.717546i
$944$	−2.55859e9	+	2.14691e9i	−0.0989918	+	0.0830640i
$945$	4.31839e9	−	1.57176e9i	0.166460	−	0.0605865i
$946$	1.46498e10	+	5.33211e9i	0.562619	+	0.204776i
$947$	8.24364e9	+	6.91724e9i	0.315424	+	0.264672i	0.786729	−	0.617298i	$-0.211773\pi$
$947$	8.24364e9	+	6.91724e9i	0.315424	+	0.264672i	−0.471306	+	0.881970i	$0.656217\pi$
$948$	2.03400e9	−	1.15354e10i	0.0775391	−	0.439746i
$949$	−1.68165e10			−0.638709
$950$	7.48252e9	−	1.62401e10i	0.283149	−	0.614547i
$951$	−3.06577e10			−1.15587
$952$	1.16761e8	−	6.62183e8i	0.00438599	−	0.0248742i
$953$	3.92097e10	+	3.29008e10i	1.46747	+	1.23135i	0.918448	+	0.395541i	$0.129443\pi$
$953$	3.92097e10	+	3.29008e10i	1.46747	+	1.23135i	0.549019	+	0.835810i	$0.315002\pi$
$954$	−3.14430e9	−	1.14443e9i	−0.117248	−	0.0426747i
$955$	3.33800e9	−	1.21493e9i	0.124015	−	0.0451378i
$956$	−7.84778e9	+	6.58507e9i	−0.290499	+	0.243757i
$957$	−1.11464e10	−	1.93062e10i	−0.411097	−	0.712041i
$958$	1.09318e10	−	1.89345e10i	0.401711	−	0.695784i
$959$	3.36906e9	+	1.91069e10i	0.123351	+	0.699559i
$960$	9.77165e7	+	5.54178e8i	0.00356466	+	0.0202162i
$961$	−2.42329e10	+	4.19727e10i	−0.880794	+	1.52558i
$962$	−2.72600e9	−	4.72157e9i	−0.0987217	−	0.170991i
$963$	1.32139e10	−	1.10878e10i	0.476802	−	0.400085i
$964$	−6.74154e9	+	2.45372e9i	−0.242376	+	0.0882176i
$965$	2.50343e9	+	9.11174e8i	0.0896789	+	0.0326404i
$966$	7.44482e9	+	6.24695e9i	0.265726	+	0.222971i
$967$	−5.19022e9	+	2.94352e10i	−0.184584	+	1.04683i	0.741906	+	0.670504i	$0.233922\pi$
$967$	−5.19022e9	+	2.94352e10i	−0.184584	+	1.04683i	−0.926489	+	0.376321i	$0.877189\pi$
$968$	1.71793e10			0.608754
$969$	−1.97212e9	−	5.18761e8i	−0.0696306	−	0.0183161i
$970$	−3.86596e9			−0.136005
$971$	6.62645e9	−	3.75805e10i	0.232281	−	1.31733i	−0.615984	−	0.787759i	$-0.711241\pi$
$971$	6.62645e9	−	3.75805e10i	0.232281	−	1.31733i	0.848265	−	0.529572i	$-0.177647\pi$
$972$	7.70460e9	+	6.46493e9i	0.269103	+	0.225804i
$973$	−3.53485e10	−	1.28658e10i	−1.23020	−	0.447756i
$974$	−2.03559e10	+	7.40896e9i	−0.705886	+	0.256922i
$975$	−8.50217e9	+	7.13417e9i	−0.293774	+	0.246506i
$976$	9.98467e8	+	1.72940e9i	0.0343763	+	0.0595415i
$977$	−1.66348e9	+	2.88123e9i	−0.0570672	+	0.0988434i	−0.893148	−	0.449763i	$-0.851508\pi$
$977$	−1.66348e9	+	2.88123e9i	−0.0570672	+	0.0988434i	0.836080	+	0.548607i	$0.184842\pi$
$978$	−6.71480e8	−	3.80815e9i	−0.0229534	−	0.130175i
$979$	8.97784e9	+	5.09159e10i	0.305796	+	1.73426i
$980$	5.86731e8	−	1.01625e9i	0.0199135	−	0.0344912i
$981$	4.61059e9	+	7.98577e9i	0.155925	+	0.270069i
$982$	1.66779e10	−	1.39944e10i	0.562018	−	0.471589i
$983$	3.80478e9	−	1.38483e9i	0.127759	−	0.0465005i	−0.277349	−	0.960769i	$-0.589456\pi$
$983$	3.80478e9	−	1.38483e9i	0.127759	−	0.0465005i	0.405109	+	0.914269i	$0.367234\pi$
$984$	−8.24073e9	−	2.99938e9i	−0.275729	−	0.100357i
$985$	2.87142e9	+	2.40941e9i	0.0957349	+	0.0803311i
$986$	−2.11866e8	+	1.20155e9i	−0.00703870	+	0.0399185i
$987$	3.99401e9			0.132221
$988$	6.30940e9	+	4.37497e9i	0.208132	+	0.144320i
$989$	1.23324e10			0.405377
$990$	4.80190e8	−	2.72330e9i	0.0157286	−	0.0892014i
$991$	−1.19766e10	−	1.00496e10i	−0.390909	−	0.328012i	0.426058	−	0.904696i	$-0.359902\pi$
$991$	−1.19766e10	−	1.00496e10i	−0.390909	−	0.328012i	−0.816967	+	0.576684i	$0.804346\pi$
$992$	8.48753e9	+	3.08921e9i	0.276052	+	0.100475i
$993$	−1.97225e10	+	7.17840e9i	−0.639204	+	0.232651i
$994$	−2.26466e9	+	1.90027e9i	−0.0731392	+	0.0613711i
$995$	−4.57635e9	−	7.92647e9i	−0.147278	−	0.255093i
$996$	4.47728e9	−	7.75488e9i	0.143584	−	0.248695i
$997$	4.39503e9	+	2.49254e10i	0.140452	+	0.796544i	0.970907	+	0.239458i	$0.0769697\pi$
$997$	4.39503e9	+	2.49254e10i	0.140452	+	0.796544i	−0.830455	+	0.557086i	$0.811919\pi$
$998$	−3.79829e9	−	2.15412e10i	−0.120957	−	0.685981i
$999$	9.44192e9	−	1.63539e10i	0.299627	−	0.518969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.17.4	yes	30
19.9	even	9	inner	38.8.e.a.9.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.9.4	✓	30	19.9	even	9	inner
38.8.e.a.17.4	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)

\(f(q)\)	\(=\)	\(q+(1.38919 - 7.87846i) q^{2} +(28.3430 + 23.7826i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-54.5194 + 19.8434i) q^{5} +(226.744 - 190.261i) q^{6} +(-356.201 - 616.958i) q^{7} +(-256.000 + 443.405i) q^{8} +(-142.054 - 805.630i) q^{9} +O(q^{10})\)	\(q+(1.38919 - 7.87846i) q^{2} +(28.3430 + 23.7826i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-54.5194 + 19.8434i) q^{5} +(226.744 - 190.261i) q^{6} +(-356.201 - 616.958i) q^{7} +(-256.000 + 443.405i) q^{8} +(-142.054 - 805.630i) q^{9} +(80.5982 + 457.095i) q^{10} +(3641.45 - 6307.17i) q^{11} +(-1183.97 - 2050.70i) q^{12} +(3073.79 - 2579.22i) q^{13} +(-5355.51 + 1949.25i) q^{14} +(-2017.18 - 734.192i) q^{15} +(3137.72 + 2632.86i) q^{16} +(320.112 - 1815.45i) q^{17} -6544.46 q^{18} +(-17260.6 - 24412.0i) q^{19} +3713.17 q^{20} +(4577.07 - 25957.9i) q^{21} +(-44632.2 - 37450.8i) q^{22} +(-43309.0 - 15763.2i) q^{23} +(-17801.2 + 6479.09i) q^{24} +(-57268.6 + 48054.1i) q^{25} +(-16050.2 - 27799.8i) q^{26} +(55592.4 - 96288.9i) q^{27} +(7917.27 + 44901.1i) q^{28} +(-14366.1 - 81474.4i) q^{29} +(-8586.53 + 14872.3i) q^{30} +(137821. + 238713. i) q^{31} +(25101.7 - 21062.9i) q^{32} +(253211. - 92161.2i) q^{33} +(-13858.2 - 5043.98i) q^{34} +(31662.4 + 26567.9i) q^{35} +(-9091.47 + 51560.3i) q^{36} +169842. q^{37} +(-216307. + 102074. i) q^{38} +148461. q^{39} +(5158.29 - 29254.1i) q^{40} +(354627. + 297567. i) q^{41} +(-198150. - 72120.6i) q^{42} +(-251443. + 91517.7i) q^{43} +(-357057. + 299607. i) q^{44} +(23731.2 + 41103.6i) q^{45} +(-184354. + 319311. i) q^{46} +(26312.5 + 149226. i) q^{47} +(26316.2 + 149246. i) q^{48} +(158013. - 273687. i) q^{49} +(299035. + 517945. i) q^{50} +(52249.0 - 43842.1i) q^{51} +(-241316. + 87831.9i) q^{52} +(480452. + 174870. i) q^{53} +(-681380. - 571746. i) q^{54} +(-73373.5 + 416122. i) q^{55} +364750. q^{56} +(91363.8 - 1.10241e6i) q^{57} -661850. q^{58} +(-141598. + 803043. i) q^{59} +(105243. + 88309.1i) q^{60} +(458131. + 166746. i) q^{61} +(2.07215e6 - 754201. i) q^{62} +(-446440. + 374608. i) q^{63} +(-131072. - 227023. i) q^{64} +(-116401. + 201612. i) q^{65} +(-374332. - 2.12294e6i) q^{66} +(-609882. - 3.45881e6i) q^{67} +(-58990.4 + 102174. i) q^{68} +(-852619. - 1.47678e6i) q^{69} +(253300. - 212544. i) q^{70} +(487438. - 177413. i) q^{71} +(393586. + 143254. i) q^{72} +(-3.21047e6 - 2.69390e6i) q^{73} +(235942. - 1.33809e6i) q^{74} -2.76602e6 q^{75} +(503696. + 1.84597e6i) q^{76} -5.18835e6 q^{77} +(206240. - 1.16965e6i) q^{78} +(3.78932e6 + 3.17962e6i) q^{79} +(-223312. - 81278.7i) q^{80} +(2.18446e6 - 795080. i) q^{81} +(2.83701e6 - 2.38054e6i) q^{82} +(1.89078e6 + 3.27493e6i) q^{83} +(-843466. + 1.46093e6i) q^{84} +(18572.4 + 105329. i) q^{85} +(371718. + 2.10812e6i) q^{86} +(1.53050e6 - 2.65090e6i) q^{87} +(1.86442e6 + 3.22927e6i) q^{88} +(-5.43816e6 + 4.56316e6i) q^{89} +(356800. - 129865. i) q^{90} +(-2.68616e6 - 977681. i) q^{91} +(2.25957e6 + 1.89601e6i) q^{92} +(-1.77096e6 + 1.00436e7i) q^{93} +1.21222e6 q^{94} +(1.42545e6 + 988417. i) q^{95} +1.21239e6 q^{96} +(-1.44635e6 + 8.20264e6i) q^{97} +(-1.93672e6 - 1.62510e6i) q^{98} +(-5.59853e6 - 2.03770e6i) 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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