LMFDB - Embedded newform 38.8.e.b.17.1

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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	38.17
Dual form			38.8.e.b.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38919 + 7.87846i) q^{2} +(-66.5349 - 55.8294i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-312.664 + 113.800i) q^{5} +(532.279 - 446.635i) q^{6} +(-817.968 - 1416.76i) q^{7} +(256.000 - 443.405i) q^{8} +(930.200 + 5275.43i) q^{9} +O(q^{10})$	\(q+(-1.38919 + 7.87846i) q^{2} +(-66.5349 - 55.8294i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-312.664 + 113.800i) q^{5} +(532.279 - 446.635i) q^{6} +(-817.968 - 1416.76i) q^{7} +(256.000 - 443.405i) q^{8} +(930.200 + 5275.43i) q^{9} +(-462.223 - 2621.40i) q^{10} +(-853.993 + 1479.16i) q^{11} +(2779.36 + 4814.00i) q^{12} +(4239.42 - 3557.30i) q^{13} +(12298.2 - 4476.18i) q^{14} +(27156.4 + 9884.13i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-3808.96 + 21601.7i) q^{17} -42854.5 q^{18} +(-15633.8 - 25484.5i) q^{19} +21294.7 q^{20} +(-24673.6 + 139931. i) q^{21} +(-10467.1 - 8782.98i) q^{22} +(6830.22 + 2486.00i) q^{23} +(-41788.0 + 15209.6i) q^{24} +(24960.9 - 20944.6i) q^{25} +(22136.7 + 38341.9i) q^{26} +(137657. - 238429. i) q^{27} +(18180.9 + 103109. i) q^{28} +(-1067.03 - 6051.43i) q^{29} +(-115597. + 200220. i) q^{30} +(-100814. - 174615. i) q^{31} +(-25101.7 + 21062.9i) q^{32} +(139401. - 50737.8i) q^{33} +(-164896. - 60017.4i) q^{34} +(416977. + 349885. i) q^{35} +(59532.8 - 337627. i) q^{36} +586562. q^{37} +(222497. - 87767.3i) q^{38} -480671. q^{39} +(-29582.3 + 167770. i) q^{40} +(-297410. - 249557. i) q^{41} +(-1.06816e6 - 388779. i) q^{42} +(-107814. + 39241.2i) q^{43} +(83737.2 - 70263.8i) q^{44} +(-891185. - 1.54358e6i) q^{45} +(-29074.3 + 50358.1i) q^{46} +(12928.6 + 73321.6i) q^{47} +(-61776.8 - 350354. i) q^{48} +(-926371. + 1.60452e6i) q^{49} +(130336. + 225749. i) q^{50} +(1.45944e6 - 1.22461e6i) q^{51} +(-332827. + 121139. i) q^{52} +(145938. + 53117.0i) q^{53} +(1.68722e6 + 1.41575e6i) q^{54} +(98683.9 - 559664. i) q^{55} -837599. q^{56} +(-382592. + 2.56843e6i) q^{57} +49158.2 q^{58} +(-440827. + 2.50005e6i) q^{59} +(-1.41684e6 - 1.18887e6i) q^{60} +(62665.0 + 22808.2i) q^{61} +(1.51575e6 - 551688. i) q^{62} +(6.71315e6 - 5.63300e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-920692. + 1.59469e6i) q^{65} +(206082. + 1.16875e6i) q^{66} +(118002. + 669225. i) q^{67} +(701917. - 1.21576e6i) q^{68} +(-315656. - 546732. i) q^{69} +(-3.33581e6 + 2.79908e6i) q^{70} +(-1.84756e6 + 672457. i) q^{71} +(2.57728e6 + 938054. i) q^{72} +(-1.17752e6 - 988054. i) q^{73} +(-814843. + 4.62121e6i) q^{74} -2.83009e6 q^{75} +(382382. + 1.87486e6i) q^{76} +2.79415e6 q^{77} +(667742. - 3.78695e6i) q^{78} +(4.53303e6 + 3.80367e6i) q^{79} +(-1.28067e6 - 466126. i) q^{80} +(-1.14615e7 + 4.17165e6i) q^{81} +(2.37928e6 - 1.99645e6i) q^{82} +(1.13583e6 + 1.96731e6i) q^{83} +(4.54686e6 - 7.87539e6i) q^{84} +(-1.26735e6 - 7.18751e6i) q^{85} +(-159386. - 903924. i) q^{86} +(-266853. + 462202. i) q^{87} +(437244. + 757330. i) q^{88} +(-3.20177e6 + 2.68661e6i) q^{89} +(1.33990e7 - 4.87685e6i) q^{90} +(-8.50756e6 - 3.09650e6i) q^{91} +(-356355. - 299017. i) q^{92} +(-3.04101e6 + 1.72464e7i) q^{93} -595622. q^{94} +(7.78824e6 + 6.18894e6i) q^{95} +2.84607e6 q^{96} +(920575. - 5.22084e6i) q^{97} +(-1.13543e7 - 9.52736e6i) q^{98} +(-8.59758e6 - 3.12926e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9}+O(q^{10}) $ 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9} + 1800 q^{11} - 38334 q^{13} + 20832 q^{14} + 111228 q^{15} - 86574 q^{17} - 285888 q^{18} - 160152 q^{19} + 48384 q^{20} - 71442 q^{21} + 129984 q^{22} + 142920 q^{23} + 43008 q^{24} - 514068 q^{25} - 77856 q^{26} + 159492 q^{27} + 204288 q^{28} - 626034 q^{29} + 82656 q^{31} + 1576494 q^{33} + 85632 q^{34} + 581760 q^{35} + 91392 q^{36} + 1090848 q^{37} - 398496 q^{38} - 282624 q^{39} + 450780 q^{41} - 898128 q^{42} + 3066264 q^{43} - 1039872 q^{44} - 1208484 q^{45} + 166080 q^{46} - 1923516 q^{47} + 688128 q^{48} - 3667500 q^{49} + 4263456 q^{50} + 5070996 q^{51} + 440448 q^{52} - 4486374 q^{53} + 1382688 q^{54} - 5711508 q^{55} - 3059712 q^{56} - 5167644 q^{57} + 1718304 q^{58} - 5420364 q^{59} - 3484416 q^{60} + 20074776 q^{61} + 5592864 q^{62} - 4282596 q^{63} - 4718592 q^{64} + 10490790 q^{65} - 6939360 q^{66} + 5235372 q^{67} - 171648 q^{68} - 11912298 q^{69} - 4654080 q^{70} + 10980792 q^{71} + 1462272 q^{72} - 11218440 q^{73} - 443088 q^{74} - 8817984 q^{75} + 470016 q^{76} + 44477160 q^{77} - 11046144 q^{78} - 30314100 q^{79} - 40768188 q^{81} - 3606240 q^{82} + 4370208 q^{83} + 14171520 q^{84} - 20507004 q^{85} + 35895744 q^{86} + 14888064 q^{87} - 921600 q^{88} + 9695220 q^{89} + 34283424 q^{90} - 24159408 q^{91} - 3868416 q^{92} + 4014432 q^{93} - 46331520 q^{94} - 16025892 q^{95} - 47992770 q^{97} - 32609808 q^{98} + 62837148 q^{99}+O(q^{100}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9 + 1800 * q^11 - 38334 * q^13 + 20832 * q^14 + 111228 * q^15 - 86574 * q^17 - 285888 * q^18 - 160152 * q^19 + 48384 * q^20 - 71442 * q^21 + 129984 * q^22 + 142920 * q^23 + 43008 * q^24 - 514068 * q^25 - 77856 * q^26 + 159492 * q^27 + 204288 * q^28 - 626034 * q^29 + 82656 * q^31 + 1576494 * q^33 + 85632 * q^34 + 581760 * q^35 + 91392 * q^36 + 1090848 * q^37 - 398496 * q^38 - 282624 * q^39 + 450780 * q^41 - 898128 * q^42 + 3066264 * q^43 - 1039872 * q^44 - 1208484 * q^45 + 166080 * q^46 - 1923516 * q^47 + 688128 * q^48 - 3667500 * q^49 + 4263456 * q^50 + 5070996 * q^51 + 440448 * q^52 - 4486374 * q^53 + 1382688 * q^54 - 5711508 * q^55 - 3059712 * q^56 - 5167644 * q^57 + 1718304 * q^58 - 5420364 * q^59 - 3484416 * q^60 + 20074776 * q^61 + 5592864 * q^62 - 4282596 * q^63 - 4718592 * q^64 + 10490790 * q^65 - 6939360 * q^66 + 5235372 * q^67 - 171648 * q^68 - 11912298 * q^69 - 4654080 * q^70 + 10980792 * q^71 + 1462272 * q^72 - 11218440 * q^73 - 443088 * q^74 - 8817984 * q^75 + 470016 * q^76 + 44477160 * q^77 - 11046144 * q^78 - 30314100 * q^79 - 40768188 * q^81 - 3606240 * q^82 + 4370208 * q^83 + 14171520 * q^84 - 20507004 * q^85 + 35895744 * q^86 + 14888064 * q^87 - 921600 * q^88 + 9695220 * q^89 + 34283424 * q^90 - 24159408 * q^91 - 3868416 * q^92 + 4014432 * q^93 - 46331520 * q^94 - 16025892 * q^95 - 47992770 * q^97 - 32609808 * q^98 + 62837148 * 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
$3$	−66.5349	−	55.8294i	−1.42274	−	1.19382i	−0.949854	−	0.312694i	$-0.898769\pi$
$3$	−66.5349	−	55.8294i	−1.42274	−	1.19382i	−0.472884	−	0.881125i	$-0.656787\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	−312.664	+	113.800i	−1.11862	+	0.407144i	−0.834148	−	0.551540i	$-0.814040\pi$
$5$	−312.664	+	113.800i	−1.11862	+	0.407144i	−0.284471	+	0.958685i	$0.591818\pi$
$6$	532.279	−	446.635i	1.00603	−	0.844157i
$7$	−817.968	−	1416.76i	−0.901349	−	1.56118i	−0.825744	−	0.564045i	$-0.809245\pi$
$7$	−817.968	−	1416.76i	−0.901349	−	1.56118i	−0.0756048	−	0.997138i	$-0.524089\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	930.200	+	5275.43i	0.425332	+	2.41217i
$10$	−462.223	−	2621.40i	−0.146168	−	0.828959i
$11$	−853.993	+	1479.16i	−0.193455	+	0.335074i	−0.946393	−	0.323018i	$-0.895303\pi$
$11$	−853.993	+	1479.16i	−0.193455	+	0.335074i	0.752938	+	0.658091i	$0.228636\pi$
$12$	2779.36	+	4814.00i	0.464313	+	0.804214i
$13$	4239.42	−	3557.30i	0.535186	−	0.449075i	−0.334701	−	0.942324i	$-0.608635\pi$
$13$	4239.42	−	3557.30i	0.535186	−	0.449075i	0.869888	+	0.493249i	$0.164191\pi$
$14$	12298.2	−	4476.18i	1.19783	−	0.435973i
$15$	27156.4	+	9884.13i	2.07756	+	0.756170i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	−3808.96	+	21601.7i	−0.188033	+	1.06639i	0.733963	+	0.679190i	$0.237669\pi$
$17$	−3808.96	+	21601.7i	−0.188033	+	1.06639i	−0.921996	+	0.387200i	$0.873442\pi$
$18$	−42854.5			−1.73198
$19$	−15633.8	−	25484.5i	−0.522908	−	0.852389i
$19$	−15633.8	−	25484.5i	−0.522908	−	0.852389i
$20$	21294.7			0.595205
$21$	−24673.6	+	139931.i	−0.581385	+	3.29720i
$22$	−10467.1	−	8782.98i	−0.209580	−	0.175858i
$23$	6830.22	+	2486.00i	0.117054	+	0.0426043i	0.399883	−	0.916566i	$-0.369051\pi$
$23$	6830.22	+	2486.00i	0.117054	+	0.0426043i	−0.282829	+	0.959170i	$0.591273\pi$
$24$	−41788.0	+	15209.6i	−0.617038	+	0.224583i
$25$	24960.9	−	20944.6i	0.319499	−	0.268091i
$26$	22136.7	+	38341.9i	0.247005	+	0.427826i
$27$	137657.	−	238429.i	1.34594	−	2.33123i
$28$	18180.9	+	103109.i	0.156518	+	0.887656i
$29$	−1067.03	−	6051.43i	−0.00812425	−	0.0460749i	0.980476	−	0.196638i	$-0.0630024\pi$
$29$	−1067.03	−	6051.43i	−0.00812425	−	0.0460749i	−0.988600	+	0.150563i	$0.951891\pi$
$30$	−115597.	+	200220.i	−0.781668	+	1.35389i
$31$	−100814.	−	174615.i	−0.607793	−	1.05273i	−0.991603	−	0.129317i	$-0.958722\pi$
$31$	−100814.	−	174615.i	−0.607793	−	1.05273i	0.383810	−	0.923412i	$-0.374612\pi$
$32$	−25101.7	+	21062.9i	−0.135419	+	0.113630i
$33$	139401.	−	50737.8i	0.675253	−	0.245772i
$34$	−164896.	−	60017.4i	−0.719507	−	0.261879i
$35$	416977.	+	349885.i	1.64389	+	1.37939i
$36$	59532.8	−	337627.i	0.212666	−	1.20609i
$37$	586562.			1.90374			0.951870	−	0.306501i	$-0.0991584\pi$
$37$	586562.			1.90374			0.951870	+	0.306501i	$0.0991584\pi$
$38$	222497.	−	87767.3i	0.657780	−	0.259472i
$39$	−480671.			−1.29754
$40$	−29582.3	+	167770.i	−0.0730839	+	0.414480i
$41$	−297410.	−	249557.i	−0.673926	−	0.565491i	0.240298	−	0.970699i	$-0.422755\pi$
$41$	−297410.	−	249557.i	−0.673926	−	0.565491i	−0.914225	+	0.405208i	$0.867199\pi$
$42$	−1.06816e6	−	388779.i	−2.22467	−	0.809712i
$43$	−107814.	+	39241.2i	−0.206794	+	0.0752667i	−0.443340	−	0.896353i	$-0.646207\pi$
$43$	−107814.	+	39241.2i	−0.206794	+	0.0752667i	0.236547	+	0.971620i	$0.423984\pi$
$44$	83737.2	−	70263.8i	0.148195	−	0.124350i
$45$	−891185.	−	1.54358e6i	−1.45789	−	2.52513i
$46$	−29074.3	+	50358.1i	−0.0440409	+	0.0762811i
$47$	12928.6	+	73321.6i	0.0181639	+	0.103012i	0.992542	−	0.121904i	$-0.0389001\pi$
$47$	12928.6	+	73321.6i	0.0181639	+	0.103012i	−0.974378	+	0.224917i	$0.927789\pi$
$48$	−61776.8	−	350354.i	−0.0806271	−	0.457259i
$49$	−926371.	+	1.60452e6i	−1.12486	+	1.94832i
$50$	130336.	+	225749.i	0.147459	+	0.255406i
$51$	1.45944e6	−	1.22461e6i	1.54060	−	1.29272i
$52$	−332827.	+	121139.i	−0.328252	+	0.119474i
$53$	145938.	+	53117.0i	0.134649	+	0.0490081i	0.408466	−	0.912774i	$-0.366064\pi$
$53$	145938.	+	53117.0i	0.134649	+	0.0490081i	−0.273817	+	0.961782i	$0.588286\pi$
$54$	1.68722e6	+	1.41575e6i	1.45812	+	1.22351i
$55$	98683.9	−	559664.i	0.0799791	−	0.453584i
$56$	−837599.			−0.637350
$57$	−382592.	+	2.56843e6i	−0.273636	+	1.83698i
$58$	49158.2			0.0330825
$59$	−440827.	+	2.50005e6i	−0.279438	+	1.58477i	0.445063	+	0.895499i	$0.353181\pi$
$59$	−440827.	+	2.50005e6i	−0.279438	+	1.58477i	−0.724501	+	0.689273i	$0.757930\pi$
$60$	−1.41684e6	−	1.18887e6i	−0.846821	−	0.710567i
$61$	62665.0	+	22808.2i	0.0353485	+	0.0128658i	0.359634	−	0.933093i	$-0.382902\pi$
$61$	62665.0	+	22808.2i	0.0353485	+	0.0128658i	−0.324285	+	0.945959i	$0.605124\pi$
$62$	1.51575e6	−	551688.i	0.807712	−	0.293983i
$63$	6.71315e6	−	5.63300e6i	3.38247	−	2.83823i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−920692.	+	1.59469e6i	−0.415832	+	0.720242i
$66$	206082.	+	1.16875e6i	0.0882340	+	0.500400i
$67$	118002.	+	669225.i	0.0479324	+	0.271838i	0.999349	−	0.0360673i	$-0.0114831\pi$
$67$	118002.	+	669225.i	0.0479324	+	0.271838i	−0.951417	+	0.307905i	$0.900372\pi$
$68$	701917.	−	1.21576e6i	0.270710	−	0.468884i
$69$	−315656.	−	546732.i	−0.115676	−	0.200356i
$70$	−3.33581e6	+	2.79908e6i	−1.16241	+	0.975376i
$71$	−1.84756e6	+	672457.i	−0.612625	+	0.222977i	−0.629651	−	0.776878i	$-0.716802\pi$
$71$	−1.84756e6	+	672457.i	−0.612625	+	0.222977i	0.0170265	+	0.999855i	$0.494580\pi$
$72$	2.57728e6	+	938054.i	0.813763	+	0.296186i
$73$	−1.17752e6	−	988054.i	−0.354272	−	0.297270i	0.448231	−	0.893918i	$-0.352054\pi$
$73$	−1.17752e6	−	988054.i	−0.354272	−	0.297270i	−0.802503	+	0.596648i	$0.796499\pi$
$74$	−814843.	+	4.62121e6i	−0.233756	+	1.32570i
$75$	−2.83009e6			−0.774616
$76$	382382.	+	1.87486e6i	0.0999195	+	0.489914i
$77$	2.79415e6			0.697482
$78$	667742.	−	3.78695e6i	0.159323	−	0.903563i
$79$	4.53303e6	+	3.80367e6i	1.03441	+	0.867976i	0.991369	−	0.131098i	$-0.0418501\pi$
$79$	4.53303e6	+	3.80367e6i	1.03441	+	0.867976i	0.0430436	+	0.999073i	$0.486295\pi$
$80$	−1.28067e6	−	466126.i	−0.279655	−	0.101786i
$81$	−1.14615e7	+	4.17165e6i	−2.39632	+	0.872188i
$82$	2.37928e6	−	1.99645e6i	0.476538	−	0.399863i
$83$	1.13583e6	+	1.96731e6i	0.218042	+	0.377660i	0.954209	−	0.299140i	$-0.0966997\pi$
$83$	1.13583e6	+	1.96731e6i	0.218042	+	0.377660i	−0.736167	+	0.676800i	$0.763366\pi$
$84$	4.54686e6	−	7.87539e6i	0.837016	−	1.44975i
$85$	−1.26735e6	−	7.18751e6i	−0.223837	−	1.26944i
$86$	−159386.	−	903924.i	−0.0270213	−	0.153245i
$87$	−266853.	+	462202.i	−0.0434464	+	0.0752514i
$88$	437244.	+	757330.i	0.0683967	+	0.118466i
$89$	−3.20177e6	+	2.68661e6i	−0.481422	+	0.403961i	−0.850940	−	0.525263i	$-0.823967\pi$
$89$	−3.20177e6	+	2.68661e6i	−0.481422	+	0.403961i	0.369519	+	0.929223i	$0.379523\pi$
$90$	1.33990e7	−	4.87685e6i	1.93742	−	0.705165i
$91$	−8.50756e6	−	3.09650e6i	−1.18348	−	0.430751i
$92$	−356355.	−	299017.i	−0.0477118	−	0.0400349i
$93$	−3.04101e6	+	1.72464e7i	−0.392037	+	2.22335i
$94$	−595622.			−0.0739644
$95$	7.78824e6	+	6.18894e6i	0.931981	+	0.740600i
$96$	2.84607e6			0.328319
$97$	920575.	−	5.22084e6i	0.102414	−	0.580817i	−0.889808	−	0.456335i	$-0.849162\pi$
$97$	920575.	−	5.22084e6i	0.102414	−	0.580817i	0.992222	−	0.124482i	$-0.0397270\pi$
$98$	−1.13543e7	−	9.52736e6i	−1.21862	−	1.02254i
$99$	−8.59758e6	−	3.12926e6i	−0.890539	−	0.324130i
$100$	−1.95962e6	+	713242.i	−0.195962	+	0.0713242i
$101$	1.38249e7	−	1.16005e7i	1.33517	−	1.12034i	0.352337	−	0.935873i	$-0.385387\pi$
$101$	1.38249e7	−	1.16005e7i	1.33517	−	1.12034i	0.982838	−	0.184471i	$-0.0590572\pi$
$102$	7.62063e6	+	1.31993e7i	0.711034	+	1.23155i
$103$	−5.82187e6	+	1.00838e7i	−0.524967	+	0.909270i	0.474610	+	0.880196i	$0.342589\pi$
$103$	−5.82187e6	+	1.00838e7i	−0.524967	+	0.909270i	−0.999577	+	0.0290739i	$0.990744\pi$
$104$	−492032.	−	2.79045e6i	−0.0428920	−	0.243253i
$105$	−8.20963e6	−	4.65591e7i	−0.692087	−	3.92502i
$106$	−621214.	+	1.07597e6i	−0.0506607	+	0.0877469i
$107$	7.97290e6	+	1.38095e7i	0.629177	+	1.08977i	0.987717	+	0.156253i	$0.0499415\pi$
$107$	7.97290e6	+	1.38095e7i	0.629177	+	1.08977i	−0.358540	+	0.933515i	$0.616725\pi$
$108$	−1.34978e7	+	1.13260e7i	−1.03105	+	0.865152i
$109$	−8.16119e6	+	2.97043e6i	−0.603616	+	0.219698i	−0.625708	−	0.780058i	$-0.715190\pi$
$109$	−8.16119e6	+	2.97043e6i	−0.603616	+	0.219698i	0.0220916	+	0.999756i	$0.492967\pi$
$110$	4.27220e6	+	1.55495e6i	0.306039	+	0.111389i
$111$	−3.90268e7	−	3.27474e7i	−2.70852	−	2.27272i
$112$	1.16358e6	−	6.59899e6i	0.0782588	−	0.443828i
$113$	2.16656e7			1.41253			0.706263	−	0.707950i	$-0.250380\pi$
$113$	2.16656e7			1.41253			0.706263	+	0.707950i	$0.250380\pi$
$114$	−1.97038e7	−	6.58226e6i	−1.24561	−	0.416110i
$115$	−2.41847e6			−0.148285
$116$	−68289.9	+	387291.i	−0.00406213	+	0.0230375i
$117$	2.27098e7	+	1.90558e7i	1.31088	+	1.09996i
$118$	−1.90842e7	−	6.94607e6i	−1.06927	−	0.389181i
$119$	3.37200e7	−	1.22731e7i	1.83431	−	0.667635i
$120$	1.13347e7	−	9.51096e6i	0.598793	−	0.502447i
$121$	8.28498e6	+	1.43500e7i	0.425150	+	0.736382i
$122$	−266747.	+	462019.i	−0.0132996	+	0.0230356i
$123$	5.85555e6	+	3.32085e7i	0.283726	+	1.60909i
$124$	2.24079e6	+	1.27082e7i	0.105542	+	0.598559i
$125$	7.57641e6	−	1.31227e7i	0.346959	−	0.600951i
$126$	3.50536e7	+	6.07146e7i	1.56112	+	2.70393i
$127$	1.39205e7	−	1.16807e7i	0.603035	−	0.506006i	−0.289385	−	0.957213i	$-0.593451\pi$
$127$	1.39205e7	−	1.16807e7i	0.603035	−	0.506006i	0.892420	+	0.451206i	$0.149006\pi$
$128$	1.97068e6	−	717268.i	0.0830579	−	0.0302306i
$129$	9.36422e6	+	3.40830e6i	0.384068	+	0.139789i
$130$	−1.12847e7	−	9.46895e6i	−0.450492	−	0.378007i
$131$	4.89259e6	−	2.77473e7i	0.190147	−	1.07838i	−0.729015	−	0.684497i	$-0.760022\pi$
$131$	4.89259e6	−	2.77473e7i	0.190147	−	1.07838i	0.919162	−	0.393879i	$-0.128867\pi$
$132$	−9.49423e6			−0.359295
$133$	−2.33175e7	+	4.29948e7i	−0.859412	+	1.58466i
$134$	−5.43639e6			−0.195184
$135$	−1.59071e7	+	9.02135e7i	−0.556445	+	3.15575i
$136$	8.60319e6	+	7.21893e6i	0.293274	+	0.246086i
$137$	−3.56316e7	−	1.29689e7i	−1.18390	−	0.430903i	−0.326320	−	0.945259i	$-0.605809\pi$
$137$	−3.56316e7	−	1.29689e7i	−1.18390	−	0.430903i	−0.857577	+	0.514356i	$0.828031\pi$
$138$	4.74592e6	−	1.72737e6i	0.153725	−	0.0559512i
$139$	4.50413e6	−	3.77942e6i	0.142252	−	0.119364i	−0.568885	−	0.822417i	$-0.692625\pi$
$139$	4.50413e6	−	3.77942e6i	0.142252	−	0.119364i	0.711137	+	0.703053i	$0.248181\pi$
$140$	−1.74184e7	−	3.01695e7i	−0.536488	−	0.929224i
$141$	3.23330e6	−	5.60024e6i	0.0971357	−	0.168244i
$142$	−2.73132e6	−	1.54901e7i	−0.0800505	−	0.453989i
$143$	1.64137e6	+	9.30869e6i	0.0469387	+	0.266203i
$144$	−1.09707e7	+	1.90019e7i	−0.306173	+	0.530308i
$145$	1.02228e6	+	1.77063e6i	0.0278471	+	0.0482326i
$146$	9.42013e6	−	7.90443e6i	0.250508	−	0.210201i
$147$	1.51215e8	−	5.50379e7i	3.92632	−	1.42906i
$148$	−3.52760e7	−	1.28394e7i	−0.894465	−	0.325559i
$149$	−3.57407e7	−	2.99900e7i	−0.885139	−	0.742720i	0.0820901	−	0.996625i	$-0.473840\pi$
$149$	−3.57407e7	−	2.99900e7i	−0.885139	−	0.742720i	−0.967229	+	0.253905i	$0.918285\pi$
$150$	3.93152e6	−	2.22968e7i	0.0951134	−	0.539415i
$151$	−3.32443e7			−0.785773			−0.392887	−	0.919587i	$-0.628524\pi$
$151$	−3.32443e7			−0.785773			−0.392887	+	0.919587i	$0.628524\pi$
$152$	−1.53022e7	+	408062.i	−0.353428	+	0.00942483i
$153$	−1.17501e8			−2.65229
$154$	−3.88160e6	+	2.20136e7i	−0.0856423	+	0.485701i
$155$	5.13922e7	+	4.31232e7i	1.10850	+	0.930144i
$156$	2.89077e7	+	1.05216e7i	0.609646	+	0.221893i
$157$	2.56005e7	−	9.31783e6i	0.527959	−	0.192161i	−0.0642679	−	0.997933i	$-0.520471\pi$
$157$	2.56005e7	−	9.31783e6i	0.527959	−	0.192161i	0.592227	+	0.805771i	$0.298249\pi$
$158$	−3.62643e7	+	3.04293e7i	−0.731441	+	0.613751i
$159$	−6.74445e6	−	1.16817e7i	−0.133063	−	0.230472i
$160$	5.45144e6	−	9.44218e6i	0.105218	−	0.182244i
$161$	−2.06483e6	−	1.17103e7i	−0.0389937	−	0.221144i
$162$	−1.69440e7	−	9.60943e7i	−0.313122	−	1.77580i
$163$	−1.78444e6	+	3.09075e6i	−0.0322735	+	0.0558994i	−0.881711	−	0.471790i	$-0.843608\pi$
$163$	−1.78444e6	+	3.09075e6i	−0.0322735	+	0.0558994i	0.849438	+	0.527689i	$0.176941\pi$
$164$	1.24237e7	+	2.15185e7i	0.219937	+	0.380942i
$165$	−3.78116e7	+	3.17277e7i	−0.655287	+	0.549851i
$166$	−1.70773e7	+	6.21563e6i	−0.289762	+	0.105465i
$167$	−1.13329e7	−	4.12485e6i	−0.188293	−	0.0685331i	0.246153	−	0.969231i	$-0.420834\pi$
$167$	−1.13329e7	−	4.12485e6i	−0.188293	−	0.0685331i	−0.434446	+	0.900698i	$0.643056\pi$
$168$	5.57295e7	+	4.67626e7i	0.906782	+	0.760881i
$169$	−5.57783e6	+	3.16334e7i	−0.0888918	+	0.504130i
$170$	5.83871e7			0.911478
$171$	1.19899e8	−	1.06180e8i	1.83370	−	1.62389i
$172$	7.34295e6			0.110033
$173$	89765.3	−	509085.i	0.00131810	−	0.00747530i	−0.984142	−	0.177385i	$-0.943236\pi$
$173$	89765.3	−	509085.i	0.00131810	−	0.00747530i	0.985460	+	0.169909i	$0.0543475\pi$
$174$	−3.27074e6	−	2.74447e6i	−0.0470677	−	0.0394945i
$175$	−5.00907e7	−	1.82315e7i	−0.706520	−	0.257152i
$176$	−6.57401e6	+	2.39274e6i	−0.0908941	+	0.0330827i
$177$	1.68907e8	−	1.41730e8i	2.28950	−	1.92112i
$178$	−1.67185e7	−	2.89572e7i	−0.222191	−	0.384846i
$179$	3.98396e7	−	6.90042e7i	0.519193	−	0.899269i	−0.480558	−	0.876963i	$-0.659566\pi$
$179$	3.98396e7	−	6.90042e7i	0.519193	−	0.899269i	0.999751	−	0.0223060i	$-0.00710082\pi$
$180$	1.98083e7	+	1.12339e8i	0.253159	+	1.43574i
$181$	1.80084e7	+	1.02131e8i	0.225736	+	1.28021i	0.861273	+	0.508143i	$0.169668\pi$
$181$	1.80084e7	+	1.02131e8i	0.225736	+	1.28021i	−0.635536	+	0.772071i	$0.719221\pi$
$182$	3.62142e7	−	6.27249e7i	0.445276	−	0.771240i
$183$	−2.89604e6	−	5.01609e6i	−0.0349322	−	0.0605043i
$184$	2.85084e6	−	2.39214e6i	0.0337373	−	0.0283090i
$185$	−1.83397e8	+	6.67509e7i	−2.12956	+	0.775097i
$186$	−1.31651e8	−	4.79169e7i	−1.50013	−	0.546001i
$187$	−2.86995e7	−	2.40817e7i	−0.320943	−	0.269303i
$188$	827429.	−	4.69258e6i	0.00908193	−	0.0515062i
$189$	−4.50396e8			−4.85264
$190$	−5.95786e7	+	5.27618e7i	−0.630163	+	0.558061i
$191$	−4.90823e7			−0.509692			−0.254846	−	0.966982i	$-0.582025\pi$
$191$	−4.90823e7			−0.509692			−0.254846	+	0.966982i	$0.582025\pi$
$192$	−3.95372e6	+	2.24226e7i	−0.0403136	+	0.228630i
$193$	−9.37713e7	−	7.86835e7i	−0.938900	−	0.787831i	0.0384934	−	0.999259i	$-0.487744\pi$
$193$	−9.37713e7	−	7.86835e7i	−0.938900	−	0.787831i	−0.977394	+	0.211428i	$0.932189\pi$
$194$	3.98534e7	+	1.45054e7i	0.391885	+	0.142635i
$195$	1.50288e8	−	5.47005e7i	1.45146	−	0.528288i
$196$	9.08341e7	−	7.62188e7i	0.861693	−	0.723046i
$197$	5.06657e7	+	8.77556e7i	0.472152	+	0.817792i	0.999492	−	0.0318624i	$-0.0101438\pi$
$197$	5.06657e7	+	8.77556e7i	0.472152	+	0.817792i	−0.527340	+	0.849654i	$0.676811\pi$
$198$	3.65974e7	−	6.33886e7i	0.335060	−	0.580340i
$199$	2.16063e7	+	1.22536e8i	0.194355	+	1.10224i	0.913334	+	0.407210i	$0.133498\pi$
$199$	2.16063e7	+	1.22536e8i	0.194355	+	1.10224i	−0.718979	+	0.695031i	$0.755390\pi$
$200$	−2.89698e6	−	1.64296e7i	−0.0256059	−	0.145218i
$201$	2.95112e7	−	5.11148e7i	0.256330	−	0.443977i
$202$	7.21886e7	+	1.25034e8i	0.616225	+	1.06733i
$203$	−7.70063e6	+	6.46160e6i	−0.0646086	+	0.0542130i
$204$	−1.14577e8	+	4.17025e7i	−0.944912	+	0.343920i
$205$	1.21389e8	+	4.41820e7i	0.984104	+	0.358184i
$206$	−7.13570e7	−	5.98756e7i	−0.568724	−	0.477216i
$207$	−6.76122e6	+	3.83448e7i	−0.0529821	+	0.300476i
$208$	2.26680e7			0.174659
$209$	5.10467e7	−	1.36126e6i	0.386772	−	0.0103140i
$210$	3.78219e8			2.81822
$211$	−49867.5	+	282813.i	−0.000365451	+	0.00207258i	−0.984990	−	0.172612i	$-0.944779\pi$
$211$	−49867.5	+	282813.i	−0.000365451	+	0.00207258i	0.984624	+	0.174684i	$0.0558905\pi$
$212$	−7.61404e6	−	6.38894e6i	−0.0548833	−	0.0460525i
$213$	1.60470e8	+	5.84064e7i	1.13780	+	0.414125i
$214$	−1.19873e8	+	4.36303e7i	−0.836130	+	0.304327i
$215$	2.92440e7	−	2.45386e7i	0.200679	−	0.168390i
$216$	−7.04804e7	−	1.22076e8i	−0.475861	−	0.824216i
$217$	−1.64926e8	+	2.85659e8i	−1.09567	+	1.89775i
$218$	−1.20650e7	−	6.84241e7i	−0.0788733	−	0.447313i
$219$	2.31835e7	+	1.31480e8i	0.149150	+	0.845873i
$220$	−1.81855e7	+	3.14983e7i	−0.115145	+	0.199438i
$221$	6.06958e7	+	1.05128e8i	0.378256	+	0.655158i
$222$	3.12214e8	−	2.61979e8i	1.91522	−	1.60706i
$223$	−2.35940e8	+	8.58750e7i	−1.42473	+	0.518561i	−0.935417	−	0.353545i	$-0.884976\pi$
$223$	−2.35940e8	+	8.58750e7i	−1.42473	+	0.518561i	−0.489317	+	0.872106i	$0.662754\pi$
$224$	5.03735e7	+	1.83344e7i	0.299457	+	0.108993i
$225$	1.33711e8	+	1.12196e8i	0.782576	+	0.656660i
$226$	−3.00976e7	+	1.70692e8i	−0.173441	+	0.983632i
$227$	1.59943e8			0.907560			0.453780	−	0.891114i	$-0.350075\pi$
$227$	1.59943e8			0.907560			0.453780	+	0.891114i	$0.350075\pi$
$228$	7.92303e7	−	1.46091e8i	0.442710	−	0.816305i
$229$	2.13662e8			1.17572			0.587859	−	0.808963i	$-0.299971\pi$
$229$	2.13662e8			1.17572			0.587859	+	0.808963i	$0.299971\pi$
$230$	3.35970e6	−	1.90538e7i	0.0182076	−	0.103261i
$231$	−1.85909e8	−	1.55996e8i	−0.992334	−	0.832667i
$232$	−2.95639e6	−	1.07604e6i	−0.0155437	−	0.00565744i
$233$	2.75600e7	−	1.00310e7i	0.142736	−	0.0519516i	−0.269664	−	0.962954i	$-0.586913\pi$
$233$	2.75600e7	−	1.00310e7i	0.142736	−	0.0519516i	0.412400	+	0.911003i	$0.364691\pi$
$234$	−1.81678e8	+	1.52446e8i	−0.926931	+	0.777787i
$235$	−1.23863e7	−	2.14537e7i	−0.0622593	−	0.107836i
$236$	8.12358e7	−	1.40705e8i	0.402305	−	0.696813i
$237$	−8.92484e7	−	5.06153e8i	−0.435493	−	2.46980i
$238$	4.98496e7	+	2.82711e8i	0.239686	+	1.35933i
$239$	−8.84175e7	+	1.53144e8i	−0.418934	+	0.725615i	−0.995833	−	0.0912008i	$-0.970929\pi$
$239$	−8.84175e7	+	1.53144e8i	−0.418934	+	0.725615i	0.576898	+	0.816816i	$0.304263\pi$
$240$	5.91857e7	+	1.02513e8i	0.276362	+	0.478672i
$241$	−1.83343e8	+	1.53843e8i	−0.843732	+	0.707975i	−0.958400	−	0.285429i	$-0.907864\pi$
$241$	−1.83343e8	+	1.53843e8i	−0.843732	+	0.707975i	0.114668	+	0.993404i	$0.463420\pi$
$242$	−1.24565e8	+	4.53381e7i	−0.564993	+	0.205641i
$243$	4.29691e8	+	1.56395e8i	1.92103	+	0.699198i
$244$	−3.26944e6	−	2.74338e6i	−0.0144082	−	0.0120899i
$245$	1.07048e8	−	6.07097e8i	0.465046	−	2.63740i
$246$	−2.69766e8			−1.15535
$247$	−1.56934e8	−	5.24255e7i	−0.662640	−	0.221362i
$248$	−1.03234e8			−0.429775
$249$	3.42617e7	−	1.94308e8i	0.140641	−	0.797613i
$250$	9.28619e7	+	7.79203e7i	0.375878	+	0.315399i
$251$	4.45892e7	+	1.62292e7i	0.177980	+	0.0647796i	0.429473	−	0.903080i	$-0.358699\pi$
$251$	4.45892e7	+	1.62292e7i	0.177980	+	0.0647796i	−0.251493	+	0.967859i	$0.580921\pi$
$252$	−5.27033e8	+	1.91824e8i	−2.07461	+	0.755096i
$253$	−9.51014e6	+	7.97996e6i	−0.0369203	+	0.0309798i
$254$	7.26878e7	+	1.25899e8i	0.278319	+	0.482063i
$255$	−3.16951e8	+	5.48976e8i	−1.19702	+	2.07330i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−1.25288e7	−	7.10542e7i	−0.0460407	−	0.261110i	0.953095	−	0.302671i	$-0.0978782\pi$
$257$	−1.25288e7	−	7.10542e7i	−0.0460407	−	0.261110i	−0.999136	+	0.0415605i	$0.986767\pi$
$258$	−3.98608e7	+	6.90409e7i	−0.144503	+	0.250287i
$259$	−4.79789e8	−	8.31018e8i	−1.71593	−	2.97209i
$260$	9.02773e7	−	7.57516e7i	0.318546	−	0.267292i
$261$	3.09313e7	−	1.12581e7i	0.107685	−	0.0391942i
$262$	2.11809e8	+	7.70922e7i	0.727595	+	0.264823i
$263$	1.52222e8	+	1.27730e8i	0.515981	+	0.432959i	0.863228	−	0.504814i	$-0.168439\pi$
$263$	1.52222e8	+	1.27730e8i	0.515981	+	0.432959i	−0.347247	+	0.937774i	$0.612883\pi$
$264$	1.31892e7	−	7.47999e7i	0.0441170	−	0.250200i
$265$	−5.16741e7			−0.170574
$266$	−3.06340e8	−	2.43434e8i	−0.997972	−	0.793040i
$267$	3.63021e8			1.16719
$268$	7.55216e6	−	4.28304e7i	0.0239662	−	0.135919i
$269$	9.89175e7	+	8.30016e7i	0.309842	+	0.259988i	0.784427	−	0.620222i	$-0.212957\pi$
$269$	9.89175e7	+	8.30016e7i	0.309842	+	0.259988i	−0.474585	+	0.880210i	$0.657402\pi$
$270$	−6.88646e8	−	2.50646e8i	−2.12923	−	0.774976i
$271$	−1.67314e8	+	6.08972e7i	−0.510669	+	0.185868i	−0.584486	−	0.811404i	$-0.698704\pi$
$271$	−1.67314e8	+	6.08972e7i	−0.510669	+	0.185868i	0.0738177	+	0.997272i	$0.476482\pi$
$272$	−6.88255e7	+	5.77515e7i	−0.207376	+	0.174009i
$273$	3.93174e8	+	6.80997e8i	1.16954	+	2.02570i
$274$	1.51674e8	−	2.62706e8i	0.445434	−	0.771514i
$275$	9.66407e6	+	5.48077e7i	0.0280218	+	0.158919i
$276$	7.01608e6	+	3.97902e7i	0.0200869	+	0.113918i
$277$	1.17841e8	−	2.04107e8i	0.333133	−	0.577004i	−0.649991	−	0.759942i	$-0.725227\pi$
$277$	1.17841e8	−	2.04107e8i	0.333133	−	0.577004i	0.983124	+	0.182938i	$0.0585608\pi$
$278$	2.35189e7	+	4.07360e7i	0.0656539	+	0.113716i
$279$	8.27393e8	−	6.94265e8i	2.28085	−	1.91386i
$280$	2.61887e8	−	9.53190e7i	0.712952	−	0.259493i
$281$	2.06746e8	+	7.52493e7i	0.555859	+	0.202316i	0.604648	−	0.796493i	$-0.293314\pi$
$281$	2.06746e8	+	7.52493e7i	0.555859	+	0.202316i	−0.0487890	+	0.998809i	$0.515536\pi$
$282$	3.96296e7	+	3.32532e7i	0.105232	+	0.0883001i
$283$	6.23512e7	−	3.53611e8i	0.163528	−	0.927414i	−0.787041	−	0.616901i	$-0.788388\pi$
$283$	6.23512e7	−	3.53611e8i	0.163528	−	0.927414i	0.950569	−	0.310513i	$-0.100501\pi$
$284$	1.25833e8			0.325971
$285$	−1.72665e8	−	8.46593e8i	−0.441822	−	2.16630i
$286$	−7.56183e7			−0.191138
$287$	−1.10291e8	+	6.25489e8i	−0.275392	+	1.56183i
$288$	−1.34465e8	−	1.12830e8i	−0.331693	−	0.278323i
$289$	−6.65312e7	−	2.42154e7i	−0.162137	−	0.0590132i
$290$	−1.53700e7	+	5.59422e6i	−0.0370067	+	0.0134693i
$291$	−3.52727e8	+	2.95973e8i	−0.839098	+	0.704087i
$292$	4.91884e7	+	8.51969e7i	0.115617	+	0.200255i
$293$	−3.21258e8	+	5.56435e8i	−0.746135	+	1.29234i	0.203528	+	0.979069i	$0.434759\pi$
$293$	−3.21258e8	+	5.56435e8i	−0.746135	+	1.29234i	−0.949663	+	0.313274i	$0.898574\pi$
$294$	2.23548e8	+	1.26780e9i	0.513044	+	2.90962i
$295$	−1.46676e8	−	8.31842e8i	−0.332646	−	1.88653i
$296$	1.50160e8	−	2.60084e8i	0.336537	−	0.582899i
$297$	2.35116e8	+	4.07233e8i	0.520757	+	0.901977i
$298$	2.85926e8	−	2.39920e8i	0.625888	−	0.525182i
$299$	3.77996e7	−	1.37579e7i	0.0817784	−	0.0297649i
$300$	1.70203e8	+	6.19487e7i	0.363950	+	0.132467i
$301$	1.43784e8	+	1.20649e8i	0.303898	+	0.255001i
$302$	4.61824e7	−	2.61914e8i	0.0964834	−	0.547185i
$303$	−1.56749e9			−3.23709
$304$	1.80427e7	−	1.21124e8i	0.0368335	−	0.247272i
$305$	−2.21886e7			−0.0447797
$306$	1.63231e8	−	9.25728e8i	0.325669	−	1.84696i
$307$	6.50891e8	+	5.46163e8i	1.28388	+	1.07730i	0.992697	+	0.120635i	$0.0384931\pi$
$307$	6.50891e8	+	5.46163e8i	1.28388	+	1.07730i	0.291182	+	0.956668i	$0.405951\pi$
$308$	−1.68041e8	−	6.11621e7i	−0.327709	−	0.119276i
$309$	9.50328e8	−	3.45891e8i	1.83239	−	0.666937i
$310$	−4.11138e8	+	3.44986e8i	−0.783829	+	0.657711i
$311$	−2.19119e7	−	3.79525e7i	−0.0413065	−	0.0715449i	0.844633	−	0.535346i	$-0.179819\pi$
$311$	−2.19119e7	−	3.79525e7i	−0.0413065	−	0.0715449i	−0.885940	+	0.463801i	$0.846485\pi$
$312$	−1.23052e8	+	2.13132e8i	−0.229376	+	0.397290i
$313$	−1.30994e8	−	7.42901e8i	−0.241460	−	1.36939i	−0.828573	−	0.559881i	$-0.810847\pi$
$313$	−1.30994e8	−	7.42901e8i	−0.241460	−	1.36939i	0.587113	−	0.809505i	$-0.300264\pi$
$314$	3.78463e7	+	2.14637e8i	0.0689874	+	0.391247i
$315$	−1.45792e9	+	2.52519e9i	−2.62813	+	4.55206i
$316$	−1.89359e8	−	3.27979e8i	−0.337583	−	0.584710i
$317$	−2.87865e8	+	2.41547e8i	−0.507553	+	0.425887i	−0.860267	−	0.509844i	$-0.829703\pi$
$317$	−2.87865e8	+	2.41547e8i	−0.507553	+	0.425887i	0.352714	+	0.935731i	$0.385259\pi$
$318$	1.01403e8	−	3.69078e7i	0.176831	−	0.0643611i
$319$	9.86226e6	+	3.58957e6i	0.0170102	+	0.00619120i
$320$	6.68168e7	+	5.60659e7i	0.113988	+	0.0956476i
$321$	2.40498e8	−	1.36393e9i	0.405830	−	2.30158i
$322$	9.51273e7			0.158785
$323$	6.10055e8	−	2.40646e8i	1.00730	−	0.397347i
$324$	7.80614e8			1.27505
$325$	3.13133e7	−	1.77586e8i	0.0505984	−	0.286958i
$326$	−2.18714e7	−	1.83523e7i	−0.0349635	−	0.0293379i
$327$	7.08841e8	+	2.57997e8i	1.12107	+	0.408035i
$328$	−1.86792e8	+	6.79866e7i	−0.292280	+	0.106381i
$329$	9.33041e7	−	7.82914e7i	0.144449	−	0.121207i
$330$	−1.97438e8	−	3.41973e8i	−0.302435	−	0.523833i
$331$	8.32346e7	−	1.44167e8i	0.126155	−	0.218508i	−0.796029	−	0.605259i	$-0.793070\pi$
$331$	8.32346e7	−	1.44167e8i	0.126155	−	0.218508i	0.922184	+	0.386751i	$0.126403\pi$
$332$	−2.52461e7	−	1.43177e8i	−0.0378626	−	0.214729i
$333$	5.45620e8	+	3.09436e9i	0.809721	+	4.59216i
$334$	4.82410e7	−	8.35558e7i	0.0708441	−	0.122706i
$335$	−1.13053e8	−	1.95814e8i	−0.164295	−	0.284568i
$336$	−4.45836e8	+	3.74101e8i	−0.641192	+	0.538024i
$337$	1.42558e8	−	5.18870e7i	0.202903	−	0.0738506i	−0.238570	−	0.971125i	$-0.576679\pi$
$337$	1.42558e8	−	5.18870e7i	0.202903	−	0.0738506i	0.441472	+	0.897275i	$0.354456\pi$
$338$	−2.41474e8	−	8.78894e7i	−0.340144	−	0.123802i
$339$	−1.44152e9	−	1.20958e9i	−2.00965	−	1.68630i
$340$	−8.11106e7	+	4.60001e8i	−0.111918	+	0.634720i
$341$	3.44379e8			0.470322
$342$	6.69976e8	+	1.09212e9i	0.905666	+	1.47632i
$343$	1.68370e9			2.25287
$344$	−1.02007e7	+	5.78512e7i	−0.0135107	+	0.0766227i
$345$	1.60913e8	+	1.35022e8i	0.210971	+	0.177026i
$346$	3.88610e6	+	1.41443e6i	0.00504368	+	0.00183575i
$347$	−8.85403e8	+	3.22260e8i	−1.13760	+	0.414051i	−0.841044	−	0.540966i	$-0.818059\pi$
$347$	−8.85403e8	+	3.22260e8i	−1.13760	+	0.414051i	−0.296551	+	0.955017i	$0.595836\pi$
$348$	2.61659e7	−	2.19558e7i	0.0332819	−	0.0279268i
$349$	4.32834e8	+	7.49691e8i	0.545045	+	0.944046i	0.998604	+	0.0528196i	$0.0168208\pi$
$349$	4.32834e8	+	7.49691e8i	0.545045	+	0.944046i	−0.453559	+	0.891226i	$0.649846\pi$
$350$	2.13222e8	−	3.69311e8i	0.265824	−	0.460420i
$351$	−2.64577e8	−	1.50049e9i	−0.326570	−	1.85207i
$352$	−9.71862e6	−	5.51170e7i	−0.0118770	−	0.0673576i
$353$	1.35250e8	−	2.34260e8i	0.163654	−	0.283457i	−0.772523	−	0.634987i	$-0.781005\pi$
$353$	1.35250e8	−	2.34260e8i	0.163654	−	0.283457i	0.936176	+	0.351531i	$0.114339\pi$
$354$	8.81968e8	+	1.52761e9i	1.05667	+	1.83021i
$355$	5.01140e8	−	4.20506e8i	0.594510	−	0.498853i
$356$	2.51364e8	−	9.14889e7i	0.295276	−	0.107472i
$357$	−2.92875e9	−	1.06598e9i	−3.40678	−	1.23997i
$358$	4.88302e8	+	4.09734e8i	0.562468	+	0.471967i
$359$	−1.70103e8	+	9.64703e8i	−0.194036	+	1.10043i	0.719749	+	0.694234i	$0.244257\pi$
$359$	−1.70103e8	+	9.64703e8i	−0.194036	+	1.10043i	−0.913785	+	0.406198i	$0.866854\pi$
$360$	−9.12573e8			−1.03088
$361$	−4.05043e8	+	7.96835e8i	−0.453134	+	0.891443i
$362$	−8.29652e8			−0.919213
$363$	2.49912e8	−	1.41732e9i	0.274229	−	1.55523i
$364$	4.43867e8	+	3.72449e8i	0.482390	+	0.404773i
$365$	4.80607e8	+	1.74927e8i	0.517327	+	0.188292i
$366$	4.35422e7	−	1.58481e7i	0.0464223	−	0.0168963i
$367$	7.20050e8	−	6.04194e8i	0.760381	−	0.638036i	−0.177845	−	0.984059i	$-0.556912\pi$
$367$	7.20050e8	−	6.04194e8i	0.760381	−	0.638036i	0.938226	+	0.346023i	$0.112468\pi$
$368$	1.48860e7	+	2.57834e7i	0.0155708	+	0.0269695i
$369$	1.03987e9	−	1.80110e9i	1.07742	−	1.86615i
$370$	−2.71123e8	−	1.53761e9i	−0.278266	−	1.57812i
$371$	−4.41182e7	−	2.50207e8i	−0.0448548	−	0.254384i
$372$	5.60399e8	−	9.70639e8i	0.564413	−	0.977592i
$373$	2.89169e8	+	5.00855e8i	0.288517	+	0.499725i	0.973456	−	0.228875i	$-0.0735046\pi$
$373$	2.89169e8	+	5.00855e8i	0.288517	+	0.499725i	−0.684939	+	0.728600i	$0.740171\pi$
$374$	2.29596e8	−	1.92654e8i	0.226941	−	0.190426i
$375$	−1.23673e9	+	4.50133e8i	−1.21106	+	0.440789i
$376$	3.58209e7	+	1.30377e7i	0.0347519	+	0.0126487i
$377$	−2.60503e7	−	2.18588e7i	−0.0250391	−	0.0210103i
$378$	6.25684e8	−	3.54843e9i	0.595845	−	3.37921i
$379$	−1.12807e9			−1.06438			−0.532192	−	0.846623i	$-0.678632\pi$
$379$	−1.12807e9			−1.06438			−0.532192	+	0.846623i	$0.678632\pi$
$380$	−3.32916e8	−	5.42684e8i	−0.311238	−	0.507346i
$381$	−1.57833e9			−1.46204
$382$	6.81844e7	−	3.86693e8i	0.0625840	−	0.354931i
$383$	−2.07508e8	−	1.74120e8i	−0.188729	−	0.158362i	0.543528	−	0.839391i	$-0.317088\pi$
$383$	−2.07508e8	−	1.74120e8i	−0.188729	−	0.158362i	−0.732256	+	0.681029i	$0.761533\pi$
$384$	−1.71163e8	−	6.22984e7i	−0.154259	−	0.0561458i
$385$	−8.73631e8	+	3.17976e8i	−0.780217	+	0.283976i
$386$	7.50171e8	−	6.29468e8i	0.663903	−	0.557081i
$387$	−3.07303e8	−	5.32264e8i	−0.269512	−	0.466809i
$388$	−1.69644e8	+	2.93832e8i	−0.147444	+	0.255381i
$389$	3.75174e8	+	2.12772e9i	0.323153	+	1.83269i	0.522346	+	0.852734i	$0.325057\pi$
$389$	3.75174e8	+	2.12772e9i	0.323153	+	1.83269i	−0.199192	+	0.979960i	$0.563832\pi$
$390$	2.22177e8	+	1.26003e9i	0.189659	+	1.07561i
$391$	−7.97177e7	+	1.38075e8i	−0.0674428	+	0.116814i
$392$	4.74302e8	+	8.21515e8i	0.397698	+	0.688833i
$393$	−1.87464e9	+	1.57301e9i	−1.55792	+	1.30725i
$394$	−7.61763e8	+	2.77259e8i	−0.627456	+	0.228375i
$395$	−1.85017e9	−	6.73408e8i	−1.51051	−	0.549779i
$396$	4.48564e8	+	3.76390e8i	0.362987	+	0.304582i
$397$	−8.08891e7	+	4.58745e8i	−0.0648819	+	0.367963i	0.935028	+	0.354573i	$0.115374\pi$
$397$	−8.08891e7	+	4.58745e8i	−0.0648819	+	0.367963i	−0.999910	+	0.0133908i	$0.995737\pi$
$398$	−9.95408e8			−0.791426
$399$	3.95180e9	−	1.55885e9i	3.11451	−	1.22857i
$400$	1.33464e8			0.104269
$401$	−3.33511e8	+	1.89143e9i	−0.258288	+	1.46483i	0.529200	+	0.848497i	$0.322492\pi$
$401$	−3.33511e8	+	1.89143e9i	−0.258288	+	1.46483i	−0.787489	+	0.616329i	$0.788619\pi$
$402$	3.61710e8	+	3.03510e8i	0.277696	+	0.233014i
$403$	−1.04855e9	−	3.81642e8i	−0.798037	−	0.290462i
$404$	−1.08536e9	+	3.95040e8i	−0.818917	+	0.298061i
$405$	3.10886e9	−	2.60865e9i	2.32546	−	1.95129i
$406$	−4.02098e7	−	6.96455e7i	−0.0298189	−	0.0516478i
$407$	−5.00920e8	+	8.67618e8i	−0.368288	+	0.637894i
$408$	−1.69384e8	−	9.60622e8i	−0.123470	−	0.700232i
$409$	−3.32409e8	−	1.88519e9i	−0.240238	−	1.36246i	−0.831297	−	0.555828i	$-0.812401\pi$
$409$	−3.32409e8	−	1.88519e9i	−0.240238	−	1.36246i	0.591060	−	0.806628i	$-0.298710\pi$
$410$	−5.16718e8	+	8.94982e8i	−0.370263	+	0.641314i
$411$	1.64670e9	+	2.85217e9i	1.16995	+	2.02642i
$412$	5.70856e8	−	4.79005e8i	0.402148	−	0.337443i
$413$	3.90256e9	−	1.42042e9i	2.72599	−	0.992179i
$414$	−2.92705e8	−	1.06536e8i	−0.202735	−	0.0737897i
$415$	−5.79014e8	−	4.85850e8i	−0.397668	−	0.333683i
$416$	−3.14900e7	+	1.78589e8i	−0.0214460	+	0.121626i
$417$	−5.10685e8			−0.344887
$418$	−6.01887e7	+	4.04060e8i	−0.0403086	+	0.270601i
$419$	7.52155e8			0.499526			0.249763	−	0.968307i	$-0.419647\pi$
$419$	7.52155e8			0.499526			0.249763	+	0.968307i	$0.419647\pi$
$420$	−5.25416e8	+	2.97978e9i	−0.346044	+	1.96251i
$421$	5.34010e8	+	4.48087e8i	0.348788	+	0.292668i	0.800303	−	0.599595i	$-0.204672\pi$
$421$	5.34010e8	+	4.48087e8i	0.348788	+	0.292668i	−0.451515	+	0.892264i	$0.649116\pi$
$422$	−2.15886e6	−	785759.i	−0.00139840	−	0.000508974i
$423$	−3.74777e8	+	1.36407e8i	−0.240758	+	0.0876288i
$424$	6.09124e7	−	5.11115e7i	0.0388083	−	0.0325641i
$425$	3.57364e8	+	6.18973e8i	0.225813	+	0.391120i
$426$	−6.83075e8	+	1.18312e9i	−0.428090	+	0.741473i
$427$	−1.89442e7	−	1.07438e8i	−0.0117755	−	0.0667820i
$428$	−1.77213e8	−	1.00503e9i	−0.109256	−	0.619619i
$429$	4.10490e8	−	7.10989e8i	0.251016	−	0.434773i
$430$	1.52701e8	+	2.64486e8i	0.0926196	+	0.160422i
$431$	−2.05167e8	+	1.72155e8i	−0.123434	+	0.103574i	−0.702415	−	0.711767i	$-0.747895\pi$
$431$	−2.05167e8	+	1.72155e8i	−0.123434	+	0.103574i	0.578981	+	0.815341i	$0.303451\pi$
$432$	1.05968e9	−	3.85691e8i	0.632384	−	0.230169i
$433$	3.11984e9	+	1.13553e9i	1.84682	+	0.672189i	0.986802	+	0.161930i	$0.0517718\pi$
$433$	3.11984e9	+	1.13553e9i	1.84682	+	0.672189i	0.860021	+	0.510259i	$0.170450\pi$
$434$	−2.02144e9	−	1.69619e9i	−1.18699	−	0.996005i
$435$	3.08364e7	−	1.74882e8i	0.0179618	−	0.101867i
$436$	5.55837e8			0.321177
$437$	−4.34277e7	−	2.12930e8i	−0.0248932	−	0.122054i
$438$	−1.06807e9			−0.607350
$439$	1.76511e7	−	1.00105e8i	0.00995742	−	0.0564714i	−0.979424	−	0.201812i	$-0.935317\pi$
$439$	1.76511e7	−	1.00105e8i	0.00995742	−	0.0564714i	0.989382	+	0.145341i	$0.0464280\pi$
$440$	−2.22895e8	−	1.87031e8i	−0.124743	−	0.104672i
$441$	−9.32625e9	−	3.39448e9i	−5.17812	−	1.88468i
$442$	−9.12566e8	+	3.32147e8i	−0.502674	+	0.182958i
$443$	−2.42881e9	+	2.03801e9i	−1.32733	+	1.11376i	−0.342641	+	0.939467i	$0.611321\pi$
$443$	−2.42881e9	+	2.03801e9i	−1.32733	+	1.11376i	−0.984693	+	0.174298i	$0.944234\pi$
$444$	1.63027e9	+	2.82371e9i	0.883932	+	1.53101i
$445$	6.95342e8	−	1.20437e9i	0.374057	−	0.647886i
$446$	−3.48799e8	−	1.97814e9i	−0.186167	−	1.05581i
$447$	7.03680e8	+	3.99077e9i	0.372648	+	2.11339i
$448$	−2.14425e8	+	3.71396e8i	−0.112669	+	0.195148i
$449$	5.62399e7	+	9.74104e7i	0.0293213	+	0.0507859i	0.880314	−	0.474392i	$-0.157332\pi$
$449$	5.62399e7	+	9.74104e7i	0.0293213	+	0.0507859i	−0.850992	+	0.525178i	$0.823999\pi$
$450$	−1.06968e9	+	8.97572e8i	−0.553365	+	0.464328i
$451$	6.23121e8	−	2.26797e8i	0.319856	−	0.116418i
$452$	−1.30298e9	−	4.74245e8i	−0.663670	−	0.241556i
$453$	2.21190e9	+	1.85601e9i	1.11795	+	0.938071i
$454$	−2.22191e8	+	1.26011e9i	−0.111437	+	0.631993i
$455$	3.01239e9			1.49924
$456$	1.04091e9	+	8.27161e8i	0.514087	+	0.408520i
$457$	2.67806e9			1.31254			0.656272	−	0.754524i	$-0.272132\pi$
$457$	2.67806e9			1.31254			0.656272	+	0.754524i	$0.272132\pi$
$458$	−2.96816e8	+	1.68333e9i	−0.144364	+	0.818729i
$459$	4.62613e9	+	3.88178e9i	2.23292	+	1.87364i
$460$	1.45448e8	+	5.29386e7i	0.0696713	+	0.0253583i
$461$	1.57167e9	−	5.72041e8i	0.747151	−	0.271941i	0.0597446	−	0.998214i	$-0.480971\pi$
$461$	1.57167e9	−	5.72041e8i	0.747151	−	0.271941i	0.687406	+	0.726273i	$0.258749\pi$
$462$	1.48727e9	−	1.24797e9i	0.701686	−	0.588784i
$463$	−1.17123e9	−	2.02864e9i	−0.548417	−	0.949885i	−0.998383	−	0.0568400i	$-0.981898\pi$
$463$	−1.17123e9	−	2.02864e9i	−0.548417	−	0.949885i	0.449967	−	0.893045i	$-0.351436\pi$
$464$	1.25845e7	−	2.17970e7i	0.00584821	−	0.0101294i
$465$	−1.01183e9	−	5.73839e9i	−0.466685	−	2.64670i
$466$	4.07430e7	+	2.31065e8i	0.0186510	+	0.105775i
$467$	−1.62616e8	+	2.81659e8i	−0.0738846	+	0.127972i	−0.900601	−	0.434647i	$-0.856873\pi$
$467$	−1.62616e8	+	2.81659e8i	−0.0738846	+	0.127972i	0.826716	+	0.562619i	$0.190206\pi$
$468$	−9.48656e8	−	1.64312e9i	−0.427808	−	0.740984i
$469$	8.51610e8	−	7.14586e8i	0.381185	−	0.319852i
$470$	1.86229e8	−	6.77819e7i	0.0827381	−	0.0301142i
$471$	−2.22354e9	−	8.09301e8i	−0.980553	−	0.356892i
$472$	9.95684e8	+	8.35478e8i	0.435837	+	0.365711i
$473$	3.40287e7	−	1.92986e8i	0.0147853	−	0.0838518i
$474$	4.11169e9			1.77336
$475$	−9.23995e8	−	3.08671e8i	−0.395587	−	0.132150i
$476$	−2.29658e9			−0.976017
$477$	−1.44463e8	+	8.19293e8i	−0.0609458	+	0.345641i
$478$	−1.08371e9	−	9.09339e8i	−0.453852	−	0.380827i
$479$	−4.20217e9	−	1.52947e9i	−1.74703	−	0.635866i	−0.747432	−	0.664338i	$-0.768713\pi$
$479$	−4.20217e9	−	1.52947e9i	−1.74703	−	0.635866i	−0.999595	+	0.0284727i	$0.990936\pi$
$480$	−8.89862e8	+	3.23883e8i	−0.367264	+	0.133673i
$481$	2.48668e9	−	2.08658e9i	1.01886	−	0.854922i
$482$	−9.57348e8	−	1.65818e9i	−0.389408	−	0.674475i
$483$	−5.16393e8	+	8.94419e8i	−0.208528	+	0.361182i
$484$	−1.84150e8	−	1.04437e9i	−0.0738266	−	0.418691i
$485$	3.06303e8	+	1.73713e9i	0.121914	+	0.691411i
$486$	−1.82907e9	+	3.16804e9i	−0.722775	+	1.25188i
$487$	1.67297e9	+	2.89767e9i	0.656353	+	1.13684i	0.981553	+	0.191191i	$0.0612349\pi$
$487$	1.67297e9	+	2.89767e9i	0.656353	+	1.13684i	−0.325200	+	0.945645i	$0.605432\pi$
$488$	2.61555e7	−	2.19471e7i	0.0101881	−	0.00854884i
$489$	2.91282e8	−	1.06018e8i	0.112650	−	0.0410014i
$490$	4.63428e9	+	1.68674e9i	1.77949	+	0.647682i
$491$	−2.27824e9	−	1.91167e9i	−0.868591	−	0.728834i	0.0952102	−	0.995457i	$-0.469648\pi$
$491$	−2.27824e9	−	1.91167e9i	−0.868591	−	0.728834i	−0.963801	+	0.266623i	$0.914092\pi$
$492$	3.74755e8	−	2.12534e9i	0.141863	−	0.804546i
$493$	1.34785e8			0.0506615
$494$	6.31043e8	−	1.16357e9i	0.235513	−	0.434258i
$495$	3.04426e9			1.12814
$496$	1.43411e8	−	8.13323e8i	0.0527711	−	0.299280i
$497$	2.46396e9	+	2.06751e9i	0.900297	+	0.755439i
$498$	1.48325e9	+	5.39859e8i	0.538160	+	0.195874i
$499$	−8.97528e8	+	3.26674e8i	−0.323367	+	0.117696i	−0.498603	−	0.866830i	$-0.666153\pi$
$499$	−8.97528e8	+	3.26674e8i	−0.323367	+	0.117696i	0.175236	+	0.984527i	$0.443931\pi$
$500$	−7.42895e8	+	6.23363e8i	−0.265786	+	0.223021i
$501$	5.23747e8	+	9.07156e8i	0.186076	+	0.322292i
$502$	−1.89804e8	+	3.28749e8i	−0.0669640	+	0.115985i
$503$	6.62879e7	+	3.75938e8i	0.0232245	+	0.131713i	0.994216	−	0.107403i	$-0.0342535\pi$
$503$	6.62879e7	+	3.75938e8i	0.0232245	+	0.131713i	−0.970991	+	0.239116i	$0.923142\pi$
$504$	−7.79135e8	−	4.41869e9i	−0.271085	−	1.53740i
$505$	−3.00241e9	+	5.20033e9i	−1.03741	+	1.79685i
$506$	−4.96585e7	−	8.60110e7i	−0.0170399	−	0.0295139i
$507$	2.13720e9	−	1.79332e9i	0.728310	−	0.611125i
$508$	−1.09287e9	+	3.97771e8i	−0.369866	+	0.134620i
$509$	−1.89023e9	−	6.87988e8i	−0.635335	−	0.231243i	0.00421672	−	0.999991i	$-0.498658\pi$
$509$	−1.89023e9	−	6.87988e8i	−0.635335	−	0.231243i	−0.639552	+	0.768748i	$0.720880\pi$
$510$	−3.88478e9	−	3.25972e9i	−1.29679	−	1.08814i
$511$	−4.36666e8	+	2.47646e9i	−0.144769	+	0.821027i
$512$	−1.34218e8			−0.0441942
$513$	−8.22833e9	+	2.19424e8i	−2.69092	+	0.0717586i
$514$	5.77202e8			0.187481
$515$	6.72751e8	−	3.81536e9i	0.217035	−	1.23086i
$516$	−4.88562e8	−	4.09952e8i	−0.156547	−	0.131359i
$517$	−1.19495e8	−	4.34927e7i	−0.0380306	−	0.0138420i
$518$	7.21366e9	−	2.62556e9i	2.28035	−	0.829980i
$519$	−3.43944e7	+	2.88603e7i	−0.0107995	+	0.00906182i
$520$	4.71394e8	+	8.16479e8i	0.147019	+	0.254644i
$521$	−2.85346e9	+	4.94234e9i	−0.883975	+	1.53109i	−0.0370907	+	0.999312i	$0.511809\pi$
$521$	−2.85346e9	+	4.94234e9i	−0.883975	+	1.53109i	−0.846884	+	0.531777i	$0.821524\pi$
$522$	4.57270e7	+	2.59331e8i	0.0140710	+	0.0798008i
$523$	−1.05408e9	−	5.97799e9i	−0.322194	−	1.82726i	−0.528699	−	0.848809i	$-0.677320\pi$
$523$	−1.05408e9	−	5.97799e9i	−0.322194	−	1.82726i	0.206504	−	0.978446i	$-0.433791\pi$
$524$	−9.01610e8	+	1.56163e9i	−0.273753	+	0.474154i
$525$	2.31493e9	+	4.00957e9i	0.698199	+	1.20932i
$526$	−1.21778e9	+	1.02184e9i	−0.364854	+	0.306149i
$527$	4.15598e9	−	1.51265e9i	1.23690	−	0.450196i
$528$	5.70986e8	+	2.07822e8i	0.168813	+	0.0614430i
$529$	−2.56778e9	−	2.15462e9i	−0.754158	−	0.632814i
$530$	7.17849e7	−	4.07113e8i	0.0209444	−	0.118782i
$531$	−1.35989e10			−3.94160
$532$	2.34345e9	−	2.07532e9i	0.674783	−	0.597576i
$533$	−2.14860e9			−0.614624
$534$	−5.04304e8	+	2.86005e9i	−0.143317	+	0.812791i
$535$	−4.06436e9	−	3.41040e9i	−1.14750	−	0.962869i
$536$	3.26946e8	+	1.18999e8i	0.0917064	+	0.0333784i
$537$	−6.50318e9	+	2.36696e9i	−1.81224	+	0.659601i
$538$	−7.91340e8	+	6.64013e8i	−0.219091	+	0.183839i
$539$	−1.58223e9	−	2.74050e9i	−0.435220	−	0.753823i
$540$	2.93137e9	−	5.07727e9i	0.801109	−	1.38756i
$541$	−3.25767e8	−	1.84752e9i	−0.0884538	−	0.501646i	−0.996558	−	0.0829015i	$-0.973581\pi$
$541$	−3.25767e8	−	1.84752e9i	−0.0884538	−	0.501646i	0.908104	−	0.418745i	$-0.137530\pi$
$542$	−2.47347e8	−	1.40277e9i	−0.0667281	−	0.378434i
$543$	4.50372e9	−	7.80067e9i	1.20718	−	2.09090i
$544$	−3.59381e8	−	6.22467e8i	−0.0957105	−	0.165775i
$545$	2.21367e9	−	1.85749e9i	0.585768	−	0.491518i
$546$	−5.91140e9	+	2.15157e9i	−1.55423	+	0.565694i
$547$	3.10174e9	+	1.12894e9i	0.810308	+	0.294928i	0.713751	−	0.700399i	$-0.246995\pi$
$547$	3.10174e9	+	1.12894e9i	0.810308	+	0.294928i	0.0965571	+	0.995327i	$0.469217\pi$
$548$	1.85902e9	+	1.55990e9i	0.482561	+	0.404916i
$549$	−6.20319e7	+	3.51801e8i	−0.0159997	+	0.0907389i
$550$	−4.45225e8			−0.114106
$551$	−1.37536e8	+	1.21799e8i	−0.0350255	+	0.0310180i
$552$	−3.23232e8			−0.0817951
$553$	1.68101e9	−	9.53350e9i	0.422701	−	2.39726i
$554$	1.44435e9	+	1.21195e9i	0.360900	+	0.302831i
$555$	1.59289e10	+	5.79766e9i	3.95513	+	1.43955i
$556$	−3.53609e8	+	1.28703e8i	−0.0872492	+	0.0317561i
$557$	2.75368e9	−	2.31061e9i	0.675180	−	0.566544i	−0.239413	−	0.970918i	$-0.576955\pi$
$557$	2.75368e9	−	2.31061e9i	0.675180	−	0.566544i	0.914594	+	0.404374i	$0.132511\pi$
$558$	4.32034e9	+	7.48305e9i	1.05268	+	1.82330i
$559$	−3.17478e8	+	5.49888e8i	−0.0768727	+	0.133147i
$560$	3.87158e8	+	2.19568e9i	0.0931601	+	0.528337i
$561$	5.65048e8	+	3.20455e9i	0.135119	+	0.766296i
$562$	−8.80057e8	+	1.52430e9i	−0.209138	+	0.362238i
$563$	−8.64630e8	−	1.49758e9i	−0.204198	−	0.353681i	0.745679	−	0.666305i	$-0.232125\pi$
$563$	−8.64630e8	−	1.49758e9i	−0.204198	−	0.353681i	−0.949877	+	0.312624i	$0.898792\pi$
$564$	−3.17037e8	+	2.66025e8i	−0.0744103	+	0.0624376i
$565$	−6.77405e9	+	2.46555e9i	−1.58008	+	0.575102i
$566$	2.69930e9	+	9.82464e8i	0.625739	+	0.227750i
$567$	1.52854e10	+	1.28260e10i	3.52156	+	2.95494i
$568$	−1.74805e8	+	9.91367e8i	−0.0400253	+	0.226994i
$569$	−1.42398e9			−0.324050			−0.162025	−	0.986787i	$-0.551803\pi$
$569$	−1.42398e9			−0.324050			−0.162025	+	0.986787i	$0.551803\pi$
$570$	6.90972e9	−	1.84261e8i	1.56278	−	0.0416746i
$571$	6.27535e8			0.141062			0.0705312	−	0.997510i	$-0.477531\pi$
$571$	6.27535e8			0.141062			0.0705312	+	0.997510i	$0.477531\pi$
$572$	1.05048e8	−	5.95756e8i	0.0234694	−	0.133101i
$573$	3.26568e9	+	2.74023e9i	0.725158	+	0.608480i
$574$	−4.77468e9	−	1.73784e9i	−1.05379	−	0.383547i
$575$	2.22556e8	−	8.10039e7i	0.0488206	−	0.0177692i
$576$	1.07572e9	−	9.02638e8i	0.234542	−	0.196804i
$577$	2.91116e9	+	5.04228e9i	0.630887	+	1.09273i	0.987371	+	0.158426i	$0.0506420\pi$
$577$	2.91116e9	+	5.04228e9i	0.630887	+	1.09273i	−0.356484	+	0.934301i	$0.616025\pi$
$578$	2.83204e8	−	4.90524e8i	0.0610032	−	0.105661i
$579$	1.84621e9	+	1.04704e10i	0.395282	+	2.24175i
$580$	−2.27221e7	−	1.28863e8i	−0.00483560	−	0.0274240i
$581$	1.85814e9	−	3.21840e9i	0.393064	−	0.680806i
$582$	−1.84181e9	−	3.19011e9i	−0.387270	−	0.670771i
$583$	−2.03198e8	+	1.70503e8i	−0.0424698	+	0.0356364i
$584$	−7.39552e8	+	2.69175e8i	−0.153647	+	0.0559229i
$585$	−9.26908e9	−	3.37367e9i	−1.91422	−	0.696718i
$586$	−3.93757e9	−	3.30401e9i	−0.808326	−	0.678266i
$587$	5.93675e8	−	3.36690e9i	0.121148	−	0.687064i	−0.862374	−	0.506272i	$-0.831023\pi$
$587$	5.93675e8	−	3.36690e9i	0.121148	−	0.687064i	0.983521	−	0.180791i	$-0.0578658\pi$
$588$	−1.02989e10			−2.08915
$589$	−2.87387e9	+	5.29909e9i	−0.579514	+	1.06856i
$590$	6.75739e9			1.35456
$591$	1.52830e9	−	8.66744e9i	0.304546	−	1.72717i
$592$	1.84047e9	+	1.54433e9i	0.364587	+	0.305925i
$593$	1.57975e9	+	5.74981e8i	0.311097	+	0.113230i	0.492850	−	0.870114i	$-0.335955\pi$
$593$	1.57975e9	+	5.74981e8i	0.311097	+	0.113230i	−0.181753	+	0.983344i	$0.558177\pi$
$594$	−3.53499e9	+	1.28663e9i	−0.692047	+	0.251885i
$595$	−9.14634e9	+	7.67469e9i	−1.78007	+	1.49366i
$596$	1.49300e9	+	2.58595e9i	0.288867	+	0.500332i
$597$	5.40352e9	−	9.35916e9i	1.03936	−	1.80023i
$598$	5.58807e7	+	3.16915e8i	0.0106858	+	0.0606023i
$599$	8.85919e8	+	5.02429e9i	0.168422	+	0.955171i	0.945465	+	0.325723i	$0.105608\pi$
$599$	8.85919e8	+	5.02429e9i	0.168422	+	0.955171i	−0.777043	+	0.629448i	$0.783281\pi$
$600$	−7.24504e8	+	1.25488e9i	−0.136934	+	0.237177i
$601$	−2.14068e9	−	3.70776e9i	−0.402245	−	0.696708i	0.591752	−	0.806120i	$-0.298437\pi$
$601$	−2.14068e9	−	3.70776e9i	−0.402245	−	0.696708i	−0.993996	+	0.109412i	$0.965103\pi$
$602$	−1.15027e9	+	9.65193e8i	−0.214888	+	0.180313i
$603$	−3.42068e9	+	1.24503e9i	−0.635334	+	0.231243i
$604$	1.99932e9	+	7.27693e8i	0.369193	+	0.134375i
$605$	−4.22345e9	−	3.54389e9i	−0.775395	−	0.650634i
$606$	2.17753e9	−	1.23494e10i	0.397475	−	2.25420i
$607$	5.21791e9			0.946970			0.473485	−	0.880802i	$-0.342996\pi$
$607$	5.21791e9			0.946970			0.473485	+	0.880802i	$0.342996\pi$
$608$	9.29210e8	+	3.10413e8i	0.167668	+	0.0560115i
$609$	8.73108e8			0.156642
$610$	3.08241e7	−	1.74812e8i	0.00549840	−	0.0311830i
$611$	3.15637e8	+	2.64851e8i	0.0559813	+	0.0469739i
$612$	7.06655e9	+	2.57201e9i	1.24617	+	0.453569i
$613$	−5.70101e9	+	2.07500e9i	−0.999631	+	0.363836i	−0.789442	−	0.613825i	$-0.789630\pi$
$613$	−5.70101e9	+	2.07500e9i	−0.999631	+	0.363836i	−0.210189	+	0.977661i	$0.567408\pi$
$614$	−5.20713e9	+	4.36930e9i	−0.907840	+	0.761768i
$615$	−5.60995e9	−	9.71672e9i	−0.972514	−	1.68444i
$616$	7.15304e8	−	1.23894e9i	0.123299	−	0.213559i
$617$	7.04466e8	+	3.99522e9i	0.120743	+	0.684767i	0.983746	+	0.179568i	$0.0574699\pi$
$617$	7.04466e8	+	3.99522e9i	0.120743	+	0.684767i	−0.863003	+	0.505199i	$0.831419\pi$
$618$	1.40491e9	+	7.96763e9i	0.239435	+	1.35791i
$619$	−1.15028e9	+	1.99234e9i	−0.194933	+	0.337635i	−0.946879	−	0.321591i	$-0.895782\pi$
$619$	−1.15028e9	+	1.99234e9i	−0.194933	+	0.337635i	0.751945	+	0.659225i	$0.229116\pi$
$620$	−2.14681e9	−	3.71838e9i	−0.361762	−	0.626589i
$621$	1.53296e9	−	1.28631e9i	0.256868	−	0.215538i
$622$	3.29447e8	−	1.19909e8i	0.0548932	−	0.0199795i
$623$	6.42523e9	+	2.33859e9i	1.06459	+	0.387477i
$624$	−1.50821e9	−	1.26554e9i	−0.248494	−	0.208511i
$625$	−1.31754e9	+	7.47215e9i	−0.215866	+	1.22424i
$626$	6.03489e9			0.983240
$627$	−3.47238e9	−	2.75933e9i	−0.562589	−	0.447062i
$628$	−1.74358e9			−0.280921
$629$	−2.23419e9	+	1.26707e10i	−0.357966	+	2.03013i
$630$	−1.78693e10	−	1.49941e10i	−2.84719	−	2.38907i
$631$	−3.07816e9	−	1.12036e9i	−0.487740	−	0.177523i	0.0864315	−	0.996258i	$-0.472454\pi$
$631$	−3.07816e9	−	1.12036e9i	−0.487740	−	0.177523i	−0.574172	+	0.818735i	$0.694676\pi$
$632$	2.84702e9	−	1.03623e9i	0.448622	−	0.163285i
$633$	1.91072e7	−	1.60328e7i	0.00299422	−	0.00251245i
$634$	−1.50312e9	−	2.60349e9i	−0.234251	−	0.405735i
$635$	−3.02317e9	+	5.23629e9i	−0.468549	+	0.811551i
$636$	1.49909e8	+	8.50175e8i	0.0231061	+	0.131041i
$637$	1.78048e9	+	1.00976e10i	0.272929	+	1.54786i
$638$	−4.19808e7	+	7.27129e7i	−0.00639997	+	0.0110851i
$639$	−5.26610e9	−	9.12115e9i	−0.798429	−	1.38292i
$640$	−5.34534e8	+	4.48527e8i	−0.0806020	+	0.0676331i
$641$	2.07097e9	−	7.53772e8i	0.310578	−	0.113041i	−0.182029	−	0.983293i	$-0.558266\pi$
$641$	2.07097e9	−	7.53772e8i	0.310578	−	0.113041i	0.492607	+	0.870252i	$0.336044\pi$
$642$	1.04116e10	+	3.78951e9i	1.55291	+	0.565211i
$643$	2.98030e9	+	2.50077e9i	0.442101	+	0.370967i	0.836495	−	0.547974i	$-0.184601\pi$
$643$	2.98030e9	+	2.50077e9i	0.442101	+	0.370967i	−0.394394	+	0.918942i	$0.629045\pi$
$644$	−1.32149e8	+	7.49457e8i	−0.0194969	+	0.110572i
$645$	−3.31572e9			−0.486540
$646$	1.04844e9	+	5.14060e9i	0.153013	+	0.750239i
$647$	3.65624e9			0.530725			0.265363	−	0.964149i	$-0.414508\pi$
$647$	3.65624e9			0.530725			0.265363	+	0.964149i	$0.414508\pi$
$648$	−1.08442e9	+	6.15003e9i	−0.156561	+	0.887902i
$649$	−3.32151e9	−	2.78708e9i	−0.476957	−	0.400215i
$650$	1.35561e9	+	4.93401e8i	0.193614	+	0.0704698i
$651$	2.69215e10	−	9.79862e9i	3.82442	−	1.39198i
$652$	1.74971e8	−	1.46818e8i	0.0247229	−	0.0207450i
$653$	−5.72381e9	−	9.91393e9i	−0.804432	−	1.39332i	−0.916674	−	0.399636i	$-0.869137\pi$
$653$	−5.72381e9	−	9.91393e9i	−0.804432	−	1.39332i	0.112242	−	0.993681i	$-0.464197\pi$
$654$	−3.01733e9	+	5.22617e9i	−0.421794	+	0.730569i
$655$	1.62791e9	+	9.23234e9i	0.226353	+	1.28371i
$656$	−2.76142e8	−	1.56608e9i	−0.0381917	−	0.216596i
$657$	4.11708e9	−	7.13099e9i	0.566383	−	0.981004i
$658$	4.87199e8	+	8.43854e8i	0.0666678	+	0.115472i
$659$	9.14843e9	−	7.67644e9i	1.24522	−	1.04487i	0.248127	−	0.968728i	$-0.420185\pi$
$659$	9.14843e9	−	7.67644e9i	1.24522	−	1.04487i	0.997097	−	0.0761392i	$-0.0242593\pi$
$660$	2.96850e9	−	1.08045e9i	0.401914	−	0.146285i
$661$	−5.98253e9	−	2.17746e9i	−0.805712	−	0.293255i	−0.0938605	−	0.995585i	$-0.529921\pi$
$661$	−5.98253e9	−	2.17746e9i	−0.805712	−	0.293255i	−0.711851	+	0.702330i	$0.752143\pi$
$662$	1.02018e9	+	8.56035e8i	0.136671	+	0.114680i
$663$	1.83086e9	−	1.03833e10i	0.243981	−	1.38369i
$664$	1.16309e9			0.154179
$665$	2.39772e9	−	1.60964e10i	0.316171	−	2.12253i
$666$	−2.51368e10			−3.29724
$667$	7.75578e6	−	4.39852e7i	0.00101201	−	0.00573940i
$668$	5.91276e8	+	4.96139e8i	0.0767489	+	0.0644000i
$669$	2.04926e10	+	7.45868e9i	2.64609	+	0.963098i
$670$	1.69976e9	−	6.18663e8i	0.218337	−	0.0794680i
$671$	−8.72524e7	+	7.32135e7i	−0.0111493	+	0.00935539i
$672$	−2.32799e9	−	4.03220e9i	−0.295930	−	0.512566i
$673$	−3.43921e9	+	5.95689e9i	−0.434917	+	0.753298i	−0.997289	−	0.0735866i	$-0.976555\pi$
$673$	−3.43921e9	+	5.95689e9i	−0.434917	+	0.753298i	0.562372	+	0.826884i	$0.309889\pi$
$674$	2.10750e8	+	1.19522e9i	0.0265129	+	0.150362i
$675$	−1.55777e9	−	8.83457e9i	−0.194958	−	1.10566i
$676$	1.02789e9	−	1.78035e9i	0.127977	−	0.221662i
$677$	−2.81946e9	−	4.88345e9i	−0.349225	−	0.604876i	0.636887	−	0.770957i	$-0.280222\pi$
$677$	−2.81946e9	−	4.88345e9i	−0.349225	−	0.604876i	−0.986112	+	0.166081i	$0.946889\pi$
$678$	1.15321e10	−	9.67662e9i	1.42104	−	1.19239i
$679$	−8.14969e9	+	2.96624e9i	−0.999072	+	0.363632i
$680$	−3.51142e9	−	1.27805e9i	−0.428254	−	0.155872i
$681$	−1.06418e10	−	8.92954e9i	−1.29122	−	1.08346i
$682$	−4.78406e8	+	2.71317e9i	−0.0577499	+	0.327516i
$683$	1.00504e9			0.120701			0.0603506	−	0.998177i	$-0.480778\pi$
$683$	1.00504e9			0.120701			0.0603506	+	0.998177i	$0.480778\pi$
$684$	−9.53497e9	+	3.76122e9i	−1.13926	+	0.449399i
$685$	1.26166e10			1.49977
$686$	−2.33898e9	+	1.32650e10i	−0.276625	+	1.56882i
$687$	−1.42160e10	−	1.19286e10i	−1.67274	−	1.40360i
$688$	−4.41608e8	−	1.60732e8i	−0.0516984	−	0.0188167i
$689$	8.07644e8	−	2.93958e8i	0.0940704	−	0.0342388i
$690$	−1.28730e9	+	1.08017e9i	−0.149179	+	0.125176i
$691$	4.40764e9	+	7.63425e9i	0.508198	+	0.880224i	0.999955	+	0.00949187i	$0.00302140\pi$
$691$	4.40764e9	+	7.63425e9i	0.508198	+	0.880224i	−0.491757	+	0.870732i	$0.663645\pi$
$692$	−1.65420e7	+	2.86516e7i	−0.00189765	+	0.00328683i
$693$	2.59912e9	+	1.47404e10i	0.296661	+	1.68245i
$694$	−1.30893e9	−	7.42329e9i	−0.148647	−	0.843021i
$695$	−9.78181e8	+	1.69426e9i	−0.110528	+	0.191440i
$696$	1.36629e8	+	2.36648e8i	0.0153606	+	0.0266054i
$697$	6.52366e9	−	5.47400e9i	0.729755	−	0.612337i
$698$	−6.50770e9	+	2.36861e9i	−0.724325	+	0.263633i
$699$	−2.39373e9	−	8.71245e8i	−0.265097	−	0.0964873i
$700$	2.61340e9	+	2.19290e9i	0.287980	+	0.241644i
$701$	−2.36236e9	+	1.33976e10i	−0.259020	+	1.46897i	0.526521	+	0.850162i	$0.323496\pi$
$701$	−2.36236e9	+	1.33976e10i	−0.259020	+	1.46897i	−0.785540	+	0.618811i	$0.787615\pi$
$702$	1.21891e10			1.32982
$703$	−9.17016e9	−	1.49482e10i	−0.995482	−	1.62273i
$704$	4.47738e8			0.0483637
$705$	−3.73626e8	+	2.11894e9i	−0.0401583	+	0.227749i
$706$	1.65772e9	+	1.39099e9i	0.177294	+	0.148768i
$707$	−2.77435e10	−	1.00978e10i	−2.95252	−	1.07463i
$708$	−1.32605e10	+	4.82641e9i	−1.40424	+	0.511103i
$709$	5.19159e9	−	4.35626e9i	0.547064	−	0.459041i	−0.326881	−	0.945065i	$-0.605998\pi$
$709$	5.19159e9	−	4.35626e9i	0.547064	−	0.459041i	0.873945	+	0.486024i	$0.161553\pi$
$710$	2.61676e9	+	4.53237e9i	0.274385	+	0.475249i
$711$	−1.58493e10	+	2.74518e10i	−1.65374	+	2.86436i
$712$	3.71601e8	+	2.10745e9i	0.0385831	+	0.218816i
$713$	−2.54490e8	−	1.44329e9i	−0.0262941	−	0.149121i
$714$	1.24669e10	−	2.15932e10i	1.28178	−	2.22011i
$715$	−1.57253e9	−	2.72370e9i	−0.160889	−	0.278669i
$716$	−3.90642e9	+	3.27787e9i	−0.397725	+	0.333731i
$717$	1.44328e10	−	5.25310e9i	1.46229	−	0.532229i
$718$	−7.36407e9	−	2.68030e9i	−0.742476	−	0.270239i
$719$	1.39128e10	+	1.16742e10i	1.39593	+	1.17132i	0.962873	+	0.269954i	$0.0870085\pi$
$719$	1.39128e10	+	1.16742e10i	1.39593	+	1.17132i	0.433054	+	0.901368i	$0.357436\pi$
$720$	1.26773e9	−	7.18967e9i	0.126580	−	0.717869i
$721$	1.90484e10			1.89272
$722$	−5.71516e9	−	4.29807e9i	−0.565129	−	0.425004i
$723$	2.07876e10			2.04560
$724$	1.15254e9	−	6.53638e9i	0.112868	−	0.640107i
$725$	−1.53379e8	−	1.28700e8i	−0.0149480	−	0.0125429i
$726$	1.08191e10	+	3.93784e9i	1.04934	+	0.381927i
$727$	−1.57815e10	+	5.74399e9i	−1.52327	+	0.554426i	−0.961963	−	0.273180i	$-0.911924\pi$
$727$	−1.57815e10	+	5.74399e9i	−1.52327	+	0.554426i	−0.561309	+	0.827606i	$0.689702\pi$
$728$	−3.55094e9	+	2.97959e9i	−0.341101	+	0.286218i
$729$	−6.52049e9	−	1.12938e10i	−0.623353	−	1.07968i
$730$	−2.04581e9	+	3.54344e9i	−0.194641	+	0.337128i
$731$	−4.37015e8	−	2.47844e9i	−0.0413795	−	0.234675i
$732$	6.43702e7	+	3.65061e8i	0.00606591	+	0.0344015i
$733$	−1.42317e9	+	2.46499e9i	−0.133472	+	0.231181i	−0.925013	−	0.379936i	$-0.875946\pi$
$733$	−1.42317e9	+	2.46499e9i	−0.133472	+	0.231181i	0.791540	+	0.611117i	$0.209279\pi$
$734$	3.75983e9	+	6.51222e9i	0.350940	+	0.607845i
$735$	−4.10162e10	+	3.44167e10i	−3.81022	+	3.19715i
$736$	−2.23813e8	+	8.14611e7i	−0.0206925	+	0.00753144i
$737$	−1.09066e9	−	3.96969e8i	−0.100359	−	0.0365276i
$738$	1.27454e10	+	1.06946e10i	1.16723	+	0.979418i
$739$	−1.28151e9	+	7.26780e9i	−0.116806	+	0.662441i	0.869034	+	0.494753i	$0.164741\pi$
$739$	−1.28151e9	+	7.26780e9i	−0.116806	+	0.662441i	−0.985840	+	0.167688i	$0.946370\pi$
$740$	1.24907e10			1.13312
$741$	7.51469e9	+	1.22496e10i	0.678497	+	1.10601i
$742$	2.03253e9			0.182652
$743$	−2.43485e9	+	1.38087e10i	−0.217776	+	1.23507i	0.658247	+	0.752802i	$0.271298\pi$
$743$	−2.43485e9	+	1.38087e10i	−0.217776	+	1.23507i	−0.876023	+	0.482269i	$0.839813\pi$
$744$	6.86864e9	+	5.76348e9i	0.611457	+	0.513073i
$745$	1.45877e10	+	5.30949e9i	1.29253	+	0.470442i
$746$	−4.34768e9	+	1.58243e9i	−0.383417	+	0.139552i
$747$	−9.32188e9	+	7.82198e9i	−0.818241	+	0.686586i
$748$	1.19886e9	+	2.07649e9i	0.104740	+	0.181416i
$749$	1.30432e10	−	2.25914e10i	1.13422	−	1.96452i
$750$	−1.82831e9	−	1.03688e10i	−0.158247	−	0.897461i
$751$	−1.25697e9	−	7.12865e9i	−0.108289	−	0.614140i	−0.989855	−	0.142079i	$-0.954621\pi$
$751$	−1.25697e9	−	7.12865e9i	−0.108289	−	0.614140i	0.881566	−	0.472061i	$-0.156490\pi$
$752$	−1.52479e8	+	2.64102e8i	−0.0130752	+	0.0226469i
$753$	−2.06068e9	−	3.56919e9i	−0.175884	−	0.304641i
$754$	2.08403e8	−	1.74871e8i	0.0177053	−	0.0148565i
$755$	1.03943e10	−	3.78321e9i	0.878982	−	0.319923i
$756$	2.70870e10	+	9.85885e9i	2.28000	+	0.829851i
$757$	−1.47064e10	−	1.23401e10i	−1.23217	−	1.03391i	−0.998095	−	0.0616950i	$-0.980349\pi$
$757$	−1.47064e10	−	1.23401e10i	−1.23217	−	1.03391i	−0.234075	−	0.972219i	$-0.575206\pi$
$758$	1.56710e9	−	8.88745e9i	0.130693	−	0.741199i
$759$	1.07827e9			0.0895122
$760$	4.73800e9	−	1.86898e9i	0.391514	−	0.154439i
$761$	−2.29119e10			−1.88458			−0.942289	−	0.334801i	$-0.891331\pi$
$761$	−2.29119e10			−1.88458			−0.942289	+	0.334801i	$0.891331\pi$
$762$	2.19259e9	−	1.24348e10i	0.179521	−	1.01811i
$763$	1.08840e10	+	9.13275e9i	0.887058	+	0.744330i
$764$	2.95182e9	+	1.07438e9i	0.239477	+	0.0871625i
$765$	3.67383e10	−	1.33717e10i	2.96691	−	1.07987i
$766$	1.66006e9	−	1.39296e9i	0.133451	−	0.111979i
$767$	7.02458e9	+	1.21669e10i	0.562130	+	0.973637i
$768$	7.28593e8	−	1.26196e9i	0.0580391	−	0.100527i
$769$	−1.76104e9	−	9.98738e9i	−0.139646	−	0.791971i	−0.971511	−	0.236993i	$-0.923838\pi$
$769$	−1.76104e9	−	9.98738e9i	−0.139646	−	0.791971i	0.831865	−	0.554977i	$-0.187273\pi$
$770$	−1.29152e9	−	7.32459e9i	−0.101949	−	0.578184i
$771$	−3.13331e9	+	5.42705e9i	−0.246214	+	0.426455i
$772$	3.91711e9	+	6.78464e9i	0.306412	+	0.530721i
$773$	8.25684e9	−	6.92831e9i	0.642962	−	0.539510i	−0.261964	−	0.965078i	$-0.584370\pi$
$773$	8.25684e9	−	6.92831e9i	0.642962	−	0.539510i	0.904926	+	0.425568i	$0.139926\pi$
$774$	4.62033e9	−	1.68166e9i	0.358162	−	0.130360i
$775$	−6.17367e9	−	2.24703e9i	−0.476417	−	0.173402i
$776$	−2.07928e9	−	1.74472e9i	−0.159734	−	0.134033i
$777$	−1.44726e10	+	8.20780e10i	−1.10681	+	6.27702i
$778$	−1.72843e10			−1.31590
$779$	−1.71018e9	+	1.14808e10i	−0.129617	+	0.870147i
$780$	−1.02358e10			−0.772305
$781$	5.83133e8	−	3.30711e9i	0.0438015	−	0.248411i
$782$	−9.77076e8	−	8.19864e8i	−0.0730642	−	0.0613082i
$783$	−1.58972e9	−	5.78610e8i	−0.118346	−	0.0430745i
$784$	−7.13117e9	+	2.59553e9i	−0.528512	+	0.192362i
$785$	−6.94398e9	+	5.82669e9i	−0.512348	+	0.429911i
$786$	−9.78867e9	−	1.69545e10i	−0.719027	−	1.24539i
$787$	8.67606e9	−	1.50274e10i	0.634470	−	1.09893i	−0.352157	−	0.935941i	$-0.614552\pi$
$787$	8.67606e9	−	1.50274e10i	0.634470	−	1.09893i	0.986627	−	0.162994i	$-0.0521150\pi$
$788$	−1.12614e9	−	6.38668e9i	−0.0819884	−	0.464979i
$789$	−2.99703e9	−	1.69970e10i	−0.217231	−	1.23198i
$790$	7.87565e9	−	1.36410e10i	0.568318	−	0.984356i
$791$	−1.77218e10	−	3.06950e10i	−1.27318	−	2.20521i
$792$	−3.58851e9	+	3.01112e9i	−0.256671	+	0.215372i
$793$	3.46799e8	−	1.26224e8i	0.0246957	−	0.00898850i
$794$	−3.50184e9	−	1.27456e9i	−0.248270	−	0.0903628i
$795$	3.43813e9	+	2.88493e9i	0.242682	+	0.203634i
$796$	1.38281e9	−	7.84228e9i	0.0971775	−	0.551121i
$797$	−3.32795e9			−0.232848			−0.116424	−	0.993200i	$-0.537143\pi$
$797$	−3.32795e9			−0.232848			−0.116424	+	0.993200i	$0.537143\pi$
$798$	6.79155e9	+	3.32996e10i	0.473107	+	2.31969i
$799$	−1.63311e9			−0.113267
$800$	−1.85407e8	+	1.05149e9i	−0.0128030	+	0.0726092i
$801$	−1.71513e10	−	1.43916e10i	−1.17919	−	0.989456i
$802$	−1.44383e10	−	5.25511e9i	−0.988338	−	0.359726i
$803$	2.46708e9	−	8.97943e8i	0.168143	−	0.0611990i
$804$	−2.89368e9	+	2.42808e9i	−0.196360	+	0.164766i
$805$	1.97823e9	+	3.42639e9i	0.133657	+	0.231500i
$806$	4.46339e9	−	7.73081e9i	0.300256	−	0.520059i
$807$	−1.94753e9	−	1.10450e10i	−0.130445	−	0.739790i
$808$	−1.60453e9	−	9.09977e9i	−0.107006	−	0.606863i
$809$	4.10336e9	−	7.10722e9i	0.272471	−	0.471933i	−0.697023	−	0.717048i	$-0.745493\pi$
$809$	4.10336e9	−	7.10722e9i	0.272471	−	0.471933i	0.969494	+	0.245116i	$0.0788259\pi$
$810$	1.62333e10	+	2.81170e10i	1.07327	+	1.85896i
$811$	−5.13564e9	+	4.30931e9i	−0.338081	+	0.283684i	−0.795983	−	0.605319i	$-0.793046\pi$
$811$	−5.13564e9	+	4.30931e9i	−0.338081	+	0.283684i	0.457902	+	0.889003i	$0.348601\pi$
$812$	6.04558e8	−	2.20041e8i	0.0396271	−	0.0144231i
$813$	1.45321e10	+	5.28923e9i	0.948440	+	0.345204i
$814$	−6.13963e9	−	5.15176e9i	−0.398985	−	0.334788i
$815$	2.06203e8	−	1.16943e9i	0.0133427	−	0.0756701i
$816$	7.80353e9			0.502777
$817$	2.68558e9	+	2.13410e9i	0.172291	+	0.136911i
$818$	1.53141e10			0.978264
$819$	8.42161e9	−	4.77613e10i	0.535675	−	3.03797i
$820$	−6.33326e9	−	5.31424e9i	−0.401124	−	0.336583i
$821$	1.35079e10	+	4.91647e9i	0.851895	+	0.310064i	0.730813	−	0.682578i	$-0.239141\pi$
$821$	1.35079e10	+	4.91647e9i	0.851895	+	0.310064i	0.121082	+	0.992642i	$0.461363\pi$
$822$	−2.47583e10	+	9.01129e9i	−1.55478	+	0.565895i
$823$	2.35715e10	−	1.97789e10i	1.47397	−	1.23681i	0.561620	−	0.827395i	$-0.310178\pi$
$823$	2.35715e10	−	1.97789e10i	1.47397	−	1.23681i	0.912349	−	0.409412i	$-0.134266\pi$
$824$	2.98080e9	+	5.16289e9i	0.185604	+	0.321476i
$825$	2.41688e9	−	4.18616e9i	0.149853	−	0.259554i
$826$	5.76931e9	+	3.27194e10i	0.356200	+	2.02011i
$827$	−2.24595e9	−	1.27374e10i	−0.138080	−	0.783091i	−0.972665	−	0.232212i	$-0.925404\pi$
$827$	−2.24595e9	−	1.27374e10i	−0.138080	−	0.783091i	0.834585	−	0.550879i	$-0.185707\pi$
$828$	1.24596e9	−	2.15807e9i	0.0762779	−	0.132117i
$829$	1.02682e10	+	1.77851e10i	0.625973	+	1.08422i	0.988352	+	0.152186i	$0.0486312\pi$
$829$	1.02682e10	+	1.77851e10i	0.625973	+	1.08422i	−0.362379	+	0.932031i	$0.618035\pi$
$830$	4.63211e9	−	3.88680e9i	0.281194	−	0.235949i
$831$	−1.92357e10	+	7.00123e9i	−1.16280	+	0.423224i
$832$	−1.36326e9	−	4.96186e8i	−0.0820629	−	0.0298685i
$833$	−3.11318e10	−	2.61227e10i	−1.86615	−	1.56589i
$834$	7.09435e8	−	4.02341e9i	0.0423479	−	0.240167i
$835$	4.01280e9			0.238531
$836$	−3.09976e9	−	1.03551e9i	−0.183487	−	0.0612960i
$837$	−5.55111e10			−3.27221
$838$	−1.04488e9	+	5.92582e9i	−0.0613357	+	0.347852i
$839$	1.87346e10	+	1.57202e10i	1.09516	+	0.918948i	0.997090	−	0.0762315i	$-0.0242888\pi$
$839$	1.87346e10	+	1.57202e10i	1.09516	+	0.918948i	0.0980695	+	0.995180i	$0.468733\pi$
$840$	−2.27462e10	−	8.27894e9i	−1.32413	−	0.481945i
$841$	1.61741e10	−	5.88689e9i	0.937636	−	0.341271i
$842$	−4.27208e9	+	3.58470e9i	−0.246631	+	0.206948i
$843$	−9.55467e9	−	1.65492e10i	−0.549312	−	0.951437i
$844$	9.18962e6	−	1.59169e7i	0.000526137	−	0.000911297i
$845$	−1.85591e9	−	1.05254e10i	−0.105818	−	0.600122i
$846$	−5.54047e8	−	3.14216e9i	−0.0314594	−	0.178415i
$847$	1.35537e10	−	2.34757e10i	0.766418	−	1.32747i
$848$	3.18062e8	+	5.50899e8i	0.0179113	+	0.0310232i
$849$	−2.38904e10	+	2.00465e10i	−1.33982	+	1.12424i
$850$	−5.37300e9	+	1.95561e9i	−0.300089	+	0.109224i
$851$	4.00635e9	+	1.45819e9i	0.222841	+	0.0811075i
$852$	−8.37225e9	−	7.02515e9i	−0.463771	−	0.389150i
$853$	−2.40253e9	+	1.36254e10i	−0.132540	+	0.751673i	0.844001	+	0.536342i	$0.180194\pi$
$853$	−2.40253e9	+	1.36254e10i	−0.132540	+	0.751673i	−0.976541	+	0.215331i	$0.930917\pi$
$854$	8.72761e8			0.0479504
$855$	−2.54047e10	+	4.68433e10i	−1.39006	+	2.56310i
$856$	8.16425e9			0.444896
$857$	−1.08191e9	+	6.13581e9i	−0.0587162	+	0.332996i	−0.999989	−	0.00465043i	$-0.998520\pi$
$857$	−1.08191e9	+	6.13581e9i	−0.0587162	+	0.332996i	0.941273	+	0.337646i	$0.109631\pi$
$858$	5.03126e9	+	4.22173e9i	0.271939	+	0.228184i
$859$	1.50462e10	+	5.47635e9i	0.809934	+	0.294792i	0.713596	−	0.700557i	$-0.247065\pi$
$859$	1.50462e10	+	5.47635e9i	0.809934	+	0.294792i	0.0963372	+	0.995349i	$0.469287\pi$
$860$	−2.29587e9	+	8.35630e8i	−0.123085	+	0.0447991i
$861$	4.22588e10	−	3.54594e10i	2.25635	−	1.89330i
$862$	−1.07130e9	−	1.85555e9i	−0.0569688	−	0.0986729i
$863$	3.81297e9	−	6.60426e9i	0.201942	−	0.349773i	−0.747212	−	0.664585i	$-0.768608\pi$
$863$	3.81297e9	−	6.60426e9i	0.201942	−	0.349773i	0.949154	+	0.314812i	$0.101942\pi$
$864$	1.56657e9	+	8.88443e9i	0.0826324	+	0.468632i
$865$	2.98676e7	+	1.69388e8i	0.00156908	+	0.00889867i
$866$	−1.32803e10	+	2.30021e10i	−0.694856	+	1.20353i
$867$	3.07472e9	+	5.32557e9i	0.160228	+	0.277523i
$868$	1.61716e10	−	1.35695e10i	0.839330	−	0.704282i
$869$	−9.49741e9	+	3.45677e9i	−0.490948	+	0.178691i
$870$	1.33496e9	+	4.85887e8i	0.0687308	+	0.0250160i
$871$	2.88090e9	+	2.41736e9i	0.147728	+	0.123959i
$872$	−7.72161e8	+	4.37914e9i	−0.0394367	+	0.223656i
$873$	2.83985e10			1.44459
$874$	1.73789e9	−	4.63442e7i	0.0880506	−	0.00234804i
$875$	−2.47890e10			−1.25093
$876$	1.48374e9	−	8.41472e9i	0.0745752	−	0.422937i
$877$	2.39270e10	+	2.00771e10i	1.19781	+	1.00509i	0.999690	+	0.0249087i	$0.00792951\pi$
$877$	2.39270e10	+	2.00771e10i	1.19781	+	1.00509i	0.198125	+	0.980177i	$0.436515\pi$
$878$	7.64150e8	+	2.78128e8i	0.0381020	+	0.0138680i
$879$	5.24403e10	−	1.90867e10i	2.60438	−	0.947916i
$880$	1.78316e9	−	1.49625e9i	0.0882065	−	0.0740140i
$881$	1.02308e10	+	1.77202e10i	0.504072	+	0.873079i	0.999989	+	0.00470885i	$0.00149888\pi$
$881$	1.02308e10	+	1.77202e10i	0.504072	+	0.873079i	−0.495916	+	0.868370i	$0.665168\pi$
$882$	3.96991e10	−	6.87609e10i	1.94823	−	3.37444i
$883$	−5.16708e8	−	2.93039e9i	−0.0252570	−	0.143240i	0.969572	−	0.244808i	$-0.0787250\pi$
$883$	−5.16708e8	−	2.93039e9i	−0.0252570	−	0.143240i	−0.994829	+	0.101568i	$0.967614\pi$
$884$	−1.34908e9	−	7.65103e9i	−0.0656834	−	0.372509i
$885$	−3.66821e10	+	6.35353e10i	−1.77891	+	3.08116i
$886$	−1.26823e10	−	2.19664e10i	−0.612606	−	1.06106i
$887$	−6.41995e9	+	5.38697e9i	−0.308886	+	0.259186i	−0.784032	−	0.620721i	$-0.786840\pi$
$887$	−6.41995e9	+	5.38697e9i	−0.308886	+	0.259186i	0.475145	+	0.879907i	$0.342396\pi$
$888$	−2.45112e10	+	8.92135e9i	−1.17468	+	0.427548i
$889$	−2.79353e10	−	1.01676e10i	−1.33351	−	0.485359i
$890$	8.52260e9	+	7.15131e9i	0.405235	+	0.340033i
$891$	3.61752e9	−	2.05160e10i	0.171332	−	0.971672i
$892$	1.60692e10			0.758085
$893$	1.66644e9	−	1.47577e9i	0.0783086	−	0.0693487i
$894$	−3.24186e10			−1.51745
$895$	−4.60369e9	+	2.61088e10i	−0.214647	+	1.21733i
$896$	−2.62815e9	−	2.20528e9i	−0.122060	−	0.102420i
$897$	−3.28309e9	−	1.19495e9i	−0.151883	−	0.0552809i
$898$	−8.45572e8	+	3.07763e8i	−0.0389658	+	0.0141824i
$899$	−9.49100e8	+	7.96390e8i	−0.0435665	+	0.0365567i
$900$	−5.58549e9	−	9.67436e9i	−0.255395	−	0.442358i
$901$	−1.70328e9	+	2.95017e9i	−0.0775801	+	0.134373i
$902$	9.21184e8	+	5.22429e9i	0.0417949	+	0.237031i
$903$	−2.83089e9	−	1.60548e10i	−0.127943	−	0.725599i
$904$	5.54640e9	−	9.60664e9i	0.249702	−	0.432496i
$905$	−1.72531e10	−	2.98833e10i	−0.773745	−	1.34017i
$906$	−1.76952e10	+	1.48481e10i	−0.790510	+	0.663316i
$907$	3.02650e9	−	1.10156e9i	0.134684	−	0.0490210i	−0.273799	−	0.961787i	$-0.588280\pi$
$907$	3.02650e9	−	1.10156e9i	0.134684	−	0.0490210i	0.408483	+	0.912766i	$0.366058\pi$
$908$	−9.61904e9	−	3.50104e9i	−0.426414	−	0.155202i
$909$	7.40575e10	+	6.21416e10i	3.27036	+	2.74416i
$910$	−4.18476e9	+	2.37330e10i	−0.184088	+	1.04402i
$911$	1.83254e10			0.803045			0.401523	−	0.915849i	$-0.368481\pi$
$911$	1.83254e10			0.803045			0.401523	+	0.915849i	$0.368481\pi$
$912$	−7.96277e9	+	7.05169e9i	−0.347602	+	0.307830i
$913$	−3.87996e9			−0.168725
$914$	−3.72033e9	+	2.10990e10i	−0.161165	+	0.914009i
$915$	1.47632e9	+	1.23878e9i	0.0637098	+	0.0534589i
$916$	−1.28497e10	−	4.67691e9i	−0.552407	−	0.201060i
$917$	−4.33132e10	+	1.57647e10i	−1.85493	+	0.675140i
$918$	−3.70090e10	+	3.10543e10i	−1.57891	+	1.32487i
$919$	−1.36544e10	−	2.36500e10i	−0.580319	−	1.00514i	−0.995441	−	0.0953765i	$-0.969595\pi$
$919$	−1.36544e10	−	2.36500e10i	−0.580319	−	1.00514i	0.415122	−	0.909766i	$-0.363739\pi$
$920$	−6.19128e8	+	1.07236e9i	−0.0262134	+	0.0454029i
$921$	−1.28150e10	−	7.26777e10i	−0.540520	−	3.06544i
$922$	2.32346e9	+	1.31770e10i	0.0976288	+	0.553680i
$923$	−5.44046e9	+	9.42316e9i	−0.227735	+	0.394449i
$924$	7.76597e9	+	1.34511e10i	0.323850	+	0.560925i
$925$	1.46411e10	−	1.22853e10i	0.608243	−	0.510377i
$926$	1.76096e10	−	6.40938e9i	0.728805	−	0.265263i
$927$	−5.86117e10	−	2.13329e10i	−2.41660	−	0.879572i
$928$	1.54245e8	+	1.29427e8i	0.00633567	+	0.00531625i
$929$	5.38811e9	−	3.05575e10i	0.220486	−	1.25044i	−0.650642	−	0.759385i	$-0.725500\pi$
$929$	5.38811e9	−	3.05575e10i	0.220486	−	1.25044i	0.871128	−	0.491056i	$-0.163389\pi$
$930$	4.66153e10			1.90037
$931$	5.53730e10	−	1.47663e9i	2.24892	−	0.0599718i
$932$	−1.87704e9			−0.0759482
$933$	−6.60960e8	+	3.74849e9i	−0.0266434	+	0.151102i
$934$	−1.99314e9	−	1.67244e9i	−0.0800429	−	0.0671640i
$935$	1.17138e10	+	4.26347e9i	0.468659	+	0.170578i
$936$	1.42631e10	−	5.19135e9i	0.568525	−	0.206926i
$937$	−2.08073e10	+	1.74594e10i	−0.826281	+	0.693332i	−0.954434	−	0.298423i	$-0.903540\pi$
$937$	−2.08073e10	+	1.74594e10i	−0.826281	+	0.693332i	0.128153	+	0.991754i	$0.459095\pi$
$938$	4.44679e9	+	7.70207e9i	0.175929	+	0.304718i
$939$	−3.27601e10	+	5.67421e10i	−1.29126	+	2.23654i
$940$	2.75310e8	+	1.56136e9i	0.0108112	+	0.0613135i
$941$	−1.90227e9	−	1.07883e10i	−0.0744233	−	0.422075i	−0.999142	−	0.0414235i	$-0.986811\pi$
$941$	−1.90227e9	−	1.07883e10i	−0.0744233	−	0.422075i	0.924718	−	0.380652i	$-0.124300\pi$
$942$	9.46495e9	−	1.63938e10i	0.368927	−	0.639000i
$943$	−1.41098e9	−	2.44389e9i	−0.0547936	−	0.0949053i
$944$	−7.96547e9	+	6.68382e9i	−0.308184	+	0.258597i
$945$	1.40822e11	−	5.12552e10i	5.42826	−	1.97572i
$946$	1.47316e9	+	5.36187e8i	0.0565759	+	0.0205920i
$947$	1.57336e10	+	1.32020e10i	0.602008	+	0.505145i	0.892091	−	0.451857i	$-0.149238\pi$
$947$	1.57336e10	+	1.32020e10i	0.602008	+	0.505145i	−0.290082	+	0.957002i	$0.593683\pi$
$948$	−5.71190e9	+	3.23938e10i	−0.217747	+	1.23490i
$949$	−8.50679e9			−0.323098
$950$	3.71545e9	−	6.85086e9i	0.140598	−	0.259246i
$951$	3.26385e10			1.23055
$952$	3.19038e9	−	1.80935e10i	0.119843	−	0.679663i
$953$	3.18786e10	+	2.67493e10i	1.19309	+	1.00112i	0.999800	+	0.0199814i	$0.00636070\pi$
$953$	3.18786e10	+	2.67493e10i	1.19309	+	1.00112i	0.193291	+	0.981141i	$0.438084\pi$
$954$	−6.25408e9	−	2.27630e9i	−0.233208	−	0.0848809i
$955$	1.53462e10	−	5.58558e9i	0.570152	−	0.207518i
$956$	8.66966e9	−	7.27471e9i	0.320922	−	0.269286i
$957$	−4.55781e8	−	7.89435e8i	−0.0168099	−	0.0291155i
$958$	1.78874e10	−	3.09819e10i	0.657308	−	1.13849i
$959$	1.07718e10	+	6.10896e10i	0.394386	+	2.23667i
$960$	−1.31552e9	−	7.46068e9i	−0.0479897	−	0.272163i
$961$	−6.57071e9	+	1.13808e10i	−0.238825	+	0.413657i
$962$	1.29845e10	+	2.24899e10i	0.470234	+	0.814469i
$963$	−6.54344e10	+	5.49060e10i	−2.36110	+	1.98120i
$964$	1.43938e10	−	5.23892e9i	0.517495	−	0.188353i
$965$	3.82731e10	+	1.39303e10i	1.37103	+	0.499015i
$966$	−6.32928e9	−	5.31090e9i	−0.225909	−	0.189561i
$967$	4.18327e9	−	2.37245e10i	0.148773	−	0.843732i	−0.815488	−	0.578775i	$-0.803531\pi$
$967$	4.18327e9	−	2.37245e10i	0.148773	−	0.843732i	0.964260	−	0.264957i	$-0.0853578\pi$
$968$	8.48382e9			0.300627
$969$	−5.40250e10	−	1.80476e10i	−1.90749	−	0.637217i
$970$	−1.41114e10			−0.496443
$971$	−7.41019e9	+	4.20253e10i	−0.259754	+	1.47314i	0.523814	+	0.851833i	$0.324509\pi$
$971$	−7.41019e9	+	4.20253e10i	−0.259754	+	1.47314i	−0.783568	+	0.621306i	$0.786603\pi$
$972$	−2.24184e10	−	1.88113e10i	−0.783019	−	0.657031i
$973$	−9.03877e9	−	3.28984e9i	−0.314568	−	0.114493i
$974$	−2.51533e10	+	9.15504e9i	−0.872244	+	0.317471i
$975$	−1.19980e10	+	1.00675e10i	−0.414564	+	0.347860i
$976$	1.36574e8	+	2.36554e8i	0.00470213	+	0.00814433i
$977$	−1.23498e10	+	2.13905e10i	−0.423672	+	0.733822i	−0.996295	−	0.0859967i	$-0.972593\pi$
$977$	−1.23498e10	+	2.13905e10i	−0.423672	+	0.733822i	0.572623	+	0.819819i	$0.305926\pi$
$978$	4.30614e8	+	2.44214e9i	0.0147198	+	0.0834802i
$979$	−1.23963e9	−	7.03028e9i	−0.0422233	−	0.239460i
$980$	−1.97268e10	+	3.41678e10i	−0.669523	+	1.15965i
$981$	−2.32618e10	−	4.02907e10i	−0.786688	−	1.36258i
$982$	1.82260e10	−	1.52934e10i	0.614186	−	0.515364i
$983$	−4.41598e10	+	1.60729e10i	−1.48283	+	0.539704i	−0.951550	−	0.307495i	$-0.900509\pi$
$983$	−4.41598e10	+	1.60729e10i	−1.48283	+	0.539704i	−0.531276	+	0.847199i	$0.678287\pi$
$984$	1.62238e10	+	5.90499e9i	0.542838	+	0.197577i
$985$	−2.58279e10	−	2.16722e10i	−0.861118	−	0.722564i
$986$	−1.87241e8	+	1.06190e9i	−0.00622061	+	0.0352788i
$987$	−1.05789e10			−0.350213
$988$	8.29050e9	+	6.58806e9i	0.273484	+	0.217324i
$989$	−8.33949e8			−0.0274127
$990$	−4.22904e9	+	2.39841e10i	−0.138522	+	0.785598i
$991$	2.32918e10	+	1.95441e10i	0.760229	+	0.637908i	0.938186	−	0.346130i	$-0.112505\pi$
$991$	2.32918e10	+	1.95441e10i	0.760229	+	0.637908i	−0.177958	+	0.984038i	$0.556949\pi$
$992$	6.20851e9	+	2.25971e9i	0.201928	+	0.0734958i
$993$	−1.35867e10	+	4.94517e9i	−0.440345	+	0.160272i
$994$	−1.97117e10	+	1.65400e10i	−0.636606	+	0.534176i
$995$	−2.07001e10	−	3.58537e10i	−0.666181	−	1.15386i
$996$	−6.31377e9	+	1.09358e10i	−0.202479	+	0.350705i
$997$	−4.63855e8	−	2.63065e9i	−0.0148234	−	0.0840680i	0.976499	−	0.215524i	$-0.0691459\pi$
$997$	−4.63855e8	−	2.63065e9i	−0.0148234	−	0.0840680i	−0.991322	+	0.131456i	$0.958035\pi$
$998$	−1.32685e9	−	7.52495e9i	−0.0422538	−	0.239633i
$999$	8.07443e10	−	1.39853e11i	2.56232	−	4.43806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.b.17.1	yes	36
19.9	even	9	inner	38.8.e.b.9.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.b.9.1	✓	36	19.9	even	9	inner
38.8.e.b.17.1	yes	36	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)

\(f(q)\)	\(=\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-66.5349 - 55.8294i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-312.664 + 113.800i) q^{5} +(532.279 - 446.635i) q^{6} +(-817.968 - 1416.76i) q^{7} +(256.000 - 443.405i) q^{8} +(930.200 + 5275.43i) q^{9} +O(q^{10})\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-66.5349 - 55.8294i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-312.664 + 113.800i) q^{5} +(532.279 - 446.635i) q^{6} +(-817.968 - 1416.76i) q^{7} +(256.000 - 443.405i) q^{8} +(930.200 + 5275.43i) q^{9} +(-462.223 - 2621.40i) q^{10} +(-853.993 + 1479.16i) q^{11} +(2779.36 + 4814.00i) q^{12} +(4239.42 - 3557.30i) q^{13} +(12298.2 - 4476.18i) q^{14} +(27156.4 + 9884.13i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-3808.96 + 21601.7i) q^{17} -42854.5 q^{18} +(-15633.8 - 25484.5i) q^{19} +21294.7 q^{20} +(-24673.6 + 139931. i) q^{21} +(-10467.1 - 8782.98i) q^{22} +(6830.22 + 2486.00i) q^{23} +(-41788.0 + 15209.6i) q^{24} +(24960.9 - 20944.6i) q^{25} +(22136.7 + 38341.9i) q^{26} +(137657. - 238429. i) q^{27} +(18180.9 + 103109. i) q^{28} +(-1067.03 - 6051.43i) q^{29} +(-115597. + 200220. i) q^{30} +(-100814. - 174615. i) q^{31} +(-25101.7 + 21062.9i) q^{32} +(139401. - 50737.8i) q^{33} +(-164896. - 60017.4i) q^{34} +(416977. + 349885. i) q^{35} +(59532.8 - 337627. i) q^{36} +586562. q^{37} +(222497. - 87767.3i) q^{38} -480671. q^{39} +(-29582.3 + 167770. i) q^{40} +(-297410. - 249557. i) q^{41} +(-1.06816e6 - 388779. i) q^{42} +(-107814. + 39241.2i) q^{43} +(83737.2 - 70263.8i) q^{44} +(-891185. - 1.54358e6i) q^{45} +(-29074.3 + 50358.1i) q^{46} +(12928.6 + 73321.6i) q^{47} +(-61776.8 - 350354. i) q^{48} +(-926371. + 1.60452e6i) q^{49} +(130336. + 225749. i) q^{50} +(1.45944e6 - 1.22461e6i) q^{51} +(-332827. + 121139. i) q^{52} +(145938. + 53117.0i) q^{53} +(1.68722e6 + 1.41575e6i) q^{54} +(98683.9 - 559664. i) q^{55} -837599. q^{56} +(-382592. + 2.56843e6i) q^{57} +49158.2 q^{58} +(-440827. + 2.50005e6i) q^{59} +(-1.41684e6 - 1.18887e6i) q^{60} +(62665.0 + 22808.2i) q^{61} +(1.51575e6 - 551688. i) q^{62} +(6.71315e6 - 5.63300e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-920692. + 1.59469e6i) q^{65} +(206082. + 1.16875e6i) q^{66} +(118002. + 669225. i) q^{67} +(701917. - 1.21576e6i) q^{68} +(-315656. - 546732. i) q^{69} +(-3.33581e6 + 2.79908e6i) q^{70} +(-1.84756e6 + 672457. i) q^{71} +(2.57728e6 + 938054. i) q^{72} +(-1.17752e6 - 988054. i) q^{73} +(-814843. + 4.62121e6i) q^{74} -2.83009e6 q^{75} +(382382. + 1.87486e6i) q^{76} +2.79415e6 q^{77} +(667742. - 3.78695e6i) q^{78} +(4.53303e6 + 3.80367e6i) q^{79} +(-1.28067e6 - 466126. i) q^{80} +(-1.14615e7 + 4.17165e6i) q^{81} +(2.37928e6 - 1.99645e6i) q^{82} +(1.13583e6 + 1.96731e6i) q^{83} +(4.54686e6 - 7.87539e6i) q^{84} +(-1.26735e6 - 7.18751e6i) q^{85} +(-159386. - 903924. i) q^{86} +(-266853. + 462202. i) q^{87} +(437244. + 757330. i) q^{88} +(-3.20177e6 + 2.68661e6i) q^{89} +(1.33990e7 - 4.87685e6i) q^{90} +(-8.50756e6 - 3.09650e6i) q^{91} +(-356355. - 299017. i) q^{92} +(-3.04101e6 + 1.72464e7i) q^{93} -595622. q^{94} +(7.78824e6 + 6.18894e6i) q^{95} +2.84607e6 q^{96} +(920575. - 5.22084e6i) q^{97} +(-1.13543e7 - 9.52736e6i) q^{98} +(-8.59758e6 - 3.12926e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9}+O(q^{10}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9	\( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9} + 1800 q^{11} - 38334 q^{13} + 20832 q^{14} + 111228 q^{15} - 86574 q^{17} - 285888 q^{18} - 160152 q^{19} + 48384 q^{20} - 71442 q^{21} + 129984 q^{22} + 142920 q^{23} + 43008 q^{24} - 514068 q^{25} - 77856 q^{26} + 159492 q^{27} + 204288 q^{28} - 626034 q^{29} + 82656 q^{31} + 1576494 q^{33} + 85632 q^{34} + 581760 q^{35} + 91392 q^{36} + 1090848 q^{37} - 398496 q^{38} - 282624 q^{39} + 450780 q^{41} - 898128 q^{42} + 3066264 q^{43} - 1039872 q^{44} - 1208484 q^{45} + 166080 q^{46} - 1923516 q^{47} + 688128 q^{48} - 3667500 q^{49} + 4263456 q^{50} + 5070996 q^{51} + 440448 q^{52} - 4486374 q^{53} + 1382688 q^{54} - 5711508 q^{55} - 3059712 q^{56} - 5167644 q^{57} + 1718304 q^{58} - 5420364 q^{59} - 3484416 q^{60} + 20074776 q^{61} + 5592864 q^{62} - 4282596 q^{63} - 4718592 q^{64} + 10490790 q^{65} - 6939360 q^{66} + 5235372 q^{67} - 171648 q^{68} - 11912298 q^{69} - 4654080 q^{70} + 10980792 q^{71} + 1462272 q^{72} - 11218440 q^{73} - 443088 q^{74} - 8817984 q^{75} + 470016 q^{76} + 44477160 q^{77} - 11046144 q^{78} - 30314100 q^{79} - 40768188 q^{81} - 3606240 q^{82} + 4370208 q^{83} + 14171520 q^{84} - 20507004 q^{85} + 35895744 q^{86} + 14888064 q^{87} - 921600 q^{88} + 9695220 q^{89} + 34283424 q^{90} - 24159408 q^{91} - 3868416 q^{92} + 4014432 q^{93} - 46331520 q^{94} - 16025892 q^{95} - 47992770 q^{97} - 32609808 q^{98} + 62837148 q^{99}+O(q^{100}) \) 36 * q - 84 * q^3 + 672 * q^6 - 2988 * q^7 + 9216 * q^8 + 1428 * q^9 + 1800 * q^11 - 38334 * q^13 + 20832 * q^14 + 111228 * q^15 - 86574 * q^17 - 285888 * q^18 - 160152 * q^19 + 48384 * q^20 - 71442 * q^21 + 129984 * q^22 + 142920 * q^23 + 43008 * q^24 - 514068 * q^25 - 77856 * q^26 + 159492 * q^27 + 204288 * q^28 - 626034 * q^29 + 82656 * q^31 + 1576494 * q^33 + 85632 * q^34 + 581760 * q^35 + 91392 * q^36 + 1090848 * q^37 - 398496 * q^38 - 282624 * q^39 + 450780 * q^41 - 898128 * q^42 + 3066264 * q^43 - 1039872 * q^44 - 1208484 * q^45 + 166080 * q^46 - 1923516 * q^47 + 688128 * q^48 - 3667500 * q^49 + 4263456 * q^50 + 5070996 * q^51 + 440448 * q^52 - 4486374 * q^53 + 1382688 * q^54 - 5711508 * q^55 - 3059712 * q^56 - 5167644 * q^57 + 1718304 * q^58 - 5420364 * q^59 - 3484416 * q^60 + 20074776 * q^61 + 5592864 * q^62 - 4282596 * q^63 - 4718592 * q^64 + 10490790 * q^65 - 6939360 * q^66 + 5235372 * q^67 - 171648 * q^68 - 11912298 * q^69 - 4654080 * q^70 + 10980792 * q^71 + 1462272 * q^72 - 11218440 * q^73 - 443088 * q^74 - 8817984 * q^75 + 470016 * q^76 + 44477160 * q^77 - 11046144 * q^78 - 30314100 * q^79 - 40768188 * q^81 - 3606240 * q^82 + 4370208 * q^83 + 14171520 * q^84 - 20507004 * q^85 + 35895744 * q^86 + 14888064 * q^87 - 921600 * q^88 + 9695220 * q^89 + 34283424 * q^90 - 24159408 * q^91 - 3868416 * q^92 + 4014432 * q^93 - 46331520 * q^94 - 16025892 * q^95 - 47992770 * q^97 - 32609808 * q^98 + 62837148 * q^99

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