LMFDB - Embedded newform 38.8.e.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	38.17
Dual form			38.8.e.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38919 - 7.87846i) q^{2} +(-21.2048 - 17.7929i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(194.773 - 70.8916i) q^{5} +(-169.638 + 142.344i) q^{6} +(-485.627 - 841.131i) q^{7} +(-256.000 + 443.405i) q^{8} +(-246.714 - 1399.18i) q^{9} +O(q^{10})$	\(q+(1.38919 - 7.87846i) q^{2} +(-21.2048 - 17.7929i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(194.773 - 70.8916i) q^{5} +(-169.638 + 142.344i) q^{6} +(-485.627 - 841.131i) q^{7} +(-256.000 + 443.405i) q^{8} +(-246.714 - 1399.18i) q^{9} +(-287.941 - 1632.99i) q^{10} +(-2515.69 + 4357.30i) q^{11} +(885.789 + 1534.23i) q^{12} +(-5805.68 + 4871.54i) q^{13} +(-7301.45 + 2657.51i) q^{14} +(-5391.49 - 1962.34i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-3730.53 + 21156.9i) q^{17} -11366.1 q^{18} +(28493.1 - 9056.32i) q^{19} -13265.5 q^{20} +(-4668.57 + 26476.8i) q^{21} +(30834.0 + 25872.8i) q^{22} +(-73884.0 - 26891.6i) q^{23} +(13317.9 - 4847.32i) q^{24} +(-26936.3 + 22602.2i) q^{25} +(30315.1 + 52507.3i) q^{26} +(-49933.1 + 86486.7i) q^{27} +(10794.0 + 61216.0i) q^{28} +(-11608.1 - 65832.6i) q^{29} +(-22950.0 + 39750.6i) q^{30} +(-147886. - 256147. i) q^{31} +(25101.7 - 21062.9i) q^{32} +(130874. - 47634.2i) q^{33} +(161501. + 58781.7i) q^{34} +(-154216. - 129403. i) q^{35} +(-15789.7 + 89547.7i) q^{36} +156076. q^{37} +(-31767.7 - 237062. i) q^{38} +209787. q^{39} +(-18428.2 + 104512. i) q^{40} +(-113672. - 95381.9i) q^{41} +(202111. + 73562.3i) q^{42} +(401253. - 146044. i) q^{43} +(246672. - 206983. i) q^{44} +(-147243. - 255033. i) q^{45} +(-314503. + 544735. i) q^{46} +(-170080. - 964573. i) q^{47} +(-19688.4 - 111659. i) q^{48} +(-59896.5 + 103744. i) q^{49} +(140651. + 243615. i) q^{50} +(455549. - 382251. i) q^{51} +(455790. - 165894. i) q^{52} +(1.34350e6 + 488993. i) q^{53} +(612016. + 513542. i) q^{54} +(-181092. + 1.02702e6i) q^{55} +497283. q^{56} +(-765329. - 314938. i) q^{57} -534786. q^{58} +(6167.73 - 34978.9i) q^{59} +(281292. + 236032. i) q^{60} +(-2.16873e6 - 789352. i) q^{61} +(-2.22348e6 + 809282. i) q^{62} +(-1.05709e6 + 887000. i) q^{63} +(-131072. - 227023. i) q^{64} +(-785438. + 1.36042e6i) q^{65} +(-193476. - 1.09726e6i) q^{66} +(-149074. - 845439. i) q^{67} +(687465. - 1.19072e6i) q^{68} +(1.08822e6 + 1.88484e6i) q^{69} +(-1.23373e6 + 1.03522e6i) q^{70} +(-4.46178e6 + 1.62395e6i) q^{71} +(683563. + 248797. i) q^{72} +(997664. + 837140. i) q^{73} +(216818. - 1.22964e6i) q^{74} +973340. q^{75} +(-1.91182e6 - 79043.2i) q^{76} +4.88674e6 q^{77} +(291433. - 1.65280e6i) q^{78} +(-2.74956e6 - 2.30715e6i) q^{79} +(797790. + 290372. i) q^{80} +(-322153. + 117254. i) q^{81} +(-909374. + 763056. i) q^{82} +(1.38264e6 + 2.39480e6i) q^{83} +(860327. - 1.49013e6i) q^{84} +(773239. + 4.38525e6i) q^{85} +(-593189. - 3.36414e6i) q^{86} +(-925209. + 1.60251e6i) q^{87} +(-1.28803e6 - 2.23094e6i) q^{88} +(4.83372e6 - 4.05597e6i) q^{89} +(-2.21382e6 + 805763. i) q^{90} +(6.91700e6 + 2.51758e6i) q^{91} +(3.85477e6 + 3.23454e6i) q^{92} +(-1.42170e6 + 8.06288e6i) q^{93} -7.83562e6 q^{94} +(4.90766e6 - 3.78384e6i) q^{95} -907048. q^{96} +(439732. - 2.49384e6i) q^{97} +(734134. + 616012. i) q^{98} +(6.71731e6 + 2.44490e6i) 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
$3$	−21.2048	−	17.7929i	−0.453430	−	0.380473i	0.387277	−	0.921963i	$-0.373416\pi$
$3$	−21.2048	−	17.7929i	−0.453430	−	0.380473i	−0.840707	+	0.541491i	$0.817860\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	194.773	−	70.8916i	0.696841	−	0.253629i	0.0307796	−	0.999526i	$-0.490201\pi$
$5$	194.773	−	70.8916i	0.696841	−	0.253629i	0.666062	+	0.745897i	$0.267979\pi$
$6$	−169.638	+	142.344i	−0.320623	+	0.269035i
$7$	−485.627	−	841.131i	−0.535131	−	0.926874i	−0.999157	−	0.0410525i	$-0.986929\pi$
$7$	−485.627	−	841.131i	−0.535131	−	0.926874i	0.464026	−	0.885822i	$-0.346404\pi$
$8$	−256.000	+	443.405i	−0.176777	+	0.306186i
$9$	−246.714	−	1399.18i	−0.112809	−	0.639772i
$10$	−287.941	−	1632.99i	−0.0910549	−	0.516398i
$11$	−2515.69	+	4357.30i	−0.569878	+	0.987058i	0.426699	+	0.904394i	$0.359676\pi$
$11$	−2515.69	+	4357.30i	−0.569878	+	0.987058i	−0.996577	+	0.0826643i	$0.973657\pi$
$12$	885.789	+	1534.23i	0.147978	+	0.256305i
$13$	−5805.68	+	4871.54i	−0.732911	+	0.614985i	−0.930923	−	0.365214i	$-0.880996\pi$
$13$	−5805.68	+	4871.54i	−0.732911	+	0.614985i	0.198013	+	0.980199i	$0.436551\pi$
$14$	−7301.45	+	2657.51i	−0.711149	+	0.258837i
$15$	−5391.49	−	1962.34i	−0.412468	−	0.150126i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	−3730.53	+	21156.9i	−0.184162	+	1.04443i	0.742866	+	0.669440i	$0.233466\pi$
$17$	−3730.53	+	21156.9i	−0.184162	+	1.04443i	−0.927028	+	0.374993i	$0.877645\pi$
$18$	−11366.1			−0.459366
$19$	28493.1	−	9056.32i	0.953019	−	0.302910i
$19$	28493.1	−	9056.32i	0.953019	−	0.302910i
$20$	−13265.5			−0.370781
$21$	−4668.57	+	26476.8i	−0.110006	+	0.623875i
$22$	30834.0	+	25872.8i	0.617378	+	0.518041i
$23$	−73884.0	−	26891.6i	−1.26620	−	0.460860i	−0.380356	−	0.924840i	$-0.624199\pi$
$23$	−73884.0	−	26891.6i	−1.26620	−	0.460860i	−0.885846	+	0.463980i	$0.846421\pi$
$24$	13317.9	−	4847.32i	0.196651	−	0.0715752i
$25$	−26936.3	+	22602.2i	−0.344785	+	0.289309i
$26$	30315.1	+	52507.3i	0.338261	+	0.585885i
$27$	−49933.1	+	86486.7i	−0.488220	+	0.845622i
$28$	10794.0	+	61216.0i	0.0929245	+	0.527001i
$29$	−11608.1	−	65832.6i	−0.0883826	−	0.501243i	−0.996575	−	0.0826904i	$-0.973649\pi$
$29$	−11608.1	−	65832.6i	−0.0883826	−	0.501243i	0.908193	−	0.418552i	$-0.137462\pi$
$30$	−22950.0	+	39750.6i	−0.155188	+	0.268794i
$31$	−147886.	−	256147.i	−0.891584	−	1.54427i	−0.837976	−	0.545706i	$-0.816261\pi$
$31$	−147886.	−	256147.i	−0.891584	−	1.54427i	−0.0536075	−	0.998562i	$-0.517072\pi$
$32$	25101.7	−	21062.9i	0.135419	−	0.113630i
$33$	130874.	−	47634.2i	0.633948	−	0.230738i
$34$	161501.	+	58781.7i	0.704693	+	0.256487i
$35$	−154216.	−	129403.i	−0.607984	−	0.510159i
$36$	−15789.7	+	89547.7i	−0.0564046	+	0.319886i
$37$	156076.			0.506558			0.253279	−	0.967393i	$-0.418491\pi$
$37$	156076.			0.506558			0.253279	+	0.967393i	$0.418491\pi$
$38$	−31767.7	−	237062.i	−0.0939167	−	0.700842i
$39$	209787.			0.566308
$40$	−18428.2	+	104512.i	−0.0455274	+	0.258199i
$41$	−113672.	−	95381.9i	−0.257578	−	0.216134i	0.504849	−	0.863208i	$-0.331548\pi$
$41$	−113672.	−	95381.9i	−0.257578	−	0.216134i	−0.762427	+	0.647074i	$0.775993\pi$
$42$	202111.	+	73562.3i	0.420937	+	0.153208i
$43$	401253.	−	146044.i	0.769624	−	0.280120i	0.0727851	−	0.997348i	$-0.476811\pi$
$43$	401253.	−	146044.i	0.769624	−	0.280120i	0.696839	+	0.717227i	$0.254589\pi$
$44$	246672.	−	206983.i	0.436552	−	0.366311i
$45$	−147243.	−	255033.i	−0.240875	−	0.417208i
$46$	−314503.	+	544735.i	−0.476400	+	0.825150i
$47$	−170080.	−	964573.i	−0.238952	−	1.35517i	−0.834128	−	0.551570i	$-0.814029\pi$
$47$	−170080.	−	964573.i	−0.238952	−	1.35517i	0.595176	−	0.803595i	$-0.297082\pi$
$48$	−19688.4	−	111659.i	−0.0256960	−	0.145730i
$49$	−59896.5	+	103744.i	−0.0727303	+	0.125973i
$50$	140651.	+	243615.i	0.159129	+	0.275619i
$51$	455549.	−	382251.i	0.480883	−	0.403508i
$52$	455790.	−	165894.i	0.449524	−	0.163613i
$53$	1.34350e6	+	488993.i	1.23957	+	0.451166i	0.876865	−	0.480738i	$-0.159631\pi$
$53$	1.34350e6	+	488993.i	1.23957	+	0.451166i	0.362705	+	0.931904i	$0.381853\pi$
$54$	612016.	+	513542.i	0.528914	+	0.443811i
$55$	−181092.	+	1.02702e6i	−0.146768	+	0.832360i
$56$	497283.			0.378395
$57$	−765329.	−	314938.i	−0.547376	−	0.225249i
$58$	−534786.			−0.359900
$59$	6167.73	−	34978.9i	0.00390970	−	0.0221730i	−0.982790	−	0.184724i	$-0.940861\pi$
$59$	6167.73	−	34978.9i	0.00390970	−	0.0221730i	0.986700	+	0.162551i	$0.0519721\pi$
$60$	281292.	+	236032.i	0.168123	+	0.141072i
$61$	−2.16873e6	−	789352.i	−1.22335	−	0.445263i	−0.352034	−	0.935987i	$-0.614510\pi$
$61$	−2.16873e6	−	789352.i	−1.22335	−	0.445263i	−0.871315	+	0.490725i	$0.836732\pi$
$62$	−2.22348e6	+	809282.i	−1.18485	+	0.431250i
$63$	−1.05709e6	+	887000.i	−0.532621	+	0.446922i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−785438.	+	1.36042e6i	−0.354744	+	0.614435i
$66$	−193476.	−	1.09726e6i	−0.0828368	−	0.469791i
$67$	−149074.	−	845439.i	−0.0605535	−	0.343416i	−1.00000		0.000719600i	$-0.999771\pi$
$67$	−149074.	−	845439.i	−0.0605535	−	0.343416i	0.939446	−	0.342696i	$-0.111340\pi$
$68$	687465.	−	1.19072e6i	0.265136	−	0.459229i
$69$	1.08822e6	+	1.88484e6i	0.398789	+	0.690723i
$70$	−1.23373e6	+	1.03522e6i	−0.429909	+	0.360737i
$71$	−4.46178e6	+	1.62395e6i	−1.47946	+	0.538480i	−0.950652	−	0.310261i	$-0.899584\pi$
$71$	−4.46178e6	+	1.62395e6i	−1.47946	+	0.538480i	−0.528810	+	0.848740i	$0.677361\pi$
$72$	683563.	+	248797.i	0.215832	+	0.0785563i
$73$	997664.	+	837140.i	0.300161	+	0.251865i	0.780411	−	0.625266i	$-0.215010\pi$
$73$	997664.	+	837140.i	0.300161	+	0.251865i	−0.480250	+	0.877132i	$0.659454\pi$
$74$	216818.	−	1.22964e6i	0.0621991	−	0.352749i
$75$	973340.			0.266410
$76$	−1.91182e6	−	79043.2i	−0.499573	−	0.0206546i
$77$	4.88674e6			1.21984
$78$	291433.	−	1.65280e6i	0.0695358	−	0.394357i
$79$	−2.74956e6	−	2.30715e6i	−0.627433	−	0.526479i	0.272697	−	0.962100i	$-0.412084\pi$
$79$	−2.74956e6	−	2.30715e6i	−0.627433	−	0.526479i	−0.900130	+	0.435621i	$0.856529\pi$
$80$	797790.	+	290372.i	0.174210	+	0.0634074i
$81$	−322153.	+	117254.i	−0.0673541	+	0.0245149i
$82$	−909374.	+	763056.i	−0.182135	+	0.152830i
$83$	1.38264e6	+	2.39480e6i	0.265421	+	0.459722i	0.967674	−	0.252205i	$-0.0811559\pi$
$83$	1.38264e6	+	2.39480e6i	0.265421	+	0.459722i	−0.702253	+	0.711927i	$0.747823\pi$
$84$	860327.	−	1.49013e6i	0.158375	−	0.274313i
$85$	773239.	+	4.38525e6i	0.136567	+	0.774513i
$86$	−593189.	−	3.36414e6i	−0.100565	−	0.570334i
$87$	−925209.	+	1.60251e6i	−0.150634	+	0.260906i
$88$	−1.28803e6	−	2.23094e6i	−0.201482	−	0.348978i
$89$	4.83372e6	−	4.05597e6i	0.726802	−	0.609859i	−0.202456	−	0.979291i	$-0.564892\pi$
$89$	4.83372e6	−	4.05597e6i	0.726802	−	0.609859i	0.929258	+	0.369432i	$0.120448\pi$
$90$	−2.21382e6	+	805763.i	−0.320105	+	0.116509i
$91$	6.91700e6	+	2.51758e6i	0.962217	+	0.350218i
$92$	3.85477e6	+	3.23454e6i	0.516109	+	0.433067i
$93$	−1.42170e6	+	8.06288e6i	−0.183281	+	1.03944i
$94$	−7.83562e6			−0.973030
$95$	4.90766e6	−	3.78384e6i	0.587276	−	0.452794i
$96$	−907048.			−0.104636
$97$	439732.	−	2.49384e6i	0.0489200	−	0.277439i	−0.950529	−	0.310636i	$-0.899458\pi$
$97$	439732.	−	2.49384e6i	0.0489200	−	0.277439i	0.999449	+	0.0331972i	$0.0105689\pi$
$98$	734134.	+	616012.i	0.0787924	+	0.0661147i
$99$	6.71731e6	+	2.44490e6i	0.695780	+	0.253243i
$100$	2.11471e6	−	769690.i	0.211471	−	0.0769690i
$101$	5.01180e6	−	4.20540e6i	0.484026	−	0.406146i	−0.367853	−	0.929884i	$-0.619907\pi$
$101$	5.01180e6	−	4.20540e6i	0.484026	−	0.406146i	0.851880	+	0.523738i	$0.175463\pi$
$102$	−2.37871e6	−	4.12004e6i	−0.221942	−	0.384415i
$103$	8.99186e6	−	1.55744e7i	0.810810	−	1.40436i	−0.101488	−	0.994837i	$-0.532360\pi$
$103$	8.99186e6	−	1.55744e7i	0.810810	−	1.40436i	0.912298	−	0.409527i	$-0.134306\pi$
$104$	−673812.	−	3.82138e6i	−0.0587384	−	0.333122i
$105$	967669.	+	5.48792e6i	0.0815764	+	0.462642i
$106$	5.71888e6	−	9.90538e6i	0.466380	−	0.807794i
$107$	−9.15466e6	−	1.58563e7i	−0.722436	−	1.25130i	−0.960021	−	0.279928i	$-0.909689\pi$
$107$	−9.15466e6	−	1.58563e7i	−0.722436	−	1.25130i	0.237585	−	0.971367i	$-0.423644\pi$
$108$	4.89613e6	−	4.10834e6i	0.373998	−	0.313822i
$109$	−2.00163e7	+	7.28535e6i	−1.48044	+	0.538838i	−0.950914	−	0.309454i	$-0.899854\pi$
$109$	−2.00163e7	+	7.28535e6i	−1.48044	+	0.538838i	−0.529530	+	0.848291i	$0.677632\pi$
$110$	7.83980e6	+	2.85346e6i	0.561605	+	0.204407i
$111$	−3.30955e6	−	2.77705e6i	−0.229688	−	0.192731i
$112$	690818.	−	3.91782e6i	0.0464623	−	0.263501i
$113$	−4.15373e6			−0.270809			−0.135405	−	0.990790i	$-0.543233\pi$
$113$	−4.15373e6			−0.270809			−0.135405	+	0.990790i	$0.543233\pi$
$114$	−3.54441e6	+	5.59210e6i	−0.224067	+	0.353515i
$115$	−1.62970e7			−0.999229
$116$	−742916.	+	4.21329e6i	−0.0441913	+	0.250621i
$117$	8.24851e6	+	6.92132e6i	0.476130	+	0.399520i
$118$	−267012.	−	97184.4i	−0.0149604	−	0.00544515i
$119$	1.96074e7	−	7.13650e6i	1.06661	−	0.388214i
$120$	2.25034e6	−	1.88826e6i	0.118881	−	0.0997531i
$121$	−2.91376e6	−	5.04679e6i	−0.149522	−	0.258980i
$122$	−9.23164e6	+	1.59897e7i	−0.460277	+	0.797224i
$123$	713262.	+	4.04511e6i	0.0345606	+	0.196003i
$124$	3.28707e6	+	1.86419e7i	0.154822	+	0.878039i
$125$	−1.17408e7	+	2.03356e7i	−0.537664	+	0.931262i
$126$	5.51971e6	+	9.56041e6i	0.245821	+	0.425775i
$127$	−6.60114e6	+	5.53901e6i	−0.285960	+	0.239949i	−0.774472	−	0.632608i	$-0.781984\pi$
$127$	−6.60114e6	+	5.53901e6i	−0.285960	+	0.239949i	0.488512	+	0.872557i	$0.337540\pi$
$128$	−1.97068e6	+	717268.i	−0.0830579	+	0.0302306i
$129$	−1.11071e7	−	4.04264e6i	−0.455549	−	0.165806i
$130$	9.62688e6	+	8.07791e6i	0.384312	+	0.322476i
$131$	2.43523e6	−	1.38109e7i	0.0946434	−	0.536749i	−0.900213	−	0.435451i	$-0.856589\pi$
$131$	2.43523e6	−	1.38109e7i	0.0946434	−	0.536749i	0.994856	−	0.101299i	$-0.0322998\pi$
$132$	−8.91347e6			−0.337317
$133$	−2.14546e7	−	1.95684e7i	−0.790750	−	0.721232i
$134$	−6.86785e6			−0.246578
$135$	−3.59445e6	+	2.03851e7i	−0.125737	+	0.713091i
$136$	−8.42605e6	−	7.07030e6i	−0.287235	−	0.241019i
$137$	4.59807e7	+	1.67356e7i	1.52776	+	0.556057i	0.963071	−	0.269249i	$-0.0867755\pi$
$137$	4.59807e7	+	1.67356e7i	1.52776	+	0.556057i	0.564685	+	0.825307i	$0.308998\pi$
$138$	1.63614e7	−	5.95507e6i	0.529961	−	0.192890i
$139$	−2.15641e7	+	1.80944e7i	−0.681050	+	0.571469i	−0.916313	−	0.400463i	$-0.868849\pi$
$139$	−2.15641e7	+	1.80944e7i	−0.681050	+	0.571469i	0.235263	+	0.971932i	$0.424405\pi$
$140$	6.44208e6	+	1.11580e7i	0.198417	+	0.343668i
$141$	−1.35561e7	+	2.34798e7i	−0.407256	+	0.705387i
$142$	6.59602e6	+	3.74079e7i	0.193318	+	1.09636i
$143$	−6.62148e6	−	3.75523e7i	−0.189356	−	1.07389i
$144$	2.90973e6	−	5.03980e6i	0.0812053	−	0.140652i
$145$	−6.92792e6	−	1.19995e7i	−0.188719	−	0.326870i
$146$	7.98132e6	−	6.69712e6i	0.212246	−	0.178096i
$147$	3.11600e6	−	1.13413e6i	0.0809072	−	0.0294478i
$148$	−9.38644e6	−	3.41639e6i	−0.238004	−	0.0866265i
$149$	7.49212e6	+	6.28663e6i	0.185546	+	0.155692i	0.730830	−	0.682560i	$-0.239133\pi$
$149$	7.49212e6	+	6.28663e6i	0.185546	+	0.155692i	−0.545283	+	0.838252i	$0.683578\pi$
$150$	1.35215e6	−	7.66842e6i	0.0327119	−	0.185518i
$151$	−4.29355e7			−1.01484			−0.507420	−	0.861699i	$-0.669401\pi$
$151$	−4.29355e7			−1.01484			−0.507420	+	0.861699i	$0.669401\pi$
$152$	−3.27861e6	+	1.49524e7i	−0.0757246	+	0.345349i
$153$	3.05227e7			0.688975
$154$	6.78859e6	−	3.85000e7i	0.149781	−	0.849451i
$155$	−4.69629e7	−	3.94066e7i	−1.01296	−	0.849978i
$156$	−1.26167e7	−	4.59209e6i	−0.266078	−	0.0968444i
$157$	1.71918e7	−	6.25732e6i	0.354547	−	0.129044i	−0.158606	−	0.987342i	$-0.550700\pi$
$157$	1.71918e7	−	6.25732e6i	0.354547	−	0.129044i	0.513152	+	0.858298i	$0.328478\pi$
$158$	−2.19964e7	+	1.84572e7i	−0.443662	+	0.372277i
$159$	−1.97880e7	−	3.42738e7i	−0.390401	−	0.676195i
$160$	3.39596e6	−	5.88198e6i	0.0655455	−	0.113528i
$161$	1.32607e7	+	7.52054e7i	0.250425	+	1.42023i
$162$	476251.	+	2.70095e6i	0.00880103	+	0.0499131i
$163$	4.99056e7	−	8.64391e7i	0.902595	−	1.56334i	0.0784807	−	0.996916i	$-0.474993\pi$
$163$	4.99056e7	−	8.64391e7i	0.902595	−	1.56334i	0.824114	−	0.566424i	$-0.191674\pi$
$164$	4.74841e6	+	8.22450e6i	0.0840611	+	0.145598i
$165$	2.21138e7	−	1.85557e7i	0.383239	−	0.321576i
$166$	2.07880e7	−	7.56623e6i	0.352724	−	0.128381i
$167$	3.82244e7	+	1.39125e7i	0.635086	+	0.231153i	0.639444	−	0.768838i	$-0.279165\pi$
$167$	3.82244e7	+	1.39125e7i	0.635086	+	0.231153i	−0.00435732	+	0.999991i	$0.501387\pi$
$168$	−1.05448e7	−	8.84812e6i	−0.171575	−	0.143969i
$169$	−922203.	+	5.23007e6i	−0.0146968	+	0.0833497i
$170$	3.56232e7			0.556112
$171$	−1.97011e7	−	3.76327e7i	−0.301303	−	0.575544i
$172$	−2.73283e7			−0.409509
$173$	−1.47533e7	+	8.36702e7i	−0.216635	+	1.22860i	0.661413	+	0.750022i	$0.269957\pi$
$173$	−1.47533e7	+	8.36702e7i	−0.216635	+	1.22860i	−0.878047	+	0.478574i	$0.841154\pi$
$174$	1.13400e7	+	9.51541e6i	0.163189	+	0.136932i
$175$	3.20925e7	+	1.16807e7i	0.452658	+	0.164754i
$176$	−1.93657e7	+	7.04852e6i	−0.267755	+	0.0974549i
$177$	−753164.	+	631979.i	−0.0102090	+	0.00856636i
$178$	−2.52399e7	−	4.37167e7i	−0.335442	−	0.581002i
$179$	8.39157e6	−	1.45346e7i	0.109360	−	0.189417i	−0.806151	−	0.591709i	$-0.798453\pi$
$179$	8.39157e6	−	1.45346e7i	0.109360	−	0.189417i	0.915511	+	0.402293i	$0.131787\pi$
$180$	3.27277e6	+	1.85608e7i	0.0418275	+	0.237216i
$181$	−9.47663e6	−	5.37446e7i	−0.118790	−	0.673690i	−0.984804	−	0.173670i	$-0.944437\pi$
$181$	−9.47663e6	−	5.37446e7i	−0.118790	−	0.673690i	0.866014	−	0.500020i	$-0.166674\pi$
$182$	2.94437e7	−	5.09979e7i	0.362028	−	0.627051i
$183$	3.19425e7	+	5.53261e7i	0.385292	+	0.667346i
$184$	3.08382e7	−	2.58763e7i	0.364944	−	0.306224i
$185$	3.03993e7	−	1.10645e7i	0.352990	−	0.128478i
$186$	6.15481e7	+	2.24017e7i	0.701325	+	0.255261i
$187$	−8.28020e7	−	6.94791e7i	−0.925966	−	0.776978i
$188$	−1.08851e7	+	6.17327e7i	−0.119476	+	0.677583i
$189$	9.69956e7			1.04505
$190$	−2.29932e7	−	4.39213e7i	−0.243199	−	0.464556i
$191$	4.69545e7			0.487596			0.243798	−	0.969826i	$-0.421607\pi$
$191$	4.69545e7			0.487596			0.243798	+	0.969826i	$0.421607\pi$
$192$	−1.26006e6	+	7.14614e6i	−0.0128480	+	0.0728648i
$193$	−6.32263e7	−	5.30532e7i	−0.633064	−	0.531204i	0.268816	−	0.963192i	$-0.413368\pi$
$193$	−6.32263e7	−	5.30532e7i	−0.633064	−	0.531204i	−0.901879	+	0.431988i	$0.857812\pi$
$194$	−1.90368e7	−	6.92882e6i	−0.187192	−	0.0681323i
$195$	4.08609e7	−	1.48722e7i	0.394627	−	0.143632i
$196$	5.87308e6	−	4.92810e6i	0.0557146	−	0.0467501i
$197$	9.25722e7	+	1.60340e8i	0.862678	+	1.49420i	0.869335	+	0.494224i	$0.164548\pi$
$197$	9.25722e7	+	1.60340e8i	0.862678	+	1.49420i	−0.00665701	+	0.999978i	$0.502119\pi$
$198$	2.85936e7	−	4.95256e7i	0.261783	−	0.453421i
$199$	2.12361e6	+	1.20436e7i	0.0191025	+	0.108335i	0.992868	−	0.119218i	$-0.0380386\pi$
$199$	2.12361e6	+	1.20436e7i	0.0191025	+	0.108335i	−0.973766	+	0.227553i	$0.926927\pi$
$200$	−3.12625e6	−	1.77299e7i	−0.0276324	−	0.156711i
$201$	−1.18818e7	+	2.05798e7i	−0.103204	+	0.178754i
$202$	−2.61698e7	−	4.53274e7i	−0.223393	−	0.386928i
$203$	−4.97367e7	+	4.17340e7i	−0.417293	+	0.350150i
$204$	−3.57640e7	+	1.30170e7i	−0.294945	+	0.107351i
$205$	−2.89020e7	−	1.05195e7i	−0.234309	−	0.0852815i
$206$	−1.10211e8	−	9.24777e7i	−0.878391	−	0.737058i
$207$	−1.93980e7	+	1.10012e8i	−0.152006	+	0.862070i
$208$	−3.10426e7			−0.239187
$209$	−3.22186e7	+	1.46936e8i	−0.244115	+	1.11331i
$210$	4.45807e7			0.332184
$211$	3.88462e6	−	2.20308e7i	0.0284682	−	0.161451i	−0.967260	−	0.253789i	$-0.918323\pi$
$211$	3.88462e6	−	2.20308e7i	0.0284682	−	0.161451i	0.995728	+	0.0923383i	$0.0294341\pi$
$212$	−7.00946e7	−	5.88164e7i	−0.505253	−	0.423958i
$213$	1.23506e8	+	4.49525e7i	0.875709	+	0.318732i
$214$	−1.37641e8	+	5.00973e7i	−0.960063	+	0.349435i
$215$	6.78000e7	−	5.68909e7i	0.465259	−	0.390399i
$216$	−2.55658e7	−	4.42812e7i	−0.172612	−	0.298973i
$217$	−1.43635e8	+	2.48784e8i	−0.954228	+	1.65277i
$218$	2.95910e7	+	1.67819e8i	0.193447	+	1.09709i
$219$	−6.26010e6	−	3.55028e7i	−0.0402742	−	0.228406i
$220$	3.33718e7	−	5.78016e7i	0.211300	−	0.365983i
$221$	−8.14084e7	−	1.41003e8i	−0.507337	−	0.878733i
$222$	−2.64764e7	+	2.22164e7i	−0.162414	+	0.136282i
$223$	−4.82326e7	+	1.75552e7i	−0.291255	+	0.106008i	−0.483516	−	0.875336i	$-0.660640\pi$
$223$	−4.82326e7	+	1.75552e7i	−0.291255	+	0.106008i	0.192261	+	0.981344i	$0.438418\pi$
$224$	−2.99067e7	−	1.08852e7i	−0.177787	−	0.0647093i
$225$	3.82702e7	+	3.21125e7i	0.223987	+	0.187947i
$226$	−5.77030e6	+	3.27250e7i	−0.0332521	+	0.188582i
$227$	−4.46035e7			−0.253092			−0.126546	−	0.991961i	$-0.540389\pi$
$227$	−4.46035e7			−0.253092			−0.126546	+	0.991961i	$0.540389\pi$
$228$	3.91333e7	+	3.56930e7i	0.218663	+	0.199439i
$229$	−2.86036e8			−1.57397			−0.786986	−	0.616970i	$-0.788360\pi$
$229$	−2.86036e8			−1.57397			−0.786986	+	0.616970i	$0.788360\pi$
$230$	−2.26395e7	+	1.28395e8i	−0.122693	+	0.695827i
$231$	−1.03622e8	−	8.69496e7i	−0.553111	−	0.464115i
$232$	3.21622e7	+	1.17061e7i	0.169098	+	0.0615465i
$233$	2.07342e8	−	7.54662e7i	1.07384	−	0.390847i	0.256230	−	0.966616i	$-0.417519\pi$
$233$	2.07342e8	−	7.54662e7i	1.07384	−	0.390847i	0.817612	+	0.575769i	$0.195297\pi$
$234$	6.59881e7	−	5.53706e7i	0.336674	−	0.282503i
$235$	−1.01507e8	−	1.75815e8i	−0.510222	−	0.883730i
$236$	−1.13659e6	+	1.96864e6i	−0.00562876	+	0.00974930i
$237$	1.72528e7	+	9.78454e7i	0.0841860	+	0.477443i
$238$	−2.89864e7	−	1.64390e8i	−0.139372	−	0.790416i
$239$	4.00103e7	−	6.92998e7i	0.189574	−	0.328352i	−0.755534	−	0.655109i	$-0.772623\pi$
$239$	4.00103e7	−	6.92998e7i	0.189574	−	0.328352i	0.945108	+	0.326757i	$0.105956\pi$
$240$	−1.17504e7	−	2.03523e7i	−0.0548674	−	0.0950330i
$241$	−1.05378e8	+	8.84226e7i	−0.484942	+	0.406915i	−0.852210	−	0.523200i	$-0.824738\pi$
$241$	−1.05378e8	+	8.84226e7i	−0.484942	+	0.406915i	0.367267	+	0.930115i	$0.380293\pi$
$242$	−4.38087e7	+	1.59451e7i	−0.198704	+	0.0723223i
$243$	2.14153e8	+	7.79455e7i	0.957421	+	0.348473i
$244$	1.13150e8	+	9.49438e7i	0.498642	+	0.418410i
$245$	−4.31166e6	+	2.44527e7i	−0.0187311	+	0.106229i
$246$	3.28601e7			0.140733
$247$	−1.21303e8	+	1.91383e8i	−0.512193	+	0.808099i
$248$	1.51436e8			0.630445
$249$	1.32919e7	−	7.53824e7i	0.0545621	−	0.309437i
$250$	1.43903e8	+	1.20749e8i	0.582479	+	0.488758i
$251$	−5.63736e7	−	2.05183e7i	−0.225018	−	0.0819000i	0.227051	−	0.973883i	$-0.427092\pi$
$251$	−5.63736e7	−	2.05183e7i	−0.225018	−	0.0819000i	−0.452069	+	0.891983i	$0.649314\pi$
$252$	8.29893e7	−	3.02056e7i	0.326678	−	0.118901i
$253$	3.03043e8	−	2.54284e8i	1.17648	−	0.987181i
$254$	3.44687e7	+	5.97016e7i	0.131980	+	0.228595i
$255$	6.16302e7	−	1.06747e8i	0.232757	−	0.403147i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−5.56959e7	−	3.15867e8i	−0.204672	−	1.16075i	−0.897956	−	0.440086i	$-0.854948\pi$
$257$	−5.56959e7	−	3.15867e8i	−0.204672	−	1.16075i	0.693284	−	0.720664i	$-0.256163\pi$
$258$	−4.72795e7	+	8.18905e7i	−0.171397	+	0.296869i
$259$	−7.57946e7	−	1.31280e8i	−0.271075	−	0.469515i
$260$	7.70151e7	−	6.46233e7i	0.271750	−	0.228025i
$261$	−8.92480e7	+	3.24836e7i	−0.310711	+	0.113090i
$262$	−1.05425e8	−	3.83717e7i	−0.362152	−	0.131813i
$263$	2.86806e8	+	2.40659e8i	0.972173	+	0.815750i	0.982890	−	0.184192i	$-0.0589670\pi$
$263$	2.86806e8	+	2.40659e8i	0.972173	+	0.815750i	−0.0107170	+	0.999943i	$0.503411\pi$
$264$	−1.23825e7	+	7.02244e7i	−0.0414184	+	0.234895i
$265$	2.96342e8			0.978212
$266$	−1.83973e8	+	1.41845e8i	−0.599335	+	0.462091i
$267$	−1.74666e8			−0.561589
$268$	−9.54071e6	+	5.41081e7i	−0.0302767	+	0.171708i
$269$	−1.71729e8	−	1.44097e8i	−0.537910	−	0.451360i	0.332912	−	0.942958i	$-0.391969\pi$
$269$	−1.71729e8	−	1.44097e8i	−0.537910	−	0.451360i	−0.870823	+	0.491597i	$0.836413\pi$
$270$	1.55610e8	+	5.66374e7i	0.481132	+	0.175118i
$271$	4.37759e8	−	1.59331e8i	1.33611	−	0.486304i	0.427525	−	0.904004i	$-0.359386\pi$
$271$	4.37759e8	−	1.59331e8i	1.33611	−	0.486304i	0.908585	+	0.417700i	$0.137164\pi$
$272$	−6.74084e7	+	5.65624e7i	−0.203106	+	0.170426i
$273$	−1.01878e8	−	1.76459e8i	−0.303049	−	0.524897i
$274$	1.95727e8	−	3.39009e8i	0.574808	−	0.995597i
$275$	−3.07214e7	−	1.74230e8i	−0.0890792	−	0.505193i
$276$	−2.41877e7	−	1.37175e8i	−0.0692490	−	0.392730i
$277$	1.32068e8	−	2.28748e8i	0.373351	−	0.646662i	−0.616728	−	0.787176i	$-0.711542\pi$
$277$	1.32068e8	−	2.28748e8i	0.373351	−	0.646662i	0.990079	+	0.140514i	$0.0448755\pi$
$278$	1.12600e8	+	1.95028e8i	0.314326	+	0.544428i
$279$	−3.21910e8	+	2.70115e8i	−0.887402	+	0.744618i
$280$	9.68572e7	−	3.52531e7i	0.263681	−	0.0959720i
$281$	−3.99589e7	−	1.45438e7i	−0.107434	−	0.0391027i	0.287744	−	0.957707i	$-0.407095\pi$
$281$	−3.99589e7	−	1.45438e7i	−0.107434	−	0.0391027i	−0.395178	+	0.918605i	$0.629317\pi$
$282$	1.66153e8	+	1.39419e8i	0.441200	+	0.370211i
$283$	−9.88448e7	+	5.60577e8i	−0.259240	+	1.47022i	0.525711	+	0.850663i	$0.323799\pi$
$283$	−9.88448e7	+	5.60577e8i	−0.259240	+	1.47022i	−0.784951	+	0.619558i	$0.787312\pi$
$284$	3.03880e8			0.787205
$285$	−1.71392e8	−	7.08611e6i	−0.438564	−	0.0181322i
$286$	−3.05053e8			−0.771070
$287$	−2.50266e7	+	1.41933e8i	−0.0624907	+	0.354402i
$288$	−3.56637e7	−	2.99254e7i	−0.0879737	−	0.0738187i
$289$	−4.81049e7	−	1.75088e7i	−0.117232	−	0.0426690i
$290$	−1.04162e8	+	3.79118e7i	−0.250793	+	0.0912812i
$291$	−5.36972e7	+	4.50573e7i	−0.127740	+	0.107186i
$292$	−4.16755e7	−	7.21840e7i	−0.0979581	−	0.169668i
$293$	4.12897e8	−	7.15159e8i	0.958971	−	1.66099i	0.233963	−	0.972246i	$-0.424831\pi$
$293$	4.12897e8	−	7.15159e8i	0.958971	−	1.66099i	0.725008	−	0.688740i	$-0.241836\pi$
$294$	−4.60651e6	−	2.61248e7i	−0.0105720	−	0.0599567i
$295$	−1.27840e6	−	7.25019e6i	−0.00289929	−	0.0164427i
$296$	−3.99554e7	+	6.92047e7i	−0.0895476	+	0.155101i
$297$	−2.51232e8	−	4.35147e8i	−0.556452	−	0.963803i
$298$	5.99369e7	−	5.02931e7i	0.131201	−	0.110091i
$299$	5.59950e8	−	2.03805e8i	1.21143	−	0.440926i
$300$	−5.85370e7	−	2.13057e7i	−0.125172	−	0.0455588i
$301$	−3.17702e8	−	2.66584e8i	−0.671486	−	0.563444i
$302$	−5.96454e7	+	3.38266e8i	−0.124610	+	0.706698i
$303$	−1.81101e8			−0.373999
$304$	1.13247e8	+	4.66020e7i	0.231190	+	0.0951365i
$305$	−4.78368e8			−0.965411
$306$	4.24017e7	−	2.40472e8i	0.0845977	−	0.479777i
$307$	4.10131e8	+	3.44141e8i	0.808982	+	0.678816i	0.950365	−	0.311139i	$-0.100710\pi$
$307$	4.10131e8	+	3.44141e8i	0.808982	+	0.678816i	−0.141383	+	0.989955i	$0.545155\pi$
$308$	−2.93890e8	−	1.06967e8i	−0.573136	−	0.208605i
$309$	−4.67784e8	+	1.70260e8i	−0.901967	+	0.328289i
$310$	−3.75703e8	+	3.15253e8i	−0.716274	+	0.601025i
$311$	−2.91198e8	−	5.04369e8i	−0.548942	−	0.950796i	−0.998347	−	0.0574680i	$-0.981697\pi$
$311$	−2.91198e8	−	5.04369e8i	−0.548942	−	0.950796i	0.449405	−	0.893328i	$-0.351636\pi$
$312$	−5.37055e7	+	9.30207e7i	−0.100110	+	0.173396i
$313$	1.83166e8	+	1.03879e9i	0.337629	+	1.91479i	0.399553	+	0.916710i	$0.369165\pi$
$313$	1.83166e8	+	1.03879e9i	0.337629	+	1.91479i	−0.0619242	+	0.998081i	$0.519724\pi$
$314$	−2.54154e7	−	1.44138e8i	−0.0463279	−	0.262739i
$315$	−1.43011e8	+	2.47702e8i	−0.257800	+	0.446522i
$316$	1.14857e8	+	1.98939e8i	0.204764	+	0.354662i
$317$	1.74872e8	−	1.46735e8i	0.308327	−	0.258717i	−0.475473	−	0.879730i	$-0.657723\pi$
$317$	1.74872e8	−	1.46735e8i	0.308327	−	0.258717i	0.783800	+	0.621013i	$0.213279\pi$
$318$	−2.97514e8	+	1.08286e8i	−0.518814	+	0.188833i
$319$	3.16054e8	+	1.15034e8i	0.545123	+	0.198409i
$320$	−4.16233e7	−	3.49261e7i	−0.0710088	−	0.0595834i
$321$	−8.80082e7	+	4.99119e8i	−0.148510	+	0.842241i
$322$	6.10925e8			1.01975
$323$	8.53092e7	+	6.36610e8i	0.140860	+	1.05115i
$324$	2.19410e7			0.0358384
$325$	4.62757e7	−	2.62443e8i	0.0747758	−	0.424075i
$326$	−6.11679e8	−	5.13259e8i	−0.977826	−	0.820494i
$327$	5.54071e8	+	2.01665e8i	0.876290	+	0.318944i
$328$	7.13928e7	−	2.59849e7i	0.111711	−	0.0406595i
$329$	−7.28737e8	+	6.11483e8i	−1.12820	+	0.946670i
$330$	−1.15470e8	−	2.00000e8i	−0.176877	−	0.306360i
$331$	−3.17568e8	+	5.50044e8i	−0.481325	+	0.833680i	−0.999770	−	0.0214312i	$-0.993178\pi$
$331$	−3.17568e8	+	5.50044e8i	−0.481325	+	0.833680i	0.518445	+	0.855111i	$0.326511\pi$
$332$	−3.07318e7	−	1.74289e8i	−0.0460898	−	0.261388i
$333$	−3.85060e7	−	2.18378e8i	−0.0571444	−	0.324082i
$334$	1.62710e8	−	2.81822e8i	0.238947	−	0.413869i
$335$	−8.89700e7	−	1.54101e8i	−0.129297	−	0.223948i
$336$	−8.43582e7	+	7.07850e7i	−0.121322	+	0.101801i
$337$	−5.43495e8	+	1.97816e8i	−0.773554	+	0.281551i	−0.698482	−	0.715627i	$-0.746141\pi$
$337$	−5.43495e8	+	1.97816e8i	−0.773554	+	0.281551i	−0.0750720	+	0.997178i	$0.523919\pi$
$338$	3.99238e7	+	1.45311e7i	0.0562372	+	0.0204687i
$339$	8.80790e7	+	7.39071e7i	0.122793	+	0.103036i
$340$	4.94873e7	−	2.80656e8i	0.0682837	−	0.387256i
$341$	1.48814e9			2.03238
$342$	−3.23856e8	+	1.02935e8i	−0.437785	+	0.139147i
$343$	−6.83521e8			−0.914581
$344$	−3.79641e7	+	2.15305e8i	−0.0502827	+	0.285167i
$345$	3.45575e8	+	2.89972e8i	0.453080	+	0.380179i
$346$	6.38697e8	+	2.32467e8i	0.828950	+	0.301713i
$347$	4.85902e8	−	1.76854e8i	0.624303	−	0.227228i	−0.0104468	−	0.999945i	$-0.503325\pi$
$347$	4.85902e8	−	1.76854e8i	0.624303	−	0.227228i	0.634750	+	0.772718i	$0.281103\pi$
$348$	9.07202e7	−	7.61233e7i	0.115392	−	0.0968256i
$349$	2.83022e8	+	4.90208e8i	0.356394	+	0.617293i	0.987356	−	0.158521i	$-0.0506726\pi$
$349$	2.83022e8	+	4.90208e8i	0.356394	+	0.617293i	−0.630961	+	0.775814i	$0.717339\pi$
$350$	1.36608e8	−	2.36613e8i	0.170310	−	0.294985i
$351$	−1.31428e8	−	7.45365e8i	−0.162223	−	0.920014i
$352$	2.86290e7	+	1.62363e8i	0.0349870	+	0.198421i
$353$	6.78430e8	−	1.17507e9i	0.820906	−	1.42185i	−0.0841029	−	0.996457i	$-0.526802\pi$
$353$	6.78430e8	−	1.17507e9i	0.820906	−	1.42185i	0.905009	−	0.425393i	$-0.139864\pi$
$354$	3.93274e6	+	6.81171e6i	0.00471177	+	0.00816102i
$355$	−7.53909e8	+	6.32605e8i	−0.894375	+	0.750470i
$356$	−3.79484e8	+	1.38121e8i	−0.445777	+	0.162250i
$357$	−5.42750e8	−	1.97545e8i	−0.631337	−	0.229788i
$358$	−1.02853e8	−	8.63039e7i	−0.118475	−	0.0994123i
$359$	−2.38783e8	+	1.35421e9i	−0.272379	+	1.54474i	0.474787	+	0.880101i	$0.342525\pi$
$359$	−2.38783e8	+	1.35421e9i	−0.272379	+	1.54474i	−0.747166	+	0.664638i	$0.768586\pi$
$360$	1.50777e8			0.170324
$361$	7.29838e8	−	5.16084e8i	0.816491	−	0.577359i
$362$	−4.36590e8			−0.483720
$363$	−2.80114e7	+	1.58861e8i	−0.0307370	+	0.174318i
$364$	−3.60883e8	−	3.02816e8i	−0.392203	−	0.329098i
$365$	2.53664e8	+	9.23263e7i	0.273045	+	0.0993803i
$366$	4.80259e8	−	1.74800e8i	0.512025	−	0.186362i
$367$	−1.06562e9	+	8.94160e8i	−1.12531	+	0.944243i	−0.998860	−	0.0477306i	$-0.984801\pi$
$367$	−1.06562e9	+	8.94160e8i	−1.12531	+	0.944243i	−0.126445	+	0.991974i	$0.540357\pi$
$368$	−1.61025e8	−	2.78904e8i	−0.168433	−	0.291734i
$369$	−1.05412e8	+	1.82580e8i	−0.109219	+	0.189173i
$370$	−4.49406e7	−	2.54871e8i	−0.0461246	−	0.261585i
$371$	−2.41132e8	−	1.36753e9i	−0.245158	−	1.39036i
$372$	2.61992e8	−	4.53784e8i	0.263869	−	0.457034i
$373$	−8.29975e8	−	1.43756e9i	−0.828102	−	1.43432i	−0.899525	−	0.436869i	$-0.856087\pi$
$373$	−8.29975e8	−	1.43756e9i	−0.828102	−	1.43432i	0.0714229	−	0.997446i	$-0.477246\pi$
$374$	−6.62416e8	+	5.55833e8i	−0.654757	+	0.549406i
$375$	6.10791e8	−	2.22310e8i	0.598113	−	0.217695i
$376$	4.71237e8	+	1.71516e8i	0.457174	+	0.166398i
$377$	3.88099e8	+	3.25654e8i	0.373033	+	0.313012i
$378$	1.34745e8	−	7.64176e8i	0.128319	−	0.727733i
$379$	1.89344e9			1.78655			0.893274	−	0.449513i	$-0.148402\pi$
$379$	1.89344e9			1.78655			0.893274	+	0.449513i	$0.148402\pi$
$380$	−3.77974e8	+	1.20136e8i	−0.353362	+	0.112313i
$381$	2.38531e8			0.220957
$382$	6.52285e7	−	3.69929e8i	0.0598708	−	0.339544i
$383$	1.23624e8	+	1.03733e8i	0.112437	+	0.0943455i	0.697273	−	0.716806i	$-0.254397\pi$
$383$	1.23624e8	+	1.03733e8i	0.112437	+	0.0943455i	−0.584836	+	0.811152i	$0.698841\pi$
$384$	5.45502e7	+	1.98546e7i	0.0491628	+	0.0178938i
$385$	9.51806e8	−	3.46429e8i	0.850033	−	0.309387i
$386$	−5.05811e8	+	4.24426e8i	−0.447644	+	0.375618i
$387$	−3.03337e8	−	5.25395e8i	−0.266034	−	0.460784i
$388$	−8.10340e7	+	1.40355e8i	−0.0704298	+	0.121988i
$389$	−2.44365e8	−	1.38586e9i	−0.210482	−	1.19370i	−0.888576	−	0.458729i	$-0.848305\pi$
$389$	−2.44365e8	−	1.38586e9i	−0.210482	−	1.19370i	0.678094	−	0.734975i	$-0.262806\pi$
$390$	−6.04063e7	−	3.42581e8i	−0.0515651	−	0.292440i
$391$	8.44569e8	−	1.46284e9i	0.714523	−	1.23759i
$392$	−3.06670e7	−	5.31168e7i	−0.0257140	−	0.0445380i
$393$	−2.97375e8	+	2.49527e8i	−0.247133	+	0.207369i
$394$	1.39183e9	−	5.06585e8i	1.14643	−	0.417268i
$395$	−6.99097e8	−	2.54450e8i	−0.570752	−	0.207737i
$396$	−3.50464e8	−	2.94074e8i	−0.283603	−	0.237971i
$397$	−2.13868e8	+	1.21291e9i	−0.171546	+	0.972884i	0.770510	+	0.637428i	$0.220001\pi$
$397$	−2.13868e8	+	1.21291e9i	−0.171546	+	0.972884i	−0.942056	+	0.335456i	$0.891110\pi$
$398$	9.78352e7			0.0777865
$399$	1.06760e8	+	7.96685e8i	0.0841403	+	0.627887i
$400$	−1.44027e8			−0.112521
$401$	1.94925e8	−	1.10548e9i	0.150960	−	0.856138i	−0.811426	−	0.584455i	$-0.801308\pi$
$401$	1.94925e8	−	1.10548e9i	0.150960	−	0.856138i	0.962387	−	0.271684i	$-0.0875804\pi$
$402$	1.45631e8	+	1.22199e8i	0.111806	+	0.0938161i
$403$	2.10641e9	+	7.66670e8i	1.60315	+	0.583500i
$404$	−3.93465e8	+	1.43209e8i	−0.296873	+	0.108053i
$405$	−5.44343e7	+	4.56758e7i	−0.0407174	+	0.0341660i
$406$	2.59707e8	+	4.49825e8i	0.192594	+	0.333582i
$407$	−3.92637e8	+	6.80068e8i	−0.288676	+	0.500002i
$408$	5.28714e7	+	2.99849e8i	0.0385399	+	0.218571i
$409$	4.42405e8	+	2.50900e9i	0.319734	+	1.81330i	0.544357	+	0.838854i	$0.316774\pi$
$409$	4.42405e8	+	2.50900e9i	0.319734	+	1.81330i	−0.224624	+	0.974446i	$0.572115\pi$
$410$	−1.23027e8	+	2.13090e8i	−0.0881573	+	0.152693i
$411$	−6.77237e8	−	1.17301e9i	−0.481165	−	0.833402i
$412$	−8.81685e8	+	7.39821e8i	−0.621116	+	0.521179i
$413$	−3.24171e7	+	1.17989e7i	−0.0226438	+	0.00824166i
$414$	8.39776e8	+	3.05653e8i	0.581650	+	0.211703i
$415$	4.39071e8	+	3.68424e8i	0.301555	+	0.253035i
$416$	−4.31240e7	+	2.44568e8i	−0.0293692	+	0.166561i
$417$	7.79215e8			0.526236
$418$	1.11287e9	+	4.57953e8i	0.745293	+	0.306693i
$419$	−8.01685e8			−0.532420			−0.266210	−	0.963915i	$-0.585772\pi$
$419$	−8.01685e8			−0.532420			−0.266210	+	0.963915i	$0.585772\pi$
$420$	6.19308e7	−	3.51227e8i	0.0407882	−	0.231321i
$421$	−1.62057e9	−	1.35982e9i	−1.05847	−	0.888165i	−0.0645145	−	0.997917i	$-0.520550\pi$
$421$	−1.62057e9	−	1.35982e9i	−1.05847	−	0.888165i	−0.993959	+	0.109752i	$0.964994\pi$
$422$	−1.68172e8	−	6.12096e7i	−0.108933	−	0.0396484i
$423$	−1.30765e9	+	4.75946e8i	−0.840042	+	0.305750i
$424$	−5.60757e8	+	4.70531e8i	−0.357268	+	0.299783i
$425$	−3.77707e8	−	6.54207e8i	−0.238667	−	0.413384i
$426$	5.25730e8	−	9.10590e8i	0.329480	−	0.570676i
$427$	3.89244e8	+	2.20751e9i	0.241950	+	1.37216i
$428$	2.03480e8	+	1.15399e9i	0.125450	+	0.711460i
$429$	−5.27759e8	+	9.14105e8i	−0.322727	+	0.558979i
$430$	−3.54026e8	−	6.13192e8i	−0.214732	−	0.371926i
$431$	5.77395e8	−	4.84492e8i	0.347378	−	0.291485i	−0.452358	−	0.891836i	$-0.649417\pi$
$431$	5.77395e8	−	4.84492e8i	0.347378	−	0.291485i	0.799736	+	0.600352i	$0.204973\pi$
$432$	−3.84383e8	+	1.39904e8i	−0.229388	+	0.0834906i
$433$	−2.24162e9	−	8.15885e8i	−1.32695	−	0.482971i	−0.421273	−	0.906934i	$-0.638416\pi$
$433$	−2.24162e9	−	8.15885e8i	−1.32695	−	0.482971i	−0.905680	+	0.423963i	$0.860639\pi$
$434$	1.76050e9	+	1.47723e9i	1.03376	+	0.867431i
$435$	−6.66014e7	+	3.77715e8i	−0.0387946	+	0.220015i
$436$	1.36326e9			0.787728
$437$	−2.34872e9	−	9.71066e7i	−1.34631	−	0.0556626i
$438$	−2.88404e8			−0.163999
$439$	3.50545e7	−	1.98804e8i	0.0197751	−	0.112150i	−0.973322	−	0.229441i	$-0.926310\pi$
$439$	3.50545e7	−	1.98804e8i	0.0197751	−	0.112150i	0.993098	+	0.117291i	$0.0374212\pi$
$440$	−4.09028e8	−	3.43215e8i	−0.228912	−	0.192080i
$441$	1.59934e8	+	5.82112e7i	0.0887984	+	0.0323200i
$442$	−1.22398e9	+	4.45493e8i	−0.674213	+	0.245393i
$443$	−7.86376e8	+	6.59848e8i	−0.429752	+	0.360604i	−0.831858	−	0.554989i	$-0.812723\pi$
$443$	−7.86376e8	+	6.59848e8i	−0.429752	+	0.360604i	0.402106	+	0.915593i	$0.368278\pi$
$444$	1.38250e8	+	2.39456e8i	0.0749592	+	0.129833i
$445$	6.53943e8	−	1.13266e9i	0.351787	−	0.609313i
$446$	7.13042e7	+	4.04386e8i	0.0380577	+	0.215836i
$447$	−4.70112e7	−	2.66614e8i	−0.0248957	−	0.141191i
$448$	−1.27304e8	+	2.20498e8i	−0.0668914	+	0.115859i
$449$	−1.66714e9	−	2.88758e9i	−0.869183	−	1.50547i	−0.862833	−	0.505489i	$-0.831312\pi$
$449$	−1.66714e9	−	2.88758e9i	−0.869183	−	1.50547i	−0.00634950	−	0.999980i	$-0.502021\pi$
$450$	3.06162e8	−	2.56900e8i	0.158382	−	0.132899i
$451$	7.01570e8	−	2.55351e8i	0.360125	−	0.131075i
$452$	2.49807e8	+	9.09222e7i	0.127239	+	0.0463111i
$453$	9.10440e8	+	7.63949e8i	0.460158	+	0.386119i
$454$	−6.19626e7	+	3.51407e8i	−0.0310766	+	0.176244i
$455$	1.52572e9			0.759338
$456$	3.35569e8	−	2.58726e8i	0.165732	−	0.127780i
$457$	9.88362e8			0.484406			0.242203	−	0.970226i	$-0.422130\pi$
$457$	9.88362e8			0.484406			0.242203	+	0.970226i	$0.422130\pi$
$458$	−3.97358e8	+	2.25353e9i	−0.193265	+	1.09606i
$459$	−1.64351e9	−	1.37907e9i	−0.793284	−	0.665645i
$460$	9.80107e8	+	3.56730e8i	0.469484	+	0.170878i
$461$	1.35673e9	−	4.93810e8i	0.644972	−	0.234751i	0.00123723	−	0.999999i	$-0.499606\pi$
$461$	1.35673e9	−	4.93810e8i	0.644972	−	0.234751i	0.643735	+	0.765249i	$0.277384\pi$
$462$	−8.28980e8	+	6.95597e8i	−0.391108	+	0.328179i
$463$	−1.68543e9	−	2.91924e9i	−0.789180	−	1.36690i	−0.926470	−	0.376369i	$-0.877173\pi$
$463$	−1.68543e9	−	2.91924e9i	−0.789180	−	1.36690i	0.137290	−	0.990531i	$-0.456161\pi$
$464$	1.36905e8	−	2.37127e8i	0.0636219	−	0.110196i
$465$	2.94681e8	+	1.67122e9i	0.135915	+	0.770811i
$466$	−3.06521e8	−	1.73837e9i	−0.140317	−	0.795777i
$467$	−1.23046e9	+	2.13122e9i	−0.559060	+	0.968321i	0.438515	+	0.898724i	$0.355505\pi$
$467$	−1.23046e9	+	2.13122e9i	−0.559060	+	0.968321i	−0.997575	+	0.0695967i	$0.977829\pi$
$468$	−3.44565e8	−	5.96805e8i	−0.155386	−	0.269136i
$469$	−6.38731e8	+	5.35959e8i	−0.285899	+	0.239898i
$470$	−1.52617e9	+	5.55480e8i	−0.678047	+	0.246789i
$471$	−4.75886e8	−	1.73208e8i	−0.209860	−	0.0763828i
$472$	1.39309e7	+	1.16894e7i	0.00609792	+	0.00511676i
$473$	−3.73069e8	+	2.11578e9i	−0.162097	+	0.919298i
$474$	7.94838e8			0.342811
$475$	−5.62805e8	+	8.87951e8i	−0.240952	+	0.380156i
$476$	−1.33541e9			−0.567531
$477$	3.52731e8	−	2.00044e9i	0.148809	−	0.843938i
$478$	−4.90394e8	−	4.11490e8i	−0.205375	−	0.172330i
$479$	−1.77885e9	−	6.47449e8i	−0.739547	−	0.269173i	−0.0553464	−	0.998467i	$-0.517626\pi$
$479$	−1.77885e9	−	6.47449e8i	−0.739547	−	0.269173i	−0.684200	+	0.729294i	$0.739849\pi$
$480$	−1.76669e8	+	6.43021e7i	−0.0729147	+	0.0265388i
$481$	−9.06125e8	+	7.60329e8i	−0.371262	+	0.311526i
$482$	5.50245e8	+	9.53052e8i	0.223816	+	0.387661i
$483$	1.05693e9	−	1.83066e9i	0.426809	−	0.739254i
$484$	6.47641e7	+	3.67296e8i	0.0259643	+	0.147251i
$485$	−9.11445e7	−	5.16906e8i	−0.0362773	−	0.205739i
$486$	9.11589e8	−	1.57892e9i	0.360224	−	0.623926i
$487$	1.05182e9	+	1.82181e9i	0.412659	+	0.714746i	0.995180	−	0.0980698i	$-0.0312668\pi$
$487$	1.05182e9	+	1.82181e9i	0.412659	+	0.714746i	−0.582521	+	0.812816i	$0.697933\pi$
$488$	9.05196e8	−	7.59550e8i	0.352593	−	0.295861i
$489$	−2.59624e9	+	9.44956e8i	−1.00407	+	0.365452i
$490$	1.86660e8	+	6.79385e7i	0.0716744	+	0.0260874i
$491$	9.35893e8	+	7.85307e8i	0.356813	+	0.299402i	0.803519	−	0.595279i	$-0.202958\pi$
$491$	9.35893e8	+	7.85307e8i	0.356813	+	0.299402i	−0.446706	+	0.894681i	$0.647403\pi$
$492$	4.56488e7	−	2.58887e8i	0.0172803	−	0.0980015i
$493$	1.43612e9			0.539791
$494$	1.33929e9	+	1.22155e9i	0.499840	+	0.455897i
$495$	1.48167e9			0.549078
$496$	2.10372e8	−	1.19308e9i	0.0774110	−	0.439019i
$497$	3.53272e9	+	2.96430e9i	1.29081	+	1.08312i
$498$	−5.75432e8	−	2.09440e8i	−0.208781	−	0.0759902i
$499$	7.07725e8	−	2.57591e8i	0.254984	−	0.0928065i	−0.211366	−	0.977407i	$-0.567791\pi$
$499$	7.07725e8	−	2.57591e8i	0.254984	−	0.0928065i	0.466350	+	0.884601i	$0.345569\pi$
$500$	1.15123e9	−	9.65993e8i	0.411875	−	0.345604i
$501$	−5.62996e8	−	9.75137e8i	−0.200020	−	0.346444i
$502$	−2.39966e8	+	4.15634e8i	−0.0846617	+	0.146638i
$503$	5.03123e7	+	2.85335e8i	0.0176273	+	0.0999695i	0.992352	−	0.123440i	$-0.0393925\pi$
$503$	5.03123e7	+	2.85335e8i	0.0176273	+	0.0999695i	−0.974725	+	0.223409i	$0.928281\pi$
$504$	−1.22686e8	−	6.95789e8i	−0.0426864	−	0.242087i
$505$	6.78036e8	−	1.17439e9i	0.234279	−	0.405783i
$506$	−1.58238e9	−	2.74076e9i	−0.542980	−	0.940470i
$507$	1.12614e8	−	9.44940e7i	0.0383763	−	0.0322015i
$508$	5.18240e8	−	1.88624e8i	0.175391	−	0.0638372i
$509$	3.74505e9	+	1.36309e9i	1.25877	+	0.458154i	0.883355	−	0.468705i	$-0.155279\pi$
$509$	3.74505e9	+	1.36309e9i	1.25877	+	0.458154i	0.375412	+	0.926858i	$0.377501\pi$
$510$	−7.55384e8	−	6.33842e8i	−0.252158	−	0.211585i
$511$	2.19651e8	−	1.24571e9i	0.0728217	−	0.412992i
$512$	1.34218e8			0.0441942
$513$	−6.39497e8	+	2.91648e9i	−0.209136	+	0.953781i
$514$	−2.56592e9			−0.833436
$515$	6.47281e8	−	3.67091e9i	0.208818	−	1.18426i
$516$	5.79491e8	+	4.86251e8i	0.185683	+	0.155807i
$517$	4.63080e9	+	1.68547e9i	1.47380	+	0.536420i
$518$	−1.13958e9	+	4.14773e8i	−0.360238	+	0.131116i
$519$	1.80158e9	−	1.51170e9i	0.565676	−	0.474658i
$520$	−4.02144e8	−	6.96534e8i	−0.125421	−	0.217235i
$521$	−8.05016e8	+	1.39433e9i	−0.249386	+	0.431949i	−0.963356	−	0.268227i	$-0.913562\pi$
$521$	−8.05016e8	+	1.39433e9i	−0.249386	+	0.431949i	0.713969	+	0.700177i	$0.246896\pi$
$522$	1.31939e8	+	7.48263e8i	0.0406000	+	0.230254i
$523$	−4.34264e8	−	2.46284e9i	−0.132739	−	0.752800i	−0.976408	−	0.215936i	$-0.930720\pi$
$523$	−4.34264e8	−	2.46284e9i	−0.132739	−	0.752800i	0.843669	−	0.536864i	$-0.180391\pi$
$524$	−4.48766e8	+	7.77285e8i	−0.136257	+	0.236005i
$525$	−4.72681e8	−	8.18707e8i	−0.142564	−	0.246928i
$526$	2.29445e9	−	1.92527e9i	0.687430	−	0.576822i
$527$	5.97096e9	−	2.17325e9i	1.77708	−	0.646804i
$528$	5.36059e8	+	1.95110e8i	0.158487	+	0.0576846i
$529$	2.12744e9	+	1.78513e9i	0.624831	+	0.524295i
$530$	4.11674e8	−	2.33472e9i	0.120113	−	0.681192i
$531$	−5.04636e7			−0.0146267
$532$	8.61946e8	+	1.64648e9i	0.248193	+	0.474094i
$533$	1.12460e9			0.321701
$534$	−2.42643e8	+	1.37610e9i	−0.0689562	+	0.391070i
$535$	−2.90716e9	−	2.43940e9i	−0.820788	−	0.688723i
$536$	4.13035e8	+	1.50332e8i	0.115854	+	0.0421673i
$537$	−4.36555e8	+	1.58893e8i	−0.121655	+	0.0442787i
$538$	−1.37383e9	+	1.15278e9i	−0.380360	+	0.319160i
$539$	−3.01362e8	−	5.21974e8i	−0.0828948	−	0.143578i
$540$	6.62387e8	−	1.14729e9i	0.181023	−	0.313541i
$541$	−7.63502e8	−	4.33003e9i	−0.207310	−	1.17571i	−0.893764	−	0.448538i	$-0.851945\pi$
$541$	−7.63502e8	−	4.33003e9i	−0.207310	−	1.17571i	0.686454	−	0.727173i	$-0.259166\pi$
$542$	−6.47156e8	−	3.67020e9i	−0.174587	−	0.990131i
$543$	−7.55325e8	+	1.30826e9i	−0.202458	+	0.350667i
$544$	3.51982e8	+	6.09650e8i	0.0937398	+	0.162362i
$545$	−3.38217e9	+	2.83798e9i	−0.894969	+	0.750968i
$546$	−1.53175e9	+	5.57512e8i	−0.402730	+	0.146582i
$547$	−3.51560e9	−	1.27958e9i	−0.918427	−	0.334280i	−0.160814	−	0.986985i	$-0.551412\pi$
$547$	−3.51560e9	−	1.27958e9i	−0.918427	−	0.334280i	−0.757612	+	0.652705i	$0.773634\pi$
$548$	−2.39897e9	−	2.01297e9i	−0.622719	−	0.522523i
$549$	−5.69393e8	+	3.22919e9i	−0.146862	+	0.832895i
$550$	−1.41534e9			−0.362736
$551$	−9.26950e8	−	1.77065e9i	−0.236062	−	0.450922i
$552$	−1.11433e9			−0.281986
$553$	−6.05358e8	+	3.43315e9i	−0.152221	+	0.863287i
$554$	−1.61871e9	−	1.35826e9i	−0.404470	−	0.339390i
$555$	−8.41481e8	−	3.06274e8i	−0.208939	−	0.0760475i
$556$	1.69294e9	−	6.16181e8i	0.417716	−	0.152036i
$557$	−4.09499e8	+	3.43611e8i	−0.100406	+	0.0842507i	−0.691609	−	0.722272i	$-0.743098\pi$
$557$	−4.09499e8	+	3.43611e8i	−0.100406	+	0.0842507i	0.591203	+	0.806523i	$0.298653\pi$
$558$	1.68090e9	+	2.91140e9i	0.409564	+	0.709385i
$559$	−1.61809e9	+	2.80261e9i	−0.391796	+	0.678611i
$560$	−1.43188e8	−	8.12059e8i	−0.0344547	−	0.195402i
$561$	5.19562e8	+	2.94658e9i	0.124242	+	0.704610i
$562$	−1.70093e8	+	2.94610e8i	−0.0404213	+	0.0700118i
$563$	5.73417e8	+	9.93188e8i	0.135423	+	0.234559i	0.925759	−	0.378114i	$-0.123427\pi$
$563$	5.73417e8	+	9.93188e8i	0.135423	+	0.234559i	−0.790336	+	0.612673i	$0.790094\pi$
$564$	1.32922e9	−	1.11535e9i	0.311976	−	0.261779i
$565$	−8.09034e8	+	2.94464e8i	−0.188711	+	0.0686852i
$566$	4.27917e9	+	1.55749e9i	0.991978	+	0.361050i
$567$	2.55072e8	+	2.14031e8i	0.0587655	+	0.0493101i
$568$	4.22145e8	−	2.39411e9i	0.0966592	−	0.548181i
$569$	−2.78275e9			−0.633258			−0.316629	−	0.948549i	$-0.602551\pi$
$569$	−2.78275e9			−0.633258			−0.316629	+	0.948549i	$0.602551\pi$
$570$	−2.93923e8	+	1.34046e9i	−0.0664769	+	0.303174i
$571$	−1.56694e9			−0.352229			−0.176114	−	0.984370i	$-0.556353\pi$
$571$	−1.56694e9			−0.352229			−0.176114	+	0.984370i	$0.556353\pi$
$572$	−4.23775e8	+	2.40335e9i	−0.0946780	+	0.536946i
$573$	−9.95661e8	−	8.35458e8i	−0.221091	−	0.185517i
$574$	1.08345e9	+	3.94342e8i	0.239120	+	0.0870326i
$575$	2.59797e9	−	9.45585e8i	0.569898	−	0.207426i
$576$	−2.85310e8	+	2.39403e8i	−0.0622068	+	0.0521977i
$577$	3.44630e9	+	5.96916e9i	0.746857	+	1.29359i	0.949322	+	0.314305i	$0.101771\pi$
$577$	3.44630e9	+	5.96916e9i	0.746857	+	1.29359i	−0.202465	+	0.979289i	$0.564895\pi$
$578$	−2.04769e8	+	3.54670e8i	−0.0441079	+	0.0763971i
$579$	3.96730e8	+	2.24997e9i	0.0849415	+	0.481727i
$580$	1.53987e8	+	8.73301e8i	0.0327706	+	0.185852i
$581$	1.34289e9	−	2.32596e9i	0.284070	−	0.492023i
$582$	2.80387e8	+	4.85644e8i	0.0589559	+	0.102115i
$583$	−5.51050e9	+	4.62386e9i	−1.15173	+	0.966417i
$584$	−6.26594e8	+	2.28062e8i	−0.130179	+	0.0473813i
$585$	2.09725e9	+	7.63337e8i	0.433117	+	0.157642i
$586$	−5.06076e9	−	4.24648e9i	−1.03890	−	0.871742i
$587$	−1.31371e9	+	7.45042e9i	−0.268081	+	1.52036i	0.492035	+	0.870576i	$0.336253\pi$
$587$	−1.31371e9	+	7.45042e9i	−0.268081	+	1.52036i	−0.760116	+	0.649788i	$0.774858\pi$
$588$	−2.12223e8			−0.0430498
$589$	−6.53348e9	−	5.95910e9i	−1.31747	−	1.20165i
$590$	−5.88963e7			−0.0118061
$591$	8.89941e8	−	5.04710e9i	0.177339	−	1.00574i
$592$	4.89721e8	+	4.10925e8i	0.0970115	+	0.0814023i
$593$	−1.31527e9	−	4.78719e8i	−0.259014	−	0.0942735i	0.209249	−	0.977862i	$-0.432898\pi$
$593$	−1.31527e9	−	4.78719e8i	−0.259014	−	0.0942735i	−0.468264	+	0.883589i	$0.655120\pi$
$594$	−3.77730e9	+	1.37482e9i	−0.739484	+	0.269150i
$595$	3.31307e9	−	2.78000e9i	0.644794	−	0.541047i
$596$	−3.12968e8	−	5.42077e8i	−0.0605534	−	0.104882i
$597$	1.69260e8	−	2.93168e8i	0.0325571	−	0.0563905i
$598$	−8.27796e8	−	4.69467e9i	−0.158296	−	0.897740i
$599$	−8.75149e8	−	4.96322e9i	−0.166375	−	0.943560i	−0.947635	−	0.319354i	$-0.896534\pi$
$599$	−8.75149e8	−	4.96322e9i	−0.166375	−	0.943560i	0.781260	−	0.624205i	$-0.214577\pi$
$600$	−2.49175e8	+	4.31584e8i	−0.0470950	+	0.0815710i
$601$	1.35927e9	+	2.35433e9i	0.255415	+	0.442391i	0.965008	−	0.262220i	$-0.0844547\pi$
$601$	1.35927e9	+	2.35433e9i	0.255415	+	0.442391i	−0.709593	+	0.704611i	$0.751121\pi$
$602$	−2.54162e9	+	2.13267e9i	−0.474812	+	0.398415i
$603$	−1.14614e9	+	4.17163e8i	−0.212877	+	0.0774809i
$604$	2.58216e9	+	9.39828e8i	0.476819	+	0.173548i
$605$	−9.25297e8	−	7.76417e8i	−0.169878	−	0.142545i
$606$	−2.51582e8	+	1.42680e9i	−0.0459226	+	0.260440i
$607$	−7.01301e9			−1.27275			−0.636376	−	0.771379i	$-0.719567\pi$
$607$	−7.01301e9			−1.27275			−0.636376	+	0.771379i	$0.719567\pi$
$608$	5.24474e8	−	8.27475e8i	0.0946371	−	0.149311i
$609$	1.79723e9			0.322435
$610$	−6.64542e8	+	3.76880e9i	−0.118541	+	0.672278i
$611$	5.68638e9	+	4.77144e9i	1.00854	+	0.846263i
$612$	−1.83565e9	−	6.68121e8i	−0.323712	−	0.117822i
$613$	4.30180e9	−	1.56573e9i	0.754291	−	0.274539i	0.0638805	−	0.997958i	$-0.479652\pi$
$613$	4.30180e9	−	1.56573e9i	0.754291	−	0.274539i	0.690410	+	0.723418i	$0.257430\pi$
$614$	3.28105e9	−	2.75313e9i	0.572037	−	0.479996i
$615$	4.25689e8	+	7.37314e8i	0.0737954	+	0.127817i
$616$	−1.25101e9	+	2.16681e9i	−0.215639	+	0.373498i
$617$	1.49243e9	+	8.46400e9i	0.255798	+	1.45070i	0.794017	+	0.607896i	$0.207986\pi$
$617$	1.49243e9	+	8.46400e9i	0.255798	+	1.45070i	−0.538219	+	0.842805i	$0.680903\pi$
$618$	6.91544e8	+	3.92194e9i	0.117858	+	0.668408i
$619$	3.11408e9	−	5.39374e9i	0.527730	−	0.914056i	−0.471747	−	0.881734i	$-0.656377\pi$
$619$	3.11408e9	−	5.39374e9i	0.527730	−	0.914056i	0.999478	−	0.0323219i	$-0.0102902\pi$
$620$	1.96178e9	+	3.39791e9i	0.330583	+	0.572586i
$621$	6.01502e9	−	5.04720e9i	1.00790	−	0.845727i
$622$	−4.37818e9	+	1.59353e9i	−0.729504	+	0.265518i
$623$	−5.75899e9	−	2.09610e9i	−0.954197	−	0.347299i
$624$	6.58253e8	+	5.52340e8i	0.108454	+	0.0910040i
$625$	−3.68133e8	+	2.08778e9i	−0.0603148	+	0.342062i
$626$	8.43850e9			1.37485
$627$	3.29761e9	−	2.54248e9i	0.534272	−	0.411927i
$628$	−1.17089e9			−0.188650
$629$	−5.82245e8	+	3.30208e9i	−0.0932886	+	0.529066i
$630$	1.75284e9	+	1.47081e9i	0.279287	+	0.234350i
$631$	−7.76299e9	−	2.82550e9i	−1.23006	−	0.447705i	−0.356442	−	0.934318i	$-0.616010\pi$
$631$	−7.76299e9	−	2.82550e9i	−1.23006	−	0.447705i	−0.873618	+	0.486612i	$0.838232\pi$
$632$	1.72689e9	−	6.28536e8i	0.272116	−	0.0990422i
$633$	−4.74365e8	+	3.98039e8i	−0.0743360	+	0.0623753i
$634$	−9.13115e8	−	1.58156e9i	−0.142303	−	0.246475i
$635$	−8.93055e8	+	1.54682e9i	−0.138411	+	0.239735i
$636$	4.39826e8	+	2.49438e9i	0.0677925	+	0.384470i
$637$	−1.57652e8	−	8.94091e8i	−0.0241664	−	0.137055i
$638$	1.34535e9	−	2.33022e9i	0.205099	−	0.355242i
$639$	3.37299e9	+	5.84219e9i	0.511401	+	0.885773i
$640$	−3.32987e8	+	2.79409e8i	−0.0502108	+	0.0421318i
$641$	5.19998e9	−	1.89264e9i	0.779827	−	0.283834i	0.0787267	−	0.996896i	$-0.474915\pi$
$641$	5.19998e9	−	1.89264e9i	0.779827	−	0.283834i	0.701101	+	0.713062i	$0.252692\pi$
$642$	3.81003e9	+	1.38674e9i	0.568272	+	0.206834i
$643$	−8.49900e9	−	7.13150e9i	−1.26075	−	1.05790i	−0.995602	−	0.0936881i	$-0.970134\pi$
$643$	−8.49900e9	−	7.13150e9i	−1.26075	−	1.05790i	−0.265149	−	0.964207i	$-0.585421\pi$
$644$	8.48688e8	−	4.81315e9i	0.125212	−	0.710115i
$645$	−2.44994e9			−0.359498
$646$	5.13401e9	+	2.12263e8i	0.749279	+	0.0309785i
$647$	1.76225e9			0.255801			0.127900	−	0.991787i	$-0.459176\pi$
$647$	1.76225e9			0.255801			0.127900	+	0.991787i	$0.459176\pi$
$648$	3.04801e7	−	1.72861e8i	0.00440052	−	0.0249566i
$649$	1.36897e8	+	1.14871e8i	0.0196580	+	0.0164950i
$650$	−2.00336e9	−	7.29163e8i	−0.286129	−	0.104142i
$651$	7.47236e9	−	2.71972e9i	1.06151	−	0.386358i
$652$	−4.89343e9	+	4.10607e9i	−0.691428	+	0.580177i
$653$	−6.28851e9	−	1.08920e10i	−0.883795	−	1.53078i	−0.847089	−	0.531452i	$-0.821647\pi$
$653$	−6.28851e9	−	1.08920e10i	−0.883795	−	1.53078i	−0.0367063	−	0.999326i	$-0.511687\pi$
$654$	2.35852e9	−	4.08507e9i	0.329699	−	0.571055i
$655$	−5.04758e8	−	2.86262e9i	−0.0701840	−	0.398033i
$656$	−1.05543e8	−	5.98563e8i	−0.0145971	−	0.0827840i
$657$	9.25174e8	−	1.60245e9i	0.127275	−	0.220448i
$658$	3.80519e9	+	6.59079e9i	0.520698	+	0.901876i
$659$	6.77053e9	−	5.68115e9i	0.921560	−	0.773281i	−0.0527228	−	0.998609i	$-0.516790\pi$
$659$	6.77053e9	−	5.68115e9i	0.921560	−	0.773281i	0.974283	+	0.225328i	$0.0723455\pi$
$660$	−1.73610e9	+	6.31890e8i	−0.235056	+	0.0855535i
$661$	−9.19228e9	−	3.34572e9i	−1.23799	−	0.450593i	−0.361665	−	0.932308i	$-0.617792\pi$
$661$	−9.19228e9	−	3.34572e9i	−1.23799	−	0.450593i	−0.876328	+	0.481715i	$0.840014\pi$
$662$	3.89234e9	+	3.26606e9i	0.521444	+	0.437543i
$663$	−7.82618e8	+	4.43845e9i	−0.104292	+	0.591471i
$664$	−1.41582e9			−0.187681
$665$	−5.56601e9	−	2.29045e9i	−0.733953	−	0.302027i
$666$	−1.77398e9			−0.232696
$667$	−9.12692e8	+	5.17614e9i	−0.119092	+	0.675407i
$668$	−1.99429e9	−	1.67341e9i	−0.258864	−	0.217212i
$669$	1.33512e9	+	4.85945e8i	0.172397	+	0.0627474i
$670$	−1.33767e9	+	4.86873e8i	−0.171826	+	0.0625394i
$671$	8.89527e9	−	7.46402e9i	1.13666	−	0.953771i
$672$	4.40487e8	+	7.62947e8i	0.0559939	+	0.0969844i
$673$	1.24146e9	−	2.15028e9i	0.156994	−	0.271921i	−0.776790	−	0.629760i	$-0.783153\pi$
$673$	1.24146e9	−	2.15028e9i	0.156994	−	0.271921i	0.933783	+	0.357839i	$0.116486\pi$
$674$	8.03470e8	+	4.55671e9i	0.101079	+	0.573247i
$675$	−6.09780e8	−	3.45823e9i	−0.0763150	−	0.432804i
$676$	1.69944e8	−	2.94352e8i	0.0211589	−	0.0366483i
$677$	2.40290e9	+	4.16195e9i	0.297629	+	0.515509i	0.975593	−	0.219586i	$-0.0704708\pi$
$677$	2.40290e9	+	4.16195e9i	0.297629	+	0.515509i	−0.677964	+	0.735095i	$0.737137\pi$
$678$	7.04632e8	−	5.91257e8i	0.0868278	−	0.0728571i
$679$	−2.31119e9	+	8.41206e8i	−0.283330	+	0.103124i
$680$	−2.14239e9	−	7.79767e8i	−0.261287	−	0.0951007i
$681$	9.45809e8	+	7.93628e8i	0.114760	+	0.0962947i
$682$	2.06731e9	−	1.17243e10i	0.249551	−	1.41527i
$683$	−4.06650e9			−0.488369			−0.244184	−	0.969729i	$-0.578520\pi$
$683$	−4.06650e9			−0.488369			−0.244184	+	0.969729i	$0.578520\pi$
$684$	3.61076e8	+	2.69448e9i	0.0431422	+	0.321943i
$685$	1.01422e10			1.20564
$686$	−9.49537e8	+	5.38509e9i	−0.112299	+	0.636881i
$687$	6.06535e9	+	5.08943e9i	0.713686	+	0.598854i
$688$	1.64353e9	+	5.98197e8i	0.192406	+	0.0700301i
$689$	−1.01820e10	+	3.70596e9i	−1.18595	+	0.431652i
$690$	2.76460e9	−	2.31977e9i	0.320376	−	0.268827i
$691$	1.15635e9	+	2.00286e9i	0.133327	+	0.230929i	0.924957	−	0.380072i	$-0.124101\pi$
$691$	1.15635e9	+	2.00286e9i	0.133327	+	0.230929i	−0.791630	+	0.611000i	$0.790767\pi$
$692$	2.71875e9	−	4.70901e9i	0.311887	−	0.540205i
$693$	−1.20563e9	−	6.83745e9i	−0.137609	−	0.780419i
$694$	−7.18328e8	−	4.07384e9i	−0.0815764	−	0.462643i
$695$	−2.91736e9	+	5.05301e9i	−0.329642	+	0.570957i
$696$	−4.73707e8	−	8.20485e8i	−0.0532571	−	0.0922440i
$697$	2.44204e9	−	2.04912e9i	0.273173	−	0.229220i
$698$	4.25526e9	−	1.54879e9i	0.473622	−	0.172384i
$699$	−5.73940e9	−	2.08897e9i	−0.635619	−	0.231346i
$700$	−1.67437e9	−	1.40496e9i	−0.184505	−	0.154818i
$701$	2.96111e9	−	1.67933e10i	0.324670	−	1.84129i	−0.187318	−	0.982299i	$-0.559979\pi$
$701$	2.96111e9	−	1.67933e10i	0.324670	−	1.84129i	0.511987	−	0.858993i	$-0.328910\pi$
$702$	−6.05491e9			−0.660584
$703$	4.44707e9	−	1.41347e9i	0.482759	−	0.153442i
$704$	1.31894e9			0.142470
$705$	−9.75837e8	+	5.53424e9i	−0.104885	+	0.594835i
$706$	−8.31531e9	−	6.97738e9i	−0.889329	−	0.746235i
$707$	−5.97116e9	−	2.17332e9i	−0.635464	−	0.231290i
$708$	5.91291e7	−	2.15212e7i	0.00626159	−	0.00227903i
$709$	8.41139e9	−	7.05799e9i	0.886351	−	0.743737i	−0.0811237	−	0.996704i	$-0.525851\pi$
$709$	8.41139e9	−	7.05799e9i	0.886351	−	0.743737i	0.967475	+	0.252967i	$0.0814064\pi$
$710$	3.93663e9	+	6.81845e9i	0.412782	+	0.714959i
$711$	−2.54977e9	+	4.41634e9i	−0.266047	+	0.460806i
$712$	5.61006e8	+	3.18162e9i	0.0582489	+	0.330346i
$713$	4.03825e9	+	2.29020e10i	0.417234	+	2.36625i
$714$	−2.31033e9	+	4.00161e9i	−0.237536	+	0.411425i
$715$	−3.95183e9	−	6.84477e9i	−0.404322	−	0.700306i
$716$	−8.22824e8	+	6.90432e8i	−0.0837744	+	0.0702951i
$717$	−2.08146e9	+	7.57589e8i	−0.210887	+	0.0767567i
$718$	1.03374e10	+	3.76249e9i	1.04226	+	0.379350i
$719$	6.03540e9	+	5.06430e9i	0.605557	+	0.508123i	0.893226	−	0.449607i	$-0.148436\pi$
$719$	6.03540e9	+	5.06430e9i	0.605557	+	0.508123i	−0.287669	+	0.957730i	$0.592880\pi$
$720$	2.09458e8	−	1.18789e9i	0.0209138	−	0.118608i
$721$	−1.74668e10			−1.73556
$722$	−3.05207e9	−	6.46694e9i	−0.301797	−	0.639468i
$723$	3.80782e9			0.374707
$724$	−6.06504e8	+	3.43966e9i	−0.0593949	+	0.336845i
$725$	1.80064e9	+	1.51092e9i	0.175487	+	0.147251i
$726$	1.21266e9	+	4.41374e8i	0.117615	+	0.0428083i
$727$	6.72634e9	−	2.44819e9i	0.649244	−	0.236306i	0.00365843	−	0.999993i	$-0.498835\pi$
$727$	6.72634e9	−	2.44819e9i	0.649244	−	0.236306i	0.645586	+	0.763688i	$0.276613\pi$
$728$	−2.88706e9	+	2.42253e9i	−0.277330	+	0.232707i
$729$	−2.77932e9	−	4.81393e9i	−0.265701	−	0.460207i
$730$	1.07978e9	−	1.87023e9i	0.102731	−	0.177936i
$731$	1.59295e9	+	9.03409e9i	0.150832	+	0.855409i
$732$	−7.09986e8	−	4.02653e9i	−0.0669053	−	0.379439i
$733$	−2.06758e9	+	3.58115e9i	−0.193909	+	0.335860i	−0.946542	−	0.322580i	$-0.895450\pi$
$733$	−2.06758e9	+	3.58115e9i	−0.193909	+	0.335860i	0.752633	+	0.658440i	$0.228783\pi$
$734$	5.56426e9	+	9.63758e9i	0.519363	+	0.899564i
$735$	5.26513e8	−	4.41797e8i	0.0489106	−	0.0410409i
$736$	−2.42103e9	+	8.81183e8i	−0.223835	+	0.0814693i
$737$	4.05885e9	+	1.47730e9i	0.373479	+	0.135935i
$738$	1.29201e9	+	1.08412e9i	0.118323	+	0.0992846i
$739$	−1.74072e9	+	9.87213e9i	−0.158662	+	0.899819i	0.796698	+	0.604377i	$0.206578\pi$
$739$	−1.74072e9	+	9.87213e9i	−0.158662	+	0.899819i	−0.955361	+	0.295442i	$0.904533\pi$
$740$	−2.07042e9			−0.187822
$741$	5.97748e9	−	1.89990e9i	0.539703	−	0.171541i
$742$	−1.11090e10			−0.998298
$743$	−1.02844e9	+	5.83259e9i	−0.0919854	+	0.521675i	0.903644	+	0.428284i	$0.140882\pi$
$743$	−1.02844e9	+	5.83259e9i	−0.0919854	+	0.521675i	−0.995630	+	0.0933910i	$0.970229\pi$
$744$	−3.21116e9	−	2.69449e9i	−0.285862	−	0.239867i
$745$	1.90493e9	+	6.93338e8i	0.168784	+	0.0614325i
$746$	−1.24787e10	+	4.54189e9i	−1.10049	+	0.400544i
$747$	3.00964e9	−	2.52539e9i	0.264176	−	0.221670i
$748$	3.45889e9	+	5.99097e9i	0.302191	+	0.523410i
$749$	−8.89151e9	+	1.54005e10i	−0.773195	+	1.33921i
$750$	−9.02957e8	−	5.12092e9i	−0.0781542	−	0.443235i
$751$	3.31282e9	+	1.87880e10i	0.285403	+	1.61860i	0.703842	+	0.710357i	$0.251466\pi$
$751$	3.31282e9	+	1.87880e10i	0.285403	+	1.61860i	−0.418439	+	0.908245i	$0.637423\pi$
$752$	2.00592e9	−	3.47435e9i	0.172009	−	0.297928i
$753$	8.30310e8	+	1.43814e9i	0.0708693	+	0.122749i
$754$	3.10479e9	−	2.60523e9i	0.263774	−	0.221333i
$755$	−8.36268e9	+	3.04377e9i	−0.707182	+	0.257393i
$756$	−5.83335e9	−	2.12317e9i	−0.491011	−	0.178714i
$757$	−4.36032e9	−	3.65874e9i	−0.365328	−	0.306546i	0.441582	−	0.897221i	$-0.354417\pi$
$757$	−4.36032e9	−	3.65874e9i	−0.365328	−	0.306546i	−0.806910	+	0.590674i	$0.798862\pi$
$758$	2.63034e9	−	1.49174e10i	0.219366	−	1.24409i
$759$	−1.09504e10			−0.909044
$760$	4.21414e8	+	3.14475e9i	0.0348226	+	0.259859i
$761$	−1.23108e10			−1.01261			−0.506303	−	0.862356i	$-0.668988\pi$
$761$	−1.23108e10			−1.01261			−0.506303	+	0.862356i	$0.668988\pi$
$762$	3.31364e8	−	1.87926e9i	0.0271308	−	0.153867i
$763$	1.58484e10	+	1.32984e10i	1.29167	+	1.08384i
$764$	−2.82386e9	−	1.02780e9i	−0.229095	−	0.0833838i
$765$	5.94500e9	−	2.16380e9i	0.480106	−	0.174744i
$766$	9.88993e8	−	8.29864e8i	0.0795046	−	0.0667123i
$767$	1.34593e8	+	2.33123e8i	0.0107706	+	0.0186552i
$768$	2.32204e8	−	4.02190e8i	0.0184972	−	0.0320381i
$769$	−2.16004e9	−	1.22502e10i	−0.171285	−	0.971405i	−0.942345	−	0.334643i	$-0.891384\pi$
$769$	−2.16004e9	−	1.22502e10i	−0.171285	−	0.971405i	0.771060	−	0.636762i	$-0.219727\pi$
$770$	−1.40709e9	−	7.98002e9i	−0.111072	−	0.629922i
$771$	−4.43919e9	+	7.68890e9i	−0.348830	+	0.604191i
$772$	2.64116e9	+	4.57462e9i	0.206601	+	0.357844i
$773$	5.14310e9	−	4.31558e9i	0.400495	−	0.336055i	−0.420190	−	0.907436i	$-0.638037\pi$
$773$	5.14310e9	−	4.31558e9i	0.400495	−	0.336055i	0.820685	+	0.571381i	$0.193592\pi$
$774$	−4.56070e9	+	1.65996e9i	−0.353540	+	0.128678i
$775$	9.77300e9	+	3.55708e9i	0.754175	+	0.274497i
$776$	9.93211e8	+	8.33403e8i	0.0763001	+	0.0640234i
$777$	−7.28650e8	+	4.13238e9i	−0.0557244	+	0.316029i
$778$	−1.12579e10			−0.857097
$779$	−4.10267e9	−	1.68828e9i	−0.310946	−	0.127957i
$780$	−2.78293e9			−0.209977
$781$	4.14838e9	−	2.35266e10i	0.311602	−	1.76718i
$782$	−1.03516e10	−	8.68605e9i	−0.774079	−	0.649529i
$783$	6.27328e9	+	2.28329e9i	0.467012	+	0.169979i
$784$	−4.61081e8	+	1.67820e8i	−0.0341721	+	0.0124376i
$785$	2.90491e9	−	2.43751e9i	0.214333	−	0.179847i
$786$	1.55278e9	+	2.68949e9i	0.114059	+	0.197557i
$787$	−2.14313e9	+	3.71201e9i	−0.156725	+	0.271455i	−0.933686	−	0.358094i	$-0.883427\pi$
$787$	−2.14313e9	+	3.71201e9i	−0.156725	+	0.271455i	0.776961	+	0.629549i	$0.216760\pi$
$788$	−2.05760e9	−	1.16692e10i	−0.149802	−	0.849572i
$789$	−1.79964e9	−	1.02063e10i	−0.130442	−	0.739771i
$790$	−2.97585e9	+	5.15433e9i	−0.214742	+	0.371944i
$791$	2.01716e9	+	3.49383e9i	0.144918	+	0.251006i
$792$	−2.80371e9	+	2.35259e9i	−0.200537	+	0.168271i
$793$	1.64363e10	−	5.98232e9i	1.17044	−	0.426004i
$794$	9.25874e9	+	3.36991e9i	0.656418	+	0.238916i
$795$	−6.28388e9	−	5.27280e9i	−0.443550	−	0.372183i
$796$	1.35911e8	−	7.70791e8i	0.00955123	−	0.0541677i
$797$	−1.90380e10			−1.33204			−0.666022	−	0.745933i	$-0.732004\pi$
$797$	−1.90380e10			−1.33204			−0.666022	+	0.745933i	$0.732004\pi$
$798$	6.42496e9	+	2.65637e8i	0.447569	+	0.0185045i
$799$	2.10418e10			1.45939
$800$	−2.00080e8	+	1.13471e9i	−0.0138162	+	0.0783557i
$801$	−6.86759e9	−	5.76259e9i	−0.472161	−	0.396190i
$802$	−8.43866e9	−	3.07142e9i	−0.577648	−	0.210247i
$803$	−6.15748e9	+	2.24114e9i	−0.419661	+	0.152744i
$804$	1.16505e9	−	9.77594e8i	0.0790586	−	0.0663380i
$805$	7.91427e9	+	1.37079e10i	0.534718	+	0.926159i
$806$	8.96637e9	−	1.55302e10i	0.603176	−	1.04473i
$807$	1.07756e9	+	6.11112e9i	0.0721742	+	0.409320i
$808$	5.81674e8	+	3.29884e9i	0.0387918	+	0.219999i
$809$	−1.41561e10	+	2.45190e10i	−0.939989	+	1.62811i	−0.174502	+	0.984657i	$0.555831\pi$
$809$	−1.41561e10	+	2.45190e10i	−0.939989	+	1.62811i	−0.765487	+	0.643451i	$0.777502\pi$
$810$	2.84236e8	+	4.92311e8i	0.0187924	+	0.0325493i
$811$	−9.35575e9	+	7.85041e9i	−0.615894	+	0.516796i	−0.896510	−	0.443024i	$-0.853906\pi$
$811$	−9.35575e9	+	7.85041e9i	−0.615894	+	0.516796i	0.280616	+	0.959820i	$0.409461\pi$
$812$	3.90471e9	−	1.42120e9i	0.255943	−	0.0931555i
$813$	−1.21176e10	−	4.41043e9i	−0.790857	−	0.287849i
$814$	4.81244e9	+	4.03812e9i	0.312738	+	0.262418i
$815$	3.59247e9	−	2.03739e10i	0.232456	−	1.31832i
$816$	2.43579e9			0.156937
$817$	1.01103e10	−	7.79512e9i	0.648615	−	0.500087i
$818$	2.03817e10			1.30198
$819$	1.81604e9	−	1.02993e10i	0.115513	−	0.655108i
$820$	1.50791e9	+	1.26529e9i	0.0955052	+	0.0801384i
$821$	−3.52837e9	−	1.28422e9i	−0.222522	−	0.0809914i	0.228353	−	0.973578i	$-0.426666\pi$
$821$	−3.52837e9	−	1.28422e9i	−0.222522	−	0.0809914i	−0.450875	+	0.892587i	$0.648888\pi$
$822$	−1.01823e10	+	3.70606e9i	−0.639433	+	0.232734i
$823$	7.39854e9	−	6.20811e9i	0.462643	−	0.388204i	−0.381459	−	0.924386i	$-0.624578\pi$
$823$	7.39854e9	−	6.20811e9i	0.462643	−	0.388204i	0.844103	+	0.536182i	$0.180134\pi$
$824$	4.60383e9	+	7.97407e9i	0.286665	+	0.496518i
$825$	−2.44862e9	+	4.24113e9i	−0.151821	+	0.262962i
$826$	4.79235e7	+	2.71788e8i	0.00295882	+	0.0167803i
$827$	−1.21199e9	−	6.87352e9i	−0.0745124	−	0.422581i	−0.999131	−	0.0416859i	$-0.986727\pi$
$827$	−1.21199e9	−	6.87352e9i	−0.0745124	−	0.422581i	0.924618	−	0.380895i	$-0.124384\pi$
$828$	3.57468e9	−	6.19153e9i	0.218842	−	0.379046i
$829$	−1.05870e10	−	1.83373e10i	−0.645406	−	1.11788i	−0.984207	−	0.177019i	$-0.943355\pi$
$829$	−1.05870e10	−	1.83373e10i	−0.645406	−	1.11788i	0.338801	−	0.940858i	$-0.389979\pi$
$830$	3.51257e9	−	2.94740e9i	0.213232	−	0.178923i
$831$	−6.87056e9	+	2.50068e9i	−0.415326	+	0.151166i
$832$	1.86691e9	+	6.79501e8i	0.112381	+	0.0409033i
$833$	−1.97145e9	−	1.65424e9i	−0.118176	−	0.0991612i
$834$	1.08247e9	−	6.13901e9i	0.0646154	−	0.366452i
$835$	8.43136e9			0.501181
$836$	5.15395e9	−	8.13151e9i	0.305083	−	0.481337i
$837$	2.95377e10			1.74116
$838$	−1.11369e9	+	6.31605e9i	−0.0653747	+	0.370759i
$839$	1.41876e10	+	1.19048e10i	0.829358	+	0.695914i	0.955143	−	0.296144i	$-0.0957008\pi$
$839$	1.41876e10	+	1.19048e10i	0.829358	+	0.695914i	−0.125786	+	0.992057i	$0.540145\pi$
$840$	−2.68110e9	−	9.75839e8i	−0.156076	−	0.0568069i
$841$	1.20104e10	−	4.37143e9i	0.696260	−	0.253418i
$842$	−1.29645e10	+	1.08785e10i	−0.748454	+	0.628027i
$843$	5.88543e8	+	1.01939e9i	0.0338362	+	0.0586060i
$844$	−7.15860e8	+	1.23991e9i	−0.0409854	+	0.0709888i
$845$	1.91148e8	+	1.08405e9i	0.0108986	+	0.0618091i
$846$	1.93315e9	+	1.09635e10i	0.109767	+	0.622518i
$847$	−2.83001e9	+	4.90172e9i	−0.160028	+	0.277176i
$848$	2.92806e9	+	5.07156e9i	0.164890	+	0.285598i
$849$	1.20703e10	−	1.01282e10i	0.676926	−	0.568008i
$850$	−5.67885e9	+	2.06693e9i	−0.317171	+	0.115441i
$851$	−1.15315e10	−	4.19712e9i	−0.641405	−	0.233452i
$852$	−6.44371e9	−	5.40692e9i	−0.356942	−	0.299510i
$853$	4.41040e8	−	2.50126e9i	0.0243308	−	0.137987i	−0.970223	−	0.242215i	$-0.922126\pi$
$853$	4.41040e8	−	2.50126e9i	0.0243308	−	0.137987i	0.994553	+	0.104228i	$0.0332372\pi$
$854$	1.79326e10			0.985234
$855$	−6.50508e9	−	5.93319e9i	−0.355935	−	0.324644i
$856$	9.37437e9			0.510839
$857$	5.26981e9	−	2.98866e10i	0.285998	−	1.62197i	−0.415703	−	0.909501i	$-0.636464\pi$
$857$	5.26981e9	−	2.98866e10i	0.285998	−	1.62197i	0.701700	−	0.712472i	$-0.252425\pi$
$858$	6.46859e9	+	5.42779e9i	0.349626	+	0.293371i
$859$	−1.58753e10	−	5.77815e9i	−0.854569	−	0.311038i	−0.122667	−	0.992448i	$-0.539145\pi$
$859$	−1.58753e10	−	5.77815e9i	−0.854569	−	0.311038i	−0.731902	+	0.681410i	$0.761367\pi$
$860$	−5.32282e9	+	1.93735e9i	−0.285362	+	0.103863i
$861$	3.05609e9	−	2.56436e9i	0.163176	−	0.136921i
$862$	−3.01494e9	−	5.22203e9i	−0.160326	−	0.277692i
$863$	−1.02206e10	+	1.77026e10i	−0.541302	+	0.937562i	0.457528	+	0.889195i	$0.348735\pi$
$863$	−1.02206e10	+	1.77026e10i	−0.541302	+	0.937562i	−0.998830	+	0.0483668i	$0.984598\pi$
$864$	5.68249e8	+	3.22270e9i	0.0299737	+	0.169990i
$865$	3.05796e9	+	1.73426e10i	0.160648	+	0.911081i
$866$	−9.54195e9	+	1.65271e10i	−0.499257	+	0.864739i
$867$	7.08523e8	+	1.22720e9i	0.0369222	+	0.0639510i
$868$	1.40840e10	−	1.18179e10i	0.730981	−	0.613366i
$869$	1.69700e10	−	6.17656e9i	0.877226	−	0.319284i
$870$	2.88329e9	+	1.04943e9i	0.148447	+	0.0540303i
$871$	4.98406e9	+	4.18212e9i	0.255576	+	0.214454i
$872$	1.89382e9	−	1.07404e10i	0.0967234	−	0.548546i
$873$	−3.59783e9			−0.183017
$874$	−4.02786e9	+	1.83694e10i	−0.204072	+	0.930690i
$875$	2.28065e10			1.15088
$876$	−4.00646e8	+	2.27218e9i	−0.0201371	+	0.114203i
$877$	6.86292e9	+	5.75867e9i	0.343566	+	0.288286i	0.798200	−	0.602392i	$-0.205786\pi$
$877$	6.86292e9	+	5.75867e9i	0.343566	+	0.288286i	−0.454634	+	0.890678i	$0.650230\pi$
$878$	−1.51757e9	−	5.52352e8i	−0.0756692	−	0.0275413i
$879$	−2.14802e10	+	7.81815e9i	−1.06679	+	0.388278i
$880$	−3.27223e9	+	2.74572e9i	−0.161865	+	0.135821i
$881$	8.94597e9	+	1.54949e10i	0.440770	+	0.763436i	0.997747	−	0.0670922i	$-0.0213722\pi$
$881$	8.94597e9	+	1.54949e10i	0.440770	+	0.763436i	−0.556977	+	0.830528i	$0.688039\pi$
$882$	6.80792e8	−	1.17917e9i	0.0334098	−	0.0578675i
$883$	−4.72383e9	−	2.67901e10i	−0.230904	−	1.30952i	−0.851071	−	0.525051i	$-0.824046\pi$
$883$	−4.72383e9	−	2.67901e10i	−0.230904	−	1.30952i	0.620167	−	0.784470i	$-0.287065\pi$
$884$	1.80946e9	+	1.02620e10i	0.0880981	+	0.499629i
$885$	−1.01894e8	+	1.76485e8i	−0.00494136	+	0.00855869i
$886$	4.10617e9	+	7.11209e9i	0.198344	+	0.343541i
$887$	5.14118e9	−	4.31396e9i	0.247360	−	0.207560i	−0.510674	−	0.859774i	$-0.670604\pi$
$887$	5.14118e9	−	4.31396e9i	0.247360	−	0.207560i	0.758035	+	0.652214i	$0.226160\pi$
$888$	2.07860e9	−	7.56549e8i	0.0996153	−	0.0362570i
$889$	7.86473e9	+	2.86253e9i	0.375429	+	0.136645i
$890$	−8.01520e9	−	6.72555e9i	−0.381109	−	0.319788i
$891$	2.99525e8	−	1.69869e9i	0.0141860	−	0.0804529i
$892$	3.28500e9			0.154974
$893$	−1.35816e10	−	2.59433e10i	−0.638220	−	1.21912i
$894$	−2.16581e9			−0.101377
$895$	6.04069e8	−	3.42584e9i	0.0281647	−	0.159730i
$896$	1.56033e9	+	1.30927e9i	0.0724668	+	0.0608069i
$897$	−1.54999e10	−	5.64151e9i	−0.717061	−	0.260989i
$898$	−2.50657e10	+	9.12315e9i	−1.15508	+	0.420415i
$899$	−1.51461e10	+	1.27091e10i	−0.695253	+	0.583386i
$900$	−1.59866e9	−	2.76897e9i	−0.0730985	−	0.126610i
$901$	−1.53575e10	+	2.66000e10i	−0.699494	+	1.21156i
$902$	−1.03716e9	−	5.88202e9i	−0.0470568	−	0.266872i
$903$	1.99350e9	+	1.13057e10i	0.0900968	+	0.510964i
$904$	1.06335e9	−	1.84178e9i	0.0478728	−	0.0829181i
$905$	−5.65583e9	−	9.79619e9i	−0.253645	−	0.439326i
$906$	7.28352e9	−	6.11160e9i	0.325381	−	0.273027i
$907$	−6.31603e9	+	2.29885e9i	−0.281073	+	0.102302i	−0.478710	−	0.877973i	$-0.658895\pi$
$907$	−6.31603e9	+	2.29885e9i	−0.281073	+	0.102302i	0.197637	+	0.980275i	$0.436673\pi$
$908$	2.68247e9	+	9.76340e8i	0.118914	+	0.0432813i
$909$	−7.12060e9	−	5.97489e9i	−0.314444	−	0.263850i
$910$	2.11951e9	−	1.20203e10i	0.0932374	−	0.528776i
$911$	−3.37402e10			−1.47854			−0.739270	−	0.673409i	$-0.764829\pi$
$911$	−3.37402e10			−1.47854			−0.739270	+	0.673409i	$0.764829\pi$
$912$	−1.57220e9	−	3.00319e9i	−0.0686318	−	0.131099i
$913$	−1.39131e10			−0.605030
$914$	1.37302e9	−	7.78677e9i	0.0594791	−	0.337323i
$915$	1.01437e10	+	8.51157e9i	0.437746	+	0.367313i
$916$	1.72023e10	+	6.26113e9i	0.739525	+	0.269165i
$917$	−1.27994e10	+	4.65859e9i	−0.548146	+	0.199509i
$918$	−1.31481e10	+	1.10326e10i	−0.560937	+	0.470682i
$919$	5.20396e9	+	9.01352e9i	0.221172	+	0.383080i	0.955164	−	0.296077i	$-0.0956786\pi$
$919$	5.20396e9	+	9.01352e9i	0.221172	+	0.383080i	−0.733992	+	0.679158i	$0.762345\pi$
$920$	4.17203e9	−	7.22617e9i	0.176640	−	0.305950i
$921$	−2.57347e9	−	1.45949e10i	−0.108545	−	0.615591i
$922$	−2.00571e9	−	1.13750e10i	−0.0842772	−	0.477960i
$923$	1.79925e10	−	3.11639e10i	0.753156	−	1.30450i
$924$	4.32863e9	+	7.49740e9i	0.180509	+	0.312650i
$925$	−4.20410e9	+	3.52766e9i	−0.174653	+	0.146552i
$926$	−2.53405e10	+	9.22319e9i	−1.04876	+	0.381718i
$927$	−2.40098e10	−	8.73884e9i	−0.989940	−	0.360309i
$928$	−1.67801e9	−	1.40801e9i	−0.0689248	−	0.0578348i
$929$	−4.89345e9	+	2.77521e10i	−0.200244	+	1.13564i	0.704506	+	0.709698i	$0.251169\pi$
$929$	−4.89345e9	+	2.77521e10i	−0.200244	+	1.13564i	−0.904750	+	0.425943i	$0.859942\pi$
$930$	1.35760e10			0.553454
$931$	−7.67099e8	+	3.49842e9i	−0.0311550	+	0.142085i
$932$	−1.41215e10			−0.571380
$933$	−2.79942e9	+	1.58763e10i	−0.112845	+	0.639977i
$934$	1.50814e10	+	1.26548e10i	0.605658	+	0.508207i
$935$	−2.10531e10	−	7.66269e9i	−0.842316	−	0.306578i
$936$	−5.18057e9	+	1.88557e9i	−0.206496	+	0.0751585i
$937$	3.05310e9	−	2.56186e9i	0.121242	−	0.101734i	−0.580151	−	0.814509i	$-0.697006\pi$
$937$	3.05310e9	−	2.56186e9i	0.121242	−	0.101734i	0.701393	+	0.712775i	$0.252562\pi$
$938$	3.33522e9	+	5.77676e9i	0.131951	+	0.228547i
$939$	1.45991e10	−	2.52863e10i	0.575434	−	0.996682i
$940$	2.25620e9	+	1.27955e10i	0.0885991	+	0.502470i
$941$	2.47626e9	+	1.40435e10i	0.0968795	+	0.549431i	0.994155	+	0.107960i	$0.0344320\pi$
$941$	2.47626e9	+	1.40435e10i	0.0968795	+	0.549431i	−0.897276	+	0.441471i	$0.854457\pi$
$942$	−2.02571e9	+	3.50863e9i	−0.0789585	+	0.136760i
$943$	5.83355e9	+	1.01040e10i	0.226539	+	0.392376i
$944$	1.11447e8	−	9.35152e7i	0.00431188	−	0.00361810i
$945$	1.88921e10	−	6.87617e9i	0.728232	−	0.265055i
$946$	1.61508e10	+	5.87842e9i	0.620263	+	0.225757i
$947$	3.37435e10	+	2.83141e10i	1.29111	+	1.08337i	0.991608	+	0.129279i	$0.0412662\pi$
$947$	3.37435e10	+	2.83141e10i	1.29111	+	1.08337i	0.299506	+	0.954094i	$0.403178\pi$
$948$	1.10418e9	−	6.26210e9i	0.0420930	−	0.238721i
$949$	−9.87028e9			−0.374885
$950$	6.21385e9	+	5.66757e9i	0.235141	+	0.214469i
$951$	−6.31896e9			−0.238240
$952$	−1.85513e9	+	1.05210e10i	−0.0696858	+	0.395208i
$953$	−1.09727e10	−	9.20719e9i	−0.410665	−	0.344589i	0.413933	−	0.910307i	$-0.364155\pi$
$953$	−1.09727e10	−	9.20719e9i	−0.410665	−	0.344589i	−0.824599	+	0.565718i	$0.808599\pi$
$954$	−1.52704e10	−	5.55796e9i	−0.569416	−	0.207251i
$955$	9.14546e9	−	3.32868e9i	0.339777	−	0.123669i
$956$	−3.92315e9	+	3.29192e9i	−0.145222	+	0.121856i
$957$	−4.65507e9	−	8.06282e9i	−0.171686	−	0.297369i
$958$	−7.57206e9	+	1.31152e10i	−0.278250	+	0.481943i
$959$	−8.25265e9	−	4.68031e10i	−0.302154	−	1.71360i
$960$	2.61176e8	+	1.48120e9i	0.00952762	+	0.0540338i
$961$	−2.99844e10	+	5.19346e10i	−1.08984	+	1.88766i
$962$	4.73145e9	+	8.19511e9i	0.171349	+	0.296785i
$963$	−1.99273e10	+	1.67210e10i	−0.719047	+	0.603352i
$964$	8.27297e9	−	3.01112e9i	0.297435	−	0.108257i
$965$	−1.60758e10	−	5.85112e9i	−0.575874	−	0.209601i
$966$	−1.29545e10	−	1.08702e10i	−0.462383	−	0.387986i
$967$	8.30307e9	−	4.70890e10i	0.295288	−	1.67466i	−0.370741	−	0.928736i	$-0.620896\pi$
$967$	8.30307e9	−	4.70890e10i	0.295288	−	1.67466i	0.666029	−	0.745926i	$-0.267993\pi$
$968$	2.98369e9			0.105728
$969$	9.51819e9	−	1.50171e10i	0.336064	−	0.530216i
$970$	−4.19904e9			−0.147723
$971$	−7.30497e9	+	4.14285e10i	−0.256065	+	1.45222i	0.537257	+	0.843418i	$0.319460\pi$
$971$	−7.30497e9	+	4.14285e10i	−0.256065	+	1.45222i	−0.793323	+	0.608801i	$0.791651\pi$
$972$	−1.11731e10	−	9.37533e9i	−0.390249	−	0.327457i
$973$	2.56919e10	+	9.35107e9i	0.894130	+	0.325437i
$974$	1.58142e10	−	5.75591e9i	0.548393	−	0.199599i
$975$	−5.65090e9	+	4.74166e9i	−0.195255	+	0.163838i
$976$	−4.72660e9	−	8.18671e9i	−0.162733	−	0.281861i
$977$	1.27746e10	−	2.21262e10i	0.438243	−	0.759059i	−0.559311	−	0.828958i	$-0.688934\pi$
$977$	1.27746e10	−	2.21262e10i	0.438243	−	0.759059i	0.997554	+	0.0698989i	$0.0222677\pi$
$978$	3.83813e9	+	2.17671e10i	0.131200	+	0.744072i
$979$	5.51295e9	+	3.12655e10i	0.187778	+	1.06494i
$980$	7.94556e8	−	1.37621e9i	0.0269670	−	0.0467083i
$981$	1.51318e10	+	2.62091e10i	0.511741	+	0.886362i
$982$	7.48714e9	−	6.28246e9i	0.252305	−	0.211709i
$983$	3.28618e10	−	1.19607e10i	1.10345	−	0.401624i	0.274865	−	0.961483i	$-0.411367\pi$
$983$	3.28618e10	−	1.19607e10i	1.10345	−	0.401624i	0.828588	+	0.559859i	$0.189145\pi$
$984$	−1.97622e9	−	7.19285e8i	−0.0661229	−	0.0240668i
$985$	2.93973e10	+	2.46673e10i	0.980123	+	0.822421i
$986$	1.99503e9	−	1.13144e10i	0.0662798	−	0.375891i
$987$	2.63328e10			0.871740
$988$	1.14845e10	−	8.85460e9i	0.378845	−	0.292092i
$989$	−3.35735e10			−1.10360
$990$	2.05832e9	−	1.16733e10i	0.0674201	−	0.382358i
$991$	−3.82939e9	−	3.21324e9i	−0.124989	−	0.104878i	0.578150	−	0.815930i	$-0.303775\pi$
$991$	−3.82939e9	−	3.21324e9i	−0.124989	−	0.104878i	−0.703140	+	0.711052i	$0.748219\pi$
$992$	−9.10739e9	−	3.31482e9i	−0.296212	−	0.107812i
$993$	1.65209e10	−	6.01310e9i	0.535440	−	0.194884i
$994$	2.82618e10	−	2.37144e10i	0.912739	−	0.765879i
$995$	1.26741e9	+	2.19522e9i	0.0407885	+	0.0706477i
$996$	−2.44945e9	+	4.24257e9i	−0.0785526	+	0.136057i
$997$	−4.00311e8	−	2.27028e9i	−0.0127928	−	0.0725514i	0.977743	−	0.209806i	$-0.0672832\pi$
$997$	−4.00311e8	−	2.27028e9i	−0.0127928	−	0.0725514i	−0.990536	+	0.137255i	$0.956172\pi$
$998$	−1.04626e9	−	5.93362e9i	−0.0333182	−	0.188957i
$999$	−7.79335e9	+	1.34985e10i	−0.247312	+	0.428357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.17.2	yes	30
19.9	even	9	inner	38.8.e.a.9.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.9.2	✓	30	19.9	even	9	inner
38.8.e.a.17.2	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.38919 - 7.87846i) q^{2} +(-21.2048 - 17.7929i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(194.773 - 70.8916i) q^{5} +(-169.638 + 142.344i) q^{6} +(-485.627 - 841.131i) q^{7} +(-256.000 + 443.405i) q^{8} +(-246.714 - 1399.18i) q^{9} +O(q^{10})\)	\(q+(1.38919 - 7.87846i) q^{2} +(-21.2048 - 17.7929i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(194.773 - 70.8916i) q^{5} +(-169.638 + 142.344i) q^{6} +(-485.627 - 841.131i) q^{7} +(-256.000 + 443.405i) q^{8} +(-246.714 - 1399.18i) q^{9} +(-287.941 - 1632.99i) q^{10} +(-2515.69 + 4357.30i) q^{11} +(885.789 + 1534.23i) q^{12} +(-5805.68 + 4871.54i) q^{13} +(-7301.45 + 2657.51i) q^{14} +(-5391.49 - 1962.34i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-3730.53 + 21156.9i) q^{17} -11366.1 q^{18} +(28493.1 - 9056.32i) q^{19} -13265.5 q^{20} +(-4668.57 + 26476.8i) q^{21} +(30834.0 + 25872.8i) q^{22} +(-73884.0 - 26891.6i) q^{23} +(13317.9 - 4847.32i) q^{24} +(-26936.3 + 22602.2i) q^{25} +(30315.1 + 52507.3i) q^{26} +(-49933.1 + 86486.7i) q^{27} +(10794.0 + 61216.0i) q^{28} +(-11608.1 - 65832.6i) q^{29} +(-22950.0 + 39750.6i) q^{30} +(-147886. - 256147. i) q^{31} +(25101.7 - 21062.9i) q^{32} +(130874. - 47634.2i) q^{33} +(161501. + 58781.7i) q^{34} +(-154216. - 129403. i) q^{35} +(-15789.7 + 89547.7i) q^{36} +156076. q^{37} +(-31767.7 - 237062. i) q^{38} +209787. q^{39} +(-18428.2 + 104512. i) q^{40} +(-113672. - 95381.9i) q^{41} +(202111. + 73562.3i) q^{42} +(401253. - 146044. i) q^{43} +(246672. - 206983. i) q^{44} +(-147243. - 255033. i) q^{45} +(-314503. + 544735. i) q^{46} +(-170080. - 964573. i) q^{47} +(-19688.4 - 111659. i) q^{48} +(-59896.5 + 103744. i) q^{49} +(140651. + 243615. i) q^{50} +(455549. - 382251. i) q^{51} +(455790. - 165894. i) q^{52} +(1.34350e6 + 488993. i) q^{53} +(612016. + 513542. i) q^{54} +(-181092. + 1.02702e6i) q^{55} +497283. q^{56} +(-765329. - 314938. i) q^{57} -534786. q^{58} +(6167.73 - 34978.9i) q^{59} +(281292. + 236032. i) q^{60} +(-2.16873e6 - 789352. i) q^{61} +(-2.22348e6 + 809282. i) q^{62} +(-1.05709e6 + 887000. i) q^{63} +(-131072. - 227023. i) q^{64} +(-785438. + 1.36042e6i) q^{65} +(-193476. - 1.09726e6i) q^{66} +(-149074. - 845439. i) q^{67} +(687465. - 1.19072e6i) q^{68} +(1.08822e6 + 1.88484e6i) q^{69} +(-1.23373e6 + 1.03522e6i) q^{70} +(-4.46178e6 + 1.62395e6i) q^{71} +(683563. + 248797. i) q^{72} +(997664. + 837140. i) q^{73} +(216818. - 1.22964e6i) q^{74} +973340. q^{75} +(-1.91182e6 - 79043.2i) q^{76} +4.88674e6 q^{77} +(291433. - 1.65280e6i) q^{78} +(-2.74956e6 - 2.30715e6i) q^{79} +(797790. + 290372. i) q^{80} +(-322153. + 117254. i) q^{81} +(-909374. + 763056. i) q^{82} +(1.38264e6 + 2.39480e6i) q^{83} +(860327. - 1.49013e6i) q^{84} +(773239. + 4.38525e6i) q^{85} +(-593189. - 3.36414e6i) q^{86} +(-925209. + 1.60251e6i) q^{87} +(-1.28803e6 - 2.23094e6i) q^{88} +(4.83372e6 - 4.05597e6i) q^{89} +(-2.21382e6 + 805763. i) q^{90} +(6.91700e6 + 2.51758e6i) q^{91} +(3.85477e6 + 3.23454e6i) q^{92} +(-1.42170e6 + 8.06288e6i) q^{93} -7.83562e6 q^{94} +(4.90766e6 - 3.78384e6i) q^{95} -907048. q^{96} +(439732. - 2.49384e6i) q^{97} +(734134. + 616012. i) q^{98} +(6.71731e6 + 2.44490e6i) 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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