LMFDB - Embedded newform 29.8.e.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(4,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, 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:	$9.05916573904$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	29.4
Dual form			29.8.e.a.22.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.35936 - 2.13621i) q^{2} +(15.2659 + 31.7000i) q^{3} +(-32.2898 - 15.5499i) q^{4} +(-15.7357 + 68.9427i) q^{5} +(-75.1613 - 329.303i) q^{6} +(-676.409 + 325.741i) q^{7} +(1229.71 + 980.664i) q^{8} +(591.731 - 742.007i) q^{9} +O(q^{10})$	\(q+(-9.35936 - 2.13621i) q^{2} +(15.2659 + 31.7000i) q^{3} +(-32.2898 - 15.5499i) q^{4} +(-15.7357 + 68.9427i) q^{5} +(-75.1613 - 329.303i) q^{6} +(-676.409 + 325.741i) q^{7} +(1229.71 + 980.664i) q^{8} +(591.731 - 742.007i) q^{9} +(294.553 - 611.645i) q^{10} +(1575.77 - 1256.63i) q^{11} -1260.97i q^{12} +(-7709.98 - 9668.00i) q^{13} +(7026.61 - 1603.78i) q^{14} +(-2425.70 + 553.651i) q^{15} +(-6554.24 - 8218.76i) q^{16} -35694.5i q^{17} +(-7123.31 + 5680.65i) q^{18} +(9234.86 - 19176.4i) q^{19} +(1580.16 - 1981.45i) q^{20} +(-20652.0 - 16469.4i) q^{21} +(-17432.6 + 8395.11i) q^{22} +(-93.8156 - 411.033i) q^{23} +(-12314.3 + 53952.6i) q^{24} +(65882.7 + 31727.4i) q^{25} +(51507.5 + 106957. i) q^{26} +(107574. + 24553.0i) q^{27} +26906.3 q^{28} +(-113726. + 65697.9i) q^{29} +23885.8 q^{30} +(-145568. - 33224.9i) q^{31} +(-43565.8 - 90465.2i) q^{32} +(63890.8 + 30768.2i) q^{33} +(-76251.1 + 334078. i) q^{34} +(-11813.7 - 51759.2i) q^{35} +(-30645.0 + 14757.9i) q^{36} +(-20660.2 - 16475.9i) q^{37} +(-127397. + 159751. i) q^{38} +(188776. - 391997. i) q^{39} +(-86960.1 + 69348.3i) q^{40} -367014. i q^{41} +(158107. + 198260. i) q^{42} +(534367. - 121966. i) q^{43} +(-70421.8 + 16073.3i) q^{44} +(41844.7 + 52471.5i) q^{45} +4047.42i q^{46} +(-604576. + 482133. i) q^{47} +(160478. - 333236. i) q^{48} +(-162049. + 203203. i) q^{49} +(-548844. - 437688. i) q^{50} +(1.13152e6 - 544909. i) q^{51} +(98616.5 + 432067. i) q^{52} +(147015. - 644115. i) q^{53} +(-954372. - 459601. i) q^{54} +(61839.9 + 128412. i) q^{55} +(-1.15123e6 - 262761. i) q^{56} +748870. q^{57} +(1.20475e6 - 371947. i) q^{58} -912506. q^{59} +(86934.6 + 19842.3i) q^{60} +(-1.29395e6 - 2.68692e6i) q^{61} +(1.29145e6 + 621929. i) q^{62} +(-158550. + 694651. i) q^{63} +(513910. + 2.25159e6i) q^{64} +(787860. - 379414. i) q^{65} +(-532250. - 424455. i) q^{66} +(-390014. + 489062. i) q^{67} +(-555047. + 1.15257e6i) q^{68} +(11597.6 - 9248.74i) q^{69} +509670. i q^{70} +(-1.88029e6 - 2.35781e6i) q^{71} +(1.45532e6 - 332167. i) q^{72} +(2.51209e6 - 573368. i) q^{73} +(158170. + 198339. i) q^{74} +2.57283e6i q^{75} +(-596383. + 475599. i) q^{76} +(-656526. + 1.36329e6i) q^{77} +(-2.60421e6 + 3.26558e6i) q^{78} +(4.59786e6 + 3.66667e6i) q^{79} +(669759. - 322539. i) q^{80} +(402017. + 1.76135e6i) q^{81} +(-784021. + 3.43502e6i) q^{82} +(-2.90107e6 - 1.39708e6i) q^{83} +(410750. + 852930. i) q^{84} +(2.46088e6 + 561679. i) q^{85} -5.26188e6 q^{86} +(-3.81876e6 - 2.60218e6i) q^{87} +3.17008e6 q^{88} +(-5.87708e6 - 1.34140e6i) q^{89} +(-279549. - 580489. i) q^{90} +(8.36436e6 + 4.02806e6i) q^{91} +(-3362.25 + 14731.0i) q^{92} +(-1.16900e6 - 5.12171e6i) q^{93} +(6.68839e6 - 3.22096e6i) q^{94} +(1.17675e6 + 938431. i) q^{95} +(2.20268e6 - 2.76207e6i) q^{96} +(2.70610e6 - 5.61927e6i) q^{97} +(1.95076e6 - 1.55568e6i) q^{98} -1.91282e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9}+O(q^{10}) $ 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9} - 7 q^{10} + 4207 q^{11} + 377 q^{13} - 7 q^{14} - 74473 q^{15} - 125851 q^{16} - 194880 q^{18} - 7 q^{19} + 162901 q^{20} + 86933 q^{21} + 252614 q^{22} + 238675 q^{23} - 490819 q^{24} - 107349 q^{25} + 367017 q^{26} + 75593 q^{27} + 1397540 q^{28} + 379863 q^{29} - 175646 q^{30} - 143885 q^{31} + 473172 q^{32} - 1419437 q^{33} - 2314463 q^{34} - 1018325 q^{35} + 1720462 q^{36} + 662991 q^{37} - 2763860 q^{38} + 42189 q^{39} + 580601 q^{40} - 3296492 q^{42} - 1587425 q^{43} + 2344398 q^{44} + 6508254 q^{45} + 526673 q^{47} + 6175806 q^{48} - 1391517 q^{49} - 4194526 q^{50} - 68204 q^{51} - 7720808 q^{52} + 1762640 q^{53} - 2032428 q^{54} + 2655709 q^{55} + 17091081 q^{56} + 4906842 q^{57} + 13231229 q^{58} - 8638324 q^{59} - 9957136 q^{60} + 2797697 q^{61} - 884069 q^{62} - 20232301 q^{63} - 17528026 q^{64} - 7454088 q^{65} - 17541475 q^{66} - 4890949 q^{67} + 22029140 q^{68} + 13204429 q^{69} - 1091301 q^{71} + 25137595 q^{72} + 14363636 q^{73} + 3185328 q^{74} - 41019881 q^{76} - 25204627 q^{77} - 15753743 q^{78} + 31186057 q^{79} + 24146022 q^{80} - 29435757 q^{81} - 51438506 q^{82} - 8367235 q^{83} + 78906093 q^{84} + 41540198 q^{85} + 65794492 q^{86} + 11089375 q^{87} + 39260390 q^{88} + 6628699 q^{89} + 32127214 q^{90} + 24315293 q^{91} - 39469980 q^{92} - 31050649 q^{93} - 102445588 q^{94} - 75684679 q^{95} - 95069050 q^{96} + 38131380 q^{97} + 19581828 q^{98}+O(q^{100}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9 - 7 * q^10 + 4207 * q^11 + 377 * q^13 - 7 * q^14 - 74473 * q^15 - 125851 * q^16 - 194880 * q^18 - 7 * q^19 + 162901 * q^20 + 86933 * q^21 + 252614 * q^22 + 238675 * q^23 - 490819 * q^24 - 107349 * q^25 + 367017 * q^26 + 75593 * q^27 + 1397540 * q^28 + 379863 * q^29 - 175646 * q^30 - 143885 * q^31 + 473172 * q^32 - 1419437 * q^33 - 2314463 * q^34 - 1018325 * q^35 + 1720462 * q^36 + 662991 * q^37 - 2763860 * q^38 + 42189 * q^39 + 580601 * q^40 - 3296492 * q^42 - 1587425 * q^43 + 2344398 * q^44 + 6508254 * q^45 + 526673 * q^47 + 6175806 * q^48 - 1391517 * q^49 - 4194526 * q^50 - 68204 * q^51 - 7720808 * q^52 + 1762640 * q^53 - 2032428 * q^54 + 2655709 * q^55 + 17091081 * q^56 + 4906842 * q^57 + 13231229 * q^58 - 8638324 * q^59 - 9957136 * q^60 + 2797697 * q^61 - 884069 * q^62 - 20232301 * q^63 - 17528026 * q^64 - 7454088 * q^65 - 17541475 * q^66 - 4890949 * q^67 + 22029140 * q^68 + 13204429 * q^69 - 1091301 * q^71 + 25137595 * q^72 + 14363636 * q^73 + 3185328 * q^74 - 41019881 * q^76 - 25204627 * q^77 - 15753743 * q^78 + 31186057 * q^79 + 24146022 * q^80 - 29435757 * q^81 - 51438506 * q^82 - 8367235 * q^83 + 78906093 * q^84 + 41540198 * q^85 + 65794492 * q^86 + 11089375 * q^87 + 39260390 * q^88 + 6628699 * q^89 + 32127214 * q^90 + 24315293 * q^91 - 39469980 * q^92 - 31050649 * q^93 - 102445588 * q^94 - 75684679 * q^95 - 95069050 * q^96 + 38131380 * q^97 + 19581828 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−9.35936	−	2.13621i	−0.827259	−	0.188816i	−0.212128	−	0.977242i	$-0.568039\pi$
$2$	−9.35936	−	2.13621i	−0.827259	−	0.188816i	−0.615130	+	0.788425i	$0.710897\pi$
$3$	15.2659	+	31.7000i	0.326436	+	0.677852i	0.998008	−	0.0630877i	$-0.0200948\pi$
$3$	15.2659	+	31.7000i	0.326436	+	0.677852i	−0.671572	+	0.740940i	$0.734381\pi$
$4$	−32.2898	−	15.5499i	−0.252264	−	0.121484i
$5$	−15.7357	+	68.9427i	−0.0562978	+	0.246657i	−0.995245	−	0.0974049i	$-0.968946\pi$
$5$	−15.7357	+	68.9427i	−0.0562978	+	0.246657i	0.938947	+	0.344062i	$0.111803\pi$
$6$	−75.1613	−	329.303i	−0.142058	−	0.622395i
$7$	−676.409	+	325.741i	−0.745360	+	0.358946i	−0.767705	−	0.640804i	$-0.778601\pi$
$7$	−676.409	+	325.741i	−0.745360	+	0.358946i	0.0223447	+	0.999750i	$0.492887\pi$
$8$	1229.71	+	980.664i	0.849159	+	0.677182i
$9$	591.731	−	742.007i	0.270567	−	0.339281i
$10$	294.553	−	611.645i	0.0931457	−	0.193419i
$11$	1575.77	−	1256.63i	0.356959	−	0.284665i	−0.428547	−	0.903520i	$-0.640974\pi$
$11$	1575.77	−	1256.63i	0.356959	−	0.284665i	0.785506	+	0.618854i	$0.212403\pi$
$12$		−	1260.97i		−	0.210654i
$13$	−7709.98	−	9668.00i	−0.973310	−	1.22049i	−0.975388	−	0.220495i	$-0.929233\pi$
$13$	−7709.98	−	9668.00i	−0.973310	−	1.22049i	0.00207804	−	0.999998i	$-0.499339\pi$
$14$	7026.61	−	1603.78i	0.684380	−	0.156205i
$15$	−2425.70	+	553.651i	−0.185574	+	0.0423562i
$16$	−6554.24	−	8218.76i	−0.400039	−	0.501633i
$17$		−	35694.5i		−	1.76210i	−0.473024	−	0.881049i	$-0.656838\pi$
$17$		−	35694.5i		−	1.76210i	0.473024	−	0.881049i	$-0.343162\pi$
$18$	−7123.31	+	5680.65i	−0.287891	+	0.229585i
$19$	9234.86	−	19176.4i	0.308882	−	0.641400i	−0.687519	−	0.726167i	$-0.741300\pi$
$19$	9234.86	−	19176.4i	0.308882	−	0.641400i	0.996401	+	0.0847662i	$0.0270143\pi$
$20$	1580.16	−	1981.45i	0.0441667	−	0.0553833i
$21$	−20652.0	−	16469.4i	−0.486625	−	0.388070i
$22$	−17432.6	+	8395.11i	−0.349047	+	0.168092i
$23$	−93.8156	−	411.033i	−0.00160778	−	0.00704416i	0.974118	−	0.226042i	$-0.0725785\pi$
$23$	−93.8156	−	411.033i	−0.00160778	−	0.00704416i	−0.975725	+	0.218997i	$0.929721\pi$
$24$	−12314.3	+	53952.6i	−0.181833	+	0.796661i
$25$	65882.7	+	31727.4i	0.843299	+	0.406111i
$26$	51507.5	+	106957.i	0.574730	+	1.19344i
$27$	107574.	+	24553.0i	1.05180	+	0.240067i
$28$	26906.3			0.231633
$29$	−113726.	+	65697.9i	−0.865900	+	0.500217i
$29$	−113726.	+	65697.9i	−0.865900	+	0.500217i
$30$	23885.8			0.161516
$31$	−145568.	−	33224.9i	−0.877607	−	0.200308i	−0.240096	−	0.970749i	$-0.577179\pi$
$31$	−145568.	−	33224.9i	−0.877607	−	0.200308i	−0.637511	+	0.770441i	$0.720036\pi$
$32$	−43565.8	−	90465.2i	−0.235028	−	0.488042i
$33$	63890.8	+	30768.2i	0.309485	+	0.149040i
$34$	−76251.1	+	334078.i	−0.332713	+	1.45771i
$35$	−11813.7	−	51759.2i	−0.0465745	−	0.204056i
$36$	−30645.0	+	14757.9i	−0.109471	+	0.0527187i
$37$	−20660.2	−	16475.9i	−0.0670545	−	0.0534742i	0.589389	−	0.807849i	$-0.299369\pi$
$37$	−20660.2	−	16475.9i	−0.0670545	−	0.0534742i	−0.656443	+	0.754375i	$0.727940\pi$
$38$	−127397.	+	159751.i	−0.376632	+	0.472282i
$39$	188776.	−	391997.i	0.509589	−	1.05817i
$40$	−86960.1	+	69348.3i	−0.214837	+	0.171327i
$41$		−	367014.i		−	0.831648i	−0.909445	−	0.415824i	$-0.863493\pi$
$41$		−	367014.i		−	0.831648i	0.909445	−	0.415824i	$-0.136507\pi$
$42$	158107.	+	198260.i	0.329291	+	0.412917i
$43$	534367.	−	121966.i	1.02494	−	0.233937i	0.323173	−	0.946340i	$-0.395250\pi$
$43$	534367.	−	121966.i	1.02494	−	0.233937i	0.701770	+	0.712403i	$0.252393\pi$
$44$	−70421.8	+	16073.3i	−0.124630	+	0.0284460i
$45$	41844.7	+	52471.5i	0.0684536	+	0.0858381i
$46$			4047.42i			0.00613092i
$47$	−604576.	+	482133.i	−0.849393	+	0.677368i	−0.948178	−	0.317741i	$-0.897076\pi$
$47$	−604576.	+	482133.i	−0.849393	+	0.677368i	0.0987848	+	0.995109i	$0.468504\pi$
$48$	160478.	−	333236.i	0.209446	−	0.434919i
$49$	−162049.	+	203203.i	−0.196771	+	0.246743i
$50$	−548844.	−	437688.i	−0.620946	−	0.495188i
$51$	1.13152e6	−	544909.i	1.19444	−	0.575213i
$52$	98616.5	+	432067.i	0.0972608	+	0.426127i
$53$	147015.	−	644115.i	0.135643	−	0.594290i	−0.860720	−	0.509078i	$-0.829986\pi$
$53$	147015.	−	644115.i	0.135643	−	0.594290i	0.996363	−	0.0852112i	$-0.0271565\pi$
$54$	−954372.	−	459601.i	−0.824783	−	0.397194i
$55$	61839.9	+	128412.i	0.0501186	+	0.104072i
$56$	−1.15123e6	−	262761.i	−0.876001	−	0.199942i
$57$	748870.			0.535605
$58$	1.20475e6	−	371947.i	0.810772	−	0.250313i
$59$	−912506.			−0.578434			−0.289217	−	0.957264i	$-0.593395\pi$
$59$	−912506.			−0.578434			−0.289217	+	0.957264i	$0.593395\pi$
$60$	86934.6	+	19842.3i	0.0519593	+	0.0118594i
$61$	−1.29395e6	−	2.68692e6i	−0.729902	−	1.51566i	−0.852230	−	0.523167i	$-0.824750\pi$
$61$	−1.29395e6	−	2.68692e6i	−0.729902	−	1.51566i	0.122328	−	0.992490i	$-0.460964\pi$
$62$	1.29145e6	+	621929.i	0.688186	+	0.331413i
$63$	−158550.	+	694651.i	−0.0798865	+	0.350005i
$64$	513910.	+	2.25159e6i	0.245051	+	1.07364i
$65$	787860.	−	379414.i	0.355838	−	0.171363i
$66$	−532250.	−	424455.i	−0.227883	−	0.181731i
$67$	−390014.	+	489062.i	−0.158423	+	0.198656i	−0.854708	−	0.519109i	$-0.826264\pi$
$67$	−390014.	+	489062.i	−0.158423	+	0.198656i	0.696285	+	0.717766i	$0.254835\pi$
$68$	−555047.	+	1.15257e6i	−0.214066	+	0.444513i
$69$	11597.6	−	9248.74i	0.00425006	−	0.00338931i
$70$			509670.i			0.177601i
$71$	−1.88029e6	−	2.35781e6i	−0.623478	−	0.781816i	0.365351	−	0.930870i	$-0.380949\pi$
$71$	−1.88029e6	−	2.35781e6i	−0.623478	−	0.781816i	−0.988829	+	0.149053i	$0.952377\pi$
$72$	1.45532e6	−	332167.i	0.459509	−	0.104880i
$73$	2.51209e6	−	573368.i	0.755796	−	0.172506i	0.172774	−	0.984962i	$-0.444727\pi$
$73$	2.51209e6	−	573368.i	0.755796	−	0.172506i	0.583023	+	0.812456i	$0.301870\pi$
$74$	158170.	+	198339.i	0.0453746	+	0.0568979i
$75$			2.57283e6i			0.704201i
$76$	−596383.	+	475599.i	−0.155840	+	0.124278i
$77$	−656526.	+	1.36329e6i	−0.163883	+	0.340307i
$78$	−2.60421e6	+	3.26558e6i	−0.621362	+	0.779164i
$79$	4.59786e6	+	3.66667e6i	1.04921	+	0.836715i	0.986898	−	0.161342i	$-0.0515824\pi$
$79$	4.59786e6	+	3.66667e6i	1.04921	+	0.836715i	0.0623083	+	0.998057i	$0.480154\pi$
$80$	669759.	−	322539.i	0.146253	−	0.0704316i
$81$	402017.	+	1.76135e6i	0.0840518	+	0.368255i
$82$	−784021.	+	3.43502e6i	−0.157029	+	0.687988i
$83$	−2.90107e6	−	1.39708e6i	−0.556909	−	0.268193i	0.134187	−	0.990956i	$-0.457158\pi$
$83$	−2.90107e6	−	1.39708e6i	−0.556909	−	0.268193i	−0.691096	+	0.722763i	$0.742872\pi$
$84$	410750.	+	852930.i	0.0756135	+	0.157013i
$85$	2.46088e6	+	561679.i	0.434634	+	0.0992023i
$86$	−5.26188e6			−0.892064
$87$	−3.81876e6	−	2.60218e6i	−0.621734	−	0.423663i
$88$	3.17008e6			0.495885
$89$	−5.87708e6	−	1.34140e6i	−0.883683	−	0.201695i	−0.243485	−	0.969905i	$-0.578291\pi$
$89$	−5.87708e6	−	1.34140e6i	−0.883683	−	0.201695i	−0.640198	+	0.768210i	$0.721148\pi$
$90$	−279549.	−	580489.i	−0.0404212	−	0.0839354i
$91$	8.36436e6	+	4.02806e6i	1.16356	+	0.560340i
$92$	−3362.25	+	14731.0i	−0.000450166	+	0.00197231i
$93$	−1.16900e6	−	5.12171e6i	−0.150704	−	0.660275i
$94$	6.68839e6	−	3.22096e6i	0.830566	−	0.399979i
$95$	1.17675e6	+	938431.i	0.140816	+	0.112297i
$96$	2.20268e6	−	2.76207e6i	0.254098	−	0.318629i
$97$	2.70610e6	−	5.61927e6i	0.301053	−	0.625142i	−0.694485	−	0.719507i	$-0.744368\pi$
$97$	2.70610e6	−	5.61927e6i	0.301053	−	0.625142i	0.995538	+	0.0943648i	$0.0300820\pi$
$98$	1.95076e6	−	1.55568e6i	0.209370	−	0.166967i
$99$		−	1.91282e6i		−	0.198130i
$100$	−1.63398e6	−	2.04894e6i	−0.163398	−	0.204894i
$101$	−3.91798e6	+	894253.i	−0.378388	+	0.0863645i	−0.407485	−	0.913212i	$-0.633594\pi$
$101$	−3.91798e6	+	894253.i	−0.378388	+	0.0863645i	0.0290969	+	0.999577i	$0.490737\pi$
$102$	−1.17543e7	+	2.68284e6i	−1.09672	+	0.250320i
$103$	−1.22827e6	−	1.54020e6i	−0.110755	−	0.138883i	0.723364	−	0.690467i	$-0.242595\pi$
$103$	−1.22827e6	−	1.54020e6i	−0.110755	−	0.138883i	−0.834119	+	0.551584i	$0.814023\pi$
$104$		−	1.94498e7i		−	1.69550i
$105$	1.46042e6	−	1.16465e6i	0.123116	−	0.0981819i
$106$	−2.75194e6	+	5.71445e6i	−0.224423	+	0.466020i
$107$	1.18063e7	−	1.48047e7i	0.931690	−	1.16830i	−0.0537976	−	0.998552i	$-0.517133\pi$
$107$	1.18063e7	−	1.48047e7i	0.931690	−	1.16830i	0.985487	−	0.169750i	$-0.0542960\pi$
$108$	−3.09173e6	−	2.46558e6i	−0.236167	−	0.188337i
$109$	−1.03689e7	+	4.99340e6i	−0.766903	+	0.369321i	−0.776078	−	0.630637i	$-0.782794\pi$
$109$	−1.03689e7	+	4.99340e6i	−0.766903	+	0.369321i	0.00917522	+	0.999958i	$0.497079\pi$
$110$	−304467.	−	1.33396e6i	−0.0218105	−	0.0955580i
$111$	206891.	−	906447.i	0.0143585	−	0.0629089i
$112$	7.11054e6	+	3.42425e6i	0.478233	+	0.230305i
$113$	−5.03650e6	−	1.04584e7i	−0.328363	−	0.681853i	0.669793	−	0.742548i	$-0.266383\pi$
$113$	−5.03650e6	−	1.04584e7i	−0.328363	−	0.681853i	−0.998156	+	0.0606945i	$0.980668\pi$
$114$	−7.00895e6	−	1.59975e6i	−0.443084	−	0.101131i
$115$	29814.0			0.00182801
$116$	4.69379e6	−	352934.i	0.279203	−	0.0209938i
$117$	−1.17360e7			−0.677435
$118$	8.54047e6	+	1.94931e6i	0.478514	+	0.109218i
$119$	1.16272e7	+	2.41441e7i	0.632499	+	1.31340i
$120$	−3.52587e6	−	1.69797e6i	−0.186265	−	0.0897005i
$121$	−3.43238e6	+	1.50383e7i	−0.176136	+	0.771700i
$122$	6.37075e6	+	2.79121e7i	0.317637	+	1.39166i
$123$	1.16343e7	−	5.60281e6i	0.563734	−	0.271480i
$124$	4.18371e6	+	3.33640e6i	0.197054	+	0.157145i
$125$	−6.66866e6	+	8.36223e6i	−0.305389	+	0.382946i
$126$	2.96785e6	−	6.16280e6i	0.132174	−	0.274461i
$127$	−652504.	+	520355.i	−0.0282664	+	0.0225417i	−0.637521	−	0.770433i	$-0.720040\pi$
$127$	−652504.	+	520355.i	−0.0282664	+	0.0225417i	0.609255	+	0.792975i	$0.291469\pi$
$128$		−	9.31891e6i		−	0.392763i
$129$	1.20239e7	+	1.50775e7i	0.493153	+	0.618394i
$130$	−8.18438e6	+	1.86803e6i	−0.326726	+	0.0745731i
$131$	−3.15862e7	+	7.20935e6i	−1.22758	+	0.280186i	−0.786674	−	0.617369i	$-0.788198\pi$
$131$	−3.15862e7	+	7.20935e6i	−1.22758	+	0.280186i	−0.440902	+	0.897555i	$0.645341\pi$
$132$	−1.58458e6	−	1.98700e6i	−0.0599659	−	0.0751949i
$133$			1.59793e7i			0.588946i
$134$	4.69503e6	−	3.74416e6i	0.168566	−	0.134427i
$135$	−3.38550e6	+	7.03007e6i	−0.118428	+	0.245919i
$136$	3.50043e7	−	4.38940e7i	1.19326	−	1.49630i
$137$	3.24038e7	+	2.58412e7i	1.07665	+	0.858599i	0.990477	−	0.137681i	$-0.0439650\pi$
$137$	3.24038e7	+	2.58412e7i	1.07665	+	0.858599i	0.0861724	+	0.996280i	$0.472536\pi$
$138$	−128303.	+	61787.5i	−0.00415585	+	0.00200135i
$139$	8.69995e6	+	3.81170e7i	0.274767	+	1.20383i	0.904313	+	0.426870i	$0.140384\pi$
$139$	8.69995e6	+	3.81170e7i	0.274767	+	1.20383i	−0.629546	+	0.776963i	$0.716759\pi$
$140$	−423390.	+	1.85499e6i	−0.0130405	+	0.0571340i
$141$	−2.45130e7	−	1.18049e7i	−0.736428	−	0.354645i
$142$	1.25615e7	+	2.60843e7i	0.368158	+	0.764487i
$143$	−2.42983e7	−	5.54592e6i	−0.694863	−	0.158598i
$144$	−9.97673e6			−0.278432
$145$	−2.73983e6	−	8.87440e6i	−0.0746337	−	0.241741i
$146$	−2.47364e7			−0.657811
$147$	−8.91538e6	−	2.03488e6i	−0.231488	−	0.0528357i
$148$	410912.	+	853268.i	0.0104192	+	0.0216356i
$149$	−1.01376e7	−	4.88200e6i	−0.251062	−	0.120905i	0.304120	−	0.952634i	$-0.401637\pi$
$149$	−1.01376e7	−	4.88200e6i	−0.251062	−	0.120905i	−0.555183	+	0.831728i	$0.687352\pi$
$150$	5.49611e6	−	2.40800e7i	0.132965	−	0.582556i
$151$	−1.41054e7	−	6.17998e7i	−0.333400	−	1.46072i	−0.812500	−	0.582961i	$-0.801894\pi$
$151$	−1.41054e7	−	6.17998e7i	−0.333400	−	1.46072i	0.479100	−	0.877761i	$-0.340963\pi$
$152$	3.01618e7	−	1.45252e7i	0.696635	−	0.335482i
$153$	−2.64856e7	−	2.11215e7i	−0.597846	−	0.476766i
$154$	9.05695e6	−	1.13571e7i	0.199829	−	0.250578i
$155$	4.58124e6	−	9.51303e6i	0.0988147	−	0.205191i
$156$	−1.21910e7	+	9.72204e6i	−0.257102	+	0.205032i
$157$			8.75400e7i			1.80534i	0.430338	+	0.902668i	$0.358394\pi$
$157$			8.75400e7i			1.80534i	−0.430338	+	0.902668i	$0.641606\pi$
$158$	−3.52003e7	−	4.41397e7i	−0.709980	−	0.890287i
$159$	2.26628e7	−	5.17263e6i	0.447119	−	0.102052i
$160$	6.92246e6	−	1.58001e6i	0.133610	−	0.0304957i
$161$	197348.	+	247467.i	0.00372685	+	0.00467333i
$162$		−	1.73439e7i		−	0.320513i
$163$	4.60971e7	−	3.67612e7i	0.833714	−	0.664865i	−0.110616	−	0.993863i	$-0.535282\pi$
$163$	4.60971e7	−	3.67612e7i	0.833714	−	0.664865i	0.944331	+	0.328998i	$0.106711\pi$
$164$	−5.70704e6	+	1.18508e7i	−0.101032	+	0.209794i
$165$	−3.12661e6	+	3.92065e6i	−0.0541851	+	0.0679460i
$166$	2.41677e7	+	1.92731e7i	0.410069	+	0.327019i
$167$	7.26160e7	−	3.49700e7i	1.20649	−	0.581016i	0.280973	−	0.959716i	$-0.409343\pi$
$167$	7.26160e7	−	3.49700e7i	1.20649	−	0.581016i	0.925520	+	0.378700i	$0.123629\pi$
$168$	−9.24508e6	−	4.05053e7i	−0.150428	−	0.659067i
$169$	−2.00637e7	+	8.79049e7i	−0.319748	+	1.40091i
$170$	−2.18324e7	−	1.05139e7i	−0.340824	−	0.164132i
$171$	−8.76446e6	−	1.81996e7i	−0.134041	−	0.278340i
$172$	−1.91511e7	−	4.37112e6i	−0.286975	−	0.0655003i
$173$	2.42628e7			0.356270			0.178135	−	0.984006i	$-0.442994\pi$
$173$	2.42628e7			0.356270			0.178135	+	0.984006i	$0.442994\pi$
$174$	3.01823e7	+	3.25125e7i	0.434340	+	0.467872i
$175$	−5.48986e7			−0.774333
$176$	−2.06559e7	−	4.71459e6i	−0.285595	−	0.0651852i
$177$	−1.39302e7	−	2.89264e7i	−0.188822	−	0.392092i
$178$	5.21402e7	+	2.51094e7i	0.692951	+	0.333708i
$179$	−2.05405e7	+	8.99937e7i	−0.267685	+	1.17281i	0.645013	+	0.764172i	$0.276852\pi$
$179$	−2.05405e7	+	8.99937e7i	−0.267685	+	1.17281i	−0.912698	+	0.408635i	$0.866005\pi$
$180$	−535225.	−	2.34497e6i	−0.00684042	−	0.0299698i
$181$	7.23326e7	−	3.48336e7i	0.906691	−	0.436639i	0.0783899	−	0.996923i	$-0.475022\pi$
$181$	7.23326e7	−	3.48336e7i	0.906691	−	0.436639i	0.828301	+	0.560283i	$0.189308\pi$
$182$	−6.96803e7	−	5.55682e7i	−0.856762	−	0.683245i
$183$	6.54221e7	−	8.20367e7i	0.789124	−	0.989531i
$184$	287719.	−	597454.i	0.00340491	−	0.00707037i
$185$	1.46100e6	−	1.16511e6i	0.0169648	−	0.0135290i
$186$			5.04332e7i			0.574674i
$187$	−4.48549e7	−	5.62463e7i	−0.501608	−	0.628997i
$188$	2.70188e7	−	6.16686e6i	0.296560	−	0.0676879i
$189$	−8.07618e7	+	1.84334e7i	−0.870141	+	0.198604i
$190$	−9.00899e6	−	1.12969e7i	−0.0952880	−	0.119487i
$191$		−	9.95921e7i		−	1.03421i	−0.855922	−	0.517104i	$-0.827010\pi$
$191$		−	9.95921e7i		−	1.03421i	0.855922	−	0.517104i	$-0.172990\pi$
$192$	−6.35300e7	+	5.06635e7i	−0.647775	+	0.516584i
$193$	−1.12727e7	+	2.34081e7i	−0.112870	+	0.234377i	−0.949750	−	0.313009i	$-0.898663\pi$
$193$	−1.12727e7	+	2.34081e7i	−0.112870	+	0.234377i	0.836880	+	0.547386i	$0.184377\pi$
$194$	−3.73313e7	+	4.68120e7i	−0.367086	+	0.460311i
$195$	2.40548e7	+	1.91831e7i	0.232317	+	0.185267i
$196$	8.39233e6	−	4.04153e6i	0.0796134	−	0.0383398i
$197$	6.78114e6	+	2.97101e7i	0.0631933	+	0.276868i	0.996646	−	0.0818322i	$-0.0260772\pi$
$197$	6.78114e6	+	2.97101e7i	0.0631933	+	0.276868i	−0.933453	+	0.358700i	$0.883220\pi$
$198$	−4.08619e6	+	1.79028e7i	−0.0374103	+	0.163905i
$199$	−1.27175e7	−	6.12443e6i	−0.114398	−	0.0550909i	0.375810	−	0.926697i	$-0.377365\pi$
$199$	−1.27175e7	−	6.12443e6i	−0.114398	−	0.0550909i	−0.490207	+	0.871606i	$0.663079\pi$
$200$	4.99029e7	+	1.03624e8i	0.441084	+	0.915920i
$201$	−2.14572e7	−	4.89746e6i	−0.186375	−	0.0425388i
$202$	3.85801e7			0.329332
$203$	5.55249e7	−	8.14840e7i	0.465856	−	0.683653i
$204$	−4.50097e7			−0.371193
$205$	2.53029e7	+	5.77523e6i	0.205132	+	0.0468200i
$206$	8.20563e6	+	1.70392e7i	0.0653999	+	0.135804i
$207$	−360503.	−	173609.i	−0.00282496	−	0.00136043i
$208$	−2.89260e7	+	1.26733e8i	−0.222877	+	0.976490i
$209$	−9.54569e6	−	4.18224e7i	−0.0723262	−	0.316882i
$210$	−1.61565e7	+	7.78057e6i	−0.120387	+	0.0579755i
$211$	9.38151e7	+	7.48150e7i	0.687518	+	0.548277i	0.903748	−	0.428065i	$-0.140805\pi$
$211$	9.38151e7	+	7.48150e7i	0.687518	+	0.548277i	−0.216230	+	0.976342i	$0.569376\pi$
$212$	−1.47630e7	+	1.85122e7i	−0.106414	+	0.133439i
$213$	4.60382e7	−	9.55994e7i	0.326430	−	0.677839i
$214$	−1.42126e8	+	1.13341e8i	−0.991343	+	0.790569i
$215$			3.87599e7i			0.265979i
$216$	1.08207e8	+	1.35687e8i	0.730577	+	0.916115i
$217$	1.09286e8	−	2.49439e7i	0.726033	−	0.165712i
$218$	1.07713e8	−	2.45849e7i	0.704161	−	0.160720i
$219$	5.65250e7	+	7.08802e7i	0.363652	+	0.456006i
$220$		−	5.10799e6i		−	0.0323423i
$221$	−3.45095e8	+	2.75204e8i	−2.15063	+	1.71507i
$222$	−3.87273e6	+	8.04181e6i	−0.0237565	+	0.0493308i
$223$	1.58494e8	−	1.98746e8i	0.957076	−	1.20014i	−0.0226393	−	0.999744i	$-0.507207\pi$
$223$	1.58494e8	−	1.98746e8i	0.957076	−	1.20014i	0.979716	−	0.200392i	$-0.0642216\pi$
$224$	5.89365e7	+	4.70003e7i	0.350362	+	0.279404i
$225$	6.25268e7	−	3.01113e7i	0.365955	−	0.176235i
$226$	2.47971e7	+	1.08643e8i	0.142896	+	0.626069i
$227$	4.09767e7	−	1.79531e8i	0.232513	−	1.01871i	−0.715034	−	0.699089i	$-0.753589\pi$
$227$	4.09767e7	−	1.79531e8i	0.232513	−	1.01871i	0.947547	−	0.319616i	$-0.103554\pi$
$228$	−2.41808e7	−	1.16449e7i	−0.135114	−	0.0650673i
$229$	−7.19769e7	−	1.49462e8i	−0.396067	−	0.822442i	−0.999683	−	0.0251668i	$-0.991988\pi$
$229$	−7.19769e7	−	1.49462e8i	−0.396067	−	0.822442i	0.603616	−	0.797275i	$-0.293726\pi$
$230$	−279040.	−	63689.0i	−0.00151223	−	0.000345157i
$231$	−5.32388e7			−0.284175
$232$	−2.04278e8	−	3.07376e7i	−1.07402	−	0.161608i
$233$	−2.58014e8			−1.33628			−0.668141	−	0.744035i	$-0.732910\pi$
$233$	−2.58014e8			−1.33628			−0.668141	+	0.744035i	$0.732910\pi$
$234$	1.09841e8	+	2.50705e7i	0.560414	+	0.127911i
$235$	−2.37261e7	−	4.92678e7i	−0.119259	−	0.247643i
$236$	2.94646e7	+	1.41894e7i	0.145918	+	0.0702703i
$237$	−4.60429e7	+	2.01727e8i	−0.224669	+	0.984341i
$238$	−5.72460e7	−	2.50811e8i	−0.275249	−	1.20595i
$239$	2.14491e8	−	1.03293e8i	1.01629	−	0.489418i	0.149852	−	0.988708i	$-0.452120\pi$
$239$	2.14491e8	−	1.03293e8i	1.01629	−	0.489418i	0.866434	+	0.499291i	$0.166406\pi$
$240$	2.04490e7	+	1.63075e7i	0.0954843	+	0.0761462i
$241$	1.04284e8	−	1.30769e8i	0.479910	−	0.601788i	−0.481656	−	0.876360i	$-0.659965\pi$
$241$	1.04284e8	−	1.30769e8i	0.479910	−	0.601788i	0.961567	+	0.274572i	$0.0885361\pi$
$242$	6.42499e7	−	1.33416e8i	0.291419	−	0.605138i
$243$	1.38969e8	−	1.10824e8i	0.621294	−	0.495465i
$244$			1.06881e8i			0.471017i
$245$	−1.14594e7	−	1.43697e7i	−0.0497831	−	0.0624260i
$246$	−1.20859e8	+	2.75852e7i	−0.517613	+	0.118142i
$247$	−2.56598e8	+	5.85668e7i	−1.08346	+	0.247293i
$248$	−1.46424e8	−	1.83610e8i	−0.609583	−	0.764393i
$249$		−	1.13292e8i		−	0.465050i
$250$	8.02779e7	−	6.40195e7i	0.324942	−	0.259133i
$251$	5.54919e7	−	1.15230e8i	0.221499	−	0.459948i	−0.760374	−	0.649485i	$-0.774985\pi$
$251$	5.54919e7	−	1.15230e8i	0.221499	−	0.459948i	0.981873	+	0.189537i	$0.0606988\pi$
$252$	1.59213e7	−	1.99647e7i	0.0626724	−	0.0785888i
$253$	−664350.	−	529801.i	−0.00257914	−	0.00205679i
$254$	7.21861e6	−	3.47630e6i	0.0276398	−	0.0133106i
$255$	1.97623e7	+	8.65843e7i	0.0746357	+	0.327001i
$256$	4.58733e7	−	2.00984e8i	0.170891	−	0.748724i
$257$	−2.86916e8	−	1.38171e8i	−1.05436	−	0.507752i	−0.175324	−	0.984511i	$-0.556097\pi$
$257$	−2.86916e8	−	1.38171e8i	−1.05436	−	0.507752i	−0.879034	+	0.476758i	$0.841812\pi$
$258$	−8.03273e7	−	1.66801e8i	−0.291202	−	0.604687i
$259$	1.93416e7	+	4.41460e6i	0.0691741	+	0.0157885i
$260$	−3.13397e7			−0.110583
$261$	−1.85470e7	+	1.23261e8i	−0.0645702	+	0.429126i
$262$	3.11028e8			1.06843
$263$	3.44364e8	+	7.85989e7i	1.16727	+	0.266423i	0.761880	−	0.647719i	$-0.224277\pi$
$263$	3.44364e8	+	7.85989e7i	1.16727	+	0.266423i	0.405395	+	0.914142i	$0.367134\pi$
$264$	4.83942e7	+	1.00492e8i	0.161875	+	0.336137i
$265$	4.20937e7	+	2.02712e7i	0.138949	+	0.0669144i
$266$	3.41351e7	−	1.49556e8i	0.111203	−	0.487211i
$267$	−4.71964e7	−	2.06781e8i	−0.151747	−	0.664846i
$268$	2.01983e7	−	9.72701e6i	0.0640979	−	0.0308679i
$269$	3.85835e8	+	3.07693e8i	1.20856	+	0.963796i	0.999899	−	0.0141920i	$-0.00451761\pi$
$269$	3.85835e8	+	3.07693e8i	1.20856	+	0.963796i	0.208662	+	0.977988i	$0.433089\pi$
$270$	4.67039e7	−	5.85648e7i	0.144404	−	0.181077i
$271$	−2.53808e8	+	5.27037e8i	−0.774662	+	1.60860i	0.0186792	+	0.999826i	$0.494054\pi$
$271$	−2.53808e8	+	5.27037e8i	−0.774662	+	1.60860i	−0.793341	+	0.608777i	$0.791660\pi$
$272$	−2.93365e8	+	2.33950e8i	−0.883927	+	0.704909i
$273$			3.26642e8i			0.971635i
$274$	−2.48077e8	−	3.11078e8i	−0.728550	−	0.913572i
$275$	1.43686e8	−	3.27953e7i	0.416629	−	0.0950928i
$276$	−518300.	+	118298.i	−0.00148388	+	0.000338686i
$277$	−1.23513e7	−	1.54880e7i	−0.0349166	−	0.0437841i	0.764067	−	0.645137i	$-0.223200\pi$
$277$	−1.23513e7	−	1.54880e7i	−0.0349166	−	0.0437841i	−0.798983	+	0.601353i	$0.794628\pi$
$278$		−	3.75335e8i		−	1.04776i
$279$	−1.10790e8	+	8.83522e7i	−0.305412	+	0.243558i
$280$	3.62309e7	−	7.52343e7i	0.0986339	−	0.204815i
$281$	−2.40718e8	+	3.01851e8i	−0.647198	+	0.811561i	−0.991882	−	0.127158i	$-0.959414\pi$
$281$	−2.40718e8	+	3.01851e8i	−0.647198	+	0.811561i	0.344684	+	0.938719i	$0.387986\pi$
$282$	2.04209e8	+	1.62851e8i	0.542253	+	0.432433i
$283$	1.60957e7	−	7.75128e6i	0.0422141	−	0.0203292i	−0.412658	−	0.910886i	$-0.635399\pi$
$283$	1.60957e7	−	7.75128e6i	0.0422141	−	0.0203292i	0.454872	+	0.890557i	$0.349685\pi$
$284$	2.40504e7	+	1.05372e8i	0.0623028	+	0.272966i
$285$	−1.17840e7	+	5.16291e7i	−0.0301534	+	0.132111i
$286$	2.15569e8	+	1.03813e8i	0.544886	+	0.262403i
$287$	1.19552e8	+	2.48252e8i	0.298517	+	0.619877i
$288$	−9.29050e7	−	2.12050e7i	−0.229174	−	0.0523075i
$289$	−8.63759e8			−2.10499
$290$	6.68542e6	+	8.89116e7i	0.0160967	+	0.214075i
$291$	2.19442e8			0.522028
$292$	−9.00305e7	−	2.05489e7i	−0.211617	−	0.0483001i
$293$	2.41088e8	+	5.00625e8i	0.559937	+	1.16272i	0.968274	+	0.249890i	$0.0803945\pi$
$293$	2.41088e8	+	5.00625e8i	0.559937	+	1.16272i	−0.408337	+	0.912831i	$0.633891\pi$
$294$	7.90953e7	+	3.80903e7i	0.181524	+	0.0874176i
$295$	1.43589e7	−	6.29106e7i	0.0325646	−	0.142675i
$296$	−9.24874e6	−	4.05214e7i	−0.0207282	−	0.0908161i
$297$	2.00366e8	−	9.64910e7i	0.443788	−	0.213717i
$298$	8.44522e7	+	6.73484e7i	0.184865	+	0.147425i
$299$	−3.25055e6	+	4.07606e6i	−0.00703247	+	0.00881844i
$300$	4.00073e7	−	8.30760e7i	0.0855490	−	0.177644i
$301$	−3.21721e8	+	2.56564e8i	−0.679981	+	0.542267i
$302$			6.08539e8i			1.27135i
$303$	−8.81593e7	−	1.10548e8i	−0.182062	−	0.228298i
$304$	−2.18134e8	+	4.97876e7i	−0.445313	+	0.101640i
$305$	2.05605e8	−	4.69280e7i	0.414939	−	0.0947072i
$306$	2.02768e8	+	2.54263e8i	0.404552	+	0.507292i
$307$			2.90344e7i			0.0572701i	0.999590	+	0.0286350i	$0.00911607\pi$
$307$			2.90344e7i			0.0572701i	−0.999590	+	0.0286350i	$0.990884\pi$
$308$	4.23981e7	−	3.38114e7i	0.0826836	−	0.0659380i
$309$	3.00738e7	−	6.24488e7i	0.0579873	−	0.120412i
$310$	−6.31993e7	+	7.92494e7i	−0.120489	+	0.151088i
$311$	7.17754e8	+	5.72390e8i	1.35305	+	1.07902i	0.989043	+	0.147628i	$0.0471637\pi$
$311$	7.17754e8	+	5.72390e8i	1.35305	+	1.07902i	0.364009	+	0.931395i	$0.381408\pi$
$312$	6.16558e8	−	2.96918e8i	1.14930	−	0.553473i
$313$	−1.89647e8	−	8.30897e8i	−0.349575	−	1.53159i	−0.778148	−	0.628081i	$-0.783841\pi$
$313$	−1.89647e8	−	8.30897e8i	−0.349575	−	1.53159i	0.428573	−	0.903507i	$-0.359016\pi$
$314$	1.87004e8	−	8.19319e8i	0.340877	−	1.49348i
$315$	−4.53962e7	−	2.18617e7i	−0.0818338	−	0.0394091i
$316$	−9.14473e7	−	1.89892e8i	−0.163030	−	0.338534i
$317$	−3.98681e8	−	9.09962e7i	−0.702939	−	0.160441i	−0.143912	−	0.989591i	$-0.545968\pi$
$317$	−3.98681e8	−	9.09962e7i	−0.702939	−	0.160441i	−0.559027	+	0.829149i	$0.688825\pi$
$318$	−2.23159e8			−0.389152
$319$	−9.66481e7	+	2.46437e8i	−0.166696	+	0.425049i
$320$	−1.63317e8			−0.278617
$321$	6.49542e8	+	1.48254e8i	1.09607	+	0.250171i
$322$	−1.31841e6	−	2.73771e6i	−0.00220067	−	0.00456974i
$323$	−6.84492e8	−	3.29634e8i	−1.13021	−	0.544281i
$324$	1.44079e7	−	6.31250e7i	0.0235338	−	0.103108i
$325$	−2.01213e8	−	8.81572e8i	−0.325136	−	1.42451i
$326$	−5.09970e8	+	2.45588e8i	−0.815235	+	0.392596i
$327$	−3.16582e8	−	2.52465e8i	−0.500690	−	0.399287i
$328$	3.59918e8	−	4.51322e8i	0.563177	−	0.706201i
$329$	2.51890e8	−	5.23055e8i	0.389964	−	0.809770i
$330$	3.76384e7	−	3.00156e7i	0.0576544	−	0.0459779i
$331$			5.72571e8i			0.867823i	0.900955	+	0.433912i	$0.142867\pi$
$331$			5.72571e8i			0.867823i	−0.900955	+	0.433912i	$0.857133\pi$
$332$	7.19503e7	+	9.02228e7i	0.107907	+	0.135311i
$333$	−2.44505e7	+	5.58067e6i	−0.0362855	+	0.00828193i
$334$	−7.54343e8	+	1.72174e8i	−1.10779	+	0.252845i
$335$	−2.75801e7	−	3.45844e7i	−0.0400811	−	0.0502601i
$336$			2.77678e8i			0.399351i
$337$	−6.05192e8	+	4.82625e8i	−0.861368	+	0.686918i	−0.951045	−	0.309053i	$-0.899988\pi$
$337$	−6.05192e8	+	4.82625e8i	−0.861368	+	0.686918i	0.0896768	+	0.995971i	$0.471417\pi$
$338$	3.75567e8	−	7.79873e8i	0.529029	−	1.09854i
$339$	2.54645e8	−	3.19314e8i	0.355006	−	0.445163i
$340$	−7.07270e7	−	5.64029e7i	−0.0975908	−	0.0778261i
$341$	−2.71133e8	+	1.30571e8i	−0.370290	+	0.178322i
$342$	4.31516e7	+	1.89059e8i	0.0583318	+	0.255568i
$343$	1.81000e8	−	7.93014e8i	0.242186	−	1.06109i
$344$	7.76725e8	+	3.74051e8i	1.02876	+	0.495423i
$345$	455137.	+	945103.i	0.000596727	+	0.00123912i
$346$	−2.27084e8	−	5.18305e7i	−0.294727	−	0.0672696i
$347$	6.42261e8			0.825199			0.412600	−	0.910913i	$-0.364621\pi$
$347$	6.42261e8			0.825199			0.412600	+	0.910913i	$0.364621\pi$
$348$	8.28430e7	+	1.43405e8i	0.105373	+	0.182405i
$349$	4.39674e8			0.553658			0.276829	−	0.960919i	$-0.410716\pi$
$349$	4.39674e8			0.553658			0.276829	+	0.960919i	$0.410716\pi$
$350$	5.13816e8	+	1.17275e8i	0.640574	+	0.146207i
$351$	−5.92013e8	−	1.22933e9i	−0.730729	−	1.51737i
$352$	−1.82331e8	−	8.78061e7i	−0.222824	−	0.107306i
$353$	−1.04301e8	+	4.56971e8i	−0.126205	+	0.552939i	0.871804	+	0.489856i	$0.162950\pi$
$353$	−1.04301e8	+	4.56971e8i	−0.126205	+	0.552939i	−0.998008	+	0.0630832i	$0.979907\pi$
$354$	6.85851e7	+	3.00491e8i	0.0821709	+	0.360014i
$355$	1.92142e8	−	9.25305e7i	0.227941	−	0.109771i
$356$	1.68911e8	+	1.34702e8i	0.198418	+	0.158233i
$357$	−5.87868e8	+	7.37163e8i	−0.683818	+	0.857481i
$358$	3.84491e8	−	7.98405e8i	0.442890	−	0.919671i
$359$	9.93100e6	−	7.91971e6i	0.0113282	−	0.00903397i	−0.617809	−	0.786328i	$-0.711980\pi$
$359$	9.93100e6	−	7.91971e6i	0.0113282	−	0.00903397i	0.629138	+	0.777294i	$0.283408\pi$
$360$			1.05561e8i			0.119246i
$361$	2.74869e8	+	3.44674e8i	0.307503	+	0.385597i
$362$	−7.51399e8	+	1.71502e8i	−0.832512	+	0.190016i
$363$	−5.29111e8	+	1.20766e8i	−0.580596	+	0.132517i
$364$	−2.07447e8	−	2.60130e8i	−0.225451	−	0.282707i
$365$			1.82212e8i			0.196134i
$366$	−7.87557e8	+	6.28056e8i	−0.839650	+	0.669598i
$367$	2.81125e8	−	5.83762e8i	0.296871	−	0.616459i	−0.698169	−	0.715933i	$-0.746002\pi$
$367$	2.81125e8	−	5.83762e8i	0.296871	−	0.616459i	0.995040	+	0.0994738i	$0.0317159\pi$
$368$	−2.76329e6	+	3.46506e6i	−0.00289041	+	0.00362446i
$369$	−2.72327e8	−	2.17174e8i	−0.282162	−	0.225017i
$370$	−1.61629e7	+	7.78366e6i	−0.0165888	+	0.00798873i
$371$	1.10373e8	+	4.83574e8i	0.112215	+	0.491648i
$372$	−4.18956e7	+	1.83557e8i	−0.0421957	+	0.184871i
$373$	1.54870e9	+	7.45816e8i	1.54521	+	0.744133i	0.995812	−	0.0914286i	$-0.0291433\pi$
$373$	1.54870e9	+	7.45816e8i	1.54521	+	0.744133i	0.549397	+	0.835562i	$0.314858\pi$
$374$	2.99659e8	+	6.22249e8i	0.296195	+	0.615055i
$375$	−3.66886e8	−	8.37393e7i	−0.359271	−	0.0820011i
$376$	−1.21627e9			−1.17997
$377$	1.51199e9	+	5.92977e8i	1.45330	+	0.569958i
$378$	7.95257e8			0.757331
$379$	4.87295e8	+	1.11222e8i	0.459785	+	0.104943i	0.446138	−	0.894964i	$-0.352799\pi$
$379$	4.87295e8	+	1.11222e8i	0.459785	+	0.104943i	0.0136466	+	0.999907i	$0.495656\pi$
$380$	−2.34046e7	−	4.86001e7i	−0.0218806	−	0.0454355i
$381$	−2.64563e7	−	1.27407e7i	−0.0245071	−	0.0118020i
$382$	−2.12750e8	+	9.32119e8i	−0.195276	+	0.855558i
$383$	−2.91932e8	−	1.27904e9i	−0.265513	−	1.16329i	−0.915172	−	0.403063i	$-0.867946\pi$
$383$	−2.91932e8	−	1.27904e9i	−0.265513	−	1.16329i	0.649659	−	0.760226i	$-0.274912\pi$
$384$	2.95409e8	−	1.42262e8i	0.266235	−	0.128212i
$385$	−8.36581e7	−	6.67151e7i	−0.0747128	−	0.0595815i
$386$	1.55510e8	−	1.95004e8i	0.137627	−	0.172579i
$387$	2.25702e8	−	4.68675e8i	0.197946	−	0.411039i
$388$	−1.74758e8	+	1.39365e8i	−0.151889	+	0.121128i
$389$			1.09872e8i			0.0946372i	0.998880	+	0.0473186i	$0.0150676\pi$
$389$			1.09872e8i			0.0946372i	−0.998880	+	0.0473186i	$0.984932\pi$
$390$	−1.84159e8	−	2.30928e8i	−0.157205	−	0.197129i
$391$	−1.46716e7	+	3.34870e6i	−0.0124125	+	0.00283307i
$392$	−3.98549e8	+	9.09661e7i	−0.334180	+	0.0762743i
$393$	−7.10729e8	−	8.91226e8i	−0.590650	−	0.740651i
$394$		−	2.92554e8i		−	0.240973i
$395$	−3.25141e8	+	2.59291e8i	−0.265449	+	0.211689i
$396$	−2.97442e7	+	6.17645e7i	−0.0240696	+	0.0499811i
$397$	−1.28753e9	+	1.61451e9i	−1.03274	+	1.29502i	−0.0781994	+	0.996938i	$0.524917\pi$
$397$	−1.28753e9	+	1.61451e9i	−1.03274	+	1.29502i	−0.954541	+	0.298078i	$0.903654\pi$
$398$	1.05945e8	+	8.44881e7i	0.0842342	+	0.0671746i
$399$	−5.06542e8	+	2.43938e8i	−0.399218	+	0.192253i
$400$	−1.71051e8	−	7.49424e8i	−0.133634	−	0.585487i
$401$	2.44497e8	−	1.07121e9i	0.189352	−	0.829603i	−0.787608	−	0.616177i	$-0.788681\pi$
$401$	2.44497e8	−	1.07121e9i	0.189352	−	0.829603i	0.976959	−	0.213426i	$-0.0684623\pi$
$402$	1.90364e8	+	9.16743e7i	0.146148	+	0.0703812i
$403$	8.01107e8	+	1.66352e9i	0.609709	+	1.26607i
$404$	1.40416e8	+	3.20491e7i	0.105945	+	0.0241813i
$405$	−1.27758e8			−0.0955646
$406$	−6.93745e8	+	6.44025e8i	−0.514468	+	0.477597i
$407$	−5.32599e7			−0.0391579
$408$	1.92581e9	+	4.39554e8i	1.40379	+	0.320407i
$409$	−5.85974e8	−	1.21679e9i	−0.423494	−	0.879394i	−0.998138	−	0.0609908i	$-0.980574\pi$
$409$	−5.85974e8	−	1.21679e9i	−0.423494	−	0.879394i	0.574645	−	0.818403i	$-0.305140\pi$
$410$	−2.24482e8	−	1.08105e8i	−0.160857	−	0.0774644i
$411$	−3.24491e8	+	1.42169e9i	−0.230546	+	1.01009i
$412$	1.57105e7	+	6.88323e7i	0.0110675	+	0.0484900i
$413$	6.17227e8	−	2.97241e8i	0.431141	−	0.207627i
$414$	3.00321e6	+	2.39498e6i	0.00208010	+	0.00165883i
$415$	1.41969e8	−	1.78023e8i	0.0975046	−	0.122267i
$416$	−5.38727e8	+	1.11868e9i	−0.366895	+	0.761866i
$417$	−1.07549e9	+	8.57678e8i	−0.726327	+	0.579226i
$418$			4.11823e8i			0.275799i
$419$	−4.14458e8	−	5.19714e8i	−0.275253	−	0.345156i	0.624920	−	0.780689i	$-0.285132\pi$
$419$	−4.14458e8	−	5.19714e8i	−0.275253	−	0.345156i	−0.900173	+	0.435532i	$0.856560\pi$
$420$	−6.52667e7	+	1.48967e7i	−0.0429852	+	0.00981110i
$421$	−2.33327e7	+	5.32555e6i	−0.0152398	+	0.00347838i	−0.230134	−	0.973159i	$-0.573916\pi$
$421$	−2.33327e7	+	5.32555e6i	−0.0152398	+	0.00347838i	0.214894	+	0.976637i	$0.431059\pi$
$422$	−7.18228e8	−	9.00630e8i	−0.465231	−	0.583382i
$423$			7.33893e8i			0.471456i
$424$	8.12447e8	−	6.47905e8i	0.517624	−	0.412792i
$425$	1.13250e9	−	2.35165e9i	0.715608	−	1.48598i
$426$	−6.35109e8	+	7.96402e8i	−0.398029	+	0.499113i
$427$	1.75048e9	+	1.39596e9i	1.08808	+	0.867714i
$428$	−6.11434e8	+	2.94451e8i	−0.376961	+	0.181535i
$429$	−1.95130e8	−	8.54919e8i	−0.119323	−	0.522787i
$430$	8.27994e7	−	3.62768e8i	0.0502213	−	0.220034i
$431$	9.58454e8	+	4.61567e8i	0.576635	+	0.277693i	0.699385	−	0.714745i	$-0.253457\pi$
$431$	9.58454e8	+	4.61567e8i	0.576635	+	0.277693i	−0.122751	+	0.992438i	$0.539171\pi$
$432$	−5.03270e8	−	1.04505e9i	−0.300336	−	0.623654i
$433$	2.70320e9	+	6.16988e8i	1.60019	+	0.365232i	0.927243	−	0.374461i	$-0.122172\pi$
$433$	2.70320e9	+	6.16988e8i	1.60019	+	0.365232i	0.672944	+	0.739693i	$0.265029\pi$
$434$	−1.07613e9			−0.631906
$435$	2.39492e8	−	2.22328e8i	0.139502	−	0.129504i
$436$	4.12457e8			0.238328
$437$	−8.74850e6	−	1.99679e6i	−0.00501474	−	0.00114458i
$438$	−3.77623e8	−	7.84143e8i	−0.214733	−	0.445898i
$439$	1.44260e9	+	6.94719e8i	0.813804	+	0.391907i	0.794016	−	0.607897i	$-0.207987\pi$
$439$	1.44260e9	+	6.94719e8i	0.813804	+	0.391907i	0.0197882	+	0.999804i	$0.493701\pi$
$440$	−4.98835e7	+	2.18554e8i	−0.0279172	+	0.122313i
$441$	5.48888e7	+	2.40483e8i	0.0304753	+	0.133521i
$442$	3.81776e9	−	1.83854e9i	2.10296	−	1.01273i
$443$	−2.49038e9	−	1.98601e9i	−1.36098	−	1.08535i	−0.987485	−	0.157713i	$-0.949588\pi$
$443$	−2.49038e9	−	1.98601e9i	−1.36098	−	1.08535i	−0.373495	−	0.927632i	$-0.621841\pi$
$444$	−2.07756e7	+	2.60518e7i	−0.0112646	+	0.0141253i
$445$	1.84960e8	−	3.84074e8i	0.0994988	−	0.206611i
$446$	−1.90797e9	+	1.52155e9i	−1.01836	+	0.812111i
$447$		−	3.95889e8i		−	0.209651i
$448$	−1.08105e9	−	1.35559e9i	−0.568031	−	0.712288i
$449$	−3.30192e9	+	7.53642e8i	−1.72149	+	0.392919i	−0.965240	−	0.261364i	$-0.915828\pi$
$449$	−3.30192e9	+	7.53642e8i	−1.72149	+	0.392919i	−0.756250	+	0.654283i	$0.772971\pi$
$450$	−6.49535e8	+	1.48252e8i	−0.336015	+	0.0766933i
$451$	−4.61202e8	−	5.78330e8i	−0.236741	−	0.296864i
$452$			4.16017e8i			0.211898i
$453$	1.74372e9	−	1.39057e9i	0.881319	−	0.702828i
$454$	−7.67032e8	+	1.59276e9i	−0.384696	+	0.798830i
$455$	−4.09325e8	+	5.13277e8i	−0.203717	+	0.255454i
$456$	9.20896e8	+	7.34390e8i	0.454814	+	0.362702i
$457$	1.00660e9	−	4.84754e8i	0.493346	−	0.237583i	−0.170632	−	0.985335i	$-0.554581\pi$
$457$	1.00660e9	−	4.84754e8i	0.493346	−	0.237583i	0.663978	+	0.747752i	$0.268867\pi$
$458$	3.54376e8	+	1.55262e9i	0.172359	+	0.755156i
$459$	8.76408e8	−	3.83979e9i	0.423021	−	1.85338i
$460$	−962686.	−	463605.i	−0.000461139	−	0.000222073i
$461$	−9.69869e8	−	2.01395e9i	−0.461063	−	0.957406i	−0.993806	−	0.111130i	$-0.964553\pi$
$461$	−9.69869e8	−	2.01395e9i	−0.461063	−	0.957406i	0.532743	−	0.846277i	$-0.321161\pi$
$462$	4.98281e8	+	1.13729e8i	0.235086	+	0.0536569i
$463$	−3.75010e9			−1.75594			−0.877970	−	0.478715i	$-0.841103\pi$
$463$	−3.75010e9			−1.75594			−0.877970	+	0.478715i	$0.841103\pi$
$464$	1.28534e9	+	5.04089e8i	0.597320	+	0.234258i
$465$	3.71500e8			0.171346
$466$	2.41485e9	+	5.51174e8i	1.10545	+	0.252312i
$467$	−1.18433e9	−	2.45928e9i	−0.538100	−	1.11738i	−0.975883	−	0.218295i	$-0.929951\pi$
$467$	−1.18433e9	−	2.45928e9i	−0.538100	−	1.11738i	0.437783	−	0.899080i	$-0.355764\pi$
$468$	3.78951e8	+	1.82493e8i	0.170892	+	0.0822974i
$469$	1.04501e8	−	4.57850e8i	0.0467753	−	0.204936i
$470$	1.16815e8	+	5.11800e8i	0.0518986	+	0.227383i
$471$	−2.77502e9	+	1.33638e9i	−1.22375	+	0.589327i
$472$	−1.12212e9	−	8.94862e8i	−0.491182	−	0.391705i
$473$	6.88772e8	−	8.63693e8i	0.299269	−	0.375271i
$474$	8.61865e8	−	1.78968e9i	0.371719	−	0.771883i
$475$	1.21684e9	−	9.70394e8i	0.520960	−	0.415452i
$476$		−	9.60408e8i		−	0.408161i
$477$	−3.90945e8	−	4.90229e8i	−0.164930	−	0.206816i
$478$	−2.22815e9	+	5.08562e8i	−0.933142	+	0.212983i
$479$	−4.52757e8	+	1.03339e8i	−0.188231	+	0.0429625i	−0.315597	−	0.948893i	$-0.602205\pi$
$479$	−4.52757e8	+	1.03339e8i	−0.188231	+	0.0429625i	0.127366	+	0.991856i	$0.459348\pi$
$480$	1.55764e8	+	1.95322e8i	0.0642868	+	0.0806131i
$481$			3.26772e8i			0.133886i
$482$	−1.25539e9	+	1.00114e9i	−0.510637	+	0.407220i
$483$	−4.83199e6	+	1.00337e7i	−0.00195124	+	0.00405180i
$484$	3.44675e8	−	4.32208e8i	0.138182	−	0.173274i
$485$	3.44825e8	+	2.74989e8i	0.137247	+	0.109451i
$486$	−1.53741e9	+	7.40377e8i	−0.607522	+	0.292567i
$487$	7.09554e8	+	3.10876e9i	0.278377	+	1.21965i	0.899845	+	0.436211i	$0.143680\pi$
$487$	7.09554e8	+	3.10876e9i	0.278377	+	1.21965i	−0.621467	+	0.783440i	$0.713463\pi$
$488$	1.04378e9	−	4.57308e9i	0.406572	−	1.78131i
$489$	1.86905e9	+	9.00085e8i	0.722834	+	0.348099i
$490$	7.65563e7	+	1.58971e8i	0.0293964	+	0.0610423i
$491$	−1.62289e9	−	3.70415e8i	−0.618735	−	0.141222i	−0.0983472	−	0.995152i	$-0.531356\pi$
$491$	−1.62289e9	−	3.70415e8i	−0.618735	−	0.141222i	−0.520388	+	0.853930i	$0.674213\pi$
$492$	−4.62793e8			−0.175190
$493$	2.34505e9	+	4.05940e9i	0.881432	+	1.52580i
$494$	2.52670e9			0.942997
$495$	1.31875e8	+	3.00996e7i	0.0488702	+	0.0111543i
$496$	6.81020e8	+	1.41415e9i	0.250596	+	0.520368i
$497$	2.03988e9	+	9.82355e8i	0.745346	+	0.358939i
$498$	−2.42015e8	+	1.06034e9i	−0.0878091	+	0.384717i
$499$	9.08221e8	+	3.97918e9i	0.327220	+	1.43364i	0.824405	+	0.566000i	$0.191510\pi$
$499$	9.08221e8	+	3.97918e9i	0.327220	+	1.43364i	−0.497185	+	0.867644i	$0.665633\pi$
$500$	3.45361e8	−	1.66317e8i	0.123560	−	0.0595035i
$501$	2.21710e9	+	1.76808e9i	0.787685	+	0.628158i
$502$	−7.65525e8	+	9.59939e8i	−0.270083	+	0.338673i
$503$	−9.29821e8	+	1.93079e9i	−0.325770	+	0.676469i	−0.997955	−	0.0639141i	$-0.979642\pi$
$503$	−9.29821e8	+	1.93079e9i	−0.325770	+	0.676469i	0.672185	+	0.740383i	$0.265356\pi$
$504$	−8.76190e8	+	6.98738e8i	−0.304854	+	0.243113i
$505$		−	2.84188e8i		−	0.0981941i
$506$	5.08612e6	+	6.37779e6i	0.00174526	+	0.00218849i
$507$	−3.09287e9	+	7.05928e8i	−1.05398	+	0.240565i
$508$	2.91607e7	−	6.65573e6i	0.00986903	−	0.00225254i
$509$	−1.98271e9	−	2.48624e9i	−0.666419	−	0.835663i	0.327606	−	0.944814i	$-0.393758\pi$
$509$	−1.98271e9	−	2.48624e9i	−0.666419	−	0.835663i	−0.994025	+	0.109151i	$0.965187\pi$
$510$		−	8.52590e8i		−	0.284606i
$511$	−1.51243e9	+	1.20612e9i	−0.501420	+	0.399869i
$512$	−1.37624e9	+	2.85778e9i	−0.453156	+	0.940988i
$513$	1.46427e9	−	1.83613e9i	0.478861	−	0.600473i
$514$	2.39018e9	+	1.90611e9i	0.776355	+	0.619123i
$515$	1.25514e8	−	6.04441e7i	0.0404916	−	0.0194997i
$516$	−1.53795e8	−	6.73820e8i	−0.0492797	−	0.215908i
$517$	−3.46807e8	+	1.51946e9i	−0.110375	+	0.483585i
$518$	−1.71595e8	−	8.26356e7i	−0.0542437	−	0.0261224i
$519$	3.70393e8	+	7.69130e8i	0.116299	+	0.241498i
$520$	1.34092e9	+	3.06056e8i	0.418207	+	0.0954530i
$521$	1.09479e9			0.339156			0.169578	−	0.985517i	$-0.445760\pi$
$521$	1.09479e9			0.339156			0.169578	+	0.985517i	$0.445760\pi$
$522$	4.36900e8	−	1.11403e9i	0.134442	−	0.342806i
$523$	3.22969e9			0.987199			0.493599	−	0.869689i	$-0.335681\pi$
$523$	3.22969e9			0.987199			0.493599	+	0.869689i	$0.335681\pi$
$524$	1.13202e9	+	2.58375e8i	0.343711	+	0.0784497i
$525$	−8.38077e8	−	1.74028e9i	−0.252770	−	0.524883i
$526$	−3.05513e9	−	1.47127e9i	−0.915333	−	0.440801i
$527$	−1.18595e9	+	5.19598e9i	−0.352963	+	1.54643i
$528$	−1.65880e8	−	7.26766e8i	−0.0490427	−	0.214870i
$529$	3.06748e9	−	1.47722e9i	0.900922	−	0.433861i
$530$	−3.50666e8	−	2.79647e8i	−0.102312	−	0.0815914i
$531$	−5.39958e8	+	6.77086e8i	−0.156505	+	0.196251i
$532$	2.48476e8	−	5.15966e8i	0.0715474	−	0.148570i
$533$	−3.54829e9	+	2.82967e9i	−1.01502	+	0.809451i
$534$			2.03616e9i			0.578652i
$535$	8.34892e8	+	1.04692e9i	0.235718	+	0.295581i
$536$	−9.59212e8	+	2.18934e8i	−0.269053	+	0.0614096i
$537$	−3.16637e9	+	7.22703e8i	−0.882371	+	0.201395i
$538$	−2.95387e9	−	3.70404e9i	−0.817813	−	1.02550i
$539$			5.23838e8i			0.144091i
$540$	2.18634e8	−	1.74355e8i	0.0597503	−	0.0476492i
$541$	2.68715e9	−	5.57992e9i	0.729628	−	1.51509i	−0.122908	−	0.992418i	$-0.539222\pi$
$541$	2.68715e9	−	5.57992e9i	0.729628	−	1.51509i	0.852535	−	0.522669i	$-0.175064\pi$
$542$	3.50134e9	−	4.39054e9i	0.944576	−	1.18446i
$543$	2.20845e9	+	1.76118e9i	0.591953	+	0.472067i
$544$	−3.22911e9	+	1.55506e9i	−0.859977	+	0.414143i
$545$	−1.81096e8	−	7.93435e8i	−0.0479206	−	0.209954i
$546$	6.97778e8	−	3.05716e9i	0.183461	−	0.803793i
$547$	4.53097e9	+	2.18200e9i	1.18368	+	0.570032i	0.918982	−	0.394299i	$-0.129013\pi$
$547$	4.53097e9	+	2.18200e9i	1.18368	+	0.570032i	0.264701	+	0.964331i	$0.414727\pi$
$548$	−6.44483e8	−	1.33828e9i	−0.167294	−	0.347389i
$549$	−2.75939e9	−	6.29813e8i	−0.711721	−	0.162446i
$550$	−1.41486e9			−0.362615
$551$	2.09602e8	+	2.78757e9i	0.0533784	+	0.709897i
$552$	2.33316e7			0.00590415
$553$	−4.30442e9	−	9.82456e8i	−1.08237	−	0.247044i
$554$	8.25143e7	+	1.71343e8i	0.0206179	+	0.0428136i
$555$	5.92373e7	+	2.85272e7i	0.0147086	+	0.00708327i
$556$	3.11797e8	−	1.36607e9i	0.0769325	−	0.337063i
$557$	−1.19400e9	−	5.23124e9i	−0.292759	−	1.28266i	−0.880668	−	0.473734i	$-0.842906\pi$
$557$	−1.19400e9	−	5.23124e9i	−0.292759	−	1.28266i	0.587909	−	0.808927i	$-0.299951\pi$
$558$	1.22567e9	−	5.90249e8i	0.298643	−	0.143819i
$559$	−5.29912e9	−	4.22591e9i	−1.28311	−	1.02324i
$560$	−3.47967e8	+	4.36336e8i	−0.0837297	+	0.104994i
$561$	1.09826e9	−	2.28055e9i	0.262623	−	0.545343i
$562$	2.89779e9	−	2.31091e9i	0.688636	−	0.549169i
$563$		−	3.57823e9i		−	0.845062i	−0.906349	−	0.422531i	$-0.861142\pi$
$563$		−	3.57823e9i		−	0.845062i	0.906349	−	0.422531i	$-0.138858\pi$
$564$	6.07955e8	+	7.62352e8i	0.142690	+	0.178928i
$565$	8.00284e8	−	1.82660e8i	0.186670	−	0.0426062i
$566$	−1.67204e8	+	3.81632e7i	−0.0387605	+	0.00884682i
$567$	−8.45673e8	−	1.06044e9i	−0.194833	−	0.244313i
$568$		−	4.74337e9i		−	1.08609i
$569$	−1.73466e9	+	1.38335e9i	−0.394749	+	0.314802i	−0.800669	−	0.599107i	$-0.795523\pi$
$569$	−1.73466e9	+	1.38335e9i	−0.394749	+	0.314802i	0.405920	+	0.913909i	$0.366951\pi$
$570$	2.20582e8	−	4.58043e8i	0.0498893	−	0.103596i
$571$	−2.91109e9	+	3.65039e9i	−0.654379	+	0.820565i	−0.992718	−	0.120459i	$-0.961563\pi$
$571$	−2.91109e9	+	3.65039e9i	−0.654379	+	0.820565i	0.338339	+	0.941024i	$0.390135\pi$
$572$	6.98347e8	+	5.56913e8i	0.156022	+	0.124423i
$573$	3.15707e9	−	1.52036e9i	0.701040	−	0.337603i
$574$	−5.88609e8	−	2.57886e9i	−0.129908	−	0.569163i
$575$	6.86020e6	−	3.00565e7i	0.00150487	−	0.00659327i
$576$	1.97479e9	+	9.51009e8i	0.430568	+	0.207351i
$577$	2.95447e9	+	6.13502e9i	0.640271	+	1.32954i	0.928270	+	0.371906i	$0.121296\pi$
$577$	2.95447e9	+	6.13502e9i	0.640271	+	1.32954i	−0.287999	+	0.957631i	$0.592990\pi$
$578$	8.08424e9	+	1.84517e9i	1.74137	+	0.397457i
$579$	−9.14125e8			−0.195718
$580$	−4.95279e7	+	3.29156e8i	−0.0105403	+	0.0700494i
$581$	2.41739e9			0.511365
$582$	−2.05384e9	−	4.68775e8i	−0.431852	−	0.0985675i
$583$	−5.77755e8	−	1.19972e9i	−0.120755	−	0.250750i
$584$	3.65143e9	+	1.75844e9i	0.758609	+	0.365327i
$585$	1.84674e8	−	8.09108e8i	0.0381381	−	0.167094i
$586$	−1.18699e9	−	5.20054e9i	−0.243672	−	1.06760i
$587$	−8.49964e8	+	4.09321e8i	−0.173447	+	0.0835278i	−0.518593	−	0.855021i	$-0.673544\pi$
$587$	−8.49964e8	+	4.09321e8i	−0.173447	+	0.0835278i	0.345145	+	0.938549i	$0.387830\pi$
$588$	2.56233e8	+	2.04339e8i	0.0519774	+	0.0414506i
$589$	−1.98144e9	+	2.48464e9i	−0.399555	+	0.501026i
$590$	−2.68781e8	+	5.58130e8i	−0.0538786	+	0.111880i
$591$	−8.38291e8	+	6.68515e8i	−0.167047	+	0.133215i
$592$			2.77788e8i			0.0550285i
$593$	−1.36331e9	−	1.70954e9i	−0.268475	−	0.336657i	0.629259	−	0.777196i	$-0.283359\pi$
$593$	−1.36331e9	−	1.70954e9i	−0.268475	−	0.336657i	−0.897733	+	0.440539i	$0.854787\pi$
$594$	−2.08142e9	+	4.75071e8i	−0.407481	+	0.0930048i
$595$	−1.84752e9	+	4.21684e8i	−0.359567	+	0.0820688i
$596$	2.51425e8	+	3.15277e8i	0.0486459	+	0.0610000i
$597$		−	4.96640e8i		−	0.0955282i
$598$	3.91304e7	−	3.12055e7i	0.00748274	−	0.00596728i
$599$	−9.44342e8	+	1.96095e9i	−0.179529	+	0.372797i	−0.971241	−	0.238098i	$-0.923476\pi$
$599$	−9.44342e8	+	1.96095e9i	−0.179529	+	0.372797i	0.791712	+	0.610895i	$0.209190\pi$
$600$	−2.52308e9	+	3.16384e9i	−0.476872	+	0.597979i
$601$	2.61723e9	+	2.08717e9i	0.491792	+	0.392191i	0.837746	−	0.546060i	$-0.183873\pi$
$601$	2.61723e9	+	2.08717e9i	0.491792	+	0.392191i	−0.345953	+	0.938252i	$0.612444\pi$
$602$	3.55918e9	−	1.71401e9i	0.664909	−	0.320203i
$603$	1.32104e8	+	5.78786e8i	0.0245361	+	0.107500i
$604$	−5.05522e8	+	2.21484e9i	−0.0933493	+	0.408990i
$605$	−9.82767e8	−	4.73276e8i	−0.180429	−	0.0868901i
$606$	5.88960e8	+	1.22299e9i	0.107506	+	0.223238i
$607$	−7.96736e9	−	1.81850e9i	−1.44595	−	0.330029i	−0.573692	−	0.819071i	$-0.694489\pi$
$607$	−7.96736e9	−	1.81850e9i	−1.44595	−	0.330029i	−0.872260	+	0.489042i	$0.837347\pi$
$608$	−2.13712e9			−0.385626
$609$	3.43068e9	+	5.16212e8i	0.615488	+	0.0926121i
$610$	−2.02458e9			−0.361144
$611$	9.32254e9	+	2.12781e9i	1.65345	+	0.377388i
$612$	5.26774e8	+	1.09386e9i	0.0928955	+	0.192899i
$613$	−1.36464e9	−	6.57175e8i	−0.239280	−	0.115231i	0.310401	−	0.950606i	$-0.399537\pi$
$613$	−1.36464e9	−	6.57175e8i	−0.239280	−	0.115231i	−0.549681	+	0.835375i	$0.685251\pi$
$614$	6.20236e7	−	2.71743e8i	0.0108135	−	0.0473772i
$615$	2.03198e8	+	8.90267e8i	0.0352254	+	0.154333i
$616$	−2.14427e9	+	1.03263e9i	−0.369613	+	0.177996i
$617$	−4.48970e9	−	3.58042e9i	−0.769520	−	0.613671i	0.158003	−	0.987439i	$-0.449494\pi$
$617$	−4.48970e9	−	3.58042e9i	−0.769520	−	0.613671i	−0.927523	+	0.373767i	$0.878066\pi$
$618$	−4.14875e8	+	5.20237e8i	−0.0707063	+	0.0886628i
$619$	−9.73531e7	+	2.02156e8i	−0.0164980	+	0.0342585i	−0.909055	−	0.416676i	$-0.863195\pi$
$619$	−9.73531e7	+	2.02156e8i	−0.0164980	+	0.0342585i	0.892557	+	0.450935i	$0.148909\pi$
$620$	−2.95854e8	+	2.35936e8i	−0.0498547	+	0.0397578i
$621$		−	4.65198e7i		−	0.00779502i
$622$	−5.49498e9	−	6.89048e9i	−0.915587	−	1.14811i
$623$	4.41226e9	−	1.00707e9i	0.731059	−	0.166860i
$624$	−4.45901e9	+	1.01774e9i	−0.734671	+	0.167684i
$625$	3.09032e9	+	3.87513e9i	0.506317	+	0.634902i
$626$			8.18179e9i			1.33302i
$627$	1.18005e9	−	9.41055e8i	0.191189	−	0.152468i
$628$	1.36124e9	−	2.82665e9i	0.219319	−	0.455421i
$629$	−5.88100e8	+	7.37455e8i	−0.0942267	+	0.118157i
$630$	3.78179e8	+	3.01587e8i	0.0602567	+	0.0480531i
$631$	3.06945e9	−	1.47817e9i	0.486360	−	0.234219i	−0.174600	−	0.984639i	$-0.555863\pi$
$631$	3.06945e9	−	1.47817e9i	0.486360	−	0.234219i	0.660961	+	0.750421i	$0.270149\pi$
$632$	2.05828e9	+	9.01791e9i	0.324336	+	1.42101i
$633$	−9.39463e8	+	4.11606e9i	−0.147220	+	0.645013i
$634$	3.53701e9	+	1.70333e9i	0.551218	+	0.265453i
$635$	−2.56070e7	−	5.31736e7i	−0.00396873	−	0.00824115i
$636$	−8.12209e8	−	1.85381e8i	−0.125190	−	0.0285737i
$637$	3.21397e9			0.492667
$638$	1.43101e9	−	2.10003e9i	0.218157	−	0.320150i
$639$	−2.86214e9			−0.433948
$640$	6.42471e8	+	1.46640e8i	0.0968776	+	0.0221117i
$641$	3.63844e8	+	7.55529e8i	0.0545647	+	0.113305i	0.926468	−	0.376373i	$-0.122829\pi$
$641$	3.63844e8	+	7.55529e8i	0.0545647	+	0.113305i	−0.871904	+	0.489678i	$0.837115\pi$
$642$	−5.76259e9	−	2.77512e9i	−0.859499	−	0.413913i
$643$	−7.66851e8	+	3.35979e9i	−0.113755	+	0.498395i	0.885664	+	0.464327i	$0.153704\pi$
$643$	−7.66851e8	+	3.35979e9i	−0.113755	+	0.498395i	−0.999419	+	0.0340687i	$0.989154\pi$
$644$	−2.52423e6	−	1.10594e7i	−0.000372416	−	0.00163166i
$645$	−1.22869e9	+	5.91705e8i	−0.180295	+	0.0868253i
$646$	5.70224e9	+	4.54738e9i	0.832207	+	0.663663i
$647$	6.10829e9	−	7.65955e9i	0.886655	−	1.11183i	−0.106417	−	0.994322i	$-0.533938\pi$
$647$	6.10829e9	−	7.65955e9i	0.886655	−	1.11183i	0.993072	−	0.117509i	$-0.0374908\pi$
$648$	−1.23293e9	+	2.56020e9i	−0.178002	+	0.369626i
$649$	−1.43790e9	+	1.14669e9i	−0.206477	+	0.164660i
$650$			8.68079e9i			1.23983i
$651$	2.45907e9	+	3.08358e9i	0.349332	+	0.438048i
$652$	−2.06010e9	+	4.70204e8i	−0.291086	+	0.0664385i
$653$	6.37334e9	−	1.45467e9i	0.895718	−	0.204442i	0.250206	−	0.968193i	$-0.419502\pi$
$653$	6.37334e9	−	1.45467e9i	0.895718	−	0.204442i	0.645511	+	0.763751i	$0.276644\pi$
$654$	2.42368e9	+	3.03920e9i	0.338808	+	0.424852i
$655$		−	2.29108e9i		−	0.318564i
$656$	−3.01640e9	+	2.40550e9i	−0.417182	+	0.332692i
$657$	1.06104e9	−	2.20327e9i	0.145966	−	0.303101i
$658$	−3.47489e9	+	4.35737e9i	−0.475499	+	0.596257i
$659$	−3.85366e9	−	3.07319e9i	−0.524535	−	0.418303i	0.325095	−	0.945681i	$-0.394604\pi$
$659$	−3.85366e9	−	3.07319e9i	−0.524535	−	0.418303i	−0.849630	+	0.527378i	$0.823175\pi$
$660$	1.61923e8	−	7.79781e7i	0.0219233	−	0.0105577i
$661$	−1.93284e9	−	8.46831e9i	−0.260309	−	1.14049i	−0.920917	−	0.389759i	$-0.872558\pi$
$661$	−1.93284e9	−	8.46831e9i	−0.260309	−	1.14049i	0.660608	−	0.750731i	$-0.270299\pi$
$662$	1.22313e9	−	5.35890e9i	0.163859	−	0.717914i
$663$	−1.39921e10	−	6.73826e9i	−1.86461	−	0.897946i
$664$	−2.19742e9	−	4.56298e9i	−0.291289	−	0.604868i
$665$	−1.10165e9	−	2.51445e8i	−0.145268	−	0.0331564i
$666$	2.40763e8			0.0315813
$667$	3.76733e7	+	4.05817e7i	0.00491579	+	0.00529530i
$668$	−2.88853e9			−0.374938
$669$	8.71979e9	+	1.99024e9i	1.12594	+	0.256988i
$670$	1.84253e8	+	3.82605e8i	0.0236675	+	0.0491460i
$671$	−5.41545e9	−	2.60794e9i	−0.692000	−	0.333250i
$672$	−5.90190e8	+	2.58579e9i	−0.0750238	+	0.328701i
$673$	−1.15271e9	−	5.05034e9i	−0.145769	−	0.638657i	−0.994033	−	0.109082i	$-0.965209\pi$
$673$	−1.15271e9	−	5.05034e9i	−0.145769	−	0.638657i	0.848263	−	0.529574i	$-0.177648\pi$
$674$	6.69520e9	−	3.22424e9i	0.842276	−	0.405619i
$675$	6.30825e9	+	5.03066e9i	0.789488	+	0.629596i
$676$	2.01477e9	−	2.52644e9i	0.250848	−	0.314554i
$677$	3.78927e9	−	7.86850e9i	0.469348	−	0.974611i	−0.523137	−	0.852248i	$-0.675239\pi$
$677$	3.78927e9	−	7.86850e9i	0.469348	−	0.974611i	0.992485	−	0.122363i	$-0.0390472\pi$
$678$	−3.06543e9	+	2.44460e9i	−0.377736	+	0.301234i
$679$			4.68241e9i			0.574018i
$680$	2.47535e9	+	3.10400e9i	0.301895	+	0.378565i
$681$	6.31667e9	−	1.44174e9i	0.766432	−	0.174933i
$682$	2.81656e9	−	6.42862e8i	0.339996	−	0.0776019i
$683$	6.70995e9	+	8.41401e9i	0.805836	+	1.01049i	0.999567	+	0.0294318i	$0.00936980\pi$
$683$	6.70995e9	+	8.41401e9i	0.805836	+	1.01049i	−0.193731	+	0.981055i	$0.562059\pi$
$684$			7.23947e8i			0.0864989i
$685$	−2.29146e9	+	1.82738e9i	−0.272392	+	0.217226i
$686$	−3.38809e9	+	7.03545e9i	−0.400702	+	0.832065i
$687$	3.63914e9	−	4.56333e9i	0.428203	−	0.536950i
$688$	−4.50478e9	−	3.59244e9i	−0.527368	−	0.420562i
$689$	−7.36079e9	+	3.54477e9i	−0.857348	+	0.412877i
$690$	−2.24086e6	−	9.81783e6i	−0.000259682	−	0.00113774i
$691$	5.24257e8	−	2.29692e9i	0.0604465	−	0.264834i	−0.935670	−	0.352876i	$-0.885204\pi$
$691$	5.24257e8	−	2.29692e9i	0.0604465	−	0.264834i	0.996117	+	0.0880421i	$0.0280610\pi$
$692$	−7.83439e8	−	3.77284e8i	−0.0898740	−	0.0432810i
$693$	6.23085e8	+	1.29385e9i	0.0711182	+	0.147678i
$694$	−6.01116e9	−	1.37201e9i	−0.682653	−	0.155811i
$695$	−2.76479e9			−0.312403
$696$	−2.14411e9	−	6.94486e9i	−0.241054	−	0.780784i
$697$	−1.31004e10			−1.46544
$698$	−4.11507e9	−	9.39237e8i	−0.458018	−	0.104540i
$699$	−3.93882e9	−	8.17905e9i	−0.436211	−	0.905801i
$700$	1.77266e9	+	8.53669e8i	0.195336	+	0.0940689i
$701$	1.59177e9	−	6.97400e9i	0.174529	−	0.764661i	−0.809568	−	0.587027i	$-0.800298\pi$
$701$	1.59177e9	−	6.97400e9i	0.174529	−	0.764661i	0.984097	−	0.177634i	$-0.0568445\pi$
$702$	2.91476e9	+	1.27704e10i	0.317997	+	1.39323i
$703$	−5.06743e8	+	2.44034e8i	−0.0550103	+	0.0264916i
$704$	3.63922e9	+	2.90218e9i	0.393101	+	0.313488i
$705$	1.19959e9	−	1.50424e9i	0.128935	−	0.161679i
$706$	1.95237e9	−	4.05415e9i	0.208808	−	0.433594i
$707$	2.35886e9	−	1.88113e9i	0.251035	−	0.200194i
$708$			1.15064e9i			0.121849i
$709$	−4.71216e8	−	5.90886e8i	−0.0496544	−	0.0622647i	0.756384	−	0.654128i	$-0.226964\pi$
$709$	−4.71216e8	−	5.90886e8i	−0.0496544	−	0.0622647i	−0.806039	+	0.591863i	$0.798393\pi$
$710$	−1.99599e9	+	4.55571e8i	−0.209293	+	0.0477697i
$711$	5.44139e9	−	1.24196e9i	0.567762	−	0.129588i
$712$	−5.91166e9	−	7.41298e9i	−0.613803	−	0.769685i
$713$			6.29503e7i			0.00650405i
$714$	7.07680e9	−	5.64356e9i	0.727601	−	0.580243i
$715$	7.64702e8	−	1.58792e9i	0.0782386	−	0.162464i
$716$	2.06264e9	−	2.58647e9i	0.210004	−	0.263337i
$717$	6.54879e9	+	5.22249e9i	0.663505	+	0.529128i
$718$	−1.09866e8	+	5.29087e7i	−0.0110771	+	0.00533447i
$719$	−4.79452e8	−	2.10062e9i	−0.0481054	−	0.210764i	0.945163	−	0.326599i	$-0.105903\pi$
$719$	−4.79452e8	−	2.10062e9i	−0.0481054	−	0.210764i	−0.993268	+	0.115835i	$0.963046\pi$
$720$	1.56991e8	−	6.87822e8i	0.0156751	−	0.0686772i
$721$	1.33252e9	+	6.41708e8i	0.132404	+	0.0637624i
$722$	−1.83630e9	−	3.81311e9i	−0.181578	−	0.377050i
$723$	5.73736e9	+	1.30952e9i	0.564583	+	0.128862i
$724$	−2.87726e9			−0.281770
$725$	−9.57702e9	+	7.20113e8i	−0.933356	+	0.0701807i
$726$	5.21012e9			0.505324
$727$	−6.97845e9	−	1.59279e9i	−0.673579	−	0.153740i	−0.127968	−	0.991778i	$-0.540845\pi$
$727$	−6.97845e9	−	1.59279e9i	−0.673579	−	0.153740i	−0.545612	+	0.838038i	$0.683703\pi$
$728$	6.33559e9	+	1.31560e10i	0.608594	+	1.26376i
$729$	9.19448e9	+	4.42783e9i	0.878984	+	0.423296i
$730$	3.89245e8	−	1.70539e9i	0.0370333	−	0.162254i
$731$	−4.35351e9	−	1.90740e10i	−0.412219	−	1.80605i
$732$	−3.38813e9	+	1.63164e9i	−0.319279	+	0.153757i
$733$	7.98924e9	+	6.37121e9i	0.749276	+	0.597528i	0.921885	−	0.387463i	$-0.126648\pi$
$733$	7.98924e9	+	6.37121e9i	0.749276	+	0.597528i	−0.172609	+	0.984990i	$0.555220\pi$
$734$	−3.87819e9	+	4.86309e9i	−0.361987	+	0.453917i
$735$	2.80580e8	−	5.82630e8i	0.0260646	−	0.0541237i
$736$	−3.30970e7	+	2.63940e7i	−0.00305997	+	0.00244024i
$737$			1.26075e9i			0.116010i
$738$	2.08488e9	+	2.61436e9i	0.190934	+	0.239424i
$739$	1.75368e10	−	4.00266e9i	1.59843	−	0.364832i	0.671780	−	0.740751i	$-0.265530\pi$
$739$	1.75368e10	−	4.00266e9i	1.59843	−	0.364832i	0.926653	+	0.375919i	$0.122673\pi$
$740$	−6.52926e7	+	1.49026e7i	−0.00592315	+	0.00135192i
$741$	−5.77377e9	−	7.24008e9i	−0.521310	−	0.653702i
$742$		−	4.76172e9i		−	0.427908i
$743$	−9.41075e9	+	7.50482e9i	−0.841712	+	0.671243i	−0.946306	−	0.323272i	$-0.895217\pi$
$743$	−9.41075e9	+	7.50482e9i	−0.841712	+	0.671243i	0.104594	+	0.994515i	$0.466646\pi$
$744$	3.58515e9	−	7.44464e9i	0.319155	−	0.662732i
$745$	4.96100e8	−	6.22090e8i	0.0439564	−	0.0551196i
$746$	−1.29016e10	−	1.02887e10i	−1.13778	−	0.907351i
$747$	−2.75329e9	+	1.32592e9i	−0.241674	+	0.116384i
$748$	5.73729e8	+	2.51367e9i	0.0501246	+	0.219610i
$749$	−3.16341e9	+	1.38598e10i	−0.275086	+	1.20523i
$750$	3.25493e9	+	1.56749e9i	0.281726	+	0.135672i
$751$	−3.84613e9	−	7.98657e9i	−0.331348	−	0.688051i	0.667027	−	0.745033i	$-0.267566\pi$
$751$	−3.84613e9	−	7.98657e9i	−0.331348	−	0.688051i	−0.998375	+	0.0569825i	$0.981852\pi$
$752$	7.92508e9	+	1.80885e9i	0.679581	+	0.155110i
$753$	4.49993e9			0.384082
$754$	−1.28846e10	−	8.77983e9i	−1.09464	−	0.745910i
$755$	4.48260e9			0.379067
$756$	2.89442e9	+	6.60631e8i	0.243632	+	0.0556074i
$757$	3.66792e9	+	7.61650e9i	0.307315	+	0.638146i	0.996235	−	0.0866910i	$-0.0276293\pi$
$757$	3.66792e9	+	7.61650e9i	0.307315	+	0.638146i	−0.688920	+	0.724837i	$0.741915\pi$
$758$	−4.32318e9	−	2.08193e9i	−0.360546	−	0.173630i
$759$	6.65279e6	−	2.91478e7i	0.000552278	−	0.00241969i
$760$	5.26786e8	+	2.30800e9i	0.0435298	+	0.190717i
$761$	−1.06480e10	+	5.12779e9i	−0.875832	+	0.421778i	−0.817100	−	0.576495i	$-0.804420\pi$
$761$	−1.06480e10	+	5.12779e9i	−0.875832	+	0.421778i	−0.0587315	+	0.998274i	$0.518706\pi$
$762$	2.20397e8	+	1.75761e8i	0.0180453	+	0.0143906i
$763$	5.38706e9	−	6.75516e9i	0.439052	−	0.550554i
$764$	−1.54865e9	+	3.21581e9i	−0.125640	+	0.260893i
$765$	1.87295e9	−	1.49362e9i	0.151255	−	0.120622i
$766$			1.25946e10i			1.01247i
$767$	7.03540e9	+	8.82211e9i	0.562995	+	0.705974i
$768$	7.07149e9	−	1.61402e9i	0.563309	−	0.128572i
$769$	−2.02242e10	+	4.61604e9i	−1.60372	+	0.366039i	−0.928429	−	0.371511i	$-0.878840\pi$
$769$	−2.02242e10	+	4.61604e9i	−1.60372	+	0.366039i	−0.675293	+	0.737550i	$0.735983\pi$
$770$	6.40468e8	+	8.03122e8i	0.0505569	+	0.0633963i
$771$		−	1.12045e10i		−	0.880448i
$772$	7.27988e8	−	5.80551e8i	0.0569460	−	0.0454130i
$773$	−1.62470e9	+	3.37372e9i	−0.126516	+	0.262712i	−0.954600	−	0.297892i	$-0.903717\pi$
$773$	−1.62470e9	+	3.37372e9i	−0.126516	+	0.262712i	0.828084	+	0.560604i	$0.189431\pi$
$774$	−3.11361e9	+	3.90435e9i	−0.241363	+	0.302660i
$775$	−8.53627e9	−	6.80745e9i	−0.658737	−	0.525326i
$776$	8.83834e9	−	4.25632e9i	0.678977	−	0.326978i
$777$	1.55325e8	+	6.80522e8i	0.0118786	+	0.0520437i
$778$	2.34709e8	−	1.02833e9i	0.0178691	−	0.0782894i
$779$	−7.03801e9	−	3.38933e9i	−0.533419	−	0.256881i
$780$	−4.78429e8	−	9.93467e8i	−0.0360982	−	0.0749588i
$781$	−5.92581e9	−	1.35253e9i	−0.445112	−	0.101594i
$782$	1.44471e8			0.0108033
$783$	−1.38470e10	+	4.27505e9i	−1.03084	+	0.318255i
$784$	2.73219e9			0.202491
$785$	−6.03525e9	−	1.37751e9i	−0.445298	−	0.101636i
$786$	4.74812e9	+	9.85957e9i	0.348773	+	0.724235i
$787$	1.85940e10	+	8.95440e9i	1.35976	+	0.654825i	0.964582	−	0.263781i	$-0.0849698\pi$
$787$	1.85940e10	+	8.95440e9i	1.35976	+	0.654825i	0.395175	+	0.918606i	$0.370684\pi$
$788$	2.43029e8	−	1.06478e9i	0.0176936	−	0.0775207i
$789$	2.76545e9	+	1.21162e10i	0.200446	+	0.878209i
$790$	3.59701e9	−	1.73223e9i	0.259566	−	0.125000i
$791$	6.81347e9	+	5.43356e9i	0.489498	+	0.390361i
$792$	1.87583e9	−	2.35222e9i	0.134170	−	0.168244i
$793$	−1.60008e10	+	3.32261e10i	−1.13943	+	2.36604i
$794$	1.54994e10	−	1.23604e10i	1.09886	−	0.876315i
$795$			1.64383e9i			0.116030i
$796$	3.15411e8	+	3.95513e8i	0.0221657	+	0.0277949i
$797$	4.04033e7	−	9.22178e6i	0.00282691	−	0.000645224i	−0.221107	−	0.975249i	$-0.570967\pi$
$797$	4.04033e7	−	9.22178e6i	0.00282691	−	0.000645224i	0.223934	+	0.974604i	$0.428110\pi$
$798$	5.26202e9	−	1.20102e9i	0.366557	−	0.0836643i
$799$	1.72095e10	+	2.15801e10i	1.19359	+	1.49671i
$800$		−	7.34232e9i		−	0.507012i
$801$	−4.47298e9	+	3.56708e9i	−0.307527	+	0.245244i
$802$	−4.57668e9	+	9.50357e9i	−0.313285	+	0.650544i
$803$	3.23796e9	−	4.06027e9i	0.220682	−	0.276726i
$804$	6.16692e8	+	4.91796e8i	0.0418478	+	0.0333725i
$805$	−2.01664e7	+	9.71164e6i	−0.00136252	+	0.000656156i
$806$	−3.94423e9	−	1.72808e10i	−0.265332	−	1.16249i
$807$	−3.86375e9	+	1.69282e10i	−0.258792	+	1.13384i
$808$	−5.69495e9	−	2.74254e9i	−0.379796	−	0.182900i
$809$	5.88276e9	+	1.22157e10i	0.390626	+	0.811144i	0.999836	+	0.0181345i	$0.00577272\pi$
$809$	5.88276e9	+	1.22157e10i	0.390626	+	0.811144i	−0.609209	+	0.793010i	$0.708513\pi$
$810$	1.19574e9	+	2.72919e8i	0.0790567	+	0.0180442i
$811$	1.52114e10			1.00137			0.500686	−	0.865629i	$-0.333081\pi$
$811$	1.52114e10			1.00137			0.500686	+	0.865629i	$0.333081\pi$
$812$	−3.05996e9	+	1.76769e9i	−0.200571	+	0.115867i
$813$	−2.05817e10			−1.34327
$814$	4.98478e8	+	1.13774e8i	0.0323937	+	0.00739366i
$815$	1.80905e9	+	3.75653e9i	0.117057	+	0.243072i
$816$	−1.18947e10	−	5.72819e9i	−0.766369	−	0.369064i
$817$	2.59594e9	−	1.13736e10i	0.166540	−	0.729658i
$818$	2.88503e9	+	1.26401e10i	0.184295	+	0.807449i
$819$	7.93830e9	−	3.82288e9i	0.504933	−	0.243163i
$820$	−7.27221e8	−	5.79940e8i	−0.0460594	−	0.0367311i
$821$	5.87087e9	−	7.36184e9i	0.370256	−	0.464286i	−0.561445	−	0.827514i	$-0.689754\pi$
$821$	5.87087e9	−	7.36184e9i	0.370256	−	0.464286i	0.931700	+	0.363229i	$0.118326\pi$
$822$	6.07407e9	−	1.26129e10i	0.381442	−	0.792072i
$823$	−7.02038e9	+	5.59856e9i	−0.438996	+	0.350088i	−0.817912	−	0.575343i	$-0.804868\pi$
$823$	−7.02038e9	+	5.59856e9i	−0.438996	+	0.350088i	0.378916	+	0.925431i	$0.376297\pi$
$824$		−	3.09853e9i		−	0.192935i
$825$	3.23310e9	+	4.05419e9i	0.200462	+	0.251371i
$826$	−6.41182e9	+	1.46346e9i	−0.395869	+	0.0903545i
$827$	1.31967e10	−	3.01205e9i	0.811326	−	0.185180i	0.203320	−	0.979112i	$-0.434827\pi$
$827$	1.31967e10	−	3.01205e9i	0.811326	−	0.185180i	0.608006	+	0.793933i	$0.291970\pi$
$828$	8.94094e6	+	1.12116e7i	0.000547365	+	0.000686374i
$829$		−	7.49870e8i		−	0.0457136i	−0.999739	−	0.0228568i	$-0.992724\pi$
$829$		−	7.49870e8i		−	0.0457136i	0.999739	−	0.0228568i	$-0.00727618\pi$
$830$	−1.70903e9	+	1.36291e9i	−0.103747	+	0.0827358i
$831$	3.02416e8	−	6.27974e8i	0.0182811	−	0.0379610i
$832$	1.78061e10	−	2.23282e10i	1.07186	−	1.34407i
$833$	7.25325e9	+	5.78427e9i	0.434785	+	0.346730i
$834$	1.18981e10	−	5.72984e9i	0.710227	−	0.342027i
$835$	1.26826e9	+	5.55662e9i	0.0753887	+	0.330300i
$836$	−3.42107e8	+	1.49887e9i	−0.0202507	+	0.0887242i
$837$	−1.48435e10	−	7.14827e9i	−0.874980	−	0.421368i
$838$	2.76885e9	+	5.74957e9i	0.162534	+	0.337506i
$839$	−3.12199e10	−	7.12575e9i	−1.82501	−	0.416547i	−0.834161	−	0.551521i	$-0.814048\pi$
$839$	−3.12199e10	−	7.12575e9i	−1.82501	−	0.416547i	−0.990849	+	0.134974i	$0.956905\pi$
$840$	2.93802e9			0.171032
$841$	8.61745e9	−	1.49432e10i	0.499566	−	0.866276i
$842$	2.29756e8			0.0132640
$843$	−1.32435e10	−	3.02274e9i	−0.761387	−	0.173782i
$844$	−1.86590e9	−	3.87458e9i	−0.106829	−	0.221833i
$845$	−5.74468e9	−	2.76649e9i	−0.327542	−	0.157736i
$846$	1.56775e9	−	6.86877e9i	0.0890187	−	0.390016i
$847$	−2.57689e9	−	1.12901e10i	−0.145715	−	0.638418i
$848$	−6.25740e9	+	3.01341e9i	−0.352378	+	0.169696i
$849$	4.91431e8	+	3.91903e8i	0.0275604	+	0.0219787i
$850$	−1.56231e10	+	1.95907e10i	−0.872569	+	1.09417i
$851$	−4.83390e6	+	1.00377e7i	−0.000268871	+	0.000558317i
$852$	−2.97313e9	+	2.37099e9i	−0.164693	+	0.131338i
$853$		−	1.89373e10i		−	1.04471i	−0.852727	−	0.522357i	$-0.825053\pi$
$853$		−	1.89373e10i		−	1.04471i	0.852727	−	0.522357i	$-0.174947\pi$
$854$	−1.34013e10	−	1.68047e10i	−0.736284	−	0.923271i
$855$	1.39264e9	−	3.17862e8i	0.0762007	−	0.0173923i
$856$	2.90368e10	−	6.62746e9i	1.58231	−	0.361151i
$857$	3.33398e9	+	4.18068e9i	0.180938	+	0.226890i	0.864026	−	0.503447i	$-0.167935\pi$
$857$	3.33398e9	+	4.18068e9i	0.180938	+	0.226890i	−0.683088	+	0.730336i	$0.739363\pi$
$858$			8.41833e9i			0.455010i
$859$	1.38660e10	−	1.10577e10i	0.746404	−	0.595237i	−0.174669	−	0.984627i	$-0.555886\pi$
$859$	1.38660e10	−	1.10577e10i	0.746404	−	0.595237i	0.921073	+	0.389390i	$0.127314\pi$
$860$	6.02713e8	−	1.25155e9i	0.0323122	−	0.0670969i
$861$	−6.04451e9	+	7.57957e9i	−0.322738	+	0.404700i
$862$	−7.98451e9	−	6.36744e9i	−0.424593	−	0.338602i
$863$	1.23092e10	−	5.92782e9i	0.651919	−	0.313948i	−0.0785332	−	0.996911i	$-0.525024\pi$
$863$	1.23092e10	−	5.92782e9i	0.651919	−	0.313948i	0.730452	+	0.682964i	$0.239309\pi$
$864$	−2.46534e9	−	1.08014e10i	−0.130041	−	0.569745i
$865$	−3.81792e8	+	1.67274e9i	−0.0200572	+	0.0878764i
$866$	−2.39822e10	−	1.15492e10i	−1.25481	−	0.604283i
$867$	−1.31861e10	−	2.73812e10i	−0.687145	−	1.42687i
$868$	−3.91670e9	−	8.93961e8i	−0.203283	−	0.0463980i
$869$	1.18528e10			0.612707
$870$	−2.71644e9	+	1.56924e9i	−0.139856	+	0.0807929i
$871$	7.73526e9			0.396653
$872$	−1.76476e10	−	4.02796e9i	−0.901320	−	0.205720i
$873$	−2.56826e9	−	5.33304e9i	−0.130644	−	0.271284i
$874$	7.76148e7	+	3.73773e7i	0.00393237	+	0.00189373i
$875$	1.78681e9	−	7.82854e9i	0.0901677	−	0.395051i
$876$	−7.22998e8	−	3.16766e9i	−0.0363390	−	0.159212i
$877$	−3.16830e9	+	1.52577e9i	−0.158609	+	0.0763820i	−0.511504	−	0.859281i	$-0.670912\pi$
$877$	−3.16830e9	+	1.52577e9i	−0.158609	+	0.0763820i	0.352895	+	0.935663i	$0.385197\pi$
$878$	−1.20177e10	−	9.58383e9i	−0.599228	−	0.477868i
$879$	−1.21894e10	+	1.52850e10i	−0.605369	+	0.759109i
$880$	6.50072e8	−	1.34989e9i	0.0321568	−	0.0667742i
$881$	1.73226e10	−	1.38143e10i	0.853489	−	0.680635i	−0.0956762	−	0.995413i	$-0.530501\pi$
$881$	1.73226e10	−	1.38143e10i	0.853489	−	0.680635i	0.949165	+	0.314778i	$0.101930\pi$
$882$		−	2.36803e9i		−	0.116211i
$883$	8.11227e9	+	1.01725e10i	0.396534	+	0.497237i	0.939515	−	0.342507i	$-0.111276\pi$
$883$	8.11227e9	+	1.01725e10i	0.396534	+	0.497237i	−0.542982	+	0.839745i	$0.682705\pi$
$884$	1.54224e10	−	3.52007e9i	0.750878	−	0.171383i
$885$	2.21347e9	−	5.05210e8i	0.107343	−	0.0245002i
$886$	1.90658e10	+	2.39077e10i	0.920952	+	1.15484i
$887$			1.57895e10i			0.759690i	0.925050	+	0.379845i	$0.124023\pi$
$887$			1.57895e10i			0.759690i	−0.925050	+	0.379845i	$0.875977\pi$
$888$	1.14334e9	−	9.11780e8i	0.0547934	−	0.0436963i
$889$	2.71858e8	−	5.64520e8i	0.0129774	−	0.0269478i
$890$	−2.55157e9	+	3.19957e9i	−0.121323	+	0.152134i
$891$	2.84686e9	+	2.27030e9i	0.134832	+	0.107525i
$892$	−8.20822e9	+	3.95287e9i	−0.387233	+	0.186481i
$893$	3.66240e9	+	1.60460e10i	0.172102	+	0.754028i
$894$	−8.45703e8	+	3.70527e9i	−0.0395855	+	0.173436i
$895$	−5.88119e9	−	2.83223e9i	−0.274211	−	0.132053i
$896$	3.03555e9	+	6.30339e9i	0.140981	+	0.292750i
$897$	−1.78834e8	−	4.08176e7i	−0.00827325	−	0.00188831i
$898$	3.25138e10			1.49831
$899$	1.87377e10	−	5.78496e9i	0.860117	−	0.265547i
$900$	−2.48720e9			−0.113727
$901$	−2.29914e10	−	5.24763e9i	−1.04720	−	0.239016i
$902$	3.08113e9	+	6.39802e9i	0.139793	+	0.290284i
$903$	−1.30444e10	−	6.28187e9i	−0.589547	−	0.283911i
$904$	4.06272e9	−	1.78000e10i	0.182906	−	0.801363i
$905$	1.26331e9	+	5.53494e9i	0.0566554	+	0.248223i
$906$	−1.92907e10	+	9.28990e9i	−0.861784	+	0.415013i
$907$	1.44654e10	+	1.15358e10i	0.643734	+	0.513361i	0.890070	−	0.455824i	$-0.150655\pi$
$907$	1.44654e10	+	1.15358e10i	0.643734	+	0.513361i	−0.246336	+	0.969184i	$0.579227\pi$
$908$	−4.11482e9	+	5.15982e9i	−0.182411	+	0.228736i
$909$	−1.65485e9	+	3.43632e9i	−0.0730776	+	0.151747i
$910$	4.92749e9	−	3.92954e9i	0.216761	−	0.172861i
$911$		−	1.36590e10i		−	0.598557i	−0.954166	−	0.299278i	$-0.903254\pi$
$911$		−	1.36590e10i		−	0.598557i	0.954166	−	0.299278i	$-0.0967459\pi$
$912$	−4.90828e9	−	6.15478e9i	−0.214263	−	0.268677i
$913$	−6.32703e9	+	1.44410e9i	−0.275139	+	0.0627987i
$914$	−1.04567e10	+	2.38667e9i	−0.452984	+	0.103391i
$915$	4.62637e9	+	5.80128e9i	0.199649	+	0.250351i
$916$			5.94531e9i			0.255588i
$917$	1.90168e10	−	1.51654e10i	0.814414	−	0.649473i
$918$	−1.64052e10	+	3.40658e10i	−0.699896	+	1.45335i
$919$	1.21451e9	−	1.52294e9i	0.0516173	−	0.0647261i	−0.755353	−	0.655318i	$-0.772534\pi$
$919$	1.21451e9	−	1.52294e9i	0.0516173	−	0.0647261i	0.806970	+	0.590592i	$0.201106\pi$
$920$	3.66626e7	+	2.92375e7i	0.00155227	+	0.00123789i
$921$	−9.20389e8	+	4.43236e8i	−0.0388206	+	0.0186950i
$922$	4.77512e9	+	2.09212e10i	0.200644	+	0.879079i
$923$	−8.29832e9	+	3.63573e10i	−0.347364	+	1.52190i
$924$	1.71907e9	+	8.27859e8i	0.0716871	+	0.0345227i
$925$	−8.38409e8	−	1.74097e9i	−0.0348305	−	0.0723263i
$926$	3.50986e10	+	8.01102e9i	1.45262	+	0.331550i
$927$	−1.86965e9			−0.0770869
$928$	1.08979e10	+	7.42609e9i	0.447638	+	0.305030i
$929$	−4.31518e10			−1.76581			−0.882905	−	0.469552i	$-0.844415\pi$
$929$	−4.31518e10			−1.76581			−0.882905	+	0.469552i	$0.844415\pi$
$930$	−3.47700e9	−	7.93603e8i	−0.141747	−	0.0323529i
$931$	2.40020e9	+	4.98408e9i	0.0974820	+	0.202423i
$932$	8.33122e9	+	4.01210e9i	0.337096	+	0.162337i
$933$	−7.18758e9	+	3.14909e10i	−0.289732	+	1.26940i
$934$	5.83100e9	+	2.55473e10i	0.234169	+	1.02596i
$935$	4.58360e9	−	2.20734e9i	0.183386	−	0.0883140i
$936$	−1.44319e10	−	1.15090e10i	−0.575250	−	0.458747i
$937$	1.29681e10	−	1.62615e10i	0.514979	−	0.645763i	−0.454556	−	0.890718i	$-0.650202\pi$
$937$	1.29681e10	−	1.62615e10i	0.514979	−	0.645763i	0.969534	+	0.244956i	$0.0787734\pi$
$938$	−1.95613e9	+	4.06194e9i	−0.0773905	+	0.160703i
$939$	2.34443e10	−	1.86962e10i	0.924076	−	0.736926i
$940$			1.95979e9i			0.0769593i
$941$	1.18790e10	+	1.48957e10i	0.464745	+	0.582772i	0.957876	−	0.287184i	$-0.0927190\pi$
$941$	1.18790e10	+	1.48957e10i	0.464745	+	0.582772i	−0.493131	+	0.869955i	$0.664148\pi$
$942$	2.88272e10	−	6.57962e9i	1.12363	−	0.256462i
$943$	−1.50855e8	+	3.44316e7i	−0.00585826	+	0.00133711i
$944$	5.98079e9	+	7.49967e9i	0.231396	+	0.290162i
$945$		−	5.85800e9i		−	0.225807i
$946$	−8.29150e9	+	6.61225e9i	−0.318430	+	0.253940i
$947$	3.74198e9	−	7.77030e9i	0.143178	−	0.297312i	−0.817031	−	0.576593i	$-0.804382\pi$
$947$	3.74198e9	−	7.77030e9i	0.143178	−	0.297312i	0.960209	+	0.279281i	$0.0900961\pi$
$948$	4.62356e9	−	5.79776e9i	0.176257	−	0.221020i
$949$	−2.49114e10	−	1.98662e10i	−0.946166	−	0.754542i
$950$	−1.34618e10	+	6.48285e9i	−0.509413	+	0.245320i
$951$	−3.20164e9	−	1.40273e10i	−0.120709	−	0.528862i
$952$	−9.37913e9	+	4.10927e10i	−0.352317	+	1.54360i
$953$	2.49999e10	+	1.20393e10i	0.935650	+	0.450585i	0.838633	−	0.544698i	$-0.183356\pi$
$953$	2.49999e10	+	1.20393e10i	0.935650	+	0.450585i	0.0970172	+	0.995283i	$0.469070\pi$
$954$	2.61176e9	+	5.42337e9i	0.0973899	+	0.202232i
$955$	6.86615e9	+	1.56715e9i	0.255095	+	0.0582237i
$956$	−8.53206e9			−0.315828
$957$	−9.28747e9	+	6.98342e8i	−0.342536	+	0.0257559i
$958$	4.45827e9			0.163828
$959$	−3.03358e10	−	6.92394e9i	−1.11068	−	0.253506i
$960$	−2.49319e9	−	5.17715e9i	−0.0909506	−	0.188861i
$961$	−4.70186e9	−	2.26430e9i	−0.170898	−	0.0823003i
$962$	6.98054e8	−	3.05837e9i	0.0252799	−	0.110759i
$963$	−3.99899e9	−	1.75207e10i	−0.144298	−	0.632209i
$964$	−5.40076e9	+	2.60087e9i	−0.194171	+	0.0935081i
$965$	−1.43643e9	−	1.14552e9i	−0.0514564	−	0.0410351i
$966$	6.66586e7	−	8.35872e7i	0.00237923	−	0.00298346i
$967$	−4.08989e9	+	8.49275e9i	−0.145452	+	0.302034i	−0.960948	−	0.276728i	$-0.910750\pi$
$967$	−4.08989e9	+	8.49275e9i	−0.145452	+	0.302034i	0.815496	+	0.578762i	$0.196464\pi$
$968$	−1.89683e10	+	1.51267e10i	−0.672149	+	0.536021i
$969$		−	2.67305e10i		−	0.943788i
$970$	−2.63991e9	−	3.31034e9i	−0.0928727	−	0.116459i
$971$	1.28765e10	−	2.93898e9i	0.451368	−	0.103022i	0.00920715	−	0.999958i	$-0.497069\pi$
$971$	1.28765e10	−	2.93898e9i	0.451368	−	0.103022i	0.442161	+	0.896936i	$0.354212\pi$
$972$	−6.21059e9	+	1.41753e9i	−0.216921	+	0.0495108i
$973$	−1.83010e10	−	2.29487e10i	−0.636912	−	0.798662i
$974$		−	3.06117e10i		−	1.06153i
$975$	2.48741e10	−	1.98365e10i	0.859472	−	0.685406i
$976$	−1.36023e10	+	2.82455e10i	−0.468315	+	0.972466i
$977$	−7.97665e9	+	1.00024e10i	−0.273646	+	0.343141i	−0.899597	−	0.436721i	$-0.856140\pi$
$977$	−7.97665e9	+	1.00024e10i	−0.273646	+	0.343141i	0.625951	+	0.779863i	$0.284711\pi$
$978$	−1.55703e10	−	1.24169e10i	−0.532244	−	0.424451i
$979$	−1.09466e10	+	5.27159e9i	−0.372854	+	0.179557i
$980$	1.46575e8	+	6.42186e8i	0.00497471	+	0.0217957i
$981$	−2.43046e9	+	1.06486e10i	−0.0821954	+	0.360121i
$982$	1.43980e10	+	6.93370e9i	0.485189	+	0.233655i
$983$	1.01318e10	+	2.10389e10i	0.340212	+	0.706458i	0.998945	−	0.0459187i	$-0.0146215\pi$
$983$	1.01318e10	+	2.10389e10i	0.340212	+	0.706458i	−0.658733	+	0.752377i	$0.728907\pi$
$984$	1.98014e10	+	4.51954e9i	0.662541	+	0.151221i
$985$	−2.15500e9			−0.0718491
$986$	−1.32765e10	−	4.30030e10i	−0.441076	−	1.42866i
$987$	2.04262e10			0.676202
$988$	9.19619e9	+	2.09897e9i	0.303360	+	0.0692400i
$989$	−1.00264e8	−	2.08200e8i	−0.00329577	−	0.00684374i
$990$	−1.16997e9	−	5.63426e8i	−0.0383222	−	0.0184550i
$991$	4.38896e9	−	1.92293e10i	0.143253	−	0.627632i	−0.851414	−	0.524494i	$-0.824255\pi$
$991$	4.38896e9	−	1.92293e10i	0.143253	−	0.627632i	0.994667	−	0.103138i	$-0.0328883\pi$
$992$	3.33608e9	+	1.46163e10i	0.108504	+	0.475387i
$993$	−1.81505e10	+	8.74082e9i	−0.588256	+	0.283289i
$994$	−1.69935e10	−	1.35518e10i	−0.548820	−	0.437669i
$995$	6.22354e8	−	7.80408e8i	0.0200289	−	0.0251154i
$996$	−1.76167e9	+	3.65816e9i	−0.0564960	+	0.117315i
$997$	2.99884e10	−	2.39150e10i	0.958343	−	0.764253i	−0.0134936	−	0.999909i	$-0.504295\pi$
$997$	2.99884e10	−	2.39150e10i	0.958343	−	0.764253i	0.971837	+	0.235656i	$0.0757239\pi$
$998$		−	3.91827e10i		−	1.24778i
$999$	−1.81796e9	−	2.27965e9i	−0.0576906	−	0.0723417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.e.a.4.5	✓	96
29.22	even	14	inner	29.8.e.a.22.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.e.a.4.5	✓	96	1.1	even	1	trivial
29.8.e.a.22.5	yes	96	29.22	even	14	inner

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.35936 - 2.13621i) q^{2} +(15.2659 + 31.7000i) q^{3} +(-32.2898 - 15.5499i) q^{4} +(-15.7357 + 68.9427i) q^{5} +(-75.1613 - 329.303i) q^{6} +(-676.409 + 325.741i) q^{7} +(1229.71 + 980.664i) q^{8} +(591.731 - 742.007i) q^{9} +O(q^{10})\)	\(q+(-9.35936 - 2.13621i) q^{2} +(15.2659 + 31.7000i) q^{3} +(-32.2898 - 15.5499i) q^{4} +(-15.7357 + 68.9427i) q^{5} +(-75.1613 - 329.303i) q^{6} +(-676.409 + 325.741i) q^{7} +(1229.71 + 980.664i) q^{8} +(591.731 - 742.007i) q^{9} +(294.553 - 611.645i) q^{10} +(1575.77 - 1256.63i) q^{11} -1260.97i q^{12} +(-7709.98 - 9668.00i) q^{13} +(7026.61 - 1603.78i) q^{14} +(-2425.70 + 553.651i) q^{15} +(-6554.24 - 8218.76i) q^{16} -35694.5i q^{17} +(-7123.31 + 5680.65i) q^{18} +(9234.86 - 19176.4i) q^{19} +(1580.16 - 1981.45i) q^{20} +(-20652.0 - 16469.4i) q^{21} +(-17432.6 + 8395.11i) q^{22} +(-93.8156 - 411.033i) q^{23} +(-12314.3 + 53952.6i) q^{24} +(65882.7 + 31727.4i) q^{25} +(51507.5 + 106957. i) q^{26} +(107574. + 24553.0i) q^{27} +26906.3 q^{28} +(-113726. + 65697.9i) q^{29} +23885.8 q^{30} +(-145568. - 33224.9i) q^{31} +(-43565.8 - 90465.2i) q^{32} +(63890.8 + 30768.2i) q^{33} +(-76251.1 + 334078. i) q^{34} +(-11813.7 - 51759.2i) q^{35} +(-30645.0 + 14757.9i) q^{36} +(-20660.2 - 16475.9i) q^{37} +(-127397. + 159751. i) q^{38} +(188776. - 391997. i) q^{39} +(-86960.1 + 69348.3i) q^{40} -367014. i q^{41} +(158107. + 198260. i) q^{42} +(534367. - 121966. i) q^{43} +(-70421.8 + 16073.3i) q^{44} +(41844.7 + 52471.5i) q^{45} +4047.42i q^{46} +(-604576. + 482133. i) q^{47} +(160478. - 333236. i) q^{48} +(-162049. + 203203. i) q^{49} +(-548844. - 437688. i) q^{50} +(1.13152e6 - 544909. i) q^{51} +(98616.5 + 432067. i) q^{52} +(147015. - 644115. i) q^{53} +(-954372. - 459601. i) q^{54} +(61839.9 + 128412. i) q^{55} +(-1.15123e6 - 262761. i) q^{56} +748870. q^{57} +(1.20475e6 - 371947. i) q^{58} -912506. q^{59} +(86934.6 + 19842.3i) q^{60} +(-1.29395e6 - 2.68692e6i) q^{61} +(1.29145e6 + 621929. i) q^{62} +(-158550. + 694651. i) q^{63} +(513910. + 2.25159e6i) q^{64} +(787860. - 379414. i) q^{65} +(-532250. - 424455. i) q^{66} +(-390014. + 489062. i) q^{67} +(-555047. + 1.15257e6i) q^{68} +(11597.6 - 9248.74i) q^{69} +509670. i q^{70} +(-1.88029e6 - 2.35781e6i) q^{71} +(1.45532e6 - 332167. i) q^{72} +(2.51209e6 - 573368. i) q^{73} +(158170. + 198339. i) q^{74} +2.57283e6i q^{75} +(-596383. + 475599. i) q^{76} +(-656526. + 1.36329e6i) q^{77} +(-2.60421e6 + 3.26558e6i) q^{78} +(4.59786e6 + 3.66667e6i) q^{79} +(669759. - 322539. i) q^{80} +(402017. + 1.76135e6i) q^{81} +(-784021. + 3.43502e6i) q^{82} +(-2.90107e6 - 1.39708e6i) q^{83} +(410750. + 852930. i) q^{84} +(2.46088e6 + 561679. i) q^{85} -5.26188e6 q^{86} +(-3.81876e6 - 2.60218e6i) q^{87} +3.17008e6 q^{88} +(-5.87708e6 - 1.34140e6i) q^{89} +(-279549. - 580489. i) q^{90} +(8.36436e6 + 4.02806e6i) q^{91} +(-3362.25 + 14731.0i) q^{92} +(-1.16900e6 - 5.12171e6i) q^{93} +(6.68839e6 - 3.22096e6i) q^{94} +(1.17675e6 + 938431. i) q^{95} +(2.20268e6 - 2.76207e6i) q^{96} +(2.70610e6 - 5.61927e6i) q^{97} +(1.95076e6 - 1.55568e6i) q^{98} -1.91282e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9}+O(q^{10}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9} - 7 q^{10} + 4207 q^{11} + 377 q^{13} - 7 q^{14} - 74473 q^{15} - 125851 q^{16} - 194880 q^{18} - 7 q^{19} + 162901 q^{20} + 86933 q^{21} + 252614 q^{22} + 238675 q^{23} - 490819 q^{24} - 107349 q^{25} + 367017 q^{26} + 75593 q^{27} + 1397540 q^{28} + 379863 q^{29} - 175646 q^{30} - 143885 q^{31} + 473172 q^{32} - 1419437 q^{33} - 2314463 q^{34} - 1018325 q^{35} + 1720462 q^{36} + 662991 q^{37} - 2763860 q^{38} + 42189 q^{39} + 580601 q^{40} - 3296492 q^{42} - 1587425 q^{43} + 2344398 q^{44} + 6508254 q^{45} + 526673 q^{47} + 6175806 q^{48} - 1391517 q^{49} - 4194526 q^{50} - 68204 q^{51} - 7720808 q^{52} + 1762640 q^{53} - 2032428 q^{54} + 2655709 q^{55} + 17091081 q^{56} + 4906842 q^{57} + 13231229 q^{58} - 8638324 q^{59} - 9957136 q^{60} + 2797697 q^{61} - 884069 q^{62} - 20232301 q^{63} - 17528026 q^{64} - 7454088 q^{65} - 17541475 q^{66} - 4890949 q^{67} + 22029140 q^{68} + 13204429 q^{69} - 1091301 q^{71} + 25137595 q^{72} + 14363636 q^{73} + 3185328 q^{74} - 41019881 q^{76} - 25204627 q^{77} - 15753743 q^{78} + 31186057 q^{79} + 24146022 q^{80} - 29435757 q^{81} - 51438506 q^{82} - 8367235 q^{83} + 78906093 q^{84} + 41540198 q^{85} + 65794492 q^{86} + 11089375 q^{87} + 39260390 q^{88} + 6628699 q^{89} + 32127214 q^{90} + 24315293 q^{91} - 39469980 q^{92} - 31050649 q^{93} - 102445588 q^{94} - 75684679 q^{95} - 95069050 q^{96} + 38131380 q^{97} + 19581828 q^{98}+O(q^{100}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9 - 7 * q^10 + 4207 * q^11 + 377 * q^13 - 7 * q^14 - 74473 * q^15 - 125851 * q^16 - 194880 * q^18 - 7 * q^19 + 162901 * q^20 + 86933 * q^21 + 252614 * q^22 + 238675 * q^23 - 490819 * q^24 - 107349 * q^25 + 367017 * q^26 + 75593 * q^27 + 1397540 * q^28 + 379863 * q^29 - 175646 * q^30 - 143885 * q^31 + 473172 * q^32 - 1419437 * q^33 - 2314463 * q^34 - 1018325 * q^35 + 1720462 * q^36 + 662991 * q^37 - 2763860 * q^38 + 42189 * q^39 + 580601 * q^40 - 3296492 * q^42 - 1587425 * q^43 + 2344398 * q^44 + 6508254 * q^45 + 526673 * q^47 + 6175806 * q^48 - 1391517 * q^49 - 4194526 * q^50 - 68204 * q^51 - 7720808 * q^52 + 1762640 * q^53 - 2032428 * q^54 + 2655709 * q^55 + 17091081 * q^56 + 4906842 * q^57 + 13231229 * q^58 - 8638324 * q^59 - 9957136 * q^60 + 2797697 * q^61 - 884069 * q^62 - 20232301 * q^63 - 17528026 * q^64 - 7454088 * q^65 - 17541475 * q^66 - 4890949 * q^67 + 22029140 * q^68 + 13204429 * q^69 - 1091301 * q^71 + 25137595 * q^72 + 14363636 * q^73 + 3185328 * q^74 - 41019881 * q^76 - 25204627 * q^77 - 15753743 * q^78 + 31186057 * q^79 + 24146022 * q^80 - 29435757 * q^81 - 51438506 * q^82 - 8367235 * q^83 + 78906093 * q^84 + 41540198 * q^85 + 65794492 * q^86 + 11089375 * q^87 + 39260390 * q^88 + 6628699 * q^89 + 32127214 * q^90 + 24315293 * q^91 - 39469980 * q^92 - 31050649 * q^93 - 102445588 * q^94 - 75684679 * q^95 - 95069050 * q^96 + 38131380 * q^97 + 19581828 * q^98

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