LMFDB - Embedded newform 38.8.e.a.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	38.23
Dual form			38.8.e.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.51754 - 2.73616i) q^{2} +(11.5048 + 65.2472i) q^{3} +(49.0268 + 41.1384i) q^{4} +(158.287 - 132.818i) q^{5} +(92.0387 - 521.978i) q^{6} +(668.912 - 1158.59i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2069.73 + 753.319i) q^{9} +O(q^{10})$	\(q+(-7.51754 - 2.73616i) q^{2} +(11.5048 + 65.2472i) q^{3} +(49.0268 + 41.1384i) q^{4} +(158.287 - 132.818i) q^{5} +(92.0387 - 521.978i) q^{6} +(668.912 - 1158.59i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2069.73 + 753.319i) q^{9} +(-1553.34 + 565.369i) q^{10} +(3797.30 + 6577.12i) q^{11} +(-2120.12 + 3672.16i) q^{12} +(1974.16 - 11196.0i) q^{13} +(-8198.66 + 6879.49i) q^{14} +(10487.1 + 8799.71i) q^{15} +(711.263 + 4033.77i) q^{16} +(1875.53 + 682.637i) q^{17} +17620.5 q^{18} +(23749.0 + 18161.9i) q^{19} +13224.2 q^{20} +(83290.5 + 30315.2i) q^{21} +(-10550.3 - 59833.8i) q^{22} +(-5803.54 - 4869.75i) q^{23} +(25985.7 - 21804.6i) q^{24} +(-6152.29 + 34891.4i) q^{25} +(-45474.8 + 78764.7i) q^{26} +(-515.392 - 892.685i) q^{27} +(80457.2 - 29284.0i) q^{28} +(185378. - 67472.0i) q^{29} +(-54759.7 - 94846.5i) q^{30} +(-122615. + 212375. i) q^{31} +(5690.10 - 32270.2i) q^{32} +(-385451. + 323432. i) q^{33} +(-12231.6 - 10263.5i) q^{34} +(-48002.0 - 272233. i) q^{35} +(-132463. - 48212.4i) q^{36} -431556. q^{37} +(-128840. - 201514. i) q^{38} +753219. q^{39} +(-99413.7 - 36183.6i) q^{40} +(-34114.5 - 193473. i) q^{41} +(-543192. - 455792. i) q^{42} +(265254. - 222574. i) q^{43} +(-84402.5 + 478670. i) q^{44} +(-227556. + 394138. i) q^{45} +(30304.0 + 52488.0i) q^{46} +(783011. - 284993. i) q^{47} +(-255009. + 92815.8i) q^{48} +(-483115. - 836780. i) q^{49} +(141719. - 245464. i) q^{50} +(-22962.5 + 130227. i) q^{51} +(557372. - 467691. i) q^{52} +(-34895.4 - 29280.7i) q^{53} +(1431.95 + 8120.99i) q^{54} +(1.47462e6 + 536719. i) q^{55} -684966. q^{56} +(-911786. + 1.75851e6i) q^{57} -1.57820e6 q^{58} +(-241337. - 87839.6i) q^{59} +(152143. + 862844. i) q^{60} +(883944. + 741717. i) q^{61} +(1.50285e6 - 1.26104e6i) q^{62} +(-511678. + 2.90187e6i) q^{63} +(-131072. + 227023. i) q^{64} +(-1.17455e6 - 2.03438e6i) q^{65} +(3.78261e6 - 1.37676e6i) q^{66} +(-1.27278e6 + 463255. i) q^{67} +(63868.7 + 110624. i) q^{68} +(250969. - 434691. i) q^{69} +(-384016. + 2.17786e6i) q^{70} +(393135. - 329880. i) q^{71} +(863876. + 724878. i) q^{72} +(-559855. - 3.17510e6i) q^{73} +(3.24424e6 + 1.18081e6i) q^{74} -2.34735e6 q^{75} +(417187. + 1.86742e6i) q^{76} +1.01602e7 q^{77} +(-5.66236e6 - 2.06093e6i) q^{78} +(-1.14908e6 - 6.51675e6i) q^{79} +(648342. + 544024. i) q^{80} +(-3.63772e6 + 3.05241e6i) q^{81} +(-272916. + 1.54778e6i) q^{82} +(3.35748e6 - 5.81533e6i) q^{83} +(2.83635e6 + 4.91270e6i) q^{84} +(387538. - 141052. i) q^{85} +(-2.60306e6 + 947435. i) q^{86} +(6.53510e6 + 1.13191e7i) q^{87} +(1.94422e6 - 3.36749e6i) q^{88} +(-2.20222e6 + 1.24894e7i) q^{89} +(2.78908e6 - 2.34032e6i) q^{90} +(-1.16510e7 - 9.77637e6i) q^{91} +(-84195.6 - 477497. i) q^{92} +(-1.52675e7 - 5.55692e6i) q^{93} -6.66610e6 q^{94} +(6.17139e6 - 279514. i) q^{95} +2.17100e6 q^{96} +(1.64314e6 + 598053. i) q^{97} +(1.34227e6 + 7.61241e6i) q^{98} +(-1.28141e7 - 1.07523e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) $ 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.51754	−	2.73616i	−0.664463	−	0.241845i
$2$	−7.51754	−	2.73616i	−0.664463	−	0.241845i
$3$	11.5048	+	65.2472i	0.246012	+	1.39520i	0.818131	+	0.575032i	$0.195011\pi$
$3$	11.5048	+	65.2472i	0.246012	+	1.39520i	−0.572119	+	0.820171i	$0.693878\pi$
$4$	49.0268	+	41.1384i	0.383022	+	0.321394i
$5$	158.287	−	132.818i	0.566304	−	0.475185i	−0.314113	−	0.949385i	$-0.601707\pi$
$5$	158.287	−	132.818i	0.566304	−	0.475185i	0.880417	+	0.474200i	$0.157263\pi$
$6$	92.0387	−	521.978i	0.173957	−	0.986558i
$7$	668.912	−	1158.59i	0.737099	−	1.27669i	−0.216697	−	0.976239i	$-0.569528\pi$
$7$	668.912	−	1158.59i	0.737099	−	1.27669i	0.953796	−	0.300454i	$-0.0971383\pi$
$8$	−256.000	−	443.405i	−0.176777	−	0.306186i
$9$	−2069.73	+	753.319i	−0.946378	+	0.344453i
$10$	−1553.34	+	565.369i	−0.491209	+	0.178785i
$11$	3797.30	+	6577.12i	0.860203	+	1.48991i	0.871733	+	0.489981i	$0.162996\pi$
$11$	3797.30	+	6577.12i	0.860203	+	1.48991i	−0.0115306	+	0.999934i	$0.503670\pi$
$12$	−2120.12	+	3672.16i	−0.354182	+	0.613461i
$13$	1974.16	−	11196.0i	0.249218	−	1.41339i	−0.561271	−	0.827632i	$-0.689687\pi$
$13$	1974.16	−	11196.0i	0.249218	−	1.41339i	0.810489	−	0.585754i	$-0.199201\pi$
$14$	−8198.66	+	6879.49i	−0.798537	+	0.670052i
$15$	10487.1	+	8799.71i	0.802297	+	0.673207i
$16$	711.263	+	4033.77i	0.0434120	+	0.246202i
$17$	1875.53	+	682.637i	0.0925876	+	0.0336991i	0.387899	−	0.921702i	$-0.373201\pi$
$17$	1875.53	+	682.637i	0.0925876	+	0.0336991i	−0.295311	+	0.955401i	$0.595423\pi$
$18$	17620.5			0.712137
$19$	23749.0	+	18161.9i	0.794343	+	0.607469i
$19$	23749.0	+	18161.9i	0.794343	+	0.607469i
$20$	13224.2			0.369628
$21$	83290.5	+	30315.2i	1.96258	+	0.714321i
$22$	−10550.3	−	59833.8i	−0.211245	−	1.19803i
$23$	−5803.54	−	4869.75i	−0.0994594	−	0.0834563i	0.591702	−	0.806157i	$-0.298456\pi$
$23$	−5803.54	−	4869.75i	−0.0994594	−	0.0834563i	−0.691161	+	0.722700i	$0.742901\pi$
$24$	25985.7	−	21804.6i	0.383703	−	0.321965i
$25$	−6152.29	+	34891.4i	−0.0787493	+	0.446610i
$26$	−45474.8	+	78764.7i	−0.507416	+	0.878871i
$27$	−515.392	−	892.685i	−0.00503923	−	0.00872821i
$28$	80457.2	−	29284.0i	0.692647	−	0.252103i
$29$	185378.	−	67472.0i	1.41145	−	0.513725i	0.479894	−	0.877327i	$-0.340675\pi$
$29$	185378.	−	67472.0i	1.41145	−	0.513725i	0.931555	+	0.363602i	$0.118453\pi$
$30$	−54759.7	−	94846.5i	−0.370285	−	0.641353i
$31$	−122615.	+	212375.i	−0.739224	+	1.28037i	0.213621	+	0.976917i	$0.431474\pi$
$31$	−122615.	+	212375.i	−0.739224	+	1.28037i	−0.952845	+	0.303457i	$0.901859\pi$
$32$	5690.10	−	32270.2i	0.0306970	−	0.174091i
$33$	−385451.	+	323432.i	−1.86711	+	1.56669i
$34$	−12231.6	−	10263.5i	−0.0533711	−	0.0447836i
$35$	−48002.0	−	272233.i	−0.189244	−	1.07325i
$36$	−132463.	−	48212.4i	−0.473189	−	0.172227i
$37$	−431556.			−1.40065			−0.700327	−	0.713822i	$-0.746963\pi$
$37$	−431556.			−1.40065			−0.700327	+	0.713822i	$0.746963\pi$
$38$	−128840.	−	201514.i	−0.380898	−	0.595749i
$39$	753219.			2.03327
$40$	−99413.7	−	36183.6i	−0.245604	−	0.0893927i
$41$	−34114.5	−	193473.i	−0.0773029	−	0.438406i	−0.998754	−	0.0499112i	$-0.984106\pi$
$41$	−34114.5	−	193473.i	−0.0773029	−	0.438406i	0.921451	−	0.388495i	$-0.127005\pi$
$42$	−543192.	−	455792.i	−1.13131	−	0.949280i
$43$	265254.	−	222574.i	0.508771	−	0.426909i	−0.351926	−	0.936028i	$-0.614473\pi$
$43$	265254.	−	222574.i	0.508771	−	0.426909i	0.860696	+	0.509119i	$0.170029\pi$
$44$	−84402.5	+	478670.i	−0.149373	+	0.847134i
$45$	−227556.	+	394138.i	−0.372258	+	0.644770i
$46$	30304.0	+	52488.0i	0.0459036	+	0.0795074i
$47$	783011.	−	284993.i	1.10008	−	0.400397i	0.272736	−	0.962089i	$-0.412071\pi$
$47$	783011.	−	284993.i	1.10008	−	0.400397i	0.827347	+	0.561692i	$0.189849\pi$
$48$	−255009.	+	92815.8i	−0.332822	+	0.121137i
$49$	−483115.	−	836780.i	−0.586630	−	1.01607i
$50$	141719.	−	245464.i	0.160336	−	0.277710i
$51$	−22962.5	+	130227.i	−0.0242395	+	0.137469i
$52$	557372.	−	467691.i	0.549710	−	0.461261i
$53$	−34895.4	−	29280.7i	−0.0321960	−	0.0270157i	0.626548	−	0.779383i	$-0.284467\pi$
$53$	−34895.4	−	29280.7i	−0.0321960	−	0.0270157i	−0.658744	+	0.752367i	$0.728912\pi$
$54$	1431.95	+	8120.99i	0.00123751	+	0.00701828i
$55$	1.47462e6	+	536719.i	1.19512	+	0.434988i
$56$	−684966.			−0.521208
$57$	−911786.	+	1.75851e6i	−0.652125	+	1.25771i
$58$	−1.57820e6			−1.06210
$59$	−241337.	−	87839.6i	−0.152983	−	0.0556812i	0.264394	−	0.964415i	$-0.414828\pi$
$59$	−241337.	−	87839.6i	−0.152983	−	0.0556812i	−0.417377	+	0.908734i	$0.637050\pi$
$60$	152143.	+	862844.i	0.0909330	+	0.515707i
$61$	883944.	+	741717.i	0.498621	+	0.418392i	0.857104	−	0.515144i	$-0.172261\pi$
$61$	883944.	+	741717.i	0.498621	+	0.418392i	−0.358483	+	0.933536i	$0.616706\pi$
$62$	1.50285e6	−	1.26104e6i	0.800839	−	0.671984i
$63$	−511678.	+	2.90187e6i	−0.257813	+	1.46213i
$64$	−131072.	+	227023.i	−0.0625000	+	0.108253i
$65$	−1.17455e6	−	2.03438e6i	−0.530487	−	0.918830i
$66$	3.78261e6	−	1.37676e6i	1.61952	−	0.589459i
$67$	−1.27278e6	+	463255.i	−0.517003	+	0.188174i	−0.587326	−	0.809351i	$-0.699819\pi$
$67$	−1.27278e6	+	463255.i	−0.517003	+	0.188174i	0.0703230	+	0.997524i	$0.477597\pi$
$68$	63868.7	+	110624.i	0.0246324	+	0.0426646i
$69$	250969.	−	434691.i	0.0919704	−	0.159297i
$70$	−384016.	+	2.17786e6i	−0.133816	+	0.758906i
$71$	393135.	−	329880.i	0.130358	−	0.109383i	−0.575278	−	0.817958i	$-0.695106\pi$
$71$	393135.	−	329880.i	0.130358	−	0.109383i	0.705636	+	0.708575i	$0.250662\pi$
$72$	863876.	+	724878.i	0.272764	+	0.228876i
$73$	−559855.	−	3.17510e6i	−0.168440	−	0.955272i	−0.945446	−	0.325779i	$-0.894374\pi$
$73$	−559855.	−	3.17510e6i	−0.168440	−	0.955272i	0.777006	−	0.629493i	$-0.216738\pi$
$74$	3.24424e6	+	1.18081e6i	0.930683	+	0.338741i
$75$	−2.34735e6			−0.642484
$76$	417187.	+	1.86742e6i	0.109014	+	0.487971i
$77$	1.01602e7			2.53622
$78$	−5.66236e6	−	2.06093e6i	−1.35103	−	0.491736i
$79$	−1.14908e6	−	6.51675e6i	−0.262213	−	1.48709i	−0.776854	−	0.629680i	$-0.783186\pi$
$79$	−1.14908e6	−	6.51675e6i	−0.262213	−	1.48709i	0.514641	−	0.857406i	$-0.327925\pi$
$80$	648342.	+	544024.i	0.141576	+	0.118796i
$81$	−3.63772e6	+	3.05241e6i	−0.760556	+	0.638182i
$82$	−272916.	+	1.54778e6i	−0.0546614	+	0.310000i
$83$	3.35748e6	−	5.81533e6i	0.644526	−	1.11635i	−0.339885	−	0.940467i	$-0.610388\pi$
$83$	3.35748e6	−	5.81533e6i	0.644526	−	1.11635i	0.984411	−	0.175884i	$-0.0562785\pi$
$84$	2.83635e6	+	4.91270e6i	0.522134	+	0.904362i
$85$	387538.	−	141052.i	0.0684460	−	0.0249123i
$86$	−2.60306e6	+	947435.i	−0.441305	+	0.160622i
$87$	6.53510e6	+	1.13191e7i	1.06398	+	1.84287i
$88$	1.94422e6	−	3.36749e6i	0.304128	−	0.526764i
$89$	−2.20222e6	+	1.24894e7i	−0.331128	+	1.87792i	0.131418	+	0.991327i	$0.458047\pi$
$89$	−2.20222e6	+	1.24894e7i	−0.331128	+	1.87792i	−0.462547	+	0.886595i	$0.653064\pi$
$90$	2.78908e6	−	2.34032e6i	0.403286	−	0.338397i
$91$	−1.16510e7	−	9.77637e6i	−1.62076	−	1.35998i
$92$	−84195.6	−	477497.i	−0.0112728	−	0.0639313i
$93$	−1.52675e7	−	5.55692e6i	−1.96824	−	0.716381i
$94$	−6.66610e6			−0.827798
$95$	6.17139e6	−	279514.i	0.738500	−	0.0334481i
$96$	2.17100e6			0.250444
$97$	1.64314e6	+	598053.i	0.182798	+	0.0665332i	0.431798	−	0.901970i	$-0.357879\pi$
$97$	1.64314e6	+	598053.i	0.182798	+	0.0665332i	−0.248999	+	0.968504i	$0.580102\pi$
$98$	1.34227e6	+	7.61241e6i	0.144062	+	0.817017i
$99$	−1.28141e7	−	1.07523e7i	−1.32728	−	1.11372i
$100$	−1.73700e6	+	1.45752e6i	−0.173700	+	0.145752i
$101$	1.70243e6	−	9.65496e6i	0.164416	−	0.932451i	−0.785248	−	0.619181i	$-0.787465\pi$
$101$	1.70243e6	−	9.65496e6i	0.164416	−	0.932451i	0.949664	−	0.313269i	$-0.101424\pi$
$102$	528943.	−	916156.i	0.0493524	−	0.0854808i
$103$	−1.11639e6	−	1.93364e6i	−0.100667	−	0.174360i	0.811293	−	0.584640i	$-0.198764\pi$
$103$	−1.11639e6	−	1.93364e6i	−0.100667	−	0.174360i	−0.911960	+	0.410280i	$0.865431\pi$
$104$	−5.46974e6	+	1.99082e6i	−0.476815	+	0.173547i
$105$	1.72102e7	−	6.26400e6i	1.45085	−	0.528067i
$106$	182211.	+	315598.i	0.0148595	+	0.0257374i
$107$	−4.31228e6	+	7.46909e6i	−0.340301	+	0.589419i	−0.984489	−	0.175448i	$-0.943862\pi$
$107$	−4.31228e6	+	7.46909e6i	−0.340301	+	0.589419i	0.644187	+	0.764868i	$0.277196\pi$
$108$	11455.6	−	64967.9i	0.000875053	−	0.00496267i
$109$	−4.81053e6	+	4.03651e6i	−0.355795	+	0.298548i	−0.803112	−	0.595828i	$-0.796824\pi$
$109$	−4.81053e6	+	4.03651e6i	−0.355795	+	0.298548i	0.447317	+	0.894376i	$0.352380\pi$
$110$	−9.61700e6	−	8.06962e6i	−0.688914	−	0.578068i
$111$	−4.96498e6	−	2.81578e7i	−0.344578	−	1.95420i
$112$	5.14926e6	+	1.87418e6i	0.346323	+	0.126051i
$113$	−7.98248e6			−0.520431			−0.260216	−	0.965551i	$-0.583794\pi$
$113$	−7.98248e6			−0.520431			−0.260216	+	0.965551i	$0.583794\pi$
$114$	1.16659e7	−	1.07249e7i	0.737485	−	0.677992i
$115$	−1.56542e6			−0.0959814
$116$	1.18642e7	+	4.31821e6i	0.705724	+	0.256863i
$117$	4.34819e6	+	2.46598e7i	0.250991	+	1.42344i
$118$	1.57392e6	+	1.32068e6i	0.0881852	+	0.0739962i
$119$	2.04546e6	−	1.71635e6i	0.111270	−	0.0933663i
$120$	1.21714e6	−	6.90275e6i	0.0642994	−	0.364660i
$121$	−1.90954e7	+	3.30742e7i	−0.979897	+	1.69723i
$122$	−4.61563e6	−	7.99450e6i	−0.230129	−	0.398595i
$123$	1.22311e7	−	4.45175e6i	0.592648	−	0.215706i
$124$	−1.47482e7	+	5.36789e6i	−0.694644	+	0.252830i
$125$	1.17318e7	+	2.03201e7i	0.537255	+	0.930552i
$126$	1.17865e7	−	2.04149e7i	0.524916	−	0.909181i
$127$	−4.02223e6	+	2.28112e7i	−0.174242	+	0.988178i	0.764772	+	0.644301i	$0.222852\pi$
$127$	−4.02223e6	+	2.28112e7i	−0.174242	+	0.988178i	−0.939015	+	0.343877i	$0.888260\pi$
$128$	1.60651e6	−	1.34802e6i	0.0677094	−	0.0568149i
$129$	1.75741e7	+	1.47464e7i	0.720789	+	0.604814i
$130$	3.26334e6	+	1.85073e7i	0.130275	+	0.738824i
$131$	−1.91150e7	−	6.95728e6i	−0.742889	−	0.270390i	−0.0572789	−	0.998358i	$-0.518242\pi$
$131$	−1.91150e7	−	6.95728e6i	−0.742889	−	0.270390i	−0.685610	+	0.727969i	$0.740465\pi$
$132$	−3.22029e7			−1.21867
$133$	3.69282e7	−	1.53666e7i	1.36106	−	0.566367i
$134$	1.08357e7			0.389038
$135$	−200145.	−	72846.7i	−0.00700125	−	0.00254825i
$136$	−177451.	−	1.00637e6i	−0.00604912	−	0.0343063i
$137$	1.23075e7	+	1.03272e7i	0.408928	+	0.343131i	0.823932	−	0.566688i	$-0.191776\pi$
$137$	1.23075e7	+	1.03272e7i	0.408928	+	0.343131i	−0.415005	+	0.909819i	$0.636220\pi$
$138$	−3.07605e6	+	2.58111e6i	−0.0996361	+	0.0836046i
$139$	−3.30271e6	+	1.87306e7i	−0.104308	+	0.591561i	0.887186	+	0.461412i	$0.152657\pi$
$139$	−3.30271e6	+	1.87306e7i	−0.104308	+	0.591561i	−0.991494	+	0.130150i	$0.958454\pi$
$140$	8.84585e6	−	1.53215e7i	0.272453	−	0.471902i
$141$	2.76034e7	+	4.78105e7i	0.829269	+	1.43634i
$142$	−3.85801e6	+	1.40420e6i	−0.113072	+	0.0411548i
$143$	8.11338e7	−	2.95303e7i	2.32020	−	0.844485i
$144$	−4.51084e6	−	7.81300e6i	−0.125889	−	0.218047i
$145$	2.03813e7	−	3.53015e7i	0.555194	−	0.961623i
$146$	−4.47884e6	+	2.54008e7i	−0.119105	+	0.675479i
$147$	4.90394e7	−	4.11489e7i	1.27331	−	1.06843i
$148$	−2.11578e7	−	1.77535e7i	−0.536482	−	0.450162i
$149$	−6.23597e6	−	3.53659e7i	−0.154437	−	0.875857i	−0.959299	−	0.282394i	$-0.908871\pi$
$149$	−6.23597e6	−	3.53659e7i	−0.154437	−	0.875857i	0.804861	−	0.593463i	$-0.202240\pi$
$150$	1.76463e7	+	6.42272e6i	0.426907	+	0.155382i
$151$	−6.85090e7			−1.61930			−0.809652	−	0.586910i	$-0.800344\pi$
$151$	−6.85090e7			−1.61930			−0.809652	+	0.586910i	$0.800344\pi$
$152$	1.97334e6	−	1.51799e7i	0.0455773	−	0.350603i
$153$	−4.39608e6			−0.0992306
$154$	−7.63801e7	−	2.78001e7i	−1.68522	−	0.613371i
$155$	8.79899e6	+	4.99015e7i	0.189789	+	1.07635i
$156$	3.69280e7	+	3.09862e7i	0.778788	+	0.653481i
$157$	−2.38845e7	+	2.00415e7i	−0.492570	+	0.413315i	−0.854946	−	0.518717i	$-0.826410\pi$
$157$	−2.38845e7	+	2.00415e7i	−0.492570	+	0.413315i	0.362376	+	0.932032i	$0.381966\pi$
$158$	−9.19263e6	+	5.21340e7i	−0.185413	+	1.05153i
$159$	1.50902e6	−	2.61370e6i	0.0297718	−	0.0515662i
$160$	−3.38540e6	−	5.86369e6i	−0.0653417	−	0.113175i
$161$	−9.52410e6	+	3.46649e6i	−0.179860	+	0.0654635i
$162$	3.56986e7	−	1.29932e7i	0.659702	−	0.240112i
$163$	−4.15136e7	−	7.19037e7i	−0.750817	−	1.30045i	−0.947427	−	0.319971i	$-0.896327\pi$
$163$	−4.15136e7	−	7.19037e7i	−0.750817	−	1.30045i	0.196610	−	0.980482i	$-0.437007\pi$
$164$	6.28664e6	−	1.08888e7i	0.111292	−	0.192764i
$165$	−1.80541e7	+	1.02390e8i	−0.312883	+	1.77445i
$166$	−4.11517e7	+	3.45304e7i	−0.698247	+	0.585899i
$167$	−2.43679e7	−	2.04471e7i	−0.404865	−	0.339722i	0.417505	−	0.908674i	$-0.362905\pi$
$167$	−2.43679e7	−	2.04471e7i	−0.404865	−	0.339722i	−0.822371	+	0.568952i	$0.807349\pi$
$168$	−7.88042e6	−	4.46921e7i	−0.128223	−	0.727191i
$169$	−6.24886e7	−	2.27440e7i	−0.995858	−	0.362463i
$170$	−3.29928e6			−0.0515048
$171$	−6.28357e7	−	1.96996e7i	−0.960993	−	0.301281i
$172$	2.21609e7			0.332076
$173$	−7.42834e7	−	2.70369e7i	−1.09076	−	0.397005i	−0.266859	−	0.963736i	$-0.585986\pi$
$173$	−7.42834e7	−	2.70369e7i	−1.09076	−	0.397005i	−0.823903	+	0.566731i	$0.808208\pi$
$174$	−1.81569e7	−	1.02973e8i	−0.261289	−	1.48184i
$175$	3.63094e7	+	3.04672e7i	0.512137	+	0.429734i
$176$	−2.38297e7	+	1.99955e7i	−0.329477	+	0.276464i
$177$	2.95474e6	−	1.67572e7i	0.0400510	−	0.227140i
$178$	5.07284e7	−	8.78641e7i	0.674188	−	1.16773i
$179$	−3.03372e7	−	5.25455e7i	−0.395357	−	0.684779i	0.597790	−	0.801653i	$-0.296046\pi$
$179$	−3.03372e7	−	5.25455e7i	−0.395357	−	0.684779i	−0.993147	+	0.116874i	$0.962712\pi$
$180$	−2.73706e7	+	9.96207e6i	−0.349808	+	0.127320i
$181$	1.19923e7	−	4.36483e6i	0.150323	−	0.0547132i	−0.265763	−	0.964038i	$-0.585624\pi$
$181$	1.19923e7	−	4.36483e6i	0.150323	−	0.0547132i	0.416086	+	0.909325i	$0.363402\pi$
$182$	6.08373e7	+	1.05373e8i	0.748032	+	1.29563i
$183$	−3.82253e7	+	6.62082e7i	−0.461076	+	0.798607i
$184$	−673565.	+	3.81998e6i	−0.00797108	+	0.0452062i
$185$	−6.83096e7	+	5.73185e7i	−0.793196	+	0.665570i
$186$	9.95695e7	+	8.35488e7i	1.13457	+	0.952017i
$187$	2.63217e6	+	1.49278e7i	0.0294353	+	0.166936i
$188$	5.01127e7	+	1.82395e7i	0.550041	+	0.200199i
$189$	−1.37901e6			−0.0148577
$190$	−4.71585e7	−	1.47847e7i	−0.498795	−	0.156377i
$191$	1.60471e8			1.66640			0.833200	−	0.552972i	$-0.186506\pi$
$191$	1.60471e8			1.66640			0.833200	+	0.552972i	$0.186506\pi$
$192$	−1.63206e7	−	5.94021e6i	−0.166411	−	0.0605686i
$193$	−1.53751e7	−	8.71968e7i	−0.153946	−	0.873071i	−0.959743	−	0.280880i	$-0.909374\pi$
$193$	−1.53751e7	−	8.71968e7i	−0.153946	−	0.873071i	0.805797	−	0.592192i	$-0.201737\pi$
$194$	−1.07160e7	−	8.99177e6i	−0.105372	−	0.0884177i
$195$	1.19225e8	−	1.00041e8i	1.15145	−	0.966180i
$196$	1.07382e7	−	6.08993e7i	0.101867	−	0.577718i
$197$	−1.99328e7	+	3.45246e7i	−0.185753	+	0.321734i	−0.943830	−	0.330431i	$-0.892806\pi$
$197$	−1.99328e7	+	3.45246e7i	−0.185753	+	0.321734i	0.758077	+	0.652165i	$0.226139\pi$
$198$	6.69102e7	+	1.15892e8i	0.612582	+	1.06102i
$199$	5.21580e7	−	1.89840e7i	0.469176	−	0.170766i	−0.0966032	−	0.995323i	$-0.530798\pi$
$199$	5.21580e7	−	1.89840e7i	0.469176	−	0.170766i	0.565779	+	0.824557i	$0.308576\pi$
$200$	1.70460e7	−	6.20424e6i	0.150667	−	0.0548382i
$201$	−4.48693e7	−	7.77159e7i	−0.389729	−	0.675031i
$202$	−3.92156e7	+	6.79235e7i	−0.334757	+	0.579816i
$203$	4.58291e7	−	2.59910e8i	0.384508	−	2.18065i
$204$	−6.48310e6	+	5.43996e6i	−0.0534659	+	0.0448632i
$205$	−3.10966e7	−	2.60932e7i	−0.252101	−	0.211538i
$206$	3.10175e6	+	1.75909e7i	0.0247213	+	0.140201i
$207$	1.56802e7	+	5.70714e6i	0.122873	+	0.0447221i
$208$	4.65662e7			0.358797
$209$	−2.92709e7	+	2.25166e8i	−0.221781	+	1.70605i
$210$	−1.46518e8			−1.09175
$211$	−1.73425e8	−	6.31214e7i	−1.27093	−	0.462581i	−0.383509	−	0.923537i	$-0.625284\pi$
$211$	−1.73425e8	−	6.31214e7i	−1.27093	−	0.462581i	−0.887423	+	0.460956i	$0.847507\pi$
$212$	−506249.	−	2.87108e6i	−0.00364912	−	0.0206952i
$213$	2.60467e7	+	2.18558e7i	0.184682	+	0.154966i
$214$	5.28544e7	−	4.43501e7i	0.368666	−	0.309347i
$215$	1.24242e7	−	7.04611e7i	0.0852577	−	0.483520i
$216$	−263881.	+	457055.i	−0.00178164	+	0.00308589i
$217$	1.64037e8	+	2.84120e8i	1.08976	+	1.88753i
$218$	4.72079e7	−	1.71823e7i	0.308615	−	0.112327i
$219$	2.00725e8	−	7.30580e7i	1.29136	−	0.470017i
$220$	5.02164e7	+	8.69773e7i	0.317955	+	0.550715i
$221$	1.13454e7	−	1.96508e7i	0.0707044	−	0.122464i
$222$	−3.97199e7	+	2.25263e8i	−0.243653	+	1.38183i
$223$	−2.10313e8	+	1.76473e8i	−1.26999	+	1.06564i	−0.275442	+	0.961318i	$0.588824\pi$
$223$	−2.10313e8	+	1.76473e8i	−1.26999	+	1.06564i	−0.994543	+	0.104327i	$0.966731\pi$
$224$	−3.35817e7	−	2.81784e7i	−0.199634	−	0.167513i
$225$	−1.35508e7	−	7.68503e7i	−0.0793095	−	0.449787i
$226$	6.00086e7	+	2.18414e7i	0.345807	+	0.125864i
$227$	2.24540e7			0.127410			0.0637050	−	0.997969i	$-0.479708\pi$
$227$	2.24540e7			0.127410			0.0637050	+	0.997969i	$0.479708\pi$
$228$	−1.17044e8	+	4.87046e7i	−0.654000	+	0.272144i
$229$	−1.30363e8			−0.717348			−0.358674	−	0.933463i	$-0.616771\pi$
$229$	−1.30363e8			−0.717348			−0.358674	+	0.933463i	$0.616771\pi$
$230$	1.17681e7	+	4.28323e6i	0.0637761	+	0.0232126i
$231$	1.16892e8	+	6.62927e8i	0.623940	+	3.53854i
$232$	−7.73742e7	−	6.49246e7i	−0.406807	−	0.341351i
$233$	−1.78067e8	+	1.49416e8i	−0.922229	+	0.773842i	−0.974406	−	0.224796i	$-0.927828\pi$
$233$	−1.78067e8	+	1.49416e8i	−0.922229	+	0.773842i	0.0521769	+	0.998638i	$0.483384\pi$
$234$	3.47855e7	−	1.97279e8i	0.177477	−	1.00652i
$235$	8.60879e7	−	1.49109e8i	0.432718	−	0.749489i
$236$	−8.21843e6	−	1.42347e7i	−0.0407002	−	0.0704949i
$237$	4.11980e8	−	1.49948e8i	2.01028	−	0.731682i
$238$	−2.00730e7	+	7.30599e6i	−0.0965148	+	0.0351285i
$239$	−1.46795e8	−	2.54257e8i	−0.695536	−	1.20470i	−0.970000	−	0.243106i	$-0.921834\pi$
$239$	−1.46795e8	−	2.54257e8i	−0.695536	−	1.20470i	0.274464	−	0.961597i	$-0.411500\pi$
$240$	−2.80369e7	+	4.85614e7i	−0.130916	+	0.226752i
$241$	5.95474e7	−	3.37710e8i	0.274033	−	1.55412i	−0.467983	−	0.883738i	$-0.655019\pi$
$241$	5.95474e7	−	3.37710e8i	0.274033	−	1.55412i	0.742016	−	0.670382i	$-0.233870\pi$
$242$	2.34047e8	−	1.96389e8i	1.06157	−	0.890764i
$243$	−2.42739e8	−	2.03682e8i	−1.08522	−	0.910608i
$244$	1.28239e7	+	7.27281e7i	0.0565141	+	0.320507i
$245$	−1.87610e8	−	6.82846e7i	−0.815034	−	0.296648i
$246$	−1.04128e8			−0.445960
$247$	2.50225e8	−	2.30039e8i	1.05655	−	0.971321i
$248$	1.25557e8			0.522710
$249$	4.18061e8	+	1.52162e8i	1.71610	+	0.624609i
$250$	−3.25953e7	−	1.84857e8i	−0.131937	−	0.748250i
$251$	8.77505e7	+	7.36314e7i	0.350261	+	0.293904i	0.800895	−	0.598805i	$-0.204358\pi$
$251$	8.77505e7	+	7.36314e7i	0.350261	+	0.293904i	−0.450634	+	0.892709i	$0.648802\pi$
$252$	−1.44464e8	+	1.21220e8i	−0.568668	+	0.477169i
$253$	9.99113e6	−	5.66625e7i	0.0387876	−	0.219975i
$254$	9.26524e7	−	1.60479e8i	0.354763	−	0.614468i
$255$	1.36618e7	+	2.36630e7i	0.0515963	+	0.0893674i
$256$	−1.57654e7	+	5.73815e6i	−0.0587308	+	0.0213763i
$257$	2.72137e7	−	9.90498e6i	0.100005	−	0.0363989i	−0.291533	−	0.956561i	$-0.594165\pi$
$257$	2.72137e7	−	9.90498e6i	0.100005	−	0.0363989i	0.391538	+	0.920162i	$0.371943\pi$
$258$	−9.17652e7	−	1.58942e8i	−0.332666	−	0.576195i
$259$	−2.88673e8	+	4.99996e8i	−1.03242	+	1.78821i
$260$	2.61067e7	−	1.48058e8i	0.0921181	−	0.522428i
$261$	−3.32854e8	+	2.79297e8i	−1.15881	+	0.972356i
$262$	1.24661e8	+	1.04603e8i	0.428230	+	0.359328i
$263$	3.45702e7	+	1.96057e8i	0.117181	+	0.664566i	0.985647	+	0.168818i	$0.0539949\pi$
$263$	3.45702e7	+	1.96057e8i	0.117181	+	0.664566i	−0.868466	+	0.495748i	$0.834894\pi$
$264$	2.42087e8	+	8.81124e7i	0.809762	+	0.294729i
$265$	−9.41249e6			−0.0310702
$266$	−3.19655e8	+	1.44778e7i	−1.04135	+	0.0471646i
$267$	−8.40236e8			−2.70154
$268$	−8.14582e7	−	2.96483e7i	−0.258501	−	0.0940868i
$269$	5.43849e7	+	3.08432e8i	0.170351	+	0.966110i	0.943374	+	0.331732i	$0.107633\pi$
$269$	5.43849e7	+	3.08432e8i	0.170351	+	0.966110i	−0.773022	+	0.634379i	$0.781256\pi$
$270$	1.30527e6	+	1.09526e6i	0.00403579	+	0.00338643i
$271$	−1.66816e8	+	1.39976e8i	−0.509150	+	0.427228i	−0.860830	−	0.508893i	$-0.830055\pi$
$271$	−1.66816e8	+	1.39976e8i	−0.509150	+	0.427228i	0.351680	+	0.936120i	$0.385611\pi$
$272$	−1.41961e6	+	8.05100e6i	−0.00427737	+	0.0242582i
$273$	5.03838e8	−	8.72672e8i	1.49872	−	2.59586i
$274$	−6.42650e7	−	1.11310e8i	−0.188733	−	0.326895i
$275$	−2.52847e8	+	9.20287e7i	−0.733151	+	0.266845i
$276$	3.01867e7	−	1.09871e7i	0.0864239	−	0.0314557i
$277$	7.97653e6	+	1.38158e7i	0.0225494	+	0.0390567i	0.877080	−	0.480345i	$-0.159488\pi$
$277$	7.97653e6	+	1.38158e7i	0.0225494	+	0.0390567i	−0.854531	+	0.519401i	$0.826155\pi$
$278$	7.60782e7	−	1.31771e8i	0.212375	−	0.367844i
$279$	9.37929e7	−	5.31926e8i	0.258556	−	1.46635i
$280$	−1.08421e8	+	9.09760e7i	−0.295162	+	0.247670i
$281$	4.83323e8	+	4.05556e8i	1.29947	+	1.09038i	0.990237	+	0.139397i	$0.0445163\pi$
$281$	4.83323e8	+	4.05556e8i	1.29947	+	1.09038i	0.309232	+	0.950987i	$0.399928\pi$
$282$	−7.66924e7	−	4.34944e8i	−0.203648	−	1.15495i
$283$	4.32206e8	+	1.57310e8i	1.13354	+	0.412577i	0.839578	−	0.543239i	$-0.182802\pi$
$283$	4.32206e8	+	1.57310e8i	1.13354	+	0.412577i	0.293967	+	0.955816i	$0.405025\pi$
$284$	3.28449e7			0.0850851
$285$	8.92384e7	+	3.99450e8i	0.228347	+	1.02213i
$286$	−6.90727e8			−1.74592
$287$	−2.46975e8	−	8.98917e7i	−0.616690	−	0.224457i
$288$	1.25328e7	+	7.10769e7i	0.0309153	+	0.175330i
$289$	−3.11286e8	−	2.61200e8i	−0.758608	−	0.636547i
$290$	−2.49808e8	+	2.09614e8i	−0.601469	+	0.504693i
$291$	−2.01172e7	+	1.14091e8i	−0.0478567	+	0.271409i
$292$	1.03171e8	−	1.78697e8i	0.242502	−	0.420026i
$293$	−2.23173e8	−	3.86547e8i	−0.518329	−	0.897772i	−0.999773	−	0.0212950i	$-0.993221\pi$
$293$	−2.23173e8	−	3.86547e8i	−0.518329	−	0.897772i	0.481445	−	0.876477i	$-0.340112\pi$
$294$	−4.81246e8	+	1.75159e8i	−1.10446	+	0.401992i
$295$	−4.98672e7	+	1.81502e7i	−0.113094	+	0.0411627i
$296$	1.10478e8	+	1.91354e8i	0.247603	+	0.428861i
$297$	3.91420e6	−	6.77959e6i	0.00866952	−	0.0150160i
$298$	−4.98877e7	+	2.82927e8i	−0.109204	+	0.619324i
$299$	−6.59788e7	+	5.53628e7i	−0.142743	+	0.119776i
$300$	−1.15083e8	−	9.65661e7i	−0.246086	−	0.206491i
$301$	−8.04409e7	−	4.56203e8i	−0.170018	−	0.964218i
$302$	5.15019e8	+	1.87452e8i	1.07597	+	0.391620i
$303$	6.49546e8			1.34141
$304$	−5.63693e7	+	1.08716e8i	−0.115076	+	0.221940i
$305$	2.38430e8			0.481185
$306$	3.30477e7	+	1.20284e7i	0.0659351	+	0.0239984i
$307$	−9.93500e6	−	5.63442e7i	−0.0195967	−	0.111139i	0.973440	−	0.228941i	$-0.0735262\pi$
$307$	−9.93500e6	−	5.63442e7i	−0.0195967	−	0.111139i	−0.993037	+	0.117802i	$0.962415\pi$
$308$	4.98125e8	+	4.17976e8i	0.971428	+	0.815125i
$309$	1.13321e8	−	9.50876e7i	0.218502	−	0.183345i
$310$	7.03919e7	−	3.99212e8i	0.134201	−	0.761094i
$311$	−1.73291e7	+	3.00149e7i	−0.0326674	+	0.0565817i	−0.881897	−	0.471442i	$-0.843734\pi$
$311$	−1.73291e7	+	3.00149e7i	−0.0326674	+	0.0565817i	0.849229	+	0.528024i	$0.177067\pi$
$312$	−1.92824e8	−	3.33981e8i	−0.359435	−	0.622560i
$313$	−3.02419e8	+	1.10072e8i	−0.557447	+	0.202894i	−0.605352	−	0.795958i	$-0.706968\pi$
$313$	−3.02419e8	+	1.10072e8i	−0.557447	+	0.202894i	0.0479050	+	0.998852i	$0.484746\pi$
$314$	2.34390e8	−	8.53109e7i	0.427253	−	0.155507i
$315$	3.04430e8	+	5.27287e8i	0.548782	+	0.950518i
$316$	2.11753e8	−	3.66767e8i	0.377507	−	0.653861i
$317$	3.01739e6	−	1.71125e7i	0.00532016	−	0.0301721i	−0.982032	−	0.188714i	$-0.939568\pi$
$317$	3.01739e6	−	1.71125e7i	0.00532016	−	0.0301721i	0.987352	+	0.158542i	$0.0506792\pi$
$318$	−1.84956e7	+	1.55196e7i	−0.0322532	+	0.0270637i
$319$	1.14771e9	+	9.63041e8i	1.97954	+	1.66103i
$320$	9.40590e6	+	5.33435e7i	0.0160463	+	0.0910032i
$321$	−5.36949e8	−	1.95434e8i	−0.906078	−	0.329785i
$322$	8.10827e7			0.135342
$323$	3.21440e7	+	5.02752e7i	0.0530751	+	0.0830128i
$324$	−3.03917e8			−0.496418
$325$	3.78498e8	+	1.37762e8i	0.611606	+	0.222606i
$326$	1.15340e8	+	6.54127e8i	0.184382	+	1.04568i
$327$	−3.18716e8	−	2.67434e8i	−0.504064	−	0.422960i
$328$	−7.70536e7	+	6.46556e7i	−0.120569	+	0.101169i
$329$	1.93576e8	−	1.09782e9i	0.299685	−	1.69960i
$330$	4.15878e8	−	7.20322e8i	0.637041	−	1.10339i
$331$	4.77479e8	+	8.27018e8i	0.723696	+	1.25348i	0.959509	+	0.281680i	$0.0908915\pi$
$331$	4.77479e8	+	8.27018e8i	0.723696	+	1.25348i	−0.235813	+	0.971799i	$0.575775\pi$
$332$	4.03840e8	−	1.46986e8i	0.605656	−	0.220441i
$333$	8.93203e8	−	3.25099e8i	1.32555	−	0.482460i
$334$	1.27240e8	+	2.20386e8i	0.186858	+	0.323647i
$335$	−1.39936e8	+	2.42376e8i	−0.203363	+	0.352235i
$336$	−6.30434e7	+	3.57537e8i	−0.0906676	+	0.514202i
$337$	−6.35382e8	+	5.33149e8i	−0.904337	+	0.758829i	−0.971033	−	0.238944i	$-0.923199\pi$
$337$	−6.35382e8	+	5.33149e8i	−0.904337	+	0.758829i	0.0666958	+	0.997773i	$0.478754\pi$
$338$	4.07529e8	+	3.41958e8i	0.574051	+	0.481686i
$339$	−9.18372e7	−	5.20835e8i	−0.128032	−	0.726107i
$340$	2.48024e7	+	9.02735e6i	0.0342230	+	0.0124562i
$341$	−1.86242e9			−2.54353
$342$	4.18469e8	+	3.20022e8i	0.565681	+	0.432601i
$343$	−1.90891e8			−0.255420
$344$	−1.66596e8	−	6.06358e7i	−0.220652	−	0.0803109i
$345$	−1.80099e7	−	1.02139e8i	−0.0236126	−	0.133914i
$346$	4.84451e8	+	4.06502e8i	0.628758	+	0.527590i
$347$	6.96023e8	−	5.84033e8i	0.894274	−	0.750385i	−0.0747890	−	0.997199i	$-0.523828\pi$
$347$	6.96023e8	−	5.84033e8i	0.894274	−	0.750385i	0.969063	+	0.246815i	$0.0793839\pi$
$348$	−1.45256e8	+	8.23785e8i	−0.184759	+	1.04782i
$349$	−5.42605e8	+	9.39820e8i	−0.683274	+	1.18347i	0.290702	+	0.956814i	$0.406111\pi$
$349$	−5.42605e8	+	9.39820e8i	−0.683274	+	1.18347i	−0.973976	+	0.226652i	$0.927222\pi$
$350$	−1.89594e8	−	3.28387e8i	−0.236367	−	0.409400i
$351$	−1.10120e7	+	4.00802e6i	−0.0135922	+	0.00494715i
$352$	2.33852e8	−	8.51151e7i	0.285786	−	0.104018i
$353$	−2.18355e8	−	3.78202e8i	−0.264212	−	0.457628i	0.703145	−	0.711046i	$-0.251778\pi$
$353$	−2.18355e8	−	3.78202e8i	−0.264212	−	0.457628i	−0.967357	+	0.253418i	$0.918445\pi$
$354$	−6.80627e7	+	1.17888e8i	−0.0815451	+	0.141240i
$355$	1.84140e7	−	1.04431e8i	0.0218449	−	0.123888i
$356$	−6.21763e8	+	5.21721e8i	−0.730382	+	0.612863i
$357$	1.35519e8	+	1.13714e8i	0.157639	+	0.132275i
$358$	8.42879e7	+	4.78021e8i	0.0970901	+	0.550625i
$359$	4.37821e8	+	1.59354e8i	0.499420	+	0.181774i	0.579433	−	0.815020i	$-0.303274\pi$
$359$	4.37821e8	+	1.59354e8i	0.499420	+	0.181774i	−0.0800134	+	0.996794i	$0.525496\pi$
$360$	2.33017e8			0.263226
$361$	2.34161e8	+	8.62656e8i	0.261962	+	0.965078i
$362$	−1.02095e8			−0.113116
$363$	−2.37769e9	−	8.65409e8i	−2.60905	−	0.949616i
$364$	−1.69029e8	−	9.58609e8i	−0.183698	−	1.04181i
$365$	−5.10329e8	−	4.28217e8i	−0.549319	−	0.460934i
$366$	4.68517e8	−	3.93132e8i	0.499507	−	0.419136i
$367$	2.05741e8	−	1.16682e9i	0.217265	−	1.23217i	−0.659667	−	0.751558i	$-0.729303\pi$
$367$	2.05741e8	−	1.16682e9i	0.217265	−	1.23217i	0.876932	−	0.480614i	$-0.159586\pi$
$368$	1.55156e7	−	2.68738e7i	0.0162294	−	0.0281101i
$369$	2.16355e8	+	3.74737e8i	0.224168	+	0.388271i
$370$	6.70353e8	−	2.43988e8i	0.688014	−	0.250417i
$371$	−5.72663e7	+	2.08432e7i	−0.0582224	+	0.0211912i
$372$	−5.19915e8	−	9.00520e8i	−0.523639	−	0.906970i
$373$	8.26089e8	−	1.43083e9i	0.824225	−	1.42760i	−0.0782847	−	0.996931i	$-0.524944\pi$
$373$	8.26089e8	−	1.43083e9i	0.824225	−	1.42760i	0.902510	−	0.430669i	$-0.141722\pi$
$374$	2.10573e7	−	1.19422e8i	0.0208139	−	0.118041i
$375$	−1.19086e9	+	9.99248e8i	−1.16614	+	0.978506i
$376$	−3.26818e8	−	2.74233e8i	−0.317065	−	0.266049i
$377$	−3.89452e8	−	2.20869e9i	−0.374333	−	2.12295i
$378$	1.03667e7	+	3.77319e6i	0.00987236	+	0.00359325i
$379$	1.24453e9			1.17427			0.587134	−	0.809490i	$-0.300256\pi$
$379$	1.24453e9			1.17427			0.587134	+	0.809490i	$0.300256\pi$
$380$	3.14063e8	+	2.40177e8i	0.293612	+	0.224538i
$381$	−1.53464e9			−1.42158
$382$	−1.20635e9	−	4.39074e8i	−1.10726	−	0.403010i
$383$	3.17300e8	+	1.79950e9i	0.288585	+	1.63665i	0.692191	+	0.721714i	$0.256645\pi$
$383$	3.17300e8	+	1.79950e9i	0.288585	+	1.63665i	−0.403606	+	0.914933i	$0.632243\pi$
$384$	1.06437e8	+	8.93116e7i	0.0959257	+	0.0804912i
$385$	1.60823e9	−	1.34947e9i	1.43627	−	1.20517i
$386$	−1.23001e8	+	6.97574e8i	−0.108856	+	0.617355i
$387$	−3.81333e8	+	6.60489e8i	−0.334439	+	0.579265i
$388$	5.59549e7	+	9.69166e7i	0.0486325	+	0.0842340i
$389$	−8.55953e8	+	3.11541e8i	−0.737270	+	0.268344i	−0.683239	−	0.730195i	$-0.739429\pi$
$389$	−8.55953e8	+	3.11541e8i	−0.737270	+	0.268344i	−0.0540309	+	0.998539i	$0.517207\pi$
$390$	−1.17000e9	+	4.25847e8i	−0.998761	+	0.363519i
$391$	−7.56045e6	−	1.30951e7i	−0.00639630	−	0.0110787i
$392$	−2.47355e8	+	4.28431e8i	−0.207405	+	0.359236i
$393$	2.34028e8	−	1.32724e9i	0.194489	−	1.10300i
$394$	2.44310e8	−	2.05001e8i	0.201236	−	0.168857i
$395$	−1.04743e9	−	8.78896e8i	−0.855134	−	0.717542i
$396$	−1.85901e8	−	1.05430e9i	−0.150435	−	0.853161i
$397$	3.33319e7	+	1.21318e7i	0.0267358	+	0.00973105i	0.355353	−	0.934732i	$-0.384361\pi$
$397$	3.33319e7	+	1.21318e7i	0.0267358	+	0.00973105i	−0.328618	+	0.944463i	$0.606583\pi$
$398$	−4.44043e8			−0.353049
$399$	1.42748e9	+	2.23267e9i	1.12504	+	1.75962i
$400$	−1.45120e8			−0.113375
$401$	−7.11101e7	−	2.58820e7i	−0.0550714	−	0.0200443i	0.314338	−	0.949311i	$-0.398218\pi$
$401$	−7.11101e7	−	2.58820e7i	−0.0550714	−	0.0200443i	−0.369409	+	0.929267i	$0.620440\pi$
$402$	1.24664e8	+	7.07002e8i	0.0957080	+	0.542787i
$403$	2.13568e9	+	1.79205e9i	1.62543	+	1.36390i
$404$	4.80655e8	−	4.03317e8i	0.362659	−	0.304307i
$405$	−1.70387e8	+	9.66310e8i	−0.127451	+	0.722810i
$406$	−1.05568e9	+	1.82849e9i	−0.782871	+	1.35597i
$407$	−1.63875e9	−	2.83840e9i	−1.20485	−	2.08686i
$408$	6.36216e7	−	2.31564e7i	0.0463761	−	0.0168795i
$409$	1.20889e9	−	4.40000e8i	0.873686	−	0.317996i	0.134027	−	0.990978i	$-0.457209\pi$
$409$	1.20889e9	−	4.40000e8i	0.873686	−	0.317996i	0.739659	+	0.672982i	$0.234987\pi$
$410$	1.62375e8	+	2.81242e8i	0.116352	+	0.201528i
$411$	−5.32225e8	+	9.21840e8i	−0.378136	+	0.654952i
$412$	2.48140e7	−	1.40727e8i	0.0174806	−	0.0991373i
$413$	−2.63204e8	+	2.20854e8i	−0.183851	+	0.154270i
$414$	−1.02261e8	−	8.58073e7i	−0.0708287	−	0.0594324i
$415$	−2.40937e8	−	1.36642e9i	−0.165476	−	0.938463i
$416$	−3.50064e8	−	1.27413e8i	−0.238408	−	0.0867733i
$417$	−1.26012e9			−0.851009
$418$	8.36137e8	−	1.61261e9i	0.559965	−	1.07997i
$419$	7.09959e8			0.471503			0.235751	−	0.971813i	$-0.424245\pi$
$419$	7.09959e8			0.471503			0.235751	+	0.971813i	$0.424245\pi$
$420$	1.10145e9	+	4.00896e8i	0.725426	+	0.264033i
$421$	−2.47853e8	−	1.40564e9i	−0.161885	−	0.918096i	−0.952218	−	0.305418i	$-0.901204\pi$
$421$	−2.47853e8	−	1.40564e9i	−0.161885	−	0.918096i	0.790333	−	0.612677i	$-0.209907\pi$
$422$	1.13102e9	+	9.49036e8i	0.732614	+	0.614736i
$423$	−1.40593e9	+	1.17971e9i	−0.903175	+	0.757854i
$424$	−4.04999e6	+	2.29686e7i	−0.00258032	+	0.0146337i
$425$	−3.53570e7	+	6.12400e7i	−0.0223416	+	0.0386967i
$426$	−1.36006e8	−	2.35569e8i	−0.0852363	−	0.147634i
$427$	1.45063e9	−	5.27985e8i	0.901692	−	0.328189i
$428$	−5.18684e8	+	1.88786e8i	−0.319779	+	0.116390i
$429$	2.86020e9	+	4.95401e9i	1.74903	+	3.02940i
$430$	−2.86192e8	+	4.95700e8i	−0.173587	+	0.300662i
$431$	−5.10652e7	+	2.89605e8i	−0.0307223	+	0.174235i	−0.996308	−	0.0858499i	$-0.972639\pi$
$431$	−5.10652e7	+	2.89605e8i	−0.0307223	+	0.174235i	0.965586	+	0.260085i	$0.0837506\pi$
$432$	3.23431e6	−	2.71391e6i	0.00193014	−	0.00161958i
$433$	7.37734e8	+	6.19032e8i	0.436709	+	0.366442i	0.834476	−	0.551044i	$-0.185770\pi$
$433$	7.37734e8	+	6.19032e8i	0.436709	+	0.366442i	−0.397767	+	0.917486i	$0.630215\pi$
$434$	−4.55755e8	−	2.58471e9i	−0.267619	−	1.51774i
$435$	2.53781e9	+	9.23686e8i	1.47824	+	0.538037i
$436$	−4.01901e8			−0.232229
$437$	−4.93844e7	−	2.21055e8i	−0.0283077	−	0.126712i
$438$	−1.70886e9			−0.971732
$439$	−2.00891e9	−	7.31182e8i	−1.13327	−	0.412477i	−0.293792	−	0.955869i	$-0.594917\pi$
$439$	−2.00891e9	−	7.31182e8i	−1.13327	−	0.412477i	−0.839479	+	0.543393i	$0.817139\pi$
$440$	−1.39520e8	−	7.91256e8i	−0.0780821	−	0.442825i
$441$	1.63028e9	+	1.36797e9i	0.905163	+	0.759522i
$442$	−1.39057e8	+	1.16683e8i	−0.0765976	+	0.0642730i
$443$	−3.09939e8	+	1.75775e9i	−0.169381	+	0.960605i	0.775051	+	0.631898i	$0.217724\pi$
$443$	−3.09939e8	+	1.75775e9i	−0.169381	+	0.960605i	−0.944432	+	0.328707i	$0.893387\pi$
$444$	9.14950e8	−	1.58474e9i	0.496086	−	0.859247i
$445$	1.31024e9	+	2.26941e9i	0.704841	+	1.22082i
$446$	2.06390e9	−	7.51196e8i	1.10158	−	0.400942i
$447$	2.23578e9	−	8.13759e8i	1.18401	−	0.430943i
$448$	1.75351e8	+	3.03717e8i	0.0921374	+	0.159587i
$449$	−1.20916e8	+	2.09433e8i	−0.0630410	+	0.109190i	−0.895823	−	0.444410i	$-0.853413\pi$
$449$	−1.20916e8	+	2.09433e8i	−0.0630410	+	0.109190i	0.832782	+	0.553601i	$0.186747\pi$
$450$	−1.08406e8	+	6.14802e8i	−0.0560803	+	0.318047i
$451$	1.14295e9	−	9.59050e8i	0.586692	−	0.492293i
$452$	−3.91356e8	−	3.28387e8i	−0.199337	−	0.167263i
$453$	−7.88186e8	−	4.47002e9i	−0.398368	−	2.25926i
$454$	−1.68799e8	−	6.14378e7i	−0.0846592	−	0.0308134i
$455$	−3.14268e9			−1.56409
$456$	1.01315e9	−	4.58874e7i	0.500375	−	0.0226630i
$457$	−1.85601e8			−0.0909648			−0.0454824	−	0.998965i	$-0.514482\pi$
$457$	−1.85601e8			−0.0909648			−0.0454824	+	0.998965i	$0.514482\pi$
$458$	9.80009e8	+	3.56694e8i	0.476651	+	0.173487i
$459$	−357253.	−	2.02608e6i	−0.000172437	−	0.000977941i
$460$	−7.67474e7	−	6.43987e7i	−0.0367630	−	0.0308478i
$461$	−1.30284e8	+	1.09322e8i	−0.0619355	+	0.0519700i	−0.673230	−	0.739433i	$-0.735094\pi$
$461$	−1.30284e8	+	1.09322e8i	−0.0619355	+	0.0519700i	0.611294	+	0.791403i	$0.290649\pi$
$462$	9.35136e8	−	5.30342e9i	0.441192	−	2.50213i
$463$	1.01777e9	−	1.76284e9i	0.476560	−	0.825426i	−0.523079	−	0.852284i	$-0.675217\pi$
$463$	1.01777e9	−	1.76284e9i	0.476560	−	0.825426i	0.999639	+	0.0268578i	$0.00855014\pi$
$464$	4.04019e8	+	6.99782e8i	0.187754	+	0.325199i
$465$	−3.15470e9	+	1.14822e9i	−1.45503	+	0.529589i
$466$	1.74746e9	−	6.36022e8i	0.799937	−	0.291153i
$467$	1.82200e9	+	3.15580e9i	0.827826	+	1.43384i	0.899740	+	0.436426i	$0.143756\pi$
$467$	1.82200e9	+	3.15580e9i	0.827826	+	1.43384i	−0.0719137	+	0.997411i	$0.522911\pi$
$468$	−8.01288e8	+	1.38787e9i	−0.361350	+	0.625876i
$469$	−3.14658e8	+	1.78451e9i	−0.140842	+	0.798756i
$470$	−1.05516e9	+	8.85380e8i	−0.468785	+	0.393357i
$471$	−1.58244e9	−	1.32782e9i	−0.697837	−	0.585555i
$472$	2.28338e7	+	1.29497e8i	0.00999498	+	0.0566844i
$473$	2.47115e9	+	8.99424e8i	1.07370	+	0.390796i
$474$	−3.50736e9			−1.51271
$475$	−7.79806e8	+	7.16899e8i	−0.333856	+	0.306924i
$476$	1.70890e8			0.0726261
$477$	9.42817e7	+	3.43157e7i	0.0397752	+	0.0144770i
$478$	4.07852e8	+	2.31304e9i	0.170807	+	0.968693i
$479$	−3.23243e9	−	2.71233e9i	−1.34386	−	1.12763i	−0.980616	−	0.195942i	$-0.937224\pi$
$479$	−3.23243e9	−	2.71233e9i	−1.34386	−	1.12763i	−0.363247	−	0.931693i	$-0.618332\pi$
$480$	3.43641e8	−	2.88349e8i	0.141827	−	0.119007i
$481$	−8.51959e8	+	4.83170e9i	−0.349069	+	1.97967i
$482$	−1.37168e9	+	2.37582e9i	−0.557941	+	0.966382i
$483$	−3.35752e8	−	5.81540e8i	−0.135583	−	0.234836i
$484$	−2.29681e9	+	8.35970e8i	−0.920802	+	0.335144i
$485$	3.39519e8	−	1.23575e8i	0.135135	−	0.0491851i
$486$	1.26749e9	+	2.19536e9i	0.500863	+	0.867520i
$487$	2.25747e9	−	3.91005e9i	0.885666	−	1.53402i	0.0407180	−	0.999171i	$-0.487035\pi$
$487$	2.25747e9	−	3.91005e9i	0.885666	−	1.53402i	0.844948	−	0.534848i	$-0.179631\pi$
$488$	1.02591e8	−	5.81825e8i	0.0399615	−	0.226633i
$489$	4.21391e9	−	3.53589e9i	1.62969	−	1.36747i
$490$	1.22353e9	+	1.02666e9i	0.469817	+	0.394223i
$491$	5.56368e8	+	3.15532e9i	0.212118	+	1.20298i	0.885839	+	0.463994i	$0.153584\pi$
$491$	5.56368e8	+	3.15532e9i	0.212118	+	1.20298i	−0.673721	+	0.738986i	$0.735305\pi$
$492$	7.82790e8	+	2.84912e8i	0.296324	+	0.107853i
$493$	3.93741e8			0.147995
$494$	−2.51050e9	+	1.04467e9i	−0.936950	+	0.389885i
$495$	−3.45639e9			−1.28087
$496$	−9.43882e8	−	3.43545e8i	−0.347322	−	0.126415i
$497$	−1.19222e8	−	6.76143e8i	−0.0435622	−	0.247053i
$498$	−2.72645e9	−	2.28777e9i	−0.989225	−	0.830059i
$499$	−1.77514e9	+	1.48952e9i	−0.639560	+	0.536655i	−0.903883	−	0.427779i	$-0.859296\pi$
$499$	−1.77514e9	+	1.48952e9i	−0.639560	+	0.536655i	0.264323	+	0.964434i	$0.414852\pi$
$500$	−2.60763e8	+	1.47886e9i	−0.0932933	+	0.529093i
$501$	1.05377e9	−	1.82518e9i	0.374380	−	0.648445i
$502$	−4.58200e8	−	7.93626e8i	−0.161656	−	0.279997i
$503$	3.63936e8	−	1.32462e8i	0.127508	−	0.0464090i	−0.277478	−	0.960732i	$-0.589499\pi$
$503$	3.63936e8	−	1.32462e8i	0.127508	−	0.0464090i	0.404986	+	0.914323i	$0.367276\pi$
$504$	1.41769e9	−	5.15998e8i	0.493259	−	0.179532i
$505$	−1.01288e9	−	1.75437e9i	−0.349977	−	0.606178i
$506$	−2.30147e8	+	3.98625e8i	−0.0789728	+	0.136785i
$507$	7.65060e8	−	4.33887e9i	0.260716	−	1.47859i
$508$	−1.13561e9	+	9.52893e8i	−0.384333	+	0.322494i
$509$	−9.34527e8	−	7.84161e8i	−0.314108	−	0.263568i	0.472079	−	0.881556i	$-0.343504\pi$
$509$	−9.34527e8	−	7.84161e8i	−0.314108	−	0.263568i	−0.786188	+	0.617988i	$0.787948\pi$
$510$	−3.79576e7	−	2.15268e8i	−0.0126708	−	0.0718596i
$511$	−4.05313e9	−	1.47522e9i	−1.34375	−	0.489084i
$512$	1.34218e8			0.0441942
$513$	3.97282e6	−	3.05609e7i	0.00129924	−	0.00999437i
$514$	−2.31682e8			−0.0752525
$515$	−4.33533e8	−	1.57793e8i	−0.139861	−	0.0509053i
$516$	2.54958e8	+	1.44594e9i	0.0816948	+	0.463314i
$517$	4.84776e9	+	4.06775e9i	1.54285	+	1.29461i
$518$	3.53818e9	−	2.96889e9i	1.11847	−	0.938511i
$519$	9.09466e8	−	5.15784e9i	0.285562	−	1.61950i
$520$	−6.01370e8	+	1.04160e9i	−0.187555	+	0.324856i
$521$	9.11262e7	+	1.57835e8i	0.0282300	+	0.0488958i	0.879795	−	0.475353i	$-0.157680\pi$
$521$	9.11262e7	+	1.57835e8i	0.0282300	+	0.0488958i	−0.851565	+	0.524249i	$0.824346\pi$
$522$	3.26644e9	−	1.18889e9i	1.00514	−	0.365843i
$523$	−4.21264e9	+	1.53327e9i	−1.28765	+	0.468667i	−0.892955	−	0.450145i	$-0.851372\pi$
$523$	−4.21264e9	+	1.53327e9i	−1.28765	+	0.468667i	−0.394695	+	0.918812i	$0.629150\pi$
$524$	−6.50935e8	−	1.12745e9i	−0.197642	−	0.342325i
$525$	−1.57017e9	+	2.71961e9i	−0.473575	+	0.820256i
$526$	2.76562e8	−	1.56846e9i	0.0828594	−	0.469919i
$527$	−3.74942e8	+	3.14614e8i	−0.111590	+	0.0936355i
$528$	−1.57881e9	−	1.32478e9i	−0.466778	−	0.391674i
$529$	−5.81275e8	−	3.29657e9i	−0.170721	−	0.968207i
$530$	7.07588e7	+	2.57541e7i	0.0206450	+	0.00751416i
$531$	5.65674e8			0.163959
$532$	2.44263e9	+	7.65791e8i	0.703344	+	0.220505i
$533$	−2.23347e9			−0.638903
$534$	6.31651e9	+	2.29902e9i	1.79508	+	0.653354i
$535$	3.09455e8	+	1.75501e9i	0.0873694	+	0.495497i
$536$	5.31242e8	+	4.45765e8i	0.149010	+	0.125034i
$537$	3.07942e9	−	2.58394e9i	0.858143	−	0.720067i
$538$	4.35079e8	−	2.46746e9i	0.120457	−	0.683143i
$539$	3.66907e9	−	6.35501e9i	1.00924	−	1.74806i
$540$	−6.81566e6	−	1.18051e7i	−0.00186264	−	0.00322619i
$541$	−5.80415e9	+	2.11254e9i	−1.57597	+	0.573606i	−0.974323	−	0.225156i	$-0.927711\pi$
$541$	−5.80415e9	+	2.11254e9i	−1.57597	+	0.573606i	−0.601647	+	0.798762i	$0.705489\pi$
$542$	1.63704e9	−	5.95835e8i	0.441634	−	0.160742i
$543$	4.22762e8	+	7.32245e8i	0.113317	+	0.196271i
$544$	3.27008e7	−	5.66394e7i	0.00870887	−	0.0150842i
$545$	−2.25320e8	+	1.27785e9i	−0.0596227	+	0.338137i
$546$	−6.17539e9	+	5.18177e9i	−1.62364	+	1.36240i
$547$	4.26904e9	+	3.58215e9i	1.11526	+	0.935811i	0.998355	−	0.0573324i	$-0.0182595\pi$
$547$	4.26904e9	+	3.58215e9i	1.11526	+	0.935811i	0.116901	+	0.993144i	$0.462704\pi$
$548$	1.78552e8	+	1.01262e9i	0.0463482	+	0.262854i
$549$	−2.38827e9	−	8.69260e8i	−0.616000	−	0.224206i
$550$	2.15259e9			0.551686
$551$	5.62797e9	+	1.76442e9i	1.43325	+	0.449337i
$552$	−2.56992e8			−0.0650329
$553$	−8.31887e9	−	3.02782e9i	−2.09183	−	0.761364i
$554$	−2.21618e7	−	1.25686e8i	−0.00553758	−	0.0314052i
$555$	−4.52576e9	−	3.79757e9i	−1.12374	−	0.942931i
$556$	−9.32468e8	+	7.82434e8i	−0.230076	+	0.193057i
$557$	−8.14549e8	+	4.61954e9i	−0.199721	+	1.13267i	0.705812	+	0.708399i	$0.250582\pi$
$557$	−8.14549e8	+	4.61954e9i	−0.199721	+	1.13267i	−0.905533	+	0.424275i	$0.860529\pi$
$558$	−2.16053e9	+	3.74214e9i	−0.526429	+	0.911802i
$559$	−1.96829e9	−	3.40918e9i	−0.476593	−	0.825483i
$560$	1.06398e9	−	3.87259e8i	0.256022	−	0.0931843i
$561$	−9.43712e8	+	3.43483e8i	−0.225668	+	0.0821363i
$562$	−2.52374e9	−	4.37124e9i	−0.599745	−	1.03879i
$563$	−5.91012e7	+	1.02366e8i	−0.0139578	+	0.0241756i	−0.872920	−	0.487863i	$-0.837776\pi$
$563$	−5.91012e7	+	1.02366e8i	−0.0139578	+	0.0241756i	0.858962	+	0.512039i	$0.171110\pi$
$564$	−6.13540e8	+	3.47956e9i	−0.144001	+	0.816671i
$565$	−1.26352e9	+	1.06022e9i	−0.294722	+	0.247301i
$566$	−2.81870e9	−	2.36517e9i	−0.653419	−	0.548284i
$567$	1.10317e9	+	6.25641e9i	0.254158	+	1.44140i
$568$	−2.46913e8	−	8.98689e7i	−0.0565359	−	0.0205774i
$569$	−4.52634e9			−1.03004			−0.515020	−	0.857178i	$-0.672215\pi$
$569$	−4.52634e9			−1.03004			−0.515020	+	0.857178i	$0.672215\pi$
$570$	4.22107e8	−	3.24705e9i	0.0954686	−	0.734391i
$571$	6.81272e8			0.153142			0.0765709	−	0.997064i	$-0.475603\pi$
$571$	6.81272e8			0.153142			0.0765709	+	0.997064i	$0.475603\pi$
$572$	5.19257e9	+	1.88994e9i	1.16010	+	0.422242i
$573$	1.84619e9	+	1.04703e10i	0.409954	+	2.32497i
$574$	1.61069e9	+	1.35153e9i	0.355484	+	0.298287i
$575$	2.05617e8	−	1.72534e8i	0.0451048	−	0.0378474i
$576$	1.00262e8	−	5.68616e8i	0.0218604	−	0.123977i
$577$	2.38731e9	−	4.13494e9i	0.517361	−	0.896095i	−0.482436	−	0.875931i	$-0.660248\pi$
$577$	2.38731e9	−	4.13494e9i	0.517361	−	0.896095i	0.999797	−	0.0201640i	$-0.00641883\pi$
$578$	1.62542e9	+	2.81531e9i	0.350121	+	0.606427i
$579$	5.51246e9	−	2.00637e9i	1.18024	−	0.429572i
$580$	2.45148e9	−	8.92266e8i	0.521711	−	0.189887i
$581$	−4.49172e9	−	7.77989e9i	−0.950159	−	1.64572i
$582$	4.63402e8	−	8.02636e8i	0.0974379	−	0.168767i
$583$	6.00744e7	−	3.40699e8i	0.0125559	−	0.0712083i
$584$	−1.26453e9	+	1.06107e9i	−0.262715	+	0.220444i
$585$	3.96354e9	+	3.32580e9i	0.818535	+	0.686832i
$586$	6.20058e8	+	3.51652e9i	0.127289	+	0.721891i
$587$	1.39360e9	+	5.07229e8i	0.284384	+	0.103507i	0.480274	−	0.877119i	$-0.340537\pi$
$587$	1.39360e9	+	5.07229e8i	0.284384	+	0.103507i	−0.195890	+	0.980626i	$0.562760\pi$
$588$	4.09705e9			0.831095
$589$	−6.76911e9	+	2.81677e9i	−1.36499	+	0.568000i
$590$	4.24541e8			0.0851015
$591$	−2.48196e9	−	9.03358e8i	−0.494582	−	0.180013i
$592$	−3.06950e8	−	1.74080e9i	−0.0608053	−	0.344844i
$593$	2.07316e9	+	1.73959e9i	0.408265	+	0.342575i	0.823678	−	0.567058i	$-0.191918\pi$
$593$	2.07316e9	+	1.73959e9i	0.408265	+	0.342575i	−0.415413	+	0.909633i	$0.636363\pi$
$594$	−4.79752e7	+	4.02560e7i	−0.00939213	+	0.00788093i
$595$	9.58071e7	−	5.43349e8i	0.0186461	−	0.105747i
$596$	1.14917e9	−	1.99042e9i	0.222342	−	0.385108i
$597$	1.83872e9	+	3.18476e9i	0.353676	+	0.612585i
$598$	6.47480e8	−	2.35663e8i	0.123815	−	0.0450648i
$599$	6.81424e9	−	2.48018e9i	1.29546	−	0.471508i	0.399943	−	0.916540i	$-0.369030\pi$
$599$	6.81424e9	−	2.48018e9i	1.29546	−	0.471508i	0.895515	+	0.445032i	$0.146808\pi$
$600$	6.00921e8	+	1.04082e9i	0.113576	+	0.196720i
$601$	3.48004e8	−	6.02760e8i	0.0653918	−	0.113262i	−0.831476	−	0.555561i	$-0.812504\pi$
$601$	3.48004e8	−	6.02760e8i	0.0653918	−	0.113262i	0.896868	+	0.442299i	$0.145837\pi$
$602$	−6.43527e8	+	3.64962e9i	−0.120221	+	0.681805i
$603$	2.28534e9	−	1.91763e9i	0.424463	−	0.356167i
$604$	−3.35878e9	−	2.81835e9i	−0.620230	−	0.520434i
$605$	1.37031e9	+	7.77143e9i	0.251580	+	1.42678i
$606$	−4.88299e9	−	1.77726e9i	−0.891315	−	0.324412i
$607$	8.00830e9			1.45338			0.726691	−	0.686964i	$-0.241057\pi$
$607$	8.00830e9			1.45338			0.726691	+	0.686964i	$0.241057\pi$
$608$	7.21223e8	−	6.63042e8i	0.130139	−	0.119641i
$609$	1.74856e10			3.13705
$610$	−1.79241e9	−	6.52383e8i	−0.319729	−	0.116372i
$611$	−1.64499e9	−	9.32920e9i	−0.291756	−	1.65463i
$612$	−2.15526e8	−	1.80848e8i	−0.0380075	−	0.0318921i
$613$	−2.33998e9	+	1.96347e9i	−0.410298	+	0.344281i	−0.824458	−	0.565923i	$-0.808520\pi$
$613$	−2.33998e9	+	1.96347e9i	−0.410298	+	0.344281i	0.414160	+	0.910204i	$0.364075\pi$
$614$	−7.94800e7	+	4.50753e8i	−0.0138570	+	0.0785868i
$615$	1.34474e9	−	2.32917e9i	0.233118	−	0.403773i
$616$	−2.60102e9	−	4.50510e9i	−0.448344	−	0.776555i
$617$	3.93000e9	−	1.43040e9i	0.673588	−	0.245166i	0.0174960	−	0.999847i	$-0.494431\pi$
$617$	3.93000e9	−	1.43040e9i	0.673588	−	0.245166i	0.656092	+	0.754681i	$0.272208\pi$
$618$	−1.11207e9	+	4.04761e8i	−0.189528	+	0.0689824i
$619$	−2.37709e9	−	4.11724e9i	−0.402836	−	0.697733i	0.591231	−	0.806503i	$-0.298642\pi$
$619$	−2.37709e9	−	4.11724e9i	−0.402836	−	0.697733i	−0.994067	+	0.108770i	$0.965309\pi$
$620$	−1.62148e9	+	2.80849e9i	−0.273238	+	0.473263i
$621$	−1.35605e6	+	7.69057e6i	−0.000227225	+	0.00128866i
$622$	2.12398e8	−	1.78223e8i	0.0353903	−	0.0296960i
$623$	1.29970e10	+	1.09058e10i	2.15346	+	1.80696i
$624$	5.35737e8	+	3.03832e9i	0.0882685	+	0.500595i
$625$	1.95486e9	+	7.11510e8i	0.320284	+	0.116574i
$626$	2.57462e9			0.419472
$627$	−1.50282e10	+	6.80658e8i	−2.43485	+	0.110279i
$628$	−1.99546e9			−0.321502
$629$	−8.09396e8	−	2.94596e8i	−0.129683	−	0.0472009i
$630$	−8.45818e8	−	4.79687e9i	−0.134767	−	0.764304i
$631$	3.19916e9	+	2.68441e9i	0.506912	+	0.425350i	0.860041	−	0.510225i	$-0.170438\pi$
$631$	3.19916e9	+	2.68441e9i	0.506912	+	0.425350i	−0.353129	+	0.935575i	$0.614882\pi$
$632$	−2.59539e9	+	2.17779e9i	−0.408972	+	0.343168i
$633$	2.12327e9	−	1.20417e10i	0.332731	−	1.88701i
$634$	−6.95059e7	+	1.20388e8i	−0.0108320	+	0.0187616i
$635$	2.39308e9	+	4.14494e9i	0.370893	+	0.642406i
$636$	1.81506e8	−	6.60627e7i	0.0279763	−	0.0101825i
$637$	−1.03223e10	+	3.75702e9i	−1.58230	+	0.575911i
$638$	−5.99290e9	−	1.03800e10i	−0.913618	−	1.58243i
$639$	−5.65178e8	+	9.78917e8i	−0.0856904	+	0.148420i
$640$	7.52472e7	−	4.26748e8i	0.0113465	−	0.0643490i
$641$	−9.58939e7	+	8.04646e7i	−0.0143810	+	0.0120671i	−0.649950	−	0.759977i	$-0.725210\pi$
$641$	−9.58939e7	+	8.04646e7i	−0.0143810	+	0.0120671i	0.635569	+	0.772044i	$0.280766\pi$
$642$	3.50180e9	+	2.93836e9i	0.522299	+	0.438261i
$643$	−5.04031e8	−	2.85850e9i	−0.0747685	−	0.424033i	−0.999099	−	0.0424404i	$-0.986487\pi$
$643$	−5.04031e8	−	2.85850e9i	−0.0747685	−	0.424033i	0.924330	−	0.381593i	$-0.124624\pi$
$644$	−6.09543e8	−	2.21855e8i	−0.0899298	−	0.0327318i
$645$	4.74033e9			0.695584
$646$	−1.04083e8	−	4.65897e8i	−0.0151903	−	0.0679949i
$647$	−9.49651e9			−1.37848			−0.689238	−	0.724535i	$-0.742054\pi$
$647$	−9.49651e9			−1.37848			−0.689238	+	0.724535i	$0.742054\pi$
$648$	2.28471e9	+	8.31566e8i	0.329851	+	0.120056i
$649$	−3.38699e8	−	1.92086e9i	−0.0486360	−	0.275828i
$650$	−2.46844e9	−	2.07126e9i	−0.352553	−	0.295827i
$651$	−1.66508e10	+	1.39717e10i	−2.36539	+	1.98479i
$652$	9.22722e8	−	5.23302e9i	0.130378	−	0.739410i
$653$	−1.68174e9	+	2.91287e9i	−0.236354	+	0.409378i	−0.959665	−	0.281144i	$-0.909286\pi$
$653$	−1.68174e9	+	2.91287e9i	−0.236354	+	0.409378i	0.723311	+	0.690522i	$0.242619\pi$
$654$	1.66421e9	+	2.88250e9i	0.232641	+	0.402947i
$655$	−3.94970e9	+	1.43757e9i	−0.549186	+	0.199887i
$656$	7.56162e8	−	2.75220e8i	0.104581	−	0.0380642i
$657$	3.55061e9	+	6.14984e9i	0.488455	+	0.846028i
$658$	−4.45904e9	+	7.72328e9i	−0.610169	+	1.05684i
$659$	1.09076e9	−	6.18601e9i	0.148467	−	0.841999i	−0.816051	−	0.577981i	$-0.803841\pi$
$659$	1.09076e9	−	6.18601e9i	0.148467	−	0.841999i	0.964518	−	0.264018i	$-0.0850479\pi$
$660$	−5.09730e9	+	4.27714e9i	−0.690138	+	0.579095i
$661$	−3.99271e9	−	3.35028e9i	−0.537729	−	0.451208i	0.333032	−	0.942916i	$-0.391928\pi$
$661$	−3.99271e9	−	3.35028e9i	−0.537729	−	0.451208i	−0.870760	+	0.491708i	$0.836373\pi$
$662$	−1.32661e9	−	7.52360e9i	−0.177722	−	1.00791i
$663$	1.41269e9	+	5.14176e8i	0.188256	+	0.0685195i
$664$	−3.43806e9			−0.455749
$665$	3.80428e9	−	7.33708e9i	0.501645	−	0.967492i
$666$	−7.60422e9			−0.997458
$667$	−1.40442e9	−	5.11167e8i	−0.183255	−	0.0666995i
$668$	−3.53520e8	−	2.00491e9i	−0.0458878	−	0.260242i
$669$	−1.39340e10	−	1.16920e10i	−1.79922	−	1.50973i
$670$	1.71515e9	−	1.43919e9i	0.220314	−	0.184865i
$671$	−1.52176e9	+	8.63033e9i	−0.194454	+	1.10280i
$672$	1.45221e9	−	2.51530e9i	0.184602	−	0.319740i
$673$	1.88384e9	+	3.26291e9i	0.238227	+	0.412622i	0.960206	−	0.279294i	$-0.0901003\pi$
$673$	1.88384e9	+	3.26291e9i	0.238227	+	0.412622i	−0.721978	+	0.691916i	$0.756767\pi$
$674$	6.23530e9	−	2.26946e9i	0.784418	−	0.285505i
$675$	3.43178e7	−	1.24907e7i	0.00429494	−	0.00156323i
$676$	−2.12797e9	−	3.68575e9i	−0.264942	−	0.458894i
$677$	2.89414e9	−	5.01281e9i	0.358476	−	0.620898i	−0.629231	−	0.777219i	$-0.716630\pi$
$677$	2.89414e9	−	5.01281e9i	0.358476	−	0.620898i	0.987706	+	0.156320i	$0.0499632\pi$
$678$	−7.34698e8	+	4.16668e9i	−0.0905325	+	0.513436i
$679$	1.79201e9	−	1.50368e9i	0.219683	−	0.184336i
$680$	−1.61753e8	−	1.35727e8i	−0.0197275	−	0.0165533i
$681$	2.58330e8	+	1.46506e9i	0.0313444	+	0.177763i
$682$	1.40008e10	+	5.09588e9i	1.69008	+	0.615139i
$683$	1.39773e10			1.67862			0.839308	−	0.543656i	$-0.182960\pi$
$683$	1.39773e10			1.67862			0.839308	+	0.543656i	$0.182960\pi$
$684$	−2.27023e9	−	3.55077e9i	−0.271252	−	0.424255i
$685$	3.31975e9			0.394628
$686$	1.43503e9	+	5.22308e8i	0.169717	+	0.0617721i
$687$	−1.49981e9	−	8.50582e9i	−0.176476	−	1.00085i
$688$	1.08648e9	+	9.11664e8i	0.127193	+	0.106727i
$689$	−3.96715e8	+	3.32884e8i	−0.0462074	+	0.0387726i
$690$	−1.44079e8	+	8.17112e8i	−0.0166966	+	0.0946912i
$691$	−6.51349e9	+	1.12817e10i	−0.751002	+	1.30077i	0.196336	+	0.980537i	$0.437096\pi$
$691$	−6.51349e9	+	1.12817e10i	−0.751002	+	1.30077i	−0.947338	+	0.320236i	$0.896238\pi$
$692$	−2.52962e9	−	4.38143e9i	−0.290191	−	0.502626i
$693$	−2.10289e10	+	7.65391e9i	−2.40022	+	0.873609i
$694$	−6.83039e9	+	2.48606e9i	−0.775688	+	0.282328i
$695$	1.96499e9	+	3.40346e9i	0.222031	+	0.384569i
$696$	3.34597e9	−	5.79540e9i	0.376175	−	0.651554i
$697$	6.80891e7	−	3.86152e8i	0.00761662	−	0.0431960i
$698$	6.65056e9	−	5.58048e9i	0.740225	−	0.621123i
$699$	−1.17976e10	−	9.89939e9i	−1.30655	−	1.09632i
$700$	5.26764e8	+	2.98743e9i	0.0580461	+	0.329196i
$701$	9.51742e9	+	3.46406e9i	1.04353	+	0.379815i	0.806219	−	0.591618i	$-0.201510\pi$
$701$	9.51742e9	+	3.46406e9i	1.04353	+	0.379815i	0.237315	+	0.971433i	$0.423733\pi$
$702$	9.37494e7			0.0102280
$703$	−1.02490e10	−	7.83789e9i	−1.11260	−	0.850855i
$704$	−1.99088e9			−0.215051
$705$	1.07194e10	+	3.90153e9i	1.15214	+	0.419346i
$706$	6.06672e8	+	3.44061e9i	0.0648840	+	0.367975i
$707$	−1.00474e10	−	8.43074e9i	−1.06926	−	0.897218i
$708$	8.34225e8	−	6.99998e8i	0.0883419	−	0.0741277i
$709$	−9.40720e8	+	5.33509e9i	−0.0991286	+	0.562186i	0.894275	+	0.447517i	$0.147692\pi$
$709$	−9.40720e8	+	5.33509e9i	−0.0991286	+	0.562186i	−0.993404	+	0.114669i	$0.963419\pi$
$710$	−4.24168e8	+	7.34681e8i	−0.0444768	+	0.0770362i
$711$	7.28747e9	+	1.26223e10i	0.760385	+	1.31702i
$712$	6.10164e9	−	2.22082e9i	0.633530	−	0.230586i
$713$	1.74581e9	−	6.35423e8i	0.180378	−	0.0656523i
$714$	−7.07632e8	−	1.22566e9i	−0.0727552	−	0.126016i
$715$	8.92024e9	−	1.54503e10i	0.912652	−	1.58076i
$716$	6.74303e8	−	3.82416e9i	0.0686530	−	0.389351i
$717$	1.49007e10	−	1.25032e10i	1.50970	−	1.26679i
$718$	−2.85532e9	−	2.39589e9i	−0.287885	−	0.241564i
$719$	3.28365e9	+	1.86225e10i	0.329462	+	1.86847i	0.476258	+	0.879306i	$0.341993\pi$
$719$	3.28365e9	+	1.86225e10i	0.329462	+	1.86847i	−0.146795	+	0.989167i	$0.546896\pi$
$720$	−1.75172e9	−	6.37572e8i	−0.174904	−	0.0636599i
$721$	−2.98707e9			−0.296805
$722$	6.00054e8	−	7.12575e9i	0.0593349	−	0.704613i
$723$	2.27197e10			2.23573
$724$	7.67505e8	+	2.79349e8i	0.0751616	+	0.0273566i
$725$	1.21369e9	+	6.88320e9i	0.118284	+	0.670822i
$726$	1.55065e10	+	1.30115e10i	1.50396	+	1.26197i
$727$	−2.83918e9	+	2.38235e9i	−0.274045	+	0.229951i	−0.769444	−	0.638715i	$-0.779466\pi$
$727$	−2.83918e9	+	2.38235e9i	−0.274045	+	0.229951i	0.495399	+	0.868666i	$0.335022\pi$
$728$	−1.35223e9	+	7.66887e9i	−0.129894	+	0.736668i
$729$	5.30432e9	−	9.18736e9i	0.507088	−	0.878303i
$730$	2.66475e9	+	4.61548e9i	0.253528	+	0.439123i
$731$	6.49429e8	−	2.36373e8i	0.0614923	−	0.0223814i
$732$	−4.59777e9	+	1.67345e9i	−0.433270	+	0.157697i
$733$	−4.16218e9	−	7.20910e9i	−0.390352	−	0.676110i	0.602144	−	0.798388i	$-0.294313\pi$
$733$	−4.16218e9	−	7.20910e9i	−0.390352	−	0.676110i	−0.992496	+	0.122278i	$0.960980\pi$
$734$	−4.73926e9	+	8.20864e9i	−0.442359	+	0.766188i
$735$	2.29695e9	−	1.30267e10i	0.213376	−	1.21012i
$736$	−1.90171e8	+	1.59572e8i	−0.0175821	+	0.0147531i
$737$	−7.88003e9	−	6.61213e9i	−0.725090	−	0.608422i
$738$	−6.01113e8	−	3.40908e9i	−0.0550502	−	0.312205i
$739$	−1.44529e10	−	5.26042e9i	−1.31734	−	0.479474i	−0.414737	−	0.909941i	$-0.636126\pi$
$739$	−1.44529e10	−	5.26042e9i	−1.31734	−	0.479474i	−0.902606	+	0.430468i	$0.858349\pi$
$740$	−5.70700e9			−0.517722
$741$	1.78882e10	+	1.36799e10i	1.61512	+	1.23515i
$742$	4.87532e8			0.0438116
$743$	−4.29981e9	−	1.56500e9i	−0.384582	−	0.139976i	0.142492	−	0.989796i	$-0.454489\pi$
$743$	−4.29981e9	−	1.56500e9i	−0.384582	−	0.139976i	−0.527073	+	0.849820i	$0.676711\pi$
$744$	1.44452e9	+	8.19226e9i	0.128593	+	0.729287i
$745$	−5.68431e9	−	4.76971e9i	−0.503653	−	0.422615i
$746$	−1.01251e10	+	8.49600e9i	−0.892925	+	0.749253i
$747$	−2.56827e9	+	1.45654e10i	−0.225434	+	1.27850i
$748$	−4.85058e8	+	8.40144e8i	−0.0423777	+	0.0734004i
$749$	5.76907e9	+	9.99233e9i	0.501672	+	0.868921i
$750$	1.16864e10	−	4.25351e9i	1.01150	−	0.368157i
$751$	1.27980e10	−	4.65810e9i	1.10256	−	0.401300i	0.274302	−	0.961644i	$-0.411553\pi$
$751$	1.27980e10	−	4.65810e9i	1.10256	−	0.401300i	0.828260	+	0.560344i	$0.189331\pi$
$752$	1.70652e9	+	2.95578e9i	0.146335	+	0.253460i
$753$	−3.79469e9	+	6.57259e9i	−0.323887	+	0.560989i
$754$	−3.11561e9	+	1.76695e10i	−0.264694	+	1.50115i
$755$	−1.08441e10	+	9.09925e9i	−0.917018	+	0.769469i
$756$	−6.76084e7	−	5.67302e7i	−0.00569081	−	0.00477516i
$757$	5.04869e8	+	2.86325e9i	0.0423002	+	0.239897i	0.998626	−	0.0524071i	$-0.0166893\pi$
$757$	5.04869e8	+	2.86325e9i	0.0423002	+	0.239897i	−0.956326	+	0.292304i	$0.905578\pi$
$758$	−9.35578e9	−	3.40523e9i	−0.780257	−	0.283990i
$759$	3.81202e9			0.316453
$760$	−1.70381e9	−	2.66487e9i	−0.140791	−	0.220206i
$761$	1.83314e10			1.50782			0.753911	−	0.656977i	$-0.228165\pi$
$761$	1.83314e10			1.50782			0.753911	+	0.656977i	$0.228165\pi$
$762$	1.15367e10	+	4.19903e9i	0.944584	+	0.343801i
$763$	1.45884e9	+	8.27350e9i	0.118897	+	0.674300i
$764$	7.86738e9	+	6.60151e9i	0.638268	+	0.535571i
$765$	−6.95841e8	+	5.83880e8i	−0.0561946	+	0.0471529i
$766$	2.53840e9	−	1.43960e10i	0.204060	−	1.15728i
$767$	−1.45989e9	+	2.52860e9i	−0.116825	+	0.202347i
$768$	−5.55777e8	−	9.62633e8i	−0.0442727	−	0.0766826i
$769$	1.45788e10	−	5.30624e9i	1.15606	−	0.420770i	0.308369	−	0.951267i	$-0.400217\pi$
$769$	1.45788e10	−	5.30624e9i	1.15606	−	0.420770i	0.847687	+	0.530497i	$0.177995\pi$
$770$	−1.57823e10	+	5.74429e9i	−1.24581	+	0.453439i
$771$	9.59362e8	+	1.66166e9i	0.0753862	+	0.130573i
$772$	2.83334e9	−	4.90749e9i	0.221635	−	0.383883i
$773$	1.51816e9	−	8.60990e9i	0.118219	−	0.670456i	−0.866886	−	0.498506i	$-0.833882\pi$
$773$	1.51816e9	−	8.60990e9i	0.118219	−	0.670456i	0.985106	−	0.171950i	$-0.0550067\pi$
$774$	4.67389e9	−	3.92186e9i	0.362314	−	0.304018i
$775$	−6.65568e9	−	5.58478e9i	−0.513614	−	0.430973i
$776$	−1.55463e8	−	8.81676e8i	−0.0119430	−	0.0677319i
$777$	−3.59445e10	−	1.30827e10i	−2.74890	−	1.00052i
$778$	7.28709e9			0.554786
$779$	2.70366e9	−	5.21438e9i	0.204913	−	0.395204i
$780$	9.96075e9			0.751555
$781$	3.66251e9	+	1.33304e9i	0.275106	+	0.100130i
$782$	2.10057e7	+	1.19129e8i	0.00157078	+	0.00890831i
$783$	−1.55773e8	−	1.30709e8i	−0.0115965	−	0.00973063i
$784$	3.03176e9	−	2.54395e9i	0.224692	−	0.188539i
$785$	−1.11873e9	+	6.34461e9i	−0.0825429	+	0.468124i
$786$	−5.39086e9	+	9.33725e9i	−0.395986	+	0.685867i
$787$	−1.07502e9	−	1.86199e9i	−0.0786148	−	0.136165i	0.824038	−	0.566535i	$-0.191716\pi$
$787$	−1.07502e9	−	1.86199e9i	−0.0786148	−	0.136165i	−0.902653	+	0.430370i	$0.858383\pi$
$788$	−2.39753e9	+	8.72629e8i	−0.174551	+	0.0635313i
$789$	−1.23945e10	+	4.51122e9i	−0.898376	+	0.326982i
$790$	5.46928e9	+	9.47306e9i	0.394671	+	0.683590i
$791$	−5.33958e9	+	9.24842e9i	−0.383609	+	0.664431i
$792$	−1.48721e9	+	8.43439e9i	−0.106374	+	0.603276i
$793$	1.00493e10	−	8.43236e9i	0.715615	−	0.600473i
$794$	−2.17380e8	−	1.82403e8i	−0.0154116	−	0.0129318i
$795$	−1.08289e8	−	6.14138e8i	−0.00764364	−	0.0433492i
$796$	3.33811e9	+	1.21497e9i	0.234588	+	0.0853830i
$797$	−1.22043e10			−0.853906			−0.426953	−	0.904274i	$-0.640413\pi$
$797$	−1.22043e10			−0.853906			−0.426953	+	0.904274i	$0.640413\pi$
$798$	−4.62222e9	−	2.06900e10i	−0.321988	−	1.44129i
$799$	1.66311e9			0.115347
$800$	1.09094e9	+	3.97071e8i	0.0753334	+	0.0274191i
$801$	−4.85052e9	−	2.75087e10i	−0.333484	−	1.89128i
$802$	4.63756e8	+	3.89137e8i	0.0317453	+	0.0266374i
$803$	1.87571e10	−	1.57390e10i	1.27838	−	1.07269i
$804$	9.97308e8	−	5.65602e9i	0.0676758	−	0.383808i
$805$	−1.04713e9	+	1.81367e9i	−0.0707478	+	0.122539i
$806$	−1.11518e10	−	1.93154e10i	−0.750189	−	1.29937i
$807$	−1.94986e10	+	7.09693e9i	−1.30601	+	0.475349i
$808$	−4.71688e9	+	1.71680e9i	−0.314568	+	0.114494i
$809$	−8.30371e9	−	1.43824e10i	−0.551381	−	0.955021i	−0.998175	−	0.0603837i	$-0.980768\pi$
$809$	−8.30371e9	−	1.43824e10i	−0.551381	−	0.955021i	0.446794	−	0.894637i	$-0.352566\pi$
$810$	3.92487e9	−	6.79807e9i	0.259494	−	0.449457i
$811$	−5.76747e8	+	3.27089e9i	−0.0379675	+	0.215325i	−0.997889	−	0.0649451i	$-0.979313\pi$
$811$	−5.76747e8	+	3.27089e9i	−0.0379675	+	0.215325i	0.959921	+	0.280270i	$0.0904239\pi$
$812$	1.29391e10	−	1.08572e10i	0.848123	−	0.711660i
$813$	−1.10522e10	−	9.27390e9i	−0.721327	−	0.605265i
$814$	4.55305e9	+	2.58216e10i	0.295881	+	1.67802i
$815$	−1.61212e10	−	5.86763e9i	−1.04315	−	0.379674i
$816$	−5.41637e8			−0.0348974
$817$	1.03419e10	−	4.68404e8i	0.663473	−	0.0300499i
$818$	−1.02918e10			−0.657437
$819$	3.14792e10	+	1.14575e10i	2.00230	+	0.728778i
$820$	−4.51138e8	−	2.55853e9i	−0.0285733	−	0.162047i
$821$	−7.76313e9	−	6.51404e9i	−0.489594	−	0.410818i	0.364287	−	0.931287i	$-0.381313\pi$
$821$	−7.76313e9	−	6.51404e9i	−0.489594	−	0.410818i	−0.853881	+	0.520469i	$0.825757\pi$
$822$	6.52332e9	−	5.47372e9i	0.409654	−	0.343741i
$823$	−9.51805e8	+	5.39795e9i	−0.0595180	+	0.337543i	−0.999997	−	0.00230750i	$-0.999265\pi$
$823$	−9.51805e8	+	5.39795e9i	−0.0595180	+	0.337543i	0.940479	+	0.339851i	$0.110377\pi$
$824$	−5.71592e8	+	9.90026e8i	−0.0355911	+	0.0616455i
$825$	−8.91358e9	−	1.54388e10i	−0.552667	−	0.957247i
$826$	2.58294e9	−	9.40112e8i	0.159472	−	0.0580429i
$827$	−5.77042e9	+	2.10026e9i	−0.354763	+	0.129123i	−0.513253	−	0.858238i	$-0.671560\pi$
$827$	−5.77042e9	+	2.10026e9i	−0.354763	+	0.129123i	0.158490	+	0.987361i	$0.449337\pi$
$828$	5.33970e8	+	9.24863e8i	0.0326897	+	0.0566202i
$829$	−3.71110e9	+	6.42781e9i	−0.226236	+	0.391852i	−0.956690	−	0.291110i	$-0.905975\pi$
$829$	−3.71110e9	+	6.42781e9i	−0.226236	+	0.391852i	0.730454	+	0.682962i	$0.239309\pi$
$830$	−1.92750e9	+	1.09314e10i	−0.117009	+	0.663593i
$831$	−8.09671e8	+	6.79394e8i	−0.0489446	+	0.0410694i
$832$	2.28300e9	+	1.91566e9i	0.137427	+	0.115315i
$833$	−3.34880e8	−	1.89920e9i	−0.0200739	−	0.113845i
$834$	9.47297e9	+	3.44788e9i	0.565464	+	0.205812i
$835$	−6.57286e9			−0.390708
$836$	−1.06981e10	+	9.83504e9i	−0.633261	+	0.582176i
$837$	2.52778e8			0.0149005
$838$	−5.33714e9	−	1.94256e9i	−0.313296	−	0.114030i
$839$	2.09165e9	+	1.18624e10i	0.122271	+	0.693433i	0.982891	+	0.184186i	$0.0589648\pi$
$839$	2.09165e9	+	1.18624e10i	0.122271	+	0.693433i	−0.860621	+	0.509247i	$0.829924\pi$
$840$	−7.18330e9	−	6.02750e9i	−0.418164	−	0.350881i
$841$	1.65983e10	−	1.39276e10i	0.962228	−	0.807405i
$842$	−1.98282e9	+	1.12451e10i	−0.114470	+	0.649192i
$843$	−2.09009e10	+	3.62014e10i	−1.20162	+	2.08127i
$844$	−5.90575e9	−	1.02291e10i	−0.338124	−	0.585649i
$845$	−1.29119e10	+	4.69956e9i	−0.736195	+	0.267953i
$846$	1.37970e10	−	5.02170e9i	0.783410	−	0.285138i
$847$	2.55463e10	+	4.42475e10i	1.44456	+	2.50205i
$848$	9.32919e7	−	1.61586e8i	0.00525362	−	0.00909953i
$849$	−5.29159e9	+	3.00101e10i	−0.296763	+	1.68302i
$850$	4.33360e8	−	3.63632e8i	0.0242037	−	0.0203094i
$851$	2.50455e9	+	2.10157e9i	0.139308	+	0.116894i
$852$	3.77875e8	+	2.14304e9i	0.0209320	+	0.118711i
$853$	1.50907e10	+	5.49257e9i	0.832508	+	0.303008i	0.722888	−	0.690965i	$-0.242814\pi$
$853$	1.50907e10	+	5.49257e9i	0.832508	+	0.303008i	0.109620	+	0.993974i	$0.465037\pi$
$854$	−1.23498e10			−0.678512
$855$	−1.25625e10	+	5.22754e9i	−0.687378	+	0.286033i
$856$	4.41578e9			0.240629
$857$	−3.20247e10	−	1.16560e10i	−1.73801	−	0.632584i	−0.738863	−	0.673856i	$-0.764637\pi$
$857$	−3.20247e10	−	1.16560e10i	−1.73801	−	0.632584i	−0.999148	+	0.0412712i	$0.986859\pi$
$858$	−7.94670e9	−	4.50680e10i	−0.429518	−	2.43592i
$859$	−7.40388e9	−	6.21259e9i	−0.398550	−	0.334424i	0.421383	−	0.906883i	$-0.361545\pi$
$859$	−7.40388e9	−	6.21259e9i	−0.398550	−	0.334424i	−0.819933	+	0.572459i	$0.805989\pi$
$860$	3.50778e9	−	2.94337e9i	0.188056	−	0.157798i
$861$	3.02377e9	−	1.71486e10i	0.161450	−	0.915627i
$862$	1.17629e9	−	2.03739e9i	0.0625517	−	0.108343i
$863$	−6.12017e9	−	1.06004e10i	−0.324135	−	0.561418i	0.657202	−	0.753714i	$-0.271740\pi$
$863$	−6.12017e9	−	1.06004e10i	−0.324135	−	0.561418i	−0.981337	+	0.192297i	$0.938406\pi$
$864$	−3.17397e7	+	1.15523e7i	−0.00167419	+	0.000609356i
$865$	−1.53491e10	+	5.58660e9i	−0.806354	+	0.293489i
$866$	−3.85217e9	−	6.67216e9i	−0.201555	−	0.349103i
$867$	1.34613e10	−	2.33156e10i	0.701486	−	1.21501i
$868$	−3.64604e9	+	2.06777e10i	−0.189235	+	1.07321i
$869$	3.84980e10	−	3.23037e10i	1.99007	−	1.66987i
$870$	−1.65507e10	−	1.38877e10i	−0.852117	−	0.715011i
$871$	2.67393e9	+	1.51646e10i	0.137116	+	0.777621i
$872$	3.02131e9	+	1.09967e9i	0.154307	+	0.0561633i
$873$	−3.85137e9			−0.195914
$874$	−2.33594e8	+	1.79692e9i	−0.0118351	+	0.0910412i
$875$	3.13902e10			1.58404
$876$	1.28464e10	+	4.67571e9i	0.645680	+	0.235008i
$877$	−1.91139e9	−	1.08400e10i	−0.0956865	−	0.542665i	−0.994535	−	0.104405i	$-0.966706\pi$
$877$	−1.91139e9	−	1.08400e10i	−0.0956865	−	0.542665i	0.898848	−	0.438260i	$-0.144405\pi$
$878$	1.31014e10	+	1.09934e10i	0.653261	+	0.548151i
$879$	2.26535e10	−	1.90086e10i	1.12506	−	0.944036i
$880$	−1.11616e9	+	6.33005e9i	−0.0552124	+	0.313125i
$881$	−1.42605e10	+	2.46999e10i	−0.702617	+	1.21697i	0.264928	+	0.964268i	$0.414652\pi$
$881$	−1.42605e10	+	2.46999e10i	−0.702617	+	1.21697i	−0.967545	+	0.252700i	$0.918682\pi$
$882$	−8.51272e9	−	1.47445e10i	−0.417761	−	0.723584i
$883$	−2.02551e9	+	7.37225e8i	−0.0990084	+	0.0360361i	−0.391049	−	0.920370i	$-0.627888\pi$
$883$	−2.02551e9	+	7.37225e8i	−0.0990084	+	0.0360361i	0.292041	+	0.956406i	$0.405666\pi$
$884$	1.36463e9	−	4.96685e8i	0.0664404	−	0.0241823i
$885$	−1.75796e9	−	3.04488e9i	−0.0852527	−	0.147662i
$886$	7.13948e9	−	1.23659e10i	0.344865	−	0.597323i
$887$	1.39075e9	−	7.88735e9i	0.0669141	−	0.379489i	−0.932899	−	0.360139i	$-0.882729\pi$
$887$	1.39075e9	−	7.88735e9i	0.0669141	−	0.379489i	0.999813	−	0.0193497i	$-0.00615958\pi$
$888$	−1.12143e10	+	9.40990e9i	−0.537435	+	0.450962i
$889$	2.37383e10	+	1.99188e10i	1.13317	+	0.950840i
$890$	−3.64034e9	−	2.06454e10i	−0.173092	−	0.981653i
$891$	−3.38895e10	−	1.23348e10i	−1.60507	−	0.584197i
$892$	−1.75708e10			−0.828924
$893$	2.37718e10	+	7.45269e9i	1.11707	+	0.350213i
$894$	−1.90342e10			−0.890949
$895$	−1.17810e10	−	4.28793e9i	−0.549289	−	0.199925i
$896$	−4.87191e8	−	2.76300e9i	−0.0226267	−	0.128322i
$897$	−4.37134e9	−	3.66799e9i	−0.202228	−	0.169689i
$898$	1.48204e9	−	1.24358e9i	0.0682955	−	0.0573067i
$899$	−8.40068e9	+	4.76426e10i	−0.385616	+	2.18694i
$900$	2.49715e9	−	4.32518e9i	0.114181	−	0.197768i
$901$	−4.54592e7	−	7.87377e7i	−0.00207055	−	0.00358630i
$902$	−1.12163e10	+	4.08240e9i	−0.508893	+	0.185222i
$903$	2.88405e10	−	1.04971e10i	1.30345	−	0.474418i
$904$	2.04352e9	+	3.53947e9i	0.0920001	+	0.159349i
$905$	1.31849e9	−	2.28369e9i	0.0591297	−	0.102416i
$906$	−6.30548e9	+	3.57602e10i	−0.281689	+	1.59754i
$907$	1.20745e10	−	1.01317e10i	0.537335	−	0.450878i	−0.333290	−	0.942824i	$-0.608159\pi$
$907$	1.20745e10	−	1.01317e10i	0.537335	−	0.450878i	0.870625	+	0.491946i	$0.163714\pi$
$908$	1.10085e9	+	9.23722e8i	0.0488008	+	0.0409488i
$909$	3.74970e9	+	2.12656e10i	0.165586	+	0.939084i
$910$	2.36252e10	+	8.59889e9i	1.03928	+	0.378266i
$911$	−1.91825e9			−0.0840603			−0.0420302	−	0.999116i	$-0.513383\pi$
$911$	−1.91825e9			−0.0840603			−0.0420302	+	0.999116i	$0.513383\pi$
$912$	−7.74194e9	−	2.42718e9i	−0.337962	−	0.105954i
$913$	5.09975e10			2.21769
$914$	1.39526e9	+	5.07834e8i	0.0604427	+	0.0219994i
$915$	2.74310e9	+	1.55569e10i	0.118377	+	0.671350i
$916$	−6.39128e9	−	5.36292e9i	−0.274760	−	0.230551i
$917$	−2.08469e10	+	1.74926e10i	−0.892788	+	0.749138i
$918$	−2.85802e6	+	1.62087e7i	−0.000121932	+	0.000691509i
$919$	1.95127e10	−	3.37971e10i	0.829305	−	1.43640i	−0.0692798	−	0.997597i	$-0.522070\pi$
$919$	1.95127e10	−	3.37971e10i	0.829305	−	1.43640i	0.898584	−	0.438801i	$-0.144597\pi$
$920$	4.00746e8	+	6.94113e8i	0.0169673	+	0.0293882i
$921$	3.56200e9	−	1.29646e9i	0.150240	−	0.0546828i
$922$	1.27854e9	−	4.65351e8i	0.0537225	−	0.0195534i
$923$	−2.91722e9	−	5.05277e9i	−0.122113	−	0.211506i
$924$	−2.15409e10	+	3.73100e10i	−0.898282	+	1.55587i
$925$	2.65506e9	−	1.50576e10i	0.110301	−	0.625546i
$926$	−1.24746e10	+	1.04674e10i	−0.516282	+	0.433212i
$927$	3.76728e9	+	3.16112e9i	0.155328	+	0.130335i
$928$	−1.12252e9	−	6.36610e9i	−0.0461078	−	0.261490i
$929$	2.49620e10	+	9.08541e9i	1.02147	+	0.371783i	0.797825	−	0.602889i	$-0.205984\pi$
$929$	2.49620e10	+	9.08541e9i	1.02147	+	0.371783i	0.223640	+	0.974672i	$0.428206\pi$
$930$	2.68573e10			1.09490
$931$	3.72402e9	−	2.86470e10i	0.151248	−	1.16347i
$932$	−1.48768e10			−0.601942
$933$	−2.15776e9	−	7.85359e8i	−0.0869795	−	0.0316579i
$934$	−5.06219e9	−	2.87091e10i	−0.203294	−	1.15294i
$935$	2.39932e9	+	2.01327e9i	0.0959946	+	0.0805491i
$936$	9.82115e9	−	8.24092e9i	0.391469	−	0.328481i
$937$	−4.17919e9	+	2.37014e10i	−0.165960	+	0.941207i	0.782109	+	0.623142i	$0.214144\pi$
$937$	−4.17919e9	+	2.37014e10i	−0.165960	+	0.941207i	−0.948069	+	0.318065i	$0.896967\pi$
$938$	7.24816e9	−	1.25542e10i	0.286760	−	0.496682i
$939$	−1.06611e10	−	1.84656e10i	−0.420217	−	0.727838i
$940$	1.03547e10	−	3.76881e9i	0.406622	−	0.147998i
$941$	−1.46272e10	+	5.32388e9i	−0.572267	+	0.208288i	−0.611912	−	0.790926i	$-0.709599\pi$
$941$	−1.46272e10	+	5.32388e9i	−0.572267	+	0.208288i	0.0396454	+	0.999214i	$0.487377\pi$
$942$	8.26291e9	+	1.43118e10i	0.322074	+	0.557848i
$943$	−7.44180e8	+	1.28896e9i	−0.0288993	+	0.0500550i
$944$	1.82671e8	−	1.03598e9i	0.00706752	−	0.0400819i
$945$	−2.18278e8	+	1.83157e8i	−0.00841394	+	0.00706014i
$946$	−1.61160e10	−	1.35229e10i	−0.618924	−	0.519339i
$947$	4.98292e9	+	2.82595e10i	0.190660	+	1.08128i	0.918465	+	0.395501i	$0.129429\pi$
$947$	4.98292e9	+	2.82595e10i	0.190660	+	1.08128i	−0.727806	+	0.685783i	$0.759460\pi$
$948$	2.63667e10	+	9.59669e9i	1.00514	+	0.365841i
$949$	−3.66536e10			−1.39215
$950$	7.82377e9	−	3.25564e9i	0.296063	−	0.123198i
$951$	1.15126e9			0.0434051
$952$	−1.28467e9	−	4.67583e8i	−0.0482574	−	0.0175642i
$953$	−7.89226e8	−	4.47592e9i	−0.0295377	−	0.167516i	0.966471	−	0.256777i	$-0.0826606\pi$
$953$	−7.89226e8	−	4.47592e9i	−0.0295377	−	0.167516i	−0.996008	+	0.0892608i	$0.971550\pi$
$954$	−6.14873e8	−	5.15940e8i	−0.0229280	−	0.0192389i
$955$	2.54004e10	−	2.13135e10i	0.943688	−	0.791848i
$956$	3.26282e9	−	1.85043e10i	0.120779	−	0.684969i
$957$	−4.96315e10	+	8.59643e10i	−1.83048	+	3.17049i
$958$	1.68786e10	+	2.92345e10i	0.620234	+	1.07428i
$959$	2.01976e10	−	7.35132e9i	0.739493	−	0.269154i
$960$	−3.37230e9	+	1.22742e9i	−0.123020	+	0.0447758i
$961$	−1.63124e10	−	2.82538e10i	−0.592905	−	1.02694i
$962$	1.96249e10	−	3.39914e10i	0.710715	−	1.23099i
$963$	3.29864e9	−	1.87075e10i	0.119026	−	0.675031i
$964$	1.68123e10	−	1.41072e10i	0.604445	−	0.507190i
$965$	−1.40150e10	−	1.17600e10i	−0.502051	−	0.421271i
$966$	9.32844e8	+	5.29042e9i	0.0332958	+	0.188830i
$967$	−8.90466e9	−	3.24103e9i	−0.316683	−	0.115263i	0.178788	−	0.983888i	$-0.442782\pi$
$967$	−8.90466e9	−	3.24103e9i	−0.316683	−	0.115263i	−0.495471	+	0.868624i	$0.665005\pi$
$968$	1.95537e10			0.692892
$969$	−2.91050e9	+	2.67571e9i	−0.102763	+	0.0944727i
$970$	−2.89047e9			−0.101687
$971$	2.88363e10	+	1.04955e10i	1.01082	+	0.367907i	0.793746	−	0.608249i	$-0.208128\pi$
$971$	2.88363e10	+	1.04955e10i	1.01082	+	0.367907i	0.217070	+	0.976156i	$0.430350\pi$
$972$	−3.52157e9	−	1.99718e10i	−0.123000	−	0.697566i
$973$	1.94919e10	+	1.63556e10i	0.678357	+	0.569209i
$974$	−2.76691e10	+	2.32172e10i	−0.959487	+	0.805105i
$975$	−4.63403e9	+	2.62809e10i	−0.160119	+	0.908079i
$976$	−2.36320e9	+	4.09318e9i	−0.0813629	+	0.140925i
$977$	8.25911e9	+	1.43052e10i	0.283337	+	0.490753i	0.972204	−	0.234134i	$-0.0752253\pi$
$977$	8.25911e9	+	1.43052e10i	0.283337	+	0.490753i	−0.688868	+	0.724887i	$0.741892\pi$
$978$	−4.13530e10	+	1.50513e10i	−1.41358	+	0.514502i
$979$	−9.05070e10	+	3.29418e10i	−3.08278	+	1.12204i
$980$	−6.38883e9	−	1.10658e10i	−0.216835	−	0.375570i
$981$	6.91570e9	−	1.19783e10i	0.233881	−	0.405094i
$982$	4.45095e9	−	2.52426e10i	0.149990	−	0.850635i
$983$	−2.23077e10	+	1.87184e10i	−0.749063	+	0.628538i	−0.935255	−	0.353975i	$-0.884830\pi$
$983$	−2.23077e10	+	1.87184e10i	−0.749063	+	0.628538i	0.186192	+	0.982513i	$0.440385\pi$
$984$	−5.10509e9	−	4.28368e9i	−0.170813	−	0.143329i
$985$	1.43040e9	+	8.11222e9i	0.0476905	+	0.270466i
$986$	−2.95996e9	−	1.07734e9i	−0.0983370	−	0.0357917i
$987$	7.38570e10			2.44501
$988$	2.17312e10	−	9.84247e8i	0.716860	−	0.0324680i
$989$	−2.62329e9			−0.0862303
$990$	2.59836e10	+	9.45724e9i	0.851090	+	0.309771i
$991$	8.24653e9	+	4.67684e10i	0.269162	+	1.52649i	0.756916	+	0.653512i	$0.226705\pi$
$991$	8.24653e9	+	4.67684e10i	0.269162	+	1.52649i	−0.487755	+	0.872981i	$0.662184\pi$
$992$	6.15568e9	+	5.16523e9i	0.200210	+	0.167996i
$993$	−4.84673e10	+	4.06689e10i	−1.57082	+	1.31807i
$994$	−9.53778e8	+	5.40914e9i	−0.0308031	+	0.174693i
$995$	5.73450e9	−	9.93245e9i	0.184550	−	0.319651i
$996$	1.42365e10	+	2.46584e10i	0.456558	+	0.790782i
$997$	7.53880e9	−	2.74390e9i	0.240918	−	0.0876870i	−0.218739	−	0.975783i	$-0.570194\pi$
$997$	7.53880e9	−	2.74390e9i	0.240918	−	0.0876870i	0.459657	+	0.888096i	$0.347972\pi$
$998$	1.74203e10	−	6.34047e9i	0.554751	−	0.201913i
$999$	2.22420e8	+	3.85244e8i	0.00705823	+	0.0122252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.23.5	yes	30
19.5	even	9	inner	38.8.e.a.5.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.5.5	✓	30	19.5	even	9	inner
38.8.e.a.23.5	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-7.51754 - 2.73616i) q^{2} +(11.5048 + 65.2472i) q^{3} +(49.0268 + 41.1384i) q^{4} +(158.287 - 132.818i) q^{5} +(92.0387 - 521.978i) q^{6} +(668.912 - 1158.59i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2069.73 + 753.319i) q^{9} +O(q^{10})\)	\(q+(-7.51754 - 2.73616i) q^{2} +(11.5048 + 65.2472i) q^{3} +(49.0268 + 41.1384i) q^{4} +(158.287 - 132.818i) q^{5} +(92.0387 - 521.978i) q^{6} +(668.912 - 1158.59i) q^{7} +(-256.000 - 443.405i) q^{8} +(-2069.73 + 753.319i) q^{9} +(-1553.34 + 565.369i) q^{10} +(3797.30 + 6577.12i) q^{11} +(-2120.12 + 3672.16i) q^{12} +(1974.16 - 11196.0i) q^{13} +(-8198.66 + 6879.49i) q^{14} +(10487.1 + 8799.71i) q^{15} +(711.263 + 4033.77i) q^{16} +(1875.53 + 682.637i) q^{17} +17620.5 q^{18} +(23749.0 + 18161.9i) q^{19} +13224.2 q^{20} +(83290.5 + 30315.2i) q^{21} +(-10550.3 - 59833.8i) q^{22} +(-5803.54 - 4869.75i) q^{23} +(25985.7 - 21804.6i) q^{24} +(-6152.29 + 34891.4i) q^{25} +(-45474.8 + 78764.7i) q^{26} +(-515.392 - 892.685i) q^{27} +(80457.2 - 29284.0i) q^{28} +(185378. - 67472.0i) q^{29} +(-54759.7 - 94846.5i) q^{30} +(-122615. + 212375. i) q^{31} +(5690.10 - 32270.2i) q^{32} +(-385451. + 323432. i) q^{33} +(-12231.6 - 10263.5i) q^{34} +(-48002.0 - 272233. i) q^{35} +(-132463. - 48212.4i) q^{36} -431556. q^{37} +(-128840. - 201514. i) q^{38} +753219. q^{39} +(-99413.7 - 36183.6i) q^{40} +(-34114.5 - 193473. i) q^{41} +(-543192. - 455792. i) q^{42} +(265254. - 222574. i) q^{43} +(-84402.5 + 478670. i) q^{44} +(-227556. + 394138. i) q^{45} +(30304.0 + 52488.0i) q^{46} +(783011. - 284993. i) q^{47} +(-255009. + 92815.8i) q^{48} +(-483115. - 836780. i) q^{49} +(141719. - 245464. i) q^{50} +(-22962.5 + 130227. i) q^{51} +(557372. - 467691. i) q^{52} +(-34895.4 - 29280.7i) q^{53} +(1431.95 + 8120.99i) q^{54} +(1.47462e6 + 536719. i) q^{55} -684966. q^{56} +(-911786. + 1.75851e6i) q^{57} -1.57820e6 q^{58} +(-241337. - 87839.6i) q^{59} +(152143. + 862844. i) q^{60} +(883944. + 741717. i) q^{61} +(1.50285e6 - 1.26104e6i) q^{62} +(-511678. + 2.90187e6i) q^{63} +(-131072. + 227023. i) q^{64} +(-1.17455e6 - 2.03438e6i) q^{65} +(3.78261e6 - 1.37676e6i) q^{66} +(-1.27278e6 + 463255. i) q^{67} +(63868.7 + 110624. i) q^{68} +(250969. - 434691. i) q^{69} +(-384016. + 2.17786e6i) q^{70} +(393135. - 329880. i) q^{71} +(863876. + 724878. i) q^{72} +(-559855. - 3.17510e6i) q^{73} +(3.24424e6 + 1.18081e6i) q^{74} -2.34735e6 q^{75} +(417187. + 1.86742e6i) q^{76} +1.01602e7 q^{77} +(-5.66236e6 - 2.06093e6i) q^{78} +(-1.14908e6 - 6.51675e6i) q^{79} +(648342. + 544024. i) q^{80} +(-3.63772e6 + 3.05241e6i) q^{81} +(-272916. + 1.54778e6i) q^{82} +(3.35748e6 - 5.81533e6i) q^{83} +(2.83635e6 + 4.91270e6i) q^{84} +(387538. - 141052. i) q^{85} +(-2.60306e6 + 947435. i) q^{86} +(6.53510e6 + 1.13191e7i) q^{87} +(1.94422e6 - 3.36749e6i) q^{88} +(-2.20222e6 + 1.24894e7i) q^{89} +(2.78908e6 - 2.34032e6i) q^{90} +(-1.16510e7 - 9.77637e6i) q^{91} +(-84195.6 - 477497. i) q^{92} +(-1.52675e7 - 5.55692e6i) q^{93} -6.66610e6 q^{94} +(6.17139e6 - 279514. i) q^{95} +2.17100e6 q^{96} +(1.64314e6 + 598053. i) q^{97} +(1.34227e6 + 7.61241e6i) q^{98} +(-1.28141e7 - 1.07523e7i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more