LMFDB - Embedded newform 54.8.e.b.31.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,8,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, 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("54.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	54.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:	$16.8687913761$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	54.31
Dual form			54.8.e.b.7.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.51754 + 2.73616i) q^{2} +(43.9672 - 15.9339i) q^{3} +(49.0268 + 41.1384i) q^{4} +(72.2267 - 409.618i) q^{5} +(374.123 + 0.517653i) q^{6} +(-152.227 + 127.734i) q^{7} +(256.000 + 443.405i) q^{8} +(1679.22 - 1401.13i) q^{9} +O(q^{10})$	\(q+(7.51754 + 2.73616i) q^{2} +(43.9672 - 15.9339i) q^{3} +(49.0268 + 41.1384i) q^{4} +(72.2267 - 409.618i) q^{5} +(374.123 + 0.517653i) q^{6} +(-152.227 + 127.734i) q^{7} +(256.000 + 443.405i) q^{8} +(1679.22 - 1401.13i) q^{9} +(1663.75 - 2881.70i) q^{10} +(-938.612 - 5323.14i) q^{11} +(2811.07 + 1027.55i) q^{12} +(-7254.96 + 2640.59i) q^{13} +(-1493.88 + 543.727i) q^{14} +(-3351.20 - 19160.6i) q^{15} +(711.263 + 4033.77i) q^{16} +(8063.48 - 13966.3i) q^{17} +(16457.4 - 5938.46i) q^{18} +(25405.5 + 44003.7i) q^{19} +(20392.1 - 17111.0i) q^{20} +(-4657.71 + 8041.67i) q^{21} +(7508.90 - 42585.1i) q^{22} +(-34815.3 - 29213.5i) q^{23} +(18320.8 + 15416.2i) q^{24} +(-89156.8 - 32450.4i) q^{25} -61764.6 q^{26} +(51505.2 - 88360.5i) q^{27} -12718.0 q^{28} +(177240. + 64510.0i) q^{29} +(27233.7 - 153210. i) q^{30} +(142294. + 119398. i) q^{31} +(-5690.10 + 32270.2i) q^{32} +(-126086. - 219087. i) q^{33} +(98831.7 - 82929.6i) q^{34} +(41327.3 + 71580.9i) q^{35} +(139967. + 387.331i) q^{36} +(286706. - 496590. i) q^{37} +(70586.0 + 400313. i) q^{38} +(-276905. + 231699. i) q^{39} +(200117. - 72836.5i) q^{40} +(-192028. + 69892.5i) q^{41} +(-57017.8 + 47709.4i) q^{42} +(105674. + 599308. i) q^{43} +(172968. - 299590. i) q^{44} +(-452645. - 789039. i) q^{45} +(-181792. - 314874. i) q^{46} +(-487813. + 409324. i) q^{47} +(95545.9 + 166020. i) q^{48} +(-136150. + 772142. i) q^{49} +(-581450. - 487895. i) q^{50} +(131990. - 742543. i) q^{51} +(-464318. - 168998. i) q^{52} +256236. q^{53} +(628961. - 523327. i) q^{54} -2.24825e6 q^{55} +(-95608.1 - 34798.5i) q^{56} +(1.81816e6 + 1.52991e6i) q^{57} +(1.15590e6 + 969913. i) q^{58} +(-135576. + 768888. i) q^{59} +(623938. - 1.07725e6i) q^{60} +(-1.90136e6 + 1.59543e6i) q^{61} +(743004. + 1.28692e6i) q^{62} +(-76651.2 + 427785. i) q^{63} +(-131072. + 227023. i) q^{64} +(557631. + 3.16248e6i) q^{65} +(-348401. - 1.99199e6i) q^{66} +(-262946. + 95704.5i) q^{67} +(969880. - 353007. i) q^{68} +(-1.99621e6 - 729691. i) q^{69} +(114822. + 651190. i) q^{70} +(-706592. + 1.22385e6i) q^{71} +(1.05115e6 + 385885. i) q^{72} +(242575. + 420152. i) q^{73} +(3.51408e6 - 2.94866e6i) q^{74} +(-4.43703e6 - 6139.28i) q^{75} +(-564688. + 3.20250e6i) q^{76} +(822828. + 690435. i) q^{77} +(-2.71561e6 + 984149. i) q^{78} +(-6.34610e6 - 2.30979e6i) q^{79} +1.70368e6 q^{80} +(856611. - 4.70564e6i) q^{81} -1.63482e6 q^{82} +(1.77558e6 + 646257. i) q^{83} +(-559174. + 202647. i) q^{84} +(-5.13847e6 - 4.31169e6i) q^{85} +(-845394. + 4.79447e6i) q^{86} +(8.82062e6 + 12204.6i) q^{87} +(2.12002e6 - 1.77891e6i) q^{88} +(3.75030e6 + 6.49572e6i) q^{89} +(-1.24384e6 - 7.17015e6i) q^{90} +(767111. - 1.32868e6i) q^{91} +(-505087. - 2.86449e6i) q^{92} +(8.15872e6 + 2.98232e6i) q^{93} +(-4.78713e6 + 1.74237e6i) q^{94} +(1.98596e7 - 7.22832e6i) q^{95} +(264011. + 1.50949e6i) q^{96} +(-433312. - 2.45743e6i) q^{97} +(-3.13622e6 + 5.43208e6i) q^{98} +(-9.03457e6 - 7.62361e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9}+O(q^{10}) $ 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9} - 3000 q^{10} - 2523 q^{11} - 5376 q^{12} - 9924 q^{13} + 13416 q^{14} - 15084 q^{15} + 29478 q^{17} + 22848 q^{18} - 61731 q^{19} - 27264 q^{20} - 36372 q^{21} + 20184 q^{22} + 255234 q^{23} + 558999 q^{25} - 316368 q^{26} - 51597 q^{27} + 263424 q^{28} + 132153 q^{29} + 610632 q^{30} + 776898 q^{31} + 645795 q^{33} + 387840 q^{34} - 321081 q^{35} - 314688 q^{36} - 759795 q^{37} + 174504 q^{38} - 84012 q^{39} - 109056 q^{40} + 349287 q^{41} + 313752 q^{42} - 1043622 q^{43} + 255552 q^{44} + 845496 q^{45} - 524472 q^{46} + 1280709 q^{47} - 872448 q^{48} + 1011003 q^{49} - 1537704 q^{50} - 7812153 q^{51} - 635136 q^{52} - 2951976 q^{53} - 1256832 q^{54} + 2539854 q^{55} + 858624 q^{56} - 3973923 q^{57} - 47496 q^{58} + 639426 q^{59} - 94464 q^{60} + 1639350 q^{61} + 2859936 q^{62} + 6955635 q^{63} - 8650752 q^{64} - 4119567 q^{65} + 712512 q^{66} - 6408441 q^{67} - 1634496 q^{68} - 1007298 q^{69} + 2380872 q^{70} + 3531612 q^{71} + 6623232 q^{72} - 6666213 q^{73} + 7873368 q^{74} + 16535910 q^{75} - 1396032 q^{76} - 8256489 q^{77} - 4117104 q^{78} - 22540695 q^{79} - 3072000 q^{80} - 13134636 q^{81} + 3798096 q^{82} + 8663238 q^{83} + 8570304 q^{84} - 15143175 q^{85} + 8348976 q^{86} + 45908613 q^{87} + 11028480 q^{88} + 21718137 q^{89} - 27904392 q^{90} - 8606796 q^{91} - 8332800 q^{92} - 20412249 q^{93} - 10358784 q^{94} - 21603363 q^{95} - 5505024 q^{96} - 17397492 q^{97} + 44171448 q^{98} + 103927383 q^{99}+O(q^{100}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9 - 3000 * q^10 - 2523 * q^11 - 5376 * q^12 - 9924 * q^13 + 13416 * q^14 - 15084 * q^15 + 29478 * q^17 + 22848 * q^18 - 61731 * q^19 - 27264 * q^20 - 36372 * q^21 + 20184 * q^22 + 255234 * q^23 + 558999 * q^25 - 316368 * q^26 - 51597 * q^27 + 263424 * q^28 + 132153 * q^29 + 610632 * q^30 + 776898 * q^31 + 645795 * q^33 + 387840 * q^34 - 321081 * q^35 - 314688 * q^36 - 759795 * q^37 + 174504 * q^38 - 84012 * q^39 - 109056 * q^40 + 349287 * q^41 + 313752 * q^42 - 1043622 * q^43 + 255552 * q^44 + 845496 * q^45 - 524472 * q^46 + 1280709 * q^47 - 872448 * q^48 + 1011003 * q^49 - 1537704 * q^50 - 7812153 * q^51 - 635136 * q^52 - 2951976 * q^53 - 1256832 * q^54 + 2539854 * q^55 + 858624 * q^56 - 3973923 * q^57 - 47496 * q^58 + 639426 * q^59 - 94464 * q^60 + 1639350 * q^61 + 2859936 * q^62 + 6955635 * q^63 - 8650752 * q^64 - 4119567 * q^65 + 712512 * q^66 - 6408441 * q^67 - 1634496 * q^68 - 1007298 * q^69 + 2380872 * q^70 + 3531612 * q^71 + 6623232 * q^72 - 6666213 * q^73 + 7873368 * q^74 + 16535910 * q^75 - 1396032 * q^76 - 8256489 * q^77 - 4117104 * q^78 - 22540695 * q^79 - 3072000 * q^80 - 13134636 * q^81 + 3798096 * q^82 + 8663238 * q^83 + 8570304 * q^84 - 15143175 * q^85 + 8348976 * q^86 + 45908613 * q^87 + 11028480 * q^88 + 21718137 * q^89 - 27904392 * q^90 - 8606796 * q^91 - 8332800 * q^92 - 20412249 * q^93 - 10358784 * q^94 - 21603363 * q^95 - 5505024 * q^96 - 17397492 * q^97 + 44171448 * q^98 + 103927383 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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
$3$	43.9672	−	15.9339i	0.940165	−	0.340720i
$3$	43.9672	−	15.9339i	0.940165	−	0.340720i
$4$	49.0268	+	41.1384i	0.383022	+	0.321394i
$5$	72.2267	−	409.618i	0.258406	−	1.46549i	−0.528770	−	0.848765i	$-0.677346\pi$
$5$	72.2267	−	409.618i	0.258406	−	1.46549i	0.787176	−	0.616729i	$-0.211542\pi$
$6$	374.123	+	0.517653i	0.707106	+	0.000978384i
$7$	−152.227	+	127.734i	−0.167745	+	0.140755i	−0.722796	−	0.691062i	$-0.757143\pi$
$7$	−152.227	+	127.734i	−0.167745	+	0.140755i	0.555051	+	0.831816i	$0.312699\pi$
$8$	256.000	+	443.405i	0.176777	+	0.306186i
$9$	1679.22	−	1401.13i	0.767820	−	0.640665i
$10$	1663.75	−	2881.70i	0.526123	−	0.911272i
$11$	−938.612	−	5323.14i	−0.212624	−	1.20585i	−0.884983	−	0.465624i	$-0.845830\pi$
$11$	−938.612	−	5323.14i	−0.212624	−	1.20585i	0.672359	−	0.740225i	$-0.265281\pi$
$12$	2811.07	+	1027.55i	0.469609	+	0.171660i
$13$	−7254.96	+	2640.59i	−0.915869	+	0.333349i	−0.756594	−	0.653885i	$-0.773138\pi$
$13$	−7254.96	+	2640.59i	−0.915869	+	0.333349i	−0.159275	+	0.987234i	$0.550916\pi$
$14$	−1493.88	+	543.727i	−0.145501	+	0.0529581i
$15$	−3351.20	−	19160.6i	−0.256378	−	1.46585i
$16$	711.263	+	4033.77i	0.0434120	+	0.246202i
$17$	8063.48	−	13966.3i	0.398062	−	0.689464i	−0.595425	−	0.803411i	$-0.703016\pi$
$17$	8063.48	−	13966.3i	0.398062	−	0.689464i	0.993487	+	0.113947i	$0.0363494\pi$
$18$	16457.4	−	5938.46i	0.665130	−	0.240005i
$19$	25405.5	+	44003.7i	0.849749	+	1.47181i	0.881432	+	0.472310i	$0.156580\pi$
$19$	25405.5	+	44003.7i	0.849749	+	1.47181i	−0.0316837	+	0.999498i	$0.510087\pi$
$20$	20392.1	−	17111.0i	0.569976	−	0.478267i
$21$	−4657.71	+	8041.67i	−0.109750	+	0.189487i
$22$	7508.90	−	42585.1i	0.150348	−	0.852664i
$23$	−34815.3	−	29213.5i	−0.596653	−	0.500652i	0.293715	−	0.955893i	$-0.405108\pi$
$23$	−34815.3	−	29213.5i	−0.596653	−	0.500652i	−0.890368	+	0.455241i	$0.849553\pi$
$24$	18320.8	+	15416.2i	0.270523	+	0.227634i
$25$	−89156.8	−	32450.4i	−1.14121	−	0.415365i
$26$	−61764.6			−0.689180
$27$	51505.2	−	88360.5i	0.503590	−	0.863942i
$28$	−12718.0			−0.109488
$29$	177240.	+	64510.0i	1.34949	+	0.491172i	0.912787	−	0.408436i	$-0.133926\pi$
$29$	177240.	+	64510.0i	1.34949	+	0.491172i	0.436698	+	0.899608i	$0.356148\pi$
$30$	27233.7	−	153210.i	0.184154	−	1.03601i
$31$	142294.	+	119398.i	0.857865	+	0.719835i	0.961507	−	0.274780i	$-0.0886051\pi$
$31$	142294.	+	119398.i	0.857865	+	0.719835i	−0.103642	+	0.994615i	$0.533050\pi$
$32$	−5690.10	+	32270.2i	−0.0306970	+	0.174091i
$33$	−126086.	−	219087.i	−0.610758	−	1.06125i
$34$	98831.7	−	82929.6i	0.431241	−	0.361854i
$35$	41327.3	+	71580.9i	0.162929	+	0.282201i
$36$	139967.	+	387.331i	0.499998	+	0.00138364i
$37$	286706.	−	496590.i	0.930532	−	1.61173i	0.148119	−	0.988970i	$-0.452678\pi$
$37$	286706.	−	496590.i	0.930532	−	1.61173i	0.782413	−	0.622760i	$-0.213989\pi$
$38$	70586.0	+	400313.i	0.208678	+	1.18347i
$39$	−276905.	+	231699.i	−0.747489	+	0.625458i
$40$	200117.	−	72836.5i	0.494394	−	0.179945i
$41$	−192028.	+	69892.5i	−0.435132	+	0.158375i	−0.550293	−	0.834972i	$-0.685484\pi$
$41$	−192028.	+	69892.5i	−0.435132	+	0.158375i	0.115161	+	0.993347i	$0.463262\pi$
$42$	−57017.8	+	47709.4i	−0.118751	+	0.0993645i
$43$	105674.	+	599308.i	0.202689	+	1.14950i	0.901036	+	0.433745i	$0.142808\pi$
$43$	105674.	+	599308.i	0.202689	+	1.14950i	−0.698347	+	0.715759i	$0.746081\pi$
$44$	172968.	−	299590.i	0.306113	−	0.530203i
$45$	−452645.	−	789039.i	−0.740482	−	1.29079i
$46$	−181792.	−	314874.i	−0.275374	−	0.476962i
$47$	−487813.	+	409324.i	−0.685348	+	0.575075i	−0.917564	−	0.397589i	$-0.869847\pi$
$47$	−487813.	+	409324.i	−0.685348	+	0.575075i	0.232216	+	0.972664i	$0.425402\pi$
$48$	95545.9	+	166020.i	0.124700	+	0.216679i
$49$	−136150.	+	772142.i	−0.165322	+	0.937586i
$50$	−581450.	−	487895.i	−0.657836	−	0.551990i
$51$	131990.	−	742543.i	0.139330	−	0.783838i
$52$	−464318.	−	168998.i	−0.457935	−	0.166675i
$53$	256236.			0.236415			0.118207	−	0.992989i	$-0.462285\pi$
$53$	256236.			0.236415			0.118207	+	0.992989i	$0.462285\pi$
$54$	628961.	−	523327.i	0.543557	−	0.452267i
$55$	−2.24825e6			−1.82211
$56$	−95608.1	−	34798.5i	−0.0727506	−	0.0264791i
$57$	1.81816e6	+	1.52991e6i	1.30038	+	1.09422i
$58$	1.15590e6	+	969913.i	0.777895	+	0.652732i
$59$	−135576.	+	768888.i	−0.0859409	+	0.487395i	0.911209	+	0.411945i	$0.135150\pi$
$59$	−135576.	+	768888.i	−0.0859409	+	0.487395i	−0.997150	+	0.0754500i	$0.975961\pi$
$60$	623938.	−	1.07725e6i	0.372917	−	0.643852i
$61$	−1.90136e6	+	1.59543e6i	−1.07253	+	0.899960i	−0.995279	−	0.0970516i	$-0.969059\pi$
$61$	−1.90136e6	+	1.59543e6i	−1.07253	+	0.899960i	−0.0772513	+	0.997012i	$0.524614\pi$
$62$	743004.	+	1.28692e6i	0.395932	+	0.685774i
$63$	−76651.2	+	427785.i	−0.0386213	+	0.215543i
$64$	−131072.	+	227023.i	−0.0625000	+	0.108253i
$65$	557631.	+	3.16248e6i	0.251855	+	1.42834i
$66$	−348401.	−	1.99199e6i	−0.149168	−	0.852872i
$67$	−262946.	+	95704.5i	−0.106808	+	0.0388750i	−0.394871	−	0.918736i	$-0.629211\pi$
$67$	−262946.	+	95704.5i	−0.106808	+	0.0388750i	0.288063	+	0.957611i	$0.406989\pi$
$68$	969880.	−	353007.i	0.374056	−	0.136145i
$69$	−1.99621e6	−	729691.i	−0.731535	−	0.267404i
$70$	114822.	+	651190.i	0.0400114	+	0.226916i
$71$	−706592.	+	1.22385e6i	−0.234296	+	0.405812i	−0.959068	−	0.283177i	$-0.908612\pi$
$71$	−706592.	+	1.22385e6i	−0.234296	+	0.405812i	0.724772	+	0.688989i	$0.241945\pi$
$72$	1.05115e6	+	385885.i	0.331896	+	0.121841i
$73$	242575.	+	420152.i	0.0729820	+	0.126409i	0.900207	−	0.435462i	$-0.143415\pi$
$73$	242575.	+	420152.i	0.0729820	+	0.126409i	−0.827225	+	0.561871i	$0.810082\pi$
$74$	3.51408e6	−	2.94866e6i	1.00809	−	0.845890i
$75$	−4.43703e6	−	6139.28i	−1.21445	−	0.00168036i
$76$	−564688.	+	3.20250e6i	−0.147557	+	0.836839i
$77$	822828.	+	690435.i	0.205396	+	0.172347i
$78$	−2.71561e6	+	984149.i	−0.647943	+	0.234817i
$79$	−6.34610e6	−	2.30979e6i	−1.44814	−	0.527081i	−0.506072	−	0.862491i	$-0.668903\pi$
$79$	−6.34610e6	−	2.30979e6i	−1.44814	−	0.527081i	−0.942072	+	0.335410i	$0.891125\pi$
$80$	1.70368e6			0.372025
$81$	856611.	−	4.70564e6i	0.179096	−	0.983832i
$82$	−1.63482e6			−0.327432
$83$	1.77558e6	+	646257.i	0.340852	+	0.124060i	0.506774	−	0.862079i	$-0.330838\pi$
$83$	1.77558e6	+	646257.i	0.340852	+	0.124060i	−0.165922	+	0.986139i	$0.553060\pi$
$84$	−559174.	+	202647.i	−0.102937	+	0.0373046i
$85$	−5.13847e6	−	4.31169e6i	−0.907544	−	0.761520i
$86$	−845394.	+	4.79447e6i	−0.143323	+	0.812823i
$87$	8.82062e6	+	12204.6i	1.43609	+	0.00198704i
$88$	2.12002e6	−	1.77891e6i	0.331628	−	0.278269i
$89$	3.75030e6	+	6.49572e6i	0.563899	+	0.976702i	0.997151	+	0.0754293i	$0.0240327\pi$
$89$	3.75030e6	+	6.49572e6i	0.563899	+	0.976702i	−0.433252	+	0.901273i	$0.642634\pi$
$90$	−1.24384e6	−	7.17015e6i	−0.179852	−	1.03676i
$91$	767111.	−	1.32868e6i	0.106712	−	0.184831i
$92$	−505087.	−	2.86449e6i	−0.0676252	−	0.383521i
$93$	8.15872e6	+	2.98232e6i	1.05180	+	0.384472i
$94$	−4.78713e6	+	1.74237e6i	−0.594467	+	0.216368i
$95$	1.98596e7	−	7.22832e6i	2.37651	−	0.864978i
$96$	264011.	+	1.50949e6i	0.0304560	+	0.174133i
$97$	−433312.	−	2.45743e6i	−0.0482058	−	0.273389i	0.951172	−	0.308662i	$-0.0998811\pi$
$97$	−433312.	−	2.45743e6i	−0.0482058	−	0.273389i	−0.999378	+	0.0352730i	$0.988770\pi$
$98$	−3.13622e6	+	5.43208e6i	−0.336600	+	0.583009i
$99$	−9.03457e6	−	7.62361e6i	−0.935803	−	0.789655i
$100$	−3.03612e6	−	5.25871e6i	−0.303612	−	0.525871i
$101$	5.99433e6	−	5.02984e6i	0.578916	−	0.485769i	−0.305675	−	0.952136i	$-0.598882\pi$
$101$	5.99433e6	−	5.02984e6i	0.578916	−	0.485769i	0.884591	+	0.466367i	$0.154438\pi$
$102$	3.02396e6	−	5.22095e6i	0.282147	−	0.487135i
$103$	1.34392e6	−	7.62177e6i	0.121184	−	0.687267i	−0.862318	−	0.506367i	$-0.830988\pi$
$103$	1.34392e6	−	7.62177e6i	0.121184	−	0.687267i	0.983502	−	0.180900i	$-0.0579009\pi$
$104$	−3.02812e6	−	2.54090e6i	−0.263971	−	0.221498i
$105$	2.95760e6	+	2.48871e6i	0.249332	+	0.209803i
$106$	1.92626e6	+	701102.i	0.157089	+	0.0571756i
$107$	3.35815e6			0.265007			0.132504	−	0.991183i	$-0.457698\pi$
$107$	3.35815e6			0.265007			0.132504	+	0.991183i	$0.457698\pi$
$108$	6.16014e6	−	2.21319e6i	0.470552	−	0.169058i
$109$	3.51748e6			0.260159			0.130079	−	0.991504i	$-0.458477\pi$
$109$	3.51748e6			0.260159			0.130079	+	0.991504i	$0.458477\pi$
$110$	−1.69013e7	−	6.15156e6i	−1.21072	−	0.440667i
$111$	4.69306e6	−	2.64020e7i	0.325706	−	1.83234i
$112$	−623523.	−	523198.i	−0.0419363	−	0.0351887i
$113$	2.97340e6	−	1.68630e7i	0.193856	−	1.09941i	−0.720182	−	0.693785i	$-0.755942\pi$
$113$	2.97340e6	−	1.68630e7i	0.193856	−	1.09941i	0.914038	−	0.405628i	$-0.132947\pi$
$114$	9.48200e6	+	1.64759e7i	0.599423	+	1.04156i
$115$	−1.44810e7	+	1.21510e7i	−0.887881	+	0.745021i
$116$	6.03567e6	+	1.04541e7i	0.359023	+	0.621846i
$117$	−8.48288e6	+	1.45993e7i	−0.489658	+	0.842718i
$118$	−3.12300e6	+	5.40919e6i	−0.174978	+	0.303072i
$119$	556495.	+	3.15604e6i	0.0302724	+	0.171683i
$120$	7.63800e6	−	6.39105e6i	0.403501	−	0.337628i
$121$	−9.14283e6	+	3.32772e6i	−0.469172	+	0.170765i
$122$	−1.86589e7	+	6.79128e6i	−0.930308	+	0.338604i
$123$	−7.32927e6	+	6.13273e6i	−0.355135	+	0.297157i
$124$	2.06434e6	+	1.17075e7i	0.0972312	+	0.551425i
$125$	−3.48423e6	+	6.03487e6i	−0.159559	+	0.276365i
$126$	−1.74672e6	+	3.00616e6i	−0.0777904	+	0.133880i
$127$	7.71646e6	+	1.33653e7i	0.334276	+	0.578983i	0.983345	−	0.181746i	$-0.0581750\pi$
$127$	7.71646e6	+	1.33653e7i	0.334276	+	0.578983i	−0.649070	+	0.760729i	$0.724842\pi$
$128$	−1.60651e6	+	1.34802e6i	−0.0677094	+	0.0568149i
$129$	1.41955e7	+	2.46661e7i	0.582220	+	1.01166i
$130$	−4.46105e6	+	2.52999e7i	−0.178088	+	1.00999i
$131$	3.66707e7	+	3.07704e7i	1.42518	+	1.19587i	0.948495	+	0.316794i	$0.102606\pi$
$131$	3.66707e7	+	3.07704e7i	1.42518	+	1.19587i	0.476685	+	0.879074i	$0.341838\pi$
$132$	2.83129e6	−	1.59282e7i	0.107146	−	0.602777i
$133$	−9.48818e6	−	3.45341e6i	−0.349705	−	0.127282i
$134$	−2.23857e6			−0.0803718
$135$	−3.24740e7	−	2.74794e7i	−1.13597	−	0.961257i
$136$	8.25700e6			0.281473
$137$	−5.13650e7	−	1.86953e7i	−1.70665	−	0.621171i	−0.710098	−	0.704103i	$-0.751349\pi$
$137$	−5.13650e7	−	1.86953e7i	−1.70665	−	0.621171i	−0.996555	+	0.0829325i	$0.973571\pi$
$138$	−1.30101e7	−	1.09474e7i	−0.421407	−	0.354598i
$139$	−5.84621e6	−	4.90555e6i	−0.184639	−	0.154930i	0.545783	−	0.837926i	$-0.316232\pi$
$139$	−5.84621e6	−	4.90555e6i	−0.184639	−	0.154930i	−0.730422	+	0.682996i	$0.760677\pi$
$140$	−918580.	+	5.20952e6i	−0.0282923	+	0.160454i
$141$	−1.49256e7	+	2.57696e7i	−0.448401	+	0.774177i
$142$	−8.66049e6	+	7.26701e6i	−0.253824	+	0.212984i
$143$	2.08658e7	+	3.61407e7i	0.596704	+	1.03352i
$144$	6.84623e6	+	5.77703e6i	0.191066	+	0.161226i
$145$	3.92259e7	−	6.79412e7i	1.06853	−	1.85074i
$146$	673963.	+	3.82223e6i	0.0179226	+	0.101644i
$147$	6.31711e6	+	3.61183e7i	0.164024	+	0.937814i
$148$	3.44852e7	−	1.25516e7i	0.874414	−	0.318261i
$149$	−5.02663e7	+	1.82955e7i	−1.24487	+	0.453097i	−0.878666	−	0.477436i	$-0.841566\pi$
$149$	−5.02663e7	+	1.82955e7i	−1.24487	+	0.453097i	−0.366208	+	0.930533i	$0.619344\pi$
$150$	−3.33388e7	−	1.21866e7i	−0.806548	−	0.294824i
$151$	6.61928e6	+	3.75398e7i	0.156456	+	0.887305i	0.957443	+	0.288623i	$0.0931975\pi$
$151$	6.61928e6	+	3.75398e7i	0.156456	+	0.887305i	−0.800987	+	0.598682i	$0.795691\pi$
$152$	−1.30076e7	+	2.25299e7i	−0.300432	+	0.520363i
$153$	−6.02837e6	−	3.47506e7i	−0.136075	−	0.784409i
$154$	4.29650e6	+	7.44176e6i	0.0947965	+	0.164192i
$155$	5.91851e7	−	4.96622e7i	1.27659	−	1.07119i
$156$	−2.31075e7	−	31972.6i	−0.487323	−	0.000674282i
$157$	6.60900e6	−	3.74815e7i	0.136297	−	0.772980i	−0.837650	−	0.546207i	$-0.816071\pi$
$157$	6.60900e6	−	3.74815e7i	0.136297	−	0.772980i	0.973948	−	0.226773i	$-0.0728176\pi$
$158$	−4.13871e7	−	3.47279e7i	−0.834767	−	0.700452i
$159$	1.12660e7	−	4.08283e6i	0.222269	−	0.0805511i
$160$	1.28075e7	+	4.66154e6i	0.247197	+	0.0899724i
$161$	9.03139e6			0.170555
$162$	1.93150e7	−	3.30310e7i	0.356937	−	0.610406i
$163$	7.93259e7			1.43469			0.717345	−	0.696718i	$-0.245357\pi$
$163$	7.93259e7			1.43469			0.717345	+	0.696718i	$0.245357\pi$
$164$	−1.22898e7	−	4.47312e6i	−0.217566	−	0.0791876i
$165$	−9.88490e7	+	3.58233e7i	−1.71308	+	0.620828i
$166$	1.15797e7	+	9.71652e6i	0.196480	+	0.164867i
$167$	2.29151e6	−	1.29958e7i	0.0380728	−	0.215921i	−0.959836	−	0.280562i	$-0.909479\pi$
$167$	2.29151e6	−	1.29958e7i	0.0380728	−	0.215921i	0.997909	+	0.0646409i	$0.0205902\pi$
$168$	−4.75809e6	−	6583.51i	−0.0774195	−	0.000107121i
$169$	−2.40640e6	+	2.01921e6i	−0.0383499	+	0.0321794i
$170$	−2.68312e7	−	4.64730e7i	−0.418860	−	0.725486i
$171$	1.04317e8	+	3.82954e7i	1.59539	+	0.585680i
$172$	−1.94737e7	+	3.37295e7i	−0.291809	+	0.505429i
$173$	9.05897e6	+	5.13760e7i	0.133020	+	0.754395i	0.976218	+	0.216791i	$0.0695591\pi$
$173$	9.05897e6	+	5.13760e7i	0.133020	+	0.754395i	−0.843198	+	0.537603i	$0.819330\pi$
$174$	6.62760e7	+	2.42264e7i	0.953749	+	0.348631i
$175$	1.77171e7	−	6.44851e6i	0.249896	−	0.0909549i
$176$	2.08047e7	−	7.57230e6i	0.287652	−	0.104697i
$177$	6.29049e6	+	3.59661e7i	0.0852664	+	0.487513i
$178$	1.04197e7	+	5.90933e7i	0.138480	+	0.785359i
$179$	1.21120e7	−	2.09786e7i	0.157845	−	0.273395i	−0.776247	−	0.630430i	$-0.782879\pi$
$179$	1.21120e7	−	2.09786e7i	0.157845	−	0.273395i	0.934091	+	0.357034i	$0.116212\pi$
$180$	1.02680e7	−	5.73052e7i	0.131230	−	0.732387i
$181$	−6.91558e7	−	1.19781e8i	−0.866869	−	1.50146i	−0.865179	−	0.501463i	$-0.832795\pi$
$181$	−6.91558e7	−	1.19781e8i	−0.866869	−	1.50146i	−0.00169054	−	0.999999i	$-0.500538\pi$
$182$	9.40226e6	−	7.88943e6i	0.115607	−	0.0970054i
$183$	−5.81760e7	+	1.00443e8i	−0.701722	+	1.21154i
$184$	4.04069e6	−	2.29159e7i	0.0478182	−	0.271191i
$185$	−1.82704e8	−	1.53307e8i	−2.12152	−	1.78017i
$186$	5.31734e7	+	4.47433e7i	0.605898	+	0.509839i
$187$	−8.19133e7	−	2.98140e7i	−0.916028	−	0.333407i
$188$	−4.07549e7			−0.447329
$189$	3.44614e6	+	2.00298e7i	0.0371292	+	0.215805i
$190$	1.69074e8			1.78829
$191$	−7.19937e7	−	2.62036e7i	−0.747614	−	0.272109i	−0.0600128	−	0.998198i	$-0.519114\pi$
$191$	−7.19937e7	−	2.62036e7i	−0.747614	−	0.272109i	−0.687602	+	0.726088i	$0.741336\pi$
$192$	−2.14550e6	+	1.20701e7i	−0.0218763	+	0.123071i
$193$	3.58107e7	+	3.00487e7i	0.358560	+	0.300868i	0.804217	−	0.594336i	$-0.202585\pi$
$193$	3.58107e7	+	3.00487e7i	0.358560	+	0.300868i	−0.445656	+	0.895204i	$0.647030\pi$
$194$	3.46649e6	−	1.96595e7i	0.0340866	−	0.193315i
$195$	7.49081e7	+	1.30160e8i	0.723449	+	1.25706i
$196$	−3.84397e7	+	3.22547e7i	−0.364656	+	0.305983i
$197$	3.16962e7	+	5.48995e7i	0.295376	+	0.511607i	0.975072	−	0.221887i	$-0.0712216\pi$
$197$	3.16962e7	+	5.48995e7i	0.295376	+	0.511607i	−0.679696	+	0.733494i	$0.737888\pi$
$198$	−4.70583e7	−	8.20308e7i	−0.430832	−	0.751016i
$199$	3.02815e7	−	5.24492e7i	0.272391	−	0.471794i	−0.697083	−	0.716991i	$-0.745519\pi$
$199$	3.02815e7	−	5.24492e7i	0.272391	−	0.471794i	0.969473	+	0.245196i	$0.0788524\pi$
$200$	−8.43546e6	−	4.78399e7i	−0.0745596	−	0.422849i
$201$	−1.00360e7	+	8.39761e6i	−0.0871719	+	0.0729406i
$202$	5.88251e7	−	2.14106e7i	0.502149	−	0.182767i
$203$	−3.52209e7	+	1.28193e7i	−0.295504	+	0.107555i
$204$	3.70181e7	−	3.09747e7i	0.305287	−	0.255447i
$205$	1.47597e7	+	8.37063e7i	0.119657	+	0.678609i
$206$	3.09574e7	−	5.36198e7i	0.246734	−	0.427356i
$207$	−9.93946e7	−	275054.i	−0.778873	−	0.00215537i
$208$	−1.58117e7	−	2.73867e7i	−0.121831	−	0.211017i
$209$	2.10391e8	−	1.76539e8i	1.59410	−	1.33761i
$210$	1.54244e7	+	2.68014e7i	0.114932	+	0.199706i
$211$	2.07595e7	−	1.17733e8i	0.152135	−	0.862799i	−0.809224	−	0.587500i	$-0.800112\pi$
$211$	2.07595e7	−	1.17733e8i	0.152135	−	0.862799i	0.961359	−	0.275299i	$-0.0887767\pi$
$212$	1.25624e7	+	1.05411e7i	0.0905520	+	0.0759822i
$213$	−1.15661e7	+	6.50681e7i	−0.0820085	+	0.461359i
$214$	2.52451e7	+	9.18845e6i	0.176087	+	0.0640906i
$215$	2.53120e8			1.73697
$216$	5.23648e7	+	217364.i	0.353550	+	0.00146757i
$217$	−3.69122e7			−0.245223
$218$	2.64428e7	+	9.62438e6i	0.172866	+	0.0629180i
$219$	1.73600e7	+	1.46077e7i	0.111685	+	0.0939784i
$220$	−1.10224e8	−	9.24892e7i	−0.697908	−	0.585614i
$221$	−2.16208e7	+	1.22618e8i	−0.134741	+	0.764153i
$222$	1.07520e8	−	1.85637e8i	0.659562	−	1.13875i
$223$	1.78111e8	−	1.49453e8i	1.07553	−	0.902478i	0.0799898	−	0.996796i	$-0.474511\pi$
$223$	1.78111e8	−	1.49453e8i	1.07553	−	0.902478i	0.995542	+	0.0943172i	$0.0300668\pi$
$224$	−3.25581e6	−	5.63923e6i	−0.0193549	−	0.0335237i
$225$	−1.95182e8	+	7.04292e7i	−1.14235	+	0.412206i
$226$	6.84926e7	−	1.18633e8i	0.394697	−	0.683636i
$227$	−3.15920e7	−	1.79167e8i	−0.179261	−	1.01664i	−0.933109	−	0.359592i	$-0.882916\pi$
$227$	−3.15920e7	−	1.79167e8i	−0.179261	−	1.01664i	0.753848	−	0.657049i	$-0.228195\pi$
$228$	2.62006e7	+	1.49803e8i	0.146399	+	0.837043i
$229$	−3.34466e8	+	1.21736e8i	−1.84046	+	0.669874i	−0.850987	+	0.525188i	$0.823995\pi$
$229$	−3.34466e8	+	1.21736e8i	−1.84046	+	0.669874i	−0.989478	+	0.144687i	$0.953783\pi$
$230$	−1.42108e8	+	5.17231e7i	−0.770144	+	0.280309i
$231$	4.71787e7	+	1.72456e7i	0.251828	+	0.0920527i
$232$	1.67693e7	+	9.51035e7i	0.0881673	+	0.500022i
$233$	−1.56754e8	+	2.71505e8i	−0.811843	+	1.40615i	0.0997294	+	0.995015i	$0.468202\pi$
$233$	−1.56754e8	+	2.71505e8i	−0.811843	+	1.40615i	−0.911573	+	0.411139i	$0.865131\pi$
$234$	−1.03716e8	+	8.65405e7i	−0.529166	+	0.441534i
$235$	1.32433e8	+	2.29381e8i	0.665671	+	1.15298i
$236$	−3.82777e7	+	3.21188e7i	−0.189563	+	0.159062i
$237$	−3.15824e8	−	436988.i	−1.54108	−	0.00213231i
$238$	−4.45196e6	+	2.52483e7i	−0.0214058	+	0.121398i
$239$	−9.93713e7	−	8.33824e7i	−0.470834	−	0.395077i	0.376264	−	0.926512i	$-0.377208\pi$
$239$	−9.93713e7	−	8.33824e7i	−0.470834	−	0.395077i	−0.847099	+	0.531435i	$0.821653\pi$
$240$	7.49059e7	−	2.71462e7i	0.349765	−	0.126756i
$241$	6.64322e7	+	2.41793e7i	0.305717	+	0.111272i	0.490323	−	0.871541i	$-0.336879\pi$
$241$	6.64322e7	+	2.41793e7i	0.305717	+	0.111272i	−0.184606	+	0.982813i	$0.559101\pi$
$242$	−7.78368e7			−0.353046
$243$	−3.73163e7	−	2.20543e8i	−0.166831	−	0.985986i
$244$	−1.58851e8			−0.700045
$245$	3.06450e8	+	1.11539e8i	1.33131	+	0.484556i
$246$	−7.18782e7	+	2.60490e7i	−0.307840	+	0.111562i
$247$	−3.00512e8	−	2.52159e8i	−1.26888	−	1.06472i
$248$	−1.65147e7	+	9.36597e7i	−0.0687528	+	0.389917i
$249$	8.83644e7	+	122265.i	0.362727	+	0.000501885i
$250$	−4.27052e7	+	3.58340e7i	−0.172859	+	0.145046i
$251$	1.14340e8	+	1.98043e8i	0.456394	+	0.790498i	0.998767	−	0.0496400i	$-0.0158074\pi$
$251$	1.14340e8	+	1.98043e8i	0.456394	+	0.790498i	−0.542373	+	0.840138i	$0.682474\pi$
$252$	−2.13564e7	+	1.78196e7i	−0.0840670	+	0.0701450i
$253$	−1.22829e8	+	2.12746e8i	−0.476848	+	0.825925i
$254$	2.14392e7	+	1.21588e8i	0.0820900	+	0.465555i
$255$	−2.94626e8	−	1.07697e8i	−1.11271	−	0.406736i
$256$	−1.57654e7	+	5.73815e6i	−0.0587308	+	0.0213763i
$257$	2.64221e8	−	9.61686e7i	0.970960	−	0.353400i	0.192641	−	0.981269i	$-0.438295\pi$
$257$	2.64221e8	−	9.61686e7i	0.970960	−	0.353400i	0.778319	+	0.627869i	$0.216073\pi$
$258$	3.92249e7	+	2.24270e8i	0.142198	+	0.813020i
$259$	1.97868e7	+	1.12217e8i	0.0707665	+	0.401337i
$260$	−1.02761e8	+	1.77987e8i	−0.362594	+	0.628031i
$261$	3.88012e8	−	1.40010e8i	1.35084	−	0.487436i
$262$	1.91481e8	+	3.31654e8i	0.657765	+	1.13928i
$263$	−2.12944e7	+	1.78681e7i	−0.0721806	+	0.0605667i	−0.678164	−	0.734910i	$-0.737224\pi$
$263$	−2.12944e7	+	1.78681e7i	−0.0721806	+	0.0605667i	0.605984	+	0.795477i	$0.292780\pi$
$264$	6.48664e7	−	1.11994e8i	0.216973	−	0.374610i
$265$	1.85071e7	−	1.04959e8i	0.0610910	−	0.346464i
$266$	−6.18787e7	−	5.19224e7i	−0.201584	−	0.169149i
$267$	2.68392e8	+	2.25841e8i	0.862940	+	0.726130i
$268$	−1.68285e7	−	6.12509e6i	−0.0534041	−	0.0194375i
$269$	−2.76676e8			−0.866638			−0.433319	−	0.901241i	$-0.642658\pi$
$269$	−2.76676e8			−0.866638			−0.433319	+	0.901241i	$0.642658\pi$
$270$	−1.68936e8	−	2.95432e8i	−0.522336	−	0.913449i
$271$	4.67820e8			1.42786			0.713930	−	0.700217i	$-0.246913\pi$
$271$	4.67820e8			1.42786			0.713930	+	0.700217i	$0.246913\pi$
$272$	6.20723e7	+	2.25925e7i	0.187028	+	0.0680727i
$273$	1.25567e7	−	7.06411e7i	0.0373515	−	0.210130i
$274$	−3.34985e8	−	2.81086e8i	−0.983781	−	0.825490i
$275$	−8.90543e7	+	5.05052e8i	−0.258220	+	1.46444i
$276$	−6.78496e7	−	1.17895e8i	−0.194252	−	0.337532i
$277$	−2.27593e8	+	1.90974e8i	−0.643399	+	0.539876i	−0.905060	−	0.425284i	$-0.860174\pi$
$277$	−2.27593e8	+	1.90974e8i	−0.643399	+	0.539876i	0.261661	+	0.965160i	$0.415730\pi$
$278$	−3.05267e7	−	5.28739e7i	−0.0852165	−	0.147599i
$279$	4.06236e8	+	1.12417e6i	1.11986	+	0.00309898i
$280$	−2.11596e7	+	3.66494e7i	−0.0576041	+	0.0997732i
$281$	−1.05795e8	−	5.99991e8i	−0.284440	−	1.61314i	−0.707278	−	0.706936i	$-0.750077\pi$
$281$	−1.05795e8	−	5.99991e8i	−0.284440	−	1.61314i	0.422837	−	0.906206i	$-0.361034\pi$
$282$	−1.82714e8	+	1.52885e8i	−0.485176	+	0.405969i
$283$	−4.85821e8	+	1.76825e8i	−1.27416	+	0.463756i	−0.888497	−	0.458883i	$-0.848250\pi$
$283$	−4.85821e8	+	1.76825e8i	−1.27416	+	0.463756i	−0.385664	+	0.922639i	$0.626027\pi$
$284$	−8.49893e7	+	3.09336e7i	−0.220166	+	0.0801338i
$285$	7.57997e8	−	6.34250e8i	1.93959	−	1.62294i
$286$	5.79730e7	+	3.28781e8i	0.146536	+	0.831047i
$287$	2.03043e7	−	3.51681e7i	0.0506992	−	0.0878136i
$288$	3.56599e7	+	6.21614e7i	0.0879644	+	0.153337i
$289$	7.51301e7	+	1.30129e8i	0.183093	+	0.317126i
$290$	4.80781e8	−	4.03423e8i	1.15759	−	0.971331i
$291$	−5.82079e7	−	1.01142e8i	−0.138470	−	0.240606i
$292$	−5.39170e6	+	3.05779e7i	−0.0126732	+	0.0718732i
$293$	−4.59415e8	−	3.85495e8i	−1.06701	−	0.895328i	−0.0722319	−	0.997388i	$-0.523012\pi$
$293$	−4.59415e8	−	3.85495e8i	−1.06701	−	0.895328i	−0.994778	+	0.102060i	$0.967457\pi$
$294$	−5.13363e7	+	2.88805e8i	−0.117817	+	0.662811i
$295$	3.05158e8	+	1.11069e8i	0.692067	+	0.251892i
$296$	2.93587e8			0.657986
$297$	−5.18698e8	−	1.91233e8i	−1.14886	−	0.423560i
$298$	−4.27939e8			−0.936752
$299$	3.29724e8	+	1.20010e8i	0.713348	+	0.259638i
$300$	−2.17281e8	−	1.82833e8i	−0.464620	−	0.390959i
$301$	−9.26386e7	−	7.77330e7i	−0.195798	−	0.164294i
$302$	−5.29543e7	+	3.00319e8i	−0.110631	+	0.627419i
$303$	1.83409e8	−	3.16661e8i	0.378766	−	0.653951i
$304$	−1.59431e8	+	1.33778e8i	−0.325473	+	0.273104i
$305$	5.16188e8	+	8.94064e8i	1.04174	+	1.80434i
$306$	4.97648e7	−	2.77734e8i	0.0992882	−	0.554120i
$307$	2.83163e8	−	4.90452e8i	0.558536	−	0.967413i	−0.439083	−	0.898447i	$-0.644696\pi$
$307$	2.83163e8	−	4.90452e8i	0.558536	−	0.967413i	0.997619	−	0.0689666i	$-0.0219702\pi$
$308$	1.19373e7	+	6.76997e7i	0.0232797	+	0.132026i
$309$	−6.23559e7	−	3.56522e8i	−0.120233	−	0.687434i
$310$	5.80811e8	−	2.11398e8i	1.10731	−	0.403027i
$311$	−5.49935e8	+	2.00160e8i	−1.03669	+	0.377326i	−0.803626	−	0.595135i	$-0.797099\pi$
$311$	−5.49935e8	+	2.00160e8i	−1.03669	+	0.377326i	−0.233068	+	0.972461i	$0.574876\pi$
$312$	−1.73624e8	−	6.34662e7i	−0.323645	−	0.118305i
$313$	−2.73287e7	−	1.54989e8i	−0.0503748	−	0.285690i	0.949206	−	0.314657i	$-0.101889\pi$
$313$	−2.73287e7	−	1.54989e8i	−0.0503748	−	0.285690i	−0.999580	+	0.0289668i	$0.990778\pi$
$314$	1.52239e8	−	2.63685e8i	0.277506	−	0.480654i
$315$	1.69692e8	+	6.22952e7i	0.305897	+	0.112297i
$316$	−2.16108e8	−	3.74310e8i	−0.385271	−	0.667309i
$317$	−6.05798e8	+	5.08325e8i	−1.06812	+	0.896260i	−0.994881	−	0.101055i	$-0.967778\pi$
$317$	−6.05798e8	+	5.08325e8i	−1.06812	+	0.896260i	−0.0732396	+	0.997314i	$0.523334\pi$
$318$	9.58636e7	+	132641.i	0.167170	+	0.000231304i
$319$	1.77036e8	−	1.00402e9i	0.305347	−	1.73171i
$320$	8.35260e7	+	7.00866e7i	0.142494	+	0.119567i
$321$	1.47649e8	−	5.35084e7i	0.249150	−	0.0902931i
$322$	6.78938e7	+	2.47113e7i	0.113327	+	0.0412478i
$323$	8.19427e8			1.35301
$324$	2.35579e8	−	1.95463e8i	0.384795	−	0.319269i
$325$	7.32517e8			1.18366
$326$	5.96336e8	+	2.17048e8i	0.953299	+	0.346972i
$327$	1.54653e8	−	5.60471e7i	0.244592	−	0.0886412i
$328$	−8.01499e7	−	6.72538e7i	−0.125414	−	0.105234i
$329$	2.19740e7	−	1.24621e8i	0.0340191	−	0.192932i
$330$	−8.41119e8	−	1.16381e6i	−1.28842	−	0.00178272i
$331$	−9.44989e8	+	7.92940e8i	−1.43228	+	1.20183i	−0.487936	+	0.872880i	$0.662250\pi$
$331$	−9.44989e8	+	7.92940e8i	−1.43228	+	1.20183i	−0.944348	+	0.328949i	$0.893306\pi$
$332$	6.04649e7	+	1.04728e8i	0.0906818	+	0.157065i
$333$	−2.14346e8	−	1.23560e9i	−0.318097	−	1.83368i
$334$	5.27852e7	−	9.14266e7i	0.0775174	−	0.134264i
$335$	2.02106e7	+	1.14620e8i	0.0293712	+	0.166572i
$336$	−3.57511e7	−	1.30684e7i	−0.0514165	−	0.0187947i
$337$	−5.23929e8	+	1.90695e8i	−0.745707	+	0.271415i	−0.686798	−	0.726848i	$-0.740984\pi$
$337$	−5.23929e8	+	1.90695e8i	−0.745707	+	0.271415i	−0.0589087	+	0.998263i	$0.518762\pi$
$338$	−2.36151e7	+	8.59519e6i	−0.0332645	+	0.0121073i
$339$	−1.37961e8	−	7.88797e8i	−0.192335	−	1.09968i
$340$	−7.45470e7	−	4.22777e8i	−0.102862	−	0.583358i
$341$	5.02016e8	−	8.69517e8i	0.685610	−	1.18751i
$342$	6.79422e8	+	5.73314e8i	0.918435	+	0.774999i
$343$	−1.59730e8	−	2.76660e8i	−0.213726	−	0.370184i
$344$	−2.38684e8	+	2.00279e8i	−0.316132	+	0.265266i
$345$	−4.43075e8	+	7.64981e8i	−0.580912	+	1.00296i
$346$	−7.24718e7	+	4.11008e8i	−0.0940595	+	0.533438i
$347$	1.31991e8	+	1.10753e8i	0.169586	+	0.142300i	0.723631	−	0.690187i	$-0.242472\pi$
$347$	1.31991e8	+	1.10753e8i	0.169586	+	0.142300i	−0.554045	+	0.832487i	$0.686916\pi$
$348$	4.31945e8	+	3.63465e8i	0.549416	+	0.462312i
$349$	−1.63483e8	−	5.95028e7i	−0.205865	−	0.0749287i	0.237030	−	0.971502i	$-0.423826\pi$
$349$	−1.63483e8	−	5.95028e7i	−0.205865	−	0.0749287i	−0.442895	+	0.896574i	$0.646048\pi$
$350$	1.50833e8			0.188044
$351$	−1.40344e8	+	7.77056e8i	−0.173229	+	0.959130i
$352$	1.77119e8			0.216455
$353$	3.41803e8	+	1.24406e8i	0.413585	+	0.150533i	0.540428	−	0.841390i	$-0.318262\pi$
$353$	3.41803e8	+	1.24406e8i	0.413585	+	0.150533i	−0.126843	+	0.991923i	$0.540484\pi$
$354$	−5.11200e7	+	2.87588e8i	−0.0612462	+	0.344556i
$355$	4.50277e8	+	3.77827e8i	0.534172	+	0.448223i
$356$	−8.33579e7	+	4.72746e8i	−0.0979201	+	0.555332i
$357$	7.47555e7	+	1.29895e8i	0.0869570	+	0.151096i
$358$	1.48453e8	−	1.24567e8i	0.171001	−	0.143487i
$359$	−5.72205e8	−	9.91087e8i	−0.652711	−	1.13053i	−0.982462	−	0.186461i	$-0.940298\pi$
$359$	−5.72205e8	−	9.91087e8i	−0.652711	−	1.13053i	0.329752	−	0.944068i	$-0.393035\pi$
$360$	2.33987e8	−	4.02699e8i	0.264322	−	0.454907i
$361$	−8.43945e8	+	1.46176e9i	−0.944146	+	1.63531i
$362$	−1.92140e8	−	1.08968e9i	−0.212882	−	1.20731i
$363$	−3.48961e8	+	2.91991e8i	−0.382916	+	0.320403i
$364$	9.22686e7	−	3.35830e7i	0.100276	−	0.0364977i
$365$	1.89622e8	−	6.90168e7i	0.204110	−	0.0742899i
$366$	−7.12167e8	+	5.95902e8i	−0.759273	+	0.635318i
$367$	1.93984e8	+	1.10014e9i	0.204850	+	1.16176i	0.897676	+	0.440657i	$0.145254\pi$
$367$	1.93984e8	+	1.10014e9i	0.204850	+	1.16176i	−0.692826	+	0.721105i	$0.743635\pi$
$368$	9.30777e7	−	1.61215e8i	0.0973595	−	0.168632i
$369$	−2.24529e8	+	3.86422e8i	−0.232638	+	0.400378i
$370$	−9.54015e8	−	1.65240e9i	−0.979150	−	1.69594i
$371$	−3.90061e7	+	3.27300e7i	−0.0396574	+	0.0332765i
$372$	2.77308e8	+	4.81851e8i	0.279295	+	0.485302i
$373$	−2.40916e8	+	1.36630e9i	−0.240373	+	1.36322i	0.590626	+	0.806946i	$0.298881\pi$
$373$	−2.40916e8	+	1.36630e9i	−0.240373	+	1.36322i	−0.830998	+	0.556275i	$0.812230\pi$
$374$	−5.34210e8	−	4.48256e8i	−0.528034	−	0.443073i
$375$	−5.70330e7	+	3.20853e8i	−0.0558492	+	0.314194i
$376$	−3.06376e8	−	1.11512e8i	−0.297234	−	0.108184i
$377$	−1.45621e9			−1.39968
$378$	−2.88984e7	+	1.60004e8i	−0.0275203	+	0.152374i
$379$	1.88328e9			1.77696			0.888481	−	0.458913i	$-0.151761\pi$
$379$	1.88328e9			1.77696			0.888481	+	0.458913i	$0.151761\pi$
$380$	1.27102e9	+	4.62613e8i	1.18825	+	0.432489i
$381$	5.52232e8	+	4.64681e8i	0.511545	+	0.430445i
$382$	−4.69518e8	−	3.93973e8i	−0.430954	−	0.361613i
$383$	6.82267e7	−	3.86933e8i	0.0620524	−	0.351917i	−0.937935	−	0.346812i	$-0.887264\pi$
$383$	6.82267e7	−	3.86933e8i	0.0620524	−	0.351917i	0.999987	−	0.00510451i	$-0.00162482\pi$
$384$	−4.91545e7	+	8.48667e7i	−0.0443000	+	0.0764853i
$385$	3.42245e8	−	2.87177e8i	0.305650	−	0.256471i
$386$	1.86990e8	+	3.23876e8i	0.165487	+	0.286631i
$387$	1.01716e9	+	8.58309e8i	0.892076	+	0.752757i
$388$	7.98509e7	−	1.38306e8i	0.0694015	−	0.120207i
$389$	−2.23687e7	−	1.26859e8i	−0.0192671	−	0.109269i	0.973658	−	0.228015i	$-0.0732236\pi$
$389$	−2.23687e7	−	1.26859e8i	−0.0192671	−	0.109269i	−0.992925	+	0.118746i	$0.962113\pi$
$390$	2.06985e8	+	1.18345e9i	0.176691	+	1.01023i
$391$	−6.88738e8	+	2.50680e8i	−0.582687	+	0.212081i
$392$	−3.77226e8	+	1.37299e8i	−0.316301	+	0.115124i
$393$	2.10260e9	+	7.68579e8i	1.74736	+	0.638726i
$394$	8.80639e7	+	4.99435e8i	0.0725372	+	0.411379i
$395$	−1.40449e9	+	2.43265e9i	−1.14664	+	1.98605i
$396$	−1.29313e8	−	7.45429e8i	−0.104643	−	0.603217i
$397$	5.90767e6	+	1.02324e7i	0.00473859	+	0.00820748i	0.868385	−	0.495891i	$-0.165158\pi$
$397$	5.90767e6	+	1.02324e7i	0.00473859	+	0.00820748i	−0.863646	+	0.504098i	$0.831825\pi$
$398$	3.71152e8	−	3.11434e8i	0.295095	−	0.247614i
$399$	−4.72195e8	−	653350.i	−0.372148	−	0.000514921i
$400$	6.74837e7	−	3.82719e8i	0.0527216	−	0.298999i
$401$	−1.19008e9	−	9.98594e8i	−0.921659	−	0.773364i	0.0526420	−	0.998613i	$-0.483236\pi$
$401$	−1.19008e9	−	9.98594e8i	−0.921659	−	0.773364i	−0.974301	+	0.225250i	$0.927680\pi$
$402$	−9.84236e7	+	3.56691e7i	−0.0755628	+	0.0273843i
$403$	−1.34762e9	−	4.90492e8i	−1.02565	−	0.373306i
$404$	5.00803e8			0.377861
$405$	−1.86564e9	−	6.90756e8i	−1.39552	−	0.516692i
$406$	−2.99850e8			−0.222363
$407$	−2.91252e9	−	1.06007e9i	−2.14136	−	0.779390i
$408$	3.63037e8	−	1.31566e8i	0.264631	−	0.0959032i
$409$	5.06116e8	+	4.24682e8i	0.365779	+	0.306925i	0.807089	−	0.590430i	$-0.201042\pi$
$409$	5.06116e8	+	4.24682e8i	0.365779	+	0.306925i	−0.441310	+	0.897355i	$0.645486\pi$
$410$	−1.18077e8	+	6.69650e8i	−0.0846103	+	0.479849i
$411$	−2.55626e9	−	3.53696e6i	−1.81618	−	0.00251295i
$412$	3.79436e8	−	3.18384e8i	0.267299	−	0.224291i
$413$	−7.75748e7	−	1.34363e8i	−0.0541870	−	0.0938547i
$414$	−7.46450e8	−	2.74027e8i	−0.517011	−	0.189798i
$415$	3.92962e8	−	6.80631e8i	0.269887	−	0.467459i
$416$	−4.39308e7	−	2.49144e8i	−0.0299187	−	0.169677i
$417$	−3.35206e8	−	1.22530e8i	−0.226379	−	0.0827500i
$418$	2.06467e9	−	7.51477e8i	1.38272	−	0.503268i
$419$	2.68686e9	−	9.77937e8i	1.78441	−	0.649474i	0.784859	−	0.619675i	$-0.212735\pi$
$419$	2.68686e9	−	9.77937e8i	1.78441	−	0.649474i	0.999556	−	0.0297992i	$-0.00948680\pi$
$420$	4.26206e7	+	2.43684e8i	0.0280703	+	0.160493i
$421$	−3.44109e8	−	1.95154e9i	−0.224755	−	1.27465i	−0.863154	−	0.504941i	$-0.831514\pi$
$421$	−3.44109e8	−	1.95154e9i	−0.224755	−	1.27465i	0.638399	−	0.769705i	$-0.279597\pi$
$422$	4.78197e8	−	8.28261e8i	0.309751	−	0.536505i
$423$	−2.45629e8	+	1.37084e9i	−0.157793	+	0.880633i
$424$	6.55964e7	+	1.13616e8i	0.0417926	+	0.0723869i
$425$	−1.17213e9	+	9.83532e8i	−0.740651	+	0.621480i
$426$	−2.64985e8	+	4.57505e8i	−0.166069	+	0.286723i
$427$	8.56484e7	−	4.85736e8i	0.0532380	−	0.301928i
$428$	1.64640e8	+	1.38149e8i	0.101504	+	0.0851716i
$429$	1.49327e9	+	1.25653e9i	0.913142	+	0.768373i
$430$	1.90284e9	+	6.92577e8i	1.15415	+	0.420077i
$431$	8.01708e8			0.482332			0.241166	−	0.970484i	$-0.422470\pi$
$431$	8.01708e8			0.482332			0.241166	+	0.970484i	$0.422470\pi$
$432$	3.93060e8	+	1.44913e8i	0.234566	+	0.0864794i
$433$	7.15327e8			0.423445			0.211723	−	0.977330i	$-0.432093\pi$
$433$	7.15327e8			0.423445			0.211723	+	0.977330i	$0.432093\pi$
$434$	−2.77489e8	−	1.00998e8i	−0.162942	−	0.0593059i
$435$	6.42084e8	−	3.61220e9i	0.374007	−	2.10407i
$436$	1.72451e8	+	1.44703e8i	0.0996466	+	0.0836134i
$437$	4.01000e8	−	2.27418e9i	0.229858	−	1.30359i
$438$	9.05352e7	+	1.57314e8i	0.0514823	+	0.0894556i
$439$	1.55245e9	−	1.30266e9i	0.875775	−	0.734863i	−0.0895308	−	0.995984i	$-0.528537\pi$
$439$	1.55245e9	−	1.30266e9i	0.875775	−	0.734863i	0.965306	+	0.261121i	$0.0840923\pi$
$440$	−5.75551e8	−	9.96883e8i	−0.322106	−	0.557905i
$441$	8.53250e8	+	1.48736e9i	0.473741	+	0.825813i
$442$	−4.98037e8	+	8.62625e8i	−0.274337	+	0.475165i
$443$	−9.54532e7	−	5.41342e8i	−0.0521648	−	0.295841i	0.947553	−	0.319599i	$-0.103548\pi$
$443$	−9.54532e7	−	5.41342e8i	−0.0521648	−	0.295841i	−0.999718	+	0.0237576i	$0.992437\pi$
$444$	1.31622e9	−	1.10134e9i	0.713656	−	0.597148i
$445$	2.93164e9	−	1.06703e9i	1.57707	−	0.574005i
$446$	1.74788e9	−	6.36177e8i	0.932911	−	0.339552i
$447$	−1.91855e9	+	1.60534e9i	−1.01601	+	0.850139i
$448$	−9.04584e6	−	5.13015e7i	−0.00475309	−	0.0269561i
$449$	−1.01317e9	+	1.75487e9i	−0.528229	+	0.914919i	0.471229	+	0.882011i	$0.343810\pi$
$449$	−1.01317e9	+	1.75487e9i	−0.528229	+	0.914919i	−0.999458	+	0.0329086i	$0.989523\pi$
$450$	−1.65999e9	−	4.59368e6i	−0.858740	−	0.00237639i
$451$	5.52287e8	+	9.56590e8i	0.283496	+	0.491030i
$452$	8.39494e8	−	7.04419e8i	0.427596	−	0.358795i
$453$	8.89186e8	+	1.54505e9i	0.449416	+	0.780905i
$454$	2.52736e8	−	1.43334e9i	0.126757	−	0.718874i
$455$	−4.88843e8	−	4.10188e8i	−0.243293	−	0.204147i
$456$	−2.12920e8	+	1.19784e9i	−0.105157	+	0.591590i
$457$	2.55318e9	+	9.29280e8i	1.25134	+	0.455449i	0.880853	−	0.473390i	$-0.156970\pi$
$457$	2.55318e9	+	9.29280e8i	1.25134	+	0.455449i	0.370483	+	0.928839i	$0.379192\pi$
$458$	−2.84745e9			−1.38493
$459$	−8.18763e8	−	1.43183e9i	−0.395197	−	0.691111i
$460$	−1.20983e9			−0.579523
$461$	−2.39763e9	−	8.72667e8i	−1.13980	−	0.414854i	−0.297960	−	0.954578i	$-0.596306\pi$
$461$	−2.39763e9	−	8.72667e8i	−1.13980	−	0.414854i	−0.841842	+	0.539724i	$0.818529\pi$
$462$	3.07481e8	+	2.58733e8i	0.145068	+	0.122069i
$463$	1.07536e9	+	9.02333e8i	0.503523	+	0.422506i	0.858843	−	0.512238i	$-0.171184\pi$
$463$	1.07536e9	+	9.02333e8i	0.503523	+	0.422506i	−0.355320	+	0.934745i	$0.615628\pi$
$464$	−1.34155e8	+	7.60828e8i	−0.0623437	+	0.353569i
$465$	1.81089e9	−	3.12656e9i	0.835232	−	1.44205i
$466$	−1.92129e9	+	1.61215e9i	−0.879511	+	0.737997i
$467$	1.36946e9	+	2.37198e9i	0.622215	+	1.07771i	0.989072	+	0.147431i	$0.0471004\pi$
$467$	1.36946e9	+	2.37198e9i	0.622215	+	1.07771i	−0.366857	+	0.930277i	$0.619566\pi$
$468$	−1.01648e9	+	3.66787e8i	−0.458394	+	0.165407i
$469$	2.78029e7	−	4.81560e7i	0.0124447	−	0.0215549i
$470$	3.67949e8	+	2.08674e9i	0.163473	+	0.927099i
$471$	−3.06647e8	−	1.75326e9i	−0.135228	−	0.773168i
$472$	−3.75636e8	+	1.36720e8i	−0.164426	+	0.0598462i
$473$	3.09101e9	−	1.12504e9i	1.34303	−	0.488824i
$474$	−2.37302e9	−	8.67430e8i	−1.02348	−	0.374119i
$475$	−8.37138e8	−	4.74764e9i	−0.358401	−	2.03259i
$476$	−1.02551e8	+	1.77624e8i	−0.0435830	+	0.0754879i
$477$	4.30277e8	−	3.59021e8i	0.181524	−	0.151463i
$478$	−5.18880e8	−	8.98727e8i	−0.217305	−	0.376383i
$479$	−5.23849e7	+	4.39561e7i	−0.0217787	+	0.0182745i	−0.653612	−	0.756830i	$-0.726747\pi$
$479$	−5.23849e7	+	4.39561e7i	−0.0217787	+	0.0182745i	0.631833	+	0.775104i	$0.282303\pi$
$480$	6.37385e8	+	881914.i	0.263061	+	0.000363984i
$481$	−7.68753e8	+	4.35982e9i	−0.314977	+	1.78632i
$482$	4.33248e8	+	3.63538e8i	0.176227	+	0.147872i
$483$	3.97085e8	−	1.43905e8i	0.160350	−	0.0581114i
$484$	−5.85141e8	−	2.12974e8i	−0.234586	−	0.0853823i
$485$	−1.03791e9			−0.413106
$486$	3.22913e8	−	1.76004e9i	0.127602	−	0.695498i
$487$	−1.03362e9			−0.405516			−0.202758	−	0.979229i	$-0.564991\pi$
$487$	−1.03362e9			−0.405516			−0.202758	+	0.979229i	$0.564991\pi$
$488$	−1.19417e9	−	4.34642e8i	−0.465154	−	0.169302i
$489$	3.48773e9	−	1.26397e9i	1.34885	−	0.488827i
$490$	1.99856e9	+	1.67699e9i	0.767417	+	0.643939i
$491$	−7.22571e8	+	4.09790e9i	−0.275483	+	1.56234i	0.461939	+	0.886912i	$0.347154\pi$
$491$	−7.22571e8	+	4.09790e9i	−0.275483	+	1.56234i	−0.737422	+	0.675432i	$0.763957\pi$
$492$	−6.11622e8	−	846267.i	−0.231529	−	0.000320354i
$493$	2.33014e9	−	1.95522e9i	0.875825	−	0.734904i
$494$	−1.56916e9	−	2.71787e9i	−0.585630	−	1.01434i
$495$	−3.77531e9	+	3.15010e9i	−1.39905	+	1.16736i
$496$	−3.80418e8	+	6.58903e8i	−0.139983	+	0.242458i
$497$	−4.87649e7	−	2.76560e8i	−0.0178181	−	0.101051i
$498$	6.63948e8	+	2.42698e8i	0.240897	+	0.0880570i
$499$	−4.62868e9	+	1.68470e9i	−1.66765	+	0.606975i	−0.991537	−	0.129822i	$-0.958559\pi$
$499$	−4.62868e9	+	1.68470e9i	−1.66765	+	0.606975i	−0.676114	+	0.736797i	$0.736337\pi$
$500$	−4.19086e8	+	1.52535e8i	−0.149937	+	0.0545725i
$501$	−1.06322e8	−	6.07902e8i	−0.0377740	−	0.215974i
$502$	3.17679e8	+	1.80165e9i	0.112079	+	0.635633i
$503$	2.60863e9	−	4.51827e9i	0.913953	−	1.58301i	0.105527	−	0.994416i	$-0.466347\pi$
$503$	2.60863e9	−	4.51827e9i	0.913953	−	1.58301i	0.808426	−	0.588597i	$-0.200320\pi$
$504$	−2.09305e8	+	7.55254e7i	−0.0728236	+	0.0262776i
$505$	−1.62736e9	−	2.81868e9i	−0.562295	−	0.973924i
$506$	−1.50548e9	+	1.26325e9i	−0.516593	+	0.433473i
$507$	−7.36287e7	+	1.27122e8i	−0.0250911	+	0.0433205i
$508$	−1.71513e8	+	9.72701e8i	−0.0580464	+	0.329197i
$509$	6.27499e8	+	5.26534e8i	0.210912	+	0.176976i	0.742124	−	0.670263i	$-0.233819\pi$
$509$	6.27499e8	+	5.26534e8i	0.210912	+	0.176976i	−0.531212	+	0.847239i	$0.678263\pi$
$510$	−1.92019e9	−	1.61576e9i	−0.640985	−	0.539363i
$511$	−9.05942e7	−	3.29736e7i	−0.0300350	−	0.0109318i
$512$	−1.34218e8			−0.0441942
$513$	5.19670e9	+	2.15713e7i	1.69948	+	0.00705448i
$514$	2.24942e9			0.730635
$515$	−3.02495e9	−	1.10099e9i	−0.975871	−	0.355188i
$516$	−3.18763e8	+	1.79328e9i	−0.102140	+	0.574612i
$517$	2.63675e9	+	2.21250e9i	0.839175	+	0.704152i
$518$	−1.58295e8	+	8.97734e8i	−0.0500394	+	0.283788i
$519$	1.21692e9	+	2.11451e9i	0.382098	+	0.663933i
$520$	−1.25951e9	+	1.05685e9i	−0.392816	+	0.329612i
$521$	−1.04673e9	−	1.81299e9i	−0.324267	−	0.561647i	0.657096	−	0.753806i	$-0.271784\pi$
$521$	−1.04673e9	−	1.81299e9i	−0.324267	−	0.561647i	−0.981364	+	0.192159i	$0.938451\pi$
$522$	3.29999e9	+	9.13204e6i	1.01547	+	0.00281010i
$523$	−1.98615e9	+	3.44010e9i	−0.607093	+	1.05152i	0.384624	+	0.923073i	$0.374331\pi$
$523$	−1.98615e9	+	3.44010e9i	−0.607093	+	1.05152i	−0.991717	+	0.128442i	$0.959002\pi$
$524$	5.32005e8	+	3.01715e9i	0.161531	+	0.916088i
$525$	6.76222e8	−	5.65825e8i	0.203954	−	0.170657i
$526$	−2.08972e8	+	7.60595e7i	−0.0626091	+	0.0227878i
$527$	2.81494e9	−	1.02455e9i	0.837784	−	0.304928i
$528$	7.94068e8	−	6.64432e8i	0.234768	−	0.196441i
$529$	−2.32566e8	−	1.31895e9i	−0.0683049	−	0.387377i
$530$	4.26312e8	−	7.38394e8i	0.124383	−	0.215438i
$531$	8.49654e8	+	1.48109e9i	0.246270	+	0.429291i
$532$	−3.23107e8	−	5.59639e8i	−0.0930371	−	0.161145i
$533$	1.20860e9	−	1.01414e9i	0.345730	−	0.290102i
$534$	1.39971e9	+	2.43214e9i	0.397781	+	0.691184i
$535$	2.42548e8	−	1.37556e9i	0.0684795	−	0.388366i
$536$	−1.09750e8	−	9.20912e7i	−0.0307842	−	0.0258310i
$537$	1.98260e8	−	1.11536e9i	0.0552490	−	0.310817i
$538$	−2.07992e9	−	7.57029e8i	−0.575849	−	0.209592i
$539$	4.23801e9			1.16574
$540$	−4.61638e8	−	2.68316e9i	−0.126160	−	0.733277i
$541$	−8.41052e8			−0.228367			−0.114183	−	0.993460i	$-0.536425\pi$
$541$	−8.41052e8			−0.228367			−0.114183	+	0.993460i	$0.536425\pi$
$542$	3.51685e9	+	1.28003e9i	0.948761	+	0.345321i
$543$	−4.94917e9	−	4.16453e9i	−1.32658	−	1.11626i
$544$	4.04815e8	+	3.39680e8i	0.107810	+	0.0904635i
$545$	2.54056e8	−	1.44082e9i	0.0672266	−	0.381261i
$546$	2.87681e8	−	4.96690e8i	0.0756376	−	0.130590i
$547$	−9.61661e8	+	8.06930e8i	−0.251227	+	0.210805i	−0.759700	−	0.650273i	$-0.774654\pi$
$547$	−9.61661e8	+	8.06930e8i	−0.251227	+	0.210805i	0.508473	+	0.861078i	$0.330210\pi$
$548$	−1.74917e9	−	3.02965e9i	−0.454045	−	0.786430i
$549$	−9.57393e8	+	5.34314e9i	−0.246938	+	1.37814i
$550$	−2.05137e9	+	3.55308e9i	−0.525745	+	0.910617i
$551$	1.66419e9	+	9.43811e9i	0.423812	+	2.40356i
$552$	−1.87482e8	−	1.07193e9i	−0.0474429	−	0.271257i
$553$	1.26109e9	−	4.58999e8i	0.317108	−	0.115418i
$554$	−2.23348e9	+	8.12919e8i	−0.558081	+	0.203125i
$555$	−1.04758e10	−	3.82929e9i	−2.60112	−	0.950809i
$556$	−8.48146e7	−	4.81008e8i	−0.0209271	−	0.118683i
$557$	−5.63835e8	+	9.76591e8i	−0.138248	+	0.239453i	−0.926834	−	0.375473i	$-0.877480\pi$
$557$	−5.63835e8	+	9.76591e8i	−0.138248	+	0.239453i	0.788585	+	0.614925i	$0.210814\pi$
$558$	3.05082e9	+	1.11998e9i	0.743356	+	0.272891i
$559$	−2.34919e9	−	4.06892e9i	−0.568823	−	0.985230i
$560$	−2.59347e8	+	2.17618e8i	−0.0624054	+	0.0523644i
$561$	−4.07655e9	−	5.64049e6i	−0.974815	−	0.00134880i
$562$	8.46356e8	−	4.79993e9i	0.201130	−	1.14066i
$563$	2.64005e9	+	2.21527e9i	0.623495	+	0.523175i	0.898900	−	0.438154i	$-0.144367\pi$
$563$	2.64005e9	+	2.21527e9i	0.623495	+	0.523175i	−0.275405	+	0.961328i	$0.588812\pi$
$564$	−1.79188e9	+	6.49383e8i	−0.420563	+	0.152414i
$565$	−6.69264e9	−	2.43592e9i	−1.56109	−	0.568190i
$566$	−4.13600e9			−0.958789
$567$	4.70670e8	+	8.25745e8i	0.108437	+	0.190242i
$568$	−7.23550e8			−0.165672
$569$	3.73011e9	+	1.35765e9i	0.848846	+	0.308955i	0.729570	−	0.683907i	$-0.239720\pi$
$569$	3.73011e9	+	1.35765e9i	0.848846	+	0.308955i	0.119276	+	0.992861i	$0.461943\pi$
$570$	7.43369e9	−	2.69400e9i	1.68129	−	0.609306i
$571$	−4.07065e9	−	3.41569e9i	−0.915035	−	0.767806i	0.0580348	−	0.998315i	$-0.481517\pi$
$571$	−4.07065e9	−	3.41569e9i	−0.915035	−	0.767806i	−0.973070	+	0.230509i	$0.925961\pi$
$572$	−4.63784e8	+	2.63025e9i	−0.103617	+	0.587639i
$573$	−3.58288e9	−	4.95744e6i	−0.795594	−	0.00110082i
$574$	2.48864e8	−	2.08822e8i	0.0549250	−	0.0460876i
$575$	2.15603e9	+	3.73435e9i	0.472952	+	0.819176i
$576$	9.79913e7	+	5.64872e8i	0.0213653	+	0.123161i
$577$	−2.51076e9	+	4.34876e9i	−0.544113	+	0.942431i	0.454549	+	0.890722i	$0.349800\pi$
$577$	−2.51076e9	+	4.34876e9i	−0.544113	+	0.942431i	−0.998662	+	0.0517096i	$0.983533\pi$
$578$	2.08739e8	+	1.18382e9i	0.0449631	+	0.254999i
$579$	2.05329e9	+	7.50554e8i	0.439617	+	0.160697i
$580$	4.71812e9	−	1.71725e9i	1.00409	−	0.365457i
$581$	−3.52840e8	+	1.28423e8i	−0.0746383	+	0.0271661i
$582$	−1.60840e8	−	9.19605e8i	−0.0338191	−	0.193362i
$583$	−2.40506e8	−	1.36398e9i	−0.0502674	−	0.285080i
$584$	−1.24198e8	+	2.15118e8i	−0.0258030	+	0.0446922i
$585$	5.36746e9	+	4.52920e9i	1.10847	+	0.935354i
$586$	−2.39889e9	−	4.15501e9i	−0.492458	−	0.852963i
$587$	−1.80670e9	+	1.51600e9i	−0.368683	+	0.309362i	−0.808240	−	0.588853i	$-0.799580\pi$
$587$	−1.80670e9	+	1.51600e9i	−0.368683	+	0.309362i	0.439557	+	0.898215i	$0.355135\pi$
$588$	−1.17614e9	+	2.03064e9i	−0.238583	+	0.411920i
$589$	−1.63893e9	+	9.29481e9i	−0.330488	+	1.87429i
$590$	1.99014e9	+	1.66992e9i	0.398934	+	0.334746i
$591$	2.26835e9	+	1.90873e9i	0.452017	+	0.380354i
$592$	2.20706e9	+	8.03302e8i	0.437207	+	0.159130i
$593$	7.17768e9			1.41349			0.706745	−	0.707468i	$-0.250163\pi$
$593$	7.17768e9			1.41349			0.706745	+	0.707468i	$0.250163\pi$
$594$	−3.37609e9	−	2.85684e9i	−0.660939	−	0.559286i
$595$	1.33297e9			0.259424
$596$	−3.21705e9	−	1.17091e9i	−0.622437	−	0.226549i
$597$	4.95675e8	−	2.78854e9i	0.0953425	−	0.536373i
$598$	2.15035e9	+	1.80436e9i	0.411202	+	0.345039i
$599$	7.22402e8	−	4.09695e9i	0.137336	−	0.778873i	−0.835868	−	0.548930i	$-0.815035\pi$
$599$	7.22402e8	−	4.09695e9i	0.137336	−	0.778873i	0.973204	−	0.229942i	$-0.0738537\pi$
$600$	−1.13316e9	−	1.96897e9i	−0.214171	−	0.372144i
$601$	−1.87482e9	+	1.57316e9i	−0.352289	+	0.295605i	−0.801708	−	0.597715i	$-0.796075\pi$
$601$	−1.87482e9	+	1.57316e9i	−0.352289	+	0.295605i	0.449420	+	0.893321i	$0.351631\pi$
$602$	−4.83724e8	−	8.37835e8i	−0.0903670	−	0.156520i
$603$	−3.07450e8	+	5.29132e8i	−0.0571037	+	0.0982774i
$604$	−1.21981e9	+	2.11277e9i	−0.225248	+	0.390141i
$605$	7.02737e8	+	3.98542e9i	0.129018	+	0.731695i
$606$	2.24522e9	−	1.87867e9i	0.409831	−	0.342924i
$607$	2.34372e9	−	8.53046e8i	0.425350	−	0.154815i	−0.120471	−	0.992717i	$-0.538440\pi$
$607$	2.34372e9	−	8.53046e8i	0.425350	−	0.154815i	0.545820	+	0.837902i	$0.316218\pi$
$608$	−1.56457e9	+	5.69455e8i	−0.282313	+	0.102754i
$609$	−1.34430e9	+	1.12484e9i	−0.241177	+	0.201803i
$610$	1.43416e9	+	8.13353e9i	0.255825	+	1.45086i
$611$	2.45821e9	−	4.25774e9i	0.435988	−	0.755153i
$612$	1.13403e9	−	1.95171e9i	0.199984	−	0.344180i
$613$	3.56128e7	+	6.16832e7i	0.00624445	+	0.0108157i	0.869131	−	0.494582i	$-0.164679\pi$
$613$	3.56128e7	+	6.16832e7i	0.00624445	+	0.0108157i	−0.862886	+	0.505398i	$0.831346\pi$
$614$	3.47064e9	−	2.91221e9i	0.605091	−	0.507731i
$615$	1.98271e9	+	3.44515e9i	0.343713	+	0.597235i
$616$	−9.54982e7	+	5.41597e8i	−0.0164612	+	0.0933564i
$617$	2.28742e9	+	1.91938e9i	0.392056	+	0.328974i	0.817414	−	0.576051i	$-0.195407\pi$
$617$	2.28742e9	+	1.91938e9i	0.392056	+	0.328974i	−0.425357	+	0.905026i	$0.639852\pi$
$618$	5.06738e8	−	2.85078e9i	0.0863622	−	0.485852i
$619$	−4.53865e9	−	1.65193e9i	−0.769148	−	0.279947i	−0.0725077	−	0.997368i	$-0.523100\pi$
$619$	−4.53865e9	−	1.65193e9i	−0.769148	−	0.279947i	−0.696640	+	0.717421i	$0.745322\pi$
$620$	4.94469e9			0.833236
$621$	−4.37448e9	+	1.57165e9i	−0.733003	+	0.263351i
$622$	−4.68183e9			−0.780099
$623$	−1.40062e9	−	5.09785e8i	−0.232067	−	0.0844654i
$624$	−1.13157e9	−	9.52174e8i	−0.186439	−	0.156881i
$625$	−3.45789e9	−	2.90151e9i	−0.566540	−	0.475384i
$626$	2.18630e8	−	1.23991e9i	0.0356204	−	0.202013i
$627$	6.43736e9	−	1.11143e10i	1.04297	−	1.80072i
$628$	1.86595e9	−	1.56572e9i	0.300636	−	0.252263i
$629$	−4.62370e9	−	8.00849e9i	−0.740820	−	1.28314i
$630$	1.10522e9	+	9.32612e8i	0.176099	+	0.148597i
$631$	−2.41582e9	+	4.18432e9i	−0.382791	+	0.663013i	−0.991460	−	0.130411i	$-0.958370\pi$
$631$	−2.41582e9	+	4.18432e9i	−0.382791	+	0.663013i	0.608669	+	0.793424i	$0.291704\pi$
$632$	−6.00428e8	−	3.40520e9i	−0.0946131	−	0.536578i
$633$	−9.63207e8	−	5.50716e9i	−0.150941	−	0.863008i
$634$	−5.94497e9	+	2.16379e9i	−0.926482	+	0.337212i
$635$	6.03200e9	−	2.19547e9i	0.934874	−	0.340266i
$636$	7.20296e8	+	2.63295e8i	0.111022	+	0.0405829i
$637$	−1.05115e9	−	5.96138e9i	−0.161130	−	0.913816i
$638$	4.07804e9	−	7.06337e9i	0.621697	−	1.07681i
$639$	5.28258e8	+	3.04515e9i	0.0800927	+	0.461696i
$640$	4.36142e8	+	7.55419e8i	0.0657654	+	0.113909i
$641$	−1.10043e9	+	9.23371e8i	−0.165029	+	0.138476i	−0.721562	−	0.692350i	$-0.756576\pi$
$641$	−1.10043e9	+	9.23371e8i	−0.165029	+	0.138476i	0.556533	+	0.830825i	$0.312131\pi$
$642$	1.25636e9	+	1.73836e6i	0.187388	+	0.000259279i
$643$	1.09805e9	−	6.22737e9i	0.162886	−	0.923775i	−0.788331	−	0.615252i	$-0.789054\pi$
$643$	1.09805e9	−	6.22737e9i	0.162886	−	0.923775i	0.951217	−	0.308523i	$-0.0998346\pi$
$644$	4.42781e8	+	3.71537e8i	0.0653263	+	0.0548153i
$645$	1.11290e10	−	4.03318e9i	1.63304	−	0.591819i
$646$	6.16008e9	+	2.24208e9i	0.899026	+	0.327219i
$647$	−1.30931e10			−1.90054			−0.950270	−	0.311428i	$-0.899193\pi$
$647$	−1.30931e10			−1.90054			−0.950270	+	0.311428i	$0.899193\pi$
$648$	2.30579e9	−	8.24817e8i	0.332896	−	0.119082i
$649$	4.22015e9			0.605998
$650$	5.50673e9	+	2.00429e9i	0.786497	+	0.286261i
$651$	−1.62293e9	+	5.88155e8i	−0.230550	+	0.0835522i
$652$	3.88910e9	+	3.26334e9i	0.549518	+	0.461101i
$653$	3.66883e8	−	2.08070e9i	0.0515622	−	0.292424i	−0.948112	−	0.317935i	$-0.897010\pi$
$653$	3.66883e8	−	2.08070e9i	0.0515622	−	0.292424i	0.999675	+	0.0255119i	$0.00812157\pi$
$654$	1.31597e9	+	1.82083e6i	0.183960	+	0.000254535i
$655$	1.52527e10	−	1.27985e10i	2.12081	−	1.77957i
$656$	−4.18513e8	−	7.24886e8i	−0.0578823	−	0.100255i
$657$	9.96027e8	+	3.65649e8i	0.137023	+	0.0503020i
$658$	5.06172e8	−	8.76716e8i	0.0692640	−	0.119969i
$659$	−3.27696e7	−	1.85846e8i	−0.00446038	−	0.0252961i	0.982496	−	0.186282i	$-0.0596438\pi$
$659$	−3.27696e7	−	1.85846e8i	−0.00446038	−	0.0252961i	−0.986957	+	0.160986i	$0.948533\pi$
$660$	−6.31997e9	−	2.31019e9i	−0.855679	−	0.312783i
$661$	−7.99210e9	+	2.90889e9i	−1.07636	+	0.391761i	−0.818550	−	0.574435i	$-0.805222\pi$
$661$	−7.99210e9	+	2.90889e9i	−1.07636	+	0.391761i	−0.257806	+	0.966197i	$0.582999\pi$
$662$	−9.27361e9	+	3.37532e9i	−1.24236	+	0.452180i
$663$	1.00317e9	+	5.73565e9i	0.133683	+	0.764338i
$664$	1.67994e8	+	9.52741e8i	0.0222692	+	0.126295i
$665$	−2.09988e9	+	3.63710e9i	−0.276897	+	0.479600i
$666$	1.76945e9	−	9.87516e9i	0.232101	−	1.29534i
$667$	−4.28609e9	−	7.42372e9i	−0.559269	−	0.968682i
$668$	6.46972e8	−	5.42874e8i	0.0839785	−	0.0704663i
$669$	5.44967e9	−	9.40901e9i	0.703685	−	1.21493i
$670$	−1.61685e8	+	9.16959e8i	−0.0207686	+	0.117784i
$671$	1.02773e10	+	8.62370e9i	1.31326	+	1.10196i
$672$	−2.33003e8	−	1.96063e8i	−0.0296190	−	0.0249232i
$673$	6.47767e9	+	2.35768e9i	0.819155	+	0.298148i	0.717400	−	0.696661i	$-0.245332\pi$
$673$	6.47767e9	+	2.35768e9i	0.819155	+	0.298148i	0.101755	+	0.994809i	$0.467554\pi$
$674$	−4.46043e9			−0.561135
$675$	−7.45937e9	+	6.20657e9i	−0.933553	+	0.776763i
$676$	−2.01045e8			−0.0250311
$677$	−5.40853e9	−	1.96854e9i	−0.669914	−	0.243829i	−0.0154029	−	0.999881i	$-0.504903\pi$
$677$	−5.40853e9	−	1.96854e9i	−0.669914	−	0.243829i	−0.654511	+	0.756053i	$0.727125\pi$
$678$	1.12115e9	−	6.30730e9i	0.138152	−	0.777212i
$679$	3.79859e8	+	3.18740e8i	0.0465670	+	0.0390744i
$680$	5.96376e8	−	3.38222e9i	0.0727342	−	0.412496i
$681$	−4.24384e9	−	7.37408e9i	−0.514925	−	0.894732i
$682$	6.15306e9	−	5.16303e9i	0.742755	−	0.623246i
$683$	1.79135e9	+	3.10272e9i	0.215134	+	0.372623i	0.953314	−	0.301981i	$-0.0976478\pi$
$683$	1.79135e9	+	3.10272e9i	0.215134	+	0.372623i	−0.738180	+	0.674604i	$0.764314\pi$
$684$	3.53890e9	+	6.16892e9i	0.422836	+	0.737077i
$685$	−1.13679e10	+	1.96897e10i	−1.35133	+	2.34058i
$686$	−4.43789e8	−	2.51685e9i	−0.0524858	−	0.297662i
$687$	−1.27658e10	+	1.06817e10i	−1.50210	+	1.25687i
$688$	−2.34231e9	+	8.52532e8i	−0.274211	+	0.0998047i
$689$	−1.85898e9	+	6.76614e8i	−0.216525	+	0.0788086i
$690$	−5.42394e9	+	4.53845e9i	−0.628555	+	0.525940i
$691$	−9.79692e8	−	5.55611e9i	−0.112958	−	0.640616i	−0.987741	−	0.156101i	$-0.950107\pi$
$691$	−9.79692e8	−	5.55611e9i	−0.112958	−	0.640616i	0.874783	−	0.484515i	$-0.161004\pi$
$692$	−1.66939e9	+	2.89147e9i	−0.191508	+	0.331702i
$693$	2.34910e9	+	6.50066e6i	0.268124	+	0.000741978i
$694$	6.89206e8	+	1.19374e9i	0.0782692	+	0.135566i
$695$	−2.43166e9	+	2.04040e9i	−0.274761	+	0.230552i
$696$	2.25267e9	+	3.91423e9i	0.253259	+	0.440062i
$697$	−5.72271e8	+	3.24551e9i	−0.0640157	+	0.363051i
$698$	−1.06618e9	−	8.94629e8i	−0.118669	−	0.0995747i
$699$	−2.56588e9	+	1.44350e10i	−0.284162	+	1.59863i
$700$	1.13390e9	+	4.12704e8i	0.124948	+	0.0454774i
$701$	−1.09326e10			−1.19870			−0.599352	−	0.800486i	$-0.704575\pi$
$701$	−1.09326e10			−1.19870			−0.599352	+	0.800486i	$0.704575\pi$
$702$	−3.18119e9	+	5.45754e9i	−0.347064	+	0.595412i
$703$	2.91357e10			3.16287
$704$	1.33150e9	+	4.84627e8i	0.143826	+	0.0523484i
$705$	9.47765e9	+	7.97506e9i	1.01868	+	0.857180i
$706$	2.22913e9	+	1.87046e9i	0.238407	+	0.200047i
$707$	−2.70020e8	+	1.53136e9i	−0.0287361	+	0.162971i
$708$	−1.17118e9	+	2.02208e9i	−0.124025	+	0.214133i
$709$	−2.05713e9	+	1.72614e9i	−0.216770	+	0.181892i	−0.744706	−	0.667392i	$-0.767411\pi$
$709$	−2.05713e9	+	1.72614e9i	−0.216770	+	0.181892i	0.527936	+	0.849284i	$0.322966\pi$
$710$	2.35118e9	+	4.07236e9i	0.246537	+	0.427014i
$711$	−1.38928e10	+	5.01309e9i	−1.44960	+	0.523072i
$712$	−1.92016e9	+	3.32581e9i	−0.199368	+	0.345316i
$713$	−1.46594e9	−	8.31377e9i	−0.151462	−	0.858984i
$714$	2.06564e8	+	1.18103e9i	0.0212378	+	0.121428i
$715$	1.63109e10	−	5.93669e9i	1.66881	−	0.607398i
$716$	1.45684e9	−	5.30246e8i	0.148326	−	0.0539861i
$717$	−5.69768e9	−	2.08272e9i	−0.577273	−	0.211015i
$718$	−1.58980e9	−	9.01618e9i	−0.160290	−	0.909049i
$719$	−4.58491e9	+	7.94130e9i	−0.460023	+	0.796784i	−0.998962	−	0.0455615i	$-0.985492\pi$
$719$	−4.58491e9	+	7.94130e9i	−0.460023	+	0.796784i	0.538938	+	0.842345i	$0.318826\pi$
$720$	2.86086e9	−	2.38708e9i	0.285649	−	0.238344i
$721$	7.68977e8	+	1.33191e9i	0.0764082	+	0.132343i
$722$	−1.03440e10	+	8.67964e9i	−1.02284	+	0.858265i
$723$	3.30611e9	+	4.57448e6i	0.325336	+	0.000450150i
$724$	1.53712e9	−	8.71746e9i	0.150530	−	0.853700i
$725$	−1.37087e10	−	1.15030e10i	−1.33603	−	1.12106i
$726$	−3.42226e9	+	1.24024e9i	−0.331921	+	0.120290i
$727$	−8.09568e8	−	2.94659e8i	−0.0781417	−	0.0284413i	0.302654	−	0.953101i	$-0.402128\pi$
$727$	−8.09568e8	−	2.94659e8i	−0.0781417	−	0.0284413i	−0.380795	+	0.924659i	$0.624350\pi$
$728$	7.85522e8			0.0754568
$729$	−5.15479e9	−	9.10204e9i	−0.492793	−	0.870146i
$730$	1.61433e9			0.153590
$731$	9.22225e9	+	3.35663e9i	0.873225	+	0.317828i
$732$	−6.98423e9	+	2.53111e9i	−0.658157	+	0.238519i
$733$	−1.39931e10	−	1.17416e10i	−1.31235	−	1.10119i	−0.987868	−	0.155298i	$-0.950366\pi$
$733$	−1.39931e10	−	1.17416e10i	−1.31235	−	1.10119i	−0.324480	−	0.945892i	$-0.605189\pi$
$734$	−1.55188e9	+	8.80112e9i	−0.144851	+	0.821489i
$735$	1.52510e10	+	2.11019e7i	1.41675	+	0.00196027i
$736$	1.14083e9	−	9.57267e8i	0.105474	−	0.0885036i
$737$	7.56253e8	+	1.30987e9i	0.0695874	+	0.120529i
$738$	−2.74522e9	+	2.29060e9i	−0.251409	+	0.209774i
$739$	−2.54598e9	+	4.40977e9i	−0.232060	+	0.401940i	−0.958414	−	0.285381i	$-0.907880\pi$
$739$	−2.54598e9	+	4.40977e9i	−0.232060	+	0.401940i	0.726354	+	0.687321i	$0.241213\pi$
$740$	−2.65061e9	−	1.50323e10i	−0.240455	−	1.36369i
$741$	−1.72305e10	−	6.29841e9i	−1.55573	−	0.568679i
$742$	−3.82785e8	+	1.39322e8i	−0.0343986	+	0.0125201i
$743$	−9.58489e9	+	3.48862e9i	−0.857287	+	0.312027i	−0.733008	−	0.680220i	$-0.761884\pi$
$743$	−9.58489e9	+	3.48862e9i	−0.857287	+	0.312027i	−0.124279	+	0.992247i	$0.539662\pi$
$744$	7.66256e8	+	4.38109e9i	0.0682132	+	0.390011i
$745$	3.86358e9	+	2.19114e10i	0.342328	+	1.94144i
$746$	−5.54952e9	+	9.61205e9i	−0.489406	+	0.847677i
$747$	3.88708e9	−	1.40261e9i	0.341194	−	0.123116i
$748$	−2.78945e9	−	4.83147e9i	−0.243704	−	0.422108i
$749$	−5.11203e8	+	4.28950e8i	−0.0444536	+	0.0373010i
$750$	−1.30665e9	+	2.25598e9i	−0.113096	+	0.195263i
$751$	−1.06507e9	+	6.04033e9i	−0.0917571	+	0.520380i	0.903936	+	0.427668i	$0.140665\pi$
$751$	−1.06507e9	+	6.04033e9i	−0.0917571	+	0.520380i	−0.995693	+	0.0927121i	$0.970446\pi$
$752$	−1.99808e9	−	1.67659e9i	−0.171337	−	0.143769i
$753$	8.18279e9	+	6.88549e9i	0.698424	+	0.587696i
$754$	−1.09471e10	−	3.98443e9i	−0.930038	−	0.338506i
$755$	1.58551e10			1.34077
$756$	−6.55043e8	+	1.12377e9i	−0.0551370	+	0.0945912i
$757$	1.91841e10			1.60733			0.803666	−	0.595080i	$-0.202880\pi$
$757$	1.91841e10			1.60733			0.803666	+	0.595080i	$0.202880\pi$
$758$	1.41576e10	+	5.15296e9i	1.18073	+	0.429749i
$759$	−2.01058e9	+	1.13110e10i	−0.166907	+	0.938977i
$760$	8.28914e9	+	6.95542e9i	0.684955	+	0.574746i
$761$	1.30936e9	−	7.42573e9i	0.107699	−	0.610791i	−0.882409	−	0.470483i	$-0.844080\pi$
$761$	1.30936e9	−	7.42573e9i	0.107699	−	0.610791i	0.990108	−	0.140308i	$-0.0448092\pi$
$762$	2.87998e9	+	5.00425e9i	0.235802	+	0.409729i
$763$	−5.35456e8	+	4.49301e8i	−0.0436404	+	0.0366186i
$764$	−2.45165e9	−	4.24638e9i	−0.198899	−	0.344503i
$765$	−1.46699e10	−	4.05959e7i	−1.18471	−	0.00327844i
$766$	1.57161e9	−	2.72211e9i	0.126341	−	0.218829i
$767$	−1.04672e9	−	5.93625e9i	−0.0837621	−	0.475038i
$768$	−6.01730e8	+	5.03494e8i	−0.0479333	+	0.0401079i
$769$	−5.29776e8	+	1.92823e8i	−0.0420097	+	0.0152903i	−0.362940	−	0.931813i	$-0.618227\pi$
$769$	−5.29776e8	+	1.92823e8i	−0.0420097	+	0.0152903i	0.320930	+	0.947103i	$0.396005\pi$
$770$	3.35860e9	−	1.22243e9i	0.265119	−	0.0964954i
$771$	1.00847e10	−	8.43832e9i	0.792452	−	0.663080i
$772$	5.19528e8	+	2.94639e9i	0.0406395	+	0.230478i
$773$	9.10600e9	−	1.57720e10i	0.709087	−	1.22817i	−0.256110	−	0.966648i	$-0.582441\pi$
$773$	9.10600e9	−	1.57720e10i	0.709087	−	1.22817i	0.965196	−	0.261526i	$-0.0842258\pi$
$774$	5.29809e9	+	9.23549e9i	0.410701	+	0.715923i
$775$	−8.81190e9	−	1.52627e10i	−0.680007	−	1.17781i
$776$	9.78710e8	−	8.21235e8i	0.0751862	−	0.0630887i
$777$	2.65802e9	+	4.61857e9i	0.203275	+	0.353211i
$778$	1.78949e8	−	1.01487e9i	0.0136239	−	0.0772650i
$779$	−7.95410e9	−	6.67428e9i	−0.602851	−	0.505852i
$780$	−1.68208e9	+	9.46295e9i	−0.126915	+	0.713995i
$781$	7.17795e9	+	2.61256e9i	0.539165	+	0.196240i
$782$	−5.86351e9			−0.438464
$783$	1.48289e10	−	1.23384e10i	1.10393	−	0.918528i
$784$	−3.21148e9			−0.238012
$785$	−1.48758e10	−	5.41433e9i	−1.09758	−	0.399486i
$786$	1.37034e10	+	1.15309e10i	1.00658	+	0.847000i
$787$	5.84960e9	+	4.90840e9i	0.427774	+	0.358945i	0.831111	−	0.556106i	$-0.187705\pi$
$787$	5.84960e9	+	4.90840e9i	0.427774	+	0.358945i	−0.403337	+	0.915052i	$0.632150\pi$
$788$	−7.04511e8	+	3.99548e9i	−0.0512916	+	0.290889i
$789$	−6.51546e8	+	1.12491e9i	−0.0472254	+	0.0815361i
$790$	−1.72144e10	+	1.44446e10i	−1.24222	+	1.04234i
$791$	1.70135e9	+	2.94682e9i	0.122229	+	0.211707i
$792$	1.06750e9	−	5.95762e9i	0.0763534	−	0.426123i
$793$	9.58141e9	−	1.65955e10i	0.682297	−	1.18177i
$794$	1.64137e7	+	9.30867e7i	0.00116368	+	0.00659957i
$795$	−8.58697e8	−	4.90963e9i	−0.0606115	−	0.346548i
$796$	3.64228e9	−	1.32568e9i	0.255963	−	0.0931631i
$797$	−4.47814e9	+	1.62991e9i	−0.313324	+	0.114041i	−0.493895	−	0.869521i	$-0.664427\pi$
$797$	−4.47814e9	+	1.62991e9i	−0.313324	+	0.114041i	0.180572	+	0.983562i	$0.442205\pi$
$798$	−3.54795e9	−	1.29691e9i	−0.247154	−	0.0903442i
$799$	1.78329e9	+	1.01135e10i	0.123683	+	0.701438i
$800$	1.55449e9	−	2.69246e9i	0.107343	−	0.185923i
$801$	1.53990e10	+	5.65308e9i	1.05871	+	0.388661i
$802$	−6.21415e9	−	1.07632e10i	−0.425374	−	0.736770i
$803$	2.00884e9	−	1.68562e9i	0.136912	−	0.114883i
$804$	−8.37500e8	−	1.15880e6i	−0.0568314	−	7.86345e-5i
$805$	6.52308e8	−	3.69942e9i	0.0440724	−	0.249947i
$806$	−8.78869e9	−	7.37459e9i	−0.591224	−	0.496095i
$807$	−1.21646e10	+	4.40852e9i	−0.814783	+	0.295281i
$808$	3.76481e9	+	1.37028e9i	0.251075	+	0.0913837i
$809$	3.69904e9			0.245623			0.122811	−	0.992430i	$-0.460809\pi$
$809$	3.69904e9			0.245623			0.122811	+	0.992430i	$0.460809\pi$
$810$	−1.21350e10	−	1.02975e10i	−0.802312	−	0.680822i
$811$	−3.63175e9			−0.239080			−0.119540	−	0.992829i	$-0.538142\pi$
$811$	−3.63175e9			−0.239080			−0.119540	+	0.992829i	$0.538142\pi$
$812$	−2.25414e9	−	8.20438e8i	−0.147752	−	0.0537774i
$813$	2.05687e10	−	7.45418e9i	1.34242	−	0.486500i
$814$	−1.89945e10	−	1.59383e10i	−1.23436	−	1.03575i
$815$	5.72945e9	−	3.24933e10i	0.370733	−	2.10253i
$816$	3.08913e9	+	4.27426e6i	0.199031	+	0.000275388i
$817$	−2.36871e10	+	1.98758e10i	−1.51962	+	1.27511i
$818$	2.64275e9	+	4.57738e9i	0.168818	+	0.292402i
$819$	−5.73503e8	−	3.30597e9i	−0.0364789	−	0.210283i
$820$	−2.71992e9	+	4.71105e9i	−0.172269	+	0.298379i
$821$	−2.59083e9	−	1.46933e10i	−0.163395	−	0.926656i	−0.950704	−	0.310099i	$-0.899638\pi$
$821$	−2.59083e9	−	1.46933e10i	−0.163395	−	0.926656i	0.787310	−	0.616558i	$-0.211473\pi$
$822$	−1.92071e10	−	7.02093e9i	−1.20618	−	0.440903i
$823$	6.69035e9	−	2.43509e9i	0.418359	−	0.152270i	−0.124259	−	0.992250i	$-0.539655\pi$
$823$	6.69035e9	−	2.43509e9i	0.418359	−	0.152270i	0.542618	+	0.839980i	$0.317433\pi$
$824$	3.72358e9	−	1.35527e9i	0.231854	−	0.0843880i
$825$	4.13197e9	+	2.36247e10i	0.256194	+	1.46480i
$826$	−2.15532e8	−	1.22234e9i	−0.0133070	−	0.0754678i
$827$	−2.97976e9	+	5.16110e9i	−0.183194	+	0.317302i	−0.942967	−	0.332887i	$-0.891977\pi$
$827$	−2.97976e9	+	5.16110e9i	−0.183194	+	0.317302i	0.759772	+	0.650189i	$0.225310\pi$
$828$	−4.86169e9	−	4.10242e9i	−0.297633	−	0.251150i
$829$	−6.36410e9	−	1.10229e10i	−0.387968	−	0.671981i	0.604208	−	0.796827i	$-0.293490\pi$
$829$	−6.36410e9	−	1.10229e10i	−0.387968	−	0.671981i	−0.992176	+	0.124846i	$0.960156\pi$
$830$	4.81643e9	−	4.04146e9i	0.292383	−	0.245338i
$831$	−6.96369e9	+	1.20230e10i	−0.420955	+	0.726791i
$832$	3.51447e8	−	1.99315e9i	0.0211557	−	0.119980i
$833$	9.68617e9	+	8.12766e9i	0.580624	+	0.487201i
$834$	−2.18466e9	−	1.83830e9i	−0.130408	−	0.109733i
$835$	−5.15781e9	−	1.87729e9i	−0.306593	−	0.111591i
$836$	1.75774e10			1.04048
$837$	1.78790e10	−	6.42349e9i	1.05391	−	0.378645i
$838$	2.28744e10			1.34275
$839$	2.21903e10	+	8.07662e9i	1.29717	+	0.472131i	0.896074	−	0.443905i	$-0.146407\pi$
$839$	2.21903e10	+	8.07662e9i	1.29717	+	0.472131i	0.401096	+	0.916036i	$0.368629\pi$
$840$	−3.46358e8	+	1.94852e9i	−0.0201627	+	0.113430i
$841$	1.40382e10	+	1.17795e10i	0.813815	+	0.682872i
$842$	2.75287e9	−	1.56123e10i	0.158925	−	0.901311i
$843$	−1.42117e10	−	2.46942e10i	−0.817050	−	1.41970i
$844$	5.86112e9	−	4.91806e9i	0.335569	−	0.281576i
$845$	6.53298e8	+	1.13155e9i	0.0372489	+	0.0645169i
$846$	−5.59736e9	+	9.63325e9i	−0.317824	+	0.546986i
$847$	9.66727e8	−	1.67442e9i	0.0546653	−	0.0946831i
$848$	1.82251e8	+	1.03360e9i	0.0102632	+	0.0582057i
$849$	−1.85427e10	+	1.55155e10i	−1.03991	+	0.870139i
$850$	−1.15026e10	+	4.18661e9i	−0.642437	+	0.233828i
$851$	−2.44889e10	+	8.91322e9i	−1.36212	+	0.495771i
$852$	−3.24385e9	+	2.71427e9i	−0.179689	+	0.150354i
$853$	−2.43859e9	−	1.38299e10i	−0.134529	−	0.762953i	−0.975186	−	0.221385i	$-0.928942\pi$
$853$	−2.43859e9	−	1.38299e10i	−0.134529	−	0.762953i	0.840657	−	0.541567i	$-0.182169\pi$
$854$	1.97292e9	−	3.41719e9i	0.108394	−	0.187744i
$855$	2.32209e10	−	3.99640e10i	1.27057	−	2.18669i
$856$	8.59688e8	+	1.48902e9i	0.0468471	+	0.0811415i
$857$	3.18580e9	−	2.67321e9i	0.172896	−	0.145077i	−0.552233	−	0.833690i	$-0.686224\pi$
$857$	3.18580e9	−	2.67321e9i	0.172896	−	0.145077i	0.725130	+	0.688612i	$0.241780\pi$
$858$	7.78767e9	+	1.35318e10i	0.420922	+	0.731394i
$859$	6.90044e8	−	3.91343e9i	0.0371450	−	0.210660i	−0.960586	−	0.277982i	$-0.910334\pi$
$859$	6.90044e8	−	3.91343e9i	0.0371450	−	0.210660i	0.997731	+	0.0673221i	$0.0214455\pi$
$860$	1.24097e10	+	1.04130e10i	0.665297	+	0.558251i
$861$	3.32359e8	−	1.86977e9i	0.0177458	−	0.0998335i
$862$	6.02687e9	+	2.19360e9i	0.320492	+	0.116649i
$863$	6.27744e9			0.332464			0.166232	−	0.986087i	$-0.446840\pi$
$863$	6.27744e9			0.332464			0.166232	+	0.986087i	$0.446840\pi$
$864$	2.55834e9	+	2.16486e9i	0.134946	+	0.114191i
$865$	2.16988e10			1.13993
$866$	5.37750e9	+	1.95725e9i	0.281364	+	0.102408i
$867$	5.37672e9	+	4.52429e9i	0.280189	+	0.235767i
$868$	−1.80969e9	−	1.51851e9i	−0.0939258	−	0.0788131i
$869$	−6.33880e9	+	3.59491e10i	−0.327671	+	1.85831i
$870$	1.47105e10	−	2.53981e10i	0.757372	−	1.30762i
$871$	1.65495e9	−	1.38867e9i	0.0848634	−	0.0712089i
$872$	9.00474e8	+	1.55967e9i	0.0459900	+	0.0796570i
$873$	−4.17082e9	−	3.51945e9i	−0.212164	−	0.179030i
$874$	9.23706e9	−	1.59991e10i	0.467998	−	0.810596i
$875$	−2.40462e8	−	1.36373e9i	−0.0121344	−	0.0688176i
$876$	2.50166e8	+	1.43033e9i	0.0125737	+	0.0718907i
$877$	−1.17345e10	+	4.27101e9i	−0.587443	+	0.213812i	−0.618605	−	0.785702i	$-0.712302\pi$
$877$	−1.17345e10	+	4.27101e9i	−0.587443	+	0.213812i	0.0311612	+	0.999514i	$0.490079\pi$
$878$	1.52349e10	−	5.54506e9i	0.759643	−	0.276487i
$879$	−2.63416e10	−	9.62886e9i	−1.30822	−	0.478205i
$880$	−1.59909e9	−	9.06891e9i	−0.0791015	−	0.448607i
$881$	−1.22122e10	+	2.11522e10i	−0.601700	+	1.04217i	0.390864	+	0.920449i	$0.372176\pi$
$881$	−1.22122e10	+	2.11522e10i	−0.601700	+	1.04217i	−0.992564	+	0.121726i	$0.961157\pi$
$882$	2.34468e9	+	1.35159e10i	0.115065	+	0.663294i
$883$	−5.16974e9	−	8.95425e9i	−0.252701	−	0.437690i	0.711568	−	0.702617i	$-0.247985\pi$
$883$	−5.16974e9	−	8.95425e9i	−0.252701	−	0.437690i	−0.964268	+	0.264927i	$0.914652\pi$
$884$	−6.10430e9	+	5.12211e9i	−0.297203	+	0.249383i
$885$	1.51867e10	+	2.10130e7i	0.736482	+	0.00101903i
$886$	7.63626e8	−	4.33074e9i	0.0368861	−	0.209191i
$887$	9.77386e9	+	8.20124e9i	0.470255	+	0.394591i	0.846888	−	0.531772i	$-0.178474\pi$
$887$	9.77386e9	+	8.20124e9i	0.470255	+	0.394591i	−0.376633	+	0.926363i	$0.622918\pi$
$888$	1.29082e10	−	4.67799e9i	0.618615	−	0.224189i
$889$	−2.88186e9	−	1.04891e9i	−0.137568	−	0.0500705i
$890$	2.49583e10			1.18672
$891$	−2.58528e10	−	1.43086e8i	−1.22443	−	0.00677679i
$892$	1.48805e10			0.702004
$893$	−3.04049e10	−	1.10665e10i	−1.42877	−	0.520031i
$894$	−1.88152e10	+	6.81872e9i	−0.880701	+	0.319170i
$895$	−7.71840e9	−	6.47651e9i	−0.359871	−	0.301967i
$896$	7.23667e7	−	4.10412e8i	0.00336094	−	0.0190608i
$897$	1.64093e10	+	2.27046e7i	0.759129	+	0.00105036i
$898$	−1.24182e10	+	1.04201e10i	−0.572257	+	0.480181i
$899$	1.75177e10	+	3.03415e10i	0.804114	+	1.39277i
$900$	−1.24665e10	−	4.57653e9i	−0.570026	−	0.209261i
$901$	2.06615e9	−	3.57868e9i	0.0941077	−	0.162999i
$902$	1.53446e9	+	8.70235e9i	0.0696198	+	0.394833i
$903$	−5.31164e9	−	1.94161e9i	−0.240061	−	0.0877514i
$904$	8.23834e9	−	2.99851e9i	0.370894	−	0.134994i
$905$	−5.40595e10	+	1.96761e10i	−2.42439	+	0.882405i
$906$	2.45699e9	+	1.40479e10i	0.109763	+	0.627572i
$907$	5.96250e9	+	3.38150e10i	0.265340	+	1.50482i	0.768065	+	0.640371i	$0.221220\pi$
$907$	5.96250e9	+	3.38150e10i	0.265340	+	1.50482i	−0.502725	+	0.864446i	$0.667669\pi$
$908$	5.82179e9	−	1.00836e10i	0.258081	−	0.447010i
$909$	3.01833e9	−	1.68451e10i	0.133289	−	0.743875i
$910$	−2.55256e9	−	4.42116e9i	−0.112287	−	0.194487i
$911$	2.20398e10	−	1.84936e10i	0.965812	−	0.810413i	−0.0160766	−	0.999871i	$-0.505118\pi$
$911$	2.20398e10	−	1.84936e10i	0.965812	−	0.810413i	0.981889	+	0.189458i	$0.0606731\pi$
$912$	−4.87811e9	+	8.42220e9i	−0.212946	+	0.367658i
$913$	1.77353e9	−	1.00582e10i	0.0771244	−	0.437394i
$914$	1.66509e10	+	1.39718e10i	0.721319	+	0.605258i
$915$	3.69412e10	+	3.10846e10i	1.59418	+	1.34144i
$916$	−2.14058e10	−	7.79107e9i	−0.920232	−	0.334937i
$917$	−9.51271e9			−0.407391
$918$	−2.23736e9	−	1.30041e10i	−0.0954523	−	0.554794i
$919$	−2.34487e10			−0.996587			−0.498293	−	0.867009i	$-0.666040\pi$
$919$	−2.34487e10			−0.996587			−0.498293	+	0.867009i	$0.666040\pi$
$920$	−9.09492e9	−	3.31028e9i	−0.385072	−	0.140155i
$921$	4.63505e9	−	2.60757e10i	0.195500	−	1.09983i
$922$	−1.56366e10	−	1.31206e10i	−0.657026	−	0.551311i
$923$	1.89460e9	−	1.07448e10i	0.0793071	−	0.449773i
$924$	1.60357e9	+	2.78635e9i	0.0668706	+	0.116194i
$925$	−4.16764e10	+	3.49706e10i	−1.73139	+	1.45281i
$926$	5.61512e9	+	9.72568e9i	0.232392	+	0.402514i
$927$	−8.42238e9	−	1.46817e10i	−0.347261	−	0.605336i
$928$	−3.09026e9	+	5.35249e9i	−0.126934	+	0.219856i
$929$	−2.51391e9	−	1.42571e10i	−0.102871	−	0.583413i	−0.992049	−	0.125851i	$-0.959834\pi$
$929$	−2.51391e9	−	1.42571e10i	−0.102871	−	0.583413i	0.889178	−	0.457562i	$-0.151277\pi$
$930$	2.21682e10	−	1.85491e10i	0.903733	−	0.756194i
$931$	−3.74360e10	+	1.36256e10i	−1.52043	+	0.553391i
$932$	−1.88544e10	+	6.86246e9i	−0.762883	+	0.277667i
$933$	−2.09898e10	+	1.75631e10i	−0.846101	+	0.707970i
$934$	3.80487e9	+	2.15785e10i	0.152801	+	0.866577i
$935$	−1.81287e10	+	3.13998e10i	−0.725313	+	1.25628i
$936$	−8.64503e9	−	2.39233e7i	−0.344589	−	0.000953578i
$937$	1.63097e10	+	2.82491e10i	0.647673	+	1.12180i	0.983677	+	0.179943i	$0.0575912\pi$
$937$	1.63097e10	+	2.82491e10i	0.647673	+	1.12180i	−0.336004	+	0.941861i	$0.609075\pi$
$938$	3.40772e8	−	2.85941e8i	0.0134820	−	0.0113127i
$939$	−3.67114e9	−	6.37896e9i	−0.144701	−	0.251432i
$940$	−2.94359e9	+	1.66939e10i	−0.115593	+	0.655558i
$941$	−1.76272e9	−	1.47910e9i	−0.0689636	−	0.0578674i	0.607654	−	0.794202i	$-0.292111\pi$
$941$	−1.76272e9	−	1.47910e9i	−0.0689636	−	0.0578674i	−0.676618	+	0.736334i	$0.736555\pi$
$942$	2.49198e9	−	1.40193e10i	0.0971329	−	0.546445i
$943$	8.72731e9	+	3.17648e9i	0.338914	+	0.123355i
$944$	−3.19795e9			−0.123728
$945$	8.45349e9	+	3.50901e7i	0.325855	+	0.00135261i
$946$	2.63151e10			1.01062
$947$	1.59827e10	+	5.81723e9i	0.611541	+	0.222583i	0.629177	−	0.777262i	$-0.283392\pi$
$947$	1.59827e10	+	5.81723e9i	0.611541	+	0.222583i	−0.0176364	+	0.999844i	$0.505614\pi$
$948$	−1.54659e10	−	1.30139e10i	−0.589583	−	0.496111i
$949$	−2.86932e9	−	2.40765e9i	−0.108980	−	0.0914452i
$950$	6.69710e9	−	3.79811e10i	0.253428	−	1.43726i
$951$	−1.85356e10	+	3.20023e10i	−0.698836	+	1.20656i
$952$	−1.25694e9	+	1.05470e9i	−0.0472156	+	0.0396186i
$953$	2.67060e9	+	4.62562e9i	0.0999503	+	0.173119i	0.911664	−	0.410937i	$-0.134798\pi$
$953$	2.67060e9	+	4.62562e9i	0.0999503	+	0.173119i	−0.811714	+	0.584056i	$0.801465\pi$
$954$	4.21696e9	−	1.52165e9i	0.157246	−	0.0567407i
$955$	−1.59333e10	+	2.75973e10i	−0.591963	+	1.02531i
$956$	−1.44164e9	−	8.17595e9i	−0.0533648	−	0.302647i
$957$	−8.21418e9	−	4.69648e10i	−0.302951	−	1.73213i
$958$	−5.14077e8	+	1.87109e8i	−0.0188907	+	0.00687566i
$959$	1.02072e10	−	3.71511e9i	0.373715	−	0.136021i
$960$	4.78915e9	+	1.75062e9i	0.174707	+	0.0638619i
$961$	1.21394e9	+	6.88461e9i	0.0441231	+	0.250235i
$962$	−1.77083e10	+	3.06717e10i	−0.641304	+	1.11077i
$963$	5.63909e9	−	4.70523e9i	0.203478	−	0.169781i
$964$	2.26226e9	+	3.91835e9i	0.0813342	+	0.140875i
$965$	1.48950e10	−	1.24984e10i	0.533574	−	0.447722i
$966$	3.37885e9	+	4.67512e6i	0.120600	+	0.000166868i
$967$	−6.83552e8	+	3.87662e9i	−0.0243097	+	0.137867i	−0.994547	−	0.104289i	$-0.966743\pi$
$967$	−6.83552e8	+	3.87662e9i	−0.0243097	+	0.137867i	0.970237	+	0.242156i	$0.0778545\pi$
$968$	−3.81609e9	−	3.20208e9i	−0.135224	−	0.113467i
$969$	3.60279e10	−	1.30567e10i	1.27205	−	0.460998i
$970$	−7.80249e9	−	2.83988e9i	−0.274494	−	0.0999075i
$971$	7.81530e8			0.0273955			0.0136977	−	0.999906i	$-0.495640\pi$
$971$	7.81530e8			0.0273955			0.0136977	+	0.999906i	$0.495640\pi$
$972$	7.24327e9	−	1.23476e10i	0.252990	−	0.431273i
$973$	1.51656e9			0.0527794
$974$	−7.77026e9	−	2.82814e9i	−0.269451	−	0.0980720i
$975$	3.22067e10	−	1.16718e10i	1.11283	−	0.403295i
$976$	−7.78797e9	−	6.53488e9i	−0.268133	−	0.224990i
$977$	−1.30187e9	+	7.38329e9i	−0.0446619	+	0.253290i	−0.998962	−	0.0455611i	$-0.985492\pi$
$977$	−1.30187e9	+	7.38329e9i	−0.0446619	+	0.253290i	0.954300	+	0.298852i	$0.0966035\pi$
$978$	2.96776e10	+	4.10633e7i	1.01448	+	0.00140368i
$979$	3.10575e10	−	2.60603e10i	1.05786	−	0.887648i
$980$	1.04357e10	+	1.80752e10i	0.354187	+	0.613469i
$981$	5.90663e9	−	4.92846e9i	0.199755	−	0.166675i
$982$	−1.66445e10	+	2.88291e10i	−0.560893	+	0.971496i
$983$	8.48968e9	+	4.81473e10i	0.285072	+	1.61672i	0.705030	+	0.709178i	$0.250934\pi$
$983$	8.48968e9	+	4.81473e10i	0.285072	+	1.61672i	−0.419958	+	0.907543i	$0.637955\pi$
$984$	−4.59558e9	−	1.67986e9i	−0.153765	−	0.0562069i
$985$	2.47771e10	−	9.01814e9i	0.826084	−	0.300670i
$986$	2.28667e10	−	8.32279e9i	0.759686	−	0.276503i
$987$	−1.01956e9	−	5.82935e9i	−0.0337521	−	0.192979i
$988$	−4.35971e9	−	2.47251e10i	−0.143816	−	0.815623i
$989$	1.38288e10	−	2.39522e10i	0.454567	−	0.787332i
$990$	−3.70002e10	+	1.33511e10i	−1.21194	+	0.437315i
$991$	−1.19879e10	−	2.07637e10i	−0.391279	−	0.677715i	0.601339	−	0.798994i	$-0.294634\pi$
$991$	−1.19879e10	−	2.07637e10i	−0.391279	−	0.677715i	−0.992619	+	0.121278i	$0.961301\pi$
$992$	−4.66267e9	+	3.91245e9i	−0.151651	+	0.127250i
$993$	−2.89139e10	+	4.99207e10i	−0.937096	+	1.61792i
$994$	3.90119e8	−	2.21248e9i	0.0125993	−	0.0714540i
$995$	−1.92970e10	−	1.61921e10i	−0.621025	−	0.521101i
$996$	4.32720e9	+	3.64116e9i	0.138771	+	0.116770i
$997$	1.18303e10	+	4.30588e9i	0.378062	+	0.137603i	0.524060	−	0.851682i	$-0.324417\pi$
$997$	1.18303e10	+	4.30588e9i	0.378062	+	0.137603i	−0.145997	+	0.989285i	$0.546639\pi$
$998$	−3.94059e10			−1.25489
$999$	−2.91121e10	−	5.09105e10i	−0.923834	−	1.61558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.e.b.31.11	yes	66
27.7	even	9	inner	54.8.e.b.7.11	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.e.b.7.11	✓	66	27.7	even	9	inner
54.8.e.b.31.11	yes	66	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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.51754 + 2.73616i) q^{2} +(43.9672 - 15.9339i) q^{3} +(49.0268 + 41.1384i) q^{4} +(72.2267 - 409.618i) q^{5} +(374.123 + 0.517653i) q^{6} +(-152.227 + 127.734i) q^{7} +(256.000 + 443.405i) q^{8} +(1679.22 - 1401.13i) q^{9} +O(q^{10})\)	\(q+(7.51754 + 2.73616i) q^{2} +(43.9672 - 15.9339i) q^{3} +(49.0268 + 41.1384i) q^{4} +(72.2267 - 409.618i) q^{5} +(374.123 + 0.517653i) q^{6} +(-152.227 + 127.734i) q^{7} +(256.000 + 443.405i) q^{8} +(1679.22 - 1401.13i) q^{9} +(1663.75 - 2881.70i) q^{10} +(-938.612 - 5323.14i) q^{11} +(2811.07 + 1027.55i) q^{12} +(-7254.96 + 2640.59i) q^{13} +(-1493.88 + 543.727i) q^{14} +(-3351.20 - 19160.6i) q^{15} +(711.263 + 4033.77i) q^{16} +(8063.48 - 13966.3i) q^{17} +(16457.4 - 5938.46i) q^{18} +(25405.5 + 44003.7i) q^{19} +(20392.1 - 17111.0i) q^{20} +(-4657.71 + 8041.67i) q^{21} +(7508.90 - 42585.1i) q^{22} +(-34815.3 - 29213.5i) q^{23} +(18320.8 + 15416.2i) q^{24} +(-89156.8 - 32450.4i) q^{25} -61764.6 q^{26} +(51505.2 - 88360.5i) q^{27} -12718.0 q^{28} +(177240. + 64510.0i) q^{29} +(27233.7 - 153210. i) q^{30} +(142294. + 119398. i) q^{31} +(-5690.10 + 32270.2i) q^{32} +(-126086. - 219087. i) q^{33} +(98831.7 - 82929.6i) q^{34} +(41327.3 + 71580.9i) q^{35} +(139967. + 387.331i) q^{36} +(286706. - 496590. i) q^{37} +(70586.0 + 400313. i) q^{38} +(-276905. + 231699. i) q^{39} +(200117. - 72836.5i) q^{40} +(-192028. + 69892.5i) q^{41} +(-57017.8 + 47709.4i) q^{42} +(105674. + 599308. i) q^{43} +(172968. - 299590. i) q^{44} +(-452645. - 789039. i) q^{45} +(-181792. - 314874. i) q^{46} +(-487813. + 409324. i) q^{47} +(95545.9 + 166020. i) q^{48} +(-136150. + 772142. i) q^{49} +(-581450. - 487895. i) q^{50} +(131990. - 742543. i) q^{51} +(-464318. - 168998. i) q^{52} +256236. q^{53} +(628961. - 523327. i) q^{54} -2.24825e6 q^{55} +(-95608.1 - 34798.5i) q^{56} +(1.81816e6 + 1.52991e6i) q^{57} +(1.15590e6 + 969913. i) q^{58} +(-135576. + 768888. i) q^{59} +(623938. - 1.07725e6i) q^{60} +(-1.90136e6 + 1.59543e6i) q^{61} +(743004. + 1.28692e6i) q^{62} +(-76651.2 + 427785. i) q^{63} +(-131072. + 227023. i) q^{64} +(557631. + 3.16248e6i) q^{65} +(-348401. - 1.99199e6i) q^{66} +(-262946. + 95704.5i) q^{67} +(969880. - 353007. i) q^{68} +(-1.99621e6 - 729691. i) q^{69} +(114822. + 651190. i) q^{70} +(-706592. + 1.22385e6i) q^{71} +(1.05115e6 + 385885. i) q^{72} +(242575. + 420152. i) q^{73} +(3.51408e6 - 2.94866e6i) q^{74} +(-4.43703e6 - 6139.28i) q^{75} +(-564688. + 3.20250e6i) q^{76} +(822828. + 690435. i) q^{77} +(-2.71561e6 + 984149. i) q^{78} +(-6.34610e6 - 2.30979e6i) q^{79} +1.70368e6 q^{80} +(856611. - 4.70564e6i) q^{81} -1.63482e6 q^{82} +(1.77558e6 + 646257. i) q^{83} +(-559174. + 202647. i) q^{84} +(-5.13847e6 - 4.31169e6i) q^{85} +(-845394. + 4.79447e6i) q^{86} +(8.82062e6 + 12204.6i) q^{87} +(2.12002e6 - 1.77891e6i) q^{88} +(3.75030e6 + 6.49572e6i) q^{89} +(-1.24384e6 - 7.17015e6i) q^{90} +(767111. - 1.32868e6i) q^{91} +(-505087. - 2.86449e6i) q^{92} +(8.15872e6 + 2.98232e6i) q^{93} +(-4.78713e6 + 1.74237e6i) q^{94} +(1.98596e7 - 7.22832e6i) q^{95} +(264011. + 1.50949e6i) q^{96} +(-433312. - 2.45743e6i) q^{97} +(-3.13622e6 + 5.43208e6i) q^{98} +(-9.03457e6 - 7.62361e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9}+O(q^{10}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9} - 3000 q^{10} - 2523 q^{11} - 5376 q^{12} - 9924 q^{13} + 13416 q^{14} - 15084 q^{15} + 29478 q^{17} + 22848 q^{18} - 61731 q^{19} - 27264 q^{20} - 36372 q^{21} + 20184 q^{22} + 255234 q^{23} + 558999 q^{25} - 316368 q^{26} - 51597 q^{27} + 263424 q^{28} + 132153 q^{29} + 610632 q^{30} + 776898 q^{31} + 645795 q^{33} + 387840 q^{34} - 321081 q^{35} - 314688 q^{36} - 759795 q^{37} + 174504 q^{38} - 84012 q^{39} - 109056 q^{40} + 349287 q^{41} + 313752 q^{42} - 1043622 q^{43} + 255552 q^{44} + 845496 q^{45} - 524472 q^{46} + 1280709 q^{47} - 872448 q^{48} + 1011003 q^{49} - 1537704 q^{50} - 7812153 q^{51} - 635136 q^{52} - 2951976 q^{53} - 1256832 q^{54} + 2539854 q^{55} + 858624 q^{56} - 3973923 q^{57} - 47496 q^{58} + 639426 q^{59} - 94464 q^{60} + 1639350 q^{61} + 2859936 q^{62} + 6955635 q^{63} - 8650752 q^{64} - 4119567 q^{65} + 712512 q^{66} - 6408441 q^{67} - 1634496 q^{68} - 1007298 q^{69} + 2380872 q^{70} + 3531612 q^{71} + 6623232 q^{72} - 6666213 q^{73} + 7873368 q^{74} + 16535910 q^{75} - 1396032 q^{76} - 8256489 q^{77} - 4117104 q^{78} - 22540695 q^{79} - 3072000 q^{80} - 13134636 q^{81} + 3798096 q^{82} + 8663238 q^{83} + 8570304 q^{84} - 15143175 q^{85} + 8348976 q^{86} + 45908613 q^{87} + 11028480 q^{88} + 21718137 q^{89} - 27904392 q^{90} - 8606796 q^{91} - 8332800 q^{92} - 20412249 q^{93} - 10358784 q^{94} - 21603363 q^{95} - 5505024 q^{96} - 17397492 q^{97} + 44171448 q^{98} + 103927383 q^{99}+O(q^{100}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9 - 3000 * q^10 - 2523 * q^11 - 5376 * q^12 - 9924 * q^13 + 13416 * q^14 - 15084 * q^15 + 29478 * q^17 + 22848 * q^18 - 61731 * q^19 - 27264 * q^20 - 36372 * q^21 + 20184 * q^22 + 255234 * q^23 + 558999 * q^25 - 316368 * q^26 - 51597 * q^27 + 263424 * q^28 + 132153 * q^29 + 610632 * q^30 + 776898 * q^31 + 645795 * q^33 + 387840 * q^34 - 321081 * q^35 - 314688 * q^36 - 759795 * q^37 + 174504 * q^38 - 84012 * q^39 - 109056 * q^40 + 349287 * q^41 + 313752 * q^42 - 1043622 * q^43 + 255552 * q^44 + 845496 * q^45 - 524472 * q^46 + 1280709 * q^47 - 872448 * q^48 + 1011003 * q^49 - 1537704 * q^50 - 7812153 * q^51 - 635136 * q^52 - 2951976 * q^53 - 1256832 * q^54 + 2539854 * q^55 + 858624 * q^56 - 3973923 * q^57 - 47496 * q^58 + 639426 * q^59 - 94464 * q^60 + 1639350 * q^61 + 2859936 * q^62 + 6955635 * q^63 - 8650752 * q^64 - 4119567 * q^65 + 712512 * q^66 - 6408441 * q^67 - 1634496 * q^68 - 1007298 * q^69 + 2380872 * q^70 + 3531612 * q^71 + 6623232 * q^72 - 6666213 * q^73 + 7873368 * q^74 + 16535910 * q^75 - 1396032 * q^76 - 8256489 * q^77 - 4117104 * q^78 - 22540695 * q^79 - 3072000 * q^80 - 13134636 * q^81 + 3798096 * q^82 + 8663238 * q^83 + 8570304 * q^84 - 15143175 * q^85 + 8348976 * q^86 + 45908613 * q^87 + 11028480 * q^88 + 21718137 * q^89 - 27904392 * q^90 - 8606796 * q^91 - 8332800 * q^92 - 20412249 * q^93 - 10358784 * q^94 - 21603363 * q^95 - 5505024 * q^96 - 17397492 * q^97 + 44171448 * q^98 + 103927383 * q^99

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