LMFDB - Embedded newform 54.8.e.b.7.9

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			7.9
Character	$\chi$	$=$	54.7
Dual form			54.8.e.b.31.9

$q$-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} +(35.4628 - 30.4859i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-84.4758 - 479.086i) q^{5} +(183.179 - 326.211i) q^{6} +(666.476 + 559.239i) q^{7} +(256.000 - 443.405i) q^{8} +(328.222 - 2162.23i) q^{9} +(-1945.91 - 3370.41i) q^{10} +(-535.039 + 3034.36i) q^{11} +(484.489 - 2953.51i) q^{12} +(-11698.2 - 4257.81i) q^{13} +(6540.43 + 2380.52i) q^{14} +(-17601.1 - 14414.4i) q^{15} +(711.263 - 4033.77i) q^{16} +(16020.8 + 27748.9i) q^{17} +(-3448.78 - 17152.7i) q^{18} +(9569.05 - 16574.1i) q^{19} +(-23850.4 - 20012.9i) q^{20} +(40684.0 - 485.889i) q^{21} +(4280.31 + 24274.9i) q^{22} +(51102.1 - 42879.7i) q^{23} +(-4439.11 - 23528.8i) q^{24} +(-148974. + 54222.1i) q^{25} -99592.1 q^{26} +(-54277.8 - 86684.9i) q^{27} +55681.4 q^{28} +(-121790. + 44328.1i) q^{29} +(-171757. - 60201.6i) q^{30} +(203893. - 171086. i) q^{31} +(-5690.10 - 32270.2i) q^{32} +(73531.0 + 123918. i) q^{33} +(196363. + 164768. i) q^{34} +(211623. - 366542. i) q^{35} +(-72859.0 - 119510. i) q^{36} +(-60074.3 - 104052. i) q^{37} +(26586.4 - 150779. i) q^{38} +(-544656. + 205637. i) q^{39} +(-234055. - 85189.1i) q^{40} +(622226. + 226472. i) q^{41} +(304514. - 114971. i) q^{42} +(-70250.4 + 398410. i) q^{43} +(98597.3 + 170776. i) q^{44} +(-1.06362e6 + 25409.3i) q^{45} +(266836. - 462174. i) q^{46} +(-221639. - 185977. i) q^{47} +(-97749.7 - 164732. i) q^{48} +(-11565.8 - 65592.8i) q^{49} +(-971558. + 815234. i) q^{50} +(1.41409e6 + 495645. i) q^{51} +(-748687. + 272500. i) q^{52} +1.35779e6 q^{53} +(-645219. - 503145. i) q^{54} +1.49892e6 q^{55} +(418587. - 152353. i) q^{56} +(-165930. - 879485. i) q^{57} +(-794276. + 666477. i) q^{58} +(350208. + 1.98613e6i) q^{59} +(-1.45591e6 + 17388.0i) q^{60} +(1.22664e6 + 1.02928e6i) q^{61} +(1.06465e6 - 1.84403e6i) q^{62} +(1.42796e6 - 1.25752e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-1.05164e6 + 5.96415e6i) q^{65} +(891832. + 730366. i) q^{66} +(862574. + 313951. i) q^{67} +(1.92700e6 + 701369. i) q^{68} +(504997. - 3.07853e6i) q^{69} +(587967. - 3.33453e6i) q^{70} +(616251. + 1.06738e6i) q^{71} +(-874719. - 699066. i) q^{72} +(-711497. + 1.23235e6i) q^{73} +(-736313. - 617840. i) q^{74} +(-3.63003e6 + 6.46447e6i) q^{75} +(-212691. - 1.20623e6i) q^{76} +(-2.05352e6 + 1.72311e6i) q^{77} +(-3.53182e6 + 3.03615e6i) q^{78} +(2.58567e6 - 941106. i) q^{79} -1.99261e6 q^{80} +(-4.56751e6 - 1.41939e6i) q^{81} +5.29727e6 q^{82} +(639688. - 232827. i) q^{83} +(1.97462e6 - 1.69750e6i) q^{84} +(1.19407e7 - 1.00195e7i) q^{85} +(562003. + 3.18728e6i) q^{86} +(-2.96765e6 + 5.28489e6i) q^{87} +(1.20848e6 + 1.01403e6i) q^{88} +(-3.01913e6 + 5.22928e6i) q^{89} +(-7.92630e6 + 3.10126e6i) q^{90} +(-5.41546e6 - 9.37985e6i) q^{91} +(741369. - 4.20452e6i) q^{92} +(2.01489e6 - 1.22831e7i) q^{93} +(-2.17504e6 - 791650. i) q^{94} +(-8.74877e6 - 3.18429e6i) q^{95} +(-1.18557e6 - 970924. i) q^{96} +(2.27013e6 - 1.28746e7i) q^{97} +(-266419. - 461450. i) q^{98} +(6.38537e6 + 2.15282e6i) 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} - 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}+ \cdots + 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

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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
$3$	35.4628	−	30.4859i	0.758314	−	0.651890i
$3$	35.4628	−	30.4859i	0.758314	−	0.651890i
$4$	49.0268	−	41.1384i	0.383022	−	0.321394i
$5$	−84.4758	−	479.086i	−0.302230	−	1.71403i	−0.636265	−	0.771471i	$-0.719521\pi$
$5$	−84.4758	−	479.086i	−0.302230	−	1.71403i	0.334035	−	0.942561i	$-0.391590\pi$
$6$	183.179	−	326.211i	0.346215	−	0.616551i
$7$	666.476	+	559.239i	0.734414	+	0.616247i	0.931331	−	0.364173i	$-0.118648\pi$
$7$	666.476	+	559.239i	0.734414	+	0.616247i	−0.196917	+	0.980420i	$0.563093\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	328.222	−	2162.23i	0.150079	−	0.988674i
$10$	−1945.91	−	3370.41i	−0.615350	−	1.06582i
$11$	−535.039	+	3034.36i	−0.121202	+	0.687373i	0.862289	+	0.506417i	$0.169030\pi$
$11$	−535.039	+	3034.36i	−0.121202	+	0.687373i	−0.983491	+	0.180956i	$0.942081\pi$
$12$	484.489	−	2953.51i	0.0809375	−	0.493406i
$13$	−11698.2	−	4257.81i	−1.47679	−	0.537508i	−0.526855	−	0.849955i	$-0.676629\pi$
$13$	−11698.2	−	4257.81i	−1.47679	−	0.537508i	−0.949935	+	0.312447i	$0.898851\pi$
$14$	6540.43	+	2380.52i	0.637027	+	0.231859i
$15$	−17601.1	−	14414.4i	−1.34654	−	1.10275i
$16$	711.263	−	4033.77i	0.0434120	−	0.246202i
$17$	16020.8	+	27748.9i	0.790886	+	1.36985i	0.925419	+	0.378945i	$0.123713\pi$
$17$	16020.8	+	27748.9i	0.790886	+	1.36985i	−0.134534	+	0.990909i	$0.542954\pi$
$18$	−3448.78	−	17152.7i	−0.139384	−	0.693233i
$19$	9569.05	−	16574.1i	0.320060	−	0.554360i	−0.660440	−	0.750879i	$-0.729630\pi$
$19$	9569.05	−	16574.1i	0.320060	−	0.554360i	0.980500	+	0.196519i	$0.0629636\pi$
$20$	−23850.4	−	20012.9i	−0.666640	−	0.559377i
$21$	40684.0	−	485.889i	0.958641	−	0.0114491i
$22$	4280.31	+	24274.9i	0.0857030	+	0.486046i
$23$	51102.1	−	42879.7i	0.875772	−	0.734860i	−0.0895334	−	0.995984i	$-0.528538\pi$
$23$	51102.1	−	42879.7i	0.875772	−	0.734860i	0.965305	+	0.261124i	$0.0840931\pi$
$24$	−4439.11	−	23528.8i	−0.0655476	−	0.347424i
$25$	−148974.	+	54222.1i	−1.90687	+	0.694043i
$26$	−99592.1			−1.11127
$27$	−54277.8	−	86684.9i	−0.530700	−	0.847560i
$28$	55681.4			0.479355
$29$	−121790.	+	44328.1i	−0.927300	+	0.337510i	−0.761139	−	0.648589i	$-0.775359\pi$
$29$	−121790.	+	44328.1i	−0.927300	+	0.337510i	−0.166161	+	0.986099i	$0.553137\pi$
$30$	−171757.	−	60201.6i	−1.16142	−	0.407083i
$31$	203893.	−	171086.i	1.22924	−	1.03145i	0.230950	−	0.972966i	$-0.425817\pi$
$31$	203893.	−	171086.i	1.22924	−	1.03145i	0.998288	−	0.0584874i	$-0.0186278\pi$
$32$	−5690.10	−	32270.2i	−0.0306970	−	0.174091i
$33$	73531.0	+	123918.i	0.356182	+	0.600255i
$34$	196363.	+	164768.i	0.856806	+	0.718946i
$35$	211623.	−	366542.i	0.834304	−	1.44506i
$36$	−72859.0	−	119510.i	−0.260270	−	0.426919i
$37$	−60074.3	−	104052.i	−0.194977	−	0.337709i	0.751916	−	0.659259i	$-0.229130\pi$
$37$	−60074.3	−	104052.i	−0.194977	−	0.337709i	−0.946893	+	0.321549i	$0.895796\pi$
$38$	26586.4	−	150779.i	0.0785989	−	0.445757i
$39$	−544656.	+	205637.i	−1.47027	+	0.555105i
$40$	−234055.	−	85189.1i	−0.578240	−	0.210462i
$41$	622226.	+	226472.i	1.40995	+	0.513181i	0.931116	−	0.364723i	$-0.118836\pi$
$41$	622226.	+	226472.i	1.40995	+	0.513181i	0.478837	+	0.877904i	$0.341058\pi$
$42$	304514.	−	114971.i	0.634213	−	0.239450i
$43$	−70250.4	+	398410.i	−0.134744	+	0.764171i	0.840294	+	0.542131i	$0.182383\pi$
$43$	−70250.4	+	398410.i	−0.134744	+	0.764171i	−0.975038	+	0.222040i	$0.928729\pi$
$44$	98597.3	+	170776.i	0.174494	+	0.302233i
$45$	−1.06362e6	+	25409.3i	−1.73998	+	0.0415670i
$46$	266836.	−	462174.i	0.404196	−	0.700088i
$47$	−221639.	−	185977.i	−0.311389	−	0.261286i	0.473677	−	0.880699i	$-0.342926\pi$
$47$	−221639.	−	185977.i	−0.311389	−	0.261286i	−0.785066	+	0.619412i	$0.787371\pi$
$48$	−97749.7	−	164732.i	−0.127577	−	0.214998i
$49$	−11565.8	−	65592.8i	−0.0140439	−	0.0796470i
$50$	−971558.	+	815234.i	−1.09919	+	0.922332i
$51$	1.41409e6	+	495645.i	1.49273	+	0.523208i
$52$	−748687.	+	272500.i	−0.738395	+	0.268754i
$53$	1.35779e6			1.25276			0.626379	−	0.779519i	$-0.284536\pi$
$53$	1.35779e6			1.25276			0.626379	+	0.779519i	$0.284536\pi$
$54$	−645219.	−	503145.i	−0.557608	−	0.434825i
$55$	1.49892e6			1.21481
$56$	418587.	−	152353.i	0.318514	−	0.115929i
$57$	−165930.	−	879485.i	−0.118676	−	0.629023i
$58$	−794276.	+	666477.i	−0.534532	+	0.448525i
$59$	350208.	+	1.98613e6i	0.221995	+	1.25900i	0.868347	+	0.495958i	$0.165183\pi$
$59$	350208.	+	1.98613e6i	0.221995	+	1.25900i	−0.646351	+	0.763040i	$0.723706\pi$
$60$	−1.45591e6	+	17388.0i	−0.870174	+	0.0103925i
$61$	1.22664e6	+	1.02928e6i	0.691932	+	0.580600i	0.919466	−	0.393170i	$-0.128622\pi$
$61$	1.22664e6	+	1.02928e6i	0.691932	+	0.580600i	−0.227533	+	0.973770i	$0.573066\pi$
$62$	1.06465e6	−	1.84403e6i	0.567332	−	0.982647i
$63$	1.42796e6	−	1.25752e6i	0.719487	−	0.633611i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−1.05164e6	+	5.96415e6i	−0.474975	+	2.69372i
$66$	891832.	+	730366.i	0.381838	+	0.312706i
$67$	862574.	+	313951.i	0.350376	+	0.127526i	0.511212	−	0.859455i	$-0.329197\pi$
$67$	862574.	+	313951.i	0.350376	+	0.127526i	−0.160836	+	0.986981i	$0.551419\pi$
$68$	1.92700e6	+	701369.i	0.743189	+	0.270499i
$69$	504997.	−	3.07853e6i	0.185062	−	1.12816i
$70$	587967.	−	3.33453e6i	0.204885	−	1.16196i
$71$	616251.	+	1.06738e6i	0.204340	+	0.353927i	0.949922	−	0.312486i	$-0.101162\pi$
$71$	616251.	+	1.06738e6i	0.204340	+	0.353927i	−0.745582	+	0.666414i	$0.767829\pi$
$72$	−874719.	−	699066.i	−0.276188	−	0.220727i
$73$	−711497.	+	1.23235e6i	−0.214064	+	0.370769i	−0.952982	−	0.303025i	$-0.902003\pi$
$73$	−711497.	+	1.23235e6i	−0.214064	+	0.370769i	0.738919	+	0.673794i	$0.235337\pi$
$74$	−736313.	−	617840.i	−0.211228	−	0.177241i
$75$	−3.63003e6	+	6.46447e6i	−0.993564	+	1.76937i
$76$	−212691.	−	1.20623e6i	−0.0555778	−	0.315198i
$77$	−2.05352e6	+	1.72311e6i	−0.512604	+	0.430126i
$78$	−3.53182e6	+	3.03615e6i	−0.842688	+	0.724423i
$79$	2.58567e6	−	941106.i	0.590035	−	0.214755i	−0.0297097	−	0.999559i	$-0.509458\pi$
$79$	2.58567e6	−	941106.i	0.590035	−	0.214755i	0.619745	+	0.784803i	$0.287236\pi$
$80$	−1.99261e6			−0.435118
$81$	−4.56751e6	−	1.41939e6i	−0.954953	−	0.296758i
$82$	5.29727e6			1.06097
$83$	639688.	−	232827.i	0.122799	−	0.0446952i	−0.279890	−	0.960032i	$-0.590298\pi$
$83$	639688.	−	232827.i	0.122799	−	0.0446952i	0.402689	+	0.915337i	$0.368076\pi$
$84$	1.97462e6	−	1.69750e6i	0.363501	−	0.312487i
$85$	1.19407e7	−	1.00195e7i	2.10894	−	1.76961i
$86$	562003.	+	3.18728e6i	0.0952784	+	0.540350i
$87$	−2.96765e6	+	5.28489e6i	−0.483165	+	0.860436i
$88$	1.20848e6	+	1.01403e6i	0.189038	+	0.158622i
$89$	−3.01913e6	+	5.22928e6i	−0.453959	+	0.786279i	−0.998628	−	0.0523717i	$-0.983322\pi$
$89$	−3.01913e6	+	5.22928e6i	−0.453959	+	0.786279i	0.544669	+	0.838651i	$0.316655\pi$
$90$	−7.92630e6	+	3.10126e6i	−1.14610	+	0.448424i
$91$	−5.41546e6	−	9.37985e6i	−0.753339	−	1.30482i
$92$	741369.	−	4.20452e6i	0.0992607	−	0.562935i
$93$	2.01489e6	−	1.22831e7i	0.259754	−	1.58349i
$94$	−2.17504e6	−	791650.i	−0.270097	−	0.0983073i
$95$	−8.74877e6	−	3.18429e6i	−1.04692	−	0.381049i
$96$	−1.18557e6	−	970924.i	−0.136766	−	0.112005i
$97$	2.27013e6	−	1.28746e7i	0.252552	−	1.43229i	−0.549728	−	0.835344i	$-0.685268\pi$
$97$	2.27013e6	−	1.28746e7i	0.252552	−	1.43229i	0.802279	−	0.596949i	$-0.203620\pi$
$98$	−266419.	−	461450.i	−0.0285939	−	0.0495261i
$99$	6.38537e6	+	2.15282e6i	0.661398	+	0.222990i
$100$	−5.07312e6	+	8.78689e6i	−0.507312	+	0.878689i
$101$	−4.15725e6	−	3.48835e6i	−0.401496	−	0.336895i	0.419576	−	0.907720i	$-0.362179\pi$
$101$	−4.15725e6	−	3.48835e6i	−0.401496	−	0.336895i	−0.821072	+	0.570825i	$0.806623\pi$
$102$	1.19867e7	−	143157.i	1.11840	−	0.0133571i
$103$	800127.	+	4.53774e6i	0.0721487	+	0.409176i	0.999397	+	0.0347281i	$0.0110565\pi$
$103$	800127.	+	4.53774e6i	0.0721487	+	0.409176i	−0.927248	+	0.374448i	$0.877832\pi$
$104$	−4.88269e6	+	4.09706e6i	−0.425640	+	0.357154i
$105$	−3.66960e6	−	1.94501e7i	−0.309354	−	1.63968i
$106$	1.02072e7	−	3.71513e6i	0.832411	−	0.302973i
$107$	1.13259e7			0.893778			0.446889	−	0.894589i	$-0.352532\pi$
$107$	1.13259e7			0.893778			0.446889	+	0.894589i	$0.352532\pi$
$108$	−6.22715e6	−	2.01699e6i	−0.475670	−	0.154071i
$109$	−1.97728e7			−1.46243			−0.731214	−	0.682148i	$-0.761046\pi$
$109$	−1.97728e7			−1.46243			−0.731214	+	0.682148i	$0.761046\pi$
$110$	1.12682e7	−	4.10128e6i	0.807196	−	0.293795i
$111$	−5.30251e6	−	1.85855e6i	−0.368003	−	0.128986i
$112$	2.72988e6	−	2.29064e6i	0.183604	−	0.154062i
$113$	−1.05457e6	−	5.98074e6i	−0.0687542	−	0.389924i	−0.999694	−	0.0247508i	$-0.992121\pi$
$113$	−1.05457e6	−	5.98074e6i	−0.0687542	−	0.389924i	0.930939	−	0.365174i	$-0.118990\pi$
$114$	−3.65380e6	−	6.15755e6i	−0.230982	−	0.389261i
$115$	−2.48600e7	−	2.08600e7i	−1.52426	−	1.27900i
$116$	−4.14741e6	+	7.18353e6i	−0.246703	+	0.427302i
$117$	−1.30460e7	+	2.38968e7i	−0.753055	+	1.37940i
$118$	8.06706e6	+	1.39726e7i	0.451990	+	0.782869i
$119$	−4.84078e6	+	2.74534e7i	−0.263330	+	1.49342i
$120$	−1.08973e7	+	4.11433e6i	−0.575685	+	0.217353i
$121$	9.39090e6	+	3.41801e6i	0.481901	+	0.175398i
$122$	1.20376e7	+	4.38133e6i	0.600179	+	0.218447i
$123$	2.89701e7	−	1.09378e7i	1.40372	−	0.529982i
$124$	2.95800e6	−	1.67756e7i	0.139323	−	0.790139i
$125$	1.95588e7	+	3.38768e7i	0.895688	+	1.55138i
$126$	7.29395e6	−	1.33606e7i	0.324837	−	0.595015i
$127$	−1.88440e6	+	3.26387e6i	−0.0816318	+	0.141390i	−0.903951	−	0.427636i	$-0.859346\pi$
$127$	−1.88440e6	+	3.26387e6i	−0.0816318	+	0.141390i	0.822319	+	0.569027i	$0.192680\pi$
$128$	−1.60651e6	−	1.34802e6i	−0.0677094	−	0.0568149i
$129$	9.65460e6	+	1.62704e7i	0.395977	+	0.667319i
$130$	8.41312e6	+	4.77132e7i	0.335858	+	1.90474i
$131$	4.96575e6	−	4.16676e6i	0.192990	−	0.161938i	−0.541173	−	0.840912i	$-0.682019\pi$
$131$	4.96575e6	−	4.16676e6i	0.192990	−	0.161938i	0.734163	+	0.678974i	$0.237575\pi$
$132$	8.70278e6	+	3.05036e6i	0.329344	+	0.115436i
$133$	1.56464e7	−	5.69483e6i	0.576679	−	0.209894i
$134$	7.34345e6			0.263653
$135$	−3.69444e7	+	3.33265e7i	−1.29235	+	1.16579i
$136$	1.64053e7			0.559241
$137$	−9.81591e6	+	3.57270e6i	−0.326143	+	0.118706i	−0.499902	−	0.866082i	$-0.666631\pi$
$137$	−9.81591e6	+	3.57270e6i	−0.326143	+	0.118706i	0.173759	+	0.984788i	$0.444409\pi$
$138$	−4.62701e6	−	2.45247e7i	−0.149873	−	0.794378i
$139$	−1.53606e7	+	1.28891e7i	−0.485127	+	0.407070i	−0.852276	−	0.523092i	$-0.824778\pi$
$139$	−1.53606e7	+	1.28891e7i	−0.485127	+	0.407070i	0.367149	+	0.930162i	$0.380334\pi$
$140$	−4.70373e6	−	2.66762e7i	−0.144875	−	0.821629i
$141$	−1.35296e7	+	161584.i	−0.406460	+	0.00485436i
$142$	7.55321e6	+	6.33789e6i	0.221372	+	0.185753i
$143$	1.91787e7	−	3.32185e7i	0.548459	−	0.949958i
$144$	−8.48849e6	−	2.86189e6i	−0.236898	−	0.0798701i
$145$	3.15253e7	+	5.46035e7i	0.858760	+	1.48742i
$146$	−1.97680e6	+	1.12110e7i	−0.0525688	+	0.298132i
$147$	−2.40981e6	−	1.97351e6i	−0.0625708	−	0.0512423i
$148$	−7.22577e6	−	2.62997e6i	−0.183218	−	0.0666859i
$149$	−1.46134e7	−	5.31885e6i	−0.361910	−	0.131724i	0.154664	−	0.987967i	$-0.450570\pi$
$149$	−1.46134e7	−	5.31885e6i	−0.361910	−	0.131724i	−0.516574	+	0.856243i	$0.672793\pi$
$150$	−9.60106e6	+	5.85293e7i	−0.232274	+	1.41597i
$151$	114488.	−	649293.i	0.00270608	−	0.0153469i	−0.983425	−	0.181316i	$-0.941964\pi$
$151$	114488.	−	649293.i	0.00270608	−	0.0153469i	0.986131	+	0.165969i	$0.0530753\pi$
$152$	−4.89935e6	−	8.48593e6i	−0.113158	−	0.195996i
$153$	6.52579e7	−	2.55329e7i	1.47303	−	0.576342i
$154$	−1.07227e7	+	1.85723e7i	−0.236583	+	0.409773i
$155$	−9.91892e7	−	8.32296e7i	−2.13946	−	1.79522i
$156$	−1.82432e7	+	3.24880e7i	−0.384737	+	0.685152i
$157$	−1.11850e7	−	6.34335e7i	−0.230669	−	1.30819i	−0.851546	−	0.524280i	$-0.824334\pi$
$157$	−1.11850e7	−	6.34335e7i	−0.230669	−	1.30819i	0.620877	−	0.783908i	$-0.286777\pi$
$158$	1.68628e7	−	1.41496e7i	0.340119	−	0.285394i
$159$	4.81510e7	−	4.13934e7i	0.949983	−	0.816660i
$160$	−1.49795e7	+	5.45210e6i	−0.289120	+	0.105231i
$161$	5.80383e7			1.09603
$162$	−3.82201e7	+	1.82715e6i	−0.706300	+	0.0337655i
$163$	−3.95070e7			−0.714526			−0.357263	−	0.934004i	$-0.616290\pi$
$163$	−3.95070e7			−0.714526			−0.357263	+	0.934004i	$0.616290\pi$
$164$	3.98225e7	−	1.44942e7i	0.704977	−	0.256591i
$165$	5.31558e7	−	4.56958e7i	0.921206	−	0.791922i
$166$	4.17183e6	−	3.50058e6i	0.0707861	−	0.0593966i
$167$	1.30723e7	+	7.41366e7i	0.217192	+	1.23176i	0.877062	+	0.480377i	$0.159500\pi$
$167$	1.30723e7	+	7.41366e7i	0.217192	+	1.23176i	−0.659870	+	0.751380i	$0.729389\pi$
$168$	1.01997e7	−	1.81639e7i	0.165960	−	0.295547i
$169$	7.06517e7	+	5.92839e7i	1.12595	+	0.944785i
$170$	6.23501e7	−	1.07994e8i	0.973343	−	1.68588i
$171$	−3.26962e7	−	2.61305e7i	−0.500047	−	0.399633i
$172$	1.29458e7	+	2.24228e7i	0.193990	+	0.336000i
$173$	−1.58655e7	+	8.99777e7i	−0.232966	+	1.32121i	0.613890	+	0.789392i	$0.289604\pi$
$173$	−1.58655e7	+	8.99777e7i	−0.232966	+	1.32121i	−0.846856	+	0.531823i	$0.821507\pi$
$174$	−7.84913e6	+	4.78493e7i	−0.112953	+	0.688579i
$175$	−1.29611e8	−	4.71744e7i	−1.82813	−	0.665386i
$176$	1.18594e7	+	4.31645e6i	0.163971	+	0.0596805i
$177$	7.29682e7	+	5.97573e7i	0.989070	+	0.809998i
$178$	−8.38825e6	+	4.75721e7i	−0.111481	+	0.632241i
$179$	−4.61499e7	−	7.99340e7i	−0.601430	−	1.04171i	−0.992605	−	0.121391i	$-0.961264\pi$
$179$	−4.61499e7	−	7.99340e7i	−0.601430	−	1.04171i	0.391175	−	0.920316i	$-0.372069\pi$
$180$	−5.11007e7	+	4.50014e7i	−0.653090	+	0.575139i
$181$	−1.72249e7	+	2.98344e7i	−0.215915	+	0.373975i	−0.953555	−	0.301219i	$-0.902607\pi$
$181$	−1.72249e7	+	2.98344e7i	−0.215915	+	0.373975i	0.737641	+	0.675194i	$0.235940\pi$
$182$	−6.63757e7	−	5.56958e7i	−0.816130	−	0.684814i
$183$	7.48786e7	−	894275.i	0.903189	−	0.0107868i
$184$	−5.93096e6	−	3.36361e7i	−0.0701879	−	0.398055i
$185$	−4.47749e7	+	3.75706e7i	−0.519917	+	0.436262i
$186$	−1.84614e7	−	9.78514e7i	−0.210363	−	1.11499i
$187$	−9.27718e7	+	3.37662e7i	−1.03746	+	0.377604i
$188$	−1.85170e7			−0.203245
$189$	1.23028e7	−	8.81277e7i	0.132552	−	0.949502i
$190$	−7.44820e7			−0.787796
$191$	3.61601e7	−	1.31612e7i	0.375502	−	0.136672i	−0.147373	−	0.989081i	$-0.547082\pi$
$191$	3.61601e7	−	1.31612e7i	0.375502	−	0.136672i	0.522875	+	0.852409i	$0.324859\pi$
$192$	−1.15692e7	−	4.05504e6i	−0.117964	−	0.0413467i
$193$	−1.37176e8	+	1.15105e8i	−1.37350	+	1.15250i	−0.401951	+	0.915661i	$0.631668\pi$
$193$	−1.37176e8	+	1.15105e8i	−1.37350	+	1.15250i	−0.971548	+	0.236842i	$0.923888\pi$
$194$	−1.81611e7	−	1.02997e8i	−0.178581	−	1.01278i
$195$	1.44528e8	+	2.43566e8i	1.39583	+	2.35231i
$196$	−3.26542e6	−	2.74001e6i	−0.0309772	−	0.0259930i
$197$	−1.29319e7	+	2.23986e7i	−0.120512	+	0.208732i	−0.919970	−	0.391990i	$-0.871787\pi$
$197$	−1.29319e7	+	2.23986e7i	−0.120512	+	0.208732i	0.799458	+	0.600722i	$0.205120\pi$
$198$	5.38927e7	−	1.28747e6i	0.493403	−	0.0117871i
$199$	1.73123e7	+	2.99858e7i	0.155729	+	0.269730i	0.933324	−	0.359035i	$-0.116894\pi$
$199$	1.73123e7	+	2.99858e7i	0.155729	+	0.269730i	−0.777595	+	0.628765i	$0.783561\pi$
$200$	−1.40950e7	+	7.99367e7i	−0.124583	+	0.706547i
$201$	4.01604e7	−	1.51627e7i	0.348828	−	0.131702i
$202$	−4.07970e7	−	1.48489e7i	−0.348256	−	0.126755i
$203$	−1.05960e8	−	3.85664e7i	−0.889011	−	0.323574i
$204$	8.97185e7	−	3.38736e7i	0.739906	−	0.279355i
$205$	5.59365e7	−	3.17231e8i	0.453478	−	2.57180i
$206$	1.84310e7	+	3.19234e7i	0.146897	+	0.254433i
$207$	−7.59430e7	−	1.24569e8i	−0.595102	−	0.976140i
$208$	−2.54956e7	+	4.41596e7i	−0.196446	+	0.340254i
$209$	4.51719e7	+	3.79037e7i	0.342260	+	0.287190i
$210$	−8.08050e7	−	1.36176e8i	−0.602103	−	1.01469i
$211$	−1.88907e7	−	1.07135e8i	−0.138440	−	0.785130i	−0.972402	−	0.233310i	$-0.925044\pi$
$211$	−1.88907e7	−	1.07135e8i	−0.138440	−	0.785130i	0.833963	−	0.551821i	$-0.186067\pi$
$212$	6.65681e7	−	5.58573e7i	0.479834	−	0.402628i
$213$	5.43939e7	+	1.90653e7i	0.385675	+	0.135181i
$214$	8.51429e7	−	3.09895e7i	0.593882	−	0.216155i
$215$	1.96807e8			1.35054
$216$	−5.23316e7	+	1.87570e6i	−0.353327	+	0.0126642i
$217$	2.31568e8			1.53840
$218$	−1.48642e8	+	5.41014e7i	−0.971729	+	0.353681i
$219$	1.23375e7	+	6.53931e7i	0.0793733	+	0.420705i
$220$	7.34872e7	−	6.16630e7i	0.465299	−	0.390432i
$221$	−6.92660e7	−	3.92827e8i	−0.431665	−	2.44809i
$222$	−4.49471e7	+	536804.i	−0.275719	+	0.00329291i
$223$	−4.76511e6	−	3.99840e6i	−0.0287744	−	0.0241446i	0.628287	−	0.777982i	$-0.283756\pi$
$223$	−4.76511e6	−	3.99840e6i	−0.0287744	−	0.0241446i	−0.657061	+	0.753837i	$0.728201\pi$
$224$	1.42544e7	−	2.46894e7i	0.0847388	−	0.146772i
$225$	6.83441e7	+	3.39913e8i	0.400002	+	1.98943i
$226$	−2.42920e7	−	4.20750e7i	−0.139986	−	0.242462i
$227$	−2.56987e7	+	1.45745e8i	−0.145821	+	0.826993i	0.820883	+	0.571096i	$0.193482\pi$
$227$	−2.56987e7	+	1.45745e8i	−0.145821	+	0.826993i	−0.966704	+	0.255897i	$0.917629\pi$
$228$	−4.43156e7	−	3.62923e7i	−0.247620	−	0.202788i
$229$	5.33858e7	+	1.94308e7i	0.293766	+	0.106922i	0.484699	−	0.874681i	$-0.338929\pi$
$229$	5.33858e7	+	1.94308e7i	0.293766	+	0.106922i	−0.190933	+	0.981603i	$0.561151\pi$
$230$	−2.43962e8	−	8.87950e7i	−1.32213	−	0.481217i
$231$	−2.02932e7	+	1.23710e8i	−0.108320	+	0.660332i
$232$	−1.15231e7	+	6.53505e7i	−0.0605842	+	0.343590i
$233$	−4.99791e7	−	8.65663e7i	−0.258847	−	0.448335i	0.707087	−	0.707127i	$-0.250009\pi$
$233$	−4.99791e7	−	8.65663e7i	−0.258847	−	0.448335i	−0.965933	+	0.258792i	$0.916676\pi$
$234$	−3.26884e7	+	2.15341e8i	−0.166778	+	1.09868i
$235$	−7.03759e7	+	1.21895e8i	−0.353742	+	0.612699i
$236$	9.88757e7	+	8.29665e7i	0.489663	+	0.410876i
$237$	6.30046e7	−	1.12201e8i	0.307435	−	0.547490i
$238$	3.87262e7	+	2.19627e8i	0.186203	+	1.05601i
$239$	−2.64213e8	+	2.21701e8i	−1.25188	+	1.05045i	−0.255377	+	0.966842i	$0.582200\pi$
$239$	−2.64213e8	+	2.21701e8i	−1.25188	+	1.05045i	−0.996499	+	0.0836070i	$0.973356\pi$
$240$	−7.06635e7	+	6.07465e7i	−0.329956	+	0.283649i
$241$	6.00382e7	−	2.18521e7i	0.276292	−	0.100562i	−0.200158	−	0.979764i	$-0.564146\pi$
$241$	6.00382e7	−	2.18521e7i	0.276292	−	0.100562i	0.476450	+	0.879202i	$0.341923\pi$
$242$	7.99487e7			0.362625
$243$	−2.05248e8	+	8.89091e7i	−0.917607	+	0.397488i
$244$	1.02481e8			0.451627
$245$	−3.04476e7	+	1.10820e7i	−0.132273	+	0.0481434i
$246$	1.87856e8	−	1.61492e8i	0.804550	−	0.691637i
$247$	−1.82510e8	+	1.53144e8i	−0.770634	+	0.646639i
$248$	−2.36640e7	−	1.34205e8i	−0.0985161	−	0.558713i
$249$	1.55872e7	−	2.77582e7i	0.0639838	−	0.113944i
$250$	2.39726e8	+	2.01154e8i	0.970343	+	0.814215i
$251$	−1.73810e8	+	3.01048e8i	−0.693772	+	1.20165i	0.276821	+	0.960921i	$0.410719\pi$
$251$	−1.73810e8	+	3.01048e8i	−0.693772	+	1.20165i	−0.970593	+	0.240726i	$0.922614\pi$
$252$	1.82759e7	−	1.20396e8i	0.0719410	−	0.473926i
$253$	1.02771e8	+	1.78004e8i	0.398977	+	0.691048i
$254$	−5.23556e6	+	2.96923e7i	−0.0200468	+	0.113691i
$255$	1.18000e8	−	7.19342e8i	0.445647	−	2.71672i
$256$	−1.57654e7	−	5.73815e6i	−0.0587308	−	0.0213763i
$257$	4.77670e8	+	1.73858e8i	1.75534	+	0.638892i	0.999867	−	0.0162862i	$-0.00518430\pi$
$257$	4.77670e8	+	1.73858e8i	1.75534	+	0.638892i	0.755474	+	0.655178i	$0.227407\pi$
$258$	1.17097e8	+	9.58967e7i	0.424500	+	0.347644i
$259$	1.81518e7	−	1.02944e8i	0.0649187	−	0.368172i
$260$	1.93797e8	+	3.35666e8i	0.683818	+	1.18441i
$261$	5.58732e7	+	2.77888e8i	0.194519	+	0.967450i
$262$	2.59293e7	−	4.49108e7i	0.0890709	−	0.154275i
$263$	4.36098e8	+	3.65930e8i	1.47822	+	1.24037i	0.908059	+	0.418843i	$0.137564\pi$
$263$	4.36098e8	+	3.65930e8i	1.47822	+	1.24037i	0.570163	+	0.821532i	$0.306880\pi$
$264$	7.37698e7	−	881033.i	0.246754	−	0.00294699i
$265$	−1.14700e8	−	6.50498e8i	−0.378621	−	2.14726i
$266$	1.02041e8	−	8.56223e7i	0.332420	−	0.278934i
$267$	5.23525e7	+	2.77486e8i	0.168325	+	0.892177i
$268$	5.52047e7	−	2.00929e7i	0.175188	−	0.0637632i
$269$	−2.93917e7			−0.0920644			−0.0460322	−	0.998940i	$-0.514658\pi$
$269$	−2.93917e7			−0.0920644			−0.0460322	+	0.998940i	$0.514658\pi$
$270$	−1.86544e8	+	3.51619e8i	−0.576778	+	1.08718i
$271$	−5.38002e7			−0.164207			−0.0821034	−	0.996624i	$-0.526164\pi$
$271$	−5.38002e7			−0.164207			−0.0821034	+	0.996624i	$0.526164\pi$
$272$	1.23328e8	−	4.48876e7i	0.371595	−	0.135249i
$273$	−4.78000e8	−	1.67541e8i	−1.42187	−	0.498369i
$274$	−6.40160e7	+	5.37158e7i	−0.188002	+	0.157752i
$275$	−8.48223e7	−	4.81051e8i	−0.245949	−	1.39485i
$276$	−1.01887e8	−	1.71705e8i	−0.291701	−	0.491589i
$277$	−1.52567e8	−	1.28019e8i	−0.431302	−	0.361905i	0.401141	−	0.916016i	$-0.368614\pi$
$277$	−1.52567e8	−	1.28019e8i	−0.431302	−	0.361905i	−0.832443	+	0.554111i	$0.813058\pi$
$278$	−8.02072e7	+	1.38923e8i	−0.223901	+	0.387809i
$279$	−3.03006e8	−	4.97018e8i	−0.835288	−	1.37011i
$280$	−1.08351e8	−	1.87669e8i	−0.294971	−	0.510905i
$281$	−6.83736e6	+	3.87766e7i	−0.0183830	+	0.104255i	−0.992619	−	0.121277i	$-0.961301\pi$
$281$	−6.83736e6	+	3.87766e7i	−0.0183830	+	0.104255i	0.974236	+	0.225532i	$0.0724121\pi$
$282$	−1.01267e8	+	3.82339e7i	−0.268904	+	0.101526i
$283$	2.43684e8	+	8.86938e7i	0.639109	+	0.232617i	0.641191	−	0.767381i	$-0.278441\pi$
$283$	2.43684e8	+	8.86938e7i	0.639109	+	0.232617i	−0.00208225	+	0.999998i	$0.500663\pi$
$284$	7.41230e7	+	2.69786e7i	0.192017	+	0.0698884i
$285$	−4.07332e8	+	1.53790e8i	−1.04230	+	0.393524i
$286$	5.32856e7	−	3.02198e8i	0.134688	−	0.763854i
$287$	2.88047e8	+	4.98911e8i	0.719244	+	1.24577i
$288$	−7.16432e7	+	1.71151e6i	−0.176726	+	0.00422189i
$289$	−3.08164e8	+	5.33756e8i	−0.751000	+	1.30077i
$290$	3.86397e8	+	3.24225e8i	0.930338	+	0.780646i
$291$	−3.11987e8	−	5.25776e8i	−0.742184	−	1.25076i
$292$	1.58144e7	+	8.96880e7i	0.0371717	+	0.210811i
$293$	2.06515e8	−	1.73287e8i	0.479641	−	0.402466i	−0.370656	−	0.928770i	$-0.620867\pi$
$293$	2.06515e8	−	1.73287e8i	0.479641	−	0.402466i	0.850296	+	0.526304i	$0.176423\pi$
$294$	−2.35157e7	−	8.24233e6i	−0.0539687	−	0.0189162i
$295$	9.21942e8	−	3.35559e8i	2.09087	−	0.761014i
$296$	−6.15160e7			−0.137869
$297$	2.92074e8	−	1.18318e8i	0.646912	−	0.262062i
$298$	−1.24410e8			−0.272332
$299$	−7.80378e8	+	2.84034e8i	−1.68832	+	0.614500i
$300$	8.79692e7	+	4.66266e8i	0.188108	+	0.997033i
$301$	−2.69627e8	+	2.26244e8i	−0.569876	+	0.478183i
$302$	−915903.	−	5.19434e6i	−0.00191349	−	0.0108519i
$303$	−2.53773e8	+	3.03081e6i	−0.524079	+	0.00625907i
$304$	−6.00500e7	−	5.03879e7i	−0.122590	−	0.102865i
$305$	3.89490e8	−	6.74617e8i	0.786044	−	1.36147i
$306$	4.20717e8	−	3.70501e8i	0.839392	−	0.739203i
$307$	1.06007e7	+	1.83610e7i	0.0209098	+	0.0362169i	0.876291	−	0.481782i	$-0.160010\pi$
$307$	1.06007e7	+	1.83610e7i	0.0209098	+	0.0362169i	−0.855381	+	0.517999i	$0.826677\pi$
$308$	−2.97917e7	+	1.68957e8i	−0.0580989	+	0.329495i
$309$	1.66712e8	+	1.36529e8i	0.321449	+	0.263250i
$310$	−9.73388e8	−	3.54284e8i	−1.85575	−	0.675439i
$311$	−8.25745e8	−	3.00547e8i	−1.55663	−	0.566566i	−0.586666	−	0.809829i	$-0.699560\pi$
$311$	−8.25745e8	−	3.00547e8i	−1.55663	−	0.566566i	−0.969960	+	0.243263i	$0.921782\pi$
$312$	−4.82513e7	+	2.94146e8i	−0.0899431	+	0.548305i
$313$	−1.11289e8	+	6.31152e8i	−0.205139	+	1.16340i	0.692082	+	0.721819i	$0.256694\pi$
$313$	−1.11289e8	+	6.31152e8i	−0.205139	+	1.16340i	−0.897221	+	0.441581i	$0.854418\pi$
$314$	−2.57648e8	−	4.46260e8i	−0.469649	−	0.813457i
$315$	−7.23088e8	−	5.77884e8i	−1.30348	−	1.04173i
$316$	8.80515e7	−	1.52510e8i	0.156976	−	0.271890i
$317$	−2.32980e8	−	1.95493e8i	−0.410781	−	0.344686i	0.413862	−	0.910340i	$-0.364180\pi$
$317$	−2.32980e8	−	1.95493e8i	−0.410781	−	0.344686i	−0.824643	+	0.565653i	$0.808624\pi$
$318$	2.48718e8	−	4.42926e8i	0.433723	−	0.772389i
$319$	−6.93446e7	−	3.93273e8i	−0.119604	−	0.678308i
$320$	−9.76914e7	+	8.19728e7i	−0.166660	+	0.139844i
$321$	4.01648e8	−	3.45280e8i	0.677764	−	0.582645i
$322$	4.36305e8	−	1.58802e8i	0.728274	−	0.265070i
$323$	6.13216e8			1.01252
$324$	−2.82322e8	+	1.18312e8i	−0.461144	+	0.193251i
$325$	1.97360e9			3.18910
$326$	−2.96996e8	+	1.08098e8i	−0.474776	+	0.172804i
$327$	−7.01198e8	+	6.02790e8i	−1.10898	+	0.953342i
$328$	2.59709e8	−	2.17921e8i	0.406376	−	0.340990i
$329$	−4.37111e7	−	2.47898e8i	−0.0676716	−	0.383785i
$330$	2.74570e8	−	4.88963e8i	0.420585	−	0.748992i
$331$	1.34542e8	+	1.12894e8i	0.203920	+	0.171109i	0.739028	−	0.673674i	$-0.235285\pi$
$331$	1.34542e8	+	1.12894e8i	0.203920	+	0.171109i	−0.535109	+	0.844783i	$0.679729\pi$
$332$	2.17837e7	−	3.77305e7i	0.0326700	−	0.0565861i
$333$	−2.44701e8	+	9.57423e7i	−0.363146	+	0.142085i
$334$	3.01121e8	+	5.21557e8i	0.442210	+	0.765931i
$335$	7.75430e7	−	4.39768e8i	0.112690	−	0.639098i
$336$	2.69771e7	−	1.64456e8i	0.0387978	−	0.236516i
$337$	−1.26485e9	−	4.60366e8i	−1.80025	−	0.655238i	−0.998328	−	0.0578117i	$-0.981588\pi$
$337$	−1.26485e9	−	4.60366e8i	−1.80025	−	0.655238i	−0.801924	−	0.597426i	$-0.796190\pi$
$338$	6.93338e8	+	2.52354e8i	0.976644	+	0.355469i
$339$	−2.19726e8	−	1.79944e8i	−0.306325	−	0.250865i
$340$	1.73232e8	−	9.82446e8i	0.239029	−	1.35560i
$341$	4.10047e8	+	7.10221e8i	0.560006	+	0.969959i
$342$	−3.17292e8	−	1.06975e8i	−0.428912	−	0.144607i
$343$	3.87224e8	−	6.70692e8i	0.518123	−	0.897415i
$344$	1.58673e8	+	1.33142e8i	0.210159	+	0.176344i
$345$	−1.51754e9	+	1.81240e7i	−1.98963	+	0.0237622i
$346$	1.26924e8	+	7.19821e8i	0.164732	+	0.934240i
$347$	−5.94398e8	+	4.98759e8i	−0.763702	+	0.640822i	−0.939088	−	0.343678i	$-0.888327\pi$
$347$	−5.94398e8	+	4.98759e8i	−0.763702	+	0.640822i	0.175386	+	0.984500i	$0.443883\pi$
$348$	7.19173e7	+	3.81186e8i	0.0914757	+	0.484852i
$349$	−1.07503e8	+	3.91280e7i	−0.135373	+	0.0492718i	−0.408818	−	0.912616i	$-0.634059\pi$
$349$	−1.07503e8	+	3.91280e7i	−0.135373	+	0.0492718i	0.273445	+	0.961888i	$0.411837\pi$
$350$	−1.10343e9			−1.37565
$351$	2.65867e8	+	1.24517e9i	0.328162	+	1.53692i
$352$	1.00964e8			0.123386
$353$	−1.06087e9	+	3.86124e8i	−1.28366	+	0.467213i	−0.891640	−	0.452745i	$-0.850445\pi$
$353$	−1.06087e9	+	3.86124e8i	−1.28366	+	0.467213i	−0.392017	+	0.919958i	$0.628223\pi$
$354$	7.12047e8	+	2.49575e8i	0.853094	+	0.299013i
$355$	4.59308e8	−	3.85405e8i	0.544884	−	0.457212i
$356$	6.71060e7	+	3.80577e8i	0.0788291	+	0.447062i
$357$	6.65274e8	+	1.12115e9i	0.773859	+	1.30414i
$358$	−5.65646e8	−	4.74633e8i	−0.651560	−	0.546723i
$359$	6.48861e8	−	1.12386e9i	0.740153	−	1.28198i	−0.212273	−	0.977210i	$-0.568087\pi$
$359$	6.48861e8	−	1.12386e9i	0.740153	−	1.28198i	0.952426	−	0.304771i	$-0.0985801\pi$
$360$	−2.61021e8	+	4.78120e8i	−0.294860	+	0.540105i
$361$	2.63802e8	+	4.56919e8i	0.295123	+	0.511168i
$362$	−4.78572e7	+	2.71412e8i	−0.0530233	+	0.300710i
$363$	4.37229e8	−	1.65078e8i	0.479772	−	0.181140i
$364$	−6.51375e8	−	2.37081e8i	−0.707907	−	0.257657i
$365$	6.50505e8	+	2.36765e8i	0.700206	+	0.254854i
$366$	5.60456e8	−	2.11603e8i	0.597527	−	0.225599i
$367$	−1.84853e8	+	1.04835e9i	−0.195207	+	1.10707i	0.716918	+	0.697158i	$0.245552\pi$
$367$	−1.84853e8	+	1.04835e9i	−0.195207	+	1.10707i	−0.912124	+	0.409914i	$0.865559\pi$
$368$	−1.36620e8	−	2.36633e8i	−0.142905	−	0.247519i
$369$	6.93913e8	−	1.27106e9i	0.718973	−	1.31697i
$370$	−2.33798e8	+	4.04950e8i	−0.239958	+	0.415619i
$371$	9.04933e8	+	7.59329e8i	0.920043	+	0.772007i
$372$	−4.06521e8	−	6.85089e8i	−0.409433	−	0.689996i
$373$	−1.03440e8	−	5.86637e8i	−0.103207	−	0.585314i	−0.991921	−	0.126854i	$-0.959512\pi$
$373$	−1.03440e8	−	5.86637e8i	−0.103207	−	0.585314i	0.888715	−	0.458460i	$-0.151599\pi$
$374$	−6.05026e8	+	5.07677e8i	−0.598031	+	0.501807i
$375$	1.72637e9	+	6.05100e8i	1.69054	+	0.592540i
$376$	−1.39203e8	+	5.06656e7i	−0.135049	+	0.0491536i
$377$	1.61347e9			1.55084
$378$	−1.48645e8	−	6.96166e8i	−0.141556	−	0.662966i
$379$	−1.82701e9			−1.72386			−0.861931	−	0.507025i	$-0.830745\pi$
$379$	−1.82701e9			−1.72386			−0.861931	+	0.507025i	$0.830745\pi$
$380$	−5.59921e8	+	2.03795e8i	−0.523461	+	0.190524i
$381$	3.26760e7	+	1.73194e8i	0.0302685	+	0.160433i
$382$	2.35824e8	−	1.97880e8i	0.216454	−	0.181626i
$383$	7.91763e7	+	4.49031e8i	0.0720111	+	0.408395i	0.999411	+	0.0343233i	$0.0109276\pi$
$383$	7.91763e7	+	4.49031e8i	0.0720111	+	0.408395i	−0.927400	+	0.374072i	$0.877961\pi$
$384$	−9.80671e7	+	1.17122e6i	−0.0883820	+	0.00105555i
$385$	9.98991e8	+	8.38253e8i	0.892173	+	0.748622i
$386$	−7.16284e8	+	1.24064e9i	−0.633913	+	1.09797i
$387$	8.38396e8	+	2.82665e8i	0.735294	+	0.247904i
$388$	−4.18342e8	−	7.24589e8i	−0.363597	−	0.629769i
$389$	1.64091e8	−	9.30608e8i	0.141339	−	0.801573i	−0.828895	−	0.559404i	$-0.811030\pi$
$389$	1.64091e8	−	9.30608e8i	0.141339	−	0.801573i	0.970234	−	0.242169i	$-0.0778589\pi$
$390$	1.75293e9	+	1.43556e9i	1.49637	+	1.22545i
$391$	2.00856e9	+	7.31057e8i	1.69929	+	0.618490i
$392$	−3.20450e7	−	1.16634e7i	−0.0268695	−	0.00977969i
$393$	4.90721e7	−	2.99150e8i	0.0407813	−	0.248608i
$394$	−3.59295e7	+	2.03766e8i	−0.0295947	+	0.167840i
$395$	−6.69298e8	−	1.15926e9i	−0.546424	−	0.946433i
$396$	4.01618e8	−	1.57138e8i	0.324997	−	0.127159i
$397$	−7.53550e8	+	1.30519e9i	−0.604429	+	1.04690i	0.387713	+	0.921780i	$0.373265\pi$
$397$	−7.53550e8	+	1.30519e9i	−0.604429	+	1.04690i	−0.992141	+	0.125121i	$0.960068\pi$
$398$	2.12192e8	+	1.78050e8i	0.168709	+	0.141563i
$399$	3.81254e8	−	6.78950e8i	0.300476	−	0.535097i
$400$	1.12760e8	+	6.39494e8i	0.0880937	+	0.499604i
$401$	5.72821e8	−	4.80654e8i	0.443622	−	0.372243i	−0.393440	−	0.919350i	$-0.628715\pi$
$401$	5.72821e8	−	4.80654e8i	0.443622	−	0.372243i	0.837063	+	0.547107i	$0.184271\pi$
$402$	2.60419e8	−	2.23872e8i	0.199932	−	0.171873i
$403$	−3.11364e9	+	1.13327e9i	−2.36974	+	0.862515i
$404$	−3.47322e8			−0.262058
$405$	−2.94164e8	+	2.30813e9i	−0.220037	+	1.72651i
$406$	−9.02085e8			−0.668970
$407$	3.47872e8	−	1.26615e8i	0.255764	−	0.0930904i
$408$	5.81779e8	−	5.00131e8i	0.424080	−	0.364563i
$409$	−4.26245e8	+	3.57662e8i	−0.308055	+	0.258489i	−0.783688	−	0.621155i	$-0.786664\pi$
$409$	−4.26245e8	+	3.57662e8i	−0.308055	+	0.258489i	0.475633	+	0.879644i	$0.342219\pi$
$410$	−4.47492e8	−	2.53785e9i	−0.320658	−	1.81854i
$411$	−2.39183e8	+	4.25944e8i	−0.169935	+	0.302626i
$412$	2.25903e8	+	1.89555e8i	0.159141	+	0.133535i
$413$	−8.77315e8	+	1.51955e9i	−0.612817	+	1.06143i
$414$	−9.11744e8	−	7.28657e8i	−0.631498	−	0.504687i
$415$	−1.65583e8	−	2.86798e8i	−0.113723	−	0.196973i
$416$	−7.08361e7	+	4.01732e8i	−0.0482423	+	0.273596i
$417$	−1.51795e8	+	9.25363e8i	−0.102514	+	0.624936i
$418$	4.43292e8	+	1.61345e8i	0.296875	+	0.108053i
$419$	9.31027e8	+	3.38866e8i	0.618320	+	0.225050i	0.632140	−	0.774855i	$-0.282177\pi$
$419$	9.31027e8	+	3.38866e8i	0.618320	+	0.225050i	−0.0138200	+	0.999904i	$0.504399\pi$
$420$	−9.80055e8	−	8.02616e8i	−0.645473	−	0.528610i
$421$	2.69015e8	−	1.52566e9i	0.175707	−	0.996484i	−0.761618	−	0.648027i	$-0.775595\pi$
$421$	2.69015e8	−	1.52566e9i	0.175707	−	0.996484i	0.937325	−	0.348457i	$-0.113294\pi$
$422$	−4.35150e8	−	7.53702e8i	−0.281868	−	0.488209i
$423$	−4.74872e8	+	4.18192e8i	−0.305060	+	0.268648i
$424$	3.47594e8	−	6.02051e8i	0.221458	−	0.383577i
$425$	−3.89129e9	−	3.26518e9i	−2.45885	−	2.06322i
$426$	4.61074e8	−	5.50661e6i	0.288960	−	0.00345105i
$427$	2.41916e8	+	1.37197e9i	0.150372	+	0.852802i
$428$	5.55273e8	−	4.65930e8i	0.342337	−	0.287255i
$429$	−3.32565e8	−	1.76270e9i	−0.203365	−	1.07790i
$430$	1.47951e9	−	5.38496e8i	0.897382	−	0.326620i
$431$	1.06137e9			0.638552			0.319276	−	0.947662i	$-0.396560\pi$
$431$	1.06137e9			0.638552			0.319276	+	0.947662i	$0.396560\pi$
$432$	−3.88273e8	+	1.57288e8i	−0.231710	+	0.0938650i
$433$	1.00405e9			0.594358			0.297179	−	0.954822i	$-0.403954\pi$
$433$	1.00405e9			0.594358			0.297179	+	0.954822i	$0.403954\pi$
$434$	1.74082e9	−	6.33607e8i	1.02221	−	0.372054i
$435$	2.78261e9	+	9.75316e8i	1.62084	+	0.568110i
$436$	−9.69396e8	+	8.13420e8i	−0.560142	+	0.470015i
$437$	−2.21694e8	−	1.25729e9i	−0.127077	−	0.720692i
$438$	2.71674e8	+	4.57838e8i	0.154486	+	0.260347i
$439$	−2.04036e9	−	1.71206e9i	−1.15101	−	0.965815i	−0.151271	−	0.988492i	$-0.548336\pi$
$439$	−2.04036e9	−	1.71206e9i	−1.15101	−	0.965815i	−0.999743	+	0.0226775i	$0.992781\pi$
$440$	3.83723e8	−	6.64627e8i	0.214750	−	0.371958i
$441$	−1.45623e8	+	3.47884e6i	−0.0808527	+	0.00193152i
$442$	−1.59555e9	−	2.76357e9i	−0.878884	−	1.52227i
$443$	5.72790e8	−	3.24845e9i	0.313027	−	1.77527i	−0.270046	−	0.962847i	$-0.587039\pi$
$443$	5.72790e8	−	3.24845e9i	0.313027	−	1.77527i	0.583074	−	0.812419i	$-0.301850\pi$
$444$	−3.36423e8	+	1.27018e8i	−0.182409	+	0.0688692i
$445$	2.76032e9	+	1.00467e9i	1.48491	+	0.540462i
$446$	−4.67622e7	−	1.70200e7i	−0.0249587	−	0.00908424i
$447$	−6.80383e8	+	2.56882e8i	−0.360311	+	0.136037i
$448$	3.96041e7	−	2.24606e8i	0.0208098	−	0.118018i
$449$	−8.00487e7	−	1.38648e8i	−0.0417342	−	0.0722857i	0.844404	−	0.535707i	$-0.179955\pi$
$449$	−8.00487e7	−	1.38648e8i	−0.0417342	−	0.0722857i	−0.886138	+	0.463422i	$0.846622\pi$
$450$	1.44384e9	+	2.36831e9i	0.746920	+	1.22517i
$451$	−1.02011e9	+	1.76689e9i	−0.523636	+	0.906965i
$452$	−2.97740e8	−	2.49834e8i	−0.151654	−	0.127253i
$453$	−1.57342e7	−	2.65160e7i	−0.00795245	−	0.0134018i
$454$	2.05590e8	+	1.16596e9i	0.103111	+	0.584772i
$455$	−4.03628e9	+	3.38684e9i	−2.00882	+	1.68560i
$456$	−4.32446e8	−	1.51574e8i	−0.213577	−	0.0748596i
$457$	8.21176e8	−	2.98884e8i	0.402466	−	0.146486i	−0.132853	−	0.991136i	$-0.542414\pi$
$457$	8.21176e8	−	2.98884e8i	0.402466	−	0.146486i	0.535319	+	0.844650i	$0.320191\pi$
$458$	4.54496e8			0.221055
$459$	1.53583e9	−	2.89491e9i	0.741310	−	1.39730i
$460$	−2.07695e9			−0.994888
$461$	2.72927e9	−	9.93373e8i	1.29746	−	0.472236i	0.401290	−	0.915951i	$-0.368562\pi$
$461$	2.72927e9	−	9.93373e8i	1.29746	−	0.472236i	0.896168	+	0.443715i	$0.146340\pi$
$462$	1.85935e8	+	9.85519e8i	0.0877232	+	0.464962i
$463$	2.05980e9	−	1.72838e9i	0.964477	−	0.809292i	−0.0171987	−	0.999852i	$-0.505475\pi$
$463$	2.05980e9	−	1.72838e9i	0.964477	−	0.809292i	0.981676	+	0.190560i	$0.0610304\pi$
$464$	9.21844e7	+	5.22804e8i	0.0428395	+	0.242955i
$465$	−6.05485e9	+	7.23131e7i	−2.79266	+	0.0333528i
$466$	−6.12579e8	−	5.14015e8i	−0.280421	−	0.235302i
$467$	2.13863e9	−	3.70421e9i	0.971686	−	1.68301i	0.281224	−	0.959642i	$-0.409260\pi$
$467$	2.13863e9	−	3.70421e9i	0.971686	−	1.68301i	0.690463	−	0.723368i	$-0.257407\pi$
$468$	3.43472e8	+	1.70828e9i	0.154892	+	0.770366i
$469$	3.99310e8	+	6.91626e8i	0.178733	+	0.309575i
$470$	−1.95530e8	+	1.10891e9i	−0.0868703	+	0.492666i
$471$	−2.33048e9	−	1.90855e9i	−1.02771	−	0.841646i
$472$	9.70312e8	+	3.53165e8i	0.424731	+	0.154590i
$473$	−1.17133e9	−	4.26330e8i	−0.508939	−	0.185239i
$474$	1.66641e8	−	1.01586e9i	0.0718716	−	0.438138i
$475$	−5.26858e8	+	2.98796e9i	−0.225562	+	1.27923i
$476$	8.92062e8	+	1.54510e9i	0.379115	+	0.656646i
$477$	4.45657e8	−	2.93585e9i	0.188012	−	1.23857i
$478$	−1.37962e9	+	2.38957e9i	−0.577780	+	1.00074i
$479$	2.71804e9	+	2.28070e9i	1.13001	+	0.948188i	0.999066	−	0.0432021i	$-0.0137559\pi$
$479$	2.71804e9	+	2.28070e9i	1.13001	+	0.948188i	0.130940	+	0.991390i	$0.458200\pi$
$480$	−3.65004e8	+	6.50011e8i	−0.150645	+	0.268273i
$481$	2.59731e8	+	1.47301e9i	0.106418	+	0.603527i
$482$	3.91549e8	−	3.28548e8i	0.159265	−	0.133639i
$483$	2.05820e9	−	1.76935e9i	0.831138	−	0.714494i
$484$	6.01017e8	−	2.18752e8i	0.240951	−	0.0876989i
$485$	−6.35980e9			−2.53132
$486$	−1.29969e9	+	1.22997e9i	−0.513586	+	0.486035i
$487$	8.14015e8			0.319360			0.159680	−	0.987169i	$-0.448954\pi$
$487$	8.14015e8			0.319360			0.159680	+	0.987169i	$0.448954\pi$
$488$	7.70407e8	−	2.80405e8i	0.300089	−	0.109224i
$489$	−1.40103e9	+	1.20441e9i	−0.541834	+	0.465792i
$490$	−1.98569e8	+	1.66619e8i	−0.0762473	+	0.0639791i
$491$	3.04195e8	+	1.72518e9i	0.115976	+	0.657731i	0.986263	+	0.165185i	$0.0528223\pi$
$491$	3.04195e8	+	1.72518e9i	0.115976	+	0.657731i	−0.870287	+	0.492545i	$0.836067\pi$
$492$	9.70349e8	−	1.72803e9i	0.367325	−	0.654143i
$493$	−3.18124e9	−	2.66938e9i	−1.19573	−	1.00333i
$494$	−9.53002e8	+	1.65065e9i	−0.355672	+	0.616042i
$495$	4.91978e8	−	3.24100e9i	0.182317	−	1.20105i
$496$	−5.45102e8	−	9.44145e8i	−0.200582	−	0.347418i
$497$	−1.86203e8	+	1.05601e9i	−0.0680363	+	0.385853i
$498$	4.12265e7	−	2.51322e8i	0.0149580	−	0.0911860i
$499$	−4.14179e9	−	1.50749e9i	−1.49223	−	0.543128i	−0.538196	−	0.842820i	$-0.680894\pi$
$499$	−4.14179e9	−	1.50749e9i	−1.49223	−	0.543128i	−0.954036	+	0.299691i	$0.903116\pi$
$500$	2.35254e9	+	8.56255e8i	0.841671	+	0.306343i
$501$	2.72370e9	+	2.23057e9i	0.967670	+	0.792473i
$502$	−4.82908e8	+	2.73871e9i	−0.170373	+	0.966236i
$503$	4.19699e8	+	7.26940e8i	0.147045	+	0.254689i	0.930134	−	0.367220i	$-0.119690\pi$
$503$	4.19699e8	+	7.26940e8i	0.147045	+	0.254689i	−0.783089	+	0.621910i	$0.786357\pi$
$504$	−1.92033e8	−	9.55088e8i	−0.0668143	−	0.332305i
$505$	−1.32003e9	+	2.28636e9i	−0.456105	+	0.789997i
$506$	1.25963e9	+	1.05696e9i	0.432232	+	0.362686i
$507$	4.31283e9	−	5.15082e7i	1.46972	−	0.0175529i
$508$	4.18844e7	+	2.37538e8i	0.0141752	+	0.0803917i
$509$	−2.68031e8	+	2.24905e8i	−0.0900892	+	0.0755938i	−0.686720	−	0.726922i	$-0.740950\pi$
$509$	−2.68031e8	+	2.24905e8i	−0.0900892	+	0.0755938i	0.596631	+	0.802516i	$0.296506\pi$
$510$	−1.08117e9	−	5.73055e9i	−0.360909	−	1.91294i
$511$	−1.16337e9	+	4.23433e8i	−0.385696	+	0.140382i
$512$	−1.34218e8			−0.0441942
$513$	−1.95611e9	+	7.01122e7i	−0.639709	+	0.0229289i
$514$	4.06660e9			1.32087
$515$	2.10638e9	−	7.66660e8i	0.679534	−	0.247330i
$516$	1.14267e9	+	4.00511e8i	0.366140	+	0.128334i
$517$	6.82906e8	−	5.73026e8i	0.217342	−	0.182372i
$518$	−1.45214e8	−	8.23550e8i	−0.0459044	−	0.260337i
$519$	2.18041e9	+	3.67453e9i	0.684625	+	1.15376i
$520$	2.37531e9	+	1.99312e9i	0.740814	+	0.621617i
$521$	−2.12512e8	+	3.68082e8i	−0.0658342	+	0.114028i	−0.897064	−	0.441901i	$-0.854304\pi$
$521$	−2.12512e8	+	3.68082e8i	−0.0658342	+	0.114028i	0.831230	+	0.555929i	$0.187638\pi$
$522$	1.18038e9	+	1.93616e9i	0.363223	+	0.595792i
$523$	−2.63710e9	−	4.56759e9i	−0.806066	−	1.39615i	−0.915569	−	0.402161i	$-0.868259\pi$
$523$	−2.63710e9	−	4.56759e9i	−0.806066	−	1.39615i	0.109503	−	0.993986i	$-0.465074\pi$
$524$	7.20412e7	−	4.08566e8i	0.0218736	−	0.124052i
$525$	−6.03451e9	+	2.27836e9i	−1.82006	+	0.687170i
$526$	4.27963e9	+	1.55766e9i	1.28220	+	0.466683i
$527$	8.01399e9	+	2.91685e9i	2.38513	+	0.868115i
$528$	5.52157e8	−	2.08469e8i	0.163246	−	0.0616344i
$529$	1.81509e8	−	1.02939e9i	0.0533092	−	0.302332i
$530$	−2.64213e9	−	4.57631e9i	−0.770884	−	1.33521i
$531$	4.40941e9	−	1.05338e8i	1.27805	−	0.0305320i
$532$	5.32818e8	−	9.22868e8i	0.153422	−	0.265735i
$533$	−6.31468e9	−	5.29864e9i	−1.80637	−	1.51572i
$534$	1.15281e9	+	1.94277e9i	0.327614	+	0.552110i
$535$	−9.56765e8	−	5.42608e9i	−0.270126	−	1.53196i
$536$	3.60026e8	−	3.02098e8i	0.100985	−	0.0847366i
$537$	−4.07346e9	−	1.42776e9i	−1.13515	−	0.397875i
$538$	−2.20953e8	+	8.04204e7i	−0.0611734	+	0.0222653i
$539$	2.05220e8			0.0564494
$540$	−4.40267e8	+	3.15373e9i	−0.120320	+	0.861879i
$541$	6.89668e9			1.87262			0.936311	−	0.351173i	$-0.114217\pi$
$541$	6.89668e9			1.87262			0.936311	+	0.351173i	$0.114217\pi$
$542$	−4.04445e8	+	1.47206e8i	−0.109109	+	0.0397125i
$543$	2.98685e8	+	1.58313e9i	0.0800596	+	0.424343i
$544$	8.04301e8	−	6.74889e8i	0.214202	−	0.179736i
$545$	1.67032e9	+	9.47286e9i	0.441990	+	2.50665i
$546$	−4.05180e9	+	4.83907e7i	−1.06531	+	0.0127230i
$547$	6.58933e8	+	5.52910e8i	0.172142	+	0.144444i	0.724788	−	0.688972i	$-0.241938\pi$
$547$	6.58933e8	+	5.52910e8i	0.172142	+	0.144444i	−0.552647	+	0.833416i	$0.686382\pi$
$548$	−3.34268e8	+	5.78969e8i	−0.0867686	+	0.150288i
$549$	2.62814e9	−	2.31445e9i	0.677869	−	0.596960i
$550$	−1.95389e9	−	3.38424e9i	−0.500761	−	0.867344i
$551$	−4.30721e8	+	2.44274e9i	−0.109690	+	0.622081i
$552$	−1.23576e9	−	1.01202e9i	−0.312713	−	0.256096i
$553$	2.24959e9	+	8.18783e8i	0.565673	+	0.205888i
$554$	−1.49721e9	−	5.44939e8i	−0.374109	−	0.136165i
$555$	−4.42471e8	+	2.69736e9i	−0.109865	+	0.669752i
$556$	−2.22845e8	+	1.26382e9i	−0.0549847	+	0.311834i
$557$	8.51662e8	+	1.47512e9i	0.208821	+	0.361689i	0.951343	−	0.308133i	$-0.0997041\pi$
$557$	8.51662e8	+	1.47512e9i	0.208821	+	0.361689i	−0.742522	+	0.669821i	$0.766371\pi$
$558$	−3.63778e9	−	2.90728e9i	−0.886373	−	0.708381i
$559$	2.51816e9	−	4.36158e9i	0.609736	−	1.05609i
$560$	−1.32803e9	−	1.11435e9i	−0.319557	−	0.268140i
$561$	−2.26056e9	+	4.02567e9i	−0.540562	+	0.962650i
$562$	5.46989e7	+	3.10213e8i	0.0129987	+	0.0737195i
$563$	−1.64703e9	+	1.38202e9i	−0.388975	+	0.326389i	−0.816214	−	0.577750i	$-0.803931\pi$
$563$	−1.64703e9	+	1.38202e9i	−0.388975	+	0.326389i	0.427239	+	0.904139i	$0.359486\pi$
$564$	−6.56666e8	+	5.64508e8i	−0.154123	+	0.132493i
$565$	−2.77620e9	+	1.01046e9i	−0.647563	+	0.235694i
$566$	2.07459e9			0.480921
$567$	−2.25036e9	−	3.50032e9i	−0.518455	−	0.806430i
$568$	6.31041e8			0.144490
$569$	2.79319e9	−	1.01664e9i	0.635636	−	0.231352i	−0.00404669	−	0.999992i	$-0.501288\pi$
$569$	2.79319e9	−	1.01664e9i	0.635636	−	0.231352i	0.639682	+	0.768639i	$0.279066\pi$
$570$	−2.64134e9	+	2.27065e9i	−0.597396	+	0.513556i
$571$	1.00064e8	−	8.39635e7i	0.0224932	−	0.0188740i	−0.631472	−	0.775399i	$-0.717549\pi$
$571$	1.00064e8	−	8.39635e7i	0.0224932	−	0.0188740i	0.653965	+	0.756525i	$0.273104\pi$
$572$	−4.26285e8	−	2.41758e9i	−0.0952388	−	0.540126i
$573$	8.81107e8	−	1.56910e9i	0.195654	−	0.348426i
$574$	3.53050e9	+	2.96244e9i	0.779193	+	0.653821i
$575$	−5.28785e9	+	9.15883e9i	−1.15996	+	2.00910i
$576$	−5.33898e8	+	2.08894e8i	−0.116407	+	0.0455456i
$577$	−3.24246e9	−	5.61610e9i	−0.702683	−	1.21708i	−0.967521	−	0.252789i	$-0.918652\pi$
$577$	−3.24246e9	−	5.61610e9i	−0.702683	−	1.21708i	0.264839	−	0.964293i	$-0.414681\pi$
$578$	−8.56195e8	+	4.85572e9i	−0.184427	+	1.04594i
$579$	−1.35559e9	+	8.26387e9i	−0.290238	+	1.76933i
$580$	3.79189e9	+	1.38013e9i	0.806970	+	0.293713i
$581$	5.56543e8	+	2.02565e8i	0.117729	+	0.0428497i
$582$	−3.78398e9	−	3.09889e9i	−0.795644	−	0.651592i
$583$	−7.26470e8	+	4.12002e9i	−0.151837	+	0.861111i
$584$	3.64286e8	+	6.30962e8i	0.0756829	+	0.131087i
$585$	1.25507e10	+	4.23146e9i	2.59192	+	0.873865i
$586$	1.07835e9	−	1.86775e9i	0.221369	−	0.383422i
$587$	−4.61115e9	−	3.86921e9i	−0.940970	−	0.789567i	0.0367839	−	0.999323i	$-0.488289\pi$
$587$	−4.61115e9	−	3.86921e9i	−0.940970	−	0.789567i	−0.977754	+	0.209756i	$0.932733\pi$
$588$	−1.99332e8	+	2.38063e6i	−0.0404350	+	0.000482915i
$589$	−8.84539e8	−	5.01647e9i	−0.178367	−	1.01157i
$590$	6.01259e9	−	5.04516e9i	1.20526	−	1.01133i
$591$	2.24242e8	+	1.18856e9i	0.0446849	+	0.236845i
$592$	−4.62449e8	+	1.68318e8i	−0.0916090	+	0.0333430i
$593$	1.93103e9			0.380274			0.190137	−	0.981758i	$-0.439107\pi$
$593$	1.93103e9			0.380274			0.190137	+	0.981758i	$0.439107\pi$
$594$	1.87194e9	−	1.68862e9i	0.366470	−	0.330583i
$595$	1.35615e10			2.63936
$596$	−9.35259e8	+	3.40406e8i	−0.180955	+	0.0658621i
$597$	1.52808e9	+	5.35599e8i	0.293925	+	0.103022i
$598$	−5.08936e9	+	4.27048e9i	−0.973216	+	0.816625i
$599$	6.65088e8	+	3.77190e9i	0.126440	+	0.717078i	0.980442	+	0.196808i	$0.0630575\pi$
$599$	6.65088e8	+	3.77190e9i	0.126440	+	0.717078i	−0.854002	+	0.520270i	$0.825831\pi$
$600$	1.93709e9	+	3.26448e9i	0.366118	+	0.616999i
$601$	2.44600e9	+	2.05244e9i	0.459616	+	0.385664i	0.842990	−	0.537930i	$-0.180793\pi$
$601$	2.44600e9	+	2.05244e9i	0.459616	+	0.385664i	−0.383374	+	0.923593i	$0.625238\pi$
$602$	−1.40789e9	+	2.43854e9i	−0.263015	+	0.455556i
$603$	9.61951e8	−	1.76204e9i	0.178666	−	0.327269i
$604$	−2.10979e7	−	3.65426e7i	−0.00389592	−	0.00674793i
$605$	8.44216e8	−	4.78779e9i	0.154992	−	0.879005i
$606$	−1.89946e9	+	7.17148e8i	−0.346717	+	0.130905i
$607$	6.68709e8	+	2.43390e8i	0.121360	+	0.0441715i	0.401986	−	0.915646i	$-0.368320\pi$
$607$	6.68709e8	+	2.43390e8i	0.121360	+	0.0441715i	−0.280626	+	0.959817i	$0.590542\pi$
$608$	−5.89298e8	−	2.14487e8i	−0.106334	−	0.0387024i
$609$	−4.93338e9	+	1.86262e9i	−0.885084	+	0.334167i
$610$	1.08215e9	−	6.13717e9i	0.193033	−	1.09475i
$611$	1.80093e9	+	3.11930e9i	0.319413	+	0.553239i
$612$	2.14900e9	−	3.93640e9i	0.378972	−	0.694176i
$613$	9.37969e8	−	1.62461e9i	0.164466	−	0.284864i	−0.771999	−	0.635623i	$-0.780743\pi$
$613$	9.37969e8	−	1.62461e9i	0.164466	−	0.284864i	0.936466	+	0.350759i	$0.114077\pi$
$614$	1.29930e8	+	1.09024e8i	0.0226527	+	0.0190079i
$615$	−7.68741e9	−	1.29552e10i	−1.33265	−	2.24585i
$616$	2.38334e8	+	1.35166e9i	0.0410821	+	0.232988i
$617$	−2.71378e9	+	2.27713e9i	−0.465132	+	0.390292i	−0.845015	−	0.534743i	$-0.820409\pi$
$617$	−2.71378e9	+	2.27713e9i	−0.465132	+	0.390292i	0.379883	+	0.925034i	$0.375964\pi$
$618$	1.62683e9	+	5.70209e8i	0.277257	+	0.0971794i
$619$	−7.13272e9	+	2.59610e9i	−1.20875	+	0.439950i	−0.866271	−	0.499574i	$-0.833490\pi$
$619$	−7.13272e9	+	2.59610e9i	−1.20875	+	0.439950i	−0.342482	+	0.939524i	$0.611268\pi$
$620$	−8.28686e9			−1.39643
$621$	−6.49073e9	−	2.10236e9i	−1.08761	−	0.352279i
$622$	−7.02991e9			−1.17134
$623$	−4.93659e9	+	1.79677e9i	−0.817936	+	0.297704i
$624$	4.42100e8	+	2.34328e9i	0.0728408	+	0.386081i
$625$	5.08979e9	−	4.27084e9i	0.833911	−	0.699735i
$626$	8.90314e8	+	5.04922e9i	0.145055	+	0.822648i
$627$	2.75745e9	−	3.29322e7i	0.446757	−	0.00533562i
$628$	−3.15792e9	−	2.64981e9i	−0.508795	−	0.426930i
$629$	1.92488e9	−	3.33399e9i	0.308408	−	0.534179i
$630$	−7.01703e9	−	2.36579e9i	−1.11805	−	0.376950i
$631$	−4.24948e9	−	7.36032e9i	−0.673338	−	1.16626i	−0.976952	−	0.213461i	$-0.931526\pi$
$631$	−4.24948e9	−	7.36032e9i	−0.673338	−	1.16626i	0.303613	−	0.952795i	$-0.401807\pi$
$632$	2.44640e8	−	1.38742e9i	0.0385494	−	0.218624i
$633$	−3.93602e9	−	3.22340e9i	−0.616799	−	0.505128i
$634$	−2.28633e9	−	8.32158e8i	−0.356309	−	0.129686i
$635$	1.72286e9	+	6.27071e8i	0.267019	+	0.0971871i
$636$	6.57835e8	−	4.01024e9i	0.101395	−	0.618117i
$637$	−1.43982e8	+	8.16565e8i	−0.0220710	+	0.125171i
$638$	−1.59736e9	−	2.76671e9i	−0.243518	−	0.421785i
$639$	2.51018e9	−	9.82138e8i	0.380586	−	0.148909i
$640$	−5.10108e8	+	8.83533e8i	−0.0769188	+	0.133227i
$641$	8.17760e9	+	6.86182e9i	1.22637	+	1.02905i	0.998466	+	0.0553660i	$0.0176326\pi$
$641$	8.17760e9	+	6.86182e9i	1.22637	+	1.02905i	0.227907	+	0.973683i	$0.426812\pi$
$642$	2.07467e9	−	3.69463e9i	0.309439	−	0.551060i
$643$	4.95130e8	+	2.80802e9i	0.0734482	+	0.416545i	0.999257	+	0.0385522i	$0.0122746\pi$
$643$	4.95130e8	+	2.80802e9i	0.0734482	+	0.416545i	−0.925808	+	0.377993i	$0.876614\pi$
$644$	2.84544e9	−	2.38760e9i	0.419806	−	0.352259i
$645$	6.97934e9	−	5.99984e9i	1.02413	−	0.880401i
$646$	4.60988e9	−	1.67786e9i	0.672784	−	0.244873i
$647$	−4.45675e9			−0.646925			−0.323462	−	0.946241i	$-0.604847\pi$
$647$	−4.45675e9			−0.646925			−0.323462	+	0.946241i	$0.604847\pi$
$648$	−1.79864e9	+	1.66189e9i	−0.259677	+	0.239933i
$649$	−6.21399e9			−0.892307
$650$	1.48366e10	−	5.40009e9i	2.11904	−	0.771266i
$651$	8.21205e9	−	7.05955e9i	1.16659	−	1.00287i
$652$	−1.93691e9	+	1.62526e9i	−0.273679	+	0.229644i
$653$	−1.14965e9	−	6.51997e9i	−0.161573	−	0.916325i	−0.952528	−	0.304451i	$-0.901527\pi$
$653$	−1.14965e9	−	6.51997e9i	−0.161573	−	0.916325i	0.790955	−	0.611874i	$-0.209584\pi$
$654$	−3.62195e9	+	6.45009e9i	−0.506315	+	0.901661i
$655$	−2.41572e9	−	2.02703e9i	−0.335894	−	0.281849i
$656$	1.35610e9	−	2.34884e9i	0.187555	−	0.324855i
$657$	2.43109e9	+	1.94290e9i	0.334443	+	0.267284i
$658$	−1.00689e9	−	1.74398e9i	−0.137782	−	0.238645i
$659$	−1.35669e9	+	7.69419e9i	−0.184664	+	1.04728i	0.741722	+	0.670707i	$0.234009\pi$
$659$	−1.35669e9	+	7.69419e9i	−0.184664	+	1.04728i	−0.926386	+	0.376575i	$0.877102\pi$
$660$	7.26209e8	−	4.42707e9i	0.0983237	−	0.599394i
$661$	−1.32788e9	−	4.83310e8i	−0.178836	−	0.0650909i	0.251050	−	0.967974i	$-0.419224\pi$
$661$	−1.32788e9	−	4.83310e8i	−0.178836	−	0.0650909i	−0.429886	+	0.902883i	$0.641446\pi$
$662$	1.32032e9	+	4.80557e8i	0.176879	+	0.0643786i
$663$	−1.44320e10	−	1.18191e10i	−1.92323	−	1.57502i
$664$	6.05233e7	−	3.43245e8i	0.00802295	−	0.0455004i
$665$	−4.05006e9	−	7.01491e9i	−0.534055	−	0.925010i
$666$	−1.57759e9	+	1.38929e9i	−0.206935	+	0.182235i
$667$	−4.32297e9	+	7.48760e9i	−0.564081	+	0.977017i
$668$	3.69076e9	+	3.09691e9i	0.479069	+	0.401986i
$669$	−2.90879e8	+	3.47397e6i	−0.0375596	+	0.000448575i
$670$	−6.20344e8	−	3.51815e9i	−0.0796840	−	0.451910i
$671$	−3.77949e9	+	3.17137e9i	−0.482953	+	0.405245i
$672$	−2.47176e8	−	1.31012e9i	−0.0314205	−	0.166539i
$673$	−2.50814e9	+	9.12887e8i	−0.317175	+	0.115442i	−0.495702	−	0.868493i	$-0.665089\pi$
$673$	−2.50814e9	+	9.12887e8i	−0.317175	+	0.115442i	0.178527	+	0.983935i	$0.442867\pi$
$674$	−1.07682e10			−1.35467
$675$	1.27862e10	+	9.97075e9i	1.60022	+	1.24786i
$676$	5.90268e9			0.734912
$677$	4.75161e9	−	1.72944e9i	0.588546	−	0.214213i	−0.0305440	−	0.999533i	$-0.509724\pi$
$677$	4.75161e9	−	1.72944e9i	0.588546	−	0.214213i	0.619090	+	0.785320i	$0.287502\pi$
$678$	−2.14416e9	−	7.51534e8i	−0.264212	−	0.0926072i
$679$	8.71296e9	−	7.31104e9i	1.06812	−	0.896262i
$680$	−1.38585e9	−	7.85957e9i	−0.169019	−	0.958556i
$681$	3.53180e9	+	5.95196e9i	0.428530	+	0.722179i
$682$	5.02582e9	+	4.21717e9i	0.606683	+	0.509067i
$683$	1.54517e8	−	2.67631e8i	0.0185568	−	0.0321413i	−0.856598	−	0.515985i	$-0.827426\pi$
$683$	1.54517e8	−	2.67631e8i	0.0185568	−	0.0321413i	0.875155	+	0.483843i	$0.160760\pi$
$684$	−2.67796e9	+	6.39749e7i	−0.319969	+	0.00764387i
$685$	2.54084e9	+	4.40086e9i	0.302037	+	0.523143i
$686$	1.07585e9	−	6.10146e9i	0.127238	−	0.721605i
$687$	2.48558e9	−	9.38440e8i	0.292468	−	0.110423i
$688$	1.55713e9	+	5.66748e8i	0.182291	+	0.0663484i
$689$	−1.58837e10	−	5.78121e9i	−1.85006	−	0.673367i
$690$	−1.13586e10	+	4.28848e9i	−1.31629	+	0.496972i
$691$	−1.41196e8	+	8.00763e8i	−0.0162798	+	0.0923275i	−0.991865	−	0.127294i	$-0.959371\pi$
$691$	−1.41196e8	+	8.00763e8i	−0.0162798	+	0.0923275i	0.975585	+	0.219621i	$0.0704821\pi$
$692$	2.92370e9	+	5.06400e9i	0.335399	+	0.580928i
$693$	3.05175e9	+	5.00575e9i	0.348323	+	0.571351i
$694$	−3.10372e9	+	5.37581e9i	−0.352472	+	0.610500i
$695$	7.47257e9	+	6.27023e9i	0.844351	+	0.708495i
$696$	1.58363e9	+	2.66880e9i	0.178041	+	0.300043i
$697$	3.68424e9	+	2.08943e10i	0.412129	+	2.33730i
$698$	−7.01100e8	+	5.88293e8i	−0.0780344	+	0.0654786i
$699$	−4.41145e9	−	1.54623e9i	−0.488552	−	0.171239i
$700$	−8.29508e9	+	3.01916e9i	−0.914066	+	0.332693i
$701$	1.25114e10			1.37181			0.685904	−	0.727692i	$-0.259407\pi$
$701$	1.25114e10			1.37181			0.685904	+	0.727692i	$0.259407\pi$
$702$	5.40564e9	+	8.63313e9i	0.589749	+	0.941864i
$703$	−2.29942e9			−0.249617
$704$	7.58999e8	−	2.76253e8i	0.0819854	−	0.0298403i
$705$	1.22034e9	+	6.46819e9i	0.131165	+	0.695218i
$706$	−6.91861e9	+	5.80540e9i	−0.739950	+	0.620891i
$707$	−8.19884e8	−	4.64980e9i	−0.0872539	−	0.494841i
$708$	6.03572e9	−	7.20846e7i	0.639164	−	0.00763354i
$709$	1.26953e10	+	1.06527e10i	1.33777	+	1.12252i	0.982192	+	0.187879i	$0.0601614\pi$
$709$	1.26953e10	+	1.06527e10i	1.33777	+	1.12252i	0.355581	+	0.934645i	$0.384283\pi$
$710$	2.39833e9	−	4.15404e9i	0.251481	−	0.435578i
$711$	−1.18621e9	−	5.89970e9i	−0.123771	−	0.615583i
$712$	1.54579e9	+	2.67739e9i	0.160499	+	0.277992i
$713$	3.08321e9	−	1.74857e10i	0.318559	−	1.80664i
$714$	8.06888e9	+	6.60800e9i	0.829601	+	0.679402i
$715$	−1.75347e10	−	6.38211e9i	−1.79402	−	0.652969i
$716$	−5.55094e9	−	2.02038e9i	−0.565159	−	0.205701i
$717$	−2.61098e9	+	1.59169e10i	−0.264538	+	1.61265i
$718$	1.80278e9	−	1.02241e10i	0.181763	−	1.03083i
$719$	3.84978e9	+	6.66802e9i	0.386265	+	0.669030i	0.991944	−	0.126679i	$-0.0404317\pi$
$719$	3.84978e9	+	6.66802e9i	0.386265	+	0.669030i	−0.605679	+	0.795709i	$0.707098\pi$
$720$	−6.54019e8	+	4.30848e9i	−0.0653021	+	0.430190i
$721$	−2.00442e9	+	3.47176e9i	−0.199166	+	0.344966i
$722$	3.23335e9	+	2.71310e9i	0.319722	+	0.268279i
$723$	1.46294e9	−	2.60525e9i	0.143960	−	0.256369i
$724$	3.82857e8	+	2.17129e9i	0.0374932	+	0.212634i
$725$	1.57400e10	−	1.32075e10i	1.53399	−	1.28717i
$726$	2.83520e9	−	2.43731e9i	0.274983	−	0.236391i
$727$	−3.09762e9	+	1.12744e9i	−0.298991	+	0.108824i	−0.487160	−	0.873313i	$-0.661967\pi$
$727$	−3.09762e9	+	1.12744e9i	−0.298991	+	0.108824i	0.188169	+	0.982137i	$0.439745\pi$
$728$	−5.54543e9			−0.532691
$729$	−4.56820e9	+	9.41013e9i	−0.436715	+	0.899600i
$730$	5.53803e9			0.526896
$731$	−1.21809e10	+	4.43348e9i	−1.15337	+	0.419792i
$732$	3.63427e9	−	3.12423e9i	0.342475	−	0.294411i
$733$	2.78725e9	−	2.33878e9i	0.261404	−	0.219344i	−0.502660	−	0.864484i	$-0.667645\pi$
$733$	2.78725e9	−	2.33878e9i	0.261404	−	0.219344i	0.764064	+	0.645140i	$0.223201\pi$
$734$	1.47882e9	+	8.38681e9i	0.138032	+	0.782818i
$735$	−7.41912e8	+	1.32122e9i	−0.0689202	+	0.122735i
$736$	−1.67451e9	−	1.40508e9i	−0.154816	−	0.129906i
$737$	−1.41415e9	+	2.44938e9i	−0.130125	+	0.225382i
$738$	1.73868e9	−	1.14539e10i	0.159229	−	1.04896i
$739$	−5.53111e9	−	9.58017e9i	−0.504147	−	0.873208i	−0.999989	−	0.00479492i	$-0.998474\pi$
$739$	−5.53111e9	−	9.58017e9i	−0.504147	−	0.873208i	0.495842	−	0.868413i	$-0.334860\pi$
$740$	−6.49577e8	+	3.68394e9i	−0.0589278	+	0.334196i
$741$	−1.80359e9	+	1.09949e10i	−0.162845	+	0.992724i
$742$	8.88052e9	+	3.23225e9i	0.798040	+	0.290463i
$743$	−5.75107e9	−	2.09322e9i	−0.514385	−	0.187221i	0.0717679	−	0.997421i	$-0.477136\pi$
$743$	−5.75107e9	−	2.09322e9i	−0.514385	−	0.187221i	−0.586153	+	0.810201i	$0.699358\pi$
$744$	−4.93056e9	−	4.03788e9i	−0.438925	−	0.359458i
$745$	−1.31371e9	+	7.45040e9i	−0.116400	+	0.660135i
$746$	−2.38275e9	−	4.12704e9i	−0.210132	−	0.363959i
$747$	−2.93466e8	−	1.45957e9i	−0.0257594	−	0.128116i
$748$	−3.15922e9	+	5.47193e9i	−0.276010	+	0.478063i
$749$	7.54844e9	+	6.33389e9i	0.656403	+	0.550788i
$750$	1.46337e10	−	1.74771e8i	1.26660	−	0.0151270i
$751$	4.17954e8	+	2.37033e9i	0.0360071	+	0.204207i	0.997504	−	0.0706090i	$-0.0224943\pi$
$751$	4.17954e8	+	2.37033e9i	0.0360071	+	0.204207i	−0.961497	+	0.274816i	$0.911383\pi$
$752$	−9.07832e8	+	7.61761e8i	−0.0778472	+	0.0653215i
$753$	3.01391e9	+	1.59747e10i	0.257246	+	1.36349i
$754$	1.21294e10	−	4.41473e9i	1.03048	−	0.375063i
$755$	−3.20739e8			−0.0271230
$756$	−3.02226e9	−	4.82674e9i	−0.254394	−	0.406282i
$757$	9.61324e9			0.805442			0.402721	−	0.915323i	$-0.368065\pi$
$757$	9.61324e9			0.805442			0.402721	+	0.915323i	$0.368065\pi$
$758$	−1.37346e10	+	4.99898e9i	−1.14544	+	0.416907i
$759$	9.07116e9	+	3.17947e9i	0.753037	+	0.263942i
$760$	−3.65162e9	+	3.06407e9i	−0.301743	+	0.253193i
$761$	−8.49369e8	−	4.81701e9i	−0.0698634	−	0.396215i	−0.999608	−	0.0280092i	$-0.991083\pi$
$761$	−8.49369e8	−	4.81701e9i	−0.0698634	−	0.396215i	0.929744	−	0.368206i	$-0.120028\pi$
$762$	7.19529e8	+	1.21258e9i	0.0589123	+	0.0992817i
$763$	−1.31781e10	−	1.10577e10i	−1.07403	−	0.901216i
$764$	1.23138e9	−	2.13282e9i	0.0999003	−	0.173032i
$765$	−1.77452e10	−	2.91072e10i	−1.43306	−	2.35064i
$766$	1.82383e9	+	3.15897e9i	0.146617	+	0.253948i
$767$	4.35974e9	−	2.47253e10i	0.348881	−	1.97860i
$768$	−7.34019e8	+	2.77132e8i	−0.0584713	+	0.0220761i
$769$	4.44815e9	+	1.61899e9i	0.352726	+	0.128382i	0.512305	−	0.858803i	$-0.328792\pi$
$769$	4.44815e9	+	1.61899e9i	0.352726	+	0.128382i	−0.159580	+	0.987185i	$0.551014\pi$
$770$	9.80355e9	+	3.56820e9i	0.773866	+	0.281664i
$771$	2.22397e10	−	8.39670e9i	1.74759	−	0.659809i
$772$	−1.99010e9	+	1.12864e10i	−0.155674	+	0.882868i
$773$	−3.15559e9	−	5.46564e9i	−0.245727	−	0.425611i	0.716609	−	0.697475i	$-0.245693\pi$
$773$	−3.15559e9	−	5.46564e9i	−0.245727	−	0.425611i	−0.962336	+	0.271864i	$0.912360\pi$
$774$	7.07609e9	−	1.69044e8i	0.548530	−	0.0131041i
$775$	−2.10981e10	+	3.65429e10i	−1.62812	+	2.81999i
$776$	−5.12750e9	−	4.30248e9i	−0.393903	−	0.330524i
$777$	−2.49462e9	−	4.20405e9i	−0.190779	−	0.321510i
$778$	−1.31273e9	−	7.44487e9i	−0.0999418	−	0.566798i
$779$	9.70768e9	−	8.14571e9i	0.735757	−	0.617373i
$780$	1.71057e10	+	5.99560e9i	1.29065	+	0.452378i
$781$	−3.56852e9	+	1.29884e9i	−0.268046	+	0.0975609i
$782$	1.70997e10			1.27869
$783$	1.04531e10	+	8.15136e9i	0.778177	+	0.606826i
$784$	−2.72813e8			−0.0202189
$785$	−2.94453e10	+	1.07172e10i	−2.17256	+	0.790747i
$786$	−4.49621e8	−	2.38314e9i	−0.0330269	−	0.175054i
$787$	−6.73198e9	+	5.64880e9i	−0.492302	+	0.413090i	−0.854850	−	0.518875i	$-0.826351\pi$
$787$	−6.73198e9	+	5.64880e9i	−0.492302	+	0.413090i	0.362549	+	0.931965i	$0.381907\pi$
$788$	2.87436e8	+	1.63013e9i	0.0209266	+	0.118681i
$789$	2.66210e10	−	3.17935e8i	1.92954	−	0.0230445i
$790$	−8.20339e9	−	6.88346e9i	−0.591968	−	0.496720i
$791$	2.64182e9	−	4.57577e9i	0.189796	−	0.328735i
$792$	2.58923e9	−	2.28018e9i	0.185196	−	0.163091i
$793$	−9.96710e9	−	1.72635e10i	−0.709762	−	1.22934i
$794$	−2.09364e9	+	1.18736e10i	−0.148433	+	0.841805i
$795$	−2.38986e10	−	1.95718e10i	−1.68689	−	1.38148i
$796$	2.08233e9	+	7.57907e8i	0.146337	+	0.0532623i
$797$	−1.01176e10	−	3.68249e9i	−0.707900	−	0.257655i	−0.0371200	−	0.999311i	$-0.511818\pi$
$797$	−1.01176e10	−	3.68249e9i	−0.707900	−	0.257655i	−0.670780	+	0.741656i	$0.734041\pi$
$798$	1.00838e9	−	6.14720e9i	0.0702447	−	0.428221i
$799$	1.60982e9	−	9.12973e9i	0.111651	−	0.633205i
$800$	2.59744e9	+	4.49889e9i	0.179362	+	0.310664i
$801$	1.03160e10	+	8.24441e9i	0.709244	+	0.566821i
$802$	2.99106e9	−	5.18066e9i	0.204746	−	0.354630i
$803$	−3.35871e9	−	2.81829e9i	−0.228911	−	0.192080i
$804$	1.34517e9	−	2.39551e9i	0.0912808	−	0.162556i
$805$	−4.90283e9	−	2.78054e10i	−0.331254	−	1.87864i
$806$	−2.03061e10	+	1.70388e10i	−1.36601	+	1.14622i
$807$	−1.04231e9	+	8.96032e8i	−0.0698137	+	0.0600159i
$808$	−2.61101e9	+	9.50329e8i	−0.174128	+	0.0633773i
$809$	9.44746e9			0.627329			0.313664	−	0.949534i	$-0.398443\pi$
$809$	9.44746e9			0.627329			0.313664	+	0.949534i	$0.398443\pi$
$810$	4.10404e9	+	1.81564e10i	0.271340	+	1.20042i
$811$	2.14580e10			1.41259			0.706296	−	0.707917i	$-0.250365\pi$
$811$	2.14580e10			1.41259			0.706296	+	0.707917i	$0.250365\pi$
$812$	−6.78146e9	+	2.46825e9i	−0.444506	+	0.161787i
$813$	−1.90790e9	+	1.64014e9i	−0.124520	+	0.107045i
$814$	2.26870e9	−	1.90367e9i	0.147432	−	0.123710i
$815$	3.33739e9	+	1.89273e10i	0.215951	+	1.22472i
$816$	3.00511e9	−	5.35159e9i	0.193618	−	0.344800i
$817$	5.93105e9	+	4.97674e9i	0.380500	+	0.319277i
$818$	−2.22570e9	+	3.85502e9i	−0.142177	+	0.246258i
$819$	−2.20589e10	+	8.63079e9i	−1.40310	+	0.548980i
$820$	−1.03080e10	−	1.78540e10i	−0.652869	−	1.13080i
$821$	−9.53325e8	+	5.40657e9i	−0.0601229	+	0.340974i	−1.00000		0.000539412i	$-0.999828\pi$
$821$	−9.53325e8	+	5.40657e9i	−0.0601229	+	0.340974i	0.939877	+	0.341513i	$0.110939\pi$
$822$	−6.32614e8	+	3.85650e9i	−0.0397272	+	0.242182i
$823$	−2.56668e10	−	9.34196e9i	−1.60499	−	0.584169i	−0.624550	−	0.780985i	$-0.714718\pi$
$823$	−2.56668e10	−	9.34196e9i	−1.60499	−	0.584169i	−0.980440	+	0.196816i	$0.936940\pi$
$824$	2.21689e9	+	8.06882e8i	0.138038	+	0.0502418i
$825$	−1.76733e10	−	1.44736e10i	−1.09579	−	0.897400i
$826$	−2.43751e9	+	1.38238e10i	−0.150493	+	0.853487i
$827$	−1.14612e9	−	1.98515e9i	−0.0704632	−	0.122046i	0.828641	−	0.559780i	$-0.189114\pi$
$827$	−1.14612e9	−	1.98515e9i	−0.0704632	−	0.122046i	−0.899104	+	0.437734i	$0.855781\pi$
$828$	−8.84779e9	−	2.98303e9i	−0.541663	−	0.182621i
$829$	−4.37381e9	+	7.57567e9i	−0.266636	+	0.461828i	−0.967991	−	0.250985i	$-0.919246\pi$
$829$	−4.37381e9	+	7.57567e9i	−0.266636	+	0.461828i	0.701355	+	0.712812i	$0.252579\pi$
$830$	−2.02950e9	−	1.70295e9i	−0.123201	−	0.103378i
$831$	−9.31322e9	+	1.11228e8i	−0.562984	+	0.00672373i
$832$	5.66689e8	+	3.21385e9i	0.0341125	+	0.193461i
$833$	1.63483e9	−	1.37179e9i	0.0979977	−	0.0822298i
$834$	1.39082e9	+	7.37179e9i	0.0830211	+	0.440040i
$835$	3.44136e10	−	1.25255e10i	2.04563	−	0.744548i
$836$	3.77393e9			0.223394
$837$	−2.58975e10	−	8.38824e9i	−1.52657	−	0.494461i
$838$	7.92622e9			0.465278
$839$	−6.49968e9	+	2.36569e9i	−0.379949	+	0.138290i	−0.524932	−	0.851144i	$-0.675909\pi$
$839$	−6.49968e9	+	2.36569e9i	−0.379949	+	0.138290i	0.144983	+	0.989434i	$0.453687\pi$
$840$	−9.56369e9	−	3.35211e9i	−0.556734	−	0.195137i
$841$	−3.46241e8	+	2.90531e8i	−0.0200721	+	0.0168425i
$842$	−2.15212e9	−	1.22053e10i	−0.124244	−	0.704620i
$843$	9.39667e8	+	1.58357e9i	0.0540228	+	0.0910418i
$844$	−5.33351e9	−	4.47534e9i	−0.305361	−	0.256229i
$845$	2.24337e10	−	3.88563e10i	1.27909	−	2.21546i
$846$	−2.42563e9	+	4.44310e9i	−0.137730	+	0.252284i
$847$	4.34732e9	+	7.52978e9i	0.245827	+	0.425785i
$848$	9.65745e8	−	5.47701e9i	0.0543847	−	0.308431i
$849$	1.13456e10	−	4.28360e9i	0.636285	−	0.240232i
$850$	−3.81870e10	−	1.38989e10i	−2.13280	−	0.776274i
$851$	−7.53163e9	−	2.74129e9i	−0.418924	−	0.152476i
$852$	3.45108e9	−	1.30297e9i	0.191168	−	0.0721765i
$853$	4.14578e9	−	2.35119e10i	0.228710	−	1.29708i	−0.626755	−	0.779217i	$-0.715617\pi$
$853$	4.14578e9	−	2.35119e10i	0.228710	−	1.29708i	0.855464	−	0.517862i	$-0.173272\pi$
$854$	5.57256e9	+	9.65195e9i	0.306162	+	0.530289i
$855$	−9.75672e9	+	1.78717e10i	−0.533854	+	0.977878i
$856$	2.89943e9	−	5.02196e9i	0.157999	−	0.273662i
$857$	−1.14006e10	−	9.56622e9i	−0.618720	−	0.519168i	0.278681	−	0.960384i	$-0.410103\pi$
$857$	−1.14006e10	−	9.56622e9i	−0.618720	−	0.519168i	−0.897401	+	0.441216i	$0.854547\pi$
$858$	−7.32311e9	−	1.23412e10i	−0.395813	−	0.667043i
$859$	4.45109e9	+	2.52434e10i	0.239602	+	1.35885i	0.832702	+	0.553722i	$0.186793\pi$
$859$	4.45109e9	+	2.52434e10i	0.239602	+	1.35885i	−0.593099	+	0.805129i	$0.702096\pi$
$860$	9.64884e9	−	8.09633e9i	0.517286	−	0.434054i
$861$	2.54247e10	+	8.91145e9i	1.35752	+	0.475814i
$862$	7.97889e9	−	2.90408e9i	0.424294	−	0.154430i
$863$	1.27446e10			0.674976			0.337488	−	0.941330i	$-0.390423\pi$
$863$	1.27446e10			0.674976			0.337488	+	0.941330i	$0.390423\pi$
$864$	−2.48849e9	+	2.24480e9i	−0.131262	+	0.118408i
$865$	4.44473e10			2.33501
$866$	7.54799e9	−	2.74724e9i	0.394929	−	0.143742i
$867$	5.34365e9	+	2.83232e10i	0.278466	+	1.47596i
$868$	1.13530e10	−	9.52633e9i	0.589241	−	0.494432i
$869$	1.47222e9	+	8.34937e9i	0.0761032	+	0.431603i
$870$	2.35870e10	−	2.81700e8i	1.21438	−	0.0145034i
$871$	−8.75385e9	−	7.34535e9i	−0.448885	−	0.376660i
$872$	−5.06183e9	+	8.76734e9i	−0.258523	+	0.447775i
$873$	−2.70927e10	−	9.13428e9i	−1.37817	−	0.464648i
$874$	−5.10674e9	−	8.84513e9i	−0.258734	−	0.448140i
$875$	−5.90979e9	+	3.35161e10i	−0.298225	+	1.69132i
$876$	3.29504e9	+	2.69847e9i	0.165614	+	0.135629i
$877$	3.46881e10	+	1.26254e10i	1.73653	+	0.632045i	0.999061	−	0.0433366i	$-0.0137988\pi$
$877$	3.46881e10	+	1.26254e10i	1.73653	+	0.632045i	0.737469	+	0.675382i	$0.236021\pi$
$878$	−2.00229e10	−	7.28776e9i	−0.998383	−	0.363382i
$879$	2.04081e9	−	1.24411e10i	0.101354	−	0.617868i
$880$	1.06612e9	−	6.04629e9i	0.0527374	−	0.299088i
$881$	−1.60436e10	−	2.77883e10i	−0.790471	−	1.36914i	−0.925676	−	0.378318i	$-0.876503\pi$
$881$	−1.60436e10	−	2.77883e10i	−0.790471	−	1.36914i	0.135205	−	0.990818i	$-0.456831\pi$
$882$	−1.08521e9	+	4.24600e8i	−0.0532565	+	0.0208372i
$883$	−3.91481e9	+	6.78065e9i	−0.191359	+	0.331443i	−0.945701	−	0.325039i	$-0.894623\pi$
$883$	−3.91481e9	+	6.78065e9i	−0.191359	+	0.331443i	0.754342	+	0.656482i	$0.227956\pi$
$884$	−1.95562e10	−	1.64096e10i	−0.952140	−	0.798940i
$885$	2.24648e10	−	4.00061e10i	1.08944	−	1.94010i
$886$	−4.58232e9	−	2.59876e10i	−0.221344	−	1.25530i
$887$	3.15330e9	−	2.64594e9i	0.151717	−	0.127305i	−0.563770	−	0.825932i	$-0.690650\pi$
$887$	3.15330e9	−	2.64594e9i	0.151717	−	0.127305i	0.715487	+	0.698627i	$0.246205\pi$
$888$	−2.18153e9	+	1.87537e9i	−0.104548	+	0.0898756i
$889$	−3.08119e9	+	1.12146e9i	−0.147083	+	0.0535338i
$890$	2.34998e10			1.11737
$891$	6.75072e9	−	1.31000e10i	0.319726	−	0.620441i
$892$	−3.98106e8			−0.0187811
$893$	−5.20327e9	+	1.89383e9i	−0.244510	+	0.0889943i
$894$	−4.41194e9	+	3.79276e9i	−0.206513	+	0.177531i
$895$	−3.43967e10	+	2.88623e10i	−1.60375	+	1.34571i
$896$	−3.16833e8	−	1.79685e9i	−0.0147147	−	0.0834514i
$897$	−1.90154e10	+	3.38632e10i	−0.879693	+	1.56659i
$898$	−9.81133e8	−	8.23269e8i	−0.0452127	−	0.0379380i
$899$	−1.72483e10	+	2.98749e10i	−0.791747	+	1.37135i
$900$	1.73342e10	+	1.38533e10i	0.792601	+	0.633438i
$901$	2.17529e10	+	3.76771e10i	0.990788	+	1.71609i
$902$	−2.83425e9	+	1.60738e10i	−0.128592	+	0.729283i
$903$	−2.66449e9	+	1.62430e10i	−0.120422	+	0.734109i
$904$	−2.92186e9	−	1.06347e9i	−0.131544	−	0.0478779i
$905$	1.57483e10	+	5.73193e9i	0.706261	+	0.257058i
$906$	−1.90835e8	−	1.56284e8i	−0.00852528	−	0.00698177i
$907$	1.61208e9	−	9.14258e9i	0.0717401	−	0.406858i	−0.927698	−	0.373332i	$-0.878215\pi$
$907$	1.61208e9	−	9.14258e9i	0.0717401	−	0.406858i	0.999438	−	0.0335262i	$-0.0106737\pi$
$908$	4.73577e9	+	8.20260e9i	0.209938	+	0.363623i
$909$	−8.90711e9	+	7.84398e9i	−0.393336	+	0.346388i
$910$	−2.10760e10	+	3.65046e10i	−0.927134	+	1.60584i
$911$	7.10100e9	+	5.95845e9i	0.311175	+	0.261107i	0.784978	−	0.619524i	$-0.212674\pi$
$911$	7.10100e9	+	5.95845e9i	0.311175	+	0.261107i	−0.473802	+	0.880631i	$0.657119\pi$
$912$	−3.66566e9	+	4.37790e7i	−0.160019	+	0.00191110i
$913$	3.64223e8	+	2.06561e9i	0.0158387	+	0.0898259i
$914$	5.35543e9	−	4.49374e9i	0.231997	−	0.194669i
$915$	−6.75387e9	−	3.57978e10i	−0.291460	−	1.54483i
$916$	3.41669e9	−	1.24357e9i	0.146883	−	0.0534610i
$917$	5.63976e9			0.241528
$918$	3.62475e9	−	2.59649e10i	0.154643	−	1.10774i
$919$	−1.89540e9			−0.0805558			−0.0402779	−	0.999189i	$-0.512824\pi$
$919$	−1.89540e9			−0.0805558			−0.0402779	+	0.999189i	$0.512824\pi$
$920$	−1.56136e10	+	5.68288e9i	−0.661067	+	0.240609i
$921$	9.35682e8	+	3.27960e8i	0.0394657	+	0.0138329i
$922$	1.77994e10	−	1.49354e10i	0.747905	−	0.627567i
$923$	−2.66436e9	−	1.51103e10i	−0.111529	−	0.632510i
$924$	4.09431e9	+	6.89993e9i	0.170738	+	0.287735i
$925$	1.45914e10	+	1.22436e10i	0.606179	+	0.508645i
$926$	1.07555e10	−	1.86291e10i	0.445136	−	0.770998i
$927$	1.00743e10	−	2.40668e8i	0.415369	−	0.00992293i
$928$	2.12348e9	+	3.67797e9i	0.0872227	+	0.151074i
$929$	−2.46729e9	+	1.39927e10i	−0.100964	+	0.572594i	0.891792	+	0.452446i	$0.149448\pi$
$929$	−2.46729e9	+	1.39927e10i	−0.100964	+	0.572594i	−0.992756	+	0.120149i	$0.961663\pi$
$930$	−4.53197e10	+	1.71107e10i	−1.84755	+	0.697552i
$931$	−1.19781e9	−	4.35969e8i	−0.0486480	−	0.0177064i
$932$	−6.01151e9	−	2.18801e9i	−0.243236	−	0.0885307i
$933$	−3.84457e10	+	1.45153e10i	−1.54975	+	0.585115i
$934$	5.94190e9	−	3.36982e10i	0.238622	−	1.35330i
$935$	2.40139e10	+	4.15933e10i	0.960775	+	1.66411i
$936$	7.25618e9	+	1.19022e10i	0.289229	+	0.474420i
$937$	−2.05414e10	+	3.55787e10i	−0.815719	+	1.41287i	0.0930909	+	0.995658i	$0.470325\pi$
$937$	−2.05414e10	+	3.55787e10i	−0.815719	+	1.41287i	−0.908810	+	0.417210i	$0.863008\pi$
$938$	4.89423e9	+	4.10675e9i	0.193631	+	0.162476i
$939$	1.52946e10	+	2.57752e10i	0.602849	+	1.01595i
$940$	1.56424e9	+	8.87126e9i	0.0614266	+	0.348368i
$941$	5.22826e8	−	4.38703e8i	0.0204547	−	0.0171636i	−0.632503	−	0.774558i	$-0.717972\pi$
$941$	5.22826e8	−	4.38703e8i	0.0204547	−	0.0171636i	0.652958	+	0.757394i	$0.273528\pi$
$942$	−2.27416e10	−	7.97100e9i	−0.886426	−	0.310695i
$943$	4.15081e10	−	1.51077e10i	1.61191	−	0.586689i
$944$	8.26067e9			0.319605
$945$	−4.32600e10	+	1.55055e9i	−1.66754	+	0.0597690i
$946$	−9.97204e9			−0.382970
$947$	3.77803e10	−	1.37509e10i	1.44557	−	0.526146i	0.504222	−	0.863574i	$-0.331779\pi$
$947$	3.77803e10	−	1.37509e10i	1.44557	−	0.526146i	0.941351	+	0.337428i	$0.109557\pi$
$948$	−1.52684e9	−	8.09275e9i	−0.0582055	−	0.308508i
$949$	1.35704e10	−	1.13869e10i	0.515418	−	0.432487i
$950$	4.21487e9	+	2.39037e10i	0.159497	+	0.904550i
$951$	−1.42219e10	+	1.69852e8i	−0.536198	+	0.00640382i
$952$	1.09337e10	+	9.17450e9i	0.410714	+	0.344630i
$953$	−1.54476e10	+	2.67561e10i	−0.578145	+	1.00138i	0.417547	+	0.908655i	$0.362890\pi$
$953$	−1.54476e10	+	2.67561e10i	−0.578145	+	1.00138i	−0.995692	+	0.0927213i	$0.970443\pi$
$954$	−4.68272e9	−	2.32898e10i	−0.174614	−	0.868453i
$955$	−9.36000e9	−	1.62120e10i	−0.347747	−	0.602316i
$956$	−3.83310e9	+	2.17386e10i	−0.141889	+	0.804690i
$957$	−1.44484e10	−	1.18325e10i	−0.532879	−	0.436401i
$958$	2.66733e10	+	9.70830e9i	0.980162	+	0.356750i
$959$	−8.54005e9	−	3.10833e9i	−0.312677	−	0.113805i
$960$	−9.65398e8	+	5.88519e9i	−0.0352174	+	0.214690i
$961$	7.52421e9	−	4.26719e10i	0.273482	−	1.55099i
$962$	5.98292e9	+	1.03627e10i	0.216671	+	0.375285i
$963$	3.71742e9	−	2.44892e10i	0.134137	−	0.883655i
$964$	2.04452e9	−	3.54121e9i	0.0735059	−	0.127316i
$965$	6.67331e10	+	5.59957e10i	2.39054	+	2.00590i
$966$	1.06314e10	−	1.89327e10i	0.379464	−	0.675761i
$967$	−9.54785e9	−	5.41485e10i	−0.339557	−	1.92572i	−0.376522	−	0.926407i	$-0.622880\pi$
$967$	−9.54785e9	−	5.41485e10i	−0.339557	−	1.92572i	0.0369654	−	0.999317i	$-0.488231\pi$
$968$	3.91963e9	−	3.28896e9i	0.138893	−	0.116545i
$969$	2.17464e10	−	1.86944e10i	0.767810	−	0.660054i
$970$	−4.78101e10	+	1.74014e10i	−1.68197	+	0.612187i
$971$	3.98514e10			1.39694			0.698468	−	0.715642i	$-0.253866\pi$
$971$	3.98514e10			1.39694			0.698468	+	0.715642i	$0.253866\pi$
$972$	−6.40508e9	+	1.28025e10i	−0.223714	+	0.447160i
$973$	−1.74455e10			−0.607140
$974$	6.11939e9	−	2.22728e9i	0.212203	−	0.0772356i
$975$	6.99895e10	−	6.01670e10i	2.41834	−	2.07894i
$976$	5.02433e9	−	4.21591e9i	0.172983	−	0.145150i
$977$	4.49380e9	+	2.54856e10i	0.154164	+	0.874306i	0.959546	+	0.281551i	$0.0908488\pi$
$977$	4.49380e9	+	2.54856e10i	0.154164	+	0.874306i	−0.805383	+	0.592755i	$0.798040\pi$
$978$	−7.23685e9	+	1.28876e10i	−0.247380	+	0.440541i
$979$	−1.42522e10	−	1.19590e10i	−0.485446	−	0.407338i
$980$	−1.03685e9	+	1.79588e9i	−0.0351905	+	0.0609517i
$981$	−6.48986e9	+	4.27532e10i	−0.219480	+	1.44586i
$982$	7.00716e9	+	1.21368e10i	0.236130	+	0.408990i
$983$	7.18253e9	−	4.07342e10i	0.241179	−	1.36780i	−0.588021	−	0.808846i	$-0.700093\pi$
$983$	7.18253e9	−	4.07342e10i	0.241179	−	1.36780i	0.829201	−	0.558951i	$-0.188796\pi$
$984$	2.56647e9	−	1.56456e10i	0.0858725	−	0.523490i
$985$	1.18233e10	+	4.30333e9i	0.394196	+	0.143476i
$986$	−3.12189e10	−	1.13628e10i	−1.03717	−	0.377498i
$987$	−9.10751e9	−	7.45859e9i	−0.301502	−	0.246915i
$988$	−2.64779e9	+	1.50164e10i	−0.0873443	+	0.495354i
$989$	1.34938e10	+	2.33719e10i	0.443554	+	0.768257i
$990$	−5.16944e9	−	2.57105e10i	−0.169325	−	0.842146i
$991$	2.78236e9	−	4.81919e9i	0.0908146	−	0.157295i	−0.817040	−	0.576582i	$-0.804386\pi$
$991$	2.78236e9	−	4.81919e9i	0.0908146	−	0.157295i	0.907854	+	0.419286i	$0.137720\pi$
$992$	−6.68116e9	−	5.60616e9i	−0.217301	−	0.182337i
$993$	8.21290e9	−	9.80867e7i	0.266179	−	0.00317898i
$994$	1.48963e9	+	8.44810e9i	0.0481089	+	0.272839i
$995$	1.29033e10	−	1.08271e10i	0.415260	−	0.348444i
$996$	−3.77736e8	−	2.00213e9i	−0.0121138	−	0.0642073i
$997$	3.23332e10	−	1.17683e10i	1.03328	−	0.376082i	0.230948	−	0.972966i	$-0.425817\pi$
$997$	3.23332e10	−	1.17683e10i	1.03328	−	0.376082i	0.802327	+	0.596884i	$0.203595\pi$
$998$	−3.52608e10			−1.12289
$999$	−5.75901e9	+	1.08552e10i	−0.182755	+	0.344477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.e.b.7.9	✓	66
27.4	even	9	inner	54.8.e.b.31.9	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.e.b.7.9	✓	66	1.1	even	1	trivial
54.8.e.b.31.9	yes	66	27.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.51754 - 2.73616i) q^{2} +(35.4628 - 30.4859i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-84.4758 - 479.086i) q^{5} +(183.179 - 326.211i) q^{6} +(666.476 + 559.239i) q^{7} +(256.000 - 443.405i) q^{8} +(328.222 - 2162.23i) q^{9} +(-1945.91 - 3370.41i) q^{10} +(-535.039 + 3034.36i) q^{11} +(484.489 - 2953.51i) q^{12} +(-11698.2 - 4257.81i) q^{13} +(6540.43 + 2380.52i) q^{14} +(-17601.1 - 14414.4i) q^{15} +(711.263 - 4033.77i) q^{16} +(16020.8 + 27748.9i) q^{17} +(-3448.78 - 17152.7i) q^{18} +(9569.05 - 16574.1i) q^{19} +(-23850.4 - 20012.9i) q^{20} +(40684.0 - 485.889i) q^{21} +(4280.31 + 24274.9i) q^{22} +(51102.1 - 42879.7i) q^{23} +(-4439.11 - 23528.8i) q^{24} +(-148974. + 54222.1i) q^{25} -99592.1 q^{26} +(-54277.8 - 86684.9i) q^{27} +55681.4 q^{28} +(-121790. + 44328.1i) q^{29} +(-171757. - 60201.6i) q^{30} +(203893. - 171086. i) q^{31} +(-5690.10 - 32270.2i) q^{32} +(73531.0 + 123918. i) q^{33} +(196363. + 164768. i) q^{34} +(211623. - 366542. i) q^{35} +(-72859.0 - 119510. i) q^{36} +(-60074.3 - 104052. i) q^{37} +(26586.4 - 150779. i) q^{38} +(-544656. + 205637. i) q^{39} +(-234055. - 85189.1i) q^{40} +(622226. + 226472. i) q^{41} +(304514. - 114971. i) q^{42} +(-70250.4 + 398410. i) q^{43} +(98597.3 + 170776. i) q^{44} +(-1.06362e6 + 25409.3i) q^{45} +(266836. - 462174. i) q^{46} +(-221639. - 185977. i) q^{47} +(-97749.7 - 164732. i) q^{48} +(-11565.8 - 65592.8i) q^{49} +(-971558. + 815234. i) q^{50} +(1.41409e6 + 495645. i) q^{51} +(-748687. + 272500. i) q^{52} +1.35779e6 q^{53} +(-645219. - 503145. i) q^{54} +1.49892e6 q^{55} +(418587. - 152353. i) q^{56} +(-165930. - 879485. i) q^{57} +(-794276. + 666477. i) q^{58} +(350208. + 1.98613e6i) q^{59} +(-1.45591e6 + 17388.0i) q^{60} +(1.22664e6 + 1.02928e6i) q^{61} +(1.06465e6 - 1.84403e6i) q^{62} +(1.42796e6 - 1.25752e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-1.05164e6 + 5.96415e6i) q^{65} +(891832. + 730366. i) q^{66} +(862574. + 313951. i) q^{67} +(1.92700e6 + 701369. i) q^{68} +(504997. - 3.07853e6i) q^{69} +(587967. - 3.33453e6i) q^{70} +(616251. + 1.06738e6i) q^{71} +(-874719. - 699066. i) q^{72} +(-711497. + 1.23235e6i) q^{73} +(-736313. - 617840. i) q^{74} +(-3.63003e6 + 6.46447e6i) q^{75} +(-212691. - 1.20623e6i) q^{76} +(-2.05352e6 + 1.72311e6i) q^{77} +(-3.53182e6 + 3.03615e6i) q^{78} +(2.58567e6 - 941106. i) q^{79} -1.99261e6 q^{80} +(-4.56751e6 - 1.41939e6i) q^{81} +5.29727e6 q^{82} +(639688. - 232827. i) q^{83} +(1.97462e6 - 1.69750e6i) q^{84} +(1.19407e7 - 1.00195e7i) q^{85} +(562003. + 3.18728e6i) q^{86} +(-2.96765e6 + 5.28489e6i) q^{87} +(1.20848e6 + 1.01403e6i) q^{88} +(-3.01913e6 + 5.22928e6i) q^{89} +(-7.92630e6 + 3.10126e6i) q^{90} +(-5.41546e6 - 9.37985e6i) q^{91} +(741369. - 4.20452e6i) q^{92} +(2.01489e6 - 1.22831e7i) q^{93} +(-2.17504e6 - 791650. i) q^{94} +(-8.74877e6 - 3.18429e6i) q^{95} +(-1.18557e6 - 970924. i) q^{96} +(2.27013e6 - 1.28746e7i) q^{97} +(-266419. - 461450. i) q^{98} +(6.38537e6 + 2.15282e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9} - 3000 q^{10} - 2523 q^{11} - 5376 q^{12} - 9924 q^{13} + 13416 q^{14} - 15084 q^{15} + 29478 q^{17} + 22848 q^{18} - 61731 q^{19} - 27264 q^{20}+ \cdots + 103927383 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more