LMFDB - Embedded newform 54.8.e.b.7.7

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			7.7
Character	$\chi$	$=$	54.7
Dual form			54.8.e.b.31.7

$q$-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} +(8.34949 + 46.0140i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-47.1028 - 267.133i) q^{5} +(188.669 + 323.066i) q^{6} +(-885.713 - 743.201i) q^{7} +(256.000 - 443.405i) q^{8} +(-2047.57 + 768.386i) q^{9} +(-1085.02 - 1879.30i) q^{10} +(-65.1109 + 369.262i) q^{11} +(2302.29 + 1912.44i) q^{12} +(-6752.16 - 2457.59i) q^{13} +(-8691.90 - 3163.59i) q^{14} +(11898.6 - 4397.81i) q^{15} +(711.263 - 4033.77i) q^{16} +(-7469.37 - 12937.3i) q^{17} +(-13290.3 + 11378.9i) q^{18} +(16538.6 - 28645.7i) q^{19} +(-13298.7 - 11159.0i) q^{20} +(26802.4 - 46960.5i) q^{21} +(520.887 + 2954.10i) q^{22} +(11898.9 - 9984.37i) q^{23} +(22540.3 + 8077.37i) q^{24} +(4272.10 - 1554.92i) q^{25} -57484.0 q^{26} +(-52452.7 - 87801.3i) q^{27} -73997.8 q^{28} +(-61044.3 + 22218.3i) q^{29} +(77414.9 - 65617.1i) q^{30} +(-144273. + 121060. i) q^{31} +(-5690.10 - 32270.2i) q^{32} +(-17534.9 + 87.1388i) q^{33} +(-91549.9 - 76819.5i) q^{34} +(-156814. + 271610. i) q^{35} +(-68775.8 + 121905. i) q^{36} +(4280.02 + 7413.22i) q^{37} +(45950.4 - 260598. i) q^{38} +(56706.2 - 331213. i) q^{39} +(-130506. - 47500.5i) q^{40} +(405912. + 147740. i) q^{41} +(72996.6 - 426363. i) q^{42} +(93410.2 - 529756. i) q^{43} +(11998.7 + 20782.3i) q^{44} +(301708. + 510781. i) q^{45} +(62131.7 - 107615. i) q^{46} +(254706. + 213724. i) q^{47} +(191549. - 951.894i) q^{48} +(89132.4 + 505495. i) q^{49} +(27861.2 - 23378.3i) q^{50} +(532932. - 451715. i) q^{51} +(-432138. + 157285. i) q^{52} -1.69085e6 q^{53} +(-634554. - 516531. i) q^{54} +101709. q^{55} +(-556282. + 202470. i) q^{56} +(1.45619e6 + 521831. i) q^{57} +(-398110. + 334054. i) q^{58} +(6005.45 + 34058.6i) q^{59} +(402430. - 705099. i) q^{60} +(2.62884e6 + 2.20586e6i) q^{61} +(-753342. + 1.30483e6i) q^{62} +(2.38463e6 + 841189. i) q^{63} +(-131072. - 227023. i) q^{64} +(-338457. + 1.91948e6i) q^{65} +(-131581. + 48633.3i) q^{66} +(2.29825e6 + 836493. i) q^{67} +(-898420. - 326998. i) q^{68} +(558770. + 464152. i) q^{69} +(-435688. + 2.47091e6i) q^{70} +(-2.32700e6 - 4.03048e6i) q^{71} +(-183472. + 1.10461e6i) q^{72} +(-3.20927e6 + 5.55862e6i) q^{73} +(52459.0 + 44018.3i) q^{74} +(107218. + 183594. i) q^{75} +(-367604. - 2.08478e6i) q^{76} +(332106. - 278670. i) q^{77} +(-479962. - 2.64507e6i) q^{78} +(583131. - 212242. i) q^{79} -1.11106e6 q^{80} +(3.60213e6 - 3.14665e6i) q^{81} +3.45570e6 q^{82} +(236435. - 86055.1i) q^{83} +(-617844. - 3.40493e6i) q^{84} +(-3.10416e6 + 2.60470e6i) q^{85} +(-747282. - 4.23805e6i) q^{86} +(-1.53204e6 - 2.62338e6i) q^{87} +(147064. + 123402. i) q^{88} +(5.51660e6 - 9.55503e6i) q^{89} +(3.66568e6 + 3.01430e6i) q^{90} +(4.15400e6 + 7.19493e6i) q^{91} +(172625. - 979004. i) q^{92} +(-6.77505e6 - 5.62781e6i) q^{93} +(2.49955e6 + 909762. i) q^{94} +(-8.43124e6 - 3.06872e6i) q^{95} +(1.43737e6 - 531264. i) q^{96} +(-878595. + 4.98276e6i) q^{97} +(2.05317e6 + 3.55620e6i) q^{98} +(-150417. - 806121. i) 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
$3$	8.34949	+	46.0140i	0.178540	+	0.983933i
$3$	8.34949	+	46.0140i	0.178540	+	0.983933i
$4$	49.0268	−	41.1384i	0.383022	−	0.321394i
$5$	−47.1028	−	267.133i	−0.168520	−	0.955724i	−0.945361	−	0.326027i	$-0.894290\pi$
$5$	−47.1028	−	267.133i	−0.168520	−	0.955724i	0.776841	−	0.629697i	$-0.216821\pi$
$6$	188.669	+	323.066i	0.356592	+	0.610608i
$7$	−885.713	−	743.201i	−0.976000	−	0.818961i	0.00748095	−	0.999972i	$-0.497619\pi$
$7$	−885.713	−	743.201i	−0.976000	−	0.818961i	−0.983481	+	0.181011i	$0.942063\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	−2047.57	+	768.386i	−0.936247	+	0.351343i
$10$	−1085.02	−	1879.30i	−0.343112	−	0.594288i
$11$	−65.1109	+	369.262i	−0.0147496	+	0.0836489i	−0.991294	−	0.131667i	$-0.957967\pi$
$11$	−65.1109	+	369.262i	−0.0147496	+	0.0836489i	0.976544	+	0.215316i	$0.0690781\pi$
$12$	2302.29	+	1912.44i	0.384615	+	0.319486i
$13$	−6752.16	−	2457.59i	−0.852395	−	0.310247i	−0.121379	−	0.992606i	$-0.538732\pi$
$13$	−6752.16	−	2457.59i	−0.852395	−	0.310247i	−0.731017	+	0.682360i	$0.760954\pi$
$14$	−8691.90	−	3163.59i	−0.846578	−	0.308129i
$15$	11898.6	−	4397.81i	0.910281	−	0.336447i
$16$	711.263	−	4033.77i	0.0434120	−	0.246202i
$17$	−7469.37	−	12937.3i	−0.368734	−	0.638665i	0.620634	−	0.784100i	$-0.286875\pi$
$17$	−7469.37	−	12937.3i	−0.368734	−	0.638665i	−0.989368	+	0.145435i	$0.953542\pi$
$18$	−13290.3	+	11378.9i	−0.537131	+	0.459881i
$19$	16538.6	−	28645.7i	0.553174	−	0.958126i	−0.444869	−	0.895596i	$-0.646750\pi$
$19$	16538.6	−	28645.7i	0.553174	−	0.958126i	0.998043	−	0.0625301i	$-0.0199169\pi$
$20$	−13298.7	−	11159.0i	−0.371711	−	0.311902i
$21$	26802.4	−	46960.5i	0.631548	−	1.10654i
$22$	520.887	+	2954.10i	0.0104295	+	0.0591487i
$23$	11898.9	−	9984.37i	0.203920	−	0.171109i	−0.535109	−	0.844783i	$-0.679729\pi$
$23$	11898.9	−	9984.37i	0.203920	−	0.171109i	0.739028	+	0.673674i	$0.235285\pi$
$24$	22540.3	+	8077.37i	0.332828	+	0.119270i
$25$	4272.10	−	1554.92i	0.0546829	−	0.0199029i
$26$	−57484.0			−0.641417
$27$	−52452.7	−	87801.3i	−0.512855	−	0.858475i
$28$	−73997.8			−0.637039
$29$	−61044.3	+	22218.3i	−0.464785	+	0.169168i	−0.563789	−	0.825919i	$-0.690657\pi$
$29$	−61044.3	+	22218.3i	−0.464785	+	0.169168i	0.0990034	+	0.995087i	$0.468435\pi$
$30$	77414.9	−	65617.1i	0.523480	−	0.443703i
$31$	−144273.	+	121060.i	−0.869802	+	0.729850i	−0.964056	−	0.265698i	$-0.914398\pi$
$31$	−144273.	+	121060.i	−0.869802	+	0.729850i	0.0942545	+	0.995548i	$0.469953\pi$
$32$	−5690.10	−	32270.2i	−0.0306970	−	0.174091i
$33$	−17534.9	+	87.1388i	−0.0849383	+	0.000422098i
$34$	−91549.9	−	76819.5i	−0.399468	−	0.335193i
$35$	−156814.	+	271610.i	−0.618226	+	1.07080i
$36$	−68775.8	+	121905.i	−0.245684	+	0.435476i
$37$	4280.02	+	7413.22i	0.0138912	+	0.0240603i	0.872887	−	0.487922i	$-0.162245\pi$
$37$	4280.02	+	7413.22i	0.0138912	+	0.0240603i	−0.858996	+	0.511982i	$0.828911\pi$
$38$	45950.4	−	260598.i	0.135846	−	0.770421i
$39$	56706.2	−	331213.i	0.153075	−	0.894091i
$40$	−130506.	−	47500.5i	−0.322420	−	0.117351i
$41$	405912.	+	147740.i	0.919790	+	0.334776i	0.758155	−	0.652074i	$-0.226101\pi$
$41$	405912.	+	147740.i	0.919790	+	0.334776i	0.161635	+	0.986851i	$0.448323\pi$
$42$	72996.6	−	426363.i	0.152030	−	0.887989i
$43$	93410.2	−	529756.i	0.179166	−	1.01610i	−0.754059	−	0.656806i	$-0.771907\pi$
$43$	93410.2	−	529756.i	0.179166	−	1.01610i	0.933225	−	0.359293i	$-0.116982\pi$
$44$	11998.7	+	20782.3i	0.0212348	+	0.0367798i
$45$	301708.	+	510781.i	0.493563	+	0.835586i
$46$	62131.7	−	107615.i	0.0941154	−	0.163013i
$47$	254706.	+	213724.i	0.357847	+	0.300269i	0.803932	−	0.594721i	$-0.202738\pi$
$47$	254706.	+	213724.i	0.357847	+	0.300269i	−0.446085	+	0.894991i	$0.647182\pi$
$48$	191549.	−	951.894i	0.249997	−	0.00124235i
$49$	89132.4	+	505495.i	0.108230	+	0.613805i
$50$	27861.2	−	23378.3i	0.0315213	−	0.0264495i
$51$	532932.	−	451715.i	0.562570	−	0.476836i
$52$	−432138.	+	157285.i	−0.426198	+	0.155123i
$53$	−1.69085e6			−1.56006			−0.780029	−	0.625743i	$-0.784796\pi$
$53$	−1.69085e6			−1.56006			−0.780029	+	0.625743i	$0.784796\pi$
$54$	−634554.	−	516531.i	−0.548391	−	0.446394i
$55$	101709.			0.0824309
$56$	−556282.	+	202470.i	−0.423289	+	0.154065i
$57$	1.45619e6	+	521831.i	1.04149	+	0.373222i
$58$	−398110.	+	334054.i	−0.267920	+	0.224812i
$59$	6005.45	+	34058.6i	0.00380683	+	0.0215896i	0.986652	−	0.162843i	$-0.0520664\pi$
$59$	6005.45	+	34058.6i	0.00380683	+	0.0215896i	−0.982845	+	0.184433i	$0.940955\pi$
$60$	402430.	−	705099.i	0.240526	−	0.421425i
$61$	2.62884e6	+	2.20586e6i	1.48289	+	1.24429i	0.903030	+	0.429577i	$0.141337\pi$
$61$	2.62884e6	+	2.20586e6i	1.48289	+	1.24429i	0.579861	+	0.814716i	$0.303107\pi$
$62$	−753342.	+	1.30483e6i	−0.401441	+	0.695316i
$63$	2.38463e6	+	841189.i	1.20151	+	0.423840i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−338457.	+	1.91948e6i	−0.152864	+	0.866938i
$66$	−131581.	+	48633.3i	−0.0563363	+	0.0208224i
$67$	2.29825e6	+	836493.i	0.933544	+	0.339782i	0.763613	−	0.645674i	$-0.223423\pi$
$67$	2.29825e6	+	836493.i	0.933544	+	0.339782i	0.169931	+	0.985456i	$0.445646\pi$
$68$	−898420.	−	326998.i	−0.346496	−	0.126114i
$69$	558770.	+	464152.i	0.204768	+	0.170094i
$70$	−435688.	+	2.47091e6i	−0.151821	+	0.861021i
$71$	−2.32700e6	−	4.03048e6i	−0.771600	−	1.33645i	−0.936686	−	0.350171i	$-0.886123\pi$
$71$	−2.32700e6	−	4.03048e6i	−0.771600	−	1.33645i	0.165086	−	0.986279i	$-0.447210\pi$
$72$	−183472.	+	1.10461e6i	−0.0579304	+	0.348775i
$73$	−3.20927e6	+	5.55862e6i	−0.965554	+	1.67239i	−0.257434	+	0.966296i	$0.582877\pi$
$73$	−3.20927e6	+	5.55862e6i	−0.965554	+	1.67239i	−0.708120	+	0.706092i	$0.750456\pi$
$74$	52459.0	+	44018.3i	0.0150490	+	0.0126276i
$75$	107218.	+	183594.i	0.0293462	+	0.0502508i
$76$	−367604.	−	2.08478e6i	−0.0960577	−	0.544770i
$77$	332106.	−	278670.i	0.0829008	−	0.0695621i
$78$	−479962.	−	2.64507e6i	−0.114519	−	0.631111i
$79$	583131.	−	212242.i	0.133067	−	0.0484326i	−0.274628	−	0.961551i	$-0.588555\pi$
$79$	583131.	−	212242.i	0.133067	−	0.0484326i	0.407695	+	0.913118i	$0.366333\pi$
$80$	−1.11106e6			−0.242617
$81$	3.60213e6	−	3.14665e6i	0.753117	−	0.657887i
$82$	3.45570e6			0.692130
$83$	236435.	−	86055.1i	0.0453876	−	0.0165197i	−0.319227	−	0.947678i	$-0.603423\pi$
$83$	236435.	−	86055.1i	0.0453876	−	0.0165197i	0.364614	+	0.931159i	$0.381201\pi$
$84$	−617844.	−	3.40493e6i	−0.113737	−	0.626803i
$85$	−3.10416e6	+	2.60470e6i	−0.548249	+	0.460035i
$86$	−747282.	−	4.23805e6i	−0.126689	−	0.718491i
$87$	−1.53204e6	−	2.62338e6i	−0.249433	−	0.427114i
$88$	147064.	+	123402.i	0.0230048	+	0.0193033i
$89$	5.51660e6	−	9.55503e6i	0.829481	−	1.43670i	−0.0689647	−	0.997619i	$-0.521970\pi$
$89$	5.51660e6	−	9.55503e6i	0.829481	−	1.43670i	0.898446	−	0.439084i	$-0.144697\pi$
$90$	3.66568e6	+	3.01430e6i	0.530036	+	0.435850i
$91$	4.15400e6	+	7.19493e6i	0.577858	+	1.00088i
$92$	172625.	−	979004.i	0.0231124	−	0.131077i
$93$	−6.77505e6	−	5.62781e6i	−0.873418	−	0.725519i
$94$	2.49955e6	+	909762.i	0.310395	+	0.112974i
$95$	−8.43124e6	−	3.06872e6i	−1.00892	−	0.367219i
$96$	1.43737e6	−	531264.i	0.165813	−	0.0612859i
$97$	−878595.	+	4.98276e6i	−0.0977435	+	0.554331i	0.896129	+	0.443795i	$0.146368\pi$
$97$	−878595.	+	4.98276e6i	−0.0977435	+	0.554331i	−0.993872	+	0.110536i	$0.964743\pi$
$98$	2.05317e6	+	3.55620e6i	0.220361	+	0.381676i
$99$	−150417.	−	806121.i	−0.0155802	−	0.0834982i
$100$	145481.	−	251980.i	0.0145481	−	0.0251980i
$101$	−1.34320e7	−	1.12708e7i	−1.29723	−	1.08850i	−0.990617	−	0.136667i	$-0.956361\pi$
$101$	−1.34320e7	−	1.12708e7i	−1.29723	−	1.08850i	−0.306610	−	0.951835i	$-0.599195\pi$
$102$	2.77037e6	−	4.85398e6i	0.258487	−	0.452895i
$103$	−2.34820e6	−	1.33173e7i	−0.211741	−	1.20084i	−0.886473	−	0.462780i	$-0.846852\pi$
$103$	−2.34820e6	−	1.33173e7i	−0.211741	−	1.20084i	0.674733	−	0.738062i	$-0.264259\pi$
$104$	−2.81826e6	+	2.36480e6i	−0.245677	+	0.206147i
$105$	−1.38072e7	−	4.94784e6i	−1.16397	−	0.417112i
$106$	−1.27111e7	+	4.62645e6i	−1.03660	+	0.377292i
$107$	−2.18222e7			−1.72209			−0.861043	−	0.508532i	$-0.830188\pi$
$107$	−2.18222e7			−1.72209			−0.861043	+	0.508532i	$0.830188\pi$
$108$	−6.18360e6	−	2.14680e6i	−0.472343	−	0.163987i
$109$	2.32300e7			1.71813			0.859067	−	0.511863i	$-0.171044\pi$
$109$	2.32300e7			1.71813			0.859067	+	0.511863i	$0.171044\pi$
$110$	764602.	−	278292.i	0.0547723	−	0.0199355i
$111$	−305376.	+	258837.i	−0.0211936	+	0.0179637i
$112$	−3.62788e6	+	3.04415e6i	−0.244000	+	0.204740i
$113$	910099.	+	5.16143e6i	0.0593354	+	0.336508i	0.999996	−	0.00284108i	$-0.000904345\pi$
$113$	910099.	+	5.16143e6i	0.0593354	+	0.336508i	−0.940661	+	0.339349i	$0.889793\pi$
$114$	1.23748e7	−	61496.1i	0.782297	−	0.00388759i
$115$	−3.22763e6	−	2.70830e6i	−0.197898	−	0.166056i
$116$	−2.07878e6	+	3.60056e6i	−0.123654	+	0.214174i
$117$	1.57139e7	−	156183.i	0.907055	−	0.00901538i
$118$	138336.	+	239605.i	0.00775083	+	0.0134248i
$119$	−2.99932e6	+	1.70100e7i	−0.163158	+	0.925316i
$120$	1.09602e6	−	6.40172e6i	0.0579009	−	0.338191i
$121$	1.81798e7	+	6.61692e6i	0.932913	+	0.339553i
$122$	2.57980e7	+	9.38969e6i	1.28625	+	0.468157i
$123$	−3.40894e6	+	1.99112e7i	−0.165178	+	0.964782i
$124$	−2.09306e6	+	1.18704e7i	−0.0985840	+	0.559098i
$125$	−1.12125e7	−	1.94205e7i	−0.513471	−	0.889357i
$126$	2.02282e7	−	201051.i	0.900865	−	0.00895385i
$127$	1.85688e7	−	3.21621e7i	0.804398	−	1.39326i	−0.112300	−	0.993674i	$-0.535822\pi$
$127$	1.85688e7	−	3.21621e7i	0.804398	−	1.39326i	0.916697	−	0.399583i	$-0.130845\pi$
$128$	−1.60651e6	−	1.34802e6i	−0.0677094	−	0.0568149i
$129$	2.51561e7	−	125012.i	1.03176	−	0.00512730i
$130$	2.70766e6	+	1.53559e7i	0.108092	+	0.613017i
$131$	−5.07232e6	+	4.25618e6i	−0.197132	+	0.165413i	−0.736010	−	0.676970i	$-0.763293\pi$
$131$	−5.07232e6	+	4.25618e6i	−0.197132	+	0.165413i	0.538879	+	0.842383i	$0.318848\pi$
$132$	−856094.	+	725629.i	−0.0323976	+	0.0274603i
$133$	−3.59380e7	+	1.30804e7i	−1.32457	+	0.482103i
$134$	1.95659e7			0.702480
$135$	−2.09840e7	+	1.81475e7i	−0.734039	+	0.634818i
$136$	−7.64863e6			−0.260734
$137$	3.74739e7	−	1.36394e7i	1.24511	−	0.453183i	0.366363	−	0.930472i	$-0.380603\pi$
$137$	3.74739e7	−	1.36394e7i	1.24511	−	0.453183i	0.878746	+	0.477289i	$0.158381\pi$
$138$	5.47057e6	+	1.96039e6i	0.177197	+	0.0634989i
$139$	−1.63674e7	+	1.37338e7i	−0.516924	+	0.433751i	−0.863558	−	0.504250i	$-0.831769\pi$
$139$	−1.63674e7	+	1.37338e7i	−0.516924	+	0.433751i	0.346634	+	0.938001i	$0.387325\pi$
$140$	3.48550e6	+	1.97673e7i	0.107354	+	0.608833i
$141$	−7.70763e6	+	1.35045e7i	−0.231555	+	0.405707i
$142$	−2.85214e7	−	2.39323e7i	−0.835913	−	0.701414i
$143$	1.34713e6	−	2.33330e6i	0.0385243	−	0.0667260i
$144$	1.64313e6	+	8.80596e6i	0.0458568	+	0.245758i
$145$	8.81060e6	+	1.52604e7i	0.240004	+	0.415698i
$146$	−8.91655e6	+	5.05682e7i	−0.237116	+	1.34475i
$147$	−2.25156e7	+	8.32196e6i	−0.584620	+	0.216080i
$148$	514804.	+	187373.i	0.0130535	+	0.00475107i
$149$	5.32679e6	+	1.93879e6i	0.131921	+	0.0480153i	0.407137	−	0.913367i	$-0.366527\pi$
$149$	5.32679e6	+	1.93879e6i	0.131921	+	0.0480153i	−0.275216	+	0.961382i	$0.588749\pi$
$150$	1.30836e6	+	1.08681e6i	0.0316524	+	0.0262926i
$151$	1.67565e6	−	9.50308e6i	0.0396063	−	0.224618i	−0.958580	−	0.284824i	$-0.908065\pi$
$151$	1.67565e6	−	9.50308e6i	0.0396063	−	0.224618i	0.998186	+	0.0602062i	$0.0191758\pi$
$152$	−8.46778e6	−	1.46666e7i	−0.195577	−	0.338749i
$153$	2.52349e7	+	2.07507e7i	0.569616	+	0.468397i
$154$	1.73413e6	−	3.00361e6i	0.0382613	−	0.0662705i
$155$	3.91347e7	+	3.28379e7i	0.844115	+	0.708296i
$156$	−1.08455e7	−	1.85712e7i	−0.228724	−	0.391654i
$157$	−4.70057e6	−	2.66583e7i	−0.0969398	−	0.549773i	−0.994136	−	0.108140i	$-0.965510\pi$
$157$	−4.70057e6	−	2.66583e7i	−0.0969398	−	0.549773i	0.897196	−	0.441633i	$-0.145601\pi$
$158$	3.80298e6	−	3.19108e6i	0.0767052	−	0.0643633i
$159$	−1.41178e7	−	7.78030e7i	−0.278533	−	1.53499i
$160$	−8.35241e6	+	3.04003e6i	−0.161210	+	0.0586756i
$161$	−1.79594e7			−0.339158
$162$	1.84694e7	−	3.35111e7i	0.341312	−	0.619279i
$163$	1.96581e7			0.355537			0.177769	−	0.984072i	$-0.443112\pi$
$163$	1.96581e7			0.355537			0.177769	+	0.984072i	$0.443112\pi$
$164$	2.59784e7	−	9.45536e6i	0.459895	−	0.167388i
$165$	849218.	+	4.68004e6i	0.0147172	+	0.0811065i
$166$	1.54195e6	−	1.29385e6i	0.0261632	−	0.0219535i
$167$	−5.20011e6	−	2.94913e7i	−0.0863983	−	0.489989i	−0.997046	−	0.0768056i	$-0.975528\pi$
$167$	−5.20011e6	−	2.94913e7i	−0.0863983	−	0.489989i	0.910648	−	0.413183i	$-0.135583\pi$
$168$	−1.39611e7	−	2.39062e7i	−0.227163	−	0.388981i
$169$	−8.51620e6	−	7.14594e6i	−0.135719	−	0.113882i
$170$	−1.62088e7	+	2.80744e7i	−0.253034	+	0.438268i
$171$	−1.18530e7	+	7.13623e7i	−0.181277	+	1.09140i
$172$	−1.72137e7	−	2.98150e7i	−0.257944	−	0.446771i
$173$	−6.16652e6	+	3.49721e7i	−0.0905480	+	0.513523i	0.905473	+	0.424404i	$0.139516\pi$
$173$	−6.16652e6	+	3.49721e7i	−0.0905480	+	0.513523i	−0.996021	+	0.0891193i	$0.971595\pi$
$174$	−1.86952e7	−	1.55295e7i	−0.269034	−	0.223478i
$175$	−4.93947e6	−	1.79782e6i	−0.0696703	−	0.0253579i
$176$	1.44321e6	+	525285.i	0.0199542	+	0.00726274i
$177$	−1.51703e6	+	560707.i	−0.0205631	+	0.00760027i
$178$	1.53272e7	−	8.69247e7i	0.203700	−	1.15524i
$179$	−1.79446e7	−	3.10810e7i	−0.233856	−	0.405051i	0.725083	−	0.688661i	$-0.241801\pi$
$179$	−1.79446e7	−	3.10810e7i	−0.233856	−	0.405051i	−0.958940	+	0.283610i	$0.908468\pi$
$180$	3.58045e7	+	1.26302e7i	0.457598	+	0.161420i
$181$	5.52270e7	−	9.56559e7i	0.692271	−	1.19905i	−0.278821	−	0.960343i	$-0.589944\pi$
$181$	5.52270e7	−	9.56559e7i	0.692271	−	1.19905i	0.971092	−	0.238705i	$-0.0767230\pi$
$182$	5.09143e7	+	4.27222e7i	0.626023	+	0.525296i
$183$	−7.95508e7	+	1.39381e8i	−0.959545	+	1.68122i
$184$	−1.38100e6	−	7.83203e6i	−0.0163430	−	0.0926856i
$185$	1.77871e6	−	1.49252e6i	0.0206540	−	0.0173308i
$186$	−6.63303e7	−	2.37696e7i	−0.755817	−	0.270849i
$187$	5.26360e6	−	1.91579e6i	0.0588623	−	0.0214241i
$188$	2.12797e7			0.233568
$189$	−1.87960e7	+	1.16750e8i	−0.202512	+	1.25788i
$190$	−7.17787e7			−0.759203
$191$	7.52342e7	−	2.73830e7i	0.781265	−	0.284357i	0.0795651	−	0.996830i	$-0.474647\pi$
$191$	7.52342e7	−	2.73830e7i	0.781265	−	0.284357i	0.701700	+	0.712472i	$0.252425\pi$
$192$	9.35186e6	−	7.92667e6i	0.0953551	−	0.0808233i
$193$	5.63231e7	−	4.72607e7i	0.563944	−	0.473205i	−0.315686	−	0.948864i	$-0.602235\pi$
$193$	5.63231e7	−	4.72607e7i	0.563944	−	0.473205i	0.879630	+	0.475659i	$0.157790\pi$
$194$	7.02876e6	+	3.98621e7i	0.0691151	+	0.391971i
$195$	−9.11491e7	+	452962.i	−0.880301	+	0.00437462i
$196$	2.51651e7	+	2.11161e7i	0.238728	+	0.200316i
$197$	8.76572e7	−	1.51827e8i	0.816875	−	1.41487i	−0.0910981	−	0.995842i	$-0.529038\pi$
$197$	8.76572e7	−	1.51827e8i	0.816875	−	1.41487i	0.907973	−	0.419028i	$-0.137629\pi$
$198$	−3.33644e6	−	5.64849e6i	−0.0305461	−	0.0517135i
$199$	−7.11533e7	−	1.23241e8i	−0.640043	−	1.10859i	−0.985423	−	0.170124i	$-0.945583\pi$
$199$	−7.11533e7	−	1.23241e8i	−0.640043	−	1.10859i	0.345380	−	0.938463i	$-0.387750\pi$
$200$	404200.	−	2.29233e6i	0.00357265	−	0.0202615i
$201$	−1.93012e7	+	1.12736e8i	−0.167648	+	0.979209i
$202$	−1.31814e8	−	4.79765e7i	−1.12521	−	0.409542i
$203$	7.05804e7	+	2.56892e7i	0.592173	+	0.215533i
$204$	7.54514e6	−	4.40702e7i	0.0622246	−	0.363445i
$205$	2.03466e7	−	1.15392e8i	0.164951	−	0.935482i
$206$	−5.40910e7	−	9.36883e7i	−0.431111	−	0.746707i
$207$	−1.66920e7	+	2.95867e7i	−0.130801	+	0.231846i
$208$	−1.47159e7	+	2.54887e7i	−0.113388	+	0.196393i
$209$	9.50095e6	+	7.97224e6i	0.0719871	+	0.0604044i
$210$	−1.17334e8	+	583087.i	−0.874292	+	0.00434476i
$211$	4.18598e7	+	2.37399e8i	0.306767	+	1.73976i	0.615070	+	0.788472i	$0.289128\pi$
$211$	4.18598e7	+	2.37399e8i	0.306767	+	1.73976i	−0.308304	+	0.951288i	$0.599761\pi$
$212$	−8.28973e7	+	6.95591e7i	−0.597537	+	0.501393i
$213$	1.66029e8	−	1.40727e8i	1.17722	−	0.997812i
$214$	−1.64049e8	+	5.97090e7i	−1.14426	+	0.416477i
$215$	−1.45915e8			−1.00130
$216$	−5.23594e7	+	780646.i	−0.353514	+	0.00527067i
$217$	2.17757e8			1.44665
$218$	1.74633e8	−	6.35611e7i	1.14164	−	0.415522i
$219$	−2.82570e8	−	1.01260e8i	−1.81791	−	0.651452i
$220$	4.98647e6	−	4.18415e6i	0.0315729	−	0.0264928i
$221$	1.86398e7	+	1.05712e8i	0.116163	+	0.658794i
$222$	−1.58745e6	+	2.78138e6i	−0.00973790	+	0.0170618i
$223$	1.13291e7	+	9.50628e6i	0.0684117	+	0.0574042i	0.676352	−	0.736578i	$-0.263560\pi$
$223$	1.13291e7	+	9.50628e6i	0.0684117	+	0.0574042i	−0.607941	+	0.793982i	$0.708004\pi$
$224$	−1.89434e7	+	3.28110e7i	−0.112614	+	0.195053i
$225$	−7.55266e6	+	6.46643e6i	−0.0442040	+	0.0378465i
$226$	2.09642e7	+	3.63111e7i	0.120809	+	0.209247i
$227$	4.35485e7	−	2.46976e8i	0.247106	−	1.40141i	−0.568445	−	0.822721i	$-0.692455\pi$
$227$	4.35485e7	−	2.46976e8i	0.247106	−	1.40141i	0.815551	−	0.578685i	$-0.196434\pi$
$228$	9.28599e7	−	3.43218e7i	0.518867	−	0.191778i
$229$	2.48842e8	+	9.05711e7i	1.36930	+	0.498385i	0.918918	−	0.394449i	$-0.129065\pi$
$229$	2.48842e8	+	9.05711e7i	1.36930	+	0.498385i	0.450385	+	0.892835i	$0.351287\pi$
$230$	−3.16742e7	−	1.15284e7i	−0.171655	−	0.0624775i
$231$	1.55956e7	+	1.29548e7i	0.0832455	+	0.0691492i
$232$	−5.77563e6	+	3.27553e7i	−0.0303663	+	0.172216i
$233$	−1.46302e7	−	2.53403e7i	−0.0757713	−	0.131240i	0.825650	−	0.564182i	$-0.190809\pi$
$233$	−1.46302e7	−	2.53403e7i	−0.0757713	−	0.131240i	−0.901421	+	0.432943i	$0.857475\pi$
$234$	1.17703e8	−	4.41699e7i	0.600524	−	0.225357i
$235$	4.50954e7	−	7.81075e7i	0.226670	−	0.392604i
$236$	1.69555e6	+	1.42273e6i	0.00839687	+	0.00704581i
$237$	1.46350e7	+	2.50601e7i	0.0714122	+	0.122282i
$238$	2.39946e7	+	1.36080e8i	0.115370	+	0.654297i
$239$	−2.64534e8	+	2.21970e8i	−1.25340	+	1.05173i	−0.257045	+	0.966399i	$0.582749\pi$
$239$	−2.64534e8	+	2.21970e8i	−1.25340	+	1.05173i	−0.996353	+	0.0853262i	$0.972807\pi$
$240$	−9.27675e6	−	5.11241e7i	−0.0433168	−	0.238719i
$241$	−2.07203e8	+	7.54159e7i	−0.953536	+	0.347059i	−0.771497	−	0.636232i	$-0.780492\pi$
$241$	−2.07203e8	+	7.54159e7i	−0.953536	+	0.347059i	−0.182039	+	0.983291i	$0.558270\pi$
$242$	1.54773e8			0.702005
$243$	1.74866e8	+	1.39476e8i	0.781778	+	0.623557i
$244$	2.19629e8			0.967888
$245$	1.30836e8	−	4.76204e7i	0.568389	−	0.206877i
$246$	2.88533e7	+	1.59011e8i	0.123573	+	0.681010i
$247$	−1.82071e8	+	1.52776e8i	−0.768778	+	0.645082i
$248$	1.67445e7	+	9.49629e7i	0.0697094	+	0.395342i
$249$	5.93385e6	+	1.01608e7i	0.0243578	+	0.0417089i
$250$	−1.37428e8	−	1.15316e8i	−0.556269	−	0.466765i
$251$	−5.58238e7	+	9.66896e7i	−0.222824	+	0.385942i	−0.955664	−	0.294458i	$-0.904861\pi$
$251$	−5.58238e7	+	9.66896e7i	−0.222824	+	0.385942i	0.732841	+	0.680400i	$0.238194\pi$
$252$	1.51516e8	−	5.68589e7i	0.596426	−	0.223819i
$253$	2.91210e6	+	5.04391e6i	0.0113054	+	0.0195815i
$254$	5.15910e7	−	2.92587e8i	0.197540	−	1.12031i
$255$	−1.45771e8	−	1.21087e8i	−0.550528	−	0.457305i
$256$	−1.57654e7	−	5.73815e6i	−0.0587308	−	0.0213763i
$257$	2.60641e8	+	9.48656e7i	0.957805	+	0.348612i	0.773173	−	0.634195i	$-0.218668\pi$
$257$	2.60641e8	+	9.48656e7i	0.957805	+	0.348612i	0.184632	+	0.982808i	$0.440891\pi$
$258$	1.88770e8	−	6.97709e7i	0.684327	−	0.252933i
$259$	1.71864e6	−	9.74690e6i	0.00614662	−	0.0348592i
$260$	6.23711e7	+	1.08030e8i	0.220078	+	0.381186i
$261$	1.07920e8	−	9.23992e7i	0.375718	−	0.321682i
$262$	−2.64858e7	+	4.58747e7i	−0.0909825	+	0.157586i
$263$	−1.50518e8	−	1.26299e8i	−0.510202	−	0.428110i	0.350998	−	0.936376i	$-0.385842\pi$
$263$	−1.50518e8	−	1.26299e8i	−0.510202	−	0.428110i	−0.861200	+	0.508266i	$0.830287\pi$
$264$	−4.45029e6	+	7.79735e6i	−0.0148859	+	0.0260816i
$265$	7.96439e7	+	4.51683e8i	0.262901	+	1.49099i
$266$	−2.34376e8	+	1.96665e8i	−0.763531	+	0.640679i
$267$	4.85726e8	+	1.74061e8i	1.56171	+	0.559645i
$268$	1.47088e8	−	5.35356e7i	0.466772	−	0.169891i
$269$	−1.79222e8			−0.561383			−0.280691	−	0.959798i	$-0.590564\pi$
$269$	−1.79222e8			−0.561383			−0.280691	+	0.959798i	$0.590564\pi$
$270$	−1.08093e8	+	1.93840e8i	−0.334215	+	0.599337i
$271$	−1.33173e7			−0.0406466			−0.0203233	−	0.999793i	$-0.506470\pi$
$271$	−1.33173e7			−0.0406466			−0.0203233	+	0.999793i	$0.506470\pi$
$272$	−5.74989e7	+	2.09279e7i	−0.173248	+	0.0630571i
$273$	−2.96384e8	+	2.51216e8i	−0.881627	+	0.747270i
$274$	2.44392e8	−	2.05069e8i	0.717729	−	0.602246i
$275$	296012.	+	1.67877e6i	0.000858312	+	0.00486773i
$276$	4.64892e7	−	231026.i	0.133098	−	0.000661424i
$277$	−3.07314e8	−	2.57867e8i	−0.868767	−	0.728982i	0.0950710	−	0.995470i	$-0.469692\pi$
$277$	−3.07314e8	−	2.57867e8i	−0.868767	−	0.728982i	−0.963838	+	0.266488i	$0.914137\pi$
$278$	−8.54643e7	+	1.48028e8i	−0.238577	+	0.413227i
$279$	2.02390e8	−	3.58736e8i	0.557922	−	0.988919i
$280$	8.02888e7	+	1.39064e8i	0.218576	+	0.378584i
$281$	−5.96845e7	+	3.38487e8i	−0.160468	+	0.910061i	0.793146	+	0.609031i	$0.208441\pi$
$281$	−5.96845e7	+	3.38487e8i	−0.160468	+	0.910061i	−0.953615	+	0.301030i	$0.902670\pi$
$282$	−2.09918e7	+	1.22610e8i	−0.0557414	+	0.325578i
$283$	−1.01270e8	−	3.68592e7i	−0.265600	−	0.0966704i	0.205788	−	0.978597i	$-0.434024\pi$
$283$	−1.01270e8	−	3.68592e7i	−0.265600	−	0.0966704i	−0.471387	+	0.881926i	$0.656247\pi$
$284$	−2.79893e8	−	1.01873e8i	−0.725067	−	0.263903i
$285$	7.08075e7	−	4.13577e8i	0.181185	−	1.05828i
$286$	3.74283e6	−	2.12267e7i	0.00946062	−	0.0536538i
$287$	−2.49721e8	−	4.32530e8i	−0.623546	−	1.08001i
$288$	3.64469e7	+	6.17033e7i	0.0899055	+	0.152207i
$289$	9.35864e7	−	1.62096e8i	0.228071	−	0.395031i
$290$	1.07989e8	+	9.06135e7i	0.260008	+	0.218173i
$291$	−2.36613e8	+	1.17584e6i	−0.562875	+	0.00279719i
$292$	7.13324e7	+	4.04546e8i	0.167667	+	0.950885i
$293$	−5.98575e8	+	5.02264e8i	−1.39021	+	1.16653i	−0.424960	+	0.905212i	$0.639712\pi$
$293$	−5.98575e8	+	5.02264e8i	−1.39021	+	1.16653i	−0.965253	+	0.261316i	$0.915844\pi$
$294$	−1.46492e8	+	1.24167e8i	−0.336200	+	0.284964i
$295$	8.81531e6	−	3.20851e6i	0.0199922	−	0.00727656i
$296$	4.38274e6			0.00982257
$297$	3.58369e7	−	1.36520e7i	0.0793749	−	0.0302376i
$298$	4.53492e7			0.0992688
$299$	−1.04881e8	+	3.81735e7i	−0.226906	+	0.0825872i
$300$	1.28093e7	+	4.59025e6i	0.0273906	+	0.00981548i
$301$	−4.76450e8	+	3.99789e8i	−1.00701	+	0.844983i
$302$	−1.34052e7	−	7.60246e7i	−0.0280059	−	0.158829i
$303$	4.06463e8	−	7.12165e8i	0.839406	−	1.47073i
$304$	−1.03787e8	−	8.70877e7i	−0.211878	−	0.177787i
$305$	4.65431e8	−	8.06151e8i	0.939304	−	1.62692i
$306$	2.46482e8	+	8.69478e7i	0.491768	+	0.173474i
$307$	−3.61739e8	−	6.26551e8i	−0.713529	−	1.23587i	−0.963524	−	0.267621i	$-0.913763\pi$
$307$	−3.61739e8	−	6.26551e8i	−0.713529	−	1.23587i	0.249996	−	0.968247i	$-0.419571\pi$
$308$	4.81807e6	−	2.73246e7i	0.00939605	−	0.0532876i
$309$	5.93176e8	−	2.19243e8i	1.14374	−	0.422737i
$310$	3.84047e8	+	1.39782e8i	0.732181	+	0.266492i
$311$	−5.67292e8	−	2.06478e8i	−1.06941	−	0.389235i	−0.253456	−	0.967347i	$-0.581567\pi$
$311$	−5.67292e8	−	2.06478e8i	−1.06941	−	0.389235i	−0.815957	+	0.578112i	$0.803790\pi$
$312$	−1.32345e8	−	1.09934e8i	−0.246698	−	0.204924i
$313$	−3.21569e7	+	1.82371e8i	−0.0592746	+	0.336163i	−0.999995	−	0.00301883i	$-0.999039\pi$
$313$	−3.21569e7	+	1.82371e8i	−0.0592746	+	0.336163i	0.940721	+	0.339182i	$0.110150\pi$
$314$	−1.08278e8	−	1.87543e8i	−0.197373	−	0.341859i
$315$	1.12387e8	−	6.76635e8i	0.202595	−	1.21974i
$316$	1.98578e7	−	3.43947e7i	0.0354018	−	0.0613178i
$317$	6.62113e8	+	5.55579e8i	1.16741	+	0.979576i	0.999980	−	0.00630766i	$-0.00200780\pi$
$317$	6.62113e8	+	5.55579e8i	1.16741	+	0.979576i	0.167433	+	0.985883i	$0.446452\pi$
$318$	−3.19012e8	−	5.46258e8i	−0.556305	−	0.952584i
$319$	−4.22973e6	−	2.39880e7i	−0.00729534	−	0.0413739i
$320$	−5.44716e7	+	4.57071e7i	−0.0929277	+	0.0779756i
$321$	−1.82204e8	−	1.00412e9i	−0.307461	−	1.69442i
$322$	−1.35011e8	+	4.91398e7i	−0.225358	+	0.0820235i
$323$	−4.94132e8			−0.815895
$324$	4.71530e7	−	3.02456e8i	0.0770197	−	0.494032i
$325$	−3.26673e7			−0.0527863
$326$	1.47781e8	−	5.37878e7i	0.236241	−	0.0859849i
$327$	1.93959e8	+	1.06891e9i	0.306756	+	1.69053i
$328$	1.69422e8	−	1.42162e8i	0.265101	−	0.222446i
$329$	−6.67568e7	−	3.78596e8i	−0.103350	−	0.586126i
$330$	1.91894e7	+	3.28588e7i	0.0293942	+	0.0503330i
$331$	3.22134e8	+	2.70303e8i	0.488246	+	0.409687i	0.853397	−	0.521261i	$-0.174538\pi$
$331$	3.22134e8	+	2.70303e8i	0.488246	+	0.409687i	−0.365151	+	0.930948i	$0.618983\pi$
$332$	8.05147e6	−	1.39456e7i	0.0120751	−	0.0209147i
$333$	−1.44599e7	−	1.18904e7i	−0.0214590	−	0.0176458i
$334$	−1.19785e8	−	2.07474e8i	−0.175910	−	0.304685i
$335$	1.15201e8	−	6.53339e8i	0.167417	−	0.949471i
$336$	−1.70365e8	−	1.41516e8i	−0.245014	−	0.203525i
$337$	6.12644e8	+	2.22984e8i	0.871975	+	0.317373i	0.738966	−	0.673742i	$-0.235314\pi$
$337$	6.12644e8	+	2.22984e8i	0.871975	+	0.317373i	0.133008	+	0.991115i	$0.457536\pi$
$338$	−8.35733e7	−	3.04182e7i	−0.117722	−	0.0428474i
$339$	−2.29899e8	+	8.49725e7i	−0.320507	+	0.118462i
$340$	−4.50340e7	+	2.55400e8i	−0.0621390	+	0.352408i
$341$	−3.53090e7	−	6.11570e7i	−0.0482220	−	0.0835230i
$342$	1.06153e8	+	5.68901e8i	0.143496	+	0.769033i
$343$	−1.79358e8	+	3.10657e8i	−0.239989	+	0.415673i
$344$	−2.10983e8	−	1.77036e8i	−0.279443	−	0.234481i
$345$	9.76706e7	−	1.71129e8i	0.128055	−	0.224366i
$346$	4.93322e7	+	2.79777e8i	0.0640271	+	0.363116i
$347$	−3.15678e8	+	2.64885e8i	−0.405594	+	0.340334i	−0.822651	−	0.568547i	$-0.807506\pi$
$347$	−3.15678e8	+	2.64885e8i	−0.405594	+	0.340334i	0.417057	+	0.908880i	$0.363061\pi$
$348$	−1.83033e8	−	6.55903e7i	−0.232810	−	0.0834281i
$349$	−1.99943e8	+	7.27735e7i	−0.251778	+	0.0916398i	−0.464826	−	0.885402i	$-0.653883\pi$
$349$	−1.99943e8	+	7.27735e7i	−0.251778	+	0.0916398i	0.213048	+	0.977042i	$0.431661\pi$
$350$	−4.20518e7			−0.0524260
$351$	1.38390e8	+	7.21756e8i	0.170816	+	0.890872i
$352$	1.22866e7			0.0150153
$353$	−2.33435e8	+	8.49633e7i	−0.282458	+	0.102806i	−0.479364	−	0.877616i	$-0.659133\pi$
$353$	−2.33435e8	+	8.49633e7i	−0.282458	+	0.102806i	0.196906	+	0.980422i	$0.436911\pi$
$354$	−9.87015e6	+	8.36597e6i	−0.0118253	+	0.0100232i
$355$	−9.67067e8	+	8.11466e8i	−1.14725	+	0.962655i
$356$	−1.22617e8	−	6.95397e8i	−0.144038	−	0.816879i
$357$	−8.07741e8	+	4.01404e6i	−0.939579	+	0.00466920i
$358$	−2.19942e8	−	1.84553e8i	−0.253348	−	0.212584i
$359$	−4.16415e8	+	7.21251e8i	−0.475002	+	0.822727i	−0.999590	−	0.0286288i	$-0.990886\pi$
$359$	−4.16415e8	+	7.21251e8i	−0.475002	+	0.822727i	0.524588	+	0.851356i	$0.324219\pi$
$360$	3.03720e8	−	3.01872e6i	0.343095	−	0.00341008i
$361$	−1.00117e8	−	1.73407e8i	−0.112003	−	0.193995i
$362$	1.53441e8	−	8.70207e8i	0.170005	−	0.964145i
$363$	−1.52678e8	+	8.91774e8i	−0.167535	+	0.978547i
$364$	4.99645e8	+	1.81856e8i	0.543009	+	0.197639i
$365$	1.63606e9	+	5.95476e8i	1.76106	+	0.640972i
$366$	−2.16657e8	+	1.26547e9i	−0.230988	+	1.34917i
$367$	−2.69874e7	+	1.53053e8i	−0.0284990	+	0.161626i	−0.995736	−	0.0922496i	$-0.970594\pi$
$367$	−2.69874e7	+	1.53053e8i	−0.0284990	+	0.161626i	0.967237	+	0.253875i	$0.0817053\pi$
$368$	−3.18114e7	−	5.50990e7i	−0.0332748	−	0.0576337i
$369$	−9.44656e8	+	9.38910e6i	−0.978772	+	0.00972818i
$370$	9.28778e6	−	1.60869e7i	0.00953248	−	0.0165107i
$371$	1.49761e9	+	1.25665e9i	1.52262	+	1.27763i
$372$	−5.63678e8	+	2.80118e6i	−0.567716	+	0.00282124i
$373$	−7.36198e7	−	4.17519e8i	−0.0734538	−	0.416577i	−0.999256	−	0.0385686i	$-0.987720\pi$
$373$	−7.36198e7	−	4.17519e8i	−0.0734538	−	0.416577i	0.925802	−	0.378008i	$-0.123391\pi$
$374$	3.43274e7	−	2.88041e7i	0.0339305	−	0.0284711i
$375$	7.99998e8	−	6.78081e8i	0.783393	−	0.664006i
$376$	1.59971e8	−	5.82247e7i	0.155197	−	0.0564872i
$377$	4.66785e8			0.448665
$378$	1.78146e8	+	9.29099e8i	0.169650	+	0.884791i
$379$	1.65343e9			1.56008			0.780042	−	0.625727i	$-0.215198\pi$
$379$	1.65343e9			1.56008			0.780042	+	0.625727i	$0.215198\pi$
$380$	−5.39599e8	+	1.96398e8i	−0.504462	+	0.183609i
$381$	1.63495e9	+	5.85887e8i	1.51449	+	0.542721i
$382$	4.90652e8	−	4.11706e8i	0.450352	−	0.377890i
$383$	1.24834e8	+	7.07966e8i	0.113537	+	0.643898i	0.987464	+	0.157842i	$0.0504536\pi$
$383$	1.24834e8	+	7.07966e8i	0.113537	+	0.643898i	−0.873928	+	0.486056i	$0.838435\pi$
$384$	4.86144e7	−	8.51773e7i	0.0438132	−	0.0767652i
$385$	−9.00850e7	−	7.55903e7i	−0.0804526	−	0.0675077i
$386$	2.94098e8	−	5.09393e8i	0.260278	−	0.450814i
$387$	2.15793e8	+	1.15649e9i	0.189256	+	1.01427i
$388$	1.61908e8	+	2.80433e8i	0.140721	+	0.243735i
$389$	−1.20993e8	+	6.86184e8i	−0.104216	+	0.591040i	0.887314	+	0.461165i	$0.152569\pi$
$389$	−1.20993e8	+	6.86184e8i	−0.104216	+	0.591040i	−0.991530	+	0.129874i	$0.958543\pi$
$390$	−6.83977e8	+	2.52804e8i	−0.583869	+	0.215803i
$391$	−2.18048e8	−	7.93631e7i	−0.184474	−	0.0671429i
$392$	2.46957e8	+	8.98850e7i	0.207071	+	0.0753678i
$393$	−2.38195e8	−	1.97861e8i	−0.197952	−	0.164432i
$394$	2.43544e8	−	1.38121e9i	0.200605	−	1.13769i
$395$	−8.41641e7	−	1.45776e8i	−0.0687127	−	0.119014i
$396$	−4.05370e7	−	3.33337e7i	−0.0328034	−	0.0269743i
$397$	3.89397e8	−	6.74455e8i	0.312338	−	0.540986i	−0.666530	−	0.745478i	$-0.732221\pi$
$397$	3.89397e8	−	6.74455e8i	0.312338	−	0.540986i	0.978868	+	0.204492i	$0.0655544\pi$
$398$	−8.72105e8	−	7.31783e8i	−0.693391	−	0.581824i
$399$	−9.01944e8	−	1.54444e9i	−0.710844	−	1.21721i
$400$	−3.23360e6	−	1.83386e7i	−0.00252625	−	0.0143271i
$401$	8.40258e8	−	7.05060e8i	0.650740	−	0.546036i	−0.256555	−	0.966530i	$-0.582588\pi$
$401$	8.40258e8	−	7.05060e8i	0.650740	−	0.546036i	0.907295	+	0.420494i	$0.138143\pi$
$402$	1.63366e8	+	9.00307e8i	0.125421	+	0.691193i
$403$	1.27167e9	−	4.62851e8i	0.967849	−	0.352268i
$404$	−1.12219e9			−0.846705
$405$	−1.01025e9	−	8.14033e8i	−0.755674	−	0.608905i
$406$	6.00881e8			0.445602
$407$	−3.01610e6	+	1.09777e6i	−0.00221751	+	0.000807106i
$408$	−6.38622e7	−	3.51944e8i	−0.0465514	−	0.256545i
$409$	−8.68015e8	+	7.28351e8i	−0.627329	+	0.526392i	−0.900098	−	0.435688i	$-0.856505\pi$
$409$	−8.68015e8	+	7.28351e8i	−0.627329	+	0.526392i	0.272769	+	0.962080i	$0.412061\pi$
$410$	−1.62773e8	−	9.23132e8i	−0.116638	−	0.661486i
$411$	9.40491e8	+	1.61044e9i	0.668203	+	1.14419i
$412$	−6.62977e8	−	5.56304e8i	−0.467045	−	0.391897i
$413$	1.99933e7	−	3.46294e7i	0.0139656	−	0.0241891i
$414$	−4.45290e7	+	2.68091e8i	−0.0308420	+	0.185687i
$415$	−3.41249e7	−	5.91060e7i	−0.0234370	−	0.0405942i
$416$	−4.08862e7	+	2.31877e8i	−0.0278452	+	0.157918i
$417$	−7.68608e8	−	6.38457e8i	−0.519073	−	0.431177i
$418$	9.32371e7	+	3.39355e7i	0.0624413	+	0.0227268i
$419$	2.82036e9	+	1.02653e9i	1.87308	+	0.681744i	0.964540	+	0.263938i	$0.0850214\pi$
$419$	2.82036e9	+	1.02653e9i	1.87308	+	0.681744i	0.908536	+	0.417806i	$0.137201\pi$
$420$	−8.80468e8	+	3.25428e8i	−0.579884	+	0.214330i
$421$	−2.33815e8	+	1.32603e9i	−0.152716	+	0.866098i	0.808128	+	0.589008i	$0.200481\pi$
$421$	−2.33815e8	+	1.32603e9i	−0.152716	+	0.866098i	−0.960844	+	0.277090i	$0.910630\pi$
$422$	9.64243e8	+	1.67012e9i	0.624587	+	1.08182i
$423$	−6.85752e8	−	2.41903e8i	−0.440531	−	0.155399i
$424$	−4.32859e8	+	7.49734e8i	−0.275782	+	0.477668i
$425$	−5.20264e7	−	4.36553e7i	−0.0328747	−	0.0275852i
$426$	8.63080e8	−	1.51220e9i	0.540901	−	0.947713i
$427$	−6.88999e8	−	3.90751e9i	−0.428274	−	2.42886i
$428$	−1.06987e9	+	8.97729e8i	−0.659597	+	0.553468i
$429$	1.18612e8	+	4.25051e7i	0.0725320	+	0.0259920i
$430$	−1.09692e9	+	3.99247e8i	−0.665329	+	0.242160i
$431$	2.95586e8			0.177833			0.0889167	−	0.996039i	$-0.471660\pi$
$431$	2.95586e8			0.177833			0.0889167	+	0.996039i	$0.471660\pi$
$432$	−3.91478e8	+	1.49132e8i	−0.233622	+	0.0889977i
$433$	−1.08732e9			−0.643652			−0.321826	−	0.946799i	$-0.604297\pi$
$433$	−1.08732e9			−0.643652			−0.321826	+	0.946799i	$0.604297\pi$
$434$	1.63699e9	−	5.95817e8i	0.961243	−	0.349864i
$435$	−6.28628e8	+	5.32827e8i	−0.366169	+	0.310366i
$436$	1.13890e9	−	9.55647e8i	0.658084	−	0.552198i
$437$	−8.92181e7	−	5.05981e8i	−0.0511408	−	0.290034i
$438$	−2.40129e9	+	1.19331e7i	−1.36548	+	0.00678571i
$439$	−8.63992e7	−	7.24975e7i	−0.0487398	−	0.0408976i	0.618092	−	0.786105i	$-0.287906\pi$
$439$	−8.63992e7	−	7.24975e7i	−0.0487398	−	0.0408976i	−0.666832	+	0.745208i	$0.732350\pi$
$440$	2.60375e7	−	4.50983e7i	0.0145719	−	0.0252392i
$441$	−5.70920e8	−	9.66549e8i	−0.316986	−	0.536647i
$442$	4.29369e8	+	7.43689e8i	0.236512	+	0.409651i
$443$	−1.81646e8	+	1.03016e9i	−0.0992687	+	0.562981i	0.894087	+	0.447894i	$0.147826\pi$
$443$	−1.81646e8	+	1.03016e9i	−0.0992687	+	0.562981i	−0.993355	+	0.115087i	$0.963285\pi$
$444$	−4.32344e6	+	2.52526e7i	−0.00234417	+	0.0136920i
$445$	−2.81231e9	−	1.02360e9i	−1.51288	−	0.550642i
$446$	1.11178e8	+	4.04655e7i	0.0593399	+	0.0215980i
$447$	−4.47356e7	+	2.61295e8i	−0.0236907	+	0.138374i
$448$	−5.26319e7	+	2.98490e8i	−0.0276552	+	0.156840i
$449$	−4.61747e8	−	7.99770e8i	−0.240737	−	0.416968i	0.720188	−	0.693779i	$-0.244056\pi$
$449$	−4.61747e8	−	7.99770e8i	−0.240737	−	0.416968i	−0.960924	+	0.276811i	$0.910722\pi$
$450$	−3.90842e7	+	6.92770e7i	−0.0202189	+	0.0358381i
$451$	−8.09841e7	+	1.40269e8i	−0.0415702	+	0.0720017i
$452$	2.56952e8	+	2.15609e8i	0.130878	+	0.109820i
$453$	4.51265e8	−	2.24255e6i	0.228081	−	0.00113344i
$454$	−3.48388e8	−	1.97581e9i	−0.174730	−	0.990944i
$455$	1.72634e9	−	1.44857e9i	0.859184	−	0.720941i
$456$	6.04168e8	−	5.12095e8i	0.298388	−	0.252914i
$457$	−2.10691e9	+	7.66853e8i	−1.03262	+	0.375842i	−0.802077	−	0.597220i	$-0.796272\pi$
$457$	−2.10691e9	+	7.66853e8i	−1.03262	+	0.375842i	−0.230541	+	0.973063i	$0.574050\pi$
$458$	2.11850e9			1.03038
$459$	−7.44126e8	+	1.33442e9i	−0.359172	+	0.644091i
$460$	−2.69655e8			−0.129169
$461$	−1.89076e9	+	6.88181e8i	−0.898842	+	0.327152i	−0.749789	−	0.661677i	$-0.769845\pi$
$461$	−1.89076e9	+	6.88181e8i	−0.898842	+	0.327152i	−0.149053	+	0.988829i	$0.547623\pi$
$462$	1.52687e8	+	5.47158e7i	0.0720369	+	0.0258146i
$463$	1.91428e9	−	1.60627e9i	0.896339	−	0.752118i	−0.0731323	−	0.997322i	$-0.523300\pi$
$463$	1.91428e9	−	1.60627e9i	0.896339	−	0.752118i	0.969471	+	0.245204i	$0.0788551\pi$
$464$	4.62051e7	+	2.62042e8i	0.0214722	+	0.121775i
$465$	−1.18425e9	+	2.07492e9i	−0.546208	+	0.957011i
$466$	−1.79318e8	−	1.50466e8i	−0.0820869	−	0.0688791i
$467$	−1.88042e8	+	3.25698e8i	−0.0854369	+	0.147981i	−0.905577	−	0.424181i	$-0.860562\pi$
$467$	−1.88042e8	+	3.25698e8i	−0.0854369	+	0.147981i	0.820140	+	0.572162i	$0.193895\pi$
$468$	7.63978e8	−	6.54103e8i	0.344525	−	0.294975i
$469$	−1.41390e9	−	2.44895e9i	−0.632871	−	1.09616i
$470$	1.25292e8	−	7.10564e8i	0.0556647	−	0.315690i
$471$	1.18741e9	−	4.38875e8i	0.523632	−	0.193539i
$472$	1.66392e7	+	6.05616e6i	0.00728340	+	0.00265094i
$473$	1.89537e8	+	6.89857e7i	0.0823530	+	0.0299740i
$474$	1.78587e8	+	1.48347e8i	0.0770241	+	0.0639813i
$475$	2.61129e7	−	1.48094e8i	0.0111796	−	0.0634029i
$476$	5.52717e8	+	9.57334e8i	0.234898	+	0.406855i
$477$	3.46215e9	−	1.29923e9i	1.46060	−	0.548115i
$478$	−1.38130e9	+	2.39248e9i	−0.578482	+	1.00196i
$479$	−2.95902e9	−	2.48292e9i	−1.23020	−	1.03226i	−0.998226	−	0.0595341i	$-0.981039\pi$
$479$	−2.95902e9	−	2.48292e9i	−1.23020	−	1.03226i	−0.231970	−	0.972723i	$-0.574517\pi$
$480$	−2.09622e8	−	3.58945e8i	−0.0865153	−	0.148144i
$481$	−1.06808e7	−	6.05738e7i	−0.00437618	−	0.0248186i
$482$	−1.35131e9	+	1.13388e9i	−0.549655	+	0.461216i
$483$	−1.49952e8	−	8.26384e8i	−0.0605532	−	0.333708i
$484$	1.16351e9	−	4.23483e8i	0.466457	−	0.169776i
$485$	1.37244e9			0.546259
$486$	1.69619e9	+	5.70052e8i	0.670266	+	0.225262i
$487$	6.75381e8			0.264971			0.132485	−	0.991185i	$-0.457704\pi$
$487$	6.75381e8			0.264971			0.132485	+	0.991185i	$0.457704\pi$
$488$	1.65107e9	−	6.00940e8i	0.643126	−	0.234079i
$489$	1.64135e8	+	9.04548e8i	0.0634776	+	0.349825i
$490$	8.53268e8	−	7.15977e8i	0.327642	−	0.274924i
$491$	−4.57178e8	−	2.59279e9i	−0.174301	−	0.988512i	−0.938947	−	0.344061i	$-0.888197\pi$
$491$	−4.57178e8	−	2.59279e9i	−0.174301	−	0.988512i	0.764646	−	0.644451i	$-0.222914\pi$
$492$	6.51985e8	+	1.11642e9i	0.246808	+	0.422620i
$493$	7.43408e8	+	6.23793e8i	0.279424	+	0.234464i
$494$	−9.50707e8	+	1.64667e9i	−0.354815	+	0.614558i
$495$	−2.08257e8	+	7.81518e7i	−0.0771757	+	0.0289615i
$496$	3.85711e8	+	6.68071e8i	0.141931	+	0.245831i
$497$	−9.34406e8	+	5.29928e9i	−0.341420	+	1.93629i
$498$	7.24095e7	+	6.01481e7i	0.0262720	+	0.0218232i
$499$	−1.46143e9	−	5.31916e8i	−0.526532	−	0.191642i	0.0650570	−	0.997882i	$-0.479277\pi$
$499$	−1.46143e9	−	5.31916e8i	−0.526532	−	0.191642i	−0.591589	+	0.806239i	$0.701499\pi$
$500$	−1.34864e9	−	4.90865e8i	−0.482505	−	0.175617i
$501$	1.31359e9	−	4.85515e8i	0.466691	−	0.172493i
$502$	−1.55099e8	+	8.79611e8i	−0.0547200	+	0.310333i
$503$	−1.38509e9	−	2.39904e9i	−0.485276	−	0.840523i	0.514581	−	0.857442i	$-0.327948\pi$
$503$	−1.38509e9	−	2.39904e9i	−0.485276	−	0.840523i	−0.999857	+	0.0169188i	$0.994614\pi$
$504$	9.83452e8	−	8.42011e8i	0.342173	−	0.292962i
$505$	−2.37812e9	+	4.11902e9i	−0.821700	+	1.42323i
$506$	3.56928e7	+	2.99498e7i	0.0122477	+	0.0102770i
$507$	2.57707e8	−	4.51529e8i	0.0878210	−	0.153871i
$508$	−4.12728e8	−	2.34070e9i	−0.139682	−	0.792177i
$509$	6.99423e7	−	5.86886e7i	0.0235086	−	0.0197261i	−0.630958	−	0.775817i	$-0.717338\pi$
$509$	6.99423e7	−	5.86886e7i	0.0235086	−	0.0197261i	0.654466	+	0.756091i	$0.272893\pi$
$510$	−1.42715e9	−	5.11423e8i	−0.476402	−	0.170720i
$511$	6.97367e9	−	2.53821e9i	2.31200	−	0.841500i
$512$	−1.34218e8			−0.0441942
$513$	−3.38263e9	+	5.04329e7i	−1.10623	+	0.0164931i
$514$	2.21895e9			0.720736
$515$	−3.44688e9	+	1.25456e9i	−1.11199	+	0.404732i
$516$	1.22818e9	−	1.04101e9i	0.393540	−	0.333566i
$517$	−9.55044e7	+	8.01377e7i	−0.0303953	+	0.0255047i
$518$	−1.37491e7	−	7.79752e7i	−0.00434631	−	0.0246492i
$519$	−1.66069e9	+	8.25275e6i	−0.521439	+	0.00259127i
$520$	7.64464e8	+	6.41461e8i	0.238421	+	0.200059i
$521$	−9.88611e8	+	1.71233e9i	−0.306262	+	0.530462i	−0.977542	−	0.210743i	$-0.932412\pi$
$521$	−9.88611e8	+	1.71233e9i	−0.306262	+	0.530462i	0.671279	+	0.741205i	$0.265745\pi$
$522$	5.58477e8	−	9.89903e8i	0.171854	−	0.304611i
$523$	−2.43382e9	−	4.21551e9i	−0.743932	−	1.28853i	−0.950692	−	0.310136i	$-0.899625\pi$
$523$	−2.43382e9	−	4.21551e9i	−0.743932	−	1.28853i	0.206760	−	0.978392i	$-0.433708\pi$
$524$	−7.35873e7	+	4.17334e8i	−0.0223431	+	0.126714i
$525$	4.14828e7	−	2.42296e8i	0.0125115	−	0.0730783i
$526$	−1.47710e9	−	5.37619e8i	−0.442546	−	0.161074i
$527$	2.64382e9	+	9.62272e8i	0.786855	+	0.286392i
$528$	−1.21204e7	+	7.07936e7i	−0.00358342	+	0.0209303i
$529$	−5.49345e8	+	3.11549e9i	−0.161343	+	0.915023i
$530$	1.83460e9	+	3.17763e9i	0.535275	+	0.927123i
$531$	−3.84668e7	−	6.51230e7i	−0.0111495	−	0.0188757i
$532$	−1.22382e9	+	2.11972e9i	−0.352393	+	0.610363i
$533$	−2.37770e9	−	1.99513e9i	−0.680162	−	0.570723i
$534$	4.12772e9	−	2.05126e7i	1.17305	−	0.00582942i
$535$	1.02788e9	+	5.82942e9i	0.290206	+	1.64584i
$536$	9.59256e8	−	8.04912e8i	0.269065	−	0.225773i
$537$	1.28033e9	−	1.08521e9i	0.356790	−	0.302417i
$538$	−1.34731e9	+	4.90381e8i	−0.373018	+	0.135767i
$539$	−1.92464e8			−0.0529405
$540$	−2.82217e8	+	1.75296e9i	−0.0771268	+	0.479065i
$541$	3.94730e9			1.07179			0.535895	−	0.844285i	$-0.319974\pi$
$541$	3.94730e9			1.07179			0.535895	+	0.844285i	$0.319974\pi$
$542$	−1.00114e8	+	3.64384e7i	−0.0270082	+	0.00983018i
$543$	4.86262e9	+	1.74253e9i	1.30338	+	0.467070i
$544$	−3.74988e8	+	3.14653e8i	−0.0998669	+	0.0837983i
$545$	−1.09420e9	−	6.20551e9i	−0.289540	−	1.64206i
$546$	−1.54071e9	+	2.69948e9i	−0.405085	+	0.709751i
$547$	5.44064e9	+	4.56524e9i	1.42133	+	1.19264i	0.950623	+	0.310347i	$0.100445\pi$
$547$	5.44064e9	+	4.56524e9i	1.42133	+	1.19264i	0.470706	+	0.882290i	$0.343999\pi$
$548$	1.27613e9	−	2.21031e9i	0.331254	−	0.573749i
$549$	−7.07768e9	−	2.49669e9i	−1.82553	−	0.643963i
$550$	6.81866e6	+	1.18103e7i	0.00174755	+	0.00302685i
$551$	−3.73129e8	+	2.11612e9i	−0.0950230	+	0.538902i
$552$	3.48852e8	−	1.28939e8i	0.0882785	−	0.0326285i
$553$	−6.74226e8	−	2.45398e8i	−0.169538	−	0.0617069i
$554$	−3.01581e9	−	1.09767e9i	−0.753564	−	0.274275i
$555$	8.35280e7	+	6.93839e7i	0.0207399	+	0.0172279i
$556$	−2.37451e8	+	1.34665e9i	−0.0585886	+	0.332272i
$557$	1.01645e9	+	1.76055e9i	0.249227	+	0.431673i	0.963311	−	0.268386i	$-0.0864903\pi$
$557$	1.01645e9	+	1.76055e9i	0.249227	+	0.431673i	−0.714085	+	0.700059i	$0.753157\pi$
$558$	5.39912e8	−	3.25059e9i	0.131554	−	0.792030i
$559$	−1.93264e9	+	3.34743e9i	−0.467961	+	0.810533i
$560$	9.84077e8	+	8.25739e8i	0.236794	+	0.198694i
$561$	1.32102e8	+	2.26203e8i	0.0315892	+	0.0540915i
$562$	4.77476e8	+	2.70790e9i	0.113468	+	0.643510i
$563$	3.75688e9	−	3.15239e9i	0.887253	−	0.744494i	−0.0804039	−	0.996762i	$-0.525621\pi$
$563$	3.75688e9	−	3.15239e9i	0.887253	−	0.744494i	0.967657	+	0.252268i	$0.0811766\pi$
$564$	1.77675e8	+	9.79164e8i	0.0417012	+	0.229815i
$565$	1.33592e9	−	4.86235e8i	0.311610	−	0.113417i
$566$	−8.62153e8			−0.199860
$567$	−5.52905e9	+	1.09919e8i	−1.27383	+	0.0253240i
$568$	−2.38285e9			−0.545604
$569$	1.15244e9	−	4.19455e8i	0.262257	−	0.0954536i	−0.207546	−	0.978225i	$-0.566548\pi$
$569$	1.15244e9	−	4.19455e8i	0.262257	−	0.0954536i	0.469802	+	0.882772i	$0.344325\pi$
$570$	−5.99315e8	−	3.30282e9i	−0.135548	−	0.747005i
$571$	2.84767e9	−	2.38948e9i	0.640122	−	0.537126i	−0.263934	−	0.964541i	$-0.585020\pi$
$571$	2.84767e9	−	2.38948e9i	0.640122	−	0.537126i	0.904056	+	0.427415i	$0.140576\pi$
$572$	−2.99427e7	−	1.69813e8i	−0.00668967	−	0.0379390i
$573$	1.88817e9	+	3.23319e9i	0.419276	+	0.717943i
$574$	−3.06076e9	−	2.56828e9i	−0.675519	−	0.566828i
$575$	3.53085e7	−	6.11561e7i	0.00774536	−	0.0134154i
$576$	4.42821e8	+	3.64133e8i	0.0965494	+	0.0793928i
$577$	−1.04697e9	−	1.81341e9i	−0.226892	−	0.392989i	0.729993	−	0.683454i	$-0.239523\pi$
$577$	−1.04697e9	−	1.81341e9i	−0.226892	−	0.392989i	−0.956885	+	0.290465i	$0.906190\pi$
$578$	2.60018e8	−	1.47463e9i	0.0560087	−	0.317641i
$579$	2.64492e9	+	2.19705e9i	0.566288	+	0.470397i
$580$	1.05975e9	+	3.85716e8i	0.225530	+	0.0820860i
$581$	−2.73369e8	−	9.94983e7i	−0.0578274	−	0.0210474i
$582$	−1.77553e9	+	6.56249e8i	−0.373333	+	0.137987i
$583$	1.10093e8	−	6.24369e8i	0.0230102	−	0.130497i
$584$	1.64315e9	+	2.84601e9i	0.341375	+	0.591278i
$585$	−7.81890e8	−	4.19035e9i	−0.161473	−	0.865376i
$586$	−3.12553e9	+	5.41358e9i	−0.641627	+	1.11133i
$587$	−3.03667e9	−	2.54807e9i	−0.619676	−	0.519970i	0.278025	−	0.960574i	$-0.410320\pi$
$587$	−3.03667e9	−	2.54807e9i	−0.619676	−	0.519970i	−0.897702	+	0.440604i	$0.854764\pi$
$588$	−7.61518e8	+	1.33426e9i	−0.154475	+	0.270657i
$589$	1.08176e9	+	6.13498e9i	0.218137	+	1.23711i
$590$	5.74904e7	−	4.82402e7i	0.0115243	−	0.00967001i
$591$	7.71804e9	+	2.76578e9i	1.53798	+	0.551140i
$592$	3.29474e7	−	1.19919e7i	0.00652673	−	0.00237554i
$593$	1.75462e8			0.0345534			0.0172767	−	0.999851i	$-0.494500\pi$
$593$	1.75462e8			0.0345534			0.0172767	+	0.999851i	$0.494500\pi$
$594$	2.32052e8	−	2.00685e8i	0.0454289	−	0.0392882i
$595$	4.68521e9			0.911842
$596$	3.40915e8	−	1.24083e8i	0.0659605	−	0.0240076i
$597$	5.07672e9	−	4.30304e9i	0.976502	−	0.827686i
$598$	−6.83997e8	+	5.73941e8i	−0.130798	+	0.109752i
$599$	−1.64719e8	−	9.34167e8i	−0.0313148	−	0.177595i	0.965139	−	0.261738i	$-0.0842957\pi$
$599$	−1.64719e8	−	9.34167e8i	−0.0313148	−	0.177595i	−0.996454	+	0.0841434i	$0.973185\pi$
$600$	1.08854e8	−	540946.i	0.0205738	−	0.000102241i
$601$	6.64628e9	+	5.57689e9i	1.24887	+	1.04793i	0.996777	+	0.0802254i	$0.0255640\pi$
$601$	6.64628e9	+	5.57689e9i	1.24887	+	1.04793i	0.252095	+	0.967702i	$0.418880\pi$
$602$	−2.48784e9	+	4.30907e9i	−0.464767	+	0.805001i
$603$	−5.34858e9	+	5.31604e7i	−0.993408	+	0.00987365i
$604$	−3.08790e8	−	5.34839e8i	−0.0570208	−	0.0987630i
$605$	9.11277e8	−	5.16811e9i	0.167304	−	0.948829i
$606$	1.10701e9	−	6.46588e9i	0.202067	−	1.18025i
$607$	1.15615e9	+	4.20805e8i	0.209824	+	0.0763697i	0.444794	−	0.895633i	$-0.353277\pi$
$607$	1.15615e9	+	4.20805e8i	0.209824	+	0.0763697i	−0.234970	+	0.972003i	$0.575499\pi$
$608$	−1.01851e9	−	3.70707e8i	−0.183782	−	0.0668911i
$609$	−5.92751e8	+	3.46218e9i	−0.106344	+	0.621139i
$610$	1.29314e9	−	7.33377e9i	0.230670	−	1.30820i
$611$	−1.19457e9	−	2.06906e9i	−0.211870	−	0.366969i
$612$	2.09084e9	−	2.07812e7i	0.368715	−	0.00366472i
$613$	−1.01842e9	+	1.76396e9i	−0.178573	+	0.309297i	−0.941392	−	0.337315i	$-0.890481\pi$
$613$	−1.01842e9	+	1.76396e9i	−0.178573	+	0.309297i	0.762819	+	0.646612i	$0.223815\pi$
$614$	−4.43373e9	−	3.72034e9i	−0.773001	−	0.648625i
$615$	5.47951e9	−	2.72302e7i	0.949902	−	0.00472050i
$616$	−3.85445e7	−	2.18597e8i	−0.00664401	−	0.0376800i
$617$	−7.45389e8	+	6.25456e8i	−0.127757	+	0.107201i	−0.704427	−	0.709776i	$-0.748796\pi$
$617$	−7.45389e8	+	6.25456e8i	−0.127757	+	0.107201i	0.576670	+	0.816977i	$0.304352\pi$
$618$	3.85934e9	−	3.27119e9i	0.657738	−	0.557501i
$619$	3.92964e8	−	1.43027e8i	0.0665940	−	0.0242382i	−0.308508	−	0.951222i	$-0.599830\pi$
$619$	3.92964e8	−	1.43027e8i	0.0665940	−	0.0242382i	0.375102	+	0.926983i	$0.377608\pi$
$620$	3.26955e9			0.550957
$621$	−1.50077e9	−	5.21033e8i	−0.251474	−	0.0873061i
$622$	−4.82960e9			−0.804720
$623$	−1.19874e10	+	4.36307e9i	−1.98618	+	0.722910i
$624$	−1.29571e9	−	4.64320e8i	−0.213482	−	0.0765017i
$625$	−4.38765e9	+	3.68167e9i	−0.718872	+	0.603206i
$626$	2.57255e8	+	1.45897e9i	0.0419135	+	0.237703i
$627$	−2.87506e8	+	5.03740e8i	−0.0465813	+	0.0816151i
$628$	−1.32713e9	−	1.11360e9i	−0.213824	−	0.179419i
$629$	6.39381e7	−	1.10744e8i	0.0102443	−	0.0177437i
$630$	−1.00651e9	−	5.39414e9i	−0.160371	−	0.859469i
$631$	4.53071e8	+	7.84741e8i	0.0717899	+	0.124344i	0.899686	−	0.436538i	$-0.143796\pi$
$631$	4.53071e8	+	7.84741e8i	0.0717899	+	0.124344i	−0.827896	+	0.560882i	$0.810462\pi$
$632$	5.51723e7	−	3.12897e8i	0.00869383	−	0.0493051i
$633$	−1.05741e10	+	3.90829e9i	−1.65704	+	0.612454i
$634$	6.49761e9	+	2.36494e9i	1.01261	+	0.368559i
$635$	−9.46620e9	−	3.44542e9i	−1.46713	−	0.533990i
$636$	−3.89284e9	−	3.23365e9i	−0.600021	−	0.498417i
$637$	6.40461e8	−	3.63223e9i	0.0981758	−	0.556783i
$638$	−9.74323e7	−	1.68758e8i	−0.0148536	−	0.0257271i
$639$	7.86167e9	+	6.46467e9i	1.19196	+	0.980152i
$640$	−2.84430e8	+	4.92648e8i	−0.0428890	+	0.0742860i
$641$	2.39360e8	+	2.00847e8i	0.0358962	+	0.0301205i	0.660559	−	0.750774i	$-0.270319\pi$
$641$	2.39360e8	+	2.00847e8i	0.0358962	+	0.0301205i	−0.624663	+	0.780894i	$0.714764\pi$
$642$	−4.11717e9	−	7.05001e9i	−0.614082	−	1.05152i
$643$	−1.52282e9	−	8.63632e9i	−0.225896	−	1.28112i	−0.860965	−	0.508665i	$-0.830139\pi$
$643$	−1.52282e9	−	8.63632e9i	−0.225896	−	1.28112i	0.635068	−	0.772456i	$-0.280972\pi$
$644$	−8.80493e8	+	7.38822e8i	−0.129905	+	0.109003i
$645$	−1.21832e9	−	6.71414e9i	−0.178773	−	0.985215i
$646$	−3.71466e9	+	1.35203e9i	−0.542132	+	0.197320i
$647$	−1.15304e10			−1.67370			−0.836851	−	0.547431i	$-0.815606\pi$
$647$	−1.15304e10			−1.67370			−0.836851	+	0.547431i	$0.815606\pi$
$648$	−4.73095e8	−	2.40275e9i	−0.0683024	−	0.346893i
$649$	−1.29676e7			−0.00186210
$650$	−2.45578e8	+	8.93829e7i	−0.0350745	+	0.0127661i
$651$	1.81816e9	+	1.00198e10i	0.258284	+	1.42340i
$652$	9.63776e8	−	8.08704e8i	0.136179	−	0.114268i
$653$	−5.85633e8	−	3.32129e9i	−0.0823056	−	0.466778i	−0.997906	−	0.0646878i	$-0.979395\pi$
$653$	−5.85633e8	−	3.32129e9i	−0.0823056	−	0.466778i	0.915600	−	0.402090i	$-0.131716\pi$
$654$	4.38279e9	+	7.50485e9i	0.612673	+	1.04911i
$655$	1.37589e9	+	1.15451e9i	0.191310	+	0.160528i
$656$	8.84660e8	−	1.53228e9i	0.122353	−	0.211921i
$657$	2.30005e9	−	1.38476e10i	0.316416	−	1.90501i
$658$	−1.53775e9	−	2.66346e9i	−0.210424	−	0.364464i
$659$	1.25450e9	−	7.11463e9i	0.170754	−	0.968397i	−0.772176	−	0.635408i	$-0.780832\pi$
$659$	1.25450e9	−	7.11463e9i	0.170754	−	0.968397i	0.942931	−	0.332988i	$-0.108057\pi$
$660$	2.34164e8	+	1.94512e8i	0.0317041	+	0.0263356i
$661$	−9.69908e9	−	3.53018e9i	−1.30625	−	0.475435i	−0.407221	−	0.913330i	$-0.633502\pi$
$661$	−9.69908e9	−	3.53018e9i	−1.30625	−	0.475435i	−0.899027	+	0.437894i	$0.855724\pi$
$662$	3.16125e9	+	1.15060e9i	0.423502	+	0.154142i
$663$	−4.70857e9	+	1.74033e9i	−0.627469	+	0.231918i
$664$	2.23700e7	−	1.26866e8i	0.00296536	−	0.0168174i
$665$	5.18698e9	+	8.98412e9i	0.683973	+	1.18468i
$666$	−1.41237e8	−	4.98219e7i	−0.0185263	−	0.00653523i
$667$	−5.04525e8	+	8.73863e8i	−0.0658328	+	0.114026i
$668$	−1.46817e9	−	1.23194e9i	−0.190572	−	0.159909i
$669$	−3.42829e8	+	6.00672e8i	−0.0442677	+	0.0775614i
$670$	−9.21610e8	−	5.22671e9i	−0.118382	−	0.671377i
$671$	−9.85705e8	+	8.27105e8i	−0.125956	+	0.105689i
$672$	−1.66793e9	−	5.97708e8i	−0.212025	−	0.0759796i
$673$	1.32040e9	−	4.80587e8i	0.166976	−	0.0607742i	−0.257180	−	0.966364i	$-0.582793\pi$
$673$	1.32040e9	−	4.80587e8i	0.166976	−	0.0607742i	0.424155	+	0.905589i	$0.360571\pi$
$674$	5.21570e9			0.656150
$675$	−3.60607e8	−	2.93537e8i	−0.0451306	−	0.0367366i
$676$	−7.11495e8			−0.0885846
$677$	1.23967e10	−	4.51202e9i	1.53548	−	0.558870i	0.570527	−	0.821279i	$-0.306739\pi$
$677$	1.23967e10	−	4.51202e9i	1.53548	−	0.558870i	0.964957	+	0.262409i	$0.0845169\pi$
$678$	−1.49578e9	+	1.26783e9i	−0.184316	+	0.156227i
$679$	4.48138e9	−	3.76032e9i	0.549373	−	0.460979i
$680$	3.60272e8	+	2.04320e9i	0.0439389	+	0.249190i
$681$	1.17279e10	−	5.82816e7i	1.42301	−	0.00707158i
$682$	−4.32773e8	−	3.63139e8i	−0.0522413	−	0.0438357i
$683$	4.77711e9	−	8.27420e9i	0.573710	−	0.993695i	−0.422470	−	0.906377i	$-0.638837\pi$
$683$	4.77711e9	−	8.27420e9i	0.573710	−	0.993695i	0.996180	−	0.0873186i	$-0.0278298\pi$
$684$	2.35461e9	+	3.98628e9i	0.281335	+	0.476290i
$685$	−5.40866e9	−	9.36807e9i	−0.642943	−	1.11361i
$686$	−4.98323e8	+	2.82613e9i	−0.0589354	+	0.334240i
$687$	−2.08983e9	+	1.22064e10i	−0.245902	+	1.43628i
$688$	−2.07047e9	−	7.53591e8i	−0.242388	−	0.0882219i
$689$	1.14169e10	+	4.15542e9i	1.32979	+	0.484003i
$690$	2.66007e8	−	1.55371e9i	0.0308263	−	0.180052i
$691$	7.55701e8	−	4.28579e9i	0.0871319	−	0.494149i	−0.909744	−	0.415169i	$-0.863722\pi$
$691$	7.55701e8	−	4.28579e9i	0.0871319	−	0.494149i	0.996876	−	0.0789803i	$-0.0251664\pi$
$692$	1.13637e9	+	1.96825e9i	0.130361	+	0.225792i
$693$	−4.65884e8	+	8.25782e8i	−0.0531755	+	0.0942539i
$694$	−1.64835e9	+	2.85503e9i	−0.187194	+	0.324230i
$695$	4.43971e9	+	3.72536e9i	0.501658	+	0.420941i
$696$	−1.55542e9	+	7.72962e6i	−0.174870	+	0.000869012i
$697$	−1.12055e9	−	6.35494e9i	−0.125348	−	0.710881i
$698$	−1.30396e9	+	1.09415e9i	−0.145135	+	0.121782i
$699$	1.04385e9	−	8.84772e8i	0.115603	−	0.0979854i
$700$	−3.16126e8	+	1.15061e8i	−0.0348351	+	0.0126790i
$701$	1.79337e10			1.96633			0.983166	−	0.182716i	$-0.0584890\pi$
$701$	1.79337e10			1.96633			0.983166	+	0.182716i	$0.0584890\pi$
$702$	3.01519e9	+	5.04717e9i	0.328954	+	0.550640i
$703$	2.83143e8			0.0307370
$704$	9.23654e7	−	3.36182e7i	0.00997711	−	0.00363137i
$705$	3.97056e9	+	1.42286e9i	0.426766	+	0.152933i
$706$	−1.52238e9	+	1.27743e9i	−0.162820	+	0.136622i
$707$	3.52043e9	+	1.99654e10i	0.374652	+	2.12476i
$708$	−5.13086e7	+	8.98979e7i	−0.00543343	+	0.00951991i
$709$	7.76991e9	+	6.51973e9i	0.818755	+	0.687017i	0.952680	−	0.303974i	$-0.0983136\pi$
$709$	7.76991e9	+	6.51973e9i	0.818755	+	0.687017i	−0.133925	+	0.990991i	$0.542758\pi$
$710$	−5.04967e9	+	8.74628e9i	−0.529491	+	0.917105i
$711$	−1.03092e9	+	8.82652e8i	−0.107568	+	0.0920971i
$712$	−2.82450e9	−	4.89218e9i	−0.293266	−	0.507951i
$713$	−5.07991e8	+	2.88096e9i	−0.0524859	+	0.297662i
$714$	−6.06124e9	+	2.24028e9i	−0.623186	+	0.230335i
$715$	−6.86756e8	−	2.49959e8i	−0.0702637	−	0.0255739i
$716$	−2.15839e9	−	7.85590e8i	−0.219753	−	0.0799835i
$717$	−1.24225e10	−	1.03189e10i	−1.25861	−	1.04548i
$718$	−1.15695e9	+	6.56141e9i	−0.116649	+	0.661549i
$719$	2.14374e9	+	3.71306e9i	0.215090	+	0.372547i	0.953300	−	0.302024i	$-0.0976622\pi$
$719$	2.14374e9	+	3.71306e9i	0.215090	+	0.372547i	−0.738210	+	0.674571i	$0.764329\pi$
$720$	2.27497e9	−	8.53720e8i	0.227149	−	0.0852417i
$721$	−7.81761e9	+	1.35405e10i	−0.776784	+	1.34543i
$722$	−1.22710e9	−	1.02966e9i	−0.121339	−	0.101815i
$723$	−5.20023e9	−	8.90457e9i	−0.511727	−	0.876252i
$724$	−1.22753e9	−	6.96165e9i	−0.120212	−	0.681754i
$725$	−2.26240e8	+	1.89838e8i	−0.0220489	+	0.0185012i
$726$	1.29227e9	+	7.12170e9i	0.125336	+	0.690726i
$727$	−2.49066e9	+	9.06525e8i	−0.240405	+	0.0875003i	−0.459413	−	0.888223i	$-0.651940\pi$
$727$	−2.49066e9	+	9.06525e8i	−0.240405	+	0.0875003i	0.219008	+	0.975723i	$0.429718\pi$
$728$	4.25369e9			0.408607
$729$	−4.95779e9	+	9.21083e9i	−0.473960	+	0.880547i
$730$	1.39284e10			1.32517
$731$	−7.55134e9	+	2.74846e9i	−0.715012	+	0.260243i
$732$	1.83379e9	+	1.01060e10i	0.172807	+	0.952337i
$733$	−4.36081e9	+	3.65915e9i	−0.408981	+	0.343176i	−0.823953	−	0.566659i	$-0.808236\pi$
$733$	−4.36081e9	+	3.65915e9i	−0.408981	+	0.343176i	0.414972	+	0.909834i	$0.363791\pi$
$734$	2.15899e8	+	1.22442e9i	0.0201518	+	0.114287i
$735$	3.28362e9	+	5.62268e9i	0.305033	+	0.522321i
$736$	−3.89903e8	−	3.27168e8i	−0.0360483	−	0.0302481i
$737$	−4.58526e8	+	7.94191e8i	−0.0421918	+	0.0730783i
$738$	−7.07580e9	+	2.65531e9i	−0.648005	+	0.243175i
$739$	−4.22955e9	−	7.32580e9i	−0.385513	−	0.667728i	0.606327	−	0.795215i	$-0.292642\pi$
$739$	−4.22955e9	−	7.32580e9i	−0.385513	−	0.667728i	−0.991840	+	0.127487i	$0.959309\pi$
$740$	2.58049e7	−	1.46347e8i	0.00234095	−	0.0132762i
$741$	−8.55001e9	−	7.10221e9i	−0.771974	−	0.641253i
$742$	1.46967e10	+	5.34918e9i	1.32071	+	0.480699i
$743$	−1.95379e10	−	7.11122e9i	−1.74750	−	0.636039i	−0.747888	−	0.663825i	$-0.768932\pi$
$743$	−1.95379e10	−	7.11122e9i	−1.74750	−	0.636039i	−0.999614	+	0.0277869i	$0.991154\pi$
$744$	−4.22981e9	+	1.56337e9i	−0.376544	+	0.139174i
$745$	2.67009e8	−	1.51428e9i	0.0236581	−	0.134172i
$746$	−1.69584e9	−	2.93728e9i	−0.149554	−	0.259036i
$747$	−4.17993e8	+	3.57877e8i	−0.0366899	+	0.0314132i
$748$	1.79245e8	−	3.10462e8i	0.0156600	−	0.0271239i
$749$	1.93282e10	+	1.62183e10i	1.68076	+	1.41032i
$750$	4.15868e9	−	7.28643e9i	0.359949	−	0.630667i
$751$	1.54454e7	+	8.75950e7i	0.00133063	+	0.00754639i	0.985466	−	0.169874i	$-0.0543360\pi$
$751$	1.54454e7	+	8.75950e7i	0.00133063	+	0.00754639i	−0.984135	+	0.177420i	$0.943225\pi$
$752$	1.04328e9	−	8.75414e8i	0.0894617	−	0.0750673i
$753$	−4.91517e9	−	1.76137e9i	−0.419524	−	0.150337i
$754$	3.50907e9	−	1.27720e9i	0.298121	−	0.108507i
$755$	−2.61751e9			−0.221348
$756$	3.88139e9	+	6.49711e9i	0.326709	+	0.546882i
$757$	1.54629e10			1.29555			0.647776	−	0.761831i	$-0.275699\pi$
$757$	1.54629e10			1.29555			0.647776	+	0.761831i	$0.275699\pi$
$758$	1.24297e10	−	4.52404e9i	1.03662	−	0.377298i
$759$	−2.07776e8	+	1.76111e8i	−0.0172484	+	0.0146198i
$760$	−3.51908e9	+	2.95286e9i	−0.290792	+	0.244003i
$761$	2.86911e9	+	1.62715e10i	0.235994	+	1.33839i	0.840511	+	0.541795i	$0.182255\pi$
$761$	2.86911e9	+	1.62715e10i	0.235994	+	1.33839i	−0.604517	+	0.796592i	$0.706634\pi$
$762$	1.38939e10	−	6.90450e7i	1.13758	−	0.00565314i
$763$	−2.05751e10	−	1.72646e10i	−1.67690	−	1.40709i
$764$	2.56200e9	−	4.43752e9i	0.207851	−	0.360009i
$765$	4.35457e9	−	7.71850e9i	0.351666	−	0.623330i
$766$	2.87555e9	+	4.98060e9i	0.231164	+	0.400388i
$767$	4.31522e7	−	2.44728e8i	0.00345318	−	0.0195839i
$768$	1.32402e8	−	7.73341e8i	0.0105470	−	0.0616037i
$769$	6.66458e9	+	2.42571e9i	0.528482	+	0.192352i	0.592460	−	0.805600i	$-0.298157\pi$
$769$	6.66458e9	+	2.42571e9i	0.528482	+	0.192352i	−0.0639783	+	0.997951i	$0.520379\pi$
$770$	−8.84045e8	−	3.21766e8i	−0.0697842	−	0.0253994i
$771$	−2.18892e9	+	1.27852e10i	−0.172005	+	1.00466i
$772$	8.17114e8	−	4.63408e9i	0.0639178	−	0.362496i
$773$	−8.02183e9	−	1.38942e10i	−0.624662	−	1.08195i	−0.988606	−	0.150526i	$-0.951903\pi$
$773$	−8.02183e9	−	1.38942e10i	−0.624662	−	1.08195i	0.363944	−	0.931421i	$-0.381430\pi$
$774$	4.78657e9	+	8.10350e9i	0.371049	+	0.628173i
$775$	−4.28113e8	+	7.41513e8i	−0.0330371	+	0.0572220i
$776$	1.98446e9	+	1.66516e9i	0.152450	+	0.127921i
$777$	4.62843e8	−	2.30008e6i	0.0353965	−	0.000175902i
$778$	9.67942e8	+	5.48947e9i	0.0736920	+	0.417928i
$779$	1.09454e10	−	9.18424e9i	0.829562	−	0.696085i
$780$	−4.45012e9	+	3.77193e9i	−0.335769	+	0.284599i
$781$	1.63982e9	−	5.96845e8i	0.123173	−	0.0448315i
$782$	−1.85634e9			−0.138814
$783$	5.15274e9	+	4.19436e9i	0.383594	+	0.312248i
$784$	2.10245e9			0.155819
$785$	−6.89990e9	+	2.51136e9i	−0.509095	+	0.185295i
$786$	−2.33202e9	−	8.35685e8i	−0.171298	−	0.0613852i
$787$	−1.97957e9	+	1.66106e9i	−0.144764	+	0.121471i	−0.712294	−	0.701882i	$-0.752344\pi$
$787$	−1.97957e9	+	1.66106e9i	−0.144764	+	0.121471i	0.567530	+	0.823353i	$0.307899\pi$
$788$	−1.94835e9	−	1.10497e10i	−0.141849	−	0.804465i
$789$	4.55478e9	−	7.98044e9i	0.330140	−	0.578439i
$790$	−1.03157e9	−	8.65594e8i	−0.0744399	−	0.0624625i
$791$	3.02989e9	−	5.24793e9i	0.217676	−	0.377025i
$792$	−3.95945e8	−	1.39672e8i	−0.0283202	−	0.00999010i
$793$	−1.23292e10	−	2.13549e10i	−0.877972	−	1.52069i
$794$	1.08189e9	−	6.13569e9i	0.0767027	−	0.435003i
$795$	−2.01188e10	+	7.43606e9i	−1.42009	+	0.524877i
$796$	−8.55836e9	−	3.11499e9i	−0.601444	−	0.218908i
$797$	1.99763e10	+	7.27078e9i	1.39769	+	0.508717i	0.927492	−	0.373843i	$-0.121960\pi$
$797$	1.99763e10	+	7.27078e9i	1.39769	+	0.508717i	0.470198	+	0.882561i	$0.344182\pi$
$798$	−1.10062e10	−	9.14251e9i	−0.766706	−	0.636877i
$799$	8.62522e8	−	4.89160e9i	0.0598214	−	0.339264i
$800$	−7.44862e7	−	1.29014e8i	−0.00514352	−	0.00890885i
$801$	−3.95368e9	+	2.38035e10i	−0.271824	+	1.63654i
$802$	4.38752e9	−	7.59940e9i	0.300337	−	0.520199i
$803$	−1.84363e9	−	1.54699e9i	−0.125652	−	0.105435i
$804$	3.69149e9	+	6.32110e9i	0.250499	+	0.428940i
$805$	8.45938e8	+	4.79755e9i	0.0571548	+	0.324141i
$806$	8.29341e9	−	6.95900e9i	0.557905	−	0.468138i
$807$	−1.49641e9	−	8.24673e9i	−0.100229	−	0.552363i
$808$	−8.43612e9	+	3.07050e9i	−0.562604	+	0.204771i
$809$	−2.75159e10			−1.82711			−0.913555	−	0.406716i	$-0.866674\pi$
$809$	−2.75159e10			−1.82711			−0.913555	+	0.406716i	$0.866674\pi$
$810$	−9.82189e9	−	3.35533e9i	−0.649378	−	0.221839i
$811$	2.35433e10			1.54987			0.774935	−	0.632042i	$-0.217783\pi$
$811$	2.35433e10			1.54987			0.774935	+	0.632042i	$0.217783\pi$
$812$	4.51715e9	−	1.64411e9i	0.296086	−	0.107767i
$813$	−1.11193e8	−	6.12783e8i	−0.00725705	−	0.0399936i
$814$	−1.96700e7	+	1.65051e7i	−0.00127826	+	0.00107258i
$815$	−9.25952e8	−	5.25133e9i	−0.0599152	−	0.339796i
$816$	−1.44306e9	−	2.47102e9i	−0.0929757	−	0.159206i
$817$	−1.36304e10	−	1.14372e10i	−0.874441	−	0.733743i
$818$	−4.53245e9	+	7.85044e9i	−0.289532	+	0.501484i
$819$	−1.40341e10	−	1.15403e10i	−0.892670	−	0.734044i
$820$	−3.74949e9	−	6.49431e9i	−0.237478	−	0.411325i
$821$	3.76505e9	−	2.13527e10i	0.237449	−	1.34664i	−0.599946	−	0.800040i	$-0.704811\pi$
$821$	3.76505e9	−	2.13527e10i	0.237449	−	1.34664i	0.837395	−	0.546598i	$-0.184077\pi$
$822$	1.14766e10	+	9.53324e9i	0.720713	+	0.598672i
$823$	3.59095e9	+	1.30700e9i	0.224548	+	0.0817289i	0.451844	−	0.892097i	$-0.350766\pi$
$823$	3.59095e9	+	1.30700e9i	0.224548	+	0.0817289i	−0.227296	+	0.973826i	$0.572988\pi$
$824$	−6.50610e9	−	2.36803e9i	−0.405112	−	0.147449i
$825$	−7.47752e7	+	2.76375e7i	−0.00463627	+	0.00171360i
$826$	5.55488e7	−	3.15033e8i	0.00342961	−	0.0194503i
$827$	−8.86278e9	−	1.53508e10i	−0.544880	−	0.943760i	−0.998614	−	0.0526230i	$-0.983242\pi$
$827$	−8.86278e9	−	1.53508e10i	−0.544880	−	0.943760i	0.453734	−	0.891137i	$-0.350091\pi$
$828$	3.98791e8	+	2.13722e9i	0.0244140	+	0.130841i
$829$	−6.07617e8	+	1.05242e9i	−0.0370416	+	0.0641579i	−0.883952	−	0.467578i	$-0.845127\pi$
$829$	−6.07617e8	+	1.05242e9i	−0.0370416	+	0.0641579i	0.846910	+	0.531736i	$0.178460\pi$
$830$	−4.18259e8	−	3.50961e8i	−0.0253905	−	0.0213052i
$831$	9.29958e9	−	1.62938e10i	0.562160	−	0.984961i
$832$	3.27090e8	+	1.85502e9i	0.0196895	+	0.111665i
$833$	5.87399e9	−	4.92886e9i	0.352108	−	0.295454i
$834$	−7.52496e9	−	2.69659e9i	−0.449183	−	0.160966i
$835$	−7.63316e9	+	2.77824e9i	−0.453735	+	0.165146i
$836$	7.93767e8			0.0469863
$837$	1.81967e10	+	6.31748e9i	1.07264	+	0.372396i
$838$	2.40109e10			1.40947
$839$	5.30409e9	−	1.93053e9i	0.310059	−	0.112852i	−0.182304	−	0.983242i	$-0.558356\pi$
$839$	5.30409e9	−	1.93053e9i	0.310059	−	0.112852i	0.492363	+	0.870390i	$0.336133\pi$
$840$	−5.72853e9	+	4.85552e9i	−0.333477	+	0.282656i
$841$	−9.98142e9	+	8.37540e9i	−0.578637	+	0.485534i
$842$	1.87052e9	+	1.06083e10i	0.107987	+	0.612424i
$843$	−1.60735e10	+	7.98766e7i	−0.924089	+	0.00459222i
$844$	1.18184e10	+	9.91686e9i	0.676647	+	0.567774i
$845$	−1.50778e9	+	2.61155e9i	−0.0859685	+	0.148902i
$846$	−5.81706e9	+	5.78167e7i	−0.330299	+	0.00328290i
$847$	−1.11844e10	−	1.93720e10i	−0.632443	−	1.09542i
$848$	−1.20264e9	+	6.82052e9i	−0.0677253	+	0.384089i
$849$	8.50488e8	−	4.96759e9i	0.0476970	−	0.278592i
$850$	−5.10558e8	−	1.85828e8i	−0.0285154	−	0.0103788i
$851$	1.24944e8	+	4.54758e7i	0.00694963	+	0.00252946i
$852$	2.35061e9	−	1.37296e10i	0.130209	−	0.760534i
$853$	−2.29409e9	+	1.30104e10i	−0.126558	+	0.717744i	0.853813	+	0.520580i	$0.174284\pi$
$853$	−2.29409e9	+	1.30104e10i	−0.126558	+	0.717744i	−0.980371	+	0.197164i	$0.936827\pi$
$854$	−1.58712e10	−	2.74897e10i	−0.871979	−	1.51031i
$855$	1.96215e10	−	1.95022e8i	1.07362	−	0.0106709i
$856$	−5.58648e9	+	9.67606e9i	−0.304425	+	0.527279i
$857$	1.33145e10	+	1.11722e10i	0.722589	+	0.606324i	0.928100	−	0.372331i	$-0.121441\pi$
$857$	1.33145e10	+	1.11722e10i	0.722589	+	0.606324i	−0.205511	+	0.978655i	$0.565886\pi$
$858$	1.00797e9	−	5.00909e6i	0.0544809	−	0.000270741i
$859$	5.69499e9	+	3.22979e10i	0.306561	+	1.73859i	0.616065	+	0.787695i	$0.288726\pi$
$859$	5.69499e9	+	3.22979e10i	0.306561	+	1.73859i	−0.309504	+	0.950898i	$0.600163\pi$
$860$	−7.15376e9	+	6.00272e9i	−0.383521	+	0.321813i
$861$	1.78174e10	−	1.51021e10i	0.951333	−	0.806353i
$862$	2.22208e9	−	8.08771e8i	0.118164	−	0.0430081i
$863$	−7.24187e9			−0.383542			−0.191771	−	0.981440i	$-0.561423\pi$
$863$	−7.24187e9			−0.383542			−0.191771	+	0.981440i	$0.561423\pi$
$864$	−2.53490e9	+	2.19226e9i	−0.133710	+	0.115636i
$865$	9.63266e9			0.506046
$866$	−8.17399e9	+	2.97509e9i	−0.427683	+	0.155664i
$867$	8.24010e9	+	2.95286e9i	0.429404	+	0.153878i
$868$	1.06759e10	−	8.95816e9i	0.554098	−	0.464943i
$869$	4.04049e7	+	2.29148e8i	0.00208865	+	0.0118453i
$870$	−3.26784e9	+	5.72558e9i	−0.168245	+	0.294783i
$871$	−1.34624e10	−	1.12963e10i	−0.690332	−	0.579258i
$872$	5.94689e9	−	1.03003e10i	0.303726	−	0.526069i
$873$	−2.02970e9	−	1.08777e10i	−0.103248	−	0.553332i
$874$	−2.05515e9	−	3.55962e9i	−0.104124	−	0.180349i
$875$	−4.50236e9	+	2.55341e10i	−0.227202	+	1.28853i
$876$	−1.80192e10	+	6.66004e9i	−0.905671	+	0.334744i
$877$	1.12856e10	+	4.10762e9i	0.564970	+	0.205632i	0.608685	−	0.793412i	$-0.291697\pi$
$877$	1.12856e10	+	4.10762e9i	0.564970	+	0.205632i	−0.0437152	+	0.999044i	$0.513919\pi$
$878$	−8.47874e8	−	3.08601e8i	−0.0422767	−	0.0153874i
$879$	−2.81089e10	−	2.33492e10i	−1.39599	−	1.15960i
$880$	7.23419e7	−	4.10271e8i	0.00357849	−	0.0202947i
$881$	9.76364e9	+	1.69111e10i	0.481056	+	0.833214i	0.999764	−	0.0217378i	$-0.00691989\pi$
$881$	9.76364e9	+	1.69111e10i	0.481056	+	0.833214i	−0.518707	+	0.854952i	$0.673587\pi$
$882$	−6.93655e9	−	5.70394e9i	−0.340411	−	0.279921i
$883$	3.18147e9	−	5.51047e9i	0.155513	−	0.269356i	−0.777733	−	0.628595i	$-0.783630\pi$
$883$	3.18147e9	−	5.51047e9i	0.155513	−	0.269356i	0.933246	+	0.359239i	$0.116964\pi$
$884$	5.26265e9	+	4.41589e9i	0.256225	+	0.214998i
$885$	2.21240e8	+	3.78838e8i	0.0107291	+	0.0183718i
$886$	1.45317e9	+	8.24132e9i	0.0701936	+	0.398088i
$887$	−3.20569e9	+	2.68989e9i	−0.154237	+	0.129420i	−0.716641	−	0.697443i	$-0.754321\pi$
$887$	−3.20569e9	+	2.68989e9i	−0.154237	+	0.129420i	0.562404	+	0.826863i	$0.309877\pi$
$888$	3.65937e7	+	2.01667e8i	0.00175372	+	0.00966474i
$889$	−4.03495e10	+	1.46860e10i	−1.92612	+	0.701049i
$890$	−2.39424e10			−1.13842
$891$	9.27402e8	+	1.53501e9i	0.0439234	+	0.0727010i
$892$	9.46506e8			0.0446525
$893$	1.03348e10	−	3.76155e9i	0.485647	−	0.176761i
$894$	3.78643e8	+	2.08670e9i	0.0177234	+	0.0976738i
$895$	−7.45752e9	+	6.25761e9i	−0.347707	+	0.291761i
$896$	4.21055e8	+	2.38792e9i	0.0195552	+	0.110903i
$897$	−2.63221e9	−	4.50725e9i	−0.121772	−	0.208515i
$898$	−5.65951e9	−	4.74889e9i	−0.260802	−	0.218839i
$899$	6.11733e9	−	1.05955e10i	0.280804	−	0.486366i
$900$	−1.04264e8	+	6.27733e8i	−0.00476746	+	0.0287029i
$901$	1.26296e10	+	2.18751e10i	0.575246	+	0.996355i
$902$	−2.25004e8	+	1.27606e9i	−0.0102086	+	0.0578960i
$903$	−2.23740e10	−	1.85853e10i	−1.01120	−	0.839968i
$904$	2.52159e9	+	9.17783e8i	0.113523	+	0.0413191i
$905$	−2.81542e10	−	1.02473e10i	−1.26262	−	0.459556i
$906$	3.38627e9	−	1.25159e9i	0.151277	−	0.0559132i
$907$	−5.61720e9	+	3.18567e10i	−0.249974	+	1.41767i	0.558679	+	0.829384i	$0.311308\pi$
$907$	−5.61720e9	+	3.18567e10i	−0.249974	+	1.41767i	−0.808653	+	0.588287i	$0.799803\pi$
$908$	−8.02515e9	−	1.39000e10i	−0.355756	−	0.616188i
$909$	3.61633e10	+	1.27568e10i	1.59696	+	0.563336i
$910$	9.01430e9	−	1.56132e10i	0.396540	−	0.686828i
$911$	2.40431e10	+	2.01746e10i	1.05360	+	0.884077i	0.993468	−	0.114114i	$-0.0364028\pi$
$911$	2.40431e10	+	2.01746e10i	1.05360	+	0.884077i	0.0601339	+	0.998190i	$0.480847\pi$
$912$	3.14068e9	−	5.50280e9i	0.137102	−	0.240216i
$913$	1.63824e7	+	9.29095e7i	0.000712412	+	0.00404029i
$914$	−1.37406e10	+	1.15297e10i	−0.595241	+	0.499467i
$915$	4.09803e10	+	1.46854e10i	1.76849	+	0.633741i
$916$	1.59259e10	−	5.79655e9i	0.684651	−	0.249193i
$917$	7.65582e9			0.327868
$918$	−1.94281e9	+	1.20676e10i	−0.0828861	+	0.514839i
$919$	2.61210e10			1.11016			0.555079	−	0.831798i	$-0.312688\pi$
$919$	2.61210e10			1.11016			0.555079	+	0.831798i	$0.312688\pi$
$920$	−2.02715e9	+	7.37821e8i	−0.0858277	+	0.0312387i
$921$	2.58098e10	−	2.18764e10i	1.08862	−	0.922716i
$922$	−1.23309e10	+	1.03469e10i	−0.518127	+	0.434760i
$923$	5.80702e9	+	3.29333e10i	0.243079	+	1.37857i
$924$	1.29754e9	−	6.44809e6i	0.0541090	−	0.000268893i
$925$	2.98116e7	+	2.50149e7i	0.00123848	+	0.00103921i
$926$	9.99567e9	−	1.73130e10i	0.413688	−	0.716529i
$927$	1.50409e10	+	2.54638e10i	0.620149	+	1.04989i
$928$	1.06434e9	+	1.84349e9i	0.0437181	+	0.0757220i
$929$	9.78977e8	−	5.55206e9i	0.0400606	−	0.227195i	−0.958204	−	0.286087i	$-0.907646\pi$
$929$	9.78977e8	−	5.55206e9i	0.0400606	−	0.227195i	0.998264	+	0.0588916i	$0.0187566\pi$
$930$	−3.22531e9	+	1.88386e10i	−0.131487	+	0.767996i
$931$	1.59544e10	+	5.80693e9i	0.647973	+	0.235843i
$932$	−1.75973e9	−	6.40490e8i	−0.0712017	−	0.0259153i
$933$	4.76425e9	−	2.78274e10i	0.192048	−	1.12172i
$934$	−5.22450e8	+	2.96296e9i	−0.0209812	+	0.118990i
$935$	−7.59702e8	−	1.31584e9i	−0.0303950	−	0.0526458i
$936$	3.95351e9	−	7.00761e9i	0.157586	−	0.279322i
$937$	−2.10407e10	+	3.64436e10i	−0.835550	+	1.44721i	0.0580321	+	0.998315i	$0.481517\pi$
$937$	−2.10407e10	+	3.64436e10i	−0.835550	+	1.44721i	−0.893582	+	0.448900i	$0.851816\pi$
$938$	−1.73298e10	−	1.45414e10i	−0.685621	−	0.575304i
$939$	−8.66009e9	+	4.30360e7i	−0.341345	+	0.00169630i
$940$	−1.00233e9	−	5.68452e9i	−0.0393609	−	0.223227i
$941$	−1.25857e10	+	1.05607e10i	−0.492396	+	0.413169i	−0.854884	−	0.518819i	$-0.826372\pi$
$941$	−1.25857e10	+	1.05607e10i	−0.492396	+	0.413169i	0.362488	+	0.931988i	$0.381927\pi$
$942$	7.72554e9	−	6.54820e9i	0.301128	−	0.255237i
$943$	6.30500e9	−	2.29483e9i	0.244847	−	0.0891169i
$944$	1.41656e8			0.00548067
$945$	3.20730e10	−	4.78189e8i	1.23631	−	0.0184327i
$946$	1.61361e9			0.0619696
$947$	−3.25574e9	+	1.18499e9i	−0.124573	+	0.0453410i	−0.403555	−	0.914956i	$-0.632225\pi$
$947$	−3.25574e9	+	1.18499e9i	−0.124573	+	0.0453410i	0.278981	+	0.960297i	$0.410003\pi$
$948$	1.74844e9	+	6.26557e8i	0.0666532	+	0.0238854i
$949$	3.53303e10	−	2.96456e10i	1.34189	−	1.12598i
$950$	−2.08903e8	−	1.18475e9i	−0.00790520	−	0.0448326i
$951$	−2.00361e10	+	3.51052e10i	−0.755407	+	1.32355i
$952$	6.77449e9	+	5.68448e9i	0.254476	+	0.213531i
$953$	−3.78375e9	+	6.55365e9i	−0.141611	+	0.245278i	−0.928103	−	0.372322i	$-0.878562\pi$
$953$	−3.78375e9	+	6.55365e9i	−0.141611	+	0.245278i	0.786492	+	0.617600i	$0.211895\pi$
$954$	2.24719e10	−	1.92400e10i	0.837956	−	0.717440i
$955$	−1.08586e10	−	1.88077e10i	−0.403426	−	0.698754i
$956$	−3.83776e9	+	2.17650e10i	−0.142061	+	0.805669i
$957$	1.06847e9	−	3.94915e8i	0.0394067	−	0.0145650i
$958$	−2.90383e10	−	1.05691e10i	−1.06707	−	0.388380i
$959$	−4.33280e10	−	1.57701e10i	−1.58637	−	0.577390i
$960$	−2.55797e9	−	2.12482e9i	−0.0933140	−	0.0775128i
$961$	1.38183e9	−	7.83677e9i	0.0502255	−	0.284843i
$962$	−2.46033e8	−	4.26141e8i	−0.00891005	−	0.0154327i
$963$	4.46825e10	−	1.67679e10i	1.61230	−	0.605042i
$964$	−7.05604e9	+	1.22214e10i	−0.253683	+	0.439392i
$965$	−1.52779e10	−	1.28196e10i	−0.547289	−	0.459230i
$966$	−3.38839e9	−	5.80208e9i	−0.120941	−	0.207092i
$967$	−3.06969e8	−	1.74091e9i	−0.0109170	−	0.0619131i	0.978863	−	0.204519i	$-0.0655630\pi$
$967$	−3.06969e8	−	1.74091e9i	−0.0109170	−	0.0619131i	−0.989780	+	0.142606i	$0.954452\pi$
$968$	7.58801e9	−	6.36710e9i	0.268884	−	0.225620i
$969$	−4.12575e9	−	2.27370e10i	−0.145670	−	0.802786i
$970$	1.03174e10	−	3.75523e9i	0.362969	−	0.132110i
$971$	2.30624e10			0.808420			0.404210	−	0.914666i	$-0.367546\pi$
$971$	2.30624e10			0.808420			0.404210	+	0.914666i	$0.367546\pi$
$972$	1.43109e10	−	3.55658e8i	0.499846	−	0.0124223i
$973$	2.47038e10			0.859743
$974$	5.07721e9	−	1.84795e9i	0.176063	−	0.0640818i
$975$	−2.72755e8	−	1.50315e9i	−0.00942446	−	0.0519381i
$976$	1.07677e10	−	9.03518e9i	0.370723	−	0.311073i
$977$	3.21929e9	+	1.82575e10i	0.110441	+	0.626340i	0.988907	+	0.148536i	$0.0474561\pi$
$977$	3.21929e9	+	1.82575e10i	0.110441	+	0.626340i	−0.878466	+	0.477804i	$0.841433\pi$
$978$	3.70888e9	+	6.35088e9i	0.126782	+	0.217094i
$979$	3.16912e9	+	2.65921e9i	0.107944	+	0.0905760i
$980$	4.45545e9	−	7.71706e9i	0.151217	−	0.261915i
$981$	−4.75652e10	+	1.78496e10i	−1.60860	+	0.603654i
$982$	−1.05311e10	−	1.82405e10i	−0.354883	−	0.614676i
$983$	4.58954e9	−	2.60286e10i	0.154110	−	0.874003i	−0.805484	−	0.592617i	$-0.798095\pi$
$983$	4.58954e9	−	2.60286e10i	0.154110	−	0.874003i	0.959595	−	0.281386i	$-0.0907941\pi$
$984$	7.95603e9	+	6.60881e9i	0.266203	+	0.221126i
$985$	−4.46868e10	−	1.62647e10i	−1.48988	−	0.542274i
$986$	7.29540e9	+	2.65531e9i	0.242371	+	0.0882157i
$987$	1.68633e10	−	6.23283e9i	0.558256	−	0.206336i
$988$	−2.64142e9	+	1.49802e10i	−0.0871339	+	0.494161i
$989$	−4.17780e9	−	7.23616e9i	−0.137328	−	0.237860i
$990$	−1.35174e9	+	1.15733e9i	−0.0442762	+	0.0379084i
$991$	−1.15813e9	+	2.00594e9i	−0.0378008	+	0.0654728i	−0.884307	−	0.466906i	$-0.845369\pi$
$991$	−1.15813e9	+	2.00594e9i	−0.0378008	+	0.0654728i	0.846506	+	0.532379i	$0.178702\pi$
$992$	4.72755e9	+	3.96689e9i	0.153761	+	0.129021i
$993$	−9.74804e9	+	1.70796e10i	−0.315933	+	0.553547i
$994$	7.47525e9	+	4.23943e10i	0.241420	+	1.36916i
$995$	−2.95702e10	+	2.48124e10i	−0.951643	+	0.798524i
$996$	7.08916e8	+	2.54042e8i	0.0227346	+	0.00814700i
$997$	−4.99676e10	+	1.81867e10i	−1.59682	+	0.581194i	−0.978773	−	0.204948i	$-0.934297\pi$
$997$	−4.99676e10	+	1.81867e10i	−1.59682	+	0.581194i	−0.618046	+	0.786142i	$0.712075\pi$
$998$	−1.24417e10			−0.396209
$999$	4.26391e8	−	7.64635e8i	0.0135310	−	0.0242647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.e.b.7.7	✓	66
27.4	even	9	inner	54.8.e.b.31.7	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.e.b.7.7	✓	66	1.1	even	1	trivial
54.8.e.b.31.7	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} +(8.34949 + 46.0140i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-47.1028 - 267.133i) q^{5} +(188.669 + 323.066i) q^{6} +(-885.713 - 743.201i) q^{7} +(256.000 - 443.405i) q^{8} +(-2047.57 + 768.386i) q^{9} +(-1085.02 - 1879.30i) q^{10} +(-65.1109 + 369.262i) q^{11} +(2302.29 + 1912.44i) q^{12} +(-6752.16 - 2457.59i) q^{13} +(-8691.90 - 3163.59i) q^{14} +(11898.6 - 4397.81i) q^{15} +(711.263 - 4033.77i) q^{16} +(-7469.37 - 12937.3i) q^{17} +(-13290.3 + 11378.9i) q^{18} +(16538.6 - 28645.7i) q^{19} +(-13298.7 - 11159.0i) q^{20} +(26802.4 - 46960.5i) q^{21} +(520.887 + 2954.10i) q^{22} +(11898.9 - 9984.37i) q^{23} +(22540.3 + 8077.37i) q^{24} +(4272.10 - 1554.92i) q^{25} -57484.0 q^{26} +(-52452.7 - 87801.3i) q^{27} -73997.8 q^{28} +(-61044.3 + 22218.3i) q^{29} +(77414.9 - 65617.1i) q^{30} +(-144273. + 121060. i) q^{31} +(-5690.10 - 32270.2i) q^{32} +(-17534.9 + 87.1388i) q^{33} +(-91549.9 - 76819.5i) q^{34} +(-156814. + 271610. i) q^{35} +(-68775.8 + 121905. i) q^{36} +(4280.02 + 7413.22i) q^{37} +(45950.4 - 260598. i) q^{38} +(56706.2 - 331213. i) q^{39} +(-130506. - 47500.5i) q^{40} +(405912. + 147740. i) q^{41} +(72996.6 - 426363. i) q^{42} +(93410.2 - 529756. i) q^{43} +(11998.7 + 20782.3i) q^{44} +(301708. + 510781. i) q^{45} +(62131.7 - 107615. i) q^{46} +(254706. + 213724. i) q^{47} +(191549. - 951.894i) q^{48} +(89132.4 + 505495. i) q^{49} +(27861.2 - 23378.3i) q^{50} +(532932. - 451715. i) q^{51} +(-432138. + 157285. i) q^{52} -1.69085e6 q^{53} +(-634554. - 516531. i) q^{54} +101709. q^{55} +(-556282. + 202470. i) q^{56} +(1.45619e6 + 521831. i) q^{57} +(-398110. + 334054. i) q^{58} +(6005.45 + 34058.6i) q^{59} +(402430. - 705099. i) q^{60} +(2.62884e6 + 2.20586e6i) q^{61} +(-753342. + 1.30483e6i) q^{62} +(2.38463e6 + 841189. i) q^{63} +(-131072. - 227023. i) q^{64} +(-338457. + 1.91948e6i) q^{65} +(-131581. + 48633.3i) q^{66} +(2.29825e6 + 836493. i) q^{67} +(-898420. - 326998. i) q^{68} +(558770. + 464152. i) q^{69} +(-435688. + 2.47091e6i) q^{70} +(-2.32700e6 - 4.03048e6i) q^{71} +(-183472. + 1.10461e6i) q^{72} +(-3.20927e6 + 5.55862e6i) q^{73} +(52459.0 + 44018.3i) q^{74} +(107218. + 183594. i) q^{75} +(-367604. - 2.08478e6i) q^{76} +(332106. - 278670. i) q^{77} +(-479962. - 2.64507e6i) q^{78} +(583131. - 212242. i) q^{79} -1.11106e6 q^{80} +(3.60213e6 - 3.14665e6i) q^{81} +3.45570e6 q^{82} +(236435. - 86055.1i) q^{83} +(-617844. - 3.40493e6i) q^{84} +(-3.10416e6 + 2.60470e6i) q^{85} +(-747282. - 4.23805e6i) q^{86} +(-1.53204e6 - 2.62338e6i) q^{87} +(147064. + 123402. i) q^{88} +(5.51660e6 - 9.55503e6i) q^{89} +(3.66568e6 + 3.01430e6i) q^{90} +(4.15400e6 + 7.19493e6i) q^{91} +(172625. - 979004. i) q^{92} +(-6.77505e6 - 5.62781e6i) q^{93} +(2.49955e6 + 909762. i) q^{94} +(-8.43124e6 - 3.06872e6i) q^{95} +(1.43737e6 - 531264. i) q^{96} +(-878595. + 4.98276e6i) q^{97} +(2.05317e6 + 3.55620e6i) q^{98} +(-150417. - 806121. i) 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

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