LMFDB - Embedded newform 54.8.e.a.13.5

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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	54.13
Dual form			54.8.e.a.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38919 + 7.87846i) q^{2} +(-14.0270 + 44.6122i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-224.372 - 188.270i) q^{5} +(-370.961 - 48.5362i) q^{6} +(356.182 + 129.640i) q^{7} +(-256.000 - 443.405i) q^{8} +(-1793.49 - 1251.55i) q^{9} +(1171.59 - 2029.25i) q^{10} +(945.954 - 793.750i) q^{11} +(-132.943 - 2990.03i) q^{12} +(1483.87 - 8415.47i) q^{13} +(-526.558 + 2986.26i) q^{14} +(11546.4 - 7368.84i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-6198.02 + 10735.3i) q^{17} +(7368.76 - 15868.6i) q^{18} +(13639.7 + 23624.6i) q^{19} +(17614.9 + 6411.29i) q^{20} +(-10779.6 + 14071.6i) q^{21} +(7567.63 + 6350.00i) q^{22} +(27929.6 - 10165.5i) q^{23} +(23372.2 - 5201.09i) q^{24} +(1330.71 + 7546.82i) q^{25} +68362.3 q^{26} +(80991.3 - 62456.1i) q^{27} -24258.6 q^{28} +(-26587.5 - 150785. i) q^{29} +(74095.2 + 80731.1i) q^{30} +(122624. - 44631.4i) q^{31} +(25101.7 + 21062.9i) q^{32} +(22142.0 + 53334.9i) q^{33} +(-93187.8 - 33917.6i) q^{34} +(-55509.8 - 96145.8i) q^{35} +(135256. + 36010.1i) q^{36} +(-149602. + 259118. i) q^{37} +(-167177. + 140278. i) q^{38} +(354618. + 184242. i) q^{39} +(-26040.8 + 147685. i) q^{40} +(149427. - 847441. i) q^{41} +(-125837. - 65379.0i) q^{42} +(545525. - 457750. i) q^{43} +(-39515.4 + 68442.6i) q^{44} +(166779. + 618472. i) q^{45} +(118888. + 205920. i) q^{46} +(-551573. - 200756. i) q^{47} +(73444.9 + 176911. i) q^{48} +(-520812. - 437013. i) q^{49} +(-57608.7 + 20967.9i) q^{50} +(-391985. - 427091. i) q^{51} +(94967.9 + 538590. i) q^{52} -1.24502e6 q^{53} +(604570. + 551324. i) q^{54} -361685. q^{55} +(-33699.7 - 191120. i) q^{56} +(-1.24527e6 + 277114. i) q^{57} +(1.15102e6 - 418937. i) q^{58} +(-1.32375e6 - 1.11076e6i) q^{59} +(-533105. + 695907. i) q^{60} +(288830. + 105125. i) q^{61} +(521974. + 904086. i) q^{62} +(-476558. - 678284. i) q^{63} +(-131072. + 227023. i) q^{64} +(-1.91732e6 + 1.60882e6i) q^{65} +(-389438. + 248537. i) q^{66} +(92450.9 - 524315. i) q^{67} +(137763. - 781294. i) q^{68} +(61739.6 + 1.38859e6i) q^{69} +(680367. - 570896. i) q^{70} +(-478554. + 828880. i) q^{71} +(-95808.2 + 1.11564e6i) q^{72} +(432025. + 748290. i) q^{73} +(-2.24928e6 - 818671. i) q^{74} +(-355346. - 46493.1i) q^{75} +(-1.33742e6 - 1.12223e6i) q^{76} +(439833. - 160086. i) q^{77} +(-958915. + 3.04979e6i) q^{78} +(-536432. - 3.04225e6i) q^{79} -1.19970e6 q^{80} +(1.65024e6 + 4.48927e6i) q^{81} +6.88411e6 q^{82} +(-154525. - 876352. i) q^{83} +(340274. - 1.08223e6i) q^{84} +(3.41179e6 - 1.24179e6i) q^{85} +(4.36420e6 + 3.66200e6i) q^{86} +(7.09980e6 + 928932. i) q^{87} +(-594117. - 216241. i) q^{88} +(-3.33231e6 - 5.77174e6i) q^{89} +(-4.64092e6 + 2.17314e6i) q^{90} +(1.61951e6 - 2.80507e6i) q^{91} +(-1.45718e6 + 1.22272e6i) q^{92} +(271066. + 6.09656e6i) q^{93} +(815412. - 4.62443e6i) q^{94} +(1.38745e6 - 7.86862e6i) q^{95} +(-1.29176e6 + 824395. i) q^{96} +(9.69544e6 - 8.13544e6i) q^{97} +(2.71949e6 - 4.71029e6i) q^{98} +(-2.68997e6 + 239677. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 213 q^{5} - 72 q^{6} + 1677 q^{7} - 15360 q^{8} - 3024 q^{9} + 3000 q^{10} - 15744 q^{11} + 2880 q^{12} + 9924 q^{13} + 13416 q^{14} + 2322 q^{15} + 29478 q^{17} + 49680 q^{18} + 61731 q^{19} - 27264 q^{20}+ \cdots + 36391797 q^{99}+O(q^{100}) $ 60 * q + 213 * q^5 - 72 * q^6 + 1677 * q^7 - 15360 * q^8 - 3024 * q^9 + 3000 * q^10 - 15744 * q^11 + 2880 * q^12 + 9924 * q^13 + 13416 * q^14 + 2322 * q^15 + 29478 * q^17 + 49680 * q^18 + 61731 * q^19 - 27264 * q^20 + 160884 * q^21 - 125952 * q^22 + 29478 * q^23 - 343017 * q^25 - 316368 * q^26 - 524124 * q^27 - 263424 * q^28 + 132153 * q^29 + 292824 * q^30 - 1372860 * q^31 - 1065834 * q^33 - 121656 * q^34 - 321081 * q^35 - 369216 * q^36 + 759795 * q^37 + 224760 * q^38 - 2283894 * q^39 + 109056 * q^40 + 704616 * q^41 + 527400 * q^42 + 2124585 * q^43 + 255552 * q^44 + 3259908 * q^45 + 524472 * q^46 + 3452931 * q^47 + 552960 * q^48 - 1987017 * q^49 + 190152 * q^50 + 5107401 * q^51 + 635136 * q^52 - 2951976 * q^53 + 1065312 * q^54 - 2539854 * q^55 + 858624 * q^56 + 5722920 * q^57 + 47496 * q^58 + 3732204 * q^59 + 2512512 * q^60 - 5504796 * q^61 + 2859936 * q^62 + 1888047 * q^63 - 7864320 * q^64 - 803499 * q^65 - 9421632 * q^66 - 7979400 * q^67 - 5893440 * q^68 - 629100 * q^69 + 1111128 * q^70 + 3531612 * q^71 + 3096576 * q^72 - 875661 * q^73 + 15158904 * q^74 + 26002422 * q^75 + 1798080 * q^76 + 5672523 * q^77 - 13012848 * q^78 - 10290369 * q^79 - 3072000 * q^80 - 42838956 * q^81 - 3798096 * q^82 - 16555878 * q^83 + 2005056 * q^84 + 30956175 * q^85 + 16996680 * q^86 + 22863879 * q^87 + 2509824 * q^88 + 32327814 * q^89 + 34182072 * q^90 + 1976658 * q^91 - 1108608 * q^92 - 17967789 * q^93 - 24396768 * q^94 - 35592135 * q^95 - 2949120 * q^96 - 25380039 * q^97 - 15123648 * q^98 + 36391797 * q^99

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	1.38919	+	7.87846i	0.122788	+	0.696364i
$2$	1.38919	+	7.87846i	0.122788	+	0.696364i
$3$	−14.0270	+	44.6122i	−0.299943	+	0.953957i
$3$	−14.0270	+	44.6122i	−0.299943	+	0.953957i
$4$	−60.1403	+	21.8893i	−0.469846	+	0.171010i
$5$	−224.372	−	188.270i	−0.802736	−	0.673576i	0.146126	−	0.989266i	$-0.453319\pi$
$5$	−224.372	−	188.270i	−0.802736	−	0.673576i	−0.948862	+	0.315690i	$0.897764\pi$
$6$	−370.961	−	48.5362i	−0.701131	−	0.0917354i
$7$	356.182	+	129.640i	0.392490	+	0.142855i	0.530723	−	0.847545i	$-0.321920\pi$
$7$	356.182	+	129.640i	0.392490	+	0.142855i	−0.138234	+	0.990400i	$0.544142\pi$
$8$	−256.000	−	443.405i	−0.176777	−	0.306186i
$9$	−1793.49	−	1251.55i	−0.820068	−	0.572266i
$10$	1171.59	−	2029.25i	0.370488	−	0.641704i
$11$	945.954	−	793.750i	0.214287	−	0.179808i	−0.529326	−	0.848419i	$-0.677555\pi$
$11$	945.954	−	793.750i	0.214287	−	0.179808i	0.743613	+	0.668611i	$0.233111\pi$
$12$	−132.943	−	2990.03i	−0.0222091	−	0.499507i
$13$	1483.87	−	8415.47i	0.187325	−	1.06237i	−0.735607	−	0.677408i	$-0.763103\pi$
$13$	1483.87	−	8415.47i	0.187325	−	1.06237i	0.922932	−	0.384963i	$-0.125786\pi$
$14$	−526.558	+	2986.26i	−0.0512859	+	0.290857i
$15$	11546.4	−	7368.84i	0.883337	−	0.563741i
$16$	3137.72	−	2632.86i	0.191511	−	0.160697i
$17$	−6198.02	+	10735.3i	−0.305972	+	0.529959i	−0.977477	−	0.211041i	$-0.932315\pi$
$17$	−6198.02	+	10735.3i	−0.305972	+	0.529959i	0.671505	+	0.741000i	$0.265648\pi$
$18$	7368.76	−	15868.6i	0.297811	−	0.641333i
$19$	13639.7	+	23624.6i	0.456211	+	0.790181i	0.998757	−	0.0498455i	$-0.0158729\pi$
$19$	13639.7	+	23624.6i	0.456211	+	0.790181i	−0.542546	+	0.840026i	$0.682540\pi$
$20$	17614.9	+	6411.29i	0.492351	+	0.179201i
$21$	−10779.6	+	14071.6i	−0.254002	+	0.331570i
$22$	7567.63	+	6350.00i	0.151524	+	0.127143i
$23$	27929.6	−	10165.5i	0.478649	−	0.174214i	−0.0914173	−	0.995813i	$-0.529140\pi$
$23$	27929.6	−	10165.5i	0.478649	−	0.174214i	0.570066	+	0.821599i	$0.306918\pi$
$24$	23372.2	−	5201.09i	0.345111	−	0.0767989i
$25$	1330.71	+	7546.82i	0.0170331	+	0.0965993i
$26$	68362.3			0.762799
$27$	80991.3	−	62456.1i	0.791891	−	0.610663i
$28$	−24258.6			−0.208839
$29$	−26587.5	−	150785.i	−0.202435	−	1.14806i	−0.901426	−	0.432934i	$-0.857478\pi$
$29$	−26587.5	−	150785.i	−0.202435	−	1.14806i	0.698991	−	0.715130i	$-0.253633\pi$
$30$	74095.2	+	80731.1i	0.501032	+	0.545904i
$31$	122624.	−	44631.4i	0.739280	−	0.269076i	0.0551925	−	0.998476i	$-0.482423\pi$
$31$	122624.	−	44631.4i	0.739280	−	0.269076i	0.684088	+	0.729400i	$0.260201\pi$
$32$	25101.7	+	21062.9i	0.135419	+	0.113630i
$33$	22142.0	+	53334.9i	0.107255	+	0.258353i
$34$	−93187.8	−	33917.6i	−0.406614	−	0.147996i
$35$	−55509.8	−	96145.8i	−0.218842	−	0.379046i
$36$	135256.	+	36010.1i	0.483169	+	0.128637i
$37$	−149602.	+	259118.i	−0.485547	+	0.840993i	−0.999862	−	0.0166089i	$-0.994713\pi$
$37$	−149602.	+	259118.i	−0.485547	+	0.840993i	0.514315	+	0.857601i	$0.328046\pi$
$38$	−167177.	+	140278.i	−0.494236	+	0.414714i
$39$	354618.	+	184242.i	0.957270	+	0.497351i
$40$	−26040.8	+	147685.i	−0.0643345	+	0.364859i
$41$	149427.	−	847441.i	0.338598	−	1.92029i	−0.0497272	−	0.998763i	$-0.515835\pi$
$41$	149427.	−	847441.i	0.338598	−	1.92029i	0.388325	−	0.921522i	$-0.373054\pi$
$42$	−125837.	−	65379.0i	−0.262082	−	0.136165i
$43$	545525.	−	457750.i	1.04634	−	0.877987i	0.0536402	−	0.998560i	$-0.482918\pi$
$43$	545525.	−	457750.i	1.04634	−	0.877987i	0.992704	+	0.120573i	$0.0384732\pi$
$44$	−39515.4	+	68442.6i	−0.0699329	+	0.121127i
$45$	166779.	+	618472.i	0.272834	+	1.01176i
$46$	118888.	+	205920.i	0.180089	+	0.311923i
$47$	−551573.	−	200756.i	−0.774926	−	0.282050i	−0.0758709	−	0.997118i	$-0.524174\pi$
$47$	−551573.	−	200756.i	−0.774926	−	0.282050i	−0.699055	+	0.715068i	$0.746396\pi$
$48$	73444.9	+	176911.i	0.0958555	+	0.230893i
$49$	−520812.	−	437013.i	−0.632404	−	0.530650i
$50$	−57608.7	+	20967.9i	−0.0651768	+	0.0237224i
$51$	−391985.	−	427091.i	−0.413784	−	0.450842i
$52$	94967.9	+	538590.i	0.0936624	+	0.531186i
$53$	−1.24502e6			−1.14871			−0.574353	−	0.818607i	$-0.694746\pi$
$53$	−1.24502e6			−1.14871			−0.574353	+	0.818607i	$0.694746\pi$
$54$	604570.	+	551324.i	0.522478	+	0.476462i
$55$	−361685.			−0.293130
$56$	−33699.7	−	191120.i	−0.0256429	−	0.145428i
$57$	−1.24527e6	+	277114.i	−0.890636	+	0.198196i
$58$	1.15102e6	−	418937.i	0.774614	−	0.281936i
$59$	−1.32375e6	−	1.11076e6i	−0.839119	−	0.704104i	0.118247	−	0.992984i	$-0.462273\pi$
$59$	−1.32375e6	−	1.11076e6i	−0.839119	−	0.704104i	−0.957365	+	0.288880i	$0.906717\pi$
$60$	−533105.	+	695907.i	−0.318627	+	0.415931i
$61$	288830.	+	105125.i	0.162925	+	0.0592998i	0.422195	−	0.906505i	$-0.361260\pi$
$61$	288830.	+	105125.i	0.162925	+	0.0592998i	−0.259270	+	0.965805i	$0.583482\pi$
$62$	521974.	+	904086.i	0.278149	+	0.481769i
$63$	−476558.	−	678284.i	−0.240118	−	0.341759i
$64$	−131072.	+	227023.i	−0.0625000	+	0.108253i
$65$	−1.91732e6	+	1.60882e6i	−0.865960	+	0.726627i
$66$	−389438.	+	248537.i	−0.166738	+	0.106411i
$67$	92450.9	−	524315.i	0.0375534	−	0.212976i	−0.960257	−	0.279118i	$-0.909958\pi$
$67$	92450.9	−	524315.i	0.0375534	−	0.212976i	0.997810	+	0.0661420i	$0.0210690\pi$
$68$	137763.	−	781294.i	0.0531315	−	0.301324i
$69$	61739.6	+	1.38859e6i	0.0226252	+	0.508865i
$70$	680367.	−	570896.i	0.237083	−	0.198936i
$71$	−478554.	+	828880.i	−0.158682	+	0.274845i	−0.934394	−	0.356242i	$-0.884058\pi$
$71$	−478554.	+	828880.i	−0.158682	+	0.274845i	0.775712	+	0.631087i	$0.217391\pi$
$72$	−95808.2	+	1.11564e6i	−0.0302509	+	0.352257i
$73$	432025.	+	748290.i	0.129981	+	0.225133i	0.923669	−	0.383192i	$-0.125175\pi$
$73$	432025.	+	748290.i	0.129981	+	0.225133i	−0.793688	+	0.608325i	$0.791842\pi$
$74$	−2.24928e6	−	818671.i	−0.645256	−	0.234854i
$75$	−355346.	−	46493.1i	−0.0972605	−	0.0127255i
$76$	−1.33742e6	−	1.12223e6i	−0.349478	−	0.293247i
$77$	439833.	−	160086.i	0.109792	−	0.0399610i
$78$	−958915.	+	3.04979e6i	−0.228796	+	0.727677i
$79$	−536432.	−	3.04225e6i	−0.122411	−	0.694226i	−0.982812	−	0.184609i	$-0.940898\pi$
$79$	−536432.	−	3.04225e6i	−0.122411	−	0.694226i	0.860401	−	0.509617i	$-0.170213\pi$
$80$	−1.19970e6			−0.261974
$81$	1.65024e6	+	4.48927e6i	0.345024	+	0.938594i
$82$	6.88411e6			1.37879
$83$	−154525.	−	876352.i	−0.0296636	−	0.168231i	0.966377	−	0.257129i	$-0.0827765\pi$
$83$	−154525.	−	876352.i	−0.0296636	−	0.168231i	−0.996041	+	0.0888982i	$0.971665\pi$
$84$	340274.	−	1.08223e6i	0.0626400	−	0.199224i
$85$	3.41179e6	−	1.24179e6i	0.602583	−	0.219322i
$86$	4.36420e6	+	3.66200e6i	0.739877	+	0.620831i
$87$	7.09980e6	+	928932.i	1.15592	+	0.151240i
$88$	−594117.	−	216241.i	−0.0929357	−	0.0338258i
$89$	−3.33231e6	−	5.77174e6i	−0.501050	−	0.867844i	−0.999999	−	0.00121272i	$-0.999614\pi$
$89$	−3.33231e6	−	5.77174e6i	−0.501050	−	0.867844i	0.498949	−	0.866631i	$-0.333719\pi$
$90$	−4.64092e6	+	2.17314e6i	−0.671050	+	0.314223i
$91$	1.61951e6	−	2.80507e6i	0.225288	−	0.390210i
$92$	−1.45718e6	+	1.22272e6i	−0.195099	+	0.163708i
$93$	271066.	+	6.09656e6i	0.0349449	+	0.785949i
$94$	815412.	−	4.62443e6i	0.101258	−	0.574263i
$95$	1.38745e6	−	7.86862e6i	0.166029	−	0.941599i
$96$	−1.29176e6	+	824395.i	−0.149016	+	0.0951012i
$97$	9.69544e6	−	8.13544e6i	1.07862	−	0.905065i	0.0828099	−	0.996565i	$-0.473611\pi$
$97$	9.69544e6	−	8.13544e6i	1.07862	−	0.905065i	0.995805	+	0.0914999i	$0.0291661\pi$
$98$	2.71949e6	−	4.71029e6i	0.291874	−	0.505541i
$99$	−2.68997e6	+	239677.i	−0.278628	+	0.0248258i
$100$	−245224.	−	424740.i	−0.0245224	−	0.0424740i
$101$	−2.60144e6	−	946846.i	−0.251240	−	0.0914438i	0.213330	−	0.976980i	$-0.431569\pi$
$101$	−2.60144e6	−	946846.i	−0.251240	−	0.0914438i	−0.464570	+	0.885536i	$0.653791\pi$
$102$	2.82028e6	−	3.68155e6i	0.263143	−	0.343502i
$103$	7.05808e6	+	5.92243e6i	0.636438	+	0.534035i	0.902922	−	0.429804i	$-0.141417\pi$
$103$	7.05808e6	+	5.92243e6i	0.636438	+	0.534035i	−0.266484	+	0.963839i	$0.585862\pi$
$104$	−4.11133e6	+	1.49640e6i	−0.358398	+	0.130446i
$105$	5.06790e6	−	1.12778e6i	0.427234	−	0.0950740i
$106$	−1.72956e6	−	9.80881e6i	−0.141047	−	0.799918i
$107$	−8.27311e6			−0.652868			−0.326434	−	0.945220i	$-0.605847\pi$
$107$	−8.27311e6			−0.652868			−0.326434	+	0.945220i	$0.605847\pi$
$108$	−3.50373e6	+	5.52897e6i	−0.267637	+	0.422339i
$109$	2.22285e7			1.64406			0.822030	−	0.569445i	$-0.192842\pi$
$109$	2.22285e7			1.64406			0.822030	+	0.569445i	$0.192842\pi$
$110$	−502447.	−	2.84952e6i	−0.0359928	−	0.204125i
$111$	−9.46137e6	−	1.03087e7i	−0.656634	−	0.715441i
$112$	1.45892e6	−	531003.i	0.0981224	−	0.0357137i
$113$	2.74753e6	+	2.30545e6i	0.179130	+	0.150308i	0.727944	−	0.685637i	$-0.240476\pi$
$113$	2.74753e6	+	2.30545e6i	0.179130	+	0.150308i	−0.548814	+	0.835944i	$0.684921\pi$
$114$	−3.91313e6	−	9.42582e6i	−0.247376	−	0.595871i
$115$	−8.18047e6	−	2.97745e6i	−0.501575	−	0.182558i
$116$	4.89957e6	+	8.48630e6i	0.291444	+	0.504795i
$117$	−1.31937e7	+	1.32359e7i	−0.761578	+	0.764018i
$118$	6.91212e6	−	1.19721e7i	0.387279	−	0.670788i
$119$	−3.59934e6	+	3.02020e6i	−0.195798	+	0.164294i
$120$	−6.22326e6	−	3.23330e6i	−0.328763	−	0.170809i
$121$	−3.11912e6	+	1.76894e7i	−0.160060	+	0.907747i
$122$	−426989.	+	2.42157e6i	−0.0212891	+	0.120736i
$123$	3.57102e7	+	1.85533e7i	1.73031	+	0.898984i
$124$	−6.39769e6	+	5.36830e6i	−0.301333	+	0.252849i
$125$	−1.03190e7	+	1.78730e7i	−0.472555	+	0.818489i
$126$	4.68181e6	−	4.69681e6i	0.208505	−	0.209173i
$127$	7.61075e6	+	1.31822e7i	0.329696	+	0.571051i	0.982452	−	0.186518i	$-0.0597203\pi$
$127$	7.61075e6	+	1.31822e7i	0.329696	+	0.571051i	−0.652755	+	0.757569i	$0.726387\pi$
$128$	−1.97068e6	−	717268.i	−0.0830579	−	0.0302306i
$129$	1.27691e7	+	3.07579e7i	0.523718	+	1.26151i
$130$	−1.53386e7	−	1.28706e7i	−0.612326	−	0.513803i
$131$	−7.53416e6	+	2.74221e6i	−0.292810	+	0.106574i	−0.484248	−	0.874931i	$-0.660907\pi$
$131$	−7.53416e6	+	2.74221e6i	−0.292810	+	0.106574i	0.191439	+	0.981505i	$0.438685\pi$
$132$	−2.49909e6	−	2.72291e6i	−0.0945744	−	0.103044i
$133$	1.79552e6	+	1.01829e7i	0.0661772	+	0.375310i
$134$	4.25923e6			0.152920
$135$	−2.99308e7	−	1.23488e6i	−1.04701	−	0.0431973i
$136$	6.34677e6			0.216355
$137$	−3.22157e6	−	1.82704e7i	−0.107040	−	0.607054i	−0.990386	−	0.138332i	$-0.955826\pi$
$137$	−3.22157e6	−	1.82704e7i	−0.107040	−	0.607054i	0.883346	−	0.468722i	$-0.155285\pi$
$138$	−1.08542e7	+	2.41542e6i	−0.351577	+	0.0782378i
$139$	−4.37265e7	+	1.59151e7i	−1.38100	+	0.502642i	−0.922480	−	0.386044i	$-0.873841\pi$
$139$	−4.37265e7	+	1.59151e7i	−1.38100	+	0.502642i	−0.458516	+	0.888686i	$0.651619\pi$
$140$	5.44294e6	+	4.56717e6i	0.167643	+	0.140669i
$141$	1.66930e7	−	2.17909e7i	0.501497	−	0.654647i
$142$	−7.19510e6	−	2.61880e6i	−0.210876	−	0.0767527i
$143$	−5.27610e6	−	9.13847e6i	−0.150882	−	0.261335i
$144$	−8.92260e6	+	795007.i	−0.249014	+	0.0221872i
$145$	−2.24229e7	+	3.88376e7i	−0.610806	+	1.05795i
$146$	−5.29521e6	+	4.44321e6i	−0.140815	+	0.118158i
$147$	2.68015e7	−	1.71046e7i	0.695902	−	0.444121i
$148$	3.32520e6	−	1.88581e7i	0.0843144	−	0.478171i
$149$	1.26664e7	−	7.18344e7i	0.313689	−	1.77902i	−0.265788	−	0.964032i	$-0.585632\pi$
$149$	1.26664e7	−	7.18344e7i	0.313689	−	1.77902i	0.579477	−	0.814988i	$-0.303257\pi$
$150$	−127347.	−	2.86416e6i	−0.00308083	−	0.0692913i
$151$	−5.22318e7	+	4.38277e7i	−1.23457	+	1.03593i	−0.236641	+	0.971597i	$0.576047\pi$
$151$	−5.22318e7	+	4.38277e7i	−1.23457	+	1.03593i	−0.997929	+	0.0643303i	$0.979509\pi$
$152$	6.98350e6	−	1.20958e7i	0.161295	−	0.279371i
$153$	2.45518e7	−	1.14965e7i	0.554196	−	0.259505i
$154$	1.87224e6	+	3.24282e6i	0.0413085	+	0.0715484i
$155$	−3.59161e7	−	1.30724e7i	−0.774690	−	0.281964i
$156$	−2.53598e7	−	3.31805e6i	−0.534822	−	0.0699756i
$157$	−4.41299e7	−	3.70294e7i	−0.910090	−	0.763657i	0.0620458	−	0.998073i	$-0.480238\pi$
$157$	−4.41299e7	−	3.70294e7i	−0.910090	−	0.763657i	−0.972136	+	0.234417i	$0.924682\pi$
$158$	2.32231e7	−	8.45251e6i	0.468403	−	0.170485i
$159$	1.74638e7	−	5.55428e7i	0.344547	−	1.09582i
$160$	−1.66661e6	−	9.45182e6i	−0.0321673	−	0.182430i
$161$	1.12659e7			0.212752
$162$	−3.30760e7	+	1.92378e7i	−0.611239	+	0.355510i
$163$	−3.36654e7			−0.608874			−0.304437	−	0.952532i	$-0.598468\pi$
$163$	−3.36654e7			−0.608874			−0.304437	+	0.952532i	$0.598468\pi$
$164$	9.56330e6	+	5.42362e7i	0.169299	+	0.960143i
$165$	5.07333e6	−	1.61355e7i	0.0879224	−	0.279634i
$166$	6.68964e6	−	2.43483e6i	0.113508	−	0.0413134i
$167$	8.22778e7	+	6.90392e7i	1.36702	+	1.14707i	0.973744	+	0.227646i	$0.0731028\pi$
$167$	8.22778e7	+	6.90392e7i	1.36702	+	1.14707i	0.393276	+	0.919420i	$0.371342\pi$
$168$	8.99900e6	+	1.17742e6i	0.146424	+	0.0191580i
$169$	−9.65390e6	−	3.51373e6i	−0.153851	−	0.0559970i
$170$	1.45230e7	+	2.51546e7i	0.226718	+	0.392687i
$171$	5.10465e6	−	5.94411e7i	0.0780691	−	0.909076i
$172$	−2.27882e7	+	3.94704e7i	−0.341476	+	0.591455i
$173$	−7.41281e7	+	6.22008e7i	−1.08848	+	0.913345i	−0.996597	−	0.0824247i	$-0.973734\pi$
$173$	−7.41281e7	+	6.22008e7i	−1.08848	+	0.913345i	−0.0918848	+	0.995770i	$0.529289\pi$
$174$	2.54439e6	+	5.72260e7i	0.0366151	+	0.823513i
$175$	−504392.	+	2.86055e6i	−0.00711435	+	0.0403475i
$176$	878307.	−	4.98113e6i	0.0121437	−	0.0688705i
$177$	6.81214e7	−	4.34747e7i	0.923373	−	0.589292i
$178$	4.08432e7	−	3.42715e7i	0.542813	−	0.455474i
$179$	3.63047e7	−	6.28816e7i	0.473127	−	0.819480i	−0.526400	−	0.850237i	$-0.676459\pi$
$179$	3.63047e7	−	6.28816e7i	0.473127	−	0.819480i	0.999527	+	0.0307573i	$0.00979190\pi$
$180$	−2.35681e7	−	3.35444e7i	−0.301211	−	0.428713i
$181$	6.51077e7	+	1.12770e8i	0.816127	+	1.41357i	0.908516	+	0.417850i	$0.137216\pi$
$181$	6.51077e7	+	1.12770e8i	0.816127	+	1.41357i	−0.0923892	+	0.995723i	$0.529450\pi$
$182$	2.43494e7	+	8.86246e6i	0.299391	+	0.108969i
$183$	−8.74127e6	+	1.14107e7i	−0.105438	+	0.137637i
$184$	−1.16574e7	−	9.78174e6i	−0.137956	−	0.115759i
$185$	8.23507e7	−	2.99732e7i	0.956238	−	0.348042i
$186$	−4.76549e7	+	1.06048e7i	−0.543016	+	0.120839i
$187$	2.65809e6	+	1.50748e7i	0.0297251	+	0.168580i
$188$	3.75662e7			0.412330
$189$	3.69444e7	−	1.17460e7i	0.398045	−	0.126554i
$190$	6.39201e7			0.676082
$191$	9.12111e6	+	5.17284e7i	0.0947177	+	0.537171i	0.994833	+	0.101520i	$0.0323706\pi$
$191$	9.12111e6	+	5.17284e7i	0.0947177	+	0.537171i	−0.900116	+	0.435651i	$0.856518\pi$
$192$	−8.28946e6	−	9.03185e6i	−0.0845224	−	0.0920921i
$193$	1.42521e8	−	5.18732e7i	1.42701	−	0.519389i	0.490937	−	0.871195i	$-0.336655\pi$
$193$	1.42521e8	−	5.18732e7i	1.42701	−	0.519389i	0.936073	+	0.351806i	$0.114432\pi$
$194$	7.75635e7	+	6.50835e7i	0.762696	+	0.639978i
$195$	−4.48789e7	−	1.08103e8i	−0.433432	−	1.04404i
$196$	4.08877e7	+	1.48819e7i	0.387879	+	0.141176i
$197$	−2.05309e6	−	3.55606e6i	−0.0191327	−	0.0331388i	0.856301	−	0.516478i	$-0.172757\pi$
$197$	−2.05309e6	−	3.55606e6i	−0.0191327	−	0.0331388i	−0.875433	+	0.483339i	$0.839424\pi$
$198$	−5.62516e6	−	2.08599e7i	−0.0514999	−	0.190978i
$199$	3.16624e7	−	5.48409e7i	0.284812	−	0.493309i	−0.687751	−	0.725946i	$-0.741402\pi$
$199$	3.16624e7	−	5.48409e7i	0.284812	−	0.493309i	0.972564	+	0.232637i	$0.0747354\pi$
$200$	3.00564e6	−	2.52203e6i	0.0265663	−	0.0222918i
$201$	2.20940e7	+	1.14790e7i	0.191906	+	0.0997051i
$202$	3.84581e6	−	2.18107e7i	0.0328290	−	0.186183i
$203$	1.00777e7	−	5.71537e7i	0.0845527	−	0.479522i
$204$	3.29228e7	+	1.71051e7i	0.271513	+	0.141065i
$205$	−1.93075e8	+	1.62009e8i	−1.56526	+	1.31341i
$206$	−3.68547e7	+	6.38342e7i	−0.293736	+	0.508766i
$207$	−6.28140e7	−	1.67234e7i	−0.492222	−	0.131047i
$208$	−1.75008e7	−	3.03122e7i	−0.134845	−	0.233559i
$209$	3.16545e7	+	1.15213e7i	0.239841	+	0.0872949i
$210$	1.59254e7	+	3.83606e7i	0.118665	+	0.285837i
$211$	−1.57456e8	−	1.32122e8i	−1.15391	−	0.968245i	−0.154106	−	0.988054i	$-0.549250\pi$
$211$	−1.57456e8	−	1.32122e8i	−1.15391	−	0.968245i	−0.999804	+	0.0198088i	$0.993694\pi$
$212$	7.48756e7	−	2.72525e7i	0.539716	−	0.196440i
$213$	−3.02655e7	−	3.29760e7i	−0.214595	−	0.233813i
$214$	−1.14929e7	−	6.51794e7i	−0.0801643	−	0.454634i
$215$	−2.08581e8			−1.43133
$216$	−4.84271e7	−	1.99232e7i	−0.326964	−	0.134515i
$217$	4.94624e7			0.328599
$218$	3.08795e7	+	1.75126e8i	0.201870	+	1.14486i
$219$	−3.94428e7	+	8.77736e6i	−0.253754	+	0.0564689i
$220$	2.17518e7	−	7.91702e6i	0.137726	−	0.0501282i
$221$	8.11454e7	+	6.80891e7i	0.505698	+	0.424331i
$222$	6.80732e7	−	8.88617e7i	0.417581	−	0.545104i
$223$	−1.88493e8	−	6.86059e7i	−1.13823	−	0.414281i	−0.296954	−	0.954892i	$-0.595971\pi$
$223$	−1.88493e8	−	6.86059e7i	−1.13823	−	0.414281i	−0.841273	+	0.540611i	$0.818193\pi$
$224$	6.21020e6	+	1.07564e7i	0.0369179	+	0.0639438i
$225$	7.05857e6	−	1.52006e7i	0.0413122	−	0.0889654i
$226$	−1.43466e7	+	2.48490e7i	−0.0826740	+	0.143196i
$227$	4.72320e7	−	3.96324e7i	0.268007	−	0.224884i	−0.498873	−	0.866675i	$-0.666253\pi$
$227$	4.72320e7	−	3.96324e7i	0.268007	−	0.224884i	0.766880	+	0.641791i	$0.221808\pi$
$228$	6.88249e7	−	4.39237e7i	0.384568	−	0.245430i
$229$	7.96726e6	−	4.51846e7i	0.0438414	−	0.248637i	−0.955009	−	0.296578i	$-0.904155\pi$
$229$	7.96726e6	−	4.51846e7i	0.0438414	−	0.248637i	0.998850	+	0.0479405i	$0.0152658\pi$
$230$	1.20935e7	−	6.85858e7i	0.0655398	−	0.371695i
$231$	972270.	+	2.18674e7i	0.00518973	+	0.116723i
$232$	−6.00526e7	+	5.03901e7i	−0.315736	+	0.264934i
$233$	1.39050e8	−	2.40841e8i	0.720153	−	1.24734i	−0.240786	−	0.970578i	$-0.577405\pi$
$233$	1.39050e8	−	2.40841e8i	0.720153	−	1.24734i	0.960938	−	0.276763i	$-0.0892616\pi$
$234$	−1.22607e8	−	8.55585e7i	−0.625547	−	0.436524i
$235$	8.59609e7	+	1.48889e8i	0.432079	+	0.748383i
$236$	1.03924e8	+	3.78254e7i	0.514666	+	0.187323i
$237$	1.43246e8	+	1.87422e7i	0.698978	+	0.0914537i
$238$	−2.87947e7	−	2.41616e7i	−0.138450	−	0.116173i
$239$	−6.44878e7	+	2.34716e7i	−0.305552	+	0.111212i	−0.490245	−	0.871584i	$-0.663093\pi$
$239$	−6.44878e7	+	2.34716e7i	−0.305552	+	0.111212i	0.184694	+	0.982796i	$0.440871\pi$
$240$	1.68282e7	−	5.35213e7i	0.0785774	−	0.249912i
$241$	2.23175e7	+	1.26569e8i	0.102704	+	0.582461i	0.992113	+	0.125349i	$0.0400050\pi$
$241$	2.23175e7	+	1.26569e8i	0.102704	+	0.582461i	−0.889409	+	0.457112i	$0.848884\pi$
$242$	−1.43698e8			−0.651776
$243$	−2.23424e8	+	1.06500e7i	−0.998866	+	0.0476131i
$244$	−1.96714e7			−0.0866905
$245$	3.45789e7	+	1.96107e8i	0.150221	+	0.851943i
$246$	−9.65631e7	+	3.07115e8i	−0.413560	+	1.31531i
$247$	2.19051e8	−	7.97282e7i	0.924925	−	0.336645i
$248$	−5.11815e7	−	4.29464e7i	−0.213075	−	0.178791i
$249$	4.12635e7	+	5.39888e6i	0.169382	+	0.0221618i
$250$	−1.55147e8	−	5.64689e7i	−0.627991	−	0.228570i
$251$	−2.12876e8	−	3.68711e8i	−0.849704	−	1.47173i	−0.881472	−	0.472236i	$-0.843447\pi$
$251$	−2.12876e8	−	3.68711e8i	−0.849704	−	1.47173i	0.0317680	−	0.999495i	$-0.489886\pi$
$252$	4.35075e7	+	3.03607e7i	0.171263	+	0.119512i
$253$	1.83512e7	−	3.17852e7i	0.0712431	−	0.123397i
$254$	−9.32827e7	+	7.82735e7i	−0.357177	+	0.299707i
$255$	7.54193e6	+	1.69626e8i	0.0284834	+	0.640622i
$256$	2.91333e6	−	1.65223e7i	0.0108530	−	0.0615505i
$257$	−6.83198e7	+	3.87461e8i	−0.251062	+	1.42384i	0.554921	+	0.831903i	$0.312748\pi$
$257$	−6.83198e7	+	3.87461e8i	−0.251062	+	1.42384i	−0.805983	+	0.591939i	$0.798363\pi$
$258$	−2.24586e8	+	1.43330e8i	−0.814167	+	0.519597i
$259$	−8.68775e7	+	7.28989e7i	−0.310712	+	0.260718i
$260$	8.00923e7	−	1.38724e8i	0.282608	−	0.489491i
$261$	−1.41030e8	+	3.03707e8i	−0.490987	+	1.05734i
$262$	−3.20708e7	−	5.55482e7i	−0.110168	−	0.190816i
$263$	−4.27344e7	−	1.55541e7i	−0.144855	−	0.0527228i	0.268575	−	0.963259i	$-0.413447\pi$
$263$	−4.27344e7	−	1.55541e7i	−0.144855	−	0.0527228i	−0.413430	+	0.910536i	$0.635669\pi$
$264$	1.79806e7	−	2.34716e7i	0.0601438	−	0.0785108i
$265$	2.79346e8	+	2.34399e8i	0.922108	+	0.773741i
$266$	−7.77311e7	+	2.82918e7i	−0.253226	+	0.0921669i
$267$	3.04232e8	−	6.77018e7i	0.978172	−	0.217676i
$268$	5.91686e6	+	3.35562e7i	0.0187767	+	0.106488i
$269$	−5.95715e8			−1.86597			−0.932987	−	0.359910i	$-0.882807\pi$
$269$	−5.95715e8			−1.86597			−0.932987	+	0.359910i	$0.882807\pi$
$270$	−3.18504e7	−	2.37524e8i	−0.0984786	−	0.734402i
$271$	3.63552e7			0.110962			0.0554810	−	0.998460i	$-0.482331\pi$
$271$	3.63552e7			0.110962			0.0554810	+	0.998460i	$0.482331\pi$
$272$	8.81685e6	+	5.00028e7i	0.0265658	+	0.150662i
$273$	1.02423e8	+	1.11596e8i	0.304670	+	0.331956i
$274$	1.39468e8	−	5.07621e7i	0.409587	−	0.149078i
$275$	7.24907e6	+	6.08269e6i	0.0210193	+	0.0176373i
$276$	−3.41083e7	−	8.21589e7i	−0.0976514	−	0.235219i
$277$	−1.79336e8	−	6.52728e7i	−0.506976	−	0.184524i	0.0758530	−	0.997119i	$-0.475832\pi$
$277$	−1.79336e8	−	6.52728e7i	−0.506976	−	0.184524i	−0.582829	+	0.812595i	$0.698054\pi$
$278$	−1.86131e8	−	3.22388e8i	−0.519591	−	0.899958i
$279$	−2.75783e8	−	7.34233e7i	−0.760243	−	0.202404i
$280$	−2.84210e7	+	4.92266e7i	−0.0773725	+	0.134013i
$281$	−2.74078e8	+	2.29979e8i	−0.736888	+	0.618323i	−0.932000	−	0.362458i	$-0.881938\pi$
$281$	−2.74078e8	+	2.29979e8i	−0.736888	+	0.618323i	0.195112	+	0.980781i	$0.437493\pi$
$282$	1.94868e8	+	1.01244e8i	0.517451	+	0.268842i
$283$	1.29097e8	−	7.32143e8i	0.338581	−	1.92019i	−0.0499520	−	0.998752i	$-0.515907\pi$
$283$	1.29097e8	−	7.32143e8i	0.338581	−	1.92019i	0.388533	−	0.921435i	$-0.372982\pi$
$284$	1.06368e7	−	6.03243e7i	0.0275548	−	0.156271i
$285$	3.31574e8	+	1.72270e8i	0.848446	+	0.440811i
$286$	6.46676e7	−	5.42626e7i	0.163458	−	0.137157i
$287$	1.63085e8	−	2.82471e8i	0.407218	−	0.705322i
$288$	−1.86586e7	−	6.91920e7i	−0.0460262	−	0.170680i
$289$	1.28338e8	+	2.22289e8i	0.312762	+	0.541720i
$290$	−3.37130e8	−	1.22705e8i	−0.811716	−	0.295441i
$291$	2.26942e8	+	5.46650e8i	0.539870	+	1.30042i
$292$	−4.23617e7	−	3.55457e7i	−0.0995711	−	0.0835501i
$293$	6.12556e8	−	2.22952e8i	1.42269	−	0.517815i	0.487860	−	0.872922i	$-0.337778\pi$
$293$	6.12556e8	−	2.22952e8i	1.42269	−	0.517815i	0.934826	+	0.355107i	$0.115556\pi$
$294$	1.71990e8	+	1.87393e8i	0.394718	+	0.430069i
$295$	8.78892e7	+	4.98444e8i	0.199324	+	1.13042i
$296$	1.53193e8			0.343334
$297$	2.70396e7	−	1.23367e8i	0.0598897	−	0.273245i
$298$	5.83541e8			1.27736
$299$	−4.41038e7	−	2.50125e8i	−0.0954172	−	0.541138i
$300$	2.23883e7	−	4.98215e6i	0.0478737	−	0.0106535i
$301$	2.53648e8	−	9.23204e7i	0.536104	−	0.195126i
$302$	−4.17854e8	−	3.50622e8i	−0.872973	−	0.732511i
$303$	7.87310e7	−	1.02774e8i	0.162591	−	0.212244i
$304$	1.04998e8	+	3.82160e7i	0.214349	+	0.0780167i
$305$	−4.50132e7	−	7.79652e7i	−0.0908428	−	0.157344i
$306$	1.24682e8	+	1.77460e8i	0.248759	+	0.354058i
$307$	4.35696e8	−	7.54647e8i	0.859407	−	1.48854i	−0.0130885	−	0.999914i	$-0.504166\pi$
$307$	4.35696e8	−	7.54647e8i	0.859407	−	1.48854i	0.872495	−	0.488622i	$-0.162500\pi$
$308$	−2.29475e7	+	1.92553e7i	−0.0447516	+	0.0375510i
$309$	−3.63216e8	+	2.31803e8i	−0.700342	+	0.446955i
$310$	5.30962e7	−	3.01123e8i	0.101227	−	0.574088i
$311$	−4.70530e7	+	2.66851e8i	−0.0887005	+	0.503045i	0.907796	+	0.419412i	$0.137764\pi$
$311$	−4.70530e7	+	2.66851e8i	−0.0887005	+	0.503045i	−0.996497	+	0.0836336i	$0.973347\pi$
$312$	−9.08829e6	−	2.04405e8i	−0.0169411	−	0.381023i
$313$	−4.33585e8	+	3.63821e8i	−0.799225	+	0.670630i	−0.948010	−	0.318240i	$-0.896908\pi$
$313$	−4.33585e8	+	3.63821e8i	−0.799225	+	0.670630i	0.148785	+	0.988870i	$0.452464\pi$
$314$	2.30430e8	−	3.99117e8i	0.420035	−	0.727522i
$315$	−2.07746e7	+	2.41909e8i	−0.0374494	+	0.436080i
$316$	9.88540e7	+	1.71220e8i	0.176234	+	0.305246i
$317$	5.57370e8	+	2.02866e8i	0.982735	+	0.357686i	0.782903	−	0.622144i	$-0.213738\pi$
$317$	5.57370e8	+	2.02866e8i	0.982735	+	0.357686i	0.199832	+	0.979830i	$0.435960\pi$
$318$	4.61852e8	+	6.04284e7i	0.805394	+	0.105377i
$319$	−1.44836e8	−	1.21532e8i	−0.249810	−	0.209616i
$320$	7.21505e7	−	2.62607e7i	0.123088	−	0.0448003i
$321$	1.16047e8	−	3.69081e8i	0.195823	−	0.622808i
$322$	1.56504e7	+	8.87577e7i	0.0261234	+	0.148153i
$323$	−3.38155e8			−0.558351
$324$	−1.97513e8	−	2.33863e8i	−0.322617	−	0.381992i
$325$	6.54846e7			0.105815
$326$	−4.67675e7	−	2.65232e8i	−0.0747624	−	0.423998i
$327$	−3.11798e8	+	9.91662e8i	−0.493124	+	1.56836i
$328$	−4.14013e8	+	1.50688e8i	−0.647821	+	0.235788i
$329$	−1.70434e8	−	1.43011e8i	−0.263858	−	0.221404i
$330$	1.34171e8	+	1.75548e7i	0.205523	+	0.0268904i
$331$	7.86775e8	+	2.86363e8i	1.19248	+	0.434029i	0.860595	−	0.509290i	$-0.170092\pi$
$331$	7.86775e8	+	2.86363e8i	1.19248	+	0.434029i	0.331889	+	0.943318i	$0.392314\pi$
$332$	2.84759e7	+	4.93217e7i	0.0427065	+	0.0739698i
$333$	5.92608e8	−	2.77492e8i	0.879453	−	0.411809i
$334$	−4.29624e8	+	7.44131e8i	−0.630922	+	1.09279i
$335$	−1.19456e8	+	1.00236e8i	−0.173601	+	0.145669i
$336$	3.22501e6	+	7.25339e7i	0.00463814	+	0.104317i
$337$	7.65059e7	−	4.33887e8i	0.108891	−	0.617549i	−0.880704	−	0.473667i	$-0.842930\pi$
$337$	7.65059e7	−	4.33887e8i	0.108891	−	0.617549i	0.989595	−	0.143882i	$-0.0459587\pi$
$338$	1.42717e7	−	8.09391e7i	0.0201034	−	0.114012i
$339$	−1.41391e8	+	9.02348e7i	−0.197116	+	0.125798i
$340$	−1.78004e8	+	1.49363e8i	−0.245615	+	0.206095i
$341$	8.05703e7	−	1.39552e8i	0.110036	−	0.190588i
$342$	4.75395e8	−	4.23579e7i	0.642634	−	0.0572589i
$343$	−2.84927e8	−	4.93509e8i	−0.381246	−	0.660337i
$344$	−3.42623e8	−	1.24704e8i	−0.453797	−	0.165169i
$345$	2.47578e8	−	3.23184e8i	0.324597	−	0.423724i
$346$	−5.93025e8	−	4.97607e8i	−0.769673	−	0.645832i
$347$	4.05295e8	−	1.47515e8i	0.520736	−	0.189533i	−0.0682610	−	0.997668i	$-0.521745\pi$
$347$	4.05295e8	−	1.47515e8i	0.520736	−	0.189533i	0.588997	+	0.808135i	$0.299523\pi$
$348$	−4.47318e8	+	9.95433e7i	−0.568969	+	0.126615i
$349$	−2.36740e8	−	1.34262e9i	−0.298115	−	1.69069i	−0.654266	−	0.756264i	$-0.727022\pi$
$349$	−2.36740e8	−	1.34262e9i	−0.298115	−	1.69069i	0.356152	−	0.934428i	$-0.384089\pi$
$350$	−2.32374e7			−0.0289701
$351$	−4.05416e8	−	7.74257e8i	−0.500410	−	0.955675i
$352$	4.04637e7			0.0494500
$353$	7.35513e7	+	4.17130e8i	0.0889977	+	0.504731i	0.996422	+	0.0845157i	$0.0269343\pi$
$353$	7.35513e7	+	4.17130e8i	0.0889977	+	0.504731i	−0.907424	+	0.420215i	$0.861955\pi$
$354$	4.37147e8	+	4.76297e8i	0.523741	+	0.570646i
$355$	2.63427e8	−	9.58797e7i	0.312508	−	0.113744i
$356$	3.26746e8	+	2.74172e8i	0.383826	+	0.322069i
$357$	−8.42501e7	−	2.02939e8i	−0.0980012	−	0.236062i
$358$	5.45845e8	+	1.98671e8i	0.628751	+	0.228846i
$359$	6.71371e8	+	1.16285e9i	0.765830	+	1.32646i	0.939807	+	0.341706i	$0.111005\pi$
$359$	6.71371e8	+	1.16285e9i	0.765830	+	1.32646i	−0.173977	+	0.984750i	$0.555662\pi$
$360$	2.31538e8	−	2.32280e8i	0.261555	−	0.262393i
$361$	7.48556e7	−	1.29654e8i	0.0837431	−	0.145047i
$362$	−7.98007e8	+	6.69607e8i	−0.884151	+	0.741891i
$363$	−7.45411e8	−	3.87279e8i	−0.817942	−	0.424963i
$364$	−3.59967e7	+	2.04147e8i	−0.0391208	+	0.221865i
$365$	4.39464e7	−	2.49232e8i	0.0473041	−	0.268275i
$366$	−1.02042e8	−	5.30162e7i	−0.108792	−	0.0565229i
$367$	−3.43670e8	+	2.88373e8i	−0.362920	+	0.304526i	−0.805953	−	0.591979i	$-0.798347\pi$
$367$	−3.43670e8	+	2.88373e8i	−0.362920	+	0.304526i	0.443033	+	0.896505i	$0.353902\pi$
$368$	6.08708e7	−	1.05431e8i	0.0636709	−	0.110281i
$369$	−1.32861e9	+	1.33286e9i	−1.37659	+	1.38100i
$370$	3.50543e8	+	6.07158e8i	0.359779	+	0.623155i
$371$	−4.43452e8	−	1.61403e8i	−0.450856	−	0.164098i
$372$	−1.49751e8	−	3.60716e8i	−0.150824	−	0.363299i
$373$	4.37083e8	+	3.66756e8i	0.436097	+	0.365929i	0.834247	−	0.551392i	$-0.185903\pi$
$373$	4.37083e8	+	3.66756e8i	0.436097	+	0.365929i	−0.398149	+	0.917321i	$0.630347\pi$
$374$	−1.15073e8	+	4.18833e7i	−0.113743	+	0.0413990i
$375$	−6.52610e8	−	7.11057e8i	−0.639064	−	0.696297i
$376$	5.21864e7	+	2.95964e8i	0.0506290	+	0.287132i
$377$	−1.30838e9			−1.25759
$378$	1.43863e8	+	2.74748e8i	0.137003	+	0.261645i
$379$	−3.62240e8			−0.341790			−0.170895	−	0.985289i	$-0.554666\pi$
$379$	−3.62240e8			−0.341790			−0.170895	+	0.985289i	$0.554666\pi$
$380$	8.87968e7	+	5.03592e8i	0.0830147	+	0.470800i
$381$	−6.94842e8	+	1.54626e8i	−0.643648	+	0.143233i
$382$	−3.94869e8	+	1.43721e8i	−0.362436	+	0.131916i
$383$	1.10255e9	+	9.25153e8i	1.00278	+	0.841430i	0.987367	−	0.158452i	$-0.0506502\pi$
$383$	1.10255e9	+	9.25153e8i	1.00278	+	0.841430i	0.0154101	+	0.999881i	$0.495095\pi$
$384$	5.96415e7	−	7.78551e7i	0.0537513	−	0.0701662i
$385$	−1.28825e8	−	4.68886e7i	−0.115051	−	0.0418750i
$386$	6.06669e8	+	1.05078e9i	0.536903	+	0.929944i
$387$	−1.55129e9	+	1.38220e8i	−1.36052	+	0.121222i
$388$	−4.05008e8	+	7.01494e8i	−0.352008	+	0.609696i
$389$	4.36307e8	−	3.66105e8i	0.375810	−	0.315342i	−0.435245	−	0.900312i	$-0.643338\pi$
$389$	4.36307e8	−	3.66105e8i	0.375810	−	0.315342i	0.811055	+	0.584970i	$0.198894\pi$
$390$	7.89338e8	−	5.03751e8i	0.673809	−	0.430021i
$391$	−6.39782e7	+	3.62838e8i	−0.0541269	+	0.306969i
$392$	−6.04459e7	+	3.42806e8i	−0.0506834	+	0.287440i
$393$	−1.66546e7	−	3.74580e8i	−0.0138408	−	0.311294i
$394$	2.51641e7	−	2.11152e7i	0.0207274	−	0.0173924i
$395$	−4.52406e8	+	7.83589e8i	−0.369350	+	0.639733i
$396$	1.56529e8	−	7.32958e7i	0.126667	−	0.0593125i
$397$	−1.48521e8	−	2.57245e8i	−0.119130	−	0.206339i	0.800293	−	0.599609i	$-0.204677\pi$
$397$	−1.48521e8	−	2.57245e8i	−0.119130	−	0.206339i	−0.919423	+	0.393270i	$0.871344\pi$
$398$	4.76047e8	+	1.73267e8i	0.378494	+	0.137761i
$399$	−4.79466e8	−	6.27329e7i	−0.377879	−	0.0494413i
$400$	2.40451e7	+	2.01762e7i	0.0187852	+	0.0157627i
$401$	8.87779e8	−	3.23125e8i	0.687542	−	0.250245i	0.0254598	−	0.999676i	$-0.491895\pi$
$401$	8.87779e8	−	3.23125e8i	0.687542	−	0.250245i	0.662083	+	0.749431i	$0.269673\pi$
$402$	−5.97440e7	+	1.90013e8i	−0.0458673	+	0.145879i
$403$	−1.93636e8	−	1.09816e9i	−0.147373	−	0.835795i
$404$	1.77177e8			0.133682
$405$	4.74928e8	−	1.31795e9i	0.355251	−	0.985843i
$406$	4.64283e8			0.344304
$407$	6.41584e7	+	3.63861e8i	0.0471708	+	0.267519i
$408$	−8.90259e7	+	2.83143e8i	−0.0648942	+	0.206393i
$409$	2.26735e7	−	8.25250e6i	0.0163866	−	0.00596422i	−0.333814	−	0.942639i	$-0.608336\pi$
$409$	2.26735e7	−	8.25250e6i	0.0163866	−	0.00596422i	0.350200	+	0.936675i	$0.386113\pi$
$410$	−1.54460e9	−	1.29607e9i	−1.10681	−	0.928722i
$411$	8.60273e8	+	1.12557e8i	0.611209	+	0.0799701i
$412$	−5.54113e8	−	2.01681e8i	−0.390354	−	0.142077i
$413$	−3.27497e8	−	5.67241e8i	−0.228761	−	0.396226i
$414$	4.44940e7	−	5.18110e8i	0.0308177	−	0.358856i
$415$	−1.30320e8	+	2.25721e8i	−0.0895041	+	0.155026i
$416$	2.14502e8	−	1.79988e8i	0.146084	−	0.122579i
$417$	−9.66594e7	−	2.17397e9i	−0.0652781	−	1.46818i
$418$	−4.67961e7	+	2.65394e8i	−0.0313395	+	0.177735i
$419$	−1.69618e8	+	9.61951e8i	−0.112648	+	0.638858i	0.875240	+	0.483689i	$0.160703\pi$
$419$	−1.69618e8	+	9.61951e8i	−0.112648	+	0.638858i	−0.987888	+	0.155169i	$0.950408\pi$
$420$	−2.80099e8	+	1.78758e8i	−0.184476	+	0.117731i
$421$	−9.46802e8	+	7.94461e8i	−0.618403	+	0.518902i	−0.897301	−	0.441419i	$-0.854475\pi$
$421$	−9.46802e8	+	7.94461e8i	−0.618403	+	0.518902i	0.278898	+	0.960321i	$0.410031\pi$
$422$	8.22179e8	−	1.42406e9i	0.532565	−	0.922430i
$423$	7.37985e8	+	1.05037e9i	0.474085	+	0.674764i
$424$	3.18724e8	+	5.52046e8i	0.203065	+	0.351718i
$425$	−8.92650e7	−	3.24898e7i	−0.0564053	−	0.0205299i
$426$	2.17756e8	−	2.84255e8i	0.136470	−	0.178145i
$427$	8.92474e7	+	7.48875e7i	0.0554751	+	0.0465491i
$428$	4.97547e8	−	1.81092e8i	0.306748	−	0.111647i
$429$	4.81694e8	−	1.07193e8i	0.294558	−	0.0655491i
$430$	−2.89757e8	−	1.64330e9i	−0.175750	−	0.996727i
$431$	1.94020e9			1.16728			0.583642	−	0.812011i	$-0.301627\pi$
$431$	1.94020e9			1.16728			0.583642	+	0.812011i	$0.301627\pi$
$432$	8.96900e7	−	4.09208e8i	0.0535243	−	0.244203i
$433$	−7.76896e8			−0.459891			−0.229946	−	0.973203i	$-0.573855\pi$
$433$	−7.76896e8			−0.459891			−0.229946	+	0.973203i	$0.573855\pi$
$434$	6.87124e7	+	3.89687e8i	0.0403479	+	0.228824i
$435$	−1.41810e9	−	1.54511e9i	−0.826029	−	0.900007i
$436$	−1.33683e9	+	4.86566e8i	−0.772455	+	0.281151i
$437$	6.21106e8	+	5.21170e8i	0.356025	+	0.298741i
$438$	−1.23945e8	−	2.98555e8i	−0.0704809	−	0.169772i
$439$	−9.57419e8	−	3.48472e8i	−0.540102	−	0.196581i	0.0575412	−	0.998343i	$-0.481674\pi$
$439$	−9.57419e8	−	3.48472e8i	−0.540102	−	0.196581i	−0.597644	+	0.801762i	$0.703896\pi$
$440$	9.25912e7	+	1.60373e8i	0.0518186	+	0.0897524i
$441$	3.87129e8	+	1.43560e9i	0.214942	+	0.797072i
$442$	−4.23711e8	+	7.33889e8i	−0.233395	+	0.404252i
$443$	2.41867e9	−	2.02951e9i	1.32180	−	1.10912i	0.335874	−	0.941907i	$-0.390968\pi$
$443$	2.41867e9	−	2.02951e9i	1.32180	−	1.10912i	0.985921	−	0.167211i	$-0.0534762\pi$
$444$	7.94660e8	+	4.12867e8i	0.430865	+	0.223856i
$445$	−3.38969e8	+	1.92239e9i	−0.182348	+	1.03414i
$446$	2.78657e8	−	1.58034e9i	0.148730	−	0.843489i
$447$	3.02702e9	+	1.57269e9i	1.60302	+	0.832851i
$448$	−7.61166e7	+	6.38694e7i	−0.0399951	+	0.0335599i
$449$	−3.72732e8	+	6.45591e8i	−0.194328	+	0.336585i	−0.946680	−	0.322176i	$-0.895586\pi$
$449$	−3.72732e8	+	6.45591e8i	−0.194328	+	0.336585i	0.752352	+	0.658761i	$0.228919\pi$
$450$	1.29563e8	+	3.44943e7i	0.0670250	+	0.0178445i
$451$	−5.31305e8	−	9.20247e8i	−0.272726	−	0.472375i
$452$	−2.15702e8	−	7.85091e7i	−0.109868	−	0.0399886i
$453$	−1.22259e9	−	2.94494e9i	−0.617929	−	1.48845i
$454$	3.77856e8	+	3.17059e8i	0.189509	+	0.159017i
$455$	−8.91481e8	+	3.24473e8i	−0.443682	+	0.161487i
$456$	4.41662e8	+	4.81216e8i	0.218129	+	0.237664i
$457$	1.81620e7	+	1.03002e8i	0.00890136	+	0.0504821i	0.988935	−	0.148350i	$-0.0473962\pi$
$457$	1.81620e7	+	1.03002e8i	0.00890136	+	0.0504821i	−0.980034	+	0.198832i	$0.936285\pi$
$458$	3.67053e8			0.178525
$459$	1.68498e8	+	1.25657e9i	0.0813299	+	0.606516i
$460$	5.57151e8			0.266883
$461$	−3.94514e8	−	2.23740e9i	−0.187546	−	1.06363i	−0.922640	−	0.385663i	$-0.873973\pi$
$461$	−3.94514e8	−	2.23740e9i	−0.187546	−	1.06363i	0.735093	−	0.677966i	$-0.237138\pi$
$462$	−1.70931e8	+	3.80379e7i	−0.0806443	+	0.0179461i
$463$	−1.81358e9	+	6.60090e8i	−0.849188	+	0.309079i	−0.729709	−	0.683758i	$-0.760345\pi$
$463$	−1.81358e9	+	6.60090e8i	−0.849188	+	0.309079i	−0.119479	+	0.992837i	$0.538122\pi$
$464$	−4.80420e8	−	4.03121e8i	−0.223259	−	0.187336i
$465$	1.08698e9	−	1.41893e9i	0.501345	−	0.654448i
$466$	2.09062e9	+	7.60925e8i	0.957030	+	0.348330i
$467$	1.93825e9	+	3.35715e9i	0.880644	+	1.52532i	0.850626	+	0.525771i	$0.176223\pi$
$467$	1.93825e9	+	3.35715e9i	0.880644	+	1.52532i	0.0300182	+	0.999549i	$0.490443\pi$
$468$	5.03746e8	−	1.08481e9i	0.227170	−	0.489208i
$469$	1.00901e8	−	1.74766e8i	0.0451639	−	0.0782262i
$470$	−1.05360e9	+	8.84074e8i	−0.468093	+	0.392777i
$471$	2.27097e9	−	1.44932e9i	1.00147	−	0.639134i
$472$	−1.53636e8	+	8.71310e8i	−0.0672504	+	0.381396i
$473$	1.52703e8	−	8.66020e8i	0.0663487	−	0.376282i
$474$	5.13357e7	+	1.15459e9i	0.0221409	+	0.497973i
$475$	−1.60140e8	+	1.34373e8i	−0.0685602	+	0.0575288i
$476$	1.50355e8	−	2.60423e8i	0.0638991	−	0.110676i
$477$	2.23292e9	+	1.55819e9i	0.942018	+	0.657366i
$478$	−2.74506e8	−	4.75458e8i	−0.114962	−	0.199120i
$479$	2.50017e9	+	9.09989e8i	1.03943	+	0.378322i	0.804665	−	0.593729i	$-0.202345\pi$
$479$	2.50017e9	+	9.09989e8i	1.03943	+	0.378322i	0.234767	+	0.972052i	$0.424567\pi$
$480$	4.45043e8	+	5.82291e7i	0.183678	+	0.0240323i
$481$	1.95861e9	+	1.64347e9i	0.802492	+	0.673371i
$482$	−9.66164e8	+	3.51655e8i	−0.392994	+	0.143038i
$483$	−1.58026e8	+	5.02594e8i	−0.0638135	+	0.202956i
$484$	−1.99624e8	−	1.13212e9i	−0.0800301	−	0.453873i
$485$	−3.70704e9			−1.47547
$486$	−3.94282e8	−	1.74544e9i	−0.155805	−	0.689728i
$487$	1.92884e8			0.0756739			0.0378369	−	0.999284i	$-0.487953\pi$
$487$	1.92884e8			0.0756739			0.0378369	+	0.999284i	$0.487953\pi$
$488$	−2.73273e7	−	1.54981e8i	−0.0106445	−	0.0603682i
$489$	4.72224e8	−	1.50189e9i	0.182628	−	0.580840i
$490$	−1.49698e9	+	5.44857e8i	−0.574818	+	0.209217i
$491$	2.59841e9	+	2.18032e9i	0.990653	+	0.831257i	0.985662	−	0.168731i	$-0.0539668\pi$
$491$	2.59841e9	+	2.18032e9i	0.990653	+	0.831257i	0.00499117	+	0.999988i	$0.498411\pi$
$492$	−2.55374e9	−	3.34129e8i	−0.966715	−	0.126484i
$493$	1.78351e9	+	6.49146e8i	0.670366	+	0.243993i
$494$	9.32438e8	+	1.61503e9i	0.347997	+	0.602749i
$495$	6.48677e8	+	4.52665e8i	0.240387	+	0.167748i
$496$	2.67251e8	−	4.62892e8i	0.0983407	−	0.170331i
$497$	−2.77908e8	+	2.33192e8i	−0.101544	+	0.0852054i
$498$	1.47878e7	+	3.32593e8i	0.00536537	+	0.120673i
$499$	−2.14007e8	+	1.21369e9i	−0.0771037	+	0.437277i	0.921679	+	0.387953i	$0.126818\pi$
$499$	−2.14007e8	+	1.21369e9i	−0.0771037	+	0.437277i	−0.998783	+	0.0493239i	$0.984293\pi$
$500$	2.29360e8	−	1.30076e9i	0.0820583	−	0.465376i
$501$	−4.23410e9	+	2.70218e9i	−1.50428	+	0.960024i
$502$	2.60915e9	−	2.18934e9i	0.920528	−	0.772414i
$503$	1.34848e9	−	2.33563e9i	0.472449	−	0.818306i	−0.527054	−	0.849832i	$-0.676703\pi$
$503$	1.34848e9	−	2.33563e9i	0.472449	−	0.818306i	0.999503	+	0.0315260i	$0.0100367\pi$
$504$	−1.78756e8	+	3.84949e8i	−0.0621947	+	0.133936i
$505$	4.05426e8	+	7.02218e8i	0.140085	+	0.242634i
$506$	2.75912e8	+	1.00424e8i	0.0946768	+	0.0344596i
$507$	2.92170e8	−	3.81394e8i	0.0995652	−	0.129971i
$508$	−7.46262e8	−	6.26188e8i	−0.252562	−	0.211925i
$509$	−3.18831e9	+	1.16045e9i	−1.07164	+	0.390044i	−0.816789	−	0.576937i	$-0.804248\pi$
$509$	−3.18831e9	+	1.16045e9i	−1.07164	+	0.390044i	−0.254848	+	0.966981i	$0.582026\pi$
$510$	−1.32592e9	+	2.95061e8i	−0.442609	+	0.0984954i
$511$	5.68716e7	+	3.22535e8i	0.0188548	+	0.106931i
$512$	1.34218e8			0.0441942
$513$	2.58019e9	+	1.06151e9i	0.843803	+	0.347146i
$514$	−3.14750e9			−1.02234
$515$	−4.68616e8	−	2.65765e9i	−0.151179	−	0.857379i
$516$	−1.44121e9	−	1.57028e9i	−0.461799	−	0.503157i
$517$	−6.81113e8	+	2.47905e8i	−0.216771	+	0.0788983i
$518$	−6.95020e8	−	5.83191e8i	−0.219707	−	0.184356i
$519$	−1.73512e9	−	4.17950e9i	−0.544809	−	1.31232i
$520$	1.20419e9	+	4.38291e8i	0.375565	+	0.136694i
$521$	5.19981e8	+	9.00633e8i	0.161085	+	0.279008i	0.935258	−	0.353966i	$-0.115167\pi$
$521$	5.19981e8	+	9.00633e8i	0.161085	+	0.279008i	−0.774173	+	0.632974i	$0.781834\pi$
$522$	−2.58866e9	−	6.89195e8i	−0.796579	−	0.212078i
$523$	2.38797e9	−	4.13608e9i	0.729916	−	1.26425i	−0.227003	−	0.973894i	$-0.572893\pi$
$523$	2.38797e9	−	4.13608e9i	0.729916	−	1.26425i	0.956918	−	0.290357i	$-0.0937740\pi$
$524$	3.93082e8	−	3.29835e8i	0.119350	−	0.100147i
$525$	−1.20540e8	−	6.26268e7i	−0.0363559	−	0.0188887i
$526$	6.31761e7	−	3.58289e8i	0.0189279	−	0.107345i
$527$	−2.80894e8	+	1.59303e9i	−0.0835998	+	0.474118i
$528$	2.09899e8	+	1.09053e8i	0.0620571	+	0.0322418i
$529$	−1.93152e9	+	1.62074e9i	−0.567290	+	0.476013i
$530$	−1.45864e9	+	2.52644e9i	−0.425582	+	0.737129i
$531$	9.83966e8	+	3.64886e9i	0.285200	+	1.05761i
$532$	−3.30879e8	−	5.73099e8i	−0.0952749	−	0.165021i
$533$	−6.90988e9	−	2.51499e9i	−1.97663	−	0.719434i
$534$	9.56021e8	+	2.30283e9i	0.271690	+	0.654436i
$535$	1.85625e9	+	1.55758e9i	0.524081	+	0.439756i
$536$	−2.56151e8	+	9.32315e7i	−0.0718489	+	0.0261509i
$537$	2.29604e9	+	2.50167e9i	0.639837	+	0.697140i
$538$	−8.27559e8	−	4.69332e9i	−0.229119	−	1.29940i
$539$	−8.39543e8			−0.230931
$540$	1.82708e9	−	5.80897e8i	0.499320	−	0.158753i
$541$	−3.27453e9			−0.889117			−0.444558	−	0.895750i	$-0.646639\pi$
$541$	−3.27453e9			−0.889117			−0.444558	+	0.895750i	$0.646639\pi$
$542$	5.05041e7	+	2.86423e8i	0.0136248	+	0.0772699i
$543$	−5.94417e9	+	1.32278e9i	−1.59328	+	0.354558i
$544$	−3.81697e8	+	1.38926e8i	−0.101654	+	0.0369989i
$545$	−4.98744e9	−	4.18496e9i	−1.31975	−	1.10740i
$546$	−7.36921e8	+	9.61966e8i	−0.193752	+	0.252921i
$547$	6.33941e9	+	2.30736e9i	1.65612	+	0.602780i	0.989747	−	0.142834i	$-0.0456216\pi$
$547$	6.33941e9	+	2.30736e9i	1.65612	+	0.602780i	0.666378	+	0.745614i	$0.267844\pi$
$548$	5.93673e8	+	1.02827e9i	0.154105	+	0.266917i
$549$	−3.86444e8	−	5.50025e8i	−0.0996743	−	0.141866i
$550$	−3.78520e7	+	6.55615e7i	−0.00970106	+	0.0168027i
$551$	3.19959e9	−	2.68478e9i	0.814825	−	0.683719i
$552$	5.99903e8	−	3.82855e8i	0.151808	−	0.0968830i
$553$	2.03329e8	−	1.15314e9i	0.0511284	−	0.289963i
$554$	2.65119e8	−	1.50356e9i	0.0662456	−	0.375697i
$555$	1.82040e8	+	4.09427e9i	0.0452003	+	1.01660i
$556$	2.28135e9	−	1.91428e9i	0.562899	−	0.472329i
$557$	−7.89513e8	+	1.36748e9i	−0.193582	+	0.335295i	−0.946435	−	0.322895i	$-0.895344\pi$
$557$	−7.89513e8	+	1.36748e9i	−0.193582	+	0.335295i	0.752852	+	0.658189i	$0.228677\pi$
$558$	1.95349e8	−	2.27474e9i	0.0475984	−	0.554259i
$559$	−3.04269e9	−	5.27009e9i	−0.736743	−	1.27608i
$560$	−4.27312e8	−	1.55529e8i	−0.102822	−	0.0374243i
$561$	−7.09803e8	−	9.28700e7i	−0.169734	−	0.0222078i
$562$	−2.19262e9	−	1.83983e9i	−0.521059	−	0.437220i
$563$	−7.15026e9	+	2.60248e9i	−1.68866	+	0.614622i	−0.994456	−	0.105156i	$-0.966466\pi$
$563$	−7.15026e9	+	2.60248e9i	−1.68866	+	0.614622i	−0.694204	+	0.719778i	$0.744244\pi$
$564$	−5.26939e8	+	1.67591e9i	−0.123675	+	0.393345i
$565$	−1.82420e8	−	1.03456e9i	−0.0425503	−	0.241315i
$566$	5.94750e9			1.37872
$567$	5.79838e6	+	1.81293e9i	0.00133588	+	0.417677i
$568$	4.90039e8			0.112205
$569$	−9.94538e8	−	5.64030e9i	−0.226323	−	1.28354i	−0.860140	−	0.510058i	$-0.829624\pi$
$569$	−9.94538e8	−	5.64030e9i	−0.226323	−	1.28354i	0.633817	−	0.773483i	$-0.281487\pi$
$570$	−8.96604e8	+	2.85161e9i	−0.202786	+	0.644954i
$571$	3.37706e9	−	1.22915e9i	0.759124	−	0.276298i	0.0666840	−	0.997774i	$-0.478758\pi$
$571$	3.37706e9	−	1.22915e9i	0.759124	−	0.276298i	0.692440	+	0.721476i	$0.256536\pi$
$572$	5.17341e8	+	4.34101e8i	0.115582	+	0.0969849i
$573$	−2.43566e9	−	3.18679e8i	−0.540848	−	0.0707641i
$574$	2.45199e9	+	8.92453e8i	0.541162	+	0.196967i
$575$	1.13884e8	+	1.97252e8i	0.0249818	+	0.0432697i
$576$	5.19206e8	−	2.43121e8i	0.113204	−	0.0530084i
$577$	−2.50102e9	+	4.33189e9i	−0.542003	+	0.938777i	0.456786	+	0.889577i	$0.349001\pi$
$577$	−2.50102e9	+	4.33189e9i	−0.542003	+	0.938777i	−0.998789	+	0.0492000i	$0.984333\pi$
$578$	−1.57301e9	+	1.31991e9i	−0.338831	+	0.284313i
$579$	3.15048e8	+	7.08577e9i	0.0674531	+	1.51709i
$580$	4.98393e8	−	2.82653e9i	0.106065	−	0.601527i
$581$	5.85711e7	−	3.32173e8i	0.0123899	−	0.0702664i
$582$	−3.99150e9	+	2.54735e9i	−0.839277	+	0.535622i
$583$	−1.17773e9	+	9.88230e8i	−0.246153	+	0.206547i
$584$	2.21197e8	−	3.83124e8i	0.0459552	−	0.0795967i
$585$	5.45221e9	−	4.85793e8i	1.12597	−	0.100324i
$586$	2.60747e9	+	4.51627e9i	0.535276	+	0.927126i
$587$	−1.18543e9	−	4.31462e8i	−0.241904	−	0.0880460i	0.218223	−	0.975899i	$-0.429974\pi$
$587$	−1.18543e9	−	4.31462e8i	−0.241904	−	0.0880460i	−0.460127	+	0.887853i	$0.652196\pi$
$588$	−1.23744e9	+	1.61534e9i	−0.251018	+	0.327675i
$589$	2.72695e9	+	2.28818e9i	0.549886	+	0.461409i
$590$	−3.80488e9	+	1.38486e9i	−0.762709	+	0.277604i
$591$	1.87442e8	−	4.17122e7i	0.0373517	−	0.00831202i
$592$	2.12813e8	+	1.20692e9i	0.0421572	+	0.239085i
$593$	−5.80505e6			−0.00114318			−0.000571590	−	1.00000i	$-0.500182\pi$
$593$	−5.80505e6			−0.00114318			−0.000571590		1.00000i	$0.500182\pi$
$594$	1.00951e9	+	4.16502e7i	0.197632	+	0.00815388i
$595$	1.37620e9			0.267839
$596$	8.10646e8	+	4.59740e9i	0.156845	+	0.889510i
$597$	2.00245e9	+	2.18178e9i	0.385168	+	0.419663i
$598$	1.90933e9	−	6.94940e8i	0.365113	−	0.132890i
$599$	2.22305e9	+	1.86536e9i	0.422625	+	0.354624i	0.829160	−	0.559011i	$-0.188819\pi$
$599$	2.22305e9	+	1.86536e9i	0.422625	+	0.354624i	−0.406536	+	0.913635i	$0.633263\pi$
$600$	7.03532e7	+	1.69464e8i	0.0132970	+	0.0320294i
$601$	7.81467e9	+	2.84431e9i	1.46842	+	0.534461i	0.947671	−	0.319249i	$-0.103431\pi$
$601$	7.81467e9	+	2.84431e9i	1.46842	+	0.534461i	0.520749	+	0.853710i	$0.325653\pi$
$602$	1.07971e9	+	1.87011e9i	0.201706	+	0.349365i
$603$	−8.22014e8	+	8.24647e8i	−0.152675	+	0.153164i
$604$	2.18188e9	−	3.77913e9i	0.402904	−	0.697851i
$605$	4.03023e9	−	3.38176e9i	0.739922	−	0.620868i
$606$	9.19076e8	+	4.77507e8i	0.167763	+	0.0871617i
$607$	−5.23368e8	+	2.96817e9i	−0.0949832	+	0.538677i	0.899769	+	0.436366i	$0.143735\pi$
$607$	−5.23368e8	+	2.96817e9i	−0.0949832	+	0.538677i	−0.994752	+	0.102311i	$0.967376\pi$
$608$	−1.55222e8	+	8.80308e8i	−0.0280086	+	0.158845i
$609$	2.40839e9	+	1.25128e9i	0.432082	+	0.224489i
$610$	5.51714e8	−	4.62943e8i	0.0984146	−	0.0825796i
$611$	−2.50792e9	+	4.34385e9i	−0.444805	+	0.770425i
$612$	−1.22490e9	+	1.22883e9i	−0.216009	+	0.216701i
$613$	−4.82619e9	−	8.35921e9i	−0.846239	−	1.46573i	−0.884541	−	0.466463i	$-0.845528\pi$
$613$	−4.82619e9	−	8.35921e9i	−0.846239	−	1.46573i	0.0383015	−	0.999266i	$-0.487805\pi$
$614$	6.55072e9	+	2.38427e9i	1.14209	+	0.415686i
$615$	−4.51932e9	−	1.08860e10i	−0.783448	−	1.88714i
$616$	−1.83580e8	−	1.54042e8i	−0.0316441	−	0.0265526i
$617$	−1.39185e9	+	5.06593e8i	−0.238558	+	0.0868282i	−0.458533	−	0.888677i	$-0.651625\pi$
$617$	−1.39185e9	+	5.06593e8i	−0.238558	+	0.0868282i	0.219974	+	0.975506i	$0.429403\pi$
$618$	−2.33082e9	−	2.53957e9i	−0.397237	−	0.432813i
$619$	−1.34269e9	−	7.61476e9i	−0.227540	−	1.29044i	−0.857770	−	0.514034i	$-0.828150\pi$
$619$	−1.34269e9	−	7.61476e9i	−0.227540	−	1.29044i	0.630230	−	0.776409i	$-0.282961\pi$
$620$	2.44615e9			0.412204
$621$	1.62715e9	−	2.56769e9i	0.272652	−	0.430252i
$622$	−2.16774e9			−0.361194
$623$	−4.38664e8	−	2.48779e9i	−0.0726815	−	0.412197i
$624$	1.59777e9	−	3.55559e8i	0.263251	−	0.0585821i
$625$	6.24283e9	−	2.27220e9i	1.02283	−	0.372278i
$626$	−3.46868e9	−	2.91057e9i	−0.565138	−	0.474207i
$627$	−9.58005e8	+	1.25057e9i	−0.155214	+	0.202614i
$628$	3.46454e9	+	1.26099e9i	0.558196	+	0.203167i
$629$	−1.85447e9	−	3.21204e9i	−0.297128	−	0.514641i
$630$	−1.93473e9	+	1.72385e8i	−0.308269	+	0.0274668i
$631$	1.90670e9	−	3.30250e9i	0.302120	−	0.523287i	−0.674496	−	0.738278i	$-0.735639\pi$
$631$	1.90670e9	−	3.30250e9i	0.302120	−	0.523287i	0.976616	+	0.214991i	$0.0689724\pi$
$632$	−1.21162e9	+	1.01667e9i	−0.190923	+	0.160203i
$633$	8.10287e9	−	5.17121e9i	1.26977	−	0.810362i
$634$	−8.23983e8	+	4.67304e9i	−0.128412	+	0.728261i
$635$	7.74179e8	−	4.39059e9i	0.119987	−	0.680479i
$636$	1.65516e8	+	3.72263e9i	0.0255117	+	0.573786i
$637$	−4.45049e9	+	3.73440e9i	−0.682212	+	0.572444i
$638$	7.56282e8	−	1.30992e9i	0.115295	−	0.199697i
$639$	1.89566e9	−	8.87655e8i	0.287414	−	0.134583i
$640$	3.07124e8	+	5.31954e8i	0.0463110	+	0.0802130i
$641$	6.04956e9	+	2.20186e9i	0.907236	+	0.330207i	0.753149	−	0.657850i	$-0.228534\pi$
$641$	6.04956e9	+	2.20186e9i	0.907236	+	0.330207i	0.154087	+	0.988057i	$0.450756\pi$
$642$	3.06900e9	+	4.01546e8i	0.457746	+	0.0598911i
$643$	−3.18129e9	−	2.66942e9i	−0.471916	−	0.395985i	0.375577	−	0.926791i	$-0.377445\pi$
$643$	−3.18129e9	−	2.66942e9i	−0.471916	−	0.395985i	−0.847493	+	0.530806i	$0.821889\pi$
$644$	−6.77533e8	+	2.46602e8i	−0.0999608	+	0.0363828i
$645$	2.92575e9	−	9.30524e9i	0.429317	−	1.36543i
$646$	−4.69761e8	−	2.66415e9i	−0.0685587	−	0.388816i
$647$	−1.14162e9			−0.165713			−0.0828564	−	0.996561i	$-0.526404\pi$
$647$	−1.14162e9			−0.165713			−0.0828564	+	0.996561i	$0.526404\pi$
$648$	1.56810e9	−	1.88098e9i	0.226392	−	0.271563i
$649$	−2.13387e9			−0.306416
$650$	9.09703e7	+	5.15918e8i	0.0129928	+	0.0736858i
$651$	−6.93806e8	+	2.20662e9i	−0.0985609	+	0.313469i
$652$	2.02465e9	−	7.36913e8i	0.286077	−	0.104124i
$653$	1.55841e8	+	1.30766e8i	0.0219021	+	0.0183780i	0.653673	−	0.756777i	$-0.273227\pi$
$653$	1.55841e8	+	1.30766e8i	0.0219021	+	0.0183780i	−0.631771	+	0.775155i	$0.717672\pi$
$654$	−8.24591e9	−	1.07889e9i	−1.15270	−	0.150818i
$655$	2.20673e9	+	8.03183e8i	0.306835	+	0.111679i
$656$	−1.76233e9	−	3.05245e9i	−0.243739	−	0.422168i
$657$	1.61686e8	−	1.88275e9i	0.0222430	−	0.259008i
$658$	8.89944e8	−	1.54143e9i	0.121779	−	0.210927i
$659$	−3.45306e7	+	2.89746e7i	−0.00470008	+	0.00394384i	−0.645135	−	0.764069i	$-0.723199\pi$
$659$	−3.45306e7	+	2.89746e7i	−0.00470008	+	0.00394384i	0.640435	+	0.768013i	$0.278754\pi$
$660$	4.80834e7	+	1.08145e9i	0.00651016	+	0.146420i
$661$	−1.86145e9	+	1.05568e10i	−0.250696	+	1.42177i	0.556188	+	0.831056i	$0.312263\pi$
$661$	−1.86145e9	+	1.05568e10i	−0.250696	+	1.42177i	−0.806884	+	0.590710i	$0.798848\pi$
$662$	−1.16312e9	+	6.59639e9i	−0.155820	+	0.883697i
$663$	−4.17582e9	+	2.66499e9i	−0.556474	+	0.355139i
$664$	−3.49021e8	+	2.92863e8i	−0.0462661	+	0.0388219i
$665$	1.51427e9	−	2.62279e9i	0.199677	−	0.345850i
$666$	3.00945e9	+	4.28335e9i	0.394755	+	0.561855i
$667$	−2.27539e9	−	3.94110e9i	−0.296904	−	0.514253i
$668$	−6.45943e9	−	2.35104e9i	−0.838449	−	0.305171i
$669$	5.70464e9	−	7.44676e9i	0.736609	−	0.961559i
$670$	−9.55650e8	−	8.01886e8i	−0.122754	−	0.103003i
$671$	3.56663e8	−	1.29815e8i	0.0455752	−	0.0165880i
$672$	−5.66976e8	+	1.26171e8i	−0.0720729	+	0.0160386i
$673$	8.93822e7	+	5.06912e8i	0.0113031	+	0.0641032i	0.989938	−	0.141505i	$-0.0451940\pi$
$673$	8.93822e7	+	5.06912e8i	0.0113031	+	0.0641032i	−0.978634	+	0.205608i	$0.934083\pi$
$674$	3.52464e9			0.443410
$675$	5.79120e8	+	5.28116e8i	0.0724779	+	0.0660946i
$676$	6.57502e8			0.0818622
$677$	−6.34939e8	−	3.60092e9i	−0.0786451	−	0.446019i	−0.998548	−	0.0538721i	$-0.982844\pi$
$677$	−6.34939e8	−	3.60092e9i	−0.0786451	−	0.446019i	0.919903	−	0.392147i	$-0.128267\pi$
$678$	−9.07329e8	−	9.88588e8i	−0.111805	−	0.121818i
$679$	4.50801e9	−	1.64078e9i	0.552638	−	0.201144i
$680$	−1.42404e9	−	1.19491e9i	−0.173676	−	0.145731i
$681$	1.10556e9	+	2.66304e9i	0.134143	+	0.323120i
$682$	1.21138e9	+	4.40907e8i	0.146230	+	0.0532233i
$683$	−5.50656e9	−	9.53765e9i	−0.661315	−	1.14543i	−0.980270	−	0.197661i	$-0.936665\pi$
$683$	−5.50656e9	−	9.53765e9i	−0.661315	−	1.14543i	0.318956	−	0.947770i	$-0.396668\pi$
$684$	9.94127e8	+	3.68654e9i	0.118781	+	0.440477i
$685$	−2.71695e9	+	4.70589e9i	−0.322972	+	0.559404i
$686$	3.49227e9	−	2.93037e9i	0.413023	−	0.346567i
$687$	1.90402e9	+	9.89238e8i	0.224039	+	0.116400i
$688$	5.06513e8	−	2.87258e9i	0.0592968	−	0.336289i
$689$	−1.84745e9	+	1.04774e10i	−0.215181	+	1.22035i
$690$	2.89012e9	+	1.50157e9i	0.334923	+	0.174010i
$691$	−1.17328e10	+	9.84503e9i	−1.35279	+	1.13513i	−0.374653	+	0.927165i	$0.622238\pi$
$691$	−1.17328e10	+	9.84503e9i	−1.35279	+	1.13513i	−0.978137	+	0.207960i	$0.933318\pi$
$692$	3.09655e9	−	5.36339e9i	0.355228	−	0.615273i
$693$	−9.89190e8	−	2.63358e8i	−0.112905	−	0.0300594i
$694$	1.72522e9	+	2.98817e9i	0.195924	+	0.339350i
$695$	1.28073e10	+	4.66148e9i	1.44714	+	0.526717i
$696$	−1.40566e9	−	3.38589e9i	−0.158033	−	0.380663i
$697$	8.17137e9	+	6.85659e9i	0.914071	+	0.766997i
$698$	1.02489e10	−	3.73030e9i	1.14073	−	0.415193i
$699$	8.79400e9	+	9.58158e9i	0.973905	+	1.06113i
$700$	−3.22811e7	−	1.83075e8i	−0.00355717	−	0.0201737i
$701$	−1.19493e10			−1.31018			−0.655089	−	0.755552i	$-0.727369\pi$
$701$	−1.19493e10			−1.31018			−0.655089	+	0.755552i	$0.727369\pi$
$702$	5.53675e9	−	4.26964e9i	0.604053	−	0.465813i
$703$	−8.16208e9			−0.886048
$704$	5.62116e7	+	3.18792e8i	0.00607186	+	0.0344352i
$705$	−7.84801e9	+	1.74645e9i	−0.843525	+	0.187713i
$706$	−3.18417e9	+	1.15894e9i	−0.340549	+	0.123950i
$707$	−8.03835e8	−	6.74498e8i	−0.0855459	−	0.0717815i
$708$	−3.14521e9	+	4.10571e9i	−0.333069	+	0.434783i
$709$	−1.92786e9	−	7.01685e8i	−0.203149	−	0.0739402i	0.238442	−	0.971157i	$-0.423363\pi$
$709$	−1.92786e9	−	7.01685e8i	−0.203149	−	0.0739402i	−0.441591	+	0.897217i	$0.645586\pi$
$710$	1.12133e9	+	1.94221e9i	0.117579	+	0.203653i
$711$	−2.84543e9	+	6.12762e9i	−0.296896	+	0.639364i
$712$	−1.70615e9	+	2.95513e9i	−0.177148	+	0.306829i
$713$	2.97113e9	−	2.49308e9i	0.306979	−	0.257586i
$714$	1.48180e9	−	9.45680e8i	0.152352	−	0.0972301i
$715$	−5.36694e8	+	3.04374e9i	−0.0549106	+	0.311413i
$716$	−8.06944e8	+	4.57641e9i	−0.0821576	+	0.465939i
$717$	−1.42553e8	−	3.20617e9i	−0.0144431	−	0.324840i
$718$	−8.22880e9	+	6.90479e9i	−0.829662	+	0.696169i
$719$	−2.09360e9	+	3.62622e9i	−0.210060	+	0.363834i	−0.951733	−	0.306927i	$-0.900699\pi$
$719$	−2.09360e9	+	3.62622e9i	−0.210060	+	0.363834i	0.741673	+	0.670761i	$0.234033\pi$
$720$	2.15165e9	+	1.50148e9i	0.214837	+	0.149919i
$721$	1.74618e9	+	3.02447e9i	0.173506	+	0.300522i
$722$	1.12546e9	+	4.09634e8i	0.111288	+	0.0405057i
$723$	−5.95955e9	−	7.79742e8i	−0.586448	−	0.0767303i
$724$	−6.38405e9	−	5.35686e9i	−0.625189	−	0.524596i
$725$	1.10257e9	−	4.01302e8i	0.107454	−	0.0391101i
$726$	2.01565e9	−	6.41070e9i	0.195496	−	0.621766i
$727$	−2.45798e9	−	1.39399e10i	−0.237251	−	1.34552i	−0.837821	−	0.545945i	$-0.816171\pi$
$727$	−2.45798e9	−	1.39399e10i	−0.237251	−	1.34552i	0.600570	−	0.799572i	$-0.294940\pi$
$728$	−1.65837e9			−0.159303
$729$	2.65883e9	−	1.01168e10i	0.254182	−	0.967156i
$730$	2.02462e9			0.192625
$731$	1.53290e9	+	8.69351e9i	0.145145	+	0.823160i
$732$	2.75930e8	−	8.77585e8i	0.0260022	−	0.0826990i
$733$	−1.84588e10	+	6.71847e9i	−1.73117	+	0.630096i	−0.998713	−	0.0507135i	$-0.983850\pi$
$733$	−1.84588e10	+	6.71847e9i	−1.73117	+	0.630096i	−0.732461	+	0.680809i	$0.761628\pi$
$734$	−2.74936e9	−	2.30699e9i	−0.256623	−	0.215332i
$735$	−9.23377e9	−	1.20814e9i	−0.857775	−	0.112231i
$736$	9.15197e8	+	3.33104e8i	0.0846140	+	0.0307970i
$737$	−3.28721e8	−	5.69361e8i	−0.0302476	−	0.0523904i
$738$	−1.23466e10	−	8.61577e9i	−1.13070	−	0.789036i
$739$	−3.34563e9	+	5.79481e9i	−0.304946	+	0.528182i	−0.977249	−	0.212094i	$-0.931972\pi$
$739$	−3.34563e9	+	5.79481e9i	−0.304946	+	0.528182i	0.672303	+	0.740276i	$0.265305\pi$
$740$	−4.29651e9	+	3.60520e9i	−0.389766	+	0.327053i
$741$	4.84223e8	+	1.08907e10i	0.0437202	+	0.983313i
$742$	6.55572e8	−	3.71794e9i	0.0589124	−	0.334109i
$743$	8.02445e8	−	4.55089e9i	0.0717719	−	0.407039i	−0.927663	−	0.373419i	$-0.878185\pi$
$743$	8.02445e8	−	4.55089e9i	0.0717719	−	0.407039i	0.999435	−	0.0336197i	$-0.0107035\pi$
$744$	2.63385e9	−	1.68091e9i	0.234469	−	0.149637i
$745$	−1.63662e10	+	1.37329e10i	−1.45011	+	1.21679i
$746$	−2.28229e9	+	3.95304e9i	−0.201272	+	0.348614i
$747$	−8.19656e8	+	1.76512e9i	−0.0719465	+	0.154936i
$748$	−4.89834e8	−	8.48418e8i	−0.0427951	−	0.0741232i
$749$	−2.94673e9	−	1.07252e9i	−0.256244	−	0.0932652i
$750$	4.69544e9	−	6.12935e9i	0.406407	−	0.530518i
$751$	−5.15052e9	−	4.32180e9i	−0.443723	−	0.372327i	0.393378	−	0.919377i	$-0.371306\pi$
$751$	−5.15052e9	−	4.32180e9i	−0.443723	−	0.372327i	−0.837100	+	0.547050i	$0.815751\pi$
$752$	−2.25924e9	+	8.22297e8i	−0.193732	+	0.0705125i
$753$	1.94350e10	−	4.32494e9i	1.65883	−	0.369146i
$754$	−1.81758e9	−	1.03080e10i	−0.154417	−	0.875742i
$755$	1.99708e10			1.68881
$756$	−1.96474e9	+	1.51510e9i	−0.165378	+	0.127530i
$757$	1.78898e10			1.49889			0.749443	−	0.662068i	$-0.230321\pi$
$757$	1.78898e10			1.49889			0.749443	+	0.662068i	$0.230321\pi$
$758$	−5.03219e8	−	2.85390e9i	−0.0419677	−	0.238010i
$759$	1.16060e9	+	1.26454e9i	0.0963463	+	0.104975i
$760$	−3.84417e9	+	1.39916e9i	−0.317655	+	0.115617i
$761$	8.96378e9	+	7.52151e9i	0.737301	+	0.618669i	0.932111	−	0.362172i	$-0.117965\pi$
$761$	8.96378e9	+	7.52151e9i	0.737301	+	0.618669i	−0.194810	+	0.980841i	$0.562409\pi$
$762$	−2.18348e9	−	5.25948e9i	−0.178775	−	0.430626i
$763$	7.91738e9	+	2.88169e9i	0.645277	+	0.234861i
$764$	−1.68084e9	−	2.91131e9i	−0.136364	−	0.236190i
$765$	−7.67317e9	−	2.04287e9i	−0.619669	−	0.164978i
$766$	−5.75713e9	+	9.97164e9i	−0.462813	+	0.801615i
$767$	−1.13118e10	+	9.49174e9i	−0.905208	+	0.759560i
$768$	6.96232e8	+	3.61728e8i	0.0554612	+	0.0288150i
$769$	1.28850e9	−	7.30744e9i	0.102174	−	0.579459i	−0.890137	−	0.455693i	$-0.849392\pi$
$769$	1.28850e9	−	7.30744e9i	0.102174	−	0.579459i	0.992311	−	0.123766i	$-0.0394974\pi$
$770$	1.90448e8	−	1.08008e9i	0.0150334	−	0.0852589i
$771$	−1.63271e10	−	8.48279e9i	−1.28298	−	0.666574i
$772$	−7.43576e9	+	6.23935e9i	−0.581654	+	0.488066i
$773$	−4.75817e9	+	8.24139e9i	−0.370520	+	0.641759i	−0.989646	−	0.143533i	$-0.954154\pi$
$773$	−4.75817e9	+	8.24139e9i	−0.370520	+	0.641759i	0.619126	+	0.785292i	$0.287487\pi$
$774$	−3.24399e9	−	1.20297e10i	−0.251470	−	0.932530i
$775$	5.00002e8	+	8.66029e8i	0.0385848	+	0.0668307i
$776$	−6.08933e9	−	2.21633e9i	−0.467793	−	0.170263i
$777$	−2.03355e9	−	4.89834e9i	−0.155518	−	0.374607i
$778$	3.49045e9	+	2.92884e9i	0.265738	+	0.222980i
$779$	2.20585e10	−	8.02865e9i	1.67184	−	0.608502i
$780$	5.06532e9	+	5.51896e9i	0.382187	+	0.416415i
$781$	2.05233e8	+	1.16393e9i	0.0154159	+	0.0874279i
$782$	−2.94749e9			−0.220408
$783$	−1.15708e10	−	1.05517e10i	−0.861386	−	0.785522i
$784$	−2.78475e9			−0.206386
$785$	2.92997e9	+	1.66167e10i	0.216182	+	1.22603i
$786$	2.92798e9	−	6.51574e8i	0.215075	−	0.0478613i
$787$	2.20005e10	−	8.00753e9i	1.60887	−	0.585581i	0.627654	−	0.778493i	$-0.284015\pi$
$787$	2.20005e10	−	8.00753e9i	1.60887	−	0.585581i	0.981216	+	0.192912i	$0.0617932\pi$
$788$	2.01313e8	+	1.68922e8i	0.0146565	+	0.0122983i
$789$	1.29333e9	−	1.68830e9i	0.0937435	−	0.122371i
$790$	−6.80195e9	−	2.47571e9i	−0.490839	−	0.178651i
$791$	6.79742e8	+	1.17735e9i	0.0488345	+	0.0845838i
$792$	7.94907e8	+	1.13139e9i	0.0568562	+	0.0809234i
$793$	1.31327e9	−	2.27464e9i	0.0935183	−	0.161978i
$794$	1.82037e9	−	1.52748e9i	0.129059	−	0.108294i
$795$	−1.43754e10	+	9.17432e9i	−1.01470	+	0.647574i
$796$	−7.03760e8	+	3.99122e9i	−0.0494571	+	0.280485i
$797$	−8.29581e7	+	4.70478e8i	−0.00580436	+	0.0329182i	−0.987572	−	0.157165i	$-0.949765\pi$
$797$	−8.29581e7	+	4.70478e8i	−0.00580436	+	0.0329182i	0.981768	+	0.190083i	$0.0608757\pi$
$798$	−1.71828e8	−	3.86460e9i	−0.0119697	−	0.269212i
$799$	5.57384e9	−	4.67700e9i	0.386581	−	0.324380i
$800$	−1.25555e8	+	2.17467e8i	−0.00866997	+	0.0150168i
$801$	−1.24712e9	+	1.45221e10i	−0.0857422	+	0.998425i
$802$	3.77902e9	+	6.54545e9i	0.258683	+	0.448053i
$803$	1.00263e9	+	3.64928e8i	0.0683340	+	0.0248715i
$804$	−1.58001e9	−	2.06727e8i	−0.107217	−	0.0140282i
$805$	−2.52774e9	−	2.12103e9i	−0.170784	−	0.143305i
$806$	8.38285e9	−	3.05111e9i	0.563922	−	0.205251i
$807$	8.35607e9	−	2.65761e10i	0.559686	−	1.78006i
$808$	2.46132e8	+	1.39588e9i	0.0164145	+	0.0930913i
$809$	2.06645e10			1.37216			0.686081	−	0.727525i	$-0.259330\pi$
$809$	2.06645e10			1.37216			0.686081	+	0.727525i	$0.259330\pi$
$810$	1.10432e10	+	1.91082e9i	0.730126	+	0.126335i
$811$	−4.03303e9			−0.265496			−0.132748	−	0.991150i	$-0.542380\pi$
$811$	−4.03303e9			−0.265496			−0.132748	+	0.991150i	$0.542380\pi$
$812$	6.44976e8	+	3.65784e9i	0.0422763	+	0.239761i
$813$	−5.09953e8	+	1.62188e9i	−0.0332823	+	0.105853i
$814$	−2.77753e9	+	1.01094e9i	−0.180499	+	0.0656961i
$815$	7.55357e9	+	6.33820e9i	0.488766	+	0.410123i
$816$	−2.35441e9	−	3.08049e8i	−0.151693	−	0.0198474i
$817$	1.82549e10	+	6.64424e9i	1.17112	+	0.426254i
$818$	9.65147e7	+	1.67168e8i	0.00616534	+	0.0106787i
$819$	−6.41523e9	+	3.00397e9i	−0.408055	+	0.191074i
$820$	8.06532e9	−	1.39695e10i	0.510826	−	0.884777i
$821$	−3.34586e9	+	2.80751e9i	−0.211012	+	0.177060i	−0.742168	−	0.670214i	$-0.766202\pi$
$821$	−3.34586e9	+	2.80751e9i	−0.211012	+	0.177060i	0.531156	+	0.847274i	$0.321758\pi$
$822$	3.08300e8	+	6.93399e9i	0.0193607	+	0.435444i
$823$	4.80817e9	−	2.72685e10i	0.300663	−	1.70515i	−0.342583	−	0.939487i	$-0.611302\pi$
$823$	4.80817e9	−	2.72685e10i	0.300663	−	1.70515i	0.643247	−	0.765659i	$-0.277587\pi$
$824$	8.19168e8	−	4.64573e9i	0.0510067	−	0.289274i
$825$	−3.73045e8	+	2.38075e8i	−0.0231298	+	0.0147613i
$826$	4.01403e9	−	3.36817e9i	0.247828	−	0.207953i
$827$	−3.71915e9	+	6.44175e9i	−0.228652	+	0.396036i	−0.957409	−	0.288736i	$-0.906765\pi$
$827$	−3.71915e9	+	6.44175e9i	−0.228652	+	0.396036i	0.728757	+	0.684772i	$0.240098\pi$
$828$	4.14372e9	−	3.69207e8i	0.253679	−	0.0226029i
$829$	7.62593e9	+	1.32085e10i	0.464892	+	0.805216i	0.999197	−	0.0400756i	$-0.0127599\pi$
$829$	7.62593e9	+	1.32085e10i	0.464892	+	0.805216i	−0.534305	+	0.845292i	$0.679427\pi$
$830$	−1.95937e9	−	7.13153e8i	−0.118944	−	0.0432922i
$831$	5.42749e9	−	7.08497e9i	0.328092	−	0.428287i
$832$	1.71601e9	+	1.43991e9i	0.103297	+	0.0866767i
$833$	7.91946e9	−	2.88245e9i	0.474721	−	0.172784i
$834$	1.69933e10	−	3.78158e9i	1.01437	−	0.225731i
$835$	−5.46277e9	−	3.09809e10i	−0.324721	−	1.84158i
$836$	−2.15590e9			−0.127617
$837$	7.14396e9	−	1.12734e10i	0.421115	−	0.664530i
$838$	−7.81433e9			−0.458709
$839$	1.12105e9	+	6.35780e9i	0.0655328	+	0.371655i	0.999883	+	0.0152988i	$0.00486996\pi$
$839$	1.12105e9	+	6.35780e9i	0.0655328	+	0.371655i	−0.934350	+	0.356356i	$0.884019\pi$
$840$	−1.79745e9	−	1.95842e9i	−0.104635	−	0.114006i
$841$	−5.81973e9	+	2.11821e9i	−0.337378	+	0.122796i
$842$	−7.57441e9	−	6.35569e9i	−0.437277	−	0.366919i
$843$	−6.41536e9	−	1.54531e10i	−0.368829	−	0.888422i
$844$	1.23615e10	+	4.49923e9i	0.707740	+	0.257596i
$845$	1.50453e9	+	2.60592e9i	0.0857832	+	0.148581i
$846$	−7.25012e9	+	7.27335e9i	−0.411670	+	0.412988i
$847$	−3.40422e9	+	5.89628e9i	−0.192498	+	0.333416i
$848$	−3.90651e9	+	3.27795e9i	−0.219990	+	0.184594i
$849$	3.08517e10	+	1.60290e10i	1.73022	+	0.898938i
$850$	1.31964e8	−	7.48406e8i	0.00737037	−	0.0417995i
$851$	−1.54425e9	+	8.75786e9i	−0.0858940	+	0.487129i
$852$	2.54200e9	+	1.32070e9i	0.140811	+	0.0731585i
$853$	−4.32807e9	+	3.63168e9i	−0.238766	+	0.200349i	−0.754317	−	0.656510i	$-0.772032\pi$
$853$	−4.32807e9	+	3.63168e9i	−0.238766	+	0.200349i	0.515551	+	0.856859i	$0.327587\pi$
$854$	−4.66017e8	+	8.07165e8i	−0.0256035	+	0.0443465i
$855$	−1.23363e10	+	1.23758e10i	−0.675000	+	0.677163i
$856$	2.11792e9	+	3.66834e9i	0.115412	+	0.199899i
$857$	−1.65547e10	−	6.02543e9i	−0.898440	−	0.327006i	−0.148813	−	0.988865i	$-0.547545\pi$
$857$	−1.65547e10	−	6.02543e9i	−0.898440	−	0.327006i	−0.749628	+	0.661860i	$0.769767\pi$
$858$	1.51368e9	+	3.64610e9i	0.0818142	+	0.197071i
$859$	−2.79090e10	−	2.34184e10i	−1.50234	−	1.26061i	−0.877224	−	0.480082i	$-0.840607\pi$
$859$	−2.79090e10	−	2.34184e10i	−1.50234	−	1.26061i	−0.625116	−	0.780532i	$-0.714948\pi$
$860$	1.25441e10	−	4.56568e9i	0.672505	−	0.244772i
$861$	1.03141e10	+	1.12378e10i	0.550705	+	0.600025i
$862$	2.69530e9	+	1.52858e10i	0.143328	+	0.812854i
$863$	2.11332e9			0.111925			0.0559626	−	0.998433i	$-0.482177\pi$
$863$	2.11332e9			0.111925			0.0559626	+	0.998433i	$0.482177\pi$
$864$	3.34853e9	+	1.38153e8i	0.176626	+	0.00728723i
$865$	2.83428e10			1.48897
$866$	−1.07925e9	−	6.12074e9i	−0.0564690	−	0.320252i
$867$	−1.17170e10	+	2.60742e9i	−0.610588	+	0.135876i
$868$	−2.97468e9	+	1.08270e9i	−0.154391	+	0.0561937i
$869$	−2.92223e9	−	2.45204e9i	−0.151058	−	0.126753i
$870$	1.02030e10	−	1.33189e10i	0.525306	−	0.685727i
$871$	−4.27517e9	−	1.55604e9i	−0.219225	−	0.0797914i
$872$	−5.69050e9	−	9.85623e9i	−0.290631	−	0.503388i
$873$	−2.75705e10	+	2.45654e9i	−1.40248	+	0.124961i
$874$	−3.24319e9	+	5.61737e9i	−0.164317	+	0.284605i
$875$	−5.99249e9	+	5.02829e9i	−0.302398	+	0.253742i
$876$	2.17997e9	−	1.39125e9i	0.109569	−	0.0699263i
$877$	2.28414e9	−	1.29540e10i	0.114347	−	0.648493i	−0.872725	−	0.488213i	$-0.837649\pi$
$877$	2.28414e9	−	1.29540e10i	0.114347	−	0.648493i	0.987072	−	0.160280i	$-0.0512398\pi$
$878$	1.41539e9	−	8.02708e9i	0.0705741	−	0.400246i
$879$	1.35408e9	+	3.04548e10i	0.0672487	+	1.51250i
$880$	−1.13486e9	+	9.52264e8i	−0.0561377	+	0.0471051i
$881$	−4.64622e8	+	8.04749e8i	−0.0228920	+	0.0396502i	−0.877244	−	0.480044i	$-0.840621\pi$
$881$	−4.64622e8	+	8.04749e8i	−0.0228920	+	0.0396502i	0.854352	+	0.519694i	$0.173954\pi$
$882$	−1.07725e10	+	5.04429e9i	−0.528660	+	0.247548i
$883$	7.60914e9	+	1.31794e10i	0.371940	+	0.644220i	0.989864	−	0.142019i	$-0.0453593\pi$
$883$	7.60914e9	+	1.31794e10i	0.371940	+	0.644220i	−0.617924	+	0.786238i	$0.712026\pi$
$884$	−6.37053e9	−	2.31868e9i	−0.310165	−	0.112891i
$885$	−2.34695e10	−	3.07073e9i	−1.13816	−	0.148916i
$886$	1.93494e10	+	1.62361e10i	0.934650	+	0.784265i
$887$	1.21719e10	−	4.43020e9i	0.585631	−	0.213152i	−0.0321755	−	0.999482i	$-0.510244\pi$
$887$	1.21719e10	−	4.43020e9i	0.585631	−	0.213152i	0.617807	+	0.786330i	$0.288021\pi$
$888$	−2.14882e9	+	6.83425e9i	−0.102981	+	0.327526i
$889$	1.00187e9	+	5.68191e9i	0.0478252	+	0.271230i
$890$	−1.56164e10			−0.742531
$891$	5.12440e9	+	2.93676e9i	0.242701	+	0.139090i
$892$	1.28378e10			0.605638
$893$	−2.78049e9	−	1.57689e10i	−0.130659	−	0.741006i
$894$	−8.18530e9	+	2.60330e10i	−0.383136	+	1.21855i
$895$	−1.99845e10	+	7.27376e9i	−0.931778	+	0.339139i
$896$	−6.08933e8	−	5.10956e8i	−0.0282808	−	0.0237304i
$897$	1.17773e10	+	1.54093e9i	0.544842	+	0.0712866i
$898$	−5.60406e9	−	2.03971e9i	−0.258247	−	0.0939943i
$899$	−9.99003e9	−	1.73032e10i	−0.458572	−	0.794271i
$900$	−9.17751e7	+	1.06868e9i	−0.00419639	+	0.0488649i
$901$	7.71663e9	−	1.33656e10i	0.351472	−	0.608768i
$902$	6.51205e9	−	5.46426e9i	0.295457	−	0.247918i
$903$	5.60701e8	+	1.26108e10i	0.0253410	+	0.569947i
$904$	3.18881e8	−	1.80846e9i	0.0143562	−	0.0814180i
$905$	6.62288e9	−	3.75602e10i	0.297014	−	1.68445i
$906$	2.15032e10	−	1.37232e10i	0.960627	−	0.613067i
$907$	−1.15682e10	+	9.70690e9i	−0.514803	+	0.431971i	−0.862816	−	0.505519i	$-0.831301\pi$
$907$	−1.15682e10	+	9.70690e9i	−0.514803	+	0.431971i	0.348012	+	0.937490i	$0.386857\pi$
$908$	−1.97302e9	+	3.41738e9i	−0.0874645	+	0.151493i
$909$	3.48063e9	+	4.95397e9i	0.153704	+	0.218766i
$910$	−3.79478e9	−	6.57275e9i	−0.166933	−	0.289136i
$911$	−8.05966e9	−	2.93348e9i	−0.353185	−	0.128549i	0.159334	−	0.987225i	$-0.449065\pi$
$911$	−8.05966e9	−	2.93348e9i	−0.353185	−	0.128549i	−0.512519	+	0.858676i	$0.671288\pi$
$912$	−3.17769e9	+	4.14811e9i	−0.138717	+	0.181079i
$913$	−8.41777e8	−	7.06335e8i	−0.0366058	−	0.0307159i
$914$	−7.86265e8	+	2.86177e8i	−0.0340610	+	0.0123972i
$915$	4.10959e9	−	9.14523e8i	0.177347	−	0.0394658i
$916$	5.09904e8	+	2.89181e9i	0.0219207	+	0.124319i
$917$	−3.03903e9			−0.130149
$918$	−9.66576e9	+	3.07311e9i	−0.412370	+	0.131108i
$919$	2.90013e10			1.23258			0.616288	−	0.787521i	$-0.288636\pi$
$919$	2.90013e10			1.23258			0.616288	+	0.787521i	$0.288636\pi$
$920$	7.73985e8	+	4.38949e9i	0.0327699	+	0.185847i
$921$	2.75549e10	+	3.00227e10i	1.16223	+	1.26631i
$922$	1.70792e10	−	6.21632e9i	0.717645	−	0.261201i
$923$	6.26530e9	+	5.25721e9i	0.262262	+	0.220064i
$924$	−5.37135e8	−	1.29383e9i	−0.0223991	−	0.0539542i
$925$	−2.15460e9	−	7.84209e8i	−0.0895096	−	0.0325788i
$926$	−7.71990e9	−	1.33713e10i	−0.319502	−	0.553393i
$927$	−5.24640e9	−	1.94553e10i	−0.216313	−	0.802157i
$928$	2.50858e9	−	4.34498e9i	0.103041	−	0.178472i
$929$	−2.95624e10	+	2.48058e10i	−1.20972	+	1.01508i	−0.210423	+	0.977610i	$0.567484\pi$
$929$	−2.95624e10	+	2.48058e10i	−1.20972	+	1.01508i	−0.999298	+	0.0374657i	$0.988072\pi$
$930$	1.26890e10	+	6.59258e9i	0.517293	+	0.268760i
$931$	3.22055e9	−	1.82647e10i	0.130800	−	0.741801i
$932$	−3.09065e9	+	1.75280e10i	−0.125053	+	0.709212i
$933$	−1.12448e10	−	5.84224e9i	−0.453279	−	0.235501i
$934$	−2.37566e10	+	1.99341e10i	−0.954046	+	0.800540i
$935$	2.24173e9	−	3.88279e9i	0.0896897	−	0.155347i
$936$	9.24645e9	+	2.46174e9i	0.368561	+	0.0981242i
$937$	8.84406e9	+	1.53184e10i	0.351207	+	0.608308i	0.986461	−	0.163995i	$-0.0524380\pi$
$937$	8.84406e9	+	1.53184e10i	0.351207	+	0.608308i	−0.635254	+	0.772303i	$0.719105\pi$
$938$	1.51706e9	+	5.52164e8i	0.0600195	+	0.0218453i
$939$	−1.01490e10	−	2.44465e10i	−0.400030	−	0.963577i
$940$	−8.42878e9	−	7.07259e9i	−0.330992	−	0.277735i
$941$	−4.28774e10	+	1.56061e10i	−1.67751	+	0.610563i	−0.992965	−	0.118410i	$-0.962220\pi$
$941$	−4.28774e10	+	1.56061e10i	−1.67751	+	0.610563i	−0.684543	+	0.728973i	$0.739998\pi$
$942$	1.45732e10	+	1.58784e10i	0.568038	+	0.618911i
$943$	−4.44127e9	−	2.51877e10i	−0.172471	−	0.978131i
$944$	−7.07801e9			−0.273848
$945$	−1.05007e10	−	4.32005e9i	−0.404769	−	0.166524i
$946$	7.03504e9			0.270176
$947$	2.95737e9	+	1.67721e10i	0.113157	+	0.641745i	0.987646	+	0.156700i	$0.0500855\pi$
$947$	2.95737e9	+	1.67721e10i	0.113157	+	0.641745i	−0.874489	+	0.485045i	$0.838803\pi$
$948$	−9.02512e9	+	2.00839e9i	−0.344052	+	0.0765631i
$949$	6.93828e9	−	2.52533e9i	0.263524	−	0.0959149i
$950$	−1.28112e9	−	1.07499e9i	−0.0484794	−	0.0406790i
$951$	−1.68685e10	+	2.20199e10i	−0.635982	+	0.830201i
$952$	2.26060e9	+	8.22793e8i	0.0849171	+	0.0309073i
$953$	−1.65667e10	−	2.86944e10i	−0.620029	−	1.07392i	−0.989480	−	0.144671i	$-0.953787\pi$
$953$	−1.65667e10	−	2.86944e10i	−0.620029	−	1.07392i	0.369451	−	0.929250i	$-0.379546\pi$
$954$	−9.17422e9	+	1.97566e10i	−0.342098	+	0.736704i
$955$	7.69239e9	−	1.33236e10i	0.285792	−	0.495006i
$956$	3.36454e9	−	2.82318e9i	0.124544	−	0.104505i
$957$	7.45342e9	−	4.75674e9i	0.274893	−	0.175435i
$958$	−3.69611e9	+	2.09617e10i	−0.135821	+	0.770277i
$959$	1.22111e9	−	6.92524e9i	0.0447083	−	0.253554i
$960$	1.59492e8	+	3.58715e9i	0.00581822	+	0.130858i
$961$	−8.03124e9	+	6.73901e9i	−0.291911	+	0.244943i
$962$	−1.02271e10	+	1.77139e10i	−0.370375	+	0.641508i
$963$	1.48377e10	+	1.03542e10i	0.535396	+	0.373614i
$964$	−4.11268e9	−	7.12337e9i	−0.147862	−	0.256104i
$965$	−4.17437e10	−	1.51935e10i	−1.49536	−	0.544266i
$966$	−4.17920e9	−	5.46803e8i	−0.149167	−	0.0195169i
$967$	1.54839e9	+	1.29925e9i	0.0550665	+	0.0462063i	0.669906	−	0.742446i	$-0.266335\pi$
$967$	1.54839e9	+	1.29925e9i	0.0550665	+	0.0462063i	−0.614839	+	0.788653i	$0.710779\pi$
$968$	8.64207e9	−	3.14546e9i	0.306234	−	0.111460i
$969$	4.74329e9	−	1.50858e10i	0.167474	−	0.532643i
$970$	−5.14977e9	−	2.92058e10i	−0.181170	−	1.02747i
$971$	−1.11064e10			−0.389319			−0.194659	−	0.980871i	$-0.562360\pi$
$971$	−1.11064e10			−0.389319			−0.194659	+	0.980871i	$0.562360\pi$
$972$	1.32037e10	−	5.53108e9i	0.461171	−	0.193187i
$973$	−1.76378e10			−0.613832
$974$	2.67952e8	+	1.51963e9i	0.00929183	+	0.0526966i
$975$	−9.18550e8	+	2.92141e9i	−0.0317385	+	0.100943i
$976$	1.18305e9	−	4.30594e8i	0.0407312	−	0.0148250i
$977$	2.50633e10	+	2.10306e10i	0.859820	+	0.721475i	0.961929	−	0.273298i	$-0.0881146\pi$
$977$	2.50633e10	+	2.10306e10i	0.859820	+	0.721475i	−0.102109	+	0.994773i	$0.532559\pi$
$978$	1.24886e10	+	1.63399e9i	0.426901	+	0.0558553i
$979$	−7.73353e9	−	2.81478e9i	−0.263414	−	0.0958748i
$980$	−6.37222e9	−	1.10370e10i	−0.216271	−	0.374593i
$981$	−3.98666e10	−	2.78200e10i	−1.34824	−	0.940839i
$982$	−1.35679e10	+	2.35003e10i	−0.457217	+	0.791924i
$983$	−5.49641e7	+	4.61204e7i	−0.00184562	+	0.00154866i	−0.643710	−	0.765270i	$-0.722606\pi$
$983$	−5.49641e7	+	4.61204e7i	−0.00184562	+	0.00154866i	0.641864	+	0.766818i	$0.278161\pi$
$984$	−9.15194e8	−	2.05837e10i	−0.0306218	−	0.688716i
$985$	−2.08844e8	+	1.18441e9i	−0.00696298	+	0.0394890i
$986$	−2.63664e9	+	1.49531e10i	−0.0875955	+	0.496779i
$987$	8.77071e9	−	5.59742e9i	0.290352	−	0.185301i
$988$	−1.14286e10	+	9.58976e9i	−0.377003	+	0.316343i
$989$	1.05830e10	−	1.83303e10i	0.347874	−	0.602536i
$990$	−2.66517e9	+	5.73941e9i	−0.0872974	+	0.187994i
$991$	2.43979e10	+	4.22585e10i	0.796334	+	1.37929i	0.921989	+	0.387217i	$0.126564\pi$
$991$	2.43979e10	+	4.22585e10i	0.796334	+	1.37929i	−0.125654	+	0.992074i	$0.540103\pi$
$992$	4.01814e9	+	1.46248e9i	0.130688	+	0.0475664i
$993$	−2.38113e10	+	3.10829e10i	−0.771722	+	1.00739i
$994$	−2.22326e9	−	1.86554e9i	−0.0718023	−	0.0602493i
$995$	−1.74291e10	+	6.34366e9i	−0.560910	+	0.204155i
$996$	−2.59978e9	+	5.78538e8i	−0.0833735	+	0.0185534i
$997$	−7.25435e9	−	4.11414e10i	−0.231828	−	1.31476i	−0.849193	−	0.528083i	$-0.822911\pi$
$997$	−7.25435e9	−	4.11414e10i	−0.231828	−	1.31476i	0.617365	−	0.786677i	$-0.288200\pi$
$998$	−9.85932e9			−0.313972
$999$	4.06704e9	+	3.03299e10i	0.129062	+	0.962480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.e.a.13.5	✓	60
27.25	even	9	inner	54.8.e.a.25.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.e.a.13.5	✓	60	1.1	even	1	trivial
54.8.e.a.25.5	yes	60	27.25	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+(1.38919 + 7.87846i) q^{2} +(-14.0270 + 44.6122i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-224.372 - 188.270i) q^{5} +(-370.961 - 48.5362i) q^{6} +(356.182 + 129.640i) q^{7} +(-256.000 - 443.405i) q^{8} +(-1793.49 - 1251.55i) q^{9} +(1171.59 - 2029.25i) q^{10} +(945.954 - 793.750i) q^{11} +(-132.943 - 2990.03i) q^{12} +(1483.87 - 8415.47i) q^{13} +(-526.558 + 2986.26i) q^{14} +(11546.4 - 7368.84i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-6198.02 + 10735.3i) q^{17} +(7368.76 - 15868.6i) q^{18} +(13639.7 + 23624.6i) q^{19} +(17614.9 + 6411.29i) q^{20} +(-10779.6 + 14071.6i) q^{21} +(7567.63 + 6350.00i) q^{22} +(27929.6 - 10165.5i) q^{23} +(23372.2 - 5201.09i) q^{24} +(1330.71 + 7546.82i) q^{25} +68362.3 q^{26} +(80991.3 - 62456.1i) q^{27} -24258.6 q^{28} +(-26587.5 - 150785. i) q^{29} +(74095.2 + 80731.1i) q^{30} +(122624. - 44631.4i) q^{31} +(25101.7 + 21062.9i) q^{32} +(22142.0 + 53334.9i) q^{33} +(-93187.8 - 33917.6i) q^{34} +(-55509.8 - 96145.8i) q^{35} +(135256. + 36010.1i) q^{36} +(-149602. + 259118. i) q^{37} +(-167177. + 140278. i) q^{38} +(354618. + 184242. i) q^{39} +(-26040.8 + 147685. i) q^{40} +(149427. - 847441. i) q^{41} +(-125837. - 65379.0i) q^{42} +(545525. - 457750. i) q^{43} +(-39515.4 + 68442.6i) q^{44} +(166779. + 618472. i) q^{45} +(118888. + 205920. i) q^{46} +(-551573. - 200756. i) q^{47} +(73444.9 + 176911. i) q^{48} +(-520812. - 437013. i) q^{49} +(-57608.7 + 20967.9i) q^{50} +(-391985. - 427091. i) q^{51} +(94967.9 + 538590. i) q^{52} -1.24502e6 q^{53} +(604570. + 551324. i) q^{54} -361685. q^{55} +(-33699.7 - 191120. i) q^{56} +(-1.24527e6 + 277114. i) q^{57} +(1.15102e6 - 418937. i) q^{58} +(-1.32375e6 - 1.11076e6i) q^{59} +(-533105. + 695907. i) q^{60} +(288830. + 105125. i) q^{61} +(521974. + 904086. i) q^{62} +(-476558. - 678284. i) q^{63} +(-131072. + 227023. i) q^{64} +(-1.91732e6 + 1.60882e6i) q^{65} +(-389438. + 248537. i) q^{66} +(92450.9 - 524315. i) q^{67} +(137763. - 781294. i) q^{68} +(61739.6 + 1.38859e6i) q^{69} +(680367. - 570896. i) q^{70} +(-478554. + 828880. i) q^{71} +(-95808.2 + 1.11564e6i) q^{72} +(432025. + 748290. i) q^{73} +(-2.24928e6 - 818671. i) q^{74} +(-355346. - 46493.1i) q^{75} +(-1.33742e6 - 1.12223e6i) q^{76} +(439833. - 160086. i) q^{77} +(-958915. + 3.04979e6i) q^{78} +(-536432. - 3.04225e6i) q^{79} -1.19970e6 q^{80} +(1.65024e6 + 4.48927e6i) q^{81} +6.88411e6 q^{82} +(-154525. - 876352. i) q^{83} +(340274. - 1.08223e6i) q^{84} +(3.41179e6 - 1.24179e6i) q^{85} +(4.36420e6 + 3.66200e6i) q^{86} +(7.09980e6 + 928932. i) q^{87} +(-594117. - 216241. i) q^{88} +(-3.33231e6 - 5.77174e6i) q^{89} +(-4.64092e6 + 2.17314e6i) q^{90} +(1.61951e6 - 2.80507e6i) q^{91} +(-1.45718e6 + 1.22272e6i) q^{92} +(271066. + 6.09656e6i) q^{93} +(815412. - 4.62443e6i) q^{94} +(1.38745e6 - 7.86862e6i) q^{95} +(-1.29176e6 + 824395. i) q^{96} +(9.69544e6 - 8.13544e6i) q^{97} +(2.71949e6 - 4.71029e6i) q^{98} +(-2.68997e6 + 239677. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 213 q^{5} - 72 q^{6} + 1677 q^{7} - 15360 q^{8} - 3024 q^{9} + 3000 q^{10} - 15744 q^{11} + 2880 q^{12} + 9924 q^{13} + 13416 q^{14} + 2322 q^{15} + 29478 q^{17} + 49680 q^{18} + 61731 q^{19} - 27264 q^{20}+ \cdots + 36391797 q^{99}+O(q^{100}) \) 60 * q + 213 * q^5 - 72 * q^6 + 1677 * q^7 - 15360 * q^8 - 3024 * q^9 + 3000 * q^10 - 15744 * q^11 + 2880 * q^12 + 9924 * q^13 + 13416 * q^14 + 2322 * q^15 + 29478 * q^17 + 49680 * q^18 + 61731 * q^19 - 27264 * q^20 + 160884 * q^21 - 125952 * q^22 + 29478 * q^23 - 343017 * q^25 - 316368 * q^26 - 524124 * q^27 - 263424 * q^28 + 132153 * q^29 + 292824 * q^30 - 1372860 * q^31 - 1065834 * q^33 - 121656 * q^34 - 321081 * q^35 - 369216 * q^36 + 759795 * q^37 + 224760 * q^38 - 2283894 * q^39 + 109056 * q^40 + 704616 * q^41 + 527400 * q^42 + 2124585 * q^43 + 255552 * q^44 + 3259908 * q^45 + 524472 * q^46 + 3452931 * q^47 + 552960 * q^48 - 1987017 * q^49 + 190152 * q^50 + 5107401 * q^51 + 635136 * q^52 - 2951976 * q^53 + 1065312 * q^54 - 2539854 * q^55 + 858624 * q^56 + 5722920 * q^57 + 47496 * q^58 + 3732204 * q^59 + 2512512 * q^60 - 5504796 * q^61 + 2859936 * q^62 + 1888047 * q^63 - 7864320 * q^64 - 803499 * q^65 - 9421632 * q^66 - 7979400 * q^67 - 5893440 * q^68 - 629100 * q^69 + 1111128 * q^70 + 3531612 * q^71 + 3096576 * q^72 - 875661 * q^73 + 15158904 * q^74 + 26002422 * q^75 + 1798080 * q^76 + 5672523 * q^77 - 13012848 * q^78 - 10290369 * q^79 - 3072000 * q^80 - 42838956 * q^81 - 3798096 * q^82 - 16555878 * q^83 + 2005056 * q^84 + 30956175 * q^85 + 16996680 * q^86 + 22863879 * q^87 + 2509824 * q^88 + 32327814 * q^89 + 34182072 * q^90 + 1976658 * q^91 - 1108608 * q^92 - 17967789 * q^93 - 24396768 * q^94 - 35592135 * q^95 - 2949120 * q^96 - 25380039 * q^97 - 15123648 * q^98 + 36391797 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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