LMFDB - Embedded newform 75.8.l.a.2.49

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,8,Mod(2,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.2"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	75.l (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4288769113$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.49
Character	$\chi$	$=$	75.2
Dual form			75.8.l.a.38.49

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.79599 - 11.3395i) q^{2} +(-12.6375 - 45.0255i) q^{3} +(-3.62242 - 1.17700i) q^{4} +(-245.145 - 134.273i) q^{5} +(-533.261 + 62.4372i) q^{6} +(-1082.77 - 1082.77i) q^{7} +(647.306 - 1270.41i) q^{8} +(-1867.59 + 1138.02i) q^{9} +(-1962.86 + 2538.65i) q^{10} +(1048.01 + 1442.46i) q^{11} +(-7.21636 + 177.975i) q^{12} +(12341.2 - 1954.65i) q^{13} +(-14222.7 + 10333.4i) q^{14} +(-2947.67 + 12734.6i) q^{15} +(-13637.6 - 9908.31i) q^{16} +(-24795.9 - 12634.1i) q^{17} +(9550.37 + 23221.3i) q^{18} +(-9446.90 + 3069.48i) q^{19} +(729.978 + 774.926i) q^{20} +(-35068.8 + 62436.0i) q^{21} +(18239.0 - 9293.22i) q^{22} +(27113.4 + 4294.35i) q^{23} +(-65381.1 - 13090.4i) q^{24} +(42066.7 + 65832.4i) q^{25} -143453. i q^{26} +(74841.6 + 69707.2i) q^{27} +(2647.84 + 5196.68i) q^{28} +(30422.4 - 93630.6i) q^{29} +(139110. + 56296.3i) q^{30} +(79487.8 + 244638. i) q^{31} +(-7797.93 + 7797.93i) q^{32} +(51703.3 - 65416.4i) q^{33} +(-187797. + 258481. i) q^{34} +(120049. + 410823. i) q^{35} +(8104.62 - 1924.25i) q^{36} +(30730.2 + 194023. i) q^{37} +(17839.7 + 112635. i) q^{38} +(-243971. - 530965. i) q^{39} +(-329265. + 224519. i) q^{40} +(269017. - 370270. i) q^{41} +(645007. + 509796. i) q^{42} +(354271. - 354271. i) q^{43} +(-2098.56 - 6458.71i) q^{44} +(610634. - 28213.9i) q^{45} +(97391.1 - 299739. i) q^{46} +(-572588. - 1.12377e6i) q^{47} +(-273781. + 739257. i) q^{48} +1.52126e6i q^{49} +(822055. - 358779. i) q^{50} +(-255499. + 1.27611e6i) q^{51} +(-47005.5 - 7444.94i) q^{52} +(-1.24027e6 + 631950. i) q^{53} +(924856. - 723469. i) q^{54} +(-63230.8 - 494331. i) q^{55} +(-2.07645e6 + 674681. i) q^{56} +(257590. + 386560. i) q^{57} +(-1.00708e6 - 513134. i) q^{58} +(654819. + 475754. i) q^{59} +(25666.3 - 42660.8i) q^{60} +(-293166. + 212998. i) q^{61} +(2.91682e6 - 461979. i) q^{62} +(3.25439e6 + 789954. i) q^{63} +(-1.19384e6 - 1.64319e6i) q^{64} +(-3.28782e6 - 1.17791e6i) q^{65} +(-648927. - 703775. i) q^{66} +(-1.05929e6 + 2.07898e6i) q^{67} +(74950.8 + 74950.8i) q^{68} +(-149292. - 1.27507e6i) q^{69} +(4.87412e6 - 623457. i) q^{70} +(-5.36074e6 - 1.74181e6i) q^{71} +(236853. + 3.10925e6i) q^{72} +(-82679.1 + 522015. i) q^{73} +2.25530e6 q^{74} +(2.43252e6 - 2.72603e6i) q^{75} +37833.4 q^{76} +(427103. - 2.69662e6i) q^{77} +(-6.45902e6 + 1.81289e6i) q^{78} +(-3.47536e6 - 1.12921e6i) q^{79} +(2.01277e6 + 4.26013e6i) q^{80} +(2.19279e6 - 4.25070e6i) q^{81} +(-3.71551e6 - 3.71551e6i) q^{82} +(786549. - 1.54369e6i) q^{83} +(200521. - 184894. i) q^{84} +(4.38216e6 + 6.42660e6i) q^{85} +(-3.38098e6 - 4.65351e6i) q^{86} +(-4.60022e6 - 186525. i) q^{87} +(2.51090e6 - 397688. i) q^{88} +(-3.56902e6 + 2.59305e6i) q^{89} +(776763. - 6.97492e6i) q^{90} +(-1.54791e7 - 1.12462e7i) q^{91} +(-93161.8 - 47468.3i) q^{92} +(1.00104e7 - 6.67059e6i) q^{93} +(-1.37713e7 + 4.47456e6i) q^{94} +(2.72800e6 + 515993. i) q^{95} +(449652. + 252559. i) q^{96} +(5.31864e6 - 2.70998e6i) q^{97} +(1.72502e7 + 2.73217e6i) q^{98} +(-3.59881e6 - 1.50127e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 34 q^{3} - 20 q^{4} - 6 q^{6} - 1364 q^{7} - 10 q^{9} + 3160 q^{10} + 2018 q^{12} - 16868 q^{13} - 37570 q^{15} + 507892 q^{16} + 106550 q^{18} + 70800 q^{19} - 6 q^{21} - 195160 q^{22} - 444200 q^{25}+ \cdots - 22089384 q^{97}+O(q^{100}) $ 544 * q - 34 * q^3 - 20 * q^4 - 6 * q^6 - 1364 * q^7 - 10 * q^9 + 3160 * q^10 + 2018 * q^12 - 16868 * q^13 - 37570 * q^15 + 507892 * q^16 + 106550 * q^18 + 70800 * q^19 - 6 * q^21 - 195160 * q^22 - 444200 * q^25 + 264158 * q^27 + 692032 * q^28 - 892390 * q^30 - 12 * q^31 + 877790 * q^33 - 1828180 * q^34 - 65542 * q^36 + 635596 * q^37 - 3868770 * q^39 + 1574020 * q^40 + 4577310 * q^42 - 1397348 * q^43 + 3411430 * q^45 - 12 * q^46 - 12135404 * q^48 - 16 * q^51 + 6428876 * q^52 + 16485420 * q^54 - 2324900 * q^55 + 4119286 * q^57 - 986360 * q^58 - 25245250 * q^60 - 12 * q^61 + 6259012 * q^63 + 363500 * q^64 - 1119750 * q^66 + 3427476 * q^67 - 12994880 * q^69 + 9814160 * q^70 - 611970 * q^72 + 10236732 * q^73 + 19853790 * q^75 - 131104 * q^76 + 24801340 * q^78 - 8474460 * q^79 + 10854734 * q^81 + 44639220 * q^82 - 52907530 * q^84 - 82807380 * q^85 - 15442020 * q^87 + 33548360 * q^88 - 11540050 * q^90 - 12 * q^91 + 14982652 * q^93 + 60673460 * q^94 + 1218042 * q^96 - 22089384 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	1.79599	−	11.3395i	0.158745	−	1.00228i	−0.771738	−	0.635941i	$-0.780612\pi$
$2$	1.79599	−	11.3395i	0.158745	−	1.00228i	0.930483	−	0.366335i	$-0.119388\pi$
$3$	−12.6375	−	45.0255i	−0.270233	−	0.962795i
$3$	−12.6375	−	45.0255i	−0.270233	−	0.962795i
$4$	−3.62242	−	1.17700i	−0.0283002	−	0.00919528i
$5$	−245.145	−	134.273i	−0.877056	−	0.480388i
$5$	−245.145	−	134.273i	−0.877056	−	0.480388i
$6$	−533.261	+	62.4372i	−1.00788	+	0.118009i
$7$	−1082.77	−	1082.77i	−1.19315	−	1.19315i	−0.976178	−	0.216971i	$-0.930382\pi$
$7$	−1082.77	−	1082.77i	−1.19315	−	1.19315i	−0.216971	−	0.976178i	$-0.569618\pi$
$8$	647.306	−	1270.41i	0.446987	−	0.877261i
$9$	−1867.59	+	1138.02i	−0.853949	+	0.520357i
$10$	−1962.86	+	2538.65i	−0.620710	+	0.802793i
$11$	1048.01	+	1442.46i	0.237406	+	0.326761i	0.911051	−	0.412294i	$-0.135272\pi$
$11$	1048.01	+	1442.46i	0.237406	+	0.326761i	−0.673645	+	0.739055i	$0.735272\pi$
$12$	−7.21636	+	177.975i	−0.00120555	+	0.0297321i
$13$	12341.2	−	1954.65i	1.55795	−	0.246755i	0.682801	−	0.730604i	$-0.260762\pi$
$13$	12341.2	−	1954.65i	1.55795	−	0.246755i	0.875152	+	0.483849i	$0.160762\pi$
$14$	−14222.7	+	10333.4i	−1.38527	+	1.00646i
$15$	−2947.67	+	12734.6i	−0.225507	+	0.974242i
$16$	−13637.6	−	9908.31i	−0.832374	−	0.604755i
$17$	−24795.9	−	12634.1i	−1.22408	−	0.623698i	−0.282102	−	0.959384i	$-0.591032\pi$
$17$	−24795.9	−	12634.1i	−1.22408	−	0.623698i	−0.941974	+	0.335687i	$0.891032\pi$
$18$	9550.37	+	23221.3i	0.385981	+	0.938496i
$19$	−9446.90	+	3069.48i	−0.315974	+	0.102666i	−0.462711	−	0.886509i	$-0.653123\pi$
$19$	−9446.90	+	3069.48i	−0.315974	+	0.102666i	0.146736	+	0.989176i	$0.453123\pi$
$20$	729.978	+	774.926i	0.0204035	+	0.0216598i
$21$	−35068.8	+	62436.0i	−0.826331	+	1.47119i
$22$	18239.0	−	9293.22i	0.365192	−	0.186075i
$23$	27113.4	+	4294.35i	0.464662	+	0.0735952i	0.384376	−	0.923177i	$-0.374417\pi$
$23$	27113.4	+	4294.35i	0.464662	+	0.0735952i	0.0802860	+	0.996772i	$0.474417\pi$
$24$	−65381.1	−	13090.4i	−0.965413	−	0.193292i
$25$	42066.7	+	65832.4i	0.538454	+	0.842655i
$26$		−	143453.i		−	1.60067i
$27$	74841.6	+	69707.2i	0.731762	+	0.681560i
$28$	2647.84	+	5196.68i	0.0227950	+	0.0447376i
$29$	30422.4	−	93630.6i	0.231633	−	0.712894i	−0.765917	−	0.642939i	$-0.777715\pi$
$29$	30422.4	−	93630.6i	0.231633	−	0.712894i	0.997550	−	0.0699542i	$-0.0222853\pi$
$30$	139110.	+	56296.3i	0.940661	+	0.380676i
$31$	79487.8	+	244638.i	0.479219	+	1.47489i	0.840182	+	0.542305i	$0.182448\pi$
$31$	79487.8	+	244638.i	0.479219	+	1.47489i	−0.360962	+	0.932580i	$0.617552\pi$
$32$	−7797.93	+	7797.93i	−0.0420683	+	0.0420683i
$33$	51703.3	−	65416.4i	0.250449	−	0.316875i
$34$	−187797.	+	258481.i	−0.819433	+	1.12785i
$35$	120049.	+	410823.i	0.473283	+	1.61963i
$36$	8104.62	−	1924.25i	0.0289517	−	0.00687389i
$37$	30730.2	+	194023.i	0.0997375	+	0.629718i	0.986027	+	0.166586i	$0.0532744\pi$
$37$	30730.2	+	194023.i	0.0997375	+	0.629718i	−0.886289	+	0.463132i	$0.846726\pi$
$38$	17839.7	+	112635.i	0.0527406	+	0.332991i
$39$	−243971.	−	530965.i	−0.658584	−	1.43331i
$40$	−329265.	+	224519.i	−0.813459	+	0.554680i
$41$	269017.	−	370270.i	0.609588	−	0.839026i	−0.386955	−	0.922098i	$-0.626473\pi$
$41$	269017.	−	370270.i	0.609588	−	0.839026i	0.996544	+	0.0830722i	$0.0264732\pi$
$42$	645007.	+	509796.i	1.34336	+	1.06175i
$43$	354271.	−	354271.i	0.679511	−	0.679511i	−0.280379	−	0.959890i	$-0.590460\pi$
$43$	354271.	−	354271.i	0.679511	−	0.679511i	0.959890	+	0.280379i	$0.0904600\pi$
$44$	−2098.56	−	6458.71i	−0.00371396	−	0.0114304i
$45$	610634.	−	28213.9i	0.998934	−	0.0461551i
$46$	97391.1	−	299739.i	0.147525	−	0.454037i
$47$	−572588.	−	1.12377e6i	−0.804451	−	1.57882i	−0.815409	−	0.578885i	$-0.803488\pi$
$47$	−572588.	−	1.12377e6i	−0.804451	−	1.57882i	0.0109578	−	0.999940i	$-0.496512\pi$
$48$	−273781.	+	739257.i	−0.357321	+	0.964830i
$49$			1.52126e6i			1.84721i
$50$	822055.	−	358779.i	0.930049	−	0.405912i
$51$	−255499.	+	1.27611e6i	−0.269708	+	1.34708i
$52$	−47005.5	−	7444.94i	−0.0463593	−	0.00734259i
$53$	−1.24027e6	+	631950.i	−1.14433	+	0.583065i	−0.920183	−	0.391490i	$-0.871960\pi$
$53$	−1.24027e6	+	631950.i	−1.14433	+	0.583065i	−0.224148	+	0.974555i	$0.571960\pi$
$54$	924856.	−	723469.i	0.799275	−	0.625233i
$55$	−63230.8	−	494331.i	−0.0512459	−	0.400635i
$56$	−2.07645e6	+	674681.i	−1.58003	+	0.513381i
$57$	257590.	+	386560.i	0.184233	+	0.276475i
$58$	−1.00708e6	−	513134.i	−0.677745	−	0.345329i
$59$	654819.	+	475754.i	0.415087	+	0.301579i	0.775658	−	0.631153i	$-0.217418\pi$
$59$	654819.	+	475754.i	0.415087	+	0.301579i	−0.360571	+	0.932732i	$0.617418\pi$
$60$	25666.3	−	42660.8i	0.0153403	−	0.0254976i
$61$	−293166.	+	212998.i	−0.165371	+	0.120149i	−0.667393	−	0.744706i	$-0.732590\pi$
$61$	−293166.	+	212998.i	−0.165371	+	0.120149i	0.502022	+	0.864855i	$0.332590\pi$
$62$	2.91682e6	−	461979.i	1.55432	−	0.246179i
$63$	3.25439e6	+	789954.i	1.63975	+	0.398025i
$64$	−1.19384e6	−	1.64319e6i	−0.569269	−	0.783532i
$65$	−3.28782e6	−	1.17791e6i	−1.48495	−	0.532004i
$66$	−648927.	−	703775.i	−0.277838	−	0.301322i
$67$	−1.05929e6	+	2.07898e6i	−0.430283	+	0.844478i	0.569464	+	0.822016i	$0.307151\pi$
$67$	−1.05929e6	+	2.07898e6i	−0.430283	+	0.844478i	−0.999748	+	0.0224624i	$0.992849\pi$
$68$	74950.8	+	74950.8i	0.0289065	+	0.0289065i
$69$	−149292.	−	1.27507e6i	−0.0547097	−	0.467262i
$70$	4.87412e6	−	623457.i	1.69845	−	0.217252i
$71$	−5.36074e6	−	1.74181e6i	−1.77754	−	0.577559i	−0.778782	−	0.627294i	$-0.784162\pi$
$71$	−5.36074e6	−	1.74181e6i	−1.77754	−	0.577559i	−0.998762	+	0.0497352i	$0.984162\pi$
$72$	236853.	+	3.10925e6i	0.0747851	+	0.981729i
$73$	−82679.1	+	522015.i	−0.0248751	+	0.157055i	−0.996999	−	0.0774115i	$-0.975334\pi$
$73$	−82679.1	+	522015.i	−0.0248751	+	0.157055i	0.972124	+	0.234467i	$0.0753345\pi$
$74$	2.25530e6			0.646984
$75$	2.43252e6	−	2.72603e6i	0.665796	−	0.746134i
$76$	37833.4			0.00988616
$77$	427103.	−	2.69662e6i	0.106614	−	0.673136i
$78$	−6.45902e6	+	1.81289e6i	−1.54112	+	0.432553i
$79$	−3.47536e6	−	1.12921e6i	−0.793059	−	0.257680i	−0.115653	−	0.993290i	$-0.536896\pi$
$79$	−3.47536e6	−	1.12921e6i	−0.793059	−	0.257680i	−0.677406	+	0.735609i	$0.736896\pi$
$80$	2.01277e6	+	4.26013e6i	0.439521	+	0.930267i
$81$	2.19279e6	−	4.25070e6i	0.458457	−	0.888717i
$82$	−3.71551e6	−	3.71551e6i	−0.744167	−	0.744167i
$83$	786549.	−	1.54369e6i	0.150991	−	0.296337i	−0.803105	−	0.595838i	$-0.796820\pi$
$83$	786549.	−	1.54369e6i	0.150991	−	0.296337i	0.954096	+	0.299501i	$0.0968200\pi$
$84$	200521.	−	184894.i	0.0369132	−	0.0340364i
$85$	4.38216e6	+	6.42660e6i	0.773966	+	1.13505i
$86$	−3.38098e6	−	4.65351e6i	−0.573188	−	0.788926i
$87$	−4.60022e6	−	186525.i	−0.748965	−	0.0303683i
$88$	2.51090e6	−	397688.i	0.392772	−	0.0622090i
$89$	−3.56902e6	+	2.59305e6i	−0.536641	+	0.389893i	−0.822836	−	0.568279i	$-0.807610\pi$
$89$	−3.56902e6	+	2.59305e6i	−0.536641	+	0.389893i	0.286195	+	0.958171i	$0.407610\pi$
$90$	776763.	−	6.97492e6i	0.112316	−	1.00853i
$91$	−1.54791e7	−	1.12462e7i	−2.15329	−	1.56445i
$92$	−93161.8	−	47468.3i	−0.0124733	−	0.00635545i
$93$	1.00104e7	−	6.67059e6i	1.29051	−	0.859952i
$94$	−1.37713e7	+	4.47456e6i	−1.71012	+	0.555652i
$95$	2.72800e6	+	515993.i	0.326447	+	0.0617463i
$96$	449652.	+	252559.i	0.0518713	+	0.0291349i
$97$	5.31864e6	−	2.70998e6i	0.591698	−	0.301485i	−0.132385	−	0.991198i	$-0.542263\pi$
$97$	5.31864e6	−	2.70998e6i	0.591698	−	0.301485i	0.724082	+	0.689713i	$0.242263\pi$
$98$	1.72502e7	+	2.73217e6i	1.85141	+	0.293235i
$99$	−3.59881e6	−	1.50127e6i	−0.372765	−	0.155502i
$100$	−74898.8	−	287985.i	−0.00748988	−	0.0287985i
$101$			3.58521e6i			0.346250i	0.984900	+	0.173125i	$0.0553864\pi$
$101$			3.58521e6i			0.346250i	−0.984900	+	0.173125i	$0.944614\pi$
$102$	1.40115e7	+	5.18911e6i	1.30733	+	0.484163i
$103$	−5.56878e6	−	1.09293e7i	−0.502145	−	0.985516i	−0.993422	−	0.114512i	$-0.963470\pi$
$103$	−5.56878e6	−	1.09293e7i	−0.502145	−	0.985516i	0.491276	−	0.871004i	$-0.336530\pi$
$104$	5.50531e6	−	1.69436e7i	0.479915	−	1.47703i
$105$	1.69804e7	−	1.05971e7i	1.43148	−	0.893353i
$106$	4.93845e6	+	1.51990e7i	0.402736	+	1.23949i
$107$	−9.55632e6	+	9.55632e6i	−0.754132	+	0.754132i	−0.975248	−	0.221116i	$-0.929030\pi$
$107$	−9.55632e6	+	9.55632e6i	−0.754132	+	0.754132i	0.221116	+	0.975248i	$0.429030\pi$
$108$	−189063.	−	340597.i	−0.0144418	−	0.0260170i
$109$	−973205.	+	1.33950e6i	−0.0719800	+	0.0990720i	−0.843489	−	0.537146i	$-0.819502\pi$
$109$	−973205.	+	1.33950e6i	−0.0719800	+	0.0990720i	0.771509	+	0.636218i	$0.219502\pi$
$110$	−5.71901e6	−	170813.i	−0.409682	−	0.0122362i
$111$	8.34760e6	−	3.83560e6i	0.579337	−	0.266197i
$112$	4.03800e6	+	2.54949e7i	0.271583	+	1.71471i
$113$	−134932.	−	851929.i	−0.00879714	−	0.0555429i	0.982899	−	0.184144i	$-0.0589513\pi$
$113$	−134932.	−	851929.i	−0.00879714	−	0.0555429i	−0.991696	+	0.128601i	$0.958951\pi$
$114$	4.84601e6	−	2.22667e6i	0.306350	−	0.140763i
$115$	−6.07010e6	−	4.69333e6i	−0.372180	−	0.287765i
$116$	−220406.	+	303362.i	−0.0131105	+	0.0180451i
$117$	−2.08237e7	+	1.76950e7i	−1.20201	+	1.02141i
$118$	6.57084e6	−	6.57084e6i	0.368158	−	0.368158i
$119$	1.31684e7	+	4.05283e7i	0.716341	+	2.20467i
$120$	1.42701e7	+	1.19879e7i	0.753866	+	0.633301i
$121$	5.03949e6	−	1.55100e7i	0.258606	−	0.795906i
$122$	1.88875e6	+	3.70689e6i	0.0941707	+	0.184820i
$123$	−2.00713e7	−	7.43333e6i	−0.972541	−	0.360176i
$124$		−	979739.i		−	0.0461460i
$125$	−1.47293e6	−	2.17869e7i	−0.0674525	−	0.997722i
$126$	1.48025e7	−	3.54843e7i	0.659233	−	1.58030i
$127$	−3.02366e6	−	478900.i	−0.130984	−	0.0207459i	0.0905980	−	0.995888i	$-0.471122\pi$
$127$	−3.02366e6	−	478900.i	−0.130984	−	0.0207459i	−0.221582	+	0.975142i	$0.571122\pi$
$128$	−2.20347e7	+	1.12272e7i	−0.928693	+	0.473193i
$129$	−2.04283e7	−	1.14741e7i	−0.837856	−	0.470604i
$130$	−1.92618e7	+	3.51666e7i	−0.768943	+	1.40388i
$131$	3.77729e6	−	1.22732e6i	0.146802	−	0.0476987i	−0.234695	−	0.972069i	$-0.575409\pi$
$131$	3.77729e6	−	1.22732e6i	0.146802	−	0.0476987i	0.381496	+	0.924370i	$0.375409\pi$
$132$	−264286.	+	176111.i	−0.0100015	+	0.00666465i
$133$	1.35524e7	+	6.90530e6i	0.499500	+	0.254508i
$134$	2.16720e7	+	1.57456e7i	0.778095	+	0.565319i
$135$	−8.98724e6	−	2.71375e7i	−0.314382	−	0.949296i
$136$	−3.21010e7	+	2.33228e7i	−1.09429	+	0.795049i
$137$	−1.90534e7	+	3.01776e6i	−0.633067	+	0.100268i	−0.464717	−	0.885459i	$-0.653844\pi$
$137$	−1.90534e7	+	3.01776e6i	−0.633067	+	0.100268i	−0.168350	+	0.985727i	$0.553844\pi$
$138$	−1.47267e7	−	597122.i	−0.477010	−	0.0193413i
$139$	2.48740e7	+	3.42361e7i	0.785585	+	1.08127i	0.994644	+	0.103362i	$0.0329600\pi$
$139$	2.48740e7	+	3.42361e7i	0.785585	+	1.08127i	−0.209059	+	0.977903i	$0.567040\pi$
$140$	48668.3	−	1.62947e6i	0.00149899	−	0.0501879i
$141$	−4.33621e7	+	3.99827e7i	−1.30270	+	1.20117i
$142$	−2.93790e7	+	5.76596e7i	−0.861050	+	1.68991i
$143$	1.57532e7	+	1.57532e7i	0.450497	+	0.450497i
$144$	3.67453e7	+	2.98473e6i	1.02549	+	0.0832982i
$145$	−2.00299e7	+	1.88681e7i	−0.545621	+	0.513974i
$146$	5.77088e6	+	1.87507e6i	0.153464	+	0.0498635i
$147$	6.84953e7	−	1.92249e7i	1.77849	−	0.499176i
$148$	117046.	−	739000.i	0.00296784	−	0.0187382i
$149$	3.16484e7			0.783791			0.391895	−	0.920010i	$-0.371820\pi$
$149$	3.16484e7			0.783791			0.391895	+	0.920010i	$0.371820\pi$
$150$	−2.65429e7	−	3.24793e7i	−0.642140	−	0.785756i
$151$	−1.07269e7			−0.253545			−0.126772	−	0.991932i	$-0.540462\pi$
$151$	−1.07269e7			−0.253545			−0.126772	+	0.991932i	$0.540462\pi$
$152$	−2.21553e6	+	1.39883e7i	−0.0511712	+	0.323082i
$153$	6.06863e7	−	4.62290e6i	1.36984	−	0.104351i
$154$	−2.98112e7	−	9.68623e6i	−0.657743	−	0.213714i
$155$	1.33622e7	−	7.06447e7i	0.288216	−	1.52377i
$156$	258821.	+	2.21053e6i	0.00545838	+	0.0466187i
$157$	−2.98230e7	−	2.98230e7i	−0.615039	−	0.615039i	0.329216	−	0.944255i	$-0.393216\pi$
$157$	−2.98230e7	−	2.98230e7i	−0.615039	−	0.615039i	−0.944255	+	0.329216i	$0.893216\pi$
$158$	−1.90464e7	+	3.73807e7i	−0.384161	+	0.753958i
$159$	4.41278e7	+	4.78576e7i	0.870608	+	0.944192i
$160$	2.95867e6	−	864572.i	0.0571053	−	0.0166871i
$161$	−2.47079e7	−	3.40075e7i	−0.466601	−	0.642221i
$162$	−4.42624e7	−	3.24992e7i	−0.817961	−	0.600580i
$163$	−1.69207e7	+	2.67998e6i	−0.306028	+	0.0484701i	−0.307560	−	0.951529i	$-0.599512\pi$
$163$	−1.69207e7	+	2.67998e6i	−0.306028	+	0.0484701i	0.00153156	+	0.999999i	$0.499512\pi$
$164$	−1.41030e6	+	1.02464e6i	−0.0249665	+	0.0181392i
$165$	−2.14584e7	+	9.09412e6i	−0.371881	+	0.157604i
$166$	−1.60920e7	−	1.16915e7i	−0.273043	−	0.198377i
$167$	−4.48640e7	−	2.28594e7i	−0.745402	−	0.379801i	0.0396642	−	0.999213i	$-0.487371\pi$
$167$	−4.48640e7	−	2.28594e7i	−0.745402	−	0.379801i	−0.785066	+	0.619412i	$0.787371\pi$
$168$	5.66190e7	+	8.49670e7i	0.921255	+	1.38251i
$169$	8.88062e7	−	2.88549e7i	1.41527	−	0.459850i
$170$	8.07444e7	−	3.81491e7i	1.26050	−	0.595544i
$171$	1.41498e7	−	1.64833e7i	0.216403	−	0.252091i
$172$	−1.70030e6	+	866344.i	−0.0254786	+	0.0129820i
$173$	5.14164e7	+	8.14356e6i	0.754989	+	0.119579i	0.522052	−	0.852913i	$-0.325167\pi$
$173$	5.14164e7	+	8.14356e6i	0.754989	+	0.119579i	0.232937	+	0.972492i	$0.425167\pi$
$174$	−1.03771e7	+	5.18290e7i	−0.149332	+	0.745849i
$175$	2.57329e7	−	1.16830e8i	0.362957	−	1.64787i
$176$		−	3.00558e7i		−	0.415560i
$177$	1.31458e7	−	3.54959e7i	0.178188	−	0.481140i
$178$	2.29938e7	+	4.51279e7i	0.305591	+	0.599756i
$179$	1.70709e7	−	5.25388e7i	0.222469	−	0.684690i	−0.776069	−	0.630648i	$-0.782789\pi$
$179$	1.70709e7	−	5.25388e7i	0.222469	−	0.684690i	0.998539	−	0.0540426i	$-0.0172107\pi$
$180$	−2.24518e6	−	616510.i	−0.0286944	−	0.00787928i
$181$	2.33978e7	+	7.20110e7i	0.293292	+	0.902659i	0.983790	+	0.179325i	$0.0573914\pi$
$181$	2.33978e7	+	7.20110e7i	0.293292	+	0.902659i	−0.690498	+	0.723334i	$0.742609\pi$
$182$	−1.55327e8	+	1.55327e8i	−1.90984	+	1.90984i
$183$	1.32952e7	+	1.05082e7i	0.160368	+	0.126750i
$184$	2.30063e7	−	3.16654e7i	0.272260	−	0.374734i
$185$	1.85186e7	−	5.16898e7i	0.215034	−	0.600211i
$186$	−5.76623e7	−	1.25493e8i	−0.657047	−	1.42996i
$187$	−7.76208e6	−	4.90079e7i	−0.0868026	−	0.548050i
$188$	751485.	+	4.74469e6i	0.00824837	+	0.0520781i
$189$	−5.55942e6	−	1.56514e8i	−0.0598981	−	1.68630i
$190$	1.07506e7	−	3.00073e7i	0.113709	−	0.317388i
$191$	6.80240e7	−	9.36270e7i	0.706391	−	0.972264i	−0.293476	−	0.955967i	$-0.594812\pi$
$191$	6.80240e7	−	9.36270e7i	0.706391	−	0.972264i	0.999867	−	0.0162978i	$-0.00518799\pi$
$192$	−5.88980e7	+	7.45192e7i	−0.600546	+	0.759826i
$193$	5.60782e7	−	5.60782e7i	0.561491	−	0.561491i	−0.368239	−	0.929731i	$-0.620039\pi$
$193$	5.60782e7	−	5.60782e7i	0.561491	−	0.561491i	0.929731	+	0.368239i	$0.120039\pi$
$194$	−2.11775e7	−	6.51776e7i	−0.208242	−	0.640903i
$195$	−1.14860e7	+	1.62922e8i	−0.110929	+	1.57347i
$196$	1.79051e6	−	5.51063e6i	0.0169856	−	0.0522763i
$197$	4.47905e7	+	8.79062e7i	0.417401	+	0.819196i	0.999979	+	0.00642141i	$0.00204401\pi$
$197$	4.47905e7	+	8.79062e7i	0.417401	+	0.819196i	−0.582578	+	0.812775i	$0.697956\pi$
$198$	−2.34870e7	+	3.81122e7i	−0.215030	+	0.348928i
$199$		−	1.96748e8i		−	1.76981i	−0.465776	−	0.884903i	$-0.654225\pi$
$199$		−	1.96748e8i		−	1.76981i	0.465776	−	0.884903i	$-0.345775\pi$
$200$	1.10864e8	−	1.08282e7i	0.979910	−	0.0957090i
$201$	1.06994e8	+	2.14220e7i	0.929336	+	0.186069i
$202$	4.06543e7	+	6.43900e6i	0.347038	+	0.0549653i
$203$	−1.34321e8	+	6.84402e7i	−1.12696	+	0.574216i
$204$	2.42750e6	−	4.32188e6i	0.0200195	−	0.0356425i
$205$	−1.15665e8	+	5.46481e7i	−0.937701	+	0.443034i
$206$	−1.33934e8	+	4.35179e7i	−1.06747	+	0.346843i
$207$	−5.55237e7	+	2.28356e7i	−0.435093	+	0.178944i
$208$	−1.87671e8	−	9.56233e7i	−1.44603	−	0.736787i
$209$	−1.43281e7	−	1.04100e7i	−0.108561	−	0.0788745i
$210$	−8.96683e7	−	2.11581e8i	−0.668146	−	1.57655i
$211$	−1.34549e8	+	9.77556e7i	−0.986034	+	0.716396i	−0.959049	−	0.283240i	$-0.908591\pi$
$211$	−1.34549e8	+	9.77556e7i	−0.986034	+	0.716396i	−0.0269854	+	0.999636i	$0.508591\pi$
$212$	5.23659e6	−	829394.i	0.0377462	−	0.00597841i
$213$	−1.06793e7	+	2.63382e8i	−0.0757209	+	1.86749i
$214$	9.12004e7	+	1.25527e8i	0.636134	+	0.875563i
$215$	−1.34417e8	+	3.92787e7i	−0.922398	+	0.269540i
$216$	1.37002e8	−	4.99576e7i	0.924994	−	0.337298i
$217$	1.78821e8	−	3.50955e8i	1.18798	−	2.33154i
$218$	1.34414e7	+	1.34414e7i	0.0878710	+	0.0878710i
$219$	2.45488e7	−	2.87431e6i	0.157934	−	0.0184918i
$220$	−352777.	+	1.86510e6i	−0.00223368	+	0.0118092i
$221$	−3.30705e8	−	1.07453e8i	−2.06095	−	0.669644i
$222$	−2.85014e7	−	1.01546e8i	−0.174836	−	0.622913i
$223$	−1.43198e7	+	9.04117e7i	−0.0864710	+	0.545956i	0.905981	+	0.423319i	$0.139135\pi$
$223$	−1.43198e7	+	9.04117e7i	−0.0864710	+	0.545956i	−0.992452	+	0.122637i	$0.960865\pi$
$224$	1.68868e7			0.100387
$225$	−1.53482e8	−	7.50749e7i	−0.898294	−	0.439396i
$226$	−9.90275e6			−0.0570658
$227$	1.27924e6	−	8.07682e6i	0.00725876	−	0.0458300i	−0.983793	−	0.179307i	$-0.942614\pi$
$227$	1.27924e6	−	8.07682e6i	0.00725876	−	0.0458300i	0.991052	+	0.133477i	$0.0426143\pi$
$228$	−478120.	−	1.70347e6i	−0.00267156	−	0.00951835i
$229$	1.00495e8	+	3.26528e7i	0.552994	+	0.179679i	0.572167	−	0.820137i	$-0.306103\pi$
$229$	1.00495e8	+	3.26528e7i	0.552994	+	0.179679i	−0.0191723	+	0.999816i	$0.506103\pi$
$230$	−6.41217e7	+	6.04024e7i	−0.347502	+	0.327346i
$231$	−1.26814e8	+	1.48481e7i	−0.676902	+	0.0792555i
$232$	−9.92566e7	−	9.92566e7i	−0.521857	−	0.521857i
$233$	−1.30819e8	+	2.56746e8i	−0.677522	+	1.32971i	0.254416	+	0.967095i	$0.418117\pi$
$233$	−1.30819e8	+	2.56746e8i	−0.677522	+	1.32971i	−0.931938	+	0.362617i	$0.881883\pi$
$234$	1.63252e8	+	2.67910e8i	0.832920	+	1.36689i
$235$	−1.05244e7	+	3.52368e8i	−0.0529003	+	1.77117i
$236$	−1.81207e6	−	2.49410e6i	−0.00897393	−	0.0123516i
$237$	−6.92340e6	+	1.70750e8i	−0.0337832	+	0.833186i
$238$	4.83219e8	−	7.65343e7i	2.32340	−	0.367991i
$239$	2.64481e8	−	1.92156e8i	1.25315	−	0.910463i	0.254745	−	0.967008i	$-0.418008\pi$
$239$	2.64481e8	−	1.92156e8i	1.25315	−	0.910463i	0.998400	+	0.0565450i	$0.0180085\pi$
$240$	1.66378e8	−	1.44464e8i	0.776884	−	0.674557i
$241$	2.39355e8	+	1.73901e8i	1.10149	+	0.800282i	0.981303	−	0.192469i	$-0.0616494\pi$
$241$	2.39355e8	+	1.73901e8i	1.10149	+	0.800282i	0.120191	+	0.992751i	$0.461649\pi$
$242$	−1.66824e8	−	8.50009e7i	−0.756665	−	0.385540i
$243$	−2.19101e8	−	4.50128e7i	−0.979542	−	0.201240i
$244$	1.31267e6	−	426512.i	0.00578483	−	0.00187960i
$245$	2.04263e8	−	3.72928e8i	0.887379	−	1.62011i
$246$	−1.20338e8	+	2.14248e8i	−0.515382	+	0.917578i
$247$	−1.10586e8	+	5.63463e7i	−0.466939	+	0.237917i
$248$	3.62244e8	+	5.73738e7i	1.50806	+	0.238854i
$249$	−7.94454e7	−	1.59063e7i	−0.326115	−	0.0652938i
$250$	−2.49697e8	−	2.24268e7i	−1.01070	−	0.0907774i
$251$		−	1.96851e7i		−	0.0785742i	−0.999228	−	0.0392871i	$-0.987491\pi$
$251$		−	1.96851e7i		−	0.0785742i	0.999228	−	0.0392871i	$-0.0125087\pi$
$252$	−1.08590e7	−	6.69195e6i	−0.0427453	−	0.0263421i
$253$	2.22208e7	+	4.36107e7i	0.0862655	+	0.169305i
$254$	−1.08609e7	+	3.34265e7i	−0.0415862	+	0.127989i
$255$	2.33981e8	−	2.78525e8i	0.883669	−	1.05190i
$256$	7.39852e6	+	2.27703e7i	0.0275616	+	0.0848260i
$257$	3.53251e8	−	3.53251e8i	1.29813	−	1.29813i	0.368502	−	0.929627i	$-0.379871\pi$
$257$	3.53251e8	−	3.53251e8i	1.29813	−	1.29813i	0.929627	−	0.368502i	$-0.120129\pi$
$258$	−1.66799e8	+	2.11039e8i	−0.604680	+	0.765056i
$259$	1.76809e8	−	2.43356e8i	0.632346	−	0.870349i
$260$	1.05235e7	+	8.13663e6i	0.0371324	+	0.0287103i
$261$	4.97371e7	+	2.09485e8i	0.173156	+	0.729307i
$262$	−7.13310e6	−	4.50366e7i	−0.0245033	−	0.154708i
$263$	1.48865e7	+	9.39899e7i	0.0504601	+	0.318593i	0.999988	+	0.00490992i	$0.00156288\pi$
$263$	1.48865e7	+	9.39899e7i	0.0504601	+	0.318593i	−0.949528	+	0.313683i	$0.898437\pi$
$264$	−4.96377e7	−	1.08029e8i	−0.166034	−	0.361348i
$265$	3.88900e8	+	1.16155e7i	1.28374	+	0.0383421i
$266$	1.02642e8	−	1.41275e8i	0.334380	−	0.460235i
$267$	1.61857e8	+	1.27927e8i	0.520405	+	0.411314i
$268$	6.28415e6	−	6.28415e6i	0.0199423	−	0.0199423i
$269$	1.32196e8	+	4.06857e8i	0.414081	+	1.27441i	0.913071	+	0.407801i	$0.133704\pi$
$269$	1.32196e8	+	4.06857e8i	0.414081	+	1.27441i	−0.498990	+	0.866608i	$0.666296\pi$
$270$	−3.23866e8	+	5.31716e7i	−1.00136	+	0.164402i
$271$	−2.07487e6	+	6.38580e6i	−0.00633285	+	0.0194905i	−0.954173	−	0.299256i	$-0.903262\pi$
$271$	−2.07487e6	+	6.38580e6i	−0.00633285	+	0.0194905i	0.947840	+	0.318746i	$0.103262\pi$
$272$	2.12974e8	+	4.17985e8i	0.641705	+	1.25942i
$273$	−3.10750e8	+	8.39080e8i	−0.924361	+	2.49594i
$274$			2.21475e8i			0.650425i
$275$	−5.08745e7	+	1.29673e8i	−0.147515	+	0.375997i
$276$	−959949.	+	4.79454e6i	−0.00274831	+	0.0137267i
$277$	−3.60973e8	−	5.71724e7i	−1.02046	−	0.161625i	−0.376284	−	0.926504i	$-0.622798\pi$
$277$	−3.60973e8	−	5.71724e7i	−1.02046	−	0.161625i	−0.644173	+	0.764880i	$0.722798\pi$
$278$	4.32892e8	−	2.20569e8i	1.20843	−	0.615728i
$279$	−4.26854e8	−	3.66424e8i	−1.17670	−	1.01011i
$280$	5.99622e8	+	1.13417e8i	1.63239	+	0.308762i
$281$	−2.37371e8	+	7.71267e7i	−0.638199	+	0.207364i	−0.610204	−	0.792244i	$-0.708912\pi$
$281$	−2.37371e8	+	7.71267e7i	−0.638199	+	0.207364i	−0.0279956	+	0.999608i	$0.508912\pi$
$282$	3.75504e8	+	5.63511e8i	0.997109	+	1.49634i
$283$	−3.12494e8	−	1.59224e8i	−0.819577	−	0.417595i	−0.00666217	−	0.999978i	$-0.502121\pi$
$283$	−3.12494e8	−	1.59224e8i	−0.819577	−	0.417595i	−0.812915	+	0.582382i	$0.802121\pi$
$284$	1.73687e7	+	1.26191e7i	0.0449940	+	0.0326900i
$285$	−1.12424e7	−	1.29350e8i	−0.0287674	−	0.330987i
$286$	2.06925e8	−	1.50340e8i	0.523037	−	0.380008i
$287$	−6.92204e8	+	1.09634e8i	−1.72841	+	0.273754i
$288$	5.68910e6	−	2.34375e7i	0.0140336	−	0.0578147i
$289$	2.14023e8	+	2.94578e8i	0.521577	+	0.717889i
$290$	1.77981e8	+	2.61015e8i	0.428529	+	0.628453i
$291$	−1.89233e8	−	2.05227e8i	−0.450164	−	0.488212i
$292$	913908.	−	1.79364e6i	0.00214814	−	0.00421596i
$293$	−2.55053e8	−	2.55053e8i	−0.592371	−	0.592371i	0.345900	−	0.938271i	$-0.387574\pi$
$293$	−2.55053e8	−	2.55053e8i	−0.592371	−	0.592371i	−0.938271	+	0.345900i	$0.887574\pi$
$294$	−9.49830e7	−	8.11228e8i	−0.217987	−	1.86177i
$295$	−9.66446e7	−	2.04553e8i	−0.219180	−	0.463904i
$296$	2.66380e8	+	8.65521e7i	0.597009	+	0.193980i
$297$	−2.21152e7	+	1.81010e8i	−0.0489829	+	0.400918i
$298$	5.68404e7	−	3.58876e8i	0.124423	−	0.785574i
$299$	3.43005e8			0.742082
$300$	−1.20201e7	+	7.01177e6i	−0.0257030	+	0.0149935i
$301$	−7.67192e8			−1.62152
$302$	−1.92654e7	+	1.21637e8i	−0.0402489	+	0.254122i
$303$	1.61426e8	−	4.53081e7i	0.333367	−	0.0935679i
$304$	1.59247e8	+	5.17423e7i	0.325097	+	0.105630i
$305$	1.00468e8	−	1.28510e7i	0.202758	−	0.0259351i
$306$	5.65711e7	−	6.96453e8i	0.112868	−	1.38953i
$307$	2.93130e8	+	2.93130e8i	0.578196	+	0.578196i	0.934406	−	0.356210i	$-0.115931\pi$
$307$	2.93130e8	+	2.93130e8i	0.578196	+	0.578196i	−0.356210	+	0.934406i	$0.615931\pi$
$308$	−4.72106e6	+	9.26560e6i	−0.00920687	+	0.0180695i
$309$	−4.21723e8	+	3.88857e8i	−0.813154	+	0.749782i
$310$	−7.77074e8	−	2.78398e8i	−1.48148	−	0.530762i
$311$	−4.85080e8	−	6.67655e8i	−0.914433	−	1.25861i	−0.965630	−	0.259921i	$-0.916304\pi$
$311$	−4.85080e8	−	6.67655e8i	−0.914433	−	1.25861i	0.0511968	−	0.998689i	$-0.483696\pi$
$312$	−8.32466e8	−	3.37540e7i	−1.55176	−	0.0629193i
$313$	3.99605e8	−	6.32912e7i	0.736590	−	0.116664i	0.223143	−	0.974786i	$-0.428368\pi$
$313$	3.99605e8	−	6.32912e7i	0.736590	−	0.116664i	0.513447	+	0.858121i	$0.328368\pi$
$314$	−3.91739e8	+	2.84615e8i	−0.714073	+	0.518804i
$315$	−6.91728e8	−	6.30629e8i	−1.24695	−	1.13681i
$316$	1.12601e7	+	8.18097e6i	0.0200742	+	0.0145848i
$317$	−3.71710e6	−	1.89396e6i	−0.00655386	−	0.00333936i	0.450710	−	0.892670i	$-0.351171\pi$
$317$	−3.71710e6	−	1.89396e6i	−0.00655386	−	0.00333936i	−0.457264	+	0.889331i	$0.651171\pi$
$318$	6.21932e8	−	4.14434e8i	1.08455	−	0.722703i
$319$	1.66942e8	−	5.42427e7i	0.287937	−	0.0935564i
$320$	7.20295e7	+	5.63119e8i	0.122881	+	0.960672i
$321$	5.51046e8	+	3.09509e8i	0.929866	+	0.522284i
$322$	−4.30002e8	+	2.19097e8i	−0.717753	+	0.365714i
$323$	2.73024e8	+	4.32428e7i	0.450809	+	0.0714011i
$324$	−1.29462e7	+	1.28169e7i	−0.0211464	+	0.0209352i
$325$	6.47831e8	+	7.30223e8i	1.04682	+	1.17995i
$326$			1.96685e8i			0.314419i
$327$	7.26106e7	+	2.68910e7i	0.114837	+	0.0425295i
$328$	−2.96259e8	−	5.81440e8i	−0.463567	−	0.909802i
$329$	−5.96803e8	+	1.83677e9i	−0.923943	+	2.84360i
$330$	6.45832e7	+	2.59660e8i	0.0989284	+	0.397746i
$331$	−1.20402e8	−	3.70558e8i	−0.182488	−	0.561641i	0.817408	−	0.576059i	$-0.195410\pi$
$331$	−1.20402e8	−	3.70558e8i	−0.182488	−	0.561641i	−0.999896	+	0.0144186i	$0.995410\pi$
$332$	−4.66612e6	+	4.66612e6i	−0.00699799	+	0.00699799i
$333$	−2.78193e8	−	3.27382e8i	−0.412849	−	0.485848i
$334$	−3.39788e8	+	4.67678e8i	−0.498994	+	0.686807i
$335$	5.38830e8	−	3.67417e8i	0.783060	−	0.533952i
$336$	1.09689e9	−	5.04006e8i	1.57752	−	0.724850i
$337$	1.02145e8	+	6.44920e8i	0.145383	+	0.917913i	0.947270	+	0.320437i	$0.103830\pi$
$337$	1.02145e8	+	6.44920e8i	0.145383	+	0.917913i	−0.801887	+	0.597476i	$0.796170\pi$
$338$	−1.67703e8	−	1.05884e9i	−0.236229	−	1.49149i
$339$	−3.66533e7	+	1.68417e7i	−0.0510992	+	0.0234794i
$340$	−8.30993e6	−	2.84376e7i	−0.0114662	−	0.0392389i
$341$	−2.69578e8	+	3.71042e8i	−0.368166	+	0.506737i
$342$	−1.61499e8	−	1.90054e8i	−0.218312	−	0.256913i
$343$	7.55467e8	−	7.55467e8i	1.01085	−	1.01085i
$344$	−2.20748e8	−	6.79392e8i	−0.292376	−	0.899841i
$345$	−1.34608e8	+	3.32621e8i	−0.176484	+	0.436097i
$346$	1.84687e8	−	5.68409e8i	0.239701	−	0.737725i
$347$	5.89002e7	+	1.15598e8i	0.0756770	+	0.148524i	0.925745	−	0.378149i	$-0.123439\pi$
$347$	5.89002e7	+	1.15598e8i	0.0756770	+	0.148524i	−0.850068	+	0.526673i	$0.823439\pi$
$348$	1.64444e7	+	6.09012e6i	0.0209166	+	0.00774637i
$349$		−	1.06922e9i		−	1.34641i	−0.739454	−	0.673207i	$-0.764916\pi$
$349$		−	1.06922e9i		−	1.34641i	0.739454	−	0.673207i	$-0.235084\pi$
$350$	−1.27858e9	−	5.01624e8i	−1.59400	−	0.625374i
$351$	1.05989e9	+	7.13978e8i	1.30823	+	0.881272i
$352$	−1.94206e7	−	3.07591e6i	−0.0237335	−	0.00375902i
$353$	2.42797e8	−	1.23711e8i	0.293786	−	0.149691i	−0.300885	−	0.953660i	$-0.597282\pi$
$353$	2.42797e8	−	1.23711e8i	0.293786	−	0.149691i	0.594671	+	0.803969i	$0.297282\pi$
$354$	−3.78894e8	−	2.12816e8i	−0.453949	−	0.254972i
$355$	1.08028e9	+	1.14680e9i	1.28155	+	1.36046i
$356$	1.59805e7	−	5.19238e6i	0.0187722	−	0.00609946i
$357$	1.65839e9	−	1.10509e9i	1.92907	−	1.28546i
$358$	−5.65102e8	−	2.87934e8i	−0.650933	−	0.331667i
$359$	−4.80350e8	−	3.48995e8i	−0.547933	−	0.398096i	0.279090	−	0.960265i	$-0.409967\pi$
$359$	−4.80350e8	−	3.48995e8i	−0.547933	−	0.398096i	−0.827023	+	0.562169i	$0.809967\pi$
$360$	3.59424e8	−	7.94018e8i	0.406020	−	0.896957i
$361$	−6.43335e8	+	4.67410e8i	−0.719718	+	0.522906i
$362$	8.58588e8	−	1.35987e8i	0.951272	−	0.150667i
$363$	−7.62030e8	−	3.08980e7i	−0.836178	−	0.0339045i
$364$	4.28351e7	+	5.89575e7i	0.0465527	+	0.0640744i
$365$	9.03607e7	−	1.16868e8i	0.0972645	−	0.125797i
$366$	1.43035e8	−	1.31888e8i	0.152496	−	0.140612i
$367$	3.98814e8	−	7.82717e8i	0.421153	−	0.826559i	−0.578786	−	0.815479i	$-0.696473\pi$
$367$	3.98814e8	−	7.82717e8i	0.421153	−	0.826559i	0.999939	−	0.0110791i	$-0.00352666\pi$
$368$	−3.27213e8	−	3.27213e8i	−0.342266	−	0.342266i
$369$	−8.10373e7	+	9.97659e8i	−0.0839639	+	1.03369i
$370$	−5.52875e8	−	3.02825e8i	−0.567441	−	0.310804i
$371$	2.02719e9	+	6.58675e8i	2.06104	+	0.669673i
$372$	−4.41132e7	+	1.23815e7i	−0.0444292	+	0.0124702i
$373$	7.21067e7	−	4.55264e8i	0.0719440	−	0.454237i	−0.925249	−	0.379361i	$-0.876144\pi$
$373$	7.21067e7	−	4.55264e8i	0.0719440	−	0.454237i	0.997193	−	0.0748760i	$-0.0238561\pi$
$374$	−5.69663e8			−0.563077
$375$	−9.62350e8	+	3.41652e8i	−0.942374	+	0.334560i
$376$	−1.79829e9			−1.74462
$377$	1.92433e8	−	1.21498e9i	0.184963	−	1.16781i
$378$	−1.78476e9	−	2.18057e8i	−1.69965	−	0.207658i
$379$	−1.01890e9	−	3.31060e8i	−0.961375	−	0.312370i	−0.214046	−	0.976824i	$-0.568664\pi$
$379$	−1.01890e9	−	3.31060e8i	−0.961375	−	0.312370i	−0.747329	+	0.664454i	$0.768664\pi$
$380$	−9.27465e6	−	5.07999e6i	−0.00867071	−	0.00474920i
$381$	1.66488e7	+	1.42194e8i	0.0154222	+	0.131717i
$382$	−9.39509e8	−	9.39509e8i	−0.862341	−	0.862341i
$383$	5.48803e8	−	1.07709e9i	0.499138	−	0.979613i	−0.494731	−	0.869046i	$-0.664733\pi$
$383$	5.48803e8	−	1.07709e9i	0.499138	−	0.979613i	0.993869	−	0.110567i	$-0.0352667\pi$
$384$	7.83976e8	+	8.50238e8i	0.706551	+	0.766269i
$385$	−4.66785e8	+	6.03714e8i	−0.416873	+	0.539161i
$386$	−5.35180e8	−	7.36612e8i	−0.473635	−	0.651903i
$387$	−2.58464e8	+	1.06480e9i	−0.226679	+	0.933856i
$388$	−2.24560e7	+	3.55668e6i	−0.0195174	+	0.00309125i
$389$	2.41064e8	−	1.75143e8i	0.207639	−	0.150859i	−0.479106	−	0.877757i	$-0.659039\pi$
$389$	2.41064e8	−	1.75143e8i	0.207639	−	0.150859i	0.686745	+	0.726899i	$0.259039\pi$
$390$	1.82681e9	+	4.22851e8i	1.55944	+	0.360962i
$391$	−6.18046e8	−	4.49037e8i	−0.522880	−	0.379895i
$392$	1.93262e9	+	9.84719e8i	1.62049	+	0.825679i
$393$	−1.02996e8	−	1.54564e8i	−0.0855946	−	0.128450i
$394$	1.07725e9	−	3.50020e8i	0.887321	−	0.288308i
$395$	7.00344e8	+	7.43467e8i	0.571770	+	0.606976i
$396$	1.12694e7	+	9.67399e6i	0.00911943	+	0.00782839i
$397$	−8.20206e7	+	4.17916e7i	−0.0657895	+	0.0335214i	−0.486576	−	0.873638i	$-0.661754\pi$
$397$	−8.20206e7	+	4.17916e7i	−0.0657895	+	0.0335214i	0.420786	+	0.907160i	$0.361754\pi$
$398$	−2.23102e9	−	3.53359e8i	−1.77383	−	0.280947i
$399$	1.39645e8	−	6.97470e8i	0.110058	−	0.549693i
$400$	7.85982e7	−	1.31461e9i	0.0614049	−	1.02704i
$401$			1.35604e9i			1.05019i	0.851045	+	0.525093i	$0.175969\pi$
$401$			1.35604e9i			1.05019i	−0.851045	+	0.525093i	$0.824031\pi$
$402$	4.35074e8	−	1.17478e9i	0.334020	−	0.901914i
$403$	1.45915e9	+	2.86375e9i	1.11054	+	2.17955i
$404$	4.21977e6	−	1.29871e7i	0.00318386	−	0.00979891i
$405$	−1.10830e9	+	7.47606e8i	−0.829022	+	0.559217i
$406$	5.34834e8	+	1.64605e9i	0.396623	+	1.22068i
$407$	−2.47665e8	+	2.47665e8i	−0.182089	+	0.182089i
$408$	1.45580e9	+	1.15062e9i	1.06118	+	0.838730i
$409$	−1.07777e9	+	1.48342e9i	−0.778924	+	1.07210i	0.216476	+	0.976288i	$0.430544\pi$
$409$	−1.07777e9	+	1.48342e9i	−0.778924	+	1.07210i	−0.995400	+	0.0958087i	$0.969456\pi$
$410$	4.11946e8	+	1.40973e9i	0.295187	+	1.01016i
$411$	3.76663e8	+	8.19750e8i	0.267613	+	0.582418i
$412$	7.30866e6	+	4.61451e7i	0.00514870	+	0.0325076i
$413$	−1.93887e8	−	1.22416e9i	−0.135433	−	0.855089i
$414$	1.59223e8	+	6.70621e8i	0.110282	+	0.464490i
$415$	−4.00093e8	+	2.72815e8i	−0.274785	+	0.187370i
$416$	−8.09933e7	+	1.11478e8i	−0.0551598	+	0.0759209i
$417$	1.22715e9	−	1.55262e9i	0.828746	−	1.04855i
$418$	−1.43776e8	+	1.43776e8i	−0.0962876	+	0.0962876i
$419$	−5.44923e8	−	1.67710e9i	−0.361898	−	1.11381i	−0.951901	−	0.306406i	$-0.900874\pi$
$419$	−5.44923e8	−	1.67710e9i	−0.361898	−	1.11381i	0.590003	−	0.807401i	$-0.299126\pi$
$420$	−7.39828e7	+	1.84012e7i	−0.0487257	+	0.0121192i
$421$	4.56633e7	−	1.40537e8i	0.0298250	−	0.0917919i	−0.935036	−	0.354553i	$-0.884633\pi$
$421$	4.56633e7	−	1.40537e8i	0.0298250	−	0.0917919i	0.964861	+	0.262761i	$0.0846331\pi$
$422$	8.66846e8	+	1.70128e9i	0.561498	+	1.10200i
$423$	2.34823e9	+	1.44712e9i	1.50851	+	0.929634i
$424$			1.98472e9i			1.26450i
$425$	−2.11346e8	−	2.16385e9i	−0.133546	−	1.36731i
$426$	2.96743e9	+	5.94130e8i	1.85972	+	0.372347i
$427$	5.48061e8	+	8.68043e7i	0.340668	+	0.0539565i
$428$	4.58647e7	−	2.33692e7i	0.0282765	−	0.0144076i
$429$	5.10213e8	−	9.08376e8i	0.311998	−	0.555476i
$430$	2.03988e8	+	1.59476e9i	0.123727	+	0.967285i
$431$	−1.74805e9	+	5.67977e8i	−1.05168	+	0.341712i	−0.783328	−	0.621608i	$-0.786480\pi$
$431$	−1.74805e9	+	5.67977e8i	−1.05168	+	0.341712i	−0.268353	+	0.963321i	$0.586480\pi$
$432$	−3.29981e8	−	1.69219e9i	−0.196923	−	1.00985i
$433$	−2.18864e9	−	1.11517e9i	−1.29559	−	0.660136i	−0.336086	−	0.941831i	$-0.609103\pi$
$433$	−2.18864e9	−	1.11517e9i	−1.29559	−	0.660136i	−0.959504	+	0.281695i	$0.909103\pi$
$434$	−3.65848e9	−	2.65804e9i	−2.14826	−	1.56080i
$435$	1.10267e9	+	6.63410e8i	0.642296	+	0.386429i
$436$	5.10195e6	−	3.70678e6i	0.00294804	−	0.00214188i
$437$	−2.69319e8	+	4.26560e7i	−0.154377	+	0.0244509i
$438$	1.14964e7	−	2.83533e8i	0.00653735	−	0.161229i
$439$	4.10283e8	+	5.64706e8i	0.231450	+	0.318564i	0.908907	−	0.416998i	$-0.136918\pi$
$439$	4.10283e8	+	5.64706e8i	0.231450	+	0.318564i	−0.677457	+	0.735563i	$0.736918\pi$
$440$	−6.68933e8	−	2.39655e8i	−0.374368	−	0.134122i
$441$	−1.73122e9	−	2.84108e9i	−0.961209	−	1.57742i
$442$	−1.81240e9	+	3.55703e9i	−0.998334	+	1.95934i
$443$	−7.14655e7	−	7.14655e7i	−0.0390556	−	0.0390556i	0.687309	−	0.726365i	$-0.258792\pi$
$443$	−7.14655e7	−	7.14655e7i	−0.0390556	−	0.0390556i	−0.726365	+	0.687309i	$0.758792\pi$
$444$	−3.47530e7	+	4.06908e6i	−0.0188431	+	0.00220625i
$445$	1.22310e9	−	1.56449e8i	0.657965	−	0.0841614i
$446$	9.99502e8	+	3.24758e8i	0.533472	+	0.173335i
$447$	−3.99958e8	−	1.42499e9i	−0.211806	−	0.754630i
$448$	−4.86535e8	+	3.07186e9i	−0.255647	+	1.61409i
$449$	−2.43027e9			−1.26704			−0.633522	−	0.773725i	$-0.718391\pi$
$449$	−2.43027e9			−1.26704			−0.633522	+	0.773725i	$0.718391\pi$
$450$	−1.12696e9	+	1.60557e9i	−0.582995	+	0.830586i
$451$	8.16035e8			0.418881
$452$	−513935.	+	3.24486e6i	−0.000261772	+	0.00165277i
$453$	1.35561e8	+	4.82983e8i	0.0685160	+	0.244112i
$454$	−8.92892e7	−	2.90118e7i	−0.0447820	−	0.0145506i
$455$	2.28456e9	+	4.83538e9i	1.13701	+	2.40653i
$456$	6.57830e8	−	7.70224e7i	0.324890	−	0.0380399i
$457$	−1.89049e9	−	1.89049e9i	−0.926548	−	0.926548i	0.0709335	−	0.997481i	$-0.477402\pi$
$457$	−1.89049e9	−	1.89049e9i	−0.926548	−	0.926548i	−0.997481	+	0.0709335i	$0.977402\pi$
$458$	5.50754e8	−	1.08092e9i	0.267873	−	0.525730i
$459$	−9.75073e8	−	2.67401e9i	−0.470644	−	1.29068i
$460$	1.64644e7	+	2.41457e7i	0.00788667	+	0.0115661i
$461$	−5.98167e8	−	8.23306e8i	−0.284360	−	0.391389i	0.642812	−	0.766024i	$-0.277768\pi$
$461$	−5.98167e8	−	8.23306e8i	−0.284360	−	0.391389i	−0.927172	+	0.374636i	$0.877768\pi$
$462$	−5.93879e7	+	1.46467e9i	−0.0280189	+	0.691024i
$463$	3.60965e7	−	5.71713e6i	0.0169018	−	0.00267698i	−0.147978	−	0.988991i	$-0.547276\pi$
$463$	3.60965e7	−	5.71713e6i	0.0169018	−	0.00267698i	0.164880	+	0.986314i	$0.447276\pi$
$464$	−1.34261e9	+	9.75463e8i	−0.623932	+	0.453313i
$465$	−3.34968e9	+	2.91134e8i	−1.54496	+	0.134279i
$466$	2.67641e9	+	1.94452e9i	1.22519	+	0.890149i
$467$	−6.01951e8	−	3.06709e8i	−0.273497	−	0.139353i	0.311863	−	0.950127i	$-0.399047\pi$
$467$	−6.01951e8	−	3.06709e8i	−0.273497	−	0.139353i	−0.585360	+	0.810773i	$0.699047\pi$
$468$	9.62593e7	−	3.95892e7i	0.0434092	−	0.0178532i
$469$	3.39804e9	−	1.10409e9i	1.52098	−	0.494197i
$470$	3.97676e9	+	7.52192e8i	1.76680	+	0.334184i
$471$	−9.65906e8	+	1.71968e9i	−0.425953	+	0.758360i
$472$	1.02827e9	−	5.23930e8i	0.450102	−	0.229338i
$473$	8.82304e8	+	1.39743e8i	0.383358	+	0.0607179i
$474$	1.92378e9	+	3.85174e8i	0.829720	+	0.166124i
$475$	−5.99471e8	−	4.92789e8i	−0.256650	−	0.210976i
$476$		−	1.62309e8i		−	0.0689794i
$477$	1.59714e9	−	2.59168e9i	0.673797	−	1.09337i
$478$	−1.70394e9	−	3.34418e9i	−0.713605	−	1.40053i
$479$	−5.08603e8	+	1.56532e9i	−0.211449	+	0.650772i	0.787938	+	0.615754i	$0.211149\pi$
$479$	−5.08603e8	+	1.56532e9i	−0.211449	+	0.650772i	−0.999387	+	0.0350174i	$0.988851\pi$
$480$	−7.63180e7	−	1.22289e8i	−0.0314980	−	0.0504713i
$481$	7.58491e8	+	2.33440e9i	0.310773	+	0.956460i
$482$	2.40182e9	−	2.40182e9i	0.976960	−	0.976960i
$483$	−1.21896e9	+	1.54226e9i	−0.492237	+	0.622790i
$484$	−3.65103e7	+	5.02521e7i	−0.0146372	+	0.0201463i
$485$	−1.66771e9	−	4.98104e7i	−0.663782	−	0.0198255i
$486$	−9.03926e8	+	2.40365e9i	−0.357195	+	0.949825i
$487$	−5.43547e8	−	3.43182e9i	−0.213248	−	1.34640i	−0.829350	−	0.558730i	$-0.811289\pi$
$487$	−5.43547e8	−	3.43182e9i	−0.213248	−	1.34640i	0.616102	−	0.787667i	$-0.288711\pi$
$488$	8.08261e7	+	5.10316e8i	0.0314834	+	0.198779i
$489$	3.34503e8	+	7.27994e8i	0.129366	+	0.281544i
$490$	−3.86194e9	−	2.98601e9i	−1.48293	−	1.14658i
$491$	2.74124e9	−	3.77299e9i	1.04511	−	1.43847i	0.152137	−	0.988359i	$-0.451384\pi$
$491$	2.74124e9	−	3.77299e9i	1.04511	−	1.43847i	0.892973	−	0.450111i	$-0.148616\pi$
$492$	6.39577e7	+	5.05505e7i	0.0242111	+	0.0191358i
$493$	−1.93729e9	+	1.93729e9i	−0.728167	+	0.728167i
$494$	4.40325e8	+	1.35518e9i	0.164335	+	0.505770i
$495$	6.80649e8	+	8.51248e8i	0.252235	+	0.315456i
$496$	1.33993e9	−	4.12387e9i	0.493055	−	1.51747i
$497$	3.91848e9	+	7.69046e9i	1.43176	+	2.80999i
$498$	−3.23052e8	+	8.72299e8i	−0.117212	+	0.316492i
$499$			1.43180e9i			0.515860i	0.966164	+	0.257930i	$0.0830403\pi$
$499$			1.43180e9i			0.515860i	−0.966164	+	0.257930i	$0.916960\pi$
$500$	−2.03075e7	+	8.06548e7i	−0.00726542	+	0.0288559i
$501$	−4.62283e8	+	2.30891e9i	−0.164239	+	0.820304i
$502$	−2.23218e8	−	3.53543e7i	−0.0787530	−	0.0124732i
$503$	2.90555e8	−	1.48045e8i	0.101798	−	0.0518689i	−0.402350	−	0.915486i	$-0.631806\pi$
$503$	2.90555e8	−	1.48045e8i	0.101798	−	0.0518689i	0.504148	+	0.863617i	$0.331806\pi$
$504$	3.11015e9	−	3.62307e9i	1.08212	−	1.26058i
$505$	4.81395e8	−	8.78894e8i	0.166334	−	0.303680i
$506$	5.34430e8	−	1.73647e8i	0.183385	−	0.0595854i
$507$	−2.42150e9	−	3.63389e9i	−0.825194	−	1.23835i
$508$	1.03893e7	+	5.29361e6i	0.00351611	+	0.00179155i
$509$	4.66230e9	+	3.38736e9i	1.56707	+	1.13854i	0.929896	+	0.367822i	$0.119896\pi$
$509$	4.66230e9	+	3.38736e9i	1.56707	+	1.13854i	0.637173	+	0.770721i	$0.280104\pi$
$510$	−2.73809e9	−	3.15345e9i	−0.914013	−	1.05266i
$511$	6.54747e8	−	4.75702e8i	0.217070	−	0.157711i
$512$	−2.85499e9	+	4.52186e8i	−0.940070	+	0.148892i
$513$	−9.20986e8	−	4.28791e8i	−0.301191	−	0.140228i
$514$	−3.37124e9	−	4.64011e9i	−1.09501	−	1.50715i
$515$	−1.02356e8	+	3.42700e9i	−0.0330208	+	1.10558i
$516$	6.04951e7	+	6.56082e7i	0.0193841	+	0.0210225i
$517$	1.02092e9	−	2.00366e9i	0.324917	−	0.637686i
$518$	−2.44198e9	−	2.44198e9i	−0.771948	−	0.771948i
$519$	−2.83109e8	−	2.41796e9i	−0.0888930	−	0.759214i
$520$	−3.62466e9	+	3.41442e9i	−1.13046	+	1.06489i
$521$	−5.90049e9	−	1.91718e9i	−1.82791	−	0.593926i	−0.999424	−	0.0339220i	$-0.989200\pi$
$521$	−5.90049e9	−	1.91718e9i	−1.82791	−	0.593926i	−0.828490	−	0.560003i	$-0.810800\pi$
$522$	2.46477e9	−	1.87759e8i	0.758454	−	0.0577767i
$523$	3.87734e8	−	2.44806e9i	0.118516	−	0.748283i	−0.854824	−	0.518918i	$-0.826335\pi$
$523$	3.87734e8	−	2.44806e9i	0.118516	−	0.748283i	0.973340	−	0.229365i	$-0.0736650\pi$
$524$	−1.51275e7			−0.00459311
$525$	−5.58554e9	+	3.17811e8i	−1.68464	+	0.0958543i
$526$	1.09253e9			0.327328
$527$	1.11982e9	−	7.07028e9i	0.333282	−	2.10426i
$528$	−1.35328e9	+	3.79831e8i	−0.400099	+	0.112298i
$529$	−2.52148e9	−	8.19280e8i	−0.740562	−	0.240623i
$530$	8.30174e8	−	4.38905e9i	0.242216	−	1.28057i
$531$	−1.76435e9	−	1.43314e8i	−0.511392	−	0.0415390i
$532$	−4.09650e7	−	4.09650e7i	−0.0117957	−	0.0117957i
$533$	2.59624e9	−	5.09540e9i	0.742675	−	1.45758i
$534$	1.74132e9	−	1.60561e9i	0.494862	−	0.456295i
$535$	3.62583e9	−	1.05953e9i	1.02369	−	0.299140i
$536$	1.95547e9	+	2.69147e9i	0.548497	+	0.754941i
$537$	−2.58132e9	−	1.04664e8i	−0.719335	−	0.0291668i
$538$	4.85096e9	−	7.68317e8i	1.34304	−	0.212717i
$539$	−2.19436e9	+	1.59429e9i	−0.603597	+	0.438539i
$540$	614834.	+	1.08881e8i	0.000168027	+	0.0297561i
$541$	6.80110e8	+	4.94129e8i	0.184667	+	0.134168i	0.676278	−	0.736647i	$-0.263592\pi$
$541$	6.80110e8	+	4.94129e8i	0.184667	+	0.134168i	−0.491611	+	0.870815i	$0.663592\pi$
$542$	6.86851e7	+	3.49968e7i	0.0185295	+	0.00944127i
$543$	2.94664e9	−	1.96354e9i	0.789819	−	0.526308i
$544$	2.91877e8	−	9.48365e7i	0.0777326	−	0.0252569i
$545$	4.18435e8	−	1.97697e8i	0.110723	−	0.0523133i
$546$	8.95661e9	+	5.03071e9i	2.35488	+	1.32268i
$547$	6.36307e9	−	3.24215e9i	1.66231	−	0.846987i	0.667567	−	0.744550i	$-0.267336\pi$
$547$	6.36307e9	−	3.24215e9i	1.66231	−	0.846987i	0.994739	−	0.102438i	$-0.0326642\pi$
$548$	7.25711e7	+	1.14941e7i	0.0188379	+	0.00298363i
$549$	3.05117e8	−	7.31421e8i	0.0786979	−	0.188653i
$550$	1.37905e9	+	8.09781e8i	0.353436	+	0.207538i
$551$			9.77899e8i			0.249037i
$552$	−1.71649e9	−	6.35696e8i	−0.434365	−	0.160865i
$553$	2.54035e9	+	4.98572e9i	0.638786	+	1.25369i
$554$	−1.29661e9	+	3.99055e9i	−0.323985	+	0.997123i
$555$	−2.56139e9	−	1.80577e8i	−0.635989	−	0.0448371i
$556$	−4.98082e7	−	1.53294e8i	−0.0122896	−	0.0378236i
$557$	−1.74584e9	+	1.74584e9i	−0.428067	+	0.428067i	−0.887969	−	0.459902i	$-0.847884\pi$
$557$	−1.74584e9	+	1.74584e9i	−0.428067	+	0.428067i	0.459902	+	0.887969i	$0.347884\pi$
$558$	−4.92168e9	+	4.18219e9i	−1.19920	+	1.01902i
$559$	3.67964e9	−	5.06460e9i	0.890973	−	1.22632i
$560$	2.43338e9	−	6.79214e9i	0.585533	−	1.63436i
$561$	−2.10851e9	+	9.68830e8i	−0.504203	+	0.231674i
$562$	4.48257e8	+	2.83018e9i	0.106525	+	0.672570i
$563$	4.51652e7	+	2.85162e8i	0.0106666	+	0.0673460i	0.992447	−	0.122671i	$-0.0391458\pi$
$563$	4.51652e7	+	2.85162e8i	0.0106666	+	0.0673460i	−0.981781	+	0.190017i	$0.939146\pi$
$564$	2.04135e8	−	9.37971e7i	0.0479116	−	0.0220147i
$565$	−8.13128e7	+	2.26963e8i	−0.0189666	+	0.0529403i
$566$	−2.36675e9	+	3.25755e9i	−0.548649	+	0.755151i
$567$	−6.97684e9	+	2.22826e9i	−1.60738	+	0.513364i
$568$	−5.68285e9	+	5.68285e9i	−1.30121	+	1.30121i
$569$	1.19974e9	+	3.69241e9i	0.273019	+	0.840267i	0.989737	+	0.142903i	$0.0456438\pi$
$569$	1.19974e9	+	3.69241e9i	0.273019	+	0.840267i	−0.716717	+	0.697364i	$0.754356\pi$
$570$	−1.48696e9	−	1.04830e8i	−0.336307	−	0.0237096i
$571$	1.46947e9	−	4.52256e9i	0.330319	−	1.01662i	−0.638663	−	0.769486i	$-0.720512\pi$
$571$	1.46947e9	−	4.52256e9i	0.330319	−	1.01662i	0.968982	−	0.247131i	$-0.0794878\pi$
$572$	−3.85232e7	−	7.56061e7i	−0.00860670	−	0.0168916i
$573$	−5.07526e9	−	1.87960e9i	−1.12698	−	0.417373i
$574$			8.04612e9i			1.77580i
$575$	8.57866e8	+	1.96559e9i	0.188184	+	0.431177i
$576$	4.09959e9	+	1.71017e9i	0.893843	+	0.372873i
$577$	3.44797e9	+	5.46105e8i	0.747220	+	0.118348i	0.518421	−	0.855126i	$-0.326520\pi$
$577$	3.44797e9	+	5.46105e8i	0.747220	+	0.118348i	0.228799	+	0.973474i	$0.426520\pi$
$578$	3.72474e9	−	1.89785e9i	0.802321	−	0.408803i
$579$	−3.23363e9	−	1.81626e9i	−0.692334	−	0.388868i
$580$	9.47645e7	−	4.47732e7i	0.0201673	−	0.00952839i
$581$	−2.52312e9	+	8.19812e8i	−0.533730	+	0.173419i
$582$	−2.66702e9	+	1.77721e9i	−0.560785	+	0.373687i
$583$	−2.21138e9	−	1.12676e9i	−0.462194	−	0.235500i
$584$	6.09654e8	+	4.42940e8i	0.126660	+	0.0920237i
$585$	7.48078e9	−	1.54177e9i	1.54490	−	0.318400i
$586$	−3.35024e9	+	2.43409e9i	−0.687755	+	0.499683i
$587$	−4.61327e9	+	7.30670e8i	−0.941403	+	0.149104i	−0.608229	−	0.793762i	$-0.708120\pi$
$587$	−4.61327e9	+	7.30670e8i	−0.941403	+	0.149104i	−0.333174	+	0.942865i	$0.608120\pi$
$588$	−2.70746e8	−	1.09779e7i	−0.0549215	−	0.00222690i
$589$	−1.50182e9	−	2.06708e9i	−0.302842	−	0.416826i
$590$	−2.49309e9	+	7.28522e8i	−0.499754	+	0.146036i
$591$	3.39198e9	−	3.12763e9i	0.675923	−	0.623245i
$592$	1.50335e9	−	2.95049e9i	0.297806	−	0.584478i
$593$	2.21231e9	+	2.21231e9i	0.435668	+	0.435668i	0.890551	−	0.454883i	$-0.150319\pi$
$593$	2.21231e9	+	2.21231e9i	0.435668	+	0.435668i	−0.454883	+	0.890551i	$0.650319\pi$
$594$	2.01284e9	+	5.75868e8i	0.394055	+	0.112738i
$595$	2.21367e9	−	1.17034e10i	0.430827	−	2.27774i
$596$	−1.14644e8	−	3.72500e7i	−0.0221814	−	0.00720717i
$597$	−8.85869e9	+	2.48641e9i	−1.70396	+	0.478259i
$598$	6.16035e8	−	3.88949e9i	0.117802	−	0.743770i
$599$	−5.90990e9			−1.12353			−0.561767	−	0.827296i	$-0.689878\pi$
$599$	−5.90990e9			−1.12353			−0.561767	+	0.827296i	$0.689878\pi$
$600$	−1.88860e9	−	4.85487e9i	−0.356952	−	0.917589i
$601$	6.40126e8			0.120283			0.0601416	−	0.998190i	$-0.480845\pi$
$601$	6.40126e8			0.120283			0.0601416	+	0.998190i	$0.480845\pi$
$602$	−1.37787e9	+	8.69954e9i	−0.257407	+	1.62521i
$603$	−3.87602e8	−	5.08817e9i	−0.0719905	−	0.945042i
$604$	3.88573e7	+	1.26255e7i	0.00717536	+	0.00233141i
$605$	−3.31797e9	+	3.12552e9i	−0.609156	+	0.573823i
$606$	−2.23850e8	−	1.91185e9i	−0.0408605	−	0.348979i
$607$	4.24950e9	+	4.24950e9i	0.771218	+	0.771218i	0.978320	−	0.207101i	$-0.0664029\pi$
$607$	4.24950e9	+	4.24950e9i	0.771218	+	0.771218i	−0.207101	+	0.978320i	$0.566403\pi$
$608$	4.97306e7	−	9.76019e7i	0.00897349	−	0.0176115i
$609$	4.77904e9	+	5.18297e9i	0.857394	+	0.929861i
$610$	3.47159e7	−	1.16233e9i	0.00619262	−	0.207336i
$611$	−9.26297e9	−	1.27494e10i	−1.64288	−	2.26123i
$612$	−2.25273e8	−	5.46815e7i	−0.0397263	−	0.00964295i
$613$	−5.01388e9	+	7.94120e8i	−0.879148	+	0.139243i	−0.579662	−	0.814857i	$-0.696815\pi$
$613$	−5.01388e9	+	7.94120e8i	−0.879148	+	0.139243i	−0.299486	+	0.954101i	$0.596815\pi$
$614$	3.85039e9	−	2.79747e9i	0.671298	−	0.487727i
$615$	3.92228e9	+	4.51727e9i	0.679948	+	0.783092i
$616$	−3.14935e9	−	2.28814e9i	−0.542861	−	0.394411i
$617$	1.66229e9	+	8.46979e8i	0.284911	+	0.145169i	0.590606	−	0.806960i	$-0.298889\pi$
$617$	1.66229e9	+	8.46979e8i	0.284911	+	0.145169i	−0.305695	+	0.952129i	$0.598889\pi$
$618$	3.65201e9	+	5.48049e9i	0.622404	+	0.934028i
$619$	−1.14748e8	+	3.72840e7i	−0.0194460	+	0.00631838i	−0.318724	−	0.947848i	$-0.603254\pi$
$619$	−1.14748e8	+	3.72840e7i	−0.0194460	+	0.00631838i	0.299278	+	0.954166i	$0.403254\pi$
$620$	−1.31552e8	+	2.40178e8i	−0.0221680	+	0.0404726i
$621$	1.72987e9	+	2.21140e9i	0.289862	+	0.370549i
$622$	−8.44205e9	+	4.30144e9i	−1.40664	+	0.716716i
$623$	6.67213e9	+	1.05676e9i	1.10549	+	0.175093i
$624$	−1.93378e9	+	9.65843e9i	−0.318612	+	1.59133i
$625$	−2.56430e9	+	5.53871e9i	−0.420135	+	0.907462i
$626$		−	4.64497e9i		−	0.756786i
$627$	−2.87642e8	+	7.76684e8i	−0.0466032	+	0.125837i
$628$	7.29299e7	+	1.43133e8i	0.0117502	+	0.0230612i
$629$	1.68933e9	−	5.19921e9i	0.270667	−	0.833029i
$630$	−8.39333e9	+	6.71121e9i	−1.33734	+	1.06932i
$631$	−6.10743e8	−	1.87967e9i	−0.0967734	−	0.297838i	0.890938	−	0.454124i	$-0.150048\pi$
$631$	−6.10743e8	−	1.87967e9i	−0.0967734	−	0.297838i	−0.987712	+	0.156286i	$0.950048\pi$
$632$	−3.68419e9	+	3.68419e9i	−0.580540	+	0.580540i
$633$	6.10186e9	+	4.82275e9i	0.956201	+	0.755756i
$634$	−2.81524e7	+	3.87484e7i	−0.00438735	+	0.00603867i
$635$	6.76930e8	+	5.23394e8i	0.104915	+	0.0811187i
$636$	−1.03521e8	−	2.25298e8i	−0.0159562	−	0.0347263i
$637$	2.97352e9	+	1.87741e10i	0.455809	+	2.87787i
$638$	−3.15256e8	−	1.99045e9i	−0.0480608	−	0.303444i
$639$	1.19939e10	−	2.84765e9i	1.81847	−	0.431752i
$640$	6.90920e9	+	2.06361e8i	1.04183	+	0.0311169i
$641$	2.24985e9	−	3.09665e9i	0.337403	−	0.464396i	−0.606277	−	0.795253i	$-0.707338\pi$
$641$	2.24985e9	−	3.09665e9i	0.337403	−	0.464396i	0.943681	+	0.330857i	$0.107338\pi$
$642$	4.49934e9	−	5.69268e9i	0.671084	−	0.849072i
$643$	7.28568e9	−	7.28568e9i	1.08077	−	1.08077i	0.0843287	−	0.996438i	$-0.473125\pi$
$643$	7.28568e9	−	7.28568e9i	1.08077	−	1.08077i	0.996438	−	0.0843287i	$-0.0268746\pi$
$644$	4.94757e7	+	1.52271e8i	0.00729948	+	0.0224655i
$645$	3.46724e9	+	5.55579e9i	0.508774	+	0.815242i
$646$	9.80700e8	−	3.01828e9i	0.143127	−	0.440500i
$647$	4.10932e9	+	8.06499e9i	0.596492	+	1.17068i	0.970011	+	0.243059i	$0.0781509\pi$
$647$	4.10932e9	+	8.06499e9i	0.596492	+	1.17068i	−0.373519	+	0.927622i	$0.621849\pi$
$648$	−3.98073e9	−	5.53724e9i	−0.574712	−	0.799431i
$649$			1.44315e9i			0.207231i
$650$	9.44383e9	−	6.03458e9i	1.34881	−	0.861887i
$651$	−1.80618e10	−	3.61628e9i	−2.56582	−	0.513722i
$652$	6.44482e7	+	1.02076e7i	0.00910635	+	0.00144230i
$653$	6.86383e9	−	3.49729e9i	0.964651	−	0.491514i	0.100605	−	0.994926i	$-0.467922\pi$
$653$	6.86383e9	−	3.49729e9i	0.964651	−	0.491514i	0.864046	+	0.503412i	$0.167922\pi$
$654$	4.35338e8	−	7.75069e8i	0.0608561	−	0.108347i
$655$	−1.09078e9	−	2.06317e8i	−0.151667	−	0.0286873i
$656$	−7.33751e9	+	2.38410e9i	−1.01481	+	0.329732i
$657$	−4.39654e8	−	1.06900e9i	−0.0604828	−	0.147061i
$658$	1.97561e10	+	1.00662e10i	2.70340	+	1.37745i
$659$	3.98480e9	+	2.89513e9i	0.542385	+	0.394066i	0.824970	−	0.565177i	$-0.191192\pi$
$659$	3.98480e9	+	2.89513e9i	0.542385	+	0.394066i	−0.282585	+	0.959242i	$0.591192\pi$
$660$	8.84352e7	−	7.68626e6i	0.0119735	−	0.00104067i
$661$	6.30974e9	−	4.58429e9i	0.849779	−	0.617401i	−0.0753059	−	0.997160i	$-0.523993\pi$
$661$	6.30974e9	−	4.58429e9i	0.849779	−	0.617401i	0.925085	+	0.379760i	$0.123993\pi$
$662$	−4.41817e9	+	6.99769e8i	−0.591888	+	0.0937458i
$663$	−6.58810e8	+	1.62481e10i	−0.0877937	+	2.16523i
$664$	−1.45198e9	−	1.99848e9i	−0.192474	−	0.264918i
$665$	−2.39511e9	−	3.51251e9i	−0.315827	−	0.463172i
$666$	−4.21197e9	+	2.56658e9i	−0.552491	+	0.336663i
$667$	1.22694e9	−	2.40800e9i	0.160097	−	0.314207i
$668$	1.35611e8	+	1.35611e8i	0.0176026	+	0.0176026i
$669$	4.25180e9	−	4.97824e8i	0.549011	−	0.0642813i
$670$	−3.19857e9	−	6.76992e9i	−0.410860	−	0.869604i
$671$	−6.14483e8	−	1.99658e8i	−0.0785201	−	0.0255127i
$672$	−2.13407e8	−	7.60336e8i	−0.0271280	−	0.0966525i
$673$	9.57432e8	−	6.04499e9i	0.121075	−	0.764439i	−0.850197	−	0.526465i	$-0.823517\pi$
$673$	9.57432e8	−	6.04499e9i	0.121075	−	0.764439i	0.971272	−	0.237973i	$-0.0764830\pi$
$674$	7.49650e9			0.943080
$675$	−1.44065e9	+	7.85935e9i	−0.180300	+	0.983612i
$676$	−3.55655e8			−0.0442809
$677$	1.12308e9	−	7.09082e9i	0.139107	−	0.878286i	−0.815140	−	0.579265i	$-0.803340\pi$
$677$	1.12308e9	−	7.09082e9i	0.139107	−	0.878286i	0.954246	−	0.299021i	$-0.0966602\pi$
$678$	1.25146e8	+	4.45876e8i	0.0154210	+	0.0549427i
$679$	−8.69319e9	−	2.82459e9i	−1.06570	−	0.346267i
$680$	1.10010e10	−	1.40716e9i	1.34169	−	0.171618i
$681$	−3.79829e8	+	4.44725e7i	−0.0460865	+	0.00539606i
$682$	3.72325e9	+	3.72325e9i	0.449446	+	0.449446i
$683$	−1.07665e9	+	2.11304e9i	−0.129301	+	0.253767i	−0.946576	−	0.322480i	$-0.895483\pi$
$683$	−1.07665e9	+	2.11304e9i	−0.129301	+	0.253767i	0.817276	+	0.576247i	$0.195483\pi$
$684$	−7.06571e7	+	4.30552e7i	−0.00844227	+	0.00514433i
$685$	5.07603e9	+	1.81856e9i	0.603403	+	0.216177i
$686$	−7.20977e9	−	9.92340e9i	−0.852682	−	1.17362i
$687$	2.00200e8	−	4.93749e9i	0.0235568	−	0.580975i
$688$	−8.34165e9	+	1.32119e9i	−0.976545	+	0.154670i
$689$	−1.40712e10	+	1.02233e10i	−1.63894	+	1.19076i
$690$	3.52999e9	+	2.12377e9i	0.409073	+	0.246114i
$691$	3.08442e9	+	2.24096e9i	0.355632	+	0.258382i	0.751228	−	0.660043i	$-0.229462\pi$
$691$	3.08442e9	+	2.24096e9i	0.355632	+	0.258382i	−0.395596	+	0.918425i	$0.629462\pi$
$692$	−1.76667e8	−	9.00163e7i	−0.0202667	−	0.0103264i
$693$	2.27116e9	+	5.52223e9i	0.259228	+	0.630301i
$694$	1.41660e9	−	4.60283e8i	0.160876	−	0.0522717i
$695$	−1.50075e9	−	1.17327e10i	−0.169575	−	1.32572i
$696$	−3.21472e9	+	5.72343e9i	−0.361419	+	0.643464i
$697$	−1.13486e10	+	5.78238e9i	−1.26948	+	0.646833i
$698$	−1.21244e10	−	1.92031e9i	−1.34948	−	0.213736i
$699$	1.32133e10	+	2.64553e9i	1.46333	+	0.292984i
$700$	−2.30724e8	+	3.92921e8i	−0.0254244	+	0.0432975i
$701$			3.67211e9i			0.402627i	0.979527	+	0.201313i	$0.0645209\pi$
$701$			3.67211e9i			0.402627i	−0.979527	+	0.201313i	$0.935479\pi$
$702$	9.99967e9	−	1.07362e10i	1.09095	−	1.17131i
$703$	−8.85853e8	−	1.73858e9i	−0.0961652	−	0.188735i
$704$	1.11907e9	−	3.44415e9i	0.120880	−	0.372030i
$705$	1.59986e10	−	3.97920e9i	1.71957	−	0.427695i
$706$	−9.66755e8	−	2.97537e9i	−0.103395	−	0.318217i
$707$	3.88197e9	−	3.88197e9i	0.413127	−	0.413127i
$708$	−8.93979e7	+	1.13109e8i	−0.00946697	+	0.0119779i
$709$	−8.08527e9	+	1.11284e10i	−0.851986	+	1.17266i	0.131436	+	0.991325i	$0.458041\pi$
$709$	−8.08527e9	+	1.11284e10i	−0.851986	+	1.17266i	−0.983422	+	0.181334i	$0.941959\pi$
$710$	1.49442e10	−	1.01901e10i	1.56700	−	1.06850i
$711$	7.77561e9	−	1.84613e9i	0.811317	−	0.192628i
$712$	9.83982e8	+	6.21262e9i	0.102166	+	0.645052i
$713$	1.10463e9	+	6.97433e9i	0.114130	+	0.720591i
$714$	−9.55268e9	−	2.07899e10i	−0.982158	−	2.13752i
$715$	−1.74659e9	−	5.97703e9i	−0.178698	−	0.611525i
$716$	−1.23676e8	+	1.70225e8i	−0.0125918	+	0.0173312i
$717$	−1.19943e10	−	9.47999e9i	−1.21523	−	0.960485i
$718$	−4.82011e9	+	4.82011e9i	−0.485984	+	0.485984i
$719$	6.94664e8	+	2.13796e9i	0.0696985	+	0.214510i	0.979839	−	0.199791i	$-0.0640262\pi$
$719$	6.94664e8	+	2.13796e9i	0.0696985	+	0.214510i	−0.910140	+	0.414301i	$0.864026\pi$
$720$	−8.60714e9	−	5.66558e9i	−0.859400	−	0.565692i
$721$	−5.80428e9	+	1.78637e10i	−0.576733	+	1.77500i
$722$	4.14475e9	+	8.13454e9i	0.409844	+	0.804364i
$723$	4.80514e9	−	1.29747e10i	0.472848	−	1.27677i
$724$		−	2.88393e8i		−	0.0282423i
$725$	7.44370e9	−	1.93595e9i	0.725447	−	0.188674i
$726$	−1.71897e9	+	8.58551e9i	−0.166721	+	0.832699i
$727$	2.01642e9	+	3.19369e8i	0.194630	+	0.0308264i	0.252988	−	0.967469i	$-0.418587\pi$
$727$	2.01642e9	+	3.19369e8i	0.194630	+	0.0308264i	−0.0583582	+	0.998296i	$0.518587\pi$
$728$	−2.43071e10	+	1.23851e10i	−2.33493	+	1.18970i
$729$	7.42174e8	+	1.04340e10i	0.0709511	+	0.997480i
$730$	−1.16293e9	−	1.23453e9i	−0.110643	−	0.117455i
$731$	−1.32604e10	+	4.30856e9i	−1.25558	+	0.407963i
$732$	−3.57928e7	−	5.37134e7i	−0.00337292	−	0.00506167i
$733$	−3.70566e9	−	1.88813e9i	−0.347538	−	0.177079i	0.271504	−	0.962437i	$-0.412479\pi$
$733$	−3.70566e9	−	1.88813e9i	−0.347538	−	0.177079i	−0.619042	+	0.785358i	$0.712479\pi$
$734$	−8.15932e9	−	5.92809e9i	−0.761584	−	0.553323i
$735$	−1.93726e10	−	4.48416e9i	−1.79963	−	0.416558i
$736$	−2.44916e8	+	1.77942e8i	−0.0226435	+	0.0164515i
$737$	−4.10901e9	+	6.50802e8i	−0.378095	+	0.0598843i
$738$	1.11674e10	+	2.71071e9i	1.02271	+	0.248248i
$739$	−9.23392e9	−	1.27094e10i	−0.841649	−	1.15843i	−0.985642	−	0.168851i	$-0.945994\pi$
$739$	−9.23392e9	−	1.27094e10i	−0.841649	−	1.15843i	0.143993	−	0.989579i	$-0.454006\pi$
$740$	−1.27921e8	+	1.65446e8i	−0.0116046	+	0.0150088i
$741$	3.93455e9	+	4.26710e9i	0.355248	+	0.385274i
$742$	1.11098e10	−	2.18043e10i	0.998377	−	1.95942i
$743$	−1.12136e10	−	1.12136e10i	−1.00296	−	1.00296i	−0.999996	−	0.00296426i	$-0.999056\pi$
$743$	−1.12136e10	−	1.12136e10i	−1.00296	−	1.00296i	−0.00296426	−	0.999996i	$-0.500944\pi$
$744$	−1.99458e9	−	1.70353e10i	−0.177561	−	1.51650i
$745$	−7.75844e9	−	4.24952e9i	−0.687428	−	0.376524i
$746$	−5.03294e9	−	1.63530e9i	−0.443850	−	0.144216i
$747$	2.87803e8	+	3.77808e9i	0.0252623	+	0.331626i
$748$	−2.95645e7	+	1.86663e8i	−0.00258294	+	0.0163081i
$749$	2.06947e10			1.79958
$750$	2.14577e9	+	1.15261e10i	0.185724	+	0.997629i
$751$	9.68503e9			0.834375			0.417187	−	0.908821i	$-0.363016\pi$
$751$	9.68503e9			0.834375			0.417187	+	0.908821i	$0.363016\pi$
$752$	−3.32590e9	+	2.09989e10i	−0.285198	+	1.80067i
$753$	−8.86332e8	+	2.48771e8i	−0.0756508	+	0.0212333i
$754$	−1.34315e10	−	4.36417e9i	−1.14111	−	0.370768i
$755$	2.62964e9	+	1.44033e9i	0.222373	+	0.121800i
$756$	−1.64077e8	+	5.73502e8i	−0.0138109	+	0.0482735i
$757$	−2.26177e9	−	2.26177e9i	−0.189501	−	0.189501i	0.605979	−	0.795481i	$-0.292781\pi$
$757$	−2.26177e9	−	2.26177e9i	−0.189501	−	0.189501i	−0.795481	+	0.605979i	$0.792781\pi$
$758$	−5.58397e9	+	1.09592e10i	−0.465694	+	0.913976i
$759$	1.68278e9	−	1.55163e9i	0.139695	−	0.128808i
$760$	2.42137e9	−	3.13168e9i	0.200085	−	0.258779i
$761$	1.76366e9	+	2.42747e9i	0.145067	+	0.199668i	0.875367	−	0.483459i	$-0.160620\pi$
$761$	1.76366e9	+	2.42747e9i	0.145067	+	0.199668i	−0.730300	+	0.683127i	$0.760620\pi$
$762$	1.64230e9	+	6.65902e7i	0.134465	+	0.00545215i
$763$	2.50414e9	−	3.96617e8i	0.204090	−	0.0323248i
$764$	−3.56610e8	+	2.59092e8i	−0.0289312	+	0.0210198i
$765$	−1.54977e10	−	7.01524e9i	−1.25156	−	0.566536i
$766$	−1.12279e10	−	8.15756e9i	−0.902607	−	0.655782i
$767$	9.01116e9	+	4.59142e9i	0.721102	+	0.367420i
$768$	9.31745e8	−	6.20882e8i	0.0742220	−	0.0494590i
$769$	−1.65830e8	+	5.38813e7i	−0.0131498	+	0.00427263i	−0.315585	−	0.948897i	$-0.602201\pi$
$769$	−1.65830e8	+	5.38813e7i	−0.0131498	+	0.00427263i	0.302435	+	0.953170i	$0.402201\pi$
$770$	6.00745e9	+	6.37735e9i	0.474212	+	0.503411i
$771$	−2.03695e10	−	1.14411e10i	−1.60063	−	0.899035i
$772$	−2.69142e8	+	1.37135e8i	−0.0210534	+	0.0107272i
$773$	2.27233e10	+	3.59901e9i	1.76947	+	0.280256i	0.954274	−	0.298932i	$-0.0966304\pi$
$773$	2.27233e10	+	3.59901e9i	1.76947	+	0.280256i	0.815194	+	0.579188i	$0.196630\pi$
$774$	1.16101e10	+	4.84322e9i	0.899997	+	0.375440i
$775$	−1.27613e10	+	1.55240e10i	−0.984782	+	1.19797i
$776$		−	8.51105e9i		−	0.653833i
$777$	−1.31917e10	−	4.88548e9i	−1.00885	−	0.373623i
$778$	−1.55308e9	−	3.04809e9i	−0.118240	−	0.232059i
$779$	−1.40484e9	+	4.32365e9i	−0.106474	+	0.327695i
$780$	2.33365e8	−	5.76652e8i	0.0176078	−	0.0435093i
$781$	−3.10562e9	−	9.55811e9i	−0.233276	−	0.717949i
$782$	−6.20184e9	+	6.20184e9i	−0.463764	+	0.463764i
$783$	8.80358e9	−	4.88680e9i	0.655380	−	0.363796i
$784$	1.50731e10	−	2.07463e10i	1.11711	−	1.53757i
$785$	3.30653e9	+	1.13154e10i	0.243966	+	0.834881i
$786$	−1.93765e9	+	8.90323e8i	−0.142330	+	0.0653986i
$787$	−2.54958e9	−	1.60974e10i	−0.186448	−	1.17719i	−0.886374	−	0.462971i	$-0.846784\pi$
$787$	−2.54958e9	−	1.60974e10i	−0.186448	−	1.17719i	0.699926	−	0.714216i	$-0.253216\pi$
$788$	−5.87846e7	−	3.71151e8i	−0.00427978	−	0.0270215i
$789$	4.04381e9	−	1.85807e9i	0.293104	−	0.134677i
$790$	9.68832e9	−	6.60625e9i	0.699123	−	0.476717i
$791$	−7.76346e8	+	1.06855e9i	−0.0557747	+	0.0767673i
$792$	−4.23675e9	+	3.60018e9i	−0.303037	+	0.257505i
$793$	−3.20167e9	+	3.20167e9i	−0.227993	+	0.227993i
$794$	3.26585e8	+	1.00513e9i	0.0231539	+	0.0712605i
$795$	−4.39174e9	−	1.76572e10i	−0.309993	−	1.24634i
$796$	−2.31572e8	+	7.12705e8i	−0.0162738	+	0.0500858i
$797$	−1.03791e10	−	2.03701e10i	−0.726197	−	1.42524i	−0.897948	−	0.440101i	$-0.854943\pi$
$797$	−1.03791e10	−	2.03701e10i	−0.726197	−	1.42524i	0.171752	−	0.985140i	$-0.445057\pi$
$798$	−7.65812e9	−	2.83615e9i	−0.533473	−	0.197569i
$799$			3.50990e10i			2.43434i
$800$	−8.41390e8	−	1.85323e8i	−0.0581009	−	0.0127972i
$801$	3.71451e9	−	8.90436e9i	0.255381	−	0.612194i
$802$	1.53767e10	+	2.43543e9i	1.05258	+	0.166712i
$803$	−8.39637e8	+	4.27816e8i	−0.0572251	+	0.0291577i
$804$	−3.62363e8	−	2.03531e8i	−0.0245894	−	0.0138113i
$805$	1.49073e9	+	1.16544e10i	0.100720	+	0.787414i
$806$	3.50940e10	−	1.14027e10i	2.36080	−	0.767072i
$807$	1.66483e10	−	1.10938e10i	1.11510	−	0.743062i
$808$	4.55468e9	+	2.32073e9i	0.303751	+	0.154769i
$809$	−6.52650e9	−	4.74178e9i	−0.433372	−	0.314863i	0.349624	−	0.936890i	$-0.386309\pi$
$809$	−6.52650e9	−	4.74178e9i	−0.433372	−	0.314863i	−0.782996	+	0.622027i	$0.786309\pi$
$810$	6.48694e9	+	1.39102e10i	0.428886	+	0.919681i
$811$	6.67415e9	−	4.84905e9i	0.439362	−	0.319215i	−0.346019	−	0.938227i	$-0.612467\pi$
$811$	6.67415e9	−	4.84905e9i	0.439362	−	0.319215i	0.785381	+	0.619012i	$0.212467\pi$
$812$	5.67122e8	−	8.98233e7i	0.0371732	−	0.00588766i
$813$	3.13745e8	+	1.27214e7i	0.0204767	+	0.000830267i
$814$	2.36358e9	+	3.25319e9i	0.153598	+	0.211409i
$815$	4.50787e9	+	1.61501e9i	0.291689	+	0.104502i
$816$	1.61285e10	−	1.48715e10i	1.03915	−	0.958165i
$817$	−2.25933e9	+	4.43419e9i	−0.144945	+	0.284471i
$818$	1.48856e10	+	1.48856e10i	0.950886	+	0.950886i
$819$	4.17071e10	+	3.38776e9i	2.65287	+	0.215486i
$820$	4.83309e8	−	6.18209e7i	0.0306109	−	0.00391550i
$821$	−8.91027e9	−	2.89512e9i	−0.561940	−	0.182585i	0.0142540	−	0.999898i	$-0.495463\pi$
$821$	−8.91027e9	−	2.89512e9i	−0.561940	−	0.182585i	−0.576194	+	0.817313i	$0.695463\pi$
$822$	9.97200e9	−	2.79889e9i	0.626226	−	0.175766i
$823$	−2.99261e9	+	1.88946e10i	−0.187133	+	1.18151i	0.697973	+	0.716124i	$0.254085\pi$
$823$	−2.99261e9	+	1.88946e10i	−0.187133	+	1.18151i	−0.885106	+	0.465389i	$0.845915\pi$
$824$	−1.74894e10			−1.08901
$825$	6.48151e9	+	6.51904e8i	0.401872	+	0.0404199i
$826$	−1.42295e10			−0.878534
$827$	−2.53360e9	+	1.59965e10i	−0.155764	+	0.983457i	0.778699	+	0.627398i	$0.215880\pi$
$827$	−2.53360e9	+	1.59965e10i	−0.155764	+	0.983457i	−0.934463	+	0.356059i	$0.884120\pi$
$828$	2.28008e8	−	1.73689e7i	0.0139586	−	0.00106333i
$829$	1.53303e10	+	4.98110e9i	0.934563	+	0.303658i	0.736427	−	0.676517i	$-0.236511\pi$
$829$	1.53303e10	+	4.98110e9i	0.934563	+	0.303658i	0.198136	+	0.980175i	$0.436511\pi$
$830$	2.37501e9	+	5.02682e9i	0.144176	+	0.305154i
$831$	1.98758e9	+	1.69755e10i	0.120149	+	1.02617i
$832$	−1.79453e10	−	1.79453e10i	−1.08024	−	1.08024i
$833$	1.92198e10	−	3.77209e10i	1.15210	−	2.26113i
$834$	−1.54019e10	−	1.67037e10i	−0.919377	−	0.997084i
$835$	7.92878e9	+	1.16279e10i	0.471307	+	0.691189i
$836$	3.96498e7	+	5.45733e7i	0.00234703	+	0.00323041i
$837$	−1.11040e10	+	2.38500e10i	−0.654549	+	1.40588i
$838$	−1.99961e10	+	3.16707e9i	−1.17379	+	0.185910i
$839$	−3.92690e9	+	2.85306e9i	−0.229553	+	0.166780i	−0.696616	−	0.717444i	$-0.745312\pi$
$839$	−3.92690e9	+	2.85306e9i	−0.229553	+	0.166780i	0.467063	+	0.884224i	$0.345312\pi$
$840$	−2.47111e9	−	2.84316e10i	−0.143851	−	1.65510i
$841$	6.11428e9	+	4.44229e9i	0.354454	+	0.257526i
$842$	−1.51161e9	−	7.70202e8i	−0.0872662	−	0.0444644i
$843$	6.47245e9	+	9.71307e9i	0.372111	+	0.558419i
$844$	6.02451e8	−	1.95748e8i	0.0344924	−	0.0112073i
$845$	−2.56448e10	−	4.85063e9i	−1.46218	−	0.276566i
$846$	2.06269e10	−	2.40286e10i	1.17122	−	1.36437i
$847$	−2.22504e10	+	1.13372e10i	−1.25819	+	0.641080i
$848$	2.31759e10	+	3.67070e9i	1.30512	+	0.206711i
$849$	−3.21997e9	+	1.60824e10i	−0.180582	+	0.901933i
$850$	−2.49164e10	−	1.48971e9i	−1.39162	−	0.0832025i
$851$			5.39258e9i			0.299946i
$852$	3.48684e8	−	9.41510e8i	0.0193150	−	0.0521539i
$853$	−4.41428e9	−	8.66351e9i	−0.243522	−	0.477939i	0.736602	−	0.676327i	$-0.236429\pi$
$853$	−4.41428e9	−	8.66351e9i	−0.243522	−	0.477939i	−0.980124	+	0.198388i	$0.936429\pi$
$854$	1.96863e9	−	6.05881e9i	0.108159	−	0.332878i
$855$	−5.68199e9	+	2.14086e9i	−0.310899	+	0.117141i
$856$	5.95458e9	+	1.83263e10i	0.324484	+	0.998658i
$857$	−1.20616e9	+	1.20616e9i	−0.0654592	+	0.0654592i	−0.739079	−	0.673619i	$-0.764739\pi$
$857$	−1.20616e9	+	1.20616e9i	−0.0654592	+	0.0654592i	0.673619	+	0.739079i	$0.264739\pi$
$858$	−9.38415e9	−	7.41698e9i	−0.507212	−	0.400887i
$859$	8.56224e9	−	1.17849e10i	0.460905	−	0.634381i	−0.513791	−	0.857915i	$-0.671759\pi$
$859$	8.56224e9	−	1.17849e10i	0.460905	−	0.634381i	0.974696	+	0.223534i	$0.0717594\pi$
$860$	5.33144e8	+	1.59237e7i	0.0285825	+	0.000853688i
$861$	1.36841e10	+	2.97813e10i	0.730642	+	1.59013i
$862$	3.30106e9	+	2.08421e10i	0.175541	+	1.10832i
$863$	−2.71723e9	−	1.71559e10i	−0.143909	−	0.908606i	−0.948959	−	0.315399i	$-0.897862\pi$
$863$	−2.71723e9	−	1.71559e10i	−0.143909	−	0.908606i	0.805050	−	0.593207i	$-0.202138\pi$
$864$	−1.12718e9	+	4.00379e7i	−0.0594560	+	0.00211190i
$865$	−1.15110e10	−	8.90017e9i	−0.604723	−	0.467565i
$866$	−1.65762e10	+	2.28152e10i	−0.867307	+	1.19375i
$867$	1.05588e10	−	1.33592e10i	0.550233	−	0.696169i
$868$	−1.06084e9	+	1.06084e9i	−0.0550591	+	0.0550591i
$869$	−2.01337e9	−	6.19651e9i	−0.104077	−	0.320316i
$870$	9.50310e9	−	1.13123e10i	0.489269	−	0.582414i
$871$	−9.00923e9	+	2.77276e10i	−0.461981	+	1.42183i
$872$	1.07176e9	+	2.10344e9i	0.0547379	+	0.107429i
$873$	−6.84900e9	+	1.11139e10i	−0.348400	+	0.565347i
$874$			3.13054e9i			0.158610i
$875$	−2.19954e10	+	2.51851e10i	−1.10995	+	1.27091i
$876$	−9.23092e7	−	1.84819e7i	−0.00463960	−	0.000928928i
$877$	1.03585e10	+	1.64062e9i	0.518557	+	0.0821313i	0.410227	−	0.911984i	$-0.365450\pi$
$877$	1.03585e10	+	1.64062e9i	0.518557	+	0.0821313i	0.108330	+	0.994115i	$0.465450\pi$
$878$	7.14033e9	−	3.63818e9i	0.356031	−	0.181407i
$879$	−8.26064e9	+	1.47071e10i	−0.410254	+	0.730410i
$880$	−4.03567e9	+	7.36801e9i	−0.199630	+	0.364469i
$881$	2.55627e9	−	8.30583e8i	0.125948	−	0.0409230i	−0.245365	−	0.969431i	$-0.578908\pi$
$881$	2.55627e9	−	8.30583e8i	0.125948	−	0.0409230i	0.371313	+	0.928508i	$0.378908\pi$
$882$	−3.53256e10	+	1.45286e10i	−1.73360	+	0.712989i
$883$	−1.41772e10	−	7.22364e9i	−0.692992	−	0.353097i	0.0717601	−	0.997422i	$-0.477138\pi$
$883$	−1.41772e10	−	7.22364e9i	−0.692992	−	0.353097i	−0.764752	+	0.644325i	$0.777138\pi$
$884$	1.07148e9	+	7.78477e8i	0.0521677	+	0.0379021i
$885$	−7.98874e9	+	6.93651e9i	−0.387415	+	0.336387i
$886$	−9.38732e8	+	6.82029e8i	−0.0453444	+	0.0329446i
$887$	3.36719e10	−	5.33311e9i	1.62008	−	0.256595i	0.720531	−	0.693423i	$-0.243898\pi$
$887$	3.36719e10	−	5.33311e9i	1.62008	−	0.256595i	0.899545	+	0.436828i	$0.143898\pi$
$888$	5.30666e8	−	1.30877e10i	0.0254317	−	0.627217i
$889$	2.75540e9	+	3.79248e9i	0.131531	+	0.181037i
$890$	4.22634e8	−	1.41503e10i	0.0200955	−	0.672822i
$891$	8.42955e9	−	1.29177e9i	0.399239	−	0.0611806i
$892$	1.58287e8	−	3.10655e8i	0.00746736	−	0.0146555i
$893$	8.85856e9	+	8.85856e9i	0.416278	+	0.416278i
$894$	−1.68769e10	+	1.97604e9i	−0.789970	+	0.0924941i
$895$	−1.12394e10	+	1.05874e10i	−0.524035	+	0.493640i
$896$	3.60152e10	+	1.17020e10i	1.67266	+	0.543480i
$897$	−4.33474e9	−	1.54440e10i	−0.200535	−	0.714472i
$898$	−4.36474e9	+	2.75579e10i	−0.201137	+	1.26993i
$899$	2.53238e10			1.16244
$900$	4.67613e8	+	4.52600e8i	0.0213815	+	0.0206950i
$901$	3.87378e10			1.76440
$902$	1.46559e9	−	9.25339e9i	0.0664952	−	0.419834i
$903$	9.69541e9	+	3.45432e10i	0.438186	+	1.56119i
$904$	−1.16964e9	−	3.80040e8i	−0.0526579	−	0.0171096i
$905$	3.93327e9	−	2.07948e10i	0.176394	−	0.932577i
$906$	5.72024e9	−	6.69757e8i	0.255544	−	0.0299205i
$907$	−2.11841e10	−	2.11841e10i	−0.942722	−	0.942722i	0.0557244	−	0.998446i	$-0.482253\pi$
$907$	−2.11841e10	−	2.11841e10i	−0.942722	−	0.942722i	−0.998446	+	0.0557244i	$0.982253\pi$
$908$	−1.41403e7	+	2.77520e7i	−0.000626844	+	0.00123025i
$909$	−4.08004e9	−	6.69568e9i	−0.180173	−	0.295679i
$910$	5.89336e10	−	1.72214e10i	2.59250	−	0.757570i
$911$	−1.21581e10	−	1.67342e10i	−0.532785	−	0.733316i	0.454766	−	0.890611i	$-0.349723\pi$
$911$	−1.21581e10	−	1.67342e10i	−0.532785	−	0.733316i	−0.987552	+	0.157295i	$0.949723\pi$
$912$	3.17241e8	−	7.82405e9i	0.0138487	−	0.341546i
$913$	3.05103e9	−	4.83235e8i	0.132678	−	0.0210141i
$914$	−2.48324e10	+	1.80418e10i	−1.07574	+	0.781571i
$915$	−1.84829e9	−	4.36121e9i	−0.0797620	−	0.188206i
$916$	−3.25603e8	−	2.36564e8i	−0.0139976	−	0.0101699i
$917$	−5.41886e9	−	2.76104e9i	−0.232068	−	0.118244i
$918$	−3.20730e10	+	6.25430e9i	−1.36833	+	0.266827i
$919$	1.92265e10	−	6.24707e9i	0.817140	−	0.265505i	0.129521	−	0.991577i	$-0.458656\pi$
$919$	1.92265e10	−	6.24707e9i	0.817140	−	0.265505i	0.687619	+	0.726072i	$0.258656\pi$
$920$	−9.89166e9	+	4.67349e9i	−0.418805	+	0.197872i
$921$	9.49387e9	−	1.69027e10i	0.400437	−	0.712932i
$922$	−1.04101e10	+	5.30424e9i	−0.437420	+	0.222877i
$923$	−6.95624e10	−	1.10176e10i	−2.91185	−	0.461191i
$924$	4.76850e8	+	9.54737e7i	0.0198852	+	0.00398136i
$925$	−1.14803e10	+	1.01849e10i	−0.476931	+	0.423118i
$926$		−	4.19583e8i		−	0.0173652i
$927$	2.28380e10	+	1.40741e10i	0.941627	+	0.580285i
$928$	4.92893e8	+	9.67357e8i	0.0202458	+	0.0397346i
$929$	−9.46355e9	+	2.91258e10i	−0.387257	+	1.19185i	0.547573	+	0.836758i	$0.315552\pi$
$929$	−9.46355e9	+	2.91258e10i	−0.387257	+	1.19185i	−0.934830	+	0.355096i	$0.884448\pi$
$930$	−2.71469e9	+	3.85064e10i	−0.110670	+	1.56979i
$931$	−4.66947e9	−	1.43712e10i	−0.189646	−	0.583671i
$932$	7.76068e8	−	7.76068e8i	0.0314011	−	0.0314011i
$933$	−2.39313e10	+	3.02785e10i	−0.964673	+	1.22053i
$934$	−4.55902e9	+	6.27495e9i	−0.183087	+	0.251997i
$935$	−4.67758e9	+	1.30562e10i	−0.187146	+	0.522369i
$936$	9.00053e9	+	3.79088e10i	0.358759	+	1.51103i
$937$	−1.21416e9	−	7.66587e9i	−0.0482154	−	0.304420i	0.951782	−	0.306776i	$-0.0992501\pi$
$937$	−1.21416e9	−	7.66587e9i	−0.0482154	−	0.304420i	−0.999997	+	0.00235572i	$0.999250\pi$
$938$	−6.41693e9	−	4.05149e10i	−0.253873	−	1.60289i
$939$	−7.89973e9	−	1.71926e10i	−0.311374	−	0.677658i
$940$	4.52860e8	−	1.26404e9i	0.0177835	−	0.0496379i
$941$	−1.60582e10	+	2.21022e10i	−0.628249	+	0.864711i	−0.997921	−	0.0644517i	$-0.979470\pi$
$941$	−1.60582e10	+	2.21022e10i	−0.628249	+	0.864711i	0.369672	+	0.929162i	$0.379470\pi$
$942$	1.77655e10	+	1.40414e10i	0.692468	+	0.547308i
$943$	8.88405e9	−	8.88405e9i	0.345001	−	0.345001i
$944$	−4.21626e9	−	1.29763e10i	−0.163127	−	0.502052i
$945$	−1.96526e10	+	3.91150e10i	−0.757547	+	1.50776i
$946$	3.16922e9	−	9.75387e9i	0.121712	−	0.374592i
$947$	−1.99555e10	−	3.91649e10i	−0.763550	−	1.49855i	−0.863935	−	0.503603i	$-0.832007\pi$
$947$	−1.99555e10	−	3.91649e10i	−0.763550	−	1.49855i	0.100384	−	0.994949i	$-0.467993\pi$
$948$	2.26052e8	−	6.10380e8i	0.00861745	−	0.0232687i
$949$			6.60388e9i			0.250823i
$950$	−6.66460e9	+	5.91263e9i	−0.252198	+	0.223742i
$951$	−3.83014e7	+	1.91299e8i	−0.00144405	+	0.00721243i
$952$	6.00115e10	+	9.50489e9i	2.25427	+	0.357041i
$953$	2.65548e10	−	1.35304e10i	0.993844	−	0.506389i	0.120093	−	0.992763i	$-0.461681\pi$
$953$	2.65548e10	−	1.35304e10i	0.993844	−	0.506389i	0.873751	+	0.486374i	$0.161681\pi$
$954$	−2.65197e10	−	2.27654e10i	−0.988895	−	0.848897i
$955$	−2.92473e10	+	1.38184e10i	−1.08661	+	0.513388i
$956$	−1.18423e9	+	3.84779e8i	−0.0438362	+	0.0142432i
$957$	−4.55203e9	−	6.83114e9i	−0.167886	−	0.251942i
$958$	1.68364e10	+	8.57859e9i	0.618686	+	0.315236i
$959$	2.38980e10	+	1.73629e10i	0.874978	+	0.635709i
$960$	2.44444e10	−	1.03596e10i	0.891724	−	0.377914i
$961$	−3.12714e10	+	2.27200e10i	−1.13662	+	0.825802i
$962$	2.78330e10	−	4.40832e9i	1.00797	−	0.159647i
$963$	6.97196e9	−	2.87225e10i	0.251572	−	1.03641i
$964$	−6.62362e8	−	9.11662e8i	−0.0238136	−	0.0327766i
$965$	−2.12770e10	+	6.21749e9i	−0.762193	+	0.222725i
$966$	1.52991e10	+	1.65922e10i	0.546068	+	0.592222i
$967$	1.36049e10	−	2.67012e10i	0.483842	−	0.949593i	−0.512042	−	0.858960i	$-0.671111\pi$
$967$	1.36049e10	−	2.67012e10i	0.483842	−	0.949593i	0.995884	−	0.0906333i	$-0.0288891\pi$
$968$	−1.64419e10	−	1.64419e10i	−0.582624	−	0.582624i
$969$	−1.50332e9	−	1.28395e10i	−0.0530786	−	0.453331i
$970$	−3.56002e9	+	1.88215e10i	−0.125243	+	0.662145i
$971$	1.72279e10	+	5.59769e9i	0.603900	+	0.196219i	0.594979	−	0.803741i	$-0.297160\pi$
$971$	1.72279e10	+	5.59769e9i	0.603900	+	0.196219i	0.00892102	+	0.999960i	$0.497160\pi$
$972$	7.40697e8	+	4.20937e8i	0.0258707	+	0.0147023i
$973$	1.01371e10	−	6.40028e10i	0.352790	−	2.22743i
$974$	−3.98912e10			−1.38331
$975$	2.46916e10	−	3.83971e10i	0.853167	−	1.32673i
$976$	6.10853e9			0.210311
$977$	4.91415e9	−	3.10267e10i	0.168584	−	1.06440i	−0.747748	−	0.663982i	$-0.768865\pi$
$977$	4.91415e9	−	3.10267e10i	0.168584	−	1.06440i	0.916333	−	0.400418i	$-0.131135\pi$
$978$	8.85583e9	−	2.48561e9i	0.302721	−	0.0849663i
$979$	−7.48075e9	−	2.43064e9i	−0.254804	−	0.0827908i
$980$	−1.17886e9	+	1.11048e9i	−0.0400103	+	0.0376896i
$981$	2.93163e8	−	3.60916e9i	0.00991443	−	0.122058i
$982$	−3.78604e10	−	3.78604e10i	−1.27584	−	1.27584i
$983$	1.48307e9	−	2.91068e9i	0.0497994	−	0.0977367i	−0.864766	−	0.502176i	$-0.832533\pi$
$983$	1.48307e9	−	2.91068e9i	0.0497994	−	0.0977367i	0.914565	+	0.404439i	$0.132533\pi$
$984$	−2.24357e10	+	2.06872e10i	−0.750682	+	0.692178i
$985$	8.23264e8	−	2.75639e10i	0.0274481	−	0.918996i
$986$	1.84885e10	+	2.54472e10i	0.614231	+	0.845416i
$987$	9.02436e10	+	3.65910e9i	2.98749	+	0.121134i
$988$	4.66908e8	−	7.39509e7i	0.0154022	−	0.00243946i
$989$	1.11269e10	−	8.08415e9i	0.365752	−	0.265734i
$990$	1.08751e10	−	6.18935e9i	0.356214	−	0.202732i
$991$	−1.05371e10	−	7.65566e9i	−0.343925	−	0.249876i	0.402391	−	0.915468i	$-0.368179\pi$
$991$	−1.05371e10	−	7.65566e9i	−0.343925	−	0.249876i	−0.746316	+	0.665592i	$0.768179\pi$
$992$	−2.52751e9	−	1.28783e9i	−0.0822058	−	0.0418859i
$993$	−1.51630e10	+	1.01041e10i	−0.491431	+	0.327472i
$994$	9.42432e10	−	3.06215e10i	3.04367	−	0.988948i
$995$	−2.64179e10	+	4.82318e10i	−0.850194	+	1.55222i
$996$	2.69063e8	+	1.51126e8i	0.00862871	+	0.00484654i
$997$	−5.63763e9	+	2.87252e9i	−0.180162	+	0.0917972i	−0.541745	−	0.840543i	$-0.682236\pi$
$997$	−5.63763e9	+	2.87252e9i	−0.180162	+	0.0917972i	0.361583	+	0.932340i	$0.382236\pi$
$998$	1.62359e10	+	2.57151e9i	0.517034	+	0.0818901i
$999$	−1.12249e10	+	1.66631e10i	−0.356207	+	0.528781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.8.l.a.2.49	yes	544
3.2	odd	2	inner	75.8.l.a.2.20	✓	544
25.13	odd	20	inner	75.8.l.a.38.20	yes	544
75.38	even	20	inner	75.8.l.a.38.49	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.8.l.a.2.20	✓	544	3.2	odd	2	inner
75.8.l.a.2.49	yes	544	1.1	even	1	trivial
75.8.l.a.38.20	yes	544	25.13	odd	20	inner
75.8.l.a.38.49	yes	544	75.38	even	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79599 - 11.3395i) q^{2} +(-12.6375 - 45.0255i) q^{3} +(-3.62242 - 1.17700i) q^{4} +(-245.145 - 134.273i) q^{5} +(-533.261 + 62.4372i) q^{6} +(-1082.77 - 1082.77i) q^{7} +(647.306 - 1270.41i) q^{8} +(-1867.59 + 1138.02i) q^{9} +(-1962.86 + 2538.65i) q^{10} +(1048.01 + 1442.46i) q^{11} +(-7.21636 + 177.975i) q^{12} +(12341.2 - 1954.65i) q^{13} +(-14222.7 + 10333.4i) q^{14} +(-2947.67 + 12734.6i) q^{15} +(-13637.6 - 9908.31i) q^{16} +(-24795.9 - 12634.1i) q^{17} +(9550.37 + 23221.3i) q^{18} +(-9446.90 + 3069.48i) q^{19} +(729.978 + 774.926i) q^{20} +(-35068.8 + 62436.0i) q^{21} +(18239.0 - 9293.22i) q^{22} +(27113.4 + 4294.35i) q^{23} +(-65381.1 - 13090.4i) q^{24} +(42066.7 + 65832.4i) q^{25} -143453. i q^{26} +(74841.6 + 69707.2i) q^{27} +(2647.84 + 5196.68i) q^{28} +(30422.4 - 93630.6i) q^{29} +(139110. + 56296.3i) q^{30} +(79487.8 + 244638. i) q^{31} +(-7797.93 + 7797.93i) q^{32} +(51703.3 - 65416.4i) q^{33} +(-187797. + 258481. i) q^{34} +(120049. + 410823. i) q^{35} +(8104.62 - 1924.25i) q^{36} +(30730.2 + 194023. i) q^{37} +(17839.7 + 112635. i) q^{38} +(-243971. - 530965. i) q^{39} +(-329265. + 224519. i) q^{40} +(269017. - 370270. i) q^{41} +(645007. + 509796. i) q^{42} +(354271. - 354271. i) q^{43} +(-2098.56 - 6458.71i) q^{44} +(610634. - 28213.9i) q^{45} +(97391.1 - 299739. i) q^{46} +(-572588. - 1.12377e6i) q^{47} +(-273781. + 739257. i) q^{48} +1.52126e6i q^{49} +(822055. - 358779. i) q^{50} +(-255499. + 1.27611e6i) q^{51} +(-47005.5 - 7444.94i) q^{52} +(-1.24027e6 + 631950. i) q^{53} +(924856. - 723469. i) q^{54} +(-63230.8 - 494331. i) q^{55} +(-2.07645e6 + 674681. i) q^{56} +(257590. + 386560. i) q^{57} +(-1.00708e6 - 513134. i) q^{58} +(654819. + 475754. i) q^{59} +(25666.3 - 42660.8i) q^{60} +(-293166. + 212998. i) q^{61} +(2.91682e6 - 461979. i) q^{62} +(3.25439e6 + 789954. i) q^{63} +(-1.19384e6 - 1.64319e6i) q^{64} +(-3.28782e6 - 1.17791e6i) q^{65} +(-648927. - 703775. i) q^{66} +(-1.05929e6 + 2.07898e6i) q^{67} +(74950.8 + 74950.8i) q^{68} +(-149292. - 1.27507e6i) q^{69} +(4.87412e6 - 623457. i) q^{70} +(-5.36074e6 - 1.74181e6i) q^{71} +(236853. + 3.10925e6i) q^{72} +(-82679.1 + 522015. i) q^{73} +2.25530e6 q^{74} +(2.43252e6 - 2.72603e6i) q^{75} +37833.4 q^{76} +(427103. - 2.69662e6i) q^{77} +(-6.45902e6 + 1.81289e6i) q^{78} +(-3.47536e6 - 1.12921e6i) q^{79} +(2.01277e6 + 4.26013e6i) q^{80} +(2.19279e6 - 4.25070e6i) q^{81} +(-3.71551e6 - 3.71551e6i) q^{82} +(786549. - 1.54369e6i) q^{83} +(200521. - 184894. i) q^{84} +(4.38216e6 + 6.42660e6i) q^{85} +(-3.38098e6 - 4.65351e6i) q^{86} +(-4.60022e6 - 186525. i) q^{87} +(2.51090e6 - 397688. i) q^{88} +(-3.56902e6 + 2.59305e6i) q^{89} +(776763. - 6.97492e6i) q^{90} +(-1.54791e7 - 1.12462e7i) q^{91} +(-93161.8 - 47468.3i) q^{92} +(1.00104e7 - 6.67059e6i) q^{93} +(-1.37713e7 + 4.47456e6i) q^{94} +(2.72800e6 + 515993. i) q^{95} +(449652. + 252559. i) q^{96} +(5.31864e6 - 2.70998e6i) q^{97} +(1.72502e7 + 2.73217e6i) q^{98} +(-3.59881e6 - 1.50127e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 34 q^{3} - 20 q^{4} - 6 q^{6} - 1364 q^{7} - 10 q^{9} + 3160 q^{10} + 2018 q^{12} - 16868 q^{13} - 37570 q^{15} + 507892 q^{16} + 106550 q^{18} + 70800 q^{19} - 6 q^{21} - 195160 q^{22} - 444200 q^{25}+ \cdots - 22089384 q^{97}+O(q^{100}) \) 544 * q - 34 * q^3 - 20 * q^4 - 6 * q^6 - 1364 * q^7 - 10 * q^9 + 3160 * q^10 + 2018 * q^12 - 16868 * q^13 - 37570 * q^15 + 507892 * q^16 + 106550 * q^18 + 70800 * q^19 - 6 * q^21 - 195160 * q^22 - 444200 * q^25 + 264158 * q^27 + 692032 * q^28 - 892390 * q^30 - 12 * q^31 + 877790 * q^33 - 1828180 * q^34 - 65542 * q^36 + 635596 * q^37 - 3868770 * q^39 + 1574020 * q^40 + 4577310 * q^42 - 1397348 * q^43 + 3411430 * q^45 - 12 * q^46 - 12135404 * q^48 - 16 * q^51 + 6428876 * q^52 + 16485420 * q^54 - 2324900 * q^55 + 4119286 * q^57 - 986360 * q^58 - 25245250 * q^60 - 12 * q^61 + 6259012 * q^63 + 363500 * q^64 - 1119750 * q^66 + 3427476 * q^67 - 12994880 * q^69 + 9814160 * q^70 - 611970 * q^72 + 10236732 * q^73 + 19853790 * q^75 - 131104 * q^76 + 24801340 * q^78 - 8474460 * q^79 + 10854734 * q^81 + 44639220 * q^82 - 52907530 * q^84 - 82807380 * q^85 - 15442020 * q^87 + 33548360 * q^88 - 11540050 * q^90 - 12 * q^91 + 14982652 * q^93 + 60673460 * q^94 + 1218042 * q^96 - 22089384 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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