LMFDB - Embedded newform 75.8.l.a.38.20

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			38.20
Character	$\chi$	$=$	75.38
Dual form			75.8.l.a.2.20

$q$-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} +(-28.9982 + 36.6893i) q^{3} +(-3.62242 + 1.17700i) q^{4} +(245.145 - 134.273i) q^{5} +(468.117 + 262.930i) q^{6} +(-1082.77 + 1082.77i) q^{7} +(-647.306 - 1270.41i) q^{8} +(-505.206 - 2127.85i) q^{9} +(-1962.86 - 2538.65i) q^{10} +(-1048.01 + 1442.46i) q^{11} +(61.8606 - 167.035i) q^{12} +(12341.2 + 1954.65i) q^{13} +(14222.7 + 10333.4i) q^{14} +(-2182.39 + 12887.8i) q^{15} +(-13637.6 + 9908.31i) q^{16} +(24795.9 - 12634.1i) q^{17} +(-23221.3 + 9550.37i) q^{18} +(-9446.90 - 3069.48i) q^{19} +(-729.978 + 774.926i) q^{20} +(-8327.68 - 71124.7i) 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} +(92719.3 + 43168.1i) q^{27} +(2647.84 - 5196.68i) q^{28} +(-30422.4 - 93630.6i) q^{29} +(150061. + 1600.62i) q^{30} +(79487.8 - 244638. i) q^{31} +(7797.93 + 7797.93i) q^{32} +(-22532.5 - 80279.7i) q^{33} +(-187797. - 258481. i) q^{34} +(-120049. + 410823. i) q^{35} +(4334.54 + 7113.33i) q^{36} +(30730.2 - 194023. i) q^{37} +(-17839.7 + 112635. i) q^{38} +(-429586. + 396107. i) q^{39} +(-329265. - 224519. i) q^{40} +(-269017. - 370270. i) q^{41} +(-791559. + 222171. i) q^{42} +(354271. + 354271. i) q^{43} +(2098.56 - 6458.71i) q^{44} +(-409560. - 453795. i) q^{45} +(97391.1 + 299739. i) q^{46} +(572588. - 1.12377e6i) q^{47} +(31937.9 - 787678. 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} +(322980. - 1.12892e6i) q^{54} +(-63230.8 + 494331. i) q^{55} +(2.07645e6 + 674681. i) q^{56} +(386560. - 257590. i) q^{57} +(-1.00708e6 + 513134. i) q^{58} +(-654819. + 475754. i) q^{59} +(-7263.40 - 49253.8i) q^{60} +(-293166. - 212998. i) q^{61} +(-2.91682e6 - 461979. i) q^{62} +(2.85100e6 + 1.75695e6i) q^{63} +(-1.19384e6 + 1.64319e6i) q^{64} +(3.28782e6 - 1.17791e6i) q^{65} +(-869859. + 399688. i) q^{66} +(-1.05929e6 - 2.07898e6i) q^{67} +(-74950.8 + 74950.8i) q^{68} +(628685. - 1.11930e6i) q^{69} +(4.87412e6 + 623457. i) q^{70} +(5.36074e6 - 1.74181e6i) q^{71} +(-2.37622e6 + 2.01919e6i) q^{72} +(-82679.1 - 522015. i) q^{73} -2.25530e6 q^{74} +(1.19548e6 + 3.45242e6i) q^{75} +37833.4 q^{76} +(-427103. - 2.69662e6i) q^{77} +(5.26317e6 + 4.15987e6i) q^{78} +(-3.47536e6 + 1.12921e6i) q^{79} +(-2.01277e6 + 4.26013e6i) q^{80} +(-4.27250e6 + 2.15000e6i) q^{81} +(-3.71551e6 + 3.71551e6i) q^{82} +(-786549. - 1.54369e6i) q^{83} +(113880. + 247842. i) q^{84} +(4.38216e6 - 6.42660e6i) q^{85} +(3.38098e6 - 4.65351e6i) q^{86} +(4.31743e6 + 1.59894e6i) q^{87} +(2.51090e6 + 397688. i) q^{88} +(3.56902e6 + 2.59305e6i) q^{89} +(-4.41022e6 + 5.45920e6i) q^{90} +(-1.54791e7 + 1.12462e7i) q^{91} +(93161.8 - 47468.3i) q^{92} +(6.67059e6 + 1.00104e7i) q^{93} +(-1.37713e7 - 4.47456e6i) q^{94} +(-2.72800e6 + 515993. i) q^{95} +(-512227. + 59974.4i) 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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	−0.930483	−	0.366335i	$-0.880612\pi$
$2$	−1.79599	−	11.3395i	−0.158745	−	1.00228i	0.771738	−	0.635941i	$-0.219388\pi$
$3$	−28.9982	+	36.6893i	−0.620079	+	0.784539i
$3$	−28.9982	+	36.6893i	−0.620079	+	0.784539i
$4$	−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
$6$	468.117	+	262.930i	0.884759	+	0.496948i
$7$	−1082.77	+	1082.77i	−1.19315	+	1.19315i	−0.216971	+	0.976178i	$0.569618\pi$
$7$	−1082.77	+	1082.77i	−1.19315	+	1.19315i	−0.976178	+	0.216971i	$0.930382\pi$
$8$	−647.306	−	1270.41i	−0.446987	−	0.877261i
$9$	−505.206	−	2127.85i	−0.231004	−	0.972953i
$10$	−1962.86	−	2538.65i	−0.620710	−	0.802793i
$11$	−1048.01	+	1442.46i	−0.237406	+	0.326761i	−0.911051	−	0.412294i	$-0.864728\pi$
$11$	−1048.01	+	1442.46i	−0.237406	+	0.326761i	0.673645	+	0.739055i	$0.264728\pi$
$12$	61.8606	−	167.035i	0.0103343	−	0.0279044i
$13$	12341.2	+	1954.65i	1.55795	+	0.246755i	0.875152	−	0.483849i	$-0.160762\pi$
$13$	12341.2	+	1954.65i	1.55795	+	0.246755i	0.682801	+	0.730604i	$0.260762\pi$
$14$	14222.7	+	10333.4i	1.38527	+	1.00646i
$15$	−2182.39	+	12887.8i	−0.166960	+	0.985964i
$16$	−13637.6	+	9908.31i	−0.832374	+	0.604755i
$17$	24795.9	−	12634.1i	1.22408	−	0.623698i	0.282102	−	0.959384i	$-0.408968\pi$
$17$	24795.9	−	12634.1i	1.22408	−	0.623698i	0.941974	+	0.335687i	$0.108968\pi$
$18$	−23221.3	+	9550.37i	−0.938496	+	0.385981i
$19$	−9446.90	−	3069.48i	−0.315974	−	0.102666i	0.146736	−	0.989176i	$-0.453123\pi$
$19$	−9446.90	−	3069.48i	−0.315974	−	0.102666i	−0.462711	+	0.886509i	$0.653123\pi$
$20$	−729.978	+	774.926i	−0.0204035	+	0.0216598i
$21$	−8327.68	−	71124.7i	−0.196226	−	1.67592i
$22$	18239.0	+	9293.22i	0.365192	+	0.186075i
$23$	−27113.4	+	4294.35i	−0.464662	+	0.0735952i	−0.384376	−	0.923177i	$-0.625583\pi$
$23$	−27113.4	+	4294.35i	−0.464662	+	0.0735952i	−0.0802860	+	0.996772i	$0.525583\pi$
$24$	65381.1	+	13090.4i	0.965413	+	0.193292i
$25$	42066.7	−	65832.4i	0.538454	−	0.842655i
$26$		−	143453.i		−	1.60067i
$27$	92719.3	+	43168.1i	0.906561	+	0.422075i
$28$	2647.84	−	5196.68i	0.0227950	−	0.0447376i
$29$	−30422.4	−	93630.6i	−0.231633	−	0.712894i	−0.997550	−	0.0699542i	$-0.977715\pi$
$29$	−30422.4	−	93630.6i	−0.231633	−	0.712894i	0.765917	−	0.642939i	$-0.222285\pi$
$30$	150061.	+	1600.62i	1.01471	+	0.0108234i
$31$	79487.8	−	244638.i	0.479219	−	1.47489i	−0.360962	−	0.932580i	$-0.617552\pi$
$31$	79487.8	−	244638.i	0.479219	−	1.47489i	0.840182	−	0.542305i	$-0.182448\pi$
$32$	7797.93	+	7797.93i	0.0420683	+	0.0420683i
$33$	−22532.5	−	80279.7i	−0.109147	−	0.388872i
$34$	−187797.	−	258481.i	−0.819433	−	1.12785i
$35$	−120049.	+	410823.i	−0.473283	+	1.61963i
$36$	4334.54	+	7113.33i	0.0154840	+	0.0254106i
$37$	30730.2	−	194023.i	0.0997375	−	0.629718i	−0.886289	−	0.463132i	$-0.846726\pi$
$37$	30730.2	−	194023.i	0.0997375	−	0.629718i	0.986027	−	0.166586i	$-0.0532744\pi$
$38$	−17839.7	+	112635.i	−0.0527406	+	0.332991i
$39$	−429586.	+	396107.i	−1.15964	+	1.06927i
$40$	−329265.	−	224519.i	−0.813459	−	0.554680i
$41$	−269017.	−	370270.i	−0.609588	−	0.839026i	0.386955	−	0.922098i	$-0.373527\pi$
$41$	−269017.	−	370270.i	−0.609588	−	0.839026i	−0.996544	+	0.0830722i	$0.973527\pi$
$42$	−791559.	+	222171.i	−1.64858	+	0.462716i
$43$	354271.	+	354271.i	0.679511	+	0.679511i	0.959890	−	0.280379i	$-0.0904600\pi$
$43$	354271.	+	354271.i	0.679511	+	0.679511i	−0.280379	+	0.959890i	$0.590460\pi$
$44$	2098.56	−	6458.71i	0.00371396	−	0.0114304i
$45$	−409560.	−	453795.i	−0.669999	−	0.742362i
$46$	97391.1	+	299739.i	0.147525	+	0.454037i
$47$	572588.	−	1.12377e6i	0.804451	−	1.57882i	−0.0109578	−	0.999940i	$-0.503488\pi$
$47$	572588.	−	1.12377e6i	0.804451	−	1.57882i	0.815409	−	0.578885i	$-0.196512\pi$
$48$	31937.9	−	787678.i	0.0416833	−	1.02803i
$49$		−	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	$-0.128040\pi$
$53$	1.24027e6	+	631950.i	1.14433	+	0.583065i	0.224148	+	0.974555i	$0.428040\pi$
$54$	322980.	−	1.12892e6i	0.279124	−	0.975626i
$55$	−63230.8	+	494331.i	−0.0512459	+	0.400635i
$56$	2.07645e6	+	674681.i	1.58003	+	0.513381i
$57$	386560.	−	257590.i	0.276475	−	0.184233i
$58$	−1.00708e6	+	513134.i	−0.677745	+	0.345329i
$59$	−654819.	+	475754.i	−0.415087	+	0.301579i	−0.775658	−	0.631153i	$-0.782582\pi$
$59$	−654819.	+	475754.i	−0.415087	+	0.301579i	0.360571	+	0.932732i	$0.382582\pi$
$60$	−7263.40	−	49253.8i	−0.00434121	−	0.0294382i
$61$	−293166.	−	212998.i	−0.165371	−	0.120149i	0.502022	−	0.864855i	$-0.332590\pi$
$61$	−293166.	−	212998.i	−0.165371	−	0.120149i	−0.667393	+	0.744706i	$0.732590\pi$
$62$	−2.91682e6	−	461979.i	−1.55432	−	0.246179i
$63$	2.85100e6	+	1.75695e6i	1.43650	+	0.885255i
$64$	−1.19384e6	+	1.64319e6i	−0.569269	+	0.783532i
$65$	3.28782e6	−	1.17791e6i	1.48495	−	0.532004i
$66$	−869859.	+	399688.i	−0.372431	+	0.171127i
$67$	−1.05929e6	−	2.07898e6i	−0.430283	−	0.844478i	−0.999748	−	0.0224624i	$-0.992849\pi$
$67$	−1.05929e6	−	2.07898e6i	−0.430283	−	0.844478i	0.569464	−	0.822016i	$-0.307151\pi$
$68$	−74950.8	+	74950.8i	−0.0289065	+	0.0289065i
$69$	628685.	−	1.11930e6i	0.230389	−	0.410181i
$70$	4.87412e6	+	623457.i	1.69845	+	0.217252i
$71$	5.36074e6	−	1.74181e6i	1.77754	−	0.577559i	0.778782	−	0.627294i	$-0.215838\pi$
$71$	5.36074e6	−	1.74181e6i	1.77754	−	0.577559i	0.998762	+	0.0497352i	$0.0158377\pi$
$72$	−2.37622e6	+	2.01919e6i	−0.750278	+	0.637548i
$73$	−82679.1	−	522015.i	−0.0248751	−	0.157055i	0.972124	−	0.234467i	$-0.0753345\pi$
$73$	−82679.1	−	522015.i	−0.0248751	−	0.157055i	−0.996999	+	0.0774115i	$0.975334\pi$
$74$	−2.25530e6			−0.646984
$75$	1.19548e6	+	3.45242e6i	0.327212	+	0.944951i
$76$	37833.4			0.00988616
$77$	−427103.	−	2.69662e6i	−0.106614	−	0.673136i
$78$	5.26317e6	+	4.15987e6i	1.25579	+	0.992541i
$79$	−3.47536e6	+	1.12921e6i	−0.793059	+	0.257680i	−0.677406	−	0.735609i	$-0.736896\pi$
$79$	−3.47536e6	+	1.12921e6i	−0.793059	+	0.257680i	−0.115653	+	0.993290i	$0.536896\pi$
$80$	−2.01277e6	+	4.26013e6i	−0.439521	+	0.930267i
$81$	−4.27250e6	+	2.15000e6i	−0.893274	+	0.449513i
$82$	−3.71551e6	+	3.71551e6i	−0.744167	+	0.744167i
$83$	−786549.	−	1.54369e6i	−0.150991	−	0.296337i	0.803105	−	0.595838i	$-0.203180\pi$
$83$	−786549.	−	1.54369e6i	−0.150991	−	0.296337i	−0.954096	+	0.299501i	$0.903180\pi$
$84$	113880.	+	247842.i	0.0209638	+	0.0456244i
$85$	4.38216e6	−	6.42660e6i	0.773966	−	1.13505i
$86$	3.38098e6	−	4.65351e6i	0.573188	−	0.788926i
$87$	4.31743e6	+	1.59894e6i	0.702924	+	0.260325i
$88$	2.51090e6	+	397688.i	0.392772	+	0.0622090i
$89$	3.56902e6	+	2.59305e6i	0.536641	+	0.389893i	0.822836	−	0.568279i	$-0.192390\pi$
$89$	3.56902e6	+	2.59305e6i	0.536641	+	0.389893i	−0.286195	+	0.958171i	$0.592390\pi$
$90$	−4.41022e6	+	5.45920e6i	−0.637693	+	0.789370i
$91$	−1.54791e7	+	1.12462e7i	−2.15329	+	1.56445i
$92$	93161.8	−	47468.3i	0.0124733	−	0.00635545i
$93$	6.67059e6	+	1.00104e7i	0.859952	+	1.29051i
$94$	−1.37713e7	−	4.47456e6i	−1.71012	−	0.555652i
$95$	−2.72800e6	+	515993.i	−0.326447	+	0.0617463i
$96$	−512227.	+	59974.4i	−0.0590899	+	0.00691857i
$97$	5.31864e6	+	2.70998e6i	0.591698	+	0.301485i	0.724082	−	0.689713i	$-0.242263\pi$
$97$	5.31864e6	+	2.70998e6i	0.591698	+	0.301485i	−0.132385	+	0.991198i	$0.542263\pi$
$98$	−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	$0.944614\pi$
$102$	1.49293e7	+	605336.i	1.39296	+	0.0564802i
$103$	−5.56878e6	+	1.09293e7i	−0.502145	+	0.985516i	0.491276	+	0.871004i	$0.336530\pi$
$103$	−5.56878e6	+	1.09293e7i	−0.502145	+	0.985516i	−0.993422	+	0.114512i	$0.963470\pi$
$104$	−5.50531e6	−	1.69436e7i	−0.479915	−	1.47703i
$105$	−1.15916e7	−	1.63177e7i	−0.977193	−	1.37561i
$106$	4.93845e6	−	1.51990e7i	0.402736	−	1.23949i
$107$	9.55632e6	+	9.55632e6i	0.754132	+	0.754132i	0.975248	−	0.221116i	$-0.0709698\pi$
$107$	9.55632e6	+	9.55632e6i	0.754132	+	0.754132i	−0.221116	+	0.975248i	$0.570970\pi$
$108$	−386677.	−	47242.9i	−0.0295369	−	0.00360872i
$109$	−973205.	−	1.33950e6i	−0.0719800	−	0.0990720i	0.771509	−	0.636218i	$-0.219502\pi$
$109$	−973205.	−	1.33950e6i	−0.0719800	−	0.0990720i	−0.843489	+	0.537146i	$0.819502\pi$
$110$	5.71901e6	−	170813.i	0.409682	−	0.0122362i
$111$	6.22743e6	+	6.75378e6i	0.432194	+	0.468723i
$112$	4.03800e6	−	2.54949e7i	0.271583	−	1.71471i
$113$	134932.	−	851929.i	0.00879714	−	0.0555429i	−0.982899	−	0.184144i	$-0.941049\pi$
$113$	134932.	−	851929.i	0.00879714	−	0.0555429i	0.991696	+	0.128601i	$0.0410487\pi$
$114$	−3.61519e6	−	3.92075e6i	−0.228541	−	0.247858i
$115$	−6.07010e6	+	4.69333e6i	−0.372180	+	0.287765i
$116$	220406.	+	303362.i	0.0131105	+	0.0180451i
$117$	−2.07564e6	−	2.72476e7i	−0.119812	−	1.57282i
$118$	6.57084e6	+	6.57084e6i	0.368158	+	0.368158i
$119$	−1.31684e7	+	4.05283e7i	−0.716341	+	2.20467i
$120$	1.77855e7	−	5.56985e6i	0.939577	−	0.294245i
$121$	5.03949e6	+	1.55100e7i	0.258606	+	0.795906i
$122$	−1.88875e6	+	3.70689e6i	−0.0941707	+	0.184820i
$123$	2.13860e7	+	867136.i	1.03624	+	0.0420164i
$124$			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	−0.221582	−	0.975142i	$-0.571122\pi$
$127$	−3.02366e6	+	478900.i	−0.130984	+	0.0207459i	0.0905980	+	0.995888i	$0.471122\pi$
$128$	2.20347e7	+	1.12272e7i	0.928693	+	0.473193i
$129$	−2.32712e7	+	2.72472e6i	−0.954454	+	0.111753i
$130$	−1.92618e7	−	3.51666e7i	−0.768943	−	1.40388i
$131$	−3.77729e6	−	1.22732e6i	−0.146802	−	0.0476987i	0.234695	−	0.972069i	$-0.424591\pi$
$131$	−3.77729e6	−	1.22732e6i	−0.146802	−	0.0476987i	−0.381496	+	0.924370i	$0.624591\pi$
$132$	176111.	+	264286.i	0.00666465	+	0.0100015i
$133$	1.35524e7	−	6.90530e6i	0.499500	−	0.254508i
$134$	−2.16720e7	+	1.57456e7i	−0.778095	+	0.565319i
$135$	2.85259e7	−	1.86723e6i	0.997865	−	0.0653175i
$136$	−3.21010e7	−	2.33228e7i	−1.09429	−	0.795049i
$137$	1.90534e7	+	3.01776e6i	0.633067	+	0.100268i	0.464717	−	0.885459i	$-0.346156\pi$
$137$	1.90534e7	+	3.01776e6i	0.633067	+	0.100268i	0.168350	+	0.985727i	$0.446156\pi$
$138$	−1.38214e7	−	5.11869e6i	−0.447687	−	0.165799i
$139$	2.48740e7	−	3.42361e7i	0.785585	−	1.08127i	−0.209059	−	0.977903i	$-0.567040\pi$
$139$	2.48740e7	−	3.42361e7i	0.785585	−	1.08127i	0.994644	−	0.103362i	$-0.0329600\pi$
$140$	−48668.3	−	1.62947e6i	−0.00149899	−	0.0501879i
$141$	2.46262e7	+	5.35951e7i	0.739827	+	1.61012i
$142$	−2.93790e7	−	5.76596e7i	−0.861050	−	1.68991i
$143$	−1.57532e7	+	1.57532e7i	−0.450497	+	0.450497i
$144$	2.79732e7	+	2.40130e7i	0.780680	+	0.670160i
$145$	−2.00299e7	−	1.88681e7i	−0.545621	−	0.513974i
$146$	−5.77088e6	+	1.87507e6i	−0.153464	+	0.0498635i
$147$	5.58138e7	+	4.41138e7i	1.44921	+	1.14542i
$148$	117046.	+	739000.i	0.00296784	+	0.0187382i
$149$	−3.16484e7			−0.783791			−0.391895	−	0.920010i	$-0.628180\pi$
$149$	−3.16484e7			−0.783791			−0.391895	+	0.920010i	$0.628180\pi$
$150$	3.70015e7	−	1.97567e7i	0.895158	−	0.477963i
$151$	−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
$153$	−3.94105e7	−	4.63790e7i	−0.889595	−	1.04689i
$154$	−2.98112e7	+	9.68623e6i	−0.657743	+	0.213714i
$155$	−1.33622e7	−	7.06447e7i	−0.288216	−	1.52377i
$156$	1.08993e6	−	1.94049e6i	0.0229859	−	0.0409237i
$157$	−2.98230e7	+	2.98230e7i	−0.615039	+	0.615039i	−0.944255	−	0.329216i	$-0.893216\pi$
$157$	−2.98230e7	+	2.98230e7i	−0.615039	+	0.615039i	0.329216	+	0.944255i	$0.393216\pi$
$158$	1.90464e7	+	3.73807e7i	0.384161	+	0.753958i
$159$	−5.91515e7	+	2.71793e7i	−1.16701	+	0.536226i
$160$	2.95867e6	+	864572.i	0.0571053	+	0.0166871i
$161$	2.47079e7	−	3.40075e7i	0.466601	−	0.642221i
$162$	3.20533e7	+	4.45865e7i	0.592338	+	0.823949i
$163$	−1.69207e7	−	2.67998e6i	−0.306028	−	0.0484701i	0.00153156	−	0.999999i	$-0.499512\pi$
$163$	−1.69207e7	−	2.67998e6i	−0.306028	−	0.0484701i	−0.307560	+	0.951529i	$0.599512\pi$
$164$	1.41030e6	+	1.02464e6i	0.0249665	+	0.0181392i
$165$	−1.63031e7	−	1.66546e7i	−0.282537	−	0.288630i
$166$	−1.60920e7	+	1.16915e7i	−0.273043	+	0.198377i
$167$	4.48640e7	−	2.28594e7i	0.745402	−	0.379801i	−0.0396642	−	0.999213i	$-0.512629\pi$
$167$	4.48640e7	−	2.28594e7i	0.745402	−	0.379801i	0.785066	+	0.619412i	$0.212629\pi$
$168$	−8.49670e7	+	5.66190e7i	−1.38251	+	0.921255i
$169$	8.88062e7	+	2.88549e7i	1.41527	+	0.459850i
$170$	−8.07444e7	−	3.81491e7i	−1.26050	−	0.595544i
$171$	−1.75876e6	+	2.16523e7i	−0.0268980	+	0.331144i
$172$	−1.70030e6	−	866344.i	−0.0254786	−	0.0129820i
$173$	−5.14164e7	+	8.14356e6i	−0.754989	+	0.119579i	−0.522052	−	0.852913i	$-0.674833\pi$
$173$	−5.14164e7	+	8.14356e6i	−0.754989	+	0.119579i	−0.232937	+	0.972492i	$0.574833\pi$
$174$	1.03771e7	−	5.18290e7i	0.149332	−	0.745849i
$175$	2.57329e7	+	1.16830e8i	0.362957	+	1.64787i
$176$		−	3.00558e7i		−	0.415560i
$177$	1.53352e6	−	3.78209e7i	0.0207866	−	0.512655i
$178$	2.29938e7	−	4.51279e7i	0.305591	−	0.599756i
$179$	−1.70709e7	−	5.25388e7i	−0.222469	−	0.684690i	−0.998539	−	0.0540426i	$-0.982789\pi$
$179$	−1.70709e7	−	5.25388e7i	−0.222469	−	0.684690i	0.776069	−	0.630648i	$-0.217211\pi$
$180$	2.01771e6	+	1.16178e6i	0.0257873	+	0.0148481i
$181$	2.33978e7	−	7.20110e7i	0.293292	−	0.902659i	−0.690498	−	0.723334i	$-0.742609\pi$
$181$	2.33978e7	−	7.20110e7i	0.293292	−	0.902659i	0.983790	−	0.179325i	$-0.0573914\pi$
$182$	1.55327e8	+	1.55327e8i	1.90984	+	1.90984i
$183$	1.63160e7	−	4.57950e6i	0.196805	−	0.0552382i
$184$	2.30063e7	+	3.16654e7i	0.272260	+	0.374734i
$185$	−1.85186e7	−	5.16898e7i	−0.215034	−	0.600211i
$186$	1.01532e8	−	9.36195e7i	1.15694	−	1.06677i
$187$	−7.76208e6	+	4.90079e7i	−0.0868026	+	0.548050i
$188$	−751485.	+	4.74469e6i	−0.00824837	+	0.0520781i
$189$	−1.47135e8	+	5.36527e7i	−1.58526	+	0.578063i
$190$	1.07506e7	+	3.00073e7i	0.113709	+	0.317388i
$191$	−6.80240e7	−	9.36270e7i	−0.706391	−	0.972264i	−0.999867	−	0.0162978i	$-0.994812\pi$
$191$	−6.80240e7	−	9.36270e7i	−0.706391	−	0.972264i	0.293476	−	0.955967i	$-0.405188\pi$
$192$	−2.56679e7	−	9.14508e7i	−0.261720	−	0.932466i
$193$	5.60782e7	+	5.60782e7i	0.561491	+	0.561491i	0.929731	−	0.368239i	$-0.120039\pi$
$193$	5.60782e7	+	5.60782e7i	0.561491	+	0.561491i	−0.368239	+	0.929731i	$0.620039\pi$
$194$	2.11775e7	−	6.51776e7i	0.208242	−	0.640903i
$195$	−5.21244e7	+	1.54785e8i	−0.503408	+	1.49489i
$196$	1.79051e6	+	5.51063e6i	0.0169856	+	0.0522763i
$197$	−4.47905e7	+	8.79062e7i	−0.417401	+	0.819196i	0.582578	+	0.812775i	$0.302044\pi$
$197$	−4.47905e7	+	8.79062e7i	−0.417401	+	0.819196i	−0.999979	+	0.00642141i	$0.997956\pi$
$198$	1.05601e7	−	4.35048e7i	0.0966808	−	0.398298i
$199$			1.96748e8i			1.76981i	0.465776	+	0.884903i	$0.345775\pi$
$199$			1.96748e8i			1.76981i	−0.465776	+	0.884903i	$0.654225\pi$
$200$	−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
$204$	−576451.	−	4.92333e6i	−0.00475397	−	0.0406025i
$205$	−1.15665e8	−	5.46481e7i	−0.937701	−	0.443034i
$206$	1.33934e8	+	4.35179e7i	1.06747	+	0.346843i
$207$	2.28356e7	+	5.55237e7i	0.178944	+	0.435093i
$208$	−1.87671e8	+	9.56233e7i	−1.44603	+	0.736787i
$209$	1.43281e7	−	1.04100e7i	0.108561	−	0.0788745i
$210$	−1.64215e8	+	1.60749e8i	−1.22362	+	1.19779i
$211$	−1.34549e8	−	9.77556e7i	−0.986034	−	0.716396i	−0.0269854	−	0.999636i	$-0.508591\pi$
$211$	−1.34549e8	−	9.77556e7i	−0.986034	−	0.716396i	−0.959049	+	0.283240i	$0.908591\pi$
$212$	−5.23659e6	−	829394.i	−0.0377462	−	0.00597841i
$213$	−9.15462e7	+	2.47191e8i	−0.649100	+	1.75269i
$214$	9.12004e7	−	1.25527e8i	0.636134	−	0.875563i
$215$	1.34417e8	+	3.92787e7i	0.922398	+	0.269540i
$216$	−5.17654e6	−	1.45734e8i	−0.0349503	−	0.983953i
$217$	1.78821e8	+	3.50955e8i	1.18798	+	2.33154i
$218$	−1.34414e7	+	1.34414e7i	−0.0878710	+	0.0878710i
$219$	2.15499e7	+	1.21041e7i	0.138641	+	0.0778712i
$220$	−352777.	−	1.86510e6i	−0.00223368	−	0.0118092i
$221$	3.30705e8	−	1.07453e8i	2.06095	−	0.669644i
$222$	6.53997e7	−	8.27454e7i	0.401181	−	0.507584i
$223$	−1.43198e7	−	9.04117e7i	−0.0864710	−	0.545956i	−0.992452	−	0.122637i	$-0.960865\pi$
$223$	−1.43198e7	−	9.04117e7i	−0.0864710	−	0.545956i	0.905981	−	0.423319i	$-0.139135\pi$
$224$	−1.68868e7			−0.100387
$225$	−1.61334e8	−	5.62526e7i	−0.944249	−	0.329233i
$226$	−9.90275e6			−0.0570658
$227$	−1.27924e6	−	8.07682e6i	−0.00725876	−	0.0458300i	0.983793	−	0.179307i	$-0.0573857\pi$
$227$	−1.27924e6	−	8.07682e6i	−0.00725876	−	0.0458300i	−0.991052	+	0.133477i	$0.957386\pi$
$228$	−1.09710e6	+	1.38808e6i	−0.00613020	+	0.00775608i
$229$	1.00495e8	−	3.26528e7i	0.552994	−	0.179679i	−0.0191723	−	0.999816i	$-0.506103\pi$
$229$	1.00495e8	−	3.26528e7i	0.552994	−	0.179679i	0.572167	+	0.820137i	$0.306103\pi$
$230$	6.41217e7	+	6.04024e7i	0.347502	+	0.327346i
$231$	1.11322e8	+	6.25272e7i	0.594211	+	0.333754i
$232$	−9.92566e7	+	9.92566e7i	−0.521857	+	0.521857i
$233$	1.30819e8	+	2.56746e8i	0.677522	+	1.32971i	0.931938	+	0.362617i	$0.118117\pi$
$233$	1.30819e8	+	2.56746e8i	0.677522	+	1.32971i	−0.254416	+	0.967095i	$0.581883\pi$
$234$	−3.05245e8	+	7.24732e7i	−1.55738	+	0.369762i
$235$	−1.05244e7	−	3.52368e8i	−0.0529003	−	1.77117i
$236$	1.81207e6	−	2.49410e6i	0.00897393	−	0.0123516i
$237$	5.93493e7	−	1.60254e8i	0.289598	−	0.781968i
$238$	4.83219e8	+	7.65343e7i	2.32340	+	0.367991i
$239$	−2.64481e8	−	1.92156e8i	−1.25315	−	0.910463i	−0.254745	−	0.967008i	$-0.581992\pi$
$239$	−2.64481e8	−	1.92156e8i	−1.25315	−	0.910463i	−0.998400	+	0.0565450i	$0.981992\pi$
$240$	−9.79342e7	−	1.97383e8i	−0.457293	−	0.921661i
$241$	2.39355e8	−	1.73901e8i	1.10149	−	0.800282i	0.120191	−	0.992751i	$-0.461649\pi$
$241$	2.39355e8	−	1.73901e8i	1.10149	−	0.800282i	0.981303	+	0.192469i	$0.0616494\pi$
$242$	1.66824e8	−	8.50009e7i	0.756665	−	0.385540i
$243$	4.50128e7	−	2.19101e8i	0.201240	−	0.979542i
$244$	1.31267e6	+	426512.i	0.00578483	+	0.00187960i
$245$	−2.04263e8	−	3.72928e8i	−0.887379	−	1.62011i
$246$	−2.85762e7	−	2.44063e8i	−0.122386	−	1.04527i
$247$	−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	$-0.0125087\pi$
$252$	−1.23955e7	−	3.00881e6i	−0.0487933	−	0.0118438i
$253$	2.22208e7	−	4.36107e7i	0.0862655	−	0.169305i
$254$	1.08609e7	+	3.34265e7i	0.0415862	+	0.127989i
$255$	1.08712e8	+	3.47138e8i	0.410571	+	1.31103i
$256$	7.39852e6	−	2.27703e7i	0.0275616	−	0.0848260i
$257$	−3.53251e8	−	3.53251e8i	−1.29813	−	1.29813i	−0.929627	−	0.368502i	$-0.879871\pi$
$257$	−3.53251e8	−	3.53251e8i	−1.29813	−	1.29813i	−0.368502	−	0.929627i	$-0.620129\pi$
$258$	7.26918e7	+	2.58989e8i	0.263522	+	0.938885i
$259$	1.76809e8	+	2.43356e8i	0.632346	+	0.870349i
$260$	−1.05235e7	+	8.13663e6i	−0.0371324	+	0.0287103i
$261$	−1.83862e8	+	1.12037e8i	−0.640104	+	0.390050i
$262$	−7.13310e6	+	4.50366e7i	−0.0245033	+	0.154708i
$263$	−1.48865e7	+	9.39899e7i	−0.0504601	+	0.318593i	0.949528	+	0.313683i	$0.101563\pi$
$263$	−1.48865e7	+	9.39899e7i	−0.0504601	+	0.318593i	−0.999988	+	0.00490992i	$0.998437\pi$
$264$	−8.74027e7	+	8.05910e7i	−0.292355	+	0.269571i
$265$	3.88900e8	−	1.16155e7i	1.28374	−	0.0383421i
$266$	−1.02642e8	−	1.41275e8i	−0.334380	−	0.460235i
$267$	−1.98632e8	+	5.57511e7i	−0.638646	+	0.179252i
$268$	6.28415e6	+	6.28415e6i	0.0199423	+	0.0199423i
$269$	−1.32196e8	+	4.06857e8i	−0.414081	+	1.27441i	0.498990	+	0.866608i	$0.333704\pi$
$269$	−1.32196e8	+	4.06857e8i	−0.414081	+	1.27441i	−0.913071	+	0.407801i	$0.866296\pi$
$270$	−7.24057e7	−	3.20115e8i	−0.223872	−	0.989767i
$271$	−2.07487e6	−	6.38580e6i	−0.00633285	−	0.0194905i	0.947840	−	0.318746i	$-0.103262\pi$
$271$	−2.07487e6	−	6.38580e6i	−0.00633285	−	0.0194905i	−0.954173	+	0.299256i	$0.903262\pi$
$272$	−2.12974e8	+	4.17985e8i	−0.641705	+	1.25942i
$273$	3.62506e7	−	8.94040e8i	0.107831	−	2.65942i
$274$		−	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	−0.644173	−	0.764880i	$-0.722798\pi$
$277$	−3.60973e8	+	5.71724e7i	−1.02046	+	0.161625i	−0.376284	+	0.926504i	$0.622798\pi$
$278$	−4.32892e8	−	2.20569e8i	−1.20843	−	0.615728i
$279$	−5.60710e8	−	4.55451e7i	−1.54570	−	0.125553i
$280$	5.99622e8	−	1.13417e8i	1.63239	−	0.308762i
$281$	2.37371e8	+	7.71267e7i	0.638199	+	0.207364i	0.610204	−	0.792244i	$-0.291088\pi$
$281$	2.37371e8	+	7.71267e7i	0.638199	+	0.207364i	0.0279956	+	0.999608i	$0.491088\pi$
$282$	5.63511e8	−	3.75504e8i	1.49634	−	0.997109i
$283$	−3.12494e8	+	1.59224e8i	−0.819577	+	0.417595i	−0.812915	−	0.582382i	$-0.802121\pi$
$283$	−3.12494e8	+	1.59224e8i	−0.819577	+	0.417595i	−0.00666217	+	0.999978i	$0.502121\pi$
$284$	−1.73687e7	+	1.26191e7i	−0.0449940	+	0.0326900i
$285$	6.01758e7	−	1.15051e8i	0.153980	−	0.294398i
$286$	2.06925e8	+	1.50340e8i	0.523037	+	0.380008i
$287$	6.92204e8	+	1.09634e8i	1.72841	+	0.273754i
$288$	1.26532e7	−	2.05324e7i	0.0312125	−	0.0506484i
$289$	2.14023e8	−	2.94578e8i	0.521577	−	0.717889i
$290$	−1.77981e8	+	2.61015e8i	−0.428529	+	0.628453i
$291$	−2.53659e8	+	1.16552e8i	−0.603426	+	0.277266i
$292$	913908.	+	1.79364e6i	0.00214814	+	0.00421596i
$293$	2.55053e8	−	2.55053e8i	0.592371	−	0.592371i	−0.345900	−	0.938271i	$-0.612426\pi$
$293$	2.55053e8	−	2.55053e8i	0.592371	−	0.592371i	0.938271	+	0.345900i	$0.112426\pi$
$294$	3.99985e8	−	7.12126e8i	0.917968	−	1.63434i
$295$	−9.66446e7	+	2.04553e8i	−0.219180	+	0.463904i
$296$	−2.66380e8	+	8.65521e7i	−0.597009	+	0.193980i
$297$	−1.59439e8	+	8.85035e7i	−0.353141	+	0.196026i
$298$	5.68404e7	+	3.58876e8i	0.124423	+	0.785574i
$299$	−3.43005e8			−0.742082
$300$	−8.39403e6	−	1.10990e7i	−0.0179492	−	0.0237334i
$301$	−7.67192e8			−1.62152
$302$	1.92654e7	+	1.21637e8i	0.0402489	+	0.254122i
$303$	−1.31539e8	−	1.03965e8i	−0.271646	−	0.214702i
$304$	1.59247e8	−	5.17423e7i	0.325097	−	0.105630i
$305$	−1.00468e8	−	1.28510e7i	−0.202758	−	0.0259351i
$306$	−4.55132e8	+	5.30190e8i	−0.908055	+	1.05781i
$307$	2.93130e8	−	2.93130e8i	0.578196	−	0.578196i	−0.356210	−	0.934406i	$-0.615931\pi$
$307$	2.93130e8	−	2.93130e8i	0.578196	−	0.578196i	0.934406	+	0.356210i	$0.115931\pi$
$308$	4.72106e6	+	9.26560e6i	0.00920687	+	0.0180695i
$309$	−2.39505e8	−	5.21246e8i	−0.461806	−	1.00505i
$310$	−7.77074e8	+	2.78398e8i	−1.48148	+	0.530762i
$311$	4.85080e8	−	6.67655e8i	0.914433	−	1.25861i	−0.0511968	−	0.998689i	$-0.516304\pi$
$311$	4.85080e8	−	6.67655e8i	0.914433	−	1.25861i	0.965630	−	0.259921i	$-0.0836964\pi$
$312$	7.81292e8	+	2.89348e8i	1.45637	+	0.539361i
$313$	3.99605e8	+	6.32912e7i	0.736590	+	0.116664i	0.513447	−	0.858121i	$-0.328368\pi$
$313$	3.99605e8	+	6.32912e7i	0.736590	+	0.116664i	0.223143	+	0.974786i	$0.428368\pi$
$314$	3.91739e8	+	2.84615e8i	0.714073	+	0.518804i
$315$	9.34819e8	+	4.78960e7i	1.68516	+	0.0863401i
$316$	1.12601e7	−	8.18097e6i	0.0200742	−	0.0145848i
$317$	3.71710e6	−	1.89396e6i	0.00655386	−	0.00333936i	−0.450710	−	0.892670i	$-0.648829\pi$
$317$	3.71710e6	−	1.89396e6i	0.00655386	−	0.00333936i	0.457264	+	0.889331i	$0.348829\pi$
$318$	4.14434e8	+	6.21932e8i	0.722703	+	1.08455i
$319$	1.66942e8	+	5.42427e7i	0.287937	+	0.0935564i
$320$	−7.20295e7	+	5.63119e8i	−0.122881	+	0.960672i
$321$	−6.27731e8	+	7.34982e7i	−1.05927	+	0.124025i
$322$	−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
$327$	7.73666e7	+	3.13698e6i	0.122359	+	0.00496129i
$328$	−2.96259e8	+	5.81440e8i	−0.463567	+	0.909802i
$329$	5.96803e8	+	1.83677e9i	0.923943	+	2.84360i
$330$	−1.59574e8	+	2.14780e8i	−0.244435	+	0.328999i
$331$	−1.20402e8	+	3.70558e8i	−0.182488	+	0.561641i	−0.999896	−	0.0144186i	$-0.995410\pi$
$331$	−1.20402e8	+	3.70558e8i	−0.182488	+	0.561641i	0.817408	+	0.576059i	$0.195410\pi$
$332$	4.66612e6	+	4.66612e6i	0.00699799	+	0.00699799i
$333$	−4.28375e8	+	3.26323e7i	−0.635726	+	0.0484277i
$334$	−3.39788e8	−	4.67678e8i	−0.498994	−	0.686807i
$335$	−5.38830e8	−	3.67417e8i	−0.783060	−	0.533952i
$336$	8.18296e8	+	8.87459e8i	1.17685	+	1.27632i
$337$	1.02145e8	−	6.44920e8i	0.145383	−	0.917913i	−0.801887	−	0.597476i	$-0.796170\pi$
$337$	1.02145e8	−	6.44920e8i	0.145383	−	0.917913i	0.947270	−	0.320437i	$-0.103830\pi$
$338$	1.67703e8	−	1.05884e9i	0.236229	−	1.49149i
$339$	2.73439e7	+	2.96550e7i	0.0381207	+	0.0413427i
$340$	−8.30993e6	+	2.84376e7i	−0.0114662	+	0.0392389i
$341$	2.69578e8	+	3.71042e8i	0.368166	+	0.506737i
$342$	2.48684e8	−	1.89440e7i	0.336168	−	0.0256082i
$343$	7.55467e8	+	7.55467e8i	1.01085	+	1.01085i
$344$	2.20748e8	−	6.79392e8i	0.292376	−	0.899841i
$345$	3.82721e6	−	3.58806e8i	0.00501782	−	0.470427i
$346$	1.84687e8	+	5.68409e8i	0.239701	+	0.737725i
$347$	−5.89002e7	+	1.15598e8i	−0.0756770	+	0.148524i	−0.925745	−	0.378149i	$-0.876561\pi$
$347$	−5.89002e7	+	1.15598e8i	−0.0756770	+	0.148524i	0.850068	+	0.526673i	$0.176561\pi$
$348$	−1.75215e7	−	710444.i	−0.0222866	−	0.000903654i
$349$			1.06922e9i			1.34641i	0.739454	+	0.673207i	$0.235084\pi$
$349$			1.06922e9i			1.34641i	−0.739454	+	0.673207i	$0.764916\pi$
$350$	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	$-0.402718\pi$
$353$	−2.42797e8	−	1.23711e8i	−0.293786	−	0.149691i	−0.594671	+	0.803969i	$0.702718\pi$
$354$	−4.31622e8	+	5.05367e7i	−0.517121	+	0.0605474i
$355$	1.08028e9	−	1.14680e9i	1.28155	−	1.36046i
$356$	−1.59805e7	−	5.19238e6i	−0.0187722	−	0.00609946i
$357$	−1.10509e9	−	1.65839e9i	−1.28546	−	1.92907i
$358$	−5.65102e8	+	2.87934e8i	−0.650933	+	0.331667i
$359$	4.80350e8	−	3.48995e8i	0.547933	−	0.398096i	−0.279090	−	0.960265i	$-0.590033\pi$
$359$	4.80350e8	−	3.48995e8i	0.547933	−	0.398096i	0.827023	+	0.562169i	$0.190033\pi$
$360$	−3.11395e8	+	8.14054e8i	−0.351765	+	0.919590i
$361$	−6.43335e8	−	4.67410e8i	−0.719718	−	0.522906i
$362$	−8.58588e8	−	1.35987e8i	−0.951272	−	0.150667i
$363$	−7.15186e8	−	2.64866e8i	−0.784776	−	0.290638i
$364$	4.28351e7	−	5.89575e7i	0.0465527	−	0.0640744i
$365$	−9.03607e7	−	1.16868e8i	−0.0972645	−	0.125797i
$366$	−8.12325e7	−	1.76790e8i	−0.0866056	−	0.188484i
$367$	3.98814e8	+	7.82717e8i	0.421153	+	0.826559i	0.999939	+	0.0110791i	$0.00352666\pi$
$367$	3.98814e8	+	7.82717e8i	0.421153	+	0.826559i	−0.578786	+	0.815479i	$0.696473\pi$
$368$	3.27213e8	−	3.27213e8i	0.342266	−	0.342266i
$369$	−6.51970e8	+	7.59491e8i	−0.675515	+	0.786919i
$370$	−5.52875e8	+	3.02825e8i	−0.567441	+	0.310804i
$371$	−2.02719e9	+	6.58675e8i	−2.06104	+	0.669673i
$372$	−3.59459e7	−	2.84107e7i	−0.0362034	−	0.0286142i
$373$	7.21067e7	+	4.55264e8i	0.0719440	+	0.454237i	0.997193	+	0.0748760i	$0.0238561\pi$
$373$	7.21067e7	+	4.55264e8i	0.0719440	+	0.454237i	−0.925249	+	0.379361i	$0.876144\pi$
$374$	5.69663e8			0.563077
$375$	7.56632e8	+	6.85821e8i	0.740927	+	0.671586i
$376$	−1.79829e9			−1.74462
$377$	−1.92433e8	−	1.21498e9i	−0.184963	−	1.16781i
$378$	8.72647e8	+	1.57208e9i	0.831031	+	1.49710i
$379$	−1.01890e9	+	3.31060e8i	−0.961375	+	0.312370i	−0.747329	−	0.664454i	$-0.768664\pi$
$379$	−1.01890e9	+	3.31060e8i	−0.961375	+	0.312370i	−0.214046	+	0.976824i	$0.568664\pi$
$380$	9.27465e6	−	5.07999e6i	0.00867071	−	0.00474920i
$381$	7.01102e7	−	1.24823e8i	0.0649447	−	0.115626i
$382$	−9.39509e8	+	9.39509e8i	−0.862341	+	0.862341i
$383$	−5.48803e8	−	1.07709e9i	−0.499138	−	0.979613i	−0.993869	−	0.110567i	$-0.964733\pi$
$383$	−5.48803e8	−	1.07709e9i	−0.499138	−	0.979613i	0.494731	−	0.869046i	$-0.335267\pi$
$384$	−1.05089e9	+	4.82867e8i	−0.947101	+	0.435179i
$385$	−4.66785e8	−	6.03714e8i	−0.416873	−	0.539161i
$386$	5.35180e8	−	7.36612e8i	0.473635	−	0.651903i
$387$	5.74855e8	−	9.32816e8i	0.504162	−	0.818102i
$388$	−2.24560e7	−	3.55668e6i	−0.0195174	−	0.00309125i
$389$	−2.41064e8	−	1.75143e8i	−0.207639	−	0.150859i	0.479106	−	0.877757i	$-0.340961\pi$
$389$	−2.41064e8	−	1.75143e8i	−0.207639	−	0.150859i	−0.686745	+	0.726899i	$0.740961\pi$
$390$	1.84879e9	+	3.13069e8i	1.57820	+	0.267248i
$391$	−6.18046e8	+	4.49037e8i	−0.522880	+	0.379895i
$392$	−1.93262e9	+	9.84719e8i	−1.62049	+	0.825679i
$393$	1.54564e8	−	1.02996e8i	0.128450	−	0.0855946i
$394$	1.07725e9	+	3.50020e8i	0.887321	+	0.288308i
$395$	−7.00344e8	+	7.43467e8i	−0.571770	+	0.606976i
$396$	−1.48034e7	−	1.20244e6i	−0.0119792	−	0.000973039i
$397$	−8.20206e7	−	4.17916e7i	−0.0657895	−	0.0335214i	0.420786	−	0.907160i	$-0.361754\pi$
$397$	−8.20206e7	−	4.17916e7i	−0.0657895	−	0.0335214i	−0.486576	+	0.873638i	$0.661754\pi$
$398$	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	$0.824031\pi$
$402$	5.07537e7	−	1.25173e9i	0.0389651	−	0.960989i
$403$	1.45915e9	−	2.86375e9i	1.11054	−	2.17955i
$404$	−4.21977e6	−	1.29871e7i	−0.00318386	−	0.00979891i
$405$	−7.58694e8	+	1.10074e9i	−0.567511	+	0.823366i
$406$	5.34834e8	−	1.64605e9i	0.396623	−	1.22068i
$407$	2.47665e8	+	2.47665e8i	0.182089	+	0.182089i
$408$	1.78657e9	−	5.01445e8i	1.30229	−	0.365522i
$409$	−1.07777e9	−	1.48342e9i	−0.778924	−	1.07210i	−0.995400	−	0.0958087i	$-0.969456\pi$
$409$	−1.07777e9	−	1.48342e9i	−0.778924	−	1.07210i	0.216476	−	0.976288i	$-0.430544\pi$
$410$	−4.11946e8	+	1.40973e9i	−0.295187	+	1.01016i
$411$	−6.63233e8	+	6.11545e8i	−0.471216	+	0.434492i
$412$	7.30866e6	−	4.61451e7i	0.00514870	−	0.0325076i
$413$	1.93887e8	−	1.22416e9i	0.135433	−	0.855089i
$414$	5.88596e8	−	3.58664e8i	0.407677	−	0.248420i
$415$	−4.00093e8	−	2.72815e8i	−0.274785	−	0.187370i
$416$	8.09933e7	+	1.11478e8i	0.0551598	+	0.0759209i
$417$	5.34796e8	+	1.90539e9i	0.361170	+	1.28679i
$418$	−1.43776e8	−	1.43776e8i	−0.0962876	−	0.0962876i
$419$	5.44923e8	−	1.67710e9i	0.361898	−	1.11381i	−0.590003	−	0.807401i	$-0.700874\pi$
$419$	5.44923e8	−	1.67710e9i	0.361898	−	1.11381i	0.951901	−	0.306406i	$-0.0991264\pi$
$420$	6.11954e7	+	4.54662e7i	0.0403038	+	0.0299444i
$421$	4.56633e7	+	1.40537e8i	0.0298250	+	0.0917919i	0.964861	−	0.262761i	$-0.0846331\pi$
$421$	4.56633e7	+	1.40537e8i	0.0298250	+	0.0917919i	−0.935036	+	0.354553i	$0.884633\pi$
$422$	−8.66846e8	+	1.70128e9i	−0.561498	+	1.10200i
$423$	−2.68048e9	−	6.50646e8i	−1.72195	−	0.417978i
$424$		−	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
$429$	−1.21159e8	−	1.03479e9i	−0.0740890	−	0.632777i
$430$	2.03988e8	−	1.59476e9i	0.123727	−	0.967285i
$431$	1.74805e9	+	5.67977e8i	1.05168	+	0.341712i	0.783328	−	0.621608i	$-0.213520\pi$
$431$	1.74805e9	+	5.67977e8i	1.05168	+	0.341712i	0.268353	+	0.963321i	$0.413520\pi$
$432$	−1.69219e9	+	3.29981e8i	−1.00985	+	0.196923i
$433$	−2.18864e9	+	1.11517e9i	−1.29559	+	0.660136i	−0.959504	−	0.281695i	$-0.909103\pi$
$433$	−2.18864e9	+	1.11517e9i	−1.29559	+	0.660136i	−0.336086	+	0.941831i	$0.609103\pi$
$434$	3.65848e9	−	2.65804e9i	2.14826	−	1.56080i
$435$	1.27309e9	−	1.87741e8i	0.741561	−	0.109357i
$436$	5.10195e6	+	3.70678e6i	0.00294804	+	0.00214188i
$437$	2.69319e8	+	4.26560e7i	0.154377	+	0.0244509i
$438$	9.85501e7	−	2.66103e8i	0.0560400	−	0.151318i
$439$	4.10283e8	−	5.64706e8i	0.231450	−	0.318564i	−0.677457	−	0.735563i	$-0.736918\pi$
$439$	4.10283e8	−	5.64706e8i	0.231450	−	0.318564i	0.908907	+	0.416998i	$0.136918\pi$
$440$	6.68933e8	−	2.39655e8i	0.374368	−	0.134122i
$441$	−3.23700e9	+	7.68549e8i	−1.79725	+	0.426714i
$442$	−1.81240e9	−	3.55703e9i	−0.998334	−	1.95934i
$443$	7.14655e7	−	7.14655e7i	0.0390556	−	0.0390556i	−0.687309	−	0.726365i	$-0.741208\pi$
$443$	7.14655e7	−	7.14655e7i	0.0390556	−	0.0390556i	0.726365	+	0.687309i	$0.241208\pi$
$444$	−3.05075e7	−	1.71354e7i	−0.0165412	−	0.00929079i
$445$	1.22310e9	+	1.56449e8i	0.657965	+	0.0841614i
$446$	−9.99502e8	+	3.24758e8i	−0.533472	+	0.173335i
$447$	9.17748e8	−	1.16116e9i	0.486012	−	0.614915i
$448$	−4.86535e8	−	3.07186e9i	−0.255647	−	1.61409i
$449$	2.43027e9			1.26704			0.633522	−	0.773725i	$-0.281609\pi$
$449$	2.43027e9			1.26704			0.633522	+	0.773725i	$0.281609\pi$
$450$	−3.48119e8	+	1.93047e9i	−0.180088	+	0.998662i
$451$	8.16035e8			0.418881
$452$	513935.	+	3.24486e6i	0.000261772	+	0.00165277i
$453$	3.11061e8	−	3.93562e8i	0.157218	−	0.198916i
$454$	−8.92892e7	+	2.90118e7i	−0.0447820	+	0.0145506i
$455$	−2.28456e9	+	4.83538e9i	−1.13701	+	2.40653i
$456$	−5.77468e8	−	3.24350e8i	−0.285201	−	0.160191i
$457$	−1.89049e9	+	1.89049e9i	−0.926548	+	0.926548i	−0.997481	−	0.0709335i	$-0.977402\pi$
$457$	−1.89049e9	+	1.89049e9i	−0.926548	+	0.926548i	0.0709335	+	0.997481i	$0.477402\pi$
$458$	−5.50754e8	−	1.08092e9i	−0.267873	−	0.525730i
$459$	2.84445e9	−	1.01036e8i	1.37295	−	0.0487675i
$460$	1.64644e7	−	2.41457e7i	0.00788667	−	0.0115661i
$461$	5.98167e8	−	8.23306e8i	0.284360	−	0.391389i	−0.642812	−	0.766024i	$-0.722232\pi$
$461$	5.98167e8	−	8.23306e8i	0.284360	−	0.391389i	0.927172	+	0.374636i	$0.122232\pi$
$462$	5.09090e8	−	1.37463e9i	0.240186	−	0.648545i
$463$	3.60965e7	+	5.71713e6i	0.0169018	+	0.00267698i	0.164880	−	0.986314i	$-0.447276\pi$
$463$	3.60965e7	+	5.71713e6i	0.0169018	+	0.00267698i	−0.147978	+	0.988991i	$0.547276\pi$
$464$	1.34261e9	+	9.75463e8i	0.623932	+	0.453313i
$465$	2.97939e9	+	1.55832e9i	1.37417	+	0.718740i
$466$	2.67641e9	−	1.94452e9i	1.22519	−	0.890149i
$467$	6.01951e8	−	3.06709e8i	0.273497	−	0.139353i	−0.311863	−	0.950127i	$-0.600953\pi$
$467$	6.01951e8	−	3.06709e8i	0.273497	−	0.139353i	0.585360	+	0.810773i	$0.300953\pi$
$468$	3.95892e7	+	9.62593e7i	0.0178532	+	0.0434092i
$469$	3.39804e9	+	1.10409e9i	1.52098	+	0.494197i
$470$	−3.97676e9	+	7.52192e8i	−1.76680	+	0.334184i
$471$	−2.29370e8	−	1.95900e9i	−0.101150	−	0.863895i
$472$	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
$477$	7.18100e8	−	2.95838e9i	0.302950	−	1.24807i
$478$	−1.70394e9	+	3.34418e9i	−0.713605	+	1.40053i
$479$	5.08603e8	+	1.56532e9i	0.211449	+	0.650772i	0.999387	+	0.0350174i	$0.0111487\pi$
$479$	5.08603e8	+	1.56532e9i	0.211449	+	0.650772i	−0.787938	+	0.615754i	$0.788851\pi$
$480$	−1.17517e8	+	8.34804e7i	−0.0485015	+	0.0344541i
$481$	7.58491e8	−	2.33440e9i	0.310773	−	0.956460i
$482$	−2.40182e9	−	2.40182e9i	−0.976960	−	0.976960i
$483$	5.31226e8	+	1.89267e9i	0.214518	+	0.764295i
$484$	−3.65103e7	−	5.02521e7i	−0.0146372	−	0.0201463i
$485$	1.66771e9	−	4.98104e7i	0.663782	−	0.0198255i
$486$	−2.56533e9	−	1.16917e8i	−1.01372	−	0.0462008i
$487$	−5.43547e8	+	3.43182e9i	−0.213248	+	1.34640i	0.616102	+	0.787667i	$0.288711\pi$
$487$	−5.43547e8	+	3.43182e9i	−0.213248	+	1.34640i	−0.829350	+	0.558730i	$0.811289\pi$
$488$	−8.08261e7	+	5.10316e8i	−0.0314834	+	0.198779i
$489$	5.88997e8	−	5.43094e8i	0.227789	−	0.210036i
$490$	−3.86194e9	+	2.98601e9i	−1.48293	+	1.14658i
$491$	−2.74124e9	−	3.77299e9i	−1.04511	−	1.43847i	−0.892973	−	0.450111i	$-0.851384\pi$
$491$	−2.74124e9	−	3.77299e9i	−1.04511	−	1.43847i	−0.152137	−	0.988359i	$-0.548616\pi$
$492$	−7.84896e7	+	2.20301e7i	−0.0297122	+	0.00833946i
$493$	−1.93729e9	−	1.93729e9i	−0.728167	−	0.728167i
$494$	−4.40325e8	+	1.35518e9i	−0.164335	+	0.505770i
$495$	1.08381e9	−	1.15194e8i	0.401637	−	0.0426885i
$496$	1.33993e9	+	4.12387e9i	0.493055	+	1.51747i
$497$	−3.91848e9	+	7.69046e9i	−1.43176	+	2.80999i
$498$	3.76857e7	−	9.29435e8i	0.0136733	−	0.337222i
$499$		−	1.43180e9i		−	0.515860i	−0.966164	−	0.257930i	$-0.916960\pi$
$499$		−	1.43180e9i		−	0.515860i	0.966164	−	0.257930i	$-0.0830403\pi$
$500$	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	$-0.368194\pi$
$503$	−2.90555e8	−	1.48045e8i	−0.101798	−	0.0518689i	−0.504148	+	0.863617i	$0.668194\pi$
$504$	3.86580e8	−	4.75923e9i	0.134503	−	1.65588i
$505$	4.81395e8	+	8.78894e8i	0.166334	+	0.303680i
$506$	−5.34430e8	−	1.73647e8i	−0.183385	−	0.0595854i
$507$	−3.63389e9	+	2.42150e9i	−1.23835	+	0.825194i
$508$	1.03893e7	−	5.29361e6i	0.00351611	−	0.00179155i
$509$	−4.66230e9	+	3.38736e9i	−1.56707	+	1.13854i	−0.637173	+	0.770721i	$0.719896\pi$
$509$	−4.66230e9	+	3.38736e9i	−1.56707	+	1.13854i	−0.929896	+	0.367822i	$0.880104\pi$
$510$	3.74111e9	−	1.85620e9i	1.24883	−	0.619625i
$511$	6.54747e8	+	4.75702e8i	0.217070	+	0.157711i
$512$	2.85499e9	+	4.52186e8i	0.940070	+	0.148892i
$513$	−7.43405e8	−	6.92405e8i	−0.243117	−	0.226438i
$514$	−3.37124e9	+	4.64011e9i	−1.09501	+	1.50715i
$515$	1.02356e8	+	3.42700e9i	0.0330208	+	1.10558i
$516$	8.10911e7	−	3.72602e7i	0.0259836	−	0.0119391i
$517$	1.02092e9	+	2.00366e9i	0.324917	+	0.637686i
$518$	2.44198e9	−	2.44198e9i	0.771948	−	0.771948i
$519$	1.19220e9	−	2.12258e9i	0.374339	−	0.666467i
$520$	−3.62466e9	−	3.41442e9i	−1.13046	−	1.06489i
$521$	5.90049e9	−	1.91718e9i	1.82791	−	0.593926i	0.828490	−	0.560003i	$-0.189200\pi$
$521$	5.90049e9	−	1.91718e9i	1.82791	−	0.593926i	0.999424	−	0.0339220i	$-0.0107998\pi$
$522$	1.60065e9	+	1.88368e9i	0.492550	+	0.579642i
$523$	3.87734e8	+	2.44806e9i	0.118516	+	0.748283i	0.973340	+	0.229365i	$0.0736650\pi$
$523$	3.87734e8	+	2.44806e9i	0.118516	+	0.748283i	−0.854824	+	0.518918i	$0.826335\pi$
$524$	1.51275e7			0.00459311
$525$	−5.03263e9	−	2.44375e9i	−1.51788	−	0.737055i
$526$	1.09253e9			0.327328
$527$	−1.11982e9	−	7.07028e9i	−0.333282	−	2.10426i
$528$	1.10273e9	+	8.71565e8i	0.326023	+	0.257680i
$529$	−2.52148e9	+	8.19280e8i	−0.740562	+	0.240623i
$530$	−8.30174e8	−	4.38905e9i	−0.242216	−	1.28057i
$531$	1.34315e9	+	1.15300e9i	0.389309	+	0.334194i
$532$	−4.09650e7	+	4.09650e7i	−0.0117957	+	0.0117957i
$533$	−2.59624e9	−	5.09540e9i	−0.742675	−	1.45758i
$534$	9.88930e8	+	2.15225e9i	0.281042	+	0.611644i
$535$	3.62583e9	+	1.05953e9i	1.02369	+	0.299140i
$536$	−1.95547e9	+	2.69147e9i	−0.548497	+	0.754941i
$537$	2.42263e9	+	8.97212e8i	0.675115	+	0.250026i
$538$	4.85096e9	+	7.68317e8i	1.34304	+	0.212717i
$539$	2.19436e9	+	1.59429e9i	0.603597	+	0.438539i
$540$	−1.01135e8	+	4.03388e7i	−0.0276391	+	0.0110241i
$541$	6.80110e8	−	4.94129e8i	0.184667	−	0.134168i	−0.491611	−	0.870815i	$-0.663592\pi$
$541$	6.80110e8	−	4.94129e8i	0.184667	−	0.134168i	0.676278	+	0.736647i	$0.263592\pi$
$542$	−6.86851e7	+	3.49968e7i	−0.0185295	+	0.00944127i
$543$	1.96354e9	+	2.94664e9i	0.526308	+	0.789819i
$544$	2.91877e8	+	9.48365e7i	0.0777326	+	0.0252569i
$545$	−4.18435e8	−	1.97697e8i	−0.110723	−	0.0523133i
$546$	−1.02030e10	+	1.19463e9i	−2.68259	+	0.314093i
$547$	6.36307e9	+	3.24215e9i	1.66231	+	0.846987i	0.994739	+	0.102438i	$0.0326642\pi$
$547$	6.36307e9	+	3.24215e9i	1.66231	+	0.846987i	0.667567	+	0.744550i	$0.267336\pi$
$548$	−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
$552$	−1.82892e9	−	7.41572e7i	−0.462816	−	0.0187658i
$553$	2.54035e9	−	4.98572e9i	0.638786	−	1.25369i
$554$	1.29661e9	+	3.99055e9i	0.323985	+	0.997123i
$555$	2.43347e9	+	8.19478e8i	0.604227	+	0.203475i
$556$	−4.98082e7	+	1.53294e8i	−0.0122896	+	0.0378236i
$557$	1.74584e9	+	1.74584e9i	0.428067	+	0.428067i	0.887969	−	0.459902i	$-0.152116\pi$
$557$	1.74584e9	+	1.74584e9i	0.428067	+	0.428067i	−0.459902	+	0.887969i	$0.652116\pi$
$558$	4.90576e8	+	6.43995e9i	0.119533	+	1.56914i
$559$	3.67964e9	+	5.06460e9i	0.890973	+	1.22632i
$560$	−2.43338e9	−	6.79214e9i	−0.585533	−	1.63436i
$561$	−1.57298e9	−	1.70593e9i	−0.376142	−	0.407934i
$562$	4.48257e8	−	2.83018e9i	0.106525	−	0.672570i
$563$	−4.51652e7	+	2.85162e8i	−0.0106666	+	0.0673460i	−0.992447	−	0.122671i	$-0.960854\pi$
$563$	−4.51652e7	+	2.85162e8i	−0.0106666	+	0.0673460i	0.981781	+	0.190017i	$0.0608542\pi$
$564$	−1.52288e8	−	1.65159e8i	−0.0357427	−	0.0387637i
$565$	−8.13128e7	−	2.26963e8i	−0.0189666	−	0.0529403i
$566$	2.36675e9	+	3.25755e9i	0.548649	+	0.755151i
$567$	2.29819e9	−	6.95412e9i	0.529474	−	1.60214i
$568$	−5.68285e9	−	5.68285e9i	−1.30121	−	1.30121i
$569$	−1.19974e9	+	3.69241e9i	−0.273019	+	0.840267i	0.716717	+	0.697364i	$0.245644\pi$
$569$	−1.19974e9	+	3.69241e9i	−0.273019	+	0.840267i	−0.989737	+	0.142903i	$0.954356\pi$
$570$	−1.41269e9	−	4.75730e8i	−0.319511	−	0.107597i
$571$	1.46947e9	+	4.52256e9i	0.330319	+	1.01662i	0.968982	+	0.247131i	$0.0794878\pi$
$571$	1.46947e9	+	4.52256e9i	0.330319	+	1.01662i	−0.638663	+	0.769486i	$0.720512\pi$
$572$	3.85232e7	−	7.56061e7i	0.00860670	−	0.0168916i
$573$	5.40768e9	+	2.19265e8i	1.20080	+	0.0486887i
$574$		−	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	0.228799	−	0.973474i	$-0.426520\pi$
$577$	3.44797e9	−	5.46105e8i	0.747220	−	0.118348i	0.518421	+	0.855126i	$0.326520\pi$
$578$	−3.72474e9	−	1.89785e9i	−0.802321	−	0.408803i
$579$	−3.68363e9	+	4.31300e8i	−0.788681	+	0.0923432i
$580$	9.47645e7	+	4.47732e7i	0.0201673	+	0.00952839i
$581$	2.52312e9	+	8.19812e8i	0.533730	+	0.173419i
$582$	1.77721e9	+	2.66702e9i	0.373687	+	0.560785i
$583$	−2.21138e9	+	1.12676e9i	−0.462194	+	0.235500i
$584$	−6.09654e8	+	4.42940e8i	−0.126660	+	0.0920237i
$585$	−4.16744e9	−	6.40090e9i	−0.860645	−	1.32189i
$586$	−3.35024e9	−	2.43409e9i	−0.687755	−	0.499683i
$587$	4.61327e9	+	7.30670e8i	0.941403	+	0.149104i	0.608229	−	0.793762i	$-0.291880\pi$
$587$	4.61327e9	+	7.30670e8i	0.941403	+	0.149104i	0.333174	+	0.942865i	$0.391880\pi$
$588$	−2.54103e8	−	9.41059e7i	−0.0515453	−	0.0190896i
$589$	−1.50182e9	+	2.06708e9i	−0.302842	+	0.416826i
$590$	2.49309e9	+	7.28522e8i	0.499754	+	0.146036i
$591$	−1.92637e9	−	4.19245e9i	−0.383870	−	0.835434i
$592$	1.50335e9	+	2.95049e9i	0.297806	+	0.584478i
$593$	−2.21231e9	+	2.21231e9i	−0.435668	+	0.435668i	−0.890551	−	0.454883i	$-0.849681\pi$
$593$	−2.21231e9	+	2.21231e9i	−0.435668	+	0.435668i	0.454883	+	0.890551i	$0.349681\pi$
$594$	1.28993e9	+	1.64900e9i	0.252531	+	0.322826i
$595$	2.21367e9	+	1.17034e10i	0.430827	+	2.27774i
$596$	1.14644e8	−	3.72500e7i	0.0221814	−	0.00720717i
$597$	−7.21856e9	−	5.70535e9i	−1.38848	−	1.09742i
$598$	6.16035e8	+	3.88949e9i	0.117802	+	0.743770i
$599$	5.90990e9			1.12353			0.561767	−	0.827296i	$-0.310122\pi$
$599$	5.90990e9			1.12353			0.561767	+	0.827296i	$0.310122\pi$
$600$	3.61214e9	−	3.75353e9i	0.682709	−	0.709431i
$601$	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
$603$	−3.88859e9	+	3.30433e9i	−0.722240	+	0.613723i
$604$	3.88573e7	−	1.26255e7i	0.00717536	−	0.00233141i
$605$	3.31797e9	+	3.12552e9i	0.609156	+	0.573823i
$606$	−9.42659e8	+	1.67830e9i	−0.172068	+	0.306347i
$607$	4.24950e9	−	4.24950e9i	0.771218	−	0.771218i	−0.207101	−	0.978320i	$-0.566403\pi$
$607$	4.24950e9	−	4.24950e9i	0.771218	−	0.771218i	0.978320	+	0.207101i	$0.0664029\pi$
$608$	−4.97306e7	−	9.76019e7i	−0.00897349	−	0.0176115i
$609$	−6.40610e9	+	2.94351e9i	−1.14930	+	0.528087i
$610$	3.47159e7	+	1.16233e9i	0.00619262	+	0.207336i
$611$	9.26297e9	−	1.27494e10i	1.64288	−	2.26123i
$612$	1.97349e8	+	1.21618e8i	0.0348021	+	0.0214471i
$613$	−5.01388e9	−	7.94120e8i	−0.879148	−	0.139243i	−0.299486	−	0.954101i	$-0.596815\pi$
$613$	−5.01388e9	−	7.94120e8i	−0.879148	−	0.139243i	−0.579662	+	0.814857i	$0.696815\pi$
$614$	−3.85039e9	−	2.79747e9i	−0.671298	−	0.487727i
$615$	5.35909e9	−	2.65898e9i	0.929026	−	0.460948i
$616$	−3.14935e9	+	2.28814e9i	−0.542861	+	0.394411i
$617$	−1.66229e9	+	8.46979e8i	−0.284911	+	0.145169i	−0.590606	−	0.806960i	$-0.701111\pi$
$617$	−1.66229e9	+	8.46979e8i	−0.284911	+	0.145169i	0.305695	+	0.952129i	$0.401111\pi$
$618$	−5.48049e9	+	3.65201e9i	−0.934028	+	0.622404i
$619$	−1.14748e8	−	3.72840e7i	−0.0194460	−	0.00631838i	0.299278	−	0.954166i	$-0.403254\pi$
$619$	−1.14748e8	−	3.72840e7i	−0.0194460	−	0.00631838i	−0.318724	+	0.947848i	$0.603254\pi$
$620$	1.31552e8	+	2.40178e8i	0.0221680	+	0.0404726i
$621$	−2.69932e9	−	7.72268e8i	−0.452307	−	0.129404i
$622$	−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
$627$	−3.35549e7	+	8.27557e8i	−0.00543650	+	0.134079i
$628$	7.29299e7	−	1.43133e8i	0.0117502	−	0.0230612i
$629$	−1.68933e9	−	5.19921e9i	−0.270667	−	0.833029i
$630$	−1.13581e9	−	1.06864e10i	−0.180974	−	1.70270i
$631$	−6.10743e8	+	1.87967e9i	−0.0967734	+	0.297838i	−0.987712	−	0.156286i	$-0.950048\pi$
$631$	−6.10743e8	+	1.87967e9i	−0.0967734	+	0.297838i	0.890938	+	0.454124i	$0.150048\pi$
$632$	3.68419e9	+	3.68419e9i	0.580540	+	0.580540i
$633$	7.48827e9	−	2.10177e9i	1.17346	−	0.329361i
$634$	−2.81524e7	−	3.87484e7i	−0.00438735	−	0.00603867i
$635$	−6.76930e8	+	5.23394e8i	−0.104915	+	0.0811187i
$636$	1.82282e8	−	1.68076e8i	0.0280959	−	0.0259063i
$637$	2.97352e9	−	1.87741e10i	0.455809	−	2.87787i
$638$	3.15256e8	−	1.99045e9i	0.0480608	−	0.303444i
$639$	−6.41459e9	−	1.05269e10i	−0.972558	−	1.59605i
$640$	6.90920e9	−	2.06361e8i	1.04183	−	0.0311169i
$641$	−2.24985e9	−	3.09665e9i	−0.337403	−	0.464396i	0.606277	−	0.795253i	$-0.292662\pi$
$641$	−2.24985e9	−	3.09665e9i	−0.337403	−	0.464396i	−0.943681	+	0.330857i	$0.892662\pi$
$642$	1.96083e9	+	6.98612e9i	0.292460	+	1.04199i
$643$	7.28568e9	+	7.28568e9i	1.08077	+	1.08077i	0.996438	+	0.0843287i	$0.0268746\pi$
$643$	7.28568e9	+	7.28568e9i	1.08077	+	1.08077i	0.0843287	+	0.996438i	$0.473125\pi$
$644$	−4.94757e7	+	1.52271e8i	−0.00729948	+	0.0224655i
$645$	−5.33895e9	+	3.79264e9i	−0.783424	+	0.556522i
$646$	9.80700e8	+	3.01828e9i	0.143127	+	0.440500i
$647$	−4.10932e9	+	8.06499e9i	−0.596492	+	1.17068i	0.373519	+	0.927622i	$0.378151\pi$
$647$	−4.10932e9	+	8.06499e9i	−0.596492	+	1.17068i	−0.970011	+	0.243059i	$0.921849\pi$
$648$	5.49700e9	+	4.03612e9i	0.793622	+	0.582708i
$649$		−	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	$-0.532078\pi$
$653$	−6.86383e9	−	3.49729e9i	−0.964651	−	0.491514i	−0.864046	+	0.503412i	$0.832078\pi$
$654$	−1.03378e8	−	8.82929e8i	−0.0144513	−	0.123425i
$655$	−1.09078e9	+	2.06317e8i	−0.151667	+	0.0286873i
$656$	7.33751e9	+	2.38410e9i	1.01481	+	0.329732i
$657$	−1.06900e9	+	4.39654e8i	−0.147061	+	0.0604828i
$658$	1.97561e10	−	1.00662e10i	2.70340	−	1.37745i
$659$	−3.98480e9	+	2.89513e9i	−0.542385	+	0.394066i	−0.824970	−	0.565177i	$-0.808808\pi$
$659$	−3.98480e9	+	2.89513e9i	−0.542385	+	0.394066i	0.282585	+	0.959242i	$0.408808\pi$
$660$	7.86590e7	+	4.11414e7i	0.0106499	+	0.00557026i
$661$	6.30974e9	+	4.58429e9i	0.849779	+	0.617401i	0.925085	−	0.379760i	$-0.123993\pi$
$661$	6.30974e9	+	4.58429e9i	0.849779	+	0.617401i	−0.0753059	+	0.997160i	$0.523993\pi$
$662$	4.41817e9	+	6.99769e8i	0.591888	+	0.0937458i
$663$	−5.64750e9	+	1.52493e10i	−0.752591	+	2.03213i
$664$	−1.45198e9	+	1.99848e9i	−0.192474	+	0.264918i
$665$	2.39511e9	−	3.51251e9i	0.315827	−	0.463172i
$666$	1.13939e9	+	4.79894e9i	0.149456	+	0.629485i
$667$	1.22694e9	+	2.40800e9i	0.160097	+	0.314207i
$668$	−1.35611e8	+	1.35611e8i	−0.0176026	+	0.0176026i
$669$	3.73239e9	+	2.09640e9i	0.481943	+	0.270696i
$670$	−3.19857e9	+	6.76992e9i	−0.410860	+	0.869604i
$671$	6.14483e8	−	1.99658e8i	0.0785201	−	0.0255127i
$672$	4.89687e8	−	6.19565e8i	0.0622481	−	0.0787579i
$673$	9.57432e8	+	6.04499e9i	0.121075	+	0.764439i	0.971272	+	0.237973i	$0.0764830\pi$
$673$	9.57432e8	+	6.04499e9i	0.121075	+	0.764439i	−0.850197	+	0.526465i	$0.823517\pi$
$674$	−7.49650e9			−0.943080
$675$	6.74226e9	−	4.28799e9i	0.843805	−	0.536650i
$676$	−3.55655e8			−0.0442809
$677$	−1.12308e9	−	7.09082e9i	−0.139107	−	0.878286i	−0.954246	−	0.299021i	$-0.903340\pi$
$677$	−1.12308e9	−	7.09082e9i	−0.139107	−	0.878286i	0.815140	−	0.579265i	$-0.196660\pi$
$678$	2.87162e8	−	3.63325e8i	0.0353853	−	0.0447704i
$679$	−8.69319e9	+	2.82459e9i	−1.06570	+	0.346267i
$680$	−1.10010e10	−	1.40716e9i	−1.34169	−	0.171618i
$681$	3.33429e8	+	1.87279e8i	0.0404565	+	0.0227234i
$682$	3.72325e9	−	3.72325e9i	0.449446	−	0.449446i
$683$	1.07665e9	+	2.11304e9i	0.129301	+	0.253767i	0.946576	−	0.322480i	$-0.104517\pi$
$683$	1.07665e9	+	2.11304e9i	0.129301	+	0.253767i	−0.817276	+	0.576247i	$0.804517\pi$
$684$	−1.91137e7	−	8.05037e7i	−0.00228375	−	0.00961877i
$685$	5.07603e9	−	1.81856e9i	0.603403	−	0.216177i
$686$	7.20977e9	−	9.92340e9i	0.852682	−	1.17362i
$687$	−1.71617e9	+	4.63397e9i	−0.201935	+	0.545261i
$688$	−8.34165e9	−	1.32119e9i	−0.976545	−	0.154670i
$689$	1.40712e10	+	1.02233e10i	1.63894	+	1.19076i
$690$	−4.07554e9	+	6.01014e8i	−0.472294	+	0.0696487i
$691$	3.08442e9	−	2.24096e9i	0.355632	−	0.258382i	−0.395596	−	0.918425i	$-0.629462\pi$
$691$	3.08442e9	−	2.24096e9i	0.355632	−	0.258382i	0.751228	+	0.660043i	$0.229462\pi$
$692$	1.76667e8	−	9.00163e7i	0.0202667	−	0.0103264i
$693$	−5.52223e9	+	2.27116e9i	−0.630301	+	0.259228i
$694$	1.41660e9	+	4.60283e8i	0.160876	+	0.0522717i
$695$	1.50075e9	−	1.17327e10i	0.169575	−	1.32572i
$696$	−7.63388e8	−	6.51992e9i	−0.0858249	−	0.733010i
$697$	−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	$0.935479\pi$
$702$	6.19258e9	−	1.33008e10i	0.675603	−	1.45110i
$703$	−8.85853e8	+	1.73858e9i	−0.0961652	+	0.188735i
$704$	−1.11907e9	−	3.44415e9i	−0.120880	−	0.372030i
$705$	1.32333e10	+	9.83193e9i	1.42235	+	1.05676i
$706$	−9.66755e8	+	2.97537e9i	−0.103395	+	0.318217i
$707$	−3.88197e9	−	3.88197e9i	−0.413127	−	0.413127i
$708$	3.89599e7	+	1.38808e8i	0.00412574	+	0.0146993i
$709$	−8.08527e9	−	1.11284e10i	−0.851986	−	1.17266i	−0.983422	−	0.181334i	$-0.941959\pi$
$709$	−8.08527e9	−	1.11284e10i	−0.851986	−	1.17266i	0.131436	−	0.991325i	$-0.458041\pi$
$710$	−1.49442e10	−	1.01901e10i	−1.56700	−	1.06850i
$711$	4.15857e9	+	6.82456e9i	0.433911	+	0.712083i
$712$	9.83982e8	−	6.21262e9i	0.102166	−	0.645052i
$713$	−1.10463e9	+	6.97433e9i	−0.114130	+	0.720591i
$714$	−1.68205e10	+	1.55096e10i	−1.72940	+	1.59462i
$715$	−1.74659e9	+	5.97703e9i	−0.178698	+	0.611525i
$716$	1.23676e8	+	1.70225e8i	0.0125918	+	0.0173312i
$717$	1.47196e10	−	4.13141e9i	1.49134	−	0.418583i
$718$	−4.82011e9	−	4.82011e9i	−0.485984	−	0.485984i
$719$	−6.94664e8	+	2.13796e9i	−0.0696985	+	0.214510i	−0.979839	−	0.199791i	$-0.935974\pi$
$719$	−6.94664e8	+	2.13796e9i	−0.0696985	+	0.214510i	0.910140	+	0.414301i	$0.135974\pi$
$720$	1.00818e10	+	2.13063e9i	1.00664	+	0.212738i
$721$	−5.80428e9	−	1.78637e10i	−0.576733	−	1.77500i
$722$	−4.14475e9	+	8.13454e9i	−0.409844	+	0.804364i
$723$	−5.60544e8	+	1.38246e10i	−0.0551602	+	1.36040i
$724$			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	−0.0583582	−	0.998296i	$-0.518587\pi$
$727$	2.01642e9	−	3.19369e8i	0.194630	−	0.0308264i	0.252988	+	0.967469i	$0.418587\pi$
$728$	2.43071e10	+	1.23851e10i	2.33493	+	1.18970i
$729$	6.73338e9	+	8.00504e9i	0.643705	+	0.765274i
$730$	−1.16293e9	+	1.23453e9i	−0.110643	+	0.117455i
$731$	1.32604e10	+	4.30856e9i	1.25558	+	0.407963i
$732$	−5.37134e7	+	3.57928e7i	−0.00506167	+	0.00337292i
$733$	−3.70566e9	+	1.88813e9i	−0.347538	+	0.177079i	−0.619042	−	0.785358i	$-0.712479\pi$
$733$	−3.70566e9	+	1.88813e9i	−0.347538	+	0.177079i	0.271504	+	0.962437i	$0.412479\pi$
$734$	8.15932e9	−	5.92809e9i	0.761584	−	0.553323i
$735$	1.96057e10	+	3.31998e9i	1.82128	+	0.308411i
$736$	−2.44916e8	−	1.77942e8i	−0.0226435	−	0.0164515i
$737$	4.10901e9	+	6.50802e8i	0.378095	+	0.0598843i
$738$	9.78314e9	+	6.02894e9i	0.895945	+	0.552133i
$739$	−9.23392e9	+	1.27094e10i	−0.841649	+	1.15843i	0.143993	+	0.989579i	$0.454006\pi$
$739$	−9.23392e9	+	1.27094e10i	−0.841649	+	1.15843i	−0.985642	+	0.168851i	$0.945994\pi$
$740$	1.27921e8	+	1.65446e8i	0.0116046	+	0.0150088i
$741$	5.27410e9	−	2.42337e9i	0.476195	−	0.218805i
$742$	1.11098e10	+	2.18043e10i	0.998377	+	1.95942i
$743$	1.12136e10	−	1.12136e10i	1.00296	−	1.00296i	0.00296426	−	0.999996i	$-0.499056\pi$
$743$	1.12136e10	−	1.12136e10i	1.00296	−	1.00296i	0.999996	−	0.00296426i	$-0.000943555\pi$
$744$	8.39942e9	−	1.49542e10i	0.747729	−	1.33124i
$745$	−7.75844e9	+	4.24952e9i	−0.687428	+	0.376524i
$746$	5.03294e9	−	1.63530e9i	0.443850	−	0.144216i
$747$	−2.88737e9	+	2.45354e9i	−0.253443	+	0.215363i
$748$	−2.95645e7	−	1.86663e8i	−0.00258294	−	0.0163081i
$749$	−2.06947e10			−1.79958
$750$	6.41793e9	−	9.81153e9i	0.555496	−	0.849224i
$751$	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
$753$	7.22233e8	+	5.70833e8i	0.0616446	+	0.0487222i
$754$	−1.34315e10	+	4.36417e9i	−1.14111	+	0.370768i
$755$	−2.62964e9	+	1.44033e9i	−0.222373	+	0.121800i
$756$	4.69837e8	−	3.67530e8i	0.0395477	−	0.0309362i
$757$	−2.26177e9	+	2.26177e9i	−0.189501	+	0.189501i	−0.795481	−	0.605979i	$-0.792781\pi$
$757$	−2.26177e9	+	2.26177e9i	−0.189501	+	0.189501i	0.605979	+	0.795481i	$0.292781\pi$
$758$	5.58397e9	+	1.09592e10i	0.465694	+	0.913976i
$759$	9.55682e8	+	2.07990e9i	0.0793354	+	0.172661i
$760$	2.42137e9	+	3.13168e9i	0.200085	+	0.258779i
$761$	−1.76366e9	+	2.42747e9i	−0.145067	+	0.199668i	−0.875367	−	0.483459i	$-0.839380\pi$
$761$	−1.76366e9	+	2.42747e9i	−0.145067	+	0.199668i	0.730300	+	0.683127i	$0.239380\pi$
$762$	−1.54134e9	−	5.70830e8i	−0.126199	−	0.0467374i
$763$	2.50414e9	+	3.96617e8i	0.204090	+	0.0323248i
$764$	3.56610e8	+	2.59092e8i	0.0289312	+	0.0210198i
$765$	−1.58887e10	−	6.07780e9i	−1.28314	−	0.490831i
$766$	−1.12279e10	+	8.15756e9i	−0.902607	+	0.655782i
$767$	−9.01116e9	+	4.59142e9i	−0.721102	+	0.367420i
$768$	6.20882e8	+	9.31745e8i	0.0494590	+	0.0742220i
$769$	−1.65830e8	−	5.38813e7i	−0.0131498	−	0.00427263i	0.302435	−	0.953170i	$-0.402201\pi$
$769$	−1.65830e8	−	5.38813e7i	−0.0131498	−	0.00427263i	−0.315585	+	0.948897i	$0.602201\pi$
$770$	−6.00745e9	+	6.37735e9i	−0.474212	+	0.503411i
$771$	2.32042e10	−	2.71688e9i	1.82338	−	0.213491i
$772$	−2.69142e8	−	1.37135e8i	−0.0210534	−	0.0107272i
$773$	−2.27233e10	+	3.59901e9i	−1.76947	+	0.280256i	−0.954274	−	0.298932i	$-0.903370\pi$
$773$	−2.27233e10	+	3.59901e9i	−1.76947	+	0.280256i	−0.815194	+	0.579188i	$0.803370\pi$
$774$	−1.16101e10	−	4.84322e9i	−0.899997	−	0.375440i
$775$	−1.27613e10	−	1.55240e10i	−0.984782	−	1.19797i
$776$		−	8.51105e9i		−	0.653833i
$777$	−1.40557e10	−	5.69916e8i	−1.07493	−	0.0435850i
$778$	−1.55308e9	+	3.04809e9i	−0.118240	+	0.232059i
$779$	1.40484e9	+	4.32365e9i	0.106474	+	0.327695i
$780$	6.63507e6	−	6.22047e8i	0.000500627	−	0.0469345i
$781$	−3.10562e9	+	9.55811e9i	−0.233276	+	0.717949i
$782$	6.20184e9	+	6.20184e9i	0.463764	+	0.463764i
$783$	1.22111e9	−	9.99464e9i	0.0909054	−	0.744048i
$784$	1.50731e10	+	2.07463e10i	1.11711	+	1.53757i
$785$	−3.30653e9	+	1.13154e10i	−0.243966	+	0.834881i
$786$	−1.44551e9	−	1.56769e9i	−0.106180	−	0.115155i
$787$	−2.54958e9	+	1.60974e10i	−0.186448	+	1.17719i	0.699926	+	0.714216i	$0.253216\pi$
$787$	−2.54958e9	+	1.60974e10i	−0.186448	+	1.17719i	−0.886374	+	0.462971i	$0.846784\pi$
$788$	5.87846e7	−	3.71151e8i	0.00427978	−	0.0270215i
$789$	−3.01674e9	−	3.27172e9i	−0.218659	−	0.237141i
$790$	9.68832e9	+	6.60625e9i	0.699123	+	0.476717i
$791$	7.76346e8	+	1.06855e9i	0.0557747	+	0.0767673i
$792$	−4.22305e8	−	5.54374e9i	−0.0302057	−	0.396519i
$793$	−3.20167e9	−	3.20167e9i	−0.227993	−	0.227993i
$794$	−3.26585e8	+	1.00513e9i	−0.0231539	+	0.0712605i
$795$	−1.08512e10	+	1.46053e10i	−0.765939	+	1.03092i
$796$	−2.31572e8	−	7.12705e8i	−0.0162738	−	0.0500858i
$797$	1.03791e10	−	2.03701e10i	0.726197	−	1.42524i	−0.171752	−	0.985140i	$-0.554943\pi$
$797$	1.03791e10	−	2.03701e10i	0.726197	−	1.42524i	0.897948	−	0.440101i	$-0.145057\pi$
$798$	8.15973e9	+	3.30852e8i	0.568415	+	0.0230475i
$799$		−	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
$804$	−4.12790e8	+	4.83318e7i	−0.0280113	+	0.00327972i
$805$	1.49073e9	−	1.16544e10i	0.100720	−	0.787414i
$806$	−3.50940e10	−	1.14027e10i	−2.36080	−	0.767072i
$807$	−1.10938e10	−	1.66483e10i	−0.743062	−	1.11510i
$808$	4.55468e9	−	2.32073e9i	0.303751	−	0.154769i
$809$	6.52650e9	−	4.74178e9i	0.433372	−	0.314863i	−0.349624	−	0.936890i	$-0.613691\pi$
$809$	6.52650e9	−	4.74178e9i	0.433372	−	0.314863i	0.782996	+	0.622027i	$0.213691\pi$
$810$	1.38444e10	+	6.62625e9i	0.915329	+	0.438097i
$811$	6.67415e9	+	4.84905e9i	0.439362	+	0.319215i	0.785381	−	0.619012i	$-0.212467\pi$
$811$	6.67415e9	+	4.84905e9i	0.439362	+	0.319215i	−0.346019	+	0.938227i	$0.612467\pi$
$812$	−5.67122e8	−	8.98233e7i	−0.0371732	−	0.00588766i
$813$	2.94458e8	+	1.09051e8i	0.0192179	+	0.00711728i
$814$	2.36358e9	−	3.25319e9i	0.153598	−	0.211409i
$815$	−4.50787e9	+	1.61501e9i	−0.291689	+	0.104502i
$816$	−9.15970e9	−	1.99347e10i	−0.590154	−	1.28438i
$817$	−2.25933e9	−	4.43419e9i	−0.144945	−	0.284471i
$818$	−1.48856e10	+	1.48856e10i	−0.950886	+	0.950886i
$819$	3.17505e10	+	2.72556e10i	2.01956	+	1.73365i
$820$	4.83309e8	+	6.18209e7i	0.0306109	+	0.00391550i
$821$	8.91027e9	−	2.89512e9i	0.561940	−	0.182585i	−0.0142540	−	0.999898i	$-0.504537\pi$
$821$	8.91027e9	−	2.89512e9i	0.561940	−	0.182585i	0.576194	+	0.817313i	$0.304537\pi$
$822$	8.12574e9	+	6.42237e9i	0.510284	+	0.403315i
$823$	−2.99261e9	−	1.88946e10i	−0.187133	−	1.18151i	−0.885106	−	0.465389i	$-0.845915\pi$
$823$	−2.99261e9	−	1.88946e10i	−0.187133	−	1.18151i	0.697973	−	0.716124i	$-0.254085\pi$
$824$	1.74894e10			1.08901
$825$	−6.23287e9	−	1.89373e9i	−0.386455	−	0.117417i
$826$	−1.42295e10			−0.878534
$827$	2.53360e9	+	1.59965e10i	0.155764	+	0.983457i	0.934463	+	0.356059i	$0.115880\pi$
$827$	2.53360e9	+	1.59965e10i	0.155764	+	0.983457i	−0.778699	+	0.627398i	$0.784120\pi$
$828$	−1.48071e8	−	1.74253e8i	−0.00906493	−	0.0106678i
$829$	1.53303e10	−	4.98110e9i	0.934563	−	0.303658i	0.198136	−	0.980175i	$-0.436511\pi$
$829$	1.53303e10	−	4.98110e9i	0.934563	−	0.303658i	0.736427	+	0.676517i	$0.236511\pi$
$830$	−2.37501e9	+	5.02682e9i	−0.144176	+	0.305154i
$831$	8.36995e9	−	1.49017e10i	0.505963	−	0.900809i
$832$	−1.79453e10	+	1.79453e10i	−1.08024	+	1.08024i
$833$	−1.92198e10	−	3.77209e10i	−1.15210	−	2.26113i
$834$	2.06456e10	−	9.48637e9i	1.23239	−	0.566264i
$835$	7.92878e9	−	1.16279e10i	0.471307	−	0.691189i
$836$	−3.96498e7	+	5.45733e7i	−0.00234703	+	0.00323041i
$837$	1.79306e10	−	1.92513e10i	1.05695	−	1.13481i
$838$	−1.99961e10	−	3.16707e9i	−1.17379	−	0.185910i
$839$	3.92690e9	+	2.85306e9i	0.229553	+	0.166780i	0.696616	−	0.717444i	$-0.254688\pi$
$839$	3.92690e9	+	2.85306e9i	0.229553	+	0.166780i	−0.467063	+	0.884224i	$0.654688\pi$
$840$	−1.32268e10	+	2.52886e10i	−0.769977	+	1.47213i
$841$	6.11428e9	−	4.44229e9i	0.354454	−	0.257526i
$842$	1.51161e9	−	7.70202e8i	0.0872662	−	0.0444644i
$843$	−9.71307e9	+	6.47245e9i	−0.558419	+	0.372111i
$844$	6.02451e8	+	1.95748e8i	0.0344924	+	0.0112073i
$845$	2.56448e10	−	4.85063e9i	1.46218	−	0.276566i
$846$	−2.56384e9	+	3.15638e10i	−0.145578	+	1.79222i
$847$	−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
$852$	4.06758e7	−	1.00318e9i	0.00225319	−	0.0555699i
$853$	−4.41428e9	+	8.66351e9i	−0.243522	+	0.477939i	−0.980124	−	0.198388i	$-0.936429\pi$
$853$	−4.41428e9	+	8.66351e9i	−0.243522	+	0.477939i	0.736602	+	0.676327i	$0.236429\pi$
$854$	−1.96863e9	−	6.05881e9i	−0.108159	−	0.332878i
$855$	2.47616e9	+	5.54409e9i	0.135487	+	0.303353i
$856$	5.95458e9	−	1.83263e10i	0.324484	−	0.998658i
$857$	1.20616e9	+	1.20616e9i	0.0654592	+	0.0654592i	0.739079	−	0.673619i	$-0.235261\pi$
$857$	1.20616e9	+	1.20616e9i	0.0654592	+	0.0654592i	−0.673619	+	0.739079i	$0.735261\pi$
$858$	−1.15163e10	+	3.23234e9i	−0.622456	+	0.174708i
$859$	8.56224e9	+	1.17849e10i	0.460905	+	0.634381i	0.974696	−	0.223534i	$-0.0717594\pi$
$859$	8.56224e9	+	1.17849e10i	0.460905	+	0.634381i	−0.513791	+	0.857915i	$0.671759\pi$
$860$	−5.33144e8	+	1.59237e7i	−0.0285825	+	0.000853688i
$861$	−2.40951e10	+	2.22173e10i	−1.28652	+	1.18626i
$862$	3.30106e9	−	2.08421e10i	0.175541	−	1.10832i
$863$	2.71723e9	−	1.71559e10i	0.143909	−	0.908606i	−0.805050	−	0.593207i	$-0.797862\pi$
$863$	2.71723e9	−	1.71559e10i	0.143909	−	0.908606i	0.948959	−	0.315399i	$-0.102138\pi$
$864$	3.86397e8	+	1.05964e9i	0.0203815	+	0.0558934i
$865$	−1.15110e10	+	8.90017e9i	−0.604723	+	0.467565i
$866$	1.65762e10	+	2.28152e10i	0.867307	+	1.19375i
$867$	4.60155e9	+	1.63946e10i	0.239794	+	0.854346i
$868$	−1.06084e9	−	1.06084e9i	−0.0550591	−	0.0550591i
$869$	2.01337e9	−	6.19651e9i	0.104077	−	0.320316i
$870$	−4.41534e9	−	1.40990e10i	−0.227325	−	0.725888i
$871$	−9.00923e9	−	2.77276e10i	−0.461981	−	1.42183i
$872$	−1.07176e9	+	2.10344e9i	−0.0547379	+	0.107429i
$873$	3.07942e9	−	1.26864e10i	0.156646	−	0.645338i
$874$		−	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	0.108330	−	0.994115i	$-0.465450\pi$
$877$	1.03585e10	−	1.64062e9i	0.518557	−	0.0821313i	0.410227	+	0.911984i	$0.365450\pi$
$878$	−7.14033e9	−	3.63818e9i	−0.356031	−	0.181407i
$879$	1.96163e9	+	1.67538e10i	0.0974217	+	0.832055i
$880$	−4.03567e9	−	7.36801e9i	−0.199630	−	0.364469i
$881$	−2.55627e9	−	8.30583e8i	−0.125948	−	0.0409230i	0.245365	−	0.969431i	$-0.421092\pi$
$881$	−2.55627e9	−	8.30583e8i	−0.125948	−	0.0409230i	−0.371313	+	0.928508i	$0.621092\pi$
$882$	1.45286e10	+	3.53256e10i	0.712989	+	1.73360i
$883$	−1.41772e10	+	7.22364e9i	−0.692992	+	0.353097i	−0.764752	−	0.644325i	$-0.777138\pi$
$883$	−1.41772e10	+	7.22364e9i	−0.692992	+	0.353097i	0.0717601	+	0.997422i	$0.477138\pi$
$884$	−1.07148e9	+	7.78477e8i	−0.0521677	+	0.0379021i
$885$	−4.70237e9	−	9.47749e9i	−0.228042	−	0.459613i
$886$	−9.38732e8	−	6.82029e8i	−0.0453444	−	0.0329446i
$887$	−3.36719e10	−	5.33311e9i	−1.62008	−	0.256595i	−0.720531	−	0.693423i	$-0.756102\pi$
$887$	−3.36719e10	−	5.33311e9i	−1.62008	−	0.256595i	−0.899545	+	0.436828i	$0.856102\pi$
$888$	4.54901e9	−	1.22831e10i	0.218008	−	0.588660i
$889$	2.75540e9	−	3.79248e9i	0.131531	−	0.181037i
$890$	−4.22634e8	−	1.41503e10i	−0.0200955	−	0.672822i
$891$	1.37633e9	−	8.41616e9i	0.0651853	−	0.398604i
$892$	1.58287e8	+	3.10655e8i	0.00746736	+	0.0146555i
$893$	−8.85856e9	+	8.85856e9i	−0.416278	+	0.416278i
$894$	−1.48152e10	−	8.32133e9i	−0.693466	−	0.389504i
$895$	−1.12394e10	−	1.05874e10i	−0.524035	−	0.493640i
$896$	−3.60152e10	+	1.17020e10i	−1.67266	+	0.543480i
$897$	9.94654e9	−	1.25846e10i	0.460149	−	0.582192i
$898$	−4.36474e9	−	2.75579e10i	−0.201137	−	1.26993i
$899$	−2.53238e10			−1.16244
$900$	6.50627e8	+	1.38814e7i	0.0297498	+	0.000634725i
$901$	3.87378e10			1.76440
$902$	−1.46559e9	−	9.25339e9i	−0.0664952	−	0.419834i
$903$	2.22472e10	−	2.81477e10i	1.00547	−	1.27214i
$904$	−1.16964e9	+	3.80040e8i	−0.0526579	+	0.0171096i
$905$	−3.93327e9	−	2.07948e10i	−0.176394	−	0.932577i
$906$	−5.02144e9	−	2.82043e9i	−0.224326	−	0.125999i
$907$	−2.11841e10	+	2.11841e10i	−0.942722	+	0.942722i	−0.998446	−	0.0557244i	$-0.982253\pi$
$907$	−2.11841e10	+	2.11841e10i	−0.942722	+	0.942722i	0.0557244	+	0.998446i	$0.482253\pi$
$908$	1.41403e7	+	2.77520e7i	0.000626844	+	0.00123025i
$909$	7.62877e9	−	1.81127e9i	0.336884	−	0.0799851i
$910$	5.89336e10	+	1.72214e10i	2.59250	+	0.757570i
$911$	1.21581e10	−	1.67342e10i	0.532785	−	0.733316i	−0.454766	−	0.890611i	$-0.650277\pi$
$911$	1.21581e10	−	1.67342e10i	0.532785	−	0.733316i	0.987552	+	0.157295i	$0.0502772\pi$
$912$	−2.71948e9	+	7.34308e9i	−0.118714	+	0.320550i
$913$	3.05103e9	+	4.83235e8i	0.132678	+	0.0210141i
$914$	2.48324e10	+	1.80418e10i	1.07574	+	0.781571i
$915$	3.38488e9	−	3.31344e9i	0.146073	−	0.142990i
$916$	−3.25603e8	+	2.36564e8i	−0.0139976	+	0.0101699i
$917$	5.41886e9	−	2.76104e9i	0.232068	−	0.118244i
$918$	−6.25430e9	−	3.20730e10i	−0.266827	−	1.36833i
$919$	1.92265e10	+	6.24707e9i	0.817140	+	0.265505i	0.687619	−	0.726072i	$-0.258656\pi$
$919$	1.92265e10	+	6.24707e9i	0.817140	+	0.265505i	0.129521	+	0.991577i	$0.458656\pi$
$920$	9.89166e9	+	4.67349e9i	0.418805	+	0.197872i
$921$	2.25448e9	+	1.92550e10i	0.0950905	+	0.812145i
$922$	−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
$927$	2.60693e10	+	6.32794e9i	1.07486	+	0.260905i
$928$	4.92893e8	−	9.67357e8i	0.0202458	−	0.0397346i
$929$	9.46355e9	+	2.91258e10i	0.387257	+	1.19185i	0.934830	+	0.355096i	$0.115552\pi$
$929$	9.46355e9	+	2.91258e10i	0.387257	+	1.19185i	−0.547573	+	0.836758i	$0.684448\pi$
$930$	1.23196e10	−	3.65833e10i	0.502233	−	1.49140i
$931$	−4.66947e9	+	1.43712e10i	−0.189646	+	0.583671i
$932$	−7.76068e8	−	7.76068e8i	−0.0314011	−	0.0314011i
$933$	1.04293e10	+	3.71580e10i	0.420408	+	1.49785i
$934$	−4.55902e9	−	6.27495e9i	−0.183087	−	0.251997i
$935$	4.67758e9	+	1.30562e10i	0.187146	+	0.522369i
$936$	−3.32721e10	+	2.02745e10i	−1.32622	+	0.808135i
$937$	−1.21416e9	+	7.66587e9i	−0.0482154	+	0.304420i	−0.999997	−	0.00235572i	$-0.999250\pi$
$937$	−1.21416e9	+	7.66587e9i	−0.0482154	+	0.304420i	0.951782	+	0.306776i	$0.0992501\pi$
$938$	6.41693e9	−	4.05149e10i	0.253873	−	1.60289i
$939$	−1.39099e10	+	1.28259e10i	−0.548271	+	0.505543i
$940$	4.52860e8	+	1.26404e9i	0.0177835	+	0.0496379i
$941$	1.60582e10	+	2.21022e10i	0.628249	+	0.864711i	0.997921	−	0.0644517i	$-0.0205298\pi$
$941$	1.60582e10	+	2.21022e10i	0.628249	+	0.864711i	−0.369672	+	0.929162i	$0.620530\pi$
$942$	−2.18020e10	+	6.11929e9i	−0.849804	+	0.238519i
$943$	8.88405e9	+	8.88405e9i	0.345001	+	0.345001i
$944$	4.21626e9	−	1.29763e10i	0.163127	−	0.502052i
$945$	−2.88654e10	+	3.29089e10i	−1.11267	+	1.26853i
$946$	3.16922e9	+	9.75387e9i	0.121712	+	0.374592i
$947$	1.99555e10	−	3.91649e10i	0.763550	−	1.49855i	−0.100384	−	0.994949i	$-0.532007\pi$
$947$	1.99555e10	−	3.91649e10i	0.763550	−	1.49855i	0.863935	−	0.503603i	$-0.167993\pi$
$948$	−2.63701e7	+	6.50360e8i	−0.00100527	+	0.0247927i
$949$		−	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	$-0.538319\pi$
$953$	−2.65548e10	−	1.35304e10i	−0.993844	−	0.506389i	−0.873751	+	0.486374i	$0.838319\pi$
$954$	−3.48361e10	−	2.82964e9i	−1.29900	−	0.105515i
$955$	−2.92473e10	−	1.38184e10i	−1.08661	−	0.513388i
$956$	1.18423e9	+	3.84779e8i	0.0438362	+	0.0142432i
$957$	−6.83114e9	+	4.55203e9i	−0.251942	+	0.167886i
$958$	1.68364e10	−	8.57859e9i	0.618686	−	0.315236i
$959$	−2.38980e10	+	1.73629e10i	−0.874978	+	0.635709i
$960$	−1.85717e10	−	1.89722e10i	−0.677489	−	0.692098i
$961$	−3.12714e10	−	2.27200e10i	−1.13662	−	0.825802i
$962$	−2.78330e10	−	4.40832e9i	−1.00797	−	0.159647i
$963$	1.55065e10	−	2.51623e10i	0.559527	−	0.907942i
$964$	−6.62362e8	+	9.11662e8i	−0.0238136	+	0.0327766i
$965$	2.12770e10	+	6.21749e9i	0.762193	+	0.222725i
$966$	2.05078e10	−	9.42305e9i	0.731980	−	0.336335i
$967$	1.36049e10	+	2.67012e10i	0.483842	+	0.949593i	0.995884	+	0.0906333i	$0.0288891\pi$
$967$	1.36049e10	+	2.67012e10i	0.483842	+	0.949593i	−0.512042	+	0.858960i	$0.671111\pi$
$968$	1.64419e10	−	1.64419e10i	0.582624	−	0.582624i
$969$	6.33067e9	−	1.12710e10i	0.223520	−	0.397952i
$970$	−3.56002e9	−	1.88215e10i	−0.125243	−	0.662145i
$971$	−1.72279e10	+	5.59769e9i	−0.603900	+	0.196219i	−0.594979	−	0.803741i	$-0.702840\pi$
$971$	−1.72279e10	+	5.59769e9i	−0.603900	+	0.196219i	−0.00892102	+	0.999960i	$0.502840\pi$
$972$	9.48259e7	+	8.46657e8i	0.00331203	+	0.0295716i
$973$	1.01371e10	+	6.40028e10i	0.352790	+	2.22743i
$974$	3.98912e10			1.38331
$975$	8.00540e9	+	4.49436e10i	0.276609	+	1.55293i
$976$	6.10853e9			0.210311
$977$	−4.91415e9	−	3.10267e10i	−0.168584	−	1.06440i	−0.916333	−	0.400418i	$-0.868865\pi$
$977$	−4.91415e9	−	3.10267e10i	−0.168584	−	1.06440i	0.747748	−	0.663982i	$-0.231135\pi$
$978$	−7.21622e9	−	5.70351e9i	−0.246674	−	0.194965i
$979$	−7.48075e9	+	2.43064e9i	−0.254804	+	0.0827908i
$980$	1.17886e9	+	1.11048e9i	0.0400103	+	0.0376896i
$981$	−2.35859e9	+	2.74756e9i	−0.0797646	+	0.0929192i
$982$	−3.78604e10	+	3.78604e10i	−1.27584	+	1.27584i
$983$	−1.48307e9	−	2.91068e9i	−0.0497994	−	0.0977367i	0.864766	−	0.502176i	$-0.167467\pi$
$983$	−1.48307e9	−	2.91068e9i	−0.0497994	−	0.0977367i	−0.914565	+	0.404439i	$0.867467\pi$
$984$	−1.27417e10	−	2.77303e10i	−0.426327	−	0.927836i
$985$	8.23264e8	+	2.75639e10i	0.0274481	+	0.918996i
$986$	−1.84885e10	+	2.54472e10i	−0.614231	+	0.845416i
$987$	−8.46960e10	−	3.13668e10i	−2.80384	−	1.03839i
$988$	4.66908e8	+	7.39509e7i	0.0154022	+	0.00243946i
$989$	−1.11269e10	−	8.08415e9i	−0.365752	−	0.265734i
$990$	−3.25274e9	−	1.20829e10i	−0.106543	−	0.395774i
$991$	−1.05371e10	+	7.65566e9i	−0.343925	+	0.249876i	−0.746316	−	0.665592i	$-0.768179\pi$
$991$	−1.05371e10	+	7.65566e9i	−0.343925	+	0.249876i	0.402391	+	0.915468i	$0.368179\pi$
$992$	2.52751e9	−	1.28783e9i	0.0822058	−	0.0418859i
$993$	−1.01041e10	−	1.51630e10i	−0.327472	−	0.491431i
$994$	9.42432e10	+	3.06215e10i	3.04367	+	0.988948i
$995$	2.64179e10	+	4.82318e10i	0.850194	+	1.55222i
$996$	−3.06506e8	+	3.58874e7i	−0.00982950	+	0.00115089i
$997$	−5.63763e9	−	2.87252e9i	−0.180162	−	0.0917972i	0.361583	−	0.932340i	$-0.382236\pi$
$997$	−5.63763e9	−	2.87252e9i	−0.180162	−	0.0917972i	−0.541745	+	0.840543i	$0.682236\pi$
$998$	−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.38.20	yes	544
3.2	odd	2	inner	75.8.l.a.38.49	yes	544
25.2	odd	20	inner	75.8.l.a.2.49	yes	544
75.2	even	20	inner	75.8.l.a.2.20	✓	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.8.l.a.2.20	✓	544	75.2	even	20	inner
75.8.l.a.2.49	yes	544	25.2	odd	20	inner
75.8.l.a.38.20	yes	544	1.1	even	1	trivial
75.8.l.a.38.49	yes	544	3.2	odd	2	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} +(-28.9982 + 36.6893i) q^{3} +(-3.62242 + 1.17700i) q^{4} +(245.145 - 134.273i) q^{5} +(468.117 + 262.930i) q^{6} +(-1082.77 + 1082.77i) q^{7} +(-647.306 - 1270.41i) q^{8} +(-505.206 - 2127.85i) q^{9} +(-1962.86 - 2538.65i) q^{10} +(-1048.01 + 1442.46i) q^{11} +(61.8606 - 167.035i) q^{12} +(12341.2 + 1954.65i) q^{13} +(14222.7 + 10333.4i) q^{14} +(-2182.39 + 12887.8i) q^{15} +(-13637.6 + 9908.31i) q^{16} +(24795.9 - 12634.1i) q^{17} +(-23221.3 + 9550.37i) q^{18} +(-9446.90 - 3069.48i) q^{19} +(-729.978 + 774.926i) q^{20} +(-8327.68 - 71124.7i) 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} +(92719.3 + 43168.1i) q^{27} +(2647.84 - 5196.68i) q^{28} +(-30422.4 - 93630.6i) q^{29} +(150061. + 1600.62i) q^{30} +(79487.8 - 244638. i) q^{31} +(7797.93 + 7797.93i) q^{32} +(-22532.5 - 80279.7i) q^{33} +(-187797. - 258481. i) q^{34} +(-120049. + 410823. i) q^{35} +(4334.54 + 7113.33i) q^{36} +(30730.2 - 194023. i) q^{37} +(-17839.7 + 112635. i) q^{38} +(-429586. + 396107. i) q^{39} +(-329265. - 224519. i) q^{40} +(-269017. - 370270. i) q^{41} +(-791559. + 222171. i) q^{42} +(354271. + 354271. i) q^{43} +(2098.56 - 6458.71i) q^{44} +(-409560. - 453795. i) q^{45} +(97391.1 + 299739. i) q^{46} +(572588. - 1.12377e6i) q^{47} +(31937.9 - 787678. 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} +(322980. - 1.12892e6i) q^{54} +(-63230.8 + 494331. i) q^{55} +(2.07645e6 + 674681. i) q^{56} +(386560. - 257590. i) q^{57} +(-1.00708e6 + 513134. i) q^{58} +(-654819. + 475754. i) q^{59} +(-7263.40 - 49253.8i) q^{60} +(-293166. - 212998. i) q^{61} +(-2.91682e6 - 461979. i) q^{62} +(2.85100e6 + 1.75695e6i) q^{63} +(-1.19384e6 + 1.64319e6i) q^{64} +(3.28782e6 - 1.17791e6i) q^{65} +(-869859. + 399688. i) q^{66} +(-1.05929e6 - 2.07898e6i) q^{67} +(-74950.8 + 74950.8i) q^{68} +(628685. - 1.11930e6i) q^{69} +(4.87412e6 + 623457. i) q^{70} +(5.36074e6 - 1.74181e6i) q^{71} +(-2.37622e6 + 2.01919e6i) q^{72} +(-82679.1 - 522015. i) q^{73} -2.25530e6 q^{74} +(1.19548e6 + 3.45242e6i) q^{75} +37833.4 q^{76} +(-427103. - 2.69662e6i) q^{77} +(5.26317e6 + 4.15987e6i) q^{78} +(-3.47536e6 + 1.12921e6i) q^{79} +(-2.01277e6 + 4.26013e6i) q^{80} +(-4.27250e6 + 2.15000e6i) q^{81} +(-3.71551e6 + 3.71551e6i) q^{82} +(-786549. - 1.54369e6i) q^{83} +(113880. + 247842. i) q^{84} +(4.38216e6 - 6.42660e6i) q^{85} +(3.38098e6 - 4.65351e6i) q^{86} +(4.31743e6 + 1.59894e6i) q^{87} +(2.51090e6 + 397688. i) q^{88} +(3.56902e6 + 2.59305e6i) q^{89} +(-4.41022e6 + 5.45920e6i) q^{90} +(-1.54791e7 + 1.12462e7i) q^{91} +(93161.8 - 47468.3i) q^{92} +(6.67059e6 + 1.00104e7i) q^{93} +(-1.37713e7 - 4.47456e6i) q^{94} +(-2.72800e6 + 515993. i) q^{95} +(-512227. + 59974.4i) 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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