LMFDB - Embedded newform 27.10.e.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(4,27)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	27.4
Dual form			27.10.e.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-31.5968 - 11.5003i) q^{2} +(132.307 + 46.6679i) q^{3} +(473.884 + 397.636i) q^{4} +(-451.726 + 2561.87i) q^{5} +(-3643.77 - 2996.12i) q^{6} +(-2730.60 + 2291.24i) q^{7} +(-1792.39 - 3104.51i) q^{8} +(15327.2 + 12349.0i) q^{9} +O(q^{10})$	\(q+(-31.5968 - 11.5003i) q^{2} +(132.307 + 46.6679i) q^{3} +(473.884 + 397.636i) q^{4} +(-451.726 + 2561.87i) q^{5} +(-3643.77 - 2996.12i) q^{6} +(-2730.60 + 2291.24i) q^{7} +(-1792.39 - 3104.51i) q^{8} +(15327.2 + 12349.0i) q^{9} +(43735.3 - 75751.7i) q^{10} +(-10297.9 - 58402.4i) q^{11} +(44141.3 + 74725.2i) q^{12} +(-14744.9 + 5366.72i) q^{13} +(112628. - 40993.2i) q^{14} +(-179323. + 317871. i) q^{15} +(-34068.5 - 193212. i) q^{16} +(-246260. + 426534. i) q^{17} +(-342274. - 566455. i) q^{18} +(-444465. - 769836. i) q^{19} +(-1.23276e6 + 1.03441e6i) q^{20} +(-468204. + 175716. i) q^{21} +(-346263. + 1.96376e6i) q^{22} +(1.21443e6 + 1.01903e6i) q^{23} +(-92264.4 - 494395. i) q^{24} +(-4.52377e6 - 1.64652e6i) q^{25} +527611. q^{26} +(1.45159e6 + 2.34914e6i) q^{27} -2.20507e6 q^{28} +(-956629. - 348184. i) q^{29} +(9.32165e6 - 7.98144e6i) q^{30} +(-449094. - 376835. i) q^{31} +(-1.46425e6 + 8.30419e6i) q^{32} +(1.36303e6 - 8.20763e6i) q^{33} +(1.26863e7 - 1.06450e7i) q^{34} +(-4.63638e6 - 8.03044e6i) q^{35} +(2.35293e6 + 1.19466e7i) q^{36} +(1.61951e6 - 2.80508e6i) q^{37} +(5.19032e6 + 2.94358e7i) q^{38} +(-2.20131e6 + 21938.3i) q^{39} +(8.76300e6 - 3.18947e6i) q^{40} +(-1.79692e7 + 6.54024e6i) q^{41} +(1.68145e7 - 167574. i) q^{42} +(-2.40636e6 - 1.36471e7i) q^{43} +(1.83429e7 - 3.17708e7i) q^{44} +(-3.85601e7 + 3.36879e7i) q^{45} +(-2.66530e7 - 4.61643e7i) q^{46} +(2.16726e6 - 1.81855e6i) q^{47} +(4.50931e6 - 2.71532e7i) q^{48} +(-4.80097e6 + 2.72276e7i) q^{49} +(1.24001e8 + 1.04049e8i) q^{50} +(-5.24873e7 + 4.49410e7i) q^{51} +(-9.12140e6 - 3.31992e6i) q^{52} -3.55712e7 q^{53} +(-1.88499e7 - 9.09190e7i) q^{54} +1.54271e8 q^{55} +(1.20075e7 + 4.37036e6i) q^{56} +(-2.28791e7 - 1.22597e8i) q^{57} +(2.62222e7 + 2.20030e7i) q^{58} +(2.06612e7 - 1.17176e8i) q^{59} +(-2.11376e8 + 7.93288e7i) q^{60} +(-3.49812e7 + 2.93527e7i) q^{61} +(9.85621e6 + 1.70715e7i) q^{62} +(-7.01469e7 + 1.39831e6i) q^{63} +(9.15409e7 - 1.58554e8i) q^{64} +(-7.08815e6 - 4.01989e7i) q^{65} +(-1.37457e8 + 2.43659e8i) q^{66} +(-3.60011e7 + 1.31033e7i) q^{67} +(-2.86304e8 + 1.04206e8i) q^{68} +(1.13122e8 + 1.91500e8i) q^{69} +(5.41422e7 + 3.07055e8i) q^{70} +(2.55520e7 - 4.42573e7i) q^{71} +(1.08652e7 - 6.97176e7i) q^{72} +(4.16970e7 + 7.22212e7i) q^{73} +(-8.34305e7 + 7.00065e7i) q^{74} +(-5.21686e8 - 4.28960e8i) q^{75} +(9.54896e7 - 5.41548e8i) q^{76} +(1.61934e8 + 1.35878e8i) q^{77} +(6.98066e7 + 2.46225e7i) q^{78} +(2.09610e8 + 7.62918e7i) q^{79} +5.10373e8 q^{80} +(8.24264e7 + 3.78551e8i) q^{81} +6.42982e8 q^{82} +(-3.03592e8 - 1.10498e8i) q^{83} +(-2.91746e8 - 1.02906e8i) q^{84} +(-9.81482e8 - 8.23561e8i) q^{85} +(-8.09128e7 + 4.58879e8i) q^{86} +(-1.10320e8 - 9.07111e7i) q^{87} +(-1.62853e8 + 1.36650e8i) q^{88} +(3.08335e8 + 5.34053e8i) q^{89} +(1.60580e9 - 6.20977e8i) q^{90} +(2.79660e7 - 4.84386e7i) q^{91} +(1.70297e8 + 9.65804e8i) q^{92} +(-4.18321e7 - 7.08161e7i) q^{93} +(-8.93923e7 + 3.25361e7i) q^{94} +(2.17299e9 - 7.90905e8i) q^{95} +(-5.81270e8 + 1.03037e9i) q^{96} +(1.29807e8 + 7.36173e8i) q^{97} +(4.64820e8 - 8.05092e8i) q^{98} +(5.63371e8 - 1.02232e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9}+O(q^{10}) $ 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17} + 922437 q^{18} - 3 q^{19} - 8448573 q^{20} - 3497394 q^{21} - 1585014 q^{22} + 9316482 q^{23} + 7959258 q^{24} + 2192178 q^{25} - 33129678 q^{26} - 3148155 q^{27} - 12 q^{28} + 19657236 q^{29} + 21174507 q^{30} - 4633692 q^{31} - 37550952 q^{32} - 19055889 q^{33} + 14341770 q^{34} + 34449663 q^{35} + 137733552 q^{36} - 3 q^{37} - 92022060 q^{38} - 89330160 q^{39} + 6645801 q^{40} - 33127221 q^{41} + 227141658 q^{42} + 2356203 q^{43} + 1001541 q^{44} - 78992532 q^{45} - 3 q^{46} - 33488952 q^{47} + 248865393 q^{48} - 93214644 q^{49} - 72027753 q^{50} - 101541537 q^{51} + 160531713 q^{52} + 4841352 q^{53} - 315431874 q^{54} - 12 q^{55} - 91770981 q^{56} - 103852992 q^{57} - 320682489 q^{58} + 538090854 q^{59} + 1127571210 q^{60} + 36683436 q^{61} - 55862958 q^{62} - 419972706 q^{63} - 956301315 q^{64} - 852347310 q^{65} + 472205277 q^{66} - 109026897 q^{67} - 508886217 q^{68} - 1234413090 q^{69} - 815297649 q^{70} + 940878639 q^{71} + 2831326452 q^{72} - 221849931 q^{73} + 838884579 q^{74} - 226667796 q^{75} + 908401146 q^{76} - 967811358 q^{77} - 1247881230 q^{78} - 1228059150 q^{79} - 2497115154 q^{80} - 392600970 q^{81} - 12 q^{82} - 297703284 q^{83} + 1027656618 q^{84} + 1535949369 q^{85} + 2930201574 q^{86} + 2687612040 q^{87} + 2837227002 q^{88} + 1774997208 q^{89} + 7127326206 q^{90} + 551343507 q^{91} - 6896645517 q^{92} - 7299151842 q^{93} + 414852915 q^{94} - 9000269169 q^{95} - 2644638174 q^{96} + 3371772333 q^{97} + 6901039926 q^{98} + 5248107342 q^{99}+O(q^{100}) \) 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−31.5968	−	11.5003i	−1.39639	−	0.508245i	−0.469287	−	0.883046i	$-0.655489\pi$
$2$	−31.5968	−	11.5003i	−1.39639	−	0.508245i	−0.927106	+	0.374800i	$0.877711\pi$
$3$	132.307	+	46.6679i	0.943054	+	0.332639i
$3$	132.307	+	46.6679i	0.943054	+	0.332639i
$4$	473.884	+	397.636i	0.925555	+	0.776633i
$5$	−451.726	+	2561.87i	−0.323229	+	1.83312i	0.198610	+	0.980079i	$0.436357\pi$
$5$	−451.726	+	2561.87i	−0.323229	+	1.83312i	−0.521839	+	0.853044i	$0.674754\pi$
$6$	−3643.77	−	2996.12i	−1.14781	−	0.943797i
$7$	−2730.60	+	2291.24i	−0.429849	+	0.360687i	−0.831895	−	0.554933i	$-0.812744\pi$
$7$	−2730.60	+	2291.24i	−0.429849	+	0.360687i	0.402045	+	0.915620i	$0.368299\pi$
$8$	−1792.39	−	3104.51i	−0.154713	−	0.267971i
$9$	15327.2	+	12349.0i	0.778703	+	0.627393i
$10$	43735.3	−	75751.7i	1.38303	−	2.39548i
$11$	−10297.9	−	58402.4i	−0.212072	−	1.20272i	−0.885916	−	0.463845i	$-0.846469\pi$
$11$	−10297.9	−	58402.4i	−0.212072	−	1.20272i	0.673845	−	0.738873i	$-0.264642\pi$
$12$	44141.3	+	74725.2i	0.614511	+	1.04028i
$13$	−14744.9	+	5366.72i	−0.143185	+	0.0521152i	−0.412619	−	0.910904i	$-0.635386\pi$
$13$	−14744.9	+	5366.72i	−0.143185	+	0.0521152i	0.269433	+	0.963019i	$0.413164\pi$
$14$	112628.	−	40993.2i	0.783556	−	0.285191i
$15$	−179323.	+	317871.i	−0.914590	+	1.62122i
$16$	−34068.5	−	193212.i	−0.129961	−	0.737045i
$17$	−246260.	+	426534.i	−0.715110	+	1.23861i	0.247807	+	0.968810i	$0.420290\pi$
$17$	−246260.	+	426534.i	−0.715110	+	1.23861i	−0.962917	+	0.269798i	$0.913043\pi$
$18$	−342274.	−	566455.i	−0.768506	−	1.27186i
$19$	−444465.	−	769836.i	−0.782431	−	1.35521i	−0.930522	−	0.366237i	$-0.880646\pi$
$19$	−444465.	−	769836.i	−0.782431	−	1.35521i	0.148090	−	0.988974i	$-0.452687\pi$
$20$	−1.23276e6	+	1.03441e6i	−1.72283	+	1.44563i
$21$	−468204.	+	175716.i	−0.525350	+	0.197162i
$22$	−346263.	+	1.96376e6i	−0.315141	+	1.78725i
$23$	1.21443e6	+	1.01903e6i	0.904894	+	0.759296i	0.971141	−	0.238507i	$-0.0766580\pi$
$23$	1.21443e6	+	1.01903e6i	0.904894	+	0.759296i	−0.0662466	+	0.997803i	$0.521102\pi$
$24$	−92264.4	−	494395.i	−0.0567654	−	0.304175i
$25$	−4.52377e6	−	1.64652e6i	−2.31617	−	0.843016i
$26$	527611.			0.226430
$27$	1.45159e6	+	2.34914e6i	0.525664	+	0.850692i
$28$	−2.20507e6			−0.677970
$29$	−956629.	−	348184.i	−0.251161	−	0.0914152i	0.213372	−	0.976971i	$-0.431556\pi$
$29$	−956629.	−	348184.i	−0.251161	−	0.0914152i	−0.464533	+	0.885556i	$0.653778\pi$
$30$	9.32165e6	−	7.98144e6i	2.10110	−	1.79902i
$31$	−449094.	−	376835.i	−0.0873393	−	0.0732864i	0.598073	−	0.801442i	$-0.295933\pi$
$31$	−449094.	−	376835.i	−0.0873393	−	0.0732864i	−0.685412	+	0.728156i	$0.740378\pi$
$32$	−1.46425e6	+	8.30419e6i	−0.246855	+	1.39998i
$33$	1.36303e6	−	8.20763e6i	0.200075	−	1.20477i
$34$	1.26863e7	−	1.06450e7i	1.62809	−	1.36613i
$35$	−4.63638e6	−	8.03044e6i	−0.522243	−	0.904551i
$36$	2.35293e6	+	1.19466e7i	0.233479	+	1.18545i
$37$	1.61951e6	−	2.80508e6i	0.142061	−	0.246058i	−0.786211	−	0.617958i	$-0.787960\pi$
$37$	1.61951e6	−	2.80508e6i	0.142061	−	0.246058i	0.928273	+	0.371900i	$0.121294\pi$
$38$	5.19032e6	+	2.94358e7i	0.403802	+	2.29007i
$39$	−2.20131e6	+	21938.3i	−0.152367	+	0.00151849i
$40$	8.76300e6	−	3.18947e6i	0.541231	−	0.196992i
$41$	−1.79692e7	+	6.54024e6i	−0.993117	+	0.361465i	−0.786926	−	0.617047i	$-0.788329\pi$
$41$	−1.79692e7	+	6.54024e6i	−0.993117	+	0.361465i	−0.206191	+	0.978512i	$0.566107\pi$
$42$	1.68145e7	−	167574.i	0.833801	−	0.00830967i
$43$	−2.40636e6	−	1.36471e7i	−0.107338	−	0.608742i	−0.990261	−	0.139225i	$-0.955539\pi$
$43$	−2.40636e6	−	1.36471e7i	−0.107338	−	0.608742i	0.882923	−	0.469518i	$-0.155572\pi$
$44$	1.83429e7	−	3.17708e7i	0.737786	−	1.27788i
$45$	−3.85601e7	+	3.36879e7i	−1.40179	+	1.22467i
$46$	−2.66530e7	−	4.61643e7i	−0.877679	−	1.52018i
$47$	2.16726e6	−	1.81855e6i	0.0647845	−	0.0543606i	−0.609820	−	0.792540i	$-0.708758\pi$
$47$	2.16726e6	−	1.81855e6i	0.0647845	−	0.0543606i	0.674605	+	0.738179i	$0.264314\pi$
$48$	4.50931e6	−	2.71532e7i	0.122610	−	0.738304i
$49$	−4.80097e6	+	2.72276e7i	−0.118972	+	0.674726i
$50$	1.24001e8	+	1.04049e8i	2.80582	+	2.35436i
$51$	−5.24873e7	+	4.49410e7i	−1.08640	+	0.930201i
$52$	−9.12140e6	−	3.31992e6i	−0.173000	−	0.0629669i
$53$	−3.55712e7			−0.619238			−0.309619	−	0.950861i	$-0.600201\pi$
$53$	−3.55712e7			−0.619238			−0.309619	+	0.950861i	$0.600201\pi$
$54$	−1.88499e7	−	9.09190e7i	−0.301673	−	1.45507i
$55$	1.54271e8			2.27328
$56$	1.20075e7	+	4.37036e6i	0.163157	+	0.0593843i
$57$	−2.28791e7	−	1.22597e8i	−0.287080	−	1.53830i
$58$	2.62222e7	+	2.20030e7i	0.304258	+	0.255303i
$59$	2.06612e7	−	1.17176e8i	0.221984	−	1.25894i	−0.646383	−	0.763013i	$-0.723719\pi$
$59$	2.06612e7	−	1.17176e8i	0.221984	−	1.25894i	0.868367	−	0.495922i	$-0.165170\pi$
$60$	−2.11376e8	+	7.93288e7i	−2.10559	+	0.790224i
$61$	−3.49812e7	+	2.93527e7i	−0.323483	+	0.271434i	−0.790038	−	0.613058i	$-0.789939\pi$
$61$	−3.49812e7	+	2.93527e7i	−0.323483	+	0.271434i	0.466555	+	0.884492i	$0.345495\pi$
$62$	9.85621e6	+	1.70715e7i	0.0847125	+	0.146726i
$63$	−7.01469e7	+	1.39831e6i	−0.561017	+	0.0111833i
$64$	9.15409e7	−	1.58554e8i	0.682033	−	1.18132i
$65$	−7.08815e6	−	4.01989e7i	−0.0492519	−	0.279321i
$66$	−1.37457e8	+	2.43659e8i	−0.891704	+	1.58065i
$67$	−3.60011e7	+	1.31033e7i	−0.218263	+	0.0794411i	−0.448837	−	0.893614i	$-0.648162\pi$
$67$	−3.60011e7	+	1.31033e7i	−0.218263	+	0.0794411i	0.230575	+	0.973055i	$0.425939\pi$
$68$	−2.86304e8	+	1.04206e8i	−1.62382	+	0.591021i
$69$	1.13122e8	+	1.91500e8i	0.600793	+	1.01706i
$70$	5.41422e7	+	3.07055e8i	0.269522	+	1.52854i
$71$	2.55520e7	−	4.42573e7i	0.119333	−	0.206692i	−0.800170	−	0.599773i	$-0.795258\pi$
$71$	2.55520e7	−	4.42573e7i	0.119333	−	0.206692i	0.919504	+	0.393081i	$0.128591\pi$
$72$	1.08652e7	−	6.97176e7i	0.0476475	−	0.305736i
$73$	4.16970e7	+	7.22212e7i	0.171851	+	0.297654i	0.939067	−	0.343734i	$-0.111692\pi$
$73$	4.16970e7	+	7.22212e7i	0.171851	+	0.297654i	−0.767216	+	0.641389i	$0.778359\pi$
$74$	−8.34305e7	+	7.00065e7i	−0.323431	+	0.271391i
$75$	−5.21686e8	−	4.28960e8i	−1.90385	−	1.56546i
$76$	9.54896e7	−	5.41548e8i	0.328318	−	1.86198i
$77$	1.61934e8	+	1.35878e8i	0.524963	+	0.440496i
$78$	6.98066e7	+	2.46225e7i	0.213536	+	0.0753194i
$79$	2.09610e8	+	7.62918e7i	0.605466	+	0.220372i	0.626518	−	0.779407i	$-0.284479\pi$
$79$	2.09610e8	+	7.62918e7i	0.605466	+	0.220372i	−0.0210521	+	0.999778i	$0.506702\pi$
$80$	5.10373e8			1.39310
$81$	8.24264e7	+	3.78551e8i	0.212757	+	0.977105i
$82$	6.42982e8			1.57049
$83$	−3.03592e8	−	1.10498e8i	−0.702164	−	0.255567i	−0.0338294	−	0.999428i	$-0.510770\pi$
$83$	−3.03592e8	−	1.10498e8i	−0.702164	−	0.255567i	−0.668335	+	0.743861i	$0.732993\pi$
$84$	−2.91746e8	−	1.02906e8i	−0.639363	−	0.225519i
$85$	−9.81482e8	−	8.23561e8i	−2.03937	−	1.71124i
$86$	−8.09128e7	+	4.58879e8i	−0.159505	+	0.904597i
$87$	−1.10320e8	−	9.07111e7i	−0.206450	−	0.169755i
$88$	−1.62853e8	+	1.36650e8i	−0.289483	+	0.242905i
$89$	3.08335e8	+	5.34053e8i	0.520917	+	0.902255i	0.999704	+	0.0243236i	$0.00774321\pi$
$89$	3.08335e8	+	5.34053e8i	0.520917	+	0.902255i	−0.478787	+	0.877931i	$0.658923\pi$
$90$	1.60580e9	−	6.20977e8i	2.57988	−	0.997664i
$91$	2.79660e7	−	4.84386e7i	0.0427509	−	0.0740466i
$92$	1.70297e8	+	9.65804e8i	0.247835	+	1.40554i
$93$	−4.18321e7	−	7.08161e7i	−0.0579878	−	0.0981655i
$94$	−8.93923e7	+	3.25361e7i	−0.118093	+	0.0429824i
$95$	2.17299e9	−	7.90905e8i	2.73717	−	0.996249i
$96$	−5.81270e8	+	1.03037e9i	−0.698486	+	1.23815i
$97$	1.29807e8	+	7.36173e8i	0.148876	+	0.844320i	0.964173	+	0.265276i	$0.0854630\pi$
$97$	1.29807e8	+	7.36173e8i	0.148876	+	0.844320i	−0.815296	+	0.579044i	$0.803426\pi$
$98$	4.64820e8	−	8.05092e8i	0.509059	−	0.881715i
$99$	5.63371e8	−	1.02232e9i	0.589436	−	1.06961i
$100$	−1.48903e9	−	2.57907e9i	−1.48903	−	2.57907i
$101$	−1.40345e9	+	1.17763e9i	−1.34199	+	1.12607i	−0.360885	+	0.932610i	$0.617525\pi$
$101$	−1.40345e9	+	1.17763e9i	−1.34199	+	1.12607i	−0.981109	+	0.193457i	$0.938030\pi$
$102$	2.17526e9	−	8.16371e8i	1.98981	−	0.746770i
$103$	−1.21161e8	+	6.87141e8i	−0.106071	+	0.601559i	0.884716	+	0.466130i	$0.154352\pi$
$103$	−1.21161e8	+	6.87141e8i	−0.106071	+	0.601559i	−0.990787	+	0.135429i	$0.956759\pi$
$104$	4.30897e7	+	3.61566e7i	0.0361180	+	0.0303066i
$105$	−2.38661e8	−	1.27885e9i	−0.191615	−	1.02676i
$106$	1.12394e9	+	4.09079e8i	0.864699	+	0.314725i
$107$	−2.05553e9			−1.51599			−0.757995	−	0.652260i	$-0.773821\pi$
$107$	−2.05553e9			−1.51599			−0.757995	+	0.652260i	$0.773821\pi$
$108$	−2.46216e8	+	1.69043e9i	−0.174144	+	1.19561i
$109$	1.54073e9			1.04546			0.522731	−	0.852498i	$-0.324913\pi$
$109$	1.54073e9			1.04546			0.522731	+	0.852498i	$0.324913\pi$
$110$	−4.87447e9	−	1.77416e9i	−3.17439	−	1.15538i
$111$	3.45180e8	−	2.95552e8i	0.215820	−	0.184791i
$112$	5.35723e8	+	4.49525e8i	0.321706	+	0.269943i
$113$	−2.58686e8	+	1.46708e9i	−0.149252	+	0.846451i	0.814602	+	0.580020i	$0.196955\pi$
$113$	−2.58686e8	+	1.46708e9i	−0.149252	+	0.846451i	−0.963854	+	0.266431i	$0.914156\pi$
$114$	−6.86991e8	+	4.13678e9i	−0.380960	+	2.29398i
$115$	−3.15921e9	+	2.65089e9i	−1.68437	+	1.41336i
$116$	−3.14881e8	−	5.45389e8i	−0.161467	−	0.279670i
$117$	−2.92272e8	−	9.98280e7i	−0.144195	−	0.0492511i
$118$	−2.00038e9	+	3.46476e9i	−0.949826	+	1.64515i
$119$	−3.04858e8	−	1.72893e9i	−0.139359	−	0.790345i
$120$	1.30825e9	−	1.30380e7i	0.575938	−	0.00573980i
$121$	−1.08905e9	+	3.96382e8i	−0.461864	+	0.168105i
$122$	1.44286e9	−	5.25157e8i	0.589664	−	0.214620i
$123$	−2.68266e9	+	2.67354e7i	−1.05680	+	0.0105321i
$124$	−6.29755e7	−	3.57152e8i	−0.0239207	−	0.135661i
$125$	3.72124e9	−	6.44538e9i	1.36330	−	2.36131i
$126$	2.23250e9	+	7.62527e8i	0.789084	+	0.269518i
$127$	−9.74503e8	−	1.68789e9i	−0.332404	−	0.575741i	0.650579	−	0.759439i	$-0.274526\pi$
$127$	−9.74503e8	−	1.68789e9i	−0.332404	−	0.575741i	−0.982983	+	0.183698i	$0.941193\pi$
$128$	−1.40853e9	+	1.18190e9i	−0.463791	+	0.389167i
$129$	3.18506e8	−	1.91791e9i	0.101266	−	0.609782i
$130$	−2.38336e8	+	1.35167e9i	−0.0731888	+	0.415074i
$131$	−1.48442e9	−	1.24558e9i	−0.440389	−	0.369530i	0.395466	−	0.918481i	$-0.370583\pi$
$131$	−1.48442e9	−	1.24558e9i	−0.440389	−	0.369530i	−0.835855	+	0.548951i	$0.815027\pi$
$132$	3.90957e9	−	3.34747e9i	1.12085	−	0.959697i
$133$	2.97754e9	+	1.08373e9i	0.825134	+	0.300324i
$134$	1.28821e9			0.345156
$135$	−6.67391e9	+	2.65762e9i	−1.72933	+	0.688639i
$136$	1.76557e9			0.442548
$137$	7.66611e9	+	2.79024e9i	1.85923	+	0.676704i	0.979572	+	0.201094i	$0.0644497\pi$
$137$	7.66611e9	+	2.79024e9i	1.85923	+	0.676704i	0.879656	+	0.475610i	$0.157772\pi$
$138$	−1.37198e9	−	7.35170e9i	−0.322027	−	1.72557i
$139$	4.21833e9	+	3.53960e9i	0.958460	+	0.804244i	0.980702	−	0.195509i	$-0.0626359\pi$
$139$	4.21833e9	+	3.53960e9i	0.958460	+	0.804244i	−0.0222416	+	0.999753i	$0.507080\pi$
$140$	9.96087e8	−	5.64909e9i	0.219140	−	1.24280i
$141$	3.71612e8	−	1.39465e8i	0.0791778	−	0.0297152i
$142$	−1.31633e9	+	1.10453e9i	−0.271686	+	0.227972i
$143$	4.65272e8	+	8.05875e8i	0.0930454	+	0.161159i
$144$	1.86379e9	−	3.38211e9i	0.361216	−	0.655476i
$145$	1.32414e9	−	2.29347e9i	0.248758	−	0.430861i
$146$	−4.86924e8	−	2.76148e9i	−0.0886898	−	0.502985i
$147$	−1.90586e9	+	3.37835e9i	−0.336637	+	0.596728i
$148$	1.88286e9	−	6.85305e8i	0.322582	−	0.117410i
$149$	−2.29214e9	+	8.34271e8i	−0.380981	+	0.138666i	−0.525409	−	0.850850i	$-0.676088\pi$
$149$	−2.29214e9	+	8.34271e8i	−0.380981	+	0.138666i	0.144429	+	0.989515i	$0.453866\pi$
$150$	1.15504e10	+	1.95533e10i	1.86289	+	3.15362i
$151$	1.55598e9	+	8.82440e9i	0.243561	+	1.38130i	0.823811	+	0.566865i	$0.191844\pi$
$151$	1.55598e9	+	8.82440e9i	0.243561	+	1.38130i	−0.580250	+	0.814439i	$0.697045\pi$
$152$	−1.59331e9	+	2.75969e9i	−0.242105	+	0.419338i
$153$	−9.04173e9	+	3.49653e9i	−1.33395	+	0.515852i
$154$	−3.55394e9	−	6.15560e9i	−0.509174	−	0.881916i
$155$	1.16827e9	−	9.80293e8i	0.162573	−	0.136415i
$156$	−1.05189e9	−	8.64925e8i	−0.142203	−	0.116928i
$157$	5.00173e8	−	2.83662e9i	0.0657010	−	0.372609i	−0.934174	−	0.356817i	$-0.883862\pi$
$157$	5.00173e8	−	2.83662e9i	0.0657010	−	0.372609i	0.999875	−	0.0157918i	$-0.00502690\pi$
$158$	−5.74562e9	−	4.82115e9i	−0.733466	−	0.615451i
$159$	−4.70632e9	−	1.66003e9i	−0.583975	−	0.205982i
$160$	−2.06128e10	−	7.50244e9i	−2.48655	−	0.905030i
$161$	−5.65097e9			−0.662836
$162$	1.74903e9	−	1.29089e10i	0.199517	−	1.47256i
$163$	1.12592e10			1.24929			0.624646	−	0.780908i	$-0.285243\pi$
$163$	1.12592e10			1.24929			0.624646	+	0.780908i	$0.285243\pi$
$164$	−1.11159e10	−	4.04587e9i	−1.19991	−	0.436732i
$165$	2.04111e10	+	7.19951e9i	2.14382	+	0.756180i
$166$	8.32175e9	+	6.98278e9i	0.850606	+	0.713743i
$167$	2.37278e9	−	1.34567e10i	0.236066	−	1.33880i	−0.604291	−	0.796764i	$-0.706544\pi$
$167$	2.37278e9	−	1.34567e10i	0.236066	−	1.33880i	0.840357	−	0.542033i	$-0.182345\pi$
$168$	1.38472e9	+	1.13859e9i	0.134112	+	0.110275i
$169$	−7.93491e9	+	6.65818e9i	−0.748258	+	0.627863i
$170$	2.15405e10	+	3.73092e10i	1.97804	+	3.42606i
$171$	2.69427e9	−	1.72881e10i	0.240968	−	1.54620i
$172$	4.28626e9	−	7.42402e9i	0.373422	−	0.646786i
$173$	6.88907e8	+	3.90699e9i	0.0584727	+	0.331615i	0.999986	−	0.00536161i	$-0.00170666\pi$
$173$	6.88907e8	+	3.90699e9i	0.0584727	+	0.331615i	−0.941513	+	0.336977i	$0.890596\pi$
$174$	2.44254e9	+	4.13488e9i	0.202008	+	0.341973i
$175$	1.61251e10	−	5.86907e9i	1.29967	−	0.473041i
$176$	−1.09332e10	+	3.97937e9i	−0.858897	+	0.312613i
$177$	8.20197e9	−	1.45389e10i	0.628114	−	1.11340i
$178$	−3.60065e9	−	2.04203e10i	−0.268838	−	1.52466i
$179$	−1.25825e10	+	2.17935e10i	−0.916070	+	1.58668i	−0.110743	+	0.993849i	$0.535323\pi$
$179$	−1.25825e10	+	2.17935e10i	−0.916070	+	1.58668i	−0.805327	+	0.592831i	$0.798010\pi$
$180$	−3.16686e10	+	6.31281e8i	−2.24855	+	0.0448225i
$181$	−3.41601e9	−	5.91671e9i	−0.236573	−	0.409757i	0.723155	−	0.690685i	$-0.242691\pi$
$181$	−3.41601e9	−	5.91671e9i	−0.236573	−	0.409757i	−0.959729	+	0.280928i	$0.909358\pi$
$182$	−1.44069e9	+	1.20889e9i	−0.0973308	+	0.0816703i
$183$	−5.99809e9	+	2.25107e9i	−0.395351	+	0.148374i
$184$	9.86851e8	−	5.59671e9i	0.0634704	−	0.359959i
$185$	6.45465e9	+	5.41610e9i	0.405135	+	0.339949i
$186$	5.07355e8	+	2.71864e9i	0.0310816	+	0.166550i
$187$	2.74466e10	+	9.98974e9i	1.64135	+	0.597403i
$188$	1.75015e9			0.102180
$189$	−9.34617e9	−	3.08860e9i	−0.532790	−	0.176070i
$190$	−7.77552e10			−4.32851
$191$	2.47638e10	+	9.01328e9i	1.34638	+	0.490041i	0.911815	−	0.410601i	$-0.134681\pi$
$191$	2.47638e10	+	9.01328e9i	1.34638	+	0.490041i	0.434562	+	0.900642i	$0.356903\pi$
$192$	1.95109e10	−	1.67057e10i	1.03615	−	0.887174i
$193$	−8.92547e9	−	7.48936e9i	−0.463045	−	0.388541i	0.381205	−	0.924491i	$-0.375509\pi$
$193$	−8.92547e9	−	7.48936e9i	−0.463045	−	0.388541i	−0.844250	+	0.535950i	$0.819954\pi$
$194$	4.36471e9	−	2.47535e10i	0.221232	−	1.25467i
$195$	9.38187e8	−	5.64938e9i	0.0464658	−	0.279798i
$196$	−1.31018e10	+	1.09937e10i	−0.634130	+	0.532098i
$197$	1.26366e10	+	2.18872e10i	0.597766	+	1.03536i	0.993150	+	0.116845i	$0.0372781\pi$
$197$	1.26366e10	+	2.18872e10i	0.597766	+	1.03536i	−0.395384	+	0.918516i	$0.629389\pi$
$198$	−2.95576e10	+	2.58229e10i	−1.36671	+	1.19402i
$199$	−5.67251e9	+	9.82508e9i	−0.256411	+	0.444117i	−0.965278	−	0.261226i	$-0.915873\pi$
$199$	−5.67251e9	+	9.82508e9i	−0.256411	+	0.444117i	0.708867	+	0.705342i	$0.249207\pi$
$200$	2.99672e9	+	1.69953e10i	0.132438	+	0.751092i
$201$	−5.37470e9	+	5.35643e7i	−0.232259	+	0.00231469i
$202$	5.78876e10	−	2.10694e10i	2.44627	−	0.890369i
$203$	3.40994e9	−	1.24112e9i	0.140934	−	0.0512957i
$204$	−4.27430e10	+	4.25977e8i	−1.72794	+	0.0172207i
$205$	−8.63808e9	−	4.89890e10i	−0.341606	−	1.93734i
$206$	1.17306e10	−	2.03180e10i	0.453856	−	0.786102i
$207$	6.02989e9	+	3.06159e10i	0.228267	+	1.15899i
$208$	1.53925e9	+	2.66607e9i	0.0570197	+	0.0987611i
$209$	−4.03832e10	+	3.38855e10i	−1.46401	+	1.22845i
$210$	−7.16626e9	+	4.31522e10i	−0.254276	+	1.53115i
$211$	1.03264e9	−	5.85639e9i	0.0358656	−	0.203404i	−0.961609	−	0.274422i	$-0.911514\pi$
$211$	1.03264e9	−	5.85639e9i	0.0358656	−	0.203404i	0.997475	+	0.0710178i	$0.0226247\pi$
$212$	−1.68566e10	−	1.41444e10i	−0.573139	−	0.480920i
$213$	5.44610e9	−	4.66309e9i	0.181292	−	0.155226i
$214$	6.49480e10	+	2.36391e10i	2.11692	+	0.770495i
$215$	3.60492e10			1.15059
$216$	4.69111e9	−	8.71706e9i	0.146634	−	0.272476i
$217$	2.08971e9			0.0639761
$218$	−4.86822e10	−	1.77189e10i	−1.45988	−	0.531351i
$219$	2.14638e9	+	1.15013e10i	0.0630533	+	0.337868i
$220$	7.31066e10	+	6.13437e10i	2.10404	+	1.76550i
$221$	1.34199e9	−	7.61083e9i	0.0378430	−	0.214618i
$222$	−1.43055e10	+	5.36881e9i	−0.395288	+	0.148351i
$223$	2.82403e8	−	2.36964e8i	0.00764712	−	0.00641669i	−0.638956	−	0.769243i	$-0.720633\pi$
$223$	2.82403e8	−	2.36964e8i	0.00764712	−	0.00641669i	0.646603	+	0.762827i	$0.276189\pi$
$224$	−1.50286e10	−	2.60304e10i	−0.398844	−	0.690819i
$225$	−4.90039e10	−	8.11004e10i	−1.27471	−	2.10961i
$226$	2.50455e10	−	4.33801e10i	0.638620	−	1.10612i
$227$	−5.10447e9	−	2.89489e10i	−0.127595	−	0.723628i	−0.979733	−	0.200310i	$-0.935805\pi$
$227$	−5.10447e9	−	2.89489e10i	−0.127595	−	0.723628i	0.852137	−	0.523318i	$-0.175306\pi$
$228$	3.79069e10	−	6.71943e10i	0.928990	−	1.64674i
$229$	−2.19819e10	+	8.00074e9i	−0.528208	+	0.192252i	−0.592338	−	0.805690i	$-0.701795\pi$
$229$	−2.19819e10	+	8.00074e9i	−0.528208	+	0.192252i	0.0641301	+	0.997942i	$0.479573\pi$
$230$	1.30307e11	−	4.74278e10i	3.07038	−	1.11753i
$231$	1.50838e10	+	2.55348e10i	0.348543	+	0.590035i
$232$	6.33709e8	+	3.59394e9i	0.0143613	+	0.0814471i
$233$	−2.92105e10	+	5.05941e10i	−0.649289	+	1.12460i	0.334004	+	0.942572i	$0.391600\pi$
$233$	−2.92105e10	+	5.05941e10i	−0.649289	+	1.12460i	−0.983293	+	0.182030i	$0.941733\pi$
$234$	8.08681e9	+	6.51546e9i	0.176322	+	0.142061i
$235$	3.67987e9	+	6.37372e9i	0.0787095	+	0.136329i
$236$	5.63843e10	−	4.73121e10i	1.18319	−	0.992814i
$237$	2.41725e10	+	1.98760e10i	0.497683	+	0.409224i
$238$	−1.02507e10	+	5.81346e10i	−0.207089	+	1.17446i
$239$	−4.71586e10	−	3.95707e10i	−0.934910	−	0.784483i	0.0417821	−	0.999127i	$-0.486696\pi$
$239$	−4.71586e10	−	3.95707e10i	−0.934910	−	0.784483i	−0.976692	+	0.214644i	$0.931141\pi$
$240$	6.75259e10	+	2.38180e10i	1.31377	+	0.463399i
$241$	−1.81946e10	−	6.62229e9i	−0.347429	−	0.126454i	0.162411	−	0.986723i	$-0.448073\pi$
$241$	−1.81946e10	−	6.62229e9i	−0.347429	−	0.126454i	−0.509839	+	0.860270i	$0.670295\pi$
$242$	3.89690e10			0.730382
$243$	−6.76059e9	+	5.39315e10i	−0.124382	+	0.992234i
$244$	−2.82488e10			−0.510205
$245$	−6.75848e10	−	2.45989e10i	−1.19840	−	0.436182i
$246$	8.50709e10	+	3.00066e10i	1.48106	+	0.522407i
$247$	1.06851e10	+	8.96587e9i	0.182660	+	0.153270i
$248$	−3.64935e8	+	2.06965e9i	−0.00612609	+	0.0347428i
$249$	−3.50105e10	−	2.87877e10i	−0.577167	−	0.474580i
$250$	−1.91703e11	+	1.60858e11i	−3.10383	+	2.60443i
$251$	8.16850e9	+	1.41483e10i	0.129900	+	0.224994i	0.923638	−	0.383266i	$-0.125201\pi$
$251$	8.16850e9	+	1.41483e10i	0.129900	+	0.224994i	−0.793737	+	0.608261i	$0.791868\pi$
$252$	−3.37975e10	−	2.72303e10i	−0.527938	−	0.425354i
$253$	4.70077e10	−	8.14197e10i	0.721317	−	1.24936i
$254$	1.13799e10	+	6.45389e10i	0.171549	+	0.972903i
$255$	−9.14229e10	−	1.54766e11i	−1.35402	−	2.29217i
$256$	−2.99875e10	+	1.09146e10i	−0.436376	+	0.158828i
$257$	−7.79202e10	+	2.83606e10i	−1.11417	+	0.405524i	−0.832521	−	0.553993i	$-0.813103\pi$
$257$	−7.79202e10	+	2.83606e10i	−1.11417	+	0.405524i	−0.281648	+	0.959518i	$0.590881\pi$
$258$	−3.21202e10	+	5.69368e10i	−0.451326	+	0.800027i
$259$	2.00488e9	+	1.13702e10i	0.0276846	+	0.157007i
$260$	1.26256e10	−	2.18681e10i	0.171345	−	0.296778i
$261$	−1.03627e10	−	1.71501e10i	−0.138227	−	0.228762i
$262$	3.25784e10	+	5.64274e10i	0.427144	+	0.739834i
$263$	−4.54679e10	+	3.81521e10i	−0.586009	+	0.491720i	−0.886914	−	0.461934i	$-0.847156\pi$
$263$	−4.54679e10	+	3.81521e10i	−0.586009	+	0.491720i	0.300905	+	0.953654i	$0.402711\pi$
$264$	−2.79237e10	+	1.04797e10i	−0.353798	+	0.132780i
$265$	1.60685e10	−	9.11287e10i	0.200156	−	1.13514i
$266$	−8.16172e10	−	6.84850e10i	−0.999573	−	0.838741i
$267$	1.58718e10	+	8.50482e10i	0.191128	+	1.02415i
$268$	−2.22707e10	−	8.10588e9i	−0.263711	−	0.0959828i
$269$	−1.27971e10			−0.149014			−0.0745070	−	0.997220i	$-0.523738\pi$
$269$	−1.27971e10			−0.149014			−0.0745070	+	0.997220i	$0.523738\pi$
$270$	2.41437e11	−	7.22041e9i	2.76483	−	0.0826847i
$271$	5.65241e10			0.636607			0.318304	−	0.947989i	$-0.396887\pi$
$271$	5.65241e10			0.636607			0.318304	+	0.947989i	$0.396887\pi$
$272$	9.08012e10	+	3.30489e10i	1.00585	+	0.366098i
$273$	5.96063e9	−	5.10364e9i	0.0649472	−	0.0556094i
$274$	−2.10136e11	−	1.76325e11i	−2.25228	−	1.88989i
$275$	−4.95751e10	+	2.81155e11i	−0.522717	+	2.96448i
$276$	−2.25405e10	+	1.35730e11i	−0.233816	+	1.40794i
$277$	−1.20881e10	+	1.01431e10i	−0.123367	+	0.103517i	−0.702384	−	0.711798i	$-0.747881\pi$
$277$	−1.20881e10	+	1.01431e10i	−0.123367	+	0.103517i	0.579017	+	0.815316i	$0.303437\pi$
$278$	−9.25792e10	−	1.60352e11i	−0.929634	−	1.61017i
$279$	−2.22984e9	−	1.13217e10i	−0.0220320	−	0.111864i
$280$	−1.66204e10	+	2.87873e10i	−0.161596	+	0.279892i
$281$	−2.26947e10	−	1.28708e11i	−0.217143	−	1.23148i	−0.877148	−	0.480219i	$-0.840557\pi$
$281$	−2.26947e10	−	1.28708e11i	−0.217143	−	1.23148i	0.660005	−	0.751261i	$-0.270554\pi$
$282$	−1.33456e10	+	1.33002e8i	−0.125666	+	0.00125239i
$283$	−9.32812e10	+	3.39516e10i	−0.864481	+	0.314645i	−0.735930	−	0.677058i	$-0.763255\pi$
$283$	−9.32812e10	+	3.39516e10i	−0.864481	+	0.314645i	−0.128551	+	0.991703i	$0.541033\pi$
$284$	2.97070e10	−	1.08125e10i	0.270973	−	0.0986262i
$285$	3.24412e11	−	3.23309e9i	2.91269	−	0.0290279i
$286$	−5.43330e9	−	3.08138e10i	−0.0480194	−	0.272332i
$287$	3.40813e10	−	5.90305e10i	0.296515	−	0.513579i
$288$	−1.24991e11	+	1.09198e11i	−1.07057	+	0.935296i
$289$	−6.19937e10	−	1.07376e11i	−0.522766	−	0.905456i
$290$	−6.82140e10	+	5.72383e10i	−0.566347	+	0.475221i
$291$	−1.71813e10	+	1.03459e11i	−0.140455	+	0.845762i
$292$	−8.95824e9	+	5.08047e10i	−0.0721107	+	0.408960i
$293$	1.18758e11	+	9.96497e10i	0.941365	+	0.789899i	0.977822	−	0.209436i	$-0.0671628\pi$
$293$	1.18758e11	+	9.96497e10i	0.941365	+	0.789899i	−0.0364570	+	0.999335i	$0.511607\pi$
$294$	9.90709e10	−	8.48271e10i	0.773362	−	0.662173i
$295$	2.90855e11	+	1.05863e11i	2.23603	+	0.813849i
$296$	−1.16112e10			−0.0879151
$297$	1.22247e11	−	1.08968e11i	0.911664	−	0.812634i
$298$	8.20186e10			0.602475
$299$	−2.33756e10	−	8.50802e9i	−0.169138	−	0.0615613i
$300$	−7.66487e10	−	4.10718e11i	−0.546335	−	2.92751i
$301$	3.78397e10	+	3.17513e10i	0.265704	+	0.222952i
$302$	5.23192e10	−	2.96717e11i	0.361934	−	2.05263i
$303$	−2.40644e11	+	9.03130e10i	−1.64015	+	0.615543i
$304$	−1.33599e11	+	1.12103e11i	−0.897167	+	0.752812i
$305$	−5.93959e10	−	1.02877e11i	−0.393013	−	0.680718i
$306$	3.25900e11	−	6.49650e9i	2.12490	−	0.0423577i
$307$	6.57967e10	−	1.13963e11i	0.422748	−	0.732221i	−0.573459	−	0.819234i	$-0.694399\pi$
$307$	6.57967e10	−	1.13963e11i	0.422748	−	0.732221i	0.996207	+	0.0870134i	$0.0277323\pi$
$308$	2.27076e10	+	1.28781e11i	0.143778	+	0.815407i
$309$	−4.80979e10	+	8.52591e10i	−0.300133	+	0.532019i
$310$	−4.81871e10	+	1.75387e10i	−0.296349	+	0.107862i
$311$	−1.15926e11	+	4.21935e10i	−0.702681	+	0.255755i	−0.668555	−	0.743663i	$-0.733087\pi$
$311$	−1.15926e11	+	4.21935e10i	−0.702681	+	0.255755i	−0.0341256	+	0.999418i	$0.510865\pi$
$312$	4.01371e9	+	6.79467e9i	0.0239801	+	0.0405950i
$313$	−3.28632e9	−	1.86377e10i	−0.0193536	−	0.109759i	0.973601	−	0.228258i	$-0.0733030\pi$
$313$	−3.28632e9	−	1.86377e10i	−0.0193536	−	0.109759i	−0.992954	+	0.118499i	$0.962192\pi$
$314$	−4.84258e10	+	8.38759e10i	−0.281121	+	0.486916i
$315$	2.81049e10	−	1.80339e11i	0.160837	−	1.03203i
$316$	6.89945e10	+	1.19502e11i	0.389244	+	0.674191i
$317$	5.41001e10	−	4.53953e10i	0.300906	−	0.252490i	−0.479815	−	0.877370i	$-0.659296\pi$
$317$	5.41001e10	−	4.53953e10i	0.300906	−	0.252490i	0.780721	+	0.624879i	$0.214852\pi$
$318$	1.29614e11	+	1.06576e11i	0.710769	+	0.584435i
$319$	−1.04835e10	+	5.94550e10i	−0.0566826	+	0.321463i
$320$	3.64842e11	+	3.06138e11i	1.94504	+	1.63209i
$321$	−2.71960e11	−	9.59272e10i	−1.42966	−	0.504277i
$322$	1.78552e11	+	6.49877e10i	0.925580	+	0.336883i
$323$	4.37815e11			2.23810
$324$	−1.11465e11	+	2.12165e11i	−0.561934	+	1.06960i
$325$	7.55391e10			0.375575
$326$	−3.55755e11	−	1.29484e11i	−1.74450	−	0.634947i
$327$	2.03850e11	+	7.19028e10i	0.985928	+	0.347761i
$328$	5.25119e10	+	4.40628e10i	0.250510	+	0.210203i
$329$	−1.75118e9	+	9.93145e9i	−0.00824043	+	0.0467338i
$330$	−5.62129e11	−	4.62215e11i	−2.60930	−	2.14551i
$331$	−7.25012e10	+	6.08357e10i	−0.331986	+	0.278569i	−0.793508	−	0.608559i	$-0.791748\pi$
$331$	−7.25012e10	+	6.08357e10i	−0.331986	+	0.278569i	0.461523	+	0.887128i	$0.347303\pi$
$332$	−9.99292e10	−	1.73082e11i	−0.451410	−	0.781865i
$333$	5.94624e10	−	2.29947e10i	0.264998	−	0.102478i
$334$	−2.29728e11	+	3.97901e11i	−1.01008	+	1.74951i
$335$	−1.73063e10	−	9.81492e10i	−0.0750765	−	0.425780i
$336$	4.99014e10	+	8.44763e10i	0.213593	+	0.361583i
$337$	2.38010e10	−	8.66284e9i	0.100522	−	0.0365869i	−0.291270	−	0.956641i	$-0.594078\pi$
$337$	2.38010e10	−	8.66284e9i	0.100522	−	0.0365869i	0.391791	+	0.920054i	$0.371855\pi$
$338$	3.27288e11	−	1.19123e11i	1.36397	−	0.496445i
$339$	−1.02692e11	+	1.82033e11i	−0.422315	+	0.748602i
$340$	−1.37631e11	−	7.80545e11i	−0.558549	−	3.16769i
$341$	−1.73833e10	+	3.01088e10i	−0.0696207	+	0.120587i
$342$	−2.83949e11	+	5.15264e11i	−1.12233	+	2.03663i
$343$	−1.21197e11	−	2.09919e11i	−0.472789	−	0.818894i
$344$	−3.80545e10	+	3.19315e10i	−0.146519	+	0.122944i
$345$	−5.41696e11	+	2.03297e11i	−2.05859	+	0.772584i
$346$	2.31642e10	−	1.31371e11i	0.0868911	−	0.492784i
$347$	−3.98438e10	−	3.34330e10i	−0.147529	−	0.123792i	0.566036	−	0.824381i	$-0.308476\pi$
$347$	−3.98438e10	−	3.34330e10i	−0.147529	−	0.123792i	−0.713565	+	0.700589i	$0.752921\pi$
$348$	−1.62087e10	−	8.68536e10i	−0.0592436	−	0.317454i
$349$	3.52382e11	+	1.28257e11i	1.27145	+	0.462770i	0.887596	−	0.460623i	$-0.152374\pi$
$349$	3.52382e11	+	1.28257e11i	1.27145	+	0.462770i	0.383855	+	0.923393i	$0.374596\pi$
$350$	−5.76998e11			−2.05527
$351$	−3.40109e10	−	2.68477e10i	−0.119601	−	0.0944115i
$352$	5.00064e11			1.73614
$353$	3.41596e11	+	1.24331e11i	1.17092	+	0.426179i	0.852986	−	0.521934i	$-0.174789\pi$
$353$	3.41596e11	+	1.24331e11i	1.17092	+	0.426179i	0.317932	+	0.948113i	$0.397011\pi$
$354$	−4.26358e11	+	3.65058e11i	−1.44298	+	1.23551i
$355$	1.01839e11	+	8.54530e10i	0.340319	+	0.285561i
$356$	−6.62433e10	+	3.75684e11i	−0.218583	+	1.23965i
$357$	4.03510e10	−	2.42977e11i	0.131476	−	0.791695i
$358$	6.48199e11	−	5.43903e11i	2.08562	−	1.75004i
$359$	8.64589e10	+	1.49751e11i	0.274716	+	0.475823i	0.970064	−	0.242851i	$-0.0780827\pi$
$359$	8.64589e10	+	1.49751e11i	0.274716	+	0.475823i	−0.695347	+	0.718674i	$0.744749\pi$
$360$	1.73699e11	+	5.93283e10i	0.545050	+	0.186166i
$361$	−2.33754e11	+	4.04874e11i	−0.724398	+	1.25469i
$362$	3.98911e10	+	2.26234e11i	0.122092	+	0.692419i
$363$	−1.62587e11	+	1.62035e9i	−0.491481	+	0.00489810i
$364$	3.25136e10	−	1.18340e10i	0.0970753	−	0.0353325i
$365$	−2.03857e11	+	7.41978e10i	−0.601184	+	0.218813i
$366$	2.15408e11	−	2.14676e9i	0.627476	−	0.00625343i
$367$	2.71277e10	+	1.53849e11i	0.0780577	+	0.442687i	0.998640	+	0.0521384i	$0.0166037\pi$
$367$	2.71277e10	+	1.53849e11i	0.0780577	+	0.442687i	−0.920582	+	0.390549i	$0.872285\pi$
$368$	1.55515e11	−	2.69360e11i	0.442035	−	0.765627i
$369$	−3.56182e11	−	1.21657e11i	−1.00012	−	0.341600i
$370$	−1.41660e11	−	2.45362e11i	−0.392951	−	0.680611i
$371$	9.71307e10	−	8.15023e10i	0.266179	−	0.223351i
$372$	8.33544e9	−	5.01926e10i	0.0225676	−	0.135893i
$373$	8.23194e10	−	4.66857e11i	0.220198	−	1.24880i	−0.651458	−	0.758684i	$-0.725842\pi$
$373$	8.23194e10	−	4.66857e11i	0.220198	−	1.24880i	0.871656	−	0.490118i	$-0.163046\pi$
$374$	−7.52339e11	−	6.31287e11i	−1.98834	−	1.66842i
$375$	7.93138e11	−	6.79105e11i	2.07113	−	1.77336i
$376$	−9.53028e9	−	3.46874e9i	−0.0245901	−	0.00895006i
$377$	1.59741e10			0.0407267
$378$	2.59789e11	+	2.05074e11i	0.654497	+	0.516650i
$379$	−1.21983e11			−0.303685			−0.151843	−	0.988405i	$-0.548521\pi$
$379$	−1.21983e11			−0.303685			−0.151843	+	0.988405i	$0.548521\pi$
$380$	1.34424e12	+	4.89263e11i	3.30712	+	1.20369i
$381$	−5.01632e10	−	2.68797e11i	−0.121962	−	0.653525i
$382$	−6.78800e11	−	5.69581e11i	−1.63101	−	1.36858i
$383$	−1.37659e11	+	7.80702e11i	−0.326896	+	1.85392i	0.169106	+	0.985598i	$0.445912\pi$
$383$	−1.37659e11	+	7.80702e11i	−0.326896	+	1.85392i	−0.496002	+	0.868322i	$0.665199\pi$
$384$	−2.41516e11	+	9.06402e10i	−0.566832	+	0.212731i
$385$	−4.21252e11	+	3.53472e11i	−0.977167	+	0.819940i
$386$	1.95886e11	+	3.39285e11i	0.449118	+	0.777896i
$387$	1.31645e11	−	2.38889e11i	0.298336	−	0.541372i
$388$	−2.31215e11	+	4.00477e11i	−0.517933	+	0.897087i
$389$	−7.78810e10	−	4.41685e11i	−0.172448	−	0.978002i	−0.941048	−	0.338273i	$-0.890157\pi$
$389$	−7.78810e10	−	4.41685e11i	−0.172448	−	0.978002i	0.768600	−	0.639730i	$-0.220954\pi$
$390$	−9.46131e10	+	1.67713e11i	−0.207091	+	0.367092i
$391$	−7.33716e11	+	2.67051e11i	−1.58757	+	0.577828i
$392$	9.31336e10	−	3.38979e10i	0.199214	−	0.0725078i
$393$	−1.38271e11	−	2.34073e11i	−0.292390	−	0.494977i
$394$	−1.47566e11	−	8.36888e11i	−0.308499	−	1.74958i
$395$	−2.90136e11	+	5.02530e11i	−0.599672	+	1.03866i
$396$	6.73482e11	−	2.60442e11i	1.37625	−	0.532210i
$397$	3.92513e11	+	6.79852e11i	0.793043	+	1.37359i	0.924075	+	0.382212i	$0.124838\pi$
$397$	3.92513e11	+	6.79852e11i	0.793043	+	1.37359i	−0.131032	+	0.991378i	$0.541829\pi$
$398$	2.92224e11	−	2.45205e11i	0.583771	−	0.489842i
$399$	3.43373e11	+	2.82341e11i	0.678247	+	0.557694i
$400$	−1.64009e11	+	9.30140e11i	−0.320330	+	1.81668i
$401$	−4.03427e11	−	3.38515e11i	−0.779139	−	0.653775i	0.163893	−	0.986478i	$-0.447595\pi$
$401$	−4.03427e11	−	3.38515e11i	−0.779139	−	0.653775i	−0.943032	+	0.332703i	$0.892039\pi$
$402$	1.70439e11	+	6.01181e10i	0.325501	+	0.114812i
$403$	8.64424e9	+	3.14624e9i	0.0163250	+	0.00594182i
$404$	−1.13334e12			−2.11663
$405$	−1.00703e12	+	4.01642e10i	−1.85992	+	0.0741808i
$406$	−1.22016e11			−0.222870
$407$	−1.80501e11	−	6.56969e10i	−0.326065	−	0.118678i
$408$	2.33597e11	+	8.23955e10i	0.417347	+	0.147209i
$409$	3.77609e11	+	3.16851e11i	0.667248	+	0.559887i	0.912249	−	0.409635i	$-0.134344\pi$
$409$	3.77609e11	+	3.16851e11i	0.667248	+	0.559887i	−0.245002	+	0.969523i	$0.578789\pi$
$410$	−2.90452e11	+	1.64723e12i	−0.507629	+	2.87891i
$411$	8.84065e11	+	7.26929e11i	1.52826	+	1.25662i
$412$	−3.30648e11	+	2.77447e11i	−0.565365	+	0.474398i
$413$	2.12060e11	+	3.67300e11i	0.358661	+	0.621220i
$414$	1.61566e11	−	1.03671e12i	0.270301	−	1.73442i
$415$	4.20222e11	−	7.27846e11i	0.695445	−	1.20455i
$416$	−2.29760e10	−	1.30303e11i	−0.0376144	−	0.213322i
$417$	3.92928e11	+	6.65174e11i	0.636358	+	1.07727i
$418$	1.66567e12	−	6.06255e11i	2.66868	−	0.971320i
$419$	5.93000e11	−	2.15834e11i	0.939921	−	0.342103i	0.173786	−	0.984783i	$-0.444400\pi$
$419$	5.93000e11	−	2.15834e11i	0.939921	−	0.342103i	0.766135	+	0.642680i	$0.222178\pi$
$420$	3.95420e11	−	7.00928e11i	0.620065	−	1.09914i
$421$	−1.90017e11	−	1.07764e12i	−0.294797	−	1.67188i	−0.668025	−	0.744139i	$-0.732860\pi$
$421$	−1.90017e11	−	1.07764e12i	−0.294797	−	1.67188i	0.373228	−	0.927740i	$-0.378251\pi$
$422$	−9.99783e10	+	1.73167e11i	−0.153462	+	0.265803i
$423$	5.56753e10	−	1.10983e9i	0.0845534	−	0.00168549i
$424$	6.37575e10	+	1.10431e11i	0.0958042	+	0.165938i
$425$	1.81632e12	−	1.52407e12i	2.70048	−	2.26597i
$426$	−2.25706e11	+	8.47069e10i	−0.332047	+	0.124617i
$427$	2.82654e10	−	1.60301e11i	0.0411462	−	0.233352i
$428$	−9.74082e11	−	8.17352e11i	−1.40313	−	1.17737i
$429$	2.39502e10	+	1.28336e11i	0.0341390	+	0.182932i
$430$	−1.13904e12	−	4.14575e11i	−1.60668	−	0.584784i
$431$	−2.63914e11			−0.368396			−0.184198	−	0.982889i	$-0.558969\pi$
$431$	−2.63914e11			−0.368396			−0.184198	+	0.982889i	$0.558969\pi$
$432$	4.04429e11	−	3.60497e11i	0.558683	−	0.497995i
$433$	4.28855e11			0.586293			0.293147	−	0.956067i	$-0.405298\pi$
$433$	4.28855e11			0.586293			0.293147	+	0.956067i	$0.405298\pi$
$434$	−6.60282e10	−	2.40323e10i	−0.0893358	−	0.0325156i
$435$	2.82224e11	−	2.41647e11i	0.377913	−	0.323579i
$436$	7.30129e11	+	6.12651e11i	0.967633	+	0.811940i
$437$	2.44713e11	−	1.38784e12i	0.320989	−	1.82042i
$438$	6.44493e10	−	3.88087e11i	0.0836729	−	0.503843i
$439$	3.62891e11	−	3.04502e11i	0.466322	−	0.391290i	−0.379129	−	0.925344i	$-0.623776\pi$
$439$	3.62891e11	−	3.04502e11i	0.466322	−	0.391290i	0.845451	+	0.534053i	$0.179332\pi$
$440$	−2.76514e11	−	4.78936e11i	−0.351706	−	0.609172i
$441$	−4.09819e11	+	3.58037e11i	−0.515962	+	0.450769i
$442$	−1.29929e11	+	2.25044e11i	−0.161922	+	0.280458i
$443$	1.09504e11	+	6.21030e11i	0.135087	+	0.766118i	0.974799	+	0.223085i	$0.0716129\pi$
$443$	1.09504e11	+	6.21030e11i	0.135087	+	0.766118i	−0.839712	+	0.543033i	$0.817276\pi$
$444$	2.81097e11	−	2.80141e9i	0.343268	−	0.00342101i
$445$	−1.50745e12	+	5.48669e11i	−1.82232	+	0.663270i
$446$	−1.16482e10	+	4.23959e9i	−0.0139396	+	0.00507361i
$447$	−3.42200e11	+	3.41036e9i	−0.405411	+	0.00404033i
$448$	1.13323e11	+	6.42688e11i	0.132913	+	0.753788i
$449$	6.40443e11	−	1.10928e12i	0.743656	−	1.28805i	−0.207164	−	0.978306i	$-0.566423\pi$
$449$	6.40443e11	−	1.10928e12i	0.743656	−	1.28805i	0.950820	−	0.309744i	$-0.100243\pi$
$450$	6.15689e11	+	3.12607e12i	0.707791	+	3.59370i
$451$	5.67011e11	+	9.82092e11i	0.645353	+	1.11778i
$452$	−7.05953e11	+	5.92365e11i	−0.795523	+	0.667523i
$453$	−2.05950e11	+	1.24014e12i	−0.229784	+	1.38366i
$454$	−1.71636e11	+	9.73394e11i	−0.189608	+	1.07532i
$455$	1.11460e11	+	9.35263e10i	0.121918	+	0.102302i
$456$	−3.39595e11	+	2.90770e11i	−0.367806	+	0.314925i
$457$	4.01738e11	+	1.46221e11i	0.430844	+	0.156814i	0.548333	−	0.836260i	$-0.315262\pi$
$457$	4.01738e11	+	1.46221e11i	0.430844	+	0.156814i	−0.117490	+	0.993074i	$0.537485\pi$
$458$	7.86567e11			0.835297
$459$	−1.35946e12	+	4.06559e10i	−1.42958	+	0.0427530i
$460$	−2.55119e12			−2.65664
$461$	−1.20936e12	−	4.40169e11i	−1.24710	−	0.453906i	−0.367676	−	0.929954i	$-0.619847\pi$
$461$	−1.20936e12	−	4.40169e11i	−1.24710	−	0.453906i	−0.879419	+	0.476048i	$0.842069\pi$
$462$	−1.82941e11	−	9.80283e11i	−0.186820	−	1.00107i
$463$	−1.37765e12	−	1.15599e12i	−1.39324	−	1.16906i	−0.964010	−	0.265867i	$-0.914342\pi$
$463$	−1.37765e12	−	1.15599e12i	−1.39324	−	1.16906i	−0.429227	−	0.903197i	$-0.641214\pi$
$464$	−3.46825e10	+	1.96694e11i	−0.0347360	+	0.196998i
$465$	2.00318e11	−	7.51789e10i	0.198693	−	0.0745689i
$466$	1.50481e12	−	1.26268e12i	1.47824	−	1.24039i
$467$	−3.75641e11	−	6.50629e11i	−0.365466	−	0.633006i	0.623385	−	0.781915i	$-0.285757\pi$
$467$	−3.75641e11	−	6.50629e11i	−0.365466	−	0.633006i	−0.988851	+	0.148909i	$0.952424\pi$
$468$	−9.88081e10	−	1.63525e11i	−0.0952108	−	0.157572i
$469$	6.82816e10	−	1.18267e11i	0.0651667	−	0.112872i
$470$	−4.29724e10	−	2.43709e11i	−0.0406209	−	0.230372i
$471$	1.98556e11	−	3.51963e11i	0.185904	−	0.329536i
$472$	−4.00806e11	+	1.45881e11i	−0.371702	+	0.135289i
$473$	−7.72245e11	+	2.81074e11i	−0.709382	+	0.258194i
$474$	−5.35192e11	−	9.06007e11i	−0.486975	−	0.824383i
$475$	7.43108e11	+	4.21438e12i	0.669778	+	3.79850i
$476$	5.43019e11	−	9.40536e11i	0.484824	−	0.839739i
$477$	−5.45208e11	−	4.39268e11i	−0.482202	−	0.388505i
$478$	1.03498e12	+	1.79264e12i	0.906792	+	1.57061i
$479$	−8.14626e11	+	6.83552e11i	−0.707047	+	0.593283i	−0.923769	−	0.382951i	$-0.874908\pi$
$479$	−8.14626e11	+	6.83552e11i	−0.707047	+	0.593283i	0.216722	+	0.976233i	$0.430464\pi$
$480$	−2.37709e12	−	1.95458e12i	−2.04390	−	1.68061i
$481$	−8.82555e9	+	5.00522e10i	−0.00751777	+	0.0426354i
$482$	4.98732e11	+	4.18486e11i	0.420877	+	0.353158i
$483$	−7.47662e11	−	2.63719e11i	−0.625091	−	0.220485i
$484$	−6.73700e11	−	2.45207e11i	−0.558036	−	0.203109i
$485$	−1.94461e12			−1.59586
$486$	8.33840e11	−	1.62631e12i	0.677984	−	1.32233i
$487$	−1.00746e12			−0.811608			−0.405804	−	0.913960i	$-0.633008\pi$
$487$	−1.00746e12			−0.811608			−0.405804	+	0.913960i	$0.633008\pi$
$488$	1.53826e11	+	5.59880e10i	0.122783	+	0.0446895i
$489$	1.48967e12	+	5.25444e11i	1.17815	+	0.415563i
$490$	1.85257e12	+	1.55449e12i	1.45175	+	1.21816i
$491$	−6.54098e10	+	3.70957e11i	−0.0507898	+	0.288043i	−0.999615	−	0.0277597i	$-0.991163\pi$
$491$	−6.54098e10	+	3.70957e11i	−0.0507898	+	0.288043i	0.948825	+	0.315803i	$0.102274\pi$
$492$	−1.28190e12	−	1.05405e12i	−0.986307	−	0.810998i
$493$	3.84092e11	−	3.22291e11i	0.292836	−	0.245718i
$494$	−2.34505e11	−	4.06174e11i	−0.177166	−	0.306861i
$495$	2.36455e12	+	1.90509e12i	1.77021	+	1.42624i
$496$	−5.75090e10	+	9.96086e10i	−0.0426647	+	0.0738974i
$497$	3.16321e10	+	1.79395e11i	0.0232555	+	0.131888i
$498$	7.75153e11	+	1.31223e12i	0.564749	+	0.956043i
$499$	−3.00403e11	+	1.09338e11i	−0.216896	+	0.0789436i	−0.448183	−	0.893942i	$-0.647929\pi$
$499$	−3.00403e11	+	1.09338e11i	−0.216896	+	0.0789436i	0.231287	+	0.972886i	$0.425706\pi$
$500$	4.32635e12	−	1.57466e12i	3.09569	−	1.12674i
$501$	9.41932e11	−	1.66968e12i	0.667959	−	1.18403i
$502$	−9.53893e10	−	5.40979e11i	−0.0670398	−	0.380202i
$503$	8.06862e11	−	1.39753e12i	0.562009	−	0.973428i	−0.435312	−	0.900280i	$-0.643362\pi$
$503$	8.06862e11	−	1.39753e12i	0.562009	−	0.973428i	0.997321	−	0.0731487i	$-0.0233048\pi$
$504$	1.30072e11	+	2.15265e11i	0.0897935	+	0.148606i
$505$	−2.38297e12	−	4.12742e12i	−1.63045	−	2.82402i
$506$	−2.42164e12	+	2.03200e12i	−1.64222	+	1.37799i
$507$	−1.36057e12	+	5.10617e11i	−0.914500	+	0.343210i
$508$	2.09364e11	−	1.18736e12i	0.139481	−	0.791036i
$509$	−1.69299e11	−	1.42059e11i	−0.111796	−	0.0938078i	0.585176	−	0.810906i	$-0.301025\pi$
$509$	−1.69299e11	−	1.42059e11i	−0.111796	−	0.0938078i	−0.696972	+	0.717098i	$0.745470\pi$
$510$	1.10881e12	+	5.94151e12i	0.725757	+	3.88894i
$511$	−2.79334e11	−	1.01669e11i	−0.181230	−	0.0659623i
$512$	2.01445e12			1.29551
$513$	1.16327e12	−	2.16160e12i	0.741571	−	1.37799i
$514$	2.78818e12			1.76192
$515$	−1.70563e12	−	6.20799e11i	−1.06845	−	0.388883i
$516$	9.13565e11	−	7.82218e11i	0.567304	−	0.485740i
$517$	−1.28526e11	−	1.07846e11i	−0.0791195	−	0.0663891i
$518$	6.74131e10	−	3.82319e11i	0.0411397	−	0.233315i
$519$	−9.11838e10	+	5.49071e11i	−0.0551651	+	0.332182i
$520$	−1.12093e11	+	9.40572e10i	−0.0672301	+	0.0564127i
$521$	1.21058e12	+	2.09679e12i	0.719820	+	1.24676i	0.961071	+	0.276302i	$0.0891090\pi$
$521$	1.21058e12	+	2.09679e12i	0.719820	+	1.24676i	−0.241251	+	0.970463i	$0.577558\pi$
$522$	1.30198e11	+	6.61061e11i	0.0767516	+	0.389695i
$523$	5.30597e11	−	9.19021e11i	0.310104	−	0.537116i	−0.668281	−	0.743909i	$-0.732970\pi$
$523$	5.30597e11	−	9.19021e11i	0.310104	−	0.537116i	0.978385	+	0.206794i	$0.0663029\pi$
$524$	−2.08157e11	−	1.18052e12i	−0.120615	−	0.684040i
$525$	2.40737e12	−	2.39918e10i	1.38301	−	0.0137831i
$526$	1.87540e12	−	6.82589e11i	1.06821	−	0.388798i
$527$	2.71327e11	−	9.87548e10i	0.153230	−	0.0557713i
$528$	−1.63225e12	+	1.62670e10i	−0.913974	+	0.00910866i
$529$	1.23657e11	+	7.01293e11i	0.0686543	+	0.389358i
$530$	−1.55572e12	+	2.69458e12i	−0.856425	+	1.48337i
$531$	1.76368e12	−	1.54083e12i	0.962707	−	0.841066i
$532$	9.80075e11	+	1.69754e12i	0.530465	+	0.918793i
$533$	2.29855e11	−	1.92871e11i	0.123362	−	0.103513i
$534$	4.76582e11	−	2.86978e12i	0.253631	−	1.52726i
$535$	9.28536e11	−	5.26599e12i	0.490012	−	2.77900i
$536$	1.05207e11	+	8.82795e10i	0.0550560	+	0.0461975i
$537$	−2.68181e12	+	2.29624e12i	−1.39169	+	1.19161i
$538$	4.04348e11	+	1.47171e11i	0.208082	+	0.0757357i
$539$	1.63960e12			0.836736
$540$	−4.21943e12	−	1.39438e12i	−2.13541	−	0.705684i
$541$	−1.20862e12			−0.606597			−0.303299	−	0.952896i	$-0.598088\pi$
$541$	−1.20862e12			−0.606597			−0.303299	+	0.952896i	$0.598088\pi$
$542$	−1.78598e12	−	6.50043e11i	−0.888954	−	0.323553i
$543$	−1.75842e11	−	9.42239e11i	−0.0868005	−	0.465117i
$544$	−3.18144e12	−	2.66954e12i	−1.55750	−	1.30690i
$545$	−6.95990e11	+	3.94715e12i	−0.337924	+	1.91646i
$546$	−2.47030e11	+	9.27097e10i	−0.118955	+	0.0446435i
$547$	−1.95325e12	+	1.63897e12i	−0.932855	+	0.782758i	−0.976328	−	0.216296i	$-0.930602\pi$
$547$	−1.95325e12	+	1.63897e12i	−0.932855	+	0.782758i	0.0434726	+	0.999055i	$0.486158\pi$
$548$	2.52335e12	+	4.37057e12i	1.19527	+	2.07026i
$549$	−8.98641e11	+	1.79135e10i	−0.422193	+	0.00841598i
$550$	4.79977e12	−	8.31345e12i	2.23660	−	3.87391i
$551$	1.57143e11	+	8.91203e11i	0.0726295	+	0.411903i
$552$	3.91754e11	−	6.94429e11i	0.179592	−	0.318348i
$553$	−7.47163e11	+	2.71945e11i	−0.339744	+	0.123657i
$554$	4.98594e11	−	1.81473e11i	0.224881	−	0.0818500i
$555$	6.01237e11	+	1.01781e12i	0.268985	+	0.455354i
$556$	5.91528e11	+	3.35472e12i	0.262506	+	1.48874i
$557$	−1.15289e12	+	1.99686e12i	−0.507502	+	0.879020i	0.492460	+	0.870335i	$0.336098\pi$
$557$	−1.15289e12	+	1.99686e12i	−0.507502	+	0.879020i	−0.999962	+	0.00868487i	$0.997235\pi$
$558$	−5.97467e10	+	3.83372e11i	−0.0260892	+	0.167404i
$559$	1.08722e11	+	1.88312e11i	0.0470939	+	0.0815690i
$560$	−1.39362e12	+	1.16939e12i	−0.598824	+	0.502473i
$561$	3.16517e12	+	2.60259e12i	1.34916	+	1.10936i
$562$	−7.63100e11	+	4.32776e12i	−0.322677	+	1.82999i
$563$	6.53231e11	+	5.48126e11i	0.274018	+	0.229928i	0.769432	−	0.638729i	$-0.220539\pi$
$563$	6.53231e11	+	5.48126e11i	0.274018	+	0.229928i	−0.495414	+	0.868657i	$0.664984\pi$
$564$	2.31557e11	+	8.16759e10i	0.0963612	+	0.0339890i
$565$	−3.64162e12	−	1.32544e12i	−1.50341	−	0.547195i
$566$	3.33784e12			1.36707
$567$	−1.09242e12	−	8.44810e11i	−0.443882	−	0.343270i
$568$	−1.83196e11			−0.0738498
$569$	4.00671e12	+	1.45832e12i	1.60245	+	0.583242i	0.979926	−	0.199362i	$-0.0638870\pi$
$569$	4.00671e12	+	1.45832e12i	1.60245	+	0.583242i	0.622519	+	0.782604i	$0.286109\pi$
$570$	−1.02875e13	−	3.62867e12i	−4.08202	−	1.43983i
$571$	−1.81900e11	−	1.52632e11i	−0.0716093	−	0.0600873i	0.606280	−	0.795251i	$-0.292661\pi$
$571$	−1.81900e11	−	1.52632e11i	−0.0716093	−	0.0600873i	−0.677890	+	0.735164i	$0.737105\pi$
$572$	−9.99598e10	+	5.66900e11i	−0.0390430	+	0.221424i
$573$	2.85579e12	+	2.34819e12i	1.10670	+	0.909993i
$574$	−1.75572e12	+	1.47323e12i	−0.675076	+	0.566456i
$575$	−3.81596e12	−	6.60943e12i	−1.45579	−	2.52150i
$576$	3.36104e12	−	1.29975e12i	1.27225	−	0.491992i
$577$	−1.95171e12	+	3.38047e12i	−0.733035	+	1.26965i	0.222545	+	0.974922i	$0.428564\pi$
$577$	−1.95171e12	+	3.38047e12i	−0.733035	+	1.26965i	−0.955580	+	0.294732i	$0.904770\pi$
$578$	7.23943e11	+	4.10568e12i	0.269792	+	1.53007i
$579$	−8.31388e11	−	1.40743e12i	−0.307433	−	0.520442i
$580$	1.53945e12	−	5.60316e11i	0.564860	−	0.205592i
$581$	1.08217e12	−	3.93876e11i	0.394004	−	0.143406i
$582$	1.73268e12	−	3.07137e12i	0.625985	−	1.10963i
$583$	3.66310e11	+	2.07745e12i	0.131323	+	0.744769i
$584$	1.49474e11	−	2.58897e11i	0.0531751	−	0.0921021i
$585$	3.87773e11	−	7.03668e11i	0.136891	−	0.248408i
$586$	−2.60637e12	−	4.51436e12i	−0.913053	−	1.58145i
$587$	1.13503e12	−	9.52399e11i	0.394579	−	0.331091i	−0.423815	−	0.905749i	$-0.639309\pi$
$587$	1.13503e12	−	9.52399e11i	0.394579	−	0.331091i	0.818394	+	0.574658i	$0.194865\pi$
$588$	−2.24651e12	+	8.43110e11i	−0.775015	+	0.290861i
$589$	−9.04943e10	+	5.13218e11i	−0.0309815	+	0.175705i
$590$	−7.97264e12	−	6.68984e12i	−2.70874	−	2.27291i
$591$	6.50476e11	+	3.48555e12i	0.219325	+	1.17524i
$592$	−5.97149e11	−	2.17344e11i	−0.199818	−	0.0727279i
$593$	7.34022e11			0.243760			0.121880	−	0.992545i	$-0.461108\pi$
$593$	7.34022e11			0.243760			0.121880	+	0.992545i	$0.461108\pi$
$594$	−5.11578e12	+	2.03716e12i	−1.68606	+	0.671407i
$595$	4.56701e12			1.49384
$596$	−1.41795e12	−	5.16090e11i	−0.460311	−	0.167539i
$597$	−1.20903e12	+	1.03520e12i	−0.389540	+	0.333534i
$598$	6.40748e11	+	5.37651e11i	0.204895	+	0.171928i
$599$	−6.43746e11	+	3.65087e12i	−0.204312	+	1.15871i	0.694206	+	0.719776i	$0.255755\pi$
$599$	−6.43746e11	+	3.65087e12i	−0.204312	+	1.15871i	−0.898519	+	0.438936i	$0.855356\pi$
$600$	−3.96646e11	+	2.38844e12i	−0.124946	+	0.752374i
$601$	4.69293e12	−	3.93784e12i	1.46727	−	1.23118i	0.548641	−	0.836058i	$-0.315146\pi$
$601$	4.69293e12	−	3.93784e12i	1.46727	−	1.23118i	0.918627	−	0.395125i	$-0.129299\pi$
$602$	−8.30463e11	−	1.43840e12i	−0.257713	−	0.446372i
$603$	−7.13609e11	−	2.43739e11i	−0.219803	−	0.0750753i
$604$	−2.77155e12	+	4.80046e12i	−0.847337	+	1.46763i
$605$	−5.23525e11	−	2.96906e12i	−0.158869	−	0.900989i
$606$	8.64219e12	−	8.61281e10i	2.60314	−	0.0259429i
$607$	3.26552e12	−	1.18855e12i	0.976346	−	0.355361i	0.195927	−	0.980618i	$-0.437228\pi$
$607$	3.26552e12	−	1.18855e12i	0.976346	−	0.355361i	0.780418	+	0.625258i	$0.215006\pi$
$608$	7.04368e12	−	2.56369e12i	2.09042	−	0.760850i
$609$	5.09079e11	−	5.07349e9i	0.149971	−	0.00149461i
$610$	6.93606e11	+	3.93364e12i	0.202828	+	1.15030i
$611$	−2.21965e10	+	3.84455e10i	−0.00644317	+	0.0111599i
$612$	−5.67508e12	−	1.93837e12i	−1.63527	−	0.558541i
$613$	−2.88454e11	−	4.99616e11i	−0.0825095	−	0.142911i	0.821818	−	0.569750i	$-0.192960\pi$
$613$	−2.88454e11	−	4.99616e11i	−0.0825095	−	0.142911i	−0.904327	+	0.426840i	$0.859627\pi$
$614$	−3.38957e12	+	2.84419e12i	−0.962470	+	0.807608i
$615$	1.14334e12	−	6.88470e12i	0.322282	−	1.94065i
$616$	1.31588e11	−	7.46271e11i	0.0368216	−	0.208825i
$617$	−3.26064e12	−	2.73600e12i	−0.905774	−	0.760035i	0.0655362	−	0.997850i	$-0.479124\pi$
$617$	−3.26064e12	−	2.73600e12i	−0.905774	−	0.760035i	−0.971310	+	0.237815i	$0.923569\pi$
$618$	2.50024e12	−	2.14077e12i	0.689499	−	0.590367i
$619$	1.00425e11	+	3.65518e10i	0.0274938	+	0.0100069i	0.355730	−	0.934589i	$-0.384232\pi$
$619$	1.00425e11	+	3.65518e10i	0.0274938	+	0.0100069i	−0.328237	+	0.944596i	$0.606454\pi$
$620$	9.43423e11			0.256415
$621$	−6.30982e11	+	4.33209e12i	−0.170257	+	1.16892i
$622$	4.14811e12			1.11120
$623$	−2.06558e12	−	7.51811e11i	−0.549347	−	0.199946i
$624$	7.92341e10	+	4.24573e11i	0.0209210	+	0.112104i
$625$	7.62847e12	+	6.40104e12i	1.99976	+	1.67799i
$626$	−1.10501e11	+	6.26683e11i	−0.0287596	+	0.163104i
$627$	−6.92435e12	+	2.59869e12i	−1.78927	+	0.671507i
$628$	1.36497e12	−	1.14534e12i	0.350190	−	0.293844i
$629$	7.97641e11	+	1.38155e12i	0.203179	+	0.351917i
$630$	−2.96197e12	+	5.37490e12i	−0.749114	+	1.35937i
$631$	−2.03298e11	+	3.52123e11i	−0.0510507	+	0.0884225i	−0.890422	−	0.455137i	$-0.849590\pi$
$631$	−2.03298e11	+	3.52123e11i	−0.0510507	+	0.0884225i	0.839371	+	0.543559i	$0.182924\pi$
$632$	−1.38854e11	−	7.87480e11i	−0.0346204	−	0.196342i
$633$	4.09931e11	−	7.26650e11i	0.101483	−	0.179891i
$634$	−2.23145e12	+	8.12180e11i	−0.548510	+	0.199641i
$635$	4.76435e12	−	1.73408e12i	1.16285	−	0.423241i
$636$	−1.57016e12	−	2.65807e12i	−0.380528	−	0.644182i
$637$	−7.53331e10	−	4.27235e11i	−0.0181284	−	0.102811i
$638$	1.01500e12	−	1.75802e12i	0.242533	−	0.420080i
$639$	9.38173e11	−	3.62801e11i	0.222602	−	0.0860824i
$640$	−2.39160e12	−	4.14237e12i	−0.563480	−	0.975976i
$641$	2.18989e12	−	1.83753e12i	0.512343	−	0.429907i	−0.349610	−	0.936895i	$-0.613686\pi$
$641$	2.18989e12	−	1.83753e12i	0.512343	−	0.429907i	0.861953	+	0.506989i	$0.169241\pi$
$642$	7.48988e12	+	6.15861e12i	1.74007	+	1.43079i
$643$	−9.46916e11	+	5.37023e12i	−0.218455	+	1.23892i	0.656354	+	0.754453i	$0.272098\pi$
$643$	−9.46916e11	+	5.37023e12i	−0.218455	+	1.23892i	−0.874809	+	0.484467i	$0.839013\pi$
$644$	−2.67790e12	−	2.24703e12i	−0.613491	−	0.514780i
$645$	4.76955e12	+	1.68234e12i	1.08507	+	0.382732i
$646$	−1.38335e13	−	5.03500e12i	−3.12527	−	1.13750i
$647$	2.37347e11			0.0532495			0.0266247	−	0.999645i	$-0.491524\pi$
$647$	2.37347e11			0.0532495			0.0266247	+	0.999645i	$0.491524\pi$
$648$	1.02747e12	−	9.34403e11i	0.228920	−	0.208184i
$649$	−7.05612e12			−1.56122
$650$	−2.38679e12	−	8.68721e11i	−0.524450	−	0.190884i
$651$	2.76484e11	+	9.75226e10i	0.0603330	+	0.0212809i
$652$	5.33556e12	+	4.47707e12i	1.15629	+	0.970241i
$653$	4.34079e11	−	2.46178e12i	0.0934241	−	0.529834i	−0.901795	−	0.432165i	$-0.857750\pi$
$653$	4.34079e11	−	2.46178e12i	0.0934241	−	0.529834i	0.995219	−	0.0976699i	$-0.0311389\pi$
$654$	−5.61409e12	−	4.61623e12i	−1.19999	−	0.986704i
$655$	3.86155e12	−	3.24023e12i	0.819740	−	0.687843i
$656$	1.87584e12	+	3.24904e12i	0.395483	+	0.684996i
$657$	−2.52760e11	+	1.62186e12i	−0.0529254	+	0.339602i
$658$	1.69546e11	−	2.93662e11i	0.0352591	−	0.0610706i
$659$	−1.33721e12	−	7.58372e12i	−0.276196	−	1.56638i	−0.735138	−	0.677917i	$-0.762883\pi$
$659$	−1.33721e12	−	7.58372e12i	−0.276196	−	1.56638i	0.458943	−	0.888466i	$-0.348228\pi$
$660$	6.80972e12	+	1.15279e13i	1.39695	+	2.36485i
$661$	5.54348e12	−	2.01766e12i	1.12947	−	0.411095i	0.291372	−	0.956610i	$-0.405888\pi$
$661$	5.54348e12	−	2.01766e12i	1.12947	−	0.411095i	0.838101	+	0.545515i	$0.183666\pi$
$662$	2.99043e12	−	1.08843e12i	0.605164	−	0.220262i
$663$	5.32737e11	−	9.44337e11i	0.107078	−	0.189809i
$664$	2.01111e11	+	1.14056e12i	0.0401495	+	0.227699i
$665$	−4.12141e12	+	7.13850e12i	−0.817238	+	1.41550i
$666$	−2.14326e12	+	4.27238e10i	−0.422126	+	0.00841465i
$667$	−8.06950e11	−	1.39768e12i	−0.157863	−	0.273427i
$668$	6.47529e12	−	5.43342e12i	1.25825	−	1.05579i
$669$	4.84225e10	−	1.81729e10i	0.00934609	−	0.00350756i
$670$	−5.81918e11	+	3.30022e12i	−0.111564	+	0.632713i
$671$	2.07451e12	+	1.74072e12i	0.395060	+	0.331495i
$672$	−7.73609e11	−	4.14535e12i	−0.146339	−	0.784151i
$673$	8.39218e11	+	3.05450e11i	0.157691	+	0.0573949i	0.419660	−	0.907682i	$-0.362149\pi$
$673$	8.39218e11	+	3.05450e11i	0.157691	+	0.0573949i	−0.261969	+	0.965076i	$0.584372\pi$
$674$	−8.51658e11			−0.158963
$675$	−2.69877e12	−	1.30170e13i	−0.500380	−	2.41349i
$676$	−6.40776e12			−1.18017
$677$	8.76272e12	+	3.18937e12i	1.60321	+	0.583520i	0.980080	−	0.198601i	$-0.0636398\pi$
$677$	8.76272e12	+	3.18937e12i	1.60321	+	0.583520i	0.623127	+	0.782121i	$0.285862\pi$
$678$	5.33816e12	−	4.57067e12i	0.970192	−	0.830703i
$679$	−2.04120e12	−	1.71277e12i	−0.368529	−	0.309233i
$680$	−7.97555e11	+	4.52316e12i	−0.143044	+	0.811244i
$681$	6.75628e11	−	4.06835e12i	0.120378	−	0.724864i
$682$	8.95516e11	−	7.51427e11i	0.158505	−	0.133002i
$683$	4.46954e11	+	7.74148e11i	0.0785905	+	0.136123i	0.902642	−	0.430392i	$-0.141625\pi$
$683$	4.46954e11	+	7.74148e11i	0.0785905	+	0.136123i	−0.824052	+	0.566515i	$0.808291\pi$
$684$	8.15115e12	−	7.12123e12i	1.42386	−	1.24395i
$685$	−1.06112e13	+	1.83791e13i	−1.84144	+	3.18946i
$686$	1.41530e12	+	8.02655e12i	0.244000	+	1.38379i
$687$	−3.28173e12	+	3.27057e10i	−0.562079	+	0.00560168i
$688$	−2.55481e12	+	9.29875e11i	−0.434721	+	0.158226i
$689$	5.24496e11	−	1.90901e11i	0.0886657	−	0.0322717i
$690$	1.94538e13	−	1.93877e11i	3.26726	−	0.0325616i
$691$	−5.57943e11	−	3.16425e12i	−0.0930977	−	0.527983i	−0.995314	−	0.0966987i	$-0.969172\pi$
$691$	−5.57943e11	−	3.16425e12i	−0.0930977	−	0.527983i	0.902216	−	0.431284i	$-0.141939\pi$
$692$	−1.22710e12	+	2.12539e12i	−0.203424	+	0.352340i
$693$	8.04032e11	+	4.08235e12i	0.132426	+	0.672374i
$694$	8.74448e11	+	1.51459e12i	0.143092	+	0.247843i
$695$	−1.09735e13	+	9.20787e12i	−1.78408	+	1.49702i
$696$	−8.38778e10	+	5.05077e11i	−0.0135489	+	0.0815861i
$697$	1.63544e12	−	9.27506e12i	0.262475	−	1.48857i
$698$	−9.65915e12	−	8.10499e12i	−1.54024	−	1.29242i
$699$	−6.22588e12	+	5.33076e12i	−0.986401	+	0.844582i
$700$	9.97521e12	+	3.63068e12i	1.57029	+	0.571540i
$701$	−1.16166e12			−0.181696			−0.0908482	−	0.995865i	$-0.528958\pi$
$701$	−1.16166e12			−0.181696			−0.0908482	+	0.995865i	$0.528958\pi$
$702$	7.65878e11	+	1.23943e12i	0.119026	+	0.192622i
$703$	−2.87926e12			−0.444613
$704$	−1.02026e13	−	3.71344e12i	−1.56543	−	0.569770i
$705$	1.89424e11	+	1.01502e12i	0.0288791	+	0.154747i
$706$	−9.36349e12	−	7.85690e12i	−1.41846	−	1.19023i
$707$	1.13401e12	−	6.43129e12i	0.170698	−	0.968078i
$708$	9.66799e12	−	3.62837e12i	1.44606	−	0.542703i
$709$	−1.31174e11	+	1.10068e11i	−0.0194957	+	0.0163589i	−0.652483	−	0.757803i	$-0.726273\pi$
$709$	−1.31174e11	+	1.10068e11i	−0.0194957	+	0.0163589i	0.632988	+	0.774162i	$0.281828\pi$
$710$	−2.23505e12	−	3.87121e12i	−0.330084	−	0.571722i
$711$	2.27061e12	+	3.75781e12i	0.333219	+	0.551469i
$712$	1.10531e12	−	1.91446e12i	0.161185	−	0.279181i
$713$	−1.61389e11	−	9.15280e11i	−0.0233867	−	0.132633i
$714$	−4.06926e12	+	7.21323e12i	−0.585968	+	1.03869i
$715$	−2.27472e12	+	8.27930e11i	−0.325500	+	0.118472i
$716$	−1.46286e13	+	5.32436e12i	−2.08014	+	0.757109i
$717$	−4.39272e12	−	7.43627e12i	−0.620722	−	1.05080i
$718$	−1.00964e12	−	5.72595e12i	−0.141777	−	0.804059i
$719$	2.70568e12	−	4.68638e12i	0.377569	−	0.653969i	−0.613139	−	0.789975i	$-0.710093\pi$
$719$	2.70568e12	−	4.68638e12i	0.377569	−	0.653969i	0.990708	+	0.136006i	$0.0434267\pi$
$720$	7.82260e12	+	6.30258e12i	1.08481	+	0.874022i
$721$	−1.24356e12	−	2.15391e12i	−0.171380	−	0.296838i
$722$	1.20420e13	−	1.01045e13i	1.64924	−	1.38387i
$723$	−2.09822e12	−	1.72528e12i	−0.285581	−	0.234821i
$724$	7.33902e11	−	4.16216e12i	0.0992692	−	0.562983i
$725$	3.75427e12	+	3.15021e12i	0.504667	+	0.423466i
$726$	5.15587e12	+	1.81860e12i	0.688790	+	0.242953i
$727$	7.61955e12	+	2.77329e12i	1.01164	+	0.368205i	0.794061	−	0.607838i	$-0.207963\pi$
$727$	7.61955e12	+	2.77329e12i	1.01164	+	0.368205i	0.217575	+	0.976044i	$0.430185\pi$
$728$	−2.00504e11			−0.0264565
$729$	−3.41134e12	+	6.82001e12i	−0.447354	+	0.894357i
$730$	7.29451e12			0.950700
$731$	6.41356e12	+	2.33434e12i	0.830751	+	0.302369i
$732$	−3.73750e12	−	1.31831e12i	−0.481151	−	0.169714i
$733$	−6.94762e11	−	5.82975e11i	−0.0888932	−	0.0745902i	0.597258	−	0.802049i	$-0.296257\pi$
$733$	−6.94762e11	−	5.82975e11i	−0.0888932	−	0.0745902i	−0.686151	+	0.727459i	$0.740701\pi$
$734$	9.12158e11	−	5.17310e12i	0.115995	−	0.657838i
$735$	−7.79396e12	−	6.40864e12i	−0.985065	−	0.809977i
$736$	−1.02405e13	+	8.59276e12i	−1.28638	+	1.07940i
$737$	1.13600e12	+	1.96762e12i	0.141833	+	0.245661i
$738$	9.85512e12	+	7.94016e12i	1.22295	+	0.985317i
$739$	−6.09465e11	+	1.05562e12i	−0.0751707	+	0.130199i	−0.901160	−	0.433486i	$-0.857284\pi$
$739$	−6.09465e11	+	1.05562e12i	−0.0751707	+	0.130199i	0.825990	+	0.563685i	$0.190617\pi$
$740$	9.05123e11	+	5.13321e12i	0.110960	+	0.629283i
$741$	9.95295e11	+	1.68490e12i	0.121275	+	0.205301i
$742$	−4.00631e12	+	1.45818e12i	−0.485207	+	0.176601i
$743$	−1.34835e13	+	4.90759e12i	−1.62313	+	0.590771i	−0.983975	−	0.178308i	$-0.942938\pi$
$743$	−1.34835e13	+	4.90759e12i	−1.62313	+	0.590771i	−0.639154	+	0.769079i	$0.720715\pi$
$744$	−1.44870e11	+	2.56798e11i	−0.0173340	+	0.0307265i
$745$	−1.10187e12	−	6.24902e12i	−0.131047	−	0.743205i
$746$	−7.97001e12	+	1.38045e13i	−0.942181	+	1.63190i
$747$	−3.28867e12	−	5.44268e12i	−0.386437	−	0.639543i
$748$	9.03423e12	+	1.56477e13i	1.05520	+	1.82766i
$749$	5.61282e12	−	4.70971e12i	0.651648	−	0.546797i
$750$	−3.28705e13	+	1.23362e13i	−3.79342	+	1.42366i
$751$	−1.88726e11	+	1.07032e12i	−0.0216497	+	0.122781i	−0.993717	−	0.111920i	$-0.964300\pi$
$751$	−1.88726e11	+	1.07032e12i	−0.0216497	+	0.122781i	0.972068	+	0.234701i	$0.0754111\pi$
$752$	−4.25201e11	−	3.56786e11i	−0.0484857	−	0.0406844i
$753$	4.20479e11	+	2.25312e12i	0.0476614	+	0.255392i
$754$	−5.04728e11	−	1.83706e11i	−0.0568705	−	0.0206992i
$755$	−2.33098e13			−2.61082
$756$	−3.20086e12	−	5.18002e12i	−0.356385	−	0.576744i
$757$	4.58078e12			0.507000			0.253500	−	0.967335i	$-0.418418\pi$
$757$	4.58078e12			0.507000			0.253500	+	0.967335i	$0.418418\pi$
$758$	3.85428e12	+	1.40284e12i	0.424064	+	0.154347i
$759$	1.00191e13	−	8.57863e12i	1.09583	−	0.938275i
$760$	−6.35022e12	−	5.32847e12i	−0.690442	−	0.579350i
$761$	−1.19014e12	+	6.74963e12i	−0.128638	+	0.729540i	0.850443	+	0.526067i	$0.176334\pi$
$761$	−1.19014e12	+	6.74963e12i	−0.128638	+	0.729540i	−0.979081	+	0.203473i	$0.934777\pi$
$762$	−1.50625e12	+	9.07001e12i	−0.161845	+	0.974564i
$763$	−4.20712e12	+	3.53020e12i	−0.449391	+	0.377084i
$764$	8.15116e12	+	1.41182e13i	0.865564	+	1.49920i
$765$	−4.87325e12	−	2.47432e13i	−0.514449	−	2.61204i
$766$	1.33279e13	−	2.30845e13i	1.39872	−	2.42266i
$767$	3.24201e11	+	1.83863e12i	0.0338248	+	0.191830i
$768$	−4.47691e12	+	4.46169e10i	−0.464358	+	0.00462780i
$769$	2.92512e11	−	1.06466e11i	0.0301630	−	0.0109784i	−0.326895	−	0.945061i	$-0.606002\pi$
$769$	2.92512e11	−	1.06466e11i	0.0301630	−	0.0109784i	0.357058	+	0.934082i	$0.383780\pi$
$770$	1.73752e13	−	6.32407e12i	1.78124	−	0.648318i
$771$	−1.16329e13	+	1.15934e11i	−1.18562	+	0.0118158i
$772$	−1.25160e12	−	7.09817e12i	−0.126820	−	0.719232i
$773$	6.52460e12	−	1.13009e13i	0.657273	−	1.13843i	−0.324045	−	0.946042i	$-0.605043\pi$
$773$	6.52460e12	−	1.13009e13i	0.657273	−	1.13843i	0.981319	−	0.192389i	$-0.0616236\pi$
$774$	−6.90685e12	+	6.03415e12i	−0.691745	+	0.604340i
$775$	1.41113e12	+	2.44415e12i	0.140511	+	0.243372i
$776$	2.05279e12	−	1.72250e12i	0.203220	−	0.170522i
$777$	−2.65366e11	+	1.59792e12i	−0.0261186	+	0.157275i
$778$	−2.61872e12	+	1.48515e13i	−0.256260	+	1.45332i
$779$	1.30216e13	+	1.09264e13i	1.26691	+	1.06306i
$780$	2.69099e12	−	2.30409e12i	0.260307	−	0.222882i
$781$	−2.84787e12	−	1.03654e12i	−0.273899	−	0.0996911i
$782$	2.62542e13			2.51055
$783$	−5.70703e11	−	2.75268e12i	−0.0542603	−	0.261715i
$784$	5.42427e12			0.512766
$785$	7.04111e12	+	2.56275e12i	0.661801	+	0.240876i
$786$	1.67699e12	+	8.98610e12i	0.156722	+	0.839788i
$787$	4.29723e12	+	3.60580e12i	0.399303	+	0.335055i	0.820224	−	0.572042i	$-0.193849\pi$
$787$	4.29723e12	+	3.60580e12i	0.399303	+	0.335055i	−0.420921	+	0.907097i	$0.638293\pi$
$788$	−2.71486e12	+	1.53967e13i	−0.250830	+	1.42253i
$789$	−7.79619e12	+	2.92589e12i	−0.716203	+	0.268789i
$790$	1.49466e13	−	1.25417e13i	1.36527	−	1.14560i
$791$	−2.65508e12	−	4.59873e12i	−0.241148	−	0.417680i
$792$	−4.18357e12	+	8.33952e10i	−0.377819	+	0.00753143i
$793$	3.58268e11	−	6.20539e11i	0.0321721	−	0.0557237i
$794$	−4.58364e12	−	2.59951e13i	−0.409278	−	2.32113i
$795$	6.37875e12	−	1.13071e13i	0.566349	−	1.00392i
$796$	−6.59492e12	+	2.40035e12i	−0.582238	+	0.211917i
$797$	1.56627e13	−	5.70077e12i	1.37501	−	0.500462i	0.454347	−	0.890825i	$-0.349873\pi$
$797$	1.56627e13	−	5.70077e12i	1.37501	−	0.500462i	0.920661	+	0.390363i	$0.127650\pi$
$798$	−7.60247e12	−	1.28699e13i	−0.663654	−	1.12348i
$799$	2.41964e11	+	1.37225e12i	0.0210034	+	0.119116i
$800$	2.02969e13	−	3.51553e13i	1.75197	−	3.03449i
$801$	−1.86908e12	+	1.19932e13i	−0.160428	+	1.02941i
$802$	8.85396e12	+	1.53355e13i	0.755706	+	1.30892i
$803$	3.78850e12	−	3.17893e12i	0.321550	−	0.269812i
$804$	−2.56828e12	−	2.11179e12i	−0.216766	−	0.178237i
$805$	2.55269e12	−	1.44770e13i	0.214248	−	1.21506i
$806$	−2.36947e11	−	1.98822e11i	−0.0197762	−	0.0165942i
$807$	−1.69315e12	−	5.97215e11i	−0.140528	−	0.0495678i
$808$	6.17150e12	+	2.24624e12i	0.509377	+	0.185398i
$809$	−1.54103e13			−1.26486			−0.632428	−	0.774619i	$-0.717942\pi$
$809$	−1.54103e13			−1.26486			−0.632428	+	0.774619i	$0.717942\pi$
$810$	3.22808e13	+	1.03121e13i	2.63488	+	0.841712i
$811$	6.25955e12			0.508100			0.254050	−	0.967191i	$-0.418237\pi$
$811$	6.25955e12			0.508100			0.254050	+	0.967191i	$0.418237\pi$
$812$	2.10943e12	+	7.67770e11i	0.170280	+	0.0619768i
$813$	7.47852e12	+	2.63786e12i	0.600355	+	0.211760i
$814$	4.94771e12	+	4.15162e12i	0.394998	+	0.331442i
$815$	−5.08608e12	+	2.88446e13i	−0.403807	+	2.29010i
$816$	1.04713e13	+	8.61011e12i	0.826789	+	0.679834i
$817$	−9.43651e12	+	7.91817e12i	−0.740990	+	0.621764i
$818$	−8.28733e12	−	1.43541e13i	−0.647180	−	1.12095i
$819$	1.02681e12	−	3.97077e11i	0.0797465	−	0.0308388i
$820$	1.53863e13	−	2.66499e13i	1.18843	−	2.05842i
$821$	3.89053e12	+	2.20643e13i	0.298858	+	1.69491i	0.651095	+	0.758997i	$0.274310\pi$
$821$	3.89053e12	+	2.20643e13i	0.298858	+	1.69491i	−0.352237	+	0.935911i	$0.614579\pi$
$822$	−1.95737e13	−	3.31356e13i	−1.49537	−	2.53146i
$823$	2.18435e13	−	7.95037e12i	1.65967	−	0.604071i	0.669361	−	0.742937i	$-0.266568\pi$
$823$	2.18435e13	−	7.95037e12i	1.65967	−	0.604071i	0.990311	+	0.138865i	$0.0443456\pi$
$824$	2.35040e12	−	8.55477e11i	0.177611	−	0.0646451i
$825$	−1.96800e13	+	3.48851e13i	−1.47905	+	2.62179i
$826$	−2.47638e12	−	1.40442e13i	−0.185100	−	1.04975i
$827$	4.11446e12	−	7.12645e12i	0.305871	−	0.529783i	−0.671584	−	0.740928i	$-0.734386\pi$
$827$	4.11446e12	−	7.12645e12i	0.305871	−	0.529783i	0.977455	+	0.211145i	$0.0677192\pi$
$828$	−9.31650e12	+	1.69061e13i	−0.688836	+	1.24999i
$829$	2.92072e12	+	5.05884e12i	0.214780	+	0.372011i	0.953205	−	0.302326i	$-0.0977631\pi$
$829$	2.92072e12	+	5.05884e12i	0.214780	+	0.372011i	−0.738424	+	0.674336i	$0.764430\pi$
$830$	−2.16481e13	+	1.81649e13i	−1.58332	+	1.32856i
$831$	−2.07270e12	+	7.77879e11i	−0.150776	+	0.0565858i
$832$	−4.98853e11	+	2.82914e12i	−0.0360926	+	0.204691i
$833$	−1.04312e13	−	8.75284e12i	−0.750642	−	0.629864i
$834$	−4.76558e12	−	2.55361e13i	−0.341089	−	1.82771i
$835$	3.34024e13	+	1.21575e13i	2.37788	+	0.865476i
$836$	−3.26111e13			−2.30907
$837$	2.33336e11	−	1.60200e12i	0.0164330	−	0.112823i
$838$	−2.12190e13			−1.48637
$839$	2.65364e12	+	9.65847e11i	0.184890	+	0.0672945i	0.432806	−	0.901487i	$-0.357523\pi$
$839$	2.65364e12	+	9.65847e11i	0.184890	+	0.0672945i	−0.247916	+	0.968782i	$0.579746\pi$
$840$	−3.54243e12	+	3.03312e12i	−0.245496	+	0.210200i
$841$	−1.03192e13	−	8.65885e12i	−0.711319	−	0.596868i
$842$	−6.38925e12	+	3.62352e13i	−0.438072	+	2.48443i
$843$	3.00387e12	−	1.80881e13i	0.204860	−	1.23358i
$844$	2.81807e12	−	2.36464e12i	0.191166	−	0.160407i
$845$	−1.34730e13	−	2.33358e13i	−0.909092	−	1.57459i
$846$	−1.77192e12	−	6.05214e11i	−0.118926	−	0.0406203i
$847$	2.06555e12	−	3.57764e12i	0.137899	−	0.238848i
$848$	1.21186e12	+	6.87279e12i	0.0804768	+	0.456406i
$849$	−1.39262e13	+	1.38789e11i	−0.919915	+	0.00916788i
$850$	−7.49169e13	+	2.72675e13i	−4.92260	+	1.79168i
$851$	4.82524e12	−	1.75624e12i	0.315381	−	0.114789i
$852$	4.43503e12	−	4.41996e10i	0.288349	−	0.00287369i
$853$	−6.47463e11	−	3.67194e12i	−0.0418740	−	0.237479i	0.956686	−	0.291121i	$-0.0940282\pi$
$853$	−6.47463e11	−	3.67194e12i	−0.0418740	−	0.237479i	−0.998560	+	0.0536418i	$0.982917\pi$
$854$	−2.73660e12	+	4.73993e12i	−0.176056	+	0.304938i
$855$	4.30728e13	+	1.47119e13i	2.75648	+	0.941499i
$856$	3.68430e12	+	6.38140e12i	0.234544	+	0.406241i
$857$	1.07719e12	−	9.03871e11i	0.0682149	−	0.0572391i	−0.608043	−	0.793904i	$-0.708045\pi$
$857$	1.07719e12	−	9.03871e11i	0.0682149	−	0.0572391i	0.676258	+	0.736665i	$0.263601\pi$
$858$	7.19152e11	−	4.33044e12i	0.0453031	−	0.272797i
$859$	−1.04457e12	+	5.92407e12i	−0.0654591	+	0.371237i	0.934427	+	0.356154i	$0.115912\pi$
$859$	−1.04457e12	+	5.92407e12i	−0.0654591	+	0.371237i	−0.999886	+	0.0150826i	$0.995199\pi$
$860$	1.70831e13	+	1.43344e13i	1.06494	+	0.893589i
$861$	7.26401e12	−	6.21963e12i	0.450466	−	0.385701i
$862$	8.33884e12	+	3.03509e12i	0.514426	+	0.187236i
$863$	−1.25347e13			−0.769246			−0.384623	−	0.923074i	$-0.625669\pi$
$863$	−1.25347e13			−0.769246			−0.384623	+	0.923074i	$0.625669\pi$
$864$	−2.16332e13	+	8.61459e12i	−1.32072	+	0.525923i
$865$	−1.03204e13			−0.626792
$866$	−1.35504e13	−	4.93195e12i	−0.818696	−	0.297981i
$867$	−3.19117e12	−	1.70997e13i	−0.191807	−	1.02779i
$868$	9.90282e11	+	8.30946e11i	0.0592134	+	0.0496860i
$869$	2.29708e12	−	1.30274e13i	0.136643	−	0.774940i
$870$	−1.16964e13	+	4.38962e12i	−0.692173	+	0.259771i
$871$	4.60513e11	−	3.86416e11i	0.0271119	−	0.0227496i
$872$	−2.76159e12	−	4.78322e12i	−0.161747	−	0.280154i
$873$	−7.10139e12	+	1.28865e13i	−0.413790	+	0.750878i
$874$	−2.36926e13	+	4.10369e13i	−1.37345	+	2.37888i
$875$	4.60672e12	+	2.61260e13i	0.265678	+	1.50673i
$876$	−3.55619e12	+	6.30375e12i	−0.204040	+	0.361685i
$877$	2.48032e13	−	9.02763e12i	1.41583	−	0.515318i	0.482992	−	0.875625i	$-0.339550\pi$
$877$	2.48032e13	−	9.02763e12i	1.41583	−	0.515318i	0.932834	+	0.360306i	$0.117328\pi$
$878$	−1.49680e13	+	5.44792e12i	−0.850040	+	0.309389i
$879$	1.10620e13	+	1.87265e13i	0.625008	+	1.05805i
$880$	−5.25578e12	−	2.98070e13i	−0.295437	−	1.67551i
$881$	−3.09920e12	+	5.36798e12i	−0.173324	+	0.300206i	−0.939580	−	0.342329i	$-0.888784\pi$
$881$	−3.09920e12	+	5.36798e12i	−0.173324	+	0.300206i	0.766256	+	0.642535i	$0.222117\pi$
$882$	1.70665e13	−	6.59977e12i	0.949587	−	0.367215i
$883$	−1.07763e13	−	1.86651e13i	−0.596548	−	1.03325i	−0.993326	−	0.115337i	$-0.963205\pi$
$883$	−1.07763e13	−	1.86651e13i	−0.596548	−	1.03325i	0.396778	−	0.917915i	$-0.370128\pi$
$884$	3.66229e12	−	3.07303e12i	0.201705	−	0.169251i
$885$	3.35418e13	+	2.75800e13i	1.83798	+	1.51129i
$886$	3.68203e12	−	2.08819e13i	0.200741	−	1.13846i
$887$	4.57163e12	+	3.83605e12i	0.247979	+	0.208079i	0.758301	−	0.651904i	$-0.226030\pi$
$887$	4.57163e12	+	3.83605e12i	0.247979	+	0.208079i	−0.510323	+	0.859983i	$0.670474\pi$
$888$	−1.53624e12	−	5.41869e11i	−0.0829087	−	0.0292440i
$889$	6.52834e12	+	2.37612e12i	0.350546	+	0.127588i
$890$	5.39405e13			2.88178
$891$	2.12595e13	−	8.71219e12i	1.13006	−	0.463103i
$892$	2.28052e11			0.0120612
$893$	−2.36326e12	−	8.60155e11i	−0.124360	−	0.0452632i
$894$	1.08516e13	+	3.82764e12i	0.568167	+	0.200406i
$895$	−5.01483e13	−	4.20794e13i	−2.61248	−	2.19213i
$896$	1.13812e12	−	6.45459e12i	0.0589931	−	0.334566i
$897$	−2.69570e12	−	2.21656e12i	−0.139029	−	0.114318i
$898$	−3.29930e13	+	2.76844e13i	−1.69308	+	1.42066i
$899$	2.98408e11	+	5.16859e11i	0.0152368	+	0.0263908i
$900$	9.02623e12	−	5.79179e13i	0.458580	−	2.94253i
$901$	8.75976e12	−	1.51723e13i	0.442823	−	0.766992i
$902$	−6.62138e12	−	3.75517e13i	−0.333057	−	1.88886i
$903$	3.52469e12	+	5.96681e12i	0.176411	+	0.298640i
$904$	5.01824e12	−	1.82649e12i	0.249916	−	0.0909619i
$905$	1.67009e13	−	6.07864e12i	0.827602	−	0.301223i
$906$	2.07693e13	−	3.68160e13i	1.02411	−	1.81535i
$907$	2.17719e12	+	1.23475e13i	0.106823	+	0.605822i	0.990477	+	0.137681i	$0.0439650\pi$
$907$	2.17719e12	+	1.23475e13i	0.106823	+	0.605822i	−0.883654	+	0.468141i	$0.844924\pi$
$908$	9.09219e12	−	1.57481e13i	0.443897	−	0.768852i
$909$	−3.60535e13	+	7.18691e11i	−1.75150	+	0.0349144i
$910$	−2.44620e12	−	4.23695e12i	−0.118251	−	0.204818i
$911$	−7.60626e12	+	6.38241e12i	−0.365880	+	0.307010i	−0.807129	−	0.590375i	$-0.798980\pi$
$911$	−7.60626e12	+	6.38241e12i	−0.365880	+	0.307010i	0.441249	+	0.897385i	$0.354535\pi$
$912$	−2.29077e13	+	8.59721e12i	−1.09649	+	0.411511i
$913$	−3.32701e12	+	1.88684e13i	−0.158466	+	0.898704i
$914$	−1.10120e13	−	9.24019e12i	−0.521927	−	0.437949i
$915$	−3.05744e12	−	1.63832e13i	−0.144199	−	0.772686i
$916$	−1.35982e13	−	4.94935e12i	−0.638195	−	0.232284i
$917$	6.90727e12			0.322585
$918$	4.34220e13	+	1.43496e13i	2.01799	+	0.666878i
$919$	3.09260e13			1.43023			0.715113	−	0.699009i	$-0.246375\pi$
$919$	3.09260e13			1.43023			0.715113	+	0.699009i	$0.246375\pi$
$920$	1.38922e13	+	5.05636e12i	0.639333	+	0.232698i
$921$	1.40238e13	−	1.20075e13i	0.642239	−	0.549902i
$922$	3.31496e13	+	2.78159e13i	1.51074	+	1.26766i
$923$	−1.39246e11	+	7.89703e11i	−0.00631502	+	0.0358143i
$924$	−3.00558e12	+	1.80984e13i	−0.135645	+	0.816800i
$925$	−1.19449e13	+	1.00230e13i	−0.536469	+	0.450151i
$926$	3.02351e13	+	5.23688e13i	1.35133	+	2.34058i
$927$	−1.03425e13	+	9.03573e12i	−0.460012	+	0.401888i
$928$	4.29214e12	−	7.43420e12i	0.189980	−	0.329055i
$929$	−3.70896e12	−	2.10346e13i	−0.163374	−	0.926537i	−0.950726	−	0.310034i	$-0.899660\pi$
$929$	−3.70896e12	−	2.10346e13i	−0.163374	−	0.926537i	0.787352	−	0.616504i	$-0.211451\pi$
$930$	−7.19398e12	+	7.16952e10i	−0.315352	+	0.00314280i
$931$	2.30947e13	−	8.40577e12i	1.00748	−	0.366694i
$932$	−3.39605e13	+	1.23606e13i	−1.47436	+	0.536621i
$933$	−1.73068e13	+	1.72480e11i	−0.747740	+	0.00745198i
$934$	4.38662e12	+	2.48778e13i	0.188612	+	1.06967i
$935$	−3.79907e13	+	6.58019e13i	−1.62564	+	2.81570i
$936$	2.13949e11	+	1.08629e12i	0.00911106	+	0.0462600i
$937$	5.75582e12	+	9.96937e12i	0.243938	+	0.422513i	0.961832	−	0.273639i	$-0.0882274\pi$
$937$	5.75582e12	+	9.96937e12i	0.243938	+	0.422513i	−0.717895	+	0.696152i	$0.754894\pi$
$938$	−3.51758e12	+	2.95160e12i	−0.148365	+	0.124493i
$939$	4.34978e11	−	2.61926e12i	0.0182588	−	0.109947i
$940$	−7.90589e11	+	4.48366e12i	−0.0330275	+	0.187308i
$941$	1.22406e13	+	1.02711e13i	0.508922	+	0.427036i	0.860750	−	0.509029i	$-0.169995\pi$
$941$	1.22406e13	+	1.02711e13i	0.508922	+	0.427036i	−0.351828	+	0.936065i	$0.614440\pi$
$942$	−1.03214e13	+	8.83743e12i	−0.427080	+	0.365676i
$943$	−2.84870e13	−	1.03684e13i	−1.17313	−	0.426983i
$944$	−2.33437e13			−0.956742
$945$	1.21345e13	−	2.25484e13i	0.494970	−	0.919758i
$946$	2.76329e13			1.12180
$947$	−2.56537e13	−	9.33717e12i	−1.03651	−	0.377260i	−0.232955	−	0.972487i	$-0.574840\pi$
$947$	−2.56537e13	−	9.33717e12i	−1.03651	−	0.377260i	−0.803557	+	0.595228i	$0.797062\pi$
$948$	3.55154e12	+	1.90307e13i	0.142817	+	0.765276i
$949$	−1.00241e12	−	8.41123e11i	−0.0401188	−	0.0336637i
$950$	2.49867e13	−	1.41707e14i	0.995297	−	5.64461i
$951$	9.27632e12	−	3.48138e12i	0.367759	−	0.138019i
$952$	−4.82106e12	+	4.04535e12i	−0.190229	+	0.159621i
$953$	−3.53738e12	−	6.12692e12i	−0.138920	−	0.240616i	0.788168	−	0.615460i	$-0.211030\pi$
$953$	−3.53738e12	−	6.12692e12i	−0.138920	−	0.240616i	−0.927088	+	0.374844i	$0.877696\pi$
$954$	1.21751e13	+	2.01495e13i	0.475888	+	0.787583i
$955$	−3.42773e13	+	5.93700e13i	−1.33349	+	2.30968i
$956$	−6.61295e12	−	3.75039e13i	−0.256056	−	1.45216i
$957$	−4.16169e12	+	7.37707e12i	−0.160386	+	0.284302i
$958$	3.36006e13	−	1.22296e13i	1.28885	−	0.469102i
$959$	−2.73262e13	+	9.94591e12i	−1.04327	+	0.379718i
$960$	3.39842e13	+	5.75306e13i	1.29139	+	2.18614i
$961$	−4.53151e12	−	2.56995e13i	−0.171391	−	0.972006i
$962$	8.54473e11	−	1.47999e12i	0.0321670	−	0.0557149i
$963$	−3.15055e13	−	2.53837e13i	−1.18051	−	0.951121i
$964$	−5.98887e12	−	1.03730e13i	−0.223356	−	0.386864i
$965$	2.32186e13	−	1.94827e13i	0.861912	−	0.723230i
$966$	2.05908e13	+	1.69310e13i	0.760812	+	0.625583i
$967$	−2.91756e12	+	1.65463e13i	−0.107300	+	0.608530i	0.882976	+	0.469418i	$0.155536\pi$
$967$	−2.91756e12	+	1.65463e13i	−0.107300	+	0.608530i	−0.990277	+	0.139112i	$0.955575\pi$
$968$	3.18257e12	+	2.67050e12i	0.116504	+	0.0977582i
$969$	5.79259e13	+	2.04319e13i	2.11065	+	0.744478i
$970$	6.14435e13	+	2.23636e13i	2.22845	+	0.811090i
$971$	−6.56530e12			−0.237011			−0.118505	−	0.992953i	$-0.537810\pi$
$971$	−6.56530e12			−0.237011			−0.118505	+	0.992953i	$0.537810\pi$
$972$	−2.46488e13	+	2.28690e13i	−0.885724	+	0.821769i
$973$	−1.96286e13			−0.702073
$974$	3.18324e13	+	1.15860e13i	1.13332	+	0.412496i
$975$	9.99434e12	+	3.52525e12i	0.354188	+	0.124931i
$976$	6.86306e12	+	5.75879e12i	0.242099	+	0.203145i
$977$	5.68877e12	−	3.22626e13i	0.199753	−	1.13285i	−0.705733	−	0.708478i	$-0.749382\pi$
$977$	5.68877e12	−	3.22626e13i	0.199753	−	1.13285i	0.905486	−	0.424377i	$-0.139507\pi$
$978$	−4.10260e13	−	3.37340e13i	−1.43395	−	1.17908i
$979$	2.80148e13	−	2.35072e13i	0.974686	−	0.817859i
$980$	−2.22460e13	−	3.85312e13i	−0.770432	−	1.33443i
$981$	2.36152e13	+	1.90265e13i	0.814105	+	0.655915i
$982$	6.33285e12	−	1.09688e13i	0.217319	−	0.376408i
$983$	−4.68500e12	−	2.65700e13i	−0.160036	−	0.907612i	−0.954036	−	0.299693i	$-0.903116\pi$
$983$	−4.68500e12	−	2.65700e13i	−0.160036	−	0.907612i	0.793999	−	0.607919i	$-0.207995\pi$
$984$	4.89137e12	+	8.28043e12i	0.166323	+	0.281563i
$985$	−6.17803e13	+	2.24862e13i	−2.09116	+	0.761120i
$986$	−1.58425e13	+	5.76620e12i	−0.533799	+	0.194287i
$987$	−6.95173e11	+	1.23227e12i	−0.0233166	+	0.0413314i
$988$	1.49835e12	+	8.49757e12i	0.0500273	+	0.283719i
$989$	1.09845e13	−	1.90257e13i	0.365087	−	0.632348i
$990$	−5.28029e13	−	8.73876e13i	−1.74703	−	2.89129i
$991$	−4.62958e12	−	8.01866e12i	−0.152479	−	0.264101i	0.779659	−	0.626204i	$-0.215392\pi$
$991$	−4.62958e12	−	8.01866e12i	−0.152479	−	0.264101i	−0.932138	+	0.362103i	$0.882059\pi$
$992$	3.78690e12	−	3.17758e12i	0.124160	−	0.104182i
$993$	−1.24315e13	+	4.66550e12i	−0.405743	+	0.152274i
$994$	1.06362e12	−	6.03207e12i	0.0345578	−	0.195987i
$995$	−2.26081e13	−	1.89705e13i	−0.731241	−	0.613584i
$996$	−5.14392e12	−	2.75635e13i	−0.165626	−	0.887497i
$997$	2.55823e13	+	9.31118e12i	0.819994	+	0.298453i	0.717746	−	0.696305i	$-0.245174\pi$
$997$	2.55823e13	+	9.31118e12i	0.819994	+	0.298453i	0.102248	+	0.994759i	$0.467396\pi$
$998$	1.07492e13			0.342994
$999$	8.94040e12	−	2.67371e11i	0.283996	−	0.00849316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.4.4	✓	156
3.2	odd	2		81.10.e.a.64.23		156
27.7	even	9	inner	27.10.e.a.7.4	yes	156
27.20	odd	18		81.10.e.a.19.23		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.4	✓	156	1.1	even	1	trivial
27.10.e.a.7.4	yes	156	27.7	even	9	inner
81.10.e.a.19.23		156	27.20	odd	18
81.10.e.a.64.23		156	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-31.5968 - 11.5003i) q^{2} +(132.307 + 46.6679i) q^{3} +(473.884 + 397.636i) q^{4} +(-451.726 + 2561.87i) q^{5} +(-3643.77 - 2996.12i) q^{6} +(-2730.60 + 2291.24i) q^{7} +(-1792.39 - 3104.51i) q^{8} +(15327.2 + 12349.0i) q^{9} +O(q^{10})\)	\(q+(-31.5968 - 11.5003i) q^{2} +(132.307 + 46.6679i) q^{3} +(473.884 + 397.636i) q^{4} +(-451.726 + 2561.87i) q^{5} +(-3643.77 - 2996.12i) q^{6} +(-2730.60 + 2291.24i) q^{7} +(-1792.39 - 3104.51i) q^{8} +(15327.2 + 12349.0i) q^{9} +(43735.3 - 75751.7i) q^{10} +(-10297.9 - 58402.4i) q^{11} +(44141.3 + 74725.2i) q^{12} +(-14744.9 + 5366.72i) q^{13} +(112628. - 40993.2i) q^{14} +(-179323. + 317871. i) q^{15} +(-34068.5 - 193212. i) q^{16} +(-246260. + 426534. i) q^{17} +(-342274. - 566455. i) q^{18} +(-444465. - 769836. i) q^{19} +(-1.23276e6 + 1.03441e6i) q^{20} +(-468204. + 175716. i) q^{21} +(-346263. + 1.96376e6i) q^{22} +(1.21443e6 + 1.01903e6i) q^{23} +(-92264.4 - 494395. i) q^{24} +(-4.52377e6 - 1.64652e6i) q^{25} +527611. q^{26} +(1.45159e6 + 2.34914e6i) q^{27} -2.20507e6 q^{28} +(-956629. - 348184. i) q^{29} +(9.32165e6 - 7.98144e6i) q^{30} +(-449094. - 376835. i) q^{31} +(-1.46425e6 + 8.30419e6i) q^{32} +(1.36303e6 - 8.20763e6i) q^{33} +(1.26863e7 - 1.06450e7i) q^{34} +(-4.63638e6 - 8.03044e6i) q^{35} +(2.35293e6 + 1.19466e7i) q^{36} +(1.61951e6 - 2.80508e6i) q^{37} +(5.19032e6 + 2.94358e7i) q^{38} +(-2.20131e6 + 21938.3i) q^{39} +(8.76300e6 - 3.18947e6i) q^{40} +(-1.79692e7 + 6.54024e6i) q^{41} +(1.68145e7 - 167574. i) q^{42} +(-2.40636e6 - 1.36471e7i) q^{43} +(1.83429e7 - 3.17708e7i) q^{44} +(-3.85601e7 + 3.36879e7i) q^{45} +(-2.66530e7 - 4.61643e7i) q^{46} +(2.16726e6 - 1.81855e6i) q^{47} +(4.50931e6 - 2.71532e7i) q^{48} +(-4.80097e6 + 2.72276e7i) q^{49} +(1.24001e8 + 1.04049e8i) q^{50} +(-5.24873e7 + 4.49410e7i) q^{51} +(-9.12140e6 - 3.31992e6i) q^{52} -3.55712e7 q^{53} +(-1.88499e7 - 9.09190e7i) q^{54} +1.54271e8 q^{55} +(1.20075e7 + 4.37036e6i) q^{56} +(-2.28791e7 - 1.22597e8i) q^{57} +(2.62222e7 + 2.20030e7i) q^{58} +(2.06612e7 - 1.17176e8i) q^{59} +(-2.11376e8 + 7.93288e7i) q^{60} +(-3.49812e7 + 2.93527e7i) q^{61} +(9.85621e6 + 1.70715e7i) q^{62} +(-7.01469e7 + 1.39831e6i) q^{63} +(9.15409e7 - 1.58554e8i) q^{64} +(-7.08815e6 - 4.01989e7i) q^{65} +(-1.37457e8 + 2.43659e8i) q^{66} +(-3.60011e7 + 1.31033e7i) q^{67} +(-2.86304e8 + 1.04206e8i) q^{68} +(1.13122e8 + 1.91500e8i) q^{69} +(5.41422e7 + 3.07055e8i) q^{70} +(2.55520e7 - 4.42573e7i) q^{71} +(1.08652e7 - 6.97176e7i) q^{72} +(4.16970e7 + 7.22212e7i) q^{73} +(-8.34305e7 + 7.00065e7i) q^{74} +(-5.21686e8 - 4.28960e8i) q^{75} +(9.54896e7 - 5.41548e8i) q^{76} +(1.61934e8 + 1.35878e8i) q^{77} +(6.98066e7 + 2.46225e7i) q^{78} +(2.09610e8 + 7.62918e7i) q^{79} +5.10373e8 q^{80} +(8.24264e7 + 3.78551e8i) q^{81} +6.42982e8 q^{82} +(-3.03592e8 - 1.10498e8i) q^{83} +(-2.91746e8 - 1.02906e8i) q^{84} +(-9.81482e8 - 8.23561e8i) q^{85} +(-8.09128e7 + 4.58879e8i) q^{86} +(-1.10320e8 - 9.07111e7i) q^{87} +(-1.62853e8 + 1.36650e8i) q^{88} +(3.08335e8 + 5.34053e8i) q^{89} +(1.60580e9 - 6.20977e8i) q^{90} +(2.79660e7 - 4.84386e7i) q^{91} +(1.70297e8 + 9.65804e8i) q^{92} +(-4.18321e7 - 7.08161e7i) q^{93} +(-8.93923e7 + 3.25361e7i) q^{94} +(2.17299e9 - 7.90905e8i) q^{95} +(-5.81270e8 + 1.03037e9i) q^{96} +(1.29807e8 + 7.36173e8i) q^{97} +(4.64820e8 - 8.05092e8i) q^{98} +(5.63371e8 - 1.02232e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9}+O(q^{10}) \) 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17} + 922437 q^{18} - 3 q^{19} - 8448573 q^{20} - 3497394 q^{21} - 1585014 q^{22} + 9316482 q^{23} + 7959258 q^{24} + 2192178 q^{25} - 33129678 q^{26} - 3148155 q^{27} - 12 q^{28} + 19657236 q^{29} + 21174507 q^{30} - 4633692 q^{31} - 37550952 q^{32} - 19055889 q^{33} + 14341770 q^{34} + 34449663 q^{35} + 137733552 q^{36} - 3 q^{37} - 92022060 q^{38} - 89330160 q^{39} + 6645801 q^{40} - 33127221 q^{41} + 227141658 q^{42} + 2356203 q^{43} + 1001541 q^{44} - 78992532 q^{45} - 3 q^{46} - 33488952 q^{47} + 248865393 q^{48} - 93214644 q^{49} - 72027753 q^{50} - 101541537 q^{51} + 160531713 q^{52} + 4841352 q^{53} - 315431874 q^{54} - 12 q^{55} - 91770981 q^{56} - 103852992 q^{57} - 320682489 q^{58} + 538090854 q^{59} + 1127571210 q^{60} + 36683436 q^{61} - 55862958 q^{62} - 419972706 q^{63} - 956301315 q^{64} - 852347310 q^{65} + 472205277 q^{66} - 109026897 q^{67} - 508886217 q^{68} - 1234413090 q^{69} - 815297649 q^{70} + 940878639 q^{71} + 2831326452 q^{72} - 221849931 q^{73} + 838884579 q^{74} - 226667796 q^{75} + 908401146 q^{76} - 967811358 q^{77} - 1247881230 q^{78} - 1228059150 q^{79} - 2497115154 q^{80} - 392600970 q^{81} - 12 q^{82} - 297703284 q^{83} + 1027656618 q^{84} + 1535949369 q^{85} + 2930201574 q^{86} + 2687612040 q^{87} + 2837227002 q^{88} + 1774997208 q^{89} + 7127326206 q^{90} + 551343507 q^{91} - 6896645517 q^{92} - 7299151842 q^{93} + 414852915 q^{94} - 9000269169 q^{95} - 2644638174 q^{96} + 3371772333 q^{97} + 6901039926 q^{98} + 5248107342 q^{99}+O(q^{100}) \) 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

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