LMFDB - Embedded newform 27.9.f.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,9,Mod(2,27)]

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([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, 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:	$10.9992224717$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	27.14
Dual form			27.9.f.a.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-18.2801 + 3.22328i) q^{2} +(61.0463 - 53.2386i) q^{3} +(83.2125 - 30.2869i) q^{4} +(-223.403 + 266.242i) q^{5} +(-944.332 + 1169.98i) q^{6} +(-1438.86 - 523.701i) q^{7} +(2691.76 - 1554.09i) q^{8} +(892.309 - 6500.04i) q^{9} +(3225.67 - 5587.03i) q^{10} +(262.444 + 312.769i) q^{11} +(3467.39 - 6279.02i) q^{12} +(-7243.71 + 41081.1i) q^{13} +(27990.6 + 4935.49i) q^{14} +(536.374 + 28146.7i) q^{15} +(-61562.3 + 51656.9i) q^{16} +(52651.8 + 30398.5i) q^{17} +(4639.91 + 121698. i) q^{18} +(81686.6 + 141485. i) q^{19} +(-10526.3 + 28920.8i) q^{20} +(-115718. + 44632.7i) q^{21} +(-5805.66 - 4871.53i) q^{22} +(88565.0 + 243330. i) q^{23} +(81584.6 - 238177. i) q^{24} +(46855.7 + 265732. i) q^{25} -774316. i q^{26} +(-291581. - 444309. i) q^{27} -135592. q^{28} +(833385. - 146948. i) q^{29} +(-100530. - 512798. i) q^{30} +(-733729. + 267056. i) q^{31} +(447401. - 533192. i) q^{32} +(32672.6 + 5121.24i) q^{33} +(-1.06047e6 - 385978. i) q^{34} +(460877. - 266087. i) q^{35} +(-122615. - 567910. i) q^{36} +(-858362. + 1.48673e6i) q^{37} +(-1.94929e6 - 2.32307e6i) q^{38} +(1.74490e6 + 2.89349e6i) q^{39} +(-187585. + 1.06385e6i) q^{40} +(-24637.0 - 4344.17i) q^{41} +(1.97148e6 - 1.18888e6i) q^{42} +(738972. - 620071. i) q^{43} +(31311.4 + 18077.7i) q^{44} +(1.53124e6 + 1.68970e6i) q^{45} +(-2.40330e6 - 4.16264e6i) q^{46} +(463987. - 1.27479e6i) q^{47} +(-1.00801e6 + 6.43096e6i) q^{48} +(-2.62005e6 - 2.19848e6i) q^{49} +(-1.71306e6 - 4.70659e6i) q^{50} +(4.83258e6 - 947388. i) q^{51} +(641451. + 3.63785e6i) q^{52} -6.06703e6i q^{53} +(6.76226e6 + 7.18218e6i) q^{54} -141903. q^{55} +(-4.68694e6 + 826433. i) q^{56} +(1.25192e7 + 4.28829e6i) q^{57} +(-1.47607e7 + 5.37247e6i) q^{58} +(-1.23794e7 + 1.47532e7i) q^{59} +(897110. + 2.32592e6i) q^{60} +(7.35050e6 + 2.67536e6i) q^{61} +(1.25519e7 - 7.24683e6i) q^{62} +(-4.68799e6 + 8.88533e6i) q^{63} +(3.82665e6 - 6.62796e6i) q^{64} +(-9.31923e6 - 1.11062e7i) q^{65} +(-613767. + 11696.2i) q^{66} +(-3.57529e6 + 2.02765e7i) q^{67} +(5.30197e6 + 934880. i) q^{68} +(1.83611e7 + 1.01394e7i) q^{69} +(-7.56721e6 + 6.34965e6i) q^{70} +(1.86096e7 + 1.07443e7i) q^{71} +(-7.69975e6 - 1.88833e7i) q^{72} +(-2.63704e7 - 4.56749e7i) q^{73} +(1.08988e7 - 2.99443e7i) q^{74} +(1.70076e7 + 1.37274e7i) q^{75} +(1.10825e7 + 9.29932e6i) q^{76} +(-213822. - 587472. i) q^{77} +(-4.12235e7 - 4.72692e7i) q^{78} +(6.77127e6 + 3.84018e7i) q^{79} -2.79308e7i q^{80} +(-4.14543e7 - 1.16001e7i) q^{81} +464371. q^{82} +(-1.82582e7 + 3.21941e6i) q^{83} +(-8.27741e6 + 7.21874e6i) q^{84} +(-1.98560e7 + 7.22697e6i) q^{85} +(-1.15098e7 + 1.37169e7i) q^{86} +(4.30518e7 - 5.33389e7i) q^{87} +(1.19251e6 + 434037. i) q^{88} +(7.85112e7 - 4.53284e7i) q^{89} +(-3.34376e7 - 2.59523e7i) q^{90} +(3.19369e7 - 5.53163e7i) q^{91} +(1.47394e7 + 1.75658e7i) q^{92} +(-3.05738e7 + 5.53655e7i) q^{93} +(-4.37272e6 + 2.47989e7i) q^{94} +(-5.59184e7 - 9.85992e6i) q^{95} +(-1.07418e6 - 5.63684e7i) q^{96} +(5.90263e7 - 4.95290e7i) q^{97} +(5.49811e7 + 3.17433e7i) q^{98} +(2.26719e6 - 1.42681e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) $ 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−18.2801	+	3.22328i	−1.14251	+	0.201455i	−0.712703	−	0.701466i	$-0.752529\pi$
$2$	−18.2801	+	3.22328i	−1.14251	+	0.201455i	−0.429806	+	0.902921i	$0.641418\pi$
$3$	61.0463	−	53.2386i	0.753658	−	0.657266i
$3$	61.0463	−	53.2386i	0.753658	−	0.657266i
$4$	83.2125	−	30.2869i	0.325049	−	0.118308i
$5$	−223.403	+	266.242i	−0.357445	+	0.425987i	−0.914561	−	0.404448i	$-0.867464\pi$
$5$	−223.403	+	266.242i	−0.357445	+	0.425987i	0.557116	+	0.830435i	$0.311908\pi$
$6$	−944.332	+	1169.98i	−0.728652	+	0.902761i
$7$	−1438.86	−	523.701i	−0.599274	−	0.218118i	0.0245293	−	0.999699i	$-0.492191\pi$
$7$	−1438.86	−	523.701i	−0.599274	−	0.218118i	−0.623804	+	0.781581i	$0.714414\pi$
$8$	2691.76	−	1554.09i	0.657168	−	0.379416i
$9$	892.309	−	6500.04i	0.136002	−	0.990709i
$10$	3225.67	−	5587.03i	0.322567	−	0.558703i
$11$	262.444	+	312.769i	0.0179253	+	0.0213625i	0.774933	−	0.632044i	$-0.217784\pi$
$11$	262.444	+	312.769i	0.0179253	+	0.0213625i	−0.757007	+	0.653406i	$0.773339\pi$
$12$	3467.39	−	6279.02i	0.167216	−	0.302808i
$13$	−7243.71	+	41081.1i	−0.253622	+	1.43836i	0.545962	+	0.837810i	$0.316164\pi$
$13$	−7243.71	+	41081.1i	−0.253622	+	1.43836i	−0.799585	+	0.600554i	$0.794947\pi$
$14$	27990.6	+	4935.49i	0.728617	+	0.128475i
$15$	536.374	+	28146.7i	0.0105950	+	0.555985i
$16$	−61562.3	+	51656.9i	−0.939367	+	0.788222i
$17$	52651.8	+	30398.5i	0.630402	+	0.363963i	0.780908	−	0.624646i	$-0.214757\pi$
$17$	52651.8	+	30398.5i	0.630402	+	0.363963i	−0.150506	+	0.988609i	$0.548090\pi$
$18$	4639.91	+	121698.i	0.0441998	+	1.15929i
$19$	81686.6	+	141485.i	0.626811	+	1.08567i	0.988188	+	0.153249i	$0.0489735\pi$
$19$	81686.6	+	141485.i	0.626811	+	1.08567i	−0.361377	+	0.932420i	$0.617693\pi$
$20$	−10526.3	+	28920.8i	−0.0657895	+	0.180755i
$21$	−115718.	+	44632.7i	−0.595010	+	0.229496i
$22$	−5805.66	−	4871.53i	−0.0247834	−	0.0207957i
$23$	88565.0	+	243330.i	0.316483	+	0.869531i	0.991309	+	0.131554i	$0.0419966\pi$
$23$	88565.0	+	243330.i	0.316483	+	0.869531i	−0.674826	+	0.737977i	$0.735781\pi$
$24$	81584.6	−	238177.i	0.245903	−	0.717884i
$25$	46855.7	+	265732.i	0.119951	+	0.680274i
$26$		−	774316.i		−	1.69444i
$27$	−291581.	−	444309.i	−0.548660	−	0.836045i
$28$	−135592.			−0.220599
$29$	833385.	−	146948.i	1.17829	−	0.207765i	0.449999	−	0.893029i	$-0.351424\pi$
$29$	833385.	−	146948.i	1.17829	−	0.207765i	0.728295	+	0.685264i	$0.240313\pi$
$30$	−100530.	−	512798.i	−0.124111	−	0.633083i
$31$	−733729.	+	267056.i	−0.794491	+	0.289171i	−0.707202	−	0.707012i	$-0.750043\pi$
$31$	−733729.	+	267056.i	−0.794491	+	0.289171i	−0.0872894	+	0.996183i	$0.527820\pi$
$32$	447401.	−	533192.i	0.426675	−	0.508492i
$33$	32672.6	+	5121.24i	0.0275504	+	0.00431836i
$34$	−1.06047e6	−	385978.i	−0.793562	−	0.288833i
$35$	460877.	−	266087.i	0.307123	−	0.177318i
$36$	−122615.	−	567910.i	−0.0730015	−	0.338119i
$37$	−858362.	+	1.48673e6i	−0.457998	+	0.793276i	−0.998855	−	0.0478387i	$-0.984767\pi$
$37$	−858362.	+	1.48673e6i	−0.457998	+	0.793276i	0.540857	+	0.841115i	$0.318100\pi$
$38$	−1.94929e6	−	2.32307e6i	−0.934850	−	1.11411i
$39$	1.74490e6	+	2.89349e6i	0.754243	+	1.25073i
$40$	−187585.	+	1.06385e6i	−0.0732754	+	0.415565i
$41$	−24637.0	−	4344.17i	−0.00871872	−	0.00153735i	0.169287	−	0.985567i	$-0.445853\pi$
$41$	−24637.0	−	4344.17i	−0.00871872	−	0.00153735i	−0.178006	+	0.984029i	$0.556965\pi$
$42$	1.97148e6	−	1.18888e6i	0.633571	−	0.382069i
$43$	738972.	−	620071.i	0.216150	−	0.181371i	−0.528284	−	0.849068i	$-0.677164\pi$
$43$	738972.	−	620071.i	0.216150	−	0.181371i	0.744433	+	0.667697i	$0.232720\pi$
$44$	31311.4	+	18077.7i	0.00835396	+	0.00482316i
$45$	1.53124e6	+	1.68970e6i	0.373415	+	0.412059i
$46$	−2.40330e6	−	4.16264e6i	−0.536756	−	0.929689i
$47$	463987.	−	1.27479e6i	0.0950854	−	0.261245i	−0.883027	−	0.469322i	$-0.844498\pi$
$47$	463987.	−	1.27479e6i	0.0950854	−	0.261245i	0.978112	+	0.208077i	$0.0667205\pi$
$48$	−1.00801e6	+	6.43096e6i	−0.189890	+	1.21146i
$49$	−2.62005e6	−	2.19848e6i	−0.454490	−	0.381362i
$50$	−1.71306e6	−	4.70659e6i	−0.274089	−	0.753054i
$51$	4.83258e6	−	947388.i	0.714328	−	0.140038i
$52$	641451.	+	3.63785e6i	0.0877304	+	0.497544i
$53$		−	6.06703e6i		−	0.768905i	−0.923145	−	0.384452i	$-0.874390\pi$
$53$		−	6.06703e6i		−	0.768905i	0.923145	−	0.384452i	$-0.125610\pi$
$54$	6.76226e6	+	7.18218e6i	0.795275	+	0.844659i
$55$	−141903.			−0.0155075
$56$	−4.68694e6	+	826433.i	−0.476581	+	0.0840341i
$57$	1.25192e7	+	4.28829e6i	1.18597	+	0.406242i
$58$	−1.47607e7	+	5.37247e6i	−1.30436	+	0.474747i
$59$	−1.23794e7	+	1.47532e7i	−1.02163	+	1.21753i	−0.0458050	+	0.998950i	$0.514585\pi$
$59$	−1.23794e7	+	1.47532e7i	−1.02163	+	1.21753i	−0.975820	+	0.218575i	$0.929859\pi$
$60$	897110.	+	2.32592e6i	0.0692215	+	0.179469i
$61$	7.35050e6	+	2.67536e6i	0.530881	+	0.193225i	0.593532	−	0.804810i	$-0.297733\pi$
$61$	7.35050e6	+	2.67536e6i	0.530881	+	0.193225i	−0.0626504	+	0.998036i	$0.519955\pi$
$62$	1.25519e7	−	7.24683e6i	0.849458	−	0.490435i
$63$	−4.68799e6	+	8.88533e6i	−0.297594	+	0.564042i
$64$	3.82665e6	−	6.62796e6i	0.228086	−	0.395057i
$65$	−9.31923e6	−	1.11062e7i	−0.522068	−	0.622176i
$66$	−613767.	+	11696.2i	−0.0323465	+	0.000616407i
$67$	−3.57529e6	+	2.02765e7i	−0.177424	+	1.00622i	0.757885	+	0.652388i	$0.226233\pi$
$67$	−3.57529e6	+	2.02765e7i	−0.177424	+	1.00622i	−0.935309	+	0.353832i	$0.884878\pi$
$68$	5.30197e6	+	934880.i	0.247971	+	0.0437240i
$69$	1.83611e7	+	1.01394e7i	0.810034	+	0.447315i
$70$	−7.56721e6	+	6.34965e6i	−0.315169	+	0.264458i
$71$	1.86096e7	+	1.07443e7i	0.732325	+	0.422808i	0.819272	−	0.573405i	$-0.194378\pi$
$71$	1.86096e7	+	1.07443e7i	0.732325	+	0.422808i	−0.0869473	+	0.996213i	$0.527711\pi$
$72$	−7.69975e6	−	1.88833e7i	−0.286515	−	0.702663i
$73$	−2.63704e7	−	4.56749e7i	−0.928593	−	1.60837i	−0.785678	−	0.618635i	$-0.787686\pi$
$73$	−2.63704e7	−	4.56749e7i	−0.928593	−	1.60837i	−0.142914	−	0.989735i	$-0.545647\pi$
$74$	1.08988e7	−	2.99443e7i	0.363457	−	0.998590i
$75$	1.70076e7	+	1.37274e7i	0.537523	+	0.433855i
$76$	1.10825e7	+	9.29932e6i	0.332188	+	0.278738i
$77$	−213822.	−	587472.i	−0.00608262	−	0.0167119i
$78$	−4.12235e7	−	4.72692e7i	−1.11370	−	1.27703i
$79$	6.77127e6	+	3.84018e7i	0.173845	+	0.985923i	0.939469	+	0.342635i	$0.111319\pi$
$79$	6.77127e6	+	3.84018e7i	0.173845	+	0.985923i	−0.765624	+	0.643289i	$0.777570\pi$
$80$		−	2.79308e7i		−	0.681904i
$81$	−4.14543e7	−	1.16001e7i	−0.963007	−	0.269477i
$82$	464371.			0.0102709
$83$	−1.82582e7	+	3.21941e6i	−0.384721	+	0.0678366i	−0.362664	−	0.931920i	$-0.618133\pi$
$83$	−1.82582e7	+	3.21941e6i	−0.384721	+	0.0678366i	−0.0220569	+	0.999757i	$0.507021\pi$
$84$	−8.27741e6	+	7.21874e6i	−0.166256	+	0.144992i
$85$	−1.98560e7	+	7.22697e6i	−0.380378	+	0.138446i
$86$	−1.15098e7	+	1.37169e7i	−0.210415	+	0.250762i
$87$	4.30518e7	−	5.33389e7i	0.751474	−	0.931037i
$88$	1.19251e6	+	434037.i	0.0198852	+	0.00723763i
$89$	7.85112e7	−	4.53284e7i	1.25133	−	0.722455i	0.279955	−	0.960013i	$-0.409680\pi$
$89$	7.85112e7	−	4.53284e7i	1.25133	−	0.722455i	0.971373	+	0.237558i	$0.0763471\pi$
$90$	−3.34376e7	−	2.59523e7i	−0.509642	−	0.395555i
$91$	3.19369e7	−	5.53163e7i	0.465722	−	0.806655i
$92$	1.47394e7	+	1.75658e7i	0.205745	+	0.245197i
$93$	−3.05738e7	+	5.53655e7i	−0.408712	+	0.740128i
$94$	−4.37272e6	+	2.47989e7i	−0.0560068	+	0.317630i
$95$	−5.59184e7	−	9.85992e6i	−0.686531	−	0.121054i
$96$	−1.07418e6	−	5.63684e7i	−0.0126471	−	0.663668i
$97$	5.90263e7	−	4.95290e7i	0.666744	−	0.559464i	−0.245356	−	0.969433i	$-0.578905\pi$
$97$	5.90263e7	−	4.95290e7i	0.666744	−	0.559464i	0.912100	+	0.409969i	$0.134460\pi$
$98$	5.49811e7	+	3.17433e7i	0.596086	+	0.344151i
$99$	2.26719e6	−	1.42681e6i	0.0236019	−	0.0148534i
$100$	1.19472e7	+	2.06931e7i	0.119472	+	0.206931i
$101$	−6.70812e7	+	1.84304e8i	−0.644637	+	1.77113i	−0.00799213	+	0.999968i	$0.502544\pi$
$101$	−6.70812e7	+	1.84304e8i	−0.644637	+	1.77113i	−0.636645	+	0.771157i	$0.719678\pi$
$102$	−8.52864e7	+	3.28951e7i	−0.787915	+	0.303900i
$103$	8.03334e7	+	6.74077e7i	0.713752	+	0.598909i	0.925649	−	0.378383i	$-0.123520\pi$
$103$	8.03334e7	+	6.74077e7i	0.713752	+	0.598909i	−0.211897	+	0.977292i	$0.567964\pi$
$104$	4.43453e7	+	1.21838e8i	0.379066	+	1.04147i
$105$	1.39687e7	−	4.07801e7i	0.114921	−	0.335499i
$106$	1.95557e7	+	1.10906e8i	0.154900	+	0.878480i
$107$			1.09060e8i			0.832017i	0.909361	+	0.416009i	$0.136571\pi$
$107$			1.09060e8i			0.832017i	−0.909361	+	0.416009i	$0.863429\pi$
$108$	−3.77199e7	−	2.81410e7i	−0.277252	−	0.206845i
$109$	7.61337e6			0.0539350			0.0269675	−	0.999636i	$-0.491415\pi$
$109$	7.61337e6			0.0539350			0.0269675	+	0.999636i	$0.491415\pi$
$110$	2.59401e6	−	457393.i	0.0177174	−	0.00312406i
$111$	2.67513e7	+	1.36457e8i	0.176219	+	0.898886i
$112$	1.15632e8	−	4.20867e7i	0.734864	−	0.267469i
$113$	−1.13330e8	+	1.35062e8i	−0.695076	+	0.828359i	−0.991960	−	0.126555i	$-0.959608\pi$
$113$	−1.13330e8	+	1.35062e8i	−0.695076	+	0.828359i	0.296884	+	0.954914i	$0.404053\pi$
$114$	−2.42674e8	−	3.80377e7i	−1.43683	−	0.225214i
$115$	−8.45704e7	−	3.07811e7i	−0.483534	−	0.175992i
$116$	6.48975e7	−	3.74686e7i	0.358423	−	0.206936i
$117$	2.60565e8	+	8.37414e7i	1.39051	+	0.446886i
$118$	1.78743e8	−	3.09593e8i	0.921939	−	1.59684i
$119$	−5.98387e7	−	7.13130e7i	−0.298397	−	0.355616i
$120$	4.51863e7	+	7.49307e7i	0.217912	+	0.361356i
$121$	3.71941e7	−	2.10938e8i	0.173513	−	0.984042i
$122$	−1.42992e8	−	2.52133e7i	−0.645463	−	0.113812i
$123$	−1.73528e6	+	1.04644e6i	−0.00758138	+	0.00457189i
$124$	−5.29672e7	+	4.44447e7i	−0.224037	+	0.187989i
$125$	−1.98791e8	−	1.14772e8i	−0.814248	−	0.470106i
$126$	5.70571e7	−	1.77536e8i	0.226375	−	0.704374i
$127$	−9.87685e7	−	1.71072e8i	−0.379668	−	0.657604i	0.611346	−	0.791363i	$-0.290628\pi$
$127$	−9.87685e7	−	1.71072e8i	−0.379668	−	0.657604i	−0.991014	+	0.133759i	$0.957295\pi$
$128$	−1.09531e8	+	3.00933e8i	−0.408033	+	1.12106i
$129$	1.20998e7	−	7.71949e7i	0.0436939	−	0.278760i
$130$	2.06155e8	+	1.72985e8i	0.721807	+	0.605668i
$131$	−9.97225e7	−	2.73985e8i	−0.338616	−	0.930341i	−0.985788	−	0.167996i	$-0.946270\pi$
$131$	−9.97225e7	−	2.73985e8i	−0.338616	−	0.930341i	0.647171	−	0.762345i	$-0.275952\pi$
$132$	2.87388e6	−	563401.i	0.00946613	−	0.00185576i
$133$	−4.34394e7	−	2.46357e8i	−0.138828	−	0.787332i
$134$		−	3.82180e8i		−	1.18536i
$135$	1.83434e8	+	2.16292e7i	0.552260	+	0.0651185i
$136$	1.88968e8			0.552373
$137$	4.29187e8	−	7.56772e7i	1.21833	−	0.214824i	0.472722	−	0.881212i	$-0.343272\pi$
$137$	4.29187e8	−	7.56772e7i	1.21833	−	0.214824i	0.745605	+	0.666388i	$0.232160\pi$
$138$	−3.68326e8	−	1.26166e8i	−1.01558	−	0.347876i
$139$	−1.12303e8	+	4.08750e7i	−0.300838	+	0.109496i	−0.488029	−	0.872827i	$-0.662284\pi$
$139$	−1.12303e8	+	4.08750e7i	−0.300838	+	0.109496i	0.187191	+	0.982324i	$0.440062\pi$
$140$	3.02918e7	−	3.61003e7i	0.0788519	−	0.0939721i
$141$	−3.95435e7	−	1.02523e8i	−0.100046	−	0.259386i
$142$	−3.74818e8	−	1.36423e8i	−0.921864	−	0.335531i
$143$	−1.47500e7	+	8.51589e6i	−0.0352733	+	0.0203651i
$144$	2.80839e8	+	4.46252e8i	0.653143	+	1.03784i
$145$	−1.47057e8	+	2.54711e8i	−0.332671	+	0.576202i
$146$	6.29278e8	+	7.49944e8i	1.38494	+	1.65051i
$147$	−2.76988e8	+	5.27838e6i	−0.593187	+	0.0113040i
$148$	−2.63981e7	+	1.49711e8i	−0.0550208	+	0.312038i
$149$	−6.60425e8	−	1.16451e8i	−1.33992	−	0.236264i	−0.542686	−	0.839936i	$-0.682593\pi$
$149$	−6.60425e8	−	1.16451e8i	−1.33992	−	0.236264i	−0.797233	+	0.603672i	$0.793704\pi$
$150$	−3.55148e8	−	1.96119e8i	−0.701527	−	0.387396i
$151$	−6.82796e8	+	5.72934e8i	−1.31336	+	1.10204i	−0.325691	+	0.945476i	$0.605597\pi$
$151$	−6.82796e8	+	5.72934e8i	−1.31336	+	1.10204i	−0.987668	+	0.156562i	$0.949959\pi$
$152$	4.39762e8	+	2.53896e8i	0.823840	+	0.475644i
$153$	2.44573e8	−	3.15114e8i	0.446317	−	0.575045i
$154$	5.80229e6	+	1.00499e7i	0.0103161	+	0.0178681i
$155$	9.28162e7	−	2.55010e8i	0.160804	−	0.441805i
$156$	2.32832e8	+	1.87927e8i	0.393138	+	0.317316i
$157$	9.14157e8	+	7.67068e8i	1.50460	+	1.26251i	0.873511	+	0.486804i	$0.161837\pi$
$157$	9.14157e8	+	7.67068e8i	1.50460	+	1.26251i	0.631092	+	0.775708i	$0.282607\pi$
$158$	−2.47560e8	−	6.80164e8i	−0.397239	−	1.09140i
$159$	−3.23000e8	−	3.70370e8i	−0.505375	−	0.579492i
$160$	4.20071e7	+	2.38234e8i	0.0640977	+	0.363516i
$161$		−	3.96499e8i		−	0.590118i
$162$	7.95180e8	+	7.84324e7i	1.15453	+	0.113877i
$163$	−8.51414e8			−1.20612			−0.603060	−	0.797696i	$-0.706052\pi$
$163$	−8.51414e8			−1.20612			−0.603060	+	0.797696i	$0.706052\pi$
$164$	−2.18168e6	+	384689.i	−0.00301589	+	0.000531783i
$165$	−8.66266e6	+	7.55471e6i	−0.0116873	+	0.0101925i
$166$	3.23385e8	−	1.17703e8i	0.425880	−	0.155008i
$167$	9.10357e8	−	1.08492e9i	1.17043	−	1.39487i	0.268338	−	0.963325i	$-0.413526\pi$
$167$	9.10357e8	−	1.08492e9i	1.17043	−	1.39487i	0.902093	−	0.431541i	$-0.142030\pi$
$168$	−2.42122e8	+	2.99977e8i	−0.303947	+	0.376574i
$169$	−8.68649e8	−	3.16162e8i	−1.06487	−	0.387582i
$170$	3.39675e8	−	1.96111e8i	0.406694	−	0.234805i
$171$	9.92550e8	−	4.04718e8i	1.16083	−	0.473334i
$172$	4.27117e7	−	7.39789e7i	0.0488015	−	0.0845267i
$173$	2.97039e8	+	3.53997e8i	0.331611	+	0.395199i	0.905926	−	0.423436i	$-0.139176\pi$
$173$	2.97039e8	+	3.53997e8i	0.331611	+	0.395199i	−0.574315	+	0.818634i	$0.694732\pi$
$174$	−6.15066e8	+	1.11381e9i	−0.671004	+	1.21511i
$175$	7.17455e7	−	4.06889e8i	0.0764967	−	0.433834i
$176$	−3.23134e7	−	5.69772e6i	−0.0336769	−	0.00593814i
$177$	2.97220e7	+	1.55969e9i	0.0302820	+	1.58908i
$178$	−1.28909e9	+	1.08167e9i	−1.28411	+	1.07750i
$179$	−6.54667e8	−	3.77972e8i	−0.637688	−	0.368170i	0.146035	−	0.989279i	$-0.453349\pi$
$179$	−6.54667e8	−	3.77972e8i	−0.637688	−	0.368170i	−0.783723	+	0.621110i	$0.786682\pi$
$180$	1.78594e8	+	9.42278e7i	0.170128	+	0.0897613i
$181$	1.30127e8	+	2.25387e8i	0.121242	+	0.209997i	0.920258	−	0.391313i	$-0.127979\pi$
$181$	1.30127e8	+	2.25387e8i	0.121242	+	0.209997i	−0.799016	+	0.601310i	$0.794646\pi$
$182$	−4.05511e8	+	1.11413e9i	−0.369587	+	1.01543i
$183$	5.91154e8	−	2.28009e8i	0.527104	−	0.203305i
$184$	6.16553e8	+	5.17349e8i	0.537897	+	0.451349i
$185$	−2.04068e8	−	5.60671e8i	−0.174216	−	0.478654i
$186$	3.80435e8	−	1.11064e9i	0.317855	−	0.927940i
$187$	4.31045e6	+	2.44458e7i	0.00352498	+	0.0199911i
$188$		−	1.20131e8i		−	0.0961668i
$189$	1.86858e8	+	7.91998e8i	0.146441	+	0.620693i
$190$	1.05398e9			0.808754
$191$	−3.97575e8	+	7.01032e7i	−0.298735	+	0.0526750i	−0.321007	−	0.947077i	$-0.604021\pi$
$191$	−3.97575e8	+	7.01032e7i	−0.298735	+	0.0526750i	0.0222719	+	0.999752i	$0.492910\pi$
$192$	−1.19260e8	−	6.08338e8i	−0.0877585	−	0.447651i
$193$	−1.13999e9	+	4.14921e8i	−0.821619	+	0.299045i	−0.718414	−	0.695615i	$-0.755132\pi$
$193$	−1.13999e9	+	4.14921e8i	−0.821619	+	0.299045i	−0.103204	+	0.994660i	$0.532910\pi$
$194$	−9.19364e8	+	1.09566e9i	−0.649053	+	0.773512i
$195$	−1.16018e9	−	1.81852e8i	−0.802396	−	0.125771i
$196$	−2.84606e8	−	1.03588e8i	−0.192850	−	0.0701916i
$197$	1.93591e9	−	1.11770e9i	1.28535	−	0.742096i	0.307527	−	0.951539i	$-0.400498\pi$
$197$	1.93591e9	−	1.11770e9i	1.28535	−	0.742096i	0.977821	+	0.209443i	$0.0671651\pi$
$198$	−3.68456e7	+	3.33901e7i	−0.0239731	+	0.0217249i
$199$	−1.14409e8	+	1.98163e8i	−0.0729540	+	0.126360i	−0.900195	−	0.435488i	$-0.856576\pi$
$199$	−1.14409e8	+	1.98163e8i	−0.0729540	+	0.126360i	0.827241	+	0.561848i	$0.189909\pi$
$200$	5.39095e8	+	6.42469e8i	0.336935	+	0.401543i
$201$	8.61231e8	+	1.42815e9i	0.527637	+	0.874961i
$202$	6.32189e8	−	3.58532e9i	0.379701	−	2.15339i
$203$	−1.27608e9	−	2.25007e8i	−0.751439	−	0.132499i
$204$	3.73437e8	−	2.25198e8i	0.215624	−	0.130030i
$205$	6.66059e6	−	5.58890e6i	0.00377135	−	0.00316454i
$206$	−1.68578e9	−	9.73285e8i	−0.936121	−	0.540470i
$207$	1.66068e9	−	3.58550e8i	0.904494	−	0.195285i
$208$	−1.67618e9	−	2.90324e9i	−0.895506	−	1.55106i
$209$	−2.28140e7	+	6.26811e7i	−0.0119569	+	0.0328512i
$210$	−1.23905e8	+	7.90490e8i	−0.0637104	+	0.406461i
$211$	2.08099e9	+	1.74615e9i	1.04988	+	0.880953i	0.993081	−	0.117433i	$-0.0374665\pi$
$211$	2.08099e9	+	1.74615e9i	1.04988	+	0.880953i	0.0567980	+	0.998386i	$0.481911\pi$
$212$	−1.83751e8	−	5.04853e8i	−0.0909677	−	0.249932i
$213$	1.70806e9	−	3.34851e8i	0.829820	−	0.162680i
$214$	−3.51533e8	−	1.99364e9i	−0.167614	−	0.950587i
$215$			3.35271e8i			0.156907i
$216$	−1.47536e9	−	7.42831e8i	−0.677771	−	0.341252i
$217$	1.19559e9			0.539192
$218$	−1.39173e8	+	2.45400e7i	−0.0616212	+	0.0108655i
$219$	−4.04148e9	−	1.38436e9i	−1.75697	−	0.601829i
$220$	−1.18081e7	+	4.29780e6i	−0.00504068	+	0.00183466i
$221$	−1.63020e9	+	1.94280e9i	−0.683395	+	0.814438i
$222$	−9.28858e8	−	2.40823e9i	−0.382417	−	0.991484i
$223$	9.99762e8	+	3.63884e8i	0.404275	+	0.147144i	0.536151	−	0.844122i	$-0.319878\pi$
$223$	9.99762e8	+	3.63884e8i	0.404275	+	0.147144i	−0.131876	+	0.991266i	$0.542100\pi$
$224$	−9.22981e8	+	5.32883e8i	−0.366607	+	0.211661i
$225$	1.76908e9	−	6.74488e7i	0.690267	−	0.0263175i
$226$	1.63635e9	−	2.83424e9i	0.627253	−	1.08643i
$227$	−1.55800e9	−	1.85676e9i	−0.586767	−	0.699281i	0.388214	−	0.921569i	$-0.373092\pi$
$227$	−1.55800e9	−	1.85676e9i	−0.586767	−	0.699281i	−0.974981	+	0.222288i	$0.928648\pi$
$228$	1.17163e9	−	2.23270e7i	0.433561	−	0.00826210i
$229$	−5.67440e8	+	3.21811e9i	−0.206337	+	1.17020i	0.688984	+	0.724777i	$0.258057\pi$
$229$	−5.67440e8	+	3.21811e9i	−0.206337	+	1.17020i	−0.895321	+	0.445421i	$0.853054\pi$
$230$	1.64517e9	+	2.90089e8i	0.587896	+	0.103662i
$231$	−4.43293e7	−	2.44794e7i	−0.0155684	−	0.00859713i
$232$	2.01490e9	−	1.69070e9i	0.695508	−	0.583600i
$233$	3.12090e9	+	1.80185e9i	1.05890	+	0.611358i	0.925129	−	0.379653i	$-0.123957\pi$
$233$	3.12090e9	+	1.80185e9i	1.05890	+	0.611358i	0.133775	+	0.991012i	$0.457290\pi$
$234$	−5.03309e9	−	6.90930e8i	−1.67869	−	0.230447i
$235$	2.35747e8	+	4.08325e8i	0.0772991	+	0.133886i
$236$	−5.83293e8	+	1.60258e9i	−0.188035	+	0.516622i
$237$	2.45782e9	+	1.98380e9i	0.779034	+	0.628787i
$238$	1.32372e9	+	1.11073e9i	0.412562	+	0.346180i
$239$	7.81125e8	+	2.14612e9i	0.239403	+	0.657754i	0.999964	+	0.00848739i	$0.00270165\pi$
$239$	7.81125e8	+	2.14612e9i	0.239403	+	0.657754i	−0.760561	+	0.649266i	$0.775076\pi$
$240$	−1.48700e9	−	1.70507e9i	−0.448193	−	0.513923i
$241$	6.31882e8	+	3.58358e9i	0.187313	+	1.06230i	0.922948	+	0.384926i	$0.125773\pi$
$241$	6.31882e8	+	3.58358e9i	0.187313	+	1.06230i	−0.735635	+	0.677379i	$0.763116\pi$
$242$			3.97586e9i			1.15923i
$243$	−3.14820e9	+	1.49882e9i	−0.902896	+	0.429858i
$244$	6.92682e8			0.195422
$245$	1.17065e9	−	2.06418e8i	0.324911	−	0.0572905i
$246$	2.83481e7	−	2.47224e7i	0.00774076	−	0.00675073i
$247$	−6.40409e9	+	2.33090e9i	−1.72056	+	0.626232i
$248$	−1.55999e9	+	1.85913e9i	−0.412398	+	0.491477i
$249$	−9.43199e8	+	1.16857e9i	−0.245361	+	0.303989i
$250$	4.00387e9	+	1.45729e9i	1.02499	+	0.373066i
$251$	3.02697e9	−	1.74762e9i	0.762629	−	0.440304i	−0.0676098	−	0.997712i	$-0.521537\pi$
$251$	3.02697e9	−	1.74762e9i	0.762629	−	0.440304i	0.830239	+	0.557408i	$0.188204\pi$
$252$	−1.20990e8	+	8.81355e8i	−0.0300019	+	0.218549i
$253$	−5.28628e7	+	9.15610e7i	−0.0129023	+	0.0223475i
$254$	2.35692e9	+	2.80886e9i	0.566251	+	0.674832i
$255$	−8.27379e8	+	1.49828e9i	−0.195679	+	0.354350i
$256$	6.92024e8	−	3.92466e9i	0.161124	−	0.913782i
$257$	1.73307e9	+	3.05588e8i	0.397269	+	0.0700493i	0.368714	−	0.929543i	$-0.379798\pi$
$257$	1.73307e9	+	3.05588e8i	0.397269	+	0.0700493i	0.0285553	+	0.999592i	$0.490909\pi$
$258$	2.76343e7	+	1.45013e9i	0.00623690	+	0.327288i
$259$	2.01366e9	−	1.68966e9i	0.447494	−	0.375492i
$260$	−1.11185e9	−	6.41927e8i	−0.243306	−	0.140473i
$261$	−2.11532e8	−	5.54816e9i	−0.0455842	−	1.19560i
$262$	2.70607e9	+	4.68706e9i	0.574294	+	0.994706i
$263$	2.40551e9	−	6.60909e9i	0.502787	−	1.38140i	−0.385755	−	0.922601i	$-0.626059\pi$
$263$	2.40551e9	−	6.60909e9i	0.502787	−	1.38140i	0.888542	−	0.458795i	$-0.151719\pi$
$264$	9.59057e7	−	3.69910e7i	0.0197437	−	0.00761518i
$265$	1.61530e9	+	1.35539e9i	0.327543	+	0.274841i
$266$	1.58815e9	+	4.36342e9i	0.317224	+	0.871566i
$267$	2.37960e9	−	6.94696e9i	0.468229	−	1.36694i
$268$	3.16602e8	+	1.79554e9i	0.0613726	+	0.348061i
$269$		−	4.63105e8i		−	0.0884445i	−0.999022	−	0.0442222i	$-0.985919\pi$
$269$		−	4.63105e8i		−	0.0884445i	0.999022	−	0.0442222i	$-0.0140810\pi$
$270$	−3.42291e9	+	1.95874e8i	−0.644080	+	0.0368572i
$271$	−9.95879e9			−1.84642			−0.923208	−	0.384301i	$-0.874442\pi$
$271$	−9.95879e9			−1.84642			−0.923208	+	0.384301i	$0.874442\pi$
$272$	−4.81167e9	+	8.48426e8i	−0.879063	+	0.155002i
$273$	−9.95332e8	−	5.07713e9i	−0.179191	−	0.914046i
$274$	−7.60166e9	+	2.76678e9i	−1.34867	+	0.490876i
$275$	−7.08157e7	+	8.43948e7i	−0.0123822	+	0.0147566i
$276$	1.83497e9	+	2.87620e8i	0.316222	+	0.0495658i
$277$	7.16936e9	+	2.60943e9i	1.21776	+	0.443228i	0.869388	−	0.494129i	$-0.164513\pi$
$277$	7.16936e9	+	2.60943e9i	1.21776	+	0.443228i	0.348370	+	0.937357i	$0.386735\pi$
$278$	1.92117e9	−	1.10919e9i	0.321652	−	0.185706i
$279$	1.08116e9	+	5.00756e9i	0.178432	+	0.826437i
$280$	8.27046e8	−	1.43249e9i	0.134554	−	0.233055i
$281$	−6.16695e9	−	7.34949e9i	−0.989112	−	1.17878i	−0.983887	−	0.178791i	$-0.942781\pi$
$281$	−6.16695e9	−	7.34949e9i	−0.989112	−	1.17878i	−0.00522454	−	0.999986i	$-0.501663\pi$
$282$	1.05332e9	+	1.74668e9i	0.166558	+	0.276196i
$283$	1.71278e9	−	9.71364e9i	0.267027	−	1.51439i	−0.496174	−	0.868223i	$-0.665262\pi$
$283$	1.71278e9	−	9.71364e9i	0.267027	−	1.51439i	0.763201	−	0.646162i	$-0.223627\pi$
$284$	1.87396e9	+	3.30430e8i	0.288063	+	0.0507933i
$285$	−3.93854e9	+	2.37510e9i	−0.596975	+	0.360000i
$286$	2.42182e8	−	2.03215e8i	0.0361974	−	0.0303733i
$287$	3.31741e7	+	1.91531e7i	0.00488958	+	0.00282300i
$288$	−3.06655e9	−	3.38390e9i	−0.445738	−	0.491867i
$289$	−1.63974e9	−	2.84011e9i	−0.235062	−	0.407139i
$290$	1.86722e9	−	5.13015e9i	0.264000	−	0.725334i
$291$	9.66490e8	−	6.16604e9i	0.134780	−	0.859873i
$292$	−3.57770e9	−	3.00204e9i	−0.492121	−	0.412939i
$293$	6.70230e8	+	1.84144e9i	0.0909396	+	0.249855i	0.976821	−	0.214057i	$-0.0686678\pi$
$293$	6.70230e8	+	1.84144e9i	0.0909396	+	0.249855i	−0.885882	+	0.463911i	$0.846446\pi$
$294$	5.04636e9	−	9.89300e8i	0.675444	−	0.132415i
$295$	−1.16232e9	−	6.59182e9i	−0.153475	−	0.870397i
$296$			5.33588e9i			0.695087i
$297$	6.24423e7	−	2.07804e8i	0.00802515	−	0.0267071i
$298$	1.24480e10			1.57846
$299$	−1.06378e10	+	1.87573e9i	−1.33097	+	0.234686i
$300$	1.83100e9	+	6.27188e8i	0.226050	+	0.0774306i
$301$	−1.38801e9	+	5.05194e8i	−0.169093	+	0.0615449i
$302$	1.06349e10	−	1.26742e10i	1.27851	−	1.52367i
$303$	5.71702e9	+	1.48224e10i	0.678265	+	1.75852i
$304$	−1.23375e10	−	4.49049e9i	−1.44455	−	0.525775i
$305$	−2.35442e9	+	1.35932e9i	−0.272072	+	0.157081i
$306$	−3.45513e9	+	6.54866e9i	−0.394075	+	0.746907i
$307$	−2.48105e9	+	4.29730e9i	−0.279307	+	0.483773i	−0.971213	−	0.238214i	$-0.923438\pi$
$307$	−2.48105e9	+	4.29730e9i	−0.279307	+	0.483773i	0.691906	+	0.721988i	$0.256771\pi$
$308$	−3.55854e7	−	4.24090e7i	−0.00395429	−	0.00471254i
$309$	8.49275e9	−	1.61841e8i	0.931568	−	0.0177523i
$310$	−8.74722e8	+	4.96080e9i	−0.0947160	+	0.537161i
$311$	−6.42742e9	−	1.13333e9i	−0.687060	−	0.121147i	−0.180790	−	0.983522i	$-0.557865\pi$
$311$	−6.42742e9	−	1.13333e9i	−0.687060	−	0.121147i	−0.506271	+	0.862375i	$0.668976\pi$
$312$	9.19359e9	+	5.07687e9i	0.970212	+	0.535769i
$313$	6.45751e9	−	5.41849e9i	0.672802	−	0.564548i	−0.241091	−	0.970502i	$-0.577505\pi$
$313$	6.45751e9	−	5.41849e9i	0.672802	−	0.564548i	0.913893	+	0.405954i	$0.133061\pi$
$314$	−1.91834e10	−	1.10755e10i	−1.97336	−	1.13932i
$315$	−1.31833e9	−	3.23315e9i	−0.133901	−	0.328385i
$316$	1.72652e9	+	2.99043e9i	0.173151	+	0.299906i
$317$	−1.74715e8	+	4.80026e8i	−0.0173019	+	0.0475366i	−0.948043	−	0.318142i	$-0.896941\pi$
$317$	−1.74715e8	+	4.80026e8i	−0.0173019	+	0.0475366i	0.930741	+	0.365679i	$0.119163\pi$
$318$	7.09829e9	+	5.72929e9i	0.694137	+	0.560264i
$319$	2.64678e8	+	2.22091e8i	0.0255597	+	0.0214471i
$320$	9.09751e8	+	2.49952e9i	0.0867607	+	0.238373i
$321$	5.80622e9	+	6.65774e9i	0.546857	+	0.627057i
$322$	1.27803e9	+	7.24806e9i	0.118882	+	0.674215i
$323$			9.93262e9i			0.912544i
$324$	−3.80085e9	+	2.90248e8i	−0.344906	+	0.0263384i
$325$	−1.12560e10			−1.00890
$326$	1.55640e10	−	2.74435e9i	1.37800	−	0.242979i
$327$	4.64768e8	−	4.05325e8i	0.0406486	−	0.0354497i
$328$	−7.30682e7	+	2.65946e7i	−0.00631296	+	0.00229773i
$329$	−1.33522e9	+	1.59125e9i	−0.113965	+	0.135818i
$330$	1.34004e8	−	1.66023e8i	0.0112995	−	0.0139995i
$331$	−7.92073e9	−	2.88291e9i	−0.659862	−	0.240170i	−0.00968542	−	0.999953i	$-0.503083\pi$
$331$	−7.92073e9	−	2.88291e9i	−0.659862	−	0.240170i	−0.650177	+	0.759783i	$0.725305\pi$
$332$	−1.42180e9	+	8.20879e8i	−0.117027	+	0.0675658i
$333$	8.89786e9	+	6.90601e9i	0.723616	+	0.561630i
$334$	−1.31444e10	+	2.27668e10i	−1.05622	+	1.82944i
$335$	−4.59971e9	−	5.48172e9i	−0.365217	−	0.435249i
$336$	4.81829e9	−	8.72534e9i	0.378038	−	0.684581i
$337$	2.27225e9	−	1.28866e10i	0.176172	−	0.999120i	−0.760611	−	0.649208i	$-0.775101\pi$
$337$	2.27225e9	−	1.28866e10i	0.176172	−	0.999120i	0.936783	−	0.349912i	$-0.113788\pi$
$338$	1.68981e10	+	2.97959e9i	1.29471	+	0.228292i
$339$	2.72097e8	+	1.42786e10i	0.0206028	+	1.08115i
$340$	−1.43338e9	+	1.20275e9i	−0.107262	+	0.0900035i
$341$	−2.76090e8	−	1.59400e8i	−0.0204189	−	0.0117889i
$342$	−1.68394e10	+	1.05976e10i	−1.23090	+	0.774643i
$343$	7.03206e9	+	1.21799e10i	0.508050	+	0.879968i
$344$	1.02549e9	−	2.81751e9i	0.0732315	−	0.201202i
$345$	−6.80146e9	+	2.62333e9i	−0.480093	+	0.185173i
$346$	−6.57095e9	−	5.51368e9i	−0.458483	−	0.384713i
$347$	−5.29741e9	−	1.45545e10i	−0.365381	−	1.00388i	−0.977096	−	0.212798i	$-0.931742\pi$
$347$	−5.29741e9	−	1.45545e10i	−0.365381	−	1.00388i	0.611715	−	0.791078i	$-0.290480\pi$
$348$	1.96698e9	−	5.74237e9i	0.134117	−	0.391538i
$349$	−4.91194e8	−	2.78570e9i	−0.0331094	−	0.187773i	0.963768	−	0.266744i	$-0.0859477\pi$
$349$	−4.91194e8	−	2.78570e9i	−0.0331094	−	0.187773i	−0.996877	+	0.0789708i	$0.974837\pi$
$350$			7.66924e9i			0.511070i
$351$	2.03648e10	−	8.76001e9i	1.34169	−	0.577133i
$352$	2.84184e8			0.0185110
$353$	1.90149e10	−	3.35285e9i	1.22461	−	0.215931i	0.476299	−	0.879284i	$-0.341978\pi$
$353$	1.90149e10	−	3.35285e9i	1.22461	−	0.215931i	0.748307	+	0.663352i	$0.230867\pi$
$354$	−5.57064e9	−	2.84155e10i	−0.354725	−	1.80943i
$355$	−7.01802e9	+	2.55435e9i	−0.441877	+	0.160830i
$356$	5.16025e9	−	6.14975e9i	0.321271	−	0.382875i
$357$	−7.44954e9	−	1.16767e9i	−0.458624	−	0.0718865i
$358$	1.31857e10	+	4.79921e9i	0.802734	+	0.292171i
$359$	−7.35567e9	+	4.24680e9i	−0.442838	+	0.255672i	−0.704801	−	0.709405i	$-0.748964\pi$
$359$	−7.35567e9	+	4.24680e9i	−0.442838	+	0.255672i	0.261963	+	0.965078i	$0.415630\pi$
$360$	6.74766e9	+	2.16859e9i	0.401738	+	0.129112i
$361$	−4.85363e9	+	8.40674e9i	−0.285784	+	0.494993i
$362$	−3.10523e9	−	3.70066e9i	−0.180825	−	0.215499i
$363$	−8.95948e9	−	1.48572e10i	−0.516008	−	0.855676i
$364$	9.82190e8	−	5.57028e9i	0.0559487	−	0.317301i
$365$	1.80518e10	+	3.18302e9i	1.01707	+	0.179336i
$366$	−1.00714e10	+	6.07349e9i	−0.561264	+	0.338465i
$367$	1.46247e10	−	1.22716e10i	0.806163	−	0.676451i	−0.143526	−	0.989647i	$-0.545844\pi$
$367$	1.46247e10	−	1.22716e10i	0.806163	−	0.676451i	0.949689	+	0.313195i	$0.101400\pi$
$368$	−1.80220e10	−	1.04050e10i	−0.982678	−	0.567349i
$369$	−5.02211e7	+	1.56265e8i	−0.00270883	+	0.00842863i
$370$	5.53759e9	+	9.59138e9i	0.295470	+	0.511769i
$371$	−3.17731e9	+	8.72959e9i	−0.167712	+	0.460785i
$372$	−8.67277e8	+	5.53308e9i	−0.0452883	+	0.288932i
$373$	2.34539e9	+	1.96802e9i	0.121166	+	0.101670i	0.701357	−	0.712810i	$-0.252578\pi$
$373$	2.34539e9	+	1.96802e9i	0.121166	+	0.101670i	−0.580191	+	0.814480i	$0.697022\pi$
$374$	−1.57591e8	−	4.32978e8i	−0.00805463	−	0.0221299i
$375$	−1.82458e10	+	3.57694e9i	−0.922650	+	0.180878i
$376$	−7.32200e8	−	4.15251e9i	−0.0366335	−	0.207759i
$377$			3.53008e10i			1.74751i
$378$	−5.96862e9	−	1.38755e10i	−0.292352	−	0.679646i
$379$	9.45638e9			0.458319			0.229160	−	0.973389i	$-0.426402\pi$
$379$	9.45638e9			0.458319			0.229160	+	0.973389i	$0.426402\pi$
$380$	−4.95173e9	+	8.73124e8i	−0.237478	+	0.0418737i
$381$	−1.51371e10	−	5.18503e9i	−0.718361	−	0.246066i
$382$	7.04176e9	−	2.56299e9i	0.330695	−	0.120363i
$383$	2.14845e9	−	2.56042e9i	0.0998459	−	0.118992i	−0.713808	−	0.700342i	$-0.753031\pi$
$383$	2.14845e9	−	2.56042e9i	0.0998459	−	0.118992i	0.813653	+	0.581350i	$0.197475\pi$
$384$	9.33480e9	+	2.42021e10i	0.429319	+	1.11308i
$385$	2.04178e8	+	7.43148e7i	0.00929323	+	0.00338246i
$386$	1.95017e10	−	1.12593e10i	0.878462	−	0.507180i
$387$	−3.37110e9	−	5.35664e9i	−0.150289	−	0.238808i
$388$	3.41165e9	−	5.90915e9i	0.150535	−	0.260734i
$389$	1.93823e9	+	2.30989e9i	0.0846461	+	0.100877i	0.806705	−	0.590954i	$-0.201249\pi$
$389$	1.93823e9	+	2.30989e9i	0.0846461	+	0.100877i	−0.722059	+	0.691831i	$0.756804\pi$
$390$	2.17945e10	−	4.15323e8i	0.942081	−	0.0179526i
$391$	−2.73378e9	+	1.55040e10i	−0.116965	+	0.663342i
$392$	−1.04692e10	−	1.84600e9i	−0.443371	−	0.0781783i
$393$	−2.06743e10	−	1.14167e10i	−0.866683	−	0.478598i
$394$	−3.17861e10	+	2.66717e10i	−1.31902	+	1.10679i
$395$	−1.17369e10	−	6.77629e9i	−0.482130	−	0.278358i
$396$	1.45445e8	−	1.87395e8i	0.00591450	−	0.00762038i
$397$	−4.50332e8	−	7.79998e8i	−0.0181289	−	0.0314001i	0.856819	−	0.515618i	$-0.172438\pi$
$397$	−4.50332e8	−	7.79998e8i	−0.0181289	−	0.0314001i	−0.874948	+	0.484218i	$0.839104\pi$
$398$	1.45268e9	−	3.99121e9i	0.0578947	−	0.159064i
$399$	−1.57675e10	−	1.27265e10i	−0.622116	−	0.502133i
$400$	−1.66114e10	−	1.39387e10i	−0.648885	−	0.544479i
$401$	3.39206e9	+	9.31962e9i	0.131186	+	0.360430i	0.987843	−	0.155457i	$-0.0496849\pi$
$401$	3.39206e9	+	9.31962e9i	0.131186	+	0.360430i	−0.856657	+	0.515886i	$0.827463\pi$
$402$	−2.03467e10	−	2.33307e10i	−0.779095	−	0.893355i
$403$	−5.65602e9	−	3.20769e10i	−0.214432	−	1.21611i
$404$			1.73681e10i			0.651968i
$405$	1.23495e10	−	8.44536e9i	0.459016	−	0.313905i
$406$	2.40522e10			0.885218
$407$	−6.90274e8	+	1.21714e8i	−0.0251561	+	0.00443570i
$408$	1.15358e10	−	1.00604e10i	0.416301	−	0.363056i
$409$	4.63141e10	−	1.68570e10i	1.65508	−	0.602402i	0.665506	−	0.746393i	$-0.268216\pi$
$409$	4.63141e10	−	1.68570e10i	1.65508	−	0.602402i	0.989579	+	0.143991i	$0.0459937\pi$
$410$	−1.03742e8	+	1.23635e8i	−0.00367129	+	0.00437527i
$411$	2.21713e10	−	2.74691e10i	0.777006	−	0.962669i
$412$	8.72631e9	+	3.17612e9i	0.302860	+	0.110232i
$413$	2.55385e10	−	1.47446e10i	0.877798	−	0.506797i
$414$	−2.92018e10	+	1.19072e10i	−0.994051	+	0.405329i
$415$	3.22180e9	−	5.58032e9i	0.108619	−	0.188134i
$416$	1.86633e10	+	2.22420e10i	0.623182	+	0.742679i
$417$	−4.67957e9	+	8.47414e9i	−0.154761	+	0.280254i
$418$	2.15005e8	−	1.21935e9i	0.00704277	−	0.0399415i
$419$	−9.07900e9	−	1.60087e9i	−0.294565	−	0.0519398i	0.0244125	−	0.999702i	$-0.492228\pi$
$419$	−9.07900e9	−	1.60087e9i	−0.294565	−	0.0519398i	−0.318978	+	0.947762i	$0.603340\pi$
$420$	−7.27282e7	−	3.81648e9i	−0.00233725	−	0.122650i
$421$	2.97544e10	−	2.49669e10i	0.947159	−	0.794761i	−0.0316579	−	0.999499i	$-0.510079\pi$
$421$	2.97544e10	−	2.49669e10i	0.947159	−	0.794761i	0.978817	+	0.204738i	$0.0656343\pi$
$422$	−4.36690e10	−	2.52123e10i	−1.37697	−	0.794993i
$423$	−7.87218e9	−	4.15344e9i	−0.245886	−	0.129732i
$424$	−9.42870e9	−	1.63310e10i	−0.291735	−	0.505300i
$425$	−5.61083e9	+	1.54156e10i	−0.171977	+	0.472504i
$426$	−3.01442e10	+	1.16267e10i	−0.915304	+	0.353034i
$427$	−9.17523e9	−	7.69893e9i	−0.275998	−	0.231590i
$428$	3.30310e9	+	9.07519e9i	0.0984344	+	0.270446i
$429$	−4.47057e8	+	1.30513e9i	−0.0131988	+	0.0385323i
$430$	−1.08067e9	−	6.12880e9i	−0.0316097	−	0.179268i
$431$			4.74289e10i			1.37447i	0.726436	+	0.687234i	$0.241175\pi$
$431$			4.74289e10i			1.37447i	−0.726436	+	0.687234i	$0.758825\pi$
$432$	4.09020e10	+	1.22905e10i	1.17438	+	0.352887i
$433$	−2.37974e10			−0.676984			−0.338492	−	0.940969i	$-0.609917\pi$
$433$	−2.37974e10			−0.676984			−0.338492	+	0.940969i	$0.609917\pi$
$434$	−2.18555e10	+	3.85372e9i	−0.616031	+	0.108623i
$435$	4.58312e9	+	2.33783e10i	0.127998	+	0.652913i
$436$	6.33527e8	−	2.30585e8i	0.0175315	−	0.00638095i
$437$	−2.71931e10	+	3.24075e10i	−0.745647	+	0.888628i
$438$	7.83410e10	+	1.22795e10i	2.12859	+	0.333644i
$439$	2.94082e10	+	1.07037e10i	0.791789	+	0.288188i	0.706080	−	0.708132i	$-0.250462\pi$
$439$	2.94082e10	+	1.07037e10i	0.791789	+	0.288188i	0.0857097	+	0.996320i	$0.472684\pi$
$440$	−3.81969e8	+	2.20530e8i	−0.0101910	+	0.00588378i
$441$	−1.66281e10	+	1.50687e10i	−0.439631	+	0.398401i
$442$	2.35381e10	−	4.07692e10i	0.616712	−	1.06818i
$443$	9.78540e8	+	1.16618e9i	0.0254076	+	0.0302796i	0.778599	−	0.627522i	$-0.215931\pi$
$443$	9.78540e8	+	1.16618e9i	0.0254076	+	0.0302796i	−0.753191	+	0.657802i	$0.771486\pi$
$444$	6.35891e9	+	1.05447e10i	0.163625	+	0.271334i
$445$	−5.47133e9	+	3.10295e10i	−0.139525	+	0.791287i
$446$	−1.94487e10	−	3.42933e9i	−0.491531	−	0.0866702i
$447$	−4.65162e10	+	2.80512e10i	−1.16513	+	0.702621i
$448$	−8.97708e9	+	7.53266e9i	−0.222855	+	0.186998i
$449$	2.91593e10	+	1.68352e10i	0.717451	+	0.414221i	0.813814	−	0.581126i	$-0.197388\pi$
$449$	2.91593e10	+	1.68352e10i	0.717451	+	0.414221i	−0.0963628	+	0.995346i	$0.530721\pi$
$450$	−3.21216e10	+	6.93521e9i	−0.783334	+	0.169126i
$451$	−5.10712e6	−	8.84580e6i	−0.000123444	−	0.000213811i
$452$	−5.33990e9	+	1.46712e10i	−0.127932	+	0.351490i
$453$	−1.11800e10	+	7.13266e10i	−0.265491	+	1.69379i
$454$	3.44654e10	+	2.89199e10i	0.811260	+	0.680728i
$455$	7.59270e9	+	2.08608e10i	0.177154	+	0.486726i
$456$	4.03629e10	−	7.91283e9i	0.933519	−	0.183009i
$457$	1.09556e10	+	6.21321e10i	0.251171	+	1.42446i	0.805713	+	0.592307i	$0.201783\pi$
$457$	1.09556e10	+	6.21321e10i	0.251171	+	1.42446i	−0.554541	+	0.832156i	$0.687106\pi$
$458$		−	6.06566e10i		−	1.37853i
$459$	−1.84591e9	−	3.22573e10i	−0.0415871	−	0.726737i
$460$	−7.96958e9			−0.177993
$461$	−3.07188e10	+	5.41656e9i	−0.680145	+	0.119928i	−0.503039	−	0.864264i	$-0.667785\pi$
$461$	−3.07188e10	+	5.41656e9i	−0.680145	+	0.119928i	−0.177106	+	0.984192i	$0.556674\pi$
$462$	8.89249e8	+	3.04602e8i	0.0195189	+	0.00668597i
$463$	4.22751e10	−	1.53869e10i	0.919942	−	0.334831i	0.161726	−	0.986836i	$-0.448294\pi$
$463$	4.22751e10	−	1.53869e10i	0.919942	−	0.334831i	0.758215	+	0.652004i	$0.226072\pi$
$464$	−4.37142e10	+	5.20966e10i	−0.943085	+	1.12393i
$465$	−7.91030e9	−	2.05088e10i	−0.169193	−	0.438661i
$466$	−6.28584e10	−	2.28786e10i	−1.33297	−	0.485161i
$467$	6.93681e10	−	4.00497e10i	1.45845	−	0.842037i	0.459516	−	0.888169i	$-0.348023\pi$
$467$	6.93681e10	−	4.00497e10i	1.45845	−	0.842037i	0.998935	+	0.0461320i	$0.0146895\pi$
$468$	2.42185e10	−	9.23369e8i	0.504853	−	0.0192483i
$469$	1.57631e10	−	2.73026e10i	0.325800	−	0.564302i
$470$	−5.62563e9	−	6.70437e9i	−0.115287	−	0.137394i
$471$	9.66435e10	−	1.84167e9i	1.96376	−	0.0374222i
$472$	−1.03946e10	+	5.89507e10i	−0.209431	+	1.18774i
$473$	3.87878e8	+	6.83934e7i	0.00774909	+	0.00136637i
$474$	−5.13236e10	−	2.83418e10i	−1.01673	−	0.561454i
$475$	−3.37697e10	+	2.83362e10i	−0.663366	+	0.556630i
$476$	−7.13918e9	−	4.12181e9i	−0.139066	−	0.0802897i
$477$	−3.94359e10	−	5.41367e9i	−0.761761	−	0.104573i
$478$	−2.11966e10	−	3.67137e10i	−0.406027	−	0.703260i
$479$	5.05947e9	−	1.39008e10i	0.0961088	−	0.264057i	−0.882317	−	0.470656i	$-0.844017\pi$
$479$	5.05947e9	−	1.39008e10i	0.0961088	−	0.264057i	0.978426	+	0.206599i	$0.0662396\pi$
$480$	1.52476e10	+	1.23069e10i	0.287235	+	0.231838i
$481$	−5.48586e10	−	4.60319e10i	−1.02486	−	0.859960i
$482$	−2.31018e10	−	6.34716e10i	−0.428013	−	1.17596i
$483$	−2.11091e10	−	2.42048e10i	−0.387865	−	0.444748i
$484$	−3.29364e9	−	1.86792e10i	−0.0600199	−	0.340390i
$485$			2.67802e10i			0.484002i
$486$	5.27185e10	−	3.75463e10i	0.944969	−	0.673010i
$487$	−1.00517e10			−0.178699			−0.0893495	−	0.996000i	$-0.528479\pi$
$487$	−1.00517e10			−0.178699			−0.0893495	+	0.996000i	$0.528479\pi$
$488$	2.39435e10	−	4.22189e9i	0.422191	−	0.0744436i
$489$	−5.19757e10	+	4.53281e10i	−0.909002	+	0.792742i
$490$	−2.07344e10	+	7.54669e9i	−0.359672	+	0.130910i
$491$	6.53311e10	−	7.78585e10i	1.12407	−	1.33962i	0.190308	−	0.981724i	$-0.439051\pi$
$491$	6.53311e10	−	7.78585e10i	1.12407	−	1.33962i	0.933763	−	0.357891i	$-0.116504\pi$
$492$	−1.12703e8	+	1.39633e8i	−0.00192343	+	0.00238303i
$493$	4.83463e10	+	1.75966e10i	0.818418	+	0.297880i
$494$	1.09554e11	−	6.32513e10i	1.83960	−	1.06209i
$495$	−1.26621e8	+	9.22375e8i	−0.00210905	+	0.0153634i
$496$	3.13748e10	−	5.43428e10i	0.518387	−	0.897873i
$497$	−2.11498e10	−	2.52053e10i	−0.346641	−	0.413111i
$498$	1.34752e10	−	2.44019e10i	0.219087	−	0.396740i
$499$	−1.13923e10	+	6.46088e10i	−0.183742	+	1.04205i	0.743819	+	0.668381i	$0.233012\pi$
$499$	−1.13923e10	+	6.46088e10i	−0.183742	+	1.04205i	−0.927561	+	0.373672i	$0.878099\pi$
$500$	−2.00180e10	−	3.52971e9i	−0.320288	−	0.0564754i
$501$	−2.18570e9	−	1.14697e11i	−0.0346928	−	1.82054i
$502$	−4.97004e10	+	4.17036e10i	−0.782609	+	0.656687i
$503$	−9.70501e9	−	5.60319e9i	−0.151609	−	0.0875313i	0.422277	−	0.906467i	$-0.361231\pi$
$503$	−9.70501e9	−	5.60319e9i	−0.151609	−	0.0875313i	−0.573885	+	0.818936i	$0.694564\pi$
$504$	1.18965e9	+	3.12027e10i	0.0184373	+	0.483582i
$505$	−3.40833e10	−	5.90339e10i	−0.524053	−	0.907687i
$506$	6.71212e8	−	1.84414e9i	0.0102390	−	0.0281314i
$507$	−6.98599e10	+	2.69451e10i	−1.05729	+	0.407800i
$508$	−1.34000e10	−	1.12440e10i	−0.201210	−	0.168836i
$509$	−9.23104e9	−	2.53621e10i	−0.137524	−	0.377845i	0.851743	−	0.523959i	$-0.175546\pi$
$509$	−9.23104e9	−	2.53621e10i	−0.137524	−	0.377845i	−0.989268	+	0.146114i	$0.953323\pi$
$510$	1.02952e10	−	3.00557e10i	0.152179	−	0.444269i
$511$	1.40233e10	+	7.95299e10i	0.205667	+	1.16640i
$512$		−	8.00907e9i		−	0.116547i
$513$	3.90450e10	−	7.75485e10i	0.563762	−	1.11971i
$514$	−3.26658e10			−0.467995
$515$	−3.58935e10	+	6.32899e9i	−0.510254	+	0.0899716i
$516$	−1.33113e9	−	6.79005e9i	−0.0187769	−	0.0957798i
$517$	5.20486e8	−	1.89441e8i	0.00728529	−	0.00265163i
$518$	−3.13638e10	+	3.73779e10i	−0.435621	+	0.519153i
$519$	3.69795e10	+	5.79631e9i	0.509672	+	0.0798881i
$520$	−4.23452e10	−	1.54124e10i	−0.579149	−	0.210793i
$521$	1.10388e11	−	6.37326e10i	1.49820	−	0.864989i	0.498207	−	0.867058i	$-0.333992\pi$
$521$	1.10388e11	−	6.37326e10i	1.49820	−	0.864989i	0.999998	+	0.00206969i	$0.000658804\pi$
$522$	2.17501e10	+	1.00739e11i	0.292941	+	1.35680i
$523$	−4.11516e10	+	7.12766e10i	−0.550022	+	0.952666i	0.448251	+	0.893908i	$0.352047\pi$
$523$	−4.11516e10	+	7.12766e10i	−0.550022	+	0.952666i	−0.998272	+	0.0587576i	$0.981286\pi$
$524$	−1.65963e10	−	1.97787e10i	−0.220134	−	0.262345i
$525$	−1.72824e10	−	2.86587e10i	−0.227492	−	0.377241i
$526$	−2.26701e10	+	1.28569e11i	−0.296149	+	1.67955i
$527$	−4.67503e10	−	8.24334e9i	−0.606096	−	0.106871i
$528$	−2.27595e9	+	1.37249e9i	−0.0292838	+	0.0176593i
$529$	8.62378e9	−	7.23621e9i	0.110122	−	0.0924035i
$530$	−3.38966e10	−	1.95702e10i	−0.429589	−	0.248023i
$531$	8.48501e10	+	9.36310e10i	1.06727	+	1.17772i
$532$	−1.10761e10	−	1.91843e10i	−0.138274	−	0.239497i
$533$	3.56927e8	−	9.80648e8i	0.00442252	−	0.0121508i
$534$	−2.11074e10	+	1.34661e11i	−0.259579	+	1.65607i
$535$	−2.90364e10	−	2.43645e10i	−0.354428	−	0.297401i
$536$	2.18876e10	+	6.01356e10i	0.265179	+	0.728573i
$537$	−6.00877e10	+	1.17797e10i	−0.722585	+	0.141657i
$538$	1.49272e9	+	8.46563e9i	0.0178176	+	0.101049i
$539$		−	1.39645e9i		−	0.0165451i
$540$	1.59190e10	−	3.75581e9i	0.187216	−	0.0441702i
$541$	−2.87855e9			−0.0336035			−0.0168017	−	0.999859i	$-0.505348\pi$
$541$	−2.87855e9			−0.0336035			−0.0168017	+	0.999859i	$0.505348\pi$
$542$	1.82048e11	−	3.21000e10i	2.10955	−	0.371970i
$543$	1.99431e10	+	6.83125e9i	0.229399	+	0.0785780i
$544$	3.97648e10	−	1.44732e10i	0.454049	−	0.165260i
$545$	−1.70085e9	+	2.02700e9i	−0.0192788	+	0.0229756i
$546$	3.45598e10	+	8.96024e10i	0.388867	+	1.00821i
$547$	−3.04941e10	−	1.10989e10i	−0.340617	−	0.123974i	0.166047	−	0.986118i	$-0.446899\pi$
$547$	−3.04941e10	−	1.10989e10i	−0.340617	−	0.123974i	−0.506665	+	0.862143i	$0.669122\pi$
$548$	3.34217e10	−	1.92960e10i	0.370600	−	0.213966i
$549$	2.39489e10	−	4.53913e10i	0.263631	−	0.499670i
$550$	1.02249e9	−	1.77101e9i	0.0111740	−	0.0193540i
$551$	8.88675e10	+	1.05908e11i	0.964132	+	1.14901i
$552$	6.51812e10	−	1.24212e9i	0.702047	−	0.0133784i
$553$	1.03682e10	−	5.88009e10i	0.110867	−	0.628757i
$554$	−1.39468e11	−	2.45919e10i	−1.48059	−	0.261068i
$555$	−4.23069e10	−	2.33627e10i	−0.445902	−	0.246235i
$556$	−8.10706e9	+	6.80263e9i	−0.0848329	+	0.0711832i
$557$	−1.21822e11	−	7.03341e10i	−1.26563	−	0.730710i	−0.291470	−	0.956580i	$-0.594144\pi$
$557$	−1.21822e11	−	7.03341e10i	−1.26563	−	0.730710i	−0.974157	+	0.225870i	$0.927478\pi$
$558$	−3.59045e10	−	8.80541e10i	−0.370350	−	0.908265i
$559$	2.01203e10	+	3.48494e10i	0.206057	+	0.356901i
$560$	−1.46274e10	+	4.01884e10i	−0.148736	+	0.408648i
$561$	1.56460e9	+	1.26284e9i	0.0157961	+	0.0127496i
$562$	1.36422e11	+	1.14472e11i	1.36754	+	1.14750i
$563$	−1.95156e10	−	5.36186e10i	−0.194244	−	0.533681i	0.803888	−	0.594781i	$-0.202761\pi$
$563$	−1.95156e10	−	5.36186e10i	−0.194244	−	0.533681i	−0.998132	+	0.0611000i	$0.980539\pi$
$564$	−6.39562e9	−	7.33358e9i	−0.0632072	−	0.0724769i
$565$	−1.06407e10	−	6.03465e10i	−0.104418	−	0.592186i
$566$			1.83087e11i			1.78399i
$567$	5.35718e10	+	3.84006e10i	0.518328	+	0.371540i
$568$	6.67901e10			0.641680
$569$	−1.32018e11	+	2.32784e10i	−1.25946	+	0.222077i	−0.763237	−	0.646118i	$-0.776391\pi$
$569$	−1.32018e11	+	2.32784e10i	−1.25946	+	0.222077i	−0.496223	+	0.868195i	$0.665280\pi$
$570$	6.43414e10	−	5.61122e10i	0.609525	−	0.531567i
$571$	5.91665e10	−	2.15349e10i	0.556585	−	0.202580i	−0.0483848	−	0.998829i	$-0.515407\pi$
$571$	5.91665e10	−	2.15349e10i	0.556585	−	0.202580i	0.604970	+	0.796248i	$0.293185\pi$
$572$	−9.69461e8	+	1.15536e9i	−0.00905621	+	0.0107928i
$573$	−2.05383e10	+	2.54459e10i	−0.190522	+	0.236047i
$574$	−6.68163e8	−	2.43192e8i	−0.00615510	−	0.00224027i
$575$	−6.05109e10	+	3.49360e10i	−0.553557	+	0.319596i
$576$	−3.96674e10	−	3.07876e10i	−0.360366	−	0.279696i
$577$	6.37070e10	−	1.10344e11i	0.574756	−	0.995507i	−0.421312	−	0.906916i	$-0.638430\pi$
$577$	6.37070e10	−	1.10344e11i	0.574756	−	0.995507i	0.996068	−	0.0885910i	$-0.0282364\pi$
$578$	3.91291e10	+	4.66322e10i	0.350581	+	0.417806i
$579$	−4.75022e10	+	8.60206e10i	−0.422668	+	0.765400i
$580$	−4.52261e9	+	2.56490e10i	−0.0399648	+	0.226651i
$581$	2.79570e10	+	4.92956e9i	0.245350	+	0.0432617i
$582$	2.20732e9	+	1.15831e11i	0.0192386	+	1.00956i
$583$	1.89758e9	−	1.59226e9i	0.0164258	−	0.0137828i
$584$	−1.41966e11	−	8.19639e10i	−1.22048	−	0.704646i
$585$	−8.05066e10	+	5.06652e10i	−0.687397	+	0.432600i
$586$	−1.81874e10	−	3.15015e10i	−0.154234	−	0.267141i
$587$	−1.06263e10	+	2.91956e10i	−0.0895015	+	0.245903i	−0.976365	−	0.216128i	$-0.930657\pi$
$587$	−1.06263e10	+	2.91956e10i	−0.0895015	+	0.245903i	0.886863	+	0.462032i	$0.152879\pi$
$588$	−2.28890e10	+	8.82833e9i	−0.191477	+	0.0738532i
$589$	−9.77203e10	−	8.19971e10i	−0.811940	−	0.681298i
$590$	4.24946e10	+	1.16753e11i	0.350692	+	0.963518i
$591$	5.86756e10	−	1.71297e11i	0.480959	−	1.40410i
$592$	−2.39570e10	−	1.35867e11i	−0.195050	−	1.10618i
$593$			7.72499e10i			0.624711i	0.949965	+	0.312356i	$0.101118\pi$
$593$			7.72499e10i			0.624711i	−0.949965	+	0.312356i	$0.898882\pi$
$594$	−4.71645e8	+	3.99995e9i	−0.00378852	+	0.0321298i
$595$	3.23547e10			0.258148
$596$	−5.84825e10	+	1.03120e10i	−0.463491	+	0.0817259i
$597$	3.56563e9	+	1.81881e10i	0.0280698	+	0.143182i
$598$	1.88415e11	−	6.85774e10i	1.47336	−	0.536261i
$599$	7.99461e10	−	9.52760e10i	0.620998	−	0.740076i	−0.360244	−	0.932858i	$-0.617307\pi$
$599$	7.99461e10	−	9.52760e10i	0.620998	−	0.740076i	0.981242	+	0.192782i	$0.0617510\pi$
$600$	6.71139e10	+	1.05197e10i	0.517854	+	0.0811705i
$601$	−2.16119e11	−	7.86608e10i	−1.65651	−	0.602921i	−0.666703	−	0.745323i	$-0.732295\pi$
$601$	−2.16119e11	−	7.86608e10i	−1.65651	−	0.602921i	−0.989809	+	0.142402i	$0.954517\pi$
$602$	2.37446e10	−	1.37090e10i	0.180792	−	0.104380i
$603$	1.28607e11	+	4.13324e10i	0.972740	+	0.312623i
$604$	−3.94648e10	+	6.83550e10i	−0.296526	+	0.513597i
$605$	4.78512e10	+	5.70269e10i	0.357167	+	0.425655i
$606$	−1.52285e11	−	2.52528e11i	−1.12919	−	1.87249i
$607$	4.05256e10	−	2.29832e11i	0.298521	−	1.69300i	−0.354016	−	0.935240i	$-0.615184\pi$
$607$	4.05256e10	−	2.29832e11i	0.298521	−	1.69300i	0.652537	−	0.757757i	$-0.273705\pi$
$608$	1.11986e11	+	1.97461e10i	0.819498	+	0.144500i
$609$	−8.98791e10	+	5.42008e10i	−0.653415	+	0.394036i
$610$	3.86576e10	−	3.24376e10i	0.279200	−	0.234277i
$611$	4.90089e10	+	2.82953e10i	0.351650	+	0.203025i
$612$	1.08078e10	−	3.36288e10i	0.0770424	−	0.239721i
$613$	7.90435e10	+	1.36907e11i	0.559789	+	0.969583i	0.997514	+	0.0704739i	$0.0224512\pi$
$613$	7.90435e10	+	1.36907e11i	0.559789	+	0.969583i	−0.437725	+	0.899109i	$0.644216\pi$
$614$	3.15025e10	−	8.65523e10i	0.221652	−	0.608983i
$615$	1.09060e8	−	6.95782e8i	0.000762366	−	0.00486377i
$616$	−1.48854e9	−	1.24904e9i	−0.0103380	−	0.00867465i
$617$	−6.27486e10	−	1.72400e11i	−0.432976	−	1.18959i	−0.943977	−	0.330011i	$-0.892948\pi$
$617$	−6.27486e10	−	1.72400e11i	−0.432976	−	1.18959i	0.511002	−	0.859580i	$-0.329275\pi$
$618$	−1.54727e11	+	3.03330e10i	−1.06075	+	0.207951i
$619$	3.91904e10	+	2.22260e11i	0.266942	+	1.51391i	0.763447	+	0.645871i	$0.223506\pi$
$619$	3.91904e10	+	2.22260e11i	0.266942	+	1.51391i	−0.496504	+	0.868034i	$0.665383\pi$
$620$		−	2.40312e10i		−	0.162633i
$621$	8.22900e10	−	1.10301e11i	0.553325	−	0.741671i
$622$	1.21147e11			0.809378
$623$	−1.36705e11	+	2.41048e10i	−0.907470	+	0.160011i
$624$	−2.56889e11	−	8.79943e10i	−1.69437	−	0.580385i
$625$	−2.40786e10	+	8.76390e9i	−0.157802	+	0.0574351i
$626$	−1.00579e11	+	1.19865e11i	−0.654951	+	0.780540i
$627$	1.94434e9	+	5.04104e9i	0.0125806	+	0.0326174i
$628$	9.93014e10	+	3.61427e10i	0.638435	+	0.232371i
$629$	−9.03887e10	+	5.21859e10i	−0.577446	+	0.333389i
$630$	3.45207e10	+	5.48530e10i	0.219138	+	0.348208i
$631$	−1.16579e11	+	2.01921e11i	−0.735368	+	1.27369i	0.219194	+	0.975681i	$0.429657\pi$
$631$	−1.16579e11	+	2.01921e11i	−0.735368	+	1.27369i	−0.954562	+	0.298013i	$0.903676\pi$
$632$	7.79064e10	+	9.28452e10i	0.488320	+	0.581958i
$633$	2.19999e11	−	4.19238e9i	1.37027	−	0.0261124i
$634$	1.64656e9	−	9.33810e9i	0.0101911	−	0.0577965i
$635$	6.76118e10	+	1.19218e10i	0.415841	+	0.0733240i
$636$	−3.80950e10	−	2.10367e10i	−0.232830	−	0.128573i
$637$	1.09295e11	−	9.17092e10i	0.663807	−	0.557000i
$638$	−5.55421e9	−	3.20673e9i	−0.0335228	−	0.0193544i
$639$	8.64436e10	−	1.11376e11i	0.518477	−	0.668018i
$640$	−5.56514e10	−	9.63910e10i	−0.331708	−	0.574535i
$641$	−7.15456e10	+	1.96570e11i	−0.423790	+	1.16435i	0.525731	+	0.850651i	$0.323792\pi$
$641$	−7.15456e10	+	1.96570e11i	−0.423790	+	1.16435i	−0.949521	+	0.313703i	$0.898430\pi$
$642$	−1.27598e11	−	1.02989e11i	−0.751112	−	0.606251i
$643$	2.36854e9	+	1.98744e9i	0.0138560	+	0.0116265i	0.649689	−	0.760200i	$-0.274899\pi$
$643$	2.36854e9	+	1.98744e9i	0.0138560	+	0.0116265i	−0.635833	+	0.771826i	$0.719343\pi$
$644$	−1.20087e10	−	3.29937e10i	−0.0698158	−	0.191817i
$645$	1.78494e10	+	2.04671e10i	0.103130	+	0.118254i
$646$	−3.20156e10	−	1.81570e11i	−0.183837	−	1.04259i
$647$		−	3.30829e10i		−	0.188793i	−0.995535	−	0.0943966i	$-0.969908\pi$
$647$		−	3.30829e10i		−	0.188793i	0.995535	−	0.0943966i	$-0.0300922\pi$
$648$	−1.29613e11	+	3.31990e10i	−0.735101	+	0.188289i
$649$	−7.86324e9			−0.0443224
$650$	2.05761e11	−	3.62812e10i	1.15268	−	0.203249i
$651$	7.29863e10	−	6.36515e10i	0.406366	−	0.354392i
$652$	−7.08483e10	+	2.57867e10i	−0.392048	+	0.142694i
$653$	7.83339e10	−	9.33547e10i	0.430821	−	0.513433i	−0.506338	−	0.862335i	$-0.669001\pi$
$653$	7.83339e10	−	9.33547e10i	0.430821	−	0.513433i	0.937159	+	0.348903i	$0.113446\pi$
$654$	−7.18955e9	+	8.90747e9i	−0.0392998	+	0.0486904i
$655$	9.52247e10	+	3.46589e10i	0.517350	+	0.188300i
$656$	1.74112e9	−	1.00524e9i	0.00940185	−	0.00542816i
$657$	−3.20419e11	+	1.30653e11i	−1.71972	+	0.701223i
$658$	1.92790e10	−	3.33921e10i	0.102844	−	0.178132i
$659$	−1.08052e11	−	1.28771e11i	−0.572916	−	0.682775i	0.399310	−	0.916816i	$-0.369250\pi$
$659$	−1.08052e11	−	1.28771e11i	−0.572916	−	0.682775i	−0.972227	+	0.234041i	$0.924805\pi$
$660$	−4.92033e8	+	8.91011e8i	−0.00259309	+	0.00469578i
$661$	3.13825e10	−	1.77979e11i	0.164392	−	0.932316i	−0.785296	−	0.619120i	$-0.787489\pi$
$661$	3.13825e10	−	1.77979e11i	0.164392	−	0.932316i	0.949689	−	0.313196i	$-0.101400\pi$
$662$	1.54084e11	+	2.71693e10i	0.802282	+	0.141464i
$663$	3.91398e9	+	2.05390e11i	0.0202565	+	1.06298i
$664$	−4.41434e10	+	3.70407e10i	−0.227088	+	0.190549i
$665$	7.52949e10	+	4.34716e10i	0.385016	+	0.222289i
$666$	−1.84914e11	−	9.75624e10i	−0.939881	−	0.495890i
$667$	1.09566e11	+	1.89773e11i	0.553569	+	0.958809i
$668$	4.28942e10	−	1.17851e11i	0.215423	−	0.591871i
$669$	8.04045e10	−	3.10121e10i	0.401398	−	0.154820i
$670$	1.01752e11	+	8.53804e10i	0.504946	+	0.423700i
$671$	1.09233e9	+	3.00114e9i	0.00538843	+	0.0148046i
$672$	−2.79746e10	+	8.16687e10i	−0.137179	+	0.400478i
$673$	1.10197e10	+	6.24957e10i	0.0537166	+	0.304642i	0.999815	−	0.0192375i	$-0.00612385\pi$
$673$	1.10197e10	+	6.24957e10i	0.0537166	+	0.304642i	−0.946098	+	0.323880i	$0.895013\pi$
$674$			2.42892e11i			1.17699i
$675$	1.04405e11	−	9.83007e10i	0.502928	−	0.473523i
$676$	−8.18580e10			−0.391990
$677$	1.72977e11	−	3.05005e10i	0.823442	−	0.145195i	0.253977	−	0.967210i	$-0.418261\pi$
$677$	1.72977e11	−	3.05005e10i	0.823442	−	0.145195i	0.569465	+	0.822015i	$0.307150\pi$
$678$	−5.09978e10	−	2.60137e11i	−0.241342	−	1.23107i
$679$	−1.10869e11	+	4.03530e10i	−0.521592	+	0.189844i
$680$	−4.22161e10	+	5.03112e10i	−0.197443	+	0.235304i
$681$	−1.93962e11	−	3.04023e10i	−0.901836	−	0.141357i
$682$	5.56075e9	+	2.02395e9i	0.0257037	+	0.00935538i
$683$	−2.25895e11	+	1.30420e11i	−1.03806	+	0.599325i	−0.919284	−	0.393596i	$-0.871231\pi$
$683$	−2.25895e11	+	1.30420e11i	−1.03806	+	0.599325i	−0.118778	+	0.992921i	$0.537898\pi$
$684$	7.03350e10	−	6.37388e10i	0.321327	−	0.291192i
$685$	−7.57333e10	+	1.31174e11i	−0.343973	+	0.595779i
$686$	−1.67806e11	−	1.99984e11i	−0.757725	−	0.903021i
$687$	1.36688e11	+	2.26664e11i	0.613624	+	1.01755i
$688$	−1.34619e10	+	7.63461e10i	−0.0600830	+	0.340748i
$689$	2.49240e11	+	4.39478e10i	1.10596	+	0.195011i
$690$	1.15876e11	−	6.98779e10i	0.511206	−	0.308279i
$691$	−4.63160e10	+	3.88637e10i	−0.203151	+	0.170464i	−0.738687	−	0.674048i	$-0.764554\pi$
$691$	−4.63160e10	+	3.88637e10i	−0.203151	+	0.170464i	0.535536	+	0.844512i	$0.320109\pi$
$692$	3.54388e10	+	2.04606e10i	0.154545	+	0.0892266i
$693$	−4.00939e9	+	8.65647e8i	−0.0173838	+	0.00375325i
$694$	1.43751e11	+	2.48984e11i	0.619687	+	1.07333i
$695$	1.42063e10	−	3.90314e10i	0.0608893	−	0.167292i
$696$	3.29917e10	−	2.10482e11i	0.140594	−	0.896969i
$697$	−1.16513e9	−	9.77658e8i	−0.00493676	−	0.00414244i
$698$	1.79582e10	+	4.93397e10i	0.0756556	+	0.207862i
$699$	2.86448e11	−	5.61558e10i	1.19988	−	0.235226i
$700$	−6.35327e9	−	3.60312e10i	−0.0264609	−	0.150067i
$701$			2.34678e11i			0.971852i	0.874000	+	0.485926i	$0.161518\pi$
$701$			2.34678e11i			0.971852i	−0.874000	+	0.485926i	$0.838482\pi$
$702$	−3.44036e11	+	2.25776e11i	−1.41663	+	0.929670i
$703$	−2.80467e11			−1.14831
$704$	3.07730e9	−	5.42611e8i	0.0125279	−	0.00220901i
$705$	3.61301e10	+	1.23759e10i	0.146256	+	0.0500982i
$706$	−3.36789e11	+	1.22581e11i	−1.35562	+	0.493406i
$707$	1.93041e11	−	2.30057e11i	0.772629	−	0.920783i
$708$	4.97114e10	+	1.28886e11i	0.197844	+	0.512945i
$709$	2.36805e11	+	8.61899e10i	0.937143	+	0.341092i	0.765037	−	0.643986i	$-0.222721\pi$
$709$	2.36805e11	+	8.61899e10i	0.937143	+	0.341092i	0.172106	+	0.985078i	$0.444943\pi$
$710$	1.20057e11	−	6.93149e10i	0.472448	−	0.272768i
$711$	2.55655e11	−	9.74725e9i	1.00041	−	0.0381420i
$712$	1.40889e11	−	2.44026e11i	0.548222	−	0.949548i
$713$	−1.29965e11	−	1.54887e11i	−0.502886	−	0.599317i
$714$	1.39942e11	−	2.66679e9i	0.538463	−	0.0102611i
$715$	1.02790e9	−	5.82953e9i	0.00393304	−	0.0223054i
$716$	−6.59241e10	−	1.16242e10i	−0.250837	−	0.0442294i
$717$	1.61941e11	+	8.94270e10i	0.612747	+	0.338370i
$718$	1.20774e11	−	1.01341e11i	0.454439	−	0.381320i
$719$	−2.59305e11	−	1.49710e11i	−0.970275	−	0.560189i	−0.0709551	−	0.997480i	$-0.522605\pi$
$719$	−2.59305e11	−	1.49710e11i	−0.970275	−	0.560189i	−0.899320	+	0.437291i	$0.855938\pi$
$720$	−1.81551e11	−	2.49229e10i	−0.675568	−	0.0927404i
$721$	−8.02868e10	−	1.39061e11i	−0.297100	−	0.514593i
$722$	6.16278e10	−	1.69321e11i	0.226792	−	0.623106i
$723$	2.29359e11	+	1.85124e11i	0.839387	+	0.677500i
$724$	1.76545e10	+	1.48139e10i	0.0642540	+	0.0539155i
$725$	7.80977e10	+	2.14572e11i	0.282674	+	0.776641i
$726$	2.11669e11	+	2.42712e11i	0.761924	+	0.873664i
$727$	3.23715e10	+	1.83588e11i	0.115885	+	0.657214i	0.986308	+	0.164911i	$0.0527337\pi$
$727$	3.23715e10	+	1.83588e11i	0.115885	+	0.657214i	−0.870424	+	0.492303i	$0.836155\pi$
$728$		−	1.98531e11i		−	0.706810i
$729$	−1.12391e11	+	2.59104e11i	−0.397944	+	0.917410i
$730$	−3.40249e11			−1.19813
$731$	5.77575e10	−	1.01842e10i	0.202273	−	0.0356663i
$732$	4.22857e10	−	3.68774e10i	0.147282	−	0.128445i
$733$	−4.74456e11	+	1.72688e11i	−1.64354	+	0.598199i	−0.987652	−	0.156661i	$-0.949927\pi$
$733$	−4.74456e11	+	1.72688e11i	−1.64354	+	0.598199i	−0.655886	+	0.754860i	$0.727705\pi$
$734$	−2.27787e11	+	2.71466e11i	−0.784774	+	0.935257i
$735$	6.04747e10	−	7.49250e10i	0.207217	−	0.256730i
$736$	1.69366e11	+	6.16442e10i	0.577185	+	0.210078i
$737$	−7.28016e9	+	4.20320e9i	−0.0246758	+	0.0142466i
$738$	4.14362e8	−	3.01843e9i	0.00139687	−	0.0101755i
$739$	−3.06215e10	+	5.30379e10i	−0.102671	+	0.177832i	−0.912784	−	0.408442i	$-0.866072\pi$
$739$	−3.06215e10	+	5.30379e10i	−0.102671	+	0.177832i	0.810113	+	0.586273i	$0.199406\pi$
$740$	−3.39620e10	−	4.04743e10i	−0.113257	−	0.134975i
$741$	−2.66853e11	+	4.83237e11i	−0.885112	+	1.60283i
$742$	2.99438e10	−	1.69820e11i	0.0987849	−	0.560237i
$743$	−3.40134e11	−	5.99748e10i	−1.11608	−	0.196795i	−0.414961	−	0.909839i	$-0.636205\pi$
$743$	−3.40134e11	−	5.99748e10i	−1.11608	−	0.196795i	−0.701119	+	0.713044i	$0.747316\pi$
$744$	3.74543e9	+	1.96545e11i	0.0122239	+	0.641461i
$745$	1.78545e11	−	1.49817e11i	0.579593	−	0.486336i
$746$	−4.92176e10	−	2.84158e10i	−0.158915	−	0.0917496i
$747$	4.63434e9	+	1.21552e11i	0.0148835	+	0.390372i
$748$	1.09907e9	+	1.90364e9i	0.00351090	+	0.00608106i
$749$	5.71151e10	−	1.56923e11i	0.181478	−	0.498607i
$750$	3.22006e11	−	1.24198e11i	1.01770	−	0.392527i
$751$	−2.09990e11	−	1.76202e11i	−0.660143	−	0.553926i	0.249987	−	0.968249i	$-0.419574\pi$
$751$	−2.09990e11	−	1.76202e11i	−0.660143	−	0.553926i	−0.910130	+	0.414324i	$0.864018\pi$
$752$	3.72878e10	+	1.02447e11i	0.116599	+	0.320353i
$753$	9.17446e10	−	2.67838e11i	0.285365	−	0.833089i
$754$	−1.13784e11	−	6.45304e11i	−0.352045	−	1.99654i
$755$		−	3.09784e11i		−	0.953392i
$756$	3.95361e10	+	6.02448e10i	0.121034	+	0.184430i
$757$	4.12942e11			1.25749			0.628747	−	0.777610i	$-0.283568\pi$
$757$	4.12942e11			1.25749			0.628747	+	0.777610i	$0.283568\pi$
$758$	−1.72864e11	+	3.04806e10i	−0.523634	+	0.0923308i
$759$	1.64750e9	+	8.40381e9i	0.00496430	+	0.0253226i
$760$	−1.65842e11	+	6.03616e10i	−0.497096	+	0.180928i
$761$	4.01928e10	−	4.78999e10i	0.119842	−	0.142822i	−0.702788	−	0.711400i	$-0.748062\pi$
$761$	4.01928e10	−	4.78999e10i	0.119842	−	0.142822i	0.822630	+	0.568577i	$0.192506\pi$
$762$	2.93421e11	+	4.59920e10i	0.870304	+	0.136415i
$763$	−1.09546e10	−	3.98713e9i	−0.0323219	−	0.0117642i
$764$	−3.09600e10	+	1.78748e10i	−0.0908715	+	0.0524647i
$765$	2.92580e10	+	1.35513e11i	0.0854276	+	0.395672i
$766$	−3.10210e10	+	5.37300e10i	−0.0901033	+	0.156064i
$767$	−5.16405e11	−	6.15427e11i	−1.49214	−	1.77826i
$768$	−1.66698e11	−	2.76429e11i	−0.479165	−	0.794581i
$769$	6.94082e10	−	3.93633e11i	0.198475	−	1.12561i	−0.708908	−	0.705301i	$-0.750812\pi$
$769$	6.94082e10	−	3.93633e11i	0.198475	−	1.12561i	0.907383	−	0.420305i	$-0.138077\pi$
$770$	−3.97194e9	−	7.00361e8i	−0.0112990	−	0.00199232i
$771$	1.22067e11	−	7.36114e10i	0.345446	−	0.208318i
$772$	−8.22944e10	+	6.90532e10i	−0.231687	+	0.194408i
$773$	3.03906e11	+	1.75460e11i	0.851179	+	0.491428i	0.861048	−	0.508523i	$-0.169808\pi$
$773$	3.03906e11	+	1.75460e11i	0.851179	+	0.491428i	−0.00986956	+	0.999951i	$0.503142\pi$
$774$	7.88901e10	+	8.70542e10i	0.219816	+	0.242564i
$775$	−1.05345e11	−	1.82462e11i	−0.292015	−	0.505785i
$776$	8.19123e10	−	2.25052e11i	0.225893	−	0.620635i
$777$	3.29714e10	−	2.10352e11i	0.0904594	−	0.577116i
$778$	−4.28766e10	−	3.59777e10i	−0.117031	−	0.0982008i
$779$	−1.39788e9	−	3.84064e9i	−0.00379594	−	0.0104293i
$780$	−1.02050e11	+	2.00060e10i	−0.275698	+	0.0540483i
$781$	1.52351e9	+	8.64027e9i	0.00409489	+	0.0232233i
$782$		−	2.92228e11i		−	0.781438i
$783$	−3.08289e11	−	3.27433e11i	−0.820184	−	0.871115i
$784$	2.74863e11			0.727531
$785$	−4.08451e11	+	7.20210e10i	−1.07563	+	0.189662i
$786$	4.14728e11	+	1.42060e11i	1.08661	+	0.372205i
$787$	−4.15833e11	+	1.51351e11i	−1.08398	+	0.394535i	−0.821386	−	0.570372i	$-0.806799\pi$
$787$	−4.15833e11	+	1.51351e11i	−1.08398	+	0.394535i	−0.262590	+	0.964907i	$0.584577\pi$
$788$	1.27240e11	−	1.51639e11i	0.330005	−	0.393285i
$789$	−2.05011e11	−	5.31526e11i	−0.529016	−	1.37157i
$790$	2.36394e11	+	8.60403e10i	0.606915	+	0.220899i
$791$	2.33798e11	−	1.34983e11i	0.597221	−	0.344806i
$792$	3.88534e9	−	7.36405e9i	0.00987481	−	0.0187161i
$793$	−1.63152e11	+	2.82587e11i	−0.412571	+	0.714594i
$794$	1.07463e10	+	1.28069e10i	0.0270381	+	0.0322228i
$795$	1.70767e11	−	3.25420e9i	0.427500	−	0.00814658i
$796$	−3.51855e9	+	1.99547e10i	−0.00876419	+	0.0497042i
$797$	4.61690e11	+	8.14084e10i	1.14424	+	0.201760i	0.713460	−	0.700696i	$-0.247127\pi$
$797$	4.61690e11	+	8.14084e10i	1.14424	+	0.201760i	0.430781	+	0.902457i	$0.358238\pi$
$798$	3.29253e11	+	1.81820e11i	0.811930	+	0.448362i
$799$	6.31816e10	−	5.30156e10i	0.155026	−	0.130082i
$800$	1.62650e11	+	9.39058e10i	0.397094	+	0.229262i
$801$	−2.24580e11	−	5.50773e11i	−0.545559	−	1.33796i
$802$	−9.20472e10	−	1.59430e11i	−0.222491	−	0.385366i
$803$	7.36492e9	−	2.02350e10i	0.0177136	−	0.0486676i
$804$	1.14919e11	+	9.27556e10i	0.275023	+	0.221981i
$805$	1.05565e11	+	8.85793e10i	0.251383	+	0.210935i
$806$	2.06786e11	+	5.68139e11i	0.489982	+	1.34621i
$807$	−2.46551e10	−	2.82709e10i	−0.0581316	−	0.0666569i
$808$	1.05858e11	+	6.00352e11i	0.248359	+	1.40851i
$809$			2.16664e11i			0.505817i	0.967490	+	0.252908i	$0.0813871\pi$
$809$			2.16664e11i			0.505817i	−0.967490	+	0.252908i	$0.918613\pi$
$810$	−1.98528e11	+	1.94188e11i	−0.461192	+	0.451110i
$811$	−1.65427e11			−0.382405			−0.191203	−	0.981551i	$-0.561239\pi$
$811$	−1.65427e11			−0.382405			−0.191203	+	0.981551i	$0.561239\pi$
$812$	−1.13001e11	+	1.99250e10i	−0.259930	+	0.0458327i
$813$	−6.07948e11	+	5.30192e11i	−1.39157	+	1.21359i
$814$	1.22260e10	−	4.44989e9i	0.0278475	−	0.0101357i
$815$	1.90209e11	−	2.26682e11i	0.431122	−	0.513791i
$816$	−2.48565e11	+	3.07959e11i	−0.560635	+	0.694597i
$817$	1.48095e11	+	5.39023e10i	0.332394	+	0.120981i
$818$	−7.92294e11	+	4.57431e11i	−1.76959	+	1.02167i
$819$	−3.31061e11	−	2.56950e11i	−0.735821	−	0.571102i
$820$	3.84974e8	−	6.66795e8i	0.000851483	−	0.00147481i
$821$	3.93958e11	+	4.69501e11i	0.867116	+	1.03339i	0.999112	+	0.0421384i	$0.0134170\pi$
$821$	3.93958e11	+	4.69501e11i	0.867116	+	1.03339i	−0.131996	+	0.991250i	$0.542139\pi$
$822$	−3.16754e11	+	5.73603e11i	−0.693801	+	1.25639i
$823$	−3.55321e10	+	2.01513e11i	−0.0774501	+	0.439241i	0.921282	+	0.388896i	$0.127143\pi$
$823$	−3.55321e10	+	2.01513e11i	−0.0774501	+	0.439241i	−0.998732	+	0.0503455i	$0.983968\pi$
$824$	3.20996e11	+	5.66002e10i	0.696290	+	0.122775i
$825$	1.70023e8	+	8.92212e9i	0.000367022	+	0.0192598i
$826$	−4.19321e11	+	3.51852e11i	−0.900795	+	0.755857i
$827$	3.20967e11	+	1.85311e11i	0.686181	+	0.396167i	0.802180	−	0.597083i	$-0.203674\pi$
$827$	3.20967e11	+	1.85311e11i	0.686181	+	0.396167i	−0.115999	+	0.993249i	$0.537007\pi$
$828$	1.27330e11	−	8.01328e10i	0.270901	−	0.170486i
$829$	1.52445e10	+	2.64043e10i	0.0322772	+	0.0559058i	0.881713	−	0.471787i	$-0.156391\pi$
$829$	1.52445e10	+	2.64043e10i	0.0322772	+	0.0559058i	−0.849436	+	0.527692i	$0.823057\pi$
$830$	−4.09080e10	+	1.12394e11i	−0.0861977	+	0.236826i
$831$	5.76585e11	−	2.22390e11i	1.20909	−	0.466349i
$832$	2.44565e11	+	2.05214e11i	0.510388	+	0.428266i
$833$	−7.11196e10	−	1.95399e11i	−0.147710	−	0.405829i
$834$	5.82287e10	−	1.69992e11i	0.120357	−	0.351370i
$835$	8.54745e10	+	4.84750e11i	0.175829	+	0.997176i
$836$			5.90681e9i			0.0120928i
$837$	3.32596e11	+	2.48134e11i	0.677666	+	0.505574i
$838$	1.71125e11			0.347007
$839$	8.55531e10	−	1.50853e10i	0.172658	−	0.0304443i	−0.0866505	−	0.996239i	$-0.527616\pi$
$839$	8.55531e10	−	1.50853e10i	0.172658	−	0.0304443i	0.259309	+	0.965794i	$0.416505\pi$
$840$	−2.57754e10	−	1.31479e11i	−0.0517711	−	0.264082i
$841$	2.02859e11	−	7.38346e10i	0.405518	−	0.147597i
$842$	−4.63439e11	+	5.52305e11i	−0.922028	+	1.09883i
$843$	−7.67746e11	−	1.20340e11i	−1.52022	−	0.238286i
$844$	2.26050e11	+	8.22753e10i	0.445486	+	0.162144i
$845$	2.78235e11	−	1.60639e11i	0.545738	−	0.315082i
$846$	1.57292e11	+	5.05512e10i	0.307062	+	0.0986847i
$847$	−1.63986e11	+	2.84031e11i	−0.318619	+	0.551865i
$848$	3.13404e11	+	3.73501e11i	0.606068	+	0.722284i
$849$	−4.12582e11	−	6.84168e11i	−0.794107	−	1.31684i
$850$	5.28778e10	−	2.99885e11i	0.101297	−	0.574485i
$851$	−4.37787e11	−	7.71936e10i	−0.834727	−	0.147185i
$852$	1.31990e11	−	7.95955e10i	0.250486	−	0.151053i
$853$	5.31783e11	−	4.46219e11i	1.00447	−	0.842853i	0.0168750	−	0.999858i	$-0.494628\pi$
$853$	5.31783e11	−	4.46219e11i	1.00447	−	0.842853i	0.987598	+	0.157005i	$0.0501838\pi$
$854$	1.92540e11	+	1.11163e11i	0.361985	+	0.208992i
$855$	−1.13986e11	+	3.54674e11i	−0.213299	+	0.663689i
$856$	1.69490e11	+	2.93565e11i	0.315681	+	0.546775i
$857$	−1.56253e10	+	4.29300e10i	−0.0289670	+	0.0795862i	−0.953333	−	0.301920i	$-0.902372\pi$
$857$	−1.56253e10	+	4.29300e10i	−0.0289670	+	0.0795862i	0.924366	+	0.381506i	$0.124595\pi$
$858$	3.96546e9	−	2.52990e10i	0.00731719	−	0.0466824i
$859$	7.59299e11	+	6.37127e11i	1.39457	+	1.17018i	0.963450	+	0.267887i	$0.0863255\pi$
$859$	7.59299e11	+	6.37127e11i	1.39457	+	1.17018i	0.431119	+	0.902295i	$0.358119\pi$
$860$	1.01543e10	+	2.78988e10i	0.0185634	+	0.0510025i
$861$	3.04484e9	−	5.96917e8i	0.00554054	−	0.00108618i
$862$	−1.52877e11	−	8.67008e11i	−0.276893	−	1.57034i
$863$		−	2.70088e11i		−	0.486926i	−0.969910	−	0.243463i	$-0.921717\pi$
$863$		−	2.70088e11i		−	0.486926i	0.969910	−	0.243463i	$-0.0782834\pi$
$864$	−3.67356e11	−	4.33159e10i	−0.659222	−	0.0777307i
$865$	−1.60608e11			−0.286882
$866$	4.35020e11	−	7.67058e10i	0.773460	−	0.136382i
$867$	−2.51303e11	−	8.60808e10i	−0.444755	−	0.152346i
$868$	9.94880e10	−	3.62107e10i	0.175264	−	0.0637907i
$869$	−1.02338e10	+	1.21962e10i	−0.0179456	+	0.0213867i
$870$	−1.59135e11	−	4.12585e11i	−0.277772	−	0.720173i
$871$	−8.07081e11	−	2.93753e11i	−1.40231	−	0.510399i
$872$	2.04934e10	−	1.18318e10i	0.0354444	−	0.0204638i
$873$	−2.69271e11	−	4.27869e11i	−0.463588	−	0.736637i
$874$	3.92635e11	−	6.80065e11i	0.672890	−	1.16548i
$875$	2.25926e11	+	2.69248e11i	0.385419	+	0.459325i
$876$	−3.78230e11	+	7.20768e9i	−0.642302	+	0.0122399i
$877$	6.08459e10	−	3.45074e11i	0.102857	−	0.583330i	−0.889198	−	0.457523i	$-0.848737\pi$
$877$	6.08459e10	−	3.45074e11i	0.102857	−	0.583330i	0.992055	−	0.125807i	$-0.0401521\pi$
$878$	−5.72086e11	−	1.00874e11i	−0.962683	−	0.169747i
$879$	1.38951e11	+	7.67312e10i	0.232758	+	0.128533i
$880$	8.73588e9	−	7.33028e9i	0.0145672	−	0.0122233i
$881$	4.63683e11	+	2.67708e11i	0.769694	+	0.444383i	0.832765	−	0.553626i	$-0.186756\pi$
$881$	4.63683e11	+	2.67708e11i	0.769694	+	0.444383i	−0.0630716	+	0.998009i	$0.520090\pi$
$882$	2.55393e11	−	3.29054e11i	0.422022	−	0.543743i
$883$	−3.50386e10	−	6.06887e10i	−0.0576374	−	0.0998309i	0.835767	−	0.549084i	$-0.185023\pi$
$883$	−3.50386e10	−	6.06887e10i	−0.0576374	−	0.0998309i	−0.893404	+	0.449253i	$0.851690\pi$
$884$	−7.68118e10	+	2.11039e11i	−0.125782	+	0.345583i
$885$	−4.21894e11	−	3.40527e11i	−0.687750	−	0.555109i
$886$	−2.16468e10	−	1.81638e10i	−0.0351284	−	0.0294762i
$887$	−2.07018e11	−	5.68777e11i	−0.334436	−	0.918856i	−0.986943	−	0.161073i	$-0.948505\pi$
$887$	−2.07018e11	−	5.68777e11i	−0.334436	−	0.918856i	0.652506	−	0.757783i	$-0.273718\pi$
$888$	2.84075e11	+	3.25736e11i	0.456857	+	0.523858i
$889$	5.25232e10	+	2.97874e11i	0.0840899	+	0.476898i
$890$		−	5.84858e11i		−	0.932161i
$891$	−7.25129e9	−	1.60100e10i	−0.0115055	−	0.0254027i
$892$	9.42136e10			0.148818
$893$	2.18266e11	−	3.84862e10i	0.343226	−	0.0605200i
$894$	7.59905e11	−	6.62714e11i	1.18962	−	1.03747i
$895$	2.46887e11	−	8.98594e10i	0.384774	−	0.140046i
$896$	3.15198e11	−	3.75638e11i	0.489048	−	0.582825i
$897$	−5.49538e11	+	6.80849e11i	−0.848845	+	1.05167i
$898$	−5.87301e11	−	2.13760e11i	−0.903141	−	0.328716i
$899$	−5.72236e11	+	3.30380e11i	−0.876064	+	0.505796i
$900$	1.45167e11	−	5.91924e10i	0.221257	−	0.0902186i
$901$	1.84429e11	−	3.19440e11i	0.279853	−	0.484719i
$902$	1.21871e8	+	1.45241e8i	0.000184109	+	0.000219413i
$903$	−5.78370e10	+	1.04736e11i	−0.0869871	+	0.157523i
$904$	−9.51599e10	+	5.39679e11i	−0.142489	+	0.808094i
$905$	−8.90782e10	−	1.57069e10i	−0.132794	−	0.0234151i
$906$	−2.55335e10	−	1.33990e12i	−0.0378964	−	1.98865i
$907$	3.57812e11	−	3.00240e11i	0.528721	−	0.443649i	−0.338939	−	0.940808i	$-0.610068\pi$
$907$	3.57812e11	−	3.00240e11i	0.528721	−	0.443649i	0.867659	+	0.497159i	$0.165624\pi$
$908$	−1.85881e11	−	1.07318e11i	−0.273458	−	0.157881i
$909$	1.13813e12	+	6.00486e11i	1.66700	+	0.879524i
$910$	−2.06036e11	−	3.56864e11i	−0.300453	−	0.520401i
$911$	−3.31123e11	+	9.09752e11i	−0.480746	+	1.32084i	0.428110	+	0.903727i	$0.359180\pi$
$911$	−3.31123e11	+	9.09752e11i	−0.480746	+	1.32084i	−0.908855	+	0.417111i	$0.863042\pi$
$912$	−9.92228e11	+	3.82704e11i	−1.43427	+	0.553202i
$913$	−5.79869e9	−	4.86568e9i	−0.00834539	−	0.00700261i
$914$	−4.00538e11	−	1.10047e12i	−0.573930	−	1.57686i
$915$	−7.13602e10	+	2.08328e11i	−0.101806	+	0.297209i
$916$	5.02485e10	+	2.84973e11i	0.0713741	+	0.404783i
$917$			4.46451e11i			0.631388i
$918$	1.37718e11	+	5.83718e11i	0.193918	+	0.821925i
$919$	3.60571e11			0.505509			0.252755	−	0.967530i	$-0.418663\pi$
$919$	3.60571e11			0.505509			0.252755	+	0.967530i	$0.418663\pi$
$920$	−2.75480e11	+	4.85745e10i	−0.384537	+	0.0678043i
$921$	7.73232e10	+	3.94422e11i	0.107466	+	0.548179i
$922$	5.44086e11	−	1.98031e11i	0.752911	−	0.274037i
$923$	−5.76188e11	+	6.86675e11i	−0.793885	+	0.946116i
$924$	−4.43015e9	−	6.94400e8i	−0.00607758	−	0.000952625i
$925$	−4.35290e11	−	1.58433e11i	−0.594582	−	0.216410i
$926$	−7.23198e11	+	4.17538e11i	−0.983588	+	0.567875i
$927$	5.09835e11	−	4.62022e11i	0.690416	−	0.625667i
$928$	2.94506e11	−	5.10099e11i	0.397102	−	0.687801i
$929$	2.68522e11	+	3.20012e11i	0.360509	+	0.429638i	0.915562	−	0.402177i	$-0.131746\pi$
$929$	2.68522e11	+	3.20012e11i	0.360509	+	0.429638i	−0.555053	+	0.831815i	$0.687302\pi$
$930$	2.10707e11	+	3.49407e11i	0.281674	+	0.467090i
$931$	9.70300e10	−	5.50285e11i	0.129154	−	0.732468i
$932$	3.14271e11	+	5.54144e10i	0.416524	+	0.0734444i
$933$	−4.52707e11	+	2.73001e11i	−0.597435	+	0.360278i
$934$	−1.13897e12	+	9.55706e11i	−1.49666	+	1.25585i
$935$	−7.47145e9	−	4.31365e9i	−0.00977594	−	0.00564414i
$936$	8.31520e11	−	1.79529e11i	1.08335	−	0.233901i
$937$	−2.31539e11	−	4.01037e11i	−0.300376	−	0.520266i	0.675845	−	0.737044i	$-0.263779\pi$
$937$	−2.31539e11	−	4.01037e11i	−0.300376	−	0.520266i	−0.976221	+	0.216777i	$0.930445\pi$
$938$	−2.00148e11	+	5.49903e11i	−0.258548	+	0.710354i
$939$	1.05734e11	−	6.74567e11i	0.136005	−	0.867687i
$940$	3.19840e10	+	2.68377e10i	0.0409658	+	0.0343744i
$941$	3.23231e11	+	8.88071e11i	0.412245	+	1.13263i	0.955994	+	0.293386i	$0.0947820\pi$
$941$	3.23231e11	+	8.88071e11i	0.412245	+	1.13263i	−0.543749	+	0.839248i	$0.682996\pi$
$942$	−1.76072e12	+	3.45175e11i	−2.23608	+	0.438365i
$943$	−1.12491e9	−	6.37968e9i	−0.00142256	−	0.00806774i
$944$		−	1.54772e12i		−	1.94897i
$945$	−2.52608e11	−	1.27186e11i	−0.316752	−	0.159482i
$946$	−7.31091e9			−0.00912866
$947$	1.13441e11	−	2.00028e10i	0.141049	−	0.0248708i	−0.102678	−	0.994715i	$-0.532741\pi$
$947$	1.13441e11	−	2.00028e10i	0.141049	−	0.0248708i	0.243727	+	0.969844i	$0.421630\pi$
$948$	2.64604e11	+	9.06370e10i	0.327615	+	0.112220i
$949$	2.06739e12	−	7.52470e11i	2.54893	−	0.927736i
$950$	5.25980e11	−	6.26838e11i	0.645765	−	0.769593i
$951$	1.48902e10	+	3.86054e10i	0.0182045	+	0.0471983i
$952$	−2.71898e11	−	9.89628e10i	−0.331023	−	0.120483i
$953$	−7.23371e11	+	4.17638e11i	−0.876980	+	0.506324i	−0.869661	−	0.493649i	$-0.835663\pi$
$953$	−7.23371e11	+	4.17638e11i	−0.876980	+	0.506324i	−0.00731829	+	0.999973i	$0.502330\pi$
$954$	7.38344e11	−	2.81505e10i	0.891385	−	0.0339854i
$955$	7.01552e10	−	1.21512e11i	0.0843424	−	0.146085i
$956$	1.29999e11	+	1.54927e11i	0.155635	+	0.185479i
$957$	2.79814e10	−	5.33224e8i	0.0333597	−	0.000635714i
$958$	−4.76817e10	+	2.70416e11i	−0.0566096	+	0.321049i
$959$	−6.57171e11	−	1.15877e11i	−0.776969	−	0.137001i
$960$	1.88608e11	+	1.04153e11i	0.222062	+	0.122627i
$961$	−1.86313e11	+	1.56335e11i	−0.218448	+	0.183300i
$962$	1.15120e12	+	6.64644e11i	1.34415	+	0.776048i
$963$	7.08897e11	+	9.73157e10i	0.824286	+	0.113156i
$964$	1.61116e11	+	2.79061e11i	0.186565	+	0.323140i
$965$	1.44207e11	−	3.96206e11i	0.166295	−	0.456891i
$966$	4.63896e11	+	3.74427e11i	0.532736	+	0.429991i
$967$	−5.96657e11	−	5.00655e11i	−0.682369	−	0.572575i	0.234329	−	0.972157i	$-0.424711\pi$
$967$	−5.96657e11	−	5.00655e11i	−0.682369	−	0.572575i	−0.916697	+	0.399582i	$0.869155\pi$
$968$	−2.27699e11	−	6.25598e11i	−0.259334	−	0.712514i
$969$	5.28798e11	+	6.06350e11i	0.599784	+	0.687746i
$970$	−8.63202e10	−	4.89546e11i	−0.0975046	−	0.552976i
$971$		−	8.97129e11i		−	1.00920i	−0.863353	−	0.504601i	$-0.831640\pi$
$971$		−	8.97129e11i		−	1.00920i	0.863353	−	0.504601i	$-0.168360\pi$
$972$	−2.16575e11	+	2.20070e11i	−0.242630	+	0.246545i
$973$	1.82995e11			0.204168
$974$	1.83746e11	−	3.23993e10i	0.204165	−	0.0359998i
$975$	−6.87136e11	+	5.99252e11i	−0.760368	+	0.663118i
$976$	−5.90715e11	+	2.15003e11i	−0.650997	+	0.236943i
$977$	−9.94842e10	+	1.18561e11i	−0.109188	+	0.130125i	−0.817871	−	0.575402i	$-0.804846\pi$
$977$	−9.94842e10	+	1.18561e11i	−0.109188	+	0.130125i	0.708682	+	0.705528i	$0.249290\pi$
$978$	8.04018e11	−	9.96136e11i	0.878841	−	1.08884i
$979$	3.47821e10	+	1.26597e10i	0.0378639	+	0.0137813i
$980$	9.11612e10	−	5.26320e10i	0.0988339	−	0.0570618i
$981$	6.79348e9	−	4.94872e10i	0.00733527	−	0.0534339i
$982$	−9.43301e11	+	1.63384e12i	−1.01439	+	1.75697i
$983$	1.17650e11	+	1.40210e11i	0.126002	+	0.150163i	0.825357	−	0.564611i	$-0.190974\pi$
$983$	1.17650e11	+	1.40210e11i	0.126002	+	0.150163i	−0.699355	+	0.714774i	$0.746529\pi$
$984$	−3.04468e9	+	5.51355e9i	−0.00324759	+	0.00588100i
$985$	−1.34911e11	+	7.65118e11i	−0.143319	+	0.812800i
$986$	−9.40495e11	−	1.65835e11i	−0.995059	−	0.175456i
$987$	3.20576e9	+	1.68226e11i	0.00337803	+	0.177265i
$988$	−4.62305e11	+	3.87920e11i	−0.485177	+	0.407112i
$989$	2.16329e11	+	1.24898e11i	0.226115	+	0.130548i
$990$	−6.58418e8	−	1.72693e10i	−0.000685426	−	0.0179777i
$991$	2.68198e11	+	4.64533e11i	0.278075	+	0.481640i	0.970906	−	0.239460i	$-0.0769703\pi$
$991$	2.68198e11	+	4.64533e11i	0.278075	+	0.481640i	−0.692831	+	0.721100i	$0.743637\pi$
$992$	−1.85880e11	+	5.10700e11i	−0.191949	+	0.527374i
$993$	−6.37014e11	+	2.45697e11i	−0.655167	+	0.252699i
$994$	4.67865e11	+	3.92585e11i	0.479264	+	0.402150i
$995$	−2.71997e10	−	7.47307e10i	−0.0277506	−	0.0762442i
$996$	−4.30935e10	+	1.25806e11i	−0.0437899	+	0.127840i
$997$	−1.28567e11	−	7.29138e11i	−0.130121	−	0.737953i	−0.978134	−	0.207977i	$-0.933312\pi$
$997$	−1.28567e11	−	7.29138e11i	−0.130121	−	0.737953i	0.848013	−	0.529976i	$-0.177799\pi$
$998$		−	1.21778e12i		−	1.22757i
$999$	9.10847e11	−	5.21228e10i	0.914500	−	0.0523318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.f.a.14.6	yes	138
3.2	odd	2		81.9.f.a.71.18		138
27.2	odd	18	inner	27.9.f.a.2.6	✓	138
27.25	even	9		81.9.f.a.8.18		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.6	✓	138	27.2	odd	18	inner
27.9.f.a.14.6	yes	138	1.1	even	1	trivial
81.9.f.a.8.18		138	27.25	even	9
81.9.f.a.71.18		138	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.2801 + 3.22328i) q^{2} +(61.0463 - 53.2386i) q^{3} +(83.2125 - 30.2869i) q^{4} +(-223.403 + 266.242i) q^{5} +(-944.332 + 1169.98i) q^{6} +(-1438.86 - 523.701i) q^{7} +(2691.76 - 1554.09i) q^{8} +(892.309 - 6500.04i) q^{9} +(3225.67 - 5587.03i) q^{10} +(262.444 + 312.769i) q^{11} +(3467.39 - 6279.02i) q^{12} +(-7243.71 + 41081.1i) q^{13} +(27990.6 + 4935.49i) q^{14} +(536.374 + 28146.7i) q^{15} +(-61562.3 + 51656.9i) q^{16} +(52651.8 + 30398.5i) q^{17} +(4639.91 + 121698. i) q^{18} +(81686.6 + 141485. i) q^{19} +(-10526.3 + 28920.8i) q^{20} +(-115718. + 44632.7i) q^{21} +(-5805.66 - 4871.53i) q^{22} +(88565.0 + 243330. i) q^{23} +(81584.6 - 238177. i) q^{24} +(46855.7 + 265732. i) q^{25} -774316. i q^{26} +(-291581. - 444309. i) q^{27} -135592. q^{28} +(833385. - 146948. i) q^{29} +(-100530. - 512798. i) q^{30} +(-733729. + 267056. i) q^{31} +(447401. - 533192. i) q^{32} +(32672.6 + 5121.24i) q^{33} +(-1.06047e6 - 385978. i) q^{34} +(460877. - 266087. i) q^{35} +(-122615. - 567910. i) q^{36} +(-858362. + 1.48673e6i) q^{37} +(-1.94929e6 - 2.32307e6i) q^{38} +(1.74490e6 + 2.89349e6i) q^{39} +(-187585. + 1.06385e6i) q^{40} +(-24637.0 - 4344.17i) q^{41} +(1.97148e6 - 1.18888e6i) q^{42} +(738972. - 620071. i) q^{43} +(31311.4 + 18077.7i) q^{44} +(1.53124e6 + 1.68970e6i) q^{45} +(-2.40330e6 - 4.16264e6i) q^{46} +(463987. - 1.27479e6i) q^{47} +(-1.00801e6 + 6.43096e6i) q^{48} +(-2.62005e6 - 2.19848e6i) q^{49} +(-1.71306e6 - 4.70659e6i) q^{50} +(4.83258e6 - 947388. i) q^{51} +(641451. + 3.63785e6i) q^{52} -6.06703e6i q^{53} +(6.76226e6 + 7.18218e6i) q^{54} -141903. q^{55} +(-4.68694e6 + 826433. i) q^{56} +(1.25192e7 + 4.28829e6i) q^{57} +(-1.47607e7 + 5.37247e6i) q^{58} +(-1.23794e7 + 1.47532e7i) q^{59} +(897110. + 2.32592e6i) q^{60} +(7.35050e6 + 2.67536e6i) q^{61} +(1.25519e7 - 7.24683e6i) q^{62} +(-4.68799e6 + 8.88533e6i) q^{63} +(3.82665e6 - 6.62796e6i) q^{64} +(-9.31923e6 - 1.11062e7i) q^{65} +(-613767. + 11696.2i) q^{66} +(-3.57529e6 + 2.02765e7i) q^{67} +(5.30197e6 + 934880. i) q^{68} +(1.83611e7 + 1.01394e7i) q^{69} +(-7.56721e6 + 6.34965e6i) q^{70} +(1.86096e7 + 1.07443e7i) q^{71} +(-7.69975e6 - 1.88833e7i) q^{72} +(-2.63704e7 - 4.56749e7i) q^{73} +(1.08988e7 - 2.99443e7i) q^{74} +(1.70076e7 + 1.37274e7i) q^{75} +(1.10825e7 + 9.29932e6i) q^{76} +(-213822. - 587472. i) q^{77} +(-4.12235e7 - 4.72692e7i) q^{78} +(6.77127e6 + 3.84018e7i) q^{79} -2.79308e7i q^{80} +(-4.14543e7 - 1.16001e7i) q^{81} +464371. q^{82} +(-1.82582e7 + 3.21941e6i) q^{83} +(-8.27741e6 + 7.21874e6i) q^{84} +(-1.98560e7 + 7.22697e6i) q^{85} +(-1.15098e7 + 1.37169e7i) q^{86} +(4.30518e7 - 5.33389e7i) q^{87} +(1.19251e6 + 434037. i) q^{88} +(7.85112e7 - 4.53284e7i) q^{89} +(-3.34376e7 - 2.59523e7i) q^{90} +(3.19369e7 - 5.53163e7i) q^{91} +(1.47394e7 + 1.75658e7i) q^{92} +(-3.05738e7 + 5.53655e7i) q^{93} +(-4.37272e6 + 2.47989e7i) q^{94} +(-5.59184e7 - 9.85992e6i) q^{95} +(-1.07418e6 - 5.63684e7i) q^{96} +(5.90263e7 - 4.95290e7i) q^{97} +(5.49811e7 + 3.17433e7i) q^{98} +(2.26719e6 - 1.42681e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) \) 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

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