LMFDB - Embedded newform 54.8.e.b.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,8,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.8687913761$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	54.7
Dual form			54.8.e.b.31.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.51754 - 2.73616i) q^{2} +(37.5285 + 27.9037i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-21.4637 - 121.726i) q^{5} +(358.471 + 107.083i) q^{6} +(674.452 + 565.932i) q^{7} +(256.000 - 443.405i) q^{8} +(629.771 + 2094.36i) q^{9} +O(q^{10})$	\(q+(7.51754 - 2.73616i) q^{2} +(37.5285 + 27.9037i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-21.4637 - 121.726i) q^{5} +(358.471 + 107.083i) q^{6} +(674.452 + 565.932i) q^{7} +(256.000 - 443.405i) q^{8} +(629.771 + 2094.36i) q^{9} +(-494.417 - 856.356i) q^{10} +(854.485 - 4846.03i) q^{11} +(2987.81 - 175.833i) q^{12} +(8397.69 + 3056.51i) q^{13} +(6618.70 + 2409.01i) q^{14} +(2591.12 - 5167.12i) q^{15} +(711.263 - 4033.77i) q^{16} +(2819.87 + 4884.16i) q^{17} +(10464.8 + 14021.3i) q^{18} +(-15908.5 + 27554.3i) q^{19} +(-6059.93 - 5084.88i) q^{20} +(9519.56 + 40058.3i) q^{21} +(-6835.88 - 38768.2i) q^{22} +(12782.4 - 10725.7i) q^{23} +(21979.9 - 9496.97i) q^{24} +(59056.8 - 21494.9i) q^{25} +71493.1 q^{26} +(-34806.1 + 96171.2i) q^{27} +56347.8 q^{28} +(-19735.6 + 7183.17i) q^{29} +(5340.75 - 45933.8i) q^{30} +(106699. - 89531.1i) q^{31} +(-5690.10 - 32270.2i) q^{32} +(167289. - 158021. i) q^{33} +(34562.4 + 29001.3i) q^{34} +(54412.8 - 94245.7i) q^{35} +(117034. + 76772.2i) q^{36} +(-179906. - 311606. i) q^{37} +(-44199.6 + 250668. i) q^{38} +(229865. + 349032. i) q^{39} +(-59468.8 - 21644.9i) q^{40} +(-356423. - 129727. i) q^{41} +(181170. + 275093. i) q^{42} +(-133408. + 756592. i) q^{43} +(-157465. - 272737. i) q^{44} +(241422. - 121613. i) q^{45} +(66745.0 - 115606. i) q^{46} +(-161286. - 135335. i) q^{47} +(139250. - 131534. i) q^{48} +(-8400.76 - 47643.1i) q^{49} +(385149. - 323178. i) q^{50} +(-30460.5 + 261980. i) q^{51} +(537452. - 195617. i) q^{52} -1.41530e6 q^{53} +(1483.70 + 818206. i) q^{54} -608230. q^{55} +(423597. - 154177. i) q^{56} +(-1.36588e6 + 590165. i) q^{57} +(-128709. + 108000. i) q^{58} +(48246.6 + 273620. i) q^{59} +(-85532.9 - 359922. i) q^{60} +(-1.20479e6 - 1.01094e6i) q^{61} +(557143. - 964999. i) q^{62} +(-760518. + 1.76896e6i) q^{63} +(-131072. - 227023. i) q^{64} +(191813. - 1.08783e6i) q^{65} +(825235. - 1.64566e6i) q^{66} +(-3.54611e6 - 1.29068e6i) q^{67} +(339176. + 123450. i) q^{68} +(778991. - 45843.5i) q^{69} +(151179. - 857378. i) q^{70} +(-1.63079e6 - 2.82461e6i) q^{71} +(1.08987e6 + 256913. i) q^{72} +(-2.60790e6 + 4.51701e6i) q^{73} +(-2.20505e6 - 1.85026e6i) q^{74} +(2.81610e6 + 841230. i) q^{75} +(353597. + 2.00535e6i) q^{76} +(3.31883e6 - 2.78483e6i) q^{77} +(2.68303e6 + 1.99492e6i) q^{78} +(-5.50965e6 + 2.00535e6i) q^{79} -506283. q^{80} +(-3.98975e6 + 2.63794e6i) q^{81} -3.03438e6 q^{82} +(4.50803e6 - 1.64079e6i) q^{83} +(2.11465e6 + 1.57231e6i) q^{84} +(534007. - 448085. i) q^{85} +(1.06726e6 + 6.05274e6i) q^{86} +(-941083. - 281122. i) q^{87} +(-1.93000e6 - 1.61947e6i) q^{88} +(5.12872e6 - 8.88321e6i) q^{89} +(1.48215e6 - 1.57480e6i) q^{90} +(3.93406e6 + 6.81399e6i) q^{91} +(185442. - 1.05170e6i) q^{92} +(6.50249e6 - 382671. i) q^{93} +(-1.58277e6 - 576081. i) q^{94} +(3.69554e6 + 1.34507e6i) q^{95} +(686915. - 1.36983e6i) q^{96} +(-591411. + 3.35406e6i) q^{97} +(-193512. - 335173. i) q^{98} +(1.06875e7 - 1.26228e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9}+O(q^{10}) $ 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9} - 3000 q^{10} - 2523 q^{11} - 5376 q^{12} - 9924 q^{13} + 13416 q^{14} - 15084 q^{15} + 29478 q^{17} + 22848 q^{18} - 61731 q^{19} - 27264 q^{20} - 36372 q^{21} + 20184 q^{22} + 255234 q^{23} + 558999 q^{25} - 316368 q^{26} - 51597 q^{27} + 263424 q^{28} + 132153 q^{29} + 610632 q^{30} + 776898 q^{31} + 645795 q^{33} + 387840 q^{34} - 321081 q^{35} - 314688 q^{36} - 759795 q^{37} + 174504 q^{38} - 84012 q^{39} - 109056 q^{40} + 349287 q^{41} + 313752 q^{42} - 1043622 q^{43} + 255552 q^{44} + 845496 q^{45} - 524472 q^{46} + 1280709 q^{47} - 872448 q^{48} + 1011003 q^{49} - 1537704 q^{50} - 7812153 q^{51} - 635136 q^{52} - 2951976 q^{53} - 1256832 q^{54} + 2539854 q^{55} + 858624 q^{56} - 3973923 q^{57} - 47496 q^{58} + 639426 q^{59} - 94464 q^{60} + 1639350 q^{61} + 2859936 q^{62} + 6955635 q^{63} - 8650752 q^{64} - 4119567 q^{65} + 712512 q^{66} - 6408441 q^{67} - 1634496 q^{68} - 1007298 q^{69} + 2380872 q^{70} + 3531612 q^{71} + 6623232 q^{72} - 6666213 q^{73} + 7873368 q^{74} + 16535910 q^{75} - 1396032 q^{76} - 8256489 q^{77} - 4117104 q^{78} - 22540695 q^{79} - 3072000 q^{80} - 13134636 q^{81} + 3798096 q^{82} + 8663238 q^{83} + 8570304 q^{84} - 15143175 q^{85} + 8348976 q^{86} + 45908613 q^{87} + 11028480 q^{88} + 21718137 q^{89} - 27904392 q^{90} - 8606796 q^{91} - 8332800 q^{92} - 20412249 q^{93} - 10358784 q^{94} - 21603363 q^{95} - 5505024 q^{96} - 17397492 q^{97} + 44171448 q^{98} + 103927383 q^{99}+O(q^{100}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9 - 3000 * q^10 - 2523 * q^11 - 5376 * q^12 - 9924 * q^13 + 13416 * q^14 - 15084 * q^15 + 29478 * q^17 + 22848 * q^18 - 61731 * q^19 - 27264 * q^20 - 36372 * q^21 + 20184 * q^22 + 255234 * q^23 + 558999 * q^25 - 316368 * q^26 - 51597 * q^27 + 263424 * q^28 + 132153 * q^29 + 610632 * q^30 + 776898 * q^31 + 645795 * q^33 + 387840 * q^34 - 321081 * q^35 - 314688 * q^36 - 759795 * q^37 + 174504 * q^38 - 84012 * q^39 - 109056 * q^40 + 349287 * q^41 + 313752 * q^42 - 1043622 * q^43 + 255552 * q^44 + 845496 * q^45 - 524472 * q^46 + 1280709 * q^47 - 872448 * q^48 + 1011003 * q^49 - 1537704 * q^50 - 7812153 * q^51 - 635136 * q^52 - 2951976 * q^53 - 1256832 * q^54 + 2539854 * q^55 + 858624 * q^56 - 3973923 * q^57 - 47496 * q^58 + 639426 * q^59 - 94464 * q^60 + 1639350 * q^61 + 2859936 * q^62 + 6955635 * q^63 - 8650752 * q^64 - 4119567 * q^65 + 712512 * q^66 - 6408441 * q^67 - 1634496 * q^68 - 1007298 * q^69 + 2380872 * q^70 + 3531612 * q^71 + 6623232 * q^72 - 6666213 * q^73 + 7873368 * q^74 + 16535910 * q^75 - 1396032 * q^76 - 8256489 * q^77 - 4117104 * q^78 - 22540695 * q^79 - 3072000 * q^80 - 13134636 * q^81 + 3798096 * q^82 + 8663238 * q^83 + 8570304 * q^84 - 15143175 * q^85 + 8348976 * q^86 + 45908613 * q^87 + 11028480 * q^88 + 21718137 * q^89 - 27904392 * q^90 - 8606796 * q^91 - 8332800 * q^92 - 20412249 * q^93 - 10358784 * q^94 - 21603363 * q^95 - 5505024 * q^96 - 17397492 * q^97 + 44171448 * q^98 + 103927383 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	7.51754	−	2.73616i	0.664463	−	0.241845i
$2$	7.51754	−	2.73616i	0.664463	−	0.241845i
$3$	37.5285	+	27.9037i	0.802484	+	0.596674i
$3$	37.5285	+	27.9037i	0.802484	+	0.596674i
$4$	49.0268	−	41.1384i	0.383022	−	0.321394i
$5$	−21.4637	−	121.726i	−0.0767907	−	0.435502i	−0.998828	−	0.0484008i	$-0.984588\pi$
$5$	−21.4637	−	121.726i	−0.0767907	−	0.435502i	0.922037	−	0.387101i	$-0.126524\pi$
$6$	358.471	+	107.083i	0.677523	+	0.202391i
$7$	674.452	+	565.932i	0.743204	+	0.623622i	0.933696	−	0.358067i	$-0.116564\pi$
$7$	674.452	+	565.932i	0.743204	+	0.623622i	−0.190492	+	0.981689i	$0.561008\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	629.771	+	2094.36i	0.287961	+	0.957642i
$10$	−494.417	−	856.356i	−0.156348	−	0.270803i
$11$	854.485	−	4846.03i	0.193566	−	1.09777i	−0.720879	−	0.693061i	$-0.756262\pi$
$11$	854.485	−	4846.03i	0.193566	−	1.09777i	0.914446	−	0.404709i	$-0.132627\pi$
$12$	2987.81	−	175.833i	0.499136	−	0.0293741i
$13$	8397.69	+	3056.51i	1.06013	+	0.385855i	0.812476	−	0.582994i	$-0.198119\pi$
$13$	8397.69	+	3056.51i	1.06013	+	0.385855i	0.247651	+	0.968849i	$0.420341\pi$
$14$	6618.70	+	2409.01i	0.644651	+	0.234634i
$15$	2591.12	−	5167.12i	0.198229	−	0.395302i
$16$	711.263	−	4033.77i	0.0434120	−	0.246202i
$17$	2819.87	+	4884.16i	0.139206	+	0.241112i	0.927196	−	0.374576i	$-0.122212\pi$
$17$	2819.87	+	4884.16i	0.139206	+	0.241112i	−0.787990	+	0.615688i	$0.788878\pi$
$18$	10464.8	+	14021.3i	0.422940	+	0.566676i
$19$	−15908.5	+	27554.3i	−0.532097	+	0.921618i	0.467201	+	0.884151i	$0.345262\pi$
$19$	−15908.5	+	27554.3i	−0.532097	+	0.921618i	−0.999298	+	0.0374673i	$0.988071\pi$
$20$	−6059.93	−	5084.88i	−0.169380	−	0.142127i
$21$	9519.56	+	40058.3i	0.224310	+	0.943897i
$22$	−6835.88	−	38768.2i	−0.136872	−	0.776240i
$23$	12782.4	−	10725.7i	0.219061	−	0.183814i	−0.526653	−	0.850081i	$-0.676553\pi$
$23$	12782.4	−	10725.7i	0.219061	−	0.183814i	0.745714	+	0.666267i	$0.232109\pi$
$24$	21979.9	−	9496.97i	0.324554	−	0.140232i
$25$	59056.8	−	21494.9i	0.755928	−	0.275135i
$26$	71493.1			0.797733
$27$	−34806.1	+	96171.2i	−0.340316	+	0.940311i
$28$	56347.8			0.485092
$29$	−19735.6	+	7183.17i	−0.150265	+	0.0546919i	−0.416058	−	0.909338i	$-0.636589\pi$
$29$	−19735.6	+	7183.17i	−0.150265	+	0.0546919i	0.265793	+	0.964030i	$0.414366\pi$
$30$	5340.75	−	45933.8i	0.0361142	−	0.310604i
$31$	106699.	−	89531.1i	0.643272	−	0.539769i	−0.261749	−	0.965136i	$-0.584299\pi$
$31$	106699.	−	89531.1i	0.643272	−	0.539769i	0.905021	+	0.425367i	$0.139855\pi$
$32$	−5690.10	−	32270.2i	−0.0306970	−	0.174091i
$33$	167289.	−	158021.i	0.810344	−	0.765447i
$34$	34562.4	+	29001.3i	0.150809	+	0.126544i
$35$	54412.8	−	94245.7i	0.214517	−	0.371555i
$36$	117034.	+	76772.2i	0.418076	+	0.274249i
$37$	−179906.	−	311606.i	−0.583900	−	1.01135i	−0.995012	−	0.0997599i	$-0.968193\pi$
$37$	−179906.	−	311606.i	−0.583900	−	1.01135i	0.411111	−	0.911585i	$-0.365141\pi$
$38$	−44199.6	+	250668.i	−0.130670	+	0.741066i
$39$	229865.	+	349032.i	0.620506	+	0.942193i
$40$	−59468.8	−	21644.9i	−0.146920	−	0.0534743i
$41$	−356423.	−	129727.i	−0.807649	−	0.293960i	−0.0949965	−	0.995478i	$-0.530284\pi$
$41$	−356423.	−	129727.i	−0.807649	−	0.293960i	−0.712652	+	0.701518i	$0.752506\pi$
$42$	181170.	+	275093.i	0.377322	+	0.572936i
$43$	−133408.	+	756592.i	−0.255883	+	1.45118i	0.537914	+	0.843000i	$0.319213\pi$
$43$	−133408.	+	756592.i	−0.255883	+	1.45118i	−0.793796	+	0.608184i	$0.791898\pi$
$44$	−157465.	−	272737.i	−0.278676	−	0.482681i
$45$	241422.	−	121613.i	0.394942	−	0.198946i
$46$	66745.0	−	115606.i	0.101103	−	0.175116i
$47$	−161286.	−	135335.i	−0.226597	−	0.190137i	0.522420	−	0.852688i	$-0.325029\pi$
$47$	−161286.	−	135335.i	−0.226597	−	0.190137i	−0.749017	+	0.662551i	$0.769474\pi$
$48$	139250.	−	131534.i	0.181740	−	0.171670i
$49$	−8400.76	−	47643.1i	−0.0102008	−	0.0578514i
$50$	385149.	−	323178.i	0.435746	−	0.365634i
$51$	−30460.5	+	261980.i	−0.0321545	+	0.276549i
$52$	537452.	−	195617.i	0.530064	−	0.192927i
$53$	−1.41530e6			−1.30582			−0.652909	−	0.757437i	$-0.726451\pi$
$53$	−1.41530e6			−1.30582			−0.652909	+	0.757437i	$0.726451\pi$
$54$	1483.70	+	818206.i	0.00128224	+	0.707106i
$55$	−608230.			−0.492945
$56$	423597.	−	154177.i	0.322326	−	0.117317i
$57$	−1.36588e6	+	590165.i	−0.976904	+	0.422096i
$58$	−128709.	+	108000.i	−0.0866185	+	0.0726815i
$59$	48246.6	+	273620.i	0.0305833	+	0.173447i	0.996274	−	0.0862502i	$-0.0274884\pi$
$59$	48246.6	+	273620.i	0.0305833	+	0.173447i	−0.965690	+	0.259697i	$0.916377\pi$
$60$	−85532.9	−	359922.i	−0.0511215	−	0.215119i
$61$	−1.20479e6	−	1.01094e6i	−0.679606	−	0.570257i	0.236285	−	0.971684i	$-0.424070\pi$
$61$	−1.20479e6	−	1.01094e6i	−0.679606	−	0.570257i	−0.915891	+	0.401427i	$0.868514\pi$
$62$	557143.	−	964999.i	0.296890	−	0.514228i
$63$	−760518.	+	1.76896e6i	−0.383193	+	0.891302i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	191813.	−	1.08783e6i	0.0866326	−	0.491318i
$66$	825235.	−	1.64566e6i	0.353325	−	0.704589i
$67$	−3.54611e6	−	1.29068e6i	−1.44043	−	0.524272i	−0.500526	−	0.865722i	$-0.666860\pi$
$67$	−3.54611e6	−	1.29068e6i	−1.44043	−	0.524272i	−0.939900	+	0.341450i	$0.889082\pi$
$68$	339176.	+	123450.i	0.130811	+	0.0476113i
$69$	778991.	−	45843.5i	0.285470	−	0.0167999i
$70$	151179.	−	857378.i	0.0526802	−	0.298765i
$71$	−1.63079e6	−	2.82461e6i	−0.540746	−	0.936599i	−0.998861	−	0.0477068i	$-0.984809\pi$
$71$	−1.63079e6	−	2.82461e6i	−0.540746	−	0.936599i	0.458115	−	0.888893i	$-0.348525\pi$
$72$	1.08987e6	+	256913.i	0.344122	+	0.0811191i
$73$	−2.60790e6	+	4.51701e6i	−0.784622	+	1.35900i	0.144603	+	0.989490i	$0.453809\pi$
$73$	−2.60790e6	+	4.51701e6i	−0.784622	+	1.35900i	−0.929225	+	0.369515i	$0.879524\pi$
$74$	−2.20505e6	−	1.85026e6i	−0.632569	−	0.530788i
$75$	2.81610e6	+	841230.i	0.770786	+	0.230250i
$76$	353597.	+	2.00535e6i	0.0923976	+	0.524013i
$77$	3.31883e6	−	2.78483e6i	0.828453	−	0.695154i
$78$	2.68303e6	+	1.99492e6i	0.640168	+	0.475986i
$79$	−5.50965e6	+	2.00535e6i	−1.25727	+	0.457610i	−0.882853	−	0.469649i	$-0.844380\pi$
$79$	−5.50965e6	+	2.00535e6i	−1.25727	+	0.457610i	−0.374420	+	0.927259i	$0.622158\pi$
$80$	−506283.			−0.110555
$81$	−3.98975e6	+	2.63794e6i	−0.834157	+	0.551527i
$82$	−3.03438e6			−0.607745
$83$	4.50803e6	−	1.64079e6i	0.865392	−	0.314977i	0.129093	−	0.991633i	$-0.458794\pi$
$83$	4.50803e6	−	1.64079e6i	0.865392	−	0.314977i	0.736300	+	0.676656i	$0.236571\pi$
$84$	2.11465e6	+	1.57231e6i	0.389278	+	0.289441i
$85$	534007.	−	448085.i	0.0943150	−	0.0791397i
$86$	1.06726e6	+	6.05274e6i	0.180936	+	1.02614i
$87$	−941083.	−	281122.i	−0.153218	−	0.0457697i
$88$	−1.93000e6	−	1.61947e6i	−0.301904	−	0.253327i
$89$	5.12872e6	−	8.88321e6i	0.771159	−	1.33569i	−0.165769	−	0.986165i	$-0.553011\pi$
$89$	5.12872e6	−	8.88321e6i	0.771159	−	1.33569i	0.936928	−	0.349522i	$-0.113656\pi$
$90$	1.48215e6	−	1.57480e6i	0.214311	−	0.227707i
$91$	3.93406e6	+	6.81399e6i	0.547263	+	0.947888i
$92$	185442.	−	1.05170e6i	0.0248285	−	0.140810i
$93$	6.50249e6	−	382671.i	0.838281	−	0.0493328i
$94$	−1.58277e6	−	576081.i	−0.196549	−	0.0715379i
$95$	3.69554e6	+	1.34507e6i	0.442227	+	0.160957i
$96$	686915.	−	1.36983e6i	0.0792417	−	0.158021i
$97$	−591411.	+	3.35406e6i	−0.0657943	+	0.373138i	0.934077	+	0.357073i	$0.116225\pi$
$97$	−591411.	+	3.35406e6i	−0.0657943	+	0.373138i	−0.999871	+	0.0160656i	$0.994886\pi$
$98$	−193512.	−	335173.i	−0.0207691	−	0.0359731i
$99$	1.06875e7	−	1.26228e6i	1.10701	−	0.130748i
$100$	2.01110e6	−	3.48333e6i	0.201110	−	0.348333i
$101$	4.72436e6	+	3.96421e6i	0.456266	+	0.382853i	0.841755	−	0.539860i	$-0.181523\pi$
$101$	4.72436e6	+	3.96421e6i	0.456266	+	0.382853i	−0.385489	+	0.922712i	$0.625967\pi$
$102$	487831.	+	2.05279e6i	0.0455165	+	0.191533i
$103$	670844.	+	3.80455e6i	0.0604911	+	0.343062i	1.00000		0.000537212i	$0.000171000\pi$
$103$	670844.	+	3.80455e6i	0.0604911	+	0.343062i	−0.939509	+	0.342525i	$0.888718\pi$
$104$	3.50508e6	−	2.94111e6i	0.305549	−	0.256386i
$105$	4.67183e6	−	2.01858e6i	0.393844	−	0.170170i
$106$	−1.06396e7	+	3.87248e6i	−0.867667	+	0.315805i
$107$	1.51526e7			1.19576			0.597879	−	0.801586i	$-0.296010\pi$
$107$	1.51526e7			1.19576			0.597879	+	0.801586i	$0.296010\pi$
$108$	2.24990e6	+	6.14683e6i	0.171862	+	0.469535i
$109$	1.12441e7			0.831637			0.415819	−	0.909448i	$-0.363495\pi$
$109$	1.12441e7			0.831637			0.415819	+	0.909448i	$0.363495\pi$
$110$	−4.57239e6	+	1.66422e6i	−0.327544	+	0.119216i
$111$	1.94336e6	−	1.67141e7i	0.134872	−	1.15999i
$112$	2.76256e6	−	2.31806e6i	0.185801	−	0.155905i
$113$	−3.25736e6	−	1.84734e7i	−0.212369	−	1.20441i	−0.885414	−	0.464804i	$-0.846125\pi$
$113$	−3.25736e6	−	1.84734e7i	−0.212369	−	1.20441i	0.673044	−	0.739602i	$-0.264986\pi$
$114$	−8.65331e6	+	8.17387e6i	−0.547035	+	0.516726i
$115$	−1.57996e6	−	1.32574e6i	−0.0968732	−	0.0812863i
$116$	−672070.	+	1.16406e6i	−0.0399771	+	0.0692424i
$117$	−1.11282e6	+	1.95127e7i	−0.0642353	+	1.12633i
$118$	1.11136e6	+	1.92494e6i	0.0622687	+	0.107853i
$119$	−862237.	+	4.88999e6i	−0.0469043	+	0.266007i
$120$	−1.62780e6	−	2.47170e6i	−0.0859938	−	0.130575i
$121$	−4.44187e6	−	1.61671e6i	−0.227938	−	0.0829626i
$122$	−1.18232e7	−	4.30328e6i	−0.589487	−	0.214556i
$123$	−9.75614e6	−	1.48140e7i	−0.472727	−	0.717801i
$124$	1.54795e6	−	8.77885e6i	0.0729089	−	0.413487i
$125$	−8.71237e6	−	1.50903e7i	−0.398980	−	0.691054i
$126$	−877077.	+	1.53791e7i	−0.0390607	+	0.684910i
$127$	−8.50522e6	+	1.47315e7i	−0.368445	+	0.638165i	−0.989323	−	0.145742i	$-0.953443\pi$
$127$	−8.50522e6	+	1.47315e7i	−0.368445	+	0.638165i	0.620878	+	0.783907i	$0.286776\pi$
$128$	−1.60651e6	−	1.34802e6i	−0.0677094	−	0.0568149i
$129$	−2.61183e7	+	2.46712e7i	−1.07122	+	1.01187i
$130$	−1.53450e6	−	8.70260e6i	−0.0612585	−	0.347414i
$131$	−1.94149e7	+	1.62910e7i	−0.754545	+	0.633138i	−0.936701	−	0.350131i	$-0.886137\pi$
$131$	−1.94149e7	+	1.62910e7i	−0.754545	+	0.633138i	0.182156	+	0.983270i	$0.441693\pi$
$132$	1.70095e6	−	1.46293e7i	0.0643700	−	0.553623i
$133$	−2.63233e7	+	9.58091e6i	−0.970198	+	0.353123i
$134$	−3.01896e7			−1.08390
$135$	1.24536e7	+	2.17264e6i	0.435640	+	0.0760009i
$136$	2.88755e6			0.0984336
$137$	−1.59839e7	+	5.81766e6i	−0.531081	+	0.193298i	−0.593621	−	0.804745i	$-0.702302\pi$
$137$	−1.59839e7	+	5.81766e6i	−0.531081	+	0.193298i	0.0625400	+	0.998042i	$0.480080\pi$
$138$	5.73066e6	−	2.47607e6i	0.185621	−	0.0802023i
$139$	1.41962e7	−	1.19120e7i	0.448352	−	0.376212i	−0.390472	−	0.920615i	$-0.627688\pi$
$139$	1.41962e7	−	1.19120e7i	0.448352	−	0.376212i	0.838824	+	0.544403i	$0.183244\pi$
$140$	−1.20943e6	−	6.85902e6i	−0.0372506	−	0.211258i
$141$	−2.27647e6	−	9.57937e6i	−0.0683903	−	0.287786i
$142$	−1.99881e7	−	1.67720e7i	−0.585817	−	0.491559i
$143$	2.19876e7	−	3.80837e7i	0.628785	−	1.08909i
$144$	8.89612e6	−	1.05071e6i	0.248274	−	0.0293234i
$145$	1.29798e6	+	2.24817e6i	0.0353574	+	0.0612408i
$146$	−7.24570e6	+	4.10924e7i	−0.192684	+	1.09276i
$147$	1.01415e6	−	2.02238e6i	0.0263324	−	0.0525113i
$148$	−2.16392e7	−	7.87601e6i	−0.548687	−	0.199706i
$149$	4.62248e7	+	1.68245e7i	1.14478	+	0.416667i	0.843639	−	0.536911i	$-0.180409\pi$
$149$	4.62248e7	+	1.68245e7i	1.14478	+	0.416667i	0.301145	+	0.953578i	$0.402631\pi$
$150$	2.34719e7	−	1.38132e6i	0.567843	−	0.0334175i
$151$	9.67803e6	−	5.48868e7i	0.228753	−	1.29732i	−0.626625	−	0.779321i	$-0.715564\pi$
$151$	9.67803e6	−	5.48868e7i	0.228753	−	1.29732i	0.855378	−	0.518004i	$-0.173325\pi$
$152$	8.14513e6	+	1.41078e7i	0.188125	+	0.325841i
$153$	−8.45334e6	+	8.98174e6i	−0.190813	+	0.202740i
$154$	1.73297e7	−	3.00159e7i	0.382357	−	0.662261i
$155$	−1.31885e7	−	1.10664e7i	−0.284468	−	0.238697i
$156$	2.56282e7	+	7.65570e6i	0.540482	+	0.161454i
$157$	1.01967e7	+	5.78282e7i	0.210286	+	1.19259i	0.888902	+	0.458097i	$0.151469\pi$
$157$	1.01967e7	+	5.78282e7i	0.210286	+	1.19259i	−0.678617	+	0.734493i	$0.737420\pi$
$158$	−3.59321e7	+	3.01506e7i	−0.724741	+	0.608130i
$159$	−5.31140e7	−	3.94920e7i	−1.04790	−	0.779147i
$160$	−3.80601e6	+	1.38527e6i	−0.0734598	+	0.0267372i
$161$	1.46911e7			0.277437
$162$	−2.27753e7	+	3.07474e7i	−0.420882	+	0.568206i
$163$	9.14404e7			1.65379			0.826897	−	0.562353i	$-0.190104\pi$
$163$	9.14404e7			1.65379			0.826897	+	0.562353i	$0.190104\pi$
$164$	−2.28111e7	+	8.30256e6i	−0.403824	+	0.146980i
$165$	−2.28259e7	−	1.69718e7i	−0.395580	−	0.294127i
$166$	2.93998e7	−	2.46694e7i	0.498846	−	0.418581i
$167$	6.66235e6	+	3.77841e7i	0.110693	+	0.627771i	0.988793	+	0.149294i	$0.0477000\pi$
$167$	6.66235e6	+	3.77841e7i	0.110693	+	0.627771i	−0.878100	+	0.478477i	$0.841189\pi$
$168$	2.01990e7	+	6.03389e6i	0.328661	+	0.0981782i
$169$	1.31108e7	+	1.10013e7i	0.208942	+	0.175323i
$170$	2.78839e6	−	4.82963e6i	0.0435293	−	0.0753950i
$171$	−6.77273e7	−	1.59652e7i	−1.03580	−	0.244168i
$172$	2.45844e7	+	4.25815e7i	0.368393	+	0.638075i
$173$	−2.12518e7	+	1.20525e8i	−0.312058	+	1.76977i	0.276205	+	0.961099i	$0.410923\pi$
$173$	−2.12518e7	+	1.20525e8i	−0.312058	+	1.76977i	−0.588263	+	0.808670i	$0.700188\pi$
$174$	−7.84383e6	+	461608.i	−0.112877	+	0.00664280i
$175$	5.19957e7	+	1.89249e7i	0.733388	+	0.266932i
$176$	−1.89400e7	−	6.89360e6i	−0.261870	−	0.0953129i
$177$	−5.82438e6	+	1.16148e7i	−0.0789484	+	0.157436i
$178$	1.42495e7	−	8.08129e7i	0.189378	−	1.07402i
$179$	−5.60536e7	−	9.70876e7i	−0.730496	−	1.26526i	−0.956672	−	0.291169i	$-0.905956\pi$
$179$	−5.60536e7	−	9.70876e7i	−0.730496	−	1.26526i	0.226176	−	0.974086i	$-0.427378\pi$
$180$	6.83323e6	−	1.58940e7i	0.0873317	−	0.203133i
$181$	3.55471e7	−	6.15694e7i	0.445584	−	0.771773i	−0.552509	−	0.833507i	$-0.686330\pi$
$181$	3.55471e7	−	6.15694e7i	0.445584	−	0.771773i	0.998093	+	0.0617335i	$0.0196629\pi$
$182$	4.82187e7	+	4.04603e7i	0.592878	+	0.497484i
$183$	−1.70050e7	−	7.15571e7i	−0.205115	−	0.863125i
$184$	−1.48354e6	−	8.41356e6i	−0.0175564	−	0.0995675i
$185$	−3.40692e7	+	2.85875e7i	−0.395605	+	0.331952i
$186$	4.78357e7	−	2.06686e7i	0.545076	−	0.235514i
$187$	2.60783e7	−	9.49173e6i	0.291631	−	0.106145i
$188$	−1.34748e7			−0.147900
$189$	−7.79014e7	+	4.51649e7i	−0.839323	+	0.486615i
$190$	3.14617e7			0.332770
$191$	1.44271e8	−	5.25104e7i	1.49818	−	0.545292i	0.542589	−	0.839999i	$-0.317444\pi$
$191$	1.44271e8	−	5.25104e7i	1.49818	−	0.545292i	0.955588	+	0.294707i	$0.0952220\pi$
$192$	1.41585e6	−	1.21772e7i	0.0144366	−	0.124164i
$193$	−1.48219e8	+	1.24370e8i	−1.48406	+	1.24528i	−0.582355	+	0.812935i	$0.697868\pi$
$193$	−1.48219e8	+	1.24370e8i	−1.48406	+	1.24528i	−0.901709	+	0.432343i	$0.857687\pi$
$194$	4.73129e6	+	2.68325e7i	0.0465236	+	0.263849i
$195$	3.75528e7	−	3.54721e7i	0.362678	−	0.342583i
$196$	−2.37182e6	−	1.99020e6i	−0.0225002	−	0.0188799i
$197$	−3.48376e7	+	6.03405e7i	−0.324651	+	0.562312i	−0.981442	−	0.191761i	$-0.938580\pi$
$197$	−3.48376e7	+	6.03405e7i	−0.324651	+	0.562312i	0.656791	+	0.754073i	$0.271913\pi$
$198$	7.68897e7	−	3.87319e7i	0.703947	−	0.354602i
$199$	6.31086e7	+	1.09307e8i	0.567679	+	0.983248i	0.996795	+	0.0799989i	$0.0254917\pi$
$199$	6.31086e7	+	1.09307e8i	0.567679	+	0.983248i	−0.429116	+	0.903249i	$0.641175\pi$
$200$	5.58759e6	−	3.16888e7i	0.0493878	−	0.280092i
$201$	−9.70655e7	−	1.47387e8i	−0.843099	−	1.28018i
$202$	4.63623e7	+	1.68745e7i	0.395763	+	0.144046i
$203$	−1.73759e7	−	6.32431e6i	−0.145784	−	0.0530612i
$204$	9.28405e6	+	1.40971e7i	0.0765653	+	0.116259i
$205$	−8.14112e6	+	4.61706e7i	−0.0660002	+	0.374306i
$206$	1.54530e7	+	2.67653e7i	0.123162	+	0.213323i
$207$	3.05135e7	+	2.00163e7i	0.239109	+	0.156851i
$208$	1.83022e7	−	3.17004e7i	0.141021	−	0.244255i
$209$	1.19935e8	+	1.00637e8i	0.908729	+	0.762514i
$210$	2.95975e7	−	2.79576e7i	0.220540	−	0.208321i
$211$	−4.83073e6	−	2.73965e7i	−0.0354017	−	0.200773i	0.961977	−	0.273130i	$-0.0880590\pi$
$211$	−4.83073e6	−	2.73965e7i	−0.0354017	−	0.200773i	−0.997379	+	0.0723570i	$0.976948\pi$
$212$	−6.93876e7	+	5.82231e7i	−0.500157	+	0.419682i
$213$	1.76159e7	−	1.51508e8i	0.124904	−	1.07425i
$214$	1.13910e8	−	4.14599e7i	0.794537	−	0.289188i
$215$	9.49607e7			0.651643
$216$	3.37324e7	+	4.00530e7i	0.227750	+	0.270425i
$217$	1.22632e8			0.814694
$218$	8.45283e7	−	3.07658e7i	0.552592	−	0.201127i
$219$	−2.23911e8	+	9.67465e7i	−1.44053	+	0.622416i
$220$	−2.98196e7	+	2.50216e7i	−0.188809	+	0.158429i
$221$	8.75193e6	+	4.96347e7i	0.0545420	+	0.309323i
$222$	−3.11232e7	−	1.30966e8i	−0.190919	−	0.803386i
$223$	−6.27441e7	−	5.26485e7i	−0.378883	−	0.317921i	0.433380	−	0.901211i	$-0.357321\pi$
$223$	−6.27441e7	−	5.26485e7i	−0.378883	−	0.317921i	−0.812264	+	0.583290i	$0.801765\pi$
$224$	1.44250e7	−	2.49849e7i	0.0857529	−	0.148528i
$225$	8.22105e7	+	1.10150e8i	0.481159	+	0.644680i
$226$	−7.50336e7	−	1.29962e8i	−0.432391	−	0.748923i
$227$	6.35654e6	−	3.60497e7i	0.0360687	−	0.204556i	−0.961448	−	0.274987i	$-0.911326\pi$
$227$	6.35654e6	−	3.60497e7i	0.0360687	−	0.204556i	0.997517	+	0.0704313i	$0.0224375\pi$
$228$	−4.26866e7	+	8.51242e7i	−0.238517	+	0.475643i
$229$	−2.72489e7	−	9.91778e6i	−0.149942	−	0.0545745i	0.265959	−	0.963984i	$-0.414312\pi$
$229$	−2.72489e7	−	9.91778e6i	−0.149942	−	0.0545745i	−0.415901	+	0.909410i	$0.636534\pi$
$230$	−1.55049e7	−	5.64331e6i	−0.0840273	−	0.0305834i
$231$	2.02258e8	−	1.19028e7i	1.07960	−	0.0635344i
$232$	−1.86726e6	+	1.05898e7i	−0.00981741	+	0.0556773i
$233$	−2.72444e7	−	4.71887e7i	−0.141101	−	0.244395i	0.786810	−	0.617195i	$-0.211731\pi$
$233$	−2.72444e7	−	4.71887e7i	−0.141101	−	0.244395i	−0.927912	+	0.372800i	$0.878398\pi$
$234$	4.50243e7	+	1.49732e8i	0.229716	+	0.763942i
$235$	−1.30120e7	+	2.25375e7i	−0.0654046	+	0.113284i
$236$	1.36217e7	+	1.14299e7i	0.0674588	+	0.0566046i
$237$	−2.62725e8	−	7.84818e7i	−1.28199	−	0.382957i
$238$	6.89790e6	+	3.91199e7i	0.0331663	+	0.188096i
$239$	−1.56138e8	+	1.31016e8i	−0.739805	+	0.620770i	−0.932785	−	0.360433i	$-0.882629\pi$
$239$	−1.56138e8	+	1.31016e8i	−0.739805	+	0.620770i	0.192981	+	0.981203i	$0.438185\pi$
$240$	−1.90000e7	−	1.41272e7i	−0.0887187	−	0.0659653i
$241$	−1.64967e8	+	6.00430e7i	−0.759167	+	0.276314i	−0.692458	−	0.721458i	$-0.743472\pi$
$241$	−1.64967e8	+	6.00430e7i	−0.759167	+	0.276314i	−0.0667088	+	0.997772i	$0.521250\pi$
$242$	−3.78155e7			−0.171520
$243$	−2.23337e8	−	1.23308e7i	−0.998479	−	0.0551274i
$244$	−1.00656e8			−0.443581
$245$	−5.61911e6	+	2.04519e6i	−0.0244111	+	0.00888490i
$246$	−1.13876e8	−	8.46704e7i	−0.487706	−	0.362626i
$247$	−2.17814e8	+	1.82768e8i	−0.919701	+	0.771721i
$248$	−1.23836e7	−	7.02308e7i	−0.0515544	−	0.292379i
$249$	2.14963e8	+	6.42142e7i	0.882402	+	0.263593i
$250$	−1.06785e8	−	8.96033e7i	−0.432235	−	0.362689i
$251$	2.01203e8	−	3.48494e8i	0.803112	−	1.39103i	−0.114446	−	0.993429i	$-0.536509\pi$
$251$	2.01203e8	−	3.48494e8i	0.803112	−	1.39103i	0.917558	−	0.397602i	$-0.130157\pi$
$252$	3.54862e7	+	1.18013e8i	0.139688	+	0.464544i
$253$	−4.10547e7	−	7.11088e7i	−0.159383	−	0.276059i
$254$	−2.36307e7	+	1.34016e8i	−0.0904811	+	0.513144i
$255$	3.25437e7	−	1.91519e6i	0.122907	−	0.00723305i
$256$	−1.57654e7	−	5.73815e6i	−0.0587308	−	0.0213763i
$257$	−5.02063e8	−	1.82736e8i	−1.84498	−	0.671519i	−0.987632	−	0.156789i	$-0.949886\pi$
$257$	−5.02063e8	−	1.82736e8i	−1.84498	−	0.671519i	−0.857352	−	0.514730i	$-0.827892\pi$
$258$	−1.28841e8	+	2.56930e8i	−0.467073	+	0.931422i
$259$	5.50101e7	−	3.11978e8i	0.196740	−	1.11577i
$260$	−3.53474e7	−	6.12235e7i	−0.124724	−	0.216029i
$261$	−2.74731e7	−	3.68098e7i	−0.0956457	−	0.128151i
$262$	−1.01377e8	+	1.75591e8i	−0.348246	+	0.603180i
$263$	1.58697e8	+	1.33162e8i	0.537927	+	0.451374i	0.870828	−	0.491588i	$-0.163583\pi$
$263$	1.58697e8	+	1.33162e8i	0.537927	+	0.451374i	−0.332901	+	0.942962i	$0.608028\pi$
$264$	−2.72411e7	−	1.14630e8i	−0.0911193	−	0.383429i
$265$	3.03775e7	+	1.72279e8i	0.100275	+	0.568686i
$266$	−1.71672e8	+	1.44050e8i	−0.559259	+	0.469274i
$267$	4.40347e8	−	1.90263e8i	1.41581	−	0.611737i
$268$	−2.26951e8	+	8.26035e7i	−0.720213	+	0.262136i
$269$	2.32202e8			0.727331			0.363666	−	0.931530i	$-0.381525\pi$
$269$	2.32202e8			0.727331			0.363666	+	0.931530i	$0.381525\pi$
$270$	9.95654e7	−	1.77423e7i	0.307847	−	0.0548576i
$271$	2.02943e8			0.619415			0.309707	−	0.950832i	$-0.399769\pi$
$271$	2.02943e8			0.619415			0.309707	+	0.950832i	$0.399769\pi$
$272$	2.17073e7	−	7.90080e6i	0.0654055	−	0.0238056i
$273$	−4.24961e7	+	3.65493e8i	−0.126410	+	1.08720i
$274$	−1.04242e8	+	8.74690e7i	−0.306136	+	0.256878i
$275$	−5.37018e7	−	3.04558e8i	−0.155713	−	0.883091i
$276$	3.63055e7	−	3.42940e7i	0.103942	−	0.0981830i
$277$	−4.25492e7	−	3.57030e7i	−0.120285	−	0.100931i	0.580661	−	0.814145i	$-0.302794\pi$
$277$	−4.25492e7	−	3.57030e7i	−0.120285	−	0.100931i	−0.700946	+	0.713214i	$0.747239\pi$
$278$	7.41271e7	−	1.28392e8i	0.206928	−	0.358411i
$279$	2.54707e8	+	1.67082e8i	0.702143	+	0.460591i
$280$	−2.78593e7	−	4.82538e7i	−0.0758434	−	0.131365i
$281$	6.95254e7	−	3.94298e8i	0.186927	−	1.06011i	−0.736528	−	0.676407i	$-0.763536\pi$
$281$	6.95254e7	−	3.94298e8i	0.186927	−	1.06011i	0.923455	−	0.383708i	$-0.125353\pi$
$282$	−4.33241e7	−	6.57845e7i	−0.115042	−	0.174683i
$283$	4.95047e7	+	1.80182e7i	0.129836	+	0.0472563i	0.406121	−	0.913819i	$-0.366881\pi$
$283$	4.95047e7	+	1.80182e7i	0.129836	+	0.0472563i	−0.276285	+	0.961076i	$0.589103\pi$
$284$	−1.96152e8	−	7.13936e7i	−0.508135	−	0.184946i
$285$	1.01156e8	+	1.53597e8i	0.258841	+	0.393031i
$286$	6.10898e7	−	3.46457e8i	0.154414	−	0.875727i
$287$	−1.66973e8	−	2.89206e8i	−0.416928	−	0.722140i
$288$	6.40020e7	−	3.22400e7i	0.157877	−	0.0795282i
$289$	1.89266e8	−	3.27818e8i	0.461243	−	0.798897i
$290$	1.59090e7	+	1.33492e7i	0.0383044	+	0.0321412i
$291$	−1.15785e8	+	1.09370e8i	−0.275441	+	0.260180i
$292$	5.79656e7	+	3.28739e8i	0.136248	+	0.772701i
$293$	−2.05223e8	+	1.72202e8i	−0.476638	+	0.399947i	−0.849209	−	0.528057i	$-0.822921\pi$
$293$	−2.05223e8	+	1.72202e8i	−0.476638	+	0.399947i	0.372571	+	0.928004i	$0.378476\pi$
$294$	2.09034e6	−	1.79782e7i	0.00479735	−	0.0412602i
$295$	3.22713e7	−	1.17458e7i	0.0731879	−	0.0266382i
$296$	−1.84223e8			−0.412880
$297$	4.36307e8	+	2.50848e8i	0.966372	+	0.555601i
$298$	3.93532e8			0.861435
$299$	1.40126e8	−	5.10017e7i	0.303158	−	0.110341i
$300$	1.72671e8	−	7.46070e7i	0.369229	−	0.159535i
$301$	−5.18157e8	+	4.34785e8i	−1.09516	+	0.918951i
$302$	−7.74242e7	−	4.39095e8i	−0.161753	−	0.917347i
$303$	6.66820e7	+	2.80598e8i	0.137708	+	0.579475i
$304$	9.98325e7	+	8.37694e7i	0.203805	+	0.171013i
$305$	−9.71989e7	+	1.68353e8i	−0.196161	+	0.339760i
$306$	−3.89728e7	+	9.06503e7i	−0.0777565	+	0.180861i
$307$	−1.08638e8	−	1.88167e8i	−0.214288	−	0.371157i	0.738764	−	0.673964i	$-0.235410\pi$
$307$	−1.08638e8	−	1.88167e8i	−0.214288	−	0.371157i	−0.953052	+	0.302807i	$0.902076\pi$
$308$	4.81484e7	−	2.73063e8i	0.0938975	−	0.532519i
$309$	−8.09851e7	+	1.61498e8i	−0.156153	+	0.311395i
$310$	−1.29424e8	−	4.71066e7i	−0.246746	−	0.0898081i
$311$	6.53760e8	+	2.37949e8i	1.23241	+	0.448562i	0.874424	−	0.485163i	$-0.161240\pi$
$311$	6.53760e8	+	2.37949e8i	1.23241	+	0.448562i	0.357990	+	0.933725i	$0.383462\pi$
$312$	2.13608e8	−	1.25708e7i	0.398177	−	0.0234327i
$313$	5.68083e7	−	3.22176e8i	0.104714	−	0.593865i	−0.886620	−	0.462500i	$-0.846953\pi$
$313$	5.68083e7	−	3.22176e8i	0.104714	−	0.593865i	0.991334	−	0.131366i	$-0.0419362\pi$
$314$	2.34881e8	+	4.06826e8i	0.428148	+	0.741575i
$315$	2.31652e8	+	5.46069e7i	0.417589	+	0.0984375i
$316$	−1.87624e8	+	3.24974e8i	−0.334490	+	0.579354i
$317$	5.08959e8	+	4.27067e8i	0.897378	+	0.752989i	0.969676	−	0.244394i	$-0.0785889\pi$
$317$	5.08959e8	+	4.27067e8i	0.897378	+	0.752989i	−0.0722982	+	0.997383i	$0.523033\pi$
$318$	−5.07343e8	−	1.51554e8i	−0.884722	−	0.264286i
$319$	1.79461e7	+	1.01777e8i	0.0309529	+	0.175543i
$320$	−2.48215e7	+	2.08277e7i	−0.0423450	+	0.0355317i
$321$	5.68653e8	+	4.22812e8i	0.959577	+	0.713477i
$322$	1.10441e8	−	4.01973e7i	0.184347	−	0.0670968i
$323$	−1.79439e8			−0.296284
$324$	−8.70841e7	+	2.93462e8i	−0.142243	+	0.479340i
$325$	5.61641e8			0.907542
$326$	6.87407e8	−	2.50196e8i	1.09889	−	0.399962i
$327$	4.21976e8	+	3.13753e8i	0.667375	+	0.496216i
$328$	−1.48766e8	+	1.24830e8i	−0.232780	+	0.195326i
$329$	−3.21891e7	−	1.82554e8i	−0.0498338	−	0.282621i
$330$	−2.18033e8	−	6.51311e7i	−0.333982	−	0.0997676i
$331$	−2.52343e8	−	2.11741e8i	−0.382467	−	0.320928i	0.431203	−	0.902255i	$-0.358089\pi$
$331$	−2.52343e8	−	2.11741e8i	−0.382467	−	0.320928i	−0.813670	+	0.581327i	$0.802534\pi$
$332$	1.53515e8	−	2.65896e8i	0.230233	−	0.398775i
$333$	5.39316e8	−	5.73028e8i	0.800366	−	0.850396i
$334$	1.53468e8	+	2.65814e8i	0.225374	+	0.390360i
$335$	−8.09973e7	+	4.59359e8i	−0.117710	+	0.667567i
$336$	1.68357e8	−	9.90778e6i	0.242127	−	0.0142491i
$337$	−1.06474e9	−	3.87534e8i	−1.51544	−	0.551576i	−0.555437	−	0.831559i	$-0.687449\pi$
$337$	−1.06474e9	−	3.87534e8i	−1.51544	−	0.551576i	−0.960005	+	0.279983i	$0.909671\pi$
$338$	1.28662e8	+	4.68293e7i	0.181235	+	0.0659643i
$339$	3.93232e8	−	7.84172e8i	0.548214	−	1.09323i
$340$	7.74717e6	−	4.39364e7i	0.0106897	−	0.0606245i
$341$	−3.42697e8	−	5.93569e8i	−0.468026	−	0.810645i
$342$	−5.52826e8	+	6.52937e7i	−0.747304	+	0.0882632i
$343$	3.83835e8	−	6.64821e8i	0.513588	−	0.889560i
$344$	3.01324e8	+	2.52841e8i	0.399098	+	0.334883i
$345$	−2.23004e7	−	9.38398e7i	−0.0292378	−	0.123033i
$346$	1.70015e8	+	9.64202e8i	0.220658	+	1.25142i
$347$	−8.78456e8	+	7.37112e8i	−1.12867	+	0.947066i	−0.999010	−	0.0444921i	$-0.985833\pi$
$347$	−8.78456e8	+	7.37112e8i	−1.12867	+	0.947066i	−0.129660	+	0.991559i	$0.541389\pi$
$348$	−5.77033e7	+	2.49321e7i	−0.0733961	+	0.0317126i
$349$	−6.50308e7	+	2.36693e7i	−0.0818899	+	0.0298055i	−0.382640	−	0.923897i	$-0.624985\pi$
$349$	−6.50308e7	+	2.36693e7i	−0.0818899	+	0.0298055i	0.300750	+	0.953703i	$0.402763\pi$
$350$	4.42661e8			0.551866
$351$	−5.86239e8	+	7.01231e8i	−0.723602	+	0.865538i
$352$	−1.61244e8			−0.197054
$353$	−7.64515e8	+	2.78261e8i	−0.925069	+	0.336698i	−0.760253	−	0.649627i	$-0.774925\pi$
$353$	−7.64515e8	+	2.78261e8i	−0.925069	+	0.336698i	−0.164816	+	0.986324i	$0.552703\pi$
$354$	−1.20051e7	+	1.03251e8i	−0.0143831	+	0.123704i
$355$	−3.08827e8	+	2.59137e8i	−0.366367	+	0.307418i
$356$	−1.13996e8	−	6.46503e8i	−0.133910	−	0.759444i
$357$	−1.68807e8	+	1.59454e8i	−0.196359	+	0.185480i
$358$	−6.87032e8	−	5.76489e8i	−0.791383	−	0.664049i
$359$	7.46418e8	−	1.29283e9i	0.851435	−	1.47473i	−0.0284788	−	0.999594i	$-0.509066\pi$
$359$	7.46418e8	−	1.29283e9i	0.851435	−	1.47473i	0.879914	−	0.475134i	$-0.157600\pi$
$360$	7.88050e6	−	1.38181e8i	0.00890216	−	0.156095i
$361$	−5.92222e7	−	1.02576e8i	−0.0662535	−	0.114754i
$362$	9.87630e7	−	5.60113e8i	0.109424	−	0.620577i
$363$	−1.21584e8	−	1.84617e8i	−0.133415	−	0.202581i
$364$	4.73191e8	+	1.72228e8i	0.514259	+	0.187175i
$365$	6.05815e8	+	2.20498e8i	0.652101	+	0.237345i
$366$	−3.23628e8	−	4.91405e8i	−0.345034	−	0.523909i
$367$	−2.22579e8	+	1.26231e9i	−0.235046	+	1.33301i	0.607471	+	0.794342i	$0.292184\pi$
$367$	−2.22579e8	+	1.26231e9i	−0.235046	+	1.33301i	−0.842517	+	0.538670i	$0.818927\pi$
$368$	−3.41734e7	−	5.91901e7i	−0.0357455	−	0.0619130i
$369$	4.72314e7	−	8.28178e8i	0.0489371	−	0.858087i
$370$	−1.77897e8	+	3.08127e8i	−0.182584	+	0.316245i
$371$	−9.54551e8	−	8.00963e8i	−0.970488	−	0.814336i
$372$	3.03054e8	−	2.86263e8i	0.305225	−	0.288314i
$373$	−2.61573e7	−	1.48346e8i	−0.0260983	−	0.148011i	0.968974	−	0.247163i	$-0.0794982\pi$
$373$	−2.61573e7	−	1.48346e8i	−0.0260983	−	0.148011i	−0.995072	+	0.0991517i	$0.968387\pi$
$374$	1.70074e8	−	1.42709e8i	0.168107	−	0.141059i
$375$	9.41119e7	−	8.09422e8i	0.0921585	−	0.792621i
$376$	−1.01297e8	+	3.68692e7i	−0.0982744	+	0.0357689i
$377$	−1.87689e8			−0.180403
$378$	−4.62048e8	+	5.52680e8i	−0.440014	+	0.526323i
$379$	−3.79927e8			−0.358479			−0.179239	−	0.983806i	$-0.557364\pi$
$379$	−3.79927e8			−0.358479			−0.179239	+	0.983806i	$0.557364\pi$
$380$	2.36514e8	−	8.60842e7i	0.221113	−	0.0804787i
$381$	−7.30250e8	+	3.15523e8i	−0.676448	+	0.292276i
$382$	9.40888e8	−	7.89499e8i	0.863607	−	0.724652i
$383$	−1.97392e7	−	1.11947e8i	−0.0179529	−	0.101816i	0.974515	−	0.224324i	$-0.0720174\pi$
$383$	−1.97392e7	−	1.11947e8i	−0.0179529	−	0.101816i	−0.992468	+	0.122508i	$0.960906\pi$
$384$	−2.26751e7	−	9.54168e7i	−0.0204357	−	0.0859935i
$385$	−4.10222e8	−	3.44217e8i	−0.366359	−	0.307411i
$386$	−7.73943e8	+	1.34051e9i	−0.684942	+	1.18635i
$387$	−1.66860e9	+	1.97076e8i	−1.46340	+	0.172840i
$388$	1.08986e8	+	1.88769e8i	0.0947236	+	0.164066i
$389$	−3.53245e8	+	2.00335e9i	−0.304265	+	1.72557i	0.322677	+	0.946509i	$0.395417\pi$
$389$	−3.53245e8	+	2.00335e9i	−0.304265	+	1.72557i	−0.626942	+	0.779066i	$0.715694\pi$
$390$	1.85247e8	−	3.69414e8i	0.158134	−	0.315346i
$391$	8.84309e7	+	3.21862e7i	0.0748144	+	0.0272302i
$392$	−2.32758e7	−	8.47169e6i	−0.0195165	−	0.00710344i
$393$	−1.18319e9	+	6.96306e7i	−0.983287	+	0.0578663i
$394$	−9.67918e7	+	5.48934e8i	−0.0797263	+	0.452150i
$395$	3.62362e8	+	6.27629e8i	0.295837	+	0.512405i
$396$	4.72044e8	−	5.01551e8i	0.381988	−	0.405865i
$397$	−4.08131e8	+	7.06904e8i	−0.327365	+	0.567014i	−0.981988	−	0.188942i	$-0.939494\pi$
$397$	−4.08131e8	+	7.06904e8i	−0.327365	+	0.567014i	0.654623	+	0.755956i	$0.272827\pi$
$398$	7.73503e8	+	6.49046e8i	0.614995	+	0.516042i
$399$	−1.25522e9	−	3.74961e8i	−0.989267	−	0.295516i
$400$	−4.47007e7	−	2.53510e8i	−0.0349224	−	0.198055i
$401$	−1.31147e9	+	1.10046e9i	−1.01567	+	0.852252i	−0.989078	−	0.147394i	$-0.952911\pi$
$401$	−1.31147e9	+	1.10046e9i	−1.01567	+	0.852252i	−0.0265965	+	0.999646i	$0.508467\pi$
$402$	−1.13297e9	−	8.42400e8i	−0.869814	−	0.646736i
$403$	1.16968e9	−	4.25728e8i	0.890223	−	0.324015i
$404$	3.94702e8			0.297806
$405$	4.06742e8	+	4.29038e8i	0.304247	+	0.320925i
$406$	−1.47928e8			−0.109701
$407$	−1.66378e9	+	6.05565e8i	−1.22325	+	0.445226i
$408$	1.08365e8	+	8.05732e7i	0.0789914	+	0.0587327i
$409$	1.78332e9	−	1.49638e9i	1.28884	−	1.08146i	0.296876	−	0.954916i	$-0.404055\pi$
$409$	1.78332e9	−	1.49638e9i	1.28884	−	1.08146i	0.991961	−	0.126547i	$-0.0403894\pi$
$410$	6.51289e7	+	3.69365e8i	0.0466692	+	0.264674i
$411$	−7.62185e8	−	2.27681e8i	−0.541520	−	0.161764i
$412$	1.89402e8	+	1.58928e8i	0.133427	+	0.111959i
$413$	−1.22310e8	+	2.11848e8i	−0.0854355	+	0.147979i
$414$	2.84154e8	+	6.69831e7i	0.196813	+	0.0463942i
$415$	−2.96486e8	−	5.13529e8i	−0.203627	−	0.352693i
$416$	5.08504e7	−	2.88387e8i	0.0346312	−	0.196403i
$417$	8.65149e8	−	5.09139e7i	0.584271	−	0.0343843i
$418$	1.17698e9	+	4.28385e8i	0.788227	+	0.286891i
$419$	1.87761e9	+	6.83393e8i	1.24697	+	0.453859i	0.879376	−	0.476128i	$-0.157960\pi$
$419$	1.87761e9	+	6.83393e8i	1.24697	+	0.453859i	0.367592	+	0.929987i	$0.380182\pi$
$420$	1.46004e8	−	2.91156e8i	0.0961593	−	0.191758i
$421$	−1.19774e7	+	6.79270e7i	−0.00782301	+	0.0443665i	−0.988469	−	0.151421i	$-0.951615\pi$
$421$	−1.19774e7	+	6.79270e7i	−0.00782301	+	0.0443665i	0.980646	+	0.195787i	$0.0627262\pi$
$422$	−1.11276e8	−	1.92736e8i	−0.0720791	−	0.124845i
$423$	1.81867e8	−	4.23021e8i	0.116832	−	0.271751i
$424$	−3.62316e8	+	6.27550e8i	−0.230838	+	0.399823i
$425$	2.71517e8	+	2.27830e8i	0.171568	+	0.143963i
$426$	−2.82122e8	−	1.18717e9i	−0.176809	−	0.744010i
$427$	−2.40450e8	−	1.36366e9i	−0.149461	−	0.847634i
$428$	7.42883e8	−	6.23353e8i	0.458002	−	0.384309i
$429$	1.88784e9	−	8.15687e8i	1.15442	−	0.498796i
$430$	7.13871e8	−	2.59828e8i	0.432992	−	0.157596i
$431$	−1.22743e9			−0.738457			−0.369228	−	0.929339i	$-0.620378\pi$
$431$	−1.22743e9			−0.738457			−0.369228	+	0.929339i	$0.620378\pi$
$432$	3.63176e8	+	2.08803e8i	0.216733	+	0.124607i
$433$	2.83081e9			1.67573			0.837863	−	0.545881i	$-0.183805\pi$
$433$	2.83081e9			1.67573			0.837863	+	0.545881i	$0.183805\pi$
$434$	9.21890e8	−	3.35541e8i	0.541334	−	0.197029i
$435$	−1.40209e7	+	1.20589e8i	−0.00816703	+	0.0702416i
$436$	5.51265e8	−	4.62566e8i	0.318535	−	0.267283i
$437$	9.21906e7	+	5.22839e8i	0.0528447	+	0.299697i
$438$	−1.41855e9	+	1.33995e9i	−0.806650	+	0.761957i
$439$	1.34301e9	+	1.12692e9i	0.757622	+	0.635721i	0.937507	−	0.347967i	$-0.113128\pi$
$439$	1.34301e9	+	1.12692e9i	0.757622	+	0.635721i	−0.179884	+	0.983688i	$0.557572\pi$
$440$	−1.55707e8	+	2.69692e8i	−0.0871412	+	0.150933i
$441$	9.44914e7	−	4.75985e7i	0.0524635	−	0.0264276i
$442$	2.01601e8	+	3.49184e8i	0.111049	+	0.192343i
$443$	1.26368e7	−	7.16668e7i	0.00690595	−	0.0391656i	−0.981160	−	0.193197i	$-0.938114\pi$
$443$	1.26368e7	−	7.16668e7i	0.00690595	−	0.0391656i	0.988066	+	0.154031i	$0.0492256\pi$
$444$	−5.92315e8	−	8.99387e8i	−0.321153	−	0.487648i
$445$	−1.19140e9	−	4.33635e8i	−0.640912	−	0.233273i
$446$	−6.15736e8	−	2.24110e8i	−0.328642	−	0.119616i
$447$	1.26528e9	+	1.92124e9i	0.670056	+	1.01743i
$448$	4.00781e7	−	2.27294e8i	0.0210588	−	0.119431i
$449$	9.97688e7	+	1.72805e8i	0.0520155	+	0.0900934i	0.890861	−	0.454276i	$-0.150102\pi$
$449$	9.97688e7	+	1.72805e8i	0.0520155	+	0.0900934i	−0.838845	+	0.544370i	$0.816769\pi$
$450$	9.19408e8	+	6.03113e8i	0.475625	+	0.312000i
$451$	−9.33221e8	+	1.61639e9i	−0.479034	+	0.829711i
$452$	−9.19666e8	−	7.71691e8i	−0.468431	−	0.393060i
$453$	1.89474e9	−	1.78977e9i	0.957651	−	0.904591i
$454$	−5.08523e7	−	2.88398e8i	−0.0255044	−	0.144643i
$455$	7.45004e8	−	6.25133e8i	0.370782	−	0.311123i
$456$	−8.79845e7	+	7.56722e8i	−0.0434540	+	0.373731i
$457$	6.93522e8	−	2.52421e8i	0.339902	−	0.123714i	−0.166429	−	0.986053i	$-0.553224\pi$
$457$	6.93522e8	−	2.52421e8i	0.339902	−	0.123714i	0.506331	+	0.862339i	$0.331001\pi$
$458$	−2.31981e8			−0.112830
$459$	−5.67864e8	+	1.01192e8i	−0.274094	+	0.0488429i
$460$	−1.31999e8			−0.0632295
$461$	−1.23011e9	+	4.47724e8i	−0.584778	+	0.212842i	−0.617431	−	0.786625i	$-0.711827\pi$
$461$	−1.23011e9	+	4.47724e8i	−0.584778	+	0.212842i	0.0326530	+	0.999467i	$0.489604\pi$
$462$	1.48791e9	−	6.42890e8i	0.701989	−	0.303312i
$463$	1.33923e9	−	1.12375e9i	0.627078	−	0.526181i	−0.272941	−	0.962031i	$-0.587996\pi$
$463$	1.33923e9	−	1.12375e9i	0.627078	−	0.526181i	0.900020	+	0.435849i	$0.143552\pi$
$464$	1.49381e7	+	8.47180e7i	0.00694195	+	0.0393698i
$465$	−1.86149e8	−	7.83312e8i	−0.0858567	−	0.361285i
$466$	−3.33927e8	−	2.80198e8i	−0.152862	−	0.128267i
$467$	−6.97093e8	+	1.20740e9i	−0.316724	+	0.548583i	−0.979803	−	0.199968i	$-0.935916\pi$
$467$	−6.97093e8	+	1.20740e9i	−0.316724	+	0.548583i	0.663078	+	0.748550i	$0.269250\pi$
$468$	7.48164e8	+	1.00243e9i	0.337393	+	0.452056i
$469$	−1.66125e9	−	2.87736e9i	−0.743582	−	1.28792i
$470$	−3.61523e7	+	2.05030e8i	−0.0160618	+	0.0910908i
$471$	−1.23095e9	+	2.45473e9i	−0.542836	+	1.08251i
$472$	1.33676e8	+	4.86540e7i	0.0585134	+	0.0212971i
$473$	3.55247e9	+	1.29299e9i	1.54354	+	0.561801i
$474$	−2.18979e9	+	1.28869e8i	−0.944448	+	0.0555807i
$475$	−3.47226e8	+	1.96922e9i	−0.148657	+	0.843075i
$476$	1.58894e8	+	2.75212e8i	0.0675277	+	0.116961i
$477$	−8.91314e8	−	2.96415e9i	−0.376025	−	1.25051i
$478$	−8.15297e8	+	1.41214e9i	−0.341443	+	0.591396i
$479$	−1.52250e9	−	1.27753e9i	−0.632970	−	0.531124i	0.268881	−	0.963174i	$-0.413346\pi$
$479$	−1.52250e9	−	1.27753e9i	−0.632970	−	0.531124i	−0.901850	+	0.432049i	$0.857791\pi$
$480$	−1.81488e8	−	5.42143e7i	−0.0749036	−	0.0223754i
$481$	−5.58366e8	−	3.16665e9i	−0.228776	−	1.29746i
$482$	−1.07586e9	+	9.02752e8i	−0.437613	+	0.367201i
$483$	5.51336e8	+	4.09937e8i	0.222639	+	0.165540i
$484$	−2.84279e8	+	1.03469e8i	−0.113969	+	0.0414813i
$485$	4.20972e8			0.167555
$486$	−1.71269e9	+	5.18390e8i	−0.676785	+	0.204847i
$487$	4.41103e9			1.73057			0.865284	−	0.501282i	$-0.167138\pi$
$487$	4.41103e9			1.73057			0.865284	+	0.501282i	$0.167138\pi$
$488$	−7.56682e8	+	2.75410e8i	−0.294743	+	0.107278i
$489$	3.43162e9	+	2.55152e9i	1.32714	+	0.986776i
$490$	−3.66460e7	+	3.07496e7i	−0.0140715	+	0.0118074i
$491$	3.03834e8	+	1.72313e9i	0.115838	+	0.656950i	0.986332	+	0.164771i	$0.0526885\pi$
$491$	3.03834e8	+	1.72313e9i	0.115838	+	0.656950i	−0.870494	+	0.492179i	$0.836200\pi$
$492$	−1.08774e9	−	3.24931e8i	−0.411762	−	0.123002i
$493$	−9.07356e7	−	7.61362e7i	−0.0341047	−	0.0286172i
$494$	−1.13734e9	+	1.96994e9i	−0.424471	+	0.735205i
$495$	−3.83046e8	−	1.27385e9i	−0.141949	−	0.472065i
$496$	−2.85257e8	−	4.94080e8i	−0.104966	−	0.181807i
$497$	4.98649e8	−	2.82798e9i	0.182200	−	1.03331i
$498$	1.79170e9	−	1.05441e8i	0.650072	−	0.0382567i
$499$	3.42094e9	+	1.24512e9i	1.23252	+	0.448600i	0.874459	−	0.485099i	$-0.161217\pi$
$499$	3.42094e9	+	1.24512e9i	1.23252	+	0.448600i	0.358059	+	0.933699i	$0.383439\pi$
$500$	−1.04793e9	−	3.81415e8i	−0.374919	−	0.136459i
$501$	−8.04286e8	+	1.60388e9i	−0.285745	+	0.569824i
$502$	5.59016e8	−	3.17034e9i	0.197225	−	1.11852i
$503$	−9.24449e8	−	1.60119e9i	−0.323888	−	0.560991i	0.657398	−	0.753543i	$-0.271657\pi$
$503$	−9.24449e8	−	1.60119e9i	−0.323888	−	0.560991i	−0.981287	+	0.192552i	$0.938324\pi$
$504$	5.89671e8	+	7.90070e8i	0.205165	+	0.274890i
$505$	3.81147e8	−	6.60166e8i	0.131696	−	0.228104i
$506$	−5.03195e8	−	4.22231e8i	−0.172667	−	0.144885i
$507$	1.85053e8	+	7.78701e8i	0.0630620	+	0.265364i
$508$	1.89045e8	+	1.07213e9i	0.0639798	+	0.362847i
$509$	3.18263e9	−	2.67054e9i	1.06973	−	0.897610i	0.0747015	−	0.997206i	$-0.476200\pi$
$509$	3.18263e9	−	2.67054e9i	1.06973	−	0.897610i	0.995028	+	0.0995964i	$0.0317552\pi$
$510$	2.39408e8	−	1.03442e8i	0.0799178	−	0.0345305i
$511$	−4.31522e9	+	1.57061e9i	−1.43064	+	0.520710i
$512$	−1.34218e8			−0.0441942
$513$	−2.09621e9	−	2.48899e9i	−0.685527	−	0.813977i
$514$	−4.27428e9			−1.38833
$515$	4.48715e8	−	1.63319e8i	0.144759	−	0.0526880i
$516$	−2.65564e8	+	2.28401e9i	−0.0850932	+	0.731855i
$517$	−7.93652e8	+	6.65953e8i	−0.252588	+	0.211947i
$518$	−4.40080e8	−	2.49582e9i	−0.139116	−	0.788968i
$519$	−4.16064e9	+	3.93012e9i	−1.30640	+	1.23401i
$520$	−4.33243e8	−	3.63534e8i	−0.135120	−	0.113379i
$521$	9.26367e8	−	1.60451e9i	0.286980	−	0.497063i	−0.686108	−	0.727500i	$-0.740682\pi$
$521$	9.26367e8	−	1.60451e9i	0.286980	−	0.497063i	0.973087	+	0.230437i	$0.0740155\pi$
$522$	−3.07247e8	−	2.01548e8i	−0.0945456	−	0.0620200i
$523$	3.53115e8	+	6.11614e8i	0.107935	+	0.186948i	0.914933	−	0.403605i	$-0.132243\pi$
$523$	3.53115e8	+	6.11614e8i	0.107935	+	0.186948i	−0.806999	+	0.590553i	$0.798910\pi$
$524$	−2.81664e8	+	1.59739e9i	−0.0855207	+	0.485012i
$525$	1.42324e9	+	2.16109e9i	0.429261	+	0.651802i
$526$	1.55736e9	+	5.66834e8i	0.466595	+	0.169827i
$527$	7.38162e8	+	2.68669e8i	0.219692	+	0.0799614i
$528$	−5.18432e8	−	7.87201e8i	−0.153276	−	0.232738i
$529$	−5.42893e8	+	3.07890e9i	−0.159448	+	0.904275i
$530$	6.99748e8	+	1.21200e9i	0.204163	+	0.353620i
$531$	−5.42676e8	+	2.73364e8i	−0.157293	+	0.0792338i
$532$	−8.96407e8	+	1.55262e9i	−0.258116	+	0.447069i
$533$	−2.59662e9	−	2.17882e9i	−0.742785	−	0.623270i
$534$	2.78974e9	−	2.63517e9i	0.792809	−	0.748883i
$535$	−3.25230e8	−	1.84447e9i	−0.0918231	−	0.520755i
$536$	−1.48010e9	+	1.24195e9i	−0.415159	+	0.348359i
$537$	6.05496e8	−	5.20765e9i	0.168734	−	1.45121i
$538$	1.74559e9	−	6.35341e8i	0.483285	−	0.175901i
$539$	−2.38058e8			−0.0654820
$540$	6.99942e8	−	4.05806e8i	0.191286	−	0.110902i
$541$	−3.24776e9			−0.881847			−0.440923	−	0.897545i	$-0.645349\pi$
$541$	−3.24776e9			−0.881847			−0.440923	+	0.897545i	$0.645349\pi$
$542$	1.52563e9	−	5.55285e8i	0.411578	−	0.149802i
$543$	3.05204e9	−	1.31871e9i	0.818071	−	0.353468i
$544$	1.41567e8	−	1.18789e8i	0.0377022	−	0.0316359i
$545$	−2.41341e8	−	1.36871e9i	−0.0638620	−	0.362180i
$546$	6.80583e8	+	2.86389e9i	0.178940	+	0.752977i
$547$	5.75985e9	+	4.83309e9i	1.50472	+	1.26261i	0.873314	+	0.487158i	$0.161967\pi$
$547$	5.75985e9	+	4.83309e9i	1.50472	+	1.26261i	0.631407	+	0.775452i	$0.282478\pi$
$548$	−5.44311e8	+	9.42774e8i	−0.141291	+	0.244723i
$549$	1.35853e9	−	3.15993e9i	0.350402	−	0.815031i
$550$	−1.23703e9	−	2.14259e9i	−0.317036	−	0.549123i
$551$	1.16036e8	−	6.58073e8i	0.0295503	−	0.167588i
$552$	1.79094e8	−	3.57144e8i	0.0453205	−	0.0903768i
$553$	−4.85089e9	−	1.76558e9i	−1.21979	−	0.443966i
$554$	−4.17554e8	−	1.51977e8i	−0.104335	−	0.0379747i
$555$	−2.07626e9	+	1.22188e8i	−0.515533	+	0.0303391i
$556$	2.05953e8	−	1.16802e9i	0.0508166	−	0.288195i
$557$	2.23850e9	+	3.87720e9i	0.548864	+	0.950660i	0.998353	+	0.0573740i	$0.0182727\pi$
$557$	2.23850e9	+	3.87720e9i	0.548864	+	0.950660i	−0.449489	+	0.893286i	$0.648394\pi$
$558$	2.37193e9	+	5.59130e8i	0.577940	+	0.136236i
$559$	−3.43285e9	+	5.94587e9i	−0.831215	+	1.43971i
$560$	−3.41464e8	−	2.86522e8i	−0.0821649	−	0.0689446i
$561$	1.24353e9	+	3.71470e8i	0.297363	+	0.0888289i
$562$	−5.56204e8	−	3.15439e9i	−0.132177	−	0.749614i
$563$	4.65461e9	−	3.90568e9i	1.09927	−	0.922397i	0.101894	−	0.994795i	$-0.467510\pi$
$563$	4.65461e9	−	3.90568e9i	1.09927	−	0.922397i	0.997376	+	0.0723985i	$0.0230653\pi$
$564$	−5.05688e8	−	3.75996e8i	−0.118688	−	0.0882483i
$565$	−2.17879e9	+	7.93015e8i	−0.508213	+	0.184974i
$566$	4.21454e8			0.0976996
$567$	−4.18379e9	−	4.78764e8i	−0.963893	−	0.110301i
$568$	−1.66993e9			−0.382365
$569$	−5.61501e9	+	2.04370e9i	−1.27779	+	0.465076i	−0.889699	−	0.456547i	$-0.849086\pi$
$569$	−5.61501e9	+	2.04370e9i	−1.27779	+	0.465076i	−0.388086	+	0.921623i	$0.626864\pi$
$570$	1.18071e9	+	8.77896e8i	0.267043	+	0.198555i
$571$	−4.93703e9	+	4.14266e9i	−1.10979	+	0.931222i	−0.998044	−	0.0625155i	$-0.980088\pi$
$571$	−4.93703e9	+	4.14266e9i	−1.10979	+	0.931222i	−0.111743	+	0.993737i	$0.535643\pi$
$572$	−4.88718e8	−	2.77166e9i	−0.109187	−	0.619232i
$573$	6.87951e9	+	2.05506e9i	1.52762	+	0.456335i
$574$	−2.04654e9	−	1.71725e9i	−0.451679	−	0.379003i
$575$	5.24340e8	−	9.08183e8i	0.115021	−	0.199221i
$576$	3.92924e8	−	4.17485e8i	0.0856702	−	0.0910253i
$577$	−4.39729e9	−	7.61633e9i	−0.952949	−	1.65056i	−0.738993	−	0.673714i	$-0.764698\pi$
$577$	−4.39729e9	−	7.61633e9i	−0.952949	−	1.65056i	−0.213957	−	0.976843i	$-0.568635\pi$
$578$	5.25851e8	−	2.98225e9i	0.113270	−	0.642387i
$579$	−9.03281e9	+	5.31580e8i	−1.93396	+	0.113813i
$580$	1.56122e8	+	5.68237e7i	0.0332251	+	0.0120929i
$581$	3.96902e9	+	1.44461e9i	0.839589	+	0.305586i
$582$	−5.71166e8	+	1.13900e9i	−0.120097	+	0.239494i
$583$	−1.20935e9	+	6.85857e9i	−0.252762	+	1.43349i
$584$	1.33524e9	+	2.31271e9i	0.277406	+	0.480481i
$585$	2.39910e9	−	2.83355e8i	0.495453	−	0.0585174i
$586$	−1.07160e9	+	1.85606e9i	−0.219983	+	0.381022i
$587$	−2.90149e9	−	2.43464e9i	−0.592089	−	0.496822i	0.296803	−	0.954939i	$-0.404080\pi$
$587$	−2.90149e9	−	2.43464e9i	−0.592089	−	0.496822i	−0.888892	+	0.458117i	$0.848524\pi$
$588$	−3.34771e7	−	1.40872e8i	−0.00679090	−	0.0285761i
$589$	7.69546e8	+	4.36431e9i	0.155178	+	0.880060i
$590$	2.10462e8	−	1.76599e8i	0.0421883	−	0.0354002i
$591$	−2.99112e9	+	1.29239e9i	−0.596044	+	0.257536i
$592$	−1.38491e9	+	5.04065e8i	−0.274343	+	0.0998528i
$593$	8.76857e8			0.172678			0.0863391	−	0.996266i	$-0.472483\pi$
$593$	8.76857e8			0.172678			0.0863391	+	0.996266i	$0.472483\pi$
$594$	3.96631e9	+	6.91954e8i	0.776487	+	0.135464i
$595$	6.13748e8			0.119449
$596$	2.95839e9	−	1.07677e9i	0.572392	−	0.208334i
$597$	−6.81705e8	+	5.86309e9i	−0.131125	+	1.12776i
$598$	9.13853e8	−	7.66814e8i	0.174752	−	0.146634i
$599$	−1.73929e9	−	9.86402e9i	−0.330658	−	1.87525i	−0.466496	−	0.884523i	$-0.654484\pi$
$599$	−1.73929e9	−	9.86402e9i	−0.330658	−	1.87525i	0.135838	−	0.990731i	$-0.456627\pi$
$600$	1.09393e9	−	1.03332e9i	0.206756	−	0.195301i
$601$	2.19151e9	+	1.83889e9i	0.411796	+	0.345538i	0.825032	−	0.565086i	$-0.191157\pi$
$601$	2.19151e9	+	1.83889e9i	0.411796	+	0.345538i	−0.413236	+	0.910624i	$0.635602\pi$
$602$	−2.70562e9	+	4.68628e9i	−0.505452	+	0.875468i
$603$	4.69913e8	−	8.23968e9i	0.0872784	−	1.53038i
$604$	−1.78347e9	−	3.08907e9i	−0.329335	−	0.570424i
$605$	−1.01457e8	+	5.75393e8i	−0.0186269	+	0.105638i
$606$	1.26904e9	+	1.92695e9i	0.231645	+	0.351736i
$607$	−2.89167e9	−	1.05248e9i	−0.524792	−	0.191009i	0.0660192	−	0.997818i	$-0.478970\pi$
$607$	−2.89167e9	−	1.05248e9i	−0.524792	−	0.191009i	−0.590812	+	0.806810i	$0.701192\pi$
$608$	9.79702e8	+	3.56582e8i	0.176779	+	0.0643424i
$609$	−4.75619e8	−	7.22193e8i	−0.0853295	−	0.129567i
$610$	−2.70054e8	+	1.53156e9i	−0.0481723	+	0.273198i
$611$	−9.40776e8	−	1.62947e9i	−0.166856	−	0.289003i
$612$	−4.49459e7	+	7.88103e8i	−0.00792611	+	0.138980i
$613$	−2.47683e9	+	4.28999e9i	−0.434295	+	0.752220i	−0.997238	−	0.0742753i	$-0.976336\pi$
$613$	−2.47683e9	+	4.28999e9i	−0.434295	+	0.752220i	0.562943	+	0.826496i	$0.309669\pi$
$614$	−1.33154e9	−	1.11730e9i	−0.232149	−	0.194796i
$615$	−1.59385e9	+	1.50554e9i	−0.276303	+	0.260994i
$616$	−3.85187e8	−	2.18450e9i	−0.0663956	−	0.376548i
$617$	1.49382e9	−	1.25346e9i	0.256036	−	0.214839i	−0.505730	−	0.862692i	$-0.668777\pi$
$617$	1.49382e9	−	1.25346e9i	0.256036	−	0.214839i	0.761766	+	0.647852i	$0.224333\pi$
$618$	−1.66924e8	+	1.43565e9i	−0.0284486	+	0.244675i
$619$	7.89175e9	−	2.87236e9i	1.33738	−	0.486768i	0.428396	−	0.903591i	$-0.359079\pi$
$619$	7.89175e9	−	2.87236e9i	1.33738	−	0.486768i	0.908988	+	0.416823i	$0.136857\pi$
$620$	−1.10184e9			−0.185673
$621$	5.86599e8	+	1.60262e9i	0.0982925	+	0.268540i
$622$	5.56573e9			0.927376
$623$	8.48637e9	−	3.08879e9i	1.40609	−	0.511776i
$624$	1.57141e9	−	6.78968e8i	0.258907	−	0.111867i
$625$	2.11133e9	−	1.77162e9i	0.345920	−	0.290262i
$626$	−4.54466e8	−	2.57741e9i	−0.0740443	−	0.419926i
$627$	1.69282e9	+	7.12340e9i	0.274268	+	1.15412i
$628$	2.87887e9	+	2.41566e9i	0.463835	+	0.389204i
$629$	1.01462e9	−	1.75738e9i	0.162565	−	0.281571i
$630$	1.89087e9	−	2.23328e8i	0.301279	−	0.0355838i
$631$	−4.80492e9	−	8.32236e9i	−0.761348	−	1.31869i	−0.942156	−	0.335175i	$-0.891204\pi$
$631$	−4.80492e9	−	8.32236e9i	−0.761348	−	1.31869i	0.180808	−	0.983519i	$-0.442129\pi$
$632$	−5.21289e8	+	2.95638e9i	−0.0821427	+	0.465854i
$633$	5.83172e8	−	1.16294e9i	0.0913868	−	0.182241i
$634$	4.99464e9	+	1.81790e9i	0.778381	+	0.283308i
$635$	1.97576e9	+	7.19119e8i	0.306215	+	0.111453i
$636$	−4.22865e9	+	2.48855e8i	−0.651781	+	0.0383572i
$637$	7.50745e7	−	4.25769e8i	0.0115081	−	0.0652658i
$638$	4.13389e8	+	7.16010e8i	0.0630211	+	0.109156i
$639$	4.88873e9	−	5.19432e9i	0.741213	−	0.787545i
$640$	−1.29609e8	+	2.24489e8i	−0.0195436	+	0.0338504i
$641$	8.76210e8	+	7.35227e8i	0.131403	+	0.110260i	0.706121	−	0.708092i	$-0.250444\pi$
$641$	8.76210e8	+	7.35227e8i	0.131403	+	0.110260i	−0.574718	+	0.818352i	$0.694888\pi$
$642$	5.43175e9	+	1.62258e9i	0.810154	+	0.242011i
$643$	−1.51158e8	−	8.57259e8i	−0.0224229	−	0.127167i	0.971542	−	0.236869i	$-0.0761213\pi$
$643$	−1.51158e8	−	8.57259e8i	−0.0224229	−	0.127167i	−0.993964	+	0.109702i	$0.965010\pi$
$644$	7.20260e8	−	6.04370e8i	0.106265	−	0.0891667i
$645$	3.56373e9	+	2.64975e9i	0.522933	+	0.388818i
$646$	−1.34894e9	+	4.90975e8i	−0.196870	+	0.0716548i
$647$	9.38829e9			1.36277			0.681383	−	0.731927i	$-0.261379\pi$
$647$	9.38829e9			1.36277			0.681383	+	0.731927i	$0.261379\pi$
$648$	1.48300e8	+	2.44439e9i	0.0214106	+	0.352904i
$649$	1.36720e9			0.196324
$650$	4.22216e9	−	1.53674e9i	0.603028	−	0.219484i
$651$	4.60219e9	+	3.42188e9i	0.653779	+	0.486106i
$652$	4.48304e9	−	3.76171e9i	0.633440	−	0.531519i
$653$	2.40380e9	+	1.36326e10i	0.337833	+	1.91595i	0.397247	+	0.917712i	$0.369966\pi$
$653$	2.40380e9	+	1.36326e10i	0.337833	+	1.91595i	−0.0594140	+	0.998233i	$0.518923\pi$
$654$	4.03070e9	+	1.20406e9i	0.563453	+	0.168316i
$655$	2.39976e9	+	2.01364e9i	0.333675	+	0.279987i
$656$	−7.76802e8	+	1.34546e9i	−0.107435	+	0.186083i
$657$	−1.11026e10	−	2.61720e9i	−1.52738	−	0.360046i
$658$	−7.41479e8	−	1.28428e9i	−0.101463	−	0.175739i
$659$	1.10989e9	−	6.29451e9i	0.151071	−	0.856768i	−0.811219	−	0.584743i	$-0.801195\pi$
$659$	1.10989e9	−	6.29451e9i	0.151071	−	0.856768i	0.962290	−	0.272025i	$-0.0876934\pi$
$660$	−1.81728e9	+	1.06947e8i	−0.246047	+	0.0144798i
$661$	3.26648e9	+	1.18890e9i	0.439921	+	0.160118i	0.552479	−	0.833527i	$-0.313682\pi$
$661$	3.26648e9	+	1.18890e9i	0.439921	+	0.160118i	−0.112558	+	0.993645i	$0.535904\pi$
$662$	−2.47636e9	−	9.01321e8i	−0.331750	−	0.120747i
$663$	−1.05654e9	+	2.10692e9i	−0.140796	+	0.280770i
$664$	4.26521e8	−	2.41892e9i	0.0565396	−	0.320652i
$665$	1.73125e9	+	2.99861e9i	0.228288	+	0.395406i
$666$	2.48643e9	−	5.78342e9i	0.326150	−	0.758621i
$667$	−1.75224e8	+	3.03496e8i	−0.0228640	+	0.0396016i
$668$	1.88101e9	+	1.57836e9i	0.244160	+	0.204874i
$669$	−8.85602e8	−	3.72661e9i	−0.114353	−	0.481196i
$670$	6.47979e8	+	3.67487e9i	0.0832337	+	0.472041i
$671$	−5.92851e9	+	4.97461e9i	−0.757560	+	0.635668i
$672$	1.23852e9	−	5.35133e8i	0.157438	−	0.0680252i
$673$	−2.32512e9	+	8.46276e8i	−0.294031	+	0.107019i	−0.484824	−	0.874612i	$-0.661116\pi$
$673$	−2.32512e9	+	8.46276e8i	−0.294031	+	0.107019i	0.190793	+	0.981630i	$0.438894\pi$
$674$	−9.06459e9			−1.14035
$675$	1.16558e7	+	6.42772e9i	0.00145874	+	0.804440i
$676$	1.09536e9			0.136377
$677$	−9.92416e9	+	3.61210e9i	−1.22923	+	0.447404i	−0.873334	−	0.487122i	$-0.838047\pi$
$677$	−9.92416e9	+	3.61210e9i	−1.22923	+	0.447404i	−0.355897	+	0.934525i	$0.615825\pi$
$678$	8.10521e8	−	6.97099e9i	0.0998758	−	0.858995i
$679$	−2.29705e9	+	1.92745e9i	−0.281596	+	0.236287i
$680$	−6.19774e7	−	3.51491e8i	−0.00755879	−	0.0428680i
$681$	1.24447e9	−	1.17552e9i	0.150998	−	0.142631i
$682$	−4.20034e9	−	3.52450e9i	−0.507036	−	0.425454i
$683$	4.81285e8	−	8.33611e8i	0.0578003	−	0.100113i	−0.835677	−	0.549221i	$-0.814925\pi$
$683$	4.81285e8	−	8.33611e8i	0.0578003	−	0.100113i	0.893478	+	0.449108i	$0.148258\pi$
$684$	−3.97724e9	+	2.00347e9i	−0.475210	+	0.239379i
$685$	1.05124e9	+	1.82080e9i	0.124964	+	0.216443i
$686$	1.06644e9	−	6.04805e9i	0.126125	−	0.715289i
$687$	−7.45866e8	−	1.13254e9i	−0.0877631	−	0.133262i
$688$	2.95703e9	+	1.07627e9i	0.346176	+	0.125998i
$689$	−1.18852e10	−	4.32587e9i	−1.38433	−	0.503856i
$690$	−4.24405e8	−	6.44427e8i	−0.0491823	−	0.0746796i
$691$	6.28156e8	−	3.56245e9i	0.0724260	−	0.410748i	−0.926942	−	0.375204i	$-0.877573\pi$
$691$	6.28156e8	−	3.56245e9i	0.0724260	−	0.410748i	0.999368	−	0.0355439i	$-0.0113164\pi$
$692$	3.91630e9	+	6.78324e9i	0.449268	+	0.778154i
$693$	7.92255e9	+	5.19703e9i	0.904271	+	0.593184i
$694$	−4.58697e9	+	7.94487e9i	−0.520916	+	0.902253i
$695$	−1.75471e9	−	1.47237e9i	−0.198270	−	0.166369i
$696$	−3.65568e8	+	3.45314e8i	−0.0410995	+	0.0388223i
$697$	−3.71458e8	−	2.10664e9i	−0.0415523	−	0.235655i
$698$	−4.24109e8	+	3.55870e8i	−0.0472045	+	0.0396093i
$699$	2.94297e8	−	2.53114e9i	0.0325923	−	0.280314i
$700$	3.32772e9	−	1.21119e9i	0.366694	−	0.133466i
$701$	−1.02292e10			−1.12158			−0.560788	−	0.827960i	$-0.689502\pi$
$701$	−1.02292e10			−1.12158			−0.560788	+	0.827960i	$0.689502\pi$
$702$	−2.48839e9	+	6.87557e9i	−0.271481	+	0.750117i
$703$	1.14481e10			1.24277
$704$	−1.21216e9	+	4.41190e8i	−0.130935	+	0.0476564i
$705$	−1.11720e9	+	4.82715e8i	−0.120080	+	0.0518834i
$706$	−4.98590e9	+	4.18367e9i	−0.533246	+	0.447446i
$707$	9.42880e8	+	5.34734e9i	0.100343	+	0.569075i
$708$	1.92263e8	+	8.09043e8i	0.0203601	+	0.0856752i
$709$	1.72005e9	+	1.44329e9i	0.181250	+	0.152087i	0.728899	−	0.684621i	$-0.240032\pi$
$709$	1.72005e9	+	1.44329e9i	0.181250	+	0.152087i	−0.547649	+	0.836708i	$0.684477\pi$
$710$	−1.61258e9	+	2.79307e9i	−0.169090	+	0.292872i
$711$	−7.66975e9	−	1.02763e10i	−0.800272	−	1.07224i
$712$	−2.62591e9	−	4.54820e9i	−0.272646	−	0.472237i
$713$	4.03585e8	−	2.28884e9i	0.0416986	−	0.236485i
$714$	−8.32722e8	+	1.66059e9i	−0.0856162	+	0.170733i
$715$	−5.10773e9	−	1.85906e9i	−0.522585	−	0.190205i
$716$	−6.74216e9	−	2.45395e9i	−0.686441	−	0.249844i
$717$	−9.51545e9	+	5.59983e8i	−0.964078	+	0.0567359i
$718$	2.07383e9	−	1.17612e10i	0.209092	−	1.18582i
$719$	−4.83298e9	−	8.37096e9i	−0.484913	−	0.839893i	0.514937	−	0.857228i	$-0.327815\pi$
$719$	−4.83298e9	−	8.37096e9i	−0.484913	−	0.839893i	−0.999850	+	0.0173346i	$0.994482\pi$
$720$	−3.18843e8	−	1.06034e9i	−0.0318356	−	0.105872i
$721$	−1.70066e9	+	2.94564e9i	−0.168984	+	0.292689i
$722$	−7.25869e8	−	6.09076e8i	−0.0717758	−	0.0602270i
$723$	−7.86637e9	−	2.34986e9i	−0.774088	−	0.231237i
$724$	−7.90104e8	−	4.48090e9i	−0.0773748	−	0.438814i
$725$	−1.01112e9	+	8.48431e8i	−0.0985416	+	0.0826863i
$726$	−1.41916e9	−	1.05519e9i	−0.137642	−	0.102342i
$727$	6.31139e9	−	2.29716e9i	0.609193	−	0.221728i	−0.0189572	−	0.999820i	$-0.506035\pi$
$727$	6.31139e9	−	2.29716e9i	0.609193	−	0.221728i	0.628150	+	0.778092i	$0.283812\pi$
$728$	4.02848e9			0.386974
$729$	−8.03743e9	−	6.69468e9i	−0.768371	−	0.640005i
$730$	5.15756e9			0.490698
$731$	−4.07151e9	+	1.48191e9i	−0.385518	+	0.140317i
$732$	−3.77745e9	−	2.80866e9i	−0.355967	−	0.264673i
$733$	1.30859e10	−	1.09803e10i	1.22727	−	1.02980i	0.228854	−	0.973461i	$-0.426502\pi$
$733$	1.30859e10	−	1.09803e10i	1.22727	−	1.02980i	0.998412	−	0.0563372i	$-0.0179422\pi$
$734$	1.78063e9	+	1.00985e10i	0.166202	+	0.942581i
$735$	−2.67945e8	−	8.00410e7i	−0.0248909	−	0.00743545i
$736$	−4.18854e8	−	3.51460e8i	−0.0387249	−	0.0324940i
$737$	−9.28477e9	+	1.60817e10i	−0.854348	+	1.47977i
$738$	−1.91097e9	−	6.35510e9i	−0.175007	−	0.582003i
$739$	−8.23808e8	−	1.42688e9i	−0.0750879	−	0.130056i	0.826037	−	0.563617i	$-0.190590\pi$
$739$	−8.23808e8	−	1.42688e9i	−0.0750879	−	0.130056i	−0.901125	+	0.433560i	$0.857257\pi$
$740$	−4.94264e8	+	2.80311e9i	−0.0448381	+	0.254290i
$741$	−1.32741e10	+	7.81181e8i	−1.19851	+	0.0705322i
$742$	−9.36744e9	−	3.40947e9i	−0.841797	−	0.306389i
$743$	6.53871e9	+	2.37990e9i	0.584832	+	0.212862i	0.617455	−	0.786606i	$-0.288164\pi$
$743$	6.53871e9	+	2.37990e9i	0.584832	+	0.212862i	−0.0326226	+	0.999468i	$0.510386\pi$
$744$	1.49496e9	−	2.98120e9i	0.133084	−	0.265391i
$745$	1.05583e9	−	5.98790e9i	0.0935506	−	0.530552i
$746$	−6.02536e8	−	1.04362e9i	−0.0531370	−	0.0920361i
$747$	6.27543e9	+	8.40812e9i	0.550835	+	0.738035i
$748$	8.88063e8	−	1.53817e9i	0.0775868	−	0.134384i
$749$	1.02197e10	+	8.57533e9i	0.888692	+	0.745701i
$750$	−1.50722e9	−	6.34237e9i	−0.130455	−	0.548955i
$751$	1.40048e9	+	7.94254e9i	0.120653	+	0.684257i	0.983795	+	0.179296i	$0.0573820\pi$
$751$	1.40048e9	+	7.94254e9i	0.120653	+	0.684257i	−0.863142	+	0.504961i	$0.831507\pi$
$752$	−6.60626e8	+	5.54331e8i	−0.0566492	+	0.0475343i
$753$	1.72751e10	−	7.46413e9i	1.47448	−	0.637084i
$754$	−1.41096e9	+	5.13547e8i	−0.119871	+	0.0436295i
$755$	−6.88891e9			−0.582554
$756$	−1.96125e9	+	5.41903e9i	−0.165084	+	0.456137i
$757$	1.28651e10			1.07790			0.538948	−	0.842339i	$-0.318822\pi$
$757$	1.28651e10			1.07790			0.538948	+	0.842339i	$0.318822\pi$
$758$	−2.85612e9	+	1.03954e9i	−0.238196	+	0.0866962i
$759$	4.43477e8	−	3.81418e9i	0.0368150	−	0.316632i
$760$	1.54247e9	−	1.29428e9i	0.127458	−	0.106950i
$761$	2.33028e9	+	1.32157e10i	0.191674	+	1.08704i	0.917077	+	0.398711i	$0.130542\pi$
$761$	2.33028e9	+	1.32157e10i	0.191674	+	1.08704i	−0.725403	+	0.688325i	$0.758346\pi$
$762$	−4.62636e9	+	4.37004e9i	−0.378789	+	0.357802i
$763$	7.58364e9	+	6.36343e9i	0.618076	+	0.518627i
$764$	4.91297e9	−	8.50951e9i	0.398581	−	0.690363i
$765$	1.27476e9	+	8.36214e8i	0.102947	+	0.0675309i
$766$	−4.54694e8	−	7.87553e8i	−0.0365526	−	0.0633110i
$767$	−4.31162e8	+	2.44524e9i	−0.0345030	+	0.195676i
$768$	−4.31537e8	−	6.55257e8i	−0.0343759	−	0.0521972i
$769$	−1.45793e10	−	5.30643e9i	−1.15610	−	0.420785i	−0.308396	−	0.951258i	$-0.599792\pi$
$769$	−1.45793e10	−	5.30643e9i	−1.15610	−	0.420785i	−0.847702	+	0.530473i	$0.822014\pi$
$770$	−4.02569e9	−	1.46523e9i	−0.317778	−	0.115662i
$771$	−1.37427e10	−	2.08672e10i	−1.07989	−	1.63974i
$772$	−2.15030e9	+	1.21950e10i	−0.168205	+	0.953938i
$773$	2.49045e9	+	4.31358e9i	0.193932	+	0.335900i	0.946550	−	0.322558i	$-0.104543\pi$
$773$	2.49045e9	+	4.31358e9i	0.193932	+	0.335900i	−0.752618	+	0.658457i	$0.771209\pi$
$774$	−1.20045e10	+	6.04707e9i	−0.930574	+	0.468761i
$775$	4.37684e9	−	7.58091e9i	0.337757	−	0.585013i
$776$	1.33581e9	+	1.12087e9i	0.102619	+	0.0861075i
$777$	1.07698e10	−	1.01731e10i	0.823631	−	0.777997i
$778$	2.82596e9	+	1.60268e10i	0.215148	+	1.22017i
$779$	9.24469e9	−	7.75721e9i	0.700666	−	0.587929i
$780$	3.81826e8	−	3.28395e9i	0.0288094	−	0.247779i
$781$	−1.50816e10	+	5.48925e9i	−1.13284	+	0.412320i
$782$	7.52849e8			0.0562969
$783$	−3.89512e6	−	2.14801e9i	−0.000289971	−	0.159908i
$784$	−1.98157e8			−0.0146860
$785$	6.82037e9	−	2.48241e9i	0.503227	−	0.183160i
$786$	−8.70416e9	+	3.76085e9i	−0.639363	+	0.276253i
$787$	5.55672e9	−	4.66264e9i	0.406356	−	0.340974i	−0.416588	−	0.909095i	$-0.636774\pi$
$787$	5.55672e9	−	4.66264e9i	0.406356	−	0.340974i	0.822944	+	0.568122i	$0.192330\pi$
$788$	7.74334e8	+	4.39147e9i	0.0563750	+	0.319719i
$789$	2.23993e9	+	9.42560e9i	0.162355	+	0.683187i
$790$	4.44136e9	+	3.72674e9i	0.320495	+	0.268927i
$791$	8.25778e9	−	1.43029e10i	0.593260	−	1.02756i
$792$	2.17629e9	−	5.06202e9i	0.155660	−	0.362064i
$793$	−7.02751e9	−	1.21720e10i	−0.500432	−	0.866774i
$794$	−1.13394e9	+	6.43089e9i	−0.0803930	+	0.455931i
$795$	−3.66720e9	+	7.31302e9i	−0.258851	+	0.516193i
$796$	7.59074e9	+	2.76280e9i	0.533443	+	0.194158i
$797$	−2.01321e10	−	7.32749e9i	−1.40859	−	0.512686i	−0.477876	−	0.878427i	$-0.658593\pi$
$797$	−2.01321e10	−	7.32749e9i	−1.40859	−	0.512686i	−0.930716	+	0.365742i	$0.880815\pi$
$798$	−1.04621e10	+	6.15693e8i	−0.728800	+	0.0428898i
$799$	2.06192e8	−	1.16937e9i	0.0143007	−	0.0811034i
$800$	−1.02968e9	−	1.78347e9i	−0.0711032	−	0.123154i
$801$	2.18346e10	+	5.14702e9i	1.50117	+	0.353869i
$802$	−6.84803e9	+	1.18611e10i	−0.468765	+	0.811925i
$803$	1.96611e10	+	1.64976e10i	1.34000	+	1.12439i
$804$	−1.08221e10	−	3.23279e9i	−0.734369	−	0.219372i
$805$	−3.15326e8	−	1.78830e9i	−0.0213046	−	0.120825i
$806$	7.62824e9	−	6.40085e9i	0.513159	−	0.430591i
$807$	8.71417e9	+	6.47928e9i	0.583672	+	0.433979i
$808$	2.96719e9	−	1.07997e9i	0.197881	−	0.0720229i
$809$	1.56094e10			1.03650			0.518248	−	0.855231i	$-0.326585\pi$
$809$	1.56094e10			1.03650			0.518248	+	0.855231i	$0.326585\pi$
$810$	4.23161e9	+	2.11240e9i	0.279775	+	0.139662i
$811$	2.80065e10			1.84368			0.921841	−	0.387569i	$-0.126685\pi$
$811$	2.80065e10			1.84368			0.921841	+	0.387569i	$0.126685\pi$
$812$	−1.11206e9	+	4.04756e8i	−0.0728922	+	0.0265306i
$813$	7.61614e9	+	5.66285e9i	0.497070	+	0.369588i
$814$	−1.08506e10	+	9.10472e9i	−0.705127	+	0.591672i
$815$	−1.96265e9	−	1.11307e10i	−0.126996	−	0.720231i
$816$	1.03510e9	+	3.09207e8i	0.0666910	+	0.0199221i
$817$	−1.87250e10	−	1.57122e10i	−1.20128	−	1.00800i
$818$	9.31184e9	−	1.61286e10i	0.594838	−	1.03029i
$819$	−1.17934e10	+	1.25306e10i	−0.750147	+	0.797037i
$820$	1.50025e9	+	2.59851e9i	0.0950201	+	0.164580i
$821$	−4.80326e9	+	2.72407e10i	−0.302925	+	1.71797i	0.330188	+	0.943915i	$0.392888\pi$
$821$	−4.80326e9	+	2.72407e10i	−0.302925	+	1.71797i	−0.633114	+	0.774059i	$0.718223\pi$
$822$	−6.35273e9	+	3.73858e8i	−0.398941	+	0.0234777i
$823$	2.28519e10	+	8.31740e9i	1.42897	+	0.520102i	0.936635	−	0.350306i	$-0.113922\pi$
$823$	2.28519e10	+	8.31740e9i	1.42897	+	0.520102i	0.492332	+	0.870408i	$0.336145\pi$
$824$	1.85869e9	+	6.76508e8i	0.115734	+	0.0421238i
$825$	6.48294e9	−	1.29281e10i	0.401960	−	0.801576i
$826$	−3.39824e8	+	1.92724e9i	−0.0209809	+	0.118988i
$827$	−6.43064e9	−	1.11382e10i	−0.395353	−	0.684771i	0.597793	−	0.801650i	$-0.296044\pi$
$827$	−6.43064e9	−	1.11382e10i	−0.395353	−	0.684771i	−0.993146	+	0.116879i	$0.962711\pi$
$828$	2.31942e9	−	2.73944e8i	0.141995	−	0.0167709i
$829$	−1.11955e10	+	1.93913e10i	−0.682503	+	1.18213i	0.291712	+	0.956506i	$0.405775\pi$
$829$	−1.11955e10	+	1.93913e10i	−0.682503	+	1.18213i	−0.974215	+	0.225623i	$0.927558\pi$
$830$	−3.63394e9	−	3.04924e9i	−0.220600	−	0.185105i
$831$	−6.00561e8	−	2.52716e9i	−0.0363039	−	0.152767i
$832$	−4.06803e8	−	2.30709e9i	−0.0244880	−	0.138878i
$833$	2.09007e8	−	1.75378e8i	0.0125287	−	0.0105128i
$834$	6.36448e9	−	2.74993e9i	0.379911	−	0.164150i
$835$	4.45632e9	−	1.62197e9i	0.264895	−	0.0964140i
$836$	1.00201e10			0.593131
$837$	4.89654e9	+	1.33776e10i	0.288636	+	0.788567i
$838$	1.59849e10			0.938328
$839$	−2.10230e10	+	7.65176e9i	−1.22893	+	0.447296i	−0.873233	−	0.487304i	$-0.837980\pi$
$839$	−2.10230e10	+	7.65176e9i	−1.22893	+	0.447296i	−0.355702	+	0.934599i	$0.615758\pi$
$840$	3.00939e8	−	2.58827e9i	0.0175187	−	0.150672i
$841$	−1.28763e10	+	1.08045e10i	−0.746456	+	0.626351i
$842$	9.58189e7	+	5.43416e8i	0.00553171	+	0.0313719i
$843$	1.36116e10	−	1.28574e10i	0.782548	−	0.739191i
$844$	−1.36388e9	−	1.14443e9i	−0.0780869	−	0.0655227i
$845$	1.05774e9	−	1.83206e9i	0.0603088	−	0.104458i
$846$	2.09741e8	−	3.67769e9i	0.0119093	−	0.208823i
$847$	−2.08088e9	−	3.60419e9i	−0.117667	−	0.203805i
$848$	−1.00665e9	+	5.70899e9i	−0.0566882	+	0.321495i
$849$	1.35506e9	+	2.05756e9i	0.0759944	+	0.115392i
$850$	2.66452e9	+	9.69807e8i	0.148817	+	0.0541651i
$851$	−5.64182e9	−	2.05345e9i	−0.313809	−	0.114217i
$852$	−5.36915e9	−	8.15266e9i	−0.297418	−	0.451607i
$853$	3.67480e9	−	2.08408e10i	0.202727	−	1.14972i	−0.698249	−	0.715855i	$-0.746037\pi$
$853$	3.67480e9	−	2.08408e10i	0.202727	−	1.14972i	0.900976	−	0.433869i	$-0.142852\pi$
$854$	−5.53879e9	−	9.59346e9i	−0.304307	−	0.527075i
$855$	−4.89714e8	+	8.58688e9i	−0.0267954	+	0.469844i
$856$	3.87906e9	−	6.71873e9i	0.211382	−	0.366125i
$857$	5.78808e9	+	4.85678e9i	0.314124	+	0.263582i	0.786194	−	0.617979i	$-0.212049\pi$
$857$	5.78808e9	+	4.85678e9i	0.314124	+	0.263582i	−0.472070	+	0.881561i	$0.656493\pi$
$858$	1.19600e10	−	1.12974e10i	0.646438	−	0.610622i
$859$	3.04095e9	+	1.72461e10i	0.163694	+	0.928357i	0.950400	+	0.311029i	$0.100674\pi$
$859$	3.04095e9	+	1.72461e10i	0.163694	+	0.928357i	−0.786706	+	0.617328i	$0.788215\pi$
$860$	4.65563e9	−	3.90653e9i	0.249594	−	0.209434i
$861$	1.80366e9	−	1.55126e10i	0.0963040	−	0.828275i
$862$	−9.22723e9	+	3.35844e9i	−0.490677	+	0.178592i
$863$	2.11601e10			1.12067			0.560337	−	0.828265i	$-0.310672\pi$
$863$	2.11601e10			1.12067			0.560337	+	0.828265i	$0.310672\pi$
$864$	3.30151e9	+	5.75974e8i	0.174146	+	0.0303812i
$865$	1.51273e10			0.794701
$866$	2.12807e10	−	7.74555e9i	1.11346	−	0.405265i
$867$	1.62502e10	−	7.02130e9i	0.846821	−	0.365890i
$868$	6.01225e9	−	5.04488e9i	0.312046	−	0.261838i
$869$	5.01006e9	+	2.84135e10i	0.258984	+	1.46877i
$870$	2.24547e8	+	9.44894e8i	0.0115609	+	0.0486481i
$871$	−2.58342e10	−	2.16775e10i	−1.32474	−	1.11159i
$872$	2.87850e9	−	4.98571e9i	0.147014	−	0.254636i
$873$	−7.39707e9	+	8.73660e8i	−0.376279	+	0.0444419i
$874$	2.12362e9	+	3.67822e9i	0.107594	+	0.186358i
$875$	2.66400e9	−	1.51083e10i	0.134433	−	0.762407i
$876$	−6.99767e9	+	1.39545e10i	−0.351714	+	0.701376i
$877$	−8.89116e9	−	3.23612e9i	−0.445102	−	0.162004i	0.109739	−	0.993960i	$-0.464999\pi$
$877$	−8.89116e9	−	3.23612e9i	−0.445102	−	0.162004i	−0.554841	+	0.831957i	$0.687221\pi$
$878$	1.31795e10	+	4.79696e9i	0.657158	+	0.239186i
$879$	−1.25068e10	+	7.36022e8i	−0.621132	+	0.0365536i
$880$	−4.32611e8	+	2.45346e9i	−0.0213997	+	0.121364i
$881$	−1.31551e10	−	2.27853e10i	−0.648154	−	1.12263i	−0.983564	−	0.180563i	$-0.942208\pi$
$881$	−1.31551e10	−	2.27853e10i	−0.648154	−	1.12263i	0.335410	−	0.942072i	$-0.391125\pi$
$882$	5.80106e8	−	6.16367e8i	0.0284687	−	0.0302482i
$883$	−1.11628e10	+	1.93345e10i	−0.545645	+	0.945085i	0.452921	+	0.891551i	$0.350382\pi$
$883$	−1.11628e10	+	1.93345e10i	−0.545645	+	0.945085i	−0.998566	+	0.0535345i	$0.982951\pi$
$884$	2.47097e9	+	2.07339e9i	0.120305	+	0.100948i
$885$	1.53884e9	+	4.59686e8i	0.0746264	+	0.0222925i
$886$	−1.01094e8	−	5.73334e8i	−0.00488325	−	0.0276943i
$887$	−1.57787e10	+	1.32399e10i	−0.759168	+	0.637018i	−0.937910	−	0.346878i	$-0.887242\pi$
$887$	−1.57787e10	+	1.32399e10i	−0.759168	+	0.637018i	0.178742	+	0.983896i	$0.442797\pi$
$888$	−6.91362e9	−	5.14051e9i	−0.331330	−	0.246355i
$889$	−1.40734e10	+	5.12229e9i	−0.671804	+	0.244517i
$890$	−1.01429e10			−0.482278
$891$	9.37434e9	+	2.15885e10i	0.443985	+	1.02247i
$892$	−5.24202e9			−0.247299
$893$	6.29486e9	−	2.29114e9i	0.295805	−	0.107664i
$894$	1.47686e10	+	1.09810e10i	0.691288	+	0.513996i
$895$	−1.06150e10	+	8.90706e9i	−0.494926	+	0.415292i
$896$	−3.20625e8	−	1.81835e9i	−0.0148908	−	0.0844501i
$897$	6.68184e9	+	1.99601e9i	0.309117	+	0.0923400i
$898$	1.22284e9	+	1.02608e9i	0.0563510	+	0.0472841i
$899$	−1.46265e9	+	2.53339e9i	−0.0671401	+	0.116290i
$900$	8.56190e9	+	2.01828e9i	0.391491	+	0.0922853i
$901$	−3.99096e9	−	6.91255e9i	−0.181778	−	0.314848i
$902$	−2.59283e9	+	1.47047e10i	−0.117639	+	0.667164i
$903$	−3.15777e10	+	1.85835e9i	−1.42716	+	0.0839885i
$904$	−9.02510e9	−	3.28487e9i	−0.406314	−	0.147886i
$905$	−8.25760e9	−	3.00552e9i	−0.370325	−	0.134787i
$906$	9.34674e9	−	1.86390e10i	0.417553	−	0.832670i
$907$	2.01019e9	−	1.14004e10i	0.0894566	−	0.507333i	−0.906849	−	0.421456i	$-0.861519\pi$
$907$	2.01019e9	−	1.14004e10i	0.0894566	−	0.507333i	0.996306	−	0.0858780i	$-0.0273695\pi$
$908$	−1.17139e9	−	2.02890e9i	−0.0519278	−	0.0899417i
$909$	−5.32723e9	+	1.23911e10i	−0.235249	+	0.547186i
$910$	3.89014e9	−	6.73791e9i	0.171128	−	0.296402i
$911$	−1.27715e10	−	1.07165e10i	−0.559664	−	0.469614i	0.318534	−	0.947911i	$-0.396809\pi$
$911$	−1.27715e10	−	1.07165e10i	−0.559664	−	0.469614i	−0.878198	+	0.478298i	$0.841254\pi$
$912$	1.40909e9	+	5.92943e9i	0.0615114	+	0.258840i
$913$	−4.09926e9	−	2.32480e10i	−0.178261	−	1.01097i
$914$	4.52291e9	−	3.79517e9i	0.195933	−	0.164407i
$915$	−8.34540e9	+	3.60584e9i	−0.360142	+	0.155608i
$916$	−1.74393e9	+	6.34738e8i	−0.0749712	+	0.0272873i
$917$	−2.23140e10			−0.955620
$918$	−3.99206e9	+	2.31448e9i	−0.170313	+	0.0987426i
$919$	2.68456e10			1.14095			0.570477	−	0.821314i	$-0.306758\pi$
$919$	2.68456e10			1.14095			0.570477	+	0.821314i	$0.306758\pi$
$920$	−9.92311e8	+	3.61172e8i	−0.0420137	+	0.0152917i
$921$	1.17352e9	−	1.00930e10i	0.0494973	−	0.425708i
$922$	−8.02237e9	+	6.73156e9i	−0.337089	+	0.282851i
$923$	−5.06141e9	−	2.87047e10i	−0.211868	−	1.20156i
$924$	9.42639e9	−	8.90412e9i	0.393091	−	0.371312i
$925$	−1.73226e10	−	1.45354e10i	−0.719643	−	0.603852i
$926$	6.99297e9	−	1.21122e10i	0.289416	−	0.501284i
$927$	−7.54563e9	+	3.80099e9i	−0.311112	+	0.156717i
$928$	3.44100e8	+	5.95998e8i	0.0141340	+	0.0244809i
$929$	3.71355e9	−	2.10606e10i	0.151962	−	0.861818i	−0.809549	−	0.587052i	$-0.800288\pi$
$929$	3.71355e9	−	2.10606e10i	0.151962	−	0.861818i	0.961511	−	0.274766i	$-0.0886004\pi$
$930$	−3.54265e9	−	5.37925e9i	−0.144423	−	0.219296i
$931$	1.44641e9	+	5.26451e8i	0.0587447	+	0.0213813i
$932$	−3.27697e9	−	1.19272e9i	−0.132592	−	0.0482595i
$933$	1.78949e10	+	2.71721e10i	0.721347	+	1.09531i
$934$	−1.93678e9	+	1.09840e10i	−0.0777798	+	0.441111i
$935$	−1.71513e9	−	2.97069e9i	−0.0686209	−	0.118855i
$936$	8.36715e9	+	5.48868e9i	0.333513	+	0.218778i
$937$	−7.92289e9	+	1.37228e10i	−0.314626	+	0.544949i	−0.979358	−	0.202133i	$-0.935213\pi$
$937$	−7.92289e9	+	1.37228e10i	−0.314626	+	0.544949i	0.664732	+	0.747082i	$0.268546\pi$
$938$	−2.03614e10	−	1.70853e10i	−0.805560	−	0.675945i
$939$	1.11218e10	−	1.05056e10i	0.438375	−	0.414087i
$940$	2.89218e8	+	1.64024e9i	0.0113574	+	0.0644109i
$941$	−1.58336e10	+	1.32860e10i	−0.619463	+	0.519791i	−0.897635	−	0.440740i	$-0.854716\pi$
$941$	−1.58336e10	+	1.32860e10i	−0.619463	+	0.519791i	0.278172	+	0.960531i	$0.410272\pi$
$942$	−2.53721e9	+	2.18216e10i	−0.0988959	+	0.850567i
$943$	−5.94736e9	+	2.16466e9i	−0.230958	+	0.0840619i
$944$	1.13804e9			0.0440306
$945$	7.16982e9	+	8.51326e9i	0.276374	+	0.328159i
$946$	3.02437e10			1.16149
$947$	−1.12800e10	+	4.10559e9i	−0.431603	+	0.157091i	−0.548680	−	0.836032i	$-0.684870\pi$
$947$	−1.12800e10	+	4.10559e9i	−0.431603	+	0.157091i	0.117077	+	0.993123i	$0.462647\pi$
$948$	−1.61092e10	+	6.96039e9i	−0.614109	+	0.265341i
$949$	−3.57066e10	+	2.99614e10i	−1.35618	+	1.13797i
$950$	2.77781e9	+	1.57537e10i	0.105116	+	0.596144i
$951$	7.18371e9	+	3.02290e10i	0.270842	+	1.13970i
$952$	1.94751e9	+	1.63416e9i	0.0731562	+	0.0613853i
$953$	5.16591e9	−	8.94762e9i	0.193340	−	0.334875i	−0.753015	−	0.658003i	$-0.771401\pi$
$953$	5.16591e9	−	8.94762e9i	0.193340	−	0.334875i	0.946355	+	0.323128i	$0.104735\pi$
$954$	−1.48109e10	−	1.98443e10i	−0.552283	−	0.739975i
$955$	−9.48850e9	−	1.64346e10i	−0.352522	−	0.610585i
$956$	−2.26520e9	+	1.28466e10i	−0.0838500	+	0.475537i
$957$	−2.16647e9	+	4.32030e9i	−0.0799025	+	0.159339i
$958$	−1.49410e10	−	5.43807e9i	−0.549035	−	0.199832i
$959$	−1.40728e10	−	5.12207e9i	−0.515246	−	0.187534i
$960$	−1.51268e9	+	8.90211e7i	−0.0551821	+	0.00324746i
$961$	−1.40866e9	+	7.98888e9i	−0.0512003	+	0.290372i
$962$	−1.28620e10	−	2.22777e10i	−0.465796	−	0.806783i
$963$	9.54265e9	+	3.17350e10i	0.344332	+	1.14511i
$964$	−5.61773e9	+	9.73019e9i	−0.201972	+	0.349826i
$965$	1.83205e10	+	1.53727e10i	0.656283	+	0.550687i
$966$	5.26634e9	+	1.57317e9i	0.187970	+	0.0561508i
$967$	1.99264e8	+	1.13008e9i	0.00708657	+	0.0401899i	0.988146	−	0.153517i	$-0.0490600\pi$
$967$	1.99264e8	+	1.13008e9i	0.00708657	+	0.0401899i	−0.981059	+	0.193707i	$0.937949\pi$
$968$	−1.85397e9	+	1.55567e9i	−0.0656961	+	0.0551256i
$969$	−6.73408e9	−	5.00701e9i	−0.237763	−	0.176785i
$970$	3.16467e9	−	1.15185e9i	0.111334	−	0.0405223i
$971$	−2.46296e10			−0.863358			−0.431679	−	0.902027i	$-0.642079\pi$
$971$	−2.46296e10			−0.863358			−0.431679	+	0.902027i	$0.642079\pi$
$972$	−1.14568e10	+	8.58320e9i	−0.400157	+	0.299790i
$973$	1.63160e10			0.567831
$974$	3.31601e10	−	1.20693e10i	1.14990	−	0.418529i
$975$	2.10775e10	+	1.56718e10i	0.728288	+	0.541506i
$976$	−4.93482e9	+	4.14081e9i	−0.169901	+	0.142564i
$977$	−4.76717e9	−	2.70360e10i	−0.163542	−	0.927494i	−0.950555	−	0.310557i	$-0.899484\pi$
$977$	−4.76717e9	−	2.70360e10i	−0.163542	−	0.927494i	0.787012	−	0.616937i	$-0.211627\pi$
$978$	3.27787e10	+	9.79172e9i	1.12048	+	0.334713i
$979$	−3.86658e10	−	3.24445e10i	−1.31701	−	1.10510i
$980$	−1.91352e8	+	3.31431e8i	−0.00649443	+	0.0112487i
$981$	7.08124e9	+	2.35493e10i	0.239479	+	0.796411i
$982$	6.99884e9	+	1.21224e10i	0.235850	+	0.408504i
$983$	1.72077e9	−	9.75895e9i	0.0577809	−	0.327692i	−0.942192	−	0.335074i	$-0.891239\pi$
$983$	1.72077e9	−	9.75895e9i	0.0577809	−	0.327692i	0.999973	+	0.00738207i	$0.00234981\pi$
$984$	−9.06617e9	+	5.33543e8i	−0.303348	+	0.0178520i
$985$	8.09278e9	+	2.94553e9i	0.269818	+	0.0982057i
$986$	−8.90430e8	−	3.24090e8i	−0.0295822	−	0.0107670i
$987$	3.88591e9	−	7.74915e9i	0.128642	−	0.256534i
$988$	−3.15997e9	+	1.79211e10i	−0.104240	+	0.591173i
$989$	6.40972e9	+	1.11020e10i	0.210694	+	0.364933i
$990$	−6.36503e9	−	8.52818e9i	−0.208486	−	0.279340i
$991$	−1.31142e10	+	2.27144e10i	−0.428039	+	0.741386i	−0.996699	−	0.0811872i	$-0.974129\pi$
$991$	−1.31142e10	+	2.27144e10i	−0.428039	+	0.741386i	0.568660	+	0.822573i	$0.307462\pi$
$992$	−3.49631e9	−	2.93375e9i	−0.113715	−	0.0954186i
$993$	−3.56170e9	−	1.49876e10i	−0.115434	−	0.485747i
$994$	−3.98919e9	−	2.26238e10i	−0.128835	−	0.730657i
$995$	1.19510e10	−	1.00281e10i	0.384614	−	0.322729i
$996$	1.31806e10	−	5.69502e9i	0.422697	−	0.182637i
$997$	4.01382e10	−	1.46091e10i	1.28270	−	0.466864i	0.391374	−	0.920232i	$-0.372000\pi$
$997$	4.01382e10	−	1.46091e10i	1.28270	−	0.466864i	0.891324	+	0.453368i	$0.149778\pi$
$998$	2.91239e10			0.927454
$999$	3.62293e10	−	6.45596e9i	1.14969	−	0.204872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.e.b.7.10	✓	66
27.4	even	9	inner	54.8.e.b.31.10	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.e.b.7.10	✓	66	1.1	even	1	trivial
54.8.e.b.31.10	yes	66	27.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.51754 - 2.73616i) q^{2} +(37.5285 + 27.9037i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-21.4637 - 121.726i) q^{5} +(358.471 + 107.083i) q^{6} +(674.452 + 565.932i) q^{7} +(256.000 - 443.405i) q^{8} +(629.771 + 2094.36i) q^{9} +O(q^{10})\)	\(q+(7.51754 - 2.73616i) q^{2} +(37.5285 + 27.9037i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-21.4637 - 121.726i) q^{5} +(358.471 + 107.083i) q^{6} +(674.452 + 565.932i) q^{7} +(256.000 - 443.405i) q^{8} +(629.771 + 2094.36i) q^{9} +(-494.417 - 856.356i) q^{10} +(854.485 - 4846.03i) q^{11} +(2987.81 - 175.833i) q^{12} +(8397.69 + 3056.51i) q^{13} +(6618.70 + 2409.01i) q^{14} +(2591.12 - 5167.12i) q^{15} +(711.263 - 4033.77i) q^{16} +(2819.87 + 4884.16i) q^{17} +(10464.8 + 14021.3i) q^{18} +(-15908.5 + 27554.3i) q^{19} +(-6059.93 - 5084.88i) q^{20} +(9519.56 + 40058.3i) q^{21} +(-6835.88 - 38768.2i) q^{22} +(12782.4 - 10725.7i) q^{23} +(21979.9 - 9496.97i) q^{24} +(59056.8 - 21494.9i) q^{25} +71493.1 q^{26} +(-34806.1 + 96171.2i) q^{27} +56347.8 q^{28} +(-19735.6 + 7183.17i) q^{29} +(5340.75 - 45933.8i) q^{30} +(106699. - 89531.1i) q^{31} +(-5690.10 - 32270.2i) q^{32} +(167289. - 158021. i) q^{33} +(34562.4 + 29001.3i) q^{34} +(54412.8 - 94245.7i) q^{35} +(117034. + 76772.2i) q^{36} +(-179906. - 311606. i) q^{37} +(-44199.6 + 250668. i) q^{38} +(229865. + 349032. i) q^{39} +(-59468.8 - 21644.9i) q^{40} +(-356423. - 129727. i) q^{41} +(181170. + 275093. i) q^{42} +(-133408. + 756592. i) q^{43} +(-157465. - 272737. i) q^{44} +(241422. - 121613. i) q^{45} +(66745.0 - 115606. i) q^{46} +(-161286. - 135335. i) q^{47} +(139250. - 131534. i) q^{48} +(-8400.76 - 47643.1i) q^{49} +(385149. - 323178. i) q^{50} +(-30460.5 + 261980. i) q^{51} +(537452. - 195617. i) q^{52} -1.41530e6 q^{53} +(1483.70 + 818206. i) q^{54} -608230. q^{55} +(423597. - 154177. i) q^{56} +(-1.36588e6 + 590165. i) q^{57} +(-128709. + 108000. i) q^{58} +(48246.6 + 273620. i) q^{59} +(-85532.9 - 359922. i) q^{60} +(-1.20479e6 - 1.01094e6i) q^{61} +(557143. - 964999. i) q^{62} +(-760518. + 1.76896e6i) q^{63} +(-131072. - 227023. i) q^{64} +(191813. - 1.08783e6i) q^{65} +(825235. - 1.64566e6i) q^{66} +(-3.54611e6 - 1.29068e6i) q^{67} +(339176. + 123450. i) q^{68} +(778991. - 45843.5i) q^{69} +(151179. - 857378. i) q^{70} +(-1.63079e6 - 2.82461e6i) q^{71} +(1.08987e6 + 256913. i) q^{72} +(-2.60790e6 + 4.51701e6i) q^{73} +(-2.20505e6 - 1.85026e6i) q^{74} +(2.81610e6 + 841230. i) q^{75} +(353597. + 2.00535e6i) q^{76} +(3.31883e6 - 2.78483e6i) q^{77} +(2.68303e6 + 1.99492e6i) q^{78} +(-5.50965e6 + 2.00535e6i) q^{79} -506283. q^{80} +(-3.98975e6 + 2.63794e6i) q^{81} -3.03438e6 q^{82} +(4.50803e6 - 1.64079e6i) q^{83} +(2.11465e6 + 1.57231e6i) q^{84} +(534007. - 448085. i) q^{85} +(1.06726e6 + 6.05274e6i) q^{86} +(-941083. - 281122. i) q^{87} +(-1.93000e6 - 1.61947e6i) q^{88} +(5.12872e6 - 8.88321e6i) q^{89} +(1.48215e6 - 1.57480e6i) q^{90} +(3.93406e6 + 6.81399e6i) q^{91} +(185442. - 1.05170e6i) q^{92} +(6.50249e6 - 382671. i) q^{93} +(-1.58277e6 - 576081. i) q^{94} +(3.69554e6 + 1.34507e6i) q^{95} +(686915. - 1.36983e6i) q^{96} +(-591411. + 3.35406e6i) q^{97} +(-193512. - 335173. i) q^{98} +(1.06875e7 - 1.26228e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9}+O(q^{10}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9} - 3000 q^{10} - 2523 q^{11} - 5376 q^{12} - 9924 q^{13} + 13416 q^{14} - 15084 q^{15} + 29478 q^{17} + 22848 q^{18} - 61731 q^{19} - 27264 q^{20} - 36372 q^{21} + 20184 q^{22} + 255234 q^{23} + 558999 q^{25} - 316368 q^{26} - 51597 q^{27} + 263424 q^{28} + 132153 q^{29} + 610632 q^{30} + 776898 q^{31} + 645795 q^{33} + 387840 q^{34} - 321081 q^{35} - 314688 q^{36} - 759795 q^{37} + 174504 q^{38} - 84012 q^{39} - 109056 q^{40} + 349287 q^{41} + 313752 q^{42} - 1043622 q^{43} + 255552 q^{44} + 845496 q^{45} - 524472 q^{46} + 1280709 q^{47} - 872448 q^{48} + 1011003 q^{49} - 1537704 q^{50} - 7812153 q^{51} - 635136 q^{52} - 2951976 q^{53} - 1256832 q^{54} + 2539854 q^{55} + 858624 q^{56} - 3973923 q^{57} - 47496 q^{58} + 639426 q^{59} - 94464 q^{60} + 1639350 q^{61} + 2859936 q^{62} + 6955635 q^{63} - 8650752 q^{64} - 4119567 q^{65} + 712512 q^{66} - 6408441 q^{67} - 1634496 q^{68} - 1007298 q^{69} + 2380872 q^{70} + 3531612 q^{71} + 6623232 q^{72} - 6666213 q^{73} + 7873368 q^{74} + 16535910 q^{75} - 1396032 q^{76} - 8256489 q^{77} - 4117104 q^{78} - 22540695 q^{79} - 3072000 q^{80} - 13134636 q^{81} + 3798096 q^{82} + 8663238 q^{83} + 8570304 q^{84} - 15143175 q^{85} + 8348976 q^{86} + 45908613 q^{87} + 11028480 q^{88} + 21718137 q^{89} - 27904392 q^{90} - 8606796 q^{91} - 8332800 q^{92} - 20412249 q^{93} - 10358784 q^{94} - 21603363 q^{95} - 5505024 q^{96} - 17397492 q^{97} + 44171448 q^{98} + 103927383 q^{99}+O(q^{100}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9 - 3000 * q^10 - 2523 * q^11 - 5376 * q^12 - 9924 * q^13 + 13416 * q^14 - 15084 * q^15 + 29478 * q^17 + 22848 * q^18 - 61731 * q^19 - 27264 * q^20 - 36372 * q^21 + 20184 * q^22 + 255234 * q^23 + 558999 * q^25 - 316368 * q^26 - 51597 * q^27 + 263424 * q^28 + 132153 * q^29 + 610632 * q^30 + 776898 * q^31 + 645795 * q^33 + 387840 * q^34 - 321081 * q^35 - 314688 * q^36 - 759795 * q^37 + 174504 * q^38 - 84012 * q^39 - 109056 * q^40 + 349287 * q^41 + 313752 * q^42 - 1043622 * q^43 + 255552 * q^44 + 845496 * q^45 - 524472 * q^46 + 1280709 * q^47 - 872448 * q^48 + 1011003 * q^49 - 1537704 * q^50 - 7812153 * q^51 - 635136 * q^52 - 2951976 * q^53 - 1256832 * q^54 + 2539854 * q^55 + 858624 * q^56 - 3973923 * q^57 - 47496 * q^58 + 639426 * q^59 - 94464 * q^60 + 1639350 * q^61 + 2859936 * q^62 + 6955635 * q^63 - 8650752 * q^64 - 4119567 * q^65 + 712512 * q^66 - 6408441 * q^67 - 1634496 * q^68 - 1007298 * q^69 + 2380872 * q^70 + 3531612 * q^71 + 6623232 * q^72 - 6666213 * q^73 + 7873368 * q^74 + 16535910 * q^75 - 1396032 * q^76 - 8256489 * q^77 - 4117104 * q^78 - 22540695 * q^79 - 3072000 * q^80 - 13134636 * q^81 + 3798096 * q^82 + 8663238 * q^83 + 8570304 * q^84 - 15143175 * q^85 + 8348976 * q^86 + 45908613 * q^87 + 11028480 * q^88 + 21718137 * q^89 - 27904392 * q^90 - 8606796 * q^91 - 8332800 * q^92 - 20412249 * q^93 - 10358784 * q^94 - 21603363 * q^95 - 5505024 * q^96 - 17397492 * q^97 + 44171448 * q^98 + 103927383 * q^99

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