LMFDB - Embedded newform 27.10.e.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	27.7
Dual form			27.10.e.a.4.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.9570 + 4.71595i) q^{2} +(-37.0275 - 135.322i) q^{3} +(-246.572 + 206.898i) q^{4} +(-222.415 - 1261.38i) q^{5} +(1117.94 + 1578.74i) q^{6} +(-4998.24 - 4194.02i) q^{7} +(5748.96 - 9957.50i) q^{8} +(-16940.9 + 10021.3i) q^{9} +(8830.42 + 15294.7i) q^{10} +(4387.44 - 24882.4i) q^{11} +(37127.8 + 25705.6i) q^{12} +(14554.5 + 5297.40i) q^{13} +(84540.9 + 30770.4i) q^{14} +(-162456. + 76803.2i) q^{15} +(1087.25 - 6166.10i) q^{16} +(187103. + 324072. i) q^{17} +(172243. - 209738. i) q^{18} +(-331545. + 574253. i) q^{19} +(315818. + 265003. i) q^{20} +(-382470. + 831665. i) q^{21} +(60496.3 + 343092. i) q^{22} +(-1.82158e6 + 1.52849e6i) q^{23} +(-1.56034e6 - 409258. i) q^{24} +(293733. - 106910. i) q^{25} -213564. q^{26} +(1.98337e6 + 1.92141e6i) q^{27} +2.10016e6 q^{28} +(2.27688e6 - 828718. i) q^{29} +(1.74274e6 - 1.76127e6i) q^{30} +(4.94152e6 - 4.14643e6i) q^{31} +(1.03725e6 + 5.88253e6i) q^{32} +(-3.52959e6 + 327618. i) q^{33} +(-3.95260e6 - 3.31663e6i) q^{34} +(-4.17856e6 + 7.23748e6i) q^{35} +(2.10377e6 - 5.97600e6i) q^{36} +(-8.89215e6 - 1.54017e7i) q^{37} +(1.58767e6 - 9.00413e6i) q^{38} +(177937. - 2.16569e6i) q^{39} +(-1.38388e7 - 5.03692e6i) q^{40} +(3.98972e6 + 1.45214e6i) q^{41} +(1.03356e6 - 1.25796e7i) q^{42} +(-2.25330e6 + 1.27791e7i) q^{43} +(4.06631e6 + 7.04305e6i) q^{44} +(1.64085e7 + 1.91400e7i) q^{45} +(1.63939e7 - 2.83951e7i) q^{46} +(-1.91163e6 - 1.60405e6i) q^{47} +(-874666. + 81187.0i) q^{48} +(385257. + 2.18490e6i) q^{49} +(-3.30171e6 + 2.77047e6i) q^{50} +(3.69260e7 - 3.73187e7i) q^{51} +(-4.68475e6 + 1.70511e6i) q^{52} -9.09978e6 q^{53} +(-3.47598e7 - 1.55422e7i) q^{54} -3.23619e7 q^{55} +(-7.04967e7 + 2.56587e7i) q^{56} +(8.99852e7 + 2.36021e7i) q^{57} +(-2.55933e7 + 2.14754e7i) q^{58} +(2.51267e7 + 1.42501e8i) q^{59} +(2.41667e7 - 5.25494e7i) q^{60} +(-1.76413e6 - 1.48028e6i) q^{61} +(-4.44728e7 + 7.70291e7i) q^{62} +(1.26704e8 + 2.09620e7i) q^{63} +(-3.95784e7 - 6.85519e7i) q^{64} +(3.44489e6 - 1.95369e7i) q^{65} +(4.41877e7 - 2.08903e7i) q^{66} +(-2.75317e8 - 1.00207e8i) q^{67} +(-1.13184e8 - 4.11957e7i) q^{68} +(2.74286e8 + 1.89903e8i) q^{69} +(2.00099e7 - 1.13482e8i) q^{70} +(3.55199e7 + 6.15222e7i) q^{71} +(2.39385e6 + 2.26301e8i) q^{72} +(-2.15747e8 + 3.73685e8i) q^{73} +(1.87849e8 + 1.57624e8i) q^{74} +(-2.53435e7 - 3.57899e7i) q^{75} +(-3.70623e7 - 2.10191e8i) q^{76} +(-1.26287e8 + 1.05967e8i) q^{77} +(7.90776e6 + 2.88999e7i) q^{78} +(3.19548e8 - 1.16306e8i) q^{79} -8.01960e6 q^{80} +(1.86569e8 - 3.39539e8i) q^{81} -5.85430e7 q^{82} +(-1.63239e8 + 5.94141e7i) q^{83} +(-7.77637e7 - 2.84197e8i) q^{84} +(3.67163e8 - 3.08086e8i) q^{85} +(-3.10697e7 - 1.76205e8i) q^{86} +(-1.96451e8 - 2.77426e8i) q^{87} +(-2.22543e8 - 1.86736e8i) q^{88} +(-2.35605e8 + 4.08079e8i) q^{89} +(-3.02868e8 - 1.70615e8i) q^{90} +(-5.05294e7 - 8.75195e7i) q^{91} +(1.32909e8 - 7.53763e8i) q^{92} +(-7.44074e8 - 5.15163e8i) q^{93} +(3.23336e7 + 1.17685e7i) q^{94} +(7.98090e8 + 2.90481e8i) q^{95} +(7.57627e8 - 3.58178e8i) q^{96} +(1.26743e8 - 7.18794e8i) q^{97} +(-1.52957e7 - 2.64928e7i) q^{98} +(1.75026e8 + 4.65499e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) $ 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−12.9570	+	4.71595i	−0.572623	+	0.208418i	−0.612070	−	0.790804i	$-0.709663\pi$
$2$	−12.9570	+	4.71595i	−0.572623	+	0.208418i	0.0394465	+	0.999222i	$0.487441\pi$
$3$	−37.0275	−	135.322i	−0.263924	−	0.964543i
$3$	−37.0275	−	135.322i	−0.263924	−	0.964543i
$4$	−246.572	+	206.898i	−0.481585	+	0.404098i
$5$	−222.415	−	1261.38i	−0.159147	−	0.902568i	−0.954896	−	0.296941i	$-0.904034\pi$
$5$	−222.415	−	1261.38i	−0.159147	−	0.902568i	0.795749	−	0.605627i	$-0.207078\pi$
$6$	1117.94	+	1578.74i	0.352157	+	0.497313i
$7$	−4998.24	−	4194.02i	−0.786821	−	0.660221i	0.158135	−	0.987417i	$-0.449452\pi$
$7$	−4998.24	−	4194.02i	−0.786821	−	0.660221i	−0.944956	+	0.327196i	$0.893896\pi$
$8$	5748.96	−	9957.50i	0.496232	−	0.859499i
$9$	−16940.9	+	10021.3i	−0.860688	+	0.509132i
$10$	8830.42	+	15294.7i	0.279242	+	0.483662i
$11$	4387.44	−	24882.4i	0.0903533	−	0.512419i	−0.905719	−	0.423878i	$-0.860668\pi$
$11$	4387.44	−	24882.4i	0.0903533	−	0.512419i	0.996073	−	0.0885409i	$-0.0282204\pi$
$12$	37127.8	+	25705.6i	0.516872	+	0.357859i
$13$	14554.5	+	5297.40i	0.141336	+	0.0514420i	0.411719	−	0.911311i	$-0.364928\pi$
$13$	14554.5	+	5297.40i	0.141336	+	0.0514420i	−0.270384	+	0.962753i	$0.587151\pi$
$14$	84540.9	+	30770.4i	0.588154	+	0.214070i
$15$	−162456.	+	76803.2i	−0.828563	+	0.391714i
$16$	1087.25	−	6166.10i	0.00414753	−	0.0235218i
$17$	187103.	+	324072.i	0.543326	+	0.941069i	0.998710	+	0.0507737i	$0.0161687\pi$
$17$	187103.	+	324072.i	0.543326	+	0.941069i	−0.455384	+	0.890295i	$0.650498\pi$
$18$	172243.	−	209738.i	0.386738	−	0.470924i
$19$	−331545.	+	574253.i	−0.583649	+	1.01091i	0.411394	+	0.911458i	$0.365042\pi$
$19$	−331545.	+	574253.i	−0.583649	+	1.01091i	−0.995042	+	0.0994513i	$0.968291\pi$
$20$	315818.	+	265003.i	0.441369	+	0.370352i
$21$	−382470.	+	831665.i	−0.429151	+	0.933171i
$22$	60496.3	+	343092.i	0.0550588	+	0.312254i
$23$	−1.82158e6	+	1.52849e6i	−1.35729	+	1.13890i	−0.380483	+	0.924788i	$0.624242\pi$
$23$	−1.82158e6	+	1.52849e6i	−1.35729	+	1.13890i	−0.976809	+	0.214114i	$0.931313\pi$
$24$	−1.56034e6	−	409258.i	−0.959992	−	0.251795i
$25$	293733.	−	106910.i	0.150391	−	0.0547380i
$26$	−213564.			−0.0916535
$27$	1.98337e6	+	1.92141e6i	0.718237	+	0.695799i
$28$	2.10016e6			0.645715
$29$	2.27688e6	−	828718.i	0.597792	−	0.217578i	−0.0253612	−	0.999678i	$-0.508074\pi$
$29$	2.27688e6	−	828718.i	0.597792	−	0.217578i	0.623153	+	0.782100i	$0.285851\pi$
$30$	1.74274e6	−	1.76127e6i	0.392814	−	0.396992i
$31$	4.94152e6	−	4.14643e6i	0.961021	−	0.806392i	−0.0200981	−	0.999798i	$-0.506398\pi$
$31$	4.94152e6	−	4.14643e6i	0.961021	−	0.806392i	0.981119	+	0.193406i	$0.0619534\pi$
$32$	1.03725e6	+	5.88253e6i	0.174867	+	0.991720i
$33$	−3.52959e6	+	327618.i	−0.518097	+	0.0480900i
$34$	−3.95260e6	−	3.31663e6i	−0.507257	−	0.425639i
$35$	−4.17856e6	+	7.23748e6i	−0.470674	+	0.815232i
$36$	2.10377e6	−	5.97600e6i	0.208755	−	0.592993i
$37$	−8.89215e6	−	1.54017e7i	−0.780008	−	1.35101i	−0.931936	−	0.362622i	$-0.881882\pi$
$37$	−8.89215e6	−	1.54017e7i	−0.780008	−	1.35101i	0.151928	−	0.988392i	$-0.451452\pi$
$38$	1.58767e6	−	9.00413e6i	0.123519	−	0.700512i
$39$	177937.	−	2.16569e6i	0.0123161	−	0.149901i
$40$	−1.38388e7	−	5.03692e6i	−0.854730	−	0.311096i
$41$	3.98972e6	+	1.45214e6i	0.220503	+	0.0802567i	0.449910	−	0.893074i	$-0.351456\pi$
$41$	3.98972e6	+	1.45214e6i	0.220503	+	0.0802567i	−0.229406	+	0.973331i	$0.573678\pi$
$42$	1.03356e6	−	1.25796e7i	0.0512523	−	0.623798i
$43$	−2.25330e6	+	1.27791e7i	−0.100510	+	0.570023i	0.892408	+	0.451229i	$0.149014\pi$
$43$	−2.25330e6	+	1.27791e7i	−0.100510	+	0.570023i	−0.992919	+	0.118795i	$0.962097\pi$
$44$	4.06631e6	+	7.04305e6i	0.163555	+	0.283285i
$45$	1.64085e7	+	1.91400e7i	0.596503	+	0.695803i
$46$	1.63939e7	−	2.83951e7i	0.539849	−	0.935045i
$47$	−1.91163e6	−	1.60405e6i	−0.0571432	−	0.0479488i	0.613769	−	0.789486i	$-0.289653\pi$
$47$	−1.91163e6	−	1.60405e6i	−0.0571432	−	0.0479488i	−0.670912	+	0.741537i	$0.734097\pi$
$48$	−874666.	+	81187.0i	−0.0237824	+	0.00220750i
$49$	385257.	+	2.18490e6i	0.00954702	+	0.0541439i
$50$	−3.30171e6	+	2.77047e6i	−0.0747092	+	0.0626885i
$51$	3.69260e7	−	3.73187e7i	0.764305	−	0.772433i
$52$	−4.68475e6	+	1.70511e6i	−0.0888528	+	0.0323398i
$53$	−9.09978e6			−0.158412			−0.0792062	−	0.996858i	$-0.525239\pi$
$53$	−9.09978e6			−0.158412			−0.0792062	+	0.996858i	$0.525239\pi$
$54$	−3.47598e7	−	1.55422e7i	−0.556296	−	0.248737i
$55$	−3.23619e7			−0.476872
$56$	−7.04967e7	+	2.56587e7i	−0.957905	+	0.348649i
$57$	8.99852e7	+	2.36021e7i	1.12910	+	0.296151i
$58$	−2.55933e7	+	2.14754e7i	−0.296962	+	0.249181i
$59$	2.51267e7	+	1.42501e8i	0.269961	+	1.53103i	0.754525	+	0.656271i	$0.227867\pi$
$59$	2.51267e7	+	1.42501e8i	0.269961	+	1.53103i	−0.484564	+	0.874756i	$0.661022\pi$
$60$	2.41667e7	−	5.25494e7i	0.240733	−	0.523464i
$61$	−1.76413e6	−	1.48028e6i	−0.0163135	−	0.0136886i	0.634594	−	0.772845i	$-0.281167\pi$
$61$	−1.76413e6	−	1.48028e6i	−0.0163135	−	0.0136886i	−0.650908	+	0.759157i	$0.725612\pi$
$62$	−4.44728e7	+	7.70291e7i	−0.382236	+	0.662052i
$63$	1.26704e8	+	2.09620e7i	1.01335	+	0.167648i
$64$	−3.95784e7	−	6.85519e7i	−0.294882	−	0.510751i
$65$	3.44489e6	−	1.95369e7i	0.0239367	−	0.135752i
$66$	4.41877e7	−	2.08903e7i	0.286651	−	0.135518i
$67$	−2.75317e8	−	1.00207e8i	−1.66916	−	0.607523i	−0.677394	−	0.735620i	$-0.736891\pi$
$67$	−2.75317e8	−	1.00207e8i	−1.66916	−	0.607523i	−0.991762	+	0.128097i	$0.959113\pi$
$68$	−1.13184e8	−	4.11957e7i	−0.641942	−	0.233648i
$69$	2.74286e8	+	1.89903e8i	1.45674	+	1.00858i
$70$	2.00099e7	−	1.13482e8i	0.0996101	−	0.564917i
$71$	3.55199e7	+	6.15222e7i	0.165886	+	0.287322i	0.936969	−	0.349411i	$-0.113618\pi$
$71$	3.55199e7	+	6.15222e7i	0.165886	+	0.287322i	−0.771084	+	0.636734i	$0.780285\pi$
$72$	2.39385e6	+	2.26301e8i	0.0104979	+	0.992408i
$73$	−2.15747e8	+	3.73685e8i	−0.889186	+	1.54011i	−0.0483457	+	0.998831i	$0.515395\pi$
$73$	−2.15747e8	+	3.73685e8i	−0.889186	+	1.54011i	−0.840840	+	0.541284i	$0.817938\pi$
$74$	1.87849e8	+	1.57624e8i	0.728226	+	0.611054i
$75$	−2.53435e7	−	3.57899e7i	−0.0924891	−	0.130612i
$76$	−3.70623e7	−	2.10191e8i	−0.127430	−	0.722690i
$77$	−1.26287e8	+	1.05967e8i	−0.409402	+	0.343529i
$78$	7.90776e6	+	2.88999e7i	0.0241896	+	0.0884038i
$79$	3.19548e8	−	1.16306e8i	0.923025	−	0.335954i	0.163584	−	0.986529i	$-0.447695\pi$
$79$	3.19548e8	−	1.16306e8i	0.923025	−	0.335954i	0.759441	+	0.650576i	$0.225472\pi$
$80$	−8.01960e6			−0.0218901
$81$	1.86569e8	−	3.39539e8i	0.481568	−	0.876409i
$82$	−5.85430e7			−0.142992
$83$	−1.63239e8	+	5.94141e7i	−0.377548	+	0.137416i	−0.523822	−	0.851828i	$-0.675494\pi$
$83$	−1.63239e8	+	5.94141e7i	−0.377548	+	0.137416i	0.146274	+	0.989244i	$0.453272\pi$
$84$	−7.77637e7	−	2.84197e8i	−0.170420	−	0.622821i
$85$	3.67163e8	−	3.08086e8i	0.762910	−	0.640157i
$86$	−3.10697e7	−	1.76205e8i	−0.0612483	−	0.347357i
$87$	−1.96451e8	−	2.77426e8i	−0.367636	−	0.519172i
$88$	−2.22543e8	−	1.86736e8i	−0.395587	−	0.331937i
$89$	−2.35605e8	+	4.08079e8i	−0.398042	+	0.689429i	−0.993484	−	0.113969i	$-0.963643\pi$
$89$	−2.35605e8	+	4.08079e8i	−0.398042	+	0.689429i	0.595443	+	0.803398i	$0.296977\pi$
$90$	−3.02868e8	−	1.70615e8i	−0.486589	−	0.274111i
$91$	−5.05294e7	−	8.75195e7i	−0.0772428	−	0.133788i
$92$	1.32909e8	−	7.53763e8i	0.193423	−	1.09696i
$93$	−7.44074e8	−	5.15163e8i	−1.03144	−	0.714120i
$94$	3.23336e7	+	1.17685e7i	0.0427149	+	0.0155469i
$95$	7.98090e8	+	2.90481e8i	1.00530	+	0.365899i
$96$	7.57627e8	−	3.58178e8i	0.910405	−	0.430405i
$97$	1.26743e8	−	7.18794e8i	0.145362	−	0.824389i	−0.821714	−	0.569900i	$-0.806982\pi$
$97$	1.26743e8	−	7.18794e8i	0.145362	−	0.824389i	0.967076	−	0.254488i	$-0.0819070\pi$
$98$	−1.52957e7	−	2.64928e7i	−0.0167514	−	0.0290142i
$99$	1.75026e8	+	4.65499e8i	0.183123	+	0.487035i
$100$	−5.03068e7	+	8.71339e7i	−0.0503068	+	0.0871339i
$101$	−9.00064e7	−	7.55243e7i	−0.0860651	−	0.0722172i	0.598740	−	0.800943i	$-0.295668\pi$
$101$	−9.00064e7	−	7.55243e7i	−0.0860651	−	0.0722172i	−0.684805	+	0.728726i	$0.740113\pi$
$102$	−3.02456e8	+	6.57679e8i	−0.276670	+	0.601607i
$103$	2.01766e8	+	1.14427e9i	0.176637	+	1.00176i	0.936238	+	0.351367i	$0.114283\pi$
$103$	2.01766e8	+	1.14427e9i	0.176637	+	1.00176i	−0.759601	+	0.650389i	$0.774606\pi$
$104$	1.36422e8	−	1.14472e8i	0.114350	−	0.0959507i
$105$	1.13411e9	+	2.97464e8i	0.910549	+	0.238826i
$106$	1.17906e8	−	4.29141e7i	0.0907106	−	0.0330160i
$107$	−1.71487e8			−0.126475			−0.0632373	−	0.997999i	$-0.520142\pi$
$107$	−1.71487e8			−0.126475			−0.0632373	+	0.997999i	$0.520142\pi$
$108$	−8.86581e8	−	6.34095e7i	−0.627063	−	0.0448484i
$109$	−1.54312e8			−0.104708			−0.0523539	−	0.998629i	$-0.516672\pi$
$109$	−1.54312e8			−0.104708			−0.0523539	+	0.998629i	$0.516672\pi$
$110$	4.19313e8	−	1.52617e8i	0.273068	−	0.0993887i
$111$	−1.75492e9	+	1.77359e9i	−1.09725	+	1.10892i
$112$	−3.12951e7	+	2.62597e7i	−0.0187930	+	0.0157692i
$113$	1.57576e8	+	8.93656e8i	0.0909151	+	0.515605i	0.995923	+	0.0902099i	$0.0287538\pi$
$113$	1.57576e8	+	8.93656e8i	0.0909151	+	0.515605i	−0.905008	+	0.425395i	$0.860135\pi$
$114$	−1.27724e9	+	1.18554e8i	−0.708274	+	0.0657424i
$115$	2.33315e9	+	1.95774e9i	1.24395	+	1.04379i
$116$	−3.89955e8	+	6.75422e8i	−0.199965	+	0.346349i
$117$	−2.99653e8	+	5.61114e7i	−0.147837	+	0.0276831i
$118$	−9.97593e8	−	1.72788e9i	−0.473679	−	0.820436i
$119$	4.23979e8	−	2.40450e9i	0.193813	−	1.09917i
$120$	−1.69187e8	+	2.05920e9i	−0.0744821	+	0.906530i
$121$	1.61586e9	+	5.88126e8i	0.685283	+	0.249423i
$122$	2.98387e7	+	1.08604e7i	0.0121944	+	0.00443841i
$123$	4.87765e7	−	5.93665e8i	0.0192149	−	0.233867i
$124$	−3.60550e8	+	2.04478e9i	−0.136952	+	0.776693i
$125$	−1.45100e9	−	2.51321e9i	−0.531585	−	0.920732i
$126$	−1.74056e9	+	3.25927e8i	−0.615207	+	0.115200i
$127$	−2.53672e9	+	4.39373e9i	−0.865279	+	1.49871i	0.00148997	+	0.999999i	$0.499526\pi$
$127$	−2.53672e9	+	4.39373e9i	−0.865279	+	1.49871i	−0.866769	+	0.498709i	$0.833808\pi$
$128$	−1.50670e9	−	1.26427e9i	−0.496115	−	0.416290i
$129$	1.81273e9	−	1.68258e8i	0.576339	−	0.0534961i
$130$	4.74999e7	+	2.69385e8i	0.0145864	+	0.0827235i
$131$	−1.39004e9	+	1.16638e9i	−0.412388	+	0.346035i	−0.825259	−	0.564755i	$-0.808971\pi$
$131$	−1.39004e9	+	1.16638e9i	−0.412388	+	0.346035i	0.412870	+	0.910790i	$0.364526\pi$
$132$	8.02512e8	−	8.11046e8i	0.230075	−	0.232521i
$133$	4.06557e9	−	1.47975e9i	1.12665	−	0.410067i
$134$	4.03985e9			1.08242
$135$	1.98249e9	−	2.92913e9i	0.513700	−	0.758992i
$136$	4.30260e9			1.07846
$137$	5.71529e9	−	2.08019e9i	1.38610	−	0.504500i	0.462080	−	0.886838i	$-0.347103\pi$
$137$	5.71529e9	−	2.08019e9i	1.38610	−	0.504500i	0.924023	+	0.382338i	$0.124881\pi$
$138$	−4.44949e9	−	1.16705e9i	−1.04437	−	0.273926i
$139$	−6.07364e9	+	5.09639e9i	−1.38001	+	1.15797i	−0.410802	+	0.911724i	$0.634751\pi$
$139$	−6.07364e9	+	5.09639e9i	−1.38001	+	1.15797i	−0.969208	+	0.246242i	$0.920804\pi$
$140$	−4.67107e8	−	2.64909e9i	−0.102764	−	0.582802i
$141$	−1.46280e8	+	3.18080e8i	−0.0311673	+	0.0677719i
$142$	−7.50366e8	−	6.29632e8i	−0.154873	−	0.129954i
$143$	1.95669e8	−	3.38909e8i	0.0391300	−	0.0677751i
$144$	4.33731e7	+	1.15355e8i	0.00840599	+	0.0223566i
$145$	−1.55174e9	−	2.68769e9i	−0.291516	−	0.504921i
$146$	1.03315e9	−	5.85929e9i	0.188181	−	1.06723i
$147$	2.81399e8	−	1.33035e8i	0.0497044	−	0.0234984i
$148$	5.37913e9	+	1.95784e9i	0.921582	+	0.335429i
$149$	−9.88175e9	−	3.59666e9i	−1.64246	−	0.597808i	−0.654996	−	0.755632i	$-0.727330\pi$
$149$	−9.88175e9	−	3.59666e9i	−1.64246	−	0.597808i	−0.987467	+	0.157824i	$0.949552\pi$
$150$	4.97158e8	+	3.44210e8i	0.0801833	+	0.0555153i
$151$	6.60043e8	−	3.74329e9i	0.103318	−	0.585945i	−0.888561	−	0.458759i	$-0.848294\pi$
$151$	6.60043e8	−	3.74329e9i	0.103318	−	0.585945i	0.991879	−	0.127186i	$-0.0405947\pi$
$152$	3.81208e9	+	6.60272e9i	0.579250	+	1.00329i
$153$	−6.41731e9	−	3.61507e9i	−0.946763	−	0.533342i
$154$	1.13656e9	−	1.96858e9i	0.162835	−	0.282039i
$155$	−6.32927e9	−	5.31089e9i	−0.880767	−	0.739052i
$156$	4.04203e8	+	5.70812e8i	0.0546435	+	0.0771671i
$157$	8.69173e7	+	4.92933e8i	0.0114172	+	0.0647499i	0.989984	−	0.141179i	$-0.0450894\pi$
$157$	8.69173e7	+	4.92933e8i	0.0114172	+	0.0647499i	−0.978567	+	0.205929i	$0.933978\pi$
$158$	−3.59188e9	+	3.01394e9i	−0.458527	+	0.384750i
$159$	3.36942e8	+	1.23140e9i	0.0418089	+	0.152796i
$160$	7.18938e9	−	2.61672e9i	0.867265	−	0.315659i
$161$	1.55152e10			1.81987
$162$	−8.16127e8	+	5.27925e9i	−0.0930979	+	0.602219i
$163$	−1.47137e10			−1.63259			−0.816295	−	0.577635i	$-0.803976\pi$
$163$	−1.47137e10			−1.63259			−0.816295	+	0.577635i	$0.803976\pi$
$164$	−1.28420e9	+	4.67410e8i	−0.138623	+	0.0504545i
$165$	1.19828e9	+	4.37927e9i	0.125858	+	0.459964i
$166$	1.83489e9	−	1.53965e9i	0.187553	−	0.157375i
$167$	9.07130e7	+	5.14459e8i	0.00902496	+	0.0511831i	0.988988	−	0.147998i	$-0.0472829\pi$
$167$	9.07130e7	+	5.14459e8i	0.00902496	+	0.0511831i	−0.979963	+	0.199181i	$0.936172\pi$
$168$	6.08249e9	+	8.58965e9i	0.589101	+	0.831924i
$169$	−7.93975e9	−	6.66224e9i	−0.748715	−	0.628246i
$170$	−3.30440e9	+	5.72339e9i	−0.303440	+	0.525573i
$171$	−1.38054e8	−	1.30509e10i	−0.0123472	−	1.16723i
$172$	−2.08837e9	−	3.61717e9i	−0.181941	−	0.315131i
$173$	−2.60634e9	+	1.47813e10i	−0.221219	+	1.25460i	0.648563	+	0.761161i	$0.275370\pi$
$173$	−2.60634e9	+	1.47813e10i	−0.221219	+	1.25460i	−0.869782	+	0.493436i	$0.835741\pi$
$174$	3.85374e9	+	2.66816e9i	0.318721	+	0.220668i
$175$	−1.91653e9	−	6.97561e8i	−0.154470	−	0.0562226i
$176$	−1.48657e8	−	5.41068e7i	−0.0116783	−	0.00425055i
$177$	1.83531e10	−	8.67663e9i	1.40549	−	0.664464i
$178$	1.12824e9	−	6.39857e9i	0.0842387	−	0.477742i
$179$	7.83220e9	+	1.35658e10i	0.570224	+	0.987656i	0.996543	+	0.0830834i	$0.0264768\pi$
$179$	7.83220e9	+	1.35658e10i	0.570224	+	0.987656i	−0.426319	+	0.904573i	$0.640190\pi$
$180$	−8.00591e9	−	1.32450e9i	−0.568439	−	0.0940427i
$181$	7.25470e9	−	1.25655e10i	0.502419	−	0.870215i	−0.497577	−	0.867420i	$-0.665777\pi$
$181$	7.25470e9	−	1.25655e10i	0.502419	−	0.870215i	0.999996	−	0.00279503i	$-0.000889686\pi$
$182$	1.06745e9	+	8.95694e8i	0.0721149	+	0.0605116i
$183$	−1.34993e8	+	2.93536e8i	−0.00889776	+	0.0193478i
$184$	4.74771e9	+	2.69256e10i	0.305354	+	1.73175i
$185$	−1.74496e10	+	1.46419e10i	−1.09525	+	0.919020i
$186$	1.20704e10	+	3.16594e9i	0.739460	+	0.193952i
$187$	8.88460e9	−	3.23373e9i	0.531313	−	0.193382i
$188$	8.03230e8			0.0468953
$189$	−1.85493e9	−	1.79220e10i	−0.105743	−	1.02166i
$190$	−1.17107e10			−0.651918
$191$	5.33447e9	−	1.94159e9i	0.290029	−	0.105562i	−0.192909	−	0.981217i	$-0.561792\pi$
$191$	5.33447e9	−	1.94159e9i	0.290029	−	0.105562i	0.482937	+	0.875655i	$0.339570\pi$
$192$	−7.81107e9	+	7.89413e9i	−0.414815	+	0.419226i
$193$	−6.22322e9	+	5.22191e9i	−0.322855	+	0.270908i	−0.789781	−	0.613389i	$-0.789806\pi$
$193$	−6.22322e9	+	5.22191e9i	−0.322855	+	0.270908i	0.466926	+	0.884296i	$0.345361\pi$
$194$	1.74760e9	+	9.91112e9i	0.0885796	+	0.502360i
$195$	−2.77132e9	+	2.57236e8i	−0.137256	+	0.0127402i
$196$	−5.47045e8	−	4.59026e8i	−0.0264771	−	0.0222170i
$197$	−9.16280e9	+	1.58704e10i	−0.433441	+	0.750743i	−0.997167	−	0.0752196i	$-0.976034\pi$
$197$	−9.16280e9	+	1.58704e10i	−0.433441	+	0.750743i	0.563726	+	0.825962i	$0.309368\pi$
$198$	−4.46307e9	−	5.20604e9i	−0.206367	−	0.240721i
$199$	−1.25288e10	−	2.17006e10i	−0.566333	−	0.980918i	−0.996924	−	0.0783710i	$-0.975028\pi$
$199$	−1.25288e10	−	2.17006e10i	−0.566333	−	0.980918i	0.430591	−	0.902547i	$-0.358305\pi$
$200$	6.24105e8	−	3.53947e9i	0.0275818	−	0.156424i
$201$	−3.36590e9	+	4.09668e10i	−0.145452	+	1.77031i
$202$	1.52238e9	+	5.54101e8i	0.0643342	+	0.0234157i
$203$	−1.48561e10	−	5.40717e9i	−0.614005	−	0.223480i
$204$	−1.38374e9	+	1.68417e10i	−0.0559395	+	0.680846i
$205$	9.44323e8	−	5.35552e9i	0.0373446	−	0.211792i
$206$	−8.01061e9	−	1.38748e10i	−0.309930	−	0.536814i
$207$	1.55419e10	−	4.41485e10i	0.588352	−	1.67128i
$208$	4.84887e7	−	8.39849e7i	0.00179620	−	0.00311111i
$209$	1.28342e10	+	1.07691e10i	0.465274	+	0.390412i
$210$	−1.60975e10	+	1.49417e9i	−0.571177	+	0.0530169i
$211$	2.99464e9	+	1.69835e10i	0.104010	+	0.589868i	0.991611	+	0.129256i	$0.0412589\pi$
$211$	2.99464e9	+	1.69835e10i	0.104010	+	0.589868i	−0.887602	+	0.460612i	$0.847630\pi$
$212$	2.24375e9	−	1.88273e9i	0.0762891	−	0.0640142i
$213$	7.01008e9	−	7.08462e9i	0.233354	−	0.235835i
$214$	2.22195e9	−	8.08723e8i	0.0724222	−	0.0263595i
$215$	1.66204e10			0.530481
$216$	3.05348e10	−	8.70331e9i	0.954450	−	0.272046i
$217$	−4.20891e10			−1.28855
$218$	1.99941e9	−	7.27727e8i	0.0599581	−	0.0218230i
$219$	5.85563e10	+	1.53586e10i	1.72018	+	0.451185i
$220$	7.97954e9	−	6.69562e9i	0.229655	−	0.192703i
$221$	1.00645e9	+	5.70786e9i	0.0283810	+	0.160956i
$222$	1.43744e10	−	3.12565e10i	0.397192	−	0.863677i
$223$	−3.04226e10	−	2.55276e10i	−0.823804	−	0.691254i	0.130056	−	0.991507i	$-0.458484\pi$
$223$	−3.04226e10	−	2.55276e10i	−0.823804	−	0.691254i	−0.953860	+	0.300253i	$0.902929\pi$
$224$	1.94870e10	−	3.37525e10i	0.517165	−	0.895757i
$225$	−3.90474e9	+	4.75473e9i	−0.101571	+	0.123682i
$226$	−6.25614e9	−	1.08360e10i	−0.159521	−	0.276299i
$227$	1.16503e10	−	6.60722e10i	0.291220	−	1.65159i	−0.390961	−	0.920407i	$-0.627857\pi$
$227$	1.16503e10	−	6.60722e10i	0.291220	−	1.65159i	0.682181	−	0.731183i	$-0.261032\pi$
$228$	−2.70710e10	+	1.27982e10i	−0.663434	+	0.313647i
$229$	8.92141e9	+	3.24713e9i	0.214375	+	0.0780261i	0.446975	−	0.894546i	$-0.352501\pi$
$229$	8.92141e9	+	3.24713e9i	0.214375	+	0.0780261i	−0.232600	+	0.972572i	$0.574723\pi$
$230$	−3.94631e10	−	1.43634e10i	−0.929857	−	0.338440i
$231$	1.90158e10	+	1.31656e10i	0.439400	+	0.304220i
$232$	4.83777e9	−	2.74363e10i	0.109635	−	0.621771i
$233$	3.72517e10	+	6.45218e10i	0.828027	+	1.43418i	0.899584	+	0.436748i	$0.143870\pi$
$233$	3.72517e10	+	6.45218e10i	0.828027	+	1.43418i	−0.0715572	+	0.997437i	$0.522797\pi$
$234$	3.61798e9	−	2.14018e9i	0.0788851	−	0.0466638i
$235$	−1.59814e9	+	2.76806e9i	−0.0341829	+	0.0592065i
$236$	−3.56787e10	−	2.99380e10i	−0.748694	−	0.628229i
$237$	−2.75708e10	−	3.89352e10i	−0.567651	−	0.801632i
$238$	5.84605e9	+	3.31546e10i	0.118104	+	0.669803i
$239$	−4.24492e10	+	3.56191e10i	−0.841548	+	0.706142i	−0.957911	−	0.287064i	$-0.907321\pi$
$239$	−4.24492e10	+	3.56191e10i	−0.841548	+	0.706142i	0.116364	+	0.993207i	$0.462876\pi$
$240$	2.96946e8	+	1.08523e9i	0.00577733	+	0.0211140i
$241$	4.96719e10	−	1.80791e10i	0.948493	−	0.345223i	0.178979	−	0.983853i	$-0.442721\pi$
$241$	4.96719e10	−	1.80791e10i	0.948493	−	0.345223i	0.769514	+	0.638630i	$0.220498\pi$
$242$	−2.37103e10			−0.444393
$243$	−5.28552e10	−	1.26746e10i	−0.972432	−	0.233188i
$244$	7.41252e8			0.0133879
$245$	2.67030e9	−	9.71908e8i	0.0473491	−	0.0172337i
$246$	2.16770e9	+	7.92213e9i	0.0377391	+	0.137922i
$247$	−7.86752e9	+	6.60163e9i	−0.134494	+	0.112853i
$248$	−1.28794e10	−	7.30428e10i	−0.216204	−	1.22615i
$249$	1.40843e10	+	1.98898e10i	0.232188	+	0.327894i
$250$	3.06528e10	+	2.57207e10i	0.496295	+	0.416441i
$251$	−2.08476e10	+	3.61091e10i	−0.331531	+	0.574229i	−0.982812	−	0.184607i	$-0.940899\pi$
$251$	−2.08476e10	+	3.61091e10i	−0.331531	+	0.574229i	0.651281	+	0.758837i	$0.274232\pi$
$252$	−3.55787e10	+	2.10462e10i	−0.555760	+	0.328755i
$253$	3.00404e10	+	5.20314e10i	0.460960	+	0.798405i
$254$	1.21476e10	−	6.88926e10i	0.183122	−	1.03853i
$255$	−5.52858e10	−	3.82774e10i	−0.818810	−	0.566907i
$256$	6.35687e10	+	2.31371e10i	0.925047	+	0.336689i
$257$	9.68995e10	+	3.52685e10i	1.38555	+	0.504299i	0.923856	−	0.382740i	$-0.125019\pi$
$257$	9.68995e10	+	3.52685e10i	1.38555	+	0.504299i	0.461694	+	0.887039i	$0.347242\pi$
$258$	−2.26939e10	+	1.07288e10i	−0.318876	+	0.150752i
$259$	−2.01498e10	+	1.14275e11i	−0.278241	+	1.57798i
$260$	3.19274e9	+	5.52999e9i	0.0433295	+	0.0750489i
$261$	−3.02677e10	+	3.68565e10i	−0.403736	+	0.491622i
$262$	1.25101e10	−	2.16681e10i	0.164023	−	0.284097i
$263$	2.32813e10	+	1.95354e10i	0.300059	+	0.251780i	0.780369	−	0.625319i	$-0.215031\pi$
$263$	2.32813e10	+	1.95354e10i	0.300059	+	0.251780i	−0.480310	+	0.877099i	$0.659476\pi$
$264$	−1.70292e10	+	3.70293e10i	−0.215763	+	0.469168i
$265$	2.02393e9	+	1.14783e10i	0.0252109	+	0.142978i
$266$	−4.56991e10	+	3.83461e10i	−0.559681	+	0.469628i
$267$	6.39458e10	+	1.67723e10i	0.770037	+	0.201972i
$268$	8.86182e10	−	3.22544e10i	1.04934	−	0.381928i
$269$	1.06100e11			1.23546			0.617732	−	0.786388i	$-0.288052\pi$
$269$	1.06100e11			1.23546			0.617732	+	0.786388i	$0.288052\pi$
$270$	−1.18735e10	+	4.73021e10i	−0.135969	+	0.541680i
$271$	−5.16724e10			−0.581965			−0.290982	−	0.956728i	$-0.593982\pi$
$271$	−5.16724e10			−0.581965			−0.290982	+	0.956728i	$0.593982\pi$
$272$	2.20169e9	−	8.01349e8i	0.0243891	−	0.00887691i
$273$	−9.97231e9	+	1.00784e10i	−0.108659	+	0.109814i
$274$	−6.42427e10	+	5.39061e10i	−0.688568	+	0.577777i
$275$	−1.37145e9	−	7.77785e9i	−0.0144604	−	0.0820092i
$276$	−1.06922e11	+	9.92454e9i	−1.10911	+	0.102948i
$277$	1.47446e10	+	1.23722e10i	0.150478	+	0.126266i	0.714919	−	0.699207i	$-0.246464\pi$
$277$	1.47446e10	+	1.23722e10i	0.150478	+	0.126266i	−0.564441	+	0.825474i	$0.690908\pi$
$278$	5.46617e10	−	9.46768e10i	0.548885	−	0.950697i
$279$	−4.21615e10	+	1.19765e11i	−0.416579	+	1.18334i
$280$	4.80448e10	+	8.32160e10i	0.467127	+	0.809088i
$281$	−4.53849e9	+	2.57391e10i	−0.0434243	+	0.246271i	−0.998791	−	0.0491497i	$-0.984349\pi$
$281$	−4.53849e9	+	2.57391e10i	−0.0434243	+	0.246271i	0.955367	+	0.295421i	$0.0954600\pi$
$282$	3.95296e8	−	4.81120e9i	0.00372222	−	0.0453036i
$283$	−1.56995e11	−	5.71417e10i	−1.45495	−	0.529559i	−0.510981	−	0.859592i	$-0.670718\pi$
$283$	−1.56995e11	−	5.71417e10i	−1.45495	−	0.529559i	−0.943969	+	0.330033i	$0.892940\pi$
$284$	−2.14870e10	−	7.82064e9i	−0.195994	−	0.0713362i
$285$	9.75709e9	−	1.18755e11i	0.0876029	−	1.06623i
$286$	−9.37001e8	+	5.31400e9i	−0.00828119	+	0.0469650i
$287$	−1.38513e10	−	2.39911e10i	−0.120510	−	0.208729i
$288$	−7.65222e10	−	8.92609e10i	−0.655423	−	0.764531i
$289$	−1.07212e10	+	1.85697e10i	−0.0904072	+	0.156590i
$290$	3.27809e10	+	2.75064e10i	0.272163	+	0.228372i
$291$	−1.01961e11	+	9.46412e9i	−0.833523	+	0.0773681i
$292$	−2.41176e10	−	1.36778e11i	−0.194139	−	1.10101i
$293$	1.34724e11	−	1.13047e11i	1.06792	−	0.896094i	0.0730601	−	0.997328i	$-0.476724\pi$
$293$	1.34724e11	−	1.13047e11i	1.06792	−	0.896094i	0.994863	+	0.101234i	$0.0322791\pi$
$294$	−3.01870e9	+	3.05080e9i	−0.0235644	+	0.0238150i
$295$	1.74158e11	−	6.33885e10i	1.33889	−	0.487317i
$296$	−2.04483e11			−1.54826
$297$	5.65113e10	−	4.09210e10i	0.421436	−	0.305170i
$298$	1.44999e11			1.06511
$299$	−3.46092e10	+	1.25967e10i	−0.250421	+	0.0911458i
$300$	1.36538e10	+	3.58125e9i	0.0973216	+	0.0255264i
$301$	6.48584e10	−	5.44227e10i	0.455425	−	0.382147i
$302$	9.10102e9	+	5.16144e10i	0.0629591	+	0.357059i
$303$	−6.88737e9	+	1.49763e10i	−0.0469420	+	0.102073i
$304$	3.18043e9	+	2.66870e9i	0.0213577	+	0.0179212i
$305$	−1.47482e9	+	2.55447e9i	−0.00975868	+	0.0169025i
$306$	1.00197e11	+	1.65767e10i	0.653296	+	0.108081i
$307$	−6.84591e10	−	1.18575e11i	−0.439854	−	0.761850i	0.557824	−	0.829959i	$-0.311637\pi$
$307$	−6.84591e10	−	1.18575e11i	−0.439854	−	0.761850i	−0.997678	+	0.0681098i	$0.978303\pi$
$308$	9.21432e9	−	5.22570e10i	0.0583425	−	0.330877i
$309$	1.47374e11	−	6.96729e10i	0.919618	−	0.434761i
$310$	1.07054e11	+	3.89645e10i	0.658379	+	0.239630i
$311$	8.66299e10	+	3.15307e10i	0.525105	+	0.191123i	0.590951	−	0.806707i	$-0.298753\pi$
$311$	8.66299e10	+	3.15307e10i	0.525105	+	0.191123i	−0.0658464	+	0.997830i	$0.520975\pi$
$312$	−2.05419e10	−	1.42223e10i	−0.122728	−	0.0849715i
$313$	−1.13520e10	+	6.43802e10i	−0.0668531	+	0.379143i	0.932963	+	0.359972i	$0.117214\pi$
$313$	−1.13520e10	+	6.43802e10i	−0.0668531	+	0.379143i	−0.999816	+	0.0191709i	$0.993897\pi$
$314$	−3.45083e9	−	5.97702e9i	−0.0200328	−	0.0346978i
$315$	−1.73994e9	−	1.64484e11i	−0.00995719	−	0.941296i
$316$	−5.47279e10	+	9.47916e10i	−0.308757	+	0.534783i
$317$	−1.34809e11	−	1.13118e11i	−0.749810	−	0.629166i	0.185642	−	0.982617i	$-0.440563\pi$
$317$	−1.34809e11	−	1.13118e11i	−0.749810	−	0.629166i	−0.935453	+	0.353452i	$0.885008\pi$
$318$	−1.01730e10	−	1.43662e10i	−0.0557861	−	0.0787806i
$319$	−1.06308e10	−	6.02903e10i	−0.0574789	−	0.325979i
$320$	−7.76669e10	+	6.51703e10i	−0.414058	+	0.347436i
$321$	6.34972e9	+	2.32058e10i	0.0333797	+	0.121990i
$322$	−2.01030e11	+	7.31690e10i	−1.04210	+	0.379294i
$323$	−2.48132e11			−1.26845
$324$	2.42472e10	+	1.22321e11i	0.122239	+	0.616666i
$325$	4.84148e9			0.0240715
$326$	1.90645e11	−	6.93891e10i	0.934859	−	0.340261i
$327$	5.71378e9	+	2.08817e10i	0.0276349	+	0.100995i
$328$	3.73964e10	−	3.13793e10i	0.178401	−	0.149696i
$329$	2.82738e9	+	1.60349e10i	0.0133046	+	0.0754542i
$330$	−3.61786e10	−	5.10911e10i	−0.167934	−	0.237155i
$331$	−2.89334e11	−	2.42780e11i	−1.32487	−	1.11170i	−0.985247	−	0.171138i	$-0.945256\pi$
$331$	−2.89334e11	−	2.42780e11i	−1.32487	−	1.11170i	−0.339624	−	0.940561i	$-0.610300\pi$
$332$	2.79574e10	−	4.84236e10i	0.126292	−	0.218744i
$333$	3.04985e11	+	1.71808e11i	1.35919	+	0.765674i
$334$	−3.60153e9	−	6.23803e9i	−0.0158354	−	0.0274276i
$335$	−6.51645e10	+	3.69567e11i	−0.282690	+	1.60321i
$336$	4.71229e9	+	3.26257e9i	0.0201700	+	0.0139648i
$337$	4.53479e10	+	1.65053e10i	0.191524	+	0.0697090i	0.436002	−	0.899946i	$-0.356394\pi$
$337$	4.53479e10	+	1.65053e10i	0.191524	+	0.0697090i	−0.244478	+	0.969655i	$0.578616\pi$
$338$	1.34294e11	+	4.88790e10i	0.559669	+	0.203703i
$339$	1.15096e11	−	5.44133e10i	0.473329	−	0.223772i
$340$	−2.67895e10	+	1.51931e11i	−0.108720	+	0.616581i
$341$	−8.14924e10	−	1.41149e11i	−0.326379	−	0.565306i
$342$	6.33361e10	+	1.68449e11i	0.250342	+	0.665810i
$343$	−1.24410e11	+	2.15485e11i	−0.485326	+	0.840609i
$344$	1.14294e11	+	9.59039e10i	0.440058	+	0.369252i
$345$	1.78534e11	−	3.88215e11i	0.678478	−	1.47532i
$346$	−3.59375e10	−	2.03812e11i	−0.134805	−	0.764517i
$347$	3.16547e10	−	2.65615e10i	0.117208	−	0.0983489i	−0.582300	−	0.812974i	$-0.697847\pi$
$347$	3.16547e10	−	2.65615e10i	0.117208	−	0.0983489i	0.699508	+	0.714625i	$0.253403\pi$
$348$	1.05838e11	+	2.77602e10i	0.386844	+	0.101465i
$349$	−3.17062e11	+	1.15401e11i	−1.14401	+	0.416386i	−0.843360	−	0.537349i	$-0.819426\pi$
$349$	−3.17062e11	+	1.15401e11i	−1.14401	+	0.416386i	−0.300650	+	0.953735i	$0.597204\pi$
$350$	2.81221e10			0.100171
$351$	1.86885e10	+	3.84719e10i	0.0657192	+	0.135289i
$352$	1.50922e11			0.523976
$353$	−1.78882e11	+	6.51076e10i	−0.613168	+	0.223175i	−0.629889	−	0.776685i	$-0.716900\pi$
$353$	−1.78882e11	+	6.51076e10i	−0.613168	+	0.223175i	0.0167207	+	0.999860i	$0.494677\pi$
$354$	−1.96881e11	+	1.98975e11i	−0.666331	+	0.673417i
$355$	6.97026e10	−	5.84874e10i	0.232928	−	0.195450i
$356$	−2.63374e10	−	1.49367e11i	−0.0869057	−	0.492867i
$357$	−3.41080e11	+	3.16593e10i	−1.11135	+	0.103156i
$358$	−1.65457e11	−	1.38835e11i	−0.532368	−	0.446710i
$359$	−2.11214e11	+	3.65833e11i	−0.671116	+	1.16241i	0.306473	+	0.951880i	$0.400851\pi$
$359$	−2.11214e11	+	3.65833e11i	−0.671116	+	1.16241i	−0.977588	+	0.210527i	$0.932482\pi$
$360$	2.84919e11	−	5.33523e10i	0.894045	−	0.167414i
$361$	−5.85005e10	−	1.01326e11i	−0.181291	−	0.314006i
$362$	−3.47406e10	+	1.97024e11i	−0.106328	+	0.603018i
$363$	1.97548e10	−	2.40438e11i	0.0597163	−	0.726814i
$364$	3.05667e10	+	1.11254e10i	0.0912626	+	0.0332169i
$365$	5.19343e11	+	1.89026e11i	1.53157	+	0.557446i
$366$	3.64795e8	−	4.43996e9i	0.00106263	−	0.0129335i
$367$	−4.99129e10	+	2.83070e11i	−0.143620	+	0.814511i	0.824844	+	0.565360i	$0.191263\pi$
$367$	−4.99129e10	+	2.83070e11i	−0.143620	+	0.814511i	−0.968465	+	0.249151i	$0.919848\pi$
$368$	7.44430e9	+	1.28939e10i	0.0211596	+	0.0366496i
$369$	−8.21418e10	+	1.53814e10i	−0.230646	+	0.0431895i
$370$	1.57043e11	−	2.72006e11i	0.435623	−	0.754521i
$371$	4.54829e10	+	3.81647e10i	0.124642	+	0.104587i
$372$	2.90054e11	−	2.69229e10i	0.785299	−	0.0728919i
$373$	−2.05333e10	−	1.16450e11i	−0.0549247	−	0.311494i	0.944952	−	0.327210i	$-0.106108\pi$
$373$	−2.05333e10	−	1.16450e11i	−0.0549247	−	0.311494i	−0.999876	+	0.0157160i	$0.994997\pi$
$374$	−9.98674e10	+	8.37987e10i	−0.263938	+	0.221470i
$375$	−2.86365e11	+	2.89410e11i	−0.747788	+	0.755740i
$376$	−2.69623e10	+	9.81346e9i	−0.0695682	+	0.0253208i
$377$	3.75289e10			0.0956820
$378$	1.08554e11	+	2.23467e11i	0.273484	+	0.562990i
$379$	4.22411e11			1.05162			0.525809	−	0.850602i	$-0.323763\pi$
$379$	4.22411e11			1.05162			0.525809	+	0.850602i	$0.323763\pi$
$380$	−2.56886e11	+	9.34990e10i	−0.631997	+	0.230028i
$381$	6.88496e11	+	1.80585e11i	1.67394	+	0.439055i
$382$	−5.99622e10	+	5.03142e10i	−0.144076	+	0.120894i
$383$	−1.06688e11	−	6.05059e11i	−0.253351	−	1.43682i	−0.800271	−	0.599639i	$-0.795311\pi$
$383$	−1.06688e11	−	6.05059e11i	−0.253351	−	1.43682i	0.546920	−	0.837185i	$-0.315800\pi$
$384$	−1.15294e11	+	2.50702e11i	−0.270593	+	0.588393i
$385$	1.61753e11	+	1.35727e11i	0.375213	+	0.314841i
$386$	5.60079e10	−	9.70086e10i	0.128412	−	0.222417i
$387$	−8.98897e10	−	2.39071e11i	−0.203709	−	0.541786i
$388$	1.17466e11	+	2.03457e11i	0.263130	+	0.455754i
$389$	−1.41597e11	+	8.03037e11i	−0.313532	+	1.77813i	0.266806	+	0.963750i	$0.414032\pi$
$389$	−1.41597e11	+	8.03037e11i	−0.313532	+	1.77813i	−0.580338	+	0.814376i	$0.697079\pi$
$390$	3.46949e10	−	1.64024e10i	0.0759407	−	0.0359019i
$391$	−8.36163e11	−	3.04339e11i	−1.80924	−	0.658509i
$392$	2.39710e10	+	8.72472e9i	0.0512741	+	0.0186623i
$393$	2.09306e11	+	1.44914e11i	0.442605	+	0.306440i
$394$	4.38780e10	−	2.48844e11i	0.0917305	−	0.520229i
$395$	−2.17778e11	−	3.77202e11i	−0.450118	−	0.779627i
$396$	−1.39467e11	−	7.85663e10i	−0.284999	−	0.160549i
$397$	1.49240e11	−	2.58492e11i	0.301529	−	0.522264i	−0.674953	−	0.737860i	$-0.735836\pi$
$397$	1.49240e11	−	2.58492e11i	0.301529	−	0.522264i	0.976482	+	0.215597i	$0.0691697\pi$
$398$	2.64675e11	+	2.22089e11i	0.528736	+	0.443662i
$399$	−3.50780e11	−	4.95369e11i	−0.692878	−	0.978477i
$400$	−3.39858e8	−	1.92743e9i	−0.000663784	−	0.00376451i
$401$	−2.63089e11	+	2.20758e11i	−0.508104	+	0.426350i	−0.860462	−	0.509515i	$-0.829825\pi$
$401$	−2.63089e11	+	2.20758e11i	−0.508104	+	0.426350i	0.352357	+	0.935866i	$0.385380\pi$
$402$	−1.49586e11	−	5.46680e11i	−0.285676	−	1.04404i
$403$	9.38865e10	−	3.41719e10i	0.177309	−	0.0645352i
$404$	3.78189e10			0.0706305
$405$	−4.69782e11	−	1.59816e11i	−0.867659	−	0.295170i
$406$	2.17990e11			0.398170
$407$	−4.22244e11	+	1.53684e11i	−0.762761	+	0.277622i
$408$	−1.59314e11	−	5.82235e11i	−0.284633	−	1.04023i
$409$	5.18351e11	−	4.34948e11i	0.915945	−	0.768569i	−0.0572959	−	0.998357i	$-0.518248\pi$
$409$	5.18351e11	−	4.34948e11i	0.915945	−	0.768569i	0.973241	+	0.229788i	$0.0738034\pi$
$410$	1.30208e10	+	7.38447e10i	0.0227568	+	0.129060i
$411$	−4.93118e11	−	6.96378e11i	−0.852438	−	1.20381i
$412$	−2.86498e11	−	2.40400e11i	−0.489873	−	0.411052i
$413$	4.72061e11	−	8.17634e11i	0.798405	−	1.38288i
$414$	6.82637e9	+	6.45326e11i	0.0114206	+	1.07964i
$415$	1.11250e11	+	1.92691e11i	0.184113	+	0.318893i
$416$	−1.60655e10	+	9.11119e10i	−0.0263011	+	0.149161i
$417$	9.14544e11	+	6.33189e11i	1.48113	+	1.02546i
$418$	−2.17079e11	−	7.90102e10i	−0.347796	−	0.126587i
$419$	3.78288e11	+	1.37685e11i	0.599597	+	0.218235i	0.623945	−	0.781468i	$-0.285529\pi$
$419$	3.78288e11	+	1.37685e11i	0.599597	+	0.218235i	−0.0243484	+	0.999704i	$0.507751\pi$
$420$	−3.41184e11	+	1.61299e11i	−0.535016	+	0.252936i
$421$	−6.68416e10	+	3.79078e11i	−0.103700	+	0.588110i	0.888032	+	0.459782i	$0.152072\pi$
$421$	−6.68416e10	+	3.79078e11i	−0.103700	+	0.588110i	−0.991732	+	0.128328i	$0.959039\pi$
$422$	−1.18895e11	−	2.05932e11i	−0.182497	−	0.316095i
$423$	4.84594e10	+	8.01714e9i	0.0735947	+	0.0121755i
$424$	−5.23143e10	+	9.06110e10i	−0.0786093	+	0.136155i
$425$	8.96050e10	+	7.51876e10i	0.133224	+	0.111788i
$426$	−5.74187e10	+	1.24855e11i	−0.0844714	+	0.183680i
$427$	2.60922e9	+	1.47976e10i	0.00379826	+	0.0215410i
$428$	4.22837e10	−	3.54803e10i	0.0609083	−	0.0511081i
$429$	−5.31068e10	−	1.39293e10i	−0.0756994	−	0.0198551i
$430$	−2.15351e11	+	7.83813e10i	−0.303765	+	0.110562i
$431$	7.95097e11			1.10987			0.554935	−	0.831894i	$-0.312743\pi$
$431$	7.95097e11			1.10987			0.554935	+	0.831894i	$0.312743\pi$
$432$	1.40041e10	−	1.01406e10i	0.0193454	−	0.0140084i
$433$	6.46577e11			0.883945			0.441972	−	0.897029i	$-0.354279\pi$
$433$	6.46577e11			0.883945			0.441972	+	0.897029i	$0.354279\pi$
$434$	5.45347e11	−	1.98490e11i	0.737852	−	0.268556i
$435$	−3.06246e11	+	3.09502e11i	−0.410080	+	0.414441i
$436$	3.80489e10	−	3.19268e10i	0.0504258	−	0.0423123i
$437$	−2.73802e11	−	1.55281e12i	−0.359146	−	2.03682i
$438$	−8.31143e11	+	7.71472e10i	−1.07905	+	0.100158i
$439$	8.41026e11	+	7.05704e11i	1.08073	+	0.906844i	0.995982	−	0.0895585i	$-0.0285456\pi$
$439$	8.41026e11	+	7.05704e11i	1.08073	+	0.906844i	0.0847525	+	0.996402i	$0.472990\pi$
$440$	−1.86048e11	+	3.22244e11i	−0.236639	+	0.409871i
$441$	−2.84220e10	−	3.31535e10i	−0.0357834	−	0.0417403i
$442$	−3.99586e10	−	6.92103e10i	−0.0497978	−	0.0862522i
$443$	2.71358e11	−	1.53895e12i	0.334754	−	1.89849i	−0.0948913	−	0.995488i	$-0.530250\pi$
$443$	2.71358e11	−	1.53895e12i	0.334754	−	1.89849i	0.429645	−	0.902998i	$-0.358639\pi$
$444$	6.57628e10	−	8.00407e11i	0.0803076	−	0.977434i
$445$	5.67143e11	+	2.06423e11i	0.685603	+	0.249539i
$446$	5.14571e11	+	1.87289e11i	0.615799	+	0.224132i
$447$	−1.20810e11	+	1.47039e12i	−0.143126	+	1.74200i
$448$	−8.96855e10	+	5.08632e11i	−0.105189	+	0.596557i
$449$	−3.60741e11	−	6.24821e11i	−0.418877	−	0.725517i	0.576950	−	0.816780i	$-0.304243\pi$
$449$	−3.60741e11	−	6.24821e11i	−0.418877	−	0.725517i	−0.995827	+	0.0912631i	$0.970910\pi$
$450$	2.81705e10	−	8.00216e10i	0.0323846	−	0.0919922i
$451$	5.36374e10	−	9.29027e10i	0.0610482	−	0.105739i
$452$	−2.23749e11	−	1.87748e11i	−0.252138	−	0.211569i
$453$	−5.30988e11	+	4.92866e10i	−0.592438	+	0.0549904i
$454$	1.60641e11	+	9.11038e11i	0.177461	+	1.00643i
$455$	−9.91566e10	+	8.32023e10i	−0.108460	+	0.0910089i
$456$	7.52339e11	−	7.60340e11i	0.814839	−	0.823504i
$457$	−6.15961e11	+	2.24192e11i	−0.660588	+	0.240434i	−0.650490	−	0.759515i	$-0.725436\pi$
$457$	−6.15961e11	+	2.24192e11i	−0.660588	+	0.240434i	−0.0100976	+	0.999949i	$0.503214\pi$
$458$	−1.30908e11			−0.139018
$459$	−2.51581e11	+	1.00226e12i	−0.264558	+	1.05396i
$460$	−9.80341e11			−1.02086
$461$	−6.52984e11	+	2.37667e11i	−0.673361	+	0.245083i	−0.655994	−	0.754766i	$-0.727751\pi$
$461$	−6.52984e11	+	2.37667e11i	−0.673361	+	0.245083i	−0.0173669	+	0.999849i	$0.505528\pi$
$462$	−3.08475e11	−	8.09095e10i	−0.315015	−	0.0826249i
$463$	−5.45783e11	+	4.57966e11i	−0.551957	+	0.463147i	−0.875603	−	0.483031i	$-0.839536\pi$
$463$	−5.45783e11	+	4.57966e11i	−0.551957	+	0.463147i	0.323646	+	0.946178i	$0.395091\pi$
$464$	−2.63442e9	−	1.49405e10i	−0.00263848	−	0.0149636i
$465$	−4.84321e11	+	1.05314e12i	−0.480392	+	1.04459i
$466$	−7.86951e11	−	6.60331e11i	−0.773057	−	0.648671i
$467$	−5.02439e11	+	8.70251e11i	−0.488830	+	0.846678i	−0.999917	−	0.0128505i	$-0.995909\pi$
$467$	−5.02439e11	+	8.70251e11i	−0.488830	+	0.846678i	0.511088	+	0.859529i	$0.329243\pi$
$468$	6.22766e10	−	7.58332e10i	0.0600093	−	0.0730723i
$469$	9.55830e11	+	1.65555e12i	0.912227	+	1.58002i
$470$	7.65301e9	−	4.34024e10i	0.00723422	−	0.0410273i
$471$	6.34862e10	−	3.00139e10i	0.0594408	−	0.0281014i
$472$	1.56340e12	+	5.69032e11i	1.44988	+	0.527713i
$473$	3.08089e11	+	1.12135e11i	0.283009	+	0.103007i
$474$	5.40850e11	+	3.74460e11i	0.492124	+	0.340724i
$475$	−3.59924e10	+	2.04123e11i	−0.0324406	+	0.183980i
$476$	3.92946e11	+	6.80603e11i	0.350834	+	0.607663i
$477$	1.54159e11	−	9.11912e10i	0.136344	−	0.0806529i
$478$	3.82035e11	−	6.61704e11i	0.334717	−	0.579747i
$479$	5.42349e11	+	4.55085e11i	0.470727	+	0.394987i	0.847060	−	0.531498i	$-0.178371\pi$
$479$	5.42349e11	+	4.55085e11i	0.470727	+	0.394987i	−0.376333	+	0.926485i	$0.622815\pi$
$480$	−6.20304e11	−	8.75989e11i	−0.533358	−	0.753205i
$481$	−4.78320e10	−	2.71268e11i	−0.0407442	−	0.231072i
$482$	−5.58338e11	+	4.68501e11i	−0.471178	+	0.395366i
$483$	−5.74489e11	−	2.09954e12i	−0.480308	−	1.75535i
$484$	−5.20108e11	+	1.89304e11i	−0.430813	+	0.156803i
$485$	−9.34860e11			−0.767201
$486$	7.44616e11	−	8.50378e10i	0.605437	−	0.0691431i
$487$	−7.20835e11			−0.580705			−0.290352	−	0.956920i	$-0.593772\pi$
$487$	−7.20835e11			−0.580705			−0.290352	+	0.956920i	$0.593772\pi$
$488$	−2.48818e10	+	9.05625e9i	−0.0198606	+	0.00722868i
$489$	5.44812e11	+	1.99108e12i	0.430880	+	1.57470i
$490$	−3.00155e10	+	2.51860e10i	−0.0235214	+	0.0197368i
$491$	−8.41069e9	−	4.76994e10i	−0.00653078	−	0.0370379i	0.981368	−	0.192136i	$-0.0615416\pi$
$491$	−8.41069e9	−	4.76994e10i	−0.00653078	−	0.0370379i	−0.987899	+	0.155099i	$0.950430\pi$
$492$	1.10801e11	+	1.56473e11i	0.0852515	+	0.120391i
$493$	6.94577e11	+	5.82819e11i	0.529552	+	0.444347i
$494$	7.08063e10	−	1.22640e11i	0.0534934	−	0.0926533i
$495$	5.48241e11	−	3.24307e11i	0.410439	−	0.242791i
$496$	−2.01946e10	−	3.49781e10i	−0.0149819	−	0.0259495i
$497$	8.04887e10	−	4.56474e11i	0.0591740	−	0.335592i
$498$	−2.76290e11	−	1.91291e11i	−0.201295	−	0.139367i
$499$	−1.77993e9	−	6.47841e8i	−0.00128514	−	0.000467752i	0.341377	−	0.939926i	$-0.389107\pi$
$499$	−1.77993e9	−	6.47841e8i	−0.00128514	−	0.000467752i	−0.342663	+	0.939459i	$0.611329\pi$
$500$	8.77754e11	+	3.19476e11i	0.628070	+	0.228599i
$501$	6.62586e10	−	3.13246e10i	0.0469864	−	0.0222134i
$502$	9.98331e10	−	5.66182e11i	0.0701630	−	0.397914i
$503$	−3.06799e11	−	5.31392e11i	−0.213697	−	0.370134i	0.739172	−	0.673517i	$-0.235217\pi$
$503$	−3.06799e11	−	5.31392e11i	−0.213697	−	0.370134i	−0.952869	+	0.303383i	$0.901884\pi$
$504$	9.37146e11	−	1.14115e12i	0.646949	−	0.787779i
$505$	−7.52459e10	+	1.30330e11i	−0.0514839	+	0.0891728i
$506$	−6.34610e11	−	5.32501e11i	−0.430358	−	0.361113i
$507$	−6.07556e11	+	1.32111e12i	−0.408367	+	0.887977i
$508$	−2.83572e11	−	1.60821e12i	−0.188919	−	1.07141i
$509$	−8.03082e11	+	6.73866e11i	−0.530310	+	0.444983i	−0.868208	−	0.496200i	$-0.834728\pi$
$509$	−8.03082e11	+	6.73866e11i	−0.530310	+	0.444983i	0.337898	+	0.941183i	$0.390284\pi$
$510$	8.96852e11	+	2.35234e11i	0.587023	+	0.153969i
$511$	2.64560e12	−	9.62920e11i	1.71645	−	0.624735i
$512$	7.42595e10			0.0477570
$513$	−1.76095e12	+	5.01923e11i	−1.12259	+	0.319970i
$514$	−1.42185e12			−0.898503
$515$	1.39848e12	−	5.09006e11i	0.876041	−	0.318853i
$516$	−4.12154e11	+	4.16537e11i	−0.255939	+	0.258661i
$517$	−4.82998e10	+	4.05284e10i	−0.0297330	+	0.0249489i
$518$	−2.77836e11	−	1.57568e12i	−0.169552	−	0.961580i
$519$	2.09673e12	−	1.94620e11i	1.26850	−	0.117743i
$520$	−1.74734e11	−	1.46619e11i	−0.104800	−	0.0879380i
$521$	4.58453e11	−	7.94065e11i	0.272600	−	0.472157i	−0.696927	−	0.717142i	$-0.745450\pi$
$521$	4.58453e11	−	7.94065e11i	0.272600	−	0.472157i	0.969527	+	0.244985i	$0.0787832\pi$
$522$	2.18365e11	−	6.20290e11i	0.128726	−	0.365660i
$523$	−1.39425e12	−	2.41491e12i	−0.814859	−	1.41138i	−0.909429	−	0.415859i	$-0.863481\pi$
$523$	−1.39425e12	−	2.41491e12i	−0.814859	−	1.41138i	0.0945696	−	0.995518i	$-0.469853\pi$
$524$	1.01422e11	−	5.75193e11i	0.0587681	−	0.333291i
$525$	−2.34307e10	+	2.85178e11i	−0.0134607	+	0.163832i
$526$	−3.93784e11	−	1.43326e11i	−0.224296	−	0.0816372i
$527$	2.26831e12	+	8.25599e11i	1.28102	+	0.466253i
$528$	−1.81742e9	+	2.21200e10i	−0.00101766	+	0.0123860i
$529$	6.69114e11	−	3.79473e12i	0.371492	−	2.10684i
$530$	−8.03549e10	−	1.39179e11i	−0.0442355	−	0.0766181i
$531$	−1.85370e12	−	2.16229e12i	−1.01185	−	1.18029i
$532$	−6.96298e11	+	1.20602e12i	−0.376871	+	0.652760i
$533$	5.03758e10	+	4.22703e10i	0.0270364	+	0.0226863i
$534$	−9.07642e11	+	8.42478e10i	−0.483035	+	0.0448356i
$535$	3.81411e10	+	2.16309e11i	0.0201280	+	0.114152i
$536$	−2.58060e12	+	2.16538e12i	−1.35045	+	1.13317i
$537$	1.54574e12	−	1.56217e12i	0.802142	−	0.810672i
$538$	−1.37474e12	+	5.00363e11i	−0.707455	+	0.257493i
$539$	5.60559e10			0.0286069
$540$	1.17205e11	+	1.13242e12i	0.0593165	+	0.573105i
$541$	−7.18636e11			−0.360679			−0.180340	−	0.983604i	$-0.557720\pi$
$541$	−7.18636e11			−0.360679			−0.180340	+	0.983604i	$0.557720\pi$
$542$	6.69518e11	−	2.43685e11i	0.333246	−	0.121292i
$543$	−1.96901e12	−	5.16448e11i	−0.971960	−	0.254934i
$544$	−1.71229e12	+	1.43678e12i	−0.838267	+	0.703389i
$545$	3.43212e10	+	1.94645e11i	0.0166640	+	0.0945060i
$546$	8.16819e10	−	1.77614e11i	0.0393332	−	0.0855284i
$547$	2.56936e12	+	2.15595e12i	1.22711	+	1.02967i	0.998421	+	0.0561655i	$0.0178875\pi$
$547$	2.56936e12	+	2.15595e12i	1.22711	+	1.02967i	0.228686	+	0.973500i	$0.426557\pi$
$548$	−9.78839e11	+	1.69540e12i	−0.463659	+	0.803081i
$549$	4.47203e10	+	7.39853e9i	0.0210101	+	0.00347592i
$550$	5.44498e10	+	9.43098e10i	0.0253726	+	0.0439466i
$551$	−2.78996e11	+	1.58227e12i	−0.128948	+	0.731303i
$552$	3.46782e12	−	1.63946e12i	1.58976	−	0.751578i
$553$	−2.08496e12	−	7.58865e11i	−0.948059	−	0.345065i
$554$	−2.49392e11	−	9.07712e10i	−0.112483	−	0.0409406i
$555$	2.62748e12	+	1.81915e12i	1.17550	+	0.813860i
$556$	4.43154e11	−	2.51325e12i	0.196661	−	1.11532i
$557$	1.76719e12	+	3.06086e12i	0.777920	+	1.34740i	0.933139	+	0.359517i	$0.117058\pi$
$557$	1.76719e12	+	3.06086e12i	0.777920	+	1.34740i	−0.155219	+	0.987880i	$0.549608\pi$
$558$	−1.85183e10	−	1.75062e12i	−0.00808627	−	0.764430i
$559$	−1.00492e11	+	1.74057e11i	−0.0435288	+	0.0753942i
$560$	4.00839e10	+	3.36344e10i	0.0172236	+	0.0144523i
$561$	−7.66568e11	−	1.08254e12i	−0.326752	−	0.461436i
$562$	−6.25791e10	−	3.54904e11i	−0.0264616	−	0.150071i
$563$	−2.27381e12	+	1.90796e12i	−0.953822	+	0.800351i	−0.979937	−	0.199308i	$-0.936131\pi$
$563$	−2.27381e12	+	1.90796e12i	−0.953822	+	0.800351i	0.0261154	+	0.999659i	$0.491686\pi$
$564$	−2.97416e10	−	1.08694e11i	−0.0123768	−	0.0452326i
$565$	1.09219e12	−	3.97525e11i	0.450900	−	0.164114i
$566$	2.30366e12			0.943507
$567$	−2.35655e12	+	9.14620e11i	−0.957531	+	0.371635i
$568$	8.16810e11			0.329271
$569$	−1.81230e12	+	6.59623e11i	−0.724811	+	0.263809i	−0.677967	−	0.735093i	$-0.737139\pi$
$569$	−1.81230e12	+	6.59623e11i	−0.724811	+	0.263809i	−0.0468440	+	0.998902i	$0.514916\pi$
$570$	4.33619e11	+	1.58472e12i	0.172057	+	0.628803i
$571$	1.10008e12	−	9.23075e11i	0.433073	−	0.363391i	−0.400037	−	0.916499i	$-0.631003\pi$
$571$	1.10008e12	−	9.23075e11i	0.433073	−	0.363391i	0.833110	+	0.553108i	$0.186558\pi$
$572$	2.18732e10	+	1.24049e11i	0.00854337	+	0.0484519i
$573$	−4.60261e11	−	6.49977e11i	−0.178365	−	0.251885i
$574$	2.92612e11	+	2.45530e11i	0.112509	+	0.0944065i
$575$	−3.71648e11	+	6.43713e11i	−0.141784	+	0.245577i
$576$	1.35747e12	+	7.64707e11i	0.513842	+	0.289463i
$577$	−1.23593e12	−	2.14069e12i	−0.464196	−	0.804011i	0.534969	−	0.844872i	$-0.320323\pi$
$577$	−1.23593e12	−	2.14069e12i	−0.464196	−	0.804011i	−0.999165	+	0.0408609i	$0.986990\pi$
$578$	5.13407e10	−	2.91167e11i	0.0191331	−	0.108509i
$579$	9.37068e11	+	6.48783e11i	0.346511	+	0.239909i
$580$	9.38693e11	+	3.41656e11i	0.344427	+	0.125361i
$581$	1.06509e12	+	3.87661e11i	0.387788	+	0.141143i
$582$	1.27648e12	−	6.03472e11i	0.461170	−	0.218024i
$583$	−3.99247e10	+	2.26424e11i	−0.0143131	+	0.0811736i
$584$	2.48065e12	+	4.29661e12i	0.882485	+	1.52851i
$585$	1.37425e11	+	3.65496e11i	0.0485136	+	0.129027i
$586$	−1.21249e12	+	2.10009e12i	−0.424755	+	0.735698i
$587$	−4.16012e12	−	3.49076e12i	−1.44622	−	1.21352i	−0.935280	−	0.353909i	$-0.884852\pi$
$587$	−4.16012e12	−	3.49076e12i	−1.44622	−	1.21352i	−0.510942	−	0.859615i	$-0.670703\pi$
$588$	−4.18604e10	+	9.10237e10i	−0.0144413	+	0.0314019i
$589$	7.42761e11	+	4.21241e12i	0.254291	+	1.44215i
$590$	−1.95763e12	+	1.64265e12i	−0.665115	+	0.558098i
$591$	2.48689e12	+	6.52283e11i	0.838519	+	0.219934i
$592$	−1.04636e11	+	3.80845e10i	−0.0350134	+	0.0127438i
$593$	−1.89941e12			−0.630771			−0.315385	−	0.948964i	$-0.602134\pi$
$593$	−1.89941e12			−0.630771			−0.315385	+	0.948964i	$0.602134\pi$
$594$	−5.39234e11	+	7.96718e11i	−0.177721	+	0.262582i
$595$	−3.12729e12			−1.02292
$596$	3.18070e12	−	1.15768e12i	1.03256	−	0.375821i
$597$	−2.47265e12	+	2.49894e12i	−0.796669	+	0.805141i
$598$	3.89025e11	−	3.26431e11i	0.124400	−	0.104384i
$599$	−7.76877e11	−	4.40589e12i	−0.246565	−	1.39834i	−0.816830	−	0.576879i	$-0.804271\pi$
$599$	−7.76877e11	−	4.40589e12i	−0.246565	−	1.39834i	0.570265	−	0.821461i	$-0.306841\pi$
$600$	−5.02077e11	+	4.66030e10i	−0.158157	+	0.0146802i
$601$	−1.00690e12	−	8.44891e11i	−0.314813	−	0.264159i	0.471665	−	0.881778i	$-0.343653\pi$
$601$	−1.00690e12	−	8.44891e11i	−0.314813	−	0.264159i	−0.786478	+	0.617619i	$0.788098\pi$
$602$	−5.83714e11	+	1.01102e12i	−0.181141	+	0.313745i
$603$	5.66833e12	−	1.06142e12i	1.74593	−	0.326934i
$604$	6.11732e11	+	1.05955e12i	0.187023	+	0.323933i
$605$	3.82456e11	−	2.16902e12i	0.116060	−	0.658209i
$606$	1.86119e10	−	2.26528e11i	0.00560615	−	0.0682331i
$607$	−1.80181e12	−	6.55806e11i	−0.538717	−	0.196077i	0.0583095	−	0.998299i	$-0.481429\pi$
$607$	−1.80181e12	−	6.55806e11i	−0.538717	−	0.196077i	−0.597026	+	0.802222i	$0.703651\pi$
$608$	−3.72195e12	−	1.35468e12i	−1.10460	−	0.402041i
$609$	−1.81624e11	+	2.21056e12i	−0.0535050	+	0.651216i
$610$	7.06250e9	−	4.00534e10i	0.00206526	−	0.0117127i
$611$	−1.93255e10	−	3.34728e10i	−0.00560979	−	0.00971643i
$612$	2.33028e12	−	4.36355e11i	0.671470	−	0.125736i
$613$	2.95639e12	−	5.12062e12i	0.845648	−	1.46470i	−0.0394096	−	0.999223i	$-0.512548\pi$
$613$	2.95639e12	−	5.12062e12i	0.845648	−	1.46470i	0.885057	−	0.465482i	$-0.154119\pi$
$614$	1.44622e12	+	1.21352e12i	0.410654	+	0.344579i
$615$	−7.59684e11	+	7.05143e10i	−0.214139	+	0.0198765i
$616$	3.29150e11	+	1.86670e12i	0.0921045	+	0.522350i
$617$	−2.81691e12	+	2.36367e12i	−0.782509	+	0.656603i	−0.943879	−	0.330291i	$-0.892853\pi$
$617$	−2.81691e12	+	2.36367e12i	−0.782509	+	0.656603i	0.161370	+	0.986894i	$0.448409\pi$
$618$	−1.58095e12	+	1.59776e12i	−0.435983	+	0.440619i
$619$	−2.12668e12	+	7.74047e11i	−0.582228	+	0.211914i	−0.616308	−	0.787505i	$-0.711372\pi$
$619$	−2.12668e12	+	7.74047e11i	−0.582228	+	0.211914i	0.0340794	+	0.999419i	$0.489150\pi$
$620$	2.65943e12			0.722814
$621$	−6.54973e12	−	4.68446e11i	−1.76730	−	0.126400i
$622$	−1.27116e12			−0.340520
$623$	2.88910e12	−	1.05155e12i	0.768363	−	0.279661i
$624$	−1.31604e10	−	3.45182e9i	−0.00347487	−	0.000911418i
$625$	−2.37970e12	+	1.99680e12i	−0.623823	+	0.523450i
$626$	−1.56527e11	−	8.87708e11i	−0.0407385	−	0.231039i
$627$	9.82081e11	−	2.13550e12i	0.253772	−	0.551816i
$628$	−1.23418e11	−	1.03560e11i	−0.0316637	−	0.0265690i
$629$	3.32750e12	−	5.76340e12i	0.847598	−	1.46808i
$630$	7.98243e11	+	2.12301e12i	0.201884	+	0.536932i
$631$	−1.36584e12	−	2.36571e12i	−0.342980	−	0.594058i	0.642005	−	0.766700i	$-0.278103\pi$
$631$	−1.36584e12	−	2.36571e12i	−0.342980	−	0.594058i	−0.984985	+	0.172642i	$0.944769\pi$
$632$	6.78953e11	−	3.85053e12i	0.169283	−	0.960050i
$633$	2.18735e12	−	1.03410e12i	0.541503	−	0.256002i
$634$	2.28017e12	+	8.29915e11i	0.560488	+	0.204001i
$635$	6.10636e12	+	2.22253e12i	1.49039	+	0.542459i
$636$	−3.37854e11	−	2.33915e11i	−0.0818790	−	0.0566893i
$637$	−5.96707e9	+	3.38410e10i	−0.00143593	+	0.00814358i
$638$	4.22070e11	+	7.31046e11i	0.100853	+	0.174683i
$639$	−1.21827e12	−	6.86290e11i	−0.289061	−	0.162837i
$640$	−1.25961e12	+	2.18171e12i	−0.296775	+	0.514029i
$641$	−1.28639e12	−	1.07941e12i	−0.300962	−	0.252537i	0.479782	−	0.877387i	$-0.340716\pi$
$641$	−1.28639e12	−	1.07941e12i	−0.300962	−	0.252537i	−0.780745	+	0.624850i	$0.785160\pi$
$642$	−1.91711e11	−	2.70733e11i	−0.0445389	−	0.0628975i
$643$	9.77213e11	+	5.54205e12i	0.225444	+	1.27856i	0.861834	+	0.507191i	$0.169316\pi$
$643$	9.77213e11	+	5.54205e12i	0.225444	+	1.27856i	−0.636389	+	0.771368i	$0.719573\pi$
$644$	−3.82561e12	+	3.21007e12i	−0.876424	+	0.735407i
$645$	−6.15414e11	−	2.24911e12i	−0.140007	−	0.511672i
$646$	3.21505e12	−	1.17018e12i	0.726342	−	0.264367i
$647$	−1.59682e12			−0.358251			−0.179125	−	0.983826i	$-0.557327\pi$
$647$	−1.59682e12			−0.358251			−0.179125	+	0.983826i	$0.557327\pi$
$648$	−2.30837e12	−	3.80976e12i	−0.514303	−	0.848809i
$649$	3.65600e12			0.808919
$650$	−6.27310e10	+	2.28322e10i	−0.0137839	+	0.00501693i
$651$	1.55845e12	+	5.69557e12i	0.340079	+	1.24286i
$652$	3.62798e12	−	3.04424e12i	0.786232	−	0.659727i
$653$	−1.01835e12	−	5.77536e12i	−0.219174	−	1.24300i	−0.873515	−	0.486797i	$-0.838165\pi$
$653$	−1.01835e12	−	5.77536e12i	−0.219174	−	1.24300i	0.654341	−	0.756199i	$-0.272946\pi$
$654$	−1.72510e11	−	2.43618e11i	−0.0368736	−	0.0520726i
$655$	1.78041e12	+	1.49394e12i	0.377950	+	0.317138i
$656$	1.32919e10	−	2.30222e10i	0.00280233	−	0.00485377i
$657$	−8.98365e10	−	8.49263e12i	−0.0188109	−	1.77827i
$658$	−1.12254e11	−	1.94430e11i	−0.0233445	−	0.0404339i
$659$	−7.78837e10	+	4.41701e11i	−0.0160865	+	0.0912313i	−0.991794	−	0.127846i	$-0.959194\pi$
$659$	−7.78837e10	+	4.41701e11i	−0.0160865	+	0.0912313i	0.975707	+	0.219077i	$0.0703047\pi$
$660$	−1.20153e12	−	8.31882e11i	−0.246482	−	0.170653i
$661$	5.62012e12	+	2.04556e12i	1.14509	+	0.416778i	0.843749	−	0.536738i	$-0.180344\pi$
$661$	5.62012e12	+	2.04556e12i	1.14509	+	0.416778i	0.301341	+	0.953517i	$0.402566\pi$
$662$	4.89384e12	+	1.78121e12i	0.990350	+	0.360458i
$663$	7.35131e11	−	3.47543e11i	0.147759	−	0.0698549i
$664$	−3.46839e11	+	1.96702e12i	−0.0692422	+	0.392692i
$665$	−2.77076e12	−	4.79910e12i	−0.549417	−	0.951618i
$666$	−4.76192e12	−	7.87814e11i	−0.937883	−	0.155163i
$667$	−2.88084e12	+	4.98977e12i	−0.563577	+	0.976144i
$668$	−1.28808e11	−	1.08083e11i	−0.0250293	−	0.0210021i
$669$	−2.32796e12	+	5.06205e12i	−0.449322	+	0.977033i
$670$	−8.98523e11	−	5.09578e12i	−0.172263	−	0.976954i
$671$	−4.45730e10	+	3.74012e10i	−0.00848829	+	0.00712252i
$672$	−5.28900e12	−	1.38725e12i	−1.00049	−	0.262417i
$673$	−1.29754e12	+	4.72267e11i	−0.243811	+	0.0887400i	−0.461035	−	0.887382i	$-0.652522\pi$
$673$	−1.29754e12	+	4.72267e11i	−0.243811	+	0.0887400i	0.217224	+	0.976122i	$0.430300\pi$
$674$	−6.65411e11			−0.124200
$675$	7.88002e11	+	3.52340e11i	0.146103	+	0.0653274i
$676$	3.33612e12			0.614443
$677$	−3.95060e12	+	1.43790e12i	−0.722794	+	0.263076i	−0.677111	−	0.735880i	$-0.736769\pi$
$677$	−3.95060e12	+	1.43790e12i	−0.722794	+	0.263076i	−0.0456826	+	0.998956i	$0.514546\pi$
$678$	−1.23469e12	+	1.24782e12i	−0.224401	+	0.226787i
$679$	−3.64813e12	+	3.06114e12i	−0.658653	+	0.552675i
$680$	−9.56961e11	−	5.42720e12i	−0.171634	−	0.973387i
$681$	−9.37238e12	+	8.69950e11i	−1.66989	+	0.155000i
$682$	1.72155e12	+	1.44455e12i	0.304712	+	0.255684i
$683$	1.96679e12	−	3.40657e12i	0.345831	−	0.598997i	−0.639674	−	0.768647i	$-0.720930\pi$
$683$	1.96679e12	−	3.40657e12i	0.345831	−	0.598997i	0.985504	+	0.169650i	$0.0542638\pi$
$684$	2.73424e12	+	3.18941e12i	0.477622	+	0.557132i
$685$	−3.89507e12	−	6.74647e12i	−0.675940	−	1.17076i
$686$	5.95765e11	−	3.37875e12i	0.102711	−	0.582502i
$687$	1.09069e11	−	1.32749e12i	0.0186809	−	0.227367i
$688$	7.63474e10	+	2.77882e10i	0.0129911	+	0.00472838i
$689$	−1.32443e11	−	4.82052e10i	−0.0223893	−	0.00814905i
$690$	−4.82458e11	+	5.87206e12i	−0.0810287	+	0.986210i
$691$	1.28113e11	−	7.26566e11i	0.0213768	−	0.121234i	−0.972252	−	0.233936i	$-0.924839\pi$
$691$	1.28113e11	−	7.26566e11i	0.0213768	−	0.121234i	0.993629	+	0.112702i	$0.0359506\pi$
$692$	−2.41557e12	−	4.18389e12i	−0.400444	−	0.693589i
$693$	1.07749e12	−	3.06073e12i	0.177466	−	0.504111i
$694$	−2.84887e11	+	4.93439e11i	−0.0466181	+	0.0807450i
$695$	7.77934e12	+	6.52764e12i	1.26477	+	1.06127i
$696$	−3.89186e12	+	3.61245e11i	−0.628660	+	0.0583526i
$697$	2.75891e11	+	1.56466e12i	0.0442782	+	0.251114i
$698$	3.56394e12	−	2.99050e12i	0.568304	−	0.476864i
$699$	7.35187e12	−	7.43005e12i	1.16480	−	1.17718i
$700$	6.16887e11	−	2.24529e11i	0.0971101	−	0.0353452i
$701$	3.66781e12			0.573688			0.286844	−	0.957977i	$-0.407394\pi$
$701$	3.66781e12			0.573688			0.286844	+	0.957977i	$0.407394\pi$
$702$	−4.23578e11	−	4.10345e11i	−0.0658289	−	0.0637724i
$703$	1.17926e13			1.82100
$704$	−1.87938e12	+	6.84040e11i	−0.288362	+	0.104955i
$705$	4.33753e11	+	1.13768e11i	0.0661289	+	0.0173449i
$706$	2.01072e12	−	1.68720e12i	0.304601	−	0.255590i
$707$	1.33123e11	+	7.54977e11i	0.0200385	+	0.113644i
$708$	−2.73016e12	+	5.93663e12i	−0.408356	+	0.887953i
$709$	1.18616e12	+	9.95307e11i	0.176293	+	0.147928i	0.726665	−	0.686992i	$-0.241069\pi$
$709$	1.18616e12	+	9.95307e11i	0.176293	+	0.147928i	−0.550371	+	0.834920i	$0.685514\pi$
$710$	−6.27311e11	+	1.08653e12i	−0.0926446	+	0.160465i
$711$	−4.24790e12	+	5.17260e12i	−0.623392	+	0.759094i
$712$	2.70896e12	+	4.69206e12i	0.395042	+	0.684233i
$713$	−2.66361e12	+	1.51061e13i	−0.385983	+	2.18902i
$714$	4.27007e12	−	2.01873e12i	0.614884	−	0.290694i
$715$	−4.71011e11	−	1.71434e11i	−0.0673991	−	0.0245313i
$716$	−4.73793e12	−	1.72447e12i	−0.673721	−	0.245215i
$717$	6.39182e12	+	4.42541e12i	0.903210	+	0.625341i
$718$	1.01144e12	−	5.73617e12i	0.142030	−	0.805493i
$719$	3.82048e12	+	6.61726e12i	0.533136	+	0.923418i	0.999251	+	0.0386944i	$0.0123199\pi$
$719$	3.82048e12	+	6.61726e12i	0.533136	+	0.923418i	−0.466115	+	0.884724i	$0.654347\pi$
$720$	1.35859e11	−	8.03665e10i	0.0188406	−	0.0111450i
$721$	3.79063e12	−	6.56556e12i	0.522399	−	0.904822i
$722$	1.23584e12	+	1.03699e12i	0.169256	+	0.142023i
$723$	−4.28572e12	−	6.05226e12i	−0.583313	−	0.823750i
$724$	8.10977e11	+	4.59928e12i	0.109695	+	0.622109i
$725$	5.80199e11	−	4.86844e11i	0.0779930	−	0.0654439i
$726$	8.77932e11	+	3.20851e12i	0.117286	+	0.428636i
$727$	−7.54231e12	+	2.74518e12i	−1.00138	+	0.364473i	−0.790117	−	0.612956i	$-0.789980\pi$
$727$	−7.54231e12	+	2.74518e12i	−1.00138	+	0.364473i	−0.211265	+	0.977429i	$0.567758\pi$
$728$	−1.16197e12			−0.153321
$729$	2.41945e11	+	7.62176e12i	0.0317280	+	0.999497i
$730$	−7.62056e12			−0.993193
$731$	−4.56295e12	+	1.66078e12i	−0.591041	+	0.215121i
$732$	−2.74467e10	−	1.00308e11i	−0.00353338	−	0.0129132i
$733$	−9.34072e11	+	7.83779e11i	−0.119512	+	0.100283i	−0.700585	−	0.713569i	$-0.747078\pi$
$733$	−9.34072e11	+	7.83779e11i	−0.119512	+	0.100283i	0.581073	+	0.813852i	$0.302633\pi$
$734$	−6.88226e11	−	3.90312e12i	−0.0875182	−	0.496341i
$735$	−2.30395e11	−	3.25362e11i	−0.0291192	−	0.0411219i
$736$	−1.08808e13	−	9.13007e12i	−1.36682	−	1.14690i
$737$	−3.70134e12	+	6.41090e12i	−0.462120	+	0.800416i
$738$	9.91772e11	−	5.86674e11i	0.123072	−	0.0728020i
$739$	5.43105e12	+	9.40686e12i	0.669860	+	1.16023i	0.977943	+	0.208872i	$0.0669791\pi$
$739$	5.43105e12	+	9.40686e12i	0.669860	+	1.16023i	−0.308083	+	0.951359i	$0.599688\pi$
$740$	1.27318e12	−	7.22056e12i	0.156080	−	0.885173i
$741$	1.18466e12	+	8.20204e11i	0.144348	+	0.0999401i
$742$	−7.69303e11	−	2.80004e11i	−0.0931709	−	0.0339114i
$743$	1.39701e13	+	5.08470e12i	1.68171	+	0.612091i	0.993542	−	0.113464i	$-0.0361946\pi$
$743$	1.39701e13	+	5.08470e12i	1.68171	+	0.612091i	0.688164	+	0.725555i	$0.258417\pi$
$744$	−9.40739e12	+	4.44746e12i	−1.12562	+	0.532150i
$745$	−2.33890e12	+	1.32646e13i	−0.278169	+	1.57757i
$746$	8.15221e11	+	1.41200e12i	0.0963720	+	0.166921i
$747$	2.17001e12	−	2.64239e12i	0.254988	−	0.310494i
$748$	−1.52164e12	+	2.63555e12i	−0.177727	+	0.307833i
$749$	8.57131e11	+	7.19218e11i	0.0995128	+	0.0835011i
$750$	2.34558e12	−	5.10036e12i	0.270691	−	0.588606i
$751$	−1.87953e12	−	1.06593e13i	−0.215610	−	1.22279i	−0.879844	−	0.475262i	$-0.842353\pi$
$751$	−1.87953e12	−	1.06593e13i	−0.215610	−	1.22279i	0.664234	−	0.747525i	$-0.268758\pi$
$752$	−1.19692e10	+	1.00433e10i	−0.00136485	+	0.00114524i
$753$	5.65829e12	+	1.48410e12i	0.641368	+	0.168224i
$754$	−4.86262e11	+	1.76985e11i	−0.0547897	+	0.0199418i
$755$	−4.86850e12			−0.545298
$756$	4.16540e12	+	4.03527e12i	0.463777	+	0.449288i
$757$	−7.14231e12			−0.790509			−0.395255	−	0.918572i	$-0.629344\pi$
$757$	−7.14231e12			−0.790509			−0.395255	+	0.918572i	$0.629344\pi$
$758$	−5.47316e12	+	1.99207e12i	−0.602181	+	0.219176i
$759$	5.92866e12	−	5.99171e12i	0.648438	−	0.655334i
$760$	7.48066e12	−	6.27702e12i	0.813352	−	0.682483i
$761$	1.46504e11	+	8.30866e11i	0.0158350	+	0.0898050i	0.991701	−	0.128565i	$-0.0410371\pi$
$761$	1.46504e11	+	8.30866e11i	0.0158350	+	0.0898050i	−0.975866	+	0.218370i	$0.929926\pi$
$762$	−9.77246e12	+	9.07085e11i	−1.05004	+	0.0974654i
$763$	7.71286e11	+	6.47186e11i	0.0823863	+	0.0691304i
$764$	−9.13618e11	+	1.58243e12i	−0.0970163	+	0.168037i
$765$	−3.13267e12	+	8.89869e12i	−0.330703	+	0.939398i
$766$	4.23579e12	+	7.33660e12i	0.444534	+	0.769955i
$767$	−3.89177e11	+	2.20713e12i	−0.0406039	+	0.230276i
$768$	7.77162e11	−	9.45894e12i	0.0806095	−	0.981108i
$769$	−8.68614e12	−	3.16150e12i	−0.895692	−	0.326005i	−0.147167	−	0.989112i	$-0.547015\pi$
$769$	−8.68614e12	−	3.16150e12i	−0.895692	−	0.326005i	−0.748525	+	0.663107i	$0.769238\pi$
$770$	−2.73591e12	−	9.95788e11i	−0.280474	−	0.102084i
$771$	1.18465e12	−	1.44185e13i	0.120738	−	1.46952i
$772$	4.54068e11	−	2.57515e12i	0.0460090	−	0.260930i
$773$	−8.26371e12	−	1.43132e13i	−0.832467	−	1.44188i	−0.896076	−	0.443901i	$-0.853594\pi$
$773$	−8.26371e12	−	1.43132e13i	−0.832467	−	1.44188i	0.0636087	−	0.997975i	$-0.479739\pi$
$774$	2.29215e12	+	2.67372e12i	0.229566	+	0.267782i
$775$	1.00819e12	−	1.74624e12i	0.100389	−	0.173879i
$776$	−6.42876e12	−	5.39437e12i	−0.636428	−	0.534026i
$777$	1.62100e13	−	1.50462e12i	1.59547	−	0.148092i
$778$	−1.95242e12	−	1.10727e13i	−0.191058	−	1.08354i
$779$	−2.15667e12	+	1.80966e12i	−0.209829	+	0.176067i
$780$	6.30108e11	−	6.36809e11i	0.0609522	−	0.0616004i
$781$	1.68666e12	−	6.13895e11i	0.162218	−	0.0590424i
$782$	1.22694e13			1.17326
$783$	6.10822e12	+	2.73118e12i	0.580747	+	0.259670i
$784$	1.38912e10			0.00131316
$785$	6.02442e11	−	2.19271e11i	0.0566242	−	0.0206095i
$786$	−3.39539e12	−	8.90572e11i	−0.317313	−	0.0832276i
$787$	−9.13055e12	+	7.66144e12i	−0.848419	+	0.711908i	−0.959441	−	0.281910i	$-0.909032\pi$
$787$	−9.13055e12	+	7.66144e12i	−0.848419	+	0.711908i	0.111022	+	0.993818i	$0.464588\pi$
$788$	−1.02428e12	−	5.80897e12i	−0.0946346	−	0.536699i
$789$	1.78151e12	−	3.87382e12i	0.163660	−	0.355871i
$790$	4.60061e12	+	3.86037e12i	0.420236	+	0.352620i
$791$	2.96041e12	−	5.12758e12i	0.268880	−	0.465713i
$792$	5.64142e12	+	9.33318e11i	0.509477	+	0.0842881i
$793$	−1.78344e10	−	3.08900e10i	−0.00160151	−	0.00277389i
$794$	−7.14668e11	+	4.05309e12i	−0.0638135	+	0.361904i
$795$	1.47832e12	−	6.98892e11i	0.131255	−	0.0620523i
$796$	7.57907e12	+	2.75856e12i	0.669125	+	0.243542i
$797$	−2.81485e12	−	1.02452e12i	−0.247111	−	0.0899412i	0.215495	−	0.976505i	$-0.430863\pi$
$797$	−2.81485e12	−	1.02452e12i	−0.247111	−	0.0899412i	−0.462606	+	0.886564i	$0.653086\pi$
$798$	6.88118e12	+	4.76422e12i	0.600690	+	0.415890i
$799$	1.62156e11	−	9.19630e11i	0.0140757	−	0.0798275i
$800$	9.33576e11	+	1.61700e12i	0.0805833	+	0.139574i
$801$	−9.81050e10	−	9.27429e12i	−0.00842064	−	0.796039i
$802$	2.36775e12	−	4.10107e12i	0.202093	−	0.350036i
$803$	8.35161e12	+	7.00783e12i	0.708843	+	0.594790i
$804$	−7.64603e12	−	1.07977e13i	−0.645333	−	0.911334i
$805$	−3.45081e12	−	1.95705e13i	−0.289627	−	1.64256i
$806$	−1.05533e12	+	8.85529e11i	−0.0880809	+	0.0739086i
$807$	−3.92862e12	−	1.43576e13i	−0.326069	−	1.19166i
$808$	−1.26948e12	+	4.62052e11i	−0.104779	+	0.0381364i
$809$	−1.91885e13			−1.57497			−0.787487	−	0.616332i	$-0.788618\pi$
$809$	−1.91885e13			−1.57497			−0.787487	+	0.616332i	$0.788618\pi$
$810$	6.84064e12	−	1.44739e11i	0.558360	−	0.0118142i
$811$	1.24781e12			0.101287			0.0506436	−	0.998717i	$-0.483873\pi$
$811$	1.24781e12			0.101287			0.0506436	+	0.998717i	$0.483873\pi$
$812$	4.78182e12	−	1.74044e12i	0.386003	−	0.140494i
$813$	1.91330e12	+	6.99239e12i	0.153594	+	0.561330i
$814$	4.74624e12	−	3.98257e12i	0.378913	−	0.317946i
$815$	3.27254e12	+	1.85595e13i	0.259822	+	1.47352i
$816$	−1.89963e11	−	2.68264e11i	−0.0149990	−	0.0211815i
$817$	−6.59137e12	−	5.53082e12i	−0.517579	−	0.434300i
$818$	−4.66507e12	+	8.08014e12i	−0.364308	+	0.630999i
$819$	1.73307e12	+	9.76293e11i	0.134598	+	0.0758233i
$820$	8.75204e11	+	1.51590e12i	0.0676001	+	0.117087i
$821$	−1.44793e12	+	8.21161e12i	−0.111225	+	0.630789i	0.877325	+	0.479897i	$0.159326\pi$
$821$	−1.44793e12	+	8.21161e12i	−0.111225	+	0.630789i	−0.988550	+	0.150893i	$0.951785\pi$
$822$	9.67341e12	+	6.69743e12i	0.739020	+	0.511664i
$823$	−2.33039e13	−	8.48193e12i	−1.77064	−	0.644460i	−0.999974	−	0.00721795i	$-0.997702\pi$
$823$	−2.33039e13	−	8.48193e12i	−1.77064	−	0.644460i	−0.770664	−	0.637242i	$-0.780075\pi$
$824$	1.25540e13	+	4.56930e12i	0.948661	+	0.345284i
$825$	−1.00173e12	+	4.73581e11i	−0.0752850	+	0.0355919i
$826$	−2.26056e12	+	1.28203e13i	−0.168969	+	0.958269i
$827$	−1.00616e13	−	1.74272e13i	−0.747983	−	1.29554i	−0.948788	−	0.315913i	$-0.897689\pi$
$827$	−1.00616e13	−	1.74272e13i	−0.747983	−	1.29554i	0.200805	−	0.979631i	$-0.435644\pi$
$828$	5.30206e12	+	1.41014e13i	0.392020	+	1.04262i
$829$	6.94330e12	−	1.20261e13i	0.510588	−	0.884364i	−0.489337	−	0.872095i	$-0.662761\pi$
$829$	6.94330e12	−	1.20261e13i	0.510588	−	0.884364i	0.999925	−	0.0122690i	$-0.00390544\pi$
$830$	−2.35019e12	−	1.97204e12i	−0.171890	−	0.144233i
$831$	1.12827e12	−	2.45337e12i	0.0820744	−	0.178467i
$832$	−2.12897e11	−	1.20740e12i	−0.0154033	−	0.0873567i
$833$	−6.35982e11	+	5.33652e11i	−0.0457660	+	0.0384022i
$834$	−1.48358e13	−	3.89126e12i	−1.06185	−	0.278512i
$835$	6.28751e11	−	2.28846e11i	0.0447599	−	0.0162913i
$836$	−5.39266e12			−0.381834
$837$	1.77679e13	+	1.27078e12i	1.25133	+	0.0894966i
$838$	−5.55079e12			−0.388827
$839$	5.97583e12	−	2.17502e12i	0.416360	−	0.151543i	−0.125341	−	0.992114i	$-0.540003\pi$
$839$	5.97583e12	−	2.17502e12i	0.416360	−	0.151543i	0.541701	+	0.840571i	$0.317780\pi$
$840$	9.48195e12	−	9.58278e12i	0.657114	−	0.664102i
$841$	−6.61569e12	+	5.55122e12i	−0.456030	+	0.382654i
$842$	−9.21647e11	−	5.22692e12i	−0.0631917	−	0.358378i
$843$	3.65110e12	−	3.38897e11i	0.249000	−	0.0231123i
$844$	−4.25224e12	−	3.56805e12i	−0.288454	−	0.242042i
$845$	−6.63768e12	+	1.14968e13i	−0.447879	+	0.775750i
$846$	−6.65696e11	+	1.24655e11i	−0.0446796	+	0.00836646i
$847$	−5.60985e12	−	9.71655e12i	−0.374521	−	0.648689i
$848$	−9.89374e9	+	5.61102e10i	−0.000657021	+	0.00372615i
$849$	−1.91936e12	+	2.33607e13i	−0.126786	+	1.54313i
$850$	−1.51559e12	−	5.51630e11i	−0.0995857	−	0.0362462i
$851$	3.97390e13	+	1.44638e13i	2.59737	+	0.945366i
$852$	−2.62691e11	+	3.19724e12i	−0.0170792	+	0.207873i
$853$	−3.54122e12	+	2.00833e13i	−0.229025	+	1.29886i	0.625815	+	0.779972i	$0.284767\pi$
$853$	−3.54122e12	+	2.00833e13i	−0.229025	+	1.29886i	−0.854840	+	0.518892i	$0.826345\pi$
$854$	−1.03592e11	−	1.79427e11i	−0.00666450	−	0.0115433i
$855$	−1.64314e13	+	3.07685e12i	−1.05154	+	0.196906i
$856$	−9.85870e11	+	1.70758e12i	−0.0627607	+	0.108705i
$857$	−7.65823e12	−	6.42602e12i	−0.484970	−	0.406938i	0.367250	−	0.930122i	$-0.380299\pi$
$857$	−7.65823e12	−	6.42602e12i	−0.484970	−	0.406938i	−0.852220	+	0.523184i	$0.824744\pi$
$858$	7.53794e11	−	6.99676e10i	0.0474854	−	0.00440762i
$859$	−3.02450e11	−	1.71528e12i	−0.0189533	−	0.107489i	0.973864	−	0.227134i	$-0.0729356\pi$
$859$	−3.02450e11	−	1.71528e12i	−0.0189533	−	0.107489i	−0.992817	+	0.119645i	$0.961824\pi$
$860$	−4.09813e12	+	3.43874e12i	−0.255472	+	0.214366i
$861$	−2.73364e12	+	2.76271e12i	−0.169522	+	0.171325i
$862$	−1.03021e13	+	3.74964e12i	−0.635537	+	0.231317i
$863$	−1.83269e12			−0.112471			−0.0562355	−	0.998418i	$-0.517910\pi$
$863$	−1.83269e12			−0.112471			−0.0562355	+	0.998418i	$0.517910\pi$
$864$	−9.24551e12	+	1.36602e13i	−0.564442	+	0.833962i
$865$	1.92244e13			1.16756
$866$	−8.37769e12	+	3.04923e12i	−0.506167	+	0.184230i
$867$	2.90986e12	+	7.63222e11i	0.174898	+	0.0458738i
$868$	1.03780e13	−	8.70816e12i	0.620546	−	0.520700i
$869$	−1.49197e12	−	8.46140e12i	−0.0887507	−	0.503330i
$870$	2.50842e12	−	5.45446e12i	0.148444	−	0.322786i
$871$	−3.47626e12	−	2.91693e12i	−0.204659	−	0.171729i
$872$	−8.87132e11	+	1.53656e12i	−0.0519594	+	0.0899963i
$873$	5.05608e12	+	1.34472e13i	0.294612	+	0.783550i
$874$	1.08706e13	+	1.88285e13i	0.630164	+	1.09148i
$875$	−3.28799e12	+	1.86471e13i	−0.189625	+	1.07541i
$876$	−1.76160e13	+	8.32819e12i	−1.01074	+	0.477839i
$877$	6.43018e12	+	2.34039e12i	0.367050	+	0.133595i	0.518959	−	0.854799i	$-0.326320\pi$
$877$	6.43018e12	+	2.34039e12i	0.367050	+	0.133595i	−0.151909	+	0.988395i	$0.548542\pi$
$878$	−1.42252e13	−	5.17756e12i	−0.807855	−	0.294035i
$879$	−2.02861e13	−	1.40452e13i	−1.14617	−	0.793557i
$880$	−3.51855e10	+	1.99547e11i	−0.00197784	+	0.0112169i
$881$	2.12745e10	+	3.68485e10i	0.00118978	+	0.00206077i	0.866620	−	0.498969i	$-0.166288\pi$
$881$	2.12745e10	+	3.68485e10i	0.00118978	+	0.00206077i	−0.865430	+	0.501030i	$0.832955\pi$
$882$	5.24614e11	+	2.95532e11i	0.0291898	+	0.0164435i
$883$	−6.88601e12	+	1.19269e13i	−0.381193	+	0.660245i	−0.991233	−	0.132125i	$-0.957820\pi$
$883$	−6.88601e12	+	1.19269e13i	−0.381193	+	0.660245i	0.610040	+	0.792370i	$0.291153\pi$
$884$	−1.42911e12	−	1.19916e12i	−0.0787100	−	0.0660456i
$885$	−1.50265e13	−	2.12203e13i	−0.823404	−	1.16281i
$886$	3.74163e12	+	2.12198e13i	0.203990	+	1.15688i
$887$	1.87682e13	−	1.57484e13i	1.01804	−	0.854239i	0.0286618	−	0.999589i	$-0.490875\pi$
$887$	1.87682e13	−	1.57484e13i	1.01804	−	0.854239i	0.989380	+	0.145350i	$0.0464310\pi$
$888$	7.57149e12	+	2.76709e13i	0.408623	+	1.49336i
$889$	3.11066e13	−	1.13219e13i	1.67030	−	0.607939i
$890$	−8.32195e12			−0.444601
$891$	−7.62998e12	−	6.13200e12i	−0.405577	−	0.325951i
$892$	1.27829e13			0.676066
$893$	1.55492e12	−	5.65946e11i	0.0818234	−	0.0297813i
$894$	−5.36897e12	−	1.96216e13i	−0.281107	−	1.02734i
$895$	1.53696e13	−	1.28966e13i	0.800677	−	0.671848i
$896$	2.22847e12	+	1.26383e13i	0.115510	+	0.655091i
$897$	2.98610e12	+	4.21695e12i	0.154006	+	0.217486i
$898$	7.62074e12	+	6.39456e12i	0.391069	+	0.328146i
$899$	7.81505e12	−	1.35361e13i	0.399037	−	0.691152i
$900$	−2.09476e10	−	1.98027e12i	−0.00106425	−	0.100608i
$901$	−1.70260e12	−	2.94898e12i	−0.0860697	−	0.149077i
$902$	−2.56854e11	+	1.45669e12i	−0.0129198	+	0.0732719i
$903$	−9.76611e12	−	6.76161e12i	−0.488795	−	0.338420i
$904$	9.80447e12	+	3.56854e12i	0.488277	+	0.177718i
$905$	−1.74634e13	−	6.35615e12i	−0.865386	−	0.314975i
$906$	6.64756e12	−	3.14272e12i	0.327782	−	0.154963i
$907$	−1.56173e12	+	8.85699e12i	−0.0766253	+	0.434564i	0.922226	+	0.386651i	$0.126368\pi$
$907$	−1.56173e12	+	8.85699e12i	−0.0766253	+	0.434564i	−0.998852	+	0.0479128i	$0.984743\pi$
$908$	1.07976e13	+	1.87020e13i	0.527157	+	0.913063i
$909$	2.28164e12	+	3.77475e11i	0.110843	+	0.0183379i
$910$	8.92392e11	−	1.54567e12i	0.0431389	−	0.0747188i
$911$	9.82893e12	+	8.24745e12i	0.472796	+	0.396723i	0.847813	−	0.530295i	$-0.177919\pi$
$911$	9.82893e12	+	8.24745e12i	0.472796	+	0.396723i	−0.375017	+	0.927018i	$0.622363\pi$
$912$	2.43369e11	−	5.29197e11i	0.0116490	−	0.0253303i
$913$	7.62164e11	+	4.32245e12i	0.0363020	+	0.205879i
$914$	6.92372e12	−	5.80969e12i	0.328157	−	0.275356i
$915$	4.00284e11	+	1.04990e11i	0.0188788	+	0.00495169i
$916$	−2.87159e12	+	1.04517e12i	−0.134770	+	0.0490523i
$917$	1.18396e13			0.552935
$918$	−1.46688e12	−	1.41727e13i	−0.0681713	−	0.658658i
$919$	−2.60634e13			−1.20535			−0.602673	−	0.797988i	$-0.705898\pi$
$919$	−2.60634e13			−1.20535			−0.602673	+	0.797988i	$0.705898\pi$
$920$	3.29074e13	−	1.19773e13i	1.51443	−	0.551206i
$921$	−1.35109e13	+	1.36545e13i	−0.618749	+	0.625329i
$922$	7.33987e12	−	6.15888e12i	0.334502	−	0.280681i
$923$	1.91066e11	+	1.08359e12i	0.00866513	+	0.0491424i
$924$	−7.41269e12	+	6.88050e11i	−0.334543	+	0.0310525i
$925$	−4.25852e12	−	3.57332e12i	−0.191258	−	0.160485i
$926$	4.91195e12	−	8.50775e12i	0.219535	−	0.380246i
$927$	−1.48851e13	−	1.73631e13i	−0.662055	−	0.772268i
$928$	7.23665e12	+	1.25342e13i	0.320311	+	0.554795i
$929$	3.73400e12	−	2.11766e13i	0.164477	−	0.932793i	−0.785126	−	0.619336i	$-0.787402\pi$
$929$	3.73400e12	−	2.11766e13i	0.164477	−	0.932793i	0.949602	−	0.313457i	$-0.101487\pi$
$930$	1.30880e12	−	1.59295e13i	0.0573718	−	0.698279i
$931$	−1.38242e12	−	5.03158e11i	−0.0603066	−	0.0219498i
$932$	−2.25347e13	−	8.20195e12i	−0.978317	−	0.356078i
$933$	1.05910e12	−	1.28904e13i	0.0457582	−	0.556928i
$934$	2.40603e12	−	1.36453e13i	0.103452	−	0.586708i
$935$	−6.05502e12	−	1.04876e13i	−0.259097	−	0.448770i
$936$	−1.16397e12	+	3.30638e12i	−0.0495677	+	0.140803i
$937$	−7.93720e12	+	1.37476e13i	−0.336387	+	0.582639i	−0.983750	−	0.179542i	$-0.942538\pi$
$937$	−7.93720e12	+	1.37476e13i	−0.336387	+	0.582639i	0.647363	+	0.762181i	$0.275872\pi$
$938$	−2.01922e13	−	1.69432e13i	−0.851667	−	0.714634i
$939$	9.13238e12	−	8.47672e11i	0.383344	−	0.0355822i
$940$	−1.78650e11	−	1.01318e12i	−0.00746325	−	0.0423262i
$941$	2.31783e13	−	1.94489e13i	0.963668	−	0.808614i	−0.0178776	−	0.999840i	$-0.505691\pi$
$941$	2.31783e13	−	1.94489e13i	0.963668	−	0.808614i	0.981546	+	0.191226i	$0.0612465\pi$
$942$	−6.81045e11	+	6.88287e11i	−0.0281804	+	0.0284800i
$943$	−9.48717e12	+	3.45305e12i	−0.390692	+	0.142200i
$944$	9.05993e11			0.0371322
$945$	−2.21938e13	+	6.32589e12i	−0.905293	+	0.258035i
$946$	−4.52072e12			−0.183526
$947$	−3.32281e13	+	1.20941e13i	−1.34255	+	0.488649i	−0.910615	−	0.413255i	$-0.864392\pi$
$947$	−3.32281e13	+	1.20941e13i	−1.34255	+	0.488649i	−0.431937	+	0.901904i	$0.642170\pi$
$948$	1.48538e13	+	3.89598e12i	0.597310	+	0.156668i
$949$	−5.11965e12	+	4.29590e12i	−0.204900	+	0.171932i
$950$	−4.96282e11	−	2.81455e12i	−0.0197684	−	0.112112i
$951$	−1.03157e13	+	2.24310e13i	−0.408965	+	0.889277i
$952$	−2.15054e13	−	1.80452e13i	−0.848558	−	0.712025i
$953$	1.03871e13	−	1.79911e13i	0.407923	−	0.706543i	−0.586734	−	0.809780i	$-0.699586\pi$
$953$	1.03871e13	−	1.79911e13i	0.407923	−	0.706543i	0.994657	+	0.103236i	$0.0329198\pi$
$954$	−1.56738e12	+	1.90857e12i	−0.0612641	+	0.0746002i
$955$	−3.63554e12	−	6.29694e12i	−0.141434	−	0.244971i
$956$	3.09724e12	−	1.75653e13i	0.119926	−	0.680135i
$957$	−7.76496e12	+	3.67098e12i	−0.299251	+	0.141475i
$958$	−9.17336e12	−	3.33883e12i	−0.351871	−	0.128071i
$959$	−3.72908e13	−	1.35727e13i	−1.42370	−	0.518183i
$960$	1.16948e13	+	8.09693e12i	0.444397	+	0.307680i
$961$	2.63456e12	−	1.49413e13i	0.0996444	−	0.565111i
$962$	1.89905e12	+	3.28925e12i	0.0714904	+	0.123825i
$963$	2.90514e12	−	1.71851e12i	0.108855	−	0.0643923i
$964$	−8.50716e12	+	1.47348e13i	−0.317276	+	0.549539i
$965$	7.97093e12	+	6.68840e12i	0.295894	+	0.248284i
$966$	1.73450e13	+	2.44945e13i	0.640881	+	0.905047i
$967$	5.22949e12	+	2.96579e13i	0.192327	+	1.09074i	0.916174	+	0.400781i	$0.131261\pi$
$967$	5.22949e12	+	2.96579e13i	0.192327	+	1.09074i	−0.723847	+	0.689961i	$0.757628\pi$
$968$	1.51458e13	−	1.27088e13i	0.554438	−	0.465229i
$969$	9.18773e12	+	3.35777e13i	0.334774	+	1.22347i
$970$	1.21130e13	−	4.40876e12i	0.439317	−	0.159898i
$971$	2.37260e13			0.856519			0.428260	−	0.903656i	$-0.359127\pi$
$971$	2.37260e13			0.856519			0.428260	+	0.903656i	$0.359127\pi$
$972$	1.56549e13	−	7.81044e12i	0.562540	−	0.280658i
$973$	5.17319e13			1.85034
$974$	9.33984e12	−	3.39942e12i	0.332525	−	0.121029i
$975$	−1.79268e11	−	6.55158e11i	−0.00635305	−	0.0232180i
$976$	−1.10456e10	+	9.26838e9i	−0.000389642	+	0.000326949i
$977$	1.62850e12	+	9.23568e12i	0.0571824	+	0.324297i	0.999958	−	0.00912959i	$-0.00290608\pi$
$977$	1.62850e12	+	9.23568e12i	0.0571824	+	0.324297i	−0.942776	+	0.333427i	$0.891795\pi$
$978$	−1.64490e13	−	2.32291e13i	−0.574928	−	0.811909i
$979$	9.12029e12	+	7.65283e12i	0.317312	+	0.266256i
$980$	−4.57333e11	+	7.92124e11i	−0.0158386	+	0.0274332i
$981$	2.61418e12	−	1.54640e12i	0.0901208	−	0.0533102i
$982$	3.33925e11	+	5.78376e11i	0.0114590	+	0.0198476i
$983$	−5.48739e11	+	3.11206e12i	−0.0187446	+	0.106306i	−0.992745	−	0.120242i	$-0.961633\pi$
$983$	−5.48739e11	+	3.11206e12i	−0.0187446	+	0.106306i	0.974000	+	0.226548i	$0.0727440\pi$
$984$	−5.63100e12	−	3.89865e12i	−0.191473	−	0.132567i
$985$	2.20566e13	+	8.02793e12i	0.746577	+	0.271732i
$986$	−1.17482e13	−	4.27598e12i	−0.395844	−	0.144075i
$987$	2.06517e12	−	9.76337e11i	0.0692675	−	0.0327471i
$988$	5.74041e11	−	3.25555e12i	0.0191662	−	0.108697i
$989$	−1.54281e13	−	2.67223e13i	−0.512779	−	0.888159i
$990$	−5.57413e12	+	6.78752e12i	−0.184425	+	0.224571i
$991$	1.11313e12	−	1.92800e12i	0.0366619	−	0.0635002i	−0.847112	−	0.531414i	$-0.821661\pi$
$991$	1.11313e12	−	1.92800e12i	0.0366619	−	0.0635002i	0.883774	+	0.467914i	$0.154994\pi$
$992$	2.95170e13	+	2.47677e13i	0.967766	+	0.812052i
$993$	−2.21401e13	+	4.81427e13i	−0.722617	+	1.57130i
$994$	1.10982e12	+	6.29410e12i	0.0360590	+	0.204501i
$995$	−2.45860e13	+	2.06301e13i	−0.795215	+	0.667265i
$996$	−7.58796e12	−	1.99024e12i	−0.244320	−	0.0640822i
$997$	4.38513e13	−	1.59606e13i	1.40558	−	0.511588i	0.475748	−	0.879582i	$-0.342178\pi$
$997$	4.38513e13	−	1.59606e13i	1.40558	−	0.511588i	0.929828	+	0.367994i	$0.119955\pi$
$998$	2.61177e10			0.000833388
$999$	1.19565e13	−	4.76327e13i	0.379803	−	1.51308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.7.10	yes	156
3.2	odd	2		81.10.e.a.19.17		156
27.4	even	9	inner	27.10.e.a.4.10	✓	156
27.23	odd	18		81.10.e.a.64.17		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.10	✓	156	27.4	even	9	inner
27.10.e.a.7.10	yes	156	1.1	even	1	trivial
81.10.e.a.19.17		156	3.2	odd	2
81.10.e.a.64.17		156	27.23	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-12.9570 + 4.71595i) q^{2} +(-37.0275 - 135.322i) q^{3} +(-246.572 + 206.898i) q^{4} +(-222.415 - 1261.38i) q^{5} +(1117.94 + 1578.74i) q^{6} +(-4998.24 - 4194.02i) q^{7} +(5748.96 - 9957.50i) q^{8} +(-16940.9 + 10021.3i) q^{9} +(8830.42 + 15294.7i) q^{10} +(4387.44 - 24882.4i) q^{11} +(37127.8 + 25705.6i) q^{12} +(14554.5 + 5297.40i) q^{13} +(84540.9 + 30770.4i) q^{14} +(-162456. + 76803.2i) q^{15} +(1087.25 - 6166.10i) q^{16} +(187103. + 324072. i) q^{17} +(172243. - 209738. i) q^{18} +(-331545. + 574253. i) q^{19} +(315818. + 265003. i) q^{20} +(-382470. + 831665. i) q^{21} +(60496.3 + 343092. i) q^{22} +(-1.82158e6 + 1.52849e6i) q^{23} +(-1.56034e6 - 409258. i) q^{24} +(293733. - 106910. i) q^{25} -213564. q^{26} +(1.98337e6 + 1.92141e6i) q^{27} +2.10016e6 q^{28} +(2.27688e6 - 828718. i) q^{29} +(1.74274e6 - 1.76127e6i) q^{30} +(4.94152e6 - 4.14643e6i) q^{31} +(1.03725e6 + 5.88253e6i) q^{32} +(-3.52959e6 + 327618. i) q^{33} +(-3.95260e6 - 3.31663e6i) q^{34} +(-4.17856e6 + 7.23748e6i) q^{35} +(2.10377e6 - 5.97600e6i) q^{36} +(-8.89215e6 - 1.54017e7i) q^{37} +(1.58767e6 - 9.00413e6i) q^{38} +(177937. - 2.16569e6i) q^{39} +(-1.38388e7 - 5.03692e6i) q^{40} +(3.98972e6 + 1.45214e6i) q^{41} +(1.03356e6 - 1.25796e7i) q^{42} +(-2.25330e6 + 1.27791e7i) q^{43} +(4.06631e6 + 7.04305e6i) q^{44} +(1.64085e7 + 1.91400e7i) q^{45} +(1.63939e7 - 2.83951e7i) q^{46} +(-1.91163e6 - 1.60405e6i) q^{47} +(-874666. + 81187.0i) q^{48} +(385257. + 2.18490e6i) q^{49} +(-3.30171e6 + 2.77047e6i) q^{50} +(3.69260e7 - 3.73187e7i) q^{51} +(-4.68475e6 + 1.70511e6i) q^{52} -9.09978e6 q^{53} +(-3.47598e7 - 1.55422e7i) q^{54} -3.23619e7 q^{55} +(-7.04967e7 + 2.56587e7i) q^{56} +(8.99852e7 + 2.36021e7i) q^{57} +(-2.55933e7 + 2.14754e7i) q^{58} +(2.51267e7 + 1.42501e8i) q^{59} +(2.41667e7 - 5.25494e7i) q^{60} +(-1.76413e6 - 1.48028e6i) q^{61} +(-4.44728e7 + 7.70291e7i) q^{62} +(1.26704e8 + 2.09620e7i) q^{63} +(-3.95784e7 - 6.85519e7i) q^{64} +(3.44489e6 - 1.95369e7i) q^{65} +(4.41877e7 - 2.08903e7i) q^{66} +(-2.75317e8 - 1.00207e8i) q^{67} +(-1.13184e8 - 4.11957e7i) q^{68} +(2.74286e8 + 1.89903e8i) q^{69} +(2.00099e7 - 1.13482e8i) q^{70} +(3.55199e7 + 6.15222e7i) q^{71} +(2.39385e6 + 2.26301e8i) q^{72} +(-2.15747e8 + 3.73685e8i) q^{73} +(1.87849e8 + 1.57624e8i) q^{74} +(-2.53435e7 - 3.57899e7i) q^{75} +(-3.70623e7 - 2.10191e8i) q^{76} +(-1.26287e8 + 1.05967e8i) q^{77} +(7.90776e6 + 2.88999e7i) q^{78} +(3.19548e8 - 1.16306e8i) q^{79} -8.01960e6 q^{80} +(1.86569e8 - 3.39539e8i) q^{81} -5.85430e7 q^{82} +(-1.63239e8 + 5.94141e7i) q^{83} +(-7.77637e7 - 2.84197e8i) q^{84} +(3.67163e8 - 3.08086e8i) q^{85} +(-3.10697e7 - 1.76205e8i) q^{86} +(-1.96451e8 - 2.77426e8i) q^{87} +(-2.22543e8 - 1.86736e8i) q^{88} +(-2.35605e8 + 4.08079e8i) q^{89} +(-3.02868e8 - 1.70615e8i) q^{90} +(-5.05294e7 - 8.75195e7i) q^{91} +(1.32909e8 - 7.53763e8i) q^{92} +(-7.44074e8 - 5.15163e8i) q^{93} +(3.23336e7 + 1.17685e7i) q^{94} +(7.98090e8 + 2.90481e8i) q^{95} +(7.57627e8 - 3.58178e8i) q^{96} +(1.26743e8 - 7.18794e8i) q^{97} +(-1.52957e7 - 2.64928e7i) q^{98} +(1.75026e8 + 4.65499e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) \) 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more