LMFDB - Embedded newform 27.10.e.a.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	27.4
Dual form			27.10.e.a.7.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-15.0855 - 5.49066i) q^{2} +(69.4935 - 121.876i) q^{3} +(-194.791 - 163.449i) q^{4} +(-120.371 + 682.656i) q^{5} +(-1717.52 + 1456.99i) q^{6} +(-4765.46 + 3998.70i) q^{7} +(6150.79 + 10653.5i) q^{8} +(-10024.3 - 16939.1i) q^{9} +(5564.08 - 9637.27i) q^{10} +(324.344 + 1839.45i) q^{11} +(-33457.1 + 12381.6i) q^{12} +(10423.0 - 3793.68i) q^{13} +(93844.8 - 34156.7i) q^{14} +(74834.1 + 62110.4i) q^{15} +(-11685.3 - 66270.8i) q^{16} +(36870.6 - 63861.7i) q^{17} +(58214.5 + 310575. i) q^{18} +(451882. + 782682. i) q^{19} +(135026. - 113301. i) q^{20} +(156175. + 858677. i) q^{21} +(5206.90 - 29529.8i) q^{22} +(1.32648e6 + 1.11305e6i) q^{23} +(1.72584e6 - 9283.55i) q^{24} +(1.38381e6 + 503665. i) q^{25} -178066. q^{26} +(-2.76109e6 + 44560.4i) q^{27} +1.58185e6 q^{28} +(-5.11051e6 - 1.86007e6i) q^{29} +(-787881. - 1.34785e6i) q^{30} +(2.20097e6 + 1.84683e6i) q^{31} +(906116. - 5.13884e6i) q^{32} +(246724. + 88300.0i) q^{33} +(-906854. + 760941. i) q^{34} +(-2.15611e6 - 3.73450e6i) q^{35} +(-816036. + 4.93804e6i) q^{36} +(-2.95439e6 + 5.11715e6i) q^{37} +(-2.51940e6 - 1.42883e7i) q^{38} +(261977. - 1.53395e6i) q^{39} +(-8.01304e6 + 2.91651e6i) q^{40} +(-1.25668e7 + 4.57393e6i) q^{41} +(2.35873e6 - 1.38111e7i) q^{42} +(4.11840e6 + 2.33566e7i) q^{43} +(237476. - 411321. i) q^{44} +(1.27702e7 - 4.80418e6i) q^{45} +(-1.38992e7 - 2.40741e7i) q^{46} +(1.67358e7 - 1.40430e7i) q^{47} +(-8.88885e6 - 3.18123e6i) q^{48} +(-287276. + 1.62922e6i) q^{49} +(-1.81099e7 - 1.51960e7i) q^{50} +(-5.22092e6 - 8.93160e6i) q^{51} +(-2.65038e6 - 964661. i) q^{52} -1.57302e7 q^{53} +(4.18970e7 + 1.44880e7i) q^{54} -1.29475e6 q^{55} +(-7.19115e7 - 2.61736e7i) q^{56} +(1.26793e8 - 682036. i) q^{57} +(6.68814e7 + 5.61201e7i) q^{58} +(-9.54196e6 + 5.41151e7i) q^{59} +(-4.42512e6 - 2.43301e7i) q^{60} +(-1.28159e8 + 1.07538e8i) q^{61} +(-2.30623e7 - 3.99451e7i) q^{62} +(1.15505e8 + 4.06386e7i) q^{63} +(-5.91119e7 + 1.02385e8i) q^{64} +(1.33515e6 + 7.57200e6i) q^{65} +(-3.23712e6 - 2.68672e6i) q^{66} +(-8.32922e7 + 3.03159e7i) q^{67} +(-1.76202e7 + 6.41322e6i) q^{68} +(2.27835e8 - 8.43158e7i) q^{69} +(1.20211e7 + 6.81752e7i) q^{70} +(-1.20867e7 + 2.09349e7i) q^{71} +(1.18803e8 - 2.10983e8i) q^{72} +(2.09303e8 + 3.62523e8i) q^{73} +(7.26649e7 - 6.09731e7i) q^{74} +(1.57550e8 - 1.33651e8i) q^{75} +(3.99061e7 - 2.26319e8i) q^{76} +(-8.90105e6 - 7.46887e6i) q^{77} +(-1.23744e7 + 2.17019e7i) q^{78} +(-3.35813e8 - 1.22226e8i) q^{79} +4.66467e7 q^{80} +(-1.86447e8 + 3.39606e8i) q^{81} +2.14690e8 q^{82} +(-6.60595e8 - 2.40437e8i) q^{83} +(1.09928e8 - 1.92789e8i) q^{84} +(3.91574e7 + 3.28570e7i) q^{85} +(6.61152e7 - 3.74958e8i) q^{86} +(-5.81844e8 + 4.93583e8i) q^{87} +(-1.76016e7 + 1.47695e7i) q^{88} +(-1.19815e7 - 2.07526e7i) q^{89} +(-2.19023e8 + 2.35638e6i) q^{90} +(-3.45009e7 + 5.97572e7i) q^{91} +(-7.64594e7 - 4.33623e8i) q^{92} +(3.78037e8 - 1.39901e8i) q^{93} +(-3.29573e8 + 1.19955e8i) q^{94} +(-5.88695e8 + 2.14268e8i) q^{95} +(-5.63330e8 - 4.67549e8i) q^{96} +(-8.54190e7 - 4.84435e8i) q^{97} +(1.32792e7 - 2.30003e7i) q^{98} +(2.79073e7 - 2.39333e7i) 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−15.0855	−	5.49066i	−0.666690	−	0.242655i	−0.0135679	−	0.999908i	$-0.504319\pi$
$2$	−15.0855	−	5.49066i	−0.666690	−	0.242655i	−0.653122	+	0.757253i	$0.726541\pi$
$3$	69.4935	−	121.876i	0.495334	−	0.868702i
$3$	69.4935	−	121.876i	0.495334	−	0.868702i
$4$	−194.791	−	163.449i	−0.380450	−	0.319236i
$5$	−120.371	+	682.656i	−0.0861302	+	0.488469i	0.910977	+	0.412458i	$0.135330\pi$
$5$	−120.371	+	682.656i	−0.0861302	+	0.488469i	−0.997107	+	0.0760110i	$0.975782\pi$
$6$	−1717.52	+	1456.99i	−0.541030	+	0.458960i
$7$	−4765.46	+	3998.70i	−0.750178	+	0.629474i	−0.935550	−	0.353195i	$-0.885095\pi$
$7$	−4765.46	+	3998.70i	−0.750178	+	0.629474i	0.185372	+	0.982668i	$0.440651\pi$
$8$	6150.79	+	10653.5i	0.530917	+	0.919575i
$9$	−10024.3	−	16939.1i	−0.509288	−	0.860596i
$10$	5564.08	−	9637.27i	0.175952	−	0.304757i
$11$	324.344	+	1839.45i	0.00667943	+	0.0378809i	0.987965	−	0.154676i	$-0.0494332\pi$
$11$	324.344	+	1839.45i	0.00667943	+	0.0378809i	−0.981286	+	0.192557i	$0.938322\pi$
$12$	−33457.1	+	12381.6i	−0.465771	+	0.172370i
$13$	10423.0	−	3793.68i	0.101216	−	0.0368396i	−0.290916	−	0.956749i	$-0.593960\pi$
$13$	10423.0	−	3793.68i	0.101216	−	0.0368396i	0.392132	+	0.919909i	$0.371738\pi$
$14$	93844.8	−	34156.7i	0.652881	−	0.237629i
$15$	74834.1	+	62110.4i	0.381671	+	0.316777i
$16$	−11685.3	−	66270.8i	−0.0445760	−	0.252803i
$17$	36870.6	−	63861.7i	0.107068	−	0.185447i	−0.807513	−	0.589850i	$-0.799187\pi$
$17$	36870.6	−	63861.7i	0.107068	−	0.185447i	0.914581	+	0.404402i	$0.132520\pi$
$18$	58214.5	+	310575.i	0.130709	+	0.697332i
$19$	451882.	+	782682.i	0.795488	+	1.37782i	0.922529	+	0.385927i	$0.126118\pi$
$19$	451882.	+	782682.i	0.795488	+	1.37782i	−0.127042	+	0.991897i	$0.540548\pi$
$20$	135026.	−	113301.i	0.188705	−	0.158342i
$21$	156175.	+	858677.i	0.175237	+	0.963481i
$22$	5206.90	−	29529.8i	0.00473890	−	0.0268756i
$23$	1.32648e6	+	1.11305e6i	0.988382	+	0.829351i	0.985333	−	0.170644i	$-0.0545848\pi$
$23$	1.32648e6	+	1.11305e6i	0.988382	+	0.829351i	0.00304966	+	0.999995i	$0.499029\pi$
$24$	1.72584e6	−	9283.55i	1.06182	−	0.00571168i
$25$	1.38381e6	+	503665.i	0.708509	+	0.257876i
$26$	−178066.			−0.0764191
$27$	−2.76109e6	+	44560.4i	−0.999870	+	0.0161366i
$28$	1.58185e6			0.486356
$29$	−5.11051e6	−	1.86007e6i	−1.34175	−	0.488359i	−0.431390	−	0.902166i	$-0.641977\pi$
$29$	−5.11051e6	−	1.86007e6i	−1.34175	−	0.488359i	−0.910365	+	0.413807i	$0.864199\pi$
$30$	−787881.	−	1.34785e6i	−0.177588	−	0.303806i
$31$	2.20097e6	+	1.84683e6i	0.428042	+	0.359170i	0.831212	−	0.555955i	$-0.187647\pi$
$31$	2.20097e6	+	1.84683e6i	0.428042	+	0.359170i	−0.403171	+	0.915125i	$0.632092\pi$
$32$	906116.	−	5.13884e6i	0.152760	−	0.866344i
$33$	246724.	+	88300.0i	0.0362158	+	0.0129613i
$34$	−906854.	+	760941.i	−0.116381	+	0.0976552i
$35$	−2.15611e6	−	3.73450e6i	−0.242865	−	0.420655i
$36$	−816036.	+	4.93804e6i	−0.0809744	+	0.489997i
$37$	−2.95439e6	+	5.11715e6i	−0.259155	+	0.448870i	−0.966016	−	0.258483i	$-0.916777\pi$
$37$	−2.95439e6	+	5.11715e6i	−0.259155	+	0.448870i	0.706861	+	0.707353i	$0.250111\pi$
$38$	−2.51940e6	−	1.42883e7i	−0.196007	−	1.11161i
$39$	261977.	−	1.53395e6i	0.0181331	−	0.106175i
$40$	−8.01304e6	+	2.91651e6i	−0.494911	+	0.180133i
$41$	−1.25668e7	+	4.57393e6i	−0.694539	+	0.252791i	−0.665077	−	0.746775i	$-0.731601\pi$
$41$	−1.25668e7	+	4.57393e6i	−0.694539	+	0.252791i	−0.0294613	+	0.999566i	$0.509379\pi$
$42$	2.35873e6	−	1.38111e7i	0.116965	−	0.684865i
$43$	4.11840e6	+	2.33566e7i	0.183705	+	1.04184i	0.927608	+	0.373554i	$0.121861\pi$
$43$	4.11840e6	+	2.33566e7i	0.183705	+	1.04184i	−0.743904	+	0.668287i	$0.767028\pi$
$44$	237476.	−	411321.i	0.00955175	−	0.0165441i
$45$	1.27702e7	−	4.80418e6i	0.464239	−	0.174648i
$46$	−1.38992e7	−	2.40741e7i	−0.457698	−	0.792756i
$47$	1.67358e7	−	1.40430e7i	0.500272	−	0.419778i	−0.357419	−	0.933944i	$-0.616343\pi$
$47$	1.67358e7	−	1.40430e7i	0.500272	−	0.419778i	0.857690	+	0.514167i	$0.171899\pi$
$48$	−8.88885e6	−	3.18123e6i	−0.241691	−	0.0864988i
$49$	−287276.	+	1.62922e6i	−0.00711897	+	0.0403737i
$50$	−1.81099e7	−	1.51960e7i	−0.409781	−	0.343847i
$51$	−5.22092e6	−	8.93160e6i	−0.108064	−	0.184869i
$52$	−2.65038e6	−	964661.i	−0.0502682	−	0.0182961i
$53$	−1.57302e7			−0.273837			−0.136919	−	0.990582i	$-0.543720\pi$
$53$	−1.57302e7			−0.273837			−0.136919	+	0.990582i	$0.543720\pi$
$54$	4.18970e7	+	1.44880e7i	0.670519	+	0.231866i
$55$	−1.29475e6			−0.0190789
$56$	−7.19115e7	−	2.61736e7i	−0.977130	−	0.355646i
$57$	1.26793e8	−	682036.i	1.59095	−	0.00855797i
$58$	6.68814e7	+	5.61201e7i	0.776031	+	0.651167i
$59$	−9.54196e6	+	5.41151e7i	−0.102519	+	0.581413i	0.889664	+	0.456617i	$0.150939\pi$
$59$	−9.54196e6	+	5.41151e7i	−0.102519	+	0.581413i	−0.992182	+	0.124796i	$0.960172\pi$
$60$	−4.42512e6	−	2.43301e7i	−0.0440803	−	0.242361i
$61$	−1.28159e8	+	1.07538e8i	−1.18513	+	0.994438i	−0.185194	+	0.982702i	$0.559291\pi$
$61$	−1.28159e8	+	1.07538e8i	−1.18513	+	0.994438i	−0.999931	+	0.0117363i	$0.996264\pi$
$62$	−2.30623e7	−	3.99451e7i	−0.198217	−	0.343321i
$63$	1.15505e8	+	4.06386e7i	0.923779	+	0.325017i
$64$	−5.91119e7	+	1.02385e8i	−0.440418	+	0.762826i
$65$	1.33515e6	+	7.57200e6i	0.00927725	+	0.0526139i
$66$	−3.23712e6	−	2.68672e6i	−0.0209996	−	0.0174291i
$67$	−8.32922e7	+	3.03159e7i	−0.504973	+	0.183795i	−0.581929	−	0.813239i	$-0.697702\pi$
$67$	−8.32922e7	+	3.03159e7i	−0.504973	+	0.183795i	0.0769565	+	0.997034i	$0.475480\pi$
$68$	−1.76202e7	+	6.41322e6i	−0.0999355	+	0.0363736i
$69$	2.27835e8	−	8.43158e7i	1.21004	−	0.447804i
$70$	1.20211e7	+	6.81752e7i	0.0598417	+	0.339379i
$71$	−1.20867e7	+	2.09349e7i	−0.0564478	+	0.0977704i	−0.892868	−	0.450318i	$-0.851311\pi$
$71$	−1.20867e7	+	2.09349e7i	−0.0564478	+	0.0977704i	0.836421	+	0.548088i	$0.184644\pi$
$72$	1.18803e8	−	2.10983e8i	0.520993	−	0.925233i
$73$	2.09303e8	+	3.62523e8i	0.862626	+	1.49411i	0.869386	+	0.494134i	$0.164515\pi$
$73$	2.09303e8	+	3.62523e8i	0.862626	+	1.49411i	−0.00675978	+	0.999977i	$0.502152\pi$
$74$	7.26649e7	−	6.09731e7i	0.281697	−	0.236372i
$75$	1.57550e8	−	1.33651e8i	0.574967	−	0.487749i
$76$	3.99061e7	−	2.26319e8i	0.137207	−	0.778142i
$77$	−8.90105e6	−	7.46887e6i	−0.0288558	−	0.0242129i
$78$	−1.23744e7	+	2.17019e7i	−0.0378530	+	0.0663854i
$79$	−3.35813e8	−	1.22226e8i	−0.970009	−	0.353054i	−0.192061	−	0.981383i	$-0.561517\pi$
$79$	−3.35813e8	−	1.22226e8i	−0.970009	−	0.353054i	−0.777948	+	0.628329i	$0.783739\pi$
$80$	4.66467e7			0.127326
$81$	−1.86447e8	+	3.39606e8i	−0.481252	+	0.876582i
$82$	2.14690e8			0.524383
$83$	−6.60595e8	−	2.40437e8i	−1.52786	−	0.556096i	−0.564765	−	0.825252i	$-0.691033\pi$
$83$	−6.60595e8	−	2.40437e8i	−1.52786	−	0.556096i	−0.963097	+	0.269155i	$0.913255\pi$
$84$	1.09928e8	−	1.92789e8i	0.240909	−	0.422499i
$85$	3.91574e7	+	3.28570e7i	0.0813634	+	0.0682720i
$86$	6.61152e7	−	3.74958e8i	0.130334	−	0.739162i
$87$	−5.81844e8	+	4.93583e8i	−1.08886	+	0.923684i
$88$	−1.76016e7	+	1.47695e7i	−0.0312881	+	0.0262538i
$89$	−1.19815e7	−	2.07526e7i	−0.0202422	−	0.0350605i	0.855727	−	0.517428i	$-0.173110\pi$
$89$	−1.19815e7	−	2.07526e7i	−0.0202422	−	0.0350605i	−0.875969	+	0.482367i	$0.839777\pi$
$90$	−2.19023e8	+	2.35638e6i	−0.351883	+	0.00378577i
$91$	−3.45009e7	+	5.97572e7i	−0.0527404	+	0.0913491i
$92$	−7.64594e7	−	4.33623e8i	−0.111272	−	0.631054i
$93$	3.78037e8	−	1.39901e8i	0.524035	−	0.193932i
$94$	−3.29573e8	+	1.19955e8i	−0.435387	+	0.158468i
$95$	−5.88695e8	+	2.14268e8i	−0.741540	+	0.269898i
$96$	−5.63330e8	−	4.67549e8i	−0.676928	−	0.561833i
$97$	−8.54190e7	−	4.84435e8i	−0.0979674	−	0.555601i	−0.993798	−	0.111204i	$-0.964529\pi$
$97$	−8.54190e7	−	4.84435e8i	−0.0979674	−	0.555601i	0.895830	−	0.444396i	$-0.146582\pi$
$98$	1.32792e7	−	2.30003e7i	0.0145430	−	0.0251893i
$99$	2.79073e7	−	2.39333e7i	0.0291984	−	0.0250406i
$100$	−1.87229e8	−	3.24291e8i	−0.187229	−	0.324291i
$101$	7.24889e8	−	6.08254e8i	0.693147	−	0.581619i	−0.226668	−	0.973972i	$-0.572783\pi$
$101$	7.24889e8	−	6.08254e8i	0.693147	−	0.581619i	0.919815	+	0.392353i	$0.128339\pi$
$102$	2.97196e7	+	1.63404e8i	0.0271858	+	0.149472i
$103$	−8.28634e6	+	4.69942e7i	−0.00725430	+	0.0411412i	−0.988220	−	0.153040i	$-0.951094\pi$
$103$	−8.28634e6	+	4.69942e7i	−0.00725430	+	0.0411412i	0.980966	+	0.194181i	$0.0622049\pi$
$104$	1.04526e8	+	8.77076e7i	0.0876141	+	0.0735169i
$105$	−6.04980e8	+	3.25428e6i	−0.485723	+	0.00261278i
$106$	2.37297e8	+	8.63691e7i	0.182564	+	0.0664480i
$107$	1.53138e9			1.12942			0.564709	−	0.825290i	$-0.308988\pi$
$107$	1.53138e9			1.12942			0.564709	+	0.825290i	$0.308988\pi$
$108$	5.45118e8	+	4.42617e8i	0.385552	+	0.313055i
$109$	2.42520e9			1.64562			0.822808	−	0.568319i	$-0.192406\pi$
$109$	2.42520e9			1.64562			0.822808	+	0.568319i	$0.192406\pi$
$110$	1.95319e7	+	7.10904e6i	0.0127197	+	0.00462961i
$111$	4.18345e8	+	7.15676e8i	0.261566	+	0.447469i
$112$	3.20683e8	+	2.69085e8i	0.192573	+	0.161588i
$113$	−4.76625e8	+	2.70308e9i	−0.274995	+	1.55957i	0.463985	+	0.885843i	$0.346419\pi$
$113$	−4.76625e8	+	2.70308e9i	−0.274995	+	1.55957i	−0.738979	+	0.673728i	$0.764692\pi$
$114$	−1.91647e9	−	6.85887e8i	−1.06275	−	0.380347i
$115$	−9.19498e8	+	7.71550e8i	−0.490242	+	0.411362i
$116$	6.91452e8	+	1.19763e9i	0.354569	+	0.614132i
$117$	−1.68745e8	−	1.38528e8i	−0.0832521	−	0.0683442i
$118$	4.41073e8	−	7.63961e8i	0.209431	−	0.362745i
$119$	7.96584e7	+	4.51765e8i	0.0364142	+	0.206515i
$120$	−2.01403e8	+	1.17927e9i	−0.0886646	+	0.519157i
$121$	2.21247e9	−	8.05272e8i	0.938302	−	0.341514i
$122$	2.52379e9	−	9.18585e8i	1.03142	−	0.375405i
$123$	−3.15858e8	+	1.84944e9i	−0.124428	+	0.728564i
$124$	−1.26866e8	−	7.19491e8i	−0.0481889	−	0.273293i
$125$	−1.18734e9	+	2.05653e9i	−0.434991	+	0.753426i
$126$	−1.51931e9	−	1.24725e9i	−0.537007	−	0.440845i
$127$	−1.37316e9	−	2.37838e9i	−0.468387	−	0.811270i	0.530960	−	0.847397i	$-0.321831\pi$
$127$	−1.37316e9	−	2.37838e9i	−0.468387	−	0.811270i	−0.999347	+	0.0361268i	$0.988498\pi$
$128$	−5.92731e8	+	4.97360e8i	−0.195170	+	0.163767i
$129$	3.13280e9	+	1.12120e9i	0.996045	+	0.356475i
$130$	2.14340e7	−	1.21558e8i	0.00658199	−	0.0373283i
$131$	2.94768e9	+	2.47340e9i	0.874501	+	0.733793i	0.965041	−	0.262100i	$-0.0844149\pi$
$131$	2.94768e9	+	2.47340e9i	0.874501	+	0.733793i	−0.0905403	+	0.995893i	$0.528859\pi$
$132$	−3.36269e7	−	5.75267e7i	−0.00964061	−	0.0164925i
$133$	−5.28313e9	−	1.92290e9i	−1.46406	−	0.532875i
$134$	1.42296e9			0.381259
$135$	3.01935e8	−	1.89024e9i	0.0782368	−	0.489795i
$136$	9.07134e8			0.227377
$137$	−1.13594e9	−	4.13448e8i	−0.275494	−	0.100272i	0.200578	−	0.979678i	$-0.435718\pi$
$137$	−1.13594e9	−	4.13448e8i	−0.275494	−	0.100272i	−0.476073	+	0.879406i	$0.657940\pi$
$138$	−3.89995e9	+	2.09784e7i	−0.915383	+	0.00492398i
$139$	−2.86124e9	−	2.40087e9i	−0.650111	−	0.545508i	0.256993	−	0.966413i	$-0.417268\pi$
$139$	−2.86124e9	−	2.40087e9i	−0.650111	−	0.545508i	−0.907105	+	0.420905i	$0.861713\pi$
$140$	−1.90408e8	+	1.07986e9i	−0.0418899	+	0.237570i
$141$	−5.48470e8	−	3.01558e9i	−0.116860	−	0.642517i
$142$	2.97281e8	−	2.49448e8i	0.0613577	−	0.0514852i
$143$	1.03589e7	+	1.79422e7i	0.00207158	+	0.00358809i
$144$	−1.00543e9	+	8.62259e8i	−0.194859	+	0.167111i
$145$	1.88494e9	−	3.26482e9i	0.354113	−	0.613342i
$146$	−1.16694e9	−	6.61805e9i	−0.212550	−	1.20543i
$147$	1.78599e8	+	1.48232e8i	0.0315465	+	0.0261827i
$148$	1.41188e9	−	5.13882e8i	0.241891	−	0.0880411i
$149$	5.78552e9	−	2.10576e9i	0.961621	−	0.350002i	0.186953	−	0.982369i	$-0.440139\pi$
$149$	5.78552e9	−	2.10576e9i	0.961621	−	0.350002i	0.774669	+	0.632367i	$0.217917\pi$
$150$	−3.11055e9	+	1.15113e9i	−0.501679	+	0.185658i
$151$	−1.39179e9	−	7.89325e9i	−0.217860	−	1.23555i	−0.875873	−	0.482541i	$-0.839714\pi$
$151$	−1.39179e9	−	7.89325e9i	−0.217860	−	1.23555i	0.658013	−	0.753007i	$-0.271397\pi$
$152$	−5.55886e9	+	9.62823e9i	−0.844675	+	1.46302i
$153$	−1.45136e9	+	1.56147e7i	−0.214124	+	0.00230367i
$154$	9.32675e7	+	1.61544e8i	0.0133625	+	0.0231445i
$155$	−1.52568e9	+	1.28020e9i	−0.212310	+	0.178150i
$156$	−3.01753e8	+	2.55979e8i	−0.0407935	+	0.0346054i
$157$	−2.01351e9	+	1.14192e10i	−0.264487	+	1.49998i	0.506005	+	0.862531i	$0.331122\pi$
$157$	−2.01351e9	+	1.14192e10i	−0.264487	+	1.49998i	−0.770492	+	0.637450i	$0.779989\pi$
$158$	4.39480e9	+	3.68767e9i	0.561025	+	0.470756i
$159$	−1.09315e9	+	1.91713e9i	−0.135641	+	0.237883i
$160$	3.39899e9	+	1.23713e9i	0.410025	+	0.149237i
$161$	−1.07720e10			−1.26352
$162$	4.67730e9	−	4.09940e9i	0.533553	−	0.467630i
$163$	3.22524e9			0.357863			0.178932	−	0.983862i	$-0.442736\pi$
$163$	3.22524e9			0.357863			0.178932	+	0.983862i	$0.442736\pi$
$164$	3.19549e9	+	1.16306e9i	0.344938	+	0.125547i
$165$	−8.99768e7	+	1.57799e8i	−0.00945045	+	0.0165739i
$166$	8.64523e9	+	7.25421e9i	0.883671	+	0.741488i
$167$	3.17625e9	−	1.80134e10i	0.316003	−	1.79214i	−0.250537	−	0.968107i	$-0.580607\pi$
$167$	3.17625e9	−	1.80134e10i	0.316003	−	1.79214i	0.566540	−	0.824034i	$-0.308282\pi$
$168$	−8.18731e9	+	6.94536e9i	−0.792957	+	0.672671i
$169$	−8.02927e9	+	6.73736e9i	−0.757157	+	0.635330i
$170$	−4.10302e8	−	7.10664e8i	−0.0376776	−	0.0652595i
$171$	8.72814e9	−	1.55003e10i	0.780619	−	1.38630i
$172$	3.01538e9	−	5.22279e9i	0.262702	−	0.455014i
$173$	−3.04290e9	−	1.72571e10i	−0.258274	−	1.46474i	−0.787528	−	0.616280i	$-0.788639\pi$
$173$	−3.04290e9	−	1.72571e10i	−0.258274	−	1.46474i	0.529254	−	0.848464i	$-0.322472\pi$
$174$	1.14875e10	−	4.25122e9i	0.950066	−	0.351595i
$175$	−8.60849e9	+	3.13323e9i	−0.693834	+	0.252535i
$176$	1.18112e8	−	4.29891e7i	0.00927867	−	0.00337716i
$177$	5.93221e9	+	4.92358e9i	0.454294	+	0.377052i
$178$	6.68014e7	+	3.78850e8i	0.00498764	+	0.0282863i
$179$	−4.72871e9	+	8.19036e9i	−0.344274	+	0.596299i	−0.985222	−	0.171285i	$-0.945208\pi$
$179$	−4.72871e9	+	8.19036e9i	−0.344274	+	0.596299i	0.640948	+	0.767584i	$0.278541\pi$
$180$	−3.27276e9	−	1.15147e9i	−0.232374	−	0.0817570i
$181$	2.04977e8	+	3.55030e8i	0.0141955	+	0.0245874i	0.873036	−	0.487656i	$-0.162148\pi$
$181$	2.04977e8	+	3.55030e8i	0.0141955	+	0.0245874i	−0.858840	+	0.512243i	$0.828815\pi$
$182$	8.48569e8	−	7.12034e8i	0.0573279	−	0.0481038i
$183$	4.20006e9	+	2.30926e10i	0.276838	+	1.52210i
$184$	−3.69894e9	+	2.09778e10i	−0.237902	+	1.34921i
$185$	−3.13763e9	−	2.63278e9i	−0.196938	−	0.165250i
$186$	−6.47101e9	+	3.48085e7i	−0.396428	+	0.00213244i
$187$	1.29429e8	+	4.71083e7i	0.00774007	+	0.00281715i
$188$	−5.55528e9			−0.324337
$189$	1.29797e10	−	1.12531e10i	0.739922	−	0.641497i
$190$	1.00572e10			0.559869
$191$	−1.05592e10	−	3.84325e9i	−0.574093	−	0.208953i	0.0386260	−	0.999254i	$-0.487702\pi$
$191$	−1.05592e10	−	3.84325e9i	−0.574093	−	0.208953i	−0.612719	+	0.790301i	$0.709924\pi$
$192$	8.37031e9	+	1.43194e10i	0.444515	+	0.760446i
$193$	2.28388e10	+	1.91641e10i	1.18486	+	0.994213i	0.999934	+	0.0114604i	$0.00364803\pi$
$193$	2.28388e10	+	1.91641e10i	1.18486	+	0.994213i	0.184923	+	0.982753i	$0.440796\pi$
$194$	−1.37128e9	+	7.77694e9i	−0.0695056	+	0.394186i
$195$	1.01563e9	+	3.63483e8i	0.0503011	+	0.0180023i
$196$	3.22253e8	−	2.70403e8i	0.0155971	−	0.0130876i
$197$	−1.00716e10	−	1.74445e10i	−0.476432	−	0.825204i	0.523203	−	0.852208i	$-0.324737\pi$
$197$	−1.00716e10	−	1.74445e10i	−0.476432	−	0.825204i	−0.999635	+	0.0270035i	$0.991403\pi$
$198$	−5.52404e8	+	2.07816e8i	−0.0255425	+	0.00960915i
$199$	5.00295e9	−	8.66537e9i	0.226145	−	0.391695i	−0.730517	−	0.682894i	$-0.760721\pi$
$199$	5.00295e9	−	8.66537e9i	0.226145	−	0.391695i	0.956662	+	0.291199i	$0.0940543\pi$
$200$	3.14573e9	+	1.78403e10i	0.139023	+	0.788438i
$201$	−2.09350e9	+	1.22580e10i	−0.0904671	+	0.529711i
$202$	−1.42750e10	+	5.19568e9i	−0.603247	+	0.219564i
$203$	3.17918e10	−	1.15713e10i	1.31396	−	0.478243i
$204$	−4.42872e8	+	2.59315e9i	−0.0179037	+	0.104831i
$205$	−1.60975e9	−	9.12935e9i	−0.0636599	−	0.361033i
$206$	3.83033e8	−	6.63432e8i	0.0148195	−	0.0256681i
$207$	5.55701e9	−	3.36269e10i	0.210366	−	1.27298i
$208$	−3.73207e8	−	6.46413e8i	−0.0138250	−	0.0239456i
$209$	−1.29314e9	+	1.08507e9i	−0.0468799	+	0.0393369i
$210$	9.14428e9	+	3.27265e9i	0.324461	+	0.116121i
$211$	−2.73448e9	+	1.55080e10i	−0.0949739	+	0.538624i	0.899781	+	0.436341i	$0.143726\pi$
$211$	−2.73448e9	+	1.55080e10i	−0.0949739	+	0.538624i	−0.994755	+	0.102283i	$0.967385\pi$
$212$	3.06409e9	+	2.57108e9i	0.104181	+	0.0874186i
$213$	1.71150e9	+	2.92792e9i	0.0569729	+	0.0974654i
$214$	−2.31015e10	−	8.40827e9i	−0.752972	−	0.274059i
$215$	−1.64402e10			−0.524729
$216$	−1.74576e10	−	2.91411e10i	−0.545686	−	0.910888i
$217$	−1.78736e10			−0.547195
$218$	−3.65853e10	−	1.33160e10i	−1.09712	−	0.399318i
$219$	5.87279e10	−	3.15906e8i	1.72523	−	0.00928025i
$220$	2.52205e8	+	2.11625e8i	0.00725859	+	0.00609068i
$221$	1.42033e8	−	8.05509e8i	0.00400520	−	0.0227146i
$222$	−2.38139e9	−	1.30933e10i	−0.0658025	−	0.361794i
$223$	−3.86647e10	+	3.24436e10i	−1.04699	+	0.878530i	−0.992774	−	0.119999i	$-0.961711\pi$
$223$	−3.86647e10	+	3.24436e10i	−1.04699	+	0.878530i	−0.0542175	+	0.998529i	$0.517266\pi$
$224$	1.62306e10	+	2.81122e10i	0.430744	+	0.746070i
$225$	−5.34008e9	−	2.84894e10i	−0.138908	−	0.741074i
$226$	2.20318e10	−	3.81602e10i	0.561774	−	0.973022i
$227$	−9.26362e9	−	5.25366e10i	−0.231561	−	1.31325i	−0.849737	−	0.527206i	$-0.823240\pi$
$227$	−9.26362e9	−	5.25366e10i	−0.231561	−	1.31325i	0.618177	−	0.786039i	$-0.287872\pi$
$228$	−2.48095e10	−	2.05912e10i	−0.608011	−	0.504633i
$229$	−5.03167e10	+	1.83138e10i	−1.20907	+	0.440067i	−0.866382	−	0.499382i	$-0.833561\pi$
$229$	−5.03167e10	+	1.83138e10i	−1.20907	+	0.440067i	−0.342691	+	0.939448i	$0.611338\pi$
$230$	1.81074e10	−	6.59055e9i	0.426658	−	0.155291i
$231$	−1.52884e9	+	5.65783e8i	−0.0353271	+	0.0130736i
$232$	−1.16174e10	−	6.58856e10i	−0.263277	−	1.49312i
$233$	−2.69059e10	+	4.66024e10i	−0.598062	+	1.03587i	0.395045	+	0.918662i	$0.370729\pi$
$233$	−2.69059e10	+	4.66024e10i	−0.598062	+	1.03587i	−0.993107	+	0.117212i	$0.962604\pi$
$234$	1.78499e9	+	3.01629e9i	0.0389193	+	0.0657660i
$235$	7.57203e9	+	1.31151e10i	0.161960	+	0.280523i
$236$	1.07037e10	−	8.98150e9i	0.224611	−	0.188471i
$237$	−3.82332e10	+	3.24335e10i	−0.787178	+	0.667769i
$238$	1.27881e9	−	7.25247e9i	0.0258350	−	0.146518i
$239$	8.68524e9	+	7.28778e9i	0.172183	+	0.144479i	0.724807	−	0.688952i	$-0.241929\pi$
$239$	8.68524e9	+	7.28778e9i	0.172183	+	0.144479i	−0.552624	+	0.833431i	$0.686373\pi$
$240$	3.24164e9	−	5.68510e9i	0.0630688	−	0.110608i
$241$	2.83803e10	+	1.03296e10i	0.541926	+	0.197245i	0.598456	−	0.801156i	$-0.295781\pi$
$241$	2.83803e10	+	1.03296e10i	0.541926	+	0.197245i	−0.0565294	+	0.998401i	$0.518003\pi$
$242$	−3.77976e10			−0.708427
$243$	2.84328e10	+	4.63237e10i	0.523109	+	0.852266i
$244$	4.25411e10			0.768342
$245$	−1.07762e9	−	3.92222e8i	−0.0191081	−	0.00695479i
$246$	1.49195e10	−	2.61654e10i	0.259745	−	0.455533i
$247$	7.67922e9	+	6.44363e9i	0.131275	+	0.110153i
$248$	−6.13750e9	+	3.48075e10i	−0.103029	+	0.584305i
$249$	−7.52105e10	+	6.38016e10i	−1.23988	+	1.05180i
$250$	2.92033e10	−	2.45045e10i	0.472827	−	0.396749i
$251$	2.83546e10	+	4.91116e10i	0.450912	+	0.781003i	0.998443	−	0.0557827i	$-0.0177654\pi$
$251$	2.83546e10	+	4.91116e10i	0.450912	+	0.781003i	−0.547531	+	0.836786i	$0.684432\pi$
$252$	−1.58570e10	−	2.67951e10i	−0.247695	−	0.418556i
$253$	−1.61716e9	+	2.80100e9i	−0.0248148	+	0.0429804i
$254$	7.65587e9	+	4.34186e10i	0.115410	+	0.654522i
$255$	6.72565e9	−	2.48899e9i	0.0996102	−	0.0368631i
$256$	6.85526e10	−	2.49511e10i	0.997571	−	0.363086i
$257$	3.34957e10	−	1.21915e10i	0.478950	−	0.174324i	−0.0912521	−	0.995828i	$-0.529087\pi$
$257$	3.34957e10	−	1.21915e10i	0.478950	−	0.174324i	0.570203	+	0.821504i	$0.306865\pi$
$258$	−4.11036e10	−	3.41150e10i	−0.577553	−	0.479354i
$259$	−6.38291e9	−	3.61993e10i	−0.0881394	−	0.499863i
$260$	9.77559e8	−	1.69318e9i	0.0132667	−	0.0229786i
$261$	1.97213e10	+	1.05213e11i	0.263059	+	1.40342i
$262$	−3.08866e10	−	5.34972e10i	−0.404962	−	0.701415i
$263$	6.96816e10	−	5.84698e10i	0.898084	−	0.753582i	−0.0717309	−	0.997424i	$-0.522852\pi$
$263$	6.96816e10	−	5.84698e10i	0.898084	−	0.753582i	0.969815	+	0.243842i	$0.0784078\pi$
$264$	5.76843e8	+	3.17158e9i	0.00730870	+	0.0401845i
$265$	1.89345e9	−	1.07383e10i	0.0235857	−	0.133761i
$266$	6.91406e10	+	5.80158e10i	0.846770	+	0.710525i
$267$	−3.36187e9	+	1.80840e7i	−0.0404838	+	0.000217768i
$268$	2.11796e10	+	7.70876e9i	0.250791	+	0.0912805i
$269$	9.42602e10			1.09760			0.548799	−	0.835954i	$-0.315085\pi$
$269$	9.42602e10			1.09760			0.548799	+	0.835954i	$0.315085\pi$
$270$	−1.49335e10	+	2.68573e10i	−0.171011	+	0.307557i
$271$	5.12096e10			0.576752			0.288376	−	0.957517i	$-0.406885\pi$
$271$	5.12096e10			0.576752			0.288376	+	0.957517i	$0.406885\pi$
$272$	−4.66302e9	−	1.69720e9i	−0.0516543	−	0.0188006i
$273$	4.88536e9	+	8.35755e9i	0.0532310	+	0.0910641i
$274$	1.48661e10	+	1.24741e10i	0.159338	+	0.133700i
$275$	−4.77635e8	+	2.70880e9i	−0.00503615	+	0.0285614i
$276$	−5.81614e10	−	2.08154e10i	−0.603315	−	0.215921i
$277$	−1.44358e11	+	1.21131e11i	−1.47327	+	1.23622i	−0.560234	+	0.828334i	$0.689289\pi$
$277$	−1.44358e11	+	1.21131e11i	−1.47327	+	1.23622i	−0.913034	+	0.407884i	$0.866267\pi$
$278$	2.99808e10	+	5.19283e10i	0.301052	+	0.521438i
$279$	9.22051e9	−	5.57957e10i	0.0911037	−	0.551292i
$280$	2.65236e10	−	4.59403e10i	0.257882	−	0.446665i
$281$	−1.48438e9	−	8.41832e9i	−0.0142025	−	0.0805466i	0.976883	−	0.213776i	$-0.0685763\pi$
$281$	−1.48438e9	−	8.41832e9i	−0.0142025	−	0.0805466i	−0.991085	+	0.133230i	$0.957465\pi$
$282$	−8.28361e9	+	4.85029e10i	−0.0780007	+	0.456717i
$283$	1.32973e11	−	4.83981e10i	1.23232	−	0.448528i	0.357928	−	0.933749i	$-0.383483\pi$
$283$	1.32973e11	−	4.83981e10i	1.23232	−	0.448528i	0.874391	+	0.485221i	$0.161261\pi$
$284$	5.77616e9	−	2.10235e9i	0.0526874	−	0.0191767i
$285$	−1.47965e10	+	8.66378e10i	−0.132849	+	0.777867i
$286$	−5.77548e7	−	3.27544e8i	−0.000510435	−	0.00289482i
$287$	4.15967e10	−	7.20477e10i	0.361902	−	0.626832i
$288$	−9.61306e10	+	3.61645e10i	−0.823371	+	0.309754i
$289$	5.65751e10	+	9.79909e10i	0.477073	+	0.826314i
$290$	−4.63613e10	+	3.89017e10i	−0.384915	+	0.322982i
$291$	−6.49769e10	−	2.32546e10i	−0.531178	−	0.190104i
$292$	1.84837e10	−	1.04826e11i	0.148788	−	0.843817i
$293$	−9.65019e10	−	8.09747e10i	−0.764947	−	0.641867i	0.174462	−	0.984664i	$-0.444181\pi$
$293$	−9.65019e10	−	8.09747e10i	−0.764947	−	0.641867i	−0.939409	+	0.342797i	$0.888626\pi$
$294$	−1.88035e9	−	3.21678e9i	−0.0146783	−	0.0251107i
$295$	−3.57934e10	−	1.30277e10i	−0.275172	−	0.100154i
$296$	−7.26873e10			−0.550359
$297$	−9.77510e8	−	5.06443e9i	−0.00728983	−	0.0377682i
$298$	−9.88393e10			−0.726033
$299$	1.80485e10	+	6.56911e9i	0.130593	+	0.0475320i
$300$	−5.25343e10	+	2.82590e8i	−0.374453	+	0.00201424i
$301$	−1.13022e11	−	9.48368e10i	−0.793623	−	0.665928i
$302$	−2.23433e10	+	1.26715e11i	−0.154567	+	0.876592i
$303$	−2.37563e10	−	1.30616e11i	−0.161915	−	0.890235i
$304$	4.65886e10	−	3.90925e10i	0.312859	−	0.262520i
$305$	−5.79849e10	−	1.00433e11i	−0.383677	−	0.664548i
$306$	2.19802e10	+	7.73339e9i	0.143313	+	0.0504224i
$307$	−7.86733e9	+	1.36266e10i	−0.0505481	+	0.0875518i	−0.890192	−	0.455585i	$-0.849430\pi$
$307$	−7.86733e9	+	1.36266e10i	−0.0505481	+	0.0875518i	0.839644	+	0.543137i	$0.182763\pi$
$308$	5.13064e8	+	2.90973e9i	0.00324858	+	0.0184236i
$309$	5.15160e9	+	4.27569e9i	0.0321461	+	0.0266805i
$310$	3.00448e10	−	1.09354e10i	0.184774	−	0.0672523i
$311$	−1.30646e11	+	4.75514e10i	−0.791909	+	0.288231i	−0.706129	−	0.708083i	$-0.749560\pi$
$311$	−1.30646e11	+	4.75514e10i	−0.791909	+	0.288231i	−0.0857796	+	0.996314i	$0.527338\pi$
$312$	1.79533e10	−	6.64404e9i	0.107263	−	0.0396951i
$313$	−1.73134e10	−	9.81890e10i	−0.101961	−	0.578247i	−0.992391	−	0.123127i	$-0.960708\pi$
$313$	−1.73134e10	−	9.81890e10i	−0.101961	−	0.578247i	0.890430	−	0.455120i	$-0.150403\pi$
$314$	9.30734e10	−	1.61208e11i	0.540309	−	0.935843i
$315$	−4.16455e10	+	7.39584e10i	−0.238326	+	0.423243i
$316$	4.54356e10	+	7.86967e10i	0.256333	+	0.443981i
$317$	−1.84111e10	+	1.54488e10i	−0.102403	+	0.0859266i	−0.692552	−	0.721368i	$-0.743514\pi$
$317$	−1.84111e10	+	1.54488e10i	−0.102403	+	0.0859266i	0.590149	+	0.807295i	$0.299069\pi$
$318$	2.70169e10	−	2.29186e10i	0.148154	−	0.125680i
$319$	1.76394e9	−	1.00038e10i	0.00953732	−	0.0540888i
$320$	−6.27782e10	−	5.26772e10i	−0.334683	−	0.280833i
$321$	1.06421e11	−	1.86637e11i	0.559440	−	0.981128i
$322$	1.62501e11	+	5.91456e10i	0.842374	+	0.306599i
$323$	6.66446e10			0.340685
$324$	9.18263e10	−	3.56776e10i	0.462929	−	0.179863i
$325$	1.63342e10			0.0812126
$326$	−4.86542e10	−	1.77087e10i	−0.238584	−	0.0868374i
$327$	1.68536e11	−	2.95573e11i	0.815131	−	1.42955i
$328$	−1.26024e11	−	1.05747e11i	−0.601203	−	0.504469i
$329$	−2.36001e10	+	1.33843e11i	−0.111053	+	0.629816i
$330$	2.22376e9	−	1.88643e9i	0.0103223	−	0.00875646i
$331$	−1.32636e11	+	1.11295e11i	−0.607346	+	0.509624i	−0.893797	−	0.448471i	$-0.851969\pi$
$331$	−1.32636e11	+	1.11295e11i	−0.607346	+	0.509624i	0.286452	+	0.958095i	$0.407524\pi$
$332$	8.93787e10	+	1.54808e11i	0.403750	+	0.699315i
$333$	1.16296e11	−	1.25118e9i	0.518280	−	0.00557597i
$334$	−1.46821e11	+	2.54301e11i	−0.645549	+	1.11812i
$335$	−1.06694e10	−	6.05091e10i	−0.0462847	−	0.262494i
$336$	5.50803e10	−	2.03838e10i	0.235760	−	0.0872485i
$337$	−2.78034e11	+	1.01196e11i	−1.17426	+	0.427394i	−0.854170	−	0.519994i	$-0.825934\pi$
$337$	−2.78034e11	+	1.01196e11i	−1.17426	+	0.427394i	−0.320086	+	0.947389i	$0.603712\pi$
$338$	1.58118e11	−	5.75502e10i	0.658955	−	0.239840i
$339$	2.96317e11	+	2.45935e11i	1.21859	+	1.01140i
$340$	−2.25707e9	−	1.28005e10i	−0.00915988	−	0.0519482i
$341$	−2.68328e9	+	4.64758e9i	−0.0107466	+	0.0186137i
$342$	−2.16775e11	+	1.85906e11i	−0.856825	+	0.734813i
$343$	−1.30663e11	−	2.26315e11i	−0.509717	−	0.882856i
$344$	−2.23498e11	+	1.87537e11i	−0.860519	+	0.722061i
$345$	3.01340e10	+	1.65682e11i	0.114517	+	0.629636i
$346$	−4.88496e10	+	2.77040e11i	−0.183239	+	1.03920i
$347$	−3.88445e11	−	3.25944e11i	−1.43829	−	1.20687i	−0.940601	−	0.339515i	$-0.889737\pi$
$347$	−3.88445e11	−	3.25944e11i	−1.43829	−	1.20687i	−0.497691	−	0.867355i	$-0.665818\pi$
$348$	1.94013e11	−	1.04363e9i	0.709129	−	0.00381451i
$349$	4.20060e11	+	1.52889e11i	1.51564	+	0.551649i	0.960055	−	0.279810i	$-0.0902715\pi$
$349$	4.20060e11	+	1.52889e11i	1.51564	+	0.551649i	0.555587	+	0.831459i	$0.312494\pi$
$350$	1.47067e11			0.523851
$351$	−2.86099e10	+	1.09391e10i	−0.100608	+	0.0384681i
$352$	9.74652e9			0.0338382
$353$	3.65490e11	+	1.33027e11i	1.25282	+	0.455990i	0.881354	−	0.472456i	$-0.156633\pi$
$353$	3.65490e11	+	1.33027e11i	1.25282	+	0.455990i	0.371467	+	0.928446i	$0.378855\pi$
$354$	−6.24564e10	−	1.06846e11i	−0.211379	−	0.361614i
$355$	−1.28364e10	−	1.07710e10i	−0.0428959	−	0.0359940i
$356$	−1.05810e9	+	6.00078e9i	−0.00349142	+	0.0198008i
$357$	6.05949e10	+	2.16863e10i	0.197437	+	0.0706609i
$358$	1.16305e11	−	9.75917e10i	0.374219	−	0.314007i
$359$	−1.42682e11	−	2.47133e11i	−0.453362	−	0.785246i	0.545230	−	0.838286i	$-0.316442\pi$
$359$	−1.42682e11	−	2.47133e11i	−0.453362	−	0.785246i	−0.998592	+	0.0530402i	$0.983109\pi$
$360$	1.29728e11	+	1.06498e11i	0.407074	+	0.334179i
$361$	−2.47050e11	+	4.27903e11i	−0.765601	+	1.32606i
$362$	−1.14282e9	−	6.48126e9i	−0.00349776	−	0.0198368i
$363$	5.56091e10	−	3.25607e11i	0.168099	−	0.984269i
$364$	1.64877e10	−	6.00103e9i	0.0492270	−	0.0179172i
$365$	−2.72673e11	+	9.92447e10i	−0.804125	+	0.292678i
$366$	6.34340e10	−	3.71424e11i	0.184781	−	1.08195i
$367$	3.40606e10	+	1.93167e11i	0.0980066	+	0.555823i	0.993784	+	0.111321i	$0.0355082\pi$
$367$	3.40606e10	+	1.93167e11i	0.0980066	+	0.555823i	−0.895778	+	0.444502i	$0.853381\pi$
$368$	5.82622e10	−	1.00913e11i	0.165604	−	0.286835i
$369$	2.03452e11	+	1.67020e11i	0.571271	+	0.468974i
$370$	3.28769e10	+	5.69445e10i	0.0911976	+	0.157959i
$371$	7.49616e10	−	6.29003e10i	0.205426	−	0.172373i
$372$	−9.65047e10	−	3.45381e10i	−0.261279	−	0.0935094i
$373$	8.64497e10	−	4.90281e11i	0.231246	−	1.31146i	−0.619132	−	0.785287i	$-0.712515\pi$
$373$	8.64497e10	−	4.90281e11i	0.231246	−	1.31146i	0.850378	−	0.526173i	$-0.176373\pi$
$374$	−1.69384e9	−	1.42130e9i	−0.00447663	−	0.00375634i
$375$	1.68129e11	+	2.87623e11i	0.439037	+	0.751075i
$376$	2.52545e11	+	9.19190e10i	0.651619	+	0.237170i
$377$	−6.03235e10			−0.153798
$378$	−2.57592e11	+	9.84915e10i	−0.648961	+	0.248134i
$379$	−1.41929e11			−0.353341			−0.176670	−	0.984270i	$-0.556533\pi$
$379$	−1.41929e11			−0.353341			−0.176670	+	0.984270i	$0.556533\pi$
$380$	1.49694e11	+	5.44842e10i	0.368280	+	0.134043i
$381$	−3.85293e11	+	2.07255e9i	−0.936760	+	0.00503897i
$382$	1.38189e11	+	1.15954e11i	0.332038	+	0.278613i
$383$	3.19474e10	−	1.81183e11i	0.0758650	−	0.430252i	−0.923092	−	0.384580i	$-0.874346\pi$
$383$	3.19474e10	−	1.81183e11i	0.0758650	−	0.430252i	0.998957	−	0.0456715i	$-0.0145427\pi$
$384$	1.94251e10	+	1.06803e11i	0.0455904	+	0.250664i
$385$	6.17009e9	−	5.17732e9i	0.0143126	−	0.0120097i
$386$	−2.39311e11	−	4.14499e11i	−0.548681	−	0.950344i
$387$	3.54356e11	−	3.03896e11i	0.803046	−	0.688692i
$388$	−6.25415e10	+	1.08325e11i	−0.140096	+	0.242653i
$389$	1.24691e11	+	7.07158e11i	0.276097	+	1.56582i	0.735455	+	0.677573i	$0.236968\pi$
$389$	1.24691e11	+	7.07158e11i	0.276097	+	1.56582i	−0.459358	+	0.888251i	$0.651921\pi$
$390$	−1.33254e10	−	1.10598e10i	−0.0291669	−	0.0242078i
$391$	1.19989e11	−	4.36725e10i	0.259625	−	0.0944958i
$392$	−1.91239e10	+	6.96053e9i	−0.0409062	+	0.0148886i
$393$	5.06292e11	−	1.87365e11i	1.07062	−	0.396208i
$394$	5.61529e10	+	3.18459e11i	0.117392	+	0.665764i
$395$	1.23860e11	−	2.14532e11i	0.256003	−	0.443410i
$396$	−9.34795e9	+	1.00571e8i	−0.0191024	+	0.000205515i
$397$	−1.21543e9	−	2.10519e9i	−0.00245569	−	0.00425337i	0.864795	−	0.502125i	$-0.167448\pi$
$397$	−1.21543e9	−	2.10519e9i	−0.00245569	−	0.00425337i	−0.867251	+	0.497872i	$0.834115\pi$
$398$	−1.23051e11	+	1.03252e11i	−0.245816	+	0.206264i
$399$	−6.01498e11	+	5.10256e11i	−1.18811	+	1.00788i
$400$	1.72080e10	−	9.75915e10i	0.0336094	−	0.190608i
$401$	−6.10998e11	−	5.12688e11i	−1.18002	−	0.990155i	−0.999979	−	0.00649664i	$-0.997932\pi$
$401$	−6.10998e11	−	5.12688e11i	−1.18002	−	0.990155i	−0.180042	−	0.983659i	$-0.557624\pi$
$402$	9.88863e10	−	1.73424e11i	0.188851	−	0.331201i
$403$	2.99471e10	+	1.08998e10i	0.0565564	+	0.0205848i
$404$	−2.40620e11			−0.449382
$405$	−2.09391e11	−	1.68158e11i	−0.386733	−	0.310577i
$406$	−5.43128e11			−0.992054
$407$	−1.03710e10	−	3.77472e9i	−0.0187346	−	0.00681884i
$408$	6.30399e10	−	1.10557e11i	0.112628	−	0.197523i
$409$	3.12103e11	+	2.61885e11i	0.551496	+	0.462760i	0.875447	−	0.483314i	$-0.160567\pi$
$409$	3.12103e11	+	2.61885e11i	0.551496	+	0.462760i	−0.323951	+	0.946074i	$0.605011\pi$
$410$	−2.58423e10	+	1.46559e11i	−0.0451652	+	0.256145i
$411$	−1.29330e11	+	1.09711e11i	−0.223568	+	0.189654i
$412$	9.29525e9	−	7.79964e9i	0.0158936	−	0.0133363i
$413$	−1.70918e11	−	2.96039e11i	−0.289077	−	0.500696i
$414$	−2.68464e11	+	4.76766e11i	−0.449143	+	0.797634i
$415$	2.43652e11	−	4.22018e11i	0.403231	−	0.698416i
$416$	−1.00506e10	−	5.69999e10i	−0.0164540	−	0.0933155i
$417$	−4.91444e11	+	1.81871e11i	−0.795907	+	0.294544i
$418$	2.54653e10	−	9.26863e9i	0.0407996	−	0.0148499i
$419$	1.01847e12	−	3.70693e11i	1.61431	−	0.587559i	0.632021	−	0.774952i	$-0.282226\pi$
$419$	1.01847e12	−	3.70693e11i	1.61431	−	0.587559i	0.982285	+	0.187392i	$0.0600036\pi$
$420$	1.18376e11	+	9.82493e10i	0.185628	+	0.154066i
$421$	−3.75761e10	−	2.13104e11i	−0.0582964	−	0.330615i	0.941686	−	0.336492i	$-0.109241\pi$
$421$	−3.75761e10	−	2.13104e11i	−0.0582964	−	0.330615i	−0.999983	+	0.00587664i	$0.998129\pi$
$422$	1.26400e11	−	2.18932e11i	0.194018	−	0.336049i
$423$	−4.05641e11	−	1.42718e11i	−0.616041	−	0.216744i
$424$	−9.67531e10	−	1.67581e11i	−0.145385	−	0.251814i
$425$	8.31867e10	−	6.98019e10i	0.123681	−	0.103781i
$426$	−9.74256e9	−	5.35663e10i	−0.0143328	−	0.0788040i
$427$	1.80724e11	−	1.02494e12i	0.263082	−	1.49201i
$428$	−2.98298e11	−	2.50301e11i	−0.429688	−	0.360551i
$429$	2.90659e9	−	1.56350e7i	0.00414311	−	2.22864e-5i
$430$	2.48009e11	+	9.02679e10i	0.349832	+	0.127328i
$431$	3.38561e11			0.472595			0.236297	−	0.971681i	$-0.424066\pi$
$431$	3.38561e11			0.472595			0.236297	+	0.971681i	$0.424066\pi$
$432$	3.52173e10	+	1.82459e11i	0.0486496	+	0.252051i
$433$	−6.24887e11			−0.854291			−0.427145	−	0.904183i	$-0.640481\pi$
$433$	−6.24887e11			−0.854291			−0.427145	+	0.904183i	$0.640481\pi$
$434$	2.69631e11	+	9.81377e10i	0.364810	+	0.132780i
$435$	−2.66910e11	−	4.56612e11i	−0.357408	−	0.611429i
$436$	−4.72407e11	−	3.96396e11i	−0.626076	−	0.525340i
$437$	−2.71751e11	+	1.54118e12i	−0.356455	+	2.02156i
$438$	−8.87673e11	−	3.17690e11i	−1.15244	−	0.412448i
$439$	4.26934e11	−	3.58240e11i	0.548618	−	0.460345i	−0.325855	−	0.945420i	$-0.605652\pi$
$439$	4.26934e11	−	3.58240e11i	0.548618	−	0.460345i	0.874473	+	0.485075i	$0.161208\pi$
$440$	−7.96375e9	−	1.37936e10i	−0.0101293	−	0.0175445i
$441$	3.04774e10	−	1.14656e10i	0.0383711	−	0.0144353i
$442$	−6.56541e9	+	1.13716e10i	−0.00818204	+	0.0141717i
$443$	1.98189e11	+	1.12399e12i	0.244491	+	1.38658i	0.821671	+	0.569962i	$0.193042\pi$
$443$	1.98189e11	+	1.12399e12i	0.244491	+	1.38658i	−0.577180	+	0.816617i	$0.695847\pi$
$444$	3.54867e10	−	2.07785e11i	0.0433354	−	0.253741i
$445$	1.56091e10	−	5.68125e9i	0.0188694	−	0.00686790i
$446$	7.61412e11	−	2.77131e11i	0.911199	−	0.331649i
$447$	1.45416e11	−	8.51450e11i	0.172277	−	1.00873i
$448$	−1.27710e11	−	7.24282e11i	−0.149787	−	0.849486i
$449$	−6.70551e11	+	1.16143e12i	−0.778616	+	1.34860i	0.154123	+	0.988052i	$0.450745\pi$
$449$	−6.70551e11	+	1.16143e12i	−0.778616	+	1.34860i	−0.932739	+	0.360551i	$0.882589\pi$
$450$	−7.58679e10	+	4.59096e11i	−0.0872171	+	0.527773i
$451$	−1.24895e10	−	2.16324e10i	−0.0142151	−	0.0246213i
$452$	5.34657e11	−	4.48630e11i	0.602493	−	0.505552i
$453$	−1.05871e12	−	3.78904e11i	−1.18124	−	0.422753i
$454$	−1.48715e11	+	8.43403e11i	−0.164287	+	0.931717i
$455$	−3.66407e10	−	3.07452e10i	−0.0400786	−	0.0336300i
$456$	7.87141e11	+	1.34659e12i	0.852533	+	1.45846i
$457$	2.86391e11	+	1.04238e11i	0.307140	+	0.111790i	0.490992	−	0.871164i	$-0.336634\pi$
$457$	2.86391e11	+	1.04238e11i	0.307140	+	0.111790i	−0.183852	+	0.982954i	$0.558857\pi$
$458$	8.59606e11			0.912861
$459$	−9.89573e10	+	1.77971e11i	−0.104062	+	0.187151i
$460$	3.05218e11			0.317834
$461$	5.78937e11	+	2.10716e11i	0.597004	+	0.217292i	0.622807	−	0.782375i	$-0.285992\pi$
$461$	5.78937e11	+	2.10716e11i	0.597004	+	0.217292i	−0.0258033	+	0.999667i	$0.508214\pi$
$462$	2.61698e10	−	1.40771e8i	0.0267246	−	0.000143755i
$463$	−4.66527e11	−	3.91463e11i	−0.471805	−	0.395891i	0.375648	−	0.926763i	$-0.377420\pi$
$463$	−4.66527e11	−	3.91463e11i	−0.471805	−	0.395891i	−0.847452	+	0.530871i	$0.821865\pi$
$464$	−6.35505e10	+	3.60413e11i	−0.0636485	+	0.360969i
$465$	5.00001e10	+	2.74909e11i	0.0495943	+	0.272678i
$466$	6.61767e11	−	5.55288e11i	0.650083	−	0.545484i
$467$	8.48195e11	+	1.46912e12i	0.825220	+	1.42932i	0.901751	+	0.432255i	$0.142282\pi$
$467$	8.48195e11	+	1.46912e12i	0.825220	+	1.42932i	−0.0765316	+	0.997067i	$0.524385\pi$
$468$	1.02278e10	+	5.45652e10i	0.00985540	+	0.0525787i
$469$	2.75702e11	−	4.77530e11i	0.263125	−	0.455746i
$470$	−4.22168e10	−	2.39424e11i	−0.0399067	−	0.226322i
$471$	1.25179e12	+	1.03895e12i	1.17203	+	0.972752i
$472$	−6.35206e11	+	2.31196e11i	−0.589081	+	0.214408i
$473$	−4.16275e10	+	1.51512e10i	−0.0382388	+	0.0139178i
$474$	7.54847e11	−	2.79349e11i	0.686841	−	0.254182i
$475$	2.31108e11	+	1.31068e12i	0.208302	+	1.18134i
$476$	5.83238e10	−	1.01020e11i	0.0520732	−	0.0901934i
$477$	1.57684e11	+	2.66455e11i	0.139462	+	0.235663i
$478$	−9.10062e10	−	1.57627e11i	−0.0797343	−	0.138104i
$479$	−1.19631e11	+	1.00382e11i	−0.103833	+	0.0871260i	−0.693226	−	0.720720i	$-0.743811\pi$
$479$	−1.19631e11	+	1.00382e11i	−0.103833	+	0.0871260i	0.589393	+	0.807846i	$0.299367\pi$
$480$	3.86984e11	−	3.28281e11i	0.332742	−	0.282267i
$481$	−1.13809e10	+	6.45443e10i	−0.00969446	+	0.0549800i
$482$	−3.71414e11	−	3.11653e11i	−0.313434	−	0.263003i
$483$	−7.48586e11	+	1.31285e12i	−0.625863	+	1.09762i
$484$	−5.62589e11	−	2.04766e11i	−0.466001	−	0.169611i
$485$	3.40984e11			0.279831
$486$	−1.74575e11	−	8.54930e11i	−0.141944	−	0.695132i
$487$	9.68948e11			0.780585			0.390292	−	0.920691i	$-0.372374\pi$
$487$	9.68948e11			0.780585			0.390292	+	0.920691i	$0.372374\pi$
$488$	−1.93393e12	−	7.03894e11i	−1.54366	−	0.561847i
$489$	2.24133e11	−	3.93077e11i	0.177262	−	0.310877i
$490$	1.41028e10	+	1.18337e10i	0.0110516	+	0.00927338i
$491$	−1.15815e11	+	6.56822e11i	−0.0899290	+	0.510013i	0.906255	+	0.422732i	$0.138929\pi$
$491$	−1.15815e11	+	6.56822e11i	−0.0899290	+	0.510013i	−0.996184	+	0.0872808i	$0.972182\pi$
$492$	3.63815e11	−	3.08627e11i	0.279922	−	0.237460i
$493$	−3.07215e11	+	2.57784e11i	−0.234224	+	0.196537i
$494$	−8.04649e10	−	1.39369e11i	−0.0607904	−	0.105292i
$495$	1.29790e10	+	2.19319e10i	0.00971667	+	0.0164193i
$496$	9.66720e10	−	1.67441e11i	0.0717188	−	0.124221i
$497$	−2.61133e10	−	1.48096e11i	−0.0191981	−	0.108878i
$498$	1.48490e12	−	5.49522e11i	1.08184	−	0.400362i
$499$	1.83615e12	−	6.68305e11i	1.32573	−	0.482528i	0.420443	−	0.907319i	$-0.361875\pi$
$499$	1.83615e12	−	6.68305e11i	1.32573	−	0.482528i	0.905291	+	0.424791i	$0.139653\pi$
$500$	5.67420e11	−	2.06524e11i	0.406013	−	0.147777i
$501$	−1.97467e12	−	1.63892e12i	−1.40031	−	1.16222i
$502$	−1.58087e11	−	8.96558e11i	−0.111104	−	0.630103i
$503$	4.59705e11	−	7.96233e11i	0.320202	−	0.554606i	−0.660328	−	0.750978i	$-0.729583\pi$
$503$	4.59705e11	−	7.96233e11i	0.320202	−	0.554606i	0.980530	+	0.196372i	$0.0629160\pi$
$504$	2.77505e11	+	1.48049e12i	0.191572	+	1.02204i
$505$	3.27973e11	+	5.68066e11i	0.224402	+	0.388676i
$506$	3.97749e10	−	3.33751e10i	0.0269732	−	0.0226332i
$507$	2.63137e11	+	1.44677e12i	0.176867	+	0.972445i
$508$	−1.21265e11	+	6.87729e11i	−0.0807884	+	0.458174i
$509$	−9.01237e10	−	7.56228e10i	−0.0595126	−	0.0499370i	0.612546	−	0.790435i	$-0.290145\pi$
$509$	−9.01237e10	−	7.56228e10i	−0.0595126	−	0.0499370i	−0.672059	+	0.740498i	$0.734590\pi$
$510$	−1.15126e11	+	6.19279e8i	−0.0753541	+	0.000405341i
$511$	−2.44705e12	−	8.90652e11i	−1.58763	−	0.577849i
$512$	−7.74984e11			−0.498400
$513$	−1.28256e12	−	2.14092e12i	−0.817617	−	1.36481i
$514$	−5.72238e11			−0.361612
$515$	−3.10834e10	−	1.13134e10i	−0.0194714	−	0.00708700i
$516$	−4.26982e11	−	7.30451e11i	−0.265146	−	0.453594i
$517$	3.12595e10	+	2.62298e10i	0.0192431	+	0.0161469i
$518$	−1.02469e11	+	5.81130e11i	−0.0625328	+	0.354641i
$519$	−2.31469e12	−	8.28404e11i	−1.40036	−	0.501175i
$520$	−7.24560e10	+	6.07978e10i	−0.0434569	+	0.0364647i
$521$	−9.73011e11	−	1.68530e12i	−0.578559	−	1.00209i	−0.995645	−	0.0932269i	$-0.970282\pi$
$521$	−9.73011e11	−	1.68530e12i	−0.578559	−	1.00209i	0.417086	−	0.908867i	$-0.363052\pi$
$522$	2.80186e11	−	1.69548e12i	0.165169	−	0.999481i
$523$	−1.09641e11	+	1.89903e11i	−0.0640787	+	0.110988i	−0.896285	−	0.443479i	$-0.853744\pi$
$523$	−1.09641e11	+	1.89903e11i	−0.0640787	+	0.110988i	0.832206	+	0.554466i	$0.187078\pi$
$524$	−1.69907e11	−	9.63591e11i	−0.0984511	−	0.558344i
$525$	−2.16369e11	+	1.26690e12i	−0.124302	+	0.727825i
$526$	−1.37222e12	+	4.99446e11i	−0.781604	+	0.284481i
$527$	1.99093e11	−	7.24639e10i	0.112437	−	0.0409236i
$528$	2.96867e9	−	1.73824e10i	0.00166230	−	0.00973323i
$529$	2.07903e11	+	1.17908e12i	0.115428	+	0.654625i
$530$	−8.75240e10	+	1.51596e11i	−0.0481821	+	0.0834539i
$531$	1.01231e12	−	3.80835e11i	0.552573	−	0.207879i
$532$	7.14809e11	+	1.23809e12i	0.386890	+	0.670113i
$533$	−1.13632e11	+	9.53485e10i	−0.0609857	+	0.0511731i
$534$	5.08148e10	+	1.81861e10i	0.0270430	+	0.00967842i
$535$	−1.84333e11	+	1.04540e12i	−0.0972770	+	0.551685i
$536$	−8.35284e11	−	7.00886e11i	−0.437112	−	0.366780i
$537$	6.69590e11	+	1.14549e12i	0.347476	+	0.594439i
$538$	−1.42196e12	−	5.17551e11i	−0.731758	−	0.266338i
$539$	−3.09005e9			−0.00157694
$540$	−3.67771e11	+	3.18850e11i	−0.186125	+	0.161367i
$541$	2.84367e12			1.42722			0.713611	−	0.700542i	$-0.247058\pi$
$541$	2.84367e12			1.42722			0.713611	+	0.700542i	$0.247058\pi$
$542$	−7.72521e11	−	2.81175e11i	−0.384515	−	0.139952i
$543$	5.75141e10	−	3.09377e8i	0.0283906	−	0.000152717i
$544$	−2.94766e11	−	2.47338e11i	−0.144305	−	0.121087i
$545$	−2.91923e11	+	1.65558e12i	−0.141737	+	0.803832i
$546$	−2.78095e10	−	1.52901e11i	−0.0133914	−	0.0736283i
$547$	−1.38051e12	+	1.15839e12i	−0.659321	+	0.553236i	−0.909883	−	0.414865i	$-0.863829\pi$
$547$	−1.38051e12	+	1.15839e12i	−0.659321	+	0.553236i	0.250562	+	0.968100i	$0.419384\pi$
$548$	1.53693e11	+	2.66204e11i	0.0728016	+	0.126096i
$549$	3.10630e12	+	1.09290e12i	1.45938	+	0.513459i
$550$	2.20785e10	−	3.82410e10i	0.0102881	−	0.0178196i
$551$	−8.53499e11	−	4.84043e12i	−0.394476	−	2.23719i
$552$	2.29962e12	+	1.90863e12i	1.05422	+	0.874975i
$553$	2.08905e12	−	7.60352e11i	0.949917	−	0.345742i
$554$	2.84280e12	−	1.03469e12i	1.28219	−	0.466678i
$555$	−5.38917e11	+	1.99439e11i	−0.241103	+	0.0892261i
$556$	1.64924e11	+	9.35332e11i	0.0731894	+	0.415078i
$557$	2.61882e11	−	4.53593e11i	0.115281	−	0.199672i	−0.802611	−	0.596503i	$-0.796557\pi$
$557$	2.61882e11	−	4.53593e11i	0.115281	−	0.199672i	0.917892	+	0.396830i	$0.129890\pi$
$558$	−4.45451e11	+	7.91077e11i	−0.194512	+	0.345434i
$559$	1.31534e11	+	2.27823e11i	0.0569749	+	0.0986834i
$560$	−2.22293e11	+	1.86526e11i	−0.0955169	+	0.0801482i
$561$	1.47358e10	−	1.25005e10i	0.00628119	−	0.00532838i
$562$	−2.38296e10	+	1.35145e11i	−0.0100764	+	0.0571459i
$563$	−2.93081e12	−	2.45924e12i	−1.22942	−	1.03161i	−0.998276	−	0.0586861i	$-0.981309\pi$
$563$	−2.93081e12	−	2.45924e12i	−1.22942	−	1.03161i	−0.231143	−	0.972920i	$-0.574247\pi$
$564$	−3.86056e11	+	6.77053e11i	−0.160655	+	0.281752i
$565$	−1.78790e12	−	6.50742e11i	−0.738117	−	0.268652i
$566$	−2.27169e12			−0.930413
$567$	−4.69476e11	−	2.36393e12i	−0.190761	−	0.960528i
$568$	−2.97372e11			−0.119876
$569$	7.29144e10	+	2.65387e10i	0.0291614	+	0.0106139i	0.356560	−	0.934273i	$-0.383950\pi$
$569$	7.29144e10	+	2.65387e10i	0.0291614	+	0.0106139i	−0.327398	+	0.944886i	$0.606172\pi$
$570$	6.98911e11	−	1.22573e12i	0.277323	−	0.486360i
$571$	3.58119e12	+	3.00497e12i	1.40982	+	1.18298i	0.956535	+	0.291619i	$0.0941939\pi$
$571$	3.58119e12	+	3.00497e12i	1.40982	+	1.18298i	0.453289	+	0.891364i	$0.350251\pi$
$572$	9.14806e8	−	5.18812e9i	0.000357311	−	0.00202641i
$573$	−1.20220e12	+	1.01983e12i	−0.465886	+	0.395214i
$574$	−1.02310e12	+	8.58479e11i	−0.393380	+	0.330085i
$575$	1.27499e12	+	2.20834e12i	0.486408	+	0.842484i
$576$	2.32686e12	−	2.50338e10i	0.880785	−	0.00947602i
$577$	1.26231e12	−	2.18638e12i	0.474104	−	0.821173i	−0.525456	−	0.850821i	$-0.676105\pi$
$577$	1.26231e12	−	2.18638e12i	0.474104	−	0.821173i	0.999560	+	0.0296480i	$0.00943862\pi$
$578$	−3.15427e11	−	1.78887e12i	−0.117550	−	0.666660i
$579$	3.92278e12	−	1.45172e12i	1.45058	−	0.536820i
$580$	−9.00800e11	+	3.27864e11i	−0.330524	+	0.120301i
$581$	4.10948e12	−	1.49573e12i	1.49622	−	0.544578i
$582$	8.52523e11	+	7.07573e11i	0.308002	+	0.255633i
$583$	−5.10200e9	−	2.89349e10i	−0.00182908	−	0.0103732i
$584$	−2.57476e12	+	4.45961e12i	−0.915965	+	1.58650i
$585$	1.14879e11	−	9.85203e10i	0.0405545	−	0.0347796i
$586$	1.01117e12	+	1.75140e12i	0.354230	+	0.613545i
$587$	−2.86438e11	+	2.40350e11i	−0.0995769	+	0.0835550i	−0.691217	−	0.722647i	$-0.742925\pi$
$587$	−2.86438e11	+	2.40350e11i	−0.0995769	+	0.0835550i	0.591640	+	0.806202i	$0.298481\pi$
$588$	−1.05610e10	−	5.80661e10i	−0.00364339	−	0.0200320i
$589$	−4.50905e11	+	2.55721e12i	−0.154371	+	0.875482i
$590$	4.68430e11	+	3.93059e11i	0.159151	+	0.133544i
$591$	−2.82597e12	+	1.52013e10i	−0.952850	+	0.00512552i
$592$	3.73641e11	+	1.35994e11i	0.125028	+	0.0455064i
$593$	−1.65567e12			−0.549830			−0.274915	−	0.961469i	$-0.588650\pi$
$593$	−1.65567e12			−0.549830			−0.274915	+	0.961469i	$0.588650\pi$
$594$	−1.30609e10	+	8.17664e10i	−0.00430460	+	0.0269486i
$595$	−3.17989e11			−0.104012
$596$	−1.47115e12	−	5.35454e11i	−0.477582	−	0.173826i
$597$	−7.08424e11	−	1.21192e12i	−0.228249	−	0.390473i
$598$	−2.36201e11	−	1.98196e11i	−0.0755313	−	0.0633782i
$599$	−1.01828e12	+	5.77498e12i	−0.323183	+	1.83286i	0.198965	+	0.980007i	$0.436242\pi$
$599$	−1.01828e12	+	5.77498e12i	−0.323183	+	1.83286i	−0.522148	+	0.852855i	$0.674869\pi$
$600$	2.39291e12	+	8.56398e11i	0.753781	+	0.269771i
$601$	2.87355e12	−	2.41120e12i	0.898430	−	0.753872i	−0.0714530	−	0.997444i	$-0.522764\pi$
$601$	2.87355e12	−	2.41120e12i	0.898430	−	0.753872i	0.969883	+	0.243572i	$0.0783192\pi$
$602$	1.18427e12	+	2.05122e12i	0.367509	+	0.636545i
$603$	1.34847e12	+	1.10700e12i	0.415350	+	0.340973i
$604$	−1.01903e12	+	1.76502e12i	−0.311546	+	0.539614i
$605$	2.83408e11	+	1.60729e12i	0.0860028	+	0.487746i
$606$	−3.58794e11	+	2.10084e12i	−0.108073	+	0.632800i
$607$	−5.35276e12	+	1.94825e12i	−1.60040	+	0.582498i	−0.979509	−	0.201399i	$-0.935451\pi$
$607$	−5.35276e12	+	1.94825e12i	−1.60040	+	0.582498i	−0.620891	+	0.783897i	$0.713229\pi$
$608$	4.43153e12	−	1.61295e12i	1.31519	−	0.478689i
$609$	7.99068e11	−	4.67877e12i	0.235400	−	1.37833i
$610$	3.23287e11	+	1.83345e12i	0.0945375	+	0.536149i
$611$	1.21163e11	−	2.09861e11i	0.0351711	−	0.0609181i
$612$	2.85264e11	+	2.34182e11i	0.0821989	+	0.0674795i
$613$	−2.66210e12	−	4.61090e12i	−0.761470	−	1.31891i	−0.942093	−	0.335353i	$-0.891145\pi$
$613$	−2.66210e12	−	4.61090e12i	−0.761470	−	1.31891i	0.180622	−	0.983553i	$-0.442189\pi$
$614$	1.93501e11	−	1.62367e11i	0.0549448	−	0.0461042i
$615$	−1.22451e12	−	4.38241e11i	−0.345163	−	0.123531i
$616$	2.48210e10	−	1.40767e11i	0.00694553	−	0.0393901i
$617$	−1.25854e12	−	1.05604e12i	−0.349610	−	0.293357i	0.451024	−	0.892512i	$-0.351059\pi$
$617$	−1.25854e12	−	1.05604e12i	−0.349610	−	0.293357i	−0.800633	+	0.599155i	$0.795503\pi$
$618$	−5.42379e10	−	9.27865e10i	−0.0149574	−	0.0255880i
$619$	−4.46032e12	−	1.62342e12i	−1.22112	−	0.444451i	−0.350572	−	0.936536i	$-0.614013\pi$
$619$	−4.46032e12	−	1.62342e12i	−1.22112	−	0.444451i	−0.870547	+	0.492085i	$0.836235\pi$
$620$	5.06436e11			0.137645
$621$	−3.71212e12	−	3.01412e12i	−1.00164	−	0.813294i
$622$	2.23195e12			0.597899
$623$	1.40081e11	+	5.09853e10i	0.0372549	+	0.0135597i
$624$	−1.04717e11	+	5.63291e8i	−0.0276496	+	0.000148731i
$625$	9.42318e11	+	7.90699e11i	0.247023	+	0.207277i
$626$	−2.77942e11	+	1.57629e12i	−0.0723386	+	0.410253i
$627$	4.23790e10	+	2.33007e11i	0.0109508	+	0.0602095i
$628$	2.25866e12	−	1.89524e12i	0.579472	−	0.486235i
$629$	2.17860e11	+	3.77345e11i	0.0554945	+	0.0961192i
$630$	1.03432e12	−	8.87036e11i	0.261592	−	0.224341i
$631$	1.17099e12	−	2.02821e12i	0.294049	−	0.509308i	−0.680714	−	0.732549i	$-0.738330\pi$
$631$	1.17099e12	−	2.02821e12i	0.294049	−	0.509308i	0.974763	+	0.223241i	$0.0716637\pi$
$632$	−7.63384e11	−	4.32937e12i	−0.190334	−	1.07944i
$633$	1.70002e12	+	1.41097e12i	0.420860	+	0.349303i
$634$	3.62565e11	−	1.31963e11i	0.0891218	−	0.0324377i
$635$	1.78891e12	−	6.51109e11i	0.436622	−	0.158917i
$636$	5.26286e11	−	1.94765e11i	0.127545	−	0.0472012i
$637$	3.18646e9	+	1.80713e10i	0.000766798	+	0.00434873i
$638$	−8.15375e10	+	1.41227e11i	−0.0194834	+	0.0337462i
$639$	4.75779e11	−	5.11872e9i	0.112889	−	0.00121453i
$640$	−2.68178e11	−	4.64499e11i	−0.0631850	−	0.109440i
$641$	1.73411e12	−	1.45509e12i	0.405710	−	0.340431i	−0.416985	−	0.908913i	$-0.636913\pi$
$641$	1.73411e12	−	1.45509e12i	0.405710	−	0.340431i	0.822696	+	0.568482i	$0.192469\pi$
$642$	−2.63017e12	+	2.23119e12i	−0.611049	+	0.518357i
$643$	5.04719e11	−	2.86240e12i	0.116439	−	0.660361i	−0.869588	−	0.493778i	$-0.835616\pi$
$643$	5.04719e11	−	2.86240e12i	0.116439	−	0.660361i	0.986027	−	0.166583i	$-0.0532734\pi$
$644$	2.09829e12	+	1.76068e12i	0.480706	+	0.403360i
$645$	−1.14249e12	+	2.00366e12i	−0.259916	+	0.455834i
$646$	−1.00536e12	−	3.65923e11i	−0.227131	−	0.0826691i
$647$	−4.82089e12			−1.08158			−0.540789	−	0.841158i	$-0.681874\pi$
$647$	−4.82089e12			−1.08158			−0.540789	+	0.841158i	$0.681874\pi$
$648$	−4.76478e12	+	1.02537e11i	−1.06159	+	0.0228450i
$649$	−1.02637e11			−0.0227092
$650$	−2.46409e11	−	8.96857e10i	−0.0541436	−	0.0197067i
$651$	−1.24210e12	+	2.17835e12i	−0.271045	+	0.475350i
$652$	−6.28246e11	−	5.27161e11i	−0.136149	−	0.114243i
$653$	1.99583e11	−	1.13189e12i	0.0429551	−	0.243610i	−0.955769	−	0.294120i	$-0.904973\pi$
$653$	1.99583e11	−	1.13189e12i	0.0429551	−	0.243610i	0.998724	+	0.0505097i	$0.0160846\pi$
$654$	−4.16533e12	+	3.53348e12i	−0.890328	+	0.755272i
$655$	−2.04330e12	+	1.71453e12i	−0.433756	+	0.363964i
$656$	4.49965e11	+	7.79362e11i	0.0948662	+	0.164313i
$657$	4.04271e12	−	7.17945e12i	0.846502	−	1.50331i
$658$	1.09090e12	−	1.88950e12i	0.226866	−	0.392944i
$659$	1.27763e12	+	7.24581e12i	0.263889	+	1.49659i	0.772180	+	0.635404i	$0.219166\pi$
$659$	1.27763e12	+	7.24581e12i	0.263889	+	1.49659i	−0.508291	+	0.861186i	$0.669722\pi$
$660$	4.33186e10	−	1.60311e10i	0.00888642	−	0.00328863i
$661$	1.95845e12	−	7.12819e11i	0.399031	−	0.145235i	−0.134707	−	0.990886i	$-0.543009\pi$
$661$	1.95845e12	−	7.12819e11i	0.399031	−	0.145235i	0.533738	+	0.845650i	$0.320787\pi$
$662$	2.61196e12	−	9.50676e11i	0.528574	−	0.192385i
$663$	−8.83015e10	−	7.32879e10i	−0.0177483	−	0.0147306i
$664$	−1.50169e12	−	8.51652e12i	−0.299795	−	1.70022i
$665$	1.94862e12	−	3.37510e12i	0.386393	−	0.669252i
$666$	−1.76125e12	−	6.19666e11i	−0.346885	−	0.122046i
$667$	−4.70863e12	−	8.15558e12i	−0.921145	−	1.59547i
$668$	−3.56298e12	+	2.98969e12i	−0.692339	+	0.580942i
$669$	1.26713e12	+	6.96690e12i	0.244570	+	1.34469i
$670$	−1.71282e11	+	9.71390e11i	−0.0328379	+	0.186233i
$671$	−2.39378e11	−	2.00862e11i	−0.0455862	−	0.0382513i
$672$	4.55412e12	−	2.44973e10i	0.861475	−	0.00463400i
$673$	3.71345e12	+	1.35158e12i	0.697765	+	0.253966i	0.666456	−	0.745544i	$-0.267810\pi$
$673$	3.71345e12	+	1.35158e12i	0.697765	+	0.253966i	0.0313089	+	0.999510i	$0.490032\pi$
$674$	4.74990e12			0.886574
$675$	−3.84326e12	−	1.32900e12i	−0.712578	−	0.246410i
$676$	2.66524e12			0.490881
$677$	4.05777e12	+	1.47691e12i	0.742401	+	0.270212i	0.685405	−	0.728162i	$-0.259625\pi$
$677$	4.05777e12	+	1.47691e12i	0.742401	+	0.270212i	0.0569965	+	0.998374i	$0.481848\pi$
$678$	−3.11973e12	−	5.33702e12i	−0.567000	−	0.969986i
$679$	2.34417e12	+	1.96699e12i	0.423229	+	0.355131i
$680$	−1.09192e11	+	6.19260e11i	−0.0195840	+	0.111066i
$681$	−7.04669e12	−	2.52194e12i	−1.25552	−	0.449338i
$682$	6.59968e10	−	5.53779e10i	0.0116814	−	0.00980182i
$683$	−2.14503e12	−	3.71531e12i	−0.377173	−	0.653283i	0.613476	−	0.789713i	$-0.289771\pi$
$683$	−2.14503e12	−	3.71531e12i	−0.377173	−	0.653283i	−0.990650	+	0.136430i	$0.956437\pi$
$684$	−4.23367e12	+	1.59271e12i	−0.739544	+	0.278218i
$685$	4.18976e11	−	7.25688e11i	0.0727080	−	0.125934i
$686$	7.28494e11	+	4.13150e12i	0.125594	+	0.712277i
$687$	−1.26468e12	+	7.40507e12i	−0.216609	+	1.26830i
$688$	1.49974e12	−	5.45859e11i	0.255192	−	0.0928822i
$689$	−1.63956e11	+	5.96752e10i	−0.0277167	+	0.0100881i
$690$	4.55118e11	−	2.66485e12i	0.0764369	−	0.447560i
$691$	5.33690e11	+	3.02671e12i	0.0890509	+	0.505033i	0.996409	+	0.0846735i	$0.0269847\pi$
$691$	5.33690e11	+	3.02671e12i	0.0890509	+	0.505033i	−0.907358	+	0.420359i	$0.861904\pi$
$692$	−2.22793e12	+	3.85889e12i	−0.369338	+	0.639712i
$693$	−3.72891e10	+	2.25646e11i	−0.00614162	+	0.0371645i
$694$	4.07023e12	+	7.04984e12i	0.666041	+	1.15362i
$695$	1.98337e12	−	1.66425e12i	0.322458	−	0.270574i
$696$	−8.83719e12	−	3.16274e12i	−1.42749	−	0.510884i
$697$	−1.71245e11	+	9.71179e11i	−0.0274834	+	0.155866i
$698$	−5.49734e12	−	4.61281e12i	−0.876603	−	0.735557i
$699$	3.80991e12	+	6.51774e12i	0.603626	+	1.03264i
$700$	2.18898e12	+	7.96722e11i	0.344588	+	0.125420i
$701$	8.81737e11			0.137914			0.0689569	−	0.997620i	$-0.478033\pi$
$701$	8.81737e11			0.137914			0.0689569	+	0.997620i	$0.478033\pi$
$702$	4.91657e11	−	7.93470e9i	0.0764091	−	0.00123314i
$703$	−5.34013e12			−0.824619
$704$	−2.07504e11	−	7.55253e10i	−0.0318383	−	0.0115882i
$705$	2.12462e12	−	1.14287e10i	0.323915	−	0.00174239i
$706$	−4.78318e12	−	4.01356e12i	−0.724595	−	0.608007i
$707$	−1.02221e12	+	5.79723e12i	−0.153869	+	0.872636i
$708$	−3.50786e11	−	1.92868e12i	−0.0524677	−	0.288476i
$709$	5.78745e12	−	4.85625e12i	0.860160	−	0.721760i	−0.101842	−	0.994801i	$-0.532474\pi$
$709$	5.78745e12	−	4.85625e12i	0.860160	−	0.721760i	0.962003	+	0.273040i	$0.0880293\pi$
$710$	1.34503e11	+	2.32967e11i	0.0198642	+	0.0344057i
$711$	1.29589e12	+	6.91361e12i	0.190176	+	1.01459i
$712$	1.47392e11	−	2.55290e11i	0.0214938	−	0.0372284i
$713$	8.63926e11	+	4.89957e12i	0.125191	+	0.709994i
$714$	−7.95030e11	−	6.59855e11i	−0.114483	−	0.0950181i
$715$	−1.34952e10	+	4.91187e9i	−0.00193109	+	0.000702861i
$716$	2.25981e12	−	8.22504e11i	0.321339	−	0.116958i
$717$	1.49177e12	−	5.52065e11i	0.210798	−	0.0780107i
$718$	7.95506e11	+	4.51154e12i	0.111708	+	0.633526i
$719$	4.50153e12	−	7.79688e12i	0.628174	−	1.08803i	−0.359744	−	0.933051i	$-0.617136\pi$
$719$	4.50153e12	−	7.79688e12i	0.628174	−	1.08803i	0.987918	−	0.154978i	$-0.0495307\pi$
$720$	−4.67601e11	−	7.90154e11i	−0.0648454	−	0.109576i
$721$	−1.48427e11	−	2.57084e11i	−0.0204553	−	0.0354296i
$722$	6.07634e12	−	5.09865e12i	0.832194	−	0.698294i
$723$	3.23117e12	−	2.74103e12i	0.439782	−	0.373070i
$724$	1.81017e10	−	1.02660e11i	0.00244847	−	0.0138860i
$725$	−6.13510e12	−	5.14796e12i	−0.824709	−	0.692013i
$726$	−2.62669e12	+	4.60660e12i	−0.350908	+	0.615412i
$727$	5.11680e12	+	1.86236e12i	0.679350	+	0.247263i	0.658569	−	0.752521i	$-0.271162\pi$
$727$	5.11680e12	+	1.86236e12i	0.679350	+	0.247263i	0.0207819	+	0.999784i	$0.493384\pi$
$728$	−8.48831e11			−0.112003
$729$	7.62163e12	−	2.46070e11i	0.999479	−	0.0322690i
$730$	4.65831e12			0.607122
$731$	1.64344e12	+	5.98163e11i	0.212876	+	0.0774804i
$732$	2.95633e12	−	5.18472e12i	0.380586	−	0.667460i
$733$	3.90516e12	+	3.27682e12i	0.499656	+	0.419261i	0.857472	−	0.514531i	$-0.172034\pi$
$733$	3.90516e12	+	3.27682e12i	0.499656	+	0.419261i	−0.357816	+	0.933792i	$0.616478\pi$
$734$	5.46797e11	−	3.10104e12i	0.0695334	−	0.394344i
$735$	−1.22690e11	+	1.04079e11i	−0.0155066	+	0.0131543i
$736$	6.92172e12	−	5.80801e12i	0.869488	−	0.729587i
$737$	−8.27799e10	−	1.43379e11i	−0.0103353	−	0.0179012i
$738$	−2.15212e12	−	3.63665e12i	−0.267062	−	0.451282i
$739$	−5.26029e12	+	9.11108e12i	−0.648798	+	1.12375i	0.334612	+	0.942356i	$0.391395\pi$
$739$	−5.26029e12	+	9.11108e12i	−0.648798	+	1.12375i	−0.983410	+	0.181395i	$0.941939\pi$
$740$	1.80856e11	+	1.02568e12i	0.0221712	+	0.125739i
$741$	1.31898e12	−	4.88119e11i	0.160715	−	0.0594763i
$742$	−1.47620e12	+	5.37291e11i	−0.178783	+	0.0650717i
$743$	4.68008e12	−	1.70341e12i	0.563383	−	0.205055i	−0.0445998	−	0.999005i	$-0.514201\pi$
$743$	4.68008e12	−	1.70341e12i	0.563383	−	0.205055i	0.607983	+	0.793950i	$0.291979\pi$
$744$	3.81566e12	+	3.16690e12i	0.456554	+	0.378928i
$745$	7.41100e11	+	4.20299e12i	0.0881401	+	0.499868i
$746$	−3.99610e12	+	6.92145e12i	−0.472402	+	0.818224i
$747$	2.54922e12	+	1.36001e13i	0.299547	+	1.59809i
$748$	−1.75118e10	−	3.03313e10i	−0.00204538	−	0.00354269i
$749$	−7.29772e12	+	6.12351e12i	−0.847264	+	0.710939i
$750$	−9.57058e11	−	5.26207e12i	−0.110449	−	0.607269i
$751$	−1.09089e12	+	6.18676e12i	−0.125142	+	0.709714i	0.856082	+	0.516840i	$0.172892\pi$
$751$	−1.09089e12	+	6.18676e12i	−0.125142	+	0.709714i	−0.981224	+	0.192874i	$0.938219\pi$
$752$	−1.12620e12	−	9.44997e11i	−0.128421	−	0.107758i
$753$	7.95597e12	−	4.27963e10i	0.901811	−	0.00485098i
$754$	9.10009e11	+	3.31216e11i	0.102536	+	0.0373199i
$755$	5.55590e12			0.622291
$756$	−4.36763e12	+	7.04878e10i	−0.486293	+	0.00784813i
$757$	−1.08955e13			−1.20591			−0.602955	−	0.797775i	$-0.706010\pi$
$757$	−1.08955e13			−1.20591			−0.602955	+	0.797775i	$0.706010\pi$
$758$	2.14106e12	+	7.79282e11i	0.235569	+	0.0857400i
$759$	2.28991e11	+	3.91743e11i	0.0250456	+	0.0428463i
$760$	−5.90364e12	−	4.95374e12i	−0.641888	−	0.538608i
$761$	−7.92582e11	+	4.49495e12i	−0.0856669	+	0.485841i	0.911544	+	0.411203i	$0.134891\pi$
$761$	−7.92582e11	+	4.49495e12i	−0.0856669	+	0.485841i	−0.997211	+	0.0746381i	$0.976220\pi$
$762$	5.82370e12	+	2.08425e12i	0.625751	+	0.223950i
$763$	−1.15572e13	+	9.69766e12i	−1.23450	+	1.03587i
$764$	1.42867e12	+	2.47452e12i	0.151709	+	0.262767i
$765$	1.64042e11	−	9.92661e11i	0.0173173	−	0.104791i
$766$	−1.47676e12	+	2.55782e12i	−0.154981	+	0.268436i
$767$	1.05839e11	+	6.00243e11i	0.0110425	+	0.0626251i
$768$	1.72303e12	−	1.00888e13i	0.178717	−	1.04644i
$769$	6.66397e12	−	2.42549e12i	0.687171	−	0.250110i	0.0252475	−	0.999681i	$-0.491963\pi$
$769$	6.66397e12	−	2.42549e12i	0.687171	−	0.250110i	0.661923	+	0.749571i	$0.269740\pi$
$770$	−1.21506e11	+	4.42244e10i	−0.0124563	+	0.00453371i
$771$	8.41896e11	−	4.92954e12i	0.0858052	−	0.502414i
$772$	−1.31645e12	−	7.46596e12i	−0.133391	−	0.756498i
$773$	−7.08813e11	+	1.22770e12i	−0.0714043	+	0.123676i	−0.899517	−	0.436886i	$-0.856081\pi$
$773$	−7.08813e11	+	1.22770e12i	−0.0714043	+	0.123676i	0.828113	+	0.560562i	$0.189415\pi$
$774$	−7.01422e12	+	2.63876e12i	−0.702498	+	0.264281i
$775$	2.11553e12	+	3.66421e12i	0.210650	+	0.364857i
$776$	4.63553e12	−	3.88967e12i	0.458904	−	0.385066i
$777$	−4.85538e12	−	1.73769e12i	−0.477891	−	0.171033i
$778$	2.00174e12	−	1.13524e13i	0.195884	−	1.11092i
$779$	−9.25862e12	−	7.76891e12i	−0.900799	−	0.755860i
$780$	−1.38424e11	−	2.36806e11i	−0.0133901	−	0.0229069i
$781$	−4.24289e10	−	1.54428e10i	−0.00408067	−	0.00148524i
$782$	−2.04989e12			−0.196019
$783$	1.41934e13	+	4.90810e12i	1.34946	+	0.466644i
$784$	1.11327e11			0.0105239
$785$	−7.55299e12	−	2.74906e12i	−0.709913	−	0.258387i
$786$	−8.66641e12	+	4.66179e10i	−0.809912	+	0.00435664i
$787$	−1.43657e13	−	1.20542e13i	−1.33487	−	1.12009i	−0.982912	−	0.184076i	$-0.941071\pi$
$787$	−1.43657e13	−	1.20542e13i	−1.33487	−	1.12009i	−0.351960	−	0.936015i	$-0.614485\pi$
$788$	−8.89433e11	+	5.04423e12i	−0.0821761	+	0.466044i
$789$	−2.28362e12	−	1.25557e13i	−0.209787	−	1.15344i
$790$	−3.04642e12	+	2.55625e12i	−0.278271	+	0.233497i
$791$	−8.53745e12	−	1.47873e13i	−0.775415	−	1.34306i
$792$	4.26625e11	+	1.50101e11i	0.0385286	+	0.0135557i
$793$	−9.27840e11	+	1.60707e12i	−0.0833190	+	0.144313i
$794$	6.77647e9	+	3.84313e10i	0.000605078	+	0.00343157i
$795$	−1.17715e12	−	9.77008e11i	−0.104516	−	0.0867453i
$796$	−2.39087e12	+	8.70206e11i	−0.211080	+	0.0768269i
$797$	−1.86553e13	+	6.78996e12i	−1.63772	+	0.596080i	−0.986638	−	0.162930i	$-0.947906\pi$
$797$	−1.86553e13	+	6.78996e12i	−1.63772	+	0.596080i	−0.651079	+	0.759010i	$0.725683\pi$
$798$	1.18755e13	−	4.39482e12i	1.03667	−	0.383644i
$799$	−2.79752e11	−	1.58655e12i	−0.0242835	−	0.137719i
$800$	3.84214e12	−	6.65479e12i	0.331641	−	0.574419i
$801$	−2.31424e11	+	4.10987e11i	−0.0198638	+	0.0352762i
$802$	6.40219e12	+	1.10889e13i	0.546442	+	0.946465i
$803$	−5.98956e11	+	5.02584e11i	−0.0508365	+	0.0426569i
$804$	2.41136e12	−	2.04557e12i	0.203521	−	0.172648i
$805$	1.29664e12	−	7.35359e12i	0.108827	−	0.617189i
$806$	−3.91918e11	−	3.28858e11i	−0.0327105	−	0.0274474i
$807$	6.55047e12	−	1.14880e13i	0.543678	−	0.953486i
$808$	1.09387e13	+	3.98135e12i	0.902846	+	0.328609i
$809$	6.10292e12			0.500921			0.250460	−	0.968127i	$-0.419418\pi$
$809$	6.10292e12			0.500921			0.250460	+	0.968127i	$0.419418\pi$
$810$	2.23547e12	+	3.68643e12i	0.182468	+	0.300901i
$811$	−1.00057e13			−0.812185			−0.406092	−	0.913832i	$-0.633109\pi$
$811$	−1.00057e13			−0.812185			−0.406092	+	0.913832i	$0.633109\pi$
$812$	−8.08406e12	−	2.94236e12i	−0.652570	−	0.237516i
$813$	3.55873e12	−	6.24120e12i	0.285685	−	0.501026i
$814$	1.35725e11	+	1.13887e11i	0.0108355	+	0.00909210i
$815$	−3.88224e11	+	2.20173e12i	−0.0308228	+	0.174805i
$816$	−5.30896e11	+	4.50363e11i	−0.0419183	+	0.0355596i
$817$	−1.64198e13	+	1.37778e13i	−1.28934	+	1.08188i
$818$	−3.27029e12	−	5.66431e12i	−0.255386	−	0.442341i
$819$	1.35808e12	−	1.46111e10i	0.105475	−	0.00113476i
$820$	−1.17862e12	+	2.04142e12i	−0.0910353	+	0.157678i
$821$	−8.18458e11	−	4.64171e12i	−0.0628713	−	0.356561i	−0.999972	−	0.00750135i	$-0.997612\pi$
$821$	−8.18458e11	−	4.64171e12i	−0.0628713	−	0.356561i	0.937101	−	0.349059i	$-0.113499\pi$
$822$	2.55339e12	−	9.44942e11i	0.195071	−	0.0721908i
$823$	6.62313e12	−	2.41062e12i	0.503227	−	0.183160i	−0.0779177	−	0.996960i	$-0.524827\pi$
$823$	6.62313e12	−	2.41062e12i	0.503227	−	0.183160i	0.581145	+	0.813800i	$0.302605\pi$
$824$	−5.51620e11	+	2.00773e11i	−0.0416838	+	0.0151717i
$825$	2.96944e11	+	2.46456e11i	0.0223168	+	0.0185224i
$826$	9.52932e11	+	5.40435e12i	0.0712281	+	0.403955i
$827$	1.22505e13	−	2.12185e13i	0.910710	−	1.57740i	0.0976464	−	0.995221i	$-0.468869\pi$
$827$	1.22505e13	−	2.12185e13i	0.910710	−	1.57740i	0.813064	−	0.582175i	$-0.197798\pi$
$828$	−6.57873e12	+	5.64192e12i	−0.486414	+	0.417148i
$829$	−3.99539e12	−	6.92022e12i	−0.293808	−	0.508891i	0.680899	−	0.732378i	$-0.261589\pi$
$829$	−3.99539e12	−	6.92022e12i	−0.293808	−	0.508891i	−0.974707	+	0.223487i	$0.928256\pi$
$830$	−5.99276e12	+	5.02852e12i	−0.438304	+	0.367781i
$831$	4.73094e12	+	2.60115e13i	0.344146	+	1.89217i
$832$	−2.27711e11	+	1.29141e12i	−0.0164751	+	0.0934351i
$833$	9.34531e10	+	7.84164e10i	0.00672498	+	0.00564293i
$834$	8.41226e12	−	4.52508e10i	0.602096	−	0.00323876i
$835$	1.19146e13	+	4.33658e12i	0.848188	+	0.308715i
$836$	4.29245e11			0.0303932
$837$	−6.15936e12	−	5.00119e12i	−0.433782	−	0.352216i
$838$	−1.73995e13			−1.21882
$839$	1.52038e13	+	5.53373e12i	1.05931	+	0.385558i	0.812169	−	0.583422i	$-0.198287\pi$
$839$	1.52038e13	+	5.53373e12i	1.05931	+	0.385558i	0.247142	+	0.968979i	$0.420509\pi$
$840$	−3.75578e12	−	6.42513e12i	−0.260281	−	0.445272i
$841$	1.15443e13	+	9.68680e12i	0.795765	+	0.667726i
$842$	−6.03232e11	+	3.42110e12i	−0.0413599	+	0.234564i
$843$	−1.12914e12	−	4.04109e11i	−0.0770060	−	0.0275597i
$844$	3.06742e12	−	2.57387e12i	0.208081	−	0.174601i
$845$	−3.63281e12	−	6.29221e12i	−0.245125	−	0.424569i
$846$	5.33566e12	+	4.38021e12i	0.358114	+	0.293987i
$847$	−7.32339e12	+	1.26845e13i	−0.488919	+	0.846833i
$848$	1.83812e11	+	1.04245e12i	0.0122066	+	0.0692269i
$849$	3.34219e12	−	1.95695e13i	0.220773	−	1.29269i
$850$	−1.63817e12	+	5.96245e11i	−0.107640	+	0.0391778i
$851$	−9.61457e12	+	3.49942e12i	−0.628415	+	0.228724i
$852$	1.45180e11	−	8.50073e11i	0.00943908	−	0.0552685i
$853$	2.73001e12	+	1.54826e13i	0.176560	+	1.00132i	0.936327	+	0.351128i	$0.114202\pi$
$853$	2.73001e12	+	1.54826e13i	0.176560	+	1.00132i	−0.759767	+	0.650195i	$0.774687\pi$
$854$	−8.35389e12	+	1.44694e13i	−0.537438	+	0.930870i
$855$	9.53077e12	+	7.82410e12i	0.609931	+	0.500710i
$856$	9.41918e12	+	1.63145e13i	0.599627	+	1.03858i
$857$	−1.08739e13	+	9.12426e12i	−0.688606	+	0.577809i	−0.918507	−	0.395405i	$-0.870604\pi$
$857$	−1.08739e13	+	9.12426e12i	−0.688606	+	0.577809i	0.229901	+	0.973214i	$0.426160\pi$
$858$	−4.39332e10	−	1.57233e10i	−0.00276758	−	0.000990489i
$859$	1.34844e12	−	7.64736e12i	0.0845008	−	0.479228i	−0.912962	−	0.408044i	$-0.866211\pi$
$859$	1.34844e12	−	7.64736e12i	0.0845008	−	0.479228i	0.997463	−	0.0711842i	$-0.0226778\pi$
$860$	3.20241e12	+	2.68714e12i	0.199634	+	0.167512i
$861$	−5.89015e12	−	1.00765e13i	−0.365268	−	0.624876i
$862$	−5.10735e12	−	1.85892e12i	−0.315074	−	0.114678i
$863$	2.85339e13			1.75110			0.875552	−	0.483124i	$-0.160498\pi$
$863$	2.85339e13			1.75110			0.875552	+	0.483124i	$0.160498\pi$
$864$	−2.27288e12	+	1.42292e13i	−0.138760	+	0.868696i
$865$	1.21470e13			0.737726
$866$	9.42671e12	+	3.43104e12i	0.569547	+	0.207298i
$867$	1.58743e13	−	8.53902e10i	0.954132	−	0.00513242i
$868$	3.48160e12	+	2.92141e12i	0.208181	+	0.174684i
$869$	1.15909e11	−	6.57354e11i	0.00689492	−	0.0391030i
$870$	1.51936e12	+	8.35373e12i	0.0899136	+	0.494360i
$871$	−7.53150e11	+	6.31968e11i	−0.0443404	+	0.0372060i
$872$	1.49169e13	+	2.58369e13i	0.873685	+	1.51327i
$873$	−7.34964e12	+	6.30305e12i	−0.428254	+	0.367271i
$874$	1.25616e13	−	2.17573e13i	0.728186	−	1.26126i
$875$	−2.56523e12	−	1.45481e13i	−0.147942	−	0.839018i
$876$	−1.14913e13	−	9.53747e12i	−0.659326	−	0.547224i
$877$	1.34487e13	−	4.89493e12i	0.767684	−	0.279414i	0.0716564	−	0.997429i	$-0.477172\pi$
$877$	1.34487e13	−	4.89493e12i	0.767684	−	0.279414i	0.696027	+	0.718015i	$0.254949\pi$
$878$	−8.40747e12	+	3.06007e12i	−0.477463	+	0.173782i
$879$	−1.65751e13	+	6.13401e12i	−0.936496	+	0.346573i
$880$	1.51296e10	+	8.58042e10i	0.000850463	+	0.00482322i
$881$	8.94202e12	−	1.54880e13i	0.500085	−	0.866173i	−0.499915	−	0.866075i	$-0.666635\pi$
$881$	8.94202e12	−	1.54880e13i	0.500085	−	0.866173i	1.00000		9.82884e-5i	$-3.12862e-5\pi$
$882$	−5.22719e11	+	5.62373e9i	−0.0290844	+	0.000312908i
$883$	−5.18249e12	−	8.97633e12i	−0.286890	−	0.496908i	0.686176	−	0.727436i	$-0.259288\pi$
$883$	−5.18249e12	−	8.97633e12i	−0.286890	−	0.496908i	−0.973066	+	0.230528i	$0.925955\pi$
$884$	−1.59326e11	+	1.33690e11i	−0.00877509	+	0.00736318i
$885$	−4.07517e12	+	3.45700e12i	−0.223307	+	0.189433i
$886$	3.18166e12	−	1.80441e13i	0.173461	−	0.983745i
$887$	−6.81254e12	−	5.71640e12i	−0.369533	−	0.310075i	0.439044	−	0.898466i	$-0.355317\pi$
$887$	−6.81254e12	−	5.71640e12i	−0.369533	−	0.310075i	−0.808577	+	0.588391i	$0.799762\pi$
$888$	−5.05130e12	+	8.85881e12i	−0.272612	+	0.478098i
$889$	1.60542e13	+	5.84325e12i	0.862046	+	0.313759i
$890$	−2.66665e11			−0.0142466
$891$	−6.85160e11	−	2.32810e11i	−0.0364202	−	0.0123752i
$892$	1.28344e13			0.678787
$893$	1.85538e13	+	6.75303e12i	0.976340	+	0.355359i
$894$	−6.86869e12	+	1.20461e13i	−0.359629	+	0.630707i
$895$	−5.02200e12	−	4.21396e12i	−0.261621	−	0.219526i
$896$	8.35844e11	−	4.74030e12i	0.0433250	−	0.245709i
$897$	2.05487e12	−	1.74316e12i	0.105978	−	0.0899023i
$898$	1.64926e13	−	1.38389e13i	0.846341	−	0.710165i
$899$	−7.81282e12	−	1.35322e13i	−0.398923	−	0.690955i
$900$	−3.61635e12	+	6.42229e12i	−0.183730	+	0.326286i
$901$	−5.79981e11	+	1.00456e12i	−0.0293192	+	0.0507824i
$902$	6.96333e10	+	3.94910e11i	0.00350258	+	0.0198641i
$903$	−1.94126e13	+	7.18409e12i	−0.971602	+	0.359565i
$904$	−3.17288e13	+	1.15483e13i	−1.58014	+	0.575124i
$905$	−2.67037e11	+	9.71934e10i	−0.0132328	+	0.00481635i
$906$	1.38908e13	+	1.15290e13i	0.684936	+	0.568479i
$907$	−5.34049e12	−	3.02874e13i	−0.262028	−	1.48604i	−0.777366	−	0.629049i	$-0.783445\pi$
$907$	−5.34049e12	−	3.02874e13i	−0.262028	−	1.48604i	0.515338	−	0.856987i	$-0.327667\pi$
$908$	−6.78258e12	+	1.17478e13i	−0.331138	+	0.573547i
$909$	−1.75698e13	−	6.18165e12i	−0.853551	−	0.300308i
$910$	3.83931e11	+	6.64988e11i	0.0185595	+	0.0321461i
$911$	1.90984e13	−	1.60255e13i	0.918681	−	0.770865i	−0.0550698	−	0.998483i	$-0.517538\pi$
$911$	1.90984e13	−	1.60255e13i	0.918681	−	0.770865i	0.973751	+	0.227618i	$0.0730937\pi$
$912$	−1.52681e12	−	8.39468e12i	−0.0730818	−	0.401816i
$913$	2.28011e11	−	1.29312e12i	0.0108602	−	0.0615912i
$914$	−3.74801e12	−	3.14495e12i	−0.177641	−	0.149058i
$915$	−1.62699e13	+	8.75181e10i	−0.767343	+	0.00412765i
$916$	1.27946e13	+	4.65685e12i	0.600478	+	0.218556i
$917$	−2.39375e13			−1.11793
$918$	2.47000e12	−	2.14143e12i	0.114790	−	0.0995205i
$919$	7.09244e12			0.328002			0.164001	−	0.986460i	$-0.447560\pi$
$919$	7.09244e12			0.328002			0.164001	+	0.986460i	$0.447560\pi$
$920$	−1.38753e13	−	5.05021e12i	−0.638555	−	0.232415i
$921$	1.11402e12	+	1.90580e12i	0.0510183	+	0.0872786i
$922$	−7.57657e12	−	6.35750e12i	−0.345290	−	0.289732i
$923$	−4.65606e10	+	2.64058e11i	−0.00211160	+	0.0119755i
$924$	3.90280e11	+	1.39677e11i	0.0176138	+	0.00630380i
$925$	−6.66563e12	+	5.59313e12i	−0.299367	+	0.251199i
$926$	4.88839e12	+	8.46694e12i	0.218482	+	0.378423i
$927$	8.79105e11	−	3.30721e11i	0.0391005	−	0.0147097i
$928$	−1.41893e13	+	2.45766e13i	−0.628052	+	1.08782i
$929$	4.60975e12	+	2.61432e13i	0.203052	+	1.15156i	0.900476	+	0.434905i	$0.143218\pi$
$929$	4.60975e12	+	2.61432e13i	0.203052	+	1.15156i	−0.697425	+	0.716658i	$0.745671\pi$
$930$	7.55158e11	−	4.42166e12i	0.0331028	−	0.193826i
$931$	−1.40498e12	+	5.11371e11i	−0.0612909	+	0.0223081i
$932$	1.28581e13	−	4.67998e12i	0.558221	−	0.203176i
$933$	−3.28372e12	+	1.92271e13i	−0.141873	+	0.830704i
$934$	−4.72900e12	−	2.68195e13i	−0.203333	−	1.15316i
$935$	−4.77382e10	+	8.26851e10i	−0.00204275	+	0.00353814i
$936$	4.37890e11	−	2.64978e12i	0.0186476	−	0.112842i
$937$	−1.02544e13	−	1.77612e13i	−0.434593	−	0.752736i	0.562670	−	0.826682i	$-0.309774\pi$
$937$	−1.02544e13	−	1.77612e13i	−0.434593	−	0.752736i	−0.997262	+	0.0739454i	$0.976441\pi$
$938$	−6.78105e12	+	5.68998e12i	−0.286012	+	0.239993i
$939$	−1.31700e13	−	4.71342e12i	−0.552829	−	0.197852i
$940$	6.68693e11	−	3.79235e12i	0.0279352	−	0.158428i
$941$	2.52986e13	+	2.12280e13i	1.05182	+	0.882585i	0.993284	−	0.115701i	$-0.0369113\pi$
$941$	2.52986e13	+	2.12280e13i	1.05182	+	0.882585i	0.0585392	+	0.998285i	$0.481356\pi$
$942$	−1.31793e13	−	2.25463e13i	−0.545335	−	0.932923i
$943$	−2.17606e13	−	7.92020e12i	−0.896123	−	0.326162i
$944$	3.69776e12			0.151553
$945$	6.11963e12	+	1.02152e13i	0.249622	+	0.416681i
$946$	7.11160e11			0.0288707
$947$	4.50715e12	+	1.64047e12i	0.182107	+	0.0662816i	0.431464	−	0.902130i	$-0.357997\pi$
$947$	4.50715e12	+	1.64047e12i	0.182107	+	0.0662816i	−0.249357	+	0.968412i	$0.580219\pi$
$948$	1.27487e13	−	6.85771e10i	0.512658	−	0.00275766i
$949$	3.55687e12	+	2.98457e12i	0.142354	+	0.119449i
$950$	3.71012e12	−	2.10411e13i	0.147785	−	0.838133i
$951$	6.03375e11	+	3.31746e12i	0.0239208	+	0.131520i
$952$	−4.32291e12	+	3.62736e12i	−0.170573	+	0.143128i
$953$	8.58128e12	+	1.48632e13i	0.337003	+	0.583707i	0.983868	−	0.178898i	$-0.0572534\pi$
$953$	8.58128e12	+	1.48632e13i	0.337003	+	0.583707i	−0.646864	+	0.762605i	$0.723920\pi$
$954$	−9.15725e11	−	4.88540e12i	−0.0357929	−	0.190955i
$955$	3.89463e12	−	6.74570e12i	0.151514	−	0.262429i
$956$	−5.00625e11	−	2.83918e12i	−0.0193844	−	0.109934i
$957$	−1.09664e12	−	9.10181e11i	−0.0422629	−	0.0350771i
$958$	2.35586e12	−	8.57462e11i	0.0903658	−	0.0328905i
$959$	7.06653e12	−	2.57201e12i	0.269788	−	0.0981948i
$960$	−1.07827e13	+	3.99041e12i	−0.409740	+	0.151634i
$961$	−3.15772e12	−	1.79083e13i	−0.119431	−	0.677329i
$962$	5.26077e11	−	9.11192e11i	0.0198044	−	0.0343022i
$963$	−1.53510e13	−	2.59402e13i	−0.575199	−	0.971973i
$964$	−3.83986e12	−	6.65083e12i	−0.143208	−	0.248044i
$965$	−1.58316e13	+	1.32843e13i	−0.587694	+	0.493134i
$966$	1.85012e13	−	1.56947e13i	0.683600	−	0.579903i
$967$	−2.13426e12	+	1.21040e13i	−0.0784924	+	0.445153i	0.920080	+	0.391731i	$0.128124\pi$
$967$	−2.13426e12	+	1.21040e13i	−0.0784924	+	0.445153i	−0.998572	+	0.0534213i	$0.982987\pi$
$968$	2.21874e13	+	1.86174e13i	0.812208	+	0.681523i
$969$	4.63136e12	−	8.12234e12i	0.168753	−	0.295954i
$970$	−5.14391e12	−	1.87223e12i	−0.186561	−	0.0679026i
$971$	1.10012e12			0.0397149			0.0198575	−	0.999803i	$-0.493679\pi$
$971$	1.10012e12			0.0397149			0.0198575	+	0.999803i	$0.493679\pi$
$972$	2.03311e12	−	1.36707e13i	0.0730570	−	0.491240i
$973$	2.32355e13			0.831082
$974$	−1.46170e13	−	5.32016e12i	−0.520408	−	0.189413i
$975$	1.13512e12	−	1.99074e12i	0.0402274	−	0.0705496i
$976$	8.62421e12	+	7.23657e12i	0.304225	+	0.255275i
$977$	1.70524e12	−	9.67088e12i	0.0598769	−	0.339579i	−0.940122	−	0.340837i	$-0.889290\pi$
$977$	1.70524e12	−	9.67088e12i	0.0598769	−	0.339579i	0.999999	+	0.00125859i	$0.000400621\pi$
$978$	−5.53941e12	+	4.69912e12i	−0.193615	+	0.164245i
$979$	3.42872e10	−	2.87704e10i	0.00119292	−	0.00100098i
$980$	1.45802e11	+	2.52537e11i	0.00504948	+	0.00874595i
$981$	−2.43110e13	−	4.10808e13i	−0.838093	−	1.41621i
$982$	5.35352e12	−	9.27257e12i	0.183712	−	0.318199i
$983$	4.23776e12	+	2.40335e13i	0.144759	+	0.820968i	0.967560	+	0.252639i	$0.0812987\pi$
$983$	4.23776e12	+	2.40335e13i	0.144759	+	0.820968i	−0.822802	+	0.568329i	$0.807590\pi$
$984$	−2.16458e13	+	8.01054e12i	−0.736030	+	0.272385i
$985$	1.31209e13	−	4.77563e12i	0.444122	−	0.161647i
$986$	6.04988e12	−	2.20198e12i	0.203845	−	0.0741937i
$987$	1.46721e13	+	1.21775e13i	0.492114	+	0.408442i
$988$	−4.42637e11	−	2.51032e12i	−0.0147789	−	0.0838152i
$989$	−2.05340e13	+	3.55660e13i	−0.682482	+	1.18209i
$990$	−7.53733e10	−	4.02117e11i	−0.00249378	−	0.0133044i
$991$	−4.10783e12	−	7.11496e12i	−0.135295	−	0.234337i	0.790415	−	0.612571i	$-0.209865\pi$
$991$	−4.10783e12	−	7.11496e12i	−0.135295	−	0.234337i	−0.925710	+	0.378234i	$0.876531\pi$
$992$	1.14849e13	−	9.63698e12i	0.376552	−	0.315965i
$993$	4.34679e12	+	2.38994e13i	0.141872	+	0.780037i
$994$	−4.19212e11	+	2.37747e12i	−0.0136206	+	0.0772461i
$995$	5.31325e12	+	4.45835e12i	0.171853	+	0.144202i
$996$	2.50786e13	−	1.34901e11i	0.807488	−	0.00434360i
$997$	4.55514e12	+	1.65793e12i	0.146007	+	0.0531422i	0.413990	−	0.910281i	$-0.364135\pi$
$997$	4.55514e12	+	1.65793e12i	0.146007	+	0.0531422i	−0.267983	+	0.963424i	$0.586357\pi$
$998$	−3.13687e13			−1.00094
$999$	7.92931e12	−	1.42606e13i	0.251878	−	0.452993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.4.9	✓	156
3.2	odd	2		81.10.e.a.64.18		156
27.7	even	9	inner	27.10.e.a.7.9	yes	156
27.20	odd	18		81.10.e.a.19.18		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.9	✓	156	1.1	even	1	trivial
27.10.e.a.7.9	yes	156	27.7	even	9	inner
81.10.e.a.19.18		156	27.20	odd	18
81.10.e.a.64.18		156	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-15.0855 - 5.49066i) q^{2} +(69.4935 - 121.876i) q^{3} +(-194.791 - 163.449i) q^{4} +(-120.371 + 682.656i) q^{5} +(-1717.52 + 1456.99i) q^{6} +(-4765.46 + 3998.70i) q^{7} +(6150.79 + 10653.5i) q^{8} +(-10024.3 - 16939.1i) q^{9} +(5564.08 - 9637.27i) q^{10} +(324.344 + 1839.45i) q^{11} +(-33457.1 + 12381.6i) q^{12} +(10423.0 - 3793.68i) q^{13} +(93844.8 - 34156.7i) q^{14} +(74834.1 + 62110.4i) q^{15} +(-11685.3 - 66270.8i) q^{16} +(36870.6 - 63861.7i) q^{17} +(58214.5 + 310575. i) q^{18} +(451882. + 782682. i) q^{19} +(135026. - 113301. i) q^{20} +(156175. + 858677. i) q^{21} +(5206.90 - 29529.8i) q^{22} +(1.32648e6 + 1.11305e6i) q^{23} +(1.72584e6 - 9283.55i) q^{24} +(1.38381e6 + 503665. i) q^{25} -178066. q^{26} +(-2.76109e6 + 44560.4i) q^{27} +1.58185e6 q^{28} +(-5.11051e6 - 1.86007e6i) q^{29} +(-787881. - 1.34785e6i) q^{30} +(2.20097e6 + 1.84683e6i) q^{31} +(906116. - 5.13884e6i) q^{32} +(246724. + 88300.0i) q^{33} +(-906854. + 760941. i) q^{34} +(-2.15611e6 - 3.73450e6i) q^{35} +(-816036. + 4.93804e6i) q^{36} +(-2.95439e6 + 5.11715e6i) q^{37} +(-2.51940e6 - 1.42883e7i) q^{38} +(261977. - 1.53395e6i) q^{39} +(-8.01304e6 + 2.91651e6i) q^{40} +(-1.25668e7 + 4.57393e6i) q^{41} +(2.35873e6 - 1.38111e7i) q^{42} +(4.11840e6 + 2.33566e7i) q^{43} +(237476. - 411321. i) q^{44} +(1.27702e7 - 4.80418e6i) q^{45} +(-1.38992e7 - 2.40741e7i) q^{46} +(1.67358e7 - 1.40430e7i) q^{47} +(-8.88885e6 - 3.18123e6i) q^{48} +(-287276. + 1.62922e6i) q^{49} +(-1.81099e7 - 1.51960e7i) q^{50} +(-5.22092e6 - 8.93160e6i) q^{51} +(-2.65038e6 - 964661. i) q^{52} -1.57302e7 q^{53} +(4.18970e7 + 1.44880e7i) q^{54} -1.29475e6 q^{55} +(-7.19115e7 - 2.61736e7i) q^{56} +(1.26793e8 - 682036. i) q^{57} +(6.68814e7 + 5.61201e7i) q^{58} +(-9.54196e6 + 5.41151e7i) q^{59} +(-4.42512e6 - 2.43301e7i) q^{60} +(-1.28159e8 + 1.07538e8i) q^{61} +(-2.30623e7 - 3.99451e7i) q^{62} +(1.15505e8 + 4.06386e7i) q^{63} +(-5.91119e7 + 1.02385e8i) q^{64} +(1.33515e6 + 7.57200e6i) q^{65} +(-3.23712e6 - 2.68672e6i) q^{66} +(-8.32922e7 + 3.03159e7i) q^{67} +(-1.76202e7 + 6.41322e6i) q^{68} +(2.27835e8 - 8.43158e7i) q^{69} +(1.20211e7 + 6.81752e7i) q^{70} +(-1.20867e7 + 2.09349e7i) q^{71} +(1.18803e8 - 2.10983e8i) q^{72} +(2.09303e8 + 3.62523e8i) q^{73} +(7.26649e7 - 6.09731e7i) q^{74} +(1.57550e8 - 1.33651e8i) q^{75} +(3.99061e7 - 2.26319e8i) q^{76} +(-8.90105e6 - 7.46887e6i) q^{77} +(-1.23744e7 + 2.17019e7i) q^{78} +(-3.35813e8 - 1.22226e8i) q^{79} +4.66467e7 q^{80} +(-1.86447e8 + 3.39606e8i) q^{81} +2.14690e8 q^{82} +(-6.60595e8 - 2.40437e8i) q^{83} +(1.09928e8 - 1.92789e8i) q^{84} +(3.91574e7 + 3.28570e7i) q^{85} +(6.61152e7 - 3.74958e8i) q^{86} +(-5.81844e8 + 4.93583e8i) q^{87} +(-1.76016e7 + 1.47695e7i) q^{88} +(-1.19815e7 - 2.07526e7i) q^{89} +(-2.19023e8 + 2.35638e6i) q^{90} +(-3.45009e7 + 5.97572e7i) q^{91} +(-7.64594e7 - 4.33623e8i) q^{92} +(3.78037e8 - 1.39901e8i) q^{93} +(-3.29573e8 + 1.19955e8i) q^{94} +(-5.88695e8 + 2.14268e8i) q^{95} +(-5.63330e8 - 4.67549e8i) q^{96} +(-8.54190e7 - 4.84435e8i) q^{97} +(1.32792e7 - 2.30003e7i) q^{98} +(2.79073e7 - 2.39333e7i) 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

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