LMFDB - Embedded newform 54.9.f.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	54.5
Dual form			54.9.f.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.27231 - 8.66680i) q^{2} +(7.33820 + 80.6669i) q^{3} +(-22.2270 + 126.055i) q^{4} +(58.6289 + 161.081i) q^{5} +(645.759 - 650.234i) q^{6} +(-371.637 - 2107.66i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6453.30 + 1183.90i) q^{9} +O(q^{10})$	\(q+(-7.27231 - 8.66680i) q^{2} +(7.33820 + 80.6669i) q^{3} +(-22.2270 + 126.055i) q^{4} +(58.6289 + 161.081i) q^{5} +(645.759 - 650.234i) q^{6} +(-371.637 - 2107.66i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6453.30 + 1183.90i) q^{9} +(969.694 - 1679.56i) q^{10} +(6809.53 - 18709.0i) q^{11} +(-10331.6 - 867.961i) q^{12} +(-1070.41 - 898.179i) q^{13} +(-15564.0 + 18548.5i) q^{14} +(-12563.7 + 5911.46i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(50482.8 + 29146.2i) q^{17} +(57191.0 + 47319.8i) q^{18} +(89325.9 + 154717. i) q^{19} +(-21608.3 + 3810.13i) q^{20} +(167291. - 45445.2i) q^{21} +(-211668. + 77041.0i) q^{22} +(-128314. - 22625.3i) q^{23} +(67612.2 + 95854.1i) q^{24} +(276726. - 232201. i) q^{25} +15808.9i q^{26} +(-142857. - 511880. i) q^{27} +273942. q^{28} +(769507. + 917062. i) q^{29} +(142601. + 65897.3i) q^{30} +(138384. - 784813. i) q^{31} +(63398.2 + 174185. i) q^{32} +(1.55917e6 + 412013. i) q^{33} +(-114522. - 649485. i) q^{34} +(317716. - 183433. i) q^{35} +(-5799.63 - 839788. i) q^{36} +(1.31302e6 - 2.27422e6i) q^{37} +(691296. - 1.89932e6i) q^{38} +(64598.5 - 92937.6i) q^{39} +(190164. + 159567. i) q^{40} +(-232825. + 277469. i) q^{41} +(-1.61046e6 - 1.11939e6i) q^{42} +(4.97942e6 + 1.81236e6i) q^{43} +(2.20702e6 + 1.27422e6i) q^{44} +(-569054. - 970097. i) q^{45} +(737054. + 1.27661e6i) q^{46} +(190199. - 33537.2i) q^{47} +(339051. - 1.28306e6i) q^{48} +(1.11303e6 - 405110. i) q^{49} +(-4.02488e6 - 709695. i) q^{50} +(-1.98068e6 + 4.28617e6i) q^{51} +(137012. - 114967. i) q^{52} +8.84487e6i q^{53} +(-3.39746e6 + 4.96067e6i) q^{54} +3.41291e6 q^{55} +(-1.99219e6 - 2.37420e6i) q^{56} +(-1.18251e7 + 8.34099e6i) q^{57} +(2.35191e6 - 1.33383e7i) q^{58} +(369812. + 1.01605e6i) q^{59} +(-465918. - 1.71512e6i) q^{60} +(1.22873e6 + 6.96846e6i) q^{61} +(-7.80819e6 + 4.50806e6i) q^{62} +(4.89354e6 + 1.31614e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(81923.2 - 225082. i) q^{65} +(-7.76792e6 - 1.65093e7i) q^{66} +(596731. + 500717. i) q^{67} +(-4.79612e6 + 5.71579e6i) q^{68} +(883516. - 1.05168e7i) q^{69} +(-3.90031e6 - 1.41960e6i) q^{70} +(-2.19784e7 - 1.26892e7i) q^{71} +(-7.23610e6 + 6.15746e6i) q^{72} +(-1.40726e7 - 2.43745e7i) q^{73} +(-2.92589e7 + 5.15913e6i) q^{74} +(2.07616e7 + 2.06187e7i) q^{75} +(-2.14884e7 + 7.82112e6i) q^{76} +(-4.19629e7 - 7.39919e6i) q^{77} +(-1.27525e6 + 116009. i) q^{78} +(5.12352e7 - 4.29914e7i) q^{79} -2.80853e6i q^{80} +(4.02435e7 - 1.52801e7i) q^{81} +4.09795e6 q^{82} +(3.12133e7 + 3.71985e7i) q^{83} +(2.01024e6 + 2.20981e7i) q^{84} +(-1.73517e6 + 9.84065e6i) q^{85} +(-2.05045e7 - 5.63357e7i) q^{86} +(-6.83298e7 + 6.88033e7i) q^{87} +(-5.00669e6 - 2.83943e7i) q^{88} +(2.76348e7 - 1.59550e7i) q^{89} +(-4.26930e6 + 1.19867e7i) q^{90} +(-1.49525e6 + 2.58985e6i) q^{91} +(5.70408e6 - 1.56718e7i) q^{92} +(6.43239e7 + 5.40387e6i) q^{93} +(-1.67385e6 - 1.40453e6i) q^{94} +(-1.96850e7 + 2.34596e7i) q^{95} +(-1.35857e7 + 6.39234e6i) q^{96} +(-1.10475e7 - 4.02096e6i) q^{97} +(-1.16053e7 - 6.70034e6i) q^{98} +(-2.17943e7 + 1.28797e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	−7.27231	−	8.66680i	−0.454519	−	0.541675i
$2$	−7.27231	−	8.66680i	−0.454519	−	0.541675i
$3$	7.33820	+	80.6669i	0.0905951	+	0.995888i
$3$	7.33820	+	80.6669i	0.0905951	+	0.995888i
$4$	−22.2270	+	126.055i	−0.0868241	+	0.492404i
$5$	58.6289	+	161.081i	0.0938062	+	0.257730i	0.977718	−	0.209924i	$-0.0673215\pi$
$5$	58.6289	+	161.081i	0.0938062	+	0.257730i	−0.883912	+	0.467654i	$0.845099\pi$
$6$	645.759	−	650.234i	0.498271	−	0.501724i
$7$	−371.637	−	2107.66i	−0.154784	−	0.877825i	−0.958983	−	0.283464i	$-0.908516\pi$
$7$	−371.637	−	2107.66i	−0.154784	−	0.877825i	0.804199	−	0.594361i	$-0.202595\pi$
$8$	1254.14	−	724.077i	0.306186	−	0.176777i
$9$	−6453.30	+	1183.90i	−0.983585	+	0.180445i
$10$	969.694	−	1679.56i	0.0969694	−	0.167956i
$11$	6809.53	−	18709.0i	0.465100	−	1.27785i	−0.456505	−	0.889721i	$-0.650899\pi$
$11$	6809.53	−	18709.0i	0.465100	−	1.27785i	0.921605	−	0.388130i	$-0.126879\pi$
$12$	−10331.6	−	867.961i	−0.498245	−	0.0418577i
$13$	−1070.41	−	898.179i	−0.0374780	−	0.0314478i	0.623856	−	0.781539i	$-0.285565\pi$
$13$	−1070.41	−	898.179i	−0.0374780	−	0.0314478i	−0.661334	+	0.750091i	$0.730010\pi$
$14$	−15564.0	+	18548.5i	−0.405144	+	0.482831i
$15$	−12563.7	+	5911.46i	−0.248172	+	0.116770i
$16$	−15395.9	−	5603.66i	−0.234923	−	0.0855050i
$17$	50482.8	+	29146.2i	0.604432	+	0.348969i	0.770783	−	0.637098i	$-0.219865\pi$
$17$	50482.8	+	29146.2i	0.604432	+	0.348969i	−0.166351	+	0.986067i	$0.553199\pi$
$18$	57191.0	+	47319.8i	0.544801	+	0.450768i
$19$	89325.9	+	154717.i	0.685430	+	1.18720i	0.973301	+	0.229531i	$0.0737191\pi$
$19$	89325.9	+	154717.i	0.685430	+	1.18720i	−0.287871	+	0.957669i	$0.592948\pi$
$20$	−21608.3	+	3810.13i	−0.135052	+	0.0238133i
$21$	167291.	−	45445.2i	0.860193	−	0.233674i
$22$	−211668.	+	77041.0i	−0.903577	+	0.328875i
$23$	−128314.	−	22625.3i	−0.458526	−	0.0808506i	−0.0603861	−	0.998175i	$-0.519233\pi$
$23$	−128314.	−	22625.3i	−0.458526	−	0.0808506i	−0.398140	+	0.917325i	$0.630344\pi$
$24$	67612.2	+	95854.1i	0.203789	+	0.288912i
$25$	276726.	−	232201.i	0.708419	−	0.594434i
$26$			15808.9i			0.0345945i
$27$	−142857.	−	511880.i	−0.268811	−	0.963193i
$28$	273942.			0.445684
$29$	769507.	+	917062.i	1.08798	+	1.29660i	0.952070	+	0.305881i	$0.0989510\pi$
$29$	769507.	+	917062.i	1.08798	+	1.29660i	0.135909	+	0.990721i	$0.456605\pi$
$30$	142601.	+	65897.3i	0.176050	+	0.0813547i
$31$	138384.	−	784813.i	0.149844	−	0.849805i	−0.813506	−	0.581557i	$-0.802444\pi$
$31$	138384.	−	784813.i	0.149844	−	0.849805i	0.963350	−	0.268249i	$-0.0864450\pi$
$32$	63398.2	+	174185.i	0.0604612	+	0.166116i
$33$	1.55917e6	+	412013.i	1.31473	+	0.347420i
$34$	−114522.	−	649485.i	−0.0856983	−	0.486019i
$35$	317716.	−	183433.i	0.211722	−	0.122238i
$36$	−5799.63	−	839788.i	−0.00345295	−	0.499988i
$37$	1.31302e6	−	2.27422e6i	0.700591	−	1.21346i	−0.267668	−	0.963511i	$-0.586253\pi$
$37$	1.31302e6	−	2.27422e6i	0.700591	−	1.21346i	0.968259	−	0.249948i	$-0.0804136\pi$
$38$	691296.	−	1.89932e6i	0.331535	−	0.910886i
$39$	64598.5	−	92937.6i	0.0279231	−	0.0401729i
$40$	190164.	+	159567.i	0.0742829	+	0.0623307i
$41$	−232825.	+	277469.i	−0.0823936	+	0.0981928i	−0.805666	−	0.592370i	$-0.798193\pi$
$41$	−232825.	+	277469.i	−0.0823936	+	0.0981928i	0.723273	+	0.690562i	$0.242637\pi$
$42$	−1.61046e6	−	1.11939e6i	−0.517550	−	0.359736i
$43$	4.97942e6	+	1.81236e6i	1.45648	+	0.530116i	0.944393	−	0.328818i	$-0.106650\pi$
$43$	4.97942e6	+	1.81236e6i	1.45648	+	0.530116i	0.512087	+	0.858933i	$0.328872\pi$
$44$	2.20702e6	+	1.27422e6i	0.588837	+	0.339965i
$45$	−569054.	−	970097.i	−0.138773	−	0.236573i
$46$	737054.	+	1.27661e6i	0.164614	+	0.285121i
$47$	190199.	−	33537.2i	0.0389778	−	0.00687284i	−0.154125	−	0.988051i	$-0.549256\pi$
$47$	190199.	−	33537.2i	0.0389778	−	0.00687284i	0.193103	+	0.981178i	$0.438145\pi$
$48$	339051.	−	1.28306e6i	0.0638705	−	0.241703i
$49$	1.11303e6	−	405110.i	0.193074	−	0.0702731i
$50$	−4.02488e6	−	709695.i	−0.643981	−	0.113551i
$51$	−1.98068e6	+	4.28617e6i	−0.292775	+	0.633561i
$52$	137012.	−	114967.i	0.0187390	−	0.0157239i
$53$			8.84487e6i			1.12095i	0.828170	+	0.560477i	$0.189382\pi$
$53$			8.84487e6i			1.12095i	−0.828170	+	0.560477i	$0.810618\pi$
$54$	−3.39746e6	+	4.96067e6i	−0.399558	+	0.583398i
$55$	3.41291e6			0.372970
$56$	−1.99219e6	−	2.37420e6i	−0.202572	−	0.241416i
$57$	−1.18251e7	+	8.34099e6i	−1.12022	+	0.790166i
$58$	2.35191e6	−	1.33383e7i	0.207830	−	1.17866i
$59$	369812.	+	1.01605e6i	0.0305192	+	0.0838508i	0.954016	−	0.299754i	$-0.0969047\pi$
$59$	369812.	+	1.01605e6i	0.0305192	+	0.0838508i	−0.923497	+	0.383605i	$0.874682\pi$
$60$	−465918.	−	1.71512e6i	−0.0359505	−	0.132339i
$61$	1.22873e6	+	6.96846e6i	0.0887434	+	0.503289i	0.996486	+	0.0837610i	$0.0266932\pi$
$61$	1.22873e6	+	6.96846e6i	0.0887434	+	0.503289i	−0.907742	+	0.419528i	$0.862196\pi$
$62$	−7.80819e6	+	4.50806e6i	−0.528425	+	0.305087i
$63$	4.89354e6	+	1.31614e7i	0.310643	+	0.835486i
$64$	1.04858e6	−	1.81619e6i	0.0625000	−	0.108253i
$65$	81923.2	−	225082.i	0.00458938	−	0.0126092i
$66$	−7.76792e6	−	1.65093e7i	−0.409382	−	0.870067i
$67$	596731.	+	500717.i	0.0296128	+	0.0248481i	0.657474	−	0.753477i	$-0.271625\pi$
$67$	596731.	+	500717.i	0.0296128	+	0.0248481i	−0.627861	+	0.778325i	$0.716069\pi$
$68$	−4.79612e6	+	5.71579e6i	−0.224313	+	0.267326i
$69$	883516.	−	1.05168e7i	0.0389779	−	0.463966i
$70$	−3.90031e6	−	1.41960e6i	−0.162445	−	0.0591253i
$71$	−2.19784e7	−	1.26892e7i	−0.864894	−	0.499347i	0.000754183	−	1.00000i	$-0.499760\pi$
$71$	−2.19784e7	−	1.26892e7i	−0.864894	−	0.499347i	−0.865648	+	0.500653i	$0.833093\pi$
$72$	−7.23610e6	+	6.15746e6i	−0.269262	+	0.229125i
$73$	−1.40726e7	−	2.43745e7i	−0.495545	−	0.858309i	0.504442	−	0.863446i	$-0.331698\pi$
$73$	−1.40726e7	−	2.43745e7i	−0.495545	−	0.858309i	−0.999987	+	0.00513672i	$0.998365\pi$
$74$	−2.92589e7	+	5.15913e6i	−0.975733	+	0.172048i
$75$	2.07616e7	+	2.06187e7i	0.656169	+	0.651653i
$76$	−2.14884e7	+	7.82112e6i	−0.644094	+	0.234431i
$77$	−4.19629e7	−	7.39919e6i	−1.19372	−	0.210485i
$78$	−1.27525e6	+	116009.i	−0.0344523	+	0.00313409i
$79$	5.12352e7	−	4.29914e7i	1.31541	−	1.10376i	0.328150	−	0.944626i	$-0.393575\pi$
$79$	5.12352e7	−	4.29914e7i	1.31541	−	1.10376i	0.987257	−	0.159132i	$-0.0508694\pi$
$80$		−	2.80853e6i		−	0.0685677i
$81$	4.02435e7	−	1.52801e7i	0.934879	−	0.354966i
$82$	4.09795e6			0.0906381
$83$	3.12133e7	+	3.71985e7i	0.657699	+	0.783815i	0.987053	−	0.160392i	$-0.0512757\pi$
$83$	3.12133e7	+	3.71985e7i	0.657699	+	0.783815i	−0.329355	+	0.944206i	$0.606831\pi$
$84$	2.01024e6	+	2.20981e7i	0.0403767	+	0.443851i
$85$	−1.73517e6	+	9.84065e6i	−0.0332405	+	0.188516i
$86$	−2.05045e7	−	5.63357e7i	−0.374848	−	1.02989i
$87$	−6.83298e7	+	6.88033e7i	−1.19271	+	1.20097i
$88$	−5.00669e6	−	2.83943e7i	−0.0834872	−	0.473479i
$89$	2.76348e7	−	1.59550e7i	0.440450	−	0.254294i	−0.263339	−	0.964703i	$-0.584824\pi$
$89$	2.76348e7	−	1.59550e7i	0.440450	−	0.254294i	0.703788	+	0.710410i	$0.251490\pi$
$90$	−4.26930e6	+	1.19867e7i	−0.0650709	+	0.182697i
$91$	−1.49525e6	+	2.58985e6i	−0.0218046	+	0.0377667i
$92$	5.70408e6	−	1.56718e7i	0.0796223	−	0.218760i
$93$	6.43239e7	+	5.40387e6i	0.859886	+	0.0722393i
$94$	−1.67385e6	−	1.40453e6i	−0.0214390	−	0.0179895i
$95$	−1.96850e7	+	2.34596e7i	−0.241680	+	0.288023i
$96$	−1.35857e7	+	6.39234e6i	−0.159955	+	0.0752618i
$97$	−1.10475e7	−	4.02096e6i	−0.124789	−	0.0454196i	0.278871	−	0.960329i	$-0.410040\pi$
$97$	−1.10475e7	−	4.02096e6i	−0.124789	−	0.0454196i	−0.403660	+	0.914909i	$0.632262\pi$
$98$	−1.16053e7	−	6.70034e6i	−0.125821	−	0.0726428i
$99$	−2.17943e7	+	1.28797e8i	−0.226883	+	1.34080i
$100$	2.31194e7	+	4.00440e7i	0.231194	+	0.400440i
$101$	−1.29650e8	+	2.28608e7i	−1.24591	+	0.219688i	−0.757447	−	0.652897i	$-0.773554\pi$
$101$	−1.29650e8	+	2.28608e7i	−1.24591	+	0.219688i	−0.488464	+	0.872584i	$0.662443\pi$
$102$	5.15516e7	−	1.40042e7i	0.476257	−	0.129377i
$103$	1.26601e8	−	4.60791e7i	1.12484	−	0.409407i	0.288421	−	0.957504i	$-0.406870\pi$
$103$	1.26601e8	−	4.60791e7i	1.12484	−	0.409407i	0.836415	+	0.548097i	$0.184647\pi$
$104$	−1.99279e6	−	351383.i	−0.0170345	−	0.00300364i
$105$	1.71285e7	+	2.42831e7i	0.140916	+	0.199778i
$106$	7.66568e7	−	6.43227e7i	0.607194	−	0.509496i
$107$		−	4.79165e7i		−	0.365553i	−0.983155	−	0.182776i	$-0.941492\pi$
$107$		−	4.79165e7i		−	0.365553i	0.983155	−	0.182776i	$-0.0585084\pi$
$108$	6.77005e7	−	6.63037e6i	0.497619	−	0.0487352i
$109$	6.02890e7			0.427103			0.213551	−	0.976932i	$-0.431497\pi$
$109$	6.02890e7			0.427103			0.213551	+	0.976932i	$0.431497\pi$
$110$	−2.48198e7	−	2.95790e7i	−0.169522	−	0.202029i
$111$	1.93089e8	+	8.92287e7i	1.27194	+	0.587777i
$112$	−6.08890e6	+	3.45319e7i	−0.0386961	+	0.219456i
$113$	−8.42957e7	−	2.31601e8i	−0.517001	−	1.42045i	−0.873808	−	0.486272i	$-0.838357\pi$
$113$	−8.42957e7	−	2.31601e8i	−0.517001	−	1.42045i	0.356806	−	0.934178i	$-0.383866\pi$
$114$	1.58285e8	+	4.18271e7i	0.937176	+	0.247650i
$115$	−3.87842e6	−	2.19956e7i	−0.0221750	−	0.125760i
$116$	−1.32704e8	+	7.66170e7i	−0.732915	+	0.423149i
$117$	7.97102e6	+	4.52897e6i	0.0425374	+	0.0241688i
$118$	6.11652e6	−	1.05941e7i	0.0315483	−	0.0546433i
$119$	4.26690e7	−	1.17232e8i	0.212777	−	0.584601i
$120$	−1.14763e7	+	1.65109e7i	−0.0553448	+	0.0796243i
$121$	−1.39449e8	−	1.17012e8i	−0.650541	−	0.545869i
$122$	5.14586e7	−	6.13259e7i	0.232283	−	0.276825i
$123$	−2.40911e7	−	1.67451e7i	−0.105253	−	0.0731590i
$124$	9.58541e7	+	3.48880e7i	0.405437	+	0.147567i
$125$	1.11617e8	+	6.44421e7i	0.457183	+	0.263955i
$126$	7.84797e7	−	1.38125e8i	0.311369	−	0.548012i
$127$	−1.10244e7	−	1.90949e7i	−0.0423781	−	0.0734010i	0.844058	−	0.536251i	$-0.180160\pi$
$127$	−1.10244e7	−	1.90949e7i	−0.0423781	−	0.0734010i	−0.886436	+	0.462850i	$0.846827\pi$
$128$	−2.33661e7	+	4.12008e6i	−0.0870455	+	0.0153485i
$129$	−1.09657e8	+	4.14974e8i	−0.395986	+	1.49852i
$130$	−2.54652e6	+	926856.i	−0.00891606	+	0.00324518i
$131$	−1.17070e7	−	2.06426e6i	−0.0397522	−	0.00700939i	0.153737	−	0.988112i	$-0.450869\pi$
$131$	−1.17070e7	−	2.06426e6i	−0.0397522	−	0.00700939i	−0.193489	+	0.981102i	$0.561980\pi$
$132$	−8.65920e7	+	1.87384e8i	−0.285221	+	0.617215i
$133$	2.92894e8	−	2.45767e8i	0.936060	−	0.785448i
$134$		−	8.81312e6i		−	0.0273344i
$135$	7.40789e7	−	5.30226e7i	0.223028	−	0.159634i
$136$	8.44165e7			0.246758
$137$	−2.39525e8	−	2.85455e8i	−0.679938	−	0.810319i	0.310162	−	0.950684i	$-0.399617\pi$
$137$	−2.39525e8	−	2.85455e8i	−0.679938	−	0.810319i	−0.990100	+	0.140365i	$0.955172\pi$
$138$	−9.75719e7	+	6.88239e7i	−0.269035	+	0.189768i
$139$	8.16191e7	−	4.62885e8i	0.218642	−	1.23998i	−0.655833	−	0.754906i	$-0.727682\pi$
$139$	8.16191e7	−	4.62885e8i	0.218642	−	1.23998i	0.874474	−	0.485072i	$-0.161206\pi$
$140$	1.60609e7	+	4.41270e7i	0.0418079	+	0.114866i
$141$	4.10107e6	+	1.50967e7i	0.0103758	+	0.0381949i
$142$	4.98587e7	+	2.82763e8i	0.122627	+	0.695454i
$143$	−2.40930e7	+	1.39101e7i	−0.0576166	+	0.0332649i
$144$	1.05989e8	+	1.79349e7i	0.246496	+	0.0417108i
$145$	−1.02606e8	+	1.77720e8i	−0.232115	+	0.402035i
$146$	−1.08908e8	+	2.99223e8i	−0.239690	+	0.658542i
$147$	4.08467e7	+	8.68121e7i	0.0874757	+	0.185913i
$148$	2.57493e8	+	2.16062e8i	0.536684	+	0.450331i
$149$	−1.83764e8	+	2.19002e8i	−0.372835	+	0.444327i	−0.919539	−	0.392999i	$-0.871438\pi$
$149$	−1.83764e8	+	2.19002e8i	−0.372835	+	0.444327i	0.546704	+	0.837326i	$0.315882\pi$
$150$	2.77135e7	−	3.29882e8i	0.0547427	−	0.651620i
$151$	−5.54387e8	−	2.01780e8i	−1.06636	−	0.388125i	−0.251548	−	0.967845i	$-0.580940\pi$
$151$	−5.54387e8	−	2.01780e8i	−1.06636	−	0.388125i	−0.814816	+	0.579720i	$0.803162\pi$
$152$	2.24054e8	+	1.29358e8i	0.419738	+	0.242336i
$153$	−3.60287e8	−	1.28323e8i	−0.657480	−	0.234174i
$154$	2.41040e8	+	4.17493e8i	0.428554	+	0.742278i
$155$	1.34532e8	−	2.37217e7i	0.233077	−	0.0410978i
$156$	1.02795e7	+	1.02087e7i	0.0173569	+	0.0172374i
$157$	−2.95235e8	+	1.07457e8i	−0.485925	+	0.176862i	−0.573353	−	0.819309i	$-0.694357\pi$
$157$	−2.95235e8	+	1.07457e8i	−0.485925	+	0.176862i	0.0874280	+	0.996171i	$0.472135\pi$
$158$	−7.45197e8	−	1.31398e8i	−1.19576	−	0.210844i
$159$	−7.13489e8	+	6.49054e7i	−1.11635	+	0.101553i
$160$	−2.43410e7	+	2.04245e7i	−0.0371414	+	0.0311654i
$161$			2.78851e8i			0.415020i
$162$	−4.25093e8	−	2.37661e8i	−0.617197	−	0.345062i
$163$	1.90229e7			0.0269480			0.0134740	−	0.999909i	$-0.495711\pi$
$163$	1.90229e7			0.0269480			0.0134740	+	0.999909i	$0.495711\pi$
$164$	−2.98015e7	−	3.55161e7i	−0.0411968	−	0.0490964i
$165$	2.50446e7	+	2.75309e8i	0.0337893	+	0.371437i
$166$	9.53997e7	−	5.41039e8i	0.125636	−	0.712518i
$167$	−1.54503e8	−	4.24493e8i	−0.198642	−	0.545763i	0.799878	−	0.600163i	$-0.204898\pi$
$167$	−1.54503e8	−	4.24493e8i	−0.198642	−	0.545763i	−0.998519	+	0.0543998i	$0.982675\pi$
$168$	1.76900e8	−	1.78126e8i	0.222071	−	0.223610i
$169$	−1.41311e8	−	8.01415e8i	−0.173233	−	0.982451i
$170$	9.79057e7	−	5.65259e7i	0.117223	−	0.0676786i
$171$	−7.59617e8	−	8.92683e8i	−0.888403	−	1.04403i
$172$	−3.39135e8	+	5.87399e8i	−0.387489	+	0.671150i
$173$	−5.15200e8	+	1.41550e9i	−0.575164	+	1.58025i	0.221068	+	0.975258i	$0.429046\pi$
$173$	−5.15200e8	+	1.41550e9i	−0.575164	+	1.58025i	−0.796232	+	0.604991i	$0.793177\pi$
$174$	1.09322e9	+	9.18418e7i	1.19264	+	0.100194i
$175$	−5.92242e8	−	4.96950e8i	−0.631461	−	0.529859i
$176$	−2.09678e8	+	2.49884e8i	−0.218525	+	0.260428i
$177$	−7.92479e7	+	3.72876e7i	−0.0807411	+	0.0379902i
$178$	−3.39247e8	−	1.23476e8i	−0.337938	−	0.122999i
$179$	1.51942e9	+	8.77240e8i	1.48002	+	0.854489i	0.999744	−	0.0226299i	$-0.00720395\pi$
$179$	1.51942e9	+	8.77240e8i	1.48002	+	0.854489i	0.480274	+	0.877119i	$0.340537\pi$
$180$	1.34934e8	−	5.01700e7i	0.128538	−	0.0477919i
$181$	9.10102e7	+	1.57634e8i	0.0847961	+	0.146871i	0.905304	−	0.424764i	$-0.139643\pi$
$181$	9.10102e7	+	1.57634e8i	0.0847961	+	0.146871i	−0.820508	+	0.571635i	$0.806309\pi$
$182$	3.33197e7	−	5.87516e6i	0.0303679	−	0.00535469i
$183$	−5.53107e8	+	1.50254e8i	−0.493179	+	0.133974i
$184$	−1.77307e8	+	6.45343e7i	−0.154687	+	0.0563015i
$185$	4.43315e8	+	7.81685e7i	0.378465	+	0.0667336i
$186$	−4.20949e8	−	5.96782e8i	−0.351705	−	0.498613i
$187$	8.89061e8	−	7.46011e8i	0.727052	−	0.610069i
$188$			2.47211e7i			0.0197895i
$189$	−1.02578e9	+	4.91328e8i	−0.803907	+	0.385056i
$190$	3.46475e8			0.265863
$191$	6.22080e8	+	7.41366e8i	0.467426	+	0.557056i	0.947328	−	0.320266i	$-0.103772\pi$
$191$	6.22080e8	+	7.41366e8i	0.467426	+	0.557056i	−0.479902	+	0.877322i	$0.659328\pi$
$192$	1.54201e8	+	7.12578e7i	0.113470	+	0.0524358i
$193$	−2.87479e8	+	1.63037e9i	−0.207194	+	1.17505i	0.686756	+	0.726888i	$0.259034\pi$
$193$	−2.87479e8	+	1.63037e9i	−0.207194	+	1.17505i	−0.893950	+	0.448167i	$0.852077\pi$
$194$	4.54920e7	+	1.24988e8i	0.0321165	+	0.0882394i
$195$	1.87579e7	+	4.95680e6i	0.0129731	+	0.00342817i
$196$	2.63270e7	+	1.49308e8i	0.0178393	+	0.101172i
$197$	1.08762e9	−	6.27936e8i	0.722123	−	0.416918i	−0.0934105	−	0.995628i	$-0.529777\pi$
$197$	1.08762e9	−	6.27936e8i	0.722123	−	0.416918i	0.815534	+	0.578710i	$0.196444\pi$
$198$	1.27475e9	−	7.47763e8i	0.829401	−	0.486523i
$199$	−1.41809e9	+	2.45621e9i	−0.904258	+	1.56622i	−0.0823476	+	0.996604i	$0.526242\pi$
$199$	−1.41809e9	+	2.45621e9i	−0.904258	+	1.56622i	−0.821910	+	0.569617i	$0.807092\pi$
$200$	1.78922e8	−	4.91583e8i	0.111826	−	0.307240i
$201$	−3.60123e7	+	5.18108e7i	−0.0220631	+	0.0317421i
$202$	1.14098e9	+	9.57400e8i	0.685290	+	0.575027i
$203$	1.64688e9	−	1.96267e9i	0.969788	−	1.15575i
$204$	−4.96270e8	−	3.44945e8i	−0.286548	−	0.199172i
$205$	−5.83454e7	−	2.12360e7i	−0.0330363	−	0.0120242i
$206$	−1.32004e9	−	7.62127e8i	−0.733025	−	0.423212i
$207$	8.54838e8	−	5.90357e6i	0.465589	−	0.00321539i
$208$	1.14468e7	+	1.98265e7i	0.00611550	+	0.0105924i
$209$	3.50287e9	−	6.17651e8i	1.83586	−	0.323711i
$210$	8.58933e7	−	3.25043e8i	0.0441654	−	0.167134i
$211$	2.94297e9	−	1.07115e9i	1.48476	−	0.540408i	0.532696	−	0.846307i	$-0.321179\pi$
$211$	2.94297e9	−	1.07115e9i	1.48476	−	0.540408i	0.952064	+	0.305898i	$0.0989568\pi$
$212$	−1.11494e9	−	1.96595e8i	−0.551963	−	0.0973259i
$213$	8.62320e8	−	1.86605e9i	0.418938	−	0.906576i
$214$	−4.15283e8	+	3.48464e8i	−0.198011	+	0.166151i
$215$			9.08348e8i			0.425107i
$216$	−5.49804e8	−	5.38529e8i	−0.252576	−	0.247397i
$217$	−1.70555e9			−0.769174
$218$	−4.38440e8	−	5.22513e8i	−0.194126	−	0.231351i
$219$	1.86295e9	−	1.31406e9i	0.809885	−	0.571266i
$220$	−7.58587e7	+	4.30216e8i	−0.0323828	+	0.183652i
$221$	−2.78586e7	−	7.65410e7i	−0.0116786	−	0.0320867i
$222$	−6.30879e8	−	2.32237e9i	−0.259737	−	0.956134i
$223$	−2.31530e8	−	1.31307e9i	−0.0936242	−	0.530969i	−0.995160	−	0.0982654i	$-0.968671\pi$
$223$	−2.31530e8	−	1.31307e9i	−0.0936242	−	0.530969i	0.901536	−	0.432704i	$-0.142441\pi$
$224$	3.43561e8	−	1.98355e8i	0.136462	−	0.0787865i
$225$	−1.51090e9	+	1.82608e9i	−0.589528	+	0.712507i
$226$	−1.39421e9	+	2.41485e9i	−0.534435	+	0.925669i
$227$	1.20114e9	−	3.30011e9i	0.452367	−	1.24287i	−0.478686	−	0.877986i	$-0.658887\pi$
$227$	1.20114e9	−	3.30011e9i	0.452367	−	1.24287i	0.931053	−	0.364883i	$-0.118891\pi$
$228$	−7.88592e8	−	1.67601e9i	−0.291819	−	0.620207i
$229$	−1.22918e9	−	1.03140e9i	−0.446964	−	0.375048i	0.391344	−	0.920245i	$-0.372010\pi$
$229$	−1.22918e9	−	1.03140e9i	−0.446964	−	0.375048i	−0.838308	+	0.545197i	$0.816455\pi$
$230$	−1.62426e8	+	1.93572e8i	−0.0580424	+	0.0691722i
$231$	2.88938e8	−	3.43931e9i	0.101474	−	1.20788i
$232$	1.62909e9	+	5.92941e8i	0.562333	+	0.204673i
$233$	4.34462e9	+	2.50837e9i	1.47410	+	0.851074i	0.999575	−	0.0291661i	$-0.00928518\pi$
$233$	4.34462e9	+	2.50837e9i	1.47410	+	0.851074i	0.474529	+	0.880240i	$0.342619\pi$
$234$	−1.87161e7	−	1.02019e8i	−0.00624241	−	0.0340266i
$235$	1.65534e7	+	2.86713e7i	0.00542770	+	0.00940105i
$236$	−1.36298e8	+	2.40331e7i	−0.0439383	+	0.00774750i
$237$	3.84396e9	+	3.81751e9i	1.21839	+	1.21000i
$238$	−1.32633e9	+	4.82745e8i	−0.413375	+	0.150456i
$239$	1.08500e9	+	1.91314e8i	0.332534	+	0.0586348i	0.337423	−	0.941353i	$-0.390445\pi$
$239$	1.08500e9	+	1.91314e8i	0.332534	+	0.0586348i	−0.00488822	+	0.999988i	$0.501556\pi$
$240$	2.26556e8	−	2.06096e7i	0.0682858	−	0.00621190i
$241$	−3.54083e9	+	2.97111e9i	−1.04963	+	0.880747i	−0.993055	−	0.117651i	$-0.962463\pi$
$241$	−3.54083e9	+	2.97111e9i	−1.04963	+	0.880747i	−0.0565781	+	0.998398i	$0.518019\pi$
$242$			2.05953e9i			0.600490i
$243$	1.52792e9	+	3.13419e9i	0.438202	+	0.898877i
$244$	−9.05722e8			−0.255526
$245$	1.30512e8	+	1.55538e8i	0.0362230	+	0.0431689i
$246$	3.00715e7	+	3.30569e8i	0.00821136	+	0.0902654i
$247$	4.33484e7	−	2.45841e8i	0.0116462	−	0.0660491i
$248$	−3.94713e8	−	1.08447e9i	−0.104346	−	0.286688i
$249$	−2.77164e9	+	2.79085e9i	−0.721007	+	0.726004i
$250$	−2.53207e8	−	1.43601e9i	−0.0648209	−	0.367618i
$251$	−2.29817e9	+	1.32685e9i	−0.579011	+	0.334292i	−0.760740	−	0.649056i	$-0.775164\pi$
$251$	−2.29817e9	+	1.32685e9i	−0.579011	+	0.334292i	0.181729	+	0.983349i	$0.441831\pi$
$252$	−1.76783e9	+	3.24320e8i	−0.438368	+	0.0804214i
$253$	−1.29706e9	+	2.24657e9i	−0.316576	+	0.548325i
$254$	−8.53185e7	+	2.34411e8i	−0.0204978	+	0.0563174i
$255$	−8.06548e8	−	6.77583e7i	−0.190752	−	0.0160251i
$256$	2.05633e8	+	1.72547e8i	0.0478778	+	0.0401742i
$257$	−3.91134e9	+	4.66136e9i	−0.896589	+	1.06851i	0.100699	+	0.994917i	$0.467892\pi$
$257$	−3.91134e9	+	4.66136e9i	−0.896589	+	1.06851i	−0.997288	+	0.0735962i	$0.976552\pi$
$258$	4.39396e9	−	2.06744e9i	0.991693	−	0.466610i
$259$	−5.28124e9	−	1.92222e9i	−1.17365	−	0.427172i
$260$	2.65519e7	+	1.53298e7i	0.00581035	+	0.00335461i
$261$	−6.05157e9	−	5.00706e9i	−1.30409	−	1.07900i
$262$	6.72466e7	+	1.16474e8i	0.0142713	+	0.0247187i
$263$	5.16134e9	−	9.10084e8i	1.07880	−	0.190221i	0.394113	−	0.919062i	$-0.371052\pi$
$263$	5.16134e9	−	9.10084e8i	1.07880	−	0.190221i	0.684683	+	0.728841i	$0.259941\pi$
$264$	2.25374e9	−	6.12237e8i	0.463969	−	0.126039i
$265$	−1.42475e9	+	5.18565e8i	−0.288904	+	0.105153i
$266$	−4.26003e9	−	7.51158e8i	−0.850915	−	0.150039i
$267$	1.48983e9	+	2.11213e9i	0.293151	+	0.415601i
$268$	−7.63816e7	+	6.40917e7i	−0.0148064	+	0.0124240i
$269$			6.38983e9i			1.22034i	0.792271	+	0.610170i	$0.208899\pi$
$269$			6.38983e9i			1.22034i	−0.792271	+	0.610170i	$0.791101\pi$
$270$	−9.98261e8	−	2.56430e8i	−0.187840	−	0.0482519i
$271$	−3.21952e8			−0.0596918			−0.0298459	−	0.999555i	$-0.509502\pi$
$271$	−3.21952e8			−0.0596918			−0.0298459	+	0.999555i	$0.509502\pi$
$272$	−6.13903e8	−	7.31621e8i	−0.112156	−	0.133663i
$273$	−2.19888e8	−	1.01613e8i	−0.0395868	−	0.0182935i
$274$	−7.32081e8	+	4.15184e9i	−0.129884	+	0.736611i
$275$	−2.45988e9	−	6.75845e9i	−0.430113	−	1.18173i
$276$	1.30606e9	+	3.45128e8i	0.225074	+	0.0594762i
$277$	−8.62910e8	−	4.89381e9i	−0.146571	−	0.831243i	−0.966093	−	0.258195i	$-0.916872\pi$
$277$	−8.62910e8	−	4.89381e9i	−0.146571	−	0.831243i	0.819522	−	0.573047i	$-0.194239\pi$
$278$	−4.60529e9	+	2.65887e9i	−0.771042	+	0.445161i
$279$	3.61082e7	+	5.22847e9i	0.00595921	+	0.862895i
$280$	2.65640e8	−	4.60102e8i	0.0432177	−	0.0748552i
$281$	2.91365e9	−	8.00518e9i	0.467317	−	1.28394i	−0.452559	−	0.891734i	$-0.649489\pi$
$281$	2.91365e9	−	8.00518e9i	0.467317	−	1.28394i	0.919876	−	0.392209i	$-0.128289\pi$
$282$	1.01016e8	−	1.45331e8i	0.0159732	−	0.0229806i
$283$	8.51310e9	+	7.14334e9i	1.32722	+	1.11367i	0.984720	+	0.174148i	$0.0557171\pi$
$283$	8.51310e9	+	7.14334e9i	1.32722	+	1.11367i	0.342497	+	0.939519i	$0.388727\pi$
$284$	2.08806e9	−	2.48845e9i	0.320974	−	0.382522i
$285$	−2.03687e9	−	1.41577e9i	−0.308733	−	0.214593i
$286$	2.95768e8	+	1.07651e8i	0.0442066	+	0.0160899i
$287$	6.71337e8	+	3.87597e8i	0.0989494	+	0.0571284i
$288$	−6.15345e8	−	1.04901e9i	−0.0894435	−	0.152479i
$289$	−1.78887e9	−	3.09842e9i	−0.256441	−	0.444169i
$290$	2.28645e9	−	4.03162e8i	0.323273	−	0.0570017i
$291$	2.43290e8	−	9.20675e8i	0.0339275	−	0.128391i
$292$	3.38532e9	−	1.23216e9i	0.465660	−	0.169486i
$293$	−1.35256e10	−	2.38492e9i	−1.83521	−	0.323596i	−0.854554	−	0.519362i	$-0.826170\pi$
$293$	−1.35256e10	−	2.38492e9i	−1.83521	−	0.323596i	−0.980651	+	0.195766i	$0.937281\pi$
$294$	4.55333e8	−	9.85334e8i	0.0609453	−	0.131885i
$295$	−1.41985e8	+	1.19140e8i	−0.0187480	+	0.0157315i
$296$		−	3.80291e9i		−	0.495393i
$297$	−1.05496e10	−	8.12944e8i	−1.35584	−	0.104480i
$298$	3.23444e9			0.410141
$299$	1.17027e8	+	1.39468e8i	0.0146421	+	0.0174497i
$300$	−3.06057e9	+	2.15882e9i	−0.377848	+	0.266521i
$301$	1.96930e9	−	1.11684e10i	0.239909	−	1.36059i
$302$	2.28288e9	+	6.27217e9i	0.274446	+	0.754033i
$303$	−2.79551e9	−	1.02907e10i	−0.331658	−	1.22088i
$304$	−5.08274e8	−	2.88256e9i	−0.0595118	−	0.337508i
$305$	−1.05045e9	+	6.06478e8i	−0.121388	+	0.0700835i
$306$	1.50797e9	+	4.05574e9i	0.171991	+	0.462577i
$307$	1.57089e9	−	2.72086e9i	0.176845	−	0.306304i	−0.763953	−	0.645272i	$-0.776744\pi$
$307$	1.57089e9	−	2.72086e9i	0.176845	−	0.306304i	0.940798	+	0.338967i	$0.110078\pi$
$308$	1.86542e9	−	5.12519e9i	0.207287	−	0.569517i
$309$	4.64608e9	+	9.87440e9i	0.509628	+	1.08312i
$310$	−1.18395e9	−	9.93453e8i	−0.128200	−	0.107572i
$311$	−3.87508e9	+	4.61814e9i	−0.414228	+	0.493657i	−0.932303	−	0.361677i	$-0.882204\pi$
$311$	−3.87508e9	+	4.61814e9i	−0.414228	+	0.493657i	0.518076	+	0.855335i	$0.326649\pi$
$312$	1.37215e7	−	1.63331e8i	0.00144805	−	0.0172365i
$313$	−6.31471e9	−	2.29837e9i	−0.657924	−	0.239465i	−0.00858426	−	0.999963i	$-0.502732\pi$
$313$	−6.31471e9	−	2.29837e9i	−0.657924	−	0.239465i	−0.649340	+	0.760498i	$0.724955\pi$
$314$	3.07834e9	+	1.77728e9i	0.316664	+	0.182826i
$315$	−1.83315e9	+	1.55990e9i	−0.186190	+	0.158436i
$316$	4.28050e9	+	7.41404e9i	0.429285	+	0.743544i
$317$	1.76296e9	−	3.10857e8i	0.174584	−	0.0307839i	−0.0856726	−	0.996323i	$-0.527304\pi$
$317$	1.76296e9	−	3.10857e8i	0.174584	−	0.0307839i	0.260257	+	0.965539i	$0.416193\pi$
$318$	5.75123e9	+	5.71165e9i	0.562409	+	0.558539i
$319$	2.23973e10	−	8.15195e9i	2.16288	−	0.787225i
$320$	3.54031e8	+	6.24252e7i	0.0337630	+	0.00595333i
$321$	3.86528e9	−	3.51621e8i	0.364049	−	0.0331173i
$322$	2.41675e9	−	2.02789e9i	0.224806	−	0.188635i
$323$			1.04141e10i			0.956775i
$324$	1.03165e9	+	5.41254e9i	0.0936166	+	0.491158i
$325$	−5.04768e8			−0.0452437
$326$	−1.38341e8	−	1.64868e8i	−0.0122484	−	0.0145971i
$327$	4.42413e8	+	4.86333e9i	0.0386934	+	0.425346i
$328$	−9.10849e7	+	5.16568e8i	−0.00786957	+	0.0446305i
$329$	−1.41370e8	−	3.88411e8i	−0.0120663	−	0.0331519i
$330$	2.20392e9	−	2.21919e9i	0.185840	−	0.187128i
$331$	−1.68286e9	−	9.54398e9i	−0.140196	−	0.795092i	−0.971099	−	0.238675i	$-0.923287\pi$
$331$	−1.68286e9	−	9.54398e9i	−0.140196	−	0.795092i	0.830903	−	0.556417i	$-0.187824\pi$
$332$	−5.38285e9	+	3.10779e9i	−0.443057	+	0.255799i
$333$	−5.78087e9	+	1.62307e10i	−0.470128	+	1.31996i
$334$	−2.55540e9	+	4.42609e9i	−0.205340	+	0.355659i
$335$	−4.56705e7	+	1.25479e8i	−0.00362624	+	0.00996302i
$336$	−2.83026e9	−	2.37771e8i	−0.222060	−	0.0186553i
$337$	1.87101e10	+	1.56996e10i	1.45063	+	1.21722i	0.932120	+	0.362149i	$0.117957\pi$
$337$	1.87101e10	+	1.56996e10i	1.45063	+	1.21722i	0.518509	+	0.855072i	$0.326487\pi$
$338$	−5.91805e9	+	7.05286e9i	−0.453432	+	0.540379i
$339$	1.80639e10	−	8.49941e9i	1.36777	−	0.643561i
$340$	−1.20190e9	−	4.37456e8i	−0.0899399	−	0.0327355i
$341$	−1.37408e10	−	7.93323e9i	−1.01623	−	0.586722i
$342$	−2.21254e9	+	1.30753e10i	−0.161728	+	0.955758i
$343$	−7.43631e9	−	1.28801e10i	−0.537256	−	0.930554i
$344$	7.55717e9	−	1.33253e9i	0.539666	−	0.0951577i
$345$	1.74586e9	−	4.74268e8i	0.123234	−	0.0334771i
$346$	1.60146e10	−	5.82882e9i	1.11741	−	0.406702i
$347$	1.01691e10	+	1.79309e9i	0.701399	+	0.123676i	0.512964	−	0.858410i	$-0.328547\pi$
$347$	1.01691e10	+	1.79309e9i	0.701399	+	0.123676i	0.188435	+	0.982086i	$0.439659\pi$
$348$	−7.15426e9	−	1.01426e10i	−0.487807	−	0.691566i
$349$	1.44701e9	−	1.21419e9i	0.0975374	−	0.0818436i	−0.592715	−	0.805412i	$-0.701944\pi$
$349$	1.44701e9	−	1.21419e9i	0.0975374	−	0.0818436i	0.690252	+	0.723569i	$0.257500\pi$
$350$			8.74682e9i			0.582878i
$351$	−3.06845e8	+	6.76232e8i	−0.0202158	+	0.0445520i
$352$	3.69054e9			0.240392
$353$	−1.51485e10	−	1.80533e10i	−0.975597	−	1.16267i	−0.986670	−	0.162732i	$-0.947969\pi$
$353$	−1.51485e10	−	1.80533e10i	−0.975597	−	1.16267i	0.0110734	−	0.999939i	$-0.496475\pi$
$354$	8.99480e8	+	4.15659e8i	0.0572767	+	0.0264682i
$355$	7.55432e8	−	4.28427e9i	0.0475644	−	0.269751i
$356$	1.39697e9	+	3.83815e9i	0.0869736	+	0.238958i
$357$	9.76988e9	+	2.58171e9i	0.601473	+	0.158940i
$358$	−3.44686e9	−	1.95481e10i	−0.209842	−	1.19007i
$359$	−1.21581e10	+	7.01946e9i	−0.731958	+	0.422596i	−0.819138	−	0.573596i	$-0.805548\pi$
$359$	−1.21581e10	+	7.01946e9i	−0.731958	+	0.422596i	0.0871800	+	0.996193i	$0.472214\pi$
$360$	−1.41610e9	−	8.04597e8i	−0.0843108	−	0.0479036i
$361$	−7.46646e9	+	1.29323e10i	−0.439629	+	0.761459i
$362$	7.04331e8	−	1.93513e9i	0.0410150	−	0.112688i
$363$	8.41568e9	−	1.21076e10i	0.484688	−	0.697319i
$364$	−2.93230e8	−	2.46049e8i	−0.0167033	−	0.0140157i
$365$	3.10121e9	−	3.69588e9i	0.174727	−	0.208232i
$366$	5.32459e9	+	3.70098e9i	0.296730	+	0.206249i
$367$	1.63335e9	+	5.94492e8i	0.0900360	+	0.0327704i	0.386645	−	0.922228i	$-0.373634\pi$
$367$	1.63335e9	+	5.94492e8i	0.0900360	+	0.0327704i	−0.296609	+	0.954999i	$0.595856\pi$
$368$	1.84874e9	+	1.06737e9i	0.100805	+	0.0582000i
$369$	1.17399e9	−	2.06623e9i	0.0633227	−	0.111448i
$370$	−2.54646e9	−	4.41059e9i	−0.135872	−	0.235337i
$371$	1.86420e10	−	3.28708e9i	0.984002	−	0.173506i
$372$	−2.11091e9	+	7.98827e9i	−0.110230	+	0.417139i
$373$	1.28343e10	−	4.67130e9i	0.663036	−	0.241325i	0.0114893	−	0.999934i	$-0.496343\pi$
$373$	1.28343e10	−	4.67130e9i	0.663036	−	0.241325i	0.651547	+	0.758609i	$0.274121\pi$
$374$	−1.29311e10	−	2.28010e9i	−0.660918	−	0.116538i
$375$	−4.37928e9	+	9.47669e9i	−0.221451	+	0.479216i
$376$	2.14253e8	−	1.79779e8i	0.0107195	−	0.00899473i
$377$		−	1.67279e9i		−	0.0828085i
$378$	1.17180e10	+	5.31712e9i	0.573967	+	0.260441i
$379$	−4.82245e9			−0.233728			−0.116864	−	0.993148i	$-0.537284\pi$
$379$	−4.82245e9			−0.233728			−0.116864	+	0.993148i	$0.537284\pi$
$380$	−2.51968e9	−	3.00283e9i	−0.120840	−	0.144011i
$381$	1.45943e9	−	1.02943e9i	0.0692599	−	0.0488536i
$382$	1.90131e9	−	1.07829e10i	0.0892895	−	0.506386i
$383$	−7.85266e9	−	2.15750e10i	−0.364940	−	1.00267i	−0.977258	−	0.212053i	$-0.931985\pi$
$383$	−7.85266e9	−	2.15750e10i	−0.364940	−	1.00267i	0.612318	−	0.790612i	$-0.290237\pi$
$384$	−5.03819e8	−	1.85464e9i	−0.0231713	−	0.0852971i
$385$	−1.26836e9	−	7.19325e9i	−0.0577299	−	0.327403i
$386$	1.62208e10	−	9.36507e9i	0.730672	−	0.421854i
$387$	−3.42793e10	−	5.80057e9i	−1.52823	−	0.258599i
$388$	7.52417e8	−	1.30322e9i	0.0331995	−	0.0575032i
$389$	−1.28725e10	+	3.53669e10i	−0.562165	+	1.54454i	0.254290	+	0.967128i	$0.418158\pi$
$389$	−1.28725e10	+	3.53669e10i	−0.562165	+	1.54454i	−0.816455	+	0.577409i	$0.804064\pi$
$390$	−9.34534e7	−	1.98618e8i	−0.00403959	−	0.00858540i
$391$	−5.81823e9	−	4.88207e9i	−0.248934	−	0.208880i
$392$	1.10257e9	−	1.31399e9i	0.0466939	−	0.0556476i
$393$	8.06093e7	−	9.59517e8i	0.00337921	−	0.0402238i
$394$	−1.33517e10	−	4.85962e9i	−0.554053	−	0.201659i
$395$	9.92899e9	+	5.73250e9i	0.407865	+	0.235481i
$396$	−1.57511e10	−	5.61005e9i	−0.640516	−	0.228132i
$397$	2.18922e10	+	3.79183e10i	0.881306	+	1.52647i	0.849890	+	0.526960i	$0.176668\pi$
$397$	2.18922e10	+	3.79183e10i	0.881306	+	1.52647i	0.0314156	+	0.999506i	$0.489998\pi$
$398$	3.16003e10	−	5.57198e9i	1.25939	−	0.222064i
$399$	2.19746e10	+	2.18234e10i	0.867020	+	0.861053i
$400$	−5.56163e9	+	2.02427e9i	−0.217251	+	0.0790730i
$401$	−2.99233e10	−	5.27628e9i	−1.15726	−	0.204056i	−0.438117	−	0.898918i	$-0.644355\pi$
$401$	−2.99233e10	−	5.27628e9i	−1.15726	−	0.204056i	−0.719144	+	0.694861i	$0.755466\pi$
$402$	7.10927e8	−	6.46724e7i	0.0272220	−	0.00247637i
$403$	−8.53030e8	+	7.15777e8i	−0.0323403	+	0.0271367i
$404$		−	1.68512e10i		−	0.632565i
$405$	4.82078e9	+	5.58662e9i	0.179183	+	0.207649i
$406$	−2.89867e10			−1.06683
$407$	−3.36073e10	−	4.00517e10i	−1.22478	−	1.45963i
$408$	6.19465e8	+	6.80962e9i	0.0223551	+	0.245744i
$409$	−7.52414e9	+	4.26715e10i	−0.268883	+	1.52491i	0.488862	+	0.872361i	$0.337412\pi$
$409$	−7.52414e9	+	4.26715e10i	−0.268883	+	1.52491i	−0.757745	+	0.652551i	$0.773699\pi$
$410$	2.40258e8	+	6.60103e8i	0.00850241	+	0.0233602i
$411$	2.12691e10	−	2.14165e10i	0.745387	−	0.750553i
$412$	2.99456e9	+	1.69830e10i	0.103931	+	0.589420i
$413$	2.00405e9	−	1.15704e9i	0.0688825	−	0.0397693i
$414$	−6.26781e9	−	7.36578e9i	−0.213361	−	0.250736i
$415$	−4.16200e9	+	7.20879e9i	−0.140317	+	0.243036i
$416$	8.85875e7	−	2.43392e8i	0.00295801	−	0.00812705i
$417$	3.79384e10	+	3.18722e9i	1.25469	+	0.105407i
$418$	−3.08270e10	−	2.58669e10i	−1.00978	−	0.847306i
$419$	−2.47929e10	+	2.95470e10i	−0.804398	+	0.958644i	−0.999756	−	0.0220879i	$-0.992969\pi$
$419$	−2.47929e10	+	2.95470e10i	−0.804398	+	0.958644i	0.195358	+	0.980732i	$0.437413\pi$
$420$	−3.44173e9	+	1.61940e9i	−0.110606	+	0.0520423i
$421$	−5.11984e10	−	1.86347e10i	−1.62978	−	0.593190i	−0.644568	−	0.764547i	$-0.722963\pi$
$421$	−5.11984e10	−	1.86347e10i	−1.62978	−	0.593190i	−0.985209	+	0.171357i	$0.945185\pi$
$422$	−3.06857e10	−	1.77164e10i	−0.967578	−	0.558631i
$423$	−1.18771e9	+	4.41603e8i	−0.0370978	+	0.0137934i
$424$	6.40437e9	+	1.10927e10i	0.198159	+	0.343221i
$425$	2.07377e10	−	3.65661e9i	0.635630	−	0.112079i
$426$	−2.24437e10	+	6.09691e9i	−0.681485	+	0.185128i
$427$	1.42305e10	−	5.17947e9i	0.428063	−	0.155802i
$428$	6.04013e9	+	1.06504e9i	0.180000	+	0.0317388i
$429$	−1.29889e9	−	1.84144e9i	−0.0383479	−	0.0543660i
$430$	7.87248e9	−	6.60579e9i	0.230270	−	0.193220i
$431$			5.21296e10i			1.51069i	0.655328	+	0.755344i	$0.272530\pi$
$431$			5.21296e10i			1.51069i	−0.655328	+	0.755344i	$0.727470\pi$
$432$	−6.68984e8	+	8.68139e9i	−0.0192079	+	0.249261i
$433$	−1.38027e10			−0.392655			−0.196328	−	0.980538i	$-0.562902\pi$
$433$	−1.38027e10			−0.392655			−0.196328	+	0.980538i	$0.562902\pi$
$434$	1.24033e10	+	1.47816e10i	0.349605	+	0.416643i
$435$	−1.50890e10	−	6.97280e9i	−0.421410	−	0.194738i
$436$	−1.34004e9	+	7.59975e9i	−0.0370828	+	0.210307i
$437$	−7.96129e9	−	2.18735e10i	−0.218302	−	0.599780i
$438$	−2.49366e10	−	6.58954e9i	−0.677549	−	0.179044i
$439$	1.05866e10	+	6.00399e10i	0.285036	+	1.61652i	0.705155	+	0.709053i	$0.250877\pi$
$439$	1.05866e10	+	6.00399e10i	0.285036	+	1.61652i	−0.420119	+	0.907469i	$0.638012\pi$
$440$	4.28026e9	−	2.47121e9i	0.114198	−	0.0659325i
$441$	−6.70312e9	+	3.93202e9i	−0.177224	+	0.103959i
$442$	−4.60769e8	+	7.98075e8i	−0.0120724	+	0.0209100i
$443$	8.02313e9	−	2.20434e10i	0.208319	−	0.572352i	−0.790897	−	0.611950i	$-0.790385\pi$
$443$	8.02313e9	−	2.20434e10i	0.208319	−	0.572352i	0.999216	+	0.0395979i	$0.0126077\pi$
$444$	−1.55395e10	+	2.23567e10i	−0.399859	+	0.575275i
$445$	4.19025e9	+	3.51603e9i	0.106856	+	0.0896629i
$446$	−9.69639e9	+	1.15557e10i	−0.245059	+	0.292050i
$447$	−1.90147e10	−	1.32166e10i	−0.476277	−	0.331048i
$448$	−4.21759e9	−	1.53508e9i	−0.104701	−	0.0381082i
$449$	5.76903e10	+	3.33075e10i	1.41944	+	0.819515i	0.996250	−	0.0865250i	$-0.0275762\pi$
$449$	5.76903e10	+	3.33075e10i	1.41944	+	0.819515i	0.423192	+	0.906040i	$0.360910\pi$
$450$	2.68140e10	−	1.85179e8i	0.653899	−	0.00451587i
$451$	3.60576e9	+	6.24535e9i	0.0871546	+	0.150956i
$452$	3.10681e10	−	5.47815e9i	0.744323	−	0.131244i
$453$	1.22088e10	−	4.62014e10i	0.289921	−	1.09714i
$454$	−3.73365e10	+	1.35894e10i	−0.878841	+	0.319872i
$455$	−5.04842e8	−	8.90173e7i	−0.0117790	−	0.00207696i
$456$	−8.79074e9	+	1.90230e10i	−0.203313	+	0.439967i
$457$	9.75571e9	−	8.18601e9i	0.223663	−	0.187675i	−0.524070	−	0.851675i	$-0.675587\pi$
$457$	9.75571e9	−	8.18601e9i	0.223663	−	0.187675i	0.747733	+	0.664000i	$0.231142\pi$
$458$			1.81537e10i			0.412576i
$459$	7.70756e9	−	3.00049e10i	0.173647	−	0.675991i
$460$	2.85887e9			0.0638503
$461$	1.41167e10	+	1.68236e10i	0.312556	+	0.372490i	0.899337	−	0.437256i	$-0.144049\pi$
$461$	1.41167e10	+	1.68236e10i	0.312556	+	0.372490i	−0.586781	+	0.809746i	$0.699605\pi$
$462$	−3.19091e10	+	2.25076e10i	−0.700401	+	0.494039i
$463$	−1.38164e9	+	7.83565e9i	−0.0300656	+	0.170511i	−0.996143	−	0.0877410i	$-0.972035\pi$
$463$	−1.38164e9	+	7.83565e9i	−0.0300656	+	0.170511i	0.966078	+	0.258252i	$0.0831463\pi$
$464$	−6.70836e9	−	1.84311e10i	−0.144725	−	0.397630i
$465$	2.90078e9	+	1.06782e10i	0.0620444	+	0.228395i
$466$	−9.85590e9	−	5.58956e10i	−0.209003	−	1.18531i
$467$	2.11774e10	−	1.22268e10i	0.445252	−	0.257066i	−0.260571	−	0.965455i	$-0.583911\pi$
$467$	2.11774e10	−	1.22268e10i	0.445252	−	0.257066i	0.705823	+	0.708388i	$0.250577\pi$
$468$	−7.48072e8	+	9.04125e8i	−0.0155941	+	0.0188471i
$469$	8.33572e8	−	1.44379e9i	0.0172287	−	0.0298409i
$470$	1.28107e8	−	3.51972e8i	0.00262532	−	0.00721301i
$471$	−1.08347e10	−	2.30271e10i	−0.220157	−	0.467903i
$472$	1.19950e9	+	1.00650e9i	0.0241674	+	0.0202789i
$473$	6.78149e10	−	8.08187e10i	1.35482	−	1.61461i
$474$	5.13109e9	−	6.10770e10i	0.101647	−	1.20994i
$475$	6.06443e10	+	2.20727e10i	1.19128	+	0.433592i
$476$	1.38294e10	+	7.98438e9i	0.269385	+	0.155530i
$477$	−1.04714e10	−	5.70786e10i	−0.202271	−	1.10255i
$478$	−6.23235e9	−	1.07947e10i	−0.119382	−	0.206776i
$479$	−4.66854e10	+	8.23189e9i	−0.886827	+	0.156371i	−0.598464	−	0.801150i	$-0.704222\pi$
$479$	−4.66854e10	+	8.23189e9i	−0.886827	+	0.156371i	−0.288363	+	0.957521i	$0.593111\pi$
$480$	−1.82620e9	−	1.81364e9i	−0.0344020	−	0.0341653i
$481$	−3.44813e9	+	1.25501e9i	−0.0644173	+	0.0234460i
$482$	5.15001e10	+	9.08086e9i	0.954157	+	0.168244i
$483$	−2.24941e10	+	2.04627e9i	−0.413314	+	0.0375988i
$484$	1.78495e10	−	1.49775e10i	0.325271	−	0.272934i
$485$		−	2.01529e9i		−	0.0364226i
$486$	1.60519e10	−	3.60349e10i	0.287728	−	0.645920i
$487$	−2.91682e10			−0.518554			−0.259277	−	0.965803i	$-0.583484\pi$
$487$	−2.91682e10			−0.518554			−0.259277	+	0.965803i	$0.583484\pi$
$488$	6.58669e9	+	7.84972e9i	0.116142	+	0.138412i
$489$	1.39594e8	+	1.53452e9i	0.00244136	+	0.0268372i
$490$	3.98893e8	−	2.26224e9i	0.00691947	−	0.0392422i
$491$	7.75336e9	+	2.13022e10i	0.133403	+	0.366520i	0.988351	−	0.152193i	$-0.0486335\pi$
$491$	7.75336e9	+	2.13022e10i	0.133403	+	0.366520i	−0.854948	+	0.518713i	$0.826411\pi$
$492$	2.64628e9	−	2.66462e9i	0.0451623	−	0.0454753i
$493$	1.21179e10	+	6.87241e10i	0.205135	+	1.16338i
$494$	−2.44590e9	+	1.41214e9i	−0.0410706	+	0.0237121i
$495$	−2.20245e10	+	4.04055e9i	−0.366848	+	0.0673006i
$496$	−6.52837e9	+	1.13075e10i	−0.107864	+	0.186827i
$497$	−1.85766e10	+	5.10388e10i	−0.304467	+	0.836517i
$498$	4.43440e10	+	3.72535e9i	0.720970	+	0.0605689i
$499$	1.63285e10	+	1.37013e10i	0.263357	+	0.220983i	0.764898	−	0.644151i	$-0.222789\pi$
$499$	1.63285e10	+	1.37013e10i	0.263357	+	0.220983i	−0.501542	+	0.865134i	$0.667234\pi$
$500$	−1.06042e10	+	1.26376e10i	−0.169667	+	0.202201i
$501$	3.31087e10	−	1.55783e10i	0.525523	−	0.247268i
$502$	2.82125e10	+	1.02685e10i	0.444250	+	0.161694i
$503$	4.46932e10	+	2.58036e10i	0.698183	+	0.403096i	0.806670	−	0.591002i	$-0.201267\pi$
$503$	4.46932e10	+	2.58036e10i	0.698183	+	0.403096i	−0.108487	+	0.994098i	$0.534601\pi$
$504$	1.56670e10	+	1.29629e10i	0.242809	+	0.200900i
$505$	−1.12837e10	−	1.95439e10i	−0.173494	−	0.300501i
$506$	2.89032e10	−	5.09641e9i	0.440904	−	0.0777432i
$507$	6.36107e10	−	1.72801e10i	0.962717	−	0.261525i
$508$	2.65205e9	−	9.65268e8i	0.0398224	−	0.0144942i
$509$	8.28333e9	+	1.46058e9i	0.123405	+	0.0217597i	0.235010	−	0.971993i	$-0.424488\pi$
$509$	8.28333e9	+	1.46058e9i	0.123405	+	0.0217597i	−0.111604	+	0.993753i	$0.535599\pi$
$510$	5.27822e9	+	7.48295e9i	0.0780202	+	0.110609i
$511$	−4.61431e10	+	3.87187e10i	−0.676743	+	0.567854i
$512$		−	3.03700e9i		−	0.0441942i
$513$	6.64357e10	−	6.78266e10i	0.959251	−	0.979334i
$514$	6.88436e10			0.986304
$515$	1.48450e10	+	1.76916e10i	0.211033	+	0.251500i
$516$	−4.98723e10	−	2.30465e10i	−0.703494	−	0.325092i
$517$	6.67717e8	−	3.78681e9i	0.00934610	−	0.0530044i
$518$	2.17474e10	+	5.97504e10i	0.302056	+	0.829893i
$519$	−1.17965e11	−	3.11724e10i	−1.62586	−	0.429636i
$520$	−6.02339e7	−	3.41603e8i	−0.000823810	−	0.00467206i
$521$	1.39337e10	−	8.04464e9i	0.189111	−	0.109183i	−0.402455	−	0.915440i	$-0.631843\pi$
$521$	1.39337e10	−	8.04464e9i	0.189111	−	0.109183i	0.591566	+	0.806256i	$0.298510\pi$
$522$	6.13678e8	+	8.88607e10i	0.00826530	+	1.19682i
$523$	2.56377e10	−	4.44058e10i	0.342667	−	0.593516i	−0.642260	−	0.766487i	$-0.722003\pi$
$523$	2.56377e10	−	4.44058e10i	0.342667	−	0.593516i	0.984927	+	0.172970i	$0.0553365\pi$
$524$	5.20423e8	−	1.42985e9i	0.00690290	−	0.0189656i
$525$	3.57414e10	−	5.14210e10i	0.470473	−	0.676867i
$526$	−4.54224e10	−	3.81139e10i	−0.593372	−	0.497898i
$527$	2.98604e10	−	3.55862e10i	0.387126	−	0.461359i
$528$	−2.16961e10	−	1.50804e10i	−0.279155	−	0.194033i
$529$	−5.76356e10	−	2.09776e10i	−0.735983	−	0.267876i
$530$	1.48555e10	+	8.57682e9i	0.188271	+	0.108698i
$531$	−3.58941e9	−	6.11906e9i	−0.0451487	−	0.0769674i
$532$	2.44701e10	+	4.23835e10i	0.305485	+	0.529115i
$533$	4.98435e8	−	8.78875e7i	0.00617589	−	0.00108898i
$534$	7.47096e9	−	2.82721e10i	0.0918779	−	0.347691i
$535$	7.71846e9	−	2.80929e9i	0.0942140	−	0.0342911i
$536$	1.11094e9	+	1.95889e8i	0.0134596	+	0.00237329i
$537$	−5.96144e10	+	1.29005e11i	−0.716893	+	1.55134i
$538$	5.53794e10	−	4.64689e10i	0.661027	−	0.554668i
$539$		−	2.35823e10i		−	0.279404i
$540$	5.03724e9	+	1.05166e10i	0.0592403	+	0.123680i
$541$	−3.18906e10			−0.372284			−0.186142	−	0.982523i	$-0.559598\pi$
$541$	−3.18906e10			−0.372284			−0.186142	+	0.982523i	$0.559598\pi$
$542$	2.34134e9	+	2.79030e9i	0.0271311	+	0.0323336i
$543$	−1.20480e10	+	8.49827e9i	−0.138585	+	0.0977532i
$544$	−1.87632e9	+	1.06412e10i	−0.0214246	+	0.121505i
$545$	3.53468e9	+	9.71144e9i	0.0400649	+	0.110077i
$546$	7.18437e8	+	2.64468e9i	0.00808385	+	0.0297579i
$547$	−1.82761e10	−	1.03649e11i	−0.204142	−	1.15775i	−0.898784	−	0.438393i	$-0.855548\pi$
$547$	−1.82761e10	−	1.03649e11i	−0.204142	−	1.15775i	0.694641	−	0.719356i	$-0.255563\pi$
$548$	4.13071e10	−	2.38487e10i	0.458039	−	0.264449i
$549$	−1.61793e10	−	4.35149e10i	−0.178103	−	0.479014i
$550$	−4.06852e10	+	7.04688e10i	−0.444617	+	0.770099i
$551$	−7.31483e10	+	2.00973e11i	−0.793593	+	2.18038i
$552$	−6.50690e9	−	1.38292e10i	−0.0700838	−	0.148950i
$553$	−1.09652e11	−	9.20091e10i	−1.17251	−	0.983853i
$554$	−3.61383e10	+	4.30680e10i	−0.383644	+	0.457210i
$555$	−3.05247e9	+	3.63345e10i	−0.0321721	+	0.382955i
$556$	5.65350e10	+	2.05771e10i	0.591586	+	0.215320i
$557$	−6.82267e10	−	3.93907e10i	−0.708817	−	0.409235i	0.101806	−	0.994804i	$-0.467538\pi$
$557$	−6.82267e10	−	3.93907e10i	−0.708817	−	0.409235i	−0.810623	+	0.585569i	$0.800871\pi$
$558$	4.50515e10	−	3.83360e10i	0.464700	−	0.395430i
$559$	−3.70219e9	−	6.41238e9i	−0.0379150	−	0.0656707i
$560$	−5.91943e9	+	1.04376e9i	−0.0601905	+	0.0106132i
$561$	6.67025e10	+	6.62435e10i	0.673427	+	0.668793i
$562$	−9.05683e10	+	3.29642e10i	−0.907885	+	0.330443i
$563$	−4.63197e10	−	8.16742e9i	−0.461033	−	0.0812926i	−0.0616927	−	0.998095i	$-0.519650\pi$
$563$	−4.63197e10	−	8.16742e9i	−0.461033	−	0.0812926i	−0.399341	+	0.916803i	$0.630761\pi$
$564$	−1.99417e9	+	1.81408e8i	−0.0197082	+	0.00179283i
$565$	3.23644e10	−	2.71570e10i	0.317595	−	0.266494i
$566$		−	1.25730e11i		−	1.22510i
$567$	−4.71612e10	−	7.91408e10i	−0.456303	−	0.765717i
$568$	−3.67520e10			−0.353091
$569$	−6.58669e10	−	7.84971e10i	−0.628374	−	0.748867i	0.354112	−	0.935203i	$-0.384783\pi$
$569$	−6.58669e10	−	7.84971e10i	−0.628374	−	0.748867i	−0.982486	+	0.186336i	$0.940339\pi$
$570$	2.54251e9	+	2.79491e10i	0.0240859	+	0.264770i
$571$	−3.65552e10	+	2.07315e11i	−0.343878	+	1.95023i	−0.0341109	+	0.999418i	$0.510860\pi$
$571$	−3.65552e10	+	2.07315e11i	−0.343878	+	1.95023i	−0.309767	+	0.950812i	$0.600251\pi$
$572$	−1.21793e9	−	3.34624e9i	−0.0113773	−	0.0312588i
$573$	−5.52388e10	+	5.56216e10i	−0.512419	+	0.515970i
$574$	−1.52295e9	−	8.63707e9i	−0.0140294	−	0.0795644i
$575$	−4.07616e10	+	2.35337e10i	−0.372889	+	0.215288i
$576$	−4.61659e9	+	1.29618e10i	−0.0419403	+	0.117754i
$577$	4.30377e10	−	7.45434e10i	0.388280	−	0.672521i	−0.603938	−	0.797031i	$-0.706403\pi$
$577$	4.30377e10	−	7.45434e10i	0.388280	−	0.672521i	0.992218	+	0.124510i	$0.0397359\pi$
$578$	−1.38441e10	+	3.80365e10i	−0.124038	+	0.340791i
$579$	−1.33627e11	−	1.12260e10i	−1.18899	−	0.0998877i
$580$	−2.01219e10	−	1.68843e10i	−0.177810	−	0.149200i
$581$	6.68018e10	−	7.96113e10i	0.586251	−	0.698667i
$582$	−9.74859e9	+	4.58689e9i	−0.0849669	+	0.0399785i
$583$	1.65479e11	+	6.02294e10i	1.43241	+	0.521356i
$584$	−3.52980e10	−	2.03793e10i	−0.303458	−	0.175202i
$585$	−2.62201e8	+	1.54951e9i	−0.00223877	+	0.0132304i
$586$	7.76924e10	+	1.34567e11i	0.658852	+	1.14117i
$587$	−1.41345e11	+	2.49230e10i	−1.19050	+	0.209917i	−0.733587	−	0.679596i	$-0.762155\pi$
$587$	−1.41345e11	+	2.49230e10i	−1.19050	+	0.209917i	−0.456911	+	0.889513i	$0.651044\pi$
$588$	−1.18510e10	+	3.21937e9i	−0.0991395	+	0.0269316i
$589$	1.33785e11	−	4.86938e10i	1.11160	−	0.404588i
$590$	2.06512e9	+	3.64137e8i	0.0170427	+	0.00300508i
$591$	5.86348e10	+	8.31268e10i	0.480624	+	0.681383i
$592$	−3.29591e10	+	2.76560e10i	−0.268342	+	0.225166i
$593$		−	1.73932e11i		−	1.40657i	−0.710910	−	0.703283i	$-0.751717\pi$
$593$		−	1.73932e11i		−	1.40657i	0.710910	−	0.703283i	$-0.248283\pi$
$594$	6.96741e10	+	9.73430e10i	0.559662	+	0.781914i
$595$	2.13856e10			0.170629
$596$	−2.35218e10	−	2.80322e10i	−0.186417	−	0.222163i
$597$	−2.08541e11	−	9.63690e10i	−1.64170	−	0.758648i
$598$	3.57680e8	−	2.02851e9i	0.00279699	−	0.0158625i
$599$	−7.14796e9	−	1.96389e10i	−0.0555232	−	0.152549i	0.908830	−	0.417166i	$-0.136977\pi$
$599$	−7.14796e9	−	1.96389e10i	−0.0555232	−	0.152549i	−0.964354	+	0.264617i	$0.914754\pi$
$600$	4.09675e10	+	1.08257e10i	0.316107	+	0.0835318i
$601$	2.96734e10	+	1.68286e11i	0.227441	+	1.28988i	0.857963	+	0.513712i	$0.171730\pi$
$601$	2.96734e10	+	1.68286e11i	0.227441	+	1.28988i	−0.630521	+	0.776172i	$0.717159\pi$
$602$	−1.11116e11	+	6.41529e10i	−0.846040	+	0.488462i
$603$	−4.44368e9	−	2.52481e9i	−0.0336104	−	0.0190967i
$604$	3.77579e10	−	6.53985e10i	0.283700	−	0.491383i
$605$	1.06727e10	−	2.93230e10i	0.0796622	−	0.218870i
$606$	−6.88577e10	+	9.90653e10i	−0.510578	+	0.734567i
$607$	−1.66357e11	−	1.39590e11i	−1.22542	−	1.02825i	−0.998523	−	0.0543324i	$-0.982697\pi$
$607$	−1.66357e11	−	1.39590e11i	−1.22542	−	1.02825i	−0.226899	−	0.973918i	$-0.572859\pi$
$608$	−2.12863e10	+	2.53680e10i	−0.155771	+	0.185640i
$609$	1.70408e11	+	1.18446e11i	1.23885	+	0.861095i
$610$	1.28954e10	+	4.69355e9i	0.0931357	+	0.0338986i
$611$	−2.33713e8	−	1.34934e8i	−0.00167694	−	0.000968184i
$612$	2.41839e10	−	4.25639e10i	0.172393	−	0.303414i
$613$	−1.11117e11	−	1.92460e11i	−0.786932	−	1.36301i	−0.927838	−	0.372984i	$-0.878335\pi$
$613$	−1.11117e11	−	1.92460e11i	−0.786932	−	1.36301i	0.140906	−	0.990023i	$-0.454999\pi$
$614$	−3.50052e10	+	6.17236e9i	−0.246297	+	0.0434288i
$615$	1.28489e9	−	4.86238e9i	0.00898186	−	0.0339898i
$616$	−5.79849e10	+	2.11048e10i	−0.402709	+	0.146574i
$617$	1.43611e11	+	2.53224e10i	0.990938	+	0.174729i	0.645539	−	0.763727i	$-0.276633\pi$
$617$	1.43611e11	+	2.53224e10i	0.990938	+	0.174729i	0.345398	+	0.938456i	$0.387744\pi$
$618$	5.17917e10	−	1.12076e11i	0.355064	−	0.768352i
$619$	−1.97635e11	+	1.65836e11i	−1.34618	+	1.12957i	−0.366182	+	0.930543i	$0.619335\pi$
$619$	−1.97635e11	+	1.65836e11i	−1.34618	+	1.12957i	−0.979993	+	0.199032i	$0.936220\pi$
$620$			1.74858e10i			0.118336i
$621$	6.74920e9	+	6.89138e10i	0.0453822	+	0.463383i
$622$	6.82053e10			0.455677
$623$	−4.38977e10	−	5.23153e10i	−0.291400	−	0.347277i
$624$	−1.51534e9	+	1.06887e9i	−0.00999477	+	0.00704997i
$625$	2.06670e10	−	1.17208e11i	0.135443	−	0.768135i
$626$	2.60030e10	+	7.14427e10i	0.169327	+	0.465223i
$627$	7.55287e10	+	2.78033e11i	0.488700	+	1.79898i
$628$	−6.98332e9	−	3.96044e10i	−0.0448976	−	0.254627i
$629$	1.32570e11	−	7.65392e10i	0.846920	−	0.488969i
$630$	2.68506e10	+	4.54351e9i	0.170448	+	0.0288423i
$631$	1.27879e11	−	2.21493e11i	0.806642	−	1.39715i	−0.108534	−	0.994093i	$-0.534616\pi$
$631$	1.27879e11	−	2.21493e11i	0.806642	−	1.39715i	0.915177	−	0.403053i	$-0.132051\pi$
$632$	3.31269e10	−	9.10155e10i	0.207641	−	0.570489i
$633$	1.08003e11	+	2.29540e11i	0.672698	+	1.42970i
$634$	−1.55149e10	−	1.30186e10i	−0.0960268	−	0.0805760i
$635$	2.42948e9	−	2.89534e9i	0.0149423	−	0.0178076i
$636$	7.67701e9	−	9.13817e10i	0.0469206	−	0.558510i
$637$	−1.55526e9	−	5.66069e8i	−0.00944595	−	0.00343804i
$638$	−2.33532e11	−	1.34830e11i	−1.40949	−	0.813771i
$639$	1.56856e11	+	5.58673e10i	0.940801	+	0.335084i
$640$	−2.03360e9	−	3.52229e9i	−0.0121212	−	0.0209945i
$641$	−5.21512e10	+	9.19566e9i	−0.308910	+	0.0544692i	−0.325954	−	0.945386i	$-0.605686\pi$
$641$	−5.21512e10	+	9.19566e9i	−0.308910	+	0.0544692i	0.0170442	+	0.999855i	$0.494574\pi$
$642$	−3.11569e10	−	3.09425e10i	−0.183406	−	0.182144i
$643$	2.23363e11	−	8.12974e10i	1.30667	−	0.475590i	0.407508	−	0.913201i	$-0.366398\pi$
$643$	2.23363e11	−	8.12974e10i	1.30667	−	0.475590i	0.899164	+	0.437612i	$0.144175\pi$
$644$	−3.51507e10	−	6.19802e9i	−0.204358	−	0.0360338i
$645$	−7.32737e10	+	6.66564e9i	−0.423359	+	0.0385126i
$646$	9.02566e10	−	7.57343e10i	0.518262	−	0.434873i
$647$			1.17413e11i			0.670038i	0.942211	+	0.335019i	$0.108743\pi$
$647$			1.17413e11i			0.670038i	−0.942211	+	0.335019i	$0.891257\pi$
$648$	3.94069e10	−	4.83028e10i	0.223497	−	0.273951i
$649$	2.15276e10			0.121343
$650$	3.67083e9	+	4.37473e9i	0.0205642	+	0.0245074i
$651$	−1.25156e10	−	1.37581e11i	−0.0696834	−	0.766011i
$652$	−4.22822e8	+	2.39794e9i	−0.00233974	+	0.0132693i
$653$	−2.00190e10	−	5.50016e10i	−0.110100	−	0.302498i	0.872390	−	0.488810i	$-0.162569\pi$
$653$	−2.00190e10	−	5.50016e10i	−0.110100	−	0.302498i	−0.982491	+	0.186312i	$0.940347\pi$
$654$	3.89321e10	−	3.92019e10i	0.212813	−	0.214287i
$655$	−3.53855e8	−	2.00681e9i	−0.00192247	−	0.0109029i
$656$	5.13939e9	−	2.96723e9i	0.0277521	−	0.0160227i
$657$	1.19672e11	+	1.40635e11i	0.642288	+	0.754801i
$658$	−2.33820e9	+	4.04987e9i	−0.0124732	+	0.0216042i
$659$	−7.30775e10	+	2.00779e11i	−0.387473	+	1.06457i	0.580662	+	0.814145i	$0.302794\pi$
$659$	−7.30775e10	+	2.00779e11i	−0.387473	+	1.06457i	−0.968135	+	0.250429i	$0.919428\pi$
$660$	−3.52609e10	−	2.96227e9i	−0.185831	−	0.0156117i
$661$	−2.36470e9	−	1.98421e9i	−0.0123871	−	0.0103940i	0.636573	−	0.771216i	$-0.280351\pi$
$661$	−2.36470e9	−	1.98421e9i	−0.0123871	−	0.0103940i	−0.648960	+	0.760822i	$0.724796\pi$
$662$	−7.04775e10	+	8.39918e10i	−0.366960	+	0.437326i
$663$	5.96989e9	−	2.80894e9i	0.0308967	−	0.0145375i
$664$	6.60804e10	+	2.40513e10i	0.339938	+	0.123727i
$665$	5.67606e10	+	3.27707e10i	0.290242	+	0.167571i
$666$	1.82709e11	−	6.79331e10i	0.928671	−	0.345290i
$667$	−7.79900e10	−	1.35083e11i	−0.394036	−	0.682490i
$668$	5.69437e10	−	1.00407e10i	0.285983	−	0.0504265i
$669$	1.04223e11	−	2.83124e10i	0.520304	−	0.141342i
$670$	1.41963e9	−	5.16703e8i	0.00704492	−	0.00256414i
$671$	1.38740e11	+	2.44636e10i	0.684403	+	0.120679i
$672$	1.85218e10	+	2.62585e10i	0.0908253	+	0.128763i
$673$	−1.05743e11	+	8.87293e10i	−0.515458	+	0.432520i	−0.863045	−	0.505127i	$-0.831446\pi$
$673$	−1.05743e11	+	8.87293e10i	−0.515458	+	0.432520i	0.347587	+	0.937648i	$0.387001\pi$
$674$		−	2.76329e11i		−	1.33902i
$675$	−1.58391e11	−	1.08479e11i	−0.762986	−	0.522554i
$676$	1.04164e11			0.498803
$677$	−1.98226e11	−	2.36237e11i	−0.943640	−	1.12459i	−0.992061	−	0.125760i	$-0.959863\pi$
$677$	−1.98226e11	−	2.36237e11i	−0.943640	−	1.12459i	0.0484204	−	0.998827i	$-0.484581\pi$
$678$	−2.05029e11	−	9.47462e10i	−0.970280	−	0.448377i
$679$	−4.36916e9	+	2.47787e10i	−0.0205550	+	0.116573i
$680$	4.94925e9	+	1.35979e10i	0.0231475	+	0.0635971i
$681$	2.75024e11	+	7.26756e10i	1.27874	+	0.337909i
$682$	3.11713e10	+	1.76781e11i	0.144085	+	0.817145i
$683$	6.92644e9	−	3.99898e9i	0.0318293	−	0.0183767i	−0.484001	−	0.875067i	$-0.660817\pi$
$683$	6.92644e9	−	3.99898e9i	0.0318293	−	0.0183767i	0.515830	+	0.856691i	$0.327484\pi$
$684$	1.29411e11	−	7.59121e10i	0.591219	−	0.346806i
$685$	3.19385e10	−	5.53190e10i	0.145061	−	0.251254i
$686$	−5.75499e10	+	1.58117e11i	−0.259865	+	0.713973i
$687$	7.41801e10	−	1.06723e11i	0.333013	−	0.479104i
$688$	−6.65069e10	−	5.58059e10i	−0.296833	−	0.249073i
$689$	7.94428e9	−	9.46763e9i	0.0352515	−	0.0420111i
$690$	−1.68068e10	−	1.16820e10i	−0.0741461	−	0.0515370i
$691$	1.22742e10	+	4.46745e9i	0.0538371	+	0.0195951i	0.368798	−	0.929509i	$-0.379769\pi$
$691$	1.22742e10	+	4.46745e9i	0.0538371	+	0.0195951i	−0.314961	+	0.949105i	$0.601992\pi$
$692$	−1.66980e11	−	9.64061e10i	−0.728183	−	0.420417i
$693$	2.79559e11	−	1.93065e9i	1.21211	−	0.00837089i
$694$	−5.84126e10	−	1.01174e11i	−0.251807	−	0.436143i
$695$	7.93474e10	−	1.39911e10i	0.340090	−	0.0599670i
$696$	−3.58761e10	+	1.35765e11i	−0.152886	+	0.578563i
$697$	−1.98408e10	+	7.22147e9i	−0.0840676	+	0.0305981i
$698$	−2.10463e10	−	3.71103e9i	−0.0886653	−	0.0156341i
$699$	−1.70460e11	+	3.68874e11i	−0.714028	+	1.54514i
$700$	7.58069e10	−	6.36096e10i	0.315731	−	0.264930i
$701$		−	3.23180e10i		−	0.133836i	−0.997758	−	0.0669179i	$-0.978683\pi$
$701$		−	3.23180e10i		−	0.133836i	0.997758	−	0.0669179i	$-0.0213166\pi$
$702$	8.09224e9	−	2.25841e9i	0.0333212	−	0.00929938i
$703$	4.69147e11			1.92082
$704$	−2.68388e10	−	3.19852e10i	−0.109263	−	0.130214i
$705$	−2.19135e9	+	1.54571e9i	−0.00887066	+	0.00625707i
$706$	−4.62996e10	+	2.62578e11i	−0.186362	+	1.05691i
$707$	9.63655e10	+	2.64762e11i	0.385695	+	1.05969i
$708$	−2.93886e9	−	1.08184e10i	−0.0116962	−	0.0430557i
$709$	1.58507e10	+	8.98936e10i	0.0627282	+	0.355749i	0.999975	+	0.00708238i	$0.00225441\pi$
$709$	1.58507e10	+	8.98936e10i	0.0627282	+	0.355749i	−0.937247	+	0.348667i	$0.886634\pi$
$710$	−4.26247e10	+	2.46094e10i	−0.167737	+	0.0968427i
$711$	−2.79739e11	+	3.38094e11i	−1.09465	+	1.32300i
$712$	2.31052e10	−	4.00195e10i	0.0899064	−	0.155722i
$713$	−3.55133e10	+	9.75719e10i	−0.137415	+	0.377543i
$714$	−4.86744e10	−	1.03449e11i	−0.187287	−	0.398045i
$715$	−3.65321e9	−	3.06541e9i	−0.0139782	−	0.0117291i
$716$	−1.44353e11	+	1.72033e11i	−0.549255	+	0.654576i
$717$	−7.47080e9	+	8.89272e10i	−0.0282677	+	0.336479i
$718$	1.49253e11	+	5.43238e10i	0.561599	+	0.204405i
$719$	−4.96883e10	−	2.86875e10i	−0.185925	−	0.107344i	0.404148	−	0.914693i	$-0.367568\pi$
$719$	−4.96883e10	−	2.86875e10i	−0.185925	−	0.107344i	−0.590074	+	0.807349i	$0.700901\pi$
$720$	3.32502e9	+	1.81243e10i	0.0123727	+	0.0674422i
$721$	−1.44169e11	−	2.49708e11i	−0.533495	−	0.924040i
$722$	1.66380e11	−	2.93373e10i	0.612283	−	0.107962i
$723$	−2.65654e11	−	2.63826e11i	−0.972216	−	0.965525i
$724$	−2.18935e10	+	7.96860e9i	−0.0796823	+	0.0290020i
$725$	4.25885e11	+	7.50951e10i	1.54149	+	0.271806i
$726$	−1.66136e11	+	1.51132e10i	−0.598021	+	0.0544014i
$727$	2.06044e11	−	1.72891e11i	0.737603	−	0.618922i	−0.194590	−	0.980885i	$-0.562338\pi$
$727$	2.06044e11	−	1.72891e11i	0.737603	−	0.618922i	0.932193	+	0.361963i	$0.117893\pi$
$728$			4.33071e9i			0.0154182i
$729$	−2.41613e11	+	1.46252e11i	−0.855481	+	0.517834i
$730$	−5.45845e10			−0.192211
$731$	1.98551e11	+	2.36624e11i	0.695350	+	0.828685i
$732$	−6.64637e9	−	7.30618e10i	−0.0231494	−	0.254476i
$733$	−8.41161e10	+	4.77046e11i	−0.291383	+	1.65251i	0.390170	+	0.920743i	$0.372416\pi$
$733$	−8.41161e10	+	4.77046e11i	−0.291383	+	1.65251i	−0.681552	+	0.731769i	$0.738695\pi$
$734$	−6.72591e9	−	1.84793e10i	−0.0231722	−	0.0636650i
$735$	−1.15890e10	+	1.16693e10i	−0.0397098	+	0.0399850i
$736$	−4.19391e9	−	2.37849e10i	−0.0142925	−	0.0810568i
$737$	1.34314e10	−	7.75461e9i	0.0455250	−	0.0262839i
$738$	−2.64453e10	+	4.85156e9i	−0.0891503	+	0.0163552i
$739$	1.06995e11	−	1.85321e11i	0.358746	−	0.621365i	−0.629006	−	0.777400i	$-0.716538\pi$
$739$	1.06995e11	−	1.85321e11i	0.358746	−	0.621365i	0.987752	+	0.156035i	$0.0498712\pi$
$740$	−1.97071e10	+	5.41449e10i	−0.0657198	+	0.180564i
$741$	2.01493e10	+	1.69275e9i	0.0668326	+	0.00561462i
$742$	−1.64059e11	−	1.37662e11i	−0.541232	−	0.454148i
$743$	2.57043e11	−	3.06332e11i	0.843433	−	1.00516i	−0.156414	−	0.987692i	$-0.549994\pi$
$743$	2.57043e11	−	3.06332e11i	0.843433	−	1.00516i	0.999847	−	0.0174727i	$-0.00556201\pi$
$744$	8.45840e10	−	3.97983e10i	0.276055	−	0.129889i
$745$	−4.60510e10	−	1.67612e10i	−0.149491	−	0.0544102i
$746$	−1.33820e11	−	7.72612e10i	−0.432083	−	0.249463i
$747$	−2.45468e11	−	2.03100e11i	−0.788338	−	0.652270i
$748$	7.42776e10	+	1.28653e11i	0.237275	+	0.410972i
$749$	−1.00992e11	+	1.78075e10i	−0.320891	+	0.0565818i
$750$	1.13980e11	−	3.09631e10i	0.360233	−	0.0978587i
$751$	1.02473e11	−	3.72970e10i	0.322143	−	0.117250i	−0.175887	−	0.984410i	$-0.556279\pi$
$751$	1.02473e11	−	3.72970e10i	0.322143	−	0.117250i	0.498030	+	0.867160i	$0.334057\pi$
$752$	−3.11622e9	−	5.49474e8i	−0.00974445	−	0.00171821i
$753$	−1.23897e11	−	1.75649e11i	−0.385373	−	0.546345i
$754$	−1.44977e10	+	1.21650e10i	−0.0448553	+	0.0376381i
$755$		−	1.01132e11i		−	0.311243i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.27231 - 8.66680i) q^{2} +(7.33820 + 80.6669i) q^{3} +(-22.2270 + 126.055i) q^{4} +(58.6289 + 161.081i) q^{5} +(645.759 - 650.234i) q^{6} +(-371.637 - 2107.66i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6453.30 + 1183.90i) q^{9} +O(q^{10})\)	\(q+(-7.27231 - 8.66680i) q^{2} +(7.33820 + 80.6669i) q^{3} +(-22.2270 + 126.055i) q^{4} +(58.6289 + 161.081i) q^{5} +(645.759 - 650.234i) q^{6} +(-371.637 - 2107.66i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6453.30 + 1183.90i) q^{9} +(969.694 - 1679.56i) q^{10} +(6809.53 - 18709.0i) q^{11} +(-10331.6 - 867.961i) q^{12} +(-1070.41 - 898.179i) q^{13} +(-15564.0 + 18548.5i) q^{14} +(-12563.7 + 5911.46i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(50482.8 + 29146.2i) q^{17} +(57191.0 + 47319.8i) q^{18} +(89325.9 + 154717. i) q^{19} +(-21608.3 + 3810.13i) q^{20} +(167291. - 45445.2i) q^{21} +(-211668. + 77041.0i) q^{22} +(-128314. - 22625.3i) q^{23} +(67612.2 + 95854.1i) q^{24} +(276726. - 232201. i) q^{25} +15808.9i q^{26} +(-142857. - 511880. i) q^{27} +273942. q^{28} +(769507. + 917062. i) q^{29} +(142601. + 65897.3i) q^{30} +(138384. - 784813. i) q^{31} +(63398.2 + 174185. i) q^{32} +(1.55917e6 + 412013. i) q^{33} +(-114522. - 649485. i) q^{34} +(317716. - 183433. i) q^{35} +(-5799.63 - 839788. i) q^{36} +(1.31302e6 - 2.27422e6i) q^{37} +(691296. - 1.89932e6i) q^{38} +(64598.5 - 92937.6i) q^{39} +(190164. + 159567. i) q^{40} +(-232825. + 277469. i) q^{41} +(-1.61046e6 - 1.11939e6i) q^{42} +(4.97942e6 + 1.81236e6i) q^{43} +(2.20702e6 + 1.27422e6i) q^{44} +(-569054. - 970097. i) q^{45} +(737054. + 1.27661e6i) q^{46} +(190199. - 33537.2i) q^{47} +(339051. - 1.28306e6i) q^{48} +(1.11303e6 - 405110. i) q^{49} +(-4.02488e6 - 709695. i) q^{50} +(-1.98068e6 + 4.28617e6i) q^{51} +(137012. - 114967. i) q^{52} +8.84487e6i q^{53} +(-3.39746e6 + 4.96067e6i) q^{54} +3.41291e6 q^{55} +(-1.99219e6 - 2.37420e6i) q^{56} +(-1.18251e7 + 8.34099e6i) q^{57} +(2.35191e6 - 1.33383e7i) q^{58} +(369812. + 1.01605e6i) q^{59} +(-465918. - 1.71512e6i) q^{60} +(1.22873e6 + 6.96846e6i) q^{61} +(-7.80819e6 + 4.50806e6i) q^{62} +(4.89354e6 + 1.31614e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(81923.2 - 225082. i) q^{65} +(-7.76792e6 - 1.65093e7i) q^{66} +(596731. + 500717. i) q^{67} +(-4.79612e6 + 5.71579e6i) q^{68} +(883516. - 1.05168e7i) q^{69} +(-3.90031e6 - 1.41960e6i) q^{70} +(-2.19784e7 - 1.26892e7i) q^{71} +(-7.23610e6 + 6.15746e6i) q^{72} +(-1.40726e7 - 2.43745e7i) q^{73} +(-2.92589e7 + 5.15913e6i) q^{74} +(2.07616e7 + 2.06187e7i) q^{75} +(-2.14884e7 + 7.82112e6i) q^{76} +(-4.19629e7 - 7.39919e6i) q^{77} +(-1.27525e6 + 116009. i) q^{78} +(5.12352e7 - 4.29914e7i) q^{79} -2.80853e6i q^{80} +(4.02435e7 - 1.52801e7i) q^{81} +4.09795e6 q^{82} +(3.12133e7 + 3.71985e7i) q^{83} +(2.01024e6 + 2.20981e7i) q^{84} +(-1.73517e6 + 9.84065e6i) q^{85} +(-2.05045e7 - 5.63357e7i) q^{86} +(-6.83298e7 + 6.88033e7i) q^{87} +(-5.00669e6 - 2.83943e7i) q^{88} +(2.76348e7 - 1.59550e7i) q^{89} +(-4.26930e6 + 1.19867e7i) q^{90} +(-1.49525e6 + 2.58985e6i) q^{91} +(5.70408e6 - 1.56718e7i) q^{92} +(6.43239e7 + 5.40387e6i) q^{93} +(-1.67385e6 - 1.40453e6i) q^{94} +(-1.96850e7 + 2.34596e7i) q^{95} +(-1.35857e7 + 6.39234e6i) q^{96} +(-1.10475e7 - 4.02096e6i) q^{97} +(-1.16053e7 - 6.70034e6i) q^{98} +(-2.17943e7 + 1.28797e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

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