LMFDB - Embedded newform 43.8.g.a.24.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$300$
Relative dimension:	$25$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.14
Character	$\chi$	$=$	43.24
Dual form			43.8.g.a.9.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.22112 - 2.78519i) q^{2} +(-37.3010 + 5.62222i) q^{3} +(25.6587 + 112.418i) q^{4} +(39.7972 - 27.1333i) q^{5} +(-67.1910 + 116.378i) q^{6} +(-76.5793 - 132.639i) q^{7} +(780.928 + 376.075i) q^{8} +(-730.081 + 225.200i) q^{9} +O(q^{10})$	\(q+(2.22112 - 2.78519i) q^{2} +(-37.3010 + 5.62222i) q^{3} +(25.6587 + 112.418i) q^{4} +(39.7972 - 27.1333i) q^{5} +(-67.1910 + 116.378i) q^{6} +(-76.5793 - 132.639i) q^{7} +(780.928 + 376.075i) q^{8} +(-730.081 + 225.200i) q^{9} +(12.8229 - 171.109i) q^{10} +(247.552 - 1084.60i) q^{11} +(-1589.14 - 4049.06i) q^{12} +(-542.368 - 7237.40i) q^{13} +(-539.517 - 81.3192i) q^{14} +(-1331.93 + 1235.85i) q^{15} +(-10516.0 + 5064.22i) q^{16} +(-23860.6 - 16267.9i) q^{17} +(-994.370 + 2533.61i) q^{18} +(-33347.5 - 10286.3i) q^{19} +(4071.42 + 3777.73i) q^{20} +(3602.21 + 4517.03i) q^{21} +(-2470.97 - 3098.50i) q^{22} +(-8253.57 - 7658.19i) q^{23} +(-31243.8 - 9637.43i) q^{24} +(-27694.7 + 70564.9i) q^{25} +(-21362.2 - 14564.5i) q^{26} +(100295. - 48299.8i) q^{27} +(12946.1 - 12012.3i) q^{28} +(-15211.5 - 2292.76i) q^{29} +(483.708 + 6454.63i) q^{30} +(-102376. - 260849. i) q^{31} +(-33940.1 + 148701. i) q^{32} +(-3136.10 + 41848.3i) q^{33} +(-98306.4 + 30323.5i) q^{34} +(-6646.57 - 3200.82i) q^{35} +(-44049.6 - 76296.1i) q^{36} +(100741. - 174489. i) q^{37} +(-102718. + 70032.0i) q^{38} +(60921.2 + 266913. i) q^{39} +(41282.9 - 6222.39i) q^{40} +(140957. - 176755. i) q^{41} +20581.7 q^{42} +(209663. + 477347. i) q^{43} +128280. q^{44} +(-22944.8 + 28771.8i) q^{45} +(-39661.7 + 5978.04i) q^{46} +(55359.6 + 242546. i) q^{47} +(363784. - 248024. i) q^{48} +(400043. - 692894. i) q^{49} +(135024. + 233868. i) q^{50} +(981486. + 472659. i) q^{51} +(799700. - 246675. i) q^{52} +(-115274. + 1.53823e6i) q^{53} +(88243.9 - 386622. i) q^{54} +(-19576.8 - 49880.8i) q^{55} +(-9920.59 - 132381. i) q^{56} +(1.30173e6 + 196204. i) q^{57} +(-40172.3 + 37274.4i) q^{58} +(-1.58742e6 + 764461. i) q^{59} +(-173107. - 118023. i) q^{60} +(-573411. + 1.46103e6i) q^{61} +(-953903. - 294240. i) q^{62} +(85779.5 + 79591.7i) q^{63} +(-592713. - 743239. i) q^{64} +(-217959. - 273312. i) q^{65} +(109590. + 101685. i) q^{66} +(-2.80244e6 - 864439. i) q^{67} +(1.21657e6 - 3.09978e6i) q^{68} +(350922. + 239255. i) q^{69} +(-23677.7 + 11402.6i) q^{70} +(-1.85678e6 + 1.72284e6i) q^{71} +(-654833. - 98700.2i) q^{72} +(-65828.0 - 878413. i) q^{73} +(-262227. - 668144. i) q^{74} +(636308. - 2.78785e6i) q^{75} +(300718. - 4.01280e6i) q^{76} +(-162817. + 50222.5i) q^{77} +(878718. + 423168. i) q^{78} +(330578. + 572578. i) q^{79} +(-281097. + 486874. i) q^{80} +(-2.08899e6 + 1.42425e6i) q^{81} +(-179213. - 785185. i) q^{82} +(-4.32122e6 + 651319. i) q^{83} +(-415369. + 520856. i) q^{84} -1.39099e6 q^{85} +(1.79519e6 + 476293. i) q^{86} +580294. q^{87} +(601210. - 753893. i) q^{88} +(-2.92399e6 + 440720. i) q^{89} +(29172.1 + 127811. i) q^{90} +(-918429. + 626174. i) q^{91} +(649145. - 1.12435e6i) q^{92} +(5.28526e6 + 9.15435e6i) q^{93} +(798498. + 384537. i) q^{94} +(-1.60624e6 + 495458. i) q^{95} +(429969. - 5.73753e6i) q^{96} +(-1.26764e6 + 5.55388e6i) q^{97} +(-1.04130e6 - 2.65320e6i) q^{98} +(63518.3 + 847592. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) $ 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

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 $

$2$	2.22112	−	2.78519i	0.196321	−	0.246179i	−0.673921	−	0.738804i	$-0.735391\pi$
$2$	2.22112	−	2.78519i	0.196321	−	0.246179i	0.870242	+	0.492625i	$0.163963\pi$
$3$	−37.3010	+	5.62222i	−0.797620	+	0.120222i	−0.535193	−	0.844730i	$-0.679761\pi$
$3$	−37.3010	+	5.62222i	−0.797620	+	0.120222i	−0.262427	+	0.964952i	$0.584523\pi$
$4$	25.6587	+	112.418i	0.200459	+	0.878268i
$5$	39.7972	−	27.1333i	0.142383	−	0.0970749i	−0.490034	−	0.871703i	$-0.663016\pi$
$5$	39.7972	−	27.1333i	0.142383	−	0.0970749i	0.632416	+	0.774629i	$0.282063\pi$
$6$	−67.1910	+	116.378i	−0.126994	+	0.219959i
$7$	−76.5793	−	132.639i	−0.0843855	−	0.146160i	0.820744	−	0.571297i	$-0.193559\pi$
$7$	−76.5793	−	132.639i	−0.0843855	−	0.146160i	−0.905129	+	0.425137i	$0.860226\pi$
$8$	780.928	+	376.075i	0.539257	+	0.259693i
$9$	−730.081	+	225.200i	−0.333828	+	0.102972i
$10$	12.8229	−	171.109i	0.00405494	−	0.0541094i
$11$	247.552	−	1084.60i	0.0560779	−	0.245694i	−0.939118	−	0.343594i	$-0.888356\pi$
$11$	247.552	−	1084.60i	0.0560779	−	0.245694i	0.995196	+	0.0979006i	$0.0312127\pi$
$12$	−1589.14	−	4049.06i	−0.265477	−	0.676425i
$13$	−542.368	−	7237.40i	−0.0684688	−	0.913653i	−0.920646	−	0.390399i	$-0.872337\pi$
$13$	−542.368	−	7237.40i	−0.0684688	−	0.913653i	0.852177	−	0.523254i	$-0.175282\pi$
$14$	−539.517	−	81.3192i	−0.0525481	−	0.00792036i
$15$	−1331.93	+	1235.85i	−0.101897	+	0.0945465i
$16$	−10516.0	+	5064.22i	−0.641843	+	0.309095i
$17$	−23860.6	−	16267.9i	−1.17790	−	0.803082i	−0.193864	−	0.981028i	$-0.562102\pi$
$17$	−23860.6	−	16267.9i	−1.17790	−	0.803082i	−0.984040	+	0.177947i	$0.943055\pi$
$18$	−994.370	+	2533.61i	−0.0401878	+	0.102397i
$19$	−33347.5	−	10286.3i	−1.11539	−	0.344051i	−0.318344	−	0.947975i	$-0.603127\pi$
$19$	−33347.5	−	10286.3i	−1.11539	−	0.344051i	−0.797042	+	0.603924i	$0.793603\pi$
$20$	4071.42	+	3777.73i	0.113800	+	0.105591i
$21$	3602.21	+	4517.03i	0.0848793	+	0.106435i
$22$	−2470.97	−	3098.50i	−0.0494752	−	0.0620400i
$23$	−8253.57	−	7658.19i	−0.141447	−	0.131244i	0.606276	−	0.795254i	$-0.292663\pi$
$23$	−8253.57	−	7658.19i	−0.141447	−	0.131244i	−0.747723	+	0.664010i	$0.768853\pi$
$24$	−31243.8	−	9637.43i	−0.461343	−	0.142306i
$25$	−27694.7	+	70564.9i	−0.354492	+	0.903230i
$26$	−21362.2	−	14564.5i	−0.238364	−	0.162514i
$27$	100295.	−	48299.8i	0.980637	−	0.472250i
$28$	12946.1	−	12012.3i	0.111452	−	0.103412i
$29$	−15211.5	−	2292.76i	−0.115819	−	0.0174568i	0.0908772	−	0.995862i	$-0.471033\pi$
$29$	−15211.5	−	2292.76i	−0.115819	−	0.0174568i	−0.206696	+	0.978405i	$0.566271\pi$
$30$	483.708	+	6454.63i	0.00327084	+	0.0436463i
$31$	−102376.	−	260849.i	−0.617207	−	1.57262i	−0.806845	−	0.590763i	$-0.798827\pi$
$31$	−102376.	−	260849.i	−0.617207	−	1.57262i	0.189639	−	0.981854i	$-0.439268\pi$
$32$	−33940.1	+	148701.i	−0.183100	+	0.802214i
$33$	−3136.10	+	41848.3i	−0.0151912	+	0.202712i
$34$	−98306.4	+	30323.5i	−0.428949	+	0.132313i
$35$	−6646.57	−	3200.82i	−0.0262035	−	0.0126189i
$36$	−44049.6	−	76296.1i	−0.157356	−	0.272548i
$37$	100741.	−	174489.i	0.326965	−	0.566320i	−0.654943	−	0.755678i	$-0.727307\pi$
$37$	100741.	−	174489.i	0.326965	−	0.566320i	0.981908	+	0.189358i	$0.0606407\pi$
$38$	−102718.	+	70032.0i	−0.303672	+	0.207040i
$39$	60921.2	+	266913.i	0.164453	+	0.720516i
$40$	41282.9	−	6222.39i	0.101991	−	0.0153726i
$41$	140957.	−	176755.i	0.319406	−	0.400523i	−0.596045	−	0.802951i	$-0.703262\pi$
$41$	140957.	−	176755.i	0.319406	−	0.400523i	0.915452	+	0.402428i	$0.131834\pi$
$42$	20581.7			0.0428657
$43$	209663.	+	477347.i	0.402144	+	0.915576i
$43$	209663.	+	477347.i	0.402144	+	0.915576i
$44$	128280.			0.227026
$45$	−22944.8	+	28771.8i	−0.0375353	+	0.0470678i
$46$	−39661.7	+	5978.04i	−0.0600785	+	0.00905537i
$47$	55359.6	+	242546.i	0.0777769	+	0.340763i	0.998813	−	0.0487151i	$-0.0155126\pi$
$47$	55359.6	+	242546.i	0.0777769	+	0.340763i	−0.921036	+	0.389478i	$0.872656\pi$
$48$	363784.	−	248024.i	0.474787	−	0.323704i
$49$	400043.	−	692894.i	0.485758	−	0.841358i
$50$	135024.	+	233868.i	0.152762	+	0.264591i
$51$	981486.	+	472659.i	1.03607	+	0.498944i
$52$	799700.	−	246675.i	0.788706	−	0.243284i
$53$	−115274.	+	1.53823e6i	−0.106357	+	1.41924i	0.647432	+	0.762123i	$0.275843\pi$
$53$	−115274.	+	1.53823e6i	−0.106357	+	1.41924i	−0.753789	+	0.657116i	$0.771776\pi$
$54$	88243.9	−	386622.i	0.0762617	−	0.334124i
$55$	−19576.8	−	49880.8i	−0.0158661	−	0.0404263i
$56$	−9920.59	−	132381.i	−0.00754883	−	0.100732i
$57$	1.30173e6	+	196204.i	0.931017	+	0.140328i
$58$	−40172.3	+	37274.4i	−0.0270351	+	0.0250849i
$59$	−1.58742e6	+	764461.i	−1.00626	+	0.484589i	−0.863058	−	0.505105i	$-0.831454\pi$
$59$	−1.58742e6	+	764461.i	−1.00626	+	0.484589i	−0.143201	+	0.989694i	$0.545740\pi$
$60$	−173107.	−	118023.i	−0.103463	−	0.0705400i
$61$	−573411.	+	1.46103e6i	−0.323453	+	0.824145i	0.672972	+	0.739668i	$0.265017\pi$
$61$	−573411.	+	1.46103e6i	−0.323453	+	0.824145i	−0.996425	+	0.0844776i	$0.973078\pi$
$62$	−953903.	−	294240.i	−0.508315	−	0.156794i
$63$	85779.5	+	79591.7i	0.0432207	+	0.0401029i
$64$	−592713.	−	743239.i	−0.282628	−	0.354404i
$65$	−217959.	−	273312.i	−0.0984415	−	0.123442i
$66$	109590.	+	101685.i	0.0469210	+	0.0435363i
$67$	−2.80244e6	−	864439.i	−1.13835	−	0.351134i	−0.332410	−	0.943135i	$-0.607862\pi$
$67$	−2.80244e6	−	864439.i	−1.13835	−	0.351134i	−0.805937	+	0.592001i	$0.798338\pi$
$68$	1.21657e6	−	3.09978e6i	0.469199	−	1.19550i
$69$	350922.	+	239255.i	0.128600	+	0.0876777i
$70$	−23677.7	+	11402.6i	−0.00825082	+	0.00397338i
$71$	−1.85678e6	+	1.72284e6i	−0.615682	+	0.571269i	−0.925132	−	0.379647i	$-0.876046\pi$
$71$	−1.85678e6	+	1.72284e6i	−0.615682	+	0.571269i	0.309450	+	0.950916i	$0.399855\pi$
$72$	−654833.	−	98700.2i	−0.206760	−	0.0311641i
$73$	−65828.0	−	878413.i	−0.0198053	−	0.264283i	−0.998312	−	0.0580703i	$-0.981505\pi$
$73$	−65828.0	−	878413.i	−0.0198053	−	0.264283i	0.978507	−	0.206213i	$-0.0661138\pi$
$74$	−262227.	−	668144.i	−0.0752258	−	0.191672i
$75$	636308.	−	2.78785e6i	0.174162	−	0.763053i
$76$	300718.	−	4.01280e6i	0.0785799	−	1.04858i
$77$	−162817.	+	50222.5i	−0.0406427	+	0.0125366i
$78$	878718.	+	423168.i	0.209661	+	0.100968i
$79$	330578.	+	572578.i	0.0754360	+	0.130659i	0.901276	−	0.433246i	$-0.142632\pi$
$79$	330578.	+	572578.i	0.0754360	+	0.130659i	−0.825840	+	0.563905i	$0.809298\pi$
$80$	−281097.	+	486874.i	−0.0613820	+	0.106317i
$81$	−2.08899e6	+	1.42425e6i	−0.436756	+	0.297775i
$82$	−179213.	−	785185.i	−0.0358940	−	0.157262i
$83$	−4.32122e6	+	651319.i	−0.829531	+	0.125032i	−0.550063	−	0.835123i	$-0.685396\pi$
$83$	−4.32122e6	+	651319.i	−0.829531	+	0.125032i	−0.279468	+	0.960155i	$0.590158\pi$
$84$	−415369.	+	520856.i	−0.0764638	+	0.0958826i
$85$	−1.39099e6			−0.245672
$86$	1.79519e6	+	476293.i	0.304345	+	0.0807475i
$87$	580294.			0.0944780
$88$	601210.	−	753893.i	0.0940452	−	0.117929i
$89$	−2.92399e6	+	440720.i	−0.439653	+	0.0662670i	−0.365139	−	0.930953i	$-0.618979\pi$
$89$	−2.92399e6	+	440720.i	−0.439653	+	0.0662670i	−0.0745139	+	0.997220i	$0.523741\pi$
$90$	29172.1	+	127811.i	0.00421812	+	0.0184808i
$91$	−918429.	+	626174.i	−0.127762	+	0.0871065i
$92$	649145.	−	1.12435e6i	0.0869129	−	0.150537i
$93$	5.28526e6	+	9.15435e6i	0.681360	+	1.18015i
$94$	798498.	+	384537.i	0.0991577	+	0.0477518i
$95$	−1.60624e6	+	495458.i	−0.192210	+	0.0592891i
$96$	429969.	−	5.73753e6i	0.0496007	−	0.661875i
$97$	−1.26764e6	+	5.55388e6i	−0.141024	+	0.617868i	0.854174	+	0.519987i	$0.174063\pi$
$97$	−1.26764e6	+	5.55388e6i	−0.141024	+	0.617868i	−0.995198	+	0.0978803i	$0.968794\pi$
$98$	−1.04130e6	−	2.65320e6i	−0.111760	−	0.284759i
$99$	63518.3	+	847592.i	0.00657924	+	0.0877938i
$100$	−8.64339e6	−	1.30278e6i	−0.864339	−	0.130278i
$101$	4.57259e6	−	4.24274e6i	0.441608	−	0.409753i	−0.427779	−	0.903883i	$-0.640704\pi$
$101$	4.57259e6	−	4.24274e6i	0.441608	−	0.409753i	0.869388	+	0.494130i	$0.164513\pi$
$102$	3.49644e6	−	1.68380e6i	0.326231	−	0.157105i
$103$	1.17204e6	+	799082.i	0.105685	+	0.0720545i	0.615009	−	0.788520i	$-0.289152\pi$
$103$	1.17204e6	+	799082.i	0.105685	+	0.0720545i	−0.509325	+	0.860575i	$0.670105\pi$
$104$	2.29826e6	−	5.85586e6i	0.200346	−	0.510474i
$105$	265920.	+	82025.3i	0.0224175	+	0.00691489i
$106$	4.02823e6	+	3.73765e6i	0.328506	+	0.304809i
$107$	−2.66088e6	−	3.33664e6i	−0.209982	−	0.263309i	0.665676	−	0.746241i	$-0.268143\pi$
$107$	−2.66088e6	−	3.33664e6i	−0.209982	−	0.263309i	−0.875658	+	0.482932i	$0.839572\pi$
$108$	8.00323e6	+	1.00357e7i	0.611339	+	0.766595i
$109$	5.70526e6	+	5.29371e6i	0.421971	+	0.391532i	0.862377	−	0.506267i	$-0.168975\pi$
$109$	5.70526e6	+	5.29371e6i	0.421971	+	0.391532i	−0.440406	+	0.897799i	$0.645165\pi$
$110$	−182410.	−	56266.0i	−0.0130669	−	0.00403062i
$111$	−2.77673e6	+	7.07500e6i	−0.192710	+	0.491017i
$112$	1.47702e6	+	1.00701e6i	0.0993397	+	0.0677287i
$113$	1.78244e7	−	8.58377e6i	1.16209	−	0.559633i	0.249447	−	0.968389i	$-0.419751\pi$
$113$	1.78244e7	−	8.58377e6i	1.16209	−	0.559633i	0.912644	+	0.408755i	$0.134037\pi$
$114$	3.43775e6	−	3.18977e6i	0.217324	−	0.201647i
$115$	−536260.	−	80828.3i	−0.0328801	−	0.00495588i
$116$	−132559.	−	1.76888e6i	−0.00788508	−	0.105219i
$117$	2.02584e6	+	5.16175e6i	0.116938	+	0.297952i
$118$	−1.39667e6	+	6.11923e6i	−0.0782543	+	0.342855i
$119$	−330531.	+	4.41063e6i	−0.0179803	+	0.239931i
$120$	−1.50491e6	+	464203.i	−0.0795016	+	0.0245230i
$121$	1.64423e7	+	7.91818e6i	0.843748	+	0.406328i
$122$	2.79563e6	+	4.84217e6i	0.139386	+	0.241424i
$123$	−4.26409e6	+	7.38562e6i	−0.206613	+	0.357865i
$124$	2.66973e7	−	1.82019e7i	1.25745	−	0.857318i
$125$	1.64984e6	+	7.22841e6i	0.0755537	+	0.331022i
$126$	412205.	−	62129.9i	0.0183576	−	0.00276696i
$127$	−1.05318e6	+	1.32064e6i	−0.0456234	+	0.0572100i	−0.804120	−	0.594467i	$-0.797363\pi$
$127$	−1.05318e6	+	1.32064e6i	−0.0456234	+	0.0572100i	0.758496	+	0.651677i	$0.225934\pi$
$128$	−2.29098e7			−0.965577
$129$	−1.05044e7	−	1.66268e7i	−0.430831	−	0.681936i
$130$	−1.24534e6			−0.0497149
$131$	−1.65803e7	+	2.07911e7i	−0.644382	+	0.808030i	−0.991543	−	0.129776i	$-0.958574\pi$
$131$	−1.65803e7	+	2.07911e7i	−0.644382	+	0.808030i	0.347161	+	0.937805i	$0.387146\pi$
$132$	−4.78499e6	+	721221.i	−0.181081	+	0.0272935i
$133$	1.18935e6	+	5.21090e6i	0.0438359	+	0.192058i
$134$	−8.63218e6	+	5.88532e6i	−0.309923	+	0.211302i
$135$	2.68095e6	−	4.64354e6i	0.0937821	−	0.162435i
$136$	−1.25155e7	−	2.16774e7i	−0.426639	−	0.738960i
$137$	3.89585e6	+	1.87614e6i	0.129444	+	0.0623367i	0.497485	−	0.867473i	$-0.334257\pi$
$137$	3.89585e6	+	1.87614e6i	0.129444	+	0.0623367i	−0.368041	+	0.929810i	$0.619971\pi$
$138$	1.44581e6	−	445974.i	0.0468312	−	0.0144455i
$139$	2.83376e6	−	3.78139e7i	0.0894975	−	1.19426i	−0.753907	−	0.656982i	$-0.771833\pi$
$139$	2.83376e6	−	3.78139e7i	0.0894975	−	1.19426i	0.843404	−	0.537280i	$-0.180548\pi$
$140$	189288.	−	829325.i	0.00583009	−	0.0255433i
$141$	−3.42862e6	−	8.73598e6i	−0.103004	−	0.262449i
$142$	674316.	+	8.99812e6i	0.0197631	+	0.263720i
$143$	−7.98393e6	−	1.20338e6i	−0.228318	−	0.0344134i
$144$	6.53704e6	−	6.06549e6i	0.182437	−	0.169277i
$145$	−667584.	+	321492.i	−0.0181852	+	0.00875753i
$146$	−2.59276e6	−	1.76772e6i	−0.0689490	−	0.0470086i
$147$	−1.10264e7	+	2.80948e7i	−0.286301	+	0.729483i
$148$	2.22006e7	+	6.84799e6i	0.562924	+	0.173639i
$149$	−4.16993e7	−	3.86913e7i	−1.03271	−	0.958211i	−0.0335556	−	0.999437i	$-0.510683\pi$
$149$	−4.16993e7	−	3.86913e7i	−1.03271	−	0.958211i	−0.999150	+	0.0412262i	$0.986874\pi$
$150$	−6.35138e6	−	7.96438e6i	−0.153656	−	0.192678i
$151$	−4.75736e6	−	5.96554e6i	−0.112447	−	0.141004i	0.722423	−	0.691452i	$-0.243028\pi$
$151$	−4.75736e6	−	5.96554e6i	−0.112447	−	0.141004i	−0.834870	+	0.550448i	$0.814457\pi$
$152$	−2.21735e7	−	2.05740e7i	−0.512132	−	0.475189i
$153$	2.10837e7	+	6.50346e6i	0.475912	+	0.146800i
$154$	−221757.	+	565028.i	−0.00489277	+	0.0124666i
$155$	−1.11519e7	−	7.60326e6i	−0.240541	−	0.163998i
$156$	−2.84428e7	+	1.36973e7i	−0.599840	+	0.288868i
$157$	−3.97423e7	+	3.68755e7i	−0.819605	+	0.760482i	−0.973763	−	0.227564i	$-0.926924\pi$
$157$	−3.97423e7	+	3.68755e7i	−0.819605	+	0.760482i	0.154158	+	0.988046i	$0.450733\pi$
$158$	2.32899e6	+	351039.i	0.0469752	+	0.00708036i
$159$	−4.34842e6	−	5.80256e7i	−0.0857910	−	1.14480i
$160$	2.68403e6	+	6.83880e6i	0.0518045	+	0.131996i
$161$	−383724.	+	1.68120e6i	−0.00724650	+	0.0317490i
$162$	−673083.	+	8.98167e6i	−0.0124384	+	0.165980i
$163$	4.63882e7	−	1.43089e7i	0.838978	−	0.258790i	0.154654	−	0.987969i	$-0.450574\pi$
$163$	4.63882e7	−	1.43089e7i	0.838978	−	0.258790i	0.684324	+	0.729178i	$0.260097\pi$
$164$	2.34872e7	+	1.13108e7i	0.415794	+	0.200236i
$165$	1.01067e6	+	1.75054e6i	0.0175153	+	0.0303374i
$166$	−7.78388e6	+	1.34821e7i	−0.132074	+	0.228759i
$167$	−7.38087e7	+	5.03219e7i	−1.22631	+	0.836084i	−0.990740	−	0.135774i	$-0.956648\pi$
$167$	−7.38087e7	+	5.03219e7i	−1.22631	+	0.836084i	−0.235570	+	0.971857i	$0.575696\pi$
$168$	1.11432e6	+	4.88218e6i	0.0181313	+	0.0794385i
$169$	9.96182e6	−	1.50150e6i	0.158758	−	0.0239289i
$170$	−3.08954e6	+	3.87416e6i	−0.0482306	+	0.0604793i
$171$	2.66628e7			0.407775
$172$	−4.82828e7	+	3.58180e7i	−0.723508	+	0.536726i
$173$	1.48057e7			0.217404			0.108702	−	0.994074i	$-0.465331\pi$
$173$	1.48057e7			0.217404			0.108702	+	0.994074i	$0.465331\pi$
$174$	1.28890e6	−	1.61623e6i	0.0185480	−	0.0232585i
$175$	1.14805e7	−	1.73041e6i	0.161930	−	0.0244070i
$176$	2.88939e6	+	1.26592e7i	0.0399495	+	0.175030i
$177$	5.49144e7	−	3.74400e7i	0.744355	−	0.507493i
$178$	−5.26703e6	+	9.12276e6i	−0.0699996	+	0.121243i
$179$	−2.28281e6	−	3.95394e6i	−0.0297498	−	0.0515281i	0.850767	−	0.525543i	$-0.176138\pi$
$179$	−2.28281e6	−	3.95394e6i	−0.0297498	−	0.0515281i	−0.880517	+	0.474015i	$0.842804\pi$
$180$	−3.82321e6	−	1.84116e6i	−0.0488624	−	0.0235309i
$181$	1.34447e8	−	4.14713e7i	1.68529	−	0.519843i	0.703644	−	0.710552i	$-0.251555\pi$
$181$	1.34447e8	−	4.14713e7i	1.68529	−	0.519843i	0.981647	+	0.190709i	$0.0610787\pi$
$182$	−295922.	+	3.94881e6i	−0.00363855	+	0.0485530i
$183$	1.31746e7	−	5.77216e7i	0.158913	−	0.696241i
$184$	−3.56539e6	−	9.08445e6i	−0.0421934	−	0.107507i
$185$	−725236.	−	9.67761e6i	−0.00842129	−	0.112374i
$186$	3.72358e7	+	5.61240e6i	0.424293	+	0.0639518i
$187$	−2.35508e7	+	2.18520e7i	−0.263366	+	0.244368i
$188$	−2.58462e7	+	1.24469e7i	−0.283690	+	0.136618i
$189$	−1.40870e7	−	9.60435e6i	−0.151776	−	0.103479i
$190$	−2.18769e6	+	5.57415e6i	−0.0231392	+	0.0589578i
$191$	−1.47185e8	−	4.54007e7i	−1.52844	−	0.471461i	−0.587267	−	0.809393i	$-0.699796\pi$
$191$	−1.47185e8	−	4.54007e7i	−1.52844	−	0.471461i	−0.941170	+	0.337932i	$0.890272\pi$
$192$	2.62875e7	+	2.43912e7i	0.268037	+	0.248702i
$193$	1.78593e7	+	2.23948e7i	0.178819	+	0.224232i	0.863160	−	0.504930i	$-0.168482\pi$
$193$	1.78593e7	+	2.23948e7i	0.178819	+	0.224232i	−0.684342	+	0.729162i	$0.739910\pi$
$194$	1.26531e7	+	1.58664e7i	0.124420	+	0.156018i
$195$	9.66672e6	+	8.96940e6i	0.0933594	+	0.0866248i
$196$	8.81586e7	+	2.71933e7i	0.836312	+	0.257968i
$197$	2.00073e7	−	5.09777e7i	0.186447	−	0.475060i	−0.806835	−	0.590777i	$-0.798821\pi$
$197$	2.00073e7	−	5.09777e7i	0.186447	−	0.475060i	0.993282	+	0.115717i	$0.0369166\pi$
$198$	2.50179e6	+	1.70569e6i	0.0229046	+	0.0156161i
$199$	1.10720e8	−	5.33200e7i	0.995957	−	0.479627i	0.136392	−	0.990655i	$-0.456449\pi$
$199$	1.10720e8	−	5.33200e7i	0.995957	−	0.479627i	0.859564	+	0.511028i	$0.170735\pi$
$200$	−4.81652e7	+	4.46908e7i	−0.425724	+	0.395014i
$201$	1.09394e8	+	1.64885e7i	0.950183	+	0.143217i
$202$	−1.66060e6	−	2.21592e7i	−0.0141754	−	0.189158i
$203$	860774.	+	2.19322e6i	0.00722192	+	0.0184012i
$204$	−2.79518e7	+	1.22465e8i	−0.230518	+	1.00996i
$205$	813766.	−	1.08590e7i	0.00659722	−	0.0880338i
$206$	4.82883e6	−	1.48950e6i	0.0384864	−	0.0118715i
$207$	7.75040e6	+	3.73240e6i	0.0607335	+	0.0292477i
$208$	4.23553e7	+	7.33616e7i	0.326352	+	0.565258i
$209$	−1.94117e7	+	3.36221e7i	−0.147080	+	0.254749i
$210$	819095.	−	558450.i	0.00610333	−	0.00416118i
$211$	1.18427e7	+	5.18861e7i	0.0867882	+	0.380244i	0.999604	−	0.0281269i	$-0.00895424\pi$
$211$	1.18427e7	+	5.18861e7i	0.0867882	+	0.380244i	−0.912816	+	0.408371i	$0.866097\pi$
$212$	−1.75883e8	+	2.65101e7i	−1.26779	+	0.191089i
$213$	5.95736e7	−	7.47029e7i	0.422401	−	0.529674i
$214$	−1.52033e7			−0.106045
$215$	2.12960e7	+	1.33082e7i	0.146138	+	0.0913242i
$216$	9.64878e7			0.651455
$217$	−2.67589e7	+	3.35546e7i	−0.177770	+	0.222917i
$218$	2.74161e7	−	4.13231e6i	0.179229	−	0.0270144i
$219$	7.39409e6	+	3.23956e7i	0.0475697	+	0.208416i
$220$	5.10520e6	−	3.48066e6i	0.0323246	−	0.0220385i
$221$	−1.04796e8	+	1.81512e8i	−0.653088	+	1.13118i
$222$	1.35378e7	+	2.34482e7i	0.0830449	+	0.143838i
$223$	1.01338e8	+	4.88016e7i	0.611933	+	0.294691i	0.714065	−	0.700080i	$-0.246852\pi$
$223$	1.01338e8	+	4.88016e7i	0.611933	+	0.294691i	−0.102132	+	0.994771i	$0.532566\pi$
$224$	2.23227e7	−	6.88565e6i	0.132703	−	0.0409333i
$225$	4.32813e6	−	5.77549e7i	0.0253316	−	0.338026i
$226$	1.56826e7	−	6.87099e7i	0.0903729	−	0.395950i
$227$	−9.36428e7	−	2.38598e8i	−0.531354	−	1.35387i	−0.904650	−	0.426155i	$-0.859868\pi$
$227$	−9.36428e7	−	2.38598e8i	−0.531354	−	1.35387i	0.373296	−	0.927712i	$-0.378228\pi$
$228$	1.13438e7	+	1.51372e8i	0.0633849	+	0.845812i
$229$	3.82427e7	+	5.76416e6i	0.210438	+	0.0317185i	0.253415	−	0.967358i	$-0.418446\pi$
$229$	3.82427e7	+	5.76416e6i	0.210438	+	0.0317185i	−0.0429770	+	0.999076i	$0.513684\pi$
$230$	−1.41622e6	+	1.31406e6i	−0.00767509	+	0.00712144i
$231$	5.79089e6	−	2.78874e6i	0.0309103	−	0.0148856i
$232$	−1.10168e7	−	7.51114e6i	−0.0579226	−	0.0394910i
$233$	4.92890e7	−	1.25586e8i	0.255273	−	0.650424i	−0.744581	−	0.667532i	$-0.767351\pi$
$233$	4.92890e7	−	1.25586e8i	0.255273	−	0.650424i	0.999854	+	0.0171079i	$0.00544589\pi$
$234$	1.88761e7	+	5.82251e6i	0.0963068	+	0.0297067i
$235$	8.78423e6	+	8.15057e6i	0.0441536	+	0.0409685i
$236$	−1.26671e8	−	1.58840e8i	−0.627313	−	0.786625i
$237$	−1.55500e7	−	1.94991e7i	−0.0758774	−	0.0951473i
$238$	1.15503e7	+	1.07171e7i	0.0555360	+	0.0515299i
$239$	−1.72463e7	−	5.31977e6i	−0.0817152	−	0.0252058i	0.253628	−	0.967302i	$-0.418376\pi$
$239$	−1.72463e7	−	5.31977e6i	−0.0817152	−	0.0252058i	−0.335343	+	0.942096i	$0.608852\pi$
$240$	7.74788e6	−	1.97413e7i	0.0361779	−	0.0921799i
$241$	−2.42960e8	−	1.65647e8i	−1.11809	−	0.762298i	−0.144247	−	0.989542i	$-0.546076\pi$
$241$	−2.42960e8	−	1.65647e8i	−1.11809	−	0.762298i	−0.973838	+	0.227244i	$0.927028\pi$
$242$	5.85739e7	−	2.82077e7i	0.265675	−	0.127942i
$243$	−1.08552e8	+	1.00721e8i	−0.485305	+	0.450298i
$244$	−1.78959e8	−	2.69738e7i	−0.788660	−	0.118871i
$245$	−2.87991e6	−	3.84297e7i	−0.0125112	−	0.166950i
$246$	1.10993e7	+	2.82806e7i	0.0475361	+	0.121120i
$247$	−5.63597e7	+	2.46928e8i	−0.237974	+	1.04263i
$248$	1.81508e7	−	2.42205e8i	0.0755638	−	1.00833i
$249$	1.57524e8	−	4.85897e7i	0.646620	−	0.199456i
$250$	2.37970e7	+	1.14600e7i	0.0963235	+	0.0463869i
$251$	−2.27800e8	−	3.94561e8i	−0.909275	−	1.57491i	−0.815073	−	0.579358i	$-0.803303\pi$
$251$	−2.27800e8	−	3.94561e8i	−0.909275	−	1.57491i	−0.0942021	−	0.995553i	$-0.530030\pi$
$252$	−6.74657e6	+	1.16854e7i	−0.0265571	+	0.0459983i
$253$	−1.03492e7	+	7.05599e6i	−0.0401778	+	0.0273928i
$254$	1.33901e6	+	5.86660e6i	0.00512704	+	0.0224630i
$255$	5.18852e7	−	7.82043e6i	0.195953	−	0.0295352i
$256$	2.49819e7	−	3.13263e7i	0.0930648	−	0.116700i
$257$	−5.33180e8			−1.95933			−0.979666	−	0.200635i	$-0.935699\pi$
$257$	−5.33180e8			−1.95933			−0.979666	+	0.200635i	$0.935699\pi$
$258$	−6.96402e7	−	7.67324e6i	−0.252459	−	0.0278170i
$259$	−3.08588e7			−0.110364
$260$	2.51327e7	−	3.15154e7i	0.0886814	−	0.111203i
$261$	1.16219e7	−	1.75173e6i	0.0404610	−	0.00609852i
$262$	2.10803e7	+	9.23588e7i	0.0724140	+	0.317266i
$263$	−3.78403e8	+	2.57991e8i	−1.28265	+	0.874499i	−0.996492	−	0.0836823i	$-0.973332\pi$
$263$	−3.78403e8	+	2.57991e8i	−1.28265	+	0.874499i	−0.286162	+	0.958181i	$0.592380\pi$
$264$	−1.81872e7	+	3.15011e7i	−0.0608347	+	0.105369i
$265$	3.71496e7	+	6.43450e7i	0.122629	+	0.212400i
$266$	1.71551e7	+	8.26144e6i	0.0558864	+	0.0269135i
$267$	1.06590e8	−	3.28786e7i	0.342710	−	0.105712i
$268$	2.52716e7	−	3.37226e8i	0.0801975	−	1.07016i
$269$	−1.55129e7	+	6.79663e7i	−0.0485914	+	0.212893i	−0.993395	−	0.114744i	$-0.963395\pi$
$269$	−1.55129e7	+	6.79663e7i	−0.0485914	+	0.212893i	0.944804	+	0.327637i	$0.106252\pi$
$270$	−6.97845e6	−	1.77808e7i	−0.0215767	−	0.0549766i
$271$	1.26320e7	+	1.68562e8i	0.0385548	+	0.514478i	0.982731	+	0.185038i	$0.0592408\pi$
$271$	1.26320e7	+	1.68562e8i	0.0385548	+	0.514478i	−0.944177	+	0.329440i	$0.893140\pi$
$272$	3.33301e8	+	5.02371e7i	1.00426	+	0.151368i
$273$	3.07378e7	−	2.85206e7i	0.0914332	−	0.0848377i
$274$	1.38786e7	−	6.68357e6i	0.0407585	−	0.0196282i
$275$	6.96785e7	+	4.75060e7i	0.202039	+	0.137748i
$276$	−1.78924e7	+	4.55891e7i	−0.0512256	+	0.130521i
$277$	1.96055e8	+	6.04749e7i	0.554241	+	0.170961i	0.559209	−	0.829027i	$-0.311105\pi$
$277$	1.96055e8	+	6.04749e7i	0.554241	+	0.170961i	−0.00496779	+	0.999988i	$0.501581\pi$
$278$	−9.90249e7	−	9.18817e7i	−0.276431	−	0.256491i
$279$	1.33486e8	+	1.67386e8i	0.367977	+	0.461428i
$280$	−3.98674e6	−	4.99922e6i	−0.0108534	−	0.0136097i
$281$	4.29249e8	+	3.98285e8i	1.15408	+	1.07083i	0.996523	+	0.0833231i	$0.0265533\pi$
$281$	4.29249e8	+	3.98285e8i	1.15408	+	1.07083i	0.157560	+	0.987509i	$0.449637\pi$
$282$	−3.19468e7	−	9.85427e6i	−0.0848310	−	0.0261669i
$283$	9.44548e7	−	2.40667e8i	0.247726	−	0.631195i	−0.751879	−	0.659301i	$-0.770852\pi$
$283$	9.44548e7	−	2.40667e8i	0.247726	−	0.631195i	0.999605	+	0.0281058i	$0.00894755\pi$
$284$	−2.41321e8	−	1.64530e8i	−0.625146	−	0.426217i
$285$	5.71287e7	−	2.75117e7i	0.146183	−	0.0703981i
$286$	−2.10849e7	+	1.95639e7i	−0.0532955	+	0.0494510i
$287$	−3.42390e7	−	5.16069e6i	−0.0854937	−	0.0128861i
$288$	−8.70854e6	−	1.16207e8i	−0.0214819	−	0.286655i
$289$	1.54771e8	+	3.94349e8i	0.377178	+	0.961033i
$290$	−587367.	+	2.57342e6i	−0.00141422	+	0.00619609i
$291$	1.60590e7	−	2.14292e8i	0.0382026	−	0.509778i
$292$	9.70607e7	−	2.99393e7i	0.228141	−	0.0703722i
$293$	7.34364e8	+	3.53651e8i	1.70559	+	0.821370i	0.992771	+	0.120023i	$0.0382968\pi$
$293$	7.34364e8	+	3.53651e8i	1.70559	+	0.821370i	0.712820	+	0.701347i	$0.247418\pi$
$294$	5.37585e7	+	9.31125e7i	0.123376	+	0.213694i
$295$	−4.24325e7	+	7.34953e7i	−0.0962325	+	0.166680i
$296$	1.44293e8	−	9.83770e7i	0.323387	−	0.220482i
$297$	−2.75574e7	−	1.20737e8i	−0.0610366	−	0.267419i
$298$	−2.00382e8	+	3.02027e7i	−0.438633	+	0.0661133i
$299$	−5.09489e7	+	6.38880e7i	−0.110227	+	0.138220i
$300$	3.29732e8			0.705077
$301$	4.72591e7	−	6.43644e7i	0.0998855	−	0.136039i
$302$	−2.71819e7			−0.0567878
$303$	−1.46709e8	+	1.83967e8i	−0.302975	+	0.379918i
$304$	4.02773e8	−	6.07082e7i	0.822248	−	0.123934i
$305$	1.68223e7	+	7.37033e7i	0.0339497	+	0.148743i
$306$	6.49428e7	−	4.42773e7i	0.129570	−	0.0883396i
$307$	−3.39774e8	+	5.88506e8i	−0.670202	+	1.16082i	0.307644	+	0.951502i	$0.400459\pi$
$307$	−3.39774e8	+	5.88506e8i	−0.670202	+	1.16082i	−0.977847	+	0.209323i	$0.932874\pi$
$308$	−9.82361e6	−	1.70150e7i	−0.0191577	−	0.0331821i
$309$	−4.82108e7	−	2.32171e7i	−0.0929587	−	0.0447665i
$310$	−4.59463e7	+	1.41726e7i	−0.0875961	+	0.0270198i
$311$	1.72402e7	−	2.30055e8i	0.0324999	−	0.433680i	−0.957093	−	0.289782i	$-0.906417\pi$
$311$	1.72402e7	−	2.30055e8i	0.0324999	−	0.433680i	0.989592	−	0.143898i	$-0.0459638\pi$
$312$	−5.28043e7	+	2.31351e8i	−0.0984302	+	0.431251i
$313$	−2.88752e8	−	7.35727e8i	−0.532254	−	1.35616i	−0.903883	−	0.427780i	$-0.859296\pi$
$313$	−2.88752e8	−	7.35727e8i	−0.532254	−	1.35616i	0.371629	−	0.928382i	$-0.378800\pi$
$314$	1.44330e7	+	1.92595e8i	0.0263089	+	0.351068i
$315$	5.57336e6	+	840049.i	0.0100469	+	0.00151432i
$316$	−5.58860e7	+	5.18546e7i	−0.0996318	+	0.0924448i
$317$	−2.00742e8	+	9.66721e7i	−0.353940	+	0.170449i	−0.602402	−	0.798193i	$-0.705789\pi$
$317$	−2.00742e8	+	9.66721e7i	−0.353940	+	0.170449i	0.248461	+	0.968642i	$0.420075\pi$
$318$	−1.71271e8	−	1.16771e8i	−0.298668	−	0.203628i
$319$	−6.25235e6	+	1.59307e7i	−0.0107839	+	0.0274769i
$320$	−4.37548e7	−	1.34966e7i	−0.0746451	−	0.0230250i
$321$	1.18013e8	+	1.09500e8i	0.199142	+	0.184777i
$322$	3.83018e6	+	4.80290e6i	0.00639329	+	0.00801693i
$323$	6.28354e8	+	7.87930e8i	1.03752	+	1.30101i
$324$	−2.13713e8	−	1.98296e8i	−0.349078	−	0.323897i
$325$	5.25727e8	+	1.62165e8i	0.849510	+	0.262039i
$326$	6.31807e7	−	1.60982e8i	0.101000	−	0.257345i
$327$	−2.42575e8	−	1.65385e8i	−0.383644	−	0.261564i
$328$	1.76550e8	−	8.50221e7i	0.276255	−	0.133037i
$329$	2.79317e7	−	2.59169e7i	0.0432426	−	0.0401233i
$330$	7.12042e6	+	1.07323e6i	0.0109070	+	0.00164397i
$331$	−8.50264e7	−	1.13460e9i	−0.128871	−	1.71967i	−0.569512	−	0.821983i	$-0.692868\pi$
$331$	−8.50264e7	−	1.13460e9i	−0.128871	−	1.71967i	0.440641	−	0.897684i	$-0.354751\pi$
$332$	−1.84097e8	−	4.69072e8i	−0.276098	−	0.703487i
$333$	−3.42543e7	+	1.50078e8i	−0.0508348	+	0.222722i
$334$	−2.37815e7	+	3.17343e8i	−0.0349243	+	0.466032i
$335$	−1.34984e8	+	4.16372e7i	−0.196167	+	0.0605096i
$336$	−6.07559e7	−	2.92585e7i	−0.0873778	−	0.0420789i
$337$	2.66128e8	+	4.60948e8i	0.378780	+	0.656066i	0.990885	−	0.134711i	$-0.0430105\pi$
$337$	2.66128e8	+	4.60948e8i	0.378780	+	0.656066i	−0.612105	+	0.790776i	$0.709677\pi$
$338$	1.79444e7	−	3.10806e7i	0.0252767	−	0.0437805i
$339$	−6.16608e8	+	4.20396e8i	−0.859627	+	0.586084i
$340$	−3.56909e7	−	1.56372e8i	−0.0492472	−	0.215766i
$341$	−3.08259e8	+	4.64626e7i	−0.420993	+	0.0634545i
$342$	5.92213e7	−	7.42612e7i	0.0800547	−	0.100385i
$343$	−2.48673e8			−0.332735
$344$	−1.57868e7	+	4.51622e8i	−0.0209093	+	0.598165i
$345$	2.04575e7			0.0268217
$346$	3.28852e7	−	4.12367e7i	0.0426809	−	0.0535202i
$347$	9.36838e7	−	1.41206e7i	0.120368	−	0.0181426i	−0.0885819	−	0.996069i	$-0.528234\pi$
$347$	9.36838e7	−	1.41206e7i	0.120368	−	0.0181426i	0.208950	+	0.977926i	$0.432995\pi$
$348$	1.48896e7	+	6.52356e7i	0.0189390	+	0.0829770i
$349$	7.92195e8	−	5.40109e8i	0.997569	−	0.680131i	0.0496912	−	0.998765i	$-0.484176\pi$
$349$	7.92195e8	−	5.40109e8i	0.997569	−	0.680131i	0.947878	+	0.318633i	$0.103224\pi$
$350$	2.06800e7	−	3.58189e7i	0.0257818	−	0.0446554i
$351$	−4.03962e8	−	6.99683e8i	−0.498615	−	0.863627i
$352$	1.52879e8	+	7.36227e7i	0.186831	+	0.0899730i
$353$	7.57114e8	−	2.33539e8i	0.916115	−	0.282584i	0.199374	−	0.979923i	$-0.436109\pi$
$353$	7.57114e8	−	2.33539e8i	0.916115	−	0.282584i	0.716741	+	0.697339i	$0.245633\pi$
$354$	1.76937e7	−	2.36106e8i	0.0211986	−	0.282876i
$355$	−2.71483e7	+	1.18945e8i	−0.0322065	+	0.141106i
$356$	−1.24571e8	−	3.17401e8i	−0.146333	−	0.372849i
$357$	−1.24684e7	−	1.66379e8i	−0.0145035	−	0.193536i
$358$	−1.60829e7	−	2.42410e6i	−0.0185256	−	0.00279229i
$359$	−8.10093e8	+	7.51656e8i	−0.924069	+	0.857410i	−0.990094	−	0.140408i	$-0.955159\pi$
$359$	−8.10093e8	+	7.51656e8i	−0.924069	+	0.857410i	0.0660251	+	0.997818i	$0.478968\pi$
$360$	−2.87386e7	+	1.38398e7i	−0.0324643	+	0.0156340i
$361$	2.67693e8	+	1.82510e8i	0.299476	+	0.204179i
$362$	1.83116e8	−	4.66573e8i	0.202884	−	0.516939i
$363$	−6.57831e8	−	2.02914e8i	−0.721840	−	0.222658i
$364$	−9.39592e7	−	8.71814e7i	−0.102114	−	0.0947477i
$365$	−2.64540e7	−	3.31723e7i	−0.0284752	−	0.0357067i
$366$	−1.31504e8	−	1.64900e8i	−0.140202	−	0.175808i
$367$	−2.07797e8	−	1.92807e8i	−0.219436	−	0.203607i	0.562793	−	0.826598i	$-0.309727\pi$
$367$	−2.07797e8	−	1.92807e8i	−0.219436	−	0.203607i	−0.782229	+	0.622991i	$0.785917\pi$
$368$	1.25577e8	+	3.87354e7i	0.131354	+	0.0405173i
$369$	−6.31049e7	+	1.60789e8i	−0.0653839	+	0.166596i
$370$	−2.85649e7	−	1.94752e7i	−0.0293174	−	0.0199883i
$371$	2.12857e8	−	1.02507e8i	0.216411	−	0.104218i
$372$	−8.93503e8	+	8.29049e8i	−0.899903	+	0.834988i
$373$	−1.20044e9	−	1.80938e8i	−1.19774	−	0.180530i	−0.480269	−	0.877121i	$-0.659461\pi$
$373$	−1.20044e9	−	1.80938e8i	−1.19774	−	0.180530i	−0.717468	+	0.696592i	$0.754699\pi$
$374$	8.55282e6	+	1.14129e8i	0.00845393	+	0.112810i
$375$	−1.02180e8	−	2.60351e8i	−0.100059	−	0.254947i
$376$	−4.79837e7	+	2.10230e8i	−0.0465518	+	0.203957i
$377$	−8.34341e6	+	1.11335e8i	−0.00801953	+	0.107013i
$378$	−5.80388e7	+	1.79026e7i	−0.0552710	+	0.0170488i
$379$	−1.23622e9	−	5.95333e8i	−1.16643	−	0.561723i	−0.252501	−	0.967597i	$-0.581253\pi$
$379$	−1.23622e9	−	5.95333e8i	−1.16643	−	0.561723i	−0.913929	+	0.405873i	$0.866967\pi$
$380$	−9.69126e7	−	1.67858e8i	−0.0906020	−	0.156927i
$381$	3.18596e7	−	5.51824e7i	0.0295123	−	0.0511168i
$382$	−4.53366e8	+	3.09099e8i	−0.416128	+	0.283711i
$383$	2.84533e8	+	1.24662e9i	0.258784	+	1.13381i	0.922553	+	0.385869i	$0.126099\pi$
$383$	2.84533e8	+	1.24662e9i	0.258784	+	1.13381i	−0.663769	+	0.747937i	$0.731044\pi$
$384$	8.54560e8	−	1.28804e8i	0.770164	−	0.116084i
$385$	−5.11697e6	+	6.41648e6i	−0.00456983	+	0.00573039i
$386$	1.02041e8			0.0903069
$387$	−2.60570e8	−	3.01286e8i	−0.228526	−	0.264235i
$388$	−6.56884e8			−0.570923
$389$	−7.04350e8	+	8.83227e8i	−0.606688	+	0.760762i	−0.986404	−	0.164341i	$-0.947450\pi$
$389$	−7.04350e8	+	8.83227e8i	−0.606688	+	0.760762i	0.379716	+	0.925103i	$0.376022\pi$
$390$	4.64525e7	−	7.00158e6i	0.0396536	−	0.00597682i
$391$	7.23525e7	+	3.16997e8i	0.0612118	+	0.268186i
$392$	5.72985e8	−	3.90654e8i	0.480443	−	0.327560i
$393$	5.01571e8	−	8.68746e8i	0.416830	−	0.721970i
$394$	−9.75443e7	−	1.68952e8i	−0.0803461	−	0.139164i
$395$	2.86920e7	+	1.38173e7i	0.0234245	+	0.0112806i
$396$	−9.36551e7	+	2.88888e7i	−0.0757876	+	0.0233774i
$397$	9.36157e7	−	1.24921e9i	0.0750900	−	1.00201i	−0.824668	−	0.565617i	$-0.808638\pi$
$397$	9.36157e7	−	1.24921e9i	0.0750900	−	1.00201i	0.899758	−	0.436389i	$-0.143743\pi$
$398$	9.74158e7	−	4.26807e8i	0.0774531	−	0.339344i
$399$	−7.36609e7	−	1.87685e8i	−0.0580540	−	0.147919i
$400$	−6.61199e7	−	8.82309e8i	−0.0516562	−	0.689304i
$401$	2.07718e9	+	3.13084e8i	1.60868	+	0.242469i	0.891031	−	0.453942i	$-0.149983\pi$
$401$	2.07718e9	+	3.13084e8i	1.60868	+	0.242469i	0.717644	+	0.696410i	$0.245221\pi$
$402$	2.88901e8	−	2.68061e8i	0.221798	−	0.205798i
$403$	−1.83234e9	+	8.82410e8i	−1.39457	+	0.671588i
$404$	5.94289e8	+	4.05179e8i	0.448397	+	0.305712i
$405$	−4.44914e7	+	1.13362e8i	−0.0332800	+	0.0847961i
$406$	8.02041e6	+	2.47397e6i	0.00594779	+	0.00183465i
$407$	−1.64311e8	−	1.52459e8i	−0.120806	−	0.112091i
$408$	5.88715e8	+	7.38225e8i	0.429135	+	0.538119i
$409$	3.94593e8	+	4.94804e8i	0.285179	+	0.357604i	0.903701	−	0.428164i	$-0.140840\pi$
$409$	3.94593e8	+	4.94804e8i	0.285179	+	0.357604i	−0.618522	+	0.785768i	$0.712268\pi$
$410$	−2.84368e7	−	2.63855e7i	−0.0203769	−	0.0189070i
$411$	−1.55867e8	−	4.80787e7i	−0.110741	−	0.0341591i
$412$	−5.97584e7	+	1.52262e8i	−0.0420977	+	0.107263i
$413$	2.22961e8	+	1.52012e8i	0.155741	+	0.106183i
$414$	2.76100e7	−	1.32963e7i	0.0191234	−	0.00920935i
$415$	−1.54300e8	+	1.43169e8i	−0.105974	+	0.0983290i
$416$	1.09462e9	+	1.64987e8i	0.745481	+	0.112363i
$417$	1.06896e8	+	1.42643e9i	0.0721914	+	0.963327i
$418$	5.05284e7	+	1.28744e8i	0.0338391	+	0.0862205i
$419$	2.94436e8	−	1.29001e9i	0.195543	−	0.856730i	−0.778007	−	0.628256i	$-0.783769\pi$
$419$	2.94436e8	−	1.29001e9i	0.195543	−	0.856730i	0.973550	−	0.228474i	$-0.0733737\pi$
$420$	−2.39799e6	+	3.19989e7i	−0.00157933	+	0.0210748i
$421$	2.27327e9	−	7.01211e8i	1.48478	−	0.457995i	0.556810	−	0.830640i	$-0.312025\pi$
$421$	2.27327e9	−	7.01211e8i	1.48478	−	0.457995i	0.927974	+	0.372644i	$0.121549\pi$
$422$	1.70817e8	+	8.22610e7i	0.110646	+	0.0532844i
$423$	−9.50385e7	−	1.64611e8i	−0.0610532	−	0.105747i
$424$	−6.68511e8	+	1.15789e9i	−0.425920	+	0.737715i
$425$	1.80875e9	−	1.23319e9i	1.14292	−	0.779233i
$426$	−7.57421e7	−	3.31848e8i	−0.0474683	−	0.207972i
$427$	2.37701e8	−	3.58276e7i	0.147752	−	0.0222700i
$428$	3.06825e8	−	3.84746e8i	0.189163	−	0.237203i
$429$	3.04574e8			0.186248
$430$	8.43669e7	−	2.97542e7i	0.0511720	−	0.0180472i
$431$	−4.07943e8			−0.245431			−0.122715	−	0.992442i	$-0.539160\pi$
$431$	−4.07943e8			−0.245431			−0.122715	+	0.992442i	$0.539160\pi$
$432$	−8.10103e8	+	1.01584e9i	−0.483445	+	0.606221i
$433$	2.09620e9	−	3.15951e8i	1.24087	−	0.187030i	0.504379	−	0.863482i	$-0.331721\pi$
$433$	2.09620e9	−	3.15951e8i	1.24087	−	0.187030i	0.736487	+	0.676452i	$0.236483\pi$
$434$	3.40214e7	+	1.49058e8i	0.0199774	+	0.0875266i
$435$	2.30941e7	−	1.57453e7i	0.0134520	−	0.00917144i
$436$	−4.48720e8	+	7.77206e8i	−0.259282	+	0.449090i
$437$	1.96461e8	+	3.40280e8i	0.112614	+	0.195053i
$438$	1.06651e8	+	5.13605e7i	0.0606466	+	0.0292059i
$439$	−1.20616e9	+	3.72051e8i	−0.680423	+	0.209883i	−0.615653	−	0.788017i	$-0.711108\pi$
$439$	−1.20616e9	+	3.72051e8i	−0.680423	+	0.209883i	−0.0647702	+	0.997900i	$0.520631\pi$
$440$	3.47088e6	−	4.63156e7i	0.00194247	−	0.0259205i
$441$	−1.36024e8	+	5.95959e8i	−0.0755231	+	0.330888i
$442$	2.72782e8	+	6.95037e8i	0.150258	+	0.382851i
$443$	−1.25819e7	−	1.67894e8i	−0.00687596	−	0.0917533i	0.992710	−	0.120528i	$-0.0384586\pi$
$443$	−1.25819e7	−	1.67894e8i	−0.00687596	−	0.0917533i	−0.999586	+	0.0287743i	$0.990840\pi$
$444$	−8.66607e8	−	1.30620e8i	−0.469875	−	0.0708222i
$445$	−1.04408e8	+	9.68767e7i	−0.0561661	+	0.0521146i
$446$	3.61005e8	−	1.73851e8i	0.192682	−	0.0927907i
$447$	1.77296e9	+	1.20878e9i	0.938905	+	0.640135i
$448$	−5.31931e7	+	1.35534e8i	−0.0279500	+	0.0712155i
$449$	−4.21163e8	−	1.29911e8i	−0.219577	−	0.0677307i	0.183015	−	0.983110i	$-0.441414\pi$
$449$	−4.21163e8	−	1.29911e8i	−0.219577	−	0.0677307i	−0.402592	+	0.915380i	$0.631891\pi$
$450$	−1.51245e8	−	1.40335e8i	−0.0782417	−	0.0725977i
$451$	−1.56813e8	−	1.96637e8i	−0.0804942	−	0.100937i
$452$	1.42232e9	+	1.78354e9i	0.724459	+	0.908443i
$453$	2.10994e8	+	1.95774e8i	0.106642	+	0.0989489i
$454$	−8.72533e8	−	2.69141e8i	−0.437609	−	0.134985i
$455$	−1.95607e7	+	4.98400e7i	−0.00973521	+	0.0248049i
$456$	9.42767e8	+	6.42768e8i	0.465615	+	0.317451i
$457$	−1.13187e9	+	5.45080e8i	−0.554741	+	0.267149i	−0.690181	−	0.723636i	$-0.742469\pi$
$457$	−1.13187e9	+	5.45080e8i	−0.554741	+	0.267149i	0.135441	+	0.990785i	$0.456755\pi$
$458$	1.00996e8	−	9.37105e7i	0.0491218	−	0.0455784i
$459$	−3.17884e9	−	4.79134e8i	−1.53435	−	0.231266i
$460$	−4.67319e6	−	6.23594e7i	−0.00223852	−	0.0298710i
$461$	−2.10795e8	−	5.37097e8i	−0.100209	−	0.255329i	0.871973	−	0.489553i	$-0.162840\pi$
$461$	−2.10795e8	−	5.37097e8i	−0.100209	−	0.255329i	−0.972183	+	0.234225i	$0.924745\pi$
$462$	5.09505e6	−	2.23229e7i	0.00240382	−	0.0105318i
$463$	2.62481e7	−	3.50257e8i	0.0122904	−	0.164004i	−0.987681	−	0.156479i	$-0.949986\pi$
$463$	2.62481e7	−	3.50257e8i	0.0122904	−	0.164004i	0.999972	−	0.00752483i	$-0.00239525\pi$
$464$	1.71574e8	−	5.29237e7i	0.0797332	−	0.0245944i
$465$	4.58726e8	+	2.20911e8i	0.211577	+	0.101890i
$466$	−2.40306e8	−	4.16222e8i	−0.110005	−	0.190535i
$467$	7.29689e8	−	1.26386e9i	0.331535	−	0.574235i	−0.651278	−	0.758839i	$-0.725767\pi$
$467$	7.29689e8	−	1.26386e9i	0.331535	−	0.574235i	0.982813	+	0.184604i	$0.0591003\pi$
$468$	−5.28295e8	+	3.60185e8i	−0.238241	+	0.162430i
$469$	9.99505e7	+	4.37912e8i	0.0447383	+	0.196011i
$470$	4.22117e7	−	6.36239e6i	0.0187539	−	0.00282669i
$471$	1.27511e9	−	1.59893e9i	0.562307	−	0.705111i
$472$	−1.52716e9			−0.668477
$473$	5.69631e8	−	1.09231e8i	0.247503	−	0.0474606i
$474$	−8.88474e7			−0.0383196
$475$	1.64940e9	−	2.06828e9i	0.706152	−	0.885487i
$476$	−5.04317e8	+	7.60135e7i	−0.214328	+	0.0323048i
$477$	−2.62250e8	−	1.14899e9i	−0.110637	−	0.484733i
$478$	−5.31226e7	+	3.62184e7i	−0.0222475	+	0.0151681i
$479$	4.56155e8	−	7.90084e8i	0.189644	−	0.328472i	−0.755488	−	0.655163i	$-0.772600\pi$
$479$	4.56155e8	−	7.90084e8i	0.189644	−	0.328472i	0.945131	+	0.326690i	$0.105933\pi$
$480$	−1.38566e8	−	2.40004e8i	−0.0571892	−	0.0990545i
$481$	−1.31749e9	−	6.34468e8i	−0.539807	−	0.259957i
$482$	−1.00100e9	+	3.08768e8i	−0.407165	+	0.125594i
$483$	4.86119e6	−	6.48680e7i	0.00196303	−	0.0261948i
$484$	−4.68260e8	+	2.05158e9i	−0.187728	+	0.822489i
$485$	1.00247e8	+	2.55424e8i	0.0399000	+	0.101664i
$486$	3.94221e7	+	5.26052e8i	0.0155781	+	0.207875i
$487$	−2.44364e9	−	3.68319e8i	−0.958706	−	0.144502i	−0.348994	−	0.937125i	$-0.613477\pi$
$487$	−2.44364e9	−	3.68319e8i	−0.958706	−	0.144502i	−0.609712	+	0.792623i	$0.708715\pi$
$488$	−9.97248e8	+	9.25311e8i	−0.388449	+	0.360428i
$489$	−1.64988e9	+	7.94539e8i	−0.638074	+	0.307280i
$490$	−1.13431e8	−	7.73358e7i	−0.0435557	−	0.0296958i
$491$	1.55904e9	−	3.97237e9i	0.594391	−	1.51448i	−0.244201	−	0.969725i	$-0.578526\pi$
$491$	1.55904e9	−	3.97237e9i	0.594391	−	1.51448i	0.838593	−	0.544759i	$-0.183379\pi$
$492$	−9.39689e8	−	2.89856e8i	−0.355718	−	0.109725i
$493$	3.25657e8	+	3.02165e8i	0.122404	+	0.113574i
$494$	5.62561e8	+	7.05429e8i	0.209955	+	0.263275i
$495$	2.55258e7	+	3.20083e7i	0.00945934	+	0.0118616i
$496$	2.39757e9	+	2.22462e9i	0.882239	+	0.818598i
$497$	3.70707e8	+	1.14348e8i	0.135451	+	0.0417812i
$498$	2.14548e8	−	5.46658e8i	0.0778432	−	0.198341i
$499$	−1.80635e9	−	1.23155e9i	−0.650803	−	0.443710i	0.192392	−	0.981318i	$-0.438376\pi$
$499$	−1.80635e9	−	1.23155e9i	−0.650803	−	0.443710i	−0.843195	+	0.537608i	$0.819328\pi$
$500$	−7.70272e8	+	3.70944e8i	−0.275581	+	0.132713i
$501$	2.47022e9	−	2.29203e9i	0.877614	−	0.814307i
$502$	−1.60490e9	−	2.41900e8i	−0.566219	−	0.0853438i
$503$	1.76007e8	+	2.34865e9i	0.0616655	+	0.822869i	0.939203	+	0.343361i	$0.111566\pi$
$503$	1.76007e8	+	2.34865e9i	0.0616655	+	0.822869i	−0.877538	+	0.479507i	$0.840815\pi$
$504$	3.70551e7	+	9.44149e7i	0.0128926	+	0.0328499i
$505$	6.68567e7	−	2.92918e8i	0.0231007	−	0.101211i
$506$	−3.33457e6	+	4.44968e7i	−0.00114423	+	0.0152687i
$507$	−3.63144e8	+	1.12015e8i	−0.123752	+	0.0381723i
$508$	−1.75487e8	−	8.45103e7i	−0.0593913	−	0.0286013i
$509$	4.64237e8	+	8.04082e8i	0.156037	+	0.270264i	0.933436	−	0.358744i	$-0.116795\pi$
$509$	4.64237e8	+	8.04082e8i	0.156037	+	0.270264i	−0.777399	+	0.629008i	$0.783461\pi$
$510$	9.34617e7	−	1.61880e8i	0.0311988	−	0.0540379i
$511$	−1.11471e8	+	7.59996e7i	−0.0369563	+	0.0251964i
$512$	−6.84295e8	−	2.99809e9i	−0.225319	−	0.987189i
$513$	−3.84143e9	+	5.79002e8i	−1.25627	+	0.189352i
$514$	−1.18426e9	+	1.48501e9i	−0.384658	+	0.482346i
$515$	6.83255e7			0.0220423
$516$	1.59962e9	−	1.60751e9i	0.512559	−	0.515085i
$517$	2.76769e8			0.0880847
$518$	−6.85409e7	+	8.59476e7i	−0.0216669	+	0.0271694i
$519$	−5.52267e8	+	8.32409e7i	−0.173406	+	0.0261367i
$520$	−6.74245e7	−	2.95406e8i	−0.0210284	−	0.0921314i
$521$	1.95765e9	−	1.33470e9i	0.606461	−	0.413478i	−0.220781	−	0.975323i	$-0.570861\pi$
$521$	1.95765e9	−	1.33470e9i	0.606461	−	0.413478i	0.827242	+	0.561845i	$0.189908\pi$
$522$	2.09348e7	−	3.62602e7i	0.00644202	−	0.0111579i
$523$	1.00270e9	+	1.73673e9i	0.306490	+	0.530856i	0.977592	−	0.210509i	$-0.0675121\pi$
$523$	1.00270e9	+	1.73673e9i	0.306490	+	0.530856i	−0.671102	+	0.741365i	$0.734179\pi$
$524$	−2.76273e9	−	1.33046e9i	−0.838839	−	0.403963i
$525$	−4.18506e8	+	1.29092e8i	−0.126225	+	0.0389351i
$526$	−1.21923e8	+	1.62695e9i	−0.0365289	+	0.487445i
$527$	−1.80071e9	+	7.88944e9i	−0.535929	+	2.34806i
$528$	−1.78950e8	−	4.55957e8i	−0.0529070	−	0.134805i
$529$	−2.44969e8	−	3.26889e9i	−0.0719477	−	0.960076i
$530$	2.61727e8	+	3.94490e7i	0.0763630	+	0.0115099i
$531$	9.86789e8	−	9.15607e8i	0.286018	−	0.265386i
$532$	−5.55283e8	+	2.67410e8i	−0.159891	+	0.0769994i
$533$	−1.35569e9	−	9.24297e8i	−0.387808	−	0.264403i
$534$	1.45175e8	−	3.69900e8i	0.0412570	−	0.105121i
$535$	−1.96430e8	−	6.05905e7i	−0.0554586	−	0.0171067i
$536$	−1.86341e9	−	1.72899e9i	−0.522675	−	0.484972i
$537$	1.07381e8	+	1.34652e8i	0.0299239	+	0.0375233i
$538$	1.54844e8	+	1.94168e8i	0.0428702	+	0.0537575i
$539$	−6.52479e8	−	6.05412e8i	−0.179476	−	0.166529i
$540$	5.90808e8	+	1.82240e8i	0.161461	+	0.0498042i
$541$	5.59672e8	−	1.42602e9i	0.151965	−	0.387200i	−0.834537	−	0.550952i	$-0.814265\pi$
$541$	5.59672e8	−	1.42602e9i	0.151965	−	0.387200i	0.986501	+	0.163752i	$0.0523598\pi$
$542$	4.97534e8	+	3.39213e8i	0.134223	+	0.0915114i
$543$	−4.78183e9	+	2.30281e9i	−1.28173	+	0.617247i
$544$	3.22889e9	−	2.99597e9i	0.859918	−	0.797887i
$545$	3.70689e8	+	5.58724e7i	0.0980894	+	0.0147846i
$546$	−1.11629e7	−	1.48958e8i	−0.00293496	−	0.0391643i
$547$	−1.64422e9	−	4.18941e9i	−0.429541	−	1.09445i	−0.967811	−	0.251679i	$-0.919017\pi$
$547$	−1.64422e9	−	4.18941e9i	−0.429541	−	1.09445i	0.538270	−	0.842773i	$-0.319078\pi$
$548$	−1.10950e8	+	4.86104e8i	−0.0288002	+	0.126182i
$549$	8.96129e7	−	1.19580e9i	0.0231136	−	0.308429i
$550$	2.87078e8	−	8.85517e7i	0.0735749	−	0.0226949i
$551$	4.83680e8	+	2.32928e8i	0.123176	+	0.0593186i
$552$	1.84067e8	+	3.18814e8i	0.0465790	+	0.0806771i
$553$	5.06308e7	−	8.76951e7i	0.0127314	−	0.0220515i
$554$	6.03895e8	−	4.11729e8i	0.150896	−	0.102879i
$555$	8.14617e7	+	3.56907e8i	0.0202268	+	0.0886196i
$556$	4.32368e9	−	6.51690e8i	1.06682	−	0.160798i
$557$	6.89273e7	−	8.64320e7i	0.0169004	−	0.0211925i	−0.773309	−	0.634029i	$-0.781400\pi$
$557$	6.89273e7	−	8.64320e7i	0.0169004	−	0.0211925i	0.790210	+	0.612836i	$0.209971\pi$
$558$	7.62689e8			0.185835
$559$	3.34104e9	−	1.77631e9i	0.808984	−	0.430108i
$560$	8.61047e7			0.0207190
$561$	7.55613e8	−	9.47509e8i	0.180688	−	0.226576i
$562$	2.06271e9	−	3.10904e8i	0.490187	−	0.0738838i
$563$	1.23535e9	+	5.41241e9i	0.291749	+	1.27824i	0.882090	+	0.471082i	$0.156136\pi$
$563$	1.23535e9	+	5.41241e9i	0.291749	+	1.27824i	−0.590341	+	0.807154i	$0.701007\pi$
$564$	8.94109e8	−	6.09593e8i	0.209852	−	0.143075i
$565$	4.76455e8	−	8.25244e8i	0.111135	−	0.192492i
$566$	−4.60509e8	−	7.97624e8i	−0.106753	−	0.184902i
$567$	3.48885e8	+	1.68014e8i	0.0803787	+	0.0387083i
$568$	−2.09793e9	+	6.47125e8i	−0.480365	+	0.148173i
$569$	−2.29684e8	+	3.06493e9i	−0.0522683	+	0.697473i	0.908103	+	0.418748i	$0.137531\pi$
$569$	−2.29684e8	+	3.06493e9i	−0.0522683	+	0.697473i	−0.960371	+	0.278725i	$0.910088\pi$
$570$	5.02641e7	−	2.20221e8i	0.0113683	−	0.0498078i
$571$	1.31510e9	+	3.35082e9i	0.295619	+	0.753225i	0.999096	+	0.0425071i	$0.0135345\pi$
$571$	1.31510e9	+	3.35082e9i	0.295619	+	0.753225i	−0.703477	+	0.710718i	$0.748370\pi$
$572$	−6.95752e7	−	9.28417e8i	−0.0155442	−	0.207423i
$573$	5.74541e9	+	8.65982e8i	1.27579	+	0.192295i
$574$	−9.04223e7	+	8.38996e7i	−0.0199565	+	0.0185169i
$575$	7.68979e8	−	3.70321e8i	0.168685	−	0.0812345i
$576$	6.00107e8	+	4.09146e8i	0.130843	+	0.0892071i
$577$	−2.40566e9	+	6.12952e9i	−0.521338	+	1.32835i	0.391558	+	0.920154i	$0.371936\pi$
$577$	−2.40566e9	+	6.12952e9i	−0.521338	+	1.32835i	−0.912896	+	0.408193i	$0.866159\pi$
$578$	1.44210e9	+	4.44830e8i	0.310634	+	0.0958178i
$579$	−7.92078e8	−	7.34941e8i	−0.169587	−	0.157354i
$580$	−5.32709e7	−	6.67996e7i	−0.0113368	−	0.0142159i
$581$	4.17306e8	+	5.23285e8i	0.0882751	+	0.110693i
$582$	−5.61177e8	−	5.20696e8i	−0.117997	−	0.109485i
$583$	1.63982e9	+	5.05818e8i	0.342734	+	0.105719i
$584$	2.78942e8	−	7.10734e8i	0.0579522	−	0.147660i
$585$	2.20678e8	+	1.50456e8i	0.0455736	+	0.0310715i
$586$	2.61610e9	−	1.25985e9i	0.537047	−	0.258628i
$587$	−3.83789e9	+	3.56105e9i	−0.783177	+	0.726682i	−0.966583	−	0.256356i	$-0.917478\pi$
$587$	−3.83789e9	+	3.56105e9i	−0.783177	+	0.726682i	0.183406	+	0.983037i	$0.441288\pi$
$588$	−3.44129e9	−	5.18691e8i	−0.698073	−	0.105218i
$589$	7.30790e8	+	9.75171e9i	0.147363	+	1.96643i
$590$	1.10451e8	+	2.81425e8i	0.0221405	+	0.0564131i
$591$	−4.59684e8	+	2.01401e9i	−0.0916015	+	0.401333i
$592$	−1.75741e8	+	2.34509e9i	−0.0348134	+	0.464552i
$593$	−4.01872e8	+	1.23961e8i	−0.0791400	+	0.0244115i	−0.334072	−	0.942547i	$-0.608423\pi$
$593$	−4.01872e8	+	1.23961e8i	−0.0791400	+	0.0244115i	0.254932	+	0.966959i	$0.417947\pi$
$594$	−3.97484e8	−	1.91418e8i	−0.0778156	−	0.0374740i
$595$	1.06521e8	+	1.84499e8i	0.0207312	+	0.0359075i
$596$	3.27965e9	−	5.68053e9i	0.634551	−	1.09907i
$597$	−3.83019e9	+	2.61138e9i	−0.736734	+	0.502296i
$598$	6.47767e7	+	2.83805e8i	0.0123870	+	0.0542708i
$599$	9.64563e9	−	1.45384e9i	1.83374	−	0.276391i	0.861050	−	0.508520i	$-0.169807\pi$
$599$	9.64563e9	−	1.45384e9i	1.83374	−	0.276391i	0.972685	+	0.232129i	$0.0745690\pi$
$600$	1.54535e9	−	1.93781e9i	0.292077	−	0.366253i
$601$	−2.70574e9			−0.508424			−0.254212	−	0.967149i	$-0.581816\pi$
$601$	−2.70574e9			−0.508424			−0.254212	+	0.967149i	$0.581816\pi$
$602$	−7.42992e7	−	2.74587e8i	−0.0138802	−	0.0512970i
$603$	2.24068e9			0.416169
$604$	5.48568e8	−	6.87883e8i	0.101298	−	0.127024i
$605$	8.69202e8	−	1.31011e8i	0.159579	−	0.0240527i
$606$	1.86526e8	+	8.17224e8i	0.0340475	+	0.149172i
$607$	2.92523e9	−	1.99439e9i	0.530884	−	0.361951i	−0.268016	−	0.963415i	$-0.586368\pi$
$607$	2.92523e9	−	1.99439e9i	0.530884	−	0.361951i	0.798900	+	0.601464i	$0.205416\pi$
$608$	2.66141e9	−	4.60970e9i	0.480230	−	0.831782i
$609$	−4.44385e7	−	7.69697e7i	−0.00797258	−	0.0138089i
$610$	2.42642e8	+	1.16850e8i	0.0432825	+	0.0208437i
$611$	1.72538e9	−	5.32209e8i	0.306013	−	0.0943926i
$612$	−1.90127e8	+	2.53706e9i	−0.0335284	+	0.447406i
$613$	6.21695e8	−	2.72383e9i	0.109010	−	0.477604i	−0.890724	−	0.454544i	$-0.849802\pi$
$613$	6.21695e8	−	2.72383e9i	0.109010	−	0.477604i	0.999734	−	0.0230594i	$-0.00734069\pi$
$614$	8.84425e8	+	2.25348e9i	0.154196	+	0.392884i
$615$	3.06972e7	+	4.09625e8i	0.00532152	+	0.0710107i
$616$	−1.46036e8	−	2.20114e7i	−0.0251726	−	0.00379415i
$617$	−7.80307e9	+	7.24019e9i	−1.33742	+	1.24094i	−0.390053	+	0.920793i	$0.627543\pi$
$617$	−7.80307e9	+	7.24019e9i	−1.33742	+	1.24094i	−0.947366	+	0.320151i	$0.896266\pi$
$618$	−1.71746e8	+	8.27085e7i	−0.0292703	+	0.0140958i
$619$	3.93126e9	+	2.68029e9i	0.666216	+	0.454218i	0.848618	−	0.529006i	$-0.177435\pi$
$619$	3.93126e9	+	2.68029e9i	0.666216	+	0.454218i	−0.182403	+	0.983224i	$0.558387\pi$
$620$	5.68601e8	−	1.44877e9i	0.0958157	−	0.244134i
$621$	−1.19768e9	−	3.69437e8i	−0.200688	−	0.0619041i
$622$	−6.02454e8	−	5.58996e8i	−0.100382	−	0.0931413i
$623$	2.82373e8	+	3.54085e8i	0.0467860	+	0.0586677i
$624$	−1.99235e9	−	2.49833e9i	−0.328262	−	0.411627i
$625$	−4.07954e9	−	3.78526e9i	−0.668391	−	0.620177i
$626$	−2.69049e9	−	8.29907e8i	−0.438351	−	0.135213i
$627$	5.35047e8	−	1.36328e9i	0.0866873	−	0.220876i
$628$	−5.16522e9	−	3.52159e9i	−0.832204	−	0.567387i
$629$	−5.24231e9	+	2.52456e9i	−0.839935	+	0.404491i
$630$	1.47188e7	−	1.36571e7i	0.00234520	−	0.00217603i
$631$	7.11639e8	+	1.07262e8i	0.112760	+	0.0169959i	0.205180	−	0.978724i	$-0.434222\pi$
$631$	7.11639e8	+	1.07262e8i	0.112760	+	0.0169959i	−0.0924196	+	0.995720i	$0.529460\pi$
$632$	4.28253e7	+	5.71464e8i	0.00674824	+	0.0900490i
$633$	−7.33458e8	−	1.86882e9i	−0.114938	−	0.292856i
$634$	−1.76620e8	+	7.73824e8i	−0.0275251	+	0.120595i
$635$	−6.08014e6	+	8.11339e7i	−0.000942336	+	0.0125746i
$636$	6.41157e9	−	1.97771e9i	0.988244	−	0.304833i
$637$	−5.23173e9	−	2.51947e9i	−0.801968	−	0.386207i
$638$	3.04830e7	+	5.27981e7i	0.00464713	+	0.00804907i
$639$	9.67616e8	−	1.67596e9i	0.146707	−	0.254104i
$640$	−9.11746e8	+	6.21618e8i	−0.137481	+	0.0937333i
$641$	−2.22716e9	−	9.75783e9i	−0.334002	−	1.46336i	−0.811308	−	0.584620i	$-0.801244\pi$
$641$	−2.22716e9	−	9.75783e9i	−0.334002	−	1.46336i	0.477306	−	0.878737i	$-0.341613\pi$
$642$	5.67100e8	−	8.54765e7i	0.0845837	−	0.0127489i
$643$	7.23150e9	−	9.06801e9i	1.07273	−	1.34516i	0.137745	−	0.990468i	$-0.456015\pi$
$643$	7.23150e9	−	9.06801e9i	1.07273	−	1.34516i	0.934983	−	0.354691i	$-0.115414\pi$
$644$	−1.98844e8			−0.0293368
$645$	−8.69183e8	−	3.76680e8i	−0.127542	−	0.0552730i
$646$	3.59019e9			0.523966
$647$	−4.98692e9	+	6.25340e9i	−0.723881	+	0.907718i	−0.998551	−	0.0538207i	$-0.982860\pi$
$647$	−4.98692e9	+	6.25340e9i	−0.723881	+	0.907718i	0.274670	+	0.961539i	$0.411431\pi$
$648$	−2.16697e9	+	3.26619e8i	−0.312854	+	0.0471551i
$649$	4.36163e8	+	1.91095e9i	0.0626314	+	0.274406i
$650$	1.61936e9	−	1.10406e9i	0.231285	−	0.157688i
$651$	8.09483e8	−	1.40207e9i	0.114994	−	0.199175i
$652$	2.79884e9	+	4.84773e9i	0.395468	+	0.684971i
$653$	−1.01773e10	−	4.90114e9i	−1.43033	−	0.688812i	−0.451274	−	0.892386i	$-0.649030\pi$
$653$	−1.01773e10	−	4.90114e9i	−1.43033	−	0.688812i	−0.979060	+	0.203573i	$0.934744\pi$
$654$	−9.99415e8	+	3.08279e8i	−0.139709	+	0.0430945i
$655$	−9.57207e7	+	1.27730e9i	−0.0133095	+	0.177603i
$656$	−5.87175e8	+	2.57258e9i	−0.0812090	+	0.355800i
$657$	2.45879e8	+	6.26489e8i	0.0338253	+	0.0861856i
$658$	−1.01438e7	−	1.35360e8i	−0.00138807	−	0.0185225i
$659$	−1.21258e10	−	1.82767e9i	−1.65049	−	0.248771i	−0.743134	−	0.669143i	$-0.766662\pi$
$659$	−1.21258e10	−	1.82767e9i	−1.65049	−	0.248771i	−0.907352	+	0.420372i	$0.861900\pi$
$660$	−1.70860e8	+	1.58535e8i	−0.0231332	+	0.0214645i
$661$	5.05330e8	−	2.43354e8i	0.0680566	−	0.0327743i	−0.399546	−	0.916713i	$-0.630832\pi$
$661$	5.05330e8	−	2.43354e8i	0.0680566	−	0.0327743i	0.467602	+	0.883939i	$0.345118\pi$
$662$	−3.34893e9	−	2.28326e9i	−0.448645	−	0.305881i
$663$	2.88850e9	−	7.35977e9i	0.384923	−	0.980769i
$664$	−3.61950e9	−	1.11647e9i	−0.479800	−	0.147999i
$665$	1.88722e8	+	1.75108e8i	0.0248855	+	0.0230903i
$666$	3.41914e8	+	4.28746e8i	0.0448494	+	0.0562394i
$667$	1.07991e8	+	1.35416e8i	0.0140911	+	0.0176697i
$668$	−7.55095e9	−	7.00625e9i	−0.980130	−	0.909428i
$669$	−4.05437e9	−	1.25061e9i	−0.523518	−	0.161484i
$670$	−1.83849e8	+	4.68439e8i	−0.0236156	+	0.0601715i
$671$	1.44268e9	+	9.83600e8i	0.184349	+	0.125687i
$672$	−7.93948e8	+	3.82345e8i	−0.100925	+	0.0486030i
$673$	7.23514e8	−	6.71323e8i	0.0914944	−	0.0848944i	−0.633100	−	0.774070i	$-0.718218\pi$
$673$	7.23514e8	−	6.71323e8i	0.0914944	−	0.0848944i	0.724594	+	0.689176i	$0.242027\pi$
$674$	1.87493e9	+	2.82601e8i	0.235872	+	0.0355519i
$675$	6.30616e8	+	8.41498e9i	0.0789226	+	1.05315i
$676$	4.24404e8	+	1.08136e9i	0.0528404	+	0.134635i
$677$	−1.27426e9	+	5.58289e9i	−0.157833	+	0.691510i	0.832642	+	0.553812i	$0.186827\pi$
$677$	−1.27426e9	+	5.58289e9i	−0.157833	+	0.691510i	−0.990474	+	0.137698i	$0.956030\pi$
$678$	−1.98674e8	+	2.65112e9i	−0.0244815	+	0.326682i
$679$	8.33737e8	−	2.57174e8i	0.102208	−	0.0315270i
$680$	−1.08626e9	−	5.23115e8i	−0.132481	−	0.0637993i
$681$	4.83442e9	+	8.37346e9i	0.586583	+	1.01599i
$682$	−5.55272e8	+	9.61760e8i	−0.0670287	+	0.116097i
$683$	−1.52972e9	+	1.04295e9i	−0.183713	+	0.125253i	−0.651684	−	0.758490i	$-0.725937\pi$
$683$	−1.52972e9	+	1.04295e9i	−0.183713	+	0.125253i	0.467972	+	0.883744i	$0.344985\pi$
$684$	6.84135e8	+	2.99739e9i	0.0817420	+	0.358135i
$685$	2.05950e8	−	3.10419e7i	0.0244819	−	0.00369005i
$686$	−5.52331e8	+	6.92601e8i	−0.0653228	+	0.0819122i
$687$	−1.45890e9			−0.171663
$688$	−4.62220e9	−	3.95798e9i	−0.541114	−	0.463356i
$689$	1.11953e10			1.30397
$690$	4.54385e7	−	5.69781e7i	0.00526565	−	0.00660292i
$691$	1.32057e10	−	1.99044e9i	1.52261	−	0.229496i	0.666190	−	0.745782i	$-0.267924\pi$
$691$	1.32057e10	−	1.99044e9i	1.52261	−	0.229496i	0.856416	+	0.516286i	$0.172686\pi$
$692$	3.79895e8	+	1.66443e9i	0.0435805	+	0.190939i
$693$	1.07560e8	−	7.33330e7i	0.0122768	−	0.00837015i
$694$	1.68754e8	−	2.92291e8i	0.0191645	−	0.0331938i
$695$	−9.13238e8	−	1.58178e9i	−0.103190	−	0.178730i
$696$	4.53168e8	+	2.18234e8i	0.0509479	+	0.0245352i
$697$	−6.23874e9	+	1.92440e9i	−0.697882	+	0.215268i
$698$	2.55249e8	−	3.40606e9i	0.0284099	−	0.379104i
$699$	−1.13246e9	+	4.96161e9i	−0.125415	+	0.549481i
$700$	4.89105e8	+	1.24622e9i	0.0538963	+	0.137325i
$701$	−9.62914e8	−	1.28492e10i	−0.105578	−	1.40884i	−0.758626	−	0.651527i	$-0.774129\pi$
$701$	−9.62914e8	−	1.28492e10i	−0.105578	−	1.40884i	0.653047	−	0.757317i	$-0.273490\pi$
$702$	−2.84600e9	−	4.28965e8i	−0.310495	−	0.0467996i
$703$	−5.15432e9	+	4.78251e9i	−0.559535	+	0.519173i
$704$	−9.52842e8	+	4.58864e8i	−0.102924	+	0.0495656i
$705$	−3.73485e8	−	2.54638e8i	−0.0401431	−	0.0273691i
$706$	1.03119e9	−	2.62743e9i	0.110286	−	0.281005i
$707$	−9.12919e8	−	2.81598e8i	−0.0971548	−	0.0299683i
$708$	5.61798e9	+	5.21272e9i	0.594927	+	0.552011i
$709$	−3.09478e9	−	3.88073e9i	−0.326113	−	0.408933i	0.591565	−	0.806257i	$-0.298510\pi$
$709$	−3.09478e9	−	3.88073e9i	−0.326113	−	0.408933i	−0.917678	+	0.397324i	$0.869939\pi$
$710$	2.70984e8	+	3.39804e8i	0.0284145	+	0.0356306i
$711$	−3.70293e8	−	3.43582e8i	−0.0386369	−	0.0358498i
$712$	−2.44916e9	−	7.55467e8i	−0.254295	−	0.0784397i
$713$	−1.15267e9	+	2.93694e9i	−0.119094	+	0.303447i
$714$	−4.91093e8	−	3.34821e8i	−0.0504917	−	0.0344246i
$715$	−3.50390e8	+	1.68739e8i	−0.0358492	+	0.0172641i
$716$	3.85921e8	−	3.58083e8i	0.0392919	−	0.0364576i
$717$	6.73213e8	+	1.01470e8i	0.0682080	+	0.0102807i
$718$	2.94197e8	+	3.92578e9i	0.0296621	+	0.395814i
$719$	1.65771e9	+	4.22379e9i	0.166325	+	0.423790i	0.989599	−	0.143855i	$-0.0459498\pi$
$719$	1.65771e9	+	4.22379e9i	0.166325	+	0.423790i	−0.823273	+	0.567645i	$0.807855\pi$
$720$	9.55794e7	−	4.18761e8i	0.00954334	−	0.0418121i
$721$	1.62358e7	−	2.16651e8i	0.00161324	−	0.0215272i
$722$	1.10290e9	−	3.40201e8i	0.109058	−	0.0336399i
$723$	9.99395e9	+	4.81283e9i	0.983452	+	0.473606i
$724$	8.11186e9	+	1.40502e10i	0.794393	+	1.37593i
$725$	5.83065e8	−	1.00990e9i	0.0568243	−	0.0984226i
$726$	−2.02628e9	+	1.38149e9i	−0.196526	+	0.133989i
$727$	−4.92532e8	−	2.15792e9i	−0.0475406	−	0.208289i	0.945579	−	0.325392i	$-0.105496\pi$
$727$	−4.92532e8	−	2.15792e9i	−0.0475406	−	0.208289i	−0.993120	+	0.117103i	$0.962639\pi$
$728$	−9.52715e8	+	1.43599e8i	−0.0915173	+	0.0137940i
$729$	6.93035e9	−	8.69039e9i	0.662535	−	0.830793i
$730$	−1.51149e8			−0.0143805
$731$	2.76274e9	−	1.48006e10i	0.261595	−	1.40142i
$732$	6.82701e9			0.643342
$733$	4.91720e9	−	6.16597e9i	0.461162	−	0.578279i	−0.495820	−	0.868425i	$-0.665132\pi$
$733$	4.91720e9	−	6.16597e9i	0.461162	−	0.578279i	0.956982	+	0.290146i	$0.0937039\pi$
$734$	−9.98547e8	+	1.50507e8i	−0.0932035	+	0.0140482i
$735$	3.23484e8	+	1.41728e9i	0.0300502	+	0.131658i
$736$	1.41891e9	−	9.67397e8i	0.131185	−	0.0894401i
$737$	−1.63132e9	+	2.82552e9i	−0.150107	+	0.259994i
$738$	3.07664e8	+	5.32890e8i	0.0281760	+	0.0488023i
$739$	4.87743e9	+	2.34885e9i	0.444565	+	0.214091i	0.642754	−	0.766072i	$-0.277792\pi$
$739$	4.87743e9	+	2.34885e9i	0.444565	+	0.214091i	−0.198189	+	0.980164i	$0.563506\pi$
$740$	1.06933e9	−	3.29845e8i	0.0970066	−	0.0299226i
$741$	7.13990e8	−	9.52753e9i	0.0644656	−	0.860234i
$742$	1.87280e8	−	8.20528e8i	0.0168298	−	0.0737360i
$743$	1.58861e9	+	4.04771e9i	0.142088	+	0.362033i	0.984148	−	0.177350i	$-0.0567526\pi$
$743$	1.58861e9	+	4.04771e9i	0.142088	+	0.362033i	−0.842060	+	0.539384i	$0.818657\pi$
$744$	6.84689e8	+	9.13654e9i	0.0609520	+	0.813348i
$745$	−2.70933e9	−	4.08366e8i	−0.240058	−	0.0361829i
$746$	−3.17028e9	+	2.94159e9i	−0.279583	+	0.259415i
$747$	3.00816e9	−	1.44865e9i	0.264046	−	0.127158i
$748$	−3.06085e9	−	2.08685e9i	−0.267415	−	0.182320i
$749$	−2.38801e8	+	6.08455e8i	−0.0207659	+	0.0529105i
$750$	−9.52083e8	−	2.93679e8i	−0.0824063	−	0.0254190i
$751$	−1.58518e10	−	1.47083e10i	−1.36565	−	1.26714i	−0.930264	−	0.366890i	$-0.880422\pi$
$751$	−1.58518e10	−	1.47083e10i	−1.36565	−	1.26714i	−0.435383	−	0.900245i	$-0.643387\pi$
$752$	−1.81047e9	−	2.27025e9i	−0.155249	−	0.194676i
$753$	1.07155e10	+	1.34368e10i	0.914595	+	1.14687i
$754$	2.91558e8	+	2.70526e8i	0.0247700	+	0.0229832i
$755$	−3.51194e8	−	1.08329e8i	−0.0296984	−	0.00916075i
$756$	7.18250e8	−	1.83007e9i	0.0604574	−	0.154043i
$757$	4.02498e9	+	2.74418e9i	0.337231	+	0.229920i	0.720081	−	0.693890i	$-0.244105\pi$
$757$	4.02498e9	+	2.74418e9i	0.337231	+	0.229920i	−0.382849	+	0.923811i	$0.625057\pi$
$758$	−4.40391e9	+	2.12081e9i	−0.367279	+	0.176872i
$759$	3.46367e8	−	3.21381e8i	0.0287534	−	0.0266793i
$760$	−1.44068e9	−	2.17148e8i	−0.119048	−	0.0179436i
$761$	5.86653e8	+	7.82834e9i	0.0482542	+	0.643908i	0.967929	+	0.251226i	$0.0808336\pi$
$761$	5.86653e8	+	7.82834e9i	0.0482542	+	0.643908i	−0.919674	+	0.392682i	$0.871547\pi$
$762$	−8.29299e7	−	2.11302e8i	−0.00678998	−	0.0173006i
$763$	2.65249e8	−	1.16213e9i	0.0216181	−	0.0947150i
$764$	1.32727e9	−	1.77112e10i	0.107680	−	1.43689i
$765$	1.01553e9	−	3.13250e8i	0.0820123	−	0.0252974i
$766$	4.10407e9	+	1.97641e9i	0.329924	+	0.158883i
$767$	6.39368e9	+	1.10742e10i	0.511643	+	0.886192i
$768$	−7.55727e8	+	1.30896e9i	−0.0602005	+	0.104270i
$769$	−1.46897e10	+	1.00153e10i	−1.16485	+	0.794184i	−0.981986	−	0.188953i	$-0.939491\pi$
$769$	−1.46897e10	+	1.00153e10i	−1.16485	+	0.794184i	−0.182868	+	0.983137i	$0.558538\pi$
$770$	6.50574e6	+	2.85035e7i	0.000513546	+	0.00224999i
$771$	1.98882e10	−	2.99766e9i	1.56280	−	0.235555i
$772$	−2.05934e9	+	2.58233e9i	−0.161090	+	0.202000i
$773$	−2.44543e10			−1.90426			−0.952130	−	0.305693i	$-0.901112\pi$
$773$	−2.44543e10			−1.90426			−0.952130	+	0.305693i	$0.901112\pi$
$774$	−1.41790e9	+	5.65449e7i	−0.109913	+	0.00438329i
$775$	2.12420e10			1.63923
$776$	−3.07861e9	+	3.86045e9i	−0.236504	+	0.296567i
$777$	1.15106e9	−	1.73495e8i	0.0880290	−	0.0132682i
$778$	8.95514e8	+	3.92350e9i	0.0681780	+	0.298707i
$779$	−6.51871e9	+	4.44438e9i	−0.494061	+	0.336845i
$780$	−7.60289e8	+	1.31686e9i	−0.0573651	+	0.0993593i
$781$	1.40894e9	+	2.44035e9i	0.105831	+	0.183305i
$782$	1.04360e9	+	5.02572e8i	0.0780389	+	0.0375816i
$783$	−1.63638e9	+	5.04757e8i	−0.121820	+	0.0375765i
$784$	−6.97864e8	+	9.31235e9i	−0.0517208	+	0.690166i
$785$	−5.81081e8	+	2.54588e9i	−0.0428739	+	0.187843i
$786$	−1.30558e9	−	3.32656e9i	−0.0959012	−	0.244352i
$787$	−1.26227e8	−	1.68439e9i	−0.00923085	−	0.123177i	0.990685	−	0.136176i	$-0.0434813\pi$
$787$	−1.26227e8	−	1.68439e9i	−0.00923085	−	0.123177i	−0.999916	+	0.0129988i	$0.995862\pi$
$788$	6.24419e9	+	9.41160e8i	0.454605	+	0.0685207i
$789$	1.26643e10	−	1.17508e10i	0.917937	−	0.851721i
$790$	1.02212e8	−	4.92228e7i	0.00737578	−	0.00355199i
$791$	−2.50352e9	−	1.70687e9i	−0.179860	−	0.122626i
$792$	−2.69155e8	+	6.85796e8i	−0.0192515	+	0.0490520i
$793$	1.08850e10	+	3.35759e9i	0.775129	+	0.239096i
$794$	−3.27137e9	−	3.03539e9i	−0.231931	−	0.215200i
$795$	−1.74748e9	−	2.19127e9i	−0.123347	−	0.154672i
$796$	8.83507e9	+	1.10788e10i	0.620890	+	0.778571i
$797$	−7.85786e9	−	7.29103e9i	−0.549794	−	0.510134i	0.355639	−	0.934623i	$-0.384263\pi$
$797$	−7.85786e9	−	7.29103e9i	−0.549794	−	0.510134i	−0.905433	+	0.424489i	$0.860454\pi$
$798$	−6.86349e8	−	2.11711e8i	−0.0478118	−	0.0147480i
$799$	2.62480e9	−	6.68788e9i	0.182047	−	0.463847i
$800$	−9.55313e9	−	6.51322e9i	−0.659676	−	0.449760i
$801$	2.03550e9	−	9.80244e8i	0.139945	−	0.0673938i
$802$	5.48566e9	−	5.08995e9i	0.375507	−	0.348420i
$803$	−9.69020e8	−	1.46056e8i	−0.0660432	−	0.00995441i
$804$	9.53304e8	+	1.27210e10i	0.0646897	+	0.863224i
$805$	3.03454e7	+	7.73189e7i	0.00205025	+	0.00522396i
$806$	−1.61217e9	+	7.06337e9i	−0.108452	+	0.475159i
$807$	1.96524e8	−	2.62243e9i	0.0131631	−	0.175649i
$808$	5.16645e9	−	1.59364e9i	0.344550	−	0.106280i
$809$	1.32582e10	+	6.38481e9i	0.880368	+	0.423963i	0.818759	−	0.574137i	$-0.194662\pi$
$809$	1.32582e10	+	6.38481e9i	0.880368	+	0.423963i	0.0616092	+	0.998100i	$0.480377\pi$
$810$	2.16915e8	+	3.75708e8i	0.0143414	+	0.0248401i
$811$	2.53392e9	−	4.38888e9i	0.166809	−	0.288922i	−0.770487	−	0.637456i	$-0.779987\pi$
$811$	2.53392e9	−	4.38888e9i	0.166809	−	0.288922i	0.937296	+	0.348533i	$0.113320\pi$
$812$	−2.24471e8	+	1.53042e8i	−0.0147134	+	0.0100315i
$813$	−1.41888e9	−	6.21650e9i	−0.0926036	−	0.405723i
$814$	−7.89582e8	+	1.19010e8i	−0.0513112	+	0.00773391i
$815$	1.45787e9	−	1.82811e9i	0.0943339	−	0.118291i
$816$	−1.27149e10			−0.819215
$817$	−2.08157e9	−	1.80750e10i	−0.133541	−	1.15958i
$818$	2.25456e9			0.144021
$819$	5.29513e8	−	6.63989e8i	0.0336809	−	0.0422345i
$820$	1.24163e9	−	1.87145e8i	0.0786398	−	0.0118530i
$821$	4.89917e9	+	2.14647e10i	0.308974	+	1.35370i	0.856168	+	0.516697i	$0.172839\pi$
$821$	4.89917e9	+	2.14647e10i	0.308974	+	1.35370i	−0.547194	+	0.837006i	$0.684304\pi$
$822$	−4.80108e8	+	3.27332e8i	−0.0301500	+	0.0205559i
$823$	4.63369e9	−	8.02579e9i	0.289753	−	0.501867i	−0.683998	−	0.729484i	$-0.739760\pi$
$823$	4.63369e9	−	8.02579e9i	0.289753	−	0.501867i	0.973751	+	0.227617i	$0.0730935\pi$
$824$	6.14762e8	+	1.06480e9i	0.0382791	+	0.0663014i
$825$	−2.86617e9	−	1.38027e9i	−0.177710	−	0.0855808i
$826$	9.18606e8	−	2.83352e8i	0.0567152	−	0.0174943i
$827$	−8.22081e8	+	1.09699e10i	−0.0505412	+	0.674425i	0.913187	+	0.407540i	$0.133613\pi$
$827$	−8.22081e8	+	1.09699e10i	−0.0505412	+	0.674425i	−0.963728	+	0.266885i	$0.914006\pi$
$828$	−2.20724e8	+	9.67055e8i	−0.0135127	+	0.0592032i
$829$	−6.63130e9	−	1.68963e10i	−0.404257	−	1.03003i	−0.977554	−	0.210683i	$-0.932431\pi$
$829$	−6.63130e9	−	1.68963e10i	−0.404257	−	1.03003i	0.573297	−	0.819348i	$-0.305664\pi$
$830$	5.60362e7	+	7.47751e8i	0.00340170	+	0.0453925i
$831$	−7.65305e9	−	1.15351e9i	−0.462627	−	0.0697298i
$832$	−5.05765e9	+	4.69282e9i	−0.304451	+	0.282489i
$833$	−2.08172e10	+	1.00250e10i	−1.24786	+	0.600936i
$834$	4.21031e9	+	2.87054e9i	0.251323	+	0.171349i
$835$	−1.57198e9	+	4.00534e9i	−0.0934426	+	0.238088i
$836$	−4.27782e9	−	1.31953e9i	−0.253222	−	0.0781085i
$837$	−2.28667e10	−	2.12172e10i	−1.34792	−	1.25069i
$838$	−2.93895e9	−	3.68533e9i	−0.172519	−	0.216333i
$839$	−6.05920e9	−	7.59800e9i	−0.354200	−	0.444153i	0.572528	−	0.819885i	$-0.305963\pi$
$839$	−6.05920e9	−	7.59800e9i	−0.354200	−	0.444153i	−0.926728	+	0.375732i	$0.877391\pi$
$840$	1.76816e8	+	1.64062e8i	0.0102931	+	0.00955057i
$841$	−1.62574e10	−	5.01474e9i	−0.942464	−	0.290712i
$842$	3.09619e9	−	7.88897e9i	0.178746	−	0.455436i
$843$	−1.82507e10	−	1.24431e10i	−1.04926	−	0.715372i
$844$	−5.52907e9	+	2.66266e9i	−0.316558	+	0.152446i
$845$	3.55712e8	−	3.30052e8i	0.0202815	−	0.0188185i
$846$	−6.69567e8	−	1.00921e8i	−0.0380187	−	0.00573040i
$847$	−2.08876e8	−	2.78726e9i	−0.0118113	−	0.157610i
$848$	−6.57771e9	−	1.67597e10i	−0.370416	−	0.943804i
$849$	−2.17018e9	+	9.50816e9i	−0.121708	+	0.533236i
$850$	5.82789e8	−	7.77678e9i	0.0325495	−	0.434344i
$851$	−2.16774e9	+	6.68661e8i	−0.120574	+	0.0371922i
$852$	9.92656e9	+	4.78038e9i	0.549870	+	0.264803i
$853$	1.59692e10	+	2.76594e10i	0.880970	+	1.52589i	0.850264	+	0.526357i	$0.176442\pi$
$853$	1.59692e10	+	2.76594e10i	0.880970	+	1.52589i	0.0307064	+	0.999528i	$0.490224\pi$
$854$	4.28175e8	−	7.41620e8i	0.0235244	−	0.0407454i
$855$	1.06111e9	−	7.23450e8i	0.0580601	−	0.0395847i
$856$	−8.23130e8	−	3.60637e9i	−0.0448549	−	0.196522i
$857$	−9.32895e9	+	1.40611e9i	−0.506291	+	0.0763111i	−0.397221	−	0.917723i	$-0.630025\pi$
$857$	−9.32895e9	+	1.40611e9i	−0.506291	+	0.0763111i	−0.109070	+	0.994034i	$0.534787\pi$
$858$	6.76495e8	−	8.48298e8i	0.0365645	−	0.0458504i
$859$	−1.89430e10			−1.01970			−0.509851	−	0.860263i	$-0.670299\pi$
$859$	−1.89430e10			−1.01970			−0.509851	+	0.860263i	$0.670299\pi$
$860$	−9.49661e8	+	2.73553e9i	−0.0509124	+	0.146655i
$861$	1.30616e9			0.0697407
$862$	−9.06089e8	+	1.13620e9i	−0.0481832	+	0.0604198i
$863$	3.04330e10	−	4.58704e9i	1.61178	−	0.242937i	0.719527	−	0.694464i	$-0.244359\pi$
$863$	3.04330e10	−	4.58704e9i	1.61178	−	0.242937i	0.892257	+	0.451527i	$0.149121\pi$
$864$	3.77820e9	+	1.65534e10i	0.199291	+	0.873149i
$865$	5.89225e8	−	4.01727e8i	0.0309546	−	0.0211045i
$866$	3.77592e9	−	6.54009e9i	0.197565	−	0.342193i
$867$	−7.99022e9	−	1.38395e10i	−0.416382	−	0.721195i
$868$	−4.45875e9	−	2.14722e9i	−0.231417	−	0.111444i
$869$	7.02851e8	−	2.16801e8i	0.0363324	−	0.0112071i
$870$	7.44102e6	−	9.92936e7i	0.000383103	−	0.00511215i
$871$	−4.73634e9	+	2.07512e10i	−0.242873	+	1.06410i
$872$	2.46457e9	+	6.27961e9i	0.125873	+	0.320719i
$873$	−3.25257e8	−	4.34026e9i	−0.0165454	−	0.220783i
$874$	1.38411e9	+	2.08621e8i	0.0701262	+	0.0105698i
$875$	8.32426e8	−	7.72379e8i	0.0420066	−	0.0389764i
$876$	−3.45214e9	+	1.66246e9i	−0.173510	+	0.0835578i
$877$	−1.01823e10	−	6.94219e9i	−0.509739	−	0.347534i	0.280980	−	0.959714i	$-0.409341\pi$
$877$	−1.01823e10	−	6.94219e9i	−0.509739	−	0.347534i	−0.790719	+	0.612179i	$0.790293\pi$
$878$	−1.64279e9	+	4.18576e9i	−0.0819127	+	0.208710i
$879$	−2.93808e10	−	9.06279e9i	−1.45916	−	0.450092i
$880$	4.58476e8	+	4.25403e8i	0.0226792	+	0.0210432i
$881$	9.85359e9	+	1.23560e10i	0.485488	+	0.608783i	0.962887	−	0.269904i	$-0.0869919\pi$
$881$	9.85359e9	+	1.23560e10i	0.485488	+	0.608783i	−0.477399	+	0.878687i	$0.658420\pi$
$882$	1.35774e9	+	1.70255e9i	0.0666309	+	0.0835525i
$883$	−9.00179e9	−	8.35244e9i	−0.440014	−	0.408273i	0.428810	−	0.903395i	$-0.358933\pi$
$883$	−9.00179e9	−	8.35244e9i	−0.440014	−	0.408273i	−0.868824	+	0.495122i	$0.835124\pi$
$884$	−2.30942e10	−	7.12362e9i	−1.12440	−	0.346831i
$885$	1.16957e9	−	2.98001e9i	0.0567185	−	0.144516i
$886$	−4.95563e8	−	3.37869e8i	−0.0239376	−	0.0163204i
$887$	3.23832e10	−	1.55949e10i	1.55807	−	0.750326i	0.561072	−	0.827767i	$-0.310389\pi$
$887$	3.23832e10	−	1.55949e10i	1.55807	−	0.750326i	0.996997	+	0.0774407i	$0.0246748\pi$
$888$	−4.82916e9	+	4.48081e9i	−0.231434	+	0.214739i
$889$	2.55820e8	+	3.85587e7i	0.0122118	+	0.00184063i
$890$	3.79173e7	+	5.05972e8i	0.00180290	+	0.0240581i
$891$	1.02760e9	+	2.61829e9i	0.0486691	+	0.124007i
$892$	−2.88600e9	+	1.26444e10i	−0.136150	+	0.596514i
$893$	6.48808e8	−	8.65775e9i	0.0304885	−	0.406841i
$894$	7.30463e9	−	2.25318e9i	0.341914	−	0.105467i
$895$	−1.98133e8	−	9.54157e7i	−0.00923795	−	0.00444876i
$896$	1.75442e9	+	3.03874e9i	0.0814807	+	0.141129i
$897$	1.54126e9	−	2.66953e9i	0.0713019	−	0.123498i
$898$	−1.29728e9	+	8.84471e8i	−0.0597815	+	0.0407583i
$899$	9.59220e8	+	4.20262e9i	0.0440311	+	0.192913i
$900$	6.60376e9	−	9.95357e8i	0.301955	−	0.0455125i
$901$	2.77742e10	−	3.48278e10i	1.26504	−	1.58631i
$902$	−8.95974e8			−0.0406511
$903$	−1.40094e9	+	2.66656e9i	−0.0633159	+	0.120516i
$904$	1.71477e10			0.771998
$905$	4.22535e9	−	5.29842e9i	0.189493	−	0.237616i
$906$	1.01391e9	−	1.52823e8i	0.0452951	−	0.00682714i
$907$	7.61407e9	+	3.33594e10i	0.338837	+	1.48454i	0.801492	+	0.598005i	$0.204040\pi$
$907$	7.61407e9	+	3.33594e10i	0.338837	+	1.48454i	−0.462655	+	0.886539i	$0.653103\pi$
$908$	2.44200e10	−	1.66493e10i	1.08254	−	0.738066i
$909$	−2.38290e9	+	4.12730e9i	−0.105228	+	0.182260i
$910$	9.53672e7	+	1.65181e8i	0.00419522	+	0.00726633i
$911$	1.52508e10	+	7.34438e9i	0.668309	+	0.321841i	0.737093	−	0.675791i	$-0.236198\pi$
$911$	1.52508e10	+	7.34438e9i	0.668309	+	0.321841i	−0.0687842	+	0.997632i	$0.521912\pi$
$912$	−1.46825e10	+	4.52896e9i	−0.640942	+	0.197704i
$913$	−3.63308e8	+	4.84801e9i	−0.0157989	+	0.210822i
$914$	−9.95865e8	+	4.36317e9i	−0.0431408	+	0.189012i
$915$	−1.04186e9	−	2.65463e9i	−0.0449612	−	0.114559i
$916$	3.33263e8	+	4.44708e9i	0.0143269	+	0.191179i
$917$	4.02742e9	+	6.07036e8i	0.172478	+	0.0259969i
$918$	−8.39507e9	+	7.78948e9i	−0.358158	+	0.332322i
$919$	7.34265e9	−	3.53603e9i	0.312067	−	0.150284i	−0.271294	−	0.962497i	$-0.587452\pi$
$919$	7.34265e9	−	3.53603e9i	0.312067	−	0.150284i	0.583361	+	0.812213i	$0.301737\pi$
$920$	−3.88383e8	−	2.64795e8i	−0.0164438	−	0.0112112i
$921$	9.36521e9	−	2.38622e10i	0.395011	−	1.00647i
$922$	−1.96412e9	−	6.05851e8i	−0.0825296	−	0.0254570i
$923$	1.34759e10	+	1.25039e10i	0.564096	+	0.523405i
$924$	4.62093e8	+	5.79446e8i	0.0192698	+	0.0241636i
$925$	9.52279e9	+	1.19412e10i	0.395611	+	0.496080i
$926$	−9.17234e8	−	8.51069e8i	−0.0379613	−	0.0352230i
$927$	−1.03564e9	−	3.19452e8i	−0.0427000	−	0.0131712i
$928$	8.57216e8	−	2.18415e9i	0.0352105	−	0.0897150i
$929$	−1.32930e10	−	9.06301e9i	−0.543961	−	0.370866i	0.259944	−	0.965624i	$-0.416296\pi$
$929$	−1.32930e10	−	9.06301e9i	−0.543961	−	0.370866i	−0.803905	+	0.594757i	$0.797248\pi$
$930$	1.63416e9	−	7.86972e8i	0.0666201	−	0.0320825i
$931$	−2.04677e10	+	1.89913e10i	−0.831278	+	0.771313i
$932$	1.53829e10	+	2.31860e9i	0.622418	+	0.0938145i
$933$	6.50341e8	+	8.67820e9i	0.0262154	+	0.349820i
$934$	−1.89937e9	−	4.83951e9i	−0.0762772	−	0.194351i
$935$	−3.44341e8	+	1.50866e9i	−0.0137768	+	0.0603601i
$936$	−3.59172e8	+	4.79282e9i	−0.0143165	+	0.191041i
$937$	3.38810e10	−	1.04509e10i	1.34545	−	0.415016i	0.463390	−	0.886155i	$-0.346633\pi$
$937$	3.38810e10	−	1.04509e10i	1.34545	−	0.415016i	0.882059	+	0.471138i	$0.156157\pi$
$938$	1.44167e9	+	6.94272e8i	0.0570369	+	0.0274675i
$939$	1.49071e10	+	2.58199e10i	0.587577	+	1.01771i
$940$	−6.90881e8	+	1.19664e9i	−0.0271304	+	0.0469912i
$941$	−3.40127e10	+	2.31895e10i	−1.33069	+	0.907251i	−0.999342	−	0.0362574i	$-0.988456\pi$
$941$	−3.40127e10	+	2.31895e10i	−1.33069	+	0.907251i	−0.331350	+	0.943508i	$0.607504\pi$
$942$	−1.62118e9	−	7.10284e9i	−0.0631906	−	0.276856i
$943$	−2.51702e9	+	3.79379e8i	−0.0977452	+	0.0147327i
$944$	1.28219e10	−	1.60781e10i	0.496077	−	0.622060i
$945$	−8.21220e8			−0.0316554
$946$	9.60988e8	−	1.82915e9i	0.0369062	−	0.0702474i
$947$	2.81651e10			1.07767			0.538836	−	0.842411i	$-0.318864\pi$
$947$	2.81651e10			1.07767			0.538836	+	0.842411i	$0.318864\pi$
$948$	1.79307e9	−	2.24843e9i	0.0683545	−	0.0857138i
$949$	−6.32173e9	+	9.52847e8i	−0.240107	+	0.0361903i
$950$	−2.09706e9	−	9.18780e9i	−0.0793555	−	0.347679i
$951$	6.94435e9	−	4.73458e9i	0.261818	−	0.178505i
$952$	−1.91685e9	+	3.32008e9i	−0.0720043	+	0.124715i
$953$	1.52055e10	+	2.63366e10i	0.569081	+	0.985678i	0.996657	+	0.0816981i	$0.0260343\pi$
$953$	1.52055e10	+	2.63366e10i	0.569081	+	0.985678i	−0.427576	+	0.903979i	$0.640632\pi$
$954$	−3.78266e9	−	1.82163e9i	−0.141051	−	0.0679268i
$955$	−7.08943e9	+	2.18680e9i	−0.263390	+	0.0812451i
$956$	1.55522e8	−	2.07530e9i	0.00575690	−	0.0768205i
$957$	1.43653e8	−	6.29385e8i	0.00529813	−	0.0232126i
$958$	−1.18736e9	−	3.02535e9i	−0.0436319	−	0.111172i
$959$	−4.94913e7	−	6.60416e8i	−0.00181202	−	0.0241798i
$960$	1.70798e9	+	2.57437e8i	0.0623065	+	0.00939120i
$961$	−3.73931e10	+	3.46958e10i	−1.35913	+	1.26109i
$962$	−4.69341e9	+	2.26023e9i	−0.169971	+	0.0818538i
$963$	2.69407e9	+	1.83679e9i	0.0972115	+	0.0662777i
$964$	1.23877e10	−	3.15634e10i	0.445371	−	1.13479i
$965$	1.31839e9	+	4.06670e8i	0.0472280	+	0.0145679i
$966$	−1.69873e8	−	1.57619e8i	−0.00606323	−	0.00562585i
$967$	2.94877e10	+	3.69764e10i	1.04869	+	1.31502i	0.947362	+	0.320165i	$0.103738\pi$
$967$	2.94877e10	+	3.69764e10i	1.04869	+	1.31502i	0.101330	+	0.994853i	$0.467690\pi$
$968$	9.86239e9	+	1.23671e10i	0.349477	+	0.438230i
$969$	−2.78681e10	−	2.58579e10i	−0.983954	−	0.912976i
$970$	9.34065e8	+	2.88121e8i	0.0328606	+	0.0101362i
$971$	1.23420e10	−	3.14468e10i	0.432630	−	1.10232i	−0.533849	−	0.845580i	$-0.679255\pi$
$971$	1.23420e10	−	3.14468e10i	0.432630	−	1.10232i	0.966479	−	0.256744i	$-0.0826497\pi$
$972$	−1.41082e10	−	9.61882e9i	−0.492766	−	0.335962i
$973$	−5.23261e9	+	2.51989e9i	−0.182106	+	0.0876974i
$974$	−6.45345e9	+	5.98792e9i	−0.223787	+	0.207644i
$975$	−2.05219e10	−	3.09318e9i	−0.709090	−	0.106878i
$976$	−1.36900e9	−	1.82680e10i	−0.0471333	−	0.628950i
$977$	1.60526e10	+	4.09014e10i	0.550699	+	1.40316i	0.887160	+	0.461461i	$0.152675\pi$
$977$	1.60526e10	+	4.09014e10i	0.550699	+	1.40316i	−0.336461	+	0.941697i	$0.609230\pi$
$978$	−1.45163e9	+	6.36000e9i	−0.0496214	+	0.217406i
$979$	−2.45835e8	+	3.28044e9i	−0.00837346	+	0.111736i
$980$	4.24631e9	−	1.30981e9i	0.144119	−	0.0444547i
$981$	−5.35745e9	−	2.58001e9i	−0.181183	−	0.0872530i
$982$	−7.60101e9	−	1.31653e10i	−0.256142	−	0.443651i
$983$	−7.37876e9	+	1.27804e10i	−0.247769	+	0.429148i	−0.962906	−	0.269836i	$-0.913031\pi$
$983$	−7.37876e9	+	1.27804e10i	−0.247769	+	0.429148i	0.715138	+	0.698983i	$0.246364\pi$
$984$	−6.10749e9	+	4.16402e9i	−0.204352	+	0.139325i
$985$	−5.86958e8	−	2.57163e9i	−0.0195695	−	0.0857397i
$986$	1.56491e9	−	2.35872e8i	0.0519900	−	0.00783624i
$987$	−8.96172e8	+	1.12376e9i	−0.0296675	+	0.0372019i
$988$	−2.92053e10			−0.963414
$989$	1.92515e9	−	5.54545e9i	0.0632816	−	0.182285i
$990$	1.45845e8			0.00477715
$991$	−1.45429e10	+	1.82363e10i	−0.474673	+	0.595221i	−0.960308	−	0.278940i	$-0.910017\pi$
$991$	−1.45429e10	+	1.82363e10i	−0.474673	+	0.595221i	0.485635	+	0.874161i	$0.338588\pi$
$992$	4.22632e10	−	6.37016e9i	1.37459	−	0.207185i
$993$	9.55054e9	+	4.18436e10i	0.309532	+	1.35615i
$994$	1.14186e9	−	7.78510e8i	0.0368776	−	0.0251427i
$995$	2.95960e9	−	5.12618e9i	0.0952472	−	0.164973i
$996$	9.50424e9	+	1.64618e10i	0.304796	+	0.527923i
$997$	−3.89706e10	−	1.87673e10i	−1.24539	−	0.599746i	−0.309115	−	0.951025i	$-0.600033\pi$
$997$	−3.89706e10	−	1.87673e10i	−1.24539	−	0.599746i	−0.936271	+	0.351278i	$0.885747\pi$
$998$	−7.44221e9	+	2.29562e9i	−0.236998	+	0.0731043i
$999$	1.67612e9	−	2.23662e10i	0.0531894	−	0.709763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.24.14	yes	300
43.9	even	21	inner	43.8.g.a.9.14	✓	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.14	✓	300	43.9	even	21	inner
43.8.g.a.24.14	yes	300	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.22112 - 2.78519i) q^{2} +(-37.3010 + 5.62222i) q^{3} +(25.6587 + 112.418i) q^{4} +(39.7972 - 27.1333i) q^{5} +(-67.1910 + 116.378i) q^{6} +(-76.5793 - 132.639i) q^{7} +(780.928 + 376.075i) q^{8} +(-730.081 + 225.200i) q^{9} +O(q^{10})\)	\(q+(2.22112 - 2.78519i) q^{2} +(-37.3010 + 5.62222i) q^{3} +(25.6587 + 112.418i) q^{4} +(39.7972 - 27.1333i) q^{5} +(-67.1910 + 116.378i) q^{6} +(-76.5793 - 132.639i) q^{7} +(780.928 + 376.075i) q^{8} +(-730.081 + 225.200i) q^{9} +(12.8229 - 171.109i) q^{10} +(247.552 - 1084.60i) q^{11} +(-1589.14 - 4049.06i) q^{12} +(-542.368 - 7237.40i) q^{13} +(-539.517 - 81.3192i) q^{14} +(-1331.93 + 1235.85i) q^{15} +(-10516.0 + 5064.22i) q^{16} +(-23860.6 - 16267.9i) q^{17} +(-994.370 + 2533.61i) q^{18} +(-33347.5 - 10286.3i) q^{19} +(4071.42 + 3777.73i) q^{20} +(3602.21 + 4517.03i) q^{21} +(-2470.97 - 3098.50i) q^{22} +(-8253.57 - 7658.19i) q^{23} +(-31243.8 - 9637.43i) q^{24} +(-27694.7 + 70564.9i) q^{25} +(-21362.2 - 14564.5i) q^{26} +(100295. - 48299.8i) q^{27} +(12946.1 - 12012.3i) q^{28} +(-15211.5 - 2292.76i) q^{29} +(483.708 + 6454.63i) q^{30} +(-102376. - 260849. i) q^{31} +(-33940.1 + 148701. i) q^{32} +(-3136.10 + 41848.3i) q^{33} +(-98306.4 + 30323.5i) q^{34} +(-6646.57 - 3200.82i) q^{35} +(-44049.6 - 76296.1i) q^{36} +(100741. - 174489. i) q^{37} +(-102718. + 70032.0i) q^{38} +(60921.2 + 266913. i) q^{39} +(41282.9 - 6222.39i) q^{40} +(140957. - 176755. i) q^{41} +20581.7 q^{42} +(209663. + 477347. i) q^{43} +128280. q^{44} +(-22944.8 + 28771.8i) q^{45} +(-39661.7 + 5978.04i) q^{46} +(55359.6 + 242546. i) q^{47} +(363784. - 248024. i) q^{48} +(400043. - 692894. i) q^{49} +(135024. + 233868. i) q^{50} +(981486. + 472659. i) q^{51} +(799700. - 246675. i) q^{52} +(-115274. + 1.53823e6i) q^{53} +(88243.9 - 386622. i) q^{54} +(-19576.8 - 49880.8i) q^{55} +(-9920.59 - 132381. i) q^{56} +(1.30173e6 + 196204. i) q^{57} +(-40172.3 + 37274.4i) q^{58} +(-1.58742e6 + 764461. i) q^{59} +(-173107. - 118023. i) q^{60} +(-573411. + 1.46103e6i) q^{61} +(-953903. - 294240. i) q^{62} +(85779.5 + 79591.7i) q^{63} +(-592713. - 743239. i) q^{64} +(-217959. - 273312. i) q^{65} +(109590. + 101685. i) q^{66} +(-2.80244e6 - 864439. i) q^{67} +(1.21657e6 - 3.09978e6i) q^{68} +(350922. + 239255. i) q^{69} +(-23677.7 + 11402.6i) q^{70} +(-1.85678e6 + 1.72284e6i) q^{71} +(-654833. - 98700.2i) q^{72} +(-65828.0 - 878413. i) q^{73} +(-262227. - 668144. i) q^{74} +(636308. - 2.78785e6i) q^{75} +(300718. - 4.01280e6i) q^{76} +(-162817. + 50222.5i) q^{77} +(878718. + 423168. i) q^{78} +(330578. + 572578. i) q^{79} +(-281097. + 486874. i) q^{80} +(-2.08899e6 + 1.42425e6i) q^{81} +(-179213. - 785185. i) q^{82} +(-4.32122e6 + 651319. i) q^{83} +(-415369. + 520856. i) q^{84} -1.39099e6 q^{85} +(1.79519e6 + 476293. i) q^{86} +580294. q^{87} +(601210. - 753893. i) q^{88} +(-2.92399e6 + 440720. i) q^{89} +(29172.1 + 127811. i) q^{90} +(-918429. + 626174. i) q^{91} +(649145. - 1.12435e6i) q^{92} +(5.28526e6 + 9.15435e6i) q^{93} +(798498. + 384537. i) q^{94} +(-1.60624e6 + 495458. i) q^{95} +(429969. - 5.73753e6i) q^{96} +(-1.26764e6 + 5.55388e6i) q^{97} +(-1.04130e6 - 2.65320e6i) q^{98} +(63518.3 + 847592. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

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