LMFDB - Embedded newform 89.10.f.a.81.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [89,10,Mod(11,89)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(89, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([21]))

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

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

chi := DirichletCharacter("89.11");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 89 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	89.f (of order $22$, degree $10$, 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:	$45.8381894186$
Analytic rank:	$0$
Dimension:	$660$
Relative dimension:	$66$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			81.20
Character	$\chi$	$=$	89.81
Dual form			89.10.f.a.11.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.7990 + 15.9249i) q^{2} +(202.658 + 29.1378i) q^{3} +(9.67508 + 67.2917i) q^{4} +(2267.64 + 1457.33i) q^{5} +(-3260.50 + 2825.24i) q^{6} +(6234.30 - 9700.76i) q^{7} +(-10281.2 - 6607.30i) q^{8} +(21335.5 + 6264.68i) q^{9} +O(q^{10})$	\(q+(-13.7990 + 15.9249i) q^{2} +(202.658 + 29.1378i) q^{3} +(9.67508 + 67.2917i) q^{4} +(2267.64 + 1457.33i) q^{5} +(-3260.50 + 2825.24i) q^{6} +(6234.30 - 9700.76i) q^{7} +(-10281.2 - 6607.30i) q^{8} +(21335.5 + 6264.68i) q^{9} +(-54499.1 + 16002.4i) q^{10} +(-6514.61 + 4186.68i) q^{11} +13919.1i q^{12} +(39028.9 + 5611.51i) q^{13} +(68456.6 + 233142. i) q^{14} +(417093. + 361413. i) q^{15} +(213693. - 62745.9i) q^{16} +(-33000.2 - 38084.3i) q^{17} +(-394174. + 253320. i) q^{18} +(-70006.7 + 238421. i) q^{19} +(-76126.3 + 166693. i) q^{20} +(1.54609e6 - 1.78428e6i) q^{21} +(23222.6 - 161517. i) q^{22} +(-532141. + 1.81231e6i) q^{23} +(-1.89104e6 - 1.63859e6i) q^{24} +(2.20705e6 + 4.83276e6i) q^{25} +(-627923. + 544099. i) q^{26} +(475519. + 217162. i) q^{27} +(713098. + 325661. i) q^{28} +(1.70389e6 - 2.65131e6i) q^{29} +(-1.15109e7 + 1.65502e6i) q^{30} +(-1.09426e6 - 3.72672e6i) q^{31} +(649834. - 1.42294e6i) q^{32} +(-1.44223e6 + 658643. i) q^{33} +1.06186e6 q^{34} +(2.82743e7 - 1.29124e7i) q^{35} +(-215138. + 1.49632e6i) q^{36} +3.70136e6i q^{37} +(-2.83081e6 - 4.40483e6i) q^{38} +(7.74601e6 + 2.27443e6i) q^{39} +(-1.36850e7 - 2.99660e7i) q^{40} +(2.37905e7 - 3.42056e6i) q^{41} +(7.08003e6 + 4.92427e7i) q^{42} +(1.60516e7 + 2.49768e7i) q^{43} +(-344758. - 397872. i) q^{44} +(3.92517e7 + 4.52989e7i) q^{45} +(-2.15178e7 - 3.34824e7i) q^{46} +(-30504.4 - 212162. i) q^{47} +(4.51349e7 - 6.48942e6i) q^{48} +(-3.84747e7 - 8.42479e7i) q^{49} +(-1.07416e8 - 3.15403e7i) q^{50} +(-5.57807e6 - 8.67964e6i) q^{51} +2.68061e6i q^{52} +(-1.45632e7 + 1.01289e8i) q^{53} +(-1.00200e7 + 4.57598e6i) q^{54} -2.08742e7 q^{55} +(-1.28192e8 + 5.85432e7i) q^{56} +(-2.11345e7 + 4.62780e7i) q^{57} +(1.87099e7 + 6.37199e7i) q^{58} +(9.31196e7 - 1.33886e7i) q^{59} +(-2.02847e7 + 3.15636e7i) q^{60} +(-1.06351e8 - 4.85690e7i) q^{61} +(7.44475e7 + 3.39990e7i) q^{62} +(1.93784e8 - 1.67915e8i) q^{63} +(6.10628e7 + 1.33709e8i) q^{64} +(8.03258e7 + 6.96027e7i) q^{65} +(9.41249e6 - 3.20560e7i) q^{66} +(2.59324e7 - 1.80364e8i) q^{67} +(2.24348e6 - 2.58911e6i) q^{68} +(-1.60649e8 + 3.51773e8i) q^{69} +(-1.84528e8 + 6.28446e8i) q^{70} +(-1.62509e8 + 1.04438e8i) q^{71} +(-1.77961e8 - 2.05378e8i) q^{72} +(-3.41233e7 + 1.00195e7i) q^{73} +(-5.89440e7 - 5.10752e7i) q^{74} +(3.06460e8 + 1.04371e9i) q^{75} +(-1.67211e7 - 2.40413e6i) q^{76} +8.92976e7i q^{77} +(-1.43108e8 + 9.19696e7i) q^{78} +(2.18206e8 - 6.40711e7i) q^{79} +(5.76021e8 + 1.69135e8i) q^{80} +(-2.78157e8 - 1.78760e8i) q^{81} +(-2.73814e8 + 4.26063e8i) q^{82} +(-1.72304e8 + 1.49302e8i) q^{83} +(1.35026e8 + 8.67759e7i) q^{84} +(-1.93315e7 - 1.34454e8i) q^{85} +(-6.19251e8 - 8.90349e7i) q^{86} +(4.22561e8 - 4.87662e8i) q^{87} +9.46404e7 q^{88} +(4.15751e8 + 4.21316e8i) q^{89} -1.26302e9 q^{90} +(2.97754e8 - 3.43626e8i) q^{91} +(-1.27102e8 - 1.82745e7i) q^{92} +(-1.13173e8 - 7.87134e8i) q^{93} +(3.79960e6 + 2.44186e6i) q^{94} +(-5.06207e8 + 4.38631e8i) q^{95} +(1.73155e8 - 2.69435e8i) q^{96} +(-5.54236e8 - 3.56186e8i) q^{97} +(1.87255e9 + 5.49832e8i) q^{98} +(-1.65221e8 + 4.85132e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9}+O(q^{10}) $ 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9	\( 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9} - 225841 q^{10} - 224944 q^{11} - 11 q^{13} + 1940664 q^{14} - 11 q^{15} - 5125641 q^{16} + 1457606 q^{17} + 2864796 q^{18} - 11 q^{19} - 5955661 q^{20} + 856653 q^{21} + 13531907 q^{22} - 11 q^{23} + 5621 q^{24} - 31973709 q^{25} - 4206763 q^{26} - 17737896 q^{27} - 11 q^{28} + 10200729 q^{29} - 81004858 q^{30} - 11 q^{31} - 44372422 q^{32} - 19516475 q^{33} + 35594328 q^{34} - 35970209 q^{35} + 71890930 q^{36} - 87132859 q^{38} + 42308203 q^{39} - 128175356 q^{40} + 60926635 q^{41} + 121333817 q^{42} + 296517661 q^{43} + 115664209 q^{44} + 48133749 q^{45} + 311125309 q^{46} - 46792325 q^{47} - 141127426 q^{48} + 164252871 q^{49} + 103838041 q^{50} - 427287971 q^{51} + 850769769 q^{53} - 329099771 q^{54} + 793594654 q^{55} - 2036185316 q^{56} - 154197519 q^{57} + 188920501 q^{58} + 405753711 q^{59} + 21484364 q^{60} + 344711653 q^{61} - 1167226764 q^{62} - 1320295229 q^{63} - 134364169 q^{64} + 1450391239 q^{65} + 863803105 q^{66} + 646170445 q^{67} + 1285178775 q^{68} - 221829309 q^{69} + 854155808 q^{70} - 1113621013 q^{71} - 2392386072 q^{72} - 314298299 q^{73} - 479039451 q^{74} - 3075936347 q^{75} - 6170784400 q^{76} - 2037231963 q^{78} - 79886655 q^{79} + 6302566534 q^{80} + 281226707 q^{81} + 5439310019 q^{82} + 1306521271 q^{83} + 1958614914 q^{84} + 4403895759 q^{85} - 3738814827 q^{86} - 4959185007 q^{87} + 2745817562 q^{88} + 3415767517 q^{89} - 10039266258 q^{90} + 1585238913 q^{91} + 8669558172 q^{92} + 1795690413 q^{93} - 8679076027 q^{94} + 10576695701 q^{95} + 12941524981 q^{96} - 2702894895 q^{97} + 1786224002 q^{98} - 9157402144 q^{99}+O(q^{100}) \) 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9 - 225841 * q^10 - 224944 * q^11 - 11 * q^13 + 1940664 * q^14 - 11 * q^15 - 5125641 * q^16 + 1457606 * q^17 + 2864796 * q^18 - 11 * q^19 - 5955661 * q^20 + 856653 * q^21 + 13531907 * q^22 - 11 * q^23 + 5621 * q^24 - 31973709 * q^25 - 4206763 * q^26 - 17737896 * q^27 - 11 * q^28 + 10200729 * q^29 - 81004858 * q^30 - 11 * q^31 - 44372422 * q^32 - 19516475 * q^33 + 35594328 * q^34 - 35970209 * q^35 + 71890930 * q^36 - 87132859 * q^38 + 42308203 * q^39 - 128175356 * q^40 + 60926635 * q^41 + 121333817 * q^42 + 296517661 * q^43 + 115664209 * q^44 + 48133749 * q^45 + 311125309 * q^46 - 46792325 * q^47 - 141127426 * q^48 + 164252871 * q^49 + 103838041 * q^50 - 427287971 * q^51 + 850769769 * q^53 - 329099771 * q^54 + 793594654 * q^55 - 2036185316 * q^56 - 154197519 * q^57 + 188920501 * q^58 + 405753711 * q^59 + 21484364 * q^60 + 344711653 * q^61 - 1167226764 * q^62 - 1320295229 * q^63 - 134364169 * q^64 + 1450391239 * q^65 + 863803105 * q^66 + 646170445 * q^67 + 1285178775 * q^68 - 221829309 * q^69 + 854155808 * q^70 - 1113621013 * q^71 - 2392386072 * q^72 - 314298299 * q^73 - 479039451 * q^74 - 3075936347 * q^75 - 6170784400 * q^76 - 2037231963 * q^78 - 79886655 * q^79 + 6302566534 * q^80 + 281226707 * q^81 + 5439310019 * q^82 + 1306521271 * q^83 + 1958614914 * q^84 + 4403895759 * q^85 - 3738814827 * q^86 - 4959185007 * q^87 + 2745817562 * q^88 + 3415767517 * q^89 - 10039266258 * q^90 + 1585238913 * q^91 + 8669558172 * q^92 + 1795690413 * q^93 - 8679076027 * q^94 + 10576695701 * q^95 + 12941524981 * q^96 - 2702894895 * q^97 + 1786224002 * q^98 - 9157402144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/89\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−13.7990	+	15.9249i	−0.609837	+	0.703789i	−0.973744	−	0.227646i	$-0.926897\pi$
$2$	−13.7990	+	15.9249i	−0.609837	+	0.703789i	0.363907	+	0.931435i	$0.381442\pi$
$3$	202.658	+	29.1378i	1.44450	+	0.207688i	0.819564	−	0.572987i	$-0.194215\pi$
$3$	202.658	+	29.1378i	1.44450	+	0.207688i	0.624937	+	0.780675i	$0.285125\pi$
$4$	9.67508	+	67.2917i	0.0188967	+	0.131429i
$5$	2267.64	+	1457.33i	1.62259	+	1.04278i	0.954287	+	0.298890i	$0.0966165\pi$
$5$	2267.64	+	1457.33i	1.62259	+	1.04278i	0.668306	+	0.743887i	$0.267020\pi$
$6$	−3260.50	+	2825.24i	−1.02708	+	0.889968i
$7$	6234.30	−	9700.76i	0.981401	−	1.52709i	0.137562	−	0.990493i	$-0.456074\pi$
$7$	6234.30	−	9700.76i	0.981401	−	1.52709i	0.843839	−	0.536596i	$-0.180290\pi$
$8$	−10281.2	−	6607.30i	−0.887436	−	0.570321i
$9$	21335.5	+	6264.68i	1.08396	+	0.318279i
$10$	−54499.1	+	16002.4i	−1.72341	+	0.506039i
$11$	−6514.61	+	4186.68i	−0.134159	+	0.0862190i	−0.605999	−	0.795465i	$-0.707226\pi$
$11$	−6514.61	+	4186.68i	−0.134159	+	0.0862190i	0.471840	+	0.881684i	$0.343590\pi$
$12$			13919.1i			0.193774i
$13$	39028.9	+	5611.51i	0.379002	+	0.0544922i	0.329183	−	0.944266i	$-0.393227\pi$
$13$	39028.9	+	5611.51i	0.379002	+	0.0544922i	0.0498185	+	0.998758i	$0.484136\pi$
$14$	68456.6	+	233142.i	0.476254	+	1.62197i
$15$	417093.	+	361413.i	2.12727	+	1.84329i
$16$	213693.	−	62745.9i	0.815174	−	0.239357i
$17$	−33000.2	−	38084.3i	−0.0958290	−	0.110593i	0.705809	−	0.708402i	$-0.250583\pi$
$17$	−33000.2	−	38084.3i	−0.0958290	−	0.110593i	−0.801638	+	0.597809i	$0.796038\pi$
$18$	−394174.	+	253320.i	−0.885038	+	0.568779i
$19$	−70006.7	+	238421.i	−0.123239	+	0.419714i	−0.997882	−	0.0650546i	$-0.979278\pi$
$19$	−70006.7	+	238421.i	−0.123239	+	0.419714i	0.874643	+	0.484768i	$0.161096\pi$
$20$	−76126.3	+	166693.i	−0.106390	+	0.232961i
$21$	1.54609e6	−	1.78428e6i	1.73479	−	2.00206i
$22$	23222.6	−	161517.i	0.0211353	−	0.146999i
$23$	−532141.	+	1.81231e6i	−0.396508	+	1.35038i	0.483468	+	0.875362i	$0.339377\pi$
$23$	−532141.	+	1.81231e6i	−0.396508	+	1.35038i	−0.879976	+	0.475019i	$0.842441\pi$
$24$	−1.89104e6	−	1.63859e6i	−1.16345	−	1.00814i
$25$	2.20705e6	+	4.83276e6i	1.13001	+	2.47437i
$26$	−627923.	+	544099.i	−0.269480	+	0.233506i
$27$	475519.	+	217162.i	0.172199	+	0.0786408i
$28$	713098.	+	325661.i	0.219249	+	0.100128i
$29$	1.70389e6	−	2.65131e6i	0.447354	−	0.696097i	−0.542201	−	0.840249i	$-0.682409\pi$
$29$	1.70389e6	−	2.65131e6i	0.447354	−	0.696097i	0.989556	+	0.144152i	$0.0460453\pi$
$30$	−1.15109e7	+	1.65502e6i	−2.59457	+	0.373043i
$31$	−1.09426e6	−	3.72672e6i	−0.212811	−	0.724768i	−0.994834	−	0.101518i	$-0.967630\pi$
$31$	−1.09426e6	−	3.72672e6i	−0.212811	−	0.724768i	0.782023	−	0.623250i	$-0.214188\pi$
$32$	649834.	−	1.42294e6i	0.109554	−	0.239889i
$33$	−1.44223e6	+	658643.i	−0.211700	+	0.0966802i
$34$	1.06186e6			0.136274
$35$	2.82743e7	−	1.29124e7i	3.18483	−	1.45446i
$36$	−215138.	+	1.49632e6i	−0.0213479	+	0.148478i
$37$			3.70136e6i			0.324679i	0.986735	+	0.162339i	$0.0519040\pi$
$37$			3.70136e6i			0.324679i	−0.986735	+	0.162339i	$0.948096\pi$
$38$	−2.83081e6	−	4.40483e6i	−0.220234	−	0.342691i
$39$	7.74601e6	+	2.27443e6i	0.536151	+	0.157428i
$40$	−1.36850e7	−	2.99660e7i	−0.845231	−	1.85080i
$41$	2.37905e7	−	3.42056e6i	1.31485	−	0.189047i	0.551036	−	0.834481i	$-0.314233\pi$
$41$	2.37905e7	−	3.42056e6i	1.31485	−	0.189047i	0.763816	+	0.645434i	$0.223323\pi$
$42$	7.08003e6	+	4.92427e7i	0.351086	+	2.44186i
$43$	1.60516e7	+	2.49768e7i	0.715997	+	1.11411i	0.988392	+	0.151928i	$0.0485480\pi$
$43$	1.60516e7	+	2.49768e7i	0.715997	+	1.11411i	−0.272395	+	0.962186i	$0.587816\pi$
$44$	−344758.	−	397872.i	−0.0138668	−	0.0160032i
$45$	3.92517e7	+	4.52989e7i	1.42693	+	1.64676i
$46$	−2.15178e7	−	3.34824e7i	−0.708578	−	1.10257i
$47$	−30504.4	−	212162.i	−0.000911846	−	0.00634203i	0.989360	−	0.145485i	$-0.0464743\pi$
$47$	−30504.4	−	212162.i	−0.000911846	−	0.00634203i	−0.990272	+	0.139143i	$0.955565\pi$
$48$	4.51349e7	−	6.48942e6i	1.22723	−	0.176449i
$49$	−3.84747e7	−	8.42479e7i	−0.953439	−	2.08774i
$50$	−1.07416e8	−	3.15403e7i	−2.43056	−	0.713676i
$51$	−5.57807e6	−	8.67964e6i	−0.115456	−	0.179654i
$52$			2.68061e6i			0.0508416i
$53$	−1.45632e7	+	1.01289e8i	−0.253522	+	1.76328i	0.323190	+	0.946334i	$0.395245\pi$
$53$	−1.45632e7	+	1.01289e8i	−0.253522	+	1.76328i	−0.576711	+	0.816948i	$0.695664\pi$
$54$	−1.00200e7	+	4.57598e6i	−0.160360	+	0.0732339i
$55$	−2.08742e7			−0.307593
$56$	−1.28192e8	+	5.85432e7i	−1.74186	+	0.795481i
$57$	−2.11345e7	+	4.62780e7i	−0.265188	+	0.580682i
$58$	1.87099e7	+	6.37199e7i	0.217092	+	0.739348i
$59$	9.31196e7	−	1.33886e7i	1.00048	−	0.143847i	0.377436	−	0.926036i	$-0.376806\pi$
$59$	9.31196e7	−	1.33886e7i	1.00048	−	0.143847i	0.623041	+	0.782189i	$0.285897\pi$
$60$	−2.02847e7	+	3.15636e7i	−0.202063	+	0.314417i
$61$	−1.06351e8	−	4.85690e7i	−0.983463	−	0.449132i	−0.142247	−	0.989831i	$-0.545433\pi$
$61$	−1.06351e8	−	4.85690e7i	−0.983463	−	0.449132i	−0.841216	+	0.540699i	$0.818160\pi$
$62$	7.44475e7	+	3.39990e7i	0.639864	+	0.292216i
$63$	1.93784e8	−	1.67915e8i	1.54984	−	1.34294i
$64$	6.10628e7	+	1.33709e8i	0.454953	+	0.996209i
$65$	8.03258e7	+	6.96027e7i	0.558142	+	0.483633i
$66$	9.41249e6	−	3.20560e7i	0.0610600	−	0.207951i
$67$	2.59324e7	−	1.80364e8i	0.157219	−	1.09348i	−0.746508	−	0.665376i	$-0.768271\pi$
$67$	2.59324e7	−	1.80364e8i	0.157219	−	1.09348i	0.903727	−	0.428108i	$-0.140820\pi$
$68$	2.24348e6	−	2.58911e6i	0.0127242	−	0.0146845i
$69$	−1.60649e8	+	3.51773e8i	−0.853214	+	1.86828i
$70$	−1.84528e8	+	6.28446e8i	−0.918590	+	3.12843i
$71$	−1.62509e8	+	1.04438e8i	−0.758953	+	0.487749i	−0.861988	−	0.506928i	$-0.830781\pi$
$71$	−1.62509e8	+	1.04438e8i	−0.758953	+	0.487749i	0.103036	+	0.994678i	$0.467144\pi$
$72$	−1.77961e8	−	2.05378e8i	−0.780422	−	0.900656i
$73$	−3.41233e7	+	1.00195e7i	−0.140636	+	0.0412946i	−0.351293	−	0.936266i	$-0.614258\pi$
$73$	−3.41233e7	+	1.00195e7i	−0.140636	+	0.0412946i	0.210657	+	0.977560i	$0.432440\pi$
$74$	−5.89440e7	−	5.10752e7i	−0.228505	−	0.198001i
$75$	3.06460e8	+	1.04371e9i	1.11840	+	3.80893i
$76$	−1.67211e7	−	2.40413e6i	−0.0574914	−	0.00826601i
$77$			8.92976e7i			0.289489i
$78$	−1.43108e8	+	9.19696e7i	−0.437761	+	0.281332i
$79$	2.18206e8	−	6.40711e7i	0.630297	−	0.185072i	0.0490462	−	0.998797i	$-0.484382\pi$
$79$	2.18206e8	−	6.40711e7i	0.630297	−	0.185072i	0.581250	+	0.813725i	$0.302564\pi$
$80$	5.76021e8	+	1.69135e8i	1.57229	+	0.461667i
$81$	−2.78157e8	−	1.78760e8i	−0.717971	−	0.461412i
$82$	−2.73814e8	+	4.26063e8i	−0.668796	+	1.04067i
$83$	−1.72304e8	+	1.49302e8i	−0.398515	+	0.345315i	−0.830947	−	0.556351i	$-0.812201\pi$
$83$	−1.72304e8	+	1.49302e8i	−0.398515	+	0.345315i	0.432432	+	0.901666i	$0.357655\pi$
$84$	1.35026e8	+	8.67759e7i	0.295910	+	0.190170i
$85$	−1.93315e7	−	1.34454e8i	−0.0401681	−	0.279375i
$86$	−6.19251e8	−	8.90349e7i	−1.22074	−	0.175516i
$87$	4.22561e8	−	4.87662e8i	0.790775	−	0.912603i
$88$	9.46404e7			0.168230
$89$	4.15751e8	+	4.21316e8i	0.702391	+	0.711792i
$89$	4.15751e8	+	4.21316e8i	0.702391	+	0.711792i
$90$	−1.26302e9			−2.02917
$91$	2.97754e8	−	3.43626e8i	0.455167	−	0.525291i
$92$	−1.27102e8	−	1.82745e7i	−0.184972	−	0.0265950i
$93$	−1.13173e8	−	7.87134e8i	−0.156880	−	1.09113i
$94$	3.79960e6	+	2.44186e6i	0.00501953	+	0.00322585i
$95$	−5.06207e8	+	4.38631e8i	−0.637635	+	0.552513i
$96$	1.73155e8	−	2.69435e8i	0.208073	−	0.323768i
$97$	−5.54236e8	−	3.56186e8i	−0.635656	−	0.408511i	0.182744	−	0.983161i	$-0.441502\pi$
$97$	−5.54236e8	−	3.56186e8i	−0.635656	−	0.408511i	−0.818400	+	0.574649i	$0.805138\pi$
$98$	1.87255e9	+	5.49832e8i	2.05077	+	0.602161i
$99$	−1.65221e8	+	4.85132e7i	−0.172865	+	0.0507577i
$100$	−3.03851e8	+	1.95273e8i	−0.303851	+	0.195273i
$101$		−	1.94749e9i		−	1.86221i	−0.364745	−	0.931107i	$-0.618844\pi$
$101$		−	1.94749e9i		−	1.86221i	0.364745	−	0.931107i	$-0.381156\pi$
$102$	2.15195e8	+	3.09403e7i	0.196848	+	0.0283024i
$103$	−6.83689e7	−	2.32843e8i	−0.0598537	−	0.203843i	0.924137	−	0.382060i	$-0.124785\pi$
$103$	−6.83689e7	−	2.32843e8i	−0.0598537	−	0.203843i	−0.983991	+	0.178217i	$0.942967\pi$
$104$	−3.64185e8	−	3.15568e8i	−0.305262	−	0.264511i
$105$	6.10626e9	−	1.79296e9i	4.90256	−	1.43952i
$106$	−1.41207e9	−	1.62961e9i	−1.08637	−	1.25374i
$107$	−5.86925e8	+	3.77194e8i	−0.432868	+	0.278187i	−0.738876	−	0.673842i	$-0.764643\pi$
$107$	−5.86925e8	+	3.77194e8i	−0.432868	+	0.278187i	0.306008	+	0.952029i	$0.401007\pi$
$108$	−1.00125e7	+	3.40996e7i	−0.00708170	+	0.0241180i
$109$	3.98482e8	−	8.72554e8i	0.270389	−	0.592070i	−0.724918	−	0.688835i	$-0.758122\pi$
$109$	3.98482e8	−	8.72554e8i	0.270389	−	0.592070i	0.995307	+	0.0967651i	$0.0308495\pi$
$110$	2.88043e8	−	3.32419e8i	0.187582	−	0.216481i
$111$	−1.07850e8	+	7.50111e8i	−0.0674319	+	0.468999i
$112$	7.23543e8	−	2.46416e9i	0.434494	−	1.47975i
$113$	1.76908e8	+	1.53291e8i	0.102069	+	0.0884433i	0.704400	−	0.709803i	$-0.251216\pi$
$113$	1.76908e8	+	1.53291e8i	0.102069	+	0.0884433i	−0.602331	+	0.798246i	$0.705761\pi$
$114$	−4.45339e8	−	9.75157e8i	−0.246956	−	0.540758i
$115$	−3.84783e9	+	3.33416e9i	−2.05152	+	1.77765i
$116$	1.94897e8	+	8.90063e7i	0.0999409	+	0.0456415i
$117$	7.97548e8	+	3.64228e8i	0.393478	+	0.179695i
$118$	−1.07175e9	+	1.66767e9i	−0.508890	+	0.791848i
$119$	−5.75180e8	+	8.26984e7i	−0.262931	+	0.0378038i
$120$	−1.90023e9	−	6.47160e9i	−0.836549	−	2.84902i
$121$	−9.54615e8	+	2.09032e9i	−0.404850	+	0.886498i
$122$	2.24100e9	−	1.02343e9i	0.915846	−	0.418253i
$123$	4.92101e9			1.93857
$124$	2.40190e8	−	1.09691e8i	0.0912342	−	0.0416653i
$125$	−1.28886e9	+	8.96420e9i	−0.472183	+	3.28410i
$126$			5.40306e9i			1.90973i
$127$	−1.53191e9	−	2.38371e9i	−0.522538	−	0.813085i	0.475230	−	0.879862i	$-0.342365\pi$
$127$	−1.53191e9	−	2.38371e9i	−0.522538	−	0.813085i	−0.997768	+	0.0667768i	$0.978728\pi$
$128$	−2.20343e9	−	6.46986e8i	−0.725529	−	0.213035i
$129$	2.52522e9	+	5.52946e9i	0.802871	+	1.75804i
$130$	−2.21684e9	+	3.18733e8i	−0.680751	+	0.0978772i
$131$	−5.11052e8	−	3.55444e9i	−0.151616	−	1.05451i	−0.913512	−	0.406811i	$-0.866641\pi$
$131$	−5.11052e8	−	3.55444e9i	−0.151616	−	1.05451i	0.761896	−	0.647699i	$-0.224269\pi$
$132$	−5.82749e7	−	9.06775e7i	−0.0167070	−	0.0259966i
$133$	1.87642e9	+	2.16550e9i	0.519993	+	0.600104i
$134$	2.51444e9	+	2.90182e9i	0.673704	+	0.777496i
$135$	7.61832e8	+	1.18543e9i	0.197405	+	0.307167i
$136$	8.76463e7	+	6.09593e8i	0.0219689	+	0.152797i
$137$	9.10853e8	−	1.30961e8i	0.220905	−	0.0317614i	−0.0309734	−	0.999520i	$-0.509861\pi$
$137$	9.10853e8	−	1.30961e8i	0.220905	−	0.0317614i	0.251879	+	0.967759i	$0.418952\pi$
$138$	−3.38515e9	−	7.41245e9i	−0.794552	−	1.73983i
$139$	−8.03476e9	−	2.35922e9i	−1.82560	−	0.536045i	−0.825985	−	0.563692i	$-0.809381\pi$
$139$	−8.03476e9	−	2.35922e9i	−1.82560	−	0.536045i	−0.999618	+	0.0276463i	$0.991199\pi$
$140$	1.14246e9	+	1.77770e9i	0.251341	+	0.391095i
$141$		−	4.38852e7i		−	0.00935045i
$142$	5.79295e8	−	4.02909e9i	0.119565	−	0.831590i
$143$	−2.77751e8	+	1.26845e8i	−0.0555449	+	0.0253665i
$144$	4.95234e9			0.959797
$145$	7.72765e9	−	3.52910e9i	1.45175	−	0.662991i
$146$	3.11308e8	−	6.81670e8i	0.0567026	−	0.124161i
$147$	−5.34241e9	−	1.81946e10i	−0.943646	−	3.21376i
$148$	−2.49071e8	+	3.58110e7i	−0.0426723	+	0.00613534i
$149$	2.85197e9	−	4.43776e9i	0.474031	−	0.737607i	−0.519087	−	0.854721i	$-0.673728\pi$
$149$	2.85197e9	−	4.43776e9i	0.474031	−	0.737607i	0.993118	+	0.117114i	$0.0373643\pi$
$150$	−2.08498e10	−	9.52178e9i	−3.36272	−	1.53570i
$151$	4.25542e9	+	1.94338e9i	0.666110	+	0.304202i	0.719623	−	0.694365i	$-0.244315\pi$
$151$	4.25542e9	+	1.94338e9i	0.666110	+	0.304202i	−0.0535133	+	0.998567i	$0.517042\pi$
$152$	2.29507e9	−	1.98869e9i	0.348738	−	0.302183i
$153$	−4.65492e8	−	1.01928e9i	−0.0686753	−	0.150378i
$154$	−1.42206e9	−	1.23222e9i	−0.203739	−	0.176541i
$155$	2.94964e9	−	1.00456e10i	0.410466	−	1.39792i
$156$	−7.81072e7	+	5.43247e8i	−0.0105592	+	0.0734407i
$157$	9.53719e9	−	1.10065e10i	1.25277	−	1.44578i	0.405953	−	0.913894i	$-0.366940\pi$
$157$	9.53719e9	−	1.10065e10i	1.25277	−	1.44578i	0.846819	−	0.531882i	$-0.178515\pi$
$158$	−1.99070e9	+	4.35903e9i	−0.254126	+	0.556459i
$159$	−5.90269e9	+	2.01027e10i	−0.732425	+	2.49441i
$160$	3.54727e9	−	2.27970e9i	0.427912	−	0.275003i
$161$	1.42632e10	+	1.64606e10i	1.67302	+	1.93077i
$162$	6.68504e9	−	1.96290e9i	0.762581	−	0.223914i
$163$	−1.10806e10	−	9.60138e9i	−1.22947	−	1.06534i	−0.995660	−	0.0930611i	$-0.970335\pi$
$163$	−1.10806e10	−	9.60138e9i	−1.22947	−	1.06534i	−0.233811	−	0.972282i	$-0.575120\pi$
$164$	4.60351e8	+	1.56781e9i	0.0496926	+	0.169237i
$165$	−4.23031e9	−	6.08227e8i	−0.444319	−	0.0638834i
$166$		−	4.80416e9i		−	0.491056i
$167$	−1.15579e10	+	7.42781e9i	−1.14989	+	0.738987i	−0.969616	−	0.244631i	$-0.921333\pi$
$167$	−1.15579e10	+	7.42781e9i	−1.14989	+	0.738987i	−0.180269	+	0.983617i	$0.557697\pi$
$168$	−2.76849e10	+	8.12901e9i	−2.68133	+	0.787311i
$169$	−8.68318e9	−	2.54961e9i	−0.818820	−	0.240427i
$170$	2.40792e9	+	1.54748e9i	0.221117	+	0.142103i
$171$	−2.98726e9	+	4.64827e9i	−0.267172	+	0.415727i
$172$	−1.52543e9	+	1.32179e9i	−0.132897	+	0.115156i
$173$	−1.68078e9	−	1.08017e9i	−0.142660	−	0.0916822i	0.467364	−	0.884065i	$-0.345204\pi$
$173$	−1.68078e9	−	1.08017e9i	−0.142660	−	0.0916822i	−0.610024	+	0.792383i	$0.708840\pi$
$174$	1.93504e9	+	1.34585e10i	0.160036	+	1.11308i
$175$	6.06409e10	+	8.71884e9i	4.88758	+	0.702728i
$176$	−1.12943e9	+	1.30343e9i	−0.0887262	+	0.102395i
$177$	1.92615e10			1.47507
$178$	−1.24464e10	+	8.07062e8i	−0.929295	+	0.0602583i
$179$	−1.31981e10			−0.960889			−0.480445	−	0.877025i	$-0.659525\pi$
$179$	−1.31981e10			−0.960889			−0.480445	+	0.877025i	$0.659525\pi$
$180$	−2.66847e9	+	3.07958e9i	−0.189468	+	0.218658i
$181$	−1.14904e10	−	1.65206e9i	−0.795756	−	0.114412i	−0.267567	−	0.963539i	$-0.586220\pi$
$181$	−1.14904e10	−	1.65206e9i	−0.795756	−	0.114412i	−0.528189	+	0.849127i	$0.677129\pi$
$182$	1.36351e9	+	9.48341e9i	0.0921163	+	0.640683i
$183$	−2.01377e10	−	1.29417e10i	−1.32733	−	0.853026i
$184$	1.74455e10	−	1.51166e10i	1.12203	−	0.972241i
$185$	−5.39409e9	+	8.39337e9i	−0.338568	+	0.526822i
$186$	1.40967e10	+	9.05941e9i	0.863595	+	0.554999i
$187$	3.74430e8	+	1.09943e8i	0.0223915	+	0.00657475i
$188$	1.39816e7	−	4.10538e6i	0.000816296	−	0.000239686i
$189$	5.07117e9	−	3.25904e9i	0.289088	−	0.185786i
$190$		−	1.41140e10i		−	0.785703i
$191$	−4.89205e9	−	7.03371e8i	−0.265975	−	0.0382414i	0.00803700	−	0.999968i	$-0.497442\pi$
$191$	−4.89205e9	−	7.03371e8i	−0.265975	−	0.0382414i	−0.274012	+	0.961726i	$0.588351\pi$
$192$	8.47888e9	+	2.88764e10i	0.450280	+	1.53351i
$193$	−1.66102e10	−	1.43929e10i	−0.861724	−	0.746688i	0.107150	−	0.994243i	$-0.465827\pi$
$193$	−1.66102e10	−	1.43929e10i	−0.861724	−	0.746688i	−0.968874	+	0.247555i	$0.920373\pi$
$194$	1.33202e10	−	3.91115e9i	0.675152	−	0.198243i
$195$	1.42506e10	+	1.64461e10i	0.705793	+	0.814528i
$196$	5.29694e9	−	3.40413e9i	0.256373	−	0.164761i
$197$	8.25233e9	−	2.81049e10i	0.390372	−	1.32949i	−0.496727	−	0.867907i	$-0.665465\pi$
$197$	8.25233e9	−	2.81049e10i	0.390372	−	1.32949i	0.887099	−	0.461579i	$-0.152717\pi$
$198$	1.50732e9	−	3.30057e9i	0.0696966	−	0.152614i
$199$	−5.13721e9	+	5.92866e9i	−0.232214	+	0.267989i	−0.859883	−	0.510491i	$-0.829464\pi$
$199$	−5.13721e9	+	5.92866e9i	−0.232214	+	0.267989i	0.627669	+	0.778480i	$0.284009\pi$
$200$	9.24049e9	−	6.42690e10i	0.408376	−	2.84032i
$201$	1.05108e10	−	3.57965e10i	0.454207	−	1.54689i
$202$	3.10137e10	+	2.68735e10i	1.31061	+	1.13565i
$203$	−1.50971e10	−	3.30581e10i	−0.623968	−	1.36630i
$204$	5.30099e8	−	4.59334e8i	0.0214300	−	0.0185692i
$205$	5.89333e10	+	2.69139e10i	2.33060	+	1.06435i
$206$	4.65143e9	+	2.12424e9i	0.179963	+	0.0821865i
$207$	−2.27070e10	+	3.53328e10i	−0.859595	+	1.33756i
$208$	8.69230e9	−	1.24976e9i	0.321996	−	0.0462960i
$209$	−5.42127e8	−	1.84631e9i	−0.0196536	−	0.0669341i
$210$	−5.57077e10	+	1.21983e11i	−1.97664	+	4.32824i
$211$	−1.87898e10	+	8.58102e9i	−0.652607	+	0.298036i	−0.714071	−	0.700074i	$-0.753150\pi$
$211$	−1.87898e10	+	8.58102e9i	−0.652607	+	0.298036i	0.0614637	+	0.998109i	$0.480423\pi$
$212$	−6.95682e9			−0.236537
$213$	−3.59768e10	+	1.64301e10i	−1.19761	+	0.546929i
$214$	2.09221e9	−	1.45516e10i	0.0681935	−	0.474296i
$215$			8.00310e10i			2.55438i
$216$	−3.45403e9	−	5.37458e9i	−0.107965	−	0.167997i
$217$	−4.29740e10	−	1.26183e10i	−1.31564	−	0.386306i
$218$	8.39670e9	+	1.83862e10i	0.251799	+	0.551363i
$219$	−7.20730e9	+	1.03625e9i	−0.211726	+	0.0304416i
$220$	−2.01959e8	−	1.40466e9i	−0.00581248	−	0.0404267i
$221$	−1.07425e9	−	1.67157e9i	−0.0302929	−	0.0471367i
$222$	−1.04572e10	−	1.20683e10i	−0.288954	−	0.333471i
$223$	1.11501e10	+	1.28679e10i	0.301931	+	0.348447i	0.886359	−	0.462999i	$-0.153226\pi$
$223$	1.11501e10	+	1.28679e10i	0.301931	+	0.348447i	−0.584428	+	0.811446i	$0.698681\pi$
$224$	−9.75232e9	−	1.51749e10i	−0.258816	−	0.402726i
$225$	1.68129e10	+	1.16936e11i	0.437341	+	3.04177i
$226$	−4.88231e9	+	7.01970e8i	−0.124491	+	0.0178991i
$227$	−1.30879e10	−	2.86585e10i	−0.327155	−	0.716369i	0.672565	−	0.740038i	$-0.265192\pi$
$227$	−1.30879e10	−	2.86585e10i	−0.327155	−	0.716369i	−0.999720	+	0.0236692i	$0.992465\pi$
$228$	−3.31861e9	−	9.74431e8i	−0.0813296	−	0.0238805i
$229$	2.51802e10	+	3.91812e10i	0.605062	+	0.941495i	0.999743	+	0.0226769i	$0.00721892\pi$
$229$	2.51802e10	+	3.91812e10i	0.605062	+	0.941495i	−0.394681	+	0.918818i	$0.629145\pi$
$230$		−	1.07284e11i		−	2.52791i
$231$	−2.60194e9	+	1.80969e10i	−0.0601233	+	0.418167i
$232$	−3.50360e10	+	1.60004e10i	−0.793997	+	0.362606i
$233$	1.53759e10			0.341774			0.170887	−	0.985291i	$-0.445337\pi$
$233$	1.53759e10			0.341774			0.170887	+	0.985291i	$0.445337\pi$
$234$	−1.68057e10	+	7.67490e9i	−0.366425	+	0.167341i
$235$	2.40017e8	−	5.25563e8i	0.00513377	−	0.0112414i
$236$	1.80188e9	+	6.13664e9i	0.0378113	+	0.128774i
$237$	4.60881e10	−	6.62647e9i	0.948902	−	0.136431i
$238$	6.61996e9	−	1.03009e10i	0.133739	−	0.208102i
$239$	6.64238e10	+	3.03347e10i	1.31684	+	0.601381i	0.945047	−	0.326935i	$-0.106016\pi$
$239$	6.64238e10	+	3.03347e10i	1.31684	+	0.601381i	0.371793	+	0.928316i	$0.378743\pi$
$240$	1.11807e11	+	5.10605e10i	2.17530	+	0.993424i
$241$	−4.80369e10	+	4.16242e10i	−0.917272	+	0.794821i	−0.979124	−	0.203264i	$-0.934845\pi$
$241$	−4.80369e10	+	4.16242e10i	−0.917272	+	0.794821i	0.0618517	+	0.998085i	$0.480299\pi$
$242$	−2.01154e10	−	4.40465e10i	−0.377015	−	0.825548i
$243$	−5.89382e10	−	5.10703e10i	−1.08435	−	0.939594i
$244$	2.23933e9	−	7.62646e9i	0.0404449	−	0.137743i
$245$	3.55297e10	−	2.47114e11i	0.630005	−	4.38178i
$246$	−6.79052e10	+	7.83667e10i	−1.18221	+	1.36434i
$247$	−4.07018e9	+	8.91246e9i	−0.0695789	+	0.152357i
$248$	−1.33733e10	+	4.55451e10i	−0.224494	+	0.764556i
$249$	−3.92691e10	+	2.52367e10i	−0.647373	+	0.416041i
$250$	−1.24969e11	−	1.44222e11i	−2.02336	−	2.33508i
$251$	6.87903e10	−	2.01987e10i	1.09394	−	0.321211i	0.315501	−	0.948925i	$-0.397827\pi$
$251$	6.87903e10	−	2.01987e10i	1.09394	−	0.321211i	0.778444	+	0.627714i	$0.216009\pi$
$252$	1.31742e10	+	1.14155e10i	0.205788	+	0.178317i
$253$	−4.12086e9	−	1.40344e10i	−0.0632333	−	0.215353i
$254$	5.90993e10	+	8.49719e9i	0.890903	+	0.128092i
$255$		−	2.78114e10i		−	0.411900i
$256$	−2.26044e10	+	1.45269e10i	−0.328937	+	0.211395i
$257$	1.06417e11	−	3.12470e10i	1.52165	−	0.446796i	0.589165	−	0.808013i	$-0.299457\pi$
$257$	1.06417e11	−	3.12470e10i	1.52165	−	0.446796i	0.932482	+	0.361217i	$0.117639\pi$
$258$	−1.22902e11	−	3.60873e10i	−1.72691	−	0.507067i
$259$	3.59060e10	+	2.30754e10i	0.495814	+	0.318640i
$260$	−3.90652e9	+	6.07867e9i	−0.0530164	+	0.0824952i
$261$	5.29631e10	−	4.58928e10i	0.706466	−	0.612156i
$262$	6.36563e10	+	4.09094e10i	0.834613	+	0.536374i
$263$	4.71840e9	+	3.28172e10i	0.0608127	+	0.422961i	0.997372	+	0.0724521i	$0.0230824\pi$
$263$	4.71840e9	+	3.28172e10i	0.0608127	+	0.422961i	−0.936559	+	0.350509i	$0.886008\pi$
$264$	1.91796e10	+	2.75761e9i	0.243009	+	0.0349394i
$265$	−1.80635e11	+	2.08464e11i	−2.25007	+	2.59672i
$266$	−6.03783e10			−0.739458
$267$	7.19791e10	+	9.74971e10i	0.866774	+	1.17406i
$268$	1.23879e10			0.146687
$269$	2.32785e10	−	2.68648e10i	0.271062	−	0.312823i	−0.603856	−	0.797094i	$-0.706370\pi$
$269$	2.32785e10	−	2.68648e10i	0.271062	−	0.312823i	0.874918	+	0.484271i	$0.160915\pi$
$270$	−2.93905e10	−	4.22571e9i	−0.336566	−	0.0483908i
$271$	−1.13572e10	−	7.89913e10i	−0.127912	−	0.889646i	−0.948195	−	0.317689i	$-0.897093\pi$
$271$	−1.13572e10	−	7.89913e10i	−0.127912	−	0.889646i	0.820283	−	0.571957i	$-0.193816\pi$
$272$	−9.44156e9	−	6.06772e9i	−0.104588	−	0.0672149i
$273$	7.03546e10	−	6.09626e10i	0.766586	−	0.664251i
$274$	−1.04833e10	+	1.63124e10i	−0.112363	+	0.174840i
$275$	−3.46113e10	−	2.22433e10i	−0.364939	−	0.234532i
$276$	−2.52257e10	−	7.40693e9i	−0.261669	−	0.0768329i
$277$	1.04787e11	−	3.07684e10i	1.06943	−	0.314012i	0.300784	−	0.953692i	$-0.402752\pi$
$277$	1.04787e11	−	3.07684e10i	1.06943	−	0.314012i	0.768641	+	0.639681i	$0.220933\pi$
$278$	1.48442e11	−	9.53980e10i	1.49058	−	0.957939i
$279$		−	8.63668e10i		−	0.853351i
$280$	−3.76009e11	−	5.40620e10i	−3.65584	−	0.525631i
$281$	7.48469e9	+	2.54905e10i	0.0716136	+	0.243894i	0.987519	−	0.157501i	$-0.0503438\pi$
$281$	7.48469e9	+	2.54905e10i	0.0716136	+	0.243894i	−0.915905	+	0.401395i	$0.868526\pi$
$282$	6.98869e8	+	6.05574e8i	0.00658074	+	0.00570225i
$283$	−1.87682e11	+	5.51084e10i	−1.73934	+	0.510715i	−0.988688	−	0.149988i	$-0.952077\pi$
$283$	−1.87682e11	+	5.51084e10i	−1.73934	+	0.510715i	−0.750648	+	0.660703i	$0.770258\pi$
$284$	−8.60011e9	−	9.92505e9i	−0.0784461	−	0.0905316i
$285$	−1.15368e11	+	7.41423e10i	−1.03581	+	0.665678i
$286$	1.81270e9	−	6.17351e9i	0.0160206	−	0.0545613i
$287$	1.15135e11	−	2.52111e11i	1.00171	−	2.19343i
$288$	2.27788e10	−	2.62881e10i	0.195103	−	0.225161i
$289$	1.65154e10	−	1.14867e11i	0.139267	−	0.968626i
$290$	−5.04334e10	+	1.71760e11i	−0.418723	+	1.42604i
$291$	−1.01942e11	−	8.83332e10i	−0.833363	−	0.722113i
$292$	−1.00437e9	−	2.19927e9i	−0.00808487	−	0.0177034i
$293$	1.21338e10	−	1.05140e10i	0.0961819	−	0.0833421i	−0.605443	−	0.795889i	$-0.707004\pi$
$293$	1.21338e10	−	1.05140e10i	0.0961819	−	0.0833421i	0.701624	+	0.712547i	$0.252458\pi$
$294$	3.63467e11	+	1.65990e11i	2.83728	+	1.29574i
$295$	2.30674e11	+	1.05345e11i	1.77337	+	0.809870i
$296$	2.44560e10	−	3.80543e10i	0.185171	−	0.288132i
$297$	−4.00701e9	+	5.76121e8i	−0.0298825	+	0.00429645i
$298$	3.13165e10	+	1.06654e11i	0.230038	+	0.783438i
$299$	−3.09386e10	+	6.77462e10i	−0.223862	+	0.490190i
$300$	−6.72677e10	+	3.07201e10i	−0.479470	+	0.218967i
$301$	3.42365e11			2.40403
$302$	−8.96688e10	+	4.09504e10i	−0.620312	+	0.283287i
$303$	5.67457e10	−	3.94675e11i	0.386760	−	2.68997i
$304$			5.53415e10i			0.371638i
$305$	−1.70386e11	−	2.65125e11i	−1.12742	−	1.75429i
$306$	2.26554e10	+	6.65222e9i	0.147715	+	0.0433730i
$307$	4.64876e10	+	1.01794e11i	0.298686	+	0.654030i	0.998160	−	0.0606270i	$-0.0193100\pi$
$307$	4.64876e10	+	1.01794e11i	0.298686	+	0.654030i	−0.699475	+	0.714657i	$0.746583\pi$
$308$	−6.00899e9	+	8.63962e8i	−0.0380472	+	0.00547037i
$309$	−7.07096e9	−	4.91796e10i	−0.0441230	−	0.306882i
$310$	1.19273e11	+	1.85592e11i	0.733522	+	1.14138i
$311$	−3.27081e10	−	3.77472e10i	−0.198260	−	0.228804i	0.647911	−	0.761716i	$-0.275643\pi$
$311$	−3.27081e10	−	3.77472e10i	−0.198260	−	0.228804i	−0.846170	+	0.532913i	$0.821097\pi$
$312$	−6.46101e10	−	7.45640e10i	−0.386015	−	0.445486i
$313$	2.01858e10	+	3.14097e10i	0.118877	+	0.184976i	0.895592	−	0.444876i	$-0.146752\pi$
$313$	2.01858e10	+	3.14097e10i	0.118877	+	0.184976i	−0.776716	+	0.629851i	$0.783116\pi$
$314$	4.36738e10	+	3.03758e11i	0.253535	+	1.76337i
$315$	6.84140e11	−	9.83645e10i	3.91514	−	0.562913i
$316$	6.42262e9	+	1.40636e10i	0.0362343	+	0.0793421i
$317$	−1.37173e10	−	4.02775e9i	−0.0762959	−	0.0224025i	0.243362	−	0.969936i	$-0.421750\pi$
$317$	−1.37173e10	−	4.02775e9i	−0.0762959	−	0.0224025i	−0.319658	+	0.947533i	$0.603568\pi$
$318$	−2.38683e11	−	3.71398e11i	−1.30888	−	2.03666i
$319$			2.44059e10i			0.131958i
$320$	−5.63888e10	+	3.92192e11i	−0.300620	+	2.09086i
$321$	−1.29936e11	+	5.93396e10i	−0.683054	+	0.311941i
$322$	−4.58953e11			−2.37912
$323$	1.13903e10	−	5.20179e9i	0.0582271	−	0.0265914i
$324$	9.33790e9	−	2.04472e10i	0.0470757	−	0.103081i
$325$	5.90196e10	+	2.01002e11i	0.293441	+	0.999369i
$326$	3.05803e11	−	4.39678e10i	1.49955	−	0.215603i
$327$	1.06180e11	−	1.65219e11i	0.513544	−	0.799090i
$328$	−2.67195e11	−	1.22024e11i	−1.27467	−	0.582120i
$329$	−2.24831e9	−	1.02677e9i	−0.0105797	−	0.00483160i
$330$	6.80602e10	−	5.89745e10i	0.315922	−	0.273748i
$331$	6.42696e9	+	1.40731e10i	0.0294293	+	0.0644412i	0.923776	−	0.382934i	$-0.125086\pi$
$331$	6.42696e9	+	1.40731e10i	0.0294293	+	0.0644412i	−0.894347	+	0.447375i	$0.852359\pi$
$332$	−1.17139e10	−	1.01501e10i	−0.0529150	−	0.0458511i
$333$	−2.31879e10	+	7.89706e10i	−0.103338	+	0.351938i
$334$	4.12004e10	−	2.86555e11i	0.181152	−	1.25994i
$335$	3.21654e11	−	3.71209e11i	1.39536	−	1.61034i
$336$	2.18432e11	−	4.78300e11i	0.934953	−	2.04726i
$337$	7.62606e10	−	2.59720e11i	0.322082	−	1.09691i	−0.626249	−	0.779623i	$-0.715410\pi$
$337$	7.62606e10	−	2.59720e11i	0.322082	−	1.09691i	0.948330	−	0.317285i	$-0.102771\pi$
$338$	1.60422e11	−	1.03097e11i	0.668556	−	0.429655i
$339$	3.13852e10	+	3.62204e10i	0.129070	+	0.148955i
$340$	8.86058e9	−	2.60170e9i	0.0359590	−	0.0105585i
$341$	2.27313e10	+	1.96968e10i	0.0910394	+	0.0788861i
$342$	−3.28020e10	−	1.11713e11i	−0.129653	−	0.441558i
$343$	−5.96538e11	−	8.57691e10i	−2.32710	−	0.334586i
$344$		−	3.62849e11i		−	1.39705i
$345$	−8.76943e11	+	5.63577e11i	−3.33262	+	2.14174i
$346$	4.03948e10	−	1.18610e10i	0.151524	−	0.0444916i
$347$	1.31131e11	+	3.85036e10i	0.485538	+	0.142567i	0.515335	−	0.856989i	$-0.327668\pi$
$347$	1.31131e11	+	3.85036e10i	0.485538	+	0.142567i	−0.0297962	+	0.999556i	$0.509486\pi$
$348$	3.69039e10	+	2.37167e10i	0.134886	+	0.0866857i
$349$	2.09186e11	−	3.25499e11i	0.754775	−	1.17445i	−0.225002	−	0.974358i	$-0.572239\pi$
$349$	2.09186e11	−	3.25499e11i	0.754775	−	1.17445i	0.979777	−	0.200094i	$-0.0641248\pi$
$350$	−9.75632e11	+	8.45390e11i	−3.47520	+	3.01128i
$351$	1.73404e10	+	1.11440e10i	0.0609785	+	0.0391885i
$352$	1.72398e9	+	1.19905e10i	0.00598535	+	0.0416290i
$353$	2.58324e11	+	3.71414e10i	0.885479	+	0.127313i	0.570024	−	0.821628i	$-0.306934\pi$
$353$	2.58324e11	+	3.71414e10i	0.885479	+	0.127313i	0.315455	+	0.948941i	$0.397843\pi$
$354$	−2.65791e11	+	3.06739e11i	−0.899549	+	1.03813i
$355$	−5.20713e11			−1.74009
$356$	−2.43286e10	+	3.20529e10i	−0.0802773	+	0.105765i
$357$	−1.18974e11			−0.387656
$358$	1.82121e11	−	2.10179e11i	0.585985	−	0.676263i
$359$	−3.21180e11	−	4.61786e10i	−1.02052	−	0.146729i	−0.388314	−	0.921527i	$-0.626942\pi$
$359$	−3.21180e11	−	4.61786e10i	−1.02052	−	0.146729i	−0.632209	+	0.774798i	$0.717852\pi$
$360$	−1.04250e11	−	7.25073e11i	−0.327125	−	2.27520i
$361$	2.19519e11	+	1.41076e11i	0.680282	+	0.437191i
$362$	1.84865e11	−	1.60186e11i	0.565803	−	0.490271i
$363$	−2.54368e11	+	3.95804e11i	−0.768921	+	1.19647i
$364$	2.60040e10	+	1.67117e10i	0.0776396	+	0.0498959i
$365$	−9.19811e10	−	2.70081e10i	−0.271257	−	0.0796482i
$366$	4.83977e11	−	1.42108e11i	1.40981	−	0.413957i
$367$	−1.85793e11	+	1.19402e11i	−0.534604	+	0.343569i	−0.779925	−	0.625873i	$-0.784743\pi$
$367$	−1.85793e11	+	1.19402e11i	−0.534604	+	0.343569i	0.245321	+	0.969442i	$0.421107\pi$
$368$			4.20667e11i			1.19570i
$369$	5.29013e11	+	7.60606e10i	1.48541	+	0.213570i
$370$	−5.92306e10	−	2.01721e11i	−0.164300	−	0.559555i
$371$	8.91791e11	+	7.72741e11i	2.44388	+	2.11764i
$372$	5.18726e10	−	1.52312e10i	0.140441	−	0.0412373i
$373$	2.71189e11	+	3.12968e11i	0.725407	+	0.837164i	0.991946	−	0.126660i	$-0.0404256\pi$
$373$	2.71189e11	+	3.12968e11i	0.725407	+	0.837164i	−0.266539	+	0.963824i	$0.585880\pi$
$374$	−6.91760e9	+	4.44567e9i	−0.0182824	+	0.0117494i
$375$	−5.22395e11	+	1.77911e12i	−1.36414	+	4.64582i
$376$	−1.08820e9	+	2.38283e9i	−0.00280778	+	0.00614819i
$377$	8.13789e10	−	9.39163e10i	0.207480	−	0.239445i
$378$	−1.80772e10	+	1.25730e11i	−0.0455426	+	0.316756i
$379$	1.09517e11	−	3.72980e11i	0.272649	−	0.928559i	−0.703361	−	0.710833i	$-0.748318\pi$
$379$	1.09517e11	−	3.72980e11i	0.272649	−	0.928559i	0.976010	−	0.217726i	$-0.0698638\pi$
$380$	−3.44138e10	−	2.98197e10i	−0.0846655	−	0.0733631i
$381$	−2.40999e11	−	5.27714e11i	−0.585939	−	1.28303i
$382$	7.87067e10	−	6.81997e10i	0.189115	−	0.163869i
$383$	3.09382e11	+	1.41290e11i	0.734683	+	0.335519i	0.747376	−	0.664401i	$-0.231313\pi$
$383$	3.09382e11	+	1.41290e11i	0.734683	+	0.335519i	−0.0126932	+	0.999919i	$0.504040\pi$
$384$	−4.27691e11	−	1.95320e11i	−1.00378	−	0.458413i
$385$	−1.30136e11	+	2.02495e11i	−0.301872	+	0.469723i
$386$	4.58410e11	−	6.59094e10i	1.05102	−	0.151114i
$387$	1.85998e11	+	6.33453e11i	0.421512	+	1.43554i
$388$	1.86061e10	−	4.07416e10i	0.0416785	−	0.0912632i
$389$	−5.33763e11	+	2.43761e11i	−1.18188	+	0.539749i	−0.906755	−	0.421659i	$-0.861448\pi$
$389$	−5.33763e11	+	2.43761e11i	−1.18188	+	0.539749i	−0.275130	+	0.961407i	$0.588721\pi$
$390$	−4.58546e11			−1.00367
$391$	8.65812e10	−	3.95403e10i	0.187339	−	0.0855548i
$392$	−1.61086e11	+	1.12038e12i	−0.344565	+	2.39650i
$393$		−	7.35227e11i		−	1.55473i
$394$	3.33694e11	+	5.19238e11i	0.697614	+	1.08551i
$395$	5.88186e11	+	1.72707e11i	1.21570	+	0.356963i
$396$	−4.86306e9	−	1.06486e10i	−0.00993760	−	0.0217603i
$397$	−2.18302e11	+	3.13871e10i	−0.441063	+	0.0634153i	−0.359269	−	0.933234i	$-0.616974\pi$
$397$	−2.18302e11	+	3.13871e10i	−0.441063	+	0.0634153i	−0.0817937	+	0.996649i	$0.526065\pi$
$398$	−2.35249e10	−	1.63619e11i	−0.0469953	−	0.326859i
$399$	3.17173e11	+	4.93531e11i	0.626497	+	0.974848i
$400$	7.74867e11	+	8.94244e11i	1.51341	+	1.74657i
$401$	−2.41639e11	−	2.78867e11i	−0.466679	−	0.538576i	0.472806	−	0.881166i	$-0.343241\pi$
$401$	−2.41639e11	−	2.78867e11i	−0.466679	−	0.538576i	−0.939485	+	0.342591i	$0.888696\pi$
$402$	4.25018e11	+	6.61341e11i	0.811690	+	1.26301i
$403$	−2.17954e10	−	1.51590e11i	−0.0411616	−	0.286285i
$404$	1.31050e11	−	1.88422e10i	0.244749	−	0.0351896i
$405$	−3.70248e11	−	8.10730e11i	−0.683825	−	1.49737i
$406$	7.34774e11	+	2.15749e11i	1.34211	+	0.394078i
$407$	−1.54964e10	−	2.41129e10i	−0.0279935	−	0.0435587i
$408$			1.26093e11i			0.225278i
$409$	−7.09795e10	+	4.93673e11i	−0.125423	+	0.872337i	0.825828	+	0.563921i	$0.190708\pi$
$409$	−7.09795e10	+	4.93673e11i	−0.125423	+	0.872337i	−0.951252	+	0.308416i	$0.900201\pi$
$410$	−1.24183e12	+	5.67123e11i	−2.17037	+	0.991173i
$411$	1.88408e11			0.325694
$412$	1.50069e10	−	6.85343e9i	0.0256599	−	0.0117185i
$413$	4.50656e11	−	9.86799e11i	0.762202	−	1.66899i
$414$	−2.49338e11	−	8.49166e11i	−0.417145	−	1.42066i
$415$	−6.08306e11	+	8.74612e10i	−1.00671	+	0.144744i
$416$	3.33471e10	−	5.18891e10i	0.0545932	−	0.0849486i
$417$	−1.55957e12	−	7.12230e11i	−2.52576	−	1.15347i
$418$	3.68832e10	+	1.68440e10i	0.0590929	+	0.0269868i
$419$	−3.20791e11	+	2.77967e11i	−0.508462	+	0.440585i	−0.870927	−	0.491413i	$-0.836481\pi$
$419$	−3.20791e11	+	2.77967e11i	−0.508462	+	0.440585i	0.362465	+	0.931997i	$0.381935\pi$
$420$	1.79730e11	+	3.93553e11i	0.281837	+	0.617137i
$421$	7.19505e10	+	6.23455e10i	0.111626	+	0.0967243i	0.708885	−	0.705324i	$-0.249198\pi$
$421$	7.19505e10	+	6.23455e10i	0.111626	+	0.0967243i	−0.597260	+	0.802048i	$0.703744\pi$
$422$	1.22629e11	−	4.17636e11i	0.188229	−	0.641050i
$423$	6.78303e8	−	4.71770e9i	0.00103013	−	0.00716471i
$424$	8.18975e11	−	9.45147e11i	1.23062	−	1.42021i
$425$	1.11219e11	−	2.43536e11i	0.165360	−	0.362087i
$426$	2.34798e11	−	7.99647e11i	0.345422	−	1.17640i
$427$	−1.13418e12	+	7.28894e11i	−1.65104	+	1.06106i
$428$	−3.10605e10	−	3.58458e10i	−0.0447417	−	0.0516346i
$429$	−5.99845e10	+	1.76130e10i	−0.0855030	+	0.0251059i
$430$	−1.27449e12	−	1.10435e12i	−1.79774	−	1.55775i
$431$	2.50174e11	+	8.52014e11i	0.349216	+	1.18932i	0.927606	+	0.373561i	$0.121863\pi$
$431$	2.50174e11	+	8.52014e11i	0.349216	+	1.18932i	−0.578389	+	0.815761i	$0.696319\pi$
$432$	1.15241e11	+	1.65692e10i	0.159196	+	0.0228889i
$433$			1.26315e12i			1.72688i	0.504456	+	0.863438i	$0.331693\pi$
$433$			1.26315e12i			1.72688i	−0.504456	+	0.863438i	$0.668307\pi$
$434$	7.93944e11	−	5.10237e11i	1.07420	−	0.690348i
$435$	1.66890e12	−	4.90033e11i	2.23475	−	0.656181i
$436$	6.25710e10	+	1.83725e10i	0.0829247	+	0.0243489i
$437$	−3.94838e11	−	2.53747e11i	−0.517908	−	0.332839i
$438$	8.29515e10	−	1.29075e11i	0.107694	−	0.167575i
$439$	−1.10091e12	+	9.53940e11i	−1.41469	+	1.22583i	−0.476742	+	0.879043i	$0.658182\pi$
$439$	−1.10091e12	+	9.53940e11i	−1.41469	+	1.22583i	−0.937943	+	0.346788i	$0.887272\pi$
$440$	2.14611e11	+	1.37922e11i	0.272969	+	0.175427i
$441$	−2.93093e11	−	2.03851e12i	−0.369004	−	2.56648i
$442$	4.14432e10	+	5.95864e9i	0.0516480	+	0.00742586i
$443$	5.56229e11	−	6.41922e11i	0.686178	−	0.791892i	−0.300638	−	0.953738i	$-0.597200\pi$
$443$	5.56229e11	−	6.41922e11i	0.686178	−	0.791892i	0.986816	+	0.161847i	$0.0517450\pi$
$444$	−5.15197e10			−0.0629144
$445$	3.28781e11	+	1.56128e12i	0.397454	+	1.88739i
$446$	−3.58782e11			−0.429362
$447$	7.07281e11	−	8.16246e11i	0.837931	−	0.967024i
$448$	1.67776e12	+	2.41226e11i	1.96779	+	0.282926i
$449$	8.79892e9	+	6.11978e10i	0.0102169	+	0.0710604i	0.994292	−	0.106693i	$-0.0340262\pi$
$449$	8.79892e9	+	6.11978e10i	0.0102169	+	0.0710604i	−0.984075	+	0.177753i	$0.943117\pi$
$450$	−2.09420e12	−	1.34586e12i	−2.40747	−	1.54719i
$451$	−1.40665e11	+	1.21887e11i	−0.160100	+	0.138728i
$452$	−8.60364e9	+	1.33875e10i	−0.00969526	+	0.0150861i
$453$	8.05768e11	+	5.17836e11i	0.899017	+	0.577763i
$454$	6.36984e11	+	1.87035e11i	0.703683	+	0.206620i
$455$	1.17597e12	−	3.45297e11i	1.28631	−	0.377695i
$456$	5.23060e11	−	3.36150e11i	0.566513	−	0.364076i
$457$			1.09202e12i			1.17114i	0.810622	+	0.585570i	$0.199129\pi$
$457$			1.09202e12i			1.17114i	−0.810622	+	0.585570i	$0.800871\pi$
$458$	−9.71421e11	−	1.39669e11i	−1.03160	−	0.148322i
$459$	−7.42177e9	−	2.52762e10i	−0.00780460	−	0.0265800i
$460$	−2.61589e11	−	2.26668e11i	−0.272402	−	0.236037i
$461$	1.59748e12	−	4.69061e11i	1.64733	−	0.483699i	0.679158	−	0.733992i	$-0.262345\pi$
$461$	1.59748e12	−	4.69061e11i	1.64733	−	0.483699i	0.968170	+	0.250293i	$0.0805268\pi$
$462$	−2.52287e11	−	2.91155e11i	−0.257636	−	0.297328i
$463$	6.36368e10	−	4.08969e10i	0.0643567	−	0.0413596i	−0.508067	−	0.861318i	$-0.669640\pi$
$463$	6.36368e10	−	4.08969e10i	0.0643567	−	0.0413596i	0.572424	+	0.819958i	$0.306003\pi$
$464$	1.97751e11	−	6.73479e11i	0.198056	−	0.674518i
$465$	8.90475e11	−	1.94987e12i	0.883250	−	1.93405i
$466$	−2.12173e11	+	2.44860e11i	−0.208426	+	0.240537i
$467$	1.49750e11	−	1.04154e12i	0.145694	−	1.01332i	−0.777471	−	0.628919i	$-0.783498\pi$
$467$	1.49750e11	−	1.04154e12i	0.145694	−	1.01332i	0.923165	−	0.384404i	$-0.125593\pi$
$468$	−1.67932e10	+	5.71923e10i	−0.0161818	+	0.0551101i
$469$	−1.58799e12	−	1.37601e12i	−1.51555	−	1.31323i
$470$	5.05756e9	+	1.10745e10i	0.00478080	+	0.0104685i
$471$	2.25349e12	−	1.95266e12i	2.10990	−	1.82824i
$472$	−1.04584e12	−	4.77619e11i	−0.969898	−	0.442938i
$473$	−2.09140e11	−	9.55111e10i	−0.192115	−	0.0877362i
$474$	−5.30445e11	+	8.25388e11i	−0.482656	+	0.751027i
$475$	−1.30674e12	+	1.87881e11i	−1.17779	+	0.169341i
$476$	−1.11298e10	−	3.79047e10i	−0.00993704	−	0.0338425i
$477$	−9.45258e11	+	2.06983e12i	−0.836022	+	1.83063i
$478$	−1.39966e12	+	6.39204e11i	−1.22630	+	0.560033i
$479$	−5.06286e11			−0.439427			−0.219713	−	0.975564i	$-0.570512\pi$
$479$	−5.06286e11			−0.439427			−0.219713	+	0.975564i	$0.570512\pi$
$480$	7.85309e11	−	3.58639e11i	0.675235	−	0.308369i
$481$	−2.07702e10	+	1.44460e11i	−0.0176925	+	0.123054i
$482$		−	1.33936e12i		−	1.13028i
$483$	2.41093e12	+	3.75148e12i	2.01568	+	3.13646i
$484$	−1.49897e11	−	4.40137e10i	−0.124162	−	0.0364572i
$485$	−7.37731e11	−	1.61541e12i	−0.605425	−	1.32570i
$486$	1.62658e12	−	2.33867e11i	1.32255	−	0.190154i
$487$	8.17924e10	+	5.68878e11i	0.0658920	+	0.458289i	0.995879	+	0.0906955i	$0.0289090\pi$
$487$	8.17924e10	+	5.68878e11i	0.0658920	+	0.458289i	−0.929987	+	0.367593i	$0.880182\pi$
$488$	7.72504e11	+	1.20204e12i	0.616611	+	0.959466i
$489$	−1.96581e12	−	2.26866e12i	−1.55471	−	1.79424i
$490$	3.44500e12	+	3.97574e12i	2.69965	+	3.11556i
$491$	−3.33457e11	−	5.18869e11i	−0.258925	−	0.402894i	0.687316	−	0.726359i	$-0.258789\pi$
$491$	−3.33457e11	−	5.18869e11i	−0.258925	−	0.402894i	−0.946240	+	0.323464i	$0.895152\pi$
$492$	4.76112e10	+	3.31143e11i	0.0366325	+	0.254784i
$493$	−1.57202e11	+	2.26023e10i	−0.119853	+	0.0172322i
$494$	−8.57656e10	−	1.87801e11i	−0.0647951	−	0.141881i
$495$	−4.45361e11	−	1.30770e11i	−0.333418	−	0.0979004i
$496$	−4.67673e11	−	7.27714e11i	−0.346956	−	0.539875i
$497$			2.22756e12i			1.63767i
$498$	1.39983e11	−	9.73601e11i	0.101986	−	0.709331i
$499$	−7.08470e11	+	3.23547e11i	−0.511528	+	0.233607i	−0.654420	−	0.756131i	$-0.727087\pi$
$499$	−7.08470e11	+	3.23547e11i	−0.511528	+	0.233607i	0.142892	+	0.989738i	$0.454360\pi$
$500$	−6.15686e11			−0.440549
$501$	−2.55873e12	+	1.16853e12i	−1.81449	+	0.828650i
$502$	−6.27577e11	+	1.37420e12i	−0.441063	+	0.965793i
$503$	2.69985e11	+	9.19485e11i	0.188055	+	0.640455i	0.998506	+	0.0546487i	$0.0174039\pi$
$503$	2.69985e11	+	9.19485e11i	0.188055	+	0.640455i	−0.810451	+	0.585806i	$0.800778\pi$
$504$	−3.10179e12	+	4.45970e11i	−2.14129	+	0.307871i
$505$	2.83813e12	−	4.41622e12i	1.94188	−	3.02162i
$506$	2.80360e11	+	1.28036e11i	0.190125	+	0.0868271i
$507$	−1.68543e12	−	7.69708e11i	−1.13285	−	0.517357i
$508$	1.45582e11	−	1.26148e11i	0.0969888	−	0.0840413i
$509$	−6.58661e11	−	1.44227e12i	−0.434943	−	0.952392i	−0.992499	−	0.122253i	$-0.960988\pi$
$509$	−6.58661e11	−	1.44227e12i	−0.434943	−	0.952392i	0.557556	−	0.830139i	$-0.311739\pi$
$510$	4.42894e11	+	3.83770e11i	0.289891	+	0.251192i
$511$	−1.15538e11	+	3.93486e11i	−0.0749602	+	0.255291i
$512$	2.47909e11	−	1.72425e12i	0.159433	−	1.10888i
$513$	−8.50656e10	+	9.81709e10i	−0.0542283	+	0.0625828i
$514$	−9.70851e11	+	2.12587e12i	−0.613506	+	1.34339i
$515$	1.84292e11	−	6.27641e11i	0.115445	−	0.393168i
$516$	−3.47655e11	+	2.23424e11i	−0.215886	+	0.138742i
$517$	1.08698e9	+	1.25444e9i	0.000669136	+	0.000772224i
$518$	−8.62942e11	+	2.53383e11i	−0.526621	+	0.154630i
$519$	−3.09149e11	−	2.67880e11i	−0.187032	−	0.162064i
$520$	−3.65956e11	−	1.24633e12i	−0.219490	−	0.747513i
$521$	−3.08497e12	−	4.43552e11i	−1.83435	−	0.263739i	−0.863659	−	0.504077i	$-0.831833\pi$
$521$	−3.08497e12	−	4.43552e11i	−1.83435	−	0.263739i	−0.970689	+	0.240338i	$0.922742\pi$
$522$			1.47671e12i			0.870518i
$523$	−8.97624e9	+	5.76868e9i	−0.00524610	+	0.00337146i	−0.543261	−	0.839564i	$-0.682811\pi$
$523$	−8.97624e9	+	5.76868e9i	−0.00524610	+	0.00337146i	0.538015	+	0.842935i	$0.319174\pi$
$524$	2.34240e11	−	6.87791e10i	0.135728	−	0.0398534i
$525$	1.20353e13	+	3.53388e12i	6.91417	+	2.03018i
$526$	−5.87721e11	−	3.77705e11i	−0.334761	−	0.215138i
$527$	−1.05819e11	+	1.64657e11i	−0.0597605	+	0.0929891i
$528$	−2.66867e11	+	2.31241e11i	−0.149431	+	0.129483i
$529$	−1.48605e12	−	9.55028e11i	−0.825057	−	0.530232i
$530$	−8.27187e11	−	5.75321e12i	−0.455368	−	3.16715i
$531$	2.07063e12	+	2.97712e11i	1.13026	+	0.162507i
$532$	−1.27566e11	+	1.47219e11i	−0.0690450	+	0.0796822i
$533$	9.47713e11			0.508633
$534$	−2.54588e12	−	1.99103e11i	−1.35488	−	0.105960i
$535$	−1.88063e12			−0.992456
$536$	−1.45833e12	+	1.68301e12i	−0.763159	+	0.880733i
$537$	−2.67470e12	−	3.84564e11i	−1.38801	−	0.199565i
$538$	1.06600e11	+	7.41416e11i	0.0548574	+	0.381542i
$539$	6.03367e11	+	3.87760e11i	0.307916	+	0.197885i
$540$	−7.23990e10	+	6.27341e10i	−0.0366405	+	0.0317491i
$541$	−2.82306e11	+	4.39277e11i	−0.141688	+	0.220471i	−0.904844	−	0.425744i	$-0.860013\pi$
$541$	−2.82306e11	+	4.39277e11i	−0.141688	+	0.220471i	0.763156	+	0.646215i	$0.223649\pi$
$542$	1.41465e12	+	9.09139e11i	0.704128	+	0.452516i
$543$	−2.28048e12	−	6.69608e11i	−1.12571	−	0.330538i
$544$	−7.56363e10	+	2.22088e10i	−0.0370284	+	0.0108725i
$545$	2.17521e12	−	1.39792e12i	1.05613	−	0.678733i
$546$			1.96162e12i			0.944599i
$547$	−1.74168e12	−	2.50415e11i	−0.831810	−	0.119596i	−0.286763	−	0.958002i	$-0.592579\pi$
$547$	−1.74168e12	−	2.50415e11i	−0.831810	−	0.119596i	−0.545047	+	0.838405i	$0.683488\pi$
$548$	1.76252e10	+	6.00258e10i	0.00834874	+	0.0284332i
$549$	−1.96479e12	−	1.70250e12i	−0.923083	−	0.799856i
$550$	8.31826e11	−	2.44246e11i	0.387615	−	0.113814i
$551$	5.12844e11	+	5.91853e11i	0.237030	+	0.273547i
$552$	3.97593e12	−	2.55517e12i	1.82269	−	1.17137i
$553$	7.38824e11	−	2.51620e12i	0.335952	−	1.14415i
$554$	−9.55981e11	+	2.09331e12i	−0.431177	+	0.944145i
$555$	−1.33772e12	+	1.54381e12i	−0.598476	+	0.690678i
$556$	8.10188e10	−	5.63498e11i	0.0359542	−	0.250067i
$557$	−2.43407e11	+	8.28969e11i	−0.107148	+	0.364913i	−0.995559	−	0.0941351i	$-0.969991\pi$
$557$	−2.43407e11	+	8.28969e11i	−0.107148	+	0.364913i	0.888411	+	0.459049i	$0.151810\pi$
$558$	1.37538e12	+	1.19178e12i	0.600579	+	0.520405i
$559$	4.86320e11	+	1.06489e12i	0.210654	+	0.461267i
$560$	5.23182e12	−	4.53340e12i	2.24805	−	1.94795i
$561$	7.26778e10	+	3.31908e10i	0.0309791	+	0.0141477i
$562$	−5.09216e11	−	2.32551e11i	−0.215322	−	0.0983343i
$563$	−1.86662e12	+	2.90451e12i	−0.783010	+	1.21839i	0.188660	+	0.982042i	$0.439586\pi$
$563$	−1.86662e12	+	2.90451e12i	−0.783010	+	1.21839i	−0.971669	+	0.236344i	$0.924051\pi$
$564$	2.95311e9	−	4.24593e8i	0.00122892	−	0.000176692i
$565$	1.77768e11	+	6.05422e11i	0.0733898	+	0.249943i
$566$	1.71223e12	−	3.74926e12i	0.701275	−	1.53558i
$567$	−3.46822e12	+	1.58388e12i	−1.40923	+	0.643576i
$568$	2.36083e12			0.951696
$569$	−8.41140e10	+	3.84136e10i	−0.0336405	+	0.0153631i	−0.432164	−	0.901795i	$-0.642250\pi$
$569$	−8.41140e10	+	3.84136e10i	−0.0336405	+	0.0153631i	0.398524	+	0.917158i	$0.369523\pi$
$570$	4.11251e11	−	2.86031e12i	0.163181	−	1.13495i
$571$			6.51807e10i			0.0256600i	0.999918	+	0.0128300i	$0.00408403\pi$
$571$			6.51807e10i			0.0256600i	−0.999918	+	0.0128300i	$0.995916\pi$
$572$	−1.12229e10	−	1.74631e10i	−0.00438351	−	0.00682087i
$573$	−9.70918e11	−	2.85087e11i	−0.376259	−	0.110480i
$574$	2.42610e12	+	5.31241e12i	0.932834	+	2.04262i
$575$	−9.93291e12	+	1.42814e12i	−3.78940	+	0.544834i
$576$	4.65165e11	+	3.23529e12i	0.176078	+	1.22465i
$577$	2.08852e12	+	3.24980e12i	0.784418	+	1.22058i	0.971221	+	0.238181i	$0.0765512\pi$
$577$	2.08852e12	+	3.24980e12i	0.784418	+	1.22058i	−0.186803	+	0.982397i	$0.559812\pi$
$578$	1.60136e12	+	1.84806e12i	0.596778	+	0.688718i
$579$	−2.94682e12	−	3.40081e12i	−1.08968	−	1.25756i
$580$	3.12245e11	+	4.85862e11i	0.114569	+	0.178274i
$581$	3.74151e11	+	2.60228e12i	0.136224	+	0.947460i
$582$	2.81340e12	−	4.04506e11i	1.01643	−	0.146141i
$583$	−3.29192e11	−	7.20831e11i	−0.118016	−	0.258419i
$584$	4.17029e11	+	1.22451e11i	0.148357	+	0.0435616i
$585$	1.27776e12	+	1.98823e12i	0.451072	+	0.701882i
$586$			3.38313e11i			0.118517i
$587$	6.93455e11	−	4.82309e12i	0.241072	−	1.67669i	−0.405698	−	0.914007i	$-0.632971\pi$
$587$	6.93455e11	−	4.82309e12i	0.241072	−	1.67669i	0.646770	−	0.762685i	$-0.276120\pi$
$588$	1.17266e12	−	5.35534e11i	0.404550	−	0.184752i
$589$	9.65133e11			0.330422
$590$	−4.86068e12	+	2.21980e12i	−1.65144	+	0.754188i
$591$	2.49132e12	−	5.45522e12i	0.840011	−	1.83937i
$592$	2.32246e11	+	7.90956e11i	0.0777141	+	0.264670i
$593$	4.61849e12	−	6.64039e11i	1.53375	−	0.220520i	0.676895	−	0.736080i	$-0.263325\pi$
$593$	4.61849e12	−	6.64039e11i	1.53375	−	0.220520i	0.856853	+	0.515560i	$0.172416\pi$
$594$	4.61182e10	−	7.17613e10i	0.0151996	−	0.0236511i
$595$	−1.42482e12	−	6.50694e11i	−0.466051	−	0.212839i
$596$	3.26217e11	+	1.48978e11i	0.105901	+	0.0483632i
$597$	−1.21384e12	+	1.05180e12i	−0.391092	+	0.338883i
$598$	−6.51930e11	−	1.42753e12i	−0.208471	−	0.456488i
$599$	2.64476e11	+	2.29170e11i	0.0839393	+	0.0727338i	0.695820	−	0.718216i	$-0.255041\pi$
$599$	2.64476e11	+	2.29170e11i	0.0839393	+	0.0727338i	−0.611881	+	0.790950i	$0.709587\pi$
$600$	3.74532e12	−	1.27554e13i	1.17980	−	4.01803i
$601$	1.08275e11	−	7.53069e11i	0.0338527	−	0.235450i	−0.965869	−	0.259030i	$-0.916597\pi$
$601$	1.08275e11	−	7.53069e11i	0.0338527	−	0.235450i	0.999722	+	0.0235795i	$0.00750628\pi$
$602$	−4.72430e12	+	5.45213e12i	−1.46607	+	1.69193i
$603$	1.68320e12	−	3.68570e12i	0.518452	−	1.13525i
$604$	−8.96020e10	+	3.05157e11i	−0.0273938	+	0.0932946i
$605$	−5.21100e12	+	3.34890e12i	−1.58133	+	1.01626i
$606$	5.50213e12	+	6.34980e12i	1.65731	+	1.91264i
$607$	2.08197e12	−	6.11323e11i	0.622481	−	0.182777i	0.0447423	−	0.998999i	$-0.485753\pi$
$607$	2.08197e12	−	6.11323e11i	0.622481	−	0.182777i	0.577739	+	0.816222i	$0.303935\pi$
$608$	2.93765e11	+	2.54549e11i	0.0871835	+	0.0755450i
$609$	−2.09631e12	−	7.13939e12i	−0.617559	−	2.10321i
$610$	6.57326e12	+	9.45092e11i	1.92219	+	0.276369i
$611$		−	8.45164e9i		−	0.00245333i
$612$	6.40857e10	−	4.11854e10i	0.0184663	−	0.0118676i
$613$	−4.47241e12	+	1.31322e12i	−1.27929	+	0.375634i	−0.849641	−	0.527361i	$-0.823182\pi$
$613$	−4.47241e12	+	1.31322e12i	−1.27929	+	0.375634i	−0.429651	+	0.902995i	$0.641363\pi$
$614$	−2.26254e12	−	6.64341e11i	−0.642448	−	0.188640i
$615$	1.11591e13	+	7.17151e12i	3.14551	+	2.02150i
$616$	5.90016e11	−	9.18083e11i	0.165101	−	0.256903i
$617$	−2.24269e12	+	1.94330e12i	−0.622997	+	0.539830i	−0.908146	−	0.418653i	$-0.862502\pi$
$617$	−2.24269e12	+	1.94330e12i	−0.622997	+	0.539830i	0.285150	+	0.958483i	$0.407957\pi$
$618$	8.80754e11	+	5.66026e11i	0.242888	+	0.156095i
$619$	−5.83202e10	−	4.05626e11i	−0.0159665	−	0.111050i	0.980280	−	0.197616i	$-0.0633198\pi$
$619$	−5.83202e10	−	4.05626e11i	−0.0159665	−	0.111050i	−0.996246	+	0.0865659i	$0.972411\pi$
$620$	7.04521e11	+	1.01295e11i	0.191484	+	0.0275312i
$621$	−6.46608e11	+	7.46226e11i	−0.174473	+	0.201353i
$622$	1.05246e12			0.281935
$623$	6.67900e12	−	1.40650e12i	1.77630	−	0.374061i
$624$	1.79798e12			0.474738
$625$	−9.19113e12	+	1.06071e13i	−2.40940	+	2.78060i
$626$	−7.78742e11	−	1.11966e11i	−0.202679	−	0.0291409i
$627$	−5.60687e10	−	3.89967e11i	−0.0144883	−	0.100768i
$628$	8.32919e11	+	5.35285e11i	0.213690	+	0.137330i
$629$	1.40964e11	−	1.22146e11i	0.0359071	−	0.0311136i
$630$	−7.87402e12	+	1.22522e13i	−1.99143	+	3.09872i
$631$	−4.42490e10	−	2.84371e10i	−0.0111115	−	0.00714091i	0.535073	−	0.844806i	$-0.320284\pi$
$631$	−4.42490e10	−	2.84371e10i	−0.0111115	−	0.00714091i	−0.546185	+	0.837665i	$0.683920\pi$
$632$	−2.66675e12	−	7.83028e11i	−0.664898	−	0.195232i
$633$	−4.05794e12	+	1.19152e12i	−1.00459	+	0.294974i
$634$	2.53427e11	−	1.62867e11i	0.0622946	−	0.0400343i
$635$		−	7.63789e12i		−	1.86420i
$636$	−1.40986e12	−	2.02707e11i	−0.341678	−	0.0491259i
$637$	−1.02887e12	−	3.50400e12i	−0.247589	−	0.843212i
$638$	−3.88662e11	−	3.36778e11i	−0.0928709	−	0.0804731i
$639$	−4.12149e12	+	1.21018e12i	−0.977913	+	0.287141i
$640$	−4.05373e12	−	4.67825e12i	−0.955091	−	1.10223i
$641$	3.47501e12	−	2.23326e12i	0.813009	−	0.522489i	−0.0668279	−	0.997765i	$-0.521288\pi$
$641$	3.47501e12	−	2.23326e12i	0.813009	−	0.522489i	0.879837	+	0.475275i	$0.157651\pi$
$642$	8.48006e11	−	2.88804e12i	0.197011	−	0.670959i
$643$	−5.11192e11	+	1.11935e12i	−0.117933	+	0.258237i	−0.959388	−	0.282090i	$-0.908972\pi$
$643$	−5.11192e11	+	1.11935e12i	−0.117933	+	0.258237i	0.841455	+	0.540327i	$0.181699\pi$
$644$	−9.69666e11	+	1.11905e12i	−0.222145	+	0.256368i
$645$	−2.33193e12	+	1.62189e13i	−0.530514	+	3.68980i
$646$	−7.43373e10	+	2.53170e11i	−0.0167943	+	0.0571960i
$647$	−8.70362e11	−	7.54173e11i	−0.195268	−	0.169201i	0.551739	−	0.834017i	$-0.313964\pi$
$647$	−8.70362e11	−	7.54173e11i	−0.195268	−	0.169201i	−0.747007	+	0.664816i	$0.768510\pi$
$648$	1.67865e12	+	3.67573e12i	0.374001	+	0.818947i
$649$	−5.50584e11	+	4.77084e11i	−0.121821	+	0.105559i
$650$	−4.01536e12	−	1.83375e12i	−0.882296	−	0.402931i
$651$	−8.34135e12	−	3.80937e12i	−1.82021	−	0.831263i
$652$	5.38888e11	−	8.38526e11i	0.116784	−	0.181720i
$653$	6.12326e11	−	8.80392e10i	0.131787	−	0.0189482i	−0.0761055	−	0.997100i	$-0.524249\pi$
$653$	6.12326e11	−	8.80392e10i	0.131787	−	0.0189482i	0.207893	+	0.978152i	$0.433339\pi$
$654$	1.16592e12	+	3.97077e12i	0.249213	+	0.848741i
$655$	4.02110e12	−	8.80498e12i	0.853609	−	1.86914i
$656$	4.86925e12	−	2.22371e12i	1.02658	−	0.468825i
$657$	−7.90807e11			−0.165587
$658$	4.73757e10	−	2.16358e10i	0.00985233	−	0.00449941i
$659$	1.97123e11	−	1.37102e12i	0.0407149	−	0.283178i	−0.959285	−	0.282441i	$-0.908856\pi$
$659$	1.97123e11	−	1.37102e12i	0.0407149	−	0.283178i	1.00000		0.000737953i	$-0.000234898\pi$
$660$		−	2.90550e11i		−	0.0596036i
$661$	3.41319e12	+	5.31103e12i	0.695431	+	1.08211i	0.991894	+	0.127067i	$0.0405563\pi$
$661$	3.41319e12	+	5.31103e12i	0.695431	+	1.08211i	−0.296464	+	0.955044i	$0.595807\pi$
$662$	−3.12799e11	−	9.18460e10i	−0.0633000	−	0.0185866i
$663$	−1.69000e11	−	3.70058e11i	−0.0339684	−	0.0743805i
$664$	2.75797e12	−	3.96537e11i	0.550597	−	0.0791638i
$665$	1.09921e12	+	7.64515e12i	0.217962	+	1.51596i
$666$	−9.37631e11	−	1.45898e12i	−0.184671	−	0.287353i
$667$	3.89828e12	+	4.49885e12i	0.762617	+	0.880106i
$668$	−6.11654e11	−	7.05886e11i	−0.118853	−	0.137164i
$669$	1.88472e12	+	2.93268e12i	0.363772	+	0.566040i
$670$	1.47296e12	+	1.02446e13i	0.282393	+	1.96408i
$671$	8.96179e11	−	1.28851e11i	0.170665	−	0.0245379i
$672$	−1.53422e12	−	3.35948e12i	−0.290219	−	0.635492i
$673$	7.34291e11	+	2.15607e11i	0.137975	+	0.0405131i	0.349991	−	0.936753i	$-0.386185\pi$
$673$	7.34291e11	+	2.15607e11i	0.137975	+	0.0405131i	−0.212016	+	0.977266i	$0.568003\pi$
$674$	3.08370e12	+	4.79833e12i	0.575575	+	0.895613i
$675$			2.77736e12i			0.514950i
$676$	8.75572e10	−	6.08973e11i	0.0161262	−	0.112160i
$677$	7.64780e11	−	3.49263e11i	0.139922	−	0.0639005i	−0.344223	−	0.938888i	$-0.611858\pi$
$677$	7.64780e11	−	3.49263e11i	0.139922	−	0.0639005i	0.484146	+	0.874987i	$0.339130\pi$
$678$	−1.00989e12			−0.183545
$679$	−6.91055e12	+	3.15594e12i	−1.24767	+	0.569790i
$680$	−6.89625e11	+	1.51007e12i	−0.123687	+	0.270836i
$681$	−1.81732e12	−	6.18922e12i	−0.323794	−	1.10274i
$682$	−6.27339e11	+	9.01978e10i	−0.111038	+	0.0159649i
$683$	2.79686e12	−	4.35200e12i	0.491788	−	0.765237i	−0.503313	−	0.864104i	$-0.667886\pi$
$683$	2.79686e12	−	4.35200e12i	0.491788	−	0.765237i	0.995101	+	0.0988674i	$0.0315220\pi$
$684$	−3.41692e11	−	1.56045e11i	−0.0596873	−	0.0272583i
$685$	2.25634e12	+	1.03044e12i	0.391559	+	0.178819i
$686$	9.59750e12	−	8.31628e12i	1.65463	−	1.43374i
$687$	3.96132e12	+	8.67408e12i	0.678476	+	1.48566i
$688$	4.99732e12	+	4.33020e12i	0.850333	+	0.736818i
$689$	−1.13677e12	+	3.87148e12i	−0.192170	+	0.654472i
$690$	3.12604e12	−	2.17421e13i	0.525017	−	3.65157i
$691$	2.73540e12	−	3.15682e12i	0.456426	−	0.526743i	−0.480160	−	0.877181i	$-0.659422\pi$
$691$	2.73540e12	−	3.15682e12i	0.456426	−	0.526743i	0.936586	+	0.350437i	$0.113967\pi$
$692$	5.64249e10	−	1.23553e11i	0.00935391	−	0.0204822i
$693$	−5.59421e11	+	1.90521e12i	−0.0921381	+	0.313794i
$694$	−2.42265e12	+	1.55694e12i	−0.396436	+	0.254774i
$695$	−1.47818e13	−	1.70591e13i	−2.40323	−	2.77348i
$696$	−7.56655e12	+	2.22174e12i	−1.22224	+	0.358882i
$697$	−9.15363e11	−	7.93167e11i	−0.146908	−	0.127297i
$698$	2.29699e12	+	7.82284e12i	0.366277	+	1.24743i
$699$	3.11605e12	+	4.48021e11i	0.493694	+	0.0709824i
$700$			4.16498e12i			0.655650i
$701$	−1.02860e13	+	6.61038e12i	−1.60884	+	1.03394i	−0.646200	+	0.763168i	$0.723643\pi$
$701$	−1.02860e13	+	6.61038e12i	−1.60884	+	1.03394i	−0.962643	+	0.270773i	$0.912721\pi$
$702$	−4.16748e11	+	1.22368e11i	−0.0647673	+	0.0190174i
$703$	−8.82482e11	−	2.59120e11i	−0.136272	−	0.0400131i
$704$	−9.57597e11	−	6.15410e11i	−0.146928	−	0.0944252i
$705$	6.39551e10	−	9.95161e10i	0.00975044	−	0.0151720i
$706$	−4.15609e12	+	3.60127e12i	−0.629599	+	0.545551i
$707$	−1.88922e13	−	1.21413e13i	−2.84377	−	1.82758i
$708$	1.86357e11	+	1.29614e12i	0.0278738	+	0.193867i
$709$	−2.06569e12	−	2.97002e11i	−0.307014	−	0.0441419i	−0.0129138	−	0.999917i	$-0.504111\pi$
$709$	−2.06569e12	−	2.97002e11i	−0.307014	−	0.0441419i	−0.294100	+	0.955775i	$0.595020\pi$
$710$	7.18533e12	−	8.29231e12i	1.06117	−	1.22465i
$711$	5.05693e12			0.742119
$712$	−1.49065e12	−	7.07861e12i	−0.217378	−	1.03226i
$713$	7.33626e12			1.06309
$714$	1.64173e12	−	1.89466e12i	0.236407	−	0.272828i
$715$	−8.14695e11	−	1.17135e11i	−0.116578	−	0.0167614i
$716$	−1.27693e11	−	8.88124e11i	−0.0181576	−	0.126289i
$717$	1.25774e13	+	8.08302e12i	1.77728	+	1.14219i
$718$	5.16736e12	−	4.47754e12i	0.725619	−	0.628752i
$719$	1.59896e12	−	2.48803e12i	0.223130	−	0.347197i	−0.711582	−	0.702603i	$-0.752021\pi$
$719$	1.59896e12	−	2.48803e12i	0.223130	−	0.347197i	0.934712	+	0.355406i	$0.115657\pi$
$720$	1.12301e13	+	7.21717e12i	1.55736	+	1.00085i
$721$	−2.68499e12	−	7.88383e11i	−0.370027	−	0.108650i
$722$	−5.27577e12	+	1.54911e12i	−0.722551	+	0.212160i
$723$	−1.09479e13	+	7.03579e12i	−1.49008	+	0.957614i
$724$		−	7.89190e11i		−	0.106748i
$725$	1.65737e13	+	2.38294e12i	2.22792	+	0.320326i
$726$	−2.79312e12	−	9.51249e12i	−0.373142	−	1.27081i
$727$	−6.55803e12	−	5.68257e12i	−0.870700	−	0.754466i	0.0999421	−	0.994993i	$-0.468134\pi$
$727$	−6.55803e12	−	5.68257e12i	−0.870700	−	0.754466i	−0.970642	+	0.240527i	$0.922680\pi$
$728$	−5.33169e12	+	1.56553e12i	−0.703516	+	0.206571i
$729$	−6.19433e12	−	7.14864e12i	−0.812308	−	0.937453i
$730$	1.69935e12	−	1.09211e12i	0.221478	−	0.142335i
$731$	4.21517e11	−	1.43556e12i	0.0545993	−	0.185948i
$732$	6.76037e11	−	1.48031e12i	0.0870303	−	0.190570i
$733$	6.25164e12	−	7.21477e12i	0.799882	−	0.923113i	−0.198493	−	0.980102i	$-0.563605\pi$
$733$	6.25164e12	−	7.21477e12i	0.799882	−	0.923113i	0.998375	+	0.0569894i	$0.0181501\pi$
$734$	6.62297e11	−	4.60637e12i	0.0842210	−	0.585770i
$735$	1.44007e13	−	4.90444e13i	1.82009	−	6.19864i
$736$	2.23300e12	+	1.93490e12i	0.280503	+	0.243057i
$737$	5.86187e11	+	1.28357e12i	0.0731867	+	0.160257i
$738$	−8.51112e12	+	7.37493e12i	−1.05617	+	0.915175i
$739$	4.83547e12	+	2.20828e12i	0.596401	+	0.272367i	0.690659	−	0.723180i	$-0.257321\pi$
$739$	4.83547e12	+	2.20828e12i	0.596401	+	0.272367i	−0.0942578	+	0.995548i	$0.530048\pi$
$740$	−6.16993e11	−	2.81771e11i	−0.0756375	−	0.0345425i
$741$	−1.08454e12	+	1.68758e12i	−0.132149	+	0.205629i
$742$	−2.46117e13	+	3.53863e12i	−2.98074	+	0.428565i
$743$	1.65514e12	+	5.63689e12i	0.199244	+	0.678563i	0.997127	+	0.0757502i	$0.0241352\pi$
$743$	1.65514e12	+	5.63689e12i	0.199244	+	0.678563i	−0.797883	+	0.602813i	$0.794047\pi$
$744$	−4.03728e12	+	8.84042e12i	−0.483071	+	1.05778i
$745$	1.29345e13	−	5.90699e12i	1.53832	−	0.702527i
$746$	−8.72614e12			−1.03157
$747$	−4.61153e12	+	2.10602e12i	−0.541879	+	0.247468i
$748$	−3.77558e9	+	2.62598e10i	−0.000440988	+	0.00306714i
$749$			8.04515e12i			0.934041i
$750$	−2.11237e13	−	3.28691e13i	−2.43778	−	3.79326i
$751$	−7.66597e12	−	2.25093e12i	−0.879402	−	0.258216i	−0.189293	−	0.981921i	$-0.560620\pi$
$751$	−7.66597e12	−	2.25093e12i	−0.879402	−	0.258216i	−0.690110	+	0.723705i	$0.742438\pi$
$752$	−1.98309e10	−	4.34236e10i	−0.00226132	−	0.00495160i
$753$	1.45294e13	−	2.08902e12i	1.64692	−	0.236791i
$754$	3.72660e11	+	2.59191e12i	0.0419896	+	0.292044i
$755$	6.81762e12	+	1.06084e13i	0.763610	+	1.18820i
$756$	2.68371e11	+	3.09716e11i	0.0298804	+	0.0344838i
$757$	−5.30994e12	−	6.12800e12i	−0.587703	−	0.678246i	0.381539	−	0.924353i	$-0.375394\pi$
$757$	−5.30994e12	−	6.12800e12i	−0.587703	−	0.678246i	−0.969243	+	0.246107i	$0.920849\pi$
$758$	4.42846e12	+	6.89081e12i	0.487238	+	0.758157i
$759$	−4.26195e11	−	2.96425e12i	−0.0466144	−	0.324210i
$760$	8.10256e12	−	1.16497e12i	0.880970	−	0.126664i
$761$	4.19149e12	+	9.17809e12i	0.453041	+	0.992022i	0.989019	+	0.147790i	$0.0472158\pi$
$761$	4.19149e12	+	9.17809e12i	0.453041	+	0.992022i	−0.535978	+	0.844232i	$0.680057\pi$
$762$	1.17293e13	+	3.44405e12i	1.26031	+	0.370060i
$763$	−5.98018e12	−	9.30534e12i	−0.638784	−	0.993967i
$764$		−	3.36000e11i		−	0.0356795i
$765$	4.29861e11	−	2.98975e12i	0.0453786	−	0.315615i
$766$	−6.51920e12	+	2.97722e12i	−0.684171	+	0.312450i
$767$	3.70948e12			0.387021
$768$	−5.00424e12	+	2.28536e12i	−0.519054	+	0.237044i
$769$	−4.13809e12	+	9.06115e12i	−0.426709	+	0.934361i	0.567141	+	0.823621i	$0.308050\pi$
$769$	−4.13809e12	+	9.06115e12i	−0.426709	+	0.934361i	−0.993849	+	0.110741i	$0.964678\pi$
$770$	−1.42897e12	−	4.86664e12i	−0.146493	−	0.498908i
$771$	2.24768e13	−	3.23168e12i	2.29082	−	0.329370i
$772$	8.07814e11	−	1.25698e12i	0.0818528	−	0.127365i
$773$	1.10555e12	+	5.04886e11i	0.111370	+	0.0508611i	0.470321	−	0.882495i	$-0.344138\pi$
$773$	1.10555e12	+	5.04886e11i	0.111370	+	0.0508611i	−0.358951	+	0.933356i	$0.616865\pi$
$774$	−1.26543e13	−	5.77902e12i	−1.26737	−	0.578788i
$775$	1.55953e13	−	1.35134e13i	1.55287	−	1.34557i
$776$	3.34476e12	+	7.32401e12i	0.331122	+	0.725056i
$777$	6.60428e12	+	5.72264e12i	0.650026	+	0.563251i
$778$	3.48353e12	−	1.18638e13i	0.340887	−	1.16096i
$779$	−8.49963e11	+	5.91162e12i	−0.0826954	+	0.575159i
$780$	−9.68807e11	+	1.11806e12i	−0.0937156	+	0.108154i
$781$	6.21432e11	−	1.36075e12i	0.0597674	−	0.130872i
$782$	−5.65060e11	+	1.92442e12i	−0.0540336	+	0.184022i
$783$	1.38600e12	−	8.90728e11i	0.131776	−	0.0846871i
$784$	−1.35080e13	−	1.55891e13i	−1.27693	−	1.47366i
$785$	3.76670e13	−	1.10600e13i	3.54036	−	1.03954i
$786$	1.17084e13	+	1.01454e13i	1.09420	+	0.948132i
$787$	−5.70187e11	−	1.94188e12i	−0.0529823	−	0.180441i	0.928751	−	0.370705i	$-0.120884\pi$
$787$	−5.70187e11	−	1.94188e12i	−0.0529823	−	0.180441i	−0.981733	+	0.190264i	$0.939066\pi$
$788$	1.97107e12	+	2.83397e11i	0.182110	+	0.0261834i
$789$			6.78815e12i			0.623599i
$790$	−1.08667e13	+	6.98363e12i	−0.992607	+	0.637910i
$791$	2.58994e12	−	7.60474e11i	0.235231	−	0.0690702i
$792$	2.01920e12	+	5.92892e11i	0.182355	+	0.0535442i
$793$	−3.87822e12	−	2.49238e12i	−0.348260	−	0.223813i
$794$	2.51252e12	−	3.90955e12i	0.224345	−	0.349088i
$795$	−4.26814e13	+	3.69837e13i	−3.78954	+	3.28366i
$796$	−4.48652e11	−	2.88331e11i	−0.0396097	−	0.0254556i
$797$	1.99757e12	+	1.38934e13i	0.175363	+	1.21968i	0.867324	+	0.497744i	$0.165838\pi$
$797$	1.99757e12	+	1.38934e13i	0.175363	+	1.21968i	−0.691961	+	0.721935i	$0.743253\pi$
$798$	−1.22361e13	−	1.75929e12i	−1.06815	−	0.153576i
$799$	−7.07341e9	+	8.16315e9i	−0.000614000	+	0.000708593i
$800$	8.31094e12			0.717373
$801$	6.23087e12	+	1.15936e13i	0.534814	+	0.995108i
$802$	7.77532e12			0.663641
$803$	1.80351e11	−	2.08136e11i	0.0153073	−	0.0176656i
$804$	2.51050e12	+	3.60956e11i	0.211889	+	0.0304650i
$805$	8.35538e12	+	5.81130e13i	0.701269	+	4.87744i
$806$	2.71482e12	+	1.74471e12i	0.226586	+	0.145618i
$807$	5.50035e12	−	4.76608e12i	0.456520	−	0.395577i
$808$	−1.28677e13	+	2.00225e13i	−1.06206	+	1.65260i
$809$	9.83487e12	+	6.32049e12i	0.807236	+	0.518779i	0.877970	−	0.478716i	$-0.158898\pi$
$809$	9.83487e12	+	6.32049e12i	0.807236	+	0.518779i	−0.0707339	+	0.997495i	$0.522534\pi$
$810$	1.80199e13	+	5.29111e12i	1.47085	+	0.431881i
$811$	8.08941e12	−	2.37526e12i	0.656633	−	0.192805i	0.0635908	−	0.997976i	$-0.479745\pi$
$811$	8.08941e12	−	2.37526e12i	0.656633	−	0.192805i	0.593043	+	0.805171i	$0.297927\pi$
$812$	2.07847e12	−	1.33575e12i	0.167781	−	0.107826i
$813$		−	1.63391e13i		−	1.31166i
$814$	5.97832e11	+	8.59553e10i	0.0477276	+	0.00686219i
$815$	−1.11345e13	−	3.79205e13i	−0.884016	−	3.01068i
$816$	−1.73661e12	−	1.50478e12i	−0.137118	−	0.118814i
$817$	−7.07872e12	+	2.07850e12i	−0.555847	+	0.163211i
$818$	−6.88226e12	−	7.94255e12i	−0.537454	−	0.620255i
$819$	8.50544e12	−	5.46611e12i	0.660571	−	0.424523i
$820$	−1.24090e12	+	4.22612e12i	−0.0958461	+	0.326422i
$821$	−1.39456e12	+	3.05366e12i	−0.107125	+	0.234572i	−0.955602	−	0.294661i	$-0.904793\pi$
$821$	−1.39456e12	+	3.05366e12i	−0.107125	+	0.234572i	0.848476	+	0.529233i	$0.177520\pi$
$822$	−2.59984e12	+	3.00038e12i	−0.198620	+	0.229220i
$823$	−1.25977e10	+	8.76192e10i	−0.000957180	+	0.00665733i	−0.990294	−	0.138985i	$-0.955616\pi$
$823$	−1.25977e10	+	8.76192e10i	−0.000957180	+	0.00665733i	0.989337	+	0.145643i	$0.0465250\pi$
$824$	−8.35553e11	+	2.84563e12i	−0.0631395	+	0.215033i
$825$	−6.36613e12	−	5.51629e12i	−0.478446	−	0.414576i
$826$	9.49609e12	+	2.07935e13i	0.709798	+	1.55424i
$827$	−1.53685e13	+	1.33169e13i	−1.14250	+	0.989983i	−0.142501	+	0.989795i	$0.545514\pi$
$827$	−1.53685e13	+	1.33169e13i	−1.14250	+	0.989983i	−1.00000		0.000187909i	$0.999940\pi$
$828$	−2.59730e12	−	1.18615e12i	−0.192037	−	0.0877005i
$829$	1.29832e13	+	5.92923e12i	0.954742	+	0.436016i	0.830984	−	0.556296i	$-0.187778\pi$
$829$	1.29832e13	+	5.92923e12i	0.954742	+	0.436016i	0.123758	+	0.992312i	$0.460505\pi$
$830$	7.00122e12	−	1.08941e13i	0.512062	−	0.796784i
$831$	2.21325e13	−	3.18218e12i	1.61000	−	0.231483i
$832$	1.63291e12	+	5.56117e12i	0.118142	+	0.402356i
$833$	−1.93885e12	+	4.24548e12i	−0.139521	+	0.305509i
$834$	3.28627e13	−	1.50079e13i	2.35210	−	1.07417i
$835$	−3.70339e13			−2.63640
$836$	1.18996e11	−	5.43439e10i	0.00842570	−	0.00384789i
$837$	2.88960e11	−	2.00976e12i	0.0203504	−	0.141540i
$838$		−	8.94423e12i		−	0.626535i
$839$	1.65314e11	+	2.57233e11i	0.0115181	+	0.0179225i	0.846965	−	0.531649i	$-0.178427\pi$
$839$	1.65314e11	+	2.57233e11i	0.0115181	+	0.0179225i	−0.835447	+	0.549571i	$0.814791\pi$
$840$	−7.46260e13	−	2.19122e13i	−5.17170	−	1.51855i
$841$	1.90029e12	+	4.16106e12i	0.130990	+	0.286828i
$842$	−1.98569e12	+	2.85500e11i	−0.136147	+	0.0195750i
$843$	7.74095e11	+	5.38395e12i	0.0527922	+	0.367178i
$844$	−7.59225e11	−	1.18138e12i	−0.0515026	−	0.0801396i
$845$	−1.59747e13	−	1.84358e13i	−1.07790	−	1.24396i
$846$	6.57691e10	+	7.59016e10i	0.00441423	+	0.00509430i
$847$	1.43263e13	+	2.22921e13i	0.956441	+	1.48825i
$848$	3.24343e12	+	2.25586e13i	0.215389	+	1.49806i
$849$	−3.96410e13	+	5.69951e12i	−2.61854	+	0.376490i
$850$	2.34358e12	+	5.13172e12i	0.153991	+	0.337192i
$851$	−6.70801e12	−	1.96965e12i	−0.438440	−	0.128738i
$852$	−1.45369e12	−	2.26198e12i	−0.0945132	−	0.147065i
$853$		−	4.24408e12i		−	0.274481i	−0.990538	−	0.137241i	$-0.956177\pi$
$853$		−	4.24408e12i		−	0.274481i	0.990538	−	0.137241i	$-0.0438234\pi$
$854$	4.04301e12	−	2.81198e13i	0.260102	−	1.80905i
$855$	−1.35481e13	+	6.18720e12i	−0.867022	+	0.395956i
$856$	8.52650e12			0.542799
$857$	−2.67611e13	+	1.22214e13i	−1.69469	+	0.773938i	−0.696265	+	0.717785i	$0.745156\pi$
$857$	−2.67611e13	+	1.22214e13i	−1.69469	+	0.773938i	−0.998422	+	0.0561533i	$0.982116\pi$
$858$	5.47242e11	−	1.19829e12i	0.0344736	−	0.0754866i
$859$	5.22033e12	+	1.77788e13i	0.327136	+	1.11412i	0.944791	+	0.327674i	$0.106265\pi$
$859$	5.22033e12	+	1.77788e13i	0.327136	+	1.11412i	−0.617654	+	0.786450i	$0.711917\pi$
$860$	−5.38542e12	+	7.74307e11i	−0.335720	+	0.0482692i
$861$	3.06790e13	−	4.77375e13i	1.90251	−	2.96037i
$862$	−1.70204e13	−	7.77297e12i	−1.05000	−	0.479517i
$863$	−2.29128e13	−	1.04639e13i	−1.40615	−	0.642165i	−0.439490	−	0.898247i	$-0.644841\pi$
$863$	−2.29128e13	−	1.04639e13i	−1.40615	−	0.642165i	−0.966655	+	0.256082i	$0.917568\pi$
$864$	6.18017e11	−	5.35515e11i	0.0377302	−	0.0326934i
$865$	−2.23725e12	−	4.89888e12i	−0.135876	−	0.297526i
$866$	−2.01156e13	−	1.74303e13i	−1.21536	−	1.05311i
$867$	6.69396e12	−	2.27975e13i	0.402344	−	1.37026i
$868$	4.33330e11	−	3.01387e12i	0.0259107	−	0.180213i
$869$	−1.15328e12	+	1.33096e12i	−0.0686035	+	0.0791727i
$870$	−1.52254e13	+	3.33391e13i	−0.901018	+	1.97295i
$871$	2.02423e12	−	6.89388e12i	0.119173	−	0.405865i
$872$	−9.86209e12	+	6.33798e12i	−0.577623	+	0.371216i
$873$	−9.59354e12	−	1.10715e13i	−0.559004	−	0.645125i
$874$	9.48928e12	−	2.78631e12i	0.550088	−	0.161520i
$875$	7.89244e13	+	6.83884e13i	4.55172	+	3.94409i
$876$	−1.39462e11	−	4.74966e11i	−0.00800182	−	0.0272517i
$877$	2.09381e13	+	3.01044e12i	1.19519	+	0.171843i	0.711047	−	0.703144i	$-0.248221\pi$
$877$	2.09381e13	+	3.01044e12i	1.19519	+	0.171843i	0.484146	+	0.874987i	$0.339130\pi$
$878$		−	3.06953e13i		−	1.74320i
$879$	2.76537e12	−	1.77720e12i	0.156244	−	0.100412i
$880$	−4.46066e12	+	1.30977e12i	−0.250742	+	0.0736246i
$881$	6.78297e10	+	1.99166e10i	0.00379340	+	0.00111384i	0.283629	−	0.958934i	$-0.408462\pi$
$881$	6.78297e10	+	1.99166e10i	0.00379340	+	0.00111384i	−0.279835	+	0.960048i	$0.590280\pi$
$882$	3.65074e13	+	2.34619e13i	2.03129	+	1.30543i
$883$	−5.01426e12	+	7.80233e12i	−0.277577	+	0.431918i	−0.951850	−	0.306564i	$-0.900821\pi$
$883$	−5.01426e12	+	7.80233e12i	−0.277577	+	0.431918i	0.674273	+	0.738482i	$0.264457\pi$
$884$	1.02089e11	−	8.84608e10i	0.00562270	−	0.00487209i
$885$	4.36783e13	+	2.80703e13i	2.39343	+	1.53817i
$886$	2.54715e12	+	1.77158e13i	0.138868	+	0.965849i
$887$	3.33330e13	+	4.79257e12i	1.80808	+	0.259963i	0.961993	−	0.273075i	$-0.0880406\pi$
$887$	3.33330e13	+	4.79257e12i	1.80808	+	0.259963i	0.846091	+	0.533038i	$0.178950\pi$
$888$	6.06503e12	−	6.99942e12i	0.327321	−	0.377749i
$889$	−3.26742e13			−1.75447
$890$	−2.94001e13	−	1.63083e13i	−1.57070	−	0.871273i
$891$	2.56049e12			0.136105
$892$	−7.58026e11	+	8.74809e11i	−0.0400906	+	0.0462670i
$893$	5.27195e10	+	7.57991e9i	0.00277421	+	0.000398871i
$894$	3.23887e12	+	2.25268e13i	0.169580	+	1.17945i
$895$	−2.99286e13	−	1.92340e13i	−1.55913	−	1.00199i
$896$	−2.00131e13	+	1.73415e13i	−1.03736	+	0.898876i
$897$	−8.24394e12	+	1.28278e13i	−0.425176	+	0.661587i
$898$	−1.09599e12	−	7.04349e11i	−0.0562422	−	0.0361447i
$899$	−1.17452e13	−	3.44870e12i	−0.599711	−	0.176091i
$900$	−7.70616e12	+	2.26273e12i	−0.391513	+	0.114959i
$901$	4.33812e12	−	2.78794e12i	0.219301	−	0.140936i
$902$		−	3.92201e12i		−	0.197278i
$903$	6.93830e13	+	9.97576e12i	3.47263	+	0.499288i
$904$	−8.05974e11	−	2.74490e12i	−0.0401387	−	0.136700i
$905$	−2.36484e13	−	2.04915e13i	−1.17188	−	1.01544i
$906$	−1.93653e13	+	5.68617e12i	−0.954877	+	0.280377i
$907$	2.10663e13	+	2.43118e13i	1.03361	+	1.19284i	0.980956	+	0.194232i	$0.0622215\pi$
$907$	2.10663e13	+	2.43118e13i	1.03361	+	1.19284i	0.0526504	+	0.998613i	$0.483233\pi$
$908$	1.80185e12	−	1.15798e12i	0.0879695	−	0.0565346i
$909$	1.22004e13	−	4.15508e13i	0.592703	−	2.01856i
$910$	−1.07285e13	+	2.34921e13i	−0.518622	+	1.13562i
$911$	−1.15274e13	+	1.33033e13i	−0.554494	+	0.639920i	−0.961924	−	0.273316i	$-0.911880\pi$
$911$	−1.15274e13	+	1.33033e13i	−0.554494	+	0.639920i	0.407430	+	0.913236i	$0.366425\pi$
$912$	−1.61253e12	+	1.12154e13i	−0.0771847	+	0.536831i
$913$	4.97412e11	−	1.69403e12i	0.0236918	−	0.0806868i
$914$	−1.73904e13	−	1.50688e13i	−0.824235	−	0.714204i
$915$	−2.68048e13	−	5.86944e13i	−1.26421	−	2.76823i
$916$	−2.39295e12	+	2.07350e12i	−0.112306	+	0.0973139i
$917$	−3.76668e13	−	1.72019e13i	−1.75913	−	0.803367i
$918$	5.04935e11	+	2.30596e11i	0.0234662	+	0.0107167i
$919$	−8.16559e9	+	1.27059e10i	−0.000377631	+	0.000587605i	−0.841442	−	0.540347i	$-0.818293\pi$
$919$	−8.16559e9	+	1.27059e10i	−0.000377631	+	0.000587605i	0.841065	+	0.540935i	$0.181929\pi$
$920$	6.15899e13	−	8.85529e12i	2.83442	−	0.407528i
$921$	6.45503e12	+	2.19838e13i	0.295618	+	1.00678i
$922$	−1.45738e13	+	3.19123e13i	−0.664179	+	1.45435i
$923$	−6.92860e12	+	3.16418e12i	−0.314223	+	0.143501i
$924$	−1.24294e12			−0.0560954
$925$	−1.78878e13	+	8.16909e12i	−0.803377	+	0.366890i
$926$	−2.26846e11	+	1.57775e12i	−0.0101387	+	0.0705161i
$927$		−	5.39614e12i		−	0.240007i
$928$	−2.66540e12	−	4.14745e12i	−0.117977	−	0.183576i
$929$	−7.59149e11	−	2.22906e11i	−0.0334392	−	0.00981864i	0.264970	−	0.964257i	$-0.414638\pi$
$929$	−7.59149e11	−	2.22906e11i	−0.0334392	−	0.00981864i	−0.298409	+	0.954438i	$0.596456\pi$
$930$	1.87638e13	+	4.10870e13i	0.822523	+	1.80107i
$931$	2.27799e13	−	3.27526e12i	0.993754	−	0.142880i
$932$	1.48763e11	+	1.03467e12i	0.00645839	+	0.0449191i
$933$	−5.52869e12	−	8.60281e12i	−0.238866	−	0.371683i
$934$	1.45200e13	+	1.67569e13i	0.624316	+	0.720499i
$935$	6.88852e11	+	7.94978e11i	0.0294764	+	0.0340175i
$936$	−5.79316e12	−	9.01433e12i	−0.246703	−	0.383877i
$937$	−4.94552e12	−	3.43968e13i	−0.209596	−	1.45777i	−0.774477	−	0.632602i	$-0.781987\pi$
$937$	−4.94552e12	−	3.43968e13i	−0.209596	−	1.45777i	0.564881	−	0.825172i	$-0.308922\pi$
$938$	4.38256e13	−	6.30116e12i	1.84848	−	0.265771i
$939$	3.17560e12	+	6.95360e12i	0.133300	+	0.291887i
$940$	3.76882e10	+	1.10663e10i	0.00157446	+	0.000462302i
$941$	2.43298e13	+	3.78579e13i	1.01155	+	1.57400i	0.802996	+	0.595984i	$0.203238\pi$
$941$	2.43298e13	+	3.78579e13i	1.01155	+	1.57400i	0.208550	+	0.978012i	$0.433126\pi$
$942$			6.28315e13i			2.59985i
$943$	−6.46082e12	+	4.49360e13i	−0.266063	+	1.85051i
$944$	1.90589e13	−	8.70393e12i	0.781133	−	0.356731i
$945$	1.62491e13			0.662805
$946$	4.40694e12	−	2.01258e12i	0.178907	−	0.0817040i
$947$	−1.82813e12	+	4.00306e12i	−0.0738641	+	0.161740i	−0.942962	−	0.332900i	$-0.891973\pi$
$947$	−1.82813e12	+	4.00306e12i	−0.0738641	+	0.161740i	0.869098	+	0.494640i	$0.164700\pi$
$948$	8.91813e11	+	3.03723e12i	0.0358621	+	0.122135i
$949$	−1.38802e12	+	1.99567e11i	−0.0555517	+	0.00798713i
$950$	1.50397e13	−	2.34023e13i	0.599079	−	0.932185i
$951$	−2.66255e12	−	1.21595e12i	−0.105557	−	0.0482062i
$952$	6.45993e12	+	2.95015e12i	0.254895	+	0.116407i
$953$	−8.44225e10	+	7.31525e10i	−0.00331543	+	0.00287284i	−0.656517	−	0.754311i	$-0.727971\pi$
$953$	−8.44225e10	+	7.31525e10i	−0.00331543	+	0.00287284i	0.653201	+	0.757184i	$0.273425\pi$
$954$	−1.99182e13	−	4.36147e13i	−0.778542	−	1.70477i
$955$	−1.00684e13	−	8.72430e12i	−0.391692	−	0.339403i
$956$	−1.39862e12	+	4.76326e12i	−0.0541551	+	0.184435i
$957$	−7.11135e11	+	4.94605e12i	−0.0274062	+	0.190614i
$958$	6.98626e12	−	8.06257e12i	0.267978	−	0.309264i
$959$	4.40811e12	−	9.65242e12i	0.168294	−	0.368513i
$960$	−2.28553e13	+	7.78379e13i	−0.868492	+	2.95781i
$961$	9.55140e12	−	6.13831e12i	0.361253	−	0.232163i
$962$	−2.01391e12	−	2.32417e12i	−0.0758144	−	0.0874945i
$963$	−1.48854e13	+	4.37073e12i	−0.557752	+	0.163771i
$964$	−3.26572e12	−	2.82977e12i	−0.121796	−	0.105537i
$965$	−1.66910e13	−	5.68444e13i	−0.619598	−	2.11016i
$966$	−9.30104e13	−	1.33729e13i	−3.43664	−	0.494115i
$967$		−	5.11607e12i		−	0.188156i	−0.995565	−	0.0940778i	$-0.970010\pi$
$967$		−	5.11607e12i		−	0.188156i	0.995565	−	0.0940778i	$-0.0299903\pi$
$968$	2.36259e13	−	1.51834e13i	0.864867	−	0.555816i
$969$	2.45991e12	−	7.22294e11i	0.0896318	−	0.0263183i
$970$	3.59052e13	+	1.05427e13i	1.30222	+	0.382366i
$971$	−7.31115e12	−	4.69859e12i	−0.263936	−	0.169622i	0.401979	−	0.915649i	$-0.368322\pi$
$971$	−7.31115e12	−	4.69859e12i	−0.263936	−	0.169622i	−0.665915	+	0.746027i	$0.731959\pi$
$972$	2.86637e12	−	4.46016e12i	0.102999	−	0.160270i
$973$	−7.29773e13	+	6.32352e13i	−2.61024	+	2.26178i
$974$	−1.01880e13	−	6.54743e12i	−0.362722	−	0.233107i
$975$	6.10402e12	+	4.24544e13i	0.216319	+	1.50453i
$976$	−2.57740e13	−	3.70574e12i	−0.909197	−	0.130723i
$977$	8.41643e12	−	9.71307e12i	0.295530	−	0.341060i	−0.588494	−	0.808502i	$-0.700279\pi$
$977$	8.41643e12	−	9.71307e12i	0.295530	−	0.341060i	0.884024	+	0.467442i	$0.154824\pi$
$978$	6.32544e13			2.21089
$979$	−4.47237e12	−	1.00409e12i	−0.155602	−	0.0349341i
$980$	1.69725e13			0.587798
$981$	1.39681e13	−	1.61201e13i	0.481534	−	0.555720i
$982$	1.28643e13	+	1.84961e12i	0.441454	+	0.0634715i
$983$	−3.31154e12	−	2.30323e13i	−0.113120	−	0.786766i	−0.964853	−	0.262790i	$-0.915357\pi$
$983$	−3.31154e12	−	2.30323e13i	−0.113120	−	0.786766i	0.851733	−	0.523976i	$-0.175552\pi$
$984$	−5.05937e13	−	3.25146e13i	−1.72036	−	1.10561i
$985$	5.96713e13	−	5.17055e13i	2.01977	−	1.75014i
$986$	1.80930e12	−	2.81532e12i	0.0609627	−	0.0948598i
$987$	−4.25720e11	−	2.73594e11i	−0.0142790	−	0.00917654i
$988$	−6.39114e11	−	1.87661e11i	−0.0213389	−	0.00626566i
$989$	−5.38074e13	+	1.57993e13i	−1.78838	+	0.525114i
$990$	8.22806e12	−	5.28785e12i	0.272232	−	0.174953i
$991$		−	2.66528e13i		−	0.877833i	−0.898528	−	0.438916i	$-0.855362\pi$
$991$		−	2.66528e13i		−	0.877833i	0.898528	−	0.438916i	$-0.144638\pi$
$992$	−6.01398e12	−	8.64680e11i	−0.197178	−	0.0283500i
$993$	8.92416e11	+	3.03929e12i	0.0291270	+	0.0991975i
$994$	−3.54737e13	−	3.07381e13i	−1.15257	−	0.998709i
$995$	−2.02893e13	+	5.95749e12i	−0.656242	+	0.192690i
$996$	−2.07816e12	−	2.39832e12i	−0.0669131	−	0.0772218i
$997$	−1.30954e13	+	8.41592e12i	−0.419751	+	0.269757i	−0.733421	−	0.679774i	$-0.762078\pi$
$997$	−1.30954e13	+	8.41592e12i	−0.419751	+	0.269757i	0.313670	+	0.949532i	$0.398441\pi$
$998$	4.62373e12	−	1.57470e13i	0.147538	−	0.502469i
$999$	−8.03797e11	+	1.76007e12i	−0.0255330	+	0.0559095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	89.10.f.a.81.20	yes	660
89.11	even	22	inner	89.10.f.a.11.20	✓	660

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
89.10.f.a.11.20	✓	660	89.11	even	22	inner
89.10.f.a.81.20	yes	660	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:	\( N \)	\(=\)	\( 89 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	89.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.7990 + 15.9249i) q^{2} +(202.658 + 29.1378i) q^{3} +(9.67508 + 67.2917i) q^{4} +(2267.64 + 1457.33i) q^{5} +(-3260.50 + 2825.24i) q^{6} +(6234.30 - 9700.76i) q^{7} +(-10281.2 - 6607.30i) q^{8} +(21335.5 + 6264.68i) q^{9} +O(q^{10})\)	\(q+(-13.7990 + 15.9249i) q^{2} +(202.658 + 29.1378i) q^{3} +(9.67508 + 67.2917i) q^{4} +(2267.64 + 1457.33i) q^{5} +(-3260.50 + 2825.24i) q^{6} +(6234.30 - 9700.76i) q^{7} +(-10281.2 - 6607.30i) q^{8} +(21335.5 + 6264.68i) q^{9} +(-54499.1 + 16002.4i) q^{10} +(-6514.61 + 4186.68i) q^{11} +13919.1i q^{12} +(39028.9 + 5611.51i) q^{13} +(68456.6 + 233142. i) q^{14} +(417093. + 361413. i) q^{15} +(213693. - 62745.9i) q^{16} +(-33000.2 - 38084.3i) q^{17} +(-394174. + 253320. i) q^{18} +(-70006.7 + 238421. i) q^{19} +(-76126.3 + 166693. i) q^{20} +(1.54609e6 - 1.78428e6i) q^{21} +(23222.6 - 161517. i) q^{22} +(-532141. + 1.81231e6i) q^{23} +(-1.89104e6 - 1.63859e6i) q^{24} +(2.20705e6 + 4.83276e6i) q^{25} +(-627923. + 544099. i) q^{26} +(475519. + 217162. i) q^{27} +(713098. + 325661. i) q^{28} +(1.70389e6 - 2.65131e6i) q^{29} +(-1.15109e7 + 1.65502e6i) q^{30} +(-1.09426e6 - 3.72672e6i) q^{31} +(649834. - 1.42294e6i) q^{32} +(-1.44223e6 + 658643. i) q^{33} +1.06186e6 q^{34} +(2.82743e7 - 1.29124e7i) q^{35} +(-215138. + 1.49632e6i) q^{36} +3.70136e6i q^{37} +(-2.83081e6 - 4.40483e6i) q^{38} +(7.74601e6 + 2.27443e6i) q^{39} +(-1.36850e7 - 2.99660e7i) q^{40} +(2.37905e7 - 3.42056e6i) q^{41} +(7.08003e6 + 4.92427e7i) q^{42} +(1.60516e7 + 2.49768e7i) q^{43} +(-344758. - 397872. i) q^{44} +(3.92517e7 + 4.52989e7i) q^{45} +(-2.15178e7 - 3.34824e7i) q^{46} +(-30504.4 - 212162. i) q^{47} +(4.51349e7 - 6.48942e6i) q^{48} +(-3.84747e7 - 8.42479e7i) q^{49} +(-1.07416e8 - 3.15403e7i) q^{50} +(-5.57807e6 - 8.67964e6i) q^{51} +2.68061e6i q^{52} +(-1.45632e7 + 1.01289e8i) q^{53} +(-1.00200e7 + 4.57598e6i) q^{54} -2.08742e7 q^{55} +(-1.28192e8 + 5.85432e7i) q^{56} +(-2.11345e7 + 4.62780e7i) q^{57} +(1.87099e7 + 6.37199e7i) q^{58} +(9.31196e7 - 1.33886e7i) q^{59} +(-2.02847e7 + 3.15636e7i) q^{60} +(-1.06351e8 - 4.85690e7i) q^{61} +(7.44475e7 + 3.39990e7i) q^{62} +(1.93784e8 - 1.67915e8i) q^{63} +(6.10628e7 + 1.33709e8i) q^{64} +(8.03258e7 + 6.96027e7i) q^{65} +(9.41249e6 - 3.20560e7i) q^{66} +(2.59324e7 - 1.80364e8i) q^{67} +(2.24348e6 - 2.58911e6i) q^{68} +(-1.60649e8 + 3.51773e8i) q^{69} +(-1.84528e8 + 6.28446e8i) q^{70} +(-1.62509e8 + 1.04438e8i) q^{71} +(-1.77961e8 - 2.05378e8i) q^{72} +(-3.41233e7 + 1.00195e7i) q^{73} +(-5.89440e7 - 5.10752e7i) q^{74} +(3.06460e8 + 1.04371e9i) q^{75} +(-1.67211e7 - 2.40413e6i) q^{76} +8.92976e7i q^{77} +(-1.43108e8 + 9.19696e7i) q^{78} +(2.18206e8 - 6.40711e7i) q^{79} +(5.76021e8 + 1.69135e8i) q^{80} +(-2.78157e8 - 1.78760e8i) q^{81} +(-2.73814e8 + 4.26063e8i) q^{82} +(-1.72304e8 + 1.49302e8i) q^{83} +(1.35026e8 + 8.67759e7i) q^{84} +(-1.93315e7 - 1.34454e8i) q^{85} +(-6.19251e8 - 8.90349e7i) q^{86} +(4.22561e8 - 4.87662e8i) q^{87} +9.46404e7 q^{88} +(4.15751e8 + 4.21316e8i) q^{89} -1.26302e9 q^{90} +(2.97754e8 - 3.43626e8i) q^{91} +(-1.27102e8 - 1.82745e7i) q^{92} +(-1.13173e8 - 7.87134e8i) q^{93} +(3.79960e6 + 2.44186e6i) q^{94} +(-5.06207e8 + 4.38631e8i) q^{95} +(1.73155e8 - 2.69435e8i) q^{96} +(-5.54236e8 - 3.56186e8i) q^{97} +(1.87255e9 + 5.49832e8i) q^{98} +(-1.65221e8 + 4.85132e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9}+O(q^{10}) \) 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9	\( 660 q - 9 q^{2} - 825 q^{3} - 16393 q^{4} - 5127 q^{5} - 11 q^{6} - 11 q^{7} + 1015 q^{8} + 489535 q^{9} - 225841 q^{10} - 224944 q^{11} - 11 q^{13} + 1940664 q^{14} - 11 q^{15} - 5125641 q^{16} + 1457606 q^{17} + 2864796 q^{18} - 11 q^{19} - 5955661 q^{20} + 856653 q^{21} + 13531907 q^{22} - 11 q^{23} + 5621 q^{24} - 31973709 q^{25} - 4206763 q^{26} - 17737896 q^{27} - 11 q^{28} + 10200729 q^{29} - 81004858 q^{30} - 11 q^{31} - 44372422 q^{32} - 19516475 q^{33} + 35594328 q^{34} - 35970209 q^{35} + 71890930 q^{36} - 87132859 q^{38} + 42308203 q^{39} - 128175356 q^{40} + 60926635 q^{41} + 121333817 q^{42} + 296517661 q^{43} + 115664209 q^{44} + 48133749 q^{45} + 311125309 q^{46} - 46792325 q^{47} - 141127426 q^{48} + 164252871 q^{49} + 103838041 q^{50} - 427287971 q^{51} + 850769769 q^{53} - 329099771 q^{54} + 793594654 q^{55} - 2036185316 q^{56} - 154197519 q^{57} + 188920501 q^{58} + 405753711 q^{59} + 21484364 q^{60} + 344711653 q^{61} - 1167226764 q^{62} - 1320295229 q^{63} - 134364169 q^{64} + 1450391239 q^{65} + 863803105 q^{66} + 646170445 q^{67} + 1285178775 q^{68} - 221829309 q^{69} + 854155808 q^{70} - 1113621013 q^{71} - 2392386072 q^{72} - 314298299 q^{73} - 479039451 q^{74} - 3075936347 q^{75} - 6170784400 q^{76} - 2037231963 q^{78} - 79886655 q^{79} + 6302566534 q^{80} + 281226707 q^{81} + 5439310019 q^{82} + 1306521271 q^{83} + 1958614914 q^{84} + 4403895759 q^{85} - 3738814827 q^{86} - 4959185007 q^{87} + 2745817562 q^{88} + 3415767517 q^{89} - 10039266258 q^{90} + 1585238913 q^{91} + 8669558172 q^{92} + 1795690413 q^{93} - 8679076027 q^{94} + 10576695701 q^{95} + 12941524981 q^{96} - 2702894895 q^{97} + 1786224002 q^{98} - 9157402144 q^{99}+O(q^{100}) \) 660 * q - 9 * q^2 - 825 * q^3 - 16393 * q^4 - 5127 * q^5 - 11 * q^6 - 11 * q^7 + 1015 * q^8 + 489535 * q^9 - 225841 * q^10 - 224944 * q^11 - 11 * q^13 + 1940664 * q^14 - 11 * q^15 - 5125641 * q^16 + 1457606 * q^17 + 2864796 * q^18 - 11 * q^19 - 5955661 * q^20 + 856653 * q^21 + 13531907 * q^22 - 11 * q^23 + 5621 * q^24 - 31973709 * q^25 - 4206763 * q^26 - 17737896 * q^27 - 11 * q^28 + 10200729 * q^29 - 81004858 * q^30 - 11 * q^31 - 44372422 * q^32 - 19516475 * q^33 + 35594328 * q^34 - 35970209 * q^35 + 71890930 * q^36 - 87132859 * q^38 + 42308203 * q^39 - 128175356 * q^40 + 60926635 * q^41 + 121333817 * q^42 + 296517661 * q^43 + 115664209 * q^44 + 48133749 * q^45 + 311125309 * q^46 - 46792325 * q^47 - 141127426 * q^48 + 164252871 * q^49 + 103838041 * q^50 - 427287971 * q^51 + 850769769 * q^53 - 329099771 * q^54 + 793594654 * q^55 - 2036185316 * q^56 - 154197519 * q^57 + 188920501 * q^58 + 405753711 * q^59 + 21484364 * q^60 + 344711653 * q^61 - 1167226764 * q^62 - 1320295229 * q^63 - 134364169 * q^64 + 1450391239 * q^65 + 863803105 * q^66 + 646170445 * q^67 + 1285178775 * q^68 - 221829309 * q^69 + 854155808 * q^70 - 1113621013 * q^71 - 2392386072 * q^72 - 314298299 * q^73 - 479039451 * q^74 - 3075936347 * q^75 - 6170784400 * q^76 - 2037231963 * q^78 - 79886655 * q^79 + 6302566534 * q^80 + 281226707 * q^81 + 5439310019 * q^82 + 1306521271 * q^83 + 1958614914 * q^84 + 4403895759 * q^85 - 3738814827 * q^86 - 4959185007 * q^87 + 2745817562 * q^88 + 3415767517 * q^89 - 10039266258 * q^90 + 1585238913 * q^91 + 8669558172 * q^92 + 1795690413 * q^93 - 8679076027 * q^94 + 10576695701 * q^95 + 12941524981 * q^96 - 2702894895 * q^97 + 1786224002 * q^98 - 9157402144 * q^99

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