LMFDB - Embedded newform 29.9.f.a.2.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(2,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.f (of order $28$, 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:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			2.16
Character	$\chi$	$=$	29.2
Dual form			29.9.f.a.15.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.6004 + 2.20843i) q^{2} +(-83.4552 - 52.4384i) q^{3} +(129.715 + 29.6067i) q^{4} +(14.4052 - 11.4877i) q^{5} +(-1519.95 - 1212.12i) q^{6} +(772.012 + 3382.40i) q^{7} +(-2289.00 - 800.955i) q^{8} +(1368.27 + 2841.25i) q^{9} +O(q^{10})$	\(q+(19.6004 + 2.20843i) q^{2} +(-83.4552 - 52.4384i) q^{3} +(129.715 + 29.6067i) q^{4} +(14.4052 - 11.4877i) q^{5} +(-1519.95 - 1212.12i) q^{6} +(772.012 + 3382.40i) q^{7} +(-2289.00 - 800.955i) q^{8} +(1368.27 + 2841.25i) q^{9} +(307.716 - 193.351i) q^{10} +(-19598.3 + 6857.75i) q^{11} +(-9272.90 - 9272.90i) q^{12} +(-21261.3 + 44149.6i) q^{13} +(7661.90 + 68001.3i) q^{14} +(-1804.58 + 203.328i) q^{15} +(-73784.4 - 35532.7i) q^{16} +(58343.9 - 58343.9i) q^{17} +(20544.0 + 58711.2i) q^{18} +(-14594.5 - 23227.1i) q^{19} +(2208.69 - 1063.65i) q^{20} +(112939. - 322762. i) q^{21} +(-399279. + 91132.9i) q^{22} +(228462. - 286483. i) q^{23} +(149028. + 186875. i) q^{24} +(-86846.7 + 380500. i) q^{25} +(-514231. + 818394. i) q^{26} +(-37602.9 + 333735. i) q^{27} +461607. i q^{28} +(-59396.6 - 704783. i) q^{29} -35819.5 q^{30} +(-1.06683e6 - 120203. i) q^{31} +(-842064. - 529104. i) q^{32} +(1.99519e6 + 455390. i) q^{33} +(1.27241e6 - 1.01471e6i) q^{34} +(49977.1 + 39855.4i) q^{35} +(93366.2 + 409064. i) q^{36} +(-652675. - 228381. i) q^{37} +(-234763. - 487490. i) q^{38} +(4.08950e6 - 2.56960e6i) q^{39} +(-42174.6 + 14757.5i) q^{40} +(826924. + 826924. i) q^{41} +(2.92645e6 - 6.07684e6i) q^{42} +(88820.7 + 788306. i) q^{43} +(-2.74524e6 + 309315. i) q^{44} +(52349.7 + 25210.3i) q^{45} +(5.11062e6 - 5.11062e6i) q^{46} +(-1.58392e6 - 4.52658e6i) q^{47} +(4.29441e6 + 6.83452e6i) q^{48} +(-5.65075e6 + 2.72126e6i) q^{49} +(-2.54254e6 + 7.26615e6i) q^{50} +(-7.92856e6 + 1.80964e6i) q^{51} +(-4.06505e6 + 5.09741e6i) q^{52} +(6.31622e6 + 7.92028e6i) q^{53} +(-1.47406e6 + 6.45828e6i) q^{54} +(-203537. + 323928. i) q^{55} +(942021. - 8.36067e6i) q^{56} +2.70373e6i q^{57} +(392269. - 1.39452e7i) q^{58} -1.26885e7 q^{59} +(-240102. - 27053.0i) q^{60} +(-5.41484e6 - 3.40237e6i) q^{61} +(-2.06449e7 - 4.71206e6i) q^{62} +(-8.55393e6 + 6.82153e6i) q^{63} +(1.05482e6 + 841189. i) q^{64} +(200906. + 880227. i) q^{65} +(3.81008e7 + 1.33320e7i) q^{66} +(8.93817e6 + 1.85603e7i) q^{67} +(9.29548e6 - 5.84074e6i) q^{68} +(-3.40891e7 + 1.19283e7i) q^{69} +(891552. + 891552. i) q^{70} +(-7.98729e6 + 1.65858e7i) q^{71} +(-856263. - 7.59954e6i) q^{72} +(1.56965e7 - 1.76857e6i) q^{73} +(-1.22883e7 - 5.91774e6i) q^{74} +(2.72006e7 - 2.72006e7i) q^{75} +(-1.20546e6 - 3.44501e6i) q^{76} +(-3.83258e7 - 6.09952e7i) q^{77} +(8.58305e7 - 4.13338e7i) q^{78} +(-2.06555e7 + 5.90300e7i) q^{79} +(-1.47107e6 + 335761. i) q^{80} +(3.35389e7 - 4.20565e7i) q^{81} +(1.43818e7 + 1.80342e7i) q^{82} +(-3.24788e6 + 1.42299e7i) q^{83} +(2.42059e7 - 3.85235e7i) q^{84} +(170214. - 1.51069e6i) q^{85} +1.56472e7i q^{86} +(-3.20007e7 + 6.19324e7i) q^{87} +5.03533e7 q^{88} +(-1.95390e7 - 2.20152e6i) q^{89} +(970399. + 609742. i) q^{90} +(-1.65746e8 - 3.78304e7i) q^{91} +(3.81169e7 - 3.03972e7i) q^{92} +(8.27295e7 + 6.59746e7i) q^{93} +(-2.10488e7 - 9.22207e7i) q^{94} +(-477063. - 166932. i) q^{95} +(4.25293e7 + 8.83129e7i) q^{96} +(1.31178e8 - 8.24246e7i) q^{97} +(-1.16766e8 + 4.08584e7i) q^{98} +(-4.63005e7 - 4.63005e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) $ 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{28}\right)$

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 $

$2$	19.6004	+	2.20843i	1.22502	+	0.138027i	0.700677	−	0.713479i	$-0.252881\pi$
$2$	19.6004	+	2.20843i	1.22502	+	0.138027i	0.524346	+	0.851506i	$0.324310\pi$
$3$	−83.4552	−	52.4384i	−1.03031	−	0.647387i	−0.0929226	−	0.995673i	$-0.529621\pi$
$3$	−83.4552	−	52.4384i	−1.03031	−	0.647387i	−0.937388	+	0.348286i	$0.886764\pi$
$4$	129.715	+	29.6067i	0.506701	+	0.115651i
$5$	14.4052	−	11.4877i	0.0230483	−	0.0183804i	−0.611898	−	0.790937i	$-0.709594\pi$
$5$	14.4052	−	11.4877i	0.0230483	−	0.0183804i	0.634946	+	0.772556i	$0.281022\pi$
$6$	−1519.95	−	1212.12i	−1.17280	−	0.935275i
$7$	772.012	+	3382.40i	0.321538	+	1.40875i	0.834817	+	0.550527i	$0.185573\pi$
$7$	772.012	+	3382.40i	0.321538	+	1.40875i	−0.513280	+	0.858221i	$0.671570\pi$
$8$	−2289.00	−	800.955i	−0.558838	−	0.195546i
$9$	1368.27	+	2841.25i	0.208546	+	0.433051i
$10$	307.716	−	193.351i	0.0307716	−	0.0193351i
$11$	−19598.3	+	6857.75i	−1.33859	+	0.468394i	−0.902183	−	0.431354i	$-0.858036\pi$
$11$	−19598.3	+	6857.75i	−1.33859	+	0.468394i	−0.436410	+	0.899748i	$0.643750\pi$
$12$	−9272.90	−	9272.90i	−0.447188	−	0.447188i
$13$	−21261.3	+	44149.6i	−0.744418	+	1.54580i	0.0907927	+	0.995870i	$0.471060\pi$
$13$	−21261.3	+	44149.6i	−0.744418	+	1.54580i	−0.835211	+	0.549930i	$0.814654\pi$
$14$	7661.90	+	68001.3i	0.199446	+	1.77013i
$15$	−1804.58	+	203.328i	−0.0356461	+	0.00401635i
$16$	−73784.4	−	35532.7i	−1.12586	−	0.542186i
$17$	58343.9	−	58343.9i	0.698554	−	0.698554i	−0.265544	−	0.964099i	$-0.585552\pi$
$17$	58343.9	−	58343.9i	0.698554	−	0.698554i	0.964099	+	0.265544i	$0.0855517\pi$
$18$	20544.0	+	58711.2i	0.195701	+	0.559283i
$19$	−14594.5	−	23227.1i	−0.111989	−	0.178230i	0.786027	−	0.618192i	$-0.212135\pi$
$19$	−14594.5	−	23227.1i	−0.111989	−	0.178230i	−0.898016	+	0.439962i	$0.854992\pi$
$20$	2208.69	−	1063.65i	0.0138043	−	0.00664780i
$21$	112939.	−	322762.i	0.580722	−	1.65961i
$22$	−399279.	+	91132.9i	−1.70446	+	0.389031i
$23$	228462.	−	286483.i	0.816401	−	1.02373i	−0.182776	−	0.983155i	$-0.558508\pi$
$23$	228462.	−	286483.i	0.816401	−	1.02373i	0.999176	−	0.0405794i	$-0.0129204\pi$
$24$	149028.	+	186875.i	0.449183	+	0.563257i
$25$	−86846.7	+	380500.i	−0.222328	+	0.974081i
$26$	−514231.	+	818394.i	−1.12529	+	1.79089i
$27$	−37602.9	+	333735.i	−0.0707565	+	0.627981i
$28$			461607.i			0.751000i
$29$	−59396.6	−	704783.i	−0.0839788	−	0.996468i
$29$	−59396.6	−	704783.i	−0.0839788	−	0.996468i
$30$	−35819.5			−0.0442217
$31$	−1.06683e6	−	120203.i	−1.15518	−	0.130158i	−0.486482	−	0.873691i	$-0.661720\pi$
$31$	−1.06683e6	−	120203.i	−1.15518	−	0.130158i	−0.668699	+	0.743533i	$0.733149\pi$
$32$	−842064.	−	529104.i	−0.803055	−	0.504593i
$33$	1.99519e6	+	455390.i	1.68240	+	0.383997i
$34$	1.27241e6	−	1.01471e6i	0.952164	−	0.759325i
$35$	49977.1	+	39855.4i	0.0333042	+	0.0265592i
$36$	93366.2	+	409064.i	0.0555878	+	0.243546i
$37$	−652675.	−	228381.i	−0.348249	−	0.121858i	0.150486	−	0.988612i	$-0.451916\pi$
$37$	−652675.	−	228381.i	−0.348249	−	0.121858i	−0.498735	+	0.866755i	$0.666202\pi$
$38$	−234763.	−	487490.i	−0.112589	−	0.233793i
$39$	4.08950e6	−	2.56960e6i	1.76771	−	1.11073i
$40$	−42174.6	+	14757.5i	−0.0164744	+	0.00576466i
$41$	826924.	+	826924.i	0.292638	+	0.292638i	0.838121	−	0.545484i	$-0.183654\pi$
$41$	826924.	+	826924.i	0.292638	+	0.292638i	−0.545484	+	0.838121i	$0.683654\pi$
$42$	2.92645e6	−	6.07684e6i	0.940468	−	1.95290i
$43$	88820.7	+	788306.i	0.0259801	+	0.230580i	0.999992	+	0.00408141i	$0.00129916\pi$
$43$	88820.7	+	788306.i	0.0259801	+	0.230580i	−0.974012	+	0.226498i	$0.927272\pi$
$44$	−2.74524e6	+	309315.i	−0.732437	+	0.0825258i
$45$	52349.7	+	25210.3i	0.0127663	+	0.00614792i
$46$	5.11062e6	−	5.11062e6i	1.14141	−	1.14141i
$47$	−1.58392e6	−	4.52658e6i	−0.324595	−	0.927639i	−0.984360	−	0.176167i	$-0.943630\pi$
$47$	−1.58392e6	−	4.52658e6i	−0.324595	−	0.927639i	0.659765	−	0.751472i	$-0.270656\pi$
$48$	4.29441e6	+	6.83452e6i	0.808982	+	1.28749i
$49$	−5.65075e6	+	2.72126e6i	−0.980216	+	0.472047i
$50$	−2.54254e6	+	7.26615e6i	−0.406806	+	1.16258i
$51$	−7.92856e6	+	1.80964e6i	−1.17196	+	0.267493i
$52$	−4.06505e6	+	5.09741e6i	−0.555971	+	0.697166i
$53$	6.31622e6	+	7.92028e6i	0.800485	+	1.00378i	0.999716	+	0.0238244i	$0.00758426\pi$
$53$	6.31622e6	+	7.92028e6i	0.800485	+	1.00378i	−0.199231	+	0.979953i	$0.563844\pi$
$54$	−1.47406e6	+	6.45828e6i	−0.173357	+	0.759525i
$55$	−203537.	+	323928.i	−0.0222430	+	0.0353995i
$56$	942021.	−	8.36067e6i	0.0957874	−	0.850137i
$57$			2.70373e6i			0.256132i
$58$	392269.	−	1.39452e7i	0.0346634	−	1.23229i
$59$	−1.26885e7			−1.04713			−0.523566	−	0.851985i	$-0.675399\pi$
$59$	−1.26885e7			−1.04713			−0.523566	+	0.851985i	$0.675399\pi$
$60$	−240102.	−	27053.0i	−0.0185264	−	0.00208743i
$61$	−5.41484e6	−	3.40237e6i	−0.391080	−	0.245732i	0.322110	−	0.946702i	$-0.395608\pi$
$61$	−5.41484e6	−	3.40237e6i	−0.391080	−	0.245732i	−0.713191	+	0.700970i	$0.752751\pi$
$62$	−2.06449e7	−	4.71206e6i	−1.39716	−	0.318892i
$63$	−8.55393e6	+	6.82153e6i	−0.543005	+	0.433032i
$64$	1.05482e6	+	841189.i	0.0628721	+	0.0501388i
$65$	200906.	+	880227.i	0.0112548	+	0.0493107i
$66$	3.81008e7	+	1.33320e7i	2.00797	+	0.702621i
$67$	8.93817e6	+	1.85603e7i	0.443557	+	0.921055i	0.996155	+	0.0876073i	$0.0279221\pi$
$67$	8.93817e6	+	1.85603e7i	0.443557	+	0.921055i	−0.552598	+	0.833448i	$0.686364\pi$
$68$	9.29548e6	−	5.84074e6i	0.434747	−	0.273169i
$69$	−3.40891e7	+	1.19283e7i	−1.50390	+	0.526237i
$70$	891552.	+	891552.i	0.0371325	+	0.0371325i
$71$	−7.98729e6	+	1.65858e7i	−0.314316	+	0.652683i	−0.996947	−	0.0780795i	$-0.975121\pi$
$71$	−7.98729e6	+	1.65858e7i	−0.314316	+	0.652683i	0.682631	+	0.730763i	$0.260835\pi$
$72$	−856263.	−	7.59954e6i	−0.0318623	−	0.282786i
$73$	1.56965e7	−	1.76857e6i	0.552729	−	0.0622776i	0.168817	−	0.985647i	$-0.446005\pi$
$73$	1.56965e7	−	1.76857e6i	0.552729	−	0.0622776i	0.383912	+	0.923370i	$0.374577\pi$
$74$	−1.22883e7	−	5.91774e6i	−0.409793	−	0.197346i
$75$	2.72006e7	−	2.72006e7i	0.859674	−	0.859674i
$76$	−1.20546e6	−	3.44501e6i	−0.0361325	−	0.103261i
$77$	−3.83258e7	−	6.09952e7i	−1.09026	−	1.73513i
$78$	8.58305e7	−	4.13338e7i	2.31880	−	1.11667i
$79$	−2.06555e7	+	5.90300e7i	−0.530307	+	1.51553i	0.297614	+	0.954686i	$0.403809\pi$
$79$	−2.06555e7	+	5.90300e7i	−0.530307	+	1.51553i	−0.827921	+	0.560844i	$0.810477\pi$
$80$	−1.47107e6	+	335761.i	−0.0359147	+	0.00819730i
$81$	3.35389e7	−	4.20565e7i	0.779129	−	0.976997i
$82$	1.43818e7	+	1.80342e7i	0.318096	+	0.398879i
$83$	−3.24788e6	+	1.42299e7i	−0.0684365	+	0.299840i	−0.997550	−	0.0699543i	$-0.977715\pi$
$83$	−3.24788e6	+	1.42299e7i	−0.0684365	+	0.299840i	0.929114	+	0.369794i	$0.120572\pi$
$84$	2.42059e7	−	3.85235e7i	0.486188	−	0.773764i
$85$	170214.	−	1.51069e6i	0.00326077	−	0.0289402i
$86$			1.56472e7i			0.286051i
$87$	−3.20007e7	+	6.19324e7i	−0.558576	+	1.08104i
$88$	5.03533e7			0.839648
$89$	−1.95390e7	−	2.20152e6i	−0.311417	−	0.0350883i	−0.0451271	−	0.998981i	$-0.514369\pi$
$89$	−1.95390e7	−	2.20152e6i	−0.311417	−	0.0350883i	−0.266290	+	0.963893i	$0.585798\pi$
$90$	970399.	+	609742.i	0.0147904	+	0.00929343i
$91$	−1.65746e8	−	3.78304e7i	−2.41700	−	0.551665i
$92$	3.81169e7	−	3.03972e7i	0.532067	−	0.424309i
$93$	8.27295e7	+	6.59746e7i	1.10593	+	0.881952i
$94$	−2.10488e7	−	9.22207e7i	−0.269597	−	1.18118i
$95$	−477063.	−	166932.i	−0.00585708	−	0.00204948i
$96$	4.25293e7	+	8.83129e7i	0.500729	+	1.03977i
$97$	1.31178e8	−	8.24246e7i	1.48175	−	0.931043i	0.483293	−	0.875459i	$-0.339441\pi$
$97$	1.31178e8	−	8.24246e7i	1.48175	−	0.931043i	0.998454	−	0.0555844i	$-0.0177022\pi$
$98$	−1.16766e8	+	4.08584e7i	−1.26594	+	0.442972i
$99$	−4.63005e7	−	4.63005e7i	−0.481997	−	0.481997i
$100$	−2.25307e7	+	4.67855e7i	−0.225307	+	0.467855i
$101$	−1.34644e6	−	1.19499e7i	−0.0129390	−	0.114837i	0.985582	−	0.169196i	$-0.0541170\pi$
$101$	−1.34644e6	−	1.19499e7i	−0.0129390	−	0.114837i	−0.998521	+	0.0543591i	$0.982688\pi$
$102$	−1.59399e8	+	1.79600e7i	−1.47260	+	0.165922i
$103$	9.91204e7	+	4.77339e7i	0.880672	+	0.424109i	0.818870	−	0.573979i	$-0.194601\pi$
$103$	9.91204e7	+	4.77339e7i	0.880672	+	0.424109i	0.0618023	+	0.998088i	$0.480315\pi$
$104$	8.40290e7	−	8.40290e7i	0.718283	−	0.718283i
$105$	−2.08090e6	−	5.94686e6i	−0.0171196	−	0.0489250i
$106$	1.06309e8	+	1.69189e8i	0.842065	+	1.34014i
$107$	−1.65564e8	+	7.97315e7i	−1.26308	+	0.608268i	−0.940988	−	0.338440i	$-0.890101\pi$
$107$	−1.65564e8	+	7.97315e7i	−1.26308	+	0.608268i	−0.322093	+	0.946708i	$0.604387\pi$
$108$	−1.47585e7	+	4.21773e7i	−0.108479	+	0.310016i
$109$	6.47953e6	−	1.47891e6i	0.0459026	−	0.0104770i	−0.199508	−	0.979896i	$-0.563934\pi$
$109$	6.47953e6	−	1.47891e6i	0.0459026	−	0.0104770i	0.245411	+	0.969419i	$0.421077\pi$
$110$	−4.70478e6	+	5.89960e6i	−0.0321342	+	0.0402951i
$111$	4.24932e7	+	5.32848e7i	0.279916	+	0.351003i
$112$	6.32235e7	−	2.77000e8i	0.401797	−	1.76039i
$113$	−4.29708e7	+	6.83876e7i	−0.263548	+	0.419434i	−0.952116	−	0.305738i	$-0.901097\pi$
$113$	−4.29708e7	+	6.83876e7i	−0.263548	+	0.419434i	0.688568	+	0.725172i	$0.258240\pi$
$114$	−5.97100e6	+	5.29941e7i	−0.0353531	+	0.313768i
$115$		−	6.75135e6i		−	0.0386011i
$116$	1.31616e7	−	9.31797e7i	0.0726906	−	0.514623i
$117$	−1.54531e8			−0.824656
$118$	−2.48699e8	−	2.80216e7i	−1.28276	−	0.144532i
$119$	2.42385e8	+	1.52301e8i	1.20870	+	0.759475i
$120$	4.29355e6	+	979974.i	0.0207058	+	0.00472596i
$121$	1.69473e8	−	1.35151e8i	0.790606	−	0.630487i
$122$	−9.86189e7	−	7.86459e7i	−0.445165	−	0.355007i
$123$	−2.56485e7	−	1.12374e8i	−0.112058	−	0.490957i
$124$	−1.34826e8	−	4.71777e7i	−0.570278	−	0.199549i
$125$	6.24281e6	+	1.29633e7i	0.0255705	+	0.0530978i
$126$	−1.82725e8	+	1.14814e8i	−0.724963	+	0.455524i
$127$	−3.49157e8	+	1.22175e8i	−1.34217	+	0.469644i	−0.903339	−	0.428928i	$-0.858891\pi$
$127$	−3.49157e8	+	1.22175e8i	−1.34217	+	0.469644i	−0.438826	+	0.898572i	$0.644606\pi$
$128$	1.98840e8	+	1.98840e8i	0.740737	+	0.740737i
$129$	3.39249e7	−	7.04458e7i	0.122507	−	0.254388i
$130$	1.99391e6	+	1.76965e7i	0.00698124	+	0.0619602i
$131$	2.57897e8	−	2.90580e7i	0.875712	−	0.0986691i	0.337347	−	0.941381i	$-0.390471\pi$
$131$	2.57897e8	−	2.90580e7i	0.875712	−	0.0986691i	0.538365	+	0.842711i	$0.319042\pi$
$132$	2.45325e8	+	1.18142e8i	0.808064	+	0.389143i
$133$	6.72962e7	−	6.72962e7i	0.215072	−	0.215072i
$134$	1.34202e8	+	3.83528e8i	0.416237	+	1.18954i
$135$	3.29218e6	+	5.23948e6i	0.00991172	+	0.0157744i
$136$	−1.80280e8	+	8.68183e7i	−0.526978	+	0.253779i
$137$	1.36210e8	−	3.89266e8i	0.386658	−	1.10501i	−0.571953	−	0.820286i	$-0.693814\pi$
$137$	1.36210e8	−	3.89266e8i	0.386658	−	1.10501i	0.958611	−	0.284719i	$-0.0919002\pi$
$138$	−6.94501e8	+	1.58515e8i	−1.91494	+	0.437074i
$139$	−1.07903e8	+	1.35306e8i	−0.289051	+	0.362458i	−0.905062	−	0.425279i	$-0.860176\pi$
$139$	−1.07903e8	+	1.35306e8i	−0.289051	+	0.362458i	0.616012	+	0.787737i	$0.288747\pi$
$140$	5.30282e6	+	6.64953e6i	0.0138037	+	0.0173093i
$141$	−1.05180e8	+	4.60825e8i	−0.266108	+	1.16590i
$142$	−1.93182e8	+	3.07448e8i	−0.475132	+	0.756168i
$143$	1.13919e8	−	1.01106e9i	0.272429	−	2.41788i
$144$		−	2.58258e8i		−	0.600626i
$145$	−8.95198e6	−	9.47018e6i	−0.0202510	−	0.0214233i
$146$	3.11563e8			0.685701
$147$	6.14283e8	+	6.92131e7i	1.31552	+	0.148224i
$148$	−7.79004e7	−	4.89481e7i	−0.162365	−	0.102021i
$149$	7.74409e8	+	1.76754e8i	1.57118	+	0.358611i	0.917365	−	0.398046i	$-0.130312\pi$
$149$	7.74409e8	+	1.76754e8i	1.57118	+	0.358611i	0.653812	+	0.756657i	$0.273169\pi$
$150$	5.93213e8	−	4.73071e8i	1.17178	−	0.934462i
$151$	6.82842e7	+	5.44548e7i	0.131345	+	0.104744i	0.686959	−	0.726697i	$-0.258945\pi$
$151$	6.82842e7	+	5.44548e7i	0.131345	+	0.104744i	−0.555614	+	0.831440i	$0.687517\pi$
$152$	1.48030e7	+	6.48563e7i	0.0277317	+	0.121500i
$153$	2.45600e8	+	8.59392e7i	0.448191	+	0.156829i
$154$	−6.16497e8	−	1.28017e9i	−1.09609	−	2.27606i
$155$	−1.67488e7	+	1.05240e7i	−0.0290173	+	0.0182328i
$156$	6.06549e8	−	2.12241e8i	1.02416	−	0.358369i
$157$	−6.71788e8	−	6.71788e8i	−1.10569	−	1.10569i	−0.993710	−	0.111980i	$-0.964281\pi$
$157$	−6.71788e8	−	6.71788e8i	−1.10569	−	1.10569i	−0.111980	−	0.993710i	$-0.535719\pi$
$158$	−5.35219e8	+	1.11139e9i	−0.858822	+	1.78336i
$159$	−1.11794e8	−	9.92201e8i	−0.174916	−	1.55243i
$160$	−1.82083e7	+	2.05158e6i	−0.0277836	+	0.00313046i
$161$	1.14538e9	+	5.51584e8i	1.70469	+	0.820934i
$162$	7.50254e8	−	7.50254e8i	1.08930	−	1.08930i
$163$	1.71099e8	+	4.88971e8i	0.242379	+	0.692681i	0.999235	+	0.0390989i	$0.0124487\pi$
$163$	1.71099e8	+	4.88971e8i	0.242379	+	0.692681i	−0.756856	+	0.653582i	$0.773266\pi$
$164$	8.27823e7	+	1.31747e8i	0.114436	+	0.182124i
$165$	3.39725e7	−	1.63603e7i	0.0458344	−	0.0220727i
$166$	−9.50854e7	+	2.71738e8i	−0.125222	+	0.357864i
$167$	−4.83023e8	+	1.10247e8i	−0.621014	+	0.141742i	−0.521440	−	0.853288i	$-0.674605\pi$
$167$	−4.83023e8	+	1.10247e8i	−0.621014	+	0.141742i	−0.0995738	+	0.995030i	$0.531748\pi$
$168$	−5.17036e8	+	6.48343e8i	−0.649058	+	0.813894i
$169$	−9.88543e8	−	1.23959e9i	−1.21185	−	1.51961i
$170$	6.67253e6	−	2.92342e7i	0.00798904	−	0.0350023i
$171$	4.60246e7	−	7.32477e7i	0.0538276	−	0.0856662i
$172$	−1.18177e7	+	1.04885e8i	−0.0135027	+	0.119840i
$173$			6.13510e8i			0.684916i	0.939533	+	0.342458i	$0.111259\pi$
$173$			6.13510e8i			0.684916i	−0.939533	+	0.342458i	$0.888741\pi$
$174$	−7.63999e8	+	1.14323e9i	−0.833481	+	1.24720i
$175$	−1.35405e9			−1.44372
$176$	1.68973e9	+	1.90386e8i	1.76102	+	0.198420i
$177$	1.05892e9	+	6.65363e8i	1.07887	+	0.677900i
$178$	−3.78110e8	−	8.63010e7i	−0.376650	−	0.0859678i
$179$	−8.28687e8	+	6.60856e8i	−0.807195	+	0.643716i	−0.937589	−	0.347746i	$-0.886947\pi$
$179$	−8.28687e8	+	6.60856e8i	−0.807195	+	0.643716i	0.130394	+	0.991462i	$0.458376\pi$
$180$	6.04418e6	+	4.82007e6i	0.00575768	+	0.00459159i
$181$	1.89642e8	+	8.30877e8i	0.176694	+	0.774145i	0.983142	+	0.182841i	$0.0585295\pi$
$181$	1.89642e8	+	8.30877e8i	0.176694	+	0.774145i	−0.806449	+	0.591304i	$0.798613\pi$
$182$	−3.16513e9	−	1.10753e9i	−2.88474	−	1.00941i
$183$	2.73482e8	+	5.67890e8i	0.243851	+	0.506361i
$184$	−7.52410e8	+	4.72771e8i	−0.656422	+	0.412457i
$185$	−1.20255e7	+	4.20790e6i	−0.0102663	+	0.00359234i
$186$	1.47583e9	+	1.47583e9i	1.23306	+	1.23306i
$187$	−7.43336e8	+	1.54355e9i	−0.607881	+	1.26228i
$188$	−7.14417e7	−	6.34063e8i	−0.0571900	−	0.507576i
$189$	−1.15786e9	+	1.30459e8i	−0.907418	+	0.102241i
$190$	−8.98195e6	−	4.32548e6i	−0.00689218	−	0.00331910i
$191$	−5.72516e8	+	5.72516e8i	−0.430184	+	0.430184i	−0.888691	−	0.458507i	$-0.848384\pi$
$191$	−5.72516e8	+	5.72516e8i	−0.430184	+	0.430184i	0.458507	+	0.888691i	$0.348384\pi$
$192$	−4.39194e7	−	1.25515e8i	−0.0323185	−	0.0923611i
$193$	−6.99829e7	−	1.11377e8i	−0.0504385	−	0.0802725i	0.820553	−	0.571570i	$-0.193666\pi$
$193$	−6.99829e7	−	1.11377e8i	−0.0504385	−	0.0802725i	−0.870992	+	0.491298i	$0.836523\pi$
$194$	2.75316e9	−	1.32585e9i	1.94368	−	0.936028i
$195$	2.93910e7	−	8.39947e7i	0.0203271	−	0.0580916i
$196$	−8.13557e8	+	1.85689e8i	−0.551269	+	0.125824i
$197$	−1.31589e9	+	1.65007e9i	−0.873684	+	1.09557i	0.121006	+	0.992652i	$0.461388\pi$
$197$	−1.31589e9	+	1.65007e9i	−0.873684	+	1.09557i	−0.994690	+	0.102913i	$0.967184\pi$
$198$	−8.05255e8	−	1.00976e9i	−0.523929	−	0.656986i
$199$	6.03545e8	−	2.64430e9i	0.384855	−	1.68616i	−0.297165	−	0.954826i	$-0.596041\pi$
$199$	6.03545e8	−	2.64430e9i	0.384855	−	1.68616i	0.682020	−	0.731334i	$-0.261102\pi$
$200$	5.03556e8	−	8.01404e8i	0.314722	−	0.500878i
$201$	2.27335e8	−	2.01766e9i	0.139278	−	1.23613i
$202$		−	2.37197e8i		−	0.142463i
$203$	2.33800e9	−	7.45004e8i	1.37677	−	0.438707i
$204$	−1.08204e9			−0.624771
$205$	2.14115e7	+	2.41249e6i	0.0121236	+	0.00136600i
$206$	1.83738e9	+	1.15450e9i	1.02030	+	0.641100i
$207$	1.12657e9	+	2.57132e8i	0.613587	+	0.140047i
$208$	3.13751e9	−	2.50208e9i	1.67622	−	1.33674i
$209$	4.45314e8	+	3.55126e8i	0.233389	+	0.186122i
$210$	−2.76531e7	−	1.21156e8i	−0.0142189	−	0.0622972i
$211$	−1.53360e8	−	5.36629e7i	−0.0773716	−	0.0270735i	0.291316	−	0.956627i	$-0.405907\pi$
$211$	−1.53360e8	−	5.36629e7i	−0.0773716	−	0.0270735i	−0.368687	+	0.929553i	$0.620193\pi$
$212$	5.84817e8	+	1.21439e9i	0.289519	+	0.601192i
$213$	1.53631e9	−	9.65329e8i	0.746382	−	0.468983i
$214$	−3.42120e9	+	1.19713e9i	−1.63126	+	0.570803i
$215$	1.03353e7	+	1.03353e7i	0.00483694	+	0.00483694i
$216$	3.53380e8	−	7.33801e8i	0.162340	−	0.337103i
$217$	−4.17032e8	−	3.70126e9i	−0.188075	−	1.66921i
$218$	1.30267e8	−	1.46776e7i	0.0576779	−	0.00649873i
$219$	−1.40270e9	−	6.75503e8i	−0.609800	−	0.293664i
$220$	−3.59924e7	+	3.59924e7i	−0.0153645	+	0.0153645i
$221$	1.33539e9	+	3.81633e9i	0.559809	+	1.59984i
$222$	7.15206e8	+	1.13824e9i	0.294455	+	0.468623i
$223$	8.60979e8	−	4.14626e8i	0.348155	−	0.167663i	−0.251630	−	0.967823i	$-0.580967\pi$
$223$	8.60979e8	−	4.14626e8i	0.348155	−	0.167663i	0.599786	+	0.800161i	$0.295252\pi$
$224$	1.13956e9	−	3.25668e9i	0.452632	−	1.29355i
$225$	−1.19993e9	+	2.73875e8i	−0.468192	+	0.106862i
$226$	−9.93273e8	+	1.24552e9i	−0.380745	+	0.477440i
$227$	2.43452e8	+	3.05279e8i	0.0916873	+	0.114972i	0.825559	−	0.564316i	$-0.190860\pi$
$227$	2.43452e8	+	3.05279e8i	0.0916873	+	0.114972i	−0.733872	+	0.679288i	$0.762289\pi$
$228$	−8.00486e7	+	3.50716e8i	−0.0296220	+	0.129782i
$229$	−6.55957e8	+	1.04395e9i	−0.238525	+	0.379610i	−0.944439	−	0.328688i	$-0.893394\pi$
$229$	−6.55957e8	+	1.04395e9i	−0.238525	+	0.379610i	0.705914	+	0.708298i	$0.250537\pi$
$230$	1.49099e7	−	1.32329e8i	0.00532798	−	0.0472872i
$231$			7.10011e9i			2.49355i
$232$	−4.28541e8	+	1.66082e9i	−0.147924	+	0.573285i
$233$	−1.43859e9			−0.488104			−0.244052	−	0.969762i	$-0.578477\pi$
$233$	−1.43859e9			−0.488104			−0.244052	+	0.969762i	$0.578477\pi$
$234$	−3.02887e9	−	3.41272e8i	−1.01022	−	0.113825i
$235$	−7.48169e7	−	4.70105e7i	−0.0245317	−	0.0154143i
$236$	−1.64589e9	−	3.75664e8i	−0.530583	−	0.121102i
$237$	4.81925e9	−	3.84322e9i	1.52752	−	1.21815i
$238$	4.41449e9	+	3.52044e9i	1.37585	+	1.09721i
$239$	−8.03750e8	−	3.52146e9i	−0.246337	−	1.07927i	−0.935127	−	0.354312i	$-0.884715\pi$
$239$	−8.03750e8	−	3.52146e9i	−0.246337	−	1.07927i	0.688790	−	0.724961i	$-0.258142\pi$
$240$	1.40375e8	+	4.91193e7i	0.0423101	+	0.0148050i
$241$	−2.22015e9	−	4.61019e9i	−0.658134	−	1.36663i	−0.916286	−	0.400525i	$-0.868828\pi$
$241$	−2.22015e9	−	4.61019e9i	−0.658134	−	1.36663i	0.258152	−	0.966104i	$-0.416886\pi$
$242$	3.62021e9	−	2.27473e9i	1.05553	−	0.663236i
$243$	−2.92454e9	+	1.02334e9i	−0.838748	+	0.293491i
$244$	−6.01655e8	−	6.01655e8i	−0.169742	−	0.169742i
$245$	−5.01389e7	+	1.04115e8i	−0.0139159	+	0.0288966i
$246$	−2.54551e8	−	2.25921e9i	−0.0695080	−	0.616901i
$247$	1.33576e9	−	1.50504e8i	0.358874	−	0.0404354i
$248$	2.34570e9	+	1.12963e9i	0.620107	+	0.298628i
$249$	1.01724e9	−	1.01724e9i	0.264623	−	0.264623i
$250$	9.37327e7	+	2.67873e8i	0.0239956	+	0.0685754i
$251$	−3.67857e9	−	5.85441e9i	−0.926796	−	1.47499i	−0.879384	−	0.476112i	$-0.842046\pi$
$251$	−3.67857e9	−	5.85441e9i	−0.926796	−	1.47499i	−0.0474118	−	0.998875i	$-0.515097\pi$
$252$	−1.31154e9	+	6.31604e8i	−0.325222	+	0.156618i
$253$	−2.51285e9	+	7.18132e9i	−0.613317	+	1.75276i
$254$	−7.11342e9	+	1.62359e9i	−1.70901	+	0.390069i
$255$	−9.34236e7	+	1.17149e8i	−0.0220951	+	0.0277064i
$256$	3.24287e9	+	4.06643e9i	0.755039	+	0.946790i
$257$	−1.21198e9	+	5.31005e9i	−0.277821	+	1.21721i	0.622722	+	0.782443i	$0.286027\pi$
$257$	−1.21198e9	+	5.31005e9i	−0.277821	+	1.21721i	−0.900542	+	0.434768i	$0.856830\pi$
$258$	8.20515e8	−	1.30584e9i	0.185186	−	0.294722i
$259$	2.68604e8	−	2.38392e9i	0.0596916	−	0.529777i
$260$			1.20127e8i			0.0262874i
$261$	1.92119e9	−	1.13310e9i	0.414008	−	0.244177i
$262$	5.11905e9			1.08639
$263$	−5.14766e9	−	5.80002e8i	−1.07594	−	0.121229i	−0.443831	−	0.896111i	$-0.646381\pi$
$263$	−5.14766e9	−	5.80002e8i	−1.07594	−	0.121229i	−0.632106	+	0.774882i	$0.717809\pi$
$264$	−4.20224e9	−	2.64045e9i	−0.865099	−	0.543578i
$265$	1.81972e8	+	4.15340e7i	0.0368996	+	0.00842210i
$266$	1.46765e9	−	1.17041e9i	0.293154	−	0.233782i
$267$	1.51519e9	+	1.20832e9i	0.298141	+	0.237759i
$268$	6.09909e8	+	2.67219e9i	0.118230	+	0.517997i
$269$	2.96328e9	+	1.03690e9i	0.565931	+	0.198028i	0.598054	−	0.801456i	$-0.295941\pi$
$269$	2.96328e9	+	1.03690e9i	0.565931	+	0.198028i	−0.0321225	+	0.999484i	$0.510227\pi$
$270$	5.29570e7	+	1.09966e8i	0.00996479	+	0.0206921i
$271$	−7.52779e9	+	4.73002e9i	−1.39569	+	0.876973i	−0.999157	−	0.0410459i	$-0.986931\pi$
$271$	−7.52779e9	+	4.73002e9i	−1.39569	+	0.876973i	−0.396537	+	0.918019i	$0.629788\pi$
$272$	−6.37799e9	+	2.23175e9i	−1.16522	+	0.407728i
$273$	1.18486e10	+	1.18486e10i	2.13312	+	2.13312i
$274$	3.52943e9	−	7.32895e9i	0.626185	−	1.30029i
$275$	−9.07326e8	−	8.05274e9i	−0.158647	−	1.40803i
$276$	−4.77504e9	+	5.38017e8i	−0.822887	+	0.0927171i
$277$	3.84207e9	+	1.85025e9i	0.652599	+	0.314275i	0.730729	−	0.682668i	$-0.239180\pi$
$277$	3.84207e9	+	1.85025e9i	0.652599	+	0.314275i	−0.0781294	+	0.996943i	$0.524895\pi$
$278$	−2.41375e9	+	2.41375e9i	−0.404123	+	0.404123i
$279$	−1.11819e9	−	3.19561e9i	−0.184544	−	0.527396i
$280$	−8.24752e7	−	1.31259e8i	−0.0134181	−	0.0213548i
$281$	6.15662e9	−	2.96487e9i	0.987454	−	0.475533i	0.130792	−	0.991410i	$-0.458248\pi$
$281$	6.15662e9	−	2.96487e9i	0.987454	−	0.475533i	0.856663	+	0.515877i	$0.172534\pi$
$282$	−3.07927e9	+	8.80005e9i	−0.486913	+	1.39152i
$283$	−6.48283e9	+	1.47966e9i	−1.01069	+	0.230684i	−0.695640	−	0.718391i	$-0.744879\pi$
$283$	−6.48283e9	+	1.47966e9i	−1.01069	+	0.230684i	−0.315052	+	0.949074i	$0.602022\pi$
$284$	−1.52713e9	+	1.91496e9i	−0.234748	+	0.294364i
$285$	3.10598e7	+	3.89477e7i	0.00470781	+	0.00590340i
$286$	4.46573e9	−	1.95656e10i	0.667464	−	2.92435i
$287$	−2.15860e9	+	3.43539e9i	−0.318159	+	0.506347i
$288$	3.51142e8	−	3.11647e9i	0.0510403	−	0.452995i
$289$			1.67727e8i			0.0240443i
$290$	−1.54548e8	−	2.05389e8i	−0.0218510	−	0.0290392i
$291$	−1.52697e10			−2.12941
$292$	2.08844e9	+	2.35311e8i	0.287271	+	0.0323676i
$293$	−8.71490e9	−	5.47594e9i	−1.18248	−	0.742998i	−0.210388	−	0.977618i	$-0.567473\pi$
$293$	−8.71490e9	−	5.47594e9i	−1.18248	−	0.742998i	−0.972087	+	0.234620i	$0.924616\pi$
$294$	1.18873e10	+	2.71320e9i	1.59109	+	0.363156i
$295$	−1.82780e8	+	1.45762e8i	−0.0241346	+	0.0192467i
$296$	1.31105e9	+	1.04553e9i	0.170786	+	0.136197i
$297$	−1.55172e9	−	6.79852e9i	−0.199428	−	0.873753i
$298$	1.47883e10	+	5.17467e9i	1.87523	+	0.656171i
$299$	7.79068e9	+	1.61775e10i	0.974745	+	2.02408i
$300$	4.33366e9	−	2.72302e9i	0.535020	−	0.336175i
$301$	−2.59780e9	+	9.09009e8i	−0.316475	+	0.110739i
$302$	1.21813e9	+	1.21813e9i	0.146443	+	0.146443i
$303$	−5.14268e8	+	1.06789e9i	−0.0610126	+	0.126694i
$304$	2.51528e8	+	2.23238e9i	0.0294505	+	0.261381i
$305$	−1.17087e8	+	1.31926e7i	−0.0135304	+	0.00152451i
$306$	4.62406e9	+	2.22683e9i	0.527397	+	0.253981i
$307$	1.18000e9	−	1.18000e9i	0.132840	−	0.132840i	−0.637560	−	0.770400i	$-0.720056\pi$
$307$	1.18000e9	−	1.18000e9i	0.132840	−	0.132840i	0.770400	+	0.637560i	$0.220056\pi$
$308$	−3.16559e9	−	9.04673e9i	−0.351764	−	1.00528i
$309$	−5.76903e9	−	9.18135e9i	−0.632803	−	1.00710i
$310$	−3.51524e8	+	1.69285e8i	−0.0380634	+	0.0183304i
$311$	−3.84503e9	+	1.09885e10i	−0.411016	+	1.17462i	0.533401	+	0.845863i	$0.320914\pi$
$311$	−3.84503e9	+	1.09885e10i	−0.411016	+	1.17462i	−0.944416	+	0.328752i	$0.893372\pi$
$312$	−1.14190e10	+	2.60631e9i	−1.20506	+	0.275048i
$313$	8.71122e9	−	1.09235e10i	0.907615	−	1.13811i	−0.0823218	−	0.996606i	$-0.526234\pi$
$313$	8.71122e9	−	1.09235e10i	0.907615	−	1.13811i	0.989937	−	0.141508i	$-0.0451950\pi$
$314$	−1.16837e10	−	1.46509e10i	−1.20188	−	1.50711i
$315$	−4.48568e7	+	1.96531e8i	−0.00455603	+	0.0199613i
$316$	−4.42702e9	+	7.04557e9i	−0.443980	+	0.706590i
$317$	4.27030e8	−	3.78999e9i	0.0422884	−	0.375320i	−0.954688	−	0.297610i	$-0.903811\pi$
$317$	4.27030e8	−	3.78999e9i	0.0422884	−	0.375320i	0.996976	−	0.0777100i	$-0.0247608\pi$
$318$		−	1.96944e10i		−	1.92590i
$319$	5.99730e9	+	1.34052e10i	0.579153	+	1.29453i
$320$	2.48582e7			0.00237066
$321$	1.79982e10	+	2.02791e9i	1.69515	+	0.190998i
$322$	2.12317e10	+	1.33407e10i	1.97497	+	1.24096i
$323$	−2.20666e9	−	5.03656e8i	−0.202733	−	0.0462726i
$324$	5.59567e9	−	4.46240e9i	0.507776	−	0.404938i
$325$	−1.49525e10	−	1.19242e10i	−1.34023	−	1.06880i
$326$	2.27373e9	+	9.96188e9i	0.201312	+	0.882004i
$327$	−6.18302e8	−	2.16353e8i	−0.0540766	−	0.0189222i
$328$	−1.23050e9	−	2.55516e9i	−0.106313	−	0.220761i
$329$	1.40879e10	−	8.85203e9i	1.20244	−	0.755544i
$330$	7.02003e8	−	2.45642e8i	0.0591948	−	0.0207131i
$331$	8.26203e9	+	8.26203e9i	0.688296	+	0.688296i	0.961855	−	0.273559i	$-0.0882010\pi$
$331$	8.26203e9	+	8.26203e9i	0.688296	+	0.688296i	−0.273559	+	0.961855i	$0.588201\pi$
$332$	−8.42601e8	+	1.74968e9i	−0.0693537	+	0.144014i
$333$	−2.44151e8	−	2.16690e9i	−0.0198555	−	0.176223i
$334$	−9.71089e9	+	1.09415e9i	−0.780321	+	0.0879210i
$335$	3.41972e8	+	1.64685e8i	0.0271526	+	0.0130760i
$336$	−1.98018e10	+	1.98018e10i	−1.55363	+	1.55363i
$337$	4.98559e9	+	1.42480e10i	0.386542	+	1.10467i	0.958673	+	0.284512i	$0.0918315\pi$
$337$	4.98559e9	+	1.42480e10i	0.386542	+	1.10467i	−0.572130	+	0.820163i	$0.693883\pi$
$338$	−1.66382e10	−	2.64796e10i	−1.27480	−	2.02883i
$339$	7.17227e9	−	3.45398e9i	0.543073	−	0.261530i
$340$	6.68061e7	−	1.90921e8i	0.00499920	−	0.0142869i
$341$	2.17325e10	−	4.96030e9i	1.60728	−	0.366851i
$342$	1.06386e9	−	1.33404e9i	0.0777643	−	0.0975133i
$343$	−1.09684e9	−	1.37539e9i	−0.0792438	−	0.0993686i
$344$	4.28087e8	−	1.87557e9i	0.0305702	−	0.133937i
$345$	−3.54030e8	+	5.63435e8i	−0.0249898	+	0.0397711i
$346$	−1.35489e9	+	1.20250e10i	−0.0945368	+	0.839037i
$347$		−	8.75402e9i		−	0.603795i	−0.953340	−	0.301897i	$-0.902380\pi$
$347$		−	8.75402e9i		−	0.603795i	0.953340	−	0.301897i	$-0.0976200\pi$
$348$	−5.98460e9	+	7.08616e9i	−0.408054	+	0.483163i
$349$	1.30015e10			0.876381			0.438191	−	0.898882i	$-0.355620\pi$
$349$	1.30015e10			0.876381			0.438191	+	0.898882i	$0.355620\pi$
$350$	−2.65399e10	−	2.99033e9i	−1.76859	−	0.199272i
$351$	−1.39348e10	−	8.75580e9i	−0.918061	−	0.576856i
$352$	2.01315e10	+	4.59489e9i	1.31131	+	0.299298i
$353$	7.46871e9	−	5.95609e9i	0.481002	−	0.383586i	−0.352757	−	0.935715i	$-0.614756\pi$
$353$	7.46871e9	−	5.95609e9i	0.481002	−	0.383586i	0.833759	+	0.552129i	$0.186184\pi$
$354$	1.92858e10	+	1.53799e10i	1.22807	+	0.979356i
$355$	7.54748e7	+	3.30677e8i	0.00475214	+	0.0208205i
$356$	−2.46933e9	−	8.64056e8i	−0.153737	−	0.0537950i
$357$	−1.22419e10	−	2.54205e10i	−0.753660	−	1.56499i
$358$	−1.77020e10	+	1.11229e10i	−1.07768	+	0.677152i
$359$	7.12634e9	−	2.49361e9i	0.429031	−	0.150124i	−0.107121	−	0.994246i	$-0.534163\pi$
$359$	7.12634e9	−	2.49361e9i	0.429031	−	0.150124i	0.536152	+	0.844122i	$0.319877\pi$
$360$	−9.96362e7	−	9.96362e7i	−0.00593208	−	0.00593208i
$361$	7.04240e9	−	1.46237e10i	0.414660	−	0.861049i
$362$	1.88212e9	+	1.67043e10i	0.109601	+	0.972734i
$363$	−2.12305e10	+	2.39210e9i	−1.22274	+	0.137770i
$364$	−2.03798e10	−	9.81437e9i	−1.16090	−	0.559058i
$365$	2.05794e8	−	2.05794e8i	0.0115948	−	0.0115948i
$366$	4.10619e9	+	1.17348e10i	0.228831	+	0.653961i
$367$	−1.26770e10	−	2.01753e10i	−0.698799	−	1.11213i	−0.987939	−	0.154846i	$-0.950512\pi$
$367$	−1.26770e10	−	2.01753e10i	−0.698799	−	1.11213i	0.289140	−	0.957287i	$-0.406631\pi$
$368$	−2.70365e10	+	1.30201e10i	−1.47421	+	0.709941i
$369$	−1.21804e9	+	3.48095e9i	−0.0656985	+	0.187756i
$370$	−2.44996e8	+	5.59189e7i	−0.0130723	+	0.00298367i
$371$	−2.19134e10	+	2.74785e10i	−1.15668	+	1.45043i
$372$	8.77801e9	+	1.10073e10i	0.458378	+	0.574788i
$373$	−2.89546e9	+	1.26858e10i	−0.149583	+	0.655366i	0.843418	+	0.537258i	$0.180540\pi$
$373$	−2.89546e9	+	1.26858e10i	−0.149583	+	0.655366i	−0.993001	+	0.118108i	$0.962317\pi$
$374$	−1.79785e10	+	2.86126e10i	−0.918896	+	1.46241i
$375$	1.58781e8	−	1.40922e9i	0.00802921	−	0.0712612i
$376$			1.16300e10i			0.581873i
$377$	3.23787e10	+	1.23623e10i	1.60285	+	0.611974i
$378$	−2.29825e10			−1.12572
$379$	4.05246e9	+	4.56602e8i	0.196409	+	0.0221300i	0.209621	−	0.977783i	$-0.432777\pi$
$379$	4.05246e9	+	4.56602e8i	0.196409	+	0.0221300i	−0.0132118	+	0.999913i	$0.504206\pi$
$380$	−5.69402e7	−	3.57779e7i	−0.00273077	−	0.00171585i
$381$	3.55456e10	+	8.11306e9i	1.68689	+	0.385021i
$382$	−1.24859e10	+	9.95715e9i	−0.586362	+	0.467608i
$383$	1.11495e10	+	8.89143e9i	0.518156	+	0.413216i	0.847340	−	0.531050i	$-0.178202\pi$
$383$	1.11495e10	+	8.89143e9i	0.518156	+	0.413216i	−0.329185	+	0.944266i	$0.606774\pi$
$384$	−6.16739e9	−	2.70211e10i	−0.283646	−	1.24273i
$385$	−1.25279e9	−	4.38369e8i	−0.0570210	−	0.0199525i
$386$	−1.12572e9	−	2.33758e9i	−0.0507086	−	0.105297i
$387$	−2.11824e9	+	1.33098e9i	−0.0944347	+	0.0593373i
$388$	1.94561e10	−	6.80800e9i	0.858479	−	0.300395i
$389$	2.49824e10	+	2.49824e10i	1.09103	+	1.09103i	0.995419	+	0.0956110i	$0.0304805\pi$
$389$	2.49824e10	+	2.49824e10i	1.09103	+	1.09103i	0.0956110	+	0.995419i	$0.469520\pi$
$390$	7.61571e8	−	1.58142e9i	0.0329194	−	0.0683578i
$391$	−3.38514e9	−	3.00439e10i	−0.144834	−	1.28543i
$392$	1.51142e10	−	1.70296e9i	0.640089	−	0.0721207i
$393$	−2.30466e10	−	1.10987e10i	−0.966133	−	0.465265i
$394$	−2.94360e10	+	2.94360e10i	−1.22150	+	1.22150i
$395$	3.80576e8	+	1.08762e9i	0.0156334	+	0.0446776i
$396$	−4.63508e9	−	7.37669e9i	−0.188485	−	0.299972i
$397$	−4.21030e10	+	2.02758e10i	−1.69493	+	0.816235i	−0.700171	+	0.713975i	$0.746893\pi$
$397$	−4.21030e10	+	2.02758e10i	−1.69493	+	0.816235i	−0.994758	+	0.102259i	$0.967393\pi$
$398$	1.76694e10	−	5.04964e10i	0.704191	−	2.01246i
$399$	−9.14511e9	+	2.08731e9i	−0.360826	+	0.0823561i
$400$	1.99281e10	−	2.49891e10i	0.778442	−	0.976136i
$401$	−3.05624e9	−	3.83240e9i	−0.118198	−	0.148215i	0.719212	−	0.694790i	$-0.244503\pi$
$401$	−3.05624e9	−	3.83240e9i	−0.118198	−	0.148215i	−0.837410	+	0.546575i	$0.815931\pi$
$402$	8.91170e9	−	3.90447e10i	0.341237	−	1.49506i
$403$	2.79892e10	−	4.45446e10i	1.06113	−	1.68879i
$404$	1.79145e8	−	1.58996e9i	0.00672480	−	0.0596842i
$405$		−	9.91118e8i		−	0.0368388i
$406$	4.74710e10	−	9.43902e9i	1.74713	−	0.347394i
$407$	1.43575e10			0.523241
$408$	1.95979e10	+	2.20815e9i	0.707244	+	0.0796873i
$409$	1.65158e10	+	1.03776e10i	0.590210	+	0.370853i	0.793778	−	0.608207i	$-0.208111\pi$
$409$	1.65158e10	+	1.03776e10i	0.590210	+	0.370853i	−0.203568	+	0.979061i	$0.565254\pi$
$410$	4.14345e8	+	9.45714e7i	0.0146631	+	0.00334676i
$411$	−3.17799e10	+	2.53436e10i	−1.11374	+	0.888181i
$412$	1.14442e10	+	9.12645e9i	0.397189	+	0.316748i
$413$	−9.79566e9	−	4.29176e10i	−0.336692	−	1.47515i
$414$	2.15133e10	+	7.52782e9i	0.732327	+	0.256252i
$415$	1.16683e8	+	2.42295e8i	0.00393383	+	0.00816868i
$416$	4.12631e10	−	2.59273e10i	1.37781	−	0.865734i
$417$	1.61003e10	−	5.63373e9i	0.532463	−	0.186317i
$418$	7.94404e9	+	7.94404e9i	0.260217	+	0.260217i
$419$	−8.74759e9	+	1.81646e10i	−0.283813	+	0.589344i	−0.993325	−	0.115350i	$-0.963201\pi$
$419$	−8.74759e9	+	1.81646e10i	−0.283813	+	0.589344i	0.709512	+	0.704693i	$0.248915\pi$
$420$	−9.38575e7	−	8.33009e8i	−0.00301628	−	0.0267702i
$421$	−2.61118e10	+	2.94209e9i	−0.831204	+	0.0936542i	−0.517304	−	0.855802i	$-0.673064\pi$
$421$	−2.61118e10	+	2.94209e9i	−0.831204	+	0.0936542i	−0.313900	+	0.949456i	$0.601636\pi$
$422$	−2.88740e9	−	1.39050e9i	−0.0910451	−	0.0438450i
$423$	1.06939e10	−	1.06939e10i	0.334022	−	0.334022i
$424$	−8.11402e9	−	2.31885e10i	−0.251057	−	0.717480i
$425$	1.71329e10	+	2.72669e10i	0.525140	+	0.835756i
$426$	3.22441e10	−	1.55280e10i	0.979067	−	0.471494i
$427$	7.32787e9	−	2.09418e10i	0.220428	−	0.629946i
$428$	−2.38368e10	+	5.44060e9i	−0.710352	+	0.162133i
$429$	−6.25257e10	+	7.84047e10i	−1.84599	+	2.31480i
$430$	1.79751e8	+	2.25401e8i	0.00525773	+	0.00659298i
$431$	−7.80515e9	+	3.41966e10i	−0.226189	+	0.991000i	0.726527	+	0.687138i	$0.241133\pi$
$431$	−7.80515e9	+	3.41966e10i	−0.226189	+	0.991000i	−0.952716	+	0.303862i	$0.901724\pi$
$432$	1.46330e10	−	2.32883e10i	0.420144	−	0.668656i
$433$	1.70270e8	−	1.51119e9i	0.00484382	−	0.0429901i	−0.991058	−	0.133433i	$-0.957400\pi$
$433$	1.70270e8	−	1.51119e9i	0.00484382	−	0.0429901i	0.995902	+	0.0904432i	$0.0288284\pi$
$434$		−	7.34670e10i		−	2.07078i
$435$	2.50488e8	+	1.25976e9i	0.00699568	+	0.0351829i
$436$	8.84281e8			0.0244706
$437$	−9.98845e9	−	1.12543e9i	−0.273888	−	0.0308597i
$438$	−2.60016e10	−	1.63379e10i	−0.706485	−	0.443914i
$439$	1.51634e10	+	3.46095e9i	0.408262	+	0.0931831i	0.421720	−	0.906726i	$-0.361427\pi$
$439$	1.51634e10	+	3.46095e9i	0.408262	+	0.0931831i	−0.0134576	+	0.999909i	$0.504284\pi$
$440$	7.25348e8	−	5.78446e8i	0.0193524	−	0.0154331i
$441$	−1.54635e10	−	1.23318e10i	−0.408841	−	0.326040i
$442$	1.77461e10	+	7.77506e10i	0.464957	+	2.03711i
$443$	4.52013e10	+	1.58166e10i	1.17364	+	0.410676i	0.845512	−	0.533956i	$-0.179295\pi$
$443$	4.52013e10	+	1.58166e10i	1.17364	+	0.410676i	0.328132	+	0.944632i	$0.393581\pi$
$444$	3.93444e9	+	8.16994e9i	0.101240	+	0.210226i
$445$	−3.06753e8	+	1.92746e8i	−0.00782256	+	0.00491524i
$446$	1.77912e10	−	6.22540e9i	0.449640	−	0.157336i
$447$	−5.53598e10	−	5.53598e10i	−1.38664	−	1.38664i
$448$	−2.03091e9	+	4.21723e9i	−0.0504172	+	0.104692i
$449$	2.68435e9	+	2.38243e10i	0.0660472	+	0.586185i	0.982529	+	0.186109i	$0.0595878\pi$
$449$	2.68435e9	+	2.38243e10i	0.0660472	+	0.586185i	−0.916482	+	0.400076i	$0.868984\pi$
$450$	−2.41238e10	+	2.71810e9i	−0.588296	+	0.0662851i
$451$	−2.18772e10	−	1.05355e10i	−0.528792	−	0.254653i
$452$	−7.59871e9	+	7.59871e9i	−0.182048	+	0.182048i
$453$	−2.84315e9	−	8.12525e9i	−0.0675160	−	0.192950i
$454$	4.09755e9	+	6.52122e9i	0.0964497	+	0.153499i
$455$	−2.82218e9	+	1.35909e9i	−0.0658475	+	0.0317105i
$456$	2.16557e9	−	6.18884e9i	0.0500856	−	0.143136i
$457$	−5.26064e10	+	1.20071e10i	−1.20607	+	0.275279i	−0.777883	−	0.628409i	$-0.783706\pi$
$457$	−5.26064e10	+	1.20071e10i	−1.20607	+	0.275279i	−0.428192	+	0.903688i	$0.640849\pi$
$458$	−1.51625e10	+	1.90132e10i	−0.344595	+	0.432108i
$459$	1.72775e10	+	2.16653e10i	0.389252	+	0.488106i
$460$	1.99885e8	−	8.75754e8i	0.00446426	−	0.0195592i
$461$	1.03613e10	−	1.64900e10i	0.229410	−	0.365104i	−0.712106	−	0.702072i	$-0.752259\pi$
$461$	1.03613e10	−	1.64900e10i	0.229410	−	0.365104i	0.941516	+	0.336968i	$0.109401\pi$
$462$	−1.56801e10	+	1.39165e11i	−0.344176	+	3.05465i
$463$			6.79043e9i			0.147766i	0.997267	+	0.0738828i	$0.0235391\pi$
$463$			6.79043e9i			0.147766i	−0.997267	+	0.0738828i	$0.976461\pi$
$464$	−2.06603e10	+	5.41125e10i	−0.445722	+	1.16742i
$465$	1.94963e9			0.0417005
$466$	−2.81968e10	−	3.17702e9i	−0.597939	−	0.0673715i
$467$	−3.39275e10	−	2.13181e10i	−0.713321	−	0.448209i	0.125870	−	0.992047i	$-0.459828\pi$
$467$	−3.39275e10	−	2.13181e10i	−0.713321	−	0.448209i	−0.839190	+	0.543838i	$0.816971\pi$
$468$	−2.00451e10	−	4.57516e9i	−0.417854	−	0.0953725i
$469$	−5.58780e10	+	4.45613e10i	−1.15491	+	0.921014i
$470$	−1.36262e9	−	1.08665e9i	−0.0279243	−	0.0222689i
$471$	2.08367e10	+	9.12916e10i	0.423395	+	1.85501i
$472$	2.90439e10	+	1.01629e10i	0.585177	+	0.204762i
$473$	−7.14674e9	−	1.48404e10i	−0.142779	−	0.296483i
$474$	1.02946e11	−	6.46856e10i	2.03938	−	1.28143i
$475$	1.01054e10	−	3.53603e9i	0.198508	−	0.0694610i
$476$	2.69320e10	+	2.69320e10i	0.524614	+	0.524614i
$477$	−1.38612e10	+	2.87831e10i	−0.267748	+	0.555985i
$478$	−7.97690e9	−	7.07969e10i	−0.152800	−	1.35613i
$479$	1.14110e10	−	1.28571e9i	0.216761	−	0.0244231i	−0.00291616	−	0.999996i	$-0.500928\pi$
$479$	1.14110e10	−	1.28571e9i	0.216761	−	0.0244231i	0.219677	+	0.975573i	$0.429500\pi$
$480$	1.62716e9	+	7.83597e8i	0.0306524	+	0.0147614i
$481$	2.39597e10	−	2.39597e10i	0.447611	−	0.447611i
$482$	−3.33345e10	−	9.52644e10i	−0.617597	−	1.76499i
$483$	−6.66634e10	−	1.06094e11i	−1.22490	−	1.94941i
$484$	2.59847e10	−	1.25136e10i	0.473518	−	0.228034i
$485$	9.42769e8	−	2.69428e9i	0.0170388	−	0.0486940i
$486$	−5.95819e10	+	1.35992e10i	−1.06800	+	0.243763i
$487$	5.28930e10	−	6.63257e10i	0.940335	−	1.17914i	−0.0433172	−	0.999061i	$-0.513793\pi$
$487$	5.28930e10	−	6.63257e10i	0.940335	−	1.17914i	0.983652	−	0.180081i	$-0.0576360\pi$
$488$	9.66941e9	+	1.21251e10i	0.170499	+	0.213798i
$489$	1.13618e10	−	4.97793e10i	0.198706	−	0.870590i
$490$	−1.21267e9	+	1.92995e9i	−0.0210358	+	0.0334783i
$491$	−1.64424e9	+	1.45930e10i	−0.0282904	+	0.251084i	0.971605	+	0.236610i	$0.0760362\pi$
$491$	−1.64424e9	+	1.45930e10i	−0.0282904	+	0.251084i	−0.999895	+	0.0144748i	$0.995392\pi$
$492$		−	1.53360e10i		−	0.261728i
$493$	−4.45852e10	−	3.76544e10i	−0.754750	−	0.637423i
$494$	2.65138e10			0.445210
$495$	−1.19885e9	−	1.35078e8i	−0.0199685	−	0.00224991i
$496$	7.44445e10	+	4.67766e10i	1.23000	+	0.772862i
$497$	−6.22661e10	−	1.42118e10i	−1.02053	−	0.232930i
$498$	2.21849e10	−	1.76919e10i	0.360695	−	0.287644i
$499$	7.10253e10	+	5.66408e10i	1.14554	+	0.913538i	0.997154	−	0.0753909i	$-0.0240205\pi$
$499$	7.10253e10	+	5.66408e10i	1.14554	+	0.913538i	0.148387	+	0.988929i	$0.452592\pi$
$500$	4.25987e8	+	1.86637e9i	0.00681580	+	0.0298620i
$501$	4.60919e10	+	1.61282e10i	0.731600	+	0.255998i
$502$	−5.91723e10	−	1.22872e11i	−0.931758	−	1.93482i
$503$	6.62360e10	−	4.16188e10i	1.03472	−	0.650156i	0.0961912	−	0.995363i	$-0.469334\pi$
$503$	6.62360e10	−	4.16188e10i	1.03472	−	0.650156i	0.938527	+	0.345207i	$0.112191\pi$
$504$	2.50437e10	−	8.76316e9i	0.388129	−	0.135812i
$505$	−1.56673e8	−	1.56673e8i	−0.00240896	−	0.00240896i
$506$	−6.51123e10	+	1.35207e11i	−0.993255	+	2.06252i
$507$	1.74968e10	+	1.55288e11i	0.264805	+	2.35021i
$508$	−4.89083e10	+	5.51064e9i	−0.734391	+	0.0827460i
$509$	−4.72569e10	−	2.27577e10i	−0.704035	−	0.339046i	0.0473783	−	0.998877i	$-0.484913\pi$
$509$	−4.72569e10	−	2.27577e10i	−0.704035	−	0.339046i	−0.751414	+	0.659831i	$0.770628\pi$
$510$	−2.08985e9	+	2.08985e9i	−0.0308912	+	0.0308912i
$511$	1.80999e10	+	5.17266e10i	0.265456	+	0.758631i
$512$	1.62812e10	+	2.59113e10i	0.236922	+	0.377059i
$513$	8.30048e9	−	3.99730e9i	0.119849	−	0.0577161i
$514$	−3.54822e10	+	1.01402e11i	−0.508344	+	1.45276i
$515$	1.97620e9	−	4.51055e8i	0.0280933	−	0.00641211i
$516$	6.48625e9	−	8.13351e9i	0.0914945	−	0.114731i
$517$	6.20844e10	+	7.78514e10i	0.869001	+	1.08969i
$518$	1.05295e10	−	4.61326e10i	0.146247	−	0.640750i
$519$	3.21715e10	−	5.12006e10i	0.443406	−	0.705676i
$520$	2.45149e8	−	2.17575e9i	0.00335287	−	0.0297575i
$521$		−	6.29231e10i		−	0.854003i	−0.904251	−	0.427001i	$-0.859570\pi$
$521$		−	6.29231e10i		−	0.854003i	0.904251	−	0.427001i	$-0.140430\pi$
$522$	4.01584e10	−	1.79663e10i	0.540872	−	0.241978i
$523$	−7.87718e10			−1.05284			−0.526422	−	0.850224i	$-0.676467\pi$
$523$	−7.87718e10			−1.05284			−0.526422	+	0.850224i	$0.676467\pi$
$524$	3.43136e10	+	3.86621e9i	0.455135	+	0.0512814i
$525$	1.13003e11	+	7.10043e10i	1.48748	+	0.934647i
$526$	−9.96151e10	−	2.27365e10i	−1.30131	−	0.297016i
$527$	−6.92564e10	+	5.52301e10i	−0.897878	+	0.716034i
$528$	−1.31033e11	−	1.04495e11i	−1.68595	−	1.34450i
$529$	−1.24515e10	−	5.45535e10i	−0.159000	−	0.696626i
$530$	3.47500e9	+	1.21595e9i	0.0440404	+	0.0154104i
$531$	−1.73613e10	−	3.60511e10i	−0.218376	−	0.453462i
$532$	1.07218e10	−	6.73694e9i	0.133851	−	0.0841039i
$533$	−5.40898e10	+	1.89269e10i	−0.670204	+	0.234514i
$534$	2.70297e10	+	2.70297e10i	0.332412	+	0.332412i
$535$	−1.46905e9	+	3.05050e9i	−0.0179316	+	0.0372354i
$536$	−5.59349e9	−	4.96436e10i	−0.0677678	−	0.601456i
$537$	1.03812e11	−	1.16968e10i	1.24839	−	0.140660i
$538$	5.57914e10	+	2.68677e10i	0.665945	+	0.320702i
$539$	9.20836e10	−	9.20836e10i	1.09101	−	1.09101i
$540$	2.71923e8	+	7.77112e8i	0.00319795	+	0.00913921i
$541$	3.18443e10	+	5.06799e10i	0.371743	+	0.591626i	0.979242	−	0.202695i	$-0.0649699\pi$
$541$	3.18443e10	+	5.06799e10i	0.371743	+	0.591626i	−0.607499	+	0.794321i	$0.707827\pi$
$542$	−1.57993e11	+	7.60856e10i	−1.83080	+	0.881668i
$543$	2.77432e10	−	7.92855e10i	0.319122	−	0.912000i
$544$	−7.99993e10	+	1.82593e10i	−0.913463	+	0.208492i
$545$	7.63494e7	−	9.57391e7i	0.000865405	−	0.00108518i
$546$	2.06070e11	+	2.58403e11i	2.31869	+	2.90755i
$547$	2.92356e10	−	1.28089e11i	0.326559	−	1.43075i	−0.499082	−	0.866555i	$-0.666329\pi$
$547$	2.92356e10	−	1.28089e11i	0.326559	−	1.43075i	0.825642	−	0.564195i	$-0.190813\pi$
$548$	2.91934e10	−	4.64611e10i	0.323715	−	0.515190i
$549$	2.25800e9	−	2.00403e10i	0.0248561	−	0.220604i
$550$		−	1.59840e11i		−	1.74677i
$551$	−1.55032e10	+	1.16656e10i	−0.168195	+	0.126561i
$552$	8.75838e10			0.943339
$553$	−2.15610e11	−	2.42934e10i	−2.30551	−	0.259769i
$554$	7.12199e10	+	4.47504e10i	0.756071	+	0.475071i
$555$	1.22424e9	+	2.79426e8i	0.0129032	+	0.00294506i
$556$	−1.80026e10	+	1.43566e10i	−0.188381	+	0.150229i
$557$	−7.93380e10	−	6.32699e10i	−0.824253	−	0.657320i	0.117706	−	0.993049i	$-0.462446\pi$
$557$	−7.93380e10	−	6.32699e10i	−0.824253	−	0.657320i	−0.941959	+	0.335729i	$0.891017\pi$
$558$	−1.48597e10	−	6.51046e10i	−0.153276	−	0.671544i
$559$	−3.66918e10	−	1.28390e10i	−0.375770	−	0.131488i
$560$	−2.27136e9	−	4.71653e9i	−0.0230959	−	0.0479591i
$561$	1.42977e11	−	8.98381e10i	1.44349	−	0.907004i
$562$	1.27220e11	−	4.45161e10i	1.27529	−	0.446243i
$563$	−1.29459e10	−	1.29459e10i	−0.128855	−	0.128855i	0.639738	−	0.768593i	$-0.279043\pi$
$563$	−1.29459e10	−	1.29459e10i	−0.128855	−	0.128855i	−0.768593	+	0.639738i	$0.779043\pi$
$564$	−2.72870e10	+	5.66621e10i	−0.269674	+	0.559985i
$565$	1.66618e8	+	1.47877e9i	0.00163504	+	0.0145113i
$566$	−1.30333e11	+	1.46851e10i	−1.26996	+	0.143090i
$567$	1.68145e11	+	8.09742e10i	1.62686	+	0.783455i
$568$	3.15674e10	−	3.15674e10i	0.303281	−	0.303281i
$569$	6.08983e10	+	1.74037e11i	0.580973	+	1.66033i	0.739648	+	0.672994i	$0.234992\pi$
$569$	6.08983e10	+	1.74037e11i	0.580973	+	1.66033i	−0.158675	+	0.987331i	$0.550722\pi$
$570$	5.22769e8	+	8.31983e8i	0.00495234	+	0.00788161i
$571$	−3.85626e10	+	1.85708e10i	−0.362762	+	0.174697i	−0.606381	−	0.795174i	$-0.707379\pi$
$571$	−3.85626e10	+	1.85708e10i	−0.362762	+	0.174697i	0.243620	+	0.969871i	$0.421665\pi$
$572$	4.47114e10	−	1.27778e11i	0.417671	−	1.19363i
$573$	7.78012e10	−	1.77576e10i	0.721718	−	0.164727i
$574$	−4.98961e10	+	6.25677e10i	−0.459641	+	0.576372i
$575$	8.91656e10	+	1.11810e11i	0.815691	+	1.02284i
$576$	−9.46749e8	+	4.14798e9i	−0.00860092	+	0.0376831i
$577$	5.14848e10	−	8.19376e10i	0.464489	−	0.739230i	−0.529547	−	0.848281i	$-0.677638\pi$
$577$	5.14848e10	−	8.19376e10i	0.464489	−	0.739230i	0.994036	+	0.109050i	$0.0347809\pi$
$578$	−3.70414e8	+	3.28751e9i	−0.00331876	+	0.0294548i
$579$			1.29648e10i			0.115359i
$580$	−8.80829e8	−	1.49347e9i	−0.00778358	−	0.0131973i
$581$	−5.06387e10			−0.444404
$582$	−2.99291e11	−	3.37221e10i	−2.60857	−	0.293915i
$583$	−1.78103e11	−	1.11909e11i	−1.54169	−	0.968706i
$584$	−3.73459e10	−	8.52395e9i	−0.321064	−	0.0732807i
$585$	−2.22605e9	+	1.77522e9i	−0.0190069	+	0.0151575i
$586$	−1.58722e11	−	1.26577e11i	−1.34600	−	1.07340i
$587$	5.46155e9	+	2.39286e10i	0.0460006	+	0.201542i	0.992706	−	0.120558i	$-0.0384684\pi$
$587$	5.46155e9	+	2.39286e10i	0.0460006	+	0.201542i	−0.946706	+	0.322100i	$0.895611\pi$
$588$	7.76328e10	+	2.71649e10i	0.649436	+	0.227247i
$589$	1.27780e10	+	2.65337e10i	0.106170	+	0.220464i
$590$	−3.90445e9	+	2.45333e9i	−0.0322220	+	0.0202464i
$591$	1.96345e11	−	6.87040e10i	1.60942	−	0.563161i
$592$	4.00422e10	+	4.00422e10i	0.326010	+	0.326010i
$593$	−1.86465e10	+	3.87198e10i	−0.150792	+	0.313123i	−0.962658	−	0.270721i	$-0.912738\pi$
$593$	−1.86465e10	+	3.87198e10i	−0.150792	+	0.313123i	0.811866	+	0.583844i	$0.198452\pi$
$594$	−1.54002e10	−	1.36680e11i	−0.123703	−	1.09789i
$595$	5.24119e9	−	5.90540e8i	0.0418179	−	0.00471174i
$596$	9.52197e10	+	4.58554e10i	0.754644	+	0.363417i
$597$	−1.89032e11	+	1.89032e11i	−1.48812	+	1.48812i
$598$	1.16973e11	+	3.34290e11i	0.914707	+	2.61408i
$599$	7.15750e8	+	1.13911e9i	0.00555974	+	0.00884827i	0.849493	−	0.527601i	$-0.176908\pi$
$599$	7.15750e8	+	1.13911e9i	0.00555974	+	0.00884827i	−0.843933	+	0.536449i	$0.819765\pi$
$600$	−8.40487e10	+	4.04757e10i	−0.648524	+	0.312312i
$601$	1.88127e10	−	5.37637e10i	0.144196	−	0.412089i	−0.849022	−	0.528358i	$-0.822808\pi$
$601$	1.88127e10	−	5.37637e10i	0.144196	−	0.412089i	0.993218	+	0.116269i	$0.0370935\pi$
$602$	−5.29253e10	+	1.20798e10i	−0.402974	+	0.0919762i
$603$	−4.05046e10	+	5.07911e10i	−0.306362	+	0.384166i
$604$	7.24529e9	+	9.08530e9i	0.0544387	+	0.0682640i
$605$	8.88719e8	−	3.89373e9i	0.00663350	−	0.0290633i
$606$	−1.24382e10	+	1.97953e10i	−0.0922290	+	0.146782i
$607$	−2.63224e10	+	2.33617e11i	−0.193897	+	1.72088i	0.400150	+	0.916449i	$0.368958\pi$
$607$	−2.63224e10	+	2.33617e11i	−0.193897	+	1.72088i	−0.594047	+	0.804430i	$0.702471\pi$
$608$			2.72807e10i			0.199637i
$609$	−2.34185e11	−	6.04267e10i	−1.70251	−	0.439299i
$610$	−2.32409e9			−0.0167854
$611$	2.33523e11	+	2.63117e10i	1.67558	+	0.188792i
$612$	2.93138e10	+	1.84191e10i	0.208961	+	0.131299i
$613$	−2.24833e11	−	5.13167e10i	−1.59228	−	0.363426i	−0.667702	−	0.744429i	$-0.732722\pi$
$613$	−2.24833e11	−	5.13167e10i	−1.59228	−	0.363426i	−0.924574	+	0.381003i	$0.875579\pi$
$614$	2.57344e10	−	2.05225e10i	0.181068	−	0.144397i
$615$	−1.66039e9	−	1.32412e9i	−0.0116067	−	0.00925605i
$616$	3.88734e10	+	1.70315e11i	0.269978	+	1.18285i
$617$	9.24276e10	+	3.23418e10i	0.637766	+	0.223164i	0.629743	−	0.776804i	$-0.283160\pi$
$617$	9.24276e10	+	3.23418e10i	0.637766	+	0.223164i	0.00802324	+	0.999968i	$0.497446\pi$
$618$	−9.27986e10	−	1.92698e11i	−0.636191	−	1.32106i
$619$	8.39391e10	−	5.27424e10i	0.571744	−	0.359250i	−0.214920	−	0.976632i	$-0.568949\pi$
$619$	8.39391e10	−	5.27424e10i	0.571744	−	0.359250i	0.786664	+	0.617381i	$0.211806\pi$
$620$	−2.48416e9	+	8.69244e8i	−0.0168117	+	0.00588267i
$621$	8.70185e10	+	8.70185e10i	0.585120	+	0.585120i
$622$	−9.96313e10	+	2.06886e11i	−0.665632	+	1.38220i
$623$	−7.63792e9	−	6.77884e10i	−0.0507017	−	0.449990i
$624$	−3.93046e11	+	4.42857e10i	−2.59242	+	0.292095i
$625$	−1.37119e11	−	6.60328e10i	−0.898621	−	0.432753i
$626$	1.94867e11	−	1.94867e11i	1.26894	−	1.26894i
$627$	−1.85415e10	−	5.29886e10i	−0.119971	−	0.342857i
$628$	−6.72519e10	−	1.07031e11i	−0.432380	−	0.688129i
$629$	−5.14043e10	+	2.47550e10i	−0.328395	+	0.158147i
$630$	−1.31323e9	+	3.75301e9i	−0.00833643	+	0.0238241i
$631$	−4.66540e10	+	1.06485e10i	−0.294287	+	0.0671691i	−0.367115	−	0.930175i	$-0.619655\pi$
$631$	−4.66540e10	+	1.06485e10i	−0.294287	+	0.0671691i	0.0728284	+	0.997344i	$0.476797\pi$
$632$	9.45608e10	−	1.18576e11i	0.592711	−	0.743236i
$633$	9.98467e9	+	1.25204e10i	0.0621898	+	0.0779835i
$634$	1.67399e10	−	7.33422e10i	0.103608	−	0.453938i
$635$	−3.62615e9	+	5.77098e9i	−0.0223024	+	0.0354940i
$636$	1.48744e10	−	1.32014e11i	0.0909096	−	0.806845i
$637$		−	3.07336e11i		−	1.86662i
$638$	8.79447e10	+	2.75992e11i	0.530795	+	1.66577i
$639$	−5.80531e10			−0.348195
$640$	5.14855e9	+	5.80102e8i	0.0306877	+	0.00345768i
$641$	7.25505e10	+	4.55865e10i	0.429743	+	0.270025i	0.729487	−	0.683994i	$-0.239759\pi$
$641$	7.25505e10	+	4.55865e10i	0.429743	+	0.270025i	−0.299745	+	0.954019i	$0.596902\pi$
$642$	3.48292e11	+	7.94955e10i	2.05024	+	0.467953i
$643$	1.62029e10	−	1.29214e10i	0.0947869	−	0.0755900i	−0.574950	−	0.818189i	$-0.694978\pi$
$643$	1.62029e10	−	1.29214e10i	0.0947869	−	0.0755900i	0.669737	+	0.742599i	$0.266407\pi$
$644$	1.32242e11	+	1.05460e11i	0.768825	+	0.613117i
$645$	−3.20569e8	−	1.40450e9i	−0.00185218	−	0.00811492i
$646$	−4.21391e10	−	1.47451e10i	−0.241966	−	0.0846676i
$647$	1.79999e10	+	3.73772e10i	0.102720	+	0.213299i	0.945994	−	0.324184i	$-0.105090\pi$
$647$	1.79999e10	+	3.73772e10i	0.102720	+	0.213299i	−0.843275	+	0.537483i	$0.819375\pi$
$648$	−1.10456e11	+	6.94041e10i	−0.626454	+	0.393627i
$649$	2.48673e11	−	8.70145e10i	1.40168	−	0.490470i
$650$	−2.66740e11	−	2.66740e11i	−1.49429	−	1.49429i
$651$	−1.59285e11	+	3.30758e11i	−0.886849	+	1.84156i
$652$	7.71729e9	+	6.84928e10i	0.0427046	+	0.379014i
$653$	1.41636e11	−	1.59586e10i	0.778973	−	0.0877692i	0.286481	−	0.958086i	$-0.407515\pi$
$653$	1.41636e11	−	1.59586e10i	0.778973	−	0.0877692i	0.492492	+	0.870317i	$0.336086\pi$
$654$	−1.16411e10	−	5.60608e9i	−0.0636333	−	0.0306442i
$655$	3.38124e9	−	3.38124e9i	0.0183701	−	0.0183701i
$656$	−3.16312e10	−	9.03969e10i	−0.170805	−	0.488133i
$657$	2.65021e10	+	4.21778e10i	0.142239	+	0.226372i
$658$	2.95678e11	−	1.42391e11i	1.57730	−	0.759589i
$659$	9.95535e10	−	2.84508e11i	0.527855	−	1.50852i	−0.303527	−	0.952823i	$-0.598164\pi$
$659$	9.95535e10	−	2.84508e11i	0.527855	−	1.50852i	0.831382	−	0.555701i	$-0.187550\pi$
$660$	4.89113e9	−	1.11637e9i	0.0257771	−	0.00588345i
$661$	−1.68321e11	+	2.11068e11i	−0.881725	+	1.10565i	0.111991	+	0.993709i	$0.464277\pi$
$661$	−1.68321e11	+	2.11068e11i	−0.881725	+	1.10565i	−0.993715	+	0.111938i	$0.964294\pi$
$662$	1.43693e11	+	1.80185e11i	0.748174	+	0.938181i
$663$	8.86768e10	−	3.88518e11i	0.458940	−	2.01075i
$664$	1.88319e10	−	2.99708e10i	0.0968773	−	0.154179i
$665$	1.96332e8	−	1.74249e9i	0.00100393	−	0.00891014i
$666$		−	4.30112e10i		−	0.218617i
$667$	−2.15478e11	−	1.44000e11i	−1.08868	−	0.727545i
$668$	−6.59195e10			−0.331061
$669$	−9.35954e10	−	1.05457e10i	−0.467251	−	0.0526465i
$670$	6.33907e9	+	3.98310e9i	0.0314577	+	0.0197662i
$671$	1.29454e11	+	2.95471e10i	0.638597	+	0.145756i
$672$	−2.65877e11	+	2.12030e11i	−1.30378	+	1.03973i
$673$	1.43797e11	+	1.14675e11i	0.700956	+	0.558994i	0.907812	−	0.419378i	$-0.137752\pi$
$673$	1.43797e11	+	1.14675e11i	0.700956	+	0.558994i	−0.206856	+	0.978371i	$0.566323\pi$
$674$	6.62537e10	+	2.90276e11i	0.321048	+	1.40660i
$675$	−1.23721e11	−	4.32917e10i	−0.595973	−	0.208540i
$676$	−9.15290e10	−	1.90062e11i	−0.438300	−	0.910140i
$677$	2.93543e11	−	1.84445e11i	1.39739	−	0.878037i	0.398160	−	0.917316i	$-0.369649\pi$
$677$	2.93543e11	−	1.84445e11i	1.39739	−	0.878037i	0.999228	+	0.0392785i	$0.0125059\pi$
$678$	1.48207e11	−	5.18599e10i	0.701374	−	0.245422i
$679$	3.80064e11	+	3.80064e11i	1.78804	+	1.78804i
$680$	−1.59962e9	+	3.32164e9i	−0.00748137	+	0.0155352i
$681$	−4.30898e9	−	3.82433e10i	−0.0200349	−	0.177814i
$682$	4.36919e11	−	4.92290e10i	2.01959	−	0.227553i
$683$	−2.00326e11	−	9.64719e10i	−0.920565	−	0.443321i	−0.0872922	−	0.996183i	$-0.527821\pi$
$683$	−2.00326e11	−	9.64719e10i	−0.920565	−	0.443321i	−0.833273	+	0.552862i	$0.813536\pi$
$684$	8.13872e9	−	8.13872e9i	0.0371819	−	0.0371819i
$685$	−2.50966e9	−	7.17219e9i	−0.0113986	−	0.0325754i
$686$	−1.84609e10	−	2.93804e10i	−0.0833600	−	0.132667i
$687$	1.09486e11	−	5.27257e10i	0.491509	−	0.236698i
$688$	2.14570e10	−	6.13207e10i	0.0957670	−	0.273686i
$689$	−4.83968e11	+	1.10463e11i	−2.14753	+	0.490161i
$690$	−8.18342e9	+	1.02617e10i	−0.0361026	+	0.0452712i
$691$	−1.48257e11	−	1.85908e11i	−0.650283	−	0.815429i	0.341963	−	0.939713i	$-0.388908\pi$
$691$	−1.48257e11	−	1.85908e11i	−0.650283	−	0.815429i	−0.992247	+	0.124284i	$0.960337\pi$
$692$	−1.81640e10	+	7.95817e10i	−0.0792113	+	0.347048i
$693$	1.20862e11	−	1.92351e11i	0.524033	−	0.833993i
$694$	1.93326e10	−	1.71582e11i	0.0833399	−	0.739662i
$695$			3.18867e9i			0.0136669i
$696$	1.22855e11	−	1.16132e11i	0.523546	−	0.494898i
$697$	9.64920e10			0.408846
$698$	2.54835e11	+	2.87130e10i	1.07359	+	0.120964i
$699$	1.20058e11	+	7.54372e10i	0.502899	+	0.315992i
$700$	−1.75642e11	−	4.00890e10i	−0.731535	−	0.166968i
$701$	−1.41866e11	+	1.13135e11i	−0.587500	+	0.468516i	−0.871559	−	0.490291i	$-0.836890\pi$
$701$	−1.41866e11	+	1.13135e11i	−0.587500	+	0.468516i	0.284059	+	0.958807i	$0.408319\pi$
$702$	−2.53790e11	−	2.02391e11i	−1.04502	−	0.833378i
$703$	4.22087e9	+	1.84928e10i	0.0172815	+	0.0757150i
$704$	−2.64413e10	−	9.25223e9i	−0.107645	−	0.0376665i
$705$	3.77870e9	+	7.84655e9i	0.0152963	+	0.0317630i
$706$	1.59543e11	−	1.00247e11i	0.642183	−	0.403510i
$707$	3.93801e10	−	1.37797e10i	0.157615	−	0.0551520i
$708$	1.17659e11	+	1.17659e11i	0.468266	+	0.468266i
$709$	1.43868e11	−	2.98746e11i	0.569351	−	1.18227i	−0.395254	−	0.918572i	$-0.629343\pi$
$709$	1.43868e11	−	2.98746e11i	0.569351	−	1.18227i	0.964605	−	0.263698i	$-0.0849423\pi$
$710$	7.49057e8	+	6.64807e9i	0.00294769	+	0.0261615i
$711$	−1.95981e11	+	2.20818e10i	−0.766896	+	0.0864084i
$712$	4.29614e10	+	2.06891e10i	0.167170	+	0.0805049i
$713$	−2.78168e11	+	2.78168e11i	−1.07634	+	1.07634i
$714$	−1.83806e11	−	5.25287e11i	−0.707240	−	2.02118i
$715$	−9.97380e9	−	1.58732e10i	−0.0381625	−	0.0607352i
$716$	−1.27059e11	+	6.11885e10i	−0.483453	+	0.232819i
$717$	−1.17583e11	+	3.36032e11i	−0.444904	+	1.27146i
$718$	1.45186e11	−	3.31377e10i	0.546294	−	0.124688i
$719$	−1.92271e11	+	2.41100e11i	−0.719446	+	0.902157i	−0.998306	−	0.0581746i	$-0.981472\pi$
$719$	−1.92271e11	+	2.41100e11i	−0.719446	+	0.902157i	0.278860	+	0.960332i	$0.410043\pi$
$720$	−2.96680e9	−	3.72025e9i	−0.0110397	−	0.0138434i
$721$	−8.49332e10	+	3.72117e11i	−0.314294	+	1.37701i
$722$	1.70329e11	−	2.71077e11i	0.626815	−	0.997571i
$723$	−5.64678e10	+	5.01165e11i	−0.206656	+	1.83412i
$724$			1.13392e11i			0.412695i
$725$	2.73328e11	+	3.86076e10i	0.989311	+	0.139740i
$726$	−4.21408e11			−1.51690
$727$	3.26332e10	+	3.67687e9i	0.116821	+	0.0131626i	0.170181	−	0.985413i	$-0.445565\pi$
$727$	3.26332e10	+	3.67687e9i	0.116821	+	0.0131626i	−0.0533603	+	0.998575i	$0.516993\pi$
$728$	3.49091e11	+	2.19349e11i	1.24284	+	0.780925i
$729$	−4.63526e10	−	1.05797e10i	−0.164121	−	0.0374596i
$730$	4.48812e9	−	3.57916e9i	0.0158042	−	0.0126034i
$731$	5.11750e10	+	4.08107e10i	0.179221	+	0.142924i
$732$	1.86614e10	+	8.17611e10i	0.0649981	+	0.284775i
$733$	−3.25063e10	−	1.13744e10i	−0.112603	−	0.0394016i	0.273389	−	0.961903i	$-0.411855\pi$
$733$	−3.25063e10	−	1.13744e10i	−0.112603	−	0.0394016i	−0.385993	+	0.922502i	$0.626141\pi$
$734$	−2.03918e11	−	4.23440e11i	−0.702541	−	1.45884i
$735$	9.64395e9	−	6.05970e9i	0.0330450	−	0.0207635i
$736$	−3.43959e11	+	1.20356e11i	−1.17218	+	0.410165i
$737$	−3.02455e11	−	3.02455e11i	−1.02516	−	1.02516i
$738$	−3.15614e10	+	6.55380e10i	−0.106397	+	0.220937i
$739$	4.97673e10	+	4.41697e11i	0.166866	+	1.48097i	0.746112	+	0.665820i	$0.231918\pi$
$739$	4.97673e10	+	4.41697e11i	0.166866	+	1.48097i	−0.579246	+	0.815152i	$0.696653\pi$
$740$	−1.68447e9	+	1.89794e8i	−0.00561742	+	0.000632931i
$741$	−1.19369e11	−	5.74849e10i	−0.395929	−	0.190669i
$742$	−4.90195e11	+	4.90195e11i	−1.61716	+	1.61716i
$743$	6.83563e10	+	1.95351e11i	0.224297	+	0.641004i	0.999952	+	0.00984635i	$0.00313424\pi$
$743$	6.83563e10	+	1.95351e11i	0.224297	+	0.641004i	−0.775654	+	0.631158i	$0.782580\pi$
$744$	−1.36525e11	−	2.17278e11i	−0.445575	−	0.709128i
$745$	1.31860e10	−	6.35004e9i	0.0428043	−	0.0206135i
$746$	−8.47678e10	+	2.42252e11i	−0.273701	+	0.782191i
$747$	−4.48747e10	+	1.02423e10i	−0.144118	+	0.0328940i
$748$	−1.42122e11	+	1.78215e11i	−0.453998	+	0.569295i
$749$	−3.97502e11	−	4.98451e11i	−1.26302	−	1.58378i
$750$	6.22432e9	−	2.72705e10i	0.0196719	−	0.0861884i
$751$	−6.67874e10	+	1.06292e11i	−0.209959	+	0.334148i	−0.935057	−	0.354498i	$-0.884652\pi$
$751$	−6.67874e10	+	1.06292e11i	−0.209959	+	0.334148i	0.725098	+	0.688646i	$0.241795\pi$
$752$	−4.39731e10	+	3.90272e11i	−0.137504	+	1.22038i
$753$			6.81479e11i			2.11969i
$754$	6.07333e11	+	3.13811e11i	1.87906	+	0.970919i
$755$	1.60921e9			0.00495250
$756$	−1.54054e11	−	1.73578e10i	−0.471614	−	0.0531381i
$757$	−4.00528e11	−	2.51668e11i	−1.21969	−	0.766382i	−0.240761	−	0.970584i	$-0.577397\pi$
$757$	−4.00528e11	−	2.51668e11i	−1.21969	−	0.766382i	−0.978929	+	0.204203i	$0.934540\pi$
$758$	7.84212e10	+	1.78991e10i	0.237551	+	0.0542195i
$759$	5.86288e11	−	4.67549e11i	1.76662	−	1.40883i
$760$	9.58292e8	+	7.64212e8i	0.00287239	+	0.00229066i
$761$	−6.67227e10	−	2.92331e11i	−0.198946	−	0.871639i	−0.971566	−	0.236770i	$-0.923911\pi$
$761$	−6.67227e10	−	2.92331e11i	−0.198946	−	0.871639i	0.772620	−	0.634869i	$-0.218946\pi$
$762$	6.78790e11	+	2.37519e11i	2.01333	+	0.704496i
$763$	1.00045e10	+	2.07747e10i	0.0295188	+	0.0612965i
$764$	−9.12144e10	+	5.73138e10i	−0.267726	+	0.168223i
$765$	4.52516e9	−	1.58342e9i	0.0132126	−	0.00462329i
$766$	1.98898e11	+	1.98898e11i	0.577718	+	0.577718i
$767$	2.69774e11	−	5.60191e11i	0.779504	−	1.61866i
$768$	−5.73973e10	−	5.09415e11i	−0.164986	−	1.46429i
$769$	−1.44768e11	+	1.63114e10i	−0.413967	+	0.0466429i	−0.316492	−	0.948595i	$-0.602505\pi$
$769$	−1.44768e11	+	1.63114e10i	−0.413967	+	0.0466429i	−0.0974751	+	0.995238i	$0.531077\pi$
$770$	−2.35870e10	−	1.13589e10i	−0.0670980	−	0.0323127i
$771$	3.79597e11	−	3.79597e11i	1.07425	−	1.07425i
$772$	−5.78035e9	−	1.65193e10i	−0.0162737	−	0.0465074i
$773$	−5.30420e10	−	8.44158e10i	−0.148560	−	0.236432i	0.764151	−	0.645037i	$-0.223158\pi$
$773$	−5.30420e10	−	8.44158e10i	−0.148560	−	0.236432i	−0.912711	+	0.408605i	$0.866015\pi$
$774$	−4.44577e10	+	2.14097e10i	−0.123875	+	0.0596550i
$775$	1.38388e11	−	3.95491e11i	0.383612	−	1.09630i
$776$	−3.66285e11	+	8.36021e10i	−1.01012	+	0.230553i
$777$	−1.47425e11	+	1.84866e11i	−0.404472	+	0.507192i
$778$	4.34493e11	+	5.44837e11i	1.18594	+	1.48713i
$779$	7.13844e9	−	3.12756e10i	0.0193845	−	0.0849289i
$780$	6.29927e9	−	1.00252e10i	0.0170181	−	0.0270842i
$781$	4.27964e10	−	3.79829e11i	0.115028	−	1.02090i
$782$		−	5.96348e11i		−	1.59468i
$783$	2.37444e11	+	6.67915e9i	0.631705	+	0.0177695i
$784$	5.13631e11			1.35952
$785$	−1.73945e10	−	1.95989e9i	−0.0458073	−	0.00516124i
$786$	−4.27211e11	−	2.68435e11i	−1.11932	−	0.703312i
$787$	3.66449e11	+	8.36397e10i	0.955245	+	0.218029i	0.671611	−	0.740904i	$-0.265603\pi$
$787$	3.66449e11	+	8.36397e10i	0.955245	+	0.218029i	0.283634	+	0.958932i	$0.408460\pi$
$788$	−2.19544e11	+	1.75081e11i	−0.569400	+	0.454081i
$789$	3.99184e11	+	3.18339e11i	1.03007	+	0.821451i
$790$	5.05748e9	+	2.21583e10i	0.0129845	+	0.0568889i
$791$	−2.64489e11	−	9.25486e10i	−0.675618	−	0.236409i
$792$	6.88971e10	+	1.43066e11i	0.175106	+	0.363611i
$793$	2.65340e11	−	1.66724e11i	0.670980	−	0.421605i
$794$	−8.70012e11	+	3.04431e11i	−2.18899	+	0.765960i
$795$	−1.30086e10	−	1.30086e10i	−0.0325657	−	0.0325657i
$796$	1.56578e11	−	3.25138e11i	0.390013	−	0.809870i
$797$	4.41726e9	+	3.92043e10i	0.0109476	+	0.0971628i	0.997998	−	0.0632492i	$-0.0201463\pi$
$797$	4.41726e9	+	3.92043e10i	0.0109476	+	0.0971628i	−0.987050	+	0.160412i	$0.948718\pi$
$798$	−1.83857e11	+	2.07157e10i	−0.453387	+	0.0510845i
$799$	−3.56511e11	−	1.71687e11i	−0.874753	−	0.421259i
$800$	2.74455e11	−	2.74455e11i	0.670055	−	0.670055i
$801$	−2.04796e10	−	5.85274e10i	−0.0497499	−	0.142177i
$802$	−5.14398e10	−	8.18659e10i	−0.124337	−	0.197882i
$803$	−2.95497e11	+	1.42304e11i	−0.710708	+	0.342259i
$804$	8.92250e10	−	2.54990e11i	0.213532	−	0.610239i
$805$	2.28358e10	−	5.21212e9i	0.0543792	−	0.0124117i
$806$	6.46972e11	−	8.11278e11i	1.53301	−	1.92234i
$807$	−1.92928e11	−	2.41924e11i	−0.454884	−	0.570407i
$808$	−6.48938e9	+	2.84318e10i	−0.0152250	+	0.0667052i
$809$	−3.96035e11	+	6.30285e11i	−0.924568	+	1.47144i	−0.0431705	+	0.999068i	$0.513746\pi$
$809$	−3.96035e11	+	6.30285e11i	−0.924568	+	1.47144i	−0.881398	+	0.472374i	$0.843397\pi$
$810$	2.18881e9	−	1.94263e10i	0.00508474	−	0.0451283i
$811$			3.29760e11i			0.762280i	0.924517	+	0.381140i	$0.124468\pi$
$811$			3.29760e11i			0.762280i	−0.924517	+	0.381140i	$0.875532\pi$
$812$	3.25333e11	−	2.74179e10i	0.748348	−	0.0630681i
$813$	8.76268e11			2.00574
$814$	2.81413e11	+	3.17076e10i	0.640982	+	0.0722214i
$815$	8.08188e9	+	5.07818e9i	0.0183182	+	0.0115101i
$816$	6.49306e11	+	1.48200e11i	1.46450	+	0.334262i
$817$	1.70137e10	−	1.35680e10i	0.0381866	−	0.0304528i
$818$	3.00798e11	+	2.39878e11i	0.671833	+	0.535769i
$819$	−1.19300e11	−	5.22687e11i	−0.265158	−	1.16173i
$820$	2.70597e9	+	9.46860e8i	0.00598505	+	0.00209426i
$821$	3.05381e11	+	6.34129e11i	0.672154	+	1.39574i	0.905920	+	0.423449i	$0.139181\pi$
$821$	3.05381e11	+	6.34129e11i	0.672154	+	1.39574i	−0.233766	+	0.972293i	$0.575105\pi$
$822$	−6.78867e11	+	4.26561e11i	−1.48695	+	0.934316i
$823$	8.54264e9	−	2.98920e9i	0.0186206	−	0.00651561i	−0.320953	−	0.947095i	$-0.604003\pi$
$823$	8.54264e9	−	2.98920e9i	0.0186206	−	0.00651561i	0.339573	+	0.940580i	$0.389717\pi$
$824$	−1.88654e11	−	1.88654e11i	−0.409220	−	0.409220i
$825$	−3.46552e11	+	7.19622e11i	−0.748087	+	1.55342i
$826$	−9.72179e10	−	8.62833e11i	−0.208846	−	1.85356i
$827$	−4.91193e11	+	5.53441e10i	−1.05010	+	0.118318i	−0.620109	−	0.784516i	$-0.712911\pi$
$827$	−4.91193e11	+	5.53441e10i	−1.05010	+	0.118318i	−0.429990	+	0.902834i	$0.641483\pi$
$828$	1.38520e11	+	6.67079e10i	0.294708	+	0.141924i
$829$	1.65382e11	−	1.65382e11i	0.350162	−	0.350162i	−0.510008	−	0.860170i	$-0.670357\pi$
$829$	1.65382e11	−	1.65382e11i	0.350162	−	0.350162i	0.860170	+	0.510008i	$0.170357\pi$
$830$	1.75194e9	+	5.00675e9i	0.00369153	+	0.0105498i
$831$	−2.23617e11	−	3.55885e11i	−0.468922	−	0.746286i
$832$	−5.95650e10	+	2.86850e10i	−0.124308	+	0.0598634i
$833$	−1.70918e11	+	4.88456e11i	−0.354984	+	1.01448i
$834$	3.28013e11	−	7.48668e10i	0.677996	−	0.154748i
$835$	−5.69154e9	+	7.13696e9i	−0.0117080	+	0.0146814i
$836$	4.72500e10	+	5.92496e10i	0.0967334	+	0.121300i
$837$	8.02321e10	−	3.51520e11i	0.163473	−	0.716222i
$838$	−2.11571e11	+	3.36713e11i	−0.429023	+	0.682786i
$839$	−2.16277e10	+	1.91952e11i	−0.0436479	+	0.387386i	0.952828	+	0.303510i	$0.0981585\pi$
$839$	−2.16277e10	+	1.91952e11i	−0.0436479	+	0.387386i	−0.996476	+	0.0838760i	$0.973270\pi$
$840$			1.52791e10i			0.0306888i
$841$	−4.93191e11	+	8.37234e10i	−0.985895	+	0.167364i
$842$	−5.18297e11			−1.03117
$843$	−6.69275e11	−	7.54091e10i	−1.32524	−	0.149319i
$844$	−1.83044e10	−	1.15014e10i	−0.0360732	−	0.0226663i
$845$	−2.84803e10	−	6.50043e9i	−0.0558621	−	0.0127502i
$846$	2.33221e11	−	1.85988e11i	0.455289	−	0.363081i
$847$	5.87969e11	+	4.68890e11i	1.14241	+	0.911039i
$848$	−1.84609e11	−	8.08825e11i	−0.357001	−	1.56412i
$849$	6.18617e11	+	2.16463e11i	1.19067	+	0.416633i
$850$	2.75594e11	+	5.72277e11i	0.527952	+	1.09630i
$851$	−2.14539e11	+	1.34804e11i	−0.409061	+	0.257030i
$852$	2.27864e11	−	7.97329e10i	0.432431	−	0.151314i
$853$	4.83396e11	+	4.83396e11i	0.913076	+	0.913076i	0.996513	−	0.0834371i	$-0.0265898\pi$
$853$	4.83396e11	+	4.83396e11i	0.913076	+	0.913076i	−0.0834371	+	0.996513i	$0.526590\pi$
$854$	1.89877e11	−	3.94285e11i	0.356978	−	0.741273i
$855$	−1.78459e8	−	1.58386e9i	−0.000333943	−	0.00296383i
$856$	4.42838e11	−	4.98958e10i	0.824802	−	0.0929328i
$857$	−3.91492e11	−	1.88533e11i	−0.725771	−	0.349513i	0.0342481	−	0.999413i	$-0.489096\pi$
$857$	−3.91492e11	−	1.88533e11i	−0.725771	−	0.349513i	−0.760019	+	0.649900i	$0.774811\pi$
$858$	−1.39868e12	+	1.39868e12i	−2.58088	+	2.58088i
$859$	−1.83429e11	−	5.24211e11i	−0.336896	−	0.962795i	−0.980343	−	0.197303i	$-0.936782\pi$
$859$	−1.83429e11	−	5.24211e11i	−0.336896	−	0.962795i	0.643446	−	0.765491i	$-0.277504\pi$
$860$	1.03466e9	+	1.64665e9i	0.00189148	+	0.00301028i
$861$	3.60292e11	−	1.73507e11i	0.655605	−	0.315723i
$862$	−2.28504e11	+	6.53028e11i	−0.413872	+	1.18278i
$863$	4.32342e11	−	9.86792e10i	0.779443	−	0.177903i	0.185753	−	0.982597i	$-0.440528\pi$
$863$	4.32342e11	−	9.86792e10i	0.779443	−	0.177903i	0.593690	+	0.804694i	$0.297671\pi$
$864$	2.08244e11	−	2.61130e11i	0.373696	−	0.468600i
$865$	7.04784e9	+	8.83771e9i	0.0125890	+	0.0157861i
$866$	6.67472e9	−	2.92439e10i	0.0118676	−	0.0519952i
$867$	8.79534e9	−	1.39977e10i	0.0155660	−	0.0247731i
$868$	5.54867e10	−	4.92458e11i	0.0977484	−	0.867541i
$869$		−	1.29854e12i		−	2.27707i
$870$	2.12756e9	+	2.52450e10i	0.00371368	+	0.0440654i
$871$	−1.00947e12			−1.75396
$872$	−1.60162e10	−	1.80459e9i	−0.0277008	−	0.00312114i
$873$	4.13676e11	+	2.59930e11i	0.712202	+	0.447506i
$874$	−1.93292e11	−	4.41176e10i	−0.331259	−	0.0756077i
$875$	−3.90277e10	+	3.11235e10i	−0.0665795	+	0.0530954i
$876$	−1.61952e11	−	1.29152e11i	−0.275024	−	0.219324i
$877$	1.21948e11	+	5.34291e11i	0.206147	+	0.903191i	0.967103	+	0.254386i	$0.0818735\pi$
$877$	1.21948e11	+	5.34291e11i	0.206147	+	0.903191i	−0.760955	+	0.648804i	$0.775269\pi$
$878$	2.89565e11	+	1.01323e11i	0.487268	+	0.170503i
$879$	4.40155e11	+	9.13990e11i	0.737309	+	1.53104i
$880$	2.65279e10	−	1.66686e10i	0.0442356	−	0.0277951i
$881$	−7.40509e9	+	2.59115e9i	−0.0122921	+	0.00430120i	−0.336418	−	0.941713i	$-0.609216\pi$
$881$	−7.40509e9	+	2.59115e9i	−0.0122921	+	0.00430120i	0.324126	+	0.946014i	$0.394930\pi$
$882$	−2.75857e11	−	2.75857e11i	−0.455838	−	0.455838i
$883$	3.99120e11	−	8.28781e11i	0.656539	−	1.36332i	−0.260871	−	0.965374i	$-0.584010\pi$
$883$	3.99120e11	−	8.28781e11i	0.656539	−	1.36332i	0.917410	−	0.397944i	$-0.130276\pi$
$884$	6.02320e10	+	5.34574e11i	0.0986321	+	0.875384i
$885$	2.28974e10	−	2.57992e9i	0.0373262	−	0.00420565i
$886$	8.51033e11	+	4.09836e11i	1.38106	+	0.665082i
$887$	7.50337e11	−	7.50337e11i	1.21217	−	1.21217i	0.241852	−	0.970313i	$-0.422245\pi$
$887$	7.50337e11	−	7.50337e11i	1.21217	−	1.21217i	0.970313	−	0.241852i	$-0.0777550\pi$
$888$	−5.45881e10	−	1.56004e11i	−0.0877903	−	0.250890i
$889$	−6.82800e11	−	1.08667e12i	−1.09317	−	1.73976i
$890$	−6.43814e9	+	3.10044e9i	−0.0102612	+	0.00494156i
$891$	−3.68894e11	+	1.05424e12i	−0.585317	+	1.67274i
$892$	1.23958e11	−	2.82926e10i	0.195801	−	0.0446903i
$893$	−8.20227e10	+	1.02853e11i	−0.128982	+	0.161738i
$894$	−9.62813e11	−	1.20733e12i	−1.50727	−	1.89006i
$895$	−4.34564e9	+	1.90395e10i	−0.00677269	+	0.0296731i
$896$	−5.19051e11	+	8.26065e11i	−0.805337	+	1.28169i
$897$	1.98150e11	−	1.75863e12i	0.306072	−	2.71647i
$898$			4.72893e11i			0.727206i
$899$	−2.13509e10	+	7.59025e11i	−0.0326872	+	1.16203i
$900$	−1.63758e11			−0.249592
$901$	8.30613e11	+	9.35877e10i	1.26037	+	0.142010i
$902$	−4.05533e11	−	2.54814e11i	−0.612633	−	0.384943i
$903$	2.64467e11	+	6.03628e10i	0.397759	+	0.0907859i
$904$	1.53136e11	−	1.22122e11i	0.229299	−	0.182860i
$905$	1.22767e10	+	9.79037e9i	0.0183016	+	0.0145950i
$906$	−3.77827e10	−	1.65537e11i	−0.0560764	−	0.245687i
$907$	−6.28505e11	−	2.19923e11i	−0.928709	−	0.324969i	−0.176808	−	0.984245i	$-0.556577\pi$
$907$	−6.28505e11	−	2.19923e11i	−0.928709	−	0.324969i	−0.751901	+	0.659276i	$0.770863\pi$
$908$	2.25411e10	+	4.68072e10i	0.0331614	+	0.0688603i
$909$	3.21105e10	−	2.01763e10i	0.0470318	−	0.0295520i
$910$	−5.83172e10	+	2.04061e10i	−0.0850416	+	0.0297573i
$911$	7.66991e11	+	7.66991e11i	1.11357	+	1.11357i	0.992664	+	0.120903i	$0.0385791\pi$
$911$	7.66991e11	+	7.66991e11i	1.11357	+	1.11357i	0.120903	+	0.992664i	$0.461421\pi$
$912$	9.60708e10	−	1.99493e11i	0.138871	−	0.288369i
$913$	−3.39321e10	−	3.01155e11i	−0.0488345	−	0.433419i
$914$	−1.05762e12	+	1.19165e11i	−1.51546	+	0.170752i
$915$	1.04633e10	+	5.03887e9i	0.0149274	+	0.00718868i
$916$	−1.15996e11	+	1.15996e11i	−0.164763	+	0.164763i
$917$	2.97386e11	+	8.49879e11i	0.420574	+	1.20193i
$918$	2.90799e11	+	4.62804e11i	0.409470	+	0.651668i
$919$	−1.20626e12	+	5.80906e11i	−1.69114	+	0.814411i	−0.695775	+	0.718260i	$0.744939\pi$
$919$	−1.20626e12	+	5.80906e11i	−1.69114	+	0.814411i	−0.995367	+	0.0961514i	$0.969347\pi$
$920$	−5.40753e9	+	1.54538e10i	−0.00754827	+	0.0215717i
$921$	−1.60355e11	+	3.65999e10i	−0.222865	+	0.0508676i
$922$	2.39503e11	−	3.00327e11i	0.331427	−	0.415596i
$923$	−5.62435e11	−	7.05271e11i	−0.774936	−	0.971738i
$924$	−2.10211e11	+	9.20994e11i	−0.288382	+	1.26348i
$925$	1.43582e11	−	2.28509e11i	0.196125	−	0.312130i
$926$	−1.49962e10	+	1.33095e11i	−0.0203956	+	0.181016i
$927$			3.46939e11i			0.469823i
$928$	−3.22887e11	+	6.24899e11i	−0.435371	+	0.842593i
$929$	4.20056e11			0.563955			0.281977	−	0.959421i	$-0.409010\pi$
$929$	4.20056e11			0.563955			0.281977	+	0.959421i	$0.409010\pi$
$930$	3.82135e10	+	4.30563e9i	0.0510840	+	0.00575578i
$931$	1.45677e11	+	9.15349e10i	0.193906	+	0.121839i
$932$	−1.86607e11	−	4.25918e10i	−0.247323	−	0.0564498i
$933$	8.97105e11	−	7.15417e11i	1.18390	−	0.944132i
$934$	−6.17913e11	−	4.92769e11i	−0.811969	−	0.647524i
$935$	7.02405e9	+	3.07744e10i	0.00919054	+	0.0402664i
$936$	3.53722e11	+	1.23773e11i	0.460849	+	0.161258i
$937$	2.29146e11	+	4.75827e11i	0.297272	+	0.617292i	0.995089	−	0.0989843i	$-0.0315594\pi$
$937$	2.29146e11	+	4.75827e11i	0.297272	+	0.617292i	−0.697817	+	0.716276i	$0.745845\pi$
$938$	−1.19364e12	+	7.50014e11i	−1.54192	+	0.968853i
$939$	−1.29981e12	+	4.54823e11i	−1.67193	+	0.585032i
$940$	−8.31308e9	−	8.31308e9i	−0.0106476	−	0.0106476i
$941$	2.25759e11	−	4.68794e11i	0.287930	−	0.597893i	−0.705962	−	0.708250i	$-0.749485\pi$
$941$	2.25759e11	−	4.68794e11i	0.287930	−	0.597893i	0.993892	+	0.110357i	$0.0351993\pi$
$942$	2.06796e11	+	1.83537e12i	0.262627	+	2.33087i
$943$	4.25820e11	−	4.79784e10i	0.538492	−	0.0606735i
$944$	9.36212e11	+	4.50856e11i	1.17892	+	0.567740i
$945$	−1.51804e10	+	1.51804e10i	−0.0190352	+	0.0190352i
$946$	−1.07305e11	−	3.06660e11i	−0.133985	−	0.382906i
$947$	−1.93364e11	−	3.07736e11i	−0.240422	−	0.382630i	0.704616	−	0.709588i	$-0.251119\pi$
$947$	−1.93364e11	−	3.07736e11i	−0.240422	−	0.382630i	−0.945039	+	0.326958i	$0.893976\pi$
$948$	7.38916e11	−	3.55843e11i	0.914875	−	0.440581i
$949$	−2.55647e11	+	7.30597e11i	−0.315193	+	0.900768i
$950$	2.05878e11	−	4.69904e10i	0.252765	−	0.0576919i
$951$	−2.34379e11	+	2.93902e11i	−0.286547	+	0.359319i
$952$	−4.32833e11	−	5.42755e11i	−0.526954	−	0.660779i
$953$	−1.51148e11	+	6.62221e11i	−0.183244	+	0.802845i	0.796829	+	0.604205i	$0.206509\pi$
$953$	−1.51148e11	+	6.62221e11i	−0.183244	+	0.802845i	−0.980073	+	0.198639i	$0.936348\pi$
$954$	−3.35250e11	+	5.33547e11i	−0.404739	+	0.644138i
$955$	−1.67027e9	+	1.48241e10i	−0.00200805	+	0.0178219i
$956$		−	4.80584e11i		−	0.575358i
$957$	2.02443e11	−	1.43323e12i	0.241354	−	1.70870i
$958$	2.26499e11			0.268908
$959$	1.42181e12	+	1.60200e11i	1.68100	+	0.189403i
$960$	−2.07455e9	−	1.30352e9i	−0.00244252	−	0.00153474i
$961$	2.92178e11	+	6.66877e10i	0.342573	+	0.0781901i
$962$	5.22531e11	−	4.16705e11i	0.610115	−	0.486551i
$963$	−4.53074e11	−	3.61315e11i	−0.526822	−	0.420127i
$964$	−1.51495e11	−	6.63744e11i	−0.175425	−	0.768586i
$965$	−2.28759e9	−	8.00461e8i	−0.00263796	−	0.000923062i
$966$	−1.07233e12	−	2.22671e12i	−1.23145	−	2.55714i
$967$	4.56096e11	−	2.86584e11i	0.521616	−	0.327753i	−0.245357	−	0.969433i	$-0.578905\pi$
$967$	4.56096e11	−	2.86584e11i	0.521616	−	0.327753i	0.766973	+	0.641680i	$0.221762\pi$
$968$	−4.96174e11	+	1.73619e11i	−0.565109	+	0.197740i
$969$	1.57746e11	+	1.57746e11i	0.178922	+	0.178922i
$970$	2.44287e10	−	5.07268e10i	0.0275940	−	0.0572995i
$971$	−4.02286e10	−	3.57038e11i	−0.0452541	−	0.401641i	−0.995836	−	0.0911662i	$-0.970941\pi$
$971$	−4.02286e10	−	3.57038e11i	−0.0452541	−	0.401641i	0.950582	−	0.310475i	$-0.100488\pi$
$972$	−4.09655e11	+	4.61571e10i	−0.458937	+	0.0517098i
$973$	−5.40962e11	−	2.60514e11i	−0.603553	−	0.290656i
$974$	1.18320e12	−	1.18320e12i	1.31468	−	1.31468i
$975$	6.22575e11	+	1.77922e12i	0.688927	+	1.96884i
$976$	2.78635e11	+	4.43445e11i	0.307069	+	0.488698i
$977$	9.02206e11	−	4.34480e11i	0.990210	−	0.476860i	0.132605	−	0.991169i	$-0.457666\pi$
$977$	9.02206e11	−	4.34480e11i	0.990210	−	0.476860i	0.857605	+	0.514309i	$0.171951\pi$
$978$	3.32630e11	−	9.50601e11i	0.363585	−	1.03907i
$979$	3.98029e11	−	9.08476e10i	0.433296	−	0.0988969i
$980$	−9.58628e9	+	1.20208e10i	−0.0103931	+	0.0130326i
$981$	1.30677e10	+	1.63864e10i	0.0141099	+	0.0176933i
$982$	−6.44554e10	+	2.82398e11i	−0.0693128	+	0.303679i
$983$	4.83668e11	−	7.69752e11i	0.518004	−	0.824398i	−0.480615	−	0.876931i	$-0.659587\pi$
$983$	4.83668e11	−	7.69752e11i	0.518004	−	0.824398i	0.998619	+	0.0525333i	$0.0167296\pi$
$984$	−3.12967e10	+	2.77766e11i	−0.0333825	+	0.296278i
$985$			3.88862e10i			0.0413095i
$986$	−7.90729e11	−	8.36502e11i	−0.836605	−	0.885033i
$987$	−1.63990e12			−1.72802
$988$	1.77725e11	+	2.00248e10i	0.186518	+	0.0210156i
$989$	2.46128e11	+	1.54653e11i	0.257262	+	0.161649i
$990$	−2.31997e10	−	5.29517e9i	−0.0241513	−	0.00551238i
$991$	−5.67449e11	+	4.52525e11i	−0.588345	+	0.469189i	−0.871844	−	0.489783i	$-0.837076\pi$
$991$	−5.67449e11	+	4.52525e11i	−0.588345	+	0.469189i	0.283499	+	0.958972i	$0.408505\pi$
$992$	8.34742e11	+	6.65685e11i	0.861997	+	0.687419i
$993$	−2.56262e11	−	1.12276e12i	−0.263565	−	1.15475i
$994$	−1.18905e12	−	4.16067e11i	−1.21802	−	0.426205i
$995$	−2.16829e10	−	4.50250e10i	−0.0221220	−	0.0459368i
$996$	1.62070e11	−	1.01835e11i	0.164689	−	0.103481i
$997$	9.76187e10	−	3.41583e10i	0.0987990	−	0.0345713i	−0.280427	−	0.959875i	$-0.590476\pi$
$997$	9.76187e10	−	3.41583e10i	0.0987990	−	0.0345713i	0.379226	+	0.925304i	$0.376190\pi$
$998$	1.26703e12	+	1.26703e12i	1.27722	+	1.27722i
$999$	1.00761e11	−	2.09233e11i	0.101165	−	0.210072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.2.16	✓	228
29.15	odd	28	inner	29.9.f.a.15.16	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.16	✓	228	1.1	even	1	trivial
29.9.f.a.15.16	yes	228	29.15	odd	28	inner

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(19.6004 + 2.20843i) q^{2} +(-83.4552 - 52.4384i) q^{3} +(129.715 + 29.6067i) q^{4} +(14.4052 - 11.4877i) q^{5} +(-1519.95 - 1212.12i) q^{6} +(772.012 + 3382.40i) q^{7} +(-2289.00 - 800.955i) q^{8} +(1368.27 + 2841.25i) q^{9} +O(q^{10})\)	\(q+(19.6004 + 2.20843i) q^{2} +(-83.4552 - 52.4384i) q^{3} +(129.715 + 29.6067i) q^{4} +(14.4052 - 11.4877i) q^{5} +(-1519.95 - 1212.12i) q^{6} +(772.012 + 3382.40i) q^{7} +(-2289.00 - 800.955i) q^{8} +(1368.27 + 2841.25i) q^{9} +(307.716 - 193.351i) q^{10} +(-19598.3 + 6857.75i) q^{11} +(-9272.90 - 9272.90i) q^{12} +(-21261.3 + 44149.6i) q^{13} +(7661.90 + 68001.3i) q^{14} +(-1804.58 + 203.328i) q^{15} +(-73784.4 - 35532.7i) q^{16} +(58343.9 - 58343.9i) q^{17} +(20544.0 + 58711.2i) q^{18} +(-14594.5 - 23227.1i) q^{19} +(2208.69 - 1063.65i) q^{20} +(112939. - 322762. i) q^{21} +(-399279. + 91132.9i) q^{22} +(228462. - 286483. i) q^{23} +(149028. + 186875. i) q^{24} +(-86846.7 + 380500. i) q^{25} +(-514231. + 818394. i) q^{26} +(-37602.9 + 333735. i) q^{27} +461607. i q^{28} +(-59396.6 - 704783. i) q^{29} -35819.5 q^{30} +(-1.06683e6 - 120203. i) q^{31} +(-842064. - 529104. i) q^{32} +(1.99519e6 + 455390. i) q^{33} +(1.27241e6 - 1.01471e6i) q^{34} +(49977.1 + 39855.4i) q^{35} +(93366.2 + 409064. i) q^{36} +(-652675. - 228381. i) q^{37} +(-234763. - 487490. i) q^{38} +(4.08950e6 - 2.56960e6i) q^{39} +(-42174.6 + 14757.5i) q^{40} +(826924. + 826924. i) q^{41} +(2.92645e6 - 6.07684e6i) q^{42} +(88820.7 + 788306. i) q^{43} +(-2.74524e6 + 309315. i) q^{44} +(52349.7 + 25210.3i) q^{45} +(5.11062e6 - 5.11062e6i) q^{46} +(-1.58392e6 - 4.52658e6i) q^{47} +(4.29441e6 + 6.83452e6i) q^{48} +(-5.65075e6 + 2.72126e6i) q^{49} +(-2.54254e6 + 7.26615e6i) q^{50} +(-7.92856e6 + 1.80964e6i) q^{51} +(-4.06505e6 + 5.09741e6i) q^{52} +(6.31622e6 + 7.92028e6i) q^{53} +(-1.47406e6 + 6.45828e6i) q^{54} +(-203537. + 323928. i) q^{55} +(942021. - 8.36067e6i) q^{56} +2.70373e6i q^{57} +(392269. - 1.39452e7i) q^{58} -1.26885e7 q^{59} +(-240102. - 27053.0i) q^{60} +(-5.41484e6 - 3.40237e6i) q^{61} +(-2.06449e7 - 4.71206e6i) q^{62} +(-8.55393e6 + 6.82153e6i) q^{63} +(1.05482e6 + 841189. i) q^{64} +(200906. + 880227. i) q^{65} +(3.81008e7 + 1.33320e7i) q^{66} +(8.93817e6 + 1.85603e7i) q^{67} +(9.29548e6 - 5.84074e6i) q^{68} +(-3.40891e7 + 1.19283e7i) q^{69} +(891552. + 891552. i) q^{70} +(-7.98729e6 + 1.65858e7i) q^{71} +(-856263. - 7.59954e6i) q^{72} +(1.56965e7 - 1.76857e6i) q^{73} +(-1.22883e7 - 5.91774e6i) q^{74} +(2.72006e7 - 2.72006e7i) q^{75} +(-1.20546e6 - 3.44501e6i) q^{76} +(-3.83258e7 - 6.09952e7i) q^{77} +(8.58305e7 - 4.13338e7i) q^{78} +(-2.06555e7 + 5.90300e7i) q^{79} +(-1.47107e6 + 335761. i) q^{80} +(3.35389e7 - 4.20565e7i) q^{81} +(1.43818e7 + 1.80342e7i) q^{82} +(-3.24788e6 + 1.42299e7i) q^{83} +(2.42059e7 - 3.85235e7i) q^{84} +(170214. - 1.51069e6i) q^{85} +1.56472e7i q^{86} +(-3.20007e7 + 6.19324e7i) q^{87} +5.03533e7 q^{88} +(-1.95390e7 - 2.20152e6i) q^{89} +(970399. + 609742. i) q^{90} +(-1.65746e8 - 3.78304e7i) q^{91} +(3.81169e7 - 3.03972e7i) q^{92} +(8.27295e7 + 6.59746e7i) q^{93} +(-2.10488e7 - 9.22207e7i) q^{94} +(-477063. - 166932. i) q^{95} +(4.25293e7 + 8.83129e7i) q^{96} +(1.31178e8 - 8.24246e7i) q^{97} +(-1.16766e8 + 4.08584e7i) q^{98} +(-4.63005e7 - 4.63005e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more