LMFDB - Embedded newform 29.9.f.a.15.16

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			15.16
Character	$\chi$	$=$	29.15
Dual form			29.9.f.a.2.16

$q$-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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{27}{28}\right)$

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	0.524346	−	0.851506i	$-0.324310\pi$
$2$	19.6004	−	2.20843i	1.22502	−	0.138027i	0.700677	+	0.713479i	$0.252881\pi$
$3$	−83.4552	+	52.4384i	−1.03031	+	0.647387i	−0.937388	−	0.348286i	$-0.886764\pi$
$3$	−83.4552	+	52.4384i	−1.03031	+	0.647387i	−0.0929226	+	0.995673i	$0.529621\pi$
$4$	129.715	−	29.6067i	0.506701	−	0.115651i
$5$	14.4052	+	11.4877i	0.0230483	+	0.0183804i	0.634946	−	0.772556i	$-0.281022\pi$
$5$	14.4052	+	11.4877i	0.0230483	+	0.0183804i	−0.611898	+	0.790937i	$0.709594\pi$
$6$	−1519.95	+	1212.12i	−1.17280	+	0.935275i
$7$	772.012	−	3382.40i	0.321538	−	1.40875i	−0.513280	−	0.858221i	$-0.671570\pi$
$7$	772.012	−	3382.40i	0.321538	−	1.40875i	0.834817	−	0.550527i	$-0.185573\pi$
$8$	−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	−0.436410	−	0.899748i	$-0.643750\pi$
$11$	−19598.3	−	6857.75i	−1.33859	−	0.468394i	−0.902183	+	0.431354i	$0.858036\pi$
$12$	−9272.90	+	9272.90i	−0.447188	+	0.447188i
$13$	−21261.3	−	44149.6i	−0.744418	−	1.54580i	−0.835211	−	0.549930i	$-0.814654\pi$
$13$	−21261.3	−	44149.6i	−0.744418	−	1.54580i	0.0907927	−	0.995870i	$-0.471060\pi$
$14$	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	0.964099	−	0.265544i	$-0.0855517\pi$
$17$	58343.9	+	58343.9i	0.698554	+	0.698554i	−0.265544	+	0.964099i	$0.585552\pi$
$18$	20544.0	−	58711.2i	0.195701	−	0.559283i
$19$	−14594.5	+	23227.1i	−0.111989	+	0.178230i	−0.898016	−	0.439962i	$-0.854992\pi$
$19$	−14594.5	+	23227.1i	−0.111989	+	0.178230i	0.786027	+	0.618192i	$0.212135\pi$
$20$	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	0.999176	+	0.0405794i	$0.0129204\pi$
$23$	228462.	+	286483.i	0.816401	+	1.02373i	−0.182776	+	0.983155i	$0.558508\pi$
$24$	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	−0.668699	−	0.743533i	$-0.733149\pi$
$31$	−1.06683e6	+	120203.i	−1.15518	+	0.130158i	−0.486482	+	0.873691i	$0.661720\pi$
$32$	−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	−0.498735	−	0.866755i	$-0.666202\pi$
$37$	−652675.	+	228381.i	−0.348249	+	0.121858i	0.150486	+	0.988612i	$0.451916\pi$
$38$	−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	−0.545484	−	0.838121i	$-0.683654\pi$
$41$	826924.	−	826924.i	0.292638	−	0.292638i	0.838121	+	0.545484i	$0.183654\pi$
$42$	2.92645e6	+	6.07684e6i	0.940468	+	1.95290i
$43$	88820.7	−	788306.i	0.0259801	−	0.230580i	−0.974012	−	0.226498i	$-0.927272\pi$
$43$	88820.7	−	788306.i	0.0259801	−	0.230580i	0.999992	−	0.00408141i	$-0.00129916\pi$
$44$	−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	0.659765	+	0.751472i	$0.270656\pi$
$47$	−1.58392e6	+	4.52658e6i	−0.324595	+	0.927639i	−0.984360	+	0.176167i	$0.943630\pi$
$48$	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	−0.199231	−	0.979953i	$-0.563844\pi$
$53$	6.31622e6	−	7.92028e6i	0.800485	−	1.00378i	0.999716	−	0.0238244i	$-0.00758426\pi$
$54$	−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	−0.713191	−	0.700970i	$-0.752751\pi$
$61$	−5.41484e6	+	3.40237e6i	−0.391080	+	0.245732i	0.322110	+	0.946702i	$0.395608\pi$
$62$	−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	−0.552598	−	0.833448i	$-0.686364\pi$
$67$	8.93817e6	−	1.85603e7i	0.443557	−	0.921055i	0.996155	−	0.0876073i	$-0.0279221\pi$
$68$	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	0.682631	−	0.730763i	$-0.260835\pi$
$71$	−7.98729e6	−	1.65858e7i	−0.314316	−	0.652683i	−0.996947	+	0.0780795i	$0.975121\pi$
$72$	−856263.	+	7.59954e6i	−0.0318623	+	0.282786i
$73$	1.56965e7	+	1.76857e6i	0.552729	+	0.0622776i	0.383912	−	0.923370i	$-0.374577\pi$
$73$	1.56965e7	+	1.76857e6i	0.552729	+	0.0622776i	0.168817	+	0.985647i	$0.446005\pi$
$74$	−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	−0.827921	−	0.560844i	$-0.810477\pi$
$79$	−2.06555e7	−	5.90300e7i	−0.530307	−	1.51553i	0.297614	−	0.954686i	$-0.403809\pi$
$80$	−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	0.929114	−	0.369794i	$-0.120572\pi$
$83$	−3.24788e6	−	1.42299e7i	−0.0684365	−	0.299840i	−0.997550	+	0.0699543i	$0.977715\pi$
$84$	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	−0.266290	−	0.963893i	$-0.585798\pi$
$89$	−1.95390e7	+	2.20152e6i	−0.311417	+	0.0350883i	−0.0451271	+	0.998981i	$0.514369\pi$
$90$	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	0.998454	+	0.0555844i	$0.0177022\pi$
$97$	1.31178e8	+	8.24246e7i	1.48175	+	0.931043i	0.483293	+	0.875459i	$0.339441\pi$
$98$	−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	−0.998521	−	0.0543591i	$-0.982688\pi$
$101$	−1.34644e6	+	1.19499e7i	−0.0129390	+	0.114837i	0.985582	+	0.169196i	$0.0541170\pi$
$102$	−1.59399e8	−	1.79600e7i	−1.47260	−	0.165922i
$103$	9.91204e7	−	4.77339e7i	0.880672	−	0.424109i	0.0618023	−	0.998088i	$-0.480315\pi$
$103$	9.91204e7	−	4.77339e7i	0.880672	−	0.424109i	0.818870	+	0.573979i	$0.194601\pi$
$104$	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	−0.322093	−	0.946708i	$-0.604387\pi$
$107$	−1.65564e8	−	7.97315e7i	−1.26308	−	0.608268i	−0.940988	+	0.338440i	$0.890101\pi$
$108$	−1.47585e7	−	4.21773e7i	−0.108479	−	0.310016i
$109$	6.47953e6	+	1.47891e6i	0.0459026	+	0.0104770i	0.245411	−	0.969419i	$-0.421077\pi$
$109$	6.47953e6	+	1.47891e6i	0.0459026	+	0.0104770i	−0.199508	+	0.979896i	$0.563934\pi$
$110$	−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	0.688568	−	0.725172i	$-0.258240\pi$
$113$	−4.29708e7	−	6.83876e7i	−0.263548	−	0.419434i	−0.952116	+	0.305738i	$0.901097\pi$
$114$	−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	−0.438826	−	0.898572i	$-0.644606\pi$
$127$	−3.49157e8	−	1.22175e8i	−1.34217	−	0.469644i	−0.903339	+	0.428928i	$0.858891\pi$
$128$	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	0.538365	−	0.842711i	$-0.319042\pi$
$131$	2.57897e8	+	2.90580e7i	0.875712	+	0.0986691i	0.337347	+	0.941381i	$0.390471\pi$
$132$	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	0.958611	+	0.284719i	$0.0919002\pi$
$137$	1.36210e8	+	3.89266e8i	0.386658	+	1.10501i	−0.571953	+	0.820286i	$0.693814\pi$
$138$	−6.94501e8	−	1.58515e8i	−1.91494	−	0.437074i
$139$	−1.07903e8	−	1.35306e8i	−0.289051	−	0.362458i	0.616012	−	0.787737i	$-0.288747\pi$
$139$	−1.07903e8	−	1.35306e8i	−0.289051	−	0.362458i	−0.905062	+	0.425279i	$0.860176\pi$
$140$	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	0.653812	−	0.756657i	$-0.273169\pi$
$149$	7.74409e8	−	1.76754e8i	1.57118	−	0.358611i	0.917365	+	0.398046i	$0.130312\pi$
$150$	5.93213e8	+	4.73071e8i	1.17178	+	0.934462i
$151$	6.82842e7	−	5.44548e7i	0.131345	−	0.104744i	−0.555614	−	0.831440i	$-0.687517\pi$
$151$	6.82842e7	−	5.44548e7i	0.131345	−	0.104744i	0.686959	+	0.726697i	$0.258945\pi$
$152$	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	−0.111980	+	0.993710i	$0.535719\pi$
$157$	−6.71788e8	+	6.71788e8i	−1.10569	+	1.10569i	−0.993710	+	0.111980i	$0.964281\pi$
$158$	−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	−0.756856	−	0.653582i	$-0.773266\pi$
$163$	1.71099e8	−	4.88971e8i	0.242379	−	0.692681i	0.999235	−	0.0390989i	$-0.0124487\pi$
$164$	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	−0.0995738	−	0.995030i	$-0.531748\pi$
$167$	−4.83023e8	−	1.10247e8i	−0.621014	−	0.141742i	−0.521440	+	0.853288i	$0.674605\pi$
$168$	−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	$-0.888741\pi$
$173$		−	6.13510e8i		−	0.684916i	0.939533	−	0.342458i	$-0.111259\pi$
$174$	−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	0.130394	−	0.991462i	$-0.458376\pi$
$179$	−8.28687e8	−	6.60856e8i	−0.807195	−	0.643716i	−0.937589	+	0.347746i	$0.886947\pi$
$180$	6.04418e6	−	4.82007e6i	0.00575768	−	0.00459159i
$181$	1.89642e8	−	8.30877e8i	0.176694	−	0.774145i	−0.806449	−	0.591304i	$-0.798613\pi$
$181$	1.89642e8	−	8.30877e8i	0.176694	−	0.774145i	0.983142	−	0.182841i	$-0.0585295\pi$
$182$	−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	0.458507	−	0.888691i	$-0.348384\pi$
$191$	−5.72516e8	−	5.72516e8i	−0.430184	−	0.430184i	−0.888691	+	0.458507i	$0.848384\pi$
$192$	−4.39194e7	+	1.25515e8i	−0.0323185	+	0.0923611i
$193$	−6.99829e7	+	1.11377e8i	−0.0504385	+	0.0802725i	−0.870992	−	0.491298i	$-0.836523\pi$
$193$	−6.99829e7	+	1.11377e8i	−0.0504385	+	0.0802725i	0.820553	+	0.571570i	$0.193666\pi$
$194$	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	−0.994690	−	0.102913i	$-0.967184\pi$
$197$	−1.31589e9	−	1.65007e9i	−0.873684	−	1.09557i	0.121006	−	0.992652i	$-0.461388\pi$
$198$	−8.05255e8	+	1.00976e9i	−0.523929	+	0.656986i
$199$	6.03545e8	+	2.64430e9i	0.384855	+	1.68616i	0.682020	+	0.731334i	$0.261102\pi$
$199$	6.03545e8	+	2.64430e9i	0.384855	+	1.68616i	−0.297165	+	0.954826i	$0.596041\pi$
$200$	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	−0.368687	−	0.929553i	$-0.620193\pi$
$211$	−1.53360e8	+	5.36629e7i	−0.0773716	+	0.0270735i	0.291316	+	0.956627i	$0.405907\pi$
$212$	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	0.599786	−	0.800161i	$-0.295252\pi$
$223$	8.60979e8	+	4.14626e8i	0.348155	+	0.167663i	−0.251630	+	0.967823i	$0.580967\pi$
$224$	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	−0.733872	−	0.679288i	$-0.762289\pi$
$227$	2.43452e8	−	3.05279e8i	0.0916873	−	0.114972i	0.825559	+	0.564316i	$0.190860\pi$
$228$	−8.00486e7	−	3.50716e8i	−0.0296220	−	0.129782i
$229$	−6.55957e8	−	1.04395e9i	−0.238525	−	0.379610i	0.705914	−	0.708298i	$-0.250537\pi$
$229$	−6.55957e8	−	1.04395e9i	−0.238525	−	0.379610i	−0.944439	+	0.328688i	$0.893394\pi$
$230$	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	0.688790	+	0.724961i	$0.258142\pi$
$239$	−8.03750e8	+	3.52146e9i	−0.246337	+	1.07927i	−0.935127	+	0.354312i	$0.884715\pi$
$240$	1.40375e8	−	4.91193e7i	0.0423101	−	0.0148050i
$241$	−2.22015e9	+	4.61019e9i	−0.658134	+	1.36663i	0.258152	+	0.966104i	$0.416886\pi$
$241$	−2.22015e9	+	4.61019e9i	−0.658134	+	1.36663i	−0.916286	+	0.400525i	$0.868828\pi$
$242$	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	−0.0474118	+	0.998875i	$0.515097\pi$
$251$	−3.67857e9	+	5.85441e9i	−0.926796	+	1.47499i	−0.879384	+	0.476112i	$0.842046\pi$
$252$	−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	−0.900542	−	0.434768i	$-0.856830\pi$
$257$	−1.21198e9	−	5.31005e9i	−0.277821	−	1.21721i	0.622722	−	0.782443i	$-0.286027\pi$
$258$	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	−0.632106	−	0.774882i	$-0.717809\pi$
$263$	−5.14766e9	+	5.80002e8i	−1.07594	+	0.121229i	−0.443831	+	0.896111i	$0.646381\pi$
$264$	−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	−0.0321225	−	0.999484i	$-0.510227\pi$
$269$	2.96328e9	−	1.03690e9i	0.565931	−	0.198028i	0.598054	+	0.801456i	$0.295941\pi$
$270$	5.29570e7	−	1.09966e8i	0.00996479	−	0.0206921i
$271$	−7.52779e9	−	4.73002e9i	−1.39569	−	0.876973i	−0.396537	−	0.918019i	$-0.629788\pi$
$271$	−7.52779e9	−	4.73002e9i	−1.39569	−	0.876973i	−0.999157	+	0.0410459i	$0.986931\pi$
$272$	−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	−0.0781294	−	0.996943i	$-0.524895\pi$
$277$	3.84207e9	−	1.85025e9i	0.652599	−	0.314275i	0.730729	+	0.682668i	$0.239180\pi$
$278$	−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	0.856663	−	0.515877i	$-0.172534\pi$
$281$	6.15662e9	+	2.96487e9i	0.987454	+	0.475533i	0.130792	+	0.991410i	$0.458248\pi$
$282$	−3.07927e9	−	8.80005e9i	−0.486913	−	1.39152i
$283$	−6.48283e9	−	1.47966e9i	−1.01069	−	0.230684i	−0.315052	−	0.949074i	$-0.602022\pi$
$283$	−6.48283e9	−	1.47966e9i	−1.01069	−	0.230684i	−0.695640	+	0.718391i	$0.744879\pi$
$284$	−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	−0.972087	−	0.234620i	$-0.924616\pi$
$293$	−8.71490e9	+	5.47594e9i	−1.18248	+	0.742998i	−0.210388	+	0.977618i	$0.567473\pi$
$294$	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	0.770400	−	0.637560i	$-0.220056\pi$
$307$	1.18000e9	+	1.18000e9i	0.132840	+	0.132840i	−0.637560	+	0.770400i	$0.720056\pi$
$308$	−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	−0.944416	−	0.328752i	$-0.893372\pi$
$311$	−3.84503e9	−	1.09885e10i	−0.411016	−	1.17462i	0.533401	−	0.845863i	$-0.320914\pi$
$312$	−1.14190e10	−	2.60631e9i	−1.20506	−	0.275048i
$313$	8.71122e9	+	1.09235e10i	0.907615	+	1.13811i	0.989937	+	0.141508i	$0.0451950\pi$
$313$	8.71122e9	+	1.09235e10i	0.907615	+	1.13811i	−0.0823218	+	0.996606i	$0.526234\pi$
$314$	−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	0.996976	+	0.0777100i	$0.0247608\pi$
$317$	4.27030e8	+	3.78999e9i	0.0422884	+	0.375320i	−0.954688	+	0.297610i	$0.903811\pi$
$318$			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	−0.273559	−	0.961855i	$-0.588201\pi$
$331$	8.26203e9	−	8.26203e9i	0.688296	−	0.688296i	0.961855	+	0.273559i	$0.0882010\pi$
$332$	−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	−0.572130	−	0.820163i	$-0.693883\pi$
$337$	4.98559e9	−	1.42480e10i	0.386542	−	1.10467i	0.958673	−	0.284512i	$-0.0918315\pi$
$338$	−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	$0.0976200\pi$
$347$			8.75402e9i			0.603795i	−0.953340	+	0.301897i	$0.902380\pi$
$348$	−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	0.833759	−	0.552129i	$-0.186184\pi$
$353$	7.46871e9	+	5.95609e9i	0.481002	+	0.383586i	−0.352757	+	0.935715i	$0.614756\pi$
$354$	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	0.536152	−	0.844122i	$-0.319877\pi$
$359$	7.12634e9	+	2.49361e9i	0.429031	+	0.150124i	−0.107121	+	0.994246i	$0.534163\pi$
$360$	−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	0.289140	+	0.957287i	$0.406631\pi$
$367$	−1.26770e10	+	2.01753e10i	−0.698799	+	1.11213i	−0.987939	+	0.154846i	$0.950512\pi$
$368$	−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	−0.993001	−	0.118108i	$-0.962317\pi$
$373$	−2.89546e9	−	1.26858e10i	−0.149583	−	0.655366i	0.843418	−	0.537258i	$-0.180540\pi$
$374$	−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	−0.0132118	−	0.999913i	$-0.504206\pi$
$379$	4.05246e9	−	4.56602e8i	0.196409	−	0.0221300i	0.209621	+	0.977783i	$0.432777\pi$
$380$	−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	−0.329185	−	0.944266i	$-0.606774\pi$
$383$	1.11495e10	−	8.89143e9i	0.518156	−	0.413216i	0.847340	+	0.531050i	$0.178202\pi$
$384$	−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	0.0956110	−	0.995419i	$-0.469520\pi$
$389$	2.49824e10	−	2.49824e10i	1.09103	−	1.09103i	0.995419	−	0.0956110i	$-0.0304805\pi$
$390$	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	−0.994758	−	0.102259i	$-0.967393\pi$
$397$	−4.21030e10	−	2.02758e10i	−1.69493	−	0.816235i	−0.700171	−	0.713975i	$-0.746893\pi$
$398$	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	−0.837410	−	0.546575i	$-0.815931\pi$
$401$	−3.05624e9	+	3.83240e9i	−0.118198	+	0.148215i	0.719212	+	0.694790i	$0.244503\pi$
$402$	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	−0.203568	−	0.979061i	$-0.565254\pi$
$409$	1.65158e10	−	1.03776e10i	0.590210	−	0.370853i	0.793778	+	0.608207i	$0.208111\pi$
$410$	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	0.709512	−	0.704693i	$-0.248915\pi$
$419$	−8.74759e9	−	1.81646e10i	−0.283813	−	0.589344i	−0.993325	+	0.115350i	$0.963201\pi$
$420$	−9.38575e7	+	8.33009e8i	−0.00301628	+	0.0267702i
$421$	−2.61118e10	−	2.94209e9i	−0.831204	−	0.0936542i	−0.313900	−	0.949456i	$-0.601636\pi$
$421$	−2.61118e10	−	2.94209e9i	−0.831204	−	0.0936542i	−0.517304	+	0.855802i	$0.673064\pi$
$422$	−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	−0.952716	−	0.303862i	$-0.901724\pi$
$431$	−7.80515e9	−	3.41966e10i	−0.226189	−	0.991000i	0.726527	−	0.687138i	$-0.241133\pi$
$432$	1.46330e10	+	2.32883e10i	0.420144	+	0.668656i
$433$	1.70270e8	+	1.51119e9i	0.00484382	+	0.0429901i	0.995902	−	0.0904432i	$-0.0288284\pi$
$433$	1.70270e8	+	1.51119e9i	0.00484382	+	0.0429901i	−0.991058	+	0.133433i	$0.957400\pi$
$434$			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	−0.0134576	−	0.999909i	$-0.504284\pi$
$439$	1.51634e10	−	3.46095e9i	0.408262	−	0.0931831i	0.421720	+	0.906726i	$0.361427\pi$
$440$	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	0.328132	−	0.944632i	$-0.393581\pi$
$443$	4.52013e10	−	1.58166e10i	1.17364	−	0.410676i	0.845512	+	0.533956i	$0.179295\pi$
$444$	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	−0.916482	−	0.400076i	$-0.868984\pi$
$449$	2.68435e9	−	2.38243e10i	0.0660472	−	0.586185i	0.982529	−	0.186109i	$-0.0595878\pi$
$450$	−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	−0.428192	−	0.903688i	$-0.640849\pi$
$457$	−5.26064e10	−	1.20071e10i	−1.20607	−	0.275279i	−0.777883	+	0.628409i	$0.783706\pi$
$458$	−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	0.941516	−	0.336968i	$-0.109401\pi$
$461$	1.03613e10	+	1.64900e10i	0.229410	+	0.365104i	−0.712106	+	0.702072i	$0.752259\pi$
$462$	−1.56801e10	−	1.39165e11i	−0.344176	−	3.05465i
$463$		−	6.79043e9i		−	0.147766i	−0.997267	−	0.0738828i	$-0.976461\pi$
$463$		−	6.79043e9i		−	0.147766i	0.997267	−	0.0738828i	$-0.0235391\pi$
$464$	−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	−0.839190	−	0.543838i	$-0.816971\pi$
$467$	−3.39275e10	+	2.13181e10i	−0.713321	+	0.448209i	0.125870	+	0.992047i	$0.459828\pi$
$468$	−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	0.219677	−	0.975573i	$-0.429500\pi$
$479$	1.14110e10	+	1.28571e9i	0.216761	+	0.0244231i	−0.00291616	+	0.999996i	$0.500928\pi$
$480$	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	0.983652	+	0.180081i	$0.0576360\pi$
$487$	5.28930e10	+	6.63257e10i	0.940335	+	1.17914i	−0.0433172	+	0.999061i	$0.513793\pi$
$488$	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	−0.999895	−	0.0144748i	$-0.995392\pi$
$491$	−1.64424e9	−	1.45930e10i	−0.0282904	−	0.251084i	0.971605	−	0.236610i	$-0.0760362\pi$
$492$			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	0.148387	−	0.988929i	$-0.452592\pi$
$499$	7.10253e10	−	5.66408e10i	1.14554	−	0.913538i	0.997154	+	0.0753909i	$0.0240205\pi$
$500$	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	0.938527	−	0.345207i	$-0.112191\pi$
$503$	6.62360e10	+	4.16188e10i	1.03472	+	0.650156i	0.0961912	+	0.995363i	$0.469334\pi$
$504$	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	−0.751414	−	0.659831i	$-0.770628\pi$
$509$	−4.72569e10	+	2.27577e10i	−0.704035	+	0.339046i	0.0473783	+	0.998877i	$0.484913\pi$
$510$	−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	$0.140430\pi$
$521$			6.29231e10i			0.854003i	−0.904251	+	0.427001i	$0.859570\pi$
$522$	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	−0.607499	−	0.794321i	$-0.707827\pi$
$541$	3.18443e10	−	5.06799e10i	0.371743	−	0.591626i	0.979242	+	0.202695i	$0.0649699\pi$
$542$	−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	0.825642	+	0.564195i	$0.190813\pi$
$547$	2.92356e10	+	1.28089e11i	0.326559	+	1.43075i	−0.499082	+	0.866555i	$0.666329\pi$
$548$	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	−0.941959	−	0.335729i	$-0.891017\pi$
$557$	−7.93380e10	+	6.32699e10i	−0.824253	+	0.657320i	0.117706	+	0.993049i	$0.462446\pi$
$558$	−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	−0.768593	−	0.639738i	$-0.779043\pi$
$563$	−1.29459e10	+	1.29459e10i	−0.128855	+	0.128855i	0.639738	+	0.768593i	$0.279043\pi$
$564$	−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	−0.158675	−	0.987331i	$-0.550722\pi$
$569$	6.08983e10	−	1.74037e11i	0.580973	−	1.66033i	0.739648	−	0.672994i	$-0.234992\pi$
$570$	5.22769e8	−	8.31983e8i	0.00495234	−	0.00788161i
$571$	−3.85626e10	−	1.85708e10i	−0.362762	−	0.174697i	0.243620	−	0.969871i	$-0.421665\pi$
$571$	−3.85626e10	−	1.85708e10i	−0.362762	−	0.174697i	−0.606381	+	0.795174i	$0.707379\pi$
$572$	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	0.994036	−	0.109050i	$-0.0347809\pi$
$577$	5.14848e10	+	8.19376e10i	0.464489	+	0.739230i	−0.529547	+	0.848281i	$0.677638\pi$
$578$	−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	−0.946706	−	0.322100i	$-0.895611\pi$
$587$	5.46155e9	−	2.39286e10i	0.0460006	−	0.201542i	0.992706	+	0.120558i	$0.0384684\pi$
$588$	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	0.811866	−	0.583844i	$-0.198452\pi$
$593$	−1.86465e10	−	3.87198e10i	−0.150792	−	0.313123i	−0.962658	+	0.270721i	$0.912738\pi$
$594$	−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	−0.843933	−	0.536449i	$-0.819765\pi$
$599$	7.15750e8	−	1.13911e9i	0.00555974	−	0.00884827i	0.849493	+	0.527601i	$0.176908\pi$
$600$	−8.40487e10	−	4.04757e10i	−0.648524	−	0.312312i
$601$	1.88127e10	+	5.37637e10i	0.144196	+	0.412089i	0.993218	−	0.116269i	$-0.0370935\pi$
$601$	1.88127e10	+	5.37637e10i	0.144196	+	0.412089i	−0.849022	+	0.528358i	$0.822808\pi$
$602$	−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	−0.594047	−	0.804430i	$-0.702471\pi$
$607$	−2.63224e10	−	2.33617e11i	−0.193897	−	1.72088i	0.400150	−	0.916449i	$-0.368958\pi$
$608$		−	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	−0.924574	−	0.381003i	$-0.875579\pi$
$613$	−2.24833e11	+	5.13167e10i	−1.59228	+	0.363426i	−0.667702	+	0.744429i	$0.732722\pi$
$614$	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	0.00802324	−	0.999968i	$-0.497446\pi$
$617$	9.24276e10	−	3.23418e10i	0.637766	−	0.223164i	0.629743	+	0.776804i	$0.283160\pi$
$618$	−9.27986e10	+	1.92698e11i	−0.636191	+	1.32106i
$619$	8.39391e10	+	5.27424e10i	0.571744	+	0.359250i	0.786664	−	0.617381i	$-0.211806\pi$
$619$	8.39391e10	+	5.27424e10i	0.571744	+	0.359250i	−0.214920	+	0.976632i	$0.568949\pi$
$620$	−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	0.0728284	−	0.997344i	$-0.476797\pi$
$631$	−4.66540e10	−	1.06485e10i	−0.294287	−	0.0671691i	−0.367115	+	0.930175i	$0.619655\pi$
$632$	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	−0.299745	−	0.954019i	$-0.596902\pi$
$641$	7.25505e10	−	4.55865e10i	0.429743	−	0.270025i	0.729487	+	0.683994i	$0.239759\pi$
$642$	3.48292e11	−	7.94955e10i	2.05024	−	0.467953i
$643$	1.62029e10	+	1.29214e10i	0.0947869	+	0.0755900i	0.669737	−	0.742599i	$-0.266407\pi$
$643$	1.62029e10	+	1.29214e10i	0.0947869	+	0.0755900i	−0.574950	+	0.818189i	$0.694978\pi$
$644$	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	−0.843275	−	0.537483i	$-0.819375\pi$
$647$	1.79999e10	−	3.73772e10i	0.102720	−	0.213299i	0.945994	+	0.324184i	$0.105090\pi$
$648$	−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	0.492492	−	0.870317i	$-0.336086\pi$
$653$	1.41636e11	+	1.59586e10i	0.778973	+	0.0877692i	0.286481	+	0.958086i	$0.407515\pi$
$654$	−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	0.831382	+	0.555701i	$0.187550\pi$
$659$	9.95535e10	+	2.84508e11i	0.527855	+	1.50852i	−0.303527	+	0.952823i	$0.598164\pi$
$660$	4.89113e9	+	1.11637e9i	0.0257771	+	0.00588345i
$661$	−1.68321e11	−	2.11068e11i	−0.881725	−	1.10565i	−0.993715	−	0.111938i	$-0.964294\pi$
$661$	−1.68321e11	−	2.11068e11i	−0.881725	−	1.10565i	0.111991	−	0.993709i	$-0.464277\pi$
$662$	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	−0.206856	−	0.978371i	$-0.566323\pi$
$673$	1.43797e11	−	1.14675e11i	0.700956	−	0.558994i	0.907812	+	0.419378i	$0.137752\pi$
$674$	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	0.999228	−	0.0392785i	$-0.0125059\pi$
$677$	2.93543e11	+	1.84445e11i	1.39739	+	0.878037i	0.398160	+	0.917316i	$0.369649\pi$
$678$	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	−0.833273	−	0.552862i	$-0.813536\pi$
$683$	−2.00326e11	+	9.64719e10i	−0.920565	+	0.443321i	−0.0872922	+	0.996183i	$0.527821\pi$
$684$	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	−0.992247	−	0.124284i	$-0.960337\pi$
$691$	−1.48257e11	+	1.85908e11i	−0.650283	+	0.815429i	0.341963	+	0.939713i	$0.388908\pi$
$692$	−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	0.284059	−	0.958807i	$-0.408319\pi$
$701$	−1.41866e11	−	1.13135e11i	−0.587500	−	0.468516i	−0.871559	+	0.490291i	$0.836890\pi$
$702$	−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	0.964605	+	0.263698i	$0.0849423\pi$
$709$	1.43868e11	+	2.98746e11i	0.569351	+	1.18227i	−0.395254	+	0.918572i	$0.629343\pi$
$710$	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	0.278860	−	0.960332i	$-0.410043\pi$
$719$	−1.92271e11	−	2.41100e11i	−0.719446	−	0.902157i	−0.998306	+	0.0581746i	$0.981472\pi$
$720$	−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	−0.0533603	−	0.998575i	$-0.516993\pi$
$727$	3.26332e10	−	3.67687e9i	0.116821	−	0.0131626i	0.170181	+	0.985413i	$0.445565\pi$
$728$	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	−0.385993	−	0.922502i	$-0.626141\pi$
$733$	−3.25063e10	+	1.13744e10i	−0.112603	+	0.0394016i	0.273389	+	0.961903i	$0.411855\pi$
$734$	−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	−0.579246	−	0.815152i	$-0.696653\pi$
$739$	4.97673e10	−	4.41697e11i	0.166866	−	1.48097i	0.746112	−	0.665820i	$-0.231918\pi$
$740$	−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	−0.775654	−	0.631158i	$-0.782580\pi$
$743$	6.83563e10	−	1.95351e11i	0.224297	−	0.641004i	0.999952	−	0.00984635i	$-0.00313424\pi$
$744$	−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	0.725098	−	0.688646i	$-0.241795\pi$
$751$	−6.67874e10	−	1.06292e11i	−0.209959	−	0.334148i	−0.935057	+	0.354498i	$0.884652\pi$
$752$	−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	−0.978929	−	0.204203i	$-0.934540\pi$
$757$	−4.00528e11	+	2.51668e11i	−1.21969	+	0.766382i	−0.240761	+	0.970584i	$0.577397\pi$
$758$	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	0.772620	+	0.634869i	$0.218946\pi$
$761$	−6.67227e10	+	2.92331e11i	−0.198946	+	0.871639i	−0.971566	+	0.236770i	$0.923911\pi$
$762$	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	−0.0974751	−	0.995238i	$-0.531077\pi$
$769$	−1.44768e11	−	1.63114e10i	−0.413967	−	0.0466429i	−0.316492	+	0.948595i	$0.602505\pi$
$770$	−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	−0.912711	−	0.408605i	$-0.866015\pi$
$773$	−5.30420e10	+	8.44158e10i	−0.148560	+	0.236432i	0.764151	+	0.645037i	$0.223158\pi$
$774$	−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	0.283634	−	0.958932i	$-0.408460\pi$
$787$	3.66449e11	−	8.36397e10i	0.955245	−	0.218029i	0.671611	+	0.740904i	$0.265603\pi$
$788$	−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	−0.987050	−	0.160412i	$-0.948718\pi$
$797$	4.41726e9	−	3.92043e10i	0.0109476	−	0.0971628i	0.997998	+	0.0632492i	$0.0201463\pi$
$798$	−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	−0.881398	−	0.472374i	$-0.843397\pi$
$809$	−3.96035e11	−	6.30285e11i	−0.924568	−	1.47144i	−0.0431705	−	0.999068i	$-0.513746\pi$
$810$	2.18881e9	+	1.94263e10i	0.00508474	+	0.0451283i
$811$		−	3.29760e11i		−	0.762280i	−0.924517	−	0.381140i	$-0.875532\pi$
$811$		−	3.29760e11i		−	0.762280i	0.924517	−	0.381140i	$-0.124468\pi$
$812$	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	−0.233766	−	0.972293i	$-0.575105\pi$
$821$	3.05381e11	−	6.34129e11i	0.672154	−	1.39574i	0.905920	−	0.423449i	$-0.139181\pi$
$822$	−6.78867e11	−	4.26561e11i	−1.48695	−	0.934316i
$823$	8.54264e9	+	2.98920e9i	0.0186206	+	0.00651561i	0.339573	−	0.940580i	$-0.389717\pi$
$823$	8.54264e9	+	2.98920e9i	0.0186206	+	0.00651561i	−0.320953	+	0.947095i	$0.604003\pi$
$824$	−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	−0.429990	−	0.902834i	$-0.641483\pi$
$827$	−4.91193e11	−	5.53441e10i	−1.05010	−	0.118318i	−0.620109	+	0.784516i	$0.712911\pi$
$828$	1.38520e11	−	6.67079e10i	0.294708	−	0.141924i
$829$	1.65382e11	+	1.65382e11i	0.350162	+	0.350162i	0.860170	−	0.510008i	$-0.170357\pi$
$829$	1.65382e11	+	1.65382e11i	0.350162	+	0.350162i	−0.510008	+	0.860170i	$0.670357\pi$
$830$	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	−0.996476	−	0.0838760i	$-0.973270\pi$
$839$	−2.16277e10	−	1.91952e11i	−0.0436479	−	0.387386i	0.952828	−	0.303510i	$-0.0981585\pi$
$840$		−	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	−0.0834371	−	0.996513i	$-0.526590\pi$
$853$	4.83396e11	−	4.83396e11i	0.913076	−	0.913076i	0.996513	+	0.0834371i	$0.0265898\pi$
$854$	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	−0.760019	−	0.649900i	$-0.774811\pi$
$857$	−3.91492e11	+	1.88533e11i	−0.725771	+	0.349513i	0.0342481	+	0.999413i	$0.489096\pi$
$858$	−1.39868e12	−	1.39868e12i	−2.58088	−	2.58088i
$859$	−1.83429e11	+	5.24211e11i	−0.336896	+	0.962795i	0.643446	+	0.765491i	$0.277504\pi$
$859$	−1.83429e11	+	5.24211e11i	−0.336896	+	0.962795i	−0.980343	+	0.197303i	$0.936782\pi$
$860$	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	0.593690	−	0.804694i	$-0.297671\pi$
$863$	4.32342e11	+	9.86792e10i	0.779443	+	0.177903i	0.185753	+	0.982597i	$0.440528\pi$
$864$	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	−0.760955	−	0.648804i	$-0.775269\pi$
$877$	1.21948e11	−	5.34291e11i	0.206147	−	0.903191i	0.967103	−	0.254386i	$-0.0818735\pi$
$878$	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	0.324126	−	0.946014i	$-0.394930\pi$
$881$	−7.40509e9	−	2.59115e9i	−0.0122921	−	0.00430120i	−0.336418	+	0.941713i	$0.609216\pi$
$882$	−2.75857e11	+	2.75857e11i	−0.455838	+	0.455838i
$883$	3.99120e11	+	8.28781e11i	0.656539	+	1.36332i	0.917410	+	0.397944i	$0.130276\pi$
$883$	3.99120e11	+	8.28781e11i	0.656539	+	1.36332i	−0.260871	+	0.965374i	$0.584010\pi$
$884$	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	0.970313	+	0.241852i	$0.0777550\pi$
$887$	7.50337e11	+	7.50337e11i	1.21217	+	1.21217i	0.241852	+	0.970313i	$0.422245\pi$
$888$	−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	−0.751901	−	0.659276i	$-0.770863\pi$
$907$	−6.28505e11	+	2.19923e11i	−0.928709	+	0.324969i	−0.176808	+	0.984245i	$0.556577\pi$
$908$	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	0.120903	−	0.992664i	$-0.461421\pi$
$911$	7.66991e11	−	7.66991e11i	1.11357	−	1.11357i	0.992664	−	0.120903i	$-0.0385791\pi$
$912$	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	−0.995367	−	0.0961514i	$-0.969347\pi$
$919$	−1.20626e12	−	5.80906e11i	−1.69114	−	0.814411i	−0.695775	−	0.718260i	$-0.744939\pi$
$920$	−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	−0.697817	−	0.716276i	$-0.745845\pi$
$937$	2.29146e11	−	4.75827e11i	0.297272	−	0.617292i	0.995089	+	0.0989843i	$0.0315594\pi$
$938$	−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	0.993892	−	0.110357i	$-0.0351993\pi$
$941$	2.25759e11	+	4.68794e11i	0.287930	+	0.597893i	−0.705962	+	0.708250i	$0.749485\pi$
$942$	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	−0.945039	−	0.326958i	$-0.893976\pi$
$947$	−1.93364e11	+	3.07736e11i	−0.240422	+	0.382630i	0.704616	+	0.709588i	$0.251119\pi$
$948$	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	−0.980073	−	0.198639i	$-0.936348\pi$
$953$	−1.51148e11	−	6.62221e11i	−0.183244	−	0.802845i	0.796829	−	0.604205i	$-0.206509\pi$
$954$	−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	0.766973	−	0.641680i	$-0.221762\pi$
$967$	4.56096e11	+	2.86584e11i	0.521616	+	0.327753i	−0.245357	+	0.969433i	$0.578905\pi$
$968$	−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	0.950582	+	0.310475i	$0.100488\pi$
$971$	−4.02286e10	+	3.57038e11i	−0.0452541	+	0.401641i	−0.995836	+	0.0911662i	$0.970941\pi$
$972$	−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	0.857605	−	0.514309i	$-0.171951\pi$
$977$	9.02206e11	+	4.34480e11i	0.990210	+	0.476860i	0.132605	+	0.991169i	$0.457666\pi$
$978$	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	0.998619	−	0.0525333i	$-0.0167296\pi$
$983$	4.83668e11	+	7.69752e11i	0.518004	+	0.824398i	−0.480615	+	0.876931i	$0.659587\pi$
$984$	−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	0.283499	−	0.958972i	$-0.408505\pi$
$991$	−5.67449e11	−	4.52525e11i	−0.588345	−	0.469189i	−0.871844	+	0.489783i	$0.837076\pi$
$992$	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	0.379226	−	0.925304i	$-0.376190\pi$
$997$	9.76187e10	+	3.41583e10i	0.0987990	+	0.0345713i	−0.280427	+	0.959875i	$0.590476\pi$
$998$	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.15.16	yes	228
29.2	odd	28	inner	29.9.f.a.2.16	✓	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.16	✓	228	29.2	odd	28	inner
29.9.f.a.15.16	yes	228	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:	\( N \)	\(=\)	\( 29 \)
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

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