LMFDB - Embedded newform 29.9.f.a.2.2

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			2.2
Character	$\chi$	$=$	29.2
Dual form			29.9.f.a.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-24.5490 - 2.76601i) q^{2} +(-135.176 - 84.9370i) q^{3} +(345.422 + 78.8403i) q^{4} +(-399.043 + 318.226i) q^{5} +(3083.51 + 2459.02i) q^{6} +(40.6060 + 177.907i) q^{7} +(-2292.28 - 802.105i) q^{8} +(8211.67 + 17051.7i) q^{9} +O(q^{10})$	\(q+(-24.5490 - 2.76601i) q^{2} +(-135.176 - 84.9370i) q^{3} +(345.422 + 78.8403i) q^{4} +(-399.043 + 318.226i) q^{5} +(3083.51 + 2459.02i) q^{6} +(40.6060 + 177.907i) q^{7} +(-2292.28 - 802.105i) q^{8} +(8211.67 + 17051.7i) q^{9} +(10676.3 - 6708.39i) q^{10} +(-20215.0 + 7073.52i) q^{11} +(-39996.5 - 39996.5i) q^{12} +(1918.80 - 3984.42i) q^{13} +(-504.747 - 4479.75i) q^{14} +(80970.4 - 9123.18i) q^{15} +(-27665.1 - 13322.8i) q^{16} +(21641.2 - 21641.2i) q^{17} +(-154423. - 441316. i) q^{18} +(32149.0 + 51164.9i) q^{19} +(-162927. + 78461.7i) q^{20} +(9621.87 - 27497.7i) q^{21} +(515823. - 117733. i) q^{22} +(-275389. + 345326. i) q^{23} +(241735. + 303126. i) q^{24} +(-28954.8 + 126859. i) q^{25} +(-58125.5 + 92506.2i) q^{26} +(221020. - 1.96161e6i) q^{27} +64654.3i q^{28} +(-587477. + 393849. i) q^{29} -2.01298e6 q^{30} +(-1.06024e6 - 119460. i) q^{31} +(1.16872e6 + 734355. i) q^{32} +(3.33339e6 + 760825. i) q^{33} +(-591131. + 471411. i) q^{34} +(-72818.1 - 58070.5i) q^{35} +(1.49213e6 + 6.53745e6i) q^{36} +(1.72813e6 + 604698. i) q^{37} +(-647705. - 1.34497e6i) q^{38} +(-597801. + 375623. i) q^{39} +(1.16997e6 - 409391. i) q^{40} +(1.18704e6 + 1.18704e6i) q^{41} +(-312267. + 648428. i) q^{42} +(-593940. - 5.27136e6i) q^{43} +(-7.54037e6 + 849596. i) q^{44} +(-8.70311e6 - 4.19120e6i) q^{45} +(7.71570e6 - 7.71570e6i) q^{46} +(-1.04726e6 - 2.99290e6i) q^{47} +(2.60807e6 + 4.15072e6i) q^{48} +(5.16390e6 - 2.48681e6i) q^{49} +(1.06170e6 - 3.03418e6i) q^{50} +(-4.76353e6 + 1.08724e6i) q^{51} +(976928. - 1.22503e6i) q^{52} +(-3.26236e6 - 4.09087e6i) q^{53} +(-1.08517e7 + 4.75443e7i) q^{54} +(5.81566e6 - 9.25557e6i) q^{55} +(49619.2 - 440383. i) q^{56} -9.64693e6i q^{57} +(1.55114e7 - 8.04365e6i) q^{58} -1.03572e7 q^{59} +(2.86882e7 + 3.23239e6i) q^{60} +(-5.71826e6 - 3.59302e6i) q^{61} +(2.56975e7 + 5.86528e6i) q^{62} +(-2.70017e6 + 2.15331e6i) q^{63} +(-2.05139e7 - 1.63593e7i) q^{64} +(502265. + 2.20057e6i) q^{65} +(-7.97270e7 - 2.78977e7i) q^{66} +(5.85423e6 + 1.21564e7i) q^{67} +(9.18156e6 - 5.76916e6i) q^{68} +(6.65571e7 - 2.32893e7i) q^{69} +(1.62699e6 + 1.62699e6i) q^{70} +(-1.91533e7 + 3.97722e7i) q^{71} +(-5.14622e6 - 4.56740e7i) q^{72} +(-3.23600e6 + 364609. i) q^{73} +(-4.07512e7 - 1.96247e7i) q^{74} +(1.46890e7 - 1.46890e7i) q^{75} +(7.07113e6 + 2.02081e7i) q^{76} +(-2.07928e6 - 3.30915e6i) q^{77} +(1.57144e7 - 7.56766e6i) q^{78} +(1.29876e7 - 3.71166e7i) q^{79} +(1.52792e7 - 3.48739e6i) q^{80} +(-1.19069e8 + 1.49308e8i) q^{81} +(-2.58574e7 - 3.24242e7i) q^{82} +(1.24899e7 - 5.47220e7i) q^{83} +(5.49154e6 - 8.73973e6i) q^{84} +(-1.74898e6 + 1.55226e7i) q^{85} +1.31050e8i q^{86} +(1.12865e8 - 3.34063e6i) q^{87} +5.20122e7 q^{88} +(2.84528e7 + 3.20586e6i) q^{89} +(2.02060e8 + 1.26963e8i) q^{90} +(786769. + 179575. i) q^{91} +(-1.22351e8 + 9.75716e7i) q^{92} +(1.33173e8 + 1.06202e8i) q^{93} +(1.74308e7 + 7.63695e7i) q^{94} +(-2.91109e7 - 1.01863e7i) q^{95} +(-9.56095e7 - 1.98535e8i) q^{96} +(-4.20609e7 + 2.64286e7i) q^{97} +(-1.33647e8 + 4.67652e7i) q^{98} +(-2.86614e8 - 2.86614e8i) 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 $

$2$	−24.5490	−	2.76601i	−1.53431	−	0.172876i	−0.695991	−	0.718050i	$-0.745035\pi$
$2$	−24.5490	−	2.76601i	−1.53431	−	0.172876i	−0.838323	+	0.545175i	$0.816463\pi$
$3$	−135.176	−	84.9370i	−1.66885	−	1.04860i	−0.924783	−	0.380494i	$-0.875754\pi$
$3$	−135.176	−	84.9370i	−1.66885	−	1.04860i	−0.744062	−	0.668111i	$-0.767103\pi$
$4$	345.422	+	78.8403i	1.34930	+	0.307970i
$5$	−399.043	+	318.226i	−0.638469	+	0.509162i	−0.888381	−	0.459106i	$-0.848170\pi$
$5$	−399.043	+	318.226i	−0.638469	+	0.509162i	0.249912	+	0.968268i	$0.419598\pi$
$6$	3083.51	+	2459.02i	2.37925	+	1.89739i
$7$	40.6060	+	177.907i	0.0169121	+	0.0740969i	0.982680	−	0.185312i	$-0.0593295\pi$
$7$	40.6060	+	177.907i	0.0169121	+	0.0740969i	−0.965768	+	0.259409i	$0.916472\pi$
$8$	−2292.28	−	802.105i	−0.559640	−	0.195826i
$9$	8211.67	+	17051.7i	1.25159	+	2.59895i
$10$	10676.3	−	6708.39i	1.06763	−	0.670839i
$11$	−20215.0	+	7073.52i	−1.38071	+	0.483131i	−0.915589	−	0.402116i	$-0.868275\pi$
$11$	−20215.0	+	7073.52i	−1.38071	+	0.483131i	−0.465121	+	0.885247i	$0.653989\pi$
$12$	−39996.5	−	39996.5i	−1.92884	−	1.92884i
$13$	1918.80	−	3984.42i	0.0671824	−	0.139506i	−0.864673	−	0.502334i	$-0.832475\pi$
$13$	1918.80	−	3984.42i	0.0671824	−	0.139506i	0.931856	+	0.362829i	$0.118189\pi$
$14$	−504.747	−	4479.75i	−0.0131390	−	0.116612i
$15$	80970.4	−	9123.18i	1.59942	−	0.180211i
$16$	−27665.1	−	13322.8i	−0.422136	−	0.203290i
$17$	21641.2	−	21641.2i	0.259111	−	0.259111i	−0.565581	−	0.824693i	$-0.691348\pi$
$17$	21641.2	−	21641.2i	0.259111	−	0.259111i	0.824693	+	0.565581i	$0.191348\pi$
$18$	−154423.	−	441316.i	−1.47103	−	4.20397i
$19$	32149.0	+	51164.9i	0.246691	+	0.392607i	0.947000	−	0.321233i	$-0.104097\pi$
$19$	32149.0	+	51164.9i	0.246691	+	0.392607i	−0.700309	+	0.713840i	$0.746954\pi$
$20$	−162927.	+	78461.7i	−1.01830	+	0.490386i
$21$	9621.87	−	27497.7i	0.0494746	−	0.141390i
$22$	515823.	−	117733.i	2.20196	−	0.502584i
$23$	−275389.	+	345326.i	−0.984090	+	1.23401i	−0.0118724	+	0.999930i	$0.503779\pi$
$23$	−275389.	+	345326.i	−0.984090	+	1.23401i	−0.972217	+	0.234080i	$0.924792\pi$
$24$	241735.	+	303126.i	0.728608	+	0.913645i
$25$	−28954.8	+	126859.i	−0.0741242	+	0.324759i
$26$	−58125.5	+	92506.2i	−0.127196	+	0.202431i
$27$	221020.	−	1.96161e6i	0.415889	−	3.69112i
$28$			64654.3i			0.105188i
$29$	−587477.	+	393849.i	−0.830613	+	0.556850i
$29$	−587477.	+	393849.i	−0.830613	+	0.556850i
$30$	−2.01298e6			−2.48516
$31$	−1.06024e6	−	119460.i	−1.14804	−	0.129353i	−0.482627	−	0.875826i	$-0.660317\pi$
$31$	−1.06024e6	−	119460.i	−1.14804	−	0.129353i	−0.665416	+	0.746473i	$0.731746\pi$
$32$	1.16872e6	+	734355.i	1.11458	+	0.700336i
$33$	3.33339e6	+	760825.i	2.81080	+	0.641548i
$34$	−591131.	+	471411.i	−0.442352	+	0.352764i
$35$	−72818.1	−	58070.5i	−0.0485252	−	0.0386975i
$36$	1.49213e6	+	6.53745e6i	0.888376	+	3.89223i
$37$	1.72813e6	+	604698.i	0.922080	+	0.322650i	0.749239	−	0.662300i	$-0.230420\pi$
$37$	1.72813e6	+	604698.i	0.922080	+	0.322650i	0.172841	+	0.984950i	$0.444705\pi$
$38$	−647705.	−	1.34497e6i	−0.310629	−	0.645029i
$39$	−597801.	+	375623.i	−0.258403	+	0.162366i
$40$	1.16997e6	−	409391.i	0.457020	−	0.159918i
$41$	1.18704e6	+	1.18704e6i	0.420080	+	0.420080i	0.885231	−	0.465151i	$-0.154000\pi$
$41$	1.18704e6	+	1.18704e6i	0.420080	+	0.420080i	−0.465151	+	0.885231i	$0.654000\pi$
$42$	−312267.	+	648428.i	−0.100353	+	0.208384i
$43$	−593940.	−	5.27136e6i	−0.173727	−	1.54187i	−0.713857	−	0.700292i	$-0.753053\pi$
$43$	−593940.	−	5.27136e6i	−0.173727	−	1.54187i	0.540129	−	0.841582i	$-0.318375\pi$
$44$	−7.54037e6	+	849596.i	−2.01179	+	0.226674i
$45$	−8.70311e6	−	4.19120e6i	−2.12239	−	1.02209i
$46$	7.71570e6	−	7.71570e6i	1.72323	−	1.72323i
$47$	−1.04726e6	−	2.99290e6i	−0.214617	−	0.613340i	0.785367	−	0.619030i	$-0.212474\pi$
$47$	−1.04726e6	−	2.99290e6i	−0.214617	−	0.613340i	−0.999984	+	0.00569085i	$0.998189\pi$
$48$	2.60807e6	+	4.15072e6i	0.491309	+	0.781913i
$49$	5.16390e6	−	2.48681e6i	0.895765	−	0.431377i
$50$	1.06170e6	−	3.03418e6i	0.169873	−	0.485469i
$51$	−4.76353e6	+	1.08724e6i	−0.704122	+	0.160711i
$52$	976928.	−	1.22503e6i	0.133613	−	0.167546i
$53$	−3.26236e6	−	4.09087e6i	−0.413455	−	0.518456i	0.530877	−	0.847449i	$-0.321862\pi$
$53$	−3.26236e6	−	4.09087e6i	−0.413455	−	0.518456i	−0.944333	+	0.328992i	$0.893291\pi$
$54$	−1.08517e7	+	4.75443e7i	−1.27621	+	5.59143i
$55$	5.81566e6	−	9.25557e6i	0.635548	−	1.01147i
$56$	49619.2	−	440383.i	0.00504543	−	0.0447794i
$57$		−	9.64693e6i		−	0.913881i
$58$	1.55114e7	−	8.04365e6i	1.37069	−	0.710790i
$59$	−1.03572e7			−0.854738			−0.427369	−	0.904077i	$-0.640559\pi$
$59$	−1.03572e7			−0.854738			−0.427369	+	0.904077i	$0.640559\pi$
$60$	2.86882e7	+	3.23239e6i	2.21360	+	0.249413i
$61$	−5.71826e6	−	3.59302e6i	−0.412995	−	0.259502i	0.309470	−	0.950909i	$-0.399848\pi$
$61$	−5.71826e6	−	3.59302e6i	−0.412995	−	0.259502i	−0.722465	+	0.691407i	$0.756991\pi$
$62$	2.56975e7	+	5.86528e6i	1.73910	+	0.396937i
$63$	−2.70017e6	+	2.15331e6i	−0.171407	+	0.136693i
$64$	−2.05139e7	−	1.63593e7i	−1.22273	−	0.975091i
$65$	502265.	+	2.20057e6i	0.0281371	+	0.123277i
$66$	−7.97270e7	−	2.78977e7i	−4.20175	−	1.47025i
$67$	5.85423e6	+	1.21564e7i	0.290516	+	0.603263i	0.994236	−	0.107215i	$-0.0341932\pi$
$67$	5.85423e6	+	1.21564e7i	0.290516	+	0.603263i	−0.703720	+	0.710478i	$0.748479\pi$
$68$	9.18156e6	−	5.76916e6i	0.429419	−	0.269822i
$69$	6.65571e7	−	2.32893e7i	2.93628	−	1.02745i
$70$	1.62699e6	+	1.62699e6i	0.0677630	+	0.0677630i
$71$	−1.91533e7	+	3.97722e7i	−0.753719	+	1.56511i	0.0696258	+	0.997573i	$0.477819\pi$
$71$	−1.91533e7	+	3.97722e7i	−0.753719	+	1.56511i	−0.823345	+	0.567541i	$0.807895\pi$
$72$	−5.14622e6	−	4.56740e7i	−0.191496	−	1.69957i
$73$	−3.23600e6	+	364609.i	−0.113951	+	0.0128391i	−0.168756	−	0.985658i	$-0.553975\pi$
$73$	−3.23600e6	+	364609.i	−0.113951	+	0.0128391i	0.0548050	+	0.998497i	$0.482546\pi$
$74$	−4.07512e7	−	1.96247e7i	−1.35898	−	0.654451i
$75$	1.46890e7	−	1.46890e7i	0.464246	−	0.464246i
$76$	7.07113e6	+	2.02081e7i	0.211950	+	0.605720i
$77$	−2.07928e6	−	3.30915e6i	−0.0591492	−	0.0941355i
$78$	1.57144e7	−	7.56766e6i	0.424541	−	0.204448i
$79$	1.29876e7	−	3.71166e7i	0.333443	−	0.952927i	−0.648078	−	0.761574i	$-0.724427\pi$
$79$	1.29876e7	−	3.71166e7i	0.333443	−	0.952927i	0.981521	−	0.191353i	$-0.0612874\pi$
$80$	1.52792e7	−	3.48739e6i	0.373028	−	0.0851412i
$81$	−1.19069e8	+	1.49308e8i	−2.76605	+	3.46851i
$82$	−2.58574e7	−	3.24242e7i	−0.571913	−	0.717156i
$83$	1.24899e7	−	5.47220e7i	0.263177	−	1.15305i	−0.654606	−	0.755970i	$-0.727165\pi$
$83$	1.24899e7	−	5.47220e7i	0.263177	−	1.15305i	0.917783	−	0.397083i	$-0.129977\pi$
$84$	5.49154e6	−	8.73973e6i	0.110300	−	0.175542i
$85$	−1.74898e6	+	1.55226e7i	−0.0335049	+	0.297364i
$86$			1.31050e8i			2.39575i
$87$	1.12865e8	−	3.34063e6i	1.97008	−	0.0583111i
$88$	5.20122e7			0.867310
$89$	2.84528e7	+	3.20586e6i	0.453487	+	0.0510957i	0.335754	−	0.941950i	$-0.391009\pi$
$89$	2.84528e7	+	3.20586e6i	0.453487	+	0.0510957i	0.117733	+	0.993045i	$0.462437\pi$
$90$	2.02060e8	+	1.26963e8i	3.07971	+	1.93511i
$91$	786769.	+	179575.i	0.0114731	+	0.00261867i
$92$	−1.22351e8	+	9.75716e7i	−1.70788	+	1.36198i
$93$	1.33173e8	+	1.06202e8i	1.78026	+	1.41971i
$94$	1.74308e7	+	7.63695e7i	0.223258	+	0.978157i
$95$	−2.91109e7	−	1.01863e7i	−0.357405	−	0.125061i
$96$	−9.56095e7	−	1.98535e8i	−1.12568	−	2.33750i
$97$	−4.20609e7	+	2.64286e7i	−0.475107	+	0.298530i	−0.748218	−	0.663453i	$-0.769090\pi$
$97$	−4.20609e7	+	2.64286e7i	−0.475107	+	0.298530i	0.273111	+	0.961983i	$0.411947\pi$
$98$	−1.33647e8	+	4.67652e7i	−1.44896	+	0.507013i
$99$	−2.86614e8	−	2.86614e8i	−2.98371	−	2.98371i
$100$	−2.00032e7	+	4.15371e7i	−0.200032	+	0.415371i
$101$	−3.01687e6	−	2.67755e7i	−0.0289916	−	0.257307i	−0.999845	−	0.0176315i	$-0.994387\pi$
$101$	−3.01687e6	−	2.67755e7i	−0.0289916	−	0.257307i	0.970853	−	0.239676i	$-0.0770412\pi$
$102$	1.19947e8	−	1.35148e7i	1.10813	−	0.124856i
$103$	1.58827e7	+	7.64869e6i	0.141115	+	0.0679576i	0.503109	−	0.864223i	$-0.332189\pi$
$103$	1.58827e7	+	7.64869e6i	0.141115	+	0.0679576i	−0.361993	+	0.932181i	$0.617904\pi$
$104$	−7.59435e6	+	7.59435e6i	−0.0649168	+	0.0649168i
$105$	4.91096e6	+	1.40347e7i	0.0404026	+	0.115464i
$106$	6.87724e7	+	1.09451e8i	0.544742	+	0.866951i
$107$	1.95614e7	−	9.42025e6i	0.149233	−	0.0718667i	−0.357777	−	0.933807i	$-0.616465\pi$
$107$	1.95614e7	−	9.42025e6i	0.149233	−	0.0718667i	0.507010	+	0.861940i	$0.330751\pi$
$108$	2.30999e8	−	6.60158e8i	1.69791	−	4.85236i
$109$	1.68099e8	−	3.83674e7i	1.19085	−	0.271804i	0.419227	−	0.907881i	$-0.362301\pi$
$109$	1.68099e8	−	3.83674e7i	1.19085	−	0.271804i	0.771626	+	0.636077i	$0.219444\pi$
$110$	−1.68370e8	+	2.11129e8i	−1.14999	+	1.44204i
$111$	−1.82241e8	−	2.28523e8i	−1.20048	−	1.50535i
$112$	1.24685e6	−	5.46279e6i	0.00792393	−	0.0347170i
$113$	−5.25359e7	+	8.36103e7i	−0.322212	+	0.512798i	−0.968077	−	0.250654i	$-0.919354\pi$
$113$	−5.25359e7	+	8.36103e7i	−0.322212	+	0.512798i	0.645864	+	0.763452i	$0.276497\pi$
$114$	−2.66835e7	+	2.36823e8i	−0.157988	+	1.40218i
$115$		−	2.25436e8i		−	1.28894i
$116$	−2.33979e8	+	8.97274e7i	−1.29224	+	0.495556i
$117$	8.36977e7			0.446653
$118$	2.54258e8	+	2.86480e7i	1.31144	+	0.147763i
$119$	4.72888e6	+	2.97135e6i	0.0235815	+	0.0148172i
$120$	−1.92925e8	−	4.40339e7i	−0.930387	−	0.212355i
$121$	1.91017e8	−	1.52331e8i	0.891111	−	0.710637i
$122$	1.30439e8	+	1.04022e8i	0.588802	+	0.469554i
$123$	−5.96365e7	−	2.61285e8i	−0.260550	−	1.14155i
$124$	−3.56812e8	−	1.24854e8i	−1.50922	−	0.528100i
$125$	−1.15320e8	−	2.39465e8i	−0.472353	−	0.980851i
$126$	7.22426e7	−	4.53930e7i	0.286623	−	0.180097i
$127$	−4.25759e7	+	1.48979e7i	−0.163662	+	0.0572679i	−0.410867	−	0.911695i	$-0.634774\pi$
$127$	−4.25759e7	+	1.48979e7i	−0.163662	+	0.0572679i	0.247204	+	0.968963i	$0.420488\pi$
$128$	2.08489e8	+	2.08489e8i	0.776682	+	0.776682i
$129$	−3.67447e8	+	7.63011e8i	−1.32689	+	2.75532i
$130$	−6.24333e6	−	5.54110e7i	−0.0218596	−	0.194009i
$131$	2.66309e8	−	3.00059e7i	0.904276	−	0.101887i	0.352435	−	0.935836i	$-0.385354\pi$
$131$	2.66309e8	−	3.00059e7i	0.904276	−	0.101887i	0.551842	+	0.833949i	$0.313925\pi$
$132$	1.09144e9	+	5.25611e8i	3.59505	+	1.73129i
$133$	−7.79713e6	+	7.79713e6i	−0.0249189	+	0.0249189i
$134$	−1.10091e8	−	3.14621e8i	−0.341454	−	0.975818i
$135$	5.36039e8	+	8.53102e8i	1.61384	+	2.56842i
$136$	−6.69664e7	+	3.22493e7i	−0.195750	+	0.0942681i
$137$	7.71540e6	−	2.20493e7i	0.0219016	−	0.0625912i	−0.932414	−	0.361393i	$-0.882301\pi$
$137$	7.71540e6	−	2.20493e7i	0.0219016	−	0.0625912i	0.954315	+	0.298802i	$0.0965870\pi$
$138$	−1.69833e9	+	3.87633e8i	−4.68280	+	1.06882i
$139$	1.94506e8	−	2.43903e8i	0.521043	−	0.653367i	−0.449787	−	0.893136i	$-0.648500\pi$
$139$	1.94506e8	−	2.43903e8i	0.521043	−	0.653367i	0.970830	+	0.239769i	$0.0770716\pi$
$140$	−2.05747e7	−	2.57998e7i	−0.0535576	−	0.0671591i
$141$	−1.12643e8	+	4.93521e8i	−0.284989	+	1.24862i
$142$	5.80204e8	−	9.23390e8i	1.42701	−	2.27108i
$143$	−1.06045e7	+	9.41176e7i	−0.0253598	+	0.225075i
$144$		−	5.81140e8i		−	1.35154i
$145$	1.09095e8	−	3.44113e8i	0.246794	−	0.778448i
$146$	8.04491e7			0.177056
$147$	−9.09260e8	−	1.02449e8i	−1.94724	−	0.219401i
$148$	5.49258e8	+	3.45122e8i	1.14480	+	0.719326i
$149$	−5.46868e8	−	1.24819e8i	−1.10953	−	0.253242i	−0.371780	−	0.928321i	$-0.621253\pi$
$149$	−5.46868e8	−	1.24819e8i	−1.10953	−	0.253242i	−0.737746	+	0.675079i	$0.764110\pi$
$150$	−4.01232e8	+	3.19971e8i	−0.792556	+	0.632042i
$151$	1.48531e8	+	1.18450e8i	0.285700	+	0.227838i	0.755844	−	0.654752i	$-0.227227\pi$
$151$	1.48531e8	+	1.18450e8i	0.285700	+	0.227838i	−0.470144	+	0.882589i	$0.655798\pi$
$152$	−3.26551e7	−	1.43071e8i	−0.0611754	−	0.268027i
$153$	5.46731e8	+	1.91309e8i	0.997718	+	0.349117i
$154$	4.18910e7	+	8.69876e7i	0.0744797	+	0.154659i
$155$	4.61098e8	−	2.89727e8i	0.798851	−	0.501952i
$156$	−2.36108e8	+	8.26177e7i	−0.398669	+	0.139500i
$157$	−7.61775e7	−	7.61775e7i	−0.125380	−	0.125380i	0.641632	−	0.767012i	$-0.278258\pi$
$157$	−7.61775e7	−	7.61775e7i	−0.125380	−	0.125380i	−0.767012	+	0.641632i	$0.778258\pi$
$158$	−4.21499e8	+	8.75251e8i	−0.676345	+	1.40444i
$159$	9.35281e7	+	8.30085e8i	0.146337	+	1.29877i
$160$	−7.00061e8	+	7.88779e7i	−1.06821	+	0.120358i
$161$	−7.26183e7	−	3.49711e7i	−0.108079	−	0.0520482i
$162$	3.33602e9	−	3.33602e9i	4.84361	−	4.84361i
$163$	9.73229e7	+	2.78133e8i	0.137868	+	0.394005i	0.992030	−	0.126003i	$-0.0402148\pi$
$163$	9.73229e7	+	2.78133e8i	0.137868	+	0.394005i	−0.854162	+	0.520008i	$0.825929\pi$
$164$	3.16444e8	+	5.03619e8i	0.437444	+	0.696188i
$165$	−1.57228e9	+	7.57171e8i	−2.12126	+	1.02155i
$166$	−4.57977e8	+	1.30882e9i	−0.603131	+	1.72365i
$167$	8.55549e8	−	1.95273e8i	1.09996	−	0.251060i	0.366249	−	0.930517i	$-0.380642\pi$
$167$	8.55549e8	−	1.95273e8i	1.09996	−	0.251060i	0.733715	+	0.679457i	$0.237785\pi$
$168$	−4.41122e7	+	5.53149e7i	−0.0553759	+	0.0694392i
$169$	4.96406e8	+	6.22473e8i	0.608541	+	0.763087i
$170$	8.58713e7	−	3.76227e8i	0.102814	−	0.450458i
$171$	−6.08452e8	+	9.68345e8i	−0.711609	+	1.13252i
$172$	2.10436e8	−	1.86767e9i	0.240440	−	2.13396i
$173$		−	7.32601e8i		−	0.817868i	−0.912564	−	0.408934i	$-0.865901\pi$
$173$		−	7.32601e8i		−	0.817868i	0.912564	−	0.408934i	$-0.134099\pi$
$174$	−2.77998e9	−	2.30178e8i	−3.03280	−	0.251111i
$175$	−2.37448e7			−0.0253173
$176$	6.53488e8	+	7.36304e7i	0.681062	+	0.0767373i
$177$	1.40005e9	+	8.79707e8i	1.42643	+	0.896282i
$178$	−6.89620e8	−	1.57401e8i	−0.686958	−	0.156794i
$179$	8.60669e8	−	6.86361e8i	0.838348	−	0.668560i	−0.107131	−	0.994245i	$-0.534166\pi$
$179$	8.60669e8	−	6.86361e8i	0.838348	−	0.668560i	0.945478	+	0.325685i	$0.105595\pi$
$180$	−2.67581e9	−	2.13389e9i	−2.54898	−	2.03274i
$181$	2.46550e8	+	1.08021e9i	0.229716	+	1.00645i	0.949872	+	0.312640i	$0.101213\pi$
$181$	2.46550e8	+	1.08021e9i	0.229716	+	1.00645i	−0.720156	+	0.693813i	$0.755930\pi$
$182$	−1.88177e7	−	6.58460e6i	−0.0171507	−	0.00600128i
$183$	4.67794e8	+	9.71384e8i	0.417110	+	0.866137i
$184$	9.08257e8	−	5.70696e8i	0.792388	−	0.497890i
$185$	−8.82028e8	+	3.08635e8i	−0.753001	+	0.263486i
$186$	−2.97551e9	−	2.97551e9i	−2.48605	−	2.48605i
$187$	−2.84397e8	+	5.90556e8i	−0.232573	+	0.482942i
$188$	−1.25786e8	−	1.11638e9i	−0.100693	−	0.893678i
$189$	3.57958e8	−	4.03322e7i	0.280534	−	0.0316086i
$190$	6.86468e8	+	3.30585e8i	0.526751	+	0.253670i
$191$	4.24678e8	−	4.24678e8i	0.319099	−	0.319099i	−0.529322	−	0.848421i	$-0.677554\pi$
$191$	4.24678e8	−	4.24678e8i	0.319099	−	0.319099i	0.848421	+	0.529322i	$0.177554\pi$
$192$	1.38349e9	+	3.95379e9i	1.01805	+	2.90943i
$193$	−1.28991e9	−	2.05289e9i	−0.929675	−	1.47957i	−0.876736	−	0.480972i	$-0.840284\pi$
$193$	−1.28991e9	−	2.05289e9i	−0.929675	−	1.47957i	−0.0529397	−	0.998598i	$-0.516859\pi$
$194$	1.10566e9	−	5.32455e8i	0.780572	−	0.375904i
$195$	1.19015e8	−	3.40126e8i	0.0823121	−	0.235235i
$196$	1.97979e9	−	4.51873e8i	1.34151	−	0.306191i
$197$	4.62242e8	−	5.79634e8i	0.306906	−	0.384847i	−0.604329	−	0.796735i	$-0.706559\pi$
$197$	4.62242e8	−	5.79634e8i	0.306906	−	0.384847i	0.911235	+	0.411887i	$0.135130\pi$
$198$	6.24332e9	+	7.82888e9i	4.06214	+	5.09376i
$199$	6.32332e7	−	2.77043e8i	0.0403211	−	0.176658i	−0.950758	−	0.309935i	$-0.899693\pi$
$199$	6.32332e7	−	2.77043e8i	0.0403211	−	0.176658i	0.991079	+	0.133277i	$0.0425499\pi$
$200$	1.68127e8	−	2.67573e8i	0.105079	−	0.167233i
$201$	2.41177e8	−	2.14050e9i	0.147758	−	1.31139i
$202$			6.65657e8i			0.399802i
$203$	−9.39235e7	−	8.85234e7i	−0.0553083	−	0.0521283i
$204$	−1.73115e9			−0.999569
$205$	−8.51431e8	−	9.59332e7i	−0.482097	−	0.0543192i
$206$	−3.68747e8	−	2.31699e8i	−0.204767	−	0.128664i
$207$	−8.14981e9	−	1.86014e9i	−4.43880	−	1.01313i
$208$	−1.06167e8	+	8.46656e7i	−0.0567202	+	0.0452328i
$209$	−1.01181e9	−	8.06890e8i	−0.530289	−	0.422891i
$210$	−8.17391e7	−	3.58122e8i	−0.0420293	−	0.184143i
$211$	−1.19108e9	−	4.16778e8i	−0.600915	−	0.210269i	0.0126417	−	0.999920i	$-0.495976\pi$
$211$	−1.19108e9	−	4.16778e8i	−0.600915	−	0.210269i	−0.613556	+	0.789651i	$0.710262\pi$
$212$	−8.04366e8	−	1.67028e9i	−0.398208	−	0.826888i
$213$	5.96720e9	−	3.74944e9i	2.89903	−	1.82158i
$214$	−5.06269e8	+	1.77151e8i	−0.241394	+	0.0844673i
$215$	1.91449e9	+	1.91449e9i	0.895984	+	0.895984i
$216$	−2.08006e9	+	4.31929e9i	−0.955566	+	1.98425i
$217$	−2.17994e7	−	1.93475e8i	−0.00983116	−	0.0872540i
$218$	−4.23278e9	+	4.76920e8i	−1.87413	+	0.211164i
$219$	4.68399e8	+	2.25569e8i	0.203629	+	0.0980626i
$220$	2.73857e9	−	2.73857e9i	1.16905	−	1.16905i
$221$	−4.47027e7	−	1.27753e8i	−0.0187398	−	0.0535552i
$222$	3.84174e9	+	6.11409e9i	1.58167	+	2.51721i
$223$	1.15249e9	−	5.55011e8i	0.466035	−	0.224431i	−0.186104	−	0.982530i	$-0.559586\pi$
$223$	1.15249e9	−	5.55011e8i	0.466035	−	0.224431i	0.652139	+	0.758099i	$0.273872\pi$
$224$	−8.31896e7	+	2.37742e8i	−0.0330428	+	0.0944309i
$225$	−2.40093e9	+	5.47997e8i	−0.936806	+	0.213820i
$226$	1.52097e9	−	1.90724e9i	0.583025	−	0.731090i
$227$	−1.15371e9	−	1.44671e9i	−0.434504	−	0.544851i	0.515581	−	0.856841i	$-0.327576\pi$
$227$	−1.15371e9	−	1.44671e9i	−0.434504	−	0.544851i	−0.950085	+	0.311990i	$0.899005\pi$
$228$	7.60567e8	−	3.33226e9i	0.281448	−	1.23310i
$229$	−6.63840e8	+	1.05649e9i	−0.241391	+	0.384172i	−0.945344	−	0.326075i	$-0.894274\pi$
$229$	−6.63840e8	+	1.05649e9i	−0.241391	+	0.384172i	0.703953	+	0.710247i	$0.251417\pi$
$230$	−6.23559e8	+	5.53423e9i	−0.222826	+	1.97764i
$231$			6.23926e8i			0.219122i
$232$	1.66257e9	−	4.31597e8i	0.573890	−	0.148979i
$233$	3.58867e9			1.21762			0.608808	−	0.793318i	$-0.291648\pi$
$233$	3.58867e9			1.21762			0.608808	+	0.793318i	$0.291648\pi$
$234$	−2.05470e9	−	2.31509e8i	−0.685306	−	0.0772154i
$235$	1.37032e9	+	8.61031e8i	0.449315	+	0.282324i
$236$	−3.57759e9	−	8.16562e8i	−1.15330	−	0.263234i
$237$	−4.90819e9	+	3.91415e9i	−1.55571	+	1.24064i
$238$	−1.07871e8	−	8.60240e7i	−0.0336198	−	0.0268109i
$239$	−5.54907e8	−	2.43121e9i	−0.170070	−	0.745127i	−0.985969	−	0.166931i	$-0.946614\pi$
$239$	−5.54907e8	−	2.43121e9i	−0.170070	−	0.745127i	0.815898	−	0.578196i	$-0.196243\pi$
$240$	−2.36160e9	−	8.26360e8i	−0.711806	−	0.249072i
$241$	1.49297e9	+	3.10018e9i	0.442570	+	0.919006i	0.996270	+	0.0862896i	$0.0275010\pi$
$241$	1.49297e9	+	3.10018e9i	0.442570	+	0.919006i	−0.553700	+	0.832716i	$0.686785\pi$
$242$	−5.11064e9	+	3.21123e9i	−1.49010	+	0.936289i
$243$	1.65524e10	−	5.79193e9i	4.74718	−	1.66111i
$244$	−1.69194e9	−	1.69194e9i	−0.477337	−	0.477337i
$245$	−1.26925e9	+	2.63563e9i	−0.352277	+	0.731511i
$246$	7.41302e8	+	6.57924e9i	0.202421	+	1.79653i
$247$	2.65550e8	−	2.99203e7i	0.0713442	−	0.00803856i
$248$	2.33456e9	+	1.12426e9i	0.617159	+	0.297208i
$249$	−6.33627e9	+	6.33627e9i	−1.64830	+	1.64830i
$250$	2.16864e9	+	6.19762e9i	0.555172	+	1.58659i
$251$	3.89774e9	+	6.20322e9i	0.982015	+	1.56287i	0.817048	+	0.576569i	$0.195609\pi$
$251$	3.89774e9	+	6.20322e9i	0.982015	+	1.56287i	0.164967	+	0.986299i	$0.447248\pi$
$252$	−1.10247e9	+	5.30919e8i	−0.273378	+	0.131652i
$253$	3.12430e9	−	8.92873e9i	0.762553	−	2.17925i
$254$	1.08640e9	−	2.47965e8i	0.261010	−	0.0595737i
$255$	1.55486e9	−	1.94974e9i	0.367732	−	0.461121i
$256$	−3.53530e8	−	4.43313e8i	−0.0823127	−	0.103217i
$257$	1.10746e8	−	4.85210e8i	0.0253861	−	0.111224i	−0.960647	−	0.277770i	$-0.910405\pi$
$257$	1.10746e8	−	4.85210e8i	0.0253861	−	0.111224i	0.986034	+	0.166547i	$0.0532617\pi$
$258$	1.11310e10	−	1.77148e10i	2.51220	−	3.99814i
$259$	−3.74073e7	+	3.31999e8i	−0.00831300	+	0.0737799i
$260$			7.99723e8i			0.175003i
$261$	−1.15400e10	−	6.78333e9i	−2.48681	−	1.46178i
$262$	−6.62063e9			−1.40506
$263$	−2.08562e9	−	2.34993e8i	−0.435926	−	0.0491171i	−0.108725	−	0.994072i	$-0.534677\pi$
$263$	−2.08562e9	−	2.34993e8i	−0.435926	−	0.0491171i	−0.327201	+	0.944955i	$0.606105\pi$
$264$	−7.03082e9	−	4.41776e9i	−1.44741	−	0.909465i
$265$	2.60365e9	+	5.94265e8i	0.527957	+	0.120503i
$266$	2.12979e8	−	1.69845e8i	0.0425412	−	0.0339255i
$267$	−3.57385e9	−	2.85005e9i	−0.703220	−	0.560799i
$268$	1.06376e9	+	4.66065e9i	0.206208	+	0.903456i
$269$	2.78272e9	+	9.73716e8i	0.531447	+	0.185961i	0.582645	−	0.812727i	$-0.302018\pi$
$269$	2.78272e9	+	9.73716e8i	0.531447	+	0.185961i	−0.0511972	+	0.998689i	$0.516304\pi$
$270$	−1.07996e10	−	2.24255e10i	−2.03213	−	4.21975i
$271$	−2.18255e9	+	1.37139e9i	−0.404658	+	0.254263i	−0.718948	−	0.695064i	$-0.755376\pi$
$271$	−2.18255e9	+	1.37139e9i	−0.404658	+	0.254263i	0.314291	+	0.949327i	$0.398233\pi$
$272$	−8.87029e8	+	3.10385e8i	−0.162055	+	0.0567054i
$273$	−9.11002e7	−	9.11002e7i	−0.0164009	−	0.0164009i
$274$	−2.50394e8	+	5.19949e8i	−0.0444244	+	0.0922483i
$275$	−3.12021e8	−	2.76926e9i	−0.0545574	−	0.484210i
$276$	2.48264e10	−	2.79727e9i	4.27836	−	0.482056i
$277$	−7.55259e9	−	3.63714e9i	−1.28285	−	0.617789i	−0.336731	−	0.941601i	$-0.609321\pi$
$277$	−7.55259e9	−	3.63714e9i	−1.28285	−	0.617789i	−0.946122	+	0.323812i	$0.895036\pi$
$278$	−5.44956e9	+	5.44956e9i	−0.912394	+	0.912394i
$279$	−6.66935e9	−	1.90599e10i	−1.10069	−	3.14560i
$280$	1.20341e8	+	1.91522e8i	0.0195786	+	0.0311592i
$281$	−6.79883e8	+	3.27415e8i	−0.109046	+	0.0525137i	−0.487611	−	0.873061i	$-0.662132\pi$
$281$	−6.79883e8	+	3.27415e8i	−0.109046	+	0.0525137i	0.378566	+	0.925574i	$0.376417\pi$
$282$	4.13036e9	−	1.18039e10i	0.653118	−	1.86650i
$283$	−3.96049e9	+	9.03955e8i	−0.617452	+	0.140929i	−0.519795	−	0.854291i	$-0.673992\pi$
$283$	−3.96049e9	+	9.03955e8i	−0.617452	+	0.140929i	−0.0976563	+	0.995220i	$0.531135\pi$
$284$	−9.75162e9	+	1.22281e10i	−1.49901	+	1.87969i
$285$	3.06991e9	+	3.84954e9i	0.465314	+	0.583485i
$286$	5.20660e8	−	2.28116e9i	0.0778198	−	0.340951i
$287$	−1.62982e8	+	2.59384e8i	−0.0240222	+	0.0382310i
$288$	−2.92487e9	+	2.59590e10i	−0.425145	+	3.77326i
$289$			6.03907e9i			0.865723i
$290$	−3.63001e9	+	8.14589e9i	−0.513234	+	1.15172i
$291$	7.93041e9			1.10592
$292$	−1.14653e9	−	1.29183e8i	−0.157708	−	0.0177694i
$293$	1.95158e9	+	1.22626e9i	0.264799	+	0.166384i	0.657887	−	0.753117i	$-0.271450\pi$
$293$	1.95158e9	+	1.22626e9i	0.264799	+	0.166384i	−0.393088	+	0.919501i	$0.628593\pi$
$294$	2.20381e10	+	5.03005e9i	2.94974	+	0.673260i
$295$	4.13296e9	−	3.29592e9i	0.545724	−	0.435200i
$296$	−3.47633e9	−	2.77228e9i	−0.452849	−	0.361135i
$297$	9.40757e9	+	4.12173e10i	1.20907	+	5.29729i
$298$	1.30798e10	+	4.57683e9i	1.65858	+	0.580363i
$299$	8.47511e8	+	1.75988e9i	0.106038	+	0.220190i
$300$	6.23201e9	−	3.91583e9i	0.769384	−	0.483436i
$301$	9.13692e8	−	3.19715e8i	0.111310	−	0.0389490i
$302$	−3.31866e9	−	3.31866e9i	−0.398965	−	0.398965i
$303$	−1.86642e9	+	3.87566e9i	−0.221431	+	0.459807i
$304$	−2.07746e8	−	1.84380e9i	−0.0243242	−	0.215883i
$305$	3.42523e9	−	3.85930e8i	0.395813	−	0.0445974i
$306$	−1.28925e10	−	6.20872e9i	−1.47046	−	0.708135i
$307$	−8.77435e9	+	8.77435e9i	−0.987783	+	0.987783i	−0.999926	−	0.0121435i	$-0.996135\pi$
$307$	−8.77435e9	+	8.77435e9i	−0.987783	+	0.987783i	0.0121435	+	0.999926i	$0.496135\pi$
$308$	−4.57333e8	−	1.30698e9i	−0.0508194	−	0.145234i
$309$	−1.49731e9	−	2.38295e9i	−0.164239	−	0.261385i
$310$	−1.21209e10	+	5.83711e9i	−1.31246	+	0.632049i
$311$	3.64861e9	−	1.04271e10i	0.390019	−	1.11461i	−0.566782	−	0.823868i	$-0.691812\pi$
$311$	3.64861e9	−	1.04271e10i	0.390019	−	1.11461i	0.956801	−	0.290743i	$-0.0939026\pi$
$312$	1.67162e9	−	3.81536e8i	0.176408	−	0.0402640i
$313$	−5.39674e9	+	6.76730e9i	−0.562282	+	0.705080i	−0.978978	−	0.203966i	$-0.934617\pi$
$313$	−5.39674e9	+	6.76730e9i	−0.562282	+	0.705080i	0.416695	+	0.909046i	$0.363188\pi$
$314$	1.65938e9	+	2.08079e9i	0.170697	+	0.214047i
$315$	3.92243e8	−	1.71853e9i	0.0398394	−	0.174548i
$316$	7.41250e9	−	1.17969e10i	0.743390	−	1.18310i
$317$	6.45544e8	−	5.72936e9i	0.0639277	−	0.567374i	−0.920394	−	0.390992i	$-0.872132\pi$
$317$	6.45544e8	−	5.72936e9i	0.0639277	−	0.567374i	0.984322	−	0.176382i	$-0.0564394\pi$
$318$		−	2.06365e10i		−	2.01803i
$319$	9.08992e9	−	1.21172e10i	0.877804	−	1.17014i
$320$	1.33919e10			1.27715
$321$	−3.44436e9	−	3.88087e8i	−0.324406	−	0.0365518i
$322$	1.68598e9	+	1.05937e9i	0.156830	+	0.0985426i
$323$	1.80302e9	+	4.11527e8i	0.165649	+	0.0378084i
$324$	−5.29007e10	+	4.21869e10i	−4.80044	+	3.82822i
$325$	4.49902e8	+	3.58785e8i	0.0403259	+	0.0321589i
$326$	−1.61986e9	−	7.09709e9i	−0.143419	−	0.628362i
$327$	−2.59818e10	−	9.09142e9i	−2.27237	−	0.795135i
$328$	−1.76891e9	−	3.67318e9i	−0.152831	−	0.317356i
$329$	4.89932e8	−	3.07845e8i	0.0418169	−	0.0262753i
$330$	4.06923e10	−	1.42389e10i	3.43128	−	1.20066i
$331$	3.09246e8	+	3.09246e8i	0.0257628	+	0.0257628i	0.719871	−	0.694108i	$-0.244201\pi$
$331$	3.09246e8	+	3.09246e8i	0.0257628	+	0.0257628i	−0.694108	+	0.719871i	$0.744201\pi$
$332$	8.62860e9	−	1.79175e10i	0.710212	−	1.47477i
$333$	3.87968e9	+	3.44331e10i	0.315514	+	2.80026i
$334$	−2.15430e10	+	2.42731e9i	−1.73109	+	0.195047i
$335$	−6.20459e9	−	2.98797e9i	−0.492644	−	0.237245i
$336$	−6.32537e8	+	6.32537e8i	−0.0496282	+	0.0496282i
$337$	2.21298e9	+	6.32432e9i	0.171576	+	0.490337i	0.997275	−	0.0737746i	$-0.0235045\pi$
$337$	2.21298e9	+	6.32432e9i	0.171576	+	0.490337i	−0.825699	+	0.564111i	$0.809219\pi$
$338$	−1.04645e10	−	1.66542e10i	−0.801774	−	1.27602i
$339$	1.42032e10	−	6.83991e9i	1.07544	−	0.517907i
$340$	−1.82794e9	+	5.22396e9i	−0.136788	+	0.390916i
$341$	2.22777e10	−	5.08475e9i	1.64761	−	0.376056i
$342$	1.76153e10	−	2.20889e10i	1.28762	−	1.61462i
$343$	1.30800e9	+	1.64018e9i	0.0944997	+	0.118499i
$344$	−2.86671e9	+	1.25599e10i	−0.204715	+	0.896915i
$345$	−1.91479e10	+	3.04737e10i	−1.35159	+	2.15104i
$346$	−2.02638e9	+	1.79846e10i	−0.141389	+	1.25487i
$347$		−	2.30212e10i		−	1.58785i	−0.608013	−	0.793927i	$-0.708033\pi$
$347$		−	2.30212e10i		−	1.58785i	0.608013	−	0.793927i	$-0.291967\pi$
$348$	3.92496e10	+	7.74442e9i	2.67620	+	0.528046i
$349$	1.04984e10			0.707656			0.353828	−	0.935310i	$-0.384880\pi$
$349$	1.04984e10			0.707656			0.353828	+	0.935310i	$0.384880\pi$
$350$	5.82912e8	+	6.56784e7i	0.0388446	+	0.00437674i
$351$	−7.39179e9	−	4.64457e9i	−0.486991	−	0.305997i
$352$	−2.88201e10	−	6.57800e9i	−1.87726	−	0.428473i
$353$	1.07009e10	−	8.53365e9i	0.689159	−	0.549586i	−0.215088	−	0.976595i	$-0.569004\pi$
$353$	1.07009e10	−	8.53365e9i	0.689159	−	0.549586i	0.904248	+	0.427008i	$0.140433\pi$
$354$	−3.19365e10	−	2.54685e10i	−2.03364	−	1.62177i
$355$	−5.01357e9	−	2.19659e10i	−0.315670	−	1.38304i
$356$	9.57546e9	+	3.35060e9i	0.596156	+	0.208604i
$357$	−3.86856e8	−	8.03314e8i	−0.0238164	−	0.0494553i
$358$	−2.30271e10	+	1.44689e10i	−1.40187	+	0.880851i
$359$	1.73813e10	−	6.08198e9i	1.04642	−	0.366157i	0.248314	−	0.968680i	$-0.420123\pi$
$359$	1.73813e10	−	6.08198e9i	1.04642	−	0.366157i	0.798102	+	0.602523i	$0.205838\pi$
$360$	1.65882e10	+	1.65882e10i	0.987621	+	0.987621i
$361$	5.78461e9	−	1.20119e10i	0.340600	−	0.707264i
$362$	−3.06471e9	−	2.72000e10i	−0.178466	−	1.58393i
$363$	−3.87596e10	+	4.36716e9i	−2.23230	+	0.251520i
$364$	2.57610e8	+	1.24058e8i	0.0146743	+	0.00706676i
$365$	1.17527e9	−	1.17527e9i	0.0662167	−	0.0662167i
$366$	−8.79702e9	−	2.51404e10i	−0.490243	−	1.40103i
$367$	8.82586e9	+	1.40463e10i	0.486511	+	0.774278i	0.996293	−	0.0860258i	$-0.0274167\pi$
$367$	8.82586e9	+	1.40463e10i	0.486511	+	0.774278i	−0.509782	+	0.860304i	$0.670274\pi$
$368$	1.22194e10	−	5.88454e9i	0.666281	−	0.320864i
$369$	−1.04935e10	+	2.99888e10i	−0.565999	+	1.61753i
$370$	2.25066e10	−	5.13699e9i	1.20089	−	0.274095i
$371$	5.95321e8	−	7.46509e8i	0.0314236	−	0.0394039i
$372$	3.76279e10	+	4.71839e10i	1.96489	+	2.46389i
$373$	1.47935e9	−	6.48145e9i	0.0764249	−	0.334839i	−0.922233	−	0.386635i	$-0.873637\pi$
$373$	1.47935e9	−	6.48145e9i	0.0764249	−	0.334839i	0.998658	+	0.0517956i	$0.0164944\pi$
$374$	8.61515e9	−	1.37109e10i	0.440328	−	0.700778i
$375$	−4.75086e9	+	4.21651e10i	−0.240241	+	2.13220i
$376$			7.70060e9i			0.385277i
$377$	4.42013e8	+	3.09647e9i	0.0218811	+	0.153286i
$378$	−8.89908e9			−0.435891
$379$	−3.42430e10	−	3.85826e9i	−1.65964	−	0.186997i	−0.768226	−	0.640178i	$-0.778861\pi$
$379$	−3.42430e10	−	3.85826e9i	−1.65964	−	0.186997i	−0.891418	+	0.453181i	$0.850289\pi$
$380$	−9.25244e9	−	5.81370e9i	−0.443733	−	0.278816i
$381$	7.02064e9	+	1.60242e9i	0.333178	+	0.0760458i
$382$	−1.16001e10	+	9.25076e9i	−0.544763	+	0.434434i
$383$	2.43605e10	+	1.94269e10i	1.13212	+	0.902834i	0.996131	−	0.0878767i	$-0.0280081\pi$
$383$	2.43605e10	+	1.94269e10i	1.13212	+	0.902834i	0.135987	+	0.990711i	$0.456580\pi$
$384$	−1.04744e10	−	4.58912e10i	−0.481729	−	2.11059i
$385$	1.88278e9	+	6.58813e8i	0.0856952	+	0.0299860i
$386$	2.59878e10	+	5.39642e10i	1.17063	+	2.43084i
$387$	8.50085e10	−	5.34144e10i	3.78982	−	2.38130i
$388$	−1.66124e10	+	5.81293e9i	−0.733002	+	0.256489i
$389$	−2.85584e10	−	2.85584e10i	−1.24720	−	1.24720i	−0.956951	−	0.290249i	$-0.906262\pi$
$389$	−2.85584e10	−	2.85584e10i	−1.24720	−	1.24720i	−0.290249	−	0.956951i	$-0.593738\pi$
$390$	−3.86250e9	+	8.02056e9i	−0.166959	+	0.346694i
$391$	1.51354e9	+	1.34330e10i	0.0647570	+	0.574734i
$392$	−1.38318e10	+	1.55847e9i	−0.585781	+	0.0660016i
$393$	−3.85474e10	−	1.85634e10i	−1.61594	−	0.778194i
$394$	−1.29509e10	+	1.29509e10i	−0.537420	+	0.537420i
$395$	6.62884e9	+	1.89441e10i	0.272301	+	0.778191i
$396$	−7.64061e10	−	1.21600e11i	−3.10704	−	4.94483i
$397$	−2.40612e10	+	1.15872e10i	−0.968623	+	0.466464i	−0.850177	−	0.526496i	$-0.823505\pi$
$397$	−2.40612e10	+	1.15872e10i	−0.968623	+	0.466464i	−0.118445	+	0.992961i	$0.537791\pi$
$398$	−2.31862e9	+	6.62622e9i	−0.0924052	+	0.264079i
$399$	1.71625e9	−	3.91724e8i	0.0677157	−	0.0154557i
$400$	2.49116e9	−	3.12381e9i	0.0973108	−	0.122024i
$401$	1.49877e10	+	1.87940e10i	0.579639	+	0.726845i	0.982051	−	0.188614i	$-0.0603995\pi$
$401$	1.49877e10	+	1.87940e10i	0.579639	+	0.726845i	−0.402412	+	0.915459i	$0.631828\pi$
$402$	−1.18413e10	+	5.18802e10i	−0.453415	+	1.98654i
$403$	−2.51037e9	+	3.99523e9i	−0.0951737	+	0.151468i
$404$	1.06889e9	−	9.48670e9i	0.0401245	−	0.356115i
$405$		−	9.74714e10i		−	3.62291i
$406$	2.06087e9	+	2.43296e9i	0.0758485	+	0.0895427i
$407$	−3.92113e10			−1.42901
$408$	1.17914e10	+	1.32858e9i	0.425526	+	0.0479453i
$409$	3.01255e10	+	1.89291e10i	1.07657	+	0.676451i	0.948967	−	0.315375i	$-0.102130\pi$
$409$	3.01255e10	+	1.89291e10i	1.07657	+	0.676451i	0.127599	+	0.991826i	$0.459273\pi$
$410$	2.06364e10	+	4.71013e9i	0.730297	+	0.166686i
$411$	−2.91574e9	+	2.32523e9i	−0.102184	+	0.0814889i
$412$	4.88320e9	+	3.89422e9i	0.169479	+	0.135155i
$413$	−4.20563e8	−	1.84261e9i	−0.0144554	−	0.0633334i
$414$	1.94925e11	+	6.82071e10i	6.63537	+	2.32182i
$415$	1.24299e10	+	2.58111e10i	0.419061	+	0.870189i
$416$	5.16852e9	−	3.24759e9i	0.172581	−	0.108440i
$417$	−4.70090e10	+	1.64491e10i	−1.55466	+	0.544000i
$418$	2.26070e10	+	2.26070e10i	0.740522	+	0.740522i
$419$	−9.72117e9	+	2.01862e10i	−0.315401	+	0.654936i	−0.997051	−	0.0767419i	$-0.975548\pi$
$419$	−9.72117e9	+	2.01862e10i	−0.315401	+	0.654936i	0.681650	+	0.731678i	$0.261263\pi$
$420$	5.89852e8	+	5.23508e9i	0.0189560	+	0.168239i
$421$	−1.86353e10	+	2.09969e9i	−0.593210	+	0.0668387i	−0.403465	−	0.914995i	$-0.632194\pi$
$421$	−1.86353e10	+	2.09969e9i	−0.593210	+	0.0668387i	−0.189744	+	0.981834i	$0.560766\pi$
$422$	2.80871e10	+	1.35261e10i	0.885641	+	0.426502i
$423$	4.24343e10	−	4.24343e10i	1.32543	−	1.32543i
$424$	4.19695e9	+	1.19942e10i	0.129859	+	0.371114i
$425$	2.11877e9	+	3.37200e9i	0.0649424	+	0.103355i
$426$	−1.56860e11	+	7.55398e10i	−4.76292	+	2.29370i
$427$	4.07026e8	−	1.16321e9i	0.0122437	−	0.0349904i
$428$	7.49962e9	−	1.71174e9i	0.223493	−	0.0510109i
$429$	9.42754e9	−	1.18218e10i	0.278336	−	0.349022i
$430$	−4.17034e10	−	5.22944e10i	−1.21983	−	1.52961i
$431$	1.28302e10	−	5.62130e10i	0.371814	−	1.62902i	−0.349868	−	0.936799i	$-0.613773\pi$
$431$	1.28302e10	−	5.62130e10i	0.371814	−	1.62902i	0.721682	−	0.692225i	$-0.243369\pi$
$432$	−3.22487e10	+	5.13235e10i	−0.925928	+	1.47361i
$433$	5.81118e9	−	5.15757e10i	0.165315	−	1.46721i	−0.587630	−	0.809130i	$-0.699939\pi$
$433$	5.81118e9	−	5.15757e10i	0.165315	−	1.46721i	0.752945	−	0.658083i	$-0.228633\pi$
$434$			4.80991e9i			0.135575i
$435$	−4.39751e10	+	3.72498e10i	−1.22815	+	1.04032i
$436$	6.10899e10			1.69053
$437$	−2.65221e10	−	2.98832e9i	−0.727247	−	0.0819410i
$438$	−1.08748e10	−	6.83310e9i	−0.295478	−	0.185661i
$439$	4.07100e9	+	9.29180e8i	0.109608	+	0.0250174i	0.276973	−	0.960878i	$-0.410669\pi$
$439$	4.07100e9	+	9.29180e8i	0.109608	+	0.0250174i	−0.167365	+	0.985895i	$0.553526\pi$
$440$	−2.07551e10	+	1.65516e10i	−0.553750	+	0.441601i
$441$	8.48086e10	+	6.76326e10i	2.24226	+	1.78814i
$442$	7.44041e8	+	3.25986e9i	0.0194943	+	0.0854101i
$443$	7.32362e9	+	2.56265e9i	0.190156	+	0.0665386i	0.423677	−	0.905813i	$-0.360739\pi$
$443$	7.32362e9	+	2.56265e9i	0.190156	+	0.0665386i	−0.233521	+	0.972352i	$0.575025\pi$
$444$	−4.49332e10	−	9.33047e10i	−1.15621	−	2.40089i
$445$	−1.23741e10	+	7.77514e9i	−0.315553	+	0.198275i
$446$	−2.98277e10	+	1.04372e10i	−0.753843	+	0.263781i
$447$	6.33219e10	+	6.33219e10i	1.58608	+	1.58608i
$448$	2.07744e9	−	4.31385e9i	0.0515723	−	0.107091i
$449$	2.41752e9	+	2.14561e10i	0.0594820	+	0.527917i	0.987754	+	0.156016i	$0.0498653\pi$
$449$	2.41752e9	+	2.14561e10i	0.0594820	+	0.527917i	−0.928272	+	0.371901i	$0.878706\pi$
$450$	6.04563e10	−	6.81179e9i	1.47432	−	0.166116i
$451$	−3.23927e10	−	1.55995e10i	−0.782961	−	0.377054i
$452$	−2.47389e10	+	2.47389e10i	−0.592689	+	0.592689i
$453$	−1.00172e10	−	2.86274e10i	−0.237877	−	0.679812i
$454$	2.43209e10	+	3.87065e10i	0.572474	+	0.911087i
$455$	−3.71100e8	+	1.78713e8i	−0.00865856	+	0.00416975i
$456$	−7.73785e9	+	2.21135e10i	−0.178962	+	0.511444i
$457$	−6.90679e9	+	1.57643e9i	−0.158348	+	0.0361418i	−0.300960	−	0.953637i	$-0.597307\pi$
$457$	−6.90679e9	+	1.57643e9i	−0.158348	+	0.0361418i	0.142612	+	0.989779i	$0.454450\pi$
$458$	1.92189e10	−	2.40997e10i	0.436784	−	0.547709i
$459$	−3.76685e10	−	4.72348e10i	−0.848648	−	1.06417i
$460$	1.77735e10	−	7.78706e10i	0.396954	−	1.73917i
$461$	3.73550e10	−	5.94502e10i	0.827076	−	1.31628i	−0.119183	−	0.992872i	$-0.538027\pi$
$461$	3.73550e10	−	5.94502e10i	0.827076	−	1.31628i	0.946258	−	0.323411i	$-0.104830\pi$
$462$	1.72579e9	−	1.53168e10i	0.0378808	−	0.336201i
$463$			1.91777e10i			0.417322i	0.977988	+	0.208661i	$0.0669106\pi$
$463$			1.91777e10i			0.417322i	−0.977988	+	0.208661i	$0.933089\pi$
$464$	2.14998e10	−	3.06904e9i	0.463833	−	0.0662110i
$465$	−8.69381e10			−1.85951
$466$	−8.80984e10	−	9.92631e9i	−1.86820	−	0.210496i
$467$	−3.30296e10	−	2.07538e10i	−0.694441	−	0.436346i	0.138020	−	0.990429i	$-0.455926\pi$
$467$	−3.30296e10	−	2.07538e10i	−0.694441	−	0.436346i	−0.832461	+	0.554083i	$0.813069\pi$
$468$	2.89110e10	+	6.59876e9i	0.602671	+	0.137556i
$469$	−1.92499e9	+	1.53513e9i	−0.0397867	+	0.0317288i
$470$	−3.12585e10	−	2.49278e10i	−0.640584	−	0.510849i
$471$	3.82712e9	+	1.67677e10i	0.0777657	+	0.340714i
$472$	2.37416e10	+	8.30754e9i	0.478345	+	0.167380i
$473$	4.92936e10	+	1.02359e11i	0.984794	+	2.04495i
$474$	1.31318e11	−	8.25125e10i	2.60142	−	1.63458i
$475$	−7.42160e9	+	2.59693e9i	−0.145788	+	0.0510136i
$476$	1.39920e9	+	1.39920e9i	0.0272553	+	0.0272553i
$477$	4.29669e10	−	8.92217e10i	0.829967	−	1.72344i
$478$	6.89768e9	+	6.12186e10i	0.132127	+	1.17266i
$479$	−7.90602e10	+	8.90794e9i	−1.50181	+	0.169214i	−0.824239	−	0.566241i	$-0.808397\pi$
$479$	−7.90602e10	+	8.90794e9i	−1.50181	+	0.169214i	−0.677573	+	0.735455i	$0.736968\pi$
$480$	1.01331e11	+	4.87986e10i	1.90888	+	0.919269i
$481$	5.72529e9	−	5.72529e9i	0.106959	−	0.106959i
$482$	−2.80757e10	−	8.02358e10i	−0.520167	−	1.48655i
$483$	6.84594e9	+	1.08953e10i	0.125790	+	0.200193i
$484$	7.79915e10	−	3.75587e10i	1.42123	−	0.684431i
$485$	8.37383e9	−	2.39310e10i	0.151341	−	0.432508i
$486$	−4.22366e11	+	9.64022e10i	−7.57083	+	1.72799i
$487$	−4.86127e9	+	6.09584e9i	−0.0864239	+	0.108372i	−0.823163	−	0.567805i	$-0.807793\pi$
$487$	−4.86127e9	+	6.09584e9i	−0.0864239	+	0.108372i	0.736740	+	0.676177i	$0.236364\pi$
$488$	1.02259e10	+	1.28229e10i	0.180311	+	0.226103i
$489$	1.04680e10	−	4.58633e10i	0.183075	−	0.802103i
$490$	3.84491e10	−	6.11914e10i	0.666964	−	1.06147i
$491$	−8.14863e9	+	7.23211e10i	−0.140203	+	1.24434i	0.704733	+	0.709473i	$0.251067\pi$
$491$	−8.14863e9	+	7.23211e10i	−0.140203	+	1.24434i	−0.844936	+	0.534867i	$0.820362\pi$
$492$		−	9.49552e10i		−	1.62053i
$493$	−4.19034e9	+	2.12371e10i	−0.0709352	+	0.359507i
$494$	−6.60175e9			−0.110854
$495$	2.05580e11	+	2.31633e10i	3.42420	+	0.385815i
$496$	2.77401e10	+	1.74303e10i	0.458334	+	0.287990i
$497$	−7.85347e9	−	1.79250e9i	−0.128717	−	0.0293788i
$498$	1.73075e11	−	1.38023e11i	2.81396	−	2.24406i
$499$	8.79487e10	+	7.01368e10i	1.41849	+	1.13121i	0.971602	+	0.236623i	$0.0760407\pi$
$499$	8.79487e10	+	7.01368e10i	1.41849	+	1.13121i	0.446892	+	0.894588i	$0.352531\pi$
$500$	−2.09547e10	−	9.18086e10i	−0.335275	−	1.46894i
$501$	−1.32236e11	−	4.62714e10i	−2.09893	−	0.734449i
$502$	−7.85276e10	−	1.63064e11i	−1.23654	−	2.56770i
$503$	−7.33428e10	+	4.60843e10i	−1.14574	+	0.719915i	−0.964645	−	0.263551i	$-0.915106\pi$
$503$	−7.33428e10	+	4.60843e10i	−1.14574	+	0.719915i	−0.181093	+	0.983466i	$0.557963\pi$
$504$	7.91674e9	−	2.77019e9i	0.122694	−	0.0429326i
$505$	9.72453e9	+	9.72453e9i	0.149521	+	0.149521i
$506$	−1.01395e11	+	2.10550e11i	−1.54674	+	3.21183i
$507$	−1.42314e10	−	1.26307e11i	−0.215385	−	1.91159i
$508$	−1.58812e10	+	1.78938e9i	−0.238467	+	0.0268688i
$509$	4.78512e10	+	2.30439e10i	0.712889	+	0.343309i	0.754929	−	0.655807i	$-0.227671\pi$
$509$	4.78512e10	+	2.30439e10i	0.712889	+	0.343309i	−0.0420398	+	0.999116i	$0.513386\pi$
$510$	−4.35634e10	+	4.35634e10i	−0.643933	+	0.643933i
$511$	−1.96267e8	−	5.60900e8i	−0.00287849	−	0.00822624i
$512$	−3.27057e10	−	5.20508e10i	−0.475931	−	0.757439i
$513$	1.07471e11	−	5.17554e10i	1.55175	−	0.747285i
$514$	−4.06080e9	+	1.16051e10i	−0.0581781	+	0.166263i
$515$	−8.77188e9	+	2.00212e9i	−0.124699	+	0.0284618i
$516$	−1.87080e11	+	2.34591e11i	−2.63894	+	3.30912i
$517$	4.23407e10	+	5.30936e10i	0.592647	+	0.743156i
$518$	1.83663e9	−	8.04679e9i	0.0255095	−	0.111764i
$519$	−6.22249e10	+	9.90304e10i	−0.857620	+	1.36489i
$520$	6.13752e8	−	5.44720e9i	0.00839420	−	0.0745006i
$521$			3.08985e9i			0.0419359i	0.999780	+	0.0209680i	$0.00667480\pi$
$521$			3.08985e9i			0.0419359i	−0.999780	+	0.0209680i	$0.993325\pi$
$522$	2.64532e11	+	1.98444e11i	3.56284	+	2.67273i
$523$	1.09043e11			1.45744			0.728719	−	0.684812i	$-0.240116\pi$
$523$	1.09043e11			1.45744			0.728719	+	0.684812i	$0.240116\pi$
$524$	9.43548e10	+	1.06312e10i	1.25152	+	0.141013i
$525$	3.20974e9	+	2.01681e9i	0.0422506	+	0.0265478i
$526$	5.05500e10	+	1.15377e10i	0.660356	+	0.150722i
$527$	−2.55302e10	+	2.03597e10i	−0.330988	+	0.263954i
$528$	−8.20822e10	−	6.54584e10i	−1.05612	−	0.842228i
$529$	−2.59856e10	−	1.13850e11i	−0.331826	−	1.45382i
$530$	−6.22732e10	−	2.17903e10i	−0.789219	−	0.276160i
$531$	−8.50496e10	−	1.76607e11i	−1.06978	−	2.22142i
$532$	−3.30803e9	+	2.07857e9i	−0.0412974	+	0.0259489i
$533$	7.00738e9	−	2.45199e9i	0.0868255	−	0.0303815i
$534$	7.98512e10	+	7.98512e10i	0.982011	+	0.982011i
$535$	−4.80805e9	+	9.98403e9i	−0.0586887	+	0.121868i
$536$	−3.66882e9	−	3.25617e10i	−0.0444496	−	0.394501i
$537$	−1.74640e11	+	1.96772e10i	−2.10013	+	0.236628i
$538$	−6.56197e10	−	3.16008e10i	−0.783259	−	0.377198i
$539$	−8.67977e10	+	8.67977e10i	−1.02838	+	1.02838i
$540$	1.17901e11	+	3.36942e11i	1.38657	+	3.96260i
$541$	−2.12669e10	−	3.38461e10i	−0.248265	−	0.395111i	0.699223	−	0.714904i	$-0.253530\pi$
$541$	−2.12669e10	−	3.38461e10i	−0.248265	−	0.395111i	−0.947488	+	0.319793i	$0.896387\pi$
$542$	5.73728e10	−	2.76293e10i	0.664828	−	0.320164i
$543$	5.84218e10	−	1.66960e11i	0.672010	−	1.92049i
$544$	4.11849e10	−	9.40018e9i	0.470265	−	0.107335i
$545$	−5.48691e10	+	6.88037e10i	−0.621930	+	0.779876i
$546$	1.98444e9	+	2.48840e9i	0.0223289	+	0.0279995i
$547$	−1.23842e10	+	5.42589e10i	−0.138331	+	0.606068i	0.857471	+	0.514533i	$0.172035\pi$
$547$	−1.23842e10	+	5.42589e10i	−0.138331	+	0.606068i	−0.995802	+	0.0915355i	$0.970823\pi$
$548$	4.40345e9	−	7.00804e9i	0.0488282	−	0.0777096i
$549$	1.43107e10	−	1.27011e11i	0.157533	−	1.39814i
$550$			6.88458e10i			0.752362i
$551$	−3.90381e10	−	1.73963e10i	−0.423528	−	0.188734i
$552$	−1.71248e11			−1.84446
$553$	7.13066e9	+	8.03432e8i	0.0762481	+	0.00859110i
$554$	1.75348e11	+	1.10179e11i	1.86150	+	1.16966i
$555$	1.45444e11	+	3.31966e10i	1.53293	+	0.349882i
$556$	8.64160e10	−	6.89144e10i	0.904263	−	0.721126i
$557$	−6.07910e9	−	4.84792e9i	−0.0631566	−	0.0503657i	0.591403	−	0.806376i	$-0.298574\pi$
$557$	−6.07910e9	−	4.84792e9i	−0.0631566	−	0.0503657i	−0.654559	+	0.756011i	$0.727146\pi$
$558$	1.11006e11	+	4.86349e11i	1.14501	+	5.01662i
$559$	−2.21430e10	−	7.74816e9i	−0.226772	−	0.0793508i
$560$	1.24086e9	+	2.57667e9i	0.0126174	+	0.0262003i
$561$	8.86039e10	−	5.56735e10i	0.894543	−	0.562079i
$562$	1.75961e10	−	6.15714e9i	0.176389	−	0.0617211i
$563$	−1.18579e11	−	1.18579e11i	−1.18025	−	1.18025i	−0.979679	−	0.200572i	$-0.935720\pi$
$563$	−1.18579e11	−	1.18579e11i	−1.18025	−	1.18025i	−0.200572	−	0.979679i	$-0.564280\pi$
$564$	−7.78187e10	+	1.61592e11i	−0.769073	+	1.59700i
$565$	−5.64293e9	−	5.00824e10i	−0.0553747	−	0.491464i
$566$	9.97264e10	−	1.12365e10i	0.971728	−	0.109487i
$567$	−3.13978e10	−	1.51204e10i	−0.303786	−	0.146296i
$568$	7.58062e10	−	7.58062e10i	0.728302	−	0.728302i
$569$	2.89745e10	+	8.28042e10i	0.276418	+	0.789957i	0.995477	+	0.0950077i	$0.0302876\pi$
$569$	2.89745e10	+	8.28042e10i	0.276418	+	0.789957i	−0.719059	+	0.694949i	$0.755427\pi$
$570$	−6.47154e10	−	1.02994e11i	−0.613067	−	0.975690i
$571$	7.84173e10	−	3.77638e10i	0.737679	−	0.355247i	−0.0270203	−	0.999635i	$-0.508602\pi$
$571$	7.84173e10	−	3.77638e10i	0.737679	−	0.355247i	0.764699	+	0.644388i	$0.222888\pi$
$572$	−1.10833e10	+	3.16742e10i	−0.103534	+	0.295884i
$573$	−9.34773e10	+	2.13356e10i	−0.867137	+	0.197918i
$574$	4.71851e9	−	5.91682e9i	0.0434667	−	0.0545056i
$575$	−3.58340e10	−	4.49344e10i	−0.327811	−	0.411062i
$576$	1.10501e11	−	4.84135e11i	1.00386	−	4.39822i
$577$	7.74206e10	−	1.23214e11i	0.698479	−	1.11162i	−0.289522	−	0.957171i	$-0.593496\pi$
$577$	7.74206e10	−	1.23214e11i	0.698479	−	1.11162i	0.988000	−	0.154451i	$-0.0493609\pi$
$578$	1.67041e10	−	1.48253e11i	0.149662	−	1.32829i
$579$			3.87063e11i			3.44404i
$580$	6.48140e10	−	1.10263e11i	0.572739	−	0.974359i
$581$	1.02426e10			0.0898885
$582$	−1.94684e11	−	2.19356e10i	−1.69683	−	0.191187i
$583$	9.48854e10	+	5.96204e10i	0.821344	+	0.516085i
$584$	7.71028e9	+	1.75982e9i	0.0662855	+	0.0151292i
$585$	−3.33990e10	+	2.66348e10i	−0.285174	+	0.227419i
$586$	−4.45176e10	−	3.55016e10i	−0.377521	−	0.301063i
$587$	2.59117e10	+	1.13527e11i	0.218245	+	0.956192i	0.958774	+	0.284169i	$0.0917176\pi$
$587$	2.59117e10	+	1.13527e11i	0.218245	+	0.956192i	−0.740530	+	0.672024i	$0.765425\pi$
$588$	−3.06001e11	−	1.07075e11i	−2.55985	−	0.895729i
$589$	−2.79735e10	−	5.80877e10i	−0.232427	−	0.482639i
$590$	−1.10577e11	+	6.94799e10i	−0.912547	+	0.573391i
$591$	−1.11717e11	+	3.90913e10i	−0.915731	+	0.320428i
$592$	−3.97525e10	−	3.97525e10i	−0.323652	−	0.323652i
$593$	2.42681e10	−	5.03931e10i	0.196253	−	0.407523i	−0.779499	−	0.626404i	$-0.784526\pi$
$593$	2.42681e10	−	5.03931e10i	0.196253	−	0.407523i	0.975752	+	0.218880i	$0.0702404\pi$
$594$	−1.16939e11	−	1.03787e12i	−0.939323	−	8.33672i
$595$	−2.83259e9	+	3.19156e8i	−0.0226004	+	0.00254645i
$596$	−1.79060e11	−	8.62305e10i	−1.41910	−	0.683402i
$597$	−3.20788e10	+	3.20788e10i	−0.252535	+	0.252535i
$598$	−1.59377e10	−	4.55474e10i	−0.124630	−	0.356172i
$599$	−3.53937e10	−	5.63288e10i	−0.274928	−	0.437545i	0.680509	−	0.732739i	$-0.261759\pi$
$599$	−3.53937e10	−	5.63288e10i	−0.274928	−	0.437545i	−0.955437	+	0.295194i	$0.904616\pi$
$600$	−4.54536e10	+	2.18893e10i	−0.350722	+	0.168899i
$601$	−4.56700e10	+	1.30517e11i	−0.350052	+	1.00039i	0.625424	+	0.780285i	$0.284926\pi$
$601$	−4.56700e10	+	1.30517e11i	−0.350052	+	1.00039i	−0.975476	+	0.220106i	$0.929360\pi$
$602$	−2.33146e10	+	5.32140e9i	−0.177518	+	0.0405173i
$603$	−1.59215e11	+	1.99649e11i	−1.20424	+	1.51007i
$604$	4.19673e10	+	5.26254e10i	0.315329	+	0.395410i
$605$	−2.77484e10	+	1.21574e11i	−0.207117	+	0.907439i
$606$	5.65389e10	−	8.99812e10i	0.419235	−	0.667208i
$607$	1.94811e10	−	1.72900e11i	0.143503	−	1.27362i	−0.691096	−	0.722763i	$-0.742872\pi$
$607$	1.94811e10	−	1.72900e11i	0.143503	−	1.27362i	0.834599	−	0.550858i	$-0.185699\pi$
$608$			8.34062e10i			0.610357i
$609$	5.17734e9	+	1.99439e10i	0.0376389	+	0.144991i
$610$	−8.51535e10			−0.615011
$611$	−1.39345e10	−	1.57004e9i	−0.0999828	−	0.0112654i
$612$	1.73770e11	+	1.09187e11i	1.23871	+	0.778332i
$613$	9.85765e9	+	2.24995e9i	0.0698123	+	0.0159342i	0.257284	−	0.966336i	$-0.417172\pi$
$613$	9.85765e9	+	2.24995e9i	0.0698123	+	0.0159342i	−0.187472	+	0.982270i	$0.560029\pi$
$614$	2.39672e11	−	1.91132e11i	1.68633	−	1.34481i
$615$	1.06945e11	+	8.52859e10i	0.747585	+	0.596179i
$616$	2.11201e9	+	9.25331e9i	0.0146681	+	0.0642649i
$617$	1.67403e11	+	5.85769e10i	1.15511	+	0.404190i	0.838786	−	0.544461i	$-0.183266\pi$
$617$	1.67403e11	+	5.85769e10i	1.15511	+	0.404190i	0.316323	+	0.948652i	$0.397552\pi$
$618$	3.01661e10	+	6.26406e10i	0.206807	+	0.429440i
$619$	1.14420e11	−	7.18948e10i	0.779361	−	0.489705i	−0.0826597	−	0.996578i	$-0.526341\pi$
$619$	1.14420e11	−	7.18948e10i	0.779361	−	0.489705i	0.862021	+	0.506873i	$0.169199\pi$
$620$	1.82115e11	−	6.37249e10i	1.23248	−	0.431263i
$621$	6.16530e11	+	6.16530e11i	4.14560	+	4.14560i
$622$	−1.18411e11	+	2.45884e11i	−0.791101	+	1.64274i
$623$	5.85011e8	+	5.19211e9i	0.00388339	+	0.0344661i
$624$	2.15426e10	−	2.42726e9i	0.142089	−	0.0160095i
$625$	7.64270e10	+	3.68053e10i	0.500872	+	0.241207i
$626$	1.51203e11	−	1.51203e11i	0.984609	−	0.984609i
$627$	6.82378e10	+	1.95012e11i	0.441524	+	1.26180i
$628$	−2.03075e10	−	3.23193e10i	−0.130563	−	0.207789i
$629$	5.04852e10	−	2.43124e10i	0.322523	−	0.155319i
$630$	−1.43827e10	+	4.11033e10i	−0.0913013	+	0.260924i
$631$	−8.87654e9	+	2.02601e9i	−0.0559920	+	0.0127798i	−0.250425	−	0.968136i	$-0.580570\pi$
$631$	−8.87654e9	+	2.02601e9i	−0.0559920	+	0.0127798i	0.194433	+	0.980916i	$0.437713\pi$
$632$	−5.95428e10	+	7.46643e10i	−0.373216	+	0.467999i
$633$	1.25607e11	+	1.57506e11i	0.782344	+	0.981029i
$634$	−3.16950e10	+	1.38865e11i	−0.196170	+	0.859478i
$635$	1.22487e10	−	1.94937e10i	0.0753347	−	0.119894i
$636$	−3.31375e10	+	2.94103e11i	−0.202531	+	1.79751i
$637$		−	2.53468e10i		−	0.153945i
$638$	−2.56665e11	+	2.72322e11i	−1.54912	+	1.64362i
$639$	−8.35464e11			−5.01100
$640$	−1.49543e11	−	1.68494e10i	−0.891344	−	0.100430i
$641$	−2.23293e11	−	1.40304e11i	−1.32264	−	0.831072i	−0.329075	−	0.944304i	$-0.606737\pi$
$641$	−2.23293e11	−	1.40304e11i	−1.32264	−	0.831072i	−0.993569	+	0.113232i	$0.963880\pi$
$642$	8.34823e10	+	1.90543e10i	0.491422	+	0.112164i
$643$	1.91901e10	−	1.53036e10i	0.112262	−	0.0895260i	−0.565750	−	0.824577i	$-0.691413\pi$
$643$	1.91901e10	−	1.53036e10i	0.112262	−	0.0895260i	0.678012	+	0.735051i	$0.262842\pi$
$644$	−2.23268e10	−	1.78050e10i	−0.129803	−	0.103514i
$645$	−9.61831e10	−	4.21406e11i	−0.555725	−	2.43479i
$646$	−4.31240e10	−	1.50897e10i	−0.247622	−	0.0866466i
$647$	−5.09636e10	−	1.05827e11i	−0.290833	−	0.603920i	0.703445	−	0.710750i	$-0.251644\pi$
$647$	−5.09636e10	−	1.05827e11i	−0.290833	−	0.603920i	−0.994277	+	0.106830i	$0.965930\pi$
$648$	3.92702e11	−	2.46751e11i	2.22722	−	1.39945i
$649$	2.09370e11	−	7.32616e10i	1.18014	−	0.412950i
$650$	−1.00522e10	−	1.00522e10i	−0.0563132	−	0.0563132i
$651$	−1.34864e10	+	2.80048e10i	−0.0750883	+	0.155922i
$652$	1.16894e10	+	1.03746e11i	0.0646847	+	0.574092i
$653$	−1.37372e11	+	1.54781e10i	−0.755520	+	0.0851267i	−0.481319	−	0.876546i	$-0.659842\pi$
$653$	−1.37372e11	+	1.54781e10i	−0.755520	+	0.0851267i	−0.274201	+	0.961672i	$0.588413\pi$
$654$	6.12681e11	+	2.95051e11i	3.34906	+	1.61282i
$655$	−9.67203e10	+	9.67203e10i	−0.525475	+	0.525475i
$656$	−1.70249e10	−	4.86545e10i	−0.0919327	−	0.262729i
$657$	−3.27901e10	−	5.21852e10i	−0.175988	−	0.280083i
$658$	−1.28788e10	+	6.20213e9i	−0.0687026	+	0.0330854i
$659$	4.88177e10	−	1.39513e11i	0.258842	−	0.739729i	−0.738977	−	0.673730i	$-0.764691\pi$
$659$	4.88177e10	−	1.39513e11i	0.258842	−	0.739729i	0.997820	−	0.0659989i	$-0.0210234\pi$
$660$	−6.02796e11	+	1.37584e11i	−3.17684	+	0.725092i
$661$	1.70617e10	−	2.13947e10i	0.0893752	−	0.112073i	−0.735133	−	0.677923i	$-0.762880\pi$
$661$	1.70617e10	−	2.13947e10i	0.0893752	−	0.112073i	0.824508	+	0.565850i	$0.191452\pi$
$662$	−6.73632e9	−	8.44708e9i	−0.0350744	−	0.0439820i
$663$	−4.80820e9	+	2.10661e10i	−0.0248845	+	0.109026i
$664$	−7.25233e10	+	1.15420e11i	−0.373083	+	0.593758i
$665$	6.30139e8	−	5.59264e9i	0.00322218	−	0.0285977i
$666$		−	8.56030e11i		−	4.35103i
$667$	2.57779e10	−	3.11333e11i	0.130240	−	1.57297i
$668$	3.10921e11			1.56151
$669$	−2.02931e11	−	2.28648e10i	−1.01308	−	0.114147i
$670$	1.44052e11	+	9.05137e10i	0.714857	+	0.449175i
$671$	1.41010e11	+	3.21846e10i	0.695599	+	0.158766i
$672$	3.14384e10	−	2.50713e10i	0.154164	−	0.122942i
$673$	−6.88929e10	−	5.49402e10i	−0.335826	−	0.267812i	0.441028	−	0.897493i	$-0.354614\pi$
$673$	−6.88929e10	−	5.49402e10i	−0.335826	−	0.267812i	−0.776853	+	0.629681i	$0.783185\pi$
$674$	−3.68333e10	−	1.61377e11i	−0.178485	−	0.781992i
$675$	2.42449e11	+	8.48365e10i	1.16790	+	0.408665i
$676$	1.22394e11	+	2.54153e11i	0.586100	+	1.21705i
$677$	−1.08075e10	+	6.79080e9i	−0.0514482	+	0.0323270i	−0.557511	−	0.830170i	$-0.688243\pi$
$677$	−1.08075e10	+	6.79080e9i	−0.0514482	+	0.0323270i	0.506062	+	0.862497i	$0.331101\pi$
$678$	−3.67595e11	+	1.28627e11i	−1.73960	+	0.608714i
$679$	−6.40975e9	−	6.40975e9i	−0.0301552	−	0.0301552i
$680$	1.64599e10	−	3.41793e10i	0.0769824	−	0.159856i
$681$	3.30756e10	+	2.93554e11i	0.153787	+	1.36489i
$682$	−5.60961e11	+	6.32052e10i	−2.59296	+	0.292156i
$683$	2.39025e11	+	1.15109e11i	1.09840	+	0.528962i	0.893155	−	0.449748i	$-0.148486\pi$
$683$	2.39025e11	+	1.15109e11i	1.09840	+	0.528962i	0.205246	+	0.978710i	$0.434201\pi$
$684$	−2.86517e11	+	2.86517e11i	−1.30896	+	1.30896i
$685$	3.93790e9	+	1.12539e10i	0.0178856	+	0.0511140i
$686$	−2.75733e10	−	4.38827e10i	−0.124507	−	0.198151i
$687$	1.79471e11	−	8.64287e10i	0.805689	−	0.387999i
$688$	−5.37979e10	+	1.53746e11i	−0.240111	+	0.686197i
$689$	−2.25596e10	+	5.14907e9i	−0.100105	+	0.0228482i
$690$	5.54352e11	−	6.95135e11i	2.44562	−	3.06671i
$691$	−4.22338e10	−	5.29596e10i	−0.185246	−	0.232291i	0.680533	−	0.732717i	$-0.261748\pi$
$691$	−4.22338e10	−	5.29596e10i	−0.185246	−	0.232291i	−0.865779	+	0.500426i	$0.833177\pi$
$692$	5.77585e10	−	2.53056e11i	0.251879	−	1.10355i
$693$	3.93523e10	−	6.26288e10i	0.170623	−	0.271545i
$694$	−6.36769e10	+	5.65148e11i	−0.274501	+	2.43627i
$695$			1.59225e11i			0.682450i
$696$	−2.61399e11	−	8.28723e10i	−1.11395	−	0.353161i
$697$	5.13782e10			0.217695
$698$	−2.57726e11	−	2.90388e10i	−1.08577	−	0.122337i
$699$	−4.85104e11	−	3.04811e11i	−2.03201	−	1.27680i
$700$	−8.20198e9	−	1.87205e9i	−0.0341607	−	0.00779696i
$701$	9.03834e10	−	7.20784e10i	0.374297	−	0.298492i	−0.418215	−	0.908348i	$-0.637344\pi$
$701$	9.03834e10	−	7.20784e10i	0.374297	−	0.298492i	0.792512	+	0.609856i	$0.208773\pi$
$702$	1.68614e11	+	1.34465e11i	0.694298	+	0.553684i
$703$	2.46183e10	+	1.07860e11i	0.100794	+	0.441610i
$704$	5.30406e11	+	1.85597e11i	2.15933	+	0.755581i
$705$	−1.12102e11	−	2.32782e11i	−0.453792	−	0.942309i
$706$	−2.86300e11	+	1.79894e11i	−1.15240	+	0.724099i
$707$	4.64104e9	−	1.62397e9i	0.0185754	−	0.00649980i
$708$	4.14250e11	+	4.14250e11i	1.64865	+	1.64865i
$709$	1.36121e10	−	2.82659e10i	0.0538693	−	0.111861i	−0.872297	−	0.488977i	$-0.837370\pi$
$709$	1.36121e10	−	2.82659e10i	0.0538693	−	0.111861i	0.926166	+	0.377117i	$0.123084\pi$
$710$	6.23204e10	+	5.53109e11i	0.245243	+	2.17659i
$711$	7.39551e11	−	8.33274e10i	2.89394	−	0.326069i
$712$	−6.26504e10	−	3.01708e10i	−0.243783	−	0.117400i
$713$	3.33231e11	−	3.33231e11i	1.28940	−	1.28940i
$714$	7.27495e9	+	2.07906e10i	0.0279922	+	0.0799972i
$715$	−2.57190e10	−	4.09316e10i	−0.0984080	−	0.156615i
$716$	3.51407e11	−	1.69229e11i	1.33708	−	0.643905i
$717$	−1.31489e11	+	3.75774e11i	−0.497523	+	1.42184i
$718$	−4.43517e11	+	1.01230e11i	−1.66883	+	0.380900i
$719$	−2.99484e11	+	3.75541e11i	−1.12062	+	1.40521i	−0.217372	+	0.976089i	$0.569749\pi$
$719$	−2.99484e11	+	3.75541e11i	−1.12062	+	1.40521i	−0.903246	+	0.429122i	$0.858823\pi$
$720$	1.84934e11	+	2.31900e11i	0.688155	+	0.862920i
$721$	−7.15820e8	+	3.13621e9i	−0.00264888	+	0.0116055i
$722$	−1.75231e11	+	2.78879e11i	−0.644856	+	1.02628i
$723$	6.15058e10	−	5.45879e11i	0.225093	−	1.99776i
$724$			3.92566e11i			1.42876i
$725$	−3.29531e10	−	8.59306e10i	−0.119274	−	0.311025i
$726$	9.63591e11			3.46854
$727$	−2.03270e11	−	2.29031e10i	−0.727674	−	0.0819891i	−0.259647	−	0.965704i	$-0.583606\pi$
$727$	−2.03270e11	−	2.29031e10i	−0.727674	−	0.0819891i	−0.468027	+	0.883714i	$0.655035\pi$
$728$	−1.65946e9	−	1.04271e9i	−0.00590802	−	0.00371225i
$729$	−1.50789e12	−	3.44166e11i	−5.33899	−	1.21859i
$730$	−3.21026e10	+	2.56010e10i	−0.113044	+	0.0901500i
$731$	−1.26932e11	−	1.01225e11i	−0.444532	−	0.354502i
$732$	8.50021e10	+	3.72418e11i	0.296064	+	1.29714i
$733$	4.65999e11	+	1.63060e11i	1.61424	+	0.564849i	0.978355	−	0.206932i	$-0.0663478\pi$
$733$	4.65999e11	+	1.63060e11i	1.61424	+	0.564849i	0.635889	+	0.771780i	$0.280634\pi$
$734$	−1.77814e11	−	3.69235e11i	−0.612607	−	1.27209i
$735$	3.95436e11	−	2.48469e11i	1.35496	−	0.851379i
$736$	−5.75444e11	+	2.01357e11i	−1.96107	+	0.686207i
$737$	−2.04332e11	−	2.04332e11i	−0.692574	−	0.692574i
$738$	3.40555e11	−	7.07170e11i	1.14805	−	2.38396i
$739$	2.83291e10	+	2.51428e11i	0.0949849	+	0.843015i	0.947379	+	0.320115i	$0.103721\pi$
$739$	2.83291e10	+	2.51428e11i	0.0949849	+	0.843015i	−0.852394	+	0.522900i	$0.824850\pi$
$740$	−3.29005e11	+	3.70699e10i	−1.09717	+	0.123622i
$741$	−3.84374e10	−	1.85105e10i	−0.127492	−	0.0613967i
$742$	−1.66794e10	+	1.66794e10i	−0.0550256	+	0.0550256i
$743$	5.61985e9	+	1.60606e10i	0.0184404	+	0.0526996i	0.952736	−	0.303801i	$-0.0982556\pi$
$743$	5.61985e9	+	1.60606e10i	0.0184404	+	0.0526996i	−0.934295	+	0.356500i	$0.883970\pi$
$744$	−2.20085e11	−	3.50264e11i	−0.718289	−	1.14315i
$745$	2.57945e11	−	1.24220e11i	0.837339	−	0.403241i
$746$	−5.42443e10	+	1.55021e11i	−0.175145	+	0.500537i
$747$	1.03567e12	−	2.36384e11i	3.32612	−	0.759164i
$748$	−1.44797e11	+	1.81569e11i	−0.462543	+	0.580011i
$749$	2.47023e9	+	3.09758e9i	0.00784894	+	0.00984226i
$750$	2.33258e11	−	1.02197e12i	0.737211	−	3.22993i
$751$	−4.81371e10	+	7.66097e10i	−0.151328	+	0.240837i	−0.913782	−	0.406205i	$-0.866852\pi$
$751$	−4.81371e10	+	7.66097e10i	−0.151328	+	0.240837i	0.762454	+	0.647043i	$0.223995\pi$
$752$	−1.09013e10	+	9.67514e10i	−0.0340883	+	0.302542i
$753$		−	1.16959e12i		−	3.63793i
$754$	−2.28612e9	−	7.72380e10i	−0.00707315	−	0.238971i
$755$	−9.69641e10			−0.298417
$756$	1.26826e11	+	1.42899e10i	0.388260	+	0.0437464i
$757$	−2.24719e11	−	1.41201e11i	−0.684317	−	0.429985i	0.144500	−	0.989505i	$-0.453843\pi$
$757$	−2.24719e11	−	1.41201e11i	−0.684317	−	0.429985i	−0.828817	+	0.559520i	$0.810985\pi$
$758$	8.29961e11	+	1.89433e11i	2.51409	+	0.573824i
$759$	−1.18071e12	+	9.41586e11i	−3.55776	+	2.83722i
$760$	5.85599e10	+	4.67000e10i	0.175528	+	0.139979i
$761$	−4.90906e10	−	2.15080e11i	−0.146373	−	0.641301i	−0.993875	−	0.110509i	$-0.964752\pi$
$761$	−4.90906e10	−	2.15080e11i	−0.146373	−	0.641301i	0.847502	−	0.530792i	$-0.178105\pi$
$762$	−1.67918e11	−	5.87569e10i	−0.498054	−	0.174277i
$763$	1.36516e10	+	2.83479e10i	0.0402797	+	0.0836417i
$764$	1.80175e11	−	1.13211e11i	0.528835	−	0.332289i
$765$	−2.79049e11	+	9.76434e10i	−0.814769	+	0.285100i
$766$	−5.44292e11	−	5.44292e11i	−1.58095	−	1.58095i
$767$	−1.98733e10	+	4.12673e10i	−0.0574233	+	0.119241i
$768$	1.01353e10	+	8.99533e10i	0.0291334	+	0.258567i
$769$	4.85572e11	−	5.47108e10i	1.38851	−	0.156447i	0.614147	−	0.789192i	$-0.289500\pi$
$769$	4.85572e11	−	5.47108e10i	1.38851	−	0.156447i	0.774361	+	0.632745i	$0.218072\pi$
$770$	−4.43981e10	−	2.13810e10i	−0.126299	−	0.0608226i
$771$	−5.61825e10	+	5.61825e10i	−0.158995	+	0.158995i
$772$	−2.83714e11	−	8.10809e11i	−0.798752	−	2.28270i
$773$	−2.33155e11	−	3.71063e11i	−0.653019	−	1.03927i	−0.995030	−	0.0995779i	$-0.968251\pi$
$773$	−2.33155e11	−	3.71063e11i	−0.653019	−	1.03927i	0.342011	−	0.939696i	$-0.388892\pi$
$774$	−2.23462e12	+	1.07614e12i	−6.22644	+	2.99850i
$775$	4.58537e10	−	1.31042e11i	0.127106	−	0.363249i
$776$	1.17614e11	−	2.68446e10i	0.324349	−	0.0740305i
$777$	3.32556e10	−	4.17012e10i	0.0912391	−	0.114410i
$778$	6.22089e11	+	7.80075e11i	1.69799	+	2.12921i
$779$	−2.25727e10	+	9.88974e10i	−0.0612962	+	0.268556i
$780$	6.79261e10	−	1.08104e11i	0.183509	−	0.292054i
$781$	1.05853e11	−	9.39474e11i	0.284512	−	2.52511i
$782$		−	3.33954e11i		−	0.893018i
$783$	6.42735e11	+	1.23945e12i	1.70995	+	3.29748i
$784$	−1.75991e11			−0.465829
$785$	5.46398e10	+	6.15643e9i	0.143890	+	0.0162125i
$786$	8.94953e11	+	5.62336e11i	2.34482	+	1.47335i
$787$	4.86360e11	+	1.11009e11i	1.26782	+	0.289373i	0.802973	−	0.596016i	$-0.203251\pi$
$787$	4.86360e11	+	1.11009e11i	1.26782	+	0.289373i	0.464852	+	0.885389i	$0.346108\pi$
$788$	2.05367e11	−	1.63775e11i	0.532631	−	0.424759i
$789$	2.61968e11	+	2.08912e11i	0.675989	+	0.539083i
$790$	−1.10332e11	−	4.83395e11i	−0.283265	−	1.24106i
$791$	−1.70081e10	−	5.95139e9i	−0.0434460	−	0.0152024i
$792$	4.27107e11	+	8.86896e11i	1.08551	+	2.25409i
$793$	−2.52883e10	+	1.58897e10i	−0.0639480	+	0.0401812i
$794$	6.22729e11	−	2.17902e11i	1.56681	−	0.548251i
$795$	−3.01476e11	−	3.01476e11i	−0.754718	−	0.754718i
$796$	4.36843e10	−	9.07113e10i	0.108811	−	0.225948i
$797$	7.76294e10	+	6.88980e11i	0.192395	+	1.70755i	0.604658	+	0.796486i	$0.293310\pi$
$797$	7.76294e10	+	6.88980e11i	0.192395	+	1.70755i	−0.412263	+	0.911065i	$0.635261\pi$
$798$	−4.32158e10	+	4.86926e9i	−0.106569	+	0.0120075i
$799$	−8.74341e10	−	4.21060e10i	−0.214533	−	0.103314i
$800$	−1.27000e11	+	1.27000e11i	−0.310058	+	0.310058i
$801$	1.78979e11	+	5.11494e11i	0.434783	+	1.24254i
$802$	−3.15949e11	−	5.02830e11i	−0.763695	−	1.21541i
$803$	6.28365e10	−	3.02604e10i	0.151130	−	0.0727802i
$804$	2.52066e11	−	7.20363e11i	0.603240	−	1.72396i
$805$	4.01066e10	−	9.15406e9i	0.0955063	−	0.0217987i
$806$	7.26779e10	−	9.11352e10i	0.172212	−	0.215946i
$807$	−2.93454e11	−	3.67979e11i	−0.691903	−	0.867619i
$808$	−1.45612e10	+	6.37969e10i	−0.0341627	+	0.149677i
$809$	−1.36928e10	+	2.17919e10i	−0.0319666	+	0.0508746i	−0.862325	−	0.506355i	$-0.830993\pi$
$809$	−1.36928e10	+	2.17919e10i	−0.0319666	+	0.0508746i	0.830359	+	0.557229i	$0.188136\pi$
$810$	−2.69607e11	+	2.39283e12i	−0.626312	+	5.55868i
$811$			2.17463e11i			0.502692i	0.967897	+	0.251346i	$0.0808732\pi$
$811$			2.17463e11i			0.502692i	−0.967897	+	0.251346i	$0.919127\pi$
$812$	−2.54640e10	−	3.79829e10i	−0.0585738	−	0.0873703i
$813$	4.11512e11			0.941933
$814$	9.62600e11	+	1.08459e11i	2.19254	+	0.247040i
$815$	−1.27345e11	−	8.00163e10i	−0.288637	−	0.181363i
$816$	1.46269e11	+	3.33848e10i	0.329906	+	0.0752989i
$817$	2.50614e11	−	1.99858e11i	0.562493	−	0.448573i
$818$	−6.87193e11	−	5.48018e11i	−1.53485	−	1.22400i
$819$	3.39863e9	+	1.48904e10i	0.00755385	+	0.0330956i
$820$	−2.86540e11	−	1.00265e11i	−0.633767	−	0.221765i
$821$	1.73694e11	+	3.60679e11i	0.382307	+	0.793868i	0.999972	+	0.00742714i	$0.00236415\pi$
$821$	1.73694e11	+	3.60679e11i	0.382307	+	0.793868i	−0.617666	+	0.786441i	$0.711922\pi$
$822$	7.80103e10	−	4.90171e10i	0.170870	−	0.107364i
$823$	5.40301e11	−	1.89060e11i	1.17771	−	0.412097i	0.330728	−	0.943726i	$-0.392706\pi$
$823$	5.40301e11	−	1.89060e11i	1.17771	−	0.412097i	0.846977	+	0.531629i	$0.178420\pi$
$824$	−3.02725e10	−	3.02725e10i	−0.0656659	−	0.0656659i
$825$	−1.93035e11	+	4.00842e11i	−0.416697	+	0.865281i
$826$	5.22774e9	+	4.63975e10i	0.0112304	+	0.0996723i
$827$	−7.51178e11	+	8.46375e10i	−1.60591	+	0.180942i	−0.868917	−	0.494959i	$-0.835183\pi$
$827$	−7.51178e11	+	8.46375e10i	−1.60591	+	0.180942i	−0.736992	+	0.675901i	$0.763755\pi$
$828$	−2.66847e12	−	1.28507e12i	−5.67729	−	2.73404i
$829$	1.04001e11	−	1.04001e11i	0.220202	−	0.220202i	−0.588382	−	0.808583i	$-0.700235\pi$
$829$	1.04001e11	−	1.04001e11i	0.220202	−	0.220202i	0.808583	+	0.588382i	$0.200235\pi$
$830$	−2.33749e11	−	6.68017e11i	−0.492536	−	1.40759i
$831$	7.12005e11	+	1.13315e12i	1.49307	+	2.37620i
$832$	−1.04544e11	+	5.03460e10i	−0.218176	+	0.105068i
$833$	5.79357e10	−	1.65571e11i	0.120328	−	0.343877i
$834$	1.19952e12	−	2.73783e11i	2.47939	−	0.565904i
$835$	−2.79260e11	+	3.50181e11i	−0.574463	+	0.720354i
$836$	−2.85885e11	−	3.58489e11i	−0.585284	−	0.733923i
$837$	−4.68670e11	+	2.05338e12i	−0.954916	+	4.18376i
$838$	2.94481e11	−	4.68663e11i	0.597146	−	0.950352i
$839$	−3.33402e10	+	2.95902e11i	−0.0672853	+	0.597174i	0.914149	+	0.405377i	$0.132860\pi$
$839$	−3.33402e10	+	2.95902e11i	−0.0672853	+	0.597174i	−0.981435	+	0.191796i	$0.938569\pi$
$840$		−	3.61107e10i		−	0.0725301i
$841$	1.90012e11	−	4.62755e11i	0.379836	−	0.925054i
$842$	4.63286e11			0.921724
$843$	1.19714e11	+	1.34885e10i	0.237047	+	0.0267088i
$844$	−3.78568e11	−	2.37870e11i	−0.746060	−	0.468781i
$845$	−3.96175e11	−	9.04243e10i	−0.777070	−	0.177361i
$846$	−1.15909e12	+	9.24347e11i	−2.26275	+	1.80449i
$847$	3.48572e10	+	2.77977e10i	0.0677266	+	0.0540101i
$848$	3.57516e10	+	1.56638e11i	0.0691373	+	0.302910i
$849$	6.12144e11	+	2.14198e11i	1.17821	+	0.412274i
$850$	−4.26868e10	−	8.86400e10i	−0.0817744	−	0.169806i
$851$	−6.84724e11	+	4.30241e11i	−1.30556	+	0.820339i
$852$	2.35681e12	−	8.24684e11i	4.47266	−	1.56505i
$853$	2.15325e11	+	2.15325e11i	0.406723	+	0.406723i	0.880594	−	0.473871i	$-0.157144\pi$
$853$	2.15325e11	+	2.15325e11i	0.406723	+	0.406723i	−0.473871	+	0.880594i	$0.657144\pi$
$854$	−1.32096e10	+	2.74299e10i	−0.0248346	+	0.0515696i
$855$	−6.53545e10	−	5.80037e11i	−0.122296	−	1.08540i
$856$	−5.23962e10	+	5.90364e9i	−0.0975899	+	0.0109957i
$857$	−7.17876e9	−	3.45711e9i	−0.0133084	−	0.00640899i	0.427218	−	0.904149i	$-0.359494\pi$
$857$	−7.17876e9	−	3.45711e9i	−0.0133084	−	0.00640899i	−0.440526	+	0.897740i	$0.645208\pi$
$858$	−2.64136e11	+	2.64136e11i	−0.487392	+	0.487392i
$859$	−2.63786e11	−	7.53857e11i	−0.484483	−	1.38457i	−0.883845	−	0.467780i	$-0.845054\pi$
$859$	−2.63786e11	−	7.53857e11i	−0.484483	−	1.38457i	0.399361	−	0.916794i	$-0.369232\pi$
$860$	5.10369e11	+	8.12248e11i	0.933019	+	1.48489i
$861$	4.40626e10	−	2.12195e10i	0.0801785	−	0.0386119i
$862$	−4.70456e11	+	1.34448e12i	−0.852098	+	2.43516i
$863$	−8.08345e11	+	1.84499e11i	−1.45731	+	0.332623i	−0.876496	−	0.481410i	$-0.840125\pi$
$863$	−8.08345e11	+	1.84499e11i	−1.45731	+	0.332623i	−0.580819	+	0.814033i	$0.697268\pi$
$864$	1.69883e12	−	2.13027e12i	3.04856	−	3.82278i
$865$	2.33133e11	+	2.92339e11i	0.416427	+	0.522183i
$866$	−2.85318e11	+	1.25006e12i	−0.507291	+	2.22259i
$867$	5.12941e11	−	8.16340e11i	0.907801	−	1.44476i
$868$	7.72363e9	−	6.85491e10i	0.0136064	−	0.120760i
$869$			8.42178e11i			1.47681i
$870$	1.18258e12	−	7.92811e11i	2.06421	−	1.38386i
$871$	5.96694e10			0.103676
$872$	−4.16105e11	−	4.68837e10i	−0.719675	−	0.0810879i
$873$	−7.96043e11	−	5.00187e11i	−1.37050	−	0.861143i
$874$	6.42825e11	+	1.46721e11i	1.10166	+	0.251446i
$875$	3.79198e10	−	3.02400e10i	0.0646895	−	0.0515881i
$876$	1.44012e11	+	1.14845e11i	0.244557	+	0.195028i
$877$	4.33199e10	+	1.89797e11i	0.0732300	+	0.320842i	0.998254	−	0.0590670i	$-0.0188126\pi$
$877$	4.33199e10	+	1.89797e11i	0.0732300	+	0.320842i	−0.925024	+	0.379909i	$0.875955\pi$
$878$	−9.73690e10	−	3.40709e10i	−0.163849	−	0.0573331i
$879$	−1.59653e11	−	3.31523e11i	−0.267437	−	0.555339i
$880$	−2.84201e11	+	1.78575e11i	−0.473909	+	0.297777i
$881$	−2.23234e11	+	7.81130e10i	−0.370559	+	0.129664i	−0.509133	−	0.860688i	$-0.670034\pi$
$881$	−2.23234e11	+	7.81130e10i	−0.370559	+	0.129664i	0.138574	+	0.990352i	$0.455748\pi$
$882$	−1.89489e12	−	1.89489e12i	−3.13120	−	3.13120i
$883$	−3.53413e11	+	7.33871e11i	−0.581353	+	1.20719i	0.378215	+	0.925718i	$0.376538\pi$
$883$	−3.53413e11	+	7.33871e11i	−0.581353	+	1.20719i	−0.959569	+	0.281475i	$0.909176\pi$
$884$	−5.36921e9	−	4.76530e10i	−0.00879227	−	0.0780336i
$885$	−8.38624e11	+	9.44903e10i	−1.36708	+	0.154033i
$886$	−1.72699e11	−	8.31676e10i	−0.280257	−	0.134964i
$887$	−4.23972e10	+	4.23972e10i	−0.0684924	+	0.0684924i	−0.740523	−	0.672031i	$-0.765422\pi$
$887$	−4.23972e10	+	4.23972e10i	−0.0684924	+	0.0684924i	0.672031	+	0.740523i	$0.265422\pi$
$888$	2.34449e11	+	6.70015e11i	0.377047	+	1.07754i
$889$	−4.37928e9	−	6.96958e9i	−0.00701125	−	0.0111583i
$890$	3.25277e11	−	1.56645e11i	0.518435	−	0.249665i
$891$	1.35085e12	−	3.86050e12i	2.14336	−	6.12537i
$892$	4.41854e11	−	1.00850e11i	0.697942	−	0.159301i
$893$	1.19463e11	−	1.49802e11i	0.187857	−	0.235565i
$894$	−1.37934e12	−	1.72964e12i	−2.15934	−	2.70773i
$895$	−1.25026e11	+	5.47775e11i	−0.194854	+	0.853710i
$896$	−2.86256e10	+	4.55574e10i	−0.0444143	+	0.0706850i
$897$	3.49150e10	−	3.09879e11i	0.0539314	−	0.478654i
$898$		−	5.33414e11i		−	0.820274i
$899$	6.69917e11	−	3.47395e11i	1.02561	−	0.531845i
$900$	−8.72539e11			−1.32989
$901$	−1.59133e11	−	1.79300e10i	−0.241469	−	0.0272070i
$902$	7.52060e11	+	4.72550e11i	1.13612	+	0.713875i
$903$	−1.50665e11	−	3.43884e10i	−0.226601	−	0.0517203i
$904$	1.87491e11	−	1.49519e11i	0.280742	−	0.223884i
$905$	−4.42135e11	−	3.52591e11i	−0.659114	−	0.525626i
$906$	1.66728e11	+	7.30482e11i	0.247454	+	1.08417i
$907$	−6.85893e11	−	2.40004e11i	−1.01351	−	0.354642i	−0.228112	−	0.973635i	$-0.573255\pi$
$907$	−6.85893e11	−	2.40004e11i	−1.01351	−	0.354642i	−0.785397	+	0.618993i	$0.787541\pi$
$908$	−2.84458e11	−	5.90684e11i	−0.418481	−	0.868984i
$909$	4.31795e11	−	2.71315e11i	0.632443	−	0.397391i
$910$	9.60447e9	−	3.36075e9i	0.0140058	−	0.00490084i
$911$	5.26778e11	+	5.26778e11i	0.764811	+	0.764811i	0.977188	−	0.212376i	$-0.0681203\pi$
$911$	5.26778e11	+	5.26778e11i	0.764811	+	0.764811i	−0.212376	+	0.977188i	$0.568120\pi$
$912$	−1.28524e11	+	2.66883e11i	−0.185783	+	0.385782i
$913$	1.34594e11	+	1.19455e12i	0.193705	+	1.71918i
$914$	1.73915e11	−	1.95955e10i	0.249203	−	0.0280784i
$915$	−4.95790e11	−	2.38760e11i	−0.707316	−	0.340625i
$916$	−3.12599e11	+	3.12599e11i	−0.444024	+	0.444024i
$917$	1.61520e10	+	4.61598e10i	0.0228428	+	0.0652809i
$918$	7.94073e11	+	1.26376e12i	1.11812	+	1.77948i
$919$	−5.54245e10	+	2.66910e10i	−0.0777033	+	0.0374199i	−0.472332	−	0.881421i	$-0.656588\pi$
$919$	−5.54245e10	+	2.66910e10i	−0.0777033	+	0.0374199i	0.394628	+	0.918841i	$0.370873\pi$
$920$	−1.80823e11	+	5.16764e11i	−0.252408	+	0.721341i
$921$	1.93135e12	−	4.40819e11i	2.68425	−	0.612663i
$922$	−1.08147e12	+	1.35612e12i	−1.49655	+	1.87661i
$923$	1.21718e11	+	1.52629e11i	0.167706	+	0.210296i
$924$	−4.91906e10	+	2.15518e11i	−0.0674829	+	0.295662i
$925$	−1.26749e11	+	2.01720e11i	−0.173132	+	0.275538i
$926$	5.30456e10	−	4.70793e11i	0.0721449	−	0.640304i
$927$			3.33635e11i			0.451807i
$928$	−9.75821e11	+	2.88827e10i	−1.31576	+	0.0389445i
$929$	−1.10768e12			−1.48714			−0.743570	−	0.668658i	$-0.766869\pi$
$929$	−1.10768e12			−1.48714			−0.743570	+	0.668658i	$0.766869\pi$
$930$	2.13424e12	+	2.40472e11i	2.85307	+	0.321464i
$931$	2.93252e11	+	1.84262e11i	0.390339	+	0.245266i
$932$	1.23961e12	+	2.82932e11i	1.64294	+	0.374989i
$933$	−1.37886e12	+	1.09960e12i	−1.81967	+	1.45114i
$934$	7.53438e11	+	6.00847e11i	0.990057	+	0.789544i
$935$	−7.44439e10	−	3.26160e11i	−0.0974053	−	0.426761i
$936$	−1.91859e11	−	6.71344e10i	−0.249965	−	0.0874665i
$937$	−2.83417e11	−	5.88522e11i	−0.367678	−	0.763492i	0.632258	−	0.774758i	$-0.282128\pi$
$937$	−2.83417e11	−	5.88522e11i	−0.367678	−	0.763492i	−0.999937	+	0.0112658i	$0.996414\pi$
$938$	5.15029e10	−	3.23614e10i	0.0665304	−	0.0418038i
$939$	1.30431e12	−	4.56397e11i	1.67771	−	0.587057i
$940$	4.05456e11	+	4.05456e11i	0.519316	+	0.519316i
$941$	4.94535e11	−	1.02691e12i	0.630723	−	1.30971i	−0.303436	−	0.952852i	$-0.598134\pi$
$941$	4.94535e11	−	1.02691e12i	0.630723	−	1.30971i	0.934159	−	0.356858i	$-0.116152\pi$
$942$	−4.75724e10	−	4.22216e11i	−0.0604159	−	0.536206i
$943$	−7.36817e11	+	8.30193e10i	−0.931778	+	0.104986i
$944$	2.86532e11	+	1.37987e11i	0.360815	+	0.173760i
$945$	−1.30006e11	+	1.30006e11i	−0.163018	+	0.163018i
$946$	−9.26982e11	−	2.64916e12i	−1.15746	−	3.30784i
$947$	−3.69119e11	−	5.87449e11i	−0.458951	−	0.730416i	0.534439	−	0.845207i	$-0.320523\pi$
$947$	−3.69119e11	−	5.87449e11i	−0.458951	−	0.730416i	−0.993390	+	0.114791i	$0.963380\pi$
$948$	−2.00399e12	+	9.65072e11i	−2.48120	+	1.19489i
$949$	−4.75646e9	+	1.35932e10i	−0.00586434	+	0.0167593i
$950$	1.89376e11	−	4.32239e10i	0.232504	−	0.0530676i
$951$	−5.73897e11	+	7.19644e11i	−0.701636	+	0.879824i
$952$	−8.45661e9	−	1.06042e10i	−0.0102955	−	0.0129102i
$953$	1.71710e11	−	7.52312e11i	0.208173	−	0.912066i	−0.757608	−	0.652709i	$-0.773632\pi$
$953$	1.71710e11	−	7.52312e11i	0.208173	−	0.912066i	0.965782	−	0.259357i	$-0.0835105\pi$
$954$	−1.30158e12	+	2.07146e12i	−1.57137	+	2.50082i
$955$	−3.43211e10	+	3.04608e11i	−0.0412618	+	0.366208i
$956$		−	8.83541e11i		−	1.05778i
$957$	−2.25794e12	+	8.65887e11i	−2.69194	+	1.03232i
$958$	1.96549e12			2.33351
$959$	4.23601e9	+	4.77284e8i	0.00500822	+	0.000564290i
$960$	−1.81027e12	−	1.13747e12i	−2.13137	−	1.33923i
$961$	2.78333e11	+	6.35278e10i	0.326341	+	0.0744852i
$962$	−1.56387e11	+	1.24714e11i	−0.182599	+	0.145618i
$963$	3.21263e11	+	2.56199e11i	0.373556	+	0.297901i
$964$	2.71285e11	+	1.18858e12i	0.314135	+	1.37632i
$965$	1.16801e12	+	4.08706e11i	1.34691	+	0.471304i
$966$	−1.37925e11	−	2.86404e11i	−0.158392	−	0.328905i
$967$	9.75995e11	−	6.13258e11i	1.11620	−	0.701354i	0.157995	−	0.987440i	$-0.449497\pi$
$967$	9.75995e11	−	6.13258e11i	1.11620	−	0.701354i	0.958204	+	0.286086i	$0.0923542\pi$
$968$	−5.60052e11	+	1.95971e11i	−0.637863	+	0.223198i
$969$	−2.08771e11	−	2.08771e11i	−0.236797	−	0.236797i
$970$	−2.71763e11	+	5.64321e11i	−0.306975	+	0.637440i
$971$	1.90281e11	+	1.68879e12i	0.214052	+	1.89976i	0.398896	+	0.916996i	$0.369393\pi$
$971$	1.90281e11	+	1.68879e12i	0.214052	+	1.89976i	−0.184845	+	0.982768i	$0.559178\pi$
$972$	6.17420e12	−	6.95665e11i	6.91696	−	0.779355i
$973$	5.12900e10	+	2.47000e10i	0.0572244	+	0.0275578i
$974$	1.36201e11	−	1.36201e11i	0.151336	−	0.151336i
$975$	−3.03420e10	−	8.67126e10i	−0.0335758	−	0.0959541i
$976$	1.10327e11	+	1.75585e11i	0.121586	+	0.193503i
$977$	3.62341e11	−	1.74494e11i	0.397685	−	0.191515i	−0.224343	−	0.974510i	$-0.572024\pi$
$977$	3.62341e11	−	1.74494e11i	0.397685	−	0.191515i	0.622027	+	0.782995i	$0.286309\pi$
$978$	−3.83838e11	+	1.09695e12i	−0.419558	+	1.19903i
$979$	−5.97848e11	+	1.36455e11i	−0.650819	+	0.148545i
$980$	−6.46222e11	+	8.10337e11i	−0.700612	+	0.878540i
$981$	2.03460e12	+	2.55131e12i	2.19686	+	2.75478i
$982$	4.00082e11	−	1.75287e12i	0.430232	−	1.88497i
$983$	5.83908e11	−	9.29284e11i	0.625360	−	0.995255i	−0.372381	−	0.928080i	$-0.621458\pi$
$983$	5.83908e11	−	9.29284e11i	0.625360	−	0.995255i	0.997741	−	0.0671752i	$-0.0213986\pi$
$984$	−7.28739e10	+	6.46773e11i	−0.0777305	+	0.689877i
$985$			3.78396e11i			0.401978i
$986$	1.61611e11	−	5.09760e11i	0.170987	−	0.539334i
$987$	−9.23746e10			−0.0973384
$988$	9.40857e10	+	1.06009e10i	0.0987407	+	0.0111254i
$989$	1.98390e12	+	1.24657e12i	2.07365	+	1.30296i
$990$	−4.98271e12	−	1.13727e12i	−5.18710	−	1.18392i
$991$	−7.19586e11	+	5.73851e11i	−0.746084	+	0.594982i	−0.920982	−	0.389604i	$-0.872612\pi$
$991$	−7.19586e11	+	5.73851e11i	−0.746084	+	0.594982i	0.174898	+	0.984587i	$0.444040\pi$
$992$	−1.15140e12	−	9.18210e11i	−1.18899	−	0.948189i
$993$	−1.55364e10	−	6.80693e10i	−0.0159791	−	0.0700091i
$994$	1.87837e11	+	6.57270e10i	0.192413	+	0.0673284i
$995$	6.29295e10	+	1.30674e11i	0.0642040	+	0.133321i
$996$	−2.68824e12	+	1.68913e12i	−2.73168	+	1.71643i
$997$	−1.52899e12	+	5.35017e11i	−1.54748	+	0.541486i	−0.962901	−	0.269854i	$-0.913025\pi$
$997$	−1.52899e12	+	5.35017e11i	−1.54748	+	0.541486i	−0.584575	+	0.811339i	$0.698739\pi$
$998$	−1.96506e12	−	1.96506e12i	−1.98086	−	1.98086i
$999$	1.56813e12	−	3.25626e12i	1.57442	−	3.26932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.2.2	✓	228
29.15	odd	28	inner	29.9.f.a.15.2	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.2	✓	228	1.1	even	1	trivial
29.9.f.a.15.2	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)

\(f(q)\)	\(=\)	\(q+(-24.5490 - 2.76601i) q^{2} +(-135.176 - 84.9370i) q^{3} +(345.422 + 78.8403i) q^{4} +(-399.043 + 318.226i) q^{5} +(3083.51 + 2459.02i) q^{6} +(40.6060 + 177.907i) q^{7} +(-2292.28 - 802.105i) q^{8} +(8211.67 + 17051.7i) q^{9} +O(q^{10})\)	\(q+(-24.5490 - 2.76601i) q^{2} +(-135.176 - 84.9370i) q^{3} +(345.422 + 78.8403i) q^{4} +(-399.043 + 318.226i) q^{5} +(3083.51 + 2459.02i) q^{6} +(40.6060 + 177.907i) q^{7} +(-2292.28 - 802.105i) q^{8} +(8211.67 + 17051.7i) q^{9} +(10676.3 - 6708.39i) q^{10} +(-20215.0 + 7073.52i) q^{11} +(-39996.5 - 39996.5i) q^{12} +(1918.80 - 3984.42i) q^{13} +(-504.747 - 4479.75i) q^{14} +(80970.4 - 9123.18i) q^{15} +(-27665.1 - 13322.8i) q^{16} +(21641.2 - 21641.2i) q^{17} +(-154423. - 441316. i) q^{18} +(32149.0 + 51164.9i) q^{19} +(-162927. + 78461.7i) q^{20} +(9621.87 - 27497.7i) q^{21} +(515823. - 117733. i) q^{22} +(-275389. + 345326. i) q^{23} +(241735. + 303126. i) q^{24} +(-28954.8 + 126859. i) q^{25} +(-58125.5 + 92506.2i) q^{26} +(221020. - 1.96161e6i) q^{27} +64654.3i q^{28} +(-587477. + 393849. i) q^{29} -2.01298e6 q^{30} +(-1.06024e6 - 119460. i) q^{31} +(1.16872e6 + 734355. i) q^{32} +(3.33339e6 + 760825. i) q^{33} +(-591131. + 471411. i) q^{34} +(-72818.1 - 58070.5i) q^{35} +(1.49213e6 + 6.53745e6i) q^{36} +(1.72813e6 + 604698. i) q^{37} +(-647705. - 1.34497e6i) q^{38} +(-597801. + 375623. i) q^{39} +(1.16997e6 - 409391. i) q^{40} +(1.18704e6 + 1.18704e6i) q^{41} +(-312267. + 648428. i) q^{42} +(-593940. - 5.27136e6i) q^{43} +(-7.54037e6 + 849596. i) q^{44} +(-8.70311e6 - 4.19120e6i) q^{45} +(7.71570e6 - 7.71570e6i) q^{46} +(-1.04726e6 - 2.99290e6i) q^{47} +(2.60807e6 + 4.15072e6i) q^{48} +(5.16390e6 - 2.48681e6i) q^{49} +(1.06170e6 - 3.03418e6i) q^{50} +(-4.76353e6 + 1.08724e6i) q^{51} +(976928. - 1.22503e6i) q^{52} +(-3.26236e6 - 4.09087e6i) q^{53} +(-1.08517e7 + 4.75443e7i) q^{54} +(5.81566e6 - 9.25557e6i) q^{55} +(49619.2 - 440383. i) q^{56} -9.64693e6i q^{57} +(1.55114e7 - 8.04365e6i) q^{58} -1.03572e7 q^{59} +(2.86882e7 + 3.23239e6i) q^{60} +(-5.71826e6 - 3.59302e6i) q^{61} +(2.56975e7 + 5.86528e6i) q^{62} +(-2.70017e6 + 2.15331e6i) q^{63} +(-2.05139e7 - 1.63593e7i) q^{64} +(502265. + 2.20057e6i) q^{65} +(-7.97270e7 - 2.78977e7i) q^{66} +(5.85423e6 + 1.21564e7i) q^{67} +(9.18156e6 - 5.76916e6i) q^{68} +(6.65571e7 - 2.32893e7i) q^{69} +(1.62699e6 + 1.62699e6i) q^{70} +(-1.91533e7 + 3.97722e7i) q^{71} +(-5.14622e6 - 4.56740e7i) q^{72} +(-3.23600e6 + 364609. i) q^{73} +(-4.07512e7 - 1.96247e7i) q^{74} +(1.46890e7 - 1.46890e7i) q^{75} +(7.07113e6 + 2.02081e7i) q^{76} +(-2.07928e6 - 3.30915e6i) q^{77} +(1.57144e7 - 7.56766e6i) q^{78} +(1.29876e7 - 3.71166e7i) q^{79} +(1.52792e7 - 3.48739e6i) q^{80} +(-1.19069e8 + 1.49308e8i) q^{81} +(-2.58574e7 - 3.24242e7i) q^{82} +(1.24899e7 - 5.47220e7i) q^{83} +(5.49154e6 - 8.73973e6i) q^{84} +(-1.74898e6 + 1.55226e7i) q^{85} +1.31050e8i q^{86} +(1.12865e8 - 3.34063e6i) q^{87} +5.20122e7 q^{88} +(2.84528e7 + 3.20586e6i) q^{89} +(2.02060e8 + 1.26963e8i) q^{90} +(786769. + 179575. i) q^{91} +(-1.22351e8 + 9.75716e7i) q^{92} +(1.33173e8 + 1.06202e8i) q^{93} +(1.74308e7 + 7.63695e7i) q^{94} +(-2.91109e7 - 1.01863e7i) q^{95} +(-9.56095e7 - 1.98535e8i) q^{96} +(-4.20609e7 + 2.64286e7i) q^{97} +(-1.33647e8 + 4.67652e7i) q^{98} +(-2.86614e8 - 2.86614e8i) 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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