LMFDB - Embedded newform 32.8.g.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,8,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, 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:	$9.99632081549$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	32.13
Dual form			32.8.g.a.5.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.01533 + 9.58206i) q^{2} +(-22.2952 + 53.8254i) q^{3} +(-55.6316 - 115.278i) q^{4} +(416.314 - 172.443i) q^{5} +(-381.645 - 537.412i) q^{6} +(881.560 - 881.560i) q^{7} +(1439.25 + 160.372i) q^{8} +(-853.657 - 853.657i) q^{9} +O(q^{10})$	\(q+(-6.01533 + 9.58206i) q^{2} +(-22.2952 + 53.8254i) q^{3} +(-55.6316 - 115.278i) q^{4} +(416.314 - 172.443i) q^{5} +(-381.645 - 537.412i) q^{6} +(881.560 - 881.560i) q^{7} +(1439.25 + 160.372i) q^{8} +(-853.657 - 853.657i) q^{9} +(-851.908 + 5026.45i) q^{10} +(-305.868 - 738.430i) q^{11} +(7445.23 - 424.237i) q^{12} +(-3350.79 - 1387.94i) q^{13} +(3144.28 + 13750.0i) q^{14} +26252.9i q^{15} +(-10194.2 + 12826.3i) q^{16} -36455.9i q^{17} +(13314.8 - 3044.76i) q^{18} +(41836.4 + 17329.2i) q^{19} +(-43039.2 - 38398.8i) q^{20} +(27795.8 + 67104.9i) q^{21} +(8915.57 + 1511.06i) q^{22} +(44765.1 + 44765.1i) q^{23} +(-40720.4 + 73892.5i) q^{24} +(88338.1 - 88338.1i) q^{25} +(33455.4 - 23758.5i) q^{26} +(-52735.3 + 21843.7i) q^{27} +(-150667. - 52582.2i) q^{28} +(4885.86 - 11795.5i) q^{29} +(-251557. - 157920. i) q^{30} -39160.8 q^{31} +(-61580.2 - 174836. i) q^{32} +46565.7 q^{33} +(349322. + 219294. i) q^{34} +(214987. - 519024. i) q^{35} +(-50917.9 + 145899. i) q^{36} +(-63716.1 + 26392.1i) q^{37} +(-417709. + 296638. i) q^{38} +(149413. - 149413. i) q^{39} +(626834. - 181423. i) q^{40} +(-214303. - 214303. i) q^{41} +(-810203. - 137317. i) q^{42} +(285302. + 688779. i) q^{43} +(-68109.1 + 76340.0i) q^{44} +(-502596. - 208182. i) q^{45} +(-698219. + 159665. i) q^{46} +148477. i q^{47} +(-463096. - 834674. i) q^{48} -730752. i q^{49} +(315078. + 1.37784e6i) q^{50} +(1.96225e6 + 812791. i) q^{51} +(26410.0 + 463487. i) q^{52} +(610579. + 1.47407e6i) q^{53} +(107913. - 636710. i) q^{54} +(-254674. - 254674. i) q^{55} +(1.41016e6 - 1.12740e6i) q^{56} +(-1.86550e6 + 1.86550e6i) q^{57} +(83635.2 + 117770. i) q^{58} +(132784. - 55001.0i) q^{59} +(3.02640e6 - 1.46049e6i) q^{60} +(1.17540e6 - 2.83767e6i) q^{61} +(235565. - 375241. i) q^{62} -1.50510e6 q^{63} +(2.04571e6 + 461631. i) q^{64} -1.63432e6 q^{65} +(-280108. + 446195. i) q^{66} +(1.10895e6 - 2.67723e6i) q^{67} +(-4.20258e6 + 2.02810e6i) q^{68} +(-3.40755e6 + 1.41145e6i) q^{69} +(3.68010e6 + 5.18212e6i) q^{70} +(-2.02890e6 + 2.02890e6i) q^{71} +(-1.09172e6 - 1.36553e6i) q^{72} +(-216388. - 216388. i) q^{73} +(130383. - 769289. i) q^{74} +(2.78532e6 + 6.72435e6i) q^{75} +(-329743. - 5.78688e6i) q^{76} +(-920611. - 381329. i) q^{77} +(532916. + 2.33045e6i) q^{78} +334646. i q^{79} +(-2.03221e6 + 7.09768e6i) q^{80} -5.96577e6i q^{81} +(3.34256e6 - 764359. i) q^{82} +(-3.39903e6 - 1.40792e6i) q^{83} +(6.18942e6 - 6.93741e6i) q^{84} +(-6.28656e6 - 1.51771e7i) q^{85} +(-8.31611e6 - 1.40946e6i) q^{86} +(525967. + 525967. i) q^{87} +(-321795. - 1.11184e6i) q^{88} +(-6.24441e6 + 6.24441e6i) q^{89} +(5.01809e6 - 3.56362e6i) q^{90} +(-4.17747e6 + 1.73037e6i) q^{91} +(2.67010e6 - 7.65081e6i) q^{92} +(873098. - 2.10784e6i) q^{93} +(-1.42272e6 - 893139. i) q^{94} +2.04054e7 q^{95} +(1.07836e7 + 583428. i) q^{96} -2.74628e6 q^{97} +(7.00211e6 + 4.39571e6i) q^{98} +(-369260. + 891471. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−6.01533	+	9.58206i	−0.531685	+	0.846942i
$2$	−6.01533	+	9.58206i	−0.531685	+	0.846942i
$3$	−22.2952	+	53.8254i	−0.476746	+	1.15097i	0.484380	+	0.874858i	$0.339045\pi$
$3$	−22.2952	+	53.8254i	−0.476746	+	1.15097i	−0.961126	+	0.276110i	$0.910955\pi$
$4$	−55.6316	−	115.278i	−0.434622	−	0.900613i
$5$	416.314	−	172.443i	1.48945	−	0.616951i	0.518253	−	0.855227i	$-0.326583\pi$
$5$	416.314	−	172.443i	1.48945	−	0.616951i	0.971197	+	0.238277i	$0.0765826\pi$
$6$	−381.645	−	537.412i	−0.721324	−	1.01573i
$7$	881.560	−	881.560i	0.971423	−	0.971423i	−0.0281795	−	0.999603i	$-0.508971\pi$
$7$	881.560	−	881.560i	0.971423	−	0.971423i	0.999603	+	0.0281795i	$0.00897099\pi$
$8$	1439.25	+	160.372i	0.993849	+	0.110743i
$9$	−853.657	−	853.657i	−0.390332	−	0.390332i
$10$	−851.908	+	5026.45i	−0.269397	+	1.58950i
$11$	−305.868	−	738.430i	−0.0692882	−	0.167276i	0.885442	−	0.464750i	$-0.153856\pi$
$11$	−305.868	−	738.430i	−0.0692882	−	0.167276i	−0.954730	+	0.297474i	$0.903856\pi$
$12$	7445.23	−	424.237i	1.24378	−	0.0708719i
$13$	−3350.79	−	1387.94i	−0.423005	−	0.175214i	0.161018	−	0.986951i	$-0.448522\pi$
$13$	−3350.79	−	1387.94i	−0.423005	−	0.175214i	−0.584023	+	0.811737i	$0.698522\pi$
$14$	3144.28	+	13750.0i	0.306248	+	1.33923i
$15$			26252.9i			2.00844i
$16$	−10194.2	+	12826.3i	−0.622207	+	0.782853i
$17$		−	36455.9i		−	1.79968i	−0.436216	−	0.899842i	$-0.643682\pi$
$17$		−	36455.9i		−	1.79968i	0.436216	−	0.899842i	$-0.356318\pi$
$18$	13314.8	−	3044.76i	0.538123	−	0.123055i
$19$	41836.4	+	17329.2i	1.39932	+	0.579617i	0.949575	−	0.313541i	$-0.101515\pi$
$19$	41836.4	+	17329.2i	1.39932	+	0.579617i	0.449744	+	0.893158i	$0.351515\pi$
$20$	−43039.2	−	38398.8i	−1.20298	−	1.07328i
$21$	27795.8	+	67104.9i	0.654954	+	1.58120i
$22$	8915.57	+	1511.06i	0.178513	+	0.0302553i
$23$	44765.1	+	44765.1i	0.767171	+	0.767171i	0.977608	−	0.210436i	$-0.0674885\pi$
$23$	44765.1	+	44765.1i	0.767171	+	0.767171i	−0.210436	+	0.977608i	$0.567488\pi$
$24$	−40720.4	+	73892.5i	−0.601275	+	1.09109i
$25$	88338.1	−	88338.1i	1.13073	−	1.13073i
$26$	33455.4	−	23758.5i	0.373302	−	0.265102i
$27$	−52735.3	+	21843.7i	−0.515618	+	0.213576i
$28$	−150667.	−	52582.2i	−1.29708	−	0.452674i
$29$	4885.86	−	11795.5i	0.0372004	−	0.0898098i	−0.904187	−	0.427136i	$-0.859523\pi$
$29$	4885.86	−	11795.5i	0.0372004	−	0.0898098i	0.941388	+	0.337326i	$0.109523\pi$
$30$	−251557.	−	157920.i	−1.70103	−	1.06786i
$31$	−39160.8			−0.236094			−0.118047	−	0.993008i	$-0.537663\pi$
$31$	−39160.8			−0.236094			−0.118047	+	0.993008i	$0.537663\pi$
$32$	−61580.2	−	174836.i	−0.332212	−	0.943205i
$33$	46565.7			0.225563
$34$	349322.	+	219294.i	1.52423	+	0.956865i
$35$	214987.	−	519024.i	0.847567	−	2.04621i
$36$	−50917.9	+	145899.i	−0.181891	+	0.521185i
$37$	−63716.1	+	26392.1i	−0.206797	+	0.0856580i	−0.483678	−	0.875246i	$-0.660699\pi$
$37$	−63716.1	+	26392.1i	−0.206797	+	0.0856580i	0.276881	+	0.960904i	$0.410699\pi$
$38$	−417709.	+	296638.i	−1.23490	+	0.876968i
$39$	149413.	−	149413.i	0.403332	−	0.403332i
$40$	626834.	−	181423.i	1.54861	−	0.448210i
$41$	−214303.	−	214303.i	−0.485606	−	0.485606i	0.421310	−	0.906917i	$-0.361570\pi$
$41$	−214303.	−	214303.i	−0.485606	−	0.485606i	−0.906917	+	0.421310i	$0.861570\pi$
$42$	−810203.	−	137317.i	−1.68741	−	0.285992i
$43$	285302.	+	688779.i	0.547224	+	1.32111i	0.919535	+	0.393007i	$0.128565\pi$
$43$	285302.	+	688779.i	0.547224	+	1.32111i	−0.372312	+	0.928108i	$0.621435\pi$
$44$	−68109.1	+	76340.0i	−0.120537	+	0.135104i
$45$	−502596.	−	208182.i	−0.822196	−	0.340565i
$46$	−698219.	+	159665.i	−1.05764	+	0.241856i
$47$			148477.i			0.208601i	0.994546	+	0.104301i	$0.0332604\pi$
$47$			148477.i			0.208601i	−0.994546	+	0.104301i	$0.966740\pi$
$48$	−463096.	−	834674.i	−0.604403	−	1.08936i
$49$		−	730752.i		−	0.887327i
$50$	315078.	+	1.37784e6i	0.356470	+	1.55885i
$51$	1.96225e6	+	812791.i	2.07138	+	0.857993i
$52$	26410.0	+	463487.i	0.0260469	+	0.457116i
$53$	610579.	+	1.47407e6i	0.563348	+	1.36004i	0.907074	+	0.420972i	$0.138311\pi$
$53$	610579.	+	1.47407e6i	0.563348	+	1.36004i	−0.343726	+	0.939070i	$0.611689\pi$
$54$	107913.	−	636710.i	0.0932599	−	0.550254i
$55$	−254674.	−	254674.i	−0.206403	−	0.206403i
$56$	1.41016e6	−	1.12740e6i	1.07303	−	0.857870i
$57$	−1.86550e6	+	1.86550e6i	−1.33424	+	1.33424i
$58$	83635.2	+	117770.i	0.0562848	+	0.0792571i
$59$	132784.	−	55001.0i	0.0841713	−	0.0348649i	−0.340201	−	0.940353i	$-0.610495\pi$
$59$	132784.	−	55001.0i	0.0841713	−	0.0348649i	0.424372	+	0.905488i	$0.360495\pi$
$60$	3.02640e6	−	1.46049e6i	1.80882	−	0.872911i
$61$	1.17540e6	−	2.83767e6i	0.663029	−	1.60069i	−0.130004	−	0.991514i	$-0.541499\pi$
$61$	1.17540e6	−	2.83767e6i	0.663029	−	1.60069i	0.793032	−	0.609179i	$-0.208501\pi$
$62$	235565.	−	375241.i	0.125528	−	0.199958i
$63$	−1.50510e6			−0.758356
$64$	2.04571e6	+	461631.i	0.975472	+	0.220123i
$65$	−1.63432e6			−0.738143
$66$	−280108.	+	446195.i	−0.119928	+	0.191039i
$67$	1.10895e6	−	2.67723e6i	0.450452	−	1.08749i	−0.521698	−	0.853130i	$-0.674701\pi$
$67$	1.10895e6	−	2.67723e6i	0.450452	−	1.08749i	0.972150	−	0.234358i	$-0.0752988\pi$
$68$	−4.20258e6	+	2.02810e6i	−1.62082	+	0.782182i
$69$	−3.40755e6	+	1.41145e6i	−1.24873	+	0.517243i
$70$	3.68010e6	+	5.18212e6i	1.28238	+	1.80578i
$71$	−2.02890e6	+	2.02890e6i	−0.672753	+	0.672753i	−0.958350	−	0.285597i	$-0.907808\pi$
$71$	−2.02890e6	+	2.02890e6i	−0.672753	+	0.672753i	0.285597	+	0.958350i	$0.407808\pi$
$72$	−1.09172e6	−	1.36553e6i	−0.344705	−	0.431158i
$73$	−216388.	−	216388.i	−0.0651033	−	0.0651033i	0.673805	−	0.738909i	$-0.264659\pi$
$73$	−216388.	−	216388.i	−0.0651033	−	0.0651033i	−0.738909	+	0.673805i	$0.764659\pi$
$74$	130383.	−	769289.i	0.0374033	−	0.220688i
$75$	2.78532e6	+	6.72435e6i	0.762360	+	1.84050i
$76$	−329743.	−	5.78688e6i	−0.0861644	−	1.51216i
$77$	−920611.	−	381329.i	−0.229804	−	0.0951881i
$78$	532916.	+	2.33045e6i	0.127153	+	0.556044i
$79$			334646.i			0.0763643i	0.999271	+	0.0381822i	$0.0121567\pi$
$79$			334646.i			0.0763643i	−0.999271	+	0.0381822i	$0.987843\pi$
$80$	−2.03221e6	+	7.09768e6i	−0.443766	+	1.54989i
$81$		−	5.96577e6i		−	1.24729i
$82$	3.34256e6	−	764359.i	0.669470	−	0.153091i
$83$	−3.39903e6	−	1.40792e6i	−0.652501	−	0.270275i	0.0317781	−	0.999495i	$-0.489883\pi$
$83$	−3.39903e6	−	1.40792e6i	−0.652501	−	0.270275i	−0.684279	+	0.729220i	$0.739883\pi$
$84$	6.18942e6	−	6.93741e6i	1.13939	−	1.27708i
$85$	−6.28656e6	−	1.51771e7i	−1.11032	−	2.68054i
$86$	−8.31611e6	−	1.40946e6i	−1.40986	−	0.238950i
$87$	525967.	+	525967.i	0.0856330	+	0.0856330i
$88$	−321795.	−	1.11184e6i	−0.0503374	−	0.173921i
$89$	−6.24441e6	+	6.24441e6i	−0.938915	+	0.938915i	−0.998239	−	0.0593234i	$-0.981106\pi$
$89$	−6.24441e6	+	6.24441e6i	−0.938915	+	0.938915i	0.0593234	+	0.998239i	$0.481106\pi$
$90$	5.01809e6	−	3.56362e6i	0.725588	−	0.515279i
$91$	−4.17747e6	+	1.73037e6i	−0.581124	+	0.240709i
$92$	2.67010e6	−	7.65081e6i	0.357495	−	1.02435i
$93$	873098.	−	2.10784e6i	0.112557	−	0.271737i
$94$	−1.42272e6	−	893139.i	−0.176673	−	0.110910i
$95$	2.04054e7			2.44181
$96$	1.07836e7	+	583428.i	1.24398	+	0.0673036i
$97$	−2.74628e6			−0.305522			−0.152761	−	0.988263i	$-0.548817\pi$
$97$	−2.74628e6			−0.305522			−0.152761	+	0.988263i	$0.548817\pi$
$98$	7.00211e6	+	4.39571e6i	0.751515	+	0.471778i
$99$	−369260.	+	891471.i	−0.0382480	+	0.0923388i
$100$	−1.50979e7	−	5.26909e6i	−1.50979	−	0.526909i
$101$	−1.86824e6	+	773851.i	−0.180430	+	0.0747364i	−0.471069	−	0.882096i	$-0.656132\pi$
$101$	−1.86824e6	+	773851.i	−0.180430	+	0.0747364i	0.290640	+	0.956833i	$0.406132\pi$
$102$	−1.95918e7	+	1.39132e7i	−1.82799	+	1.29815i
$103$	−1.93754e6	+	1.93754e6i	−0.174711	+	0.174711i	−0.789046	−	0.614335i	$-0.789425\pi$
$103$	−1.93754e6	+	1.93754e6i	−0.174711	+	0.174711i	0.614335	+	0.789046i	$0.289425\pi$
$104$	−4.60003e6	−	2.53497e6i	−0.400999	−	0.220981i
$105$	2.31435e7	+	2.31435e7i	1.95104	+	1.95104i
$106$	−1.77974e7	−	3.01640e6i	−1.45140	−	0.245991i
$107$	−3.87505e6	−	9.35521e6i	−0.305798	−	0.738261i	−0.999832	−	0.0183194i	$-0.994168\pi$
$107$	−3.87505e6	−	9.35521e6i	−0.305798	−	0.738261i	0.694034	−	0.719942i	$-0.255832\pi$
$108$	5.45186e6	+	4.86405e6i	0.416449	+	0.371548i
$109$	1.56021e7	+	6.46262e6i	1.15396	+	0.477987i	0.875860	−	0.482565i	$-0.160295\pi$
$109$	1.56021e7	+	6.46262e6i	1.15396	+	0.477987i	0.278102	+	0.960552i	$0.410295\pi$
$110$	3.97225e6	−	908353.i	0.284552	−	0.0650699i
$111$		−	4.01797e6i		−	0.278853i
$112$	2.32027e6	+	2.02939e7i	0.156055	+	1.36491i
$113$			2.58259e7i			1.68376i	0.539664	+	0.841880i	$0.318551\pi$
$113$			2.58259e7i			1.68376i	−0.539664	+	0.841880i	$0.681449\pi$
$114$	−6.65374e6	−	2.90970e7i	−0.420629	−	1.83942i
$115$	2.63558e7	+	1.09169e7i	1.61597	+	0.669357i
$116$	−1.63158e6	+	92969.0i	−0.0970520	+	0.00553013i
$117$	1.67560e6	+	4.04525e6i	0.0967206	+	0.233504i
$118$	−271718.	+	1.60319e6i	−0.0152241	+	0.0898254i
$119$	−3.21380e7	−	3.21380e7i	−1.74825	−	1.74825i
$120$	−4.21025e6	+	3.77845e7i	−0.222420	+	1.99608i
$121$	1.33278e7	−	1.33278e7i	0.683926	−	0.683926i
$122$	2.01203e7	+	2.83323e7i	1.00317	+	1.41261i
$123$	1.63129e7	−	6.75701e6i	0.790428	−	0.327406i
$124$	2.17858e6	+	4.51439e6i	0.102612	+	0.212629i
$125$	8.07100e6	−	1.94851e7i	0.369609	−	0.892315i
$126$	9.05366e6	−	1.44219e7i	0.403206	−	0.642283i
$127$	−3.71712e7			−1.61025			−0.805126	−	0.593104i	$-0.797902\pi$
$127$	−3.71712e7			−1.61025			−0.805126	+	0.593104i	$0.797902\pi$
$128$	−1.67290e7	+	1.68253e7i	−0.705075	+	0.709132i
$129$	−4.34347e7			−1.78145
$130$	9.83098e6	−	1.56602e7i	0.392460	−	0.625165i
$131$	6.92011e6	−	1.67066e7i	0.268945	−	0.649290i	−0.730489	−	0.682924i	$-0.760708\pi$
$131$	6.92011e6	−	1.67066e7i	0.268945	−	0.649290i	0.999434	+	0.0336338i	$0.0107080\pi$
$132$	−2.59052e6	−	5.36802e6i	−0.0980345	−	0.203145i
$133$	5.21580e7	−	2.16045e7i	1.92238	−	0.796277i
$134$	1.89827e7	+	2.67304e7i	0.681541	+	0.959708i
$135$	−1.81877e7	+	1.81877e7i	−0.636222	+	0.636222i
$136$	5.84652e6	−	5.24690e7i	0.199302	−	1.78861i
$137$	1.26375e7	+	1.26375e7i	0.419894	+	0.419894i	0.885167	−	0.465273i	$-0.154044\pi$
$137$	1.26375e7	+	1.26375e7i	0.419894	+	0.419894i	−0.465273	+	0.885167i	$0.654044\pi$
$138$	6.97291e6	−	4.11417e7i	0.225859	−	1.33262i
$139$	8.27113e6	+	1.99683e7i	0.261224	+	0.630651i	0.999015	−	0.0443789i	$-0.0141309\pi$
$139$	8.27113e6	+	1.99683e7i	0.261224	+	0.630651i	−0.737791	+	0.675030i	$0.764131\pi$
$140$	−7.17924e7	+	4.09081e6i	−2.21121	+	0.125997i
$141$	−7.99184e6	−	3.31033e6i	−0.240093	−	0.0994499i
$142$	−7.23652e6	−	3.16455e7i	−0.212090	−	0.927475i
$143$			2.89885e6i			0.0828990i
$144$	1.96516e7	−	2.24683e6i	0.548440	−	0.0627050i
$145$		−	5.75317e6i		−	0.156718i
$146$	3.37509e6	−	771797.i	0.0897532	−	0.0205243i
$147$	3.93330e7	+	1.62923e7i	1.02128	+	0.423030i
$148$	6.58707e6	+	5.87686e6i	0.167023	+	0.149015i
$149$	−1.04310e7	−	2.51826e7i	−0.258329	−	0.623661i	0.740499	−	0.672057i	$-0.234589\pi$
$149$	−1.04310e7	−	2.51826e7i	−0.258329	−	0.623661i	−0.998828	+	0.0483962i	$0.984589\pi$
$150$	−8.11877e7	−	1.37601e7i	−1.96413	−	0.332892i
$151$	−1.70659e7	−	1.70659e7i	−0.403375	−	0.403375i	0.476045	−	0.879421i	$-0.342070\pi$
$151$	−1.70659e7	−	1.70659e7i	−0.403375	−	0.403375i	−0.879421	+	0.476045i	$0.842070\pi$
$152$	5.74338e7	+	3.16504e7i	1.32652	+	0.731016i
$153$	−3.11208e7	+	3.11208e7i	−0.702474	+	0.702474i
$154$	9.19170e6	−	6.52752e6i	0.202802	−	0.144021i
$155$	−1.63032e7	+	6.75299e6i	−0.351650	+	0.145658i
$156$	−2.55362e7	−	8.91202e6i	−0.538543	−	0.187949i
$157$	−1.33479e7	+	3.22246e7i	−0.275273	+	0.664567i	−0.999693	−	0.0247917i	$-0.992108\pi$
$157$	−1.33479e7	+	3.22246e7i	−0.275273	+	0.664567i	0.724420	+	0.689359i	$0.242108\pi$
$158$	−3.20659e6	−	2.01300e6i	−0.0646762	−	0.0406018i
$159$	−9.29554e7			−1.83394
$160$	−5.57859e7	−	6.21676e7i	−1.07672	−	1.19990i
$161$	7.89262e7			1.49050
$162$	5.71644e7	+	3.58861e7i	1.05639	+	0.663168i
$163$	−1.21292e7	+	2.92824e7i	−0.219369	+	0.529603i	−0.994802	−	0.101826i	$-0.967531\pi$
$163$	−1.21292e7	+	2.92824e7i	−0.219369	+	0.529603i	0.775433	+	0.631429i	$0.217531\pi$
$164$	−1.27825e7	+	3.66265e7i	−0.226288	+	0.648398i
$165$	1.93859e7	−	8.02992e6i	0.335964	−	0.139161i
$166$	3.39371e7	−	2.41005e7i	0.575832	−	0.408930i
$167$	−5.07074e7	+	5.07074e7i	−0.842488	+	0.842488i	−0.989182	−	0.146694i	$-0.953137\pi$
$167$	−5.07074e7	+	5.07074e7i	−0.842488	+	0.842488i	0.146694	+	0.989182i	$0.453137\pi$
$168$	2.92432e7	+	1.01038e8i	0.475819	+	1.64400i
$169$	−3.50685e7	−	3.50685e7i	−0.558874	−	0.558874i
$170$	1.83243e8	+	3.10570e7i	2.86060	+	0.484829i
$171$	−2.09207e7	−	5.05071e7i	−0.319956	−	0.772442i
$172$	6.35296e7	−	7.12071e7i	0.951978	−	1.06702i
$173$	−5.39177e7	−	2.23334e7i	−0.791717	−	0.327940i	−0.0500835	−	0.998745i	$-0.515949\pi$
$173$	−5.39177e7	−	2.23334e7i	−0.791717	−	0.327940i	−0.741634	+	0.670805i	$0.765949\pi$
$174$	−8.20371e6	+	1.87598e6i	−0.118056	+	0.0269964i
$175$		−	1.55751e8i		−	2.19683i
$176$	1.25894e7	+	3.60460e6i	0.174064	+	0.0498382i
$177$			8.37342e6i			0.113500i
$178$	−2.22721e7	−	9.73965e7i	−0.296000	−	1.29441i
$179$	−2.61434e7	−	1.08289e7i	−0.340703	−	0.141124i	0.205770	−	0.978600i	$-0.434030\pi$
$179$	−2.61434e7	−	1.08289e7i	−0.340703	−	0.141124i	−0.546473	+	0.837477i	$0.684030\pi$
$180$	3.96132e6	+	6.95200e7i	0.0506275	+	0.888497i
$181$	2.84426e7	+	6.86665e7i	0.356528	+	0.860736i	0.995783	+	0.0917404i	$0.0292430\pi$
$181$	2.84426e7	+	6.86665e7i	0.356528	+	0.860736i	−0.639255	+	0.768995i	$0.720757\pi$
$182$	8.54841e6	−	5.04375e7i	0.105108	−	0.620160i
$183$	1.26533e8	+	1.26533e8i	1.52625	+	1.52625i
$184$	5.72490e7	+	7.16072e7i	0.677494	+	0.847411i
$185$	−2.19748e7	+	2.19748e7i	−0.255167	+	0.255167i
$186$	1.49455e7	+	2.10454e7i	0.170300	+	0.239808i
$187$	−2.69201e7	+	1.11507e7i	−0.301045	+	0.124697i
$188$	1.71162e7	−	8.26002e6i	0.187869	−	0.0906627i
$189$	−2.72328e7	+	6.57458e7i	−0.293411	+	0.708357i
$190$	−1.22745e8	+	1.95525e8i	−1.29827	+	2.06807i
$191$	−4.14764e7			−0.430710			−0.215355	−	0.976536i	$-0.569091\pi$
$191$	−4.14764e7			−0.430710			−0.215355	+	0.976536i	$0.569091\pi$
$192$	−7.04571e7	+	9.98192e7i	−0.718407	+	1.01779i
$193$	−3.83582e7			−0.384067			−0.192034	−	0.981388i	$-0.561508\pi$
$193$	−3.83582e7			−0.384067			−0.192034	+	0.981388i	$0.561508\pi$
$194$	1.65198e7	−	2.63150e7i	0.162442	−	0.258760i
$195$	3.64375e7	−	8.79680e7i	0.351907	−	0.849579i
$196$	−8.42399e7	+	4.06529e7i	−0.799138	+	0.385652i
$197$	9.91070e7	−	4.10514e7i	0.923575	−	0.382557i	0.130338	−	0.991470i	$-0.458394\pi$
$197$	9.91070e7	−	4.10514e7i	0.923575	−	0.382557i	0.793238	+	0.608912i	$0.208394\pi$
$198$	−6.32091e6	−	8.90076e6i	−0.0578697	−	0.0814890i
$199$	3.85414e7	−	3.85414e7i	0.346690	−	0.346690i	−0.512185	−	0.858875i	$-0.671164\pi$
$199$	3.85414e7	−	3.85414e7i	0.346690	−	0.346690i	0.858875	+	0.512185i	$0.171164\pi$
$200$	1.41307e8	−	1.12973e8i	1.24899	−	0.998553i
$201$	1.19379e8	+	1.19379e8i	1.03691	+	1.03691i
$202$	3.82300e6	−	2.25566e7i	0.0326343	−	0.192550i
$203$	−6.09127e6	−	1.47056e7i	−0.0511060	−	0.123381i
$204$	−1.54659e7	−	2.71422e8i	−0.127547	−	2.23841i
$205$	−1.26172e8	−	5.22622e7i	−1.02288	−	0.423691i
$206$	−6.91068e6	−	3.02206e7i	−0.0550789	−	0.240861i
$207$		−	7.64281e7i		−	0.598903i
$208$	5.19609e7	−	2.88291e7i	0.400364	−	0.222131i
$209$		−	3.61937e7i		−	0.274234i
$210$	−3.60978e8	+	8.25466e7i	−2.68976	+	0.615080i
$211$	1.60823e8	+	6.66153e7i	1.17858	+	0.488186i	0.884022	−	0.467446i	$-0.154826\pi$
$211$	1.60823e8	+	6.66153e7i	1.17858	+	0.488186i	0.294563	+	0.955632i	$0.404826\pi$
$212$	1.35961e8	−	1.52391e8i	0.980028	−	1.09846i
$213$	−6.39715e7	−	1.54441e8i	−0.453584	−	1.09505i
$214$	1.12952e8	+	1.91437e7i	0.787853	+	0.133529i
$215$	2.37550e8	+	2.37550e8i	1.63012	+	1.63012i
$216$	−7.94023e7	+	2.29812e7i	−0.536099	+	0.155161i
$217$	−3.45225e7	+	3.45225e7i	−0.229347	+	0.229347i
$218$	−1.55777e8	+	1.10626e8i	−1.01837	+	0.723201i
$219$	1.64716e7	−	6.82275e6i	0.105970	−	0.0438940i
$220$	−1.51905e7	+	4.35264e7i	−0.0961817	+	0.275596i
$221$	−5.05986e7	+	1.22156e8i	−0.315330	+	0.761275i
$222$	3.85004e7	+	2.41694e7i	0.236173	+	0.148262i
$223$	−4.17193e7			−0.251924			−0.125962	−	0.992035i	$-0.540202\pi$
$223$	−4.17193e7			−0.251924			−0.125962	+	0.992035i	$0.540202\pi$
$224$	−2.08415e8	−	9.98418e7i	−1.23897	−	0.593532i
$225$	−1.50821e8			−0.882719
$226$	−2.47465e8	−	1.55351e8i	−1.42605	−	0.895230i
$227$	−4.68363e7	+	1.13073e8i	−0.265761	+	0.641605i	−0.999275	−	0.0380698i	$-0.987879\pi$
$227$	−4.68363e7	+	1.13073e8i	−0.265761	+	0.641605i	0.733514	+	0.679675i	$0.237879\pi$
$228$	3.18833e8	+	1.11271e8i	1.78152	+	0.621744i
$229$	2.35252e8	−	9.74446e7i	1.29452	−	0.536208i	0.374191	−	0.927352i	$-0.377920\pi$
$229$	2.35252e8	−	9.74446e7i	1.29452	−	0.536208i	0.920330	+	0.391143i	$0.127920\pi$
$230$	−2.63145e8	+	1.86874e8i	−1.42609	+	1.01275i
$231$	4.10504e7	−	4.10504e7i	0.219117	−	0.219117i
$232$	8.92364e6	−	1.61931e7i	0.0469174	−	0.0851377i
$233$	−1.64512e8	−	1.64512e8i	−0.852025	−	0.852025i	0.138358	−	0.990382i	$-0.455818\pi$
$233$	−1.64512e8	−	1.64512e8i	−0.852025	−	0.852025i	−0.990382	+	0.138358i	$0.955818\pi$
$234$	−4.88411e7	−	8.27784e6i	−0.249189	−	0.0422339i
$235$	2.56038e7	+	6.18131e7i	0.128697	+	0.310701i
$236$	−1.37274e7	−	1.22474e7i	−0.0679825	−	0.0606527i
$237$	−1.80124e7	−	7.46100e6i	−0.0878928	−	0.0364064i
$238$	5.01269e8	−	1.14628e8i	2.41019	−	0.551150i
$239$		−	1.41157e8i		−	0.668822i	−0.942427	−	0.334411i	$-0.891463\pi$
$239$		−	1.41157e8i		−	0.668822i	0.942427	−	0.334411i	$-0.108537\pi$
$240$	−3.36727e8	−	2.67629e8i	−1.57231	−	1.24966i
$241$		−	1.24529e8i		−	0.573073i	−0.958069	−	0.286536i	$-0.907496\pi$
$241$		−	1.24529e8i		−	0.573073i	0.958069	−	0.286536i	$-0.0925039\pi$
$242$	4.75366e7	+	2.07879e8i	0.215613	+	0.942879i
$243$	2.05778e8	+	8.52361e7i	0.919977	+	0.381067i
$244$	−3.92512e8	+	2.23658e7i	−1.72977	+	0.0985642i
$245$	−1.26013e8	−	3.04222e8i	−0.547437	−	1.32163i
$246$	−3.33812e7	+	1.96956e8i	−0.142965	+	0.843523i
$247$	−1.16133e8	−	1.16133e8i	−0.490361	−	0.490361i
$248$	−5.63620e7	−	6.28031e6i	−0.234642	−	0.0261457i
$249$	1.51564e8	−	1.51564e8i	0.622155	−	0.622155i
$250$	1.38158e8	+	1.94546e8i	0.559224	+	0.787468i
$251$	−3.84859e8	+	1.59414e8i	−1.53618	+	0.636309i	−0.980753	−	0.195253i	$-0.937447\pi$
$251$	−3.84859e8	+	1.59414e8i	−1.53618	+	0.636309i	−0.555432	+	0.831562i	$0.687447\pi$
$252$	8.37311e7	+	1.73505e8i	0.329598	+	0.682985i
$253$	1.93637e7	−	4.67481e7i	0.0751738	−	0.181486i
$254$	2.23597e8	−	3.56177e8i	0.856147	−	1.36379i
$255$	9.57073e8			3.61455
$256$	−6.05902e7	−	2.61508e8i	−0.225716	−	0.974193i
$257$	−1.39826e8			−0.513832			−0.256916	−	0.966434i	$-0.582706\pi$
$257$	−1.39826e8			−0.513832			−0.256916	+	0.966434i	$0.582706\pi$
$258$	2.61274e8	−	4.16194e8i	0.947169	−	1.50878i
$259$	−3.29034e7	+	7.94358e7i	−0.117677	+	0.284097i
$260$	9.09199e7	+	1.88402e8i	0.320813	+	0.664781i
$261$	−1.42402e7	+	5.89847e6i	−0.0495762	+	0.0205351i
$262$	1.18457e8	+	1.66805e8i	0.406917	+	0.572999i
$263$	−2.64185e8	+	2.64185e8i	−0.895494	+	0.895494i	−0.995034	−	0.0995397i	$-0.968263\pi$
$263$	−2.64185e8	+	2.64185e8i	−0.895494	+	0.895494i	0.0995397	+	0.995034i	$0.468263\pi$
$264$	6.70195e7	+	7.46786e6i	0.224175	+	0.0249794i
$265$	5.08385e8	+	5.08385e8i	1.67816	+	1.67816i
$266$	−1.06731e8	+	6.29739e8i	−0.347702	+	2.05152i
$267$	−1.96888e8	−	4.75329e8i	−0.633037	−	1.52829i
$268$	−3.70320e8	+	2.11012e7i	−1.17518	+	0.0669631i
$269$	−2.96246e8	−	1.22709e8i	−0.927939	−	0.384365i	−0.133043	−	0.991110i	$-0.542475\pi$
$269$	−2.96246e8	−	1.22709e8i	−0.927939	−	0.384365i	−0.794896	+	0.606745i	$0.792475\pi$
$270$	−6.48704e7	−	2.83680e8i	−0.200574	−	0.877113i
$271$			2.80251e8i			0.855372i	0.903927	+	0.427686i	$0.140671\pi$
$271$			2.80251e8i			0.855372i	−0.903927	+	0.427686i	$0.859329\pi$
$272$	4.67592e8	+	3.71640e8i	1.40889	+	1.11978i
$273$		−	2.63433e8i		−	0.783612i
$274$	−1.97112e8	+	4.50746e7i	−0.578877	+	0.132375i
$275$	−9.22512e7	−	3.82117e7i	−0.267490	−	0.110798i
$276$	3.52278e8	+	3.14296e8i	1.00856	+	0.899822i
$277$	2.51446e8	+	6.07043e8i	0.710829	+	1.71609i	0.697920	+	0.716176i	$0.254109\pi$
$277$	2.51446e8	+	6.07043e8i	0.710829	+	1.71609i	0.0129084	+	0.999917i	$0.495891\pi$
$278$	−2.41091e8	−	4.08613e7i	−0.673014	−	0.114066i
$279$	3.34298e7	+	3.34298e7i	0.0921551	+	0.0921551i
$280$	3.92657e8	−	7.12526e8i	1.06896	−	1.93976i
$281$	3.09654e8	−	3.09654e8i	0.832539	−	0.832539i	−0.155325	−	0.987863i	$-0.549642\pi$
$281$	3.09654e8	−	3.09654e8i	0.832539	−	0.832539i	0.987863	+	0.155325i	$0.0496423\pi$
$282$	7.97933e7	−	5.66656e7i	0.211882	−	0.150469i
$283$	−2.67045e8	+	1.10614e8i	−0.700377	+	0.290106i	−0.704316	−	0.709886i	$-0.748746\pi$
$283$	−2.67045e8	+	1.10614e8i	−0.700377	+	0.290106i	0.00393880	+	0.999992i	$0.498746\pi$
$284$	3.46759e8	+	1.21017e8i	0.898283	+	0.313497i
$285$	−4.54942e8	+	1.09833e9i	−1.16412	+	2.81044i
$286$	−2.77769e7	−	1.74375e7i	−0.0702107	−	0.0440762i
$287$	−3.77841e8			−0.943458
$288$	−9.66816e7	+	2.01818e8i	−0.238490	+	0.497836i
$289$	−9.18691e8			−2.23886
$290$	5.51272e7	+	3.46072e7i	0.132731	+	0.0833246i
$291$	6.12288e7	−	1.47819e8i	0.145657	−	0.351646i
$292$	−1.29069e7	+	3.69829e7i	−0.0303375	+	0.0869282i
$293$	−4.26790e8	+	1.76782e8i	−0.991238	+	0.410584i	−0.818577	−	0.574397i	$-0.805237\pi$
$293$	−4.26790e8	+	1.76782e8i	−0.991238	+	0.410584i	−0.172661	+	0.984981i	$0.555237\pi$
$294$	−3.92715e8	+	2.78888e8i	−0.901283	+	0.640050i
$295$	4.57954e7	−	4.57954e7i	0.103859	−	0.103859i
$296$	−9.59359e7	+	2.77664e7i	−0.215011	+	0.0622299i
$297$	3.22601e7	+	3.22601e7i	0.0714525	+	0.0714525i
$298$	3.04047e8	+	5.15314e7i	0.665554	+	0.112802i
$299$	−8.78670e7	−	2.12130e8i	−0.190098	−	0.458936i
$300$	6.20221e8	−	6.95174e8i	1.32624	−	1.48651i
$301$	8.58711e8	+	3.55690e8i	1.81495	+	0.751776i
$302$	2.66183e8	−	6.08694e7i	0.556104	−	0.127167i
$303$		−	1.17812e8i		−	0.243299i
$304$	−6.48759e8	+	3.59946e8i	−1.32442	+	0.734818i
$305$		−	1.38405e9i		−	2.79321i
$306$	−1.10999e8	−	4.85403e8i	−0.221460	−	0.968450i
$307$	3.40670e8	+	1.41110e8i	0.671969	+	0.278339i	0.692465	−	0.721451i	$-0.256525\pi$
$307$	3.40670e8	+	1.41110e8i	0.671969	+	0.278339i	−0.0204961	+	0.999790i	$0.506525\pi$
$308$	7.25600e6	+	1.27341e8i	0.0141504	+	0.248336i
$309$	−6.10910e7	−	1.47487e8i	−0.117794	−	0.284380i
$310$	3.33614e7	−	1.96839e8i	0.0636030	−	0.375272i
$311$	4.62293e7	+	4.62293e7i	0.0871477	+	0.0871477i	0.749337	−	0.662189i	$-0.230372\pi$
$311$	4.62293e7	+	4.62293e7i	0.0871477	+	0.0871477i	−0.662189	+	0.749337i	$0.730372\pi$
$312$	2.39004e8	−	1.91081e8i	0.445517	−	0.356185i
$313$	2.41271e8	−	2.41271e8i	0.444734	−	0.444734i	−0.448865	−	0.893600i	$-0.648172\pi$
$313$	2.41271e8	−	2.41271e8i	0.444734	−	0.444734i	0.893600	+	0.448865i	$0.148172\pi$
$314$	−2.28486e8	−	3.21742e8i	−0.416492	−	0.586481i
$315$	−6.26594e8	+	2.59544e8i	−1.12953	+	0.467868i
$316$	3.85774e7	−	1.86169e7i	0.0687747	−	0.0331896i
$317$	−9.08553e7	+	2.19344e8i	−0.160193	+	0.386739i	−0.983513	−	0.180838i	$-0.942119\pi$
$317$	−9.08553e7	+	2.19344e8i	−0.160193	+	0.386739i	0.823320	+	0.567577i	$0.192119\pi$
$318$	5.59157e8	−	8.90704e8i	0.975077	−	1.55324i
$319$	−1.02046e7			−0.0176006
$320$	9.31264e8	−	1.60585e8i	1.58872	−	0.273956i
$321$	5.89943e8			0.995503
$322$	−4.74767e8	+	7.56276e8i	−0.792474	+	1.26236i
$323$	6.31751e8	−	1.52518e9i	1.04313	−	2.51833i
$324$	−6.87725e8	+	3.31886e8i	−1.12333	+	0.542102i
$325$	−4.18610e8	+	1.73394e8i	−0.676423	+	0.280183i
$326$	−2.07625e8	−	2.92366e8i	−0.331908	−	0.467375i
$327$	−6.95707e8	+	6.95707e8i	−1.10029	+	1.10029i
$328$	−2.74066e8	−	3.42803e8i	−0.428842	−	0.536397i
$329$	1.30891e8	+	1.30891e8i	0.202640	+	0.202640i
$330$	−3.96697e7	+	2.34060e8i	−0.0607659	+	0.358532i
$331$	2.41221e7	+	5.82360e7i	0.0365610	+	0.0882660i	0.941105	−	0.338114i	$-0.109789\pi$
$331$	2.41221e7	+	5.82360e7i	0.0365610	+	0.0882660i	−0.904544	+	0.426380i	$0.859789\pi$
$332$	2.67902e7	+	4.70160e8i	0.0401784	+	0.705118i
$333$	7.69215e7	+	3.18619e7i	0.114154	+	0.0472843i
$334$	−1.80860e8	−	7.90903e8i	−0.265600	−	1.16148i
$335$		−	1.30580e9i		−	1.89767i
$336$	−1.14406e9	−	3.27568e8i	−1.64536	−	0.471101i
$337$		−	3.01452e8i		−	0.429056i	−0.976718	−	0.214528i	$-0.931179\pi$
$337$		−	3.01452e8i		−	0.429056i	0.976718	−	0.214528i	$-0.0688213\pi$
$338$	5.46977e8	−	1.25080e8i	0.770479	−	0.176189i
$339$	−1.39009e9	−	5.75793e8i	−1.93795	−	0.802727i
$340$	−1.39986e9	+	1.56903e9i	−1.93156	+	2.16499i
$341$	1.19780e7	+	2.89175e7i	0.0163585	+	0.0394930i
$342$	6.09807e8	+	1.03353e8i	0.824330	+	0.139712i
$343$	8.18009e7	+	8.18009e7i	0.109453	+	0.109453i
$344$	3.00159e8	+	1.03708e9i	0.397554	+	1.37359i
$345$	−1.17522e9	+	1.17522e9i	−1.54082	+	1.54082i
$346$	5.38333e8	−	3.82300e8i	0.698690	−	0.496178i
$347$	−7.59083e8	+	3.14422e8i	−0.975295	+	0.403980i	−0.812681	−	0.582709i	$-0.801993\pi$
$347$	−7.59083e8	+	3.14422e8i	−0.975295	+	0.403980i	−0.162614	+	0.986690i	$0.551993\pi$
$348$	3.13723e7	−	8.98930e7i	0.0399042	−	0.114340i
$349$	1.38071e7	−	3.33333e7i	0.0173866	−	0.0419748i	−0.914948	−	0.403572i	$-0.867768\pi$
$349$	1.38071e7	−	3.33333e7i	0.0173866	−	0.0419748i	0.932334	+	0.361597i	$0.117768\pi$
$350$	1.49241e9	+	9.36891e8i	1.86059	+	1.16802i
$351$	2.07023e8			0.255531
$352$	−1.10269e8	+	9.89493e7i	−0.134758	+	0.120924i
$353$	1.22131e9			1.47779			0.738896	−	0.673819i	$-0.235347\pi$
$353$	1.22131e9			1.47779			0.738896	+	0.673819i	$0.235347\pi$
$354$	−8.02346e7	−	5.03689e7i	−0.0961281	−	0.0603463i
$355$	−4.94789e8	+	1.19453e9i	−0.586977	+	1.41709i
$356$	1.06723e9	+	3.72459e8i	1.25367	+	0.437526i
$357$	2.44637e9	−	1.01332e9i	2.84566	−	1.17871i
$358$	2.61024e8	−	1.85368e8i	0.300670	−	0.213522i
$359$	−2.48924e8	+	2.48924e8i	−0.283946	+	0.283946i	−0.834680	−	0.550735i	$-0.814348\pi$
$359$	−2.48924e8	+	2.48924e8i	−0.283946	+	0.283946i	0.550735	+	0.834680i	$0.314348\pi$
$360$	−6.89973e8	−	3.80228e8i	−0.779424	−	0.429522i
$361$	8.17919e8	+	8.17919e8i	0.915030	+	0.915030i
$362$	−8.29058e8	−	1.40513e8i	−0.918554	−	0.155681i
$363$	4.20228e8	+	1.01452e9i	0.461117	+	1.11324i
$364$	4.31874e8	+	3.85310e8i	0.469355	+	0.418750i
$365$	−1.27400e8	−	5.27708e7i	−0.137134	−	0.0568026i
$366$	−1.97359e9	+	4.51309e8i	−2.10413	+	0.481161i
$367$		−	1.15385e9i		−	1.21848i	−0.792986	−	0.609239i	$-0.791475\pi$
$367$		−	1.15385e9i		−	1.21848i	0.792986	−	0.609239i	$-0.208525\pi$
$368$	−1.03052e9	+	1.17822e8i	−1.07792	+	0.123242i
$369$			3.65882e8i			0.379095i
$370$	−7.83781e7	−	3.42749e8i	−0.0804431	−	0.351780i
$371$	1.83774e9	+	7.61218e8i	1.86843	+	0.773927i
$372$	−2.91561e8	+	1.66134e7i	−0.293649	+	0.0167324i
$373$	3.66026e8	+	8.83665e8i	0.365200	+	0.881671i	0.994522	+	0.104526i	$0.0333327\pi$
$373$	3.66026e8	+	8.83665e8i	0.365200	+	0.881671i	−0.629322	+	0.777145i	$0.716667\pi$
$374$	5.50869e7	−	3.25025e8i	0.0544500	−	0.321267i
$375$	8.68850e8	+	8.68850e8i	0.850816	+	0.850816i
$376$	−2.38116e7	+	2.13695e8i	−0.0231011	+	0.207318i
$377$	−3.27430e7	+	3.27430e7i	−0.0314719	+	0.0314719i
$378$	−4.66166e8	−	6.56429e8i	−0.443935	−	0.625125i
$379$	5.10376e8	−	2.11405e8i	0.481563	−	0.199470i	−0.128677	−	0.991687i	$-0.541073\pi$
$379$	5.10376e8	−	2.11405e8i	0.481563	−	0.199470i	0.610240	+	0.792217i	$0.291073\pi$
$380$	−1.13518e9	−	2.35230e9i	−1.06126	−	2.19913i
$381$	8.28740e8	−	2.00076e9i	0.767681	−	1.85335i
$382$	2.49494e8	−	3.97429e8i	0.229002	−	0.364786i
$383$	−2.41587e8			−0.219724			−0.109862	−	0.993947i	$-0.535041\pi$
$383$	−2.41587e8			−0.219724			−0.109862	+	0.993947i	$0.535041\pi$
$384$	−5.32650e8	−	1.27557e9i	−0.480046	−	1.14960i
$385$	−4.49021e8			−0.401009
$386$	2.30737e8	−	3.67550e8i	0.204203	−	0.325283i
$387$	3.44431e8	−	8.31531e8i	0.302075	−	0.729273i
$388$	1.52780e8	+	3.16586e8i	0.132787	+	0.275157i
$389$	−1.16547e9	+	4.82752e8i	−1.00387	+	0.415816i	−0.823214	−	0.567731i	$-0.807821\pi$
$389$	−1.16547e9	+	4.82752e8i	−1.00387	+	0.415816i	−0.180654	+	0.983547i	$0.557821\pi$
$390$	6.23731e8	+	8.78303e8i	0.532440	+	0.749753i
$391$	1.63195e9	−	1.63195e9i	1.38067	−	1.38067i
$392$	1.17193e8	−	1.05173e9i	0.0982649	−	0.881869i
$393$	7.44955e8	+	7.44955e8i	0.619093	+	0.619093i
$394$	−2.02804e8	+	1.19659e9i	−0.167047	+	0.985615i
$395$	5.77073e7	+	1.39318e8i	0.0471130	+	0.113741i
$396$	1.23310e8	−	7.02633e6i	0.0997849	−	0.00568585i
$397$	−1.58501e9	−	6.56533e8i	−1.27135	−	0.526611i	−0.357976	−	0.933731i	$-0.616533\pi$
$397$	−1.58501e9	−	6.56533e8i	−1.27135	−	0.526611i	−0.913375	+	0.407120i	$0.866533\pi$
$398$	1.37467e8	+	6.01145e8i	0.109297	+	0.477957i
$399$			3.28910e9i			2.59222i
$400$	2.32507e8	+	2.03359e9i	0.181646	+	1.58874i
$401$			1.36037e9i			1.05354i	0.850006	+	0.526772i	$0.176598\pi$
$401$			1.36037e9i			1.05354i	−0.850006	+	0.526772i	$0.823402\pi$
$402$	−1.86200e9	+	4.25793e8i	−1.42952	+	0.326894i
$403$	1.31219e8	+	5.43529e7i	0.0998689	+	0.0413671i
$404$	1.93142e8	+	1.72317e8i	0.145727	+	0.130015i
$405$	−1.02876e9	−	2.48363e9i	−0.769519	−	1.85778i
$406$	1.77551e8	+	3.00923e7i	0.131669	+	0.0223159i
$407$	3.89774e7	+	3.89774e7i	0.0286571	+	0.0286571i
$408$	2.69382e9	+	1.48450e9i	1.96362	+	1.08210i
$409$	9.41366e8	−	9.41366e8i	0.680341	−	0.680341i	−0.279736	−	0.960077i	$-0.590247\pi$
$409$	9.41366e8	−	9.41366e8i	0.680341	−	0.680341i	0.960077	+	0.279736i	$0.0902468\pi$
$410$	1.25975e9	−	8.94615e8i	0.902693	−	0.641051i
$411$	−9.61976e8	+	3.98463e8i	−0.683467	+	0.283101i
$412$	3.31145e8	+	1.15568e8i	0.233280	+	0.0814138i
$413$	6.85705e7	−	1.65544e8i	0.0478974	−	0.115635i
$414$	7.32338e8	+	4.59740e8i	0.507236	+	0.318428i
$415$	−1.65785e9			−1.13861
$416$	−3.63201e7	+	6.71308e8i	−0.0247355	+	0.457188i
$417$	−1.25921e9			−0.850396
$418$	3.46810e8	+	2.17717e8i	0.232260	+	0.145806i
$419$	−4.23961e8	+	1.02353e9i	−0.281564	+	0.679755i	−0.999872	−	0.0159692i	$-0.994917\pi$
$419$	−4.23961e8	+	1.02353e9i	−0.281564	+	0.679755i	0.718309	+	0.695725i	$0.244917\pi$
$420$	1.38044e9	−	3.95546e9i	0.909168	−	2.60510i
$421$	1.83686e8	−	7.60854e7i	0.119975	−	0.0496951i	−0.321889	−	0.946778i	$-0.604318\pi$
$421$	1.83686e8	−	7.60854e7i	0.119975	−	0.0496951i	0.441863	+	0.897082i	$0.354318\pi$
$422$	−1.60572e9	+	1.14031e9i	−1.04010	+	0.738632i
$423$	1.26748e8	−	1.26748e8i	0.0814238	−	0.0814238i
$424$	6.42374e8	+	2.21947e9i	0.409268	+	1.41406i
$425$	−3.22044e9	−	3.22044e9i	−2.03495	−	2.03495i
$426$	1.86467e9	+	3.16034e8i	1.16861	+	0.198062i
$427$	−1.46539e9	−	3.53777e9i	−0.910869	−	2.19903i
$428$	−8.62878e8	+	9.67155e8i	−0.531981	+	0.596270i
$429$	−1.56032e8	−	6.46305e7i	−0.0954141	−	0.0395218i
$430$	−3.70516e9	+	8.47277e8i	−2.24733	+	0.513908i
$431$		−	3.01258e9i		−	1.81246i	−0.422788	−	0.906228i	$-0.638949\pi$
$431$		−	3.01258e9i		−	1.81246i	0.422788	−	0.906228i	$-0.361051\pi$
$432$	2.57424e8	−	8.99076e8i	0.153623	−	0.536542i
$433$			2.62662e9i			1.55485i	0.628974	+	0.777426i	$0.283475\pi$
$433$			2.62662e9i			1.55485i	−0.628974	+	0.777426i	$0.716525\pi$
$434$	−1.23132e8	−	5.38461e8i	−0.0723034	−	0.316184i
$435$	3.09667e8	+	1.28268e8i	0.180377	+	0.0747147i
$436$	−1.22972e8	−	2.15812e9i	−0.0710564	−	1.24702i
$437$	1.09707e9	+	2.64855e9i	0.628851	+	1.51818i
$438$	−3.37060e7	+	1.98873e8i	−0.0191667	+	0.113088i
$439$	−9.89956e8	−	9.89956e8i	−0.558457	−	0.558457i	0.370411	−	0.928868i	$-0.379217\pi$
$439$	−9.89956e8	−	9.89956e8i	−0.558457	−	0.558457i	−0.928868	+	0.370411i	$0.879217\pi$
$440$	−3.25696e8	−	4.07382e8i	−0.182275	−	0.227991i
$441$	−6.23811e8	+	6.23811e8i	−0.346352	+	0.346352i
$442$	−8.66137e8	−	1.21965e9i	−0.477099	−	0.671825i
$443$	2.62239e9	−	1.08623e9i	1.43313	−	0.593621i	0.475006	−	0.879982i	$-0.342446\pi$
$443$	2.62239e9	−	1.08623e9i	1.43313	−	0.593621i	0.958122	+	0.286361i	$0.0924458\pi$
$444$	−4.63185e8	+	2.23526e8i	−0.251139	+	0.121196i
$445$	−1.52283e9	+	3.67644e9i	−0.819203	+	1.97773i
$446$	2.50955e8	−	3.99757e8i	0.133944	−	0.213365i
$447$	1.58802e9			0.840970
$448$	2.21037e9	−	1.39646e9i	1.16143	−	0.733764i
$449$	−5.42432e8			−0.282802			−0.141401	−	0.989952i	$-0.545161\pi$
$449$	−5.42432e8			−0.282802			−0.141401	+	0.989952i	$0.545161\pi$
$450$	9.07237e8	−	1.44517e9i	0.469328	−	0.747612i
$451$	−9.26993e7	+	2.23796e8i	−0.0475837	+	0.114877i
$452$	2.97717e9	−	1.43673e9i	1.51642	−	0.731799i
$453$	1.29907e9	−	5.38091e8i	0.656580	−	0.271964i
$454$	−8.01734e8	−	1.12896e9i	−0.402101	−	0.566216i
$455$	−1.44075e9	+	1.44075e9i	−0.717050	+	0.717050i
$456$	−2.98409e9	+	2.38574e9i	−1.47379	+	1.17828i
$457$	8.36612e8	+	8.36612e8i	0.410032	+	0.410032i	0.881750	−	0.471718i	$-0.156366\pi$
$457$	8.36612e8	+	8.36612e8i	0.410032	+	0.410032i	−0.471718	+	0.881750i	$0.656366\pi$
$458$	−4.81399e8	+	2.84036e9i	−0.234140	+	1.38148i
$459$	7.96330e8	+	1.92251e9i	0.384369	+	0.927950i
$460$	−2.07729e8	−	3.64558e9i	−0.0995049	−	1.74628i
$461$	−1.44153e9	−	5.97100e8i	−0.685282	−	0.283853i	0.0127510	−	0.999919i	$-0.495941\pi$
$461$	−1.44153e9	−	5.97100e8i	−0.685282	−	0.283853i	−0.698033	+	0.716066i	$0.745941\pi$
$462$	1.46416e8	+	6.40279e8i	0.0690782	+	0.302080i
$463$			2.90661e9i			1.36099i	0.732754	+	0.680493i	$0.238234\pi$
$463$			2.90661e9i			1.36099i	−0.732754	+	0.680493i	$0.761766\pi$
$464$	1.01485e8	+	1.82914e8i	0.0471614	+	0.0850028i
$465$		−	1.02808e9i		−	0.474180i
$466$	2.56596e9	−	5.86770e8i	1.17462	−	0.268607i
$467$	−5.10399e8	−	2.11414e8i	−0.231900	−	0.0960560i	0.263708	−	0.964603i	$-0.415055\pi$
$467$	−5.10399e8	−	2.11414e8i	−0.231900	−	0.0960560i	−0.495608	+	0.868547i	$0.665055\pi$
$468$	3.73114e8	−	4.18204e8i	0.168260	−	0.188594i
$469$	−1.38254e9	−	3.33774e9i	−0.618832	−	1.49399i
$470$	−7.46312e8	−	1.26489e8i	−0.331572	−	0.0561966i
$471$	−1.43691e9	−	1.43691e9i	−0.633660	−	0.633660i
$472$	1.99930e8	−	5.78651e7i	0.0875146	−	0.0253291i
$473$	4.21351e8	−	4.21351e8i	0.183075	−	0.183075i
$474$	1.79843e8	−	1.27716e8i	0.0775654	−	0.0550834i
$475$	5.22657e9	−	2.16492e9i	2.23764	−	0.926859i
$476$	−1.91693e9	+	5.49271e9i	−0.814671	+	2.33433i
$477$	7.37123e8	−	1.77957e9i	0.310975	−	0.750761i
$478$	1.35258e9	+	8.49108e8i	0.566454	+	0.355603i
$479$	−2.78085e9			−1.15612			−0.578061	−	0.815994i	$-0.696190\pi$
$479$	−2.78085e9			−1.15612			−0.578061	+	0.815994i	$0.696190\pi$
$480$	4.58996e9	−	1.61666e9i	1.89437	−	0.667228i
$481$	2.50130e8			0.102484
$482$	1.19324e9	+	7.49081e8i	0.485359	+	0.304694i
$483$	−1.75968e9	+	4.24824e9i	−0.710588	+	1.71551i
$484$	−2.27785e9	−	7.94960e8i	−0.913202	−	0.318703i
$485$	−1.14331e9	+	4.73576e8i	−0.455060	+	0.188492i
$486$	−2.05456e9	+	1.45905e9i	−0.811880	+	0.576560i
$487$	−1.03981e9	+	1.03981e9i	−0.407947	+	0.407947i	−0.881022	−	0.473075i	$-0.843144\pi$
$487$	−1.03981e9	+	1.03981e9i	−0.407947	+	0.407947i	0.473075	+	0.881022i	$0.343144\pi$
$488$	2.14678e9	−	3.89561e9i	0.836215	−	1.51742i
$489$	−1.30572e9	−	1.30572e9i	−0.504973	−	0.504973i
$490$	3.67308e9	+	6.22533e8i	1.41041	+	0.239043i
$491$	1.72322e9	+	4.16023e9i	0.656986	+	1.58611i	0.802435	+	0.596740i	$0.203537\pi$
$491$	1.72322e9	+	4.16023e9i	0.656986	+	1.58611i	−0.145449	+	0.989366i	$0.546463\pi$
$492$	−1.68645e9	−	1.50462e9i	−0.638403	−	0.569572i
$493$	−4.30015e8	−	1.78118e8i	−0.161629	−	0.0669490i
$494$	1.81137e9	−	4.14215e8i	0.676025	−	0.154590i
$495$			4.34808e8i			0.161131i
$496$	3.99214e8	−	5.02286e8i	0.146899	−	0.184827i
$497$			3.57719e9i			1.30706i
$498$	5.40588e8	+	2.36400e9i	0.196139	+	0.857720i
$499$	2.11737e9	+	8.77043e8i	0.762860	+	0.315987i	0.729977	−	0.683472i	$-0.239531\pi$
$499$	2.11737e9	+	8.77043e8i	0.762860	+	0.315987i	0.0328835	+	0.999459i	$0.489531\pi$
$500$	−2.69522e9	+	1.53576e8i	−0.964270	+	0.0549452i
$501$	−1.59881e9	−	3.85988e9i	−0.568023	−	1.37133i
$502$	7.87541e8	−	4.64667e9i	0.277850	−	1.63938i
$503$	1.48830e9	+	1.48830e9i	0.521436	+	0.521436i	0.918005	−	0.396569i	$-0.129799\pi$
$503$	1.48830e9	+	1.48830e9i	0.521436	+	0.521436i	−0.396569	+	0.918005i	$0.629799\pi$
$504$	−2.16621e9	−	2.41376e8i	−0.753691	−	0.0839823i
$505$	−6.44330e8	+	6.44330e8i	−0.222632	+	0.222632i
$506$	3.31464e8	+	4.66749e8i	0.113739	+	0.160161i
$507$	2.66944e9	−	1.10572e9i	0.909687	−	0.376804i
$508$	2.06789e9	+	4.28504e9i	0.699851	+	1.45021i
$509$	1.87076e9	−	4.51642e9i	0.628791	−	1.51804i	−0.212336	−	0.977197i	$-0.568107\pi$
$509$	1.87076e9	−	4.51642e9i	0.628791	−	1.51804i	0.841126	−	0.540838i	$-0.181893\pi$
$510$	−5.75711e9	+	9.17073e9i	−1.92180	+	3.06132i
$511$	−3.81518e8			−0.126486
$512$	2.87025e9	+	9.92478e8i	0.945095	+	0.326795i
$513$	−2.58479e9			−0.845306
$514$	8.41098e8	−	1.33982e9i	0.273197	−	0.435186i
$515$	−4.72510e8	+	1.14074e9i	−0.152435	+	0.368012i
$516$	2.41634e9	+	5.00709e9i	0.774256	+	1.60439i
$517$	1.09640e8	−	4.54144e7i	0.0348941	−	0.0144536i
$518$	−5.63234e8	−	7.93115e8i	−0.178047	−	0.250716i
$519$	2.40421e9	−	2.40421e9i	0.754897	−	0.754897i
$520$	−2.35219e9	−	2.62100e8i	−0.733603	−	0.0817439i
$521$	−1.27881e9	−	1.27881e9i	−0.396162	−	0.396162i	0.480715	−	0.876877i	$-0.340377\pi$
$521$	−1.27881e9	−	1.27881e9i	−0.396162	−	0.396162i	−0.876877	+	0.480715i	$0.840377\pi$
$522$	2.91398e7	−	1.71931e8i	0.00896685	−	0.0529064i
$523$	7.48486e7	+	1.80700e8i	0.0228785	+	0.0552336i	0.934906	−	0.354896i	$-0.115484\pi$
$523$	7.48486e7	+	1.80700e8i	0.0228785	+	0.0552336i	−0.912027	+	0.410129i	$0.865484\pi$
$524$	−2.31089e9	+	1.31677e8i	−0.701649	+	0.0399807i
$525$	8.38334e9	+	3.47249e9i	2.52848	+	1.04733i
$526$	−9.42275e8	−	4.12059e9i	−0.282311	−	1.23455i
$527$			1.42764e9i			0.424895i
$528$	−4.74702e8	+	5.97263e8i	−0.140347	+	0.176582i
$529$			6.03005e8i			0.177103i
$530$	−7.92948e9	+	1.81327e9i	−2.31355	+	0.529051i
$531$	−1.60304e8	−	6.64001e7i	−0.0464637	−	0.0192459i
$532$	−5.39217e9	−	4.81080e9i	−1.55265	−	1.38524i
$533$	4.20643e8	+	1.01552e9i	0.120329	+	0.290499i
$534$	5.73897e9	+	9.72670e8i	1.63095	+	0.276421i
$535$	−3.22648e9	−	3.22648e9i	−0.910941	−	0.910941i
$536$	2.02540e9	−	3.67536e9i	0.568113	−	1.03091i
$537$	1.16574e9	−	1.16574e9i	0.324858	−	0.324858i
$538$	2.95782e9	−	2.10051e9i	0.818906	−	0.581550i
$539$	−5.39609e8	+	2.23513e8i	−0.148429	+	0.0614813i
$540$	3.10845e9	+	1.08484e9i	0.849506	+	0.296474i
$541$	3.92347e8	−	9.47209e8i	0.106532	−	0.257191i	−0.861620	−	0.507554i	$-0.830550\pi$
$541$	3.92347e8	−	9.47209e8i	0.106532	−	0.257191i	0.968152	+	0.250363i	$0.0805499\pi$
$542$	−2.68538e9	−	1.68580e9i	−0.724451	−	0.454788i
$543$	−4.33014e9			−1.16065
$544$	−6.37380e9	+	2.24496e9i	−1.69747	+	0.597877i
$545$	7.60983e9			2.01366
$546$	2.52423e9	+	1.58464e9i	0.663674	+	0.416635i
$547$	2.54600e9	−	6.14659e9i	0.665124	−	1.60575i	−0.124541	−	0.992214i	$-0.539746\pi$
$547$	2.54600e9	−	6.14659e9i	0.665124	−	1.60575i	0.789665	−	0.613538i	$-0.210254\pi$
$548$	7.53788e8	−	2.15988e9i	0.195667	−	0.560657i
$549$	−3.42579e9	+	1.41901e9i	−0.883603	+	0.366001i
$550$	9.21068e8	−	6.54101e8i	0.236060	−	0.167639i
$551$	4.08813e8	−	4.08813e8i	0.104110	−	0.104110i
$552$	−5.13066e9	+	1.48495e9i	−1.29834	+	0.375773i
$553$	2.95010e8	+	2.95010e8i	0.0741821	+	0.0741821i
$554$	−7.32925e9	−	1.24220e9i	−1.83137	−	0.310390i
$555$	−6.92870e8	−	1.67274e9i	−0.172039	−	0.415338i
$556$	1.84178e9	−	2.06435e9i	0.454438	−	0.509356i
$557$	2.68232e8	+	1.11105e8i	0.0657684	+	0.0272422i	0.415325	−	0.909673i	$-0.363668\pi$
$557$	2.68232e8	+	1.11105e8i	0.0657684	+	0.0272422i	−0.349557	+	0.936915i	$0.613668\pi$
$558$	−5.21418e8	+	1.19235e8i	−0.127048	+	0.0290526i
$559$		−	2.70394e9i		−	0.654719i
$560$	4.46551e9	+	8.04854e9i	1.07452	+	1.93668i
$561$		−	1.69759e9i		−	0.405941i
$562$	1.10445e9	+	4.82979e9i	0.262464	+	1.14776i
$563$	−2.24942e9	−	9.31741e8i	−0.531241	−	0.220047i	0.100906	−	0.994896i	$-0.467826\pi$
$563$	−2.24942e9	−	9.31741e8i	−0.531241	−	0.220047i	−0.632147	+	0.774849i	$0.717826\pi$
$564$	6.29895e7	+	1.10545e9i	0.0147840	+	0.259454i
$565$	4.45349e9	+	1.07517e10i	1.03880	+	2.50788i
$566$	5.46457e8	−	3.22422e9i	0.126677	−	0.747424i
$567$	−5.25918e9	−	5.25918e9i	−1.21165	−	1.21165i
$568$	−3.24546e9	+	2.59470e9i	−0.743117	+	0.594112i
$569$	−5.81325e9	+	5.81325e9i	−1.32290	+	1.32290i	−0.411478	+	0.911420i	$0.634987\pi$
$569$	−5.81325e9	+	5.81325e9i	−1.32290	+	1.32290i	−0.911420	+	0.411478i	$0.865013\pi$
$570$	−7.78761e9	−	1.09661e10i	−1.76134	−	2.48022i
$571$	−8.64359e8	+	3.58029e8i	−0.194298	+	0.0804808i	−0.477711	−	0.878517i	$-0.658533\pi$
$571$	−8.64359e8	+	3.58029e8i	−0.194298	+	0.0804808i	0.283413	+	0.958998i	$0.408533\pi$
$572$	3.34175e8	−	1.61268e8i	0.0746599	−	0.0360298i
$573$	9.24726e8	−	2.23249e9i	0.205339	−	0.495733i
$574$	2.27284e9	−	3.62050e9i	0.501623	−	0.799055i
$575$	7.90893e9			1.73492
$576$	−1.35226e9	−	2.14041e9i	−0.294837	−	0.466679i
$577$	6.60634e9			1.43168			0.715840	−	0.698265i	$-0.246044\pi$
$577$	6.60634e9			1.43168			0.715840	+	0.698265i	$0.246044\pi$
$578$	5.52623e9	−	8.80295e9i	1.19037	−	1.89619i
$579$	8.55204e8	−	2.06465e9i	0.183103	−	0.442049i
$580$	−6.63216e8	+	3.20058e8i	−0.141142	+	0.0681131i
$581$	−4.23761e9	+	1.75528e9i	−0.896406	+	0.371304i
$582$	1.04810e9	+	1.47588e9i	0.220381	+	0.310328i
$583$	9.01740e8	−	9.01740e8i	0.188470	−	0.188470i
$584$	−2.76733e8	−	3.46138e8i	−0.0574931	−	0.0719126i
$585$	1.39515e9	+	1.39515e9i	0.288121	+	0.288121i
$586$	8.73346e8	−	5.15294e9i	0.179285	−	1.05782i
$587$	4.92843e8	+	1.18983e9i	0.100572	+	0.242801i	0.966154	−	0.257965i	$-0.0830518\pi$
$587$	4.92843e8	+	1.18983e9i	0.100572	+	0.242801i	−0.865583	+	0.500766i	$0.833052\pi$
$588$	−3.10012e8	−	5.44062e9i	−0.0628866	−	1.10364i
$589$	−1.63834e9	−	6.78624e8i	−0.330371	−	0.136844i
$590$	1.63340e8	+	7.14288e8i	0.0327423	+	0.143183i
$591$			6.24972e9i			1.24539i
$592$	3.11026e8	−	1.08629e9i	0.0616128	−	0.215188i
$593$			3.23317e8i			0.0636703i	0.999493	+	0.0318352i	$0.0101352\pi$
$593$			3.23317e8i			0.0636703i	−0.999493	+	0.0318352i	$0.989865\pi$
$594$	−5.03173e8	+	1.15063e8i	−0.0985064	+	0.0225259i
$595$	−1.89215e10	−	7.83753e9i	−3.68253	−	1.52535i
$596$	−2.32272e9	+	2.60341e9i	−0.449402	+	0.503711i
$597$	1.21522e9	+	2.93380e9i	0.233746	+	0.564313i
$598$	2.56119e9	+	4.34084e8i	0.489765	+	0.0830079i
$599$	6.29460e9	+	6.29460e9i	1.19667	+	1.19667i	0.975158	+	0.221512i	$0.0710992\pi$
$599$	6.29460e9	+	6.29460e9i	1.19667	+	1.19667i	0.221512	+	0.975158i	$0.428901\pi$
$600$	2.93036e9	+	1.01247e10i	0.553849	+	1.91361i
$601$	5.08895e9	−	5.08895e9i	0.956241	−	0.956241i	−0.0428413	−	0.999082i	$-0.513641\pi$
$601$	5.08895e9	−	5.08895e9i	0.956241	−	0.956241i	0.999082	+	0.0428413i	$0.0136410\pi$
$602$	−8.57367e9	+	6.08862e9i	−1.60169	+	1.13745i
$603$	−3.23210e9	+	1.33878e9i	−0.600308	+	0.248656i
$604$	−1.01793e9	+	2.91673e9i	−0.187969	+	0.538601i
$605$	3.25026e9	−	7.84683e9i	0.596725	−	1.44062i
$606$	1.12888e9	+	7.08678e8i	0.206060	+	0.129358i
$607$	1.86456e9			0.338389			0.169195	−	0.985583i	$-0.445883\pi$
$607$	1.86456e9			0.338389			0.169195	+	0.985583i	$0.445883\pi$
$608$	4.53476e8	−	8.38164e9i	0.0818260	−	1.51240i
$609$	9.27342e8			0.166372
$610$	1.32621e10	+	8.32554e9i	2.36569	+	1.48511i
$611$	2.06078e8	−	4.97515e8i	0.0365499	−	0.0882394i
$612$	5.31886e9	+	1.85626e9i	0.937968	+	0.327347i
$613$	8.93947e8	−	3.70285e8i	0.156747	−	0.0649269i	−0.302930	−	0.953013i	$-0.597965\pi$
$613$	8.93947e8	−	3.70285e8i	0.156747	−	0.0649269i	0.459678	+	0.888086i	$0.347965\pi$
$614$	−3.40137e9	+	2.41549e9i	−0.593013	+	0.421131i
$615$	5.62607e9	−	5.62607e9i	0.975310	−	0.975310i
$616$	−1.26383e9	−	6.96468e8i	−0.217850	−	0.120052i
$617$	−1.71421e9	−	1.71421e9i	−0.293809	−	0.293809i	0.544774	−	0.838583i	$-0.316616\pi$
$617$	−1.71421e9	−	1.71421e9i	−0.293809	−	0.293809i	−0.838583	+	0.544774i	$0.816616\pi$
$618$	1.78071e9	+	3.01804e8i	0.303482	+	0.0514358i
$619$	1.71183e9	+	4.13272e9i	0.290097	+	0.700356i	0.999992	−	0.00395129i	$-0.00125774\pi$
$619$	1.71183e9	+	4.13272e9i	0.290097	+	0.700356i	−0.709895	+	0.704307i	$0.751258\pi$
$620$	1.68545e9	+	1.50372e9i	0.284017	+	0.253395i
$621$	−3.33854e9	−	1.38287e9i	−0.559417	−	0.231718i
$622$	−7.21056e8	+	1.64887e8i	−0.120144	+	0.0274739i
$623$			1.10096e10i			1.82417i
$624$	3.93257e8	+	3.43957e9i	0.0647933	+	0.566706i
$625$			2.56354e8i			0.0420011i
$626$	8.60550e8	+	3.76320e9i	0.140206	+	0.613123i
$627$	1.94814e9	+	8.06946e8i	0.315634	+	0.130740i
$628$	4.45737e9	−	2.53986e8i	0.718158	−	0.0409214i
$629$	9.62147e8	+	2.32283e9i	0.154157	+	0.372169i
$630$	1.28221e9	−	7.56529e9i	0.204299	−	1.20541i
$631$	−2.46041e9	−	2.46041e9i	−0.389856	−	0.389856i	0.484780	−	0.874636i	$-0.338900\pi$
$631$	−2.46041e9	−	2.46041e9i	−0.389856	−	0.389856i	−0.874636	+	0.484780i	$0.838900\pi$
$632$	−5.36680e7	+	4.81638e8i	−0.00845679	+	0.0758946i
$633$	−7.17119e9	+	7.17119e9i	−1.12377	+	1.12377i
$634$	−1.55524e9	−	2.19001e9i	−0.242374	−	0.341298i
$635$	−1.54749e10	+	6.40991e9i	−2.39839	+	0.993445i
$636$	5.17126e9	+	1.07158e10i	0.797070	+	1.65167i
$637$	−1.01424e9	+	2.44860e9i	−0.155472	+	0.375344i
$638$	6.13839e7	−	9.77809e7i	0.00935798	−	0.0149067i
$639$	3.46396e9			0.525194
$640$	−4.06312e9	+	9.88940e9i	−0.612675	+	1.49121i
$641$	2.63800e9			0.395614			0.197807	−	0.980241i	$-0.436618\pi$
$641$	2.63800e9			0.395614			0.197807	+	0.980241i	$0.436618\pi$
$642$	−3.54870e9	+	5.65287e9i	−0.529294	+	0.843133i
$643$	5.73673e8	−	1.38497e9i	0.0850993	−	0.205448i	−0.875601	−	0.483035i	$-0.839535\pi$
$643$	5.73673e8	−	1.38497e9i	0.0850993	−	0.205448i	0.960701	+	0.277587i	$0.0895345\pi$
$644$	−4.39079e9	−	9.09849e9i	−0.647802	−	1.34236i
$645$	−1.80825e10	+	7.49001e9i	−2.65338	+	1.09906i
$646$	1.08142e10	+	1.52279e10i	1.57827	+	2.22243i
$647$	1.90568e9	−	1.90568e9i	0.276621	−	0.276621i	−0.555138	−	0.831759i	$-0.687334\pi$
$647$	1.90568e9	−	1.90568e9i	0.276621	−	0.276621i	0.831759	+	0.555138i	$0.187334\pi$
$648$	9.56746e8	−	8.58622e9i	0.138129	−	1.23962i
$649$	−8.12288e7	−	8.12288e7i	−0.0116642	−	0.0116642i
$650$	8.56607e8	−	5.05417e9i	0.122345	−	0.721860i
$651$	−1.08850e9	−	2.62788e9i	−0.154631	−	0.373312i
$652$	4.05040e9	−	2.30796e8i	0.572310	−	0.0326108i
$653$	2.06090e9	+	8.53652e8i	0.289641	+	0.119973i	0.522773	−	0.852472i	$-0.324897\pi$
$653$	2.06090e9	+	8.53652e8i	0.289641	+	0.119973i	−0.233132	+	0.972445i	$0.574897\pi$
$654$	−2.48140e9	−	1.08512e10i	−0.346876	−	1.51690i
$655$		−	8.14852e9i		−	1.13301i
$656$	4.93336e9	−	5.64047e8i	0.682306	−	0.0780103i
$657$			3.69442e8i			0.0508238i
$658$	−2.04156e9	+	4.66854e8i	−0.279365	+	0.0638838i
$659$	6.38860e9	+	2.64624e9i	0.869574	+	0.360190i	0.772445	−	0.635082i	$-0.219034\pi$
$659$	6.38860e9	+	2.64624e9i	0.869574	+	0.360190i	0.0971299	+	0.995272i	$0.469034\pi$
$660$	−2.00415e9	−	1.78806e9i	−0.271348	−	0.242091i
$661$	−2.25026e9	−	5.43261e9i	−0.303059	−	0.731650i	−0.999896	−	0.0144201i	$-0.995410\pi$
$661$	−2.25026e9	−	5.43261e9i	−0.303059	−	0.731650i	0.696837	−	0.717230i	$-0.254590\pi$
$662$	−7.03123e8	−	1.19169e8i	−0.0941951	−	0.0159647i
$663$	−5.44698e9	−	5.44698e9i	−0.725870	−	0.725870i
$664$	−4.66625e9	−	2.57146e9i	−0.618557	−	0.340872i
$665$	1.79886e10	−	1.79886e10i	2.37203	−	2.37203i
$666$	−7.68011e8	+	5.45406e8i	−0.100741	+	0.0715419i
$667$	7.46743e8	−	3.09311e8i	0.0974386	−	0.0403604i
$668$	8.66641e9	+	3.02454e9i	1.12492	+	0.392592i
$669$	9.30141e8	−	2.24556e9i	0.120104	−	0.289957i
$670$	1.25123e10	+	7.85482e9i	1.60721	+	1.00896i
$671$	−2.45494e9			−0.313698
$672$	1.00207e10	−	8.99203e9i	1.27381	−	1.14305i
$673$	−1.11708e10			−1.41264			−0.706322	−	0.707891i	$-0.749647\pi$
$673$	−1.11708e10			−1.41264			−0.706322	+	0.707891i	$0.749647\pi$
$674$	2.88853e9	+	1.81333e9i	0.363385	+	0.228123i
$675$	−2.72891e9	+	6.58817e9i	−0.341527	+	0.824520i
$676$	−2.09172e9	+	5.99356e9i	−0.260430	+	0.746228i
$677$	1.06370e10	−	4.40600e9i	1.31753	−	0.545738i	0.390455	−	0.920622i	$-0.372318\pi$
$677$	1.06370e10	−	4.40600e9i	1.31753	−	0.545738i	0.927072	+	0.374884i	$0.122318\pi$
$678$	1.38791e10	−	9.85632e9i	1.71024	−	1.21454i
$679$	−2.42101e9	+	2.42101e9i	−0.296792	+	0.296792i
$680$	−6.61392e9	−	2.28518e10i	−0.806636	−	2.78701i
$681$	−5.04197e9	−	5.04197e9i	−0.611766	−	0.611766i
$682$	−3.49141e8	−	5.91742e7i	−0.0421459	−	0.00714310i
$683$	−1.53694e9	−	3.71050e9i	−0.184580	−	0.445615i	0.804320	−	0.594196i	$-0.202530\pi$
$683$	−1.53694e9	−	3.71050e9i	−0.184580	−	0.445615i	−0.988900	+	0.148580i	$0.952530\pi$
$684$	−4.65852e9	+	5.22150e9i	−0.556611	+	0.623877i
$685$	7.44043e9	+	3.08193e9i	0.884465	+	0.366358i
$686$	−1.27588e9	+	2.91762e8i	−0.150895	+	0.0345059i
$687$			1.48351e10i			1.74559i
$688$	−1.17429e10	−	3.36223e9i	−1.37472	−	0.393612i
$689$		−	5.78674e9i		−	0.674011i
$690$	−4.19167e9	−	1.83303e10i	−0.485753	−	2.12421i
$691$	−7.03736e9	−	2.91497e9i	−0.811402	−	0.336094i	−0.0618890	−	0.998083i	$-0.519712\pi$
$691$	−7.03736e9	−	2.91497e9i	−0.811402	−	0.336094i	−0.749513	+	0.661989i	$0.769712\pi$
$692$	4.24965e8	+	7.45800e9i	0.0487508	+	0.855561i
$693$	4.60361e8	+	1.11141e9i	0.0525451	+	0.126855i
$694$	1.55332e9	−	9.16493e9i	0.176402	−	1.04081i
$695$	6.88678e9	+	6.88678e9i	0.778160	+	0.778160i
$696$	6.72646e8	+	8.41347e8i	0.0756230	+	0.0945895i
$697$	−7.81259e9	+	7.81259e9i	−0.873937	+	0.873937i
$698$	2.36347e8	+	3.32811e8i	0.0263061	+	0.0370428i
$699$	1.25228e10	−	5.18710e9i	1.38685	−	0.574453i
$700$	−1.79547e10	+	8.66466e9i	−1.97849	+	0.954791i
$701$	−3.69628e9	+	8.92362e9i	−0.405277	+	0.978426i	0.581086	+	0.813842i	$0.302628\pi$
$701$	−3.69628e9	+	8.92362e9i	−0.405277	+	0.978426i	−0.986363	+	0.164584i	$0.947372\pi$
$702$	−1.24531e9	+	1.98370e9i	−0.135862	+	0.216420i
$703$	−3.12301e9			−0.339023
$704$	−2.84835e8	−	1.65181e9i	−0.0307673	−	0.178425i
$705$	−3.89796e9			−0.418963
$706$	−7.34657e9	+	1.17026e10i	−0.785720	+	1.25160i
$707$	−9.64770e8	+	2.32916e9i	−0.102673	+	0.247874i
$708$	9.65275e8	−	4.65827e8i	0.102220	−	0.0493297i
$709$	−6.26382e9	+	2.59456e9i	−0.660050	+	0.273402i	−0.687460	−	0.726222i	$-0.741274\pi$
$709$	−6.26382e9	+	2.59456e9i	−0.660050	+	0.273402i	0.0274093	+	0.999624i	$0.491274\pi$
$710$	−8.46970e9	−	1.19266e10i	−0.888104	−	1.25058i
$711$	2.85673e8	−	2.85673e8i	0.0298075	−	0.0298075i
$712$	−9.98868e9	+	7.98582e9i	−1.03712	+	0.829162i
$713$	−1.75304e9	−	1.75304e9i	−0.181125	−	0.181125i
$714$	−5.00603e9	+	2.95367e10i	−0.514695	+	3.03681i
$715$	4.99886e8	+	1.20683e9i	0.0511446	+	0.123474i
$716$	2.06055e8	+	3.61620e9i	0.0209791	+	0.368177i
$717$	7.59785e9	+	3.14713e9i	0.769793	+	0.318859i
$718$	−8.87843e8	−	3.88256e9i	−0.0895160	−	0.391456i
$719$		−	8.13590e9i		−	0.816309i	−0.912913	−	0.408154i	$-0.866173\pi$
$719$		−	8.13590e9i		−	0.816309i	0.912913	−	0.408154i	$-0.133827\pi$
$720$	7.79379e9	−	4.32417e9i	0.778188	−	0.431756i
$721$			3.41611e9i			0.339437i
$722$	−1.27574e10	+	2.91729e9i	−1.26148	+	0.288470i
$723$	6.70281e9	+	2.77639e9i	0.659588	+	0.273210i
$724$	6.33346e9	−	7.09884e9i	0.620234	−	0.695189i
$725$	−6.10385e8	−	1.47360e9i	−0.0594868	−	0.143614i
$726$	−1.22490e10	−	2.07602e9i	−1.18802	−	0.201351i
$727$	−4.10504e9	−	4.10504e9i	−0.396230	−	0.396230i	0.480671	−	0.876901i	$-0.340393\pi$
$727$	−4.10504e9	−	4.10504e9i	−0.396230	−	0.396230i	−0.876901	+	0.480671i	$0.840393\pi$
$728$	−6.28992e9	+	1.82047e9i	−0.604206	+	0.174874i
$729$	4.99905e7	−	4.99905e7i	0.00477904	−	0.00477904i
$730$	1.27200e9	−	9.03319e8i	0.121020	−	0.0859432i
$731$	2.51100e10	−	1.04009e10i	2.37759	−	0.984829i
$732$	7.54730e9	−	2.16258e10i	0.711218	−	2.03790i
$733$	−4.13574e9	+	9.98457e9i	−0.387873	+	0.936408i	0.602517	+	0.798106i	$0.294165\pi$
$733$	−4.13574e9	+	9.98457e9i	−0.387873	+	0.936408i	−0.990390	+	0.138302i	$0.955835\pi$
$734$	1.10563e10	+	6.94079e9i	1.03198	+	0.647847i
$735$	1.91844e10			1.78214
$736$	5.06991e9	−	1.05832e10i	0.468735	−	0.978463i
$737$	−2.31614e9			−0.213122
$738$	−3.50590e9	−	2.20090e9i	−0.321072	−	0.201559i
$739$	−4.75081e9	+	1.14695e10i	−0.433025	+	1.04541i	0.545282	+	0.838253i	$0.316422\pi$
$739$	−4.75081e9	+	1.14695e10i	−0.433025	+	1.04541i	−0.978307	+	0.207161i	$0.933578\pi$
$740$	3.75571e9	+	1.31073e9i	0.340707	+	0.118905i
$741$	8.84011e9	−	3.66170e9i	0.798168	−	0.330612i
$742$	−1.83487e10	+	1.30304e10i	−1.64889	+	1.17096i
$743$	−5.53966e9	+	5.53966e9i	−0.495475	+	0.495475i	−0.910026	−	0.414551i	$-0.863939\pi$
$743$	−5.53966e9	+	5.53966e9i	−0.495475	+	0.495475i	0.414551	+	0.910026i	$0.363939\pi$
$744$	1.59464e9	−	2.89369e9i	0.141957	−	0.257600i
$745$	−8.68512e9	−	8.68512e9i	−0.769536	−	0.769536i
$746$	−1.06691e10	−	1.80825e9i	−0.940896	−	0.159468i
$747$	1.69972e9	+	4.10348e9i	0.149195	+	0.360189i
$748$	2.78304e9	+	2.48298e9i	0.243144	+	0.216929i
$749$	−1.16633e10	−	4.83108e9i	−1.01422	−	0.420105i
$750$	−1.35518e10	+	3.09895e9i	−1.17296	+	0.268226i
$751$		−	1.23188e10i		−	1.06128i	−0.847599	−	0.530638i	$-0.821952\pi$
$751$		−	1.23188e10i		−	1.06128i	0.847599	−	0.530638i	$-0.178048\pi$
$752$	−1.90441e9	−	1.51361e9i	−0.163304	−	0.129793i
$753$		−	2.42694e10i		−	2.07146i
$754$	−1.16785e8	−	5.10705e8i	−0.00992175	−	0.0433881i
$755$	−1.00477e10	−	4.16188e9i	−0.849670	−	0.351945i
$756$	9.09408e9	−	5.18191e8i	0.765478	−	0.0436177i
$757$	1.50374e9	+	3.63036e9i	0.125991	+	0.304168i	0.974271	−	0.225379i	$-0.0723619\pi$
$757$	1.50374e9	+	3.63036e9i	0.125991	+	0.304168i	−0.848281	+	0.529547i	$0.822362\pi$
$758$	−1.04439e9	+	6.16212e9i	−0.0871004	+	0.513911i
$759$	2.08452e9	+	2.08452e9i	0.173045	+	0.173045i
$760$	2.93684e10	+	3.27246e9i	2.42679	+	0.270413i
$761$	1.04778e10	−	1.04778e10i	0.861836	−	0.861836i	−0.129715	−	0.991551i	$-0.541406\pi$
$761$	1.04778e10	−	1.04778e10i	0.861836	−	0.861836i	0.991551	+	0.129715i	$0.0414064\pi$
$762$	1.41862e10	+	1.99762e10i	1.16151	+	1.63558i
$763$	1.94514e10	−	8.05704e9i	1.58531	−	0.656658i
$764$	2.30740e9	+	4.78134e9i	0.187196	+	0.387903i
$765$	−7.58946e9	+	1.83226e10i	−0.612909	+	1.47969i
$766$	1.45322e9	−	2.31490e9i	0.116824	−	0.186094i
$767$	−5.21270e8			−0.0417137
$768$	1.54266e10	+	2.56908e9i	1.22887	+	0.204651i
$769$	1.61930e10			1.28406			0.642029	−	0.766680i	$-0.278093\pi$
$769$	1.61930e10			1.28406			0.642029	+	0.766680i	$0.278093\pi$
$770$	2.70101e9	−	4.30254e9i	0.213210	−	0.339631i
$771$	3.11745e9	−	7.52618e9i	0.244968	−	0.591404i
$772$	2.13393e9	+	4.42187e9i	0.166924	+	0.345896i
$773$	−1.25851e10	+	5.21291e9i	−0.980003	+	0.405930i	−0.814427	−	0.580267i	$-0.802948\pi$
$773$	−1.25851e10	+	5.21291e9i	−0.980003	+	0.405930i	−0.165576	+	0.986197i	$0.552948\pi$
$774$	5.89591e9	+	8.30229e9i	0.457043	+	0.643583i
$775$	−3.45939e9	+	3.45939e9i	−0.266958	+	0.266958i
$776$	−3.95257e9	−	4.40427e8i	−0.303643	−	0.0338344i
$777$	−3.54208e9	−	3.54208e9i	−0.270885	−	0.270885i
$778$	2.38491e9	−	1.40715e10i	0.181570	−	1.07130i
$779$	−5.25196e9	−	1.26793e10i	−0.398052	−	0.960983i
$780$	−1.21679e10	+	6.93340e8i	−0.918088	+	0.0523136i
$781$	2.11877e9	+	8.77624e8i	0.159150	+	0.0659219i
$782$	5.82072e9	+	2.54542e10i	0.435265	+	1.90342i
$783$			7.28765e8i			0.0542527i
$784$	9.37281e9	+	7.44946e9i	0.694646	+	0.552101i
$785$			1.57173e10i			1.15967i
$786$	−1.16194e10	+	2.65705e9i	−0.853499	+	0.195174i
$787$	1.92112e10	+	7.95755e9i	1.40489	+	0.581926i	0.951017	−	0.309139i	$-0.100041\pi$
$787$	1.92112e10	+	7.95755e9i	1.40489	+	0.581926i	0.453877	+	0.891065i	$0.350041\pi$
$788$	−1.02458e10	−	9.14114e9i	−0.745942	−	0.665516i
$789$	−8.32980e9	−	2.01099e10i	−0.603761	−	1.45761i
$790$	−1.68208e9	−	2.85087e8i	−0.121381	−	0.0205723i
$791$	2.27670e10	+	2.27670e10i	1.63564	+	1.63564i
$792$	−6.74423e8	+	1.22383e9i	−0.0482386	+	0.0875352i
$793$	−7.87705e9	+	7.87705e9i	−0.560929	+	0.560929i
$794$	1.58253e10	−	1.12384e10i	1.12197	−	0.796769i
$795$	−3.86986e10	+	1.60295e10i	−2.73156	+	1.13145i
$796$	−6.58711e9	−	2.29887e9i	−0.462913	−	0.161555i
$797$	−1.60736e9	+	3.88051e9i	−0.112463	+	0.271509i	−0.970083	−	0.242775i	$-0.921942\pi$
$797$	−1.60736e9	+	3.88051e9i	−0.112463	+	0.271509i	0.857620	+	0.514284i	$0.171942\pi$
$798$	−3.15164e10	−	1.97850e10i	−2.19546	−	1.37825i
$799$	5.41286e9			0.375416
$800$	−2.08845e10	−	1.00048e10i	−1.44215	−	0.690865i
$801$	1.06612e10			0.732978
$802$	−1.30352e10	−	8.18310e9i	−0.892292	−	0.560154i
$803$	−9.36012e7	+	2.25973e8i	−0.00637936	+	0.0154011i
$804$	7.12058e9	−	2.04031e10i	0.483192	−	1.38452i
$805$	3.28581e10	−	1.36103e10i	2.22002	−	0.919562i
$806$	−1.31014e9	+	9.30402e8i	−0.0881343	+	0.0625890i
$807$	1.32097e10	−	1.32097e10i	0.884783	−	0.884783i
$808$	−2.81297e9	+	8.14148e8i	−0.187596	+	0.0542955i
$809$	1.04029e10	+	1.04029e10i	0.690769	+	0.690769i	0.962401	−	0.271632i	$-0.0875634\pi$
$809$	1.04029e10	+	1.04029e10i	0.690769	+	0.690769i	−0.271632	+	0.962401i	$0.587563\pi$
$810$	2.99866e10	+	5.08229e9i	1.98258	+	0.336017i
$811$	−5.43830e9	−	1.31292e10i	−0.358006	−	0.864303i	−0.995580	−	0.0939142i	$-0.970062\pi$
$811$	−5.43830e9	−	1.31292e10i	−0.358006	−	0.864303i	0.637574	−	0.770389i	$-0.279938\pi$
$812$	−1.35637e9	+	1.52029e9i	−0.0889065	+	0.0996507i
$813$	−1.50846e10	−	6.24826e9i	−0.984505	−	0.407795i
$814$	−6.07946e8	+	1.39022e8i	−0.0395075	+	0.00903436i
$815$			1.42823e10i			0.924157i
$816$	−3.04287e10	+	1.68826e10i	−1.96051	+	1.08773i
$817$			3.37601e10i			2.16584i
$818$	3.35760e9	+	1.46828e10i	0.214482	+	0.937937i
$819$	5.04327e9	+	2.08899e9i	0.320788	+	0.132875i
$820$	9.94455e8	+	1.74524e10i	0.0629849	+	1.10537i
$821$	4.79466e9	+	1.15753e10i	0.302383	+	0.730016i	0.999909	+	0.0134574i	$0.00428375\pi$
$821$	4.79466e9	+	1.15753e10i	0.302383	+	0.730016i	−0.697527	+	0.716559i	$0.745716\pi$
$822$	1.96850e9	−	1.16146e10i	0.123619	−	0.729378i
$823$	1.31979e10	+	1.31979e10i	0.825286	+	0.825286i	0.986860	−	0.161575i	$-0.0516574\pi$
$823$	1.31979e10	+	1.31979e10i	0.825286	+	0.825286i	−0.161575	+	0.986860i	$0.551657\pi$
$824$	−3.09933e9	+	2.47787e9i	−0.192984	+	0.154288i
$825$	4.11352e9	−	4.11352e9i	0.255050	−	0.255050i
$826$	1.17378e9	+	1.65285e9i	0.0724695	+	0.102048i
$827$	−7.96090e9	+	3.29751e9i	−0.489432	+	0.202730i	−0.613731	−	0.789515i	$-0.710332\pi$
$827$	−7.96090e9	+	3.29751e9i	−0.489432	+	0.202730i	0.124298	+	0.992245i	$0.460332\pi$
$828$	−8.81051e9	+	4.25182e9i	−0.539380	+	0.260297i
$829$	9.30086e9	−	2.24543e10i	0.566999	−	1.36886i	−0.337074	−	0.941478i	$-0.609437\pi$
$829$	9.30086e9	−	2.24543e10i	0.566999	−	1.36886i	0.904073	−	0.427378i	$-0.140563\pi$
$830$	9.97251e9	−	1.58856e10i	0.605384	−	0.964340i
$831$	−3.82804e10			−2.31405
$832$	−6.21404e9	−	4.38616e9i	−0.374061	−	0.264030i
$833$	−2.66402e10			−1.59691
$834$	7.57455e9	−	1.20658e10i	0.452143	−	0.720236i
$835$	−1.23661e10	+	2.98543e10i	−0.735071	+	1.77462i
$836$	−4.17235e9	+	2.01351e9i	−0.246978	+	0.119188i
$837$	2.06515e9	−	8.55415e8i	0.121734	−	0.0504241i
$838$	−7.25728e9	−	1.02193e10i	−0.426010	−	0.599884i
$839$	5.34040e9	−	5.34040e9i	0.312181	−	0.312181i	−0.533573	−	0.845754i	$-0.679151\pi$
$839$	5.34040e9	−	5.34040e9i	0.312181	−	0.312181i	0.845754	+	0.533573i	$0.179151\pi$
$840$	2.95977e10	+	3.70208e10i	1.72298	+	2.15511i
$841$	1.20822e10	+	1.20822e10i	0.700425	+	0.700425i
$842$	−3.75879e8	+	2.21777e9i	−0.0216998	+	0.128034i
$843$	9.76345e9	+	2.35711e10i	0.561315	+	1.35514i
$844$	−1.26757e9	−	2.22454e10i	−0.0725725	−	1.27363i
$845$	−2.06468e10	−	8.55219e9i	−1.17721	−	0.487617i
$846$	4.52077e8	+	1.97694e9i	0.0256694	+	0.112253i
$847$		−	2.34985e10i		−	1.32876i
$848$	−2.51312e10	−	7.19557e9i	−1.41523	−	0.405210i
$849$		−	1.68400e10i		−	0.944418i
$850$	5.02305e10	−	1.14864e10i	2.80544	−	0.641533i
$851$	−4.03371e9	−	1.67082e9i	−0.224363	−	0.0929341i
$852$	−1.42449e10	+	1.59663e10i	−0.789078	+	0.884436i
$853$	6.73115e8	+	1.62504e9i	0.0371337	+	0.0896486i	0.941358	−	0.337408i	$-0.109550\pi$
$853$	6.73115e8	+	1.62504e9i	0.0371337	+	0.0896486i	−0.904225	+	0.427057i	$0.859550\pi$
$854$	4.27139e10	+	7.23937e9i	2.34675	+	0.397739i
$855$	−1.74192e10	−	1.74192e10i	−0.953117	−	0.953117i
$856$	−4.07684e9	−	1.40859e10i	−0.222160	−	0.767585i
$857$	4.95206e9	−	4.95206e9i	0.268753	−	0.268753i	−0.559845	−	0.828597i	$-0.689139\pi$
$857$	4.95206e9	−	4.95206e9i	0.268753	−	0.268753i	0.828597	+	0.559845i	$0.189139\pi$
$858$	1.55788e9	−	1.10633e9i	0.0842029	−	0.0597971i
$859$	−2.63260e10	+	1.09046e10i	−1.41713	+	0.586993i	−0.954137	−	0.299370i	$-0.903223\pi$
$859$	−2.63260e10	+	1.09046e10i	−1.41713	+	0.586993i	−0.462990	+	0.886364i	$0.653223\pi$
$860$	1.41691e10	−	4.05997e10i	0.759623	−	2.17660i
$861$	8.42405e9	−	2.03375e10i	0.449790	−	1.08589i
$862$	2.88667e10	+	1.81216e10i	1.53505	+	0.963656i
$863$	−1.99509e10			−1.05664			−0.528318	−	0.849046i	$-0.677177\pi$
$863$	−1.99509e10			−1.05664			−0.528318	+	0.849046i	$0.677177\pi$
$864$	7.06651e9	+	7.87489e9i	0.372741	+	0.415381i
$865$	−2.62979e10			−1.38155
$866$	−2.51684e10	−	1.58000e10i	−1.31687	−	0.826692i
$867$	2.04824e10	−	4.94489e10i	1.06737	−	2.57686i
$868$	5.90025e9	+	2.05916e9i	0.306233	+	0.106874i
$869$	2.47112e8	−	1.02357e8i	0.0127740	−	0.00529115i
$870$	−3.09182e9	+	2.19567e9i	−0.159183	+	0.113044i
$871$	−7.43169e9	+	7.43169e9i	−0.381087	+	0.381087i
$872$	2.14189e10	+	1.18035e10i	1.09393	+	0.602840i
$873$	2.34438e9	+	2.34438e9i	0.119255	+	0.119255i
$874$	−3.19778e10	−	5.41977e9i	−1.62016	−	0.274594i
$875$	−1.00622e10	−	2.42924e10i	−0.507769	−	1.22586i
$876$	−1.70286e9	−	1.51926e9i	−0.0855882	−	0.0763602i
$877$	−1.34034e10	−	5.55185e9i	−0.670988	−	0.277932i	0.0210659	−	0.999778i	$-0.493294\pi$
$877$	−1.34034e10	−	5.55185e9i	−0.670988	−	0.277932i	−0.692054	+	0.721846i	$0.743294\pi$
$878$	1.54407e10	−	3.53090e9i	0.769905	−	0.176058i
$879$		−	2.69136e10i		−	1.33663i
$880$	5.86272e9	−	6.70305e8i	0.290008	−	0.0331576i
$881$		−	7.06843e9i		−	0.348263i	−0.984722	−	0.174132i	$-0.944288\pi$
$881$		−	7.06843e9i		−	0.348263i	0.984722	−	0.174132i	$-0.0557118\pi$
$882$	−2.22496e9	−	9.72982e9i	−0.109190	−	0.477491i
$883$	−2.11976e9	−	8.78035e8i	−0.103616	−	0.0429190i	0.330273	−	0.943885i	$-0.392859\pi$
$883$	−2.11976e9	−	8.78035e8i	−0.103616	−	0.0429190i	−0.433889	+	0.900966i	$0.642859\pi$
$884$	1.68968e10	−	9.62799e8i	0.822664	−	0.0468762i
$885$	1.44394e9	+	3.48597e9i	0.0700240	+	0.169053i
$886$	−5.36624e9	+	3.16620e10i	−0.259210	+	1.52940i
$887$	−1.86475e10	−	1.86475e10i	−0.897198	−	0.897198i	0.0979898	−	0.995187i	$-0.468759\pi$
$887$	−1.86475e10	−	1.86475e10i	−0.897198	−	0.897198i	−0.995187	+	0.0979898i	$0.968759\pi$
$888$	6.44371e8	−	5.78285e9i	0.0308810	−	0.277138i
$889$	−3.27686e10	+	3.27686e10i	−1.56424	+	1.56424i
$890$	−2.60675e10	−	3.67069e10i	−1.23947	−	1.74535i
$891$	−4.40530e9	+	1.82474e9i	−0.208643	+	0.0864228i
$892$	2.32091e9	+	4.80934e9i	0.109492	+	0.226886i
$893$	−2.57299e9	+	6.21175e9i	−0.120909	+	0.291900i
$894$	−9.55249e9	+	1.52165e10i	−0.447131	+	0.712253i
$895$	−1.27512e10			−0.594526
$896$	8.48584e7	+	2.95801e10i	0.00394109	+	1.37379i
$897$	1.33770e10			0.618849
$898$	3.26291e9	−	5.19761e9i	0.150362	−	0.239517i
$899$	−1.91334e8	+	4.61921e8i	−0.00878280	+	0.0212036i
$900$	8.39040e9	+	1.73864e10i	0.383649	+	0.794988i
$901$	5.37385e10	−	2.22592e10i	2.44764	−	1.01385i
$902$	−1.58681e9	−	2.23446e9i	−0.0719948	−	0.101379i
$903$	−3.82903e10	+	3.82903e10i	−1.73054	+	1.73054i
$904$	−4.14176e9	+	3.71698e10i	−0.186464	+	1.67340i
$905$	2.36821e10	+	2.36821e10i	1.06206	+	1.06206i
$906$	−2.65829e9	+	1.56845e10i	−0.118756	+	0.700684i
$907$	6.38194e9	+	1.54074e10i	0.284006	+	0.685650i	0.999921	−	0.0125363i	$-0.00399055\pi$
$907$	6.38194e9	+	1.54074e10i	0.284006	+	0.685650i	−0.715916	+	0.698187i	$0.753991\pi$
$908$	1.56404e10	−	8.91209e8i	0.693344	−	0.0395075i
$909$	2.25544e9	+	9.34233e8i	0.0995996	+	0.0412555i
$910$	−5.13877e9	−	2.24720e10i	−0.226055	−	0.988544i
$911$		−	8.83576e9i		−	0.387195i	−0.981081	−	0.193597i	$-0.937984\pi$
$911$		−	8.83576e9i		−	0.387195i	0.981081	−	0.193597i	$-0.0620155\pi$
$912$	−4.91002e9	−	4.29448e10i	−0.214339	−	1.87469i
$913$			2.94058e9i			0.127875i
$914$	−1.30490e10	+	2.98397e9i	−0.565281	+	0.129265i
$915$	7.44972e10	+	3.08578e10i	3.21489	+	1.33165i
$916$	−2.43207e10	−	2.16985e10i	−1.04554	−	0.932815i
$917$	−8.62739e9	−	2.08284e10i	−0.369476	−	0.891995i
$918$	−2.32118e10	−	3.93406e9i	−0.990283	−	0.167838i
$919$	1.00368e10	+	1.00368e10i	0.426572	+	0.426572i	0.887459	−	0.460887i	$-0.152469\pi$
$919$	1.00368e10	+	1.00368e10i	0.426572	+	0.426572i	−0.460887	+	0.887459i	$0.652469\pi$
$920$	3.61817e10	+	1.99389e10i	1.53190	+	0.844196i
$921$	−1.51906e10	+	1.51906e10i	−0.640718	+	0.640718i
$922$	1.43927e10	−	1.02210e10i	0.604761	−	0.429474i
$923$	9.61439e9	−	3.98241e9i	0.402454	−	0.166702i
$924$	−7.01593e9	−	2.44853e9i	−0.292572	−	0.102106i
$925$	−3.29714e9	+	7.95999e9i	−0.136975	+	0.330686i
$926$	−2.78513e10	−	1.74842e10i	−1.15268	−	0.723616i
$927$	3.30799e9			0.136391
$928$	−2.36315e9	−	1.27855e8i	−0.0970675	−	0.00525168i
$929$	2.88374e10			1.18005			0.590025	−	0.807385i	$-0.299118\pi$
$929$	2.88374e10			1.18005			0.590025	+	0.807385i	$0.299118\pi$
$930$	9.85116e9	+	6.18427e9i	0.401603	+	0.252115i
$931$	1.26633e10	−	3.05720e10i	0.514309	−	1.24165i
$932$	−9.81263e9	+	2.81168e10i	−0.397036	+	1.13765i
$933$	−3.51900e9	+	1.45762e9i	−0.141852	+	0.0587568i
$934$	5.09600e9	−	3.61894e9i	0.204652	−	0.145334i
$935$	−9.28436e9	+	9.28436e9i	−0.371459	+	0.371459i
$936$	1.76285e9	+	6.09083e9i	0.0702668	+	0.242779i
$937$	−1.18815e10	−	1.18815e10i	−0.471826	−	0.471826i	0.430679	−	0.902505i	$-0.358274\pi$
$937$	−1.18815e10	−	1.18815e10i	−0.471826	−	0.471826i	−0.902505	+	0.430679i	$0.858274\pi$
$938$	4.02989e10	+	6.83006e9i	1.59435	+	0.270218i
$939$	7.60734e9	+	1.83657e10i	0.299849	+	0.723900i
$940$	5.70134e9	−	6.39033e9i	0.223887	−	0.250944i
$941$	3.04956e10	+	1.26317e10i	1.19309	+	0.494194i	0.888760	−	0.458373i	$-0.151568\pi$
$941$	3.04956e10	+	1.26317e10i	1.19309	+	0.494194i	0.304329	+	0.952567i	$0.401568\pi$
$942$	2.24120e10	−	5.12507e9i	0.873581	−	0.199766i
$943$		−	1.91866e10i		−	0.745086i
$944$	−6.48177e8	+	2.26382e9i	−0.0250779	+	0.0875869i
$945$			3.20670e10i			1.23608i
$946$	1.50284e9	+	6.57197e9i	0.0577158	+	0.252393i
$947$	−3.34341e10	−	1.38489e10i	−1.27928	−	0.529894i	−0.363506	−	0.931592i	$-0.618420\pi$
$947$	−3.34341e10	−	1.38489e10i	−1.27928	−	0.529894i	−0.915772	+	0.401698i	$0.868420\pi$
$948$	1.41969e8	+	2.49151e9i	0.00541209	+	0.0949805i
$949$	4.24736e8	+	1.02540e9i	0.0161320	+	0.0389460i
$950$	−1.06952e10	+	6.31040e10i	−0.404721	+	2.38795i
$951$	−9.78065e9	−	9.78065e9i	−0.368753	−	0.368753i
$952$	−4.11005e10	−	5.14086e10i	−1.54390	−	1.93111i
$953$	−1.72605e10	+	1.72605e10i	−0.645993	+	0.645993i	−0.952022	−	0.306029i	$-0.901000\pi$
$953$	−1.72605e10	+	1.72605e10i	−0.645993	+	0.645993i	0.306029	+	0.952022i	$0.401000\pi$
$954$	1.26179e10	+	1.77679e10i	0.470510	+	0.662546i
$955$	−1.72672e10	+	7.15232e9i	−0.641520	+	0.265726i
$956$	−1.62724e10	+	7.85281e9i	−0.602350	+	0.290685i
$957$	2.27513e8	−	5.49266e8i	0.00839103	−	0.0202577i
$958$	1.67277e10	−	2.66463e10i	0.614693	−	0.979168i
$959$	2.22815e10			0.815790
$960$	−1.21192e10	+	5.37060e10i	−0.442103	+	1.95917i
$961$	−2.59790e10			−0.944260
$962$	−1.50461e9	+	2.39676e9i	−0.0544895	+	0.0867984i
$963$	−4.67817e9	+	1.12941e10i	−0.168804	+	0.407530i
$964$	−1.43555e10	+	6.92773e9i	−0.516117	+	0.249070i
$965$	−1.59690e10	+	6.61460e9i	−0.572049	+	0.236951i
$966$	−3.01218e10	−	4.24159e10i	−1.07513	−	1.51394i
$967$	8.91694e9	−	8.91694e9i	0.317119	−	0.317119i	−0.530540	−	0.847660i	$-0.678011\pi$
$967$	8.91694e9	−	8.91694e9i	0.317119	−	0.317119i	0.847660	+	0.530540i	$0.178011\pi$
$968$	2.13194e10	−	1.70446e10i	0.755459	−	0.603980i
$969$	6.80085e10	+	6.80085e10i	2.40121	+	2.40121i
$970$	2.33957e9	−	1.38040e10i	0.0823068	−	0.485628i
$971$	−3.33222e8	−	8.04468e8i	−0.0116806	−	0.0281995i	0.917932	−	0.396739i	$-0.129858\pi$
$971$	−3.33222e8	−	8.04468e8i	−0.0116806	−	0.0281995i	−0.929612	+	0.368539i	$0.879858\pi$
$972$	−1.62189e9	−	2.84636e10i	−0.0566485	−	0.994163i
$973$	2.48947e10	+	1.03117e10i	0.866388	+	0.358870i
$974$	−3.70873e9	−	1.62184e10i	−0.128608	−	0.562407i
$975$		−	2.63977e10i		−	0.912117i
$976$	2.44144e10	+	4.40040e10i	0.840565	+	1.51502i
$977$		−	5.37339e10i		−	1.84339i	−0.387914	−	0.921695i	$-0.626804\pi$
$977$		−	5.37339e10i		−	1.84339i	0.387914	−	0.921695i	$-0.373196\pi$
$978$	2.03658e10	−	4.65713e9i	0.696169	−	0.159196i
$979$	6.52102e9	+	2.70110e9i	0.222114	+	0.0920027i
$980$	−2.80600e10	+	3.14510e10i	−0.952348	+	1.06744i
$981$	−7.80202e9	−	1.88357e10i	−0.263855	−	0.637002i
$982$	−5.02293e10	−	8.51312e9i	−1.69265	−	0.286879i
$983$	−2.43306e9	−	2.43306e9i	−0.0816986	−	0.0816986i	0.665077	−	0.746775i	$-0.268399\pi$
$983$	−2.43306e9	−	2.43306e9i	−0.0816986	−	0.0816986i	−0.746775	+	0.665077i	$0.768399\pi$
$984$	2.45619e10	−	7.10887e9i	0.821824	−	0.237858i
$985$	3.41806e10	−	3.41806e10i	1.13960	−	1.13960i
$986$	4.29342e9	−	3.04899e9i	0.142638	−	0.101295i
$987$	−9.96354e9	+	4.12703e9i	−0.329840	+	0.136624i
$988$	−6.92696e9	+	1.98483e10i	−0.228504	+	0.654748i
$989$	−1.80617e10	+	4.36049e10i	−0.593707	+	1.43334i
$990$	−4.16636e9	−	2.61551e9i	−0.136469	−	0.0856710i
$991$	4.66448e9			0.152246			0.0761230	−	0.997098i	$-0.475746\pi$
$991$	4.66448e9			0.152246			0.0761230	+	0.997098i	$0.475746\pi$
$992$	2.41153e9	+	6.84671e9i	0.0784334	+	0.222685i
$993$	−3.67238e9			−0.119022
$994$	−3.42768e10	−	2.15179e10i	−1.10700	−	0.694942i
$995$	9.39913e9	−	2.26915e10i	0.302487	−	0.730269i
$996$	−2.59038e10	−	9.04032e9i	−0.830723	−	0.289919i
$997$	−2.36599e10	+	9.80025e9i	−0.756101	+	0.313187i	−0.727228	−	0.686396i	$-0.759192\pi$
$997$	−2.36599e10	+	9.80025e9i	−0.756101	+	0.313187i	−0.0288730	+	0.999583i	$0.509192\pi$
$998$	−2.11406e10	+	1.50131e10i	−0.673224	+	0.478093i
$999$	2.78359e9	−	2.78359e9i	0.0883336	−	0.0883336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.13.10	yes	108
32.5	even	8	inner	32.8.g.a.5.10	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.5.10	✓	108	32.5	even	8	inner
32.8.g.a.13.10	yes	108	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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.01533 + 9.58206i) q^{2} +(-22.2952 + 53.8254i) q^{3} +(-55.6316 - 115.278i) q^{4} +(416.314 - 172.443i) q^{5} +(-381.645 - 537.412i) q^{6} +(881.560 - 881.560i) q^{7} +(1439.25 + 160.372i) q^{8} +(-853.657 - 853.657i) q^{9} +O(q^{10})\)	\(q+(-6.01533 + 9.58206i) q^{2} +(-22.2952 + 53.8254i) q^{3} +(-55.6316 - 115.278i) q^{4} +(416.314 - 172.443i) q^{5} +(-381.645 - 537.412i) q^{6} +(881.560 - 881.560i) q^{7} +(1439.25 + 160.372i) q^{8} +(-853.657 - 853.657i) q^{9} +(-851.908 + 5026.45i) q^{10} +(-305.868 - 738.430i) q^{11} +(7445.23 - 424.237i) q^{12} +(-3350.79 - 1387.94i) q^{13} +(3144.28 + 13750.0i) q^{14} +26252.9i q^{15} +(-10194.2 + 12826.3i) q^{16} -36455.9i q^{17} +(13314.8 - 3044.76i) q^{18} +(41836.4 + 17329.2i) q^{19} +(-43039.2 - 38398.8i) q^{20} +(27795.8 + 67104.9i) q^{21} +(8915.57 + 1511.06i) q^{22} +(44765.1 + 44765.1i) q^{23} +(-40720.4 + 73892.5i) q^{24} +(88338.1 - 88338.1i) q^{25} +(33455.4 - 23758.5i) q^{26} +(-52735.3 + 21843.7i) q^{27} +(-150667. - 52582.2i) q^{28} +(4885.86 - 11795.5i) q^{29} +(-251557. - 157920. i) q^{30} -39160.8 q^{31} +(-61580.2 - 174836. i) q^{32} +46565.7 q^{33} +(349322. + 219294. i) q^{34} +(214987. - 519024. i) q^{35} +(-50917.9 + 145899. i) q^{36} +(-63716.1 + 26392.1i) q^{37} +(-417709. + 296638. i) q^{38} +(149413. - 149413. i) q^{39} +(626834. - 181423. i) q^{40} +(-214303. - 214303. i) q^{41} +(-810203. - 137317. i) q^{42} +(285302. + 688779. i) q^{43} +(-68109.1 + 76340.0i) q^{44} +(-502596. - 208182. i) q^{45} +(-698219. + 159665. i) q^{46} +148477. i q^{47} +(-463096. - 834674. i) q^{48} -730752. i q^{49} +(315078. + 1.37784e6i) q^{50} +(1.96225e6 + 812791. i) q^{51} +(26410.0 + 463487. i) q^{52} +(610579. + 1.47407e6i) q^{53} +(107913. - 636710. i) q^{54} +(-254674. - 254674. i) q^{55} +(1.41016e6 - 1.12740e6i) q^{56} +(-1.86550e6 + 1.86550e6i) q^{57} +(83635.2 + 117770. i) q^{58} +(132784. - 55001.0i) q^{59} +(3.02640e6 - 1.46049e6i) q^{60} +(1.17540e6 - 2.83767e6i) q^{61} +(235565. - 375241. i) q^{62} -1.50510e6 q^{63} +(2.04571e6 + 461631. i) q^{64} -1.63432e6 q^{65} +(-280108. + 446195. i) q^{66} +(1.10895e6 - 2.67723e6i) q^{67} +(-4.20258e6 + 2.02810e6i) q^{68} +(-3.40755e6 + 1.41145e6i) q^{69} +(3.68010e6 + 5.18212e6i) q^{70} +(-2.02890e6 + 2.02890e6i) q^{71} +(-1.09172e6 - 1.36553e6i) q^{72} +(-216388. - 216388. i) q^{73} +(130383. - 769289. i) q^{74} +(2.78532e6 + 6.72435e6i) q^{75} +(-329743. - 5.78688e6i) q^{76} +(-920611. - 381329. i) q^{77} +(532916. + 2.33045e6i) q^{78} +334646. i q^{79} +(-2.03221e6 + 7.09768e6i) q^{80} -5.96577e6i q^{81} +(3.34256e6 - 764359. i) q^{82} +(-3.39903e6 - 1.40792e6i) q^{83} +(6.18942e6 - 6.93741e6i) q^{84} +(-6.28656e6 - 1.51771e7i) q^{85} +(-8.31611e6 - 1.40946e6i) q^{86} +(525967. + 525967. i) q^{87} +(-321795. - 1.11184e6i) q^{88} +(-6.24441e6 + 6.24441e6i) q^{89} +(5.01809e6 - 3.56362e6i) q^{90} +(-4.17747e6 + 1.73037e6i) q^{91} +(2.67010e6 - 7.65081e6i) q^{92} +(873098. - 2.10784e6i) q^{93} +(-1.42272e6 - 893139. i) q^{94} +2.04054e7 q^{95} +(1.07836e7 + 583428. i) q^{96} -2.74628e6 q^{97} +(7.00211e6 + 4.39571e6i) q^{98} +(-369260. + 891471. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Introduction

L-functions

Modular forms

Varieties

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