LMFDB - Embedded newform 32.8.g.a.21.4

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			21.4
Character	$\chi$	$=$	32.21
Dual form			32.8.g.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.5959 + 3.96560i) q^{2} +(-22.5968 + 9.35989i) q^{3} +(96.5480 - 84.0385i) q^{4} +(-139.101 + 335.820i) q^{5} +(202.317 - 188.787i) q^{6} +(319.530 + 319.530i) q^{7} +(-689.754 + 1273.34i) q^{8} +(-1123.44 + 1123.44i) q^{9} +O(q^{10})$	\(q+(-10.5959 + 3.96560i) q^{2} +(-22.5968 + 9.35989i) q^{3} +(96.5480 - 84.0385i) q^{4} +(-139.101 + 335.820i) q^{5} +(202.317 - 188.787i) q^{6} +(319.530 + 319.530i) q^{7} +(-689.754 + 1273.34i) q^{8} +(-1123.44 + 1123.44i) q^{9} +(142.181 - 4109.95i) q^{10} +(1461.61 + 605.418i) q^{11} +(-1395.08 + 2802.68i) q^{12} +(-3132.97 - 7563.65i) q^{13} +(-4652.85 - 2118.60i) q^{14} -8890.43i q^{15} +(2259.05 - 16227.5i) q^{16} -24559.7i q^{17} +(7448.77 - 16359.0i) q^{18} +(-11269.5 - 27207.0i) q^{19} +(14791.9 + 44112.7i) q^{20} +(-10211.1 - 4229.58i) q^{21} +(-17888.0 - 618.821i) q^{22} +(-69019.8 + 69019.8i) q^{23} +(3667.91 - 35229.4i) q^{24} +(-38183.4 - 38183.4i) q^{25} +(63191.1 + 67719.9i) q^{26} +(35340.9 - 85320.4i) q^{27} +(57702.9 + 3997.16i) q^{28} +(145056. - 60084.1i) q^{29} +(35255.9 + 94202.5i) q^{30} -175945. q^{31} +(40415.1 + 180904. i) q^{32} -38694.3 q^{33} +(97394.1 + 260234. i) q^{34} +(-151752. + 62857.7i) q^{35} +(-14053.6 + 202877. i) q^{36} +(19858.5 - 47942.7i) q^{37} +(227304. + 243594. i) q^{38} +(141590. + 141590. i) q^{39} +(-331667. - 408757. i) q^{40} +(-125962. + 125962. i) q^{41} +(124969. + 4323.22i) q^{42} +(95136.0 + 39406.6i) q^{43} +(191994. - 64379.5i) q^{44} +(-221001. - 533544. i) q^{45} +(457625. - 1.00503e6i) q^{46} -203922. i q^{47} +(100841. + 387834. i) q^{48} -619344. i q^{49} +(556009. + 253169. i) q^{50} +(229876. + 554971. i) q^{51} +(-938120. - 466966. i) q^{52} +(-1.20758e6 - 500196. i) q^{53} +(-36123.3 + 1.04420e6i) q^{54} +(-406623. + 406623. i) q^{55} +(-627268. + 186473. i) q^{56} +(509310. + 509310. i) q^{57} +(-1.29873e6 + 1.21188e6i) q^{58} +(28673.6 - 69224.3i) q^{59} +(-747139. - 858353. i) q^{60} +(2.47882e6 - 1.02676e6i) q^{61} +(1.86430e6 - 697726. i) q^{62} -717944. q^{63} +(-1.14563e6 - 1.75658e6i) q^{64} +2.97583e6 q^{65} +(410002. - 153446. i) q^{66} +(-4.01036e6 + 1.66115e6i) q^{67} +(-2.06396e6 - 2.37119e6i) q^{68} +(913607. - 2.20564e6i) q^{69} +(1.35869e6 - 1.26782e6i) q^{70} +(2.46042e6 + 2.46042e6i) q^{71} +(-655619. - 2.20541e6i) q^{72} +(-1.10035e6 + 1.10035e6i) q^{73} +(-20298.2 + 586750. i) q^{74} +(1.22021e6 + 505429. i) q^{75} +(-3.37449e6 - 1.67971e6i) q^{76} +(273579. + 660477. i) q^{77} +(-2.06177e6 - 938789. i) q^{78} +7.83101e6i q^{79} +(5.13529e6 + 3.01590e6i) q^{80} -1.21591e6i q^{81} +(835168. - 1.83419e6i) q^{82} +(362067. + 874106. i) q^{83} +(-1.34131e6 + 449770. i) q^{84} +(8.24766e6 + 3.41629e6i) q^{85} +(-1.16433e6 - 40279.1i) q^{86} +(-2.71542e6 + 2.71542e6i) q^{87} +(-1.77905e6 + 1.44353e6i) q^{88} +(-4.18977e6 - 4.18977e6i) q^{89} +(4.45754e6 + 4.77700e6i) q^{90} +(1.41574e6 - 3.41789e6i) q^{91} +(-863403. + 1.24640e7i) q^{92} +(3.97578e6 - 1.64682e6i) q^{93} +(808672. + 2.16074e6i) q^{94} +1.07043e7 q^{95} +(-2.60649e6 - 3.70957e6i) q^{96} -1.41147e7 q^{97} +(2.45607e6 + 6.56253e6i) q^{98} +(-2.32217e6 + 961875. 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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

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

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 $

$2$	−10.5959	+	3.96560i	−0.936558	+	0.350513i
$2$	−10.5959	+	3.96560i	−0.936558	+	0.350513i
$3$	−22.5968	+	9.35989i	−0.483195	+	0.200146i	−0.610964	−	0.791658i	$-0.709218\pi$
$3$	−22.5968	+	9.35989i	−0.483195	+	0.200146i	0.127770	+	0.991804i	$0.459218\pi$
$4$	96.5480	−	84.0385i	0.754282	−	0.656551i
$5$	−139.101	+	335.820i	−0.497664	+	1.20147i	0.453074	+	0.891473i	$0.350327\pi$
$5$	−139.101	+	335.820i	−0.497664	+	1.20147i	−0.950738	+	0.309994i	$0.899673\pi$
$6$	202.317	−	188.787i	0.382386	−	0.356814i
$7$	319.530	+	319.530i	0.352102	+	0.352102i	0.860891	−	0.508789i	$-0.169907\pi$
$7$	319.530	+	319.530i	0.352102	+	0.352102i	−0.508789	+	0.860891i	$0.669907\pi$
$8$	−689.754	+	1273.34i	−0.476299	+	0.879283i
$9$	−1123.44	+	1123.44i	−0.513688	+	0.513688i
$10$	142.181	−	4109.95i	0.0449615	−	1.29968i
$11$	1461.61	+	605.418i	0.331098	+	0.137145i	0.542039	−	0.840354i	$-0.317653\pi$
$11$	1461.61	+	605.418i	0.331098	+	0.137145i	−0.210941	+	0.977499i	$0.567653\pi$
$12$	−1395.08	+	2802.68i	−0.233059	+	0.468208i
$13$	−3132.97	−	7563.65i	−0.395507	−	0.954838i	−0.988718	−	0.149791i	$-0.952140\pi$
$13$	−3132.97	−	7563.65i	−0.395507	−	0.954838i	0.593211	−	0.805047i	$-0.297860\pi$
$14$	−4652.85	−	2118.60i	−0.453181	−	0.206348i
$15$		−	8890.43i		−	0.680148i
$16$	2259.05	−	16227.5i	0.137881	−	0.990449i
$17$		−	24559.7i		−	1.21242i	−0.795305	−	0.606209i	$-0.792689\pi$
$17$		−	24559.7i		−	1.21242i	0.795305	−	0.606209i	$-0.207311\pi$
$18$	7448.77	−	16359.0i	0.301044	−	0.661153i
$19$	−11269.5	−	27207.0i	−0.376936	−	0.910005i	−0.992537	−	0.121946i	$-0.961086\pi$
$19$	−11269.5	−	27207.0i	−0.376936	−	0.910005i	0.615600	−	0.788059i	$-0.288914\pi$
$20$	14791.9	+	44112.7i	0.413446	+	1.23299i
$21$	−10211.1	−	4229.58i	−0.240606	−	0.0996621i
$22$	−17888.0	−	618.821i	−0.358164	−	0.0123904i
$23$	−69019.8	+	69019.8i	−1.18284	+	1.18284i	−0.203835	+	0.979005i	$0.565341\pi$
$23$	−69019.8	+	69019.8i	−1.18284	+	1.18284i	−0.979005	+	0.203835i	$0.934659\pi$
$24$	3667.91	−	35229.4i	0.0541602	−	0.520194i
$25$	−38183.4	−	38183.4i	−0.488747	−	0.488747i
$26$	63191.1	+	67719.9i	0.705098	+	0.755631i
$27$	35340.9	−	85320.4i	0.345545	−	0.834218i
$28$	57702.9	+	3997.16i	0.496757	+	0.0344111i
$29$	145056.	−	60084.1i	1.10444	−	0.457474i	0.245421	−	0.969417i	$-0.421074\pi$
$29$	145056.	−	60084.1i	1.10444	−	0.457474i	0.859020	+	0.511942i	$0.171074\pi$
$30$	35255.9	+	94202.5i	0.238400	+	0.636998i
$31$	−175945.			−1.06074			−0.530372	−	0.847765i	$-0.677948\pi$
$31$	−175945.			−1.06074			−0.530372	+	0.847765i	$0.677948\pi$
$32$	40415.1	+	180904.i	0.218031	+	0.975942i
$33$	−38694.3			−0.187434
$34$	97394.1	+	260234.i	0.424968	+	1.13550i
$35$	−151752.	+	62857.7i	−0.598268	+	0.247811i
$36$	−14053.6	+	202877.i	−0.0502030	+	0.724728i
$37$	19858.5	−	47942.7i	0.0644527	−	0.155603i	−0.888371	−	0.459125i	$-0.848163\pi$
$37$	19858.5	−	47942.7i	0.0644527	−	0.155603i	0.952824	+	0.303523i	$0.0981629\pi$
$38$	227304.	+	243594.i	0.671991	+	0.720151i
$39$	141590.	+	141590.i	0.382213	+	0.382213i
$40$	−331667.	−	408757.i	−0.819393	−	1.00985i
$41$	−125962.	+	125962.i	−0.285427	+	0.285427i	−0.835269	−	0.549842i	$-0.814688\pi$
$41$	−125962.	+	125962.i	−0.285427	+	0.285427i	0.549842	+	0.835269i	$0.314688\pi$
$42$	124969.	+	4323.22i	0.260274	+	0.00900399i
$43$	95136.0	+	39406.6i	0.182476	+	0.0755840i	0.472051	−	0.881571i	$-0.343514\pi$
$43$	95136.0	+	39406.6i	0.182476	+	0.0755840i	−0.289575	+	0.957155i	$0.593514\pi$
$44$	191994.	−	64379.5i	0.339784	−	0.113937i
$45$	−221001.	−	533544.i	−0.361535	−	0.872823i
$46$	457625.	−	1.00503e6i	0.693198	−	1.52240i
$47$		−	203922.i		−	0.286498i	−0.989687	−	0.143249i	$-0.954245\pi$
$47$		−	203922.i		−	0.286498i	0.989687	−	0.143249i	$-0.0457549\pi$
$48$	100841.	+	387834.i	0.131611	+	0.506176i
$49$		−	619344.i		−	0.752048i
$50$	556009.	+	253169.i	0.629052	+	0.286428i
$51$	229876.	+	554971.i	0.242660	+	0.585834i
$52$	−938120.	−	466966.i	−0.925223	−	0.460546i
$53$	−1.20758e6	−	500196.i	−1.11417	−	0.461503i	−0.251796	−	0.967780i	$-0.581021\pi$
$53$	−1.20758e6	−	500196.i	−1.11417	−	0.461503i	−0.862371	+	0.506277i	$0.831021\pi$
$54$	−36123.3	+	1.04420e6i	−0.0312183	+	0.902412i
$55$	−406623.	+	406623.i	−0.329551	+	0.329551i
$56$	−627268.	+	186473.i	−0.477304	+	0.141892i
$57$	509310.	+	509310.i	0.364267	+	0.364267i
$58$	−1.29873e6	+	1.21188e6i	−0.874022	+	0.815572i
$59$	28673.6	−	69224.3i	0.0181761	−	0.0438810i	−0.914531	−	0.404516i	$-0.867440\pi$
$59$	28673.6	−	69224.3i	0.0181761	−	0.0438810i	0.932707	+	0.360635i	$0.117440\pi$
$60$	−747139.	−	858353.i	−0.446552	−	0.513023i
$61$	2.47882e6	−	1.02676e6i	1.39827	−	0.579182i	0.448967	−	0.893548i	$-0.351792\pi$
$61$	2.47882e6	−	1.02676e6i	1.39827	−	0.579182i	0.949302	+	0.314366i	$0.101792\pi$
$62$	1.86430e6	−	697726.i	0.993448	−	0.371804i
$63$	−717944.			−0.361742
$64$	−1.14563e6	−	1.75658e6i	−0.546279	−	0.837603i
$65$	2.97583e6			1.34404
$66$	410002.	−	153446.i	0.175543	−	0.0656980i
$67$	−4.01036e6	+	1.66115e6i	−1.62900	+	0.674755i	−0.995120	−	0.0986741i	$-0.968540\pi$
$67$	−4.01036e6	+	1.66115e6i	−1.62900	+	0.674755i	−0.633883	+	0.773429i	$0.718540\pi$
$68$	−2.06396e6	−	2.37119e6i	−0.796014	−	0.914505i
$69$	913607.	−	2.20564e6i	0.334802	−	0.808283i
$70$	1.35869e6	−	1.26782e6i	0.473452	−	0.441790i
$71$	2.46042e6	+	2.46042e6i	0.815842	+	0.815842i	0.985503	−	0.169661i	$-0.0542672\pi$
$71$	2.46042e6	+	2.46042e6i	0.815842	+	0.815842i	−0.169661	+	0.985503i	$0.554267\pi$
$72$	−655619.	−	2.20541e6i	−0.207008	−	0.696347i
$73$	−1.10035e6	+	1.10035e6i	−0.331056	+	0.331056i	−0.852987	−	0.521931i	$-0.825212\pi$
$73$	−1.10035e6	+	1.10035e6i	−0.331056	+	0.331056i	0.521931	+	0.852987i	$0.325212\pi$
$74$	−20298.2	+	586750.i	−0.00582299	+	0.168322i
$75$	1.22021e6	+	505429.i	0.333981	+	0.138339i
$76$	−3.37449e6	−	1.67971e6i	−0.881781	−	0.438922i
$77$	273579.	+	660477.i	0.0682912	+	0.164870i
$78$	−2.06177e6	−	938789.i	−0.491936	−	0.223994i
$79$			7.83101e6i			1.78699i	0.449069	+	0.893497i	$0.351756\pi$
$79$			7.83101e6i			1.78699i	−0.449069	+	0.893497i	$0.648244\pi$
$80$	5.13529e6	+	3.01590e6i	1.12137	+	0.658571i
$81$		−	1.21591e6i		−	0.254216i
$82$	835168.	−	1.83419e6i	0.167273	−	0.367364i
$83$	362067.	+	874106.i	0.0695048	+	0.167800i	0.954814	−	0.297202i	$-0.0960536\pi$
$83$	362067.	+	874106.i	0.0695048	+	0.167800i	−0.885310	+	0.465002i	$0.846054\pi$
$84$	−1.34131e6	+	449770.i	−0.246918	+	0.0827966i
$85$	8.24766e6	+	3.41629e6i	1.45668	+	0.603377i
$86$	−1.16433e6	−	40279.1i	−0.197392	−	0.00682865i
$87$	−2.71542e6	+	2.71542e6i	−0.442098	+	0.442098i
$88$	−1.77905e6	+	1.44353e6i	−0.278291	+	0.225807i
$89$	−4.18977e6	−	4.18977e6i	−0.629978	−	0.629978i	0.318085	−	0.948062i	$-0.396960\pi$
$89$	−4.18977e6	−	4.18977e6i	−0.629978	−	0.629978i	−0.948062	+	0.318085i	$0.896960\pi$
$90$	4.45754e6	+	4.77700e6i	0.644535	+	0.690727i
$91$	1.41574e6	−	3.41789e6i	0.196942	−	0.475459i
$92$	−863403.	+	1.24640e7i	−0.115600	+	1.66879i
$93$	3.97578e6	−	1.64682e6i	0.512545	−	0.212303i
$94$	808672.	+	2.16074e6i	0.100421	+	0.268322i
$95$	1.07043e7			1.28093
$96$	−2.60649e6	−	3.70957e6i	−0.300682	−	0.427932i
$97$	−1.41147e7			−1.57025			−0.785126	−	0.619336i	$-0.787402\pi$
$97$	−1.41147e7			−1.57025			−0.785126	+	0.619336i	$0.787402\pi$
$98$	2.45607e6	+	6.56253e6i	0.263602	+	0.704336i
$99$	−2.32217e6	+	961875.i	−0.240531	+	0.0996312i
$100$	−6.89540e6	−	477655.i	−0.689540	−	0.0477655i
$101$	−514694.	+	1.24258e6i	−0.0497077	+	0.120005i	−0.946783	−	0.321873i	$-0.895688\pi$
$101$	−514694.	+	1.24258e6i	−0.0497077	+	0.120005i	0.897075	+	0.441878i	$0.145688\pi$
$102$	−4.63655e6	−	4.96884e6i	−0.432608	−	0.463612i
$103$	−4.56124e6	−	4.56124e6i	−0.411294	−	0.411294i	0.470895	−	0.882189i	$-0.343931\pi$
$103$	−4.56124e6	−	4.56124e6i	−0.411294	−	0.411294i	−0.882189	+	0.470895i	$0.843931\pi$
$104$	1.17921e7	+	1.22773e6i	1.02795	+	0.107026i
$105$	2.84076e6	−	2.84076e6i	0.239482	−	0.239482i
$106$	1.47790e7	+	511270.i	1.20524	+	0.0416946i
$107$	−1.28040e7	−	5.30357e6i	−1.01042	−	0.418529i	−0.184810	−	0.982774i	$-0.559167\pi$
$107$	−1.28040e7	−	5.30357e6i	−1.01042	−	0.418529i	−0.825607	+	0.564246i	$0.809167\pi$
$108$	−3.75811e6	−	1.12075e7i	−0.287069	−	0.856103i
$109$	−8.51398e6	−	2.05546e7i	−0.629709	−	1.52025i	−0.839985	−	0.542610i	$-0.817436\pi$
$109$	−8.51398e6	−	2.05546e7i	−0.629709	−	1.52025i	0.210276	−	0.977642i	$-0.432564\pi$
$110$	2.69605e6	−	5.92106e6i	0.193132	−	0.424156i
$111$			1.26922e6i			0.0880862i
$112$	5.90702e6	−	4.46335e6i	0.397288	−	0.300191i
$113$			2.32706e7i			1.51716i	0.651578	+	0.758581i	$0.274107\pi$
$113$			2.32706e7i			1.51716i	−0.651578	+	0.758581i	$0.725893\pi$
$114$	−7.41634e6	−	3.37690e6i	−0.468838	−	0.213477i
$115$	−1.35775e7	−	3.27790e7i	−0.832487	−	2.00980i
$116$	8.95548e6	−	1.79913e7i	0.532704	−	1.07019i
$117$	1.20170e7	+	4.97759e6i	0.693656	+	0.287322i
$118$	−29308.4	+	847204.i	−0.00164212	+	0.0474680i
$119$	7.84758e6	−	7.84758e6i	0.426895	−	0.426895i
$120$	1.13205e7	+	6.13221e6i	0.598043	+	0.323954i
$121$	−1.20097e7	−	1.20097e7i	−0.616290	−	0.616290i
$122$	−2.21937e7	+	2.07095e7i	−1.10655	+	1.03255i
$123$	1.66734e6	−	4.02531e6i	0.0807897	−	0.195043i
$124$	−1.69871e7	+	1.47861e7i	−0.800099	+	0.696432i
$125$	−8.10186e6	+	3.35590e6i	−0.371022	+	0.153682i
$126$	7.60729e6	−	2.84708e6i	0.338792	−	0.126795i
$127$	4.94350e6			0.214152			0.107076	−	0.994251i	$-0.465851\pi$
$127$	4.94350e6			0.214152			0.107076	+	0.994251i	$0.465851\pi$
$128$	1.91049e7	+	1.40695e7i	0.805213	+	0.592986i
$129$	−2.51861e6			−0.103299
$130$	−3.15317e7	+	1.18009e7i	−1.25877	+	0.471102i
$131$	6.11927e6	−	2.53468e6i	0.237821	−	0.0985086i	−0.260590	−	0.965450i	$-0.583917\pi$
$131$	6.11927e6	−	2.53468e6i	0.237821	−	0.0985086i	0.498411	+	0.866941i	$0.333917\pi$
$132$	−3.73586e6	+	3.25181e6i	−0.141378	+	0.123060i
$133$	5.09252e6	−	1.22944e7i	0.187695	−	0.453135i
$134$	3.59061e7	−	3.35049e7i	1.28915	−	1.20293i
$135$	2.37364e7	+	2.37364e7i	0.830321	+	0.830321i
$136$	3.12729e7	+	1.69402e7i	1.06606	+	0.577473i
$137$	−2.69072e7	+	2.69072e7i	−0.894019	+	0.894019i	−0.994899	−	0.100880i	$-0.967834\pi$
$137$	−2.69072e7	+	2.69072e7i	−0.894019	+	0.894019i	0.100880	+	0.994899i	$0.467834\pi$
$138$	−933833.	+	2.69939e7i	−0.0302477	+	0.874356i
$139$	−8.74240e6	−	3.62122e6i	−0.276108	−	0.114368i	0.240333	−	0.970691i	$-0.422743\pi$
$139$	−8.74240e6	−	3.62122e6i	−0.276108	−	0.114368i	−0.516441	+	0.856323i	$0.672743\pi$
$140$	−9.36887e6	+	1.88218e7i	−0.288562	+	0.579713i
$141$	1.90869e6	+	4.60797e6i	0.0573413	+	0.138434i
$142$	−3.58276e7	−	1.63135e7i	−1.05005	−	0.478120i
$143$		−	1.29518e7i		−	0.370387i
$144$	1.56927e7	+	2.07685e7i	0.437954	+	0.579610i
$145$			5.70705e7i			1.55462i
$146$	7.29571e6	−	1.60228e7i	0.194014	−	0.426093i
$147$	5.79699e6	+	1.39952e7i	0.150519	+	0.363385i
$148$	−2.11174e6	−	6.29766e6i	−0.0535456	−	0.159685i
$149$	1.67410e6	+	693437.i	0.0414601	+	0.0171733i	0.403317	−	0.915060i	$-0.367857\pi$
$149$	1.67410e6	+	693437.i	0.0414601	+	0.0171733i	−0.361857	+	0.932234i	$0.617857\pi$
$150$	−1.49336e7	−	516618.i	−0.361282	−	0.0124983i
$151$	−7.05028e6	+	7.05028e6i	−0.166643	+	0.166643i	−0.785502	−	0.618859i	$-0.787595\pi$
$151$	−7.05028e6	+	7.05028e6i	−0.166643	+	0.166643i	0.618859	+	0.785502i	$0.287595\pi$
$152$	4.24170e7	+	4.41626e6i	0.979687	+	0.102000i
$153$	2.75913e7	+	2.75913e7i	0.622805	+	0.622805i
$154$	−5.51801e6	−	5.91348e6i	−0.121748	−	0.130473i
$155$	2.44741e7	−	5.90858e7i	0.527894	−	1.27445i
$156$	2.55692e7	+	1.77122e6i	0.539239	+	0.0373539i
$157$	1.42345e7	−	5.89613e6i	0.293558	−	0.121596i	−0.231044	−	0.972943i	$-0.574214\pi$
$157$	1.42345e7	−	5.89613e6i	0.293558	−	0.121596i	0.524602	+	0.851348i	$0.324214\pi$
$158$	−3.10547e7	−	8.29770e7i	−0.626364	−	1.67362i
$159$	3.19692e7			0.630727
$160$	−6.63731e7	−	1.15918e7i	−1.28107	−	0.223734i
$161$	−4.41078e7			−0.832962
$162$	4.82180e6	+	1.28837e7i	0.0891059	+	0.238088i
$163$	−2.90111e7	+	1.20168e7i	−0.524696	+	0.217336i	−0.629278	−	0.777180i	$-0.716649\pi$
$163$	−2.90111e7	+	1.20168e7i	−0.524696	+	0.217336i	0.104582	+	0.994516i	$0.466649\pi$
$164$	−1.57572e6	+	2.27470e7i	−0.0278949	+	0.402689i
$165$	5.38242e6	−	1.29943e7i	0.0932791	−	0.225196i
$166$	−7.30279e6	−	7.82617e6i	−0.123911	−	0.132792i
$167$	4.89771e7	+	4.89771e7i	0.813739	+	0.813739i	0.985192	−	0.171453i	$-0.0548463\pi$
$167$	4.89771e7	+	4.89771e7i	0.813739	+	0.813739i	−0.171453	+	0.985192i	$0.554846\pi$
$168$	1.24289e7	−	1.00848e7i	0.202231	−	0.164092i
$169$	−3.02342e6	+	3.02342e6i	−0.0481831	+	0.0481831i
$170$	−1.00939e8	−	3.49192e6i	−1.57576	−	0.0545122i
$171$	4.32260e7	+	1.79048e7i	0.661086	+	0.273831i
$172$	1.24969e7	−	4.19046e6i	0.187263	−	0.0627931i
$173$	2.69100e6	+	6.49664e6i	0.0395141	+	0.0953954i	0.942404	−	0.334475i	$-0.108559\pi$
$173$	2.69100e6	+	6.49664e6i	0.0395141	+	0.0953954i	−0.902890	+	0.429871i	$0.858559\pi$
$174$	1.80041e7	−	3.95406e7i	0.259090	−	0.569012i
$175$		−	2.44015e7i		−	0.344178i
$176$	1.31263e7	−	2.23506e7i	0.181488	−	0.309026i
$177$			1.83263e6i			0.0248409i
$178$	6.10095e7	+	2.77796e7i	0.810826	+	0.369195i
$179$	−3.13275e7	−	7.56312e7i	−0.408262	−	0.985633i	−0.985595	−	0.169124i	$-0.945906\pi$
$179$	−3.13275e7	−	7.56312e7i	−0.408262	−	0.985633i	0.577332	−	0.816509i	$-0.304094\pi$
$180$	−6.61755e7	−	3.29400e7i	−0.845753	−	0.420988i
$181$	1.09965e8	+	4.55489e7i	1.37841	+	0.570956i	0.944056	−	0.329786i	$-0.106977\pi$
$181$	1.09965e8	+	4.55489e7i	1.37841	+	0.570956i	0.434354	+	0.900742i	$0.356977\pi$
$182$	−1.44708e6	+	4.18300e7i	−0.0177927	+	0.514326i
$183$	−4.64030e7	+	4.64030e7i	−0.559715	+	0.559715i
$184$	−4.02789e7	−	1.35492e8i	−0.476667	−	1.60344i
$185$	1.33378e7	+	1.33378e7i	0.154876	+	0.154876i
$186$	−3.55965e7	+	3.32160e7i	−0.405614	+	0.378488i
$187$	1.48689e7	−	3.58967e7i	0.166277	−	0.401429i
$188$	−1.71373e7	−	1.96883e7i	−0.188100	−	0.216100i
$189$	3.85549e7	−	1.59700e7i	0.415397	−	0.172063i
$190$	−1.13422e8	+	4.24489e7i	−1.19966	+	0.448982i
$191$	−1.32555e8			−1.37651			−0.688255	−	0.725469i	$-0.741623\pi$
$191$	−1.32555e8			−1.37651			−0.688255	+	0.725469i	$0.741623\pi$
$192$	4.23289e7	+	2.89701e7i	0.431602	+	0.295390i
$193$	−1.44840e8			−1.45023			−0.725116	−	0.688627i	$-0.758214\pi$
$193$	−1.44840e8			−1.45023			−0.725116	+	0.688627i	$0.758214\pi$
$194$	1.49558e8	−	5.59731e7i	1.47063	−	0.550393i
$195$	−6.72441e7	+	2.78534e7i	−0.649431	+	0.269003i
$196$	−5.20488e7	−	5.97964e7i	−0.493758	−	0.567256i
$197$	−3.21637e6	+	7.76500e6i	−0.0299733	+	0.0723619i	−0.938157	−	0.346209i	$-0.887469\pi$
$197$	−3.21637e6	+	7.76500e6i	−0.0299733	+	0.0723619i	0.908184	+	0.418571i	$0.137469\pi$
$198$	2.07912e7	−	1.94008e7i	0.190349	−	0.177620i
$199$	1.36145e8	+	1.36145e8i	1.22466	+	1.22466i	0.965957	+	0.258703i	$0.0832949\pi$
$199$	1.36145e8	+	1.36145e8i	1.22466	+	1.22466i	0.258703	+	0.965957i	$0.416705\pi$
$200$	7.49575e7	−	2.22832e7i	0.662537	−	0.196958i
$201$	7.50731e7	−	7.50731e7i	0.652076	−	0.652076i
$202$	526088.	−	1.52074e7i	0.00449085	−	0.129815i
$203$	6.55485e7	+	2.71511e7i	0.549954	+	0.227798i
$204$	6.88330e7	+	3.42629e7i	0.567664	+	0.282565i
$205$	−2.47790e7	−	5.98219e7i	−0.200884	−	0.484977i
$206$	6.64186e7	+	3.02426e7i	0.529364	+	0.241037i
$207$		−	1.55079e8i		−	1.21522i
$208$	−1.29817e8	+	3.37536e7i	−1.00025	+	0.260075i
$209$		−	4.65888e7i		−	0.352996i
$210$	−1.88352e7	+	4.13659e7i	−0.140347	+	0.308230i
$211$	4.01304e6	+	9.68834e6i	0.0294093	+	0.0710004i	0.937902	−	0.346901i	$-0.112766\pi$
$211$	4.01304e6	+	9.68834e6i	0.0294093	+	0.0710004i	−0.908493	+	0.417901i	$0.862766\pi$
$212$	−1.58625e8	+	5.31903e7i	−1.14340	+	0.383404i
$213$	−7.86270e7	−	3.25684e7i	−0.557497	−	0.230923i
$214$	1.56702e8	+	5.42099e6i	1.09301	+	0.0378120i
$215$	−2.64671e7	+	2.64671e7i	−0.181623	+	0.181623i
$216$	8.42652e7	+	1.03851e8i	0.568932	+	0.701169i
$217$	−5.62197e7	−	5.62197e7i	−0.373490	−	0.373490i
$218$	1.71725e8	+	1.84032e8i	1.12263	+	1.20308i
$219$	1.45652e7	−	3.51636e7i	0.0937050	−	0.226224i
$220$	−5.08665e6	+	7.34307e7i	−0.0322072	+	0.464942i
$221$	−1.85761e8	+	7.69448e7i	−1.15766	+	0.479520i
$222$	−5.03324e6	−	1.34486e7i	−0.0308754	−	0.0824979i
$223$	6.72018e7			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$223$	6.72018e7			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$224$	−4.48906e7	+	7.07182e7i	−0.266862	+	0.420401i
$225$	8.57931e7			0.502127
$226$	−9.22817e7	−	2.46573e8i	−0.531785	−	1.42091i
$227$	−3.06644e8	+	1.27016e8i	−1.73998	+	0.720724i	−0.741204	+	0.671280i	$0.765745\pi$
$227$	−3.06644e8	+	1.27016e8i	−1.73998	+	0.720724i	−0.998777	+	0.0494437i	$0.984255\pi$
$228$	9.19745e7	+	6.37121e6i	0.513920	+	0.0356000i
$229$	4.88801e7	−	1.18007e8i	0.268973	−	0.649357i	−0.730463	−	0.682952i	$-0.760696\pi$
$229$	4.88801e7	−	1.18007e8i	0.268973	−	0.649357i	0.999436	+	0.0335951i	$0.0106957\pi$
$230$	2.73855e8	+	2.93481e8i	1.48413	+	1.59050i
$231$	−1.23640e7	−	1.23640e7i	−0.0659959	−	0.0659959i
$232$	−2.35455e7	+	2.26149e8i	−0.123794	+	1.18901i
$233$	2.61805e8	−	2.61805e8i	1.35591	−	1.35591i	0.477020	−	0.878892i	$-0.341717\pi$
$233$	2.61805e8	−	2.61805e8i	1.35591	−	1.35591i	0.878892	−	0.477020i	$-0.158283\pi$
$234$	−1.47070e8	−	5.08779e6i	−0.750359	−	0.0259581i
$235$	6.84811e7	+	2.83658e7i	0.344218	+	0.142580i
$236$	−3.04912e6	−	9.09316e6i	−0.0151002	−	0.0450321i
$237$	−7.32974e7	−	1.76956e8i	−0.357659	−	0.863466i
$238$	−5.20321e7	+	1.14273e8i	−0.250180	+	0.549444i
$239$		−	2.03577e8i		−	0.964575i	−0.876013	−	0.482287i	$-0.839806\pi$
$239$		−	2.03577e8i		−	0.964575i	0.876013	−	0.482287i	$-0.160194\pi$
$240$	−1.44270e8	−	2.00839e7i	−0.673651	−	0.0937797i
$241$			1.40865e8i			0.648250i	0.946014	+	0.324125i	$0.105070\pi$
$241$			1.40865e8i			0.648250i	−0.946014	+	0.324125i	$0.894930\pi$
$242$	1.74880e8	+	7.96287e7i	0.793208	+	0.361174i
$243$	8.86712e7	+	2.14071e8i	0.396425	+	0.957054i
$244$	1.53038e8	−	3.07448e8i	0.674426	−	1.35490i
$245$	2.07988e8	+	8.61515e7i	0.903561	+	0.374267i
$246$	−1.70425e6	+	4.92640e7i	−0.00729896	+	0.210987i
$247$	−1.70477e8	+	1.70477e8i	−0.719826	+	0.719826i
$248$	1.21359e8	−	2.24037e8i	0.505231	−	0.932694i
$249$	−1.63631e7	−	1.63631e7i	−0.0671687	−	0.0671687i
$250$	7.25387e7	−	6.76876e7i	0.293616	−	0.273980i
$251$	−1.86559e8	+	4.50394e8i	−0.744661	+	1.79777i	−0.158887	+	0.987297i	$0.550790\pi$
$251$	−1.86559e8	+	4.50394e8i	−0.744661	+	1.79777i	−0.585774	+	0.810474i	$0.699210\pi$
$252$	−6.93160e7	+	6.03349e7i	−0.272855	+	0.237502i
$253$	−1.42666e8	+	5.90941e7i	−0.553857	+	0.229415i
$254$	−5.23811e7	+	1.96040e7i	−0.200566	+	0.0750630i
$255$	−2.18347e8			−0.824623
$256$	−2.58229e8	−	7.33174e7i	−0.961977	−	0.273129i
$257$	1.40539e8			0.516454			0.258227	−	0.966084i	$-0.416862\pi$
$257$	1.40539e8			0.516454			0.258227	+	0.966084i	$0.416862\pi$
$258$	2.66870e7	−	9.98779e6i	0.0967456	−	0.0362077i
$259$	2.16646e7	−	8.97375e6i	0.0774820	−	0.0320941i
$260$	2.87310e8	−	2.50084e8i	1.01378	−	0.882428i
$261$	−9.54604e7	+	2.30462e8i	−0.332339	+	0.802337i
$262$	−5.47879e7	+	5.11239e7i	−0.188204	+	0.175618i
$263$	−1.63862e8	−	1.63862e8i	−0.555436	−	0.555436i	0.372569	−	0.928005i	$-0.378477\pi$
$263$	−1.63862e8	−	1.63862e8i	−0.555436	−	0.555436i	−0.928005	+	0.372569i	$0.878477\pi$
$264$	2.66895e7	−	4.92709e7i	0.0892745	−	0.164807i
$265$	3.35952e8	−	3.35952e8i	1.10896	−	1.10896i
$266$	−5.20526e6	+	1.50466e8i	−0.0169573	+	0.490177i
$267$	1.33891e8	+	5.54595e7i	0.430489	+	0.178314i
$268$	−2.47592e8	+	4.97405e8i	−0.785716	+	1.57848i
$269$	−1.44205e8	−	3.48141e8i	−0.451696	−	1.09049i	−0.971677	−	0.236313i	$-0.924061\pi$
$269$	−1.44205e8	−	3.48141e8i	−0.451696	−	1.09049i	0.519981	−	0.854178i	$-0.325939\pi$
$270$	−3.45638e8	−	1.57380e8i	−1.06868	−	0.486605i
$271$		−	5.17449e7i		−	0.157934i	−0.996877	−	0.0789669i	$-0.974838\pi$
$271$		−	5.17449e7i		−	0.157934i	0.996877	−	0.0789669i	$-0.0251621\pi$
$272$	−3.98543e8	−	5.54816e7i	−1.20084	−	0.167170i
$273$			9.04845e7i			0.269156i
$274$	1.78404e8	−	3.91811e8i	0.523936	−	1.15067i
$275$	−3.26922e7	−	7.89260e7i	−0.0947938	−	0.228853i
$276$	−9.71520e7	−	2.89729e8i	−0.278144	−	0.829487i
$277$	4.79256e8	+	1.98515e8i	1.35484	+	0.561194i	0.937636	−	0.347618i	$-0.113009\pi$
$277$	4.79256e8	+	1.98515e8i	1.35484	+	0.561194i	0.417206	+	0.908812i	$0.363009\pi$
$278$	1.06994e8	+	3.70139e6i	0.298678	+	0.0103326i
$279$	1.97663e8	−	1.97663e8i	0.544891	−	0.544891i
$280$	2.46324e7	−	2.36588e8i	0.0670585	−	0.644079i
$281$	−3.31701e8	−	3.31701e8i	−0.891815	−	0.891815i	0.102878	−	0.994694i	$-0.467195\pi$
$281$	−3.31701e8	−	3.31701e8i	−0.891815	−	0.891815i	−0.994694	+	0.102878i	$0.967195\pi$
$282$	−3.84977e7	−	4.12568e7i	−0.102226	−	0.109553i
$283$	2.57819e8	−	6.22430e8i	0.676180	−	1.63244i	−0.0947334	−	0.995503i	$-0.530200\pi$
$283$	2.57819e8	−	6.22430e8i	0.676180	−	1.63244i	0.770913	−	0.636940i	$-0.219800\pi$
$284$	4.44320e8	+	3.07787e7i	1.15102	+	0.0797326i
$285$	−2.41882e8	+	1.00191e8i	−0.618938	+	0.256372i
$286$	5.13618e7	+	1.37237e8i	0.129825	+	0.346889i
$287$	−8.04970e7			−0.200999
$288$	−2.48638e8	−	1.57831e8i	−0.613330	−	0.389330i
$289$	−1.92842e8			−0.469958
$290$	−2.26319e8	−	6.04716e8i	−0.544914	−	1.45599i
$291$	3.18946e8	−	1.32112e8i	0.758737	−	0.314279i
$292$	−1.37649e7	+	1.98709e8i	−0.0323543	+	0.467065i
$293$	−1.69310e8	+	4.08749e8i	−0.393228	+	0.949337i	0.596004	+	0.802982i	$0.296754\pi$
$293$	−1.69310e8	+	4.08749e8i	−0.393228	+	0.949337i	−0.989232	+	0.146355i	$0.953246\pi$
$294$	−1.16924e8	−	1.25304e8i	−0.268341	−	0.287573i
$295$	1.92584e7	+	1.92584e7i	0.0436760	+	0.0436760i
$296$	4.73498e7	+	5.83553e7i	0.106120	+	0.130786i
$297$	1.03309e8	−	1.03309e8i	0.228818	−	0.228818i
$298$	−2.04886e7	−	708789.i	−0.0448493	−	0.00155153i
$299$	7.38278e8	+	3.05805e8i	1.59724	+	0.661600i
$300$	1.60285e8	−	5.37468e7i	0.342742	−	0.114929i
$301$	1.78072e7	+	4.29904e7i	0.0376369	+	0.0908635i
$302$	4.67458e7	−	1.02663e8i	0.0976603	−	0.214481i
$303$		−	3.28958e7i		−	0.0679346i
$304$	−4.66961e8	+	1.21414e8i	−0.953286	+	0.247863i
$305$			9.75262e8i			1.96821i
$306$	−4.01772e8	−	1.82940e8i	−0.801594	−	0.364992i
$307$	1.95711e8	+	4.72489e8i	0.386039	+	0.931982i	0.990770	+	0.135552i	$0.0432807\pi$
$307$	1.95711e8	+	4.72489e8i	0.386039	+	0.931982i	−0.604731	+	0.796430i	$0.706719\pi$
$308$	8.19191e7	+	4.07766e7i	0.159756	+	0.0795214i
$309$	1.45762e8	+	6.03765e7i	0.281054	+	0.116416i
$310$	−2.50160e7	+	7.23125e8i	−0.0476927	+	1.37863i
$311$	−5.20653e8	+	5.20653e8i	−0.981493	+	0.981493i	−0.999832	−	0.0183393i	$-0.994162\pi$
$311$	−5.20653e8	+	5.20653e8i	−0.981493	+	0.981493i	0.0183393	+	0.999832i	$0.494162\pi$
$312$	−2.77954e8	+	8.26296e7i	−0.518122	+	0.154026i
$313$	2.51835e8	+	2.51835e8i	0.464206	+	0.464206i	0.900031	−	0.435825i	$-0.143543\pi$
$313$	2.51835e8	+	2.51835e8i	0.464206	+	0.464206i	−0.435825	+	0.900031i	$0.643543\pi$
$314$	−1.27446e8	+	1.18923e8i	−0.232313	+	0.216777i
$315$	9.98669e7	−	2.41100e8i	0.180026	−	0.434621i
$316$	6.58107e8	+	7.56069e8i	1.17325	+	1.34790i
$317$	−8.99273e8	+	3.72491e8i	−1.58557	+	0.656763i	−0.989283	−	0.146012i	$-0.953356\pi$
$317$	−8.99273e8	+	3.72491e8i	−1.58557	+	0.656763i	−0.596283	+	0.802775i	$0.703356\pi$
$318$	−3.38744e8	+	1.26777e8i	−0.590713	+	0.221078i
$319$	2.48391e8			0.428419
$320$	7.49254e8	−	1.40383e8i	1.27822	−	0.239491i
$321$	3.38969e8			0.571995
$322$	4.67364e8	−	1.74914e8i	0.780117	−	0.291964i
$323$	−6.68198e8	+	2.76777e8i	−1.10331	+	0.457004i
$324$	−1.02183e8	−	1.17393e8i	−0.166906	−	0.191750i
$325$	−1.69178e8	+	4.08433e8i	−0.273371	+	0.659977i
$326$	2.59746e8	−	2.42376e8i	0.415229	−	0.387460i
$327$	3.84777e8	+	3.84777e8i	0.608544	+	0.608544i
$328$	−7.35092e7	−	2.47274e8i	−0.115023	−	0.386919i
$329$	6.51592e7	−	6.51592e7i	0.100877	−	0.100877i
$330$	−5.50159e6	+	1.59032e8i	−0.00842731	+	0.243604i
$331$	7.47860e8	+	3.09774e8i	1.13350	+	0.469512i	0.868970	−	0.494865i	$-0.164783\pi$
$331$	7.47860e8	+	3.09774e8i	1.13350	+	0.469512i	0.264532	+	0.964377i	$0.414783\pi$
$332$	1.08415e8	+	5.39657e7i	0.162595	+	0.0809346i
$333$	3.15508e7	+	7.61704e7i	0.0468226	+	0.113040i
$334$	−7.13181e8	−	3.24735e8i	−1.04734	−	0.476888i
$335$		−	1.57783e9i		−	2.29299i
$336$	−9.17030e7	+	1.56146e8i	−0.131885	+	0.224566i
$337$		−	6.17497e8i		−	0.878882i	−0.898272	−	0.439441i	$-0.855177\pi$
$337$		−	6.17497e8i		−	0.878882i	0.898272	−	0.439441i	$-0.144823\pi$
$338$	2.00463e7	−	4.40256e7i	0.0282375	−	0.0620150i
$339$	−2.17810e8	−	5.25839e8i	−0.303654	−	0.733085i
$340$	1.08340e9	−	3.63285e8i	1.49489	−	0.501269i
$341$	−2.57162e8	−	1.06520e8i	−0.351210	−	0.145476i
$342$	−5.29023e8	−	1.83012e7i	−0.715127	−	0.0247393i
$343$	4.61046e8	−	4.61046e8i	0.616900	−	0.616900i
$344$	−1.15798e8	+	9.39595e7i	−0.153373	+	0.124447i
$345$	6.13615e8	+	6.13615e8i	0.804506	+	0.804506i
$346$	−5.42767e7	−	5.81666e7i	−0.0704445	−	0.0754932i
$347$	2.23420e8	−	5.39385e8i	0.287058	−	0.693019i	−0.712908	−	0.701258i	$-0.752622\pi$
$347$	2.23420e8	−	5.39385e8i	0.287058	−	0.693019i	0.999966	+	0.00823814i	$0.00262231\pi$
$348$	−3.39685e7	+	4.90368e8i	−0.0432065	+	0.623727i
$349$	6.32793e8	−	2.62111e8i	0.796843	−	0.330063i	0.0531515	−	0.998586i	$-0.483073\pi$
$349$	6.32793e8	−	2.62111e8i	0.796843	−	0.330063i	0.743691	+	0.668523i	$0.233073\pi$
$350$	9.67665e7	+	2.58557e8i	0.120639	+	0.322343i
$351$	−7.56055e8			−0.933209
$352$	−5.04517e7	+	2.88879e8i	−0.0616562	+	0.353034i
$353$	−5.94237e8			−0.719032			−0.359516	−	0.933139i	$-0.617058\pi$
$353$	−5.94237e8			−0.719032			−0.359516	+	0.933139i	$0.617058\pi$
$354$	−7.26746e6	−	1.94184e7i	−0.00870706	−	0.0232650i
$355$	−1.16851e9	+	4.84012e8i	−1.38622	+	0.574192i
$356$	−7.56616e8	−	5.24119e7i	−0.888793	−	0.0615680i
$357$	−1.03877e8	+	2.50782e8i	−0.120832	+	0.291715i
$358$	6.31867e8	+	6.77151e8i	0.727838	+	0.780001i
$359$	−8.72029e8	−	8.72029e8i	−0.994719	−	0.994719i	0.00526706	−	0.999986i	$-0.498323\pi$
$359$	−8.72029e8	−	8.72029e8i	−0.994719	−	0.994719i	−0.999986	+	0.00526706i	$0.998323\pi$
$360$	8.31819e8	+	8.66050e7i	0.939658	+	0.0978328i
$361$	1.88418e7	−	1.88418e7i	0.0210788	−	0.0210788i
$362$	−1.34581e9	−	4.65573e7i	−1.49109	−	0.0515831i
$363$	3.83791e8	+	1.58972e8i	0.421136	+	0.174440i
$364$	−1.50548e8	−	4.48967e8i	−0.163614	−	0.487933i
$365$	−2.16460e8	−	5.22581e8i	−0.232998	−	0.562508i
$366$	3.07668e8	−	6.75699e8i	0.328018	−	0.720393i
$367$		−	4.58178e8i		−	0.483841i	−0.970296	−	0.241921i	$-0.922223\pi$
$367$		−	4.58178e8i		−	0.483841i	0.970296	−	0.241921i	$-0.0777774\pi$
$368$	9.64101e8	+	1.27594e9i	1.00845	+	1.33463i
$369$		−	2.83019e8i		−	0.293241i
$370$	−1.94219e8	−	8.84342e7i	−0.199336	−	0.0907641i
$371$	−2.26031e8	−	5.45686e8i	−0.229804	−	0.554797i
$372$	2.45457e8	−	4.93117e8i	0.247216	−	0.496649i
$373$	−6.29019e8	−	2.60548e8i	−0.627600	−	0.259960i	0.0461329	−	0.998935i	$-0.485310\pi$
$373$	−6.29019e8	−	2.60548e8i	−0.627600	−	0.259960i	−0.673733	+	0.738975i	$0.735310\pi$
$374$	−1.51981e7	+	4.39324e8i	−0.0150224	+	0.434244i
$375$	1.51665e8	−	1.51665e8i	0.148517	−	0.148517i
$376$	2.59661e8	+	1.40656e8i	0.251913	+	0.136459i
$377$	−9.08911e8	−	9.08911e8i	−0.873628	−	0.873628i
$378$	−3.45195e8	+	3.22110e8i	−0.328733	+	0.306749i
$379$	−4.01281e7	+	9.68779e7i	−0.0378627	+	0.0914087i	−0.941680	−	0.336511i	$-0.890753\pi$
$379$	−4.01281e7	+	9.68779e7i	−0.0378627	+	0.0914087i	0.903817	+	0.427919i	$0.140753\pi$
$380$	1.03348e9	−	8.99572e8i	0.966181	−	0.840995i
$381$	−1.11707e8	+	4.62707e7i	−0.103477	+	0.0428616i
$382$	1.40455e9	−	5.25660e8i	1.28918	−	0.482484i
$383$	6.34018e8			0.576641			0.288321	−	0.957534i	$-0.406903\pi$
$383$	6.34018e8			0.576641			0.288321	+	0.957534i	$0.406903\pi$
$384$	−5.63399e8	−	1.39106e8i	−0.507758	−	0.125368i
$385$	−2.59857e8			−0.232071
$386$	1.53471e9	−	5.74377e8i	1.35823	−	0.508325i
$387$	−1.51150e8	+	6.26084e7i	−0.132562	+	0.0549091i
$388$	−1.36274e9	+	1.18618e9i	−1.18441	+	1.03095i
$389$	1.91057e8	−	4.61254e8i	0.164566	−	0.397298i	−0.819987	−	0.572382i	$-0.806020\pi$
$389$	1.91057e8	−	4.61254e8i	0.164566	−	0.397298i	0.984554	+	0.175084i	$0.0560196\pi$
$390$	6.02059e8	−	5.61796e8i	0.513941	−	0.479571i
$391$	1.69511e9	+	1.69511e9i	1.43410	+	1.43410i
$392$	7.88634e8	+	4.27195e8i	0.661263	+	0.358200i
$393$	−1.14551e8	+	1.14551e8i	−0.0951976	+	0.0951976i
$394$	3.28758e6	−	9.50324e7i	0.00270794	−	0.0782771i
$395$	−2.62981e9	−	1.08930e9i	−2.14701	−	0.889323i
$396$	−1.43367e8	+	2.88019e8i	−0.116015	+	0.233071i
$397$	7.06306e7	+	1.70517e8i	0.0566534	+	0.136773i	0.949672	−	0.313247i	$-0.101417\pi$
$397$	7.06306e7	+	1.70517e8i	0.0566534	+	0.136773i	−0.893018	+	0.450020i	$0.851417\pi$
$398$	−1.98248e9	−	9.02687e8i	−1.57622	−	0.717706i
$399$			3.25480e8i			0.256519i
$400$	−7.05879e8	+	5.33363e8i	−0.551468	+	0.416690i
$401$			6.35599e8i			0.492241i	0.969239	+	0.246121i	$0.0791559\pi$
$401$			6.35599e8i			0.492241i	−0.969239	+	0.246121i	$0.920844\pi$
$402$	−4.97760e8	+	1.09318e9i	−0.382146	+	0.839268i
$403$	5.51229e8	+	1.33078e9i	0.419531	+	1.01284i
$404$	5.47320e7	+	1.63223e8i	0.0412958	+	0.123153i
$405$	4.08326e8	+	1.69134e8i	0.305432	+	0.126514i
$406$	−8.02218e8	−	2.77522e7i	−0.594910	−	0.0205805i
$407$	5.80508e7	−	5.80508e7i	0.0426803	−	0.0426803i
$408$	−8.65224e8	−	9.00830e7i	−0.630693	−	0.0656648i
$409$	−2.56854e8	−	2.56854e8i	−0.185633	−	0.185633i	0.608172	−	0.793805i	$-0.291903\pi$
$409$	−2.56854e8	−	2.56854e8i	−0.185633	−	0.185633i	−0.793805	+	0.608172i	$0.791903\pi$
$410$	4.99787e8	+	5.35605e8i	0.358130	+	0.383797i
$411$	3.56168e8	−	8.59865e8i	0.253051	−	0.610919i
$412$	−8.23698e8	−	5.70588e7i	−0.580267	−	0.0401959i
$413$	3.12813e7	−	1.29572e7i	0.0218504	−	0.00905075i
$414$	6.14980e8	+	1.64320e9i	0.425951	+	1.13813i
$415$	−3.43906e8			−0.236196
$416$	1.24168e9	−	8.72452e8i	0.845633	−	0.594176i
$417$	2.31444e8			0.156304
$418$	1.84753e8	+	4.93652e8i	0.123730	+	0.330601i
$419$	1.97693e9	−	8.18871e8i	1.31293	−	0.543834i	0.387193	−	0.921999i	$-0.373445\pi$
$419$	1.97693e9	−	8.18871e8i	1.31293	−	0.543834i	0.925738	+	0.378165i	$0.123445\pi$
$420$	3.55365e7	−	5.13003e8i	0.0234046	−	0.337868i
$421$	4.74837e8	−	1.14636e9i	0.310140	−	0.748743i	−0.689560	−	0.724229i	$-0.742196\pi$
$421$	4.74837e8	−	1.14636e9i	0.310140	−	0.748743i	0.999699	−	0.0245147i	$-0.00780405\pi$
$422$	−8.09420e7	−	8.67429e7i	−0.0524301	−	0.0561876i
$423$	2.29093e8	+	2.29093e8i	0.147170	+	0.147170i
$424$	1.46985e9	−	1.19265e9i	0.936468	−	0.759855i
$425$	−9.37773e8	+	9.37773e8i	−0.592566	+	0.592566i
$426$	9.62280e8	+	3.32894e7i	0.603070	+	0.0208628i
$427$	1.12014e9	+	4.63977e8i	0.696265	+	0.288402i
$428$	−1.68190e9	+	5.63976e8i	−1.03692	+	0.347702i
$429$	1.21228e8	+	2.92670e8i	0.0741314	+	0.178969i
$430$	1.75486e8	−	3.85402e8i	0.106439	−	0.233762i
$431$			2.18766e9i			1.31616i	0.752947	+	0.658081i	$0.228631\pi$
$431$			2.18766e9i			1.31616i	−0.752947	+	0.658081i	$0.771369\pi$
$432$	−1.30470e9	−	7.66237e8i	−0.778606	−	0.457267i
$433$		−	9.67461e8i		−	0.572698i	−0.958125	−	0.286349i	$-0.907558\pi$
$433$		−	9.67461e8i		−	0.572698i	0.958125	−	0.286349i	$-0.0924417\pi$
$434$	8.18645e8	+	3.72756e8i	0.480708	+	0.218882i
$435$	−5.34174e8	−	1.28961e9i	−0.311150	−	0.751183i
$436$	−2.54938e9	−	1.26900e9i	−1.47310	−	0.733262i
$437$	2.65564e9	+	1.10000e9i	1.52225	+	0.630535i
$438$	−1.48877e7	+	4.30351e8i	−0.00846580	+	0.244717i
$439$	−1.42443e9	+	1.42443e9i	−0.803552	+	0.803552i	−0.983649	−	0.180097i	$-0.942359\pi$
$439$	−1.42443e9	+	1.42443e9i	−0.803552	+	0.803552i	0.180097	+	0.983649i	$0.442359\pi$
$440$	−2.37299e8	−	7.98239e8i	−0.132804	−	0.446734i
$441$	6.95793e8	+	6.95793e8i	0.386318	+	0.386318i
$442$	1.66318e9	−	1.55196e9i	0.916141	−	0.854874i
$443$	−1.11103e9	+	2.68226e9i	−0.607172	+	1.46584i	0.258891	+	0.965907i	$0.416643\pi$
$443$	−1.11103e9	+	2.68226e9i	−0.607172	+	1.46584i	−0.866063	+	0.499935i	$0.833357\pi$
$444$	1.06664e8	+	1.22541e8i	0.0578331	+	0.0664418i
$445$	1.98981e9	−	8.24207e8i	1.07041	−	0.443380i
$446$	−7.12067e8	+	2.66496e8i	−0.380057	+	0.142239i
$447$	−4.43199e7			−0.0234705
$448$	1.95218e8	−	9.27344e8i	0.102576	−	0.487268i
$449$	−8.02659e8			−0.418474			−0.209237	−	0.977865i	$-0.567098\pi$
$449$	−8.02659e8			−0.418474			−0.209237	+	0.977865i	$0.567098\pi$
$450$	−9.09059e8	+	3.40221e8i	−0.470271	+	0.176002i
$451$	−2.60366e8	+	1.07847e8i	−0.133649	+	0.0553593i
$452$	1.95562e9	+	2.24673e9i	0.996095	+	1.14437i
$453$	9.33237e7	−	2.25303e8i	0.0471681	−	0.113874i
$454$	2.74549e9	−	2.56189e9i	1.37697	−	1.28489i
$455$	9.50867e8	+	9.50867e8i	0.473238	+	0.473238i
$456$	−9.99823e8	+	2.97225e8i	−0.493794	+	0.146794i
$457$	7.64925e8	−	7.64925e8i	0.374897	−	0.374897i	−0.494360	−	0.869257i	$-0.664598\pi$
$457$	7.64925e8	−	7.64925e8i	0.374897	−	0.374897i	0.869257	+	0.494360i	$0.164598\pi$
$458$	−4.99623e7	+	1.44423e9i	−0.0243004	+	0.702439i
$459$	−2.09545e9	−	8.67962e8i	−1.01142	−	0.418944i
$460$	−4.06558e9	−	2.02371e9i	−1.94747	−	0.969386i
$461$	7.77868e8	+	1.87794e9i	0.369788	+	0.892746i	0.993785	+	0.111320i	$0.0355078\pi$
$461$	7.77868e8	+	1.87794e9i	0.369788	+	0.892746i	−0.623997	+	0.781427i	$0.714492\pi$
$462$	1.80039e8	+	8.19775e7i	0.0849414	+	0.0386766i
$463$			3.40146e9i			1.59269i	0.604840	+	0.796347i	$0.293237\pi$
$463$			3.40146e9i			1.59269i	−0.604840	+	0.796347i	$0.706763\pi$
$464$	−6.47328e8	−	2.48963e9i	−0.300823	−	1.15697i
$465$			1.56422e9i			0.721462i
$466$	−1.73586e9	+	3.81228e9i	−0.794626	+	1.74516i
$467$	−8.90077e8	−	2.14884e9i	−0.404407	−	0.976324i	−0.986583	−	0.163262i	$-0.947799\pi$
$467$	−8.90077e8	−	2.14884e9i	−0.404407	−	0.976324i	0.582176	−	0.813063i	$-0.302201\pi$
$468$	1.57852e9	−	5.29312e8i	0.711853	−	0.238699i
$469$	−1.81222e9	−	7.50646e8i	−0.811158	−	0.335993i
$470$	−8.38109e8	−	2.89938e7i	−0.372356	−	0.0128814i
$471$	−2.66467e8	+	2.66467e8i	−0.117509	+	0.117509i
$472$	6.83682e7	+	8.42590e7i	0.0299266	+	0.0368824i
$473$	1.15194e8	+	1.15194e8i	0.0500514	+	0.0500514i
$474$	1.47839e9	+	1.58434e9i	0.637624	+	0.683322i
$475$	−6.08548e8	+	1.46916e9i	−0.260536	+	0.628989i
$476$	9.81693e7	−	1.41717e9i	0.0417207	−	0.602278i
$477$	1.91858e9	−	7.94700e8i	0.809403	−	0.335266i
$478$	8.07305e8	+	2.15709e9i	0.338096	+	0.903380i
$479$	3.26438e9			1.35715			0.678574	−	0.734532i	$-0.262598\pi$
$479$	3.26438e9			1.35715			0.678574	+	0.734532i	$0.262598\pi$
$480$	1.60832e9	−	3.59307e8i	0.663785	−	0.148293i
$481$	−4.24838e8			−0.174067
$482$	−5.58613e8	−	1.49259e9i	−0.227220	−	0.607124i
$483$	9.96694e8	−	4.12844e8i	0.402483	−	0.166714i
$484$	−2.16880e9	−	1.50236e8i	−0.869482	−	0.0602303i
$485$	1.96337e9	−	4.73999e9i	0.781458	−	1.88661i
$486$	−1.78848e9	−	1.91665e9i	−0.706734	−	0.757385i
$487$	−1.92124e9	−	1.92124e9i	−0.753754	−	0.753754i	0.221424	−	0.975178i	$-0.428930\pi$
$487$	−1.92124e9	−	1.92124e9i	−0.753754	−	0.753754i	−0.975178	+	0.221424i	$0.928930\pi$
$488$	−4.02363e8	+	3.86459e9i	−0.156729	+	1.50534i
$489$	5.43081e8	−	5.43081e8i	0.210031	−	0.210031i
$490$	−2.54547e9	−	8.80589e7i	−0.977423	−	0.0338132i
$491$	−1.11469e8	−	4.61722e7i	−0.0424982	−	0.0176033i	0.361333	−	0.932437i	$-0.382322\pi$
$491$	−1.11469e8	−	4.61722e7i	−0.0424982	−	0.0176033i	−0.403831	+	0.914833i	$0.632322\pi$
$492$	−1.77303e8	−	5.28756e8i	−0.0671179	−	0.200160i
$493$	−1.47565e9	−	3.56253e9i	−0.554650	−	1.33904i
$494$	1.13032e9	−	2.48242e9i	0.421851	−	0.926467i
$495$		−	9.13630e8i		−	0.338573i
$496$	−3.97468e8	+	2.85515e9i	−0.146257	+	1.05061i
$497$			1.57236e9i			0.574519i
$498$	2.38272e8	+	1.08493e8i	0.0864509	+	0.0393639i
$499$	7.41794e8	+	1.79085e9i	0.267258	+	0.645219i	0.999352	−	0.0359850i	$-0.0114569\pi$
$499$	7.41794e8	+	1.79085e9i	0.267258	+	0.645219i	−0.732094	+	0.681204i	$0.761457\pi$
$500$	−5.00194e8	+	1.00487e9i	−0.178955	+	0.359515i
$501$	−1.56514e9	−	6.48304e8i	−0.556060	−	0.230328i
$502$	1.90689e8	−	5.51217e9i	0.0672766	−	1.94473i
$503$	5.23936e8	−	5.23936e8i	0.183565	−	0.183565i	−0.609342	−	0.792907i	$-0.708566\pi$
$503$	5.23936e8	−	5.23936e8i	0.183565	−	0.183565i	0.792907	+	0.609342i	$0.208566\pi$
$504$	4.95205e8	−	9.14185e8i	0.172297	−	0.318073i
$505$	−3.45689e8	−	3.45689e8i	−0.119444	−	0.119444i
$506$	1.27733e9	−	1.19191e9i	0.438306	−	0.408995i
$507$	4.00206e7	−	9.66183e7i	0.0136382	−	0.0329254i
$508$	4.77286e8	−	4.15445e8i	0.161531	−	0.140602i
$509$	−8.69565e8	+	3.60186e8i	−0.292274	+	0.121064i	−0.524003	−	0.851717i	$-0.675562\pi$
$509$	−8.69565e8	+	3.60186e8i	−0.292274	+	0.121064i	0.231729	+	0.972780i	$0.425562\pi$
$510$	2.31359e9	−	8.65875e8i	0.772308	−	0.289041i
$511$	−7.03191e8			−0.233131
$512$	3.02693e9	−	2.47165e8i	0.996683	−	0.0813845i
$513$	−2.71959e9			−0.889391
$514$	−1.48915e9	+	5.57322e8i	−0.483689	+	0.181024i
$515$	2.16623e9	−	8.97281e8i	0.698842	−	0.289470i
$516$	−2.43167e8	+	2.11660e8i	−0.0779166	+	0.0678212i
$517$	1.23458e8	−	2.98054e8i	0.0392918	−	0.0948588i
$518$	−1.93970e8	+	1.80998e8i	−0.0613170	+	0.0572164i
$519$	−1.21616e8	−	1.21616e8i	−0.0381860	−	0.0381860i
$520$	−2.05259e9	+	3.78923e9i	−0.640163	+	1.18179i
$521$	−3.86048e9	+	3.86048e9i	−1.19594	+	1.19594i	−0.220569	+	0.975371i	$0.570791\pi$
$521$	−3.86048e9	+	3.86048e9i	−1.19594	+	1.19594i	−0.975371	+	0.220569i	$0.929209\pi$
$522$	9.75738e7	−	2.82052e9i	0.0300252	−	0.867925i
$523$	−4.39794e9	−	1.82169e9i	−1.34429	−	0.556824i	−0.409594	−	0.912268i	$-0.634330\pi$
$523$	−4.39794e9	−	1.82169e9i	−1.34429	−	0.556824i	−0.934698	+	0.355444i	$0.884330\pi$
$524$	3.77792e8	−	7.58973e8i	0.114708	−	0.230445i
$525$	2.28395e8	+	5.51395e8i	0.0688857	+	0.166305i
$526$	2.38609e9	+	1.08646e9i	0.714885	+	0.325511i
$527$			4.32116e9i			1.28606i
$528$	−8.74122e7	+	6.27912e8i	−0.0258436	+	0.185644i
$529$		−	6.12264e9i		−	1.79822i
$530$	−2.22748e9	+	4.89198e9i	−0.649902	+	1.42731i
$531$	4.55560e7	+	1.09982e8i	0.0132043	+	0.0318780i
$532$	−5.41533e8	−	1.61497e9i	−0.155932	−	0.465022i
$533$	1.34736e9	+	5.58096e8i	0.385424	+	0.159648i
$534$	−1.63863e9	−	5.66873e7i	−0.465680	−	0.0161099i
$535$	3.56209e9	−	3.56209e9i	1.00570	−	1.00570i
$536$	6.50963e8	−	6.25233e9i	0.182591	−	1.75374i
$537$	1.41580e9	+	1.41580e9i	0.394540	+	0.394540i
$538$	2.90857e9	+	3.11702e9i	0.805271	+	0.862983i
$539$	3.74962e8	−	9.05238e8i	0.103140	−	0.249002i
$540$	4.28647e9	+	2.96930e8i	1.17144	+	0.0811476i
$541$	−1.11070e9	+	4.60067e8i	−0.301583	+	0.124920i	−0.528343	−	0.849031i	$-0.677187\pi$
$541$	−1.11070e9	+	4.60067e8i	−0.301583	+	0.124920i	0.226760	+	0.973951i	$0.427187\pi$
$542$	2.05200e8	+	5.48286e8i	0.0553578	+	0.147914i
$543$	−2.91118e9			−0.780315
$544$	4.44296e9	−	9.92583e8i	1.18325	−	0.264345i
$545$	8.08695e9			2.13992
$546$	−3.58825e8	−	9.58768e8i	−0.0943428	−	0.252081i
$547$	−5.83763e8	+	2.41803e8i	−0.152504	+	0.0631692i	−0.457630	−	0.889143i	$-0.651301\pi$
$547$	−5.83763e8	+	2.41803e8i	−0.152504	+	0.0631692i	0.305126	+	0.952312i	$0.401301\pi$
$548$	−3.36596e8	+	4.85908e9i	−0.0873729	+	1.26131i
$549$	−1.63130e9	+	3.93830e9i	−0.420755	+	1.01579i
$550$	6.59394e8	+	7.06651e8i	0.168996	+	0.181107i
$551$	−3.26942e9	−	3.26942e9i	−0.832608	−	0.832608i
$552$	2.17836e9	+	2.68468e9i	0.551244	+	0.679370i
$553$	−2.50225e9	+	2.50225e9i	−0.629205	+	0.629205i
$554$	−5.86540e9	−	2.02909e8i	−1.46559	−	0.0507012i
$555$	−4.26231e8	−	1.76551e8i	−0.105833	−	0.0438374i
$556$	−1.14838e9	+	3.85077e8i	−0.283351	+	0.0950135i
$557$	1.78297e9	+	4.30446e9i	0.437170	+	1.05542i	0.976922	+	0.213597i	$0.0685180\pi$
$557$	1.78297e9	+	4.30446e9i	0.437170	+	1.05542i	−0.539752	+	0.841824i	$0.681482\pi$
$558$	−1.31057e9	+	2.87827e9i	−0.319331	+	0.701314i
$559$		−	8.43035e8i		−	0.204129i
$560$	6.77209e8	+	2.60455e9i	0.162954	+	0.626722i
$561$			9.50321e8i			0.227248i
$562$	4.83008e9	+	2.19929e9i	1.14783	+	0.522644i
$563$	−1.10666e9	−	2.67171e9i	−0.261357	−	0.630971i	0.737666	−	0.675165i	$-0.235928\pi$
$563$	−1.10666e9	−	2.67171e9i	−0.261357	−	0.630971i	−0.999023	+	0.0441948i	$0.985928\pi$
$564$	5.71527e8	+	2.84488e8i	0.134141	+	0.0667708i
$565$	−7.81472e9	−	3.23696e9i	−1.82282	−	0.755037i
$566$	−2.63527e8	+	7.61764e9i	−0.0610896	+	1.76589i
$567$	3.88519e8	−	3.88519e8i	0.0895099	−	0.0895099i
$568$	−4.83004e9	+	1.43586e9i	−1.10594	+	0.328772i
$569$	5.78179e8	+	5.78179e8i	0.131574	+	0.131574i	0.769827	−	0.638253i	$-0.220343\pi$
$569$	5.78179e8	+	5.78179e8i	0.131574	+	0.131574i	−0.638253	+	0.769827i	$0.720343\pi$
$570$	2.16565e9	−	2.02083e9i	0.489809	−	0.457053i
$571$	−2.09736e7	+	5.06348e7i	−0.00471463	+	0.0113821i	−0.926219	−	0.376985i	$-0.876961\pi$
$571$	−2.09736e7	+	5.06348e7i	−0.00471463	+	0.0113821i	0.921505	+	0.388367i	$0.126961\pi$
$572$	−1.08845e9	−	1.25048e9i	−0.243178	−	0.279376i
$573$	2.99532e9	−	1.24070e9i	0.665122	−	0.275503i
$574$	8.52942e8	−	3.19219e8i	0.188247	−	0.0704526i
$575$	5.27082e9			1.15622
$576$	3.26045e9	+	6.86365e8i	0.710884	+	0.149650i
$577$	−1.35695e9			−0.294069			−0.147035	−	0.989131i	$-0.546973\pi$
$577$	−1.35695e9			−0.294069			−0.147035	+	0.989131i	$0.546973\pi$
$578$	2.04334e9	−	7.64733e8i	0.440143	−	0.164726i
$579$	3.27291e9	−	1.35568e9i	0.700744	−	0.290258i
$580$	4.79612e9	+	5.51005e9i	1.02069	+	1.17262i
$581$	−1.63612e8	+	3.94994e8i	−0.0346098	+	0.0835554i
$582$	−2.85563e9	+	2.66466e9i	−0.600442	+	0.560288i
$583$	−1.46218e9	−	1.46218e9i	−0.305606	−	0.305606i
$584$	−6.42148e8	−	2.16009e9i	−0.133411	−	0.448774i
$585$	−3.34315e9	+	3.34315e9i	−0.690415	+	0.690415i
$586$	1.73058e8	−	5.00250e9i	0.0355263	−	1.02694i
$587$	−1.94331e8	−	8.04944e7i	−0.0396559	−	0.0164260i	0.362767	−	0.931880i	$-0.381832\pi$
$587$	−1.94331e8	−	8.04944e7i	−0.0396559	−	0.0164260i	−0.402423	+	0.915454i	$0.631832\pi$
$588$	1.73582e9	+	8.64036e8i	0.352115	+	0.175271i
$589$	1.98281e9	+	4.78694e9i	0.399833	+	0.965282i
$590$	−2.80432e8	−	1.27690e8i	−0.0562141	−	0.0255961i
$591$		−	2.05569e8i		−	0.0409639i
$592$	−7.33130e8	−	4.30559e8i	−0.145230	−	0.0852918i
$593$		−	3.72706e9i		−	0.733965i	−0.930228	−	0.366983i	$-0.880391\pi$
$593$		−	3.72706e9i		−	0.733965i	0.930228	−	0.366983i	$-0.119609\pi$
$594$	−6.84974e8	+	1.50434e9i	−0.134098	+	0.294505i
$595$	1.54377e9	+	3.72698e9i	0.300450	+	0.725351i
$596$	2.19907e8	−	7.37393e7i	0.0425478	−	0.0142672i
$597$	−4.35073e9	−	1.80213e9i	−0.836859	−	0.346638i
$598$	−9.03545e9	−	3.12575e8i	−1.72781	−	0.0597723i
$599$	1.99541e9	−	1.99541e9i	0.379349	−	0.379349i	−0.491518	−	0.870867i	$-0.663558\pi$
$599$	1.99541e9	−	1.99541e9i	0.379349	−	0.379349i	0.870867	+	0.491518i	$0.163558\pi$
$600$	−1.48523e9	+	1.20512e9i	−0.280714	+	0.227773i
$601$	−2.21207e9	−	2.21207e9i	−0.415659	−	0.415659i	0.468045	−	0.883705i	$-0.344958\pi$
$601$	−2.21207e9	−	2.21207e9i	−0.415659	−	0.415659i	−0.883705	+	0.468045i	$0.844958\pi$
$602$	−3.59167e8	−	3.84908e8i	−0.0670979	−	0.0719067i
$603$	2.63919e9	−	6.37158e9i	0.490186	−	1.18341i
$604$	−8.81954e7	+	1.27319e9i	−0.0162861	+	0.235105i
$605$	5.70369e9	−	2.36254e9i	1.04716	−	0.433747i
$606$	1.30451e8	+	3.48562e8i	0.0238119	+	0.0636247i
$607$	1.74822e8			0.0317275			0.0158637	−	0.999874i	$-0.494950\pi$
$607$	1.74822e8			0.0317275			0.0158637	+	0.999874i	$0.494950\pi$
$608$	4.46641e9	−	3.13828e9i	0.805928	−	0.566277i
$609$	−1.73531e9			−0.311328
$610$	−3.86750e9	−	1.03338e10i	−0.689883	−	1.84334i
$611$	−1.54239e9	+	6.38880e8i	−0.273559	+	0.113312i
$612$	4.98262e9	+	3.45153e8i	0.878673	+	0.0608670i
$613$	−3.55944e9	+	8.59325e9i	−0.624123	+	1.50677i	0.222698	+	0.974888i	$0.428514\pi$
$613$	−3.55944e9	+	8.59325e9i	−0.624123	+	1.50677i	−0.846821	+	0.531879i	$0.821486\pi$
$614$	−3.94745e9	−	4.23035e9i	−0.688220	−	0.737543i
$615$	1.11985e9	+	1.11985e9i	0.194132	+	0.194132i
$616$	−1.02971e9	−	1.07209e8i	−0.177494	−	0.0184798i
$617$	−2.29978e9	+	2.29978e9i	−0.394174	+	0.394174i	−0.876172	−	0.481998i	$-0.839911\pi$
$617$	−2.29978e9	+	2.29978e9i	−0.394174	+	0.394174i	0.481998	+	0.876172i	$0.339911\pi$
$618$	−1.78391e9	−	6.17132e7i	−0.304028	−	0.0105176i
$619$	4.41319e9	+	1.82800e9i	0.747886	+	0.309784i	0.723879	−	0.689927i	$-0.242358\pi$
$619$	4.41319e9	+	1.82800e9i	0.747886	+	0.309784i	0.0240071	+	0.999712i	$0.492358\pi$
$620$	−2.60255e9	−	7.76139e9i	−0.438560	−	1.30788i
$621$	3.44958e9	+	8.32802e9i	0.578023	+	1.39547i
$622$	3.45211e9	−	7.58151e9i	0.575199	−	1.26325i
$623$		−	2.67752e9i		−	0.443633i
$624$	2.61751e9	−	1.97779e9i	0.431263	−	0.325863i
$625$		−	7.40628e9i		−	1.21345i
$626$	−3.66711e9	−	1.66975e9i	−0.597467	−	0.272046i
$627$	4.36066e8	+	1.05276e9i	0.0706506	+	0.170566i
$628$	8.78812e8	−	1.76551e9i	0.141591	−	0.284453i
$629$	−1.17746e9	−	4.87720e8i	−0.188655	−	0.0781436i
$630$	−1.02078e8	+	2.95071e9i	−0.0162645	+	0.470149i
$631$	−1.46189e9	+	1.46189e9i	−0.231639	+	0.231639i	−0.813377	−	0.581737i	$-0.802373\pi$
$631$	−1.46189e9	+	1.46189e9i	−0.231639	+	0.231639i	0.581737	+	0.813377i	$0.302373\pi$
$632$	−9.97153e9	−	5.40148e9i	−1.57127	−	0.851143i
$633$	−1.81364e8	−	1.81364e8i	−0.0284208	−	0.0284208i
$634$	8.05150e9	−	7.51305e9i	1.25477	−	1.17086i
$635$	−6.87648e8	+	1.66013e9i	−0.106576	+	0.257296i
$636$	3.08656e9	−	2.68664e9i	0.475746	−	0.414105i
$637$	−4.68450e9	+	1.94038e9i	−0.718084	+	0.297440i
$638$	−2.63194e9	+	9.85019e8i	−0.401239	+	0.150166i
$639$	−5.52826e9			−0.838176
$640$	−7.38235e9	+	4.45873e9i	−1.11318	+	0.672328i
$641$	8.33813e9			1.25045			0.625224	−	0.780446i	$-0.285008\pi$
$641$	8.33813e9			1.25045			0.625224	+	0.780446i	$0.285008\pi$
$642$	−3.59169e9	+	1.34421e9i	−0.535706	+	0.200492i
$643$	9.38600e9	−	3.88781e9i	1.39233	−	0.576722i	0.444581	−	0.895739i	$-0.353353\pi$
$643$	9.38600e9	−	3.88781e9i	1.39233	−	0.576722i	0.947749	+	0.319017i	$0.103353\pi$
$644$	−4.25852e9	+	3.70676e9i	−0.628288	+	0.546882i
$645$	3.50342e8	−	8.45800e8i	0.0514083	−	0.124111i
$646$	5.98260e9	−	5.58251e9i	0.873124	−	0.814734i
$647$	−3.15249e9	−	3.15249e9i	−0.457602	−	0.457602i	0.440265	−	0.897868i	$-0.354884\pi$
$647$	−3.15249e9	−	3.15249e9i	−0.457602	−	0.457602i	−0.897868	+	0.440265i	$0.854884\pi$
$648$	1.54826e9	+	8.38676e8i	0.223528	+	0.121083i
$649$	8.38192e7	−	8.38192e7i	0.0120361	−	0.0120361i
$650$	1.72924e8	−	4.99862e9i	0.0246978	−	0.713927i
$651$	1.79659e9	+	7.44173e8i	0.255221	+	0.105716i
$652$	−1.79109e9	+	3.59825e9i	−0.253076	+	0.508422i
$653$	−7.19454e8	−	1.73692e9i	−0.101113	−	0.244108i	0.865225	−	0.501383i	$-0.167175\pi$
$653$	−7.19454e8	−	1.73692e9i	−0.101113	−	0.244108i	−0.966338	+	0.257275i	$0.917175\pi$
$654$	−5.60295e9	−	2.55120e9i	−0.783239	−	0.356634i
$655$			2.40755e9i			0.334758i
$656$	1.75949e9	+	2.32860e9i	0.243345	+	0.322055i
$657$		−	2.47235e9i		−	0.340119i
$658$	−4.32028e8	+	9.48818e8i	−0.0591182	+	0.129835i
$659$	8.95419e8	+	2.16173e9i	0.121879	+	0.294241i	0.973030	−	0.230680i	$-0.0740950\pi$
$659$	8.95419e8	+	2.16173e9i	0.121879	+	0.294241i	−0.851151	+	0.524921i	$0.824095\pi$
$660$	−5.72361e8	−	1.70691e9i	−0.0774937	−	0.231103i
$661$	3.81349e9	+	1.57960e9i	0.513592	+	0.212737i	0.624399	−	0.781105i	$-0.285344\pi$
$661$	3.81349e9	+	1.57960e9i	0.513592	+	0.212737i	−0.110808	+	0.993842i	$0.535344\pi$
$662$	−9.15272e9	−	3.16632e8i	−1.22616	−	0.0424181i
$663$	3.47741e9	−	3.47741e9i	0.463403	−	0.463403i
$664$	−1.36277e9	−	1.41885e8i	−0.180648	−	0.0188083i
$665$	3.42034e9	+	3.42034e9i	0.451018	+	0.451018i
$666$	−6.36372e8	−	6.81979e8i	−0.0834740	−	0.0894564i
$667$	−5.86474e9	+	1.41587e10i	−0.765258	+	1.84750i
$668$	8.84460e9	+	6.12678e8i	1.14805	+	0.0795271i
$669$	−1.51854e9	+	6.29002e8i	−0.196081	+	0.0812195i
$670$	6.25704e9	+	1.67186e10i	0.803724	+	2.14752i
$671$	4.24468e9			0.542396
$672$	3.52467e8	−	2.01817e9i	0.0448049	−	0.256547i
$673$	1.09783e10			1.38830			0.694148	−	0.719832i	$-0.255781\pi$
$673$	1.09783e10			1.38830			0.694148	+	0.719832i	$0.255781\pi$
$674$	2.44875e9	+	6.54297e9i	0.308059	+	0.823124i
$675$	−4.60725e9	+	1.90839e9i	−0.576606	+	0.238838i
$676$	−3.78214e7	+	5.45988e8i	−0.00470895	+	0.0679783i
$677$	−1.58392e9	+	3.82392e9i	−0.196188	+	0.473640i	−0.991106	−	0.133078i	$-0.957514\pi$
$677$	−1.58392e9	+	3.82392e9i	−0.196188	+	0.473640i	0.794918	+	0.606717i	$0.207514\pi$
$678$	4.39317e9	+	4.70802e9i	0.541345	+	0.580142i
$679$	−4.51006e9	−	4.51006e9i	−0.552889	−	0.552889i
$680$	−1.00390e10	+	8.14566e9i	−1.22435	+	0.993447i
$681$	5.74031e9	−	5.74031e9i	0.696499	−	0.696499i
$682$	3.14729e9	+	1.08878e8i	0.379920	+	0.0131431i
$683$	−5.53927e9	−	2.29444e9i	−0.665242	−	0.275552i	0.0244005	−	0.999702i	$-0.492232\pi$
$683$	−5.53927e9	−	2.29444e9i	−0.665242	−	0.275552i	−0.689643	+	0.724150i	$0.742232\pi$
$684$	5.67807e9	−	1.90398e9i	0.678429	−	0.227491i
$685$	−5.29316e9	−	1.27788e10i	−0.629213	−	1.51906i
$686$	−3.05689e9	+	6.71354e9i	−0.361531	+	0.793994i
$687$			3.12409e9i			0.367600i
$688$	8.54388e8	−	1.45480e9i	0.100022	−	0.170311i
$689$			1.07008e10i			1.24638i
$690$	−8.93519e9	−	4.06848e9i	−1.03546	−	0.471477i
$691$	5.18200e9	+	1.25105e10i	0.597481	+	1.44245i	0.876140	+	0.482057i	$0.160110\pi$
$691$	5.18200e9	+	1.25105e10i	0.597481	+	1.44245i	−0.278659	+	0.960390i	$0.589890\pi$
$692$	8.05779e8	+	4.01091e8i	0.0924367	+	0.0460120i
$693$	−1.04935e9	−	4.34656e8i	−0.119772	−	0.0496112i
$694$	−2.28367e8	+	6.60128e9i	−0.0259343	+	0.749670i
$695$	2.43216e9	−	2.43216e9i	0.274818	−	0.274818i
$696$	−1.58467e9	−	5.33061e9i	−0.178159	−	0.599301i
$697$	3.09358e9	+	3.09358e9i	0.346056	+	0.346056i
$698$	−5.66561e9	+	5.28672e9i	−0.630598	+	0.588427i
$699$	−3.46548e9	+	8.36640e9i	−0.383789	+	0.926550i
$700$	−2.05066e9	−	2.35591e9i	−0.225970	−	0.259607i
$701$	−6.86968e9	+	2.84551e9i	−0.753222	+	0.311995i	−0.726056	−	0.687636i	$-0.758649\pi$
$701$	−6.86968e9	+	2.84551e9i	−0.753222	+	0.311995i	−0.0271667	+	0.999631i	$0.508649\pi$
$702$	8.01112e9	−	2.99821e9i	0.874004	−	0.327102i
$703$	−1.52818e9			−0.165894
$704$	−6.10996e8	−	3.26102e9i	−0.0659985	−	0.352248i
$705$	−1.81295e9			−0.194861
$706$	6.29651e9	−	2.35651e9i	0.673416	−	0.252030i
$707$	−5.61502e8	+	2.32582e8i	−0.0597563	+	0.0247519i
$708$	1.54011e8	+	1.76937e8i	0.0163093	+	0.0187370i
$709$	2.60473e9	−	6.28836e9i	0.274473	−	0.662637i	−0.725191	−	0.688548i	$-0.758249\pi$
$709$	2.60473e9	−	6.28836e9i	0.274473	−	0.662637i	0.999664	+	0.0259106i	$0.00824851\pi$
$710$	1.04621e10	−	9.76240e9i	1.09702	−	1.02365i
$711$	−8.79764e9	−	8.79764e9i	−0.917958	−	0.917958i
$712$	8.22491e9	−	2.44508e9i	0.853987	−	0.253871i
$713$	1.21437e10	−	1.21437e10i	1.25469	−	1.25469i
$714$	1.06177e8	−	3.06921e9i	0.0109166	−	0.315561i
$715$	4.34949e9	+	1.80162e9i	0.445008	+	0.184328i
$716$	−9.38054e9	−	4.66933e9i	−0.955063	−	0.475399i
$717$	1.90546e9	+	4.60018e9i	0.193056	+	0.466077i
$718$	1.26981e10	+	5.78185e9i	1.28027	+	0.582950i
$719$		−	4.21199e9i		−	0.422607i	−0.977421	−	0.211303i	$-0.932229\pi$
$719$		−	4.21199e9i		−	0.422607i	0.977421	−	0.211303i	$-0.0677708\pi$
$720$	−9.15734e9	+	2.38100e9i	−0.914336	+	0.237736i
$721$		−	2.91491e9i		−	0.289635i
$722$	−1.24927e8	+	2.74365e8i	−0.0123532	+	0.0271300i
$723$	−1.31848e9	−	3.18309e9i	−0.129744	−	0.313231i
$724$	1.44447e10	−	4.84362e9i	1.41457	−	0.474335i
$725$	−7.83294e9	−	3.24451e9i	−0.763382	−	0.316203i
$726$	−4.69705e9	−	1.62491e8i	−0.455561	−	0.0157598i
$727$	−9.49843e9	+	9.49843e9i	−0.916814	+	0.916814i	−0.996796	−	0.0799822i	$-0.974514\pi$
$727$	−9.49843e9	+	9.49843e9i	−0.916814	+	0.916814i	0.0799822	+	0.996796i	$0.474514\pi$
$728$	3.37562e9	+	4.16022e9i	0.324261	+	0.399628i
$729$	−2.12704e9	−	2.12704e9i	−0.203343	−	0.203343i
$730$	4.36594e9	+	4.67884e9i	0.415383	+	0.445152i
$731$	9.67816e8	−	2.33652e9i	0.0916394	−	0.221237i
$732$	−5.80478e8	+	8.37975e9i	−0.0547012	+	0.789664i
$733$	1.50444e9	−	6.23159e8i	0.141095	−	0.0584433i	−0.311019	−	0.950404i	$-0.600670\pi$
$733$	1.50444e9	−	6.23159e8i	0.141095	−	0.0584433i	0.452113	+	0.891960i	$0.350670\pi$
$734$	1.81695e9	+	4.85483e9i	0.169593	+	0.453145i
$735$	−5.50623e9			−0.511504
$736$	−1.52754e10	−	9.69654e9i	−1.41228	−	0.896488i
$737$	−6.86727e9			−0.631899
$738$	1.12234e9	+	2.99886e9i	0.102785	+	0.274637i
$739$	1.02972e10	−	4.26525e9i	0.938566	−	0.388767i	0.139644	−	0.990202i	$-0.455404\pi$
$739$	1.02972e10	−	4.26525e9i	0.938566	−	0.388767i	0.798922	+	0.601435i	$0.205404\pi$
$740$	2.40863e9	+	1.66849e8i	0.218504	+	0.0151361i
$741$	2.25659e9	−	5.44789e9i	0.203746	−	0.491886i
$742$	4.55898e9	+	4.88571e9i	0.409689	+	0.439050i
$743$	−1.15542e9	−	1.15542e9i	−0.103342	−	0.103342i	0.653545	−	0.756888i	$-0.273281\pi$
$743$	−1.15542e9	−	1.15542e9i	−0.103342	−	0.103342i	−0.756888	+	0.653545i	$0.773281\pi$
$744$	−6.45350e8	+	6.19842e9i	−0.0574500	+	0.551793i
$745$	−4.65740e8	+	4.65740e8i	−0.0412664	+	0.0412664i
$746$	7.69828e9	+	2.66317e8i	0.678903	+	0.0234862i
$747$	−1.38876e9	−	5.75243e8i	−0.121900	−	0.0504928i
$748$	−1.58114e9	−	4.71532e9i	−0.138139	−	0.411960i
$749$	−2.39660e9	−	5.78590e9i	−0.208405	−	0.503135i
$750$	−1.00559e9	+	2.20848e9i	−0.0870376	+	0.191152i
$751$			1.77502e10i			1.52919i	0.644508	+	0.764597i	$0.277062\pi$
$751$			1.77502e10i			1.52919i	−0.644508	+	0.764597i	$0.722938\pi$
$752$	−3.30914e9	−	4.60669e8i	−0.283761	−	0.0395027i
$753$		−	1.19236e10i		−	1.01771i
$754$	1.32351e10	+	6.02639e9i	1.12442	+	0.511985i
$755$	−1.38692e9	−	3.34833e9i	−0.117284	−	0.283148i
$756$	2.38031e9	−	4.78197e9i	0.200358	−	0.402514i
$757$	3.24023e9	+	1.34215e9i	0.271481	+	0.112451i	0.514271	−	0.857628i	$-0.328063\pi$
$757$	3.24023e9	+	1.34215e9i	0.271481	+	0.112451i	−0.242790	+	0.970079i	$0.578063\pi$
$758$	4.10165e7	−	1.18564e9i	0.00342071	−	0.0988809i
$759$	2.67067e9	−	2.67067e9i	0.221704	−	0.221704i
$760$	−7.38333e9	+	1.36302e10i	−0.610105	+	1.12630i
$761$	−1.18635e8	−	1.18635e8i	−0.00975816	−	0.00975816i	0.702211	−	0.711969i	$-0.252196\pi$
$761$	−1.18635e8	−	1.18635e8i	−0.00975816	−	0.00975816i	−0.711969	+	0.702211i	$0.752196\pi$
$762$	1.00015e9	−	9.33268e8i	0.0818887	−	0.0764124i
$763$	3.84733e9	−	9.28828e9i	0.313562	−	0.757006i
$764$	−1.27979e10	+	1.11397e10i	−1.03828	+	0.903749i
$765$	−1.31037e10	+	5.42773e9i	−1.05823	+	0.438332i
$766$	−6.71802e9	+	2.51426e9i	−0.540058	+	0.202120i
$767$	−6.13422e8			−0.0490880
$768$	6.52138e9	−	7.60256e8i	0.519488	−	0.0605613i
$769$	−1.13898e10			−0.903181			−0.451590	−	0.892225i	$-0.649143\pi$
$769$	−1.13898e10			−0.903181			−0.451590	+	0.892225i	$0.649143\pi$
$770$	2.75343e9	−	1.03049e9i	0.217348	−	0.0813440i
$771$	−3.17573e9	+	1.31543e9i	−0.249548	+	0.103366i
$772$	−1.39840e10	+	1.21721e10i	−1.09388	+	0.952151i
$773$	2.51286e9	−	6.06657e9i	0.195677	−	0.472406i	−0.795337	−	0.606168i	$-0.792706\pi$
$773$	2.51286e9	−	6.06657e9i	0.195677	−	0.472406i	0.991013	+	0.133762i	$0.0427059\pi$
$774$	1.35330e9	−	1.26280e9i	0.104906	−	0.0978903i
$775$	6.71816e9	+	6.71816e9i	0.518435	+	0.518435i
$776$	9.73565e9	−	1.79727e10i	0.747909	−	1.38070i
$777$	−4.05556e8	+	4.05556e8i	−0.0310154	+	0.0310154i
$778$	−1.95287e8	+	5.64507e9i	−0.0148678	+	0.429775i
$779$	4.84657e9	+	2.00751e9i	0.367327	+	0.152152i
$780$	−4.15152e9	+	8.34029e9i	−0.313239	+	0.629289i
$781$	2.10659e9	+	5.08576e9i	0.158235	+	0.382012i
$782$	−2.46834e10	−	1.12391e10i	−1.84578	−	0.840446i
$783$		−	1.44997e10i		−	1.07942i
$784$	−1.00504e10	−	1.39913e9i	−0.744865	−	0.103693i
$785$			5.60039e9i			0.413214i
$786$	7.59515e8	−	1.66804e9i	0.0557901	−	0.122526i
$787$	−4.80604e9	−	1.16028e10i	−0.351460	−	0.848499i	−0.996440	−	0.0842999i	$-0.973135\pi$
$787$	−4.80604e9	−	1.16028e10i	−0.351460	−	0.848499i	0.644981	−	0.764199i	$-0.276865\pi$
$788$	3.42025e8	+	1.01999e9i	0.0249010	+	0.0742602i
$789$	5.23649e9	+	2.16903e9i	0.379552	+	0.157215i
$790$	3.21851e10	+	1.11342e9i	2.32252	+	0.0803460i
$791$	−7.43564e9	+	7.43564e9i	−0.534196	+	0.534196i
$792$	3.76936e8	−	3.62037e9i	0.0269606	−	0.258949i
$793$	−1.55321e10	−	1.55321e10i	−1.10605	−	1.10605i
$794$	−1.42460e9	−	1.52670e9i	−0.101000	−	0.108239i
$795$	−4.44696e9	+	1.07359e10i	−0.313890	+	0.757798i
$796$	2.45859e10	+	1.70310e9i	1.72779	+	0.119687i
$797$	9.45209e9	−	3.91518e9i	0.661338	−	0.273935i	−0.0266633	−	0.999644i	$-0.508488\pi$
$797$	9.45209e9	−	3.91518e9i	0.661338	−	0.273935i	0.688002	+	0.725709i	$0.258488\pi$
$798$	−1.29072e9	−	3.44877e9i	−0.0899131	−	0.240245i
$799$	−5.00827e9			−0.347355
$800$	5.36435e9	−	8.45072e9i	0.370427	−	0.583551i
$801$	9.41388e9			0.647224
$802$	−2.52053e9	−	6.73477e9i	−0.172537	−	0.461012i
$803$	−2.27446e9	+	9.42111e8i	−0.155015	+	0.0642092i
$804$	9.39127e8	−	1.35572e10i	0.0637277	−	0.919970i
$805$	6.13546e9	−	1.48123e10i	0.414535	−	1.00078i
$806$	−1.11181e10	−	1.19150e10i	−0.747928	−	0.801531i
$807$	6.51712e9	+	6.51712e9i	0.436514	+	0.436514i
$808$	−1.22721e9	−	1.51245e9i	−0.0818428	−	0.100865i
$809$	−5.55861e9	+	5.55861e9i	−0.369102	+	0.369102i	−0.867150	−	0.498048i	$-0.834050\pi$
$809$	−5.55861e9	+	5.55861e9i	−0.369102	+	0.369102i	0.498048	+	0.867150i	$0.334050\pi$
$810$	−4.99732e9	−	1.72879e8i	−0.330399	−	0.0114299i
$811$	−1.26323e10	−	5.23246e9i	−0.831588	−	0.344455i	−0.0740570	−	0.997254i	$-0.523595\pi$
$811$	−1.26323e10	−	5.23246e9i	−0.831588	−	0.344455i	−0.757531	+	0.652799i	$0.773595\pi$
$812$	8.61031e9	−	2.88722e9i	0.564381	−	0.189249i
$813$	4.84327e8	+	1.16927e9i	0.0316098	+	0.0763127i
$814$	−3.84897e8	+	8.45309e8i	−0.0250126	+	0.0549326i
$815$		−	1.14141e10i		−	0.738565i
$816$	9.52510e9	−	2.47662e9i	0.613697	−	0.159567i
$817$		−	3.03246e9i		−	0.194544i
$818$	3.74019e9	+	1.70303e9i	0.238922	+	0.108789i
$819$	2.24929e9	+	5.43027e9i	0.143071	+	0.345405i
$820$	−7.41971e9	−	3.69329e9i	−0.469936	−	0.233919i
$821$	1.43569e10	+	5.94683e9i	0.905441	+	0.375046i	0.786310	−	0.617832i	$-0.211989\pi$
$821$	1.43569e10	+	5.94683e9i	0.905441	+	0.375046i	0.119131	+	0.992878i	$0.461989\pi$
$822$	−3.64053e8	+	1.05235e10i	−0.0228619	+	0.660859i
$823$	3.84284e9	−	3.84284e9i	0.240299	−	0.240299i	−0.576675	−	0.816974i	$-0.695650\pi$
$823$	3.84284e9	−	3.84284e9i	0.240299	−	0.240299i	0.816974	+	0.576675i	$0.195650\pi$
$824$	8.95413e9	−	2.66186e9i	0.557543	−	0.165745i
$825$	1.47748e9	+	1.47748e9i	0.0916077	+	0.0916077i
$826$	−2.80072e8	+	2.61343e8i	−0.0172918	+	0.0161354i
$827$	5.06421e9	−	1.22261e10i	0.311345	−	0.751655i	−0.688310	−	0.725416i	$-0.741647\pi$
$827$	5.06421e9	−	1.22261e10i	0.311345	−	0.751655i	0.999656	−	0.0262381i	$-0.00835280\pi$
$828$	−1.30326e10	−	1.49725e10i	−0.797856	−	0.916620i
$829$	1.14557e10	−	4.74509e9i	0.698360	−	0.289270i	−0.00511846	−	0.999987i	$-0.501629\pi$
$829$	1.14557e10	−	4.74509e9i	0.698360	−	0.289270i	0.703478	+	0.710717i	$0.251629\pi$
$830$	3.64401e9	−	1.36380e9i	0.221211	−	0.0827896i
$831$	−1.26877e10			−0.766973
$832$	−9.69695e9	+	1.41685e10i	−0.583718	+	0.852886i
$833$	−1.52109e10			−0.911797
$834$	−2.45237e9	+	9.17815e8i	−0.146388	+	0.0547866i
$835$	−2.32603e10	+	9.63471e9i	−1.38265	+	0.572712i
$836$	−3.91526e9	−	4.49806e9i	−0.231760	−	0.266258i
$837$	−6.21804e9	+	1.50117e10i	−0.366534	+	0.884892i
$838$	−1.77001e10	+	1.65164e10i	−1.03902	+	0.969531i
$839$	2.03405e10	+	2.03405e10i	1.18903	+	1.18903i	0.977335	+	0.211700i	$0.0679000\pi$
$839$	2.03405e10	+	2.03405e10i	1.18903	+	1.18903i	0.211700	+	0.977335i	$0.432100\pi$
$840$	1.65782e9	+	5.57668e9i	0.0965074	+	0.324637i
$841$	5.23362e9	−	5.23362e9i	0.303400	−	0.303400i
$842$	−4.85350e8	+	1.40298e10i	−0.0280196	+	0.809950i
$843$	1.06001e10	+	4.39069e9i	0.609413	+	0.252427i
$844$	1.20164e9	+	5.98140e8i	0.0687983	+	0.0342455i
$845$	−5.94763e8	−	1.43589e9i	−0.0339114	−	0.0818694i
$846$	−3.33595e9	−	1.51897e9i	−0.189419	−	0.0862485i
$847$		−	7.67495e9i		−	0.433994i
$848$	−1.08449e10	+	1.84660e10i	−0.610718	+	1.03989i
$849$			1.64781e10i			0.924122i
$850$	6.21776e9	−	1.36554e10i	0.347270	−	0.762674i
$851$	1.93837e9	+	4.67963e9i	0.107816	+	0.260290i
$852$	−1.03283e10	+	3.46328e9i	−0.572123	+	0.191845i
$853$	9.45269e9	+	3.91543e9i	0.521475	+	0.216002i	0.627865	−	0.778322i	$-0.283929\pi$
$853$	9.45269e9	+	3.91543e9i	0.521475	+	0.216002i	−0.106390	+	0.994325i	$0.533929\pi$
$854$	−1.37089e10	−	4.74249e8i	−0.753181	−	0.0260558i
$855$	−1.20256e10	+	1.20256e10i	−0.657998	+	0.657998i
$856$	1.55848e10	−	1.26456e10i	0.849266	−	0.689099i
$857$	2.42235e10	+	2.42235e10i	1.31463	+	1.31463i	0.917962	+	0.396668i	$0.129834\pi$
$857$	2.42235e10	+	2.42235e10i	1.31463	+	1.31463i	0.396668	+	0.917962i	$0.370166\pi$
$858$	−2.44514e9	−	2.62037e9i	−0.132159	−	0.141631i
$859$	4.35550e9	−	1.05151e10i	0.234457	−	0.566028i	−0.762235	−	0.647300i	$-0.775898\pi$
$859$	4.35550e9	−	1.05151e10i	0.234457	−	0.566028i	0.996692	+	0.0812717i	$0.0258981\pi$
$860$	−3.31090e8	+	4.77960e9i	−0.0177501	+	0.256240i
$861$	1.81897e9	−	7.53443e8i	0.0971215	−	0.0402290i
$862$	−8.67538e9	−	2.31803e10i	−0.461331	−	1.23266i
$863$	1.32839e10			0.703539			0.351770	−	0.936087i	$-0.385580\pi$
$863$	1.32839e10			0.703539			0.351770	+	0.936087i	$0.385580\pi$
$864$	1.68631e10	+	2.94508e9i	0.889488	+	0.155346i
$865$	−2.55603e9			−0.134279
$866$	3.83656e9	+	1.02512e10i	0.200738	+	0.536365i
$867$	4.35760e9	−	1.80498e9i	0.227081	−	0.0940600i
$868$	−1.01525e10	−	7.03280e8i	−0.526932	−	0.0365014i
$869$	−4.74104e9	+	1.14459e10i	−0.245078	+	0.591670i
$870$	1.07741e10	+	1.15463e10i	0.554709	+	0.594464i
$871$	2.51287e10	+	2.51287e10i	1.28856	+	1.28856i
$872$	3.20455e10	+	3.33642e9i	1.63666	+	0.170402i
$873$	1.58569e10	−	1.58569e10i	0.806620	−	0.806620i
$874$	−3.25012e10	−	1.12436e9i	−1.64668	−	0.0569658i
$875$	−3.66110e9	−	1.51648e9i	−0.184750	−	0.0765258i
$876$	−1.54885e9	−	4.61901e9i	−0.0778476	−	0.232159i
$877$	−2.60719e9	−	6.29432e9i	−0.130519	−	0.315101i	0.845087	−	0.534629i	$-0.179549\pi$
$877$	−2.60719e9	−	6.29432e9i	−0.130519	−	0.315101i	−0.975606	+	0.219527i	$0.929549\pi$
$878$	9.44443e9	−	2.07418e10i	0.470918	−	1.03423i
$879$		−	1.08211e10i		−	0.537417i
$880$	5.67990e9	+	7.51707e9i	0.280965	+	0.371842i
$881$			3.47733e10i			1.71329i	0.515910	+	0.856643i	$0.327454\pi$
$881$			3.47733e10i			1.71329i	−0.515910	+	0.856643i	$0.672546\pi$
$882$	−1.01318e10	−	4.61335e9i	−0.497219	−	0.226400i
$883$	−5.46956e9	−	1.32047e10i	−0.267356	−	0.645455i	0.732001	−	0.681304i	$-0.238587\pi$
$883$	−5.46956e9	−	1.32047e10i	−0.267356	−	0.645455i	−0.999357	+	0.0358485i	$0.988587\pi$
$884$	−1.14686e10	+	2.30400e10i	−0.558375	+	1.12176i
$885$	−6.15433e8	−	2.54921e8i	−0.0298455	−	0.0123624i
$886$	1.13562e9	−	3.28269e10i	0.0548550	−	1.58567i
$887$	2.05657e10	−	2.05657e10i	0.989488	−	0.989488i	−0.0104576	−	0.999945i	$-0.503329\pi$
$887$	2.05657e10	−	2.05657e10i	0.989488	−	0.989488i	0.999945	+	0.0104576i	$0.00332883\pi$
$888$	−1.61615e9	−	8.75453e8i	−0.0774528	−	0.0419554i
$889$	1.57960e9	+	1.57960e9i	0.0754034	+	0.0754034i
$890$	−1.78155e10	+	1.66241e10i	−0.847095	+	0.790445i
$891$	7.36131e8	−	1.77718e9i	0.0348645	−	0.0841703i
$892$	6.48821e9	−	5.64754e9i	0.306089	−	0.266430i
$893$	−5.54811e9	+	2.29810e9i	−0.260714	+	0.107991i
$894$	4.69611e8	−	1.75755e8i	0.0219815	−	0.00822670i
$895$	2.97562e10			1.38738
$896$	1.60896e9	+	1.06002e10i	0.0747253	+	0.492309i
$897$	−1.95450e10			−0.904195
$898$	8.50493e9	−	3.18302e9i	0.391926	−	0.146681i
$899$	−2.55218e10	+	1.05715e10i	−1.17153	+	0.485263i
$900$	8.28316e9	−	7.20993e9i	0.378745	−	0.329672i
$901$	−1.22847e10	+	2.96578e10i	−0.559535	+	1.35084i
$902$	2.33114e9	−	2.17525e9i	0.105766	−	0.0986929i
$903$	−8.04772e8	−	8.04772e8i	−0.0363719	−	0.0363719i
$904$	−2.96313e10	−	1.60510e10i	−1.33402	−	0.722623i
$905$	−3.05925e10	+	3.05925e10i	−1.37197	+	1.37197i
$906$	−9.53898e7	+	2.75739e9i	−0.00426141	+	0.123182i
$907$	3.74904e10	+	1.55290e10i	1.66838	+	0.691066i	0.998670	−	0.0515572i	$-0.0164185\pi$
$907$	3.74904e10	+	1.55290e10i	1.66838	+	0.691066i	0.669710	+	0.742623i	$0.266418\pi$
$908$	−1.89317e10	+	3.80331e10i	−0.839244	+	1.68601i
$909$	−8.17734e8	−	1.97418e9i	−0.0361109	−	0.0871795i
$910$	−1.38461e10	−	6.30457e9i	−0.609091	−	0.277339i
$911$		−	7.59426e9i		−	0.332791i	−0.986059	−	0.166395i	$-0.946787\pi$
$911$		−	7.59426e9i		−	0.332791i	0.986059	−	0.166395i	$-0.0532128\pi$
$912$	9.41539e9	−	7.11428e9i	0.411014	−	0.310562i
$913$			1.49680e9i			0.0650904i
$914$	−5.07171e9	+	1.11385e10i	−0.219707	+	0.482519i
$915$	−9.12834e9	−	2.20378e10i	−0.393929	−	0.951029i
$916$	−5.19786e9	−	1.55012e10i	−0.223455	−	0.666392i
$917$	2.76520e9	+	1.14538e9i	0.118422	+	0.0490522i
$918$	2.56452e10	+	8.87178e8i	1.09410	+	0.0378496i
$919$	−2.40899e10	+	2.40899e10i	−1.02384	+	1.02384i	−0.0241299	+	0.999709i	$0.507682\pi$
$919$	−2.40899e10	+	2.40899e10i	−1.02384	+	1.02384i	−0.999709	+	0.0241299i	$0.992318\pi$
$920$	5.11039e10	+	5.32070e9i	2.16370	+	0.225274i
$921$	−8.84489e9	−	8.84489e9i	−0.373064	−	0.373064i
$922$	−1.56894e10	−	1.68138e10i	−0.659247	−	0.706493i
$923$	1.09014e10	−	2.63182e10i	0.456326	−	1.10167i
$924$	−2.23277e9	−	1.54667e8i	−0.0931091	−	0.00644981i
$925$	−2.58888e9	+	1.07235e9i	−0.107551	+	0.0445492i
$926$	−1.34888e10	−	3.60417e10i	−0.558259	−	1.49165i
$927$	1.02485e10			0.422554
$928$	1.67319e10	+	2.38129e10i	0.687271	+	0.978126i
$929$	−1.06702e10			−0.436632			−0.218316	−	0.975878i	$-0.570056\pi$
$929$	−1.06702e10			−0.436632			−0.218316	+	0.975878i	$0.570056\pi$
$930$	−6.20309e9	−	1.65744e10i	−0.252882	−	0.675691i
$931$	−1.68505e10	+	6.97971e9i	−0.684367	+	0.283474i
$932$	3.27505e9	−	4.72784e10i	0.132514	−	1.91297i
$933$	6.89182e9	−	1.66383e10i	0.277810	−	0.670693i
$934$	1.79526e10	+	1.92393e10i	0.720965	+	0.772635i
$935$	9.98656e9	+	9.98656e9i	0.399554	+	0.399554i
$936$	−1.46269e10	+	1.18683e10i	−0.583025	+	0.473069i
$937$	−8.76811e9	+	8.76811e9i	−0.348191	+	0.348191i	−0.859435	−	0.511244i	$-0.829185\pi$
$937$	−8.76811e9	+	8.76811e9i	−0.348191	+	0.348191i	0.511244	+	0.859435i	$0.329185\pi$
$938$	2.21789e10	+	7.67264e8i	0.877467	+	0.0303553i
$939$	−8.04781e9	−	3.33351e9i	−0.317211	−	0.131393i
$940$	8.99553e9	−	3.01639e9i	0.353248	−	0.118451i
$941$	−1.63551e10	−	3.94848e10i	−0.639869	−	1.54478i	−0.826854	−	0.562417i	$-0.809872\pi$
$941$	−1.63551e10	−	3.94848e10i	−0.639869	−	1.54478i	0.186985	−	0.982363i	$-0.440128\pi$
$942$	1.76677e9	−	3.88017e9i	0.0688654	−	0.151242i
$943$		−	1.73877e10i		−	0.675228i
$944$	−1.05856e9	−	6.21683e8i	−0.0409557	−	0.0240529i
$945$			1.51690e10i			0.584716i
$946$	−1.67740e9	−	7.63777e8i	−0.0644197	−	0.0293324i
$947$	−3.91244e9	−	9.44547e9i	−0.149700	−	0.361409i	0.831185	−	0.555996i	$-0.187663\pi$
$947$	−3.91244e9	−	9.44547e9i	−0.149700	−	0.361409i	−0.980885	+	0.194588i	$0.937663\pi$
$948$	−2.19478e10	−	1.09249e10i	−0.836685	−	0.416475i
$949$	1.17700e10	+	4.87531e9i	0.447040	+	0.185170i
$950$	6.22021e8	−	1.79804e10i	0.0235381	−	0.680405i
$951$	1.68342e10	−	1.68342e10i	0.634688	−	0.634688i
$952$	4.57972e9	+	1.54055e10i	0.172032	+	0.578692i
$953$	−1.64203e10	−	1.64203e10i	−0.614547	−	0.614547i	0.329581	−	0.944127i	$-0.393093\pi$
$953$	−1.64203e10	−	1.64203e10i	−0.614547	−	0.614547i	−0.944127	+	0.329581i	$0.893093\pi$
$954$	−1.71777e10	+	1.60289e10i	−0.640538	+	0.597702i
$955$	1.84386e10	−	4.45147e10i	0.685040	−	1.65383i
$956$	−1.71083e10	−	1.96550e10i	−0.633293	−	0.727561i
$957$	−5.61283e9	+	2.32491e9i	−0.207010	+	0.0857462i
$958$	−3.45892e10	+	1.29452e10i	−1.27105	+	0.475698i
$959$	−1.71953e10			−0.629572
$960$	−1.56168e10	+	1.01851e10i	−0.569694	+	0.371550i
$961$	3.44394e9			0.125177
$962$	4.50156e9	−	1.68474e9i	0.163024	−	0.0610126i
$963$	2.03426e10	−	8.42620e9i	0.734033	−	0.304046i
$964$	1.18381e10	+	1.36002e10i	0.425609	+	0.488963i
$965$	2.01474e10	−	4.86401e10i	0.721728	−	1.74241i
$966$	−8.92374e9	+	8.32697e9i	−0.318513	+	0.297212i
$967$	−1.69550e10	−	1.69550e10i	−0.602984	−	0.602984i	0.338119	−	0.941103i	$-0.390209\pi$
$967$	−1.69550e10	−	1.69550e10i	−0.602984	−	0.602984i	−0.941103	+	0.338119i	$0.890209\pi$
$968$	2.35762e10	−	7.00870e9i	0.835431	−	0.248355i
$969$	1.25085e10	−	1.25085e10i	0.441644	−	0.441644i
$970$	−2.00683e9	+	5.80106e10i	−0.0706009	+	2.04083i
$971$	−2.62320e10	−	1.08656e10i	−0.919525	−	0.380880i	−0.127830	−	0.991796i	$-0.540801\pi$
$971$	−2.62320e10	−	1.08656e10i	−0.919525	−	0.380880i	−0.791695	+	0.610916i	$0.790801\pi$
$972$	2.65513e10	+	1.32164e10i	0.927371	+	0.461615i
$973$	−1.63637e9	−	3.95055e9i	−0.0569491	−	0.137487i
$974$	2.79762e10	+	1.27385e10i	0.970134	+	0.441734i
$975$		−	1.08128e10i		−	0.373611i
$976$	−1.10620e10	−	4.25446e10i	−0.380855	−	1.46477i
$977$		−	1.68863e10i		−	0.579299i	−0.957133	−	0.289649i	$-0.906461\pi$
$977$		−	1.68863e10i		−	0.579299i	0.957133	−	0.289649i	$-0.0935387\pi$
$978$	−3.60082e9	+	7.90810e9i	−0.123088	+	0.270325i
$979$	−3.58724e9	−	8.66037e9i	−0.122186	−	0.294983i
$980$	2.73209e10	−	9.16126e9i	0.927265	−	0.310931i
$981$	3.26567e10	+	1.35268e10i	1.10441	+	0.457461i
$982$	1.36422e9	+	4.71944e7i	0.0459722	+	0.00159038i
$983$	−4.76231e9	+	4.76231e9i	−0.159912	+	0.159912i	−0.782528	−	0.622616i	$-0.786070\pi$
$983$	−4.76231e9	+	4.76231e9i	−0.159912	+	0.159912i	0.622616	+	0.782528i	$0.286070\pi$
$984$	3.97553e9	+	4.89956e9i	0.133019	+	0.163936i
$985$	−2.16024e9	−	2.16024e9i	−0.0720238	−	0.0720238i
$986$	2.97635e10	+	3.18966e10i	0.988814	+	1.05968i
$987$	−8.62505e8	+	2.08227e9i	−0.0285530	+	0.0689330i
$988$	−2.13259e9	+	3.07859e10i	−0.0703490	+	1.01555i
$989$	−9.28611e9	+	3.84643e9i	−0.305244	+	0.126436i
$990$	3.62309e9	+	9.68078e9i	0.118674	+	0.317093i
$991$	−2.55019e10			−0.832367			−0.416184	−	0.909281i	$-0.636633\pi$
$991$	−2.55019e10			−0.832367			−0.416184	+	0.909281i	$0.636633\pi$
$992$	−7.11082e9	−	3.18292e10i	−0.231275	−	1.03522i
$993$	−1.97987e10			−0.641673
$994$	−6.23535e9	−	1.66606e10i	−0.201376	−	0.538071i
$995$	−6.46581e10	+	2.67823e10i	−2.08086	+	0.861919i
$996$	−2.95495e9	−	2.04694e8i	−0.0947638	−	0.00656443i
$997$	−4.43135e9	+	1.06982e10i	−0.141613	+	0.341884i	−0.978734	−	0.205134i	$-0.934237\pi$
$997$	−4.43135e9	+	1.06982e10i	−0.141613	+	0.341884i	0.837121	+	0.547018i	$0.184237\pi$
$998$	−1.49618e10	−	1.60341e10i	−0.476460	−	0.510607i
$999$	−3.38868e9	−	3.38868e9i	−0.107535	−	0.107535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.21.4	✓	108
32.29	even	8	inner	32.8.g.a.29.4	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.21.4	✓	108	1.1	even	1	trivial
32.8.g.a.29.4	yes	108	32.29	even	8	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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.5959 + 3.96560i) q^{2} +(-22.5968 + 9.35989i) q^{3} +(96.5480 - 84.0385i) q^{4} +(-139.101 + 335.820i) q^{5} +(202.317 - 188.787i) q^{6} +(319.530 + 319.530i) q^{7} +(-689.754 + 1273.34i) q^{8} +(-1123.44 + 1123.44i) q^{9} +O(q^{10})\)	\(q+(-10.5959 + 3.96560i) q^{2} +(-22.5968 + 9.35989i) q^{3} +(96.5480 - 84.0385i) q^{4} +(-139.101 + 335.820i) q^{5} +(202.317 - 188.787i) q^{6} +(319.530 + 319.530i) q^{7} +(-689.754 + 1273.34i) q^{8} +(-1123.44 + 1123.44i) q^{9} +(142.181 - 4109.95i) q^{10} +(1461.61 + 605.418i) q^{11} +(-1395.08 + 2802.68i) q^{12} +(-3132.97 - 7563.65i) q^{13} +(-4652.85 - 2118.60i) q^{14} -8890.43i q^{15} +(2259.05 - 16227.5i) q^{16} -24559.7i q^{17} +(7448.77 - 16359.0i) q^{18} +(-11269.5 - 27207.0i) q^{19} +(14791.9 + 44112.7i) q^{20} +(-10211.1 - 4229.58i) q^{21} +(-17888.0 - 618.821i) q^{22} +(-69019.8 + 69019.8i) q^{23} +(3667.91 - 35229.4i) q^{24} +(-38183.4 - 38183.4i) q^{25} +(63191.1 + 67719.9i) q^{26} +(35340.9 - 85320.4i) q^{27} +(57702.9 + 3997.16i) q^{28} +(145056. - 60084.1i) q^{29} +(35255.9 + 94202.5i) q^{30} -175945. q^{31} +(40415.1 + 180904. i) q^{32} -38694.3 q^{33} +(97394.1 + 260234. i) q^{34} +(-151752. + 62857.7i) q^{35} +(-14053.6 + 202877. i) q^{36} +(19858.5 - 47942.7i) q^{37} +(227304. + 243594. i) q^{38} +(141590. + 141590. i) q^{39} +(-331667. - 408757. i) q^{40} +(-125962. + 125962. i) q^{41} +(124969. + 4323.22i) q^{42} +(95136.0 + 39406.6i) q^{43} +(191994. - 64379.5i) q^{44} +(-221001. - 533544. i) q^{45} +(457625. - 1.00503e6i) q^{46} -203922. i q^{47} +(100841. + 387834. i) q^{48} -619344. i q^{49} +(556009. + 253169. i) q^{50} +(229876. + 554971. i) q^{51} +(-938120. - 466966. i) q^{52} +(-1.20758e6 - 500196. i) q^{53} +(-36123.3 + 1.04420e6i) q^{54} +(-406623. + 406623. i) q^{55} +(-627268. + 186473. i) q^{56} +(509310. + 509310. i) q^{57} +(-1.29873e6 + 1.21188e6i) q^{58} +(28673.6 - 69224.3i) q^{59} +(-747139. - 858353. i) q^{60} +(2.47882e6 - 1.02676e6i) q^{61} +(1.86430e6 - 697726. i) q^{62} -717944. q^{63} +(-1.14563e6 - 1.75658e6i) q^{64} +2.97583e6 q^{65} +(410002. - 153446. i) q^{66} +(-4.01036e6 + 1.66115e6i) q^{67} +(-2.06396e6 - 2.37119e6i) q^{68} +(913607. - 2.20564e6i) q^{69} +(1.35869e6 - 1.26782e6i) q^{70} +(2.46042e6 + 2.46042e6i) q^{71} +(-655619. - 2.20541e6i) q^{72} +(-1.10035e6 + 1.10035e6i) q^{73} +(-20298.2 + 586750. i) q^{74} +(1.22021e6 + 505429. i) q^{75} +(-3.37449e6 - 1.67971e6i) q^{76} +(273579. + 660477. i) q^{77} +(-2.06177e6 - 938789. i) q^{78} +7.83101e6i q^{79} +(5.13529e6 + 3.01590e6i) q^{80} -1.21591e6i q^{81} +(835168. - 1.83419e6i) q^{82} +(362067. + 874106. i) q^{83} +(-1.34131e6 + 449770. i) q^{84} +(8.24766e6 + 3.41629e6i) q^{85} +(-1.16433e6 - 40279.1i) q^{86} +(-2.71542e6 + 2.71542e6i) q^{87} +(-1.77905e6 + 1.44353e6i) q^{88} +(-4.18977e6 - 4.18977e6i) q^{89} +(4.45754e6 + 4.77700e6i) q^{90} +(1.41574e6 - 3.41789e6i) q^{91} +(-863403. + 1.24640e7i) q^{92} +(3.97578e6 - 1.64682e6i) q^{93} +(808672. + 2.16074e6i) q^{94} +1.07043e7 q^{95} +(-2.60649e6 - 3.70957e6i) q^{96} -1.41147e7 q^{97} +(2.45607e6 + 6.56253e6i) q^{98} +(-2.32217e6 + 961875. 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

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