LMFDB - Embedded newform 19.7.f.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,7,Mod(2,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, 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:	$4.37102758878$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	19.2
Dual form			19.7.f.a.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.2866 - 2.34278i) q^{2} +(-30.7619 + 36.6606i) q^{3} +(110.904 + 40.3656i) q^{4} +(-169.577 + 61.7209i) q^{5} +(494.607 - 415.025i) q^{6} +(-29.1620 - 50.5101i) q^{7} +(-631.184 - 364.414i) q^{8} +(-271.115 - 1537.57i) q^{9} +O(q^{10})$	\(q+(-13.2866 - 2.34278i) q^{2} +(-30.7619 + 36.6606i) q^{3} +(110.904 + 40.3656i) q^{4} +(-169.577 + 61.7209i) q^{5} +(494.607 - 415.025i) q^{6} +(-29.1620 - 50.5101i) q^{7} +(-631.184 - 364.414i) q^{8} +(-271.115 - 1537.57i) q^{9} +(2397.69 - 422.777i) q^{10} +(-267.061 + 462.562i) q^{11} +(-4891.43 + 2824.07i) q^{12} +(2282.40 + 2720.06i) q^{13} +(269.129 + 739.426i) q^{14} +(2953.78 - 8115.43i) q^{15} +(1746.31 + 1465.33i) q^{16} +(-230.723 + 1308.49i) q^{17} +21064.2i q^{18} +(-3369.80 - 5974.14i) q^{19} -21298.1 q^{20} +(2748.81 + 484.689i) q^{21} +(4632.00 - 5520.20i) q^{22} +(-5716.82 - 2080.75i) q^{23} +(32776.1 - 11929.5i) q^{24} +(12977.4 - 10889.3i) q^{25} +(-23952.8 - 41487.4i) q^{26} +(34494.6 + 19915.5i) q^{27} +(-1195.30 - 6778.91i) q^{28} +(-11855.6 + 2090.46i) q^{29} +(-58258.2 + 100906. i) q^{30} +(14864.0 - 8581.75i) q^{31} +(10213.3 + 12171.7i) q^{32} +(-8742.52 - 24019.9i) q^{33} +(6131.02 - 16844.8i) q^{34} +(8062.74 + 6765.44i) q^{35} +(31997.4 - 181466. i) q^{36} +17337.3i q^{37} +(30777.0 + 87270.4i) q^{38} -169930. q^{39} +(129526. + 22839.0i) q^{40} +(54796.0 - 65303.4i) q^{41} +(-35386.7 - 12879.7i) q^{42} +(-83694.2 + 30462.2i) q^{43} +(-48289.6 + 40519.8i) q^{44} +(140875. + 244003. i) q^{45} +(71082.1 + 41039.3i) q^{46} +(-21289.2 - 120737. i) q^{47} +(-107440. + 18944.5i) q^{48} +(57123.6 - 98941.1i) q^{49} +(-197936. + 114278. i) q^{50} +(-40872.6 - 48710.1i) q^{51} +(143330. + 393795. i) q^{52} +(8760.41 - 24069.0i) q^{53} +(-411657. - 345421. i) q^{54} +(16737.5 - 94923.1i) q^{55} +42508.3i q^{56} +(322677. + 60236.9i) q^{57} +162418. q^{58} +(-32344.5 - 5703.21i) q^{59} +(655169. - 780800. i) q^{60} +(251440. + 91516.8i) q^{61} +(-217597. + 79198.8i) q^{62} +(-69756.7 + 58532.8i) q^{63} +(-180133. - 311999. i) q^{64} +(-554927. - 320387. i) q^{65} +(59884.8 + 339623. i) q^{66} +(-125216. + 22078.9i) q^{67} +(-78406.1 + 135803. i) q^{68} +(252142. - 145574. i) q^{69} +(-91276.1 - 108779. i) q^{70} +(112194. + 308250. i) q^{71} +(-389189. + 1.06929e6i) q^{72} +(-240588. - 201877. i) q^{73} +(40617.5 - 230353. i) q^{74} +810733. i q^{75} +(-132573. - 798578. i) q^{76} +31152.1 q^{77} +(2.25778e6 + 398108. i) q^{78} +(-478243. + 569948. i) q^{79} +(-386576. - 140702. i) q^{80} +(-721691. + 262674. i) q^{81} +(-881042. + 739282. i) q^{82} +(-142692. - 247150. i) q^{83} +(285288. + 164711. i) q^{84} +(-41636.2 - 236130. i) q^{85} +(1.18337e6 - 208661. i) q^{86} +(288063. - 498940. i) q^{87} +(337129. - 194641. i) q^{88} +(32759.9 + 39041.7i) q^{89} +(-1.30010e6 - 3.57200e6i) q^{90} +(70831.1 - 194607. i) q^{91} +(-550026. - 461526. i) q^{92} +(-142633. + 808915. i) q^{93} +1.65405e6i q^{94} +(940169. + 805088. i) q^{95} -760402. q^{96} +(-411219. - 72509.1i) q^{97} +(-990774. + 1.18076e6i) q^{98} +(783627. + 285217. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9}+O(q^{10}) $ 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} - 1689 q^{10} + 1677 q^{11} - 9 q^{12} - 10506 q^{13} + 6105 q^{14} + 24138 q^{15} + 23760 q^{16} - 3438 q^{17} - 30918 q^{19} - 76650 q^{20} - 59055 q^{21} + 20490 q^{22} + 42498 q^{23} + 31848 q^{24} + 7914 q^{25} + 109989 q^{26} + 124821 q^{27} - 109476 q^{28} - 27726 q^{29} - 153516 q^{30} - 30789 q^{31} - 114375 q^{32} + 126039 q^{33} + 359796 q^{34} + 160161 q^{35} + 184995 q^{36} - 245244 q^{38} - 390564 q^{39} - 372678 q^{40} - 24708 q^{41} - 244893 q^{42} - 30726 q^{43} - 301419 q^{44} + 293037 q^{45} + 69246 q^{46} - 71454 q^{47} + 1024041 q^{48} - 350346 q^{49} - 104148 q^{50} - 180672 q^{51} + 921801 q^{52} + 822558 q^{53} + 308469 q^{54} + 623517 q^{55} - 17862 q^{57} - 1150644 q^{58} - 463812 q^{59} - 908130 q^{60} - 583698 q^{61} - 429732 q^{62} - 2576043 q^{63} - 328293 q^{64} - 1056789 q^{65} - 1038756 q^{66} + 1120464 q^{67} + 717270 q^{68} + 3771567 q^{69} + 4845345 q^{70} + 94494 q^{71} + 2351634 q^{72} + 950850 q^{73} + 55149 q^{74} - 218814 q^{76} - 343086 q^{77} + 1833471 q^{78} - 4936494 q^{79} - 9642039 q^{80} - 769551 q^{81} - 8627793 q^{82} - 412131 q^{83} - 3125205 q^{84} - 896910 q^{85} + 8878236 q^{86} + 610737 q^{87} + 13604751 q^{88} + 6653022 q^{89} + 3142734 q^{90} + 3409821 q^{91} - 3043740 q^{92} - 816393 q^{93} + 4839186 q^{95} - 5667138 q^{96} - 853656 q^{97} - 17679315 q^{98} - 13991937 q^{99}+O(q^{100}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9 - 1689 * q^10 + 1677 * q^11 - 9 * q^12 - 10506 * q^13 + 6105 * q^14 + 24138 * q^15 + 23760 * q^16 - 3438 * q^17 - 30918 * q^19 - 76650 * q^20 - 59055 * q^21 + 20490 * q^22 + 42498 * q^23 + 31848 * q^24 + 7914 * q^25 + 109989 * q^26 + 124821 * q^27 - 109476 * q^28 - 27726 * q^29 - 153516 * q^30 - 30789 * q^31 - 114375 * q^32 + 126039 * q^33 + 359796 * q^34 + 160161 * q^35 + 184995 * q^36 - 245244 * q^38 - 390564 * q^39 - 372678 * q^40 - 24708 * q^41 - 244893 * q^42 - 30726 * q^43 - 301419 * q^44 + 293037 * q^45 + 69246 * q^46 - 71454 * q^47 + 1024041 * q^48 - 350346 * q^49 - 104148 * q^50 - 180672 * q^51 + 921801 * q^52 + 822558 * q^53 + 308469 * q^54 + 623517 * q^55 - 17862 * q^57 - 1150644 * q^58 - 463812 * q^59 - 908130 * q^60 - 583698 * q^61 - 429732 * q^62 - 2576043 * q^63 - 328293 * q^64 - 1056789 * q^65 - 1038756 * q^66 + 1120464 * q^67 + 717270 * q^68 + 3771567 * q^69 + 4845345 * q^70 + 94494 * q^71 + 2351634 * q^72 + 950850 * q^73 + 55149 * q^74 - 218814 * q^76 - 343086 * q^77 + 1833471 * q^78 - 4936494 * q^79 - 9642039 * q^80 - 769551 * q^81 - 8627793 * q^82 - 412131 * q^83 - 3125205 * q^84 - 896910 * q^85 + 8878236 * q^86 + 610737 * q^87 + 13604751 * q^88 + 6653022 * q^89 + 3142734 * q^90 + 3409821 * q^91 - 3043740 * q^92 - 816393 * q^93 + 4839186 * q^95 - 5667138 * q^96 - 853656 * q^97 - 17679315 * q^98 - 13991937 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−13.2866	−	2.34278i	−1.66082	−	0.292847i	−0.737062	−	0.675825i	$-0.763788\pi$
$2$	−13.2866	−	2.34278i	−1.66082	−	0.292847i	−0.923758	+	0.382978i	$0.874899\pi$
$3$	−30.7619	+	36.6606i	−1.13933	+	1.35780i	−0.214813	+	0.976655i	$0.568914\pi$
$3$	−30.7619	+	36.6606i	−1.13933	+	1.35780i	−0.924516	+	0.381144i	$0.875530\pi$
$4$	110.904	+	40.3656i	1.73287	+	0.630713i
$5$	−169.577	+	61.7209i	−1.35661	+	0.493767i	−0.915006	−	0.403441i	$-0.867814\pi$
$5$	−169.577	+	61.7209i	−1.35661	+	0.493767i	−0.441608	+	0.897208i	$0.645592\pi$
$6$	494.607	−	415.025i	2.28985	−	1.92141i
$7$	−29.1620	−	50.5101i	−0.0850205	−	0.147260i	0.820379	−	0.571820i	$-0.193762\pi$
$7$	−29.1620	−	50.5101i	−0.0850205	−	0.147260i	−0.905400	+	0.424560i	$0.860429\pi$
$8$	−631.184	−	364.414i	−1.23278	−	0.711747i
$9$	−271.115	−	1537.57i	−0.371900	−	2.10915i
$10$	2397.69	−	422.777i	2.39769	−	0.422777i
$11$	−267.061	+	462.562i	−0.200647	+	0.347530i	−0.948737	−	0.316067i	$-0.897638\pi$
$11$	−267.061	+	462.562i	−0.200647	+	0.347530i	0.748090	+	0.663597i	$0.230971\pi$
$12$	−4891.43	+	2824.07i	−2.83069	+	1.63430i
$13$	2282.40	+	2720.06i	1.03887	+	1.23808i	0.970672	+	0.240407i	$0.0772809\pi$
$13$	2282.40	+	2720.06i	1.03887	+	1.23808i	0.0681993	+	0.997672i	$0.478275\pi$
$14$	269.129	+	739.426i	0.0980791	+	0.269470i
$15$	2953.78	−	8115.43i	0.875193	−	2.40457i
$16$	1746.31	+	1465.33i	0.426346	+	0.357747i
$17$	−230.723	+	1308.49i	−0.0469617	+	0.266333i	−0.999244	−	0.0388869i	$-0.987619\pi$
$17$	−230.723	+	1308.49i	−0.0469617	+	0.266333i	0.952282	+	0.305220i	$0.0987299\pi$
$18$			21064.2i			3.61183i
$19$	−3369.80	−	5974.14i	−0.491296	−	0.870993i
$19$	−3369.80	−	5974.14i	−0.491296	−	0.870993i
$20$	−21298.1			−2.66226
$21$	2748.81	+	484.689i	0.296816	+	0.0523366i
$22$	4632.00	−	5520.20i	0.435011	−	0.518426i
$23$	−5716.82	−	2080.75i	−0.469863	−	0.171016i	0.0962274	−	0.995359i	$-0.469322\pi$
$23$	−5716.82	−	2080.75i	−0.469863	−	0.171016i	−0.566090	+	0.824343i	$0.691545\pi$
$24$	32776.1	−	11929.5i	2.37095	−	0.862956i
$25$	12977.4	−	10889.3i	0.830551	−	0.696915i
$26$	−23952.8	−	41487.4i	−1.36281	−	2.36046i
$27$	34494.6	+	19915.5i	1.75251	+	1.01181i
$28$	−1195.30	−	6778.91i	−0.0544508	−	0.308806i
$29$	−11855.6	+	2090.46i	−0.486105	+	0.0857134i	−0.411329	−	0.911487i	$-0.634935\pi$
$29$	−11855.6	+	2090.46i	−0.486105	+	0.0857134i	−0.0747759	+	0.997200i	$0.523824\pi$
$30$	−58258.2	+	100906.i	−2.15771	+	3.73726i
$31$	14864.0	−	8581.75i	0.498944	−	0.288065i	−0.229334	−	0.973348i	$-0.573655\pi$
$31$	14864.0	−	8581.75i	0.498944	−	0.288065i	0.728277	+	0.685283i	$0.240321\pi$
$32$	10213.3	+	12171.7i	0.311685	+	0.371452i
$33$	−8742.52	−	24019.9i	−0.243274	−	0.668389i
$34$	6131.02	−	16844.8i	0.155990	−	0.428578i
$35$	8062.74	+	6765.44i	0.188052	+	0.157795i
$36$	31997.4	−	181466.i	0.685815	−	3.88945i
$37$			17337.3i			0.342276i	0.985247	+	0.171138i	$0.0547444\pi$
$37$			17337.3i			0.342276i	−0.985247	+	0.171138i	$0.945256\pi$
$38$	30777.0	+	87270.4i	0.560886	+	1.59044i
$39$	−169930.			−2.86468
$40$	129526.	+	22839.0i	2.02385	+	0.356859i
$41$	54796.0	−	65303.4i	0.795056	−	0.947511i	−0.204452	−	0.978877i	$-0.565541\pi$
$41$	54796.0	−	65303.4i	0.795056	−	0.947511i	0.999508	+	0.0313659i	$0.00998573\pi$
$42$	−35386.7	−	12879.7i	−0.477631	−	0.173843i
$43$	−83694.2	+	30462.2i	−1.05266	+	0.383138i	−0.809668	−	0.586889i	$-0.800353\pi$
$43$	−83694.2	+	30462.2i	−1.05266	+	0.383138i	−0.242996	+	0.970027i	$0.578130\pi$
$44$	−48289.6	+	40519.8i	−0.566886	+	0.475674i
$45$	140875.	+	244003.i	1.54595	+	2.67767i
$46$	71082.1	+	41039.3i	0.730276	+	0.421625i
$47$	−21289.2	−	120737.i	−0.205053	−	1.16291i	−0.897357	−	0.441306i	$-0.854516\pi$
$47$	−21289.2	−	120737.i	−0.205053	−	1.16291i	0.692304	−	0.721606i	$-0.256596\pi$
$48$	−107440.	+	18944.5i	−0.971497	+	0.171301i
$49$	57123.6	−	98941.1i	0.485543	−	0.840985i
$50$	−197936.	+	114278.i	−1.58349	+	0.914226i
$51$	−40872.6	−	48710.1i	−0.308122	−	0.367205i
$52$	143330.	+	393795.i	1.01936	+	2.80066i
$53$	8760.41	−	24069.0i	0.0588432	−	0.161670i	−0.906788	−	0.421588i	$-0.861473\pi$
$53$	8760.41	−	24069.0i	0.0588432	−	0.161670i	0.965631	+	0.259917i	$0.0836952\pi$
$54$	−411657.	−	345421.i	−2.61429	−	2.19365i
$55$	16737.5	−	94923.1i	0.100601	−	0.570537i
$56$			42508.3i			0.242052i
$57$	322677.	+	60236.9i	1.74238	+	0.325266i
$58$	162418.			0.832434
$59$	−32344.5	−	5703.21i	−0.157487	−	0.0277692i	0.0943487	−	0.995539i	$-0.469923\pi$
$59$	−32344.5	−	5703.21i	−0.157487	−	0.0277692i	−0.251836	+	0.967770i	$0.581034\pi$
$60$	655169.	−	780800.i	3.03319	−	3.61482i
$61$	251440.	+	91516.8i	1.10776	+	0.403191i	0.830171	−	0.557509i	$-0.188243\pi$
$61$	251440.	+	91516.8i	1.10776	+	0.403191i	0.277588	+	0.960700i	$0.410465\pi$
$62$	−217597.	+	79198.8i	−0.913014	+	0.332310i
$63$	−69756.7	+	58532.8i	−0.278974	+	0.234087i
$64$	−180133.	−	311999.i	−0.687152	−	1.19018i
$65$	−554927.	−	320387.i	−2.02067	−	1.16663i
$66$	59884.8	+	339623.i	0.208298	+	1.18132i
$67$	−125216.	+	22078.9i	−0.416326	+	0.0734095i	−0.377888	−	0.925851i	$-0.623349\pi$
$67$	−125216.	+	22078.9i	−0.416326	+	0.0734095i	−0.0384385	+	0.999261i	$0.512238\pi$
$68$	−78406.1	+	135803.i	−0.249358	+	0.431901i
$69$	252142.	−	145574.i	0.767534	−	0.443136i
$70$	−91276.1	−	108779.i	−0.266111	−	0.317139i
$71$	112194.	+	308250.i	0.313468	+	0.861247i	0.991950	+	0.126630i	$0.0404160\pi$
$71$	112194.	+	308250.i	0.313468	+	0.861247i	−0.678482	+	0.734617i	$0.737362\pi$
$72$	−389189.	+	1.06929e6i	−1.04271	+	2.86482i
$73$	−240588.	−	201877.i	−0.618451	−	0.518942i	0.278865	−	0.960330i	$-0.410042\pi$
$73$	−240588.	−	201877.i	−0.618451	−	0.518942i	−0.897316	+	0.441388i	$0.854486\pi$
$74$	40617.5	−	230353.i	0.100235	−	0.568459i
$75$			810733.i			1.92174i
$76$	−132573.	−	798578.i	−0.302006	−	1.81918i
$77$	31152.1			0.0682363
$78$	2.25778e6	+	398108.i	4.75771	+	0.838913i
$79$	−478243.	+	569948.i	−0.969990	+	1.15599i	0.0177438	+	0.999843i	$0.494352\pi$
$79$	−478243.	+	569948.i	−0.969990	+	1.15599i	−0.987734	+	0.156147i	$0.950093\pi$
$80$	−386576.	−	140702.i	−0.755031	−	0.274809i
$81$	−721691.	+	262674.i	−1.35799	+	0.494268i
$82$	−881042.	+	739282.i	−1.59792	+	1.34081i
$83$	−142692.	−	247150.i	−0.249555	−	0.432242i	0.713847	−	0.700301i	$-0.246951\pi$
$83$	−142692.	−	247150.i	−0.249555	−	0.432242i	−0.963402	+	0.268059i	$0.913618\pi$
$84$	285288.	+	164711.i	0.481334	+	0.277898i
$85$	−41636.2	−	236130.i	−0.0677975	−	0.384499i
$86$	1.18337e6	−	208661.i	1.86049	−	0.328054i
$87$	288063.	−	498940.i	0.437452	−	0.757689i
$88$	337129.	−	194641.i	0.494707	−	0.285619i
$89$	32759.9	+	39041.7i	0.0464699	+	0.0553807i	0.788779	−	0.614677i	$-0.210714\pi$
$89$	32759.9	+	39041.7i	0.0464699	+	0.0553807i	−0.742309	+	0.670058i	$0.766269\pi$
$90$	−1.30010e6	−	3.57200e6i	−1.78340	−	4.89986i
$91$	70831.1	−	194607.i	0.0939939	−	0.258246i
$92$	−550026.	−	461526.i	−0.706349	−	0.592697i
$93$	−142633.	+	808915.i	−0.177326	+	1.00567i
$94$			1.65405e6i			1.99144i
$95$	940169.	+	805088.i	1.09657	+	0.939015i
$96$	−760402.			−0.859468
$97$	−411219.	−	72509.1i	−0.450566	−	0.0794469i	−0.0562394	−	0.998417i	$-0.517911\pi$
$97$	−411219.	−	72509.1i	−0.450566	−	0.0794469i	−0.394327	+	0.918970i	$0.629022\pi$
$98$	−990774.	+	1.18076e6i	−1.05268	+	1.25453i
$99$	783627.	+	285217.i	0.807614	+	0.293947i
$100$	1.87879e6	−	683824.i	1.87879	−	0.683824i
$101$	721072.	−	605051.i	0.699865	−	0.587256i	−0.221870	−	0.975076i	$-0.571216\pi$
$101$	721072.	−	605051.i	0.699865	−	0.587256i	0.921735	+	0.387820i	$0.126772\pi$
$102$	428940.	+	742945.i	0.404199	+	0.700094i
$103$	−1.11357e6	−	642919.i	−1.01907	−	0.588362i	−0.105238	−	0.994447i	$-0.533560\pi$
$103$	−1.11357e6	−	642919.i	−1.01907	−	0.588362i	−0.913835	+	0.406085i	$0.866894\pi$
$104$	−449387.	−	2.54860e6i	−0.399503	−	2.26569i
$105$	−496050.	+	87467.0i	−0.428506	+	0.0755573i
$106$	−172784.	+	299271.i	−0.145073	+	0.251273i
$107$	1.10100e6	−	635662.i	0.898743	−	0.518890i	0.0219511	−	0.999759i	$-0.493012\pi$
$107$	1.10100e6	−	635662.i	0.898743	−	0.518890i	0.876792	+	0.480869i	$0.159679\pi$
$108$	3.02168e6	+	3.60110e6i	2.39871	+	2.85867i
$109$	−453240.	−	1.24527e6i	−0.349984	−	0.961574i	−0.982374	−	0.186924i	$-0.940148\pi$
$109$	−453240.	−	1.24527e6i	−0.349984	−	0.961574i	0.632390	−	0.774650i	$-0.282074\pi$
$110$	−444767.	+	1.22199e6i	−0.334160	+	0.918098i
$111$	−635596.	−	533328.i	−0.464742	−	0.389965i
$112$	23088.0	−	130939.i	0.0164336	−	0.0931996i
$113$			1.40547e6i			0.974060i	0.873385	+	0.487030i	$0.161920\pi$
$113$			1.40547e6i			0.974060i	−0.873385	+	0.487030i	$0.838080\pi$
$114$	−4.14614e6	−	1.55630e6i	−2.79853	−	1.05046i
$115$	1.09787e6			0.721865
$116$	−1.39921e6	−	246719.i	−0.896417	−	0.158063i
$117$	3.56349e6	−	4.24680e6i	2.22494	−	2.65158i
$118$	416386.	+	151552.i	0.253425	+	0.0922393i
$119$	72820.5	−	26504.5i	0.0432128	−	0.0157282i
$120$	−4.82176e6	+	4.04593e6i	−2.79037	+	2.34140i
$121$	743138.	+	1.28715e6i	0.419482	+	0.726564i
$122$	−3.12637e6	−	1.80501e6i	−1.72172	−	0.994033i
$123$	708431.	+	4.01771e6i	0.380699	+	2.15905i
$124$	1.99488e6	−	351752.i	1.04629	−	0.184489i
$125$	−118719.	+	205628.i	−0.0607843	+	0.105282i
$126$	1.06396e6	−	614275.i	0.531878	−	0.307080i
$127$	−2.32319e6	−	2.76867e6i	−1.13416	−	1.35164i	−0.927765	−	0.373166i	$-0.878272\pi$
$127$	−2.32319e6	−	2.76867e6i	−1.13416	−	1.35164i	−0.206392	−	0.978469i	$-0.566172\pi$
$128$	1.31460e6	+	3.61183e6i	0.626849	+	1.72225i
$129$	1.45783e6	−	4.00535e6i	0.679105	−	1.86583i
$130$	6.62247e6	+	5.55691e6i	3.01432	+	2.52932i
$131$	155623.	−	882584.i	0.0692247	−	0.392593i	−0.930434	−	0.366460i	$-0.880570\pi$
$131$	155623.	−	882584.i	0.0692247	−	0.392593i	0.999658	−	0.0261326i	$-0.00831921\pi$
$132$		−	3.01679e6i		−	1.31167i
$133$	−203484.	+	344427.i	−0.0864920	+	0.146400i
$134$	1.71541e6			0.712941
$135$	−7.07868e6	−	1.24816e6i	−2.87707	−	0.507306i
$136$	622462.	−	741821.i	0.247455	−	0.294905i
$137$	−423996.	−	154322.i	−0.164892	−	0.0600159i	0.258255	−	0.966077i	$-0.416853\pi$
$137$	−423996.	−	154322.i	−0.164892	−	0.0600159i	−0.423147	+	0.906061i	$0.639075\pi$
$138$	−3.69114e6	+	1.34347e6i	−1.40451	+	0.511199i
$139$	−3.44095e6	+	2.88730e6i	−1.28125	+	1.07510i	−0.288181	+	0.957576i	$0.593050\pi$
$139$	−3.44095e6	+	2.88730e6i	−1.28125	+	1.07510i	−0.993070	+	0.117521i	$0.962505\pi$
$140$	621096.	+	1.07577e6i	0.226347	+	0.392044i
$141$	5.08118e6	+	2.93362e6i	1.81262	+	1.04652i
$142$	−768507.	−	4.35842e6i	−0.268400	−	1.52217i
$143$	−1.86774e6	+	329332.i	−0.638716	+	0.112623i
$144$	1.77960e6	−	3.08236e6i	0.595984	−	1.03228i
$145$	1.88141e6	−	1.08623e6i	0.617134	−	0.356303i
$146$	2.72363e6	+	3.24590e6i	0.875165	+	1.04298i
$147$	1.87001e6	+	5.13780e6i	0.588696	+	1.61743i
$148$	−699832.	+	1.92277e6i	−0.215878	+	0.593120i
$149$	−1.74717e6	−	1.46605e6i	−0.528173	−	0.443190i	0.339297	−	0.940679i	$-0.389811\pi$
$149$	−1.74717e6	−	1.46605e6i	−0.528173	−	0.443190i	−0.867470	+	0.497490i	$0.834255\pi$
$150$	1.89937e6	−	1.07718e7i	0.562776	−	3.19166i
$151$		−	1.89531e6i		−	0.550489i	−0.961374	−	0.275244i	$-0.911241\pi$
$151$		−	1.89531e6i		−	0.550489i	0.961374	−	0.275244i	$-0.0887587\pi$
$152$	−50097.5	+	4.99879e6i	−0.0142655	+	1.42342i
$153$	2.07445e6			0.579201
$154$	−413905.	−	72982.6i	−0.113328	−	0.0199828i
$155$	−1.99092e6	+	2.37269e6i	−0.534637	+	0.637155i
$156$	−1.88458e7	−	6.85933e6i	−4.96412	−	1.80679i
$157$	−27884.0	+	10148.9i	−0.00720535	+	0.00262253i	−0.345620	−	0.938374i	$-0.612331\pi$
$157$	−27884.0	+	10148.9i	−0.00720535	+	0.00262253i	0.338415	+	0.940997i	$0.390109\pi$
$158$	7.68946e6	−	6.45223e6i	1.94951	−	1.63583i
$159$	612898.	+	1.06157e6i	0.152474	+	0.264093i
$160$	−2.48319e6	−	1.43367e6i	−0.606247	−	0.350017i
$161$	61615.1	+	349437.i	0.0147642	+	0.0837318i
$162$	1.02042e7	−	1.79927e6i	2.40012	−	0.423206i
$163$	4.04458e6	−	7.00542e6i	0.933922	−	1.61760i	0.157377	−	0.987539i	$-0.449696\pi$
$163$	4.04458e6	−	7.00542e6i	0.933922	−	1.61760i	0.776545	−	0.630062i	$-0.216971\pi$
$164$	8.71310e6	−	5.03051e6i	1.97534	−	1.14046i
$165$	2.96506e6	+	3.53362e6i	0.660057	+	0.786625i
$166$	1.31687e6	+	3.61807e6i	0.287885	+	0.790958i
$167$	656365.	−	1.80335e6i	0.140928	−	0.387195i	−0.849070	−	0.528281i	$-0.822837\pi$
$167$	656365.	−	1.80335e6i	0.140928	−	0.387195i	0.989997	+	0.141085i	$0.0450591\pi$
$168$	−1.55838e6	−	1.30763e6i	−0.328659	−	0.275777i
$169$	−1.35120e6	+	7.66305e6i	−0.279937	+	1.58760i
$170$			3.23490e6i			0.658438i
$171$	−8.27206e6	+	6.80099e6i	−1.65434	+	1.36014i
$172$	−1.05116e7			−2.06578
$173$	6.79347e6	+	1.19787e6i	1.31206	+	0.231351i	0.785539	−	0.618812i	$-0.212386\pi$
$173$	6.79347e6	+	1.19787e6i	1.31206	+	0.231351i	0.526519	+	0.850163i	$0.323497\pi$
$174$	−4.99628e6	+	5.95433e6i	−0.948416	+	1.13028i
$175$	−928467.	−	337934.i	−0.173242	−	0.0630548i
$176$	−1.14418e6	+	416447.i	−0.209873	+	0.0763875i
$177$	1.20406e6	−	1.01033e6i	0.217134	−	0.182197i
$178$	−343800.	−	595479.i	−0.0609601	−	0.105586i
$179$	−3.24755e6	−	1.87498e6i	−0.566235	−	0.326916i	0.189409	−	0.981898i	$-0.439343\pi$
$179$	−3.24755e6	−	1.87498e6i	−0.566235	−	0.326916i	−0.755644	+	0.654982i	$0.772676\pi$
$180$	5.77424e6	+	3.27473e7i	0.990096	+	5.61511i
$181$	−8.68118e6	+	1.53073e6i	−1.46401	+	0.258144i	−0.848168	−	0.529728i	$-0.822294\pi$
$181$	−8.68118e6	+	1.53073e6i	−1.46401	+	0.258144i	−0.615839	+	0.787872i	$0.711183\pi$
$182$	−1.39702e6	+	2.41971e6i	−0.231734	+	0.401375i
$183$	−1.10898e7	+	6.40272e6i	−1.80956	+	1.04475i
$184$	2.85011e6	+	3.39663e6i	0.457518	+	0.545249i
$185$	−1.07007e6	−	2.94000e6i	−0.169005	−	0.464337i
$186$	3.79022e6	−	1.04135e7i	0.589013	−	1.61830i
$187$	−543643.	−	456171.i	−0.0831359	−	0.0697593i
$188$	2.51258e6	−	1.42495e7i	0.378134	−	2.14450i
$189$		−	2.32310e6i		−	0.344099i
$190$	−1.06055e7	−	1.28995e7i	−1.54621	−	1.88066i
$191$	−1.67335e6			−0.240153			−0.120076	−	0.992765i	$-0.538314\pi$
$191$	−1.67335e6			−0.240153			−0.120076	+	0.992765i	$0.538314\pi$
$192$	1.69793e7	+	2.99391e6i	2.39892	+	0.422994i
$193$	1.07959e6	−	1.28661e6i	0.150172	−	0.178968i	−0.685714	−	0.727871i	$-0.740510\pi$
$193$	1.07959e6	−	1.28661e6i	0.150172	−	0.178968i	0.835886	+	0.548903i	$0.184954\pi$
$194$	5.29382e6	+	1.92679e6i	0.725043	+	0.263894i
$195$	2.88162e7	−	1.04882e7i	3.88626	−	1.41448i
$196$	1.03290e7	−	8.66710e6i	1.37180	−	1.15108i
$197$	−3.23204e6	−	5.59805e6i	−0.422744	−	0.732214i	0.573463	−	0.819232i	$-0.305600\pi$
$197$	−3.23204e6	−	5.59805e6i	−0.422744	−	0.732214i	−0.996207	+	0.0870173i	$0.972266\pi$
$198$	−9.74351e6	−	5.62542e6i	−1.25522	−	0.724701i
$199$	−1.49251e6	−	8.46442e6i	−0.189390	−	1.07408i	−0.920184	−	0.391485i	$-0.871961\pi$
$199$	−1.49251e6	−	8.46442e6i	−0.189390	−	1.07408i	0.730794	−	0.682598i	$-0.239150\pi$
$200$	−1.21593e7	+	2.14402e6i	−1.51992	+	0.268002i
$201$	3.04244e6	−	5.26966e6i	0.374657	−	0.648925i
$202$	−1.09981e7	+	6.34973e6i	−1.33433	+	0.770373i
$203$	451324.	+	537867.i	0.0539511	+	0.0642964i
$204$	−2.56671e6	−	7.05198e6i	−0.302334	−	0.830655i
$205$	−5.26155e6	+	1.44560e7i	−0.610734	+	1.67798i
$206$	1.32893e7	+	1.11510e7i	1.52020	+	1.27560i
$207$	−1.64939e6	+	9.35415e6i	−0.185957	+	1.05461i
$208$			8.09455e6i			0.899504i
$209$	3.66335e6	+	36713.9i	0.401273	+	0.00402153i
$210$	6.79571e6			0.733799
$211$	−6.10655e6	−	1.07675e6i	−0.650053	−	0.114622i	−0.161108	−	0.986937i	$-0.551507\pi$
$211$	−6.10655e6	−	1.07675e6i	−0.650053	−	0.114622i	−0.488945	+	0.872315i	$0.662618\pi$
$212$	1.94312e6	−	2.31572e6i	0.203935	−	0.243041i
$213$	−1.47519e7	−	5.36925e6i	−1.52654	−	0.555616i
$214$	−1.61177e7	+	5.86637e6i	−1.64461	+	0.598588i
$215$	1.23124e7	−	1.03314e7i	1.23888	−	1.03954i
$216$	−1.45150e7	−	2.51407e7i	−1.44031	−	2.49468i
$217$	−866931.	−	500523.i	−0.0848409	−	0.0489829i
$218$	3.10461e6	+	1.76071e7i	0.299666	+	1.69949i
$219$	1.48019e7	−	2.60997e6i	1.40924	−	0.248487i
$220$	5.68788e6	−	9.85170e6i	0.534174	−	0.925216i
$221$	−4.08578e6	+	2.35893e6i	−0.378528	+	0.218543i
$222$	7.19541e6	+	8.57516e6i	0.657653	+	0.783760i
$223$	1.72311e6	+	4.73422e6i	0.155382	+	0.426907i	0.992819	−	0.119626i	$-0.0381695\pi$
$223$	1.72311e6	+	4.73422e6i	0.155382	+	0.426907i	−0.837438	+	0.546533i	$0.815947\pi$
$224$	316955.	−	870827.i	0.0282003	−	0.0774797i
$225$	−2.02614e7	−	1.70014e7i	−1.77878	−	1.49258i
$226$	3.29270e6	−	1.86738e7i	0.285251	−	1.61774i
$227$			2.24475e7i			1.91907i	0.281587	+	0.959536i	$0.409139\pi$
$227$			2.24475e7i			1.91907i	−0.281587	+	0.959536i	$0.590861\pi$
$228$	3.33545e7	+	1.97055e7i	2.81417	+	1.66259i
$229$	2.07706e7			1.72959			0.864793	−	0.502129i	$-0.167450\pi$
$229$	2.07706e7			1.72959			0.864793	+	0.502129i	$0.167450\pi$
$230$	−1.45869e7	−	2.57206e6i	−1.19889	−	0.211396i
$231$	−958298.	+	1.14206e6i	−0.0777436	+	0.0926512i
$232$	8.24487e6	+	3.00089e6i	0.660267	+	0.240318i
$233$	−1.46477e7	+	5.33132e6i	−1.15798	+	0.421470i	−0.848375	−	0.529396i	$-0.822419\pi$
$233$	−1.46477e7	+	5.33132e6i	−1.15798	+	0.421470i	−0.309604	+	0.950866i	$0.600197\pi$
$234$	−5.72959e7	+	4.80769e7i	−4.47173	+	3.75223i
$235$	1.10621e7	+	1.91602e7i	0.852385	+	1.47637i
$236$	−3.35691e6	−	1.93811e6i	−0.255390	−	0.147450i
$237$	−6.18296e6	−	3.50653e7i	−0.464464	−	2.63410i
$238$	−1.02963e6	+	181551.i	−0.0763747	+	0.0134669i
$239$	3.76938e6	−	6.52876e6i	0.276106	−	0.478230i	−0.694307	−	0.719679i	$-0.744289\pi$
$239$	3.76938e6	−	6.52876e6i	0.276106	−	0.478230i	0.970414	+	0.241449i	$0.0776225\pi$
$240$	1.70500e7	−	9.84384e6i	1.23336	−	0.712083i
$241$	1.49105e7	+	1.77697e7i	1.06523	+	1.26949i	0.961477	+	0.274885i	$0.0886398\pi$
$241$	1.49105e7	+	1.77697e7i	1.06523	+	1.26949i	0.103750	+	0.994603i	$0.466916\pi$
$242$	−6.85823e6	−	1.88428e7i	−0.483912	−	1.32954i
$243$	2.63963e6	−	7.25233e6i	0.183960	−	0.505427i
$244$	2.41915e7	+	2.02991e7i	1.66530	+	1.39736i
$245$	−3.58011e6	+	2.03038e7i	−0.243444	+	1.38064i
$246$		−	5.50412e7i		−	3.69728i
$247$	8.55878e6	−	2.28014e7i	0.567964	−	1.51311i
$248$	−1.25093e7			−0.820118
$249$	1.34502e7	+	2.37163e6i	0.871223	+	0.153620i
$250$	2.05911e6	−	2.45395e6i	0.131783	−	0.157053i
$251$	−1.73222e7	−	6.30475e6i	−1.09542	−	0.398701i	−0.269795	−	0.962918i	$-0.586956\pi$
$251$	−1.73222e7	−	6.30475e6i	−1.09542	−	0.398701i	−0.825626	+	0.564217i	$0.809178\pi$
$252$	−1.00990e7	+	3.67573e6i	−0.631068	+	0.229690i
$253$	2.48922e6	−	2.08870e6i	0.153710	−	0.128978i
$254$	2.43808e7	+	4.22288e7i	1.48781	+	2.57696i
$255$	9.93748e6	+	5.73741e6i	0.599316	+	0.346015i
$256$	−5.00097e6	−	2.83619e7i	−0.298081	−	1.69050i
$257$	−2.36659e7	+	4.17294e6i	−1.39420	+	0.245835i	−0.819757	−	0.572711i	$-0.805892\pi$
$257$	−2.36659e7	+	4.17294e6i	−1.39420	+	0.245835i	−0.574441	+	0.818546i	$0.694780\pi$
$258$	−2.87532e7	+	4.98019e7i	−1.67427	+	2.89993i
$259$	875710.	−	505592.i	0.0504035	−	0.0291005i
$260$	−4.86108e7	−	5.79321e7i	−2.76575	−	3.29609i
$261$	6.42848e6	+	1.76621e7i	0.361565	+	0.993392i
$262$	−4.13540e6	+	1.13619e7i	−0.229939	+	0.631753i
$263$	−1.00048e7	−	8.39500e6i	−0.549971	−	0.461481i	0.324960	−	0.945728i	$-0.394649\pi$
$263$	−1.00048e7	−	8.39500e6i	−0.549971	−	0.461481i	−0.874931	+	0.484247i	$0.839094\pi$
$264$	−3.23505e6	+	1.83469e7i	−0.175820	+	0.997127i
$265$			4.62225e6i			0.248379i
$266$	3.51052e6	−	4.09953e6i	0.186521	−	0.217816i
$267$	−2.43904e6			−0.128140
$268$	−1.47781e7	−	2.60578e6i	−0.767739	−	0.135373i
$269$	1.81222e7	−	2.15972e7i	0.931009	−	1.10953i	−0.0627555	−	0.998029i	$-0.519989\pi$
$269$	1.81222e7	−	2.15972e7i	0.931009	−	1.10953i	0.993764	−	0.111504i	$-0.0355667\pi$
$270$	9.11272e7	+	3.31676e7i	4.62974	+	1.68509i
$271$	9.72164e6	−	3.53839e6i	0.488463	−	0.177786i	−0.0860347	−	0.996292i	$-0.527420\pi$
$271$	9.72164e6	−	3.53839e6i	0.488463	−	0.177786i	0.574498	+	0.818506i	$0.305197\pi$
$272$	−2.32029e6	+	1.94696e6i	−0.115302	+	0.0967496i
$273$	4.95550e6	+	8.58318e6i	0.243557	+	0.421852i
$274$	5.27191e6	+	3.04374e6i	0.256281	+	0.147964i
$275$	1.57124e6	+	8.91094e6i	0.0755517	+	0.428475i
$276$	3.38396e7	−	5.96684e6i	1.60953	−	0.283803i
$277$	−1.50557e7	+	2.60772e7i	−0.708371	+	1.22693i	0.257090	+	0.966387i	$0.417236\pi$
$277$	−1.50557e7	+	2.60772e7i	−0.708371	+	1.22693i	−0.965461	+	0.260547i	$0.916097\pi$
$278$	5.24827e7	−	3.03009e7i	2.44277	−	1.41033i
$279$	−1.72249e7	−	2.05279e7i	−0.793130	−	0.945216i
$280$	−2.62365e6	−	7.20842e6i	−0.119518	−	0.328372i
$281$	6.84830e6	−	1.88155e7i	0.308648	−	0.848004i	−0.684273	−	0.729226i	$-0.739880\pi$
$281$	6.84830e6	−	1.88155e7i	0.308648	−	0.848004i	0.992921	−	0.118778i	$-0.0378976\pi$
$282$	−6.06386e7	−	5.08818e7i	−2.70397	−	2.26890i
$283$	983810.	−	5.57946e6i	0.0434062	−	0.246169i	−0.955383	−	0.295371i	$-0.904557\pi$
$283$	983810.	−	5.57946e6i	0.0434062	−	0.246169i	0.998789	+	0.0492021i	$0.0156678\pi$
$284$			3.87148e7i			1.69014i
$285$	−5.84363e7	+	9.70112e6i	−2.52434	+	0.419071i
$286$	2.55873e7			1.09377
$287$	−4.89645e6	−	863376.i	−0.207126	−	0.0365220i
$288$	1.59459e7	−	1.90036e7i	0.667532	−	0.795534i
$289$	2.10230e7	+	7.65174e6i	0.870965	+	0.317005i
$290$	−2.75423e7	+	1.00246e7i	−1.12929	+	0.411028i
$291$	1.53081e7	−	1.28450e7i	0.621216	−	0.521262i
$292$	−1.85332e7	−	3.21004e7i	−0.744392	−	1.28932i
$293$	−1.84441e6	−	1.06487e6i	−0.0733255	−	0.0423345i	0.462889	−	0.886416i	$-0.346813\pi$
$293$	−1.84441e6	−	1.06487e6i	−0.0733255	−	0.0423345i	−0.536215	+	0.844082i	$0.680146\pi$
$294$	−1.28092e7	−	7.26447e7i	−0.504058	−	2.85866i
$295$	5.83689e6	−	1.02920e6i	0.227361	−	0.0400898i
$296$	6.31797e6	−	1.09430e7i	0.243614	−	0.421952i
$297$	−1.84243e7	+	1.06373e7i	−0.703269	+	0.406033i
$298$	1.97792e7	+	2.35720e7i	0.747413	+	0.890732i
$299$	−7.38831e6	−	2.02992e7i	−0.276396	−	0.759391i
$300$	−3.27257e7	+	8.99133e7i	−1.21206	+	3.33012i
$301$	3.97934e6	+	3.33906e6i	0.145919	+	0.122441i
$302$	−4.44028e6	+	2.51821e7i	−0.161209	+	0.914262i
$303$			4.50474e7i			1.61935i
$304$	2.86937e6	−	1.53706e7i	0.102133	−	0.547104i
$305$	−4.82869e7			−1.70188
$306$	−2.75624e7	−	4.85999e6i	−0.961949	−	0.169618i
$307$	1.13647e7	−	1.35439e7i	0.392773	−	0.468089i	−0.533029	−	0.846097i	$-0.678946\pi$
$307$	1.13647e7	−	1.35439e7i	0.392773	−	0.468089i	0.925802	+	0.378008i	$0.123391\pi$
$308$	3.45489e6	+	1.25748e6i	0.118245	+	0.0430375i
$309$	5.78252e7	−	2.10467e7i	1.95994	−	0.713359i
$310$	3.20112e7	−	2.68606e7i	1.07452	−	0.901633i
$311$	5.41096e6	+	9.37206e6i	0.179884	+	0.311569i	0.941841	−	0.336060i	$-0.109094\pi$
$311$	5.41096e6	+	9.37206e6i	0.179884	+	0.311569i	−0.761957	+	0.647628i	$0.775761\pi$
$312$	1.07257e8	+	6.19249e7i	3.53152	+	2.03893i
$313$	−4.14340e6	−	2.34984e7i	−0.135121	−	0.766311i	−0.974775	−	0.223189i	$-0.928353\pi$
$313$	−4.14340e6	−	2.34984e7i	−0.135121	−	0.766311i	0.839654	−	0.543122i	$-0.182758\pi$
$314$	394258.	−	69518.4i	0.0127348	−	0.00224549i
$315$	8.21642e6	−	1.42312e7i	0.262876	−	0.455314i
$316$	−7.60452e7	+	4.39047e7i	−2.40996	+	1.39139i
$317$	−1.90942e7	−	2.27556e7i	−0.599410	−	0.714349i	0.377975	−	0.925816i	$-0.376620\pi$
$317$	−1.90942e7	−	2.27556e7i	−0.599410	−	0.714349i	−0.977385	+	0.211467i	$0.932176\pi$
$318$	−5.65628e6	−	1.55405e7i	−0.175893	−	0.483263i
$319$	2.19920e6	−	6.04224e6i	0.0677473	−	0.186134i
$320$	4.98032e7	+	4.17898e7i	1.51987	+	1.27532i
$321$	−1.05651e7	+	5.99174e7i	−0.319416	+	1.81150i
$322$		−	4.78716e6i		−	0.143387i
$323$	8.59461e6	−	3.03099e6i	0.255046	−	0.0899450i
$324$	−9.06412e7			−2.66496
$325$	5.92391e7	+	1.04454e7i	1.72567	+	0.304282i
$326$	−7.01507e7	+	8.36023e7i	−2.02479	+	2.41305i
$327$	5.95947e7	+	2.16907e7i	1.70437	+	0.620340i
$328$	−5.83839e7	+	2.12500e7i	−1.65452	+	0.602195i
$329$	−5.47760e6	+	4.59626e6i	−0.153817	+	0.129067i
$330$	−3.11169e7	−	5.38961e7i	−0.865874	−	1.49974i
$331$	−1.43644e7	−	8.29331e6i	−0.396100	−	0.228688i	0.288700	−	0.957420i	$-0.406777\pi$
$331$	−1.43644e7	−	8.29331e6i	−0.396100	−	0.228688i	−0.684800	+	0.728731i	$0.740110\pi$
$332$	−5.84872e6	−	3.31698e7i	−0.159826	−	0.906417i
$333$	2.66574e7	−	4.70041e6i	0.721912	−	0.127293i
$334$	−1.29457e7	+	2.24226e7i	−0.347444	+	0.601791i
$335$	1.98709e7	−	1.14725e7i	0.528547	−	0.305157i
$336$	4.09006e6	+	4.87434e6i	0.107823	+	0.128498i
$337$	1.20038e7	+	3.29802e7i	0.313639	+	0.861715i	0.991915	+	0.126908i	$0.0405053\pi$
$337$	1.20038e7	+	3.29802e7i	0.313639	+	0.861715i	−0.678276	+	0.734807i	$0.737273\pi$
$338$	3.59057e7	−	9.86500e7i	0.929850	−	2.55474i
$339$	−5.15253e7	−	4.32348e7i	−1.32258	−	1.10977i
$340$	4.91395e6	−	2.78684e7i	0.125024	−	0.709047i
$341$			9.16739e6i			0.231197i
$342$	1.25840e8	−	7.09821e7i	3.14588	−	1.77448i
$343$	−1.35251e7			−0.335166
$344$	6.39273e7	+	1.12721e7i	1.57040	+	0.276904i
$345$	−3.37724e7	+	4.02484e7i	−0.822441	+	0.980147i
$346$	−8.74554e7	−	3.18312e7i	−2.11134	−	0.768466i
$347$	−6.82633e7	+	2.48458e7i	−1.63380	+	0.594655i	−0.985939	−	0.167103i	$-0.946559\pi$
$347$	−6.82633e7	+	2.48458e7i	−1.63380	+	0.594655i	−0.647861	+	0.761758i	$0.724336\pi$
$348$	5.20873e7	−	4.37064e7i	1.23593	−	1.03707i
$349$	−2.67355e7	−	4.63073e7i	−0.628945	−	1.08936i	−0.987764	−	0.155957i	$-0.950154\pi$
$349$	−2.67355e7	−	4.63073e7i	−0.628945	−	1.08936i	0.358819	−	0.933407i	$-0.383180\pi$
$350$	1.15444e7	+	6.66517e6i	0.269258	+	0.155456i
$351$	2.45593e7	+	1.39282e8i	0.567929	+	3.22088i
$352$	−8.35775e6	+	1.47370e6i	−0.191629	+	0.0337894i
$353$	3.32266e6	−	5.75501e6i	0.0755373	−	0.130835i	−0.825782	−	0.563989i	$-0.809266\pi$
$353$	3.32266e6	−	5.75501e6i	0.0755373	−	0.130835i	0.901320	+	0.433154i	$0.142599\pi$
$354$	−1.83648e7	+	1.06029e7i	−0.413977	+	0.239010i
$355$	−3.80509e7	−	4.53473e7i	−0.850511	−	1.01360i
$356$	2.05725e6	+	5.65224e6i	0.0455970	+	0.125277i
$357$	−1.26843e6	+	3.48497e6i	−0.0278779	+	0.0765939i
$358$	3.87561e7	+	3.25203e7i	0.844678	+	0.708769i
$359$	5.26012e6	−	2.98316e7i	0.113687	−	0.644753i	−0.873704	−	0.486457i	$-0.838289\pi$
$359$	5.26012e6	−	2.98316e7i	0.113687	−	0.644753i	0.987392	−	0.158296i	$-0.0505999\pi$
$360$		−	2.05348e8i		−	4.40131i
$361$	−2.43348e7	+	4.02633e7i	−0.517256	+	0.855831i
$362$	1.18929e8			2.50705
$363$	−7.00481e7	−	1.23514e7i	−1.46446	−	0.258223i
$364$	1.57109e7	−	1.87235e7i	0.325759	−	0.388224i
$365$	5.32582e7	+	1.93844e7i	1.09524	+	0.398633i
$366$	1.62346e8	−	5.90891e7i	3.31130	−	1.20521i
$367$	6.37072e6	−	5.34567e6i	0.128882	−	0.108144i	−0.576069	−	0.817401i	$-0.695414\pi$
$367$	6.37072e6	−	5.34567e6i	0.128882	−	0.108144i	0.704950	+	0.709257i	$0.250969\pi$
$368$	−6.93438e6	−	1.20107e7i	−0.139144	−	0.241004i
$369$	−1.15265e8	−	6.65481e7i	−2.29413	−	1.32451i
$370$	7.32982e6	+	4.15695e7i	0.144707	+	0.820672i
$371$	−1.47120e6	+	259412.i	−0.0288105	+	0.00508006i
$372$	−4.84709e7	+	8.39541e7i	−0.941570	+	1.63085i
$373$	−3.51617e7	+	2.03006e7i	−0.677553	+	0.391185i	−0.798932	−	0.601421i	$-0.794602\pi$
$373$	−3.51617e7	+	2.03006e7i	−0.677553	+	0.391185i	0.121380	+	0.992606i	$0.461268\pi$
$374$	6.15444e6	+	7.33457e6i	0.117645	+	0.140204i
$375$	−3.88641e6	−	1.06778e7i	−0.0736978	−	0.202483i
$376$	−3.05609e7	+	8.39653e7i	−0.574913	+	1.57956i
$377$	−3.27454e7	−	2.74767e7i	−0.611120	−	0.512791i
$378$	−5.44252e6	+	3.08660e7i	−0.100768	+	0.571486i
$379$		−	1.82339e7i		−	0.334936i	−0.985877	−	0.167468i	$-0.946441\pi$
$379$		−	1.82339e7i		−	0.334936i	0.985877	−	0.167468i	$-0.0535591\pi$
$380$	7.17703e7	+	1.27238e8i	1.30796	+	2.31881i
$381$	1.72967e8			3.12743
$382$	2.22331e7	+	3.92029e6i	0.398850	+	0.0703280i
$383$	4.62230e7	−	5.50864e7i	0.822738	−	0.980501i	−0.177255	−	0.984165i	$-0.556722\pi$
$383$	4.62230e7	−	5.50864e7i	0.822738	−	0.980501i	0.999993	+	0.00366357i	$0.00116615\pi$
$384$	−1.72851e8	−	6.29127e7i	−3.05266	−	1.11108i
$385$	−5.28268e6	+	1.92274e6i	−0.0925704	+	0.0336929i
$386$	−1.73583e7	+	1.45653e7i	−0.301818	+	0.253255i
$387$	6.95285e7	+	1.20427e8i	1.19958	+	2.07774i
$388$	−4.26789e7	−	2.46407e7i	−0.730664	−	0.421849i
$389$	1.32257e7	+	7.50065e7i	0.224682	+	1.27424i	0.863292	+	0.504705i	$0.168399\pi$
$389$	1.32257e7	+	7.50065e7i	0.224682	+	1.27424i	−0.638610	+	0.769531i	$0.720490\pi$
$390$	−4.07439e8	+	7.18425e7i	−6.86861	+	1.21112i
$391$	4.04165e6	−	7.00034e6i	0.0676127	−	0.117109i
$392$	−7.21111e7	+	4.16334e7i	−1.19714	+	0.691167i
$393$	2.75688e7	+	3.28552e7i	0.454192	+	0.541285i
$394$	2.98277e7	+	8.19508e7i	0.487675	+	1.33988i
$395$	4.59212e7	−	1.26167e8i	0.745113	−	2.04718i
$396$	7.53942e7	+	6.32632e7i	1.21409	+	1.01875i
$397$	9.81926e6	−	5.56878e7i	0.156930	−	0.889997i	−0.800069	−	0.599908i	$-0.795204\pi$
$397$	9.81926e6	−	5.56878e7i	0.156930	−	0.889997i	0.957000	−	0.290089i	$-0.0936849\pi$
$398$			1.15960e8i			1.83932i
$399$	−6.36734e6	−	1.80551e7i	−0.100240	−	0.284237i
$400$	3.86190e7			0.603422
$401$	−9.42156e7	−	1.66128e7i	−1.46113	−	0.257637i	−0.614121	−	0.789212i	$-0.710489\pi$
$401$	−9.42156e7	−	1.66128e7i	−1.46113	−	0.257637i	−0.847012	+	0.531574i	$0.821601\pi$
$402$	−5.27692e7	+	6.28879e7i	−0.812274	+	0.968030i
$403$	5.72685e7	+	2.08440e7i	0.874986	+	0.318469i
$404$	1.04393e8	−	3.79959e7i	1.58317	−	0.576225i
$405$	1.06170e8	−	8.90868e7i	1.59821	−	1.34106i
$406$	−4.73644e6	−	8.20375e6i	−0.0707740	−	0.122584i
$407$	−8.01959e6	−	4.63011e6i	−0.118951	−	0.0686765i
$408$	8.04750e6	+	4.56396e7i	0.118490	+	0.671988i
$409$	7.93907e7	−	1.39987e7i	1.16038	−	0.204606i	0.439876	−	0.898058i	$-0.355022\pi$
$409$	7.93907e7	−	1.39987e7i	1.16038	−	0.204606i	0.720503	+	0.693452i	$0.243911\pi$
$410$	1.03775e8	−	1.79744e8i	1.50571	−	2.60797i
$411$	1.87005e7	−	1.07967e7i	0.269356	−	0.155513i
$412$	−9.75470e7	−	1.16252e8i	−1.39483	−	1.66230i
$413$	655162.	+	1.80004e6i	0.00930034	+	0.0255525i
$414$	4.38294e7	−	1.20420e8i	0.617681	−	1.69707i
$415$	3.94516e7	+	3.31039e7i	0.551977	+	0.463164i
$416$	−9.79699e6	+	5.55615e7i	−0.136086	+	0.771781i
$417$		−	2.14966e8i		−	2.96457i
$418$	−4.85873e7	−	9.07023e6i	−0.665264	−	0.124191i
$419$	−9.19806e7			−1.25042			−0.625208	−	0.780458i	$-0.714986\pi$
$419$	−9.19806e7			−1.25042			−0.625208	+	0.780458i	$0.714986\pi$
$420$	−5.85444e7	−	1.03230e7i	−0.790201	−	0.139334i
$421$	−8.62320e6	+	1.02767e7i	−0.115564	+	0.137724i	−0.820725	−	0.571323i	$-0.806430\pi$
$421$	−8.62320e6	+	1.02767e7i	−0.115564	+	0.137724i	0.705161	+	0.709047i	$0.250875\pi$
$422$	7.86125e7	+	2.86126e7i	1.04605	+	0.380733i
$423$	−1.79870e8	+	6.54673e7i	−2.37650	+	0.864974i
$424$	−1.43005e7	+	1.19996e7i	−0.187609	+	0.157423i
$425$	1.12544e7	+	1.94932e7i	0.146607	+	0.253931i
$426$	1.83423e8	+	1.05899e8i	2.37260	+	1.36982i
$427$	−2.70999e6	−	1.53691e7i	−0.0348084	−	0.197408i
$428$	1.47764e8	−	2.60547e7i	1.88468	−	0.332319i
$429$	4.53816e7	−	7.86032e7i	0.574788	−	0.995562i
$430$	−1.87794e8	+	1.08423e8i	−2.36198	+	1.36369i
$431$	1.83792e7	+	2.19034e7i	0.229559	+	0.273578i	0.868512	−	0.495668i	$-0.165077\pi$
$431$	1.83792e7	+	2.19034e7i	0.229559	+	0.273578i	−0.638953	+	0.769246i	$0.720632\pi$
$432$	3.10557e7	+	8.53247e7i	0.385203	+	1.05834i
$433$	−2.29311e7	+	6.30026e7i	−0.282463	+	0.776059i	0.714605	+	0.699529i	$0.246607\pi$
$433$	−2.29311e7	+	6.30026e7i	−0.282463	+	0.776059i	−0.997067	+	0.0765309i	$0.975616\pi$
$434$	1.03459e7	+	8.68125e6i	0.126561	+	0.106197i
$435$	−1.80538e7	+	1.02388e8i	−0.219331	+	1.24389i
$436$		−	1.56400e8i		−	1.88702i
$437$	6.83384e6	+	4.11648e7i	0.0818880	+	0.493267i
$438$	−2.02781e8			−2.41326
$439$	1.34452e8	+	2.37075e7i	1.58918	+	0.280215i	0.897174	−	0.441677i	$-0.145616\pi$
$439$	1.34452e8	+	2.37075e7i	1.58918	+	0.280215i	0.692005	+	0.721892i	$0.256727\pi$
$440$	−4.51558e7	+	5.38146e7i	−0.530097	+	0.631745i
$441$	−1.67616e8	−	6.10073e7i	−1.95434	−	0.711321i
$442$	5.98124e7	−	2.17699e7i	0.692667	−	0.252110i
$443$	4.76885e7	−	4.00154e7i	0.548532	−	0.460273i	−0.325911	−	0.945400i	$-0.605671\pi$
$443$	4.76885e7	−	4.00154e7i	0.548532	−	0.460273i	0.874444	+	0.485127i	$0.161227\pi$
$444$	−4.89618e7	−	8.48043e7i	−0.559382	−	0.968878i
$445$	−7.96500e6	−	4.59859e6i	−0.0903869	−	0.0521849i
$446$	−1.18030e7	−	6.69383e7i	−0.133042	−	0.754519i
$447$	1.07492e8	−	1.89538e7i	1.20353	−	0.212214i
$448$	−1.05061e7	+	1.81971e7i	−0.116844	+	0.202380i
$449$	−1.70389e6	+	983743.i	−0.0188236	+	0.0108678i	−0.509382	−	0.860540i	$-0.670126\pi$
$449$	−1.70389e6	+	983743.i	−0.0188236	+	0.0108678i	0.490559	+	0.871408i	$0.336793\pi$
$450$	2.29374e8	+	2.73358e8i	2.51714	+	2.99981i
$451$	1.55730e7	+	4.27866e7i	0.169763	+	0.466421i
$452$	−5.67326e7	+	1.55872e8i	−0.614352	+	1.68792i
$453$	6.94830e7	+	5.83032e7i	0.747453	+	0.627188i
$454$	5.25896e7	−	2.98251e8i	0.561995	−	3.18723i
$455$			3.73726e7i			0.396752i
$456$	−1.81717e8	−	1.55609e8i	−1.91647	−	1.64112i
$457$	−3.98098e7			−0.417101			−0.208551	−	0.978012i	$-0.566875\pi$
$457$	−3.98098e7			−0.417101			−0.208551	+	0.978012i	$0.566875\pi$
$458$	−2.75969e8	−	4.86609e7i	−2.87253	−	0.506504i
$459$	−3.40179e7	+	4.05410e7i	−0.351779	+	0.419234i
$460$	1.21757e8	+	4.43161e7i	1.25090	+	0.455290i
$461$	−8.55059e7	+	3.11216e7i	−0.872757	+	0.317658i	−0.739283	−	0.673395i	$-0.764835\pi$
$461$	−8.55059e7	+	3.11216e7i	−0.872757	+	0.317658i	−0.133474	+	0.991052i	$0.542613\pi$
$462$	1.54081e7	−	1.29289e7i	0.156251	−	0.131110i
$463$	9.62191e6	+	1.66656e7i	0.0969434	+	0.167911i	0.910418	−	0.413690i	$-0.135760\pi$
$463$	9.62191e6	+	1.66656e7i	0.0969434	+	0.167911i	−0.813475	+	0.581600i	$0.802427\pi$
$464$	−2.37669e7	−	1.37218e7i	−0.237913	−	0.137359i
$465$	−2.57396e7	−	1.45977e8i	−0.256002	−	1.45186i
$466$	2.07107e8	−	3.65186e7i	2.04662	−	0.360875i
$467$	−5.72264e7	+	9.91190e7i	−0.561883	+	0.973209i	0.435449	+	0.900213i	$0.356589\pi$
$467$	−5.72264e7	+	9.91190e7i	−0.561883	+	0.973209i	−0.997332	+	0.0729963i	$0.976744\pi$
$468$	5.66629e8	−	3.27144e8i	5.52792	−	3.19154i
$469$	4.76675e6	+	5.68079e6i	0.0462066	+	0.0550668i
$470$	−1.02090e8	−	2.80489e8i	−0.983305	−	2.70161i
$471$	485697.	−	1.33444e6i	0.00464839	−	0.0127714i
$472$	1.83370e7	+	1.53866e7i	0.174382	+	0.146324i
$473$	8.26075e6	−	4.68490e7i	0.0780613	−	0.442708i
$474$			4.80383e8i			4.51079i
$475$	−1.08785e8	−	4.08338e7i	−1.01505	−	0.381012i
$476$	9.14593e6			0.0848022
$477$	−3.93829e7	−	6.94427e6i	−0.362871	−	0.0639840i
$478$	−6.53775e7	+	7.79139e7i	−0.598611	+	0.713397i
$479$	−2.35984e7	−	8.58912e6i	−0.214722	−	0.0781524i	0.232420	−	0.972616i	$-0.425336\pi$
$479$	−2.35984e7	−	8.58912e6i	−0.214722	−	0.0781524i	−0.447141	+	0.894463i	$0.647558\pi$
$480$	1.28947e8	−	4.69327e7i	1.16597	−	0.424377i
$481$	−4.71585e7	+	3.95707e7i	−0.423765	+	0.355581i
$482$	−1.56479e8	−	2.71030e8i	−1.39738	−	2.42034i
$483$	−1.47059e7	−	8.49048e6i	−0.130512	−	0.0753513i
$484$	3.04600e7	+	1.72747e8i	0.268654	+	1.52361i
$485$	7.42086e7	−	1.30850e7i	0.650472	−	0.114696i
$486$	−5.20622e7	+	9.01744e7i	−0.453538	+	0.785551i
$487$	4.27877e6	−	2.47035e6i	0.0370452	−	0.0213881i	−0.481363	−	0.876521i	$-0.659858\pi$
$487$	4.27877e6	−	2.47035e6i	0.0370452	−	0.0213881i	0.518408	+	0.855133i	$0.326525\pi$
$488$	−1.25355e8	−	1.49392e8i	−1.07866	−	1.28549i
$489$	1.32404e8	+	3.63776e8i	1.13233	+	3.11106i
$490$	9.51347e7	−	2.61381e8i	0.808632	−	2.22170i
$491$	−1.72102e7	−	1.44411e7i	−0.145393	−	0.121999i	0.567190	−	0.823587i	$-0.308030\pi$
$491$	−1.72102e7	−	1.44411e7i	−0.145393	−	0.121999i	−0.712583	+	0.701588i	$0.752475\pi$
$492$	−8.36098e7	+	4.74175e8i	−0.702040	+	3.98147i
$493$		−	1.59953e7i		−	0.133491i
$494$	−1.67135e8	+	2.82901e8i	−1.38640	+	2.34668i
$495$	−1.50489e8			−1.24076
$496$	3.85324e7	+	6.79430e6i	0.315777	+	0.0556801i
$497$	1.22979e7	−	1.46561e7i	0.100176	−	0.119385i
$498$	−1.73150e8	−	6.30215e7i	−1.40196	−	0.510271i
$499$	−2.67778e7	+	9.74631e6i	−0.215513	+	0.0784402i	−0.447520	−	0.894274i	$-0.647693\pi$
$499$	−2.67778e7	+	9.74631e6i	−0.215513	+	0.0784402i	0.232008	+	0.972714i	$0.425471\pi$
$500$	−2.14667e7	+	1.80127e7i	−0.171734	+	0.144102i
$501$	4.59208e7	+	7.95371e7i	0.365171	+	0.632494i
$502$	2.15381e8	+	1.24350e8i	1.70254	+	0.982961i
$503$	−6.18135e6	−	3.50562e7i	−0.0485712	−	0.275461i	0.950843	−	0.309672i	$-0.100219\pi$
$503$	−6.18135e6	−	3.50562e7i	−0.0485712	−	0.275461i	−0.999415	+	0.0342110i	$0.989108\pi$
$504$	6.53595e7	−	1.15246e7i	0.510525	−	0.0900194i
$505$	−8.49327e7	+	1.47108e8i	−0.659479	+	1.14225i
$506$	−3.79665e7	+	2.19200e7i	−0.293055	+	0.169195i
$507$	−2.39366e8	−	2.85266e8i	−1.83670	−	2.18890i
$508$	−1.45891e8	−	4.00832e8i	−1.11285	−	3.05754i
$509$	−7.75699e7	+	2.13122e8i	−0.588220	+	1.61612i	0.185536	+	0.982638i	$0.440598\pi$
$509$	−7.75699e7	+	2.13122e8i	−0.588220	+	1.61612i	−0.773756	+	0.633484i	$0.781624\pi$
$510$	−1.18593e8	−	9.95117e7i	−0.894026	−	0.750177i
$511$	−3.18081e6	+	1.80393e7i	−0.0238383	+	0.135194i
$512$			1.42556e8i			1.06212i
$513$	2.73786e6	−	2.73187e8i	0.0202796	−	2.02352i
$514$	3.24215e8			2.38750
$515$	2.28517e8	+	4.02937e7i	1.67300	+	0.294996i
$516$	3.23357e8	−	3.85362e8i	2.35360	−	2.80491i
$517$	6.15339e7	+	2.23965e7i	0.445290	+	0.162072i
$518$	−1.28197e7	+	4.66598e6i	−0.0922332	+	0.0335701i
$519$	−2.52894e8	+	2.12204e8i	−1.80899	+	1.51793i
$520$	2.33507e8	+	4.04446e8i	1.66070	+	2.87641i
$521$	1.81769e8	+	1.04944e8i	1.28531	+	0.742072i	0.977813	−	0.209478i	$-0.0671765\pi$
$521$	1.81769e8	+	1.04944e8i	1.28531	+	0.742072i	0.307493	+	0.951550i	$0.400510\pi$
$522$	−4.40340e7	−	2.49729e8i	−0.309582	−	1.75573i
$523$	−1.16557e8	+	2.05522e7i	−0.814769	+	0.143666i	−0.565478	−	0.824763i	$-0.691308\pi$
$523$	−1.16557e8	+	2.05522e7i	−0.814769	+	0.143666i	−0.249290	+	0.968429i	$0.580197\pi$
$524$	5.28853e7	−	9.15999e7i	0.367571	−	0.636651i
$525$	4.09502e7	−	2.36426e7i	0.282995	−	0.163387i
$526$	1.13261e8	+	1.34980e8i	0.778260	+	0.927494i
$527$	7.79969e6	+	2.14295e7i	0.0532900	+	0.146413i
$528$	1.99299e7	−	5.47570e7i	0.135395	−	0.371996i
$529$	−8.50496e7	−	7.13650e7i	−0.574520	−	0.482079i
$530$	1.08289e7	−	6.14137e7i	0.0727372	−	0.412513i
$531$			5.12782e7i			0.342491i
$532$	−3.64702e7	+	2.99845e7i	−0.242216	+	0.199141i
$533$	3.02696e8			1.99905
$534$	3.24065e7	+	5.71414e6i	0.212818	+	0.0375256i
$535$	−1.47470e8	+	1.75748e8i	−0.963037	+	1.14770i
$536$	8.70799e7	+	3.16945e7i	0.565488	+	0.205821i
$537$	1.68638e8	−	6.13794e7i	1.08901	−	0.396369i
$538$	−2.91379e8	+	2.44496e8i	−1.87116	+	1.57009i
$539$	3.05110e7	+	5.28465e7i	0.194845	+	0.337482i
$540$	−7.34669e8	−	4.24161e8i	−4.66563	−	2.69370i
$541$	−3.20517e7	−	1.81774e8i	−0.202423	−	1.14800i	−0.901444	−	0.432895i	$-0.857492\pi$
$541$	−3.20517e7	−	1.81774e8i	−0.202423	−	1.14800i	0.699022	−	0.715100i	$-0.253619\pi$
$542$	−1.37457e8	+	2.42373e7i	−0.863313	+	0.152225i
$543$	2.10932e8	−	3.65345e8i	1.31748	−	2.28194i
$544$	−1.82831e7	+	1.05557e7i	−0.113567	+	0.0655679i
$545$	1.53718e8	+	1.83194e8i	0.949587	+	1.13167i
$546$	−4.57331e7	−	1.25651e8i	−0.280965	−	0.771945i
$547$	2.45057e7	−	6.73288e7i	0.149729	−	0.411376i	−0.842041	−	0.539414i	$-0.818646\pi$
$547$	2.45057e7	−	6.73288e7i	0.149729	−	0.411376i	0.991769	+	0.128038i	$0.0408680\pi$
$548$	−4.07934e7	−	3.42298e7i	−0.247884	−	0.207999i
$549$	7.25443e7	−	4.11419e8i	0.438416	−	2.48638i
$550$		−	1.22077e8i		−	0.733745i
$551$	5.24398e7	+	6.37826e7i	0.313477	+	0.381283i
$552$	−2.12197e8			−1.26160
$553$	4.27347e7	+	7.53528e6i	0.252700	+	0.0445578i
$554$	2.61131e8	−	3.11204e8i	1.53578	−	1.83027i
$555$	1.40700e8	+	5.12105e7i	0.823028	+	0.299558i
$556$	−4.98162e8	+	1.81316e8i	−2.89832	+	1.05490i
$557$	1.55939e8	−	1.30849e8i	0.902381	−	0.757188i	−0.0682729	−	0.997667i	$-0.521749\pi$
$557$	1.55939e8	−	1.30849e8i	0.902381	−	0.757188i	0.970654	+	0.240479i	$0.0773044\pi$
$558$	1.80768e8	+	3.13099e8i	1.04044	+	1.80210i
$559$	−2.73883e8	−	1.58126e8i	−1.56794	−	0.905249i
$560$	4.16646e6	+	2.36292e7i	0.0237248	+	0.134550i
$561$	3.34469e7	−	5.89760e6i	0.189438	−	0.0334031i
$562$	−1.35071e8	+	2.33950e8i	−0.760945	+	1.31799i
$563$	2.18410e7	−	1.26099e7i	0.122391	−	0.0706622i	−0.437555	−	0.899192i	$-0.644155\pi$
$563$	2.18410e7	−	1.26099e7i	0.122391	−	0.0706622i	0.559945	+	0.828530i	$0.310822\pi$
$564$	4.45104e8	+	5.30454e8i	2.48099	+	2.95672i
$565$	−8.67467e7	−	2.38335e8i	−0.480959	−	1.32142i
$566$	−2.61429e7	+	7.18270e7i	−0.144180	+	0.396131i
$567$	3.43137e7	+	2.87926e7i	0.188243	+	0.157954i
$568$	4.15157e7	−	2.35447e8i	0.226552	−	1.28484i
$569$		−	2.47998e8i		−	1.34620i	−0.739550	−	0.673102i	$-0.764962\pi$
$569$		−	2.47998e8i		−	1.34620i	0.739550	−	0.673102i	$-0.235038\pi$
$570$	7.99145e8	+	8.00899e6i	4.31520	+	0.0432467i
$571$	−4.09854e7			−0.220151			−0.110075	−	0.993923i	$-0.535109\pi$
$571$	−4.09854e7			−0.220151			−0.110075	+	0.993923i	$0.535109\pi$
$572$	−2.20433e8	−	3.88682e7i	−1.17784	−	0.207686i
$573$	5.14754e7	−	6.13460e7i	0.273613	−	0.326079i
$574$	6.30342e7	+	2.29426e7i	0.333304	+	0.121313i
$575$	−9.68472e7	+	3.52495e7i	−0.509429	+	0.185417i
$576$	−4.30884e8	+	3.61555e8i	−2.25472	+	1.89194i
$577$	−6.13823e7	−	1.06317e8i	−0.319533	−	0.553447i	0.660858	−	0.750511i	$-0.270193\pi$
$577$	−6.13823e7	−	1.06317e8i	−0.319533	−	0.553447i	−0.980391	+	0.197064i	$0.936859\pi$
$578$	−2.61397e8	−	1.50917e8i	−1.35368	−	0.781548i
$579$	1.39575e7	+	7.91569e7i	0.0719072	+	0.407806i
$580$	2.52502e8	−	4.45229e7i	1.29414	−	0.228191i
$581$	−8.32240e6	+	1.44148e7i	−0.0424346	+	0.0734989i
$582$	−2.33485e8	+	1.34803e8i	−1.18438	+	0.683801i
$583$	8.79387e6	+	1.04801e7i	0.0443787	+	0.0528884i
$584$	7.82883e7	+	2.15095e8i	0.393060	+	1.07992i
$585$	−3.42169e8	+	9.40101e8i	−1.70912	+	4.69577i
$586$	2.20111e7	+	1.84695e7i	0.109383	+	0.0917832i
$587$	−4.30299e7	+	2.44034e8i	−0.212743	+	1.20653i	0.672037	+	0.740518i	$0.265420\pi$
$587$	−4.30299e7	+	2.44034e8i	−0.212743	+	1.20653i	−0.884780	+	0.466009i	$0.845692\pi$
$588$			6.45285e8i			3.17409i
$589$	−1.01357e8	−	5.98810e7i	−0.496032	−	0.293051i
$590$	−7.99633e7			−0.389345
$591$	3.04651e8	+	5.37183e7i	1.47584	+	0.260231i
$592$	−2.54049e7	+	3.02764e7i	−0.122448	+	0.145928i
$593$	−2.79761e8	−	1.01825e8i	−1.34160	−	0.488302i	−0.431283	−	0.902217i	$-0.641939\pi$
$593$	−2.79761e8	−	1.01825e8i	−1.34160	−	0.488302i	−0.910316	+	0.413915i	$0.864161\pi$
$594$	2.69716e8	−	9.81687e7i	1.28691	−	0.468397i
$595$	−1.07128e7	+	8.98909e6i	−0.0508571	+	0.0426742i
$596$	−1.34589e8	−	2.33116e8i	−0.635729	−	1.10112i
$597$	3.56223e8	+	2.05665e8i	1.67417	+	0.966580i
$598$	5.06086e7	+	2.87016e8i	0.236658	+	1.34215i
$599$	−3.14079e8	+	5.53806e7i	−1.46136	+	0.257678i	−0.847104	−	0.531427i	$-0.821656\pi$
$599$	−3.14079e8	+	5.53806e7i	−1.46136	+	0.257678i	−0.614259	+	0.789105i	$0.710545\pi$
$600$	2.95443e8	−	5.11722e8i	1.36779	−	2.36908i
$601$	1.03357e8	−	5.96731e7i	0.476120	−	0.274888i	−0.242678	−	0.970107i	$-0.578026\pi$
$601$	1.03357e8	−	5.96731e7i	0.476120	−	0.274888i	0.718798	+	0.695219i	$0.244693\pi$
$602$	−4.50491e7	−	5.36874e7i	−0.206489	−	0.246084i
$603$	6.78957e7	+	1.86542e8i	0.309664	+	0.850794i
$604$	7.65052e7	−	2.10196e8i	0.347200	−	0.953925i
$605$	−2.05463e8	−	1.72404e8i	−0.927828	−	0.778541i
$606$	1.05536e8	−	5.98525e8i	0.474224	−	2.68946i
$607$		−	4.13597e8i		−	1.84932i	−0.380797	−	0.924659i	$-0.624350\pi$
$607$		−	4.13597e8i		−	1.84932i	0.380797	−	0.924659i	$-0.375650\pi$
$608$	3.82988e7	−	1.02032e8i	0.170402	−	0.453968i
$609$	−3.36021e7			−0.148770
$610$	6.41567e8	+	1.13126e8i	2.82652	+	0.498392i
$611$	2.79821e8	−	3.33478e8i	1.22675	−	1.46199i
$612$	2.30065e8	+	8.37367e7i	1.00368	+	0.365310i
$613$	−2.70246e8	+	9.83614e7i	−1.17321	+	0.427015i	−0.853801	−	0.520600i	$-0.825708\pi$
$613$	−2.70246e8	+	9.83614e7i	−1.17321	+	0.427015i	−0.319414	+	0.947615i	$0.603486\pi$
$614$	−1.82728e8	+	1.53327e8i	−0.789405	+	0.662389i
$615$	−3.68110e8	−	6.37585e8i	−1.58253	−	2.74102i
$616$	−1.96627e7	−	1.13523e7i	−0.0841205	−	0.0485670i
$617$	5.80962e7	+	3.29480e8i	0.247339	+	1.40273i	0.814998	+	0.579464i	$0.196738\pi$
$617$	5.80962e7	+	3.29480e8i	0.247339	+	1.40273i	−0.567660	+	0.823263i	$0.692151\pi$
$618$	−8.17606e8	+	1.44166e8i	−3.46401	+	0.610798i
$619$	−2.18156e7	+	3.77857e7i	−0.0919802	+	0.159314i	−0.908344	−	0.418223i	$-0.862653\pi$
$619$	−2.18156e7	+	3.77857e7i	−0.0919802	+	0.159314i	0.816364	+	0.577538i	$0.195986\pi$
$620$	−3.16575e8	+	1.82775e8i	−1.32832	+	0.766905i
$621$	−1.55760e8	−	1.85628e8i	−0.650402	−	0.775119i
$622$	−4.99364e7	−	1.37199e8i	−0.207513	−	0.570138i
$623$	1.01666e6	−	2.79324e6i	0.00420446	−	0.0115517i
$624$	−2.96751e8	−	2.49004e8i	−1.22135	−	1.02483i
$625$	−3.85240e7	+	2.18481e8i	−0.157794	+	0.894896i
$626$			3.21920e8i			1.31227i
$627$	−1.14038e8	+	1.33171e8i	−0.462642	+	0.540266i
$628$	−3.50210e6			−0.0141400
$629$	−2.26857e7	−	4.00011e6i	−0.0911593	−	0.0160739i
$630$	−1.42509e8	+	1.69835e8i	−0.569927	+	0.679213i
$631$	4.46730e6	+	1.62596e6i	0.0177810	+	0.00647176i	0.350895	−	0.936415i	$-0.385877\pi$
$631$	4.46730e6	+	1.62596e6i	0.0177810	+	0.00647176i	−0.333114	+	0.942886i	$0.608100\pi$
$632$	5.09557e8	−	1.85463e8i	2.01856	−	0.734695i
$633$	2.27323e8	−	1.90747e8i	0.896257	−	0.752049i
$634$	2.00385e8	+	3.47077e8i	0.786317	+	1.36194i
$635$	5.64843e8	+	3.26112e8i	2.20601	+	1.27364i
$636$	2.51217e7	+	1.42472e8i	0.0976510	+	0.553807i
$637$	3.99505e8	−	7.04434e7i	1.54562	−	0.272535i
$638$	−4.33754e7	+	7.51284e7i	−0.167025	+	0.289296i
$639$	4.43538e8	−	2.56077e8i	1.69992	−	0.981450i
$640$	−4.45851e8	−	5.31344e8i	−1.70079	−	2.02692i
$641$	−1.43768e8	−	3.94999e8i	−0.545868	−	1.49976i	−0.839240	−	0.543761i	$-0.817000\pi$
$641$	−1.43768e8	−	3.94999e8i	−0.545868	−	1.49976i	0.293373	−	0.955998i	$-0.405222\pi$
$642$	2.80747e8	−	7.71345e8i	1.06099	−	2.91503i
$643$	3.03863e8	+	2.54971e8i	1.14300	+	0.959088i	0.999533	−	0.0305679i	$-0.00973158\pi$
$643$	3.03863e8	+	2.54971e8i	1.14300	+	0.959088i	0.143464	+	0.989656i	$0.454176\pi$
$644$	−7.27189e6	+	4.12409e7i	−0.0272264	+	0.154408i
$645$			7.69193e8i			2.86653i
$646$	−1.21294e8	+	2.01362e7i	−0.449926	+	0.0746929i
$647$	−4.28383e7			−0.158168			−0.0790841	−	0.996868i	$-0.525200\pi$
$647$	−4.28383e7			−0.158168			−0.0790841	+	0.996868i	$0.525200\pi$
$648$	5.51242e8	+	9.71989e7i	2.02590	+	0.357220i
$649$	1.12760e7	−	1.34383e7i	0.0412499	−	0.0491597i
$650$	−7.62612e8	−	2.77568e8i	−2.77692	−	1.01072i
$651$	4.50179e7	−	1.63852e7i	0.163171	−	0.0593893i
$652$	7.31337e8	−	6.13665e8i	2.63861	−	2.21405i
$653$	−1.27564e8	−	2.20948e8i	−0.458131	−	0.793507i	0.540731	−	0.841196i	$-0.318148\pi$
$653$	−1.27564e8	−	2.20948e8i	−0.458131	−	0.793507i	−0.998862	+	0.0476889i	$0.984814\pi$
$654$	−7.40992e8	−	4.27812e8i	−2.64899	−	1.52939i
$655$	2.80838e7	+	1.59271e8i	0.0999381	+	0.566777i
$656$	1.91382e8	−	3.37459e7i	0.677938	−	0.119539i
$657$	−2.45174e8	+	4.24653e8i	−0.864525	+	1.49740i
$658$	8.35465e7	−	4.82356e7i	0.293259	−	0.169313i
$659$	1.15730e8	+	1.37922e8i	0.404382	+	0.481923i	0.929351	−	0.369198i	$-0.120368\pi$
$659$	1.15730e8	+	1.37922e8i	0.404382	+	0.481923i	−0.524969	+	0.851121i	$0.675923\pi$
$660$	1.86199e8	+	5.11578e8i	0.647658	+	1.77943i
$661$	−4.44380e7	+	1.22092e8i	−0.153869	+	0.422750i	−0.992545	−	0.121880i	$-0.961108\pi$
$661$	−4.44380e7	+	1.22092e8i	−0.153869	+	0.422750i	0.838676	+	0.544630i	$0.183330\pi$
$662$	1.71424e8	+	1.43842e8i	0.590879	+	0.495807i
$663$	3.92067e7	−	2.22352e8i	0.134530	−	0.762958i
$664$			2.07997e8i			0.710480i
$665$	1.32479e7	−	7.09661e7i	0.0450486	−	0.241316i
$666$	−3.65197e8			−1.23624
$667$	7.21262e7	+	1.27178e7i	0.243061	+	0.0428582i
$668$	1.45587e8	−	1.73503e8i	0.488418	−	0.582074i
$669$	−2.26565e8	−	8.24630e7i	−0.756685	−	0.275411i
$670$	−2.90893e8	+	1.05877e8i	−0.967185	+	0.352027i
$671$	−1.09482e8	+	9.18663e7i	−0.362389	+	0.304081i
$672$	2.21749e7	+	3.84080e7i	0.0730725	+	0.126565i
$673$	−2.52524e8	−	1.45795e8i	−0.828432	−	0.478296i	0.0248833	−	0.999690i	$-0.492079\pi$
$673$	−2.52524e8	−	1.45795e8i	−0.828432	−	0.478296i	−0.853316	+	0.521395i	$0.825412\pi$
$674$	−8.22241e7	−	4.66316e8i	−0.268546	−	1.52300i
$675$	6.64514e8	−	1.17172e8i	2.16069	−	0.380989i
$676$	−4.59177e8	+	7.95318e8i	−1.48642	+	2.57455i
$677$	−3.07042e8	+	1.77271e8i	−0.989535	+	0.571309i	−0.905135	−	0.425123i	$-0.860231\pi$
$677$	−3.07042e8	+	1.77271e8i	−0.989535	+	0.571309i	−0.0844000	+	0.996432i	$0.526897\pi$
$678$	5.83304e8	+	6.95154e8i	1.87157	+	2.23045i
$679$	8.32955e6	+	2.28853e7i	0.0266080	+	0.0731049i
$680$	−5.97692e7	+	1.64215e8i	−0.190086	+	0.522258i
$681$	−8.22940e8	−	6.90528e8i	−2.60571	−	2.18645i
$682$	2.14772e7	−	1.21803e8i	0.0677055	−	0.383977i
$683$			2.24322e8i			0.704060i	0.935989	+	0.352030i	$0.114509\pi$
$683$			2.24322e8i			0.704060i	−0.935989	+	0.352030i	$0.885491\pi$
$684$	−1.19193e9	+	4.20348e8i	−3.72462	+	1.31353i
$685$	8.14248e7			0.253329
$686$	1.79703e8	+	3.16864e7i	0.556650	+	0.0981524i
$687$	−6.38942e8	+	7.61461e8i	−1.97057	+	2.34843i
$688$	−1.90794e8	−	6.94432e7i	−0.585866	−	0.213238i
$689$	8.54639e7	−	3.11063e7i	0.261291	−	0.0951023i
$690$	5.43012e8	−	4.55641e8i	1.65296	−	1.38700i
$691$	3.45305e7	+	5.98086e7i	0.104657	+	0.181271i	0.913598	−	0.406618i	$-0.133292\pi$
$691$	3.45305e7	+	5.98086e7i	0.104657	+	0.181271i	−0.808941	+	0.587890i	$0.799959\pi$
$692$	7.05068e8	+	4.07071e8i	2.12771	+	1.22843i
$693$	−8.44582e6	−	4.78986e7i	−0.0253771	−	0.143921i
$694$	9.65193e8	−	1.70190e8i	2.88759	−	0.509160i
$695$	4.05299e8	−	7.01998e8i	1.20732	−	2.09113i
$696$	−3.63642e8	+	2.09949e8i	−1.07856	+	0.622710i
$697$	7.28063e7	+	8.67672e7i	0.215016	+	0.256246i
$698$	2.46735e8	+	6.77900e8i	0.725547	+	1.99342i
$699$	2.55141e8	−	7.00993e8i	0.747048	−	2.05250i
$700$	−8.93294e7	−	7.49563e7i	−0.260436	−	0.218531i
$701$	−1.77061e7	+	1.00416e8i	−0.0514007	+	0.291508i	−0.999662	−	0.0259817i	$-0.991729\pi$
$701$	−1.77061e7	+	1.00416e8i	−0.0514007	+	0.291508i	0.948262	+	0.317490i	$0.102840\pi$
$702$		−	1.90812e9i		−	5.51562i
$703$	1.03576e8	−	5.84233e7i	0.298120	−	0.168159i
$704$	1.92425e8			0.551498
$705$	−1.04272e9	−	1.83859e8i	−2.97576	−	0.524708i
$706$	−5.76294e7	+	6.86801e7i	−0.163768	+	0.195172i
$707$	−5.15891e7	−	1.87769e7i	−0.145982	−	0.0531332i
$708$	1.74317e8	−	6.34463e7i	0.491180	−	0.178775i
$709$	5.54987e7	−	4.65690e7i	0.155720	−	0.130665i	−0.561599	−	0.827410i	$-0.689814\pi$
$709$	5.54987e7	−	4.65690e7i	0.155720	−	0.130665i	0.717319	+	0.696745i	$0.245369\pi$
$710$	3.99327e8	+	6.91654e8i	1.11572	+	1.93248i
$711$	1.00599e9	+	5.80811e8i	2.79890	+	1.61594i
$712$	−6.45016e6	−	3.65806e7i	−0.0178702	−	0.101347i
$713$	−1.02832e8	+	1.81320e7i	−0.283699	+	0.0500238i
$714$	2.50175e7	−	4.33316e7i	0.0687305	−	0.119045i
$715$	2.96398e8	−	1.71125e8i	0.810881	−	0.468162i
$716$	−2.84481e8	−	3.39031e8i	−0.775022	−	0.923635i
$717$	1.23395e8	+	3.39024e8i	0.334764	+	0.919758i
$718$	−1.39778e8	+	3.84036e8i	−0.377628	+	1.03752i
$719$	3.73421e8	+	3.13338e8i	1.00464	+	0.842997i	0.987621	−	0.156859i	$-0.0501367\pi$
$719$	3.73421e8	+	3.13338e8i	1.00464	+	0.842997i	0.0170231	+	0.999855i	$0.494581\pi$
$720$	−1.11533e8	+	6.32535e8i	−0.298817	+	1.69468i
$721$			7.49954e7i			0.200091i
$722$	4.17653e8	−	4.77950e8i	1.10970	−	1.26990i
$723$	−1.11012e9			−2.93735
$724$	−1.02456e9	−	1.80658e8i	−2.69975	−	0.476038i
$725$	−1.31091e8	+	1.56228e8i	−0.344000	+	0.409963i
$726$	9.01761e8	+	3.28214e8i	2.35658	+	0.857724i
$727$	−3.86026e8	+	1.40502e8i	−1.00465	+	0.365661i	−0.791374	−	0.611332i	$-0.790634\pi$
$727$	−3.86026e8	+	1.40502e8i	−1.00465	+	0.365661i	−0.213272	+	0.976993i	$0.568412\pi$
$728$	−1.15625e8	+	9.70209e7i	−0.299680	+	0.251461i
$729$	−9.52642e7	−	1.65002e8i	−0.245894	−	0.425900i
$730$	−6.62204e8	−	3.82324e8i	−1.70225	−	0.982795i
$731$	−2.05494e7	−	1.16542e8i	−0.0526075	−	0.298352i
$732$	−1.48835e9	+	2.62437e8i	−3.79466	+	0.669101i
$733$	2.18126e8	−	3.77805e8i	0.553854	−	0.959304i	−0.444137	−	0.895959i	$-0.646490\pi$
$733$	2.18126e8	−	3.77805e8i	0.553854	−	0.959304i	0.997992	−	0.0633450i	$-0.0201768\pi$
$734$	−9.71687e7	+	5.61004e7i	−0.245719	+	0.141866i
$735$	−6.34219e8	−	7.55833e8i	−1.59727	−	1.90355i
$736$	−3.30612e7	−	9.08349e7i	−0.0829250	−	0.227834i
$737$	2.32273e7	−	6.38164e7i	0.0580224	−	0.159415i
$738$	1.37556e9	+	1.15423e9i	3.42225	+	2.87161i
$739$	1.95693e7	−	1.10983e8i	0.0484889	−	0.274994i	−0.950918	−	0.309444i	$-0.899857\pi$
$739$	1.95693e7	−	1.10983e8i	0.0484889	−	0.274994i	0.999406	+	0.0344503i	$0.0109680\pi$
$740$		−	3.69252e8i		−	0.911228i
$741$	5.72630e8	+	1.01518e9i	1.40741	+	2.49511i
$742$	2.01549e7			0.0493367
$743$	3.32446e8	+	5.86193e7i	0.810504	+	0.142914i	0.563516	−	0.826105i	$-0.309448\pi$
$743$	3.32446e8	+	5.86193e7i	0.810504	+	0.142914i	0.246988	+	0.969019i	$0.420559\pi$
$744$	3.84808e8	−	4.58596e8i	0.934384	−	1.11356i
$745$	3.86765e8	+	1.40771e8i	0.935359	+	0.340443i
$746$	5.14738e8	−	1.87349e8i	1.23985	−	0.451269i
$747$	−3.41325e8	+	2.86406e8i	−0.818854	+	0.687100i
$748$	−4.18784e7	−	7.25355e7i	−0.100066	−	0.173319i
$749$	−6.42148e7	−	3.70744e7i	−0.152823	−	0.0882326i
$750$	2.66212e7	+	1.50976e8i	0.0631022	+	0.357870i
$751$	−6.57223e8	+	1.15886e8i	−1.55165	+	0.273597i	−0.882781	−	0.469785i	$-0.844331\pi$
$751$	−6.57223e8	+	1.15886e8i	−1.55165	+	0.273597i	−0.668867	+	0.743382i	$0.733220\pi$
$752$	1.39742e8	−	2.42040e8i	0.328605	−	0.569160i
$753$	7.63998e8	−	4.41095e8i	1.78940	−	1.03311i
$754$	3.70702e8	+	4.41786e8i	0.864791	+	1.03062i
$755$	1.16980e8	+	3.21400e8i	0.271813	+	0.746801i
$756$	9.37736e7	−	2.57641e8i	0.217028	−	0.596278i
$757$	5.57272e8	+	4.67607e8i	1.28464	+	1.07794i	0.992587	+	0.121533i	$0.0387812\pi$
$757$	5.57272e8	+	4.67607e8i	1.28464	+	1.07794i	0.292048	+	0.956404i	$0.405663\pi$
$758$	−4.27180e7	+	2.42266e8i	−0.0980852	+	0.556269i
$759$			1.55508e8i			0.355655i
$760$	−3.00034e8	−	8.50770e8i	−0.683486	−	1.93808i
$761$	−1.71747e8			−0.389705			−0.194853	−	0.980833i	$-0.562423\pi$
$761$	−1.71747e8			−0.389705			−0.194853	+	0.980833i	$0.562423\pi$
$762$	−2.29813e9	−	4.05222e8i	−5.19409	−	0.915858i
$763$	−4.96812e7	+	5.92077e7i	−0.111845	+	0.133292i
$764$	−1.85581e8	−	6.75459e7i	−0.416153	−	0.151467i
$765$	−3.51779e8	+	1.28037e8i	−0.785753	+	0.285991i
$766$	−7.43200e8	+	6.23619e8i	−1.65356	+	1.38750i
$767$	−5.83101e7	−	1.00996e8i	−0.129228	−	0.223830i
$768$	1.19360e9	+	6.89127e8i	2.63497	+	1.52130i
$769$	−7.84793e6	−	4.45078e7i	−0.0172574	−	0.0978717i	0.974962	−	0.222370i	$-0.0713791\pi$
$769$	−7.84793e6	−	4.45078e7i	−0.0172574	−	0.0978717i	−0.992220	+	0.124498i	$0.960268\pi$
$770$	7.46932e7	−	1.31704e7i	0.163610	−	0.0288488i
$771$	5.75026e8	−	9.95975e8i	1.25466	−	2.17313i
$772$	1.71665e8	−	9.91111e7i	0.373105	−	0.215412i
$773$	1.07269e8	+	1.27838e8i	0.232240	+	0.276772i	0.869561	−	0.493826i	$-0.164402\pi$
$773$	1.07269e8	+	1.27838e8i	0.232240	+	0.276772i	−0.637321	+	0.770598i	$0.719958\pi$
$774$	−6.41661e8	−	1.76295e9i	−1.38383	−	3.80204i
$775$	9.94466e7	−	2.73227e8i	0.213641	−	0.586974i
$776$	2.33132e8	+	1.95621e8i	0.498903	+	0.418630i
$777$	−8.40321e6	+	4.76570e7i	−0.0179136	+	0.101593i
$778$		−	1.02756e9i		−	2.18207i
$779$	−5.74783e8	−	1.07300e8i	−1.21588	−	0.226980i
$780$	3.61918e9			7.62652
$781$	−1.72547e8	−	3.04247e7i	−0.362205	−	0.0638666i
$782$	−7.00999e7	+	8.35418e7i	−0.146588	+	0.174696i
$783$	−4.50587e8	−	1.64000e8i	−0.938628	−	0.341633i
$784$	2.44737e8	−	8.90771e7i	0.507869	−	0.184849i
$785$	4.10207e6	−	3.44204e6i	0.00847996	−	0.00711553i
$786$	−2.89322e8	−	5.01120e8i	−0.595817	−	1.03199i
$787$	−5.87521e8	−	3.39205e8i	−1.20531	−	0.695887i	−0.243580	−	0.969881i	$-0.578322\pi$
$787$	−5.87521e8	−	3.39205e8i	−1.20531	−	0.695887i	−0.961731	+	0.273994i	$0.911655\pi$
$788$	−1.32476e8	−	7.51308e8i	−0.270744	−	1.53546i
$789$	6.15531e8	−	1.08535e8i	1.25320	−	0.220972i
$790$	−9.05717e8	+	1.56875e9i	−1.83701	+	3.18179i
$791$	7.09904e7	−	4.09863e7i	0.143440	−	0.0828151i
$792$	−3.90676e8	−	4.65589e8i	−0.786396	−	0.937190i
$793$	3.24956e8	+	8.92810e8i	0.651637	+	1.79036i
$794$	−2.60928e8	+	7.16894e8i	−0.521266	+	1.43217i
$795$	−1.69454e8	−	1.42189e8i	−0.337249	−	0.282986i
$796$	1.76147e8	−	9.98981e8i	0.349250	−	1.98070i
$797$		−	6.39980e8i		−	1.26413i	−0.774916	−	0.632065i	$-0.782208\pi$
$797$		−	6.39980e8i		−	1.26413i	0.774916	−	0.632065i	$-0.217792\pi$
$798$	4.23010e7	+	2.54807e8i	0.0832418	+	0.501421i
$799$	1.62895e8			0.319351
$800$	2.65083e8	+	4.67413e7i	0.517740	+	0.0912916i
$801$	5.11477e7	−	6.09554e7i	0.0995241	−	0.118608i
$802$	1.21288e9	+	4.41453e8i	2.35123	+	0.855778i
$803$	1.57632e8	−	5.73735e7i	0.304438	−	0.110806i
$804$	5.50131e8	−	4.61615e8i	1.05852	−	0.888201i
$805$	−3.20160e7	−	5.54534e7i	−0.0613733	−	0.106302i
$806$	−7.12069e8	−	4.11113e8i	−1.35993	−	0.785156i
$807$	2.34293e8	+	1.32874e9i	0.445798	+	2.52825i
$808$	−6.75618e8	+	1.19130e8i	−1.28076	+	0.225832i
$809$	6.19560e7	−	1.07311e8i	0.117014	−	0.202674i	−0.801569	−	0.597902i	$-0.796001\pi$
$809$	6.19560e7	−	1.07311e8i	0.117014	−	0.202674i	0.918583	+	0.395228i	$0.129334\pi$
$810$	−1.61934e9	+	9.34925e8i	−3.04707	+	1.75923i
$811$	6.48150e7	+	7.72435e7i	0.121510	+	0.144810i	0.823370	−	0.567505i	$-0.192091\pi$
$811$	6.48150e7	+	7.72435e7i	0.121510	+	0.144810i	−0.701860	+	0.712315i	$0.747647\pi$
$812$	2.83421e7	+	7.78693e7i	0.0529376	+	0.145445i
$813$	−1.69337e8	+	4.65248e8i	−0.315122	+	0.865791i
$814$	9.57054e7	+	8.03064e7i	0.177445	+	0.148894i
$815$	−2.53486e8	+	1.43759e9i	−0.468254	+	2.65560i
$816$		−	1.44955e8i		−	0.266786i
$817$	4.64018e8	+	3.97349e8i	0.850880	+	0.728628i
$818$	−1.08763e9			−1.98710
$819$	−3.18425e8	−	5.61470e7i	−0.579637	−	0.102206i
$820$	−1.16705e9	+	1.39084e9i	−2.11665	+	2.52252i
$821$	−1.29328e8	−	4.70715e7i	−0.233702	−	0.0850607i	0.222514	−	0.974929i	$-0.428574\pi$
$821$	−1.29328e8	−	4.70715e7i	−0.233702	−	0.0850607i	−0.456217	+	0.889869i	$0.650796\pi$
$822$	−2.73759e8	+	9.96401e7i	−0.492893	+	0.179398i
$823$	7.31606e8	−	6.13890e8i	1.31244	−	1.10126i	0.324585	−	0.945857i	$-0.394776\pi$
$823$	7.31606e8	−	6.13890e8i	1.31244	−	1.10126i	0.987851	−	0.155407i	$-0.0496689\pi$
$824$	4.68578e8	+	8.11601e8i	0.837530	+	1.45064i
$825$	−3.75015e8	−	2.16515e8i	−0.667861	−	0.385590i
$826$	−4.48775e6	−	2.54513e7i	−0.00796321	−	0.0451616i
$827$	−2.29404e8	+	4.04501e7i	−0.405587	+	0.0715160i	−0.372720	−	0.927944i	$-0.621575\pi$
$827$	−2.29404e8	+	4.04501e7i	−0.405587	+	0.0715160i	−0.0328671	+	0.999460i	$0.510464\pi$
$828$	−5.60509e8	+	9.70831e8i	−0.987397	+	1.71022i
$829$	4.75264e8	−	2.74394e8i	0.834201	−	0.481626i	−0.0210876	−	0.999778i	$-0.506713\pi$
$829$	4.75264e8	−	2.74394e8i	0.834201	−	0.481626i	0.855289	+	0.518151i	$0.173380\pi$
$830$	−4.46622e8	−	5.32263e8i	−0.781098	−	0.930876i
$831$	−4.92864e8	−	1.35413e9i	−0.858863	−	2.35971i
$832$	4.37521e8	−	1.20208e9i	0.759676	−	2.08719i
$833$	1.16284e8	+	9.75738e7i	0.201180	+	0.168810i
$834$	−5.03618e8	+	2.85616e9i	−0.868167	+	4.92362i
$835$			3.46317e8i			0.594860i
$836$	4.04797e8	+	1.51945e8i	0.692817	+	0.260057i
$837$	6.83638e8			1.16587
$838$	1.22211e9	+	2.15490e8i	2.07671	+	0.366181i
$839$	−1.89377e8	+	2.25691e8i	−0.320658	+	0.382145i	−0.902161	−	0.431399i	$-0.858020\pi$
$839$	−1.89377e8	+	2.25691e8i	−0.320658	+	0.382145i	0.581504	+	0.813544i	$0.302465\pi$
$840$	3.44973e8	+	1.25560e8i	0.582033	+	0.211843i
$841$	−4.22766e8	+	1.53874e8i	−0.710741	+	0.258689i
$842$	1.38649e8	−	1.16340e8i	0.232263	−	0.194892i
$843$	4.79122e8	+	8.29864e8i	0.799767	+	1.38524i
$844$	−6.33775e8	−	3.65910e8i	−1.05416	−	0.608622i
$845$	−2.43838e8	−	1.38287e9i	−0.404139	−	2.29199i
$846$	2.54323e9	−	4.48439e8i	4.20024	−	0.740615i
$847$	4.33428e7	−	7.50720e7i	0.0713292	−	0.123546i
$848$	5.05675e7	−	2.91952e7i	0.0829247	−	0.0478766i
$849$	1.74283e8	+	2.07702e8i	0.284794	+	0.339404i
$850$	−1.03864e8	−	2.85364e8i	−0.169125	−	0.464668i
$851$	3.60747e7	−	9.91143e7i	0.0585347	−	0.160823i
$852$	−1.41931e9	−	1.19094e9i	−2.29487	−	1.92562i
$853$	1.47579e8	−	8.36962e8i	0.237781	−	1.34852i	−0.598896	−	0.800827i	$-0.704394\pi$
$853$	1.47579e8	−	8.36962e8i	0.237781	−	1.34852i	0.836677	−	0.547697i	$-0.184495\pi$
$854$			2.10551e8i			0.338053i
$855$	9.82986e8	−	1.66385e9i	1.57271	−	2.66205i
$856$	−9.26578e8			−1.47727
$857$	3.16467e8	+	5.58017e7i	0.502789	+	0.0886553i	0.419290	−	0.907853i	$-0.362279\pi$
$857$	3.16467e8	+	5.58017e7i	0.502789	+	0.0886553i	0.0834995	+	0.996508i	$0.473390\pi$
$858$	−7.87115e8	+	9.38047e8i	−1.24617	+	1.48512i
$859$	−2.31214e8	−	8.41551e7i	−0.364783	−	0.132770i	0.153124	−	0.988207i	$-0.451067\pi$
$859$	−2.31214e8	−	8.41551e7i	−0.364783	−	0.132770i	−0.517907	+	0.855437i	$0.673289\pi$
$860$	1.78253e9	−	6.48786e8i	2.80247	−	1.02001i
$861$	1.82276e8	−	1.52948e8i	0.285575	−	0.239626i
$862$	−1.92881e8	−	3.34080e8i	−0.301139	−	0.521589i
$863$	3.43872e8	+	1.98535e8i	0.535013	+	0.308890i	0.743056	−	0.669230i	$-0.233376\pi$
$863$	3.43872e8	+	1.98535e8i	0.535013	+	0.308890i	−0.208042	+	0.978120i	$0.566709\pi$
$864$	1.09898e8	+	6.23261e8i	0.170391	+	0.966338i
$865$	−1.22595e9	+	2.16168e8i	−1.89419	+	0.333997i
$866$	4.52276e8	−	7.83366e8i	0.696386	−	1.20618i
$867$	−9.27223e8	+	5.35333e8i	−1.42274	+	0.821422i
$868$	−7.59419e7	−	9.05041e7i	−0.116124	−	0.138391i
$869$	−1.35917e8	−	3.73428e8i	−0.207116	−	0.569046i
$870$	4.79746e8	−	1.31809e9i	0.728540	−	2.00165i
$871$	−3.45848e8	−	2.90201e8i	−0.523396	−	0.439182i
$872$	−1.67715e8	+	9.51159e8i	−0.252943	+	1.43451i
$873$			6.51937e8i			0.979858i
$874$	5.64184e6	−	5.62949e8i	0.00845058	−	0.843208i
$875$	1.38484e7			0.0206717
$876$	1.74694e9	+	3.08032e8i	2.59875	+	0.458230i
$877$	−1.53451e8	+	1.82876e8i	−0.227495	+	0.271118i	−0.867702	−	0.497084i	$-0.834404\pi$
$877$	−1.53451e8	+	1.82876e8i	−0.227495	+	0.271118i	0.640207	+	0.768202i	$0.278848\pi$
$878$	−1.73086e9	−	6.29981e8i	−2.55728	−	0.930774i
$879$	9.57764e7	−	3.48598e7i	0.141024	−	0.0513284i
$880$	1.68323e8	−	1.41240e8i	0.246999	−	0.207257i
$881$	−6.29703e8	−	1.09068e9i	−0.920890	−	1.59503i	−0.798041	−	0.602603i	$-0.794130\pi$
$881$	−6.29703e8	−	1.09068e9i	−0.920890	−	1.59503i	−0.122849	−	0.992425i	$-0.539203\pi$
$882$	2.08411e9	+	1.20326e9i	3.03750	+	1.75370i
$883$	−8.62557e7	−	4.89181e8i	−0.125287	−	0.710538i	−0.981137	−	0.193314i	$-0.938077\pi$
$883$	−8.62557e7	−	4.89181e8i	−0.125287	−	0.710538i	0.855850	−	0.517224i	$-0.173035\pi$
$884$	−5.48348e8	+	9.66885e7i	−0.793778	+	0.139964i
$885$	−1.41822e8	+	2.45644e8i	−0.204605	+	0.354385i
$886$	−7.27363e8	+	4.19943e8i	−1.04580	+	0.603795i
$887$	1.61844e8	+	1.92878e8i	0.231913	+	0.276384i	0.869433	−	0.494050i	$-0.164484\pi$
$887$	1.61844e8	+	1.92878e8i	0.231913	+	0.276384i	−0.637520	+	0.770434i	$0.720040\pi$
$888$	2.06826e8	+	5.68249e8i	0.295369	+	0.811521i
$889$	−7.20969e7	+	1.98085e8i	−0.102615	+	0.281933i
$890$	9.50539e7	+	7.97597e7i	0.134834	+	0.113139i
$891$	7.12320e7	−	4.03977e8i	0.100703	−	0.571115i
$892$			5.94597e8i			0.837776i
$893$	−6.49559e8	+	5.34044e8i	−0.912146	+	0.749933i
$894$	−1.47261e9			−2.06098
$895$	6.66435e8	+	1.17510e8i	0.929583	+	0.163911i
$896$	1.44098e8	−	1.71729e8i	0.200324	−	0.238737i
$897$	9.71459e8	+	3.53582e8i	1.34601	+	0.489906i
$898$	2.49436e7	−	9.07871e6i	0.0344453	−	0.0125370i
$899$	−1.58282e8	+	1.32815e8i	−0.217848	+	0.182796i
$900$	−1.56080e9	−	2.70338e9i	−2.14101	−	3.70834i
$901$	2.94729e7	+	1.70162e7i	0.0402948	+	0.0232642i
$902$	−1.06673e8	−	6.04970e8i	−0.145356	−	0.824355i
$903$	−2.44824e8	+	4.31691e7i	−0.332499	+	0.0586286i
$904$	5.12173e8	−	8.87109e8i	0.693284	−	1.20080i
$905$	1.37765e9	−	7.95386e8i	1.85863	−	1.07308i
$906$	−7.86598e8	−	9.37431e8i	−1.05771	−	1.26054i
$907$	2.28772e8	+	6.28546e8i	0.306606	+	0.842394i	0.993312	+	0.115458i	$0.0368337\pi$
$907$	2.28772e8	+	6.28546e8i	0.306606	+	0.842394i	−0.686706	+	0.726935i	$0.740944\pi$
$908$	−9.06109e8	+	2.48951e9i	−1.21038	+	3.32550i
$909$	−1.12580e9	−	9.44660e8i	−1.49889	−	1.25772i
$910$	8.75556e7	−	4.96553e8i	0.116188	−	0.658933i
$911$			9.44506e7i			0.124925i	0.998047	+	0.0624625i	$0.0198954\pi$
$911$			9.44506e7i			0.124925i	−0.998047	+	0.0624625i	$0.980105\pi$
$912$	4.75228e8	+	5.78021e8i	0.626495	+	0.762007i
$913$	1.52430e8			0.200289
$914$	5.28935e8	+	9.32656e7i	0.692730	+	0.122147i
$915$	1.48540e9	−	1.77023e9i	1.93901	−	2.31082i
$916$	2.30353e9	+	8.38417e8i	2.99715	+	1.09087i
$917$	−4.91177e7	+	1.78774e7i	−0.0636987	+	0.0231844i
$918$	5.46960e8	−	4.58954e8i	0.707013	−	0.593254i
$919$	4.61739e8	+	7.99755e8i	0.594908	+	1.03041i	0.993560	+	0.113308i	$0.0361447\pi$
$919$	4.61739e8	+	7.99755e8i	0.594908	+	1.03041i	−0.398652	+	0.917102i	$0.630522\pi$
$920$	−6.92956e8	−	4.00078e8i	−0.889902	−	0.513785i
$921$	1.46928e8	+	8.33272e8i	0.188073	+	1.06662i
$922$	1.20899e9	−	2.13178e8i	1.54252	−	0.271987i
$923$	−5.82386e8	+	1.00872e9i	−0.740638	+	1.28282i
$924$	−1.52379e8	+	8.79758e7i	−0.193156	+	0.111519i
$925$	1.88791e8	+	2.24993e8i	0.238537	+	0.284278i
$926$	−8.87981e7	−	2.43971e8i	−0.111833	−	0.307259i
$927$	−6.86629e8	+	1.88650e9i	−0.861951	+	2.36819i
$928$	−1.46529e8	−	1.22953e8i	−0.183350	−	0.153849i
$929$	6.90700e7	−	3.91715e8i	0.0861474	−	0.488566i	−0.910956	−	0.412504i	$-0.864654\pi$
$929$	6.90700e7	−	3.91715e8i	0.0861474	−	0.488566i	0.997103	−	0.0760621i	$-0.0242347\pi$
$930$			1.99983e9i			2.48624i
$931$	−7.83583e8	−	7.85302e6i	−0.971037	−	0.00973168i
$932$	−1.83968e9			−2.27245
$933$	−5.10036e8	−	8.99331e7i	−0.627995	−	0.110732i
$934$	9.92556e8	−	1.18288e9i	1.21819	−	1.45178i
$935$	1.20344e8	+	4.38018e7i	0.147228	+	0.0535867i
$936$	−3.79682e9	+	1.38193e9i	−4.63012	+	1.68522i
$937$	8.58713e8	−	7.20545e8i	1.04383	−	0.875876i	0.0513971	−	0.998678i	$-0.483633\pi$
$937$	8.58713e8	−	7.20545e8i	1.04383	−	0.875876i	0.992431	+	0.122802i	$0.0391881\pi$
$938$	−5.00248e7	−	8.66456e7i	−0.0606146	−	0.104988i
$939$	9.88923e8	+	5.70955e8i	1.19444	+	0.689612i
$940$	4.53419e8	+	2.57147e9i	0.545904	+	3.09597i
$941$	−4.31255e8	+	7.60419e7i	−0.517565	+	0.0912607i	−0.426328	−	0.904569i	$-0.640193\pi$
$941$	−4.31255e8	+	7.60419e7i	−0.517565	+	0.0912607i	−0.0912369	+	0.995829i	$0.529082\pi$
$942$	−9.57954e6	+	1.65923e7i	−0.0114602	+	0.0198496i
$943$	−4.49139e8	+	2.59311e8i	−0.535607	+	0.309233i
$944$	−4.81266e7	−	5.73551e7i	−0.0572097	−	0.0681798i
$945$	1.43384e8	+	3.93944e8i	0.169905	+	0.466809i
$946$	−2.19514e8	+	6.03109e8i	−0.259292	+	0.712398i
$947$	1.11212e8	+	9.33180e7i	0.130949	+	0.109879i	0.705910	−	0.708302i	$-0.250538\pi$
$947$	1.11212e8	+	9.33180e7i	0.130949	+	0.109879i	−0.574961	+	0.818181i	$0.694983\pi$
$948$	7.29721e8	−	4.13845e9i	0.856509	−	4.85750i
$949$		−	1.11518e9i		−	1.30481i
$950$	1.34972e9	+	7.97400e8i	1.57424	+	0.930049i
$951$	1.42161e9			1.65287
$952$	−5.56218e7	−	9.80762e6i	−0.0644665	−	0.0113672i
$953$	−1.41781e7	+	1.68968e7i	−0.0163809	+	0.0195220i	−0.774173	−	0.632974i	$-0.781834\pi$
$953$	−1.41781e7	+	1.68968e7i	−0.0163809	+	0.0195220i	0.757792	+	0.652496i	$0.226278\pi$
$954$	5.06994e8	+	1.84531e8i	0.583926	+	0.212532i
$955$	2.83762e8	−	1.03281e8i	0.325794	−	0.118579i
$956$	6.81575e8	−	5.71910e8i	0.780082	−	0.654566i
$957$	1.53861e8	+	2.66495e8i	0.175546	+	0.304055i
$958$	2.93419e8	+	1.69406e8i	0.333728	+	0.192678i
$959$	4.56977e6	+	2.59165e7i	0.00518130	+	0.0293846i
$960$	−3.06408e9	+	5.40280e8i	−3.46327	+	0.610668i
$961$	−2.96459e8	+	5.13482e8i	−0.334037	+	0.578569i
$962$	7.19280e8	−	4.15276e8i	0.807928	−	0.466457i
$963$	−1.27587e9	−	1.52053e9i	−1.42866	−	1.70261i
$964$	9.36349e8	+	2.57260e9i	1.04522	+	2.87171i
$965$	−1.03663e8	+	2.84812e8i	−0.115357	+	0.316940i
$966$	1.75500e8	+	1.47262e8i	0.194691	+	0.163365i
$967$	6.76563e7	−	3.83698e8i	0.0748219	−	0.424336i	−0.924270	−	0.381739i	$-0.875325\pi$
$967$	6.76563e7	−	3.83698e8i	0.0748219	−	0.424336i	0.999092	−	0.0425978i	$-0.0135634\pi$
$968$		−	1.08324e9i		−	1.19426i
$969$	−1.53268e8	+	4.08322e8i	−0.168454	+	0.448778i
$970$	−1.01663e9			−1.11391
$971$	−9.13543e8	−	1.61082e8i	−0.997864	−	0.175950i	−0.349219	−	0.937041i	$-0.613553\pi$
$971$	−9.13543e8	−	1.61082e8i	−0.997864	−	0.175950i	−0.648645	+	0.761091i	$0.724664\pi$
$972$	5.85490e8	−	6.97760e8i	0.637559	−	0.759813i
$973$	2.46183e8	+	8.96034e7i	0.267251	+	0.0972715i
$974$	−6.26376e7	+	2.27982e7i	−0.0677889	+	0.0246731i
$975$	−2.20524e9	+	1.85042e9i	−2.37926	+	1.99644i
$976$	3.04991e8	+	5.28261e8i	0.328049	+	0.568197i
$977$	−1.21915e9	−	7.03877e8i	−1.30730	−	0.754767i	−0.325651	−	0.945490i	$-0.605584\pi$
$977$	−1.21915e9	−	7.03877e8i	−1.30730	−	0.754767i	−0.981644	+	0.190723i	$0.938917\pi$
$978$	−9.06943e8	−	5.14353e9i	−0.969535	−	5.49851i
$979$	−2.68081e7	+	4.72699e6i	−0.0285705	+	0.00503775i
$980$	−1.21662e9	+	2.10726e9i	−1.29264	+	2.23892i
$981$	−1.79181e9	+	1.03450e9i	−1.89795	+	1.09578i
$982$	1.94833e8	+	2.32192e8i	0.205744	+	0.245196i
$983$	2.66457e8	+	7.32083e8i	0.280521	+	0.770726i	0.997301	+	0.0734259i	$0.0233932\pi$
$983$	2.66457e8	+	7.32083e8i	0.280521	+	0.770726i	−0.716779	+	0.697300i	$0.754385\pi$
$984$	1.01696e9	−	2.79408e9i	1.06738	−	2.93260i
$985$	8.93595e8	+	7.49815e8i	0.935044	+	0.784595i
$986$	−3.74735e7	+	2.12523e8i	−0.0390925	+	0.221704i
$987$		−	3.42202e8i		−	0.355902i
$988$	1.86959e9	−	2.18328e9i	1.93855	−	2.26381i
$989$	5.41849e8			0.560131
$990$	1.99948e9	+	3.52562e8i	2.06068	+	0.363354i
$991$	3.42975e8	−	4.08741e8i	0.352404	−	0.419979i	−0.560499	−	0.828155i	$-0.689391\pi$
$991$	3.42975e8	−	4.08741e8i	0.352404	−	0.419979i	0.912903	+	0.408176i	$0.133835\pi$
$992$	2.56265e8	+	9.32730e7i	0.262515	+	0.0955478i
$993$	7.45914e8	−	2.71491e8i	0.761800	−	0.277273i
$994$	−1.97733e8	+	1.65918e8i	−0.201336	+	0.168941i
$995$	7.75526e8	+	1.34325e9i	0.787276	+	1.36360i
$996$	1.39594e9	+	8.05946e8i	1.41283	+	0.815696i
$997$	−1.23735e8	−	7.01733e8i	−0.124855	−	0.708087i	−0.981394	−	0.192005i	$-0.938501\pi$
$997$	−1.23735e8	−	7.01733e8i	−0.124855	−	0.708087i	0.856539	−	0.516082i	$-0.172610\pi$
$998$	3.78618e8	−	6.67605e7i	0.380899	−	0.0671627i
$999$	−3.45281e8	+	5.98044e8i	−0.346319	+	0.599841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.7.f.a.2.2	✓	54
19.10	odd	18	inner	19.7.f.a.10.2	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.7.f.a.2.2	✓	54	1.1	even	1	trivial
19.7.f.a.10.2	yes	54	19.10	odd	18	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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.2866 - 2.34278i) q^{2} +(-30.7619 + 36.6606i) q^{3} +(110.904 + 40.3656i) q^{4} +(-169.577 + 61.7209i) q^{5} +(494.607 - 415.025i) q^{6} +(-29.1620 - 50.5101i) q^{7} +(-631.184 - 364.414i) q^{8} +(-271.115 - 1537.57i) q^{9} +O(q^{10})\)	\(q+(-13.2866 - 2.34278i) q^{2} +(-30.7619 + 36.6606i) q^{3} +(110.904 + 40.3656i) q^{4} +(-169.577 + 61.7209i) q^{5} +(494.607 - 415.025i) q^{6} +(-29.1620 - 50.5101i) q^{7} +(-631.184 - 364.414i) q^{8} +(-271.115 - 1537.57i) q^{9} +(2397.69 - 422.777i) q^{10} +(-267.061 + 462.562i) q^{11} +(-4891.43 + 2824.07i) q^{12} +(2282.40 + 2720.06i) q^{13} +(269.129 + 739.426i) q^{14} +(2953.78 - 8115.43i) q^{15} +(1746.31 + 1465.33i) q^{16} +(-230.723 + 1308.49i) q^{17} +21064.2i q^{18} +(-3369.80 - 5974.14i) q^{19} -21298.1 q^{20} +(2748.81 + 484.689i) q^{21} +(4632.00 - 5520.20i) q^{22} +(-5716.82 - 2080.75i) q^{23} +(32776.1 - 11929.5i) q^{24} +(12977.4 - 10889.3i) q^{25} +(-23952.8 - 41487.4i) q^{26} +(34494.6 + 19915.5i) q^{27} +(-1195.30 - 6778.91i) q^{28} +(-11855.6 + 2090.46i) q^{29} +(-58258.2 + 100906. i) q^{30} +(14864.0 - 8581.75i) q^{31} +(10213.3 + 12171.7i) q^{32} +(-8742.52 - 24019.9i) q^{33} +(6131.02 - 16844.8i) q^{34} +(8062.74 + 6765.44i) q^{35} +(31997.4 - 181466. i) q^{36} +17337.3i q^{37} +(30777.0 + 87270.4i) q^{38} -169930. q^{39} +(129526. + 22839.0i) q^{40} +(54796.0 - 65303.4i) q^{41} +(-35386.7 - 12879.7i) q^{42} +(-83694.2 + 30462.2i) q^{43} +(-48289.6 + 40519.8i) q^{44} +(140875. + 244003. i) q^{45} +(71082.1 + 41039.3i) q^{46} +(-21289.2 - 120737. i) q^{47} +(-107440. + 18944.5i) q^{48} +(57123.6 - 98941.1i) q^{49} +(-197936. + 114278. i) q^{50} +(-40872.6 - 48710.1i) q^{51} +(143330. + 393795. i) q^{52} +(8760.41 - 24069.0i) q^{53} +(-411657. - 345421. i) q^{54} +(16737.5 - 94923.1i) q^{55} +42508.3i q^{56} +(322677. + 60236.9i) q^{57} +162418. q^{58} +(-32344.5 - 5703.21i) q^{59} +(655169. - 780800. i) q^{60} +(251440. + 91516.8i) q^{61} +(-217597. + 79198.8i) q^{62} +(-69756.7 + 58532.8i) q^{63} +(-180133. - 311999. i) q^{64} +(-554927. - 320387. i) q^{65} +(59884.8 + 339623. i) q^{66} +(-125216. + 22078.9i) q^{67} +(-78406.1 + 135803. i) q^{68} +(252142. - 145574. i) q^{69} +(-91276.1 - 108779. i) q^{70} +(112194. + 308250. i) q^{71} +(-389189. + 1.06929e6i) q^{72} +(-240588. - 201877. i) q^{73} +(40617.5 - 230353. i) q^{74} +810733. i q^{75} +(-132573. - 798578. i) q^{76} +31152.1 q^{77} +(2.25778e6 + 398108. i) q^{78} +(-478243. + 569948. i) q^{79} +(-386576. - 140702. i) q^{80} +(-721691. + 262674. i) q^{81} +(-881042. + 739282. i) q^{82} +(-142692. - 247150. i) q^{83} +(285288. + 164711. i) q^{84} +(-41636.2 - 236130. i) q^{85} +(1.18337e6 - 208661. i) q^{86} +(288063. - 498940. i) q^{87} +(337129. - 194641. i) q^{88} +(32759.9 + 39041.7i) q^{89} +(-1.30010e6 - 3.57200e6i) q^{90} +(70831.1 - 194607. i) q^{91} +(-550026. - 461526. i) q^{92} +(-142633. + 808915. i) q^{93} +1.65405e6i q^{94} +(940169. + 805088. i) q^{95} -760402. q^{96} +(-411219. - 72509.1i) q^{97} +(-990774. + 1.18076e6i) q^{98} +(783627. + 285217. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9}+O(q^{10}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} - 1689 q^{10} + 1677 q^{11} - 9 q^{12} - 10506 q^{13} + 6105 q^{14} + 24138 q^{15} + 23760 q^{16} - 3438 q^{17} - 30918 q^{19} - 76650 q^{20} - 59055 q^{21} + 20490 q^{22} + 42498 q^{23} + 31848 q^{24} + 7914 q^{25} + 109989 q^{26} + 124821 q^{27} - 109476 q^{28} - 27726 q^{29} - 153516 q^{30} - 30789 q^{31} - 114375 q^{32} + 126039 q^{33} + 359796 q^{34} + 160161 q^{35} + 184995 q^{36} - 245244 q^{38} - 390564 q^{39} - 372678 q^{40} - 24708 q^{41} - 244893 q^{42} - 30726 q^{43} - 301419 q^{44} + 293037 q^{45} + 69246 q^{46} - 71454 q^{47} + 1024041 q^{48} - 350346 q^{49} - 104148 q^{50} - 180672 q^{51} + 921801 q^{52} + 822558 q^{53} + 308469 q^{54} + 623517 q^{55} - 17862 q^{57} - 1150644 q^{58} - 463812 q^{59} - 908130 q^{60} - 583698 q^{61} - 429732 q^{62} - 2576043 q^{63} - 328293 q^{64} - 1056789 q^{65} - 1038756 q^{66} + 1120464 q^{67} + 717270 q^{68} + 3771567 q^{69} + 4845345 q^{70} + 94494 q^{71} + 2351634 q^{72} + 950850 q^{73} + 55149 q^{74} - 218814 q^{76} - 343086 q^{77} + 1833471 q^{78} - 4936494 q^{79} - 9642039 q^{80} - 769551 q^{81} - 8627793 q^{82} - 412131 q^{83} - 3125205 q^{84} - 896910 q^{85} + 8878236 q^{86} + 610737 q^{87} + 13604751 q^{88} + 6653022 q^{89} + 3142734 q^{90} + 3409821 q^{91} - 3043740 q^{92} - 816393 q^{93} + 4839186 q^{95} - 5667138 q^{96} - 853656 q^{97} - 17679315 q^{98} - 13991937 q^{99}+O(q^{100}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9 - 1689 * q^10 + 1677 * q^11 - 9 * q^12 - 10506 * q^13 + 6105 * q^14 + 24138 * q^15 + 23760 * q^16 - 3438 * q^17 - 30918 * q^19 - 76650 * q^20 - 59055 * q^21 + 20490 * q^22 + 42498 * q^23 + 31848 * q^24 + 7914 * q^25 + 109989 * q^26 + 124821 * q^27 - 109476 * q^28 - 27726 * q^29 - 153516 * q^30 - 30789 * q^31 - 114375 * q^32 + 126039 * q^33 + 359796 * q^34 + 160161 * q^35 + 184995 * q^36 - 245244 * q^38 - 390564 * q^39 - 372678 * q^40 - 24708 * q^41 - 244893 * q^42 - 30726 * q^43 - 301419 * q^44 + 293037 * q^45 + 69246 * q^46 - 71454 * q^47 + 1024041 * q^48 - 350346 * q^49 - 104148 * q^50 - 180672 * q^51 + 921801 * q^52 + 822558 * q^53 + 308469 * q^54 + 623517 * q^55 - 17862 * q^57 - 1150644 * q^58 - 463812 * q^59 - 908130 * q^60 - 583698 * q^61 - 429732 * q^62 - 2576043 * q^63 - 328293 * q^64 - 1056789 * q^65 - 1038756 * q^66 + 1120464 * q^67 + 717270 * q^68 + 3771567 * q^69 + 4845345 * q^70 + 94494 * q^71 + 2351634 * q^72 + 950850 * q^73 + 55149 * q^74 - 218814 * q^76 - 343086 * q^77 + 1833471 * q^78 - 4936494 * q^79 - 9642039 * q^80 - 769551 * q^81 - 8627793 * q^82 - 412131 * q^83 - 3125205 * q^84 - 896910 * q^85 + 8878236 * q^86 + 610737 * q^87 + 13604751 * q^88 + 6653022 * q^89 + 3142734 * q^90 + 3409821 * q^91 - 3043740 * q^92 - 816393 * q^93 + 4839186 * q^95 - 5667138 * q^96 - 853656 * q^97 - 17679315 * q^98 - 13991937 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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