LMFDB - Embedded newform 29.8.e.a.22.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(4,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, 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:	$9.05916573904$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			22.16
Character	$\chi$	$=$	29.22
Dual form			29.8.e.a.4.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.1958 - 4.38132i) q^{2} +(-23.2918 + 48.3658i) q^{3} +(233.959 - 112.669i) q^{4} +(36.5819 + 160.276i) q^{5} +(-235.198 + 1030.47i) q^{6} +(541.526 + 260.785i) q^{7} +(2026.99 - 1616.47i) q^{8} +(-433.175 - 543.185i) q^{9} +O(q^{10})$	\(q+(19.1958 - 4.38132i) q^{2} +(-23.2918 + 48.3658i) q^{3} +(233.959 - 112.669i) q^{4} +(36.5819 + 160.276i) q^{5} +(-235.198 + 1030.47i) q^{6} +(541.526 + 260.785i) q^{7} +(2026.99 - 1616.47i) q^{8} +(-433.175 - 543.185i) q^{9} +(1404.44 + 2916.35i) q^{10} +(2129.34 + 1698.09i) q^{11} +13939.9i q^{12} +(-1921.80 + 2409.86i) q^{13} +(11537.6 + 2633.39i) q^{14} +(-8603.92 - 1963.79i) q^{15} +(11103.6 - 13923.4i) q^{16} -37148.8i q^{17} +(-10695.0 - 8528.99i) q^{18} +(-18984.2 - 39421.2i) q^{19} +(26616.7 + 33376.3i) q^{20} +(-25226.2 + 20117.2i) q^{21} +(48314.3 + 23267.0i) q^{22} +(-7058.45 + 30925.1i) q^{23} +(30969.7 + 135687. i) q^{24} +(46038.1 - 22170.8i) q^{25} +(-26332.1 + 54679.1i) q^{26} +(-78098.1 + 17825.4i) q^{27} +156077. q^{28} +(-10685.2 - 130903. i) q^{29} -173763. q^{30} +(3778.37 - 862.388i) q^{31} +(8152.75 - 16929.4i) q^{32} +(-131726. + 63435.8i) q^{33} +(-162761. - 713101. i) q^{34} +(-21987.5 + 96333.5i) q^{35} +(-162545. - 78277.7i) q^{36} +(158260. - 126208. i) q^{37} +(-537135. - 673546. i) q^{38} +(-71792.7 - 149079. i) q^{39} +(333231. + 265743. i) q^{40} +718435. i q^{41} +(-396097. + 496690. i) q^{42} +(278766. + 63626.5i) q^{43} +(689501. + 157374. i) q^{44} +(71212.9 - 89298.2i) q^{45} +624557. i q^{46} +(-495480. - 395132. i) q^{47} +(414797. + 861334. i) q^{48} +(-288229. - 361428. i) q^{49} +(786602. - 627294. i) q^{50} +(1.79673e6 + 865260. i) q^{51} +(-178106. + 780334. i) q^{52} +(-180885. - 792508. i) q^{53} +(-1.42106e6 + 684345. i) q^{54} +(-194268. + 403401. i) q^{55} +(1.51922e6 - 346751. i) q^{56} +2.34882e6 q^{57} +(-778641. - 2.46598e6i) q^{58} +2.65624e6 q^{59} +(-2.23422e6 + 509947. i) q^{60} +(-1.08586e6 + 2.25482e6i) q^{61} +(68750.4 - 33108.5i) q^{62} +(-92921.2 - 407114. i) q^{63} +(-424915. + 1.86167e6i) q^{64} +(-456544. - 219860. i) q^{65} +(-2.25065e6 + 1.79483e6i) q^{66} +(1.09962e6 + 1.37888e6i) q^{67} +(-4.18551e6 - 8.69129e6i) q^{68} +(-1.33131e6 - 1.06169e6i) q^{69} +1.94553e6i q^{70} +(1.42357e6 - 1.78510e6i) q^{71} +(-1.75608e6 - 400814. i) q^{72} +(1.61857e6 + 369428. i) q^{73} +(2.48497e6 - 3.11606e6i) q^{74} +2.74307e6i q^{75} +(-8.88308e6 - 7.08402e6i) q^{76} +(710257. + 1.47486e6i) q^{77} +(-2.03128e6 - 2.54715e6i) q^{78} +(838507. - 668687. i) q^{79} +(2.63778e6 + 1.27029e6i) q^{80} +(1.29501e6 - 5.67380e6i) q^{81} +(3.14769e6 + 1.37909e7i) q^{82} +(-2.18172e6 + 1.05066e6i) q^{83} +(-3.63532e6 + 7.54881e6i) q^{84} +(5.95405e6 - 1.35897e6i) q^{85} +5.62991e6 q^{86} +(6.58013e6 + 2.53217e6i) q^{87} +7.06106e6 q^{88} +(-9.66496e6 + 2.20596e6i) q^{89} +(975746. - 2.02616e6i) q^{90} +(-1.66916e6 + 803824. i) q^{91} +(1.83290e6 + 8.03047e6i) q^{92} +(-46294.7 + 202830. i) q^{93} +(-1.12423e7 - 5.41402e6i) q^{94} +(5.62378e6 - 4.48482e6i) q^{95} +(628911. + 788629. i) q^{96} +(-5.50297e6 - 1.14270e7i) q^{97} +(-7.11632e6 - 5.67508e6i) q^{98} -1.89220e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9}+O(q^{10}) $ 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9} - 7 q^{10} + 4207 q^{11} + 377 q^{13} - 7 q^{14} - 74473 q^{15} - 125851 q^{16} - 194880 q^{18} - 7 q^{19} + 162901 q^{20} + 86933 q^{21} + 252614 q^{22} + 238675 q^{23} - 490819 q^{24} - 107349 q^{25} + 367017 q^{26} + 75593 q^{27} + 1397540 q^{28} + 379863 q^{29} - 175646 q^{30} - 143885 q^{31} + 473172 q^{32} - 1419437 q^{33} - 2314463 q^{34} - 1018325 q^{35} + 1720462 q^{36} + 662991 q^{37} - 2763860 q^{38} + 42189 q^{39} + 580601 q^{40} - 3296492 q^{42} - 1587425 q^{43} + 2344398 q^{44} + 6508254 q^{45} + 526673 q^{47} + 6175806 q^{48} - 1391517 q^{49} - 4194526 q^{50} - 68204 q^{51} - 7720808 q^{52} + 1762640 q^{53} - 2032428 q^{54} + 2655709 q^{55} + 17091081 q^{56} + 4906842 q^{57} + 13231229 q^{58} - 8638324 q^{59} - 9957136 q^{60} + 2797697 q^{61} - 884069 q^{62} - 20232301 q^{63} - 17528026 q^{64} - 7454088 q^{65} - 17541475 q^{66} - 4890949 q^{67} + 22029140 q^{68} + 13204429 q^{69} - 1091301 q^{71} + 25137595 q^{72} + 14363636 q^{73} + 3185328 q^{74} - 41019881 q^{76} - 25204627 q^{77} - 15753743 q^{78} + 31186057 q^{79} + 24146022 q^{80} - 29435757 q^{81} - 51438506 q^{82} - 8367235 q^{83} + 78906093 q^{84} + 41540198 q^{85} + 65794492 q^{86} + 11089375 q^{87} + 39260390 q^{88} + 6628699 q^{89} + 32127214 q^{90} + 24315293 q^{91} - 39469980 q^{92} - 31050649 q^{93} - 102445588 q^{94} - 75684679 q^{95} - 95069050 q^{96} + 38131380 q^{97} + 19581828 q^{98}+O(q^{100}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9 - 7 * q^10 + 4207 * q^11 + 377 * q^13 - 7 * q^14 - 74473 * q^15 - 125851 * q^16 - 194880 * q^18 - 7 * q^19 + 162901 * q^20 + 86933 * q^21 + 252614 * q^22 + 238675 * q^23 - 490819 * q^24 - 107349 * q^25 + 367017 * q^26 + 75593 * q^27 + 1397540 * q^28 + 379863 * q^29 - 175646 * q^30 - 143885 * q^31 + 473172 * q^32 - 1419437 * q^33 - 2314463 * q^34 - 1018325 * q^35 + 1720462 * q^36 + 662991 * q^37 - 2763860 * q^38 + 42189 * q^39 + 580601 * q^40 - 3296492 * q^42 - 1587425 * q^43 + 2344398 * q^44 + 6508254 * q^45 + 526673 * q^47 + 6175806 * q^48 - 1391517 * q^49 - 4194526 * q^50 - 68204 * q^51 - 7720808 * q^52 + 1762640 * q^53 - 2032428 * q^54 + 2655709 * q^55 + 17091081 * q^56 + 4906842 * q^57 + 13231229 * q^58 - 8638324 * q^59 - 9957136 * q^60 + 2797697 * q^61 - 884069 * q^62 - 20232301 * q^63 - 17528026 * q^64 - 7454088 * q^65 - 17541475 * q^66 - 4890949 * q^67 + 22029140 * q^68 + 13204429 * q^69 - 1091301 * q^71 + 25137595 * q^72 + 14363636 * q^73 + 3185328 * q^74 - 41019881 * q^76 - 25204627 * q^77 - 15753743 * q^78 + 31186057 * q^79 + 24146022 * q^80 - 29435757 * q^81 - 51438506 * q^82 - 8367235 * q^83 + 78906093 * q^84 + 41540198 * q^85 + 65794492 * q^86 + 11089375 * q^87 + 39260390 * q^88 + 6628699 * q^89 + 32127214 * q^90 + 24315293 * q^91 - 39469980 * q^92 - 31050649 * q^93 - 102445588 * q^94 - 75684679 * q^95 - 95069050 * q^96 + 38131380 * q^97 + 19581828 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{14}\right)$

Coefficient data

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

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

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

$2$	19.1958	−	4.38132i	1.69669	−	0.387257i	0.738691	−	0.674044i	$-0.235444\pi$
$2$	19.1958	−	4.38132i	1.69669	−	0.387257i	0.957995	+	0.286786i	$0.0925870\pi$
$3$	−23.2918	+	48.3658i	−0.498056	+	1.03422i	0.488767	+	0.872415i	$0.337447\pi$
$3$	−23.2918	+	48.3658i	−0.498056	+	1.03422i	−0.986822	+	0.161809i	$0.948267\pi$
$4$	233.959	−	112.669i	1.82781	−	0.880225i
$5$	36.5819	+	160.276i	0.130879	+	0.573420i	0.997256	+	0.0740289i	$0.0235857\pi$
$5$	36.5819	+	160.276i	0.130879	+	0.573420i	−0.866377	+	0.499391i	$0.833557\pi$
$6$	−235.198	+	1030.47i	−0.444533	+	1.94763i
$7$	541.526	+	260.785i	0.596728	+	0.287369i	0.707766	−	0.706447i	$-0.249703\pi$
$7$	541.526	+	260.785i	0.596728	+	0.287369i	−0.111038	+	0.993816i	$0.535418\pi$
$8$	2026.99	−	1616.47i	1.39970	−	1.11623i
$9$	−433.175	−	543.185i	−0.198068	−	0.248370i
$10$	1404.44	+	2916.35i	0.444122	+	0.922229i
$11$	2129.34	+	1698.09i	0.482360	+	0.384669i	0.834262	−	0.551368i	$-0.185894\pi$
$11$	2129.34	+	1698.09i	0.482360	+	0.384669i	−0.351903	+	0.936037i	$0.614465\pi$
$12$			13939.9i			2.32876i
$13$	−1921.80	+	2409.86i	−0.242608	+	0.304221i	−0.888196	−	0.459465i	$-0.848041\pi$
$13$	−1921.80	+	2409.86i	−0.242608	+	0.304221i	0.645588	+	0.763686i	$0.276613\pi$
$14$	11537.6	+	2633.39i	1.12375	+	0.256488i
$15$	−8603.92	−	1963.79i	−0.658229	−	0.150237i
$16$	11103.6	−	13923.4i	0.677708	−	0.849819i
$17$		−	37148.8i		−	1.83389i	−0.399014	−	0.916945i	$-0.630648\pi$
$17$		−	37148.8i		−	1.83389i	0.399014	−	0.916945i	$-0.369352\pi$
$18$	−10695.0	−	8528.99i	−0.432243	−	0.344702i
$19$	−18984.2	−	39421.2i	−0.634974	−	1.31854i	−0.931580	−	0.363537i	$-0.881569\pi$
$19$	−18984.2	−	39421.2i	−0.634974	−	1.31854i	0.296606	−	0.955000i	$-0.404145\pi$
$20$	26616.7	+	33376.3i	0.743960	+	0.932897i
$21$	−25226.2	+	20117.2i	−0.594407	+	0.474024i
$22$	48314.3	+	23267.0i	0.967379	+	0.465865i
$23$	−7058.45	+	30925.1i	−0.120966	+	0.529985i	0.877741	+	0.479136i	$0.159050\pi$
$23$	−7058.45	+	30925.1i	−0.120966	+	0.529985i	−0.998706	+	0.0508490i	$0.983807\pi$
$24$	30969.7	+	135687.i	0.457297	+	2.00355i
$25$	46038.1	−	22170.8i	0.589288	−	0.283786i
$26$	−26332.1	+	54679.1i	−0.293818	+	0.610120i
$27$	−78098.1	+	17825.4i	−0.763602	+	0.174287i
$28$	156077.			1.34365
$29$	−10685.2	−	130903.i	−0.0813561	−	0.996685i
$29$	−10685.2	−	130903.i	−0.0813561	−	0.996685i
$30$	−173763.			−1.17499
$31$	3778.37	−	862.388i	0.0227792	−	0.00519920i	−0.211116	−	0.977461i	$-0.567710\pi$
$31$	3778.37	−	862.388i	0.0227792	−	0.00519920i	0.233895	+	0.972262i	$0.424853\pi$
$32$	8152.75	−	16929.4i	0.0439824	−	0.0913304i
$33$	−131726.	+	63435.8i	−0.638076	+	0.307281i
$34$	−162761.	−	713101.i	−0.710188	−	3.11153i
$35$	−21987.5	+	96333.5i	−0.0866837	+	0.379786i
$36$	−162545.	−	78277.7i	−0.580652	−	0.279627i
$37$	158260.	−	126208.i	0.513647	−	0.409620i	−0.332067	−	0.943256i	$-0.607746\pi$
$37$	158260.	−	126208.i	0.513647	−	0.409620i	0.845715	+	0.533636i	$0.179175\pi$
$38$	−537135.	−	673546.i	−1.58796	−	1.99124i
$39$	−71792.7	−	149079.i	−0.193800	−	0.402430i
$40$	333231.	+	265743.i	0.823258	+	0.656526i
$41$			718435.i			1.62796i	0.580892	+	0.813981i	$0.302704\pi$
$41$			718435.i			1.62796i	−0.580892	+	0.813981i	$0.697296\pi$
$42$	−396097.	+	496690.i	−0.824953	+	1.03446i
$43$	278766.	+	63626.5i	0.534688	+	0.122039i	0.481335	−	0.876537i	$-0.340152\pi$
$43$	278766.	+	63626.5i	0.534688	+	0.122039i	0.0533528	+	0.998576i	$0.483009\pi$
$44$	689501.	+	157374.i	1.22026	+	0.278515i
$45$	71212.9	−	89298.2i	0.116497	−	0.146083i
$46$			624557.i			0.946063i
$47$	−495480.	−	395132.i	−0.696119	−	0.555136i	0.210238	−	0.977650i	$-0.432576\pi$
$47$	−495480.	−	395132.i	−0.696119	−	0.555136i	−0.906356	+	0.422514i	$0.861148\pi$
$48$	414797.	+	861334.i	0.541366	+	1.12416i
$49$	−288229.	−	361428.i	−0.349987	−	0.438869i
$50$	786602.	−	627294.i	0.889938	−	0.709702i
$51$	1.79673e6	+	865260.i	1.89665	+	0.913379i
$52$	−178106.	+	780334.i	−0.175658	+	0.769607i
$53$	−180885.	−	792508.i	−0.166892	−	0.731204i	−0.987227	−	0.159320i	$-0.949070\pi$
$53$	−180885.	−	792508.i	−0.166892	−	0.731204i	0.820335	−	0.571884i	$-0.193787\pi$
$54$	−1.42106e6	+	684345.i	−1.22810	+	0.591421i
$55$	−194268.	+	403401.i	−0.157446	+	0.326940i
$56$	1.51922e6	−	346751.i	1.15601	−	0.263852i
$57$	2.34882e6			1.67991
$58$	−778641.	−	2.46598e6i	−0.524009	−	1.65956i
$59$	2.65624e6			1.68378			0.841890	−	0.539650i	$-0.181443\pi$
$59$	2.65624e6			1.68378			0.841890	+	0.539650i	$0.181443\pi$
$60$	−2.23422e6	+	509947.i	−1.33536	+	0.304787i
$61$	−1.08586e6	+	2.25482e6i	−0.612521	+	1.27191i	0.331944	+	0.943299i	$0.392296\pi$
$61$	−1.08586e6	+	2.25482e6i	−0.612521	+	1.27191i	−0.944465	+	0.328613i	$0.893419\pi$
$62$	68750.4	−	33108.5i	0.0366357	−	0.0176428i
$63$	−92921.2	−	407114.i	−0.0468191	−	0.205128i
$64$	−424915.	+	1.86167e6i	−0.202615	+	0.887715i
$65$	−456544.	−	219860.i	−0.206199	−	0.0993001i
$66$	−2.25065e6	+	1.79483e6i	−0.963617	+	0.768459i
$67$	1.09962e6	+	1.37888e6i	0.446662	+	0.560097i	0.953286	−	0.302071i	$-0.0976779\pi$
$67$	1.09962e6	+	1.37888e6i	0.446662	+	0.560097i	−0.506623	+	0.862168i	$0.669106\pi$
$68$	−4.18551e6	−	8.69129e6i	−1.61424	−	3.35199i
$69$	−1.33131e6	−	1.06169e6i	−0.487875	−	0.389067i
$70$			1.94553e6i			0.677947i
$71$	1.42357e6	−	1.78510e6i	0.472036	−	0.591915i	−0.487632	−	0.873049i	$-0.662139\pi$
$71$	1.42357e6	−	1.78510e6i	0.472036	−	0.591915i	0.959668	+	0.281135i	$0.0907107\pi$
$72$	−1.75608e6	−	400814.i	−0.554473	−	0.126555i
$73$	1.61857e6	+	369428.i	0.486969	+	0.111147i	0.458954	−	0.888460i	$-0.348224\pi$
$73$	1.61857e6	+	369428.i	0.486969	+	0.111147i	0.0280147	+	0.999608i	$0.491081\pi$
$74$	2.48497e6	−	3.11606e6i	0.712870	−	0.893911i
$75$			2.74307e6i			0.750797i
$76$	−8.88308e6	−	7.08402e6i	−2.32122	−	1.85111i
$77$	710257.	+	1.47486e6i	0.177295	+	0.368158i
$78$	−2.03128e6	−	2.54715e6i	−0.484662	−	0.607747i
$79$	838507.	−	668687.i	0.191343	−	0.152591i	−0.523133	−	0.852251i	$-0.675237\pi$
$79$	838507.	−	668687.i	0.191343	−	0.152591i	0.714475	+	0.699660i	$0.246665\pi$
$80$	2.63778e6	+	1.27029e6i	0.576001	+	0.277387i
$81$	1.29501e6	−	5.67380e6i	0.270754	−	1.18625i
$82$	3.14769e6	+	1.37909e7i	0.630440	+	2.76214i
$83$	−2.18172e6	+	1.05066e6i	−0.418818	+	0.201692i	−0.631411	−	0.775449i	$-0.717524\pi$
$83$	−2.18172e6	+	1.05066e6i	−0.418818	+	0.201692i	0.212592	+	0.977141i	$0.431809\pi$
$84$	−3.63532e6	+	7.54881e6i	−0.669213	+	1.38964i
$85$	5.95405e6	−	1.35897e6i	1.05159	−	0.240018i
$86$	5.62991e6			0.954458
$87$	6.58013e6	+	2.53217e6i	1.07131	+	0.412264i
$88$	7.06106e6			1.10454
$89$	−9.66496e6	+	2.20596e6i	−1.45323	+	0.331691i	−0.874977	−	0.484165i	$-0.839124\pi$
$89$	−9.66496e6	+	2.20596e6i	−1.45323	+	0.331691i	−0.578256	+	0.815855i	$0.696266\pi$
$90$	975746.	−	2.02616e6i	0.141087	−	0.292971i
$91$	−1.66916e6	+	803824.i	−0.232195	+	0.111819i
$92$	1.83290e6	+	8.03047e6i	0.245404	+	1.07519i
$93$	−46294.7	+	202830.i	−0.00596817	+	0.0261482i
$94$	−1.12423e7	−	5.41402e6i	−1.39608	−	0.672314i
$95$	5.62378e6	−	4.48482e6i	0.672970	−	0.536676i
$96$	628911.	+	788629.i	0.0725504	+	0.0909753i
$97$	−5.50297e6	−	1.14270e7i	−0.612204	−	1.27126i	−0.944634	−	0.328127i	$-0.893583\pi$
$97$	−5.50297e6	−	1.14270e7i	−0.612204	−	1.27126i	0.332429	−	0.943128i	$-0.392132\pi$
$98$	−7.11632e6	−	5.67508e6i	−0.763773	−	0.609089i
$99$		−	1.89220e6i		−	0.195994i
$100$	8.27308e6	−	1.03741e7i	0.827308	−	1.03741i
$101$	−1.51258e7	−	3.45236e6i	−1.46081	−	0.333419i	−0.583014	−	0.812462i	$-0.698127\pi$
$101$	−1.51258e7	−	3.45236e6i	−1.46081	−	0.333419i	−0.877792	+	0.479042i	$0.840984\pi$
$102$	3.82807e7	+	8.73732e6i	3.57173	+	0.815225i
$103$	−1.28925e7	+	1.61667e7i	−1.16254	+	1.45778i	−0.298456	+	0.954423i	$0.596472\pi$
$103$	−1.28925e7	+	1.61667e7i	−1.16254	+	1.45778i	−0.864081	+	0.503352i	$0.832100\pi$
$104$			7.99126e6i			0.696625i
$105$	−4.14712e6	−	3.30722e6i	−0.349610	−	0.278805i
$106$	−6.94446e6	−	1.44203e7i	−0.566328	−	1.17599i
$107$	8.48965e6	+	1.06457e7i	0.669957	+	0.840099i	0.994386	−	0.105811i	$-0.0337438\pi$
$107$	8.48965e6	+	1.06457e7i	0.669957	+	0.840099i	−0.324430	+	0.945910i	$0.605172\pi$
$108$	−1.62634e7	+	1.29696e7i	−1.24230	+	0.990705i
$109$	−4.07118e6	−	1.96057e6i	−0.301111	−	0.145008i	0.277227	−	0.960804i	$-0.410584\pi$
$109$	−4.07118e6	−	1.96057e6i	−0.301111	−	0.145008i	−0.578339	+	0.815797i	$0.696299\pi$
$110$	−1.96170e6	+	8.59476e6i	−0.140526	+	0.615686i
$111$	2.41801e6	+	1.05940e7i	0.167814	+	0.735240i
$112$	9.64389e6	−	4.64425e6i	0.648619	−	0.312358i
$113$	−5.14241e6	+	1.06783e7i	−0.335268	+	0.696192i	−0.998642	−	0.0520964i	$-0.983410\pi$
$113$	−5.14241e6	+	1.06783e7i	−0.335268	+	0.696192i	0.663374	+	0.748288i	$0.269124\pi$
$114$	4.50874e7	−	1.02909e7i	2.85029	−	0.650559i
$115$	−5.21475e6			−0.319736
$116$	−1.72486e7	−	2.94222e7i	−1.02601	−	1.75014i
$117$	2.14147e6			0.123612
$118$	5.09887e7	−	1.16378e7i	2.85684	−	0.652056i
$119$	9.68785e6	−	2.01170e7i	0.527003	−	1.09433i
$120$	−2.06144e7	+	9.92739e6i	−1.08902	+	0.524446i
$121$	−2.68573e6	−	1.17669e7i	−0.137820	−	0.603830i
$122$	−1.09649e7	+	4.80406e7i	−0.546698	+	2.39524i
$123$	−3.47477e7	−	1.67336e7i	−1.68368	−	0.810815i
$124$	786819.	−	627467.i	0.0370595	−	0.0295539i
$125$	1.32454e7	+	1.66092e7i	0.606570	+	0.760615i
$126$	−3.56740e6	−	7.40777e6i	−0.158875	−	0.329906i
$127$	−8.55497e6	−	6.82236e6i	−0.370600	−	0.295544i	0.420425	−	0.907327i	$-0.361881\pi$
$127$	−8.55497e6	−	6.82236e6i	−0.370600	−	0.295544i	−0.791025	+	0.611784i	$0.790452\pi$
$128$			4.00032e7i			1.68601i
$129$	−9.57030e6	+	1.20008e7i	−0.392520	+	0.492204i
$130$	−9.72701e6	−	2.22013e6i	−0.388309	−	0.0886291i
$131$	1.88785e7	+	4.30889e6i	0.733699	+	0.167462i	0.573016	−	0.819544i	$-0.305773\pi$
$131$	1.88785e7	+	4.30889e6i	0.733699	+	0.167462i	0.160683	+	0.987006i	$0.448630\pi$
$132$	−2.36712e7	+	2.96828e7i	−0.895802	+	1.12330i
$133$		−	2.62984e7i		−	0.969279i
$134$	2.71493e7	+	2.16509e7i	0.974747	+	0.777335i
$135$	−5.71395e6	−	1.18651e7i	−0.199879	−	0.415054i
$136$	−6.00498e7	−	7.53000e7i	−2.04703	−	2.56690i
$137$	−1.89187e7	+	1.50871e7i	−0.628591	+	0.501285i	−0.885188	−	0.465234i	$-0.845970\pi$
$137$	−1.89187e7	+	1.50871e7i	−0.628591	+	0.501285i	0.256597	+	0.966519i	$0.417399\pi$
$138$	−3.02072e7	−	1.45470e7i	−0.978440	−	0.471192i
$139$	5.77664e6	−	2.53091e7i	0.182441	−	0.799328i	−0.798022	−	0.602628i	$-0.794120\pi$
$139$	5.77664e6	−	2.53091e7i	0.182441	−	0.799328i	0.980464	−	0.196700i	$-0.0630225\pi$
$140$	5.70960e6	+	2.50154e7i	0.175856	+	0.770477i
$141$	3.06515e7	−	1.47610e7i	0.920840	−	0.443453i
$142$	1.95055e7	−	4.05036e7i	0.571674	−	1.18709i
$143$	−8.18432e6	+	1.86802e6i	−0.234049	+	0.0534201i
$144$	−1.23728e7			−0.345302
$145$	2.05898e7	−	6.50127e6i	0.560871	−	0.177097i
$146$	3.26883e7			0.869275
$147$	2.41941e7	−	5.52215e6i	0.628202	−	0.143383i
$148$	2.28067e7	−	4.73585e7i	0.578290	−	1.20083i
$149$	−4.26385e7	+	2.05336e7i	−1.05597	+	0.508527i	−0.879559	−	0.475790i	$-0.842162\pi$
$149$	−4.26385e7	+	2.05336e7i	−1.05597	+	0.508527i	−0.176408	+	0.984317i	$0.556448\pi$
$150$	1.20183e7	+	5.26554e7i	0.290752	+	1.27387i
$151$	1.10252e6	−	4.83046e6i	0.0260596	−	0.114175i	−0.960225	−	0.279226i	$-0.909922\pi$
$151$	1.10252e6	−	4.83046e6i	0.0260596	−	0.114175i	0.986285	+	0.165052i	$0.0527791\pi$
$152$	−1.02204e8	−	4.92188e7i	−2.36056	−	1.13679i
$153$	−2.01786e7	+	1.60919e7i	−0.455483	+	0.363235i
$154$	2.00958e7	+	2.51993e7i	0.443387	+	0.555989i
$155$	276440.	+	574033.i	0.00596265	+	0.0123816i
$156$	−3.35931e7	−	2.67896e7i	−0.708458	−	0.564976i
$157$			1.25273e7i			0.258350i	0.991622	+	0.129175i	$0.0412329\pi$
$157$			1.25273e7i			0.258350i	−0.991622	+	0.129175i	$0.958767\pi$
$158$	1.31661e7	−	1.65098e7i	0.265557	−	0.332997i
$159$	4.25434e7	+	9.71026e6i	0.839349	+	0.191576i
$160$	3.01161e6	+	687380.i	0.0581271	+	0.0132671i
$161$	−1.18871e7	+	1.49060e7i	−0.224485	+	0.281495i
$162$		−	1.14587e8i		−	2.11755i
$163$	3.50567e7	+	2.79568e7i	0.634037	+	0.505628i	0.886952	−	0.461861i	$-0.152818\pi$
$163$	3.50567e7	+	2.79568e7i	0.634037	+	0.505628i	−0.252915	+	0.967488i	$0.581389\pi$
$164$	8.09452e7	+	1.68084e8i	1.43297	+	2.97560i
$165$	−1.49860e7	−	1.87918e7i	−0.259712	−	0.325668i
$166$	−3.72766e7	+	2.97271e7i	−0.632497	+	0.504399i
$167$	−4.44681e6	−	2.14147e6i	−0.0738824	−	0.0355799i	0.396578	−	0.918001i	$-0.370198\pi$
$167$	−4.44681e6	−	2.14147e6i	−0.0738824	−	0.0355799i	−0.470460	+	0.882421i	$0.655912\pi$
$168$	−1.86143e7	+	8.15546e7i	−0.302876	+	1.32698i
$169$	1.18488e7	+	5.19128e7i	0.188829	+	0.827315i
$170$	1.08339e8	−	5.21731e7i	1.69127	−	0.814471i
$171$	−1.31895e7	+	2.73882e7i	−0.201716	+	0.418869i
$172$	7.23886e7	−	1.65222e7i	1.08473	−	0.247582i
$173$	9.20291e7			1.35134			0.675669	−	0.737205i	$-0.263855\pi$
$173$	9.20291e7			1.35134			0.675669	+	0.737205i	$0.263855\pi$
$174$	1.37405e8	+	1.97774e7i	1.97734	+	0.284608i
$175$	3.07127e7			0.433196
$176$	4.72866e7	−	1.07929e7i	0.653798	−	0.149225i
$177$	−6.18685e7	+	1.28471e8i	−0.838616	+	1.74140i
$178$	−1.75862e8	+	8.46906e7i	−2.33723	+	1.12555i
$179$	1.45926e7	+	6.39344e7i	0.190172	+	0.833199i	0.976522	+	0.215418i	$0.0691112\pi$
$179$	1.45926e7	+	6.39344e7i	0.190172	+	0.833199i	−0.786350	+	0.617782i	$0.788032\pi$
$180$	6.59980e6	−	2.89156e7i	0.0843484	−	0.369555i
$181$	821721.	+	395720.i	0.0103003	+	0.00496036i	0.439027	−	0.898474i	$-0.355323\pi$
$181$	821721.	+	395720.i	0.0103003	+	0.00496036i	−0.428727	+	0.903434i	$0.641038\pi$
$182$	−2.85190e7	+	2.27432e7i	−0.350659	+	0.279641i
$183$	−8.37645e7	−	1.05037e8i	−1.01037	−	1.26697i
$184$	3.56820e7	+	7.40945e7i	0.422267	+	0.876846i
$185$	2.60175e7	+	2.07483e7i	0.302110	+	0.240925i
$186$			4.09632e6i			0.0466766i
$187$	6.30821e7	−	7.91024e7i	0.705441	−	0.884595i
$188$	−1.60441e8	−	3.66196e7i	−1.76101	−	0.401940i
$189$	−4.69407e7	−	1.07139e7i	−0.505747	−	0.115433i
$190$	8.83036e7	−	1.10729e8i	0.933987	−	1.17118i
$191$		−	1.36582e8i		−	1.41833i	−0.705041	−	0.709166i	$-0.749072\pi$
$191$		−	1.36582e8i		−	1.41833i	0.705041	−	0.709166i	$-0.250928\pi$
$192$	−8.01444e7	−	6.39130e7i	−0.817182	−	0.651681i
$193$	−2.26072e7	−	4.69444e7i	−0.226359	−	0.470038i	0.756597	−	0.653881i	$-0.226860\pi$
$193$	−2.26072e7	−	4.69444e7i	−0.226359	−	0.470038i	−0.982956	+	0.183843i	$0.941146\pi$
$194$	−1.55700e8	−	1.95241e8i	−1.53102	−	1.91984i
$195$	2.12674e7	−	1.69602e7i	0.205397	−	0.163799i
$196$	−1.08155e8	−	5.20849e7i	−1.02601	−	0.494101i
$197$	−5.65302e6	+	2.47675e7i	−0.0526803	+	0.230808i	−0.994414	−	0.105553i	$-0.966339\pi$
$197$	−5.65302e6	+	2.47675e7i	−0.0526803	+	0.230808i	0.941733	+	0.336360i	$0.109196\pi$
$198$	−8.29032e6	−	3.63223e7i	−0.0759003	−	0.332541i
$199$	7.18097e7	−	3.45817e7i	0.645947	−	0.311072i	−0.0820740	−	0.996626i	$-0.526154\pi$
$199$	7.18097e7	−	3.45817e7i	0.645947	−	0.311072i	0.728021	+	0.685554i	$0.240440\pi$
$200$	5.74803e7	−	1.19359e8i	0.508059	−	1.05499i
$201$	−9.23024e7	+	2.10674e7i	−0.801728	+	0.182989i
$202$	−3.05477e8			−2.60765
$203$	2.83514e7	−	7.36741e7i	0.237869	−	0.618129i
$204$	5.17849e8			4.27069
$205$	−1.15148e8	+	2.62817e7i	−0.933505	+	0.213066i
$206$	−1.76651e8	+	3.66819e8i	−1.40793	+	2.92359i
$207$	1.98556e7	−	9.56194e6i	0.155592	−	0.0749290i
$208$	1.22147e7	+	5.35160e7i	0.0941153	+	0.412346i
$209$	2.65169e7	−	1.16178e8i	0.200914	−	0.880264i
$210$	−9.40973e7	−	4.53149e7i	−0.701148	−	0.337655i
$211$	4.21962e7	−	3.36504e7i	0.309232	−	0.246605i	−0.456560	−	0.889693i	$-0.650919\pi$
$211$	4.21962e7	−	3.36504e7i	0.309232	−	0.246605i	0.765792	+	0.643088i	$0.222347\pi$
$212$	−1.31611e8	−	1.65034e8i	−0.948671	−	1.18960i
$213$	5.31805e7	+	1.10430e8i	0.377072	+	0.782997i
$214$	2.09608e8	+	1.67157e8i	1.46204	+	1.16594i
$215$			4.70070e7i			0.322573i
$216$	−1.29490e8	+	1.62375e8i	−0.874272	+	1.09630i
$217$	2.27098e6	+	518337.i	0.0150871	+	0.00344352i
$218$	−8.67394e7	−	1.97977e7i	−0.567047	−	0.129425i
$219$	−5.55670e7	+	6.96788e7i	−0.357489	+	0.448277i
$220$			1.16267e8i			0.736170i
$221$	8.95232e7	+	7.13924e7i	0.557908	+	0.444917i
$222$	9.28312e7	+	1.92766e8i	0.569454	+	1.18248i
$223$	−2.64132e7	−	3.31211e7i	−0.159497	−	0.200003i	0.695661	−	0.718370i	$-0.255112\pi$
$223$	−2.64132e7	−	3.31211e7i	−0.159497	−	0.200003i	−0.855158	+	0.518367i	$0.826540\pi$
$224$	8.82985e6	−	7.04157e6i	0.0524911	−	0.0418602i
$225$	−3.19854e7	−	1.54034e7i	−0.187203	−	0.0901523i
$226$	−5.19276e7	+	2.27510e8i	−0.299240	+	1.31105i
$227$	5.79925e7	+	2.54082e8i	0.329065	+	1.44173i	0.820916	+	0.571048i	$0.193463\pi$
$227$	5.79925e7	+	2.54082e8i	0.329065	+	1.44173i	−0.491851	+	0.870679i	$0.663680\pi$
$228$	5.49527e8	−	2.64638e8i	3.07056	−	1.47870i
$229$	6.09399e7	−	1.26543e8i	0.335334	−	0.696329i	−0.663312	−	0.748343i	$-0.730850\pi$
$229$	6.09399e7	−	1.26543e8i	0.335334	−	0.696329i	0.998646	+	0.0520143i	$0.0165641\pi$
$230$	−1.00101e8	+	2.28475e7i	−0.542491	+	0.123820i
$231$	−8.78761e7			−0.469060
$232$	−2.33260e8	−	2.48067e8i	−1.22640	−	1.30425i
$233$	−2.14944e8			−1.11322			−0.556608	−	0.830775i	$-0.687897\pi$
$233$	−2.14944e8			−1.11322			−0.556608	+	0.830775i	$0.687897\pi$
$234$	4.11073e7	−	9.38247e6i	0.209731	−	0.0478698i
$235$	4.52044e7	−	9.38680e7i	0.227218	−	0.471824i
$236$	6.21452e8	−	2.99275e8i	3.07762	−	1.48210i
$237$	1.28113e7	+	5.61300e7i	0.0625135	+	0.273890i
$238$	9.78270e7	−	4.28608e8i	0.470370	−	2.06082i
$239$	2.94655e8	+	1.41898e8i	1.39611	+	0.672333i	0.972369	−	0.233448i	$-0.0750010\pi$
$239$	2.94655e8	+	1.41898e8i	1.39611	+	0.672333i	0.423745	+	0.905782i	$0.360715\pi$
$240$	−1.22877e8	+	9.79911e7i	−0.573761	+	0.457559i
$241$	−2.65621e8	−	3.33078e8i	−1.22237	−	1.53280i	−0.765746	−	0.643143i	$-0.777630\pi$
$241$	−2.65621e8	−	3.33078e8i	−1.22237	−	1.53280i	−0.456623	−	0.889660i	$-0.650941\pi$
$242$	−1.03109e8	−	2.14109e8i	−0.467676	−	0.971138i
$243$	1.07284e8	+	8.55561e7i	0.479637	+	0.382498i
$244$			6.49878e8i			2.86396i
$245$	4.73841e7	−	5.94178e7i	0.205850	−	0.258128i
$246$	−7.40326e8	−	1.68975e8i	−3.17066	−	0.723683i
$247$	1.31483e8	+	3.00102e7i	0.555177	+	0.126715i
$248$	6.26467e6	−	7.85565e6i	0.0260806	−	0.0327040i
$249$		−	1.29992e8i		−	0.533606i
$250$	3.27027e8	+	2.60795e8i	1.32371	+	1.05563i
$251$	7.39045e7	+	1.53464e8i	0.294994	+	0.612561i	0.994809	−	0.101763i	$-0.0324485\pi$
$251$	7.39045e7	+	1.53464e8i	0.294994	+	0.612561i	−0.699815	+	0.714324i	$0.746734\pi$
$252$	−6.76089e7	−	8.47788e7i	−0.266135	−	0.333722i
$253$	−6.75435e7	+	5.38642e7i	−0.262218	+	0.209112i
$254$	−1.94110e8	−	9.34787e7i	−0.743243	−	0.357927i
$255$	−7.29524e7	+	3.19625e8i	−0.275517	+	1.20712i
$256$	1.20877e8	+	5.29599e8i	0.450304	+	1.97291i
$257$	−3.28011e7	+	1.57962e7i	−0.120538	+	0.0580479i	−0.493181	−	0.869927i	$-0.664166\pi$
$257$	−3.28011e7	+	1.57962e7i	−0.120538	+	0.0580479i	0.372643	+	0.927975i	$0.378452\pi$
$258$	−1.31130e8	+	2.72295e8i	−0.475373	+	0.987122i
$259$	1.18615e8	−	2.70731e7i	0.424220	−	0.0968254i
$260$	−1.31584e8			−0.464298
$261$	−6.64762e7	+	6.25082e7i	−0.231432	+	0.217618i
$262$	3.81267e8			1.30971
$263$	2.97659e8	−	6.79388e7i	1.00896	−	0.230289i	0.314067	−	0.949401i	$-0.398308\pi$
$263$	2.97659e8	−	6.79388e7i	1.00896	−	0.230289i	0.694894	+	0.719112i	$0.255451\pi$
$264$	−1.64464e8	+	3.41514e8i	−0.550121	+	1.14234i
$265$	1.20403e8	−	5.79829e7i	0.397444	−	0.191399i
$266$	−1.15222e8	−	5.04819e8i	−0.375361	−	1.64456i
$267$	1.18421e8	−	5.18835e8i	0.380748	−	1.66817i
$268$	4.12621e8	+	1.98708e8i	1.30942	+	0.630585i
$269$	1.75505e8	−	1.39960e8i	0.549738	−	0.438402i	−0.308818	−	0.951121i	$-0.599933\pi$
$269$	1.75505e8	−	1.39960e8i	0.549738	−	0.438402i	0.858556	+	0.512719i	$0.171362\pi$
$270$	−1.61669e8	−	2.02726e8i	−0.499865	−	0.626811i
$271$	−9.33100e7	−	1.93760e8i	−0.284797	−	0.591387i	0.708666	−	0.705545i	$-0.249298\pi$
$271$	−9.33100e7	−	1.93760e8i	−0.284797	−	0.591387i	−0.993463	+	0.114157i	$0.963583\pi$
$272$	−5.17238e8	−	4.12484e8i	−1.55847	−	1.24284i
$273$		−	9.94526e7i		−	0.295833i
$274$	−2.97057e8	+	3.72498e8i	−0.872396	+	1.09395i
$275$	1.35679e8	+	3.09678e7i	0.393413	+	0.0897938i
$276$	−4.31092e8	−	9.83940e7i	−1.23421	−	0.281700i
$277$	−3.47841e8	+	4.36179e8i	−0.983335	+	1.23306i	−0.0108880	+	0.999941i	$0.503466\pi$
$277$	−3.47841e8	+	4.36179e8i	−0.983335	+	1.23306i	−0.972447	+	0.233123i	$0.925106\pi$
$278$		−	5.11138e8i		−	1.42686i
$279$	−2.10513e6	−	1.67879e6i	−0.00580316	−	0.00462786i
$280$	1.11152e8	+	2.30809e8i	0.302596	+	0.628346i
$281$	2.06578e8	+	2.59040e8i	0.555407	+	0.696458i	0.977701	−	0.210000i	$-0.0673465\pi$
$281$	2.06578e8	+	2.59040e8i	0.555407	+	0.696458i	−0.422294	+	0.906459i	$0.638775\pi$
$282$	5.23707e8	−	4.17643e8i	1.39065	−	1.10900i
$283$	−7.22496e7	−	3.47936e7i	−0.189489	−	0.0912529i	0.336734	−	0.941600i	$-0.390678\pi$
$283$	−7.22496e7	−	3.47936e7i	−0.189489	−	0.0912529i	−0.526222	+	0.850347i	$0.676392\pi$
$284$	1.31932e8	−	5.78033e8i	0.341772	−	1.49740i
$285$	8.59241e7	+	3.76458e8i	0.219866	+	0.963296i
$286$	−1.48920e8	+	7.17162e7i	−0.376420	+	0.181274i
$287$	−1.87357e8	+	3.89051e8i	−0.467825	+	0.971449i
$288$	−1.27273e7	+	2.90493e6i	−0.0313952	+	0.00716576i
$289$	−9.69692e8			−2.36315
$290$	3.66753e8	−	2.15007e8i	0.883040	−	0.517679i
$291$	6.80852e8			1.61967
$292$	4.20302e8	−	9.59311e7i	0.987919	−	0.225486i
$293$	−2.71806e8	+	5.64411e8i	−0.631280	+	1.31087i	0.302544	+	0.953135i	$0.402164\pi$
$293$	−2.71806e8	+	5.64411e8i	−0.631280	+	1.31087i	−0.933825	+	0.357731i	$0.883550\pi$
$294$	4.40231e8	−	2.12004e8i	1.01034	−	0.486552i
$295$	9.71702e7	+	4.25731e8i	0.220372	+	0.965512i
$296$	1.16779e8	−	5.11644e8i	0.261725	−	1.14669i
$297$	−1.96567e8	−	9.46615e7i	−0.435374	−	0.209665i
$298$	−7.28517e8	+	5.80973e8i	−1.59471	+	1.27174i
$299$	−6.09601e7	−	7.64416e7i	−0.131885	−	0.165379i
$300$	3.09058e8	+	6.41766e8i	0.660870	+	1.37231i
$301$	1.34366e8	+	1.07153e8i	0.283993	+	0.226477i
$302$		−	9.75552e7i		−	0.203810i
$303$	5.19282e8	−	6.51159e8i	1.07239	−	1.34474i
$304$	−7.59671e8	−	1.73390e8i	−1.55084	−	0.353970i
$305$	−4.01116e8	−	9.15520e7i	−0.809506	−	0.184764i
$306$	−3.16842e8	+	3.97307e8i	−0.632146	+	0.792685i
$307$			1.54515e8i			0.304780i	0.988320	+	0.152390i	$0.0486970\pi$
$307$			1.54515e8i			0.304780i	−0.988320	+	0.152390i	$0.951303\pi$
$308$	3.32342e8	+	2.65034e8i	0.648123	+	0.516861i
$309$	−4.81626e8	−	1.00011e9i	−0.928657	−	1.92838i
$310$	7.82150e6	+	9.80785e6i	0.0149116	+	0.0186986i
$311$	−3.66061e8	+	2.91924e8i	−0.690069	+	0.550312i	−0.904524	−	0.426422i	$-0.859774\pi$
$311$	−3.66061e8	+	2.91924e8i	−0.690069	+	0.550312i	0.214455	+	0.976734i	$0.431202\pi$
$312$	−3.86504e8	−	1.86131e8i	−0.720465	−	0.346958i
$313$	1.88639e8	−	8.26480e8i	0.347717	−	1.52345i	−0.434634	−	0.900607i	$-0.643122\pi$
$313$	1.88639e8	−	8.26480e8i	0.347717	−	1.52345i	0.782350	−	0.622838i	$-0.214021\pi$
$314$	5.48861e7	+	2.40472e8i	0.100048	+	0.438339i
$315$	6.18513e7	−	2.97860e7i	0.111497	−	0.0536940i
$316$	1.20836e8	−	2.50919e8i	0.215423	−	0.447331i
$317$	5.98991e8	−	1.36716e8i	1.05612	−	0.241052i	0.341006	−	0.940061i	$-0.389232\pi$
$317$	5.98991e8	−	1.36716e8i	1.05612	−	0.241052i	0.715113	+	0.699009i	$0.246375\pi$
$318$	8.59200e8			1.49830
$319$	1.99534e8	−	2.96883e8i	0.344151	−	0.512056i
$320$	−3.13925e8			−0.535552
$321$	−7.12626e8	+	1.62652e8i	−1.20253	+	0.274469i
$322$	−1.62875e8	+	3.38214e8i	−0.271869	+	0.564542i
$323$	−1.46445e9	+	7.05241e8i	−2.41805	+	1.16447i
$324$	−3.36282e8	−	1.47335e9i	−0.549282	−	2.40656i
$325$	−3.50475e7	+	1.53553e8i	−0.0566324	+	0.248123i
$326$	7.95430e8	+	3.83059e8i	1.27157	+	0.612356i
$327$	1.89650e8	−	1.51241e8i	0.299940	−	0.239194i
$328$	1.16133e9	+	1.45626e9i	1.81717	+	2.27866i
$329$	−1.65271e8	−	3.43188e8i	−0.255864	−	0.531308i
$330$	−3.70001e8	−	2.95066e8i	−0.566767	−	0.451982i
$331$		−	7.15114e8i		−	1.08387i	−0.840420	−	0.541935i	$-0.817692\pi$
$331$		−	7.15114e8i		−	1.08387i	0.840420	−	0.541935i	$-0.182308\pi$
$332$	−3.92057e8	+	4.91624e8i	−0.587984	+	0.737309i
$333$	−1.37109e8	−	3.12942e7i	−0.203475	−	0.0464417i
$334$	−9.47425e7	−	2.16244e7i	−0.139134	−	0.0317564i
$335$	−1.80774e8	+	2.26684e8i	−0.262712	+	0.329430i
$336$			5.74608e8i			0.826388i
$337$	−7.91829e7	−	6.31463e7i	−0.112701	−	0.0898759i	0.565518	−	0.824736i	$-0.308676\pi$
$337$	−7.91829e7	−	6.31463e7i	−0.112701	−	0.0898759i	−0.678219	+	0.734860i	$0.737248\pi$
$338$	4.54893e8	+	9.44595e8i	0.640768	+	1.33057i
$339$	−3.96691e8	−	4.97434e8i	−0.553035	−	0.693484i
$340$	1.23989e9	−	9.88779e8i	1.71083	−	1.36434i
$341$	9.50985e6	+	4.57970e6i	0.0129877	+	0.00625456i
$342$	−1.33186e8	+	5.83527e8i	−0.180040	+	0.788805i
$343$	−1.71974e8	−	7.53467e8i	−0.230109	−	1.00817i
$344$	6.67905e8	−	3.21646e8i	0.884627	−	0.426014i
$345$	1.21461e8	−	2.52216e8i	0.159246	−	0.330678i
$346$	1.76657e9	−	4.03209e8i	2.29280	−	0.523316i
$347$	8.86672e8			1.13923			0.569613	−	0.821913i	$-0.307093\pi$
$347$	8.86672e8			1.13923			0.569613	+	0.821913i	$0.307093\pi$
$348$	1.82478e9	−	1.48951e8i	2.32104	−	0.189459i
$349$	−1.10186e9			−1.38751			−0.693757	−	0.720209i	$-0.744046\pi$
$349$	−1.10186e9			−1.38751			−0.693757	+	0.720209i	$0.744046\pi$
$350$	5.89554e8	−	1.34562e8i	0.734997	−	0.167758i
$351$	1.07132e8	−	2.22462e8i	0.132234	−	0.274587i
$352$	4.61076e7	−	2.22043e7i	0.0563473	−	0.0271354i
$353$	1.63900e8	+	7.18094e8i	0.198321	+	0.868901i	0.971936	+	0.235245i	$0.0755892\pi$
$353$	1.63900e8	+	7.18094e8i	0.198321	+	0.868901i	−0.773615	+	0.633656i	$0.781554\pi$
$354$	−6.24742e8	+	2.73717e9i	−0.748496	+	3.27938i
$355$	3.38186e8	+	1.62862e8i	0.401195	+	0.193205i
$356$	−2.01266e9	+	1.60505e9i	−2.36427	+	1.88544i
$357$	7.47330e8	+	9.37122e8i	0.869308	+	1.09008i
$358$	5.60234e8	+	1.16334e9i	0.645325	+	1.34003i
$359$	−2.96398e8	−	2.36370e8i	−0.338100	−	0.269626i	0.439690	−	0.898149i	$-0.355088\pi$
$359$	−2.96398e8	−	2.36370e8i	−0.338100	−	0.269626i	−0.777791	+	0.628523i	$0.783660\pi$
$360$		−	2.96120e8i		−	0.334509i
$361$	−6.36309e8	+	7.97906e8i	−0.711857	+	0.892641i
$362$	1.75074e7	+	3.99594e6i	0.0193973	+	0.00442731i
$363$	6.31673e8	+	1.44175e8i	0.693137	+	0.158204i
$364$	−2.99949e8	+	3.76124e8i	−0.325981	+	0.408767i
$365$			2.72931e8i			0.293784i
$366$	−2.06813e9	−	1.64928e9i	−2.20493	−	1.75837i
$367$	−2.46570e8	−	5.12009e8i	−0.260381	−	0.540687i	0.729262	−	0.684234i	$-0.239863\pi$
$367$	−2.46570e8	−	5.12009e8i	−0.260381	−	0.540687i	−0.989643	+	0.143547i	$0.954149\pi$
$368$	3.52209e8	+	4.41657e8i	0.368412	+	0.461974i
$369$	3.90243e8	−	3.11208e8i	0.404336	−	0.322447i
$370$	5.90333e8	+	2.84289e8i	0.605886	+	0.291779i
$371$	1.08721e8	−	4.76336e8i	0.110536	−	0.484289i
$372$	1.20216e7	+	5.26700e7i	0.0121077	+	0.0530473i
$373$	1.73510e9	−	8.35579e8i	1.73118	−	0.833694i	0.745201	−	0.666840i	$-0.232353\pi$
$373$	1.73510e9	−	8.35579e8i	1.73118	−	0.833694i	0.985982	−	0.166854i	$-0.0533609\pi$
$374$	8.64339e8	−	1.79482e9i	0.854345	−	1.77407i
$375$	−1.11183e9	+	2.53768e8i	−1.08875	+	0.248500i
$376$	−1.64305e9			−1.59402
$377$	3.35993e8	+	2.25820e8i	0.322950	+	0.217054i
$378$	−9.48006e8			−0.902797
$379$	−4.77893e8	+	1.09076e8i	−0.450914	+	0.102918i	−0.441946	−	0.897042i	$-0.645712\pi$
$379$	−4.77893e8	+	1.09076e8i	−0.450914	+	0.102918i	−0.00896789	+	0.999960i	$0.502855\pi$
$380$	8.10436e8	−	1.68289e9i	0.757663	−	1.57330i
$381$	5.29229e8	−	2.54863e8i	0.490237	−	0.236086i
$382$	−5.98411e8	−	2.62181e9i	−0.549260	−	2.40646i
$383$	−4.02517e8	+	1.76354e9i	−0.366091	+	1.60395i	0.371321	+	0.928505i	$0.378905\pi$
$383$	−4.02517e8	+	1.76354e9i	−0.366091	+	1.60395i	−0.737411	+	0.675444i	$0.763952\pi$
$384$	−1.93479e9	−	9.31744e8i	−1.74371	−	0.839725i
$385$	−2.10402e8	+	1.67790e8i	−0.187905	+	0.149849i
$386$	−6.39643e8	−	8.02087e8i	−0.566085	−	0.709849i
$387$	−8.61936e7	−	1.78983e8i	−0.0755939	−	0.156972i
$388$	−2.57494e9	−	2.05345e9i	−2.23798	−	1.78473i
$389$			6.62243e8i			0.570419i	0.958465	+	0.285209i	$0.0920631\pi$
$389$			6.62243e8i			0.570419i	−0.958465	+	0.285209i	$0.907937\pi$
$390$	3.33938e8	−	4.18744e8i	0.285062	−	0.357456i
$391$	1.14883e9	+	2.62213e8i	0.971934	+	0.221838i
$392$	−1.16847e9	−	2.66696e8i	−0.979755	−	0.223623i
$393$	−6.48117e8	+	8.12713e8i	−0.538616	+	0.675403i
$394$			5.00200e8i			0.412009i
$395$	1.37848e8	+	1.09930e8i	0.112541	+	0.0897487i
$396$	−2.13192e8	−	4.42697e8i	−0.172519	−	0.358240i
$397$	5.20789e8	+	6.53049e8i	0.417730	+	0.523817i	0.945523	−	0.325557i	$-0.105552\pi$
$397$	5.20789e8	+	6.53049e8i	0.417730	+	0.523817i	−0.527793	+	0.849373i	$0.676980\pi$
$398$	1.22693e9	−	9.78445e8i	0.975505	−	0.777939i
$399$	1.27194e9	+	6.12536e8i	1.00245	+	0.482755i
$400$	2.02494e8	−	8.87183e8i	0.158198	−	0.693112i
$401$	7.62258e7	+	3.33967e8i	0.0590333	+	0.258642i	0.995830	−	0.0912338i	$-0.0290811\pi$
$401$	7.62258e7	+	3.33967e8i	0.0590333	+	0.258642i	−0.936796	+	0.349875i	$0.886224\pi$
$402$	−1.67952e9	+	8.08813e8i	−1.28942	+	0.620950i
$403$	−5.18302e6	+	1.07627e7i	−0.00394471	+	0.00819128i
$404$	−3.92778e9	+	8.96491e8i	−2.96355	+	0.676412i
$405$	9.56747e8			0.715656
$406$	2.21437e8	−	1.53845e9i	0.164214	−	1.14089i
$407$	5.51303e8			0.405331
$408$	5.04061e9	−	1.15049e9i	3.67428	−	0.838631i
$409$	6.45866e8	−	1.34115e9i	0.466778	−	0.969275i	−0.526131	−	0.850403i	$-0.676358\pi$
$409$	6.45866e8	−	1.34115e9i	0.466778	−	0.969275i	0.992910	−	0.118872i	$-0.0379277\pi$
$410$	−2.09520e9	+	1.00900e9i	−1.50135	+	0.723014i
$411$	−2.89053e8	−	1.26642e9i	−0.205367	−	0.899771i
$412$	−1.19484e9	+	5.23493e9i	−0.841722	+	3.68783i
$413$	1.43842e9	+	6.92708e8i	1.00476	+	0.483866i
$414$	3.39250e8	−	2.70543e8i	0.234973	−	0.187385i
$415$	−2.48207e8	−	3.11242e8i	−0.170469	−	0.213761i
$416$	2.51294e7	+	5.21817e7i	0.0171142	+	0.0355379i
$417$	1.08955e9	+	8.68885e8i	0.735817	+	0.586795i
$418$		−	2.34631e9i		−	1.57134i
$419$	−1.99340e8	+	2.49964e8i	−0.132387	+	0.166008i	−0.843606	−	0.536962i	$-0.819572\pi$
$419$	−1.99340e8	+	2.49964e8i	−0.132387	+	0.166008i	0.711220	+	0.702970i	$0.248143\pi$
$420$	−1.34288e9	−	3.06503e8i	−0.884431	−	0.201866i
$421$	7.01803e8	+	1.60182e8i	0.458383	+	0.104623i	0.445476	−	0.895294i	$-0.353034\pi$
$421$	7.01803e8	+	1.60182e8i	0.458383	+	0.104623i	0.0129065	+	0.999917i	$0.495892\pi$
$422$	6.62558e8	−	8.30821e8i	0.429171	−	0.538163i
$423$			4.40298e8i			0.282850i
$424$	−1.64771e9	−	1.31401e9i	−1.04979	−	0.837178i
$425$	−8.23618e8	−	1.71026e9i	−0.520432	−	1.08069i
$426$	1.50467e9	+	1.88680e9i	0.942993	+	1.18248i
$427$	−1.17605e9	+	9.37866e8i	−0.731016	+	0.582966i
$428$	3.18567e9	+	1.53414e9i	1.96403	+	0.945826i
$429$	1.00279e8	−	4.39351e8i	0.0613210	−	0.268665i
$430$	2.05953e8	+	9.02337e8i	0.124919	+	0.547305i
$431$	−1.98288e9	+	9.54907e8i	−1.19296	+	0.574501i	−0.921662	−	0.387994i	$-0.873168\pi$
$431$	−1.98288e9	+	9.54907e8i	−1.19296	+	0.574501i	−0.271301	+	0.962495i	$0.587454\pi$
$432$	−6.18977e8	+	1.28532e9i	−0.369387	+	0.767039i
$433$	2.50735e9	−	5.72287e8i	1.48425	−	0.338771i	0.597820	−	0.801630i	$-0.296034\pi$
$433$	2.50735e9	−	5.72287e8i	1.48425	−	0.338771i	0.886432	+	0.462859i	$0.153176\pi$
$434$	4.58643e7			0.0269315
$435$	−1.65132e8	+	1.14727e9i	−0.0961876	+	0.668270i
$436$	−1.17338e9			−0.678012
$437$	1.35310e9	−	3.08837e8i	0.775614	−	0.177029i
$438$	−7.61368e8	+	1.58100e9i	−0.432947	+	0.899025i
$439$	5.85275e8	−	2.81854e8i	0.330167	−	0.159000i	−0.261454	−	0.965216i	$-0.584202\pi$
$439$	5.85275e8	−	2.81854e8i	0.330167	−	0.159000i	0.591622	+	0.806216i	$0.298488\pi$
$440$	2.58307e8	+	1.13172e9i	0.144561	+	0.633364i
$441$	−7.14684e7	+	3.13123e8i	−0.0396806	+	0.173852i
$442$	2.03126e9	+	9.78205e8i	1.11889	+	0.538830i
$443$	2.42117e9	−	1.93082e9i	1.32316	−	1.05518i	0.329334	−	0.944214i	$-0.393176\pi$
$443$	2.42117e9	−	1.93082e9i	1.32316	−	1.05518i	0.993824	−	0.110969i	$-0.0353955\pi$
$444$	1.75933e9	+	2.20613e9i	0.953907	+	1.19616i
$445$	−7.07125e8	−	1.46836e9i	−0.380396	−	0.789901i
$446$	−6.52137e8	−	5.20062e8i	−0.348070	−	0.277577i
$447$		−	2.54051e9i		−	1.34538i
$448$	−7.15599e8	+	8.97333e8i	−0.376008	+	0.471499i
$449$	−7.54188e8	−	1.72139e8i	−0.393204	−	0.0897462i	0.0213476	−	0.999772i	$-0.493204\pi$
$449$	−7.54188e8	−	1.72139e8i	−0.393204	−	0.0897462i	−0.414551	+	0.910026i	$0.636061\pi$
$450$	−6.81473e8	−	1.55542e8i	−0.352537	−	0.0804643i
$451$	−1.21997e9	+	1.52979e9i	−0.626226	+	0.785263i
$452$			3.07768e9i			1.56762i
$453$	2.07950e8	+	1.65834e8i	0.105103	+	0.0838168i
$454$	2.22643e9	+	4.62322e9i	1.11664	+	2.31873i
$455$	−1.89894e8	−	2.38120e8i	−0.0945088	−	0.118510i
$456$	4.76101e9	−	3.79678e9i	2.35138	−	1.87516i
$457$	−1.25310e9	−	6.03461e8i	−0.614156	−	0.295762i	0.100827	−	0.994904i	$-0.467851\pi$
$457$	−1.25310e9	−	6.03461e8i	−0.614156	−	0.295762i	−0.714983	+	0.699142i	$0.753565\pi$
$458$	6.15366e8	−	2.69609e9i	0.299298	−	1.31131i
$459$	6.62191e8	+	2.90125e9i	0.319623	+	1.40036i
$460$	−1.22004e9	+	5.87540e8i	−0.584415	+	0.281439i
$461$	−6.90940e8	+	1.43475e9i	−0.328463	+	0.682061i	−0.998164	−	0.0605700i	$-0.980708\pi$
$461$	−6.90940e8	+	1.43475e9i	−0.328463	+	0.682061i	0.669701	+	0.742631i	$0.266422\pi$
$462$	−1.68685e9	+	3.85013e8i	−0.795848	+	0.181647i
$463$	−1.91604e9			−0.897162			−0.448581	−	0.893742i	$-0.648070\pi$
$463$	−1.91604e9			−0.897162			−0.448581	+	0.893742i	$0.648070\pi$
$464$	−1.94127e9	−	1.30472e9i	−0.902137	−	0.606323i
$465$	−3.42023e7			−0.0157750
$466$	−4.12602e9	+	9.41737e8i	−1.88878	+	0.431101i
$467$	1.71770e9	−	3.56683e9i	0.780436	−	1.62059i	−0.00369340	−	0.999993i	$-0.501176\pi$
$467$	1.71770e9	−	3.56683e9i	0.780436	−	1.62059i	0.784129	−	0.620598i	$-0.213110\pi$
$468$	5.01017e8	−	2.41277e8i	0.225939	−	0.108807i
$469$	2.35881e8	+	1.03346e9i	0.105581	+	0.462582i
$470$	4.56470e8	−	1.99993e9i	0.202801	−	0.888529i
$471$	−6.05894e8	−	2.91783e8i	−0.267192	−	0.128673i
$472$	5.38416e9	−	4.29372e9i	2.35679	−	1.87948i
$473$	4.85544e8	+	6.08853e8i	0.210967	+	0.264545i
$474$	4.91847e8	+	1.02133e9i	0.212132	+	0.440496i
$475$	−1.74800e9	−	1.39398e9i	−0.748365	−	0.596801i
$476$		−	5.79808e9i		−	2.46411i
$477$	−3.52124e8	+	4.41549e8i	−0.148553	+	0.186279i
$478$	6.27784e9	+	1.43288e9i	2.62913	+	0.600083i
$479$	−2.93370e9	−	6.69599e8i	−1.21967	−	0.278382i	−0.436221	−	0.899839i	$-0.643684\pi$
$479$	−2.93370e9	−	6.69599e8i	−1.21967	−	0.278382i	−0.783448	+	0.621458i	$0.786541\pi$
$480$	−1.03391e8	+	1.29649e8i	−0.0426717	+	0.0535086i
$481$			6.23930e8i			0.255640i
$482$	−6.55813e9	−	5.22993e9i	−2.66757	−	2.12731i
$483$	−4.44069e8	−	9.22118e8i	−0.179323	−	0.372367i
$484$	−1.95412e9	−	2.45039e9i	−0.783415	−	0.982372i
$485$	1.63017e9	−	1.30002e9i	0.648838	−	0.517431i
$486$	2.43425e9	+	1.17227e9i	0.961918	+	0.463235i
$487$	−4.77278e8	+	2.09109e9i	−0.187249	+	0.820392i	0.790810	+	0.612062i	$0.209660\pi$
$487$	−4.77278e8	+	2.09109e9i	−0.187249	+	0.820392i	−0.978059	+	0.208330i	$0.933197\pi$
$488$	1.44381e9	+	6.32575e9i	0.562394	+	2.46401i
$489$	−2.16869e9	+	1.04438e9i	−0.838718	+	0.403905i
$490$	6.49249e8	−	1.34818e9i	0.249301	−	0.517680i
$491$	−6.17296e8	+	1.40894e8i	−0.235347	+	0.0537163i	−0.338567	−	0.940942i	$-0.609942\pi$
$491$	−6.17296e8	+	1.40894e8i	−0.235347	+	0.0537163i	0.103221	+	0.994658i	$0.467085\pi$
$492$	−1.00149e10			−3.79113
$493$	−4.86290e9	+	3.96942e8i	−1.82781	+	0.149198i
$494$	2.65541e9			0.991032
$495$	3.03273e8	−	6.92202e7i	0.112387	−	0.0256516i
$496$	2.99459e7	−	6.21834e7i	0.0110193	−	0.0228817i
$497$	1.23643e9	−	5.95433e8i	0.451775	−	0.217563i
$498$	−5.69538e8	−	2.49531e9i	−0.206643	−	0.905361i
$499$	3.76671e8	−	1.65030e9i	0.135710	−	0.594582i	−0.860640	−	0.509214i	$-0.829936\pi$
$499$	3.76671e8	−	1.65030e9i	0.135710	−	0.594582i	0.996349	−	0.0853683i	$-0.0272067\pi$
$500$	4.97023e9	+	2.39354e9i	1.77820	+	0.856338i
$501$	2.07148e8	−	1.65195e8i	0.0735950	−	0.0586901i
$502$	2.09103e9	+	2.62207e9i	0.737730	+	0.925085i
$503$	2.00665e9	+	4.16685e9i	0.703046	+	1.45989i	0.879657	+	0.475609i	$0.157772\pi$
$503$	2.00665e9	+	4.16685e9i	0.703046	+	1.45989i	−0.176611	+	0.984281i	$0.556513\pi$
$504$	−8.46437e8	−	6.75011e8i	−0.294502	−	0.234857i
$505$		−	2.55059e9i		−	0.881293i
$506$	−1.06056e9	+	1.32990e9i	−0.363921	+	0.456343i
$507$	−2.78678e9	−	6.36065e8i	−0.949676	−	0.216757i
$508$	−2.77018e9	−	6.32276e8i	−0.937530	−	0.213985i
$509$	3.46249e9	−	4.34182e9i	1.16379	−	1.45935i	0.301124	−	0.953585i	$-0.402638\pi$
$509$	3.46249e9	−	4.34182e9i	1.16379	−	1.45935i	0.862670	−	0.505767i	$-0.168790\pi$
$510$			6.45509e9i			2.15480i
$511$	7.80155e8	+	6.22153e8i	0.258647	+	0.206264i
$512$	2.41902e9	+	5.02315e9i	0.796517	+	1.65398i
$513$	2.18533e9	+	2.74032e9i	0.714671	+	0.896169i
$514$	−5.60436e8	+	4.46933e8i	−0.182035	+	0.145168i
$515$	−3.06276e9	−	1.47495e9i	−0.988070	−	0.475829i
$516$	−8.86946e8	+	3.88597e9i	−0.284200	+	1.24516i
$517$	−3.84075e8	−	1.68274e9i	−0.122236	−	0.535550i
$518$	2.15830e9	−	1.03938e9i	0.682271	−	0.328565i
$519$	−2.14352e9	+	4.45107e9i	−0.673042	+	1.39759i
$520$	−1.28081e9	+	2.92335e8i	−0.399458	+	0.0911738i
$521$	−8.73492e8			−0.270600			−0.135300	−	0.990805i	$-0.543200\pi$
$521$	−8.73492e8			−0.270600			−0.135300	+	0.990805i	$0.543200\pi$
$522$	−1.00220e9	+	1.49115e9i	−0.308394	+	0.458854i
$523$	2.50895e9			0.766896			0.383448	−	0.923562i	$-0.374737\pi$
$523$	2.50895e9			0.766896			0.383448	+	0.923562i	$0.374737\pi$
$524$	4.90228e9	−	1.11891e9i	1.48846	−	0.339732i
$525$	−7.15352e8	+	1.48544e9i	−0.215756	+	0.448021i
$526$	5.41615e9	−	2.60828e9i	1.62271	−	0.781455i
$527$	−3.20366e7	−	1.40362e8i	−0.00953476	−	0.0417745i
$528$	−5.79382e8	+	2.53844e9i	−0.171296	+	0.750495i
$529$	2.16110e9	+	1.04073e9i	0.634718	+	0.305664i
$530$	2.05719e9	−	1.64055e9i	0.600217	−	0.478657i
$531$	−1.15062e9	−	1.44283e9i	−0.333503	−	0.418200i
$532$	−2.96301e9	−	6.15275e9i	−0.853184	−	1.77165i
$533$	−1.73133e9	−	1.38069e9i	−0.495260	−	0.394957i
$534$		−	1.04783e10i		−	2.97780i
$535$	−1.39568e9	+	1.75012e9i	−0.394046	+	0.494118i
$536$	4.45781e9	+	1.01747e9i	1.25039	+	0.285393i
$537$	−3.43213e9	−	7.83360e8i	−0.956430	−	0.218299i
$538$	2.75575e9	−	3.45560e9i	0.762959	−	0.956721i
$539$		−	1.25904e9i		−	0.346322i
$540$	−2.67366e9	−	2.13217e9i	−0.730682	−	0.582699i
$541$	−7.82316e8	−	1.62450e9i	−0.212418	−	0.441091i	0.767349	−	0.641229i	$-0.221575\pi$
$541$	−7.82316e8	−	1.62450e9i	−0.212418	−	0.441091i	−0.979768	+	0.200138i	$0.935861\pi$
$542$	−2.64009e9	−	3.31056e9i	−0.712230	−	0.893109i
$543$	−3.82787e7	+	3.05262e7i	−0.0102602	+	0.00818226i
$544$	−6.28905e8	−	3.02865e8i	−0.167490	−	0.0806589i
$545$	1.65301e8	−	7.24232e8i	0.0437410	−	0.191642i
$546$	−4.35734e8	−	1.90907e9i	−0.114564	−	0.501936i
$547$	4.10217e8	−	1.97550e8i	0.107166	−	0.0516086i	−0.379533	−	0.925178i	$-0.623915\pi$
$547$	4.10217e8	−	1.97550e8i	0.107166	−	0.0516086i	0.486699	+	0.873570i	$0.338201\pi$
$548$	−2.72635e9	+	5.66131e9i	−0.707700	+	1.46955i
$549$	1.69515e9	−	3.86907e8i	0.437225	−	0.0997939i
$550$	2.74015e9			0.702271
$551$	−4.95752e9	+	2.90633e9i	−1.26251	+	0.740140i
$552$	−4.41474e9			−1.11717
$553$	6.28457e8	−	1.43441e8i	0.158029	−	0.0360692i
$554$	−4.76605e9	+	9.89681e9i	−1.19090	+	2.47293i
$555$	−1.60950e9	+	7.75096e8i	−0.399638	+	0.192455i
$556$	−1.50005e9	−	6.57214e9i	−0.370121	−	1.62161i
$557$	9.66988e8	−	4.23665e9i	0.237098	−	1.03879i	−0.706503	−	0.707710i	$-0.749728\pi$
$557$	9.66988e8	−	4.23665e9i	0.237098	−	1.03879i	0.943601	−	0.331084i	$-0.107414\pi$
$558$	−4.77650e7	−	2.30024e7i	−0.0116383	−	0.00560472i
$559$	−6.89062e8	+	5.49509e8i	−0.166846	+	0.133056i
$560$	1.09715e9	+	1.37579e9i	0.264003	+	0.331049i
$561$	2.35656e9	+	4.89345e9i	0.563519	+	1.17016i
$562$	5.10037e9	+	4.06741e9i	1.21206	+	0.966586i
$563$			5.98538e9i			1.41355i	0.707436	+	0.706777i	$0.249852\pi$
$563$			5.98538e9i			1.41355i	−0.707436	+	0.706777i	$0.750148\pi$
$564$	5.50809e9	−	6.90693e9i	1.29278	−	1.62109i
$565$	−1.89960e9	−	4.33571e8i	−0.443090	−	0.101132i
$566$	−1.53933e9	−	3.51342e8i	−0.356841	−	0.0814466i
$567$	2.18093e9	−	2.73479e9i	0.502458	−	0.630063i
$568$		−	5.91954e9i		−	1.35540i
$569$	2.29317e7	+	1.82874e7i	0.00521846	+	0.00416159i	0.626096	−	0.779746i	$-0.284652\pi$
$569$	2.29317e7	+	1.82874e7i	0.00521846	+	0.00416159i	−0.620877	+	0.783908i	$0.713223\pi$
$570$	3.29876e9	+	6.84996e9i	0.746087	+	1.54927i
$571$	−1.67784e9	−	2.10394e9i	−0.377158	−	0.472941i	0.556634	−	0.830758i	$-0.312093\pi$
$571$	−1.67784e9	−	2.10394e9i	−0.377158	−	0.472941i	−0.933792	+	0.357817i	$0.883521\pi$
$572$	−1.70433e9	+	1.35916e9i	−0.380774	+	0.303657i
$573$	6.60592e9	+	3.18124e9i	1.46687	+	0.706408i
$574$	−1.89192e9	+	8.28903e9i	−0.417552	+	1.82941i
$575$	3.60676e8	+	1.58022e9i	0.0791188	+	0.346642i
$576$	1.19530e9	−	5.75624e8i	0.260613	−	0.125505i
$577$	3.34231e9	−	6.94038e9i	0.724322	−	1.50407i	−0.134013	−	0.990980i	$-0.542786\pi$
$577$	3.34231e9	−	6.94038e9i	0.724322	−	1.50407i	0.858335	−	0.513090i	$-0.171499\pi$
$578$	−1.86140e10	+	4.24853e9i	−4.00953	+	0.915148i
$579$	2.79707e9			0.598864
$580$	4.08467e9	−	3.84085e9i	0.869279	−	0.817391i
$581$	−1.45546e9			−0.307881
$582$	1.30695e10	−	2.98303e9i	2.74808	−	0.627231i
$583$	9.60588e8	−	1.99468e9i	0.200769	−	0.416901i
$584$	3.87798e9	−	1.86754e9i	0.805677	−	0.387993i
$585$	7.83391e7	+	3.43226e8i	0.0161783	+	0.0708818i
$586$	−2.74467e9	+	1.20252e10i	−0.563441	+	2.46860i
$587$	3.69799e9	+	1.78086e9i	0.754628	+	0.363410i	0.771317	−	0.636451i	$-0.219598\pi$
$587$	3.69799e9	+	1.78086e9i	0.754628	+	0.363410i	−0.0166891	+	0.999861i	$0.505313\pi$
$588$	5.03826e9	−	4.01788e9i	1.02202	−	0.815035i
$589$	−1.05726e8	−	1.32576e8i	−0.0213195	−	0.0267338i
$590$	3.73052e9	+	7.74651e9i	0.747804	+	1.55283i
$591$	−1.06623e9	−	8.50291e8i	−0.212469	−	0.169438i
$592$		−	3.60488e9i		−	0.714110i
$593$	−1.70755e9	+	2.14120e9i	−0.336265	+	0.421663i	−0.921001	−	0.389561i	$-0.872627\pi$
$593$	−1.70755e9	+	2.14120e9i	−0.336265	+	0.421663i	0.584736	+	0.811224i	$0.301198\pi$
$594$	−4.18800e9	−	9.55883e8i	−0.819887	−	0.187134i
$595$	3.57867e9	+	8.16808e8i	0.696486	+	0.158968i
$596$	−7.66218e9	+	9.60807e9i	−1.48248	+	1.85898i
$597$			4.27860e9i			0.822985i
$598$	−1.50509e9	−	1.20027e9i	−0.287812	−	0.229523i
$599$	−4.74399e8	−	9.85100e8i	−0.0901883	−	0.187278i	0.850995	−	0.525173i	$-0.175999\pi$
$599$	−4.74399e8	−	9.85100e8i	−0.0901883	−	0.187278i	−0.941184	+	0.337895i	$0.890285\pi$
$600$	4.43408e9	+	5.56016e9i	0.838058	+	1.05089i
$601$	2.46251e8	−	1.96379e8i	0.0462719	−	0.0369006i	−0.600081	−	0.799939i	$-0.704865\pi$
$601$	2.46251e8	−	1.96379e8i	0.0462719	−	0.0369006i	0.646353	+	0.763039i	$0.276293\pi$
$602$	3.04874e9	+	1.46820e9i	0.569551	+	0.274281i
$603$	2.72657e8	−	1.19459e9i	0.0506415	−	0.221875i
$604$	−2.86297e8	−	1.25435e9i	−0.0528674	−	0.231627i
$605$	1.78771e9	−	8.60914e8i	0.328210	−	0.158058i
$606$	7.11510e9	−	1.47747e10i	1.29875	−	2.69689i
$607$	−2.48739e9	+	5.67731e8i	−0.451423	+	0.103034i	−0.442187	−	0.896923i	$-0.645797\pi$
$607$	−2.48739e9	+	5.67731e8i	−0.451423	+	0.103034i	−0.00923636	+	0.999957i	$0.502940\pi$
$608$	−8.22149e8			−0.148350
$609$	2.90296e9	+	3.08724e9i	0.520811	+	0.553872i
$610$	−8.10086e9			−1.44503
$611$	1.90442e9	−	4.34672e8i	0.337768	−	0.0770934i
$612$	−2.90792e9	+	6.03836e9i	−0.512805	+	1.06485i
$613$	−3.83013e9	+	1.84449e9i	−0.671587	+	0.323419i	−0.738416	−	0.674345i	$-0.764426\pi$
$613$	−3.83013e9	+	1.84449e9i	−0.671587	+	0.323419i	0.0668294	+	0.997764i	$0.478712\pi$
$614$	6.76979e8	+	2.96604e9i	0.118028	+	0.517116i
$615$	1.41086e9	−	6.18136e9i	0.244579	−	1.07157i
$616$	3.82375e9	+	1.84142e9i	0.659108	+	0.317410i
$617$	1.60080e9	−	1.27660e9i	0.274372	−	0.218804i	−0.476630	−	0.879104i	$-0.658142\pi$
$617$	1.60080e9	−	1.27660e9i	0.274372	−	0.218804i	0.751003	+	0.660299i	$0.229571\pi$
$618$	−1.36270e10	−	1.70877e10i	−2.32242	−	2.91222i
$619$	1.92022e9	+	3.98737e9i	0.325411	+	0.675724i	0.997927	−	0.0643595i	$-0.0205004\pi$
$619$	1.92022e9	+	3.98737e9i	0.325411	+	0.675724i	−0.672515	+	0.740083i	$0.734786\pi$
$620$	1.29351e8	+	1.03154e8i	0.0217971	+	0.0173826i
$621$		−	2.54101e9i		−	0.425780i
$622$	−5.74783e9	+	7.20755e9i	−0.957718	+	1.20094i
$623$	−5.80911e9	−	1.32589e9i	−0.962502	−	0.219685i
$624$	−2.87285e9	−	6.55708e8i	−0.473333	−	0.108035i
$625$	3.11499e8	−	3.90607e8i	0.0510359	−	0.0639970i
$626$		−	1.66914e10i		−	2.71946i
$627$	5.00143e9	+	3.98851e9i	0.810323	+	0.646211i
$628$	1.41144e9	+	2.93088e9i	0.227406	+	0.472214i
$629$	−4.68848e9	−	5.87916e9i	−0.751198	−	0.941973i
$630$	1.05678e9	−	8.42757e8i	0.168381	−	0.134280i
$631$	−7.88991e9	−	3.79958e9i	−1.25017	−	0.602050i	−0.312613	−	0.949881i	$-0.601204\pi$
$631$	−7.88991e9	−	3.79958e9i	−1.25017	−	0.602050i	−0.937558	+	0.347830i	$0.886919\pi$
$632$	6.18731e8	−	2.71084e9i	0.0974972	−	0.427163i
$633$	6.44704e8	+	2.82463e9i	0.101029	+	0.442638i
$634$	1.08991e10	−	5.24874e9i	1.69855	−	0.817980i
$635$	7.80502e8	−	1.62073e9i	0.120967	−	0.251190i
$636$	1.10475e10	−	2.52151e9i	1.70280	−	0.388652i
$637$	1.42491e9			0.218423
$638$	2.52948e9	−	6.57312e9i	0.385619	−	1.00207i
$639$	−1.58630e9			−0.240509
$640$	−6.41153e9	+	1.46339e9i	−0.966790	+	0.220663i
$641$	3.95782e9	−	8.21849e9i	0.593543	−	1.23251i	−0.360478	−	0.932768i	$-0.617387\pi$
$641$	3.95782e9	−	8.21849e9i	0.593543	−	1.23251i	0.954022	−	0.299738i	$-0.0968992\pi$
$642$	−1.29668e10	+	6.24449e9i	−1.93402	+	0.931374i
$643$	−1.02659e9	−	4.49779e9i	−0.152286	−	0.667207i	−0.992218	−	0.124515i	$-0.960262\pi$
$643$	−1.02659e9	−	4.49779e9i	−0.152286	−	0.667207i	0.839932	−	0.542692i	$-0.182595\pi$
$644$	−1.10166e9	+	4.82671e9i	−0.162536	+	0.712115i
$645$	−2.27353e9	−	1.09488e9i	−0.333612	−	0.160659i
$646$	−2.50214e10	+	1.99539e10i	−3.65172	+	2.91215i
$647$	7.48270e9	+	9.38300e9i	1.08616	+	1.36200i	0.927136	+	0.374724i	$0.122263\pi$
$647$	7.48270e9	+	9.38300e9i	1.08616	+	1.36200i	0.159022	+	0.987275i	$0.449166\pi$
$648$	−6.54655e9	−	1.35941e10i	−0.945149	−	1.96262i
$649$	5.65604e9	+	4.51054e9i	0.812187	+	0.647698i
$650$			3.10113e9i			0.442918i
$651$	−7.79649e7	+	9.77649e7i	−0.0110756	+	0.0138883i
$652$	1.13517e10	+	2.59095e9i	1.60396	+	0.366094i
$653$	−2.08841e9	−	4.76666e8i	−0.293508	−	0.0669912i	0.0732317	−	0.997315i	$-0.476669\pi$
$653$	−2.08841e9	−	4.76666e8i	−0.293508	−	0.0669912i	−0.366739	+	0.930324i	$0.619526\pi$
$654$	2.97785e9	−	3.73410e9i	0.416275	−	0.521992i
$655$			3.18339e9i			0.442635i
$656$	1.00031e10	+	7.97719e9i	1.38347	+	1.10328i
$657$	−5.00456e8	−	1.03921e9i	−0.0688474	−	0.142963i
$658$	−4.67612e9	−	5.86367e9i	−0.639874	−	0.802377i
$659$	−3.29831e9	+	2.63032e9i	−0.448945	+	0.358022i	−0.821712	−	0.569903i	$-0.806981\pi$
$659$	−3.29831e9	+	2.63032e9i	−0.448945	+	0.358022i	0.372767	+	0.927925i	$0.378409\pi$
$660$	−5.62337e9	−	2.70807e9i	−0.761364	−	0.366654i
$661$	−1.20039e9	+	5.25924e9i	−0.161665	+	0.708301i	0.827497	+	0.561471i	$0.189764\pi$
$661$	−1.20039e9	+	5.25924e9i	−0.161665	+	0.708301i	−0.989162	+	0.146830i	$0.953093\pi$
$662$	−3.13314e9	−	1.37272e10i	−0.419737	−	1.83899i
$663$	−5.53810e9	+	2.66701e9i	−0.738012	+	0.355408i
$664$	−2.72396e9	+	5.65636e9i	−0.361087	+	0.749805i
$665$	4.21500e9	−	9.62046e8i	0.555804	−	0.126859i
$666$	−2.76902e9			−0.363217
$667$	4.12362e9	+	5.93534e8i	0.538069	+	0.0774471i
$668$	−1.28165e9			−0.166361
$669$	2.21714e9	−	5.06047e8i	0.286287	−	0.0653431i
$670$	−2.47693e9	+	5.14340e9i	−0.318165	+	0.660677i
$671$	−6.14107e9	+	2.95738e9i	−0.784721	+	0.377902i
$672$	1.34909e8	+	5.91074e8i	0.0171493	+	0.0751362i
$673$	5.17649e8	−	2.26797e9i	0.0654610	−	0.286804i	−0.931593	−	0.363502i	$-0.881581\pi$
$673$	5.17649e8	−	2.26797e9i	0.0654610	−	0.286804i	0.997054	+	0.0766988i	$0.0244380\pi$
$674$	−1.79664e9	−	8.65218e8i	−0.226023	−	0.108847i
$675$	−3.20029e9	+	2.55214e9i	−0.400521	+	0.319405i
$676$	8.62107e9	+	1.08105e10i	1.07337	+	1.34596i
$677$	−1.77749e8	−	3.69100e8i	−0.0220164	−	0.0457176i	0.889671	−	0.456603i	$-0.150934\pi$
$677$	−1.77749e8	−	3.69100e8i	−0.0220164	−	0.0457176i	−0.911687	+	0.410885i	$0.865220\pi$
$678$	−9.79421e9	−	7.81063e9i	−1.20688	−	0.962458i
$679$		−	7.62314e9i		−	0.934522i
$680$	9.87203e9	−	1.23791e10i	1.20400	−	1.50976i
$681$	−1.36396e10	−	3.11316e9i	−1.65496	−	0.377734i
$682$	2.02614e8	+	4.62454e7i	0.0244582	+	0.00558243i
$683$	2.55289e9	−	3.20123e9i	0.306592	−	0.384454i	−0.604536	−	0.796578i	$-0.706641\pi$
$683$	2.55289e9	−	3.20123e9i	0.306592	−	0.384454i	0.911128	+	0.412124i	$0.135213\pi$
$684$			7.89377e9i			0.943166i
$685$	−3.11018e9	−	2.48029e9i	−0.369716	−	0.294839i
$686$	−6.60236e9	−	1.37099e10i	−0.780845	−	1.62144i
$687$	4.70096e9	+	5.89482e9i	0.553144	+	0.693621i
$688$	3.98120e9	−	3.17490e9i	0.466073	−	0.371681i
$689$	2.25745e9	+	1.08713e9i	0.262937	+	0.126624i
$690$	1.22650e9	−	5.37364e9i	0.142133	−	0.622726i
$691$	2.05189e9	+	8.98994e9i	0.236582	+	1.03653i	0.944054	+	0.329792i	$0.106979\pi$
$691$	2.05189e9	+	8.98994e9i	0.236582	+	1.03653i	−0.707472	+	0.706742i	$0.750164\pi$
$692$	2.15311e10	−	1.03688e10i	2.46998	−	1.18948i
$693$	4.93457e8	−	1.02467e9i	0.0563227	−	0.116955i
$694$	1.70204e10	−	3.88479e9i	1.93291	−	0.441174i
$695$	4.26775e9			0.482228
$696$	1.74310e10	−	5.50389e9i	1.95970	−	0.618781i
$697$	2.66890e10			2.98550
$698$	−2.11511e10	+	4.82760e9i	−2.35418	+	0.537326i
$699$	5.00642e9	−	1.03959e10i	0.554443	−	1.15131i
$700$	7.18551e9	−	3.46036e9i	0.791798	−	0.381310i
$701$	2.74673e9	+	1.20342e10i	0.301164	+	1.31949i	0.868372	+	0.495913i	$0.165166\pi$
$701$	2.74673e9	+	1.20342e10i	0.301164	+	1.31949i	−0.567208	+	0.823575i	$0.691976\pi$
$702$	1.08181e9	−	4.73971e9i	0.118024	−	0.517097i
$703$	−7.97972e9	−	3.84283e9i	−0.866252	−	0.417165i
$704$	−4.06608e9	+	3.24259e9i	−0.439210	+	0.350258i
$705$	3.48711e9	+	4.37270e9i	0.374804	+	0.469989i
$706$	6.29240e9	+	1.30663e10i	0.672977	+	1.39745i
$707$	−7.29067e9	−	5.81412e9i	−0.775889	−	0.618751i
$708$			3.70277e10i			3.92112i
$709$	−8.25894e9	+	1.03564e10i	−0.870287	+	1.09131i	0.124788	+	0.992183i	$0.460175\pi$
$709$	−8.25894e9	+	1.03564e10i	−0.870287	+	1.09131i	−0.995075	+	0.0991222i	$0.968397\pi$
$710$	7.20530e9	+	1.64456e9i	0.755523	+	0.172443i
$711$	−7.26441e8	−	1.65805e8i	−0.0757978	−	0.0173004i
$712$	−1.60249e10	+	2.00946e10i	−1.66385	+	2.08640i
$713$			1.22933e8i			0.0127015i
$714$	1.84514e10	+	1.47145e10i	1.89708	+	1.51287i
$715$	−5.98796e8	−	1.24341e9i	−0.0612643	−	0.127217i
$716$	1.06175e10	+	1.33139e10i	1.08100	+	1.35553i
$717$	−1.37261e10	+	1.09462e10i	−1.39068	+	1.10903i
$718$	−6.72522e9	−	3.23870e9i	−0.678065	−	0.326539i
$719$	2.46765e9	−	1.08115e10i	0.247590	−	1.08476i	−0.686333	−	0.727287i	$-0.740781\pi$
$719$	2.46765e9	−	1.08115e10i	0.247590	−	1.08476i	0.933923	−	0.357474i	$-0.116362\pi$
$720$	−4.52620e8	−	1.98306e9i	−0.0451929	−	0.198003i
$721$	−1.11977e10	+	5.39251e9i	−1.11264	+	0.535818i
$722$	−8.71859e9	+	1.81043e10i	−0.862116	+	1.79020i
$723$	2.22964e10	−	5.08900e9i	2.19407	−	0.500782i
$724$	2.36834e8			0.0231932
$725$	−3.39416e9	−	5.78965e9i	−0.330788	−	0.564247i
$726$	1.27572e10			1.23730
$727$	6.00467e8	−	1.37053e8i	0.0579587	−	0.0132287i	−0.193443	−	0.981111i	$-0.561966\pi$
$727$	6.00467e8	−	1.37053e8i	0.0579587	−	0.0132287i	0.251402	+	0.967883i	$0.419108\pi$
$728$	−2.08400e9	+	4.32748e9i	−0.200188	+	0.415695i
$729$	4.83046e9	−	2.32623e9i	0.461787	−	0.222385i
$730$	1.19580e9	+	5.23914e9i	0.113770	+	0.498460i
$731$	2.36365e9	−	1.03558e10i	0.223806	−	0.980558i
$732$	−3.14319e10	−	1.51368e10i	−2.96198	−	1.42641i
$733$	1.54102e9	−	1.22892e9i	0.144525	−	0.115255i	−0.548558	−	0.836112i	$-0.684823\pi$
$733$	1.54102e9	−	1.22892e9i	0.144525	−	0.115255i	0.693083	+	0.720857i	$0.256252\pi$
$734$	−6.97639e9	−	8.74812e9i	−0.651170	−	0.816542i
$735$	1.77013e9	+	3.67572e9i	0.164437	+	0.341457i
$736$	4.65996e8	+	3.71619e8i	0.0430834	+	0.0343579i
$737$			4.80335e9i			0.441985i
$738$	6.12753e9	−	7.68368e9i	0.561162	−	0.703674i
$739$	−2.09111e10	−	4.77283e9i	−1.90600	−	0.435031i	−0.999929	−	0.0118951i	$-0.996214\pi$
$739$	−2.09111e10	−	4.77283e9i	−1.90600	−	0.435031i	−0.906066	−	0.423136i	$-0.860929\pi$
$740$	8.42473e9	+	1.92289e9i	0.764267	+	0.174439i
$741$	−4.51394e9	+	5.66031e9i	−0.407561	+	0.511065i
$742$		−	9.61999e9i		−	0.864492i
$743$	−1.58290e9	−	1.26232e9i	−0.141577	−	0.112904i	0.550141	−	0.835072i	$-0.314574\pi$
$743$	−1.58290e9	−	1.26232e9i	−0.141577	−	0.112904i	−0.691717	+	0.722168i	$0.743146\pi$
$744$	2.34030e8	+	4.85968e8i	0.0208337	+	0.0432616i
$745$	−4.85084e9	−	6.08276e9i	−0.429804	−	0.538957i
$746$	2.96457e10	−	2.36416e10i	2.61442	−	2.08493i
$747$	1.51577e9	+	7.29957e8i	0.133049	+	0.0640730i
$748$	5.84626e9	−	2.56141e10i	0.510766	−	2.23781i
$749$	1.82113e9	+	7.97889e9i	0.158363	+	0.693835i
$750$	−2.02306e10	+	9.74255e9i	−1.75103	+	0.843254i
$751$	1.90826e9	−	3.96254e9i	0.164398	−	0.341376i	−0.802454	−	0.596714i	$-0.796473\pi$
$751$	1.90826e9	−	3.96254e9i	0.164398	−	0.341376i	0.966852	+	0.255338i	$0.0821868\pi$
$752$	−1.10032e10	+	2.51140e9i	−0.943530	+	0.215355i
$753$	−9.14379e9			−0.780448
$754$	7.43905e9	+	2.86270e9i	0.632001	+	0.243207i
$755$	8.14538e8			0.0688807
$756$	−1.21893e10	+	2.78214e9i	−1.02602	+	0.234181i
$757$	7.40498e9	−	1.53766e10i	0.620424	−	1.28832i	−0.319710	−	0.947516i	$-0.603585\pi$
$757$	7.40498e9	−	1.53766e10i	0.620424	−	1.28832i	0.940133	−	0.340807i	$-0.110700\pi$
$758$	−8.69565e9	+	4.18761e9i	−0.725204	+	0.349240i
$759$	−1.03198e9	−	4.52139e9i	−0.0856691	−	0.375341i
$760$	4.14977e9	−	1.81813e10i	0.342907	−	1.50237i
$761$	6.68696e9	+	3.22027e9i	0.550025	+	0.264878i	0.688189	−	0.725531i	$-0.258406\pi$
$761$	6.68696e9	+	3.22027e9i	0.550025	+	0.264878i	−0.138164	+	0.990409i	$0.544120\pi$
$762$	9.04235e9	−	7.21103e9i	0.740353	−	0.590412i
$763$	−1.69336e9	−	2.12340e9i	−0.138011	−	0.173060i
$764$	−1.53886e10	−	3.19547e10i	−1.24845	−	2.59244i
$765$	−3.31732e9	−	2.64547e9i	−0.267900	−	0.213643i
$766$			3.56162e10i			2.86317i
$767$	−5.10475e9	+	6.40115e9i	−0.408499	+	0.512241i
$768$	−2.84299e10	−	6.48895e9i	−2.26470	−	0.516904i
$769$	1.51915e10	+	3.46736e9i	1.20464	+	0.274952i	0.777296	−	0.629135i	$-0.216591\pi$
$769$	1.51915e10	+	3.46736e9i	1.20464	+	0.274952i	0.427348	+	0.904087i	$0.359448\pi$
$770$	−3.30370e9	+	4.14271e9i	−0.260785	+	0.327014i
$771$		−	1.95438e9i		−	0.153574i
$772$	−1.05783e10	−	8.43595e9i	−0.827479	−	0.659893i
$773$	−9.08226e9	−	1.88595e10i	−0.707238	−	1.46860i	−0.875684	−	0.482885i	$-0.839589\pi$
$773$	−9.08226e9	−	1.88595e10i	−0.707238	−	1.46860i	0.168446	−	0.985711i	$-0.446125\pi$
$774$	−2.43874e9	−	3.05808e9i	−0.189048	−	0.237058i
$775$	1.54829e8	−	1.23472e8i	0.0119480	−	0.00952824i
$776$	−2.96259e10	−	1.42671e10i	−2.27591	−	1.09602i
$777$	−1.45334e9	+	6.36750e9i	−0.111146	+	0.486962i
$778$	2.90150e9	+	1.27123e10i	0.220899	+	0.967821i
$779$	2.83216e10	−	1.36389e10i	2.14653	−	1.03371i
$780$	3.06482e9	−	6.36417e9i	0.231246	−	0.480188i
$781$	6.06254e9	−	1.38374e9i	0.455382	−	0.103938i
$782$	2.32015e10			1.73497
$783$	3.16790e9	+	1.00328e10i	0.235833	+	0.746891i
$784$	−8.23269e9			−0.610148
$785$	−2.00782e9	+	4.58273e8i	−0.148143	+	0.0338127i
$786$	−8.88037e9	+	1.84403e10i	−0.652307	+	1.35453i
$787$	5.26070e9	−	2.53342e9i	0.384709	−	0.185266i	−0.231526	−	0.972829i	$-0.574372\pi$
$787$	5.26070e9	−	2.53342e9i	0.384709	−	0.185266i	0.616234	+	0.787563i	$0.288657\pi$
$788$	1.46795e9	+	6.43150e9i	0.106873	+	0.468242i
$789$	−3.64709e9	+	1.59789e10i	−0.264349	+	1.15819i
$790$	3.12775e9	+	1.50625e9i	0.225703	+	0.108693i
$791$	−5.56950e9	+	4.44153e9i	−0.400128	+	0.319091i
$792$	−3.05868e9	−	3.83546e9i	−0.218774	−	0.274334i
$793$	−3.34698e9	−	6.95008e9i	−0.238340	−	0.494918i
$794$	1.28582e10	+	1.02541e10i	0.911608	+	0.726983i
$795$			7.17390e9i			0.506373i
$796$	1.29043e10	−	1.61814e10i	0.906853	−	1.13716i
$797$	−2.89832e7	−	6.61523e6i	−0.00202788	−	0.000462850i	0.221507	−	0.975159i	$-0.428902\pi$
$797$	−2.89832e7	−	6.61523e6i	−0.00202788	−	0.000462850i	−0.223535	+	0.974696i	$0.571760\pi$
$798$	2.70997e10	+	6.18534e9i	1.88779	+	0.430877i
$799$	−1.46787e10	+	1.84065e10i	−1.01806	+	1.27660i
$800$		−	9.60149e8i		−	0.0663015i
$801$	5.38487e9	+	4.29429e9i	0.370221	+	0.295242i
$802$	2.92643e9	+	6.07680e9i	0.200322	+	0.415973i
$803$	2.81916e9	+	3.53512e9i	0.192139	+	0.240935i
$804$	−1.92214e10	+	1.53285e10i	−1.30433	+	1.04017i
$805$	−2.82392e9	−	1.35993e9i	−0.190795	−	0.0918821i
$806$	−5.23377e7	+	2.29306e8i	−0.00352080	+	0.0154256i
$807$	2.68149e9	+	1.17484e10i	0.179605	+	0.786901i
$808$	−3.62403e10	+	1.74524e10i	−2.41687	+	1.16390i
$809$	−9.47814e9	+	1.96816e10i	−0.629366	+	1.30689i	0.305602	+	0.952159i	$0.401142\pi$
$809$	−9.47814e9	+	1.96816e10i	−0.629366	+	1.30689i	−0.934968	+	0.354732i	$0.884572\pi$
$810$	1.83655e10	−	4.19181e9i	1.21424	−	0.277143i
$811$	1.63716e10			1.07775			0.538874	−	0.842387i	$-0.318850\pi$
$811$	1.63716e10			1.07775			0.538874	+	0.842387i	$0.318850\pi$
$812$	−1.66772e9	−	2.04311e10i	−0.109314	−	1.33920i
$813$	1.15447e10			0.753471
$814$	1.05827e10	−	2.41543e9i	0.687720	−	0.156967i
$815$	−3.19835e9	+	6.64145e9i	−0.206955	+	0.429746i
$816$	3.19975e10	−	1.54092e10i	2.06158	−	0.992806i
$817$	−2.78393e9	−	1.21972e10i	−0.178600	−	0.782497i
$818$	6.52189e9	−	2.85743e10i	0.416617	−	1.82532i
$819$	1.15966e9	+	5.58464e8i	0.0737629	+	0.0355223i
$820$	−2.39787e10	+	1.91224e10i	−1.51872	+	1.21114i
$821$	−1.26280e10	−	1.58350e10i	−0.796404	−	0.998659i	−0.999809	−	0.0195644i	$-0.993772\pi$
$821$	−1.26280e10	−	1.58350e10i	−0.796404	−	0.998659i	0.203404	−	0.979095i	$-0.434799\pi$
$822$	−1.10972e10	−	2.30436e10i	−0.696886	−	1.44710i
$823$	1.66948e10	+	1.33137e10i	1.04396	+	0.832527i	0.986159	−	0.165802i	$-0.0530212\pi$
$823$	1.66948e10	+	1.33137e10i	1.04396	+	0.832527i	0.0577962	+	0.998328i	$0.481593\pi$
$824$			5.36099e10i			3.33811i
$825$	−4.65799e9	+	5.84093e9i	−0.288808	+	0.362154i
$826$	3.06467e10	+	6.99490e9i	1.89214	+	0.431868i
$827$	3.74611e9	+	8.55024e8i	0.230309	+	0.0525665i	0.336118	−	0.941820i	$-0.390886\pi$
$827$	3.74611e9	+	8.55024e8i	0.230309	+	0.0525665i	−0.105809	+	0.994386i	$0.533743\pi$
$828$	3.56806e9	−	4.47421e9i	0.218437	−	0.273911i
$829$		−	1.66062e10i		−	1.01234i	−0.862432	−	0.506172i	$-0.831060\pi$
$829$		−	1.66062e10i		−	1.01234i	0.862432	−	0.506172i	$-0.168940\pi$
$830$	−6.12818e9	−	4.88706e9i	−0.372013	−	0.296671i
$831$	−1.29943e10	−	2.69830e10i	−0.785507	−	1.63112i
$832$	−3.66977e9	−	4.60174e9i	−0.220906	−	0.277007i
$833$	−1.34266e10	+	1.07074e10i	−0.804838	+	0.641837i
$834$	2.47216e10	+	1.19053e10i	1.47569	+	0.710656i
$835$	1.80553e8	−	7.91054e8i	0.0107325	−	0.0470223i
$836$	−6.88578e9	−	3.01686e10i	−0.407597	−	1.78580i
$837$	−2.79711e8	+	1.34702e8i	−0.0164881	+	0.00794024i
$838$	−2.73131e9	+	5.67163e9i	−0.160331	+	0.332931i
$839$	−1.22750e9	+	2.80170e8i	−0.0717557	+	0.0163778i	−0.258248	−	0.966079i	$-0.583145\pi$
$839$	−1.22750e9	+	2.80170e8i	−0.0717557	+	0.0163778i	0.186492	+	0.982456i	$0.440288\pi$
$840$	−1.37522e10			−0.800560
$841$	−1.70215e10	+	2.79746e9i	−0.986762	+	0.162173i
$842$	1.41735e10			0.818247
$843$	−1.73403e10	+	3.95780e9i	−0.996917	+	0.227540i
$844$	6.08085e9	−	1.26270e10i	0.348149	−	0.722940i
$845$	−7.88691e9	+	3.79813e9i	−0.449685	+	0.216557i
$846$	1.92909e9	+	8.45188e9i	0.109536	+	0.479907i
$847$	1.61425e9	−	7.07250e9i	0.0912808	−	0.399927i
$848$	−1.30429e10	−	6.28113e9i	−0.734495	−	0.353714i
$849$	3.36564e9	−	2.68401e9i	0.188752	−	0.150524i
$850$	−2.33032e10	−	2.92213e10i	−1.30152	−	1.63205i
$851$	2.78593e9	+	5.78504e9i	0.154959	+	0.321775i
$852$	2.48841e10	+	1.98444e10i	1.37843	+	1.09926i
$853$		−	6.19882e9i		−	0.341969i	−0.985274	−	0.170985i	$-0.945305\pi$
$853$		−	6.19882e9i		−	0.341969i	0.985274	−	0.170985i	$-0.0546949\pi$
$854$	−1.84661e10	+	2.31557e10i	−1.01455	+	1.27220i
$855$	−4.87217e9	−	1.11204e9i	−0.266588	−	0.0608470i
$856$	3.44168e10	+	7.85541e9i	1.87548	+	0.428066i
$857$	−7.19405e8	+	9.02106e8i	−0.0390428	+	0.0489581i	−0.800970	−	0.598705i	$-0.795682\pi$
$857$	−7.19405e8	+	9.02106e8i	−0.0390428	+	0.0489581i	0.761927	+	0.647663i	$0.224254\pi$
$858$		−	8.87305e9i		−	0.479587i
$859$	−2.45010e9	−	1.95389e9i	−0.131889	−	0.105178i	0.555324	−	0.831634i	$-0.312594\pi$
$859$	−2.45010e9	−	1.95389e9i	−0.131889	−	0.105178i	−0.687212	+	0.726457i	$0.741166\pi$
$860$	5.29622e9	+	1.09977e10i	0.283937	+	0.589601i
$861$	−1.44529e10	−	1.81234e10i	−0.771692	−	0.967672i
$862$	−3.38793e10	+	2.70179e10i	−1.80160	+	1.43673i
$863$	3.04602e10	+	1.46689e10i	1.61323	+	0.776889i	0.999916	−	0.0129531i	$-0.00412321\pi$
$863$	3.04602e10	+	1.46689e10i	1.61323	+	0.776889i	0.613310	+	0.789842i	$0.289837\pi$
$864$	−3.34942e8	+	1.46748e9i	−0.0176673	+	0.0774057i
$865$	3.36660e9	+	1.47500e10i	0.176862	+	0.774884i
$866$	4.56233e10	−	2.19710e10i	2.38712	−	1.14958i
$867$	2.25858e10	−	4.69000e10i	1.17698	−	2.44403i
$868$	5.89717e8	−	1.34599e8i	0.0306073	−	0.00698591i
$869$	2.92096e9			0.150993
$870$	1.85670e9	+	2.27462e10i	0.0955924	+	1.17109i
$871$	−5.43613e9			−0.278757
$872$	−1.14214e10	+	2.60686e9i	−0.583327	+	0.133141i
$873$	−3.82324e9	+	7.93904e9i	−0.194483	+	0.403848i
$874$	2.46208e10	−	1.18568e10i	1.24742	−	0.600725i
$875$	2.84130e9	+	1.24485e10i	0.143380	+	0.628189i
$876$	−5.14978e9	+	2.25626e10i	−0.258836	+	1.13403i
$877$	4.44285e9	+	2.13956e9i	0.222414	+	0.107109i	0.541773	−	0.840525i	$-0.317753\pi$
$877$	4.44285e9	+	2.13956e9i	0.222414	+	0.107109i	−0.319359	+	0.947634i	$0.603467\pi$
$878$	9.99994e9	−	7.97468e9i	0.498616	−	0.397633i
$879$	−2.09674e10	−	2.62922e10i	−1.04132	−	1.30577i
$880$	3.45966e9	+	7.18407e9i	0.171137	+	0.355370i
$881$	−2.35607e10	−	1.87890e10i	−1.16084	−	0.925739i	−0.162698	−	0.986676i	$-0.552020\pi$
$881$	−2.35607e10	−	1.87890e10i	−1.16084	−	0.925739i	−0.998142	+	0.0609372i	$0.980591\pi$
$882$			6.32378e9i			0.310339i
$883$	−1.30064e9	+	1.63095e9i	−0.0635764	+	0.0797222i	−0.812603	−	0.582818i	$-0.801950\pi$
$883$	−1.30064e9	+	1.63095e9i	−0.0635764	+	0.0797222i	0.749027	+	0.662540i	$0.230522\pi$
$884$	2.89885e10	+	6.61643e9i	1.41137	+	0.322137i
$885$	−2.28541e10	−	5.21630e9i	−1.10831	−	0.252965i
$886$	3.80167e10	−	4.76715e10i	1.83636	−	2.30272i
$887$			3.59724e10i			1.73076i	0.501117	+	0.865380i	$0.332923\pi$
$887$			3.59724e10i			1.73076i	−0.501117	+	0.865380i	$0.667077\pi$
$888$	2.20261e10	+	1.75652e10i	1.05558	+	0.841799i
$889$	−2.85357e9	−	5.92549e9i	−0.136217	−	0.282858i
$890$	−2.00072e10	−	2.50882e10i	−0.951308	−	1.19290i
$891$	1.23922e10	−	9.88242e9i	0.586915	−	0.468049i
$892$	−9.91132e9	−	4.77304e9i	−0.467578	−	0.225174i
$893$	−6.17026e9	+	2.70337e10i	−0.289950	+	1.27035i
$894$	−1.11308e10	−	4.87672e10i	−0.521009	−	2.28269i
$895$	−9.71330e9	+	4.67768e9i	−0.452883	+	0.218097i
$896$	−1.04322e10	+	2.16628e10i	−0.484506	+	1.00609i
$897$	5.11703e9	−	1.16793e9i	0.236725	−	0.0540309i
$898$	−1.52315e10			−0.701898
$899$	−1.53262e8	−	4.85386e8i	−0.00703519	−	0.0222807i
$900$	−9.21876e9			−0.421525
$901$	−2.94407e10	+	6.71965e9i	−1.34095	+	0.306062i
$902$	−1.67158e10	+	3.47107e10i	−0.758410	+	1.57486i
$903$	−8.31219e9	+	4.00294e9i	−0.375672	+	0.180914i
$904$	6.83757e9	+	2.99574e10i	0.307831	+	1.34870i
$905$	−3.33642e7	+	1.46178e8i	−0.00149627	+	0.00655560i
$906$	4.71834e9	+	2.27223e9i	0.210785	+	0.101509i
$907$	1.61814e10	−	1.29042e10i	0.720097	−	0.574258i	−0.193392	−	0.981122i	$-0.561949\pi$
$907$	1.61814e10	−	1.29042e10i	0.720097	−	0.574258i	0.913489	+	0.406864i	$0.133378\pi$
$908$	4.21950e10	+	5.29108e10i	1.87051	+	2.34555i
$909$	4.67684e9	+	9.71156e9i	0.206528	+	0.428860i
$910$	−4.68846e9	−	3.73892e9i	−0.206246	−	0.164475i
$911$		−	1.47661e10i		−	0.647071i	−0.946216	−	0.323536i	$-0.895128\pi$
$911$		−	1.47661e10i		−	0.647071i	0.946216	−	0.323536i	$-0.104872\pi$
$912$	2.60802e10	−	3.27036e10i	1.13849	−	1.42762i
$913$	−6.42975e9	−	1.46755e9i	−0.279606	−	0.0638182i
$914$	−2.66982e10	−	6.09369e9i	−1.15657	−	0.263979i
$915$	1.37707e10	−	1.72679e10i	0.594267	−	0.745187i
$916$		−	3.64719e10i		−	1.56792i
$917$	9.09950e9	+	7.25661e9i	0.389695	+	0.310772i
$918$	2.54226e10	+	5.27905e10i	1.08460	+	2.25220i
$919$	−7.45857e8	−	9.35275e8i	−0.0316994	−	0.0397498i	0.765729	−	0.643163i	$-0.222378\pi$
$919$	−7.45857e8	−	9.35275e8i	−0.0316994	−	0.0397498i	−0.797429	+	0.603413i	$0.793807\pi$
$920$	−1.05702e10	+	8.42947e9i	−0.447535	+	0.356897i
$921$	−7.47324e9	−	3.59893e9i	−0.315210	−	0.151797i
$922$	−6.97705e9	+	3.05684e10i	−0.293166	+	1.28444i
$923$	1.56603e9	+	6.86121e9i	0.0655531	+	0.287207i
$924$	−2.05594e10	+	9.90089e9i	−0.857351	+	0.412879i
$925$	4.48786e9	−	9.31914e9i	0.186442	−	0.387150i
$926$	−3.67799e10	+	8.39478e9i	−1.52220	+	0.347433i
$927$	1.43662e10			0.592329
$928$	−2.30322e9	−	8.86329e8i	−0.0946059	−	0.0364063i
$929$	−2.07425e9			−0.0848801			−0.0424400	−	0.999099i	$-0.513513\pi$
$929$	−2.07425e9			−0.0848801			−0.0424400	+	0.999099i	$0.513513\pi$
$930$	−6.56541e8	+	1.49851e8i	−0.0267653	+	0.00610900i
$931$	−8.77611e9	+	1.82238e10i	−0.356433	+	0.740141i
$932$	−5.02881e10	+	2.42175e10i	−2.03474	+	0.979880i
$933$	−5.59294e9	−	2.45043e10i	−0.225452	−	0.987771i
$934$	1.73451e10	−	7.59940e10i	0.696568	−	3.05186i
$935$	1.49859e10	+	7.21681e9i	0.599572	+	0.288738i
$936$	4.34073e9	−	3.46162e9i	0.173020	−	0.137979i
$937$	4.77716e9	+	5.99037e9i	0.189706	+	0.237884i	0.867584	−	0.497291i	$-0.165672\pi$
$937$	4.77716e9	+	5.99037e9i	0.189706	+	0.237884i	−0.677878	+	0.735174i	$0.737100\pi$
$938$	9.05584e9	+	1.88046e10i	0.358277	+	0.743970i
$939$	3.55796e10	+	2.83738e10i	1.40240	+	1.11838i
$940$		−	2.70544e10i		−	1.06241i
$941$	9.45086e9	−	1.18510e10i	0.369750	−	0.463651i	−0.561796	−	0.827276i	$-0.689889\pi$
$941$	9.45086e9	−	1.18510e10i	0.369750	−	0.463651i	0.931546	+	0.363624i	$0.118461\pi$
$942$	−1.29090e10	−	2.94640e9i	−0.503170	−	0.114845i
$943$	−2.22177e10	−	5.07104e9i	−0.862795	−	0.196927i
$944$	2.94937e10	−	3.69840e10i	1.14111	−	1.43091i
$945$		−	7.91539e9i		−	0.305113i
$946$	1.19880e10	+	9.56011e9i	0.460392	+	0.367150i
$947$	−2.13994e9	−	4.44364e9i	−0.0818799	−	0.170025i	0.856009	−	0.516961i	$-0.172937\pi$
$947$	−2.13994e9	−	4.44364e9i	−0.0818799	−	0.170025i	−0.937889	+	0.346935i	$0.887222\pi$
$948$	9.32142e9	+	1.16887e10i	0.355347	+	0.445591i
$949$	−4.00082e9	+	3.19055e9i	−0.151956	+	0.121181i
$950$	−3.96617e10	−	1.91001e10i	−1.50086	−	0.722774i
$951$	−7.33918e9	+	3.21551e10i	−0.276704	+	1.21232i
$952$	−1.28814e10	−	5.64370e10i	−0.483875	−	2.11999i
$953$	−5.96059e9	+	2.87047e9i	−0.223082	+	0.107430i	−0.542087	−	0.840323i	$-0.682366\pi$
$953$	−5.96059e9	+	2.87047e9i	−0.223082	+	0.107430i	0.319005	+	0.947753i	$0.396651\pi$
$954$	−4.82473e9	+	1.00187e10i	−0.179909	+	0.373586i
$955$	2.18908e10	−	4.99644e9i	0.813300	−	0.185630i
$956$	8.49247e10			3.14363
$957$	9.71148e9	+	1.65655e10i	0.358174	+	0.610961i
$958$	−5.92486e10			−2.17720
$959$	−1.41794e10	+	3.23637e9i	−0.519152	+	0.118493i
$960$	7.31187e9	−	1.51833e10i	0.266734	−	0.553880i
$961$	−2.47745e10	+	1.19308e10i	−0.900477	+	0.433647i
$962$	2.73364e9	+	1.19768e10i	0.0989984	+	0.433740i
$963$	2.10507e9	−	9.22290e9i	0.0759581	−	0.332794i
$964$	−9.96719e10	−	4.79995e10i	−3.58347	−	1.72571i
$965$	6.69703e9	−	5.34071e9i	0.239904	−	0.191317i
$966$	−1.25644e10	−	1.57552e10i	−0.448456	−	0.562346i
$967$	1.68882e10	+	3.50686e10i	0.600606	+	1.24717i	0.950600	+	0.310419i	$0.100469\pi$
$967$	1.68882e10	+	3.50686e10i	0.600606	+	1.24717i	−0.349994	+	0.936752i	$0.613816\pi$
$968$	−2.44648e10	−	1.95100e10i	−0.866918	−	0.691344i
$969$		−	8.72556e10i		−	3.08078i
$970$	2.55966e10	−	3.20971e10i	0.900495	−	1.12919i
$971$	3.28946e10	+	7.50798e9i	1.15307	+	0.263182i	0.755979	−	0.654596i	$-0.227161\pi$
$971$	3.28946e10	+	7.50798e9i	1.15307	+	0.263182i	0.397095	+	0.917777i	$0.370018\pi$
$972$	3.47396e10	+	7.92908e9i	1.21337	+	0.276943i
$973$	9.72844e9	−	1.21991e10i	0.338570	−	0.424553i
$974$			4.22313e10i			1.46446i
$975$	−6.61040e9	−	5.27162e9i	−0.228408	−	0.182149i
$976$	1.93379e10	+	4.01555e10i	0.665785	+	1.38252i
$977$	1.50714e9	+	1.88989e9i	0.0517038	+	0.0648345i	0.807011	−	0.590536i	$-0.201084\pi$
$977$	1.50714e9	+	1.88989e9i	0.0517038	+	0.0648345i	−0.755307	+	0.655371i	$0.772512\pi$
$978$	−3.70539e10	+	2.95495e10i	−1.26662	+	1.01010i
$979$	−2.43260e10	−	1.17148e10i	−0.828572	−	0.399019i
$980$	4.39142e9	−	1.92401e10i	0.149044	−	0.653003i
$981$	6.98579e8	+	3.06067e9i	0.0236251	+	0.103508i
$982$	−1.12322e10	+	5.40914e9i	−0.378507	+	0.182280i
$983$	1.80430e10	−	3.74666e10i	0.605858	−	1.25808i	−0.342095	−	0.939666i	$-0.611136\pi$
$983$	1.80430e10	−	3.74666e10i	0.605858	−	1.25808i	0.947953	−	0.318411i	$-0.103149\pi$
$984$	−9.74824e10	+	2.22497e10i	−3.26170	+	0.744461i
$985$	−4.17642e9			−0.139244
$986$	−9.16082e10	+	2.89255e10i	−3.04344	+	0.960976i
$987$	2.04480e10			0.676926
$988$	3.41429e10	−	7.79290e9i	1.12629	−	0.257069i
$989$	−3.93531e9	+	8.17176e9i	−0.129358	+	0.268614i
$990$	5.51830e9	−	2.65747e9i	0.180752	−	0.0870454i
$991$	6.90243e9	+	3.02415e10i	0.225291	+	0.987065i	0.953425	+	0.301630i	$0.0975307\pi$
$991$	6.90243e9	+	3.02415e10i	0.225291	+	0.987065i	−0.728134	+	0.685435i	$0.759612\pi$
$992$	1.62044e7	−	7.09961e7i	0.000527038	−	0.00230911i
$993$	3.45871e10	+	1.66563e10i	1.12096	+	0.539828i
$994$	2.11255e10	−	1.68470e10i	0.682267	−	0.544090i
$995$	8.16954e9	+	1.02443e10i	0.262916	+	0.329686i
$996$	−1.46461e10	−	3.04129e10i	−0.469693	−	0.975328i
$997$	2.90822e10	+	2.31922e10i	0.929381	+	0.741156i	0.966100	−	0.258169i	$-0.0831193\pi$
$997$	2.90822e10	+	2.31922e10i	0.929381	+	0.741156i	−0.0367191	+	0.999326i	$0.511691\pi$
$998$		−	3.33292e10i		−	1.06137i
$999$	−1.01101e10	+	1.26777e10i	−0.320831	+	0.402309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.e.a.22.16	yes	96
29.4	even	14	inner	29.8.e.a.4.16	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.e.a.4.16	✓	96	29.4	even	14	inner
29.8.e.a.22.16	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(19.1958 - 4.38132i) q^{2} +(-23.2918 + 48.3658i) q^{3} +(233.959 - 112.669i) q^{4} +(36.5819 + 160.276i) q^{5} +(-235.198 + 1030.47i) q^{6} +(541.526 + 260.785i) q^{7} +(2026.99 - 1616.47i) q^{8} +(-433.175 - 543.185i) q^{9} +O(q^{10})\)	\(q+(19.1958 - 4.38132i) q^{2} +(-23.2918 + 48.3658i) q^{3} +(233.959 - 112.669i) q^{4} +(36.5819 + 160.276i) q^{5} +(-235.198 + 1030.47i) q^{6} +(541.526 + 260.785i) q^{7} +(2026.99 - 1616.47i) q^{8} +(-433.175 - 543.185i) q^{9} +(1404.44 + 2916.35i) q^{10} +(2129.34 + 1698.09i) q^{11} +13939.9i q^{12} +(-1921.80 + 2409.86i) q^{13} +(11537.6 + 2633.39i) q^{14} +(-8603.92 - 1963.79i) q^{15} +(11103.6 - 13923.4i) q^{16} -37148.8i q^{17} +(-10695.0 - 8528.99i) q^{18} +(-18984.2 - 39421.2i) q^{19} +(26616.7 + 33376.3i) q^{20} +(-25226.2 + 20117.2i) q^{21} +(48314.3 + 23267.0i) q^{22} +(-7058.45 + 30925.1i) q^{23} +(30969.7 + 135687. i) q^{24} +(46038.1 - 22170.8i) q^{25} +(-26332.1 + 54679.1i) q^{26} +(-78098.1 + 17825.4i) q^{27} +156077. q^{28} +(-10685.2 - 130903. i) q^{29} -173763. q^{30} +(3778.37 - 862.388i) q^{31} +(8152.75 - 16929.4i) q^{32} +(-131726. + 63435.8i) q^{33} +(-162761. - 713101. i) q^{34} +(-21987.5 + 96333.5i) q^{35} +(-162545. - 78277.7i) q^{36} +(158260. - 126208. i) q^{37} +(-537135. - 673546. i) q^{38} +(-71792.7 - 149079. i) q^{39} +(333231. + 265743. i) q^{40} +718435. i q^{41} +(-396097. + 496690. i) q^{42} +(278766. + 63626.5i) q^{43} +(689501. + 157374. i) q^{44} +(71212.9 - 89298.2i) q^{45} +624557. i q^{46} +(-495480. - 395132. i) q^{47} +(414797. + 861334. i) q^{48} +(-288229. - 361428. i) q^{49} +(786602. - 627294. i) q^{50} +(1.79673e6 + 865260. i) q^{51} +(-178106. + 780334. i) q^{52} +(-180885. - 792508. i) q^{53} +(-1.42106e6 + 684345. i) q^{54} +(-194268. + 403401. i) q^{55} +(1.51922e6 - 346751. i) q^{56} +2.34882e6 q^{57} +(-778641. - 2.46598e6i) q^{58} +2.65624e6 q^{59} +(-2.23422e6 + 509947. i) q^{60} +(-1.08586e6 + 2.25482e6i) q^{61} +(68750.4 - 33108.5i) q^{62} +(-92921.2 - 407114. i) q^{63} +(-424915. + 1.86167e6i) q^{64} +(-456544. - 219860. i) q^{65} +(-2.25065e6 + 1.79483e6i) q^{66} +(1.09962e6 + 1.37888e6i) q^{67} +(-4.18551e6 - 8.69129e6i) q^{68} +(-1.33131e6 - 1.06169e6i) q^{69} +1.94553e6i q^{70} +(1.42357e6 - 1.78510e6i) q^{71} +(-1.75608e6 - 400814. i) q^{72} +(1.61857e6 + 369428. i) q^{73} +(2.48497e6 - 3.11606e6i) q^{74} +2.74307e6i q^{75} +(-8.88308e6 - 7.08402e6i) q^{76} +(710257. + 1.47486e6i) q^{77} +(-2.03128e6 - 2.54715e6i) q^{78} +(838507. - 668687. i) q^{79} +(2.63778e6 + 1.27029e6i) q^{80} +(1.29501e6 - 5.67380e6i) q^{81} +(3.14769e6 + 1.37909e7i) q^{82} +(-2.18172e6 + 1.05066e6i) q^{83} +(-3.63532e6 + 7.54881e6i) q^{84} +(5.95405e6 - 1.35897e6i) q^{85} +5.62991e6 q^{86} +(6.58013e6 + 2.53217e6i) q^{87} +7.06106e6 q^{88} +(-9.66496e6 + 2.20596e6i) q^{89} +(975746. - 2.02616e6i) q^{90} +(-1.66916e6 + 803824. i) q^{91} +(1.83290e6 + 8.03047e6i) q^{92} +(-46294.7 + 202830. i) q^{93} +(-1.12423e7 - 5.41402e6i) q^{94} +(5.62378e6 - 4.48482e6i) q^{95} +(628911. + 788629. i) q^{96} +(-5.50297e6 - 1.14270e7i) q^{97} +(-7.11632e6 - 5.67508e6i) q^{98} -1.89220e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9}+O(q^{10}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9	\( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9} - 7 q^{10} + 4207 q^{11} + 377 q^{13} - 7 q^{14} - 74473 q^{15} - 125851 q^{16} - 194880 q^{18} - 7 q^{19} + 162901 q^{20} + 86933 q^{21} + 252614 q^{22} + 238675 q^{23} - 490819 q^{24} - 107349 q^{25} + 367017 q^{26} + 75593 q^{27} + 1397540 q^{28} + 379863 q^{29} - 175646 q^{30} - 143885 q^{31} + 473172 q^{32} - 1419437 q^{33} - 2314463 q^{34} - 1018325 q^{35} + 1720462 q^{36} + 662991 q^{37} - 2763860 q^{38} + 42189 q^{39} + 580601 q^{40} - 3296492 q^{42} - 1587425 q^{43} + 2344398 q^{44} + 6508254 q^{45} + 526673 q^{47} + 6175806 q^{48} - 1391517 q^{49} - 4194526 q^{50} - 68204 q^{51} - 7720808 q^{52} + 1762640 q^{53} - 2032428 q^{54} + 2655709 q^{55} + 17091081 q^{56} + 4906842 q^{57} + 13231229 q^{58} - 8638324 q^{59} - 9957136 q^{60} + 2797697 q^{61} - 884069 q^{62} - 20232301 q^{63} - 17528026 q^{64} - 7454088 q^{65} - 17541475 q^{66} - 4890949 q^{67} + 22029140 q^{68} + 13204429 q^{69} - 1091301 q^{71} + 25137595 q^{72} + 14363636 q^{73} + 3185328 q^{74} - 41019881 q^{76} - 25204627 q^{77} - 15753743 q^{78} + 31186057 q^{79} + 24146022 q^{80} - 29435757 q^{81} - 51438506 q^{82} - 8367235 q^{83} + 78906093 q^{84} + 41540198 q^{85} + 65794492 q^{86} + 11089375 q^{87} + 39260390 q^{88} + 6628699 q^{89} + 32127214 q^{90} + 24315293 q^{91} - 39469980 q^{92} - 31050649 q^{93} - 102445588 q^{94} - 75684679 q^{95} - 95069050 q^{96} + 38131380 q^{97} + 19581828 q^{98}+O(q^{100}) \) 96 * q - 7 * q^2 - 7 * q^3 + 709 * q^4 + 191 * q^5 + 1801 * q^6 - 667 * q^7 + 9086 * q^8 + 9103 * q^9 - 7 * q^10 + 4207 * q^11 + 377 * q^13 - 7 * q^14 - 74473 * q^15 - 125851 * q^16 - 194880 * q^18 - 7 * q^19 + 162901 * q^20 + 86933 * q^21 + 252614 * q^22 + 238675 * q^23 - 490819 * q^24 - 107349 * q^25 + 367017 * q^26 + 75593 * q^27 + 1397540 * q^28 + 379863 * q^29 - 175646 * q^30 - 143885 * q^31 + 473172 * q^32 - 1419437 * q^33 - 2314463 * q^34 - 1018325 * q^35 + 1720462 * q^36 + 662991 * q^37 - 2763860 * q^38 + 42189 * q^39 + 580601 * q^40 - 3296492 * q^42 - 1587425 * q^43 + 2344398 * q^44 + 6508254 * q^45 + 526673 * q^47 + 6175806 * q^48 - 1391517 * q^49 - 4194526 * q^50 - 68204 * q^51 - 7720808 * q^52 + 1762640 * q^53 - 2032428 * q^54 + 2655709 * q^55 + 17091081 * q^56 + 4906842 * q^57 + 13231229 * q^58 - 8638324 * q^59 - 9957136 * q^60 + 2797697 * q^61 - 884069 * q^62 - 20232301 * q^63 - 17528026 * q^64 - 7454088 * q^65 - 17541475 * q^66 - 4890949 * q^67 + 22029140 * q^68 + 13204429 * q^69 - 1091301 * q^71 + 25137595 * q^72 + 14363636 * q^73 + 3185328 * q^74 - 41019881 * q^76 - 25204627 * q^77 - 15753743 * q^78 + 31186057 * q^79 + 24146022 * q^80 - 29435757 * q^81 - 51438506 * q^82 - 8367235 * q^83 + 78906093 * q^84 + 41540198 * q^85 + 65794492 * q^86 + 11089375 * q^87 + 39260390 * q^88 + 6628699 * q^89 + 32127214 * q^90 + 24315293 * q^91 - 39469980 * q^92 - 31050649 * q^93 - 102445588 * q^94 - 75684679 * q^95 - 95069050 * q^96 + 38131380 * q^97 + 19581828 * q^98

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