LMFDB - Embedded newform 13.8.e.a.4.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,8,Mod(4,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.4"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	13.e (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.06100533129$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 1279 x^{12} + 629380 x^{10} + 148562016 x^{8} + 16872573312 x^{6} + 790180980480 x^{4} + \cdots + 4669637050368 $ x^14 + 1279x^12 + 629380x^10 + 148562016x^8 + 16872573312x^6 + 790180980480x^4 + 10484997239808x^2 + 4669637050368
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.6
Root			$14.7644i$ of defining polynomial
Character	$\chi$	$=$	13.4
Dual form			13.8.e.a.10.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.7863 + 7.38219i) q^{2} +(-22.6982 + 39.3144i) q^{3} +(44.9933 + 77.9308i) q^{4} +248.787i q^{5} +(-580.452 + 335.124i) q^{6} +(497.017 - 286.953i) q^{7} -561.243i q^{8} +(63.0878 + 109.271i) q^{9} +(-1836.59 + 3181.07i) q^{10} +(3411.39 + 1969.56i) q^{11} -4085.06 q^{12} +(2867.43 - 7384.20i) q^{13} +8473.37 q^{14} +(-9780.91 - 5647.01i) q^{15} +(9902.35 - 17151.4i) q^{16} +(-7791.62 - 13495.5i) q^{17} +1862.90i q^{18} +(-1742.44 + 1006.00i) q^{19} +(-19388.2 + 11193.8i) q^{20} +26053.2i q^{21} +(29079.4 + 50367.0i) q^{22} +(-33680.6 + 58336.5i) q^{23} +(22064.9 + 12739.2i) q^{24} +16229.9 q^{25} +(91175.3 - 73248.9i) q^{26} -105010. q^{27} +(44724.9 + 25822.0i) q^{28} +(-94582.0 + 163821. i) q^{29} +(-83374.5 - 144409. i) q^{30} -281068. i q^{31} +(191015. - 110282. i) q^{32} +(-154864. + 89410.9i) q^{33} -230077. i q^{34} +(71390.3 + 123652. i) q^{35} +(-5677.07 + 9832.97i) q^{36} +(228285. + 131800. i) q^{37} -29705.8 q^{38} +(225220. + 280339. i) q^{39} +139630. q^{40} +(-125678. - 72560.2i) q^{41} +(-192330. + 333125. i) q^{42} +(-371259. - 643040. i) q^{43} +354469. i q^{44} +(-27185.3 + 15695.4i) q^{45} +(-861302. + 497273. i) q^{46} -1.08055e6i q^{47} +(449530. + 778609. i) q^{48} +(-247087. + 427968. i) q^{49} +(207521. + 119812. i) q^{50} +707422. q^{51} +(704471. - 108779. i) q^{52} +1.63799e6 q^{53} +(-1.34269e6 - 775201. i) q^{54} +(-490002. + 848709. i) q^{55} +(-161050. - 278947. i) q^{56} -91337.1i q^{57} +(-2.41871e6 + 1.39644e6i) q^{58} +(778187. - 449287. i) q^{59} -1.01631e6i q^{60} +(-254459. - 440737. i) q^{61} +(2.07490e6 - 3.59383e6i) q^{62} +(62711.5 + 36206.5i) q^{63} +721500. q^{64} +(1.83709e6 + 713379. i) q^{65} -2.64019e6 q^{66} +(315772. + 182311. i) q^{67} +(701142. - 1.21441e6i) q^{68} +(-1.52897e6 - 2.64826e6i) q^{69} +2.10806e6i q^{70} +(-2.46548e6 + 1.42345e6i) q^{71} +(61327.8 - 35407.6i) q^{72} +4.44132e6i q^{73} +(1.94595e6 + 3.37048e6i) q^{74} +(-368390. + 638070. i) q^{75} +(-156796. - 90526.4i) q^{76} +2.26069e6 q^{77} +(810220. + 5.24711e6i) q^{78} -6.66251e6 q^{79} +(4.26704e6 + 2.46358e6i) q^{80} +(2.24555e6 - 3.88941e6i) q^{81} +(-1.07131e6 - 1.85556e6i) q^{82} +4.05229e6i q^{83} +(-2.03035e6 + 1.17222e6i) q^{84} +(3.35750e6 - 1.93846e6i) q^{85} -1.09628e7i q^{86} +(-4.29367e6 - 7.43686e6i) q^{87} +(1.10540e6 - 1.91462e6i) q^{88} +(-1.01547e6 - 586279. i) q^{89} -463467. q^{90} +(-693759. - 4.49289e6i) q^{91} -6.06161e6 q^{92} +(1.10500e7 + 6.37973e6i) q^{93} +(7.97686e6 - 1.38163e7i) q^{94} +(-250279. - 433496. i) q^{95} +1.00128e7i q^{96} +(-1.12996e7 + 6.52384e6i) q^{97} +(-6.31867e6 + 3.64809e6i) q^{98} +497022. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} + 26 q^{3} + 383 q^{4} - 264 q^{6} - 2772 q^{7} - 3491 q^{9} - 509 q^{10} + 6516 q^{11} + 38380 q^{12} + 5109 q^{13} - 47916 q^{14} - 19266 q^{15} - 633 q^{16} - 38403 q^{17} + 43254 q^{19}+ \cdots + 16173003 q^{98}+O(q^{100}) $ 14 * q - 3 * q^2 + 26 * q^3 + 383 * q^4 - 264 * q^6 - 2772 * q^7 - 3491 * q^9 - 509 * q^10 + 6516 * q^11 + 38380 * q^12 + 5109 * q^13 - 47916 * q^14 - 19266 * q^15 - 633 * q^16 - 38403 * q^17 + 43254 * q^19 + 89409 * q^20 - 125882 * q^22 - 68550 * q^23 + 224454 * q^24 + 39380 * q^25 + 361959 * q^26 - 432400 * q^27 - 234780 * q^28 + 221583 * q^29 - 157890 * q^30 - 878067 * q^32 + 219756 * q^33 + 659616 * q^35 + 635675 * q^36 - 565347 * q^37 + 953640 * q^38 + 30082 * q^39 - 77182 * q^40 + 1716057 * q^41 + 206406 * q^42 - 882692 * q^43 - 4616853 * q^45 - 3267480 * q^46 + 1133630 * q^48 + 2653979 * q^49 + 145128 * q^50 - 38964 * q^51 + 4962178 * q^52 - 1791210 * q^53 + 9597234 * q^54 + 2453536 * q^55 - 7457952 * q^56 - 14978127 * q^58 - 1189032 * q^59 + 3858525 * q^61 + 1904142 * q^62 + 7718520 * q^63 + 14570922 * q^64 + 10424661 * q^65 - 31956396 * q^66 + 4674330 * q^67 + 9569619 * q^68 - 13743840 * q^69 - 25203126 * q^71 - 6851607 * q^72 + 8640105 * q^74 + 10316152 * q^75 + 12934506 * q^76 + 19599336 * q^77 + 50085750 * q^78 - 30688440 * q^79 + 29127963 * q^80 + 13886221 * q^81 - 37359719 * q^82 - 96398508 * q^84 - 22436313 * q^85 + 12769686 * q^87 + 27045536 * q^88 + 2123160 * q^89 + 41193546 * q^90 + 37205532 * q^91 - 47685588 * q^92 + 36638964 * q^93 + 19138810 * q^94 - 43420386 * q^95 - 68556288 * q^97 + 16173003 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	12.7863	+	7.38219i	1.13016	+	0.652499i	0.943976	−	0.330015i	$-0.107054\pi$
$2$	12.7863	+	7.38219i	1.13016	+	0.652499i	0.186186	+	0.982514i	$0.440387\pi$
$3$	−22.6982	+	39.3144i	−0.485362	+	0.840672i	−0.999859	−	0.0168204i	$-0.994646\pi$
$3$	−22.6982	+	39.3144i	−0.485362	+	0.840672i	0.514496	+	0.857493i	$0.327979\pi$
$4$	44.9933	+	77.9308i	0.351510	+	0.608834i
$5$			248.787i			0.890088i	0.895509	+	0.445044i	$0.146812\pi$
$5$			248.787i			0.890088i	−0.895509	+	0.445044i	$0.853188\pi$
$6$	−580.452	+	335.124i	−1.09708	+	0.633397i
$7$	497.017	−	286.953i	0.547682	−	0.316204i	−0.200505	−	0.979693i	$-0.564258\pi$
$7$	497.017	−	286.953i	0.547682	−	0.316204i	0.748187	+	0.663488i	$0.230925\pi$
$8$		−	561.243i		−	0.387557i
$9$	63.0878	+	109.271i	0.0288468	+	0.0499640i
$10$	−1836.59	+	3181.07i	−0.580782	+	1.00594i
$11$	3411.39	+	1969.56i	0.772781	+	0.446165i	0.833866	−	0.551967i	$-0.186123\pi$
$11$	3411.39	+	1969.56i	0.772781	+	0.446165i	−0.0610849	+	0.998133i	$0.519456\pi$
$12$	−4085.06			−0.682440
$13$	2867.43	−	7384.20i	0.361985	−	0.932184i
$13$	2867.43	−	7384.20i	0.361985	−	0.932184i
$14$	8473.37			0.825292
$15$	−9780.91	−	5647.01i	−0.748272	−	0.432015i
$16$	9902.35	−	17151.4i	0.604391	−	1.04684i
$17$	−7791.62	−	13495.5i	−0.384642	−	0.666220i	0.607077	−	0.794643i	$-0.292342\pi$
$17$	−7791.62	−	13495.5i	−0.384642	−	0.666220i	−0.991719	+	0.128423i	$0.959008\pi$
$18$			1862.90i			0.0752899i
$19$	−1742.44	+	1006.00i	−0.0582800	+	0.0336480i	−0.528857	−	0.848711i	$-0.677379\pi$
$19$	−1742.44	+	1006.00i	−0.0582800	+	0.0336480i	0.470577	+	0.882359i	$0.344046\pi$
$20$	−19388.2	+	11193.8i	−0.541916	+	0.312875i
$21$			26053.2i			0.613895i
$22$	29079.4	+	50367.0i	0.582245	+	1.00848i
$23$	−33680.6	+	58336.5i	−0.577208	+	0.999753i	0.418590	+	0.908175i	$0.362524\pi$
$23$	−33680.6	+	58336.5i	−0.577208	+	0.999753i	−0.995798	+	0.0915781i	$0.970809\pi$
$24$	22064.9	+	12739.2i	0.325809	+	0.188106i
$25$	16229.9			0.207743
$26$	91175.3	−	73248.9i	1.01735	−	0.817324i
$27$	−105010.			−1.02673
$28$	44724.9	+	25822.0i	0.385032	+	0.222298i
$29$	−94582.0	+	163821.i	−0.720138	+	1.24732i	0.240807	+	0.970573i	$0.422588\pi$
$29$	−94582.0	+	163821.i	−0.720138	+	1.24732i	−0.960944	+	0.276742i	$0.910745\pi$
$30$	−83374.5	−	144409.i	−0.563779	−	0.976494i
$31$		−	281068.i		−	1.69452i	−0.531181	−	0.847258i	$-0.678252\pi$
$31$		−	281068.i		−	1.69452i	0.531181	−	0.847258i	$-0.321748\pi$
$32$	191015.	−	110282.i	1.03049	−	0.594951i
$33$	−154864.	+	89410.9i	−0.750158	+	0.433104i
$34$		−	230077.i		−	1.00391i
$35$	71390.3	+	123652.i	0.281450	+	0.487485i
$36$	−5677.07	+	9832.97i	−0.0202799	+	0.0351258i
$37$	228285.	+	131800.i	0.740920	+	0.427770i	0.822404	−	0.568904i	$-0.192633\pi$
$37$	228285.	+	131800.i	0.740920	+	0.427770i	−0.0814838	+	0.996675i	$0.525966\pi$
$38$	−29705.8			−0.0878212
$39$	225220.	+	280339.i	0.607967	+	0.756758i
$40$	139630.			0.344960
$41$	−125678.	−	72560.2i	−0.284784	−	0.164420i	0.350803	−	0.936449i	$-0.385909\pi$
$41$	−125678.	−	72560.2i	−0.284784	−	0.164420i	−0.635587	+	0.772029i	$0.719242\pi$
$42$	−192330.	+	333125.i	−0.400566	+	0.693800i
$43$	−371259.	−	643040.i	−0.712095	−	1.23338i	−0.964069	−	0.265650i	$-0.914413\pi$
$43$	−371259.	−	643040.i	−0.712095	−	1.23338i	0.251975	−	0.967734i	$-0.418920\pi$
$44$			354469.i			0.627327i
$45$	−27185.3	+	15695.4i	−0.0444724	+	0.0256761i
$46$	−861302.	+	497273.i	−1.30468	+	0.753255i
$47$		−	1.08055e6i		−	1.51811i	−0.651024	−	0.759057i	$-0.725660\pi$
$47$		−	1.08055e6i		−	1.51811i	0.651024	−	0.759057i	$-0.274340\pi$
$48$	449530.	+	778609.i	0.586698	+	1.01619i
$49$	−247087.	+	427968.i	−0.300030	+	0.519667i
$50$	207521.	+	119812.i	0.234784	+	0.135552i
$51$	707422.			0.746763
$52$	704471.	−	108779.i	0.694787	−	0.107284i
$53$	1.63799e6			1.51128			0.755642	−	0.654985i	$-0.227325\pi$
$53$	1.63799e6			1.51128			0.755642	+	0.654985i	$0.227325\pi$
$54$	−1.34269e6	−	775201.i	−1.16037	−	0.669940i
$55$	−490002.	+	848709.i	−0.397126	+	0.687843i
$56$	−161050.	−	278947.i	−0.122547	−	0.212258i
$57$		−	91337.1i		−	0.0653259i
$58$	−2.41871e6	+	1.39644e6i	−1.62774	+	0.939779i
$59$	778187.	−	449287.i	0.493290	−	0.284801i	−0.232649	−	0.972561i	$-0.574739\pi$
$59$	778187.	−	449287.i	0.493290	−	0.284801i	0.725938	+	0.687760i	$0.241406\pi$
$60$		−	1.01631e6i		−	0.607431i
$61$	−254459.	−	440737.i	−0.143537	−	0.248614i	0.785289	−	0.619129i	$-0.212514\pi$
$61$	−254459.	−	440737.i	−0.143537	−	0.248614i	−0.928826	+	0.370516i	$0.879181\pi$
$62$	2.07490e6	−	3.59383e6i	1.10567	−	1.91508i
$63$	62711.5	+	36206.5i	0.0315977	+	0.0182429i
$64$	721500.			0.344038
$65$	1.83709e6	+	713379.i	0.829726	+	0.322198i
$66$	−2.64019e6			−1.13040
$67$	315772.	+	182311.i	0.128266	+	0.0740544i	0.562760	−	0.826620i	$-0.309739\pi$
$67$	315772.	+	182311.i	0.128266	+	0.0740544i	−0.434494	+	0.900675i	$0.643073\pi$
$68$	701142.	−	1.21441e6i	0.270411	−	0.468366i
$69$	−1.52897e6	−	2.64826e6i	−0.560310	−	0.970485i
$70$			2.10806e6i			0.734583i
$71$	−2.46548e6	+	1.42345e6i	−0.817518	+	0.471994i	−0.849560	−	0.527492i	$-0.823132\pi$
$71$	−2.46548e6	+	1.42345e6i	−0.817518	+	0.471994i	0.0320418	+	0.999487i	$0.489799\pi$
$72$	61327.8	−	35407.6i	0.0193639	−	0.0111798i
$73$			4.44132e6i			1.33623i	0.744057	+	0.668116i	$0.232899\pi$
$73$			4.44132e6i			1.33623i	−0.744057	+	0.668116i	$0.767101\pi$
$74$	1.94595e6	+	3.37048e6i	0.558240	+	0.966899i
$75$	−368390.	+	638070.i	−0.100831	+	0.174644i
$76$	−156796.	−	90526.4i	−0.0409721	−	0.0236552i
$77$	2.26069e6			0.564318
$78$	810220.	+	5.24711e6i	0.193318	+	1.25196i
$79$	−6.66251e6			−1.52035			−0.760174	−	0.649720i	$-0.774886\pi$
$79$	−6.66251e6			−1.52035			−0.760174	+	0.649720i	$0.774886\pi$
$80$	4.26704e6	+	2.46358e6i	0.931776	+	0.537961i
$81$	2.24555e6	−	3.88941e6i	0.469489	−	0.813179i
$82$	−1.07131e6	−	1.85556e6i	−0.214568	−	0.371643i
$83$			4.05229e6i			0.777906i	0.921258	+	0.388953i	$0.127163\pi$
$83$			4.05229e6i			0.777906i	−0.921258	+	0.388953i	$0.872837\pi$
$84$	−2.03035e6	+	1.17222e6i	−0.373760	+	0.215790i
$85$	3.35750e6	−	1.93846e6i	0.592994	−	0.342365i
$86$		−	1.09628e7i		−	1.85856i
$87$	−4.29367e6	−	7.43686e6i	−0.699056	−	1.21080i
$88$	1.10540e6	−	1.91462e6i	0.172915	−	0.299497i
$89$	−1.01547e6	−	586279.i	−0.152686	−	0.0881535i	0.421710	−	0.906731i	$-0.361430\pi$
$89$	−1.01547e6	−	586279.i	−0.152686	−	0.0881535i	−0.574397	+	0.818577i	$0.694763\pi$
$90$	−463467.			−0.0670147
$91$	−693759.	−	4.49289e6i	−0.0965081	−	0.625002i
$92$	−6.06161e6			−0.811578
$93$	1.10500e7	+	6.37973e6i	1.42453	+	0.822454i
$94$	7.97686e6	−	1.38163e7i	0.990568	−	1.71571i
$95$	−250279.	−	433496.i	−0.0299497	−	0.0518744i
$96$			1.00128e7i			1.15507i
$97$	−1.12996e7	+	6.52384e6i	−1.25708	+	0.725776i	−0.972506	−	0.232878i	$-0.925186\pi$
$97$	−1.12996e7	+	6.52384e6i	−1.25708	+	0.725776i	−0.284574	+	0.958654i	$0.591852\pi$
$98$	−6.31867e6	+	3.64809e6i	−0.678164	+	0.391538i
$99$			497022.i			0.0514817i
$100$	730240.	+	1.26481e6i	0.0730240	+	0.126481i
$101$	712550.	−	1.23417e6i	0.0688162	−	0.119193i	−0.829564	−	0.558411i	$-0.811411\pi$
$101$	712550.	−	1.23417e6i	0.0688162	−	0.119193i	0.898380	+	0.439218i	$0.144744\pi$
$102$	9.04532e6	+	5.22232e6i	0.843963	+	0.487262i
$103$	3.43743e6			0.309959			0.154979	−	0.987918i	$-0.450469\pi$
$103$	3.43743e6			0.309959			0.154979	+	0.987918i	$0.450469\pi$
$104$	−4.14433e6	−	1.60932e6i	−0.361275	−	0.140290i
$105$	−6.48171e6			−0.546420
$106$	2.09439e7	+	1.20920e7i	1.70800	+	0.986112i
$107$	4.55117e6	−	7.88286e6i	0.359153	−	0.622072i	−0.628666	−	0.777675i	$-0.716399\pi$
$107$	4.55117e6	−	7.88286e6i	0.359153	−	0.622072i	0.987820	+	0.155604i	$0.0497322\pi$
$108$	−4.72473e6	−	8.18348e6i	−0.360906	−	0.625108i
$109$			3.25125e6i			0.240468i	0.992746	+	0.120234i	$0.0383646\pi$
$109$			3.25125e6i			0.240468i	−0.992746	+	0.120234i	$0.961635\pi$
$110$	−1.25307e7	+	7.23458e6i	−0.897634	+	0.518249i
$111$	−1.03633e7	+	5.98325e6i	−0.719229	+	0.415247i
$112$		−	1.13660e7i		−	0.764445i
$113$	1.18415e7	+	2.05100e7i	0.772023	+	1.33718i	0.936452	+	0.350794i	$0.114088\pi$
$113$	1.18415e7	+	2.05100e7i	0.772023	+	1.33718i	−0.164429	+	0.986389i	$0.552578\pi$
$114$	674268.	−	1.16787e6i	0.0426251	−	0.0738288i
$115$	−1.45134e7	−	8.37930e6i	−0.889868	−	0.513766i
$116$	−1.70222e7			−1.01254
$117$	987781.	−	152526.i	0.0570178	−	0.00880426i
$118$	1.32669e7			0.743329
$119$	−7.74515e6	−	4.47166e6i	−0.421323	−	0.243251i
$120$	−3.16934e6	+	5.48946e6i	−0.167431	+	0.289998i
$121$	−1.98522e6	−	3.43850e6i	−0.101873	−	0.176449i
$122$		−	7.51387e6i		−	0.374631i
$123$	5.70531e6	−	3.29396e6i	0.276447	−	0.159607i
$124$	2.19039e7	−	1.26462e7i	1.03168	−	0.595640i
$125$			2.34743e7i			1.07500i
$126$	534566.	+	925896.i	0.0238070	+	0.0412349i
$127$	9.29215e6	−	1.60945e7i	0.402535	−	0.697210i	−0.591497	−	0.806308i	$-0.701463\pi$
$127$	9.29215e6	−	1.60945e7i	0.402535	−	0.697210i	0.994031	+	0.109097i	$0.0347960\pi$
$128$	−1.52246e7	−	8.78990e6i	−0.641667	−	0.370467i
$129$	3.37076e7			1.38250
$130$	1.82234e7	+	2.26833e7i	0.727490	+	0.905532i
$131$	−1.85251e7			−0.719964			−0.359982	−	0.932959i	$-0.617217\pi$
$131$	−1.85251e7			−0.719964			−0.359982	+	0.932959i	$0.617217\pi$
$132$	−1.39357e7	−	8.04579e6i	−0.527376	−	0.304481i
$133$	−577348.	+	999996.i	−0.0212793	+	0.0368568i
$134$	2.69171e6	+	4.66217e6i	0.0966409	+	0.167387i
$135$		−	2.61250e7i		−	0.913879i
$136$	−7.57425e6	+	4.37299e6i	−0.258198	+	0.149071i
$137$	−4.37505e6	+	2.52594e6i	−0.145366	+	0.0839268i	−0.570919	−	0.821007i	$-0.693413\pi$
$137$	−4.37505e6	+	2.52594e6i	−0.145366	+	0.0839268i	0.425553	+	0.904933i	$0.360080\pi$
$138$		−	4.51487e7i		−	1.46241i
$139$	−7.79200e6	−	1.34961e7i	−0.246092	−	0.426244i	0.716346	−	0.697745i	$-0.245813\pi$
$139$	−7.79200e6	−	1.34961e7i	−0.246092	−	0.426244i	−0.962438	+	0.271501i	$0.912480\pi$
$140$	−6.42417e6	+	1.11270e7i	−0.197865	+	0.342712i
$141$	4.24813e7	+	2.45266e7i	1.27624	+	0.736835i
$142$	−4.20326e7			−1.23190
$143$	2.43255e7	−	1.95428e7i	0.695643	−	0.558869i
$144$	2.49887e6			0.0697389
$145$	−4.07565e7	−	2.35308e7i	−1.11022	−	0.640986i
$146$	−3.27866e7	+	5.67881e7i	−0.871890	+	1.51016i
$147$	−1.12168e7	−	1.94282e7i	−0.291246	−	0.504453i
$148$			2.37206e7i			0.601463i
$149$	3.21304e7	−	1.85505e7i	0.795727	−	0.459413i	−0.0462480	−	0.998930i	$-0.514726\pi$
$149$	3.21304e7	−	1.85505e7i	0.795727	−	0.459413i	0.841975	+	0.539517i	$0.181393\pi$
$150$	−9.42070e6	+	5.43904e6i	−0.227910	+	0.131584i
$151$			4.72742e7i			1.11739i	0.829373	+	0.558695i	$0.188698\pi$
$151$			4.72742e7i			1.11739i	−0.829373	+	0.558695i	$0.811302\pi$
$152$	564609.	+	977931.i	0.0130405	+	0.0225869i
$153$	983114.	−	1.70280e6i	0.0221913	−	0.0384365i
$154$	2.89059e7	+	1.66888e7i	0.637770	+	0.368217i
$155$	6.99262e7			1.50827
$156$	−1.17136e7	+	3.01649e7i	−0.247033	+	0.636159i
$157$	6.68124e7			1.37787			0.688935	−	0.724823i	$-0.258078\pi$
$157$	6.68124e7			1.37787			0.688935	+	0.724823i	$0.258078\pi$
$158$	−8.51889e7	−	4.91839e7i	−1.71824	−	0.992025i
$159$	−3.71794e7	+	6.43966e7i	−0.733520	+	1.27049i
$160$	2.74368e7	+	4.75220e7i	0.529559	+	0.917223i
$161$			3.86590e7i			0.730063i
$162$	5.74247e7	−	3.31542e7i	1.06120	−	0.612682i
$163$	−4.15217e7	+	2.39725e7i	−0.750962	+	0.433568i	−0.826041	−	0.563609i	$-0.809412\pi$
$163$	−4.15217e7	+	2.39725e7i	−0.750962	+	0.433568i	0.0750793	+	0.997178i	$0.476079\pi$
$164$		−	1.30589e7i		−	0.231181i
$165$	−2.22443e7	−	3.85282e7i	−0.385500	−	0.667706i
$166$	−2.99148e7	+	5.18139e7i	−0.507583	+	0.879160i
$167$	−4.11000e7	−	2.37291e7i	−0.682864	−	0.394252i	0.118069	−	0.993005i	$-0.462330\pi$
$167$	−4.11000e7	−	2.37291e7i	−0.682864	−	0.394252i	−0.800933	+	0.598753i	$0.795663\pi$
$168$	1.46222e7			0.237919
$169$	−4.63043e7	−	4.23473e7i	−0.737934	−	0.674873i
$170$	5.72402e7			0.893572
$171$	−219853.	−	126932.i	−0.00336238	−	0.00194127i
$172$	3.34084e7	−	5.78650e7i	0.500617	−	0.867095i
$173$	−5.19255e7	−	8.99376e7i	−0.762464	−	1.32063i	−0.941577	−	0.336798i	$-0.890656\pi$
$173$	−5.19255e7	−	8.99376e7i	−0.762464	−	1.32063i	0.179113	−	0.983828i	$-0.442677\pi$
$174$		−	1.26787e8i		−	1.82453i
$175$	8.06657e6	−	4.65723e6i	0.113777	−	0.0656893i
$176$	6.75614e7	−	3.90066e7i	0.934124	−	0.539317i
$177$			4.07919e7i			0.552927i
$178$	−8.65604e6	−	1.49927e7i	−0.115040	−	0.199255i
$179$	−1.01888e7	+	1.76475e7i	−0.132782	+	0.229984i	−0.924748	−	0.380581i	$-0.875724\pi$
$179$	−1.01888e7	+	1.76475e7i	−0.132782	+	0.229984i	0.791966	+	0.610565i	$0.209058\pi$
$180$	−2.44632e6	−	1.41238e6i	−0.0312650	−	0.0180509i
$181$	−5.61052e7			−0.703280			−0.351640	−	0.936135i	$-0.614376\pi$
$181$	−5.61052e7			−0.703280			−0.351640	+	0.936135i	$0.614376\pi$
$182$	2.42967e7	−	6.25690e7i	0.298743	−	0.769324i
$183$	2.31030e7			0.278670
$184$	3.27409e7	+	1.89030e7i	0.387462	+	0.223701i
$185$	−3.27902e7	+	5.67944e7i	−0.380753	+	0.659484i
$186$	9.41927e7	+	1.63147e8i	1.07330	+	1.85901i
$187$		−	6.13844e7i		−	0.686456i
$188$	8.42085e7	−	4.86178e7i	0.924279	−	0.533633i
$189$	−5.21916e7	+	3.01328e7i	−0.562321	+	0.324656i
$190$		−	7.39043e6i		−	0.0781686i
$191$	4.54840e7	+	7.87807e7i	0.472326	+	0.818093i	0.999499	−	0.0316651i	$-0.0100810\pi$
$191$	4.54840e7	+	7.87807e7i	0.472326	+	0.818093i	−0.527172	+	0.849759i	$0.676748\pi$
$192$	−1.63767e7	+	2.83653e7i	−0.166983	+	0.289223i
$193$	−5.70124e7	−	3.29162e7i	−0.570846	−	0.329578i	0.186641	−	0.982428i	$-0.440240\pi$
$193$	−5.70124e7	−	3.29162e7i	−0.570846	−	0.329578i	−0.757487	+	0.652850i	$0.773573\pi$
$194$	−1.92641e8			−1.89427
$195$	−6.97446e7	+	5.60318e7i	−0.673581	+	0.541145i
$196$	−4.44691e7			−0.421854
$197$	1.26253e8	+	7.28923e7i	1.17655	+	0.679281i	0.955214	−	0.295916i	$-0.0956250\pi$
$197$	1.26253e8	+	7.28923e7i	1.17655	+	0.679281i	0.221336	+	0.975198i	$0.428958\pi$
$198$	−3.66911e6	+	6.35509e6i	−0.0335918	+	0.0581826i
$199$	4.88672e7	+	8.46405e7i	0.439574	+	0.761364i	0.997657	−	0.0684210i	$-0.0217961\pi$
$199$	4.88672e7	+	8.46405e7i	0.439574	+	0.761364i	−0.558083	+	0.829785i	$0.688463\pi$
$200$		−	9.10894e6i		−	0.0805124i
$201$	−1.43349e7	+	8.27625e6i	−0.124511	+	0.0718865i
$202$	1.82218e7	−	1.05204e7i	0.155547	−	0.0898050i
$203$			1.08562e8i			0.910843i
$204$	3.18293e7	+	5.51299e7i	0.262495	+	0.454655i
$205$	1.80520e7	−	3.12670e7i	0.146348	−	0.253483i
$206$	4.39521e7	+	2.53758e7i	0.350304	+	0.202248i
$207$	−8.49934e6			−0.0666023
$208$	−9.82549e7	−	1.22301e8i	−0.757064	−	0.942343i
$209$	−7.92551e6			−0.0600503
$210$	−8.28772e7	−	4.78492e7i	−0.617543	−	0.356539i
$211$	6.34096e7	−	1.09829e8i	0.464693	−	0.804872i	−0.534494	−	0.845172i	$-0.679498\pi$
$211$	6.34096e7	−	1.09829e8i	0.464693	−	0.804872i	0.999188	+	0.0402998i	$0.0128313\pi$
$212$	7.36987e7	+	1.27650e8i	0.531232	+	0.920121i
$213$		−	1.29238e8i		−	0.916353i
$214$	1.16385e8	−	6.71951e7i	0.811802	−	0.468694i
$215$	1.59980e8	−	9.23645e7i	1.09782	−	0.633827i
$216$			5.89359e7i			0.397916i
$217$	−8.06534e7	−	1.39696e8i	−0.535813	−	0.928056i
$218$	−2.40014e7	+	4.15716e7i	−0.156905	+	0.271768i
$219$	−1.74608e8	−	1.00810e8i	−1.12333	−	0.648557i
$220$	−8.81874e7			−0.558376
$221$	−1.21995e8	+	1.88376e7i	−0.760274	+	0.117396i
$222$	−1.76678e8			−1.08379
$223$	1.54510e8	+	8.92066e7i	0.933019	+	0.538679i	0.887765	−	0.460296i	$-0.152257\pi$
$223$	1.54510e8	+	8.92066e7i	0.933019	+	0.538679i	0.0452542	+	0.998976i	$0.485590\pi$
$224$	6.32918e7	−	1.09625e8i	0.376252	−	0.651688i
$225$	1.02391e6	+	1.77347e6i	0.00599272	+	0.0103797i
$226$			3.49663e8i			2.01498i
$227$	9.00440e7	−	5.19869e7i	0.510934	−	0.294988i	−0.222284	−	0.974982i	$-0.571351\pi$
$227$	9.00440e7	−	5.19869e7i	0.510934	−	0.294988i	0.733217	+	0.679994i	$0.238018\pi$
$228$	7.11797e6	−	4.10956e6i	0.0397726	−	0.0229627i
$229$			4.93769e7i			0.271706i	0.990729	+	0.135853i	$0.0433776\pi$
$229$			4.93769e7i			0.271706i	−0.990729	+	0.135853i	$0.956622\pi$
$230$	−1.23715e8	−	2.14281e8i	−0.670464	−	1.16128i
$231$	−5.13135e7	+	8.88776e7i	−0.273899	+	0.474406i
$232$	9.19433e7	+	5.30835e7i	0.483406	+	0.279095i
$233$	2.49971e8			1.29462			0.647312	−	0.762225i	$-0.275893\pi$
$233$	2.49971e8			1.29462			0.647312	+	0.762225i	$0.275893\pi$
$234$	1.37561e7	+	5.34174e6i	0.0701841	+	0.0272538i
$235$	2.68828e8			1.35126
$236$	7.00265e7	+	4.04298e7i	0.346793	+	0.200221i
$237$	1.51227e8	−	2.61932e8i	0.737919	−	1.27811i
$238$	−6.60213e7	−	1.14352e8i	−0.317442	−	0.549826i
$239$		−	3.95989e7i		−	0.187625i	−0.995590	−	0.0938124i	$-0.970095\pi$
$239$		−	3.95989e7i		−	0.187625i	0.995590	−	0.0938124i	$-0.0299054\pi$
$240$	−1.93708e8	+	1.11837e8i	−0.904498	+	0.522212i
$241$	−1.70708e8	+	9.85581e7i	−0.785585	+	0.453558i	−0.838406	−	0.545046i	$-0.816512\pi$
$241$	−1.70708e8	+	9.85581e7i	−0.785585	+	0.453558i	0.0528210	+	0.998604i	$0.483179\pi$
$242$		−	5.86210e7i		−	0.265889i
$243$	−1.28883e7	−	2.23232e7i	−0.0576201	−	0.0998009i
$244$	2.28980e7	−	3.96604e7i	0.100910	−	0.174781i
$245$	−1.06473e8	−	6.14721e7i	−0.462549	−	0.267053i
$246$	9.72666e7			0.416573
$247$	2.43217e6	+	1.57511e7i	0.0102696	+	0.0665078i
$248$	−1.57747e8			−0.656722
$249$	−1.59313e8	−	9.19795e7i	−0.653964	−	0.377567i
$250$	−1.73292e8	+	3.00150e8i	−0.701435	+	1.21492i
$251$	1.40289e7	+	2.42988e7i	0.0559972	+	0.0969900i	0.892665	−	0.450720i	$-0.148833\pi$
$251$	1.40289e7	+	2.42988e7i	0.0559972	+	0.0969900i	−0.836668	+	0.547710i	$0.815500\pi$
$252$			6.51621e6i			0.0256503i
$253$	−2.29795e8	+	1.32672e8i	−0.892110	+	0.515060i
$254$	2.37625e8	−	1.37193e8i	0.909858	−	0.525307i
$255$			1.75997e8i			0.664685i
$256$	−1.75953e8	−	3.04760e8i	−0.655477	−	1.13532i
$257$	5.58401e7	−	9.67178e7i	0.205201	−	0.355419i	−0.744996	−	0.667069i	$-0.767548\pi$
$257$	5.58401e7	−	9.67178e7i	0.205201	−	0.355419i	0.950197	+	0.311650i	$0.100882\pi$
$258$	4.30996e8	+	2.48836e8i	1.56244	+	0.902077i
$259$	1.51282e8			0.541051
$260$	2.70629e7	+	1.75263e8i	0.0954920	+	0.618421i
$261$	−2.38679e7			−0.0830945
$262$	−2.36868e8	−	1.36756e8i	−0.813676	−	0.469776i
$263$	−1.61308e8	+	2.79393e8i	−0.546776	+	0.947044i	0.451717	+	0.892162i	$0.350812\pi$
$263$	−1.61308e8	+	2.79393e8i	−0.546776	+	0.947044i	−0.998493	+	0.0548828i	$0.982521\pi$
$264$	5.01812e7	+	8.69165e7i	0.167852	+	0.290729i
$265$			4.07511e8i			1.34518i
$266$	−1.47643e7	+	8.52418e6i	−0.0480981	+	0.0277694i
$267$	4.60984e7	−	2.66149e7i	0.148216	−	0.0855727i
$268$			3.28111e7i			0.104124i
$269$	2.11106e8	+	3.65647e8i	0.661254	+	1.14532i	0.980287	+	0.197581i	$0.0633086\pi$
$269$	2.11106e8	+	3.65647e8i	0.661254	+	1.14532i	−0.319033	+	0.947744i	$0.603358\pi$
$270$	1.92860e8	−	3.34043e8i	0.596306	−	1.03283i
$271$	−1.37631e8	−	7.94615e7i	−0.420073	−	0.242529i	0.275036	−	0.961434i	$-0.411310\pi$
$271$	−1.37631e8	−	7.94615e7i	−0.420073	−	0.242529i	−0.695108	+	0.718905i	$0.744644\pi$
$272$	−3.08621e8			−0.929897
$273$	1.92382e8	+	7.47057e7i	0.572263	+	0.222221i
$274$	−7.45878e7			−0.219049
$275$	5.53666e7	+	3.19659e7i	0.160540	+	0.0926879i
$276$	1.37587e8	−	2.38308e8i	0.393910	−	0.682272i
$277$	−1.43949e8	−	2.49327e8i	−0.406940	−	0.704840i	0.587605	−	0.809148i	$-0.300071\pi$
$277$	−1.43949e8	−	2.49327e8i	−0.406940	−	0.704840i	−0.994545	+	0.104307i	$0.966737\pi$
$278$		−	2.30088e8i		−	0.642299i
$279$	3.07127e7	−	1.77320e7i	0.0846649	−	0.0488813i
$280$	6.93985e7	−	4.00673e7i	0.188928	−	0.109078i
$281$		−	6.26146e8i		−	1.68346i	−0.539897	−	0.841731i	$-0.681537\pi$
$281$		−	6.26146e8i		−	1.68346i	0.539897	−	0.841731i	$-0.318463\pi$
$282$	3.62120e8	+	6.27210e8i	0.961569	+	1.66549i
$283$	2.36259e7	−	4.09212e7i	0.0619634	−	0.107324i	−0.833380	−	0.552701i	$-0.813597\pi$
$283$	2.36259e7	−	4.09212e7i	0.0619634	−	0.107324i	0.895343	+	0.445377i	$0.146930\pi$
$284$	−2.21860e8	−	1.28091e8i	−0.574732	−	0.331822i
$285$	2.27235e7			0.0581458
$286$	4.55303e8	−	7.03044e7i	1.15085	−	0.177706i
$287$	−8.32855e7			−0.207961
$288$	2.41014e7	+	1.39150e7i	0.0594523	+	0.0343248i
$289$	8.37505e7	−	1.45060e8i	0.204101	−	0.353513i
$290$	−3.47417e8	−	6.01745e8i	−0.836486	−	1.44884i
$291$		−	5.92317e8i		−	1.40906i
$292$	−3.46115e8	+	1.99830e8i	−0.813543	+	0.469700i
$293$	−6.60540e8	+	3.81363e8i	−1.53413	+	0.885730i	−0.534965	+	0.844874i	$0.679675\pi$
$293$	−6.60540e8	+	3.81363e8i	−1.53413	+	0.885730i	−0.999165	+	0.0408560i	$0.986992\pi$
$294$		−	3.31219e8i		−	0.760152i
$295$	1.11777e8	+	1.93603e8i	0.253498	+	0.439071i
$296$	7.39720e7	−	1.28123e8i	0.165785	−	0.287149i
$297$	−3.58228e8	−	2.06823e8i	−0.793437	−	0.458091i
$298$	5.47772e8			1.19907
$299$	3.34192e8	+	4.15980e8i	0.723014	+	0.899959i
$300$	−6.63004e7			−0.141772
$301$	−3.69045e8	−	2.13068e8i	−0.780003	−	0.450335i
$302$	−3.48987e8	+	6.04463e8i	−0.729096	+	1.26283i
$303$	3.23471e7	+	5.60269e7i	0.0668016	+	0.115704i
$304$			3.98469e7i			0.0813462i
$305$	1.09650e8	−	6.33063e7i	0.221288	−	0.127761i
$306$	2.51408e7	−	1.45151e7i	0.0501596	−	0.0289597i
$307$		−	4.52948e8i		−	0.893436i	−0.894675	−	0.446718i	$-0.852593\pi$
$307$		−	4.52948e8i		−	0.893436i	0.894675	−	0.446718i	$-0.147407\pi$
$308$	1.01716e8	+	1.76177e8i	0.198364	+	0.343576i
$309$	−7.80234e7	+	1.35140e8i	−0.150442	+	0.260574i
$310$	8.94098e8	+	5.16208e8i	1.70459	+	0.984144i
$311$	−4.98788e8			−0.940274			−0.470137	−	0.882594i	$-0.655795\pi$
$311$	−4.98788e8			−0.940274			−0.470137	+	0.882594i	$0.655795\pi$
$312$	1.57338e8	−	1.26403e8i	0.293287	−	0.235622i
$313$	9.49928e8			1.75100			0.875498	−	0.483221i	$-0.160533\pi$
$313$	9.49928e8			1.75100			0.875498	+	0.483221i	$0.160533\pi$
$314$	8.54285e8	+	4.93222e8i	1.55722	+	0.899059i
$315$	−9.00772e6	+	1.56018e7i	−0.0162378	+	0.0281247i
$316$	−2.99768e8	−	5.19214e8i	−0.534418	−	0.925639i
$317$			8.74259e8i			1.54146i	0.637161	+	0.770731i	$0.280109\pi$
$317$			8.74259e8i			1.54146i	−0.637161	+	0.770731i	$0.719891\pi$
$318$	−9.50775e8	+	5.48930e8i	−1.65799	+	0.957243i
$319$	−6.45311e8	+	3.72571e8i	−1.11302	+	0.642601i
$320$			1.79500e8i			0.306224i
$321$	2.06606e8	+	3.57852e8i	0.348639	+	0.603860i
$322$	−2.85388e8	+	4.94306e8i	−0.476365	+	0.825089i
$323$	2.71529e7	+	1.56767e7i	0.0448339	+	0.0258849i
$324$	4.04139e8			0.660121
$325$	4.65382e7	−	1.19845e8i	0.0751999	−	0.193655i
$326$	−7.07879e8			−1.13161
$327$	−1.27821e8	−	7.37974e7i	−0.202155	−	0.116714i
$328$	−4.07239e7	+	7.05358e7i	−0.0637222	+	0.110370i
$329$	−3.10069e8	−	5.37055e8i	−0.480034	−	0.831444i
$330$		−	6.56846e8i		−	1.00615i
$331$	7.98662e8	−	4.61108e8i	1.21050	−	0.698883i	0.247632	−	0.968854i	$-0.420348\pi$
$331$	7.98662e8	−	4.61108e8i	1.21050	−	0.698883i	0.962868	+	0.269971i	$0.0870142\pi$
$332$	−3.15798e8	+	1.82326e8i	−0.473616	+	0.273442i
$333$			3.32600e7i			0.0493591i
$334$	−3.50345e8	−	6.06816e8i	−0.514498	−	0.891137i
$335$	−4.53566e7	+	7.85600e7i	−0.0659150	+	0.114168i
$336$	4.46848e8	+	2.57988e8i	0.642647	+	0.371033i
$337$	1.85249e8			0.263664			0.131832	−	0.991272i	$-0.457914\pi$
$337$	1.85249e8			0.263664			0.131832	+	0.991272i	$0.457914\pi$
$338$	−2.79446e8	−	8.83293e8i	−0.393631	−	1.24422i
$339$	−1.07512e9			−1.49884
$340$	3.02131e8	+	1.74435e8i	0.416887	+	0.240690i
$341$	5.53582e8	−	9.58832e8i	0.756034	−	1.30949i
$342$	−1.87408e6	−	3.24600e6i	−0.00253336	−	0.00438790i
$343$			7.56246e8i			1.01189i
$344$	−3.60902e8	+	2.08367e8i	−0.478007	+	0.275977i
$345$	6.58853e8	−	3.80389e8i	0.863817	−	0.498725i
$346$		−	1.53329e9i		−	1.99003i
$347$	−7.10332e7	−	1.23033e8i	−0.0912658	−	0.158077i	0.816778	−	0.576952i	$-0.195758\pi$
$347$	−7.10332e7	−	1.23033e8i	−0.0912658	−	0.158077i	−0.908044	+	0.418875i	$0.862425\pi$
$348$	3.86373e8	−	6.69218e8i	0.491451	−	0.851218i
$349$	4.07258e8	+	2.35130e8i	0.512838	+	0.296087i	0.734000	−	0.679150i	$-0.237651\pi$
$349$	4.07258e8	+	2.35130e8i	0.512838	+	0.296087i	−0.221161	+	0.975237i	$0.570985\pi$
$350$	1.37522e8			0.171449
$351$	−3.01107e8	+	7.75412e8i	−0.371660	+	0.957101i
$352$	8.68833e8			1.06179
$353$	3.93517e8	+	2.27197e8i	0.476159	+	0.274911i	0.718814	−	0.695202i	$-0.244685\pi$
$353$	3.93517e8	+	2.27197e8i	0.476159	+	0.274911i	−0.242655	+	0.970113i	$0.578018\pi$
$354$	−3.01133e8	+	5.21578e8i	−0.360784	+	0.624896i
$355$	−3.54135e8	−	6.13380e8i	−0.420116	−	0.727663i
$356$		−	1.05515e8i		−	0.123947i
$357$	3.51601e8	−	2.02997e8i	0.408989	−	0.236130i
$358$	−2.60555e8	+	1.50431e8i	−0.300129	+	0.173280i
$359$			1.21160e9i			1.38207i	0.722821	+	0.691035i	$0.242845\pi$
$359$			1.21160e9i			1.38207i	−0.722821	+	0.691035i	$0.757155\pi$
$360$	8.80896e6	+	1.52576e7i	0.00995098	+	0.0172356i
$361$	−4.44912e8	+	7.70610e8i	−0.497736	+	0.862103i
$362$	−7.17379e8	−	4.14179e8i	−0.794820	−	0.458890i
$363$	1.80243e8			0.197782
$364$	3.18920e8	−	2.56215e8i	0.346599	−	0.278452i
$365$	−1.10494e9			−1.18936
$366$	2.95403e8	+	1.70551e8i	0.314942	+	0.181832i
$367$	6.89733e8	−	1.19465e9i	0.728366	−	1.26157i	−0.229208	−	0.973377i	$-0.573614\pi$
$367$	6.89733e8	−	1.19465e9i	0.728366	−	1.26157i	0.957574	−	0.288189i	$-0.0930531\pi$
$368$	6.67034e8	+	1.15534e9i	0.697719	+	1.20848i
$369$		−	1.83107e7i		−	0.0189719i
$370$	−8.38533e8	+	4.84127e8i	−0.860626	+	0.496882i
$371$	8.14110e8	−	4.70027e8i	0.827703	−	0.477875i
$372$			1.14818e9i			1.15641i
$373$	−7.04597e7	−	1.22040e8i	−0.0703007	−	0.121764i	0.828732	−	0.559645i	$-0.189063\pi$
$373$	−7.04597e7	−	1.22040e8i	−0.0703007	−	0.121764i	−0.899033	+	0.437881i	$0.855729\pi$
$374$	4.53151e8	−	7.84881e8i	0.447912	−	0.775806i
$375$	−9.22877e8	−	5.32823e8i	−0.903721	−	0.521764i
$376$	−6.06454e8			−0.588356
$377$	9.38479e8	+	1.16816e9i	0.902048	+	1.12281i
$378$	−8.89785e8			−0.847352
$379$	−1.25855e9	−	7.26626e8i	−1.18750	−	0.685604i	−0.229763	−	0.973247i	$-0.573795\pi$
$379$	−1.25855e9	−	7.26626e8i	−1.18750	−	0.685604i	−0.957738	+	0.287642i	$0.907129\pi$
$380$	2.25218e7	−	3.90089e7i	0.0210553	−	0.0364688i
$381$	4.21829e8	+	7.30630e8i	0.390750	+	0.676799i
$382$			1.34309e9i			1.23277i
$383$	8.94535e8	−	5.16460e8i	0.813583	−	0.469722i	−0.0346157	−	0.999401i	$-0.511021\pi$
$383$	8.94535e8	−	5.16460e8i	0.813583	−	0.469722i	0.848199	+	0.529678i	$0.177687\pi$
$384$	6.91138e8	−	3.99029e8i	0.622882	−	0.359621i
$385$			5.62431e8i			0.502292i
$386$	−4.85986e8	−	8.41753e8i	−0.430099	−	0.744953i
$387$	4.68439e7	−	8.11360e7i	0.0410832	−	0.0711582i
$388$	−1.01682e9	−	5.87059e8i	−0.883754	−	0.510235i
$389$	−3.93410e8			−0.338861			−0.169431	−	0.985542i	$-0.554193\pi$
$389$	−3.93410e8			−0.338861			−0.169431	+	0.985542i	$0.554193\pi$
$390$	−1.30541e9	+	2.01572e8i	−1.11435	+	0.172070i
$391$	1.04971e9			0.888074
$392$	2.40194e8	+	1.38676e8i	0.201401	+	0.116279i
$393$	4.20485e8	−	7.28302e8i	0.349443	−	0.605254i
$394$	1.07621e9	+	1.86405e9i	0.886461	+	1.53540i
$395$		−	1.65755e9i		−	1.35324i
$396$	−3.87333e7	+	2.23627e7i	−0.0313438	+	0.0180963i
$397$	9.23207e8	−	5.33014e8i	0.740512	−	0.427535i	−0.0817434	−	0.996653i	$-0.526049\pi$
$397$	9.23207e8	−	5.33014e8i	0.740512	−	0.427535i	0.822255	+	0.569119i	$0.192715\pi$
$398$			1.44299e9i			1.14729i
$399$	−2.62095e7	−	4.53961e7i	−0.0206563	−	0.0357778i
$400$	1.60715e8	−	2.78366e8i	0.125558	−	0.217473i
$401$	6.63509e8	+	3.83077e8i	0.513856	+	0.296675i	0.734417	−	0.678698i	$-0.237455\pi$
$401$	6.63509e8	+	3.83077e8i	0.513856	+	0.296675i	−0.220561	+	0.975373i	$0.570789\pi$
$402$	−2.44387e8			−0.187623
$403$	−2.07546e9	−	8.05942e8i	−1.57960	−	0.613389i
$404$	1.28240e8			0.0967584
$405$	9.67635e8	+	5.58664e8i	0.723801	+	0.417887i
$406$	−8.01428e8	+	1.38811e9i	−0.594324	+	1.02940i
$407$	5.19179e8	+	8.99244e8i	0.381712	+	0.661145i
$408$		−	3.97035e8i		−	0.289413i
$409$	−1.94247e9	+	1.12148e9i	−1.40386	+	0.810516i	−0.994786	−	0.101987i	$-0.967480\pi$
$409$	−1.94247e9	+	1.12148e9i	−1.40386	+	0.810516i	−0.409069	+	0.912503i	$0.634147\pi$
$410$	4.61638e8	−	2.66527e8i	0.330795	−	0.190984i
$411$		−	2.29337e8i		−	0.162940i
$412$	1.54662e8	+	2.67882e8i	0.108954	+	0.188714i
$413$	2.57848e8	−	4.46606e8i	0.180111	−	0.311961i
$414$	−1.08675e8	−	6.27437e7i	−0.0752714	−	0.0434579i
$415$	−1.00816e9			−0.692405
$416$	−2.66627e8	−	1.72672e9i	−0.181584	−	1.17597i
$417$	7.07456e8			0.477775
$418$	−1.01338e8	−	5.85076e7i	−0.0678665	−	0.0391828i
$419$	7.01906e8	−	1.21574e9i	0.466154	−	0.807403i	−0.533098	−	0.846053i	$-0.678972\pi$
$419$	7.01906e8	−	1.21574e9i	0.466154	−	0.807403i	0.999253	+	0.0386502i	$0.0123058\pi$
$420$	−2.91634e8	−	5.05124e8i	−0.192072	−	0.332679i
$421$			1.81487e9i			1.18538i	0.805429	+	0.592692i	$0.201935\pi$
$421$			1.81487e9i			1.18538i	−0.805429	+	0.592692i	$0.798065\pi$
$422$	1.62155e9	−	9.36203e8i	1.05036	−	0.606424i
$423$	1.18074e8	−	6.81699e7i	0.0758511	−	0.0437927i
$424$		−	9.19311e8i		−	0.585709i
$425$	−1.26458e8	−	2.19031e8i	−0.0799068	−	0.138403i
$426$	9.54062e8	−	1.65248e9i	0.597920	−	1.03563i
$427$	−2.52942e8	−	1.46036e8i	−0.157225	−	0.0907741i
$428$	8.19089e8			0.504984
$429$	2.16166e8	+	1.39993e9i	0.132187	+	0.856062i
$430$	2.72741e9			1.65429
$431$	−1.54287e9	−	8.90776e8i	−0.928237	−	0.535918i	−0.0419833	−	0.999118i	$-0.513368\pi$
$431$	−1.54287e9	−	8.90776e8i	−0.928237	−	0.535918i	−0.886254	+	0.463201i	$0.846701\pi$
$432$	−1.03984e9	+	1.80106e9i	−0.620546	+	1.07482i
$433$	−7.17382e8	−	1.24254e9i	−0.424662	−	0.735536i	0.571727	−	0.820444i	$-0.306274\pi$
$433$	−7.17382e8	−	1.24254e9i	−0.424662	−	0.735536i	−0.996389	+	0.0849082i	$0.972940\pi$
$434$		−	2.38159e9i		−	1.39847i
$435$	1.85020e9	−	1.06821e9i	1.07772	−	0.622221i
$436$	−2.53373e8	+	1.46285e8i	−0.146405	+	0.0845272i
$437$		−	1.35530e8i		−	0.0776876i
$438$	−1.48839e9	−	2.57797e9i	−0.846366	−	1.46595i
$439$	−1.57839e9	+	2.73385e9i	−0.890406	+	1.54223i	−0.0510165	+	0.998698i	$0.516246\pi$
$439$	−1.57839e9	+	2.73385e9i	−0.890406	+	1.54223i	−0.839389	+	0.543530i	$0.817087\pi$
$440$	4.76332e8	+	2.75010e8i	0.266579	+	0.153909i
$441$	−6.23528e7			−0.0346195
$442$	−1.69893e9	−	6.59728e8i	−0.935833	−	0.363402i
$443$	8.24759e8			0.450727			0.225364	−	0.974275i	$-0.427643\pi$
$443$	8.24759e8			0.450727			0.225364	+	0.974275i	$0.427643\pi$
$444$	−9.32558e8	−	5.38413e8i	−0.505633	−	0.291927i
$445$	1.45859e8	−	2.52635e8i	0.0784643	−	0.135904i
$446$	1.31708e9	+	2.28125e9i	0.702975	+	1.21759i
$447$			1.68425e9i			0.891927i
$448$	3.58598e8	−	2.07037e8i	0.188423	−	0.108786i
$449$	−1.94207e9	+	1.12126e9i	−1.01252	+	0.584578i	−0.911928	−	0.410350i	$-0.865407\pi$
$449$	−1.94207e9	+	1.12126e9i	−1.01252	+	0.584578i	−0.100591	+	0.994928i	$0.532073\pi$
$450$			3.02348e7i			0.0156410i
$451$	−2.85824e8	−	4.95061e8i	−0.146717	−	0.254121i
$452$	−1.06557e9	+	1.84563e9i	−0.542748	+	0.940068i
$453$	−1.85855e9	−	1.07304e9i	−0.939359	−	0.542339i
$454$	1.53511e9			0.769917
$455$	1.11777e9	−	1.72598e8i	0.556306	−	0.0859007i
$456$	−5.12623e7			−0.0253175
$457$	−9.49936e8	−	5.48446e8i	−0.465573	−	0.268799i	0.248812	−	0.968552i	$-0.419960\pi$
$457$	−9.49936e8	−	5.48446e8i	−0.465573	−	0.268799i	−0.714385	+	0.699753i	$0.753293\pi$
$458$	−3.64510e8	+	6.31349e8i	−0.177288	+	0.307072i
$459$	8.18196e8	+	1.41716e9i	0.394923	+	0.684027i
$460$		−	1.50805e9i		−	0.722376i
$461$	1.37164e9	−	7.91917e8i	0.652059	−	0.376467i	−0.137186	−	0.990545i	$-0.543806\pi$
$461$	1.37164e9	−	7.91917e8i	0.652059	−	0.376467i	0.789245	+	0.614079i	$0.210472\pi$
$462$	−1.31222e9	+	7.57612e8i	−0.619099	+	0.357437i
$463$			2.25948e9i			1.05798i	0.848629	+	0.528988i	$0.177428\pi$
$463$			2.25948e9i			1.05798i	−0.848629	+	0.528988i	$0.822572\pi$
$464$	1.87317e9	+	3.24442e9i	0.870490	+	1.50773i
$465$	−1.58719e9	+	2.74910e9i	−0.732057	+	1.26796i
$466$	3.19621e9	+	1.84533e9i	1.46314	+	0.844742i
$467$	−2.17106e9			−0.986421			−0.493211	−	0.869910i	$-0.664177\pi$
$467$	−2.17106e9			−0.986421			−0.493211	+	0.869910i	$0.664177\pi$
$468$	5.63300e7	+	7.01159e7i	0.0254027	+	0.0316196i
$469$	2.09259e8			0.0936653
$470$	3.43732e9	+	1.98454e9i	1.52714	+	0.881693i
$471$	−1.51652e9	+	2.62669e9i	−0.668766	+	1.15834i
$472$	−2.52159e8	−	4.36752e8i	−0.110377	−	0.191178i
$473$		−	2.92488e9i		−	1.27085i
$474$	3.86726e9	−	2.23277e9i	1.66794	−	0.962983i
$475$	−2.82797e7	+	1.63273e7i	−0.0121073	+	0.00699015i
$476$		−	8.04780e8i		−	0.342021i
$477$	1.03337e8	+	1.78986e8i	0.0435956	+	0.0755098i
$478$	2.92326e8	−	5.06324e8i	0.122425	−	0.212046i
$479$	−5.66356e8	−	3.26986e8i	−0.235459	−	0.135942i	0.377629	−	0.925957i	$-0.376739\pi$
$479$	−5.66356e8	−	3.26986e8i	−0.235459	−	0.135942i	−0.613088	+	0.790015i	$0.710073\pi$
$480$	−2.49106e9			−1.02811
$481$	1.62783e9	−	1.30777e9i	0.666962	−	0.535827i
$482$	−2.91030e9			−1.18378
$483$	−1.51985e9	−	8.77488e8i	−0.613743	−	0.354345i
$484$	1.78643e8	−	3.09419e8i	0.0716190	−	0.124048i
$485$	−1.62305e9	−	2.81120e9i	−0.646004	−	1.11891i
$486$		−	3.80575e8i		−	0.150388i
$487$	2.35359e9	−	1.35885e9i	0.923377	−	0.533112i	0.0386663	−	0.999252i	$-0.487689\pi$
$487$	2.35359e9	−	1.35885e9i	0.923377	−	0.533112i	0.884711	+	0.466140i	$0.154356\pi$
$488$	−2.47360e8	+	1.42814e8i	−0.0963520	+	0.0556288i
$489$		−	2.17653e9i		−	0.841751i
$490$	−9.07598e8	−	1.57201e9i	−0.348503	−	0.603626i
$491$	1.39241e8	−	2.41173e8i	0.0530864	−	0.0919483i	−0.838261	−	0.545269i	$-0.816427\pi$
$491$	1.39241e8	−	2.41173e8i	0.0530864	−	0.0919483i	0.891347	+	0.453321i	$0.149761\pi$
$492$	5.13402e8	+	2.96413e8i	0.194348	+	0.112207i
$493$	2.94779e9			1.10798
$494$	−8.51793e7	+	2.19354e8i	−0.0317899	+	0.0818655i
$495$	−1.23653e8			−0.0458232
$496$	−4.82070e9	−	2.78323e9i	−1.77388	−	1.02415i
$497$	−8.16924e8	+	1.41495e9i	−0.298493	+	0.517006i
$498$	−1.35802e9	−	2.35216e9i	−0.492724	−	0.853422i
$499$		−	1.57082e9i		−	0.565947i	−0.959128	−	0.282973i	$-0.908679\pi$
$499$		−	1.57082e9i		−	0.565947i	0.959128	−	0.282973i	$-0.0913208\pi$
$500$	−1.82937e9	+	1.05619e9i	−0.654495	+	0.377873i
$501$	1.86579e9	−	1.07721e9i	0.662873	−	0.382710i
$502$			4.14257e8i			0.146153i
$503$	1.85784e9	+	3.21787e9i	0.650909	+	1.12741i	0.982903	+	0.184126i	$0.0589455\pi$
$503$	1.85784e9	+	3.21787e9i	0.650909	+	1.12741i	−0.331993	+	0.943282i	$0.607721\pi$
$504$	2.03206e7	−	3.51964e7i	0.00707018	−	0.0122459i
$505$	3.07046e8	+	1.77273e8i	0.106092	+	0.0612525i
$506$	−3.91764e9			−1.34431
$507$	2.71588e9	−	8.59217e8i	0.925512	−	0.292803i
$508$	1.67234e9			0.565980
$509$	4.81978e8	+	2.78270e8i	0.162000	+	0.0935308i	0.578808	−	0.815464i	$-0.303518\pi$
$509$	4.81978e8	+	2.78270e8i	0.162000	+	0.0935308i	−0.416808	+	0.908994i	$0.636851\pi$
$510$	−1.29925e9	+	2.25036e9i	−0.433706	+	0.751202i
$511$	1.27445e9	+	2.20741e9i	0.422522	+	0.731830i
$512$		−	2.94547e9i		−	0.969860i
$513$	1.82973e8	−	1.05639e8i	0.0598378	−	0.0345474i
$514$	1.42798e9	−	8.24443e8i	0.463821	−	0.267787i
$515$			8.55189e8i			0.275891i
$516$	1.51662e9	+	2.62686e9i	0.485962	+	0.841710i
$517$	2.12822e9	−	3.68619e9i	0.677330	−	1.17317i
$518$	1.93434e9	+	1.11679e9i	0.611476	+	0.353036i
$519$	4.71445e9			1.48028
$520$	4.00379e8	−	1.03106e9i	0.124870	−	0.321566i
$521$	−1.65430e9			−0.512486			−0.256243	−	0.966612i	$-0.582485\pi$
$521$	−1.65430e9			−0.512486			−0.256243	+	0.966612i	$0.582485\pi$
$522$	−3.05183e8	−	1.76197e8i	−0.0939103	−	0.0542191i
$523$	9.42609e8	−	1.63265e9i	0.288122	−	0.499041i	−0.685240	−	0.728318i	$-0.740303\pi$
$523$	9.42609e8	−	1.63265e9i	0.288122	−	0.499041i	0.973361	+	0.229276i	$0.0736359\pi$
$524$	−8.33506e8	−	1.44367e9i	−0.253075	−	0.438339i
$525$			4.22842e8i			0.127533i
$526$	−4.12506e9	+	2.38161e9i	−1.23589	+	0.713542i
$527$	−3.79315e9	+	2.18998e9i	−1.12892	+	0.651782i
$528$			3.54151e9i			1.04706i
$529$	−5.66351e8	−	9.80949e8i	−0.166338	−	0.288106i
$530$	−3.00832e9	+	5.21057e9i	−0.877726	+	1.52027i
$531$	9.81883e7	+	5.66890e7i	0.0284596	+	0.0164312i
$532$	−1.03907e8			−0.0299196
$533$	−8.96171e8	+	7.19970e8i	−0.256357	+	0.205953i
$534$	7.85905e8			0.223345
$535$	1.96115e9	+	1.13227e9i	0.553698	+	0.319678i
$536$	1.02321e8	−	1.77225e8i	0.0287003	−	0.0497104i
$537$	−4.62534e8	−	8.01132e8i	−0.128894	−	0.223251i
$538$			6.23370e9i			1.72587i
$539$	−1.68582e9	+	9.73309e8i	−0.463714	+	0.267726i
$540$	2.03594e9	−	1.17545e9i	0.556401	−	0.321238i
$541$		−	4.62326e7i		−	0.0125533i	−0.999980	−	0.00627665i	$-0.998002\pi$
$541$		−	4.62326e7i		−	0.0125533i	0.999980	−	0.00627665i	$-0.00199793\pi$
$542$	−1.17320e9	−	2.03204e9i	−0.316500	−	0.548194i
$543$	1.27348e9	−	2.20574e9i	0.341346	−	0.591228i
$544$	−2.97663e9	−	1.71856e9i	−0.792736	−	0.457686i
$545$	−8.08870e8			−0.214038
$546$	1.90837e9	+	2.37541e9i	0.501751	+	0.624546i
$547$	5.53529e9			1.44605			0.723027	−	0.690819i	$-0.242750\pi$
$547$	5.53529e9			1.44605			0.723027	+	0.690819i	$0.242750\pi$
$548$	−3.93697e8	−	2.27301e8i	−0.102195	−	0.0590023i
$549$	3.21066e7	−	5.56103e7i	0.00828116	−	0.0143434i
$550$	4.71957e8	+	8.17453e8i	0.120958	+	0.209505i
$551$		−	3.80597e8i		−	0.0969248i
$552$	−1.48632e9	+	8.58126e8i	−0.376119	+	0.217152i
$553$	−3.31138e9	+	1.91183e9i	−0.832667	+	0.480740i
$554$		−	4.25064e9i		−	1.06211i
$555$	−1.48856e9	−	2.57825e9i	−0.369607	−	0.640177i
$556$	7.01176e8	−	1.21447e9i	0.173008	−	0.299658i
$557$	−4.15944e9	−	2.40146e9i	−1.01986	−	0.588819i	−0.105799	−	0.994387i	$-0.533740\pi$
$557$	−4.15944e9	−	2.40146e9i	−1.01986	−	0.588819i	−0.914065	+	0.405569i	$0.867073\pi$
$558$	5.23603e8			0.127580
$559$	−5.81289e9	+	8.97583e8i	−1.40751	+	0.217337i
$560$	2.82772e9			0.680423
$561$	2.41329e9	+	1.39331e9i	0.577084	+	0.333180i
$562$	4.62232e9	−	8.00610e9i	1.09846	−	1.90258i
$563$	2.91491e8	+	5.04878e8i	0.0688409	+	0.119236i	0.898391	−	0.439196i	$-0.144737\pi$
$563$	2.91491e8	+	5.04878e8i	0.0688409	+	0.119236i	−0.829550	+	0.558432i	$0.811403\pi$
$564$			4.41413e9i			1.03602i
$565$	−5.10262e9	+	2.94600e9i	−1.19021	+	0.687169i
$566$	6.04176e8	−	3.48821e8i	0.140057	−	0.0808621i
$567$		−	2.57747e9i		−	0.593818i
$568$	7.98899e8	+	1.38373e9i	0.182925	+	0.316835i
$569$	1.09595e9	−	1.89824e9i	0.249401	−	0.431975i	−0.713959	−	0.700188i	$-0.753100\pi$
$569$	1.09595e9	−	1.89824e9i	0.249401	−	0.431975i	0.963360	+	0.268213i	$0.0864330\pi$
$570$	2.90550e8	+	1.67749e8i	0.0657142	+	0.0379401i
$571$	3.96943e9			0.892281			0.446140	−	0.894963i	$-0.352798\pi$
$571$	3.96943e9			0.892281			0.446140	+	0.894963i	$0.352798\pi$
$572$	2.61747e9	+	1.01641e9i	0.584784	+	0.227083i
$573$	−4.12961e9			−0.916998
$574$	−1.06491e9	−	6.14829e8i	−0.235030	−	0.135695i
$575$	−5.46634e8	+	9.46798e8i	−0.119911	+	0.207692i
$576$	4.55179e7	+	7.88392e7i	0.00992437	+	0.0171895i
$577$			5.01942e9i			1.08777i	0.839159	+	0.543886i	$0.183048\pi$
$577$			5.01942e9i			1.08777i	−0.839159	+	0.543886i	$0.816952\pi$
$578$	2.14172e9	−	1.23652e9i	0.461334	−	0.266351i
$579$	2.58815e9	−	1.49427e9i	0.554134	−	0.319930i
$580$		−	4.23492e9i		−	0.901253i
$581$	1.16282e9	+	2.01406e9i	0.245977	+	0.426045i
$582$	4.37259e9	−	7.57355e9i	0.919408	−	1.59246i
$583$	5.58782e9	+	3.22613e9i	1.16789	+	0.674282i
$584$	2.49266e9			0.517866
$585$	3.79465e7	+	2.45747e8i	0.00783656	+	0.0507508i
$586$	−1.12612e10			−2.31175
$587$	3.33458e9	+	1.92522e9i	0.680468	+	0.392868i	0.800031	−	0.599958i	$-0.204816\pi$
$587$	3.33458e9	+	1.92522e9i	0.680468	+	0.392868i	−0.119563	+	0.992827i	$0.538149\pi$
$588$	1.00937e9	−	1.74827e9i	0.204752	−	0.354641i
$589$	2.82754e8	+	4.89744e8i	0.0570171	+	0.0987565i
$590$			3.30063e9i			0.661629i
$591$	−5.73142e9	+	3.30904e9i	−1.14211	+	0.659395i
$592$	4.52111e9	−	2.61027e9i	0.895611	−	0.517081i
$593$		−	3.30871e9i		−	0.651580i	−0.945442	−	0.325790i	$-0.894370\pi$
$593$		−	3.30871e9i		−	0.651580i	0.945442	−	0.325790i	$-0.105630\pi$
$594$	−3.05361e9	−	5.28902e9i	−0.597808	−	1.03543i
$595$	1.11249e9	−	1.92689e9i	0.216515	−	0.375015i
$596$	2.89131e9	+	1.66930e9i	0.559413	+	0.322977i
$597$	−4.43678e9			−0.853411
$598$	1.20224e9	+	7.78591e9i	0.229899	+	1.48887i
$599$	−1.42968e9			−0.271797			−0.135899	−	0.990723i	$-0.543392\pi$
$599$	−1.42968e9			−0.271797			−0.135899	+	0.990723i	$0.543392\pi$
$600$	3.58112e8	+	2.06756e8i	0.0676846	+	0.0390777i
$601$	−9.80155e8	+	1.69768e9i	−0.184176	+	0.319003i	−0.943299	−	0.331945i	$-0.892295\pi$
$601$	−9.80155e8	+	1.69768e9i	−0.184176	+	0.319003i	0.759122	+	0.650948i	$0.225628\pi$
$602$	−3.14582e9	−	5.44871e9i	−0.587686	−	1.01790i
$603$			4.60064e7i			0.00854492i
$604$	−3.68411e9	+	2.12702e9i	−0.680305	+	0.392774i
$605$	8.55455e8	−	4.93897e8i	0.157056	−	0.0906761i
$606$			9.55170e8i			0.174352i
$607$	−2.47671e9	−	4.28978e9i	−0.449484	−	0.778529i	0.548868	−	0.835909i	$-0.315059\pi$
$607$	−2.47671e9	−	4.28978e9i	−0.449484	−	0.778529i	−0.998352	+	0.0573795i	$0.981726\pi$
$608$	−2.21888e8	+	3.84321e8i	−0.0400378	+	0.0693475i
$609$	−4.26806e9	−	2.46417e9i	−0.765720	−	0.442089i
$610$	1.86935e9			0.333455
$611$	−7.97903e9	−	3.09841e9i	−1.41516	−	0.549534i
$612$	1.76934e8			0.0312020
$613$	5.81190e9	+	3.35550e9i	1.01908	+	0.588363i	0.913836	−	0.406084i	$-0.133106\pi$
$613$	5.81190e9	+	3.35550e9i	1.01908	+	0.588363i	0.105239	+	0.994447i	$0.466439\pi$
$614$	3.34374e9	−	5.79153e9i	0.582967	−	1.00973i
$615$	8.19496e8	+	1.41941e9i	0.142064	+	0.246062i
$616$		−	1.26880e9i		−	0.218705i
$617$	2.06965e9	−	1.19491e9i	0.354730	−	0.204804i	−0.312036	−	0.950070i	$-0.601011\pi$
$617$	2.06965e9	−	1.19491e9i	0.354730	−	0.204804i	0.666767	+	0.745267i	$0.267678\pi$
$618$	−1.99526e9	+	1.15197e9i	−0.340048	+	0.196327i
$619$			3.61543e9i			0.612693i	0.951920	+	0.306346i	$0.0991066\pi$
$619$			3.61543e9i			0.612693i	−0.951920	+	0.306346i	$0.900893\pi$
$620$	3.14621e9	+	5.44940e9i	0.530172	+	0.918285i
$621$	3.53679e9	−	6.12589e9i	0.592636	−	1.02648i
$622$	−6.37766e9	−	3.68214e9i	−1.06266	−	0.613528i
$623$	−6.72938e8			−0.111498
$624$	7.03839e9	−	1.08682e9i	1.15965	−	0.179065i
$625$	−4.57214e9			−0.749099
$626$	1.21461e10	+	7.01254e9i	1.97891	+	1.14252i
$627$	1.79894e8	−	3.11586e8i	0.0291461	−	0.0504826i
$628$	3.00611e9	+	5.20674e9i	0.484336	+	0.838894i
$629$		−	4.10776e9i		−	0.658154i
$630$	−2.30351e8	+	1.32993e8i	−0.0367027	+	0.0211903i
$631$	5.59855e7	−	3.23232e7i	0.00887100	−	0.00512167i	−0.495558	−	0.868575i	$-0.665036\pi$
$631$	5.59855e7	−	3.23232e7i	0.00887100	−	0.00512167i	0.504429	+	0.863453i	$0.331703\pi$
$632$			3.73928e9i			0.589221i
$633$	2.87856e9	+	4.98581e9i	0.451089	+	0.781309i
$634$	−6.45394e9	+	1.11786e10i	−1.00580	+	1.74210i
$635$	4.00410e9	+	2.31177e9i	0.620578	+	0.358291i
$636$	−6.69130e9			−1.03136
$637$	2.45169e9	+	3.05171e9i	0.375819	+	0.467794i
$638$	−1.10015e10			−1.67719
$639$	−3.11084e8	−	1.79604e8i	−0.0471655	−	0.0272310i
$640$	2.18681e9	−	3.78767e9i	0.329748	−	0.571140i
$641$	−2.88121e9	−	4.99039e9i	−0.432087	−	0.748397i	0.564966	−	0.825114i	$-0.308889\pi$
$641$	−2.88121e9	−	4.99039e9i	−0.432087	−	0.748397i	−0.997053	+	0.0767177i	$0.975556\pi$
$642$			6.10082e9i			0.909946i
$643$	−1.98357e9	+	1.14522e9i	−0.294245	+	0.169883i	−0.639855	−	0.768496i	$-0.721005\pi$
$643$	−1.98357e9	+	1.14522e9i	−0.294245	+	0.169883i	0.345610	+	0.938378i	$0.387672\pi$
$644$	−3.01273e9	+	1.73940e9i	−0.444487	+	0.256625i
$645$			8.38602e9i			1.23054i
$646$	2.31457e8	+	4.00895e8i	0.0337797	+	0.0585082i
$647$	−4.23115e9	+	7.32857e9i	−0.614177	+	1.06379i	0.376352	+	0.926477i	$0.377178\pi$
$647$	−4.23115e9	+	7.32857e9i	−0.614177	+	1.06379i	−0.990528	+	0.137308i	$0.956155\pi$
$648$	−2.18290e9	−	1.26030e9i	−0.315153	−	0.181954i
$649$	3.53959e9			0.508273
$650$	1.47977e9	−	1.18883e9i	0.211348	−	0.169794i
$651$	7.32273e9			1.04025
$652$	−3.73640e9	−	2.15721e9i	−0.527942	−	0.304808i
$653$	1.94059e9	−	3.36119e9i	0.272732	−	0.472386i	−0.696828	−	0.717238i	$-0.745406\pi$
$653$	1.94059e9	−	3.36119e9i	0.272732	−	0.472386i	0.969560	+	0.244852i	$0.0787393\pi$
$654$	−1.08957e9	−	1.88720e9i	−0.152312	−	0.263812i
$655$		−	4.60880e9i		−	0.640831i
$656$	−2.48901e9	+	1.43703e9i	−0.344242	+	0.198748i
$657$	−4.85309e8	+	2.80193e8i	−0.0667635	+	0.0385460i
$658$		−	9.15594e9i		−	1.25289i
$659$	−6.98230e8	−	1.20937e9i	−0.0950385	−	0.164612i	0.814586	−	0.580043i	$-0.196964\pi$
$659$	−6.98230e8	−	1.20937e9i	−0.0950385	−	0.164612i	−0.909625	+	0.415431i	$0.863631\pi$
$660$	2.00169e9	−	3.46703e9i	0.271015	−	0.469411i
$661$	4.16961e9	+	2.40733e9i	0.561552	+	0.324212i	0.753768	−	0.657140i	$-0.228234\pi$
$661$	4.16961e9	+	2.40733e9i	0.561552	+	0.324212i	−0.192216	+	0.981353i	$0.561567\pi$
$662$	1.36159e10			1.82408
$663$	2.02848e9	−	5.22374e9i	0.270317	−	0.696121i
$664$	2.27432e9			0.301483
$665$	−2.48786e8	−	1.43637e8i	−0.0328058	−	0.0189404i
$666$	−2.45532e8	+	4.25273e8i	−0.0322068	+	0.0557838i
$667$	−6.37116e9	−	1.10352e10i	−0.831338	−	1.43992i
$668$		−	4.27061e9i		−	0.554335i
$669$	−7.01420e9	+	4.04965e9i	−0.905705	+	0.522909i
$670$	−1.15989e9	+	6.69662e8i	−0.148989	+	0.0860189i
$671$		−	2.00470e9i		−	0.256165i
$672$	2.87321e9	+	4.97655e9i	0.365237	+	0.632610i
$673$	7.05428e9	−	1.22184e10i	0.892072	−	1.54511i	0.0546842	−	0.998504i	$-0.482585\pi$
$673$	7.05428e9	−	1.22184e10i	0.892072	−	1.54511i	0.837387	−	0.546610i	$-0.184082\pi$
$674$	2.36865e9	+	1.36754e9i	0.297983	+	0.172040i
$675$	−1.70430e9			−0.213296
$676$	1.21677e9	−	5.51387e9i	0.151494	−	0.686504i
$677$	6.91643e8			0.0856686			0.0428343	−	0.999082i	$-0.486361\pi$
$677$	6.91643e8			0.0856686			0.0428343	+	0.999082i	$0.486361\pi$
$678$	−1.37468e10	−	7.93671e9i	−1.69394	−	0.977995i
$679$	−3.74407e9	+	6.48493e9i	−0.458987	+	0.794988i
$680$	−1.08794e9	−	1.88438e9i	−0.132686	−	0.229819i
$681$			4.72003e9i			0.572704i
$682$	1.41565e10	−	8.17329e9i	1.70888	−	0.986624i
$683$	2.97479e8	−	1.71750e8i	0.0357260	−	0.0206264i	−0.482031	−	0.876154i	$-0.660101\pi$
$683$	2.97479e8	−	1.71750e8i	0.0357260	−	0.0206264i	0.517757	+	0.855528i	$0.326767\pi$
$684$		−	2.28445e7i		−	0.00272951i
$685$	−6.28421e8	−	1.08846e9i	−0.0747023	−	0.129388i
$686$	−5.58275e9	+	9.66961e9i	−0.660258	+	1.14360i
$687$	−1.94122e9	−	1.12077e9i	−0.228416	−	0.131876i
$688$	−1.47054e10			−1.72154
$689$	4.69682e9	−	1.20953e10i	0.547062	−	1.40879i
$690$	1.12324e10			1.30167
$691$	3.75457e7	+	2.16770e7i	0.00432899	+	0.00249935i	0.502163	−	0.864773i	$-0.332538\pi$
$691$	3.75457e7	+	2.16770e7i	0.00432899	+	0.00249935i	−0.497834	+	0.867272i	$0.665871\pi$
$692$	4.67260e9	−	8.09318e9i	0.536028	−	0.928428i
$693$	1.42622e8	+	2.47029e8i	0.0162787	+	0.0281956i
$694$		−	2.09752e9i		−	0.238204i
$695$	3.35767e9	−	1.93855e9i	0.379394	−	0.219043i
$696$	−4.17388e9	+	2.40979e9i	−0.469254	+	0.270924i
$697$			2.26145e9i			0.252971i
$698$	3.47155e9	+	6.01291e9i	0.386394	+	0.669253i
$699$	−5.67388e9	+	9.82745e9i	−0.628362	+	1.08835i
$700$	7.25884e8	+	4.19089e8i	0.0799878	+	0.0461810i
$701$	−3.13161e9			−0.343364			−0.171682	−	0.985152i	$-0.554920\pi$
$701$	−3.13161e9			−0.343364			−0.171682	+	0.985152i	$0.554920\pi$
$702$	−9.57429e9	+	7.69184e9i	−1.04454	+	0.839170i
$703$	−5.30363e8			−0.0575745
$704$	2.46131e9	+	1.42104e9i	0.265866	+	0.153498i
$705$	−6.10190e9	+	1.05688e10i	−0.655848	+	1.13596i
$706$	3.35442e9	+	5.81003e9i	0.358758	+	0.621387i
$707$		−	8.17874e8i		−	0.0870399i
$708$	−3.17894e9	+	1.83536e9i	−0.336640	+	0.194359i
$709$	−1.36402e8	+	7.87519e7i	−0.0143734	+	0.00829850i	−0.507169	−	0.861846i	$-0.669308\pi$
$709$	−1.36402e8	+	7.87519e7i	−0.0143734	+	0.00829850i	0.492796	+	0.870145i	$0.335975\pi$
$710$		−	1.04572e10i		−	1.09650i
$711$	−4.20323e8	−	7.28021e8i	−0.0438571	−	0.0759627i
$712$	−3.29045e8	+	5.69922e8i	−0.0341645	+	0.0591747i
$713$	1.63965e10	+	9.46654e9i	1.69410	+	0.978088i
$714$	5.99424e9			0.616298
$715$	4.86199e9	+	6.05188e9i	0.497443	+	0.619184i
$716$	−1.83371e9			−0.186696
$717$	1.55680e9	+	8.98821e8i	0.157731	+	0.0910660i
$718$	−8.94429e9	+	1.54920e10i	−0.901800	+	1.56196i
$719$	6.01180e9	+	1.04127e10i	0.603189	+	1.04475i	0.992335	+	0.123578i	$0.0394368\pi$
$719$	6.01180e9	+	1.04127e10i	0.603189	+	1.04475i	−0.389146	+	0.921176i	$0.627230\pi$
$720$			6.21687e8i			0.0620738i
$721$	1.70846e9	−	9.86383e8i	0.169759	−	0.0980104i
$722$	−1.13776e10	+	6.56884e9i	−1.12504	+	0.649544i
$723$		−	8.94834e9i		−	0.880559i
$724$	−2.52436e9	−	4.37232e9i	−0.247210	−	0.428181i
$725$	−1.53506e9	+	2.65880e9i	−0.149604	+	0.259121i
$726$	2.30465e9	+	1.33059e9i	0.223525	+	0.129052i
$727$	2.27511e9			0.219600			0.109800	−	0.993954i	$-0.464979\pi$
$727$	2.27511e9			0.219600			0.109800	+	0.993954i	$0.464979\pi$
$728$	−2.52160e9	+	3.89367e8i	−0.242224	+	0.0374024i
$729$	1.09922e10			1.05084
$730$	−1.41282e10	−	8.15689e9i	−1.34417	−	0.776059i
$731$	−5.78543e9	+	1.00207e10i	−0.547803	+	0.948823i
$732$	1.03948e9	+	1.80044e9i	0.0979554	+	0.169664i
$733$		−	1.24052e10i		−	1.16343i	−0.813394	−	0.581713i	$-0.802383\pi$
$733$		−	1.24052e10i		−	1.16343i	0.813394	−	0.581713i	$-0.197617\pi$
$734$	1.76383e10	−	1.01835e10i	1.64634	−	0.950516i
$735$	4.83347e9	−	2.79061e9i	0.449008	−	0.259235i
$736$			1.48575e10i			1.37364i
$737$	7.18146e8	+	1.24387e9i	0.0660810	+	0.114456i
$738$	1.35173e8	−	2.34126e8i	0.0123792	−	0.0214414i
$739$	−1.03072e10	−	5.95087e9i	−0.939475	−	0.542406i	−0.0496793	−	0.998765i	$-0.515820\pi$
$739$	−1.03072e10	−	5.95087e9i	−0.939475	−	0.542406i	−0.889796	+	0.456359i	$0.849153\pi$
$740$	−5.90137e9			−0.535355
$741$	−6.74451e8	−	2.61902e8i	−0.0608958	−	0.0236470i
$742$	1.38793e10			1.24725
$743$	−7.70983e9	−	4.45127e9i	−0.689579	−	0.398128i	0.113876	−	0.993495i	$-0.463673\pi$
$743$	−7.70983e9	−	4.45127e9i	−0.689579	−	0.398128i	−0.803454	+	0.595367i	$0.797007\pi$
$744$	3.58058e9	−	6.20174e9i	0.318748	−	0.552088i
$745$	4.61512e9	+	7.99363e9i	0.408918	+	0.708267i
$746$		−	2.08059e9i		−	0.183485i
$747$	−4.42799e8	+	2.55650e8i	−0.0388673	+	0.0224401i
$748$	4.78373e9	−	2.76189e9i	0.417938	−	0.241296i
$749$		−	5.22389e9i		−	0.454263i
$750$	−7.86680e9	−	1.36257e10i	−0.680901	−	1.17935i
$751$	9.35730e9	−	1.62073e10i	0.806141	−	1.39628i	−0.109378	−	0.994000i	$-0.534886\pi$
$751$	9.35730e9	−	1.62073e10i	0.806141	−	1.39628i	0.915518	−	0.402276i	$-0.131781\pi$
$752$	−1.85330e10	−	1.07000e10i	−1.58922	−	0.917535i
$753$	−1.27372e9			−0.108716
$754$	3.37614e9	+	2.18644e10i	0.286828	+	1.85754i
$755$	−1.17612e10			−0.994575
$756$	−4.69655e9	−	2.71155e9i	−0.395324	−	0.228240i
$757$	−1.12646e10	+	1.95108e10i	−0.943799	+	1.63471i	−0.185660	+	0.982614i	$0.559442\pi$
$757$	−1.12646e10	+	1.95108e10i	−0.943799	+	1.63471i	−0.758139	+	0.652093i	$0.773891\pi$
$758$	−1.07282e10	−	1.85817e10i	−0.894712	−	1.54969i
$759$		−	1.20457e10i		−	0.999963i
$760$	−2.43297e8	+	1.40467e8i	−0.0201043	+	0.0116072i
$761$	6.90340e9	−	3.98568e9i	0.567828	−	0.327835i	−0.188454	−	0.982082i	$-0.560348\pi$
$761$	6.90340e9	−	3.98568e9i	0.567828	−	0.327835i	0.756281	+	0.654247i	$0.227014\pi$
$762$			1.24561e10i			1.01986i
$763$	9.32957e8	+	1.61593e9i	0.0760372	+	0.131700i
$764$	−4.09296e9	+	7.08921e9i	−0.332055	+	0.575137i
$765$	4.23635e8	+	2.44586e8i	0.0342119	+	0.0197523i
$766$	1.52504e10			1.22597
$767$	−1.08623e9	−	7.03458e9i	−0.0869235	−	0.562930i
$768$	1.59753e10			1.27258
$769$	−5.04153e9	−	2.91073e9i	−0.399779	−	0.230813i	0.286610	−	0.958047i	$-0.407472\pi$
$769$	−5.04153e9	−	2.91073e9i	−0.399779	−	0.230813i	−0.686389	+	0.727235i	$0.740805\pi$
$770$	−4.15197e9	+	7.19142e9i	−0.327745	+	0.567672i
$771$	2.53493e9	+	4.39063e9i	0.199194	+	0.345014i
$772$		−	5.92403e9i		−	0.463401i
$773$	1.74452e10	−	1.00720e10i	1.35846	−	0.784308i	0.369045	−	0.929412i	$-0.379685\pi$
$773$	1.74452e10	−	1.00720e10i	1.35846	−	0.784308i	0.989416	+	0.145104i	$0.0463517\pi$
$774$	1.19792e9	−	6.91621e8i	0.0928614	−	0.0536136i
$775$		−	4.56172e9i		−	0.352024i
$776$	3.66146e9	+	6.34183e9i	0.281280	+	0.487191i
$777$	−3.43382e9	+	5.94756e9i	−0.262606	+	0.454847i
$778$	−5.03027e9	−	2.90423e9i	−0.382968	−	0.221107i
$779$	2.91981e8			0.0221296
$780$	−7.50464e9	−	2.91420e9i	−0.566238	−	0.219881i
$781$	−1.12143e10			−0.842350
$782$	1.34219e10	+	7.74913e9i	1.00367	+	0.579467i
$783$	9.93202e9	−	1.72028e10i	0.739386	−	1.28065i
$784$	4.89349e9	+	8.47577e9i	0.362671	+	0.628164i
$785$			1.66221e10i			1.22643i
$786$	1.07529e10	−	6.20820e9i	0.789855	−	0.456023i
$787$	7.31133e8	−	4.22120e8i	0.0534669	−	0.0308691i	−0.473028	−	0.881047i	$-0.656839\pi$
$787$	7.31133e8	−	4.22120e8i	0.0534669	−	0.0308691i	0.526495	+	0.850178i	$0.323506\pi$
$788$			1.31187e10i			0.955098i
$789$	−7.32277e9	−	1.26834e10i	−0.530769	−	0.919319i
$790$	1.22363e10	−	2.11939e10i	0.882990	−	1.52938i
$791$	1.17708e10	+	6.79588e9i	0.845646	+	0.488234i
$792$	2.78950e8			0.0199521
$793$	−3.98413e9	+	6.15200e8i	−0.283712	+	0.0438087i
$794$	1.57392e10			1.11586
$795$	−1.60210e10	−	9.24975e9i	−1.13085	−	0.652898i
$796$	−4.39740e9	+	7.61652e9i	−0.309030	+	0.535255i
$797$	8.84381e9	+	1.53179e10i	0.618779	+	1.07176i	0.989709	+	0.143095i	$0.0457055\pi$
$797$	8.84381e9	+	1.53179e10i	0.618779	+	1.07176i	−0.370930	+	0.928661i	$0.620961\pi$
$798$		−	7.73933e8i		−	0.0539130i
$799$	−1.45826e10	+	8.41928e9i	−1.01140	+	0.583931i
$800$	3.10016e9	−	1.78988e9i	0.214076	−	0.123597i
$801$		−	1.47948e8i		−	0.0101718i
$802$	5.65590e9	+	9.79630e9i	0.387161	+	0.670582i
$803$	−8.74746e9	+	1.51510e10i	−0.596180	+	1.03261i
$804$	−1.28995e9	−	7.44752e8i	−0.0875339	−	0.0505377i
$805$	−9.61786e9			−0.649820
$806$	−2.05879e10	−	2.56265e10i	−1.38497	−	1.72392i
$807$	−1.91669e10			−1.28379
$808$	−6.92671e8	−	3.99914e8i	−0.0461942	−	0.0266702i
$809$	6.07311e9	−	1.05189e10i	0.403266	−	0.698477i	−0.590852	−	0.806780i	$-0.701208\pi$
$809$	6.07311e9	−	1.05189e10i	0.403266	−	0.698477i	0.994118	+	0.108303i	$0.0345417\pi$
$810$	8.24833e9	+	1.42865e10i	0.545341	+	0.944559i
$811$		−	9.76645e9i		−	0.642930i	−0.946921	−	0.321465i	$-0.895825\pi$
$811$		−	9.76645e9i		−	0.642930i	0.946921	−	0.321465i	$-0.104175\pi$
$812$	−8.46035e9	+	4.88459e9i	−0.554552	+	0.320171i
$813$	6.24795e9	−	3.60726e9i	0.407775	−	0.235429i
$814$			1.53307e10i			0.996268i
$815$	−5.96406e9	−	1.03301e10i	−0.385914	−	0.668422i
$816$	7.00514e9	−	1.21333e10i	0.451337	−	0.781739i
$817$	1.29379e9	+	7.46972e8i	0.0830018	+	0.0479211i
$818$	−3.31160e10			−2.11544
$819$	4.47177e8	−	3.59255e8i	0.0284437	−	0.0228512i
$820$	3.24889e9			0.205772
$821$	7.00087e9	+	4.04196e9i	0.441521	+	0.254912i	0.704243	−	0.709959i	$-0.251287\pi$
$821$	7.00087e9	+	4.04196e9i	0.441521	+	0.254912i	−0.262722	+	0.964872i	$0.584620\pi$
$822$	1.69301e9	−	2.93237e9i	0.106318	−	0.184148i
$823$	5.48917e9	+	9.50753e9i	0.343248	+	0.594522i	0.985034	−	0.172361i	$-0.0551397\pi$
$823$	5.48917e9	+	9.50753e9i	0.343248	+	0.594522i	−0.641786	+	0.766884i	$0.721806\pi$
$824$		−	1.92924e9i		−	0.120127i
$825$	−2.51344e9	+	1.45113e9i	−0.155840	+	0.0899744i
$826$	6.59386e9	−	3.80697e9i	0.407108	−	0.235044i
$827$			1.39129e10i			0.855357i	0.903931	+	0.427678i	$0.140668\pi$
$827$			1.39129e10i			0.855357i	−0.903931	+	0.427678i	$0.859332\pi$
$828$	−3.82414e8	−	6.62360e8i	−0.0234114	−	0.0405497i
$829$	−1.31171e10	+	2.27195e10i	−0.799646	+	1.38503i	0.120200	+	0.992750i	$0.461646\pi$
$829$	−1.31171e10	+	2.27195e10i	−0.799646	+	1.38503i	−0.919847	+	0.392278i	$0.871687\pi$
$830$	−1.28906e10	−	7.44241e9i	−0.782530	−	0.451794i
$831$	1.30695e10			0.790053
$832$	2.06885e9	−	5.32770e9i	0.124536	−	0.320707i
$833$	7.70085e9			0.461616
$834$	9.04576e9	+	5.22257e9i	0.539963	+	0.311748i
$835$	5.90350e9	−	1.02252e10i	0.350919	−	0.607809i
$836$	−3.56595e8	−	6.17641e8i	−0.0211083	−	0.0365606i
$837$			2.95149e10i			1.73981i
$838$	1.79496e10	−	1.03632e10i	1.05366	−	0.608331i
$839$	−1.04861e10	+	6.05413e9i	−0.612979	+	0.353904i	−0.774130	−	0.633026i	$-0.781813\pi$
$839$	−1.04861e10	+	6.05413e9i	−0.612979	+	0.353904i	0.161151	+	0.986930i	$0.448479\pi$
$840$			3.63781e9i			0.211769i
$841$	−9.26658e9	−	1.60502e10i	−0.537197	−	0.930452i
$842$	−1.33977e10	+	2.32056e10i	−0.773462	+	1.33968i
$843$	2.46165e10	+	1.42124e10i	1.41524	+	0.817089i
$844$	1.14120e10			0.653378
$845$	1.05355e10	−	1.15199e10i	0.600696	−	0.656826i
$846$	2.01297e9			0.114299
$847$	−1.97338e9	−	1.13933e9i	−0.111588	−	0.0644255i
$848$	1.62200e10	−	2.80938e10i	0.913407	−	1.58207i
$849$	1.07253e9	+	1.85767e9i	0.0601494	+	0.104182i
$850$		−	3.73414e9i		−	0.208557i
$851$	−1.53775e10	+	8.87823e9i	−0.855330	+	0.493825i
$852$	1.00716e10	−	5.81486e9i	0.557907	−	0.322108i
$853$			1.60323e10i			0.884453i	0.896903	+	0.442227i	$0.145811\pi$
$853$			1.60323e10i			0.884453i	−0.896903	+	0.442227i	$0.854189\pi$
$854$	−2.15613e9	−	3.73452e9i	−0.118460	−	0.205179i
$855$	3.15792e7	−	5.46967e7i	0.00172790	−	0.00299281i
$856$	−4.42420e9	−	2.55431e9i	−0.241088	−	0.139192i
$857$	−2.24463e10			−1.21818			−0.609092	−	0.793100i	$-0.708466\pi$
$857$	−2.24463e10			−1.21818			−0.609092	+	0.793100i	$0.708466\pi$
$858$	−7.57055e9	+	1.94957e10i	−0.409187	+	1.05374i
$859$	−1.36041e10			−0.732310			−0.366155	−	0.930554i	$-0.619326\pi$
$859$	−1.36041e10			−0.732310			−0.366155	+	0.930554i	$0.619326\pi$
$860$	1.43961e10	+	8.31158e9i	0.771791	+	0.445594i
$861$	1.89043e9	−	3.27431e9i	0.100937	−	0.174827i
$862$	−1.31518e10	−	2.27795e10i	−0.699372	−	1.21135i
$863$			1.13911e10i			0.603290i	0.953420	+	0.301645i	$0.0975358\pi$
$863$			1.13911e10i			0.603290i	−0.953420	+	0.301645i	$0.902464\pi$
$864$	−2.00584e10	+	1.15807e10i	−1.05803	+	0.610854i
$865$	2.23753e10	−	1.29184e10i	1.17547	−	0.678660i
$866$		−	2.11834e10i		−	1.10837i
$867$	3.80196e9	+	6.58519e9i	0.198126	+	0.343164i
$868$	7.25773e9	−	1.25708e10i	0.376688	−	0.652443i
$869$	−2.27284e10	−	1.31222e10i	−1.17490	−	0.678326i
$870$	3.15429e10			1.62399
$871$	2.25167e9	−	1.80896e9i	0.115463	−	0.0927610i
$872$	1.82474e9			0.0931953
$873$	−1.42574e9	−	8.23150e8i	−0.0725254	−	0.0418725i
$874$	1.00051e9	−	1.73293e9i	0.0506911	−	0.0877995i
$875$	6.73602e9	+	1.16671e10i	0.339919	+	0.588757i
$876$		−	1.81431e10i		−	0.911898i
$877$	2.38991e10	−	1.37981e10i	1.19642	−	0.690752i	0.236662	−	0.971592i	$-0.423946\pi$
$877$	2.38991e10	−	1.37981e10i	1.19642	−	0.690752i	0.959755	+	0.280840i	$0.0906131\pi$
$878$	−4.03636e10	+	2.33039e10i	−2.01261	+	1.16198i
$879$		−	3.46249e10i		−	1.71960i
$880$	9.70434e9	+	1.68084e10i	0.480039	+	0.831453i
$881$	5.80856e9	−	1.00607e10i	0.286189	−	0.495694i	−0.686708	−	0.726934i	$-0.740945\pi$
$881$	5.80856e9	−	1.00607e10i	0.286189	−	0.495694i	0.972897	+	0.231240i	$0.0742781\pi$
$882$	−7.97263e8	−	4.60300e8i	−0.0391257	−	0.0225892i
$883$	−2.60345e10			−1.27258			−0.636292	−	0.771449i	$-0.719532\pi$
$883$	−2.60345e10			−1.27258			−0.636292	+	0.771449i	$0.719532\pi$
$884$	−6.95700e9	−	8.65962e9i	−0.338719	−	0.421615i
$885$	−1.01485e10			−0.492153
$886$	1.05456e10	+	6.08852e9i	0.509395	+	0.294099i
$887$	1.36152e10	−	2.35823e10i	0.655078	−	1.13463i	−0.326796	−	0.945095i	$-0.605969\pi$
$887$	1.36152e10	−	2.35823e10i	0.655078	−	1.13463i	0.981874	−	0.189533i	$-0.0606975\pi$
$888$	3.35806e9	+	5.81632e9i	0.160932	+	0.278742i
$889$		−	1.06656e10i		−	0.509133i
$890$	3.72999e9	−	2.15351e9i	0.177355	−	0.102396i
$891$	1.53209e10	−	8.84551e9i	0.725624	−	0.418939i
$892$			1.60548e10i			0.757405i
$893$	1.08704e9	+	1.88280e9i	0.0510815	+	0.0884757i
$894$	−1.24334e10	+	2.15353e10i	−0.581982	+	1.00802i
$895$	−4.39048e9	−	2.53484e9i	−0.204706	−	0.118187i
$896$	−1.00892e10			−0.468573
$897$	−2.39395e10	+	3.69656e9i	−1.10749	+	0.171011i
$898$	−3.31093e10			−1.52575
$899$	4.60448e10	+	2.65840e10i	2.11360	+	1.22029i
$900$	−9.21385e7	+	1.59589e8i	−0.00421301	+	0.00729714i
$901$	−1.27626e10	−	2.21055e10i	−0.581303	−	1.00685i
$902$		−	8.44002e9i		−	0.382931i
$903$	1.67533e10	−	9.67250e9i	0.757168	−	0.437151i
$904$	1.15111e10	−	6.64593e9i	0.518235	−	0.299203i
$905$		−	1.39583e10i		−	0.625981i
$906$	−1.58427e10	−	2.74404e10i	−0.707752	−	1.22586i
$907$	1.45545e10	−	2.52092e10i	0.647698	−	1.12185i	−0.335974	−	0.941871i	$-0.609065\pi$
$907$	1.45545e10	−	2.52092e10i	0.647698	−	1.12185i	0.983671	−	0.179974i	$-0.0576013\pi$
$908$	8.10276e9	+	4.67813e9i	0.359197	+	0.207382i
$909$	1.79813e8			0.00794049
$910$	1.55664e10	+	6.04472e9i	0.684766	+	0.265908i
$911$	−1.86121e9			−0.0815606			−0.0407803	−	0.999168i	$-0.512984\pi$
$911$	−1.86121e9			−0.0815606			−0.0407803	+	0.999168i	$0.512984\pi$
$912$	−1.56656e9	−	9.04452e8i	−0.0683855	−	0.0394824i
$913$	−7.98125e9	+	1.38239e10i	−0.347075	+	0.601151i
$914$	−8.09745e9	−	1.40252e10i	−0.350782	−	0.607572i
$915$			5.74774e9i			0.248041i
$916$	−3.84798e9	+	2.22163e9i	−0.165424	+	0.0955077i
$917$	−9.20729e9	+	5.31583e9i	−0.394311	+	0.227656i
$918$			2.41603e10i			1.03075i
$919$	1.67606e10	+	2.90302e10i	0.712336	+	1.23380i	0.963978	+	0.265982i	$0.0856962\pi$
$919$	1.67606e10	+	2.90302e10i	0.712336	+	1.23380i	−0.251642	+	0.967820i	$0.580970\pi$
$920$	−4.70282e9	+	8.14552e9i	−0.199114	+	0.344875i
$921$	1.78073e10	+	1.02811e10i	0.751087	+	0.433640i
$922$	2.33843e10			0.982576
$923$	3.44143e9	+	2.22872e10i	0.144056	+	0.932932i
$924$	−9.23506e9			−0.385113
$925$	3.70505e9	+	2.13911e9i	0.153921	+	0.0888664i
$926$	−1.66799e10	+	2.88905e10i	−0.690328	+	1.19568i
$927$	2.16860e8	+	3.75613e8i	0.00894131	+	0.0154868i
$928$			4.17229e10i			1.71379i
$929$	−1.54742e10	+	8.93401e9i	−0.633216	+	0.365588i	−0.781997	−	0.623283i	$-0.785799\pi$
$929$	−1.54742e10	+	8.93401e9i	−0.633216	+	0.365588i	0.148780	+	0.988870i	$0.452465\pi$
$930$	−4.05888e10	+	2.34339e10i	−1.65469	+	0.955333i
$931$		−	9.94277e8i		−	0.0403816i
$932$	1.12470e10	+	1.94804e10i	0.455074	+	0.788211i
$933$	1.13216e10	−	1.96095e10i	0.456373	−	0.790462i
$934$	−2.77599e10	−	1.60272e10i	−1.11482	−	0.643639i
$935$	1.52717e10			0.611006
$936$	−8.56040e7	−	5.54385e8i	−0.00341215	−	0.0220976i
$937$	2.15006e10			0.853811			0.426905	−	0.904296i	$-0.359604\pi$
$937$	2.15006e10			0.853811			0.426905	+	0.904296i	$0.359604\pi$
$938$	2.67565e9	+	1.54479e9i	0.105857	+	0.0611166i
$939$	−2.15616e10	+	3.73458e10i	−0.849868	+	1.47201i
$940$	1.20955e10	+	2.09500e10i	0.474980	+	0.822690i
$941$		−	1.20772e10i		−	0.472502i	−0.971692	−	0.236251i	$-0.924081\pi$
$941$		−	1.20772e10i		−	0.472502i	0.971692	−	0.236251i	$-0.0759188\pi$
$942$	−3.87814e10	+	2.23904e10i	−1.51163	+	0.872739i
$943$	8.46581e9	−	4.88774e9i	0.328759	−	0.189809i
$944$		−	1.77960e10i		−	0.688525i
$945$	−7.49666e9	−	1.29846e10i	−0.288973	−	0.500515i
$946$	2.15920e10	−	3.73984e10i	0.829227	−	1.43626i
$947$	3.63894e10	+	2.10094e10i	1.39235	+	0.803876i	0.993576	−	0.113171i	$-0.0361007\pi$
$947$	3.63894e10	+	2.10094e10i	1.39235	+	0.803876i	0.398779	+	0.917047i	$0.369434\pi$
$948$	2.72168e10			1.03755
$949$	3.27956e10	+	1.27351e10i	1.24561	+	0.483696i
$950$	−4.82124e8			−0.0182443
$951$	−3.43709e10	−	1.98441e10i	−1.29586	−	0.748168i
$952$	−2.50969e9	+	4.34691e9i	−0.0942737	+	0.163287i
$953$	−1.06091e10	−	1.83754e10i	−0.397056	−	0.687722i	0.596305	−	0.802758i	$-0.296635\pi$
$953$	−1.06091e10	−	1.83754e10i	−0.397056	−	0.687722i	−0.993361	+	0.115036i	$0.963302\pi$
$954$			3.05142e9i			0.113784i
$955$	−1.95996e10	+	1.13158e10i	−0.728175	+	0.420412i
$956$	3.08597e9	−	1.78169e9i	0.114232	−	0.0659521i
$957$		−	3.38267e10i		−	1.24758i
$958$	−4.82774e9	−	8.36188e9i	−0.177404	−	0.307273i
$959$	−1.44965e9	+	2.51087e9i	−0.0530761	+	0.0919304i
$960$	−7.05692e9	−	4.07431e9i	−0.257434	−	0.148630i
$961$	−5.14867e10			−1.87139
$962$	3.04682e10	−	4.70467e9i	1.10340	−	0.170379i
$963$	1.14849e9			0.0414416
$964$	−1.53614e10	−	8.86891e9i	−0.552283	−	0.318861i
$965$	8.18912e9	−	1.41840e10i	0.293354	−	0.508103i
$966$	−1.29556e10	−	2.24397e10i	−0.462420	−	0.800934i
$967$		−	2.68721e10i		−	0.955671i	−0.878449	−	0.477836i	$-0.841421\pi$
$967$		−	2.68721e10i		−	0.955671i	0.878449	−	0.477836i	$-0.158579\pi$
$968$	−1.92983e9	+	1.11419e9i	−0.0683843	+	0.0394817i
$969$	−1.23264e9	+	7.11665e8i	−0.0435214	+	0.0251271i
$970$		−	4.79266e10i		−	1.68607i
$971$	1.52953e10	+	2.64923e10i	0.536157	+	0.928651i	0.999106	+	0.0422666i	$0.0134579\pi$
$971$	1.52953e10	+	2.64923e10i	0.536157	+	0.928651i	−0.462949	+	0.886385i	$0.653209\pi$
$972$	1.15978e9	−	2.00879e9i	0.0405081	−	0.0701621i
$973$	−7.74552e9	−	4.47188e9i	−0.269560	−	0.155631i
$974$	4.01250e10			1.39142
$975$	3.65530e9	+	4.54988e9i	0.126301	+	0.157211i
$976$	−1.00790e10			−0.347010
$977$	−2.41063e10	−	1.39178e10i	−0.826990	−	0.477463i	0.0258312	−	0.999666i	$-0.491777\pi$
$977$	−2.41063e10	−	1.39178e10i	−0.826990	−	0.477463i	−0.852821	+	0.522204i	$0.825110\pi$
$978$	1.60675e10	−	2.78298e10i	0.549242	−	0.951315i
$979$	−2.30943e9	−	4.00005e9i	−0.0786620	−	0.136247i
$980$		−	1.10633e10i		−	0.375487i
$981$	−3.55269e8	+	2.05115e8i	−0.0120148	+	0.00693673i
$982$	3.56077e9	−	2.05581e9i	0.119992	−	0.0692777i
$983$			2.17619e8i			0.00730735i	0.999993	+	0.00365368i	$0.00116300\pi$
$983$			2.17619e8i			0.00730735i	−0.999993	+	0.00365368i	$0.998837\pi$
$984$	−1.84871e9	−	3.20206e9i	−0.0618567	−	0.107139i
$985$	−1.81347e10	+	3.14101e10i	−0.604620	+	1.04723i
$986$	3.76914e10	+	2.17611e10i	1.25220	+	0.722957i
$987$	2.81519e10			0.931962
$988$	−1.11807e9	+	8.98237e8i	−0.0368823	+	0.0296307i
$989$	5.00169e10			1.64411
$990$	−1.58106e9	−	9.12828e8i	−0.0517877	−	0.0298996i
$991$	−1.81782e9	+	3.14855e9i	−0.0593325	+	0.102767i	−0.894166	−	0.447736i	$-0.852231\pi$
$991$	−1.81782e9	+	3.14855e9i	−0.0593325	+	0.102767i	0.834833	+	0.550503i	$0.185564\pi$
$992$	−3.09969e10	−	5.36882e10i	−1.00815	−	1.74617i
$993$			4.18652e10i			1.35685i
$994$	−2.08909e10	+	1.20614e10i	−0.674691	+	0.389533i
$995$	−2.10575e10	+	1.21575e10i	−0.677681	+	0.391259i
$996$		−	1.65539e10i		−	0.530874i
$997$	2.88782e9	+	5.00185e9i	0.0922862	+	0.159844i	0.908473	−	0.417944i	$-0.137249\pi$
$997$	2.88782e9	+	5.00185e9i	0.0922862	+	0.159844i	−0.816187	+	0.577788i	$0.803916\pi$
$998$	1.15961e10	−	2.00851e10i	0.369280	−	0.639612i
$999$	−2.39721e10	−	1.38403e10i	−0.760724	−	0.439204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.e.a.4.6	✓	14
3.2	odd	2		117.8.q.b.82.2		14
4.3	odd	2		208.8.w.a.17.6		14
13.4	even	6		169.8.b.d.168.11		14
13.6	odd	12		169.8.a.g.1.4		14
13.7	odd	12		169.8.a.g.1.11		14
13.9	even	3		169.8.b.d.168.4		14
13.10	even	6	inner	13.8.e.a.10.6	yes	14
39.23	odd	6		117.8.q.b.10.2		14
52.23	odd	6		208.8.w.a.49.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.e.a.4.6	✓	14	1.1	even	1	trivial
13.8.e.a.10.6	yes	14	13.10	even	6	inner
117.8.q.b.10.2		14	39.23	odd	6
117.8.q.b.82.2		14	3.2	odd	2
169.8.a.g.1.4		14	13.6	odd	12
169.8.a.g.1.11		14	13.7	odd	12
169.8.b.d.168.4		14	13.9	even	3
169.8.b.d.168.11		14	13.4	even	6
208.8.w.a.17.6		14	4.3	odd	2
208.8.w.a.49.6		14	52.23	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	13.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.7863 + 7.38219i) q^{2} +(-22.6982 + 39.3144i) q^{3} +(44.9933 + 77.9308i) q^{4} +248.787i q^{5} +(-580.452 + 335.124i) q^{6} +(497.017 - 286.953i) q^{7} -561.243i q^{8} +(63.0878 + 109.271i) q^{9} +(-1836.59 + 3181.07i) q^{10} +(3411.39 + 1969.56i) q^{11} -4085.06 q^{12} +(2867.43 - 7384.20i) q^{13} +8473.37 q^{14} +(-9780.91 - 5647.01i) q^{15} +(9902.35 - 17151.4i) q^{16} +(-7791.62 - 13495.5i) q^{17} +1862.90i q^{18} +(-1742.44 + 1006.00i) q^{19} +(-19388.2 + 11193.8i) q^{20} +26053.2i q^{21} +(29079.4 + 50367.0i) q^{22} +(-33680.6 + 58336.5i) q^{23} +(22064.9 + 12739.2i) q^{24} +16229.9 q^{25} +(91175.3 - 73248.9i) q^{26} -105010. q^{27} +(44724.9 + 25822.0i) q^{28} +(-94582.0 + 163821. i) q^{29} +(-83374.5 - 144409. i) q^{30} -281068. i q^{31} +(191015. - 110282. i) q^{32} +(-154864. + 89410.9i) q^{33} -230077. i q^{34} +(71390.3 + 123652. i) q^{35} +(-5677.07 + 9832.97i) q^{36} +(228285. + 131800. i) q^{37} -29705.8 q^{38} +(225220. + 280339. i) q^{39} +139630. q^{40} +(-125678. - 72560.2i) q^{41} +(-192330. + 333125. i) q^{42} +(-371259. - 643040. i) q^{43} +354469. i q^{44} +(-27185.3 + 15695.4i) q^{45} +(-861302. + 497273. i) q^{46} -1.08055e6i q^{47} +(449530. + 778609. i) q^{48} +(-247087. + 427968. i) q^{49} +(207521. + 119812. i) q^{50} +707422. q^{51} +(704471. - 108779. i) q^{52} +1.63799e6 q^{53} +(-1.34269e6 - 775201. i) q^{54} +(-490002. + 848709. i) q^{55} +(-161050. - 278947. i) q^{56} -91337.1i q^{57} +(-2.41871e6 + 1.39644e6i) q^{58} +(778187. - 449287. i) q^{59} -1.01631e6i q^{60} +(-254459. - 440737. i) q^{61} +(2.07490e6 - 3.59383e6i) q^{62} +(62711.5 + 36206.5i) q^{63} +721500. q^{64} +(1.83709e6 + 713379. i) q^{65} -2.64019e6 q^{66} +(315772. + 182311. i) q^{67} +(701142. - 1.21441e6i) q^{68} +(-1.52897e6 - 2.64826e6i) q^{69} +2.10806e6i q^{70} +(-2.46548e6 + 1.42345e6i) q^{71} +(61327.8 - 35407.6i) q^{72} +4.44132e6i q^{73} +(1.94595e6 + 3.37048e6i) q^{74} +(-368390. + 638070. i) q^{75} +(-156796. - 90526.4i) q^{76} +2.26069e6 q^{77} +(810220. + 5.24711e6i) q^{78} -6.66251e6 q^{79} +(4.26704e6 + 2.46358e6i) q^{80} +(2.24555e6 - 3.88941e6i) q^{81} +(-1.07131e6 - 1.85556e6i) q^{82} +4.05229e6i q^{83} +(-2.03035e6 + 1.17222e6i) q^{84} +(3.35750e6 - 1.93846e6i) q^{85} -1.09628e7i q^{86} +(-4.29367e6 - 7.43686e6i) q^{87} +(1.10540e6 - 1.91462e6i) q^{88} +(-1.01547e6 - 586279. i) q^{89} -463467. q^{90} +(-693759. - 4.49289e6i) q^{91} -6.06161e6 q^{92} +(1.10500e7 + 6.37973e6i) q^{93} +(7.97686e6 - 1.38163e7i) q^{94} +(-250279. - 433496. i) q^{95} +1.00128e7i q^{96} +(-1.12996e7 + 6.52384e6i) q^{97} +(-6.31867e6 + 3.64809e6i) q^{98} +497022. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} + 26 q^{3} + 383 q^{4} - 264 q^{6} - 2772 q^{7} - 3491 q^{9} - 509 q^{10} + 6516 q^{11} + 38380 q^{12} + 5109 q^{13} - 47916 q^{14} - 19266 q^{15} - 633 q^{16} - 38403 q^{17} + 43254 q^{19}+ \cdots + 16173003 q^{98}+O(q^{100}) \) 14 * q - 3 * q^2 + 26 * q^3 + 383 * q^4 - 264 * q^6 - 2772 * q^7 - 3491 * q^9 - 509 * q^10 + 6516 * q^11 + 38380 * q^12 + 5109 * q^13 - 47916 * q^14 - 19266 * q^15 - 633 * q^16 - 38403 * q^17 + 43254 * q^19 + 89409 * q^20 - 125882 * q^22 - 68550 * q^23 + 224454 * q^24 + 39380 * q^25 + 361959 * q^26 - 432400 * q^27 - 234780 * q^28 + 221583 * q^29 - 157890 * q^30 - 878067 * q^32 + 219756 * q^33 + 659616 * q^35 + 635675 * q^36 - 565347 * q^37 + 953640 * q^38 + 30082 * q^39 - 77182 * q^40 + 1716057 * q^41 + 206406 * q^42 - 882692 * q^43 - 4616853 * q^45 - 3267480 * q^46 + 1133630 * q^48 + 2653979 * q^49 + 145128 * q^50 - 38964 * q^51 + 4962178 * q^52 - 1791210 * q^53 + 9597234 * q^54 + 2453536 * q^55 - 7457952 * q^56 - 14978127 * q^58 - 1189032 * q^59 + 3858525 * q^61 + 1904142 * q^62 + 7718520 * q^63 + 14570922 * q^64 + 10424661 * q^65 - 31956396 * q^66 + 4674330 * q^67 + 9569619 * q^68 - 13743840 * q^69 - 25203126 * q^71 - 6851607 * q^72 + 8640105 * q^74 + 10316152 * q^75 + 12934506 * q^76 + 19599336 * q^77 + 50085750 * q^78 - 30688440 * q^79 + 29127963 * q^80 + 13886221 * q^81 - 37359719 * q^82 - 96398508 * q^84 - 22436313 * q^85 + 12769686 * q^87 + 27045536 * q^88 + 2123160 * q^89 + 41193546 * q^90 + 37205532 * q^91 - 47685588 * q^92 + 36638964 * q^93 + 19138810 * q^94 - 43420386 * q^95 - 68556288 * q^97 + 16173003 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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