LMFDB - Embedded newform 27.11.f.a.2.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,11,Mod(2,27)] 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("27.2"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$17.1546458222$
Analytic rank:	$0$
Dimension:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.19
Character	$\chi$	$=$	27.2
Dual form			27.11.f.a.14.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.8751 + 2.27023i) q^{2} +(-242.999 + 0.792606i) q^{3} +(-801.631 - 291.770i) q^{4} +(-2001.83 - 2385.69i) q^{5} +(-3130.43 - 541.458i) q^{6} +(-5414.20 + 1970.61i) q^{7} +(-21252.6 - 12270.2i) q^{8} +(59047.7 - 385.204i) q^{9} +(-20357.7 - 35260.6i) q^{10} +(5862.12 - 6986.20i) q^{11} +(195027. + 70264.3i) q^{12} +(50114.5 + 284213. i) q^{13} +(-74182.1 + 13080.3i) q^{14} +(488334. + 578133. i) q^{15} +(423406. + 355280. i) q^{16} +(-483672. + 279248. i) q^{17} +(761120. + 129092. i) q^{18} +(461520. - 799376. i) q^{19} +(908659. + 2.49652e6i) q^{20} +(1.31408e6 - 483147. i) q^{21} +(91335.7 - 76639.7i) q^{22} +(-547430. + 1.50405e6i) q^{23} +(5.17408e6 + 2.96480e6i) q^{24} +(11593.0 - 65747.1i) q^{25} +3.77305e6i q^{26} +(-1.43482e7 + 140406. i) q^{27} +4.91516e6 q^{28} +(1.05674e7 + 1.86331e6i) q^{29} +(4.97485e6 + 8.55216e6i) q^{30} +(3.50314e7 + 1.27504e7i) q^{31} +(2.07977e7 + 2.47857e7i) q^{32} +(-1.41895e6 + 1.70228e6i) q^{33} +(-6.86129e6 + 2.49731e6i) q^{34} +(1.55396e7 + 8.97179e6i) q^{35} +(-4.74469e7 - 1.69196e7i) q^{36} +(8.95940e6 + 1.55181e7i) q^{37} +(7.75688e6 - 9.24429e6i) q^{38} +(-1.24030e7 - 6.90238e7i) q^{39} +(1.32713e7 + 7.52651e7i) q^{40} +(1.02384e7 - 1.80531e6i) q^{41} +(1.80158e7 - 3.23730e6i) q^{42} +(-9.64927e7 - 8.09670e7i) q^{43} +(-6.73762e6 + 3.88997e6i) q^{44} +(-1.19123e8 - 1.40099e8i) q^{45} +(-1.04628e7 + 1.81220e7i) q^{46} +(-1.34535e8 - 3.69632e8i) q^{47} +(-1.03169e8 - 8.59970e7i) q^{48} +(-1.90958e8 + 1.60233e8i) q^{49} +(298522. - 820182. i) q^{50} +(1.17310e8 - 6.82404e7i) q^{51} +(4.27516e7 - 2.42456e8i) q^{52} +2.30982e8i q^{53} +(-1.85054e8 - 3.07660e7i) q^{54} -2.84019e7 q^{55} +(1.39246e8 + 2.45528e7i) q^{56} +(-1.11515e8 + 1.94613e8i) q^{57} +(1.31826e8 + 4.79807e7i) q^{58} +(4.14069e8 + 4.93469e8i) q^{59} +(-2.22782e8 - 6.05931e8i) q^{60} +(-1.44479e8 + 5.25861e7i) q^{61} +(4.22086e8 + 2.43692e8i) q^{62} +(-3.18937e8 + 1.18446e8i) q^{63} +(-7.14884e7 - 1.23821e8i) q^{64} +(5.77725e8 - 6.88506e8i) q^{65} +(-2.21337e7 + 1.86957e7i) q^{66} +(3.88344e8 + 2.20241e9i) q^{67} +(4.69203e8 - 8.27332e7i) q^{68} +(1.31833e8 - 3.65916e8i) q^{69} +(1.79706e8 + 1.50791e8i) q^{70} +(2.85073e9 - 1.64587e9i) q^{71} +(-1.25964e9 - 7.16341e8i) q^{72} +(-1.88036e9 + 3.25688e9i) q^{73} +(8.01235e7 + 2.20137e8i) q^{74} +(-2.76497e6 + 1.59857e7i) q^{75} +(-6.03202e8 + 5.06147e8i) q^{76} +(-1.79716e7 + 4.93766e7i) q^{77} +(-2.99054e6 - 9.16846e8i) q^{78} +(-8.39932e8 + 4.76349e9i) q^{79} -1.72133e9i q^{80} +(3.48649e9 - 4.54909e7i) q^{81} +1.35919e8 q^{82} +(6.01546e9 + 1.06069e9i) q^{83} +(-1.19438e9 + 3.89578e6i) q^{84} +(1.63443e9 + 5.94885e8i) q^{85} +(-1.05854e9 - 1.26152e9i) q^{86} +(-2.56933e9 - 4.44407e8i) q^{87} +(-2.10307e8 + 7.65456e7i) q^{88} +(-5.85736e7 - 3.38175e7i) q^{89} +(-1.21566e9 - 2.07422e9i) q^{90} +(-8.31403e8 - 1.44003e9i) q^{91} +(8.77673e8 - 1.04597e9i) q^{92} +(-8.52269e9 - 3.07056e9i) q^{93} +(-8.93003e8 - 5.06447e9i) q^{94} +(-2.83095e9 + 4.99173e8i) q^{95} +(-5.07345e9 - 6.00641e9i) q^{96} +(-4.70128e9 - 3.94484e9i) q^{97} +(-2.82237e9 + 1.62950e9i) q^{98} +(3.43454e8 - 4.14778e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 4965 q^{5} + 18234 q^{6} - 6 q^{7} - 9 q^{8} + 119124 q^{9} - 3 q^{10} - 978 q^{11} - 1015107 q^{12} - 6 q^{13} + 2134569 q^{14} - 2548539 q^{15} - 3078 q^{16} - 9 q^{17}+ \cdots - 72892391589 q^{99}+O(q^{100}) $ 174 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 4965 * q^5 + 18234 * q^6 - 6 * q^7 - 9 * q^8 + 119124 * q^9 - 3 * q^10 - 978 * q^11 - 1015107 * q^12 - 6 * q^13 + 2134569 * q^14 - 2548539 * q^15 - 3078 * q^16 - 9 * q^17 + 6676947 * q^18 - 3 * q^19 + 15925353 * q^20 - 21049824 * q^21 + 10420410 * q^22 + 8437692 * q^23 + 87359400 * q^24 - 14881965 * q^25 - 60562494 * q^27 - 12 * q^28 + 7820868 * q^29 + 216153117 * q^30 - 51711531 * q^31 + 76244832 * q^32 - 198927081 * q^33 + 92236410 * q^34 - 260153622 * q^35 + 199074744 * q^36 - 3 * q^37 + 250645020 * q^38 + 152777949 * q^39 - 26151153 * q^40 - 837714012 * q^41 - 1627952634 * q^42 - 213300456 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 - 3 * q^46 - 1685998563 * q^47 - 1664196711 * q^48 - 183168366 * q^49 + 2548576023 * q^50 + 1007158626 * q^51 - 912655665 * q^52 - 1206704682 * q^54 - 12 * q^55 - 4260806997 * q^56 - 1000586442 * q^57 - 496853331 * q^58 + 1806342150 * q^59 + 1176655374 * q^60 - 1784159286 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 8858370045 * q^64 - 2961878001 * q^65 - 5594499243 * q^66 - 915608058 * q^67 + 11412166995 * q^68 - 7767764199 * q^69 + 1945422669 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 2110132140 * q^73 + 22008588729 * q^74 + 15296936925 * q^75 + 11875694586 * q^76 - 2702962221 * q^77 - 12511026108 * q^78 + 6660721974 * q^79 + 440880768 * q^81 - 12 * q^82 + 7670489421 * q^83 - 31766160684 * q^84 - 6965484381 * q^85 - 33241766118 * q^86 - 10927113525 * q^87 + 28790289402 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 - 991980102 * q^91 + 40280154009 * q^92 + 57140838285 * q^93 - 62587945905 * q^94 - 12104972679 * q^95 - 78182924274 * q^96 + 48297833958 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	12.8751	+	2.27023i	0.402347	+	0.0709446i	0.371160	−	0.928569i	$-0.378960\pi$
$2$	12.8751	+	2.27023i	0.402347	+	0.0709446i	0.0311870	+	0.999514i	$0.490071\pi$
$3$	−242.999	+	0.792606i	−0.999995	+	0.00326175i
$3$	−242.999	+	0.792606i	−0.999995	+	0.00326175i
$4$	−801.631	−	291.770i	−0.782843	−	0.284931i
$5$	−2001.83	−	2385.69i	−0.640587	−	0.763421i	0.343876	−	0.939015i	$-0.388260\pi$
$5$	−2001.83	−	2385.69i	−0.640587	−	0.763421i	−0.984463	+	0.175594i	$0.943816\pi$
$6$	−3130.43	−	541.458i	−0.402576	−	0.0696319i
$7$	−5414.20	+	1970.61i	−0.322140	+	0.117249i	−0.498028	−	0.867161i	$-0.665942\pi$
$7$	−5414.20	+	1970.61i	−0.322140	+	0.117249i	0.175889	+	0.984410i	$0.443720\pi$
$8$	−21252.6	−	12270.2i	−0.648578	−	0.374457i
$9$	59047.7	−	385.204i	0.999979	−	0.00652347i
$10$	−20357.7	−	35260.6i	−0.203577	−	0.352606i
$11$	5862.12	−	6986.20i	0.0363992	−	0.0433788i	−0.747538	−	0.664219i	$-0.768764\pi$
$11$	5862.12	−	6986.20i	0.0363992	−	0.0433788i	0.783937	+	0.620841i	$0.213209\pi$
$12$	195027.	+	70264.3i	0.783768	+	0.282376i
$13$	50114.5	+	284213.i	0.134973	+	0.765470i	0.974879	+	0.222737i	$0.0714991\pi$
$13$	50114.5	+	284213.i	0.134973	+	0.765470i	−0.839906	+	0.542732i	$0.817390\pi$
$14$	−74182.1	+	13080.3i	−0.137930	+	0.0243208i
$15$	488334.	+	578133.i	0.643073	+	0.761328i
$16$	423406.	+	355280.i	0.403792	+	0.338821i
$17$	−483672.	+	279248.i	−0.340649	+	0.196674i	−0.660559	−	0.750774i	$-0.729681\pi$
$17$	−483672.	+	279248.i	−0.340649	+	0.196674i	0.319910	+	0.947448i	$0.396347\pi$
$18$	761120.	+	129092.i	0.402801	+	0.0683184i
$19$	461520.	−	799376.i	0.186390	−	0.322837i	−0.757654	−	0.652656i	$-0.773655\pi$
$19$	461520.	−	799376.i	0.186390	−	0.322837i	0.944044	+	0.329820i	$0.106988\pi$
$20$	908659.	+	2.49652e6i	0.283956	+	0.780162i
$21$	1.31408e6	−	483147.i	0.321756	−	0.118299i
$22$	91335.7	−	76639.7i	0.0177226	−	0.0148710i
$23$	−547430.	+	1.50405e6i	−0.0850529	+	0.233681i	−0.974927	−	0.222526i	$-0.928570\pi$
$23$	−547430.	+	1.50405e6i	−0.0850529	+	0.233681i	0.889874	+	0.456206i	$0.150792\pi$
$24$	5.17408e6	+	2.96480e6i	0.649796	+	0.372339i
$25$	11593.0	−	65747.1i	0.00118712	−	0.00673251i
$26$			3.77305e6i			0.317560i
$27$	−1.43482e7	+	140406.i	−0.999952	+	0.00978512i
$28$	4.91516e6			0.285593
$29$	1.05674e7	+	1.86331e6i	0.515201	+	0.0908438i	0.425203	−	0.905098i	$-0.360203\pi$
$29$	1.05674e7	+	1.86331e6i	0.515201	+	0.0908438i	0.0899982	+	0.995942i	$0.471314\pi$
$30$	4.97485e6	+	8.55216e6i	0.204726	+	0.351941i
$31$	3.50314e7	+	1.27504e7i	1.22363	+	0.445364i	0.871410	−	0.490555i	$-0.163206\pi$
$31$	3.50314e7	+	1.27504e7i	1.22363	+	0.445364i	0.352216	+	0.935919i	$0.385428\pi$
$32$	2.07977e7	+	2.47857e7i	0.619819	+	0.738671i
$33$	−1.41895e6	+	1.70228e6i	−0.0362575	+	0.0434973i
$34$	−6.86129e6	+	2.49731e6i	−0.151012	+	0.0549638i
$35$	1.55396e7	+	8.97179e6i	0.295869	+	0.170820i
$36$	−4.74469e7	−	1.69196e7i	−0.784685	−	0.279819i
$37$	8.95940e6	+	1.55181e7i	0.129202	+	0.223785i	0.923368	−	0.383917i	$-0.125425\pi$
$37$	8.95940e6	+	1.55181e7i	0.129202	+	0.223785i	−0.794165	+	0.607702i	$0.792092\pi$
$38$	7.75688e6	−	9.24429e6i	0.0978969	−	0.116669i
$39$	−1.24030e7	−	6.90238e7i	−0.137469	−	0.765025i
$40$	1.32713e7	+	7.52651e7i	0.129602	+	0.735010i
$41$	1.02384e7	−	1.80531e6i	0.0883718	−	0.0155823i	−0.129287	−	0.991607i	$-0.541269\pi$
$41$	1.02384e7	−	1.80531e6i	0.0883718	−	0.0155823i	0.217659	+	0.976025i	$0.430158\pi$
$42$	1.80158e7	−	3.23730e6i	0.137850	−	0.0247706i
$43$	−9.64927e7	−	8.09670e7i	−0.656375	−	0.550764i	0.252623	−	0.967565i	$-0.418707\pi$
$43$	−9.64927e7	−	8.09670e7i	−0.656375	−	0.550764i	−0.908998	+	0.416801i	$0.863151\pi$
$44$	−6.73762e6	+	3.88997e6i	−0.0408548	+	0.0235875i
$45$	−1.19123e8	−	1.40099e8i	−0.645553	−	0.759226i
$46$	−1.04628e7	+	1.81220e7i	−0.0507992	+	0.0879868i
$47$	−1.34535e8	−	3.69632e8i	−0.586605	−	1.61168i	−0.776667	−	0.629912i	$-0.783091\pi$
$47$	−1.34535e8	−	3.69632e8i	−0.586605	−	1.61168i	0.190062	−	0.981772i	$-0.439131\pi$
$48$	−1.03169e8	−	8.59970e7i	−0.404895	−	0.337502i
$49$	−1.90958e8	+	1.60233e8i	−0.676018	+	0.567246i
$50$	298522.	−	820182.i	0.000955270	−	0.00262458i
$51$	1.17310e8	−	6.82404e7i	0.340005	−	0.197784i
$52$	4.27516e7	−	2.42456e8i	0.112444	−	0.637700i
$53$			2.30982e8i			0.552331i	0.961110	+	0.276166i	$0.0890638\pi$
$53$			2.30982e8i			0.552331i	−0.961110	+	0.276166i	$0.910936\pi$
$54$	−1.85054e8	−	3.07660e7i	−0.403022	−	0.0670042i
$55$	−2.84019e7			−0.0564331
$56$	1.39246e8	+	2.45528e7i	0.252837	+	0.0445821i
$57$	−1.11515e8	+	1.94613e8i	−0.185336	+	0.323443i
$58$	1.31826e8	+	4.79807e7i	0.200845	+	0.0731015i
$59$	4.14069e8	+	4.93469e8i	0.579179	+	0.690239i	0.973488	−	0.228739i	$-0.0734602\pi$
$59$	4.14069e8	+	4.93469e8i	0.579179	+	0.690239i	−0.394308	+	0.918978i	$0.629016\pi$
$60$	−2.22782e8	−	6.05931e8i	−0.286499	−	0.779232i
$61$	−1.44479e8	+	5.25861e7i	−0.171063	+	0.0622618i	−0.426132	−	0.904661i	$-0.640124\pi$
$61$	−1.44479e8	+	5.25861e7i	−0.171063	+	0.0622618i	0.255069	+	0.966923i	$0.417902\pi$
$62$	4.22086e8	+	2.43692e8i	0.460726	+	0.266000i
$63$	−3.18937e8	+	1.18446e8i	−0.321368	+	0.119348i
$64$	−7.14884e7	−	1.23821e8i	−0.0665787	−	0.115318i
$65$	5.77725e8	−	6.88506e8i	0.497914	−	0.593391i
$66$	−2.21337e7	+	1.86957e7i	−0.0176740	+	0.0149287i
$67$	3.88344e8	+	2.20241e9i	0.287636	+	1.63126i	0.695715	+	0.718318i	$0.255088\pi$
$67$	3.88344e8	+	2.20241e9i	0.287636	+	1.63126i	−0.408079	+	0.912947i	$0.633801\pi$
$68$	4.69203e8	−	8.27332e7i	0.322713	−	0.0569030i
$69$	1.31833e8	−	3.65916e8i	0.0842902	−	0.233957i
$70$	1.79706e8	+	1.50791e8i	0.106923	+	0.0897192i
$71$	2.85073e9	−	1.64587e9i	1.58002	−	0.912228i	0.585171	−	0.810910i	$-0.301027\pi$
$71$	2.85073e9	−	1.64587e9i	1.58002	−	0.912228i	0.994854	−	0.101318i	$-0.0323059\pi$
$72$	−1.25964e9	−	7.16341e8i	−0.651007	−	0.370218i
$73$	−1.88036e9	+	3.25688e9i	−0.907040	+	1.57104i	−0.0888837	+	0.996042i	$0.528330\pi$
$73$	−1.88036e9	+	3.25688e9i	−0.907040	+	1.57104i	−0.818156	+	0.574997i	$0.805003\pi$
$74$	8.01235e7	+	2.20137e8i	0.0361078	+	0.0992054i
$75$	−2.76497e6	+	1.59857e7i	−0.00116516	+	0.00673634i
$76$	−6.03202e8	+	5.06147e8i	−0.237900	+	0.199622i
$77$	−1.79716e7	+	4.93766e7i	−0.00663948	+	0.0182418i
$78$	−2.99054e6	−	9.16846e8i	−0.00103580	−	0.317558i
$79$	−8.39932e8	+	4.76349e9i	−0.272966	+	1.54807i	0.472383	+	0.881393i	$0.343394\pi$
$79$	−8.39932e8	+	4.76349e9i	−0.272966	+	1.54807i	−0.745349	+	0.666675i	$0.767717\pi$
$80$		−	1.72133e9i		−	0.525308i
$81$	3.48649e9	−	4.54909e7i	0.999915	−	0.0130467i
$82$	1.35919e8			0.0366616
$83$	6.01546e9	+	1.06069e9i	1.52714	+	0.269276i	0.873234	−	0.487302i	$-0.162019\pi$
$83$	6.01546e9	+	1.06069e9i	1.52714	+	0.269276i	0.653904	+	0.756578i	$0.273130\pi$
$84$	−1.19438e9	+	3.89578e6i	−0.285591	+	0.000931533i
$85$	1.63443e9	+	5.94885e8i	0.368360	+	0.134072i
$86$	−1.05854e9	−	1.26152e9i	−0.225017	−	0.268165i
$87$	−2.56933e9	−	4.44407e8i	−0.515495	−	0.0891629i
$88$	−2.10307e8	+	7.65456e7i	−0.0398512	+	0.0145046i
$89$	−5.85736e7	−	3.38175e7i	−0.0104894	−	0.00605607i	0.494746	−	0.869038i	$-0.335261\pi$
$89$	−5.85736e7	−	3.38175e7i	−0.0104894	−	0.00605607i	−0.505236	+	0.862981i	$0.668594\pi$
$90$	−1.21566e9	−	2.07422e9i	−0.205873	−	0.351271i
$91$	−8.31403e8	−	1.44003e9i	−0.133231	−	0.230763i
$92$	8.77673e8	−	1.04597e9i	0.133166	−	0.158701i
$93$	−8.52269e9	−	3.07056e9i	−1.22507	−	0.441370i
$94$	−8.93003e8	−	5.06447e9i	−0.121678	−	0.690072i
$95$	−2.83095e9	+	4.99173e8i	−0.365859	+	0.0645109i
$96$	−5.07345e9	−	6.00641e9i	−0.622225	−	0.736646i
$97$	−4.70128e9	−	3.94484e9i	−0.547466	−	0.459379i	0.326616	−	0.945157i	$-0.394092\pi$
$97$	−4.70128e9	−	3.94484e9i	−0.547466	−	0.459379i	−0.874082	+	0.485779i	$0.838536\pi$
$98$	−2.82237e9	+	1.62950e9i	−0.312237	+	0.180270i
$99$	3.43454e8	−	4.14778e8i	0.0361154	−	0.0436153i
$100$	−2.84763e7	+	4.93225e7i	−0.00284763	+	0.00493225i
$101$	2.83333e9	+	7.78451e9i	0.269582	+	0.740670i	0.998431	+	0.0559955i	$0.0178333\pi$
$101$	2.83333e9	+	7.78451e9i	0.269582	+	0.740670i	−0.728849	+	0.684674i	$0.759945\pi$
$102$	1.66531e9	−	6.12280e8i	0.150832	−	0.0554561i
$103$	−1.26630e9	+	1.06255e9i	−0.109232	+	0.0916568i	−0.695768	−	0.718267i	$-0.744936\pi$
$103$	−1.26630e9	+	1.06255e9i	−0.109232	+	0.0916568i	0.586536	+	0.809923i	$0.300491\pi$
$104$	2.42229e9	−	6.65519e9i	0.199095	−	0.547008i
$105$	−3.78321e9	−	2.16782e9i	−0.296425	−	0.169854i
$106$	−5.24383e8	+	2.97392e9i	−0.0391849	+	0.222229i
$107$		−	2.10630e9i		−	0.150177i	−0.997177	−	0.0750883i	$-0.976076\pi$
$107$		−	2.10630e9i		−	0.150177i	0.997177	−	0.0750883i	$-0.0239239\pi$
$108$	1.15429e10	+	4.07382e9i	0.785593	+	0.277258i
$109$	1.14750e10			0.745797			0.372899	−	0.927872i	$-0.378364\pi$
$109$	1.14750e10			0.745797			0.372899	+	0.927872i	$0.378364\pi$
$110$	−3.65678e8	−	6.44788e7i	−0.0227057	−	0.00400363i
$111$	−2.18942e9	−	3.76379e9i	−0.129932	−	0.223362i
$112$	−2.99252e9	−	1.08919e9i	−0.169804	−	0.0618035i
$113$	6.10448e9	+	7.27503e9i	0.331327	+	0.394860i	0.905829	−	0.423643i	$-0.139249\pi$
$113$	6.10448e9	+	7.27503e9i	0.331327	+	0.394860i	−0.574503	+	0.818503i	$0.694804\pi$
$114$	−1.87758e9	+	2.25250e9i	−0.0975159	+	0.116988i
$115$	4.68406e9	−	1.70486e9i	0.232881	−	0.0847617i
$116$	−7.92747e9	−	4.57693e9i	−0.377437	−	0.217913i
$117$	3.06863e9	+	1.67629e10i	0.139964	+	0.764573i
$118$	4.21090e9	+	7.29349e9i	0.184062	+	0.318805i
$119$	2.06841e9	−	2.46504e9i	0.0866766	−	0.103297i
$120$	−3.28455e9	−	1.82788e10i	−0.131999	−	0.734584i
$121$	4.48954e9	+	2.54615e10i	0.173091	+	0.981650i
$122$	−1.97957e9	+	3.49051e8i	−0.0732438	+	0.0129149i
$123$	−2.48649e9	+	4.46803e8i	−0.0883205	+	0.0158705i
$124$	−2.43621e10	−	2.04422e10i	−0.831009	−	0.697299i
$125$	−2.65186e10	+	1.53105e10i	−0.868960	+	0.501694i
$126$	−4.37525e9	+	8.00938e8i	−0.137769	+	0.0252201i
$127$	1.30512e10	−	2.26054e10i	0.395033	−	0.684217i	−0.598073	−	0.801442i	$-0.704067\pi$
$127$	1.30512e10	−	2.26054e10i	0.395033	−	0.684217i	0.993105	+	0.117225i	$0.0373999\pi$
$128$	−1.19711e10	−	3.28904e10i	−0.348405	−	0.957236i
$129$	2.35118e10	+	1.95984e10i	0.658168	+	0.548620i
$130$	9.00133e9	−	7.55301e9i	0.242432	−	0.203425i
$131$	−5.98262e9	+	1.64371e10i	−0.155072	+	0.426058i	−0.992763	−	0.120086i	$-0.961683\pi$
$131$	−5.98262e9	+	1.64371e10i	−0.155072	+	0.426058i	0.837691	+	0.546144i	$0.183905\pi$
$132$	1.63415e9	−	9.50597e8i	0.0407776	−	0.0237207i
$133$	−9.23505e8	+	5.23746e9i	−0.0221912	+	0.125853i
$134$			2.92379e10i			0.676740i
$135$	2.90577e10	+	3.39494e10i	0.648026	+	0.757117i
$136$	1.37057e10			0.294583
$137$	6.32409e10	+	1.11511e10i	1.31037	+	0.231054i	0.784829	−	0.619712i	$-0.212751\pi$
$137$	6.32409e10	+	1.11511e10i	1.31037	+	0.231054i	0.525544	+	0.850766i	$0.323862\pi$
$138$	2.52807e9	−	4.41192e9i	0.0505119	−	0.0881520i
$139$	3.42328e10	+	1.24597e10i	0.659734	+	0.240123i	0.650121	−	0.759830i	$-0.274718\pi$
$139$	3.42328e10	+	1.24597e10i	0.659734	+	0.240123i	0.00961236	+	0.999954i	$0.496940\pi$
$140$	−9.83932e9	−	1.17260e10i	−0.182947	−	0.218028i
$141$	3.29848e10	+	8.97134e10i	0.591859	+	1.60976i
$142$	4.04399e10	−	1.47189e10i	0.700436	−	0.254938i
$143$	2.27935e9	+	1.31598e9i	0.0381181	+	0.0220075i
$144$	2.51380e10	+	2.08154e10i	0.405993	+	0.336180i
$145$	−1.67088e10	−	2.89405e10i	−0.260679	−	0.451509i
$146$	−3.16036e10	+	3.76638e10i	−0.476401	+	0.567753i
$147$	4.62756e10	−	3.90878e10i	0.674164	−	0.569448i
$148$	−2.65441e9	−	1.50539e10i	−0.0373817	−	0.212002i
$149$	−1.14907e11	+	2.02612e10i	−1.56465	+	0.275889i	−0.887798	−	0.460234i	$-0.847766\pi$
$149$	−1.14907e11	+	2.02612e10i	−1.56465	+	0.275889i	−0.676848	+	0.736123i	$0.736655\pi$
$150$	−7.18904e7	+	1.99540e8i	−0.000946705	+	0.00262769i
$151$	−1.14129e11	−	9.57657e10i	−1.45382	−	1.21990i	−0.929730	−	0.368242i	$-0.879960\pi$
$151$	−1.14129e11	−	9.57657e10i	−1.45382	−	1.21990i	−0.524093	−	0.851661i	$-0.675596\pi$
$152$	−1.96170e10	+	1.13259e10i	−0.241777	+	0.139590i
$153$	−2.84522e10	+	1.66753e10i	−0.339358	+	0.198892i
$154$	−3.43483e8	+	5.94930e8i	−0.00396553	+	0.00686850i
$155$	−3.97085e10	−	1.09098e11i	−0.443839	−	1.21944i
$156$	−1.01964e10	+	5.89504e10i	−0.110363	+	0.638064i
$157$	7.27878e10	−	6.10762e10i	0.763063	−	0.640285i	−0.175860	−	0.984415i	$-0.556270\pi$
$157$	7.27878e10	−	6.10762e10i	0.763063	−	0.640285i	0.938922	+	0.344130i	$0.111826\pi$
$158$	−2.16284e10	+	5.94236e10i	−0.219654	+	0.603495i
$159$	−1.83078e8	−	5.61284e10i	−0.00180157	−	0.552328i
$160$	1.74976e10	−	9.92337e10i	0.166870	−	0.946366i
$161$		−	9.22200e9i		−	0.0852503i
$162$	4.49922e10	+	7.32942e9i	0.403238	+	0.0656893i
$163$	−2.01365e11			−1.75003			−0.875017	−	0.484093i	$-0.839150\pi$
$163$	−2.01365e11			−1.75003			−0.875017	+	0.484093i	$0.839150\pi$
$164$	−8.73417e9	−	1.54007e9i	−0.0736211	−	0.0129814i
$165$	6.90163e9	−	2.25115e7i	0.0564328	−	0.000184071i
$166$	7.50416e10	+	2.73129e10i	0.595335	+	0.216684i
$167$	−1.28130e11	−	1.52699e11i	−0.986435	−	1.17559i	−0.984463	−	0.175590i	$-0.943817\pi$
$167$	−1.28130e11	−	1.52699e11i	−0.986435	−	1.17559i	−0.00197178	−	0.999998i	$-0.500628\pi$
$168$	−3.38560e10	−	5.85592e9i	−0.252982	−	0.0437571i
$169$	5.12788e10	−	1.86639e10i	0.371967	−	0.135385i
$170$	1.96930e10	+	1.13697e10i	0.138697	+	0.0800766i
$171$	2.69438e10	−	4.73791e10i	0.184280	−	0.324046i
$172$	5.37278e10	+	9.30593e10i	0.356908	+	0.618184i
$173$	3.38764e10	−	4.03723e10i	0.218608	−	0.260527i	−0.645583	−	0.763690i	$-0.723386\pi$
$173$	3.38764e10	−	4.03723e10i	0.218608	−	0.260527i	0.864192	+	0.503162i	$0.167830\pi$
$174$	−3.20715e10	−	1.15548e10i	−0.201082	−	0.0724460i
$175$	6.67950e7	+	3.78814e8i	0.000406962	+	0.00230800i
$176$	4.96411e9	−	8.75307e8i	0.0293953	−	0.00518319i
$177$	−1.01009e11	−	1.19584e11i	−0.581428	−	0.688346i
$178$	−6.77367e8	−	5.68379e8i	−0.00379074	−	0.00318081i
$179$	3.79620e10	−	2.19174e10i	0.206578	−	0.119268i	−0.393142	−	0.919478i	$-0.628612\pi$
$179$	3.79620e10	−	2.19174e10i	0.206578	−	0.119268i	0.599720	+	0.800210i	$0.295279\pi$
$180$	5.46159e10	+	1.47064e11i	0.289039	+	0.778293i
$181$	−1.42121e11	+	2.46160e11i	−0.731585	+	1.26714i	0.224621	+	0.974446i	$0.427886\pi$
$181$	−1.42121e11	+	2.46160e11i	−0.731585	+	1.26714i	−0.956206	+	0.292696i	$0.905448\pi$
$182$	−7.43520e9	−	2.04280e10i	−0.0372337	−	0.102299i
$183$	3.50666e10	−	1.28929e10i	0.170859	−	0.0628195i
$184$	3.00893e10	−	2.52479e10i	0.142667	−	0.119712i
$185$	1.90863e10	−	5.24391e10i	0.0880770	−	0.241989i
$186$	−1.02760e11	−	5.88822e10i	−0.461591	−	0.264496i
$187$	−8.84460e8	+	5.01602e9i	−0.00386785	+	0.0219357i
$188$			3.35561e11i			1.42884i
$189$	7.74075e10	−	2.90349e10i	0.320977	−	0.120396i
$190$	−3.75820e10			−0.151779
$191$	4.24220e11	+	7.48015e10i	1.66888	+	0.294268i	0.926663	−	0.375894i	$-0.122664\pi$
$191$	4.24220e11	+	7.48015e10i	1.66888	+	0.294268i	0.742215	+	0.670162i	$0.233775\pi$
$192$	1.74697e10	+	3.00318e10i	0.0669545	+	0.115100i
$193$	1.38420e11	+	5.03809e10i	0.516908	+	0.188139i	0.587283	−	0.809382i	$-0.300197\pi$
$193$	1.38420e11	+	5.03809e10i	0.516908	+	0.188139i	−0.0703754	+	0.997521i	$0.522420\pi$
$194$	−5.15737e10	−	6.14632e10i	−0.187681	−	0.223669i
$195$	−1.39841e11	+	1.67764e11i	−0.495976	+	0.595012i
$196$	1.99829e11	−	7.27319e10i	0.690842	−	0.251446i
$197$	3.50254e11	+	2.02219e11i	1.18046	+	0.681540i	0.956121	−	0.292971i	$-0.0946441\pi$
$197$	3.50254e11	+	2.02219e11i	1.18046	+	0.681540i	0.224340	+	0.974511i	$0.427977\pi$
$198$	5.36364e9	−	4.56059e9i	0.0176252	−	0.0149863i
$199$	1.06945e11	+	1.85235e11i	0.342686	+	0.593549i	0.984931	−	0.172950i	$-0.0553300\pi$
$199$	1.06945e11	+	1.85235e11i	0.342686	+	0.593549i	−0.642245	+	0.766500i	$0.721997\pi$
$200$	−1.05311e9	+	1.25505e9i	−0.00329097	+	0.00392203i
$201$	−9.61129e10	−	5.34875e11i	−0.292955	−	1.63032i
$202$	1.88068e10	+	1.06659e11i	0.0559188	+	0.317132i
$203$	−6.08857e10	+	1.07358e10i	−0.176618	+	0.0311425i
$204$	−1.13950e11	+	2.04759e10i	−0.322526	+	0.0579553i
$205$	−2.48025e10	−	2.08118e10i	−0.0685057	−	0.0574831i
$206$	−1.87160e10	+	1.08057e10i	−0.0504518	+	0.0291284i
$207$	−3.17451e10	+	8.90217e10i	−0.0835267	+	0.234231i
$208$	−7.97566e10	+	1.38142e11i	−0.204856	+	0.354822i
$209$	−2.87912e9	−	7.91031e9i	−0.00721984	−	0.0198364i
$210$	−4.37878e10	−	3.64996e10i	−0.107215	−	0.0893700i
$211$	2.74310e11	−	2.30173e11i	0.655887	−	0.550354i	−0.252964	−	0.967476i	$-0.581405\pi$
$211$	2.74310e11	−	2.30173e11i	0.655887	−	0.550354i	0.908851	+	0.417122i	$0.136961\pi$
$212$	6.73937e10	−	1.85163e11i	0.157377	−	0.432389i
$213$	−6.91419e11	+	4.02203e11i	−1.57704	+	0.917377i
$214$	4.78179e9	−	2.71189e10i	0.0106542	−	0.0604231i
$215$			3.92284e11i			0.853903i
$216$	3.06660e11	+	1.73071e11i	0.652211	+	0.368092i
$217$	−2.14793e11			−0.446397
$218$	1.47742e11	+	2.60509e10i	0.300069	+	0.0529103i
$219$	4.54343e11	−	7.92907e11i	0.901910	−	1.57399i
$220$	2.27679e10	+	8.28682e9i	0.0441783	+	0.0160796i
$221$	−1.03605e11	−	1.23472e11i	−0.196526	−	0.234211i
$222$	−1.96444e10	−	5.34296e10i	−0.0364312	−	0.0990871i
$223$	−8.54608e11	+	3.11052e11i	−1.54968	+	0.564038i	−0.968343	−	0.249623i	$-0.919693\pi$
$223$	−8.54608e11	+	3.11052e11i	−1.54968	+	0.564038i	−0.581339	+	0.813661i	$0.697471\pi$
$224$	−1.61446e11	−	9.32107e10i	−0.286277	−	0.165282i
$225$	6.59214e8	−	3.88669e9i	0.00114318	−	0.00674011i
$226$	6.20798e10	+	1.07525e11i	0.105295	+	0.182376i
$227$	5.38250e11	−	6.41461e11i	0.893007	−	1.06424i	−0.104559	−	0.994519i	$-0.533343\pi$
$227$	5.38250e11	−	6.41461e11i	0.893007	−	1.06424i	0.997566	−	0.0697255i	$-0.0222123\pi$
$228$	1.46176e11	−	1.23471e11i	0.237248	−	0.200397i
$229$	1.07722e11	+	6.10920e11i	0.171051	+	0.970078i	0.942604	+	0.333913i	$0.108369\pi$
$229$	1.07722e11	+	6.10920e11i	0.171051	+	0.970078i	−0.771553	+	0.636165i	$0.780520\pi$
$230$	6.41782e10	−	1.13164e10i	0.0997123	−	0.0175820i
$231$	4.32795e9	−	1.20127e10i	0.00657994	−	0.0182634i
$232$	−2.01721e11	−	1.69264e11i	−0.300131	−	0.251840i
$233$	−1.50960e11	+	8.71569e10i	−0.219828	+	0.126918i	−0.605871	−	0.795563i	$-0.707175\pi$
$233$	−1.50960e11	+	8.71569e10i	−0.219828	+	0.126918i	0.386043	+	0.922481i	$0.373842\pi$
$234$	1.45340e9	+	2.22790e11i	0.00207159	+	0.317553i
$235$	−6.12511e11	+	1.06090e12i	−0.854623	+	1.48025i
$236$	−1.87952e11	−	5.16393e11i	−0.256736	−	0.705375i
$237$	2.00327e11	−	1.15819e12i	0.267915	−	1.54895i
$238$	3.22272e10	−	2.70418e10i	0.0422025	−	0.0354121i
$239$	2.63210e11	−	7.23163e11i	0.337530	−	0.927356i	−0.648563	−	0.761161i	$-0.724630\pi$
$239$	2.63210e11	−	7.23163e11i	0.337530	−	0.927356i	0.986093	−	0.166195i	$-0.0531481\pi$
$240$	1.36433e9	+	4.18280e11i	0.00171342	+	0.525305i
$241$	1.27734e11	−	7.24418e11i	0.157117	−	0.891054i	−0.799708	−	0.600389i	$-0.795012\pi$
$241$	1.27734e11	−	7.24418e11i	0.157117	−	0.891054i	0.956825	−	0.290665i	$-0.0938764\pi$
$242$			3.38011e11i			0.407244i
$243$	−8.47176e11	+	1.38176e10i	−0.999867	+	0.0163081i
$244$	1.31162e11			0.151656
$245$	7.64533e11	+	1.34808e11i	0.866096	+	0.152716i
$246$	−3.30282e10	+	1.07730e8i	−0.0366614	+	0.000119581i
$247$	2.50322e11	+	9.11098e10i	0.272279	+	0.0991015i
$248$	−5.88058e11	−	7.00821e11i	−0.626848	−	0.747048i
$249$	−1.46259e12	−	2.52978e11i	−1.52801	−	0.264293i
$250$	−3.76188e11	+	1.36921e11i	−0.385216	+	0.140207i
$251$	5.01926e11	+	2.89787e11i	0.503815	+	0.290878i	0.730288	−	0.683140i	$-0.239386\pi$
$251$	5.01926e11	+	2.89787e11i	0.503815	+	0.290878i	−0.226472	+	0.974018i	$0.572719\pi$
$252$	2.90229e11	−	1.89334e9i	0.285587	−	0.00186306i
$253$	7.29850e9	+	1.26414e10i	0.00704095	+	0.0121953i
$254$	2.19355e11	−	2.61418e11i	0.207482	−	0.247267i
$255$	−3.97636e11	−	1.43261e11i	−0.368795	−	0.132870i
$256$	−5.40372e10	−	3.06460e11i	−0.0491465	−	0.278724i
$257$	−2.29445e11	+	4.04573e10i	−0.204650	+	0.0360854i	−0.275034	−	0.961435i	$-0.588689\pi$
$257$	−2.29445e11	+	4.04573e10i	−0.204650	+	0.0360854i	0.0703830	+	0.997520i	$0.477578\pi$
$258$	2.58224e11	+	3.05708e11i	0.225890	+	0.267429i
$259$	−7.90881e10	−	6.63628e10i	−0.0678598	−	0.0569411i
$260$	−6.64007e11	+	3.83365e11i	−0.558864	+	0.322660i
$261$	6.24697e11	+	1.05954e11i	0.515783	+	0.0874810i
$262$	−1.14343e11	+	1.98047e11i	−0.0926194	+	0.160422i
$263$	6.73609e10	+	1.85073e11i	0.0535339	+	0.147083i	0.963577	−	0.267429i	$-0.0861742\pi$
$263$	6.73609e10	+	1.85073e11i	0.0535339	+	0.147083i	−0.910043	+	0.414513i	$0.863952\pi$
$264$	5.10437e10	−	1.87672e10i	0.0398037	−	0.0146345i
$265$	5.51053e11	−	4.62388e11i	0.421662	−	0.353816i
$266$	−2.37804e10	+	6.53362e10i	−0.0178571	+	0.0490621i
$267$	1.42601e10	+	8.17117e9i	0.0105091	+	0.00602183i
$268$	3.31288e11	−	1.87883e12i	0.239625	−	1.35898i
$269$			1.49158e12i			1.05897i	0.848318	+	0.529487i	$0.177616\pi$
$269$			1.49158e12i			1.05897i	−0.848318	+	0.529487i	$0.822384\pi$
$270$	2.97048e11	+	5.03069e11i	0.207018	+	0.350598i
$271$	−3.91112e11			−0.267581			−0.133790	−	0.991010i	$-0.542715\pi$
$271$	−3.91112e11			−0.267581			−0.133790	+	0.991010i	$0.542715\pi$
$272$	−3.04001e11	−	5.36036e10i	−0.204188	−	0.0360039i
$273$	2.03171e11	+	3.49267e11i	0.133983	+	0.230327i
$274$	7.88917e11	+	2.87142e11i	0.510833	+	0.185928i
$275$	−3.91363e8	−	4.66409e8i	−0.000248838	−	0.000296554i
$276$	−2.12444e11	+	2.54865e11i	−0.132648	+	0.159135i
$277$	6.11171e11	−	2.22448e11i	0.374769	−	0.136405i	−0.147766	−	0.989022i	$-0.547208\pi$
$277$	6.11171e11	−	2.22448e11i	0.374769	−	0.136405i	0.522536	+	0.852617i	$0.324986\pi$
$278$	4.12465e11	+	2.38137e11i	0.248406	+	0.143417i
$279$	2.07344e12	+	7.39387e11i	1.22651	+	0.437372i
$280$	−2.20171e11	−	3.81348e11i	−0.127929	−	0.221580i
$281$	1.93872e11	−	2.31048e11i	0.110658	−	0.131878i	−0.707872	−	0.706341i	$-0.750345\pi$
$281$	1.93872e11	−	2.31048e11i	0.110658	−	0.131878i	0.818530	+	0.574463i	$0.194789\pi$
$282$	2.21013e11	+	1.22995e12i	0.123929	+	0.689672i
$283$	2.19715e11	+	1.24606e12i	0.121040	+	0.686449i	0.983582	+	0.180464i	$0.0577599\pi$
$283$	2.19715e11	+	1.24606e12i	0.121040	+	0.686449i	−0.862542	+	0.505985i	$0.831129\pi$
$284$	−2.76545e12	+	4.87623e11i	−1.49683	+	0.263932i
$285$	6.87522e11	−	1.23542e11i	0.365647	−	0.0657039i
$286$	2.63593e10	+	2.21181e10i	0.0137754	+	0.0115589i
$287$	−5.18753e10	+	2.99502e10i	−0.0266411	+	0.0153812i
$288$	1.23760e12	+	1.45553e12i	0.624624	+	0.734612i
$289$	−8.52038e11	+	1.47577e12i	−0.422639	+	0.732032i
$290$	−1.49426e11	−	4.10545e11i	−0.0728512	−	0.200157i
$291$	1.14553e12	+	9.54865e11i	0.548962	+	0.457590i
$292$	2.45761e12	−	2.06218e12i	1.15771	−	0.971432i
$293$	−9.02468e11	+	2.47951e12i	−0.417920	+	1.14823i	0.534959	+	0.844878i	$0.320327\pi$
$293$	−9.02468e11	+	2.47951e12i	−0.417920	+	1.14823i	−0.952880	+	0.303349i	$0.901895\pi$
$294$	6.84542e11	−	3.98203e11i	0.311647	−	0.181287i
$295$	3.48366e11	−	1.97568e12i	0.155929	−	0.884316i
$296$		−	4.39734e11i		−	0.193523i
$297$	−8.31301e10	+	1.01063e11i	−0.0359729	+	0.0437329i
$298$	−1.52544e12			−0.649103
$299$	−4.54906e11	−	8.02121e10i	−0.190355	−	0.0335648i
$300$	6.88062e9	−	1.20079e10i	0.00283153	−	0.00494151i
$301$	6.81985e11	+	2.48222e11i	0.276021	+	0.100463i
$302$	−1.25201e12	−	1.49209e12i	−0.498396	−	0.593965i
$303$	−6.94666e11	−	1.88938e12i	−0.271996	−	0.739786i
$304$	4.79412e11	−	1.74492e11i	0.184647	−	0.0672059i
$305$	4.14678e11	+	2.39414e11i	0.157113	+	0.0907091i
$306$	−4.04182e11	+	1.50103e11i	−0.150650	+	0.0559478i
$307$	4.65939e11	+	8.07030e11i	0.170859	+	0.295936i	0.938720	−	0.344680i	$-0.112013\pi$
$307$	4.65939e11	+	8.07030e11i	0.170859	+	0.295936i	−0.767862	+	0.640616i	$0.778679\pi$
$308$	2.88132e10	−	3.43383e10i	0.0103953	−	0.0123887i
$309$	3.06868e11	−	2.59203e11i	0.108933	−	0.0920126i
$310$	−2.63573e11	−	1.49480e12i	−0.0920646	−	0.522124i
$311$	−2.64487e12	+	4.66363e11i	−0.909082	+	0.160296i	−0.608587	−	0.793487i	$-0.708263\pi$
$311$	−2.64487e12	+	4.66363e11i	−0.909082	+	0.160296i	−0.300496	+	0.953783i	$0.597152\pi$
$312$	−5.83339e11	+	1.61912e12i	−0.197309	+	0.547655i
$313$	−7.51264e11	−	6.30385e11i	−0.250075	−	0.209838i	0.509129	−	0.860690i	$-0.329967\pi$
$313$	−7.51264e11	−	6.30385e11i	−0.250075	−	0.209838i	−0.759205	+	0.650852i	$0.774412\pi$
$314$	1.07581e12	−	6.21117e11i	0.352441	−	0.203482i
$315$	9.21034e11	+	5.23778e11i	0.296977	+	0.168886i
$316$	2.06316e12	−	3.57350e12i	0.654783	−	1.13412i
$317$	9.83978e11	+	2.70346e12i	0.307390	+	0.844546i	0.993164	+	0.116731i	$0.0372416\pi$
$317$	9.83978e11	+	2.70346e12i	0.307390	+	0.844546i	−0.685774	+	0.727815i	$0.740536\pi$
$318$	1.25067e11	−	7.23075e11i	0.0384599	−	0.222355i
$319$	7.49646e10	−	6.29028e10i	0.0226936	−	0.0190422i
$320$	−1.52292e11	+	4.18419e11i	−0.0453866	+	0.124699i
$321$	1.66947e9	+	5.11829e11i	0.000489839	+	0.150176i
$322$	2.09360e10	−	1.18734e11i	0.00604805	−	0.0343002i
$323$			5.15515e11i			0.146632i
$324$	−2.80815e12	−	9.80785e11i	−0.786493	−	0.274694i
$325$	1.92672e10			0.00531376
$326$	−2.59260e12	−	4.57145e11i	−0.704121	−	0.124155i
$327$	−2.78841e12	+	9.09517e9i	−0.745793	+	0.00243261i
$328$	−2.39745e11	−	8.72599e10i	−0.0631509	−	0.0229851i
$329$	1.45680e12	+	1.73614e12i	0.377937	+	0.450408i
$330$	8.89103e10	+	1.53784e10i	0.0227186	+	0.00392955i
$331$	−1.46270e12	+	5.32380e11i	−0.368142	+	0.133993i	−0.519465	−	0.854492i	$-0.673869\pi$
$331$	−1.46270e12	+	5.32380e11i	−0.368142	+	0.133993i	0.151323	+	0.988484i	$0.451647\pi$
$332$	−4.51270e12	−	2.60541e12i	−1.11878	−	0.645930i
$333$	5.35010e11	+	9.12860e11i	0.130659	+	0.222937i
$334$	−1.30302e12	−	2.25690e12i	−0.313488	−	0.542976i
$335$	4.47687e12	−	5.33533e12i	1.06109	−	1.26455i
$336$	7.28043e11	+	2.62300e11i	0.170005	+	0.0612493i
$337$	9.10879e11	+	5.16585e12i	0.209561	+	1.18848i	0.890099	+	0.455768i	$0.150635\pi$
$337$	9.10879e11	+	5.16585e12i	0.209561	+	1.18848i	−0.680537	+	0.732714i	$0.738254\pi$
$338$	7.02591e11	−	1.23886e11i	0.159265	−	0.0280826i
$339$	−1.48915e12	−	1.76299e12i	−0.332613	−	0.393777i
$340$	−1.13664e12	−	9.53756e11i	−0.250167	−	0.209915i
$341$	2.94435e11	−	1.69992e11i	0.0638583	−	0.0368686i
$342$	4.54465e11	−	5.48842e11i	0.0971338	−	0.117305i
$343$	1.53190e12	−	2.65332e12i	0.322670	−	0.558881i
$344$	1.05724e12	+	2.90474e12i	0.219473	+	0.602997i
$345$	−1.13687e12	+	4.17991e11i	−0.232603	+	0.0855208i
$346$	5.27817e11	−	4.42891e11i	0.106439	−	0.0893133i
$347$	1.30766e12	−	3.59276e12i	0.259924	−	0.714135i	−0.739247	−	0.673434i	$-0.764819\pi$
$347$	1.30766e12	−	3.59276e12i	0.259924	−	0.714135i	0.999171	−	0.0407013i	$-0.0129592\pi$
$348$	1.92999e12	+	1.10590e12i	0.378146	+	0.216681i
$349$	−7.01546e11	+	3.97867e12i	−0.135497	+	0.768441i	0.839016	+	0.544107i	$0.183132\pi$
$349$	−7.01546e11	+	3.97867e12i	−0.135497	+	0.768441i	−0.974512	+	0.224333i	$0.927980\pi$
$350$			5.02890e9i			0.000957487i
$351$	−7.58959e11	−	4.07092e12i	−0.142457	−	0.764112i
$352$	2.95076e11			0.0546036
$353$	−1.94975e12	−	3.43793e11i	−0.355717	−	0.0627225i	−0.00706577	−	0.999975i	$-0.502249\pi$
$353$	−1.94975e12	−	3.43793e11i	−0.355717	−	0.0627225i	−0.348651	+	0.937253i	$0.613360\pi$
$354$	−1.02902e12	−	1.76897e12i	−0.185101	−	0.318203i
$355$	−9.63322e12	−	3.50620e12i	−1.70856	−	0.621864i
$356$	3.70875e10	+	4.41991e10i	0.00648600	+	0.00772972i
$357$	−5.00667e11	+	6.00640e11i	−0.0863392	+	0.103579i
$358$	5.38522e11	−	1.96006e11i	0.0915773	−	0.0333314i
$359$	−4.24855e12	−	2.45290e12i	−0.712473	−	0.411347i	0.0995028	−	0.995037i	$-0.468275\pi$
$359$	−4.24855e12	−	2.45290e12i	−0.712473	−	0.411347i	−0.811976	+	0.583691i	$0.801608\pi$
$360$	8.12630e11	+	4.43912e12i	0.134394	+	0.734149i
$361$	2.63953e12	+	4.57180e12i	0.430518	+	0.745678i
$362$	−2.38866e12	+	2.84669e12i	−0.384248	+	0.457929i
$363$	−1.11113e12	−	6.18355e12i	−0.176292	−	0.981080i
$364$	2.46321e11	+	1.39695e12i	0.0385473	+	0.218612i
$365$	1.15341e13	−	2.03377e12i	1.78040	−	0.313933i
$366$	4.80755e11	−	8.63880e10i	0.0732013	−	0.0131537i
$367$	−2.24222e12	−	1.88144e12i	−0.336781	−	0.282593i	0.458675	−	0.888604i	$-0.348324\pi$
$367$	−2.24222e12	−	1.88144e12i	−0.336781	−	0.282593i	−0.795456	+	0.606011i	$0.792769\pi$
$368$	−7.66144e11	+	4.42333e11i	−0.113520	+	0.0655406i
$369$	6.03860e11	−	1.10543e11i	0.0882683	−	0.0161585i
$370$	3.64786e11	−	6.31828e11i	0.0526053	−	0.0911151i
$371$	−4.55176e11	−	1.25059e12i	−0.0647604	−	0.177928i
$372$	5.93615e12	+	4.94812e12i	0.833279	+	0.694585i
$373$	−6.53194e12	+	5.48095e12i	−0.904686	+	0.759122i	−0.971101	−	0.238670i	$-0.923289\pi$
$373$	−6.53194e12	+	5.48095e12i	−0.904686	+	0.759122i	0.0664144	+	0.997792i	$0.478844\pi$
$374$	−2.27750e10	+	6.25739e10i	−0.00311244	+	0.00855136i
$375$	6.43184e12	−	3.74145e12i	0.867319	−	0.504526i
$376$	−1.67624e12	+	9.50640e12i	−0.223047	+	1.26496i
$377$			3.09677e12i			0.406632i
$378$	1.06254e12	−	1.98095e11i	0.137686	−	0.0256693i
$379$	9.94813e12			1.27217			0.636086	−	0.771619i	$-0.280553\pi$
$379$	9.94813e12			1.27217			0.636086	+	0.771619i	$0.280553\pi$
$380$	2.41502e12	+	4.25833e11i	0.304792	+	0.0537430i
$381$	−3.15352e12	+	5.50343e12i	−0.392799	+	0.685502i
$382$	5.29206e12	+	1.92615e12i	0.650591	+	0.236796i
$383$	5.36395e12	+	6.39250e12i	0.650865	+	0.775670i	0.986044	−	0.166484i	$-0.0532414\pi$
$383$	5.36395e12	+	6.39250e12i	0.650865	+	0.775670i	−0.335179	+	0.942154i	$0.608797\pi$
$384$	2.93503e12	+	7.98283e12i	0.351526	+	0.956094i
$385$	1.53774e11	−	5.59690e10i	0.0181794	−	0.00661674i
$386$	1.66780e12	+	9.62904e11i	0.194629	+	0.112369i
$387$	−5.72886e12	−	4.74375e12i	−0.659954	−	0.546471i
$388$	2.61770e12	+	4.53400e12i	0.297688	+	0.515611i
$389$	−8.74661e11	+	1.04238e12i	−0.0981955	+	0.117025i	−0.812904	−	0.582397i	$-0.802115\pi$
$389$	−8.74661e11	+	1.04238e12i	−0.0981955	+	0.117025i	0.714709	+	0.699422i	$0.246559\pi$
$390$	−2.18133e12	+	1.84251e12i	−0.241767	+	0.204214i
$391$	−1.55227e11	−	8.80337e11i	−0.0169857	−	0.0963308i
$392$	6.02445e12	−	1.06227e12i	0.650859	−	0.114764i
$393$	1.44074e12	−	3.99894e12i	0.153682	−	0.426562i
$394$	4.05047e12	+	3.39875e12i	0.426603	+	0.357963i
$395$	1.30456e13	−	7.53190e12i	1.35669	−	0.783284i
$396$	−3.96343e11	+	2.32289e11i	−0.0407001	+	0.0238535i
$397$	−1.97136e12	+	3.41449e12i	−0.199900	+	0.346237i	−0.948496	−	0.316790i	$-0.897395\pi$
$397$	−1.97136e12	+	3.41449e12i	−0.199900	+	0.346237i	0.748596	+	0.663026i	$0.230728\pi$
$398$	9.56406e11	+	2.62770e12i	0.0957695	+	0.263124i
$399$	2.20259e11	−	1.27343e12i	0.0217806	−	0.125924i
$400$	2.82672e10	−	2.37190e10i	0.00276047	−	0.00231631i
$401$	−6.86161e11	+	1.88521e12i	−0.0661765	+	0.181819i	−0.968373	−	0.249507i	$-0.919732\pi$
$401$	−6.86161e11	+	1.88521e12i	−0.0661765	+	0.181819i	0.902197	+	0.431325i	$0.141954\pi$
$402$	−2.31741e10	−	7.10477e12i	−0.00220736	−	0.676737i
$403$	−1.86825e12	+	1.05954e13i	−0.175756	+	0.996761i
$404$		−	7.06699e12i		−	0.656640i
$405$	−7.08789e12	−	8.22662e12i	−0.650492	−	0.754999i
$406$	−8.08282e11			−0.0732711
$407$	1.60934e11	+	2.83770e10i	0.0144104	+	0.00254094i
$408$	−3.33048e12	+	1.08632e10i	−0.294581	+	0.000960857i
$409$	−1.39696e13	−	5.08453e12i	−1.22059	−	0.444257i	−0.350222	−	0.936667i	$-0.613894\pi$
$409$	−1.39696e13	−	5.08453e12i	−1.22059	−	0.444257i	−0.870363	+	0.492410i	$0.836116\pi$
$410$	−2.72088e11	−	3.24261e11i	−0.0234849	−	0.0279883i
$411$	−1.53763e13	−	2.65957e12i	−1.31112	−	0.226779i
$412$	1.32513e12	−	4.82307e11i	0.111628	−	0.0406291i
$413$	−3.21429e12	−	1.85577e12i	−0.267507	−	0.154445i
$414$	−6.10821e11	+	1.07409e12i	−0.0502241	+	0.0883163i
$415$	−9.51147e12	−	1.64743e13i	−0.772693	−	1.33834i
$416$	−6.00217e12	+	7.15310e12i	−0.481772	+	0.574153i
$417$	−8.32841e12	−	3.00056e12i	−0.660513	−	0.237970i
$418$	−1.91107e10	−	1.08382e11i	−0.00149760	−	0.00849331i
$419$	6.19419e12	−	1.09220e12i	0.479639	−	0.0845733i	0.0713990	−	0.997448i	$-0.477254\pi$
$419$	6.19419e12	−	1.09220e12i	0.479639	−	0.0845733i	0.408240	+	0.912874i	$0.366143\pi$
$420$	2.40024e12	+	2.84162e12i	0.183657	+	0.217430i
$421$	1.21559e13	+	1.02000e13i	0.919130	+	0.771241i	0.973834	−	0.227261i	$-0.0729771\pi$
$421$	1.21559e13	+	1.02000e13i	0.919130	+	0.771241i	−0.0547041	+	0.998503i	$0.517422\pi$
$422$	4.05431e12	−	2.34076e12i	0.302939	−	0.174902i
$423$	−8.08637e12	−	2.17741e13i	−0.597106	−	1.60782i
$424$	2.83420e12	−	4.90898e12i	0.206824	−	0.358230i
$425$	1.27526e10	+	3.50374e10i	0.000919715	+	0.00252690i
$426$	−9.81518e12	+	3.60873e12i	−0.699601	+	0.257221i
$427$	6.78613e11	−	5.69424e11i	0.0478060	−	0.0401140i
$428$	−6.14556e11	+	1.68848e12i	−0.0427900	+	0.117565i
$429$	−5.54922e11	−	3.17976e11i	−0.0381896	−	0.0218830i
$430$	−8.90575e11	+	5.05070e12i	−0.0605798	+	0.343565i
$431$		−	9.69546e12i		−	0.651902i	−0.945387	−	0.325951i	$-0.894316\pi$
$431$		−	9.69546e12i		−	0.651902i	0.945387	−	0.325951i	$-0.105684\pi$
$432$	−6.12501e12	−	5.03819e12i	−0.407088	−	0.334854i
$433$	−4.86634e12			−0.319715			−0.159858	−	0.987140i	$-0.551103\pi$
$433$	−4.86634e12			−0.319715			−0.159858	+	0.987140i	$0.551103\pi$
$434$	−2.76548e12	−	4.87629e11i	−0.179606	−	0.0316695i
$435$	4.08316e12	+	7.01927e12i	0.262150	+	0.450656i
$436$	−9.19873e12	−	3.34806e12i	−0.583842	−	0.212501i
$437$	9.49652e11	+	1.13175e12i	0.0595878	+	0.0710140i
$438$	7.64979e12	−	9.17729e12i	0.474547	−	0.569304i
$439$	2.07869e13	−	7.56583e12i	1.27488	−	0.464017i	0.386142	−	0.922440i	$-0.373808\pi$
$439$	2.07869e13	−	7.56583e12i	1.27488	−	0.464017i	0.888734	+	0.458423i	$0.151585\pi$
$440$	6.03615e11	+	3.48497e11i	0.0366013	+	0.0211318i
$441$	−1.12139e13	+	9.53496e12i	−0.672303	+	0.571644i
$442$	−1.05362e12	−	1.82492e12i	−0.0624557	−	0.108176i
$443$	−1.42070e13	+	1.69312e13i	−0.832690	+	0.992362i	0.167289	+	0.985908i	$0.446499\pi$
$443$	−1.42070e13	+	1.69312e13i	−0.832690	+	0.992362i	−0.999979	+	0.00645366i	$0.997946\pi$
$444$	6.56950e11	+	3.65597e12i	0.0380730	+	0.211879i
$445$	3.65765e10	+	2.07435e11i	0.00209605	+	0.0118873i
$446$	−1.17093e13	+	2.06467e12i	−0.663525	+	0.116997i
$447$	2.79062e13	−	5.01453e12i	1.56374	−	0.280991i
$448$	6.31056e11	+	5.29519e11i	0.0349686	+	0.0293421i
$449$	1.84551e13	−	1.06551e13i	1.01131	−	0.583881i	0.0997359	−	0.995014i	$-0.468200\pi$
$449$	1.84551e13	−	1.06551e13i	1.01131	−	0.583881i	0.911575	+	0.411133i	$0.134867\pi$
$450$	1.73111e10	−	4.85449e10i	0.000938129	−	0.00263076i
$451$	4.74066e10	−	8.21106e10i	0.00254072	−	0.00440065i
$452$	−2.77090e12	−	7.61299e12i	−0.146869	−	0.403518i
$453$	2.78091e13	+	2.31805e13i	1.45779	+	1.21515i
$454$	8.38629e12	−	7.03693e12i	0.434801	−	0.364841i
$455$	−1.77114e12	+	4.86618e12i	−0.0908232	+	0.249535i
$456$	4.75793e12	−	2.76772e12i	0.241320	−	0.140378i
$457$	−1.11818e12	+	6.34153e12i	−0.0560960	+	0.318136i	−0.999924	−	0.0123000i	$-0.996085\pi$
$457$	−1.11818e12	+	6.34153e12i	−0.0560960	+	0.318136i	0.943828	+	0.330436i	$0.107196\pi$
$458$			8.11021e12i			0.402443i
$459$	6.90063e12	−	4.07463e12i	0.338708	−	0.199998i
$460$	−4.25232e12			−0.206460
$461$	−2.41288e13	−	4.25455e12i	−1.15886	−	0.204338i	−0.439019	−	0.898478i	$-0.644674\pi$
$461$	−2.41288e13	−	4.25455e12i	−1.15886	−	0.204338i	−0.719840	+	0.694140i	$0.755785\pi$
$462$	8.29943e10	−	1.44839e11i	0.00394311	−	0.00688140i
$463$	−1.35103e13	−	4.91736e12i	−0.634981	−	0.231114i	0.00441674	−	0.999990i	$-0.498594\pi$
$463$	−1.35103e13	−	4.91736e12i	−0.634981	−	0.231114i	−0.639398	+	0.768876i	$0.720816\pi$
$464$	3.81229e12	+	4.54331e12i	0.177254	+	0.211243i
$465$	9.73559e12	+	2.64793e13i	0.447814	+	1.21798i
$466$	−2.14149e12	+	7.79440e11i	−0.0974512	+	0.0354693i
$467$	−2.90321e13	−	1.67617e13i	−1.30706	−	0.754630i	−0.325453	−	0.945558i	$-0.605517\pi$
$467$	−2.90321e13	−	1.67617e13i	−1.30706	−	0.754630i	−0.981604	+	0.190929i	$0.938850\pi$
$468$	2.43099e12	−	1.43330e13i	0.108281	−	0.638420i
$469$	−6.44266e12	−	1.11590e13i	−0.283923	−	0.491770i
$470$	−1.02946e13	+	1.22687e13i	−0.448871	+	0.534943i
$471$	−1.76389e13	+	1.48991e13i	−0.760970	+	0.642771i
$472$	−2.74510e12	−	1.55682e13i	−0.117178	−	0.664552i
$473$	−1.13130e12	+	1.99479e11i	−0.0477830	+	0.00842543i
$474$	5.20858e12	−	1.44570e13i	0.217685	−	0.604208i
$475$	−4.72063e10	−	3.96108e10i	−0.00195223	−	0.00163812i
$476$	−2.37733e12	+	1.37255e12i	−0.0972868	+	0.0561685i
$477$	8.89755e10	+	1.36390e13i	0.00360312	+	0.552320i
$478$	5.03060e12	−	8.71325e12i	0.201595	−	0.349173i
$479$	−6.26922e12	−	1.72245e13i	−0.248620	−	0.683077i	−0.999738	−	0.0229090i	$-0.992707\pi$
$479$	−6.26922e12	−	1.72245e13i	−0.248620	−	0.683077i	0.751118	−	0.660168i	$-0.229515\pi$
$480$	−4.17324e12	+	2.41275e13i	−0.163782	+	0.946905i
$481$	−3.96147e12	+	3.32407e12i	−0.153862	+	0.129105i
$482$	3.28919e12	−	9.03696e12i	0.126431	−	0.347366i
$483$	7.30941e9	+	2.24093e12i	0.000278065	+	0.0852498i
$484$	3.82993e12	−	2.17206e13i	0.144200	−	0.817797i
$485$			1.91127e13i			0.712219i
$486$	−1.09388e13	−	1.74538e12i	−0.403450	−	0.0643737i
$487$	3.15810e13			1.15287			0.576436	−	0.817142i	$-0.304443\pi$
$487$	3.15810e13			1.15287			0.576436	+	0.817142i	$0.304443\pi$
$488$	3.71580e12	+	6.55196e11i	0.134262	+	0.0236740i
$489$	4.89315e13	−	1.59603e11i	1.75002	−	0.00570818i
$490$	9.53740e12	+	3.47133e12i	0.337637	+	0.122890i
$491$	1.90991e13	+	2.27614e13i	0.669275	+	0.797611i	0.988685	−	0.150006i	$-0.0479293\pi$
$491$	1.90991e13	+	2.27614e13i	0.669275	+	0.797611i	−0.319410	+	0.947617i	$0.603485\pi$
$492$	2.12361e12	+	3.67312e11i	0.0736631	+	0.0127412i
$493$	−5.63147e12	+	2.04969e12i	−0.193369	+	0.0703806i
$494$	3.01608e12	+	1.74134e12i	0.102520	+	0.0591900i
$495$	−1.67707e12	+	1.09405e10i	−0.0564319	+	0.000368140i
$496$	1.03025e13	+	1.78445e13i	0.343191	+	0.594425i
$497$	−1.21910e13	+	1.45287e13i	−0.402031	+	0.479121i
$498$	−1.82567e13	−	6.57752e12i	−0.596039	−	0.214741i
$499$	−5.16349e11	−	2.92836e12i	−0.0166894	−	0.0946503i	0.975325	−	0.220773i	$-0.0708579\pi$
$499$	−5.16349e11	−	2.92836e12i	−0.0166894	−	0.0946503i	−0.992015	+	0.126122i	$0.959747\pi$
$500$	2.57252e13	−	4.53605e12i	0.823208	−	0.145154i
$501$	3.12565e13	+	3.70042e13i	0.990264	+	1.17236i
$502$	5.80447e12	+	4.87053e12i	0.182072	+	0.152777i
$503$	6.97565e12	−	4.02739e12i	0.216643	−	0.125079i	−0.387752	−	0.921764i	$-0.626748\pi$
$503$	6.97565e12	−	4.02739e12i	0.216643	−	0.125079i	0.604395	+	0.796685i	$0.293415\pi$
$504$	8.23160e12	+	1.39615e12i	0.253123	+	0.0429317i
$505$	1.28996e13	−	2.23428e13i	0.392753	−	0.680268i
$506$	6.52702e10	+	1.79328e11i	0.00196771	+	0.00540625i
$507$	−1.24459e13	+	4.57596e12i	−0.371523	+	0.136597i
$508$	−1.70579e13	+	1.43132e13i	−0.504203	+	0.423077i
$509$	−2.86140e12	+	7.86164e12i	−0.0837510	+	0.230104i	−0.974498	−	0.224395i	$-0.927959\pi$
$509$	−2.86140e12	+	7.86164e12i	−0.0837510	+	0.230104i	0.890747	+	0.454499i	$0.150182\pi$
$510$	−4.79438e12	−	2.74722e12i	−0.138957	−	0.0796238i
$511$	3.76261e12	−	2.13388e13i	0.107990	−	0.612444i
$512$			3.17729e13i			0.903039i
$513$	−6.50975e12	+	1.15344e13i	−0.183222	+	0.324645i
$514$	−3.04597e12			−0.0849006
$515$	5.06985e12	+	8.93951e11i	0.139946	+	0.0246762i
$516$	−1.31295e13	−	2.25707e13i	−0.358923	−	0.617016i
$517$	−3.37098e12	−	1.22694e12i	−0.0912649	−	0.0332177i
$518$	−8.67609e11	−	1.03398e12i	−0.0232635	−	0.0277244i
$519$	−8.19993e12	+	9.83728e12i	−0.217757	+	0.261239i
$520$	−2.07263e13	+	7.54374e12i	−0.545135	+	0.198413i
$521$	−5.10994e13	−	2.95023e13i	−1.33115	−	0.768540i	−0.345675	−	0.938354i	$-0.612350\pi$
$521$	−5.10994e13	−	2.95023e13i	−1.33115	−	0.768540i	−0.985476	+	0.169814i	$0.945683\pi$
$522$	7.80250e12	+	2.78237e12i	0.201317	+	0.0717897i
$523$	−7.53885e12	−	1.30577e13i	−0.192662	−	0.333701i	0.753469	−	0.657483i	$-0.228379\pi$
$523$	−7.53885e12	−	1.30577e13i	−0.192662	−	0.333701i	−0.946132	+	0.323782i	$0.895045\pi$
$524$	9.59170e12	−	1.14309e13i	0.242795	−	0.289351i
$525$	−1.65314e10	−	9.19983e10i	−0.000414488	−	0.00230666i
$526$	4.47122e11	+	2.53575e12i	0.0111044	+	0.0629765i
$527$	−2.05042e13	+	3.61545e12i	−0.504418	+	0.0889425i
$528$	−1.20558e12	+	2.16633e11i	−0.0293783	+	0.00527904i
$529$	2.97721e13	+	2.49817e13i	0.718672	+	0.603037i
$530$	8.14459e12	−	4.70228e12i	0.194756	−	0.112442i
$531$	2.46400e13	+	2.89787e13i	0.583670	+	0.686446i
$532$	2.26844e12	−	3.92906e12i	0.0532316	−	0.0921998i
$533$	1.02619e12	+	2.81943e12i	0.0238556	+	0.0655427i
$534$	1.65050e11	+	1.37578e11i	0.00380110	+	0.00316843i
$535$	−5.02499e12	+	4.21647e12i	−0.114648	+	0.0962011i
$536$	1.87707e13	−	5.15720e13i	0.424283	−	1.16571i
$537$	−9.20734e12	+	5.35598e12i	−0.206188	+	0.119941i
$538$	−3.38623e12	+	1.92043e13i	−0.0751286	+	0.426075i
$539$			2.27338e12i			0.0499721i
$540$	−1.33882e13	−	3.56930e13i	−0.291576	−	0.777346i
$541$	2.98697e13			0.644533			0.322267	−	0.946649i	$-0.395555\pi$
$541$	2.98697e13			0.644533			0.322267	+	0.946649i	$0.395555\pi$
$542$	−5.03561e12	−	8.87914e11i	−0.107660	−	0.0189834i
$543$	3.43401e13	−	5.99293e13i	0.727448	−	1.26952i
$544$	−1.69806e13	−	6.18044e12i	−0.356418	−	0.129725i
$545$	−2.29711e13	−	2.73759e13i	−0.477748	−	0.569358i
$546$	1.82294e12	+	4.95810e12i	0.0375671	+	0.102177i
$547$	−5.24289e13	+	1.90826e13i	−1.07062	+	0.389673i	−0.816407	−	0.577477i	$-0.804037\pi$
$547$	−5.24289e13	+	1.90826e13i	−1.07062	+	0.389673i	−0.254209	+	0.967149i	$0.581815\pi$
$548$	−4.74423e13	−	2.73908e13i	−0.959982	−	0.554246i
$549$	−8.51091e12	+	3.16075e12i	−0.170653	+	0.0633764i
$550$	−3.97999e9	−	6.89354e9i	−7.90803e−5	−	0.000136971i
$551$	6.36653e12	−	7.58734e12i	0.125356	−	0.149393i
$552$	−7.29165e12	+	6.15906e12i	−0.142276	+	0.120176i
$553$	−4.83941e12	−	2.74457e13i	−0.0935766	−	0.530699i
$554$	8.37390e12	−	1.47654e12i	0.160464	−	0.0282942i
$555$	−4.59637e12	+	1.27578e13i	−0.0872872	+	0.242275i
$556$	−2.38067e13	−	1.99762e13i	−0.448049	−	0.375958i
$557$	1.63464e13	−	9.43761e12i	0.304893	−	0.176030i	−0.339746	−	0.940517i	$-0.610341\pi$
$557$	1.63464e13	−	9.43761e12i	0.304893	−	0.176030i	0.644639	+	0.764487i	$0.277008\pi$
$558$	2.50171e13	+	1.42269e13i	0.462452	+	0.262989i
$559$	1.81762e13	−	3.14821e13i	0.333000	−	0.576773i
$560$	3.39206e12	+	9.31962e12i	0.0615919	+	0.169222i
$561$	2.10947e11	−	1.21959e12i	0.00379629	−	0.0219482i
$562$	3.02066e12	−	2.53463e12i	0.0538791	−	0.0452099i
$563$	−3.17116e13	+	8.71268e13i	−0.560629	+	1.54032i	0.258090	+	0.966121i	$0.416907\pi$
$563$	−3.17116e13	+	8.71268e13i	−0.560629	+	1.54032i	−0.818719	+	0.574195i	$0.805315\pi$
$564$	−2.65968e11	−	8.15410e13i	−0.00466051	−	1.42883i
$565$	5.13584e12	−	2.91268e13i	0.0892009	−	0.505884i
$566$			1.65420e13i			0.284778i
$567$	−1.87869e13	+	7.11680e12i	−0.320583	+	0.121442i
$568$	−8.07805e13			−1.36636
$569$	5.70413e13	+	1.00579e13i	0.956375	+	0.168635i	0.629991	−	0.776603i	$-0.283059\pi$
$569$	5.70413e13	+	1.00579e13i	0.956375	+	0.168635i	0.326384	+	0.945237i	$0.394170\pi$
$570$	9.13238e12	−	2.97877e10i	0.151778	−	0.000495066i
$571$	6.76791e13	+	2.46332e13i	1.11500	+	0.405826i	0.832824	−	0.553538i	$-0.186723\pi$
$571$	6.76791e13	+	2.46332e13i	1.11500	+	0.405826i	0.282173	+	0.959364i	$0.408945\pi$
$572$	−1.44323e12	−	1.71998e12i	−0.0235698	−	0.0280894i
$573$	−1.03144e14	−	1.78404e13i	−1.66983	−	0.288823i
$574$	−7.35894e11	+	2.67844e11i	−0.0118102	+	0.00429855i
$575$	9.25407e10	+	5.34284e10i	0.00147229	+	0.000850027i
$576$	−4.26892e12	−	7.28384e12i	−0.0673296	−	0.114881i
$577$	4.92174e12	+	8.52471e12i	0.0769556	+	0.133291i	0.901935	−	0.431872i	$-0.142147\pi$
$577$	4.92174e12	+	8.52471e12i	0.0769556	+	0.133291i	−0.824979	+	0.565163i	$0.808813\pi$
$578$	−1.43204e13	+	1.70664e13i	−0.221981	+	0.264547i
$579$	−3.36759e13	−	1.21328e13i	−0.517519	−	0.186452i
$580$	4.95033e12	+	2.80747e13i	0.0754214	+	0.427736i
$581$	−3.46591e13	+	6.11133e12i	−0.523524	+	0.0923114i
$582$	1.25811e13	+	1.48946e13i	0.188409	+	0.223056i
$583$	1.61369e12	+	1.35405e12i	0.0239595	+	0.0201044i
$584$	7.99250e13	−	4.61447e13i	1.17657	−	0.679294i
$585$	3.38481e13	−	4.08773e13i	0.494032	−	0.596626i
$586$	−1.72484e13	+	2.98751e13i	−0.249610	+	0.432336i
$587$	3.72007e12	+	1.02208e13i	0.0533779	+	0.146654i	0.963516	−	0.267650i	$-0.0862471\pi$
$587$	3.72007e12	+	1.02208e13i	0.0533779	+	0.146654i	−0.910138	+	0.414304i	$0.864025\pi$
$588$	−4.85006e13	+	1.78321e13i	−0.690018	+	0.253698i
$589$	2.63600e13	−	2.21187e13i	0.371851	−	0.312020i
$590$	8.97051e12	−	2.46463e13i	0.125475	−	0.344740i
$591$	−8.52715e13	−	4.88614e13i	−1.18268	−	0.677686i
$592$	−1.71982e12	+	9.75357e12i	−0.0236523	+	0.134139i
$593$			1.02116e14i			1.39259i	0.717758	+	0.696293i	$0.245169\pi$
$593$			1.02116e14i			1.39259i	−0.717758	+	0.696293i	$0.754831\pi$
$594$	−1.29974e12	+	1.11247e12i	−0.0175762	+	0.0150437i
$595$	−1.00214e13			−0.134383
$596$	9.80248e13	+	1.72844e13i	1.30348	+	0.229839i
$597$	−2.61344e13	−	4.49270e13i	−0.344620	−	0.592428i
$598$	−5.67486e12	−	2.06548e12i	−0.0742077	−	0.0270094i
$599$	−1.29030e13	−	1.53772e13i	−0.167324	−	0.199409i	0.675866	−	0.737024i	$-0.263770\pi$
$599$	−1.29030e13	−	1.53772e13i	−0.167324	−	0.199409i	−0.843190	+	0.537615i	$0.819325\pi$
$600$	2.54910e11	−	3.05810e11i	0.00327816	−	0.00393274i
$601$	5.47511e13	−	1.99278e13i	0.698265	−	0.254148i	0.0315953	−	0.999501i	$-0.489941\pi$
$601$	5.47511e13	−	1.99278e13i	0.698265	−	0.254148i	0.666670	+	0.745353i	$0.267719\pi$
$602$	8.21710e12	+	4.74415e12i	0.103929	+	0.0600034i
$603$	2.37792e13	+	1.29898e14i	0.298271	+	1.62935i
$604$	6.35479e13	+	1.10068e14i	0.790526	+	1.36923i
$605$	5.17559e13	−	6.16803e13i	0.638533	−	0.760973i
$606$	−4.65457e12	−	2.59030e13i	−0.0569530	−	0.316947i
$607$	9.96951e12	+	5.65399e13i	0.120985	+	0.686138i	0.983612	+	0.180298i	$0.0577062\pi$
$607$	9.96951e12	+	5.65399e13i	0.120985	+	0.686138i	−0.862627	+	0.505840i	$0.831183\pi$
$608$	2.94116e13	−	5.18606e12i	0.353998	−	0.0624194i
$609$	1.47866e13	−	2.65704e12i	0.176516	−	0.0317184i
$610$	4.79549e12	+	4.02389e12i	0.0567785	+	0.0476428i
$611$	9.83121e13	−	5.67605e13i	1.15452	−	0.666562i
$612$	2.76735e13	−	5.06595e12i	0.322335	−	0.0590070i
$613$	−7.06986e13	+	1.22454e14i	−0.816786	+	1.41471i	0.0912525	+	0.995828i	$0.470913\pi$
$613$	−7.06986e13	+	1.22454e14i	−0.816786	+	1.41471i	−0.908038	+	0.418887i	$0.862420\pi$
$614$	4.16687e12	+	1.14484e13i	0.0477494	+	0.131190i
$615$	6.04348e12	+	5.03758e12i	0.0686928	+	0.0572594i
$616$	9.87805e11	−	8.28867e11i	0.0111370	−	0.00934504i
$617$	9.19988e12	−	2.52765e13i	0.102886	−	0.282677i	−0.877559	−	0.479468i	$-0.840830\pi$
$617$	9.19988e12	−	2.52765e13i	0.102886	−	0.282677i	0.980446	+	0.196791i	$0.0630520\pi$
$618$	4.53940e12	−	2.64060e12i	0.0503566	−	0.0292928i
$619$	5.65772e12	−	3.20865e13i	0.0622570	−	0.353077i	−0.937727	−	0.347374i	$-0.887073\pi$
$619$	5.65772e12	−	3.20865e13i	0.0622570	−	0.353077i	0.999984	−	0.00570323i	$-0.00181541\pi$
$620$			9.90423e13i			1.08109i
$621$	7.64346e12	−	2.16573e13i	0.0827622	−	0.234502i
$622$	−3.51118e13			−0.377139
$623$	3.83770e11	+	6.76690e10i	0.00408913	+	0.000721024i
$624$	1.92712e13	−	3.36316e13i	0.203698	−	0.355488i
$625$	8.89992e13	+	3.23931e13i	0.933225	+	0.339666i
$626$	−8.24148e12	−	9.82182e12i	−0.0857302	−	0.102169i
$627$	7.05891e11	+	1.91991e12i	0.00728451	+	0.0198127i
$628$	−7.61691e13	+	2.77233e13i	−0.779795	+	0.283822i
$629$	−8.66683e12	−	5.00380e12i	−0.0880252	−	0.0508214i
$630$	1.06693e13	+	8.83465e12i	0.107506	+	0.0890198i
$631$	−2.60764e13	−	4.51656e13i	−0.260676	−	0.451504i	0.705746	−	0.708465i	$-0.250612\pi$
$631$	−2.60764e13	−	4.51656e13i	−0.260676	−	0.451504i	−0.966422	+	0.256961i	$0.917279\pi$
$632$	7.62997e13	−	9.09305e13i	0.756724	−	0.901829i
$633$	−6.64744e13	+	5.61492e13i	−0.654088	+	0.552491i
$634$	6.53135e12	+	3.70411e13i	0.0637613	+	0.361608i
$635$	−8.00560e13	+	1.41160e13i	−0.775399	+	0.136724i
$636$	−1.62298e13	+	4.50477e13i	−0.155965	+	0.432900i
$637$	−5.51102e13	−	4.62429e13i	−0.525454	−	0.440908i
$638$	1.10798e12	−	6.39693e11i	0.0104816	−	0.00605157i
$639$	1.67695e14	−	9.82829e13i	1.57404	−	0.922516i
$640$	−5.45021e13	+	9.44004e13i	−0.507591	+	0.879173i
$641$	−3.03698e13	−	8.34403e13i	−0.280641	−	0.771056i	−0.997287	−	0.0736179i	$-0.976545\pi$
$641$	−3.03698e13	−	8.34403e13i	−0.280641	−	0.771056i	0.716645	−	0.697438i	$-0.245677\pi$
$642$	−1.14047e12	+	6.59364e12i	−0.0104571	+	0.0604575i
$643$	−9.16496e13	+	7.69031e13i	−0.833826	+	0.699663i	−0.956166	−	0.292825i	$-0.905405\pi$
$643$	−9.16496e13	+	7.69031e13i	−0.833826	+	0.699663i	0.122340	+	0.992488i	$0.460960\pi$
$644$	−2.69070e12	+	7.39264e12i	−0.0242905	+	0.0667376i
$645$	−3.10927e11	−	9.53246e13i	−0.00278522	−	0.853898i
$646$	−1.17034e12	+	6.63730e12i	−0.0104027	+	0.0589969i
$647$			1.01695e14i			0.896974i	0.893789	+	0.448487i	$0.148037\pi$
$647$			1.01695e14i			0.896974i	−0.893789	+	0.448487i	$0.851963\pi$
$648$	−7.46551e13	−	4.18131e13i	−0.653408	−	0.365963i
$649$	5.87480e12			0.0510234
$650$	2.48067e11	+	4.37409e10i	0.00213797	+	0.000376983i
$651$	5.21944e13	−	1.70246e11i	0.446395	−	0.00145604i
$652$	1.61421e14	+	5.87523e13i	1.37000	+	0.498640i
$653$	−5.56385e13	−	6.63073e13i	−0.468608	−	0.558465i	0.479036	−	0.877795i	$-0.340986\pi$
$653$	−5.56385e13	−	6.63073e13i	−0.468608	−	0.558465i	−0.947643	+	0.319331i	$0.896542\pi$
$654$	−3.59218e13	−	6.21324e12i	−0.300240	−	0.0519313i
$655$	5.11901e13	−	1.86317e13i	0.424599	−	0.154541i
$656$	4.97640e12	+	2.87313e12i	0.0409634	+	0.0236502i
$657$	−1.09776e14	+	1.93035e14i	−0.896772	+	1.57692i
$658$	1.48150e13	+	2.56603e13i	0.120108	+	0.208033i
$659$	1.09446e14	−	1.30433e14i	0.880590	−	1.04945i	−0.117818	−	0.993035i	$-0.537590\pi$
$659$	1.09446e14	−	1.30433e14i	0.880590	−	1.04945i	0.998408	−	0.0564110i	$-0.0179657\pi$
$660$	−5.53913e12	−	1.99564e12i	−0.0442305	−	0.0159354i
$661$	−1.35548e13	−	7.68732e13i	−0.107420	−	0.609211i	−0.990226	−	0.139472i	$-0.955459\pi$
$661$	−1.35548e13	−	7.68732e13i	−0.107420	−	0.609211i	0.882806	−	0.469738i	$-0.155652\pi$
$662$	−2.00410e13	+	3.53378e12i	−0.157627	+	0.0277939i
$663$	2.52738e13	+	2.99214e13i	0.197289	+	0.233568i
$664$	−1.14829e14	−	9.63532e13i	−0.889636	−	0.746493i
$665$	1.43437e13	−	8.28132e12i	0.110294	−	0.0636782i
$666$	4.81591e12	+	1.29678e13i	0.0367542	+	0.0989677i
$667$	−8.58740e12	+	1.48738e13i	−0.0650478	+	0.112666i
$668$	5.81599e13	+	1.59793e14i	0.437262	+	1.20137i
$669$	2.07422e14	−	7.62626e13i	1.54783	−	0.569090i
$670$	6.97526e13	−	5.85294e13i	0.516638	−	0.433511i
$671$	−4.79577e11	+	1.31763e12i	−0.00352570	+	0.00968679i
$672$	3.93050e13	+	2.25221e13i	0.286815	+	0.164347i
$673$	2.46024e13	−	1.39527e14i	0.178198	−	1.01061i	−0.756189	−	0.654353i	$-0.772941\pi$
$673$	2.46024e13	−	1.39527e14i	0.178198	−	1.01061i	0.934387	−	0.356258i	$-0.115948\pi$
$674$			6.85788e13i			0.493049i
$675$	−1.57108e11	+	9.44982e11i	−0.00112119	+	0.00674380i
$676$	−4.65522e13			−0.329767
$677$	−2.46472e14	−	4.34596e13i	−1.73310	−	0.305592i	−0.784046	−	0.620703i	$-0.786847\pi$
$677$	−2.46472e14	−	4.34596e13i	−1.73310	−	0.305592i	−0.949055	+	0.315111i	$0.897958\pi$
$678$	−1.51705e13	−	2.60793e13i	−0.105889	−	0.182032i
$679$	3.32274e13	+	1.20938e13i	0.230222	+	0.0837941i
$680$	−2.74366e13	−	3.26977e13i	−0.188706	−	0.224891i
$681$	−1.30286e14	+	1.56301e14i	−0.889531	+	1.06715i
$682$	4.17680e12	−	1.52023e12i	0.0283088	−	0.0103036i
$683$	−1.66554e14	−	9.61598e13i	−1.12060	−	0.646979i	−0.179046	−	0.983841i	$-0.557301\pi$
$683$	−1.66554e14	−	9.61598e13i	−1.12060	−	0.646979i	−0.941554	+	0.336862i	$0.890634\pi$
$684$	−3.54228e13	+	3.01192e13i	−0.236593	+	0.201170i
$685$	−9.99947e13	−	1.73196e14i	−0.663016	−	1.14838i
$686$	2.57469e13	−	3.06840e13i	0.169475	−	0.201972i
$687$	−2.66604e13	−	1.48367e14i	−0.174214	−	0.969515i
$688$	−1.20897e13	−	6.85638e13i	−0.0784281	−	0.444788i
$689$	−6.56483e13	+	1.15756e13i	−0.422793	+	0.0745498i
$690$	−1.55863e13	+	2.80073e12i	−0.0996544	+	0.0179071i
$691$	−1.62990e14	−	1.36765e14i	−1.03459	−	0.868127i	−0.0432034	−	0.999066i	$-0.513756\pi$
$691$	−1.62990e14	−	1.36765e14i	−1.03459	−	0.868127i	−0.991390	+	0.130939i	$0.958201\pi$
$692$	−3.89358e13	+	2.24796e13i	−0.245368	+	0.141664i
$693$	−1.04216e12	+	2.92250e12i	−0.00652033	+	0.0182847i
$694$	2.49926e13	−	4.32884e13i	0.155244	−	0.268890i
$695$	−3.88033e13	−	1.06611e14i	−0.239301	−	0.657475i
$696$	4.91521e13	+	4.09710e13i	0.300951	+	0.250859i
$697$	−4.44791e12	+	3.73224e12i	−0.0270391	+	0.0226885i
$698$	−1.80650e13	+	4.96331e13i	−0.109033	+	0.299567i
$699$	3.66140e13	−	2.12987e13i	0.219413	−	0.127634i
$700$	5.69814e10	−	3.23157e11i	0.000339034	−	0.00192275i
$701$			2.95802e14i			1.74748i	0.486397	+	0.873738i	$0.338311\pi$
$701$			2.95802e14i			1.74748i	−0.486397	+	0.873738i	$0.661689\pi$
$702$	−5.29758e11	−	5.41365e13i	−0.00310736	−	0.317545i
$703$	1.65398e13			0.0963280
$704$	−1.28412e12	−	2.26424e11i	−0.00742576	−	0.00130936i
$705$	1.47998e14	−	2.58283e14i	0.849790	−	1.48303i
$706$	−2.43227e13	−	8.85274e12i	−0.138672	−	0.0504724i
$707$	−3.06804e13	−	3.65635e13i	−0.173686	−	0.206991i
$708$	4.60813e13	+	1.25334e14i	0.259035	+	0.704534i
$709$	2.58665e14	−	9.41462e13i	1.44380	−	0.525499i	0.502944	−	0.864319i	$-0.332250\pi$
$709$	2.58665e14	−	9.41462e13i	1.44380	−	0.525499i	0.940851	+	0.338820i	$0.110028\pi$
$710$	−1.16069e14	−	6.70123e13i	−0.643315	−	0.371418i
$711$	−4.77612e13	+	2.81597e14i	−0.262862	+	1.54982i
$712$	8.29894e11	+	1.43742e12i	0.00453547	+	0.00785567i
$713$	−3.83544e13	+	4.57090e13i	−0.208146	+	0.248059i
$714$	−7.80973e12	+	6.59667e12i	−0.0420867	+	0.0355495i
$715$	−1.42335e12	−	8.07221e12i	−0.00761695	−	0.0431978i
$716$	−3.68263e13	+	6.49347e12i	−0.195701	+	0.0345074i
$717$	−6.33864e13	+	1.75936e14i	−0.334503	+	0.928452i
$718$	−4.91319e13	−	4.12265e13i	−0.257479	−	0.216050i
$719$	1.35697e14	−	7.83447e13i	0.706197	−	0.407723i	−0.103454	−	0.994634i	$-0.532990\pi$
$719$	1.35697e14	−	7.83447e13i	0.706197	−	0.407723i	0.809651	+	0.586911i	$0.199656\pi$
$720$	−6.63063e11	−	1.01641e14i	−0.00342683	−	0.525296i
$721$	4.76214e12	−	8.24826e12i	0.0244414	−	0.0423337i
$722$	2.36052e13	+	6.48548e13i	0.120316	+	0.330564i
$723$	−3.04651e13	+	1.76134e14i	−0.154210	+	0.891561i
$724$	1.85751e14	−	1.55863e14i	0.933764	−	0.783521i
$725$	2.45015e11	−	6.73173e11i	0.00122321	−	0.00336075i
$726$	−2.67910e11	−	8.21363e13i	−0.00132833	−	0.407242i
$727$	−2.47932e13	+	1.40609e14i	−0.122084	+	0.692374i	0.860913	+	0.508753i	$0.169893\pi$
$727$	−2.47932e13	+	1.40609e14i	−0.122084	+	0.692374i	−0.982997	+	0.183622i	$0.941218\pi$
$728$			4.08059e13i			0.199557i
$729$	2.05852e14	−	4.02915e12i	0.999809	−	0.0195693i
$730$	1.53119e14			0.738611
$731$	6.92808e13	+	1.22161e13i	0.331914	+	0.0585254i
$732$	−3.18722e13	+	1.03960e11i	−0.151655	+	0.000494664i
$733$	−4.89041e13	−	1.77996e13i	−0.231113	−	0.0841184i	0.223868	−	0.974620i	$-0.428132\pi$
$733$	−4.89041e13	−	1.77996e13i	−0.231113	−	0.0841184i	−0.454981	+	0.890501i	$0.650354\pi$
$734$	−2.45975e13	−	2.93141e13i	−0.115454	−	0.137593i
$735$	−1.85887e14	−	3.21522e13i	−0.866590	−	0.149890i
$736$	−4.86642e13	+	1.77123e13i	−0.225331	+	0.0820137i
$737$	1.76630e13	+	1.01977e13i	0.0812320	+	0.0468993i
$738$	8.02572e12	−	5.23567e10i	0.0366608	−	0.000239161i
$739$	8.12019e13	+	1.40646e14i	0.368421	+	0.638123i	0.989319	−	0.145768i	$-0.0465653\pi$
$739$	8.12019e13	+	1.40646e14i	0.368421	+	0.638123i	−0.620898	+	0.783891i	$0.713232\pi$
$740$	−3.06003e13	+	3.64680e13i	−0.137901	+	0.164344i
$741$	−6.09002e13	−	2.19412e13i	−0.272601	−	0.0982129i
$742$	−3.02132e12	−	1.71348e13i	−0.0134331	−	0.0761831i
$743$	−6.03736e12	+	1.06455e12i	−0.0266626	+	0.00470134i	−0.186964	−	0.982367i	$-0.559865\pi$
$743$	−6.03736e12	+	1.06455e12i	−0.0266626	+	0.00470134i	0.160301	+	0.987068i	$0.448754\pi$
$744$	1.43453e14	+	1.69832e14i	0.629281	+	0.744999i
$745$	2.78362e14	+	2.33574e14i	1.21291	+	1.01775i
$746$	−9.65424e13	+	5.57388e13i	−0.417853	+	0.241248i
$747$	3.55608e14	+	6.03140e13i	1.52886	+	0.259308i
$748$	2.17253e12	−	3.76294e12i	0.00927809	−	0.0160701i
$749$	4.15070e12	+	1.14040e13i	0.0176081	+	0.0483778i
$750$	9.13046e13	−	3.35698e13i	0.384757	−	0.141463i
$751$	−8.16514e13	+	6.85137e13i	−0.341794	+	0.286799i	−0.797485	−	0.603339i	$-0.793837\pi$
$751$	−8.16514e13	+	6.85137e13i	−0.341794	+	0.286799i	0.455691	+	0.890138i	$0.349392\pi$
$752$	7.43598e13	−	2.04302e14i	0.309207	−	0.849538i
$753$	−1.22197e14	−	7.00201e13i	−0.504762	−	0.289233i
$754$	−7.03037e12	+	3.98712e13i	−0.0288484	+	0.163607i
$755$			4.63984e14i			1.89133i
$756$	−7.05237e13	+	6.90116e11i	−0.285579	+	0.00279456i
$757$	−2.30843e13			−0.0928619			−0.0464309	−	0.998922i	$-0.514785\pi$
$757$	−2.30843e13			−0.0928619			−0.0464309	+	0.998922i	$0.514785\pi$
$758$	1.28083e14	+	2.25845e13i	0.511854	+	0.0902537i
$759$	−1.78355e12	−	3.06605e12i	−0.00708069	−	0.0121723i
$760$	6.62900e13	+	2.41276e13i	0.261445	+	0.0951581i
$761$	4.75616e13	+	5.66818e13i	0.186352	+	0.222085i	0.851129	−	0.524956i	$-0.175918\pi$
$761$	4.75616e13	+	5.66818e13i	0.186352	+	0.222085i	−0.664778	+	0.747041i	$0.731474\pi$
$762$	−5.30959e13	+	6.36980e13i	−0.206674	+	0.247943i
$763$	−6.21281e13	+	2.26128e13i	−0.240251	+	0.0874442i
$764$	−3.18243e14	−	1.83738e14i	−1.22262	−	0.705881i
$765$	9.67387e13	+	3.44970e13i	0.369227	+	0.131666i
$766$	5.45489e13	+	9.44815e13i	0.206844	+	0.358264i
$767$	−1.19500e14	+	1.42414e14i	−0.450184	+	0.536508i
$768$	1.33739e13	+	7.44266e13i	0.0500554	+	0.278562i
$769$	−5.23121e13	−	2.96677e14i	−0.194523	−	1.10319i	−0.913097	−	0.407743i	$-0.866316\pi$
$769$	−5.23121e13	−	2.96677e14i	−0.194523	−	1.10319i	0.718574	−	0.695451i	$-0.244795\pi$
$770$	2.10691e12	−	3.71506e11i	0.00778383	−	0.00137250i
$771$	5.57227e13	−	1.00129e13i	0.204532	−	0.0367527i
$772$	−9.62623e13	−	8.07737e13i	−0.351051	−	0.294567i
$773$	4.33167e14	−	2.50089e14i	1.56949	−	0.906144i	0.573258	−	0.819375i	$-0.305679\pi$
$773$	4.33167e14	−	2.50089e14i	1.56949	−	0.906144i	0.996228	−	0.0867690i	$-0.0276542\pi$
$774$	−6.29903e13	−	7.40821e13i	−0.226761	−	0.266691i
$775$	1.24442e12	−	2.15540e12i	0.00445101	−	0.00770937i
$776$	5.15104e13	+	1.41524e14i	0.183057	+	0.502945i
$777$	1.92709e13	+	1.60634e13i	0.0680452	+	0.0567195i
$778$	−1.36278e13	+	1.14351e13i	−0.0478109	+	0.0401181i
$779$	3.28211e12	−	9.01753e12i	0.0114411	−	0.0314341i
$780$	1.61049e14	−	9.36835e13i	0.557809	−	0.324481i
$781$	5.21294e12	−	2.95640e13i	0.0179402	−	0.101744i
$782$		−	1.16868e13i		−	0.0399634i
$783$	−1.51885e14	−	2.52515e13i	−0.516065	−	0.0857982i
$784$	−1.37781e14			−0.465165
$785$	−2.91418e14	−	5.13848e13i	−0.977615	−	0.172380i
$786$	2.76282e13	−	4.82159e13i	0.0920957	−	0.160723i
$787$	−1.93246e14	−	7.03358e13i	−0.640084	−	0.232971i	0.00153054	−	0.999999i	$-0.499513\pi$
$787$	−1.93246e14	−	7.03358e13i	−0.640084	−	0.232971i	−0.641614	+	0.767027i	$0.721735\pi$
$788$	−2.21773e14	−	2.64299e14i	−0.729923	−	0.869889i
$789$	−1.65153e13	−	4.49190e13i	−0.0540134	−	0.146908i
$790$	1.85063e14	−	6.73574e13i	0.601429	−	0.218902i
$791$	−4.73871e13	−	2.73590e13i	−0.153030	−	0.0883522i
$792$	−1.23887e13	+	4.60086e12i	−0.0397557	+	0.0147643i
$793$	−2.21862e13	−	3.84276e13i	−0.0707484	−	0.122540i
$794$	−3.31331e13	+	3.94865e13i	−0.104993	+	0.125125i
$795$	−1.33539e14	+	1.12797e14i	−0.420505	+	0.355190i
$796$	−3.16848e13	−	1.79693e14i	−0.0991483	−	0.562298i
$797$	1.17657e14	−	2.07462e13i	0.365871	−	0.0645129i	0.0123095	−	0.999924i	$-0.496082\pi$
$797$	1.17657e14	−	2.07462e13i	0.365871	−	0.0645129i	0.353561	+	0.935411i	$0.384971\pi$
$798$	5.72683e12	−	1.58955e13i	0.0176970	−	0.0491200i
$799$	1.68290e14	+	1.41212e14i	0.516802	+	0.433648i
$800$	1.87070e12	−	1.08005e12i	0.00570891	−	0.00329604i
$801$	−3.47166e12	−	1.97428e12i	−0.0105287	−	0.00598752i
$802$	−1.31143e13	+	2.27145e13i	−0.0395250	+	0.0684593i
$803$	1.17303e13	+	3.22288e13i	0.0351343	+	0.0965308i
$804$	−7.90134e13	+	4.56815e14i	−0.235191	+	1.35975i
$805$	−2.20009e13	+	1.84609e13i	−0.0650819	+	0.0546102i
$806$	−4.81078e13	+	1.32175e14i	−0.141430	+	0.388575i
$807$	−1.18224e12	−	3.62452e14i	−0.00345411	−	1.05897i
$808$	3.53018e13	−	2.00207e14i	0.102504	−	0.581329i
$809$		−	2.13433e14i		−	0.615911i	−0.951401	−	0.307956i	$-0.900355\pi$
$809$		−	2.13433e14i		−	0.615911i	0.951401	−	0.307956i	$-0.0996448\pi$
$810$	−7.25811e13	−	1.22010e14i	−0.208160	−	0.349920i
$811$	−2.61791e14			−0.746192			−0.373096	−	0.927793i	$-0.621704\pi$
$811$	−2.61791e14			−0.746192			−0.373096	+	0.927793i	$0.621704\pi$
$812$	5.19402e13	+	9.15847e12i	0.147138	+	0.0259443i
$813$	9.50398e13	−	3.09998e11i	0.267579	−	0.000872782i
$814$	2.00762e12	+	7.30713e11i	0.00561771	+	0.00204468i
$815$	4.03100e14	+	4.80395e14i	1.12105	+	1.33601i
$816$	7.39144e13	+	1.27847e13i	0.204305	+	0.0353377i
$817$	−1.09256e14	+	3.97660e13i	−0.300149	+	0.109245i
$818$	−1.68317e14	−	9.71780e13i	−0.459581	−	0.265339i
$819$	−4.96472e13	−	8.47104e13i	−0.134733	−	0.229889i
$820$	1.38102e13	+	2.39200e13i	0.0372504	+	0.0645197i
$821$	−1.41353e14	+	1.68457e14i	−0.378955	+	0.451621i	−0.921484	−	0.388416i	$-0.873022\pi$
$821$	−1.41353e14	+	1.68457e14i	−0.378955	+	0.451621i	0.542529	+	0.840037i	$0.317467\pi$
$822$	−1.91933e14	−	6.91499e13i	−0.511436	−	0.184261i
$823$	8.18590e13	+	4.64245e14i	0.216804	+	1.22956i	0.877749	+	0.479122i	$0.159045\pi$
$823$	8.18590e13	+	4.64245e14i	0.216804	+	1.22956i	−0.660945	+	0.750435i	$0.729844\pi$
$824$	3.99500e13	−	7.04425e12i	0.105167	−	0.0185438i
$825$	9.54705e10	+	1.13026e11i	0.000249804	+	0.000295740i
$826$	−3.71713e13	−	3.11904e13i	−0.0966734	−	0.0811187i
$827$	5.64853e14	−	3.26118e14i	1.46019	−	0.843039i	0.461166	−	0.887314i	$-0.347431\pi$
$827$	5.64853e14	−	3.26118e14i	1.46019	−	0.843039i	0.999019	+	0.0442753i	$0.0140979\pi$
$828$	5.14217e13	−	6.21003e13i	0.132128	−	0.159566i
$829$	1.66209e14	−	2.87883e14i	0.424505	−	0.735265i	−0.571869	−	0.820345i	$-0.693781\pi$
$829$	1.66209e14	−	2.87883e14i	0.424505	−	0.735265i	0.996374	+	0.0850804i	$0.0271147\pi$
$830$	−8.50606e13	−	2.33702e14i	−0.215942	−	0.593297i
$831$	−1.48337e14	+	5.45390e13i	−0.374322	+	0.137626i
$832$	3.16091e13	−	2.65232e13i	0.0792859	−	0.0665288i
$833$	4.76165e13	−	1.30825e14i	0.118722	−	0.326187i
$834$	−1.00417e14	−	5.75400e13i	−0.248873	−	0.142606i
$835$	−1.07799e14	+	6.11358e14i	−0.265572	+	1.50613i
$836$			7.18119e12i			0.0175859i
$837$	−5.04428e14	−	1.78027e14i	−1.22793	−	0.433369i
$838$	8.22304e13			0.198981
$839$	6.04111e14	+	1.06521e14i	1.45314	+	0.256227i	0.843789	−	0.536675i	$-0.180320\pi$
$839$	6.04111e14	+	1.06521e14i	1.45314	+	0.256227i	0.609349	+	0.792902i	$0.291431\pi$
$840$	5.38036e13	+	9.24925e13i	0.128651	+	0.221162i
$841$	−2.87138e14	−	1.04510e14i	−0.682513	−	0.248414i
$842$	1.33352e14	+	1.58923e14i	0.315094	+	0.375514i
$843$	−4.69276e13	+	5.62981e13i	−0.110228	+	0.132238i
$844$	−2.87053e14	+	1.04479e14i	−0.670269	+	0.243958i
$845$	−1.47178e14	−	8.49733e13i	−0.341633	−	0.197242i
$846$	−5.46806e13	−	2.98701e14i	−0.126177	−	0.689264i
$847$	−7.44819e13	−	1.29006e14i	−0.170857	−	0.295934i
$848$	−8.20634e13	+	9.77994e13i	−0.187142	+	0.223027i
$849$	−5.43781e13	−	3.02618e14i	−0.123278	−	0.686051i
$850$	8.46478e10	+	4.80061e11i	0.000190775	+	0.00108194i
$851$	−2.82447e13	+	4.98030e12i	−0.0632833	+	0.0111586i
$852$	6.71613e14	−	1.20684e14i	1.49596	−	0.268813i
$853$	3.34474e14	+	2.80657e14i	0.740657	+	0.621485i	0.933014	−	0.359840i	$-0.117169\pi$
$853$	3.34474e14	+	2.80657e14i	0.740657	+	0.621485i	−0.192357	+	0.981325i	$0.561613\pi$
$854$	1.00299e13	−	5.79078e12i	0.0220805	−	0.0127482i
$855$	−1.66969e14	+	3.05655e13i	−0.365431	+	0.0668962i
$856$	−2.58448e13	+	4.47644e13i	−0.0562346	+	0.0974012i
$857$	−2.63403e14	−	7.23695e14i	−0.569793	−	1.56549i	−0.804829	−	0.593507i	$-0.797743\pi$
$857$	−2.63403e14	−	7.23695e14i	−0.569793	−	1.56549i	0.235035	−	0.971987i	$-0.424479\pi$
$858$	−6.42280e12	−	5.35377e12i	−0.0138130	−	0.0115139i
$859$	−5.90258e14	+	4.95285e14i	−1.26205	+	1.05898i	−0.266587	+	0.963811i	$0.585896\pi$
$859$	−5.90258e14	+	4.95285e14i	−1.26205	+	1.05898i	−0.995461	+	0.0951729i	$0.969660\pi$
$860$	1.14457e14	−	3.14467e14i	0.243304	−	0.668472i
$861$	1.25819e13	−	7.31898e12i	0.0265907	−	0.0154680i
$862$	2.20109e13	−	1.24830e14i	0.0462489	−	0.262291i
$863$		−	2.54952e14i		−	0.532605i	−0.963890	−	0.266302i	$-0.914198\pi$
$863$		−	2.54952e14i		−	0.532605i	0.963890	−	0.266302i	$-0.0858019\pi$
$864$	−3.01890e14	−	3.52711e14i	−0.627017	−	0.732571i
$865$	−1.64131e14			−0.338930
$866$	−6.26546e13	−	1.10477e13i	−0.128636	−	0.0226821i
$867$	2.05874e14	−	3.59286e14i	0.420249	−	0.733407i
$868$	1.72185e14	+	6.26701e13i	0.349459	+	0.127193i
$869$	2.83549e13	+	3.37921e13i	0.0572176	+	0.0681893i
$870$	3.66358e13	+	9.96435e13i	0.0735037	+	0.199918i
$871$	−6.06493e14	+	2.20745e14i	−1.20986	+	0.440353i
$872$	−2.43874e14	−	1.40801e14i	−0.483708	−	0.279269i
$873$	−2.79119e14	−	2.31123e14i	−0.550451	−	0.455797i
$874$	9.65753e12	+	1.67273e13i	0.0189369	+	0.0327997i
$875$	1.13406e14	−	1.35152e14i	0.221103	−	0.263501i
$876$	−5.95562e14	+	5.03055e14i	−1.15453	+	0.975203i
$877$	1.40337e14	+	7.95891e14i	0.270505	+	1.53411i	0.752889	+	0.658148i	$0.228660\pi$
$877$	1.40337e14	+	7.95891e14i	0.270505	+	1.53411i	−0.482384	+	0.875960i	$0.660229\pi$
$878$	2.84810e14	−	5.02197e13i	0.545862	−	0.0962502i
$879$	2.17333e14	−	6.03233e14i	0.414173	−	1.14958i
$880$	−1.20255e13	−	1.00906e13i	−0.0227872	−	0.0191208i
$881$	7.59349e14	−	4.38410e14i	1.43074	−	0.826040i	0.433566	−	0.901122i	$-0.357255\pi$
$881$	7.59349e14	−	4.38410e14i	1.43074	−	0.826040i	0.997177	+	0.0750815i	$0.0239217\pi$
$882$	−1.66027e14	+	9.73054e13i	−0.311054	+	0.182303i
$883$	1.36395e14	−	2.36244e14i	0.254095	−	0.440105i	−0.710554	−	0.703642i	$-0.751556\pi$
$883$	1.36395e14	−	2.36244e14i	0.254095	−	0.440105i	0.964649	+	0.263537i	$0.0848891\pi$
$884$	4.70278e13	+	1.29208e14i	0.0871150	+	0.239346i
$885$	−8.30867e13	+	4.80365e14i	−0.153044	+	0.884820i
$886$	−2.21354e14	+	1.85738e14i	−0.405433	+	0.340199i
$887$	−3.17061e14	+	8.71118e14i	−0.577464	+	1.58657i	0.214977	+	0.976619i	$0.431032\pi$
$887$	−3.17061e14	+	8.71118e14i	−0.577464	+	1.58657i	−0.792441	+	0.609949i	$0.791190\pi$
$888$	3.48536e11	+	1.06855e14i	0.000631223	+	0.193522i
$889$	−2.61156e13	+	1.48109e14i	−0.0470318	+	0.266731i
$890$			2.75379e12i			0.00493152i
$891$	2.01204e13	−	2.46240e13i	0.0358301	−	0.0438500i
$892$	7.75836e14			1.37387
$893$	−3.57565e14	−	6.30484e13i	−0.629648	−	0.111024i
$894$	3.70680e14	−	1.20907e12i	0.649100	−	0.00211721i
$895$	−1.28282e14	−	4.66907e13i	−0.223383	−	0.0813046i
$896$	1.29628e14	+	1.54485e14i	0.224470	+	0.267513i
$897$	1.10605e14	+	1.91309e13i	0.190464	+	0.0329437i
$898$	2.61801e14	−	9.52877e13i	0.448321	−	0.163176i
$899$	3.46431e14	+	2.00012e14i	0.589955	+	0.340611i
$900$	−1.66246e12	+	2.92335e12i	−0.00281540	+	0.00495072i
$901$	−6.45015e13	−	1.11720e14i	−0.108629	−	0.188151i
$902$	7.96775e11	−	9.49559e11i	0.00133445	−	0.00159034i
$903$	−1.65918e14	−	5.97771e13i	−0.276347	−	0.0995626i
$904$	−4.04700e13	−	2.29517e14i	−0.0670333	−	0.380165i
$905$	8.71765e14	−	1.53716e14i	1.43601	−	0.253207i
$906$	3.05420e14	+	3.61584e14i	0.500331	+	0.592336i
$907$	6.23629e14	+	5.23287e14i	1.01599	+	0.852518i	0.989119	−	0.147121i	$-0.0470005\pi$
$907$	6.23629e14	+	5.23287e14i	1.01599	+	0.852518i	0.0268732	+	0.999639i	$0.491445\pi$
$908$	−6.18637e14	+	3.57170e14i	−1.00232	+	0.578690i
$909$	1.70300e14	+	4.58566e14i	0.274408	+	0.738895i
$910$	−3.38510e13	+	5.86316e13i	−0.0542456	+	0.0939561i
$911$	2.73888e14	+	7.52502e14i	0.436497	+	1.19927i	0.941756	+	0.336298i	$0.109175\pi$
$911$	2.73888e14	+	7.52502e14i	0.436497	+	1.19927i	−0.505258	+	0.862968i	$0.668603\pi$
$912$	−1.16358e14	+	4.27813e13i	−0.184426	+	0.0678078i
$913$	4.26735e13	−	3.58073e13i	0.0672674	−	0.0564440i
$914$	−2.87934e13	+	7.91093e13i	−0.0451401	+	0.124021i
$915$	−1.00956e14	−	5.78487e13i	−0.157408	−	0.0901961i
$916$	9.18950e13	−	5.21162e14i	0.142500	−	0.808157i
$917$		−	1.00783e14i		−	0.155432i
$918$	9.80967e13	−	3.67953e13i	0.150467	−	0.0564389i
$919$	7.91215e14			1.20703			0.603513	−	0.797353i	$-0.293767\pi$
$919$	7.91215e14			1.20703			0.603513	+	0.797353i	$0.293767\pi$
$920$	−1.20468e14	−	2.12417e13i	−0.182781	−	0.0322292i
$921$	−1.13862e14	−	1.95738e14i	−0.171823	−	0.295377i
$922$	−3.01002e14	−	1.09556e14i	−0.451767	−	0.164430i
$923$	6.10641e14	+	7.27733e14i	0.911543	+	1.08633i
$924$	−6.97436e12	+	8.36699e12i	−0.0103549	+	0.0124225i
$925$	1.12414e12	−	4.09153e11i	0.00166001	−	0.000604195i
$926$	−1.62783e14	−	9.39830e13i	−0.239086	−	0.138037i
$927$	−7.43630e13	+	6.32292e13i	−0.108632	+	0.0923674i
$928$	1.73593e14	+	3.00672e14i	0.252228	+	0.436871i
$929$	−3.54193e14	+	4.22111e14i	−0.511873	+	0.610026i	−0.958639	−	0.284625i	$-0.908131\pi$
$929$	−3.54193e14	+	4.22111e14i	−0.511873	+	0.610026i	0.446766	+	0.894651i	$0.352575\pi$
$930$	6.52327e13	+	3.63025e14i	0.0937672	+	0.521821i
$931$	3.99554e13	+	2.26598e14i	0.0571251	+	0.323972i
$932$	1.46444e14	−	2.58220e13i	0.208253	−	0.0367207i
$933$	6.42331e14	−	1.15422e14i	0.908554	−	0.163260i
$934$	−3.35739e14	−	2.81718e14i	−0.472353	−	0.396352i
$935$	1.37372e13	−	7.93119e12i	0.0192239	−	0.0110989i
$936$	1.40467e14	−	3.93907e14i	0.195522	−	0.548295i
$937$	5.79781e14	−	1.00421e15i	0.802723	−	1.39036i	−0.115095	−	0.993355i	$-0.536717\pi$
$937$	5.79781e14	−	1.00421e15i	0.802723	−	1.39036i	0.917818	−	0.397002i	$-0.129950\pi$
$938$	−5.76164e13	−	1.58300e14i	−0.0793473	−	0.218005i
$939$	1.83056e14	+	1.52587e14i	0.250758	+	0.209021i
$940$	8.00546e14	−	6.71738e14i	1.09080	−	0.915294i
$941$	−1.69971e14	+	4.66991e14i	−0.230370	+	0.632937i	−0.999984	−	0.00557188i	$-0.998226\pi$
$941$	−1.69971e14	+	4.66991e14i	−0.230370	+	0.632937i	0.769614	+	0.638509i	$0.220449\pi$
$942$	−2.60927e14	+	1.51783e14i	−0.351775	+	0.204630i
$943$	−2.88954e12	+	1.63874e13i	−0.00387499	+	0.0219761i
$944$			3.56048e14i			0.474951i
$945$	−2.24225e14	−	1.26547e14i	−0.297526	−	0.167917i
$946$	−1.50185e13			−0.0198231
$947$	−4.34307e14	−	7.65800e13i	−0.570225	−	0.100546i	−0.118901	−	0.992906i	$-0.537937\pi$
$947$	−4.34307e14	−	7.65800e13i	−0.570225	−	0.100546i	−0.451324	+	0.892360i	$0.649048\pi$
$948$	−4.98513e14	+	8.69990e14i	−0.651080	+	1.13625i
$949$	−1.01988e15	−	3.71206e14i	−1.32501	−	0.482263i
$950$	−5.17860e11	−	6.17162e11i	−0.000669259	−	0.000797592i
$951$	−2.41248e14	−	6.56157e14i	−0.310143	−	0.843539i
$952$	−7.42056e13	+	2.70086e13i	−0.0948969	+	0.0345396i
$953$	−1.04006e15	−	6.00480e14i	−1.32311	−	0.763896i	−0.338883	−	0.940828i	$-0.610049\pi$
$953$	−1.04006e15	−	6.00480e14i	−1.32311	−	0.763896i	−0.984223	+	0.176932i	$0.943383\pi$
$954$	−2.98181e13	+	1.75805e14i	−0.0377344	+	0.222480i
$955$	−6.70765e14	−	1.16180e15i	−0.844410	−	1.46256i
$956$	−4.21994e14	+	5.02913e14i	−0.528466	+	0.629801i
$957$	−1.81665e13	+	1.53447e13i	−0.0226313	+	0.0191161i
$958$	−4.16132e13	−	2.36000e14i	−0.0515708	−	0.292472i
$959$	−3.64373e14	+	6.42488e13i	−0.449214	+	0.0792086i
$960$	3.66752e13	−	1.01796e14i	0.0449796	−	0.124846i
$961$	4.36754e14	+	3.66480e14i	0.532868	+	0.447129i
$962$	−5.85507e13	+	3.38042e13i	−0.0710651	+	0.0410295i
$963$	−8.11358e11	−	1.24373e14i	−0.000979673	−	0.150173i
$964$	−3.13759e14	+	5.43447e14i	−0.376887	+	0.652787i
$965$	−1.56901e14	−	4.31082e14i	−0.187495	−	0.515138i
$966$	−4.99332e12	+	2.88689e13i	−0.00593614	+	0.0343197i
$967$	−2.53618e14	+	2.12811e14i	−0.299949	+	0.251687i	−0.780323	−	0.625376i	$-0.784945\pi$
$967$	−2.53618e14	+	2.12811e14i	−0.299949	+	0.251687i	0.480374	+	0.877064i	$0.340501\pi$
$968$	2.17003e14	−	5.96210e14i	0.255322	−	0.701492i
$969$	−4.08600e11	−	1.25269e14i	−0.000478277	−	0.146631i
$970$	−4.33902e13	+	2.46078e14i	−0.0505281	+	0.286559i
$971$		−	9.10849e14i		−	1.05524i	−0.849481	−	0.527619i	$-0.823085\pi$
$971$		−	9.10849e14i		−	1.05524i	0.849481	−	0.527619i	$-0.176915\pi$
$972$	6.83154e14	+	2.36104e14i	0.787385	+	0.272127i
$973$	−2.09897e14			−0.240681
$974$	4.06609e14	+	7.16961e13i	0.463855	+	0.0817901i
$975$	−4.68190e12	+	1.52713e10i	−0.00531373	+	1.73322e-5i
$976$	−7.98562e13	−	2.90653e13i	−0.0901694	−	0.0328190i
$977$	−1.01387e15	−	1.20829e15i	−1.13897	−	1.35737i	−0.924747	−	0.380582i	$-0.875724\pi$
$977$	−1.01387e15	−	1.20829e15i	−1.13897	−	1.35737i	−0.214219	−	0.976786i	$-0.568721\pi$
$978$	6.30360e14	+	1.09031e14i	0.704522	+	0.121858i
$979$	−5.79621e11	+	2.10965e11i	−0.000644511	+	0.000234583i
$980$	−5.73541e14	−	3.31134e14i	−0.634503	−	0.366331i
$981$	6.77574e14	−	4.42023e12i	0.745782	−	0.00486519i
$982$	1.94229e14	+	3.36414e14i	0.212694	+	0.368398i
$983$	−5.04430e14	+	6.01156e14i	−0.549583	+	0.654967i	−0.967308	−	0.253606i	$-0.918383\pi$
$983$	−5.04430e14	+	6.01156e14i	−0.549583	+	0.654967i	0.417725	+	0.908574i	$0.362828\pi$
$984$	5.83268e13	+	2.10140e13i	0.0632256	+	0.0227790i
$985$	−2.18717e14	−	1.24041e15i	−0.235886	−	1.33777i
$986$	−7.71590e13	+	1.36052e13i	−0.0827946	+	0.0145989i
$987$	−3.55376e14	−	4.20726e14i	−0.379404	−	0.449173i
$988$	−1.74083e14	−	1.46073e14i	−0.184915	−	0.155162i
$989$	1.74601e14	−	1.00806e14i	0.184530	−	0.106538i
$990$	−2.16173e13	−	3.66647e12i	−0.0227313	−	0.00385542i
$991$	2.81731e14	−	4.87972e14i	0.294758	−	0.510536i	−0.680170	−	0.733054i	$-0.738094\pi$
$991$	2.81731e14	−	4.87972e14i	0.294758	−	0.510536i	0.974929	+	0.222518i	$0.0714275\pi$
$992$	4.12544e14	+	1.13346e15i	0.429449	+	1.17990i
$993$	3.55012e14	−	1.30527e14i	0.367703	−	0.135193i
$994$	−1.89945e14	+	1.59382e14i	−0.195747	+	0.164251i
$995$	2.27826e14	−	6.25947e14i	0.233608	−	0.641834i
$996$	1.09865e15	+	6.29534e14i	1.12088	+	0.642277i
$997$	−1.13387e14	+	6.43047e14i	−0.115103	+	0.652780i	0.871597	+	0.490224i	$0.163085\pi$
$997$	−1.13387e14	+	6.43047e14i	−0.115103	+	0.652780i	−0.986699	+	0.162556i	$0.948026\pi$
$998$		−	3.88752e13i		−	0.0392663i
$999$	−1.30730e14	−	2.21400e14i	−0.131386	−	0.222510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.f.a.2.19	✓	174
3.2	odd	2		81.11.f.a.8.11		174
27.13	even	9		81.11.f.a.71.11		174
27.14	odd	18	inner	27.11.f.a.14.19	yes	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.f.a.2.19	✓	174	1.1	even	1	trivial
27.11.f.a.14.19	yes	174	27.14	odd	18	inner
81.11.f.a.8.11		174	3.2	odd	2
81.11.f.a.71.11		174	27.13	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(12.8751 + 2.27023i) q^{2} +(-242.999 + 0.792606i) q^{3} +(-801.631 - 291.770i) q^{4} +(-2001.83 - 2385.69i) q^{5} +(-3130.43 - 541.458i) q^{6} +(-5414.20 + 1970.61i) q^{7} +(-21252.6 - 12270.2i) q^{8} +(59047.7 - 385.204i) q^{9} +(-20357.7 - 35260.6i) q^{10} +(5862.12 - 6986.20i) q^{11} +(195027. + 70264.3i) q^{12} +(50114.5 + 284213. i) q^{13} +(-74182.1 + 13080.3i) q^{14} +(488334. + 578133. i) q^{15} +(423406. + 355280. i) q^{16} +(-483672. + 279248. i) q^{17} +(761120. + 129092. i) q^{18} +(461520. - 799376. i) q^{19} +(908659. + 2.49652e6i) q^{20} +(1.31408e6 - 483147. i) q^{21} +(91335.7 - 76639.7i) q^{22} +(-547430. + 1.50405e6i) q^{23} +(5.17408e6 + 2.96480e6i) q^{24} +(11593.0 - 65747.1i) q^{25} +3.77305e6i q^{26} +(-1.43482e7 + 140406. i) q^{27} +4.91516e6 q^{28} +(1.05674e7 + 1.86331e6i) q^{29} +(4.97485e6 + 8.55216e6i) q^{30} +(3.50314e7 + 1.27504e7i) q^{31} +(2.07977e7 + 2.47857e7i) q^{32} +(-1.41895e6 + 1.70228e6i) q^{33} +(-6.86129e6 + 2.49731e6i) q^{34} +(1.55396e7 + 8.97179e6i) q^{35} +(-4.74469e7 - 1.69196e7i) q^{36} +(8.95940e6 + 1.55181e7i) q^{37} +(7.75688e6 - 9.24429e6i) q^{38} +(-1.24030e7 - 6.90238e7i) q^{39} +(1.32713e7 + 7.52651e7i) q^{40} +(1.02384e7 - 1.80531e6i) q^{41} +(1.80158e7 - 3.23730e6i) q^{42} +(-9.64927e7 - 8.09670e7i) q^{43} +(-6.73762e6 + 3.88997e6i) q^{44} +(-1.19123e8 - 1.40099e8i) q^{45} +(-1.04628e7 + 1.81220e7i) q^{46} +(-1.34535e8 - 3.69632e8i) q^{47} +(-1.03169e8 - 8.59970e7i) q^{48} +(-1.90958e8 + 1.60233e8i) q^{49} +(298522. - 820182. i) q^{50} +(1.17310e8 - 6.82404e7i) q^{51} +(4.27516e7 - 2.42456e8i) q^{52} +2.30982e8i q^{53} +(-1.85054e8 - 3.07660e7i) q^{54} -2.84019e7 q^{55} +(1.39246e8 + 2.45528e7i) q^{56} +(-1.11515e8 + 1.94613e8i) q^{57} +(1.31826e8 + 4.79807e7i) q^{58} +(4.14069e8 + 4.93469e8i) q^{59} +(-2.22782e8 - 6.05931e8i) q^{60} +(-1.44479e8 + 5.25861e7i) q^{61} +(4.22086e8 + 2.43692e8i) q^{62} +(-3.18937e8 + 1.18446e8i) q^{63} +(-7.14884e7 - 1.23821e8i) q^{64} +(5.77725e8 - 6.88506e8i) q^{65} +(-2.21337e7 + 1.86957e7i) q^{66} +(3.88344e8 + 2.20241e9i) q^{67} +(4.69203e8 - 8.27332e7i) q^{68} +(1.31833e8 - 3.65916e8i) q^{69} +(1.79706e8 + 1.50791e8i) q^{70} +(2.85073e9 - 1.64587e9i) q^{71} +(-1.25964e9 - 7.16341e8i) q^{72} +(-1.88036e9 + 3.25688e9i) q^{73} +(8.01235e7 + 2.20137e8i) q^{74} +(-2.76497e6 + 1.59857e7i) q^{75} +(-6.03202e8 + 5.06147e8i) q^{76} +(-1.79716e7 + 4.93766e7i) q^{77} +(-2.99054e6 - 9.16846e8i) q^{78} +(-8.39932e8 + 4.76349e9i) q^{79} -1.72133e9i q^{80} +(3.48649e9 - 4.54909e7i) q^{81} +1.35919e8 q^{82} +(6.01546e9 + 1.06069e9i) q^{83} +(-1.19438e9 + 3.89578e6i) q^{84} +(1.63443e9 + 5.94885e8i) q^{85} +(-1.05854e9 - 1.26152e9i) q^{86} +(-2.56933e9 - 4.44407e8i) q^{87} +(-2.10307e8 + 7.65456e7i) q^{88} +(-5.85736e7 - 3.38175e7i) q^{89} +(-1.21566e9 - 2.07422e9i) q^{90} +(-8.31403e8 - 1.44003e9i) q^{91} +(8.77673e8 - 1.04597e9i) q^{92} +(-8.52269e9 - 3.07056e9i) q^{93} +(-8.93003e8 - 5.06447e9i) q^{94} +(-2.83095e9 + 4.99173e8i) q^{95} +(-5.07345e9 - 6.00641e9i) q^{96} +(-4.70128e9 - 3.94484e9i) q^{97} +(-2.82237e9 + 1.62950e9i) q^{98} +(3.43454e8 - 4.14778e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 4965 q^{5} + 18234 q^{6} - 6 q^{7} - 9 q^{8} + 119124 q^{9} - 3 q^{10} - 978 q^{11} - 1015107 q^{12} - 6 q^{13} + 2134569 q^{14} - 2548539 q^{15} - 3078 q^{16} - 9 q^{17}+ \cdots - 72892391589 q^{99}+O(q^{100}) \) 174 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 4965 * q^5 + 18234 * q^6 - 6 * q^7 - 9 * q^8 + 119124 * q^9 - 3 * q^10 - 978 * q^11 - 1015107 * q^12 - 6 * q^13 + 2134569 * q^14 - 2548539 * q^15 - 3078 * q^16 - 9 * q^17 + 6676947 * q^18 - 3 * q^19 + 15925353 * q^20 - 21049824 * q^21 + 10420410 * q^22 + 8437692 * q^23 + 87359400 * q^24 - 14881965 * q^25 - 60562494 * q^27 - 12 * q^28 + 7820868 * q^29 + 216153117 * q^30 - 51711531 * q^31 + 76244832 * q^32 - 198927081 * q^33 + 92236410 * q^34 - 260153622 * q^35 + 199074744 * q^36 - 3 * q^37 + 250645020 * q^38 + 152777949 * q^39 - 26151153 * q^40 - 837714012 * q^41 - 1627952634 * q^42 - 213300456 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 - 3 * q^46 - 1685998563 * q^47 - 1664196711 * q^48 - 183168366 * q^49 + 2548576023 * q^50 + 1007158626 * q^51 - 912655665 * q^52 - 1206704682 * q^54 - 12 * q^55 - 4260806997 * q^56 - 1000586442 * q^57 - 496853331 * q^58 + 1806342150 * q^59 + 1176655374 * q^60 - 1784159286 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 8858370045 * q^64 - 2961878001 * q^65 - 5594499243 * q^66 - 915608058 * q^67 + 11412166995 * q^68 - 7767764199 * q^69 + 1945422669 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 2110132140 * q^73 + 22008588729 * q^74 + 15296936925 * q^75 + 11875694586 * q^76 - 2702962221 * q^77 - 12511026108 * q^78 + 6660721974 * q^79 + 440880768 * q^81 - 12 * q^82 + 7670489421 * q^83 - 31766160684 * q^84 - 6965484381 * q^85 - 33241766118 * q^86 - 10927113525 * q^87 + 28790289402 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 - 991980102 * q^91 + 40280154009 * q^92 + 57140838285 * q^93 - 62587945905 * q^94 - 12104972679 * q^95 - 78182924274 * q^96 + 48297833958 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

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