LMFDB - Embedded newform 100.9.j.b.91.70

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			91.70
Character	$\chi$	$=$	100.91
Dual form			100.9.j.b.11.70

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.15303 + 15.1475i) q^{2} +(-38.8019 + 12.6075i) q^{3} +(-202.893 + 156.111i) q^{4} +(209.784 + 588.741i) q^{5} +(-390.919 - 522.784i) q^{6} +437.907i q^{7} +(-3410.20 - 2268.87i) q^{8} +(-3961.32 + 2878.07i) q^{9} +(-7836.93 + 6211.49i) q^{10} +(14053.1 - 19342.4i) q^{11} +(5904.45 - 8615.36i) q^{12} +(-42733.3 + 31047.5i) q^{13} +(-6633.19 + 2256.55i) q^{14} +(-15562.5 - 20199.4i) q^{15} +(16794.9 - 63347.5i) q^{16} +(7025.45 - 21622.1i) q^{17} +(-64008.3 - 45173.3i) q^{18} +(-81270.3 - 26406.3i) q^{19} +(-134472. - 86701.7i) q^{20} +(-5520.91 - 16991.6i) q^{21} +(365405. + 113197. i) q^{22} +(-196806. + 270880. i) q^{23} +(160927. + 45042.4i) q^{24} +(-302607. + 247016. i) q^{25} +(-690498. - 487313. i) q^{26} +(274760. - 378175. i) q^{27} +(-68362.0 - 88848.1i) q^{28} +(-156464. - 481548. i) q^{29} +(225776. - 339821. i) q^{30} +(765749. + 248807. i) q^{31} +(1.04610e6 - 72031.2i) q^{32} +(-301427. + 927697. i) q^{33} +(363723. - 5001.39i) q^{34} +(-257814. + 91865.7i) q^{35} +(354426. - 1.20234e6i) q^{36} +(1.16899e6 - 849318. i) q^{37} +(-18798.5 - 1.36711e6i) q^{38} +(1.26670e6 - 1.74346e6i) q^{39} +(620374. - 2.48369e6i) q^{40} +(1.65146e6 - 1.19986e6i) q^{41} +(228931. - 171186. i) q^{42} -5.16180e6i q^{43} +(168291. + 6.11828e6i) q^{44} +(-2.52546e6 - 1.72842e6i) q^{45} +(-5.11730e6 - 1.58526e6i) q^{46} +(-4.59776e6 + 1.49390e6i) q^{47} +(146981. + 2.66974e6i) q^{48} +5.57304e6 q^{49} +(-5.30102e6 - 3.31085e6i) q^{50} +927551. i q^{51} +(3.82341e6 - 1.29704e7i) q^{52} +(2.19512e6 + 6.75590e6i) q^{53} +(7.14424e6 + 2.21318e6i) q^{54} +(1.43358e7 + 4.21591e6i) q^{55} +(993555. - 1.49335e6i) q^{56} +3.48636e6 q^{57} +(6.48798e6 - 4.85147e6i) q^{58} +(-3.48368e6 - 4.79488e6i) q^{59} +(6.31087e6 + 1.66883e6i) q^{60} +(1.86328e7 + 1.35375e7i) q^{61} +(177125. + 1.28813e7i) q^{62} +(-1.26033e6 - 1.73469e6i) q^{63} +(6.48167e6 + 1.54746e7i) q^{64} +(-2.72437e7 - 1.86456e7i) q^{65} +(-1.56055e7 + 214585. i) q^{66} +(-2.57291e6 - 835989. i) q^{67} +(1.95003e6 + 5.48371e6i) q^{68} +(4.22132e6 - 1.29919e7i) q^{69} +(-2.72006e6 - 3.43185e6i) q^{70} +(4.57537e6 - 1.48663e6i) q^{71} +(2.00389e7 - 827053. i) q^{72} +(-1.30242e7 - 9.46260e6i) q^{73} +(1.88889e7 + 1.33306e7i) q^{74} +(8.62745e6 - 1.33998e7i) q^{75} +(2.06115e7 - 7.32952e6i) q^{76} +(8.47019e6 + 6.15395e6i) q^{77} +(3.29364e7 + 1.02032e7i) q^{78} +(7.05366e6 - 2.29187e6i) q^{79} +(4.08185e7 - 3.40143e6i) q^{80} +(4.03402e6 - 1.24154e7i) q^{81} +(2.66849e7 + 1.88326e7i) q^{82} +(-3.72653e7 - 1.21082e7i) q^{83} +(3.77273e6 + 2.58560e6i) q^{84} +(1.42036e7 - 399792. i) q^{85} +(7.81883e7 - 2.65989e7i) q^{86} +(1.21422e7 + 1.67123e7i) q^{87} +(-9.18093e7 + 3.40768e7i) q^{88} +(-5.51749e7 - 4.00869e7i) q^{89} +(1.31675e7 - 4.71609e7i) q^{90} +(-1.35959e7 - 1.87132e7i) q^{91} +(-2.35683e6 - 8.56831e7i) q^{92} -3.28493e7 q^{93} +(-4.63213e7 - 6.19464e7i) q^{94} +(-1.50269e6 - 5.33867e7i) q^{95} +(-3.96825e7 + 1.59836e7i) q^{96} +(3.82139e6 + 1.17610e7i) q^{97} +(2.87180e7 + 8.44175e7i) q^{98} +1.17067e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	5.15303	+	15.1475i	0.322064	+	0.946718i
$2$	5.15303	+	15.1475i	0.322064	+	0.946718i
$3$	−38.8019	+	12.6075i	−0.479035	+	0.155648i	−0.538574	−	0.842578i	$-0.681037\pi$
$3$	−38.8019	+	12.6075i	−0.479035	+	0.155648i	0.0595390	+	0.998226i	$0.481037\pi$
$4$	−202.893	+	156.111i	−0.792549	+	0.609808i
$5$	209.784	+	588.741i	0.335654	+	0.941985i
$5$	209.784	+	588.741i	0.335654	+	0.941985i
$6$	−390.919	−	522.784i	−0.301635	−	0.403383i
$7$			437.907i			0.182385i	0.995833	+	0.0911926i	$0.0290679\pi$
$7$			437.907i			0.182385i	−0.995833	+	0.0911926i	$0.970932\pi$
$8$	−3410.20	−	2268.87i	−0.832568	−	0.553924i
$9$	−3961.32	+	2878.07i	−0.603768	+	0.438663i
$10$	−7836.93	+	6211.49i	−0.783693	+	0.621149i
$11$	14053.1	−	19342.4i	0.959846	−	1.32111i	0.0128332	−	0.999918i	$-0.495915\pi$
$11$	14053.1	−	19342.4i	0.959846	−	1.32111i	0.947013	−	0.321197i	$-0.104085\pi$
$12$	5904.45	−	8615.36i	0.284744	−	0.415478i
$13$	−42733.3	+	31047.5i	−1.49621	+	1.08706i	−0.524350	+	0.851503i	$0.675692\pi$
$13$	−42733.3	+	31047.5i	−1.49621	+	1.08706i	−0.971860	+	0.235558i	$0.924308\pi$
$14$	−6633.19	+	2256.55i	−0.172667	+	0.0587398i
$15$	−15562.5	−	20199.4i	−0.307408	−	0.399001i
$16$	16794.9	−	63347.5i	0.256269	−	0.966605i
$17$	7025.45	−	21622.1i	0.0841159	−	0.258882i	−0.900149	−	0.435583i	$-0.856542\pi$
$17$	7025.45	−	21622.1i	0.0841159	−	0.258882i	0.984265	+	0.176700i	$0.0565424\pi$
$18$	−64008.3	−	45173.3i	−0.609743	−	0.430321i
$19$	−81270.3	−	26406.3i	−0.623616	−	0.202625i	−0.0198709	−	0.999803i	$-0.506326\pi$
$19$	−81270.3	−	26406.3i	−0.623616	−	0.202625i	−0.603745	+	0.797177i	$0.706326\pi$
$20$	−134472.	−	86701.7i	−0.840452	−	0.541886i
$21$	−5520.91	−	16991.6i	−0.0283879	−	0.0873690i
$22$	365405.	+	113197.i	1.55985	+	0.483220i
$23$	−196806.	+	270880.i	−0.703278	+	0.967979i	0.296638	+	0.954990i	$0.404135\pi$
$23$	−196806.	+	270880.i	−0.703278	+	0.967979i	−0.999916	+	0.0129886i	$0.995865\pi$
$24$	160927.	+	45042.4i	0.485046	+	0.135761i
$25$	−302607.	+	247016.i	−0.774673	+	0.632362i
$26$	−690498.	−	487313.i	−1.51102	−	1.06639i
$27$	274760.	−	378175.i	0.517010	−	0.711603i
$28$	−68362.0	−	88848.1i	−0.111220	−	0.144549i
$29$	−156464.	−	481548.i	−0.221220	−	0.680844i	−0.998653	−	0.0518792i	$-0.983479\pi$
$29$	−156464.	−	481548.i	−0.221220	−	0.680844i	0.777434	−	0.628965i	$-0.216521\pi$
$30$	225776.	−	339821.i	0.278736	−	0.419533i
$31$	765749.	+	248807.i	0.829163	+	0.269411i	0.692693	−	0.721233i	$-0.256424\pi$
$31$	765749.	+	248807.i	0.829163	+	0.269411i	0.136470	+	0.990644i	$0.456424\pi$
$32$	1.04610e6	−	72031.2i	0.997638	−	0.0686943i
$33$	−301427.	+	927697.i	−0.254171	+	0.782259i
$34$	363723.	−	5001.39i	0.272179	−	0.00374261i
$35$	−257814.	+	91865.7i	−0.171804	+	0.0612183i
$36$	354426.	−	1.20234e6i	0.211016	−	0.715845i
$37$	1.16899e6	−	849318.i	0.623738	−	0.453173i	−0.230487	−	0.973075i	$-0.574032\pi$
$37$	1.16899e6	−	849318.i	0.623738	−	0.453173i	0.854225	+	0.519903i	$0.174032\pi$
$38$	−18798.5	−	1.36711e6i	−0.00901550	−	0.655647i
$39$	1.26670e6	−	1.74346e6i	0.547539	−	0.753623i
$40$	620374.	−	2.48369e6i	0.242334	−	0.970193i
$41$	1.65146e6	−	1.19986e6i	0.584431	−	0.424614i	−0.255888	−	0.966706i	$-0.582368\pi$
$41$	1.65146e6	−	1.19986e6i	0.584431	−	0.424614i	0.840319	+	0.542092i	$0.182368\pi$
$42$	228931.	−	171186.i	0.0735711	−	0.0550138i
$43$		−	5.16180e6i		−	1.50983i	−0.655823	−	0.754914i	$-0.727678\pi$
$43$		−	5.16180e6i		−	1.50983i	0.655823	−	0.754914i	$-0.272322\pi$
$44$	168291.	+	6.11828e6i	0.0449004	+	1.63237i
$45$	−2.52546e6	−	1.72842e6i	−0.615872	−	0.421502i
$46$	−5.11730e6	−	1.58526e6i	−1.14290	−	0.354054i
$47$	−4.59776e6	+	1.49390e6i	−0.942226	+	0.306148i	−0.739553	−	0.673099i	$-0.764963\pi$
$47$	−4.59776e6	+	1.49390e6i	−0.942226	+	0.306148i	−0.202673	+	0.979246i	$0.564963\pi$
$48$	146981.	+	2.66974e6i	0.0276882	+	0.502926i
$49$	5.57304e6			0.966736
$50$	−5.30102e6	−	3.31085e6i	−0.848163	−	0.529736i
$51$			927551.i			0.137106i
$52$	3.82341e6	−	1.29704e7i	0.522923	−	1.77395i
$53$	2.19512e6	+	6.75590e6i	0.278199	+	0.856208i	0.988355	+	0.152164i	$0.0486243\pi$
$53$	2.19512e6	+	6.75590e6i	0.278199	+	0.856208i	−0.710156	+	0.704044i	$0.751376\pi$
$54$	7.14424e6	+	2.21318e6i	0.840197	+	0.260281i
$55$	1.43358e7	+	4.21591e6i	1.56665	+	0.460724i
$56$	993555.	−	1.49335e6i	0.101028	−	0.151848i
$57$	3.48636e6			0.330272
$58$	6.48798e6	−	4.85147e6i	0.573320	−	0.428708i
$59$	−3.48368e6	−	4.79488e6i	−0.287495	−	0.395703i	0.640703	−	0.767789i	$-0.278643\pi$
$59$	−3.48368e6	−	4.79488e6i	−0.287495	−	0.395703i	−0.928199	+	0.372085i	$0.878643\pi$
$60$	6.31087e6	+	1.66883e6i	0.486950	+	0.128768i
$61$	1.86328e7	+	1.35375e7i	1.34573	+	0.977732i	0.999212	+	0.0396904i	$0.0126372\pi$
$61$	1.86328e7	+	1.35375e7i	1.34573	+	0.977732i	0.346521	+	0.938042i	$0.387363\pi$
$62$	177125.	+	1.28813e7i	0.0119871	+	0.871751i
$63$	−1.26033e6	−	1.73469e6i	−0.0800058	−	0.110118i
$64$	6.48167e6	+	1.54746e7i	0.386337	+	0.922358i
$65$	−2.72437e7	−	1.86456e7i	−1.52620	−	1.04453i
$66$	−1.56055e7	+	214585.i	−0.822438	+	0.0113090i
$67$	−2.57291e6	−	835989.i	−0.127681	−	0.0414860i	0.244480	−	0.969654i	$-0.421383\pi$
$67$	−2.57291e6	−	835989.i	−0.127681	−	0.0414860i	−0.372160	+	0.928168i	$0.621383\pi$
$68$	1.95003e6	+	5.48371e6i	0.0912023	+	0.256471i
$69$	4.22132e6	−	1.29919e7i	0.186231	−	0.573160i
$70$	−2.72006e6	−	3.43185e6i	−0.113288	−	0.142934i
$71$	4.57537e6	−	1.48663e6i	0.180050	−	0.0585018i	−0.217604	−	0.976037i	$-0.569824\pi$
$71$	4.57537e6	−	1.48663e6i	0.180050	−	0.0585018i	0.397654	+	0.917535i	$0.369824\pi$
$72$	2.00389e7	−	827053.i	0.745664	−	0.0307754i
$73$	−1.30242e7	−	9.46260e6i	−0.458625	−	0.333211i	0.334366	−	0.942443i	$-0.391478\pi$
$73$	−1.30242e7	−	9.46260e6i	−0.458625	−	0.333211i	−0.792992	+	0.609232i	$0.791478\pi$
$74$	1.88889e7	+	1.33306e7i	0.629910	+	0.444554i
$75$	8.62745e6	−	1.33998e7i	0.272670	−	0.423500i
$76$	2.06115e7	−	7.32952e6i	0.617809	−	0.219695i
$77$	8.47019e6	+	6.15395e6i	0.240952	+	0.175062i
$78$	3.29364e7	+	1.02032e7i	0.889811	+	0.275650i
$79$	7.05366e6	−	2.29187e6i	0.181095	−	0.0588413i	−0.217066	−	0.976157i	$-0.569649\pi$
$79$	7.05366e6	−	2.29187e6i	0.181095	−	0.0588413i	0.398161	+	0.917316i	$0.369649\pi$
$80$	4.08185e7	−	3.40143e6i	0.996546	−	0.0830427i
$81$	4.03402e6	−	1.24154e7i	0.0937127	−	0.288418i
$82$	2.66849e7	+	1.88326e7i	0.590214	+	0.416538i
$83$	−3.72653e7	−	1.21082e7i	−0.785221	−	0.255134i	−0.111153	−	0.993803i	$-0.535454\pi$
$83$	−3.72653e7	−	1.21082e7i	−0.785221	−	0.255134i	−0.674068	+	0.738669i	$0.735454\pi$
$84$	3.77273e6	+	2.58560e6i	0.0757771	+	0.0519331i
$85$	1.42036e7	−	399792.i	0.272097	−	0.00765877i
$86$	7.81883e7	−	2.65989e7i	1.42938	−	0.486262i
$87$	1.21422e7	+	1.67123e7i	0.211944	+	0.291716i
$88$	−9.18093e7	+	3.40768e7i	−1.53093	+	0.568236i
$89$	−5.51749e7	−	4.00869e7i	−0.879390	−	0.638914i	0.0537002	−	0.998557i	$-0.482898\pi$
$89$	−5.51749e7	−	4.00869e7i	−0.879390	−	0.638914i	−0.933090	+	0.359643i	$0.882898\pi$
$90$	1.31675e7	−	4.71609e7i	0.200693	−	0.718807i
$91$	−1.35959e7	−	1.87132e7i	−0.198264	−	0.272887i
$92$	−2.35683e6	−	8.56831e7i	−0.0328985	−	1.19604i
$93$	−3.28493e7			−0.439132
$94$	−4.63213e7	−	6.19464e7i	−0.593293	−	0.793423i
$95$	−1.50269e6	−	5.33867e7i	−0.0184490	−	0.655449i
$96$	−3.96825e7	+	1.59836e7i	−0.467212	+	0.188187i
$97$	3.82139e6	+	1.17610e7i	0.0431653	+	0.132849i	0.970317	−	0.241838i	$-0.0777502\pi$
$97$	3.82139e6	+	1.17610e7i	0.0431653	+	0.132849i	−0.927151	+	0.374687i	$0.877750\pi$
$98$	2.87180e7	+	8.44175e7i	0.311351	+	0.915226i
$99$			1.17067e8i			1.21870i
$100$	2.28348e7	−	9.73580e7i	0.228348	−	0.973580i
$101$	−1.38153e8			−1.32762			−0.663811	−	0.747900i	$-0.731062\pi$
$101$	−1.38153e8			−1.32762			−0.663811	+	0.747900i	$0.731062\pi$
$102$	−1.40501e7	+	4.77969e6i	−0.129801	+	0.0441570i
$103$	−7.69723e7	+	2.50098e7i	−0.683889	+	0.222209i	−0.630297	−	0.776354i	$-0.717067\pi$
$103$	−7.69723e7	+	2.50098e7i	−0.683889	+	0.222209i	−0.0535920	+	0.998563i	$0.517067\pi$
$104$	2.16172e8	−	8.92194e6i	1.84784	−	0.0762651i
$105$	8.84546e6	−	6.81495e6i	0.0727718	−	0.0560667i
$106$	−9.10233e7	+	6.80639e7i	−0.720990	+	0.539130i
$107$		−	1.97007e8i		−	1.50296i	−0.659756	−	0.751480i	$-0.729340\pi$
$107$		−	1.97007e8i		−	1.50296i	0.659756	−	0.751480i	$-0.270660\pi$
$108$	3.29036e6	+	1.19622e8i	0.0241851	+	0.879257i
$109$	2.65307e7	−	1.92757e7i	0.187950	−	0.136554i	−0.489831	−	0.871817i	$-0.662942\pi$
$109$	2.65307e7	−	1.92757e7i	0.187950	−	0.136554i	0.677781	+	0.735264i	$0.262942\pi$
$110$	1.00122e7	+	2.38876e8i	0.0683849	+	1.63155i
$111$	−3.46511e7	+	4.76931e7i	−0.228257	+	0.314169i
$112$	2.77403e7	+	7.35459e6i	0.176295	+	0.0467397i
$113$	1.18181e8	−	8.58632e7i	0.724823	−	0.526615i	−0.163098	−	0.986610i	$-0.552149\pi$
$113$	1.18181e8	−	8.58632e7i	0.724823	−	0.526615i	0.887922	+	0.459995i	$0.152149\pi$
$114$	1.79653e7	+	5.28095e7i	0.106369	+	0.312675i
$115$	−2.00765e8	−	5.90415e7i	−1.14788	−	0.337572i
$116$	1.06920e8	+	7.32768e7i	0.590511	+	0.404701i
$117$	7.99233e7	−	2.45979e8i	0.426511	−	1.31267i
$118$	5.46788e7	−	7.74772e7i	0.282027	−	0.399619i
$119$	9.46847e6	+	3.07649e6i	0.0472163	+	0.0153415i
$120$	7.24148e6	+	1.04193e8i	0.0349222	+	0.502476i
$121$	−1.10400e8	−	3.39775e8i	−0.515022	−	1.58508i
$122$	−1.09044e8	+	3.51999e8i	−0.492224	+	1.58892i
$123$	−4.89526e7	+	6.73775e7i	−0.213873	+	0.294371i
$124$	−1.94206e8	+	6.90606e7i	−0.821441	+	0.292108i
$125$	−2.08910e8	−	1.26337e8i	−0.855697	−	0.517477i
$126$	1.97817e7	−	2.80297e7i	0.0784841	−	0.111208i
$127$	−2.30023e8	+	3.16600e8i	−0.884214	+	1.21702i	0.0910222	+	0.995849i	$0.470987\pi$
$127$	−2.30023e8	+	3.16600e8i	−0.884214	+	1.21702i	−0.975236	+	0.221167i	$0.929013\pi$
$128$	−2.01001e8	+	1.77922e8i	−0.748787	+	0.662811i
$129$	6.50774e7	+	2.00288e8i	0.235002	+	0.723261i
$130$	1.42046e8	−	5.08754e8i	0.497342	−	1.78129i
$131$	−2.27189e8	−	7.38183e7i	−0.771441	−	0.250656i	−0.103259	−	0.994654i	$-0.532927\pi$
$131$	−2.27189e8	−	7.38183e7i	−0.771441	−	0.250656i	−0.668182	+	0.743998i	$0.732927\pi$
$132$	−8.36662e7	−	2.35279e8i	−0.275584	−	0.774974i
$133$	1.15635e7	−	3.55888e7i	0.0369558	−	0.113738i
$134$	−595137.	−	4.32810e7i	−0.00184586	−	0.134239i
$135$	2.80287e8	+	8.24277e7i	0.843855	+	0.248163i
$136$	−7.30159e7	+	5.77958e7i	−0.213433	+	0.168943i
$137$	−8.02661e7	+	5.83167e7i	−0.227850	+	0.165543i	−0.695853	−	0.718184i	$-0.744974\pi$
$137$	−8.02661e7	+	5.83167e7i	−0.227850	+	0.165543i	0.468003	+	0.883727i	$0.344974\pi$
$138$	2.18547e8	−	3.00514e6i	0.602599	−	0.00828607i
$139$	−2.41052e8	+	3.31779e8i	−0.645730	+	0.888772i	−0.998905	−	0.0467859i	$-0.985102\pi$
$139$	−2.41052e8	+	3.31779e8i	−0.645730	+	0.888772i	0.353175	+	0.935557i	$0.385102\pi$
$140$	3.79673e7	−	5.88864e7i	0.0988320	−	0.153286i
$141$	1.59567e8	−	1.15932e8i	0.403708	−	0.293311i
$142$	4.60957e7	+	6.16448e7i	0.113372	+	0.151615i
$143$			1.26288e9i			3.02008i
$144$	1.15789e8	+	2.99277e8i	0.269287	+	0.696022i
$145$	2.50683e8	−	1.93138e8i	0.567092	−	0.436913i
$146$	7.62208e7	−	2.46044e8i	0.167750	−	0.541504i
$147$	−2.16244e8	+	7.02620e7i	−0.463101	+	0.150471i
$148$	−1.04591e8	+	3.54812e8i	−0.217995	+	0.739522i
$149$	−4.91274e8			−0.996733			−0.498367	−	0.866966i	$-0.666067\pi$
$149$	−4.91274e8			−0.996733			−0.498367	+	0.866966i	$0.666067\pi$
$150$	2.47431e8	+	6.16347e7i	0.488752	+	0.121747i
$151$		−	3.94717e8i		−	0.759237i	−0.925143	−	0.379619i	$-0.876055\pi$
$151$		−	3.94717e8i		−	0.759237i	0.925143	−	0.379619i	$-0.123945\pi$
$152$	2.17235e8	+	2.74442e8i	0.406964	+	0.514135i
$153$	3.43999e7	+	1.05872e8i	0.0627756	+	0.193203i
$154$	−4.95698e7	+	1.60014e8i	−0.0881321	+	0.284494i
$155$	1.41587e7	+	5.03023e8i	0.0245299	+	0.871488i
$156$	1.51692e7	+	5.51481e8i	0.0256132	+	0.931177i
$157$	−8.44046e8			−1.38921			−0.694604	−	0.719392i	$-0.744420\pi$
$157$	−8.44046e8			−1.38921			−0.694604	+	0.719392i	$0.744420\pi$
$158$	7.10638e7	+	9.50351e7i	0.114030	+	0.152495i
$159$	−1.70350e8	−	2.34466e8i	−0.266534	−	0.366853i
$160$	2.61862e8	+	6.00770e8i	0.399570	+	0.916703i
$161$	−1.18620e8	−	8.61827e7i	−0.176545	−	0.128267i
$162$	2.08850e8	−	2.87181e6i	0.303232	−	0.00416961i
$163$	2.00389e8	+	2.75812e8i	0.283873	+	0.390717i	0.927012	−	0.375032i	$-0.122368\pi$
$163$	2.00389e8	+	2.75812e8i	0.283873	+	0.390717i	−0.643139	+	0.765749i	$0.722368\pi$
$164$	−1.47759e8	+	5.01253e8i	−0.204258	+	0.692918i
$165$	−6.09408e8	+	1.71531e7i	−0.822190	+	0.0231423i
$166$	−8.61980e6	−	6.26869e8i	−0.0113518	−	0.825552i
$167$	−1.23109e9	−	4.00006e8i	−1.58280	−	0.514281i	−0.620020	−	0.784586i	$-0.712876\pi$
$167$	−1.23109e9	−	4.00006e8i	−1.58280	−	0.514281i	−0.962775	+	0.270305i	$0.912876\pi$
$168$	−1.97244e7	+	7.04710e7i	−0.0247609	+	0.0884653i
$169$	6.10108e8	−	1.87772e9i	0.747928	−	2.30189i
$170$	7.92476e7	+	2.13089e8i	0.0948834	+	0.255133i
$171$	3.97937e8	−	1.29298e8i	0.465404	−	0.151219i
$172$	8.05813e8	+	1.04729e9i	0.920705	+	1.19661i
$173$	2.98918e7	+	2.17177e7i	0.0333709	+	0.0242454i	0.604346	−	0.796722i	$-0.293435\pi$
$173$	2.98918e7	+	2.17177e7i	0.0333709	+	0.0242454i	−0.570975	+	0.820968i	$0.693435\pi$
$174$	−1.90581e8	+	2.70043e8i	−0.207913	+	0.294603i
$175$	−1.08170e8	−	1.32514e8i	−0.115333	−	0.141289i
$176$	−9.89274e8	−	1.21508e9i	−1.03102	−	1.26635i
$177$	1.95625e8	+	1.42130e8i	0.199311	+	0.144808i
$178$	3.22898e8	−	1.04233e9i	0.321651	−	1.03831i
$179$	1.29400e9	−	4.20445e8i	1.26044	−	0.409541i	0.398787	−	0.917044i	$-0.369431\pi$
$179$	1.29400e9	−	4.20445e8i	1.26044	−	0.409541i	0.861650	+	0.507503i	$0.169431\pi$
$180$	7.82222e8	−	4.35671e7i	0.745144	−	0.0415020i
$181$	2.35206e8	−	7.23888e8i	0.219146	−	0.674462i	−0.779687	−	0.626169i	$-0.784622\pi$
$181$	2.35206e8	−	7.23888e8i	0.219146	−	0.674462i	0.998833	−	0.0482927i	$-0.0153780\pi$
$182$	2.13398e8	−	3.02374e8i	0.194493	−	0.275587i
$183$	−8.93662e8	−	2.90368e8i	−0.796836	−	0.258908i
$184$	1.28574e9	−	4.77227e8i	1.12171	−	0.416346i
$185$	7.45263e8	+	5.10057e8i	0.636242	+	0.435444i
$186$	−1.69273e8	−	4.97585e8i	−0.141429	−	0.415734i
$187$	−3.19495e8	−	4.39747e8i	−0.261275	−	0.359614i
$188$	6.99638e8	−	1.02086e9i	0.560069	−	0.817214i
$189$	1.65605e8	+	1.20319e8i	0.129786	+	0.0942949i
$190$	8.00932e8	−	2.97865e8i	0.614584	−	0.228563i
$191$	−2.26296e8	−	3.11470e8i	−0.170037	−	0.234036i	0.715491	−	0.698622i	$-0.246203\pi$
$191$	−2.26296e8	−	3.11470e8i	−0.170037	−	0.234036i	−0.885528	+	0.464586i	$0.846203\pi$
$192$	−4.46597e8	−	5.18726e8i	−0.328632	−	0.381709i
$193$	−6.76698e8			−0.487715			−0.243857	−	0.969811i	$-0.578413\pi$
$193$	−6.76698e8			−0.487715			−0.243857	+	0.969811i	$0.578413\pi$
$194$	−1.58458e8	+	1.18489e8i	−0.111869	+	0.0836513i
$195$	1.29218e9	+	3.80008e8i	0.893685	+	0.262818i
$196$	−1.13073e9	+	8.70011e8i	−0.766186	+	0.589523i
$197$	7.22720e8	+	2.22430e9i	0.479850	+	1.47683i	0.839304	+	0.543663i	$0.182963\pi$
$197$	7.22720e8	+	2.22430e9i	0.479850	+	1.47683i	−0.359454	+	0.933163i	$0.617037\pi$
$198$	−1.77328e9	+	6.03252e8i	−1.15376	+	0.392498i
$199$		−	2.87954e9i		−	1.83616i	−0.396391	−	0.918082i	$-0.629738\pi$
$199$		−	2.87954e9i		−	1.83616i	0.396391	−	0.918082i	$-0.370262\pi$
$200$	1.59240e9	−	1.55798e8i	0.995248	−	0.0973740i
$201$	1.10373e8			0.0676208
$202$	−7.11906e8	−	2.09267e9i	−0.427580	−	1.25688i
$203$	2.10873e8	−	6.85169e7i	0.124176	−	0.0403472i
$204$	−1.44801e8	−	1.88193e8i	−0.0836084	−	0.108663i
$205$	1.05285e9	+	7.20573e8i	0.596147	+	0.408002i
$206$	−7.75477e8	−	1.03706e9i	−0.430626	−	0.575885i
$207$		−	1.63947e9i		−	0.892937i
$208$	1.24908e9	+	3.22848e9i	0.667326	+	1.72483i
$209$	−1.65286e9	+	1.20087e9i	−0.866266	+	0.629379i
$210$	1.48810e8	+	9.88689e7i	0.0765166	+	0.0508373i
$211$	−2.71224e8	+	3.73307e8i	−0.136835	+	0.188337i	−0.871935	−	0.489621i	$-0.837135\pi$
$211$	−2.71224e8	+	3.73307e8i	−0.136835	+	0.188337i	0.735100	+	0.677959i	$0.237135\pi$
$212$	−1.50004e9	−	1.02804e9i	−0.742609	−	0.508940i
$213$	−1.58790e8	+	1.15368e8i	−0.0771446	+	0.0560489i
$214$	2.98417e9	−	1.01518e9i	1.42288	−	0.484049i
$215$	3.03896e9	−	1.08286e9i	1.42224	−	0.506779i
$216$	−1.79502e9	+	6.66255e8i	−0.824619	+	0.306073i
$217$	−1.08954e8	+	3.35327e8i	−0.0491367	+	0.151227i
$218$	4.28691e8	+	3.02545e8i	0.189810	+	0.133956i
$219$	6.24661e8	+	2.02965e8i	0.271561	+	0.0882356i
$220$	−3.56678e9	+	1.38259e9i	−1.52260	+	0.590206i
$221$	3.71093e8	+	1.14211e9i	0.155565	+	0.478781i
$222$	−9.00989e8	−	2.79113e8i	−0.370943	−	0.114913i
$223$	−2.74367e8	+	3.77633e8i	−0.110946	+	0.152704i	−0.860879	−	0.508810i	$-0.830086\pi$
$223$	−2.74367e8	+	3.77633e8i	−0.110946	+	0.152704i	0.749933	+	0.661514i	$0.230086\pi$
$224$	3.15430e7	+	4.58094e8i	0.0125288	+	0.181954i
$225$	4.87793e8	−	1.84944e9i	0.190329	−	0.721621i
$226$	1.90960e9	+	1.34768e9i	0.731995	+	0.516599i
$227$	2.23346e9	−	3.07410e9i	0.841154	−	1.15775i	−0.144589	−	0.989492i	$-0.546186\pi$
$227$	2.23346e9	−	3.07410e9i	0.841154	−	1.15775i	0.985743	−	0.168257i	$-0.0538139\pi$
$228$	−7.07356e8	+	5.44258e8i	−0.261757	+	0.201403i
$229$	1.33927e8	+	4.12186e8i	0.0486998	+	0.149883i	0.972449	−	0.233115i	$-0.0748918\pi$
$229$	1.33927e8	+	4.12186e8i	0.0486998	+	0.149883i	−0.923749	+	0.382997i	$0.874892\pi$
$230$	−1.40216e8	−	3.34533e9i	−0.0501055	−	1.19544i
$231$	−4.06245e8	−	1.31997e8i	−0.142672	−	0.0463571i
$232$	−5.58996e8	+	1.99717e9i	−0.192955	+	0.689387i
$233$	1.53649e9	−	4.72884e9i	0.521323	−	1.60447i	−0.250151	−	0.968207i	$-0.580480\pi$
$233$	1.53649e9	−	4.72884e9i	0.521323	−	1.60447i	0.771474	−	0.636260i	$-0.219520\pi$
$234$	4.13781e9	−	5.68971e7i	1.38009	−	0.0189770i
$235$	−1.84406e9	−	2.39349e9i	−0.604648	−	0.784804i
$236$	1.45535e9	+	4.29005e8i	0.469157	+	0.138298i
$237$	−2.44800e8	+	1.77858e8i	−0.0775923	+	0.0563741i
$238$	2.19014e6	+	1.59277e8i	0.000682597	+	0.0496415i
$239$	−2.43847e9	+	3.35627e9i	−0.747353	+	1.02864i	0.250808	+	0.968037i	$0.419304\pi$
$239$	−2.43847e9	+	3.35627e9i	−0.747353	+	1.02864i	−0.998162	+	0.0606070i	$0.980696\pi$
$240$	−1.54095e9	+	6.46601e8i	−0.464455	+	0.194891i
$241$	−3.31798e9	+	2.41065e9i	−0.983569	+	0.714605i	−0.958504	−	0.285081i	$-0.907980\pi$
$241$	−3.31798e9	+	2.41065e9i	−0.983569	+	0.714605i	−0.0250660	+	0.999686i	$0.507980\pi$
$242$	4.57784e9	−	3.42314e9i	1.33475	−	0.998076i
$243$			3.59954e9i			1.03234i
$244$	−5.89381e9	+	1.62117e8i	−1.66279	+	0.0457372i
$245$	1.16913e9	+	3.28108e9i	0.324488	+	0.910651i
$246$	−1.27285e9	−	3.94311e8i	−0.347567	−	0.107671i
$247$	4.29280e9	−	1.39481e9i	1.15333	−	0.374739i
$248$	−2.04684e9	−	2.58587e9i	−0.541101	−	0.683596i
$249$	1.59862e9			0.415860
$250$	8.37167e8	−	3.81549e9i	0.214315	−	0.976765i
$251$			2.00933e9i			0.506239i	0.967435	+	0.253119i	$0.0814565\pi$
$251$			2.00933e9i			0.506239i	−0.967435	+	0.253119i	$0.918543\pi$
$252$	5.26515e8	+	1.55206e8i	0.130560	+	0.0384862i
$253$	2.47375e9	+	7.61341e9i	0.603772	+	1.85822i
$254$	−5.98101e9	−	1.85283e9i	−1.43694	−	0.445144i
$255$	−5.46087e8	+	1.94585e8i	−0.129152	+	0.0460202i
$256$	−3.73083e9	−	2.12782e9i	−0.868652	−	0.495422i
$257$	1.04629e9			0.239839			0.119919	−	0.992784i	$-0.461736\pi$
$257$	1.04629e9			0.239839			0.119919	+	0.992784i	$0.461736\pi$
$258$	−2.69851e9	+	2.01785e9i	−0.609039	+	0.455417i
$259$	3.71923e8	+	5.11907e8i	0.0826520	+	0.113761i
$260$	8.43832e9	−	4.69986e8i	1.84656	−	0.102847i
$261$	2.00574e9	+	1.45725e9i	0.432227	+	0.314031i
$262$	−5.25510e7	−	3.82174e9i	−0.0111526	−	0.811065i
$263$	4.35277e9	+	5.99107e9i	0.909793	+	1.25222i	0.967237	+	0.253874i	$0.0817050\pi$
$263$	4.35277e9	+	5.99107e9i	0.909793	+	1.25222i	−0.0574438	+	0.998349i	$0.518295\pi$
$264$	3.13275e9	−	2.47973e9i	0.644926	−	0.510492i
$265$	−3.51697e9	+	2.70963e9i	−0.713157	+	0.549449i
$266$	5.98668e8	−	8.23202e6i	0.119580	−	0.00164430i
$267$	2.64628e9	+	8.59830e8i	0.520705	+	0.169187i
$268$	6.52531e8	−	2.32043e8i	0.126492	−	0.0449810i
$269$	1.77601e9	−	5.46599e9i	0.339184	−	1.04390i	−0.625440	−	0.780272i	$-0.715081\pi$
$269$	1.77601e9	−	5.46599e9i	0.339184	−	1.04390i	0.964624	−	0.263629i	$-0.0849194\pi$
$270$	1.95755e8	+	4.67040e9i	0.0368347	+	0.878818i
$271$	−1.27556e9	+	4.14453e8i	−0.236495	+	0.0768419i	−0.424867	−	0.905256i	$-0.639679\pi$
$271$	−1.27556e9	+	4.14453e8i	−0.236495	+	0.0768419i	0.188372	+	0.982098i	$0.439679\pi$
$272$	−1.25171e9	−	8.08184e8i	−0.228681	−	0.147650i
$273$	7.63474e8	+	5.54697e8i	0.137450	+	0.0998631i
$274$	−1.29697e9	−	9.15322e8i	−0.230105	−	0.162395i
$275$	5.25333e8	+	9.32450e9i	0.0918552	+	1.63040i
$276$	1.17170e9	+	3.29495e9i	0.201920	+	0.567823i
$277$	4.59876e9	+	3.34120e9i	0.781128	+	0.567523i	0.905317	−	0.424736i	$-0.139633\pi$
$277$	4.59876e9	+	3.34120e9i	0.781128	+	0.567523i	−0.124189	+	0.992259i	$0.539633\pi$
$278$	−6.26777e9	−	1.94166e9i	−1.04938	−	0.325083i
$279$	−3.74946e9	+	1.21827e9i	−0.618803	+	0.201061i
$280$	1.08763e9	+	2.71666e8i	0.176949	+	0.0441981i
$281$	1.68200e9	−	5.17667e9i	0.269775	−	0.830282i	−0.720780	−	0.693164i	$-0.756216\pi$
$281$	1.68200e9	−	5.17667e9i	0.269775	−	0.830282i	0.990555	−	0.137118i	$-0.0437839\pi$
$282$	2.57834e9	+	1.81964e9i	0.407703	+	0.287733i
$283$	−3.92137e8	−	1.27413e8i	−0.0611353	−	0.0198641i	0.278290	−	0.960497i	$-0.410232\pi$
$283$	−3.92137e8	−	1.27413e8i	−0.0611353	−	0.0198641i	−0.339425	+	0.940633i	$0.610232\pi$
$284$	−6.96231e8	+	1.01589e9i	−0.107024	+	0.156161i
$285$	7.31380e8	+	2.05256e9i	0.110857	+	0.311112i
$286$	−1.91295e10	+	6.50765e9i	−2.85916	+	0.972658i
$287$	5.25426e8	+	7.23187e8i	0.0774434	+	0.106592i
$288$	−3.93663e9	+	3.29609e9i	−0.572208	+	0.479103i
$289$	5.22535e9	+	3.79644e9i	0.749072	+	0.544233i
$290$	4.21733e9	+	2.80198e9i	0.596274	+	0.396162i
$291$	−2.96554e8	−	4.08172e8i	−0.0413554	−	0.0569208i
$292$	4.11972e9	−	1.13318e8i	0.566678	−	0.0155872i
$293$	−1.30441e10			−1.76988			−0.884940	−	0.465705i	$-0.845801\pi$
$293$	−1.30441e10			−1.76988			−0.884940	+	0.465705i	$0.845801\pi$
$294$	−2.17861e9	−	2.91350e9i	−0.291601	−	0.389964i
$295$	2.09212e9	−	3.05687e9i	0.276248	−	0.403635i
$296$	−5.91347e9	+	2.44063e8i	−0.770327	+	0.0317933i
$297$	−3.45359e9	−	1.06291e10i	−0.443859	−	1.36606i
$298$	−2.53155e9	−	7.44157e9i	−0.321012	−	0.943625i
$299$		−	1.76859e10i		−	2.21281i
$300$	3.41407e8	+	4.06556e9i	0.0421490	+	0.501921i
$301$	2.26039e9			0.275371
$302$	5.97896e9	−	2.03398e9i	0.718784	−	0.244523i
$303$	5.36059e9	−	1.74176e9i	0.635978	−	0.206642i
$304$	−3.03770e9	+	4.70477e9i	−0.355672	+	0.550864i
$305$	−4.06124e9	+	1.38098e10i	−0.469310	+	1.59584i
$306$	−1.42643e9	+	1.06663e9i	−0.162691	+	0.121655i
$307$		−	3.90914e9i		−	0.440076i	−0.975491	−	0.220038i	$-0.929382\pi$
$307$		−	3.90914e9i		−	0.440076i	0.975491	−	0.220038i	$-0.0706181\pi$
$308$	−2.67924e9	+	7.36959e7i	−0.297720	+	0.00818918i
$309$	2.67136e9	−	1.94086e9i	0.293021	−	0.212892i
$310$	−7.54658e9	+	2.80656e9i	−0.817153	+	0.303898i
$311$	−1.66948e9	+	2.29784e9i	−0.178460	+	0.245629i	−0.888870	−	0.458159i	$-0.848509\pi$
$311$	−1.66948e9	+	2.29784e9i	−0.178460	+	0.245629i	0.710411	+	0.703787i	$0.248509\pi$
$312$	−8.27538e9	+	3.07157e9i	−0.873313	+	0.324147i
$313$	−3.17018e9	+	2.30327e9i	−0.330298	+	0.239976i	−0.740557	−	0.671993i	$-0.765438\pi$
$313$	−3.17018e9	+	2.30327e9i	−0.330298	+	0.239976i	0.410259	+	0.911969i	$0.365438\pi$
$314$	−4.34939e9	−	1.27852e10i	−0.447414	−	1.31519i
$315$	7.56888e8	−	1.10592e9i	0.0768758	−	0.112326i
$316$	−1.07335e9	+	1.56616e9i	−0.107645	+	0.157068i
$317$	−4.79801e9	+	1.47667e10i	−0.475142	+	1.46234i	0.370623	+	0.928783i	$0.379144\pi$
$317$	−4.79801e9	+	1.47667e10i	−0.475142	+	1.46234i	−0.845766	+	0.533555i	$0.820856\pi$
$318$	2.67376e9	−	3.78858e9i	0.261465	−	0.370483i
$319$	−1.15131e10	−	3.74084e9i	−1.11181	−	0.361249i
$320$	−7.75078e9	+	7.06234e9i	−0.739172	+	0.673517i
$321$	2.48377e9	+	7.64425e9i	0.233933	+	0.719971i
$322$	6.94198e8	−	2.24090e9i	0.0645743	−	0.208449i
$323$	−1.14192e9	+	1.57172e9i	−0.104912	+	0.144399i
$324$	1.11971e9	+	3.14876e9i	0.101608	+	0.285732i
$325$	5.26213e9	−	1.99510e10i	0.471659	−	1.78826i
$326$	−3.14525e9	+	4.45666e9i	−0.278474	+	0.394583i
$327$	−7.86422e8	+	1.08242e9i	−0.0687803	+	0.0946680i
$328$	−8.35413e9	+	3.44796e8i	−0.721782	+	0.0297897i
$329$	−6.54191e8	−	2.01339e9i	−0.0558369	−	0.171848i
$330$	−3.40012e9	−	9.14260e9i	−0.286707	−	0.770928i
$331$	−9.88092e9	−	3.21051e9i	−0.823162	−	0.267462i	−0.133000	−	0.991116i	$-0.542461\pi$
$331$	−9.88092e9	−	3.21051e9i	−0.823162	−	0.267462i	−0.690163	+	0.723654i	$0.742461\pi$
$332$	9.45108e9	−	3.36084e9i	0.777909	−	0.276628i
$333$	−2.18634e9	+	6.72885e9i	−0.177803	+	0.547222i
$334$	−2.84763e8	−	2.07092e10i	−0.0228822	−	1.66409i
$335$	−4.75731e7	−	1.69015e9i	−0.00377730	−	0.134198i
$336$	−1.16910e9	+	6.43638e7i	−0.0917263	+	0.00504992i
$337$	1.47525e8	−	1.07183e8i	0.0114379	−	0.00831012i	−0.582052	−	0.813152i	$-0.697750\pi$
$337$	1.47525e8	−	1.07183e8i	0.0114379	−	0.00831012i	0.593490	+	0.804842i	$0.297750\pi$
$338$	3.15866e10	−	4.34333e8i	2.42012	−	0.0332779i
$339$	−3.50311e9	+	4.82161e9i	−0.265249	+	0.365085i
$340$	−2.81940e9	+	2.29846e9i	−0.210980	+	0.171997i
$341$	1.55737e10	−	1.13149e10i	1.15179	−	0.836825i
$342$	4.00911e9	+	5.36147e9i	0.293052	+	0.391904i
$343$			4.96492e9i			0.358704i
$344$	−1.17115e10	+	1.76028e10i	−0.836330	+	1.25703i
$345$	8.53442e9	−	2.40220e8i	0.602417	−	0.0169563i
$346$	−1.74935e8	+	5.64698e8i	−0.0122060	+	0.0394014i
$347$	2.71481e10	−	8.82097e9i	1.87250	−	0.608413i	0.881937	−	0.471368i	$-0.156240\pi$
$347$	2.71481e10	−	8.82097e9i	1.87250	−	0.608413i	0.990565	−	0.137045i	$-0.0437604\pi$
$348$	−5.07255e9	−	1.49528e9i	−0.345867	−	0.101954i
$349$	−2.07194e10			−1.39661			−0.698307	−	0.715799i	$-0.746063\pi$
$349$	−2.07194e10			−1.39661			−0.698307	+	0.715799i	$0.746063\pi$
$350$	1.44984e9	−	2.32135e9i	0.0966161	−	0.154692i
$351$			2.46913e10i			1.62673i
$352$	1.33077e10	−	2.12464e10i	0.866825	−	1.38393i
$353$	−2.01811e9	−	6.21109e9i	−0.129971	−	0.400008i	0.864803	−	0.502111i	$-0.167443\pi$
$353$	−2.01811e9	−	6.21109e9i	−0.129971	−	0.400008i	−0.994774	+	0.102102i	$0.967443\pi$
$354$	−1.14485e9	+	3.69562e9i	−0.0729013	+	0.235328i
$355$	1.83508e9	+	2.38184e9i	0.115542	+	0.149968i
$356$	1.74526e10	−	4.80056e8i	1.08657	−	0.0298876i
$357$	−4.06181e8			−0.0250062
$358$	1.30367e10	+	1.74342e10i	0.793661	+	1.06138i
$359$	−1.80808e10	−	2.48861e10i	−1.08853	−	1.49823i	−0.849771	−	0.527153i	$-0.823260\pi$
$359$	−1.80808e10	−	2.48861e10i	−1.08853	−	1.49823i	−0.238758	−	0.971079i	$-0.576740\pi$
$360$	4.69074e9	+	1.16242e10i	0.279275	+	0.692075i
$361$	−7.83243e9	−	5.69059e9i	−0.461177	−	0.335065i
$362$	1.21771e10	−	1.67442e8i	0.709104	−	0.00975057i
$363$	8.56742e9	+	1.17920e10i	0.493428	+	0.679145i
$364$	5.67985e9	+	1.67430e9i	0.323542	+	0.0953734i
$365$	2.83877e9	−	9.65295e9i	0.159940	−	0.543862i
$366$	−2.06712e8	−	1.50330e10i	−0.0115197	−	0.837764i
$367$	−1.01564e10	−	3.30002e9i	−0.559856	−	0.181908i	0.0154005	−	0.999881i	$-0.495098\pi$
$367$	−1.01564e10	−	3.30002e9i	−0.559856	−	0.181908i	−0.575256	+	0.817973i	$0.695098\pi$
$368$	1.38542e10	+	1.70165e10i	0.755425	+	0.927855i
$369$	−3.08870e9	+	9.50605e9i	−0.166598	+	0.512737i
$370$	−3.88573e9	+	1.39172e10i	−0.207332	+	0.742582i
$371$	−2.95845e9	+	9.61260e8i	−0.156160	+	0.0507394i
$372$	6.66489e9	−	5.12813e9i	0.348034	−	0.267786i
$373$	−2.19475e10	−	1.59458e10i	−1.13383	−	0.823778i	−0.147585	−	0.989049i	$-0.547150\pi$
$373$	−2.19475e10	−	1.59458e10i	−1.13383	−	0.823778i	−0.986248	+	0.165271i	$0.947150\pi$
$374$	5.01469e9	−	7.10557e9i	0.256306	−	0.363172i
$375$	9.69891e9	+	2.26828e9i	0.490454	+	0.114702i
$376$	1.90687e10	+	5.33722e9i	0.954049	+	0.267032i
$377$	2.16371e10	+	1.57203e10i	1.07111	+	0.778207i
$378$	−9.69167e8	+	3.12851e9i	−0.0474713	+	0.153240i
$379$	6.41304e9	−	2.08372e9i	0.310819	−	0.100991i	−0.149454	−	0.988769i	$-0.547752\pi$
$379$	6.41304e9	−	2.08372e9i	0.310819	−	0.100991i	0.460273	+	0.887778i	$0.347752\pi$
$380$	8.63913e9	+	1.05972e10i	0.414320	+	0.508225i
$381$	4.93381e9	−	1.51847e10i	0.234144	−	0.720620i
$382$	3.55188e9	−	5.03283e9i	0.166803	−	0.236352i
$383$	1.10067e9	+	3.57630e8i	0.0511521	+	0.0166203i	0.334481	−	0.942402i	$-0.391439\pi$
$383$	1.10067e9	+	3.57630e8i	0.0511521	+	0.0166203i	−0.283329	+	0.959023i	$0.591439\pi$
$384$	5.55606e9	−	9.43782e9i	0.255530	−	0.434057i
$385$	−1.84618e9	+	6.27774e9i	−0.0840293	+	0.285733i
$386$	−3.48704e9	−	1.02503e10i	−0.157075	−	0.461728i
$387$	1.48560e10	+	2.04476e10i	0.662307	+	0.911587i
$388$	−2.61136e9	−	1.78967e9i	−0.115223	−	0.0789670i
$389$	−1.76069e10	−	1.27922e10i	−0.768928	−	0.558659i	0.132708	−	0.991155i	$-0.457633\pi$
$389$	−1.76069e10	−	1.27922e10i	−0.768928	−	0.558659i	−0.901636	+	0.432496i	$0.857633\pi$
$390$	9.02469e8	+	2.15315e10i	0.0390098	+	0.930712i
$391$	4.47435e9	+	6.15841e9i	0.191436	+	0.263488i
$392$	−1.90052e10	−	1.26445e10i	−0.804873	−	0.535498i
$393$	9.74604e9			0.408562
$394$	−2.99684e10	+	2.24093e10i	−1.24359	+	0.929915i
$395$	2.82906e9	+	3.67198e9i	0.116213	+	0.150838i
$396$	−1.82755e10	−	2.37521e10i	−0.743170	−	0.965877i
$397$	6.43475e9	+	1.98041e10i	0.259041	+	0.797248i	0.993006	+	0.118060i	$0.0376676\pi$
$397$	6.43475e9	+	1.98041e10i	0.259041	+	0.797248i	−0.733965	+	0.679187i	$0.762332\pi$
$398$	4.36178e10	−	1.48384e10i	1.73833	−	0.591362i
$399$			1.52670e9i			0.0602368i
$400$	1.05656e10	+	2.33180e10i	0.412719	+	0.910858i
$401$	−1.68962e10			−0.653450			−0.326725	−	0.945119i	$-0.605945\pi$
$401$	−1.68962e10			−0.653450			−0.326725	+	0.945119i	$0.605945\pi$
$402$	5.68757e8	+	1.67188e9i	0.0217782	+	0.0640178i
$403$	−4.04478e10	+	1.31423e10i	−1.53347	+	0.498254i
$404$	2.80302e10	−	2.15672e10i	1.05221	−	0.809594i
$405$	8.15575e9	−	2.29561e8i	0.303141	−	0.00853255i
$406$	2.12449e9	+	2.84113e9i	0.0781900	+	0.104565i
$407$		−	3.45466e10i		−	1.25901i
$408$	2.10449e9	−	3.16313e9i	0.0759464	−	0.114150i
$409$	1.91670e10	−	1.39257e10i	0.684954	−	0.497648i	−0.190044	−	0.981776i	$-0.560863\pi$
$409$	1.91670e10	−	1.39257e10i	0.684954	−	0.497648i	0.874997	+	0.484127i	$0.160863\pi$
$410$	−5.48948e9	+	1.96612e10i	−0.194266	+	0.695786i
$411$	2.37925e9	−	3.27475e9i	0.0833820	−	0.114765i
$412$	1.17128e10	−	1.70905e10i	0.406511	−	0.593153i
$413$	2.09971e9	−	1.52553e9i	0.0721704	−	0.0524349i
$414$	2.48338e10	−	8.44821e9i	0.845359	−	0.287583i
$415$	−6.89034e8	−	2.44797e10i	−0.0232300	−	0.825304i
$416$	−4.24668e10	+	3.55569e10i	−1.41800	+	1.18727i
$417$	5.17036e9	−	1.59127e10i	0.170992	−	0.526260i
$418$	−2.67075e10	−	1.88486e10i	−0.874838	−	0.617409i
$419$	−1.14741e10	−	3.72815e9i	−0.372273	−	0.120959i	0.116905	−	0.993143i	$-0.462703\pi$
$419$	−1.14741e10	−	3.72815e9i	−0.372273	−	0.120959i	−0.489177	+	0.872184i	$0.662703\pi$
$420$	−7.30793e8	+	2.76357e9i	−0.0234854	+	0.0888125i
$421$	−3.14320e9	−	9.67378e9i	−0.100056	−	0.307941i	0.888482	−	0.458911i	$-0.151760\pi$
$421$	−3.14320e9	−	9.67378e9i	−0.100056	−	0.307941i	−0.988538	+	0.150970i	$0.951760\pi$
$422$	−7.05229e9	−	2.18469e9i	−0.222372	−	0.0688876i
$423$	1.39137e10	−	1.91505e10i	0.434590	−	0.598162i
$424$	7.84245e9	−	2.80194e10i	0.242655	−	0.866952i
$425$	3.21506e9	+	8.27839e9i	0.0985448	+	0.253741i
$426$	−2.56578e9	−	1.81078e9i	−0.0779080	−	0.0549829i
$427$	−5.92818e9	+	8.15944e9i	−0.178324	+	0.245442i
$428$	3.07550e10	+	3.99714e10i	0.916516	+	1.19117i
$429$	−1.59217e10	−	4.90021e10i	−0.470069	−	1.44672i
$430$	3.20625e10	+	4.04527e10i	0.937828	+	1.18324i
$431$	−5.42796e10	−	1.76365e10i	−1.57299	−	0.511097i	−0.612755	−	0.790273i	$-0.709939\pi$
$431$	−5.42796e10	−	1.76365e10i	−1.57299	−	0.511097i	−0.960240	+	0.279176i	$0.909939\pi$
$432$	−1.93419e10	−	2.37567e10i	−0.555345	−	0.682106i
$433$	−4.33385e9	+	1.33382e10i	−0.123288	+	0.379443i	−0.993585	−	0.113085i	$-0.963927\pi$
$433$	−4.33385e9	+	1.33382e10i	−0.123288	+	0.379443i	0.870297	+	0.492527i	$0.163927\pi$
$434$	−5.64080e9	+	7.75642e7i	−0.158995	+	0.00218626i
$435$	−7.29200e9	+	1.06546e10i	−0.203652	+	0.297564i
$436$	−2.37374e9	+	8.05261e9i	−0.0656881	+	0.222839i
$437$	2.31474e10	−	1.68176e10i	0.634712	−	0.461145i
$438$	1.44490e8	+	1.05079e10i	0.00392591	+	0.285510i
$439$	−3.33213e10	+	4.58628e10i	−0.897147	+	1.23482i	0.0742218	+	0.997242i	$0.476353\pi$
$439$	−3.33213e10	+	4.58628e10i	−0.897147	+	1.23482i	−0.971369	+	0.237576i	$0.923647\pi$
$440$	−3.93225e10	−	4.69031e10i	−1.04913	−	1.25139i
$441$	−2.20766e10	+	1.60396e10i	−0.583684	+	0.424072i
$442$	−1.53878e10	+	1.15064e10i	−0.403169	+	0.301475i
$443$			7.96140e9i			0.206716i	0.994644	+	0.103358i	$0.0329588\pi$
$443$			7.96140e9i			0.206716i	−0.994644	+	0.103358i	$0.967041\pi$
$444$	−4.14960e8	−	1.50860e10i	−0.0106776	−	0.388188i
$445$	1.20260e10	−	4.08933e10i	0.306677	−	1.04283i
$446$	−7.13401e9	−	2.21001e9i	−0.180299	−	0.0558541i
$447$	1.90624e10	−	6.19374e9i	0.477471	−	0.155140i
$448$	−6.77643e9	+	2.83837e9i	−0.168224	+	0.0704623i
$449$	3.61991e10			0.890662			0.445331	−	0.895366i	$-0.353086\pi$
$449$	3.61991e10			0.890662			0.445331	+	0.895366i	$0.353086\pi$
$450$	3.05279e10	−	2.14135e9i	0.744470	−	0.0522200i
$451$		−	4.88050e10i		−	1.17966i
$452$	−1.05738e10	+	3.58703e10i	−0.253324	+	0.859371i
$453$	4.97639e9	+	1.53157e10i	0.118174	+	0.363702i
$454$	5.80740e10	+	1.79904e10i	1.36697	+	0.423466i
$455$	8.16502e9	−	1.19302e10i	0.190507	−	0.278357i
$456$	−1.18892e10	−	7.91009e9i	−0.274974	−	0.182946i
$457$	−6.09538e10			−1.39745			−0.698725	−	0.715390i	$-0.746249\pi$
$457$	−6.09538e10			−1.39745			−0.698725	+	0.715390i	$0.746249\pi$
$458$	−5.55345e9	+	4.15267e9i	−0.126212	+	0.0943767i
$459$	−6.24662e9	−	8.59774e9i	−0.140732	−	0.193702i
$460$	4.99507e10	−	1.93625e10i	1.11561	−	0.432443i
$461$	7.21419e10	+	5.24142e10i	1.59729	+	1.16050i	0.892462	+	0.451123i	$0.148977\pi$
$461$	7.21419e10	+	5.24142e10i	1.59729	+	1.16050i	0.704830	+	0.709377i	$0.251023\pi$
$462$	−9.39682e7	−	6.83378e9i	−0.00206259	−	0.150001i
$463$	4.45557e10	+	6.13256e10i	0.969570	+	1.33450i	0.942264	+	0.334871i	$0.108693\pi$
$463$	4.45557e10	+	6.13256e10i	0.969570	+	1.33450i	0.0273057	+	0.999627i	$0.491307\pi$
$464$	−3.31326e10	+	1.82409e9i	−0.714799	+	0.0393527i
$465$	−6.89125e9	−	1.93397e10i	−0.147396	−	0.413656i
$466$	7.95476e10	−	1.09382e9i	1.68688	−	0.0231955i
$467$	6.54554e10	+	2.12678e10i	1.37619	+	0.447151i	0.901415	−	0.432956i	$-0.142530\pi$
$467$	6.54554e10	+	2.12678e10i	1.37619	+	0.447151i	0.474775	+	0.880107i	$0.342530\pi$
$468$	2.21841e10	+	6.23842e10i	0.462443	+	1.30044i
$469$	3.66086e8	−	1.12670e9i	0.00756643	−	0.0232871i
$470$	2.67530e10	−	4.02666e10i	0.548252	−	0.825188i
$471$	3.27506e10	−	1.06413e10i	0.665480	−	0.216228i
$472$	1.00108e9	+	2.42555e10i	0.0201698	+	0.488700i
$473$	−9.98418e10	−	7.25393e10i	−1.99466	−	1.44920i
$474$	−3.95556e9	−	2.79160e9i	−0.0783601	−	0.0553019i
$475$	3.11157e10	−	1.20844e10i	0.611231	−	0.237383i
$476$	−2.40136e9	+	8.53932e8i	−0.0467766	+	0.0166340i
$477$	−2.81395e10	−	2.04446e10i	−0.543555	−	0.394916i
$478$	−6.34045e10	−	1.96418e10i	−1.21453	−	0.376244i
$479$	−7.32194e10	+	2.37904e10i	−1.39086	+	0.451918i	−0.906224	−	0.422797i	$-0.861048\pi$
$479$	−7.32194e10	+	2.37904e10i	−1.39086	+	0.451918i	−0.484637	+	0.874715i	$0.661048\pi$
$480$	−1.77349e10	−	2.00096e10i	−0.334091	−	0.376941i
$481$	−2.35854e10	+	7.25883e10i	−0.440618	+	1.35608i
$482$	−5.36129e10	−	3.78368e10i	−0.993302	−	0.701014i
$483$	5.68924e9	+	1.84855e9i	0.104536	+	0.0339658i
$484$	7.54418e10	+	5.17033e10i	1.37477	+	0.942186i
$485$	−6.12254e9	+	4.71708e9i	−0.110653	+	0.0852524i
$486$	−5.45240e10	+	1.85485e10i	−0.977333	+	0.332479i
$487$	−3.12969e10	−	4.30765e10i	−0.556398	−	0.765816i	0.434465	−	0.900689i	$-0.356937\pi$
$487$	−3.12969e10	−	4.30765e10i	−0.556398	−	0.765816i	−0.990863	+	0.134873i	$0.956937\pi$
$488$	−3.28266e10	−	8.84411e10i	−0.578825	−	1.55946i
$489$	−1.12528e10	−	8.17561e9i	−0.196799	−	0.142983i
$490$	−4.36755e10	+	3.46169e10i	−0.757623	+	0.600487i
$491$	−3.84123e10	−	5.28700e10i	−0.660913	−	0.909669i	0.338598	−	0.940931i	$-0.390047\pi$
$491$	−3.84123e10	−	5.28700e10i	−0.660913	−	0.909669i	−0.999511	+	0.0312620i	$0.990047\pi$
$492$	−5.86226e8	−	2.13124e10i	−0.0100047	−	0.363725i
$493$	−1.15113e10			−0.194867
$494$	4.32488e10	+	5.78375e10i	0.726217	+	0.971185i
$495$	−6.89224e10	+	2.45588e10i	−1.14799	+	0.409060i
$496$	2.86219e10	−	4.43296e10i	0.472903	−	0.732431i
$497$	6.51005e8	+	2.00359e9i	0.0106699	+	0.0328385i
$498$	8.23771e9	+	2.42150e10i	0.133934	+	0.393702i
$499$			1.05688e11i			1.70461i	0.523047	+	0.852304i	$0.324795\pi$
$499$			1.05688e11i			1.70461i	−0.523047	+	0.852304i	$0.675205\pi$
$500$	6.21090e10	−	6.98032e9i	0.993744	−	0.111685i
$501$	5.28118e10			0.838262
$502$	−3.04362e10	+	1.03541e10i	−0.479265	+	0.163041i
$503$	−5.75444e10	+	1.86973e10i	−0.898940	+	0.292083i	−0.721800	−	0.692102i	$-0.756685\pi$
$503$	−5.75444e10	+	1.86973e10i	−0.898940	+	0.292083i	−0.177141	+	0.984186i	$0.556685\pi$
$504$	3.62172e8	+	8.77516e9i	0.00561298	+	0.135998i
$505$	−2.89822e10	−	8.13363e10i	−0.445621	−	1.25060i
$506$	−1.02577e11	+	7.67032e10i	−1.56476	+	1.17007i
$507$			8.05509e10i			1.21910i
$508$	−2.75462e9	−	1.00145e11i	−0.0413625	−	1.50375i
$509$	1.01616e11	−	7.38283e10i	1.51388	−	1.09990i	0.549456	−	0.835523i	$-0.314835\pi$
$509$	1.01616e11	−	7.38283e10i	1.51388	−	1.09990i	0.964421	−	0.264373i	$-0.0851649\pi$
$510$	−5.76147e9	−	7.26915e9i	−0.0851634	−	0.107449i
$511$	4.14374e9	−	5.70337e9i	0.0607727	−	0.0836465i
$512$	1.30061e10	−	6.74775e10i	0.189264	−	0.981926i
$513$	−3.23160e10	+	2.34790e10i	−0.466604	+	0.339008i
$514$	5.39156e9	+	1.58487e10i	0.0772435	+	0.227060i
$515$	−3.08718e10	−	4.00701e10i	−0.438868	−	0.569629i
$516$	−4.44708e10	−	3.04776e10i	−0.627301	−	0.429914i
$517$	−3.57171e10	+	1.09926e11i	−0.499935	+	1.53864i
$518$	−5.83758e9	+	8.27156e9i	−0.0810801	+	0.114886i
$519$	−1.43366e9	−	4.65826e8i	−0.0197596	−	0.00642028i
$520$	5.06020e10	+	1.25397e11i	0.692076	+	1.71504i
$521$	4.02676e9	+	1.23931e10i	0.0546518	+	0.168201i	0.974657	−	0.223706i	$-0.0718155\pi$
$521$	4.02676e9	+	1.23931e10i	0.0546518	+	0.168201i	−0.920005	+	0.391907i	$0.871816\pi$
$522$	−1.17381e10	+	3.78911e10i	−0.158094	+	0.510335i
$523$	−3.58209e10	+	4.93032e10i	−0.478773	+	0.658975i	−0.978269	−	0.207342i	$-0.933519\pi$
$523$	−3.58209e10	+	4.93032e10i	−0.478773	+	0.658975i	0.499496	+	0.866316i	$0.333519\pi$
$524$	5.76189e10	−	2.04895e10i	0.764258	−	0.271773i
$525$	5.86787e9	+	3.77802e9i	0.0772402	+	0.0497310i
$526$	−6.83198e10	+	9.68057e10i	−0.892490	+	1.26461i
$527$	1.07595e10	−	1.48091e10i	0.139492	−	0.191994i
$528$	5.37048e10	+	3.46752e10i	0.690999	+	0.446152i
$529$	−1.04440e10	−	3.21434e10i	−0.133366	−	0.410459i
$530$	−5.91672e10	−	3.93105e10i	−0.749855	−	0.498201i
$531$	2.76000e10	+	8.96778e9i	0.347161	+	0.112799i
$532$	3.20965e9	+	9.02590e9i	0.0400692	+	0.112679i
$533$	−3.33198e10	+	1.02548e11i	−0.412851	+	1.27062i
$534$	6.12109e8	+	4.45153e10i	0.00752773	+	0.547449i
$535$	1.15986e11	−	4.13289e10i	1.41577	−	0.504474i
$536$	6.87738e9	+	8.68849e9i	0.0833228	+	0.105265i
$537$	−4.49087e10	+	3.26281e10i	−0.540050	+	0.392369i
$538$	9.19477e10	−	1.26433e9i	1.09752	−	0.0150915i
$539$	7.83185e10	−	1.07796e11i	0.927917	−	1.27717i
$540$	−6.97360e10	+	2.70319e10i	−0.820129	+	0.317908i
$541$	3.68706e10	−	2.67881e10i	0.430419	−	0.312718i	−0.351398	−	0.936226i	$-0.614293\pi$
$541$	3.68706e10	−	2.67881e10i	0.430419	−	0.312718i	0.781816	+	0.623509i	$0.214293\pi$
$542$	−1.28509e10	−	1.71858e10i	−0.148914	−	0.199146i
$543$			3.10536e10i			0.357201i
$544$	5.79185e9	−	2.31249e10i	0.0661335	−	0.264049i
$545$	1.69141e10	+	1.15760e10i	0.191718	+	0.131211i
$546$	−4.46806e9	+	1.44231e10i	−0.0502745	+	0.162288i
$547$	−1.03816e11	+	3.37320e10i	−1.15962	+	0.376784i	−0.824760	−	0.565483i	$-0.808690\pi$
$547$	−1.03816e11	+	3.37320e10i	−1.15962	+	0.376784i	−0.334863	+	0.942267i	$0.608690\pi$
$548$	7.18153e9	−	2.43624e10i	0.0796333	−	0.270146i
$549$	−1.12773e11			−1.24141
$550$	−1.38536e11	+	5.60068e10i	−1.51395	+	0.612055i
$551$			4.32672e10i			0.469410i
$552$	−4.38724e10	+	3.47272e10i	−0.472537	+	0.374037i
$553$	1.00363e9	+	3.08885e9i	0.0107318	+	0.0330290i
$554$	−2.69132e10	+	8.68770e10i	−0.285711	+	0.922286i
$555$	−3.53481e10	−	1.03953e10i	−0.372558	−	0.109563i
$556$	−2.88669e9	−	1.04946e11i	−0.0302065	−	1.09817i
$557$	9.35906e10			0.972325			0.486163	−	0.873868i	$-0.338396\pi$
$557$	9.35906e10			0.972325			0.486163	+	0.873868i	$0.338396\pi$
$558$	−3.77749e10	−	5.05172e10i	−0.389643	−	0.521077i
$559$	1.60261e11	+	2.20581e11i	1.64128	+	2.25902i
$560$	1.48951e9	+	1.78747e10i	0.0151458	+	0.181755i
$561$	1.79411e10	+	1.30350e10i	0.181133	+	0.131601i
$562$	8.70810e10	−	1.19741e9i	0.872928	−	0.0120032i
$563$	−8.80346e10	−	1.21169e11i	−0.876233	−	1.20603i	−0.977450	−	0.211167i	$-0.932273\pi$
$563$	−8.80346e10	−	1.21169e11i	−0.876233	−	1.20603i	0.101216	−	0.994864i	$-0.467727\pi$
$564$	−1.42767e10	+	4.84320e10i	−0.141095	+	0.478648i
$565$	7.53435e10	+	5.15650e10i	0.739353	+	0.506013i
$566$	−9.07048e7	−	6.59645e9i	−0.000883822	−	0.0642754i
$567$	5.43681e9	+	1.76653e9i	0.0526032	+	0.0170918i
$568$	−1.89759e10	−	5.31123e9i	−0.182309	−	0.0510272i
$569$	−3.30947e10	+	1.01855e11i	−0.315726	+	0.971704i	0.659729	+	0.751504i	$0.270671\pi$
$569$	−3.30947e10	+	1.01855e11i	−0.315726	+	0.971704i	−0.975455	+	0.220200i	$0.929329\pi$
$570$	−2.73223e10	+	2.16555e10i	−0.258832	+	0.205148i
$571$	1.47109e11	−	4.77985e10i	1.38386	−	0.449645i	0.479926	−	0.877309i	$-0.340663\pi$
$571$	1.47109e11	−	4.77985e10i	1.38386	−	0.449645i	0.903938	+	0.427664i	$0.140663\pi$
$572$	−1.97149e11	−	2.56229e11i	−1.84167	−	2.39356i
$573$	1.27076e10	+	9.23259e9i	0.117881	+	0.0856456i
$574$	−8.24693e9	+	1.16855e10i	−0.0759705	+	0.107646i
$575$	−7.35699e9	−	1.30584e11i	−0.0673022	−	1.19459i
$576$	−7.02129e10	−	4.26452e10i	−0.637863	−	0.387418i
$577$	6.84246e10	+	4.97133e10i	0.617318	+	0.448508i	0.851984	−	0.523569i	$-0.175400\pi$
$577$	6.84246e10	+	4.97133e10i	0.617318	+	0.448508i	−0.234666	+	0.972076i	$0.575400\pi$
$578$	−3.05801e10	+	9.87140e10i	−0.273986	+	0.884438i
$579$	2.62572e10	−	8.53147e9i	0.233633	−	0.0759118i
$580$	−2.07109e10	+	7.83206e10i	−0.183015	+	0.692093i
$581$	5.30228e9	−	1.63187e10i	0.0465327	−	0.143213i
$582$	4.65463e9	−	6.59537e9i	0.0405689	−	0.0574841i
$583$	1.61524e11	+	5.24823e10i	1.39818	+	0.454295i
$584$	2.29455e10	+	6.18194e10i	0.197263	+	0.531464i
$585$	1.61584e11	−	4.54814e9i	1.37967	−	0.0388339i
$586$	−6.72166e10	−	1.97585e11i	−0.570015	−	1.67558i
$587$	4.11794e10	+	5.66785e10i	0.346838	+	0.477382i	0.946423	−	0.322929i	$-0.104668\pi$
$587$	4.11794e10	+	5.66785e10i	0.346838	+	0.477382i	−0.599585	+	0.800311i	$0.704668\pi$
$588$	3.29057e10	−	4.80137e10i	0.275272	−	0.401658i
$589$	−5.56626e10	−	4.04412e10i	−0.462490	−	0.336018i
$590$	5.70847e10	+	1.59382e10i	0.471098	+	0.131532i
$591$	−5.60858e10	−	7.71955e10i	−0.459730	−	0.632764i
$592$	−3.41692e10	−	8.83165e10i	−0.278194	−	0.719043i
$593$	−2.09456e10			−0.169385			−0.0846925	−	0.996407i	$-0.526991\pi$
$593$	−2.09456e10			−0.169385			−0.0846925	+	0.996407i	$0.526991\pi$
$594$	1.43207e11	−	1.07085e11i	1.15032	−	0.860167i
$595$	1.75072e8	+	6.21987e9i	0.00139685	+	0.0496265i
$596$	9.96760e10	−	7.66932e10i	0.789961	−	0.607816i
$597$	3.63038e10	+	1.11732e11i	0.285795	+	0.879587i
$598$	2.67897e11	−	9.11361e10i	2.09490	−	0.712665i
$599$		−	9.63751e10i		−	0.748613i	−0.927305	−	0.374307i	$-0.877881\pi$
$599$		−	9.63751e10i		−	0.748613i	0.927305	−	0.374307i	$-0.122119\pi$
$600$	−5.98237e10	+	2.61214e10i	−0.461603	+	0.201554i
$601$	9.12544e10			0.699449			0.349725	−	0.936853i	$-0.386275\pi$
$601$	9.12544e10			0.699449			0.349725	+	0.936853i	$0.386275\pi$
$602$	1.16478e10	+	3.42392e10i	0.0886870	+	0.260698i
$603$	1.25982e10	−	4.09339e9i	0.0952880	−	0.0309609i
$604$	6.16195e10	+	8.00851e10i	0.462989	+	0.601733i
$605$	1.76879e11	−	1.36276e11i	1.32025	−	1.01718i
$606$	5.40066e10	+	7.22242e10i	0.400457	+	0.535540i
$607$			8.58393e10i			0.632312i	0.948707	+	0.316156i	$0.102392\pi$
$607$			8.58393e10i			0.632312i	−0.948707	+	0.316156i	$0.897608\pi$
$608$	−8.69188e10	−	2.17696e10i	−0.636062	−	0.159308i
$609$	−7.31845e9	+	5.31717e9i	−0.0532047	+	0.0386555i
$610$	−2.30112e11	+	9.64491e9i	−1.66196	+	0.0696592i
$611$	1.50095e11	−	2.06589e11i	1.07697	−	1.48232i
$612$	−2.35072e10	−	1.61104e10i	−0.167570	−	0.114842i
$613$	9.22797e9	−	6.70451e9i	0.0653528	−	0.0474816i	−0.554629	−	0.832098i	$-0.687140\pi$
$613$	9.22797e9	−	6.70451e9i	0.0653528	−	0.0474816i	0.619982	+	0.784616i	$0.287140\pi$
$614$	5.92136e10	−	2.01439e10i	0.416627	−	0.141733i
$615$	−4.99374e10	−	1.46857e10i	−0.349080	−	0.102659i
$616$	−1.49225e10	−	4.02040e10i	−0.103638	−	0.279220i
$617$	−5.48704e10	+	1.68874e11i	−0.378615	+	1.16526i	0.562392	+	0.826871i	$0.309881\pi$
$617$	−5.48704e10	+	1.68874e11i	−0.378615	+	1.16526i	−0.941007	+	0.338387i	$0.890119\pi$
$618$	4.31647e10	+	3.04631e10i	0.295920	+	0.208843i
$619$	−1.86024e11	−	6.04428e10i	−1.26708	−	0.411701i	−0.403071	−	0.915169i	$-0.632057\pi$
$619$	−1.86024e11	−	6.04428e10i	−1.26708	−	0.411701i	−0.864014	+	0.503468i	$0.832057\pi$
$620$	−8.14001e10	−	9.98494e10i	−0.550881	−	0.675739i
$621$	4.83656e10	+	1.48854e11i	0.325215	+	1.00091i
$622$	−4.34095e10	−	1.34476e10i	−0.290017	−	0.0898428i
$623$	1.75543e10	−	2.41615e10i	0.116529	−	0.160388i
$624$	−8.91698e10	−	1.09523e11i	−0.588138	−	0.722384i
$625$	3.05538e10	−	1.49498e11i	0.200237	−	0.979747i
$626$	−5.12247e10	−	3.61514e10i	−0.333566	−	0.235412i
$627$	4.89941e10	−	6.74346e10i	0.317011	−	0.436328i
$628$	1.71251e11	−	1.31765e11i	1.10102	−	0.847150i
$629$	−1.01514e10	−	3.12428e10i	−0.0648520	−	0.199594i
$630$	2.06521e10	+	5.76614e9i	0.131100	+	0.0366035i
$631$	8.84234e10	+	2.87305e10i	0.557763	+	0.181228i	0.574314	−	0.818635i	$-0.305269\pi$
$631$	8.84234e10	+	2.87305e10i	0.557763	+	0.181228i	−0.0165514	+	0.999863i	$0.505269\pi$
$632$	−2.92543e10	−	8.18810e9i	−0.183367	−	0.0513233i
$633$	5.81752e9	−	1.79045e10i	0.0362345	−	0.111518i
$634$	−2.48403e11	+	3.41568e9i	−1.53745	+	0.0211407i
$635$	−2.34651e11	−	6.90067e10i	−1.44320	−	0.424421i
$636$	7.11654e10	+	2.09781e10i	0.434951	+	0.128214i
$637$	−2.38154e11	+	1.73029e11i	−1.44644	+	1.05090i
$638$	−2.66309e9	−	1.93672e11i	−0.0160732	−	1.16892i
$639$	−1.38459e10	+	1.90573e10i	−0.0830459	+	0.114303i
$640$	−1.46917e11	−	8.10124e10i	−0.875691	−	0.482872i
$641$	5.27702e10	−	3.83398e10i	0.312577	−	0.227100i	−0.420425	−	0.907327i	$-0.638119\pi$
$641$	5.27702e10	−	3.83398e10i	0.312577	−	0.227100i	0.733001	+	0.680227i	$0.238119\pi$
$642$	−1.02992e11	+	7.70139e10i	−0.606268	+	0.453345i
$643$			1.69187e10i			0.0989743i	0.998775	+	0.0494871i	$0.0157587\pi$
$643$			1.69187e10i			0.0989743i	−0.998775	+	0.0494871i	$0.984241\pi$
$644$	3.75212e10	−	1.03207e9i	0.218139	−	0.00600020i
$645$	−1.04265e11	+	8.03308e10i	−0.602422	+	0.464134i
$646$	−2.96919e10	−	9.19811e9i	−0.170494	−	0.0528164i
$647$	8.67093e10	−	2.81735e10i	0.494821	−	0.160777i	−0.0509669	−	0.998700i	$-0.516230\pi$
$647$	8.67093e10	−	2.81735e10i	0.494821	−	0.160777i	0.545788	+	0.837923i	$0.316230\pi$
$648$	−4.19259e10	+	3.31864e10i	−0.237784	+	0.188218i
$649$	−1.41701e11			−0.798720
$650$	3.29323e11	−	2.31000e10i	1.84488	−	0.129407i
$651$		−	1.43850e10i		−	0.0800911i
$652$	−8.37147e10	−	2.46773e10i	−0.463245	−	0.136555i
$653$	1.66640e10	+	5.12864e10i	0.0916485	+	0.282065i	0.986366	−	0.164568i	$-0.0526230\pi$
$653$	1.66640e10	+	5.12864e10i	0.0916485	+	0.282065i	−0.894717	+	0.446633i	$0.852623\pi$
$654$	−2.04483e10	−	6.33459e9i	−0.111776	−	0.0346264i
$655$	−4.20073e9	−	1.49242e11i	−0.0228223	−	0.810820i
$656$	−4.82719e10	−	1.24767e11i	−0.260663	−	0.673730i
$657$	7.88269e10			0.423071
$658$	2.71268e10	−	2.02844e10i	0.144709	−	0.108208i
$659$	1.83356e10	+	2.52369e10i	0.0972198	+	0.133812i	0.854856	−	0.518866i	$-0.173646\pi$
$659$	1.83356e10	+	2.52369e10i	0.0972198	+	0.133812i	−0.757636	+	0.652678i	$0.773646\pi$
$660$	1.20967e11	−	9.86153e10i	0.637514	−	0.519719i
$661$	7.94128e10	+	5.76968e10i	0.415992	+	0.302236i	0.776023	−	0.630704i	$-0.217234\pi$
$661$	7.94128e10	+	5.76968e10i	0.415992	+	0.302236i	−0.360031	+	0.932940i	$0.617234\pi$
$662$	−2.28555e9	−	1.66215e11i	−0.0119003	−	0.865442i
$663$	−2.87982e10	−	3.96373e10i	−0.149043	−	0.205140i
$664$	9.96099e10	+	1.25842e11i	0.512425	+	0.647369i
$665$	2.33784e10	−	6.58037e8i	0.119544	−	0.00336483i
$666$	−1.13191e11	+	1.55644e9i	−0.575329	+	0.00791110i
$667$	1.61235e11	+	5.23884e10i	0.814621	+	0.264687i
$668$	3.12225e11	−	1.11028e11i	1.56806	−	0.557607i
$669$	5.88493e9	−	1.81119e10i	0.0293790	−	0.0904192i
$670$	2.53564e10	−	9.43002e9i	0.125831	−	0.0467965i
$671$	5.23698e11	−	1.70160e11i	2.58339	−	0.839395i
$672$	−6.99934e9	−	1.73772e10i	−0.0343226	−	0.0852125i
$673$	5.60823e9	+	4.07462e9i	0.0273379	+	0.0198622i	0.601370	−	0.798970i	$-0.294622\pi$
$673$	5.60823e9	+	4.07462e9i	0.0273379	+	0.0198622i	−0.574032	+	0.818833i	$0.694622\pi$
$674$	2.38376e9	+	1.68232e9i	0.0115511	+	0.00815207i
$675$	1.02711e10	+	1.82308e11i	0.0494767	+	0.878196i
$676$	1.69346e11	+	4.76220e11i	0.810938	+	2.28045i
$677$	−9.43088e10	−	6.85193e10i	−0.448949	−	0.326181i	0.340231	−	0.940342i	$-0.389495\pi$
$677$	−9.43088e10	−	6.85193e10i	−0.448949	−	0.326181i	−0.789181	+	0.614161i	$0.789495\pi$
$678$	−9.10869e10	−	2.82174e10i	−0.431059	−	0.133536i
$679$	−5.15024e9	+	1.67341e9i	−0.0242297	+	0.00787271i
$680$	−4.93443e10	−	3.08629e10i	−0.230782	−	0.144345i
$681$	−4.79059e10	+	1.47439e11i	−0.222741	+	0.685527i
$682$	2.51645e11	+	1.77596e11i	1.16319	+	0.820910i
$683$	2.09100e11	+	6.79408e10i	0.960886	+	0.312211i	0.747131	−	0.664676i	$-0.231431\pi$
$683$	2.09100e11	+	6.79408e10i	0.960886	+	0.312211i	0.213755	+	0.976887i	$0.431431\pi$
$684$	−6.05538e10	+	8.83558e10i	−0.276641	+	0.403655i
$685$	−5.11719e10	−	3.50220e10i	−0.232418	−	0.159067i
$686$	−7.52061e10	+	2.55844e10i	−0.339591	+	0.115526i
$687$	−1.03933e10	−	1.43051e10i	−0.0466578	−	0.0642190i
$688$	−3.26987e11	−	8.66918e10i	−1.45941	−	0.386923i
$689$	−3.03559e11	−	2.20548e11i	−1.34699	−	0.978649i
$690$	4.76168e10	+	1.28037e11i	0.210070	+	0.564858i
$691$	5.06644e10	+	6.97336e10i	0.222224	+	0.305865i	0.905543	−	0.424255i	$-0.139464\pi$
$691$	5.06644e10	+	6.97336e10i	0.222224	+	0.305865i	−0.683319	+	0.730120i	$0.739464\pi$
$692$	−9.45520e9	+	2.60078e8i	−0.0412331	+	0.00113417i
$693$	−5.12647e10			−0.222272
$694$	2.73511e11	+	3.65771e11i	1.17906	+	1.57678i
$695$	−2.45901e11	−	7.23152e10i	−1.05395	−	0.309949i
$696$	−3.48924e9	−	8.45415e10i	−0.0148694	−	0.360274i
$697$	−1.43412e10	−	4.41376e10i	−0.0607651	−	0.187016i
$698$	−1.06768e11	−	3.13847e11i	−0.449799	−	1.32220i
$699$			2.02859e11i			0.849739i
$700$	4.26337e10	+	9.99952e9i	0.177567	+	0.0416473i
$701$	3.94363e11			1.63314			0.816571	−	0.577245i	$-0.195872\pi$
$701$	3.94363e11			1.63314			0.816571	+	0.577245i	$0.195872\pi$
$702$	−3.74011e11	+	1.27235e11i	−1.54005	+	0.523911i
$703$	−1.17431e11	+	3.81557e10i	−0.480798	+	0.156221i
$704$	3.90404e11	+	9.20948e10i	1.58936	+	0.374925i
$705$	1.01729e11	+	6.96231e10i	0.411801	+	0.281836i
$706$	8.36830e10	−	6.25751e10i	0.336836	−	0.251874i
$707$		−	6.04982e10i		−	0.242139i
$708$	−6.18788e10	+	1.70206e9i	−0.246269	+	0.00677394i
$709$	1.21590e11	−	8.83402e10i	0.481185	−	0.349601i	−0.320599	−	0.947215i	$-0.603884\pi$
$709$	1.21590e11	−	8.83402e10i	0.481185	−	0.349601i	0.801784	+	0.597613i	$0.203884\pi$
$710$	−2.66227e10	+	4.00705e10i	−0.104765	+	0.157685i
$711$	−2.13457e10	+	2.93798e10i	−0.0835278	+	0.114966i
$712$	9.72052e10	+	2.61889e11i	0.378242	+	1.01905i
$713$	−2.18101e11	+	1.58460e11i	−0.843916	+	0.613141i
$714$	−2.09306e9	−	6.15262e9i	−0.00805359	−	0.0236738i
$715$	−7.43509e11	+	2.64931e11i	−2.84487	+	1.01370i
$716$	−1.96906e11	+	2.87312e11i	−0.749217	+	1.09321i
$717$	5.23031e10	−	1.60972e11i	0.197902	−	0.609081i
$718$	2.83791e11	−	4.02117e11i	1.06783	−	1.51306i
$719$	−9.60619e10	−	3.12124e10i	−0.359448	−	0.116792i	0.123725	−	0.992316i	$-0.460516\pi$
$719$	−9.60619e10	−	3.12124e10i	−0.359448	−	0.116792i	−0.483173	+	0.875525i	$0.660516\pi$
$720$	−1.51906e11	+	1.30953e11i	−0.565255	+	0.487287i
$721$	−1.09520e10	−	3.37067e10i	−0.0405277	−	0.124731i
$722$	4.58375e10	−	1.47965e11i	0.168683	−	0.544517i
$723$	9.83514e10	−	1.35369e11i	0.359938	−	0.495412i
$724$	6.52853e10	+	1.83590e11i	0.237608	+	0.668181i
$725$	1.66297e11	+	1.07070e11i	0.601913	+	0.387541i
$726$	−1.34472e11	+	1.90540e11i	−0.484043	+	0.685865i
$727$	−2.38436e11	+	3.28179e11i	−0.853561	+	1.17483i	0.129506	+	0.991579i	$0.458661\pi$
$727$	−2.38436e11	+	3.28179e11i	−0.853561	+	1.17483i	−0.983067	+	0.183247i	$0.941339\pi$
$728$	3.90698e9	+	9.46631e10i	0.0139096	+	0.337020i
$729$	−1.89139e10	−	5.82111e10i	−0.0669687	−	0.206108i
$730$	1.60846e11	−	6.74170e9i	0.566395	−	0.0237398i
$731$	−1.11609e11	−	3.62640e10i	−0.390868	−	0.127001i
$732$	2.26647e11	−	8.05967e10i	0.789416	−	0.280720i
$733$	1.10613e11	−	3.40432e11i	0.383169	−	1.17927i	−0.554631	−	0.832097i	$-0.687140\pi$
$733$	1.10613e11	−	3.40432e11i	0.383169	−	1.17927i	0.937800	−	0.347177i	$-0.112860\pi$
$734$	−2.34927e9	−	1.70849e11i	−0.00809373	−	0.588612i
$735$	−8.67306e10	−	1.12572e11i	−0.297182	−	0.385728i
$736$	−1.86367e11	+	2.97544e11i	−0.635122	+	1.01400i
$737$	−5.23274e10	+	3.80181e10i	−0.177362	+	0.128861i
$738$	−1.59909e11	+	2.19884e9i	−0.539073	+	0.00741255i
$739$	−1.35860e11	+	1.86995e11i	−0.455526	+	0.626978i	−0.973574	−	0.228374i	$-0.926659\pi$
$739$	−1.35860e11	+	1.86995e11i	−0.455526	+	0.626978i	0.518047	+	0.855352i	$0.326659\pi$
$740$	−2.30834e11	+	1.28567e10i	−0.769790	+	0.0428747i
$741$	−1.48983e11	+	1.08243e11i	−0.494157	+	0.359026i
$742$	−2.98057e10	−	3.98598e10i	−0.0983294	−	0.131498i
$743$			1.90045e11i			0.623595i	0.950149	+	0.311797i	$0.100931\pi$
$743$			1.90045e11i			0.623595i	−0.950149	+	0.311797i	$0.899069\pi$
$744$	1.12023e11	+	7.45309e10i	0.365607	+	0.243245i
$745$	−1.03061e11	−	2.89233e11i	−0.334557	−	0.938908i
$746$	1.28442e11	−	4.14618e11i	0.414718	−	1.33873i
$747$	1.82468e11	−	5.92875e10i	0.586010	−	0.190406i
$748$	1.33472e11	+	3.93448e10i	0.426368	+	0.125684i
$749$	8.62709e10			0.274118
$750$	1.56201e10	+	1.58603e11i	0.0493671	+	0.501263i
$751$		−	6.82448e9i		−	0.0214541i	−0.999942	−	0.0107270i	$-0.996585\pi$
$751$		−	6.82448e9i		−	0.0214541i	0.999942	−	0.0107270i	$-0.00341459\pi$
$752$	1.74162e10	+	3.16346e11i	0.0544606	+	0.989217i
$753$	−2.53326e10	−	7.79656e10i	−0.0787951	−	0.242506i
$754$	−1.26626e11	+	4.08755e11i	−0.391776	+	1.26467i
$755$	2.32386e11	−	8.28050e10i	0.715191	−	0.254841i
$756$	−5.23833e10	+	1.44087e9i	−0.160363	+	0.00441101i
$757$	−1.08744e11			−0.331147			−0.165573	−	0.986197i	$-0.552947\pi$
$757$	−1.08744e11			−0.331147			−0.165573	+	0.986197i	$0.552947\pi$
$758$	6.46097e10	+	8.64039e10i	0.195714	+	0.261732i
$759$	−1.91972e11	−	2.64227e11i	−0.578457	−	0.796177i
$760$	−1.16003e11	+	1.85469e11i	−0.347709	+	0.555925i
$761$	5.45393e10	+	3.96251e10i	0.162619	+	0.118150i	0.666119	−	0.745846i	$-0.267954\pi$
$761$	5.45393e10	+	3.96251e10i	0.162619	+	0.118150i	−0.503500	+	0.863995i	$0.667954\pi$
$762$	2.55434e11	−	3.51236e9i	0.757633	−	0.0104179i
$763$	8.44094e9	+	1.16180e10i	0.0249054	+	0.0342793i
$764$	9.45377e10	+	2.78677e10i	0.277480	+	0.0817952i
$765$	−5.51146e10	+	4.24628e10i	−0.160924	+	0.123983i
$766$	2.54596e8	+	1.85153e10i	0.000739496	+	0.0537794i
$767$	2.97738e11	+	9.67410e10i	0.860307	+	0.279531i
$768$	1.71590e11	+	3.55271e10i	0.493227	+	0.102121i
$769$	1.89471e11	−	5.83133e11i	0.541799	−	1.66749i	−0.186683	−	0.982420i	$-0.559774\pi$
$769$	1.89471e11	−	5.83133e11i	0.541799	−	1.66749i	0.728482	−	0.685065i	$-0.240226\pi$
$770$	−1.04605e11	+	4.38443e9i	−0.297572	+	0.0124724i
$771$	−4.05980e10	+	1.31911e10i	−0.114891	+	0.0373304i
$772$	1.37297e11	−	1.05640e11i	0.386538	−	0.297412i
$773$	2.58712e11	+	1.87965e11i	0.724600	+	0.526453i	0.887851	−	0.460132i	$-0.152198\pi$
$773$	2.58712e11	+	1.87965e11i	0.724600	+	0.526453i	−0.163251	+	0.986585i	$0.552198\pi$
$774$	−2.33176e11	+	3.30398e11i	−0.649710	+	0.920607i
$775$	−2.93180e11	+	1.13862e11i	−0.812696	+	0.315625i
$776$	1.36526e10	−	4.87777e10i	0.0376502	−	0.134516i
$777$	−2.08852e10	−	1.51740e10i	−0.0572999	−	0.0416308i
$778$	1.03041e11	−	3.32619e11i	0.281248	−	0.907882i
$779$	−1.65899e11	+	5.39037e10i	−0.450498	+	0.146376i
$780$	−3.21497e11	+	1.24622e11i	−0.868558	+	0.336680i
$781$	3.55432e10	−	1.09391e11i	0.0955327	−	0.294019i
$782$	−7.02280e10	+	9.95096e10i	−0.187795	+	0.266096i
$783$	−2.25100e11	−	7.31393e10i	−0.598863	−	0.194582i
$784$	9.35984e10	−	3.53038e11i	0.247745	−	0.934452i
$785$	−1.77067e11	−	4.96924e11i	−0.466293	−	1.30861i
$786$	5.02216e10	+	1.47628e11i	0.131583	+	0.386793i
$787$	1.28302e11	+	1.76593e11i	0.334453	+	0.460335i	0.942811	−	0.333327i	$-0.108171\pi$
$787$	1.28302e11	+	1.76593e11i	0.334453	+	0.460335i	−0.608358	+	0.793663i	$0.708171\pi$
$788$	−4.93872e11	−	3.38471e11i	−1.28088	−	0.877841i
$789$	−2.44428e11	−	1.77587e11i	−0.630729	−	0.458252i
$790$	−4.10430e10	+	6.17749e10i	−0.105373	+	0.158600i
$791$	3.76001e10	+	5.17521e10i	0.0960468	+	0.132197i
$792$	2.65611e11	−	3.99223e11i	0.675065	−	1.01465i
$793$	−1.21655e12			−3.07635
$794$	−2.66824e11	+	1.99521e11i	−0.671341	+	0.502004i
$795$	1.02303e11	−	1.49479e11i	0.256107	−	0.374207i
$796$	4.49528e11	+	5.84238e11i	1.11971	+	1.45525i
$797$	3.98917e10	+	1.22774e11i	0.0988666	+	0.304280i	0.988242	−	0.152897i	$-0.0488604\pi$
$797$	3.98917e10	+	1.22774e11i	0.0988666	+	0.304280i	−0.889375	+	0.457177i	$0.848860\pi$
$798$	−2.31257e10	+	7.86712e9i	−0.0570273	+	0.0194001i
$799$			1.09909e11i			0.269677i
$800$	−2.98764e11	+	2.80201e11i	−0.729404	+	0.684083i
$801$	3.33939e11			0.811216
$802$	−8.70667e10	−	2.55935e11i	−0.210453	−	0.618633i
$803$	−3.66059e11	+	1.18940e11i	−0.880419	+	0.286065i
$804$	−2.23940e10	+	1.72305e10i	−0.0535928	+	0.0412357i
$805$	2.58547e10	−	8.79163e10i	0.0615681	−	0.209356i
$806$	−4.07501e11	−	5.44960e11i	−0.965581	−	1.29129i
$807$			2.34481e11i			0.552859i
$808$	4.71129e11	+	3.13451e11i	1.10534	+	0.735401i
$809$	−5.51671e11	+	4.00813e11i	−1.28791	+	0.935723i	−0.999761	−	0.0218615i	$-0.993041\pi$
$809$	−5.51671e11	+	4.00813e11i	−1.28791	+	0.935723i	−0.288152	+	0.957585i	$0.593041\pi$
$810$	4.55041e10	+	1.22356e11i	0.105709	+	0.284241i
$811$	−1.33731e11	+	1.84065e11i	−0.309135	+	0.425488i	−0.935111	−	0.354354i	$-0.884701\pi$
$811$	−1.33731e11	+	1.84065e11i	−0.309135	+	0.425488i	0.625976	+	0.779842i	$0.284701\pi$
$812$	−3.20884e10	+	4.68212e10i	−0.0738115	+	0.107701i
$813$	4.42687e10	−	3.21631e10i	0.101329	−	0.0736200i
$814$	5.23294e11	−	1.78020e11i	1.19192	−	0.405480i
$815$	−1.20343e11	+	1.75838e11i	−0.272767	+	0.398550i
$816$	5.87580e10	+	1.55781e10i	0.132528	+	0.0351361i
$817$	−1.36304e11	+	4.19501e11i	−0.305929	+	0.941553i
$818$	3.09707e11	+	2.18573e11i	0.691732	+	0.488184i
$819$	1.07716e11	+	3.49990e10i	0.239411	+	0.0777893i
$820$	−3.26106e11	+	1.81630e10i	−0.721279	+	0.0401728i
$821$	−2.75767e10	−	8.48724e10i	−0.0606973	−	0.186807i	0.916110	−	0.400927i	$-0.131312\pi$
$821$	−2.75767e10	−	8.48724e10i	−0.0606973	−	0.186807i	−0.976807	+	0.214119i	$0.931312\pi$
$822$	6.18646e10	+	1.91647e10i	0.135505	+	0.0419774i
$823$	2.02375e11	−	2.78545e11i	0.441120	−	0.607150i	−0.529340	−	0.848410i	$-0.677561\pi$
$823$	2.02375e11	−	2.78545e11i	0.441120	−	0.607150i	0.970461	+	0.241260i	$0.0775605\pi$
$824$	3.19235e11	+	8.93519e10i	0.692471	+	0.193818i
$825$	−1.37942e11	−	3.55185e11i	−0.297771	−	0.766723i
$826$	3.39278e10	+	2.39443e10i	0.0728846	+	0.0514376i
$827$	−1.19932e11	+	1.65072e11i	−0.256396	+	0.352899i	−0.917738	−	0.397185i	$-0.869987\pi$
$827$	−1.19932e11	+	1.65072e11i	−0.256396	+	0.352899i	0.661342	+	0.750084i	$0.269987\pi$
$828$	2.55938e11	+	3.32635e11i	0.544520	+	0.707697i
$829$	6.69431e10	+	2.06030e11i	0.141738	+	0.436226i	0.996577	−	0.0826678i	$-0.0263440\pi$
$829$	6.69431e10	+	2.06030e11i	0.141738	+	0.436226i	−0.854839	+	0.518894i	$0.826344\pi$
$830$	3.67255e11	−	1.36582e11i	0.773848	−	0.287793i
$831$	−2.20565e11	−	7.16658e10i	−0.462522	−	0.150282i
$832$	−7.57431e11	−	4.60040e11i	−1.58070	−	0.960069i
$833$	3.91531e10	−	1.20501e11i	0.0813179	−	0.250271i
$834$	2.67681e11	−	3.68076e9i	0.553290	−	0.00760804i
$835$	−2.27629e10	−	8.08709e11i	−0.0468254	−	1.66359i
$836$	1.47884e11	−	5.01678e11i	0.302758	−	1.02707i
$837$	3.04490e11	−	2.21225e11i	0.620399	−	0.450746i
$838$	−2.65405e9	−	1.93014e11i	−0.00538188	−	0.391394i
$839$	−3.01679e11	+	4.15225e11i	−0.608831	+	0.837984i	−0.996481	−	0.0838229i	$-0.973287\pi$
$839$	−3.01679e11	+	4.15225e11i	−0.608831	+	0.837984i	0.387650	+	0.921807i	$0.373287\pi$
$840$	−4.56270e10	+	3.17109e9i	−0.0916442	+	0.00636930i
$841$	1.97300e11	−	1.43347e11i	0.394406	−	0.286553i
$842$	1.30336e11	−	9.74608e10i	0.259309	−	0.193902i
$843$			2.22070e11i			0.439724i
$844$	−3.24801e9	−	1.18082e11i	−0.00640099	−	0.232710i
$845$	1.23348e12	−	3.47190e10i	2.41939	−	0.0680989i
$846$	3.61780e11	+	1.12074e11i	0.706257	+	0.218788i
$847$	1.48790e11	−	4.83448e10i	0.289094	−	0.0939325i
$848$	4.64836e11	−	2.55912e10i	0.898909	−	0.0494888i
$849$	1.68220e10			0.0323778
$850$	−1.08830e11	+	9.13589e10i	−0.208483	+	0.175015i
$851$			4.83806e11i			0.922472i
$852$	1.42072e10	−	4.81962e10i	0.0269619	−	0.0914649i
$853$	−1.59091e11	−	4.89631e11i	−0.300503	−	0.924853i	−0.981317	−	0.192397i	$-0.938374\pi$
$853$	−1.59091e11	−	4.89631e11i	−0.300503	−	0.924853i	0.680814	−	0.732456i	$-0.261626\pi$
$854$	−1.54143e11	−	4.77512e10i	−0.289796	−	0.0897745i
$855$	1.59603e11	+	2.07157e11i	0.298661	+	0.387647i
$856$	−4.46984e11	+	6.71834e11i	−0.832525	+	1.25132i
$857$	−8.38332e11			−1.55415			−0.777075	−	0.629408i	$-0.783297\pi$
$857$	−8.38332e11			−1.55415			−0.777075	+	0.629408i	$0.783297\pi$
$858$	6.60213e11	−	4.93683e11i	1.21825	−	0.910960i
$859$	−6.74135e10	−	9.27868e10i	−0.123815	−	0.170417i	0.742610	−	0.669725i	$-0.233588\pi$
$859$	−6.74135e10	−	9.27868e10i	−0.123815	−	0.170417i	−0.866425	+	0.499307i	$0.833588\pi$
$860$	−4.47537e11	+	6.94120e11i	−0.818155	+	1.26894i
$861$	−2.95051e10	−	2.14367e10i	−0.0536889	−	0.0390073i
$862$	−1.25554e10	−	9.13080e11i	−0.0227405	−	1.65379i
$863$	−2.23736e11	−	3.07946e11i	−0.403359	−	0.555176i	0.558224	−	0.829690i	$-0.311483\pi$
$863$	−2.23736e11	−	3.07946e11i	−0.403359	−	0.555176i	−0.961583	+	0.274514i	$0.911483\pi$
$864$	2.60186e11	−	4.15400e11i	0.466905	−	0.745437i
$865$	−6.51528e9	+	2.21546e10i	−0.0116377	+	0.0395730i
$866$	−2.24373e11	+	3.08525e9i	−0.398932	+	0.00548554i
$867$	−2.50617e11	−	8.14303e10i	−0.443541	−	0.144115i
$868$	−3.02421e10	−	8.50443e10i	−0.0532762	−	0.149819i
$869$	5.47954e10	−	1.68643e11i	0.0960870	−	0.295725i
$870$	−1.98966e11	−	5.55521e10i	−0.347298	−	0.0969668i
$871$	1.35904e11	−	4.41580e10i	0.236135	−	0.0767249i
$872$	−1.34209e11	+	5.53912e9i	−0.232121	+	0.00958021i
$873$	−4.89869e10	−	3.55910e10i	−0.0843379	−	0.0612751i
$874$	3.74023e11	+	2.63964e11i	0.640992	+	0.452375i
$875$	5.53239e10	−	9.14834e10i	0.0943801	−	0.156067i
$876$	−1.58424e11	+	5.63363e10i	−0.269033	+	0.0956691i
$877$	3.43316e10	+	2.49434e10i	0.0580358	+	0.0421654i	0.616425	−	0.787414i	$-0.288580\pi$
$877$	3.43316e10	+	2.49434e10i	0.0580358	+	0.0421654i	−0.558389	+	0.829579i	$0.688580\pi$
$878$	−8.66412e11	−	2.68401e11i	−1.45796	−	0.451655i
$879$	5.06136e11	−	1.64453e11i	0.847835	−	0.275478i
$880$	5.07835e11	−	8.37330e11i	0.846821	−	1.39626i
$881$	−1.58252e11	+	4.87051e11i	−0.262692	+	0.808483i	0.729524	+	0.683955i	$0.239742\pi$
$881$	−1.58252e11	+	4.87051e11i	−0.262692	+	0.808483i	−0.992216	+	0.124528i	$0.960258\pi$
$882$	−3.56721e11	−	2.51753e11i	−0.589460	−	0.416006i
$883$	3.66664e11	+	1.19136e11i	0.603150	+	0.195975i	0.594645	−	0.803988i	$-0.297293\pi$
$883$	3.66664e11	+	1.19136e11i	0.603150	+	0.195975i	0.00850527	+	0.999964i	$0.497293\pi$
$884$	−2.53587e11	−	1.73793e11i	−0.415258	−	0.284593i
$885$	−4.26387e10	+	1.44989e11i	−0.0695074	+	0.236353i
$886$	−1.20595e11	+	4.10253e10i	−0.195702	+	0.0665759i
$887$	−4.77374e10	−	6.57049e10i	−0.0771196	−	0.106146i	0.768714	−	0.639592i	$-0.220897\pi$
$887$	−4.77374e10	−	6.57049e10i	−0.0771196	−	0.106146i	−0.845834	+	0.533446i	$0.820897\pi$
$888$	2.26377e11	−	8.40241e10i	0.364066	−	0.135130i
$889$	−1.38641e11	−	1.00729e11i	−0.221966	−	0.161268i
$890$	6.81401e11	−	2.85602e10i	1.08603	−	0.0455199i
$891$	−1.83454e11	−	2.52503e11i	−0.291083	−	0.400642i
$892$	−3.28564e9	−	1.19451e11i	−0.00518992	−	0.188681i
$893$	4.13110e11			0.649621
$894$	1.92048e11	+	2.56830e11i	0.300650	+	0.402065i
$895$	5.18992e11	+	6.73626e11i	0.808851	+	1.04985i
$896$	−7.79133e10	−	8.80197e10i	−0.120887	−	0.136568i
$897$	2.22975e11	+	6.86247e11i	0.344419	+	1.06001i
$898$	1.86535e11	+	5.48326e11i	0.286850	+	0.843206i
$899$		−	4.07674e11i		−	0.624130i
$900$	1.89747e11	+	4.51387e11i	0.289205	+	0.687984i
$901$	1.61498e11			0.245058
$902$	7.39273e11	−	2.51494e11i	1.11681	−	0.379927i
$903$	−8.77074e10	+	2.84979e10i	−0.131912	+	0.0428609i
$904$	−5.97831e11	+	2.46740e10i	−0.895169	+	0.0369458i
$905$	4.75525e11	−	1.33847e10i	0.708890	−	0.0199533i
$906$	−2.06352e11	+	1.54302e11i	−0.306263	+	0.229013i
$907$		−	1.02567e12i		−	1.51558i	−0.652501	−	0.757788i	$-0.726280\pi$
$907$		−	1.02567e12i		−	1.51558i	0.652501	−	0.757788i	$-0.273720\pi$
$908$	2.67466e10	+	9.72380e11i	0.0393482	+	1.43052i
$909$	5.47269e11	−	3.97614e11i	0.801577	−	0.582379i
$910$	2.22787e11	+	6.22029e10i	0.324881	+	0.0907079i
$911$	1.90138e11	−	2.61702e11i	0.276055	−	0.379957i	−0.648367	−	0.761328i	$-0.724548\pi$
$911$	1.90138e11	−	2.61702e11i	0.276055	−	0.379957i	0.924422	+	0.381371i	$0.124548\pi$
$912$	5.85529e10	−	2.20852e11i	0.0846386	−	0.319243i
$913$	−7.57895e11	+	5.50643e11i	−1.09075	+	0.792478i
$914$	−3.14097e11	−	9.23297e11i	−0.450068	−	1.32299i
$915$	−1.65238e10	−	5.87050e11i	−0.0235736	−	0.837511i
$916$	−9.15195e10	−	6.27220e10i	−0.129997	−	0.0890918i
$917$	3.23256e10	−	9.94879e10i	0.0457161	−	0.140700i
$918$	9.80451e10	−	1.38925e11i	0.138056	−	0.195618i
$919$	4.19858e11	+	1.36420e11i	0.588627	+	0.191256i	0.588162	−	0.808743i	$-0.299852\pi$
$919$	4.19858e11	+	1.36420e11i	0.588627	+	0.191256i	0.000465282		1.00000i	$0.499852\pi$
$920$	5.50690e11	+	6.56853e11i	0.768698	+	0.916889i
$921$	4.92844e10	+	1.51682e11i	0.0684969	+	0.210812i
$922$	−4.22194e11	+	1.36286e12i	−0.584236	+	1.88594i
$923$	−1.49364e11	+	2.05583e11i	−0.205798	+	0.283256i
$924$	1.03030e11	−	3.66380e10i	0.141344	−	0.0502625i
$925$	−1.43948e11	+	5.45768e11i	−0.196625	+	0.745489i
$926$	−6.99332e11	+	9.90919e11i	−0.951130	+	1.34770i
$927$	2.32932e11	−	3.20604e11i	0.315436	−	0.434160i
$928$	−1.98364e11	−	4.92477e11i	−0.267467	−	0.664039i
$929$	−2.08018e11	−	6.40215e11i	−0.279280	−	0.859534i	−0.988055	−	0.154100i	$-0.950752\pi$
$929$	−2.08018e11	−	6.40215e11i	−0.279280	−	0.859534i	0.708776	−	0.705434i	$-0.249248\pi$
$930$	2.57438e11	−	2.04043e11i	0.344144	−	0.272766i
$931$	−4.52922e11	−	1.47163e11i	−0.602872	−	0.195885i
$932$	4.26479e11	+	1.19931e12i	0.565242	+	1.58953i
$933$	3.58090e10	−	1.10209e11i	0.0472569	−	0.145442i
$934$	1.51404e10	+	1.10108e12i	0.0198953	+	1.44687i
$935$	1.91872e11	−	2.80351e11i	0.251053	−	0.366823i
$936$	−8.30648e11	+	6.57500e11i	−1.08222	+	0.856628i
$937$	2.43192e11	−	1.76689e11i	0.315494	−	0.229220i	−0.418756	−	0.908099i	$-0.637534\pi$
$937$	2.43192e11	−	1.76689e11i	0.315494	−	0.229220i	0.734250	+	0.678879i	$0.237534\pi$
$938$	1.89531e10	−	2.60615e8i	0.0244832	−	0.000336657i
$939$	9.39703e10	−	1.29339e11i	0.120873	−	0.166367i
$940$	7.47796e11	+	1.97745e11i	0.957793	+	0.253276i
$941$	−8.30687e10	+	6.03529e10i	−0.105945	+	0.0769733i	−0.639496	−	0.768794i	$-0.720857\pi$
$941$	−8.30687e10	+	6.03529e10i	−0.105945	+	0.0769733i	0.533552	+	0.845768i	$0.320857\pi$
$942$	3.29953e11	+	4.41254e11i	0.419034	+	0.560383i
$943$			6.83487e11i			0.864338i
$944$	−3.62251e11	+	1.40153e11i	−0.456165	+	0.176488i
$945$	−3.60957e10	+	1.22740e11i	−0.0452614	+	0.153907i
$946$	5.84301e11	−	1.88615e12i	0.729579	−	2.35511i
$947$	−3.11484e11	+	1.01207e11i	−0.387290	+	0.125838i	−0.496189	−	0.868215i	$-0.665268\pi$
$947$	−3.11484e11	+	1.01207e11i	−0.387290	+	0.125838i	0.108899	+	0.994053i	$0.465268\pi$
$948$	2.19027e10	−	7.43020e10i	0.0271184	−	0.0919956i
$949$	8.50355e11			1.04842
$950$	3.43388e11	+	4.09054e11i	0.421590	+	0.502211i
$951$		−	6.33468e11i		−	0.774467i
$952$	−2.53092e10	−	3.19742e10i	−0.0308127	−	0.0389271i
$953$	4.10733e11	+	1.26411e12i	0.497952	+	1.53254i	0.812305	+	0.583233i	$0.198213\pi$
$953$	4.10733e11	+	1.26411e12i	0.497952	+	1.53254i	−0.314353	+	0.949306i	$0.601787\pi$
$954$	1.64680e11	−	5.31595e11i	0.198814	−	0.641781i
$955$	1.35902e11	−	1.98571e11i	0.163385	−	0.238728i
$956$	−2.92016e10	−	1.06163e12i	−0.0349603	−	1.27099i
$957$	4.93893e11			0.588824
$958$	−7.37666e11	−	9.86497e11i	−0.875786	−	1.17121i
$959$	−2.55373e10	−	3.51491e10i	−0.0301926	−	0.0415566i
$960$	2.11706e11	−	3.71750e11i	0.249258	−	0.437689i
$961$	−1.65537e11	−	1.20269e11i	−0.194089	−	0.141014i
$962$	−1.22107e12	+	1.67903e10i	−1.42574	+	0.0196046i
$963$	5.67001e11	+	7.80410e11i	0.659294	+	0.907440i
$964$	2.96864e11	−	1.00707e12i	0.343756	−	1.16615i
$965$	−1.41960e11	−	3.98400e11i	−0.163703	−	0.459420i
$966$	1.31597e9	+	9.57033e10i	0.00151126	+	0.109905i
$967$	6.35562e11	+	2.06507e11i	0.726862	+	0.236172i	0.648996	−	0.760792i	$-0.275189\pi$
$967$	6.35562e11	+	2.06507e11i	0.726862	+	0.236172i	0.0778663	+	0.996964i	$0.475189\pi$
$968$	−3.94421e11	+	1.40918e12i	−0.449220	+	1.60497i
$969$	2.44932e10	−	7.53823e10i	0.0277812	−	0.0855016i
$970$	−1.03002e11	−	6.84338e10i	−0.116347	−	0.0773008i
$971$	1.32019e12	−	4.28956e11i	1.48511	−	0.482543i	0.549478	−	0.835508i	$-0.314827\pi$
$971$	1.32019e12	−	4.28956e11i	1.48511	−	0.482543i	0.935636	+	0.352966i	$0.114827\pi$
$972$	−5.61927e11	−	7.30320e11i	−0.629527	−	0.818179i
$973$	−1.45289e11	−	1.05558e11i	−0.162099	−	0.117772i
$974$	4.91227e11	−	6.96043e11i	0.545816	−	0.773393i
$975$	4.73517e10	+	8.40479e11i	0.0523983	+	0.930054i
$976$	1.17050e12	−	9.52980e11i	1.28995	−	1.05023i
$977$	3.51951e11	+	2.55707e11i	0.386282	+	0.280650i	0.763930	−	0.645299i	$-0.223267\pi$
$977$	3.51951e11	+	2.55707e11i	0.386282	+	0.280650i	−0.377649	+	0.925949i	$0.623267\pi$
$978$	6.58542e10	−	2.12580e11i	0.0719827	−	0.232363i
$979$	−1.55076e12	+	5.03871e11i	−1.68816	+	0.548515i
$980$	−7.49419e11	−	4.83192e11i	−0.812495	−	0.523860i
$981$	−4.96199e10	+	1.52714e11i	−0.0535771	+	0.164893i
$982$	6.02908e11	−	8.54291e11i	0.648344	−	0.918670i
$983$	1.33745e12	+	4.34565e11i	1.43240	+	0.465415i	0.919519	−	0.393044i	$-0.128578\pi$
$983$	1.33745e12	+	4.34565e11i	1.43240	+	0.465415i	0.512881	+	0.858460i	$0.328578\pi$
$984$	3.19809e11	−	1.18703e11i	0.341122	−	0.126614i
$985$	−1.15792e12	+	8.92117e11i	−1.23009	+	0.947713i
$986$	−5.93181e10	−	1.74367e11i	−0.0627595	−	0.184484i
$987$	5.07677e10	+	6.98757e10i	0.0534957	+	0.0736305i
$988$	−6.53231e11	+	9.53149e11i	−0.685550	+	1.00031i
$989$	1.39823e12	+	1.01587e12i	1.46148	+	1.06183i
$990$	−7.27163e11	−	9.17449e11i	−0.756992	−	0.955083i
$991$	−9.24175e11	−	1.27202e12i	−0.958208	−	1.31886i	−0.947784	−	0.318914i	$-0.896682\pi$
$991$	−9.24175e11	−	1.27202e12i	−0.958208	−	1.31886i	−0.0104239	−	0.999946i	$-0.503318\pi$
$992$	8.18971e11	+	2.05119e11i	0.845711	+	0.211816i
$993$	4.23875e11			0.435954
$994$	−2.69947e10	+	2.01856e10i	−0.0276524	+	0.0206774i
$995$	1.69530e12	−	6.04081e11i	1.72964	−	0.616315i
$996$	−3.24348e11	+	2.49561e11i	−0.329589	+	0.253595i
$997$	−1.19356e11	−	3.67340e11i	−0.120799	−	0.371782i	0.872313	−	0.488948i	$-0.162619\pi$
$997$	−1.19356e11	−	3.67340e11i	−0.120799	−	0.371782i	−0.993112	+	0.117166i	$0.962619\pi$
$998$	−1.60091e12	+	5.44614e11i	−1.61378	+	0.548993i
$999$		−	6.75440e11i		−	0.678148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.91.70	yes	464
4.3	odd	2	inner	100.9.j.b.91.116	yes	464
25.11	even	5	inner	100.9.j.b.11.116	yes	464
100.11	odd	10	inner	100.9.j.b.11.70	✓	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.70	✓	464	100.11	odd	10	inner
100.9.j.b.11.116	yes	464	25.11	even	5	inner
100.9.j.b.91.70	yes	464	1.1	even	1	trivial
100.9.j.b.91.116	yes	464	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(5.15303 + 15.1475i) q^{2} +(-38.8019 + 12.6075i) q^{3} +(-202.893 + 156.111i) q^{4} +(209.784 + 588.741i) q^{5} +(-390.919 - 522.784i) q^{6} +437.907i q^{7} +(-3410.20 - 2268.87i) q^{8} +(-3961.32 + 2878.07i) q^{9} +(-7836.93 + 6211.49i) q^{10} +(14053.1 - 19342.4i) q^{11} +(5904.45 - 8615.36i) q^{12} +(-42733.3 + 31047.5i) q^{13} +(-6633.19 + 2256.55i) q^{14} +(-15562.5 - 20199.4i) q^{15} +(16794.9 - 63347.5i) q^{16} +(7025.45 - 21622.1i) q^{17} +(-64008.3 - 45173.3i) q^{18} +(-81270.3 - 26406.3i) q^{19} +(-134472. - 86701.7i) q^{20} +(-5520.91 - 16991.6i) q^{21} +(365405. + 113197. i) q^{22} +(-196806. + 270880. i) q^{23} +(160927. + 45042.4i) q^{24} +(-302607. + 247016. i) q^{25} +(-690498. - 487313. i) q^{26} +(274760. - 378175. i) q^{27} +(-68362.0 - 88848.1i) q^{28} +(-156464. - 481548. i) q^{29} +(225776. - 339821. i) q^{30} +(765749. + 248807. i) q^{31} +(1.04610e6 - 72031.2i) q^{32} +(-301427. + 927697. i) q^{33} +(363723. - 5001.39i) q^{34} +(-257814. + 91865.7i) q^{35} +(354426. - 1.20234e6i) q^{36} +(1.16899e6 - 849318. i) q^{37} +(-18798.5 - 1.36711e6i) q^{38} +(1.26670e6 - 1.74346e6i) q^{39} +(620374. - 2.48369e6i) q^{40} +(1.65146e6 - 1.19986e6i) q^{41} +(228931. - 171186. i) q^{42} -5.16180e6i q^{43} +(168291. + 6.11828e6i) q^{44} +(-2.52546e6 - 1.72842e6i) q^{45} +(-5.11730e6 - 1.58526e6i) q^{46} +(-4.59776e6 + 1.49390e6i) q^{47} +(146981. + 2.66974e6i) q^{48} +5.57304e6 q^{49} +(-5.30102e6 - 3.31085e6i) q^{50} +927551. i q^{51} +(3.82341e6 - 1.29704e7i) q^{52} +(2.19512e6 + 6.75590e6i) q^{53} +(7.14424e6 + 2.21318e6i) q^{54} +(1.43358e7 + 4.21591e6i) q^{55} +(993555. - 1.49335e6i) q^{56} +3.48636e6 q^{57} +(6.48798e6 - 4.85147e6i) q^{58} +(-3.48368e6 - 4.79488e6i) q^{59} +(6.31087e6 + 1.66883e6i) q^{60} +(1.86328e7 + 1.35375e7i) q^{61} +(177125. + 1.28813e7i) q^{62} +(-1.26033e6 - 1.73469e6i) q^{63} +(6.48167e6 + 1.54746e7i) q^{64} +(-2.72437e7 - 1.86456e7i) q^{65} +(-1.56055e7 + 214585. i) q^{66} +(-2.57291e6 - 835989. i) q^{67} +(1.95003e6 + 5.48371e6i) q^{68} +(4.22132e6 - 1.29919e7i) q^{69} +(-2.72006e6 - 3.43185e6i) q^{70} +(4.57537e6 - 1.48663e6i) q^{71} +(2.00389e7 - 827053. i) q^{72} +(-1.30242e7 - 9.46260e6i) q^{73} +(1.88889e7 + 1.33306e7i) q^{74} +(8.62745e6 - 1.33998e7i) q^{75} +(2.06115e7 - 7.32952e6i) q^{76} +(8.47019e6 + 6.15395e6i) q^{77} +(3.29364e7 + 1.02032e7i) q^{78} +(7.05366e6 - 2.29187e6i) q^{79} +(4.08185e7 - 3.40143e6i) q^{80} +(4.03402e6 - 1.24154e7i) q^{81} +(2.66849e7 + 1.88326e7i) q^{82} +(-3.72653e7 - 1.21082e7i) q^{83} +(3.77273e6 + 2.58560e6i) q^{84} +(1.42036e7 - 399792. i) q^{85} +(7.81883e7 - 2.65989e7i) q^{86} +(1.21422e7 + 1.67123e7i) q^{87} +(-9.18093e7 + 3.40768e7i) q^{88} +(-5.51749e7 - 4.00869e7i) q^{89} +(1.31675e7 - 4.71609e7i) q^{90} +(-1.35959e7 - 1.87132e7i) q^{91} +(-2.35683e6 - 8.56831e7i) q^{92} -3.28493e7 q^{93} +(-4.63213e7 - 6.19464e7i) q^{94} +(-1.50269e6 - 5.33867e7i) q^{95} +(-3.96825e7 + 1.59836e7i) q^{96} +(3.82139e6 + 1.17610e7i) q^{97} +(2.87180e7 + 8.44175e7i) q^{98} +1.17067e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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