LMFDB - Embedded newform 100.9.j.b.11.116

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			11.116
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.116

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(15.9985 - 0.219988i) q^{2} +(38.8019 + 12.6075i) q^{3} +(255.903 - 7.03895i) q^{4} +(209.784 - 588.741i) q^{5} +(623.545 + 193.165i) q^{6} +437.907i q^{7} +(4092.52 - 168.908i) q^{8} +(-3961.32 - 2878.07i) q^{9} +(3226.70 - 9465.11i) q^{10} +(-14053.1 - 19342.4i) q^{11} +(10018.3 + 2953.17i) q^{12} +(-42733.3 - 31047.5i) q^{13} +(96.3343 + 7005.85i) q^{14} +(15562.5 - 20199.4i) q^{15} +(65436.9 - 3602.58i) q^{16} +(7025.45 + 21622.1i) q^{17} +(-64008.3 - 45173.3i) q^{18} +(81270.3 - 26406.3i) q^{19} +(49540.2 - 152137. i) q^{20} +(-5520.91 + 16991.6i) q^{21} +(-229083. - 306358. 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} +(3082.41 + 112062. i) q^{28} +(-156464. + 481548. i) q^{29} +(244533. - 326583. i) q^{30} +(-765749. + 248807. i) q^{31} +(1.04610e6 - 72031.2i) q^{32} +(-301427. - 927697. i) q^{33} +(117153. + 344375. i) q^{34} +(257814. + 91865.7i) q^{35} +(-1.03397e6 - 708624. i) q^{36} +(1.16899e6 + 849318. i) q^{37} +(1.29439e6 - 440340. i) q^{38} +(-1.26670e6 - 1.74346e6i) q^{39} +(759099. - 2.44487e6i) q^{40} +(1.65146e6 + 1.19986e6i) q^{41} +(-84588.3 + 273055. i) q^{42} -5.16180e6i q^{43} +(-3.73238e6 - 4.85087e6i) q^{44} +(-2.52546e6 + 1.72842e6i) q^{45} +(3.20819e6 + 4.29038e6i) q^{46} +(4.59776e6 + 1.49390e6i) q^{47} +(2.58449e6 + 685208. i) q^{48} +5.57304e6 q^{49} +(-4.89559e6 - 3.88532e6i) q^{50} +927551. i q^{51} +(-1.11541e7 - 7.64437e6i) q^{52} +(2.19512e6 - 6.75590e6i) q^{53} +(-4.47894e6 - 5.98978e6i) q^{54} +(-1.43358e7 + 4.21591e6i) q^{55} +(73966.1 + 1.79214e6i) q^{56} +3.48636e6 q^{57} +(-2.39726e6 + 7.73846e6i) q^{58} +(3.48368e6 - 4.79488e6i) q^{59} +(3.84032e6 - 5.27864e6i) q^{60} +(1.86328e7 - 1.35375e7i) q^{61} +(-1.21961e7 + 4.14899e6i) q^{62} +(1.26033e6 - 1.73469e6i) q^{63} +(1.67202e7 - 1.38252e6i) q^{64} +(-2.72437e7 + 1.86456e7i) q^{65} +(-5.02646e6 - 1.47754e7i) q^{66} +(2.57291e6 - 835989. i) q^{67} +(1.95003e6 + 5.48371e6i) q^{68} +(4.22132e6 + 1.29919e7i) q^{69} +(4.14484e6 + 1.41300e6i) q^{70} +(-4.57537e6 - 1.48663e6i) q^{71} +(-1.66979e7 - 1.11094e7i) 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} +(-2.06488e7 - 2.76141e7i) q^{78} +(-7.05366e6 - 2.29187e6i) q^{79} +(1.16066e7 - 3.92811e7i) q^{80} +(4.03402e6 + 1.24154e7i) q^{81} +(2.66849e7 + 1.88326e7i) q^{82} +(3.72653e7 - 1.21082e7i) q^{83} +(-1.29322e6 + 4.38707e6i) q^{84} +(1.42036e7 + 399792. i) q^{85} +(-1.13553e6 - 8.25810e7i) q^{86} +(-1.21422e7 + 1.67123e7i) q^{87} +(-6.07796e7 - 7.67855e7i) q^{88} +(-5.51749e7 + 4.00869e7i) q^{89} +(-4.00233e7 + 2.82077e7i) q^{90} +(1.35959e7 - 1.87132e7i) q^{91} +(5.22700e7 + 6.79338e7i) q^{92} -3.28493e7 q^{93} +(7.38859e7 + 2.28887e7i) q^{94} +(1.50269e6 - 5.33867e7i) q^{95} +(4.14987e7 + 1.03937e7i) q^{96} +(3.82139e6 - 1.17610e7i) q^{97} +(8.91602e7 - 1.22600e6i) 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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	15.9985	−	0.219988i	0.999905	−	0.0137492i
$2$	15.9985	−	0.219988i	0.999905	−	0.0137492i
$3$	38.8019	+	12.6075i	0.479035	+	0.155648i	0.538574	−	0.842578i	$-0.318963\pi$
$3$	38.8019	+	12.6075i	0.479035	+	0.155648i	−0.0595390	+	0.998226i	$0.518963\pi$
$4$	255.903	−	7.03895i	0.999622	−	0.0274959i
$5$	209.784	−	588.741i	0.335654	−	0.941985i
$5$	209.784	−	588.741i	0.335654	−	0.941985i
$6$	623.545	+	193.165i	0.481130	+	0.149047i
$7$			437.907i			0.182385i	0.995833	+	0.0911926i	$0.0290679\pi$
$7$			437.907i			0.182385i	−0.995833	+	0.0911926i	$0.970932\pi$
$8$	4092.52	−	168.908i	0.999149	−	0.0412374i
$9$	−3961.32	−	2878.07i	−0.603768	−	0.438663i
$10$	3226.70	−	9465.11i	0.322670	−	0.946511i
$11$	−14053.1	−	19342.4i	−0.959846	−	1.32111i	−0.947013	−	0.321197i	$-0.895915\pi$
$11$	−14053.1	−	19342.4i	−0.959846	−	1.32111i	−0.0128332	−	0.999918i	$-0.504085\pi$
$12$	10018.3	+	2953.17i	0.483134	+	0.142418i
$13$	−42733.3	−	31047.5i	−1.49621	−	1.08706i	−0.971860	−	0.235558i	$-0.924308\pi$
$13$	−42733.3	−	31047.5i	−1.49621	−	1.08706i	−0.524350	−	0.851503i	$-0.675692\pi$
$14$	96.3343	+	7005.85i	0.00250766	+	0.182368i
$15$	15562.5	−	20199.4i	0.307408	−	0.399001i
$16$	65436.9	−	3602.58i	0.998488	−	0.0549710i
$17$	7025.45	+	21622.1i	0.0841159	+	0.258882i	0.984265	−	0.176700i	$-0.0565424\pi$
$17$	7025.45	+	21622.1i	0.0841159	+	0.258882i	−0.900149	+	0.435583i	$0.856542\pi$
$18$	−64008.3	−	45173.3i	−0.609743	−	0.430321i
$19$	81270.3	−	26406.3i	0.623616	−	0.202625i	0.0198709	−	0.999803i	$-0.493674\pi$
$19$	81270.3	−	26406.3i	0.623616	−	0.202625i	0.603745	+	0.797177i	$0.293674\pi$
$20$	49540.2	−	152137.i	0.309626	−	0.950858i
$21$	−5520.91	+	16991.6i	−0.0283879	+	0.0873690i
$22$	−229083.	−	306358.i	−0.977919	−	1.30779i
$23$	196806.	+	270880.i	0.703278	+	0.967979i	0.999916	+	0.0129886i	$0.00413453\pi$
$23$	196806.	+	270880.i	0.703278	+	0.967979i	−0.296638	+	0.954990i	$0.595865\pi$
$24$	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
$28$	3082.41	+	112062.i	0.00501485	+	0.182316i
$29$	−156464.	+	481548.i	−0.221220	+	0.680844i	0.777434	+	0.628965i	$0.216521\pi$
$29$	−156464.	+	481548.i	−0.221220	+	0.680844i	−0.998653	+	0.0518792i	$0.983479\pi$
$30$	244533.	−	326583.i	0.301893	−	0.403190i
$31$	−765749.	+	248807.i	−0.829163	+	0.269411i	−0.692693	−	0.721233i	$-0.743576\pi$
$31$	−765749.	+	248807.i	−0.829163	+	0.269411i	−0.136470	+	0.990644i	$0.543576\pi$
$32$	1.04610e6	−	72031.2i	0.997638	−	0.0686943i
$33$	−301427.	−	927697.i	−0.254171	−	0.782259i
$34$	117153.	+	344375.i	0.0876674	+	0.257701i
$35$	257814.	+	91865.7i	0.171804	+	0.0612183i
$36$	−1.03397e6	−	708624.i	−0.615602	−	0.421896i
$37$	1.16899e6	+	849318.i	0.623738	+	0.453173i	0.854225	−	0.519903i	$-0.174032\pi$
$37$	1.16899e6	+	849318.i	0.623738	+	0.453173i	−0.230487	+	0.973075i	$0.574032\pi$
$38$	1.29439e6	−	440340.i	0.620771	−	0.211180i
$39$	−1.26670e6	−	1.74346e6i	−0.547539	−	0.753623i
$40$	759099.	−	2.44487e6i	0.296523	−	0.955026i
$41$	1.65146e6	+	1.19986e6i	0.584431	+	0.424614i	0.840319	−	0.542092i	$-0.182368\pi$
$41$	1.65146e6	+	1.19986e6i	0.584431	+	0.424614i	−0.255888	+	0.966706i	$0.582368\pi$
$42$	−84588.3	+	273055.i	−0.0271840	+	0.0877511i
$43$		−	5.16180e6i		−	1.50983i	−0.655823	−	0.754914i	$-0.727678\pi$
$43$		−	5.16180e6i		−	1.50983i	0.655823	−	0.754914i	$-0.272322\pi$
$44$	−3.73238e6	−	4.85087e6i	−0.995808	−	1.29422i
$45$	−2.52546e6	+	1.72842e6i	−0.615872	+	0.421502i
$46$	3.20819e6	+	4.29038e6i	0.716520	+	0.958218i
$47$	4.59776e6	+	1.49390e6i	0.942226	+	0.306148i	0.739553	−	0.673099i	$-0.235037\pi$
$47$	4.59776e6	+	1.49390e6i	0.942226	+	0.306148i	0.202673	+	0.979246i	$0.435037\pi$
$48$	2.58449e6	+	685208.i	0.486867	+	0.129080i
$49$	5.57304e6			0.966736
$50$	−4.89559e6	−	3.88532e6i	−0.783295	−	0.621651i
$51$			927551.i			0.137106i
$52$	−1.11541e7	−	7.64437e6i	−1.52553	−	1.04551i
$53$	2.19512e6	−	6.75590e6i	0.278199	−	0.856208i	−0.710156	−	0.704044i	$-0.751376\pi$
$53$	2.19512e6	−	6.75590e6i	0.278199	−	0.856208i	0.988355	−	0.152164i	$-0.0486243\pi$
$54$	−4.47894e6	−	5.98978e6i	−0.526745	−	0.704427i
$55$	−1.43358e7	+	4.21591e6i	−1.56665	+	0.460724i
$56$	73966.1	+	1.79214e6i	0.00752109	+	0.182230i
$57$	3.48636e6			0.330272
$58$	−2.39726e6	+	7.73846e6i	−0.211838	+	0.683821i
$59$	3.48368e6	−	4.79488e6i	0.287495	−	0.395703i	−0.640703	−	0.767789i	$-0.721357\pi$
$59$	3.48368e6	−	4.79488e6i	0.287495	−	0.395703i	0.928199	+	0.372085i	$0.121357\pi$
$60$	3.84032e6	−	5.27864e6i	0.296321	−	0.407302i
$61$	1.86328e7	−	1.35375e7i	1.34573	−	0.977732i	0.346521	−	0.938042i	$-0.387363\pi$
$61$	1.86328e7	−	1.35375e7i	1.34573	−	0.977732i	0.999212	−	0.0396904i	$-0.0126372\pi$
$62$	−1.21961e7	+	4.14899e6i	−0.825380	+	0.280786i
$63$	1.26033e6	−	1.73469e6i	0.0800058	−	0.110118i
$64$	1.67202e7	−	1.38252e6i	0.996599	−	0.0824045i
$65$	−2.72437e7	+	1.86456e7i	−1.52620	+	1.04453i
$66$	−5.02646e6	−	1.47754e7i	−0.264903	−	0.778690i
$67$	2.57291e6	−	835989.i	0.127681	−	0.0414860i	−0.244480	−	0.969654i	$-0.578617\pi$
$67$	2.57291e6	−	835989.i	0.127681	−	0.0414860i	0.372160	+	0.928168i	$0.378617\pi$
$68$	1.95003e6	+	5.48371e6i	0.0912023	+	0.256471i
$69$	4.22132e6	+	1.29919e7i	0.186231	+	0.573160i
$70$	4.14484e6	+	1.41300e6i	0.172630	+	0.0588503i
$71$	−4.57537e6	−	1.48663e6i	−0.180050	−	0.0585018i	0.217604	−	0.976037i	$-0.430176\pi$
$71$	−4.57537e6	−	1.48663e6i	−0.180050	−	0.0585018i	−0.397654	+	0.917535i	$0.630176\pi$
$72$	−1.66979e7	−	1.11094e7i	−0.621344	−	0.413392i
$73$	−1.30242e7	+	9.46260e6i	−0.458625	+	0.333211i	−0.792992	−	0.609232i	$-0.791478\pi$
$73$	−1.30242e7	+	9.46260e6i	−0.458625	+	0.333211i	0.334366	+	0.942443i	$0.391478\pi$
$74$	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
$78$	−2.06488e7	−	2.76141e7i	−0.557849	−	0.746023i
$79$	−7.05366e6	−	2.29187e6i	−0.181095	−	0.0588413i	0.217066	−	0.976157i	$-0.430351\pi$
$79$	−7.05366e6	−	2.29187e6i	−0.181095	−	0.0588413i	−0.398161	+	0.917316i	$0.630351\pi$
$80$	1.16066e7	−	3.92811e7i	0.283364	−	0.959012i
$81$	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	$-0.464546\pi$
$83$	3.72653e7	−	1.21082e7i	0.785221	−	0.255134i	0.674068	+	0.738669i	$0.264546\pi$
$84$	−1.29322e6	+	4.38707e6i	−0.0259749	+	0.0881165i
$85$	1.42036e7	+	399792.i	0.272097	+	0.00765877i
$86$	−1.13553e6	−	8.25810e7i	−0.0207590	−	1.50969i
$87$	−1.21422e7	+	1.67123e7i	−0.211944	+	0.291716i
$88$	−6.07796e7	−	7.67855e7i	−1.01351	−	1.28041i
$89$	−5.51749e7	+	4.00869e7i	−0.879390	+	0.638914i	−0.933090	−	0.359643i	$-0.882898\pi$
$89$	−5.51749e7	+	4.00869e7i	−0.879390	+	0.638914i	0.0537002	+	0.998557i	$0.482898\pi$
$90$	−4.00233e7	+	2.82077e7i	−0.610018	+	0.429930i
$91$	1.35959e7	−	1.87132e7i	0.198264	−	0.272887i
$92$	5.22700e7	+	6.79338e7i	0.729627	+	0.948275i
$93$	−3.28493e7			−0.439132
$94$	7.38859e7	+	2.28887e7i	0.946346	+	0.293164i
$95$	1.50269e6	−	5.33867e7i	0.0184490	−	0.655449i
$96$	4.14987e7	+	1.03937e7i	0.488596	+	0.122373i
$97$	3.82139e6	−	1.17610e7i	0.0431653	−	0.132849i	−0.927151	−	0.374687i	$-0.877750\pi$
$97$	3.82139e6	−	1.17610e7i	0.0431653	−	0.132849i	0.970317	+	0.241838i	$0.0777502\pi$
$98$	8.91602e7	−	1.22600e6i	0.966644	−	0.0132919i
$99$			1.17067e8i			1.21870i
$100$	−7.91768e7	−	6.10822e7i	−0.791768	−	0.610822i
$101$	−1.38153e8			−1.32762			−0.663811	−	0.747900i	$-0.731062\pi$
$101$	−1.38153e8			−1.32762			−0.663811	+	0.747900i	$0.731062\pi$
$102$	204050.	+	1.48394e7i	0.00188511	+	0.137093i
$103$	7.69723e7	+	2.50098e7i	0.683889	+	0.222209i	0.630297	−	0.776354i	$-0.282933\pi$
$103$	7.69723e7	+	2.50098e7i	0.683889	+	0.222209i	0.0535920	+	0.998563i	$0.482933\pi$
$104$	−1.80131e8	−	1.19845e8i	−1.53977	−	1.02444i
$105$	8.84546e6	+	6.81495e6i	0.0727718	+	0.0560667i
$106$	3.36324e7	−	1.08567e8i	0.266400	−	0.859952i
$107$		−	1.97007e8i		−	1.50296i	−0.659756	−	0.751480i	$-0.729340\pi$
$107$		−	1.97007e8i		−	1.50296i	0.659756	−	0.751480i	$-0.270660\pi$
$108$	−7.29739e7	−	9.48421e7i	−0.536380	−	0.697118i
$109$	2.65307e7	+	1.92757e7i	0.187950	+	0.136554i	0.677781	−	0.735264i	$-0.262942\pi$
$109$	2.65307e7	+	1.92757e7i	0.187950	+	0.136554i	−0.489831	+	0.871817i	$0.662942\pi$
$110$	−2.28424e8	+	7.06019e7i	−1.56016	+	0.482221i
$111$	3.46511e7	+	4.76931e7i	0.228257	+	0.314169i
$112$	1.57760e6	+	2.86553e7i	0.0100259	+	0.182110i
$113$	1.18181e8	+	8.58632e7i	0.724823	+	0.526615i	0.887922	−	0.459995i	$-0.152149\pi$
$113$	1.18181e8	+	8.58632e7i	0.724823	+	0.526615i	−0.163098	+	0.986610i	$0.552149\pi$
$114$	5.57764e7	−	766956.i	0.330241	−	0.00454100i
$115$	2.00765e8	−	5.90415e7i	1.14788	−	0.337572i
$116$	−3.66502e7	+	1.24331e8i	−0.202416	+	0.686669i
$117$	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
$120$	6.02781e7	−	8.52950e7i	0.290693	−	0.411338i
$121$	−1.10400e8	+	3.39775e8i	−0.515022	+	1.58508i
$122$	2.95119e8	−	2.20679e8i	1.33216	−	0.996143i
$123$	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	0.975236	+	0.221167i	$0.0709866\pi$
$127$	2.30023e8	+	3.16600e8i	0.884214	+	1.21702i	−0.0910222	+	0.995849i	$0.529013\pi$
$128$	2.67193e8	−	2.57964e7i	0.995372	−	0.0960992i
$129$	6.50774e7	−	2.00288e8i	0.235002	−	0.723261i
$130$	−4.31756e8	+	3.04294e8i	−1.51170	+	1.06542i
$131$	2.27189e8	−	7.38183e7i	0.771441	−	0.250656i	0.103259	−	0.994654i	$-0.467073\pi$
$131$	2.27189e8	−	7.38183e7i	0.771441	−	0.250656i	0.668182	+	0.743998i	$0.267073\pi$
$132$	−8.36662e7	−	2.35279e8i	−0.275584	−	0.774974i
$133$	1.15635e7	+	3.55888e7i	0.0369558	+	0.113738i
$134$	4.09788e7	−	1.39406e7i	0.127098	−	0.0432376i
$135$	−2.80287e8	+	8.24277e7i	−0.843855	+	0.248163i
$136$	3.24039e7	+	8.73021e7i	0.0947200	+	0.255193i
$137$	−8.02661e7	−	5.83167e7i	−0.227850	−	0.165543i	0.468003	−	0.883727i	$-0.344974\pi$
$137$	−8.02661e7	−	5.83167e7i	−0.227850	−	0.165543i	−0.695853	+	0.718184i	$0.744974\pi$
$138$	7.03928e7	+	2.06922e8i	0.194094	+	0.570545i
$139$	2.41052e8	+	3.31779e8i	0.645730	+	0.888772i	0.998905	−	0.0467859i	$-0.0148978\pi$
$139$	2.41052e8	+	3.31779e8i	0.645730	+	0.888772i	−0.353175	+	0.935557i	$0.614898\pi$
$140$	6.66220e7	+	2.16940e7i	0.173423	+	0.0564712i
$141$	1.59567e8	+	1.15932e8i	0.403708	+	0.293311i
$142$	−7.35261e7	−	2.27773e7i	−0.180837	−	0.0560207i
$143$			1.26288e9i			3.02008i
$144$	−2.69585e8	−	1.74061e8i	−0.626969	−	0.404810i
$145$	2.50683e8	+	1.93138e8i	0.567092	+	0.436913i
$146$	−2.06285e8	+	1.54252e8i	−0.454001	+	0.339485i
$147$	2.16244e8	+	7.02620e7i	0.463101	+	0.150471i
$148$	3.05126e8	+	2.09115e8i	0.635963	+	0.435851i
$149$	−4.91274e8			−0.996733			−0.498367	−	0.866966i	$-0.666067\pi$
$149$	−4.91274e8			−0.996733			−0.498367	+	0.866966i	$0.666067\pi$
$150$	−1.40974e8	−	2.12479e8i	−0.278467	−	0.419711i
$151$		−	3.94717e8i		−	0.759237i	−0.925143	−	0.379619i	$-0.876055\pi$
$151$		−	3.94717e8i		−	0.759237i	0.925143	−	0.379619i	$-0.123945\pi$
$152$	3.28140e8	−	1.21795e8i	0.614730	−	0.228169i
$153$	3.43999e7	−	1.05872e8i	0.0627756	−	0.193203i
$154$	1.34156e8	−	1.00317e8i	0.238522	−	0.178358i
$155$	−1.41587e7	+	5.03023e8i	−0.0245299	+	0.871488i
$156$	−3.36425e8	−	4.37241e8i	−0.568053	−	0.738283i
$157$	−8.44046e8			−1.38921			−0.694604	−	0.719392i	$-0.744420\pi$
$157$	−8.44046e8			−1.38921			−0.694604	+	0.719392i	$0.744420\pi$
$158$	−1.13352e8	−	3.51148e7i	−0.181887	−	0.0563458i
$159$	1.70350e8	−	2.34466e8i	0.266534	−	0.366853i
$160$	1.77047e8	−	6.30992e8i	0.270152	−	0.962818i
$161$	−1.18620e8	+	8.61827e7i	−0.176545	+	0.128267i
$162$	6.72695e7	+	1.97741e8i	0.0976693	+	0.287102i
$163$	−2.00389e8	+	2.75812e8i	−0.283873	+	0.390717i	−0.927012	−	0.375032i	$-0.877632\pi$
$163$	−2.00389e8	+	2.75812e8i	−0.283873	+	0.390717i	0.643139	+	0.765749i	$0.277632\pi$
$164$	4.31060e8	+	2.95423e8i	0.595885	+	0.408384i
$165$	−6.09408e8	−	1.71531e7i	−0.822190	−	0.0231423i
$166$	5.93524e8	−	2.01911e8i	0.781639	−	0.265906i
$167$	1.23109e9	−	4.00006e8i	1.58280	−	0.514281i	0.620020	−	0.784586i	$-0.287124\pi$
$167$	1.23109e9	−	4.00006e8i	1.58280	−	0.514281i	0.962775	+	0.270305i	$0.0871244\pi$
$168$	−1.97244e7	+	7.04710e7i	−0.0247609	+	0.0884653i
$169$	6.10108e8	+	1.87772e9i	0.747928	+	2.30189i
$170$	2.27325e8	+	3.27144e6i	0.272177	+	0.00391691i
$171$	−3.97937e8	−	1.29298e8i	−0.465404	−	0.151219i
$172$	−3.63337e7	−	1.32092e9i	−0.0415141	−	1.50926i
$173$	2.98918e7	−	2.17177e7i	0.0333709	−	0.0242454i	−0.570975	−	0.820968i	$-0.693435\pi$
$173$	2.98918e7	−	2.17177e7i	0.0333709	−	0.0242454i	0.604346	+	0.796722i	$0.293435\pi$
$174$	−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
$178$	−8.73896e8	+	6.53468e8i	−0.870522	+	0.650945i
$179$	−1.29400e9	−	4.20445e8i	−1.26044	−	0.409541i	−0.398787	−	0.917044i	$-0.630569\pi$
$179$	−1.29400e9	−	4.20445e8i	−1.26044	−	0.409541i	−0.861650	+	0.507503i	$0.830569\pi$
$180$	−6.34107e8	+	4.60085e8i	−0.604049	+	0.438277i
$181$	2.35206e8	+	7.23888e8i	0.219146	+	0.674462i	0.998833	+	0.0482927i	$0.0153780\pi$
$181$	2.35206e8	+	7.23888e8i	0.219146	+	0.674462i	−0.779687	+	0.626169i	$0.784622\pi$
$182$	2.13398e8	−	3.02374e8i	0.194493	−	0.275587i
$183$	8.93662e8	−	2.90368e8i	0.796836	−	0.258908i
$184$	8.51185e8	+	1.07534e9i	0.742596	+	0.938154i
$185$	7.45263e8	−	5.10057e8i	0.636242	−	0.435444i
$186$	−5.25540e8	+	7.22646e6i	−0.439090	+	0.00603773i
$187$	3.19495e8	−	4.39747e8i	0.261275	−	0.359614i
$188$	1.18710e9	+	3.49931e8i	0.950288	+	0.280125i
$189$	1.65605e8	−	1.20319e8i	0.129786	−	0.0942949i
$190$	1.22963e7	−	8.54438e8i	0.00943537	−	0.655641i
$191$	2.26296e8	−	3.11470e8i	0.170037	−	0.234036i	−0.715491	−	0.698622i	$-0.753797\pi$
$191$	2.26296e8	−	3.11470e8i	0.170037	−	0.234036i	0.885528	+	0.464586i	$0.153797\pi$
$192$	6.66203e8	+	1.57155e8i	0.490232	+	0.115644i
$193$	−6.76698e8			−0.487715			−0.243857	−	0.969811i	$-0.578413\pi$
$193$	−6.76698e8			−0.487715			−0.243857	+	0.969811i	$0.578413\pi$
$194$	5.85492e7	−	1.88999e8i	0.0413346	−	0.133430i
$195$	−1.29218e9	+	3.80008e8i	−0.893685	+	0.262818i
$196$	1.42616e9	−	3.92283e7i	0.966370	−	0.0265813i
$197$	7.22720e8	−	2.22430e9i	0.479850	−	1.47683i	−0.359454	−	0.933163i	$-0.617037\pi$
$197$	7.22720e8	−	2.22430e9i	0.479850	−	1.47683i	0.839304	−	0.543663i	$-0.182963\pi$
$198$	2.57534e7	+	1.87290e9i	0.0167562	+	1.21858i
$199$		−	2.87954e9i		−	1.83616i	−0.396391	−	0.918082i	$-0.629738\pi$
$199$		−	2.87954e9i		−	1.83616i	0.396391	−	0.918082i	$-0.370262\pi$
$200$	−1.28015e9	−	9.59805e8i	−0.800091	−	0.599878i
$201$	1.10373e8			0.0676208
$202$	−2.21024e9	+	3.03920e7i	−1.32750	+	0.0182538i
$203$	−2.10873e8	−	6.85169e7i	−0.124176	−	0.0403472i
$204$	6.52899e6	+	2.37363e8i	0.00376986	+	0.137054i
$205$	1.05285e9	−	7.20573e8i	0.596147	−	0.408002i
$206$	1.23694e9	+	3.83186e8i	0.686880	+	0.212785i
$207$		−	1.63947e9i		−	0.892937i
$208$	−2.90818e9	−	1.87770e9i	−1.55370	−	1.00317i
$209$	−1.65286e9	−	1.20087e9i	−0.866266	−	0.629379i
$210$	1.43013e8	+	1.07083e8i	0.0735358	+	0.0550609i
$211$	2.71224e8	+	3.73307e8i	0.136835	+	0.188337i	0.871935	−	0.489621i	$-0.162865\pi$
$211$	2.71224e8	+	3.73307e8i	0.136835	+	0.188337i	−0.735100	+	0.677959i	$0.762865\pi$
$212$	5.14185e8	−	1.74431e9i	0.254552	−	0.863534i
$213$	−1.58790e8	−	1.15368e8i	−0.0771446	−	0.0560489i
$214$	−4.33393e7	−	3.15182e9i	−0.0206646	−	1.50282i
$215$	−3.03896e9	−	1.08286e9i	−1.42224	−	0.506779i
$216$	−1.18834e9	−	1.50128e9i	−0.545914	−	0.689677i
$217$	−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
$220$	−3.63890e9	+	1.17977e9i	−1.55339	+	0.503626i
$221$	3.71093e8	−	1.14211e9i	0.155565	−	0.478781i
$222$	5.64857e8	+	7.55395e8i	0.232555	+	0.311001i
$223$	2.74367e8	+	3.77633e8i	0.110946	+	0.152704i	0.860879	−	0.508810i	$-0.169914\pi$
$223$	2.74367e8	+	3.77633e8i	0.110946	+	0.152704i	−0.749933	+	0.661514i	$0.769914\pi$
$224$	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	−0.985743	−	0.168257i	$-0.946186\pi$
$227$	−2.23346e9	−	3.07410e9i	−0.841154	−	1.15775i	0.144589	−	0.989492i	$-0.453814\pi$
$228$	8.92170e8	−	2.45403e7i	0.330148	−	0.00908114i
$229$	1.33927e8	−	4.12186e8i	0.0486998	−	0.149883i	−0.923749	−	0.382997i	$-0.874892\pi$
$229$	1.33927e8	−	4.12186e8i	0.0486998	−	0.149883i	0.972449	+	0.233115i	$0.0748918\pi$
$230$	3.19895e9	−	9.88741e8i	1.14313	−	0.353322i
$231$	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	0.771474	+	0.636260i	$0.219520\pi$
$233$	1.53649e9	+	4.72884e9i	0.521323	+	1.60447i	−0.250151	+	0.968207i	$0.580480\pi$
$234$	1.33276e9	+	3.91771e9i	0.444519	+	1.30668i
$235$	1.84406e9	−	2.39349e9i	0.604648	−	0.784804i
$236$	8.57735e8	−	1.25155e9i	0.276506	−	0.403459i
$237$	−2.44800e8	−	1.77858e8i	−0.0775923	−	0.0563741i
$238$	−1.50804e8	+	5.13022e7i	−0.0470009	+	0.0159892i
$239$	2.43847e9	+	3.35627e9i	0.747353	+	1.02864i	0.998162	+	0.0606070i	$0.0193036\pi$
$239$	2.43847e9	+	3.35627e9i	0.747353	+	1.02864i	−0.250808	+	0.968037i	$0.580696\pi$
$240$	9.45594e8	−	1.37785e9i	0.285010	−	0.415296i
$241$	−3.31798e9	−	2.41065e9i	−0.983569	−	0.714605i	−0.0250660	−	0.999686i	$-0.507980\pi$
$241$	−3.31798e9	−	2.41065e9i	−0.983569	−	0.714605i	−0.958504	+	0.285081i	$0.907980\pi$
$242$	−1.69148e9	+	5.46017e9i	−0.493180	+	1.59201i
$243$			3.59954e9i			1.03234i
$244$	4.67291e9	−	3.59545e9i	1.31834	−	1.01436i
$245$	1.16913e9	−	3.28108e9i	0.324488	−	0.910651i
$246$	7.97990e8	+	1.06717e9i	0.217900	+	0.291402i
$247$	−4.29280e9	−	1.39481e9i	−1.15333	−	0.374739i
$248$	−3.09181e9	+	1.14759e9i	−0.817348	+	0.303375i
$249$	1.59862e9			0.415860
$250$	−3.31446e9	+	2.06716e9i	−0.848502	+	0.529193i
$251$			2.00933e9i			0.506239i	0.967435	+	0.253119i	$0.0814565\pi$
$251$			2.00933e9i			0.506239i	−0.967435	+	0.253119i	$0.918543\pi$
$252$	3.10311e8	−	4.52785e8i	0.0769477	−	0.112277i
$253$	2.47375e9	−	7.61341e9i	0.603772	−	1.85822i
$254$	3.74968e9	+	5.01452e9i	0.900863	+	1.20474i
$255$	5.46087e8	+	1.94585e8i	0.129152	+	0.0460202i
$256$	4.26901e9	−	4.71483e8i	0.993956	−	0.109776i
$257$	1.04629e9			0.239839			0.119919	−	0.992784i	$-0.461736\pi$
$257$	1.04629e9			0.239839			0.119919	+	0.992784i	$0.461736\pi$
$258$	9.97079e8	−	3.21862e9i	0.225035	−	0.726424i
$259$	−3.71923e8	+	5.11907e8i	−0.0826520	+	0.113761i
$260$	−6.84050e9	+	4.96323e9i	−1.49691	+	1.08610i
$261$	2.00574e9	−	1.45725e9i	0.432227	−	0.314031i
$262$	3.61845e9	−	1.23096e9i	0.767922	−	0.261240i
$263$	−4.35277e9	+	5.99107e9i	−0.909793	+	1.25222i	0.0574438	+	0.998349i	$0.481705\pi$
$263$	−4.35277e9	+	5.99107e9i	−0.909793	+	1.25222i	−0.967237	+	0.253874i	$0.918295\pi$
$264$	−1.39029e9	−	3.74570e9i	−0.286213	−	0.771112i
$265$	−3.51697e9	−	2.70963e9i	−0.713157	−	0.549449i
$266$	1.92828e8	+	5.66824e8i	0.0385162	+	0.113220i
$267$	−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	0.964624	+	0.263629i	$0.0849194\pi$
$269$	1.77601e9	+	5.46599e9i	0.339184	+	1.04390i	−0.625440	+	0.780272i	$0.715081\pi$
$270$	−4.46604e9	+	1.38038e9i	−0.840364	+	0.259742i
$271$	1.27556e9	+	4.14453e8i	0.236495	+	0.0768419i	0.424867	−	0.905256i	$-0.360321\pi$
$271$	1.27556e9	+	4.14453e8i	0.236495	+	0.0768419i	−0.188372	+	0.982098i	$0.560321\pi$
$272$	5.37619e8	+	1.38957e9i	0.0982198	+	0.253867i
$273$	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	−0.124189	−	0.992259i	$-0.539633\pi$
$277$	4.59876e9	−	3.34120e9i	0.781128	−	0.567523i	0.905317	+	0.424736i	$0.139633\pi$
$278$	3.92945e9	+	5.25494e9i	0.657889	+	0.879809i
$279$	3.74946e9	+	1.21827e9i	0.618803	+	0.201061i
$280$	1.07062e9	+	3.32415e8i	0.174183	+	0.0540815i
$281$	1.68200e9	+	5.17667e9i	0.269775	+	0.830282i	0.990555	+	0.137118i	$0.0437839\pi$
$281$	1.68200e9	+	5.17667e9i	0.269775	+	0.830282i	−0.720780	+	0.693164i	$0.756216\pi$
$282$	2.57834e9	+	1.81964e9i	0.407703	+	0.287733i
$283$	3.92137e8	−	1.27413e8i	0.0611353	−	0.0198641i	−0.278290	−	0.960497i	$-0.589768\pi$
$283$	3.92137e8	−	1.27413e8i	0.0611353	−	0.0198641i	0.339425	+	0.940633i	$0.389768\pi$
$284$	−1.18132e9	−	3.48227e8i	−0.181590	−	0.0535290i
$285$	7.31380e8	−	2.05256e9i	0.110857	−	0.311112i
$286$	2.77818e8	+	2.02042e10i	0.0415238	+	3.01979i
$287$	−5.25426e8	+	7.23187e8i	−0.0774434	+	0.106592i
$288$	−4.35125e9	−	2.72541e9i	−0.632476	−	0.396152i
$289$	5.22535e9	−	3.79644e9i	0.749072	−	0.544233i
$290$	4.05304e9	+	3.03477e9i	0.573046	+	0.429075i
$291$	2.96554e8	−	4.08172e8i	0.0413554	−	0.0569208i
$292$	−3.26632e9	+	2.51319e9i	−0.449290	+	0.345695i
$293$	−1.30441e10			−1.76988			−0.884940	−	0.465705i	$-0.845801\pi$
$293$	−1.30441e10			−1.76988			−0.884940	+	0.465705i	$0.845801\pi$
$294$	3.47504e9	+	1.07652e9i	0.465126	+	0.144089i
$295$	−2.09212e9	−	3.05687e9i	−0.276248	−	0.403635i
$296$	4.92755e9	+	3.27840e9i	0.641896	+	0.427066i
$297$	−3.45359e9	+	1.06291e10i	−0.443859	+	1.36606i
$298$	−7.85965e9	+	1.08074e8i	−0.996639	+	0.0137043i
$299$		−	1.76859e10i		−	2.21281i
$300$	−2.30211e9	−	3.36833e9i	−0.284212	−	0.415843i
$301$	2.26039e9			0.275371
$302$	−8.68329e7	−	6.31487e9i	−0.0104389	−	0.759166i
$303$	−5.36059e9	−	1.74176e9i	−0.635978	−	0.206642i
$304$	5.22294e9	−	2.02073e9i	0.611535	−	0.236600i
$305$	−4.06124e9	−	1.38098e10i	−0.469310	−	1.59584i
$306$	5.27055e8	−	1.70136e9i	0.0601133	−	0.194048i
$307$		−	3.90914e9i		−	0.440076i	−0.975491	−	0.220038i	$-0.929382\pi$
$307$		−	3.90914e9i		−	0.440076i	0.975491	−	0.220038i	$-0.0706181\pi$
$308$	2.12423e9	−	1.63444e9i	0.236047	−	0.181621i
$309$	2.67136e9	+	1.94086e9i	0.293021	+	0.212892i
$310$	−1.15859e8	+	8.05073e9i	−0.0125453	+	0.871743i
$311$	1.66948e9	+	2.29784e9i	0.178460	+	0.245629i	0.888870	−	0.458159i	$-0.151491\pi$
$311$	1.66948e9	+	2.29784e9i	0.178460	+	0.245629i	−0.710411	+	0.703787i	$0.751491\pi$
$312$	−5.47847e9	−	6.92119e9i	−0.578151	−	0.730403i
$313$	−3.17018e9	−	2.30327e9i	−0.330298	−	0.239976i	0.410259	−	0.911969i	$-0.365438\pi$
$313$	−3.17018e9	−	2.30327e9i	−0.330298	−	0.239976i	−0.740557	+	0.671993i	$0.765438\pi$
$314$	−1.35035e10	+	1.85680e8i	−1.38908	+	0.0191006i
$315$	−7.56888e8	−	1.10592e9i	−0.0768758	−	0.112326i
$316$	−1.82119e9	−	5.36847e8i	−0.182644	−	0.0538397i
$317$	−4.79801e9	−	1.47667e10i	−0.475142	−	1.46234i	−0.845766	−	0.533555i	$-0.820856\pi$
$317$	−4.79801e9	−	1.47667e10i	−0.475142	−	1.46234i	0.370623	−	0.928783i	$-0.379144\pi$
$318$	2.67376e9	−	3.78858e9i	0.261465	−	0.370483i
$319$	1.15131e10	−	3.74084e9i	1.11181	−	0.361249i
$320$	2.69367e9	−	1.01339e10i	0.256888	−	0.966441i
$321$	2.48377e9	−	7.64425e9i	0.233933	−	0.719971i
$322$	−1.87879e9	+	1.40489e9i	−0.174765	+	0.130683i
$323$	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
$328$	6.96130e9	+	4.63149e9i	0.601444	+	0.400152i
$329$	−6.54191e8	+	2.01339e9i	−0.0558369	+	0.171848i
$330$	−9.75337e9	−	1.40361e8i	−0.822430	−	0.0118356i
$331$	9.88092e9	−	3.21051e9i	0.823162	−	0.267462i	0.133000	−	0.991116i	$-0.457539\pi$
$331$	9.88092e9	−	3.21051e9i	0.823162	−	0.267462i	0.690163	+	0.723654i	$0.257539\pi$
$332$	9.45108e9	−	3.36084e9i	0.777909	−	0.276628i
$333$	−2.18634e9	−	6.72885e9i	−0.177803	−	0.547222i
$334$	1.96076e10	−	6.67032e9i	1.57557	−	0.535995i
$335$	4.75731e7	−	1.69015e9i	0.00377730	−	0.134198i
$336$	−3.00058e8	+	1.13177e9i	−0.0235422	+	0.0887974i
$337$	1.47525e8	+	1.07183e8i	0.0114379	+	0.00831012i	0.593490	−	0.804842i	$-0.297750\pi$
$337$	1.47525e8	+	1.07183e8i	0.0114379	+	0.00831012i	−0.582052	+	0.813152i	$0.697750\pi$
$338$	1.01739e10	+	2.99065e10i	0.779507	+	2.29139i
$339$	3.50311e9	+	4.82161e9i	0.265249	+	0.365085i
$340$	3.63757e9	+	2.32944e6i	0.272205	+	0.000174315i
$341$	1.55737e10	+	1.13149e10i	1.15179	+	0.836825i
$342$	−6.39484e9	−	1.98102e9i	−0.467439	−	0.144806i
$343$			4.96492e9i			0.358704i
$344$	−8.71871e8	−	2.11248e10i	−0.0622613	−	1.50854i
$345$	8.53442e9	+	2.40220e8i	0.602417	+	0.0169563i
$346$	4.73447e8	−	3.54026e8i	0.0330344	−	0.0247019i
$347$	−2.71481e10	−	8.82097e9i	−1.87250	−	0.608413i	−0.990565	−	0.137045i	$-0.956240\pi$
$347$	−2.71481e10	−	8.82097e9i	−1.87250	−	0.608413i	−0.881937	−	0.471368i	$-0.843760\pi$
$348$	−2.98960e9	+	4.36221e9i	−0.203843	+	0.297433i
$349$	−2.07194e10			−1.39661			−0.698307	−	0.715799i	$-0.746063\pi$
$349$	−2.07194e10			−1.39661			−0.698307	+	0.715799i	$0.746063\pi$
$350$	1.70141e9	−	2.14381e9i	0.113380	−	0.142861i
$351$			2.46913e10i			1.62673i
$352$	−1.60942e10	−	1.92218e10i	−1.04833	−	1.25206i
$353$	−2.01811e9	+	6.21109e9i	−0.129971	+	0.400008i	−0.994774	−	0.102102i	$-0.967443\pi$
$353$	−2.01811e9	+	6.21109e9i	−0.129971	+	0.400008i	0.864803	+	0.502111i	$0.167443\pi$
$354$	3.09843e9	−	2.31690e9i	0.197301	−	0.147534i
$355$	−1.83508e9	+	2.38184e9i	−0.115542	+	0.149968i
$356$	−1.38373e10	+	1.06467e10i	−0.861490	+	0.662852i
$357$	−4.06181e8			−0.0250062
$358$	−2.07945e10	−	6.44182e9i	−1.26595	−	0.392172i
$359$	1.80808e10	−	2.48861e10i	1.08853	−	1.49823i	0.238758	−	0.971079i	$-0.423260\pi$
$359$	1.80808e10	−	2.48861e10i	1.08853	−	1.49823i	0.849771	−	0.527153i	$-0.176740\pi$
$360$	−1.00435e10	+	7.50017e9i	−0.597966	+	0.446540i
$361$	−7.83243e9	+	5.69059e9i	−0.461177	+	0.335065i
$362$	3.92218e9	+	1.15294e10i	0.228399	+	0.671385i
$363$	−8.56742e9	+	1.17920e10i	−0.493428	+	0.679145i
$364$	3.34752e9	−	4.88447e9i	0.190686	−	0.278235i
$365$	2.83877e9	+	9.65295e9i	0.159940	+	0.543862i
$366$	1.42334e10	−	4.84205e9i	0.793201	−	0.269839i
$367$	1.01564e10	−	3.30002e9i	0.559856	−	0.181908i	−0.0154005	−	0.999881i	$-0.504902\pi$
$367$	1.01564e10	−	3.30002e9i	0.559856	−	0.181908i	0.575256	+	0.817973i	$0.304902\pi$
$368$	1.38542e10	+	1.70165e10i	0.755425	+	0.927855i
$369$	−3.08870e9	−	9.50605e9i	−0.166598	−	0.512737i
$370$	1.18109e10	−	8.32409e9i	0.630195	−	0.444150i
$371$	2.95845e9	+	9.61260e8i	0.156160	+	0.0507394i
$372$	−8.40625e9	+	2.31225e8i	−0.438966	+	0.0120743i
$373$	−2.19475e10	+	1.59458e10i	−1.13383	+	0.823778i	−0.986248	−	0.165271i	$-0.947150\pi$
$373$	−2.19475e10	+	1.59458e10i	−1.13383	+	0.823778i	−0.147585	+	0.989049i	$0.547150\pi$
$374$	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
$378$	2.62297e9	−	1.96136e9i	0.128477	−	0.0960705i
$379$	−6.41304e9	−	2.08372e9i	−0.310819	−	0.100991i	0.149454	−	0.988769i	$-0.452248\pi$
$379$	−6.41304e9	−	2.08372e9i	−0.310819	−	0.100991i	−0.460273	+	0.887778i	$0.652248\pi$
$380$	8.75558e6	−	1.36724e10i	0.000419905	−	0.655709i
$381$	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	$-0.608561\pi$
$383$	−1.10067e9	+	3.57630e8i	−0.0511521	+	0.0166203i	0.283329	+	0.959023i	$0.408561\pi$
$384$	1.06928e10	+	2.36768e9i	0.491776	+	0.108893i
$385$	−1.84618e9	−	6.27774e9i	−0.0840293	−	0.285733i
$386$	−1.08261e10	+	1.48865e8i	−0.487668	+	0.00670571i
$387$	−1.48560e10	+	2.04476e10i	−0.662307	+	0.911587i
$388$	8.95121e8	−	3.03659e9i	0.0394962	−	0.133986i
$389$	−1.76069e10	+	1.27922e10i	−0.768928	+	0.558659i	−0.901636	−	0.432496i	$-0.857633\pi$
$389$	−1.76069e10	+	1.27922e10i	−0.768928	+	0.558659i	0.132708	+	0.991155i	$0.457633\pi$
$390$	−2.05893e10	+	6.36382e9i	−0.889987	+	0.275080i
$391$	−4.47435e9	+	6.15841e9i	−0.191436	+	0.263488i
$392$	2.28077e10	−	9.41332e8i	0.965913	−	0.0398656i
$393$	9.74604e9			0.408562
$394$	1.10731e10	−	3.57445e10i	0.459499	−	1.48328i
$395$	−2.82906e9	+	3.67198e9i	−0.116213	+	0.150838i
$396$	8.24032e8	+	2.99579e10i	0.0335091	+	1.21824i
$397$	6.43475e9	−	1.98041e10i	0.259041	−	0.797248i	−0.733965	−	0.679187i	$-0.762332\pi$
$397$	6.43475e9	−	1.98041e10i	0.259041	−	0.797248i	0.993006	−	0.118060i	$-0.0376676\pi$
$398$	−6.33465e8	−	4.60683e10i	−0.0252459	−	1.83599i
$399$			1.52670e9i			0.0602368i
$400$	−2.06915e10	−	1.50738e10i	−0.808264	−	0.588821i
$401$	−1.68962e10			−0.653450			−0.326725	−	0.945119i	$-0.605945\pi$
$401$	−1.68962e10			−0.653450			−0.326725	+	0.945119i	$0.605945\pi$
$402$	1.76581e9	−	2.42808e7i	0.0676144	−	0.000929735i
$403$	4.04478e10	+	1.31423e10i	1.53347	+	0.498254i
$404$	−3.53538e10	+	9.72452e8i	−1.32712	+	0.0365042i
$405$	8.15575e9	+	2.29561e8i	0.303141	+	0.00853255i
$406$	−3.38873e9	−	1.04978e9i	−0.124719	−	0.0386361i
$407$		−	3.45466e10i		−	1.25901i
$408$	1.56671e8	+	3.79602e9i	0.00565390	+	0.136990i
$409$	1.91670e10	+	1.39257e10i	0.684954	+	0.497648i	0.874997	−	0.484127i	$-0.160863\pi$
$409$	1.91670e10	+	1.39257e10i	0.684954	+	0.497648i	−0.190044	+	0.981776i	$0.560863\pi$
$410$	1.66856e10	−	1.17597e10i	0.590481	−	0.416160i
$411$	−2.37925e9	−	3.27475e9i	−0.0833820	−	0.114765i
$412$	1.98735e10	+	5.85829e9i	0.689741	+	0.203321i
$413$	2.09971e9	+	1.52553e9i	0.0721704	+	0.0524349i
$414$	−3.60663e8	−	2.62290e10i	−0.0122772	−	0.892853i
$415$	6.89034e8	−	2.44797e10i	0.0232300	−	0.825304i
$416$	−4.69396e10	−	2.94007e10i	−1.56735	−	0.981712i
$417$	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	$-0.537297\pi$
$419$	1.14741e10	−	3.72815e9i	0.372273	−	0.120959i	0.489177	+	0.872184i	$0.337297\pi$
$420$	2.31155e9	+	1.68170e9i	0.0742859	+	0.0540446i
$421$	−3.14320e9	+	9.67378e9i	−0.100056	+	0.307941i	−0.988538	−	0.150970i	$-0.951760\pi$
$421$	−3.14320e9	+	9.67378e9i	−0.100056	+	0.307941i	0.888482	+	0.458911i	$0.151760\pi$
$422$	4.42129e9	+	5.91269e9i	0.139412	+	0.186438i
$423$	−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
$428$	−1.38673e9	−	5.04148e10i	−0.0413252	−	1.50239i
$429$	−1.59217e10	+	4.90021e10i	−0.470069	+	1.44672i
$430$	−4.88571e10	−	1.66556e10i	−1.42907	−	0.487177i
$431$	5.42796e10	−	1.76365e10i	1.57299	−	0.511097i	0.612755	−	0.790273i	$-0.290061\pi$
$431$	5.42796e10	−	1.76365e10i	1.57299	−	0.511097i	0.960240	+	0.279176i	$0.0900613\pi$
$432$	−1.93419e10	−	2.37567e10i	−0.555345	−	0.682106i
$433$	−4.33385e9	−	1.33382e10i	−0.123288	−	0.379443i	0.870297	−	0.492527i	$-0.163927\pi$
$433$	−4.33385e9	−	1.33382e10i	−0.123288	−	0.379443i	−0.993585	+	0.113085i	$0.963927\pi$
$434$	−1.81687e9	−	5.34076e9i	−0.0512113	−	0.150537i
$435$	7.29200e9	+	1.06546e10i	0.203652	+	0.297564i
$436$	6.92496e9	+	4.74595e9i	0.191633	+	0.131334i
$437$	2.31474e10	+	1.68176e10i	0.634712	+	0.461145i
$438$	−9.94898e9	+	3.38455e9i	−0.270323	+	0.0919611i
$439$	3.33213e10	+	4.58628e10i	0.897147	+	1.23482i	0.971369	+	0.237576i	$0.0763527\pi$
$439$	3.33213e10	+	4.58628e10i	0.897147	+	1.23482i	−0.0742218	+	0.997242i	$0.523647\pi$
$440$	−5.79574e10	+	1.96751e10i	−1.54631	+	0.524936i
$441$	−2.20766e10	−	1.60396e10i	−0.583684	−	0.424072i
$442$	5.68567e9	−	1.83536e10i	0.148968	−	0.480875i
$443$			7.96140e9i			0.206716i	0.994644	+	0.103358i	$0.0329588\pi$
$443$			7.96140e9i			0.206716i	−0.994644	+	0.103358i	$0.967041\pi$
$444$	9.20303e9	+	1.19609e10i	0.236809	+	0.307774i
$445$	1.20260e10	+	4.08933e10i	0.306677	+	1.04283i
$446$	4.47252e9	+	5.98120e9i	0.113035	+	0.151164i
$447$	−1.90624e10	−	6.19374e9i	−0.477471	−	0.155140i
$448$	6.05415e8	+	7.32187e9i	0.0150294	+	0.181765i
$449$	3.61991e10			0.890662			0.445331	−	0.895366i	$-0.353086\pi$
$449$	3.61991e10			0.890662			0.445331	+	0.895366i	$0.353086\pi$
$450$	8.21081e9	+	2.94809e10i	0.200233	+	0.718936i
$451$		−	4.88050e10i		−	1.17966i
$452$	3.08472e10	+	2.11408e10i	0.739029	+	0.506486i
$453$	4.97639e9	−	1.53157e10i	0.118174	−	0.363702i
$454$	−3.64083e10	−	4.86896e10i	−0.856992	−	1.14607i
$455$	−8.16502e9	−	1.19302e10i	−0.190507	−	0.278357i
$456$	1.42680e10	−	5.88874e8i	0.329991	−	0.0136196i
$457$	−6.09538e10			−1.39745			−0.698725	−	0.715390i	$-0.746249\pi$
$457$	−6.09538e10			−1.39745			−0.698725	+	0.715390i	$0.746249\pi$
$458$	2.05196e9	−	6.62381e9i	0.0466344	−	0.150538i
$459$	6.24662e9	−	8.59774e9i	0.140732	−	0.193702i
$460$	5.09608e10	−	1.65221e10i	1.13816	−	0.369006i
$461$	7.21419e10	−	5.24142e10i	1.59729	−	1.16050i	0.704830	−	0.709377i	$-0.251023\pi$
$461$	7.21419e10	−	5.24142e10i	1.59729	−	1.16050i	0.892462	−	0.451123i	$-0.148977\pi$
$462$	6.47027e9	−	2.20112e9i	0.142022	−	0.0483144i
$463$	−4.45557e10	+	6.13256e10i	−0.969570	+	1.33450i	−0.0273057	+	0.999627i	$0.508693\pi$
$463$	−4.45557e10	+	6.13256e10i	−0.969570	+	1.33450i	−0.942264	+	0.334871i	$0.891307\pi$
$464$	−8.50373e9	+	3.20747e10i	−0.183458	+	0.691975i
$465$	−6.89125e9	+	1.93397e10i	−0.147396	+	0.413656i
$466$	2.56218e10	+	7.53163e10i	0.543334	+	1.59715i
$467$	−6.54554e10	+	2.12678e10i	−1.37619	+	0.447151i	−0.901415	−	0.432956i	$-0.857470\pi$
$467$	−6.54554e10	+	2.12678e10i	−1.37619	+	0.447151i	−0.474775	+	0.880107i	$0.657470\pi$
$468$	2.21841e10	+	6.23842e10i	0.462443	+	1.30044i
$469$	3.66086e8	+	1.12670e9i	0.00756643	+	0.0232871i
$470$	2.89756e10	−	3.86980e10i	0.593801	−	0.793043i
$471$	−3.27506e10	−	1.06413e10i	−0.665480	−	0.216228i
$472$	1.34471e10	−	2.02115e10i	0.270933	−	0.407222i
$473$	−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
$478$	3.97502e10	+	5.31588e10i	0.761426	+	1.01827i
$479$	7.32194e10	+	2.37904e10i	1.39086	+	0.451918i	0.906224	−	0.422797i	$-0.138952\pi$
$479$	7.32194e10	+	2.37904e10i	1.39086	+	0.451918i	0.484637	+	0.874715i	$0.338952\pi$
$480$	1.48250e10	−	2.22516e10i	0.279273	−	0.419175i
$481$	−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
$484$	−2.58599e10	+	8.77266e10i	−0.471244	+	1.59864i
$485$	−6.12254e9	−	4.71708e9i	−0.110653	−	0.0852524i
$486$	7.91855e8	+	5.75872e10i	0.0141939	+	1.03224i
$487$	3.12969e10	−	4.30765e10i	0.556398	−	0.765816i	−0.434465	−	0.900689i	$-0.643063\pi$
$487$	3.12969e10	−	4.30765e10i	0.556398	−	0.765816i	0.990863	+	0.134873i	$0.0430626\pi$
$488$	7.39685e10	−	5.85498e10i	1.30427	−	1.03240i
$489$	−1.12528e10	+	8.17561e9i	−0.196799	+	0.142983i
$490$	1.79825e10	−	5.27494e10i	0.311937	−	0.915026i
$491$	3.84123e10	−	5.28700e10i	0.660913	−	0.909669i	−0.338598	−	0.940931i	$-0.609953\pi$
$491$	3.84123e10	−	5.28700e10i	0.660913	−	0.909669i	0.999511	+	0.0312620i	$0.00995262\pi$
$492$	1.30014e10	+	1.68975e10i	0.221886	+	0.288379i
$493$	−1.15113e10			−0.194867
$494$	−6.89851e10	−	2.13705e10i	−1.15837	−	0.358846i
$495$	6.89224e10	+	2.45588e10i	1.14799	+	0.409060i
$496$	−4.92119e10	+	1.90398e10i	−0.813099	+	0.314584i
$497$	6.51005e8	−	2.00359e9i	0.0106699	−	0.0328385i
$498$	2.55755e10	−	3.51676e8i	0.415821	−	0.00571776i
$499$			1.05688e11i			1.70461i	0.523047	+	0.852304i	$0.324795\pi$
$499$			1.05688e11i			1.70461i	−0.523047	+	0.852304i	$0.675205\pi$
$500$	−5.25716e10	+	3.38006e10i	−0.841145	+	0.540809i
$501$	5.28118e10			0.838262
$502$	4.42027e8	+	3.21462e10i	0.00696040	+	0.506191i
$503$	5.75444e10	+	1.86973e10i	0.898940	+	0.292083i	0.721800	−	0.692102i	$-0.243315\pi$
$503$	5.75444e10	+	1.86973e10i	0.898940	+	0.292083i	0.177141	+	0.984186i	$0.443315\pi$
$504$	4.86491e9	−	7.31213e9i	0.0753967	−	0.113324i
$505$	−2.89822e10	+	8.13363e10i	−0.445621	+	1.25060i
$506$	3.79014e10	−	1.22347e11i	0.578166	−	1.86635i
$507$			8.05509e10i			1.21910i
$508$	6.10923e10	+	7.93999e10i	0.917342	+	1.19224i
$509$	1.01616e11	+	7.38283e10i	1.51388	+	1.09990i	0.964421	+	0.264373i	$0.0851649\pi$
$509$	1.01616e11	+	7.38283e10i	1.51388	+	1.09990i	0.549456	+	0.835523i	$0.314835\pi$
$510$	8.77938e9	+	2.99293e9i	0.129773	+	0.0442401i
$511$	−4.14374e9	−	5.70337e9i	−0.0607727	−	0.0836465i
$512$	6.81940e10	−	8.48215e9i	0.992353	−	0.123432i
$513$	−3.23160e10	−	2.34790e10i	−0.466604	−	0.339008i
$514$	1.67391e10	−	2.30171e8i	0.239816	−	0.00329760i
$515$	3.08718e10	−	4.00701e10i	0.438868	−	0.569629i
$516$	1.52437e10	−	5.17123e10i	0.215026	−	0.729450i
$517$	−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
$520$	−1.08346e11	+	8.09089e10i	−1.48183	+	1.10658i
$521$	4.02676e9	−	1.23931e10i	0.0546518	−	0.168201i	−0.920005	−	0.391907i	$-0.871816\pi$
$521$	4.02676e9	−	1.23931e10i	0.0546518	−	0.168201i	0.974657	+	0.223706i	$0.0718155\pi$
$522$	3.17682e10	−	2.37551e10i	0.427868	−	0.319944i
$523$	3.58209e10	+	4.93032e10i	0.478773	+	0.658975i	0.978269	−	0.207342i	$-0.0664813\pi$
$523$	3.58209e10	+	4.93032e10i	0.478773	+	0.658975i	−0.499496	+	0.866316i	$0.666481\pi$
$524$	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
$528$	−2.30666e10	−	5.96197e10i	−0.296788	−	0.767104i
$529$	−1.04440e10	+	3.21434e10i	−0.133366	+	0.410459i
$530$	−5.68623e10	−	4.25764e10i	−0.720644	−	0.539591i
$531$	−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
$534$	−4.21474e10	+	1.43381e10i	−0.518329	+	0.176330i
$535$	−1.15986e11	−	4.13289e10i	−1.41577	−	0.504474i
$536$	1.03885e10	−	3.85588e9i	0.125861	−	0.0467159i
$537$	−4.49087e10	−	3.26281e10i	−0.540050	−	0.392369i
$538$	2.96159e10	+	8.70568e10i	0.353505	+	1.03914i
$539$	−7.83185e10	−	1.07796e11i	−0.927917	−	1.27717i
$540$	−7.11462e10	+	2.30664e10i	−0.836713	+	0.271272i
$541$	3.68706e10	+	2.67881e10i	0.430419	+	0.312718i	0.781816	−	0.623509i	$-0.214293\pi$
$541$	3.68706e10	+	2.67881e10i	0.430419	+	0.312718i	−0.351398	+	0.936226i	$0.614293\pi$
$542$	2.04981e10	+	6.35002e9i	0.237529	+	0.0735830i
$543$			3.10536e10i			0.357201i
$544$	8.90678e9	+	2.21128e10i	0.101701	+	0.252492i
$545$	1.69141e10	−	1.15760e10i	0.191718	−	0.131211i
$546$	1.20924e10	−	9.04226e9i	0.136064	−	0.101743i
$547$	1.03816e11	+	3.37320e10i	1.15962	+	0.376784i	0.824760	−	0.565483i	$-0.191310\pi$
$547$	1.03816e11	+	3.37320e10i	1.15962	+	0.376784i	0.334863	+	0.942267i	$0.391310\pi$
$548$	−2.09508e10	−	1.43584e10i	−0.232316	−	0.159215i
$549$	−1.12773e11			−1.24141
$550$	−6.35325e9	+	1.49293e11i	−0.0694297	+	1.63151i
$551$			4.32672e10i			0.469410i
$552$	1.94702e10	+	5.24565e10i	0.209708	+	0.564993i
$553$	1.00363e9	−	3.08885e9i	0.0107318	−	0.0330290i
$554$	7.28383e10	−	5.44658e10i	0.773251	−	0.578209i
$555$	3.53481e10	−	1.03953e10i	0.372558	−	0.109563i
$556$	6.40213e10	+	8.32066e10i	0.669924	+	0.870681i
$557$	9.35906e10			0.972325			0.486163	−	0.873868i	$-0.338396\pi$
$557$	9.35906e10			0.972325			0.486163	+	0.873868i	$0.338396\pi$
$558$	6.02538e10	+	1.86657e10i	0.621509	+	0.192534i
$559$	−1.60261e11	+	2.20581e11i	−1.64128	+	2.25902i
$560$	1.72015e10	+	5.08261e9i	0.174910	+	0.0516815i
$561$	1.79411e10	−	1.30350e10i	0.181133	−	0.131601i
$562$	2.80483e10	+	8.24489e10i	0.281165	+	0.826494i
$563$	8.80346e10	−	1.21169e11i	0.876233	−	1.20603i	−0.101216	−	0.994864i	$-0.532273\pi$
$563$	8.80346e10	−	1.21169e11i	0.876233	−	1.20603i	0.977450	−	0.211167i	$-0.0677265\pi$
$564$	4.16499e10	+	2.85443e10i	0.411621	+	0.282100i
$565$	7.53435e10	−	5.15650e10i	0.739353	−	0.506013i
$566$	6.24557e9	−	2.12468e9i	0.0608564	−	0.0207027i
$567$	−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	−0.975455	−	0.220200i	$-0.929329\pi$
$569$	−3.30947e10	−	1.01855e11i	−0.315726	−	0.971704i	0.659729	−	0.751504i	$-0.270671\pi$
$570$	1.12494e10	−	3.29988e10i	0.106569	−	0.312607i
$571$	−1.47109e11	−	4.77985e10i	−1.38386	−	0.449645i	−0.479926	−	0.877309i	$-0.659337\pi$
$571$	−1.47109e11	−	4.77985e10i	−1.38386	−	0.449645i	−0.903938	+	0.427664i	$0.859337\pi$
$572$	8.88935e9	+	3.23175e11i	0.0830397	+	3.01893i
$573$	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	−0.234666	−	0.972076i	$-0.575400\pi$
$577$	6.84246e10	−	4.97133e10i	0.617318	−	0.448508i	0.851984	+	0.523569i	$0.175400\pi$
$578$	8.27625e10	−	6.18868e10i	0.741519	−	0.554481i
$579$	−2.62572e10	−	8.53147e9i	−0.233633	−	0.0759118i
$580$	6.55102e10	+	4.76601e10i	0.578891	+	0.421156i
$581$	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
$584$	−5.17032e10	+	4.09257e10i	−0.444494	+	0.351840i
$585$	1.61584e11	+	4.54814e9i	1.37967	+	0.0388339i
$586$	−2.08686e11	+	2.86955e9i	−1.76971	+	0.0243345i
$587$	−4.11794e10	+	5.66785e10i	−0.346838	+	0.477382i	−0.946423	−	0.322929i	$-0.895332\pi$
$587$	−4.11794e10	+	5.66785e10i	−0.346838	+	0.477382i	0.599585	+	0.800311i	$0.295332\pi$
$588$	5.58322e10	+	1.64581e10i	0.467063	+	0.137680i
$589$	−5.56626e10	+	4.04412e10i	−0.462490	+	0.336018i
$590$	−3.41433e10	−	4.84451e10i	−0.281771	−	0.399799i
$591$	5.60858e10	−	7.71955e10i	0.459730	−	0.632764i
$592$	7.95546e10	+	5.13654e10i	0.647707	+	0.418200i
$593$	−2.09456e10			−0.169385			−0.0846925	−	0.996407i	$-0.526991\pi$
$593$	−2.09456e10			−0.169385			−0.0846925	+	0.996407i	$0.526991\pi$
$594$	−5.29139e10	+	1.70809e11i	−0.425035	+	1.37203i
$595$	−1.75072e8	+	6.21987e9i	−0.00139685	+	0.0496265i
$596$	−1.25719e11	+	3.45806e9i	−0.996357	+	0.0274061i
$597$	3.63038e10	−	1.11732e11i	0.285795	−	0.879587i
$598$	−3.89069e9	−	2.82948e11i	−0.0304244	−	2.21260i
$599$		−	9.63751e10i		−	0.748613i	−0.927305	−	0.374307i	$-0.877881\pi$
$599$		−	9.63751e10i		−	0.748613i	0.927305	−	0.374307i	$-0.122119\pi$
$600$	−3.75713e10	−	5.33817e10i	−0.289902	−	0.411896i
$601$	9.12544e10			0.699449			0.349725	−	0.936853i	$-0.386275\pi$
$601$	9.12544e10			0.699449			0.349725	+	0.936853i	$0.386275\pi$
$602$	3.61628e10	−	4.97259e8i	0.275345	−	0.00378614i
$603$	−1.25982e10	−	4.09339e9i	−0.0952880	−	0.0309609i
$604$	−2.77839e9	−	1.01009e11i	−0.0208759	−	0.758950i
$605$	1.76879e11	+	1.36276e11i	1.32025	+	1.01718i
$606$	−8.61445e10	−	2.66863e10i	−0.638759	−	0.197878i
$607$			8.58393e10i			0.632312i	0.948707	+	0.316156i	$0.102392\pi$
$607$			8.58393e10i			0.632312i	−0.948707	+	0.316156i	$0.897608\pi$
$608$	8.31147e10	−	3.34776e10i	0.608224	−	0.244985i
$609$	−7.31845e9	−	5.31717e9i	−0.0532047	−	0.0386555i
$610$	−6.80117e10	−	2.20043e11i	−0.491207	−	1.58924i
$611$	−1.50095e11	−	2.06589e11i	−1.07697	−	1.48232i
$612$	8.05781e9	−	2.73351e10i	0.0574396	−	0.194856i
$613$	9.22797e9	+	6.70451e9i	0.0653528	+	0.0474816i	0.619982	−	0.784616i	$-0.287140\pi$
$613$	9.22797e9	+	6.70451e9i	0.0653528	+	0.0474816i	−0.554629	+	0.832098i	$0.687140\pi$
$614$	−8.59963e8	−	6.25403e10i	−0.00605071	−	0.440034i
$615$	4.99374e10	−	1.46857e10i	0.349080	−	0.102659i
$616$	3.36249e10	−	2.66158e10i	0.233528	−	0.184849i
$617$	−5.48704e10	−	1.68874e11i	−0.378615	−	1.16526i	−0.941007	−	0.338387i	$-0.890119\pi$
$617$	−5.48704e10	−	1.68874e11i	−0.378615	−	1.16526i	0.562392	−	0.826871i	$-0.309881\pi$
$618$	4.31647e10	+	3.04631e10i	0.295920	+	0.208843i
$619$	1.86024e11	−	6.04428e10i	1.26708	−	0.411701i	0.403071	−	0.915169i	$-0.367943\pi$
$619$	1.86024e11	−	6.04428e10i	1.26708	−	0.411701i	0.864014	+	0.503468i	$0.167943\pi$
$620$	−8.24973e7	+	1.28825e11i	−0.000558307	+	0.871833i
$621$	4.83656e10	−	1.48854e11i	0.325215	−	1.00091i
$622$	2.72147e10	+	3.63948e10i	0.181820	+	0.243152i
$623$	−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
$628$	−2.15994e11	+	5.94120e9i	−1.38868	+	0.0381975i
$629$	−1.01514e10	+	3.12428e10i	−0.0648520	+	0.199594i
$630$	−1.23524e10	−	1.75265e10i	−0.0784129	−	0.111258i
$631$	−8.84234e10	+	2.87305e10i	−0.557763	+	0.181228i	−0.574314	−	0.818635i	$-0.694731\pi$
$631$	−8.84234e10	+	2.87305e10i	−0.557763	+	0.181228i	0.0165514	+	0.999863i	$0.494731\pi$
$632$	−2.92543e10	−	8.18810e9i	−0.183367	−	0.0513233i
$633$	5.81752e9	+	1.79045e10i	0.0362345	+	0.111518i
$634$	−8.00093e10	−	2.35190e11i	−0.495203	−	1.45567i
$635$	2.34651e11	−	6.90067e10i	1.44320	−	0.424421i
$636$	4.19427e10	−	6.11998e10i	0.256347	−	0.374043i
$637$	−2.38154e11	−	1.73029e11i	−1.44644	−	1.05090i
$638$	1.83370e11	−	6.23805e10i	1.10674	−	0.376501i
$639$	1.38459e10	+	1.90573e10i	0.0830459	+	0.114303i
$640$	4.08653e10	−	1.62719e11i	0.243576	−	0.969882i
$641$	5.27702e10	+	3.83398e10i	0.312577	+	0.227100i	0.733001	−	0.680227i	$-0.238119\pi$
$641$	5.27702e10	+	3.83398e10i	0.312577	+	0.227100i	−0.420425	+	0.907327i	$0.638119\pi$
$642$	3.80549e10	−	1.22843e11i	0.224012	−	0.723119i
$643$			1.69187e10i			0.0989743i	0.998775	+	0.0494871i	$0.0157587\pi$
$643$			1.69187e10i			0.0989743i	−0.998775	+	0.0494871i	$0.984241\pi$
$644$	−2.97487e10	+	2.28894e10i	−0.172951	+	0.133073i
$645$	−1.04265e11	−	8.03308e10i	−0.602422	−	0.464134i
$646$	1.86147e10	+	2.48939e10i	0.106888	+	0.142943i
$647$	−8.67093e10	−	2.81735e10i	−0.494821	−	0.160777i	0.0509669	−	0.998700i	$-0.483770\pi$
$647$	−8.67093e10	−	2.81735e10i	−0.494821	−	0.160777i	−0.545788	+	0.837923i	$0.683770\pi$
$648$	1.86064e10	+	5.01290e10i	0.105527	+	0.284308i
$649$	−1.41701e11			−0.798720
$650$	8.85751e10	+	3.18028e11i	0.496202	+	1.78161i
$651$		−	1.43850e10i		−	0.0800911i
$652$	−4.93388e10	+	7.19917e10i	−0.273022	+	0.398375i
$653$	1.66640e10	−	5.12864e10i	0.0916485	−	0.282065i	−0.894717	−	0.446633i	$-0.852623\pi$
$653$	1.66640e10	−	5.12864e10i	0.0916485	−	0.282065i	0.986366	+	0.164568i	$0.0526230\pi$
$654$	1.28197e10	+	1.71440e10i	0.0700755	+	0.0937134i
$655$	4.20073e9	−	1.49242e11i	0.0228223	−	0.810820i
$656$	1.12389e11	+	7.25655e10i	0.606889	+	0.391845i
$657$	7.88269e10			0.423071
$658$	−1.00231e10	+	3.23552e10i	−0.0534688	+	0.172600i
$659$	−1.83356e10	+	2.52369e10i	−0.0972198	+	0.133812i	−0.854856	−	0.518866i	$-0.826354\pi$
$659$	−1.83356e10	+	2.52369e10i	−0.0972198	+	0.133812i	0.757636	+	0.652678i	$0.226354\pi$
$660$	−1.56070e11	−	9.99446e7i	−0.822515	−	0.000526725i
$661$	7.94128e10	−	5.76968e10i	0.415992	−	0.302236i	−0.360031	−	0.932940i	$-0.617234\pi$
$661$	7.94128e10	−	5.76968e10i	0.415992	−	0.302236i	0.776023	+	0.630704i	$0.217234\pi$
$662$	1.57374e11	−	5.35369e10i	0.819407	−	0.278754i
$663$	2.87982e10	−	3.96373e10i	0.149043	−	0.205140i
$664$	1.50464e11	−	5.58475e10i	0.774032	−	0.287297i
$665$	2.33784e10	+	6.58037e8i	0.119544	+	0.00336483i
$666$	−3.64583e10	−	1.07170e11i	−0.185310	−	0.544726i
$667$	−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
$670$	3.89284e8	−	2.70504e10i	0.00193182	−	0.134238i
$671$	−5.23698e11	−	1.70160e11i	−2.58339	−	0.839395i
$672$	−4.55149e9	+	1.81726e10i	−0.0223191	+	0.0891127i
$673$	5.60823e9	−	4.07462e9i	0.0273379	−	0.0198622i	−0.574032	−	0.818833i	$-0.694622\pi$
$673$	5.60823e9	−	4.07462e9i	0.0273379	−	0.0198622i	0.601370	+	0.798970i	$0.294622\pi$
$674$	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	−0.789181	−	0.614161i	$-0.789495\pi$
$677$	−9.43088e10	+	6.85193e10i	−0.448949	+	0.326181i	0.340231	+	0.940342i	$0.389495\pi$
$678$	5.71051e10	+	7.63679e10i	0.270244	+	0.361403i
$679$	5.15024e9	+	1.67341e9i	0.0242297	+	0.00787271i
$680$	5.81961e10	−	7.62954e8i	0.272181	−	0.00356831i
$681$	−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	$-0.768569\pi$
$683$	−2.09100e11	+	6.79408e10i	−0.960886	+	0.312211i	−0.213755	+	0.976887i	$0.568569\pi$
$684$	−1.02744e11	−	3.02866e10i	−0.469386	−	0.138365i
$685$	−5.11719e10	+	3.50220e10i	−0.232418	+	0.159067i
$686$	1.09222e9	+	7.94312e10i	0.00493191	+	0.358670i
$687$	1.03933e10	−	1.43051e10i	0.0466578	−	0.0642190i
$688$	−1.85958e10	−	3.37772e11i	−0.0829968	−	1.50755i
$689$	−3.03559e11	+	2.20548e11i	−1.34699	+	0.978649i
$690$	1.36591e11	+	1.96568e9i	0.602594	+	0.00867196i
$691$	−5.06644e10	+	6.97336e10i	−0.222224	+	0.305865i	−0.905543	−	0.424255i	$-0.860536\pi$
$691$	−5.06644e10	+	6.97336e10i	−0.222224	+	0.305865i	0.683319	+	0.730120i	$0.260536\pi$
$692$	7.49655e9	−	5.76803e9i	0.0326917	−	0.0251538i
$693$	−5.12647e10			−0.222272
$694$	−4.36270e11	−	1.35150e11i	−1.88069	−	0.582610i
$695$	2.45901e11	−	7.23152e10i	1.05395	−	0.309949i
$696$	−4.68694e10	+	7.04464e10i	−0.199734	+	0.300208i
$697$	−1.43412e10	+	4.41376e10i	−0.0607651	+	0.187016i
$698$	−3.31480e11	+	4.55803e9i	−1.39648	+	0.0192024i
$699$			2.02859e11i			0.849739i
$700$	2.67483e10	−	3.46721e10i	0.111405	−	0.144407i
$701$	3.94363e11			1.63314			0.816571	−	0.577245i	$-0.195872\pi$
$701$	3.94363e11			1.63314			0.816571	+	0.577245i	$0.195872\pi$
$702$	5.43178e9	+	3.95023e11i	0.0223663	+	1.62657i
$703$	1.17431e11	+	3.81557e10i	0.480798	+	0.156221i
$704$	−2.61711e11	−	3.03980e11i	−1.06545	−	1.23753i
$705$	1.01729e11	−	6.96231e10i	0.411801	−	0.281836i
$706$	−3.09203e10	+	9.98120e10i	−0.124458	+	0.401757i
$707$		−	6.04982e10i		−	0.242139i
$708$	4.90606e10	−	3.77484e10i	0.195254	−	0.150233i
$709$	1.21590e11	+	8.83402e10i	0.481185	+	0.349601i	0.801784	−	0.597613i	$-0.203884\pi$
$709$	1.21590e11	+	8.83402e10i	0.481185	+	0.349601i	−0.320599	+	0.947215i	$0.603884\pi$
$710$	−2.88345e10	+	3.85095e10i	−0.113469	+	0.151543i
$711$	2.13457e10	+	2.93798e10i	0.0835278	+	0.114966i
$712$	−2.19033e11	+	1.73376e11i	−0.852295	+	0.674634i
$713$	−2.18101e11	−	1.58460e11i	−0.843916	−	0.613141i
$714$	−6.49829e9	+	8.93550e7i	−0.0250038	+	0.000343816i
$715$	7.43509e11	+	2.64931e11i	2.84487	+	1.01370i
$716$	−3.34097e11	−	9.84848e10i	−1.27122	−	0.374729i
$717$	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	$-0.539484\pi$
$719$	9.60619e10	−	3.12124e10i	0.359448	−	0.116792i	0.483173	+	0.875525i	$0.339484\pi$
$720$	−1.59031e11	+	1.22201e11i	−0.591770	+	0.454720i
$721$	−1.09520e10	+	3.37067e10i	−0.0405277	+	0.124731i
$722$	−1.24055e11	+	9.27639e10i	−0.456526	+	0.341374i
$723$	−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	0.983067	+	0.183247i	$0.0586607\pi$
$727$	2.38436e11	+	3.28179e11i	0.853561	+	1.17483i	−0.129506	+	0.991579i	$0.541339\pi$
$728$	5.24808e10	−	7.88805e10i	0.186842	−	0.280831i
$729$	−1.89139e10	+	5.82111e10i	−0.0669687	+	0.206108i
$730$	4.75395e10	+	1.53808e11i	0.167403	+	0.541611i
$731$	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	0.937800	+	0.347177i	$0.112860\pi$
$733$	1.10613e11	+	3.40432e11i	0.383169	+	1.17927i	−0.554631	+	0.832097i	$0.687140\pi$
$734$	1.61761e11	−	5.50296e10i	0.557302	−	0.189589i
$735$	8.67306e10	−	1.12572e11i	0.297182	−	0.385728i
$736$	2.25390e11	+	2.69191e11i	0.768111	+	0.917381i
$737$	−5.23274e10	−	3.80181e10i	−0.177362	−	0.128861i
$738$	−5.15058e10	−	1.51403e11i	−0.173632	−	0.510398i
$739$	1.35860e11	+	1.86995e11i	0.455526	+	0.626978i	0.973574	−	0.228374i	$-0.0733408\pi$
$739$	1.35860e11	+	1.86995e11i	0.455526	+	0.626978i	−0.518047	+	0.855352i	$0.673341\pi$
$740$	1.87125e11	−	1.35771e11i	0.624029	−	0.452773i
$741$	−1.48983e11	−	1.08243e11i	−0.494157	−	0.359026i
$742$	4.75423e10	+	1.47279e10i	0.156843	+	0.0485875i
$743$			1.90045e11i			0.623595i	0.950149	+	0.311797i	$0.100931\pi$
$743$			1.90045e11i			0.623595i	−0.950149	+	0.311797i	$0.899069\pi$
$744$	−1.34436e11	+	5.54852e9i	−0.438758	+	0.0181086i
$745$	−1.03061e11	+	2.89233e11i	−0.334557	+	0.938908i
$746$	−3.47618e11	+	2.59936e11i	−1.12240	+	0.839289i
$747$	−1.82468e11	−	5.92875e10i	−0.586010	−	0.190406i
$748$	7.86644e10	−	1.14782e11i	0.251288	−	0.366662i
$749$	8.62709e10			0.274118
$750$	−1.54669e11	+	3.84226e10i	−0.488830	+	0.121434i
$751$		−	6.82448e9i		−	0.0214541i	−0.999942	−	0.0107270i	$-0.996585\pi$
$751$		−	6.82448e9i		−	0.0214541i	0.999942	−	0.0107270i	$-0.00341459\pi$
$752$	3.06245e11	+	8.11926e10i	0.957631	+	0.253890i
$753$	−2.53326e10	+	7.79656e10i	−0.0787951	+	0.242506i
$754$	3.42703e11	−	2.56261e11i	1.06031	−	0.792860i
$755$	−2.32386e11	−	8.28050e10i	−0.715191	−	0.254841i
$756$	4.15320e10	−	3.19558e10i	0.127144	−	0.0978279i
$757$	−1.08744e11			−0.331147			−0.165573	−	0.986197i	$-0.552947\pi$
$757$	−1.08744e11			−0.331147			−0.165573	+	0.986197i	$0.552947\pi$
$758$	−1.03057e11	−	3.19256e10i	−0.312178	−	0.0967080i
$759$	1.91972e11	−	2.64227e11i	0.578457	−	0.796177i
$760$	−2.86769e9	−	2.18740e11i	−0.00859564	−	0.655652i
$761$	5.45393e10	−	3.96251e10i	0.162619	−	0.118150i	−0.503500	−	0.863995i	$-0.667954\pi$
$761$	5.45393e10	−	3.96251e10i	0.162619	−	0.118150i	0.666119	+	0.745846i	$0.267954\pi$
$762$	8.22739e10	+	2.41847e11i	0.244029	+	0.717332i
$763$	−8.44094e9	+	1.16180e10i	−0.0249054	+	0.0342793i
$764$	5.57175e10	−	8.12991e10i	0.163538	−	0.238623i
$765$	−5.51146e10	−	4.24628e10i	−0.160924	−	0.123983i
$766$	−1.75304e10	+	5.96368e9i	−0.0509187	+	0.0173221i
$767$	−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	0.728482	+	0.685065i	$0.240226\pi$
$769$	1.89471e11	+	5.83133e11i	0.541799	+	1.66749i	−0.186683	+	0.982420i	$0.559774\pi$
$770$	−3.09171e10	−	1.00028e11i	−0.0879499	−	0.284551i
$771$	4.05980e10	+	1.31911e10i	0.114891	+	0.0373304i
$772$	−1.73169e11	+	4.76324e9i	−0.487530	+	0.0134102i
$773$	2.58712e11	−	1.87965e11i	0.724600	−	0.526453i	−0.163251	−	0.986585i	$-0.552198\pi$
$773$	2.58712e11	−	1.87965e11i	0.724600	−	0.526453i	0.887851	+	0.460132i	$0.152198\pi$
$774$	−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
$778$	−2.78870e11	+	2.08529e11i	−0.761174	+	0.569178i
$779$	1.65899e11	+	5.39037e10i	0.450498	+	0.146376i
$780$	−3.27998e11	+	1.06341e11i	−0.886121	+	0.287291i
$781$	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
$784$	3.64682e11	−	2.00773e10i	0.965274	−	0.0531424i
$785$	−1.77067e11	+	4.96924e11i	−0.466293	+	1.30861i
$786$	1.55922e11	−	2.14401e9i	0.408523	−	0.00561742i
$787$	−1.28302e11	+	1.76593e11i	−0.334453	+	0.460335i	−0.942811	−	0.333327i	$-0.891829\pi$
$787$	−1.28302e11	+	1.76593e11i	−0.334453	+	0.460335i	0.608358	+	0.793663i	$0.291829\pi$
$788$	1.69290e11	−	5.74294e11i	0.439062	−	1.48946i
$789$	−2.44428e11	+	1.77587e11i	−0.630729	+	0.458252i
$790$	−4.44529e10	+	5.93685e10i	−0.114128	+	0.152422i
$791$	−3.76001e10	+	5.17521e10i	−0.0960468	+	0.132197i
$792$	1.97737e10	+	4.79100e11i	0.0502558	+	1.21766i
$793$	−1.21655e12			−3.07635
$794$	9.85895e10	−	3.18251e11i	0.248055	−	0.800734i
$795$	−1.02303e11	−	1.49479e11i	−0.256107	−	0.374207i
$796$	−2.02690e10	−	7.36884e11i	−0.0504870	−	1.83547i
$797$	3.98917e10	−	1.22774e11i	0.0988666	−	0.304280i	−0.889375	−	0.457177i	$-0.848860\pi$
$797$	3.98917e10	−	1.22774e11i	0.0988666	−	0.304280i	0.988242	+	0.152897i	$0.0488604\pi$
$798$	3.35856e8	+	2.44249e10i	0.000828211	+	0.0602311i
$799$			1.09909e11i			0.269677i
$800$	−3.34350e11	−	2.36606e11i	−0.816283	−	0.577652i
$801$	3.33939e11			0.811216
$802$	−2.70314e11	+	3.71697e9i	−0.653388	+	0.00898445i
$803$	3.66059e11	+	1.18940e11i	0.880419	+	0.286065i
$804$	2.82449e10	−	7.76913e8i	0.0675952	−	0.00185929i
$805$	2.58547e10	+	8.79163e10i	0.0615681	+	0.209356i
$806$	6.49995e11	+	2.01359e11i	1.54017	+	0.477123i
$807$			2.34481e11i			0.552859i
$808$	−5.65393e11	+	2.33352e10i	−1.32649	+	0.0547476i
$809$	−5.51671e11	−	4.00813e11i	−1.28791	−	0.935723i	−0.288152	−	0.957585i	$-0.593041\pi$
$809$	−5.51671e11	−	4.00813e11i	−1.28791	−	0.935723i	−0.999761	+	0.0218615i	$0.993041\pi$
$810$	1.30530e11	+	1.87847e9i	0.303229	+	0.00436379i
$811$	1.33731e11	+	1.84065e11i	0.309135	+	0.425488i	0.935111	−	0.354354i	$-0.115299\pi$
$811$	1.33731e11	+	1.84065e11i	0.309135	+	0.425488i	−0.625976	+	0.779842i	$0.715299\pi$
$812$	−5.44454e10	−	1.60494e10i	−0.125238	−	0.0369176i
$813$	4.42687e10	+	3.21631e10i	0.101329	+	0.0736200i
$814$	−7.59984e9	−	5.52693e11i	−0.0173104	−	1.25889i
$815$	1.20343e11	+	1.75838e11i	0.272767	+	0.398550i
$816$	3.34158e9	+	6.06961e10i	0.00753687	+	0.136899i
$817$	−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
$820$	2.64357e11	−	1.91808e11i	0.584703	−	0.424240i
$821$	−2.75767e10	+	8.48724e10i	−0.0606973	+	0.186807i	−0.976807	−	0.214119i	$-0.931312\pi$
$821$	−2.75767e10	+	8.48724e10i	−0.0606973	+	0.186807i	0.916110	+	0.400927i	$0.131312\pi$
$822$	−3.87848e10	−	5.18677e10i	−0.0849520	−	0.113608i
$823$	−2.02375e11	−	2.78545e11i	−0.441120	−	0.607150i	0.529340	−	0.848410i	$-0.322439\pi$
$823$	−2.02375e11	−	2.78545e11i	−0.441120	−	0.607150i	−0.970461	+	0.241260i	$0.922439\pi$
$824$	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	$-0.130013\pi$
$827$	1.19932e11	+	1.65072e11i	0.256396	+	0.352899i	−0.661342	+	0.750084i	$0.730013\pi$
$828$	−1.15401e10	−	4.19544e11i	−0.0245521	−	0.892599i
$829$	6.69431e10	−	2.06030e11i	0.141738	−	0.436226i	−0.854839	−	0.518894i	$-0.826344\pi$
$829$	6.69431e10	−	2.06030e11i	0.141738	−	0.436226i	0.996577	+	0.0826678i	$0.0263440\pi$
$830$	5.63827e9	−	3.91790e11i	0.0118805	−	0.825545i
$831$	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
$834$	8.62185e10	+	2.53442e11i	0.178212	+	0.523859i
$835$	2.27629e10	−	8.08709e11i	0.0468254	−	1.66359i
$836$	−4.31426e11	−	2.95673e11i	−0.883244	−	0.605323i
$837$	3.04490e11	+	2.21225e11i	0.620399	+	0.450746i
$838$	1.82748e11	−	6.21689e10i	0.370574	−	0.126066i
$839$	3.01679e11	+	4.15225e11i	0.608831	+	0.837984i	0.996481	−	0.0838229i	$-0.0267130\pi$
$839$	3.01679e11	+	4.15225e11i	0.608831	+	0.837984i	−0.387650	+	0.921807i	$0.626713\pi$
$840$	3.73513e10	+	2.63962e10i	0.0750220	+	0.0530181i
$841$	1.97300e11	+	1.43347e11i	0.394406	+	0.286553i
$842$	−4.81584e10	+	1.55457e11i	−0.0958127	+	0.309288i
$843$			2.22070e11i			0.439724i
$844$	7.20347e10	+	9.36214e10i	0.141962	+	0.184504i
$845$	1.23348e12	+	3.47190e10i	2.41939	+	0.0680989i
$846$	−2.26811e11	−	3.03319e11i	−0.442774	−	0.592131i
$847$	−1.48790e11	−	4.83448e10i	−0.289094	−	0.0939325i
$848$	1.19303e11	−	4.49993e11i	0.230712	−	0.870207i
$849$	1.68220e10			0.0323778
$850$	4.96150e10	−	1.33149e11i	0.0950468	−	0.255072i
$851$			4.83806e11i			0.922472i
$852$	−4.14470e10	−	2.84053e10i	−0.0786566	−	0.0539065i
$853$	−1.59091e11	+	4.89631e11i	−0.300503	+	0.924853i	0.680814	+	0.732456i	$0.261626\pi$
$853$	−1.59091e11	+	4.89631e11i	−0.300503	+	0.924853i	−0.981317	+	0.192397i	$0.938374\pi$
$854$	9.66369e10	+	1.29235e11i	0.181682	+	0.242967i
$855$	−1.59603e11	+	2.07157e11i	−0.298661	+	0.387647i
$856$	−3.32762e10	−	8.06256e11i	−0.0619781	−	1.50168i
$857$	−8.38332e11			−1.55415			−0.777075	−	0.629408i	$-0.783297\pi$
$857$	−8.38332e11			−1.55415			−0.777075	+	0.629408i	$0.783297\pi$
$858$	−2.43944e11	+	7.87462e11i	−0.450133	+	1.45305i
$859$	6.74135e10	−	9.27868e10i	0.123815	−	0.170417i	−0.742610	−	0.669725i	$-0.766412\pi$
$859$	6.74135e10	−	9.27868e10i	0.123815	−	0.170417i	0.866425	+	0.499307i	$0.166412\pi$
$860$	−7.85303e11	−	2.55717e11i	−1.43563	−	0.467482i
$861$	−2.95051e10	+	2.14367e10i	−0.0536889	+	0.0390073i
$862$	8.64511e11	−	2.94098e11i	1.56582	−	0.532676i
$863$	2.23736e11	−	3.07946e11i	0.403359	−	0.555176i	−0.558224	−	0.829690i	$-0.688517\pi$
$863$	2.23736e11	−	3.07946e11i	0.403359	−	0.555176i	0.961583	+	0.274514i	$0.0885170\pi$
$864$	−3.14667e11	−	3.75817e11i	−0.564671	−	0.674406i
$865$	−6.51528e9	−	2.21546e10i	−0.0116377	−	0.0395730i
$866$	−7.22693e10	−	2.12438e11i	−0.128494	−	0.377712i
$867$	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
$870$	1.19005e11	+	1.68853e11i	0.207724	+	0.294736i
$871$	−1.35904e11	−	4.41580e10i	−0.236135	−	0.0767249i
$872$	1.11833e11	+	7.44047e10i	0.193421	+	0.128687i
$873$	−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	−0.558389	−	0.829579i	$-0.688580\pi$
$877$	3.43316e10	−	2.49434e10i	0.0580358	−	0.0421654i	0.616425	+	0.787414i	$0.288580\pi$
$878$	5.43180e11	+	7.26406e11i	0.914040	+	1.22237i
$879$	−5.06136e11	−	1.64453e11i	−0.847835	−	0.275478i
$880$	−9.22902e11	+	3.27522e11i	−1.53895	+	0.546147i
$881$	−1.58252e11	−	4.87051e11i	−0.262692	−	0.808483i	−0.992216	−	0.124528i	$-0.960258\pi$
$881$	−1.58252e11	−	4.87051e11i	−0.262692	−	0.808483i	0.729524	−	0.683955i	$-0.239742\pi$
$882$	−3.56721e11	−	2.51753e11i	−0.589460	−	0.416006i
$883$	−3.66664e11	+	1.19136e11i	−0.603150	+	0.195975i	−0.594645	−	0.803988i	$-0.702707\pi$
$883$	−3.66664e11	+	1.19136e11i	−0.603150	+	0.195975i	−0.00850527	+	0.999964i	$0.502707\pi$
$884$	8.69246e10	−	2.94881e11i	0.142342	−	0.482878i
$885$	−4.26387e10	−	1.44989e11i	−0.0695074	−	0.236353i
$886$	1.75141e9	+	1.27370e11i	0.00284219	+	0.206697i
$887$	4.77374e10	−	6.57049e10i	0.0771196	−	0.106146i	−0.768714	−	0.639592i	$-0.779103\pi$
$887$	4.77374e10	−	6.57049e10i	0.0771196	−	0.106146i	0.845834	+	0.533446i	$0.179103\pi$
$888$	1.49866e11	+	1.89332e11i	0.241019	+	0.304489i
$889$	−1.38641e11	+	1.00729e11i	−0.221966	+	0.161268i
$890$	2.01394e11	+	6.51585e11i	0.320987	+	1.03851i
$891$	1.83454e11	−	2.52503e11i	0.291083	−	0.400642i
$892$	7.28694e10	+	9.47063e10i	0.115103	+	0.149596i
$893$	4.13110e11			0.649621
$894$	−3.06332e11	−	9.48969e10i	−0.479559	−	0.148560i
$895$	−5.18992e11	+	6.73626e11i	−0.808851	+	1.04985i
$896$	1.12964e10	+	1.17006e11i	0.0175271	+	0.181541i
$897$	2.22975e11	−	6.86247e11i	0.344419	−	1.06001i
$898$	5.79132e11	−	7.96338e9i	0.890578	−	0.0122459i
$899$		−	4.07674e11i		−	0.624130i
$900$	1.37846e11	+	4.69843e11i	0.210099	+	0.716115i
$901$	1.61498e11			0.245058
$902$	−1.07365e10	−	7.80807e11i	−0.0162195	−	1.17955i
$903$	8.77074e10	+	2.84979e10i	0.131912	+	0.0428609i
$904$	4.98159e11	+	3.31435e11i	0.745923	+	0.496277i
$905$	4.75525e11	+	1.33847e10i	0.708890	+	0.0199533i
$906$	7.62454e10	−	2.46123e11i	0.113162	−	0.365292i
$907$		−	1.02567e12i		−	1.51558i	−0.652501	−	0.757788i	$-0.726280\pi$
$907$		−	1.02567e12i		−	1.51558i	0.652501	−	0.757788i	$-0.273720\pi$
$908$	−5.93189e11	−	7.70950e11i	−0.872669	−	1.13418i
$909$	5.47269e11	+	3.97614e11i	0.801577	+	0.582379i
$910$	−1.33253e11	−	1.89069e11i	−0.194317	−	0.275711i
$911$	−1.90138e11	−	2.61702e11i	−0.276055	−	0.379957i	0.648367	−	0.761328i	$-0.275452\pi$
$911$	−1.90138e11	−	2.61702e11i	−0.276055	−	0.379957i	−0.924422	+	0.381371i	$0.875452\pi$
$912$	2.28136e11	−	1.25599e10i	0.329773	−	0.0181554i
$913$	−7.57895e11	−	5.50643e11i	−1.09075	−	0.792478i
$914$	−9.75169e11	+	1.34091e10i	−1.39732	+	0.0192139i
$915$	1.65238e10	−	5.87050e11i	0.0235736	−	0.837511i
$916$	3.13711e10	−	1.06422e11i	0.0445602	−	0.151165i
$917$	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	$-0.700148\pi$
$919$	−4.19858e11	+	1.36420e11i	−0.588627	+	0.191256i	−0.000465282		1.00000i	$0.500148\pi$
$920$	8.11661e11	−	2.75539e11i	1.13298	−	0.384620i
$921$	4.92844e10	−	1.51682e11i	0.0684969	−	0.210812i
$922$	1.14263e12	−	8.54418e11i	1.58118	−	1.18235i
$923$	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
$928$	−1.28991e11	+	5.15017e11i	−0.173927	+	0.694432i
$929$	−2.08018e11	+	6.40215e11i	−0.279280	+	0.859534i	0.708776	+	0.705434i	$0.249248\pi$
$929$	−2.08018e11	+	6.40215e11i	−0.279280	+	0.859534i	−0.988055	+	0.154100i	$0.950752\pi$
$930$	−1.05995e11	+	3.10923e11i	−0.141695	+	0.415643i
$931$	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
$934$	−1.04251e12	+	3.54651e11i	−1.36991	+	0.466030i
$935$	−1.91872e11	−	2.80351e11i	−0.251053	−	0.366823i
$936$	3.68635e11	+	9.93172e11i	0.480279	+	1.29396i
$937$	2.43192e11	+	1.76689e11i	0.315494	+	0.229220i	0.734250	−	0.678879i	$-0.237534\pi$
$937$	2.43192e11	+	1.76689e11i	0.315494	+	0.229220i	−0.418756	+	0.908099i	$0.637534\pi$
$938$	6.10467e9	+	1.79449e10i	0.00788590	+	0.0231809i
$939$	−9.39703e10	−	1.29339e11i	−0.120873	−	0.166367i
$940$	4.55052e11	−	6.25483e11i	0.582841	−	0.801132i
$941$	−8.30687e10	−	6.03529e10i	−0.105945	−	0.0769733i	0.533552	−	0.845768i	$-0.320857\pi$
$941$	−8.30687e10	−	6.03529e10i	−0.105945	−	0.0769733i	−0.639496	+	0.768794i	$0.720857\pi$
$942$	−5.26300e11	−	1.63040e11i	−0.668390	−	0.207057i
$943$			6.83487e11i			0.864338i
$944$	2.10688e11	−	3.26312e11i	0.265308	−	0.410909i
$945$	−3.60957e10	−	1.22740e11i	−0.0452614	−	0.153907i
$946$	−1.58136e12	+	1.18248e12i	−1.97454	+	1.47649i
$947$	3.11484e11	+	1.01207e11i	0.387290	+	0.125838i	0.496189	−	0.868215i	$-0.334732\pi$
$947$	3.11484e11	+	1.01207e11i	0.387290	+	0.125838i	−0.108899	+	0.994053i	$0.534732\pi$
$948$	−6.38971e10	−	4.37913e10i	−0.0791130	−	0.0542193i
$949$	8.50355e11			1.04842
$950$	−5.00463e11	−	1.86486e11i	−0.614437	−	0.228956i
$951$		−	6.33468e11i		−	0.774467i
$952$	−3.82302e10	+	1.41899e10i	−0.0465435	+	0.0172755i
$953$	4.10733e11	−	1.26411e12i	0.497952	−	1.53254i	−0.314353	−	0.949306i	$-0.601787\pi$
$953$	4.10733e11	−	1.26411e12i	0.497952	−	1.53254i	0.812305	−	0.583233i	$-0.198213\pi$
$954$	−4.45693e11	+	3.33273e11i	−0.538074	+	0.402352i
$955$	−1.35902e11	−	1.98571e11i	−0.163385	−	0.238728i
$956$	6.47637e11	+	8.41715e11i	0.775354	+	1.00771i
$957$	4.93893e11			0.588824
$958$	1.17663e12	+	3.64503e11i	1.39694	+	0.432752i
$959$	2.55373e10	−	3.51491e10i	0.0301926	−	0.0415566i
$960$	2.32282e11	−	3.59253e11i	0.273483	−	0.422975i
$961$	−1.65537e11	+	1.20269e11i	−0.194089	+	0.141014i
$962$	−3.93299e11	−	1.15611e12i	−0.459222	−	1.34990i
$963$	−5.67001e11	+	7.80410e11i	−0.659294	+	0.907440i
$964$	−8.66049e11	−	5.93538e11i	−1.00285	−	0.687291i
$965$	−1.41960e11	+	3.98400e11i	−0.163703	+	0.459420i
$966$	−9.06125e10	+	3.08255e10i	−0.104059	+	0.0353999i
$967$	−6.35562e11	+	2.06507e11i	−0.726862	+	0.236172i	−0.648996	−	0.760792i	$-0.724811\pi$
$967$	−6.35562e11	+	2.06507e11i	−0.726862	+	0.236172i	−0.0778663	+	0.996964i	$0.524811\pi$
$968$	−3.94421e11	+	1.40918e12i	−0.449220	+	1.60497i
$969$	2.44932e10	+	7.53823e10i	0.0277812	+	0.0855016i
$970$	−9.89891e10	−	7.41193e10i	−0.111815	−	0.0837229i
$971$	−1.32019e12	−	4.28956e11i	−1.48511	−	0.482543i	−0.549478	−	0.835508i	$-0.685173\pi$
$971$	−1.32019e12	−	4.28956e11i	−1.48511	−	0.482543i	−0.935636	+	0.352966i	$0.885173\pi$
$972$	2.53370e10	+	9.21134e11i	0.0283851	+	1.03195i
$973$	−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	−0.377649	−	0.925949i	$-0.623267\pi$
$977$	3.51951e11	−	2.55707e11i	0.386282	−	0.280650i	0.763930	+	0.645299i	$0.223267\pi$
$978$	−1.78229e11	+	1.33273e11i	−0.194815	+	0.145675i
$979$	1.55076e12	+	5.03871e11i	1.68816	+	0.548515i
$980$	2.76089e11	−	8.47867e11i	0.299326	−	0.919229i
$981$	−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	$-0.871422\pi$
$983$	−1.33745e12	+	4.34565e11i	−1.43240	+	0.465415i	−0.512881	+	0.858460i	$0.671422\pi$
$984$	2.11720e11	+	2.67475e11i	0.225830	+	0.285301i
$985$	−1.15792e12	−	8.92117e11i	−1.23009	−	0.947713i
$986$	−1.84164e11	+	2.53235e9i	−0.194848	+	0.00267927i
$987$	−5.07677e10	+	6.98757e10i	−0.0534957	+	0.0736305i
$988$	−1.10836e12	−	3.26721e11i	−1.16319	−	0.342885i
$989$	1.39823e12	−	1.01587e12i	1.46148	−	1.06183i
$990$	1.10806e12	+	3.77742e11i	1.15351	+	0.393237i
$991$	9.24175e11	−	1.27202e12i	0.958208	−	1.31886i	0.0104239	−	0.999946i	$-0.496682\pi$
$991$	9.24175e11	−	1.27202e12i	0.958208	−	1.31886i	0.947784	−	0.318914i	$-0.103318\pi$
$992$	−7.83128e11	+	3.15435e11i	−0.808697	+	0.325734i
$993$	4.23875e11			0.435954
$994$	9.97433e9	−	3.21976e10i	0.0102174	−	0.0329821i
$995$	−1.69530e12	−	6.04081e11i	−1.72964	−	0.616315i
$996$	4.09091e11	−	1.12526e10i	0.415703	−	0.0114344i
$997$	−1.19356e11	+	3.67340e11i	−0.120799	+	0.371782i	−0.993112	−	0.117166i	$-0.962619\pi$
$997$	−1.19356e11	+	3.67340e11i	−0.120799	+	0.371782i	0.872313	+	0.488948i	$0.162619\pi$
$998$	2.32501e10	+	1.69085e12i	0.0234371	+	1.70445i
$999$		−	6.75440e11i		−	0.678148i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.70	✓	464	4.3	odd	2	inner
100.9.j.b.11.116	yes	464	1.1	even	1	trivial
100.9.j.b.91.70	yes	464	25.16	even	5	inner
100.9.j.b.91.116	yes	464	100.91	odd	10	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+(15.9985 - 0.219988i) q^{2} +(38.8019 + 12.6075i) q^{3} +(255.903 - 7.03895i) q^{4} +(209.784 - 588.741i) q^{5} +(623.545 + 193.165i) q^{6} +437.907i q^{7} +(4092.52 - 168.908i) q^{8} +(-3961.32 - 2878.07i) q^{9} +(3226.70 - 9465.11i) q^{10} +(-14053.1 - 19342.4i) q^{11} +(10018.3 + 2953.17i) q^{12} +(-42733.3 - 31047.5i) q^{13} +(96.3343 + 7005.85i) q^{14} +(15562.5 - 20199.4i) q^{15} +(65436.9 - 3602.58i) q^{16} +(7025.45 + 21622.1i) q^{17} +(-64008.3 - 45173.3i) q^{18} +(81270.3 - 26406.3i) q^{19} +(49540.2 - 152137. i) q^{20} +(-5520.91 + 16991.6i) q^{21} +(-229083. - 306358. 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} +(3082.41 + 112062. i) q^{28} +(-156464. + 481548. i) q^{29} +(244533. - 326583. i) q^{30} +(-765749. + 248807. i) q^{31} +(1.04610e6 - 72031.2i) q^{32} +(-301427. - 927697. i) q^{33} +(117153. + 344375. i) q^{34} +(257814. + 91865.7i) q^{35} +(-1.03397e6 - 708624. i) q^{36} +(1.16899e6 + 849318. i) q^{37} +(1.29439e6 - 440340. i) q^{38} +(-1.26670e6 - 1.74346e6i) q^{39} +(759099. - 2.44487e6i) q^{40} +(1.65146e6 + 1.19986e6i) q^{41} +(-84588.3 + 273055. i) q^{42} -5.16180e6i q^{43} +(-3.73238e6 - 4.85087e6i) q^{44} +(-2.52546e6 + 1.72842e6i) q^{45} +(3.20819e6 + 4.29038e6i) q^{46} +(4.59776e6 + 1.49390e6i) q^{47} +(2.58449e6 + 685208. i) q^{48} +5.57304e6 q^{49} +(-4.89559e6 - 3.88532e6i) q^{50} +927551. i q^{51} +(-1.11541e7 - 7.64437e6i) q^{52} +(2.19512e6 - 6.75590e6i) q^{53} +(-4.47894e6 - 5.98978e6i) q^{54} +(-1.43358e7 + 4.21591e6i) q^{55} +(73966.1 + 1.79214e6i) q^{56} +3.48636e6 q^{57} +(-2.39726e6 + 7.73846e6i) q^{58} +(3.48368e6 - 4.79488e6i) q^{59} +(3.84032e6 - 5.27864e6i) q^{60} +(1.86328e7 - 1.35375e7i) q^{61} +(-1.21961e7 + 4.14899e6i) q^{62} +(1.26033e6 - 1.73469e6i) q^{63} +(1.67202e7 - 1.38252e6i) q^{64} +(-2.72437e7 + 1.86456e7i) q^{65} +(-5.02646e6 - 1.47754e7i) q^{66} +(2.57291e6 - 835989. i) q^{67} +(1.95003e6 + 5.48371e6i) q^{68} +(4.22132e6 + 1.29919e7i) q^{69} +(4.14484e6 + 1.41300e6i) q^{70} +(-4.57537e6 - 1.48663e6i) q^{71} +(-1.66979e7 - 1.11094e7i) 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} +(-2.06488e7 - 2.76141e7i) q^{78} +(-7.05366e6 - 2.29187e6i) q^{79} +(1.16066e7 - 3.92811e7i) q^{80} +(4.03402e6 + 1.24154e7i) q^{81} +(2.66849e7 + 1.88326e7i) q^{82} +(3.72653e7 - 1.21082e7i) q^{83} +(-1.29322e6 + 4.38707e6i) q^{84} +(1.42036e7 + 399792. i) q^{85} +(-1.13553e6 - 8.25810e7i) q^{86} +(-1.21422e7 + 1.67123e7i) q^{87} +(-6.07796e7 - 7.67855e7i) q^{88} +(-5.51749e7 + 4.00869e7i) q^{89} +(-4.00233e7 + 2.82077e7i) q^{90} +(1.35959e7 - 1.87132e7i) q^{91} +(5.22700e7 + 6.79338e7i) q^{92} -3.28493e7 q^{93} +(7.38859e7 + 2.28887e7i) q^{94} +(1.50269e6 - 5.33867e7i) q^{95} +(4.14987e7 + 1.03937e7i) q^{96} +(3.82139e6 - 1.17610e7i) q^{97} +(8.91602e7 - 1.22600e6i) 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

Related objects

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