LMFDB - Embedded newform 100.9.j.b.11.28

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			11.28
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.0924 - 11.5307i) q^{2} +(-36.9043 - 11.9909i) q^{3} +(-9.91611 + 255.808i) q^{4} +(-624.781 - 16.5320i) q^{5} +(271.094 + 558.543i) q^{6} +802.640i q^{7} +(3059.65 - 2723.19i) q^{8} +(-4089.81 - 2971.42i) q^{9} +(6739.72 + 7387.57i) q^{10} +(-13197.2 - 18164.3i) q^{11} +(3433.33 - 9321.52i) q^{12} +(-16151.5 - 11734.7i) q^{13} +(9255.03 - 8903.22i) q^{14} +(22858.9 + 8101.82i) q^{15} +(-65339.3 - 5073.24i) q^{16} +(-25864.7 - 79603.4i) q^{17} +(11103.2 + 80118.9i) q^{18} +(-135137. + 43908.6i) q^{19} +(10424.4 - 159660. i) q^{20} +(9624.41 - 29620.9i) q^{21} +(-63059.8 + 353660. i) q^{22} +(-152647. - 210100. i) q^{23} +(-145568. + 63809.5i) q^{24} +(390078. + 20657.8i) q^{25} +(43848.8 + 316405. i) q^{26} +(264946. + 364667. i) q^{27} +(-205322. - 7959.06i) q^{28} +(30864.7 - 94991.6i) q^{29} +(-160141. - 353449. i) q^{30} +(-1.36260e6 + 442736. i) q^{31} +(666274. + 809686. i) q^{32} +(269225. + 828590. i) q^{33} +(-630984. + 1.18123e6i) q^{34} +(13269.2 - 501474. i) q^{35} +(800668. - 1.01674e6i) q^{36} +(-2.18913e6 - 1.59049e6i) q^{37} +(2.00529e6 + 1.07117e6i) q^{38} +(455349. + 626734. i) q^{39} +(-1.95663e6 + 1.65082e6i) q^{40} +(-2.37789e6 - 1.72764e6i) q^{41} +(-448309. + 217591. i) q^{42} +729028. i q^{43} +(4.77745e6 - 3.19582e6i) q^{44} +(2.50612e6 + 1.92410e6i) q^{45} +(-729388. + 4.09065e6i) q^{46} +(1.50061e6 + 487578. i) q^{47} +(2.35047e6 + 970705. i) q^{48} +5.12057e6 q^{49} +(-4.08872e6 - 4.72704e6i) q^{50} +3.24785e6i q^{51} +(3.16200e6 - 4.01531e6i) q^{52} +(-638611. + 1.96544e6i) q^{53} +(1.26599e6 - 7.10006e6i) q^{54} +(7.94505e6 + 1.15669e7i) q^{55} +(2.18574e6 + 2.45580e6i) q^{56} +5.51364e6 q^{57} +(-1.43769e6 + 697795. i) q^{58} +(5.70995e6 - 7.85907e6i) q^{59} +(-2.29918e6 + 5.76715e6i) q^{60} +(2.23671e7 - 1.62507e7i) q^{61} +(2.02196e7 + 1.08008e7i) q^{62} +(2.38498e6 - 3.28265e6i) q^{63} +(1.94569e6 - 1.66640e7i) q^{64} +(9.89714e6 + 7.59865e6i) q^{65} +(6.56790e6 - 1.22954e7i) q^{66} +(-1.74623e7 + 5.67384e6i) q^{67} +(2.06197e7 - 5.82704e6i) q^{68} +(3.11403e6 + 9.58398e6i) q^{69} +(-5.92956e6 + 5.40956e6i) q^{70} +(3.19530e7 + 1.03821e7i) q^{71} +(-2.06051e7 + 2.04583e6i) q^{72} +(-3.24076e7 + 2.35455e7i) q^{73} +(5.94315e6 + 4.28847e7i) q^{74} +(-1.41479e7 - 5.43977e6i) q^{75} +(-9.89213e6 - 3.50044e7i) q^{76} +(1.45794e7 - 1.05926e7i) q^{77} +(2.17578e6 - 1.22025e7i) q^{78} +(2.86034e7 + 9.29380e6i) q^{79} +(4.07389e7 + 4.24985e6i) q^{80} +(4.84444e6 + 1.49097e7i) q^{81} +(6.45561e6 + 4.65825e7i) q^{82} +(-6.50527e7 + 2.11369e7i) q^{83} +(7.48182e6 + 2.75572e6i) q^{84} +(1.48438e7 + 5.01623e7i) q^{85} +(8.40623e6 - 8.08669e6i) q^{86} +(-2.27808e6 + 3.13551e6i) q^{87} +(-8.98437e7 - 1.96381e7i) q^{88} +(6.65941e7 - 4.83835e7i) q^{89} +(-5.61257e6 - 5.02403e7i) q^{90} +(9.41876e6 - 1.29638e7i) q^{91} +(5.52589e7 - 3.69648e7i) q^{92} +5.55947e7 q^{93} +(-1.10233e7 - 2.27116e7i) q^{94} +(8.51568e7 - 2.51992e7i) q^{95} +(-1.48795e7 - 3.78702e7i) q^{96} +(9.40676e6 - 2.89510e7i) q^{97} +(-5.67996e7 - 5.90440e7i) q^{98} +1.13503e8i 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 $

$2$	−11.0924	−	11.5307i	−0.693277	−	0.720671i
$2$	−11.0924	−	11.5307i	−0.693277	−	0.720671i
$3$	−36.9043	−	11.9909i	−0.455609	−	0.148036i	0.0722168	−	0.997389i	$-0.476993\pi$
$3$	−36.9043	−	11.9909i	−0.455609	−	0.148036i	−0.527826	+	0.849353i	$0.676993\pi$
$4$	−9.91611	+	255.808i	−0.0387348	+	0.999250i
$5$	−624.781	−	16.5320i	−0.999650	−	0.0264512i
$5$	−624.781	−	16.5320i	−0.999650	−	0.0264512i
$6$	271.094	+	558.543i	0.209178	+	0.430975i
$7$			802.640i			0.334294i	0.985932	+	0.167147i	$0.0534554\pi$
$7$			802.640i			0.334294i	−0.985932	+	0.167147i	$0.946545\pi$
$8$	3059.65	−	2723.19i	0.746985	−	0.664841i
$9$	−4089.81	−	2971.42i	−0.623352	−	0.452892i
$10$	6739.72	+	7387.57i	0.673972	+	0.738757i
$11$	−13197.2	−	18164.3i	−0.901384	−	1.24065i	−0.970024	−	0.243008i	$-0.921866\pi$
$11$	−13197.2	−	18164.3i	−0.901384	−	1.24065i	0.0686399	−	0.997642i	$-0.478134\pi$
$12$	3433.33	−	9321.52i	0.165573	−	0.449533i
$13$	−16151.5	−	11734.7i	−0.565508	−	0.410865i	0.267963	−	0.963429i	$-0.413650\pi$
$13$	−16151.5	−	11734.7i	−0.565508	−	0.410865i	−0.833471	+	0.552564i	$0.813650\pi$
$14$	9255.03	−	8903.22i	0.240916	−	0.231758i
$15$	22858.9	+	8101.82i	0.451534	+	0.160036i
$16$	−65339.3	−	5073.24i	−0.996999	−	0.0774115i
$17$	−25864.7	−	79603.4i	−0.309679	−	0.953094i	−0.977890	−	0.209122i	$-0.932939\pi$
$17$	−25864.7	−	79603.4i	−0.309679	−	0.953094i	0.668210	−	0.743972i	$-0.267061\pi$
$18$	11103.2	+	80118.9i	0.105769	+	0.763211i
$19$	−135137.	+	43908.6i	−1.03695	+	0.336926i	−0.777535	−	0.628839i	$-0.783530\pi$
$19$	−135137.	+	43908.6i	−1.03695	+	0.336926i	−0.259417	+	0.965765i	$0.583530\pi$
$20$	10424.4	−	159660.i	0.0651526	−	0.997875i
$21$	9624.41	−	29620.9i	0.0494877	−	0.152307i
$22$	−63059.8	+	353660.i	−0.269192	+	1.50972i
$23$	−152647.	−	210100.i	−0.545476	−	0.750784i	0.443913	−	0.896070i	$-0.353590\pi$
$23$	−152647.	−	210100.i	−0.545476	−	0.750784i	−0.989390	+	0.145286i	$0.953590\pi$
$24$	−145568.	+	63809.5i	−0.438754	+	0.192327i
$25$	390078.	+	20657.8i	0.998601	+	0.0528839i
$26$	43848.8	+	316405.i	0.0959544	+	0.692389i
$27$	264946.	+	364667.i	0.498542	+	0.686185i
$28$	−205322.	−	7959.06i	−0.334043	−	0.0129488i
$29$	30864.7	−	94991.6i	0.0436385	−	0.134305i	−0.926864	−	0.375398i	$-0.877506\pi$
$29$	30864.7	−	94991.6i	0.0436385	−	0.134305i	0.970502	+	0.241093i	$0.0775059\pi$
$30$	−160141.	−	353449.i	−0.197705	−	0.436357i
$31$	−1.36260e6	+	442736.i	−1.47544	+	0.479400i	−0.932748	−	0.360530i	$-0.882596\pi$
$31$	−1.36260e6	+	442736.i	−1.47544	+	0.479400i	−0.542694	+	0.839930i	$0.682596\pi$
$32$	666274.	+	809686.i	0.635408	+	0.772176i
$33$	269225.	+	828590.i	0.227018	+	0.698689i
$34$	−630984.	+	1.18123e6i	−0.472175	+	0.883935i
$35$	13269.2	−	501474.i	0.00884247	−	0.334177i
$36$	800668.	−	1.01674e6i	0.476697	−	0.605342i
$37$	−2.18913e6	−	1.59049e6i	−1.16806	−	0.848642i	−0.177281	−	0.984160i	$-0.556730\pi$
$37$	−2.18913e6	−	1.59049e6i	−1.16806	−	0.848642i	−0.990775	+	0.135518i	$0.956730\pi$
$38$	2.00529e6	+	1.07117e6i	0.961708	+	0.513719i
$39$	455349.	+	626734.i	0.196827	+	0.270910i
$40$	−1.95663e6	+	1.65082e6i	−0.764309	+	0.644850i
$41$	−2.37789e6	−	1.72764e6i	−0.841503	−	0.611388i	0.0812868	−	0.996691i	$-0.474097\pi$
$41$	−2.37789e6	−	1.72764e6i	−0.841503	−	0.611388i	−0.922790	+	0.385303i	$0.874097\pi$
$42$	−448309.	+	217591.i	−0.144072	+	0.0699268i
$43$			729028.i			0.213241i	0.994300	+	0.106620i	$0.0340030\pi$
$43$			729028.i			0.213241i	−0.994300	+	0.106620i	$0.965997\pi$
$44$	4.77745e6	−	3.19582e6i	1.27463	−	0.852652i
$45$	2.50612e6	+	1.92410e6i	0.611154	+	0.469222i
$46$	−729388.	+	4.09065e6i	−0.162902	+	0.913610i
$47$	1.50061e6	+	487578.i	0.307522	+	0.0999200i	0.458713	−	0.888585i	$-0.348311\pi$
$47$	1.50061e6	+	487578.i	0.307522	+	0.0999200i	−0.151191	+	0.988505i	$0.548311\pi$
$48$	2.35047e6	+	970705.i	0.442782	+	0.182862i
$49$	5.12057e6			0.888248
$50$	−4.08872e6	−	4.72704e6i	−0.654195	−	0.756326i
$51$			3.24785e6i			0.480082i
$52$	3.16200e6	−	4.01531e6i	0.432462	−	0.549169i
$53$	−638611.	+	1.96544e6i	−0.0809343	+	0.249090i	−0.983334	−	0.181811i	$-0.941804\pi$
$53$	−638611.	+	1.96544e6i	−0.0809343	+	0.249090i	0.902399	+	0.430901i	$0.141804\pi$
$54$	1.26599e6	−	7.10006e6i	0.148886	−	0.835001i
$55$	7.94505e6	+	1.15669e7i	0.868252	+	1.26406i
$56$	2.18574e6	+	2.45580e6i	0.222252	+	0.249712i
$57$	5.51364e6			0.522322
$58$	−1.43769e6	+	697795.i	−0.127044	+	0.0616618i
$59$	5.70995e6	−	7.85907e6i	0.471221	−	0.648579i	−0.505568	−	0.862787i	$-0.668717\pi$
$59$	5.70995e6	−	7.85907e6i	0.471221	−	0.648579i	0.976788	+	0.214208i	$0.0687169\pi$
$60$	−2.29918e6	+	5.76715e6i	−0.177406	+	0.444996i
$61$	2.23671e7	−	1.62507e7i	1.61544	−	1.17369i	0.774454	−	0.632631i	$-0.218025\pi$
$61$	2.23671e7	−	1.62507e7i	1.61544	−	1.17369i	0.840987	−	0.541055i	$-0.181975\pi$
$62$	2.02196e7	+	1.08008e7i	1.36838	+	0.730952i
$63$	2.38498e6	−	3.28265e6i	0.151399	−	0.208383i
$64$	1.94569e6	−	1.66640e7i	0.115972	−	0.993252i
$65$	9.89714e6	+	7.59865e6i	0.554442	+	0.425680i
$66$	6.56790e6	−	1.22954e7i	0.346139	−	0.647990i
$67$	−1.74623e7	+	5.67384e6i	−0.866567	+	0.281565i	−0.708369	−	0.705843i	$-0.750569\pi$
$67$	−1.74623e7	+	5.67384e6i	−0.866567	+	0.281565i	−0.158198	+	0.987407i	$0.550569\pi$
$68$	2.06197e7	−	5.82704e6i	0.964375	−	0.272529i
$69$	3.11403e6	+	9.58398e6i	0.137381	+	0.422814i
$70$	−5.92956e6	+	5.40956e6i	−0.246962	+	0.225305i
$71$	3.19530e7	+	1.03821e7i	1.25741	+	0.408558i	0.860572	−	0.509329i	$-0.170107\pi$
$71$	3.19530e7	+	1.03821e7i	1.25741	+	0.408558i	0.396841	+	0.917887i	$0.370107\pi$
$72$	−2.06051e7	+	2.04583e6i	−0.766736	+	0.0761270i
$73$	−3.24076e7	+	2.35455e7i	−1.14118	+	0.829119i	−0.987284	−	0.158968i	$-0.949183\pi$
$73$	−3.24076e7	+	2.35455e7i	−1.14118	+	0.829119i	−0.153900	+	0.988086i	$0.549183\pi$
$74$	5.94315e6	+	4.28847e7i	0.198194	+	1.43013i
$75$	−1.41479e7	−	5.43977e6i	−0.447143	−	0.171924i
$76$	−9.89213e6	−	3.50044e7i	−0.296507	−	1.04923i
$77$	1.45794e7	−	1.05926e7i	0.414741	−	0.301327i
$78$	2.17578e6	−	1.22025e7i	0.0587811	−	0.329663i
$79$	2.86034e7	+	9.29380e6i	0.734359	+	0.238608i	0.652238	−	0.758014i	$-0.273830\pi$
$79$	2.86034e7	+	9.29380e6i	0.734359	+	0.238608i	0.0821217	+	0.996622i	$0.473830\pi$
$80$	4.07389e7	+	4.24985e6i	0.994603	+	0.103756i
$81$	4.84444e6	+	1.49097e7i	0.112539	+	0.346360i
$82$	6.45561e6	+	4.65825e7i	0.142785	+	1.03031i
$83$	−6.50527e7	+	2.11369e7i	−1.37073	+	0.445378i	−0.899612	−	0.436690i	$-0.856151\pi$
$83$	−6.50527e7	+	2.11369e7i	−1.37073	+	0.445378i	−0.471121	+	0.882068i	$0.656151\pi$
$84$	7.48182e6	+	2.75572e6i	0.150276	+	0.0553501i
$85$	1.48438e7	+	5.01623e7i	0.284360	+	0.960952i
$86$	8.40623e6	−	8.08669e6i	0.153677	−	0.147835i
$87$	−2.27808e6	+	3.13551e6i	−0.0397642	+	0.0547307i
$88$	−8.98437e7	−	1.96381e7i	−1.49816	−	0.327468i
$89$	6.65941e7	−	4.83835e7i	1.06139	−	0.771147i	0.0870470	−	0.996204i	$-0.472257\pi$
$89$	6.65941e7	−	4.83835e7i	1.06139	−	0.771147i	0.974346	+	0.225057i	$0.0722570\pi$
$90$	−5.61257e6	−	5.02403e7i	−0.0855444	−	0.765742i
$91$	9.41876e6	−	1.29638e7i	0.137350	−	0.189046i
$92$	5.52589e7	−	3.69648e7i	0.771349	−	0.515986i
$93$	5.55947e7			0.743193
$94$	−1.10233e7	−	2.27116e7i	−0.141188	−	0.290895i
$95$	8.51568e7	−	2.51992e7i	1.04550	−	0.309380i
$96$	−1.48795e7	−	3.78702e7i	−0.175188	−	0.445874i
$97$	9.40676e6	−	2.89510e7i	0.106256	−	0.327022i	−0.883767	−	0.467927i	$-0.845001\pi$
$97$	9.40676e6	−	2.89510e7i	0.106256	−	0.327022i	0.990023	+	0.140905i	$0.0450011\pi$
$98$	−5.67996e7	−	5.90440e7i	−0.615801	−	0.640135i
$99$			1.13503e8i			1.18159i
$100$	−9.15248e6	+	9.95803e7i	−0.0915248	+	0.995803i
$101$	−1.01600e8			−0.976353			−0.488177	−	0.872745i	$-0.662338\pi$
$101$	−1.01600e8			−0.976353			−0.488177	+	0.872745i	$0.662338\pi$
$102$	3.74502e7	−	3.60266e7i	0.345982	−	0.332830i
$103$	−817360.	−	265576.i	−0.00726214	−	0.00235961i	0.305384	−	0.952229i	$-0.401215\pi$
$103$	−817360.	−	265576.i	−0.00726214	−	0.00235961i	−0.312646	+	0.949870i	$0.601215\pi$
$104$	−8.13737e7	+	8.07937e6i	−0.695586	+	0.0690628i
$105$	−6.50284e6	+	1.83475e7i	−0.0534991	+	0.150945i
$106$	2.97467e7	−	1.44379e7i	0.235622	−	0.114361i
$107$			2.34293e8i			1.78741i	0.448658	+	0.893704i	$0.351902\pi$
$107$			2.34293e8i			1.78741i	−0.448658	+	0.893704i	$0.648098\pi$
$108$	−9.59119e7	+	6.41592e7i	−0.704981	+	0.471589i
$109$	−1.41189e8	−	1.02580e8i	−1.00022	−	0.726700i	−0.0380825	−	0.999275i	$-0.512125\pi$
$109$	−1.41189e8	−	1.02580e8i	−1.00022	−	0.726700i	−0.962135	+	0.272574i	$0.912125\pi$
$110$	4.52453e7	−	2.19918e8i	0.309031	−	1.50207i
$111$	6.17167e7	+	8.49458e7i	0.406547	+	0.559564i
$112$	4.07198e6	−	5.24439e7i	0.0258782	−	0.333291i
$113$	−8.03495e7	−	5.83773e7i	−0.492798	−	0.358039i	0.313461	−	0.949601i	$-0.398511\pi$
$113$	−8.03495e7	−	5.83773e7i	−0.492798	−	0.358039i	−0.806259	+	0.591562i	$0.798511\pi$
$114$	−6.11596e7	−	6.35763e7i	−0.362114	−	0.376423i
$115$	9.18974e7	+	1.33790e8i	0.525426	+	0.764950i
$116$	2.39935e7	+	8.83737e6i	0.132514	+	0.0488080i
$117$	3.11876e7	+	9.59857e7i	0.166433	+	0.512228i
$118$	−1.53958e8	+	2.13362e7i	−0.794099	+	0.110050i
$119$	6.38928e7	−	2.07600e7i	0.318614	−	0.103524i
$120$	9.20030e7	−	3.74604e7i	0.443688	−	0.180654i
$121$	−8.95376e7	+	2.75569e8i	−0.417700	+	1.28555i
$122$	−4.35488e8	−	7.76503e7i	−1.96579	−	0.350513i
$123$	6.70384e7	+	9.22704e7i	0.292889	+	0.403127i
$124$	−9.97437e7	−	3.52954e8i	−0.421889	−	1.49290i
$125$	−2.43372e8	−	1.93554e7i	−0.996852	−	0.0792795i
$126$	−6.43066e7	+	8.91190e6i	−0.255137	+	0.0353580i
$127$	1.16361e8	+	1.60158e8i	0.447295	+	0.615648i	0.971814	−	0.235750i	$-0.0757548\pi$
$127$	1.16361e8	+	1.60158e8i	0.447295	+	0.615648i	−0.524519	+	0.851399i	$0.675755\pi$
$128$	−2.13731e8	+	1.62409e8i	−0.796209	+	0.605021i
$129$	8.74173e6	−	2.69043e7i	0.0315674	−	0.0971544i
$130$	−2.21651e7	−	1.98409e8i	−0.0776063	−	0.694685i
$131$	1.63526e8	−	5.31328e7i	0.555266	−	0.180417i	−0.0179238	−	0.999839i	$-0.505706\pi$
$131$	1.63526e8	−	5.31328e7i	0.555266	−	0.180417i	0.573190	+	0.819422i	$0.305706\pi$
$132$	−2.14629e8	+	6.06535e7i	−0.706958	+	0.199784i
$133$	−3.52428e7	−	1.08466e8i	−0.112632	−	0.346647i
$134$	2.59123e8	+	1.38417e8i	0.803686	+	0.429308i
$135$	−1.59505e8	−	2.32217e8i	−0.480218	−	0.699132i
$136$	−2.95912e8	−	1.73124e8i	−0.864982	−	0.506059i
$137$	−3.14632e8	−	2.28594e8i	−0.893143	−	0.648906i	0.0435527	−	0.999051i	$-0.486132\pi$
$137$	−3.14632e8	−	2.28594e8i	−0.893143	−	0.648906i	−0.936696	+	0.350145i	$0.886132\pi$
$138$	7.59684e7	−	1.42217e8i	0.209467	−	0.392134i
$139$	−9.38694e7	−	1.29200e8i	−0.251458	−	0.346102i	0.664563	−	0.747232i	$-0.268618\pi$
$139$	−9.38694e7	−	1.29200e8i	−0.251458	−	0.346102i	−0.916021	+	0.401130i	$0.868618\pi$
$140$	1.28149e8	+	8.36705e6i	0.333584	+	0.0217801i
$141$	−4.95325e7	−	3.59875e7i	−0.125318	−	0.0910490i
$142$	−2.34722e8	−	4.83605e8i	−0.577299	−	1.18943i
$143$			4.48246e8i			1.07194i
$144$	2.52151e8	+	2.14899e8i	0.586422	+	0.499787i
$145$	−2.08541e7	+	5.88387e7i	−0.0471757	+	0.133104i
$146$	6.30976e8	+	1.12507e8i	1.38868	+	0.247610i
$147$	−1.88971e8	−	6.14005e7i	−0.404694	−	0.131493i
$148$	4.28568e8	−	5.44224e8i	0.893250	−	1.13431i
$149$	2.20328e8			0.447018			0.223509	−	0.974702i	$-0.428249\pi$
$149$	2.20328e8			0.447018			0.223509	+	0.974702i	$0.428249\pi$
$150$	9.42097e7	+	2.23476e8i	0.186093	+	0.441434i
$151$			2.34652e8i			0.451353i	0.974202	+	0.225677i	$0.0724592\pi$
$151$			2.34652e8i			0.451353i	−0.974202	+	0.225677i	$0.927541\pi$
$152$	−2.93899e8	+	5.02348e8i	−0.550585	+	0.941088i
$153$	−1.30754e8	+	4.02418e8i	−0.238609	+	0.734365i
$154$	−2.83861e8	−	5.06143e7i	−0.504689	−	0.0899891i
$155$	8.58647e8	−	2.54087e8i	1.48761	−	0.440205i
$156$	−1.64839e8	+	1.10267e8i	−0.278331	+	0.186186i
$157$	−7.59257e7			−0.124966			−0.0624828	−	0.998046i	$-0.519902\pi$
$157$	−7.59257e7			−0.124966			−0.0624828	+	0.998046i	$0.519902\pi$
$158$	−2.10116e8	−	4.32909e8i	−0.337156	−	0.694653i
$159$	4.71350e7	−	6.48758e7i	0.0737488	−	0.101507i
$160$	−4.02890e8	−	5.16891e8i	−0.614761	−	0.788714i
$161$	1.68635e8	−	1.22520e8i	0.250982	−	0.182349i
$162$	1.18183e8	−	2.21244e8i	0.171591	−	0.321227i
$163$	−1.13640e8	+	1.56412e8i	−0.160983	+	0.221575i	−0.881887	−	0.471461i	$-0.843727\pi$
$163$	−1.13640e8	+	1.56412e8i	−0.160983	+	0.221575i	0.720904	+	0.693035i	$0.243727\pi$
$164$	4.65522e8	−	5.91151e8i	0.643525	−	0.817190i
$165$	−1.54509e8	−	5.22138e8i	−0.208457	−	0.704449i
$166$	9.65317e8	+	5.15646e8i	1.27127	+	0.679078i
$167$	1.34259e9	−	4.36233e8i	1.72614	−	0.560858i	0.733259	−	0.679950i	$-0.237998\pi$
$167$	1.34259e9	−	4.36233e8i	1.72614	−	0.560858i	0.992883	+	0.119092i	$0.0379984\pi$
$168$	−5.12160e7	−	1.16839e8i	−0.0642937	−	0.146673i
$169$	−1.28909e8	−	3.96740e8i	−0.158028	−	0.486361i
$170$	4.13755e8	−	7.27582e8i	0.495391	−	0.871136i
$171$	6.83155e8	+	2.21970e8i	0.798978	+	0.259604i
$172$	−1.86491e8	−	7.22912e6i	−0.213081	−	0.00825984i
$173$	−3.31196e8	+	2.40628e8i	−0.369744	+	0.268634i	−0.757105	−	0.653294i	$-0.773387\pi$
$173$	−3.31196e8	+	2.40628e8i	−0.369744	+	0.268634i	0.387361	+	0.921928i	$0.373387\pi$
$174$	6.14242e7	−	8.51244e6i	0.0670104	−	0.00928660i
$175$	−1.65807e7	+	3.13092e8i	−0.0176788	+	0.333826i
$176$	7.70142e8	+	1.25380e9i	0.802639	+	1.30670i
$177$	−3.04960e8	+	2.21566e8i	−0.310706	+	0.225741i
$178$	−1.29659e9	−	2.31190e8i	−1.29158	−	0.230297i
$179$	−6.84272e8	−	2.22333e8i	−0.666525	−	0.216567i	−0.0438387	−	0.999039i	$-0.513959\pi$
$179$	−6.84272e8	−	2.22333e8i	−0.666525	−	0.216567i	−0.622686	+	0.782472i	$0.713959\pi$
$180$	−5.17051e8	+	6.22004e8i	−0.492543	+	0.592521i
$181$	1.55875e8	+	4.79733e8i	0.145232	+	0.446977i	0.997041	−	0.0768755i	$-0.0244944\pi$
$181$	1.55875e8	+	4.79733e8i	0.145232	+	0.446977i	−0.851809	+	0.523852i	$0.824494\pi$
$182$	−2.53959e8	+	3.51948e7i	−0.231461	+	0.0320770i
$183$	−1.02031e9	+	3.31517e8i	−0.909758	+	0.295598i
$184$	−1.03919e9	−	2.27147e8i	−0.906615	−	0.198169i
$185$	1.34143e9	+	1.02990e9i	1.14520	+	0.879242i
$186$	−6.16681e8	−	6.41049e8i	−0.515239	−	0.535598i
$187$	−1.10460e9	+	1.52036e9i	−0.903316	+	1.24331i
$188$	−1.39606e8	+	3.79033e8i	−0.111757	+	0.303421i
$189$	−2.92696e8	+	2.12656e8i	−0.229387	+	0.166660i
$190$	−1.23516e9	−	7.02401e8i	−0.947783	−	0.538978i
$191$	−4.97692e8	+	6.85014e8i	−0.373961	+	0.514714i	−0.953972	−	0.299895i	$-0.903048\pi$
$191$	−4.97692e8	+	6.85014e8i	−0.373961	+	0.514714i	0.580011	+	0.814609i	$0.303048\pi$
$192$	−2.71622e8	+	5.91644e8i	−0.199875	+	0.435367i
$193$	4.27868e8			0.308376			0.154188	−	0.988042i	$-0.450724\pi$
$193$	4.27868e8			0.308376			0.154188	+	0.988042i	$0.450724\pi$
$194$	−4.38171e8	+	2.12670e8i	−0.309340	+	0.150141i
$195$	−2.74132e8	−	3.99099e8i	−0.189593	−	0.276021i
$196$	−5.07761e7	+	1.30988e9i	−0.0344061	+	0.887581i
$197$	6.37990e8	−	1.96353e9i	0.423593	−	1.30369i	−0.480741	−	0.876862i	$-0.659632\pi$
$197$	6.37990e8	−	1.96353e9i	0.423593	−	1.30369i	0.904335	−	0.426824i	$-0.140368\pi$
$198$	1.30878e9	−	1.25903e9i	0.851539	−	0.819169i
$199$			3.41119e8i			0.217517i	0.994068	+	0.108759i	$0.0346875\pi$
$199$			3.41119e8i			0.217517i	−0.994068	+	0.108759i	$0.965312\pi$
$200$	1.24976e9	−	9.99052e8i	0.781099	−	0.624408i
$201$	7.12469e8			0.436498
$202$	1.12699e9	+	1.17152e9i	0.676883	+	0.703630i
$203$	7.62440e7	+	2.47732e7i	0.0448975	+	0.0145881i
$204$	−8.30827e8	−	3.22061e7i	−0.479722	−	0.0185959i
$205$	1.45710e9	+	1.11871e9i	0.825037	+	0.633433i
$206$	6.00422e6	+	1.23707e7i	0.00333417	+	0.00686948i
$207$			1.31285e9i			0.715044i
$208$	9.95793e8	+	8.48680e8i	0.532005	+	0.453409i
$209$	2.58099e9	+	1.87520e9i	1.35270	+	0.982794i
$210$	2.83692e8	−	1.28535e8i	0.145871	−	0.0660915i
$211$	6.86972e8	+	9.45536e8i	0.346584	+	0.477033i	0.946350	−	0.323143i	$-0.104740\pi$
$211$	6.86972e8	+	9.45536e8i	0.346584	+	0.477033i	−0.599766	+	0.800176i	$0.704740\pi$
$212$	−4.96443e8	−	1.82851e8i	−0.245768	−	0.0905220i
$213$	−1.05471e9	−	7.66293e8i	−0.512407	−	0.372286i
$214$	2.70157e9	−	2.59887e9i	1.28813	−	1.23917i
$215$	1.20523e7	−	4.55483e8i	0.00564047	−	0.213166i
$216$	1.80370e9	+	3.94254e8i	0.828608	+	0.181118i
$217$	−3.55358e8	−	1.09368e9i	−0.160261	−	0.493231i
$218$	3.83307e8	+	2.76587e9i	0.169715	+	1.22463i
$219$	1.47831e9	−	4.80334e8i	0.642674	−	0.208817i
$220$	−3.03769e9	+	1.91771e9i	−1.29674	+	0.818638i
$221$	−5.16371e8	+	1.58923e9i	−0.216468	+	0.666219i
$222$	2.94900e8	−	1.65389e9i	0.121412	−	0.680920i
$223$	−9.02310e8	−	1.24192e9i	−0.364868	−	0.502198i	0.586629	−	0.809856i	$-0.300455\pi$
$223$	−9.02310e8	−	1.24192e9i	−0.364868	−	0.502198i	−0.951497	+	0.307658i	$0.900455\pi$
$224$	−6.49886e8	+	5.34778e8i	−0.258134	+	0.212413i
$225$	−1.53396e9	−	1.24357e9i	−0.598529	−	0.485223i
$226$	2.18137e8	+	1.57404e9i	0.0836172	+	0.603366i
$227$	−9.26171e8	−	1.27477e9i	−0.348809	−	0.480095i	0.598179	−	0.801362i	$-0.295891\pi$
$227$	−9.26171e8	−	1.27477e9i	−0.348809	−	0.480095i	−0.946988	+	0.321268i	$0.895891\pi$
$228$	−5.46738e7	+	1.41043e9i	−0.0202321	+	0.521930i
$229$	1.53791e9	−	4.73319e9i	0.559226	−	1.72112i	−0.125286	−	0.992121i	$-0.539985\pi$
$229$	1.53791e9	−	4.73319e9i	0.559226	−	1.72112i	0.684512	−	0.729001i	$-0.260015\pi$
$230$	5.23335e8	−	2.54370e9i	0.187011	−	0.908982i
$231$	−6.65059e8	+	2.16091e8i	−0.233567	+	0.0758907i
$232$	−1.64245e8	−	3.74691e8i	−0.0566945	−	0.129337i
$233$	1.11051e9	+	3.41779e9i	0.376789	+	1.15964i	0.942264	+	0.334871i	$0.108693\pi$
$233$	1.11051e9	+	3.41779e9i	0.376789	+	1.15964i	−0.565475	+	0.824765i	$0.691307\pi$
$234$	7.60840e8	−	1.42433e9i	0.253764	−	0.475059i
$235$	−9.29493e8	−	3.29438e8i	−0.304772	−	0.108019i
$236$	1.95379e9	+	1.53858e9i	0.629840	+	0.495989i
$237$	−9.44147e8	−	6.85963e8i	−0.299258	−	0.217424i
$238$	−9.48106e8	−	5.06453e8i	−0.295494	−	0.157845i
$239$	−2.66662e9	−	3.67029e9i	−0.817277	−	1.12489i	−0.990160	−	0.139943i	$-0.955308\pi$
$239$	−2.66662e9	−	3.67029e9i	−0.817277	−	1.12489i	0.172883	−	0.984942i	$-0.444692\pi$
$240$	−1.45248e9	−	6.45336e8i	−0.437790	−	0.194510i
$241$	−1.13252e9	−	8.22824e8i	−0.335720	−	0.243915i	0.407134	−	0.913369i	$-0.366528\pi$
$241$	−1.13252e9	−	8.22824e8i	−0.335720	−	0.243915i	−0.742854	+	0.669453i	$0.766528\pi$
$242$	4.17070e9	−	2.02429e9i	1.21604	−	0.590216i
$243$		−	3.56571e9i		−	1.02264i
$244$	3.93526e9	+	5.88283e9i	1.11023	+	1.65969i
$245$	−3.19924e9	−	8.46532e7i	−0.887937	−	0.0234952i
$246$	3.20328e8	−	1.79651e9i	0.0874691	−	0.490555i
$247$	2.69791e9	+	8.76604e8i	0.724836	+	0.235514i
$248$	−2.96343e9	+	5.06524e9i	−0.783407	+	1.33904i
$249$	2.65418e9			0.690451
$250$	2.47641e9	+	3.02096e9i	0.633960	+	0.773366i
$251$		−	2.51075e9i		−	0.632570i	−0.948664	−	0.316285i	$-0.897564\pi$
$251$		−	2.51075e9i		−	0.632570i	0.948664	−	0.316285i	$-0.102436\pi$
$252$	8.16077e8	+	6.42648e8i	0.202362	+	0.159357i
$253$	−1.80183e9	+	5.54545e9i	−0.439775	+	1.35349i
$254$	5.56007e8	−	3.11827e9i	0.133581	−	0.749167i
$255$	5.36935e7	−	2.02920e9i	0.0126987	−	0.479914i
$256$	4.24349e9	+	6.62964e8i	0.988015	+	0.154358i
$257$	7.85276e9			1.80007			0.900036	−	0.435815i	$-0.143540\pi$
$257$	7.85276e9			1.80007			0.900036	+	0.435815i	$0.143540\pi$
$258$	−4.07193e8	+	1.97635e8i	−0.0919014	+	0.0446052i
$259$	1.27659e9	−	1.75708e9i	0.283696	−	0.390474i
$260$	−2.04194e9	+	2.45642e9i	−0.446837	+	0.537537i
$261$	−4.08491e8	+	2.96786e8i	−0.0880279	+	0.0639560i
$262$	−2.42656e9	−	1.29620e9i	−0.514975	−	0.275086i
$263$	3.71644e9	−	5.11523e9i	0.776790	−	1.06916i	−0.218839	−	0.975761i	$-0.570227\pi$
$263$	3.71644e9	−	5.11523e9i	0.776790	−	1.06916i	0.995629	−	0.0933987i	$-0.0297731\pi$
$264$	3.08014e9	+	1.80204e9i	0.634096	+	0.370979i
$265$	4.31485e8	−	1.21741e9i	0.0874947	−	0.246862i
$266$	−8.59767e8	+	1.60953e9i	−0.171733	+	0.321493i
$267$	−3.03778e9	+	9.87034e8i	−0.597738	+	0.194217i
$268$	−1.27826e9	−	4.52325e9i	−0.247787	−	0.876823i
$269$	−2.92992e9	−	9.01736e9i	−0.559560	−	1.72215i	−0.683587	−	0.729869i	$-0.739581\pi$
$269$	−2.92992e9	−	9.01736e9i	−0.559560	−	1.72215i	0.124027	−	0.992279i	$-0.460419\pi$
$270$	−9.08342e8	+	4.41506e9i	−0.170921	+	0.830771i
$271$	−7.21651e9	−	2.34479e9i	−1.33798	−	0.434737i	−0.449349	−	0.893356i	$-0.648344\pi$
$271$	−7.21651e9	−	2.34479e9i	−1.33798	−	0.434737i	−0.888633	+	0.458620i	$0.848344\pi$
$272$	1.28614e9	+	5.33245e9i	0.234969	+	0.974207i
$273$	−5.03041e8	+	3.65481e8i	−0.0905635	+	0.0657982i
$274$	8.54180e8	+	6.16360e9i	0.151547	+	1.09353i
$275$	−4.77270e9	−	7.35814e9i	−0.834513	−	1.28658i
$276$	−2.48254e9	+	7.01556e8i	−0.427818	+	0.120900i
$277$	−3.24686e9	+	2.35898e9i	−0.551498	+	0.400687i	−0.828337	−	0.560229i	$-0.810713\pi$
$277$	−3.24686e9	+	2.35898e9i	−0.551498	+	0.400687i	0.276840	+	0.960916i	$0.410713\pi$
$278$	−4.48534e8	+	2.51553e9i	−0.0750960	+	0.421163i
$279$	6.88834e9	+	2.23816e9i	1.13684	+	0.369380i
$280$	−1.32501e9	−	1.57047e9i	−0.215569	−	0.255504i
$281$	1.34285e9	+	4.13285e9i	0.215378	+	0.662864i	0.999127	+	0.0417865i	$0.0133049\pi$
$281$	1.34285e9	+	4.13285e9i	0.215378	+	0.662864i	−0.783749	+	0.621078i	$0.786695\pi$
$282$	1.34473e8	+	9.70335e8i	0.0212638	+	0.153435i
$283$	−7.34402e9	+	2.38622e9i	−1.14495	+	0.372018i	−0.819240	−	0.573451i	$-0.805604\pi$
$283$	−7.34402e9	+	2.38622e9i	−1.14495	+	0.372018i	−0.325713	+	0.945469i	$0.605604\pi$
$284$	−2.97268e9	+	8.07087e9i	−0.456957	+	1.24064i
$285$	−3.44482e9	−	9.11514e7i	−0.522140	−	0.0138160i
$286$	5.16861e9	−	4.97214e9i	0.772520	−	0.743154i
$287$	1.38667e9	−	1.90859e9i	0.204383	−	0.281309i
$288$	−3.19016e8	−	5.29124e9i	−0.0463706	−	0.769109i
$289$	−2.42119e7	+	1.75910e7i	−0.00347086	+	0.00252173i
$290$	9.09777e8	−	4.12202e8i	0.128630	−	0.0582798i
$291$	−6.94300e8	+	9.55623e8i	−0.0968223	+	0.133264i
$292$	−5.70177e9	−	8.52360e9i	−0.784293	−	1.17244i
$293$	−7.29957e9			−0.990437			−0.495218	−	0.868769i	$-0.664912\pi$
$293$	−7.29957e9			−0.990437			−0.495218	+	0.868769i	$0.664912\pi$
$294$	1.38816e9	+	2.86006e9i	0.185802	+	0.382812i
$295$	−3.69740e9	+	4.81580e9i	−0.488211	+	0.635888i
$296$	−1.10292e10	+	1.09506e9i	−1.43673	+	0.142649i
$297$	3.12740e9	−	9.62514e9i	0.401936	−	1.23703i
$298$	−2.44397e9	−	2.54055e9i	−0.309907	−	0.322153i
$299$			5.18469e9i			0.648691i
$300$	1.53183e9	−	3.56520e9i	0.189115	−	0.440148i
$301$	−5.85147e8			−0.0712851
$302$	2.70571e9	−	2.60286e9i	0.325277	−	0.312913i
$303$	3.74947e9	+	1.21828e9i	0.444836	+	0.144536i
$304$	9.05250e9	−	2.18338e9i	1.05992	−	0.255643i
$305$	−1.42432e10	+	9.78334e9i	−1.64592	+	1.13055i
$306$	6.09055e9	−	2.95611e9i	0.694658	−	0.337159i
$307$		−	1.52043e10i		−	1.71164i	−0.517272	−	0.855821i	$-0.673052\pi$
$307$		−	1.52043e10i		−	1.71164i	0.517272	−	0.855821i	$-0.326948\pi$
$308$	2.56509e9	+	3.83457e9i	0.285036	+	0.426102i
$309$	2.69796e7	+	1.96019e7i	0.00295939	+	0.00215012i
$310$	−1.24543e10	−	7.08240e9i	−1.34857	−	0.766891i
$311$	−2.54204e9	−	3.49882e9i	−0.271732	−	0.374007i	0.651241	−	0.758871i	$-0.274249\pi$
$311$	−2.54204e9	−	3.49882e9i	−0.271732	−	0.374007i	−0.922973	+	0.384864i	$0.874249\pi$
$312$	3.09992e9	+	6.77584e8i	0.327139	+	0.0715064i
$313$	6.79602e7	+	4.93760e7i	0.00708072	+	0.00514444i	0.591320	−	0.806437i	$-0.298607\pi$
$313$	6.79602e7	+	4.93760e7i	0.00708072	+	0.00514444i	−0.584239	+	0.811581i	$0.698607\pi$
$314$	8.42201e8	+	8.75480e8i	0.0866357	+	0.0900591i
$315$	−1.54436e9	+	2.01151e9i	−0.156858	+	0.204305i
$316$	−2.66106e9	+	7.22481e9i	−0.266874	+	0.724566i
$317$	−1.46233e9	−	4.50059e9i	−0.144813	−	0.445690i	0.852174	−	0.523259i	$-0.175284\pi$
$317$	−1.46233e9	−	4.50059e9i	−0.144813	−	0.445690i	−0.996987	+	0.0775695i	$0.975284\pi$
$318$	−1.27091e9	+	1.76128e8i	−0.124281	+	0.0172235i
$319$	−2.13279e9	+	6.92984e8i	−0.205961	+	0.0669207i
$320$	−1.49112e9	+	1.03792e10i	−0.142204	+	0.989837i
$321$	2.80939e9	−	8.64642e9i	0.264601	−	0.814359i
$322$	−3.28332e9	−	5.85436e8i	−0.305414	−	0.0544573i
$323$	6.99054e9	+	9.62166e9i	0.642245	+	0.883975i
$324$	−3.86204e9	+	1.09140e9i	−0.350459	+	0.0990385i
$325$	−6.05793e9	−	4.91112e9i	−0.542988	−	0.440197i
$326$	3.06409e9	−	4.24636e8i	0.271289	−	0.0375964i
$327$	3.98045e9	+	5.47862e9i	0.348130	+	0.479160i
$328$	−1.19802e10	+	1.18948e9i	−1.03507	+	0.102769i
$329$	−3.91349e8	+	1.20445e9i	−0.0334027	+	0.102803i
$330$	−4.30677e9	+	7.57338e9i	−0.363158	+	0.638607i
$331$	−1.26568e10	+	4.11246e9i	−1.05442	+	0.342602i	−0.784401	−	0.620254i	$-0.787030\pi$
$331$	−1.26568e10	+	4.11246e9i	−1.05442	+	0.342602i	−0.270018	+	0.962855i	$0.587030\pi$
$332$	−4.76192e9	−	1.68506e10i	−0.391949	−	1.38696i
$333$	4.22709e9	+	1.30096e10i	0.343767	+	1.05801i
$334$	−1.99226e10	−	1.06421e10i	−1.60089	−	0.855152i
$335$	1.10039e10	−	3.25622e9i	0.873711	−	0.258544i
$336$	−7.79126e8	+	1.88658e9i	−0.0611295	+	0.148019i
$337$	−1.83050e10	−	1.32993e10i	−1.41922	−	1.03112i	−0.991900	−	0.127022i	$-0.959458\pi$
$337$	−1.83050e10	−	1.32993e10i	−1.41922	−	1.03112i	−0.427319	−	0.904101i	$-0.640542\pi$
$338$	−3.14480e9	+	5.88722e9i	−0.240949	+	0.451070i
$339$	2.26525e9	+	3.11784e9i	0.171521	+	0.236078i
$340$	−1.29791e10	+	3.29974e9i	−0.971246	+	0.246925i
$341$	2.60245e10	+	1.89079e10i	1.92471	+	1.39838i
$342$	−5.01836e9	−	1.03395e10i	−0.366824	−	0.755777i
$343$			8.73703e9i			0.631230i
$344$	1.98528e9	+	2.23057e9i	0.141771	+	0.159288i
$345$	−1.78714e9	−	6.03937e9i	−0.126149	−	0.426300i
$346$	6.44839e9	+	1.14979e9i	0.449932	+	0.0802257i
$347$	−2.14268e9	−	6.96199e8i	−0.147788	−	0.0480193i	0.234189	−	0.972191i	$-0.424757\pi$
$347$	−2.14268e9	−	6.96199e8i	−0.147788	−	0.0480193i	−0.381977	+	0.924172i	$0.624757\pi$
$348$	−7.79498e8	−	6.13843e8i	−0.0531493	−	0.0418543i
$349$	2.58260e10			1.74082			0.870412	−	0.492323i	$-0.163852\pi$
$349$	2.58260e10			1.74082			0.870412	+	0.492323i	$0.163852\pi$
$350$	3.79411e9	−	3.28177e9i	0.252835	−	0.218693i
$351$		−	8.99897e9i		−	0.592877i
$352$	5.91448e9	−	2.27880e10i	0.385253	−	1.48435i
$353$	−6.33448e9	+	1.94955e10i	−0.407955	+	1.25556i	0.510447	+	0.859909i	$0.329480\pi$
$353$	−6.33448e9	+	1.94955e10i	−0.407955	+	1.25556i	−0.918402	+	0.395648i	$0.870520\pi$
$354$	5.93757e9	+	1.05871e9i	0.378090	+	0.0674158i
$355$	−1.97920e10	−	7.01482e9i	−1.24617	−	0.441675i
$356$	1.17165e10	+	1.75151e10i	0.729455	+	1.09047i
$357$	−2.60686e9			−0.160489
$358$	5.02657e9	+	1.03564e10i	0.306013	+	0.630487i
$359$	−2.38164e9	+	3.27805e9i	−0.143383	+	0.197350i	−0.874668	−	0.484722i	$-0.838921\pi$
$359$	−2.38164e9	+	3.27805e9i	−0.143383	+	0.197350i	0.731285	+	0.682072i	$0.238921\pi$
$360$	1.29075e10	−	9.37551e8i	0.768481	−	0.0558193i
$361$	2.59397e9	−	1.88463e9i	0.152734	−	0.110968i
$362$	3.80265e9	−	7.11875e9i	0.221438	−	0.414543i
$363$	6.60866e9	−	9.09603e9i	0.380616	−	0.523872i
$364$	3.22285e9	+	2.53794e9i	0.183584	+	0.144569i
$365$	2.06369e10	−	1.41750e10i	1.16272	−	0.798643i
$366$	1.51403e10	+	8.08755e9i	0.843743	+	0.450705i
$367$	7.49650e9	−	2.43576e9i	0.413232	−	0.134267i	−0.0950204	−	0.995475i	$-0.530292\pi$
$367$	7.49650e9	−	2.43576e9i	0.413232	−	0.134267i	0.508253	+	0.861208i	$0.330292\pi$
$368$	8.90794e9	+	1.45022e10i	0.485720	+	0.790757i
$369$	4.59158e9	+	1.41314e10i	0.247660	+	0.762220i
$370$	−3.00420e9	−	2.68918e10i	−0.160296	−	1.43487i
$371$	−1.57754e9	−	5.12574e8i	−0.0832693	−	0.0270559i
$372$	−5.51283e8	+	1.42216e10i	−0.0287875	+	0.742636i
$373$	6.63143e9	−	4.81802e9i	0.342588	−	0.248905i	−0.403165	−	0.915127i	$-0.632090\pi$
$373$	6.63143e9	−	4.81802e9i	0.342588	−	0.248905i	0.745753	+	0.666223i	$0.232090\pi$
$374$	2.97836e10	−	4.12754e9i	1.52226	−	0.210962i
$375$	8.74940e9	+	3.63256e9i	0.442439	+	0.183691i
$376$	5.91911e9	−	2.59463e9i	0.296145	−	0.129815i
$377$	−1.61321e9	+	1.17207e9i	−0.0798593	+	0.0580212i
$378$	5.69879e9	+	1.01613e9i	0.279136	+	0.0497717i
$379$	2.07144e10	+	6.73052e9i	1.00396	+	0.326206i	0.764446	−	0.644687i	$-0.223012\pi$
$379$	2.07144e10	+	6.73052e9i	1.00396	+	0.326206i	0.239513	+	0.970893i	$0.423012\pi$
$380$	5.60172e9	+	2.20337e10i	0.268650	+	1.05670i
$381$	−2.37380e9	−	7.30580e9i	−0.112653	−	0.346711i
$382$	1.34193e10	−	1.85971e9i	0.630198	−	0.0873357i
$383$	1.11815e10	−	3.63309e9i	0.519642	−	0.168842i	−0.0374407	−	0.999299i	$-0.511921\pi$
$383$	1.11815e10	−	3.63309e9i	0.519642	−	0.168842i	0.557083	+	0.830457i	$0.311921\pi$
$384$	9.83504e9	−	3.43077e9i	0.452325	−	0.157785i
$385$	−9.28407e9	+	6.37701e9i	−0.422567	+	0.290251i
$386$	−4.74609e9	−	4.93363e9i	−0.213790	−	0.222238i
$387$	2.16625e9	−	2.98159e9i	0.0965750	−	0.132924i
$388$	7.31262e9	+	2.69340e9i	0.322661	+	0.118843i
$389$	−2.00727e10	+	1.45837e10i	−0.876613	+	0.636897i	−0.932353	−	0.361548i	$-0.882248\pi$
$389$	−2.00727e10	+	1.45837e10i	−0.876613	+	0.636897i	0.0557399	+	0.998445i	$0.482248\pi$
$390$	−1.56112e9	+	7.58793e9i	−0.0674805	+	0.327993i
$391$	−1.27765e10	+	1.75854e10i	−0.546645	+	0.752393i
$392$	1.56671e10	−	1.39443e10i	0.663507	−	0.590544i
$393$	−6.67193e9			−0.279693
$394$	−2.97179e10	+	1.44238e10i	−1.23320	+	0.598544i
$395$	−1.77172e10	−	6.27946e9i	−0.727791	−	0.257949i
$396$	−2.90350e10	−	1.12551e9i	−1.18070	−	0.0457687i
$397$	5.02527e9	−	1.54662e10i	0.202301	−	0.622617i	−0.797513	−	0.603302i	$-0.793851\pi$
$397$	5.02527e9	−	1.54662e10i	0.202301	−	0.622617i	0.999813	−	0.0193153i	$-0.00614864\pi$
$398$	3.93335e9	−	3.78384e9i	0.156758	−	0.150800i
$399$			4.42546e9i			0.174609i
$400$	−2.53827e10	−	3.32872e9i	−0.991510	−	0.130028i
$401$	3.37735e10			1.30617			0.653084	−	0.757285i	$-0.273475\pi$
$401$	3.37735e10			1.30617			0.653084	+	0.757285i	$0.273475\pi$
$402$	−7.90301e9	−	8.21530e9i	−0.302614	−	0.314571i
$403$	2.72034e10	+	8.83892e9i	1.03134	+	0.335104i
$404$	1.00747e9	−	2.59900e10i	0.0378189	−	0.975621i
$405$	−2.78023e9	−	9.39536e9i	−0.103338	−	0.349215i
$406$	−5.60078e8	−	1.15395e9i	−0.0206132	−	0.0424699i
$407$			6.07540e10i			2.21410i
$408$	8.84452e9	+	9.93729e9i	0.319179	+	0.358614i
$409$	1.47269e9	+	1.06997e9i	0.0526282	+	0.0382366i	0.613788	−	0.789471i	$-0.289645\pi$
$409$	1.47269e9	+	1.06997e9i	0.0526282	+	0.0382366i	−0.561160	+	0.827707i	$0.689645\pi$
$410$	−3.26324e9	−	2.92106e10i	−0.115482	−	1.03372i
$411$	8.87024e9	+	1.22088e10i	0.310862	+	0.427865i
$412$	7.60416e7	−	2.06454e8i	0.00263914	−	0.00716529i
$413$	6.30800e9	+	4.58303e9i	0.216816	+	0.157526i
$414$	1.51381e10	−	1.45627e10i	0.515312	−	0.495724i
$415$	4.09931e10	−	1.21305e10i	1.38203	−	0.408965i
$416$	−1.25986e9	−	2.08962e10i	−0.0420676	−	0.697739i
$417$	1.91496e9	+	5.89363e9i	0.0633308	+	0.194912i
$418$	−7.00701e9	−	5.05613e10i	−0.229524	−	1.65620i
$419$	2.23007e10	−	7.24592e9i	0.723538	−	0.235092i	0.0759817	−	0.997109i	$-0.475791\pi$
$419$	2.23007e10	−	7.24592e9i	0.723538	−	0.235092i	0.647557	+	0.762017i	$0.275791\pi$
$420$	−4.62894e9	−	1.84541e9i	−0.148760	−	0.0593057i
$421$	−6.65166e9	+	2.04717e10i	−0.211739	+	0.651667i	0.787630	+	0.616149i	$0.211308\pi$
$421$	−6.65166e9	+	2.04717e10i	−0.211739	+	0.651667i	−0.999369	+	0.0355180i	$0.988692\pi$
$422$	3.28254e9	−	1.84096e10i	0.103505	−	0.580489i
$423$	−4.68841e9	−	6.45305e9i	−0.146442	−	0.201560i
$424$	3.39835e9	+	7.75262e9i	0.105149	+	0.239875i
$425$	−8.44484e9	−	3.15859e10i	−0.258842	−	0.968138i
$426$	2.86338e9	+	2.06617e10i	0.0869443	+	0.627374i
$427$	1.30434e10	+	1.79527e10i	0.392356	+	0.540032i
$428$	−5.99339e10	−	2.32327e9i	−1.78607	−	0.0692349i
$429$	5.37490e9	−	1.65422e10i	0.158687	−	0.488388i
$430$	−5.38575e9	+	4.91344e9i	−0.157533	+	0.143718i
$431$	−4.11426e10	+	1.33681e10i	−1.19229	+	0.387399i	−0.836920	−	0.547325i	$-0.815646\pi$
$431$	−4.11426e10	+	1.33681e10i	−1.19229	+	0.387399i	−0.355373	+	0.934725i	$0.615646\pi$
$432$	−1.54613e10	−	2.51712e10i	−0.443928	−	0.722719i
$433$	−5.99426e9	−	1.84484e10i	−0.170523	−	0.524817i	0.828877	−	0.559430i	$-0.188980\pi$
$433$	−5.99426e9	−	1.84484e10i	−0.170523	−	0.524817i	−0.999401	+	0.0346132i	$0.988980\pi$
$434$	−8.66914e9	+	1.62291e10i	−0.244353	+	0.457441i
$435$	1.47514e9	−	1.92135e9i	0.0411979	−	0.0536597i
$436$	2.76407e10	−	3.51000e10i	0.764898	−	0.971318i
$437$	2.98534e10	+	2.16897e10i	0.818592	+	0.594742i
$438$	−2.19367e10	−	1.17180e10i	−0.596039	−	0.318388i
$439$	6.63526e8	+	9.13266e8i	0.0178649	+	0.0245889i	0.817856	−	0.575423i	$-0.195163\pi$
$439$	6.63526e8	+	9.13266e8i	0.0178649	+	0.0245889i	−0.799991	+	0.600012i	$0.795163\pi$
$440$	5.58080e10	+	1.37548e10i	1.48897	+	0.366982i
$441$	−2.09422e10	−	1.52154e10i	−0.553691	−	0.402280i
$442$	2.40528e10	−	1.16742e10i	0.630197	−	0.305872i
$443$			5.58401e10i			1.44988i	0.688814	+	0.724938i	$0.258132\pi$
$443$			5.58401e10i			1.44988i	−0.688814	+	0.724938i	$0.741868\pi$
$444$	−2.23418e10	+	1.49453e10i	−0.574892	+	0.384567i
$445$	−4.24067e10	+	2.91282e10i	−1.08142	+	0.742802i
$446$	−4.31149e9	+	2.41802e10i	−0.108965	+	0.611113i
$447$	−8.13106e9	−	2.64194e9i	−0.203665	−	0.0661749i
$448$	1.33752e10	+	1.56168e9i	0.332038	+	0.0387687i
$449$	5.27476e10			1.29783			0.648915	−	0.760861i	$-0.275223\pi$
$449$	5.27476e10			1.29783			0.648915	+	0.760861i	$0.275223\pi$
$450$	2.67606e9	+	3.14820e10i	0.0652597	+	0.767737i
$451$			6.59927e10i			1.59511i
$452$	1.57301e10	−	1.99752e10i	0.376859	−	0.478560i
$453$	2.81370e9	−	8.65968e9i	0.0668167	−	0.205641i
$454$	−4.42551e9	+	2.48197e10i	−0.104169	+	0.584215i
$455$	−6.09898e9	+	7.94383e9i	−0.142302	+	0.185347i
$456$	1.68698e10	−	1.50147e10i	0.390167	−	0.347262i
$457$	−5.87114e10			−1.34604			−0.673020	−	0.739625i	$-0.735003\pi$
$457$	−5.87114e10			−1.34604			−0.673020	+	0.739625i	$0.735003\pi$
$458$	−7.16363e10	+	3.47693e10i	−1.62806	+	0.790195i
$459$	2.21760e10	−	3.05226e10i	0.499611	−	0.687655i
$460$	−3.51358e10	+	2.21814e10i	−0.784728	+	0.495402i
$461$	−1.41676e10	+	1.02934e10i	−0.313685	+	0.227906i	−0.733476	−	0.679715i	$-0.762103\pi$
$461$	−1.41676e10	+	1.02934e10i	−0.313685	+	0.227906i	0.419791	+	0.907621i	$0.362103\pi$
$462$	9.86881e9	+	5.27165e9i	0.216619	+	0.115712i
$463$	1.51247e10	−	2.08174e10i	0.329126	−	0.453004i	−0.612100	−	0.790781i	$-0.709675\pi$
$463$	1.51247e10	−	2.08174e10i	0.329126	−	0.453004i	0.941226	+	0.337777i	$0.109675\pi$
$464$	−2.49859e9	+	6.05011e9i	−0.0539043	+	0.130524i
$465$	−3.47346e10	−	9.19092e8i	−0.742933	−	0.0196583i
$466$	2.70914e10	−	5.07166e10i	0.574498	−	1.07549i
$467$	−2.37809e10	+	7.72687e9i	−0.499989	+	0.162456i	−0.548144	−	0.836384i	$-0.684666\pi$
$467$	−2.37809e10	+	7.72687e9i	−0.499989	+	0.162456i	0.0481558	+	0.998840i	$0.484666\pi$
$468$	−2.48632e10	+	7.02624e9i	−0.518290	+	0.146467i
$469$	−4.55405e9	−	1.40159e10i	−0.0941253	−	0.289688i
$470$	6.51167e9	+	1.43720e10i	0.133445	+	0.294528i
$471$	2.80199e9	+	9.10422e8i	0.0569355	+	0.0184995i
$472$	−3.93131e9	−	3.95953e10i	−0.0792080	−	0.797766i
$473$	1.32423e10	−	9.62110e9i	0.264557	−	0.192212i
$474$	2.56322e9	+	1.84957e10i	0.0507776	+	0.366402i
$475$	−5.36210e10	+	1.43362e10i	−1.05332	+	0.281617i
$476$	4.67701e9	+	1.65502e10i	0.0911047	+	0.322385i
$477$	8.45196e9	−	6.14071e9i	0.163261	−	0.118616i
$478$	−1.27419e10	+	7.14605e10i	−0.244074	+	1.36885i
$479$	1.83548e10	+	5.96382e9i	0.348664	+	0.113288i	0.478113	−	0.878298i	$-0.341321\pi$
$479$	1.83548e10	+	5.96382e9i	0.348664	+	0.113288i	−0.129449	+	0.991586i	$0.541321\pi$
$480$	8.67036e9	+	2.39066e10i	0.163332	+	0.450352i
$481$	1.66936e10	+	5.13776e10i	0.311867	+	0.959828i
$482$	3.07462e9	+	2.21859e10i	0.0569644	+	0.411045i
$483$	−7.69249e9	+	2.49944e9i	−0.141344	+	0.0459255i
$484$	−6.96047e10	−	2.56370e10i	−1.26840	−	0.467182i
$485$	−6.35578e9	+	1.79325e10i	−0.114869	+	0.324097i
$486$	−4.11153e10	+	3.95524e10i	−0.736984	+	0.708969i
$487$	−2.93440e10	+	4.03886e10i	−0.521679	+	0.718030i	−0.985834	−	0.167724i	$-0.946358\pi$
$487$	−2.93440e10	+	4.03886e10i	−0.521679	+	0.718030i	0.464155	+	0.885754i	$0.346358\pi$
$488$	2.41819e10	−	1.10631e11i	0.426394	−	1.95074i
$489$	6.06934e9	−	4.40964e9i	0.106147	−	0.0771201i
$490$	3.45112e10	+	3.78286e10i	0.598654	+	0.656199i
$491$	3.46739e10	−	4.77246e10i	0.596592	−	0.821138i	−0.398799	−	0.917038i	$-0.630573\pi$
$491$	3.46739e10	−	4.77246e10i	0.596592	−	0.821138i	0.995391	+	0.0959002i	$0.0305730\pi$
$492$	−2.42683e10	+	1.62340e10i	−0.414170	+	0.277054i
$493$	−8.35996e9			−0.141520
$494$	−1.98185e10	−	4.08326e10i	−0.332784	−	0.685645i
$495$	1.87643e9	−	7.09146e10i	0.0312545	−	1.18118i
$496$	9.12776e10	−	2.20153e10i	1.50813	−	0.363745i
$497$	−8.33312e9	+	2.56467e10i	−0.136578	+	0.420345i
$498$	−2.94413e10	−	3.06047e10i	−0.478674	−	0.497588i
$499$		−	1.21059e11i		−	1.95251i	−0.216617	−	0.976257i	$-0.569502\pi$
$499$		−	1.21059e11i		−	1.95251i	0.216617	−	0.976257i	$-0.430498\pi$
$500$	7.36456e9	−	6.20646e10i	0.117833	−	0.993033i
$501$	−5.47781e10			−0.869473
$502$	−2.89508e10	+	2.78503e10i	−0.455875	+	0.438546i
$503$	1.17187e10	+	3.80763e9i	0.183066	+	0.0594816i	0.399115	−	0.916901i	$-0.369317\pi$
$503$	1.17187e10	+	3.80763e9i	0.183066	+	0.0594816i	−0.216050	+	0.976382i	$0.569317\pi$
$504$	−1.64206e9	−	1.65385e10i	−0.0254488	−	0.256315i
$505$	6.34776e10	+	1.67965e9i	0.976012	+	0.0258257i
$506$	8.39298e10	−	4.07361e10i	1.28031	−	0.621409i
$507$			1.61872e10i			0.244985i
$508$	−4.21234e10	+	2.81780e10i	−0.632512	+	0.423112i
$509$	−1.72238e10	−	1.25138e10i	−0.256600	−	0.186431i	0.452047	−	0.891994i	$-0.350694\pi$
$509$	−1.72238e10	−	1.25138e10i	−0.256600	−	0.186431i	−0.708647	+	0.705563i	$0.750694\pi$
$510$	−2.39938e10	+	2.18896e10i	−0.354664	+	0.323562i
$511$	−1.88986e10	−	2.60116e10i	−0.277169	−	0.381491i
$512$	−3.94262e10	−	5.62845e10i	−0.573726	−	0.819047i
$513$	−5.18159e10	−	3.76465e10i	−0.748158	−	0.543569i
$514$	−8.71062e10	−	9.05482e10i	−1.24795	−	1.29726i
$515$	5.06281e8	+	1.79440e8i	0.00719719	+	0.00255088i
$516$	6.79564e9	+	2.50299e9i	0.0958588	+	0.0353070i
$517$	−1.09473e10	−	3.36922e10i	−0.153230	−	0.471594i
$518$	−3.44209e10	+	4.77021e9i	−0.478083	+	0.0662549i
$519$	1.51079e10	−	4.90886e9i	0.208226	−	0.0676568i
$520$	5.09743e10	−	3.70257e9i	0.697169	−	0.0506396i
$521$	1.75727e10	−	5.40831e10i	0.238499	−	0.734025i	−0.758139	−	0.652093i	$-0.773891\pi$
$521$	1.75727e10	−	5.40831e10i	0.238499	−	0.734025i	0.996638	−	0.0819317i	$-0.0261089\pi$
$522$	7.95332e9	+	1.41813e9i	0.107119	+	0.0191000i
$523$	2.86767e10	+	3.94701e10i	0.383286	+	0.527548i	0.956451	−	0.291892i	$-0.0942848\pi$
$523$	2.86767e10	+	3.94701e10i	0.383286	+	0.527548i	−0.573166	+	0.819440i	$0.694285\pi$
$524$	1.19702e10	+	4.23581e10i	0.158773	+	0.561838i
$525$	4.36618e9	−	1.13557e10i	0.0574730	−	0.149477i
$526$	−1.00207e11	+	1.38871e10i	−1.30904	+	0.181413i
$527$	7.04866e10	+	9.70165e10i	0.913827	+	1.25778i
$528$	−1.33874e10	−	5.55054e10i	−0.172250	−	0.714166i
$529$	3.35838e9	−	1.03360e10i	0.0428852	−	0.131987i
$530$	−1.88239e10	+	8.52873e9i	−0.238565	+	0.108089i
$531$	−4.67052e10	+	1.51755e10i	−0.587473	+	0.190881i
$532$	2.80959e10	−	7.93981e9i	0.350750	−	0.0991206i
$533$	1.81330e10	+	5.58077e10i	0.224679	+	0.691489i
$534$	4.50776e10	+	2.40792e10i	0.554364	+	0.296127i
$535$	3.87332e9	−	1.46382e11i	0.0472791	−	1.78678i
$536$	−3.79775e10	+	6.49131e10i	−0.460116	+	0.786454i
$537$	2.25866e10	+	1.64101e10i	0.271615	+	0.197340i
$538$	−7.14770e10	+	1.33809e11i	−0.853173	+	1.59718i
$539$	−6.75770e10	−	9.30118e10i	−0.800653	−	1.10200i
$540$	6.09846e10	−	3.84998e10i	0.717208	−	0.452776i
$541$	−3.66117e10	−	2.66000e10i	−0.427397	−	0.310522i	0.353210	−	0.935544i	$-0.385090\pi$
$541$	−3.66117e10	−	2.66000e10i	−0.427397	−	0.310522i	−0.780607	+	0.625022i	$0.785090\pi$
$542$	5.30115e10	+	1.09221e11i	0.614289	+	1.26564i
$543$		−	1.95733e10i		−	0.225146i
$544$	4.72208e10	−	7.39799e10i	0.539184	−	0.844731i
$545$	8.65163e10	+	6.64240e10i	0.980645	+	0.752903i
$546$	9.79422e9	+	1.74637e9i	0.110204	+	0.0196501i
$547$	5.22052e10	+	1.69625e10i	0.583129	+	0.189470i	0.585702	−	0.810527i	$-0.300819\pi$
$547$	5.22052e10	+	1.69625e10i	0.583129	+	0.189470i	−0.00257281	+	0.999997i	$0.500819\pi$
$548$	6.15960e10	−	7.82186e10i	0.683015	−	0.867337i
$549$	−1.39765e11			−1.53854
$550$	−3.19041e10	+	1.36652e11i	−0.348655	+	1.49337i
$551$			1.41921e10i			0.153971i
$552$	3.56268e10	+	2.08435e10i	0.383726	+	0.224499i
$553$	−7.45957e9	+	2.29582e10i	−0.0797652	+	0.245492i
$554$	6.32163e10	+	1.12719e10i	0.671104	+	0.119662i
$555$	−3.71551e10	−	5.40928e10i	−0.391604	−	0.570122i
$556$	3.39812e10	−	2.27314e10i	0.355582	−	0.237863i
$557$	−7.97183e10			−0.828204			−0.414102	−	0.910230i	$-0.635904\pi$
$557$	−7.97183e10			−0.828204			−0.414102	+	0.910230i	$0.635904\pi$
$558$	−5.06008e10	−	1.04254e11i	−0.521940	−	1.07537i
$559$	8.55494e9	−	1.17749e10i	0.0876133	−	0.120589i
$560$	−3.41110e9	+	3.26987e10i	−0.0346851	+	0.332490i
$561$	5.89951e10	−	4.28625e10i	0.595614	−	0.432739i
$562$	3.27595e10	−	6.13274e10i	0.328391	−	0.614765i
$563$	2.91808e10	−	4.01640e10i	0.290445	−	0.399763i	−0.638714	−	0.769445i	$-0.720533\pi$
$563$	2.91808e10	−	4.01640e10i	0.290445	−	0.399763i	0.929159	+	0.369681i	$0.120533\pi$
$564$	9.69705e9	−	1.23140e10i	0.0958348	−	0.121697i
$565$	4.92358e10	+	3.78014e10i	0.483155	+	0.370949i
$566$	1.08978e11	+	5.82131e10i	1.06187	+	0.567224i
$567$	−1.19671e10	+	3.88834e9i	−0.115786	+	0.0376211i
$568$	1.26037e11	−	5.52483e10i	1.21089	−	0.530793i
$569$	5.36406e10	+	1.65089e11i	0.511735	+	1.57496i	0.789146	+	0.614206i	$0.210524\pi$
$569$	5.36406e10	+	1.65089e11i	0.511735	+	1.57496i	−0.277411	+	0.960751i	$0.589476\pi$
$570$	3.71603e10	+	4.07324e10i	0.352030	+	0.385870i
$571$	−1.45356e11	−	4.72291e10i	−1.36738	−	0.444288i	−0.468879	−	0.883262i	$-0.655342\pi$
$571$	−1.45356e11	−	4.72291e10i	−1.36738	−	0.444288i	−0.898500	+	0.438974i	$0.855342\pi$
$572$	−1.14665e11	−	4.44486e9i	−1.07114	−	0.0415216i
$573$	2.65809e10	−	1.93122e10i	0.246577	−	0.179148i
$574$	−3.73890e10	+	5.18153e9i	−0.344426	+	0.0477321i
$575$	−5.52040e10	−	8.51088e10i	−0.505009	−	0.778580i
$576$	−5.74733e10	+	6.23712e10i	−0.522127	+	0.566623i
$577$	−5.79393e10	+	4.20954e10i	−0.522721	+	0.379779i	−0.817628	−	0.575747i	$-0.804711\pi$
$577$	−5.79393e10	+	4.20954e10i	−0.522721	+	0.379779i	0.294907	+	0.955526i	$0.404711\pi$
$578$	4.71406e8	+	8.40546e7i	0.00422361	+	0.000753096i
$579$	−1.57902e10	−	5.13054e9i	−0.140499	−	0.0456508i
$580$	−1.48446e10	−	5.91808e9i	−0.131177	−	0.0522961i
$581$	−1.69653e10	−	5.22139e10i	−0.148887	−	0.458228i
$582$	1.87205e10	−	2.59437e9i	0.163165	−	0.0226121i
$583$	4.41288e10	−	1.43383e10i	0.381987	−	0.124115i
$584$	−3.50370e10	+	1.60293e11i	−0.301214	+	1.37805i
$585$	−1.78986e10	−	6.04857e10i	−0.152826	−	0.516451i
$586$	8.09699e10	+	8.41695e10i	0.686647	+	0.713780i
$587$	−1.18377e11	+	1.62932e11i	−0.997044	+	1.37231i	−0.0699223	+	0.997552i	$0.522275\pi$
$587$	−1.18377e11	+	1.62932e11i	−0.997044	+	1.37231i	−0.927122	+	0.374761i	$0.877725\pi$
$588$	1.75806e10	−	4.77315e10i	0.147070	−	0.399297i
$589$	1.64698e11	−	1.19660e11i	1.36844	−	0.994230i
$590$	9.65429e10	−	1.07852e10i	0.796732	−	0.0890064i
$591$	−4.70892e10	+	6.48128e10i	−0.385986	+	0.531264i
$592$	1.34967e11	+	1.15028e11i	1.09886	+	0.936517i
$593$	3.20722e10			0.259364			0.129682	−	0.991556i	$-0.458604\pi$
$593$	3.20722e10			0.259364			0.129682	+	0.991556i	$0.458604\pi$
$594$	−1.45675e11	+	7.07049e10i	−1.17015	+	0.567942i
$595$	−4.02623e10	+	1.19142e10i	−0.321241	+	0.0950599i
$596$	−2.18480e9	+	5.63616e10i	−0.0173151	+	0.446682i
$597$	4.09034e9	−	1.25888e10i	0.0322004	−	0.0991028i
$598$	5.97833e10	−	5.75108e10i	0.467493	−	0.449723i
$599$		−	1.16139e10i		−	0.0902131i	−0.998982	−	0.0451066i	$-0.985637\pi$
$599$		−	1.16139e10i		−	0.0902131i	0.998982	−	0.0451066i	$-0.0143627\pi$
$600$	−5.81011e10	+	2.18836e10i	−0.448311	+	0.168855i
$601$	−2.42278e9			−0.0185701			−0.00928507	−	0.999957i	$-0.502956\pi$
$601$	−2.42278e9			−0.0185701			−0.00928507	+	0.999957i	$0.502956\pi$
$602$	6.49070e9	+	6.74717e9i	0.0494203	+	0.0513731i
$603$	8.82769e10	+	2.86829e10i	0.667694	+	0.216947i
$604$	−6.00258e10	−	2.32683e9i	−0.451014	−	0.0174831i
$605$	6.04971e10	−	1.70690e11i	0.451558	−	1.27405i
$606$	−2.75431e10	−	5.67478e10i	−0.204231	−	0.420784i
$607$			3.66781e10i			0.270179i	0.990833	+	0.135090i	$0.0431323\pi$
$607$			3.66781e10i			0.270179i	−0.990833	+	0.135090i	$0.956868\pi$
$608$	−1.25590e11	−	8.01631e10i	−0.919055	−	0.586625i
$609$	−2.51668e9	−	1.82848e9i	−0.0182961	−	0.0132929i
$610$	2.70801e11	+	5.57139e10i	1.95583	+	0.402387i
$611$	−1.85155e10	−	2.54843e10i	−0.132853	−	0.182856i
$612$	−1.01645e11	−	3.74382e10i	−0.724571	−	0.266876i
$613$	−3.70908e10	−	2.69480e10i	−0.262678	−	0.190847i	0.448649	−	0.893708i	$-0.351905\pi$
$613$	−3.70908e10	−	2.69480e10i	−0.262678	−	0.190847i	−0.711327	+	0.702861i	$0.751905\pi$
$614$	−1.75317e11	+	1.68653e11i	−1.23353	+	1.18664i
$615$	−4.03589e10	−	5.87571e10i	−0.282123	−	0.410733i
$616$	1.57623e10	−	7.21121e10i	0.109471	−	0.500824i
$617$	4.81883e10	+	1.48308e11i	0.332507	+	1.02335i	0.967937	+	0.251193i	$0.0808230\pi$
$617$	4.81883e10	+	1.48308e11i	0.332507	+	1.02335i	−0.635430	+	0.772159i	$0.719177\pi$
$618$	−7.32457e7	−	5.28527e8i	−0.000502144	−	0.00362338i
$619$	2.39674e11	−	7.78747e10i	1.63252	−	0.530437i	0.657668	−	0.753307i	$-0.271543\pi$
$619$	2.39674e11	−	7.78747e10i	1.63252	−	0.530437i	0.974848	+	0.222871i	$0.0715428\pi$
$620$	5.64829e10	+	2.22168e11i	0.382253	+	1.50354i
$621$	3.61734e10	−	1.11330e11i	0.243233	−	0.748595i
$622$	−1.21466e10	+	6.81220e10i	−0.0811507	+	0.455120i
$623$	3.88345e10	+	5.34511e10i	0.257790	+	0.354817i
$624$	−2.65726e10	−	4.32605e10i	−0.175265	−	0.285334i
$625$	1.51734e11	+	1.61163e10i	0.994407	+	0.105620i
$626$	−1.84502e8	−	1.33133e9i	−0.00120144	−	0.00866939i
$627$	−7.27644e10	−	1.00152e11i	−0.470813	−	0.648019i
$628$	7.52888e8	−	1.94224e10i	0.00484052	−	0.124872i
$629$	−6.99875e10	+	2.15399e11i	−0.447114	+	1.37607i
$630$	4.03249e10	−	4.50487e9i	0.255983	−	0.0285970i
$631$	1.59146e11	−	5.17097e10i	1.00387	−	0.326178i	0.239460	−	0.970906i	$-0.423030\pi$
$631$	1.59146e11	−	5.17097e10i	1.00387	−	0.326178i	0.764412	+	0.644728i	$0.223030\pi$
$632$	1.12825e11	−	4.94566e10i	0.707192	−	0.309996i
$633$	−1.40144e10	−	4.31318e10i	−0.0872889	−	0.268648i
$634$	−3.56744e10	+	6.67842e10i	−0.220800	+	0.413349i
$635$	−7.00527e10	−	1.01987e11i	−0.430854	−	0.627264i
$636$	1.61283e10	+	1.27008e10i	0.0985738	+	0.0776253i
$637$	−8.27047e10	−	6.00885e10i	−0.502311	−	0.364950i
$638$	3.16484e10	+	1.69057e10i	0.191016	+	0.102036i
$639$	−9.98319e10	−	1.37407e11i	−0.598778	−	0.824147i
$640$	1.36220e11	−	9.79368e10i	0.811934	−	0.583749i
$641$	−4.48731e10	−	3.26022e10i	−0.265799	−	0.193114i	0.446901	−	0.894584i	$-0.352528\pi$
$641$	−4.48731e10	−	3.26022e10i	−0.265799	−	0.193114i	−0.712700	+	0.701469i	$0.752528\pi$
$642$	−1.30863e11	+	6.35154e10i	−0.770327	+	0.373886i
$643$			2.53512e11i			1.48305i	0.670926	+	0.741524i	$0.265897\pi$
$643$			2.53512e11i			1.48305i	−0.670926	+	0.741524i	$0.734103\pi$
$644$	2.96694e10	+	4.43530e10i	0.172491	+	0.257857i
$645$	−5.90645e9	+	1.66648e10i	−0.0341262	+	0.0962855i
$646$	3.34028e10	−	1.87334e11i	0.191802	−	1.07569i
$647$	−1.67032e11	−	5.42719e10i	−0.953196	−	0.309712i	−0.209182	−	0.977877i	$-0.567080\pi$
$647$	−1.67032e11	−	5.42719e10i	−0.953196	−	0.309712i	−0.744014	+	0.668164i	$0.767080\pi$
$648$	5.54241e10	+	3.24260e10i	0.314339	+	0.183905i
$649$	−2.18110e11			−1.22941
$650$	1.05683e10	+	1.24329e11i	0.0592039	+	0.696494i
$651$			4.46225e10i			0.248445i
$652$	−3.88846e10	−	3.06210e10i	−0.215173	−	0.169445i
$653$	5.85342e10	−	1.80150e11i	0.321927	−	0.990789i	−0.650882	−	0.759179i	$-0.725601\pi$
$653$	5.85342e10	−	1.80150e11i	0.321927	−	0.990789i	0.972809	−	0.231610i	$-0.0743993\pi$
$654$	1.90197e10	−	1.06669e11i	0.103966	−	0.583078i
$655$	−1.03046e11	+	3.04930e10i	−0.559844	+	0.165666i
$656$	1.46605e11	+	1.24946e11i	0.791650	+	0.674695i
$657$	2.02505e11			1.08686
$658$	1.82292e10	−	8.84772e9i	0.0972443	−	0.0471984i
$659$	7.35473e10	−	1.01229e11i	0.389965	−	0.536740i	−0.568225	−	0.822873i	$-0.692370\pi$
$659$	7.35473e10	−	1.01229e11i	0.389965	−	0.536740i	0.958190	+	0.286133i	$0.0923698\pi$
$660$	1.35099e11	−	3.43469e10i	0.711995	−	0.181014i
$661$	−1.32073e11	+	9.59568e10i	−0.691845	+	0.502655i	−0.877266	−	0.480004i	$-0.840635\pi$
$661$	−1.32073e11	+	9.59568e10i	−0.691845	+	0.502655i	0.185421	+	0.982659i	$0.440635\pi$
$662$	1.87815e11	+	1.00326e11i	0.977908	+	0.522372i
$663$	3.81127e10	−	5.24576e10i	0.197249	−	0.271490i
$664$	−1.41479e11	+	2.41822e11i	−0.727811	+	1.24401i
$665$	2.02259e10	+	6.83502e10i	0.103424	+	0.349505i
$666$	1.03122e11	−	1.93050e11i	0.524149	−	0.981234i
$667$	−2.46691e10	+	8.01549e9i	−0.124638	+	0.0404973i
$668$	9.82786e10	+	3.47770e11i	0.493575	+	1.74657i
$669$	1.84073e10	+	5.66519e10i	0.0918938	+	0.282820i
$670$	−1.59607e11	−	9.07639e10i	−0.792049	−	0.450416i
$671$	−5.90366e11	−	1.91821e11i	−2.91227	−	0.946253i
$672$	3.03961e10	−	1.19429e10i	0.149053	−	0.0585641i
$673$	2.04701e11	−	1.48724e11i	0.997837	−	0.724971i	0.0362135	−	0.999344i	$-0.488470\pi$
$673$	2.04701e11	−	1.48724e11i	0.997837	−	0.724971i	0.961623	+	0.274373i	$0.0884704\pi$
$674$	4.96953e10	+	3.58592e11i	0.240811	+	1.73764i
$675$	9.58165e10	+	1.47722e11i	0.461557	+	0.711589i
$676$	1.02767e11	−	2.90417e10i	0.492118	−	0.139071i
$677$	2.27054e11	−	1.64965e11i	1.08087	−	0.785301i	0.103039	−	0.994677i	$-0.467143\pi$
$677$	2.27054e11	−	1.64965e11i	1.08087	−	0.785301i	0.977835	+	0.209376i	$0.0671433\pi$
$678$	1.08240e10	−	6.07044e10i	0.0512234	−	0.287277i
$679$	2.32372e10	+	7.55024e9i	0.109321	+	0.0355207i
$680$	1.82018e11	+	1.13057e11i	0.851294	+	0.528762i
$681$	1.88941e10	+	5.81501e10i	0.0878492	+	0.270372i
$682$	−7.06526e10	−	5.09816e11i	−0.326581	−	2.35655i
$683$	1.68873e11	−	5.48702e10i	0.776029	−	0.252147i	0.105885	−	0.994378i	$-0.466232\pi$
$683$	1.68873e11	−	5.48702e10i	0.776029	−	0.252147i	0.670144	+	0.742231i	$0.266232\pi$
$684$	−6.35560e10	+	1.72555e11i	−0.290357	+	0.788322i
$685$	1.92797e11	+	1.48023e11i	0.875666	+	0.672304i
$686$	1.00744e11	−	9.69149e10i	0.454909	−	0.437617i
$687$	−1.13511e11	+	1.56234e11i	−0.509577	+	0.701373i
$688$	3.69853e9	−	4.76342e10i	0.0165073	−	0.212601i
$689$	3.33784e10	−	2.42508e10i	0.148112	−	0.107609i
$690$	−4.98147e10	+	8.75984e10i	−0.219767	+	0.386456i
$691$	−9.21560e10	+	1.26842e11i	−0.404214	+	0.556353i	−0.961795	−	0.273770i	$-0.911729\pi$
$691$	−9.21560e10	+	1.26842e11i	−0.404214	+	0.556353i	0.557581	+	0.830122i	$0.311729\pi$
$692$	−5.82703e10	−	8.71086e10i	−0.254111	−	0.379872i
$693$	−9.11021e10			−0.394999
$694$	1.57398e10	+	3.24292e10i	0.0678519	+	0.139797i
$695$	5.65119e10	+	8.22737e10i	0.242215	+	0.352632i
$696$	1.56846e9	+	1.57972e10i	0.00668400	+	0.0673198i
$697$	−7.60224e10	+	2.33973e11i	−0.322114	+	0.991366i
$698$	−2.86473e11	−	2.97793e11i	−1.20687	−	1.25456i
$699$		−	1.39447e11i		−	0.584119i
$700$	−7.99271e10	−	7.34614e9i	−0.332891	−	0.0305962i
$701$	−3.53512e11			−1.46397			−0.731985	−	0.681320i	$-0.761406\pi$
$701$	−3.53512e11			−1.46397			−0.731985	+	0.681320i	$0.761406\pi$
$702$	−1.03765e11	+	9.98204e10i	−0.427269	+	0.411028i
$703$	3.65667e11	+	1.18813e11i	1.49715	+	0.486453i
$704$	−3.28368e11	+	1.84576e11i	−1.33681	+	0.751422i
$705$	3.03520e10	+	2.33032e10i	0.122866	+	0.0943319i
$706$	2.95063e11	−	1.43212e11i	1.18767	−	0.576447i
$707$		−	8.15480e10i		−	0.326389i
$708$	−5.36544e10	−	8.02082e10i	−0.213536	−	0.319217i
$709$	−2.91983e11	−	2.12138e11i	−1.15551	−	0.839524i	−0.166303	−	0.986075i	$-0.553183\pi$
$709$	−2.91983e11	−	2.12138e11i	−1.15551	−	0.839524i	−0.989203	+	0.146550i	$0.953183\pi$
$710$	1.38655e11	+	3.06028e11i	0.545635	+	1.20428i
$711$	−8.93666e10	−	1.23003e11i	−0.349701	−	0.481322i
$712$	7.19973e10	−	3.29385e11i	0.280154	−	1.28169i
$713$	3.01015e11	+	2.18700e11i	1.16474	+	0.846236i
$714$	2.89164e10	+	3.00590e10i	0.111263	+	0.115660i
$715$	7.41040e9	−	2.80056e11i	0.0283542	−	1.07157i
$716$	6.36599e10	−	1.72837e11i	0.242222	−	0.657636i
$717$	5.43996e10	+	1.67425e11i	0.205835	+	0.633495i
$718$	6.42165e10	−	8.89942e9i	0.241629	−	0.0334860i
$719$	1.65223e11	−	5.36842e10i	0.618237	−	0.200877i	0.0168797	−	0.999858i	$-0.494627\pi$
$719$	1.65223e11	−	5.36842e10i	0.618237	−	0.200877i	0.601358	+	0.798980i	$0.294627\pi$
$720$	−1.53986e11	−	1.38434e11i	−0.572997	−	0.515124i
$721$	2.13162e8	−	6.56046e8i	0.000788804	−	0.00242769i
$722$	−5.05046e10	−	9.00529e9i	−0.185858	−	0.0331397i
$723$	3.19285e10	+	4.39458e10i	0.116849	+	0.160829i
$724$	−1.24265e11	+	3.51169e10i	−0.452267	+	0.127809i
$725$	1.40019e10	−	3.64166e10i	0.0506800	−	0.131810i
$726$	−1.78190e11	+	2.46944e10i	−0.641412	+	0.0888897i
$727$	2.46840e11	+	3.39747e11i	0.883646	+	1.21624i	0.975398	+	0.220453i	$0.0707536\pi$
$727$	2.46840e11	+	3.39747e11i	0.883646	+	1.21624i	−0.0917511	+	0.995782i	$0.529246\pi$
$728$	−6.48482e9	−	6.53138e10i	−0.0230873	−	0.232530i
$729$	−1.09719e10	+	3.37680e10i	−0.0388482	+	0.119562i
$730$	−3.92362e11	−	8.07236e10i	−1.38164	−	0.284256i
$731$	5.80331e10	−	1.88561e10i	0.203239	−	0.0660362i
$732$	−7.46873e10	−	2.64290e11i	−0.260137	−	0.920525i
$733$	−1.23159e10	−	3.79046e10i	−0.0426631	−	0.131303i	0.927456	−	0.373932i	$-0.121991\pi$
$733$	−1.23159e10	−	3.79046e10i	−0.0426631	−	0.131303i	−0.970119	+	0.242628i	$0.921991\pi$
$734$	−1.11240e11	−	5.94217e10i	−0.383247	−	0.204720i
$735$	1.17051e11	+	4.14860e10i	0.401074	+	0.142152i
$736$	6.84106e10	−	2.63580e11i	0.233137	−	0.898258i
$737$	3.33514e11	+	2.42312e11i	1.13043	+	0.821307i
$738$	1.12014e11	−	2.09696e11i	0.377613	−	0.706911i
$739$	2.89315e11	+	3.98208e11i	0.970049	+	1.33516i	0.942022	+	0.335551i	$0.108922\pi$
$739$	2.89315e11	+	3.98208e11i	0.970049	+	1.33516i	0.0280267	+	0.999607i	$0.491078\pi$
$740$	−2.76758e11	+	3.32936e11i	−0.922941	+	1.11028i
$741$	−8.90533e10	−	6.47010e10i	−0.295377	−	0.214604i
$742$	1.15884e10	+	2.38759e10i	0.0382303	+	0.0787670i
$743$		−	7.72300e10i		−	0.253414i	−0.991940	−	0.126707i	$-0.959559\pi$
$743$		−	7.72300e10i		−	0.253414i	0.991940	−	0.126707i	$-0.0404408\pi$
$744$	1.70100e11	−	1.51395e11i	0.555154	−	0.494106i
$745$	−1.37657e11	−	3.64246e9i	−0.446861	−	0.0118241i
$746$	−1.29114e11	−	2.30218e10i	−0.416887	−	0.0743335i
$747$	3.28860e11	+	1.06853e11i	1.05616	+	0.343166i
$748$	−3.77965e11	−	2.97642e11i	−1.20738	−	0.950797i
$749$	−1.88053e11			−0.597519
$750$	−5.51660e10	−	1.41181e11i	−0.174352	−	0.446202i
$751$			5.54731e11i			1.74390i	0.489592	+	0.871952i	$0.337146\pi$
$751$			5.54731e11i			1.74390i	−0.489592	+	0.871952i	$0.662854\pi$
$752$	−9.55753e10	−	3.94710e10i	−0.298864	−	0.123426i
$753$	−3.01063e10	+	9.26575e10i	−0.0936433	+	0.288205i
$754$	3.14092e10	+	5.60046e9i	0.0971788	+	0.0173276i
$755$	3.87926e9	−	1.46606e11i	0.0119388	−	0.451195i
$756$	−5.14967e10	−	7.69827e10i	−0.157649	−	0.235671i
$757$	−2.98110e11			−0.907807			−0.453904	−	0.891051i	$-0.649969\pi$
$757$	−2.98110e11			−0.907807			−0.453904	+	0.891051i	$0.649969\pi$
$758$	−1.52165e11	−	3.13511e11i	−0.460934	−	0.949676i
$759$	1.32990e11	−	1.83046e11i	0.400731	−	0.551560i
$760$	1.91928e11	−	3.08999e11i	0.575285	−	0.926195i
$761$	1.69004e11	−	1.22789e11i	0.503917	−	0.366117i	−0.306594	−	0.951840i	$-0.599189\pi$
$761$	1.69004e11	−	1.22789e11i	0.503917	−	0.366117i	0.810511	+	0.585723i	$0.199189\pi$
$762$	−5.79101e10	+	1.08411e11i	−0.171765	+	0.321553i
$763$	8.23345e10	−	1.13324e11i	0.242931	−	0.334367i
$764$	−1.70297e11	−	1.34106e11i	−0.499842	−	0.393618i
$765$	8.83451e10	−	2.49262e11i	0.257951	−	0.727796i
$766$	−1.65922e11	−	8.86311e10i	−0.481936	−	0.257437i
$767$	−1.84448e11	+	5.99308e10i	−0.532958	+	0.173168i
$768$	−1.48654e11	−	7.53497e10i	−0.427298	−	0.216589i
$769$	−6.87369e10	−	2.11550e11i	−0.196555	−	0.604935i	−0.999955	−	0.00949457i	$-0.996978\pi$
$769$	−6.87369e10	−	2.11550e11i	−0.196555	−	0.604935i	0.803400	−	0.595440i	$-0.203022\pi$
$770$	1.76515e11	+	3.63156e10i	0.502132	+	0.103307i
$771$	−2.89801e11	−	9.41621e10i	−0.820130	−	0.266476i
$772$	−4.24278e9	+	1.09452e11i	−0.0119449	+	0.308144i
$773$	−4.26109e11	+	3.09586e11i	−1.19345	+	0.867089i	−0.993624	−	0.112744i	$-0.964036\pi$
$773$	−4.26109e11	+	3.09586e11i	−1.19345	+	0.867089i	−0.199821	+	0.979832i	$0.564036\pi$
$774$	−5.84089e10	+	8.09457e9i	−0.162748	+	0.0225543i
$775$	−5.40667e11	+	1.44553e11i	−1.49873	+	0.400702i
$776$	−5.00578e10	−	1.14196e11i	−0.138046	−	0.314924i
$777$	−6.81808e10	+	4.95363e10i	−0.187059	+	0.135906i
$778$	3.90816e11	+	6.96850e10i	1.06673	+	0.190205i
$779$	3.97198e11	+	1.29057e11i	1.07859	+	0.350456i
$780$	1.04811e11	−	6.61677e10i	0.283158	−	0.178759i
$781$	−2.33104e11	−	7.17420e11i	−0.626535	−	1.92828i
$782$	3.44495e11	−	4.77417e10i	0.921204	−	0.127665i
$783$	4.28177e10	−	1.39123e10i	0.113914	−	0.0370129i
$784$	−3.34575e11	−	2.59779e10i	−0.885582	−	0.0687605i
$785$	4.74370e10	+	1.25520e9i	0.124922	+	0.00330549i
$786$	7.40079e10	+	7.69323e10i	0.193904	+	0.201567i
$787$	−1.46488e11	+	2.01624e11i	−0.381860	+	0.525585i	−0.956076	−	0.293119i	$-0.905307\pi$
$787$	−1.46488e11	+	2.01624e11i	−0.381860	+	0.525585i	0.574216	+	0.818704i	$0.305307\pi$
$788$	4.95961e11	+	1.82674e11i	1.28630	+	0.473774i
$789$	−1.98489e11	+	1.44211e11i	−0.512187	+	0.372126i
$790$	1.24120e11	+	2.73947e11i	0.318664	+	0.703328i
$791$	4.68560e10	−	6.44917e10i	0.119690	−	0.164740i
$792$	3.09091e11	+	3.47280e11i	0.785570	+	0.882630i
$793$	−5.51959e11			−1.39577
$794$	−2.34079e11	+	1.13612e11i	−0.588953	+	0.285854i
$795$	−3.05216e10	+	3.97539e10i	−0.0764080	+	0.0995203i
$796$	−8.72609e10	−	3.38257e9i	−0.217354	−	0.00842548i
$797$	1.06878e10	−	3.28936e10i	0.0264883	−	0.0815226i	−0.936938	−	0.349494i	$-0.886353\pi$
$797$	1.06878e10	−	3.28936e10i	0.0264883	−	0.0815226i	0.963427	+	0.267972i	$0.0863534\pi$
$798$	5.10289e10	−	4.90891e10i	0.125836	−	0.121053i
$799$		−	1.32065e11i		−	0.324041i
$800$	2.43173e11	+	3.29605e11i	0.593683	+	0.804699i
$801$	−4.16125e11			−1.01087
$802$	−3.74631e11	−	3.89434e11i	−0.905536	−	0.941318i
$803$	8.55378e11	+	2.77929e11i	2.05729	+	0.668454i
$804$	−7.06492e9	+	1.82255e11i	−0.0169076	+	0.436170i
$805$	−1.07385e11	+	7.37605e10i	−0.255718	+	0.175647i
$806$	−1.99832e11	−	4.11720e11i	−0.473506	−	0.975579i
$807$			3.67912e11i			0.867462i
$808$	−3.10859e11	+	2.76675e11i	−0.729321	+	0.649120i
$809$	6.03704e11	+	4.38616e11i	1.40939	+	1.02398i	0.993411	+	0.114602i	$0.0365593\pi$
$809$	6.03704e11	+	4.38616e11i	1.40939	+	1.02398i	0.415974	+	0.909377i	$0.363441\pi$
$810$	−7.74960e10	+	1.36275e11i	−0.180028	+	0.316576i
$811$	−2.46302e11	−	3.39006e11i	−0.569358	−	0.783654i	0.423121	−	0.906073i	$-0.360935\pi$
$811$	−2.46302e11	−	3.39006e11i	−0.569358	−	0.783654i	−0.992478	+	0.122420i	$0.960935\pi$
$812$	−7.09322e9	+	1.92582e10i	−0.0163162	+	0.0442987i
$813$	2.38204e11	+	1.73066e11i	0.545240	+	0.396140i
$814$	7.00539e11	−	6.73910e11i	1.59564	−	1.53498i
$815$	7.35860e10	−	9.58447e10i	0.166788	−	0.217239i
$816$	1.64771e10	−	2.12213e11i	0.0371639	−	0.478642i
$817$	−3.20106e10	−	9.85184e10i	−0.0718464	−	0.221121i
$818$	−3.99814e9	−	2.88498e10i	−0.00892986	−	0.0644362i
$819$	−7.70419e10	+	2.50324e10i	−0.171235	+	0.0556375i
$820$	−3.00623e11	+	3.61644e11i	−0.664915	+	0.799882i
$821$	1.13343e11	−	3.48834e11i	0.249472	−	0.767797i	−0.745396	−	0.666622i	$-0.767740\pi$
$821$	1.13343e11	−	3.48834e11i	0.249472	−	0.767797i	0.994869	−	0.101175i	$-0.0322603\pi$
$822$	4.23845e10	−	2.37706e11i	0.0928367	−	0.520659i
$823$	1.97219e11	+	2.71449e11i	0.429882	+	0.591682i	0.967926	−	0.251235i	$-0.0808366\pi$
$823$	1.97219e11	+	2.71449e11i	0.429882	+	0.591682i	−0.538044	+	0.842917i	$0.680837\pi$
$824$	−3.22405e9	+	1.41326e9i	−0.00699348	+	0.00306558i
$825$	8.79021e10	+	3.28777e11i	0.189751	+	0.709717i
$826$	−1.71253e10	−	1.23573e11i	−0.0367890	−	0.265462i
$827$	1.45995e11	+	2.00945e11i	0.312116	+	0.429591i	0.936040	−	0.351895i	$-0.114462\pi$
$827$	1.45995e11	+	2.00945e11i	0.312116	+	0.429591i	−0.623924	+	0.781485i	$0.714462\pi$
$828$	−3.35837e11	−	1.30183e10i	−0.714508	−	0.0276971i
$829$	−5.76662e10	+	1.77478e11i	−0.122097	+	0.375775i	−0.993361	−	0.115039i	$-0.963301\pi$
$829$	−5.76662e10	+	1.77478e11i	−0.122097	+	0.375775i	0.871264	+	0.490814i	$0.163301\pi$
$830$	−5.94587e11	−	3.38125e11i	−1.25286	−	0.712467i
$831$	1.48109e11	−	4.81237e10i	0.310584	−	0.100915i
$832$	−2.26973e11	+	2.46316e11i	−0.473676	+	0.514043i
$833$	−1.32442e11	−	4.07615e11i	−0.275072	−	0.846584i
$834$	4.67164e10	−	8.74556e10i	0.0965618	−	0.180769i
$835$	−8.46035e11	+	2.50355e11i	−1.74037	+	0.515003i
$836$	−5.05285e11	+	6.41643e11i	−1.03445	+	1.31362i
$837$	−5.22467e11	−	3.79594e11i	−1.06453	−	0.773424i
$838$	−3.30919e11	−	1.76768e11i	−0.671036	−	0.358450i
$839$	−3.18716e11	−	4.38674e11i	−0.643214	−	0.885308i	0.355568	−	0.934650i	$-0.384287\pi$
$839$	−3.18716e11	−	4.38674e11i	−0.643214	−	0.885308i	−0.998782	+	0.0493423i	$0.984287\pi$
$840$	3.00672e10	+	7.38453e10i	0.0603916	+	0.148322i
$841$	3.96637e11	+	2.88174e11i	0.792883	+	0.576063i
$842$	3.09837e11	−	1.50382e11i	0.616432	−	0.299191i
$843$		−	1.68622e11i		−	0.333891i
$844$	−2.48688e11	+	1.66357e11i	−0.490099	+	0.327847i
$845$	7.39808e10	+	2.50007e11i	0.145108	+	0.490371i
$846$	−2.24026e10	+	1.25641e11i	−0.0437337	+	0.245273i
$847$	−2.21182e11	−	7.18665e10i	−0.429751	−	0.139634i
$848$	5.16976e10	−	1.25181e11i	0.0999739	−	0.242078i
$849$	2.99639e11			0.576724
$850$	−2.70535e11	+	4.47739e11i	−0.518260	+	0.857728i
$851$			7.02719e11i			1.33987i
$852$	2.06482e11	−	2.62205e11i	0.391854	−	0.497602i
$853$	6.13886e10	−	1.88935e11i	0.115956	−	0.356875i	−0.876190	−	0.481967i	$-0.839923\pi$
$853$	6.13886e10	−	1.88935e11i	0.115956	−	0.356875i	0.992145	+	0.125092i	$0.0399226\pi$
$854$	6.23252e10	−	3.49540e11i	0.117174	−	0.657151i
$855$	−4.23153e11	−	1.49977e11i	−0.791831	−	0.280647i
$856$	6.38023e11	+	7.16853e11i	1.18834	+	1.33517i
$857$	1.39895e11			0.259346			0.129673	−	0.991557i	$-0.458607\pi$
$857$	1.39895e11			0.259346			0.129673	+	0.991557i	$0.458607\pi$
$858$	−2.50365e11	+	1.21517e11i	−0.461981	+	0.224227i
$859$	−1.46029e11	+	2.00992e11i	−0.268205	+	0.369153i	−0.921783	−	0.387707i	$-0.873267\pi$
$859$	−1.46029e11	+	2.00992e11i	−0.268205	+	0.369153i	0.653578	+	0.756860i	$0.273267\pi$
$860$	1.16397e11	+	7.59969e9i	0.212788	+	0.0138932i
$861$	−7.40599e10	+	5.38077e10i	−0.134763	+	0.0979110i
$862$	6.10515e11	+	3.26121e11i	1.10578	+	0.590676i
$863$	−3.03283e11	+	4.17433e11i	−0.546770	+	0.752564i	−0.989569	−	0.144057i	$-0.953985\pi$
$863$	−3.03283e11	+	4.17433e11i	−0.546770	+	0.752564i	0.442800	+	0.896620i	$0.353985\pi$
$864$	−1.18739e11	+	4.57491e11i	−0.213078	+	0.820970i
$865$	2.10903e11	−	1.44865e11i	0.376720	−	0.258760i
$866$	−1.46233e11	+	2.73756e11i	−0.260001	+	0.486735i
$867$	1.10446e9	−	3.58860e8i	0.00195467	−	0.000635109i
$868$	2.83295e11	−	8.00582e10i	0.499069	−	0.141035i
$869$	−2.08668e11	−	6.42213e11i	−0.365912	−	1.12616i
$870$	−3.85174e10	+	4.30295e9i	−0.0672326	+	0.00751085i
$871$	3.48623e11	+	1.13274e11i	0.605735	+	0.196815i
$872$	−7.11332e11	+	7.06262e10i	−1.23029	+	0.122152i
$873$	−1.24498e11	+	9.04528e10i	−0.214340	+	0.155727i
$874$	−8.10474e10	−	5.84823e11i	−0.138897	−	1.00226i
$875$	1.55354e10	−	1.95340e11i	0.0265027	−	0.333242i
$876$	1.08214e11	+	3.82928e11i	0.183767	+	0.650280i
$877$	1.12031e11	−	8.13952e10i	0.189382	−	0.137594i	−0.489054	−	0.872253i	$-0.662658\pi$
$877$	1.12031e11	−	8.13952e10i	0.189382	−	0.137594i	0.678436	+	0.734659i	$0.262658\pi$
$878$	3.17051e9	−	1.77813e10i	0.00533521	−	0.0299216i
$879$	2.69386e11	+	8.75288e10i	0.451252	+	0.146621i
$880$	−4.60443e11	−	7.96082e11i	−0.767794	−	1.32748i
$881$	1.74465e11	+	5.36949e11i	0.289604	+	0.891310i	0.984981	+	0.172665i	$0.0552377\pi$
$881$	1.74465e11	+	5.36949e11i	0.289604	+	0.891310i	−0.695376	+	0.718646i	$0.744762\pi$
$882$	5.68549e10	+	4.10254e11i	0.0939493	+	0.677921i
$883$	−3.65788e10	+	1.18852e10i	−0.0601710	+	0.0195507i	−0.338948	−	0.940805i	$-0.610071\pi$
$883$	−3.65788e10	+	1.18852e10i	−0.0601710	+	0.0195507i	0.278777	+	0.960356i	$0.410071\pi$
$884$	−4.01416e11	−	1.47851e11i	−0.657334	−	0.242111i
$885$	1.94196e11	−	1.33389e11i	0.316568	−	0.217443i
$886$	6.43877e11	−	6.19402e11i	1.04488	−	1.00517i
$887$	6.71260e11	−	9.23910e11i	1.08442	−	1.49257i	0.229853	−	0.973225i	$-0.426176\pi$
$887$	6.71260e11	−	9.23910e11i	1.08442	−	1.49257i	0.854564	−	0.519346i	$-0.173824\pi$
$888$	4.20155e11	+	9.18379e10i	0.675706	+	0.147696i
$889$	−1.28549e11	+	9.33962e10i	−0.205808	+	0.149528i
$890$	8.06262e11	+	1.65878e11i	1.28504	+	0.264381i
$891$	2.06891e11	−	2.84761e11i	0.328270	−	0.451825i
$892$	3.26641e11	−	2.18503e11i	0.515954	−	0.345142i
$893$	−2.24196e11			−0.352552
$894$	5.97296e10	+	1.23063e11i	0.0935061	+	0.192653i
$895$	4.23845e11	+	1.50222e11i	0.660563	+	0.234122i
$896$	−1.30356e11	−	1.71549e11i	−0.202255	−	0.266168i
$897$	6.21694e10	−	1.91338e11i	0.0960299	−	0.295550i
$898$	−5.85099e11	−	6.08219e11i	−0.899755	−	0.935309i
$899$			1.43101e11i			0.219080i
$900$	3.33327e11	−	3.80069e11i	0.508043	−	0.579285i
$901$	1.72973e11			0.262470
$902$	7.60945e11	−	7.32019e11i	1.14955	−	1.10585i
$903$	2.15944e10	+	7.01646e9i	0.0324781	+	0.0105528i
$904$	−4.04814e11	+	4.01928e10i	−0.606152	+	0.0601832i
$905$	−8.94566e10	−	3.02305e11i	−0.133358	−	0.450662i
$906$	−1.31063e11	+	6.36128e10i	−0.194522	+	0.0944130i
$907$			1.08346e12i			1.60098i	0.599348	+	0.800489i	$0.295427\pi$
$907$			1.08346e12i			1.60098i	−0.599348	+	0.800489i	$0.704573\pi$
$908$	3.35279e11	−	2.24281e11i	0.493245	−	0.329951i
$909$	4.15524e11	+	3.01896e11i	0.608612	+	0.442182i
$910$	1.59251e11	−	1.77906e10i	0.232229	−	0.0259433i
$911$	−6.66674e10	−	9.17598e10i	−0.0967921	−	0.133223i	0.757874	−	0.652401i	$-0.226238\pi$
$911$	−6.66674e10	−	9.17598e10i	−0.0967921	−	0.133223i	−0.854666	+	0.519178i	$0.826238\pi$
$912$	−3.60257e11	−	2.79720e10i	−0.520755	−	0.0404337i
$913$	1.24245e12	+	9.02692e11i	1.78812	+	1.29914i
$914$	6.51252e11	+	6.76986e11i	0.933178	+	0.970052i
$915$	6.42948e11	−	1.90258e11i	0.917258	−	0.271431i
$916$	1.19554e12	+	4.40343e11i	1.69817	+	0.625474i
$917$	4.26465e10	+	1.31252e11i	0.0603123	+	0.185622i
$918$	−5.97933e11	+	8.28643e10i	−0.841942	+	0.116680i
$919$	4.19153e11	−	1.36191e11i	0.587639	−	0.190935i	−8.09630e−5	−	1.00000i	$-0.500026\pi$
$919$	4.19153e11	−	1.36191e11i	0.587639	−	0.190935i	0.587720	+	0.809065i	$0.300026\pi$
$920$	6.45510e11	+	1.59097e11i	0.901055	+	0.222080i
$921$	−1.82314e11	+	5.61105e11i	−0.253385	+	0.779840i
$922$	2.75844e11	+	4.91847e10i	0.381716	+	0.0680623i
$923$	−3.94256e11	−	5.42646e11i	−0.543214	−	0.747670i
$924$	−4.86829e10	−	1.72270e11i	−0.0667865	−	0.236332i
$925$	−8.21074e11	−	6.65639e11i	−1.12154	−	0.909226i
$926$	−4.07809e11	+	5.65160e10i	−0.554642	+	0.0768648i
$927$	2.55371e9	+	3.51488e9i	0.00345822	+	0.00475983i
$928$	9.74777e10	−	3.82998e10i	0.131436	−	0.0516421i
$929$	−1.20696e9	+	3.71464e9i	−0.00162043	+	0.00498717i	−0.951863	−	0.306522i	$-0.900835\pi$
$929$	−1.20696e9	+	3.71464e9i	−0.00162043	+	0.00498717i	0.950243	+	0.311510i	$0.100835\pi$
$930$	3.74693e11	+	4.10710e11i	0.500891	+	0.549040i
$931$	−6.91977e11	+	2.24837e11i	−0.921071	+	0.299274i
$932$	−8.85310e11	+	2.50185e11i	−1.17336	+	0.331588i
$933$	5.18582e10	+	1.59603e11i	0.0684370	+	0.210627i
$934$	3.52884e11	+	1.88501e11i	0.463708	+	0.247700i
$935$	7.15270e11	−	9.31628e11i	0.935887	−	1.21898i
$936$	3.56810e11	+	2.08753e11i	0.464873	+	0.271975i
$937$	−3.24092e11	−	2.35467e11i	−0.420446	−	0.305472i	0.357371	−	0.933962i	$-0.383673\pi$
$937$	−3.24092e11	−	2.35467e11i	−0.420446	−	0.305472i	−0.777817	+	0.628490i	$0.783673\pi$
$938$	−1.11099e11	+	2.07982e11i	−0.143515	+	0.268667i
$939$	−1.91596e9	−	2.63710e9i	−0.00246448	−	0.00339206i
$940$	9.34897e10	−	2.34505e11i	0.119744	−	0.300359i
$941$	1.04002e12	+	7.55615e11i	1.32642	+	0.963701i	0.999828	+	0.0185352i	$0.00590029\pi$
$941$	1.04002e12	+	7.55615e11i	1.32642	+	0.963701i	0.326592	+	0.945165i	$0.394100\pi$
$942$	−2.05830e10	−	4.24078e10i	−0.0261400	−	0.0538570i
$943$			7.63312e11i			0.965285i
$944$	−4.12955e11	+	4.84539e11i	−0.520014	+	0.610155i
$945$	1.86387e11	−	1.28025e11i	0.233715	−	0.160534i
$946$	−2.57828e11	−	4.59723e10i	−0.321933	−	0.0574026i
$947$	7.11567e10	+	2.31202e10i	0.0884740	+	0.0287470i	0.352920	−	0.935654i	$-0.385189\pi$
$947$	7.11567e10	+	2.31202e10i	0.0884740	+	0.0287470i	−0.264446	+	0.964401i	$0.585189\pi$
$948$	1.84837e11	−	2.34718e11i	0.228852	−	0.290612i
$949$	7.99731e11			0.986005
$950$	7.60093e11	+	4.59267e11i	0.933195	+	0.563859i
$951$			1.83626e11i			0.224498i
$952$	1.38956e11	−	2.37511e11i	0.169173	−	0.289158i
$953$	2.57869e11	−	7.93641e11i	0.312628	−	0.962171i	−0.664091	−	0.747651i	$-0.731181\pi$
$953$	2.57869e11	−	7.93641e11i	0.312628	−	0.962171i	0.976720	−	0.214520i	$-0.0688186\pi$
$954$	−1.64560e11	−	2.93420e10i	−0.198669	−	0.0354239i
$955$	3.22273e11	−	4.19756e11i	0.387445	−	0.504642i
$956$	9.65330e11	−	6.45747e11i	1.15570	−	0.773091i
$957$	8.70186e10			0.103744
$958$	−1.34831e11	−	2.77797e11i	−0.160077	−	0.329812i
$959$	1.83478e11	−	2.52536e11i	0.216925	−	0.298572i
$960$	1.79485e11	−	3.65158e11i	0.211321	−	0.429928i
$961$	9.70664e11	−	7.05229e11i	1.13809	−	0.826868i
$962$	4.07249e11	−	7.62391e11i	0.475510	−	0.890180i
$963$	6.96183e11	−	9.58213e11i	0.809502	−	1.11418i
$964$	2.21715e11	−	2.81548e11i	0.256736	−	0.326020i
$965$	−2.67324e11	−	7.07350e9i	−0.308268	−	0.00815690i
$966$	1.14149e11	+	6.09752e10i	0.131088	+	0.0700237i
$967$	−4.07188e11	+	1.32303e11i	−0.465682	+	0.151309i	−0.532454	−	0.846459i	$-0.678730\pi$
$967$	−4.07188e11	+	1.32303e11i	−0.465682	+	0.151309i	0.0667720	+	0.997768i	$0.478730\pi$
$968$	4.76472e11	+	1.08697e12i	0.542670	+	1.23799i
$969$	−1.42609e11	−	4.38904e11i	−0.161752	−	0.497823i
$970$	2.77277e11	−	1.25629e11i	0.313203	−	0.141906i
$971$	−1.17860e12	−	3.82952e11i	−1.32584	−	0.430791i	−0.441343	−	0.897339i	$-0.645498\pi$
$971$	−1.17860e12	−	3.82952e11i	−1.32584	−	0.430791i	−0.884496	+	0.466547i	$0.845498\pi$
$972$	9.12137e11	+	3.53580e10i	1.02187	+	0.0396116i
$973$	1.03701e11	−	7.53433e10i	0.115700	−	0.0840608i
$974$	7.91206e11	−	1.09649e11i	0.879132	−	0.121834i
$975$	1.64675e11	+	2.53882e11i	0.182225	+	0.280940i
$976$	−1.54390e12	+	9.48334e11i	−1.70145	+	1.04511i
$977$	−5.97718e10	+	4.34268e10i	−0.0656022	+	0.0476628i	−0.620103	−	0.784520i	$-0.712909\pi$
$977$	−5.97718e10	+	4.34268e10i	−0.0656022	+	0.0476628i	0.554501	+	0.832183i	$0.312909\pi$
$978$	−1.18170e11	−	2.10705e10i	−0.129167	−	0.0230313i
$979$	−1.75771e12	−	5.71114e11i	−1.91345	−	0.621716i
$980$	5.33789e10	−	8.17551e11i	0.0578716	−	0.886360i
$981$	2.72628e11	+	8.39063e11i	0.294371	+	0.905980i
$982$	−9.34918e11	+	1.29565e11i	−1.00537	+	0.139329i
$983$	−1.19682e12	+	3.88871e11i	−1.28179	+	0.416478i	−0.869209	−	0.494444i	$-0.835372\pi$
$983$	−1.19682e12	+	3.88871e11i	−1.28179	+	0.416478i	−0.412578	+	0.910922i	$0.635372\pi$
$984$	4.56384e11	+	9.97568e10i	0.486799	+	0.106405i
$985$	−4.31066e11	+	1.21623e12i	−0.457929	+	1.29203i
$986$	9.27323e10	+	9.63966e10i	0.0981122	+	0.101989i
$987$	2.88850e10	−	3.97568e10i	0.0304371	−	0.0418931i
$988$	−2.50995e11	+	6.81454e11i	−0.263413	+	0.715170i
$989$	1.53169e11	−	1.11284e11i	0.160098	−	0.116318i
$990$	−8.38513e11	+	7.64979e11i	−0.872909	+	0.796359i
$991$	−2.40938e11	+	3.31622e11i	−0.249810	+	0.343834i	−0.915445	−	0.402444i	$-0.868161\pi$
$991$	−2.40938e11	+	3.31622e11i	−0.249810	+	0.343834i	0.665635	+	0.746278i	$0.268161\pi$
$992$	−1.26634e12	−	8.08296e11i	−1.30769	−	0.834687i
$993$	5.16405e11			0.531121
$994$	3.88160e11	−	1.88397e11i	0.397618	−	0.192987i
$995$	5.63937e9	−	2.13125e11i	0.00575358	−	0.217441i
$996$	−2.63191e10	+	6.78960e11i	−0.0267445	+	0.689933i
$997$	−8.24666e10	+	2.53806e11i	−0.0834637	+	0.256875i	−0.984076	−	0.177749i	$-0.943119\pi$
$997$	−8.24666e10	+	2.53806e11i	−0.0834637	+	0.256875i	0.900612	+	0.434624i	$0.143119\pi$
$998$	−1.39590e12	+	1.34284e12i	−1.40712	+	1.35363i
$999$		−	1.21970e12i		−	1.22459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.28	✓	464
4.3	odd	2	inner	100.9.j.b.11.76	yes	464
25.16	even	5	inner	100.9.j.b.91.76	yes	464
100.91	odd	10	inner	100.9.j.b.91.28	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.28	✓	464	1.1	even	1	trivial
100.9.j.b.11.76	yes	464	4.3	odd	2	inner
100.9.j.b.91.28	yes	464	100.91	odd	10	inner
100.9.j.b.91.76	yes	464	25.16	even	5	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+(-11.0924 - 11.5307i) q^{2} +(-36.9043 - 11.9909i) q^{3} +(-9.91611 + 255.808i) q^{4} +(-624.781 - 16.5320i) q^{5} +(271.094 + 558.543i) q^{6} +802.640i q^{7} +(3059.65 - 2723.19i) q^{8} +(-4089.81 - 2971.42i) q^{9} +(6739.72 + 7387.57i) q^{10} +(-13197.2 - 18164.3i) q^{11} +(3433.33 - 9321.52i) q^{12} +(-16151.5 - 11734.7i) q^{13} +(9255.03 - 8903.22i) q^{14} +(22858.9 + 8101.82i) q^{15} +(-65339.3 - 5073.24i) q^{16} +(-25864.7 - 79603.4i) q^{17} +(11103.2 + 80118.9i) q^{18} +(-135137. + 43908.6i) q^{19} +(10424.4 - 159660. i) q^{20} +(9624.41 - 29620.9i) q^{21} +(-63059.8 + 353660. i) q^{22} +(-152647. - 210100. i) q^{23} +(-145568. + 63809.5i) q^{24} +(390078. + 20657.8i) q^{25} +(43848.8 + 316405. i) q^{26} +(264946. + 364667. i) q^{27} +(-205322. - 7959.06i) q^{28} +(30864.7 - 94991.6i) q^{29} +(-160141. - 353449. i) q^{30} +(-1.36260e6 + 442736. i) q^{31} +(666274. + 809686. i) q^{32} +(269225. + 828590. i) q^{33} +(-630984. + 1.18123e6i) q^{34} +(13269.2 - 501474. i) q^{35} +(800668. - 1.01674e6i) q^{36} +(-2.18913e6 - 1.59049e6i) q^{37} +(2.00529e6 + 1.07117e6i) q^{38} +(455349. + 626734. i) q^{39} +(-1.95663e6 + 1.65082e6i) q^{40} +(-2.37789e6 - 1.72764e6i) q^{41} +(-448309. + 217591. i) q^{42} +729028. i q^{43} +(4.77745e6 - 3.19582e6i) q^{44} +(2.50612e6 + 1.92410e6i) q^{45} +(-729388. + 4.09065e6i) q^{46} +(1.50061e6 + 487578. i) q^{47} +(2.35047e6 + 970705. i) q^{48} +5.12057e6 q^{49} +(-4.08872e6 - 4.72704e6i) q^{50} +3.24785e6i q^{51} +(3.16200e6 - 4.01531e6i) q^{52} +(-638611. + 1.96544e6i) q^{53} +(1.26599e6 - 7.10006e6i) q^{54} +(7.94505e6 + 1.15669e7i) q^{55} +(2.18574e6 + 2.45580e6i) q^{56} +5.51364e6 q^{57} +(-1.43769e6 + 697795. i) q^{58} +(5.70995e6 - 7.85907e6i) q^{59} +(-2.29918e6 + 5.76715e6i) q^{60} +(2.23671e7 - 1.62507e7i) q^{61} +(2.02196e7 + 1.08008e7i) q^{62} +(2.38498e6 - 3.28265e6i) q^{63} +(1.94569e6 - 1.66640e7i) q^{64} +(9.89714e6 + 7.59865e6i) q^{65} +(6.56790e6 - 1.22954e7i) q^{66} +(-1.74623e7 + 5.67384e6i) q^{67} +(2.06197e7 - 5.82704e6i) q^{68} +(3.11403e6 + 9.58398e6i) q^{69} +(-5.92956e6 + 5.40956e6i) q^{70} +(3.19530e7 + 1.03821e7i) q^{71} +(-2.06051e7 + 2.04583e6i) q^{72} +(-3.24076e7 + 2.35455e7i) q^{73} +(5.94315e6 + 4.28847e7i) q^{74} +(-1.41479e7 - 5.43977e6i) q^{75} +(-9.89213e6 - 3.50044e7i) q^{76} +(1.45794e7 - 1.05926e7i) q^{77} +(2.17578e6 - 1.22025e7i) q^{78} +(2.86034e7 + 9.29380e6i) q^{79} +(4.07389e7 + 4.24985e6i) q^{80} +(4.84444e6 + 1.49097e7i) q^{81} +(6.45561e6 + 4.65825e7i) q^{82} +(-6.50527e7 + 2.11369e7i) q^{83} +(7.48182e6 + 2.75572e6i) q^{84} +(1.48438e7 + 5.01623e7i) q^{85} +(8.40623e6 - 8.08669e6i) q^{86} +(-2.27808e6 + 3.13551e6i) q^{87} +(-8.98437e7 - 1.96381e7i) q^{88} +(6.65941e7 - 4.83835e7i) q^{89} +(-5.61257e6 - 5.02403e7i) q^{90} +(9.41876e6 - 1.29638e7i) q^{91} +(5.52589e7 - 3.69648e7i) q^{92} +5.55947e7 q^{93} +(-1.10233e7 - 2.27116e7i) q^{94} +(8.51568e7 - 2.51992e7i) q^{95} +(-1.48795e7 - 3.78702e7i) q^{96} +(9.40676e6 - 2.89510e7i) q^{97} +(-5.67996e7 - 5.90440e7i) q^{98} +1.13503e8i 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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