LMFDB - Embedded newform 100.9.j.b.11.51

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			11.51
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.51

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82276 + 15.7490i) q^{2} +(30.1760 + 9.80478i) q^{3} +(-240.064 - 88.9114i) q^{4} +(134.651 + 610.323i) q^{5} +(-239.595 + 447.567i) q^{6} -4004.03i q^{7} +(2077.91 - 3529.80i) q^{8} +(-4493.50 - 3264.72i) q^{9} +(-9992.08 + 397.832i) q^{10} +(11360.2 + 15636.0i) q^{11} +(-6372.42 - 5036.77i) q^{12} +(-16467.4 - 11964.3i) q^{13} +(63059.6 + 11302.4i) q^{14} +(-1920.85 + 19737.3i) q^{15} +(49725.5 + 42688.9i) q^{16} +(20987.7 + 64593.4i) q^{17} +(64100.3 - 61552.8i) q^{18} +(73896.4 - 24010.4i) q^{19} +(21939.8 - 158489. i) q^{20} +(39258.7 - 120826. i) q^{21} +(-278318. + 134775. i) q^{22} +(251943. + 346769. i) q^{23} +(97312.0 - 86141.9i) q^{24} +(-354363. + 164361. i) q^{25} +(234909. - 225573. i) q^{26} +(-225947. - 310990. i) q^{27} +(-356004. + 961224. i) q^{28} +(111105. - 341947. i) q^{29} +(-305422. - 85965.2i) q^{30} +(197863. - 64289.5i) q^{31} +(-812671. + 662629. i) q^{32} +(189498. + 583215. i) q^{33} +(-1.07653e6 + 148204. i) q^{34} +(2.44375e6 - 539147. i) q^{35} +(788458. + 1.18327e6i) q^{36} +(2.39339e6 + 1.73890e6i) q^{37} +(169549. + 1.23157e6i) q^{38} +(-379613. - 522493. i) q^{39} +(2.43411e6 + 792905. i) q^{40} +(3.15324e6 + 2.29096e6i) q^{41} +(1.79207e6 + 959348. i) q^{42} +2.21535e6i q^{43} +(-1.33696e6 - 4.76368e6i) q^{44} +(1.38748e6 - 3.18209e6i) q^{45} +(-6.17246e6 + 2.98901e6i) q^{46} +(-3.71652e6 - 1.20757e6i) q^{47} +(1.08196e6 + 1.77573e6i) q^{48} -1.02675e7 q^{49} +(-1.58825e6 - 6.04483e6i) q^{50} +2.15495e6i q^{51} +(2.88947e6 + 4.33633e6i) q^{52} +(133657. - 411353. i) q^{53} +(5.53559e6 - 2.68061e6i) q^{54} +(-8.01332e6 + 9.03878e6i) q^{55} +(-1.41334e7 - 8.32002e6i) q^{56} +2.46532e6 q^{57} +(5.07171e6 + 2.71503e6i) q^{58} +(-6.06914e6 + 8.35346e6i) q^{59} +(2.21600e6 - 4.56744e6i) q^{60} +(-5.78776e6 + 4.20506e6i) q^{61} +(453979. + 3.29762e6i) q^{62} +(-1.30720e7 + 1.79921e7i) q^{63} +(-8.14179e6 - 1.46692e7i) q^{64} +(5.08471e6 - 1.16614e7i) q^{65} +(-9.71998e6 + 1.33814e6i) q^{66} +(-2.12190e7 + 6.89449e6i) q^{67} +(704704. - 1.73726e7i) q^{68} +(4.20263e6 + 1.29344e7i) q^{69} +(1.59293e6 + 4.00086e7i) q^{70} +(4.44116e7 + 1.44302e7i) q^{71} +(-2.08609e7 + 9.07737e6i) q^{72} +(-9.05014e6 + 6.57531e6i) q^{73} +(-3.41420e7 + 3.27851e7i) q^{74} +(-1.23048e7 + 1.48532e6i) q^{75} +(-1.98747e7 - 806198. i) q^{76} +(6.26069e7 - 4.54866e7i) q^{77} +(9.30032e6 - 4.50367e6i) q^{78} +(2.61741e7 + 8.50449e6i) q^{79} +(-1.93584e7 + 3.60967e7i) q^{80} +(7.49207e6 + 2.30582e7i) q^{81} +(-4.49813e7 + 4.31937e7i) q^{82} +(-5.64019e7 + 1.83261e7i) q^{83} +(-2.01674e7 + 2.55154e7i) q^{84} +(-3.65968e7 + 2.15068e7i) q^{85} +(-3.48895e7 - 6.25338e6i) q^{86} +(6.70543e6 - 9.22924e6i) q^{87} +(7.87973e7 - 7.60909e6i) q^{88} +(4.55623e7 - 3.31030e7i) q^{89} +(4.61983e7 + 3.08337e7i) q^{90} +(-4.79053e7 + 6.59360e7i) q^{91} +(-2.96506e7 - 1.05647e8i) q^{92} +6.60105e6 q^{93} +(2.95089e7 - 5.51229e7i) q^{94} +(2.46043e7 + 4.18676e7i) q^{95} +(-3.10201e7 + 1.20274e7i) q^{96} +(4.54762e7 - 1.39961e8i) q^{97} +(2.89826e7 - 1.61703e8i) q^{98} -1.07348e8i 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 $

$2$	−2.82276	+	15.7490i	−0.176422	+	0.984315i
$2$	−2.82276	+	15.7490i	−0.176422	+	0.984315i
$3$	30.1760	+	9.80478i	0.372543	+	0.121047i	0.489304	−	0.872113i	$-0.337251\pi$
$3$	30.1760	+	9.80478i	0.372543	+	0.121047i	−0.116760	+	0.993160i	$0.537251\pi$
$4$	−240.064	−	88.9114i	−0.937750	−	0.347310i
$5$	134.651	+	610.323i	0.215442	+	0.976517i
$5$	134.651	+	610.323i	0.215442	+	0.976517i
$6$	−239.595	+	447.567i	−0.184873	+	0.345345i
$7$		−	4004.03i		−	1.66765i	−0.552028	−	0.833826i	$-0.686146\pi$
$7$		−	4004.03i		−	1.66765i	0.552028	−	0.833826i	$-0.313854\pi$
$8$	2077.91	−	3529.80i	0.507302	−	0.861768i
$9$	−4493.50	−	3264.72i	−0.684881	−	0.497595i
$10$	−9992.08	+	397.832i	−0.999208	+	0.0397832i
$11$	11360.2	+	15636.0i	0.775916	+	1.06796i	0.995721	+	0.0924131i	$0.0294580\pi$
$11$	11360.2	+	15636.0i	0.775916	+	1.06796i	−0.219805	+	0.975544i	$0.570542\pi$
$12$	−6372.42	−	5036.77i	−0.307312	−	0.242900i
$13$	−16467.4	−	11964.3i	−0.576569	−	0.418902i	0.260916	−	0.965361i	$-0.415975\pi$
$13$	−16467.4	−	11964.3i	−0.576569	−	0.418902i	−0.837486	+	0.546459i	$0.815975\pi$
$14$	63059.6	+	11302.4i	1.64149	+	0.294211i
$15$	−1920.85	+	19737.3i	−0.0379427	+	0.389873i
$16$	49725.5	+	42688.9i	0.758751	+	0.651380i
$17$	20987.7	+	64593.4i	0.251286	+	0.773379i	0.994539	+	0.104368i	$0.0332820\pi$
$17$	20987.7	+	64593.4i	0.251286	+	0.773379i	−0.743253	+	0.669011i	$0.766718\pi$
$18$	64100.3	−	61552.8i	0.610618	−	0.586351i
$19$	73896.4	−	24010.4i	0.567034	−	0.184240i	−0.0114499	−	0.999934i	$-0.503645\pi$
$19$	73896.4	−	24010.4i	0.567034	−	0.184240i	0.578484	+	0.815694i	$0.303645\pi$
$20$	21939.8	−	158489.i	0.137123	−	0.990554i
$21$	39258.7	−	120826.i	0.201864	−	0.621273i
$22$	−278318.	+	134775.i	−1.18809	+	0.575334i
$23$	251943.	+	346769.i	0.900307	+	1.23917i	0.970370	+	0.241623i	$0.0776798\pi$
$23$	251943.	+	346769.i	0.900307	+	1.23917i	−0.0700635	+	0.997543i	$0.522320\pi$
$24$	97312.0	−	86141.9i	0.293306	−	0.259639i
$25$	−354363.	+	164361.i	−0.907170	+	0.420765i
$26$	234909.	−	225573.i	0.514051	−	0.493622i
$27$	−225947.	−	310990.i	−0.425160	−	0.585183i
$28$	−356004.	+	961224.i	−0.579192	+	1.56384i
$29$	111105.	−	341947.i	0.157088	−	0.483467i	−0.841279	−	0.540602i	$-0.818197\pi$
$29$	111105.	−	341947.i	0.157088	−	0.483467i	0.998366	+	0.0571349i	$0.0181965\pi$
$30$	−305422.	−	85965.2i	−0.377064	−	0.106130i
$31$	197863.	−	64289.5i	0.214248	−	0.0696134i	−0.199926	−	0.979811i	$-0.564070\pi$
$31$	197863.	−	64289.5i	0.214248	−	0.0696134i	0.414175	+	0.910197i	$0.364070\pi$
$32$	−812671.	+	662629.i	−0.775024	+	0.631932i
$33$	189498.	+	583215.i	0.159790	+	0.491782i
$34$	−1.07653e6	+	148204.i	−0.805581	+	0.110903i
$35$	2.44375e6	−	539147.i	1.62849	−	0.359282i
$36$	788458.	+	1.18327e6i	0.469427	+	0.704486i
$37$	2.39339e6	+	1.73890e6i	1.27705	+	0.927830i	0.999460	−	0.0328704i	$-0.0104649\pi$
$37$	2.39339e6	+	1.73890e6i	1.27705	+	0.927830i	0.277588	+	0.960700i	$0.410465\pi$
$38$	169549.	+	1.23157e6i	0.0813131	+	0.590644i
$39$	−379613.	−	522493.i	−0.164090	−	0.225851i
$40$	2.43411e6	+	792905.i	0.950825	+	0.309728i
$41$	3.15324e6	+	2.29096e6i	1.11589	+	0.810743i	0.983581	−	0.180466i	$-0.0577605\pi$
$41$	3.15324e6	+	2.29096e6i	1.11589	+	0.810743i	0.132310	+	0.991208i	$0.457761\pi$
$42$	1.79207e6	+	959348.i	0.575914	+	0.308304i
$43$			2.21535e6i			0.647989i	0.946059	+	0.323995i	$0.105026\pi$
$43$			2.21535e6i			0.647989i	−0.946059	+	0.323995i	$0.894974\pi$
$44$	−1.33696e6	−	4.76368e6i	−0.356703	−	1.27096i
$45$	1.38748e6	−	3.18209e6i	0.338358	−	0.776000i
$46$	−6.17246e6	+	2.98901e6i	−1.37856	+	0.667568i
$47$	−3.71652e6	−	1.20757e6i	−0.761632	−	0.247469i	−0.0976529	−	0.995221i	$-0.531133\pi$
$47$	−3.71652e6	−	1.20757e6i	−0.761632	−	0.247469i	−0.663979	+	0.747751i	$0.731133\pi$
$48$	1.08196e6	+	1.77573e6i	0.203820	+	0.334512i
$49$	−1.02675e7			−1.78106
$50$	−1.58825e6	−	6.04483e6i	−0.254120	−	0.967173i
$51$			2.15495e6i			0.318535i
$52$	2.88947e6	+	4.33633e6i	0.395189	+	0.593074i
$53$	133657.	−	411353.i	0.0169390	−	0.0521328i	−0.942230	−	0.334967i	$-0.891275\pi$
$53$	133657.	−	411353.i	0.0169390	−	0.0521328i	0.959169	+	0.282835i	$0.0912747\pi$
$54$	5.53559e6	−	2.68061e6i	0.651011	−	0.315252i
$55$	−8.01332e6	+	9.03878e6i	−0.875713	+	0.987778i
$56$	−1.41334e7	−	8.32002e6i	−1.43713	−	0.846004i
$57$	2.46532e6			0.233546
$58$	5.07171e6	+	2.71503e6i	0.448170	+	0.239918i
$59$	−6.06914e6	+	8.35346e6i	−0.500864	+	0.689379i	−0.982345	−	0.187077i	$-0.940099\pi$
$59$	−6.06914e6	+	8.35346e6i	−0.500864	+	0.689379i	0.481482	+	0.876456i	$0.340099\pi$
$60$	2.21600e6	−	4.56744e6i	0.170988	−	0.352426i
$61$	−5.78776e6	+	4.20506e6i	−0.418015	+	0.303705i	−0.776839	−	0.629700i	$-0.783178\pi$
$61$	−5.78776e6	+	4.20506e6i	−0.418015	+	0.303705i	0.358824	+	0.933405i	$0.383178\pi$
$62$	453979.	+	3.29762e6i	0.0307234	+	0.223169i
$63$	−1.30720e7	+	1.79921e7i	−0.829815	+	1.14214i
$64$	−8.14179e6	−	1.46692e7i	−0.485288	−	0.874354i
$65$	5.08471e6	−	1.16614e7i	0.284848	−	0.653279i
$66$	−9.71998e6	+	1.33814e6i	−0.512259	+	0.0705220i
$67$	−2.12190e7	+	6.89449e6i	−1.05300	+	0.342139i	−0.783843	−	0.620958i	$-0.786744\pi$
$67$	−2.12190e7	+	6.89449e6i	−1.05300	+	0.342139i	−0.269152	+	0.963098i	$0.586744\pi$
$68$	704704.	−	1.73726e7i	0.0329588	−	0.812511i
$69$	4.20263e6	+	1.29344e7i	0.185406	+	0.570622i
$70$	1.59293e6	+	4.00086e7i	0.0663445	+	1.66633i
$71$	4.44116e7	+	1.44302e7i	1.74769	+	0.567858i	0.995810	−	0.0914466i	$-0.0291491\pi$
$71$	4.44116e7	+	1.44302e7i	1.74769	+	0.567858i	0.751876	+	0.659304i	$0.229149\pi$
$72$	−2.08609e7	+	9.07737e6i	−0.776253	+	0.337777i
$73$	−9.05014e6	+	6.57531e6i	−0.318687	+	0.231539i	−0.735615	−	0.677400i	$-0.763107\pi$
$73$	−9.05014e6	+	6.57531e6i	−0.318687	+	0.231539i	0.416928	+	0.908939i	$0.363107\pi$
$74$	−3.41420e7	+	3.27851e7i	−1.13858	+	1.09333i
$75$	−1.23048e7	+	1.48532e6i	−0.388892	+	0.0469434i
$76$	−1.98747e7	−	806198.i	−0.595725	−	0.0241650i
$77$	6.26069e7	−	4.54866e7i	1.78098	−	1.29396i
$78$	9.30032e6	−	4.50367e6i	0.251258	−	0.121671i
$79$	2.61741e7	+	8.50449e6i	0.671992	+	0.218343i	0.625086	−	0.780556i	$-0.285064\pi$
$79$	2.61741e7	+	8.50449e6i	0.671992	+	0.218343i	0.0469057	+	0.998899i	$0.485064\pi$
$80$	−1.93584e7	+	3.60967e7i	−0.472617	+	0.881268i
$81$	7.49207e6	+	2.30582e7i	0.174045	+	0.535655i
$82$	−4.49813e7	+	4.31937e7i	−0.994894	+	0.955355i
$83$	−5.64019e7	+	1.83261e7i	−1.18845	+	0.386151i	−0.835500	−	0.549491i	$-0.814822\pi$
$83$	−5.64019e7	+	1.83261e7i	−1.18845	+	0.386151i	−0.352951	+	0.935642i	$0.614822\pi$
$84$	−2.01674e7	+	2.55154e7i	−0.405072	+	0.512489i
$85$	−3.65968e7	+	2.15068e7i	−0.701080	+	0.412003i
$86$	−3.48895e7	−	6.25338e6i	−0.637825	−	0.114320i
$87$	6.70543e6	−	9.22924e6i	0.117044	−	0.161097i
$88$	7.87973e7	−	7.60909e6i	1.31396	−	0.126883i
$89$	4.55623e7	−	3.31030e7i	0.726183	−	0.527603i	−0.162171	−	0.986763i	$-0.551850\pi$
$89$	4.55623e7	−	3.31030e7i	0.726183	−	0.527603i	0.888354	+	0.459160i	$0.151850\pi$
$90$	4.61983e7	+	3.08337e7i	0.704134	+	0.469954i
$91$	−4.79053e7	+	6.59360e7i	−0.698583	+	0.961517i
$92$	−2.96506e7	−	1.05647e8i	−0.413888	−	1.47471i
$93$	6.60105e6			0.0882432
$94$	2.95089e7	−	5.51229e7i	0.377956	−	0.706026i
$95$	2.46043e7	+	4.18676e7i	0.302077	+	0.514025i
$96$	−3.10201e7	+	1.20274e7i	−0.365223	+	0.141608i
$97$	4.54762e7	−	1.39961e8i	0.513685	−	1.58096i	−0.271976	−	0.962304i	$-0.587677\pi$
$97$	4.54762e7	−	1.39961e8i	0.513685	−	1.58096i	0.785662	−	0.618656i	$-0.212323\pi$
$98$	2.89826e7	−	1.61703e8i	0.314219	−	1.75313i
$99$		−	1.07348e8i		−	1.11752i
$100$	9.96835e7	−	7.95034e6i	0.996835	−	0.0795034i
$101$	−1.07255e8			−1.03070			−0.515348	−	0.856981i	$-0.672337\pi$
$101$	−1.07255e8			−1.03070			−0.515348	+	0.856981i	$0.672337\pi$
$102$	−3.39384e7	−	6.08290e6i	−0.313538	−	0.0561966i
$103$	1.19672e8	+	3.88839e7i	1.06327	+	0.345478i	0.787864	−	0.615849i	$-0.211187\pi$
$103$	1.19672e8	+	3.88839e7i	1.06327	+	0.345478i	0.275408	+	0.961327i	$0.411187\pi$
$104$	−7.64493e7	+	3.32660e7i	−0.653492	+	0.284359i
$105$	7.90289e7	+	7.69113e6i	0.650173	+	0.0632752i
$106$	6.10113e6	+	3.26611e6i	0.0483267	+	0.0258707i
$107$			1.20009e6i			0.00915540i	0.999990	+	0.00457770i	$0.00145713\pi$
$107$			1.20009e6i			0.00915540i	−0.999990	+	0.00457770i	$0.998543\pi$
$108$	2.65913e7	+	9.47468e7i	0.195454	+	0.696418i
$109$	1.31728e8	+	9.57061e7i	0.933195	+	0.678006i	0.946773	−	0.321902i	$-0.104322\pi$
$109$	1.31728e8	+	9.57061e7i	0.933195	+	0.678006i	−0.0135778	+	0.999908i	$0.504322\pi$
$110$	−1.19732e8	−	1.51716e8i	−0.817789	−	1.03624i
$111$	5.51735e7	+	7.59398e7i	0.363445	+	0.500239i
$112$	1.70928e8	−	1.99103e8i	1.08628	−	1.26533i
$113$	2.35698e8	+	1.71245e8i	1.44558	+	1.05028i	0.986839	+	0.161709i	$0.0517004\pi$
$113$	2.35698e8	+	1.71245e8i	1.44558	+	1.05028i	0.458744	+	0.888569i	$0.348300\pi$
$114$	−6.95899e6	+	3.88263e7i	−0.0412028	+	0.229883i
$115$	−1.77717e8	+	2.00459e8i	−1.01610	+	1.14613i
$116$	−5.70754e7	+	7.22107e7i	−0.315222	+	0.398813i
$117$	3.49363e7	+	1.07523e8i	0.186438	+	0.573796i
$118$	−1.14427e8	−	1.19163e8i	−0.590203	−	0.614629i
$119$	2.58634e8	−	8.40353e7i	1.28973	−	0.419058i
$120$	6.56775e7	+	4.77926e7i	0.316732	+	0.230482i
$121$	−4.91888e7	+	1.51387e8i	−0.229469	+	0.706234i
$122$	−4.98881e7	−	1.03022e8i	−0.225195	−	0.465038i
$123$	7.26899e7	+	1.00049e8i	0.317580	+	0.437112i
$124$	−5.32158e7	−	2.15865e6i	−0.225089	−	0.00913052i
$125$	−1.48029e8	−	1.94144e8i	−0.606326	−	0.795216i
$126$	−2.46459e8	−	2.56659e8i	−0.977830	−	1.01830i
$127$	−6.01652e7	−	8.28103e7i	−0.231276	−	0.318324i	0.677568	−	0.735460i	$-0.263034\pi$
$127$	−6.01652e7	−	8.28103e7i	−0.231276	−	0.318324i	−0.908844	+	0.417136i	$0.863034\pi$
$128$	2.54008e8	−	8.68176e7i	0.946255	−	0.323421i
$129$	−2.17210e7	+	6.68503e7i	−0.0784369	+	0.241404i
$130$	1.69303e8	+	1.12997e8i	0.592778	+	0.395633i
$131$	−9.74816e7	+	3.16737e7i	−0.331007	+	0.107551i	−0.469806	−	0.882770i	$-0.655676\pi$
$131$	−9.74816e7	+	3.16737e7i	−0.331007	+	0.107551i	0.138798	+	0.990321i	$0.455676\pi$
$132$	6.36278e6	−	1.56858e8i	0.0209581	−	0.516666i
$133$	−9.61384e7	−	2.95884e8i	−0.307249	−	0.945615i
$134$	−4.86853e7	−	3.53641e8i	−0.151001	−	1.09684i
$135$	1.59380e8	−	1.79776e8i	0.479843	−	0.541249i
$136$	2.71612e8	+	6.01370e7i	0.793951	+	0.175787i
$137$	3.84314e8	+	2.79221e8i	1.09095	+	0.792620i	0.979559	−	0.201157i	$-0.0644700\pi$
$137$	3.84314e8	+	2.79221e8i	1.09095	+	0.792620i	0.111389	+	0.993777i	$0.464470\pi$
$138$	−2.15567e8	+	2.96768e7i	−0.594382	+	0.0818277i
$139$	1.57097e8	+	2.16226e8i	0.420832	+	0.579226i	0.965819	−	0.259219i	$-0.0834652\pi$
$139$	1.57097e8	+	2.16226e8i	0.420832	+	0.579226i	−0.544986	+	0.838445i	$0.683465\pi$
$140$	−6.34593e8	−	8.78475e7i	−1.65190	−	0.228674i
$141$	−1.00310e8	−	7.28793e7i	−0.253786	−	0.184386i
$142$	−3.52625e8	+	6.58707e8i	−0.867281	+	1.62009i
$143$		−	3.93400e8i		−	0.940784i
$144$	−8.40746e7	−	3.54162e8i	−0.195531	−	0.823669i
$145$	2.23659e8	+	2.17666e7i	0.505957	+	0.0492400i
$146$	−7.80085e7	−	1.61092e8i	−0.171684	−	0.354537i
$147$	−3.09831e8	−	1.00670e8i	−0.663523	−	0.215592i
$148$	−4.19960e8	−	6.30248e8i	−0.875308	−	1.31360i
$149$	7.01139e8			1.42252			0.711261	−	0.702928i	$-0.248125\pi$
$149$	7.01139e8			1.42252			0.711261	+	0.702928i	$0.248125\pi$
$150$	1.13411e7	−	1.97981e8i	0.0224022	−	0.391074i
$151$			3.34523e8i			0.643456i	0.946832	+	0.321728i	$0.104264\pi$
$151$			3.34523e8i			0.643456i	−0.946832	+	0.321728i	$0.895736\pi$
$152$	6.87982e7	−	3.10731e8i	0.128885	−	0.582117i
$153$	1.16571e8	−	3.58769e8i	0.212729	−	0.654711i
$154$	5.39645e8	+	1.11440e9i	0.959457	+	1.98133i
$155$	6.58798e7	+	1.12103e8i	0.114137	+	0.194219i
$156$	4.46760e7	+	1.59184e8i	0.0754355	+	0.268782i
$157$	−5.37166e8			−0.884117			−0.442059	−	0.896986i	$-0.645752\pi$
$157$	−5.37166e8			−0.884117			−0.442059	+	0.896986i	$0.645752\pi$
$158$	−2.07821e8	+	3.88211e8i	−0.333473	+	0.622930i
$159$	8.06645e6	−	1.11025e7i	0.0126210	−	0.0173713i
$160$	−5.13845e8	−	4.06768e8i	−0.784065	−	0.620679i
$161$	1.38848e9	−	1.00879e9i	2.06650	−	1.50140i
$162$	−3.84293e8	+	5.29051e7i	−0.557959	+	0.0768135i
$163$	−1.75750e8	+	2.41899e8i	−0.248969	+	0.342676i	−0.915150	−	0.403114i	$-0.867928\pi$
$163$	−1.75750e8	+	2.41899e8i	−0.248969	+	0.342676i	0.666181	+	0.745790i	$0.267928\pi$
$164$	−5.53287e8	−	8.30337e8i	−0.764848	−	1.14783i
$165$	−3.30433e8	+	1.94186e8i	−0.445808	+	0.261988i
$166$	−1.29409e8	−	9.40005e8i	−0.170425	−	1.23793i
$167$	8.74094e8	−	2.84010e8i	1.12381	−	0.365148i	0.312589	−	0.949889i	$-0.398804\pi$
$167$	8.74094e8	−	2.84010e8i	1.12381	−	0.365148i	0.811220	+	0.584741i	$0.198804\pi$
$168$	−3.44915e8	−	3.89640e8i	−0.432987	−	0.489133i
$169$	−1.24043e8	−	3.81765e8i	−0.152064	−	0.468004i
$170$	−2.35408e8	−	6.37073e8i	−0.281855	−	0.762770i
$171$	−4.10441e8	−	1.33360e8i	−0.480028	−	0.155970i
$172$	1.96969e8	−	5.31825e8i	0.225053	−	0.607652i
$173$	3.02437e8	−	2.19733e8i	0.337637	−	0.245308i	−0.406027	−	0.913861i	$-0.633086\pi$
$173$	3.02437e8	−	2.19733e8i	0.337637	−	0.245308i	0.743664	+	0.668553i	$0.233086\pi$
$174$	1.26424e8	+	1.31656e8i	0.137921	+	0.143629i
$175$	6.58108e8	+	1.41888e9i	0.701690	+	1.51284i
$176$	−1.02590e8	+	1.26246e9i	−0.106919	+	1.31573i
$177$	−2.65046e8	+	1.92568e8i	−0.270040	+	0.196196i
$178$	3.92729e8	+	8.11005e8i	0.391212	+	0.807873i
$179$	5.87154e8	+	1.90778e8i	0.571926	+	0.185830i	0.580680	−	0.814132i	$-0.302787\pi$
$179$	5.87154e8	+	1.90778e8i	0.571926	+	0.185830i	−0.00875439	+	0.999962i	$0.502787\pi$
$180$	−6.16007e8	+	6.40542e8i	−0.586808	+	0.610179i
$181$	−7.62881e7	−	2.34791e8i	−0.0710792	−	0.218759i	0.909206	−	0.416346i	$-0.136690\pi$
$181$	−7.62881e7	−	2.34791e8i	−0.0710792	−	0.218759i	−0.980285	+	0.197587i	$0.936690\pi$
$182$	−9.03203e8	−	9.40583e8i	−0.823189	−	0.857258i
$183$	−2.15881e8	+	7.01441e7i	−0.192491	+	0.0625442i
$184$	1.74754e9	−	1.68752e8i	1.52460	−	0.147224i
$185$	−7.39019e8	+	1.69489e9i	−0.630912	+	1.44695i
$186$	−1.86332e7	+	1.03960e8i	−0.0155681	+	0.0868591i
$187$	−7.71556e8	+	1.06196e9i	−0.630959	+	0.868440i
$188$	7.84836e8	+	6.20335e8i	0.628272	+	0.496587i
$189$	−1.24521e9	+	9.04701e8i	−0.975881	+	0.709019i
$190$	−7.28827e8	+	2.69312e8i	−0.559255	+	0.206653i
$191$	−1.18166e9	+	1.62642e9i	−0.887891	+	1.22208i	0.0862810	+	0.996271i	$0.472502\pi$
$191$	−1.18166e9	+	1.62642e9i	−0.887891	+	1.22208i	−0.974172	+	0.225806i	$0.927498\pi$
$192$	−1.01858e8	−	5.22487e8i	−0.0749533	−	0.384477i
$193$	6.36373e8			0.458651			0.229326	−	0.973350i	$-0.426348\pi$
$193$	6.36373e8			0.458651			0.229326	+	0.973350i	$0.426348\pi$
$194$	2.07589e9	+	1.11128e9i	1.46554	+	0.784544i
$195$	2.67774e8	−	3.02041e8i	0.185195	−	0.208895i
$196$	2.46485e9	+	9.12895e8i	1.67019	+	0.618581i
$197$	3.23994e8	−	9.97152e8i	0.215116	−	0.662058i	−0.784030	−	0.620724i	$-0.786839\pi$
$197$	3.23994e8	−	9.97152e8i	0.215116	−	0.662058i	0.999145	−	0.0413349i	$-0.0131610\pi$
$198$	1.69063e9	+	3.03017e8i	1.09999	+	0.197155i
$199$			1.63340e7i			0.0104155i	0.999986	+	0.00520776i	$0.00165769\pi$
$199$			1.63340e7i			0.0104155i	−0.999986	+	0.00520776i	$0.998342\pi$
$200$	−1.56172e8	+	1.59236e9i	−0.0976075	+	0.995225i
$201$	−7.07905e8			−0.433702
$202$	3.02754e8	−	1.68916e9i	0.181838	−	1.01453i
$203$	−1.36917e9	−	4.44869e8i	−0.806255	−	0.261968i
$204$	1.91600e8	−	5.17326e8i	0.110630	−	0.298706i
$205$	−9.73641e8	+	2.23298e9i	−0.551294	+	1.26435i
$206$	−9.50189e8	+	1.77496e9i	−0.527644	+	0.985645i
$207$		−	2.38073e9i		−	1.29667i
$208$	−3.08109e8	−	1.29790e9i	−0.164608	−	0.693408i
$209$	1.21490e9	+	8.82678e8i	0.636732	+	0.462613i
$210$	−3.44207e8	+	1.22292e9i	−0.176988	+	0.628812i
$211$	−2.54808e8	−	3.50713e8i	−0.128553	−	0.176938i	0.739889	−	0.672729i	$-0.234878\pi$
$211$	−2.54808e8	−	3.50713e8i	−0.128553	−	0.176938i	−0.868442	+	0.495791i	$0.834878\pi$
$212$	−6.86601e7	+	8.68674e7i	−0.0339908	+	0.0430045i
$213$	1.19868e9	+	8.70893e8i	0.582352	+	0.423103i
$214$	−1.89002e7	−	3.38755e6i	−0.00901180	−	0.00161522i
$215$	−1.35208e9	+	2.98299e8i	−0.632772	+	0.139604i
$216$	−1.56723e9	+	1.51340e8i	−0.719976	+	0.0695248i
$217$	−2.57417e8	−	7.92248e8i	−0.116091	−	0.357291i
$218$	−1.87911e9	+	1.80444e9i	−0.832008	+	0.798942i
$219$	−3.37567e8	+	1.09682e8i	−0.146752	+	0.0476825i
$220$	2.72736e9	−	1.45741e9i	1.16427	−	0.622145i
$221$	4.27200e8	−	1.31479e9i	0.179086	−	0.551171i
$222$	−1.35172e9	+	6.54570e8i	−0.556513	+	0.269491i
$223$	−8.89207e8	−	1.22389e9i	−0.359570	−	0.494906i	0.590459	−	0.807068i	$-0.298947\pi$
$223$	−8.89207e8	−	1.22389e9i	−0.359570	−	0.494906i	−0.950029	+	0.312162i	$0.898947\pi$
$224$	2.65319e9	+	3.25396e9i	1.05384	+	1.29247i
$225$	2.12893e9	+	4.18338e8i	0.830674	+	0.163229i
$226$	−3.36226e9	+	3.22864e9i	−1.28884	+	1.23762i
$227$	5.50942e8	+	7.58307e8i	0.207493	+	0.285589i	0.900062	−	0.435762i	$-0.143521\pi$
$227$	5.50942e8	+	7.58307e8i	0.207493	+	0.285589i	−0.692569	+	0.721352i	$0.743521\pi$
$228$	−5.91834e8	−	2.19195e8i	−0.219008	−	0.0811130i
$229$	−4.70533e8	+	1.44815e9i	−0.171099	+	0.526589i	−0.999434	−	0.0336443i	$-0.989289\pi$
$229$	−4.70533e8	+	1.44815e9i	−0.171099	+	0.526589i	0.828335	+	0.560234i	$0.189289\pi$
$230$	−2.65539e9	−	3.36472e9i	−0.948892	−	1.20237i
$231$	2.33521e9	−	7.58756e8i	0.820122	−	0.266474i
$232$	−9.76138e8	−	1.10272e9i	−0.336945	−	0.380637i
$233$	−1.35916e9	−	4.18307e9i	−0.461156	−	1.41929i	−0.863753	−	0.503915i	$-0.831892\pi$
$233$	−1.35916e9	−	4.18307e9i	−0.461156	−	1.41929i	0.402597	−	0.915377i	$-0.368108\pi$
$234$	−1.79200e9	+	2.46702e8i	−0.597687	+	0.0822828i
$235$	2.36574e8	−	2.43088e9i	0.0775704	−	0.797061i
$236$	2.19970e9	−	1.46575e9i	0.709113	−	0.472511i
$237$	7.06446e8	+	5.13263e8i	0.223916	+	0.162685i
$238$	5.93413e8	+	4.31045e9i	0.184948	+	1.34343i
$239$	6.59654e7	+	9.07936e7i	0.0202174	+	0.0278268i	0.819006	−	0.573785i	$-0.194525\pi$
$239$	6.59654e7	+	9.07936e7i	0.0202174	+	0.0278268i	−0.798789	+	0.601612i	$0.794525\pi$
$240$	−9.38080e8	+	8.99451e8i	−0.282745	+	0.271102i
$241$	−4.47106e9	−	3.24842e9i	−1.32539	−	0.962949i	−0.999848	−	0.0174201i	$-0.994455\pi$
$241$	−4.47106e9	−	3.24842e9i	−1.32539	−	0.962949i	−0.325538	−	0.945529i	$-0.605545\pi$
$242$	−2.24536e9	−	1.20201e9i	−0.654673	−	0.350465i
$243$			3.29134e9i			0.943948i
$244$	1.76331e9	−	4.94885e8i	0.497473	−	0.139619i
$245$	−1.38253e9	−	6.26647e9i	−0.383715	−	1.73924i
$246$	−1.78086e9	+	8.62381e8i	−0.486284	+	0.235483i
$247$	−1.50415e9	−	4.88727e8i	−0.404113	−	0.131304i
$248$	1.84212e8	−	8.32004e8i	0.0486980	−	0.219947i
$249$	−1.88167e9			−0.489492
$250$	3.47544e9	−	1.78329e9i	0.889712	−	0.456522i
$251$			3.71969e9i			0.937156i	0.883422	+	0.468578i	$0.155234\pi$
$251$			3.71969e9i			0.937156i	−0.883422	+	0.468578i	$0.844766\pi$
$252$	4.73783e9	−	3.15701e9i	1.17484	−	0.782841i
$253$	−2.55996e9	+	7.87873e9i	−0.624813	+	1.92298i
$254$	1.47401e9	−	7.13791e8i	0.354133	−	0.171489i
$255$	−1.31522e9	+	2.90167e8i	−0.311054	+	0.0686257i
$256$	6.50289e8	+	4.24545e9i	0.151407	+	0.988471i
$257$	−1.86356e8			−0.0427180			−0.0213590	−	0.999772i	$-0.506799\pi$
$257$	−1.86356e8			−0.0427180			−0.0213590	+	0.999772i	$0.506799\pi$
$258$	−9.91515e8	−	5.30787e8i	−0.223779	−	0.119796i
$259$	6.96262e9	−	9.58322e9i	1.54730	−	2.12967i
$260$	−2.25749e9	+	2.34740e9i	−0.494006	+	0.513682i
$261$	−1.61561e9	+	1.17381e9i	−0.348157	+	0.252951i
$262$	−2.23663e8	−	1.62465e9i	−0.0474667	−	0.344790i
$263$	−3.33649e9	+	4.59229e9i	−0.697376	+	0.959856i	0.302601	+	0.953117i	$0.402145\pi$
$263$	−3.33649e9	+	4.59229e9i	−0.697376	+	0.959856i	−0.999977	+	0.00673832i	$0.997855\pi$
$264$	2.45239e9	+	5.42978e8i	0.504864	+	0.111781i
$265$	2.69055e8	+	2.61846e7i	0.0545579	+	0.00530960i
$266$	4.93125e9	−	6.78879e8i	0.984988	−	0.135602i
$267$	1.69946e9	−	5.52187e8i	0.334399	−	0.108653i
$268$	5.70693e9	+	2.31496e8i	1.10628	+	0.0448751i
$269$	−2.35348e9	−	7.24325e9i	−0.449470	−	1.38333i	−0.877506	−	0.479565i	$-0.840795\pi$
$269$	−2.35348e9	−	7.24325e9i	−0.449470	−	1.38333i	0.428037	−	0.903761i	$-0.359205\pi$
$270$	2.38141e9	+	3.01755e9i	0.448104	+	0.567805i
$271$	3.66465e8	+	1.19072e8i	0.0679447	+	0.0220766i	0.342792	−	0.939411i	$-0.388627\pi$
$271$	3.66465e8	+	1.19072e8i	0.0679447	+	0.0220766i	−0.274847	+	0.961488i	$0.588627\pi$
$272$	−1.71380e9	+	4.10788e9i	−0.313100	+	0.750485i
$273$	−2.09208e9	+	1.51998e9i	−0.376641	+	0.273646i
$274$	−5.48228e9	+	5.26440e9i	−0.972655	+	0.934000i
$275$	−6.59558e9	−	3.67363e9i	−1.15325	−	0.642340i
$276$	1.41112e8	−	3.47874e9i	0.0243180	−	0.599495i
$277$	−3.82028e9	+	2.77559e9i	−0.648897	+	0.471451i	−0.862895	−	0.505383i	$-0.831351\pi$
$277$	−3.82028e9	+	2.77559e9i	−0.648897	+	0.471451i	0.213998	+	0.976834i	$0.431351\pi$
$278$	−3.84879e9	+	1.86378e9i	−0.644385	+	0.312043i
$279$	−1.09898e9	−	3.57081e8i	−0.181374	−	0.0589319i
$280$	3.17482e9	−	9.74626e9i	0.516519	−	1.58564i
$281$	3.44563e9	+	1.06045e10i	0.552641	+	1.70085i	0.702094	+	0.712084i	$0.252249\pi$
$281$	3.44563e9	+	1.06045e10i	0.552641	+	1.70085i	−0.149453	+	0.988769i	$0.547751\pi$
$282$	1.43093e9	−	1.37406e9i	0.226267	−	0.217275i
$283$	4.18643e9	−	1.36025e9i	0.652677	−	0.212068i	0.0360830	−	0.999349i	$-0.488512\pi$
$283$	4.18643e9	−	1.36025e9i	0.652677	−	0.212068i	0.616594	+	0.787281i	$0.288512\pi$
$284$	−9.37863e9	−	7.41288e9i	−1.44167	−	1.13950i
$285$	3.31958e8	+	1.50464e9i	0.0503157	+	0.228062i
$286$	6.19567e9	+	1.11047e9i	0.926028	+	0.165975i
$287$	9.17309e9	−	1.26257e10i	1.35204	−	1.86092i
$288$	5.81504e9	−	3.24379e8i	0.845245	−	0.0471501i
$289$	1.91168e9	−	1.38892e9i	0.274047	−	0.199106i
$290$	−9.74136e8	+	3.46096e9i	−0.137730	+	0.489334i
$291$	2.74458e9	−	3.77759e9i	0.382740	−	0.526796i
$292$	2.75723e9	−	7.73836e8i	0.379265	−	0.106443i
$293$	−1.37513e10			−1.86584			−0.932921	−	0.360081i	$-0.882749\pi$
$293$	−1.37513e10			−1.86584			−0.932921	+	0.360081i	$0.882749\pi$
$294$	2.46004e9	−	4.59537e9i	0.329270	−	0.615080i
$295$	−5.91553e9	−	2.57933e9i	−0.781098	−	0.340580i
$296$	1.11112e10	−	4.83492e9i	1.44742	−	0.629829i
$297$	2.29582e9	−	7.06581e9i	0.295061	−	0.908105i
$298$	−1.97914e9	+	1.10423e10i	−0.250965	+	1.40021i
$299$		−	8.72470e9i		−	1.09161i
$300$	3.08600e9	+	7.37465e8i	0.380988	+	0.0910450i
$301$	8.87031e9			1.08062
$302$	−5.26842e9	−	9.44278e8i	−0.633363	−	0.113520i
$303$	−3.23652e9	−	1.05161e9i	−0.383979	−	0.124762i
$304$	4.69951e9	+	1.96062e9i	0.550248	+	0.229562i
$305$	−3.34577e9	−	2.96619e9i	−0.386631	−	0.342767i
$306$	5.32122e9	+	2.84860e9i	0.606912	+	0.324897i
$307$		−	1.18554e10i		−	1.33464i	−0.744773	−	0.667318i	$-0.767442\pi$
$307$		−	1.18554e10i		−	1.33464i	0.744773	−	0.667318i	$-0.232558\pi$
$308$	−1.90739e10	+	5.35322e9i	−2.11952	+	0.594857i
$309$	3.22998e9	+	2.34672e9i	0.354296	+	0.257411i
$310$	−1.95148e9	+	7.21102e8i	−0.211309	+	0.0780818i
$311$	8.84531e9	+	1.21745e10i	0.945521	+	1.30140i	0.953488	+	0.301430i	$0.0974640\pi$
$311$	8.84531e9	+	1.21745e10i	0.945521	+	1.30140i	−0.00796689	+	0.999968i	$0.502536\pi$
$312$	−2.63310e9	+	2.54266e8i	−0.277875	+	0.0268331i
$313$	2.75091e9	+	1.99865e9i	0.286615	+	0.208238i	0.721797	−	0.692104i	$-0.243316\pi$
$313$	2.75091e9	+	1.99865e9i	0.286615	+	0.208238i	−0.435183	+	0.900342i	$0.643316\pi$
$314$	1.51629e9	−	8.45985e9i	0.155978	−	0.870250i
$315$	−1.27412e10	−	5.55551e9i	−1.29410	−	0.564263i
$316$	−5.52732e9	−	4.36880e9i	−0.554327	−	0.438141i
$317$	2.92215e9	+	8.99345e9i	0.289378	+	0.890613i	0.985052	+	0.172256i	$0.0551057\pi$
$317$	2.92215e9	+	8.99345e9i	0.289378	+	0.890613i	−0.695674	+	0.718357i	$0.744894\pi$
$318$	1.52084e8	+	1.58378e8i	0.0148722	+	0.0154877i
$319$	6.60885e9	−	2.14734e9i	0.638209	−	0.207367i
$320$	7.85667e9	−	6.94435e9i	0.749270	−	0.662265i
$321$	−1.17666e7	+	3.62138e7i	−0.00110823	+	0.00341079i
$322$	1.19681e10	+	2.47147e10i	1.11327	+	2.29896i
$323$	3.10183e9	+	4.26930e9i	0.284975	+	0.392235i
$324$	2.51561e8	−	6.20158e9i	0.0228278	−	0.562759i
$325$	7.80190e9	+	1.53309e9i	0.699306	+	0.137415i
$326$	−3.31358e9	−	3.45072e9i	−0.293378	−	0.305519i
$327$	3.03665e9	+	4.17959e9i	0.265585	+	0.365547i
$328$	1.46388e10	−	6.36990e9i	1.26477	−	0.550348i
$329$	−4.83515e9	+	1.48811e10i	−0.412692	+	1.27014i
$330$	−2.12550e9	−	5.75215e9i	−0.179228	−	0.485036i
$331$	1.33495e10	−	4.33751e9i	1.11212	−	0.361350i	0.305366	−	0.952235i	$-0.401221\pi$
$331$	1.33495e10	−	4.33751e9i	1.11212	−	0.361350i	0.806756	+	0.590885i	$0.201221\pi$
$332$	1.51695e10	+	6.15335e8i	1.24858	+	0.0506477i
$333$	−5.07769e9	−	1.56275e10i	−0.412942	−	1.27091i
$334$	2.00553e9	+	1.45678e10i	0.161155	+	1.17060i
$335$	−7.06503e9	−	1.20221e10i	−0.560964	−	0.954557i
$336$	7.11007e9	−	4.33222e9i	0.557849	−	0.339901i
$337$	−5.92916e9	−	4.30779e9i	−0.459699	−	0.333991i	0.333714	−	0.942674i	$-0.391698\pi$
$337$	−5.92916e9	−	4.30779e9i	−0.459699	−	0.333991i	−0.793413	+	0.608684i	$0.791698\pi$
$338$	6.36258e9	−	8.75928e8i	0.487491	−	0.0671122i
$339$	5.43342e9	+	7.47846e9i	0.411410	+	0.566257i
$340$	1.06978e10	−	1.90914e9i	0.800531	−	0.142864i
$341$	3.25298e9	+	2.36343e9i	0.240583	+	0.174794i
$342$	3.25887e9	−	6.08760e9i	0.238212	−	0.444981i
$343$			1.80288e10i			1.30254i
$344$	7.81973e9	+	4.60329e9i	0.558416	+	0.328726i
$345$	−7.32825e9	+	4.30659e9i	−0.517278	+	0.303988i
$346$	2.60688e9	+	5.38334e9i	0.181893	+	0.375619i
$347$	−1.97004e10	−	6.40106e9i	−1.35881	−	0.441503i	−0.463163	−	0.886273i	$-0.653286\pi$
$347$	−1.97004e10	−	6.40106e9i	−1.35881	−	0.441503i	−0.895645	+	0.444770i	$0.853286\pi$
$348$	−2.43032e9	+	1.61942e9i	−0.165709	+	0.110419i
$349$	−5.59524e8			−0.0377153			−0.0188576	−	0.999822i	$-0.506003\pi$
$349$	−5.59524e8			−0.0377153			−0.0188576	+	0.999822i	$0.506003\pi$
$350$	−2.42037e10	+	6.35941e9i	−1.61291	+	0.423784i
$351$			7.82449e9i			0.515499i
$352$	−1.95929e10	−	5.17931e9i	−1.27623	−	0.337366i
$353$	8.75635e9	−	2.69493e10i	0.563929	−	1.73560i	−0.107183	−	0.994239i	$-0.534183\pi$
$353$	8.75635e9	−	2.69493e10i	0.563929	−	1.73560i	0.671112	−	0.741356i	$-0.265817\pi$
$354$	−2.28459e9	−	4.71780e9i	−0.145477	−	0.300418i
$355$	−2.82701e9	+	2.90485e10i	−0.177998	+	1.82899i
$356$	−1.38811e10	+	3.89583e9i	−0.864220	+	0.242549i
$357$	8.62849e9			0.531205
$358$	−4.66196e9	+	8.70859e9i	−0.283816	+	0.530170i
$359$	−7.87771e9	+	1.08427e10i	−0.474266	+	0.652771i	−0.977390	−	0.211443i	$-0.932184\pi$
$359$	−7.87771e9	+	1.08427e10i	−0.474266	+	0.652771i	0.503124	+	0.864214i	$0.332184\pi$
$360$	−8.34908e9	−	1.15096e10i	−0.497082	−	0.685253i
$361$	−8.85581e9	+	6.43412e9i	−0.521434	+	0.378844i
$362$	3.91307e9	−	5.38707e8i	0.227868	−	0.0313703i
$363$	−2.96864e9	+	4.08599e9i	−0.170975	+	0.235326i
$364$	1.73628e10	−	1.15695e10i	0.989041	−	0.659038i
$365$	−5.23168e9	−	4.63814e9i	−0.294761	−	0.261320i
$366$	−4.95321e8	−	3.59792e9i	−0.0276034	−	0.200506i
$367$	2.20536e10	−	7.16564e9i	1.21567	−	0.394994i	0.370165	−	0.928966i	$-0.379301\pi$
$367$	2.20536e10	−	7.16564e9i	1.21567	−	0.394994i	0.845503	+	0.533971i	$0.179301\pi$
$368$	−2.27521e9	+	2.79984e10i	−0.124059	+	1.52666i
$369$	−6.68974e9	−	2.05889e10i	−0.360831	−	1.11052i
$370$	−2.46068e10	−	1.64231e10i	−1.31295	−	0.876290i
$371$	−1.64707e9	−	5.35165e8i	−0.0869393	−	0.0282483i
$372$	−1.58467e9	−	5.86908e8i	−0.0827501	−	0.0306478i
$373$	−4.17167e9	+	3.03090e9i	−0.215514	+	0.156580i	−0.690305	−	0.723519i	$-0.742524\pi$
$373$	−4.17167e9	+	3.03090e9i	−0.215514	+	0.156580i	0.474791	+	0.880099i	$0.342524\pi$
$374$	−1.45469e10	−	1.51489e10i	−0.743503	−	0.774274i
$375$	−2.56338e9	−	7.30990e9i	−0.129625	−	0.369646i
$376$	−1.19851e10	+	1.06094e10i	−0.599639	+	0.530808i
$377$	−5.92076e9	+	4.30168e9i	−0.293097	+	0.212948i
$378$	−1.07332e10	−	2.21647e10i	−0.525730	−	1.08566i
$379$	3.54985e9	+	1.15342e9i	0.172050	+	0.0559023i	0.393775	−	0.919207i	$-0.371169\pi$
$379$	3.54985e9	+	1.15342e9i	0.172050	+	0.0559023i	−0.221725	+	0.975109i	$0.571169\pi$
$380$	−2.18411e9	−	1.22385e10i	−0.104746	−	0.586941i
$381$	−1.00361e9	−	3.08879e9i	−0.0476283	−	0.146585i
$382$	−2.22790e10	−	2.32010e10i	−1.04626	−	1.08957i
$383$	−2.54016e10	+	8.25348e9i	−1.18050	+	0.383568i	−0.832552	−	0.553946i	$-0.813121\pi$
$383$	−2.54016e10	+	8.25348e9i	−1.18050	+	0.383568i	−0.347948	+	0.937514i	$0.613121\pi$
$384$	8.51619e9	−	1.29312e8i	0.391670	−	0.00594723i
$385$	3.61916e10	+	3.20856e10i	1.64727	+	1.46038i
$386$	−1.79633e9	+	1.00223e10i	−0.0809164	+	0.451457i
$387$	7.23248e9	−	9.95466e9i	0.322436	−	0.443795i
$388$	−2.33613e10	+	2.95563e10i	−1.03079	+	1.30414i
$389$	3.57210e9	−	2.59529e9i	0.156000	−	0.113341i	−0.507047	−	0.861919i	$-0.669263\pi$
$389$	3.57210e9	−	2.59529e9i	0.156000	−	0.113341i	0.663047	+	0.748578i	$0.269263\pi$
$390$	4.00099e9	+	5.06977e9i	0.172946	+	0.219144i
$391$	−1.71113e10	+	2.35517e10i	−0.732110	+	1.00766i
$392$	−2.13349e10	+	3.62421e10i	−0.903537	+	1.53486i
$393$	−3.25216e9			−0.136333
$394$	1.47896e10	+	7.91731e9i	0.613722	+	0.328543i
$395$	−1.66611e9	+	1.71198e10i	−0.0684408	+	0.703251i
$396$	−9.54447e9	+	2.57704e10i	−0.388124	+	1.04795i
$397$	7.79625e9	−	2.39944e10i	0.313851	−	0.965934i	−0.662374	−	0.749174i	$-0.730451\pi$
$397$	7.79625e9	−	2.39944e10i	0.313851	−	0.965934i	0.976225	−	0.216761i	$-0.0695491\pi$
$398$	−2.57245e8	−	4.61070e7i	−0.0102521	−	0.00183753i
$399$		−	9.87120e9i		−	0.389474i
$400$	−2.46373e10	−	6.95440e9i	−0.962394	−	0.271656i
$401$	4.42105e10			1.70981			0.854905	−	0.518785i	$-0.173616\pi$
$401$	4.42105e10			1.70981			0.854905	+	0.518785i	$0.173616\pi$
$402$	1.99824e9	−	1.11488e10i	0.0765146	−	0.426899i
$403$	−4.02746e9	−	1.30860e9i	−0.152690	−	0.0496120i
$404$	2.57480e10	+	9.53616e9i	0.966536	+	0.357971i
$405$	−1.30641e10	+	7.67739e9i	−0.485580	+	0.285360i
$406$	1.08711e10	−	2.03073e10i	0.400100	−	0.747391i
$407$			5.71773e10i			2.08375i
$408$	7.60655e9	+	4.47780e9i	0.274503	+	0.161593i
$409$	1.40540e9	+	1.02108e9i	0.0502236	+	0.0364896i	0.612614	−	0.790382i	$-0.290118\pi$
$409$	1.40540e9	+	1.02108e9i	0.0502236	+	0.0364896i	−0.562390	+	0.826872i	$0.690118\pi$
$410$	−3.24189e10	−	2.16370e10i	−1.14726	−	0.765707i
$411$	8.85937e9	+	1.21939e10i	0.310482	+	0.427341i
$412$	−2.52718e10	−	1.99748e10i	−0.877096	−	0.693258i
$413$	3.34475e10	+	2.43010e10i	1.14964	+	0.835266i
$414$	3.74942e10	+	6.72023e9i	1.27633	+	0.228761i
$415$	−1.87794e10	−	3.19557e10i	−0.633125	−	1.07735i
$416$	2.13104e10	−	1.18875e9i	0.711573	−	0.0396935i
$417$	2.62052e9	+	8.06513e9i	0.0866649	+	0.266727i
$418$	−1.73307e10	+	1.66420e10i	−0.567690	+	0.545129i
$419$	−2.57845e10	+	8.37789e9i	−0.836570	+	0.271818i	−0.695810	−	0.718226i	$-0.744955\pi$
$419$	−2.57845e10	+	8.37789e9i	−0.836570	+	0.271818i	−0.140760	+	0.990044i	$0.544955\pi$
$420$	−1.82882e10	−	8.87294e9i	−0.587724	−	0.285148i
$421$	1.52328e10	−	4.68816e10i	0.484898	−	1.49236i	−0.347232	−	0.937779i	$-0.612878\pi$
$421$	1.52328e10	−	4.68816e10i	0.484898	−	1.49236i	0.832129	−	0.554582i	$-0.187122\pi$
$422$	6.24265e9	−	3.02300e9i	0.196843	−	0.0953210i
$423$	1.27578e10	+	1.75596e10i	0.398487	+	0.548471i
$424$	−1.17427e9	−	1.32654e9i	−0.0363332	−	0.0410446i
$425$	−1.80539e10	−	1.94400e10i	−0.553370	−	0.595854i
$426$	−1.70993e10	+	1.64198e10i	−0.519207	+	0.498572i
$427$	1.68372e10	+	2.31744e10i	0.506475	+	0.697103i
$428$	1.06701e8	−	2.88098e8i	0.00317976	−	0.00858548i
$429$	3.85720e9	−	1.18712e10i	0.113879	−	0.350483i
$430$	−8.81336e8	−	2.21359e10i	−0.0257791	−	0.647476i
$431$	1.60855e10	−	5.22650e9i	0.466150	−	0.151461i	−0.0665186	−	0.997785i	$-0.521189\pi$
$431$	1.60855e10	−	5.22650e9i	0.466150	−	0.151461i	0.532669	+	0.846324i	$0.321189\pi$
$432$	2.04045e9	−	2.51096e10i	0.0585857	−	0.720949i
$433$	2.18365e9	+	6.72058e9i	0.0621199	+	0.191185i	0.977300	−	0.211859i	$-0.0679519\pi$
$433$	2.18365e9	+	6.72058e9i	0.0621199	+	0.191185i	−0.915180	+	0.403045i	$0.867952\pi$
$434$	1.32038e10	−	1.81775e9i	0.372168	−	0.0512359i
$435$	6.53571e9	+	2.84975e9i	0.182531	+	0.0795884i
$436$	−2.31138e10	−	3.46877e10i	−0.639626	−	0.959909i
$437$	2.69437e10	+	1.95758e10i	0.738809	+	0.536776i
$438$	−7.74518e8	−	5.62596e9i	−0.0210443	−	0.152862i
$439$	1.41193e10	+	1.94335e10i	0.380150	+	0.523231i	0.955624	−	0.294589i	$-0.0951826\pi$
$439$	1.41193e10	+	1.94335e10i	0.380150	+	0.523231i	−0.575474	+	0.817820i	$0.695183\pi$
$440$	1.52541e10	+	4.70672e10i	0.406984	+	1.25576i
$441$	4.61369e10	+	3.35204e10i	1.21981	+	0.886247i
$442$	1.95007e10	+	1.04393e10i	0.510931	+	0.273516i
$443$		−	5.78029e10i		−	1.50084i	−0.660961	−	0.750421i	$-0.729851\pi$
$443$		−	5.78029e10i		−	1.50084i	0.660961	−	0.750421i	$-0.270149\pi$
$444$	−6.49326e9	−	2.31360e10i	−0.167083	−	0.595328i
$445$	2.63385e10	+	2.33504e10i	0.671663	+	0.595462i
$446$	2.17851e10	−	1.05494e10i	0.550579	−	0.266618i
$447$	2.11576e10	+	6.87451e9i	0.529951	+	0.172192i
$448$	−5.87361e10	+	3.26000e10i	−1.45812	+	0.809292i
$449$	−7.77920e10			−1.91403			−0.957016	−	0.290034i	$-0.906333\pi$
$449$	−7.77920e10			−1.91403			−0.957016	+	0.290034i	$0.906333\pi$
$450$	−1.25979e10	+	3.23477e10i	−0.307218	+	0.788847i
$451$			7.53298e10i			1.82079i
$452$	−4.13571e10	−	6.20660e10i	−0.990824	−	1.48696i
$453$	−3.27993e9	+	1.00946e10i	−0.0778882	+	0.239715i
$454$	−1.34978e10	+	6.53629e9i	−0.317716	+	0.153854i
$455$	−4.66927e10	−	2.03593e10i	−1.08944	−	0.475027i
$456$	5.12271e9	−	8.70208e9i	0.118479	−	0.201263i
$457$	−4.05139e10			−0.928837			−0.464419	−	0.885616i	$-0.653737\pi$
$457$	−4.05139e10			−0.928837			−0.464419	+	0.885616i	$0.653737\pi$
$458$	−2.14788e10	−	1.14982e10i	−0.488144	−	0.261318i
$459$	1.53458e10	−	2.11217e10i	0.345731	−	0.475858i
$460$	6.04866e10	−	3.23220e10i	1.35091	−	0.721884i
$461$	−2.76175e10	+	2.00653e10i	−0.611477	+	0.444264i	−0.849934	−	0.526889i	$-0.823358\pi$
$461$	−2.76175e10	+	2.00653e10i	−0.611477	+	0.444264i	0.238457	+	0.971153i	$0.423358\pi$
$462$	5.35794e9	+	3.89191e10i	0.117606	+	0.854270i
$463$	3.36282e10	−	4.62852e10i	0.731778	−	1.00721i	−0.267272	−	0.963621i	$-0.586122\pi$
$463$	3.36282e10	−	4.62852e10i	0.731778	−	1.00721i	0.999050	−	0.0435843i	$-0.0138777\pi$
$464$	2.01221e10	−	1.22605e10i	0.434112	−	0.264507i
$465$	8.88839e8	+	4.02877e9i	0.0190113	+	0.0861709i
$466$	6.97160e10	−	9.59770e9i	1.47839	−	0.203528i
$467$	−3.23995e10	+	1.05272e10i	−0.681193	+	0.221333i	−0.629118	−	0.777310i	$-0.716584\pi$
$467$	−3.23995e10	+	1.05272e10i	−0.681193	+	0.221333i	−0.0520756	+	0.998643i	$0.516584\pi$
$468$	1.17306e9	−	2.89186e10i	0.0244532	−	0.602829i
$469$	2.76057e10	+	8.49617e10i	0.570569	+	1.75603i
$470$	3.76162e10	+	1.05876e10i	0.770874	+	0.216973i
$471$	−1.62095e10	−	5.26680e9i	−0.329372	−	0.107019i
$472$	1.68749e10	+	3.87806e10i	0.339996	+	0.781352i
$473$	−3.46391e10	+	2.51667e10i	−0.692024	+	0.502785i
$474$	−1.00775e10	+	9.67703e9i	−0.199637	+	0.191703i
$475$	−2.22398e10	+	2.06541e10i	−0.436874	+	0.405725i
$476$	−6.95604e10	−	2.82166e9i	−1.35498	−	0.0549637i
$477$	−1.94354e9	+	1.41206e9i	−0.0375422	+	0.0272760i
$478$	−1.61612e9	+	7.82603e8i	−0.0309571	+	0.0149910i
$479$	6.05878e9	+	1.96862e9i	0.115091	+	0.0373955i	0.365997	−	0.930616i	$-0.380728\pi$
$479$	6.05878e9	+	1.96862e9i	0.115091	+	0.0373955i	−0.250905	+	0.968012i	$0.580728\pi$
$480$	−1.15175e10	−	1.73128e10i	−0.216967	−	0.326138i
$481$	−1.86083e10	−	5.72704e10i	−0.347637	−	1.06992i
$482$	6.37801e10	−	6.12454e10i	1.18167	−	1.13471i
$483$	5.17896e10	−	1.68275e10i	0.951599	−	0.309193i
$484$	2.52685e10	−	3.19693e10i	0.460467	−	0.582574i
$485$	9.15450e10	+	8.90921e9i	1.65450	+	0.161017i
$486$	−5.18355e10	−	9.29066e9i	−0.929142	−	0.166533i
$487$	4.81253e10	−	6.62387e10i	0.855573	−	1.17760i	−0.127034	−	0.991898i	$-0.540546\pi$
$487$	4.81253e10	−	6.62387e10i	0.855573	−	1.17760i	0.982607	−	0.185697i	$-0.0594544\pi$
$488$	2.81656e9	+	2.91674e10i	0.0496638	+	0.514302i
$489$	−7.67521e9	+	5.57636e9i	−0.134232	+	0.0975249i
$490$	1.02593e11	−	4.08473e9i	1.77965	−	0.0708564i
$491$	−2.93136e10	+	4.03468e10i	−0.504364	+	0.694197i	−0.982956	−	0.183840i	$-0.941147\pi$
$491$	−2.93136e10	+	4.03468e10i	−0.504364	+	0.694197i	0.478593	+	0.878037i	$0.341147\pi$
$492$	−8.55473e9	−	3.04811e10i	−0.145998	−	0.520201i
$493$	2.44194e10			0.413377
$494$	1.19428e10	−	2.23093e10i	0.200539	−	0.374609i
$495$	6.55170e10	−	1.44545e10i	1.09127	−	0.240760i
$496$	1.25833e10	+	5.24970e9i	0.207906	+	0.0867377i
$497$	5.77790e10	−	1.77826e11i	0.946989	−	2.91453i
$498$	5.31149e9	−	2.96344e10i	0.0863572	−	0.481814i
$499$		−	4.88329e10i		−	0.787609i	−0.919194	−	0.393804i	$-0.871159\pi$
$499$		−	4.88329e10i		−	0.787609i	0.919194	−	0.393804i	$-0.128841\pi$
$500$	1.82748e10	+	5.97686e10i	0.292396	+	0.956297i
$501$	2.91613e10			0.462867
$502$	−5.85815e10	−	1.04998e10i	−0.922457	−	0.165335i
$503$	1.46575e10	+	4.76250e9i	0.228974	+	0.0743983i	0.421257	−	0.906941i	$-0.361589\pi$
$503$	1.46575e10	+	4.76250e9i	0.228974	+	0.0743983i	−0.192283	+	0.981340i	$0.561589\pi$
$504$	3.63461e10	+	8.35278e10i	0.563295	+	1.29452i
$505$	−1.44420e10	−	6.54600e10i	−0.222055	−	1.00649i
$506$	−1.16856e11	−	6.25566e10i	−1.78258	−	0.954269i
$507$		−	1.27364e10i		−	0.192759i
$508$	7.08073e9	+	2.52292e10i	0.106322	+	0.378833i
$509$	−4.91741e10	−	3.57271e10i	−0.732597	−	0.532263i	0.157787	−	0.987473i	$-0.449564\pi$
$509$	−4.91741e10	−	3.57271e10i	−0.732597	−	0.532263i	−0.890384	+	0.455210i	$0.849564\pi$
$510$	−8.57309e8	−	2.15324e10i	−0.0126723	−	0.318282i
$511$	2.63278e10	+	3.62371e10i	0.386127	+	0.531458i
$512$	−6.86974e10	−	1.74245e9i	−0.999678	−	0.0253560i
$513$	−2.41637e10	−	1.75560e10i	−0.348894	−	0.253487i
$514$	5.26038e8	−	2.93493e9i	0.00753641	−	0.0420480i
$515$	−7.61771e9	+	7.82745e10i	−0.108292	+	1.11273i
$516$	1.11582e10	−	1.41171e10i	0.157396	−	0.199135i
$517$	−2.33388e10	−	7.18296e10i	−0.326676	−	1.00541i
$518$	1.31273e11	+	1.36706e11i	1.82329	+	1.89875i
$519$	1.12808e10	−	3.66534e9i	0.155478	−	0.0505179i
$520$	−3.05970e10	−	4.21794e10i	−0.418471	−	0.576883i
$521$	−9.32291e9	+	2.86930e10i	−0.126532	+	0.389426i	−0.994177	−	0.107758i	$-0.965633\pi$
$521$	−9.32291e9	+	2.86930e10i	−0.126532	+	0.389426i	0.867645	+	0.497184i	$0.165633\pi$
$522$	−1.39259e10	−	2.87577e10i	−0.187561	−	0.387322i
$523$	−2.27294e10	−	3.12843e10i	−0.303795	−	0.418138i	0.629639	−	0.776888i	$-0.283203\pi$
$523$	−2.27294e10	−	3.12843e10i	−0.303795	−	0.418138i	−0.933434	+	0.358750i	$0.883203\pi$
$524$	2.62180e10	+	1.06351e9i	0.347756	+	0.0141064i
$525$	5.94726e9	+	4.92688e10i	0.0782852	+	0.648537i
$526$	−6.29059e10	−	6.55094e10i	−0.821767	−	0.855777i
$527$	8.30535e9	+	1.14313e10i	0.107675	+	0.148202i
$528$	−1.54739e10	+	3.70901e10i	−0.199097	+	0.477225i
$529$	−3.25745e10	+	1.00254e11i	−0.415963	+	1.28020i
$530$	−1.17186e9	+	4.16344e9i	−0.0148516	+	0.0527654i
$531$	5.45434e10	−	1.77222e10i	0.686063	−	0.222916i
$532$	−3.22804e9	+	7.95788e10i	−0.0402988	+	0.993461i
$533$	−2.45160e10	−	7.54524e10i	−0.303767	−	0.934899i
$534$	3.89926e9	+	2.83235e10i	0.0479531	+	0.348323i
$535$	−7.32440e8	+	1.61593e8i	−0.00894041	+	0.00197246i
$536$	−1.97551e10	+	8.92252e10i	−0.239343	+	1.08101i
$537$	1.58474e10	+	1.15138e10i	0.190573	+	0.138459i
$538$	1.20718e11	−	1.66190e10i	1.44092	−	0.198370i
$539$	−1.16640e11	−	1.60542e11i	−1.38195	−	1.90210i
$540$	−5.42456e10	+	2.89871e10i	−0.637954	+	0.340902i
$541$	−7.33142e10	−	5.32659e10i	−0.855853	−	0.621813i	0.0709008	−	0.997483i	$-0.477413\pi$
$541$	−7.33142e10	−	5.32659e10i	−0.855853	−	0.621813i	−0.926754	+	0.375670i	$0.877413\pi$
$542$	−2.90971e9	+	5.43537e9i	−0.0337173	+	0.0629842i
$543$		−	7.83304e9i		−	0.0901013i
$544$	−5.98575e10	−	3.85862e10i	−0.683476	−	0.440591i
$545$	−4.06743e10	+	9.32836e10i	−0.461035	+	1.05735i
$546$	−1.80328e10	−	3.72388e10i	−0.202905	−	0.419010i
$547$	−1.41563e11	−	4.59964e10i	−1.58124	−	0.513777i	−0.618867	−	0.785495i	$-0.712408\pi$
$547$	−1.41563e11	−	4.59964e10i	−1.58124	−	0.513777i	−0.962377	+	0.271718i	$0.912408\pi$
$548$	−6.74341e10	−	1.01201e11i	−0.747752	−	1.12218i
$549$	3.97357e10			0.437412
$550$	7.64739e10	−	9.35042e10i	0.835723	−	1.02183i
$551$		−	2.79363e10i		−	0.303084i
$552$	5.43884e10	+	1.20420e10i	0.585801	+	0.129701i
$553$	3.40522e10	−	1.04802e11i	0.364121	−	1.12065i
$554$	−3.29292e10	−	6.80005e10i	−0.349576	−	0.721893i
$555$	−3.89186e10	+	4.38991e10i	−0.410191	+	0.462683i
$556$	−1.84885e10	−	6.58757e10i	−0.193465	−	0.689329i
$557$	−1.97341e10			−0.205020			−0.102510	−	0.994732i	$-0.532687\pi$
$557$	−1.97341e10			−0.205020			−0.102510	+	0.994732i	$0.532687\pi$
$558$	8.72585e9	−	1.63000e10i	0.0900059	−	0.168132i
$559$	2.65050e10	−	3.64810e10i	0.271444	−	0.373611i
$560$	1.44532e11	+	7.75116e10i	1.46965	+	0.788160i
$561$	−3.36947e10	+	2.44806e10i	−0.340181	+	0.247156i
$562$	−1.76737e11	+	2.43312e10i	−1.77167	+	0.243904i
$563$	8.07950e10	−	1.11205e11i	0.804175	−	1.10685i	−0.188021	−	0.982165i	$-0.560207\pi$
$563$	8.07950e10	−	1.11205e11i	0.804175	−	1.10685i	0.992196	−	0.124687i	$-0.0397927\pi$
$564$	1.76010e10	+	2.64144e10i	0.173948	+	0.261050i
$565$	−7.27776e10	+	1.66910e11i	−0.714174	+	1.63791i
$566$	9.60541e9	+	6.97720e10i	0.0935945	+	0.679853i
$567$	9.23258e10	−	2.99985e10i	0.893287	−	0.290246i
$568$	1.43219e11	−	1.26780e11i	1.37597	−	1.21802i
$569$	1.16661e10	+	3.59046e10i	0.111295	+	0.342532i	0.991156	−	0.132699i	$-0.0423644\pi$
$569$	1.16661e10	+	3.59046e10i	0.111295	+	0.342532i	−0.879861	+	0.475231i	$0.842364\pi$
$570$	−2.46336e10	+	9.80782e8i	−0.233361	+	0.00929122i
$571$	−1.42709e11	−	4.63689e10i	−1.34248	−	0.436197i	−0.452322	−	0.891855i	$-0.649404\pi$
$571$	−1.42709e11	−	4.63689e10i	−1.34248	−	0.436197i	−0.890155	+	0.455658i	$0.849404\pi$
$572$	−3.49777e10	+	9.44412e10i	−0.326744	+	0.882221i
$573$	−5.16045e10	+	3.74929e10i	−0.478706	+	0.347801i
$574$	1.72949e11	+	1.80107e11i	1.59320	+	1.65914i
$575$	−1.46275e11	−	8.14726e10i	−1.33813	−	0.745316i
$576$	−1.13058e10	+	9.24969e10i	−0.102710	+	0.840305i
$577$	6.00738e10	−	4.36462e10i	0.541978	−	0.393770i	−0.282841	−	0.959167i	$-0.591277\pi$
$577$	6.00738e10	−	4.36462e10i	0.541978	−	0.393770i	0.824819	+	0.565397i	$0.191277\pi$
$578$	1.64779e10	+	3.40277e10i	0.147635	+	0.304875i
$579$	1.92032e10	+	6.23950e9i	0.170868	+	0.0555182i
$580$	−5.17571e10	−	2.51112e10i	−0.457360	−	0.221899i
$581$	7.33782e10	+	2.25835e11i	0.643965	+	1.98192i
$582$	5.17461e10	+	5.38877e10i	0.451010	+	0.469675i
$583$	7.95026e9	−	2.58320e9i	0.0688188	−	0.0223606i
$584$	4.40416e9	+	4.56081e10i	0.0378627	+	0.392095i
$585$	−6.09195e10	+	3.58005e10i	−0.520155	+	0.305679i
$586$	3.88167e10	−	2.16570e11i	0.329176	−	1.83658i
$587$	−1.29839e10	+	1.78708e10i	−0.109358	+	0.150519i	−0.860188	−	0.509977i	$-0.829654\pi$
$587$	−1.29839e10	+	1.78708e10i	−0.109358	+	0.150519i	0.750830	+	0.660496i	$0.229654\pi$
$588$	6.54286e10	+	5.17148e10i	0.547342	+	0.432619i
$589$	1.30777e10	−	9.50152e9i	0.108660	−	0.0789463i
$590$	5.73201e10	−	8.58830e10i	0.473041	−	0.708760i
$591$	1.95537e10	−	2.69134e10i	0.160280	−	0.220606i
$592$	4.47810e10	+	1.88639e11i	0.364592	+	1.53584i
$593$	−1.83259e11			−1.48200			−0.740999	−	0.671507i	$-0.765647\pi$
$593$	−1.83259e11			−1.48200			−0.740999	+	0.671507i	$0.765647\pi$
$594$	1.04799e11	+	5.61020e10i	0.841806	+	0.450643i
$595$	8.61140e10	+	1.46535e11i	0.687078	+	1.16916i
$596$	−1.68318e11	−	6.23392e10i	−1.33397	−	0.494056i
$597$	−1.60152e8	+	4.92896e8i	−0.00126076	+	0.00388023i
$598$	1.37406e11	+	2.46277e10i	1.07448	+	0.192584i
$599$			1.78293e11i			1.38492i	0.721454	+	0.692462i	$0.243474\pi$
$599$			1.78293e11i			1.38492i	−0.721454	+	0.692462i	$0.756526\pi$
$600$	−2.03254e10	+	4.65198e10i	−0.156832	+	0.358949i
$601$	−2.04813e10			−0.156986			−0.0784928	−	0.996915i	$-0.525011\pi$
$601$	−2.04813e10			−0.156986			−0.0784928	+	0.996915i	$0.525011\pi$
$602$	−2.50387e10	+	1.39699e11i	−0.190645	+	1.06367i
$603$	1.17856e11	+	3.82939e10i	0.891423	+	0.289641i
$604$	2.97429e10	−	8.03070e10i	0.223479	−	0.603401i
$605$	−9.90186e10	−	9.63654e9i	−0.739086	−	0.0719283i
$606$	2.56977e10	−	4.80036e10i	0.190548	−	0.355945i
$607$			1.69234e11i			1.24662i	0.781976	+	0.623309i	$0.214212\pi$
$607$			1.69234e11i			1.24662i	−0.781976	+	0.623309i	$0.785788\pi$
$608$	−4.41435e10	+	6.84784e10i	−0.323037	+	0.501117i
$609$	−3.69542e10	−	2.68488e10i	−0.268654	−	0.195189i
$610$	5.61589e10	−	4.43198e10i	0.405601	−	0.320095i
$611$	4.67537e10	+	6.43510e10i	0.335468	+	0.461732i
$612$	−5.98833e10	+	7.57631e10i	−0.426874	+	0.540073i
$613$	−1.57949e11	−	1.14757e11i	−1.11860	−	0.812710i	−0.134603	−	0.990900i	$-0.542976\pi$
$613$	−1.57949e11	−	1.14757e11i	−1.11860	−	0.812710i	−0.983996	+	0.178190i	$0.942976\pi$
$614$	1.86711e11	+	3.34649e10i	1.31370	+	0.235460i
$615$	−5.12744e10	+	5.78360e10i	−0.358427	+	0.404295i
$616$	−3.04670e10	−	3.15507e11i	−0.211596	−	2.19122i
$617$	−5.25151e10	−	1.61625e11i	−0.362363	−	1.11524i	−0.951616	−	0.307289i	$-0.900578\pi$
$617$	−5.25151e10	−	1.61625e11i	−0.362363	−	1.11524i	0.589254	−	0.807948i	$-0.299422\pi$
$618$	−4.60760e10	+	4.42449e10i	−0.315879	+	0.303326i
$619$	7.24708e10	−	2.35472e10i	0.493629	−	0.160390i	−0.0516153	−	0.998667i	$-0.516437\pi$
$619$	7.24708e10	−	2.35472e10i	0.493629	−	0.160390i	0.545244	+	0.838277i	$0.316437\pi$
$620$	−5.84809e9	−	3.27695e10i	−0.0395774	−	0.221770i
$621$	5.09160e10	−	1.56703e11i	0.342364	−	1.05369i
$622$	−2.16705e11	+	1.04939e11i	−1.44780	+	0.701095i
$623$	−1.32545e11	−	1.82433e11i	−0.879858	−	1.21102i
$624$	3.42816e9	−	4.21865e10i	0.0226111	−	0.278250i
$625$	9.85586e10	−	1.16487e11i	0.645913	−	0.763411i
$626$	−3.92419e10	+	3.76824e10i	−0.255537	+	0.245381i
$627$	2.80065e10	+	3.85476e10i	0.181212	+	0.249417i
$628$	1.28954e11	+	4.77602e10i	0.829081	+	0.307063i
$629$	−6.20898e10	+	1.91093e11i	−0.396660	+	1.22079i
$630$	1.23459e11	−	1.84979e11i	0.783720	−	1.17425i
$631$	−3.06625e10	+	9.96285e9i	−0.193415	+	0.0628443i	−0.404123	−	0.914705i	$-0.632423\pi$
$631$	−3.06625e10	+	9.96285e9i	−0.193415	+	0.0628443i	0.210708	+	0.977549i	$0.432423\pi$
$632$	8.44067e10	−	7.47179e10i	0.529064	−	0.468335i
$633$	−4.25042e9	−	1.30815e10i	−0.0264739	−	0.0814782i
$634$	−1.49887e11	+	2.06347e10i	−0.927696	+	0.127715i
$635$	4.24397e10	−	4.78707e10i	0.261022	−	0.294425i
$636$	−2.92360e9	+	1.94812e9i	−0.0178686	+	0.0119066i
$637$	1.69078e11	+	1.22843e11i	1.02691	+	0.746091i
$638$	1.51634e10	+	1.10144e11i	0.0915197	+	0.664783i
$639$	−1.52453e11	−	2.09834e11i	−0.914393	−	1.25855i
$640$	8.71893e10	+	1.43337e11i	0.519689	+	0.854356i
$641$	2.29533e11	+	1.66765e11i	1.35960	+	0.987810i	0.998470	+	0.0552965i	$0.0176104\pi$
$641$	2.29533e11	+	1.66765e11i	1.35960	+	0.987810i	0.361134	+	0.932514i	$0.382390\pi$
$642$	−5.37119e8	−	2.87535e8i	−0.00316177	−	0.00169259i
$643$		−	1.35882e11i		−	0.794912i	−0.917621	−	0.397456i	$-0.869893\pi$
$643$		−	1.35882e11i		−	0.794912i	0.917621	−	0.397456i	$-0.130107\pi$
$644$	−4.23016e11	+	1.18722e11i	−2.45931	+	0.690221i
$645$	−4.37250e10	−	4.25534e9i	−0.252634	−	0.0245864i
$646$	−7.59930e10	+	3.67996e10i	−0.436359	+	0.211306i
$647$	3.15894e11	+	1.02640e11i	1.80270	+	0.585734i	0.999944	−	0.0105671i	$-0.00336367\pi$
$647$	3.15894e11	+	1.02640e11i	1.80270	+	0.585734i	0.802761	+	0.596301i	$0.203364\pi$
$648$	9.69588e10	+	2.14674e10i	0.549904	+	0.121753i
$649$	−1.99561e11			−1.12486
$650$	−4.61676e10	+	1.18545e11i	−0.258633	+	0.664094i
$651$		−	2.64308e10i		−	0.147159i
$652$	6.36989e10	−	4.24451e10i	0.352486	−	0.234875i
$653$	−2.16948e10	+	6.67696e10i	−0.119317	+	0.367220i	−0.992823	−	0.119594i	$-0.961841\pi$
$653$	−2.16948e10	+	6.67696e10i	−0.119317	+	0.367220i	0.873506	+	0.486813i	$0.161841\pi$
$654$	−7.43963e10	+	3.60264e10i	−0.406668	+	0.196929i
$655$	−3.24572e10	−	5.52304e10i	−0.176338	−	0.300063i
$656$	5.89980e10	+	2.48528e11i	0.318582	+	1.34202i
$657$	6.21334e10			0.333475
$658$	−2.20714e11	−	1.18155e11i	−1.17741	−	0.630299i
$659$	−4.39311e10	+	6.04660e10i	−0.232933	+	0.320605i	−0.909443	−	0.415829i	$-0.863492\pi$
$659$	−4.39311e10	+	6.04660e10i	−0.232933	+	0.320605i	0.676510	+	0.736433i	$0.263492\pi$
$660$	9.65905e10	−	1.72377e10i	0.509048	−	0.0908455i
$661$	2.86844e11	−	2.08404e11i	1.50259	−	1.09169i	0.533248	−	0.845959i	$-0.320971\pi$
$661$	2.86844e11	−	2.08404e11i	1.50259	−	1.09169i	0.969337	−	0.245734i	$-0.0790289\pi$
$662$	3.06292e10	+	2.22485e11i	0.159479	+	1.15843i
$663$	2.57824e10	−	3.54864e10i	0.133435	−	0.183657i
$664$	−5.25106e10	+	2.37167e11i	−0.270131	+	1.22006i
$665$	1.67639e11	−	9.85165e10i	0.857214	−	0.503759i
$666$	2.60451e11	−	3.58560e10i	1.32382	−	0.182249i
$667$	1.46569e11	−	4.76231e10i	0.740523	−	0.240611i
$668$	−2.35090e11	−	9.53623e9i	−1.18067	−	0.0478929i
$669$	−1.48328e10	−	4.56506e10i	−0.0740487	−	0.227899i
$670$	2.09280e11	−	7.73319e10i	1.03855	−	0.383760i
$671$	−1.31500e11	−	4.27270e10i	−0.648689	−	0.210772i
$672$	4.81582e10	+	1.24206e11i	0.236153	+	0.609065i
$673$	2.15376e11	−	1.56480e11i	1.04987	−	0.762778i	0.0776850	−	0.996978i	$-0.475247\pi$
$673$	2.15376e11	−	1.56480e11i	1.04987	−	0.762778i	0.972188	+	0.234200i	$0.0752472\pi$
$674$	8.45800e10	−	8.12187e10i	0.409853	−	0.393565i
$675$	1.31182e11	+	7.30664e10i	0.631917	+	0.351967i
$676$	−4.16500e9	+	1.02677e11i	−0.0199447	+	0.491684i
$677$	−1.07049e11	+	7.77753e10i	−0.509596	+	0.370243i	−0.812670	−	0.582724i	$-0.801987\pi$
$677$	−1.07049e11	+	7.77753e10i	−0.509596	+	0.370243i	0.303074	+	0.952967i	$0.401987\pi$
$678$	−1.33116e11	+	6.44612e10i	−0.629957	+	0.305056i
$679$	−5.60409e11	−	1.82088e11i	−2.63649	−	0.856648i
$680$	−1.30080e8	+	1.73869e11i	−0.000608379	+	0.813179i
$681$	9.19021e9	+	2.82845e10i	0.0427304	+	0.131511i
$682$	−4.64041e10	+	4.45600e10i	−0.214496	+	0.205972i
$683$	2.64646e11	−	8.59888e10i	1.21614	−	0.395147i	0.370464	−	0.928847i	$-0.379199\pi$
$683$	2.64646e11	−	8.59888e10i	1.21614	−	0.395147i	0.845674	+	0.533699i	$0.179199\pi$
$684$	8.66749e10	+	6.85079e10i	0.395976	+	0.312980i
$685$	−1.18666e11	+	2.72153e11i	−0.538971	+	1.23609i
$686$	−2.83936e11	−	5.08910e10i	−1.28211	−	0.229797i
$687$	−2.83976e10	+	3.90860e10i	−0.127484	+	0.175466i
$688$	−9.45706e10	+	1.10159e11i	−0.422087	+	0.491663i
$689$	−7.12251e9	+	5.17481e9i	−0.0316050	+	0.0229624i
$690$	−4.71387e10	−	1.27569e11i	−0.207961	−	0.562794i
$691$	−1.56843e11	+	2.15875e11i	−0.687943	+	0.946872i	−0.999995	−	0.00319325i	$-0.998984\pi$
$691$	−1.56843e11	+	2.15875e11i	−0.687943	+	0.946872i	0.312052	+	0.950065i	$0.398984\pi$
$692$	−9.21410e10	+	2.58600e10i	−0.401817	+	0.112773i
$693$	−4.29825e11			−1.86363
$694$	1.56420e11	−	2.92194e11i	0.674302	−	1.25960i
$695$	−1.10814e11	+	1.24995e11i	−0.474959	+	0.535739i
$696$	−1.86441e10	−	4.28464e10i	−0.0794519	−	0.182590i
$697$	−8.18020e10	+	2.51761e11i	−0.346603	+	1.06674i
$698$	1.57940e9	−	8.81197e9i	0.00665382	−	0.0371237i
$699$		−	1.39555e11i		−	0.584570i
$700$	−3.18334e10	−	3.99136e11i	−0.132584	−	1.66237i
$701$	−1.13860e11			−0.471520			−0.235760	−	0.971811i	$-0.575758\pi$
$701$	−1.13860e11			−0.471520			−0.235760	+	0.971811i	$0.575758\pi$
$702$	−1.23228e11	−	2.20866e10i	−0.507413	−	0.0909455i
$703$	2.18615e11	+	7.10323e10i	0.895073	+	0.290827i
$704$	1.36875e11	−	2.93950e11i	0.557230	−	1.19669i
$705$	3.09731e10	−	7.10347e10i	0.125380	−	0.287550i
$706$	3.99708e11	+	2.13975e11i	1.60888	+	0.861281i
$707$			4.29451e11i			1.71884i
$708$	8.07496e10	−	2.26629e10i	0.321371	−	0.0901950i
$709$	−8.57784e10	−	6.23217e10i	−0.339463	−	0.246635i	0.404972	−	0.914329i	$-0.367281\pi$
$709$	−8.57784e10	−	6.23217e10i	−0.339463	−	0.246635i	−0.744435	+	0.667694i	$0.767281\pi$
$710$	−4.49506e11	−	1.26520e11i	−1.76889	−	0.497880i
$711$	−8.98487e10	−	1.23666e11i	−0.351588	−	0.483919i
$712$	−2.21725e10	−	2.29611e11i	−0.0862768	−	0.893456i
$713$	7.21437e10	+	5.24154e10i	0.279152	+	0.202815i
$714$	−2.43561e10	+	1.35890e11i	−0.0937164	+	0.522873i
$715$	2.40101e11	−	5.29717e10i	0.918691	−	0.202684i
$716$	−1.23992e11	−	9.80036e10i	−0.471783	−	0.372898i
$717$	1.10036e9	+	3.38656e9i	0.00416350	+	0.0128139i
$718$	−1.48526e11	−	1.54673e11i	−0.558861	−	0.581990i
$719$	−4.87739e11	+	1.58476e11i	−1.82504	+	0.592991i	−0.825446	+	0.564481i	$0.809076\pi$
$719$	−4.87739e11	+	1.58476e11i	−1.82504	+	0.592991i	−0.999594	+	0.0285102i	$0.990924\pi$
$720$	2.04833e11	−	9.90010e10i	0.762201	−	0.368392i
$721$	1.55692e11	−	4.79172e11i	0.576137	−	1.77317i
$722$	−7.63334e10	−	1.57632e11i	−0.280909	−	0.580092i
$723$	−1.03069e11	−	1.41862e11i	−0.377202	−	0.519174i
$724$	−2.56153e9	+	6.31477e10i	−0.00932277	+	0.229828i
$725$	1.68313e10	+	1.39435e11i	0.0609206	+	0.504684i
$726$	−5.59706e10	−	5.82870e10i	−0.201471	−	0.209810i
$727$	2.17445e11	+	2.99288e11i	0.778416	+	1.07140i	0.995455	+	0.0952352i	$0.0303603\pi$
$727$	2.17445e11	+	2.99288e11i	0.778416	+	1.07140i	−0.217038	+	0.976163i	$0.569640\pi$
$728$	1.33198e11	+	3.06105e11i	0.474212	+	1.08980i
$729$	1.68845e10	−	5.19653e10i	0.0597832	−	0.183994i
$730$	8.78139e10	−	6.93015e10i	0.309223	−	0.244035i
$731$	−1.43097e11	+	4.64949e10i	−0.501141	+	0.162831i
$732$	5.80620e10	+	2.35523e9i	0.202231	+	0.00820331i
$733$	−3.54322e10	−	1.09049e11i	−0.122739	−	0.377752i	0.870743	−	0.491738i	$-0.163638\pi$
$733$	−3.54322e10	−	1.09049e11i	−0.122739	−	0.377752i	−0.993482	+	0.113986i	$0.963638\pi$
$734$	5.06001e10	+	3.67550e11i	0.174328	+	1.26629i
$735$	1.97222e10	−	2.02652e11i	0.0675782	−	0.694389i
$736$	−4.34526e11	−	1.14865e11i	−1.48083	−	0.391450i
$737$	−3.48854e11	−	2.53458e11i	−1.18243	−	0.859083i
$738$	3.43139e11	−	4.72395e10i	1.15676	−	0.159250i
$739$	−7.38987e10	−	1.01713e11i	−0.247776	−	0.341034i	0.666955	−	0.745098i	$-0.267597\pi$
$739$	−7.38987e10	−	1.01713e11i	−0.247776	−	0.341034i	−0.914731	+	0.404064i	$0.867597\pi$
$740$	3.28107e11	−	3.41175e11i	1.09418	−	1.13776i
$741$	−4.05973e10	−	2.94957e10i	−0.134656	−	0.0978331i
$742$	1.30776e10	−	2.44291e10i	0.0431433	−	0.0805920i
$743$			2.43343e11i			0.798479i	0.916847	+	0.399240i	$0.130726\pi$
$743$			2.43343e11i			0.798479i	−0.916847	+	0.399240i	$0.869274\pi$
$744$	1.37164e10	−	2.33004e10i	0.0447660	−	0.0760452i
$745$	9.44091e10	+	4.27921e11i	0.306471	+	1.38912i
$746$	−3.59581e10	−	7.42553e10i	−0.116102	−	0.239758i
$747$	3.13271e11	+	1.01788e11i	1.00609	+	0.326900i
$748$	2.79643e11	−	1.86337e11i	0.893300	−	0.595242i
$749$	4.80519e9			0.0152680
$750$	1.22360e11	−	1.97367e10i	0.386717	−	0.0623776i
$751$			3.20021e11i			1.00605i	0.864272	+	0.503025i	$0.167779\pi$
$751$			3.20021e11i			1.00605i	−0.864272	+	0.503025i	$0.832221\pi$
$752$	−1.33256e11	−	2.18701e11i	−0.416693	−	0.683879i
$753$	−3.64708e10	+	1.12245e11i	−0.113440	+	0.349131i
$754$	−5.10345e10	−	1.05389e11i	−0.157899	−	0.326069i
$755$	−2.04167e11	+	4.50440e10i	−0.628345	+	0.138627i
$756$	3.79369e11	−	1.06472e11i	1.16138	−	0.325949i
$757$	3.00113e11			0.913907			0.456953	−	0.889491i	$-0.348941\pi$
$757$	3.00113e11			0.913907			0.456953	+	0.889491i	$0.348941\pi$
$758$	−2.81856e10	+	5.26509e10i	−0.0853788	+	0.159488i
$759$	−1.54498e11	+	2.12649e11i	−0.465540	+	0.640761i
$760$	1.98910e11	+	1.48815e8i	0.596214	+	0.000446058i
$761$	2.96781e11	−	2.15624e11i	0.884906	−	0.642922i	−0.0496389	−	0.998767i	$-0.515807\pi$
$761$	2.96781e11	−	2.15624e11i	0.884906	−	0.642922i	0.934545	+	0.355845i	$0.115807\pi$
$762$	5.14784e10	−	7.08697e9i	0.152688	−	0.0210204i
$763$	3.83210e11	−	5.27444e11i	1.13068	−	1.55624i
$764$	4.28282e11	−	2.85381e11i	1.25706	−	0.837630i
$765$	2.34662e11	+	2.28374e10i	0.685167	+	0.0666808i
$766$	−5.82818e10	−	4.23348e11i	−0.169285	−	1.22965i
$767$	1.99886e11	−	6.49469e10i	0.577565	−	0.187662i
$768$	−2.20026e10	+	1.34487e11i	−0.0632454	+	0.386576i
$769$	−3.92598e10	−	1.20829e11i	−0.112265	−	0.345515i	0.879102	−	0.476633i	$-0.158143\pi$
$769$	−3.92598e10	−	1.20829e11i	−0.112265	−	0.345515i	−0.991367	+	0.131119i	$0.958143\pi$
$770$	−6.07477e11	+	4.79412e11i	−1.72809	+	1.36379i
$771$	−5.62349e9	−	1.82718e9i	−0.0159143	−	0.00517088i
$772$	−1.52770e11	−	5.65808e10i	−0.430101	−	0.159294i
$773$	3.55020e11	−	2.57937e11i	0.994338	−	0.722429i	0.0334716	−	0.999440i	$-0.489344\pi$
$773$	3.55020e11	−	2.57937e11i	0.994338	−	0.722429i	0.960867	+	0.277010i	$0.0893437\pi$
$774$	1.36361e11	+	1.42004e11i	0.379949	+	0.395674i
$775$	−5.95485e10	+	5.53028e10i	−0.165068	+	0.153299i
$776$	−3.99540e11	−	4.51349e11i	−1.10183	−	1.24470i
$777$	3.04066e11	−	2.20917e11i	0.834225	−	0.606100i
$778$	3.07901e10	+	6.35830e10i	0.0840412	+	0.173549i
$779$	2.88020e11	+	9.35834e10i	0.782120	+	0.254126i
$780$	−9.11378e10	+	4.87010e10i	−0.246218	+	0.131571i
$781$	2.78894e11	+	8.58349e11i	0.749610	+	2.30706i
$782$	−3.22616e11	−	3.35968e11i	−0.862697	−	0.898401i
$783$	−1.31446e11	+	4.27094e10i	−0.349704	+	0.113626i
$784$	−5.10555e11	−	4.38306e11i	−1.35138	−	1.16015i
$785$	−7.23300e10	−	3.27845e11i	−0.190476	−	0.863355i
$786$	9.18006e9	−	5.12184e10i	0.0240522	−	0.134195i
$787$	−1.83698e11	+	2.52839e11i	−0.478858	+	0.659091i	−0.978285	−	0.207265i	$-0.933544\pi$
$787$	−1.83698e11	+	2.52839e11i	−0.478858	+	0.659091i	0.499427	+	0.866356i	$0.333544\pi$
$788$	−1.66438e11	+	2.10574e11i	−0.431664	+	0.546134i
$789$	−1.45708e11	+	1.05863e11i	−0.375990	+	0.273173i
$790$	−2.64917e11	−	7.45646e10i	−0.680146	−	0.191436i
$791$	6.85670e11	−	9.43744e11i	1.75150	−	2.41073i
$792$	−3.78917e11	−	2.23060e11i	−0.963039	−	0.566918i
$793$	1.45620e11			0.368237
$794$	3.55881e11	+	1.90514e11i	0.895413	+	0.479341i
$795$	7.86228e9	+	3.42817e9i	0.0196825	+	0.00858211i
$796$	1.45228e9	−	3.92121e9i	0.00361742	−	0.00976716i
$797$	1.52170e11	−	4.68330e11i	0.377133	−	1.16070i	−0.564895	−	0.825163i	$-0.691083\pi$
$797$	1.52170e11	−	4.68330e11i	0.377133	−	1.16070i	0.942028	−	0.335534i	$-0.108917\pi$
$798$	1.55462e11	+	2.78640e10i	0.383365	+	0.0687119i
$799$		−	2.65407e11i		−	0.651216i
$800$	1.79070e11	−	3.68383e11i	0.437183	−	0.899372i
$801$	−3.12806e11			−0.759881
$802$	−1.24795e11	+	6.96272e11i	−0.301649	+	1.68299i
$803$	−2.05623e11	−	6.68109e10i	−0.494548	−	0.160689i
$804$	1.69943e11	+	6.29408e10i	0.406704	+	0.150629i
$805$	8.02645e11	+	7.11584e11i	1.91135	+	1.69450i
$806$	3.19777e10	−	5.97347e10i	0.0757718	−	0.141542i
$807$		−	2.41648e11i		−	0.569756i
$808$	−2.22866e11	+	3.78588e11i	−0.522875	+	0.888221i
$809$	−2.27852e11	−	1.65544e11i	−0.531936	−	0.386474i	0.289146	−	0.957285i	$-0.406629\pi$
$809$	−2.27852e11	−	1.65544e11i	−0.531936	−	0.386474i	−0.821081	+	0.570811i	$0.806629\pi$
$810$	−8.40346e10	−	2.27419e11i	−0.195217	−	0.528307i
$811$	−1.65843e11	−	2.28263e11i	−0.383365	−	0.527657i	0.573107	−	0.819481i	$-0.305738\pi$
$811$	−1.65843e11	−	2.28263e11i	−0.383365	−	0.527657i	−0.956472	+	0.291824i	$0.905738\pi$
$812$	2.89134e11	+	2.28532e11i	0.665081	+	0.525681i
$813$	9.89099e9	+	7.18623e9i	0.0226401	+	0.0164490i
$814$	−9.00487e11	−	1.61398e11i	−2.05107	−	0.367620i
$815$	−1.71302e11	−	7.46923e10i	−0.388267	−	0.169295i
$816$	−9.19924e10	+	1.07156e11i	−0.207487	+	0.241689i
$817$	5.31913e10	+	1.63706e11i	0.119386	+	0.367432i
$818$	−2.00482e10	+	1.92515e10i	−0.0447778	+	0.0429982i
$819$	4.30525e11	−	1.39886e11i	0.956892	−	0.310913i
$820$	4.32273e11	−	4.49490e11i	0.956099	−	0.994179i
$821$	−1.10241e11	+	3.39287e11i	−0.242644	+	0.746783i	0.753370	+	0.657596i	$0.228427\pi$
$821$	−1.10241e11	+	3.39287e11i	−0.242644	+	0.746783i	−0.996015	+	0.0891866i	$0.971573\pi$
$822$	−2.17050e11	+	1.05106e11i	−0.475414	+	0.230219i
$823$	2.05208e11	+	2.82444e11i	0.447296	+	0.615650i	0.971814	−	0.235750i	$-0.0757545\pi$
$823$	2.05208e11	+	2.82444e11i	0.447296	+	0.615650i	−0.524518	+	0.851399i	$0.675754\pi$
$824$	3.85921e11	−	3.41622e11i	0.837123	−	0.741032i
$825$	−1.63009e11	−	1.75524e11i	−0.351881	−	0.378896i
$826$	−4.77132e11	+	4.58170e11i	−1.02499	+	0.984253i
$827$	−2.17317e11	−	2.99111e11i	−0.464591	−	0.639455i	0.510862	−	0.859663i	$-0.329326\pi$
$827$	−2.17317e11	−	2.99111e11i	−0.464591	−	0.639455i	−0.975453	+	0.220208i	$0.929326\pi$
$828$	−2.11674e11	+	5.71528e11i	−0.450346	+	1.21595i
$829$	−2.83105e10	+	8.71307e10i	−0.0599417	+	0.184482i	−0.976544	−	0.215319i	$-0.930921\pi$
$829$	−2.83105e10	+	8.71307e10i	−0.0599417	+	0.184482i	0.916602	+	0.399801i	$0.130921\pi$
$830$	5.56281e11	−	2.05554e11i	1.17215	−	0.433126i
$831$	−1.42495e11	+	4.62994e10i	−0.298810	+	0.0970892i
$832$	−4.14325e10	+	3.38975e11i	−0.0864664	+	0.707414i
$833$	−2.15490e11	−	6.63210e11i	−0.447556	−	1.37744i
$834$	−1.34415e11	+	1.85047e10i	−0.277833	+	0.0382489i
$835$	2.91036e11	+	4.95237e11i	0.598688	+	1.01875i
$836$	−2.13174e11	−	3.19918e11i	−0.436425	−	0.654958i
$837$	−6.46999e10	−	4.70073e10i	−0.131826	−	0.0957774i
$838$	−5.91603e10	−	4.29729e11i	−0.119965	−	0.871403i
$839$	2.70701e11	+	3.72588e11i	0.546313	+	0.751935i	0.989506	−	0.144491i	$-0.0461544\pi$
$839$	2.70701e11	+	3.72588e11i	0.546313	+	0.751935i	−0.443193	+	0.896426i	$0.646154\pi$
$840$	1.91363e11	−	2.62975e11i	0.384363	−	0.528199i
$841$	3.00124e11	+	2.18053e11i	0.599953	+	0.435892i
$842$	6.95341e11	+	3.72236e11i	1.38341	+	0.740577i
$843$			3.53787e11i			0.700537i
$844$	2.99879e10	+	1.06849e11i	0.0590984	+	0.210572i
$845$	2.16298e11	−	1.27112e11i	0.424253	−	0.249321i
$846$	−3.12559e11	+	1.51357e11i	−0.610170	+	0.295474i
$847$	6.06160e11	+	1.96953e11i	1.17775	+	0.382675i
$848$	2.42063e10	−	1.47491e10i	0.0468107	−	0.0285221i
$849$	1.39667e11			0.268821
$850$	3.57122e11	−	2.29457e11i	0.684134	−	0.439568i
$851$			1.26806e12i			2.41781i
$852$	−2.10328e11	−	3.15647e11i	−0.399152	−	0.599022i
$853$	−2.10517e11	+	6.47904e11i	−0.397640	+	1.22381i	0.529246	+	0.848468i	$0.322475\pi$
$853$	−2.10517e11	+	6.47904e11i	−0.397640	+	1.22381i	−0.926886	+	0.375342i	$0.877525\pi$
$854$	−4.12502e11	+	1.99754e11i	−0.775522	+	0.375546i
$855$	2.61265e10	−	2.68459e11i	0.0488897	−	0.502357i
$856$	4.23607e9	+	2.49367e9i	0.00788984	+	0.00464456i
$857$	−2.16483e11			−0.401329			−0.200665	−	0.979660i	$-0.564310\pi$
$857$	−2.16483e11			−0.401329			−0.200665	+	0.979660i	$0.564310\pi$
$858$	1.76073e11	+	9.42568e10i	0.324895	+	0.173926i
$859$	−4.08216e10	+	5.61862e10i	−0.0749752	+	0.103195i	−0.844858	−	0.534991i	$-0.820315\pi$
$859$	−4.08216e10	+	5.61862e10i	−0.0749752	+	0.103195i	0.769882	+	0.638186i	$0.220315\pi$
$860$	3.51107e11	+	4.86041e10i	0.641868	+	0.0888545i
$861$	4.00600e11	−	2.91053e11i	0.728950	−	0.529613i
$862$	3.69068e10	+	2.68084e11i	0.0668463	+	0.485559i
$863$	2.88471e11	−	3.97046e11i	0.520067	−	0.715810i	−0.465510	−	0.885043i	$-0.654129\pi$
$863$	2.88471e11	−	3.97046e11i	0.520067	−	0.715810i	0.985576	+	0.169233i	$0.0541289\pi$
$864$	3.89692e11	+	1.03013e11i	0.699305	+	0.184858i
$865$	1.74832e11	+	1.54997e11i	0.312288	+	0.276859i
$866$	−1.12006e11	+	1.54198e10i	−0.199146	+	0.0274162i
$867$	7.13050e10	−	2.31684e10i	0.126195	−	0.0410034i
$868$	−8.64330e9	+	2.13078e11i	−0.0152265	+	0.375369i
$869$	1.64367e11	+	5.05870e11i	0.288228	+	0.887074i
$870$	−6.33296e10	+	9.48869e10i	−0.110543	+	0.165626i
$871$	4.31910e11	+	1.40336e11i	0.750448	+	0.243835i
$872$	6.11543e11	−	2.66105e11i	1.05770	−	0.460244i
$873$	−6.61282e11	+	4.80449e11i	−1.13849	+	0.827162i
$874$	−3.84355e11	+	3.69080e11i	−0.658699	+	0.632521i
$875$	−7.77361e11	+	5.92712e11i	−1.32614	+	1.01114i
$876$	9.07896e10	+	3.68280e9i	0.154177	+	0.00625405i
$877$	6.50911e11	−	4.72914e11i	1.10033	−	0.799437i	0.119216	−	0.992868i	$-0.461962\pi$
$877$	6.50911e11	−	4.72914e11i	1.10033	−	0.799437i	0.981114	+	0.193432i	$0.0619618\pi$
$878$	−3.45915e11	+	1.67509e11i	−0.582091	+	0.281877i
$879$	−4.14961e11	−	1.34829e11i	−0.695107	−	0.225854i
$880$	−7.84322e11	+	1.07379e11i	−1.30787	+	0.179055i
$881$	−9.05303e10	−	2.78624e11i	−0.150276	−	0.462503i	0.847375	−	0.530994i	$-0.178181\pi$
$881$	−9.05303e10	−	2.78624e11i	−0.150276	−	0.462503i	−0.997652	+	0.0684915i	$0.978181\pi$
$882$	−6.58147e11	+	6.31991e11i	−1.08755	+	1.04433i
$883$	−4.72619e11	+	1.53563e11i	−0.777442	+	0.252606i	−0.670748	−	0.741686i	$-0.734027\pi$
$883$	−4.72619e11	+	1.53563e11i	−0.777442	+	0.252606i	−0.106694	+	0.994292i	$0.534027\pi$
$884$	−2.19455e11	+	2.77650e11i	−0.359365	+	0.454662i
$885$	−1.53217e11	−	1.35834e11i	−0.249767	−	0.221430i
$886$	9.10340e11	+	1.63164e11i	1.47730	+	0.264782i
$887$	−2.12789e11	+	2.92879e11i	−0.343760	+	0.473145i	−0.945535	−	0.325521i	$-0.894460\pi$
$887$	−2.12789e11	+	2.92879e11i	−0.343760	+	0.473145i	0.601775	+	0.798666i	$0.294460\pi$
$888$	3.82698e11	−	3.69554e10i	0.615467	−	0.0594328i
$889$	−3.31575e11	+	2.40903e11i	−0.530854	+	0.385688i
$890$	−4.42093e11	+	3.48894e11i	−0.704618	+	0.556075i
$891$	−2.75426e11	+	3.79091e11i	−0.437013	+	0.601496i
$892$	1.04649e11	+	3.72872e11i	0.165301	+	0.588980i
$893$	−3.03632e11			−0.477465
$894$	−1.67990e11	+	3.13806e11i	−0.262986	+	0.491260i
$895$	−3.73751e10	+	3.84042e11i	−0.0582493	+	0.598531i
$896$	−3.47620e11	−	1.01706e12i	−0.539353	−	1.57802i
$897$	8.55438e10	−	2.63277e11i	0.132135	−	0.406670i
$898$	2.19588e11	−	1.22515e12i	0.337678	−	1.88401i
$899$		−	7.48014e10i		−	0.114517i
$900$	−4.73884e11	−	2.89714e11i	−0.722273	−	0.441569i
$901$	2.93758e10			0.0445749
$902$	−1.18637e12	−	2.12638e11i	−1.79223	−	0.321228i
$903$	2.67671e11	+	8.69715e10i	0.402578	+	0.130805i
$904$	1.09422e12	−	4.76137e11i	1.63844	−	0.712949i
$905$	1.33026e11	−	7.81752e10i	0.198309	−	0.116540i
$906$	−1.49721e11	−	8.01503e10i	−0.222214	−	0.118958i
$907$		−	1.01888e12i		−	1.50554i	−0.658284	−	0.752770i	$-0.728717\pi$
$907$		−	1.01888e12i		−	1.50554i	0.658284	−	0.752770i	$-0.271283\pi$
$908$	−6.48393e10	−	2.31027e11i	−0.0953883	−	0.339875i
$909$	4.81949e11	+	3.50157e11i	0.705904	+	0.512869i
$910$	4.52442e11	−	6.77896e11i	0.659778	−	0.988547i
$911$	2.67461e11	+	3.68128e11i	0.388317	+	0.534472i	0.957764	−	0.287556i	$-0.0928426\pi$
$911$	2.67461e11	+	3.68128e11i	0.388317	+	0.534472i	−0.569447	+	0.822028i	$0.692843\pi$
$912$	1.22589e11	+	1.05242e11i	0.177204	+	0.152128i
$913$	−9.27281e11	−	6.73709e11i	−1.33453	−	0.969593i
$914$	1.14361e11	−	6.38055e11i	0.163868	−	0.914268i
$915$	−7.18792e10	−	1.22312e11i	−0.102546	−	0.174496i
$916$	2.41715e11	−	3.05813e11i	0.343338	−	0.434385i
$917$	1.26822e11	+	3.90319e11i	0.179357	+	0.552005i
$918$	2.89328e11	+	3.01303e11i	0.407399	+	0.424260i
$919$	−4.81197e11	+	1.56350e11i	−0.674623	+	0.219198i	−0.626240	−	0.779631i	$-0.715407\pi$
$919$	−4.81197e11	+	1.56350e11i	−0.674623	+	0.219198i	−0.0483831	+	0.998829i	$0.515407\pi$
$920$	3.38302e11	+	1.04384e12i	0.472229	+	1.45708i
$921$	1.16240e11	−	3.57749e11i	0.161553	−	0.497210i
$922$	−2.38051e11	−	4.91587e11i	−0.329417	−	0.680263i
$923$	−5.58697e11	−	7.68981e11i	−0.769785	−	1.05952i
$924$	−6.28063e11	−	2.54768e10i	−0.861618	−	0.0349508i
$925$	−1.13394e12	−	2.22821e11i	−1.54890	−	0.304362i
$926$	6.34023e11	+	6.60263e11i	0.862305	+	0.897993i
$927$	−4.10803e11	−	5.65421e11i	−0.556307	−	0.765690i
$928$	1.36292e11	+	3.51512e11i	0.183771	+	0.473967i
$929$	1.50975e11	−	4.64654e11i	0.202695	−	0.623831i	−0.797105	−	0.603841i	$-0.793636\pi$
$929$	1.50975e11	−	4.64654e11i	0.202695	−	0.623831i	0.999800	−	0.0199907i	$-0.00636368\pi$
$930$	−6.59582e10	+	2.62611e9i	−0.0881733	+	0.00351060i
$931$	−7.58729e11	+	2.46526e11i	−1.00992	+	0.328144i
$932$	−4.56367e10	+	1.12505e12i	−0.0604854	+	1.49111i
$933$	1.47548e11	+	4.54105e11i	0.194718	+	0.599280i
$934$	−7.43378e10	−	5.39976e11i	−0.0976837	−	0.709557i
$935$	−7.52027e11	−	3.27905e11i	−0.983981	−	0.429043i
$936$	4.52129e11	+	1.00105e11i	0.589059	+	0.130422i
$937$	−6.62004e11	−	4.80974e11i	−0.858821	−	0.623970i	0.0687432	−	0.997634i	$-0.478101\pi$
$937$	−6.62004e11	−	4.80974e11i	−0.858821	−	0.623970i	−0.927564	+	0.373665i	$0.878101\pi$
$938$	−1.41599e12	+	1.94937e11i	−1.82915	+	0.251816i
$939$	6.34150e10	+	8.72833e10i	0.0815699	+	0.112271i
$940$	−2.72926e11	+	5.62532e11i	−0.349569	+	0.720503i
$941$	7.30763e11	+	5.30930e11i	0.932005	+	0.677141i	0.946483	−	0.322754i	$-0.104609\pi$
$941$	7.30763e11	+	5.30930e11i	0.932005	+	0.677141i	−0.0144782	+	0.999895i	$0.504609\pi$
$942$	1.28703e11	−	2.40418e11i	0.163449	−	0.305325i
$943$			1.67064e12i			2.11269i
$944$	−6.58391e11	+	1.56295e11i	−0.829079	+	0.196815i
$945$	−7.19829e11	−	6.38164e11i	−0.902614	−	0.800211i
$946$	−2.98574e11	−	6.16571e11i	−0.372810	−	0.769872i
$947$	−9.31540e11	−	3.02676e11i	−1.15825	−	0.376338i	−0.334004	−	0.942572i	$-0.608400\pi$
$947$	−9.31540e11	−	3.02676e11i	−1.15825	−	0.376338i	−0.824244	+	0.566234i	$0.808400\pi$
$948$	−1.23957e11	−	1.86027e11i	−0.153476	−	0.230326i
$949$	2.27701e11			0.280737
$950$	−2.62505e11	−	4.08557e11i	−0.322287	−	0.501600i
$951$			3.00037e11i			0.366820i
$952$	2.40791e11	−	1.08754e12i	0.293151	−	1.32403i
$953$	2.10943e11	−	6.49217e11i	0.255737	−	0.787079i	−0.737946	−	0.674860i	$-0.764204\pi$
$953$	2.10943e11	−	6.49217e11i	0.255737	−	0.787079i	0.993683	−	0.112219i	$-0.0357958\pi$
$954$	−1.67525e10	−	3.45948e10i	−0.0202249	−	0.0417654i
$955$	−1.15175e12	−	5.02196e11i	−1.38467	−	0.603754i
$956$	−7.76334e9	−	2.76613e10i	−0.00929431	−	0.0331163i
$957$	2.20483e11			0.262862
$958$	−4.81063e10	+	8.98630e10i	−0.0571136	+	0.106689i
$959$	1.11801e12	−	1.53881e12i	1.32181	−	1.81932i
$960$	3.05171e11	−	1.32520e11i	0.359301	−	0.156026i
$961$	−6.54987e11	+	4.75876e11i	−0.767961	+	0.557956i
$962$	9.54480e11	−	1.31402e11i	1.11447	−	0.153427i
$963$	3.91795e9	−	5.39259e9i	0.00455568	−	0.00627036i
$964$	7.84520e11	+	1.17736e12i	0.908439	+	1.36333i
$965$	8.56884e10	+	3.88393e11i	0.0988127	+	0.447881i
$966$	1.18827e11	+	8.63136e11i	0.136460	+	0.991221i
$967$	−1.79420e11	+	5.82972e10i	−0.205194	+	0.0666717i	−0.409811	−	0.912171i	$-0.634405\pi$
$967$	−1.79420e11	+	5.82972e10i	−0.205194	+	0.0666717i	0.204616	+	0.978842i	$0.434405\pi$
$968$	4.32158e11	+	4.88196e11i	0.492199	+	0.556023i
$969$	5.17412e10	+	1.59243e11i	0.0586870	+	0.180620i
$970$	−3.98721e11	+	1.41660e12i	−0.450383	+	1.60014i
$971$	8.53786e11	+	2.77412e11i	0.960445	+	0.312067i	0.746952	−	0.664877i	$-0.231516\pi$
$971$	8.53786e11	+	2.77412e11i	0.960445	+	0.312067i	0.213492	+	0.976945i	$0.431516\pi$
$972$	2.92638e11	−	7.90133e11i	0.327843	−	0.885188i
$973$	8.65774e11	−	6.29022e11i	0.965947	−	0.701801i
$974$	9.07350e11	+	9.44902e11i	1.00818	+	1.04991i
$975$	2.20399e11	+	1.22758e11i	0.243888	+	0.135842i
$976$	−4.67309e11	−	3.79744e10i	−0.514997	−	0.0418496i
$977$	−4.15512e11	+	3.01887e11i	−0.456043	+	0.331334i	−0.791977	−	0.610551i	$-0.790948\pi$
$977$	−4.15512e11	+	3.01887e11i	−0.456043	+	0.331334i	0.335934	+	0.941885i	$0.390948\pi$
$978$	−6.61571e10	−	1.36618e11i	−0.0723138	−	0.149332i
$979$	1.03519e12	+	3.36355e11i	1.12691	+	0.366157i
$980$	−2.25266e11	+	1.62728e12i	−0.244225	+	1.76424i
$981$	−2.79467e11	−	8.60111e11i	−0.301755	−	0.928707i
$982$	−5.52677e11	−	5.75550e11i	−0.594327	−	0.618924i
$983$	6.62840e11	−	2.15370e11i	0.709896	−	0.230659i	0.0682591	−	0.997668i	$-0.478256\pi$
$983$	6.62840e11	−	2.15370e11i	0.709896	−	0.230659i	0.641637	+	0.767008i	$0.278256\pi$
$984$	5.04196e11	−	4.86879e10i	0.537798	−	0.0519327i
$985$	6.52211e11	+	6.34735e10i	0.692856	+	0.0674291i
$986$	−6.89299e10	+	3.84581e11i	−0.0729290	+	0.406893i
$987$	−2.91811e11	+	4.01644e11i	−0.307492	+	0.423226i
$988$	3.17639e11	+	2.51062e11i	0.333354	+	0.263483i
$989$	−7.68214e11	+	5.58140e11i	−0.802966	+	0.583389i
$990$	4.27065e10	+	1.07263e12i	0.0444583	+	1.11663i
$991$	1.79545e11	−	2.47122e11i	0.186157	−	0.256223i	−0.705731	−	0.708480i	$-0.749381\pi$
$991$	1.79545e11	−	2.47122e11i	0.186157	−	0.256223i	0.891887	+	0.452257i	$0.149381\pi$
$992$	−1.18197e11	+	1.83356e11i	−0.122056	+	0.189342i
$993$	4.45363e11			0.458054
$994$	2.63749e12	+	1.41192e12i	2.70175	+	1.44632i
$995$	−9.96903e9	+	2.19940e9i	−0.0101709	+	0.00224394i
$996$	4.51721e11	+	1.67302e11i	0.459021	+	0.170005i
$997$	−5.34463e11	+	1.64491e12i	−0.540925	+	1.66480i	0.189560	+	0.981869i	$0.439294\pi$
$997$	−5.34463e11	+	1.64491e12i	−0.540925	+	1.66480i	−0.730486	+	0.682928i	$0.760706\pi$
$998$	7.69071e11	+	1.37843e11i	0.775255	+	0.138952i
$999$		−	1.13722e12i		−	1.14178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.51	yes	464
4.3	odd	2	inner	100.9.j.b.11.4	✓	464
25.16	even	5	inner	100.9.j.b.91.4	yes	464
100.91	odd	10	inner	100.9.j.b.91.51	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.4	✓	464	4.3	odd	2	inner
100.9.j.b.11.51	yes	464	1.1	even	1	trivial
100.9.j.b.91.4	yes	464	25.16	even	5	inner
100.9.j.b.91.51	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+(-2.82276 + 15.7490i) q^{2} +(30.1760 + 9.80478i) q^{3} +(-240.064 - 88.9114i) q^{4} +(134.651 + 610.323i) q^{5} +(-239.595 + 447.567i) q^{6} -4004.03i q^{7} +(2077.91 - 3529.80i) q^{8} +(-4493.50 - 3264.72i) q^{9} +(-9992.08 + 397.832i) q^{10} +(11360.2 + 15636.0i) q^{11} +(-6372.42 - 5036.77i) q^{12} +(-16467.4 - 11964.3i) q^{13} +(63059.6 + 11302.4i) q^{14} +(-1920.85 + 19737.3i) q^{15} +(49725.5 + 42688.9i) q^{16} +(20987.7 + 64593.4i) q^{17} +(64100.3 - 61552.8i) q^{18} +(73896.4 - 24010.4i) q^{19} +(21939.8 - 158489. i) q^{20} +(39258.7 - 120826. i) q^{21} +(-278318. + 134775. i) q^{22} +(251943. + 346769. i) q^{23} +(97312.0 - 86141.9i) q^{24} +(-354363. + 164361. i) q^{25} +(234909. - 225573. i) q^{26} +(-225947. - 310990. i) q^{27} +(-356004. + 961224. i) q^{28} +(111105. - 341947. i) q^{29} +(-305422. - 85965.2i) q^{30} +(197863. - 64289.5i) q^{31} +(-812671. + 662629. i) q^{32} +(189498. + 583215. i) q^{33} +(-1.07653e6 + 148204. i) q^{34} +(2.44375e6 - 539147. i) q^{35} +(788458. + 1.18327e6i) q^{36} +(2.39339e6 + 1.73890e6i) q^{37} +(169549. + 1.23157e6i) q^{38} +(-379613. - 522493. i) q^{39} +(2.43411e6 + 792905. i) q^{40} +(3.15324e6 + 2.29096e6i) q^{41} +(1.79207e6 + 959348. i) q^{42} +2.21535e6i q^{43} +(-1.33696e6 - 4.76368e6i) q^{44} +(1.38748e6 - 3.18209e6i) q^{45} +(-6.17246e6 + 2.98901e6i) q^{46} +(-3.71652e6 - 1.20757e6i) q^{47} +(1.08196e6 + 1.77573e6i) q^{48} -1.02675e7 q^{49} +(-1.58825e6 - 6.04483e6i) q^{50} +2.15495e6i q^{51} +(2.88947e6 + 4.33633e6i) q^{52} +(133657. - 411353. i) q^{53} +(5.53559e6 - 2.68061e6i) q^{54} +(-8.01332e6 + 9.03878e6i) q^{55} +(-1.41334e7 - 8.32002e6i) q^{56} +2.46532e6 q^{57} +(5.07171e6 + 2.71503e6i) q^{58} +(-6.06914e6 + 8.35346e6i) q^{59} +(2.21600e6 - 4.56744e6i) q^{60} +(-5.78776e6 + 4.20506e6i) q^{61} +(453979. + 3.29762e6i) q^{62} +(-1.30720e7 + 1.79921e7i) q^{63} +(-8.14179e6 - 1.46692e7i) q^{64} +(5.08471e6 - 1.16614e7i) q^{65} +(-9.71998e6 + 1.33814e6i) q^{66} +(-2.12190e7 + 6.89449e6i) q^{67} +(704704. - 1.73726e7i) q^{68} +(4.20263e6 + 1.29344e7i) q^{69} +(1.59293e6 + 4.00086e7i) q^{70} +(4.44116e7 + 1.44302e7i) q^{71} +(-2.08609e7 + 9.07737e6i) q^{72} +(-9.05014e6 + 6.57531e6i) q^{73} +(-3.41420e7 + 3.27851e7i) q^{74} +(-1.23048e7 + 1.48532e6i) q^{75} +(-1.98747e7 - 806198. i) q^{76} +(6.26069e7 - 4.54866e7i) q^{77} +(9.30032e6 - 4.50367e6i) q^{78} +(2.61741e7 + 8.50449e6i) q^{79} +(-1.93584e7 + 3.60967e7i) q^{80} +(7.49207e6 + 2.30582e7i) q^{81} +(-4.49813e7 + 4.31937e7i) q^{82} +(-5.64019e7 + 1.83261e7i) q^{83} +(-2.01674e7 + 2.55154e7i) q^{84} +(-3.65968e7 + 2.15068e7i) q^{85} +(-3.48895e7 - 6.25338e6i) q^{86} +(6.70543e6 - 9.22924e6i) q^{87} +(7.87973e7 - 7.60909e6i) q^{88} +(4.55623e7 - 3.31030e7i) q^{89} +(4.61983e7 + 3.08337e7i) q^{90} +(-4.79053e7 + 6.59360e7i) q^{91} +(-2.96506e7 - 1.05647e8i) q^{92} +6.60105e6 q^{93} +(2.95089e7 - 5.51229e7i) q^{94} +(2.46043e7 + 4.18676e7i) q^{95} +(-3.10201e7 + 1.20274e7i) q^{96} +(4.54762e7 - 1.39961e8i) q^{97} +(2.89826e7 - 1.61703e8i) q^{98} -1.07348e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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