LMFDB - Embedded newform 100.9.j.b.11.85

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			11.85
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.85

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.6807 - 11.9131i) q^{2} +(23.9193 + 7.77186i) q^{3} +(-27.8462 - 254.481i) q^{4} +(-439.267 - 444.600i) q^{5} +(348.062 - 201.946i) q^{6} -3464.57i q^{7} +(-3329.09 - 2386.29i) q^{8} +(-4796.23 - 3484.66i) q^{9} +(-9988.26 + 484.430i) q^{10} +(1192.15 + 1640.85i) q^{11} +(1311.73 - 6303.43i) q^{12} +(8835.97 + 6419.71i) q^{13} +(-41274.0 - 37004.0i) q^{14} +(-7051.61 - 14048.5i) q^{15} +(-63985.2 + 14172.7i) q^{16} +(31685.0 + 97516.3i) q^{17} +(-92740.3 + 19919.6i) q^{18} +(162540. - 52812.3i) q^{19} +(-100910. + 124166. i) q^{20} +(26926.2 - 82870.2i) q^{21} +(32280.7 + 3323.17i) q^{22} +(-56834.9 - 78226.6i) q^{23} +(-61083.5 - 82951.7i) q^{24} +(-4713.17 + 390597. i) q^{25} +(170853. - 36697.4i) q^{26} +(-184631. - 254123. i) q^{27} +(-881668. + 96475.2i) q^{28} +(-98761.9 + 303958. i) q^{29} +(-242677. - 66040.1i) q^{30} +(-803046. + 260926. i) q^{31} +(-514564. + 913639. i) q^{32} +(15762.9 + 48513.4i) q^{33} +(1.50014e6 + 664073. i) q^{34} +(-1.54035e6 + 1.52187e6i) q^{35} +(-753224. + 1.31758e6i) q^{36} +(1.01903e6 + 740371. i) q^{37} +(1.10687e6 - 2.50043e6i) q^{38} +(161457. + 222227. i) q^{39} +(401413. + 2.52833e6i) q^{40} +(-2.18509e6 - 1.58756e6i) q^{41} +(-699656. - 1.20589e6i) q^{42} -5.79619e6i q^{43} +(384370. - 349071. i) q^{44} +(557546. + 3.66310e6i) q^{45} +(-1.53896e6 - 158430. i) q^{46} +(-3.45085e6 - 1.12125e6i) q^{47} +(-1.64063e6 - 158283. i) q^{48} -6.23846e6 q^{49} +(4.60289e6 + 4.22799e6i) q^{50} +2.57877e6i q^{51} +(1.38765e6 - 2.42735e6i) q^{52} +(-1.99603e6 + 6.14316e6i) q^{53} +(-4.99939e6 - 514668. i) q^{54} +(205851. - 1.25080e6i) q^{55} +(-8.26749e6 + 1.15339e7i) q^{56} +4.29829e6 q^{57} +(2.56625e6 + 4.42304e6i) q^{58} +(9.22018e6 - 1.26905e7i) q^{59} +(-3.37870e6 + 2.18570e6i) q^{60} +(1.63904e6 - 1.19083e6i) q^{61} +(-5.46864e6 + 1.23537e7i) q^{62} +(-1.20729e7 + 1.66169e7i) q^{63} +(5.38842e6 + 1.58884e7i) q^{64} +(-1.02715e6 - 6.74844e6i) q^{65} +(746306. + 330369. i) q^{66} +(7.74657e6 - 2.51701e6i) q^{67} +(2.39337e7 - 1.07787e7i) q^{68} +(-751487. - 2.31284e6i) q^{69} +(1.67834e6 + 3.46051e7i) q^{70} +(6.69742e6 + 2.17612e6i) q^{71} +(7.65163e6 + 2.30460e7i) q^{72} +(-1.94672e7 + 1.41437e7i) q^{73} +(1.97041e7 - 4.23223e6i) q^{74} +(-3.14840e6 + 9.30617e6i) q^{75} +(-1.79658e7 - 3.98926e7i) q^{76} +(5.68486e6 - 4.13029e6i) q^{77} +(4.37190e6 + 450070. i) q^{78} +(4.62870e7 + 1.50396e7i) q^{79} +(3.44078e7 + 2.22222e7i) q^{80} +(9.57848e6 + 2.94795e7i) q^{81} +(-4.22511e7 + 9.07508e6i) q^{82} +(-8.40252e7 + 2.73014e7i) q^{83} +(-2.18387e7 - 4.54458e6i) q^{84} +(2.94376e7 - 5.69229e7i) q^{85} +(-6.90509e7 - 6.19072e7i) q^{86} +(-4.72463e6 + 6.50290e6i) q^{87} +(-53211.1 - 8.30737e6i) q^{88} +(1.73204e7 - 1.25840e7i) q^{89} +(4.95940e7 + 3.24823e7i) q^{90} +(2.22415e7 - 3.06129e7i) q^{91} +(-1.83245e7 + 1.66417e7i) q^{92} -2.12362e7 q^{93} +(-5.02151e7 + 2.91348e7i) q^{94} +(-9.48787e7 - 4.90664e7i) q^{95} +(-1.94087e7 + 1.78545e7i) q^{96} +(-4.13620e6 + 1.27299e7i) q^{97} +(-6.66310e7 + 7.43198e7i) q^{98} -1.20242e7i 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 $

$2$	10.6807	−	11.9131i	0.667542	−	0.744572i
$2$	10.6807	−	11.9131i	0.667542	−	0.744572i
$3$	23.9193	+	7.77186i	0.295300	+	0.0959489i	0.452920	−	0.891551i	$-0.350382\pi$
$3$	23.9193	+	7.77186i	0.295300	+	0.0959489i	−0.157620	+	0.987500i	$0.550382\pi$
$4$	−27.8462	−	254.481i	−0.108774	−	0.994066i
$5$	−439.267	−	444.600i	−0.702828	−	0.711360i
$5$	−439.267	−	444.600i	−0.702828	−	0.711360i
$6$	348.062	−	201.946i	0.268566	−	0.155822i
$7$		−	3464.57i		−	1.44297i	−0.692430	−	0.721485i	$-0.743460\pi$
$7$		−	3464.57i		−	1.44297i	0.692430	−	0.721485i	$-0.256540\pi$
$8$	−3329.09	−	2386.29i	−0.812765	−	0.582591i
$9$	−4796.23	−	3484.66i	−0.731021	−	0.531118i
$10$	−9988.26	+	484.430i	−0.998826	+	0.0484430i
$11$	1192.15	+	1640.85i	0.0814255	+	0.112073i	0.847787	−	0.530337i	$-0.177935\pi$
$11$	1192.15	+	1640.85i	0.0814255	+	0.112073i	−0.766361	+	0.642410i	$0.777935\pi$
$12$	1311.73	−	6303.43i	0.0632585	−	0.303985i
$13$	8835.97	+	6419.71i	0.309372	+	0.224772i	0.731627	−	0.681705i	$-0.238761\pi$
$13$	8835.97	+	6419.71i	0.309372	+	0.224772i	−0.422255	+	0.906477i	$0.638761\pi$
$14$	−41274.0	−	37004.0i	−1.07440	−	0.963244i
$15$	−7051.61	−	14048.5i	−0.139291	−	0.277500i
$16$	−63985.2	+	14172.7i	−0.976336	+	0.216258i
$17$	31685.0	+	97516.3i	0.379365	+	1.16757i	0.940486	+	0.339832i	$0.110370\pi$
$17$	31685.0	+	97516.3i	0.379365	+	1.16757i	−0.561121	+	0.827734i	$0.689630\pi$
$18$	−92740.3	+	19919.6i	−0.883443	+	0.189754i
$19$	162540.	−	52812.3i	1.24722	−	0.405248i	0.390299	−	0.920688i	$-0.372372\pi$
$19$	162540.	−	52812.3i	1.24722	−	0.405248i	0.856926	+	0.515440i	$0.172372\pi$
$20$	−100910.	+	124166.i	−0.630689	+	0.776035i
$21$	26926.2	−	82870.2i	0.138451	−	0.426110i
$22$	32280.7	+	3323.17i	0.137801	+	0.0141861i
$23$	−56834.9	−	78226.6i	−0.203097	−	0.279539i	0.695303	−	0.718716i	$-0.255270\pi$
$23$	−56834.9	−	78226.6i	−0.203097	−	0.279539i	−0.898401	+	0.439177i	$0.855270\pi$
$24$	−61083.5	−	82951.7i	−0.184111	−	0.250023i
$25$	−4713.17	+	390597.i	−0.0120657	+	0.999927i
$26$	170853.	−	36697.4i	0.373878	−	0.0803048i
$27$	−184631.	−	254123.i	−0.347416	−	0.478177i
$28$	−881668.	+	96475.2i	−1.43441	+	0.156958i
$29$	−98761.9	+	303958.i	−0.139636	+	0.429755i	−0.996282	−	0.0861489i	$-0.972544\pi$
$29$	−98761.9	+	303958.i	−0.139636	+	0.429755i	0.856646	+	0.515904i	$0.172544\pi$
$30$	−242677.	−	66040.1i	−0.299602	−	0.0815310i
$31$	−803046.	+	260926.i	−0.869549	+	0.282533i	−0.709611	−	0.704594i	$-0.751129\pi$
$31$	−803046.	+	260926.i	−0.869549	+	0.282533i	−0.159938	+	0.987127i	$0.551129\pi$
$32$	−514564.	+	913639.i	−0.490727	+	0.871314i
$33$	15762.9	+	48513.4i	0.0132917	+	0.0409077i
$34$	1.50014e6	+	664073.i	1.12258	+	0.496935i
$35$	−1.54035e6	+	1.52187e6i	−1.02647	+	1.01416i
$36$	−753224.	+	1.31758e6i	−0.448450	+	0.784455i
$37$	1.01903e6	+	740371.i	0.543728	+	0.395041i	0.825468	−	0.564449i	$-0.190911\pi$
$37$	1.01903e6	+	740371.i	0.543728	+	0.395041i	−0.281740	+	0.959491i	$0.590911\pi$
$38$	1.10687e6	−	2.50043e6i	0.530839	−	1.19917i
$39$	161457.	+	222227.i	0.0697910	+	0.0960591i
$40$	401413.	+	2.52833e6i	0.156802	+	0.987630i
$41$	−2.18509e6	−	1.58756e6i	−0.773275	−	0.561817i	0.129678	−	0.991556i	$-0.458606\pi$
$41$	−2.18509e6	−	1.58756e6i	−0.773275	−	0.561817i	−0.902953	+	0.429739i	$0.858606\pi$
$42$	−699656.	−	1.20589e6i	−0.224847	−	0.387533i
$43$		−	5.79619e6i		−	1.69539i	−0.530487	−	0.847693i	$-0.677991\pi$
$43$		−	5.79619e6i		−	1.69539i	0.530487	−	0.847693i	$-0.322009\pi$
$44$	384370.	−	349071.i	0.102551	−	0.0931330i
$45$	557546.	+	3.66310e6i	0.135966	+	0.893303i
$46$	−1.53896e6	−	158430.i	−0.343713	−	0.0353839i
$47$	−3.45085e6	−	1.12125e6i	−0.707188	−	0.229779i	−0.0667287	−	0.997771i	$-0.521256\pi$
$47$	−3.45085e6	−	1.12125e6i	−0.707188	−	0.229779i	−0.640460	+	0.767992i	$0.721256\pi$
$48$	−1.64063e6	−	158283.i	−0.309062	−	0.0298174i
$49$	−6.23846e6			−1.08216
$50$	4.60289e6	+	4.22799e6i	0.736463	+	0.676478i
$51$			2.57877e6i			0.381182i
$52$	1.38765e6	−	2.42735e6i	0.189786	−	0.331986i
$53$	−1.99603e6	+	6.14316e6i	−0.252967	+	0.778553i	0.741256	+	0.671222i	$0.234230\pi$
$53$	−1.99603e6	+	6.14316e6i	−0.252967	+	0.778553i	−0.994223	+	0.107331i	$0.965770\pi$
$54$	−4.99939e6	−	514668.i	−0.587952	−	0.0605274i
$55$	205851.	−	1.25080e6i	0.0224958	−	0.136691i
$56$	−8.26749e6	+	1.15339e7i	−0.840662	+	1.17280i
$57$	4.29829e6			0.407189
$58$	2.56625e6	+	4.42304e6i	0.226771	+	0.390849i
$59$	9.22018e6	−	1.26905e7i	0.760907	−	1.04730i	−0.236231	−	0.971697i	$-0.575912\pi$
$59$	9.22018e6	−	1.26905e7i	0.760907	−	1.04730i	0.997138	−	0.0756014i	$-0.0240877\pi$
$60$	−3.37870e6	+	2.18570e6i	−0.260702	+	0.168650i
$61$	1.63904e6	−	1.19083e6i	0.118377	−	0.0860062i	−0.527021	−	0.849852i	$-0.676691\pi$
$61$	1.63904e6	−	1.19083e6i	0.118377	−	0.0860062i	0.645399	+	0.763846i	$0.276691\pi$
$62$	−5.46864e6	+	1.23537e7i	−0.370094	+	0.836044i
$63$	−1.20729e7	+	1.66169e7i	−0.766387	+	1.05484i
$64$	5.38842e6	+	1.58884e7i	0.321175	+	0.947020i
$65$	−1.02715e6	−	6.74844e6i	−0.0575415	−	0.378051i
$66$	746306.	+	330369.i	0.0393316	+	0.0174110i
$67$	7.74657e6	−	2.51701e6i	0.384424	−	0.124907i	−0.110428	−	0.993884i	$-0.535222\pi$
$67$	7.74657e6	−	2.51701e6i	0.384424	−	0.124907i	0.494852	+	0.868977i	$0.335222\pi$
$68$	2.39337e7	−	1.07787e7i	1.11937	−	0.504115i
$69$	−751487.	−	2.31284e6i	−0.0331532	−	0.102035i
$70$	1.67834e6	+	3.46051e7i	0.0699018	+	1.44128i
$71$	6.69742e6	+	2.17612e6i	0.263557	+	0.0856348i	0.437815	−	0.899065i	$-0.355753\pi$
$71$	6.69742e6	+	2.17612e6i	0.263557	+	0.0856348i	−0.174258	+	0.984700i	$0.555753\pi$
$72$	7.65163e6	+	2.30460e7i	0.284724	+	0.857561i
$73$	−1.94672e7	+	1.41437e7i	−0.685507	+	0.498050i	−0.875180	−	0.483797i	$-0.839257\pi$
$73$	−1.94672e7	+	1.41437e7i	−0.685507	+	0.498050i	0.189673	+	0.981847i	$0.439257\pi$
$74$	1.97041e7	−	4.23223e6i	0.657098	−	0.141138i
$75$	−3.14840e6	+	9.30617e6i	−0.0995049	+	0.294121i
$76$	−1.79658e7	−	3.98926e7i	−0.538509	−	1.19574i
$77$	5.68486e6	−	4.13029e6i	0.161717	−	0.117495i
$78$	4.37190e6	+	450070.i	0.118111	+	0.0121591i
$79$	4.62870e7	+	1.50396e7i	1.18837	+	0.386124i	0.835469	−	0.549538i	$-0.185196\pi$
$79$	4.62870e7	+	1.50396e7i	1.18837	+	0.386124i	0.352898	+	0.935662i	$0.385196\pi$
$80$	3.44078e7	+	2.22222e7i	0.840033	+	0.542535i
$81$	9.57848e6	+	2.94795e7i	0.222514	+	0.684827i
$82$	−4.22511e7	+	9.07508e6i	−0.934507	+	0.200722i
$83$	−8.40252e7	+	2.73014e7i	−1.77050	+	0.575272i	−0.998200	−	0.0599807i	$-0.980896\pi$
$83$	−8.40252e7	+	2.73014e7i	−1.77050	+	0.575272i	−0.772305	+	0.635252i	$0.780896\pi$
$84$	−2.18387e7	−	4.54458e6i	−0.438641	−	0.0912802i
$85$	2.94376e7	−	5.69229e7i	0.563931	−	1.09046i
$86$	−6.90509e7	−	6.19072e7i	−1.26234	−	1.13174i
$87$	−4.72463e6	+	6.50290e6i	−0.0824691	+	0.113509i
$88$	−53211.1	−	8.30737e6i	−0.000887303	−	0.138526i
$89$	1.73204e7	−	1.25840e7i	0.276057	−	0.200567i	−0.441139	−	0.897439i	$-0.645425\pi$
$89$	1.73204e7	−	1.25840e7i	0.276057	−	0.200567i	0.717196	+	0.696872i	$0.245425\pi$
$90$	4.95940e7	+	3.24823e7i	0.755892	+	0.495081i
$91$	2.22415e7	−	3.06129e7i	0.324339	−	0.446415i
$92$	−1.83245e7	+	1.66417e7i	−0.255789	+	0.232299i
$93$	−2.12362e7			−0.283887
$94$	−5.02151e7	+	2.91348e7i	−0.643166	+	0.373165i
$95$	−9.48787e7	−	4.90664e7i	−1.16486	−	0.602406i
$96$	−1.94087e7	+	1.78545e7i	−0.228513	+	0.210214i
$97$	−4.13620e6	+	1.27299e7i	−0.0467212	+	0.143793i	−0.971696	−	0.236236i	$-0.924086\pi$
$97$	−4.13620e6	+	1.27299e7i	−0.0467212	+	0.143793i	0.924974	+	0.380029i	$0.124086\pi$
$98$	−6.66310e7	+	7.43198e7i	−0.722391	+	0.805749i
$99$		−	1.20242e7i		−	0.125174i
$100$	9.95307e7	−	9.67722e6i	0.995307	−	0.0967722i
$101$	−1.00930e8			−0.969921			−0.484960	−	0.874536i	$-0.661166\pi$
$101$	−1.00930e8			−0.969921			−0.484960	+	0.874536i	$0.661166\pi$
$102$	3.07213e7	+	2.75431e7i	0.283818	+	0.254455i
$103$	1.55361e8	+	5.04798e7i	1.38036	+	0.448507i	0.902788	−	0.430085i	$-0.141516\pi$
$103$	1.55361e8	+	5.04798e7i	1.38036	+	0.448507i	0.477573	+	0.878592i	$0.341516\pi$
$104$	−1.40964e7	−	4.24570e7i	−0.120497	−	0.362924i
$105$	−4.86719e7	+	2.44308e7i	−0.400425	+	0.200993i
$106$	5.18653e7	+	8.93921e7i	0.410822	+	0.708069i
$107$		−	1.87567e8i		−	1.43094i	−0.698643	−	0.715470i	$-0.746213\pi$
$107$		−	1.87567e8i		−	1.43094i	0.698643	−	0.715470i	$-0.253787\pi$
$108$	−5.95282e7	+	5.40615e7i	−0.437550	+	0.397368i
$109$	−1.81443e8	−	1.31826e8i	−1.28539	−	0.933887i	−0.285684	−	0.958324i	$-0.592221\pi$
$109$	−1.81443e8	−	1.31826e8i	−1.28539	−	0.933887i	−0.999701	+	0.0244370i	$0.992221\pi$
$110$	−1.27024e7	−	1.58118e7i	−0.0867590	−	0.107997i
$111$	1.86205e7	+	2.56290e7i	0.122659	+	0.168826i
$112$	4.91022e7	+	2.21681e8i	0.312053	+	1.40882i
$113$	−1.57722e8	−	1.14592e8i	−0.967340	−	0.702814i	−0.0124963	−	0.999922i	$-0.503978\pi$
$113$	−1.57722e8	−	1.14592e8i	−0.967340	−	0.702814i	−0.954844	+	0.297108i	$0.903978\pi$
$114$	4.59086e7	−	5.12061e7i	0.271816	−	0.303181i
$115$	−9.81379e6	+	5.96312e7i	−0.0561107	+	0.340943i
$116$	8.01016e7	+	1.66689e7i	0.442394	+	0.0920611i
$117$	−2.00088e7	−	6.15808e7i	−0.106777	−	0.328626i
$118$	−5.27059e7	−	2.45384e8i	−0.271851	−	1.26567i
$119$	3.37852e8	−	1.09775e8i	1.68476	−	0.547413i
$120$	−1.00483e7	+	6.35957e7i	−0.0484583	+	0.306692i
$121$	6.49694e7	−	1.99955e8i	0.303087	−	0.932805i
$122$	3.31949e6	−	3.22449e7i	0.0149841	−	0.145553i
$123$	−3.99276e7	−	5.49556e7i	−0.174443	−	0.240100i
$124$	8.87624e7	+	1.97094e8i	0.375442	+	0.833657i
$125$	1.75730e8	−	1.69481e8i	0.719788	−	0.694194i
$126$	6.90129e7	+	3.21306e8i	0.273809	+	1.27478i
$127$	4.00416e7	+	5.51125e7i	0.153920	+	0.211853i	0.879013	−	0.476799i	$-0.158203\pi$
$127$	4.00416e7	+	5.51125e7i	0.153920	+	0.211853i	−0.725092	+	0.688652i	$0.758203\pi$
$128$	2.46832e8	+	1.05505e8i	0.919522	+	0.393038i
$129$	4.50472e7	−	1.38641e8i	0.162670	−	0.500648i
$130$	−9.13659e7	−	5.98413e7i	−0.319897	−	0.209521i
$131$	−1.25876e8	+	4.08997e7i	−0.427424	+	0.138878i	−0.514826	−	0.857295i	$-0.672143\pi$
$131$	−1.25876e8	+	4.08997e7i	−0.427424	+	0.138878i	0.0874022	+	0.996173i	$0.472143\pi$
$132$	1.19068e7	−	5.36228e6i	0.0392192	−	0.0176626i
$133$	−1.82972e8	−	5.63130e8i	−0.584761	−	1.79971i
$134$	5.27530e7	−	1.19169e8i	0.163617	−	0.369612i
$135$	−3.18806e7	+	1.93715e8i	−0.0959824	+	0.583214i
$136$	1.27221e8	−	4.00250e8i	0.371879	−	1.16997i
$137$	−3.13928e8	−	2.28082e8i	−0.891144	−	0.647454i	0.0450323	−	0.998986i	$-0.485661\pi$
$137$	−3.13928e8	−	2.28082e8i	−0.891144	−	0.647454i	−0.936176	+	0.351532i	$0.885661\pi$
$138$	−3.55796e7	−	1.57501e7i	−0.0981035	−	0.0434278i
$139$	7.12932e6	+	9.81267e6i	0.0190981	+	0.0262862i	0.818459	−	0.574565i	$-0.194829\pi$
$139$	7.12932e6	+	9.81267e6i	0.0190981	+	0.0262862i	−0.799361	+	0.600851i	$0.794829\pi$
$140$	4.30181e8	+	3.49611e8i	1.11980	+	0.910066i
$141$	−7.38279e7	−	5.36391e7i	−0.186786	−	0.135708i
$142$	9.74575e7	−	5.65449e7i	0.239697	−	0.139072i
$143$			2.21518e7i			0.0529743i
$144$	3.56274e8	+	1.54992e8i	0.828581	+	0.360461i
$145$	1.78522e8	−	8.96092e7i	0.403851	−	0.202713i
$146$	−3.94263e7	+	3.82980e8i	−0.0867711	+	0.842879i
$147$	−1.49220e8	−	4.84845e7i	−0.319564	−	0.103832i
$148$	1.60034e8	−	2.79941e8i	0.333554	−	0.583472i
$149$	6.45551e8			1.30974			0.654870	−	0.755741i	$-0.272723\pi$
$149$	6.45551e8			1.30974			0.654870	+	0.755741i	$0.272723\pi$
$150$	7.72388e7	+	1.36904e8i	0.152571	+	0.270427i
$151$			2.16983e8i			0.417366i	0.977983	+	0.208683i	$0.0669177\pi$
$151$			2.16983e8i			0.417366i	−0.977983	+	0.208683i	$0.933082\pi$
$152$	−6.67134e8	−	2.12051e8i	−1.24980	−	0.397251i
$153$	1.87843e8	−	5.78122e8i	0.342791	−	1.05500i
$154$	1.15134e7	−	1.11839e8i	0.0204701	−	0.198843i
$155$	4.68760e8	+	2.42418e8i	0.812126	+	0.419990i
$156$	5.20566e7	−	4.72760e7i	0.0878976	−	0.0798256i
$157$	−4.30892e8			−0.709202			−0.354601	−	0.935018i	$-0.615383\pi$
$157$	−4.30892e8			−0.709202			−0.354601	+	0.935018i	$0.615383\pi$
$158$	6.73545e8	−	3.90791e8i	1.08078	−	0.627071i
$159$	−9.54875e7	+	1.31427e8i	−0.149403	+	0.205635i
$160$	6.32235e8	−	1.72557e8i	0.964714	−	0.263300i
$161$	−2.71022e8	+	1.96909e8i	−0.403367	+	0.293063i
$162$	4.53499e8	+	2.00752e8i	0.658440	+	0.291473i
$163$	6.87915e8	−	9.46834e8i	0.974506	−	1.34129i	0.0347684	−	0.999395i	$-0.488931\pi$
$163$	6.87915e8	−	9.46834e8i	0.974506	−	1.34129i	0.939737	−	0.341897i	$-0.111069\pi$
$164$	−3.43158e8	+	6.00272e8i	−0.474371	+	0.829798i
$165$	1.46449e7	−	2.83185e7i	0.0197583	−	0.0382063i
$166$	−5.72200e8	+	1.29260e9i	−0.753556	+	1.70229i
$167$	−1.76511e8	+	5.73520e7i	−0.226938	+	0.0737366i	−0.420279	−	0.907395i	$-0.638068\pi$
$167$	−1.76511e8	+	5.73520e7i	−0.226938	+	0.0737366i	0.193341	+	0.981132i	$0.438068\pi$
$168$	−2.87392e8	+	2.11628e8i	−0.360776	+	0.265667i
$169$	−2.15213e8	−	6.62357e8i	−0.263828	−	0.811980i
$170$	−3.63717e8	−	9.58669e8i	−0.435480	−	1.14782i
$171$	−9.63610e8	−	3.13096e8i	−1.12698	−	0.366179i
$172$	−1.47502e9	+	1.61402e8i	−1.68533	+	0.184414i
$173$	5.29750e7	−	3.84886e7i	0.0591407	−	0.0429682i	−0.557822	−	0.829961i	$-0.688363\pi$
$173$	5.29750e7	−	3.84886e7i	0.0591407	−	0.0429682i	0.616963	+	0.786992i	$0.288363\pi$
$174$	2.70077e7	+	1.25741e8i	0.0294639	+	0.137176i
$175$	1.35325e9	+	1.63291e7i	1.44287	+	0.0174105i
$176$	−9.95353e7	−	8.80944e7i	−0.103735	−	0.0918116i
$177$	3.19169e8	−	2.31890e8i	0.325183	−	0.236259i
$178$	3.50786e7	−	3.40747e8i	0.0349431	−	0.339431i
$179$	−8.02598e8	−	2.60780e8i	−0.781783	−	0.254017i	−0.109182	−	0.994022i	$-0.534823\pi$
$179$	−8.02598e8	−	2.60780e8i	−0.781783	−	0.254017i	−0.672601	+	0.740005i	$0.734823\pi$
$180$	9.16664e8	−	2.43888e8i	0.873213	−	0.232328i
$181$	3.23446e8	+	9.95465e8i	0.301362	+	0.927496i	0.981010	+	0.193957i	$0.0621324\pi$
$181$	3.23446e8	+	9.95465e8i	0.301362	+	0.927496i	−0.679648	+	0.733538i	$0.737868\pi$
$182$	−1.27141e8	−	5.91933e8i	−0.115878	−	0.539494i
$183$	4.84596e7	−	1.57455e7i	0.0432091	−	0.0140395i
$184$	2.53680e6	+	3.96048e8i	0.00221317	+	0.345523i
$185$	−1.18459e8	−	7.78283e8i	−0.101131	−	0.664432i
$186$	−2.26817e8	+	2.52990e8i	−0.189506	+	0.211374i
$187$	−1.22237e8	+	1.68245e8i	−0.0999622	+	0.137586i
$188$	−1.89244e8	+	9.09399e8i	−0.151492	+	0.727986i
$189$	−8.80428e8	+	6.39668e8i	−0.689996	+	0.501311i
$190$	−1.59790e9	+	6.06242e8i	−1.22613	+	0.465191i
$191$	3.24386e8	−	4.46480e8i	0.243741	−	0.335481i	−0.669566	−	0.742753i	$-0.733520\pi$
$191$	3.24386e8	−	4.46480e8i	0.243741	−	0.335481i	0.913307	+	0.407272i	$0.133520\pi$
$192$	5.40522e6	+	4.21917e8i	0.00397749	+	0.310472i
$193$	−1.63881e9			−1.18114			−0.590568	−	0.806988i	$-0.701096\pi$
$193$	−1.63881e9			−1.18114			−0.590568	+	0.806988i	$0.701096\pi$
$194$	1.07476e8	+	1.85239e8i	0.0758760	+	0.130775i
$195$	2.78791e7	−	1.69401e8i	0.0192815	−	0.117159i
$196$	1.73718e8	+	1.58757e9i	0.117712	+	1.07574i
$197$	−6.50063e8	+	2.00069e9i	−0.431609	+	1.32836i	0.464913	+	0.885356i	$0.346086\pi$
$197$	−6.50063e8	+	2.00069e9i	−0.431609	+	1.32836i	−0.896522	+	0.443000i	$0.853914\pi$
$198$	−1.43246e8	−	1.28426e8i	−0.0932010	−	0.0835589i
$199$			1.50650e9i			0.960629i	0.877096	+	0.480315i	$0.159477\pi$
$199$			1.50650e9i			0.960629i	−0.877096	+	0.480315i	$0.840523\pi$
$200$	9.47769e8	−	1.28908e9i	0.592355	−	0.805677i
$201$	2.04854e8			0.125505
$202$	−1.07800e9	+	1.20240e9i	−0.647463	+	0.722176i
$203$	1.05308e9	+	3.42168e8i	0.620124	+	0.201491i
$204$	6.56249e8	−	7.18091e7i	0.378921	−	0.0414628i
$205$	2.54010e8	+	1.66886e9i	0.143825	+	0.944938i
$206$	2.26073e9	−	1.31168e9i	1.25540	−	0.728381i
$207$			5.73243e8i			0.312218i
$208$	−6.56355e8	−	2.85537e8i	−0.350660	−	0.152549i
$209$	2.80429e8	+	2.03744e8i	0.146973	+	0.106782i
$210$	−2.28801e8	+	8.40773e8i	−0.117647	+	0.432316i
$211$	−1.84943e9	−	2.54552e9i	−0.933055	−	1.28424i	−0.958656	−	0.284567i	$-0.908150\pi$
$211$	−1.84943e9	−	2.54552e9i	−0.933055	−	1.28424i	0.0256014	−	0.999672i	$-0.491850\pi$
$212$	1.61890e9	+	3.36889e8i	0.801450	+	0.166780i
$213$	1.43285e8	+	1.04103e8i	0.0696118	+	0.0505760i
$214$	−2.23451e9	−	2.00334e9i	−1.06544	−	0.955213i
$215$	−2.57699e9	+	2.54608e9i	−1.20603	+	1.19157i
$216$	8.24093e6	+	1.28658e9i	0.00378583	+	0.591047i
$217$	9.03996e8	+	2.78221e9i	0.407688	+	1.25473i
$218$	−3.50839e9	+	7.53564e8i	−1.55339	+	0.333652i
$219$	−5.75565e8	+	1.87013e8i	−0.250218	+	0.0813007i
$220$	−3.24038e8	−	1.75550e7i	−0.138326	−	0.00749393i
$221$	−3.46059e8	+	1.06506e9i	−0.145071	+	0.446483i
$222$	5.04201e8	+	5.19056e7i	0.207583	+	0.0213699i
$223$	−1.71556e9	−	2.36127e9i	−0.693725	−	0.954830i	−0.999996	−	0.00288605i	$-0.999081\pi$
$223$	−1.71556e9	−	2.36127e9i	−0.693725	−	0.954830i	0.306271	−	0.951944i	$-0.400919\pi$
$224$	3.16537e9	+	1.78274e9i	1.25728	+	0.708104i
$225$	1.38370e9	−	1.85697e9i	0.539899	−	0.724559i
$226$	−3.04973e9	+	6.55049e8i	−1.16904	+	0.251096i
$227$	7.60375e8	+	1.04657e9i	0.286368	+	0.394152i	0.927830	−	0.373003i	$-0.121672\pi$
$227$	7.60375e8	+	1.04657e9i	0.286368	+	0.394152i	−0.641462	+	0.767155i	$0.721672\pi$
$228$	−1.19691e8	−	1.09383e9i	−0.0442917	−	0.404773i
$229$	−6.78367e8	+	2.08780e9i	−0.246674	+	0.759183i	0.748683	+	0.662928i	$0.230686\pi$
$229$	−6.78367e8	+	2.08780e9i	−0.246674	+	0.759183i	−0.995357	+	0.0962551i	$0.969314\pi$
$230$	6.05577e8	+	7.53815e8i	0.216401	+	0.269373i
$231$	1.68078e8	−	5.46119e7i	0.0590287	−	0.0191796i
$232$	1.05412e9	−	7.76227e8i	0.363863	−	0.267939i
$233$	−1.95782e8	−	6.02556e8i	−0.0664278	−	0.204444i	0.912333	−	0.409449i	$-0.134279\pi$
$233$	−1.95782e8	−	6.02556e8i	−0.0664278	−	0.204444i	−0.978761	+	0.205005i	$0.934279\pi$
$234$	−9.47328e8	−	4.19357e8i	−0.315964	−	0.139869i
$235$	1.01734e9	+	2.02678e9i	0.333576	+	0.664561i
$236$	−3.48624e9	−	1.99298e9i	−1.12385	−	0.642473i
$237$	9.90268e8	+	7.19472e8i	0.313877	+	0.228045i
$238$	2.30073e9	−	5.19736e9i	0.717063	−	1.61985i
$239$	−2.78749e9	−	3.83665e9i	−0.854323	−	1.17587i	−0.982894	−	0.184174i	$-0.941039\pi$
$239$	−2.78749e9	−	3.83665e9i	−0.854323	−	1.17587i	0.128571	−	0.991700i	$-0.458961\pi$
$240$	6.50303e8	+	7.98953e8i	0.196007	+	0.240811i
$241$	−1.46664e9	−	1.06558e9i	−0.434765	−	0.315876i	0.348786	−	0.937202i	$-0.386594\pi$
$241$	−1.46664e9	−	1.06558e9i	−0.434765	−	0.315876i	−0.783552	+	0.621327i	$0.786594\pi$
$242$	−1.68818e9	−	2.90965e9i	−0.492217	−	0.848357i
$243$			2.84047e9i			0.814639i
$244$	−3.48684e8	−	3.83943e8i	−0.0983723	−	0.108320i
$245$	2.74035e9	+	2.77362e9i	0.760576	+	0.769809i
$246$	−1.08115e9	−	1.11300e8i	−0.295219	−	0.0303917i
$247$	1.77523e9	+	5.76809e8i	0.476945	+	0.154969i
$248$	3.29606e9	+	1.04766e9i	0.871340	+	0.276958i
$249$	−2.22201e9			−0.578027
$250$	−1.42140e8	−	3.90366e9i	−0.0363879	−	0.999338i
$251$			1.85764e9i			0.468023i	0.972234	+	0.234011i	$0.0751853\pi$
$251$			1.85764e9i			0.468023i	−0.972234	+	0.234011i	$0.924815\pi$
$252$	4.56487e9	+	2.60960e9i	1.13195	+	0.647100i
$253$	6.06026e7	−	1.86516e8i	0.0147914	−	0.0455233i
$254$	1.08423e9	+	1.11618e8i	0.260488	+	0.0268162i
$255$	1.14652e9	−	1.13277e9i	0.271158	−	0.267906i
$256$	3.89324e9	−	1.81368e9i	0.906465	−	0.422280i
$257$	7.76046e9			1.77891			0.889456	−	0.457020i	$-0.151083\pi$
$257$	7.76046e9			1.77891			0.889456	+	0.457020i	$0.151083\pi$
$258$	−1.17052e9	−	2.01743e9i	−0.264179	−	0.455324i
$259$	2.56507e9	−	3.53052e9i	0.570033	−	0.784583i
$260$	−1.68875e9	+	4.49309e8i	−0.369548	+	0.0983223i
$261$	1.53287e9	−	1.11370e9i	0.330327	−	0.239997i
$262$	−8.57200e8	+	1.93642e9i	−0.181919	+	0.410955i
$263$	1.67073e9	−	2.29957e9i	0.349208	−	0.480644i	−0.597894	−	0.801575i	$-0.703996\pi$
$263$	1.67073e9	−	2.29957e9i	0.349208	−	0.480644i	0.947103	+	0.320931i	$0.103996\pi$
$264$	6.32909e7	−	1.99120e8i	0.0130294	−	0.0409920i
$265$	3.60804e9	−	1.81105e9i	0.731624	−	0.367238i
$266$	−8.66292e9	−	3.83484e9i	−1.73037	−	0.765986i
$267$	5.12095e8	−	1.66390e8i	0.100764	−	0.0327402i
$268$	−8.56244e8	−	1.90126e9i	−0.165981	−	0.368556i
$269$	2.20205e9	+	6.77721e9i	0.420550	+	1.29432i	0.907191	+	0.420718i	$0.138222\pi$
$269$	2.20205e9	+	6.77721e9i	0.420550	+	1.29432i	−0.486641	+	0.873602i	$0.661778\pi$
$270$	1.96725e9	+	2.44881e9i	0.370173	+	0.460786i
$271$	5.83782e9	+	1.89682e9i	1.08236	+	0.351682i	0.795292	−	0.606227i	$-0.207318\pi$
$271$	5.83782e9	+	1.89682e9i	1.08236	+	0.351682i	0.287073	+	0.957909i	$0.407318\pi$
$272$	−3.40943e9	−	5.79054e9i	−0.622883	−	1.05790i
$273$	7.69922e8	−	5.59381e8i	0.138610	−	0.100706i
$274$	−6.07014e9	+	1.30380e9i	−1.07695	+	0.231318i
$275$	−6.46531e8	+	4.57916e8i	−0.113047	+	0.0800673i
$276$	−5.67648e8	+	2.55643e8i	−0.0978234	+	0.0440552i
$277$	5.50037e9	−	3.99625e9i	0.934271	−	0.678788i	−0.0127639	−	0.999919i	$-0.504063\pi$
$277$	5.50037e9	−	3.99625e9i	0.934271	−	0.678788i	0.947035	+	0.321131i	$0.104063\pi$
$278$	1.93046e8	+	1.98733e7i	0.0323207	+	0.00332729i
$279$	4.76083e9	+	1.54689e9i	0.785717	+	0.255295i
$280$	8.75959e9	−	1.39073e9i	1.42512	−	0.226261i
$281$	2.14215e9	+	6.59285e9i	0.343577	+	1.05742i	0.962341	+	0.271845i	$0.0876337\pi$
$281$	2.14215e9	+	6.59285e9i	0.343577	+	1.05742i	−0.618764	+	0.785577i	$0.712366\pi$
$282$	−1.42754e9	+	3.06621e8i	−0.225732	+	0.0484847i
$283$	−6.65383e9	+	2.16196e9i	−1.03735	+	0.337056i	−0.777693	−	0.628644i	$-0.783610\pi$
$283$	−6.65383e9	+	2.16196e9i	−1.03735	+	0.337056i	−0.259659	+	0.965700i	$0.583610\pi$
$284$	3.67285e8	−	1.76496e9i	0.0564585	−	0.271308i
$285$	−1.88810e9	−	1.91102e9i	−0.286184	−	0.289658i
$286$	2.63898e8	+	2.36596e8i	0.0394431	+	0.0353626i
$287$	−5.50022e9	+	7.57041e9i	−0.810686	+	1.11581i
$288$	5.65169e9	−	2.58894e9i	0.821502	−	0.376315i
$289$	−2.86199e9	+	2.07936e9i	−0.410276	+	0.298083i
$290$	8.39213e8	−	3.08385e9i	0.118653	−	0.436015i
$291$	−1.97870e8	+	2.72345e8i	−0.0275936	+	0.0379793i
$292$	4.14140e9	+	4.56018e9i	0.569660	+	0.627265i
$293$	7.81142e9			1.05989			0.529943	−	0.848033i	$-0.322213\pi$
$293$	7.81142e9			1.05989			0.529943	+	0.848033i	$0.322213\pi$
$294$	−2.17137e9	+	1.25983e9i	−0.290633	+	0.168625i
$295$	−9.69232e9	+	1.47523e9i	−1.27979	+	0.194792i
$296$	−1.62571e9	−	4.89647e9i	−0.211775	−	0.637847i
$297$	1.96871e8	−	6.05906e8i	0.0253020	−	0.0778716i
$298$	6.89492e9	−	7.69054e9i	0.874307	−	0.975196i
$299$		−	1.05607e9i		−	0.132132i
$300$	2.45592e9	+	5.42066e8i	0.303199	+	0.0669217i
$301$	−2.00813e10			−2.44639
$302$	2.58495e9	+	2.31752e9i	0.310759	+	0.278610i
$303$	−2.41419e9	−	7.84417e8i	−0.286418	−	0.0930628i
$304$	−9.65163e9	+	5.68282e9i	−1.13007	+	0.665380i
$305$	−1.24942e9	−	2.05623e8i	−0.144380	−	0.0237614i
$306$	−4.88096e9	−	8.41254e9i	−0.556698	−	0.959492i
$307$		−	8.82727e9i		−	0.993740i	−0.867825	−	0.496870i	$-0.834483\pi$
$307$		−	8.82727e9i		−	0.993740i	0.867825	−	0.496870i	$-0.165517\pi$
$308$	−1.20938e9	−	1.33168e9i	−0.134388	−	0.147978i
$309$	3.32381e9	+	2.41489e9i	0.364587	+	0.264888i
$310$	7.89464e9	−	2.99521e9i	0.854841	−	0.324325i
$311$	−6.24118e9	−	8.59024e9i	−0.667152	−	0.918256i	0.332539	−	0.943089i	$-0.392095\pi$
$311$	−6.24118e9	−	8.59024e9i	−0.667152	−	0.918256i	−0.999692	+	0.0248332i	$0.992095\pi$
$312$	−7.20658e6	−	1.12510e9i	−0.000760520	−	0.118733i
$313$	−1.40012e10	−	1.01725e10i	−1.45877	−	1.05986i	−0.983681	−	0.179922i	$-0.942415\pi$
$313$	−1.40012e10	−	1.01725e10i	−1.45877	−	1.05986i	−0.475090	−	0.879937i	$-0.657585\pi$
$314$	−4.60222e9	+	5.13328e9i	−0.473422	+	0.528051i
$315$	1.26911e10	−	1.93166e9i	1.28901	−	0.196195i
$316$	2.53836e9	−	1.21980e10i	0.254569	−	1.22332i
$317$	−1.46148e9	−	4.49797e9i	−0.144729	−	0.445430i	0.852247	−	0.523139i	$-0.175239\pi$
$317$	−1.46148e9	−	4.49797e9i	−0.144729	−	0.445430i	−0.996976	+	0.0777096i	$0.975239\pi$
$318$	5.45841e8	+	2.54129e9i	0.0533774	+	0.248511i
$319$	−6.16489e8	+	2.00310e8i	−0.0595337	+	0.0193437i
$320$	4.69701e9	−	9.37493e9i	0.447941	−	0.894063i
$321$	1.45774e9	−	4.48648e9i	0.137297	−	0.422557i
$322$	−5.48892e8	+	5.33184e9i	−0.0510580	+	0.495968i
$323$	1.03001e10	+	1.41769e10i	0.946308	+	1.30248i
$324$	7.23526e9	−	3.25844e9i	0.656559	−	0.295685i
$325$	−2.54916e9	+	3.42104e9i	−0.228488	+	0.306637i
$326$	−3.93237e9	−	1.83081e10i	−0.348164	−	1.62096i
$327$	−3.31545e9	−	4.56333e9i	−0.289969	−	0.399108i
$328$	3.48597e9	+	1.04994e10i	0.301181	+	0.907129i
$329$	−3.88465e9	+	1.19557e10i	−0.331565	+	1.02045i
$330$	−1.80946e8	−	4.76928e8i	−0.0152578	−	0.0402158i
$331$	1.98698e9	−	6.45609e8i	0.165532	−	0.0537846i	−0.225079	−	0.974341i	$-0.572264\pi$
$331$	1.98698e9	−	6.45609e8i	0.165532	−	0.0537846i	0.390611	+	0.920556i	$0.372264\pi$
$332$	9.28748e9	+	2.06226e10i	0.764444	+	1.69742i
$333$	−2.30757e9	−	7.10198e9i	−0.187663	−	0.577567i
$334$	−1.20202e9	+	2.71537e9i	−0.0965885	+	0.218194i
$335$	−4.52188e9	−	2.33848e9i	−0.359037	−	0.185676i
$336$	−5.48384e8	+	5.68408e9i	−0.0430257	+	0.445968i
$337$	1.62370e10	+	1.17968e10i	1.25888	+	0.914631i	0.998702	−	0.0509293i	$-0.0162183\pi$
$337$	1.62370e10	+	1.17968e10i	1.25888	+	0.914631i	0.260179	+	0.965560i	$0.416218\pi$
$338$	−1.01894e10	−	4.51056e9i	−0.780694	−	0.345592i
$339$	−2.88202e9	−	3.96676e9i	−0.218222	−	0.300356i
$340$	−1.53055e10	−	5.90622e9i	−1.14533	−	0.441971i
$341$	−1.38549e9	−	1.00662e9i	−0.102468	−	0.0744471i
$342$	−1.40220e10	+	8.13555e9i	−1.02495	+	0.594679i
$343$			1.64104e9i			0.118561i
$344$	−1.38314e10	+	1.92960e10i	−0.987717	+	1.37795i
$345$	−6.98184e8	+	1.35007e9i	−0.0492826	+	0.0952969i
$346$	1.07289e8	−	1.04218e9i	0.00748599	−	0.0727176i
$347$	2.29216e10	+	7.44769e9i	1.58099	+	0.513693i	0.962310	−	0.271953i	$-0.0876697\pi$
$347$	2.29216e10	+	7.44769e9i	1.58099	+	0.513693i	0.618675	+	0.785647i	$0.287670\pi$
$348$	1.78643e9	+	1.02125e9i	0.121806	+	0.0696329i
$349$	−7.47328e9			−0.503744			−0.251872	−	0.967761i	$-0.581046\pi$
$349$	−7.47328e9			−0.503744			−0.251872	+	0.967761i	$0.581046\pi$
$350$	1.46482e10	−	1.59471e10i	0.976137	−	1.06269i
$351$		−	3.43070e9i		−	0.226024i
$352$	−2.11259e9	+	2.44870e8i	−0.137608	+	0.0159502i
$353$	3.30154e9	−	1.01611e10i	0.212626	−	0.654397i	−0.786687	−	0.617352i	$-0.788206\pi$
$353$	3.30154e9	−	1.01611e10i	0.212626	−	0.654397i	0.999314	−	0.0370450i	$-0.0117945\pi$
$354$	6.46404e8	−	6.27905e9i	0.0411615	−	0.399835i
$355$	−1.97446e9	−	3.93357e9i	−0.124318	−	0.247670i
$356$	−3.68471e9	−	4.05731e9i	−0.229405	−	0.252603i
$357$	8.93435e9			0.550035
$358$	−1.16790e10	+	6.77616e9i	−0.711007	+	0.412526i
$359$	−1.27535e10	+	1.75537e10i	−0.767807	+	1.05680i	0.228717	+	0.973493i	$0.426547\pi$
$359$	−1.27535e10	+	1.75537e10i	−0.767807	+	1.05680i	−0.996524	+	0.0833026i	$0.973453\pi$
$360$	6.88512e9	−	1.35253e10i	0.409922	−	0.805259i
$361$	9.88999e9	−	7.18550e9i	0.582327	−	0.423086i
$362$	1.53138e10	+	6.77898e9i	0.891759	+	0.394757i
$363$	3.10805e9	−	4.27786e9i	0.179003	−	0.246377i
$364$	−8.40973e9	−	4.80760e9i	−0.479046	−	0.273856i
$365$	1.48396e10	+	2.44223e9i	0.836086	+	0.137599i
$366$	3.30003e8	−	7.45478e8i	0.0183905	−	0.0415442i
$367$	−1.15797e10	+	3.76247e9i	−0.638311	+	0.207400i	−0.610253	−	0.792206i	$-0.708932\pi$
$367$	−1.15797e10	+	3.76247e9i	−0.638311	+	0.207400i	−0.0280579	+	0.999606i	$0.508932\pi$
$368$	4.74527e9	+	4.19984e9i	0.258744	+	0.229003i
$369$	4.94808e9	+	1.52286e10i	0.266889	+	0.821400i
$370$	−1.05370e10	−	6.90137e9i	−0.562226	−	0.368238i
$371$	2.12834e10	+	6.91540e9i	1.12343	+	0.365024i
$372$	5.91348e8	+	5.40421e9i	0.0308796	+	0.282202i
$373$	1.75503e10	−	1.27510e10i	0.906668	−	0.658733i	−0.0335020	−	0.999439i	$-0.510666\pi$
$373$	1.75503e10	−	1.27510e10i	0.906668	−	0.658733i	0.940170	+	0.340706i	$0.110666\pi$
$374$	6.98750e8	+	3.25319e9i	0.0357138	+	0.166274i
$375$	5.52051e9	−	2.68812e9i	0.279161	−	0.135933i
$376$	8.81256e9	+	1.19675e10i	0.440911	+	0.598759i
$377$	−2.82398e9	+	2.05174e9i	−0.139796	+	0.101568i
$378$	−1.78310e9	+	1.73208e10i	−0.0873392	+	0.848398i
$379$	−2.39038e10	−	7.76682e9i	−1.15854	−	0.376432i	−0.334185	−	0.942507i	$-0.608461\pi$
$379$	−2.39038e10	−	7.76682e9i	−1.15854	−	0.376432i	−0.824353	+	0.566076i	$0.808461\pi$
$380$	−9.84445e9	+	2.55111e10i	−0.472125	+	1.22348i
$381$	5.29441e8	+	1.62945e9i	0.0251256	+	0.0773288i
$382$	−1.85431e9	−	8.63317e9i	−0.0870821	−	0.405431i
$383$	2.69126e10	−	8.74445e9i	1.25072	−	0.406385i	0.392543	−	0.919733i	$-0.371595\pi$
$383$	2.69126e10	−	8.74445e9i	1.25072	−	0.406385i	0.858180	+	0.513349i	$0.171595\pi$
$384$	5.08409e9	+	4.44196e9i	0.233824	+	0.204291i
$385$	−4.33350e9	−	7.13185e8i	−0.197241	−	0.0324608i
$386$	−1.75036e10	+	1.95234e10i	−0.788458	+	0.879440i
$387$	−2.01978e10	+	2.77998e10i	−0.900450	+	1.23936i
$388$	3.35470e9	+	6.98104e8i	0.148022	+	0.0308030i
$389$	−3.04611e10	+	2.21313e10i	−1.33029	+	0.966514i	−0.330551	+	0.943788i	$0.607235\pi$
$389$	−3.04611e10	+	2.21313e10i	−1.33029	+	0.966514i	−0.999742	+	0.0227260i	$0.992765\pi$
$390$	−1.72033e9	−	2.14145e9i	−0.0743624	−	0.0925654i
$391$	5.82755e9	−	8.02094e9i	0.249333	−	0.343177i
$392$	2.07684e10	+	1.48868e10i	0.879546	+	0.630460i
$393$	−3.32874e9			−0.139544
$394$	1.68914e10	+	2.91130e10i	0.700939	+	1.20810i
$395$	−1.36458e10	−	2.71856e10i	−0.560545	−	1.11674i
$396$	−3.05992e9	+	3.34827e8i	−0.124431	+	0.0136157i
$397$	7.39580e9	−	2.27619e10i	0.297730	−	0.916320i	−0.684560	−	0.728956i	$-0.740006\pi$
$397$	7.39580e9	−	2.27619e10i	0.297730	−	0.916320i	0.982291	−	0.187364i	$-0.0599943\pi$
$398$	1.79471e10	+	1.60904e10i	0.715257	+	0.641261i
$399$		−	1.48917e10i		−	0.587562i
$400$	−5.23422e9	−	2.50592e10i	−0.204462	−	0.978875i
$401$	−1.23172e10			−0.476357			−0.238179	−	0.971221i	$-0.576550\pi$
$401$	−1.23172e10			−0.476357			−0.238179	+	0.971221i	$0.576550\pi$
$402$	2.18798e9	−	2.44046e9i	0.0837799	−	0.0934475i
$403$	−8.77076e9	−	2.84979e9i	−0.332519	−	0.108042i
$404$	2.81053e9	+	2.56849e10i	0.105502	+	0.964166i
$405$	8.89908e9	−	1.72080e10i	0.330769	−	0.639603i
$406$	1.53239e10	−	8.89096e9i	0.563983	−	0.327224i
$407$			2.55472e9i			0.0931034i
$408$	6.15372e9	−	8.58497e9i	0.222074	−	0.309812i
$409$	−2.87948e10	−	2.09206e10i	−1.02901	−	0.747621i	−0.0609016	−	0.998144i	$-0.519398\pi$
$409$	−2.87948e10	−	2.09206e10i	−1.02901	−	0.747621i	−0.968111	+	0.250523i	$0.919398\pi$
$410$	2.25943e10	+	1.47984e10i	0.799583	+	0.523698i
$411$	−5.73632e9	−	7.89537e9i	−0.201033	−	0.276698i
$412$	8.51995e9	−	4.09421e10i	0.295698	−	1.42096i
$413$	−4.39671e10	−	3.19440e10i	−1.51122	−	1.09797i
$414$	6.82913e9	+	6.12263e9i	0.232468	+	0.208419i
$415$	4.90477e10	+	2.53649e10i	1.65359	+	0.855149i
$416$	−1.04120e10	+	4.76953e9i	−0.347664	+	0.159258i
$417$	9.42659e7	+	2.90121e8i	0.00311753	+	0.00959476i
$418$	5.42240e9	−	1.16467e9i	0.177618	−	0.0381504i
$419$	−2.88691e10	+	9.38013e9i	−0.936649	+	0.304336i	−0.737279	−	0.675589i	$-0.763890\pi$
$419$	−2.88691e10	+	9.38013e9i	−0.936649	+	0.304336i	−0.199370	+	0.979924i	$0.563890\pi$
$420$	7.57251e9	+	1.17058e10i	0.243356	+	0.376186i
$421$	−1.25600e9	+	3.86558e9i	−0.0399818	+	0.123051i	−0.969055	−	0.246844i	$-0.920606\pi$
$421$	−1.25600e9	+	3.86558e9i	−0.0399818	+	0.123051i	0.929073	+	0.369895i	$0.120606\pi$
$422$	−5.00782e10	−	5.15536e9i	−1.57906	−	0.162558i
$423$	1.26439e10	+	1.74028e10i	0.394930	+	0.543574i
$424$	2.13043e10	−	1.56880e10i	0.659181	−	0.485404i
$425$	−3.82389e10	+	1.19164e10i	−1.17206	+	0.365250i
$426$	2.77058e9	−	5.95090e8i	0.0841263	−	0.0180694i
$427$	−4.12571e9	−	5.67856e9i	−0.124104	−	0.170815i
$428$	−4.77323e10	+	5.22303e9i	−1.42245	+	0.155649i
$429$	−1.72161e8	+	5.29856e8i	−0.00508282	+	0.0156433i
$430$	2.80785e9	+	5.78938e10i	0.0821296	+	1.69340i
$431$	−5.68231e10	+	1.84629e10i	−1.64670	+	0.535047i	−0.978022	−	0.208502i	$-0.933141\pi$
$431$	−5.68231e10	+	1.84629e10i	−1.64670	+	0.535047i	−0.668682	+	0.743548i	$0.733141\pi$
$432$	1.54153e10	+	1.36434e10i	0.442604	+	0.391730i
$433$	−5.63126e9	−	1.73312e10i	−0.160197	−	0.493035i	0.838453	−	0.544973i	$-0.183460\pi$
$433$	−5.63126e9	−	1.73312e10i	−0.160197	−	0.493035i	−0.998650	+	0.0519380i	$0.983460\pi$
$434$	4.28002e10	+	1.89465e10i	1.20639	+	0.534035i
$435$	4.96657e9	−	7.55941e8i	0.138707	−	0.0211121i
$436$	−2.84947e10	+	4.98445e10i	−0.788529	+	1.37934i
$437$	−1.33693e10	−	9.71333e9i	−0.366591	−	0.266344i
$438$	−3.91952e9	+	8.85422e9i	−0.106497	+	0.240577i
$439$	−7.92249e9	−	1.09044e10i	−0.213306	−	0.293591i	0.688934	−	0.724824i	$-0.258079\pi$
$439$	−7.92249e9	−	1.09044e10i	−0.213306	−	0.293591i	−0.902241	+	0.431233i	$0.858079\pi$
$440$	−3.67008e9	+	3.67281e9i	−0.0979186	+	0.0979915i
$441$	2.99211e10	+	2.17390e10i	0.791085	+	0.574757i
$442$	8.99207e9	+	1.54982e10i	0.235597	+	0.406062i
$443$		−	6.25024e10i		−	1.62286i	−0.584448	−	0.811431i	$-0.698689\pi$
$443$		−	6.25024e10i		−	1.62286i	0.584448	−	0.811431i	$-0.301311\pi$
$444$	6.00357e9	−	5.45224e9i	0.154482	−	0.140295i
$445$	−1.32032e10	−	2.17291e9i	−0.336696	−	0.0554117i
$446$	−4.64535e10	−	4.78221e9i	−1.17403	−	0.120862i
$447$	1.54411e10	+	5.01713e9i	0.386767	+	0.125668i
$448$	5.50464e10	−	1.86686e10i	1.36652	−	0.463446i
$449$	−3.15632e10			−0.776598			−0.388299	−	0.921533i	$-0.626937\pi$
$449$	−3.15632e10			−0.776598			−0.388299	+	0.921533i	$0.626937\pi$
$450$	−7.34343e9	−	3.63179e10i	−0.179081	−	0.885668i
$451$		−	5.47803e9i		−	0.132409i
$452$	−2.47695e10	+	4.33283e10i	−0.593422	+	1.03805i
$453$	−1.68636e9	+	5.19008e9i	−0.0400458	+	0.123248i
$454$	2.05892e10	+	2.11958e9i	0.484637	+	0.0498915i
$455$	−2.33805e10	+	3.55865e9i	−0.545516	+	0.0830308i
$456$	−1.43094e10	−	1.02570e10i	−0.330949	−	0.237225i
$457$	5.82091e10			1.33452			0.667261	−	0.744824i	$-0.267466\pi$
$457$	5.82091e10			1.33452			0.667261	+	0.744824i	$0.267466\pi$
$458$	1.76268e10	+	3.03806e10i	0.400601	+	0.690453i
$459$	1.89311e10	−	2.60564e10i	0.426506	−	0.587035i
$460$	1.54483e10	+	8.36921e8i	0.345024	+	0.0186919i
$461$	−2.88614e9	+	2.09690e9i	−0.0639019	+	0.0464275i	−0.619278	−	0.785172i	$-0.712574\pi$
$461$	−2.88614e9	+	2.09690e9i	−0.0639019	+	0.0464275i	0.555376	+	0.831600i	$0.312574\pi$
$462$	1.14459e9	−	2.58563e9i	0.0251236	−	0.0567543i
$463$	2.85953e10	−	3.93581e10i	0.622258	−	0.856465i	−0.375257	−	0.926921i	$-0.622445\pi$
$463$	2.85953e10	−	3.93581e10i	0.622258	−	0.856465i	0.997515	+	0.0704559i	$0.0224454\pi$
$464$	2.01140e9	−	2.08485e10i	0.0433938	−	0.449783i
$465$	9.32837e9	+	9.44161e9i	0.199524	+	0.201946i
$466$	−9.26943e9	−	4.10333e9i	−0.196566	−	0.0870146i
$467$	−4.21899e9	+	1.37083e9i	−0.0887036	+	0.0288215i	−0.353033	−	0.935611i	$-0.614850\pi$
$467$	−4.21899e9	+	1.37083e9i	−0.0887036	+	0.0288215i	0.264329	+	0.964433i	$0.414850\pi$
$468$	−1.51140e10	+	6.80665e9i	−0.315061	+	0.141889i
$469$	−8.72037e9	−	2.68385e10i	−0.180237	−	0.554712i
$470$	3.50112e10	+	9.52764e9i	0.717489	+	0.195251i
$471$	−1.03066e10	−	3.34883e9i	−0.209427	−	0.0680471i
$472$	−6.09780e10	+	2.02457e10i	−1.22859	+	0.407910i
$473$	9.51070e9	−	6.90993e9i	0.190006	−	0.138048i
$474$	1.91479e10	−	4.11276e9i	0.379322	−	0.0814743i
$475$	1.98622e10	+	6.37363e10i	0.390170	+	1.25202i
$476$	−3.73435e10	−	8.29202e10i	−0.727424	−	1.61522i
$477$	3.09803e10	−	2.25085e10i	0.598428	−	0.434783i
$478$	−7.54789e10	−	7.77026e9i	−1.44582	−	0.148841i
$479$	8.65100e10	+	2.81088e10i	1.64333	+	0.533950i	0.977279	−	0.211957i	$-0.0679838\pi$
$479$	8.65100e10	+	2.81088e10i	1.64333	+	0.533950i	0.666050	+	0.745907i	$0.267984\pi$
$480$	1.64637e10	+	7.86205e8i	0.310144	+	0.0148105i
$481$	4.25118e9	+	1.30838e10i	0.0794199	+	0.244429i
$482$	−2.83591e10	+	6.09122e9i	−0.525416	+	0.112854i
$483$	−8.01300e9	+	2.60358e9i	−0.147234	+	0.0478391i
$484$	−5.26939e10	−	1.09655e10i	−0.960239	−	0.199823i
$485$	7.47661e9	−	3.75288e9i	0.135126	−	0.0678263i
$486$	3.38389e10	+	3.03382e10i	0.606557	+	0.543806i
$487$	−1.20061e10	+	1.65250e10i	−0.213445	+	0.293782i	−0.902292	−	0.431125i	$-0.858117\pi$
$487$	−1.20061e10	+	1.65250e10i	−0.213445	+	0.293782i	0.688847	+	0.724906i	$0.258117\pi$
$488$	−8.29816e9	+	5.31521e7i	−0.146320	+	0.000937220i
$489$	2.38131e10	−	1.73012e10i	0.416467	−	0.302581i
$490$	6.23114e10	−	3.02210e9i	1.08089	−	0.0524233i
$491$	3.68642e10	−	5.07393e10i	0.634277	−	0.873008i	−0.364017	−	0.931392i	$-0.618595\pi$
$491$	3.68642e10	−	5.07393e10i	0.634277	−	0.873008i	0.998294	+	0.0583844i	$0.0185949\pi$
$492$	−1.28733e10	+	1.16911e10i	−0.219700	+	0.199524i
$493$	−3.27701e10			−0.554741
$494$	2.58323e10	−	1.49879e10i	0.433766	−	0.251671i
$495$	−5.34594e9	+	5.28182e9i	−0.0890437	+	0.0879757i
$496$	4.76851e10	−	2.80767e10i	0.787872	−	0.463894i
$497$	7.53934e9	−	2.32037e10i	0.123569	−	0.380305i
$498$	−2.37325e10	+	2.64711e10i	−0.385858	+	0.430383i
$499$			3.96359e10i			0.639274i	0.947540	+	0.319637i	$0.103561\pi$
$499$			3.96359e10i			0.639274i	−0.947540	+	0.319637i	$0.896439\pi$
$500$	−4.80231e10	−	4.00004e10i	−0.768369	−	0.640007i
$501$	−4.66777e9			−0.0740898
$502$	2.21304e10	+	1.98409e10i	0.348477	+	0.312425i
$503$	−5.71150e9	−	1.85578e9i	−0.0892233	−	0.0289904i	0.264065	−	0.964505i	$-0.414937\pi$
$503$	−5.71150e9	−	1.85578e9i	−0.0892233	−	0.0289904i	−0.353288	+	0.935514i	$0.614937\pi$
$504$	7.98444e10	−	2.65096e10i	1.23743	−	0.410848i
$505$	4.43354e10	+	4.48736e10i	0.681688	+	0.689963i
$506$	−1.57471e9	−	2.71408e9i	−0.0240214	−	0.0414020i
$507$		−	1.75157e10i		−	0.265092i
$508$	1.29101e10	−	1.17245e10i	0.193854	−	0.176051i
$509$	−7.29382e10	−	5.29927e10i	−1.08664	−	0.789487i	−0.107807	−	0.994172i	$-0.534383\pi$
$509$	−7.29382e10	−	5.29927e10i	−1.08664	−	0.789487i	−0.978828	+	0.204685i	$0.934383\pi$
$510$	−1.24924e9	−	2.57575e10i	−0.0184656	−	0.380735i
$511$	4.90020e10	+	6.74455e10i	0.718672	+	0.989167i
$512$	1.99758e10	−	6.57521e10i	0.290686	−	0.956819i
$513$	−4.34307e10	−	3.15543e10i	−0.627086	−	0.455605i
$514$	8.28869e10	−	9.24515e10i	1.18750	−	1.32453i
$515$	−4.58017e10	−	9.12476e10i	−0.651107	−	1.29716i
$516$	−3.65359e10	−	7.60302e9i	−0.515372	−	0.107248i
$517$	−2.27413e9	−	6.99905e9i	−0.0318312	−	0.0979663i
$518$	−1.46629e10	−	6.82664e10i	−0.203657	−	0.948173i
$519$	1.56625e9	−	5.08906e8i	0.0215870	−	0.00701405i
$520$	−1.26843e10	+	2.49172e10i	−0.173481	+	0.340790i
$521$	1.03612e10	−	3.18886e10i	0.140624	−	0.432797i	−0.855798	−	0.517310i	$-0.826933\pi$
$521$	1.03612e10	−	3.18886e10i	0.140624	−	0.432797i	0.996422	+	0.0845131i	$0.0269335\pi$
$522$	3.10449e9	−	3.01564e10i	0.0418126	−	0.406161i
$523$	3.19783e10	+	4.40143e10i	0.427413	+	0.588284i	0.967357	−	0.253417i	$-0.0815545\pi$
$523$	3.19783e10	+	4.40143e10i	0.427413	+	0.588284i	−0.539944	+	0.841701i	$0.681554\pi$
$524$	1.39134e10	+	3.08942e10i	0.184547	+	0.409781i
$525$	3.22419e10	+	1.09079e10i	0.424408	+	0.143583i
$526$	−9.55053e9	−	4.44647e10i	−0.124763	−	0.580861i
$527$	−5.08890e10	−	7.00427e10i	−0.659753	−	0.908072i
$528$	−1.69616e9	−	2.88073e9i	−0.0218238	−	0.0370653i
$529$	2.13102e10	−	6.55862e10i	0.272123	−	0.837509i
$530$	1.69610e10	−	6.23264e10i	0.214955	−	0.789893i
$531$	−8.84442e10	+	2.87373e10i	−1.11248	+	0.361466i
$532$	−1.38211e11	+	6.22440e10i	−1.72542	+	0.777053i
$533$	−9.11571e9	−	2.80553e10i	−0.112949	−	0.347621i
$534$	3.48729e9	−	7.87781e9i	0.0428868	−	0.0968814i
$535$	−8.33923e10	+	8.23921e10i	−1.01791	+	1.00570i
$536$	−3.17953e10	−	1.01062e10i	−0.385216	−	0.122442i
$537$	−1.71709e10	−	1.24754e10i	−0.206488	−	0.150022i
$538$	1.04257e11	+	4.61518e10i	1.24445	+	0.550884i
$539$	−7.43719e9	−	1.02364e10i	−0.0881158	−	0.121281i
$540$	5.01845e10	+	2.71878e9i	0.590194	+	0.0319742i
$541$	1.28810e11	+	9.35858e10i	1.50369	+	1.09250i	0.968881	+	0.247528i	$0.0796183\pi$
$541$	1.28810e11	+	9.35858e10i	1.50369	+	1.09250i	0.534814	+	0.844970i	$0.320382\pi$
$542$	8.49490e10	−	4.92875e10i	0.984377	−	0.571136i
$543$			2.63246e10i			0.302805i
$544$	−1.05399e11	−	2.12298e10i	−1.20348	−	0.242410i
$545$	2.10921e10	+	1.38576e11i	0.239075	+	1.57073i
$546$	1.55930e9	−	1.51468e10i	0.0175452	−	0.170431i
$547$	1.17480e11	+	3.81715e10i	1.31224	+	0.426374i	0.879824	−	0.475299i	$-0.157660\pi$
$547$	1.17480e11	+	3.81715e10i	1.31224	+	0.426374i	0.432419	+	0.901673i	$0.357660\pi$
$548$	−4.93008e10	+	8.62399e10i	−0.546679	+	0.956282i
$549$	−1.20108e10			−0.132216
$550$	−1.45016e9	+	1.25931e10i	−0.0158477	+	0.137620i
$551$			5.46210e10i			0.592589i
$552$	−3.01735e9	+	9.49291e9i	−0.0324990	+	0.102245i
$553$	5.21056e10	−	1.60365e11i	0.557166	−	1.71478i
$554$	1.11397e10	−	1.08209e11i	0.118259	−	1.14875i
$555$	3.21524e9	−	1.95367e10i	0.0338877	−	0.205910i
$556$	2.29861e9	−	2.08752e9i	0.0240529	−	0.0218440i
$557$	−1.79428e10			−0.186410			−0.0932050	−	0.995647i	$-0.529711\pi$
$557$	−1.79428e10			−0.186410			−0.0932050	+	0.995647i	$0.529711\pi$
$558$	6.92772e10	−	4.01947e10i	0.714585	−	0.414602i
$559$	3.72098e10	−	5.12150e10i	0.381075	−	0.524505i
$560$	7.69905e10	−	1.19208e11i	0.782862	−	1.21214i
$561$	−4.23140e9	+	3.07429e9i	−0.0427201	+	0.0310380i
$562$	1.01421e11	+	4.48964e10i	1.01668	+	0.450056i
$563$	−3.38043e10	+	4.65276e10i	−0.336463	+	0.463102i	−0.943404	−	0.331645i	$-0.892396\pi$
$563$	−3.38043e10	+	4.65276e10i	−0.336463	+	0.463102i	0.606941	+	0.794747i	$0.292396\pi$
$564$	−1.15943e10	+	2.02814e10i	−0.114585	+	0.200439i
$565$	1.83347e10	+	1.20460e11i	0.179920	+	1.18208i
$566$	−4.53117e10	+	1.02359e11i	−0.441514	+	0.997382i
$567$	1.02134e11	−	3.31854e10i	0.988185	−	0.321081i
$568$	−1.71034e10	−	2.32265e10i	−0.164320	−	0.223147i
$569$	2.20454e9	+	6.78487e9i	0.0210314	+	0.0647280i	0.961021	−	0.276474i	$-0.0891660\pi$
$569$	2.20454e9	+	6.78487e9i	0.0210314	+	0.0647280i	−0.939990	+	0.341202i	$0.889166\pi$
$570$	−4.29324e10	+	2.08222e9i	−0.406711	+	0.0197254i
$571$	1.33445e11	+	4.33590e10i	1.25533	+	0.407882i	0.859829	−	0.510582i	$-0.170570\pi$
$571$	1.33445e11	+	4.33590e10i	1.25533	+	0.407882i	0.395504	+	0.918464i	$0.370570\pi$
$572$	5.63721e9	−	6.16844e8i	0.0526599	−	0.00576224i
$573$	1.12291e10	−	8.15840e9i	0.104166	−	0.0756810i
$574$	3.14413e10	+	1.46382e11i	0.289636	+	1.34847i
$575$	3.08229e10	−	2.18308e10i	0.281970	−	0.199710i
$576$	2.95215e10	−	9.49810e10i	0.268194	−	0.862873i
$577$	5.29049e10	−	3.84376e10i	0.477301	−	0.346779i	−0.322979	−	0.946406i	$-0.604684\pi$
$577$	5.29049e10	−	3.84376e10i	0.477301	−	0.346779i	0.800280	+	0.599627i	$0.204684\pi$
$578$	−5.79630e9	+	5.63042e10i	−0.0519325	+	0.504463i
$579$	−3.91992e10	−	1.27366e10i	−0.348790	−	0.113329i
$580$	−2.77750e10	−	4.29353e10i	−0.245438	−	0.379405i
$581$	9.45878e10	+	2.91111e11i	0.830100	+	2.55479i
$582$	1.13110e9	+	5.26608e9i	0.00985844	+	0.0458982i
$583$	−1.24596e10	+	4.04837e9i	−0.107852	+	0.0350434i
$584$	9.85591e10	−	6.31300e8i	0.847316	−	0.00542731i
$585$	−1.85896e10	+	3.59463e10i	−0.158725	+	0.306924i
$586$	8.34312e10	−	9.30586e10i	0.707519	−	0.789161i
$587$	−8.05310e10	+	1.10841e11i	−0.678282	+	0.933576i	−0.999912	−	0.0132899i	$-0.995770\pi$
$587$	−8.05310e10	+	1.10841e11i	−0.678282	+	0.933576i	0.321629	+	0.946866i	$0.395770\pi$
$588$	−8.18317e9	+	3.93237e10i	−0.0684561	+	0.328962i
$589$	−1.16747e11	+	8.48215e10i	−0.970027	+	0.704766i
$590$	−8.59459e10	+	1.31222e11i	−0.709279	+	1.08293i
$591$	−3.10981e10	+	4.28029e10i	−0.254909	+	0.350851i
$592$	−7.56961e10	−	3.29304e10i	−0.616292	−	0.268108i
$593$	−1.43738e11			−1.16239			−0.581197	−	0.813763i	$-0.697416\pi$
$593$	−1.43738e11			−1.16239			−0.581197	+	0.813763i	$0.697416\pi$
$594$	−5.11553e9	−	8.81684e9i	−0.0410908	−	0.0708218i
$595$	−1.97213e11	−	1.01989e11i	−1.57351	−	0.813736i
$596$	−1.79761e10	−	1.64280e11i	−0.142466	−	1.30197i
$597$	−1.17083e10	+	3.60344e10i	−0.0921713	+	0.283674i
$598$	−1.25811e10	−	1.12796e10i	−0.0983819	−	0.0882038i
$599$		−	4.20154e10i		−	0.326363i	−0.986596	−	0.163182i	$-0.947824\pi$
$599$		−	4.20154e10i		−	0.326363i	0.986596	−	0.163182i	$-0.0521756\pi$
$600$	3.26886e10	−	2.34681e10i	0.252227	−	0.181081i
$601$	2.17535e11			1.66737			0.833683	−	0.552243i	$-0.186228\pi$
$601$	2.17535e11			1.66737			0.833683	+	0.552243i	$0.186228\pi$
$602$	−2.14482e11	+	2.39232e11i	−1.63307	+	1.82152i
$603$	−4.59252e10	−	1.49220e10i	−0.347362	−	0.112865i
$604$	5.52179e10	−	6.04214e9i	0.414890	−	0.0453987i
$605$	−1.17439e11	+	5.89484e10i	−0.876578	+	0.439998i
$606$	−3.51300e10	+	2.03825e10i	−0.260488	+	0.151135i
$607$		−	2.53898e11i		−	1.87027i	−0.354288	−	0.935136i	$-0.615277\pi$
$607$		−	2.53898e11i		−	1.87027i	0.354288	−	0.935136i	$-0.384723\pi$
$608$	−3.53857e10	+	1.75678e11i	−0.258948	+	1.28559i
$609$	2.25298e10	+	1.63688e10i	0.163790	+	0.119000i
$610$	−1.57942e10	+	1.26883e10i	−0.114072	+	0.0916398i
$611$	−2.32935e10	−	3.20608e10i	−0.167136	−	0.230043i
$612$	−1.52352e11	−	3.17040e10i	−1.08603	−	0.226000i
$613$	1.46554e11	+	1.06478e11i	1.03790	+	0.754080i	0.969875	−	0.243604i	$-0.0783296\pi$
$613$	1.46554e11	+	1.06478e11i	1.03790	+	0.754080i	0.0680270	+	0.997683i	$0.478330\pi$
$614$	−1.05161e11	−	9.42812e10i	−0.739911	−	0.663364i
$615$	−6.89437e9	+	4.18920e10i	−0.0481941	+	0.292840i
$616$	−2.87815e10	+	1.84354e8i	−0.199890	+	0.00128035i
$617$	−1.90443e10	−	5.86122e10i	−0.131408	−	0.404434i	0.863606	−	0.504168i	$-0.168201\pi$
$617$	−1.90443e10	−	5.86122e10i	−0.131408	−	0.404434i	−0.995014	+	0.0997343i	$0.968201\pi$
$618$	6.42694e10	−	1.38044e10i	0.440606	−	0.0946374i
$619$	1.71875e11	−	5.58457e10i	1.17071	−	0.380388i	0.341805	−	0.939771i	$-0.388962\pi$
$619$	1.71875e11	−	5.58457e10i	1.17071	−	0.380388i	0.828910	+	0.559383i	$0.188962\pi$
$620$	4.86377e10	−	1.26041e11i	0.329159	−	0.852991i
$621$	−9.38567e9	+	2.88861e10i	−0.0631101	+	0.194233i
$622$	−1.68997e11	−	1.73976e10i	−1.12906	−	0.116232i
$623$	−4.35983e10	−	6.00079e10i	−0.289413	−	0.398342i
$624$	−1.34804e10	−	1.19310e10i	−0.0889130	−	0.0786931i
$625$	−1.52543e11	−	3.68189e9i	−0.999709	−	0.0241297i
$626$	−2.70728e11	+	5.81494e10i	−1.76293	+	0.378659i
$627$	5.12421e9	+	7.05286e9i	0.0331556	+	0.0456347i
$628$	1.19987e10	+	1.09654e11i	0.0771429	+	0.704993i
$629$	−3.99102e10	+	1.22831e11i	−0.254966	+	0.784703i
$630$	1.12537e11	−	1.71822e11i	0.714388	−	1.09073i
$631$	−2.35172e11	+	7.64119e10i	−1.48343	+	0.481996i	−0.935136	−	0.354289i	$-0.884723\pi$
$631$	−2.35172e11	+	7.64119e10i	−1.48343	+	0.481996i	−0.548295	+	0.836285i	$0.684723\pi$
$632$	−1.18205e11	−	1.60522e11i	−0.740911	−	1.00616i
$633$	−2.44536e10	−	7.52605e10i	−0.152310	−	0.468762i
$634$	−6.91945e10	−	3.06305e10i	−0.428267	−	0.189582i
$635$	6.91405e9	−	4.20116e10i	0.0425243	−	0.258389i
$636$	3.61047e10	+	2.06400e10i	0.220666	+	0.126148i
$637$	−5.51229e10	−	4.00491e10i	−0.334791	−	0.243240i
$638$	−4.19821e9	+	9.48377e9i	−0.0253385	+	0.0572398i
$639$	−2.45393e10	−	3.37755e10i	−0.147183	−	0.202581i
$640$	−6.15177e10	−	1.56087e11i	−0.366674	−	0.930349i
$641$	1.55495e11	+	1.12974e11i	0.921051	+	0.669182i	0.943785	−	0.330559i	$-0.107237\pi$
$641$	1.55495e11	+	1.12974e11i	0.921051	+	0.669182i	−0.0227347	+	0.999742i	$0.507237\pi$
$642$	−3.78784e10	−	6.52850e10i	−0.222972	−	0.384302i
$643$			8.41991e10i			0.492565i	0.969198	+	0.246283i	$0.0792091\pi$
$643$			8.41991e10i			0.492565i	−0.969198	+	0.246283i	$0.920791\pi$
$644$	5.76565e10	+	6.34867e10i	0.335200	+	0.369096i
$645$	−8.14275e10	+	4.08725e10i	−0.470470	+	0.236152i
$646$	2.78904e11	+	2.87121e10i	1.60149	+	0.164867i
$647$	−2.03938e11	−	6.62634e10i	−1.16381	−	0.378144i	−0.337479	−	0.941333i	$-0.609574\pi$
$647$	−2.03938e11	−	6.62634e10i	−1.16381	−	0.378144i	−0.826328	+	0.563190i	$0.809574\pi$
$648$	3.84592e10	−	1.20997e11i	0.218123	−	0.686238i
$649$	3.18151e10			0.179331
$650$	1.35286e10	+	6.69076e10i	0.0757879	+	0.374819i
$651$			7.35744e10i			0.409640i
$652$	−2.60107e11	−	1.48696e11i	−1.43933	−	0.822826i
$653$	−1.05900e11	+	3.25926e11i	−0.582428	+	1.79253i	0.0269360	+	0.999637i	$0.491425\pi$
$653$	−1.05900e11	+	3.25926e11i	−0.582428	+	1.79253i	−0.609364	+	0.792891i	$0.708575\pi$
$654$	−8.97749e10	−	9.24197e9i	−0.490732	−	0.0505189i
$655$	7.34774e10	+	3.79987e10i	0.399198	+	0.206445i
$656$	1.62313e11	+	7.06118e10i	0.876474	+	0.381296i
$657$	1.42655e11			0.765643
$658$	1.00940e11	+	1.73974e11i	0.538466	+	0.928069i
$659$	−1.29239e11	+	1.77882e11i	−0.685254	+	0.943172i	−0.999982	−	0.00601044i	$-0.998087\pi$
$659$	−1.29239e11	+	1.77882e11i	−0.685254	+	0.943172i	0.314728	+	0.949182i	$0.398087\pi$
$660$	−7.61434e9	−	2.93828e9i	−0.0401288	−	0.0154852i
$661$	1.22923e11	−	8.93089e10i	0.643914	−	0.467831i	−0.217279	−	0.976110i	$-0.569718\pi$
$661$	1.22923e11	−	8.93089e10i	0.643914	−	0.467831i	0.861193	+	0.508279i	$0.169718\pi$
$662$	1.35311e10	−	3.05668e10i	0.0704531	−	0.159154i
$663$	−1.65550e10	+	2.27860e10i	−0.0856790	+	0.117927i
$664$	3.44876e11	+	1.09620e11i	1.77415	+	0.563920i
$665$	−1.69994e11	+	3.28714e11i	−0.869255	+	1.68086i
$666$	−1.09253e11	−	4.83635e10i	−0.555313	−	0.245822i
$667$	2.93907e10	−	9.54962e9i	0.148493	−	0.0482484i
$668$	1.95102e10	+	4.33218e10i	0.0979841	+	0.217571i
$669$	−2.26837e10	−	6.98131e10i	−0.113242	−	0.348524i
$670$	−7.61554e10	+	2.88932e10i	−0.377921	+	0.143383i
$671$	3.90795e9	+	1.26977e9i	0.0192779	+	0.00626376i
$672$	6.18582e10	+	6.72428e10i	0.303333	+	0.329738i
$673$	1.93412e11	−	1.40522e11i	0.942806	−	0.684989i	−0.00628815	−	0.999980i	$-0.502002\pi$
$673$	1.93412e11	−	1.40522e11i	0.942806	−	0.684989i	0.949095	+	0.314991i	$0.102002\pi$
$674$	3.13959e11	−	6.74350e10i	1.52137	−	0.326773i
$675$	1.00130e11	−	7.09186e10i	0.482334	−	0.341621i
$676$	−1.62565e11	+	7.32117e10i	−0.778465	+	0.350586i
$677$	1.79053e11	−	1.30089e11i	0.852366	−	0.619280i	−0.0734311	−	0.997300i	$-0.523395\pi$
$677$	1.79053e11	−	1.30089e11i	0.852366	−	0.619280i	0.925797	+	0.378020i	$0.123395\pi$
$678$	−7.80384e10	−	8.03375e9i	−0.369309	−	0.0380189i
$679$	4.41037e10	+	1.43302e10i	0.207489	+	0.0674174i
$680$	−2.33835e11	+	1.19254e11i	−1.09364	+	0.557749i
$681$	1.00539e10	+	3.09427e10i	0.0467461	+	0.143870i
$682$	−2.67900e10	+	5.75421e9i	−0.123833	+	0.0265979i
$683$	2.79983e10	−	9.09719e9i	0.128661	−	0.0418047i	−0.243979	−	0.969781i	$-0.578453\pi$
$683$	2.79983e10	−	9.09719e9i	0.128661	−	0.0418047i	0.372640	+	0.927976i	$0.378453\pi$
$684$	−5.28441e10	+	2.53939e11i	−0.241419	+	1.16013i
$685$	3.64931e10	+	2.39761e11i	0.165748	+	1.08897i
$686$	1.95500e10	+	1.75275e10i	0.0882775	+	0.0791448i
$687$	−3.24521e10	+	4.46665e10i	−0.145686	+	0.200519i
$688$	8.21474e10	+	3.70870e11i	0.366640	+	1.65527i
$689$	−5.70741e10	+	4.14668e10i	−0.253258	+	0.184002i
$690$	8.62646e9	+	2.27372e10i	0.0380571	+	0.100309i
$691$	−8.19248e10	+	1.12760e11i	−0.359338	+	0.494587i	−0.949964	−	0.312359i	$-0.898881\pi$
$691$	−8.19248e10	+	1.12760e11i	−0.359338	+	0.494587i	0.590626	+	0.806945i	$0.298881\pi$
$692$	−1.12698e10	−	1.24094e10i	−0.0491463	−	0.0541159i
$693$	−4.16586e10			−0.180622
$694$	3.33544e11	−	1.93523e11i	1.43786	−	0.834245i
$695$	1.23103e9	−	7.48008e9i	0.00527631	−	0.0320603i
$696$	3.12465e10	−	1.03744e10i	0.133157	−	0.0442104i
$697$	8.55786e10	−	2.63384e11i	0.362605	−	1.11598i
$698$	−7.98197e10	+	8.90303e10i	−0.336270	+	0.375073i
$699$		−	1.59343e10i		−	0.0667460i
$700$	−3.35274e10	−	3.44831e11i	−0.139639	−	1.43620i
$701$	2.23129e11			0.924025			0.462013	−	0.886873i	$-0.347127\pi$
$701$	2.23129e11			0.924025			0.462013	+	0.886873i	$0.347127\pi$
$702$	−4.08705e10	−	3.66422e10i	−0.168291	−	0.150881i
$703$	2.04734e11	+	6.65221e10i	0.838241	+	0.272361i
$704$	−1.96467e10	+	2.77829e10i	−0.0799832	+	0.113106i
$705$	8.58225e9	+	5.63858e10i	0.0347412	+	0.228251i
$706$	−8.57878e10	−	1.47859e11i	−0.345308	−	0.595153i
$707$			3.49681e11i			1.39957i
$708$	−6.78992e10	−	7.47652e10i	−0.270229	−	0.297555i
$709$	−3.10106e11	−	2.25305e11i	−1.22723	−	0.891634i	−0.230550	−	0.973060i	$-0.574053\pi$
$709$	−3.10106e11	−	2.25305e11i	−1.22723	−	0.891634i	−0.996679	+	0.0814261i	$0.974053\pi$
$710$	−6.79498e10	−	1.84913e10i	−0.267396	−	0.0727668i
$711$	−1.69595e11	−	2.33428e11i	−0.663644	−	0.913428i
$712$	−8.76905e10	+	5.61683e8i	−0.341218	+	0.00218560i
$713$	6.60524e10	+	4.79899e10i	0.255582	+	0.185691i
$714$	9.54250e10	−	1.06436e11i	0.367172	−	0.409541i
$715$	9.84869e9	−	9.73057e9i	0.0376838	−	0.0372318i
$716$	−4.40142e10	+	2.11508e11i	−0.167472	+	0.804774i
$717$	−3.68570e10	−	1.13434e11i	−0.139458	−	0.429207i
$718$	7.29037e10	+	3.39420e11i	0.274316	+	1.27714i
$719$	1.39189e11	−	4.52251e10i	0.520821	−	0.169225i	−0.0367971	−	0.999323i	$-0.511716\pi$
$719$	1.39189e11	−	4.52251e10i	0.520821	−	0.169225i	0.557618	+	0.830098i	$0.311716\pi$
$720$	−8.75906e10	−	2.26482e11i	−0.325932	−	0.842761i
$721$	1.74891e11	−	5.38259e11i	0.647182	−	1.99182i
$722$	2.00299e10	−	1.94567e11i	0.0737106	−	0.716012i
$723$	−2.67995e10	−	3.68864e10i	−0.0980784	−	0.134993i
$724$	2.44320e11	−	1.10031e11i	0.889212	−	0.400461i
$725$	−1.18259e11	−	4.00086e10i	−0.428039	−	0.144811i
$726$	−1.77667e10	−	8.27170e10i	−0.0639530	−	0.297748i
$727$	2.86354e11	+	3.94132e11i	1.02510	+	1.41092i	0.908568	+	0.417737i	$0.137177\pi$
$727$	2.86354e11	+	3.94132e11i	1.02510	+	1.41092i	0.116529	+	0.993187i	$0.462823\pi$
$728$	−1.47095e11	+	4.88380e10i	−0.523689	+	0.173873i
$729$	4.07687e10	−	1.25473e11i	0.144350	−	0.444263i
$730$	1.87592e11	−	1.50702e11i	0.660575	−	0.530673i
$731$	5.65223e11	−	1.83652e11i	1.97948	−	0.643171i
$732$	−5.35634e9	−	1.18936e10i	−0.0186562	−	0.0414256i
$733$	−1.65412e11	−	5.09085e11i	−0.572995	−	1.76350i	−0.642908	−	0.765943i	$-0.722272\pi$
$733$	−1.65412e11	−	5.09085e11i	−0.572995	−	1.76350i	0.0699133	−	0.997553i	$-0.477728\pi$
$734$	−7.88560e10	+	1.78136e11i	−0.271676	+	0.613717i
$735$	4.39912e10	+	8.76408e10i	0.150736	+	0.300301i
$736$	1.00716e11	−	1.16740e10i	0.343232	−	0.0397840i
$737$	1.33651e10	+	9.71033e9i	0.0453005	+	0.0329127i
$738$	2.34270e11	+	1.03705e11i	0.789751	+	0.349601i
$739$	−1.14640e11	−	1.57788e11i	−0.384378	−	0.529051i	0.572360	−	0.820003i	$-0.306028\pi$
$739$	−1.14640e11	−	1.57788e11i	−0.384378	−	0.529051i	−0.956738	+	0.290952i	$0.906028\pi$
$740$	−1.94760e11	+	5.18179e10i	−0.649489	+	0.172804i
$741$	3.79795e10	+	2.75937e10i	0.125973	+	0.0915246i
$742$	3.09705e11	−	1.79691e11i	1.02172	−	0.592804i
$743$		−	5.75184e11i		−	1.88735i	−0.330878	−	0.943673i	$-0.607345\pi$
$743$		−	5.75184e11i		−	1.88735i	0.330878	−	0.943673i	$-0.392655\pi$
$744$	7.06972e10	+	5.06758e10i	0.230733	+	0.165390i
$745$	−2.83569e11	−	2.87012e11i	−0.920522	−	0.931697i
$746$	3.55440e10	−	3.45268e11i	0.114765	−	1.11481i
$747$	4.98140e11	+	1.61856e11i	1.59981	+	0.519811i
$748$	4.62189e10	+	2.64220e10i	0.147643	+	0.0844032i
$749$	−6.49840e11			−2.06481
$750$	2.69388e10	−	9.44777e10i	0.0851400	−	0.298596i
$751$		−	2.79969e11i		−	0.880138i	−0.897964	−	0.440069i	$-0.854954\pi$
$751$		−	2.79969e11i		−	0.880138i	0.897964	−	0.440069i	$-0.145046\pi$
$752$	2.36695e11	+	2.28356e10i	0.740145	+	0.0714071i
$753$	−1.44373e10	+	4.44335e10i	−0.0449063	+	0.138207i
$754$	−5.71931e9	+	5.55564e10i	−0.0176953	+	0.171889i
$755$	9.64704e10	−	9.53134e10i	0.296897	−	0.293337i
$756$	1.87300e11	+	2.06240e11i	0.573391	+	0.631372i
$757$	1.77947e10			0.0541884			0.0270942	−	0.999633i	$-0.491375\pi$
$757$	1.77947e10			0.0541884			0.0270942	+	0.999633i	$0.491375\pi$
$758$	−3.47836e11	+	2.01815e11i	−1.05365	+	0.611331i
$759$	2.89915e9	−	3.99034e9i	0.00873581	−	0.0120238i
$760$	1.98773e11	+	3.89755e11i	0.595803	+	1.16825i
$761$	1.00511e11	−	7.30252e10i	0.299690	−	0.217738i	−0.427770	−	0.903888i	$-0.640701\pi$
$761$	1.00511e11	−	7.30252e10i	0.299690	−	0.217738i	0.727460	+	0.686150i	$0.240701\pi$
$762$	2.50667e10	+	1.10963e10i	0.0743493	+	0.0329124i
$763$	−4.56720e11	+	6.28621e11i	−1.34757	+	1.85477i
$764$	−1.22654e11	−	7.01174e10i	−0.360003	−	0.205803i
$765$	−3.39546e11	+	1.70435e11i	−0.991410	+	0.497638i
$766$	1.83271e11	−	4.14011e11i	0.532328	−	1.20253i
$767$	1.62938e11	−	5.29419e10i	0.470806	−	0.152974i
$768$	1.07219e11	−	1.31243e10i	0.308197	−	0.0377252i
$769$	−1.43340e11	−	4.41156e11i	−0.409886	−	1.26150i	−0.916746	−	0.399470i	$-0.869194\pi$
$769$	−1.43340e11	−	4.41156e11i	−0.409886	−	1.26150i	0.506860	−	0.862028i	$-0.330806\pi$
$770$	−5.47810e10	+	4.40084e10i	−0.155836	+	0.125191i
$771$	1.85625e11	+	6.03132e10i	0.525313	+	0.170685i
$772$	4.56347e10	+	4.17046e11i	0.128477	+	1.17413i
$773$	1.64137e10	−	1.19252e10i	0.0459715	−	0.0334002i	−0.564562	−	0.825391i	$-0.690955\pi$
$773$	1.64137e10	−	1.19252e10i	0.0459715	−	0.0334002i	0.610534	+	0.791990i	$0.290955\pi$
$774$	1.15458e11	+	5.37540e11i	0.321706	+	1.49778i
$775$	−9.81318e10	−	3.14897e11i	−0.272021	−	0.872894i
$776$	4.41471e10	−	3.25088e10i	0.121746	−	0.0896507i
$777$	8.87934e10	−	6.45122e10i	0.243611	−	0.176994i
$778$	−6.16919e10	+	5.99265e11i	−0.168388	+	1.63569i
$779$	−4.39007e11	−	1.42642e11i	−1.19212	−	0.387344i
$780$	−4.38857e10	−	2.37753e9i	−0.118562	−	0.00642316i
$781$	4.41363e9	+	1.35838e10i	0.0118629	+	0.0365104i
$782$	−3.33124e10	−	1.55094e11i	−0.0890798	−	0.414731i
$783$	9.54772e10	−	3.10224e10i	0.254011	−	0.0825332i
$784$	3.99169e11	−	8.84157e10i	1.05656	−	0.234026i
$785$	1.89277e11	+	1.91574e11i	0.498447	+	0.504498i
$786$	−3.55532e10	+	3.96558e10i	−0.0931513	+	0.103900i
$787$	2.42304e11	−	3.33503e11i	0.631628	−	0.869362i	−0.366506	−	0.930416i	$-0.619446\pi$
$787$	2.42304e11	−	3.33503e11i	0.631628	−	0.869362i	0.998134	+	0.0610540i	$0.0194462\pi$
$788$	5.27239e11	+	1.09717e11i	1.36742	+	0.284557i
$789$	5.78348e10	−	4.20194e10i	0.149239	−	0.108428i
$790$	−4.69612e11	−	1.27796e11i	−1.20568	−	0.328103i
$791$	−3.97012e11	+	5.46440e11i	−1.01414	+	1.39584i
$792$	−2.86932e10	+	4.00295e10i	−0.0729252	+	0.101737i
$793$	2.21272e10			0.0559544
$794$	−1.92174e11	−	3.31220e11i	−0.483518	−	0.833364i
$795$	1.00377e11	−	1.52780e10i	0.251285	−	0.0382470i
$796$	3.83375e11	−	4.19502e10i	0.954929	−	0.104492i
$797$	1.55447e11	−	4.78416e11i	0.385255	−	1.18569i	−0.551040	−	0.834479i	$-0.685769\pi$
$797$	1.55447e11	−	4.78416e11i	0.385255	−	1.18569i	0.936295	−	0.351214i	$-0.114231\pi$
$798$	−1.77407e11	−	1.59054e11i	−0.437482	−	0.392222i
$799$		−	3.72041e11i		−	0.912860i
$800$	−3.54439e11	−	2.05293e11i	−0.865329	−	0.501204i
$801$	−1.26924e11			−0.308328
$802$	−1.31556e11	+	1.46736e11i	−0.317989	+	0.354682i
$803$	−4.64157e10	−	1.50814e10i	−0.111636	−	0.0362726i
$804$	−5.70442e9	−	5.21316e10i	−0.0136517	−	0.124760i
$805$	2.06597e11	+	3.40006e10i	0.491971	+	0.0809661i
$806$	−1.27628e11	+	7.40496e10i	−0.302416	+	0.175462i
$807$			1.79220e11i			0.422564i
$808$	3.36006e11	+	2.40850e11i	0.788318	+	0.565068i
$809$	1.15794e11	+	8.41292e10i	0.270329	+	0.196405i	0.714688	−	0.699443i	$-0.246569\pi$
$809$	1.15794e11	+	8.41292e10i	0.270329	+	0.196405i	−0.444359	+	0.895849i	$0.646569\pi$
$810$	−1.09953e11	−	2.89809e11i	−0.255427	−	0.673243i
$811$	−1.47000e11	−	2.02328e11i	−0.339808	−	0.467705i	0.604577	−	0.796546i	$-0.293342\pi$
$811$	−1.47000e11	−	2.02328e11i	−0.339808	−	0.467705i	−0.944385	+	0.328841i	$0.893342\pi$
$812$	5.77508e10	−	2.77518e11i	0.132841	−	0.638362i
$813$	1.24895e11	+	9.07415e10i	0.285879	+	0.207703i
$814$	3.04348e10	+	2.72861e10i	0.0693222	+	0.0621505i
$815$	−7.23141e11	+	1.10066e11i	−1.63905	+	0.249473i
$816$	−3.65481e10	−	1.65003e11i	−0.0824336	−	0.372162i
$817$	−3.06110e11	−	9.42110e11i	−0.687052	−	2.11453i
$818$	−5.56778e11	+	1.19590e11i	−1.24357	+	0.267105i
$819$	−2.13351e11	+	6.93220e10i	−0.474197	+	0.154076i
$820$	4.17619e11	−	1.11112e11i	0.923686	−	0.245757i
$821$	−1.00941e11	+	3.10664e11i	−0.222174	+	0.683782i	0.776392	+	0.630251i	$0.217048\pi$
$821$	−1.00941e11	+	3.10664e11i	−0.222174	+	0.683782i	−0.998566	+	0.0535318i	$0.982952\pi$
$822$	−1.55327e11	−	1.59903e10i	−0.340219	−	0.0350242i
$823$	9.59342e10	+	1.32042e11i	0.209110	+	0.287815i	0.900670	−	0.434504i	$-0.143076\pi$
$823$	9.59342e10	+	1.32042e11i	0.209110	+	0.287815i	−0.691560	+	0.722319i	$0.743076\pi$
$824$	−3.96750e11	−	5.38789e11i	−0.860614	−	1.16872i
$825$	−1.90234e10	+	5.92830e9i	−0.0410651	+	0.0127972i
$826$	−8.50152e11	+	1.82603e11i	−1.82632	+	0.392273i
$827$	−6.09143e10	−	8.38414e10i	−0.130226	−	0.179241i	0.738925	−	0.673788i	$-0.235334\pi$
$827$	−6.09143e10	−	8.38414e10i	−0.130226	−	0.179241i	−0.869151	+	0.494547i	$0.835334\pi$
$828$	1.45880e11	−	1.59626e10i	0.310365	−	0.0339612i
$829$	−6.56104e10	+	2.01928e11i	−0.138917	+	0.427542i	−0.996179	−	0.0873388i	$-0.972164\pi$
$829$	−6.56104e10	+	2.01928e11i	−0.138917	+	0.427542i	0.857262	+	0.514881i	$0.172164\pi$
$830$	8.26039e11	−	3.13398e11i	1.74056	−	0.660365i
$831$	1.62623e11	−	5.28396e10i	0.341019	−	0.110804i
$832$	−5.43867e10	+	1.74981e11i	−0.113501	+	0.365172i
$833$	−1.97666e11	−	6.08352e11i	−0.410536	−	1.26350i
$834$	4.46307e9	+	1.97568e9i	0.00922507	+	0.00408369i
$835$	1.03034e11	+	5.32841e10i	0.211952	+	0.109610i
$836$	4.40400e10	−	7.70374e10i	0.0901617	−	0.157716i
$837$	2.14575e11	+	1.55898e11i	0.437196	+	0.317642i
$838$	−1.96594e11	+	4.44108e11i	−0.398653	+	0.900559i
$839$	5.72264e11	+	7.87653e11i	1.15491	+	1.58960i	0.728462	+	0.685086i	$0.240235\pi$
$839$	5.72264e11	+	7.87653e11i	1.15491	+	1.58960i	0.426448	+	0.904512i	$0.359765\pi$
$840$	2.20332e11	+	3.48131e10i	0.442548	+	0.0699239i
$841$	3.22071e11	+	2.33999e11i	0.643826	+	0.467767i
$842$	3.26363e10	+	5.62500e10i	0.0649310	+	0.111911i
$843$			1.74345e11i			0.345223i
$844$	−5.96286e11	+	5.41527e11i	−1.17513	+	1.06721i
$845$	−1.99948e11	+	3.86636e11i	−0.392184	+	0.758359i
$846$	3.42368e11	+	3.52454e10i	0.668362	+	0.0688052i
$847$	−6.92759e11	−	2.25091e11i	−1.34601	−	0.437345i
$848$	4.06516e10	−	4.21360e11i	0.0786130	−	0.814835i
$849$	−1.75958e11			−0.338670
$850$	−2.66455e11	+	5.82821e11i	−0.510444	+	1.11650i
$851$		−	1.21794e11i		−	0.232225i
$852$	2.25022e10	−	3.93623e10i	0.0427039	−	0.0747002i
$853$	6.37165e10	−	1.96099e11i	0.120353	−	0.370408i	−0.872673	−	0.488305i	$-0.837615\pi$
$853$	6.37165e10	−	1.96099e11i	0.120353	−	0.370408i	0.993026	+	0.117897i	$0.0376154\pi$
$854$	−1.11715e11	−	1.15006e10i	−0.210029	−	0.0216217i
$855$	2.84080e11	+	5.65954e11i	0.531590	+	1.05905i
$856$	−4.47590e11	+	6.24427e11i	−0.833653	+	1.16302i
$857$	5.70275e11			1.05721			0.528605	−	0.848868i	$-0.322715\pi$
$857$	5.70275e11			1.05721			0.528605	+	0.848868i	$0.322715\pi$
$858$	4.47346e9	+	7.71020e9i	0.00825457	+	0.0142271i
$859$	2.72726e11	−	3.75375e11i	0.500903	−	0.689434i	−0.481449	−	0.876474i	$-0.659889\pi$
$859$	2.72726e11	−	3.75375e11i	0.500903	−	0.689434i	0.982352	+	0.187040i	$0.0598894\pi$
$860$	7.19688e11	+	5.84895e11i	1.31568	+	1.06926i
$861$	−1.90398e11	+	1.38332e11i	−0.346457	+	0.251716i
$862$	−3.86957e11	+	8.74138e11i	−0.700864	+	1.58326i
$863$	4.95473e11	−	6.81960e11i	0.893258	−	1.22946i	−0.0793116	−	0.996850i	$-0.525272\pi$
$863$	4.95473e11	−	6.81960e11i	0.893258	−	1.22946i	0.972569	−	0.232614i	$-0.0747278\pi$
$864$	3.27181e11	−	3.79236e10i	0.587129	−	0.0680541i
$865$	−4.03822e10	−	6.64589e9i	−0.0721316	−	0.0118710i
$866$	−2.66615e11	−	1.18023e11i	−0.474038	−	0.209844i
$867$	−8.46172e10	+	2.74938e10i	−0.149755	+	0.0486585i
$868$	6.82848e11	−	3.07524e11i	1.20294	−	0.541751i
$869$	3.05034e10	+	9.38797e10i	0.0534895	+	0.164624i
$870$	4.40407e10	−	6.72414e10i	0.0768735	−	0.117371i
$871$	8.46069e10	+	2.74904e10i	0.147005	+	0.0477649i
$872$	2.89463e11	+	8.71835e11i	0.500642	+	1.50789i
$873$	6.41976e10	−	4.66423e10i	0.110525	−	0.0803014i
$874$	−2.58509e11	+	5.55249e10i	−0.443027	+	0.0951574i
$875$	−5.87179e11	−	6.08828e11i	−1.00170	−	1.03863i
$876$	6.36184e10	+	1.41263e11i	0.108036	+	0.239890i
$877$	−6.28734e11	+	4.56802e11i	−1.06284	+	0.772199i	−0.974612	−	0.223901i	$-0.928121\pi$
$877$	−6.28734e11	+	4.56802e11i	−1.06284	+	0.772199i	−0.0882293	+	0.996100i	$0.528121\pi$
$878$	−2.14523e11	−	2.20843e10i	−0.360990	−	0.0371625i
$879$	1.86844e11	+	6.07092e10i	0.312985	+	0.101695i
$880$	4.55582e9	+	8.29504e10i	0.00759690	+	0.138321i
$881$	1.13216e11	+	3.48444e11i	0.187934	+	0.578401i	0.999987	−	0.00518288i	$-0.00164977\pi$
$881$	1.13216e11	+	3.48444e11i	0.187934	+	0.578401i	−0.812053	+	0.583584i	$0.801650\pi$
$882$	5.78557e11	−	1.24268e11i	0.956031	−	0.205345i
$883$	9.49886e10	−	3.08637e10i	0.156253	−	0.0507697i	−0.229846	−	0.973227i	$-0.573822\pi$
$883$	9.49886e10	−	3.08637e10i	0.156253	−	0.0507697i	0.386099	+	0.922457i	$0.373822\pi$
$884$	2.80674e11	+	5.84075e10i	0.459614	+	0.0956444i
$885$	−2.43299e11	−	4.00409e10i	−0.396613	−	0.0652725i
$886$	−7.44600e11	−	6.67568e11i	−1.20834	−	1.08333i
$887$	3.41841e11	−	4.70504e11i	0.552242	−	0.760096i	−0.438072	−	0.898940i	$-0.644339\pi$
$887$	3.41841e11	−	4.70504e11i	0.552242	−	0.760096i	0.990314	+	0.138844i	$0.0443386\pi$
$888$	−8.31119e8	−	1.29755e11i	−0.00133663	−	0.208676i
$889$	1.90941e11	−	1.38727e11i	0.305698	−	0.222103i
$890$	−1.66905e11	+	1.34083e11i	−0.266017	+	0.213705i
$891$	−3.69526e10	+	5.08610e10i	−0.0586320	+	0.0807000i
$892$	−5.53127e11	+	5.02331e11i	−0.873706	+	0.793470i
$893$	−6.20116e11			−0.975141
$894$	2.24692e11	−	1.30366e11i	0.351752	−	0.204087i
$895$	2.36613e11	+	4.71387e11i	0.368762	+	0.734659i
$896$	3.65531e11	−	8.55169e11i	0.567143	−	1.32684i
$897$	8.20764e9	−	2.52605e10i	0.0126779	−	0.0390187i
$898$	−3.37117e11	+	3.76018e11i	−0.518412	+	0.578233i
$899$		−	2.69862e11i		−	0.413145i
$900$	−5.11094e11	−	3.00417e11i	−0.778987	−	0.457883i
$901$	−6.62302e11			−1.00498
$902$	−6.52606e10	−	5.85091e10i	−0.0985881	−	0.0883887i
$903$	−4.80332e11	−	1.56069e11i	−0.722421	−	0.234729i
$904$	2.51621e11	+	7.57858e11i	0.376767	+	1.13479i
$905$	3.00504e11	−	5.81080e11i	0.447978	−	0.866246i
$906$	4.38187e10	+	7.55234e10i	0.0650349	+	0.112090i
$907$			1.44384e11i			0.213349i	0.994294	+	0.106674i	$0.0340202\pi$
$907$			1.44384e11i			0.213349i	−0.994294	+	0.106674i	$0.965980\pi$
$908$	2.45158e11	−	2.22644e11i	0.360664	−	0.327543i
$909$	4.84085e11	+	3.51708e11i	0.709033	+	0.515142i
$910$	−2.07325e11	+	3.16544e11i	−0.302333	+	0.461602i
$911$	6.87415e11	+	9.46146e11i	0.998035	+	1.37368i	0.926524	+	0.376237i	$0.122782\pi$
$911$	6.87415e11	+	9.46146e11i	0.998035	+	1.37368i	0.0715110	+	0.997440i	$0.477218\pi$
$912$	−2.75027e11	+	6.09182e10i	−0.397553	+	0.0880577i
$913$	−1.44968e11	−	1.05326e11i	−0.208636	−	0.151583i
$914$	6.21712e11	−	6.93453e11i	0.890850	−	0.993648i
$915$	−2.82871e10	−	1.46286e10i	−0.0403557	−	0.0208699i
$916$	5.50195e11	+	1.14494e11i	0.781510	+	0.162630i
$917$	1.41700e11	+	4.36108e11i	0.200398	+	0.616760i
$918$	−1.08217e11	−	5.03829e11i	−0.152379	−	0.709435i
$919$	7.09728e11	−	2.30605e11i	0.995015	−	0.323300i	0.234143	−	0.972202i	$-0.424771\pi$
$919$	7.09728e11	−	2.30605e11i	0.995015	−	0.323300i	0.760872	+	0.648902i	$0.224771\pi$
$920$	1.74969e11	−	1.75099e11i	0.244235	−	0.244417i
$921$	6.86043e10	−	2.11142e11i	0.0953483	−	0.293452i
$922$	−5.84521e9	+	5.67794e10i	−0.00808866	+	0.0785719i
$923$	4.52081e10	+	6.22237e10i	0.0622888	+	0.0857332i
$924$	−1.85780e10	−	4.12519e10i	−0.0254866	−	0.0565922i
$925$	−2.93989e11	+	3.94541e11i	−0.401573	+	0.538922i
$926$	−1.63461e11	−	7.61031e11i	−0.222316	−	1.03504i
$927$	−5.69241e11	−	7.83493e11i	−0.770863	−	1.06100i
$928$	−2.26888e11	−	2.46638e11i	−0.305929	−	0.332559i
$929$	−1.80536e11	+	5.55632e11i	−0.242382	+	0.745975i	0.753674	+	0.657249i	$0.228280\pi$
$929$	−1.80536e11	+	5.55632e11i	−0.242382	+	0.745975i	−0.996056	+	0.0887268i	$0.971720\pi$
$930$	2.12113e11	−	1.02874e10i	0.283553	−	0.0137523i
$931$	−1.01400e12	+	3.29468e11i	−1.34970	+	0.438545i
$932$	−1.47887e11	+	6.66018e10i	−0.196005	+	0.0882719i
$933$	−8.25226e10	−	2.53978e11i	−0.108905	−	0.335174i
$934$	−2.87308e10	+	6.49029e10i	−0.0377537	+	0.0852858i
$935$	1.28496e11	−	1.95579e10i	0.168129	−	0.0255903i
$936$	−8.03388e10	+	2.52755e11i	−0.104670	+	0.329303i
$937$	1.09534e12	+	7.95809e11i	1.42099	+	1.03241i	0.991608	+	0.129281i	$0.0412670\pi$
$937$	1.09534e12	+	7.95809e11i	1.42099	+	1.03241i	0.429377	+	0.903125i	$0.358733\pi$
$938$	−4.12871e11	−	1.82767e11i	−0.533339	−	0.236095i
$939$	−2.55840e11	−	3.52133e11i	−0.329083	−	0.452944i
$940$	4.87448e11	−	3.15332e11i	0.624333	−	0.403884i
$941$	−6.51321e10	−	4.73212e10i	−0.0830685	−	0.0603528i	0.545476	−	0.838127i	$-0.316349\pi$
$941$	−6.51321e10	−	4.73212e10i	−0.0830685	−	0.0603528i	−0.628544	+	0.777774i	$0.716349\pi$
$942$	−1.49977e11	+	8.70168e10i	−0.190468	+	0.110509i
$943$			2.61161e11i			0.330264i
$944$	−4.10097e11	+	9.42678e11i	−0.516415	+	1.18707i
$945$	6.71140e11	+	1.10453e11i	0.841561	+	0.138500i
$946$	1.92617e10	−	1.87105e11i	0.0240509	−	0.233626i
$947$	−6.39643e11	−	2.07833e11i	−0.795312	−	0.258413i	−0.116948	−	0.993138i	$-0.537311\pi$
$947$	−6.39643e11	−	2.07833e11i	−0.795312	−	0.258413i	−0.678365	+	0.734725i	$0.737311\pi$
$948$	1.55517e11	−	2.72039e11i	0.192550	−	0.336820i
$949$	−2.62810e11			−0.324024
$950$	9.71442e11	+	4.44125e11i	1.19268	+	0.545270i
$951$		−	1.18947e11i		−	0.145422i
$952$	−1.38669e12	−	4.40765e11i	−1.68824	−	0.536611i
$953$	1.02687e11	−	3.16039e11i	0.124493	−	0.383150i	−0.869315	−	0.494258i	$-0.835440\pi$
$953$	1.02687e11	−	3.16039e11i	0.124493	−	0.383150i	0.993808	+	0.111108i	$0.0354399\pi$
$954$	6.27434e10	−	6.09478e11i	0.0757486	−	0.735808i
$955$	−3.40997e11	+	5.19018e10i	−0.409956	+	0.0623978i
$956$	−8.98734e11	+	8.16200e11i	−1.07597	+	0.977158i
$957$	−1.63028e10			−0.0194363
$958$	1.25885e12	−	7.30386e11i	1.49456	−	0.867142i
$959$	−7.90207e11	+	1.08763e12i	−0.934257	+	1.28589i
$960$	1.85210e11	−	1.87737e11i	0.218062	−	0.221038i
$961$	−1.13202e11	+	8.22460e10i	−0.132727	+	0.0964320i
$962$	2.01275e11	+	8.90988e10i	0.235011	+	0.104033i
$963$	−6.53608e11	+	8.99615e11i	−0.759998	+	1.04605i
$964$	−2.30328e11	+	4.02904e11i	−0.266710	+	0.466545i
$965$	7.19876e11	+	7.28615e11i	0.830135	+	0.840212i
$966$	−5.45674e10	+	1.23268e11i	−0.0626650	+	0.141561i
$967$	−1.98103e11	+	6.43675e10i	−0.226561	+	0.0736140i	−0.420097	−	0.907479i	$-0.638004\pi$
$967$	−1.98103e11	+	6.43675e10i	−0.226561	+	0.0736140i	0.193537	+	0.981093i	$0.438004\pi$
$968$	−6.93440e11	+	5.10632e11i	−0.789783	+	0.581576i
$969$	1.36191e11	+	4.19153e11i	0.154473	+	0.475420i
$970$	3.51467e10	−	1.29153e11i	0.0397006	−	0.145888i
$971$	5.06931e11	+	1.64712e11i	0.570259	+	0.185288i	0.579932	−	0.814665i	$-0.303079\pi$
$971$	5.06931e11	+	1.64712e11i	0.570259	+	0.185288i	−0.00967299	+	0.999953i	$0.503079\pi$
$972$	7.22846e11	−	7.90963e10i	0.809805	−	0.0886117i
$973$	3.39967e10	−	2.47001e10i	0.0379302	−	0.0275579i
$974$	6.86312e10	+	3.19528e11i	0.0762581	+	0.355037i
$975$	−8.75621e10	+	6.20173e10i	−0.0968941	+	0.0686269i
$976$	−8.79967e10	+	9.94249e10i	−0.0969767	+	0.109571i
$977$	−7.52045e11	+	5.46393e11i	−0.825402	+	0.599690i	−0.918255	−	0.395990i	$-0.870401\pi$
$977$	−7.52045e11	+	5.46393e11i	−0.825402	+	0.599690i	0.0928527	+	0.995680i	$0.470401\pi$
$978$	4.82280e10	−	4.68478e11i	0.0527162	−	0.512076i
$979$	4.12971e10	+	1.34183e10i	0.0449562	+	0.0146071i
$980$	6.29525e11	−	7.74603e11i	0.682510	−	0.839798i
$981$	4.10872e11	+	1.26453e12i	0.443639	+	1.36538i
$982$	−2.10729e11	−	9.81099e11i	−0.226610	−	1.05503i
$983$	9.30659e11	−	3.02389e11i	0.996728	−	0.323856i	0.235170	−	0.971954i	$-0.424435\pi$
$983$	9.30659e11	−	3.02389e11i	0.996728	−	0.323856i	0.761557	+	0.648098i	$0.224435\pi$
$984$	1.78215e9	+	2.78231e11i	0.00190092	+	0.296773i
$985$	1.17506e12	−	5.89819e11i	1.24829	−	0.626576i
$986$	−3.50007e11	+	3.90395e11i	−0.370313	+	0.413044i
$987$	−1.85837e11	+	2.55782e11i	−0.195823	+	0.269527i
$988$	9.73533e10	−	4.67825e11i	0.102170	−	0.490971i
$989$	−4.53416e11	+	3.29426e11i	−0.473927	+	0.344328i
$990$	5.82486e9	+	1.20100e11i	0.00606380	+	0.125027i
$991$	2.23072e11	−	3.07032e11i	0.231286	−	0.318338i	−0.677561	−	0.735466i	$-0.736963\pi$
$991$	2.23072e11	−	3.07032e11i	0.231286	−	0.318338i	0.908848	+	0.417128i	$0.136963\pi$
$992$	1.74827e11	−	8.67957e11i	0.180535	−	0.896296i
$993$	5.25448e10			0.0540422
$994$	−1.95904e11	−	3.37649e11i	−0.200677	−	0.345875i
$995$	6.69788e11	−	6.61755e11i	0.683353	−	0.675157i
$996$	6.18745e10	+	5.65459e11i	0.0628745	+	0.574597i
$997$	−1.03652e11	+	3.19008e11i	−0.104905	+	0.322865i	−0.989708	−	0.143101i	$-0.954293\pi$
$997$	−1.03652e11	+	3.19008e11i	−0.104905	+	0.322865i	0.884803	+	0.465965i	$0.154293\pi$
$998$	4.72189e11	+	4.23339e11i	0.475985	+	0.426743i
$999$		−	3.95655e11i		−	0.397242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.85	✓	464
4.3	odd	2	inner	100.9.j.b.11.102	yes	464
25.16	even	5	inner	100.9.j.b.91.102	yes	464
100.91	odd	10	inner	100.9.j.b.91.85	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.85	✓	464	1.1	even	1	trivial
100.9.j.b.11.102	yes	464	4.3	odd	2	inner
100.9.j.b.91.85	yes	464	100.91	odd	10	inner
100.9.j.b.91.102	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+(10.6807 - 11.9131i) q^{2} +(23.9193 + 7.77186i) q^{3} +(-27.8462 - 254.481i) q^{4} +(-439.267 - 444.600i) q^{5} +(348.062 - 201.946i) q^{6} -3464.57i q^{7} +(-3329.09 - 2386.29i) q^{8} +(-4796.23 - 3484.66i) q^{9} +(-9988.26 + 484.430i) q^{10} +(1192.15 + 1640.85i) q^{11} +(1311.73 - 6303.43i) q^{12} +(8835.97 + 6419.71i) q^{13} +(-41274.0 - 37004.0i) q^{14} +(-7051.61 - 14048.5i) q^{15} +(-63985.2 + 14172.7i) q^{16} +(31685.0 + 97516.3i) q^{17} +(-92740.3 + 19919.6i) q^{18} +(162540. - 52812.3i) q^{19} +(-100910. + 124166. i) q^{20} +(26926.2 - 82870.2i) q^{21} +(32280.7 + 3323.17i) q^{22} +(-56834.9 - 78226.6i) q^{23} +(-61083.5 - 82951.7i) q^{24} +(-4713.17 + 390597. i) q^{25} +(170853. - 36697.4i) q^{26} +(-184631. - 254123. i) q^{27} +(-881668. + 96475.2i) q^{28} +(-98761.9 + 303958. i) q^{29} +(-242677. - 66040.1i) q^{30} +(-803046. + 260926. i) q^{31} +(-514564. + 913639. i) q^{32} +(15762.9 + 48513.4i) q^{33} +(1.50014e6 + 664073. i) q^{34} +(-1.54035e6 + 1.52187e6i) q^{35} +(-753224. + 1.31758e6i) q^{36} +(1.01903e6 + 740371. i) q^{37} +(1.10687e6 - 2.50043e6i) q^{38} +(161457. + 222227. i) q^{39} +(401413. + 2.52833e6i) q^{40} +(-2.18509e6 - 1.58756e6i) q^{41} +(-699656. - 1.20589e6i) q^{42} -5.79619e6i q^{43} +(384370. - 349071. i) q^{44} +(557546. + 3.66310e6i) q^{45} +(-1.53896e6 - 158430. i) q^{46} +(-3.45085e6 - 1.12125e6i) q^{47} +(-1.64063e6 - 158283. i) q^{48} -6.23846e6 q^{49} +(4.60289e6 + 4.22799e6i) q^{50} +2.57877e6i q^{51} +(1.38765e6 - 2.42735e6i) q^{52} +(-1.99603e6 + 6.14316e6i) q^{53} +(-4.99939e6 - 514668. i) q^{54} +(205851. - 1.25080e6i) q^{55} +(-8.26749e6 + 1.15339e7i) q^{56} +4.29829e6 q^{57} +(2.56625e6 + 4.42304e6i) q^{58} +(9.22018e6 - 1.26905e7i) q^{59} +(-3.37870e6 + 2.18570e6i) q^{60} +(1.63904e6 - 1.19083e6i) q^{61} +(-5.46864e6 + 1.23537e7i) q^{62} +(-1.20729e7 + 1.66169e7i) q^{63} +(5.38842e6 + 1.58884e7i) q^{64} +(-1.02715e6 - 6.74844e6i) q^{65} +(746306. + 330369. i) q^{66} +(7.74657e6 - 2.51701e6i) q^{67} +(2.39337e7 - 1.07787e7i) q^{68} +(-751487. - 2.31284e6i) q^{69} +(1.67834e6 + 3.46051e7i) q^{70} +(6.69742e6 + 2.17612e6i) q^{71} +(7.65163e6 + 2.30460e7i) q^{72} +(-1.94672e7 + 1.41437e7i) q^{73} +(1.97041e7 - 4.23223e6i) q^{74} +(-3.14840e6 + 9.30617e6i) q^{75} +(-1.79658e7 - 3.98926e7i) q^{76} +(5.68486e6 - 4.13029e6i) q^{77} +(4.37190e6 + 450070. i) q^{78} +(4.62870e7 + 1.50396e7i) q^{79} +(3.44078e7 + 2.22222e7i) q^{80} +(9.57848e6 + 2.94795e7i) q^{81} +(-4.22511e7 + 9.07508e6i) q^{82} +(-8.40252e7 + 2.73014e7i) q^{83} +(-2.18387e7 - 4.54458e6i) q^{84} +(2.94376e7 - 5.69229e7i) q^{85} +(-6.90509e7 - 6.19072e7i) q^{86} +(-4.72463e6 + 6.50290e6i) q^{87} +(-53211.1 - 8.30737e6i) q^{88} +(1.73204e7 - 1.25840e7i) q^{89} +(4.95940e7 + 3.24823e7i) q^{90} +(2.22415e7 - 3.06129e7i) q^{91} +(-1.83245e7 + 1.66417e7i) q^{92} -2.12362e7 q^{93} +(-5.02151e7 + 2.91348e7i) q^{94} +(-9.48787e7 - 4.90664e7i) q^{95} +(-1.94087e7 + 1.78545e7i) q^{96} +(-4.13620e6 + 1.27299e7i) q^{97} +(-6.66310e7 + 7.43198e7i) q^{98} -1.20242e7i 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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