LMFDB - Embedded newform 100.9.j.b.11.62

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			11.62
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.62

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.59100 + 15.7888i) q^{2} +(-23.9209 - 7.77239i) q^{3} +(-242.573 + 81.8176i) q^{4} +(443.111 - 440.770i) q^{5} +(60.7377 - 397.822i) q^{6} +2979.31i q^{7} +(-1920.31 - 3617.96i) q^{8} +(-4796.16 - 3484.61i) q^{9} +(8107.33 + 5854.16i) q^{10} +(1572.76 + 2164.72i) q^{11} +(6438.50 - 71.7785i) q^{12} +(-7228.32 - 5251.68i) q^{13} +(-47039.8 + 7719.39i) q^{14} +(-14025.5 + 7099.60i) q^{15} +(52147.8 - 39693.5i) q^{16} +(-5405.02 - 16634.9i) q^{17} +(42591.1 - 84754.3i) q^{18} +(72375.6 - 23516.2i) q^{19} +(-71424.2 + 143173. i) q^{20} +(23156.4 - 71267.9i) q^{21} +(-30103.3 + 30440.8i) q^{22} +(-55583.6 - 76504.3i) q^{23} +(17815.4 + 101470. i) q^{24} +(2069.22 - 390620. i) q^{25} +(64189.3 - 127734. i) q^{26} +(184642. + 254139. i) q^{27} +(-243760. - 722702. i) q^{28} +(105628. - 325091. i) q^{29} +(-148434. - 203050. i) q^{30} +(1.08360e6 - 352082. i) q^{31} +(761829. + 720506. i) q^{32} +(-20796.9 - 64006.1i) q^{33} +(248641. - 128440. i) q^{34} +(1.31319e6 + 1.32016e6i) q^{35} +(1.44852e6 + 452865. i) q^{36} +(1.80740e6 + 1.31315e6i) q^{37} +(558819. + 1.08179e6i) q^{38} +(132090. + 181807. i) q^{39} +(-2.44560e6 - 756742. i) q^{40} +(2.33729e6 + 1.69814e6i) q^{41} +(1.18523e6 + 180956. i) q^{42} -210225. i q^{43} +(-558621. - 396423. i) q^{44} +(-3.66114e6 + 569932. i) q^{45} +(1.06390e6 - 1.07582e6i) q^{46} +(534618. + 173708. i) q^{47} +(-1.55594e6 + 544194. i) q^{48} -3.11150e6 q^{49} +(6.17278e6 - 979424. i) q^{50} +439933. i q^{51} +(2.18308e6 + 682515. i) q^{52} +(-2.11588e6 + 6.51200e6i) q^{53} +(-3.53414e6 + 3.57376e6i) q^{54} +(1.65105e6 + 265985. i) q^{55} +(1.07790e7 - 5.72120e6i) q^{56} -1.91407e6 q^{57} +(5.40649e6 + 825439. i) q^{58} +(5.55230e6 - 7.64209e6i) q^{59} +(2.82133e6 - 2.86970e6i) q^{60} +(-1.62764e6 + 1.18255e6i) q^{61} +(8.36655e6 + 1.61965e7i) q^{62} +(1.03817e7 - 1.42893e7i) q^{63} +(-9.40204e6 + 1.38952e7i) q^{64} +(-5.51773e6 + 858948. i) q^{65} +(956697. - 494197. i) q^{66} +(-1.60727e7 + 5.22233e6i) q^{67} +(2.67214e6 + 3.59297e6i) q^{68} +(734992. + 2.26207e6i) q^{69} +(-1.74414e7 + 2.41543e7i) q^{70} +(3.07619e7 + 9.99514e6i) q^{71} +(-3.39708e6 + 2.40438e7i) q^{72} +(-2.43171e7 + 1.76674e7i) q^{73} +(-1.60502e7 + 3.19391e7i) q^{74} +(-3.08554e6 + 9.32791e6i) q^{75} +(-1.56324e7 + 1.16260e7i) q^{76} +(-6.44936e6 + 4.68574e6i) q^{77} +(-2.52826e6 + 2.55661e6i) q^{78} +(5.19131e7 + 1.68676e7i) q^{79} +(5.61153e6 - 4.05738e7i) q^{80} +(9.57799e6 + 2.94780e7i) q^{81} +(-2.07558e7 + 4.13030e7i) q^{82} +(8.13518e7 - 2.64328e7i) q^{83} +(213850. + 1.91823e7i) q^{84} +(-9.72719e6 - 4.98875e6i) q^{85} +(3.31920e6 - 544691. i) q^{86} +(-5.05347e6 + 6.95550e6i) q^{87} +(4.81167e6 - 9.84710e6i) q^{88} +(8.23488e7 - 5.98299e7i) q^{89} +(-1.84846e7 - 5.63284e7i) q^{90} +(1.56464e7 - 2.15354e7i) q^{91} +(1.97425e7 + 1.40102e7i) q^{92} -2.86572e7 q^{93} +(-1.35745e6 + 8.89106e6i) q^{94} +(2.17051e7 - 4.23213e7i) q^{95} +(-1.26236e7 - 2.31564e7i) q^{96} +(2.82622e7 - 8.69821e7i) q^{97} +(-8.06188e6 - 4.91268e7i) q^{98} -1.58628e7i 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 $

$2$	2.59100	+	15.7888i	0.161937	+	0.986801i
$2$	2.59100	+	15.7888i	0.161937	+	0.986801i
$3$	−23.9209	−	7.77239i	−0.295320	−	0.0959554i	0.157610	−	0.987501i	$-0.449621\pi$
$3$	−23.9209	−	7.77239i	−0.295320	−	0.0959554i	−0.452930	+	0.891546i	$0.649621\pi$
$4$	−242.573	+	81.8176i	−0.947553	+	0.319600i
$5$	443.111	−	440.770i	0.708977	−	0.705231i
$5$	443.111	−	440.770i	0.708977	−	0.705231i
$6$	60.7377	−	397.822i	0.0468655	−	0.306961i
$7$			2979.31i			1.24086i	0.784261	+	0.620431i	$0.213042\pi$
$7$			2979.31i			1.24086i	−0.784261	+	0.620431i	$0.786958\pi$
$8$	−1920.31	−	3617.96i	−0.468826	−	0.883291i
$9$	−4796.16	−	3484.61i	−0.731010	−	0.531110i
$10$	8107.33	+	5854.16i	0.810733	+	0.585416i
$11$	1572.76	+	2164.72i	0.107422	+	0.147853i	0.859343	−	0.511400i	$-0.170873\pi$
$11$	1572.76	+	2164.72i	0.107422	+	0.147853i	−0.751922	+	0.659253i	$0.770873\pi$
$12$	6438.50	−	71.7785i	0.310499	−	0.00346154i
$13$	−7228.32	−	5251.68i	−0.253084	−	0.183876i	0.454009	−	0.890997i	$-0.349993\pi$
$13$	−7228.32	−	5251.68i	−0.253084	−	0.183876i	−0.707092	+	0.707121i	$0.749993\pi$
$14$	−47039.8	+	7719.39i	−1.22448	+	0.200942i
$15$	−14025.5	+	7099.60i	−0.277046	+	0.140239i
$16$	52147.8	−	39693.5i	0.795712	−	0.605675i
$17$	−5405.02	−	16634.9i	−0.0647144	−	0.199171i	0.913471	−	0.406904i	$-0.133391\pi$
$17$	−5405.02	−	16634.9i	−0.0647144	−	0.199171i	−0.978186	+	0.207733i	$0.933391\pi$
$18$	42591.1	−	84754.3i	0.405722	−	0.807368i
$19$	72375.6	−	23516.2i	0.555364	−	0.180449i	−0.0178702	−	0.999840i	$-0.505689\pi$
$19$	72375.6	−	23516.2i	0.555364	−	0.180449i	0.573234	+	0.819392i	$0.305689\pi$
$20$	−71424.2	+	143173.i	−0.446401	+	0.894833i
$21$	23156.4	−	71267.9i	0.119067	−	0.366452i
$22$	−30103.3	+	30440.8i	−0.128506	+	0.129947i
$23$	−55583.6	−	76504.3i	−0.198626	−	0.273385i	0.698073	−	0.716027i	$-0.254041\pi$
$23$	−55583.6	−	76504.3i	−0.198626	−	0.273385i	−0.896698	+	0.442642i	$0.854041\pi$
$24$	17815.4	+	101470.i	0.0536972	+	0.305840i
$25$	2069.22	−	390620.i	0.00529719	−	0.999986i
$26$	64189.3	−	127734.i	0.140465	−	0.279520i
$27$	184642.	+	254139.i	0.347437	+	0.478206i
$28$	−243760.	−	722702.i	−0.396580	−	1.17578i
$29$	105628.	−	325091.i	0.149344	−	0.459635i	−0.848200	−	0.529677i	$-0.822313\pi$
$29$	105628.	−	325091.i	0.149344	−	0.459635i	0.997544	+	0.0700418i	$0.0223133\pi$
$30$	−148434.	−	203050.i	−0.183252	−	0.250679i
$31$	1.08360e6	−	352082.i	1.17333	−	0.381238i	0.343446	−	0.939172i	$-0.388406\pi$
$31$	1.08360e6	−	352082.i	1.17333	−	0.381238i	0.829885	+	0.557934i	$0.188406\pi$
$32$	761829.	+	720506.i	0.726536	+	0.687128i
$33$	−20796.9	−	64006.1i	−0.0175365	−	0.0539717i
$34$	248641.	−	128440.i	0.186062	−	0.0961134i
$35$	1.31319e6	+	1.32016e6i	0.875095	+	0.879743i
$36$	1.44852e6	+	452865.i	0.862413	+	0.269624i
$37$	1.80740e6	+	1.31315e6i	0.964379	+	0.700663i	0.954164	−	0.299285i	$-0.0967482\pi$
$37$	1.80740e6	+	1.31315e6i	0.964379	+	0.700663i	0.0102157	+	0.999948i	$0.496748\pi$
$38$	558819.	+	1.08179e6i	0.268001	+	0.518812i
$39$	132090.	+	181807.i	0.0570968	+	0.0785871i
$40$	−2.44560e6	−	756742.i	−0.955311	−	0.295602i
$41$	2.33729e6	+	1.69814e6i	0.827138	+	0.600951i	0.918748	−	0.394844i	$-0.129201\pi$
$41$	2.33729e6	+	1.69814e6i	0.827138	+	0.600951i	−0.0916101	+	0.995795i	$0.529201\pi$
$42$	1.18523e6	+	180956.i	0.380897	+	0.0581537i
$43$		−	210225.i		−	0.0614907i	−0.999527	−	0.0307454i	$-0.990212\pi$
$43$		−	210225.i		−	0.0614907i	0.999527	−	0.0307454i	$-0.00978809\pi$
$44$	−558621.	−	396423.i	−0.149041	−	0.105767i
$45$	−3.66114e6	+	569932.i	−0.892825	+	0.138987i
$46$	1.06390e6	−	1.07582e6i	0.237612	−	0.240275i
$47$	534618.	+	173708.i	0.109560	+	0.0355982i	0.363284	−	0.931678i	$-0.381655\pi$
$47$	534618.	+	173708.i	0.109560	+	0.0355982i	−0.253724	+	0.967277i	$0.581655\pi$
$48$	−1.55594e6	+	544194.i	−0.293108	+	0.102515i
$49$	−3.11150e6			−0.539740
$50$	6.17278e6	−	979424.i	0.987645	−	0.156708i
$51$			439933.i			0.0650288i
$52$	2.18308e6	+	682515.i	0.298577	+	0.0933467i
$53$	−2.11588e6	+	6.51200e6i	−0.268156	+	0.825299i	0.722794	+	0.691064i	$0.242858\pi$
$53$	−2.11588e6	+	6.51200e6i	−0.268156	+	0.825299i	−0.990950	+	0.134235i	$0.957142\pi$
$54$	−3.53414e6	+	3.57376e6i	−0.415632	+	0.420291i
$55$	1.65105e6	+	265985.i	0.180430	+	0.0290674i
$56$	1.07790e7	−	5.72120e6i	1.09604	−	0.581748i
$57$	−1.91407e6			−0.181325
$58$	5.40649e6	+	825439.i	0.477753	+	0.0729412i
$59$	5.55230e6	−	7.64209e6i	0.458211	−	0.630673i	−0.515926	−	0.856633i	$-0.672552\pi$
$59$	5.55230e6	−	7.64209e6i	0.458211	−	0.630673i	0.974136	+	0.225960i	$0.0725520\pi$
$60$	2.82133e6	−	2.86970e6i	0.217695	−	0.221428i
$61$	−1.62764e6	+	1.18255e6i	−0.117554	+	0.0854082i	−0.645009	−	0.764175i	$-0.723146\pi$
$61$	−1.62764e6	+	1.18255e6i	−0.117554	+	0.0854082i	0.527455	+	0.849583i	$0.323146\pi$
$62$	8.36655e6	+	1.61965e7i	0.566213	+	1.09611i
$63$	1.03817e7	−	1.42893e7i	0.659035	−	0.907084i
$64$	−9.40204e6	+	1.38952e7i	−0.560405	+	0.828219i
$65$	−5.51773e6	+	858948.i	−0.309106	+	0.0481186i
$66$	956697.	−	494197.i	0.0504195	−	0.0260450i
$67$	−1.60727e7	+	5.22233e6i	−0.797607	+	0.259158i	−0.679340	−	0.733824i	$-0.737734\pi$
$67$	−1.60727e7	+	5.22233e6i	−0.797607	+	0.259158i	−0.118267	+	0.992982i	$0.537734\pi$
$68$	2.67214e6	+	3.59297e6i	0.124975	+	0.168042i
$69$	734992.	+	2.26207e6i	0.0324255	+	0.0997953i
$70$	−1.74414e7	+	2.41543e7i	−0.726421	+	1.00601i
$71$	3.07619e7	+	9.99514e6i	1.21054	+	0.393329i	0.843629	−	0.536927i	$-0.180415\pi$
$71$	3.07619e7	+	9.99514e6i	1.21054	+	0.393329i	0.366912	+	0.930256i	$0.380415\pi$
$72$	−3.39708e6	+	2.40438e7i	−0.126408	+	0.894693i
$73$	−2.43171e7	+	1.76674e7i	−0.856288	+	0.622130i	−0.926873	−	0.375376i	$-0.877514\pi$
$73$	−2.43171e7	+	1.76674e7i	−0.856288	+	0.622130i	0.0705845	+	0.997506i	$0.477514\pi$
$74$	−1.60502e7	+	3.19391e7i	−0.535246	+	1.06511i
$75$	−3.08554e6	+	9.32791e6i	−0.0975184	+	0.294808i
$76$	−1.56324e7	+	1.16260e7i	−0.468565	+	0.348479i
$77$	−6.44936e6	+	4.68574e6i	−0.183465	+	0.133295i
$78$	−2.52826e6	+	2.55661e6i	−0.0683037	+	0.0690694i
$79$	5.19131e7	+	1.68676e7i	1.33281	+	0.433057i	0.886876	−	0.462008i	$-0.152871\pi$
$79$	5.19131e7	+	1.68676e7i	1.33281	+	0.433057i	0.445936	+	0.895065i	$0.352871\pi$
$80$	5.61153e6	−	4.05738e7i	0.137000	−	0.990571i
$81$	9.57799e6	+	2.94780e7i	0.222502	+	0.684792i
$82$	−2.07558e7	+	4.13030e7i	−0.459075	+	0.913537i
$83$	8.13518e7	−	2.64328e7i	1.71417	−	0.556969i	0.723155	−	0.690686i	$-0.242691\pi$
$83$	8.13518e7	−	2.64328e7i	1.71417	−	0.556969i	0.991020	+	0.133717i	$0.0426914\pi$
$84$	213850.	+	1.91823e7i	0.00429529	+	0.385286i
$85$	−9.72719e6	−	4.98875e6i	−0.186342	−	0.0955687i
$86$	3.31920e6	−	544691.i	0.0606791	−	0.00995764i
$87$	−5.05347e6	+	6.95550e6i	−0.0882089	+	0.121409i
$88$	4.81167e6	−	9.84710e6i	0.0802353	−	0.164202i
$89$	8.23488e7	−	5.98299e7i	1.31249	−	0.953583i	0.312501	−	0.949918i	$-0.398833\pi$
$89$	8.23488e7	−	5.98299e7i	1.31249	−	0.953583i	0.999993	−	0.00366510i	$-0.00116664\pi$
$90$	−1.84846e7	−	5.63284e7i	−0.281734	−	0.858534i
$91$	1.56464e7	−	2.15354e7i	0.228165	−	0.314042i
$92$	1.97425e7	+	1.40102e7i	0.275582	+	0.195566i
$93$	−2.86572e7			−0.383090
$94$	−1.35745e6	+	8.89106e6i	−0.0173865	+	0.113879i
$95$	2.17051e7	−	4.23213e7i	0.266482	−	0.519594i
$96$	−1.26236e7	−	2.31564e7i	−0.148627	−	0.272638i
$97$	2.82622e7	−	8.69821e7i	0.319241	−	0.982523i	−0.654732	−	0.755861i	$-0.727219\pi$
$97$	2.82622e7	−	8.69821e7i	0.319241	−	0.982523i	0.973973	−	0.226662i	$-0.0727814\pi$
$98$	−8.06188e6	−	4.91268e7i	−0.0874041	−	0.532616i
$99$		−	1.58628e7i		−	0.165135i
$100$	3.14576e7	+	9.49232e7i	0.314576	+	0.949232i
$101$	9.68254e7			0.930473			0.465236	−	0.885186i	$-0.345969\pi$
$101$	9.68254e7			0.930473			0.465236	+	0.885186i	$0.345969\pi$
$102$	−6.94602e6	+	1.13987e6i	−0.0641705	+	0.0105306i
$103$	−3.12222e6	−	1.01447e6i	−0.0277405	−	0.00901344i	0.295114	−	0.955462i	$-0.404642\pi$
$103$	−3.12222e6	−	1.01447e6i	−0.0277405	−	0.00901344i	−0.322854	+	0.946449i	$0.604642\pi$
$104$	−5.11976e6	+	3.62366e7i	−0.0437639	+	0.309752i
$105$	−2.11519e7	−	4.17862e7i	−0.174017	−	0.343776i
$106$	−1.08299e8	−	1.65346e7i	−0.857830	−	0.130970i
$107$		−	9.48926e7i		−	0.723931i	−0.932191	−	0.361966i	$-0.882106\pi$
$107$		−	9.48926e7i		−	0.723931i	0.932191	−	0.361966i	$-0.117894\pi$
$108$	−6.55823e7	−	4.65403e7i	−0.482050	−	0.342085i
$109$	−1.27808e8	−	9.28580e7i	−0.905425	−	0.657830i	0.0344288	−	0.999407i	$-0.489039\pi$
$109$	−1.27808e8	−	9.28580e7i	−0.905425	−	0.657830i	−0.939854	+	0.341578i	$0.889039\pi$
$110$	78273.7	+	2.67572e7i	0.000534620	+	0.182756i
$111$	−3.30284e7	−	4.54597e7i	−0.217568	−	0.299457i
$112$	1.18259e8	+	1.55364e8i	0.751560	+	0.987369i
$113$	−1.30711e8	−	9.49672e7i	−0.801676	−	0.582452i	0.109730	−	0.993961i	$-0.465002\pi$
$113$	−1.30711e8	−	9.49672e7i	−0.801676	−	0.582452i	−0.911405	+	0.411510i	$0.865002\pi$
$114$	−4.95935e6	−	3.02209e7i	−0.0293633	−	0.178932i
$115$	−5.83505e7	−	9.40030e6i	−0.333621	−	0.0537465i
$116$	975486.	+	8.75007e7i	0.00538752	+	0.483259i
$117$	1.63681e7	+	5.03758e7i	0.0873483	+	0.268831i
$118$	1.35046e8	+	6.78637e7i	0.696550	+	0.350033i
$119$	4.95606e7	−	1.61032e7i	0.247143	−	0.0803017i
$120$	5.26193e7	+	3.71101e7i	0.253758	+	0.178965i
$121$	6.40281e7	−	1.97058e8i	0.298696	−	0.919291i
$122$	−2.28883e7	−	2.26345e7i	−0.103317	−	0.102172i
$123$	−4.27117e7	−	5.87876e7i	−0.186606	−	0.256841i
$124$	−2.34045e8	+	1.74063e8i	−0.989949	+	0.736240i
$125$	−1.71256e8	−	1.74000e8i	−0.701466	−	0.712703i
$126$	2.52509e8	+	1.26892e8i	1.00183	+	0.503446i
$127$	1.09892e8	+	1.51253e8i	0.422425	+	0.581418i	0.966194	−	0.257817i	$-0.0830032\pi$
$127$	1.09892e8	+	1.51253e8i	0.422425	+	0.581418i	−0.543769	+	0.839235i	$0.683003\pi$
$128$	−2.43749e8	−	1.12445e8i	−0.908037	−	0.418889i
$129$	−1.63395e6	+	5.02877e6i	−0.00590036	+	0.0181595i
$130$	−2.78582e7	−	8.48929e7i	−0.0975393	−	0.297234i
$131$	1.99289e8	−	6.47530e7i	0.676704	−	0.219874i	0.0495521	−	0.998772i	$-0.484221\pi$
$131$	1.99289e8	−	6.47530e7i	0.676704	−	0.219874i	0.627152	+	0.778897i	$0.284221\pi$
$132$	1.02816e7	+	1.38246e7i	0.0338661	+	0.0455364i
$133$	7.00622e7	+	2.15629e8i	0.223912	+	0.689130i
$134$	−1.24099e8	−	2.40237e8i	−0.384900	−	0.745112i
$135$	1.93834e8	+	3.12267e7i	0.583571	+	0.0940137i
$136$	−4.98052e7	+	5.14993e7i	−0.145586	+	0.150538i
$137$	1.45244e8	+	1.05526e8i	0.412304	+	0.299556i	0.774534	−	0.632533i	$-0.217985\pi$
$137$	1.45244e8	+	1.05526e8i	0.412304	+	0.299556i	−0.362230	+	0.932089i	$0.617985\pi$
$138$	−3.38111e7	+	1.74657e7i	−0.0932272	+	0.0481581i
$139$	−2.35524e8	−	3.24171e8i	−0.630923	−	0.868392i	0.367167	−	0.930155i	$-0.380328\pi$
$139$	−2.35524e8	−	3.24171e8i	−0.630923	−	0.868392i	−0.998091	+	0.0617633i	$0.980328\pi$
$140$	−4.26558e8	−	2.12795e8i	−1.11036	−	0.553923i
$141$	−1.14384e7	−	8.31052e6i	−0.0289395	−	0.0210258i
$142$	−7.81075e7	+	5.11591e8i	−0.192105	+	1.25826i
$143$		−	2.39069e7i		−	0.0571714i
$144$	−3.88426e8	+	8.66166e6i	−0.903354	+	0.0201442i
$145$	−9.64852e7	−	1.90609e8i	−0.218267	−	0.431193i
$146$	−3.41953e8	−	3.38162e8i	−0.752583	−	0.744240i
$147$	7.44299e7	+	2.41837e7i	0.159396	+	0.0517910i
$148$	−5.45867e8	−	1.70659e8i	−1.13773	−	0.355699i
$149$	−8.58273e8			−1.74133			−0.870663	−	0.491879i	$-0.836310\pi$
$149$	−8.58273e8			−1.74133			−0.870663	+	0.491879i	$0.836310\pi$
$150$	−1.55271e8	−	2.45485e7i	−0.306709	−	0.0484909i
$151$			5.85568e7i			0.112634i	0.998413	+	0.0563170i	$0.0179358\pi$
$151$			5.85568e7i			0.112634i	−0.998413	+	0.0563170i	$0.982064\pi$
$152$	−2.24064e8	−	2.16693e8i	−0.419757	−	0.405949i
$153$	−3.20430e7	+	9.86181e7i	−0.0584746	+	0.179966i
$154$	−9.06925e7	−	8.96871e7i	−0.161246	−	0.159458i
$155$	3.24966e8	−	6.33627e8i	0.563004	−	1.09776i
$156$	−4.69165e7	−	3.32941e7i	−0.0792187	−	0.0562172i
$157$	5.04632e8			0.830571			0.415285	−	0.909691i	$-0.363682\pi$
$157$	5.04632e8			0.830571			0.415285	+	0.909691i	$0.363682\pi$
$158$	−1.31813e8	+	8.63351e8i	−0.211509	+	1.38535i
$159$	1.01228e8	−	1.39328e8i	0.158384	−	0.217997i
$160$	6.55152e8	−	1.65271e7i	0.999682	−	0.0252183i
$161$	2.27930e8	−	1.65601e8i	0.339233	−	0.246467i
$162$	−4.40607e8	+	2.27603e8i	−0.639722	+	0.330459i
$163$	−1.99928e8	+	2.75178e8i	−0.283220	+	0.389819i	−0.926797	−	0.375563i	$-0.877450\pi$
$163$	−1.99928e8	+	2.75178e8i	−0.283220	+	0.389819i	0.643577	+	0.765381i	$0.277450\pi$
$164$	−7.05904e8	−	2.20693e8i	−0.975821	−	0.305080i
$165$	−3.74273e7	−	1.91952e7i	−0.0504955	−	0.0258974i
$166$	6.28125e8	+	1.21596e9i	0.827206	+	1.60135i
$167$	1.02615e9	−	3.33417e8i	1.31931	−	0.428669i	0.437050	−	0.899437i	$-0.356023\pi$
$167$	1.02615e9	−	3.33417e8i	1.31931	−	0.428669i	0.882257	+	0.470768i	$0.156023\pi$
$168$	−3.02312e8	+	5.30777e7i	−0.379506	+	0.0666309i
$169$	−2.27406e8	−	6.99884e8i	−0.278776	−	0.857985i
$170$	5.35633e7	−	1.66507e8i	0.0641315	−	0.199359i
$171$	−4.29070e8	−	1.39413e8i	−0.501815	−	0.163050i
$172$	1.72001e7	+	5.09949e7i	0.0196524	+	0.0582657i
$173$	−3.06541e8	+	2.22715e8i	−0.342219	+	0.248637i	−0.745598	−	0.666396i	$-0.767836\pi$
$173$	−3.06541e8	+	2.22715e8i	−0.342219	+	0.248637i	0.403378	+	0.915033i	$0.367836\pi$
$174$	−1.22913e8	−	6.17666e7i	−0.134091	−	0.0673840i
$175$	1.16378e9	+	6.16484e6i	1.24085	+	0.00657309i
$176$	1.67941e8	+	5.04568e7i	0.175028	+	0.0525859i
$177$	−1.92214e8	+	1.39651e8i	−0.195835	+	0.142283i
$178$	1.15801e9	+	1.14517e9i	1.15354	+	1.14075i
$179$	2.28414e6	+	742164.i	0.00222491	+	0.000722915i	0.310129	−	0.950694i	$-0.399628\pi$
$179$	2.28414e6	+	742164.i	0.00222491	+	0.000722915i	−0.307904	+	0.951417i	$0.599628\pi$
$180$	8.41465e8	−	4.37796e8i	0.801579	−	0.417044i
$181$	−5.59385e8	−	1.72161e9i	−0.521190	−	1.60406i	−0.771729	−	0.635952i	$-0.780608\pi$
$181$	−5.59385e8	−	1.72161e9i	−0.521190	−	1.60406i	0.250539	−	0.968107i	$-0.419392\pi$
$182$	3.80559e8	+	1.91240e8i	0.346845	+	0.174298i
$183$	4.81259e7	−	1.56370e7i	0.0429116	−	0.0139428i
$184$	−1.70052e8	+	3.48011e8i	−0.148357	+	0.303614i
$185$	1.37968e9	−	2.14775e8i	1.17785	−	0.183357i
$186$	−7.42506e7	−	4.52463e8i	−0.0620366	−	0.378034i
$187$	2.75091e7	−	3.78630e7i	0.0224963	−	0.0309634i
$188$	−1.43897e8	+	1.60420e6i	−0.115191	+	0.00128419i
$189$	−7.57158e8	+	5.50107e8i	−0.593389	+	0.431122i
$190$	7.24440e8	+	2.33044e8i	0.555889	+	0.178823i
$191$	−9.39990e8	+	1.29378e9i	−0.706301	+	0.972139i	0.293568	+	0.955938i	$0.405157\pi$
$191$	−9.39990e8	+	1.29378e9i	−0.706301	+	0.972139i	−0.999869	+	0.0162013i	$0.994843\pi$
$192$	3.32905e8	−	2.59310e8i	0.244971	−	0.190816i
$193$	1.02147e9			0.736203			0.368102	−	0.929786i	$-0.380008\pi$
$193$	1.02147e9			0.736203			0.368102	+	0.929786i	$0.380008\pi$
$194$	1.44657e9	+	2.20856e8i	1.02125	+	0.155920i
$195$	1.38665e8	+	2.23391e7i	0.0959024	+	0.0154499i
$196$	7.54766e8	−	2.54575e8i	0.511432	−	0.172501i
$197$	−6.67059e8	+	2.05300e9i	−0.442894	+	1.36309i	0.441884	+	0.897072i	$0.354310\pi$
$197$	−6.67059e8	+	2.05300e9i	−0.442894	+	1.36309i	−0.884777	+	0.466014i	$0.845690\pi$
$198$	2.50454e8	−	4.11004e7i	0.162955	−	0.0267415i
$199$			1.17695e9i			0.750492i	0.926925	+	0.375246i	$0.122442\pi$
$199$			1.17695e9i			0.750492i	−0.926925	+	0.375246i	$0.877558\pi$
$200$	−1.41722e9	+	7.42624e8i	−0.885762	+	0.464140i
$201$	4.25064e8			0.260417
$202$	2.50874e8	+	1.52876e9i	0.150678	+	0.918191i
$203$	9.68547e8	+	3.14700e8i	0.570344	+	0.185316i
$204$	−3.59942e7	−	1.06716e8i	−0.0207832	−	0.0616182i
$205$	1.78417e9	−	2.77743e8i	1.01023	−	0.157263i
$206$	7.92763e6	−	5.19246e7i	0.00440225	−	0.0288340i
$207$			5.60614e8i			0.305339i
$208$	−5.85399e8	+	1.30540e7i	−0.312751	+	0.00697415i
$209$	1.64735e8	+	1.19687e8i	0.0863379	+	0.0627282i
$210$	6.04950e8	−	4.42232e8i	0.311059	−	0.227391i
$211$	−1.32474e9	−	1.82335e9i	−0.668345	−	0.919898i	0.331376	−	0.943499i	$-0.392487\pi$
$211$	−1.32474e9	−	1.82335e9i	−0.668345	−	0.919898i	−0.999721	+	0.0236005i	$0.992487\pi$
$212$	−1.95403e7	−	1.75276e9i	−0.00967358	−	0.867717i
$213$	−6.58167e8	−	4.78186e8i	−0.319755	−	0.232316i
$214$	1.49824e9	−	2.45866e8i	0.714376	−	0.117231i
$215$	−9.26606e7	−	9.31527e7i	−0.0433652	−	0.0435955i
$216$	5.64892e8	−	1.15605e9i	0.259508	−	0.531084i
$217$	1.04896e9	+	3.22837e9i	0.473065	+	1.45594i
$218$	1.13497e9	−	2.25853e9i	0.502525	−	1.00000i
$219$	7.19005e8	−	2.33619e8i	0.312576	−	0.101562i
$220$	−4.22263e8	+	7.05638e7i	−0.180257	+	0.0301225i
$221$	−4.82922e7	+	1.48628e8i	−0.0202445	+	0.0623062i
$222$	6.32179e8	−	6.39266e8i	0.260272	−	0.263190i
$223$	−2.06285e9	−	2.83927e9i	−0.834157	−	1.14812i	−0.987135	−	0.159889i	$-0.948886\pi$
$223$	−2.06285e9	−	2.83927e9i	−0.834157	−	1.14812i	0.152978	−	0.988230i	$-0.451114\pi$
$224$	−2.14661e9	+	2.26972e9i	−0.852631	+	0.901532i
$225$	−1.37108e9	+	1.86626e9i	−0.534975	+	0.728187i
$226$	1.16075e9	−	2.30983e9i	0.444943	−	0.885415i
$227$	4.56586e8	+	6.28437e8i	0.171957	+	0.236678i	0.886294	−	0.463124i	$-0.153272\pi$
$227$	4.56586e8	+	6.28437e8i	0.171957	+	0.236678i	−0.714337	+	0.699802i	$0.753272\pi$
$228$	4.64302e8	−	1.56604e8i	0.171815	−	0.0579515i
$229$	4.81681e8	−	1.48246e9i	0.175153	−	0.539066i	−0.824487	−	0.565880i	$-0.808536\pi$
$229$	4.81681e8	−	1.48246e9i	0.175153	−	0.539066i	0.999640	+	0.0268148i	$0.00853643\pi$
$230$	−2.76631e6	−	9.45641e8i	−0.000988529	−	0.337921i
$231$	1.90694e8	−	6.19603e7i	0.0669714	−	0.0217603i
$232$	−1.37901e9	+	2.42116e8i	−0.476008	+	0.0835740i
$233$	2.00742e8	+	6.17821e8i	0.0681106	+	0.209623i	0.979319	−	0.202323i	$-0.0648492\pi$
$233$	2.00742e8	+	6.17821e8i	0.0681106	+	0.209623i	−0.911208	+	0.411946i	$0.864849\pi$
$234$	−7.52965e8	+	3.88956e8i	−0.251137	+	0.129729i
$235$	3.13460e8	−	1.58672e8i	0.102781	−	0.0520269i
$236$	−7.21584e8	+	2.30804e9i	−0.232616	+	0.744040i
$237$	−1.11071e9	−	8.06978e8i	−0.352052	−	0.255781i
$238$	3.82662e8	+	7.40780e8i	0.119264	+	0.230877i
$239$	2.45716e9	+	3.38199e9i	0.753081	+	1.03653i	0.997758	+	0.0669226i	$0.0213181\pi$
$239$	2.45716e9	+	3.38199e9i	0.753081	+	1.03653i	−0.244677	+	0.969605i	$0.578682\pi$
$240$	−4.49588e8	+	9.26948e8i	−0.135510	+	0.279390i
$241$	1.03476e9	+	7.51799e8i	0.306742	+	0.222861i	0.730497	−	0.682916i	$-0.239288\pi$
$241$	1.03476e9	+	7.51799e8i	0.306742	+	0.222861i	−0.423756	+	0.905777i	$0.639288\pi$
$242$	3.27721e9	+	5.00351e8i	0.955528	+	0.145886i
$243$		−	2.84061e9i		−	0.814679i
$244$	2.98069e8	−	4.20024e8i	0.0840925	−	0.118499i
$245$	−1.37874e9	+	1.37145e9i	−0.382664	+	0.380642i
$246$	8.17520e8	−	8.26685e8i	0.223233	−	0.225735i
$247$	−6.46654e8	−	2.10111e8i	−0.173734	−	0.0564495i
$248$	−3.35466e9	−	3.24430e9i	−0.886832	−	0.857658i
$249$	−2.15146e9			−0.559675
$250$	2.30353e9	−	3.15477e9i	0.589703	−	0.807621i
$251$			5.34789e9i			1.34737i	0.739018	+	0.673686i	$0.235290\pi$
$251$			5.34789e9i			1.34737i	−0.739018	+	0.673686i	$0.764710\pi$
$252$	−1.34923e9	+	4.31560e9i	−0.334566	+	1.07014i
$253$	7.81905e7	−	2.40646e8i	0.0190841	−	0.0587348i
$254$	−2.10337e9	+	2.12695e9i	−0.505337	+	0.511002i
$255$	1.93909e8	+	1.94939e8i	0.0458604	+	0.0461039i
$256$	1.14381e9	−	4.13986e9i	0.266315	−	0.963886i
$257$	1.11535e9			0.255670			0.127835	−	0.991795i	$-0.459197\pi$
$257$	1.11535e9			0.255670			0.127835	+	0.991795i	$0.459197\pi$
$258$	−8.36319e7	−	1.27686e7i	−0.0188753	−	0.00288179i
$259$	−3.91230e9	+	5.38481e9i	−0.869426	+	1.19666i
$260$	1.26818e9	−	6.59805e8i	0.277515	−	0.144385i
$261$	−1.63943e9	+	1.19111e9i	−0.353289	+	0.256680i
$262$	1.53873e9	+	2.97877e9i	0.326556	+	0.632166i
$263$	−2.32880e9	+	3.20531e9i	−0.486753	+	0.669958i	−0.979785	−	0.200053i	$-0.935889\pi$
$263$	−2.32880e9	+	3.20531e9i	−0.486753	+	0.669958i	0.493032	+	0.870011i	$0.335889\pi$
$264$	−1.91635e8	+	1.98154e8i	−0.0394511	+	0.0407931i
$265$	1.93273e9	+	3.81815e9i	0.391910	+	0.774230i
$266$	−3.22300e9	+	1.66489e9i	−0.643775	+	0.332552i
$267$	−2.43488e9	+	7.91141e8i	−0.479107	+	0.155671i
$268$	3.47153e9	−	2.58183e9i	0.672948	−	0.500481i
$269$	2.62041e8	+	8.06479e8i	0.0500449	+	0.154023i	0.972956	−	0.230991i	$-0.0741968\pi$
$269$	2.62041e8	+	8.06479e8i	0.0500449	+	0.154023i	−0.922911	+	0.385013i	$0.874197\pi$
$270$	9.18936e6	+	3.14131e9i	0.00172914	+	0.591093i
$271$	−5.60697e9	−	1.82181e9i	−1.03956	−	0.337775i	−0.260999	−	0.965339i	$-0.584052\pi$
$271$	−5.60697e9	−	1.82181e9i	−1.03956	−	0.337775i	−0.778565	+	0.627564i	$0.784052\pi$
$272$	−9.42159e8	−	6.52930e8i	−0.172127	−	0.119286i
$273$	−5.41658e8	+	3.93538e8i	−0.0975157	+	0.0708493i
$274$	−1.28981e9	+	2.56665e9i	−0.228835	+	0.455371i
$275$	8.48835e8	−	6.09871e8i	0.148420	−	0.106637i
$276$	−3.63367e8	−	4.88583e8i	−0.0626194	−	0.0841981i
$277$	5.75953e8	−	4.18455e8i	0.0978292	−	0.0710770i	−0.537795	−	0.843075i	$-0.680743\pi$
$277$	5.75953e8	−	4.18455e8i	0.0978292	−	0.0710770i	0.635624	+	0.771998i	$0.280743\pi$
$278$	4.50804e9	−	4.55858e9i	0.754760	−	0.763221i
$279$	−6.42397e9	−	2.08727e9i	−1.06020	−	0.344479i
$280$	2.25457e9	−	7.28619e9i	0.366802	−	1.18541i
$281$	−2.20741e9	−	6.79372e9i	−0.354045	−	1.08964i	−0.956561	−	0.291532i	$-0.905835\pi$
$281$	−2.20741e9	−	6.79372e9i	−0.354045	−	1.08964i	0.602516	−	0.798107i	$-0.294165\pi$
$282$	1.01576e8	−	2.02132e8i	0.0160619	−	0.0319624i
$283$	3.20196e8	−	1.04038e8i	0.0499194	−	0.0162198i	−0.283951	−	0.958839i	$-0.591645\pi$
$283$	3.20196e8	−	1.04038e8i	0.0499194	−	0.0162198i	0.333870	+	0.942619i	$0.391645\pi$
$284$	−8.27979e9	+	9.23057e7i	−1.27276	+	0.0141891i
$285$	−8.48145e8	+	8.43664e8i	−0.128555	+	0.127876i
$286$	3.77462e8	−	6.19427e7i	0.0564168	−	0.00925819i
$287$	−5.05930e9	+	6.96353e9i	−0.745698	+	1.02636i
$288$	−1.14317e9	−	6.11034e9i	−0.166165	−	0.888168i
$289$	5.39600e9	−	3.92042e9i	0.773536	−	0.562007i
$290$	2.75950e9	−	2.01725e9i	0.390156	−	0.285213i
$291$	−1.35212e9	+	1.86103e9i	−0.188557	+	0.259526i
$292$	4.45317e9	−	6.27520e9i	0.612545	−	0.863170i
$293$	5.10197e9			0.692257			0.346128	−	0.938187i	$-0.387496\pi$
$293$	5.10197e9			0.692257			0.346128	+	0.938187i	$0.387496\pi$
$294$	−1.88985e8	+	1.23782e9i	−0.0252952	+	0.165679i
$295$	−9.08116e8	−	5.83358e9i	−0.119909	−	0.770277i
$296$	1.28017e9	−	9.06077e9i	0.166763	−	1.18032i
$297$	−2.59740e8	+	7.99397e8i	−0.0333820	+	0.102739i
$298$	−2.22378e9	−	1.35511e10i	−0.281986	−	1.71834i
$299$			8.44905e8i			0.105712i
$300$	−1.47154e7	−	2.51515e9i	−0.00181672	−	0.310513i
$301$	6.26324e8			0.0763015
$302$	−9.24543e8	+	1.51721e8i	−0.111147	+	0.0182397i
$303$	−2.31615e9	−	7.52564e8i	−0.274787	−	0.0892839i
$304$	2.84078e9	−	4.09916e9i	0.332616	−	0.479955i
$305$	−1.99993e8	+	1.24141e9i	−0.0231108	+	0.143455i
$306$	−1.64009e9	−	2.50401e8i	−0.187060	−	0.0285595i
$307$			3.79168e9i			0.426853i	0.976959	+	0.213426i	$0.0684624\pi$
$307$			3.79168e9i			0.426853i	−0.976959	+	0.213426i	$0.931538\pi$
$308$	1.18107e9	−	1.66431e9i	0.131242	−	0.184940i
$309$	6.68016e7	+	4.85342e7i	0.00732745	+	0.00532370i
$310$	1.08462e10	+	3.48910e9i	1.17444	+	0.377804i
$311$	−9.16918e9	−	1.26203e10i	−0.980142	−	1.34905i	−0.936753	−	0.349992i	$-0.886184\pi$
$311$	−9.16918e9	−	1.26203e10i	−0.980142	−	1.34905i	−0.0433897	−	0.999058i	$-0.513816\pi$
$312$	4.04115e8	−	8.27022e8i	0.0426468	−	0.0872767i
$313$	1.02960e10	+	7.48047e9i	1.07273	+	0.779384i	0.976401	−	0.215965i	$-0.0692898\pi$
$313$	1.02960e10	+	7.48047e9i	1.07273	+	0.779384i	0.0963294	+	0.995350i	$0.469290\pi$
$314$	1.30750e9	+	7.96755e9i	0.134500	+	0.819608i
$315$	−1.69800e9	−	1.09077e10i	−0.172463	−	1.10787i
$316$	−1.39728e10	+	1.55773e8i	−1.40131	+	0.0156223i
$317$	−1.85012e9	−	5.69408e9i	−0.183216	−	0.563880i	0.816697	−	0.577066i	$-0.195803\pi$
$317$	−1.85012e9	−	5.69408e9i	−0.183216	−	0.563880i	−0.999913	+	0.0131863i	$0.995803\pi$
$318$	2.46210e9	+	1.23727e9i	0.240767	+	0.120991i
$319$	8.69858e8	−	2.82634e8i	0.0840012	−	0.0272936i
$320$	1.95844e9	+	1.03012e10i	0.186771	+	0.982403i
$321$	−7.37542e8	+	2.26992e9i	−0.0694651	+	0.213792i
$322$	3.20521e9	+	3.16967e9i	0.298149	+	0.294843i
$323$	−7.82382e8	−	1.07686e9i	−0.0718801	−	0.0989345i
$324$	−4.73519e9	−	6.36694e9i	−0.429692	−	0.577764i
$325$	−2.06637e9	+	2.81266e9i	−0.185214	+	0.252106i
$326$	−4.86274e9	−	2.44365e9i	−0.430537	−	0.216355i
$327$	2.33556e9	+	3.21463e9i	0.204268	+	0.281151i
$328$	1.65549e9	−	1.17172e10i	0.143031	−	1.01234i
$329$	−5.17530e8	+	1.59279e9i	−0.0441725	+	0.135949i
$330$	2.06095e8	−	6.40667e8i	0.0173785	−	0.0540227i
$331$	−4.78995e9	+	1.55635e9i	−0.399043	+	0.129657i	−0.501662	−	0.865064i	$-0.667278\pi$
$331$	−4.78995e9	+	1.55635e9i	−0.399043	+	0.129657i	0.102619	+	0.994721i	$0.467278\pi$
$332$	−1.75711e10	+	1.30679e10i	−1.44626	+	1.07561i
$333$	−4.09275e9	−	1.25962e10i	−0.332842	−	1.02438i
$334$	7.92302e9	+	1.53378e10i	0.636656	+	1.23248i
$335$	−4.82013e9	+	9.39842e9i	−0.382719	+	0.746235i
$336$	−1.62132e9	−	4.63562e9i	−0.127207	−	0.363706i
$337$	−9.27479e9	−	6.73853e9i	−0.719092	−	0.522451i	0.167002	−	0.985957i	$-0.446591\pi$
$337$	−9.27479e9	−	6.73853e9i	−0.719092	−	0.522451i	−0.886094	+	0.463506i	$0.846591\pi$
$338$	1.04611e10	−	5.40387e9i	0.801516	−	0.414036i
$339$	2.38861e9	+	3.28764e9i	0.180862	+	0.248935i
$340$	2.76773e9	+	4.14283e8i	0.207113	+	0.0310014i
$341$	2.46639e9	+	1.79194e9i	0.182408	+	0.132527i
$342$	1.08945e9	−	7.13572e9i	0.0796349	−	0.521595i
$343$			7.90502e9i			0.571119i
$344$	−7.60584e8	+	4.03696e8i	−0.0543142	+	0.0288284i
$345$	1.32274e9	+	6.78386e8i	0.0933677	+	0.0478851i
$346$	−4.31066e9	−	4.26287e9i	−0.300773	−	0.297439i
$347$	1.63695e10	+	5.31878e9i	1.12906	+	0.366855i	0.813220	−	0.581957i	$-0.197713\pi$
$347$	1.63695e10	+	5.31878e9i	1.12906	+	0.366855i	0.315843	+	0.948812i	$0.397713\pi$
$348$	6.56755e8	−	2.10068e9i	0.0447802	−	0.143233i
$349$	9.89300e9			0.666847			0.333423	−	0.942777i	$-0.391796\pi$
$349$	9.89300e9			0.666847			0.333423	+	0.942777i	$0.391796\pi$
$350$	2.91801e9	+	1.83906e10i	0.194453	+	1.22553i
$351$		−	2.80668e9i		−	0.184912i
$352$	−3.61518e8	+	2.78232e9i	−0.0235483	+	0.181233i
$353$	4.48663e9	−	1.38084e10i	0.288949	−	0.889295i	−0.696238	−	0.717811i	$-0.745144\pi$
$353$	4.48663e9	−	1.38084e10i	0.288949	−	0.889295i	0.985187	−	0.171484i	$-0.0548560\pi$
$354$	−2.70295e9	−	2.67299e9i	−0.172118	−	0.170210i
$355$	1.80365e10	−	9.12995e9i	1.13563	−	0.574851i
$356$	−1.50805e10	+	2.12507e10i	−0.938892	+	1.32304i
$357$	−1.31070e9			−0.0806918
$358$	−5.79967e6	+	3.79869e7i	−0.000353079	+	0.00231261i
$359$	−4.99405e9	+	6.87372e9i	−0.300660	+	0.413823i	−0.932440	−	0.361325i	$-0.882325\pi$
$359$	−4.99405e9	+	6.87372e9i	−0.300660	+	0.413823i	0.631780	+	0.775148i	$0.282325\pi$
$360$	9.09251e9	+	1.21514e10i	0.541345	+	0.723464i
$361$	−9.05478e9	+	6.57868e9i	−0.533150	+	0.387356i
$362$	2.57328e10	−	1.32927e10i	1.49849	−	0.774068i
$363$	−3.06323e9	+	4.21617e9i	−0.176422	+	0.242824i
$364$	−2.03343e9	+	6.50407e9i	−0.115830	+	0.370493i
$365$	−2.98791e9	+	1.85468e10i	−0.168343	+	1.04496i
$366$	3.71584e8	+	7.19335e8i	0.0207078	+	0.0400873i
$367$	1.95260e10	−	6.34438e9i	1.07634	−	0.349724i	0.283386	−	0.959006i	$-0.408542\pi$
$367$	1.95260e10	−	6.34438e9i	1.07634	−	0.349724i	0.792953	+	0.609282i	$0.208542\pi$
$368$	−5.93529e9	−	1.78322e9i	−0.323631	−	0.0972329i
$369$	−5.29266e9	−	1.62891e10i	−0.285475	−	0.878603i
$370$	6.96579e9	+	2.12270e10i	0.371675	+	1.13261i
$371$	−1.94013e10	−	6.30386e9i	−1.02408	−	0.332745i
$372$	6.95147e9	−	2.34466e9i	0.362998	−	0.122436i
$373$	2.84965e10	−	2.07039e10i	1.47216	−	1.06959i	0.492183	−	0.870492i	$-0.336199\pi$
$373$	2.84965e10	−	2.07039e10i	1.47216	−	1.06959i	0.979980	−	0.199098i	$-0.0638011\pi$
$374$	6.69089e8	+	3.36233e8i	0.0341977	+	0.0171852i
$375$	2.74422e9	+	5.49331e9i	0.138769	+	0.277785i
$376$	−3.98164e8	−	2.26780e9i	−0.0199210	−	0.113463i
$377$	−2.47079e9	+	1.79514e9i	−0.122312	+	0.0888652i
$378$	−1.06473e10	−	1.05293e10i	−0.521523	−	0.515742i
$379$	1.81242e10	+	5.88891e9i	0.878420	+	0.285416i	0.713301	−	0.700858i	$-0.247199\pi$
$379$	1.81242e10	+	5.88891e9i	0.878420	+	0.285416i	0.165119	+	0.986274i	$0.447199\pi$
$380$	−1.80247e9	+	1.20419e10i	−0.0864438	+	0.577510i
$381$	−1.45311e9	−	4.47223e9i	−0.0689604	−	0.212238i
$382$	−2.28628e10	−	1.14891e10i	−1.07368	−	0.539553i
$383$	3.62521e10	−	1.17790e10i	1.68476	−	0.547412i	0.698935	−	0.715185i	$-0.253658\pi$
$383$	3.62521e10	−	1.17790e10i	1.68476	−	0.547412i	0.985826	+	0.167773i	$0.0536576\pi$
$384$	4.95675e9	+	4.58430e9i	0.227967	+	0.210837i
$385$	−7.92451e8	+	4.91898e9i	−0.0360686	+	0.223889i
$386$	2.64663e9	+	1.61279e10i	0.119219	+	0.726486i
$387$	−7.32551e8	+	1.00827e9i	−0.0326583	+	0.0449503i
$388$	2.61003e8	+	2.34119e10i	0.0115165	+	1.03302i
$389$	−2.69563e10	+	1.95849e10i	−1.17723	+	0.855308i	−0.991857	−	0.127360i	$-0.959350\pi$
$389$	−2.69563e10	+	1.95849e10i	−1.17723	+	0.855308i	−0.185374	+	0.982668i	$0.559350\pi$
$390$	6.57392e6	+	2.24724e9i	0.000284162	+	0.0971385i
$391$	−9.72213e8	+	1.33814e9i	−0.0415963	+	0.0572523i
$392$	5.97503e9	+	1.12573e10i	0.253044	+	0.476748i
$393$	−5.27047e9			−0.220943
$394$	−3.41427e10	−	5.21277e9i	−1.41682	−	0.216313i
$395$	3.04380e10	−	1.54075e10i	1.25034	−	0.632914i
$396$	1.29785e9	+	3.84789e9i	0.0527770	+	0.156474i
$397$	−1.40201e10	+	4.31493e10i	−0.564401	+	1.73705i	0.105323	+	0.994438i	$0.466412\pi$
$397$	−1.40201e10	+	4.31493e10i	−0.564401	+	1.73705i	−0.669724	+	0.742610i	$0.733588\pi$
$398$	−1.85827e10	+	3.04947e9i	−0.740586	+	0.121533i
$399$		−	5.70261e9i		−	0.225000i
$400$	−1.53972e10	−	2.04521e10i	−0.601452	−	0.798909i
$401$	−4.35465e10			−1.68413			−0.842065	−	0.539376i	$-0.818660\pi$
$401$	−4.35465e10			−1.68413			−0.842065	+	0.539376i	$0.818660\pi$
$402$	1.10134e9	+	6.71125e9i	0.0421713	+	0.256980i
$403$	−9.68160e9	−	3.14574e9i	−0.367051	−	0.119262i
$404$	−2.34873e10	+	7.92201e9i	−0.881672	+	0.297379i
$405$	1.72371e10	+	8.84034e9i	0.640686	+	0.328586i
$406$	−2.45924e9	+	1.61076e10i	−0.0905100	+	0.592825i
$407$			5.97779e9i			0.217853i
$408$	1.59166e9	−	8.44808e8i	0.0574394	−	0.0304872i
$409$	−1.31774e10	−	9.57392e9i	−0.470908	−	0.342134i	0.326887	−	0.945063i	$-0.394000\pi$
$409$	−1.31774e10	−	9.57392e9i	−0.470908	−	0.342134i	−0.797795	+	0.602929i	$0.794000\pi$
$410$	9.00801e9	+	2.74503e10i	0.318782	+	0.971431i
$411$	−2.65419e9	−	3.65318e9i	−0.0930176	−	0.128028i
$412$	8.40369e8	−	9.36870e6i	0.0291663	−	0.000325155i
$413$	2.27682e10	+	1.65420e10i	0.782578	+	0.568577i
$414$	−8.85143e9	+	1.45255e9i	−0.301309	+	0.0494458i
$415$	2.43971e10	−	4.75701e10i	0.822518	−	1.60377i
$416$	−1.72287e9	−	9.20893e9i	−0.0575281	−	0.307493i
$417$	3.11438e9	+	9.58507e9i	0.102998	+	0.316994i
$418$	−1.46289e9	+	2.91108e9i	−0.0479189	+	0.0953564i
$419$	3.54437e10	−	1.15164e10i	1.14996	−	0.373645i	0.328833	−	0.944388i	$-0.393345\pi$
$419$	3.54437e10	−	1.15164e10i	1.14996	−	0.373645i	0.821129	+	0.570743i	$0.193345\pi$
$420$	8.54974e9	+	8.40563e9i	0.274761	+	0.270130i
$421$	6.25257e8	−	1.92434e9i	0.0199035	−	0.0612568i	−0.940611	−	0.339485i	$-0.889747\pi$
$421$	6.25257e8	−	1.92434e9i	0.0199035	−	0.0612568i	0.960515	+	0.278228i	$0.0897472\pi$
$422$	2.53561e10	−	2.56404e10i	0.799526	−	0.808489i
$423$	−1.95881e9	−	2.69607e9i	−0.0611830	−	0.0842111i
$424$	2.76233e10	−	4.84990e9i	0.854697	−	0.150062i
$425$	−6.50911e9	+	2.07688e9i	−0.199511	+	0.0636585i
$426$	5.84469e9	−	1.16307e10i	0.177469	−	0.353156i
$427$	−3.52318e9	−	4.84924e9i	−0.105980	−	0.145869i
$428$	7.76388e9	+	2.30184e10i	0.231368	+	0.685963i
$429$	−1.85814e8	+	5.71875e8i	−0.00548591	+	0.0168839i
$430$	1.23069e9	−	1.70436e9i	0.0359977	−	0.0498525i
$431$	−1.35314e10	+	4.39662e9i	−0.392134	+	0.127412i	−0.498446	−	0.866921i	$-0.666096\pi$
$431$	−1.35314e10	+	4.39662e9i	−0.392134	+	0.127412i	0.106312	+	0.994333i	$0.466096\pi$
$432$	1.97163e10	+	5.92365e9i	0.566098	+	0.170080i
$433$	−4.55944e9	−	1.40325e10i	−0.129706	−	0.399194i	0.865023	−	0.501732i	$-0.167304\pi$
$433$	−4.55944e9	−	1.40325e10i	−0.129706	−	0.399194i	−0.994729	+	0.102538i	$0.967304\pi$
$434$	−4.82543e10	+	2.49266e10i	−1.36012	+	0.702592i
$435$	8.26528e8	+	5.30947e9i	0.0230834	+	0.148284i
$436$	3.86003e10	+	1.20679e10i	1.06818	+	0.333955i
$437$	−5.82199e9	−	4.22992e9i	−0.159641	−	0.115986i
$438$	5.55151e9	+	1.07469e10i	0.150839	+	0.292004i
$439$	3.59392e10	+	4.94660e10i	0.967632	+	1.33183i	0.943234	+	0.332128i	$0.107767\pi$
$439$	3.59392e10	+	4.94660e10i	0.967632	+	1.33183i	0.0243973	+	0.999702i	$0.492233\pi$
$440$	−2.20820e9	−	6.48419e9i	−0.0589152	−	0.173000i
$441$	1.49232e10	+	1.08424e10i	0.394556	+	0.286662i
$442$	−2.47179e9	−	3.77381e8i	−0.0647622	−	0.00988761i
$443$		−	4.13606e10i		−	1.07392i	−0.843608	−	0.536960i	$-0.819573\pi$
$443$		−	4.13606e10i		−	1.07392i	0.843608	−	0.536960i	$-0.180427\pi$
$444$	1.17312e10	+	8.32502e9i	0.301864	+	0.214217i
$445$	1.01184e10	−	6.28081e10i	0.258032	−	1.60168i
$446$	3.94838e10	−	3.99265e10i	0.997883	−	1.00907i
$447$	2.05307e10	+	6.67083e9i	0.514249	+	0.167090i
$448$	−4.13981e10	−	2.80116e10i	−1.02771	−	0.695386i
$449$	−3.57981e10			−0.880794			−0.440397	−	0.897803i	$-0.645162\pi$
$449$	−3.57981e10			−0.880794			−0.440397	+	0.897803i	$0.645162\pi$
$450$	−3.30186e10	−	1.68123e10i	−0.805208	−	0.409993i
$451$			7.73035e9i			0.186850i
$452$	3.94770e10	+	1.23421e10i	0.945781	+	0.295688i
$453$	4.55126e8	−	1.40073e9i	0.0108078	−	0.0332631i
$454$	−8.73926e9	+	8.83723e9i	−0.205708	+	0.208014i
$455$	−2.55907e9	−	1.64390e10i	−0.0597086	−	0.383558i
$456$	3.67561e9	+	6.92502e9i	0.0850099	+	0.160163i
$457$	2.73470e10			0.626966			0.313483	−	0.949594i	$-0.398504\pi$
$457$	2.73470e10			0.626966			0.313483	+	0.949594i	$0.398504\pi$
$458$	2.46543e10	+	3.76412e9i	0.560314	+	0.0855463i
$459$	3.22958e9	−	4.44514e9i	0.0727604	−	0.100146i
$460$	1.49234e10	−	2.49383e9i	0.333301	−	0.0556975i
$461$	6.71775e10	−	4.88073e10i	1.48737	−	1.08064i	0.512287	−	0.858814i	$-0.328798\pi$
$461$	6.71775e10	−	4.88073e10i	1.48737	−	1.08064i	0.975086	−	0.221826i	$-0.0712016\pi$
$462$	1.47237e9	+	2.85030e9i	0.0323183	+	0.0625637i
$463$	−3.09475e10	+	4.25956e10i	−0.673445	+	0.926917i	−0.999832	−	0.0183191i	$-0.994169\pi$
$463$	−3.09475e10	+	4.25956e10i	−0.673445	+	0.926917i	0.326388	+	0.945236i	$0.394169\pi$
$464$	−7.39572e9	−	2.11455e10i	−0.159554	−	0.456191i
$465$	−1.26983e10	+	1.26312e10i	−0.271602	+	0.270167i
$466$	−9.23454e9	+	4.77025e9i	−0.195826	+	0.101157i
$467$	−6.65587e10	+	2.16262e10i	−1.39939	+	0.454688i	−0.908992	−	0.416813i	$-0.863147\pi$
$467$	−6.65587e10	+	2.16262e10i	−1.39939	+	0.454688i	−0.490394	+	0.871501i	$0.663147\pi$
$468$	−8.09209e9	−	1.08806e10i	−0.168685	−	0.226815i
$469$	−1.55589e10	−	4.78855e10i	−0.321580	−	0.989721i
$470$	3.31741e9	+	4.53805e9i	0.0679842	+	0.0929989i
$471$	−1.20713e10	−	3.92220e9i	−0.245284	−	0.0796977i
$472$	−3.83109e10	−	5.41283e9i	−0.771888	−	0.109058i
$473$	4.55076e8	−	3.30632e8i	0.00909159	−	0.00660543i
$474$	9.86338e9	−	1.96277e10i	0.195395	−	0.388826i
$475$	−9.03614e9	−	2.83200e10i	−0.177504	−	0.556312i
$476$	−1.07046e10	+	7.96114e9i	−0.208517	+	0.155077i
$477$	3.28399e10	−	2.38596e10i	0.634349	−	0.460882i
$478$	−4.70311e10	+	4.75584e10i	−0.900894	+	0.910994i
$479$	4.06306e10	+	1.32017e10i	0.771812	+	0.250777i	0.668341	−	0.743855i	$-0.267005\pi$
$479$	4.06306e10	+	1.32017e10i	0.771812	+	0.250777i	0.103472	+	0.994632i	$0.467005\pi$
$480$	−1.58003e10	−	4.69675e9i	−0.297646	−	0.0884774i
$481$	−6.16821e9	−	1.89838e10i	−0.115234	−	0.354652i
$482$	−9.18895e9	+	1.82856e10i	−0.170246	+	0.338782i
$483$	−6.73942e9	+	2.18977e9i	−0.123832	+	0.0402355i
$484$	5.91304e8	+	5.30397e10i	0.0107753	+	0.966540i
$485$	−2.58158e10	−	5.09998e10i	−0.466572	−	0.921726i
$486$	4.48499e10	−	7.36001e9i	0.803926	−	0.131927i
$487$	−4.42546e10	+	6.09113e10i	−0.786761	+	1.08288i	0.207743	+	0.978183i	$0.433388\pi$
$487$	−4.42546e10	+	6.09113e10i	−0.786761	+	1.08288i	−0.994504	+	0.104700i	$0.966612\pi$
$488$	7.40398e9	+	3.61787e9i	0.130553	+	0.0637931i
$489$	6.92126e9	−	5.02859e9i	0.121046	−	0.0879449i
$490$	−2.52259e10	−	1.82152e10i	−0.437585	−	0.315973i
$491$	2.76936e10	−	3.81169e10i	0.476489	−	0.655831i	−0.501336	−	0.865252i	$-0.667158\pi$
$491$	2.76936e10	−	3.81169e10i	0.476489	−	0.655831i	0.977825	+	0.209422i	$0.0671581\pi$
$492$	1.51706e10	+	1.07657e10i	0.258906	+	0.183731i
$493$	−5.97879e9			−0.101210
$494$	1.64192e9	−	1.07543e10i	0.0275705	−	0.180582i
$495$	−6.99183e9	−	7.02897e9i	−0.116458	−	0.117077i
$496$	4.25318e10	−	6.13720e10i	0.702727	−	1.01401i
$497$	−2.97786e10	+	9.16492e10i	−0.488067	+	1.50212i
$498$	−5.57442e9	−	3.39690e10i	−0.0906322	−	0.552287i
$499$		−	5.50740e10i		−	0.888268i	−0.895960	−	0.444134i	$-0.853511\pi$
$499$		−	5.50740e10i		−	0.888268i	0.895960	−	0.444134i	$-0.146489\pi$
$500$	5.57785e10	+	2.81959e10i	0.892456	+	0.451135i
$501$	−2.71380e10			−0.430751
$502$	−8.44369e10	+	1.38564e10i	−1.32959	+	0.218190i
$503$	8.02755e10	+	2.60831e10i	1.25404	+	0.407462i	0.859367	−	0.511360i	$-0.170858\pi$
$503$	8.02755e10	+	2.60831e10i	1.25404	+	0.407462i	0.394672	+	0.918822i	$0.370858\pi$
$504$	−7.16341e10	−	1.01210e10i	−1.11019	−	0.156855i
$505$	4.29044e10	−	4.26777e10i	0.659684	−	0.656199i
$506$	4.00210e9	+	6.11023e8i	0.0610500	+	0.00932085i
$507$			1.85094e10i			0.280130i
$508$	−3.90319e10	−	2.76988e10i	−0.586091	−	0.415917i
$509$	2.55058e10	+	1.85310e10i	0.379986	+	0.276076i	0.761340	−	0.648353i	$-0.224542\pi$
$509$	2.55058e10	+	1.85310e10i	0.379986	+	0.276076i	−0.381354	+	0.924429i	$0.624542\pi$
$510$	−2.57544e9	+	3.56668e9i	−0.0380689	+	0.0527210i
$511$	−5.26367e10	−	7.24481e10i	−0.771978	−	1.06254i
$512$	6.83271e10	+	7.33311e9i	0.994290	+	0.106711i
$513$	1.93400e10	+	1.40513e10i	0.279246	+	0.202884i
$514$	2.88987e9	+	1.76101e10i	0.0414025	+	0.252295i
$515$	−1.83064e9	+	9.26657e8i	−0.0260239	+	0.0131732i
$516$	−1.50896e7	−	1.35353e9i	−0.000212852	−	0.0190928i
$517$	4.64797e8	+	1.43050e9i	0.00650580	+	0.0200228i
$518$	−9.51566e10	−	4.78185e10i	−1.32166	−	0.664166i
$519$	9.06378e9	−	2.94500e9i	0.124922	−	0.0405897i
$520$	1.37034e10	+	1.83135e10i	0.187419	+	0.250471i
$521$	−1.90322e10	+	5.85750e10i	−0.258308	+	0.794989i	0.734852	+	0.678227i	$0.237251\pi$
$521$	−1.90322e10	+	5.85750e10i	−0.258308	+	0.794989i	−0.993160	+	0.116762i	$0.962749\pi$
$522$	−2.30540e10	−	2.27984e10i	−0.310502	−	0.307060i
$523$	1.51439e10	+	2.08438e10i	0.202410	+	0.278594i	0.898140	−	0.439710i	$-0.144919\pi$
$523$	1.51439e10	+	2.08438e10i	0.202410	+	0.278594i	−0.695730	+	0.718304i	$0.744919\pi$
$524$	−4.30443e10	+	3.20127e10i	−0.570941	+	0.424617i
$525$	−2.77907e10	−	9.19279e9i	−0.365816	−	0.121007i
$526$	−5.66420e10	−	2.84640e10i	−0.739939	−	0.371837i
$527$	−1.17137e10	−	1.61225e10i	−0.151863	−	0.209021i
$528$	−3.62514e9	−	2.51228e9i	−0.0466433	−	0.0323245i
$529$	2.14361e10	−	6.59734e10i	0.273730	−	0.842454i
$530$	−5.52765e10	+	4.04083e10i	−0.700546	+	0.512114i
$531$	−5.32595e10	+	1.73050e10i	−0.669913	+	0.217668i
$532$	−3.46375e10	−	4.65736e10i	−0.432414	−	0.581425i
$533$	−7.97660e9	−	2.45495e10i	−0.0988346	−	0.304182i
$534$	−1.88000e10	−	3.63941e10i	−0.231202	−	0.447575i
$535$	−4.18258e10	−	4.20479e10i	−0.510539	−	0.513251i
$536$	4.97587e10	+	4.81218e10i	0.602851	+	0.583019i
$537$	−4.88705e7	−	3.55065e7i	−0.000587692	−	0.000426983i
$538$	−1.20544e10	+	6.22690e9i	−0.143885	+	0.0743264i
$539$	−4.89363e9	−	6.73551e9i	−0.0579797	−	0.0798023i
$540$	−4.95738e10	+	8.28422e9i	−0.583011	+	0.0974263i
$541$	5.26721e10	+	3.82685e10i	0.614881	+	0.446737i	0.851130	−	0.524955i	$-0.175918\pi$
$541$	5.26721e10	+	3.82685e10i	0.614881	+	0.446737i	−0.236249	+	0.971693i	$0.575918\pi$
$542$	1.42367e10	−	9.32477e10i	0.164972	−	1.08054i
$543$			4.55303e10i			0.523722i
$544$	7.86787e9	−	1.65673e10i	0.0898383	−	0.189172i
$545$	−9.75621e10	+	1.51875e10i	−1.10585	+	0.172148i
$546$	−7.61693e9	−	7.53249e9i	−0.0857056	−	0.0847555i
$547$	−9.48039e10	−	3.08036e10i	−1.05895	−	0.344075i	−0.272777	−	0.962077i	$-0.587942\pi$
$547$	−9.48039e10	−	3.08036e10i	−1.05895	−	0.344075i	−0.786176	+	0.618003i	$0.787942\pi$
$548$	−4.38663e10	−	1.37143e10i	−0.486417	−	0.152073i
$549$	1.19271e10			0.131295
$550$	1.18285e10	+	1.18219e10i	0.129264	+	0.129193i
$551$		−	2.60126e10i		−	0.282214i
$552$	6.77267e9	−	7.00305e9i	0.0729464	−	0.0754277i
$553$	−5.02538e10	+	1.54665e11i	−0.537364	+	1.65384i
$554$	8.09920e9	+	8.00941e9i	0.0859811	+	0.0850279i
$555$	−3.46725e10	−	5.58576e9i	−0.365438	−	0.0588723i
$556$	8.36549e10	+	5.93654e10i	0.875371	+	0.621204i
$557$	3.65008e10			0.379211			0.189606	−	0.981860i	$-0.439279\pi$
$557$	3.65008e10			0.379211			0.189606	+	0.981860i	$0.439279\pi$
$558$	1.63111e10	−	1.06835e11i	0.168247	−	1.10199i
$559$	−1.10403e9	+	1.51957e9i	−0.0113067	+	0.0155623i
$560$	1.20882e11	+	1.67185e10i	1.22916	+	0.169999i
$561$	−9.52330e8	+	6.91908e8i	−0.00961471	+	0.00698549i
$562$	1.01545e11	−	5.24550e10i	1.01792	−	0.525825i
$563$	−1.08423e11	+	1.49232e11i	−1.07917	+	1.48535i	−0.218732	+	0.975785i	$0.570192\pi$
$563$	−1.08423e11	+	1.49232e11i	−1.07917	+	1.48535i	−0.860435	+	0.509561i	$0.829808\pi$
$564$	3.45461e9	+	1.08005e9i	0.0341415	+	0.0106740i
$565$	−9.97781e10	+	1.55325e10i	−0.979133	+	0.152422i
$566$	2.47226e9	+	4.78595e9i	0.0240895	+	0.0466340i
$567$	−8.78242e10	+	2.85358e10i	−0.849732	+	0.276095i
$568$	−2.29103e10	−	1.30489e11i	−0.220109	−	1.25366i
$569$	1.13831e10	+	3.50335e10i	0.108595	+	0.334221i	0.990557	−	0.137099i	$-0.0437778\pi$
$569$	1.13831e10	+	3.50335e10i	0.108595	+	0.334221i	−0.881962	+	0.471320i	$0.843778\pi$
$570$	−1.55180e10	−	1.12053e10i	−0.147006	−	0.106151i
$571$	3.14761e10	+	1.02272e10i	0.296099	+	0.0962084i	0.453299	−	0.891358i	$-0.350247\pi$
$571$	3.14761e10	+	1.02272e10i	0.296099	+	0.0962084i	−0.157200	+	0.987567i	$0.550247\pi$
$572$	1.95600e9	+	5.79918e9i	0.0182720	+	0.0541729i
$573$	3.25412e10	−	2.36426e10i	0.301867	−	0.219319i
$574$	−1.23055e11	−	6.18379e10i	−1.13357	−	0.569649i
$575$	−2.99991e10	+	2.15537e10i	−0.274433	+	0.197175i
$576$	9.35131e10	−	3.38811e10i	0.849537	−	0.307799i
$577$	1.33842e11	−	9.72418e10i	1.20750	−	0.877303i	0.212502	−	0.977161i	$-0.431839\pi$
$577$	1.33842e11	−	9.72418e10i	1.20750	−	0.877303i	0.995002	+	0.0998578i	$0.0318388\pi$
$578$	7.58799e10	+	7.50386e10i	0.679853	+	0.672316i
$579$	−2.44346e10	−	7.93929e9i	−0.217416	−	0.0706427i
$580$	3.89999e10	+	3.83425e10i	0.344629	+	0.338820i
$581$	7.87516e10	+	2.42372e11i	0.691122	+	2.12705i
$582$	−3.28868e10	−	1.65264e10i	−0.286635	−	0.144041i
$583$	−1.74244e10	+	5.66153e9i	−0.150829	+	0.0490072i
$584$	1.10616e11	+	5.40513e10i	0.950971	+	0.464681i
$585$	2.94570e10	+	1.51075e10i	0.251516	+	0.128994i
$586$	1.32192e10	+	8.05540e10i	0.112102	+	0.683120i
$587$	−1.27053e11	+	1.74873e11i	−1.07012	+	1.47289i	−0.200158	+	0.979764i	$0.564146\pi$
$587$	−1.27053e11	+	1.74873e11i	−1.07012	+	1.47289i	−0.869958	+	0.493125i	$0.835854\pi$
$588$	−2.00334e10	+	2.23338e8i	−0.167589	+	0.00186833i
$589$	7.01462e10	−	5.09642e10i	0.582832	−	0.423452i
$590$	8.97524e10	−	2.94529e10i	0.740693	−	0.243063i
$591$	3.19134e10	−	4.39250e10i	0.261591	−	0.360049i
$592$	1.46376e11	−	3.26409e9i	1.19174	−	0.0265751i
$593$	−1.07772e10			−0.0871537			−0.0435768	−	0.999050i	$-0.513875\pi$
$593$	−1.07772e10			−0.0871537			−0.0435768	+	0.999050i	$0.513875\pi$
$594$	−1.32945e10	−	2.02975e9i	−0.106789	−	0.0163041i
$595$	1.48630e10	−	2.89803e10i	0.118588	−	0.231225i
$596$	2.08194e11	−	7.02218e10i	1.65000	−	0.556528i
$597$	9.14771e9	−	2.81538e10i	0.0720137	−	0.221635i
$598$	−1.33401e10	+	2.18915e9i	−0.104316	+	0.0171187i
$599$			5.81919e10i			0.452018i	0.974125	+	0.226009i	$0.0725678\pi$
$599$			5.81919e10i			0.452018i	−0.974125	+	0.226009i	$0.927432\pi$
$600$	3.96732e10	−	6.74910e9i	0.306120	−	0.0520764i
$601$	−1.58431e11			−1.21434			−0.607172	−	0.794570i	$-0.707696\pi$
$601$	−1.58431e11			−1.21434			−0.607172	+	0.794570i	$0.707696\pi$
$602$	1.62280e9	+	9.88892e9i	0.0123561	+	0.0752944i
$603$	9.52849e10	+	3.09599e10i	0.720700	+	0.234170i
$604$	−4.79098e9	−	1.42043e10i	−0.0359978	−	0.106727i
$605$	−5.84858e10	−	1.15540e11i	−0.436545	−	0.862406i
$606$	5.88095e9	−	3.85192e10i	0.0436071	−	0.285619i
$607$		−	1.13850e11i		−	0.838648i	−0.907837	−	0.419324i	$-0.862267\pi$
$607$		−	1.13850e11i		−	0.838648i	0.907837	−	0.419324i	$-0.137733\pi$
$608$	7.20814e10	+	3.42317e10i	0.527483	+	0.250503i
$609$	−2.07226e10	−	1.50558e10i	−0.150652	−	0.109455i
$610$	−2.01186e10	+	5.88536e7i	−0.145305	+	0.000425063i
$611$	−2.95213e9	−	4.06326e9i	−0.0211822	−	0.0291548i
$612$	−2.95919e8	−	2.65438e10i	−0.00210944	−	0.189216i
$613$	3.67488e10	+	2.66996e10i	0.260256	+	0.189087i	0.710260	−	0.703939i	$-0.248577\pi$
$613$	3.67488e10	+	2.66996e10i	0.260256	+	0.189087i	−0.450004	+	0.893027i	$0.648577\pi$
$614$	−5.98661e10	+	9.82423e9i	−0.421219	+	0.0691234i
$615$	−4.48378e10	−	7.22339e9i	−0.313432	−	0.0504941i
$616$	2.93376e10	+	1.43355e10i	0.203752	+	0.0995610i
$617$	4.42547e10	+	1.36202e11i	0.305364	+	0.939815i	0.979541	+	0.201245i	$0.0644986\pi$
$617$	4.42547e10	+	1.36202e11i	0.305364	+	0.939815i	−0.674177	+	0.738570i	$0.735501\pi$
$618$	−5.93215e8	+	1.18047e9i	−0.00406685	+	0.00809284i
$619$	2.37811e11	−	7.72694e10i	1.61983	−	0.526314i	0.647927	−	0.761703i	$-0.275636\pi$
$619$	2.37811e11	−	7.72694e10i	1.61983	−	0.526314i	0.971901	+	0.235389i	$0.0756363\pi$
$620$	−2.69863e10	+	1.80289e11i	−0.182632	+	1.22012i
$621$	9.17959e9	−	2.82519e10i	0.0617244	−	0.189968i
$622$	1.75502e11	−	1.77470e11i	1.17252	−	1.18567i
$623$	1.78252e11	+	2.45343e11i	1.18327	+	1.62862i
$624$	1.41048e10	+	4.23768e9i	0.0930309	+	0.0279505i
$625$	−1.52579e11	−	1.61655e9i	−0.999944	−	0.0105942i
$626$	−9.14309e10	+	1.81943e11i	−0.595382	+	1.18478i
$627$	−3.01037e9	−	4.14342e9i	−0.0194782	−	0.0268095i
$628$	−1.22410e11	+	4.12878e10i	−0.787009	+	0.265450i
$629$	1.20752e10	−	3.71636e10i	0.0771421	−	0.237419i
$630$	1.67820e11	−	5.50712e10i	1.06532	−	0.349593i
$631$	−1.70625e11	+	5.54394e10i	−1.07628	+	0.349704i	−0.792930	−	0.609313i	$-0.791445\pi$
$631$	−1.70625e11	+	5.54394e10i	−1.07628	+	0.349704i	−0.283349	+	0.959017i	$0.591445\pi$
$632$	−3.86630e10	−	2.20211e11i	−0.242341	−	1.38029i
$633$	1.75173e10	+	5.39126e10i	0.109107	+	0.335796i
$634$	8.51091e10	−	4.39645e10i	0.526768	−	0.272111i
$635$	1.15362e11	+	1.85848e10i	0.709524	+	0.114305i
$636$	−1.31557e10	+	4.20794e10i	−0.0804053	+	0.257183i
$637$	2.24909e10	+	1.63406e10i	0.136599	+	0.0992453i
$638$	6.71625e9	+	1.30017e10i	0.0405363	+	0.0784726i
$639$	−1.12710e11	−	1.55132e11i	−0.676017	−	0.930458i
$640$	−1.57570e11	+	5.76119e10i	−0.939191	+	0.343394i
$641$	1.31921e11	+	9.58461e10i	0.781415	+	0.567731i	0.905403	−	0.424553i	$-0.139569\pi$
$641$	1.31921e11	+	9.58461e10i	0.781415	+	0.567731i	−0.123989	+	0.992284i	$0.539569\pi$
$642$	−3.77503e10	−	5.76356e9i	−0.222219	−	0.0339274i
$643$			3.04362e11i			1.78052i	0.455454	+	0.890259i	$0.349477\pi$
$643$			3.04362e11i			1.78052i	−0.455454	+	0.890259i	$0.650523\pi$
$644$	−4.17407e10	+	5.88191e10i	−0.242670	+	0.341959i
$645$	1.49251e9	+	2.94850e9i	0.00862340	+	0.0170358i
$646$	1.49751e10	−	1.51430e10i	0.0859886	−	0.0869526i
$647$	−5.08883e10	−	1.65346e10i	−0.290403	−	0.0943575i	0.160193	−	0.987086i	$-0.448788\pi$
$647$	−5.08883e10	−	1.65346e10i	−0.290403	−	0.0943575i	−0.450596	+	0.892728i	$0.648788\pi$
$648$	8.82576e10	−	9.12597e10i	0.500555	−	0.517582i
$649$	2.52754e10			0.142469
$650$	−4.97625e10	−	2.53379e10i	−0.278772	−	0.141944i
$651$		−	8.53786e10i		−	0.475363i
$652$	2.59829e10	−	8.31084e10i	0.143780	−	0.459891i
$653$	1.76184e10	−	5.42240e10i	0.0968980	−	0.298221i	−0.890846	−	0.454306i	$-0.849887\pi$
$653$	1.76184e10	−	5.42240e10i	0.0968980	−	0.298221i	0.987744	+	0.156085i	$0.0498873\pi$
$654$	−4.47037e10	+	4.52048e10i	−0.244361	+	0.247101i
$655$	5.97660e10	−	1.16533e11i	0.324705	−	0.633119i
$656$	1.89290e11	−	4.22105e9i	1.02214	−	0.0227932i
$657$	1.78193e11			0.956375
$658$	−2.64892e10	−	4.04426e9i	−0.141308	−	0.0215743i
$659$	1.83069e11	−	2.51973e11i	0.970672	−	1.33602i	0.0289657	−	0.999580i	$-0.490779\pi$
$659$	1.83069e11	−	2.51973e11i	0.970672	−	1.33602i	0.941707	−	0.336435i	$-0.109221\pi$
$660$	1.06494e10	+	1.59403e9i	0.0561239	+	0.00840083i
$661$	−8.86777e10	+	6.44281e10i	−0.464525	+	0.337497i	−0.795304	−	0.606211i	$-0.792689\pi$
$661$	−8.86777e10	+	6.44281e10i	−0.464525	+	0.337497i	0.330779	+	0.943708i	$0.392689\pi$
$662$	−3.69837e10	−	7.15952e10i	−0.192565	−	0.372779i
$663$	2.31039e9	−	3.17998e9i	0.0119572	−	0.0164577i
$664$	−2.51854e11	−	2.43568e11i	−1.29561	−	1.25299i
$665$	1.26088e11	+	6.46664e10i	0.644745	+	0.330668i
$666$	1.88275e11	−	9.72564e10i	0.956963	−	0.494335i
$667$	−3.07421e10	+	9.98870e9i	−0.155321	+	0.0504668i
$668$	−2.21638e11	+	1.64835e11i	−1.11311	+	0.827837i
$669$	2.72774e10	+	8.39512e10i	0.136175	+	0.419105i
$670$	−1.60879e11	−	5.17529e10i	−0.798362	−	0.256824i
$671$	−5.11976e9	−	1.66351e9i	−0.0252557	−	0.00820608i
$672$	6.89902e10	−	3.76097e10i	0.338306	−	0.184426i
$673$	−1.10494e10	+	8.02786e9i	−0.0538615	+	0.0391327i	−0.614390	−	0.789002i	$-0.710598\pi$
$673$	−1.10494e10	+	8.02786e9i	−0.0538615	+	0.0391327i	0.560529	+	0.828135i	$0.310598\pi$
$674$	8.23624e10	−	1.63897e11i	0.399107	−	0.794205i
$675$	9.96535e10	−	7.15991e10i	0.480040	−	0.344899i
$676$	1.12426e11	+	1.51168e11i	0.538367	+	0.723889i
$677$	−1.41619e11	+	1.02893e11i	−0.674168	+	0.489812i	−0.871418	−	0.490541i	$-0.836799\pi$
$677$	−1.41619e11	+	1.02893e11i	−0.674168	+	0.489812i	0.197250	+	0.980353i	$0.436799\pi$
$678$	−4.57191e10	+	4.62316e10i	−0.216361	+	0.218786i
$679$	2.59147e11	+	8.42019e10i	1.21918	+	0.396135i
$680$	6.30133e8	+	4.47725e10i	0.00294711	+	0.209400i
$681$	−6.03752e9	−	1.85816e10i	−0.0280718	−	0.0863960i
$682$	−2.19022e10	+	4.35843e10i	−0.101239	+	0.201462i
$683$	−1.16477e11	+	3.78457e10i	−0.535251	+	0.173914i	−0.564156	−	0.825669i	$-0.690798\pi$
$683$	−1.16477e11	+	3.78457e10i	−0.535251	+	0.173914i	0.0289043	+	0.999582i	$0.490798\pi$
$684$	1.15487e11	−	1.28749e9i	0.527607	−	0.00588192i
$685$	1.10872e11	−	1.72595e10i	0.503570	−	0.0783910i
$686$	−1.24811e11	+	2.04819e10i	−0.563581	+	0.0924855i
$687$	−2.30445e10	+	3.17181e10i	−0.103452	+	0.142390i
$688$	−8.34455e9	−	1.09627e10i	−0.0372434	−	0.0489289i
$689$	4.94932e10	−	3.59589e10i	0.219619	−	0.159562i
$690$	−7.28371e9	+	2.26421e10i	−0.0321334	+	0.0998897i
$691$	−1.47645e11	+	2.03216e11i	−0.647601	+	0.891346i	−0.998992	−	0.0448828i	$-0.985709\pi$
$691$	−1.47645e11	+	2.03216e11i	−0.647601	+	0.891346i	0.351392	+	0.936229i	$0.385709\pi$
$692$	5.61367e10	−	7.91052e10i	0.244806	−	0.344970i
$693$	4.72602e10			0.204910
$694$	−4.15639e10	+	2.72236e11i	−0.179175	+	1.17357i
$695$	−2.47248e11	−	3.98319e10i	−1.05973	−	0.170723i
$696$	3.48689e10	+	4.92652e9i	0.148594	+	0.0209944i
$697$	1.56154e10	−	4.80592e10i	0.0661640	−	0.203632i
$698$	2.56327e10	+	1.56199e11i	0.107987	+	0.658045i
$699$		−	1.63391e10i		−	0.0684415i
$700$	−2.82806e11	+	9.37220e10i	−1.17787	+	0.390346i
$701$	−2.98200e11			−1.23491			−0.617455	−	0.786606i	$-0.711836\pi$
$701$	−2.98200e11			−1.23491			−0.617455	+	0.786606i	$0.711836\pi$
$702$	4.43141e10	−	7.27209e9i	0.182471	−	0.0299441i
$703$	1.61692e11	+	5.25370e10i	0.662015	+	0.215102i
$704$	−4.48663e10	+	1.50105e9i	−0.182654	+	0.00611088i
$705$	−8.73152e9	+	1.35924e9i	−0.0353454	+	0.00550224i
$706$	2.29644e11	+	3.50610e10i	0.924349	+	0.141126i
$707$			2.88473e11i			1.15459i
$708$	3.52000e10	−	4.96022e10i	0.140091	−	0.197409i
$709$	−5.31939e10	−	3.86477e10i	−0.210512	−	0.152946i	0.477533	−	0.878614i	$-0.341531\pi$
$709$	−5.31939e10	−	3.86477e10i	−0.210512	−	0.152946i	−0.688045	+	0.725668i	$0.741531\pi$
$710$	1.90884e11	+	2.61119e11i	0.751165	+	1.02755i
$711$	−1.90207e11	−	2.61797e11i	−0.744299	−	1.02444i
$712$	−3.74597e11	−	1.83043e11i	−1.45762	−	0.712250i
$713$	−8.71659e10	−	6.33298e10i	−0.337279	−	0.245047i
$714$	−3.39601e9	−	2.06944e10i	−0.0130670	−	0.0796268i
$715$	−1.05374e10	−	1.05934e10i	−0.0403191	−	0.0405332i
$716$	−6.14795e8	+	6.85393e6i	−0.00233926	+	2.60788e-5i
$717$	−3.24914e10	−	9.99984e10i	−0.122940	−	0.378370i
$718$	−1.21468e11	−	6.10404e10i	−0.457049	−	0.229678i
$719$	2.15612e11	−	7.00564e10i	0.806782	−	0.262139i	0.123548	−	0.992339i	$-0.460573\pi$
$719$	2.15612e11	−	7.00564e10i	0.806782	−	0.262139i	0.683234	+	0.730199i	$0.260573\pi$
$720$	−1.68298e11	+	1.75044e11i	−0.626251	+	0.651355i
$721$	3.02242e9	−	9.30206e9i	0.0111844	−	0.0344222i
$722$	−1.27331e11	−	1.25919e11i	−0.468580	−	0.463385i
$723$	−1.89092e10	−	2.60263e10i	−0.0692023	−	0.0952488i
$724$	2.76550e11	+	3.71849e11i	1.00651	+	1.35336i
$725$	−1.26768e11	−	4.19332e10i	−0.458837	−	0.151777i
$726$	−7.45051e10	−	3.74406e10i	−0.268188	−	0.134771i
$727$	−1.59372e11	−	2.19356e11i	−0.570524	−	0.785259i	0.422093	−	0.906553i	$-0.361296\pi$
$727$	−1.59372e11	−	2.19356e11i	−0.570524	−	0.785259i	−0.992617	+	0.121294i	$0.961296\pi$
$728$	−1.07960e11	−	1.52534e10i	−0.384360	−	0.0543050i
$729$	4.07629e10	−	1.25455e11i	0.144329	−	0.444200i
$730$	−3.00574e11	+	8.79278e8i	−1.05843	+	0.00309624i
$731$	−3.49707e9	+	1.13627e9i	−0.0122471	+	0.00397934i
$732$	−1.03947e10	+	7.73067e9i	−0.0362048	+	0.0269261i
$733$	−1.40103e11	−	4.31193e11i	−0.485324	−	1.49367i	−0.831511	−	0.555508i	$-0.812524\pi$
$733$	−1.40103e11	−	4.31193e11i	−0.485324	−	1.49367i	0.346187	−	0.938165i	$-0.387476\pi$
$734$	1.50762e11	+	2.91854e11i	0.519407	+	1.00550i
$735$	4.36402e10	−	2.20904e10i	0.149533	−	0.0756926i
$736$	1.27766e10	−	9.83315e10i	0.0435415	−	0.335105i
$737$	−3.65833e10	−	2.65793e10i	−0.123997	−	0.0900894i
$738$	2.43473e11	−	1.25770e11i	0.820777	−	0.423986i
$739$	8.21413e10	+	1.13058e11i	0.275413	+	0.379073i	0.924208	−	0.381890i	$-0.124727\pi$
$739$	8.21413e10	+	1.13058e11i	0.275413	+	0.379073i	−0.648795	+	0.760963i	$0.724727\pi$
$740$	−3.17101e11	+	1.64981e11i	−1.05748	+	0.550182i
$741$	1.38355e10	+	1.00521e10i	0.0458904	+	0.0333414i
$742$	4.92618e10	−	3.22657e11i	0.162516	−	1.06445i
$743$			3.20508e11i			1.05168i	0.850584	+	0.525840i	$0.176249\pi$
$743$			3.20508e11i			1.05168i	−0.850584	+	0.525840i	$0.823751\pi$
$744$	5.50306e10	+	1.03680e11i	0.179603	+	0.338380i
$745$	−3.80310e11	+	3.78301e11i	−1.23456	+	1.22804i
$746$	4.00724e11	+	3.96282e11i	1.29387	+	1.27953i
$747$	−4.82284e11	−	1.56704e11i	−1.54889	−	0.503265i
$748$	−3.57512e9	+	1.14353e10i	−0.0114205	+	0.0365293i
$749$	2.82715e11			0.898299
$750$	−7.96226e10	+	5.75611e10i	−0.251647	+	0.181922i
$751$		−	3.58573e11i		−	1.12724i	−0.826033	−	0.563621i	$-0.809408\pi$
$751$		−	3.58573e11i		−	1.12724i	0.826033	−	0.563621i	$-0.190592\pi$
$752$	3.47742e10	−	1.21624e10i	0.108739	−	0.0380319i
$753$	4.15659e10	−	1.27927e11i	0.129288	−	0.397906i
$754$	−3.47449e10	−	3.43597e10i	−0.107499	−	0.106307i
$755$	2.58101e10	+	2.59472e10i	0.0794331	+	0.0798550i
$756$	1.38658e11	−	1.95390e11i	0.424480	−	0.598158i
$757$	6.53419e10			0.198979			0.0994897	−	0.995039i	$-0.468279\pi$
$757$	6.53419e10			0.198979			0.0994897	+	0.995039i	$0.468279\pi$
$758$	−4.60192e10	+	3.01418e11i	−0.139400	+	0.913046i
$759$	−3.74078e9	+	5.14874e9i	−0.0112718	+	0.0155144i
$760$	−1.94797e11	+	2.74159e9i	−0.583886	+	0.00821767i
$761$	−4.52282e11	+	3.28602e11i	−1.34856	+	0.979786i	−0.349478	+	0.936945i	$0.613641\pi$
$761$	−4.52282e11	+	3.28602e11i	−1.34856	+	0.979786i	−0.999082	+	0.0428416i	$0.986359\pi$
$762$	6.68462e10	−	3.45305e10i	0.198270	−	0.102420i
$763$	2.76653e11	−	3.80780e11i	0.816276	−	1.12351i
$764$	1.22162e11	−	3.90745e11i	0.358561	−	1.14689i
$765$	2.92693e10	+	5.78223e10i	0.0854607	+	0.168830i
$766$	2.79906e11	+	5.41859e11i	0.813012	+	1.57388i
$767$	−8.02677e10	+	2.60805e10i	−0.231931	+	0.0753590i
$768$	−5.95377e10	+	9.01392e10i	−0.171138	+	0.259101i
$769$	−7.79853e10	−	2.40014e11i	−0.223001	−	0.686328i	−0.998488	−	0.0549640i	$-0.982496\pi$
$769$	−7.79853e10	−	2.40014e11i	−0.223001	−	0.686328i	0.775487	−	0.631364i	$-0.217504\pi$
$770$	−7.97182e10	+	2.33202e8i	−0.226775	+	0.000663390i
$771$	−2.66803e10	−	8.66895e9i	−0.0755045	−	0.0245329i
$772$	−2.47782e11	+	8.35745e10i	−0.697591	+	0.235290i
$773$	4.86746e11	−	3.53642e11i	1.36328	−	0.990479i	0.365049	−	0.930988i	$-0.381052\pi$
$773$	4.86746e11	−	3.53642e11i	1.36328	−	0.990479i	0.998229	−	0.0594910i	$-0.0189478\pi$
$774$	−1.78174e10	−	8.95369e9i	−0.0496457	−	0.0249481i
$775$	−1.35288e11	−	4.24002e11i	−0.375018	−	1.17533i
$776$	−3.68970e11	+	6.47811e10i	−1.01752	+	0.178649i
$777$	1.35439e11	−	9.84020e10i	0.371585	−	0.269973i
$778$	−3.79066e11	−	3.74863e11i	−1.03466	−	1.02319i
$779$	2.09097e11	+	6.79397e10i	0.567803	+	0.184491i
$780$	−3.54643e10	+	5.92639e9i	−0.0958104	+	0.0160108i
$781$	2.67444e10	+	8.23107e10i	0.0718833	+	0.221234i
$782$	−2.36466e10	−	1.18830e10i	−0.0632327	−	0.0317759i
$783$	1.02122e11	−	3.31813e10i	0.271688	−	0.0882768i
$784$	−1.62258e11	+	1.23506e11i	−0.429478	+	0.326907i
$785$	2.23608e11	−	2.22427e11i	0.588856	−	0.585744i
$786$	−1.36558e10	−	8.32145e10i	−0.0357788	−	0.218026i
$787$	1.28274e10	−	1.76554e10i	0.0334380	−	0.0460234i	−0.791971	−	0.610559i	$-0.790945\pi$
$787$	1.28274e10	−	1.76554e10i	0.0334380	−	0.0460234i	0.825409	+	0.564536i	$0.190945\pi$
$788$	−6.16033e9	−	5.52580e11i	−0.0159772	−	1.43314i
$789$	8.06200e10	−	5.85738e10i	0.208034	−	0.151146i
$790$	3.22131e11	+	4.40659e11i	0.827036	+	1.13134i
$791$	2.82937e11	−	3.89429e11i	0.722742	−	0.994770i
$792$	−5.73909e10	+	3.04614e10i	−0.145862	+	0.0774194i
$793$	1.79755e10			0.0454556
$794$	−7.17602e11	−	1.09560e11i	−1.80552	−	0.275659i
$795$	−1.65565e10	−	1.06356e11i	−0.0414475	−	0.266252i
$796$	−9.62952e10	−	2.85497e11i	−0.239857	−	0.711130i
$797$	3.44524e10	−	1.06034e11i	0.0853859	−	0.262791i	−0.899243	−	0.437449i	$-0.855882\pi$
$797$	3.44524e10	−	1.06034e11i	0.0853859	−	0.262791i	0.984629	+	0.174658i	$0.0558821\pi$
$798$	9.00374e10	−	1.47754e10i	0.222030	−	0.0364358i
$799$		−	9.83223e9i		−	0.0241249i
$800$	2.83020e11	−	2.96094e11i	0.690967	−	0.722886i
$801$	−6.03442e11			−1.46590
$802$	−1.12829e11	−	6.87548e11i	−0.272723	−	1.66190i
$803$	−7.64898e10	−	2.48530e10i	−0.183968	−	0.0597747i
$804$	−1.03109e11	+	3.47777e10i	−0.246759	+	0.0832293i
$805$	2.80064e10	−	1.73844e11i	0.0666920	−	0.413977i
$806$	2.45826e10	−	1.61012e11i	0.0582488	−	0.381520i
$807$		−	2.13284e10i		−	0.0502881i
$808$	−1.85935e11	−	3.50310e11i	−0.436229	−	0.821878i
$809$	2.16456e11	+	1.57264e11i	0.505330	+	0.367144i	0.811049	−	0.584978i	$-0.198897\pi$
$809$	2.16456e11	+	1.57264e11i	0.505330	+	0.367144i	−0.305719	+	0.952122i	$0.598897\pi$
$810$	−9.49172e10	+	2.95059e11i	−0.220498	+	0.685440i
$811$	2.76061e11	+	3.79965e11i	0.638147	+	0.878334i	0.998515	−	0.0544760i	$-0.0173488\pi$
$811$	2.76061e11	+	3.79965e11i	0.638147	+	0.878334i	−0.360368	+	0.932810i	$0.617349\pi$
$812$	−2.60692e11	+	2.90628e9i	−0.599658	+	0.00668517i
$813$	1.19964e11	+	8.71591e10i	0.274593	+	0.199503i
$814$	−9.43822e10	+	1.54884e10i	−0.214977	+	0.0352785i
$815$	3.26996e10	+	2.10056e11i	0.0741160	+	0.476108i
$816$	1.74625e10	+	2.29415e10i	0.0393863	+	0.0517442i
$817$	−4.94369e9	−	1.52151e10i	−0.0110959	−	0.0341497i
$818$	1.17018e11	−	2.32861e11i	0.261361	−	0.520096i
$819$	−1.50085e11	+	4.87656e10i	−0.333582	+	0.108387i
$820$	−4.10068e11	+	2.13350e11i	−0.906986	+	0.471885i
$821$	2.35145e11	−	7.23703e11i	0.517564	−	1.59290i	−0.261005	−	0.965338i	$-0.584054\pi$
$821$	2.35145e11	−	7.23703e11i	0.517564	−	1.59290i	0.778568	−	0.627560i	$-0.215946\pi$
$822$	5.08024e10	−	5.13719e10i	0.111275	−	0.112522i
$823$	4.57837e11	+	6.30158e11i	0.997955	+	1.37357i	0.926571	+	0.376119i	$0.122742\pi$
$823$	4.57837e11	+	6.30158e11i	0.997955	+	1.37357i	0.0713839	+	0.997449i	$0.477258\pi$
$824$	2.32531e9	+	1.32442e10i	0.00504397	+	0.0287287i
$825$	−2.50451e10	+	7.99122e9i	−0.0540638	+	0.0172503i
$826$	−2.02187e11	+	4.02343e11i	−0.434343	+	0.864323i
$827$	3.06625e10	+	4.22033e10i	0.0655519	+	0.0902244i	0.840534	−	0.541759i	$-0.182241\pi$
$827$	3.06625e10	+	4.22033e10i	0.0655519	+	0.0902244i	−0.774982	+	0.631983i	$0.782241\pi$
$828$	−4.58681e10	−	1.35990e11i	−0.0975864	−	0.289325i
$829$	1.78666e11	−	5.49878e11i	0.378290	−	1.16426i	−0.562943	−	0.826496i	$-0.690331\pi$
$829$	1.78666e11	−	5.49878e11i	0.378290	−	1.16426i	0.941232	−	0.337760i	$-0.109669\pi$
$830$	8.14288e11	+	2.61947e11i	1.71580	+	0.551952i
$831$	−1.70297e10	+	5.53330e9i	−0.0357112	+	0.0116033i
$832$	1.40934e11	−	5.10625e10i	0.294119	−	0.106563i
$833$	1.68177e10	+	5.17595e10i	0.0349290	+	0.107500i
$834$	−1.43268e11	+	7.40073e10i	−0.296131	+	0.152971i
$835$	3.07739e11	−	6.00037e11i	0.633048	−	1.23433i
$836$	−4.97529e10	−	1.55547e10i	−0.101858	−	0.0318447i
$837$	2.89555e11	+	2.10374e11i	0.589970	+	0.428638i
$838$	2.73664e11	+	5.29776e11i	0.554935	+	1.07428i
$839$	3.03165e11	+	4.17270e11i	0.611830	+	0.842111i	0.996726	−	0.0808483i	$-0.0257629\pi$
$839$	3.03165e11	+	4.17270e11i	0.611830	+	0.842111i	−0.384897	+	0.922960i	$0.625763\pi$
$840$	−1.10563e11	+	1.56769e11i	−0.222071	+	0.314879i
$841$	3.10181e11	+	2.25360e11i	0.620057	+	0.450497i
$842$	3.20031e10	+	4.88610e9i	0.0636714	+	0.00972107i
$843$			1.79669e11i			0.355765i
$844$	4.70529e11	+	3.33909e11i	0.927291	+	0.658049i
$845$	−4.09254e11	−	2.09892e11i	−0.802724	−	0.411690i
$846$	3.74925e10	−	3.79128e10i	0.0731918	−	0.0740123i
$847$	5.87098e11	+	1.90760e11i	1.14071	+	0.370641i
$848$	1.48146e11	+	4.23573e11i	0.286488	+	0.819116i
$849$	−8.46801e9			−0.0162986
$850$	−4.96566e10	−	9.73900e10i	−0.0951265	−	0.186569i
$851$		−	2.11264e11i		−	0.402816i
$852$	1.98778e11	+	6.21457e10i	0.377233	+	0.117938i
$853$	−1.11735e11	+	3.43886e11i	−0.211054	+	0.649558i	0.788356	+	0.615219i	$0.210932\pi$
$853$	−1.11735e11	+	3.43886e11i	−0.211054	+	0.649558i	−0.999410	+	0.0343386i	$0.989068\pi$
$854$	6.74353e10	−	6.81912e10i	0.126781	−	0.128203i
$855$	−2.51575e11	+	1.27345e11i	−0.470763	+	0.238297i
$856$	−3.43318e11	+	1.82223e11i	−0.639442	+	0.339397i
$857$	−1.03972e12			−1.92749			−0.963746	−	0.266821i	$-0.914027\pi$
$857$	−1.03972e12			−1.92749			−0.963746	+	0.266821i	$0.914027\pi$
$858$	−9.51068e9	−	1.45205e9i	−0.0175494	−	0.00267937i
$859$	2.63350e11	−	3.62471e11i	0.483684	−	0.665733i	−0.495524	−	0.868594i	$-0.665024\pi$
$859$	2.63350e11	−	3.62471e11i	0.483684	−	0.665733i	0.979208	+	0.202861i	$0.0650239\pi$
$860$	3.00985e10	+	1.50151e10i	0.0550239	+	0.0274495i
$861$	1.75146e11	−	1.27251e11i	0.318705	−	0.231553i
$862$	−1.04477e11	−	2.02253e11i	−0.189231	−	0.366325i
$863$	7.02512e10	−	9.66925e10i	0.126652	−	0.174321i	−0.740982	−	0.671525i	$-0.765640\pi$
$863$	7.02512e10	−	9.66925e10i	0.126652	−	0.174321i	0.867634	+	0.497204i	$0.165640\pi$
$864$	−4.24424e10	+	3.26646e11i	−0.0761631	+	0.586168i
$865$	−3.76656e10	+	2.33801e11i	−0.0672791	+	0.417621i
$866$	2.09743e11	−	1.08346e11i	0.372921	−	0.192638i
$867$	−1.59548e11	+	5.18404e10i	−0.282368	+	0.0917471i
$868$	−5.18587e11	−	6.97293e11i	−0.913573	−	1.22839i
$869$	4.51333e10	+	1.38906e11i	0.0791439	+	0.243580i
$870$	−8.16887e10	+	2.68067e10i	−0.142589	+	0.0467915i
$871$	1.43604e11	+	4.66599e10i	0.249514	+	0.0810721i
$872$	−9.05254e10	+	6.40721e11i	−0.156569	+	1.10816i
$873$	−4.38649e11	+	3.18697e11i	−0.755197	+	0.548683i
$874$	5.17007e10	−	1.02882e11i	0.0886035	−	0.176317i
$875$	5.18399e11	−	5.10226e11i	0.884367	−	0.870423i
$876$	−1.55297e11	+	1.15497e11i	−0.263723	+	0.196135i
$877$	4.92028e11	−	3.57479e11i	0.831747	−	0.604299i	−0.0883061	−	0.996093i	$-0.528145\pi$
$877$	4.92028e11	−	3.57479e11i	0.831747	−	0.604299i	0.920053	+	0.391794i	$0.128145\pi$
$878$	−6.87892e11	+	6.95603e11i	−1.15756	+	1.17053i
$879$	−1.22044e11	−	3.96545e10i	−0.204437	−	0.0664257i
$880$	9.66563e10	−	5.16654e10i	0.161176	−	0.0861527i
$881$	1.81024e11	+	5.57134e11i	0.300491	+	0.924817i	0.981321	+	0.192376i	$0.0616192\pi$
$881$	1.81024e11	+	5.57134e11i	0.300491	+	0.924817i	−0.680830	+	0.732441i	$0.738381\pi$
$882$	−1.32522e11	+	2.63713e11i	−0.218985	+	0.435769i
$883$	−3.78994e11	+	1.23143e11i	−0.623432	+	0.202565i	−0.603664	−	0.797239i	$-0.706293\pi$
$883$	−3.78994e11	+	1.23143e11i	−0.623432	+	0.202565i	−0.0197686	+	0.999805i	$0.506293\pi$
$884$	−4.45981e8	−	4.00044e10i	−0.000730310	−	0.0655086i
$885$	−2.36178e10	+	1.46603e11i	−0.0385005	+	0.238984i
$886$	6.53035e11	−	1.07165e11i	1.05975	−	0.173908i
$887$	−2.34632e11	+	3.22943e11i	−0.379046	+	0.521712i	−0.955332	−	0.295536i	$-0.904502\pi$
$887$	−2.34632e11	+	3.22943e11i	−0.379046	+	0.521712i	0.576285	+	0.817249i	$0.304502\pi$
$888$	−1.01047e11	+	2.06792e11i	−0.162506	+	0.332569i
$889$	−4.50629e11	+	3.27401e11i	−0.721460	+	0.524171i
$890$	1.01788e12	−	2.97764e9i	1.62232	−	0.00474583i
$891$	−4.87477e10	+	6.70955e10i	−0.0773470	+	0.106459i
$892$	7.32694e11	+	5.19954e11i	1.15735	+	0.821306i
$893$	4.27782e10			0.0672693
$894$	−5.21295e10	+	3.41440e11i	−0.0816081	+	0.534520i
$895$	1.33925e9	−	6.77921e8i	0.00208723	−	0.00105654i
$896$	3.35008e11	−	7.26206e11i	0.519784	−	1.12675i
$897$	6.56693e9	−	2.02109e10i	0.0101436	−	0.0312188i
$898$	−9.27527e10	−	5.65209e11i	−0.142633	−	0.869168i
$899$		−	3.89457e11i		−	0.596240i
$900$	1.79895e11	−	5.64884e11i	0.274189	−	0.860973i
$901$	1.19763e11			0.181729
$902$	−1.22053e11	+	2.00293e10i	−0.184384	+	0.0302580i
$903$	−1.49823e10	−	4.86803e9i	−0.0225334	−	0.00732154i
$904$	−9.25816e10	+	6.55274e11i	−0.138628	+	0.981181i
$905$	−1.00670e12	−	5.16304e11i	−1.50074	−	0.769681i
$906$	2.32952e10	+	3.55661e9i	0.0345743	+	0.00527865i
$907$			7.43208e11i			1.09820i	0.835757	+	0.549100i	$0.185029\pi$
$907$			7.43208e11i			1.09820i	−0.835757	+	0.549100i	$0.814971\pi$
$908$	−1.62173e11	−	1.15085e11i	−0.238580	−	0.169308i
$909$	−4.64390e11	−	3.37399e11i	−0.680185	−	0.494183i
$910$	2.52922e11	−	8.29982e10i	0.368826	−	0.121033i
$911$	−4.99846e11	−	6.87979e11i	−0.725709	−	0.998853i	−0.999315	−	0.0370108i	$-0.988216\pi$
$911$	−4.99846e11	−	6.87979e11i	−0.725709	−	0.998853i	0.273606	−	0.961842i	$-0.411784\pi$
$912$	−9.98145e10	+	7.59762e10i	−0.144283	+	0.109824i
$913$	1.85166e11	+	1.34531e11i	0.266489	+	0.193615i
$914$	7.08559e10	+	4.31776e11i	0.101529	+	0.618691i
$915$	1.44328e10	−	2.81414e10i	0.0205904	−	0.0401477i
$916$	4.44835e9	+	3.99016e11i	0.00631855	+	0.566772i
$917$	1.92919e11	+	5.93745e11i	0.272834	+	0.839697i
$918$	7.85513e10	+	3.94739e10i	0.110607	+	0.0555827i
$919$	2.54991e11	−	8.28514e10i	0.357488	−	0.116155i	−0.124766	−	0.992186i	$-0.539818\pi$
$919$	2.54991e11	−	8.28514e10i	0.357488	−	0.116155i	0.482255	+	0.876031i	$0.339818\pi$
$920$	7.80411e10	+	2.29161e11i	0.108936	+	0.319882i
$921$	2.94704e10	−	9.07006e10i	0.0409588	−	0.126058i
$922$	9.44666e11	+	9.34193e11i	1.30724	+	1.29275i
$923$	−1.69865e11	−	2.33800e11i	−0.234044	−	0.322134i
$924$	−4.11879e10	+	3.06321e10i	−0.0565044	+	0.0420231i
$925$	5.16684e11	−	7.03289e11i	0.705761	−	0.960654i
$926$	−7.52719e11	−	3.78260e11i	−1.02374	−	0.514453i
$927$	1.14396e10	+	1.57453e10i	0.0154915	+	0.0213222i
$928$	3.14701e11	−	1.71558e11i	0.424332	−	0.231323i
$929$	−2.72545e11	+	8.38809e11i	−0.365912	+	1.12616i	0.583497	+	0.812115i	$0.301684\pi$
$929$	−2.72545e11	+	8.38809e11i	−0.365912	+	1.12616i	−0.949408	+	0.314044i	$0.898316\pi$
$930$	−2.32333e11	−	1.67764e11i	−0.310584	−	0.224267i
$931$	−2.25196e11	+	7.31707e10i	−0.299752	+	0.0973954i
$932$	−9.92433e10	−	1.33443e11i	−0.131534	−	0.176861i
$933$	1.21246e11	+	3.73156e11i	0.160007	+	0.492452i
$934$	−5.13906e11	−	9.94850e11i	−0.675299	−	1.30728i
$935$	−4.49930e9	−	2.89027e10i	−0.00588706	−	0.0378174i
$936$	1.50826e11	−	1.55956e11i	0.196504	−	0.203189i
$937$	5.08403e11	+	3.69376e11i	0.659553	+	0.479193i	0.866512	−	0.499156i	$-0.166357\pi$
$937$	5.08403e11	+	3.69376e11i	0.659553	+	0.479193i	−0.206959	+	0.978350i	$0.566357\pi$
$938$	7.15742e11	−	3.69729e11i	0.924582	−	0.477608i
$939$	−1.88149e11	−	2.58964e11i	−0.242013	−	0.333102i
$940$	−6.30550e10	+	6.41361e10i	−0.0807622	+	0.0821468i
$941$	1.52284e11	+	1.10641e11i	0.194221	+	0.141110i	0.680646	−	0.732613i	$-0.261699\pi$
$941$	1.52284e11	+	1.10641e11i	0.194221	+	0.141110i	−0.486425	+	0.873722i	$0.661699\pi$
$942$	3.06502e10	−	2.00754e11i	0.0389251	−	0.254953i
$943$		−	2.73202e11i		−	0.345491i
$944$	−1.38013e10	−	6.18909e11i	−0.0173793	−	0.779361i
$945$	−9.30341e10	+	5.77491e11i	−0.116658	+	0.724132i
$946$	6.39940e9	+	6.32845e9i	0.00799051	+	0.00790192i
$947$	−7.07205e11	−	2.29785e11i	−0.879317	−	0.285707i	−0.165643	−	0.986186i	$-0.552970\pi$
$947$	−7.07205e11	−	2.29785e11i	−0.879317	−	0.285707i	−0.713674	+	0.700478i	$0.752970\pi$
$948$	3.35454e11	+	1.04876e11i	0.415336	+	0.129850i
$949$	2.68555e11			0.331107
$950$	4.23726e11	−	2.16047e11i	0.520225	−	0.265249i
$951$			1.50588e11i			0.184106i
$952$	−1.53433e11	−	1.48385e11i	−0.186797	−	0.180652i
$953$	−3.79555e11	+	1.16815e12i	−0.460154	+	1.41621i	0.404823	+	0.914395i	$0.367333\pi$
$953$	−3.79555e11	+	1.16815e12i	−0.460154	+	1.41621i	−0.864976	+	0.501813i	$0.832667\pi$
$954$	4.61803e11	+	4.56683e11i	0.557523	+	0.551343i
$955$	1.53742e11	+	9.87609e11i	0.184832	+	1.18733i
$956$	−8.72748e11	−	6.19342e11i	−1.04486	−	0.741480i
$957$	−2.30046e10			−0.0274262
$958$	−1.03165e11	+	6.75715e11i	−0.122482	+	0.802235i
$959$	−3.14395e11	+	4.32728e11i	−0.371708	+	0.511612i
$960$	3.32176e10	−	2.61637e11i	0.0391095	−	0.308045i
$961$	3.60215e11	−	2.61712e11i	0.422346	−	0.306853i
$962$	2.83750e11	−	1.46576e11i	0.331311	−	0.171144i
$963$	−3.30664e11	+	4.55120e11i	−0.384487	+	0.529201i
$964$	−3.12516e11	−	9.77048e10i	−0.361880	−	0.113138i
$965$	4.52626e11	−	4.50234e11i	0.521951	−	0.519194i
$966$	−5.20357e10	−	1.00734e11i	−0.0597575	−	0.115682i
$967$	1.39747e12	−	4.54064e11i	1.59821	−	0.519291i	0.631550	−	0.775335i	$-0.282419\pi$
$967$	1.39747e12	−	4.54064e11i	1.59821	−	0.519291i	0.966665	+	0.256044i	$0.0824192\pi$
$968$	−8.35902e11	+	1.46762e11i	−0.952038	+	0.167152i
$969$	1.03456e10	+	3.18404e10i	0.0117344	+	0.0361147i
$970$	7.38338e11	−	5.39741e11i	0.834004	−	0.609675i
$971$	−7.12341e11	−	2.31454e11i	−0.801330	−	0.260368i	−0.120408	−	0.992724i	$-0.538420\pi$
$971$	−7.12341e11	−	2.31454e11i	−0.801330	−	0.260368i	−0.680921	+	0.732357i	$0.738420\pi$
$972$	2.32412e11	+	6.89056e11i	0.260371	+	0.771951i
$973$	9.65808e11	−	7.01700e11i	1.07755	−	0.782889i
$974$	−1.07638e12	−	5.40907e11i	−1.19600	−	0.601017i
$975$	7.12905e10	−	5.12208e10i	0.0788884	−	0.0566797i
$976$	−3.79382e10	+	1.26274e11i	−0.0418097	+	0.139160i
$977$	−1.28096e12	+	9.30672e11i	−1.40591	+	1.02145i	−0.412008	+	0.911180i	$0.635173\pi$
$977$	−1.28096e12	+	9.30672e11i	−1.40591	+	1.02145i	−0.993901	+	0.110273i	$0.964827\pi$
$978$	9.73284e10	+	9.62494e10i	0.106386	+	0.105207i
$979$	2.59030e11	+	8.41638e10i	0.281980	+	0.0916209i
$980$	2.22236e11	−	4.45483e11i	0.240941	−	0.482977i
$981$	2.89414e11	+	8.90724e11i	0.312495	+	0.961760i
$982$	6.73575e11	+	3.38488e11i	0.724336	+	0.363996i
$983$	−2.41989e11	+	7.86271e10i	−0.259168	+	0.0842089i	−0.435719	−	0.900083i	$-0.643506\pi$
$983$	−2.41989e11	+	7.86271e10i	−0.259168	+	0.0842089i	0.176551	+	0.984292i	$0.443506\pi$
$984$	−1.30671e11	+	2.67419e11i	−0.139380	+	0.285241i
$985$	6.09318e11	+	1.20372e12i	0.647290	+	1.27874i
$986$	−1.54910e10	−	9.43980e10i	−0.0163898	−	0.0998746i
$987$	2.47596e10	−	3.40787e10i	0.0260901	−	0.0359099i
$988$	1.74052e11	−	1.94038e9i	0.182663	−	0.00203638i
$989$	−1.60831e10	+	1.16850e10i	−0.0168106	+	0.0122136i
$990$	9.28633e10	−	1.28605e11i	0.0966725	−	0.133880i
$991$	−7.51916e11	+	1.03492e12i	−0.779605	+	1.07303i	0.215721	+	0.976455i	$0.430790\pi$
$991$	−7.51916e11	+	1.03492e12i	−0.779605	+	1.07303i	−0.995325	+	0.0965788i	$0.969210\pi$
$992$	1.07919e12	+	5.12511e11i	1.11443	+	0.529245i
$993$	1.26677e11			0.130287
$994$	−1.52419e12	−	2.32707e11i	−1.56133	−	0.238376i
$995$	5.18764e11	+	5.21519e11i	0.529270	+	0.532081i
$996$	5.21887e11	−	1.76027e11i	0.530321	−	0.178872i
$997$	3.60361e11	−	1.10908e12i	0.364718	−	1.12249i	−0.585439	−	0.810716i	$-0.699078\pi$
$997$	3.60361e11	−	1.10908e12i	0.364718	−	1.12249i	0.950157	−	0.311771i	$-0.100922\pi$
$998$	8.69553e11	−	1.42696e11i	0.876544	−	0.143844i
$999$			7.01795e11i			0.704609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.62	yes	464
4.3	odd	2	inner	100.9.j.b.11.18	✓	464
25.16	even	5	inner	100.9.j.b.91.18	yes	464
100.91	odd	10	inner	100.9.j.b.91.62	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.18	✓	464	4.3	odd	2	inner
100.9.j.b.11.62	yes	464	1.1	even	1	trivial
100.9.j.b.91.18	yes	464	25.16	even	5	inner
100.9.j.b.91.62	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+(2.59100 + 15.7888i) q^{2} +(-23.9209 - 7.77239i) q^{3} +(-242.573 + 81.8176i) q^{4} +(443.111 - 440.770i) q^{5} +(60.7377 - 397.822i) q^{6} +2979.31i q^{7} +(-1920.31 - 3617.96i) q^{8} +(-4796.16 - 3484.61i) q^{9} +(8107.33 + 5854.16i) q^{10} +(1572.76 + 2164.72i) q^{11} +(6438.50 - 71.7785i) q^{12} +(-7228.32 - 5251.68i) q^{13} +(-47039.8 + 7719.39i) q^{14} +(-14025.5 + 7099.60i) q^{15} +(52147.8 - 39693.5i) q^{16} +(-5405.02 - 16634.9i) q^{17} +(42591.1 - 84754.3i) q^{18} +(72375.6 - 23516.2i) q^{19} +(-71424.2 + 143173. i) q^{20} +(23156.4 - 71267.9i) q^{21} +(-30103.3 + 30440.8i) q^{22} +(-55583.6 - 76504.3i) q^{23} +(17815.4 + 101470. i) q^{24} +(2069.22 - 390620. i) q^{25} +(64189.3 - 127734. i) q^{26} +(184642. + 254139. i) q^{27} +(-243760. - 722702. i) q^{28} +(105628. - 325091. i) q^{29} +(-148434. - 203050. i) q^{30} +(1.08360e6 - 352082. i) q^{31} +(761829. + 720506. i) q^{32} +(-20796.9 - 64006.1i) q^{33} +(248641. - 128440. i) q^{34} +(1.31319e6 + 1.32016e6i) q^{35} +(1.44852e6 + 452865. i) q^{36} +(1.80740e6 + 1.31315e6i) q^{37} +(558819. + 1.08179e6i) q^{38} +(132090. + 181807. i) q^{39} +(-2.44560e6 - 756742. i) q^{40} +(2.33729e6 + 1.69814e6i) q^{41} +(1.18523e6 + 180956. i) q^{42} -210225. i q^{43} +(-558621. - 396423. i) q^{44} +(-3.66114e6 + 569932. i) q^{45} +(1.06390e6 - 1.07582e6i) q^{46} +(534618. + 173708. i) q^{47} +(-1.55594e6 + 544194. i) q^{48} -3.11150e6 q^{49} +(6.17278e6 - 979424. i) q^{50} +439933. i q^{51} +(2.18308e6 + 682515. i) q^{52} +(-2.11588e6 + 6.51200e6i) q^{53} +(-3.53414e6 + 3.57376e6i) q^{54} +(1.65105e6 + 265985. i) q^{55} +(1.07790e7 - 5.72120e6i) q^{56} -1.91407e6 q^{57} +(5.40649e6 + 825439. i) q^{58} +(5.55230e6 - 7.64209e6i) q^{59} +(2.82133e6 - 2.86970e6i) q^{60} +(-1.62764e6 + 1.18255e6i) q^{61} +(8.36655e6 + 1.61965e7i) q^{62} +(1.03817e7 - 1.42893e7i) q^{63} +(-9.40204e6 + 1.38952e7i) q^{64} +(-5.51773e6 + 858948. i) q^{65} +(956697. - 494197. i) q^{66} +(-1.60727e7 + 5.22233e6i) q^{67} +(2.67214e6 + 3.59297e6i) q^{68} +(734992. + 2.26207e6i) q^{69} +(-1.74414e7 + 2.41543e7i) q^{70} +(3.07619e7 + 9.99514e6i) q^{71} +(-3.39708e6 + 2.40438e7i) q^{72} +(-2.43171e7 + 1.76674e7i) q^{73} +(-1.60502e7 + 3.19391e7i) q^{74} +(-3.08554e6 + 9.32791e6i) q^{75} +(-1.56324e7 + 1.16260e7i) q^{76} +(-6.44936e6 + 4.68574e6i) q^{77} +(-2.52826e6 + 2.55661e6i) q^{78} +(5.19131e7 + 1.68676e7i) q^{79} +(5.61153e6 - 4.05738e7i) q^{80} +(9.57799e6 + 2.94780e7i) q^{81} +(-2.07558e7 + 4.13030e7i) q^{82} +(8.13518e7 - 2.64328e7i) q^{83} +(213850. + 1.91823e7i) q^{84} +(-9.72719e6 - 4.98875e6i) q^{85} +(3.31920e6 - 544691. i) q^{86} +(-5.05347e6 + 6.95550e6i) q^{87} +(4.81167e6 - 9.84710e6i) q^{88} +(8.23488e7 - 5.98299e7i) q^{89} +(-1.84846e7 - 5.63284e7i) q^{90} +(1.56464e7 - 2.15354e7i) q^{91} +(1.97425e7 + 1.40102e7i) q^{92} -2.86572e7 q^{93} +(-1.35745e6 + 8.89106e6i) q^{94} +(2.17051e7 - 4.23213e7i) q^{95} +(-1.26236e7 - 2.31564e7i) q^{96} +(2.82622e7 - 8.69821e7i) q^{97} +(-8.06188e6 - 4.91268e7i) q^{98} -1.58628e7i 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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