LMFDB - Embedded newform 100.9.j.b.11.35

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			11.35
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.11381 - 13.1506i) q^{2} +(-59.1564 - 19.2211i) q^{3} +(-89.8770 + 239.704i) q^{4} +(-437.861 - 445.986i) q^{5} +(286.371 + 953.120i) q^{6} -3669.49i q^{7} +(3971.38 - 1002.68i) q^{8} +(-2177.93 - 1582.36i) q^{9} +(-1874.40 + 9822.76i) q^{10} +(14576.8 + 20063.3i) q^{11} +(9924.17 - 12452.5i) q^{12} +(13678.3 + 9937.90i) q^{13} +(-48256.0 + 33443.0i) q^{14} +(17329.9 + 34799.1i) q^{15} +(-49380.3 - 43087.8i) q^{16} +(11426.5 + 35167.2i) q^{17} +(-959.740 + 43062.4i) q^{18} +(-215843. + 70131.7i) q^{19} +(146258. - 64873.2i) q^{20} +(-70531.6 + 217074. i) q^{21} +(130994. - 374547. i) q^{22} +(244002. + 335840. i) q^{23} +(-254205. - 17019.1i) q^{24} +(-7181.20 + 390559. i) q^{25} +(6027.58 - 270451. i) q^{26} +(338298. + 465628. i) q^{27} +(879592. + 329803. i) q^{28} +(228540. - 703375. i) q^{29} +(299687. - 545051. i) q^{30} +(1.46107e6 - 474730. i) q^{31} +(-116588. + 1.04207e6i) q^{32} +(-476675. - 1.46706e6i) q^{33} +(358330. - 470772. i) q^{34} +(-1.63654e6 + 1.60672e6i) q^{35} +(575044. - 379841. i) q^{36} +(-747765. - 543283. i) q^{37} +(2.88943e6 + 2.19930e6i) q^{38} +(-618144. - 850803. i) q^{39} +(-2.18609e6 - 1.33214e6i) q^{40} +(338142. + 245674. i) q^{41} +(3.49746e6 - 1.05084e6i) q^{42} -1.26186e6i q^{43} +(-6.11938e6 + 1.69090e6i) q^{44} +(247921. + 1.66418e6i) q^{45} +(2.19271e6 - 6.26956e6i) q^{46} +(3.60074e6 + 1.16995e6i) q^{47} +(2.09297e6 + 3.49806e6i) q^{48} -7.70035e6 q^{49} +(5.20154e6 - 3.46504e6i) q^{50} -2.29999e6i q^{51} +(-3.61152e6 + 2.38557e6i) q^{52} +(1.53500e6 - 4.72426e6i) q^{53} +(3.04010e6 - 8.69247e6i) q^{54} +(2.56532e6 - 1.52860e7i) q^{55} +(-3.67933e6 - 1.45729e7i) q^{56} +1.41165e7 q^{57} +(-1.13327e7 + 3.40498e6i) q^{58} +(1.24006e6 - 1.70679e6i) q^{59} +(-9.89904e6 + 1.02643e6i) q^{60} +(-1.40648e7 + 1.02187e7i) q^{61} +(-1.95589e7 - 1.48873e7i) q^{62} +(-5.80645e6 + 7.99189e6i) q^{63} +(1.47665e7 - 7.96406e6i) q^{64} +(-1.55705e6 - 1.04518e7i) q^{65} +(-1.49483e7 + 1.96390e7i) q^{66} +(-5.66838e6 + 1.84177e6i) q^{67} +(-9.45670e6 - 421736. i) q^{68} +(-7.97908e6 - 2.45571e7i) q^{69} +(3.60445e7 + 6.87810e6i) q^{70} +(-2.49453e6 - 810522. i) q^{71} +(-1.02360e7 - 4.10037e6i) q^{72} +(5.41028e6 - 3.93080e6i) q^{73} +(-329515. + 1.47849e7i) q^{74} +(7.93178e6 - 2.29660e7i) q^{75} +(2.58846e6 - 5.80418e7i) q^{76} +(7.36221e7 - 5.34896e7i) q^{77} +(-5.55492e6 + 1.58830e7i) q^{78} +(3.03544e7 + 9.86273e6i) q^{79} +(2.40515e6 + 4.08893e7i) q^{80} +(-5.60459e6 - 1.72491e7i) q^{81} +(149008. - 6.68580e6i) q^{82} +(-1.49363e7 + 4.85311e6i) q^{83} +(-4.56944e7 - 3.64166e7i) q^{84} +(1.06808e7 - 2.04944e7i) q^{85} +(-1.65942e7 + 1.15003e7i) q^{86} +(-2.70393e7 + 3.72164e7i) q^{87} +(7.80073e7 + 6.50630e7i) q^{88} +(-1.76107e6 + 1.27949e6i) q^{89} +(1.96254e7 - 1.84273e7i) q^{90} +(3.64670e7 - 5.01925e7i) q^{91} +(-1.02432e8 + 2.83041e7i) q^{92} -9.55564e7 q^{93} +(-1.74309e7 - 5.80146e7i) q^{94} +(1.25787e8 + 6.55550e7i) q^{95} +(2.69267e7 - 5.94044e7i) q^{96} +(-1.20159e7 + 3.69811e7i) q^{97} +(7.01795e7 + 1.01264e8i) q^{98} -6.67623e7i 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 $

$2$	−9.11381	−	13.1506i	−0.569613	−	0.821913i
$2$	−9.11381	−	13.1506i	−0.569613	−	0.821913i
$3$	−59.1564	−	19.2211i	−0.730326	−	0.237297i	−0.0798316	−	0.996808i	$-0.525438\pi$
$3$	−59.1564	−	19.2211i	−0.730326	−	0.237297i	−0.650494	+	0.759511i	$0.725438\pi$
$4$	−89.8770	+	239.704i	−0.351082	+	0.936345i
$5$	−437.861	−	445.986i	−0.700577	−	0.713577i
$5$	−437.861	−	445.986i	−0.700577	−	0.713577i
$6$	286.371	+	953.120i	0.220966	+	0.735432i
$7$		−	3669.49i		−	1.52832i	−0.645028	−	0.764159i	$-0.723154\pi$
$7$		−	3669.49i		−	1.52832i	0.645028	−	0.764159i	$-0.276846\pi$
$8$	3971.38	−	1002.68i	0.969575	−	0.244796i
$9$	−2177.93	−	1582.36i	−0.331951	−	0.241176i
$10$	−1874.40	+	9822.76i	−0.187440	+	0.982276i
$11$	14576.8	+	20063.3i	0.995618	+	1.37035i	0.927976	+	0.372641i	$0.121548\pi$
$11$	14576.8	+	20063.3i	0.995618	+	1.37035i	0.0676424	+	0.997710i	$0.478452\pi$
$12$	9924.17	−	12452.5i	0.478596	−	0.600526i
$13$	13678.3	+	9937.90i	0.478917	+	0.347953i	0.800906	−	0.598790i	$-0.204352\pi$
$13$	13678.3	+	9937.90i	0.478917	+	0.347953i	−0.321989	+	0.946743i	$0.604352\pi$
$14$	−48256.0	+	33443.0i	−1.25614	+	0.870549i
$15$	17329.9	+	34799.1i	0.342320	+	0.687389i
$16$	−49380.3	−	43087.8i	−0.753483	−	0.657467i
$17$	11426.5	+	35167.2i	0.136810	+	0.421058i	0.995867	−	0.0908219i	$-0.0289494\pi$
$17$	11426.5	+	35167.2i	0.136810	+	0.421058i	−0.859057	+	0.511880i	$0.828949\pi$
$18$	−959.740	+	43062.4i	−0.00914247	+	0.410212i
$19$	−215843.	+	70131.7i	−1.65624	+	0.538146i	−0.980079	−	0.198606i	$-0.936359\pi$
$19$	−215843.	+	70131.7i	−1.65624	+	0.538146i	−0.676163	+	0.736752i	$0.736359\pi$
$20$	146258.	−	64873.2i	0.914114	−	0.405458i
$21$	−70531.6	+	217074.i	−0.362666	+	1.11617i
$22$	130994.	−	374547.i	0.559192	−	1.59888i
$23$	244002.	+	335840.i	0.871931	+	1.20011i	0.978591	+	0.205815i	$0.0659844\pi$
$23$	244002.	+	335840.i	0.871931	+	1.20011i	−0.106660	+	0.994296i	$0.534016\pi$
$24$	−254205.	−	17019.1i	−0.766195	−	0.0512969i
$25$	−7181.20	+	390559.i	−0.0183839	+	0.999831i
$26$	6027.58	−	270451.i	0.0131901	−	0.591827i
$27$	338298.	+	465628.i	0.636568	+	0.876161i
$28$	879592.	+	329803.i	1.43103	+	0.536564i
$29$	228540.	−	703375.i	0.323125	−	0.994478i	−0.649154	−	0.760657i	$-0.724877\pi$
$29$	228540.	−	703375.i	0.323125	−	0.994478i	0.972280	−	0.233821i	$-0.0751230\pi$
$30$	299687.	−	545051.i	0.369984	−	0.672903i
$31$	1.46107e6	−	474730.i	1.58206	−	0.514044i	0.619476	−	0.785015i	$-0.287345\pi$
$31$	1.46107e6	−	474730.i	1.58206	−	0.514044i	0.962587	+	0.270972i	$0.0873450\pi$
$32$	−116588.	+	1.04207e6i	−0.111187	+	0.993799i
$33$	−476675.	−	1.46706e6i	−0.401945	−	1.23706i
$34$	358330.	−	470772.i	0.268144	−	0.352286i
$35$	−1.63654e6	+	1.60672e6i	−1.09057	+	1.07070i
$36$	575044.	−	379841.i	0.342366	−	0.226148i
$37$	−747765.	−	543283.i	−0.398987	−	0.289881i	0.370141	−	0.928975i	$-0.379309\pi$
$37$	−747765.	−	543283.i	−0.398987	−	0.289881i	−0.769128	+	0.639095i	$0.779309\pi$
$38$	2.88943e6	+	2.19930e6i	1.38573	+	1.05475i
$39$	−618144.	−	850803.i	−0.267197	−	0.367765i
$40$	−2.18609e6	−	1.33214e6i	−0.853942	−	0.520368i
$41$	338142.	+	245674.i	0.119664	+	0.0869409i	0.646008	−	0.763331i	$-0.276437\pi$
$41$	338142.	+	245674.i	0.119664	+	0.0869409i	−0.526344	+	0.850272i	$0.676437\pi$
$42$	3.49746e6	−	1.05084e6i	1.12397	−	0.337705i
$43$		−	1.26186e6i		−	0.369093i	−0.982824	−	0.184546i	$-0.940918\pi$
$43$		−	1.26186e6i		−	0.369093i	0.982824	−	0.184546i	$-0.0590816\pi$
$44$	−6.11938e6	+	1.69090e6i	−1.63266	+	0.451136i
$45$	247921.	+	1.66418e6i	0.0604592	+	0.405835i
$46$	2.19271e6	−	6.26956e6i	0.489723	−	1.40025i
$47$	3.60074e6	+	1.16995e6i	0.737904	+	0.239760i	0.653768	−	0.756695i	$-0.273187\pi$
$47$	3.60074e6	+	1.16995e6i	0.737904	+	0.239760i	0.0841358	+	0.996454i	$0.473187\pi$
$48$	2.09297e6	+	3.49806e6i	0.394273	+	0.658965i
$49$	−7.70035e6			−1.33575
$50$	5.20154e6	−	3.46504e6i	0.832246	−	0.554407i
$51$		−	2.29999e6i		−	0.339974i
$52$	−3.61152e6	+	2.38557e6i	−0.493943	+	0.326271i
$53$	1.53500e6	−	4.72426e6i	0.194539	−	0.598729i	−0.805443	−	0.592673i	$-0.798073\pi$
$53$	1.53500e6	−	4.72426e6i	0.194539	−	0.598729i	0.999982	−	0.00605535i	$-0.00192749\pi$
$54$	3.04010e6	−	8.69247e6i	0.357530	−	1.02228i
$55$	2.56532e6	−	1.52860e7i	0.280343	−	1.67049i
$56$	−3.67933e6	−	1.45729e7i	−0.374125	−	1.48182i
$57$	1.41165e7			1.33730
$58$	−1.13327e7	+	3.40498e6i	−1.00143	+	0.300887i
$59$	1.24006e6	−	1.70679e6i	0.102337	−	0.140855i	−0.754777	−	0.655981i	$-0.772255\pi$
$59$	1.24006e6	−	1.70679e6i	0.102337	−	0.140855i	0.857114	+	0.515126i	$0.172255\pi$
$60$	−9.89904e6	+	1.02643e6i	−0.763815	+	0.0791996i
$61$	−1.40648e7	+	1.02187e7i	−1.01582	+	0.738033i	−0.965421	−	0.260696i	$-0.916048\pi$
$61$	−1.40648e7	+	1.02187e7i	−1.01582	+	0.738033i	−0.0503948	+	0.998729i	$0.516048\pi$
$62$	−1.95589e7	−	1.48873e7i	−1.32366	−	1.00751i
$63$	−5.80645e6	+	7.99189e6i	−0.368594	+	0.507326i
$64$	1.47665e7	−	7.96406e6i	0.880150	−	0.474695i
$65$	−1.55705e6	−	1.04518e7i	−0.0872265	−	0.585512i
$66$	−1.49483e7	+	1.96390e7i	−0.787803	+	1.03501i
$67$	−5.66838e6	+	1.84177e6i	−0.281293	+	0.0913978i	−0.446266	−	0.894900i	$-0.647246\pi$
$67$	−5.66838e6	+	1.84177e6i	−0.281293	+	0.0913978i	0.164973	+	0.986298i	$0.447246\pi$
$68$	−9.45670e6	−	421736.i	−0.442287	−	0.0197244i
$69$	−7.97908e6	−	2.45571e7i	−0.352011	−	1.08338i
$70$	3.60445e7	+	6.87810e6i	1.50123	+	0.286468i
$71$	−2.49453e6	−	810522.i	−0.0981648	−	0.0318957i	0.259523	−	0.965737i	$-0.416435\pi$
$71$	−2.49453e6	−	810522.i	−0.0981648	−	0.0318957i	−0.357688	+	0.933841i	$0.616435\pi$
$72$	−1.02360e7	−	4.10037e6i	−0.380890	−	0.152578i
$73$	5.41028e6	−	3.93080e6i	0.190515	−	0.138417i	−0.488439	−	0.872598i	$-0.662434\pi$
$73$	5.41028e6	−	3.93080e6i	0.190515	−	0.138417i	0.678954	+	0.734181i	$0.262434\pi$
$74$	−329515.	+	1.47849e7i	−0.0109887	+	0.493052i
$75$	7.93178e6	−	2.29660e7i	0.250683	−	0.725840i
$76$	2.58846e6	−	5.80418e7i	0.0775867	−	1.73975i
$77$	7.36221e7	−	5.34896e7i	2.09433	−	1.52162i
$78$	−5.55492e6	+	1.58830e7i	−0.150072	+	0.429096i
$79$	3.03544e7	+	9.86273e6i	0.779314	+	0.253215i	0.671547	−	0.740962i	$-0.265630\pi$
$79$	3.03544e7	+	9.86273e6i	0.779314	+	0.253215i	0.107767	+	0.994176i	$0.465630\pi$
$80$	2.40515e6	+	4.08893e7i	0.0587194	+	0.998275i
$81$	−5.60459e6	−	1.72491e7i	−0.130198	−	0.400707i
$82$	149008.	−	6.68580e6i	0.00329574	−	0.147876i
$83$	−1.49363e7	+	4.85311e6i	−0.314725	+	0.102260i	−0.462120	−	0.886817i	$-0.652911\pi$
$83$	−1.49363e7	+	4.85311e6i	−0.314725	+	0.102260i	0.147395	+	0.989078i	$0.452911\pi$
$84$	−4.56944e7	−	3.64166e7i	−0.917794	−	0.731447i
$85$	1.06808e7	−	2.04944e7i	0.204611	−	0.392608i
$86$	−1.65942e7	+	1.15003e7i	−0.303362	+	0.210240i
$87$	−2.70393e7	+	3.72164e7i	−0.471974	+	0.649616i
$88$	7.80073e7	+	6.50630e7i	1.30078	+	1.08493i
$89$	−1.76107e6	+	1.27949e6i	−0.0280684	+	0.0203929i	−0.601731	−	0.798699i	$-0.705522\pi$
$89$	−1.76107e6	+	1.27949e6i	−0.0280684	+	0.0203929i	0.573663	+	0.819092i	$0.305522\pi$
$90$	1.96254e7	−	1.84273e7i	0.299123	−	0.280861i
$91$	3.64670e7	−	5.01925e7i	0.531783	−	0.731937i
$92$	−1.02432e8	+	2.83041e7i	−1.42984	+	0.395091i
$93$	−9.55564e7			−1.27740
$94$	−1.74309e7	−	5.80146e7i	−0.223258	−	0.743063i
$95$	1.25787e8	+	6.55550e7i	1.54433	+	0.804844i
$96$	2.69267e7	−	5.94044e7i	0.317029	−	0.699413i
$97$	−1.20159e7	+	3.69811e7i	−0.135728	+	0.417727i	−0.995703	−	0.0926096i	$-0.970479\pi$
$97$	−1.20159e7	+	3.69811e7i	−0.135728	+	0.417727i	0.859975	+	0.510337i	$0.170479\pi$
$98$	7.01795e7	+	1.01264e8i	0.760862	+	1.09787i
$99$		−	6.67623e7i		−	0.695009i
$100$	−9.29732e7	−	3.68236e7i	−0.929732	−	0.368236i
$101$	−1.09452e8			−1.05181			−0.525904	−	0.850544i	$-0.676273\pi$
$101$	−1.09452e8			−1.05181			−0.525904	+	0.850544i	$0.676273\pi$
$102$	−3.02463e7	+	2.09617e7i	−0.279429	+	0.193654i
$103$	1.25549e8	+	4.07933e7i	1.11549	+	0.362443i	0.808043	−	0.589124i	$-0.200527\pi$
$103$	1.25549e8	+	4.07933e7i	1.11549	+	0.362443i	0.307442	+	0.951567i	$0.400527\pi$
$104$	6.42864e7	+	2.57521e7i	0.549523	+	0.220130i
$105$	1.27695e8	−	6.35920e7i	1.05055	−	0.523173i
$106$	−7.61166e7	+	2.28697e7i	−0.602915	+	0.181150i
$107$		−	1.77164e8i		−	1.35157i	−0.737097	−	0.675787i	$-0.763804\pi$
$107$		−	1.77164e8i		−	1.35157i	0.737097	−	0.675787i	$-0.236196\pi$
$108$	−1.42018e8	+	3.92424e7i	−1.04388	+	0.288443i
$109$	2.12954e8	+	1.54720e8i	1.50862	+	1.09608i	0.966784	+	0.255594i	$0.0822709\pi$
$109$	2.12954e8	+	1.54720e8i	1.50862	+	1.09608i	0.541837	+	0.840484i	$0.317729\pi$
$110$	−2.24400e8	+	1.05578e8i	−1.53268	+	0.721113i
$111$	3.37926e7	+	4.65115e7i	0.222602	+	0.306386i
$112$	−1.58110e8	+	1.81200e8i	−1.00482	+	1.15156i
$113$	−1.11370e8	−	8.09150e7i	−0.683052	−	0.496267i	0.191317	−	0.981528i	$-0.438724\pi$
$113$	−1.11370e8	−	8.09150e7i	−0.683052	−	0.496267i	−0.874369	+	0.485262i	$0.838724\pi$
$114$	−1.28655e8	−	1.85641e8i	−0.761742	−	1.09914i
$115$	4.29409e7	−	2.55873e8i	0.245516	−	1.46296i
$116$	1.48062e8	+	1.17999e8i	0.817731	+	0.651700i
$117$	−1.40651e7	−	4.32881e7i	−0.0750587	−	0.231007i
$118$	−3.37470e7	−	752125.i	−0.174063	−	0.00387937i
$119$	1.29046e8	−	4.19294e7i	0.643510	−	0.209089i
$120$	1.03716e8	+	1.20824e8i	0.500174	+	0.582676i
$121$	−1.23811e8	+	3.81052e8i	−0.577589	+	1.77764i
$122$	2.62566e8	+	9.18298e7i	1.18522	+	0.414519i
$123$	−1.52811e7	−	2.10327e7i	−0.0667628	−	0.0918911i
$124$	−1.75216e7	+	3.92892e8i	−0.0741118	+	1.66183i
$125$	1.77328e8	−	1.67808e8i	0.726336	−	0.687340i
$126$	1.58017e8	+	3.52175e6i	0.626934	+	0.0139726i
$127$	2.32976e8	+	3.20665e8i	0.895565	+	1.23264i	0.971861	+	0.235554i	$0.0756906\pi$
$127$	2.32976e8	+	3.20665e8i	0.895565	+	1.23264i	−0.0762961	+	0.997085i	$0.524309\pi$
$128$	−2.39311e8	−	1.21605e8i	−0.891503	−	0.453014i
$129$	−2.42542e7	+	7.46468e7i	−0.0875848	+	0.269558i
$130$	−1.23256e8	+	1.15731e8i	−0.431555	+	0.405208i
$131$	3.07629e8	−	9.99547e7i	1.04458	−	0.339405i	0.264041	−	0.964511i	$-0.414945\pi$
$131$	3.07629e8	−	9.99547e7i	1.04458	−	0.339405i	0.780539	+	0.625107i	$0.214945\pi$
$132$	3.94502e8	+	1.75934e7i	1.29943	+	0.0579501i
$133$	2.57348e8	+	7.92034e8i	0.822458	+	2.53126i
$134$	7.58809e7	+	5.77571e7i	0.235349	+	0.179137i
$135$	5.95357e7	−	3.54756e8i	0.179243	−	1.06806i
$136$	8.06404e7	+	1.28205e8i	0.235720	+	0.374756i
$137$	−1.21554e8	−	8.83139e7i	−0.345053	−	0.250696i	0.401738	−	0.915755i	$-0.368406\pi$
$137$	−1.21554e8	−	8.83139e7i	−0.345053	−	0.250696i	−0.746791	+	0.665059i	$0.768406\pi$
$138$	−2.50221e8	+	3.28738e8i	−0.689933	+	0.906429i
$139$	−9.47705e7	−	1.30440e8i	−0.253872	−	0.349424i	0.662991	−	0.748627i	$-0.269287\pi$
$139$	−9.47705e7	−	1.30440e8i	−0.253872	−	0.349424i	−0.916862	+	0.399203i	$0.869287\pi$
$140$	−2.38052e8	−	5.36693e8i	−0.619668	−	1.39706i
$141$	−1.90519e8	−	1.38420e8i	−0.482016	−	0.350205i
$142$	1.20758e7	+	4.01916e7i	0.0297005	+	0.0988511i
$143$			4.19296e8i			1.00271i
$144$	3.93664e7	+	1.71979e8i	0.0915537	+	0.399969i
$145$	−4.13764e8	+	2.06055e8i	−0.936011	+	0.466133i
$146$	−1.01001e8	−	3.53239e7i	−0.222286	−	0.0777423i
$147$	4.55525e8	+	1.48009e8i	0.975535	+	0.316971i
$148$	1.97434e8	−	1.30414e8i	0.411505	−	0.271817i
$149$	−7.63183e8			−1.54840			−0.774201	−	0.632940i	$-0.781848\pi$
$149$	−7.63183e8			−1.54840			−0.774201	+	0.632940i	$0.781848\pi$
$150$	−3.74306e8	+	1.05000e8i	−0.739370	+	0.207408i
$151$		−	8.49455e8i		−	1.63393i	−0.576689	−	0.816964i	$-0.695656\pi$
$151$		−	8.49455e8i		−	1.63393i	0.576689	−	0.816964i	$-0.304344\pi$
$152$	−7.86875e8	+	4.94942e8i	−1.47412	+	0.927213i
$153$	3.07609e7	−	9.46724e7i	0.0561350	−	0.172766i
$154$	−1.37440e9	−	4.80681e8i	−2.44360	−	0.854623i
$155$	−8.51467e8	−	4.43750e8i	−1.47517	−	0.768797i
$156$	2.59498e8	−	7.17043e7i	0.438163	−	0.121073i
$157$	−3.60141e8			−0.592754			−0.296377	−	0.955071i	$-0.595778\pi$
$157$	−3.60141e8			−0.592754			−0.296377	+	0.955071i	$0.595778\pi$
$158$	−1.46943e8	−	4.89065e8i	−0.235787	−	0.784763i
$159$	−1.81611e8	+	2.49966e8i	−0.284153	+	0.391104i
$160$	5.15799e8	−	4.04287e8i	0.787047	−	0.616892i
$161$	1.23236e9	−	8.95363e8i	1.83415	−	1.33259i
$162$	−1.75758e8	+	2.30909e8i	−0.255184	+	0.335259i
$163$	−1.56783e8	+	2.15793e8i	−0.222100	+	0.305695i	−0.905497	−	0.424352i	$-0.860502\pi$
$163$	−1.56783e8	+	2.15793e8i	−0.222100	+	0.305695i	0.683397	+	0.730047i	$0.260502\pi$
$164$	−8.92803e7	+	5.89735e7i	−0.123418	+	0.0815233i
$165$	−4.45568e8	+	8.54956e8i	−0.601144	+	1.15347i
$166$	1.99948e8	+	1.52192e8i	0.263321	+	0.200428i
$167$	4.75179e8	−	1.54395e8i	0.610929	−	0.198503i	0.0128204	−	0.999918i	$-0.495919\pi$
$167$	4.75179e8	−	1.54395e8i	0.610929	−	0.198503i	0.598109	+	0.801415i	$0.295919\pi$
$168$	−6.24514e7	+	9.32803e8i	−0.0783980	+	1.17099i
$169$	−1.63739e8	−	5.03938e8i	−0.200727	−	0.617775i
$170$	−3.66856e8	+	4.63224e7i	−0.439239	+	0.0554619i
$171$	5.81065e8	+	1.88799e8i	0.679579	+	0.220809i
$172$	3.02472e8	+	1.13412e8i	0.345598	+	0.129582i
$173$	2.93925e8	−	2.13549e8i	0.328135	−	0.238404i	−0.411504	−	0.911408i	$-0.634996\pi$
$173$	2.93925e8	−	2.13549e8i	0.328135	−	0.238404i	0.739639	+	0.673004i	$0.234996\pi$
$174$	7.35848e8	+	1.64000e7i	0.802770	+	0.0178915i
$175$	1.43315e9	+	2.63513e7i	1.52806	+	0.0280964i
$176$	1.44675e8	−	1.61882e9i	0.150779	−	1.68712i
$177$	−1.06164e8	+	7.71324e7i	−0.108164	+	0.0785857i
$178$	3.28762e7	+	1.14981e7i	0.0327493	+	0.0114537i
$179$	−6.27292e8	−	2.03819e8i	−0.611023	−	0.198533i	−0.0128723	−	0.999917i	$-0.504098\pi$
$179$	−6.27292e8	−	2.03819e8i	−0.611023	−	0.198533i	−0.598150	+	0.801384i	$0.704098\pi$
$180$	−4.21193e8	−	9.01436e7i	−0.401228	−	0.0858707i
$181$	2.68289e8	+	8.25708e8i	0.249970	+	0.769329i	0.994779	+	0.102051i	$0.0325406\pi$
$181$	2.68289e8	+	8.25708e8i	0.249970	+	0.769329i	−0.744809	+	0.667278i	$0.767459\pi$
$182$	−9.92415e8	−	2.21181e7i	−0.904499	−	0.0201587i
$183$	1.02844e9	−	3.34160e8i	0.917010	−	0.297955i
$184$	1.30577e9	+	1.08909e9i	1.13918	+	0.950152i
$185$	8.51205e7	+	5.71375e8i	0.0726686	+	0.487791i
$186$	8.70883e8	+	1.25662e9i	0.727626	+	1.04991i
$187$	−5.39007e8	+	7.41879e8i	−0.440786	+	0.606690i
$188$	−6.04065e8	+	7.57960e8i	−0.483562	+	0.606758i
$189$	1.70862e9	−	1.24138e9i	1.33905	−	0.972878i
$190$	−2.84310e8	−	2.25163e9i	−0.218161	−	1.72776i
$191$	5.92078e8	−	8.14925e8i	0.444882	−	0.612328i	−0.526406	−	0.850233i	$-0.676461\pi$
$191$	5.92078e8	−	8.14925e8i	0.444882	−	0.612328i	0.971288	+	0.237905i	$0.0764608\pi$
$192$	−1.02661e9	+	1.87298e8i	−0.755441	+	0.137825i
$193$	2.38055e9			1.71573			0.857864	−	0.513877i	$-0.171791\pi$
$193$	2.38055e9			1.71573			0.857864	+	0.513877i	$0.171791\pi$
$194$	5.95834e8	−	1.79022e8i	0.420648	−	0.126386i
$195$	−1.08785e8	+	6.48216e8i	−0.0752366	+	0.448313i
$196$	6.92084e8	−	1.84581e9i	0.468959	−	1.25073i
$197$	1.44847e6	−	4.45792e6i	0.000961708	−	0.00295983i	−0.950575	−	0.310497i	$-0.899505\pi$
$197$	1.44847e6	−	4.45792e6i	0.000961708	−	0.00295983i	0.951536	+	0.307537i	$0.0995047\pi$
$198$	−8.77964e8	+	6.08458e8i	−0.571237	+	0.395886i
$199$		−	5.77553e8i		−	0.368281i	−0.982900	−	0.184140i	$-0.941050\pi$
$199$		−	5.77553e8i		−	0.368281i	0.982900	−	0.184140i	$-0.0589501\pi$
$200$	3.63087e8	+	1.55826e9i	0.226930	+	0.973911i
$201$	3.70722e8			0.227124
$202$	9.97521e8	+	1.43935e9i	0.599124	+	0.864495i
$203$	−2.58103e9	−	8.38627e8i	−1.51988	−	0.493838i
$204$	5.51318e8	+	2.06716e8i	0.318333	+	0.119359i
$205$	−3.84917e7	−	2.58377e8i	−0.0217947	−	0.146298i
$206$	−6.07772e8	−	2.02283e9i	−0.337498	−	1.12328i
$207$		−	1.11753e9i		−	0.608667i
$208$	−2.47238e8	−	1.08011e9i	−0.132088	−	0.577049i
$209$	−4.55339e9	−	3.30823e9i	−2.38643	−	1.73385i
$210$	−2.00006e9	−	1.09970e9i	−1.02841	−	0.565453i
$211$	2.25672e9	+	3.10610e9i	1.13854	+	1.56706i	0.770732	+	0.637159i	$0.219891\pi$
$211$	2.25672e9	+	3.10610e9i	1.13854	+	1.56706i	0.367805	+	0.929903i	$0.380109\pi$
$212$	9.94463e8	+	7.92549e8i	0.492317	+	0.392358i
$213$	1.31988e8	+	9.58952e7i	0.0641235	+	0.0465885i
$214$	−2.32981e9	+	1.61464e9i	−1.11088	+	0.769874i
$215$	−5.62769e8	+	5.52517e8i	−0.263376	+	0.258578i
$216$	1.81039e9	+	1.50998e9i	0.831681	+	0.693674i
$217$	−1.74202e9	−	5.36138e9i	−0.785622	−	2.41789i
$218$	9.38417e7	−	4.21057e9i	0.0415499	−	1.86430i
$219$	−3.95607e8	+	1.28540e8i	−0.171984	+	0.0558809i
$220$	3.43355e9	+	1.98878e9i	1.46573	+	0.848975i
$221$	−1.93192e8	+	5.94584e8i	−0.0809879	+	0.249255i
$222$	3.03676e8	−	8.68291e8i	0.125025	−	0.357481i
$223$	9.70563e8	+	1.33587e9i	0.392468	+	0.540186i	0.958834	−	0.283968i	$-0.0916510\pi$
$223$	9.70563e8	+	1.33587e9i	0.392468	+	0.540186i	−0.566366	+	0.824154i	$0.691651\pi$
$224$	3.82388e9	+	4.27819e8i	1.51884	+	0.169929i
$225$	6.33644e8	−	8.39247e8i	0.247238	−	0.327461i
$226$	−4.90769e7	+	2.20203e9i	−0.0188124	+	0.844089i
$227$	2.16377e9	+	2.97817e9i	0.814905	+	1.12162i	0.990548	+	0.137166i	$0.0437995\pi$
$227$	2.16377e9	+	2.97817e9i	0.814905	+	1.12162i	−0.175643	+	0.984454i	$0.556201\pi$
$228$	−1.26875e9	+	3.38379e9i	−0.469501	+	1.25217i
$229$	8.49964e8	−	2.61592e9i	0.309071	−	0.951224i	−0.669055	−	0.743213i	$-0.733301\pi$
$229$	8.49964e8	−	2.61592e9i	0.309071	−	0.951224i	0.978126	−	0.208011i	$-0.0666990\pi$
$230$	−3.75623e9	+	1.76727e9i	−1.34227	+	0.631528i
$231$	−5.38335e9	+	1.74915e9i	−1.89062	+	0.614300i
$232$	2.02359e8	−	3.02252e9i	0.0698505	−	1.04332i
$233$	9.23762e8	+	2.84305e9i	0.313427	+	0.964629i	0.976397	+	0.215983i	$0.0692957\pi$
$233$	9.23762e8	+	2.84305e9i	0.313427	+	0.964629i	−0.662970	+	0.748646i	$0.730704\pi$
$234$	−4.41077e8	+	5.79485e8i	−0.147113	+	0.193276i
$235$	−1.05484e9	−	2.11815e9i	−0.345872	−	0.694521i
$236$	2.97672e8	+	4.50648e8i	0.0959601	+	0.145274i
$237$	−1.60608e9	−	1.16689e9i	−0.509066	−	0.369858i
$238$	−1.72749e9	−	1.31489e9i	−0.538404	−	0.409809i
$239$	−2.12550e9	−	2.92550e9i	−0.651434	−	0.896622i	0.347727	−	0.937596i	$-0.386954\pi$
$239$	−2.12550e9	−	2.92550e9i	−0.651434	−	0.896622i	−0.999160	+	0.0409745i	$0.986954\pi$
$240$	6.43657e8	−	2.46510e9i	0.194004	−	0.743000i
$241$	7.48422e8	+	5.43760e8i	0.221860	+	0.161190i	0.693163	−	0.720781i	$-0.256216\pi$
$241$	7.48422e8	+	5.43760e8i	0.221860	+	0.161190i	−0.471304	+	0.881971i	$0.656216\pi$
$242$	6.13946e9	−	1.84464e9i	1.79006	−	0.537837i
$243$		−	2.64804e9i		−	0.759452i
$244$	−1.18536e9	−	4.28982e9i	−0.334419	−	1.21026i
$245$	3.37168e9	+	3.43425e9i	0.935798	+	0.953163i
$246$	−1.37323e8	+	3.92644e8i	−0.0374975	+	0.107216i
$247$	−3.64934e9	−	1.18574e9i	−0.980452	−	0.318568i
$248$	5.32645e9	−	3.35032e9i	1.40809	−	0.885686i
$249$	9.76862e8			0.254118
$250$	−3.82291e9	−	8.02604e8i	−0.978664	−	0.205467i
$251$			8.06032e8i			0.203075i	0.994832	+	0.101538i	$0.0323762\pi$
$251$			8.06032e8i			0.203075i	−0.994832	+	0.101538i	$0.967624\pi$
$252$	−1.39382e9	−	2.11012e9i	−0.345626	−	0.523244i
$253$	−3.18128e9	+	9.79098e9i	−0.776462	+	2.38970i
$254$	2.09363e9	−	5.98626e9i	0.502997	−	1.43820i
$255$	−1.02576e9	+	1.00708e9i	−0.242598	+	0.238178i
$256$	5.81854e8	+	4.25537e9i	0.135473	+	0.990781i
$257$	1.49213e9			0.342038			0.171019	−	0.985268i	$-0.445294\pi$
$257$	1.49213e9			0.342038			0.171019	+	0.985268i	$0.445294\pi$
$258$	1.20270e9	−	3.61359e8i	0.271443	−	0.0815568i
$259$	−1.99357e9	+	2.74392e9i	−0.443030	+	0.609778i
$260$	2.64527e9	+	5.66141e8i	0.578865	+	0.123889i
$261$	−1.61074e9	+	1.17027e9i	−0.347106	+	0.252188i
$262$	−4.11814e9	−	3.13454e9i	−0.873968	−	0.665225i
$263$	−1.95745e9	+	2.69420e9i	−0.409136	+	0.563128i	−0.963007	−	0.269475i	$-0.913150\pi$
$263$	−1.95745e9	+	2.69420e9i	−0.409136	+	0.563128i	0.553871	+	0.832602i	$0.313150\pi$
$264$	−3.36405e9	−	5.34828e9i	−0.692543	−	1.10103i
$265$	−2.77907e9	+	1.38398e9i	−0.563528	+	0.280637i
$266$	8.07032e9	−	1.06027e10i	1.61200	−	2.11783i
$267$	1.28772e8	−	4.18405e7i	0.0253382	−	0.00823289i
$268$	6.79770e7	−	1.52427e9i	0.0131772	−	0.295476i
$269$	2.55944e9	+	7.87714e9i	0.488805	+	1.50439i	0.826394	+	0.563092i	$0.190388\pi$
$269$	2.55944e9	+	7.87714e9i	0.488805	+	1.50439i	−0.337590	+	0.941293i	$0.609612\pi$
$270$	−5.20786e9	+	2.45025e9i	−0.979950	+	0.461058i
$271$	−1.01310e9	−	3.29177e8i	−0.187835	−	0.0610312i	0.213589	−	0.976924i	$-0.431485\pi$
$271$	−1.01310e9	−	3.29177e8i	−0.187835	−	0.0610312i	−0.401424	+	0.915892i	$0.631485\pi$
$272$	9.51031e8	−	2.22891e9i	0.173748	−	0.407208i
$273$	−3.12201e9	+	2.26827e9i	−0.562062	+	0.408362i
$274$	−5.35646e7	+	2.40338e9i	−0.00950332	+	0.426403i
$275$	−7.94058e9	+	5.54904e9i	−1.38842	+	0.970257i
$276$	6.60357e9	+	2.94496e8i	1.13800	+	0.0507509i
$277$	5.12747e9	−	3.72532e9i	0.870931	−	0.632769i	−0.0599053	−	0.998204i	$-0.519080\pi$
$277$	5.12747e9	−	3.72532e9i	0.870931	−	0.632769i	0.930837	+	0.365435i	$0.119080\pi$
$278$	−8.51650e8	+	2.43510e9i	−0.142588	+	0.407697i
$279$	−3.93330e9	−	1.27801e9i	−0.649143	−	0.210919i
$280$	−4.88828e9	+	8.02184e9i	−0.795287	+	1.30509i
$281$	−1.17849e9	−	3.62702e9i	−0.189017	−	0.581735i	0.810977	−	0.585077i	$-0.198936\pi$
$281$	−1.17849e9	−	3.62702e9i	−0.189017	−	0.581735i	−0.999994	+	0.00334294i	$0.998936\pi$
$282$	−8.39553e7	+	3.76698e9i	−0.0132755	+	0.595657i
$283$	2.69784e9	−	8.76582e8i	0.420601	−	0.136662i	−0.0910668	−	0.995845i	$-0.529028\pi$
$283$	2.69784e9	−	8.76582e8i	0.420601	−	0.136662i	0.511668	+	0.859183i	$0.329028\pi$
$284$	4.18487e8	−	5.25103e8i	0.0643292	−	0.0807181i
$285$	−6.18107e9	−	6.29576e9i	−0.936880	−	0.954265i
$286$	5.51400e9	−	3.82138e9i	0.824142	−	0.571158i
$287$	9.01499e8	−	1.24081e9i	0.132873	−	0.182884i
$288$	1.90286e9	−	2.08508e9i	0.276590	−	0.303077i
$289$	4.53734e9	−	3.29657e9i	0.650444	−	0.472576i
$290$	6.48071e9	+	3.56331e9i	0.916285	+	0.503804i
$291$	1.42163e9	−	1.95671e9i	0.198251	−	0.272869i
$292$	4.55970e8	+	1.65015e9i	0.0627198	+	0.226983i
$293$	−5.90320e8			−0.0800971			−0.0400486	−	0.999198i	$-0.512751\pi$
$293$	−5.90320e8			−0.0800971			−0.0400486	+	0.999198i	$0.512751\pi$
$294$	−2.20516e9	−	7.33936e9i	−0.295155	−	0.982356i
$295$	−1.30418e9	+	1.94289e8i	−0.172206	+	0.0256543i
$296$	−3.51440e9	−	1.40781e9i	−0.457809	−	0.183391i
$297$	−4.41071e9	+	1.35748e10i	−0.566869	+	1.74464i
$298$	6.95550e9	+	1.00363e10i	0.881990	+	1.27265i
$299$			7.01860e9i			0.878144i
$300$	4.79217e9	+	3.96540e9i	0.591626	+	0.489555i
$301$	−4.63036e9			−0.564091
$302$	−1.11709e10	+	7.74177e9i	−1.34295	+	0.930706i
$303$	6.47476e9	+	2.10378e9i	0.768163	+	0.249591i
$304$	1.36802e10	+	5.83708e9i	1.60176	+	0.683442i
$305$	1.07158e10	+	1.79835e9i	1.23830	+	0.207813i
$306$	−1.52535e9	+	4.58301e8i	−0.173974	+	0.0522716i
$307$			1.21084e10i			1.36311i	0.731766	+	0.681556i	$0.238696\pi$
$307$			1.21084e10i			1.36311i	−0.731766	+	0.681556i	$0.761304\pi$
$308$	6.20475e9	+	2.24550e10i	0.689480	+	2.49523i
$309$	−6.64293e9	−	4.82637e9i	−0.728661	−	0.529403i
$310$	1.92453e9	+	1.52416e10i	0.208390	+	1.65038i
$311$	−2.15591e9	−	2.96736e9i	−0.230457	−	0.317197i	0.678091	−	0.734978i	$-0.262808\pi$
$311$	−2.15591e9	−	2.96736e9i	−0.230457	−	0.317197i	−0.908547	+	0.417782i	$0.862808\pi$
$312$	−3.30797e9	−	2.75906e9i	−0.349095	−	0.291167i
$313$	5.66043e9	+	4.11254e9i	0.589756	+	0.428483i	0.842228	−	0.539121i	$-0.181244\pi$
$313$	5.66043e9	+	4.11254e9i	0.589756	+	0.428483i	−0.252472	+	0.967604i	$0.581244\pi$
$314$	3.28226e9	+	4.73608e9i	0.337640	+	0.487192i
$315$	6.10668e9	−	9.09742e8i	0.620245	−	0.0924008i
$316$	−5.09229e9	+	6.38964e9i	−0.510699	+	0.640808i
$317$	−5.29809e9	−	1.63058e10i	−0.524665	−	1.61475i	−0.764978	−	0.644057i	$-0.777250\pi$
$317$	−5.29809e9	−	1.63058e10i	−0.524665	−	1.61475i	0.240313	−	0.970695i	$-0.422750\pi$
$318$	4.94237e9	+	1.10151e8i	0.483311	+	0.0107716i
$319$	1.74434e10	−	5.66771e9i	1.68449	−	0.547325i
$320$	−1.00175e10	−	3.09848e9i	−0.955344	−	0.295494i
$321$	−3.40528e9	+	1.04804e10i	−0.320725	+	0.987089i
$322$	−2.30061e10	−	8.04613e9i	−2.14003	−	0.748452i
$323$	−4.93267e9	−	6.78923e9i	−0.453181	−	0.623750i
$324$	4.63842e9	+	2.06857e8i	0.420910	+	0.0187711i
$325$	−3.97956e9	+	5.27083e9i	−0.356699	+	0.472439i
$326$	4.26671e9	+	9.50929e7i	0.377766	+	0.00841933i
$327$	−9.62371e9	−	1.32459e10i	−0.841689	−	1.15849i
$328$	1.58922e9	+	6.36617e8i	0.137306	+	0.0550025i
$329$	4.29312e9	−	1.32129e10i	0.366429	−	1.12775i
$330$	1.53040e10	−	1.93241e9i	1.29048	−	0.162946i
$331$	−1.73984e10	+	5.65309e9i	−1.44943	+	0.470949i	−0.924824	−	0.380396i	$-0.875788\pi$
$331$	−1.73984e10	+	5.65309e9i	−1.44943	+	0.470949i	−0.524607	+	0.851344i	$0.675788\pi$
$332$	1.79121e8	−	4.01648e9i	0.0147433	−	0.330593i
$333$	7.68911e8	+	2.36647e9i	0.0625316	+	0.192452i
$334$	−6.36107e9	−	4.84176e9i	−0.511145	−	0.389061i
$335$	3.30336e9	+	1.72158e9i	0.262287	+	0.136693i
$336$	1.28361e10	−	7.68011e9i	1.00711	−	0.602574i
$337$	−7.56484e9	−	5.49618e9i	−0.586517	−	0.426129i	0.254551	−	0.967059i	$-0.418072\pi$
$337$	−7.56484e9	−	5.49618e9i	−0.586517	−	0.426129i	−0.841068	+	0.540930i	$0.818072\pi$
$338$	−5.13480e9	+	6.74607e9i	−0.393421	+	0.516873i
$339$	5.03297e9	+	6.92729e9i	0.381088	+	0.524523i
$340$	3.95263e9	+	4.40221e9i	0.295781	+	0.329424i
$341$	3.08224e10	+	2.23938e10i	2.27955	+	1.65619i
$342$	−2.81289e9	−	9.36204e9i	−0.205612	−	0.684331i
$343$			7.10248e9i			0.513137i
$344$	−1.26524e9	−	5.01130e9i	−0.0903523	−	0.357863i
$345$	−7.45838e9	+	1.43111e10i	−0.526463	+	1.01018i
$346$	−5.48708e9	−	1.91905e9i	−0.382857	−	0.133900i
$347$	1.41320e9	+	4.59176e8i	0.0974732	+	0.0316710i	0.357348	−	0.933971i	$-0.383681\pi$
$347$	1.41320e9	+	4.59176e8i	0.0974732	+	0.0316710i	−0.259874	+	0.965642i	$0.583681\pi$
$348$	−6.49071e9	−	9.82632e9i	−0.442563	−	0.669999i
$349$	−2.23460e9			−0.150626			−0.0753128	−	0.997160i	$-0.523996\pi$
$349$	−2.23460e9			−0.150626			−0.0753128	+	0.997160i	$0.523996\pi$
$350$	−1.27149e10	−	1.90870e10i	−0.847310	−	1.27194i
$351$			9.73099e9i			0.641104i
$352$	−2.26069e10	+	1.28510e10i	−1.47255	+	0.837079i
$353$	2.80638e9	−	8.63716e9i	0.180737	−	0.556253i	−0.819111	−	0.573634i	$-0.805533\pi$
$353$	2.80638e9	−	8.63716e9i	0.180737	−	0.556253i	0.999849	+	0.0173817i	$0.00553305\pi$
$354$	1.98189e9	+	6.93146e8i	0.126202	+	0.0441379i
$355$	7.30776e8	+	1.46742e9i	0.0460120	+	0.0923935i
$356$	−1.48420e8	−	5.37133e8i	−0.00924046	−	0.0334412i
$357$	−8.43980e9			−0.519588
$358$	3.03667e9	+	1.01068e10i	0.184869	+	0.615295i
$359$	6.82937e9	−	9.39982e9i	0.411152	−	0.565903i	−0.552347	−	0.833615i	$-0.686267\pi$
$359$	6.82937e9	−	9.39982e9i	0.411152	−	0.565903i	0.963499	+	0.267712i	$0.0862675\pi$
$360$	2.65323e9	+	6.36049e9i	0.157966	+	0.378687i
$361$	2.79298e10	−	2.02922e10i	1.64452	−	1.19482i
$362$	8.41343e9	−	1.10535e10i	0.489935	−	0.643674i
$363$	1.46485e10	−	2.01619e10i	0.843656	−	1.16119i
$364$	8.75382e9	+	1.32524e10i	0.498646	+	0.754902i
$365$	−4.12203e9	−	6.91765e8i	−0.232241	−	0.0389751i
$366$	−1.37674e10	−	1.04791e10i	−0.767234	−	0.583984i
$367$	−2.27448e9	+	7.39023e8i	−0.125377	+	0.0407374i	−0.371033	−	0.928620i	$-0.620996\pi$
$367$	−2.27448e9	+	7.39023e8i	−0.125377	+	0.0407374i	0.245657	+	0.969357i	$0.420996\pi$
$368$	2.42171e9	−	2.70974e10i	0.132048	−	1.47753i
$369$	−3.47704e8	−	1.07012e9i	−0.0187544	−	0.0577202i
$370$	6.73815e9	−	6.32679e9i	0.359529	−	0.337580i
$371$	−1.73356e10	−	5.63268e9i	−0.915047	−	0.297317i
$372$	8.58832e9	−	2.29053e10i	0.448473	−	1.19609i
$373$	2.56642e10	−	1.86461e10i	1.32584	−	0.963281i	0.326003	−	0.945369i	$-0.394298\pi$
$373$	2.56642e10	−	1.86461e10i	1.32584	−	0.963281i	0.999840	−	0.0179127i	$-0.00570209\pi$
$374$	1.46686e10	+	3.26921e8i	0.749724	+	0.0167092i
$375$	−1.37155e10	+	6.51846e9i	−0.693566	+	0.329625i
$376$	1.54730e10	+	1.03592e9i	0.774145	+	0.0518292i
$377$	1.01161e10	−	7.34979e9i	0.500782	−	0.363839i
$378$	−3.18969e10	−	1.11556e10i	−1.56236	−	0.546420i
$379$	1.63542e10	+	5.31380e9i	0.792634	+	0.257542i	0.677225	−	0.735776i	$-0.263182\pi$
$379$	1.63542e10	+	5.31380e9i	0.792634	+	0.257542i	0.115409	+	0.993318i	$0.463182\pi$
$380$	−2.70192e10	+	2.42598e10i	−1.29580	+	1.16346i
$381$	−7.61853e9	−	2.34474e10i	−0.361552	−	1.11274i
$382$	−1.61128e10	−	3.59110e8i	−0.756691	−	0.0168645i
$383$	2.28186e10	−	7.41421e9i	1.06046	−	0.344564i	0.273694	−	0.961817i	$-0.411754\pi$
$383$	2.28186e10	−	7.41421e9i	1.06046	−	0.344564i	0.786765	+	0.617253i	$0.211754\pi$
$384$	1.18194e10	+	1.17935e10i	0.543589	+	0.542400i
$385$	−5.60918e10	−	9.41341e9i	−2.55303	−	0.428454i
$386$	−2.16959e10	−	3.13057e10i	−0.977301	−	1.41018i
$387$	−1.99671e9	+	2.74823e9i	−0.0890165	+	0.122521i
$388$	−7.78457e9	−	6.20400e9i	−0.343485	−	0.273744i
$389$	1.38521e10	−	1.00642e10i	0.604949	−	0.439521i	−0.242683	−	0.970106i	$-0.578028\pi$
$389$	1.38521e10	−	1.00642e10i	0.604949	−	0.439521i	0.847632	+	0.530585i	$0.178028\pi$
$390$	9.51588e9	−	4.47714e9i	0.411330	−	0.193527i
$391$	−9.02245e9	+	1.24183e10i	−0.386027	+	0.531320i
$392$	−3.05810e10	+	7.72101e9i	−1.29511	+	0.326986i
$393$	−2.01195e10			−0.843424
$394$	−7.18254e7	+	2.15804e7i	−0.00298053	+	0.000895520i
$395$	−8.89234e9	−	1.78561e10i	−0.365282	−	0.733497i
$396$	1.60032e10	+	6.00039e9i	0.650768	+	0.244005i
$397$	−1.31241e10	+	4.03918e10i	−0.528332	+	1.62604i	0.229299	+	0.973356i	$0.426357\pi$
$397$	−1.31241e10	+	4.03918e10i	−0.528332	+	1.62604i	−0.757631	+	0.652683i	$0.773643\pi$
$398$	−7.59517e9	+	5.26370e9i	−0.302695	+	0.209778i
$399$		−	5.18004e10i		−	2.04382i
$400$	1.71829e10	−	1.89765e10i	0.671208	−	0.741269i
$401$	1.50348e10			0.581460			0.290730	−	0.956805i	$-0.406102\pi$
$401$	1.50348e10			0.581460			0.290730	+	0.956805i	$0.406102\pi$
$402$	−3.37869e9	−	4.87522e9i	−0.129373	−	0.186676i
$403$	2.47028e10	+	8.02643e9i	0.936540	+	0.304300i
$404$	9.83717e9	−	2.62360e10i	0.369271	−	0.984855i
$405$	−5.23884e9	+	1.00523e10i	−0.194722	+	0.373632i
$406$	1.24945e10	+	4.15852e10i	0.459850	+	1.53050i
$407$		−	2.29220e10i		−	0.835362i
$408$	−2.30616e9	−	9.13414e9i	−0.0832241	−	0.329630i
$409$	−1.86634e9	−	1.35598e9i	−0.0666956	−	0.0484572i	0.553938	−	0.832558i	$-0.313125\pi$
$409$	−1.86634e9	−	1.35598e9i	−0.0666956	−	0.0484572i	−0.620634	+	0.784101i	$0.713125\pi$
$410$	−3.04701e9	+	2.86099e9i	−0.107830	+	0.101247i
$411$	5.49319e9	+	7.56072e9i	0.192512	+	0.264970i
$412$	−2.10623e10	+	2.64282e10i	−0.730998	+	0.917232i
$413$	−6.26305e9	−	4.55037e9i	−0.215271	−	0.156404i
$414$	−1.46963e10	+	1.01850e10i	−0.500271	+	0.346705i
$415$	8.70445e9	+	4.53640e9i	0.293460	+	0.152939i
$416$	−1.19508e10	+	1.30952e10i	−0.399045	+	0.437259i
$417$	3.09908e9	+	9.53798e9i	0.102492	+	0.315437i
$418$	−2.00652e9	+	9.00304e10i	−0.0657263	+	2.94906i
$419$	−1.73892e10	+	5.65011e9i	−0.564189	+	0.183316i	−0.577205	−	0.816599i	$-0.695857\pi$
$419$	−1.73892e10	+	5.65011e9i	−0.564189	+	0.183316i	0.0130162	+	0.999915i	$0.495857\pi$
$420$	3.76646e9	+	3.63244e10i	0.121042	+	1.16735i
$421$	1.12121e10	−	3.45073e10i	0.356910	−	1.09846i	−0.597983	−	0.801509i	$-0.704031\pi$
$421$	1.12121e10	−	3.45073e10i	0.356910	−	1.09846i	0.954894	−	0.296948i	$-0.0959690\pi$
$422$	2.02799e10	−	5.79856e10i	0.639463	−	1.82840i
$423$	−5.99087e9	−	8.24573e9i	−0.187124	−	0.257554i
$424$	1.35915e9	−	2.03009e10i	0.0420538	−	0.628134i
$425$	−1.38169e10	+	4.21018e9i	−0.423502	+	0.129046i
$426$	5.81628e7	−	2.60970e9i	0.00176607	−	0.0792414i
$427$	3.74974e10	+	5.16107e10i	1.12795	+	1.55249i
$428$	4.24669e10	+	1.59229e10i	1.26554	+	0.474513i
$429$	8.05932e9	−	2.48040e10i	0.237941	−	0.732307i
$430$	1.23949e10	+	2.36522e9i	0.362551	+	0.0691829i
$431$	5.95630e10	−	1.93532e10i	1.72611	−	0.560846i	0.733228	−	0.679983i	$-0.238013\pi$
$431$	5.95630e10	−	1.93532e10i	1.72611	−	0.560846i	0.992878	+	0.119137i	$0.0380129\pi$
$432$	3.35760e9	−	3.75694e10i	0.0964038	−	1.07870i
$433$	1.59107e10	+	4.89680e10i	0.452623	+	1.39303i	0.873903	+	0.486100i	$0.161581\pi$
$433$	1.59107e10	+	4.89680e10i	0.452623	+	1.39303i	−0.421280	+	0.906931i	$0.638419\pi$
$434$	−5.46290e10	+	7.17711e10i	−1.53980	+	2.02298i
$435$	2.84374e10	−	4.23645e9i	0.794205	−	0.118317i
$436$	−5.62268e10	+	3.71402e10i	−1.55596	+	1.02778i
$437$	−7.62192e10	−	5.53765e10i	−2.08996	−	1.51845i
$438$	5.29587e9	+	4.03098e9i	0.143893	+	0.109525i
$439$	−3.14233e10	−	4.32504e10i	−0.846045	−	1.16448i	−0.984720	−	0.174143i	$-0.944284\pi$
$439$	−3.14233e10	−	4.32504e10i	−0.846045	−	1.16448i	0.138675	−	0.990338i	$-0.455716\pi$
$440$	−5.13915e9	−	6.32787e10i	−0.137114	−	1.68829i
$441$	1.67708e10	+	1.21847e10i	0.443404	+	0.322152i
$442$	9.57985e9	−	2.87833e9i	0.250998	−	0.0754139i
$443$			1.46560e10i			0.380539i	0.981732	+	0.190269i	$0.0609362\pi$
$443$			1.46560e10i			0.380539i	−0.981732	+	0.190269i	$0.939064\pi$
$444$	−1.41862e10	+	3.91992e9i	−0.365035	+	0.100866i
$445$	1.34174e9	+	2.25173e8i	0.0342159	+	0.00574217i
$446$	8.72191e9	−	2.49383e10i	0.220431	−	0.630271i
$447$	4.51472e10	+	1.46692e10i	1.13084	+	0.367432i
$448$	−2.92240e10	−	5.41854e10i	−0.725485	−	1.34515i
$449$	1.82989e10			0.450235			0.225117	−	0.974332i	$-0.427723\pi$
$449$	1.82989e10			0.450235			0.225117	+	0.974332i	$0.427723\pi$
$450$	−1.68115e10	−	6.84075e8i	−0.409975	−	0.0166822i
$451$			1.03654e10i			0.250541i
$452$	2.94052e10	−	1.94234e10i	0.704484	−	0.465342i
$453$	−1.63274e10	+	5.02507e10i	−0.387727	+	1.19330i
$454$	1.94446e10	−	5.55973e10i	0.457694	−	1.30867i
$455$	−3.83526e10	+	5.71357e9i	−0.894848	+	0.133310i
$456$	5.60620e10	−	1.41544e10i	1.29661	−	0.327365i
$457$	7.75835e9			0.177871			0.0889354	−	0.996037i	$-0.471654\pi$
$457$	7.75835e9			0.177871			0.0889354	+	0.996037i	$0.471654\pi$
$458$	−4.21474e10	+	1.26635e10i	−0.957874	+	0.287800i
$459$	−1.25092e10	+	1.72175e10i	−0.281825	+	0.387899i
$460$	5.74743e10	+	3.32902e10i	1.28364	+	0.743506i
$461$	1.31857e10	−	9.57995e9i	0.291943	−	0.212109i	−0.432167	−	0.901794i	$-0.642251\pi$
$461$	1.31857e10	−	9.57995e9i	0.291943	−	0.212109i	0.724110	+	0.689685i	$0.242251\pi$
$462$	7.20652e10	+	5.48528e10i	1.58182	+	1.20401i
$463$	4.46114e10	−	6.14023e10i	0.970782	−	1.33617i	0.0291309	−	0.999576i	$-0.490726\pi$
$463$	4.46114e10	−	6.14023e10i	0.970782	−	1.33617i	0.941651	−	0.336591i	$-0.109274\pi$
$464$	−4.15923e10	+	2.48856e10i	−0.897306	+	0.536878i
$465$	4.18404e10	+	4.26168e10i	0.894919	+	0.911526i
$466$	2.89688e10	−	3.80590e10i	0.614309	−	0.807075i
$467$	6.82881e10	−	2.21881e10i	1.43575	−	0.466502i	0.515177	−	0.857084i	$-0.327726\pi$
$467$	6.82881e10	−	2.21881e10i	1.43575	−	0.466502i	0.920568	+	0.390582i	$0.127726\pi$
$468$	1.16405e10	+	5.19124e8i	0.242654	+	0.0108215i
$469$	6.75835e9	+	2.08001e10i	0.139685	+	0.429906i
$470$	−1.82414e10	+	3.31762e10i	−0.373823	+	0.679885i
$471$	2.13047e10	+	6.92231e9i	0.432904	+	0.140659i
$472$	3.21336e9	−	8.02169e9i	0.0647428	−	0.161621i
$473$	2.53170e10	−	1.83939e10i	0.505787	−	0.367476i
$474$	−7.07746e8	+	3.17557e10i	−0.0140205	+	0.629084i
$475$	−2.58406e10	−	8.48031e10i	−0.507607	−	1.66586i
$476$	−1.54755e9	+	3.47012e10i	−0.0301452	+	0.675954i
$477$	−1.08186e10	+	7.86017e9i	−0.208977	+	0.151830i
$478$	−1.91007e10	+	5.46141e10i	−0.365880	+	1.04615i
$479$	4.40206e10	+	1.43031e10i	0.836206	+	0.271700i	0.695657	−	0.718374i	$-0.255113\pi$
$479$	4.40206e10	+	1.43031e10i	0.836206	+	0.271700i	0.140549	+	0.990074i	$0.455113\pi$
$480$	−3.82837e10	+	1.40019e10i	−0.721188	+	0.263768i
$481$	−4.82909e9	−	1.48624e10i	−0.0902164	−	0.277657i
$482$	3.29804e8	−	1.47979e10i	0.00611038	−	0.274165i
$483$	−9.01119e10	+	2.92791e10i	−1.65575	+	0.537985i
$484$	−8.02120e10	−	6.39259e10i	−1.46170	−	1.16492i
$485$	2.17543e10	−	1.08336e10i	0.393168	−	0.195798i
$486$	−3.48234e10	+	2.41338e10i	−0.624203	+	0.432594i
$487$	−4.20212e10	+	5.78373e10i	−0.747056	+	1.02823i	0.251126	+	0.967954i	$0.419199\pi$
$487$	−4.20212e10	+	5.78373e10i	−0.747056	+	1.02823i	−0.998182	+	0.0602794i	$0.980801\pi$
$488$	−4.56106e10	+	5.46848e10i	−0.804242	+	0.964246i
$489$	1.34225e10	−	9.75203e9i	0.234746	−	0.170553i
$490$	1.44336e10	−	7.56387e10i	0.250374	−	1.31208i
$491$	−4.95680e10	+	6.82245e10i	−0.852855	+	1.17385i	0.130371	+	0.991465i	$0.458383\pi$
$491$	−4.95680e10	+	6.82245e10i	−0.852855	+	1.17385i	−0.983226	+	0.182389i	$0.941617\pi$
$492$	6.41504e9	−	1.77260e9i	0.109481	−	0.0302517i
$493$	2.73471e10			0.462939
$494$	1.76661e10	+	5.87976e10i	0.296643	+	0.987307i
$495$	−2.97750e10	+	2.92326e10i	−0.495942	+	0.486907i
$496$	−9.26030e10	−	3.95119e10i	−1.53002	−	0.652832i
$497$	−2.97420e9	+	9.15366e9i	−0.0487467	+	0.150027i
$498$	−8.90293e9	−	1.28463e10i	−0.144749	−	0.208863i
$499$		−	4.32936e10i		−	0.698266i	−0.937073	−	0.349133i	$-0.886476\pi$
$499$		−	4.32936e10i		−	0.698266i	0.937073	−	0.349133i	$-0.113524\pi$
$500$	2.42865e10	+	5.75883e10i	0.388584	+	0.921413i
$501$	−3.10775e10			−0.493282
$502$	1.05998e10	−	7.34602e9i	0.166910	−	0.115674i
$503$	1.06145e11	+	3.44886e10i	1.65817	+	0.538771i	0.980487	−	0.196586i	$-0.0629854\pi$
$503$	1.06145e11	+	3.44886e10i	1.65817	+	0.538771i	0.677680	+	0.735357i	$0.262985\pi$
$504$	−1.50463e10	+	3.75608e10i	−0.233188	+	0.582121i
$505$	4.79245e10	+	4.88138e10i	0.736872	+	0.750546i
$506$	1.57751e11	−	4.73973e10i	2.40641	−	0.723022i
$507$			3.29584e10i			0.498809i
$508$	−9.78039e10	+	2.70251e10i	−1.46859	+	0.405800i
$509$	5.94874e9	+	4.32202e9i	0.0886246	+	0.0643895i	0.631215	−	0.775608i	$-0.282556\pi$
$509$	5.94874e9	+	4.32202e9i	0.0886246	+	0.0643895i	−0.542591	+	0.839997i	$0.682556\pi$
$510$	2.25923e10	+	4.31111e9i	0.333948	+	0.0637248i
$511$	−1.44240e10	−	1.98530e10i	−0.211545	−	0.291167i
$512$	5.06578e10	−	4.64344e10i	0.737168	−	0.675709i
$513$	−1.05675e11	−	7.67772e10i	−1.52581	−	1.10857i
$514$	−1.35990e10	−	1.96224e10i	−0.194829	−	0.281126i
$515$	−3.67797e10	−	7.38547e10i	−0.522852	−	1.04990i
$516$	−1.57133e10	−	1.25229e10i	−0.221650	−	0.176647i
$517$	2.90143e10	+	8.92969e10i	0.406116	+	1.24990i
$518$	5.42532e10	+	1.20915e9i	0.753540	+	0.0167943i
$519$	−2.14922e10	+	6.98324e9i	−0.296218	+	0.0962471i
$520$	−1.66634e10	−	3.99466e10i	−0.227903	−	0.546345i
$521$	−3.15396e10	+	9.70690e10i	−0.428061	+	1.31744i	0.471971	+	0.881614i	$0.343543\pi$
$521$	−3.15396e10	+	9.70690e10i	−0.428061	+	1.31744i	−0.900033	+	0.435823i	$0.856457\pi$
$522$	3.00697e10	+	1.05166e10i	0.404992	+	0.141642i
$523$	1.41234e9	+	1.94393e9i	0.0188770	+	0.0259820i	0.818351	−	0.574718i	$-0.194888\pi$
$523$	1.41234e9	+	1.94393e9i	0.0188770	+	0.0259820i	−0.799474	+	0.600700i	$0.794888\pi$
$524$	−3.68918e9	+	8.27236e10i	−0.0489334	+	1.09725i
$525$	−8.42736e10	−	2.91056e10i	−1.10931	−	0.383124i
$526$	5.32702e10	+	1.18724e9i	0.695891	+	0.0155095i
$527$	3.33898e10	+	4.59571e10i	0.432884	+	0.595814i
$528$	−3.96738e10	+	9.29825e10i	−0.510468	+	1.19637i
$529$	−2.90521e10	+	8.94132e10i	−0.370984	+	1.14177i
$530$	4.35280e10	+	2.39331e10i	0.551652	+	0.303317i
$531$	−5.40151e9	+	1.75506e9i	−0.0679418	+	0.0220756i
$532$	−2.12984e11	−	9.49833e9i	−2.65889	−	0.118577i
$533$	2.18373e9	+	6.72083e9i	0.0270577	+	0.0832749i
$534$	−1.72383e9	−	1.31210e9i	−0.0211997	−	0.0161363i
$535$	−7.90124e10	+	7.75730e10i	−0.964451	+	0.946881i
$536$	−2.06646e10	+	1.29979e10i	−0.250361	+	0.157476i
$537$	3.31907e10	+	2.41145e10i	0.399134	+	0.289988i
$538$	8.02629e10	−	1.05449e11i	0.958045	−	1.25867i
$539$	−1.12247e11	−	1.54494e11i	−1.32990	−	1.83045i
$540$	7.96857e10	+	4.61554e10i	0.937142	+	0.542809i
$541$	−7.83131e10	−	5.68978e10i	−0.914209	−	0.664212i	0.0278668	−	0.999612i	$-0.491129\pi$
$541$	−7.83131e10	−	5.68978e10i	−0.914209	−	0.664212i	−0.942076	+	0.335400i	$0.891129\pi$
$542$	4.90435e9	+	1.63230e10i	0.0568308	+	0.189148i
$543$		−	5.40027e10i		−	0.621178i
$544$	−3.79790e10	+	7.80719e9i	−0.433658	+	0.0891455i
$545$	−2.42412e10	−	1.62720e11i	−0.274770	−	1.84440i
$546$	5.82826e10	+	2.03837e10i	0.655795	+	0.229358i
$547$	7.47324e10	+	2.42820e10i	0.834756	+	0.271229i	0.695047	−	0.718964i	$-0.255383\pi$
$547$	7.47324e10	+	2.42820e10i	0.834756	+	0.271229i	0.139709	+	0.990193i	$0.455383\pi$
$548$	3.20941e10	−	2.11995e10i	0.355879	−	0.235074i
$549$	4.68018e10			0.515197
$550$	1.45342e11	+	5.38506e10i	1.58833	+	0.588491i
$551$			1.67847e11i			1.82099i
$552$	−5.63109e10	−	8.95250e10i	−0.606507	−	0.964246i
$553$	3.61912e10	−	1.11385e11i	0.386992	−	1.19104i
$554$	−9.57211e10	−	3.34774e10i	−1.01617	−	0.355396i
$555$	5.94702e9	−	3.54366e10i	0.0626798	−	0.373491i
$556$	3.97848e10	−	1.09933e10i	0.416311	−	0.115035i
$557$	1.80141e11			1.87151			0.935757	−	0.352646i	$-0.114718\pi$
$557$	1.80141e11			1.87151			0.935757	+	0.352646i	$0.114718\pi$
$558$	1.90408e10	+	6.33728e10i	0.196403	+	0.653681i
$559$	1.25402e10	−	1.72601e10i	0.128427	−	0.176765i
$560$	1.50043e11	−	8.82566e9i	1.52568	−	0.0897419i
$561$	4.61454e10	−	3.35266e10i	0.465884	−	0.338484i
$562$	−3.69570e10	+	4.85539e10i	−0.370469	+	0.486719i
$563$	−6.26655e9	+	8.62517e9i	−0.0623728	+	0.0858488i	−0.839064	−	0.544033i	$-0.816897\pi$
$563$	−6.26655e9	+	8.62517e9i	−0.0623728	+	0.0858488i	0.776691	+	0.629882i	$0.216897\pi$
$564$	5.03032e10	−	3.32274e10i	0.497140	−	0.328383i
$565$	1.26776e10	+	8.50988e10i	0.124406	+	0.835083i
$566$	−3.61152e10	−	2.74893e10i	−0.351904	−	0.267853i
$567$	−6.32955e10	+	2.05660e10i	−0.612408	+	0.198983i
$568$	−1.07194e10	−	7.17668e8i	−0.102986	−	0.00689494i
$569$	−2.43009e10	−	7.47905e10i	−0.231832	−	0.713506i	−0.997526	−	0.0703005i	$-0.977604\pi$
$569$	−2.43009e10	−	7.47905e10i	−0.231832	−	0.713506i	0.765694	−	0.643205i	$-0.222396\pi$
$570$	−2.64600e10	+	1.38663e11i	−0.250663	+	1.31360i
$571$	−9.07847e10	−	2.94977e10i	−0.854020	−	0.277488i	−0.150891	−	0.988550i	$-0.548214\pi$
$571$	−9.07847e10	−	2.94977e10i	−0.854020	−	0.277488i	−0.703129	+	0.711062i	$0.748214\pi$
$572$	−1.00507e11	−	3.76850e10i	−0.938885	−	0.352034i
$573$	−5.06889e10	+	3.68277e10i	−0.470213	+	0.341630i
$574$	−2.45335e10	−	5.46782e8i	−0.226001	−	0.00503693i
$575$	−1.32918e11	+	9.28855e10i	−1.21594	+	0.849721i
$576$	−4.47623e10	−	6.02069e9i	−0.406652	−	0.0546961i
$577$	1.34168e11	−	9.74791e10i	1.21045	−	0.879444i	0.215179	−	0.976575i	$-0.430966\pi$
$577$	1.34168e11	−	9.74791e10i	1.21045	−	0.879444i	0.995272	+	0.0971303i	$0.0309664\pi$
$578$	−8.47044e10	−	2.96245e10i	−0.758918	−	0.265423i
$579$	−1.40825e11	−	4.57568e10i	−1.25304	−	0.407137i
$580$	−1.22043e10	−	1.17701e11i	−0.107845	−	1.04008i
$581$	1.78084e10	+	5.48087e10i	0.156286	+	0.481000i
$582$	−3.86884e10	−	8.62255e8i	−0.337201	−	0.00751526i
$583$	1.17160e11	−	3.80675e10i	1.01415	−	0.329519i
$584$	1.75449e10	−	2.10355e10i	0.150834	−	0.180843i
$585$	−1.31473e10	+	2.52270e10i	−0.112257	+	0.215398i
$586$	5.38006e9	+	7.76307e9i	0.0456244	+	0.0658329i
$587$	−4.92225e9	+	6.77489e9i	−0.0414582	+	0.0570624i	−0.829243	−	0.558888i	$-0.811228\pi$
$587$	−4.92225e9	+	6.77489e9i	−0.0414582	+	0.0570624i	0.787785	+	0.615951i	$0.211228\pi$
$588$	−7.64196e10	+	9.58887e10i	−0.639287	+	0.802155i
$589$	−2.82068e11	+	2.04935e11i	−2.34365	+	1.70276i
$590$	1.44410e10	+	1.53800e10i	0.119176	+	0.126925i
$591$	−1.71372e8	+	2.35873e8i	−0.00140472	+	0.00193343i
$592$	1.35160e10	+	5.90470e10i	0.110043	+	0.480741i
$593$	9.32764e9			0.0754315			0.0377158	−	0.999289i	$-0.487992\pi$
$593$	9.32764e9			0.0754315			0.0377158	+	0.999289i	$0.487992\pi$
$594$	2.18715e11	−	6.57143e10i	1.75684	−	0.527855i
$595$	−7.52039e10	−	3.91932e10i	−0.600029	−	0.312711i
$596$	6.85926e10	−	1.82938e11i	0.543616	−	1.44984i
$597$	−1.11012e10	+	3.41659e10i	−0.0873921	+	0.268965i
$598$	9.22989e10	−	6.39662e10i	0.721758	−	0.500202i
$599$		−	2.19173e10i		−	0.170247i	−0.996370	−	0.0851237i	$-0.972871\pi$
$599$		−	2.19173e10i		−	0.170247i	0.996370	−	0.0851237i	$-0.0271285\pi$
$600$	8.47246e9	−	9.91599e10i	0.0653739	−	0.765122i
$601$	−1.01501e11			−0.777988			−0.388994	−	0.921240i	$-0.627177\pi$
$601$	−1.01501e11			−0.777988			−0.388994	+	0.921240i	$0.627177\pi$
$602$	4.22003e10	+	6.08921e10i	0.321314	+	0.463634i
$603$	1.52597e10	+	4.95817e9i	0.115419	+	0.0375018i
$604$	2.03618e11	+	7.63465e10i	1.52992	+	0.573642i
$605$	2.24156e11	−	1.11630e11i	1.67312	−	0.833216i
$606$	−3.13438e10	−	1.04320e11i	−0.232413	−	0.773533i
$607$			3.66330e10i			0.269847i	0.990856	+	0.134924i	$0.0430789\pi$
$607$			3.66330e10i			0.269847i	−0.990856	+	0.134924i	$0.956921\pi$
$608$	−4.79177e10	−	2.33101e11i	−0.350656	−	1.70581i
$609$	1.36565e11	+	9.92203e10i	0.992820	+	0.721326i
$610$	−7.40126e10	−	1.57309e11i	−0.534548	−	1.13615i
$611$	3.76253e10	+	5.17867e10i	0.269970	+	0.371581i
$612$	1.99287e10	+	1.58824e10i	0.142060	+	0.113217i
$613$	−2.57240e10	−	1.86896e10i	−0.182178	−	0.132360i	0.492959	−	0.870053i	$-0.335915\pi$
$613$	−2.57240e10	−	1.86896e10i	−0.182178	−	0.132360i	−0.675137	+	0.737693i	$0.735915\pi$
$614$	1.59232e11	−	1.10353e11i	1.12036	−	0.776446i
$615$	−2.68926e9	+	1.60245e10i	−0.0187989	+	0.112017i
$616$	2.38748e11	−	2.86247e11i	1.65812	−	1.98801i
$617$	6.64443e9	+	2.04495e10i	0.0458476	+	0.141105i	0.971360	−	0.237613i	$-0.0763651\pi$
$617$	6.64443e9	+	2.04495e10i	0.0458476	+	0.141105i	−0.925512	+	0.378718i	$0.876365\pi$
$618$	−2.92731e9	+	1.31345e11i	−0.0200685	+	0.900451i
$619$	1.43512e11	−	4.66298e10i	0.977518	−	0.317615i	0.223671	−	0.974665i	$-0.428196\pi$
$619$	1.43512e11	−	4.66298e10i	0.977518	−	0.317615i	0.753847	+	0.657050i	$0.228196\pi$
$620$	1.82896e11	−	1.64217e11i	1.23776	−	1.11135i
$621$	−7.38310e10	+	2.27228e11i	−0.496446	+	1.52790i
$622$	−1.93740e10	+	5.53955e10i	−0.129437	+	0.370095i
$623$	4.69509e9	+	6.46224e9i	0.0311668	+	0.0428974i
$624$	−6.13507e9	+	6.86473e10i	−0.0404651	+	0.452778i
$625$	−1.52485e11	−	5.60936e9i	−0.999324	−	0.0367615i
$626$	2.49436e9	−	1.11919e11i	0.0162428	−	0.728797i
$627$	2.05774e11	+	2.83224e11i	1.33144	+	1.83257i
$628$	3.23684e10	−	8.63274e10i	0.208105	−	0.555022i
$629$	1.05614e10	−	3.25046e10i	0.0674712	−	0.207655i
$630$	−6.76188e10	−	7.20154e10i	−0.429245	−	0.457154i
$631$	−1.76976e11	+	5.75030e10i	−1.11634	+	0.362721i	−0.808370	−	0.588675i	$-0.799650\pi$
$631$	−1.76976e11	+	5.75030e10i	−1.11634	+	0.362721i	−0.307971	+	0.951396i	$0.599650\pi$
$632$	1.30438e11	+	8.73284e9i	0.817589	+	0.0547378i
$633$	−7.37966e10	−	2.27123e11i	−0.459644	−	1.41464i
$634$	−1.66146e11	+	2.18281e11i	−1.02833	+	1.35101i
$635$	4.10006e10	−	2.44311e11i	0.252171	−	1.50261i
$636$	−4.35952e10	−	6.59990e10i	−0.266447	−	0.403375i
$637$	−1.05328e11	−	7.65253e10i	−0.639714	−	0.464780i
$638$	−2.33510e11	−	1.77737e11i	−1.40936	−	1.07274i
$639$	4.15038e9	+	5.71250e9i	0.0248934	+	0.0342628i
$640$	5.05508e10	+	1.59975e11i	0.301306	+	0.953528i
$641$	−2.75826e10	−	2.00399e10i	−0.163382	−	0.118704i	0.503090	−	0.864234i	$-0.332196\pi$
$641$	−2.75826e10	−	2.00399e10i	−0.163382	−	0.118704i	−0.666472	+	0.745530i	$0.732196\pi$
$642$	1.68858e11	−	5.07346e10i	0.993990	−	0.298651i
$643$			1.89569e11i			1.10898i	0.832191	+	0.554489i	$0.187086\pi$
$643$			1.89569e11i			1.10898i	−0.832191	+	0.554489i	$0.812914\pi$
$644$	1.03861e11	+	3.75875e11i	0.603825	+	2.18524i
$645$	4.39114e10	−	2.18679e10i	0.253710	−	0.126348i
$646$	−4.43271e10	+	1.26743e11i	−0.254530	+	0.727771i
$647$	−2.28724e11	−	7.43170e10i	−1.30525	−	0.424103i	−0.427847	−	0.903851i	$-0.640728\pi$
$647$	−2.28724e11	−	7.43170e10i	−1.30525	−	0.424103i	−0.877406	+	0.479748i	$0.840728\pi$
$648$	−3.95533e10	−	6.28832e10i	−0.224328	−	0.356644i
$649$	5.23199e10			0.294909
$650$	1.05584e11	+	4.29629e9i	0.591484	+	0.0240680i
$651$			3.50643e11i			1.95228i
$652$	−3.76354e10	−	5.69765e10i	−0.208260	−	0.315286i
$653$	4.91933e10	−	1.51401e11i	0.270554	−	0.832679i	−0.719808	−	0.694173i	$-0.755770\pi$
$653$	4.91933e10	−	1.51401e11i	0.270554	−	0.832679i	0.990362	−	0.138505i	$-0.0442298\pi$
$654$	−8.64830e10	+	2.47278e11i	−0.472737	+	1.35168i
$655$	−1.79277e11	−	9.34318e10i	−0.974000	−	0.507609i
$656$	−6.11196e9	−	2.67012e10i	−0.0330039	−	0.144184i
$657$	−1.80031e10			−0.0966244
$658$	−2.12884e11	+	6.39624e10i	−1.13564	+	0.341210i
$659$	−6.29239e10	+	8.66073e10i	−0.333637	+	0.459212i	−0.942569	−	0.334010i	$-0.891598\pi$
$659$	−6.29239e10	+	8.66073e10i	−0.333637	+	0.459212i	0.608933	+	0.793222i	$0.291598\pi$
$660$	−1.64890e11	−	1.83645e11i	−0.868999	−	0.967842i
$661$	−6.84393e10	+	4.97241e10i	−0.358509	+	0.260472i	−0.752430	−	0.658672i	$-0.771118\pi$
$661$	−6.84393e10	+	4.97241e10i	−0.358509	+	0.260472i	0.393921	+	0.919144i	$0.371118\pi$
$662$	2.32907e11	+	1.77278e11i	1.21269	+	0.923048i
$663$	2.28571e10	−	3.14601e10i	0.118295	−	0.162819i
$664$	−5.44517e10	+	3.42499e10i	−0.280117	+	0.176192i
$665$	2.40554e11	−	4.61574e11i	1.23006	−	2.36023i
$666$	2.41127e10	−	3.16792e10i	0.122560	−	0.161019i
$667$	2.91986e11	−	9.48720e10i	1.47523	−	0.479330i
$668$	−5.69849e9	+	1.27779e11i	−0.0286190	+	0.641731i
$669$	−3.17382e10	−	9.76803e10i	−0.158445	−	0.487643i
$670$	−7.46642e9	−	5.91313e10i	−0.0370521	−	0.293439i
$671$	−4.10041e11	−	1.33231e11i	−2.02273	−	0.657224i
$672$	−2.17984e11	−	9.88074e10i	−1.06893	−	0.484521i
$673$	−1.13576e10	+	8.25180e9i	−0.0553640	+	0.0402243i	−0.615123	−	0.788431i	$-0.710894\pi$
$673$	−1.13576e10	+	8.25180e9i	−0.0553640	+	0.0402243i	0.559759	+	0.828655i	$0.310894\pi$
$674$	−3.33357e9	+	1.49573e11i	−0.0161536	+	0.724794i
$675$	−1.84285e11	+	1.28782e11i	−0.887715	+	0.620353i
$676$	1.35513e11	+	6.04339e9i	0.648922	+	0.0289397i
$677$	−2.43284e10	+	1.76756e10i	−0.115813	+	0.0841432i	−0.644184	−	0.764870i	$-0.722803\pi$
$677$	−2.43284e10	+	1.76756e10i	−0.115813	+	0.0841432i	0.528371	+	0.849014i	$0.322803\pi$
$678$	4.52285e10	−	1.29321e11i	0.214039	−	0.611996i
$679$	1.35702e11	+	4.40921e10i	0.638419	+	0.207435i
$680$	2.18683e10	−	9.21004e10i	0.102277	−	0.430750i
$681$	−7.07570e10	−	2.17768e11i	−0.328989	−	1.01252i
$682$	1.35824e10	−	6.09426e11i	0.0627826	−	2.81698i
$683$	1.62024e11	−	5.26447e10i	0.744554	−	0.241920i	0.0879176	−	0.996128i	$-0.471979\pi$
$683$	1.62024e11	−	5.26447e10i	0.744554	−	0.241920i	0.656636	+	0.754208i	$0.271979\pi$
$684$	−9.74804e10	+	1.22315e11i	−0.445341	+	0.558799i
$685$	1.38368e10	+	9.28803e10i	0.0628455	+	0.421853i
$686$	9.34019e10	−	6.47306e10i	0.421754	−	0.292290i
$687$	−1.00562e11	+	1.38411e11i	−0.451446	+	0.621362i
$688$	−5.43705e10	+	6.23107e10i	−0.242667	+	0.278105i
$689$	6.79455e10	−	4.93653e10i	0.301498	−	0.219051i
$690$	2.56174e11	−	3.23467e10i	1.13016	−	0.142703i
$691$	1.37905e11	−	1.89810e11i	0.604879	−	0.832544i	−0.391265	−	0.920278i	$-0.627963\pi$
$691$	1.37905e11	−	1.89810e11i	0.604879	−	0.832544i	0.996144	+	0.0877339i	$0.0279625\pi$
$692$	2.47716e10	+	8.96483e10i	0.108026	+	0.390947i
$693$	−2.44983e11			−1.06219
$694$	−6.84118e9	−	2.27693e10i	−0.0294912	−	0.0981547i
$695$	−1.66783e10	+	9.93810e10i	−0.0714845	+	0.425955i
$696$	−7.00670e10	+	1.74912e11i	−0.298591	+	0.745389i
$697$	−4.77589e9	+	1.46987e10i	−0.0202359	+	0.0622798i
$698$	2.03657e10	+	2.93864e10i	0.0857983	+	0.123801i
$699$		−	1.85940e11i		−	0.778869i
$700$	−1.35124e11	+	3.41164e11i	−0.562782	+	1.42093i
$701$	−1.98738e11			−0.823019			−0.411509	−	0.911406i	$-0.634998\pi$
$701$	−1.98738e11			−0.823019			−0.411509	+	0.911406i	$0.634998\pi$
$702$	1.27968e11	−	8.86864e10i	0.526932	−	0.365181i
$703$	1.99501e11	+	6.48219e10i	0.816817	+	0.265400i
$704$	3.75034e11	+	1.80173e11i	1.52679	+	0.733500i
$705$	2.16874e10	+	1.45577e11i	0.0877911	+	0.589302i
$706$	−1.39161e11	+	4.18118e10i	−0.560142	+	0.168298i
$707$			4.01631e11i			1.60750i
$708$	−8.94730e9	−	3.23803e10i	−0.0356089	−	0.128869i
$709$	1.24979e11	+	9.08025e10i	0.494597	+	0.359346i	0.806949	−	0.590620i	$-0.201117\pi$
$709$	1.24979e11	+	9.08025e10i	0.494597	+	0.359346i	−0.312352	+	0.949966i	$0.601117\pi$
$710$	1.26373e10	−	2.29839e10i	0.0497304	−	0.0904464i
$711$	−5.05033e10	−	6.95118e10i	−0.197625	−	0.272007i
$712$	−5.71096e9	+	6.84715e9i	−0.0222223	+	0.0266434i
$713$	5.15937e11	+	3.74850e11i	1.99636	+	1.45044i
$714$	7.69187e10	+	1.10988e11i	0.295964	+	0.427056i
$715$	1.87000e11	−	1.83593e11i	0.715512	−	0.702477i
$716$	1.05235e11	−	1.32046e11i	0.400415	−	0.502427i
$717$	6.95058e10	+	2.13917e11i	0.262993	+	0.809410i
$718$	−1.85855e11	−	4.14218e9i	−0.699321	−	0.0155859i
$719$	4.38968e11	−	1.42629e11i	1.64254	−	0.533695i	0.665439	−	0.746452i	$-0.268244\pi$
$719$	4.38968e11	−	1.42629e11i	1.64254	−	0.533695i	0.977105	+	0.212757i	$0.0682444\pi$
$720$	5.94633e10	−	9.28599e10i	0.221268	−	0.345540i
$721$	1.49691e11	−	4.60700e11i	0.553928	−	1.70482i
$722$	−5.21402e11	−	1.82355e11i	−1.91878	−	0.671072i
$723$	−3.38223e10	−	4.65524e10i	−0.123780	−	0.170368i
$724$	−2.22039e11	−	9.90215e9i	−0.808117	−	0.0360392i
$725$	2.73068e11	+	9.43096e10i	0.988369	+	0.341353i
$726$	−3.98644e11	−	8.88465e9i	−1.43496	−	0.0319812i
$727$	−1.76716e11	−	2.43229e11i	−0.632613	−	0.870717i	0.365582	−	0.930779i	$-0.380870\pi$
$727$	−1.76716e11	−	2.43229e11i	−0.632613	−	0.870717i	−0.998195	+	0.0600622i	$0.980870\pi$
$728$	9.44971e10	−	2.35898e11i	0.336429	−	0.839845i
$729$	−8.76700e10	+	2.69820e11i	−0.310414	+	0.955355i
$730$	2.84702e10	+	6.05118e10i	0.100254	+	0.213083i
$731$	4.43759e10	−	1.44186e10i	0.155409	−	0.0504956i
$732$	−1.23334e10	+	2.76554e11i	−0.0429573	+	0.963244i
$733$	1.18947e11	+	3.66081e11i	0.412038	+	1.26812i	0.914873	+	0.403741i	$0.132290\pi$
$733$	1.18947e11	+	3.66081e11i	0.412038	+	1.26812i	−0.502835	+	0.864382i	$0.667710\pi$
$734$	3.04478e10	+	2.31755e10i	0.104899	+	0.0798443i
$735$	−1.33447e11	−	2.67965e11i	−0.457255	−	0.918182i
$736$	−3.78418e11	+	2.15113e11i	−1.28962	+	0.733088i
$737$	−1.19579e11	−	8.68792e10i	−0.405308	−	0.294473i
$738$	−1.09039e10	+	1.43254e10i	−0.0367582	+	0.0482927i
$739$	−2.63214e11	−	3.62283e11i	−0.882533	−	1.21470i	−0.975713	−	0.219053i	$-0.929703\pi$
$739$	−2.63214e11	−	3.62283e11i	−0.882533	−	1.21470i	0.0931806	−	0.995649i	$-0.470297\pi$
$740$	−1.44611e11	−	3.09497e10i	−0.482254	−	0.103212i
$741$	1.93091e11	+	1.40288e11i	0.640454	+	0.465317i
$742$	8.39203e10	+	2.79309e11i	0.276854	+	0.921445i
$743$		−	3.78673e11i		−	1.24253i	−0.783599	−	0.621267i	$-0.786618\pi$
$743$		−	3.78673e11i		−	1.24253i	0.783599	−	0.621267i	$-0.213382\pi$
$744$	−3.79491e11	+	9.58127e10i	−1.23854	+	0.312703i
$745$	3.34168e11	+	3.40369e11i	1.08477	+	1.10490i
$746$	−4.79106e11	−	1.67562e11i	−1.54695	−	0.541030i
$747$	4.02096e10	+	1.30649e10i	0.129136	+	0.0419589i
$748$	−1.29387e11	−	1.95880e11i	−0.413319	−	0.625726i
$749$	−6.50100e11			−2.06563
$750$	2.10723e11	+	1.20960e11i	0.665987	+	0.382292i
$751$			5.15538e11i			1.62069i	0.585951	+	0.810347i	$0.300721\pi$
$751$			5.15538e11i			1.62069i	−0.585951	+	0.810347i	$0.699279\pi$
$752$	−1.27395e11	−	2.12920e11i	−0.398364	−	0.665803i
$753$	1.54928e10	−	4.76819e10i	0.0481892	−	0.148311i
$754$	−1.88851e11	−	6.60485e10i	−0.584296	−	0.204352i
$755$	−3.78845e11	+	3.71943e11i	−1.16593	+	1.14469i
$756$	1.43999e11	+	5.21134e11i	0.440832	+	1.59537i
$757$	−5.40690e10			−0.164651			−0.0823257	−	0.996605i	$-0.526235\pi$
$757$	−5.40690e10			−0.164651			−0.0823257	+	0.996605i	$0.526235\pi$
$758$	−7.91694e10	−	2.63497e11i	−0.239817	−	0.798175i
$759$	3.76386e11	−	5.18051e11i	1.13414	−	1.56101i
$760$	5.65279e11	+	1.34219e11i	1.69437	+	0.402310i
$761$	−3.55961e11	+	2.58621e11i	−1.06136	+	0.771125i	−0.974340	−	0.225082i	$-0.927735\pi$
$761$	−3.55961e11	+	2.58621e11i	−1.06136	+	0.771125i	−0.0870222	+	0.996206i	$0.527735\pi$
$762$	−2.38914e11	+	3.13884e11i	−0.708634	+	0.930998i
$763$	5.67744e11	−	7.81433e11i	1.67515	−	2.30565i
$764$	1.42127e11	+	2.15167e11i	0.417160	+	0.631541i
$765$	−5.56915e10	+	2.77344e10i	−0.162609	+	0.0809791i
$766$	−3.05466e11	−	2.32507e11i	−0.887253	−	0.675337i
$767$	3.39238e10	−	1.10225e10i	0.0980219	−	0.0318492i
$768$	4.73725e10	−	2.62916e11i	0.136170	−	0.755741i
$769$	−1.60600e11	−	4.94274e11i	−0.459239	−	1.41339i	−0.866085	−	0.499896i	$-0.833372\pi$
$769$	−1.60600e11	−	4.94274e11i	−0.459239	−	1.41339i	0.406846	−	0.913497i	$-0.366628\pi$
$770$	3.87418e11	+	8.23433e11i	1.10209	+	2.34242i
$771$	−8.82691e10	−	2.86804e10i	−0.249799	−	0.0811647i
$772$	−2.13957e11	+	5.70628e11i	−0.602361	+	1.60651i
$773$	−8.79993e10	+	6.39352e10i	−0.246468	+	0.179070i	−0.704160	−	0.710041i	$-0.748676\pi$
$773$	−8.79993e10	+	6.39352e10i	−0.246468	+	0.179070i	0.457692	+	0.889111i	$0.348676\pi$
$774$	5.43385e10	+	1.21105e9i	0.151406	+	0.00337442i
$775$	1.74918e11	+	5.74043e11i	0.484872	+	1.59125i
$776$	−1.06393e10	+	1.58914e11i	−0.0293405	+	0.438243i
$777$	1.70674e11	−	1.24002e11i	0.468255	−	0.340207i
$778$	−2.58596e11	−	9.04411e10i	−0.705834	−	0.246858i
$779$	−9.02151e10	−	2.93127e10i	−0.244979	−	0.0795986i
$780$	−1.45603e11	−	8.43359e10i	−0.393362	−	0.227842i
$781$	−2.01006e10	−	6.18634e10i	−0.0540264	−	0.166276i
$782$	2.45538e11	+	5.47234e9i	0.656585	+	0.0146334i
$783$	4.04826e11	−	1.31536e11i	1.07701	−	0.349943i
$784$	3.80245e11	+	3.31791e11i	1.00647	+	0.878214i
$785$	1.57692e11	+	1.60618e11i	0.415270	+	0.422976i
$786$	1.83365e11	+	2.64583e11i	0.480425	+	0.693221i
$787$	2.31125e11	−	3.18116e11i	0.602487	−	0.829253i	−0.393446	−	0.919348i	$-0.628717\pi$
$787$	2.31125e11	−	3.18116e11i	0.602487	−	0.829253i	0.995933	+	0.0900951i	$0.0287171\pi$
$788$	9.38399e8	+	7.47868e8i	0.00243379	+	0.00193963i
$789$	1.67581e11	−	1.21755e11i	0.432431	−	0.314180i
$790$	−1.53775e11	+	2.79677e11i	−0.394801	+	0.718039i
$791$	−2.96917e11	+	4.08671e11i	−0.758453	+	1.04392i
$792$	−6.69413e10	−	2.65138e11i	−0.170135	−	0.673863i
$793$	−2.93936e11			−0.743292
$794$	6.50787e11	−	1.95533e11i	1.63741	−	0.491970i
$795$	1.91001e11	−	2.84544e10i	0.478154	−	0.0712329i
$796$	1.38442e11	+	5.19087e10i	0.344838	+	0.129297i
$797$	1.45903e11	−	4.49042e11i	0.361601	−	1.11289i	−0.590481	−	0.807052i	$-0.701062\pi$
$797$	1.45903e11	−	4.49042e11i	0.361601	−	1.11289i	0.952082	−	0.305843i	$-0.0989382\pi$
$798$	−6.81207e11	+	4.72099e11i	−1.67984	+	1.16418i
$799$			1.39996e11i			0.343502i
$800$	−4.06154e11	−	5.30179e10i	−0.991587	−	0.129438i
$801$	5.86011e9			0.0142356
$802$	−1.37024e11	−	1.97716e11i	−0.331207	−	0.477909i
$803$	1.57730e11	+	5.12494e10i	0.379359	+	0.123261i
$804$	−3.33193e10	+	8.88636e10i	−0.0797392	+	0.212667i
$805$	−9.38922e11	−	1.57571e11i	−2.23587	−	0.375226i
$806$	−1.19584e11	−	3.98008e11i	−0.283357	−	0.943088i
$807$		−	5.15178e11i		−	1.21468i
$808$	−4.34674e11	+	1.09745e11i	−1.01981	+	0.257478i
$809$	−1.60553e11	−	1.16648e11i	−0.374821	−	0.272323i	0.384386	−	0.923172i	$-0.374413\pi$
$809$	−1.60553e11	−	1.16648e11i	−0.374821	−	0.272323i	−0.759207	+	0.650849i	$0.774413\pi$
$810$	1.79939e11	−	2.27207e10i	0.418010	−	0.0527814i
$811$	4.42578e11	+	6.09156e11i	1.02307	+	1.40814i	0.910027	+	0.414548i	$0.136060\pi$
$811$	4.42578e11	+	6.09156e11i	1.02307	+	1.40814i	0.113045	+	0.993590i	$0.463940\pi$
$812$	4.32997e11	−	5.43310e11i	0.996004	−	1.24975i
$813$	5.36044e10	+	3.89458e10i	0.122698	+	0.0891454i
$814$	−3.01438e11	+	2.08907e11i	−0.686595	+	0.475833i
$815$	1.64890e11	−	2.45644e10i	0.373735	−	0.0556771i
$816$	−9.91016e10	+	1.13574e11i	−0.223522	+	0.256165i
$817$	8.84961e10	+	2.72363e11i	0.198626	+	0.611307i
$818$	−8.22433e8	+	3.69016e10i	−0.00183691	+	0.0824199i
$819$	−1.58845e11	+	5.16119e10i	−0.353052	+	0.114713i
$820$	6.53937e10	+	1.39955e10i	0.144637	+	0.0309552i
$821$	−2.21092e11	+	6.80452e11i	−0.486632	+	1.49770i	0.342971	+	0.939346i	$0.388567\pi$
$821$	−2.21092e11	+	6.80452e11i	−0.486632	+	1.49770i	−0.829603	+	0.558353i	$0.811433\pi$
$822$	4.93643e10	−	1.41146e11i	0.108125	−	0.309158i
$823$	4.35118e10	+	5.98889e10i	0.0948435	+	0.130541i	0.853801	−	0.520599i	$-0.174291\pi$
$823$	4.35118e10	+	5.98889e10i	0.0948435	+	0.130541i	−0.758958	+	0.651140i	$0.774291\pi$
$824$	5.39505e11	+	3.61200e10i	1.17027	+	0.0783499i
$825$	5.76395e11	−	1.75635e11i	1.24424	−	0.379135i
$826$	−2.75991e9	+	1.23834e11i	−0.00592891	+	0.266024i
$827$	2.96193e11	+	4.07675e11i	0.633217	+	0.871549i	0.998231	−	0.0594532i	$-0.0189357\pi$
$827$	2.96193e11	+	4.07675e11i	0.633217	+	0.871549i	−0.365014	+	0.931002i	$0.618936\pi$
$828$	2.67878e11	+	1.00441e11i	0.569922	+	0.213692i
$829$	−1.00849e11	+	3.10383e11i	−0.213528	+	0.657172i	0.785727	+	0.618574i	$0.212289\pi$
$829$	−1.00849e11	+	3.10383e11i	−0.213528	+	0.657172i	−0.999255	+	0.0385985i	$0.987711\pi$
$830$	−1.96742e10	−	1.55813e11i	−0.0414558	−	0.328315i
$831$	−3.74927e11	+	1.21821e11i	−0.786218	+	0.255458i
$832$	2.81127e11	+	3.78125e10i	0.586690	+	0.0789118i
$833$	−8.79881e10	−	2.70799e11i	−0.182744	−	0.562429i
$834$	9.71858e10	−	1.27682e11i	0.200881	−	0.263916i
$835$	−2.76920e11	−	1.44319e11i	−0.569650	−	0.296878i
$836$	1.20224e12	−	7.94133e11i	2.46131	−	1.62580i
$837$	7.15325e11	+	5.19714e11i	1.45748	+	1.05892i
$838$	2.32785e11	+	1.77185e11i	0.472039	+	0.359295i
$839$	2.24477e11	+	3.08965e11i	0.453026	+	0.623537i	0.973044	−	0.230618i	$-0.0740749\pi$
$839$	2.24477e11	+	3.08965e11i	0.453026	+	0.623537i	−0.520018	+	0.854155i	$0.674075\pi$
$840$	4.43362e11	−	3.80585e11i	0.890514	−	0.764425i
$841$	−3.77981e10	−	2.74619e10i	−0.0755589	−	0.0548968i
$842$	−5.55978e11	+	1.67047e11i	−1.10614	+	0.332346i
$843$			2.37213e11i			0.469709i
$844$	−9.47373e11	+	2.61777e11i	−1.86703	+	0.515896i
$845$	−1.53054e11	+	2.93680e11i	−0.300205	+	0.576033i
$846$	−5.38367e10	+	1.53934e11i	−0.105099	+	0.300505i
$847$	1.39827e12	+	4.54324e11i	2.71679	+	0.882739i
$848$	−2.79357e11	+	1.67145e11i	−0.540226	+	0.323229i
$849$	−1.76443e11			−0.339606
$850$	1.81291e11	+	1.43330e11i	0.347297	+	0.274575i
$851$		−	3.83692e11i		−	0.731584i
$852$	−3.48492e10	+	2.30194e10i	−0.0661355	+	0.0436854i
$853$	2.50223e11	−	7.70106e11i	0.472640	−	1.45464i	−0.376474	−	0.926427i	$-0.622864\pi$
$853$	2.50223e11	−	7.70106e11i	0.472640	−	1.45464i	0.849114	−	0.528209i	$-0.177136\pi$
$854$	3.36968e11	−	9.63484e11i	0.633516	−	1.81139i
$855$	−1.70224e11	−	3.41814e11i	−0.318534	−	0.639626i
$856$	−1.77639e11	−	7.03584e11i	−0.330859	−	1.31045i
$857$	−1.16059e11			−0.215157			−0.107578	−	0.994197i	$-0.534310\pi$
$857$	−1.16059e11			−0.215157			−0.107578	+	0.994197i	$0.534310\pi$
$858$	−3.99639e11	+	1.20074e11i	−0.737427	+	0.221565i
$859$	−6.84055e10	+	9.41521e10i	−0.125637	+	0.172925i	−0.867202	−	0.497956i	$-0.834084\pi$
$859$	−6.84055e10	+	9.41521e10i	−0.125637	+	0.172925i	0.741565	+	0.670881i	$0.234084\pi$
$860$	−8.18606e10	−	1.84557e11i	−0.149652	−	0.337393i
$861$	−7.71791e10	+	5.60739e10i	−0.140439	+	0.102035i
$862$	−7.97352e11	−	6.06908e11i	−1.44418	−	1.09924i
$863$	−1.30241e11	+	1.79261e11i	−0.234803	+	0.323179i	−0.910117	−	0.414352i	$-0.864008\pi$
$863$	−1.30241e11	+	1.79261e11i	−0.234803	+	0.323179i	0.675314	+	0.737531i	$0.264008\pi$
$864$	−5.24660e11	+	2.98245e11i	−0.941506	+	0.535203i
$865$	−2.23938e11	−	3.75816e10i	−0.400003	−	0.0671292i
$866$	4.98952e11	−	6.55520e11i	0.887130	−	1.16551i
$867$	−3.31777e11	+	1.07801e11i	−0.587177	+	0.190786i
$868$	1.44171e12	+	6.42953e10i	2.53980	+	0.113266i
$869$	2.44592e11	+	7.52776e11i	0.428907	+	1.32004i
$870$	−3.14885e11	−	3.35359e11i	−0.549636	−	0.585373i
$871$	−9.58373e10	−	3.11394e10i	−0.166518	−	0.0541051i
$872$	1.00086e12	+	4.00927e11i	1.73104	+	0.693425i
$873$	8.46870e10	−	6.15287e10i	0.145801	−	0.105931i
$874$	−3.35872e10	+	1.50702e12i	−0.0575610	+	2.58270i
$875$	−6.15768e11	−	6.50703e11i	−1.05047	−	1.11007i
$876$	4.74424e9	−	1.06381e11i	0.00805658	−	0.180655i
$877$	−3.89741e11	+	2.83164e11i	−0.658837	+	0.478673i	−0.866270	−	0.499576i	$-0.833489\pi$
$877$	−3.89741e11	+	2.83164e11i	−0.658837	+	0.478673i	0.207433	+	0.978249i	$0.433489\pi$
$878$	−2.82384e11	+	8.07411e11i	−0.475184	+	1.35868i
$879$	3.49212e10	+	1.13466e10i	0.0584970	+	0.0190068i
$880$	−7.85315e11	+	6.44292e11i	−1.30952	+	1.07437i
$881$	1.29961e11	+	3.99979e11i	0.215729	+	0.663947i	0.999101	+	0.0423932i	$0.0134982\pi$
$881$	1.29961e11	+	3.99979e11i	0.215729	+	0.663947i	−0.783372	+	0.621554i	$0.786502\pi$
$882$	7.39033e9	−	3.31596e11i	0.0122121	−	0.547942i
$883$	−1.34056e11	+	4.35575e10i	−0.220518	+	0.0716506i	−0.417192	−	0.908818i	$-0.636986\pi$
$883$	−1.34056e11	+	4.35575e10i	−0.220518	+	0.0716506i	0.196674	+	0.980469i	$0.436986\pi$
$884$	−1.25161e11	−	9.97483e10i	−0.204955	−	0.163341i
$885$	8.08848e10	+	1.35742e10i	0.131854	+	0.0221280i
$886$	1.92735e11	−	1.33572e11i	0.312770	−	0.216760i
$887$	−1.37525e11	+	1.89286e11i	−0.222170	+	0.305791i	−0.905523	−	0.424297i	$-0.860521\pi$
$887$	−1.37525e11	+	1.89286e11i	−0.222170	+	0.305791i	0.683353	+	0.730088i	$0.260521\pi$
$888$	1.80840e11	+	1.50832e11i	0.290832	+	0.242572i
$889$	1.17668e12	−	8.54905e11i	1.88386	−	1.36871i
$890$	−9.26720e9	−	1.96969e10i	−0.0147703	−	0.0313933i
$891$	2.64378e11	−	3.63885e11i	0.419482	−	0.577368i
$892$	−4.07444e11	+	1.12585e11i	−0.643589	+	0.177836i
$893$	−8.59245e11			−1.35117
$894$	−2.18554e11	−	7.27405e11i	−0.342143	−	1.13874i
$895$	1.83766e11	+	3.69008e11i	0.286400	+	0.575100i
$896$	−4.46229e11	+	8.78149e11i	−0.692350	+	1.36250i
$897$	1.34905e11	−	4.15195e11i	0.208381	−	0.641332i
$898$	−1.66772e11	−	2.40641e11i	−0.256460	−	0.370054i
$899$		−	1.13617e12i		−	1.73943i
$900$	1.44221e11	+	2.27316e11i	0.219816	+	0.346466i
$901$	1.83678e11			0.278714
$902$	1.36311e11	−	9.44682e10i	0.205923	−	0.142712i
$903$	2.73916e11	+	8.90006e10i	0.411970	+	0.133857i
$904$	−5.23424e11	−	2.09675e11i	−0.783754	−	0.313959i
$905$	2.50781e11	−	4.81198e11i	0.373852	−	0.717347i
$906$	8.09633e11	−	2.43260e11i	1.20164	−	0.361042i
$907$			2.23491e11i			0.330241i	0.986273	+	0.165121i	$0.0528013\pi$
$907$			2.23491e11i			0.330241i	−0.986273	+	0.165121i	$0.947199\pi$
$908$	−9.08352e11	+	2.50995e11i	−1.33632	+	0.369251i
$909$	2.38378e11	+	1.73192e11i	0.349149	+	0.253671i
$910$	4.24675e11	+	4.52288e11i	0.619286	+	0.659552i
$911$	−4.50810e11	−	6.20487e11i	−0.654516	−	0.900864i	0.344768	−	0.938688i	$-0.387957\pi$
$911$	−4.50810e11	−	6.20487e11i	−0.654516	−	0.900864i	−0.999284	+	0.0378237i	$0.987957\pi$
$912$	−6.97077e11	−	6.08249e11i	−1.00763	−	0.879230i
$913$	−3.15094e11	−	2.28929e11i	−0.453479	−	0.329472i
$914$	−7.07081e10	−	1.02027e11i	−0.101317	−	0.146194i
$915$	−5.99343e11	−	3.12353e11i	−0.855050	−	0.445617i
$916$	5.50655e11	+	4.38851e11i	0.782164	+	0.623355i
$917$	−3.66783e11	−	1.12884e12i	−0.518718	−	1.59645i
$918$	3.40427e11	+	7.58716e9i	0.479351	+	0.0106834i
$919$	−1.09300e12	+	3.55138e11i	−1.53235	+	0.497892i	−0.949255	−	0.314508i	$-0.898160\pi$
$919$	−1.09300e12	+	3.55138e11i	−1.53235	+	0.497892i	−0.583100	+	0.812401i	$0.698160\pi$
$920$	−8.60243e10	−	1.05922e12i	−0.120080	−	1.47855i
$921$	2.32736e11	−	7.16287e11i	0.323463	−	0.995516i
$922$	−2.46154e11	−	8.60897e10i	−0.340630	−	0.119132i
$923$	−2.60662e10	−	3.58770e10i	−0.0359145	−	0.0494321i
$924$	6.45588e10	−	1.44762e12i	0.0885661	−	1.98594i
$925$	2.17554e11	−	2.88145e11i	0.297167	−	0.393590i
$926$	−1.21406e12	−	2.70579e10i	−1.65118	−	0.0368002i
$927$	−2.08887e11	−	2.87508e11i	−0.282874	−	0.389342i
$928$	7.06324e11	+	3.20161e11i	0.952384	+	0.431695i
$929$	−1.13025e11	+	3.47855e11i	−0.151744	+	0.467020i	−0.997816	−	0.0660481i	$-0.978961\pi$
$929$	−1.13025e11	+	3.47855e11i	−0.151744	+	0.467020i	0.846073	+	0.533068i	$0.178961\pi$
$930$	1.79111e11	−	9.38628e11i	0.239437	−	1.25476i
$931$	1.66207e12	−	5.40039e11i	2.21233	−	0.718830i
$932$	−7.64516e11	−	3.40947e10i	−1.01326	−	0.0451881i
$933$	7.05002e10	+	2.16977e11i	0.0930388	+	0.286344i
$934$	−9.14152e11	−	6.95811e11i	−1.20124	−	0.914332i
$935$	5.66877e11	−	8.44505e10i	0.741725	−	0.110498i
$936$	−9.92622e10	−	1.57810e11i	−0.129324	−	0.205604i
$937$	4.50969e11	+	3.27648e11i	0.585044	+	0.425059i	0.840539	−	0.541751i	$-0.182239\pi$
$937$	4.50969e11	+	3.27648e11i	0.585044	+	0.425059i	−0.255495	+	0.966810i	$0.582239\pi$
$938$	2.11939e11	−	2.78444e11i	0.273779	−	0.359689i
$939$	−2.55803e11	−	3.52083e11i	−0.329036	−	0.452880i
$940$	6.02536e11	−	6.24766e10i	0.771741	−	0.0800214i
$941$	−8.26366e10	−	6.00390e10i	−0.105394	−	0.0765729i	0.533840	−	0.845585i	$-0.320748\pi$
$941$	−8.26366e10	−	6.00390e10i	−0.105394	−	0.0765729i	−0.639234	+	0.769012i	$0.720748\pi$
$942$	−1.03134e11	−	3.43258e11i	−0.130978	−	0.435930i
$943$			1.73507e11i			0.219416i
$944$	−1.34776e11	+	3.08505e10i	−0.169717	+	0.0388485i
$945$	−1.30177e12	−	2.18466e11i	−1.63233	−	0.273940i
$946$	−4.72625e11	−	1.65296e11i	−0.590136	−	0.206394i
$947$	−6.51375e11	−	2.11645e11i	−0.809900	−	0.263152i	−0.125344	−	0.992113i	$-0.540004\pi$
$947$	−6.51375e11	−	2.11645e11i	−0.809900	−	0.263152i	−0.684555	+	0.728961i	$0.740004\pi$
$948$	4.24058e11	−	2.80108e11i	0.525039	−	0.346811i
$949$	1.13067e11			0.139403
$950$	−8.79707e11	+	1.11270e12i	−1.08005	+	1.36610i
$951$			1.06643e12i			1.30380i
$952$	4.70447e11	−	2.95909e11i	0.572747	−	0.360256i
$953$	6.51228e10	−	2.00427e11i	0.0789517	−	0.242988i	−0.903789	−	0.427979i	$-0.859226\pi$
$953$	6.51228e10	−	2.00427e11i	0.0789517	−	0.242988i	0.982740	+	0.184991i	$0.0592256\pi$
$954$	2.01965e11	+	7.06350e10i	0.243827	+	0.0852760i
$955$	−6.22692e11	+	9.27655e10i	−0.748618	+	0.111525i
$956$	8.92290e11	−	2.46557e11i	1.06825	−	0.295179i
$957$	−1.14083e12			−1.36011
$958$	−2.13100e11	−	7.09253e11i	−0.253000	−	0.842053i
$959$	−3.24067e11	+	4.46040e11i	−0.383142	+	0.527350i
$960$	5.33044e11	+	3.75843e11i	0.627593	+	0.442508i
$961$	1.21935e12	−	8.85910e11i	1.42967	−	1.03871i
$962$	−1.51438e11	+	1.98959e11i	−0.176822	+	0.232307i
$963$	−2.80336e11	+	3.85850e11i	−0.325968	+	0.448656i
$964$	−1.97608e11	+	1.30528e11i	−0.228821	+	0.151146i
$965$	−1.04235e12	−	1.06169e12i	−1.20200	−	1.22430i
$966$	1.20630e12	+	9.18182e11i	1.38531	+	1.05444i
$967$	8.21037e10	−	2.66771e10i	0.0938981	−	0.0305093i	−0.261691	−	0.965152i	$-0.584280\pi$
$967$	8.21037e10	−	2.66771e10i	0.0938981	−	0.0305093i	0.355589	+	0.934642i	$0.384280\pi$
$968$	−1.09627e11	+	1.63744e12i	−0.124858	+	1.86494i
$969$	1.61302e11	+	4.96438e11i	0.182956	+	0.563079i
$970$	−3.40734e11	−	1.87347e11i	−0.384882	−	0.211621i
$971$	−1.24549e12	−	4.04683e11i	−1.40108	−	0.455237i	−0.491538	−	0.870856i	$-0.663565\pi$
$971$	−1.24549e12	−	4.04683e11i	−1.40108	−	0.455237i	−0.909539	+	0.415619i	$0.863565\pi$
$972$	6.34748e11	+	2.37998e11i	0.711109	+	0.266630i
$973$	−4.78650e11	+	3.47759e11i	−0.534031	+	0.387996i
$974$	1.14357e12	+	2.54869e10i	1.27065	+	0.0283192i
$975$	3.36728e11	−	2.35312e11i	0.372615	−	0.260391i
$976$	1.13483e12	+	1.01420e11i	1.25063	+	0.111770i
$977$	4.35871e11	−	3.16679e11i	0.478388	−	0.347569i	−0.322313	−	0.946633i	$-0.604461\pi$
$977$	4.35871e11	−	3.16679e11i	0.478388	−	0.347569i	0.800701	+	0.599064i	$0.204461\pi$
$978$	−2.50575e11	−	8.76361e10i	−0.273894	−	0.0957916i
$979$	−5.13417e10	−	1.66819e10i	−0.0558907	−	0.0181600i
$980$	−1.12624e12	+	4.99547e11i	−1.22103	+	0.541591i
$981$	−2.18976e11	−	6.73940e11i	−0.236440	−	0.727688i
$982$	1.34895e12	+	3.00642e10i	1.45060	+	0.0323299i
$983$	−8.21880e11	+	2.67045e11i	−0.880227	+	0.286003i	−0.714051	−	0.700093i	$-0.753142\pi$
$983$	−8.21880e11	+	2.67045e11i	−0.880227	+	0.286003i	−0.166175	+	0.986096i	$0.553142\pi$
$984$	−8.17762e10	−	6.82065e10i	−0.0872261	−	0.0727521i
$985$	−2.62239e9	+	1.30595e9i	−0.00278582	+	0.00138734i
$986$	−2.49236e11	−	3.59631e11i	−0.263696	−	0.380496i
$987$	−5.07931e11	+	6.99107e11i	−0.535225	+	0.736674i
$988$	6.12219e11	−	7.68191e11i	0.642509	−	0.806198i
$989$	4.23782e11	−	3.07895e11i	0.442952	−	0.321824i
$990$	6.55790e11	+	1.25139e11i	0.682690	+	0.130273i
$991$	−2.12581e11	+	2.92593e11i	−0.220410	+	0.303368i	−0.904875	−	0.425678i	$-0.860036\pi$
$991$	−2.12581e11	+	2.92593e11i	−0.220410	+	0.303368i	0.684465	+	0.729045i	$0.260036\pi$
$992$	3.24361e11	+	1.57789e12i	0.334951	+	1.62941i
$993$	1.13789e12			1.17031
$994$	1.47482e11	−	4.43121e10i	0.151076	−	0.0453917i
$995$	−2.57580e11	+	2.52888e11i	−0.262797	+	0.258009i
$996$	−8.77974e10	+	2.34158e11i	−0.0892163	+	0.237942i
$997$	−5.18527e11	+	1.59586e12i	−0.524796	+	1.61516i	0.239922	+	0.970792i	$0.422878\pi$
$997$	−5.18527e11	+	1.59586e12i	−0.524796	+	1.61516i	−0.764718	+	0.644365i	$0.777122\pi$
$998$	−5.69337e11	+	3.94569e11i	−0.573914	+	0.397742i
$999$		−	5.31972e11i		−	0.534105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.35	✓	464
4.3	odd	2	inner	100.9.j.b.11.82	yes	464
25.16	even	5	inner	100.9.j.b.91.82	yes	464
100.91	odd	10	inner	100.9.j.b.91.35	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.35	✓	464	1.1	even	1	trivial
100.9.j.b.11.82	yes	464	4.3	odd	2	inner
100.9.j.b.91.35	yes	464	100.91	odd	10	inner
100.9.j.b.91.82	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+(-9.11381 - 13.1506i) q^{2} +(-59.1564 - 19.2211i) q^{3} +(-89.8770 + 239.704i) q^{4} +(-437.861 - 445.986i) q^{5} +(286.371 + 953.120i) q^{6} -3669.49i q^{7} +(3971.38 - 1002.68i) q^{8} +(-2177.93 - 1582.36i) q^{9} +(-1874.40 + 9822.76i) q^{10} +(14576.8 + 20063.3i) q^{11} +(9924.17 - 12452.5i) q^{12} +(13678.3 + 9937.90i) q^{13} +(-48256.0 + 33443.0i) q^{14} +(17329.9 + 34799.1i) q^{15} +(-49380.3 - 43087.8i) q^{16} +(11426.5 + 35167.2i) q^{17} +(-959.740 + 43062.4i) q^{18} +(-215843. + 70131.7i) q^{19} +(146258. - 64873.2i) q^{20} +(-70531.6 + 217074. i) q^{21} +(130994. - 374547. i) q^{22} +(244002. + 335840. i) q^{23} +(-254205. - 17019.1i) q^{24} +(-7181.20 + 390559. i) q^{25} +(6027.58 - 270451. i) q^{26} +(338298. + 465628. i) q^{27} +(879592. + 329803. i) q^{28} +(228540. - 703375. i) q^{29} +(299687. - 545051. i) q^{30} +(1.46107e6 - 474730. i) q^{31} +(-116588. + 1.04207e6i) q^{32} +(-476675. - 1.46706e6i) q^{33} +(358330. - 470772. i) q^{34} +(-1.63654e6 + 1.60672e6i) q^{35} +(575044. - 379841. i) q^{36} +(-747765. - 543283. i) q^{37} +(2.88943e6 + 2.19930e6i) q^{38} +(-618144. - 850803. i) q^{39} +(-2.18609e6 - 1.33214e6i) q^{40} +(338142. + 245674. i) q^{41} +(3.49746e6 - 1.05084e6i) q^{42} -1.26186e6i q^{43} +(-6.11938e6 + 1.69090e6i) q^{44} +(247921. + 1.66418e6i) q^{45} +(2.19271e6 - 6.26956e6i) q^{46} +(3.60074e6 + 1.16995e6i) q^{47} +(2.09297e6 + 3.49806e6i) q^{48} -7.70035e6 q^{49} +(5.20154e6 - 3.46504e6i) q^{50} -2.29999e6i q^{51} +(-3.61152e6 + 2.38557e6i) q^{52} +(1.53500e6 - 4.72426e6i) q^{53} +(3.04010e6 - 8.69247e6i) q^{54} +(2.56532e6 - 1.52860e7i) q^{55} +(-3.67933e6 - 1.45729e7i) q^{56} +1.41165e7 q^{57} +(-1.13327e7 + 3.40498e6i) q^{58} +(1.24006e6 - 1.70679e6i) q^{59} +(-9.89904e6 + 1.02643e6i) q^{60} +(-1.40648e7 + 1.02187e7i) q^{61} +(-1.95589e7 - 1.48873e7i) q^{62} +(-5.80645e6 + 7.99189e6i) q^{63} +(1.47665e7 - 7.96406e6i) q^{64} +(-1.55705e6 - 1.04518e7i) q^{65} +(-1.49483e7 + 1.96390e7i) q^{66} +(-5.66838e6 + 1.84177e6i) q^{67} +(-9.45670e6 - 421736. i) q^{68} +(-7.97908e6 - 2.45571e7i) q^{69} +(3.60445e7 + 6.87810e6i) q^{70} +(-2.49453e6 - 810522. i) q^{71} +(-1.02360e7 - 4.10037e6i) q^{72} +(5.41028e6 - 3.93080e6i) q^{73} +(-329515. + 1.47849e7i) q^{74} +(7.93178e6 - 2.29660e7i) q^{75} +(2.58846e6 - 5.80418e7i) q^{76} +(7.36221e7 - 5.34896e7i) q^{77} +(-5.55492e6 + 1.58830e7i) q^{78} +(3.03544e7 + 9.86273e6i) q^{79} +(2.40515e6 + 4.08893e7i) q^{80} +(-5.60459e6 - 1.72491e7i) q^{81} +(149008. - 6.68580e6i) q^{82} +(-1.49363e7 + 4.85311e6i) q^{83} +(-4.56944e7 - 3.64166e7i) q^{84} +(1.06808e7 - 2.04944e7i) q^{85} +(-1.65942e7 + 1.15003e7i) q^{86} +(-2.70393e7 + 3.72164e7i) q^{87} +(7.80073e7 + 6.50630e7i) q^{88} +(-1.76107e6 + 1.27949e6i) q^{89} +(1.96254e7 - 1.84273e7i) q^{90} +(3.64670e7 - 5.01925e7i) q^{91} +(-1.02432e8 + 2.83041e7i) q^{92} -9.55564e7 q^{93} +(-1.74309e7 - 5.80146e7i) q^{94} +(1.25787e8 + 6.55550e7i) q^{95} +(2.69267e7 - 5.94044e7i) q^{96} +(-1.20159e7 + 3.69811e7i) q^{97} +(7.01795e7 + 1.01264e8i) q^{98} -6.67623e7i 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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