LMFDB - Embedded newform 100.9.j.b.11.75

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			11.75
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.75

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.29871 - 14.2383i) q^{2} +(-21.5758 - 7.01039i) q^{3} +(-149.458 - 207.842i) q^{4} +(-500.682 + 374.089i) q^{5} +(-257.291 + 256.035i) q^{6} +2756.23i q^{7} +(-4050.17 + 611.039i) q^{8} +(-4891.59 - 3553.95i) q^{9} +(1672.05 + 9859.22i) q^{10} +(-7970.26 - 10970.1i) q^{11} +(1767.61 + 5532.11i) q^{12} +(-32422.0 - 23555.9i) q^{13} +(39243.9 + 20116.9i) q^{14} +(13425.1 - 4561.27i) q^{15} +(-20860.8 + 62127.2i) q^{16} +(35808.3 + 110207. i) q^{17} +(-86304.5 + 43708.6i) q^{18} +(217351. - 70621.5i) q^{19} +(152582. + 48152.5i) q^{20} +(19322.2 - 59467.7i) q^{21} +(-214368. + 33415.1i) q^{22} +(218659. + 300959. i) q^{23} +(91669.1 + 15209.6i) q^{24} +(110740. - 374599. i) q^{25} +(-572035. + 289705. i) q^{26} +(168113. + 231388. i) q^{27} +(572860. - 411939. i) q^{28} +(225502. - 694024. i) q^{29} +(33041.3 - 224442. i) q^{30} +(734789. - 238747. i) q^{31} +(732328. + 750471. i) q^{32} +(95059.6 + 292563. i) q^{33} +(1.83051e6 + 294517. i) q^{34} +(-1.03107e6 - 1.37999e6i) q^{35} +(-7575.41 + 1.54784e6i) q^{36} +(-2.85415e6 - 2.07366e6i) q^{37} +(580850. - 3.61014e6i) q^{38} +(534392. + 735528. i) q^{39} +(1.79926e6 - 1.82106e6i) q^{40} +(2.24016e6 + 1.62757e6i) q^{41} +(-705691. - 709153. i) q^{42} +3.06866e6i q^{43} +(-1.08884e6 + 3.29613e6i) q^{44} +(3.77863e6 - 50490.0i) q^{45} +(5.88107e6 - 916723. i) q^{46} +(142628. + 46342.5i) q^{47} +(885625. - 1.19420e6i) q^{48} -1.83198e6 q^{49} +(-4.52539e6 - 4.31084e6i) q^{50} -2.62882e6i q^{51} +(-50210.6 + 1.02593e7i) q^{52} +(140322. - 431867. i) q^{53} +(4.52158e6 - 704810. i) q^{54} +(8.09437e6 + 2.51096e6i) q^{55} +(-1.68416e6 - 1.11632e7i) q^{56} -5.18459e6 q^{57} +(-8.23584e6 - 8.27624e6i) q^{58} +(5.82950e6 - 8.02361e6i) q^{59} +(-2.95451e6 - 2.10859e6i) q^{60} +(-5.10299e6 + 3.70754e6i) q^{61} +(1.96366e6 - 1.22047e7i) q^{62} +(9.79549e6 - 1.34823e7i) q^{63} +(1.60305e7 - 4.94962e6i) q^{64} +(2.50451e7 - 334653. i) q^{65} +(4.85942e6 + 781850. i) q^{66} +(-2.94518e7 + 9.56947e6i) q^{67} +(1.75538e7 - 2.39137e7i) q^{68} +(-2.60790e6 - 8.02630e6i) q^{69} +(-2.71742e7 + 4.60854e6i) q^{70} +(2.76946e6 + 899851. i) q^{71} +(2.19834e7 + 1.14051e7i) q^{72} +(-8.00180e6 + 5.81365e6i) q^{73} +(-5.03570e7 + 2.55031e7i) q^{74} +(-5.01539e6 + 7.30593e6i) q^{75} +(-4.71628e7 - 3.46197e7i) q^{76} +(3.02361e7 - 2.19678e7i) q^{77} +(1.43730e7 - 2.24043e6i) q^{78} +(2.10637e7 + 6.84401e6i) q^{79} +(-1.27964e7 - 3.89098e7i) q^{80} +(1.02537e7 + 3.15575e7i) q^{81} +(3.95242e7 - 2.00169e7i) q^{82} +(7.43986e6 - 2.41736e6i) q^{83} +(-1.52478e7 + 4.87192e6i) q^{84} +(-5.91556e7 - 4.17830e7i) q^{85} +(4.36925e7 + 2.23973e7i) q^{86} +(-9.73076e6 + 1.33932e7i) q^{87} +(3.89841e7 + 3.95607e7i) q^{88} +(1.96687e7 - 1.42902e7i) q^{89} +(2.68602e7 - 5.41697e7i) q^{90} +(6.49255e7 - 8.93622e7i) q^{91} +(2.98717e7 - 9.04272e7i) q^{92} -1.75273e7 q^{93} +(1.70084e6 - 1.69253e6i) q^{94} +(-8.24048e7 + 1.16667e8i) q^{95} +(-1.05394e7 - 2.13259e7i) q^{96} +(-2.17117e7 + 6.68217e7i) q^{97} +(-1.33711e7 + 2.60842e7i) q^{98} +8.19873e7i 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 $

$2$	7.29871	−	14.2383i	0.456169	−	0.889893i
$2$	7.29871	−	14.2383i	0.456169	−	0.889893i
$3$	−21.5758	−	7.01039i	−0.266367	−	0.0865480i	0.172788	−	0.984959i	$-0.444722\pi$
$3$	−21.5758	−	7.01039i	−0.266367	−	0.0865480i	−0.439156	+	0.898411i	$0.644722\pi$
$4$	−149.458	−	207.842i	−0.583819	−	0.811884i
$5$	−500.682	+	374.089i	−0.801091	+	0.598542i
$5$	−500.682	+	374.089i	−0.801091	+	0.598542i
$6$	−257.291	+	256.035i	−0.198527	+	0.197558i
$7$			2756.23i			1.14795i	0.818873	+	0.573975i	$0.194599\pi$
$7$			2756.23i			1.14795i	−0.818873	+	0.573975i	$0.805401\pi$
$8$	−4050.17	+	611.039i	−0.988810	+	0.149180i
$9$	−4891.59	−	3553.95i	−0.745556	−	0.541678i
$10$	1672.05	+	9859.22i	0.167205	+	0.985922i
$11$	−7970.26	−	10970.1i	−0.544380	−	0.749274i	0.444857	−	0.895602i	$-0.353255\pi$
$11$	−7970.26	−	10970.1i	−0.544380	−	0.749274i	−0.989236	+	0.146328i	$0.953255\pi$
$12$	1767.61	+	5532.11i	0.0852434	+	0.266788i
$13$	−32422.0	−	23555.9i	−1.13518	−	0.824759i	−0.148742	−	0.988876i	$-0.547522\pi$
$13$	−32422.0	−	23555.9i	−1.13518	−	0.824759i	−0.986441	+	0.164117i	$0.947522\pi$
$14$	39243.9	+	20116.9i	1.02155	+	0.523659i
$15$	13425.1	−	4561.27i	0.265187	−	0.0900992i
$16$	−20860.8	+	62127.2i	−0.318311	+	0.947986i
$17$	35808.3	+	110207.i	0.428734	+	1.31951i	0.899373	+	0.437182i	$0.144023\pi$
$17$	35808.3	+	110207.i	0.428734	+	1.31951i	−0.470639	+	0.882326i	$0.655977\pi$
$18$	−86304.5	+	43708.6i	−0.822135	+	0.416368i
$19$	217351.	−	70621.5i	1.66781	−	0.541904i	0.685323	−	0.728239i	$-0.259661\pi$
$19$	217351.	−	70621.5i	1.66781	−	0.541904i	0.982486	+	0.186335i	$0.0596611\pi$
$20$	152582.	+	48152.5i	0.953639	+	0.300953i
$21$	19322.2	−	59467.7i	0.0993527	−	0.305776i
$22$	−214368.	+	33415.1i	−0.915103	+	0.142643i
$23$	218659.	+	300959.i	0.781370	+	1.07546i	0.995129	+	0.0985772i	$0.0314291\pi$
$23$	218659.	+	300959.i	0.781370	+	1.07546i	−0.213759	+	0.976886i	$0.568571\pi$
$24$	91669.1	+	15209.6i	0.276298	+	0.0458430i
$25$	110740.	−	374599.i	0.283495	−	0.958974i
$26$	−572035.	+	289705.i	−1.25178	+	0.633962i
$27$	168113.	+	231388.i	0.316335	+	0.435398i
$28$	572860.	−	411939.i	0.932001	−	0.670194i
$29$	225502.	−	694024.i	0.318829	−	0.981256i	−0.655320	−	0.755351i	$-0.727466\pi$
$29$	225502.	−	694024.i	0.318829	−	0.981256i	0.974149	−	0.225905i	$-0.0725338\pi$
$30$	33041.3	−	224442.i	0.0407917	−	0.277089i
$31$	734789.	−	238747.i	0.795638	−	0.258519i	0.117135	−	0.993116i	$-0.462629\pi$
$31$	734789.	−	238747.i	0.795638	−	0.258519i	0.678503	+	0.734597i	$0.262629\pi$
$32$	732328.	+	750471.i	0.698402	+	0.715705i
$33$	95059.6	+	292563.i	0.0801568	+	0.246697i
$34$	1.83051e6	+	294517.i	1.36980	+	0.220392i
$35$	−1.03107e6	−	1.37999e6i	−0.687096	−	0.919612i
$36$	−7575.41	+	1.54784e6i	−0.00451020	+	0.921547i
$37$	−2.85415e6	−	2.07366e6i	−1.52289	−	1.10645i	−0.960030	−	0.279897i	$-0.909700\pi$
$37$	−2.85415e6	−	2.07366e6i	−1.52289	−	1.10645i	−0.562863	−	0.826550i	$-0.690300\pi$
$38$	580850.	−	3.61014e6i	0.278567	−	1.73137i
$39$	534392.	+	735528.i	0.230995	+	0.317937i
$40$	1.79926e6	−	1.82106e6i	0.702837	−	0.711351i
$41$	2.24016e6	+	1.62757e6i	0.792765	+	0.575977i	0.908783	−	0.417270i	$-0.137013\pi$
$41$	2.24016e6	+	1.62757e6i	0.792765	+	0.575977i	−0.116018	+	0.993247i	$0.537013\pi$
$42$	−705691.	−	709153.i	−0.226786	−	0.227899i
$43$			3.06866e6i			0.897585i	0.893636	+	0.448792i	$0.148146\pi$
$43$			3.06866e6i			0.897585i	−0.893636	+	0.448792i	$0.851854\pi$
$44$	−1.08884e6	+	3.29613e6i	−0.290505	+	0.879413i
$45$	3.77863e6	−	50490.0i	0.921476	−	0.0123128i
$46$	5.88107e6	−	916723.i	1.31348	−	0.204742i
$47$	142628.	+	46342.5i	0.0292289	+	0.00949704i	0.323595	−	0.946196i	$-0.395108\pi$
$47$	142628.	+	46342.5i	0.0292289	+	0.00949704i	−0.294366	+	0.955693i	$0.595108\pi$
$48$	885625.	−	1.19420e6i	0.166834	−	0.224964i
$49$	−1.83198e6			−0.317787
$50$	−4.52539e6	−	4.31084e6i	−0.724062	−	0.689735i
$51$		−	2.62882e6i		−	0.388580i
$52$	−50210.6	+	1.02593e7i	−0.00686723	+	1.40315i
$53$	140322.	−	431867.i	0.0177837	−	0.0547326i	−0.941771	−	0.336255i	$-0.890839\pi$
$53$	140322.	−	431867.i	0.0177837	−	0.0547326i	0.959555	+	0.281523i	$0.0908395\pi$
$54$	4.52158e6	−	704810.i	0.531760	−	0.0828891i
$55$	8.09437e6	+	2.51096e6i	0.884570	+	0.274403i
$56$	−1.68416e6	−	1.11632e7i	−0.171250	−	1.13510i
$57$	−5.18459e6			−0.491151
$58$	−8.23584e6	−	8.27624e6i	−0.727773	−	0.731343i
$59$	5.82950e6	−	8.02361e6i	0.481086	−	0.662158i	−0.497627	−	0.867391i	$-0.665795\pi$
$59$	5.82950e6	−	8.02361e6i	0.481086	−	0.662158i	0.978713	+	0.205233i	$0.0657951\pi$
$60$	−2.95451e6	−	2.10859e6i	−0.227971	−	0.162700i
$61$	−5.10299e6	+	3.70754e6i	−0.368558	+	0.267773i	−0.756613	−	0.653863i	$-0.773147\pi$
$61$	−5.10299e6	+	3.70754e6i	−0.368558	+	0.267773i	0.388055	+	0.921636i	$0.373147\pi$
$62$	1.96366e6	−	1.22047e7i	0.132892	−	0.825961i
$63$	9.79549e6	−	1.34823e7i	0.621819	−	0.855860i
$64$	1.60305e7	−	4.94962e6i	0.955491	−	0.295020i
$65$	2.50451e7	−	334653.i	1.40304	−	0.0187474i
$66$	4.85942e6	+	781850.i	0.256099	+	0.0412048i
$67$	−2.94518e7	+	9.56947e6i	−1.46155	+	0.474885i	−0.928542	−	0.371227i	$-0.878937\pi$
$67$	−2.94518e7	+	9.56947e6i	−1.46155	+	0.474885i	−0.533005	+	0.846112i	$0.678937\pi$
$68$	1.75538e7	−	2.39137e7i	0.820984	−	1.11844i
$69$	−2.60790e6	−	8.02630e6i	−0.115052	−	0.354095i
$70$	−2.71742e7	+	4.60854e6i	−1.13179	+	0.191942i
$71$	2.76946e6	+	899851.i	0.108984	+	0.0354109i	0.363001	−	0.931789i	$-0.381752\pi$
$71$	2.76946e6	+	899851.i	0.108984	+	0.0354109i	−0.254018	+	0.967200i	$0.581752\pi$
$72$	2.19834e7	+	1.14051e7i	0.818021	+	0.424395i
$73$	−8.00180e6	+	5.81365e6i	−0.281771	+	0.204719i	−0.719689	−	0.694296i	$-0.755716\pi$
$73$	−8.00180e6	+	5.81365e6i	−0.281771	+	0.204719i	0.437919	+	0.899015i	$0.355716\pi$
$74$	−5.03570e7	+	2.55031e7i	−1.67932	+	0.850485i
$75$	−5.01539e6	+	7.30593e6i	−0.158511	+	0.230903i
$76$	−4.71628e7	−	3.46197e7i	−1.41366	−	1.03769i
$77$	3.02361e7	−	2.19678e7i	0.860129	−	0.624920i
$78$	1.43730e7	−	2.24043e6i	0.388302	−	0.0605274i
$79$	2.10637e7	+	6.84401e6i	0.540787	+	0.175712i	0.566658	−	0.823953i	$-0.308236\pi$
$79$	2.10637e7	+	6.84401e6i	0.540787	+	0.175712i	−0.0258712	+	0.999665i	$0.508236\pi$
$80$	−1.27964e7	−	3.89098e7i	−0.312413	−	0.949946i
$81$	1.02537e7	+	3.15575e7i	0.238199	+	0.733100i
$82$	3.95242e7	−	2.00169e7i	0.874193	−	0.442733i
$83$	7.43986e6	−	2.41736e6i	0.156766	−	0.0509364i	−0.229583	−	0.973289i	$-0.573736\pi$
$83$	7.43986e6	−	2.41736e6i	0.156766	−	0.0509364i	0.386349	+	0.922353i	$0.373736\pi$
$84$	−1.52478e7	+	4.87192e6i	−0.306259	+	0.0978551i
$85$	−5.91556e7	−	4.17830e7i	−1.13324	−	0.800431i
$86$	4.36925e7	+	2.23973e7i	0.798754	+	0.409451i
$87$	−9.73076e6	+	1.33932e7i	−0.169852	+	0.233781i
$88$	3.89841e7	+	3.95607e7i	0.650064	+	0.659680i
$89$	1.96687e7	−	1.42902e7i	0.313485	−	0.227760i	−0.419905	−	0.907568i	$-0.637937\pi$
$89$	1.96687e7	−	1.42902e7i	0.313485	−	0.227760i	0.733390	+	0.679808i	$0.237937\pi$
$90$	2.68602e7	−	5.41697e7i	0.409392	−	0.825631i
$91$	6.49255e7	−	8.93622e7i	0.946781	−	1.30313i
$92$	2.98717e7	−	9.04272e7i	0.416973	−	1.26226i
$93$	−1.75273e7			−0.234306
$94$	1.70084e6	−	1.69253e6i	0.0217847	−	0.0216783i
$95$	−8.24048e7	+	1.16667e8i	−1.01172	+	1.43237i
$96$	−1.05394e7	−	2.13259e7i	−0.124089	−	0.251086i
$97$	−2.17117e7	+	6.68217e7i	−0.245249	+	0.754798i	0.750347	+	0.661044i	$0.229886\pi$
$97$	−2.17117e7	+	6.68217e7i	−0.245249	+	0.754798i	−0.995595	+	0.0937533i	$0.970114\pi$
$98$	−1.33711e7	+	2.60842e7i	−0.144965	+	0.282796i
$99$			8.19873e7i			0.853504i
$100$	−9.44085e7	+	3.29702e7i	−0.944085	+	0.329702i
$101$	1.16527e8			1.11980			0.559899	−	0.828561i	$-0.310840\pi$
$101$	1.16527e8			1.11980			0.559899	+	0.828561i	$0.310840\pi$
$102$	−3.74299e7	−	1.91870e7i	−0.345795	−	0.177258i
$103$	2.04858e8	+	6.65623e7i	1.82013	+	0.591397i	0.999810	+	0.0194966i	$0.00620636\pi$
$103$	2.04858e8	+	6.65623e7i	1.82013	+	0.591397i	0.820323	+	0.571900i	$0.193794\pi$
$104$	1.45708e8	+	7.55944e7i	1.24552	+	0.646184i
$105$	1.25719e7	+	3.70026e7i	0.103429	+	0.304422i
$106$	−5.12487e6	−	5.15002e6i	−0.0405938	−	0.0407929i
$107$		−	3.64071e7i		−	0.277748i	−0.990310	−	0.138874i	$-0.955652\pi$
$107$		−	3.64071e7i		−	0.277748i	0.990310	−	0.138874i	$-0.0443483\pi$
$108$	2.29664e7	−	6.95238e7i	0.168810	−	0.511020i
$109$	1.77701e8	+	1.29107e8i	1.25888	+	0.914629i	0.998702	−	0.0509323i	$-0.0162193\pi$
$109$	1.77701e8	+	1.29107e8i	1.25888	+	0.914629i	0.260176	+	0.965561i	$0.416219\pi$
$110$	9.48302e7	−	9.69231e7i	0.647703	−	0.661998i
$111$	4.70433e7	+	6.47495e7i	0.309888	+	0.426525i
$112$	−1.71237e8	−	5.74972e7i	−1.08824	−	0.365405i
$113$	1.00054e8	+	7.26936e7i	0.613650	+	0.445843i	0.850698	−	0.525655i	$-0.176180\pi$
$113$	1.00054e8	+	7.26936e7i	0.613650	+	0.445843i	−0.237047	+	0.971498i	$0.576180\pi$
$114$	−3.78408e7	+	7.38197e7i	−0.224048	+	0.437072i
$115$	−2.22064e8	−	6.88867e7i	−1.26966	−	0.393862i
$116$	−1.77951e8	+	5.68583e7i	−0.982805	+	0.314023i
$117$	7.48784e7	+	2.30452e8i	0.399589	+	1.22981i
$118$	−7.16947e7	−	1.41564e8i	−0.369793	−	0.730172i
$119$	−3.03754e8	+	9.86957e7i	−1.51473	+	0.492165i
$120$	−5.15868e7	+	2.66772e7i	−0.248779	+	0.128652i
$121$	9.42199e6	−	2.89979e7i	0.0439543	−	0.135277i
$122$	1.55438e7	+	9.97182e7i	0.0701644	+	0.450127i
$123$	−3.69233e7	−	5.08206e7i	−0.161317	−	0.222034i
$124$	−1.59442e8	−	1.17038e8i	−0.674396	−	0.495038i
$125$	8.46876e7	+	2.28982e8i	0.346880	+	0.937909i
$126$	−1.20471e8	−	2.37875e8i	−0.477969	−	0.943769i
$127$	−5.76834e7	−	7.93944e7i	−0.221736	−	0.305193i	0.683627	−	0.729831i	$-0.260401\pi$
$127$	−5.76834e7	−	7.93944e7i	−0.221736	−	0.305193i	−0.905363	+	0.424638i	$0.860401\pi$
$128$	4.65277e7	−	2.64372e8i	0.173329	−	0.984864i
$129$	2.15125e7	−	6.62088e7i	0.0776842	−	0.239087i
$130$	1.78032e8	−	3.59042e8i	0.623340	−	1.25711i
$131$	−4.03719e8	+	1.31176e8i	−1.37086	+	0.445420i	−0.899654	−	0.436603i	$-0.856181\pi$
$131$	−4.03719e8	+	1.31176e8i	−1.37086	+	0.445420i	−0.471207	+	0.882023i	$0.656181\pi$
$132$	4.65997e7	−	6.34833e7i	0.153493	−	0.209105i
$133$	1.94649e8	+	5.99067e8i	0.622078	+	1.91456i
$134$	−7.87074e7	+	4.89188e8i	−0.244116	+	1.51725i
$135$	−1.70731e8	−	5.29626e7i	−0.514017	−	0.159454i
$136$	−2.12370e8	−	4.24475e8i	−0.620780	−	1.24078i
$137$	−3.68515e8	−	2.67742e8i	−1.04610	−	0.760036i	−0.0746331	−	0.997211i	$-0.523779\pi$
$137$	−3.68515e8	−	2.67742e8i	−1.04610	−	0.760036i	−0.971467	+	0.237175i	$0.923779\pi$
$138$	−1.33315e8	−	2.14496e7i	−0.367590	−	0.0591429i
$139$	−2.12696e8	−	2.92750e8i	−0.569770	−	0.784221i	0.422758	−	0.906243i	$-0.361062\pi$
$139$	−2.12696e8	−	2.92750e8i	−0.569770	−	0.784221i	−0.992527	+	0.122022i	$0.961062\pi$
$140$	−1.32719e8	+	4.20551e8i	−0.345479	+	1.09473i
$141$	−2.75242e6	−	1.99975e6i	−0.00696368	−	0.00505941i
$142$	3.30258e7	−	3.28646e7i	0.0812269	−	0.0808303i
$143$			5.43420e8i			1.29955i
$144$	3.22840e8	−	2.29763e8i	0.750822	−	0.534355i
$145$	1.46722e8	+	4.31843e8i	0.331911	+	0.976909i
$146$	2.43736e7	+	1.56364e8i	0.0536423	+	0.344132i
$147$	3.95263e7	+	1.28429e7i	0.0846481	+	0.0275038i
$148$	−4.42010e6	+	9.03137e8i	−0.00921267	+	1.88238i
$149$	7.08633e7			0.143773			0.0718863	−	0.997413i	$-0.477098\pi$
$149$	7.08633e7			0.143773			0.0718863	+	0.997413i	$0.477098\pi$
$150$	6.74180e7	+	1.24734e8i	0.133171	+	0.246389i
$151$		−	2.05634e8i		−	0.395537i	−0.980249	−	0.197769i	$-0.936631\pi$
$151$		−	2.05634e8i		−	0.395537i	0.980249	−	0.197769i	$-0.0633695\pi$
$152$	−8.37153e8	+	4.18838e8i	−1.56831	+	0.784643i
$153$	2.16509e8	−	6.66346e8i	0.395103	−	1.21600i
$154$	−9.20995e7	−	5.90848e8i	−0.163747	−	1.05049i
$155$	−2.78583e8	+	3.94413e8i	−0.482645	+	0.683320i
$156$	7.30048e7	−	2.21000e8i	0.123269	−	0.373158i
$157$	9.78496e8			1.61050			0.805249	−	0.592937i	$-0.202032\pi$
$157$	9.78496e8			1.61050			0.805249	+	0.592937i	$0.202032\pi$
$158$	2.51185e8	−	2.49959e8i	0.403056	−	0.401088i
$159$	−6.05511e6	+	8.33414e6i	−0.00947400	+	0.0130398i
$160$	−6.47406e8	−	1.01792e8i	−0.987864	−	0.155322i
$161$	−8.29510e8	+	6.02675e8i	−1.23458	+	0.896973i
$162$	5.24164e8	+	8.43347e7i	0.761039	+	0.122447i
$163$	−4.43673e8	+	6.10663e8i	−0.628510	+	0.865070i	−0.997938	−	0.0641897i	$-0.979554\pi$
$163$	−4.43673e8	+	6.10663e8i	−0.628510	+	0.865070i	0.369428	+	0.929259i	$0.379554\pi$
$164$	3.46925e6	−	7.08854e8i	0.00479579	−	0.979900i
$165$	−1.57039e8	−	1.10921e8i	−0.211872	−	0.149650i
$166$	1.98824e7	−	1.23574e8i	0.0261840	−	0.162741i
$167$	5.07468e8	−	1.64887e8i	0.652444	−	0.211992i	0.0359525	−	0.999354i	$-0.488554\pi$
$167$	5.07468e8	−	1.64887e8i	0.652444	−	0.211992i	0.616491	+	0.787362i	$0.288554\pi$
$168$	−4.19211e7	+	2.52661e8i	−0.0526254	+	0.317176i
$169$	2.44227e8	+	7.51653e8i	0.299397	+	0.921448i
$170$	−1.02668e9	+	5.37312e8i	−1.22925	+	0.643326i
$171$	−1.31418e9	−	4.27001e8i	−1.53698	−	0.499396i
$172$	6.37798e8	−	4.58635e8i	0.728735	−	0.524027i
$173$	7.89718e8	−	5.73764e8i	0.881633	−	0.640544i	−0.0520500	−	0.998644i	$-0.516576\pi$
$173$	7.89718e8	−	5.73764e8i	0.881633	−	0.640544i	0.933683	+	0.358101i	$0.116576\pi$
$174$	1.19675e8	+	2.36303e8i	0.130559	+	0.257793i
$175$	1.03248e9	+	3.05225e8i	1.10085	+	0.325438i
$176$	8.47810e8	−	2.66324e8i	0.883584	−	0.277562i
$177$	−1.82025e8	+	1.32249e8i	−0.185454	+	0.134740i
$178$	−5.99112e7	−	3.84349e8i	−0.0596799	−	0.382865i
$179$	6.27141e8	+	2.03771e8i	0.610876	+	0.198486i	0.598085	−	0.801433i	$-0.295928\pi$
$179$	6.27141e8	+	2.03771e8i	0.610876	+	0.198486i	0.0127909	+	0.999918i	$0.495928\pi$
$180$	−5.75238e8	−	7.77812e8i	−0.547971	−	0.740943i
$181$	−1.49482e8	−	4.60057e8i	−0.139275	−	0.428645i	0.856955	−	0.515391i	$-0.172353\pi$
$181$	−1.49482e8	−	4.60057e8i	−0.139275	−	0.428645i	−0.996230	+	0.0867460i	$0.972353\pi$
$182$	−7.98493e8	−	1.57666e9i	−0.727756	−	1.43698i
$183$	1.36092e8	−	4.42191e7i	0.121347	−	0.0394281i
$184$	−1.06950e9	−	1.08532e9i	−0.933064	−	0.946865i
$185$	2.20475e9	−	2.94599e7i	1.88223	−	0.0251504i
$186$	−1.27927e8	+	2.49559e8i	−0.106883	+	0.208508i
$187$	9.23578e8	−	1.27120e9i	0.755279	−	1.03955i
$188$	−1.16848e7	−	3.65703e7i	−0.00935388	−	0.0292750i
$189$	−6.37758e8	+	4.63358e8i	−0.499814	+	0.363136i
$190$	1.05969e9	+	2.02482e9i	0.813141	+	1.55372i
$191$	8.26026e8	−	1.13693e9i	0.620669	−	0.854278i	−0.376732	−	0.926322i	$-0.622952\pi$
$191$	8.26026e8	−	1.13693e9i	0.620669	−	0.854278i	0.997401	+	0.0720443i	$0.0229523\pi$
$192$	−3.80569e8	−	5.58806e6i	−0.280045	−	0.00411203i
$193$	−1.32082e9			−0.951951			−0.475975	−	0.879459i	$-0.657905\pi$
$193$	−1.32082e9			−0.951951			−0.475975	+	0.879459i	$0.657905\pi$
$194$	7.92959e8	+	7.96849e8i	0.559814	+	0.562561i
$195$	−5.42714e8	−	1.68356e8i	−0.375346	−	0.116437i
$196$	2.73803e8	+	3.80763e8i	0.185530	+	0.258006i
$197$	−1.62501e8	+	5.00127e8i	−0.107892	+	0.332059i	−0.990398	−	0.138242i	$-0.955855\pi$
$197$	−1.62501e8	+	5.00127e8i	−0.107892	+	0.332059i	0.882506	+	0.470301i	$0.155855\pi$
$198$	1.16736e9	+	5.98402e8i	0.759527	+	0.389343i
$199$			2.13024e9i			1.35836i	0.733971	+	0.679181i	$0.237665\pi$
$199$			2.13024e9i			1.35836i	−0.733971	+	0.679181i	$0.762335\pi$
$200$	−2.19622e8	+	1.58486e9i	−0.137264	+	0.990535i
$201$	7.02531e8			0.430409
$202$	8.50494e8	−	1.65914e9i	0.510817	−	0.996500i
$203$	1.91289e9	+	6.21534e8i	1.12643	+	0.366000i
$204$	−5.46380e8	+	3.92897e8i	−0.315482	+	0.226860i
$205$	−1.73047e9	+	2.31225e7i	−0.979824	+	0.0130924i
$206$	2.44293e9	−	2.43100e9i	1.35657	−	1.34995i
$207$		−	2.24927e9i		−	1.22507i
$208$	2.13981e9	−	1.52289e9i	1.14320	−	0.813608i
$209$	−2.50707e9	−	1.82149e9i	−1.31396	−	0.954645i
$210$	6.18613e8	+	9.10693e7i	0.318084	+	0.0468268i
$211$	1.52940e9	+	2.10503e9i	0.771596	+	1.06201i	0.996160	+	0.0875519i	$0.0279044\pi$
$211$	1.52940e9	+	2.10503e9i	0.771596	+	1.06201i	−0.224564	+	0.974459i	$0.572096\pi$
$212$	−1.10732e8	+	3.53809e7i	−0.0548190	+	0.0175156i
$213$	−5.34448e7	−	3.88299e7i	−0.0259649	−	0.0188646i
$214$	−5.18375e8	−	2.65725e8i	−0.247166	−	0.126700i
$215$	−1.14795e9	−	1.53642e9i	−0.537242	−	0.719047i
$216$	−8.22274e8	−	8.34437e8i	−0.377748	−	0.383335i
$217$	6.58041e8	+	2.02524e9i	0.296766	+	0.913352i
$218$	3.13526e9	−	1.58784e9i	1.38818	−	0.703041i
$219$	2.13401e8	−	6.93382e7i	0.0927726	−	0.0301437i
$220$	−6.87881e8	−	2.05763e9i	−0.293645	−	0.878370i
$221$	1.43504e9	−	4.41661e9i	0.601584	−	1.85148i
$222$	1.26528e9	−	1.97227e8i	0.520923	−	0.0811999i
$223$	2.08884e9	+	2.87504e9i	0.844668	+	1.16259i	0.985013	+	0.172483i	$0.0551789\pi$
$223$	2.08884e9	+	2.87504e9i	0.844668	+	1.16259i	−0.140345	+	0.990103i	$0.544821\pi$
$224$	−2.06847e9	+	2.01846e9i	−0.821593	+	0.801730i
$225$	−1.87300e9	+	1.43882e9i	−0.730816	+	0.561405i
$226$	1.76530e9	−	8.94030e8i	0.676681	−	0.342703i
$227$	1.50097e9	+	2.06591e9i	0.565287	+	0.778051i	0.991987	−	0.126342i	$-0.0403238\pi$
$227$	1.50097e9	+	2.06591e9i	0.565287	+	0.778051i	−0.426700	+	0.904393i	$0.640324\pi$
$228$	7.74876e8	+	1.07758e9i	0.286743	+	0.398757i
$229$	1.00902e9	−	3.10546e9i	0.366910	−	1.12923i	−0.581866	−	0.813284i	$-0.697677\pi$
$229$	1.00902e9	−	3.10546e9i	0.366910	−	1.12923i	0.948776	−	0.315949i	$-0.102323\pi$
$230$	−2.60161e9	+	2.65903e9i	−0.929675	+	0.950193i
$231$	−8.06371e8	+	2.62006e8i	−0.283196	+	0.0920159i
$232$	−4.89245e8	+	2.94870e9i	−0.168878	+	1.01784i
$233$	−1.42942e8	−	4.39932e8i	−0.0484995	−	0.149266i	0.923874	−	0.382697i	$-0.125005\pi$
$233$	−1.42942e8	−	4.39932e8i	−0.0484995	−	0.149266i	−0.972373	+	0.233431i	$0.925005\pi$
$234$	3.82776e9	+	6.15863e8i	1.27668	+	0.205410i
$235$	−8.87473e7	+	3.01525e7i	−0.0290994	+	0.00988672i
$236$	−2.53891e9	−	1.24258e7i	−0.818463	−	0.00400569i
$237$	−4.06486e8	−	2.95330e8i	−0.128841	−	0.0936081i
$238$	−8.11756e8	+	5.04529e9i	−0.252998	+	1.57246i
$239$	−4.67236e8	−	6.43096e8i	−0.143201	−	0.197099i	0.731392	−	0.681957i	$-0.238871\pi$
$239$	−4.67236e8	−	6.43096e8i	−0.143201	−	0.197099i	−0.874593	+	0.484859i	$0.838871\pi$
$240$	3.32007e6	+	9.29217e8i	0.00100070	+	0.280074i
$241$	−6.75902e8	−	4.91072e8i	−0.200362	−	0.145572i	0.483080	−	0.875576i	$-0.339518\pi$
$241$	−6.75902e8	−	4.91072e8i	−0.200362	−	0.145572i	−0.683442	+	0.730004i	$0.739518\pi$
$242$	−3.44112e8	−	3.45800e8i	−0.100332	−	0.100824i
$243$		−	2.62928e9i		−	0.754071i
$244$	1.53327e9	+	5.06498e8i	0.432572	+	0.142895i
$245$	9.17239e8	−	6.85323e8i	0.254576	−	0.190209i
$246$	−9.93091e8	+	1.54800e8i	−0.271174	+	0.0422698i
$247$	−8.71049e9	−	2.83021e9i	−2.34021	−	0.760380i
$248$	−2.83013e9	+	1.41595e9i	−0.748170	+	0.374319i
$249$	−1.77467e8			−0.0461659
$250$	3.87842e9	+	4.65466e8i	0.992875	+	0.119159i
$251$		−	4.01372e9i		−	1.01123i	−0.862758	−	0.505617i	$-0.831265\pi$
$251$		−	4.01372e9i		−	1.01123i	0.862758	−	0.505617i	$-0.168735\pi$
$252$	−4.26621e9	−	2.08795e7i	−1.05789	−	0.00517748i
$253$	1.55878e9	−	4.79744e9i	0.380455	−	1.17092i
$254$	−1.55145e9	+	2.41836e8i	−0.372738	+	0.0581013i
$255$	9.83412e8	+	1.31620e9i	0.232581	+	0.311288i
$256$	−3.42462e9	−	2.59205e9i	−0.797356	−	0.603509i
$257$	−6.41920e9			−1.47146			−0.735730	−	0.677275i	$-0.763161\pi$
$257$	−6.41920e9			−1.47146			−0.735730	+	0.677275i	$0.763161\pi$
$258$	−7.85685e8	−	7.89540e8i	−0.177325	−	0.178195i
$259$	5.71547e9	−	7.86667e9i	1.27014	−	1.74820i
$260$	−3.81274e9	−	5.15542e9i	−0.834341	−	1.12816i
$261$	−3.56959e9	+	2.59346e9i	−0.769230	+	0.558878i
$262$	−1.07890e9	+	6.70568e9i	−0.228969	+	1.42311i
$263$	2.76502e9	−	3.80572e9i	0.577930	−	0.795452i	−0.415537	−	0.909576i	$-0.636406\pi$
$263$	2.76502e9	−	3.80572e9i	0.577930	−	0.795452i	0.993466	+	0.114124i	$0.0364062\pi$
$264$	−5.63775e8	−	1.12685e9i	−0.116062	−	0.231979i
$265$	9.12997e7	+	2.68721e8i	0.0185134	+	0.0544901i
$266$	9.95037e9	+	1.60095e9i	1.98753	+	0.319781i
$267$	−5.24548e8	+	1.70436e8i	−0.103214	+	0.0335364i
$268$	6.39074e9	+	4.69110e9i	1.23883	+	0.909360i
$269$	−1.11500e9	−	3.43163e9i	−0.212945	−	0.655378i	−0.999293	−	0.0375938i	$-0.988031\pi$
$269$	−1.11500e9	−	3.43163e9i	−0.212945	−	0.655378i	0.786348	−	0.617784i	$-0.211969\pi$
$270$	−2.00021e9	+	2.04436e9i	−0.376375	+	0.384682i
$271$	9.55205e9	+	3.10365e9i	1.77100	+	0.575434i	0.998242	−	0.0592627i	$-0.0188750\pi$
$271$	9.55205e9	+	3.10365e9i	1.77100	+	0.575434i	0.772761	+	0.634697i	$0.218875\pi$
$272$	−7.59382e9	−	7.43326e7i	−1.38735	−	0.0135801i
$273$	−2.02728e9	+	1.47291e9i	−0.364975	+	0.265170i
$274$	−6.50187e9	+	3.29285e9i	−1.15355	+	0.584212i
$275$	−4.99203e9	+	1.77082e9i	−0.872863	+	0.309630i
$276$	−1.27843e9	+	1.74163e9i	−0.220314	+	0.300136i
$277$	7.73171e8	−	5.61741e8i	0.131328	−	0.0954152i	−0.520182	−	0.854055i	$-0.674136\pi$
$277$	7.73171e8	−	5.61741e8i	0.131328	−	0.0954152i	0.651510	+	0.758640i	$0.274136\pi$
$278$	−5.72067e9	+	8.91720e8i	−0.957784	+	0.149296i
$279$	−4.44278e9	−	1.44355e9i	−0.733227	−	0.238240i
$280$	5.01925e9	+	4.95918e9i	0.816594	+	0.806821i
$281$	8.84544e8	+	2.72235e9i	0.141871	+	0.436635i	0.996595	−	0.0824478i	$-0.0262738\pi$
$281$	8.84544e8	+	2.72235e9i	0.141871	+	0.436635i	−0.854724	+	0.519082i	$0.826274\pi$
$282$	−4.85622e7	+	2.45942e7i	−0.00767895	+	0.00388898i
$283$	−7.86142e9	+	2.55433e9i	−1.22562	+	0.398227i	−0.849125	−	0.528192i	$-0.822870\pi$
$283$	−7.86142e9	+	2.55433e9i	−1.22562	+	0.398227i	−0.376493	+	0.926419i	$0.622870\pi$
$284$	−2.26889e8	−	7.10100e8i	−0.0348771	−	0.109156i
$285$	2.59583e9	−	1.93950e9i	0.393457	−	0.293974i
$286$	7.73737e9	+	3.96627e9i	1.15646	+	0.592813i
$287$	−4.48596e9	+	6.17440e9i	−0.661193	+	0.910054i
$288$	−9.15112e8	−	6.27366e9i	−0.133016	−	0.911908i
$289$	−5.21975e9	+	3.79237e9i	−0.748270	+	0.543650i
$290$	7.21959e9	+	1.06283e9i	1.02075	+	0.150270i
$291$	9.36892e8	−	1.28952e9i	0.130653	−	0.179828i
$292$	2.40425e9	+	7.94219e8i	0.330711	+	0.109247i
$293$	1.01787e10			1.38110			0.690548	−	0.723286i	$-0.257369\pi$
$293$	1.01787e10			1.38110			0.690548	+	0.723286i	$0.257369\pi$
$294$	4.71352e8	−	4.69051e8i	0.0630894	−	0.0627813i
$295$	8.28181e7	+	6.19803e9i	0.0109355	+	0.818400i
$296$	1.28269e10	+	6.65467e9i	1.67091	+	0.866881i
$297$	1.19845e9	−	3.68845e9i	0.154026	−	0.474043i
$298$	5.17210e8	−	1.00897e9i	0.0655847	−	0.127942i
$299$		−	1.49084e10i		−	1.86529i
$300$	2.26807e9	−	4.95160e7i	0.280009	−	0.00611309i
$301$	−8.45793e9			−1.03038
$302$	−2.92788e9	−	1.50086e9i	−0.351986	−	0.180432i
$303$	−2.51415e9	−	8.16897e8i	−0.298278	−	0.0969163i
$304$	−1.46600e8	+	1.49766e10i	−0.0171648	+	1.75355i
$305$	1.16803e9	−	3.76527e9i	0.134975	−	0.435108i
$306$	−7.90739e9	−	7.94619e9i	−0.901878	−	0.906302i
$307$			2.25662e9i			0.254042i	0.991900	+	0.127021i	$0.0405415\pi$
$307$			2.25662e9i			0.254042i	−0.991900	+	0.127021i	$0.959458\pi$
$308$	−9.08487e9	−	3.00109e9i	−1.00952	−	0.333485i
$309$	−3.95333e9	−	2.87226e9i	−0.433640	−	0.315058i
$310$	3.58246e9	+	6.84525e9i	0.387914	+	0.741212i
$311$	2.40671e9	+	3.31255e9i	0.257266	+	0.354096i	0.918039	−	0.396490i	$-0.129772\pi$
$311$	2.40671e9	+	3.31255e9i	0.257266	+	0.354096i	−0.660774	+	0.750585i	$0.729772\pi$
$312$	−2.61381e9	−	2.65248e9i	−0.275839	−	0.279919i
$313$	−4.64045e9	−	3.37148e9i	−0.483484	−	0.351272i	0.319189	−	0.947691i	$-0.396590\pi$
$313$	−4.64045e9	−	3.37148e9i	−0.483484	−	0.351272i	−0.802673	+	0.596419i	$0.796590\pi$
$314$	7.14176e9	−	1.39321e10i	0.734660	−	1.43317i
$315$	1.39162e8	+	1.04147e10i	0.0141344	+	1.05781i
$316$	−1.72566e9	−	5.40082e9i	−0.173064	−	0.541641i
$317$	2.25148e9	+	6.92936e9i	0.222963	+	0.686208i	0.998492	+	0.0548969i	$0.0174830\pi$
$317$	2.25148e9	+	6.92936e9i	0.222963	+	0.686208i	−0.775529	+	0.631311i	$0.782517\pi$
$318$	7.44694e7	+	1.47043e8i	0.00728232	+	0.0143792i
$319$	−9.41084e9	+	3.05777e9i	−0.908794	+	0.295285i
$320$	−6.17458e9	+	8.47501e9i	−0.588854	+	0.808240i
$321$	−2.55228e8	+	7.85512e8i	−0.0240386	+	0.0739831i
$322$	2.52670e9	+	1.62096e10i	0.235033	+	1.50781i
$323$	1.55659e10	+	2.14246e10i	1.43009	+	1.96835i
$324$	5.02650e9	−	6.84766e9i	0.456127	−	0.621387i
$325$	−1.24144e10	+	9.53665e9i	−1.11274	+	0.854796i
$326$	5.45656e9	+	1.07742e10i	0.483112	+	0.953925i
$327$	−2.92894e9	−	4.03134e9i	−0.256165	−	0.352581i
$328$	−1.00676e10	−	5.22312e9i	−0.869818	−	0.451268i
$329$	−1.27730e8	+	3.93114e8i	−0.0109021	+	0.0335533i
$330$	−2.72550e9	+	1.42639e9i	−0.229822	+	0.120277i
$331$	8.85901e9	−	2.87847e9i	0.738029	−	0.239800i	0.0842065	−	0.996448i	$-0.473164\pi$
$331$	8.85901e9	−	2.87847e9i	0.738029	−	0.239800i	0.653822	+	0.756648i	$0.273164\pi$
$332$	−1.61437e9	−	1.18503e9i	−0.132878	−	0.0975383i
$333$	6.59164e9	+	2.02870e10i	0.536064	+	1.64984i
$334$	1.35616e9	−	8.42894e9i	0.108975	−	0.677309i
$335$	1.11662e10	−	1.58089e10i	0.886594	−	1.25522i
$336$	3.29148e9	+	2.44098e9i	0.258247	+	0.191517i
$337$	1.07729e10	+	7.82699e9i	0.835245	+	0.606841i	0.921038	−	0.389472i	$-0.127342\pi$
$337$	1.07729e10	+	7.82699e9i	0.835245	+	0.606841i	−0.0857932	+	0.996313i	$0.527342\pi$
$338$	1.24848e10	+	2.00873e9i	0.956566	+	0.153906i
$339$	−1.64913e9	−	2.26984e9i	−0.124870	−	0.171868i
$340$	1.56982e8	+	1.85398e10i	0.0117472	+	1.38736i
$341$	−8.47555e9	−	6.15784e9i	−0.626831	−	0.455419i
$342$	−1.56716e10	+	1.55950e10i	−1.14553	+	1.13994i
$343$			1.08397e10i			0.783146i
$344$	−1.87507e9	−	1.24286e10i	−0.133901	−	0.887541i
$345$	4.30828e9	+	3.04304e9i	0.304108	+	0.214799i
$346$	−2.40549e9	−	1.54320e10i	−0.167841	−	1.07676i
$347$	−1.61247e10	−	5.23923e9i	−1.11218	−	0.361368i	−0.305399	−	0.952225i	$-0.598790\pi$
$347$	−1.61247e10	−	5.23923e9i	−1.11218	−	0.361368i	−0.806776	+	0.590857i	$0.798790\pi$
$348$	4.23802e9	+	2.07416e7i	0.288965	+	0.00141424i
$349$	−6.52771e9			−0.440006			−0.220003	−	0.975499i	$-0.570607\pi$
$349$	−6.52771e9			−0.440006			−0.220003	+	0.975499i	$0.570607\pi$
$350$	1.18817e10	−	1.24730e10i	0.791780	−	0.831186i
$351$		−	1.14621e10i		−	0.755156i
$352$	2.39592e9	−	1.40152e10i	0.156064	−	0.912910i
$353$	7.40966e9	−	2.28046e10i	0.477199	−	1.46867i	−0.365770	−	0.930705i	$-0.619194\pi$
$353$	7.40966e9	−	2.28046e10i	0.477199	−	1.46867i	0.842969	−	0.537963i	$-0.180806\pi$
$354$	5.54448e8	+	3.55696e9i	0.0353060	+	0.226499i
$355$	−1.72324e9	+	5.85483e8i	−0.108501	+	0.0368639i
$356$	−5.90975e9	−	1.95222e9i	−0.367933	−	0.121543i
$357$	7.24562e9			0.446070
$358$	7.47867e9	−	7.44215e9i	0.455294	−	0.453071i
$359$	1.57672e10	−	2.17017e10i	0.949241	−	1.30652i	−0.00262294	−	0.999997i	$-0.500835\pi$
$359$	1.57672e10	−	2.17017e10i	0.949241	−	1.30652i	0.951864	−	0.306521i	$-0.0991651\pi$
$360$	−1.52732e10	+	2.51338e9i	−0.909328	+	0.149640i
$361$	2.85139e10	−	2.07165e10i	1.67891	−	1.21980i
$362$	−7.64145e9	−	1.22946e9i	−0.444981	−	0.0715947i
$363$	−4.06573e8	+	5.59600e8i	−0.0234160	+	0.0322293i
$364$	−2.82769e10	−	1.38392e8i	−1.61074	−	0.00788323i
$365$	1.83154e9	−	5.90417e9i	0.103192	−	0.332650i
$366$	3.63695e8	−	2.26046e9i	0.0202681	−	0.125972i
$367$	−1.48769e10	+	4.83379e9i	−0.820064	+	0.266455i	−0.688854	−	0.724900i	$-0.741886\pi$
$367$	−1.48769e10	+	4.83379e9i	−0.820064	+	0.266455i	−0.131210	+	0.991355i	$0.541886\pi$
$368$	−2.32592e10	+	7.30645e9i	−1.26824	+	0.398396i
$369$	−5.17365e9	−	1.59229e10i	−0.279056	−	0.858847i
$370$	1.56724e10	−	3.16069e10i	0.836235	−	1.68646i
$371$	1.19032e9	+	3.86759e8i	0.0628303	+	0.0204148i
$372$	2.61959e9	+	3.64292e9i	0.136793	+	0.190230i
$373$	1.01528e10	−	7.37644e9i	0.524506	−	0.381076i	−0.293793	−	0.955869i	$-0.594917\pi$
$373$	1.01528e10	−	7.37644e9i	0.524506	−	0.381076i	0.818299	+	0.574793i	$0.194917\pi$
$374$	−1.13587e10	−	2.24283e10i	−0.580555	−	1.14633i
$375$	−2.21948e8	−	5.53415e9i	−0.0112234	−	0.279850i
$376$	−6.05983e8	−	1.00544e8i	−0.0303186	−	0.00503042i
$377$	−2.36596e10	+	1.71897e10i	−1.17123	+	0.850948i
$378$	1.94262e9	+	1.24625e10i	0.0951524	+	0.610433i
$379$	2.61589e10	+	8.49953e9i	1.26783	+	0.411944i	0.864279	−	0.503012i	$-0.167775\pi$
$379$	2.61589e10	+	8.49953e9i	1.26783	+	0.411944i	0.403553	+	0.914956i	$0.367775\pi$
$380$	3.65644e10	−	3.09602e8i	1.75358	−	0.0148480i
$381$	6.87978e8	+	2.11738e9i	0.0326493	+	0.100484i
$382$	−1.01590e10	−	2.00593e10i	−0.477086	−	0.942025i
$383$	5.58615e9	−	1.81505e9i	0.259608	−	0.0843517i	−0.176321	−	0.984333i	$-0.556420\pi$
$383$	5.58615e9	−	1.81505e9i	0.259608	−	0.0843517i	0.435929	+	0.899981i	$0.356420\pi$
$384$	−2.85723e9	+	5.37786e9i	−0.131407	+	0.247334i
$385$	−6.92077e9	+	2.23099e10i	−0.315001	+	1.01544i
$386$	−9.64029e9	+	1.88062e10i	−0.434251	+	0.847134i
$387$	1.09059e10	−	1.50106e10i	0.486202	−	0.669199i
$388$	1.71333e10	−	5.47440e9i	0.755989	−	0.241552i
$389$	−8.10207e8	+	5.88650e8i	−0.0353832	+	0.0257074i	−0.605336	−	0.795970i	$-0.706961\pi$
$389$	−8.10207e8	+	5.88650e8i	−0.0353832	+	0.0257074i	0.569953	+	0.821677i	$0.306961\pi$
$390$	−6.35821e9	+	6.49853e9i	−0.274838	+	0.280903i
$391$	−2.53378e10	+	3.48745e10i	−1.08408	+	1.49211i
$392$	7.41982e9	−	1.11941e9i	0.314231	−	0.0474073i
$393$	9.63013e9			0.403703
$394$	5.93490e9	+	5.96402e9i	0.246280	+	0.247488i
$395$	−1.31065e10	+	4.45302e9i	−0.538391	+	0.182922i
$396$	1.70404e10	−	1.22536e10i	0.692946	−	0.498292i
$397$	−3.35311e9	+	1.03198e10i	−0.134985	+	0.415442i	−0.995588	−	0.0938355i	$-0.970087\pi$
$397$	−3.35311e9	+	1.03198e10i	−0.134985	+	0.415442i	0.860603	+	0.509277i	$0.170087\pi$
$398$	3.03309e10	+	1.55480e10i	1.20880	+	0.619644i
$399$		−	1.42899e10i		−	0.563816i
$400$	2.09627e10	+	1.46944e10i	0.818854	+	0.574002i
$401$	−1.44989e10			−0.560734			−0.280367	−	0.959893i	$-0.590456\pi$
$401$	−1.44989e10			−0.560734			−0.280367	+	0.959893i	$0.590456\pi$
$402$	5.12757e9	−	1.00028e10i	0.196339	−	0.383018i
$403$	−2.94472e10	−	9.56798e9i	−1.11641	−	0.362744i
$404$	−1.74158e10	−	2.42192e10i	−0.653759	−	0.909146i
$405$	−1.69391e10	−	1.19645e10i	−0.629610	−	0.444708i
$406$	2.28112e10	−	2.26998e10i	0.839545	−	0.835446i
$407$			4.78380e10i			1.74339i
$408$	1.60631e9	+	1.06472e10i	0.0579682	+	0.384232i
$409$	2.47888e10	+	1.80101e10i	0.885854	+	0.643611i	0.934794	−	0.355191i	$-0.115584\pi$
$409$	2.47888e10	+	1.80101e10i	0.885854	+	0.643611i	−0.0489397	+	0.998802i	$0.515584\pi$
$410$	−1.23010e10	+	2.48077e10i	−0.435315	+	0.877911i
$411$	6.07402e9	+	8.36018e9i	0.212867	+	0.292987i
$412$	−1.67831e10	−	5.25263e10i	−0.582482	−	1.82301i
$413$	2.21149e10	+	1.60674e10i	0.760124	+	0.552262i
$414$	−3.20258e10	−	1.64168e10i	−1.09018	−	0.558839i
$415$	−2.82070e9	+	3.99349e9i	−0.0950965	+	0.134636i
$416$	−6.06546e9	−	4.15824e10i	−0.202530	−	1.38847i
$417$	2.53678e9	+	7.80739e9i	0.0838954	+	0.258203i
$418$	−4.42333e10	+	2.24018e10i	−1.44892	+	0.733800i
$419$	7.98160e9	−	2.59338e9i	0.258961	−	0.0841414i	−0.176659	−	0.984272i	$-0.556529\pi$
$419$	7.98160e9	−	2.59338e9i	0.258961	−	0.0841414i	0.435620	+	0.900131i	$0.356529\pi$
$420$	5.81175e9	−	8.14330e9i	0.186771	−	0.261700i
$421$	−5.41124e9	+	1.66541e10i	−0.172254	+	0.530142i	−0.999497	−	0.0317011i	$-0.989908\pi$
$421$	−5.41124e9	+	1.66541e10i	−0.172254	+	0.530142i	0.827244	+	0.561843i	$0.189908\pi$
$422$	4.11347e10	−	6.41195e9i	1.29706	−	0.202181i
$423$	−5.32977e8	−	7.33580e8i	−0.0166474	−	0.0229132i
$424$	−3.04440e8	+	1.83487e9i	−0.00941972	+	0.0567731i
$425$	4.52487e10	−	1.20944e9i	1.38692	−	0.0370706i
$426$	−9.42950e8	+	4.77554e8i	−0.0286319	+	0.0145005i
$427$	−1.02188e10	−	1.40650e10i	−0.307390	−	0.423086i
$428$	−7.56694e9	+	5.44132e9i	−0.225499	+	0.162155i
$429$	3.80959e9	−	1.17247e10i	0.112473	−	0.346157i
$430$	−3.02546e10	+	5.13095e9i	−0.884949	+	0.150080i
$431$	1.82685e10	−	5.93578e9i	0.529411	−	0.172016i	−0.0321010	−	0.999485i	$-0.510220\pi$
$431$	1.82685e10	−	5.93578e9i	0.529411	−	0.172016i	0.561512	+	0.827469i	$0.310220\pi$
$432$	−1.78825e10	+	5.61746e9i	−0.513444	+	0.161289i
$433$	−1.24242e10	−	3.82377e10i	−0.353440	−	1.08778i	−0.956908	−	0.290390i	$-0.906215\pi$
$433$	−1.24242e10	−	3.82377e10i	−0.353440	−	1.08778i	0.603468	−	0.797387i	$-0.293785\pi$
$434$	3.36389e10	+	5.41228e9i	0.948161	+	0.152553i
$435$	−1.38242e8	−	1.03459e10i	−0.00386086	−	0.288943i
$436$	2.75198e8	−	5.62299e10i	0.00761552	−	1.55604i
$437$	6.87799e10	+	4.99715e10i	1.88597	+	1.37024i
$438$	5.70295e8	−	3.54454e9i	0.0154954	−	0.0963083i
$439$	6.40909e8	+	8.82136e8i	0.0172559	+	0.0237508i	0.817558	−	0.575847i	$-0.195327\pi$
$439$	6.40909e8	+	8.82136e8i	0.0172559	+	0.0237508i	−0.800302	+	0.599597i	$0.795327\pi$
$440$	−3.43178e10	−	5.22383e9i	−0.915607	−	0.139373i
$441$	8.96129e9	+	6.51076e9i	0.236928	+	0.172138i
$442$	−5.24110e10	−	5.26681e10i	−1.37320	−	1.37994i
$443$			3.91864e10i			1.01747i	0.860924	+	0.508734i	$0.169886\pi$
$443$			3.91864e10i			1.01747i	−0.860924	+	0.508734i	$0.830114\pi$
$444$	6.42671e9	−	1.94549e10i	0.165370	−	0.500607i
$445$	−4.50200e9	+	1.45127e10i	−0.114806	+	0.370091i
$446$	5.61815e10	−	8.75741e9i	1.41989	−	0.221328i
$447$	−1.52893e9	−	4.96779e8i	−0.0382963	−	0.0124432i
$448$	1.36423e10	+	4.41836e10i	0.338668	+	1.09685i
$449$	−2.84703e10			−0.700497			−0.350249	−	0.936657i	$-0.613903\pi$
$449$	−2.84703e10			−0.700497			−0.350249	+	0.936657i	$0.613903\pi$
$450$	6.81583e9	+	3.71699e10i	0.166214	+	0.906444i
$451$		−	3.75471e10i		−	0.907549i
$452$	1.54950e8	−	3.16601e10i	0.00371225	−	0.758505i
$453$	−1.44158e9	+	4.43671e9i	−0.0342330	+	0.105358i
$454$	4.03702e10	−	6.29278e9i	0.950249	−	0.148122i
$455$	9.22379e8	+	6.90300e10i	0.0215211	+	1.61062i
$456$	2.09984e10	−	3.16799e9i	0.485655	−	0.0732696i
$457$	−4.37713e9			−0.100352			−0.0501758	−	0.998740i	$-0.515978\pi$
$457$	−4.37713e9			−0.100352			−0.0501758	+	0.998740i	$0.515978\pi$
$458$	−3.68518e10	−	3.70326e10i	−0.837523	−	0.841632i
$459$	−1.94806e10	+	2.68128e10i	−0.438887	+	0.604076i
$460$	1.88716e10	+	5.64500e10i	0.421480	+	1.26076i
$461$	−5.63053e10	+	4.09082e10i	−1.24665	+	0.905746i	−0.998023	−	0.0628529i	$-0.979980\pi$
$461$	−5.63053e10	+	4.09082e10i	−1.24665	+	0.905746i	−0.248629	+	0.968599i	$0.579980\pi$
$462$	−2.15496e9	+	1.33936e10i	−0.0473010	+	0.293989i
$463$	1.62733e10	−	2.23982e10i	0.354120	−	0.487404i	−0.594379	−	0.804185i	$-0.702602\pi$
$463$	1.62733e10	−	2.23982e10i	0.354120	−	0.487404i	0.948499	+	0.316781i	$0.102602\pi$
$464$	3.84136e10	+	2.84877e10i	0.828730	+	0.614591i
$465$	8.77563e9	−	6.55678e9i	0.187701	−	0.140242i
$466$	−7.30717e9	−	1.17568e9i	−0.154955	−	0.0249313i
$467$	3.75040e9	−	1.21858e9i	0.0788516	−	0.0256204i	−0.269326	−	0.963049i	$-0.586801\pi$
$467$	3.75040e9	−	1.21858e9i	0.0788516	−	0.0256204i	0.348177	+	0.937429i	$0.386801\pi$
$468$	3.67065e10	−	5.00057e10i	0.765174	−	1.04240i
$469$	−2.63756e10	−	8.11758e10i	−0.545144	−	1.67778i
$470$	−2.18421e8	+	1.48368e9i	−0.00447614	+	0.0304054i
$471$	−2.11118e10	−	6.85964e9i	−0.428984	−	0.139385i
$472$	−1.87077e10	+	3.60590e10i	−0.376922	+	0.726517i
$473$	3.36636e10	−	2.44580e10i	0.672537	−	0.488627i
$474$	−7.17181e9	+	3.63214e9i	−0.142074	+	0.0719531i
$475$	−2.38528e9	−	8.92400e10i	−0.0468559	−	1.75301i
$476$	6.59115e10	+	4.83821e10i	1.28391	+	0.942448i
$477$	−2.22123e9	+	1.61382e9i	−0.0429062	+	0.0311732i
$478$	−1.25668e10	+	1.95888e9i	−0.240721	+	0.0375228i
$479$	2.48259e10	+	8.06642e9i	0.471588	+	0.153228i	0.535163	−	0.844749i	$-0.320250\pi$
$479$	2.48259e10	+	8.06642e9i	0.471588	+	0.153228i	−0.0635751	+	0.997977i	$0.520250\pi$
$480$	1.32547e10	+	6.73481e9i	0.249692	+	0.126871i
$481$	4.36901e10	+	1.34464e11i	0.816211	+	2.51204i
$482$	−1.19252e10	+	6.03950e9i	−0.220942	+	0.111896i
$483$	2.21223e10	−	7.18797e9i	0.406483	−	0.132074i
$484$	−7.43518e9	+	2.37567e9i	−0.135491	+	0.0432917i
$485$	−1.41266e10	−	4.15785e10i	−0.255311	−	0.751453i
$486$	−3.74365e10	−	1.91904e10i	−0.671042	−	0.343984i
$487$	7.37908e8	−	1.01564e9i	0.0131186	−	0.0180562i	−0.802407	−	0.596777i	$-0.796448\pi$
$487$	7.37908e8	−	1.01564e9i	0.0131186	−	0.0180562i	0.815526	+	0.578721i	$0.196448\pi$
$488$	1.84025e10	−	1.81343e10i	0.324488	−	0.319758i
$489$	1.38536e10	−	1.00652e10i	0.242285	−	0.176030i
$490$	−3.06315e9	−	1.80619e10i	−0.0531355	−	0.313313i
$491$	7.52217e9	−	1.03534e10i	0.129425	−	0.178138i	−0.739387	−	0.673281i	$-0.764884\pi$
$491$	7.52217e9	−	1.03534e10i	0.129425	−	0.178138i	0.868811	+	0.495143i	$0.164884\pi$
$492$	−5.04420e9	+	1.52698e10i	−0.0860858	+	0.260598i
$493$	8.45608e10			1.43147
$494$	−1.03873e11	+	1.03366e11i	−1.74419	+	1.73567i
$495$	−3.06705e10	−	4.10496e10i	−0.510858	−	0.683735i
$496$	−4.95603e8	+	5.06309e10i	−0.00818856	+	0.836544i
$497$	−2.48019e9	+	7.63325e9i	−0.0406499	+	0.125108i
$498$	−1.29528e9	+	2.52683e9i	−0.0210595	+	0.0410827i
$499$			9.71748e10i			1.56730i	0.621204	+	0.783649i	$0.286644\pi$
$499$			9.71748e10i			1.56730i	−0.621204	+	0.783649i	$0.713356\pi$
$500$	3.49349e10	−	5.18247e10i	0.558958	−	0.829196i
$501$	−1.21049e10			−0.192137
$502$	−5.71484e10	−	2.92950e10i	−0.899890	−	0.461294i
$503$	1.75468e10	+	5.70129e9i	0.274110	+	0.0890638i	0.442847	−	0.896597i	$-0.353969\pi$
$503$	1.75468e10	+	5.70129e9i	0.274110	+	0.0890638i	−0.168736	+	0.985661i	$0.553969\pi$
$504$	−3.14351e10	+	6.05911e10i	−0.487184	+	0.939046i
$505$	−5.83428e10	+	4.35913e10i	−0.897060	+	0.670246i
$506$	−5.69302e10	−	5.72095e10i	−0.868442	−	0.872703i
$507$		−	1.79296e10i		−	0.271356i
$508$	−7.88029e9	+	2.38551e10i	−0.118328	+	0.358201i
$509$	−4.47383e10	−	3.25043e10i	−0.666513	−	0.484250i	0.202343	−	0.979315i	$-0.435144\pi$
$509$	−4.47383e10	−	3.25043e10i	−0.666513	−	0.484250i	−0.868856	+	0.495065i	$0.835144\pi$
$510$	2.59181e10	−	4.39551e9i	0.383110	−	0.0649724i
$511$	−1.60237e10	−	2.20548e10i	−0.235007	−	0.323459i
$512$	−6.19017e10	+	2.98420e10i	−0.900788	+	0.434259i
$513$	5.28805e10	+	3.84199e10i	0.763530	+	0.554737i
$514$	−4.68519e10	+	9.13985e10i	−0.671235	+	1.30944i
$515$	−1.27469e11	+	4.33084e10i	−1.81207	+	0.615663i
$516$	−1.69762e10	+	5.42419e9i	−0.239465	+	0.0765131i
$517$	−6.28396e8	−	1.93401e9i	−0.00879572	−	0.0270704i
$518$	−7.02924e10	−	1.38795e11i	−0.976313	−	1.92777i
$519$	−2.10611e10	+	6.84316e9i	−0.290276	+	0.0943164i
$520$	−1.01232e11	+	1.66589e10i	−1.38454	+	0.227842i
$521$	1.20605e10	−	3.71183e10i	0.163687	−	0.503776i	−0.835250	−	0.549870i	$-0.814677\pi$
$521$	1.20605e10	−	3.71183e10i	0.163687	−	0.503776i	0.998937	+	0.0460937i	$0.0146773\pi$
$522$	1.08730e10	+	6.97538e10i	0.146443	+	0.939476i
$523$	2.97545e10	+	4.09536e10i	0.397692	+	0.547376i	0.960163	−	0.279441i	$-0.0901492\pi$
$523$	2.97545e10	+	4.09536e10i	0.397692	+	0.547376i	−0.562471	+	0.826817i	$0.690149\pi$
$524$	8.76028e10	+	6.43045e10i	1.16196	+	0.852936i
$525$	−2.01368e10	−	1.38236e10i	−0.265065	−	0.181963i
$526$	−3.40059e10	−	6.71460e10i	−0.444233	−	0.877157i
$527$	5.26230e10	+	7.24294e10i	0.682234	+	0.939015i
$528$	−2.01592e10	−	1.97330e8i	−0.259380	−	0.00253896i
$529$	−1.85649e10	+	5.71367e10i	−0.237066	+	0.729613i
$530$	4.49249e9	+	6.61364e8i	0.0569356	+	0.00838180i
$531$	−5.70310e10	+	1.85305e10i	−0.717353	+	0.233082i
$532$	9.54198e10	−	1.29991e11i	1.19122	−	1.62281i
$533$	−3.42915e10	−	1.05538e11i	−0.424891	−	1.30768i
$534$	−1.40181e9	+	8.71263e9i	−0.0172395	+	0.107148i
$535$	1.36195e10	+	1.82284e10i	0.166244	+	0.222502i
$536$	1.13437e11	−	5.67542e10i	1.37435	−	0.687604i
$537$	−1.21025e10	−	8.79301e9i	−0.145539	−	0.105740i
$538$	−5.69987e10	−	9.17074e9i	−0.680355	−	0.109465i
$539$	1.46013e10	+	2.00970e10i	0.172997	+	0.238110i
$540$	1.45092e10	+	4.34008e10i	0.170635	+	0.510414i
$541$	−3.49328e10	−	2.53801e10i	−0.407797	−	0.296282i	0.364912	−	0.931042i	$-0.381099\pi$
$541$	−3.49328e10	−	2.53801e10i	−0.407797	−	0.296282i	−0.772709	+	0.634760i	$0.781099\pi$
$542$	1.13908e11	−	1.13352e11i	1.31995	−	1.31351i
$543$			1.09740e10i			0.126231i
$544$	−5.64835e10	+	1.07580e11i	−0.644950	+	1.22839i
$545$	−1.37269e11	+	1.83419e9i	−1.55592	+	0.0207902i
$546$	6.17512e9	+	3.96153e10i	0.0694824	+	0.445751i
$547$	−9.87187e10	−	3.20756e10i	−1.10268	−	0.358283i	−0.299547	−	0.954081i	$-0.596836\pi$
$547$	−9.87187e10	−	3.20756e10i	−1.10268	−	0.358283i	−0.803134	+	0.595799i	$0.796836\pi$
$548$	−5.70705e8	+	1.16609e11i	−0.00632833	+	1.29304i
$549$	3.81382e10			0.419827
$550$	−1.12220e10	+	8.40026e10i	−0.122636	+	0.917999i
$551$		−	1.66772e11i		−	1.80932i
$552$	1.54668e10	+	3.09143e10i	0.166589	+	0.332969i
$553$	−1.88636e10	+	5.80563e10i	−0.201709	+	0.620796i
$554$	−2.35509e9	−	1.51086e10i	−0.0250016	−	0.160393i
$555$	−4.77758e10	−	1.48206e10i	−0.503542	−	0.156204i
$556$	−2.90569e10	+	8.79609e10i	−0.304054	+	0.920430i
$557$	4.72167e10			0.490540			0.245270	−	0.969455i	$-0.421123\pi$
$557$	4.72167e10			0.490540			0.245270	+	0.969455i	$0.421123\pi$
$558$	−5.29802e10	+	5.27216e10i	−0.546484	+	0.543815i
$559$	7.22852e10	−	9.94921e10i	0.740291	−	1.01892i
$560$	1.07244e11	−	3.52699e10i	1.09049	−	0.358634i
$561$	−2.88385e10	+	2.09524e10i	−0.291153	+	0.211535i
$562$	4.52176e10	+	7.27523e9i	0.453275	+	0.0729292i
$563$	5.78914e8	−	7.96807e8i	0.00576210	−	0.00793085i	−0.806126	−	0.591744i	$-0.798440\pi$
$563$	5.78914e8	−	7.96807e8i	0.00576210	−	0.00793085i	0.811888	+	0.583813i	$0.198440\pi$
$564$	−4.26256e6	+	8.70948e8i	−4.21264e−5	+	0.00860747i
$565$	−7.72891e10	+	1.03274e9i	−0.758446	+	0.0101344i
$566$	−2.10089e10	+	1.30576e11i	−0.204710	+	1.27233i
$567$	−8.69797e10	+	2.82614e10i	−0.841561	+	0.273440i
$568$	−1.17666e10	−	1.95230e9i	−0.113047	−	0.0187566i
$569$	2.86757e9	+	8.82549e9i	0.0273568	+	0.0841956i	0.963803	−	0.266616i	$-0.0859056\pi$
$569$	2.86757e9	+	8.82549e9i	0.0273568	+	0.0841956i	−0.936446	+	0.350812i	$0.885906\pi$
$570$	−8.66888e9	−	5.11160e10i	−0.0821227	−	0.484237i
$571$	−5.91490e10	−	1.92187e10i	−0.556421	−	0.180792i	0.0172894	−	0.999851i	$-0.494496\pi$
$571$	−5.91490e10	−	1.92187e10i	−0.556421	−	0.180792i	−0.573710	+	0.819059i	$0.694496\pi$
$572$	1.12946e11	−	8.12182e10i	1.05508	−	0.758699i
$573$	−2.57925e10	+	1.87393e10i	−0.239262	+	0.173834i
$574$	5.51711e10	+	1.08938e11i	0.508234	+	1.00353i
$575$	1.36953e11	−	4.85813e10i	1.25286	−	0.444425i
$576$	−9.60053e10	−	3.27600e10i	−0.872178	−	0.297614i
$577$	9.88882e10	−	7.18465e10i	0.892157	−	0.648190i	−0.0442823	−	0.999019i	$-0.514100\pi$
$577$	9.88882e10	−	7.18465e10i	0.892157	−	0.648190i	0.936440	+	0.350829i	$0.114100\pi$
$578$	1.58994e10	+	1.02000e11i	0.142452	+	0.913876i
$579$	2.84977e10	+	9.25947e9i	0.253569	+	0.0823895i
$580$	6.78266e10	−	9.50372e10i	0.599361	−	0.839811i
$581$	6.66278e9	+	2.05059e10i	0.0584724	+	0.179960i
$582$	−1.15225e10	−	2.27516e10i	−0.100428	−	0.198299i
$583$	−5.85603e9	+	1.90274e9i	−0.0506908	+	0.0164704i
$584$	2.88563e10	−	2.84357e10i	0.248078	−	0.244462i
$585$	−1.23700e11	−	8.73721e10i	−1.05620	−	0.746018i
$586$	7.42918e10	−	1.44928e11i	0.630014	−	1.22903i
$587$	8.34362e10	−	1.14840e11i	0.702752	−	0.967256i	−0.297170	−	0.954824i	$-0.596043\pi$
$587$	8.34362e10	−	1.14840e11i	0.702752	−	0.967256i	0.999923	−	0.0124311i	$-0.00395704\pi$
$588$	−3.23822e9	−	1.01347e10i	−0.0270892	−	0.0847817i
$589$	1.42846e11	−	1.03784e11i	1.18688	−	0.862319i
$590$	8.88538e10	+	4.40584e10i	0.733277	+	0.363598i
$591$	7.01217e9	−	9.65142e9i	0.0574781	−	0.0791118i
$592$	1.88371e11	−	1.34062e11i	1.53365	−	1.09149i
$593$	1.84179e10			0.148943			0.0744715	−	0.997223i	$-0.476273\pi$
$593$	1.84179e10			0.148943			0.0744715	+	0.997223i	$0.476273\pi$
$594$	−4.37700e10	−	4.39848e10i	−0.351586	−	0.353311i
$595$	1.15163e11	−	1.63046e11i	0.918854	−	1.30090i
$596$	−1.05911e10	−	1.47284e10i	−0.0839371	−	0.116727i
$597$	1.49338e10	−	4.59615e10i	0.117564	−	0.361824i
$598$	−2.12270e11	−	1.08812e11i	−1.65991	−	0.850888i
$599$			3.55347e10i			0.276023i	0.990431	+	0.138012i	$0.0440711\pi$
$599$			3.55347e10i			0.276023i	−0.990431	+	0.138012i	$0.955929\pi$
$600$	1.58490e10	−	3.26548e10i	0.122291	−	0.251966i
$601$	−1.23230e11			−0.944539			−0.472270	−	0.881454i	$-0.656565\pi$
$601$	−1.23230e11			−0.944539			−0.472270	+	0.881454i	$0.656565\pi$
$602$	−6.17320e10	+	1.20426e11i	−0.470028	+	0.916929i
$603$	1.78076e11	+	5.78603e10i	1.34690	+	0.437634i
$604$	−4.27395e10	+	3.07336e10i	−0.321130	+	0.230922i
$605$	6.13037e9	+	1.80434e10i	0.0457578	+	0.134678i
$606$	−2.99813e10	+	2.98349e10i	−0.222310	+	0.221225i
$607$			1.27831e11i			0.941633i	0.882231	+	0.470816i	$0.156041\pi$
$607$			1.27831e11i			0.941633i	−0.882231	+	0.470816i	$0.843959\pi$
$608$	2.12171e11	+	1.11397e11i	1.55265	+	0.815193i
$609$	−3.69148e10	−	2.68202e10i	−0.268368	−	0.194981i
$610$	−4.50859e10	−	4.41124e10i	−0.325628	−	0.318597i
$611$	−3.53263e9	−	4.86224e9i	−0.0253474	−	0.0348877i
$612$	−1.70854e11	+	5.45908e10i	−1.21792	+	0.389147i
$613$	−4.82676e10	−	3.50684e10i	−0.341833	−	0.248356i	0.403602	−	0.914935i	$-0.367758\pi$
$613$	−4.82676e10	−	3.50684e10i	−0.341833	−	0.248356i	−0.745435	+	0.666579i	$0.767758\pi$
$614$	3.21304e10	+	1.64704e10i	0.226070	+	0.115886i
$615$	3.74983e10	+	1.16324e10i	0.262126	+	0.0813145i
$616$	−1.09038e11	+	1.07449e11i	−0.757279	+	0.746241i
$617$	1.94794e10	+	5.99513e10i	0.134411	+	0.413674i	0.995498	−	0.0947836i	$-0.0302159\pi$
$617$	1.94794e10	+	5.99513e10i	0.134411	+	0.413674i	−0.861087	+	0.508457i	$0.830216\pi$
$618$	−6.97503e10	+	3.53248e10i	−0.478181	+	0.242173i
$619$	1.23057e11	−	3.99836e10i	0.838191	−	0.272345i	0.141700	−	0.989910i	$-0.454743\pi$
$619$	1.23057e11	−	3.99836e10i	0.838191	−	0.272345i	0.696492	+	0.717565i	$0.254743\pi$
$620$	1.23612e11	−	1.04666e9i	0.836554	−	0.00708334i
$621$	−3.28787e10	+	1.01190e11i	−0.221080	+	0.680413i
$622$	6.47309e10	−	1.00900e10i	0.432464	−	0.0674112i
$623$	3.93870e10	+	5.42115e10i	0.261457	+	0.359865i
$624$	−5.68442e10	+	1.78566e10i	−0.374928	+	0.117777i
$625$	−1.28061e11	−	8.29664e10i	−0.839261	−	0.543729i
$626$	−8.18734e10	+	4.14645e10i	−0.533145	+	0.270010i
$627$	4.13225e10	+	5.68756e10i	0.267372	+	0.368007i
$628$	−1.46244e11	−	2.03373e11i	−0.940239	−	1.30754i
$629$	1.26329e11	−	3.88800e11i	0.807048	−	2.48384i
$630$	1.49304e11	+	7.40328e10i	0.947783	+	0.469961i
$631$	−2.41211e11	+	7.83741e10i	−1.52152	+	0.494373i	−0.946208	−	0.323558i	$-0.895121\pi$
$631$	−2.41211e11	+	7.83741e10i	−1.52152	+	0.494373i	−0.575316	+	0.817931i	$0.695121\pi$
$632$	−8.94934e10	−	1.48486e10i	−0.560948	−	0.0930718i
$633$	−1.82408e10	−	5.61394e10i	−0.113613	−	0.349665i
$634$	1.15095e11	+	1.85181e10i	0.712361	+	0.114614i
$635$	5.85816e10	+	1.81726e10i	0.360302	+	0.111769i
$636$	2.63717e9	+	1.29067e7i	0.0161179	+	7.88839e-5i
$637$	5.93963e10	+	4.31540e10i	0.360746	+	0.262098i
$638$	−2.51496e10	+	1.56312e11i	−0.151792	+	0.943430i
$639$	−1.03490e10	−	1.42442e10i	−0.0620720	−	0.0854348i
$640$	7.56031e10	+	1.49772e11i	0.450630	+	0.892711i
$641$	7.91923e10	+	5.75366e10i	0.469084	+	0.340810i	0.797084	−	0.603868i	$-0.206375\pi$
$641$	7.91923e10	+	5.75366e10i	0.469084	+	0.340810i	−0.328000	+	0.944678i	$0.606375\pi$
$642$	9.32150e9	+	9.36724e9i	0.0548714	+	0.0551406i
$643$		−	5.19447e10i		−	0.303877i	−0.988390	−	0.151938i	$-0.951448\pi$
$643$		−	5.19447e10i		−	0.303877i	0.988390	−	0.151938i	$-0.0485515\pi$
$644$	2.49238e11	+	8.23330e10i	1.44901	+	0.478664i
$645$	1.39970e10	+	4.11971e10i	0.0808717	+	0.238028i
$646$	4.18661e11	−	6.52596e10i	2.40399	−	0.374726i
$647$	1.57381e11	+	5.11363e10i	0.898124	+	0.291818i	0.721463	−	0.692453i	$-0.243470\pi$
$647$	1.57381e11	+	5.11363e10i	0.898124	+	0.291818i	0.176662	+	0.984272i	$0.443470\pi$
$648$	−6.08119e10	−	1.21548e11i	−0.344897	−	0.689362i
$649$	−1.34483e11			−0.758032
$650$	4.51760e10	+	2.46366e11i	0.253078	+	1.38015i
$651$		−	4.83093e10i		−	0.268972i
$652$	1.93232e11	+	9.45709e8i	1.06927	+	0.00523320i
$653$	9.21364e10	−	2.83567e11i	0.506732	−	1.55956i	−0.291107	−	0.956690i	$-0.594024\pi$
$653$	9.21364e10	−	2.83567e11i	0.506732	−	1.55956i	0.797839	−	0.602870i	$-0.205976\pi$
$654$	−7.87769e10	+	1.22795e10i	−0.430614	+	0.0671228i
$655$	1.53063e11	−	2.16704e11i	0.831583	−	1.17734i
$656$	−1.47848e11	+	1.05223e11i	−0.798365	+	0.568190i
$657$	5.98030e10			0.320968
$658$	4.66500e9	+	4.68789e9i	0.0248856	+	0.0250077i
$659$	−9.77689e10	+	1.34567e11i	−0.518393	+	0.713506i	−0.985306	−	0.170797i	$-0.945366\pi$
$659$	−9.77689e10	+	1.34567e11i	−0.518393	+	0.713506i	0.466914	+	0.884303i	$0.345366\pi$
$660$	4.16738e8	+	4.92173e10i	0.00219628	+	0.259384i
$661$	−3.01701e11	+	2.19198e11i	−1.58041	+	1.14824i	−0.664193	+	0.747561i	$0.731225\pi$
$661$	−3.01701e11	+	2.19198e11i	−1.58041	+	1.14824i	−0.916220	+	0.400677i	$0.868775\pi$
$662$	2.36749e10	−	1.47146e11i	0.123270	−	0.766156i
$663$	−6.19243e10	+	8.52315e10i	−0.320485	+	0.441109i
$664$	−2.86556e10	+	1.43367e10i	−0.147413	+	0.0737527i
$665$	−3.21561e11	−	2.27126e11i	−1.64429	−	1.16140i
$666$	3.36963e11	+	5.42152e10i	1.71271	+	0.275565i
$667$	2.58181e11	−	8.38880e10i	1.30443	−	0.423835i
$668$	−1.10115e11	−	8.08299e10i	−0.553022	−	0.405944i
$669$	−2.49132e10	−	7.66748e10i	−0.124373	−	0.382779i
$670$	−1.43592e11	−	2.74371e11i	−0.712578	−	1.36157i
$671$	8.13444e10	+	2.64304e10i	0.401271	+	0.130381i
$672$	5.87790e10	−	2.90491e10i	0.288234	−	0.142448i
$673$	9.88124e10	−	7.17914e10i	0.481672	−	0.349955i	−0.320301	−	0.947316i	$-0.603784\pi$
$673$	9.88124e10	−	7.17914e10i	0.481672	−	0.349955i	0.801973	+	0.597361i	$0.203784\pi$
$674$	1.90071e11	−	9.62610e10i	0.921037	−	0.466456i
$675$	1.05295e11	−	3.73511e10i	0.507214	−	0.179924i
$676$	1.19724e11	−	1.63101e11i	0.573315	−	0.781034i
$677$	5.15873e10	−	3.74804e10i	0.245577	−	0.178422i	−0.458187	−	0.888856i	$-0.651501\pi$
$677$	5.15873e10	−	3.74804e10i	0.245577	−	0.178422i	0.703764	+	0.710433i	$0.251501\pi$
$678$	−4.43551e10	+	6.91395e9i	−0.209906	+	0.0327195i
$679$	−1.84176e11	−	5.98423e10i	−0.866469	−	0.281533i
$680$	2.65121e11	+	1.33082e11i	1.23996	+	0.622419i
$681$	−1.79018e10	−	5.50960e10i	−0.0832353	−	0.256172i
$682$	−1.49538e11	+	7.57329e10i	−0.691215	+	0.350064i
$683$	2.06326e11	−	6.70393e10i	0.948136	−	0.308068i	0.206178	−	0.978515i	$-0.433897\pi$
$683$	2.06326e11	−	6.70393e10i	0.948136	−	0.308068i	0.741958	+	0.670447i	$0.233897\pi$
$684$	1.07665e11	+	3.36960e11i	0.491868	+	1.53941i
$685$	2.84668e11	−	3.80374e9i	1.29294	−	0.0172762i
$686$	1.54339e11	+	7.91162e10i	0.696916	+	0.357247i
$687$	−4.35409e10	+	5.99290e10i	−0.195466	+	0.269036i
$688$	−1.90648e11	−	6.40149e10i	−0.850898	−	0.285711i
$689$	−1.47225e10	+	1.06966e10i	−0.0653290	+	0.0474643i
$690$	7.47726e10	−	3.91323e10i	0.329872	−	0.172639i
$691$	−2.11086e11	+	2.90535e11i	−0.925864	+	1.27434i	0.0355876	+	0.999367i	$0.488670\pi$
$691$	−2.11086e11	+	2.90535e11i	−0.925864	+	1.27434i	−0.961451	+	0.274975i	$0.911330\pi$
$692$	−2.37282e11	−	7.83835e10i	−1.03476	−	0.341822i
$693$	−2.25975e11			−0.979779
$694$	−1.92287e11	+	1.91348e11i	−0.828919	+	0.824872i
$695$	2.16008e11	+	6.70079e10i	0.925827	+	0.287201i
$696$	3.12274e10	−	6.01907e10i	0.133076	−	0.256503i
$697$	−9.91530e10	+	3.05161e11i	−0.420121	+	1.29300i
$698$	−4.76439e10	+	9.29434e10i	−0.200717	+	0.391559i
$699$			1.04939e10i			0.0439572i
$700$	−9.08732e10	−	2.60211e11i	−0.378481	−	1.08376i
$701$	3.74253e11			1.54986			0.774932	−	0.632044i	$-0.217784\pi$
$701$	3.74253e11			1.54986			0.774932	+	0.632044i	$0.217784\pi$
$702$	−1.63201e11	−	8.36587e10i	−0.672008	−	0.344479i
$703$	−7.66795e11	−	2.49147e11i	−3.13948	−	1.02008i
$704$	−1.82065e11	−	1.36407e11i	−0.741201	−	0.555322i
$705$	2.12617e9	−	2.84099e7i	0.00860681	−	0.000115004i
$706$	−2.70617e11	−	2.71945e11i	−1.08927	−	1.09462i
$707$			3.21174e11i			1.28547i
$708$	5.46918e10	+	1.80668e10i	0.217665	+	0.0719034i
$709$	−5.72132e10	−	4.15678e10i	−0.226418	−	0.164503i	0.468793	−	0.883308i	$-0.344689\pi$
$709$	−5.72132e10	−	4.15678e10i	−0.226418	−	0.164503i	−0.695211	+	0.718806i	$0.744689\pi$
$710$	−4.24117e9	+	2.88093e10i	−0.0166898	+	0.113370i
$711$	−7.87118e10	−	1.08337e11i	−0.308007	−	0.423936i
$712$	−7.09298e10	+	6.98960e10i	−0.276000	+	0.271977i
$713$	2.32522e11	+	1.68937e11i	0.899715	+	0.653681i
$714$	5.28837e10	−	1.03165e11i	0.203483	−	0.396954i
$715$	−2.03287e11	−	2.72081e11i	−0.777832	−	1.04105i
$716$	−5.13789e10	−	1.60802e11i	−0.195494	−	0.611840i
$717$	5.57263e9	+	1.71508e10i	0.0210855	+	0.0648945i
$718$	−1.93914e11	−	3.82892e11i	−0.729646	−	1.44072i
$719$	3.88450e11	−	1.26215e11i	1.45352	−	0.472276i	0.527434	−	0.849596i	$-0.323154\pi$
$719$	3.88450e11	−	1.26215e11i	1.45352	−	0.472276i	0.926083	+	0.377320i	$0.123154\pi$
$720$	−7.56885e10	+	2.35809e11i	−0.281644	+	0.877465i
$721$	−1.83461e11	+	5.64634e11i	−0.678894	+	2.08942i
$722$	−8.68535e10	−	5.57193e11i	−0.319623	−	2.05049i
$723$	1.11405e10	+	1.53336e10i	0.0407710	+	0.0561165i
$724$	−7.32781e10	+	9.98276e10i	−0.266698	+	0.363326i
$725$	−2.35009e11	−	1.61329e11i	−0.850612	−	0.583930i
$726$	5.00029e9	+	9.87327e9i	0.0179990	+	0.0355398i
$727$	−1.71338e11	−	2.35826e11i	−0.613360	−	0.844217i	0.383489	−	0.923546i	$-0.374722\pi$
$727$	−1.71338e11	−	2.35826e11i	−0.613360	−	0.844217i	−0.996849	+	0.0793283i	$0.974722\pi$
$728$	−2.08355e11	+	4.01604e11i	−0.741786	+	1.42979i
$729$	4.88420e10	−	1.50320e11i	0.172935	−	0.532240i
$730$	−7.06974e10	−	6.91708e10i	−0.248950	−	0.243574i
$731$	−3.38187e11	+	1.09884e11i	−1.18437	+	0.384825i
$732$	−2.95306e10	−	2.16769e10i	−0.102856	−	0.0755009i
$733$	1.67255e11	+	5.14757e11i	0.579378	+	1.78314i	0.620762	+	0.783999i	$0.286823\pi$
$733$	1.67255e11	+	5.14757e11i	0.579378	+	1.78314i	−0.0413839	+	0.999143i	$0.513177\pi$
$734$	−3.97572e10	+	2.47102e11i	−0.136972	+	0.851318i
$735$	−2.45945e10	+	8.35615e9i	−0.0842731	+	0.0286324i
$736$	−6.57306e10	+	3.84498e11i	−0.224004	+	1.31034i
$737$	3.39717e11	+	2.46819e11i	1.15146	+	0.836582i
$738$	−2.64475e11	−	4.25525e10i	−0.891579	−	0.143450i
$739$	−7.03823e9	−	9.68729e9i	−0.0235986	−	0.0324806i	0.797055	−	0.603907i	$-0.206390\pi$
$739$	−7.03823e9	−	9.68729e9i	−0.0235986	−	0.0324806i	−0.820653	+	0.571426i	$0.806390\pi$
$740$	−3.35640e11	−	4.53838e11i	−1.11930	−	1.51347i
$741$	1.68095e11	+	1.22128e11i	0.557546	+	0.405081i
$742$	1.41946e10	−	1.41253e10i	0.0468282	−	0.0465996i
$743$		−	4.90727e11i		−	1.61022i	−0.593127	−	0.805109i	$-0.702107\pi$
$743$		−	4.90727e11i		−	1.61022i	0.593127	−	0.805109i	$-0.297893\pi$
$744$	7.09886e10	−	1.07099e10i	0.231685	−	0.0349537i
$745$	−3.54800e10	+	2.65091e10i	−0.115175	+	0.0860539i
$746$	−3.09255e10	−	1.98397e11i	−0.0998532	−	0.640590i
$747$	−4.49839e10	−	1.46162e10i	−0.144469	−	0.0469409i
$748$	−4.02244e11	−	1.96865e9i	−1.28494	−	0.00628872i
$749$	1.00346e11			0.318841
$750$	−8.04168e10	−	3.72320e10i	−0.254157	−	0.117672i
$751$			4.55505e11i			1.43197i	0.698116	+	0.715985i	$0.254022\pi$
$751$			4.55505e11i			1.43197i	−0.698116	+	0.715985i	$0.745978\pi$
$752$	−5.85447e9	+	7.89432e9i	−0.0183069	+	0.0246856i
$753$	−2.81377e10	+	8.65990e10i	−0.0875204	+	0.269360i
$754$	7.20674e10	+	4.62335e11i	0.222973	+	1.43045i
$755$	7.69254e10	+	1.02957e11i	0.236746	+	0.316862i
$756$	1.91623e11	+	6.33007e10i	0.586625	+	0.193785i
$757$	4.31141e11			1.31291			0.656456	−	0.754364i	$-0.272055\pi$
$757$	4.31141e11			1.31291			0.656456	+	0.754364i	$0.272055\pi$
$758$	3.11945e11	−	3.10422e11i	0.944932	−	0.940319i
$759$	−6.72639e10	+	9.25808e10i	−0.202682	+	0.278968i
$760$	2.62465e11	−	5.22875e11i	0.786714	−	1.56727i
$761$	−1.96933e11	+	1.43080e11i	−0.587192	+	0.426620i	−0.841310	−	0.540553i	$-0.818215\pi$
$761$	−1.96933e11	+	1.43080e11i	−0.587192	+	0.426620i	0.254118	+	0.967173i	$0.418215\pi$
$762$	3.51692e10	+	5.65851e9i	0.104314	+	0.0167835i
$763$	−3.55849e11	+	4.89784e11i	−1.04995	+	1.44513i
$764$	−3.59757e11	−	1.76071e9i	−1.05593	−	0.00516791i
$765$	1.40870e11	+	4.14621e11i	0.411315	+	1.21061i
$766$	1.49285e10	−	9.27848e10i	0.0433612	−	0.269502i
$767$	−3.78007e11	+	1.22822e11i	−1.09224	+	0.354891i
$768$	5.57174e10	+	7.99334e10i	0.160157	+	0.229765i
$769$	−2.23636e9	−	6.88281e9i	−0.00639494	−	0.0196816i	0.947808	−	0.318841i	$-0.103294\pi$
$769$	−2.23636e9	−	6.88281e9i	−0.00639494	−	0.0196816i	−0.954203	+	0.299160i	$0.903294\pi$
$770$	2.67142e11	+	2.61374e11i	0.759940	+	0.743530i
$771$	1.38499e11	+	4.50011e10i	0.391949	+	0.127352i
$772$	1.97407e11	+	2.74522e11i	0.555767	+	0.772874i
$773$	3.67300e11	−	2.66859e11i	1.02873	−	0.747418i	0.0606783	−	0.998157i	$-0.480674\pi$
$773$	3.67300e11	−	2.66859e11i	1.02873	−	0.747418i	0.968055	+	0.250739i	$0.0806736\pi$
$774$	−1.34127e11	−	2.64839e11i	−0.373725	−	0.737936i
$775$	−8.06381e9	−	3.01690e11i	−0.0223529	−	0.836285i
$776$	4.71052e10	−	2.83906e11i	0.129904	−	0.782938i
$777$	−1.78464e11	+	1.29662e11i	−0.489629	+	0.355736i
$778$	2.46790e9	+	1.58323e10i	0.00673610	+	0.0432142i
$779$	6.01843e11	+	1.95551e11i	1.63431	+	0.531018i
$780$	4.61212e10	+	1.37961e11i	0.124601	+	0.372716i
$781$	−1.22018e10	−	3.75533e10i	−0.0327960	−	0.100936i
$782$	3.11620e11	+	6.15306e11i	0.833294	+	1.64537i
$783$	1.98499e11	−	6.44962e10i	0.528093	−	0.171588i
$784$	3.82166e10	−	1.13816e11i	0.101155	−	0.301258i
$785$	−4.89915e11	+	3.66044e11i	−1.29016	+	0.963951i
$786$	7.02876e10	−	1.37117e11i	0.184157	−	0.359253i
$787$	−3.63936e11	+	5.00915e11i	−0.948694	+	1.30577i	0.00341051	+	0.999994i	$0.498914\pi$
$787$	−3.63936e11	+	5.00915e11i	−0.948694	+	1.30577i	−0.952105	+	0.305772i	$0.901086\pi$
$788$	1.28234e11	−	4.09731e10i	0.332583	−	0.106266i
$789$	−8.63370e10	+	6.27275e10i	−0.222787	+	0.161864i
$790$	−3.22571e10	+	2.19115e11i	−0.0828166	+	0.562554i
$791$	−2.00360e11	+	2.75772e11i	−0.511805	+	0.704439i
$792$	−5.00974e10	−	3.32062e11i	−0.127325	−	0.843954i
$793$	2.52784e11			0.639229
$794$	1.22463e11	+	1.23064e11i	0.308122	+	0.309634i
$795$	−8.60234e7	−	6.43790e9i	−0.000215352	−	0.0161167i
$796$	4.42753e11	−	3.18380e11i	1.10283	−	0.793038i
$797$	1.72196e11	−	5.29965e11i	0.426767	−	1.31345i	−0.474526	−	0.880241i	$-0.657381\pi$
$797$	1.72196e11	−	5.29965e11i	0.426767	−	1.31345i	0.901293	−	0.433211i	$-0.142619\pi$
$798$	−2.03464e11	−	1.04298e11i	−0.501736	−	0.257196i
$799$			1.73779e10i			0.0426394i
$800$	3.62224e11	−	1.91222e11i	0.884336	−	0.466851i
$801$	−1.46998e11			−0.357093
$802$	−1.05823e11	+	2.06439e11i	−0.255790	+	0.498994i
$803$	1.27553e11	+	4.14444e10i	0.306781	+	0.0996791i
$804$	−1.04999e11	−	1.46016e11i	−0.251281	−	0.349442i
$805$	1.89867e11	−	6.12059e11i	0.452133	−	1.45750i
$806$	−3.51158e11	+	3.49444e11i	−0.832076	+	0.828013i
$807$			8.18567e10i			0.193001i
$808$	−4.71952e11	+	7.12023e10i	−1.10727	+	0.167051i
$809$	1.87694e11	+	1.36368e11i	0.438184	+	0.318359i	0.784913	−	0.619606i	$-0.212708\pi$
$809$	1.87694e11	+	1.36368e11i	0.438184	+	0.318359i	−0.346729	+	0.937965i	$0.612708\pi$
$810$	−2.93988e11	+	1.53859e11i	−0.682951	+	0.357423i
$811$	−3.28094e11	−	4.51583e11i	−0.758429	−	1.04389i	−0.997343	−	0.0728469i	$-0.976792\pi$
$811$	−3.28094e11	−	4.51583e11i	−0.758429	−	1.04389i	0.238914	−	0.971041i	$-0.423208\pi$
$812$	−1.56714e11	−	4.90472e11i	−0.360483	−	1.12821i
$813$	−1.84335e11	−	1.33927e11i	−0.421935	−	0.306554i
$814$	6.81130e11	+	3.49155e11i	1.55143	+	0.795282i
$815$	−6.30314e9	−	4.71721e11i	−0.0142865	−	1.06919i
$816$	1.63321e11	+	5.48394e10i	0.368368	+	0.123689i
$817$	2.16713e11	+	6.66976e11i	0.486405	+	1.49700i
$818$	4.37359e11	−	2.21499e11i	0.976844	−	0.494720i
$819$	−6.35178e11	+	2.06382e11i	−1.41176	+	0.458707i
$820$	2.63437e11	+	3.56209e11i	0.582669	+	0.787860i
$821$	6.81785e10	−	2.09832e11i	0.150063	−	0.461847i	−0.847564	−	0.530693i	$-0.821932\pi$
$821$	6.81785e10	−	2.09832e11i	0.150063	−	0.461847i	0.997627	+	0.0688458i	$0.0219316\pi$
$822$	1.63367e11	−	2.54652e10i	0.357831	−	0.0557775i
$823$	2.62792e11	+	3.61703e11i	0.572814	+	0.788410i	0.992885	−	0.119081i	$-0.0379948\pi$
$823$	2.62792e11	+	3.61703e11i	0.572814	+	0.788410i	−0.420071	+	0.907491i	$0.637995\pi$
$824$	−8.70379e11	−	1.44412e11i	−1.88799	−	0.313253i
$825$	1.20121e11	−	3.21069e9i	0.259300	−	0.00693078i
$826$	3.90183e11	−	1.97607e11i	0.838200	−	0.424504i
$827$	1.63679e11	+	2.25284e11i	0.349921	+	0.481625i	0.947306	−	0.320330i	$-0.103794\pi$
$827$	1.63679e11	+	2.25284e11i	0.349921	+	0.481625i	−0.597385	+	0.801954i	$0.703794\pi$
$828$	−4.67494e11	+	3.36171e11i	−0.994614	+	0.715218i
$829$	−7.09536e10	+	2.18373e11i	−0.150230	+	0.462360i	−0.997646	−	0.0685687i	$-0.978157\pi$
$829$	−7.09536e10	+	2.18373e11i	−0.150230	+	0.462360i	0.847417	+	0.530929i	$0.178157\pi$
$830$	3.62731e10	+	6.93093e10i	0.0764314	+	0.146042i
$831$	−2.06198e10	+	6.69977e9i	−0.0432394	+	0.0140493i
$832$	−6.36333e11	−	2.17136e11i	−1.32798	−	0.453147i
$833$	−6.56000e10	−	2.01896e11i	−0.136246	−	0.419322i
$834$	1.29679e11	+	2.08646e10i	0.268044	+	0.0431266i
$835$	−1.92398e11	+	2.72394e11i	−0.395781	+	0.560340i
$836$	−3.88259e9	+	7.93310e11i	−0.00794871	+	1.62412i
$837$	1.78771e11	+	1.29885e11i	0.364246	+	0.264641i
$838$	2.13301e10	−	1.32573e11i	0.0432531	−	0.268830i
$839$	1.36535e11	+	1.87924e11i	0.275547	+	0.379258i	0.924253	−	0.381781i	$-0.124689\pi$
$839$	1.36535e11	+	1.87924e11i	0.275547	+	0.379258i	−0.648705	+	0.761040i	$0.724689\pi$
$840$	−7.35283e10	−	1.42185e11i	−0.147685	−	0.285586i
$841$	−2.61101e10	−	1.89701e10i	−0.0521946	−	0.0379216i
$842$	1.97630e11	+	1.98600e11i	0.393193	+	0.395122i
$843$		−	6.49377e10i		−	0.128584i
$844$	2.08935e11	−	6.32487e11i	0.411758	−	1.24647i
$845$	−4.03465e11	−	2.84977e11i	−0.791369	−	0.558963i
$846$	−1.43350e10	+	2.23449e9i	−0.0279844	+	0.00436212i
$847$	7.99248e10	+	2.59691e10i	0.155292	+	0.0504573i
$848$	2.39034e10	+	1.77269e10i	0.0462250	+	0.0342807i
$849$	1.87523e11			0.360931
$850$	3.13037e11	−	6.53091e11i	0.599680	−	1.25112i
$851$		−	1.31241e12i		−	2.50236i
$852$	−8.27678e7	+	1.69115e10i	−0.000157074	+	0.0320940i
$853$	5.36749e9	−	1.65194e10i	0.0101385	−	0.0312032i	−0.945859	−	0.324577i	$-0.894778\pi$
$853$	5.36749e9	−	1.65194e10i	0.0101385	−	0.0312032i	0.955998	+	0.293374i	$0.0947781\pi$
$854$	−2.74846e11	+	4.28421e10i	−0.516723	+	0.0805452i
$855$	8.17721e11	−	2.77826e11i	1.53017	−	0.519887i
$856$	2.22462e10	+	1.47455e11i	0.0414343	+	0.274640i
$857$	−2.24939e10			−0.0417005			−0.0208502	−	0.999783i	$-0.506637\pi$
$857$	−2.24939e10			−0.0417005			−0.0208502	+	0.999783i	$0.506637\pi$
$858$	−1.39135e11	−	1.39817e11i	−0.256736	−	0.257995i
$859$	8.45237e10	−	1.16337e11i	0.155241	−	0.213671i	−0.724311	−	0.689473i	$-0.757842\pi$
$859$	8.45237e10	−	1.16337e11i	0.155241	−	0.213671i	0.879552	+	0.475802i	$0.157842\pi$
$860$	−1.47764e11	+	4.68223e11i	−0.270131	+	0.855971i
$861$	1.40073e11	−	1.01769e11i	0.254884	−	0.185184i
$862$	4.88209e10	−	3.03435e11i	0.0884253	−	0.549588i
$863$	−2.78980e11	+	3.83984e11i	−0.502957	+	0.692261i	−0.982712	−	0.185142i	$-0.940726\pi$
$863$	−2.78980e11	+	3.83984e11i	−0.502957	+	0.692261i	0.479755	+	0.877402i	$0.340726\pi$
$864$	−5.05361e10	+	2.95616e11i	−0.0906873	+	0.530485i
$865$	−1.80759e11	+	5.82698e11i	−0.322876	+	1.04083i
$866$	−6.35120e11	−	1.02187e11i	−1.12923	−	0.181687i
$867$	1.39206e11	−	4.52308e10i	0.246367	−	0.0800493i
$868$	3.22582e11	−	4.39457e11i	0.568278	−	0.774172i
$869$	−9.28035e10	−	2.85620e11i	−0.162737	−	0.500852i
$870$	−1.48317e11	−	7.35436e10i	−0.258890	−	0.128371i
$871$	1.18030e12	+	3.83504e11i	2.05079	+	0.666342i
$872$	−7.98608e11	−	4.14324e11i	−1.38124	−	0.716595i
$873$	3.43686e11	−	2.49702e11i	0.591704	−	0.429898i
$874$	1.21351e12	−	6.14580e11i	2.07969	−	1.05325i
$875$	−6.31125e11	+	2.33418e11i	−1.07667	+	0.398201i
$876$	−4.63058e10	−	3.39906e10i	−0.0786355	−	0.0577222i
$877$	1.41124e11	−	1.02532e11i	0.238562	−	0.173325i	−0.462080	−	0.886838i	$-0.652897\pi$
$877$	1.41124e11	−	1.02532e11i	0.238562	−	0.173325i	0.700642	+	0.713513i	$0.252897\pi$
$878$	1.72379e10	−	2.68699e9i	0.0290073	−	0.00452156i
$879$	−2.19614e11	−	7.13570e10i	−0.367879	−	0.119531i
$880$	−3.24854e11	+	4.50500e11i	−0.541699	+	0.751214i
$881$	2.98256e11	+	9.17937e11i	0.495091	+	1.52373i	0.816814	+	0.576900i	$0.195738\pi$
$881$	2.98256e11	+	9.17937e11i	0.495091	+	1.52373i	−0.321723	+	0.946834i	$0.604262\pi$
$882$	1.58108e11	−	8.00733e10i	0.261264	−	0.132316i
$883$	6.40241e11	−	2.08027e11i	1.05318	−	0.342198i	0.269262	−	0.963067i	$-0.413220\pi$
$883$	6.40241e11	−	2.08027e11i	1.05318	−	0.342198i	0.783914	+	0.620869i	$0.213220\pi$
$884$	−1.13244e12	+	3.61833e11i	−1.85441	+	0.592515i
$885$	4.16637e10	−	1.34308e11i	0.0679180	−	0.218942i
$886$	5.57947e11	+	2.86010e11i	0.905437	+	0.464138i
$887$	−5.12856e11	+	7.05885e11i	−0.828515	+	1.14035i	0.159682	+	0.987168i	$0.448953\pi$
$887$	−5.12856e11	+	7.05885e11i	−0.828515	+	1.14035i	−0.988198	+	0.153185i	$0.951047\pi$
$888$	−2.30097e11	−	2.33501e11i	−0.370050	−	0.375523i
$889$	2.18829e11	−	1.58988e11i	0.350346	−	0.254541i
$890$	1.73777e11	+	1.70025e11i	0.276970	+	0.270989i
$891$	2.64466e11	−	3.64006e11i	0.419622	−	0.577560i
$892$	2.85362e11	−	8.63847e11i	0.450752	−	1.36451i
$893$	3.42730e10			0.0538947
$894$	−1.82325e10	+	1.81435e10i	−0.0285428	+	0.0284034i
$895$	−3.90227e11	+	1.32582e11i	−0.608170	+	0.206630i
$896$	7.28670e11	+	1.28241e11i	1.13057	+	0.198973i
$897$	−1.04514e11	+	3.21660e11i	−0.161437	+	0.496853i
$898$	−2.07796e11	+	4.05368e11i	−0.319545	+	0.623367i
$899$		−	5.63799e11i		−	0.863148i
$900$	5.78982e11	+	1.74247e11i	0.882460	+	0.265579i
$901$	5.26192e10			0.0798446
$902$	−5.34606e11	−	2.74045e11i	−0.807621	−	0.413996i
$903$	1.82486e11	+	5.92934e10i	0.274460	+	0.0891775i
$904$	−4.49654e11	−	2.33284e11i	−0.673294	−	0.349310i
$905$	2.46945e11	+	1.74423e11i	0.368134	+	0.260022i
$906$	5.26496e10	+	5.29079e10i	0.0781415	+	0.0785249i
$907$		−	1.12717e12i		−	1.66557i	−0.553600	−	0.832783i	$-0.686746\pi$
$907$		−	1.12717e12i		−	1.66557i	0.553600	−	0.832783i	$-0.313254\pi$
$908$	2.05052e11	−	6.20731e11i	0.301662	−	0.913188i
$909$	−5.70000e11	−	4.14130e11i	−0.834872	−	0.606570i
$910$	9.89601e11	+	4.90697e11i	1.44309	+	0.715563i
$911$	2.21653e11	+	3.05079e11i	0.321810	+	0.442933i	0.939019	−	0.343866i	$-0.111737\pi$
$911$	2.21653e11	+	3.05079e11i	0.321810	+	0.442933i	−0.617209	+	0.786799i	$0.711737\pi$
$912$	1.08155e11	−	3.22104e11i	0.156339	−	0.465604i
$913$	−8.58163e10	−	6.23492e10i	−0.123506	−	0.0897321i
$914$	−3.19474e10	+	6.23228e10i	−0.0457773	+	0.0893022i
$915$	−5.15972e10	+	7.30503e10i	−0.0736108	+	0.104217i
$916$	−7.96252e11	+	2.54416e11i	−1.13102	+	0.361379i
$917$	−3.61551e11	−	1.11274e12i	−0.511319	−	1.57368i
$918$	2.39585e11	+	4.73070e11i	0.337356	+	0.666123i
$919$	−1.36360e11	+	4.43062e10i	−0.191173	+	0.0621158i	−0.403039	−	0.915183i	$-0.632046\pi$
$919$	−1.36360e11	+	4.43062e10i	−0.191173	+	0.0621158i	0.211866	+	0.977299i	$0.432046\pi$
$920$	9.41489e11	+	1.43313e11i	1.31421	+	0.200048i
$921$	1.58198e10	−	4.86883e10i	0.0219868	−	0.0676685i
$922$	1.71506e11	+	1.10027e12i	0.237332	+	1.52256i
$923$	−6.85944e10	−	9.44121e10i	−0.0945109	−	0.130083i
$924$	1.74974e11	+	1.28439e11i	0.240041	+	0.176202i
$925$	−1.09286e12	+	8.39523e11i	−1.49279	+	1.14674i
$926$	−2.00138e11	−	3.95181e11i	−0.272199	−	0.537468i
$927$	−7.65521e11	−	1.05365e12i	−1.03666	−	1.42685i
$928$	6.85987e11	−	3.39020e11i	0.924962	−	0.457124i
$929$	1.05487e11	−	3.24654e11i	0.141623	−	0.435871i	−0.854938	−	0.518730i	$-0.826405\pi$
$929$	1.05487e11	−	3.24654e11i	0.141623	−	0.435871i	0.996561	+	0.0828586i	$0.0264050\pi$
$930$	−2.93065e10	−	1.72806e11i	−0.0391771	−	0.231008i
$931$	−3.98182e11	+	1.29377e11i	−0.530008	+	0.172210i
$932$	−7.00726e10	+	9.54606e10i	−0.0928719	+	0.126520i
$933$	−2.87043e10	−	8.83427e10i	−0.0378809	−	0.116585i
$934$	1.00226e10	−	6.22934e10i	0.0131702	−	0.0818567i
$935$	1.31210e10	+	9.81966e11i	0.0171681	+	1.28484i
$936$	−4.44085e11	−	8.87616e11i	−0.578579	−	1.15644i
$937$	−2.22838e11	−	1.61901e11i	−0.289089	−	0.210035i	0.433783	−	0.901017i	$-0.357178\pi$
$937$	−2.22838e11	−	1.61901e11i	−0.289089	−	0.210035i	−0.722872	+	0.690982i	$0.757178\pi$
$938$	−1.34831e12	−	2.16935e11i	−1.74172	−	0.280233i
$939$	7.64858e10	+	1.05274e11i	0.0983826	+	0.135412i
$940$	1.95309e10	+	1.39389e10i	0.0250156	+	0.0178533i
$941$	−2.34705e11	−	1.70523e11i	−0.299339	−	0.217482i	0.427970	−	0.903793i	$-0.359229\pi$
$941$	−2.34705e11	−	1.70523e11i	−0.299339	−	0.217482i	−0.727308	+	0.686311i	$0.759229\pi$
$942$	−2.51758e11	+	2.50529e11i	−0.319728	+	0.318167i
$943$			1.03008e12i			1.30264i
$944$	3.76877e11	+	5.29550e11i	0.474582	+	0.666836i
$945$	1.45977e11	−	4.70573e11i	0.183045	−	0.590065i
$946$	−1.02540e11	−	6.57824e11i	−0.128035	−	0.821382i
$947$	8.50471e11	+	2.76335e11i	1.05745	+	0.343586i	0.785588	−	0.618750i	$-0.212361\pi$
$947$	8.50471e11	+	2.76335e11i	1.05745	+	0.343586i	0.271861	+	0.962336i	$0.412361\pi$
$948$	−6.29509e8	+	1.28624e11i	−0.000779414	+	0.159254i
$949$	3.96380e11			0.488705
$950$	−1.28803e12	−	6.17374e11i	−1.58137	−	0.757974i
$951$		−	1.65290e11i		−	0.202081i
$952$	1.16995e12	−	5.85340e11i	1.42436	−	0.712624i
$953$	−7.85683e10	+	2.41808e11i	−0.0952524	+	0.293157i	−0.987319	−	0.158746i	$-0.949255\pi$
$953$	−7.85683e10	+	2.41808e11i	−0.0952524	+	0.293157i	0.892067	+	0.451903i	$0.149255\pi$
$954$	6.76589e9	+	4.34053e10i	0.00816829	+	0.0524022i
$955$	1.17351e10	+	8.78246e11i	0.0141083	+	1.05585i
$956$	−6.38305e10	+	1.93227e11i	−0.0764181	+	0.231332i
$957$	2.24482e11			0.267630
$958$	2.96049e11	−	2.94603e11i	0.351481	−	0.349765i
$959$	7.37957e11	−	1.01571e12i	0.872483	−	1.20087i
$960$	1.92634e11	−	1.39569e11i	0.226803	−	0.164325i
$961$	−2.07089e11	+	1.50459e11i	−0.242809	+	0.176411i
$962$	2.23342e12	+	3.59344e11i	2.60778	+	0.419575i
$963$	−1.29389e11	+	1.78089e11i	−0.150450	+	0.207077i
$964$	−1.04674e9	+	2.13876e11i	−0.00121208	+	0.247658i
$965$	6.61311e11	−	4.94104e11i	0.762600	−	0.569782i
$966$	5.91199e10	−	3.67447e11i	0.0678931	−	0.421974i
$967$	7.15774e11	−	2.32569e11i	0.818597	−	0.265978i	0.130362	−	0.991466i	$-0.458386\pi$
$967$	7.15774e11	−	2.32569e11i	0.818597	−	0.265978i	0.688235	+	0.725488i	$0.258386\pi$
$968$	−2.04418e10	+	1.23204e11i	−0.0232818	+	0.140321i
$969$	−1.85651e11	−	5.71376e11i	−0.210573	−	0.648077i
$970$	−6.95113e11	−	1.02331e11i	−0.785178	−	0.115590i
$971$	−2.61961e11	−	8.51164e10i	−0.294686	−	0.0957494i	0.157943	−	0.987448i	$-0.449514\pi$
$971$	−2.61961e11	−	8.51164e10i	−0.294686	−	0.0957494i	−0.452629	+	0.891699i	$0.649514\pi$
$972$	−5.46476e11	+	3.92966e11i	−0.612218	+	0.440241i
$973$	8.06886e11	−	5.86237e11i	0.900245	−	0.654067i
$974$	−9.07524e9	−	1.79194e10i	−0.0100838	−	0.0199108i
$975$	3.34707e11	−	1.18730e11i	0.370379	−	0.131384i
$976$	−1.23887e11	−	3.94377e11i	−0.136529	−	0.434623i
$977$	−9.08552e11	+	6.60102e11i	−0.997175	+	0.724490i	−0.961481	−	0.274873i	$-0.911364\pi$
$977$	−9.08552e11	+	6.60102e11i	−0.997175	+	0.724490i	−0.0356945	+	0.999363i	$0.511364\pi$
$978$	−4.21981e10	−	2.70714e11i	−0.0461251	−	0.295907i
$979$	−3.13530e11	−	1.01872e11i	−0.341310	−	0.110898i
$980$	−2.79527e11	−	8.82144e10i	−0.303054	−	0.0956390i
$981$	−4.10400e11	−	1.26308e12i	−0.443130	−	1.36381i
$982$	−9.25123e10	−	1.82669e11i	−0.0994840	−	0.196435i
$983$	7.81397e11	−	2.53891e11i	0.836870	−	0.271915i	0.140934	−	0.990019i	$-0.454990\pi$
$983$	7.81397e11	−	2.53891e11i	0.836870	−	0.271915i	0.695936	+	0.718104i	$0.254990\pi$
$984$	1.80599e11	+	1.83270e11i	0.192635	+	0.195484i
$985$	−1.05730e11	−	3.11194e11i	−0.112319	−	0.330588i
$986$	6.17185e11	−	1.20400e12i	0.652992	−	1.27385i
$987$	5.51177e9	−	7.58630e9i	0.00580794	−	0.00799394i
$988$	7.13611e11	+	2.23340e12i	0.748918	+	2.34390i
$989$	−9.23541e11	+	6.70992e11i	−0.965319	+	0.701346i
$990$	−8.08331e11	+	1.37087e11i	−0.841489	+	0.142710i
$991$	4.80193e11	−	6.60929e11i	0.497876	−	0.685267i	−0.483940	−	0.875101i	$-0.660795\pi$
$991$	4.80193e11	−	6.60929e11i	0.497876	−	0.685267i	0.981816	+	0.189834i	$0.0607949\pi$
$992$	7.17279e11	+	3.76597e11i	0.740699	+	0.388893i
$993$	−2.11319e11			−0.217341
$994$	9.05821e10	+	9.10265e10i	0.0927891	+	0.0932443i
$995$	−7.96898e11	−	1.06657e12i	−0.813037	−	1.08817i
$996$	2.65238e10	+	3.68852e10i	0.0269525	+	0.0374813i
$997$	−3.31740e11	+	1.02099e12i	−0.335751	+	1.03333i	0.630600	+	0.776108i	$0.282809\pi$
$997$	−3.31740e11	+	1.02099e12i	−0.335751	+	1.03333i	−0.966351	+	0.257227i	$0.917191\pi$
$998$	1.38360e12	+	7.09251e11i	1.39473	+	0.714953i
$999$		−	1.00903e12i		−	1.01307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.75	✓	464
4.3	odd	2	inner	100.9.j.b.11.109	yes	464
25.16	even	5	inner	100.9.j.b.91.109	yes	464
100.91	odd	10	inner	100.9.j.b.91.75	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.75	✓	464	1.1	even	1	trivial
100.9.j.b.11.109	yes	464	4.3	odd	2	inner
100.9.j.b.91.75	yes	464	100.91	odd	10	inner
100.9.j.b.91.109	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+(7.29871 - 14.2383i) q^{2} +(-21.5758 - 7.01039i) q^{3} +(-149.458 - 207.842i) q^{4} +(-500.682 + 374.089i) q^{5} +(-257.291 + 256.035i) q^{6} +2756.23i q^{7} +(-4050.17 + 611.039i) q^{8} +(-4891.59 - 3553.95i) q^{9} +(1672.05 + 9859.22i) q^{10} +(-7970.26 - 10970.1i) q^{11} +(1767.61 + 5532.11i) q^{12} +(-32422.0 - 23555.9i) q^{13} +(39243.9 + 20116.9i) q^{14} +(13425.1 - 4561.27i) q^{15} +(-20860.8 + 62127.2i) q^{16} +(35808.3 + 110207. i) q^{17} +(-86304.5 + 43708.6i) q^{18} +(217351. - 70621.5i) q^{19} +(152582. + 48152.5i) q^{20} +(19322.2 - 59467.7i) q^{21} +(-214368. + 33415.1i) q^{22} +(218659. + 300959. i) q^{23} +(91669.1 + 15209.6i) q^{24} +(110740. - 374599. i) q^{25} +(-572035. + 289705. i) q^{26} +(168113. + 231388. i) q^{27} +(572860. - 411939. i) q^{28} +(225502. - 694024. i) q^{29} +(33041.3 - 224442. i) q^{30} +(734789. - 238747. i) q^{31} +(732328. + 750471. i) q^{32} +(95059.6 + 292563. i) q^{33} +(1.83051e6 + 294517. i) q^{34} +(-1.03107e6 - 1.37999e6i) q^{35} +(-7575.41 + 1.54784e6i) q^{36} +(-2.85415e6 - 2.07366e6i) q^{37} +(580850. - 3.61014e6i) q^{38} +(534392. + 735528. i) q^{39} +(1.79926e6 - 1.82106e6i) q^{40} +(2.24016e6 + 1.62757e6i) q^{41} +(-705691. - 709153. i) q^{42} +3.06866e6i q^{43} +(-1.08884e6 + 3.29613e6i) q^{44} +(3.77863e6 - 50490.0i) q^{45} +(5.88107e6 - 916723. i) q^{46} +(142628. + 46342.5i) q^{47} +(885625. - 1.19420e6i) q^{48} -1.83198e6 q^{49} +(-4.52539e6 - 4.31084e6i) q^{50} -2.62882e6i q^{51} +(-50210.6 + 1.02593e7i) q^{52} +(140322. - 431867. i) q^{53} +(4.52158e6 - 704810. i) q^{54} +(8.09437e6 + 2.51096e6i) q^{55} +(-1.68416e6 - 1.11632e7i) q^{56} -5.18459e6 q^{57} +(-8.23584e6 - 8.27624e6i) q^{58} +(5.82950e6 - 8.02361e6i) q^{59} +(-2.95451e6 - 2.10859e6i) q^{60} +(-5.10299e6 + 3.70754e6i) q^{61} +(1.96366e6 - 1.22047e7i) q^{62} +(9.79549e6 - 1.34823e7i) q^{63} +(1.60305e7 - 4.94962e6i) q^{64} +(2.50451e7 - 334653. i) q^{65} +(4.85942e6 + 781850. i) q^{66} +(-2.94518e7 + 9.56947e6i) q^{67} +(1.75538e7 - 2.39137e7i) q^{68} +(-2.60790e6 - 8.02630e6i) q^{69} +(-2.71742e7 + 4.60854e6i) q^{70} +(2.76946e6 + 899851. i) q^{71} +(2.19834e7 + 1.14051e7i) q^{72} +(-8.00180e6 + 5.81365e6i) q^{73} +(-5.03570e7 + 2.55031e7i) q^{74} +(-5.01539e6 + 7.30593e6i) q^{75} +(-4.71628e7 - 3.46197e7i) q^{76} +(3.02361e7 - 2.19678e7i) q^{77} +(1.43730e7 - 2.24043e6i) q^{78} +(2.10637e7 + 6.84401e6i) q^{79} +(-1.27964e7 - 3.89098e7i) q^{80} +(1.02537e7 + 3.15575e7i) q^{81} +(3.95242e7 - 2.00169e7i) q^{82} +(7.43986e6 - 2.41736e6i) q^{83} +(-1.52478e7 + 4.87192e6i) q^{84} +(-5.91556e7 - 4.17830e7i) q^{85} +(4.36925e7 + 2.23973e7i) q^{86} +(-9.73076e6 + 1.33932e7i) q^{87} +(3.89841e7 + 3.95607e7i) q^{88} +(1.96687e7 - 1.42902e7i) q^{89} +(2.68602e7 - 5.41697e7i) q^{90} +(6.49255e7 - 8.93622e7i) q^{91} +(2.98717e7 - 9.04272e7i) q^{92} -1.75273e7 q^{93} +(1.70084e6 - 1.69253e6i) q^{94} +(-8.24048e7 + 1.16667e8i) q^{95} +(-1.05394e7 - 2.13259e7i) q^{96} +(-2.17117e7 + 6.68217e7i) q^{97} +(-1.33711e7 + 2.60842e7i) q^{98} +8.19873e7i 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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