LMFDB - Embedded newform 75.8.l.a.2.55

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,8,Mod(2,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.2"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	75.l (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.4288769113$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.55
Character	$\chi$	$=$	75.2
Dual form			75.8.l.a.38.55

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.30743 - 14.5685i) q^{2} +(43.9293 - 16.0379i) q^{3} +(-85.1830 - 27.6776i) q^{4} +(102.175 - 260.164i) q^{5} +(-132.284 - 676.993i) q^{6} +(-331.771 - 331.771i) q^{7} +(257.366 - 505.109i) q^{8} +(1672.57 - 1409.07i) q^{9} +(-3554.45 - 2088.85i) q^{10} +(1796.34 + 2472.45i) q^{11} +(-4185.92 + 150.293i) q^{12} +(796.184 - 126.103i) q^{13} +(-5598.96 + 4067.88i) q^{14} +(316.001 - 13067.5i) q^{15} +(-16039.9 - 11653.6i) q^{16} +(6327.92 + 3224.24i) q^{17} +(-16668.7 - 27618.3i) q^{18} +(3985.23 - 1294.88i) q^{19} +(-15904.3 + 19333.6i) q^{20} +(-19895.4 - 9253.58i) q^{21} +(40165.0 - 20465.1i) q^{22} +(-25524.8 - 4042.74i) q^{23} +(3205.05 - 26316.7i) q^{24} +(-57245.6 - 53164.4i) q^{25} -11890.2i q^{26} +(50876.7 - 88723.8i) q^{27} +(19078.6 + 37443.9i) q^{28} +(3266.26 - 10052.5i) q^{29} +(-189645. - 34756.0i) q^{30} +(23122.7 + 71164.3i) q^{31} +(-155478. + 155478. i) q^{32} +(118565. + 79803.7i) q^{33} +(61573.7 - 84748.9i) q^{34} +(-120213. + 52416.2i) q^{35} +(-181474. + 73735.5i) q^{36} +(83507.9 + 527248. i) q^{37} +(-9668.87 - 61046.8i) q^{38} +(32953.4 - 18308.7i) q^{39} +(-105115. - 118567. i) q^{40} +(43960.7 - 60506.7i) q^{41} +(-180718. + 268495. i) q^{42} +(-462464. + 462464. i) q^{43} +(-84586.1 - 260329. i) q^{44} +(-195693. - 579115. i) q^{45} +(-117794. + 362531. i) q^{46} +(50997.8 + 100089. i) q^{47} +(-891519. - 254692. i) q^{48} -603399. i q^{49} +(-906619. + 711312. i) q^{50} +(329691. + 40152.3i) q^{51} +(-71311.6 - 11294.6i) q^{52} +(-1.21243e6 + 617764. i) q^{53} +(-1.17518e6 - 945923. i) q^{54} +(826784. - 214721. i) q^{55} +(-252967. + 82194.0i) q^{56} +(154301. - 120798. i) q^{57} +(-138914. - 70780.1i) q^{58} +(1.86748e6 + 1.35681e6i) q^{59} +(-388595. + 1.10438e6i) q^{60} +(2.57918e6 - 1.87388e6i) q^{61} +(1.09011e6 - 172657. i) q^{62} +(-1.02240e6 - 87424.5i) q^{63} +(414663. + 570735. i) q^{64} +(48542.5 - 220023. i) q^{65} +(1.43620e6 - 1.54318e6i) q^{66} +(1.64799e6 - 3.23437e6i) q^{67} +(-449792. - 449792. i) q^{68} +(-1.18613e6 + 231769. i) q^{69} +(486243. + 1.87228e6i) q^{70} +(2.43157e6 + 790064. i) q^{71} +(-281268. - 1.20748e6i) q^{72} +(197445. - 1.24662e6i) q^{73} +7.87392e6 q^{74} +(-3.36741e6 - 1.41738e6i) q^{75} -375313. q^{76} +(224314. - 1.41626e6i) q^{77} +(-190694. - 522330. i) q^{78} +(-1.48041e6 - 481014. i) q^{79} +(-4.67073e6 + 2.98228e6i) q^{80} +(812039. - 4.71353e6i) q^{81} +(-780058. - 780058. i) q^{82} +(-2.93578e6 + 5.76180e6i) q^{83} +(1.43863e6 + 1.33890e6i) q^{84} +(1.48539e6 - 1.31686e6i) q^{85} +(5.67032e6 + 7.80453e6i) q^{86} +(-17736.2 - 493984. i) q^{87} +(1.71118e6 - 271024. i) q^{88} +(7.85725e6 - 5.70863e6i) q^{89} +(-8.88840e6 + 1.51470e6i) q^{90} +(-305988. - 222313. i) q^{91} +(2.06239e6 + 1.05084e6i) q^{92} +(2.15709e6 + 2.75536e6i) q^{93} +(1.57582e6 - 512016. i) q^{94} +(70309.3 - 1.16912e6i) q^{95} +(-4.33650e6 + 9.32356e6i) q^{96} +(3.07505e6 - 1.56682e6i) q^{97} +(-8.79065e6 - 1.39230e6i) q^{98} +(6.48836e6 + 1.60420e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 34 q^{3} - 20 q^{4} - 6 q^{6} - 1364 q^{7} - 10 q^{9} + 3160 q^{10} + 2018 q^{12} - 16868 q^{13} - 37570 q^{15} + 507892 q^{16} + 106550 q^{18} + 70800 q^{19} - 6 q^{21} - 195160 q^{22} - 444200 q^{25}+ \cdots - 22089384 q^{97}+O(q^{100}) $ 544 * q - 34 * q^3 - 20 * q^4 - 6 * q^6 - 1364 * q^7 - 10 * q^9 + 3160 * q^10 + 2018 * q^12 - 16868 * q^13 - 37570 * q^15 + 507892 * q^16 + 106550 * q^18 + 70800 * q^19 - 6 * q^21 - 195160 * q^22 - 444200 * q^25 + 264158 * q^27 + 692032 * q^28 - 892390 * q^30 - 12 * q^31 + 877790 * q^33 - 1828180 * q^34 - 65542 * q^36 + 635596 * q^37 - 3868770 * q^39 + 1574020 * q^40 + 4577310 * q^42 - 1397348 * q^43 + 3411430 * q^45 - 12 * q^46 - 12135404 * q^48 - 16 * q^51 + 6428876 * q^52 + 16485420 * q^54 - 2324900 * q^55 + 4119286 * q^57 - 986360 * q^58 - 25245250 * q^60 - 12 * q^61 + 6259012 * q^63 + 363500 * q^64 - 1119750 * q^66 + 3427476 * q^67 - 12994880 * q^69 + 9814160 * q^70 - 611970 * q^72 + 10236732 * q^73 + 19853790 * q^75 - 131104 * q^76 + 24801340 * q^78 - 8474460 * q^79 + 10854734 * q^81 + 44639220 * q^82 - 52907530 * q^84 - 82807380 * q^85 - 15442020 * q^87 + 33548360 * q^88 - 11540050 * q^90 - 12 * q^91 + 14982652 * q^93 + 60673460 * q^94 + 1218042 * q^96 - 22089384 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.30743	−	14.5685i	0.203950	−	1.28769i	−0.647019	−	0.762474i	$-0.723985\pi$
$2$	2.30743	−	14.5685i	0.203950	−	1.28769i	0.850969	−	0.525216i	$-0.176015\pi$
$3$	43.9293	−	16.0379i	0.939356	−	0.342943i
$3$	43.9293	−	16.0379i	0.939356	−	0.342943i
$4$	−85.1830	−	27.6776i	−0.665492	−	0.216231i
$5$	102.175	−	260.164i	0.365552	−	0.930791i
$5$	102.175	−	260.164i	0.365552	−	0.930791i
$6$	−132.284	−	676.993i	−0.250023	−	1.27954i
$7$	−331.771	−	331.771i	−0.365591	−	0.365591i	0.500276	−	0.865866i	$-0.333232\pi$
$7$	−331.771	−	331.771i	−0.365591	−	0.365591i	−0.865866	+	0.500276i	$0.833232\pi$
$8$	257.366	−	505.109i	0.177720	−	0.348795i
$9$	1672.57	−	1409.07i	0.764780	−	0.644291i
$10$	−3554.45	−	2088.85i	−1.12402	−	0.660552i
$11$	1796.34	+	2472.45i	0.406925	+	0.560085i	0.962465	−	0.271405i	$-0.0874884\pi$
$11$	1796.34	+	2472.45i	0.406925	+	0.560085i	−0.555540	+	0.831490i	$0.687488\pi$
$12$	−4185.92	+	150.293i	−0.699289	+	0.0251075i
$13$	796.184	−	126.103i	0.100511	−	0.0159193i	−0.105977	−	0.994369i	$-0.533797\pi$
$13$	796.184	−	126.103i	0.100511	−	0.0159193i	0.206487	+	0.978449i	$0.433797\pi$
$14$	−5598.96	+	4067.88i	−0.545329	+	0.396205i
$15$	316.001	−	13067.5i	0.0241751	−	0.999708i
$16$	−16039.9	−	11653.6i	−0.978995	−	0.711281i
$17$	6327.92	+	3224.24i	0.312385	+	0.159168i	0.603153	−	0.797626i	$-0.293911\pi$
$17$	6327.92	+	3224.24i	0.312385	+	0.159168i	−0.290768	+	0.956794i	$0.593911\pi$
$18$	−16668.7	−	27618.3i	−0.673670	−	1.11620i
$19$	3985.23	−	1294.88i	0.133296	−	0.0433104i	−0.241610	−	0.970374i	$-0.577675\pi$
$19$	3985.23	−	1294.88i	0.133296	−	0.0433104i	0.374905	+	0.927063i	$0.377675\pi$
$20$	−15904.3	+	19333.6i	−0.444538	+	0.540390i
$21$	−19895.4	−	9253.58i	−0.468797	−	0.218043i
$22$	40165.0	−	20465.1i	0.804207	−	0.409764i
$23$	−25524.8	−	4042.74i	−0.437437	−	0.0692832i	−0.0661678	−	0.997809i	$-0.521077\pi$
$23$	−25524.8	−	4042.74i	−0.437437	−	0.0692832i	−0.371269	+	0.928525i	$0.621077\pi$
$24$	3205.05	−	26316.7i	0.0473255	−	0.388591i
$25$	−57245.6	−	53164.4i	−0.732744	−	0.680505i
$26$		−	11890.2i		−	0.132673i
$27$	50876.7	−	88723.8i	0.497446	−	0.867495i
$28$	19078.6	+	37443.9i	0.164245	+	0.322350i
$29$	3266.26	−	10052.5i	0.0248690	−	0.0765388i	−0.937852	−	0.347036i	$-0.887188\pi$
$29$	3266.26	−	10052.5i	0.0248690	−	0.0765388i	0.962721	+	0.270497i	$0.0871881\pi$
$30$	−189645.	−	34756.0i	−1.28238	−	0.235020i
$31$	23122.7	+	71164.3i	0.139403	+	0.429039i	0.996249	−	0.0865341i	$-0.0275792\pi$
$31$	23122.7	+	71164.3i	0.139403	+	0.429039i	−0.856846	+	0.515573i	$0.827579\pi$
$32$	−155478.	+	155478.i	−0.838770	+	0.838770i
$33$	118565.	+	79803.7i	0.574325	+	0.386567i
$34$	61573.7	−	84748.9i	0.268670	−	0.369792i
$35$	−120213.	+	52416.2i	−0.473931	+	0.206646i
$36$	−181474.	+	73735.5i	−0.648271	+	0.263401i
$37$	83507.9	+	527248.i	0.271032	+	1.71123i	0.628922	+	0.777468i	$0.283496\pi$
$37$	83507.9	+	527248.i	0.271032	+	1.71123i	−0.357890	+	0.933764i	$0.616504\pi$
$38$	−9668.87	−	61046.8i	−0.0285847	−	0.180476i
$39$	32953.4	−	18308.7i	0.0889559	−	0.0494233i
$40$	−105115.	−	118567.i	−0.259689	−	0.292923i
$41$	43960.7	−	60506.7i	0.0996141	−	0.137107i	−0.756300	−	0.654225i	$-0.772995\pi$
$41$	43960.7	−	60506.7i	0.0996141	−	0.137107i	0.855914	+	0.517118i	$0.172995\pi$
$42$	−180718.	+	268495.i	−0.376383	+	0.559195i
$43$	−462464.	+	462464.i	−0.887030	+	0.887030i	−0.994237	−	0.107207i	$-0.965809\pi$
$43$	−462464.	+	462464.i	−0.887030	+	0.887030i	0.107207	+	0.994237i	$0.465809\pi$
$44$	−84586.1	−	260329.i	−0.149698	−	0.460722i
$45$	−195693.	−	579115.i	−0.320134	−	0.947372i
$46$	−117794.	+	362531.i	−0.178430	+	0.549153i
$47$	50997.8	+	100089.i	0.0716489	+	0.140619i	0.924053	−	0.382265i	$-0.124856\pi$
$47$	50997.8	+	100089.i	0.0716489	+	0.140619i	−0.852404	+	0.522884i	$0.824856\pi$
$48$	−891519.	−	254692.i	−1.16355	−	0.332407i
$49$		−	603399.i		−	0.732687i
$50$	−906619.	+	711312.i	−1.02572	+	0.804757i
$51$	329691.	+	40152.3i	0.348026	+	0.0423853i
$52$	−71311.6	−	11294.6i	−0.0703313	−	0.0111394i
$53$	−1.21243e6	+	617764.i	−1.11864	+	0.569977i	−0.912717	−	0.408591i	$-0.866020\pi$
$53$	−1.21243e6	+	617764.i	−1.11864	+	0.569977i	−0.205925	+	0.978568i	$0.566020\pi$
$54$	−1.17518e6	−	945923.i	−1.01561	−	0.817481i
$55$	826784.	−	214721.i	0.670074	−	0.174022i
$56$	−252967.	+	82194.0i	−0.192489	+	0.0625434i
$57$	154301.	−	120798.i	0.110359	−	0.0863966i
$58$	−138914.	−	70780.1i	−0.0934862	−	0.0476336i
$59$	1.86748e6	+	1.35681e6i	1.18379	+	0.860074i	0.992594	−	0.121478i	$-0.0387635\pi$
$59$	1.86748e6	+	1.35681e6i	1.18379	+	0.860074i	0.191196	+	0.981552i	$0.438764\pi$
$60$	−388595.	+	1.10438e6i	−0.232257	+	0.660070i
$61$	2.57918e6	−	1.87388e6i	1.45488	−	1.05703i	0.470218	−	0.882550i	$-0.344175\pi$
$61$	2.57918e6	−	1.87388e6i	1.45488	−	1.05703i	0.984661	−	0.174481i	$-0.0558247\pi$
$62$	1.09011e6	−	172657.i	0.580900	−	0.0920055i
$63$	−1.02240e6	−	87424.5i	−0.515143	−	0.0440495i
$64$	414663.	+	570735.i	0.197727	+	0.272148i
$65$	48542.5	−	220023.i	0.0219243	−	0.0993737i
$66$	1.43620e6	−	1.54318e6i	0.614911	−	0.660712i
$67$	1.64799e6	−	3.23437e6i	0.669413	−	1.31380i	−0.267272	−	0.963621i	$-0.586122\pi$
$67$	1.64799e6	−	3.23437e6i	0.669413	−	1.31380i	0.936684	−	0.350175i	$-0.113878\pi$
$68$	−449792.	−	449792.i	−0.173472	−	0.173472i
$69$	−1.18613e6	+	231769.i	−0.434669	+	0.0849344i
$70$	486243.	+	1.87228e6i	0.169438	+	0.652421i
$71$	2.43157e6	+	790064.i	0.806272	+	0.261974i	0.683018	−	0.730401i	$-0.260667\pi$
$71$	2.43157e6	+	790064.i	0.806272	+	0.261974i	0.123254	+	0.992375i	$0.460667\pi$
$72$	−281268.	−	1.20748e6i	−0.0888090	−	0.381255i
$73$	197445.	−	1.24662e6i	0.0594041	−	0.375063i	−0.940020	−	0.341120i	$-0.889194\pi$
$73$	197445.	−	1.24662e6i	0.0594041	−	0.375063i	0.999424	−	0.0339427i	$-0.0108064\pi$
$74$	7.87392e6			2.25881
$75$	−3.36741e6	−	1.41738e6i	−0.921682	−	0.387947i
$76$	−375313.			−0.0980722
$77$	224314.	−	1.41626e6i	0.0559936	−	0.353530i
$78$	−190694.	−	522330.i	−0.0454994	−	0.124627i
$79$	−1.48041e6	−	481014.i	−0.337821	−	0.109765i	0.135194	−	0.990819i	$-0.456834\pi$
$79$	−1.48041e6	−	481014.i	−0.337821	−	0.109765i	−0.473015	+	0.881054i	$0.656834\pi$
$80$	−4.67073e6	+	2.98228e6i	−1.01993	+	0.651229i
$81$	812039.	−	4.71353e6i	0.169777	−	0.985482i
$82$	−780058.	−	780058.i	−0.156235	−	0.156235i
$83$	−2.93578e6	+	5.76180e6i	−0.563573	+	1.10607i	0.416814	+	0.908992i	$0.363147\pi$
$83$	−2.93578e6	+	5.76180e6i	−0.563573	+	1.10607i	−0.980387	+	0.197083i	$0.936853\pi$
$84$	1.43863e6	+	1.33890e6i	0.264833	+	0.246474i
$85$	1.48539e6	−	1.31686e6i	0.262345	−	0.232581i
$86$	5.67032e6	+	7.80453e6i	0.961309	+	1.32313i
$87$	−17736.2	−	493984.i	−0.00288764	−	0.0804259i
$88$	1.71118e6	−	271024.i	0.267673	−	0.0423953i
$89$	7.85725e6	−	5.70863e6i	1.18142	−	0.858354i	0.189092	−	0.981959i	$-0.439446\pi$
$89$	7.85725e6	−	5.70863e6i	1.18142	−	0.858354i	0.992331	+	0.123605i	$0.0394456\pi$
$90$	−8.88840e6	+	1.51470e6i	−1.28521	+	0.219016i
$91$	−305988.	−	222313.i	−0.0425657	−	0.0309258i
$92$	2.06239e6	+	1.05084e6i	0.276130	+	0.140695i
$93$	2.15709e6	+	2.75536e6i	0.278085	+	0.355213i
$94$	1.57582e6	−	512016.i	0.195686	−	0.0635823i
$95$	70309.3	−	1.16912e6i	0.00841356	−	0.139902i
$96$	−4.33650e6	+	9.32356e6i	−0.500254	+	1.07555i
$97$	3.07505e6	−	1.56682e6i	0.342099	−	0.174308i	−0.274497	−	0.961588i	$-0.588511\pi$
$97$	3.07505e6	−	1.56682e6i	0.342099	−	0.174308i	0.616596	+	0.787280i	$0.288511\pi$
$98$	−8.79065e6	−	1.39230e6i	−0.943473	−	0.149431i
$99$	6.48836e6	+	1.60420e6i	0.672066	+	0.166163i
$100$	3.40488e6	+	6.11313e6i	0.340488	+	0.611313i
$101$		−	783845.i		−	0.0757017i	−0.999283	−	0.0378508i	$-0.987949\pi$
$101$		−	783845.i		−	0.0757017i	0.999283	−	0.0378508i	$-0.0120512\pi$
$102$	1.34570e6	−	4.71047e6i	0.125559	−	0.439505i
$103$	−750.039	−	1472.03i	−6.76322e−5	−	0.000132736i	0.890973	−	0.454057i	$-0.150024\pi$
$103$	−750.039	−	1472.03i	−6.76322e−5	−	0.000132736i	−0.891040	+	0.453924i	$0.850024\pi$
$104$	141215.	−	434615.i	0.0123102	−	0.0378868i
$105$	−4.44026e6	+	4.23058e6i	−0.374322	+	0.356646i
$106$	6.20232e6	+	1.90888e7i	0.505806	+	1.55671i
$107$	1.10071e7	−	1.10071e7i	0.868621	−	0.868621i	−0.123699	−	0.992320i	$-0.539476\pi$
$107$	1.10071e7	−	1.10071e7i	0.868621	−	0.868621i	0.992320	+	0.123699i	$0.0394757\pi$
$108$	−6.78949e6	+	6.14961e6i	−0.518626	+	0.469748i
$109$	3.57371e6	−	4.91879e6i	0.264318	−	0.363802i	−0.656143	−	0.754636i	$-0.727813\pi$
$109$	3.57371e6	−	4.91879e6i	0.264318	−	0.363802i	0.920461	+	0.390834i	$0.127813\pi$
$110$	−1.22042e6	−	1.25405e7i	−0.0874252	−	0.898339i
$111$	1.21244e7	+	2.18224e7i	0.841451	+	1.51451i
$112$	1.45522e6	+	9.18789e6i	0.0978735	+	0.617949i
$113$	772488.	+	4.87730e6i	0.0503636	+	0.317983i	0.999989	+	0.00459735i	$0.00146339\pi$
$113$	772488.	+	4.87730e6i	0.0503636	+	0.317983i	−0.949626	+	0.313386i	$0.898537\pi$
$114$	−1.40381e6	−	2.52668e6i	−0.0887443	−	0.159729i
$115$	−3.65977e6	+	6.22758e6i	−0.224394	+	0.381836i
$116$	−556459.	+	765901.i	−0.0331002	+	0.0455585i
$117$	1.15399e6	−	1.33279e6i	0.0666118	−	0.0769329i
$118$	2.40758e7	−	2.40758e7i	1.34894	−	1.34894i
$119$	−1.02971e6	−	3.16913e6i	−0.0560146	−	0.172395i
$120$	−6.51918e6	−	3.52274e6i	−0.344397	−	0.186100i
$121$	3.13569e6	−	9.65066e6i	0.160910	−	0.495231i
$122$	−2.13485e7	−	4.18987e7i	−1.06441	−	2.08901i
$123$	960766.	−	3.36305e6i	0.0465532	−	0.162954i
$124$		−	6.70197e6i		−	0.315665i
$125$	−1.96805e7	+	9.46117e6i	−0.901264	+	0.433271i
$126$	−3.63276e6	+	1.46931e7i	−0.161786	+	0.654361i
$127$	8.41296e6	+	1.33248e6i	0.364448	+	0.0577229i	0.335973	−	0.941872i	$-0.390935\pi$
$127$	8.41296e6	+	1.33248e6i	0.364448	+	0.0577229i	0.0284752	+	0.999595i	$0.490935\pi$
$128$	−1.58053e7	+	8.05321e6i	−0.666144	+	0.339417i
$129$	−1.28988e7	+	2.77327e7i	−0.529036	+	1.13744i
$130$	−3.09341e6	−	1.21488e6i	−0.123491	−	0.0484989i
$131$	−2.37323e7	+	7.71110e6i	−0.922339	+	0.299686i	−0.731426	−	0.681921i	$-0.761145\pi$
$131$	−2.37323e7	+	7.71110e6i	−0.922339	+	0.299686i	−0.190913	+	0.981607i	$0.561145\pi$
$132$	−7.89094e6	−	1.00795e7i	−0.298621	−	0.381444i
$133$	−1.75179e6	−	892580.i	−0.0645655	−	0.0328978i
$134$	−4.33174e7	−	3.14720e7i	−1.55524	−	1.12994i
$135$	−1.78844e7	−	2.23016e7i	−0.625614	−	0.780132i
$136$	3.25718e6	−	2.36648e6i	0.111034	−	0.0806709i
$137$	−1.36651e7	+	2.16433e6i	−0.454035	+	0.0719121i	−0.379264	−	0.925289i	$-0.623823\pi$
$137$	−1.36651e7	+	2.16433e6i	−0.454035	+	0.0719121i	−0.0747715	+	0.997201i	$0.523823\pi$
$138$	639633.	+	1.78149e7i	0.0207183	+	0.577041i
$139$	−1.72812e7	−	2.37856e7i	−0.545786	−	0.751211i	0.443646	−	0.896202i	$-0.353685\pi$
$139$	−1.72812e7	−	2.37856e7i	−0.545786	−	0.751211i	−0.989433	+	0.144991i	$0.953685\pi$
$140$	1.16909e7	−	1.13774e6i	0.360081	−	0.0350426i
$141$	3.84551e6	+	3.57894e6i	0.115528	+	0.107520i
$142$	1.71207e7	−	3.36014e7i	0.501780	−	0.984799i
$143$	1.74200e6	+	1.74200e6i	0.0498165	+	0.0498165i
$144$	−4.32486e7	+	3.10963e6i	−1.20699	+	0.0867841i
$145$	−2.28157e6	−	1.87688e6i	−0.0621507	−	0.0511267i
$146$	−1.77059e7	−	5.75298e6i	−0.470849	−	0.152988i
$147$	−9.67723e6	−	2.65069e7i	−0.251270	−	0.688254i
$148$	7.47952e6	−	4.72238e7i	0.189652	−	1.19742i
$149$	3.72125e7			0.921587			0.460794	−	0.887507i	$-0.347565\pi$
$149$	3.72125e7			0.921587			0.460794	+	0.887507i	$0.347565\pi$
$150$	−2.84192e7	+	4.57877e7i	−0.687532	+	1.10772i
$151$	5.87579e7			1.38882			0.694411	−	0.719579i	$-0.255665\pi$
$151$	5.87579e7			1.38882			0.694411	+	0.719579i	$0.255665\pi$
$152$	371607.	−	2.34623e6i	0.00858284	−	0.0541899i
$153$	1.51271e7	−	3.52368e6i	0.341456	−	0.0795383i
$154$	−2.01153e7	−	6.53585e6i	−0.443817	−	0.144205i
$155$	2.08770e7	+	1.25551e6i	0.450304	+	0.0270808i
$156$	−3.31381e6	+	647519.i	−0.0698863	+	0.0136558i
$157$	2.95703e7	+	2.95703e7i	0.609827	+	0.609827i	0.942901	−	0.333074i	$-0.108086\pi$
$157$	2.95703e7	+	2.95703e7i	0.609827	+	0.609827i	−0.333074	+	0.942901i	$0.608086\pi$
$158$	−1.04236e7	+	2.04575e7i	−0.210242	+	0.412622i
$159$	−4.33536e7	+	4.65828e7i	−0.855334	+	0.919042i
$160$	2.45638e7	+	5.63356e7i	0.474106	+	1.08733i
$161$	7.12713e6	+	9.80966e6i	0.134594	+	0.185252i
$162$	−6.67956e7	−	2.27064e7i	−1.23437	−	0.419609i
$163$	−6.11692e7	+	9.68825e6i	−1.10631	+	0.175222i	−0.682754	−	0.730649i	$-0.739218\pi$
$163$	−6.11692e7	+	9.68825e6i	−1.10631	+	0.175222i	−0.423555	+	0.905871i	$0.639218\pi$
$164$	−5.41938e6	+	3.93741e6i	−0.0959392	+	0.0697039i
$165$	3.28764e7	−	2.26924e7i	0.569758	−	0.393266i
$166$	7.71669e7	+	5.60650e7i	1.30934	+	0.951291i
$167$	7.35096e7	+	3.74550e7i	1.22134	+	0.622304i	0.941263	−	0.337674i	$-0.109640\pi$
$167$	7.35096e7	+	3.74550e7i	1.22134	+	0.622304i	0.280076	+	0.959978i	$0.409640\pi$
$168$	−9.79446e6	+	7.66778e6i	−0.159367	+	0.124763i
$169$	−5.90594e7	+	1.91896e7i	−0.941208	+	0.305817i
$170$	−1.57573e7	−	2.46785e7i	−0.245987	−	0.385254i
$171$	4.84102e6	−	7.78123e6i	0.0740373	−	0.119004i
$172$	5.21939e7	−	2.65941e7i	0.782115	−	0.398507i
$173$	3.42071e7	+	5.41787e6i	0.502290	+	0.0795549i	0.402438	−	0.915447i	$-0.368163\pi$
$173$	3.42071e7	+	5.41787e6i	0.502290	+	0.0795549i	0.0998522	+	0.995002i	$0.468163\pi$
$174$	−7.23755e6	−	881444.i	−0.104152	−	0.0126845i
$175$	1.35401e6	+	3.66308e7i	0.0190980	+	0.516670i
$176$		−	6.05917e7i		−	0.837758i
$177$	1.03798e8	+	2.96531e7i	1.40696	+	0.401943i
$178$	−6.50363e7	−	1.27641e8i	−0.864342	−	1.69637i
$179$	−4.02166e7	+	1.23774e8i	−0.524107	+	1.61304i	0.241967	+	0.970285i	$0.422207\pi$
$179$	−4.02166e7	+	1.23774e8i	−0.524107	+	1.61304i	−0.766074	+	0.642752i	$0.777793\pi$
$180$	641195.	+	5.47470e7i	0.00819476	+	0.699692i
$181$	4.44783e7	+	1.36890e8i	0.557537	+	1.71592i	0.689148	+	0.724620i	$0.257985\pi$
$181$	4.44783e7	+	1.36890e8i	0.557537	+	1.71592i	−0.131612	+	0.991301i	$0.542015\pi$
$182$	−3.94483e6	+	3.94483e6i	−0.0485041	+	0.0485041i
$183$	8.32485e7	−	1.23683e8i	1.00415	−	1.49187i
$184$	−8.61124e6	+	1.18524e7i	−0.101907	+	0.140263i
$185$	1.45703e8	+	3.21457e7i	1.69188	+	0.373269i
$186$	4.51190e7	−	2.50678e7i	0.514119	−	0.285642i
$187$	3.39534e6	+	2.14373e7i	0.0379697	+	0.239731i
$188$	−1.57392e6	−	9.93737e6i	−0.0172755	−	0.109073i
$189$	−4.63154e7	+	1.25566e7i	−0.499010	+	0.135287i
$190$	−1.68701e7	−	3.72196e6i	−0.178435	−	0.0393672i
$191$	3.43991e7	−	4.73463e7i	0.357216	−	0.491665i	−0.592155	−	0.805824i	$-0.701723\pi$
$191$	3.43991e7	−	4.73463e7i	0.357216	−	0.491665i	0.949370	+	0.314159i	$0.101723\pi$
$192$	2.73693e7	+	1.84217e7i	0.279067	+	0.187835i
$193$	−5.13817e7	+	5.13817e7i	−0.514468	+	0.514468i	−0.915892	−	0.401425i	$-0.868515\pi$
$193$	−5.13817e7	+	5.13817e7i	−0.514468	+	0.514468i	0.401425	+	0.915892i	$0.368515\pi$
$194$	−1.57308e7	−	4.84144e7i	−0.154684	−	0.476067i
$195$	−1.39626e6	−	1.04440e7i	−0.0134848	−	0.100866i
$196$	−1.67007e7	+	5.13993e7i	−0.158430	+	0.487597i
$197$	5.04074e7	+	9.89300e7i	0.469745	+	0.921926i	0.997372	+	0.0724503i	$0.0230819\pi$
$197$	5.04074e7	+	9.89300e7i	0.469745	+	0.921926i	−0.527627	+	0.849476i	$0.676918\pi$
$198$	3.83423e7	−	9.08244e7i	0.351034	−	0.831523i
$199$		−	1.13443e8i		−	1.02045i	−0.860040	−	0.510226i	$-0.829562\pi$
$199$		−	1.13443e8i		−	1.02045i	0.860040	−	0.510226i	$-0.170438\pi$
$200$	−4.15869e7	+	1.52326e7i	−0.367580	+	0.134638i
$201$	2.05229e7	−	1.68514e8i	0.178260	−	1.46369i
$202$	−1.14195e7	−	1.80867e6i	−0.0974802	−	0.0154394i
$203$	−4.41878e6	+	2.25148e6i	−0.0370737	+	0.0188900i
$204$	−2.69728e7	−	1.25454e7i	−0.222444	−	0.103461i
$205$	−1.12500e7	−	1.76192e7i	−0.0912039	−	0.142840i
$206$	−23176.1	+	7530.36i	−0.000184716	+	6.00178e-5i
$207$	−4.83887e7	+	2.92044e7i	−0.379182	+	0.228850i
$208$	−1.42402e7	−	7.25576e6i	−0.109722	−	0.0559064i
$209$	1.03604e7	+	7.52724e6i	0.0784988	+	0.0570327i
$210$	5.13877e7	+	7.44498e7i	0.382906	+	0.554748i
$211$	−1.41671e8	+	1.02930e8i	−1.03823	+	0.754317i	−0.969939	−	0.243349i	$-0.921754\pi$
$211$	−1.41671e8	+	1.02930e8i	−1.03823	+	0.754317i	−0.0682892	+	0.997666i	$0.521754\pi$
$212$	1.20377e8	−	1.90658e7i	0.867694	−	0.137429i
$213$	1.19488e8	−	4.29014e6i	0.847219	−	0.0304188i
$214$	−1.34959e8	−	1.85756e8i	−0.941359	−	1.29567i
$215$	7.30643e7	+	1.67569e8i	0.501384	+	1.14989i
$216$	−3.17213e7	−	4.85328e7i	−0.214172	−	0.327678i
$217$	1.59388e7	−	3.12817e7i	0.105888	−	0.207817i
$218$	−6.34135e7	−	6.34135e7i	−0.414557	−	0.414557i
$219$	−1.13195e7	−	5.79298e7i	−0.0728236	−	0.372690i
$220$	−7.63709e7	−	4.59285e6i	−0.483558	−	0.0290806i
$221$	5.44478e6	+	1.76912e6i	0.0339318	+	0.0110251i
$222$	3.45896e8	−	1.26281e8i	2.12183	−	0.774644i
$223$	5.08251e7	−	3.20897e8i	0.306910	−	1.93775i	−0.0383923	−	0.999263i	$-0.512224\pi$
$223$	5.08251e7	−	3.20897e8i	0.306910	−	1.93775i	0.345302	−	0.938491i	$-0.387776\pi$
$224$	1.03166e8			0.613293
$225$	−1.70660e8	−	8.25869e6i	−0.998831	−	0.0483362i
$226$	7.28375e7			0.419736
$227$	−5.20636e7	+	3.28716e8i	−0.295422	+	1.86522i	0.177502	+	0.984121i	$0.443199\pi$
$227$	−5.20636e7	+	3.28716e8i	−0.295422	+	1.86522i	−0.472924	+	0.881103i	$0.656801\pi$
$228$	−1.64872e7	+	6.01921e6i	−0.0921247	+	0.0336332i
$229$	4.63093e7	+	1.50468e7i	0.254826	+	0.0827980i	0.433644	−	0.901084i	$-0.357227\pi$
$229$	4.63093e7	+	1.50468e7i	0.254826	+	0.0827980i	−0.178818	+	0.983882i	$0.557227\pi$
$230$	8.22820e7	+	6.76872e7i	0.445921	+	0.366825i
$231$	−1.28599e7	−	6.58130e7i	−0.0686427	−	0.351293i
$232$	−4.23699e6	−	4.23699e6i	−0.0222766	−	0.0222766i
$233$	1.33207e8	−	2.61434e8i	0.689895	−	1.35399i	−0.234334	−	0.972156i	$-0.575291\pi$
$233$	1.33207e8	−	2.61434e8i	0.689895	−	1.35399i	0.924229	−	0.381839i	$-0.124709\pi$
$234$	−1.67541e7	−	1.98873e7i	−0.0854802	−	0.101466i
$235$	3.12502e7	−	3.04123e6i	0.157078	−	0.0152866i
$236$	−1.21525e8	−	1.67264e8i	−0.601827	−	0.828344i
$237$	−7.27478e7	+	2.61196e6i	−0.354978	+	0.0127452i
$238$	−4.85456e7	+	7.68886e6i	−0.233416	+	0.0369694i
$239$	−2.24679e8	+	1.63239e8i	−1.06456	+	0.773446i	−0.974926	−	0.222529i	$-0.928569\pi$
$239$	−2.24679e8	+	1.63239e8i	−1.06456	+	0.773446i	−0.0896309	+	0.995975i	$0.528569\pi$
$240$	−1.57352e8	+	2.05918e8i	−0.734741	+	0.961513i
$241$	−6.66431e6	−	4.84190e6i	−0.0306687	−	0.0222821i	0.572345	−	0.820013i	$-0.306034\pi$
$241$	−6.66431e6	−	4.84190e6i	−0.0306687	−	0.0222821i	−0.603014	+	0.797731i	$0.706034\pi$
$242$	−1.33361e8	−	6.79506e7i	−0.604886	−	0.308205i
$243$	−3.99226e7	−	2.20086e8i	−0.178483	−	0.983943i
$244$	−2.71567e8	+	8.82373e7i	−1.19677	+	0.388855i
$245$	−1.56983e8	−	6.16522e7i	−0.681978	−	0.267835i
$246$	−4.67779e7	−	2.17570e7i	−0.200340	−	0.0931806i
$247$	3.00969e6	−	1.53351e6i	0.0127081	−	0.00647512i
$248$	4.18967e7	+	6.63579e6i	0.174421	+	0.0276256i
$249$	−3.65601e7	+	3.00196e8i	−0.150075	+	1.23227i
$250$	9.24240e7	+	3.08548e8i	0.374106	+	1.24891i
$251$		−	1.27644e8i		−	0.509498i	−0.967007	−	0.254749i	$-0.918007\pi$
$251$		−	1.27644e8i		−	0.509498i	0.967007	−	0.254749i	$-0.0819928\pi$
$252$	8.46712e7	+	3.57446e7i	0.333299	+	0.140705i
$253$	−3.58559e7	−	7.03711e7i	−0.139200	−	0.273195i
$254$	3.88247e7	−	1.19490e8i	0.148658	−	0.457524i
$255$	4.41324e7	−	8.16713e7i	0.166673	−	0.308446i
$256$	1.08758e8	+	3.34723e8i	0.405155	+	1.24694i
$257$	−5.89957e7	+	5.89957e7i	−0.216797	+	0.216797i	−0.807147	−	0.590350i	$-0.798990\pi$
$257$	−5.89957e7	+	5.89957e7i	−0.216797	+	0.216797i	0.590350	+	0.807147i	$0.298990\pi$
$258$	3.74261e8	+	2.51908e8i	1.35677	+	0.913215i
$259$	1.47220e8	−	2.02631e8i	0.526523	−	0.724697i
$260$	−1.02247e7	+	1.73987e7i	−0.0360782	+	0.0613917i
$261$	−8.70159e6	−	2.14160e7i	−0.0302940	−	0.0745582i
$262$	5.75788e7	+	3.63538e8i	0.197792	+	1.24881i
$263$	−1.74955e7	−	1.10462e8i	−0.0593037	−	0.374429i	−0.999435	−	0.0336158i	$-0.989298\pi$
$263$	−1.74955e7	−	1.10462e8i	−0.0593037	−	0.374429i	0.940131	−	0.340813i	$-0.110702\pi$
$264$	7.08242e7	−	3.93495e7i	0.236902	−	0.131621i
$265$	3.68401e7	+	3.78551e8i	0.121607	+	1.24958i
$266$	−1.70457e7	+	2.34614e7i	−0.0555302	+	0.0764308i
$267$	2.53610e8	−	3.76790e8i	0.815411	−	1.21146i
$268$	−2.29901e8	+	2.29901e8i	−0.729573	+	0.729573i
$269$	9.71316e7	+	2.98940e8i	0.304248	+	0.936379i	0.979957	+	0.199210i	$0.0638377\pi$
$269$	9.71316e7	+	2.98940e8i	0.304248	+	0.936379i	−0.675709	+	0.737169i	$0.736162\pi$
$270$	−3.66169e8	+	2.09091e8i	−1.13216	+	0.646489i
$271$	−3.13466e7	+	9.64750e7i	−0.0956749	+	0.294457i	−0.987429	−	0.158063i	$-0.949475\pi$
$271$	−3.13466e7	+	9.64750e7i	−0.0956749	+	0.294457i	0.891754	+	0.452520i	$0.149475\pi$
$272$	−6.39249e7	−	1.25460e8i	−0.192610	−	0.378018i
$273$	−1.70073e7	−	4.85869e6i	−0.0505901	−	0.0144527i
$274$			2.04074e8i			0.599323i
$275$	2.86139e7	−	2.37039e8i	0.0829684	−	0.687313i
$276$	1.07453e8	+	1.30864e7i	0.307634	+	0.0374660i
$277$	−5.04494e8	−	7.99041e7i	−1.42619	−	0.225886i	−0.604856	−	0.796335i	$-0.706769\pi$
$277$	−5.04494e8	−	7.99041e7i	−1.42619	−	0.225886i	−0.821333	+	0.570449i	$0.806769\pi$
$278$	−3.86396e8	+	1.96879e8i	−1.07864	+	0.549594i
$279$	1.38950e8	+	8.64462e7i	0.383039	+	0.238304i
$280$	−4.46296e6	+	7.42111e7i	−0.0121498	+	0.202030i
$281$	−3.72942e8	+	1.21176e8i	−1.00270	+	0.325795i	−0.763942	−	0.645285i	$-0.776739\pi$
$281$	−3.72942e8	+	1.21176e8i	−1.00270	+	0.325795i	−0.238753	+	0.971080i	$0.576739\pi$
$282$	6.10132e7	−	4.77654e7i	0.162014	−	0.126836i
$283$	−5.10319e8	−	2.60021e8i	−1.33841	−	0.681955i	−0.369469	−	0.929243i	$-0.620461\pi$
$283$	−5.10319e8	−	2.60021e8i	−1.33841	−	0.681955i	−0.968942	+	0.247288i	$0.920461\pi$
$284$	−1.85261e8	−	1.34600e8i	−0.479921	−	0.348683i
$285$	−1.56615e7	−	5.24862e7i	−0.0400753	−	0.134304i
$286$	2.93980e7	−	2.13589e7i	0.0743082	−	0.0539881i
$287$	−3.46592e7	+	5.48948e6i	−0.0865430	+	0.0137071i
$288$	−4.09697e7	+	4.79126e8i	−0.101062	+	1.18189i
$289$	−2.11544e8	−	2.91166e8i	−0.515535	−	0.709574i
$290$	−3.26079e7	+	2.89084e7i	−0.0785110	+	0.0696036i
$291$	1.09957e8	−	1.18147e8i	0.261575	−	0.281058i
$292$	−5.13225e7	+	1.00726e8i	−0.120633	+	0.236756i
$293$	−2.15406e8	−	2.15406e8i	−0.500288	−	0.500288i	0.411239	−	0.911527i	$-0.365096\pi$
$293$	−2.15406e8	−	2.15406e8i	−0.500288	−	0.500288i	−0.911527	+	0.411239i	$0.865096\pi$
$294$	−4.08497e8	+	7.98203e7i	−0.937504	+	0.183188i
$295$	5.43802e8	−	3.47220e8i	1.23329	−	0.787459i
$296$	2.87810e8	+	9.35151e7i	0.645037	+	0.209585i
$297$	3.10757e8	−	3.35881e7i	0.688294	−	0.0743941i
$298$	8.58652e7	−	5.42131e8i	0.187958	−	1.18672i
$299$	−2.08323e7			−0.0450700
$300$	2.47616e8	+	2.13939e8i	0.529485	+	0.457472i
$301$	3.06864e8			0.648580
$302$	1.35580e8	−	8.56016e8i	0.283250	−	1.78837i
$303$	−1.25712e7	−	3.44338e7i	−0.0259614	−	0.0711108i
$304$	−7.90125e7	−	2.56727e7i	−0.161301	−	0.0524100i
$305$	−2.23989e8	−	8.62473e8i	−0.452041	−	1.74059i
$306$	−1.64302e7	−	2.28510e8i	−0.0327807	−	0.455912i
$307$	−3.46971e8	−	3.46971e8i	−0.684399	−	0.684399i	0.276589	−	0.960988i	$-0.410796\pi$
$307$	−3.46971e8	−	3.46971e8i	−0.684399	−	0.684399i	−0.960988	+	0.276589i	$0.910796\pi$
$308$	−5.83065e7	+	1.14433e8i	−0.113708	+	0.223164i
$309$	−56557.0	−	52636.5i	−0.000109051	−	0.000101492i
$310$	6.64631e7	−	3.01250e8i	0.126711	−	0.574329i
$311$	4.99844e8	+	6.87976e8i	0.942264	+	1.29692i	0.954879	+	0.296995i	$0.0959845\pi$
$311$	4.99844e8	+	6.87976e8i	0.942264	+	1.29692i	−0.0126146	+	0.999920i	$0.504015\pi$
$312$	−766813.	−	2.13571e7i	−0.00142938	−	0.0398109i
$313$	−4.86186e8	+	7.70042e7i	−0.896183	+	0.141941i	−0.587501	−	0.809224i	$-0.699888\pi$
$313$	−4.86186e8	+	7.70042e7i	−0.896183	+	0.141941i	−0.308683	+	0.951165i	$0.599888\pi$
$314$	4.99027e8	−	3.62564e8i	0.909642	−	0.660893i
$315$	−1.27208e8	+	2.57059e8i	−0.229313	+	0.463388i
$316$	1.12792e8	+	8.19484e7i	0.201083	+	0.146095i
$317$	−6.50771e8	−	3.31584e8i	−1.14741	−	0.584637i	−0.226350	−	0.974046i	$-0.572679\pi$
$317$	−6.50771e8	−	3.31584e8i	−1.14741	−	0.584637i	−0.921065	+	0.389409i	$0.872679\pi$
$318$	5.78607e8	+	7.39086e8i	1.00899	+	1.28884i
$319$	3.07217e7	−	9.98208e6i	0.0529880	−	0.0172169i
$320$	1.90853e8	−	4.95657e7i	0.325592	−	0.0845583i
$321$	3.07005e8	−	6.60066e8i	0.518057	−	1.11383i
$322$	1.59358e8	−	8.11968e7i	0.265998	−	0.135533i
$323$	2.93932e7	+	4.65543e6i	0.0485331	+	0.00768689i
$324$	−1.99631e8	+	3.79037e8i	−0.326078	+	0.619119i
$325$	−5.22823e7	−	3.51098e7i	−0.0844817	−	0.0567332i
$326$			9.13501e8i			1.46032i
$327$	7.81038e7	−	2.73394e8i	0.123525	−	0.432386i
$328$	−1.92485e7	−	3.77773e7i	−0.0301188	−	0.0591115i
$329$	1.62870e7	−	5.01262e7i	0.0252148	−	0.0776031i
$330$	−2.54735e8	−	5.31323e8i	−0.390203	−	0.813879i
$331$	1.72045e8	+	5.29501e8i	0.260763	+	0.802545i	0.992639	+	0.121108i	$0.0386446\pi$
$331$	1.72045e8	+	5.29501e8i	0.260763	+	0.802545i	−0.731877	+	0.681437i	$0.761355\pi$
$332$	4.09551e8	−	4.09551e8i	0.614222	−	0.614222i
$333$	8.82600e8	+	7.64193e8i	1.30981	+	1.13409i
$334$	7.15283e8	−	9.84503e8i	1.05043	−	1.44579i
$335$	−6.73083e8	−	7.59220e8i	−0.978165	−	1.10334i
$336$	2.11281e8	+	3.80279e8i	0.303860	+	0.546909i
$337$	1.93475e8	+	1.22155e9i	0.275373	+	1.73863i	0.606531	+	0.795060i	$0.292560\pi$
$337$	1.93475e8	+	1.22155e9i	0.275373	+	1.73863i	−0.331159	+	0.943575i	$0.607440\pi$
$338$	1.43288e8	+	9.04688e8i	0.201838	+	1.27435i
$339$	1.12156e8	+	2.01867e8i	0.156360	+	0.281428i
$340$	−1.62977e8	+	7.10622e7i	−0.224880	+	0.0980534i
$341$	−1.34414e8	+	1.85005e8i	−0.183571	+	0.252664i
$342$	−1.02191e8	−	8.84813e7i	−0.138140	−	0.119608i
$343$	−4.73418e8	+	4.73418e8i	−0.633454	+	0.633454i
$344$	1.14572e8	+	3.52617e8i	0.151749	+	0.467034i
$345$	−6.08943e7	+	3.32268e8i	−0.0798381	+	0.435634i
$346$	1.57861e8	−	4.85846e8i	0.204884	−	0.630568i
$347$	−1.02439e8	−	2.01048e8i	−0.131617	−	0.258313i	0.815787	−	0.578352i	$-0.196304\pi$
$347$	−1.02439e8	−	2.01048e8i	−0.131617	−	0.258313i	−0.947404	+	0.320039i	$0.896304\pi$
$348$	−1.21615e7	+	4.25699e7i	−0.0154689	+	0.0541471i
$349$		−	6.21336e7i		−	0.0782416i	−0.999234	−	0.0391208i	$-0.987544\pi$
$349$		−	6.21336e7i		−	0.0782416i	0.999234	−	0.0391208i	$-0.0124557\pi$
$350$	5.36782e8	+	6.47972e7i	0.669206	+	0.0807826i
$351$	2.93189e7	−	7.70562e7i	0.0361886	−	0.0951115i
$352$	−6.63702e8	−	1.05120e8i	−0.811099	−	0.128465i
$353$	3.47583e8	−	1.77102e8i	0.420579	−	0.214296i	−0.230876	−	0.972983i	$-0.574159\pi$
$353$	3.47583e8	−	1.77102e8i	0.420579	−	0.214296i	0.651455	+	0.758688i	$0.274159\pi$
$354$	6.71509e8	−	1.44376e9i	0.804526	−	1.72975i
$355$	4.53991e8	−	5.51881e8i	0.538577	−	0.654706i
$356$	−8.27305e8	+	2.68808e8i	−0.971831	+	0.315767i
$357$	−9.60606e7	−	1.22703e8i	−0.111739	−	0.142731i
$358$	1.71041e9	+	8.71498e8i	1.97020	+	1.00387i
$359$	1.25747e9	+	9.13609e8i	1.43439	+	1.04215i	0.989177	+	0.146726i	$0.0468736\pi$
$359$	1.25747e9	+	9.13609e8i	1.43439	+	1.04215i	0.445217	+	0.895423i	$0.353126\pi$
$360$	−3.42881e8	−	5.01981e7i	−0.387333	−	0.0567059i
$361$	−7.08952e8	+	5.15084e8i	−0.793125	+	0.576239i
$362$	2.09692e9	−	3.32120e8i	2.32328	−	0.367972i
$363$	−1.70272e7	−	4.74237e8i	−0.0186840	−	0.520382i
$364$	1.99119e7	+	2.74063e7i	0.0216400	+	0.0297849i
$365$	−3.04152e8	−	1.78741e8i	−0.327390	−	0.192398i
$366$	−1.60979e9	−	1.49820e9i	−1.71627	−	1.59730i
$367$	−7.27723e8	+	1.42824e9i	−0.768484	+	1.50823i	0.0903107	+	0.995914i	$0.471214\pi$
$367$	−7.27723e8	+	1.42824e9i	−0.768484	+	1.50823i	−0.858794	+	0.512320i	$0.828786\pi$
$368$	3.62302e8	+	3.62302e8i	0.378969	+	0.378969i
$369$	−1.17304e7	−	1.63145e8i	−0.0121540	−	0.169037i
$370$	8.04517e8	−	2.04851e9i	0.825713	−	2.10248i
$371$	6.07205e8	+	1.97293e8i	0.617343	+	0.200587i
$372$	−1.07485e8	−	2.94413e8i	−0.108255	−	0.296522i
$373$	−3.67596e7	+	2.32091e8i	−0.0366767	+	0.231567i	−0.999217	−	0.0395722i	$-0.987401\pi$
$373$	−3.67596e7	+	2.32091e8i	−0.0366767	+	0.231567i	0.962540	+	0.271140i	$0.0874005\pi$
$374$	3.20145e8			0.316444
$375$	−7.12816e8	+	7.31257e8i	−0.698020	+	0.716078i
$376$	6.36809e7			0.0617806
$377$	1.33289e6	−	8.41554e6i	0.00128115	−	0.00808886i
$378$	7.60615e7	+	7.03721e8i	0.0724342	+	0.670161i
$379$	5.27313e8	+	1.71334e8i	0.497544	+	0.161662i	0.547030	−	0.837113i	$-0.315758\pi$
$379$	5.27313e8	+	1.71334e8i	0.497544	+	0.161662i	−0.0494862	+	0.998775i	$0.515758\pi$
$380$	−3.83475e7	+	9.76429e7i	−0.0358505	+	0.0912847i
$381$	3.90946e8	−	7.63909e7i	0.362143	−	0.0707626i
$382$	−6.10393e8	−	6.10393e8i	−0.560258	−	0.560258i
$383$	1.02201e7	−	2.00581e7i	0.00929525	−	0.0182429i	−0.886312	−	0.463088i	$-0.846741\pi$
$383$	1.02201e7	−	2.00581e7i	0.00929525	−	0.0182429i	0.895607	+	0.444845i	$0.146741\pi$
$384$	−5.65161e8	+	6.07255e8i	−0.509346	+	0.547283i
$385$	−3.45541e8	−	2.03065e8i	−0.308594	−	0.181352i
$386$	6.29997e8	+	8.67116e8i	0.557549	+	0.767400i
$387$	−1.21863e8	+	1.42515e9i	−0.106877	+	1.24989i
$388$	−3.05308e8	+	4.83560e7i	−0.265355	+	0.0420281i
$389$	−7.34333e8	+	5.33524e8i	−0.632513	+	0.459548i	−0.857270	−	0.514867i	$-0.827841\pi$
$389$	−7.34333e8	+	5.33524e8i	−0.632513	+	0.459548i	0.224757	+	0.974415i	$0.427841\pi$
$390$	−1.55375e8	−	3.75732e6i	−0.132634	−	0.00320739i
$391$	−1.48484e8	−	1.07880e8i	−0.125621	−	0.0912690i
$392$	−3.04782e8	−	1.55294e8i	−0.255557	−	0.130213i
$393$	−9.18876e8	+	7.19359e8i	−0.763630	+	0.597822i
$394$	1.55758e9	−	5.06088e8i	1.28296	−	0.416859i
$395$	−2.76403e8	+	3.36002e8i	−0.225659	+	0.274316i
$396$	−5.08298e8	−	3.16233e8i	−0.411325	−	0.255902i
$397$	9.22687e8	−	4.70132e8i	0.740095	−	0.377097i	−0.0429376	−	0.999078i	$-0.513672\pi$
$397$	9.22687e8	−	4.70132e8i	0.740095	−	0.377097i	0.783033	+	0.621980i	$0.213672\pi$
$398$	−1.65270e9	−	2.61762e8i	−1.31403	−	0.208121i
$399$	−9.12699e7	−	1.11155e7i	−0.0719320	−	0.00876042i
$400$	2.98652e8	+	1.51987e9i	0.233322	+	1.18740i
$401$		−	1.48011e8i		−	0.114627i	−0.998356	−	0.0573136i	$-0.981747\pi$
$401$		−	1.48011e8i		−	0.114627i	0.998356	−	0.0573136i	$-0.0182535\pi$
$402$	−2.40765e9	−	6.87824e8i	−1.84843	−	0.528063i
$403$	2.73840e7	+	5.37441e7i	0.0208415	+	0.0409037i
$404$	−2.16950e7	+	6.67703e7i	−0.0163691	+	0.0503789i
$405$	−1.14332e9	−	6.92868e8i	−0.855216	−	0.518272i
$406$	2.26048e7	+	6.95704e7i	0.0167633	+	0.0515921i
$407$	−1.15359e9	+	1.15359e9i	−0.848145	+	0.848145i
$408$	1.05133e8	−	1.56196e8i	0.0766350	−	0.113857i
$409$	4.52660e8	−	6.23033e8i	0.327145	−	0.450276i	−0.613487	−	0.789705i	$-0.710234\pi$
$409$	4.52660e8	−	6.23033e8i	0.327145	−	0.450276i	0.940632	+	0.339429i	$0.110234\pi$
$410$	−2.82645e8	+	1.23241e8i	−0.202534	+	0.0883101i
$411$	−5.65586e8	+	3.14236e8i	−0.401839	+	0.223259i
$412$	23148.1	+	146152.i	1.63071e−5	+	0.000102959i
$413$	−1.69428e8	−	1.06972e9i	−0.118348	−	0.747217i
$414$	3.13812e8	+	7.72339e8i	0.217354	+	0.534942i
$415$	1.19905e9	+	1.35250e9i	0.823509	+	0.928897i
$416$	−1.04183e8	+	1.43395e8i	−0.0709527	+	0.0976580i
$417$	−1.14062e9	−	7.67730e8i	−0.770310	−	0.518481i
$418$	1.33567e8	−	1.33567e8i	0.0894502	−	0.0894502i
$419$	−1.21056e7	−	3.72572e7i	−0.00803965	−	0.0247435i	0.946956	−	0.321363i	$-0.104141\pi$
$419$	−1.21056e7	−	3.72572e7i	−0.00803965	−	0.0247435i	−0.954996	+	0.296619i	$0.904141\pi$
$420$	4.95326e8	−	2.37477e8i	0.326226	−	0.156405i
$421$	6.70341e8	−	2.06310e9i	0.437833	−	1.34751i	−0.452323	−	0.891854i	$-0.649405\pi$
$421$	6.70341e8	−	2.06310e9i	0.437833	−	1.34751i	0.890156	−	0.455656i	$-0.150595\pi$
$422$	1.17265e9	+	2.30145e9i	0.759579	+	1.49076i
$423$	2.26329e8	+	9.55468e7i	0.145395	+	0.0613797i
$424$			7.71401e8i			0.491473i
$425$	−1.90831e8	−	5.20994e8i	−0.120583	−	0.329209i
$426$	2.13209e8	−	1.75067e9i	0.133620	−	1.09716i
$427$	−1.47740e9	−	2.33996e8i	−0.918331	−	0.145449i
$428$	−1.24227e9	+	6.32968e8i	−0.765883	+	0.390237i
$429$	1.04463e8	+	4.85871e7i	0.0638796	+	0.0297112i
$430$	2.60982e9	−	6.77787e8i	1.58296	−	0.411106i
$431$	1.78525e9	−	5.80062e8i	1.07406	−	0.348983i	0.281991	−	0.959417i	$-0.409005\pi$
$431$	1.78525e9	−	5.80062e8i	1.07406	−	0.348983i	0.792067	+	0.610434i	$0.209005\pi$
$432$	−1.85001e9	+	8.30219e8i	−1.10403	+	0.495449i
$433$	−4.90994e8	−	2.50174e8i	−0.290649	−	0.148093i	0.302587	−	0.953122i	$-0.402150\pi$
$433$	−4.90994e8	−	2.50174e8i	−0.290649	−	0.148093i	−0.593236	+	0.805029i	$0.702150\pi$
$434$	−4.18951e8	−	3.04386e8i	−0.246008	−	0.178735i
$435$	−1.30329e8	−	4.58585e7i	−0.0759152	−	0.0267120i
$436$	−4.40559e8	+	3.20085e8i	−0.254567	+	0.184954i
$437$	−1.06957e8	+	1.69403e7i	−0.0613091	+	0.00971040i
$438$	−8.70072e8	+	3.12394e7i	−0.494761	+	0.0177641i
$439$	−2.07966e8	−	2.86241e8i	−0.117319	−	0.161475i	0.746319	−	0.665589i	$-0.231819\pi$
$439$	−2.07966e8	−	2.86241e8i	−0.117319	−	0.161475i	−0.863638	+	0.504113i	$0.831819\pi$
$440$	1.04329e8	−	4.72878e8i	0.0583874	−	0.264646i
$441$	−8.50229e8	−	1.00923e9i	−0.472064	−	0.560344i
$442$	3.83369e7	−	7.52404e7i	0.0211173	−	0.0414451i
$443$	−3.39333e8	−	3.39333e8i	−0.185444	−	0.185444i	0.608279	−	0.793723i	$-0.291860\pi$
$443$	−3.39333e8	−	3.39333e8i	−0.185444	−	0.185444i	−0.793723	+	0.608279i	$0.791860\pi$
$444$	−4.28799e8	−	2.19447e9i	−0.232495	−	1.18984i
$445$	−6.82365e8	−	2.62745e9i	−0.367077	−	1.41343i
$446$	−4.55773e9	−	1.48090e9i	−2.43263	−	0.790410i
$447$	1.63472e9	−	5.96808e8i	0.865699	−	0.316052i
$448$	5.17801e7	−	3.26927e8i	0.0272076	−	0.171782i
$449$	1.19146e9			0.621178			0.310589	−	0.950544i	$-0.399474\pi$
$449$	1.19146e9			0.621178			0.310589	+	0.950544i	$0.399474\pi$
$450$	−5.14102e8	+	2.46721e9i	−0.265954	+	1.27633i
$451$	2.28568e8			0.117327
$452$	6.91891e7	−	4.36843e8i	0.0352414	−	0.222506i
$453$	2.58119e9	−	9.42350e8i	1.30460	−	0.476287i
$454$	4.66879e9	+	1.51698e9i	2.34158	+	0.760825i
$455$	−8.91023e7	+	5.68923e7i	−0.0443454	+	0.0283148i
$456$	−2.13041e7	−	1.09028e8i	−0.0105217	−	0.0538471i
$457$	−1.25931e9	−	1.25931e9i	−0.617200	−	0.617200i	0.327612	−	0.944812i	$-0.393756\pi$
$457$	−1.25931e9	−	1.25931e9i	−0.617200	−	0.617200i	−0.944812	+	0.327612i	$0.893756\pi$
$458$	3.26065e8	−	6.39939e8i	0.158590	−	0.311250i
$459$	6.08010e8	−	3.97399e8i	0.293472	−	0.191815i
$460$	4.84115e8	−	4.29190e8i	0.231897	−	0.205588i
$461$	−2.11798e9	−	2.91515e9i	−1.00686	−	1.38582i	−0.921021	−	0.389513i	$-0.872643\pi$
$461$	−2.11798e9	−	2.91515e9i	−1.00686	−	1.38582i	−0.0858372	−	0.996309i	$-0.527357\pi$
$462$	−9.88472e8	+	3.54905e7i	−0.466356	+	0.0167442i
$463$	−1.30891e9	+	2.07310e8i	−0.612879	+	0.0970705i	−0.455154	−	0.890413i	$-0.650416\pi$
$463$	−1.30891e9	+	2.07310e8i	−0.612879	+	0.0970705i	−0.157725	+	0.987483i	$0.550416\pi$
$464$	−1.69539e8	+	1.23177e8i	−0.0787872	+	0.0572423i
$465$	9.37247e8	−	2.79668e8i	0.432283	−	0.128990i
$466$	−3.50135e9	−	2.54388e9i	−1.60282	−	1.16452i
$467$	3.62054e9	+	1.84476e9i	1.64499	+	0.838166i	0.997073	+	0.0764578i	$0.0243611\pi$
$467$	3.62054e9	+	1.84476e9i	1.64499	+	0.838166i	0.647920	+	0.761708i	$0.275639\pi$
$468$	−1.35189e8	+	8.15915e7i	−0.0609649	+	0.0367947i
$469$	−1.61983e9	+	5.26314e8i	−0.725043	+	0.235581i
$470$	2.78014e7	−	4.62288e8i	0.0123516	−	0.205385i
$471$	1.77325e9	+	8.24759e8i	0.781981	+	0.363709i
$472$	1.16596e9	−	5.94087e8i	0.510372	−	0.260048i
$473$	−1.97416e9	−	3.12677e8i	−0.857767	−	0.135857i
$474$	−1.29808e8	+	1.06586e9i	−0.0559858	+	0.459700i
$475$	−2.96978e8	−	1.37746e8i	−0.127144	−	0.0589729i
$476$			2.98456e8i			0.126840i
$477$	−1.15741e9	+	2.74165e9i	−0.488284	+	1.15664i
$478$	1.85972e9	+	3.64990e9i	0.778842	+	1.52856i
$479$	−8.29859e8	+	2.55404e9i	−0.345009	+	1.06183i	0.616570	+	0.787300i	$0.288522\pi$
$479$	−8.29859e8	+	2.55404e9i	−0.345009	+	1.06183i	−0.961579	+	0.274528i	$0.911478\pi$
$480$	1.98257e9	+	2.08083e9i	0.818248	+	0.858802i
$481$	1.32975e8	+	4.09256e8i	0.0544833	+	0.167682i
$482$	−8.59169e7	+	8.59169e7i	−0.0349473	+	0.0349473i
$483$	4.70416e8	+	3.16628e8i	0.189962	+	0.127860i
$484$	−5.34214e8	+	7.35283e8i	−0.214169	+	0.294779i
$485$	−9.34365e7	−	9.60108e8i	−0.0371895	−	0.382141i
$486$	−3.29845e9	+	7.37821e7i	−1.30341	+	0.0291558i
$487$	6.42820e8	+	4.05860e9i	0.252196	+	1.59230i	0.710625	+	0.703571i	$0.248412\pi$
$487$	6.42820e8	+	4.05860e9i	0.252196	+	1.59230i	−0.458430	+	0.888731i	$0.651588\pi$
$488$	−2.82722e8	−	1.78504e9i	−0.110126	−	0.695310i
$489$	−2.53174e9	+	1.40662e9i	−0.979126	+	0.543997i
$490$	−1.26041e9	+	2.14475e9i	−0.483978	+	0.823551i
$491$	−1.59241e9	+	2.19176e9i	−0.607112	+	0.835618i	−0.996336	−	0.0855253i	$-0.972743\pi$
$491$	−1.59241e9	+	2.19176e9i	−0.607112	+	0.835618i	0.389224	+	0.921143i	$0.372743\pi$
$492$	−1.74922e8	+	2.59883e8i	−0.0662166	+	0.0983785i
$493$	5.30803e7	−	5.30803e7i	0.0199512	−	0.0199512i
$494$	−1.53964e7	−	4.73853e7i	−0.00574612	−	0.0176847i
$495$	1.08030e9	−	1.52413e9i	0.400338	−	0.564812i
$496$	4.58439e8	−	1.41093e9i	0.168692	−	0.519182i
$497$	−5.44603e8	−	1.06884e9i	−0.198991	−	0.390541i
$498$	4.28905e9	+	1.22531e9i	1.55618	+	0.444572i
$499$		−	6.57247e7i		−	0.0236797i	−0.999930	−	0.0118399i	$-0.996231\pi$
$499$		−	6.57247e7i		−	0.0236797i	0.999930	−	0.0118399i	$-0.00376883\pi$
$500$	1.93831e9	−	2.61220e8i	0.693470	−	0.0934570i
$501$	3.82993e9	+	4.66437e8i	1.36069	+	0.165715i
$502$	−1.85959e9	−	2.94529e8i	−0.656075	−	0.103912i
$503$	3.13698e9	−	1.59837e9i	1.09906	−	0.560001i	0.192171	−	0.981361i	$-0.438447\pi$
$503$	3.13698e9	−	1.59837e9i	1.09906	−	0.560001i	0.906893	+	0.421360i	$0.138447\pi$
$504$	−3.07289e8	+	4.93923e8i	−0.106916	+	0.171851i
$505$	−2.03928e8	−	8.00893e7i	−0.0704624	−	0.0276729i
$506$	−1.10794e9	+	3.59991e8i	−0.380180	+	0.123528i
$507$	−2.28668e9	+	1.79017e9i	−0.779251	+	0.610052i
$508$	−6.79761e8	−	3.46356e8i	−0.230056	−	0.117219i
$509$	−8.82697e8	−	6.41317e8i	−0.296688	−	0.215556i	0.429476	−	0.903078i	$-0.358698\pi$
$509$	−8.82697e8	−	6.41317e8i	−0.296688	−	0.215556i	−0.726163	+	0.687522i	$0.758698\pi$
$510$	−1.08800e9	−	8.31395e8i	−0.363189	−	0.277531i
$511$	−4.79099e8	+	3.48086e8i	−0.158837	+	0.115402i
$512$	2.88477e9	−	4.56903e8i	0.949876	−	0.150446i
$513$	8.78686e7	−	4.19464e8i	0.0287358	−	0.137178i
$514$	7.23352e8	+	9.95609e8i	0.234952	+	0.323384i
$515$	−459605.	+	44728.2i	−0.000148272	+	1.44297e-5i
$516$	1.86633e9	−	2.00534e9i	0.598019	−	0.642561i
$517$	−1.55856e8	+	3.05884e8i	−0.0496027	+	0.0973508i
$518$	−2.61234e9	−	2.61234e9i	−0.825801	−	0.825801i
$519$	1.58958e9	−	3.10605e8i	0.499112	−	0.0975265i
$520$	−9.86425e7	−	8.11457e7i	−0.0307647	−	0.0253078i
$521$	2.41642e9	+	7.85142e8i	0.748584	+	0.243230i	0.658372	−	0.752693i	$-0.271246\pi$
$521$	2.41642e9	+	7.85142e8i	0.748584	+	0.243230i	0.0902121	+	0.995923i	$0.471246\pi$
$522$	−3.32077e8	+	7.73536e7i	−0.102186	+	0.0238031i
$523$	−4.25978e8	+	2.68952e9i	−0.130206	+	0.822088i	0.832990	+	0.553288i	$0.186627\pi$
$523$	−4.25978e8	+	2.68952e9i	−0.130206	+	0.822088i	−0.963196	+	0.268800i	$0.913373\pi$
$524$	2.23501e9			0.678611
$525$	6.46961e8	+	1.58745e9i	0.195128	+	0.478788i
$526$	−1.64965e9			−0.494243
$527$	−8.31321e7	+	5.24876e8i	−0.0247418	+	0.156214i
$528$	−9.71761e8	−	2.66175e9i	−0.287303	−	0.786953i
$529$	−2.60301e9	−	8.45769e8i	−0.764506	−	0.248403i
$530$	5.59994e9	+	3.36773e8i	1.63387	+	0.0982590i
$531$	5.03533e9	−	3.62047e8i	1.45948	−	0.104938i
$532$	1.24518e8	+	1.24518e8i	0.0358543	+	0.0358543i
$533$	2.73707e7	−	5.37180e7i	0.00782962	−	0.0153665i
$534$	−4.90409e9	−	4.56414e9i	−1.39368	−	1.29707i
$535$	−1.73900e9	−	3.98831e9i	−0.490979	−	1.12603i
$536$	−1.20957e9	−	1.66483e9i	−0.339278	−	0.466976i
$537$	2.18381e8	+	6.08230e9i	0.0608562	+	1.69495i
$538$	4.57925e9	−	7.25282e8i	1.26782	−	0.200802i
$539$	1.49188e9	−	1.08391e9i	0.410367	−	0.298149i
$540$	9.06192e8	+	2.39472e9i	0.247652	+	0.654449i
$541$	1.08056e8	+	7.85071e7i	0.0293398	+	0.0213166i	0.602359	−	0.798226i	$-0.294228\pi$
$541$	1.08056e8	+	7.85071e7i	0.0293398	+	0.0213166i	−0.573019	+	0.819542i	$0.694228\pi$
$542$	1.33317e9	+	6.79284e8i	0.359656	+	0.183254i
$543$	4.14933e9	+	5.30016e9i	1.11219	+	1.42066i
$544$	−1.48515e9	+	4.82554e8i	−0.395524	+	0.128514i
$545$	−9.14548e8	−	1.43233e9i	−0.242002	−	0.379013i
$546$	−1.10027e8	+	2.36560e8i	−0.0289285	+	0.0621968i
$547$	4.30848e9	−	2.19528e9i	1.12556	−	0.573501i	0.210811	−	0.977527i	$-0.432390\pi$
$547$	4.30848e9	−	2.19528e9i	1.12556	−	0.573501i	0.914747	+	0.404026i	$0.132390\pi$
$548$	1.22393e9	+	1.93852e8i	0.317706	+	0.0503198i
$549$	1.67344e9	−	6.76844e9i	0.431626	−	1.74576i
$550$	−3.38728e9	−	9.63813e8i	−0.868124	−	0.247015i
$551$		−	4.42910e7i		−	0.0112794i
$552$	−1.88200e8	+	6.58772e8i	−0.0476247	+	0.166705i
$553$	3.31570e8	+	6.50743e8i	0.0833753	+	0.163633i
$554$	−2.32817e9	+	7.16538e9i	−0.581742	+	1.79042i
$555$	6.91620e9	−	9.24628e8i	1.71728	−	0.229584i
$556$	8.13738e8	+	2.50443e9i	0.200781	+	0.617941i
$557$	3.14880e9	−	3.14880e9i	0.772061	−	0.772061i	−0.206406	−	0.978467i	$-0.566177\pi$
$557$	3.14880e9	−	3.14880e9i	0.772061	−	0.772061i	0.978467	+	0.206406i	$0.0661766\pi$
$558$	1.58001e9	−	1.82482e9i	0.384982	−	0.444633i
$559$	−3.09888e8	+	4.26525e8i	−0.0750350	+	0.103277i
$560$	2.53905e9	+	5.60176e8i	0.610959	+	0.134793i
$561$	4.92964e8	+	8.87274e8i	0.117881	+	0.212172i
$562$	9.04822e8	+	5.71282e9i	0.215024	+	1.35761i
$563$	1.39380e8	+	8.80012e8i	0.0329171	+	0.207830i	0.998665	−	0.0516511i	$-0.0164484\pi$
$563$	1.39380e8	+	8.80012e8i	0.0329171	+	0.207830i	−0.965748	+	0.259481i	$0.916448\pi$
$564$	−2.28516e8	−	4.11300e8i	−0.0536338	−	0.0965342i
$565$	1.34783e9	+	2.97364e8i	0.314387	+	0.0693614i
$566$	−4.96565e9	+	6.83463e9i	−1.15111	+	1.58437i
$567$	−1.83322e9	+	1.29440e9i	−0.422352	+	0.298214i
$568$	1.02487e9	−	1.02487e9i	0.234666	−	0.234666i
$569$	−1.72288e9	−	5.30248e9i	−0.392069	−	1.20666i	−0.931221	−	0.364455i	$-0.881255\pi$
$569$	−1.72288e9	−	5.30248e9i	−0.392069	−	1.20666i	0.539152	−	0.842208i	$-0.318745\pi$
$570$	−8.00785e8	+	1.07057e8i	−0.181115	+	0.0242133i
$571$	1.77701e9	−	5.46907e9i	0.399451	−	1.22938i	−0.525990	−	0.850491i	$-0.676305\pi$
$571$	1.77701e9	−	5.46907e9i	0.399451	−	1.22938i	0.925441	−	0.378892i	$-0.123695\pi$
$572$	−1.00175e8	−	1.96604e8i	−0.0223806	−	0.0439244i
$573$	7.51797e8	−	2.63158e9i	0.166940	−	0.584353i
$574$			5.17601e8i			0.114236i
$575$	1.24625e9	+	1.58844e9i	0.273382	+	0.348445i
$576$	1.49776e9	+	3.70309e8i	0.326560	+	0.0807394i
$577$	−6.09877e9	−	9.65950e8i	−1.32168	−	0.209334i	−0.544580	−	0.838709i	$-0.683311\pi$
$577$	−6.09877e9	−	9.65950e8i	−1.32168	−	0.209334i	−0.777102	+	0.629375i	$0.783311\pi$
$578$	−4.72998e9	+	2.41005e9i	−1.01885	+	0.519132i
$579$	−1.43311e9	+	3.08122e9i	−0.306835	+	0.659701i
$580$	1.42404e8	+	2.23026e8i	0.0303056	+	0.0474634i
$581$	2.88560e9	−	9.37589e8i	0.610408	−	0.198334i
$582$	−1.46751e9	−	1.87452e9i	−0.308567	−	0.394149i
$583$	−3.70533e9	−	1.88796e9i	−0.774439	−	0.394596i
$584$	−5.78864e8	−	4.20569e8i	−0.120263	−	0.0873760i
$585$	−2.28836e8	−	4.36405e8i	−0.0472584	−	0.0901247i
$586$	−3.63518e9	+	2.64111e9i	−0.746249	+	0.542182i
$587$	−1.61531e8	+	2.55839e7i	−0.0329626	+	0.00522077i	−0.172894	−	0.984940i	$-0.555312\pi$
$587$	−1.61531e8	+	2.55839e7i	−0.0329626	+	0.00522077i	0.139931	+	0.990161i	$0.455312\pi$
$588$	9.06865e7	+	2.52578e9i	0.0183959	+	0.512360i
$589$	1.84298e8	+	2.53665e8i	0.0371636	+	0.0511514i
$590$	−3.80371e9	−	8.72359e9i	−0.762474	−	1.74869i
$591$	3.80099e9	+	3.53750e9i	0.757426	+	0.704921i
$592$	4.80490e9	−	9.43015e9i	0.951828	−	1.86807i
$593$	1.12540e9	+	1.12540e9i	0.221624	+	0.221624i	0.809182	−	0.587558i	$-0.199911\pi$
$593$	1.12540e9	+	1.12540e9i	0.221624	+	0.221624i	−0.587558	+	0.809182i	$0.699911\pi$
$594$	2.27721e8	−	4.60478e9i	0.0445810	−	0.901481i
$595$	−9.29704e8	−	5.59113e7i	−0.180940	−	0.0108815i
$596$	−3.16987e9	−	1.02995e9i	−0.613309	−	0.199276i
$597$	−1.81939e9	−	4.98349e9i	−0.349957	−	0.958568i
$598$	−4.80690e7	+	3.03496e8i	−0.00919202	+	0.0580362i
$599$	8.59373e9			1.63376			0.816879	−	0.576809i	$-0.195702\pi$
$599$	8.59373e9			1.63376			0.816879	+	0.576809i	$0.195702\pi$
$600$	−1.58259e9	+	1.33612e9i	−0.299115	+	0.252532i
$601$	5.88695e9			1.10619			0.553095	−	0.833118i	$-0.313447\pi$
$601$	5.88695e9			1.10619			0.553095	+	0.833118i	$0.313447\pi$
$602$	7.08068e8	−	4.47056e9i	0.132278	−	0.835169i
$603$	−1.80105e9	−	7.73186e9i	−0.334514	−	1.43606i
$604$	−5.00517e9	−	1.62628e9i	−0.924250	−	0.300307i
$605$	−2.19036e9	−	1.80185e9i	−0.402136	−	0.330807i
$606$	−5.30658e8	+	1.03690e8i	−0.0968635	+	0.0189271i
$607$	−3.18214e9	−	3.18214e9i	−0.577510	−	0.577510i	0.356707	−	0.934216i	$-0.383900\pi$
$607$	−3.18214e9	−	3.18214e9i	−0.577510	−	0.577510i	−0.934216	+	0.356707i	$0.883900\pi$
$608$	−4.18289e8	+	8.20939e8i	−0.0754769	+	0.148132i
$609$	−1.58005e8	+	1.69774e8i	−0.0283473	+	0.0304586i
$610$	−1.30818e10	+	1.27310e9i	−2.33353	+	0.227096i
$611$	5.32252e7	+	7.32582e7i	0.00944003	+	0.0129931i
$612$	−1.38610e9	−	1.18524e8i	−0.244435	−	0.0209015i
$613$	−1.49080e9	+	2.36119e8i	−0.261401	+	0.0414018i	−0.285759	−	0.958301i	$-0.592246\pi$
$613$	−1.49080e9	+	2.36119e8i	−0.261401	+	0.0414018i	0.0243584	+	0.999703i	$0.492246\pi$
$614$	−5.85548e9	+	4.25426e9i	−1.02088	+	0.741710i
$615$	−7.76779e8	−	5.93576e8i	−0.134659	−	0.102900i
$616$	−6.57636e8	−	4.77801e8i	−0.113358	−	0.0823596i
$617$	−3.72950e9	−	1.90028e9i	−0.639223	−	0.325701i	0.104166	−	0.994560i	$-0.466783\pi$
$617$	−3.72950e9	−	1.90028e9i	−0.639223	−	0.325701i	−0.743389	+	0.668859i	$0.766783\pi$
$618$	−897338.	+	702498.i	−0.000152931	+	0.000119725i
$619$	−4.41500e9	+	1.43452e9i	−0.748193	+	0.243103i	−0.658204	−	0.752840i	$-0.728683\pi$
$619$	−4.41500e9	+	1.43452e9i	−0.748193	+	0.243103i	−0.0899897	+	0.995943i	$0.528683\pi$
$620$	−1.74361e9	−	6.84773e8i	−0.293818	−	0.115392i
$621$	−1.65731e9	+	2.05898e9i	−0.277704	+	0.345010i
$622$	1.11762e10	−	5.69454e9i	1.86220	−	0.948838i
$623$	−4.50076e9	−	7.12851e8i	−0.745724	−	0.118111i
$624$	−7.41931e8	−	9.03580e7i	−0.122241	−	0.0148875i
$625$	4.50600e8	+	6.08686e9i	0.0738263	+	0.997271i
$626$			7.26070e9i			1.18295i
$627$	5.75845e8	+	1.64509e8i	0.0932973	+	0.0266534i
$628$	−1.70045e9	−	3.33732e9i	−0.273971	−	0.537699i
$629$	−1.17154e9	+	3.60563e9i	−0.187707	+	0.577703i
$630$	3.45145e9	+	2.44638e9i	0.549932	+	0.389791i
$631$	1.16141e9	+	3.57444e9i	0.184027	+	0.566376i	0.999930	−	0.0118118i	$-0.00375990\pi$
$631$	1.16141e9	+	3.57444e9i	0.184027	+	0.566376i	−0.815903	+	0.578188i	$0.803760\pi$
$632$	−6.23972e8	+	6.23972e8i	−0.0983230	+	0.0983230i
$633$	−4.57274e9	+	6.79375e9i	−0.716578	+	1.06463i
$634$	−6.33231e9	+	8.71567e9i	−0.986846	+	1.35828i
$635$	1.20626e9	−	2.05260e9i	0.186953	−	0.318125i
$636$	4.98229e9	−	2.76813e9i	0.767943	−	0.426665i
$637$	−7.60906e7	−	4.80417e8i	−0.0116639	−	0.0736428i
$638$	−7.45362e7	−	4.70603e8i	−0.0113631	−	0.0717435i
$639$	5.18022e9	−	2.10479e9i	0.785409	−	0.319122i
$640$	4.80249e8	+	4.93481e9i	0.0724163	+	0.744115i
$641$	−5.34541e9	+	7.35733e9i	−0.801638	+	1.10336i	0.190923	+	0.981605i	$0.438852\pi$
$641$	−5.34541e9	+	7.35733e9i	−0.801638	+	1.10336i	−0.992560	+	0.121754i	$0.961148\pi$
$642$	−8.90781e9	−	5.99567e9i	−1.32861	−	0.894262i
$643$	3.60886e9	−	3.60886e9i	0.535342	−	0.535342i	−0.386815	−	0.922157i	$-0.626425\pi$
$643$	3.60886e9	−	3.60886e9i	0.535342	−	0.535342i	0.922157	+	0.386815i	$0.126425\pi$
$644$	−3.35602e8	−	1.03288e9i	−0.0495136	−	0.152387i
$645$	5.89711e9	+	6.18939e9i	0.865327	+	0.908215i
$646$	1.35646e8	−	4.17474e8i	0.0197967	−	0.0609279i
$647$	2.94139e8	+	5.77281e8i	0.0426961	+	0.0837958i	0.911369	−	0.411590i	$-0.135027\pi$
$647$	2.94139e8	+	5.77281e8i	0.0426961	+	0.0837958i	−0.868673	+	0.495386i	$0.835027\pi$
$648$	−2.17186e9	−	1.62327e9i	−0.313559	−	0.234357i
$649$			7.05455e9i			1.01301i
$650$	−6.32137e8	+	6.80663e8i	−0.0902848	+	0.0972154i
$651$	1.98490e8	−	1.62981e9i	0.0281972	−	0.231528i
$652$	5.47872e9	+	8.67744e8i	0.774128	+	0.122610i
$653$	−7.64684e9	+	3.89626e9i	−1.07470	+	0.547585i	−0.899488	−	0.436946i	$-0.856060\pi$
$653$	−7.64684e9	+	3.89626e9i	−1.07470	+	0.547585i	−0.175208	+	0.984531i	$0.556060\pi$
$654$	−3.80273e9	−	1.76870e9i	−0.531586	−	0.247247i
$655$	−4.18697e8	+	6.96218e9i	−0.0582177	+	0.968056i
$656$	−1.41024e9	+	4.58216e8i	−0.195043	+	0.0633734i
$657$	−1.42633e9	−	2.36328e9i	−0.196219	−	0.325114i
$658$	−6.92684e8	−	3.52940e8i	−0.0947861	−	0.0482959i
$659$	5.67650e9	+	4.12422e9i	0.772648	+	0.561362i	0.902764	−	0.430137i	$-0.141535\pi$
$659$	5.67650e9	+	4.12422e9i	0.772648	+	0.561362i	−0.130115	+	0.991499i	$0.541535\pi$
$660$	−3.42858e9	+	1.02306e9i	−0.464206	+	0.138516i
$661$	−6.55167e9	+	4.76007e9i	−0.882363	+	0.641074i	−0.933876	−	0.357598i	$-0.883596\pi$
$661$	−6.55167e9	+	4.76007e9i	−0.882363	+	0.641074i	0.0515128	+	0.998672i	$0.483596\pi$
$662$	8.11105e9	−	1.28466e9i	1.08661	−	0.172102i
$663$	2.67558e8	−	9.60651e6i	0.0356551	−	0.00128017i
$664$	2.15477e9	+	2.96578e9i	0.285635	+	0.393143i
$665$	−4.11206e8	+	3.64552e8i	−0.0542230	+	0.0480711i
$666$	1.31697e10	−	1.10949e10i	1.72749	−	1.45533i
$667$	−1.24010e8	+	2.43384e8i	−0.0161815	+	0.0317579i
$668$	−5.22510e9	−	5.22510e9i	−0.678230	−	0.678230i
$669$	−2.91379e9	−	1.49119e10i	−0.376241	−	1.92549i
$670$	−1.26138e10	+	8.05399e9i	−1.62026	+	1.03455i
$671$	9.26617e9	+	3.01076e9i	1.18405	+	0.384722i
$672$	4.53201e9	−	1.65456e9i	0.576101	−	0.210325i
$673$	−1.06649e9	+	6.73357e9i	−0.134867	+	0.851515i	0.823779	+	0.566912i	$0.191862\pi$
$673$	−1.06649e9	+	6.73357e9i	−0.134867	+	0.851515i	−0.958645	+	0.284603i	$0.908138\pi$
$674$	1.82427e10			2.29498
$675$	−7.62942e9	+	2.37422e9i	−0.954835	+	0.297137i
$676$	5.56197e9			0.692493
$677$	1.85053e9	−	1.16838e10i	0.229211	−	1.44718i	−0.557664	−	0.830067i	$-0.688302\pi$
$677$	1.85053e9	−	1.16838e10i	0.229211	−	1.44718i	0.786875	−	0.617113i	$-0.211698\pi$
$678$	3.19971e9	−	1.16816e9i	0.394281	−	0.143945i
$679$	−1.54004e9	−	5.00389e8i	−0.188794	−	0.0613428i
$680$	−2.82871e8	−	1.08920e9i	−0.0344991	−	0.132839i
$681$	2.98479e9	+	1.52753e10i	0.362159	+	1.85342i
$682$	2.38511e9	+	2.38511e9i	0.287914	+	0.287914i
$683$	−4.71317e9	+	9.25011e9i	−0.566031	+	1.11090i	0.413669	+	0.910428i	$0.364247\pi$
$683$	−4.71317e9	+	9.25011e9i	−0.566031	+	1.11090i	−0.979700	+	0.200471i	$0.935753\pi$
$684$	−6.27738e8	+	5.28840e8i	−0.0750036	+	0.0631871i
$685$	−8.33144e8	+	3.77630e9i	−0.0990383	+	0.448900i
$686$	5.80463e9	+	7.98939e9i	0.686499	+	0.944885i
$687$	2.27566e9	−	8.17059e7i	0.267768	−	0.00961402i
$688$	1.28072e10	−	2.02847e9i	1.49933	−	0.237470i
$689$	−8.87416e8	+	6.44745e8i	−0.103362	+	0.0750967i
$690$	4.70015e9	+	1.65383e9i	0.544679	+	0.191654i
$691$	−5.71021e9	−	4.14871e9i	−0.658384	−	0.478344i	0.207733	−	0.978186i	$-0.433391\pi$
$691$	−5.71021e9	−	4.14871e9i	−0.658384	−	0.478344i	−0.866117	+	0.499842i	$0.833391\pi$
$692$	−2.76391e9	−	1.40828e9i	−0.317068	−	0.161554i
$693$	−1.62042e9	−	2.68488e9i	−0.184953	−	0.306449i
$694$	−3.16534e9	+	1.02848e9i	−0.359470	+	0.116799i
$695$	−7.95386e9	+	2.06567e9i	−0.898733	+	0.233407i
$696$	−2.54081e8	−	1.18176e8i	−0.0285653	−	0.0132861i
$697$	4.73268e8	−	2.41142e8i	0.0529410	−	0.0269748i
$698$	−9.05197e8	−	1.43369e8i	−0.100751	−	0.0159574i
$699$	1.65887e9	−	1.36210e10i	0.183714	−	1.50848i
$700$	8.98516e8	−	3.15780e9i	0.0990108	−	0.347970i
$701$			2.36364e9i			0.259160i	0.991569	+	0.129580i	$0.0413629\pi$
$701$			2.36364e9i			0.259160i	−0.991569	+	0.129580i	$0.958637\pi$
$702$	−1.05495e9	−	6.04935e8i	−0.115093	−	0.0659977i
$703$	1.01552e9	+	1.99307e9i	0.110241	+	0.216361i
$704$	−6.66239e8	+	2.05047e9i	−0.0719657	+	0.221488i
$705$	1.32403e9	−	6.34786e8i	0.142310	−	0.0682284i
$706$	−1.77810e9	−	5.47243e9i	−0.190169	−	0.585280i
$707$	−2.60057e8	+	2.60057e8i	−0.0276758	+	0.0276758i
$708$	−8.02105e9	−	5.39881e9i	−0.849405	−	0.571718i
$709$	5.39092e9	−	7.41996e9i	0.568069	−	0.781879i	−0.424256	−	0.905542i	$-0.639464\pi$
$709$	5.39092e9	−	7.41996e9i	0.568069	−	0.781879i	0.992324	+	0.123663i	$0.0394642\pi$
$710$	−6.99255e9	−	7.88741e9i	−0.733215	−	0.827047i
$711$	−3.15387e9	+	1.28146e9i	−0.329080	+	0.133709i
$712$	−8.61290e8	−	5.43797e9i	−0.0894272	−	0.564621i
$713$	−3.02504e8	−	1.90994e9i	−0.0312549	−	0.197336i
$714$	−2.00926e9	+	1.11633e9i	−0.206582	+	0.114776i
$715$	6.31196e8	−	2.75218e8i	0.0645792	−	0.0281582i
$716$	6.85155e9	−	9.43034e9i	0.697578	−	0.960134i
$717$	−7.25198e9	+	1.07743e10i	−0.734750	+	1.09162i
$718$	1.62115e10	−	1.62115e10i	1.63451	−	1.63451i
$719$	1.72827e9	+	5.31907e9i	0.173405	+	0.533685i	0.999557	−	0.0297622i	$-0.00947499\pi$
$719$	1.72827e9	+	5.31907e9i	0.173405	+	0.533685i	−0.826152	+	0.563447i	$0.809475\pi$
$720$	−3.60990e9	+	1.15694e10i	−0.360439	+	1.15518i
$721$	−239537.	+	737219.i	−2.38012e−5	+	7.32526e-5i
$722$	5.86816e9	+	1.15169e10i	0.580259	+	1.13882i
$723$	−3.70412e8	−	1.05820e8i	−0.0364503	−	0.0104132i
$724$		−	1.28918e10i		−	1.26249i
$725$	−7.21415e8	+	4.01813e8i	−0.0703076	+	0.0391599i
$726$	−6.94823e9	−	8.46207e8i	−0.673901	−	0.0820727i
$727$	7.48836e9	+	1.18604e9i	0.722797	+	0.114480i	0.506985	−	0.861955i	$-0.330760\pi$
$727$	7.48836e9	+	1.18604e9i	0.722797	+	0.114480i	0.215812	+	0.976435i	$0.430760\pi$
$728$	−1.91043e8	+	9.73415e7i	−0.0183515	+	0.00935057i
$729$	−5.28348e9	−	9.02795e9i	−0.505096	−	0.863063i
$730$	−3.30581e9	+	4.01861e9i	−0.314520	+	0.382337i
$731$	−4.41753e9	+	1.43534e9i	−0.418282	+	0.135908i
$732$	−1.05146e10	+	8.23155e9i	−0.990841	+	0.775699i
$733$	−1.41949e10	−	7.23264e9i	−1.33127	−	0.678318i	−0.363844	−	0.931460i	$-0.618536\pi$
$733$	−1.41949e10	−	7.23264e9i	−1.33127	−	0.678318i	−0.967429	+	0.253142i	$0.918536\pi$
$734$	1.91281e10	+	1.38974e10i	1.78540	+	1.29717i
$735$	−7.88492e9	−	1.90675e8i	−0.732473	−	0.0177128i
$736$	4.59710e9	−	3.33999e9i	0.425022	−	0.308796i
$737$	1.09572e10	−	1.73545e9i	1.00824	−	0.159689i
$738$	−2.40386e9	−	2.05552e8i	−0.220146	−	0.0188245i
$739$	−9.19296e9	−	1.26530e10i	−0.837915	−	1.15329i	−0.986398	−	0.164376i	$-0.947439\pi$
$739$	−9.19296e9	−	1.26530e10i	−0.837915	−	1.15329i	0.148483	−	0.988915i	$-0.452561\pi$
$740$	−1.15217e10	−	6.77099e9i	−1.04522	−	0.614244i
$741$	1.07619e8	−	1.15635e8i	0.00971688	−	0.0104406i
$742$	4.27535e9	−	8.39085e9i	0.384201	−	0.754037i
$743$	−4.14332e9	−	4.14332e9i	−0.370584	−	0.370584i	0.497106	−	0.867690i	$-0.334396\pi$
$743$	−4.14332e9	−	4.14332e9i	−0.370584	−	0.370584i	−0.867690	+	0.497106i	$0.834396\pi$
$744$	1.94692e9	−	3.80428e8i	0.173318	−	0.0338663i
$745$	3.80218e9	−	9.68134e9i	0.336888	−	0.857805i
$746$	3.29641e9	+	1.07107e9i	0.290707	+	0.0944563i
$747$	3.20843e9	+	1.37737e10i	0.281625	+	1.20901i
$748$	3.04109e8	−	1.92007e9i	0.0265689	−	0.167750i
$749$	−7.30368e9			−0.635120
$750$	9.00857e9	+	1.20720e10i	0.779725	+	1.04488i
$751$	1.24342e10			1.07122			0.535611	−	0.844465i	$-0.320081\pi$
$751$	1.24342e10			1.07122			0.535611	+	0.844465i	$0.320081\pi$
$752$	3.48402e8	−	2.19972e9i	0.0298757	−	0.188628i
$753$	−2.04714e9	−	5.60731e9i	−0.174729	−	0.478600i
$754$	−1.19527e8	−	3.88366e7i	−0.0101547	−	0.00329945i
$755$	6.00358e9	−	1.52867e10i	0.507687	−	1.29270i
$756$	4.29282e9	+	2.12293e8i	0.361340	+	0.0178694i
$757$	8.31009e9	+	8.31009e9i	0.696258	+	0.696258i	0.963601	−	0.267344i	$-0.0861459\pi$
$757$	8.31009e9	+	8.31009e9i	0.696258	+	0.696258i	−0.267344	+	0.963601i	$0.586146\pi$
$758$	3.71283e9	−	7.28684e9i	0.309644	−	0.607711i
$759$	−2.70373e9	−	2.51630e9i	−0.224448	−	0.208890i
$760$	−5.72436e8	−	3.36405e8i	−0.0473020	−	0.0277981i
$761$	−3.22472e9	−	4.43845e9i	−0.265244	−	0.365077i	0.655533	−	0.755167i	$-0.272444\pi$
$761$	−3.22472e9	−	4.43845e9i	−0.265244	−	0.365077i	−0.920777	+	0.390089i	$0.872444\pi$
$762$	−2.10822e8	−	5.87178e9i	−0.0172613	−	0.480759i
$763$	−2.81756e9	+	4.46258e8i	−0.229635	+	0.0363706i
$764$	−4.24065e9	+	3.08101e9i	−0.344038	+	0.249958i
$765$	6.28873e8	−	4.29555e9i	0.0507864	−	0.346900i
$766$	−2.68636e8	−	1.95175e8i	−0.0215955	−	0.0156900i
$767$	1.65796e9	+	8.44772e8i	0.132675	+	0.0676014i
$768$	1.01459e10	+	1.29599e10i	0.808214	+	1.03238i
$769$	−5.77156e9	+	1.87529e9i	−0.457669	+	0.148706i	−0.528773	−	0.848763i	$-0.677348\pi$
$769$	−5.77156e9	+	1.87529e9i	−0.457669	+	0.148706i	0.0711042	+	0.997469i	$0.477348\pi$
$770$	−3.75567e9	+	4.56547e9i	−0.296463	+	0.360386i
$771$	−1.64548e9	+	3.53781e9i	−0.129301	+	0.277999i
$772$	5.79897e9	−	2.95472e9i	0.453618	−	0.231130i
$773$	2.16964e9	+	3.43638e8i	0.168951	+	0.0267592i	0.240337	−	0.970690i	$-0.422742\pi$
$773$	2.16964e9	+	3.43638e8i	0.168951	+	0.0267592i	−0.0713858	+	0.997449i	$0.522742\pi$
$774$	2.04811e10	+	5.06380e9i	1.58767	+	0.392539i
$775$	2.45974e9	−	5.30315e9i	0.189816	−	0.409240i
$776$		−	1.95648e9i		−	0.150300i
$777$	3.21751e9	−	1.12625e10i	0.246063	−	0.861317i
$778$	6.07825e9	+	1.19292e10i	0.462754	+	0.908205i
$779$	9.68445e7	−	2.98057e8i	0.00733996	−	0.0225901i
$780$	−1.70127e8	+	9.28295e8i	−0.0128364	+	0.0700414i
$781$	2.41453e9	+	7.43116e9i	0.181365	+	0.558185i
$782$	−1.91428e9	+	1.91428e9i	−0.143147	+	0.143147i
$783$	−7.25721e8	−	8.01234e8i	−0.0540261	−	0.0596476i
$784$	−7.03179e9	+	9.67843e9i	−0.521147	+	0.717297i
$785$	1.07145e10	−	4.67178e9i	0.790545	−	0.344698i
$786$	8.35977e9	+	1.50466e10i	0.614067	+	1.10524i
$787$	4.93153e8	+	3.11364e9i	0.0360637	+	0.227697i	0.999137	−	0.0415433i	$-0.0132274\pi$
$787$	4.93153e8	+	3.11364e9i	0.0360637	+	0.227697i	−0.963073	+	0.269240i	$0.913227\pi$
$788$	−1.55570e9	−	9.82231e9i	−0.113262	−	0.715108i
$789$	−2.54015e9	−	4.57195e9i	−0.184115	−	0.331384i
$790$	4.25727e9	+	4.80209e9i	0.307211	+	0.346526i
$791$	1.36186e9	−	1.87443e9i	0.0978393	−	0.134664i
$792$	2.48018e9	−	2.86447e9i	0.177396	−	0.204883i
$793$	1.81720e9	−	1.81720e9i	0.129404	−	0.129404i
$794$	−4.72011e9	−	1.45270e10i	−0.334642	−	1.02992i
$795$	7.68950e9	+	1.60386e10i	0.542767	+	1.13209i
$796$	−3.13984e9	+	9.66343e9i	−0.220654	+	0.679103i
$797$	3.57165e9	+	7.00976e9i	0.249899	+	0.490455i	0.981545	−	0.191230i	$-0.0612476\pi$
$797$	3.57165e9	+	7.00976e9i	0.249899	+	0.490455i	−0.731646	+	0.681685i	$0.761248\pi$
$798$	−3.72536e8	+	1.30402e9i	−0.0259512	+	0.0908394i
$799$			7.97784e8i			0.0553314i
$800$	1.71663e10	−	6.34528e8i	1.18539	−	0.0438163i
$801$	5.09800e9	−	2.06195e10i	0.350499	−	1.41763i
$802$	−2.15630e9	−	3.41524e8i	−0.147604	−	0.0233782i
$803$	3.43689e9	−	1.75118e9i	0.234240	−	0.119351i
$804$	−6.41227e9	+	1.37865e10i	−0.435127	+	0.935531i
$805$	3.28033e9	−	8.51923e8i	0.221632	−	0.0575592i
$806$	8.46160e8	−	2.74934e8i	0.0569219	−	0.0184951i
$807$	9.06129e9	+	1.15745e10i	0.606922	+	0.775254i
$808$	−3.95927e8	−	2.01735e8i	−0.0264044	−	0.0134537i
$809$	−2.04496e10	−	1.48575e10i	−1.35789	−	0.986568i	−0.998576	−	0.0533526i	$-0.983009\pi$
$809$	−2.04496e10	−	1.48575e10i	−1.35789	−	0.986568i	−0.359318	−	0.933215i	$-0.616991\pi$
$810$	−1.27322e10	+	1.50578e10i	−0.841795	+	0.995551i
$811$	1.86113e10	−	1.35219e10i	1.22519	−	0.890153i	0.228670	−	0.973504i	$-0.426562\pi$
$811$	1.86113e10	−	1.35219e10i	1.22519	−	0.890153i	0.996520	+	0.0833513i	$0.0265624\pi$
$812$	4.38721e8	−	6.94865e7i	0.0287569	−	0.00455464i
$813$	1.70216e8	+	4.74081e9i	0.0111092	+	0.309411i
$814$	1.41443e10	+	1.94679e10i	0.919168	+	1.26513i
$815$	−3.72942e9	+	1.69039e10i	−0.241318	+	1.09379i
$816$	−4.82028e9	−	4.48614e9i	−0.310568	−	0.289039i
$817$	−1.24419e9	+	2.44186e9i	−0.0798196	+	0.156655i
$818$	−8.03220e9	−	8.03220e9i	−0.513095	−	0.513095i
$819$	−8.25042e8	+	5.93217e7i	−0.0524786	+	0.00377329i
$820$	4.70648e8	+	1.81223e9i	0.0298090	+	0.114780i
$821$	−1.98668e10	−	6.45510e9i	−1.25293	−	0.407101i	−0.393959	−	0.919128i	$-0.628895\pi$
$821$	−1.98668e10	−	6.45510e9i	−1.25293	−	0.407101i	−0.858969	+	0.512027i	$0.828895\pi$
$822$	3.27291e9	+	8.96484e9i	0.205534	+	0.562978i
$823$	−3.69060e9	+	2.33015e10i	−0.230780	+	1.45709i	0.551508	+	0.834170i	$0.314053\pi$
$823$	−3.69060e9	+	2.33015e10i	−0.230780	+	1.45709i	−0.782288	+	0.622917i	$0.785947\pi$
$824$	−936572.			−5.83171e−5
$825$	−2.54460e9	−	1.08719e10i	−0.157772	−	0.674085i
$826$	−1.59753e10			−0.986321
$827$	−4.36116e8	+	2.75353e9i	−0.0268122	+	0.169286i	−0.997461	−	0.0712161i	$-0.977312\pi$
$827$	−4.36116e8	+	2.75353e9i	−0.0268122	+	0.169286i	0.970649	+	0.240502i	$0.0773120\pi$
$828$	4.93020e9	−	1.14843e9i	0.301827	−	0.0703071i
$829$	5.13617e9	+	1.66884e9i	0.313111	+	0.101736i	0.461357	−	0.887215i	$-0.347363\pi$
$829$	5.13617e9	+	1.66884e9i	0.313111	+	0.101736i	−0.148246	+	0.988951i	$0.547363\pi$
$830$	2.24706e10	−	1.43476e10i	1.36409	−	0.870976i
$831$	−2.34436e10	+	4.58088e9i	−1.41717	+	0.276914i
$832$	4.02120e8	+	4.02120e8i	0.0242061	+	0.0242061i
$833$	1.94550e9	−	3.81826e9i	0.116620	−	0.228880i
$834$	−1.38166e10	+	1.48457e10i	−0.824747	+	0.886176i
$835$	1.72553e10	−	1.52976e10i	1.02570	−	0.909328i
$836$	−6.74190e8	−	9.27943e8i	−0.0399080	−	0.0549287i
$837$	7.49038e9	+	1.56907e9i	0.441535	+	0.0924919i
$838$	−5.70716e8	+	9.03925e7i	−0.0335016	+	0.00530614i
$839$	−1.57010e10	+	1.14074e10i	−0.917826	+	0.666840i	−0.942982	−	0.332844i	$-0.891992\pi$
$839$	−1.57010e10	+	1.14074e10i	−0.917826	+	0.666840i	0.0251557	+	0.999684i	$0.491992\pi$
$840$	9.94132e8	+	3.33162e9i	0.0578717	+	0.193945i
$841$	1.38651e10	+	1.00736e10i	0.803777	+	0.583978i
$842$	−2.85095e10	−	1.45263e10i	−1.64588	−	0.838617i
$843$	−1.44397e10	+	1.13044e10i	−0.830159	+	0.649905i
$844$	1.49168e10	−	4.84677e9i	0.854039	−	0.277494i
$845$	−1.04195e9	+	1.73258e10i	−0.0594087	+	0.987859i
$846$	1.91422e9	−	3.07682e9i	0.108691	−	0.174705i
$847$	−4.24214e9	+	2.16148e9i	−0.239879	+	0.122225i
$848$	2.66464e10	+	4.22037e9i	1.50056	+	0.237665i
$849$	−2.65882e10	−	3.23811e9i	−1.49112	−	0.181599i
$850$	−8.03045e9	+	1.57797e9i	−0.448512	+	0.0881318i
$851$		−	1.37955e10i		−	0.767334i
$852$	−1.02971e10	−	2.94170e9i	−0.570395	−	0.162952i
$853$	−4.28852e9	−	8.41669e9i	−0.236584	−	0.464323i	0.741937	−	0.670470i	$-0.233907\pi$
$853$	−4.28852e9	−	8.41669e9i	−0.236584	−	0.464323i	−0.978521	+	0.206147i	$0.933907\pi$
$854$	−6.81797e9	+	2.09836e10i	−0.374587	+	1.15286i
$855$	−1.52976e9	−	2.05451e9i	−0.0837034	−	0.112415i
$856$	−2.72694e9	−	8.39265e9i	−0.148599	−	0.457342i
$857$	−1.41252e10	+	1.41252e10i	−0.766588	+	0.766588i	−0.977504	−	0.210916i	$-0.932355\pi$
$857$	−1.41252e10	+	1.41252e10i	−0.766588	+	0.766588i	0.210916	+	0.977504i	$0.432355\pi$
$858$	9.48884e8	−	1.40976e9i	0.0512870	−	0.0761975i
$859$	−5.12384e9	+	7.05236e9i	−0.275816	+	0.379628i	−0.924342	−	0.381564i	$-0.875386\pi$
$859$	−5.12384e9	+	7.05236e9i	−0.275816	+	0.379628i	0.648526	+	0.761192i	$0.275386\pi$
$860$	−1.58593e9	−	1.62962e10i	−0.0850235	−	0.873661i
$861$	−1.43452e9	+	7.97009e8i	−0.0765940	+	0.0425552i
$862$	−4.33132e9	−	2.73469e10i	−0.230327	−	1.45423i
$863$	1.09309e9	+	6.90148e9i	0.0578918	+	0.365514i	0.999579	+	0.0290241i	$0.00923994\pi$
$863$	1.09309e9	+	6.90148e9i	0.0578918	+	0.365514i	−0.941687	+	0.336490i	$0.890760\pi$
$864$	5.88438e9	+	2.17048e10i	0.310387	+	1.14487i
$865$	4.90464e9	−	8.34588e9i	0.257662	−	0.438445i
$866$	−4.77760e9	+	6.57580e9i	−0.249975	+	0.344062i
$867$	−1.39627e10	−	9.39799e9i	−0.727615	−	0.489743i
$868$	−2.22352e9	+	2.22352e9i	−0.115404	+	0.115404i
$869$	−1.47004e9	−	4.52431e9i	−0.0759905	−	0.233875i
$870$	−9.68816e8	+	1.79289e9i	−0.0498797	+	0.0923073i
$871$	9.04243e8	−	2.78297e9i	0.0463683	−	0.142707i
$872$	−1.56477e9	−	3.07104e9i	−0.0799178	−	0.156848i
$873$	2.93551e9	−	6.95357e9i	0.149325	−	0.353719i
$874$			1.59730e9i			0.0809275i
$875$	9.66837e9	+	3.39049e9i	0.487894	+	0.171094i
$876$	−6.39132e8	+	5.24793e9i	−0.0321238	+	0.263769i
$877$	5.87211e9	+	9.30051e8i	0.293965	+	0.0465595i	0.301675	−	0.953411i	$-0.402454\pi$
$877$	5.87211e9	+	9.30051e8i	0.293965	+	0.0465595i	−0.00771012	+	0.999970i	$0.502454\pi$
$878$	−4.64999e9	+	2.36929e9i	−0.231857	+	0.118137i
$879$	−1.29173e10	−	6.00798e9i	−0.641519	−	0.298378i
$880$	−1.57638e10	−	6.19095e9i	−0.779778	−	0.306244i
$881$	−2.18908e10	+	7.11275e9i	−1.07856	+	0.350447i	−0.793817	−	0.608156i	$-0.791909\pi$
$881$	−2.18908e10	+	7.11275e9i	−1.07856	+	0.350447i	−0.284746	+	0.958603i	$0.591909\pi$
$882$	−1.66649e10	+	1.00579e10i	−0.817827	+	0.493589i
$883$	−1.46832e10	−	7.48147e9i	−0.717725	−	0.365699i	0.0566771	−	0.998393i	$-0.481949\pi$
$883$	−1.46832e10	−	7.48147e9i	−0.717725	−	0.365699i	−0.774403	+	0.632693i	$0.781949\pi$
$884$	−4.14838e8	−	3.01397e8i	−0.0201974	−	0.0146743i
$885$	1.83202e10	−	2.39746e10i	0.888440	−	1.16265i
$886$	−5.72657e9	+	4.16060e9i	−0.276616	+	0.200973i
$887$	2.34506e10	−	3.71421e9i	1.12829	−	0.178704i	0.435740	−	0.900072i	$-0.356487\pi$
$887$	2.34506e10	−	3.71421e9i	1.12829	−	0.178704i	0.692551	+	0.721369i	$0.256487\pi$
$888$	1.41431e10	−	5.07798e8i	0.677795	−	0.0243358i
$889$	−2.34910e9	−	3.23326e9i	−0.112136	−	0.154342i
$890$	−3.98526e10	+	3.87841e9i	−1.89493	+	0.184412i
$891$	1.31127e10	−	6.45939e9i	0.621040	−	0.305928i
$892$	−1.32111e10	+	2.59282e10i	−0.623250	+	1.22320i
$893$	3.32841e8	+	3.32841e8i	0.0156407	+	0.0156407i
$894$	−4.92263e9	−	2.51926e10i	−0.230418	−	1.17921i
$895$	2.80924e10	+	2.31095e10i	1.30981	+	1.07748i
$896$	7.91556e9	+	2.57192e9i	0.367624	+	0.119448i
$897$	−9.15148e8	+	3.34105e8i	−0.0423368	+	0.0154564i
$898$	2.74921e9	−	1.73578e10i	0.126689	−	0.799885i
$899$	7.90905e8			0.0363049
$900$	1.43087e10	+	5.42695e9i	0.654262	+	0.248146i
$901$	−9.66398e9			−0.440169
$902$	5.27405e8	−	3.32991e9i	0.0239288	−	0.151081i
$903$	1.34803e10	−	4.92144e9i	0.609247	−	0.222426i
$904$	2.66238e9	+	8.65059e8i	0.119862	+	0.0389454i
$905$	4.01585e10	+	2.41508e9i	1.80097	+	0.108308i
$906$	−7.77274e9	−	3.97786e10i	−0.347237	−	1.77706i
$907$	−6.97627e9	−	6.97627e9i	−0.310455	−	0.310455i	0.534631	−	0.845086i	$-0.320451\pi$
$907$	−6.97627e9	−	6.97627e9i	−0.310455	−	0.310455i	−0.845086	+	0.534631i	$0.820451\pi$
$908$	1.35330e10	−	2.65600e10i	0.599921	−	1.17741i
$909$	−1.10449e9	−	1.31104e9i	−0.0487739	−	0.0578951i
$910$	6.23240e8	+	1.42936e9i	0.0274164	+	0.0628779i
$911$	−1.87030e10	−	2.57425e10i	−0.819593	−	1.12807i	−0.989772	−	0.142659i	$-0.954435\pi$
$911$	−1.87030e10	−	2.57425e10i	−0.819593	−	1.12807i	0.170179	−	0.985413i	$-0.445565\pi$
$912$	−3.88270e9	+	1.39406e8i	−0.169493	+	0.00608554i
$913$	−1.95194e10	+	3.09158e9i	−0.848828	+	0.134441i
$914$	−2.12521e10	+	1.54405e10i	−0.920640	+	0.668884i
$915$	−2.36719e10	−	3.42955e10i	−1.02155	−	1.48001i
$916$	−3.52830e9	−	2.56346e9i	−0.151681	−	0.110203i
$917$	1.04320e10	+	5.31538e9i	0.446761	+	0.227636i
$918$	−4.38658e9	−	9.77480e9i	−0.187144	−	0.417021i
$919$	1.70491e10	−	5.53959e9i	0.724598	−	0.235436i	0.0765827	−	0.997063i	$-0.475599\pi$
$919$	1.70491e10	−	5.53959e9i	0.724598	−	0.235436i	0.648016	+	0.761627i	$0.275599\pi$
$920$	2.20370e9	+	3.45135e9i	0.0933031	+	0.146127i
$921$	−2.08069e10	−	9.67755e9i	−0.877604	−	0.408185i
$922$	−4.73565e10	+	2.41294e10i	−1.98986	+	1.01388i
$923$	2.03560e9	+	3.22408e8i	0.0852094	+	0.0134958i
$924$	−7.26106e8	+	5.96207e9i	−0.0302795	+	0.248625i
$925$	2.32504e10	−	3.46223e10i	0.965904	−	1.43833i
$926$			1.95472e10i			0.808996i
$927$	−3.32869e6	−	1.40523e6i	−0.000137244	−	5.79387e-5i
$928$	1.05511e9	+	2.07077e9i	0.0433391	+	0.0850578i
$929$	−7.58780e8	+	2.33528e9i	−0.0310499	+	0.0955619i	−0.965380	−	0.260846i	$-0.915999\pi$
$929$	−7.58780e8	+	2.33528e9i	−0.0310499	+	0.0955619i	0.934331	+	0.356408i	$0.115999\pi$
$930$	−1.91172e9	−	1.42996e10i	−0.0779353	−	0.582954i
$931$	−7.81329e8	−	2.40468e9i	−0.0317329	−	0.0976639i
$932$	−1.85829e10	+	1.85829e10i	−0.751896	+	0.751896i
$933$	3.29915e10	+	2.22059e10i	1.32989	+	0.895123i
$934$	3.52296e10	−	4.84893e10i	1.41479	−	1.94730i
$935$	5.92414e9	+	1.30701e9i	0.237020	+	0.0522924i
$936$	−3.76208e8	−	9.25906e8i	−0.0149956	−	0.0369064i
$937$	−3.54225e9	−	2.23649e10i	−0.140667	−	0.888134i	−0.952565	−	0.304335i	$-0.901566\pi$
$937$	−3.54225e9	−	2.23649e10i	−0.140667	−	0.888134i	0.811898	−	0.583799i	$-0.198434\pi$
$938$	3.92999e9	+	2.48129e10i	0.155482	+	0.981677i
$939$	−2.01228e10	+	1.11801e10i	−0.793157	+	0.440673i
$940$	−2.74616e9	−	6.05871e8i	−0.107840	−	0.0237921i
$941$	−2.31483e10	+	3.18609e10i	−0.905639	+	1.24651i	0.0629945	+	0.998014i	$0.479935\pi$
$941$	−2.31483e10	+	3.18609e10i	−0.905639	+	1.24651i	−0.968634	+	0.248492i	$0.920065\pi$
$942$	1.61072e10	−	2.39305e10i	0.627829	−	0.932770i
$943$	−1.36670e9	+	1.36670e9i	−0.0530741	+	0.0530741i
$944$	−1.41424e10	−	4.35259e10i	−0.547170	−	1.68401i
$945$	−1.46550e9	+	1.33326e10i	−0.0564903	+	0.513928i
$946$	−9.11049e9	+	2.80392e10i	−0.349883	+	1.07683i
$947$	1.78382e10	+	3.50094e10i	0.682536	+	1.33955i	0.928884	+	0.370371i	$0.120770\pi$
$947$	1.78382e10	+	3.50094e10i	0.682536	+	1.33955i	−0.246347	+	0.969182i	$0.579230\pi$
$948$	6.26917e9	+	1.79099e9i	0.238991	+	0.0682755i
$949$		−	1.01744e9i		−	0.0386435i
$950$	−2.69202e9	+	4.00870e9i	−0.101870	+	0.151695i
$951$	−3.39058e10	−	4.12931e9i	−1.27833	−	0.155684i
$952$	−1.86577e9	−	2.95509e8i	−0.0700855	−	0.0111005i
$953$	−2.39782e10	+	1.22175e10i	−0.897410	+	0.457253i	−0.840926	−	0.541150i	$-0.817989\pi$
$953$	−2.39782e10	+	1.22175e10i	−0.897410	+	0.457253i	−0.0564841	+	0.998403i	$0.517989\pi$
$954$	3.72712e10	+	2.31879e10i	1.38981	+	0.864655i
$955$	−8.80308e9	−	1.37870e10i	−0.327057	−	0.512222i
$956$	2.36568e10	−	7.68657e9i	0.875697	−	0.284531i
$957$	1.18949e9	−	9.31217e8i	0.0438702	−	0.0343446i
$958$	3.52939e10	+	1.79831e10i	1.29694	+	0.660824i
$959$	5.25173e9	+	3.81561e9i	0.192282	+	0.139701i
$960$	7.58912e9	−	5.23826e9i	0.276848	−	0.191090i
$961$	1.77285e10	−	1.28805e10i	0.644376	−	0.468167i
$962$	6.26909e9	−	9.92927e8i	0.227035	−	0.0359587i
$963$	2.90047e9	−	3.39200e10i	0.104659	−	1.22395i
$964$	4.33673e8	+	5.96900e8i	0.0155917	+	0.0214601i
$965$	8.11775e9	+	1.86176e10i	0.290797	+	0.666926i
$966$	5.69826e9	−	6.12268e9i	0.203387	−	0.218535i
$967$	−2.31873e10	+	4.55077e10i	−0.824629	+	1.61842i	−0.0393959	+	0.999224i	$0.512543\pi$
$967$	−2.31873e10	+	4.55077e10i	−0.824629	+	1.61842i	−0.785233	+	0.619201i	$0.787457\pi$
$968$	−4.06761e9	−	4.06761e9i	−0.144137	−	0.144137i
$969$	1.36589e9	−	2.66894e8i	0.0482261	−	0.00942337i
$970$	−1.42030e10	−	8.54149e8i	−0.499664	−	0.0300492i
$971$	2.60145e10	+	8.45263e9i	0.911902	+	0.296295i	0.727141	−	0.686488i	$-0.240849\pi$
$971$	2.60145e10	+	8.45263e9i	0.911902	+	0.296295i	0.184762	+	0.982783i	$0.440849\pi$
$972$	−2.69072e9	+	1.98525e10i	−0.0939803	+	0.693400i
$973$	−2.15795e9	+	1.36248e10i	−0.0751012	+	0.474170i
$974$	6.06112e10			2.10183
$975$	−2.85981e9	−	7.03857e8i	−0.0988146	−	0.0243203i
$976$	−6.32072e10			−2.17617
$977$	6.64852e9	−	4.19771e10i	0.228084	−	1.44006i	−0.562037	−	0.827112i	$-0.689982\pi$
$977$	6.64852e9	−	4.19771e10i	0.228084	−	1.44006i	0.790121	−	0.612951i	$-0.210018\pi$
$978$	1.46506e10	+	4.01295e10i	0.500806	+	1.37176i
$979$	2.82286e10	+	9.17203e9i	0.961502	+	0.312411i
$980$	1.16659e10	+	9.59663e9i	0.395937	+	0.325707i
$981$	−9.53601e8	−	1.32626e10i	−0.0322497	−	0.448526i
$982$	2.82564e10	+	2.82564e10i	0.952196	+	0.952196i
$983$	1.33017e10	−	2.61061e10i	0.446653	−	0.876605i	−0.552421	−	0.833565i	$-0.686296\pi$
$983$	1.33017e10	−	2.61061e10i	0.446653	−	0.876605i	0.999073	−	0.0430398i	$-0.0137042\pi$
$984$	−1.45144e9	−	1.35083e9i	−0.0485642	−	0.0451977i
$985$	3.08884e10	−	3.00602e9i	1.02984	−	0.100222i
$986$	−6.50824e8	−	8.95782e8i	−0.0216219	−	0.0297600i
$987$	−8.84403e7	−	2.46322e9i	−0.00292779	−	0.0815442i
$988$	−2.98818e8	+	4.73281e7i	−0.00985729	+	0.00156124i
$989$	1.36739e10	−	9.93469e9i	0.449476	−	0.326563i
$990$	−1.97116e10	−	1.92552e10i	−0.645653	−	0.630705i
$991$	1.45040e10	+	1.05378e10i	0.473402	+	0.343947i	0.798766	−	0.601642i	$-0.205487\pi$
$991$	1.45040e10	+	1.05378e10i	0.473402	+	0.343947i	−0.325364	+	0.945589i	$0.605487\pi$
$992$	−1.46595e10	−	7.46940e9i	−0.476792	−	0.242938i
$993$	1.60499e10	+	2.05014e10i	0.520176	+	0.664448i
$994$	−1.68281e10	+	5.46779e9i	−0.543479	+	0.176587i
$995$	−2.95138e10	−	1.15910e10i	−0.949828	−	0.373028i
$996$	1.14230e10	−	2.45596e10i	0.366330	−	0.787616i
$997$	−4.53994e10	+	2.31321e10i	−1.45083	+	0.739236i	−0.989025	−	0.147745i	$-0.952798\pi$
$997$	−4.53994e10	+	2.31321e10i	−1.45083	+	0.739236i	−0.461806	+	0.886981i	$0.652798\pi$
$998$	−9.57513e8	−	1.51655e8i	−0.0304921	−	0.00482948i
$999$	5.10281e10	+	1.94155e10i	1.61931	+	0.616125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.8.l.a.2.55	yes	544
3.2	odd	2	inner	75.8.l.a.2.14	✓	544
25.13	odd	20	inner	75.8.l.a.38.14	yes	544
75.38	even	20	inner	75.8.l.a.38.55	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.8.l.a.2.14	✓	544	3.2	odd	2	inner
75.8.l.a.2.55	yes	544	1.1	even	1	trivial
75.8.l.a.38.14	yes	544	25.13	odd	20	inner
75.8.l.a.38.55	yes	544	75.38	even	20	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.30743 - 14.5685i) q^{2} +(43.9293 - 16.0379i) q^{3} +(-85.1830 - 27.6776i) q^{4} +(102.175 - 260.164i) q^{5} +(-132.284 - 676.993i) q^{6} +(-331.771 - 331.771i) q^{7} +(257.366 - 505.109i) q^{8} +(1672.57 - 1409.07i) q^{9} +(-3554.45 - 2088.85i) q^{10} +(1796.34 + 2472.45i) q^{11} +(-4185.92 + 150.293i) q^{12} +(796.184 - 126.103i) q^{13} +(-5598.96 + 4067.88i) q^{14} +(316.001 - 13067.5i) q^{15} +(-16039.9 - 11653.6i) q^{16} +(6327.92 + 3224.24i) q^{17} +(-16668.7 - 27618.3i) q^{18} +(3985.23 - 1294.88i) q^{19} +(-15904.3 + 19333.6i) q^{20} +(-19895.4 - 9253.58i) q^{21} +(40165.0 - 20465.1i) q^{22} +(-25524.8 - 4042.74i) q^{23} +(3205.05 - 26316.7i) q^{24} +(-57245.6 - 53164.4i) q^{25} -11890.2i q^{26} +(50876.7 - 88723.8i) q^{27} +(19078.6 + 37443.9i) q^{28} +(3266.26 - 10052.5i) q^{29} +(-189645. - 34756.0i) q^{30} +(23122.7 + 71164.3i) q^{31} +(-155478. + 155478. i) q^{32} +(118565. + 79803.7i) q^{33} +(61573.7 - 84748.9i) q^{34} +(-120213. + 52416.2i) q^{35} +(-181474. + 73735.5i) q^{36} +(83507.9 + 527248. i) q^{37} +(-9668.87 - 61046.8i) q^{38} +(32953.4 - 18308.7i) q^{39} +(-105115. - 118567. i) q^{40} +(43960.7 - 60506.7i) q^{41} +(-180718. + 268495. i) q^{42} +(-462464. + 462464. i) q^{43} +(-84586.1 - 260329. i) q^{44} +(-195693. - 579115. i) q^{45} +(-117794. + 362531. i) q^{46} +(50997.8 + 100089. i) q^{47} +(-891519. - 254692. i) q^{48} -603399. i q^{49} +(-906619. + 711312. i) q^{50} +(329691. + 40152.3i) q^{51} +(-71311.6 - 11294.6i) q^{52} +(-1.21243e6 + 617764. i) q^{53} +(-1.17518e6 - 945923. i) q^{54} +(826784. - 214721. i) q^{55} +(-252967. + 82194.0i) q^{56} +(154301. - 120798. i) q^{57} +(-138914. - 70780.1i) q^{58} +(1.86748e6 + 1.35681e6i) q^{59} +(-388595. + 1.10438e6i) q^{60} +(2.57918e6 - 1.87388e6i) q^{61} +(1.09011e6 - 172657. i) q^{62} +(-1.02240e6 - 87424.5i) q^{63} +(414663. + 570735. i) q^{64} +(48542.5 - 220023. i) q^{65} +(1.43620e6 - 1.54318e6i) q^{66} +(1.64799e6 - 3.23437e6i) q^{67} +(-449792. - 449792. i) q^{68} +(-1.18613e6 + 231769. i) q^{69} +(486243. + 1.87228e6i) q^{70} +(2.43157e6 + 790064. i) q^{71} +(-281268. - 1.20748e6i) q^{72} +(197445. - 1.24662e6i) q^{73} +7.87392e6 q^{74} +(-3.36741e6 - 1.41738e6i) q^{75} -375313. q^{76} +(224314. - 1.41626e6i) q^{77} +(-190694. - 522330. i) q^{78} +(-1.48041e6 - 481014. i) q^{79} +(-4.67073e6 + 2.98228e6i) q^{80} +(812039. - 4.71353e6i) q^{81} +(-780058. - 780058. i) q^{82} +(-2.93578e6 + 5.76180e6i) q^{83} +(1.43863e6 + 1.33890e6i) q^{84} +(1.48539e6 - 1.31686e6i) q^{85} +(5.67032e6 + 7.80453e6i) q^{86} +(-17736.2 - 493984. i) q^{87} +(1.71118e6 - 271024. i) q^{88} +(7.85725e6 - 5.70863e6i) q^{89} +(-8.88840e6 + 1.51470e6i) q^{90} +(-305988. - 222313. i) q^{91} +(2.06239e6 + 1.05084e6i) q^{92} +(2.15709e6 + 2.75536e6i) q^{93} +(1.57582e6 - 512016. i) q^{94} +(70309.3 - 1.16912e6i) q^{95} +(-4.33650e6 + 9.32356e6i) q^{96} +(3.07505e6 - 1.56682e6i) q^{97} +(-8.79065e6 - 1.39230e6i) q^{98} +(6.48836e6 + 1.60420e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 34 q^{3} - 20 q^{4} - 6 q^{6} - 1364 q^{7} - 10 q^{9} + 3160 q^{10} + 2018 q^{12} - 16868 q^{13} - 37570 q^{15} + 507892 q^{16} + 106550 q^{18} + 70800 q^{19} - 6 q^{21} - 195160 q^{22} - 444200 q^{25}+ \cdots - 22089384 q^{97}+O(q^{100}) \) 544 * q - 34 * q^3 - 20 * q^4 - 6 * q^6 - 1364 * q^7 - 10 * q^9 + 3160 * q^10 + 2018 * q^12 - 16868 * q^13 - 37570 * q^15 + 507892 * q^16 + 106550 * q^18 + 70800 * q^19 - 6 * q^21 - 195160 * q^22 - 444200 * q^25 + 264158 * q^27 + 692032 * q^28 - 892390 * q^30 - 12 * q^31 + 877790 * q^33 - 1828180 * q^34 - 65542 * q^36 + 635596 * q^37 - 3868770 * q^39 + 1574020 * q^40 + 4577310 * q^42 - 1397348 * q^43 + 3411430 * q^45 - 12 * q^46 - 12135404 * q^48 - 16 * q^51 + 6428876 * q^52 + 16485420 * q^54 - 2324900 * q^55 + 4119286 * q^57 - 986360 * q^58 - 25245250 * q^60 - 12 * q^61 + 6259012 * q^63 + 363500 * q^64 - 1119750 * q^66 + 3427476 * q^67 - 12994880 * q^69 + 9814160 * q^70 - 611970 * q^72 + 10236732 * q^73 + 19853790 * q^75 - 131104 * q^76 + 24801340 * q^78 - 8474460 * q^79 + 10854734 * q^81 + 44639220 * q^82 - 52907530 * q^84 - 82807380 * q^85 - 15442020 * q^87 + 33548360 * q^88 - 11540050 * q^90 - 12 * q^91 + 14982652 * q^93 + 60673460 * q^94 + 1218042 * q^96 - 22089384 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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