LMFDB - Embedded newform 75.8.l.a.38.14

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			38.14
Character	$\chi$	$=$	75.38
Dual form			75.8.l.a.2.14

$q$-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} +(-38.7959 - 26.1128i) q^{3} +(-85.1830 + 27.6776i) q^{4} +(-102.175 - 260.164i) q^{5} +(-290.906 + 625.453i) q^{6} +(-331.771 + 331.771i) q^{7} +(-257.366 - 505.109i) q^{8} +(823.247 + 2026.14i) q^{9} +(-3554.45 + 2088.85i) q^{10} +(-1796.34 + 2472.45i) q^{11} +(4027.49 + 1150.58i) q^{12} +(796.184 + 126.103i) q^{13} +(5598.96 + 4067.88i) q^{14} +(-2829.63 + 12761.4i) q^{15} +(-16039.9 + 11653.6i) q^{16} +(-6327.92 + 3224.24i) q^{17} +(27618.3 - 16668.7i) q^{18} +(3985.23 + 1294.88i) q^{19} +(15904.3 + 19333.6i) q^{20} +(21534.8 - 4207.90i) 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} +(20969.4 - 100103. i) q^{27} +(19078.6 - 37443.9i) q^{28} +(-3266.26 - 10052.5i) q^{29} +(192444. + 11777.7i) q^{30} +(23122.7 - 71164.3i) q^{31} +(155478. + 155478. i) q^{32} +(134253. - 49013.6i) q^{33} +(61573.7 + 84748.9i) q^{34} +(120213. + 52416.2i) q^{35} +(-126205. - 149807. i) q^{36} +(83507.9 - 527248. i) q^{37} +(9668.87 - 61046.8i) q^{38} +(-27595.8 - 25682.9i) q^{39} +(-105115. + 118567. i) q^{40} +(-43960.7 - 60506.7i) q^{41} +(-110993. - 304021. i) q^{42} +(-462464. - 462464. i) q^{43} +(84586.1 - 260329. i) q^{44} +(443013. - 421200. i) q^{45} +(-117794. - 362531. i) q^{46} +(-50997.8 + 100089. i) q^{47} +(926589. - 33268.6i) 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} +(-1.50674e6 - 74513.1i) q^{54} +(826784. + 214721. i) q^{55} +(252967. + 82194.0i) q^{56} +(-120798. - 154301. i) q^{57} +(-138914. + 70780.1i) q^{58} +(-1.86748e6 + 1.35681e6i) q^{59} +(-112168. - 1.16537e6i) q^{60} +(2.57918e6 + 1.87388e6i) q^{61} +(-1.09011e6 - 172657. i) q^{62} +(-945343. - 399084. i) q^{63} +(414663. - 570735. i) q^{64} +(-48542.5 - 220023. i) q^{65} +(-1.02384e6 - 1.84278e6i) q^{66} +(1.64799e6 + 3.23437e6i) q^{67} +(449792. - 449792. i) q^{68} +(-1.09583e6 - 509682. i) q^{69} +(486243. - 1.87228e6i) q^{70} +(-2.43157e6 + 790064. i) q^{71} +(811545. - 937288. i) q^{72} +(197445. + 1.24662e6i) q^{73} -7.87392e6 q^{74} +(3.60917e6 - 567723. i) q^{75} -375313. q^{76} +(-224314. - 1.41626e6i) q^{77} +(-310487. + 461292. i) q^{78} +(-1.48041e6 + 481014. i) q^{79} +(4.67073e6 + 2.98228e6i) q^{80} +(-3.42750e6 + 3.33602e6i) q^{81} +(-780058. + 780058. i) q^{82} +(2.93578e6 + 5.76180e6i) q^{83} +(-1.71793e6 + 954474. i) q^{84} +(1.48539e6 + 1.31686e6i) q^{85} +(-5.67032e6 + 7.80453e6i) q^{86} +(-135781. + 475288. i) q^{87} +(1.71118e6 + 271024. i) q^{88} +(-7.85725e6 - 5.70863e6i) q^{89} +(-7.15848e6 - 5.48216e6i) q^{90} +(-305988. + 222313. i) q^{91} +(-2.06239e6 + 1.05084e6i) q^{92} +(-2.75536e6 + 2.15709e6i) q^{93} +(1.57582e6 + 512016. i) q^{94} +(-70309.3 - 1.16912e6i) q^{95} +(-1.97195e6 - 1.00918e7i) 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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	−0.850969	−	0.525216i	$-0.823985\pi$
$2$	−2.30743	−	14.5685i	−0.203950	−	1.28769i	0.647019	−	0.762474i	$-0.276015\pi$
$3$	−38.7959	−	26.1128i	−0.829586	−	0.558378i
$3$	−38.7959	−	26.1128i	−0.829586	−	0.558378i
$4$	−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
$6$	−290.906	+	625.453i	−0.549824	+	1.18213i
$7$	−331.771	+	331.771i	−0.365591	+	0.365591i	−0.865866	−	0.500276i	$-0.833232\pi$
$7$	−331.771	+	331.771i	−0.365591	+	0.365591i	0.500276	+	0.865866i	$0.333232\pi$
$8$	−257.366	−	505.109i	−0.177720	−	0.348795i
$9$	823.247	+	2026.14i	0.376427	+	0.926446i
$10$	−3554.45	+	2088.85i	−1.12402	+	0.660552i
$11$	−1796.34	+	2472.45i	−0.406925	+	0.560085i	−0.962465	−	0.271405i	$-0.912512\pi$
$11$	−1796.34	+	2472.45i	−0.406925	+	0.560085i	0.555540	+	0.831490i	$0.312512\pi$
$12$	4027.49	+	1150.58i	0.672822	+	0.192214i
$13$	796.184	+	126.103i	0.100511	+	0.0159193i	0.206487	−	0.978449i	$-0.433797\pi$
$13$	796.184	+	126.103i	0.100511	+	0.0159193i	−0.105977	+	0.994369i	$0.533797\pi$
$14$	5598.96	+	4067.88i	0.545329	+	0.396205i
$15$	−2829.63	+	12761.4i	−0.216476	+	0.976288i
$16$	−16039.9	+	11653.6i	−0.978995	+	0.711281i
$17$	−6327.92	+	3224.24i	−0.312385	+	0.159168i	−0.603153	−	0.797626i	$-0.706089\pi$
$17$	−6327.92	+	3224.24i	−0.312385	+	0.159168i	0.290768	+	0.956794i	$0.406089\pi$
$18$	27618.3	−	16668.7i	1.11620	−	0.673670i
$19$	3985.23	+	1294.88i	0.133296	+	0.0433104i	0.374905	−	0.927063i	$-0.377675\pi$
$19$	3985.23	+	1294.88i	0.133296	+	0.0433104i	−0.241610	+	0.970374i	$0.577675\pi$
$20$	15904.3	+	19333.6i	0.444538	+	0.540390i
$21$	21534.8	−	4207.90i	0.507427	−	0.0991512i
$22$	40165.0	+	20465.1i	0.804207	+	0.409764i
$23$	25524.8	−	4042.74i	0.437437	−	0.0692832i	0.0661678	−	0.997809i	$-0.478923\pi$
$23$	25524.8	−	4042.74i	0.437437	−	0.0692832i	0.371269	+	0.928525i	$0.378923\pi$
$24$	−3205.05	+	26316.7i	−0.0473255	+	0.388591i
$25$	−57245.6	+	53164.4i	−0.732744	+	0.680505i
$26$		−	11890.2i		−	0.132673i
$27$	20969.4	−	100103.i	0.205028	−	0.978756i
$28$	19078.6	−	37443.9i	0.164245	−	0.322350i
$29$	−3266.26	−	10052.5i	−0.0248690	−	0.0765388i	0.937852	−	0.347036i	$-0.112812\pi$
$29$	−3266.26	−	10052.5i	−0.0248690	−	0.0765388i	−0.962721	+	0.270497i	$0.912812\pi$
$30$	192444.	+	11777.7i	1.30131	+	0.0796406i
$31$	23122.7	−	71164.3i	0.139403	−	0.429039i	−0.856846	−	0.515573i	$-0.827579\pi$
$31$	23122.7	−	71164.3i	0.139403	−	0.429039i	0.996249	+	0.0865341i	$0.0275792\pi$
$32$	155478.	+	155478.i	0.838770	+	0.838770i
$33$	134253.	−	49013.6i	0.650319	−	0.237420i
$34$	61573.7	+	84748.9i	0.268670	+	0.369792i
$35$	120213.	+	52416.2i	0.473931	+	0.206646i
$36$	−126205.	−	149807.i	−0.450836	−	0.535147i
$37$	83507.9	−	527248.i	0.271032	−	1.71123i	−0.357890	−	0.933764i	$-0.616504\pi$
$37$	83507.9	−	527248.i	0.271032	−	1.71123i	0.628922	−	0.777468i	$-0.283496\pi$
$38$	9668.87	−	61046.8i	0.0285847	−	0.180476i
$39$	−27595.8	−	25682.9i	−0.0744933	−	0.0693294i
$40$	−105115.	+	118567.i	−0.259689	+	0.292923i
$41$	−43960.7	−	60506.7i	−0.0996141	−	0.137107i	0.756300	−	0.654225i	$-0.227005\pi$
$41$	−43960.7	−	60506.7i	−0.0996141	−	0.137107i	−0.855914	+	0.517118i	$0.827005\pi$
$42$	−110993.	−	304021.i	−0.231166	−	0.633186i
$43$	−462464.	−	462464.i	−0.887030	−	0.887030i	0.107207	−	0.994237i	$-0.465809\pi$
$43$	−462464.	−	462464.i	−0.887030	−	0.887030i	−0.994237	+	0.107207i	$0.965809\pi$
$44$	84586.1	−	260329.i	0.149698	−	0.460722i
$45$	443013.	−	421200.i	0.724724	−	0.689039i
$46$	−117794.	−	362531.i	−0.178430	−	0.549153i
$47$	−50997.8	+	100089.i	−0.0716489	+	0.140619i	−0.924053	−	0.382265i	$-0.875144\pi$
$47$	−50997.8	+	100089.i	−0.0716489	+	0.140619i	0.852404	+	0.522884i	$0.175144\pi$
$48$	926589.	−	33268.6i	1.20932	−	0.0434200i
$49$			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	$-0.133980\pi$
$53$	1.21243e6	+	617764.i	1.11864	+	0.569977i	0.205925	+	0.978568i	$0.433980\pi$
$54$	−1.50674e6	−	74513.1i	−1.30215	−	0.0643953i
$55$	826784.	+	214721.i	0.670074	+	0.174022i
$56$	252967.	+	82194.0i	0.192489	+	0.0625434i
$57$	−120798.	−	154301.i	−0.0863966	−	0.110359i
$58$	−138914.	+	70780.1i	−0.0934862	+	0.0476336i
$59$	−1.86748e6	+	1.35681e6i	−1.18379	+	0.860074i	−0.992594	−	0.121478i	$-0.961236\pi$
$59$	−1.86748e6	+	1.35681e6i	−1.18379	+	0.860074i	−0.191196	+	0.981552i	$0.561236\pi$
$60$	−112168.	−	1.16537e6i	−0.0670408	−	0.696521i
$61$	2.57918e6	+	1.87388e6i	1.45488	+	1.05703i	0.984661	+	0.174481i	$0.0558247\pi$
$61$	2.57918e6	+	1.87388e6i	1.45488	+	1.05703i	0.470218	+	0.882550i	$0.344175\pi$
$62$	−1.09011e6	−	172657.i	−0.580900	−	0.0920055i
$63$	−945343.	−	399084.i	−0.476318	−	0.201082i
$64$	414663.	−	570735.i	0.197727	−	0.272148i
$65$	−48542.5	−	220023.i	−0.0219243	−	0.0993737i
$66$	−1.02384e6	−	1.84278e6i	−0.438356	−	0.788987i
$67$	1.64799e6	+	3.23437e6i	0.669413	+	1.31380i	0.936684	+	0.350175i	$0.113878\pi$
$67$	1.64799e6	+	3.23437e6i	0.669413	+	1.31380i	−0.267272	+	0.963621i	$0.586122\pi$
$68$	449792.	−	449792.i	0.173472	−	0.173472i
$69$	−1.09583e6	−	509682.i	−0.401578	−	0.186779i
$70$	486243.	−	1.87228e6i	0.169438	−	0.652421i
$71$	−2.43157e6	+	790064.i	−0.806272	+	0.261974i	−0.683018	−	0.730401i	$-0.739333\pi$
$71$	−2.43157e6	+	790064.i	−0.806272	+	0.261974i	−0.123254	+	0.992375i	$0.539333\pi$
$72$	811545.	−	937288.i	0.256241	−	0.295944i
$73$	197445.	+	1.24662e6i	0.0594041	+	0.375063i	0.999424	+	0.0339427i	$0.0108064\pi$
$73$	197445.	+	1.24662e6i	0.0594041	+	0.375063i	−0.940020	+	0.341120i	$0.889194\pi$
$74$	−7.87392e6			−2.25881
$75$	3.60917e6	−	567723.i	0.987853	−	0.155390i
$76$	−375313.			−0.0980722
$77$	−224314.	−	1.41626e6i	−0.0559936	−	0.353530i
$78$	−310487.	+	461292.i	−0.0740818	+	0.110064i
$79$	−1.48041e6	+	481014.i	−0.337821	+	0.109765i	−0.473015	−	0.881054i	$-0.656834\pi$
$79$	−1.48041e6	+	481014.i	−0.337821	+	0.109765i	0.135194	+	0.990819i	$0.456834\pi$
$80$	4.67073e6	+	2.98228e6i	1.01993	+	0.651229i
$81$	−3.42750e6	+	3.33602e6i	−0.716605	+	0.697480i
$82$	−780058.	+	780058.i	−0.156235	+	0.156235i
$83$	2.93578e6	+	5.76180e6i	0.563573	+	1.10607i	0.980387	+	0.197083i	$0.0631468\pi$
$83$	2.93578e6	+	5.76180e6i	0.563573	+	1.10607i	−0.416814	+	0.908992i	$0.636853\pi$
$84$	−1.71793e6	+	954474.i	−0.316249	+	0.175706i
$85$	1.48539e6	+	1.31686e6i	0.262345	+	0.232581i
$86$	−5.67032e6	+	7.80453e6i	−0.961309	+	1.32313i
$87$	−135781.	+	475288.i	−0.0221066	+	0.0773819i
$88$	1.71118e6	+	271024.i	0.267673	+	0.0423953i
$89$	−7.85725e6	−	5.70863e6i	−1.18142	−	0.858354i	−0.189092	−	0.981959i	$-0.560554\pi$
$89$	−7.85725e6	−	5.70863e6i	−1.18142	−	0.858354i	−0.992331	+	0.123605i	$0.960554\pi$
$90$	−7.15848e6	−	5.48216e6i	−1.03508	−	0.792690i
$91$	−305988.	+	222313.i	−0.0425657	+	0.0309258i
$92$	−2.06239e6	+	1.05084e6i	−0.276130	+	0.140695i
$93$	−2.75536e6	+	2.15709e6i	−0.355213	+	0.278085i
$94$	1.57582e6	+	512016.i	0.195686	+	0.0635823i
$95$	−70309.3	−	1.16912e6i	−0.00841356	−	0.139902i
$96$	−1.97195e6	−	1.00918e7i	−0.227481	−	1.16418i
$97$	3.07505e6	+	1.56682e6i	0.342099	+	0.174308i	0.616596	−	0.787280i	$-0.288511\pi$
$97$	3.07505e6	+	1.56682e6i	0.342099	+	0.174308i	−0.274497	+	0.961588i	$0.588511\pi$
$98$	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	$-0.0120512\pi$
$102$	−175779.	−	4.89577e6i	−0.0164009	−	0.456794i
$103$	−750.039	+	1472.03i	−6.76322e−5	+	0.000132736i	−0.891040	−	0.453924i	$-0.850024\pi$
$103$	−750.039	+	1472.03i	−6.76322e−5	+	0.000132736i	0.890973	+	0.454057i	$0.150024\pi$
$104$	−141215.	−	434615.i	−0.0123102	−	0.0378868i
$105$	−3.29506e6	−	5.17264e6i	−0.277780	−	0.436064i
$106$	6.20232e6	−	1.90888e7i	0.505806	−	1.55671i
$107$	−1.10071e7	−	1.10071e7i	−0.868621	−	0.868621i	0.123699	−	0.992320i	$-0.460524\pi$
$107$	−1.10071e7	−	1.10071e7i	−0.868621	−	0.868621i	−0.992320	+	0.123699i	$0.960524\pi$
$108$	984378.	+	9.10746e6i	0.0751932	+	0.695688i
$109$	3.57371e6	+	4.91879e6i	0.264318	+	0.363802i	0.920461	−	0.390834i	$-0.127813\pi$
$109$	3.57371e6	+	4.91879e6i	0.264318	+	0.363802i	−0.656143	+	0.754636i	$0.727813\pi$
$110$	1.22042e6	−	1.25405e7i	0.0874252	−	0.898339i
$111$	−1.70077e7	+	1.82744e7i	−1.18036	+	1.26828i
$112$	1.45522e6	−	9.18789e6i	0.0978735	−	0.617949i
$113$	−772488.	+	4.87730e6i	−0.0503636	+	0.317983i	0.949626	+	0.313386i	$0.101463\pi$
$113$	−772488.	+	4.87730e6i	−0.0503636	+	0.317983i	−0.999989	+	0.00459735i	$0.998537\pi$
$114$	−1.96921e6	+	2.11589e6i	−0.124488	+	0.133760i
$115$	−3.65977e6	−	6.22758e6i	−0.224394	−	0.381836i
$116$	556459.	+	765901.i	0.0331002	+	0.0455585i
$117$	399954.	+	1.71699e6i	0.0230866	+	0.0991101i
$118$	2.40758e7	+	2.40758e7i	1.34894	+	1.34894i
$119$	1.02971e6	−	3.16913e6i	0.0560146	−	0.172395i
$120$	7.17413e6	−	1.85507e6i	0.378996	−	0.0979999i
$121$	3.13569e6	+	9.65066e6i	0.160910	+	0.495231i
$122$	2.13485e7	−	4.18987e7i	1.06441	−	2.08901i
$123$	125498.	+	3.49535e6i	0.00608092	+	0.169364i
$124$			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	0.0284752	−	0.999595i	$-0.490935\pi$
$127$	8.41296e6	−	1.33248e6i	0.364448	−	0.0577229i	0.335973	+	0.941872i	$0.390935\pi$
$128$	1.58053e7	+	8.05321e6i	0.666144	+	0.339417i
$129$	5.86550e6	+	3.00179e7i	0.240570	+	1.23117i
$130$	−3.09341e6	+	1.21488e6i	−0.123491	+	0.0484989i
$131$	2.37323e7	+	7.71110e6i	0.922339	+	0.299686i	0.731426	−	0.681921i	$-0.238855\pi$
$131$	2.37323e7	+	7.71110e6i	0.922339	+	0.299686i	0.190913	+	0.981607i	$0.438855\pi$
$132$	−1.00795e7	+	7.89094e6i	−0.381444	+	0.298621i
$133$	−1.75179e6	+	892580.i	−0.0645655	+	0.0328978i
$134$	4.33174e7	−	3.14720e7i	1.55524	−	1.12994i
$135$	−2.81858e7	+	4.77253e6i	−0.985966	+	0.166948i
$136$	3.25718e6	+	2.36648e6i	0.111034	+	0.0806709i
$137$	1.36651e7	+	2.16433e6i	0.454035	+	0.0719121i	0.379264	−	0.925289i	$-0.376177\pi$
$137$	1.36651e7	+	2.16433e6i	0.454035	+	0.0719121i	0.0747715	+	0.997201i	$0.476177\pi$
$138$	−4.89678e6	+	1.71406e7i	−0.158611	+	0.555201i
$139$	−1.72812e7	+	2.37856e7i	−0.545786	+	0.751211i	−0.989433	−	0.144991i	$-0.953685\pi$
$139$	−1.72812e7	+	2.37856e7i	−0.545786	+	0.751211i	0.443646	+	0.896202i	$0.353685\pi$
$140$	−1.16909e7	−	1.13774e6i	−0.360081	−	0.0350426i
$141$	4.59211e6	−	2.55135e6i	0.137957	−	0.0766483i
$142$	1.71207e7	+	3.36014e7i	0.501780	+	0.984799i
$143$	−1.74200e6	+	1.74200e6i	−0.0498165	+	0.0498165i
$144$	−3.68166e7	−	2.29051e7i	−1.02748	−	0.639240i
$145$	−2.28157e6	+	1.87688e6i	−0.0621507	+	0.0511267i
$146$	1.77059e7	−	5.75298e6i	0.470849	−	0.152988i
$147$	1.57564e7	−	2.34094e7i	0.409116	−	0.607827i
$148$	7.47952e6	+	4.72238e7i	0.189652	+	1.19742i
$149$	−3.72125e7			−0.921587			−0.460794	−	0.887507i	$-0.652435\pi$
$149$	−3.72125e7			−0.921587			−0.460794	+	0.887507i	$0.652435\pi$
$150$	−1.65988e7	−	5.12703e7i	−0.401566	−	1.24036i
$151$	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
$153$	−1.17422e7	−	1.01669e7i	−0.265051	−	0.229492i
$154$	−2.01153e7	+	6.53585e6i	−0.443817	+	0.144205i
$155$	−2.08770e7	+	1.25551e6i	−0.450304	+	0.0270808i
$156$	3.06153e6	+	1.42396e6i	0.0645658	+	0.0300304i
$157$	2.95703e7	−	2.95703e7i	0.609827	−	0.609827i	−0.333074	−	0.942901i	$-0.608086\pi$
$157$	2.95703e7	−	2.95703e7i	0.609827	−	0.609827i	0.942901	+	0.333074i	$0.108086\pi$
$158$	1.04236e7	+	2.04575e7i	0.210242	+	0.412622i
$159$	−3.09058e7	−	5.56266e7i	−0.609748	−	1.09747i
$160$	2.45638e7	−	5.63356e7i	0.474106	−	1.08733i
$161$	−7.12713e6	+	9.80966e6i	−0.134594	+	0.185252i
$162$	5.65097e7	+	4.22360e7i	1.04429	+	0.780513i
$163$	−6.11692e7	−	9.68825e6i	−1.10631	−	0.175222i	−0.423555	−	0.905871i	$-0.639218\pi$
$163$	−6.11692e7	−	9.68825e6i	−1.10631	−	0.175222i	−0.682754	+	0.730649i	$0.739218\pi$
$164$	5.41938e6	+	3.93741e6i	0.0959392	+	0.0697039i
$165$	−2.64689e7	−	2.99199e7i	−0.458714	−	0.518521i
$166$	7.71669e7	−	5.60650e7i	1.30934	−	0.951291i
$167$	−7.35096e7	+	3.74550e7i	−1.22134	+	0.622304i	−0.941263	−	0.337674i	$-0.890360\pi$
$167$	−7.35096e7	+	3.74550e7i	−1.22134	+	0.622304i	−0.280076	+	0.959978i	$0.590360\pi$
$168$	−7.66778e6	−	9.79446e6i	−0.124763	−	0.159367i
$169$	−5.90594e7	−	1.91896e7i	−0.941208	−	0.305817i
$170$	1.57573e7	−	2.46785e7i	0.245987	−	0.385254i
$171$	657224.	+	9.14063e6i	0.0100514	+	0.139794i
$172$	5.21939e7	+	2.65941e7i	0.782115	+	0.398507i
$173$	−3.42071e7	+	5.41787e6i	−0.502290	+	0.0795549i	−0.402438	−	0.915447i	$-0.631837\pi$
$173$	−3.42071e7	+	5.41787e6i	−0.502290	+	0.0795549i	−0.0998522	+	0.995002i	$0.531837\pi$
$174$	7.23755e6	+	881444.i	0.104152	+	0.0126845i
$175$	1.35401e6	−	3.66308e7i	0.0190980	−	0.516670i
$176$		−	6.05917e7i		−	0.837758i
$177$	1.07881e8	−	3.87338e6i	1.46230	−	0.0525030i
$178$	−6.50363e7	+	1.27641e8i	−0.864342	+	1.69637i
$179$	4.02166e7	+	1.23774e8i	0.524107	+	1.61304i	0.766074	+	0.642752i	$0.222207\pi$
$179$	4.02166e7	+	1.23774e8i	0.524107	+	1.61304i	−0.241967	+	0.970285i	$0.577793\pi$
$180$	−2.60793e7	+	4.81406e7i	−0.333306	+	0.615258i
$181$	4.44783e7	−	1.36890e8i	0.557537	−	1.71592i	−0.131612	−	0.991301i	$-0.542015\pi$
$181$	4.44783e7	−	1.36890e8i	0.557537	−	1.71592i	0.689148	−	0.724620i	$-0.257985\pi$
$182$	3.94483e6	+	3.94483e6i	0.0485041	+	0.0485041i
$183$	−5.11293e7	−	1.40048e8i	−0.616724	−	1.68927i
$184$	−8.61124e6	−	1.18524e7i	−0.101907	−	0.140263i
$185$	−1.45703e8	+	3.21457e7i	−1.69188	+	0.373269i
$186$	3.77834e7	+	3.51643e7i	0.430533	+	0.400688i
$187$	3.39534e6	−	2.14373e7i	0.0379697	−	0.239731i
$188$	1.57392e6	−	9.93737e6i	0.0172755	−	0.109073i
$189$	2.62543e7	+	4.01684e7i	0.282868	+	0.432781i
$190$	−1.68701e7	+	3.72196e6i	−0.178435	+	0.0393672i
$191$	−3.43991e7	−	4.73463e7i	−0.357216	−	0.491665i	0.592155	−	0.805824i	$-0.298277\pi$
$191$	−3.43991e7	−	4.73463e7i	−0.357216	−	0.491665i	−0.949370	+	0.314159i	$0.898277\pi$
$192$	−3.09907e7	+	1.13142e7i	−0.315993	+	0.115364i
$193$	−5.13817e7	−	5.13817e7i	−0.514468	−	0.514468i	0.401425	−	0.915892i	$-0.368515\pi$
$193$	−5.13817e7	−	5.13817e7i	−0.514468	−	0.514468i	−0.915892	+	0.401425i	$0.868515\pi$
$194$	1.57308e7	−	4.84144e7i	0.154684	−	0.476067i
$195$	−3.86216e6	+	9.80358e6i	−0.0373000	+	0.0946811i
$196$	−1.67007e7	−	5.13993e7i	−0.158430	−	0.487597i
$197$	−5.04074e7	+	9.89300e7i	−0.469745	+	0.921926i	0.527627	+	0.849476i	$0.323082\pi$
$197$	−5.04074e7	+	9.89300e7i	−0.469745	+	0.921926i	−0.997372	+	0.0724503i	$0.976918\pi$
$198$	−8.39937e6	+	9.82276e7i	−0.0768986	+	0.899301i
$199$			1.13443e8i			1.02045i	0.860040	+	0.510226i	$0.170438\pi$
$199$			1.13443e8i			1.02045i	−0.860040	+	0.510226i	$0.829562\pi$
$200$	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
$204$	−2.91954e7	+	5.70478e6i	−0.240774	+	0.0470472i
$205$	−1.12500e7	+	1.76192e7i	−0.0912039	+	0.142840i
$206$	23176.1	+	7530.36i	0.000184716	+	6.00178e-5i
$207$	2.92044e7	+	4.83887e7i	0.228850	+	0.379182i
$208$	−1.42402e7	+	7.25576e6i	−0.109722	+	0.0559064i
$209$	−1.03604e7	+	7.52724e6i	−0.0784988	+	0.0570327i
$210$	−6.77547e7	+	5.99397e7i	−0.504861	+	0.446629i
$211$	−1.41671e8	−	1.02930e8i	−1.03823	−	0.754317i	−0.0682892	−	0.997666i	$-0.521754\pi$
$211$	−1.41671e8	−	1.02930e8i	−1.03823	−	0.754317i	−0.969939	+	0.243349i	$0.921754\pi$
$212$	−1.20377e8	−	1.90658e7i	−0.867694	−	0.137429i
$213$	1.14966e8	+	3.28437e7i	0.815153	+	0.232875i
$214$	−1.34959e8	+	1.85756e8i	−0.941359	+	1.29567i
$215$	−7.30643e7	+	1.67569e8i	−0.501384	+	1.14989i
$216$	−5.59598e7	+	1.51713e7i	−0.377823	+	0.102432i
$217$	1.59388e7	+	3.12817e7i	0.105888	+	0.207817i
$218$	6.34135e7	−	6.34135e7i	0.414557	−	0.414557i
$219$	2.48926e7	−	5.35196e7i	0.160146	−	0.344317i
$220$	−7.63709e7	+	4.59285e6i	−0.483558	+	0.0290806i
$221$	−5.44478e6	+	1.76912e6i	−0.0339318	+	0.0110251i
$222$	3.05476e8	+	2.05610e8i	1.87388	+	1.26127i
$223$	5.08251e7	+	3.20897e8i	0.306910	+	1.93775i	0.345302	+	0.938491i	$0.387776\pi$
$223$	5.08251e7	+	3.20897e8i	0.306910	+	1.93775i	−0.0383923	+	0.999263i	$0.512224\pi$
$224$	−1.03166e8			−0.613293
$225$	−1.54846e8	−	7.22200e7i	−0.906276	−	0.422687i
$226$	7.28375e7			0.419736
$227$	5.20636e7	+	3.28716e8i	0.295422	+	1.86522i	0.472924	+	0.881103i	$0.343199\pi$
$227$	5.20636e7	+	3.28716e8i	0.295422	+	1.86522i	−0.177502	+	0.984121i	$0.556801\pi$
$228$	1.45606e7	+	9.80045e6i	0.0813593	+	0.0547614i
$229$	4.63093e7	−	1.50468e7i	0.254826	−	0.0827980i	−0.178818	−	0.983882i	$-0.557227\pi$
$229$	4.63093e7	−	1.50468e7i	0.254826	−	0.0827980i	0.433644	+	0.901084i	$0.357227\pi$
$230$	−8.22820e7	+	6.76872e7i	−0.445921	+	0.366825i
$231$	−2.82801e7	+	6.08026e7i	−0.150952	+	0.324549i
$232$	−4.23699e6	+	4.23699e6i	−0.0222766	+	0.0222766i
$233$	−1.33207e8	−	2.61434e8i	−0.689895	−	1.35399i	−0.924229	−	0.381839i	$-0.875291\pi$
$233$	−1.33207e8	−	2.61434e8i	−0.689895	−	1.35399i	0.234334	−	0.972156i	$-0.424709\pi$
$234$	2.40912e7	−	9.78859e6i	0.122915	−	0.0499418i
$235$	3.12502e7	+	3.04123e6i	0.157078	+	0.0152866i
$236$	1.21525e8	−	1.67264e8i	0.601827	−	0.828344i
$237$	6.99945e7	+	1.99962e7i	0.341542	+	0.0975727i
$238$	−4.85456e7	−	7.68886e6i	−0.233416	−	0.0369694i
$239$	2.24679e8	+	1.63239e8i	1.06456	+	0.773446i	0.974926	−	0.222529i	$-0.0714312\pi$
$239$	2.24679e8	+	1.63239e8i	1.06456	+	0.773446i	0.0896309	+	0.995975i	$0.471431\pi$
$240$	−1.03329e8	−	2.37666e8i	−0.482486	−	1.10976i
$241$	−6.66431e6	+	4.84190e6i	−0.0306687	+	0.0222821i	−0.603014	−	0.797731i	$-0.706034\pi$
$241$	−6.66431e6	+	4.84190e6i	−0.0306687	+	0.0222821i	0.572345	+	0.820013i	$0.306034\pi$
$242$	1.33361e8	−	6.79506e7i	0.604886	−	0.308205i
$243$	2.20086e8	−	3.99226e7i	0.983943	−	0.178483i
$244$	−2.71567e8	−	8.82373e7i	−1.19677	−	0.388855i
$245$	1.56983e8	−	6.16522e7i	0.681978	−	0.267835i
$246$	5.06325e7	−	9.89359e6i	0.216849	−	0.0423722i
$247$	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	$-0.0819928\pi$
$252$	9.15728e7	+	7.83032e6i	0.360466	+	0.0308232i
$253$	−3.58559e7	+	7.03711e7i	−0.139200	+	0.273195i
$254$	−3.88247e7	−	1.19490e8i	−0.148658	−	0.457524i
$255$	−2.32400e7	−	8.98764e7i	−0.0877698	−	0.339434i
$256$	1.08758e8	−	3.34723e8i	0.405155	−	1.24694i
$257$	5.89957e7	+	5.89957e7i	0.216797	+	0.216797i	0.807147	−	0.590350i	$-0.201010\pi$
$257$	5.89957e7	+	5.89957e7i	0.216797	+	0.216797i	−0.590350	+	0.807147i	$0.701010\pi$
$258$	4.23783e8	−	1.54716e8i	1.53630	−	0.560876i
$259$	1.47220e8	+	2.02631e8i	0.526523	+	0.724697i
$260$	1.02247e7	+	1.73987e7i	0.0360782	+	0.0613917i
$261$	1.76788e7	−	1.48936e7i	0.0615477	−	0.0518511i
$262$	5.75788e7	−	3.63538e8i	0.197792	−	1.24881i
$263$	1.74955e7	−	1.10462e8i	0.0593037	−	0.374429i	−0.940131	−	0.340813i	$-0.889298\pi$
$263$	1.74955e7	−	1.10462e8i	0.0593037	−	0.374429i	0.999435	−	0.0336158i	$-0.0107023\pi$
$264$	−5.93095e7	−	5.51981e7i	−0.198386	−	0.184634i
$265$	3.68401e7	−	3.78551e8i	0.121607	−	1.24958i
$266$	1.70457e7	+	2.34614e7i	0.0555302	+	0.0764308i
$267$	1.55761e8	+	4.26646e8i	0.500806	+	1.37176i
$268$	−2.29901e8	−	2.29901e8i	−0.729573	−	0.729573i
$269$	−9.71316e7	+	2.98940e8i	−0.304248	+	0.936379i	0.675709	+	0.737169i	$0.263838\pi$
$269$	−9.71316e7	+	2.98940e8i	−0.304248	+	0.936379i	−0.979957	+	0.199210i	$0.936162\pi$
$270$	1.34566e8	+	3.99613e8i	0.416065	+	1.23557i
$271$	−3.13466e7	−	9.64750e7i	−0.0956749	−	0.294457i	0.891754	−	0.452520i	$-0.149475\pi$
$271$	−3.13466e7	−	9.64750e7i	−0.0956749	−	0.294457i	−0.987429	+	0.158063i	$0.949475\pi$
$272$	6.39249e7	−	1.25460e8i	0.192610	−	0.378018i
$273$	1.76763e7	−	634656.i	0.0525802	−	0.00188786i
$274$		−	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	−0.821333	−	0.570449i	$-0.806769\pi$
$277$	−5.04494e8	+	7.99041e7i	−1.42619	+	0.225886i	−0.604856	+	0.796335i	$0.706769\pi$
$278$	3.86396e8	+	1.96879e8i	1.07864	+	0.549594i
$279$	1.63224e8	−	1.17361e7i	0.449956	−	0.0323525i
$280$	−4.46296e6	−	7.42111e7i	−0.0121498	−	0.202030i
$281$	3.72942e8	+	1.21176e8i	1.00270	+	0.325795i	0.763942	−	0.645285i	$-0.223261\pi$
$281$	3.72942e8	+	1.21176e8i	1.00270	+	0.325795i	0.238753	+	0.971080i	$0.423261\pi$
$282$	−4.77654e7	−	6.10132e7i	−0.126836	−	0.162014i
$283$	−5.10319e8	+	2.60021e8i	−1.33841	+	0.681955i	−0.968942	−	0.247288i	$-0.920461\pi$
$283$	−5.10319e8	+	2.60021e8i	−1.33841	+	0.681955i	−0.369469	+	0.929243i	$0.620461\pi$
$284$	1.85261e8	−	1.34600e8i	0.479921	−	0.348683i
$285$	−2.78012e7	+	4.71929e7i	−0.0711387	+	0.120759i
$286$	2.93980e7	+	2.13589e7i	0.0743082	+	0.0539881i
$287$	3.46592e7	+	5.48948e6i	0.0865430	+	0.0137071i
$288$	−1.87023e8	+	4.43016e8i	−0.461339	+	1.09281i
$289$	−2.11544e8	+	2.91166e8i	−0.515535	+	0.709574i
$290$	3.26079e7	+	2.89084e7i	0.0785110	+	0.0696036i
$291$	−7.83856e7	−	1.41084e8i	−0.186471	−	0.335624i
$292$	−5.13225e7	−	1.00726e8i	−0.120633	−	0.236756i
$293$	2.15406e8	−	2.15406e8i	0.500288	−	0.500288i	−0.411239	−	0.911527i	$-0.634904\pi$
$293$	2.15406e8	−	2.15406e8i	0.500288	−	0.500288i	0.911527	+	0.411239i	$0.134904\pi$
$294$	−3.77398e8	−	1.75532e8i	−0.866132	−	0.402849i
$295$	5.43802e8	+	3.47220e8i	1.23329	+	0.787459i
$296$	−2.87810e8	+	9.35151e7i	−0.645037	+	0.209585i
$297$	2.09832e8	+	2.31665e8i	0.464755	+	0.513114i
$298$	8.58652e7	+	5.42131e8i	0.187958	+	1.18672i
$299$	2.08323e7			0.0450700
$300$	−2.91726e8	+	1.48253e8i	−0.623808	+	0.317015i
$301$	3.06864e8			0.648580
$302$	−1.35580e8	−	8.56016e8i	−0.283250	−	1.78837i
$303$	−2.04684e7	+	3.04100e7i	−0.0422702	+	0.0628011i
$304$	−7.90125e7	+	2.56727e7i	−0.161301	+	0.0524100i
$305$	2.23989e8	−	8.62473e8i	0.452041	−	1.74059i
$306$	−1.21023e8	+	1.94526e8i	−0.241458	+	0.388108i
$307$	−3.46971e8	+	3.46971e8i	−0.684399	+	0.684399i	−0.960988	−	0.276589i	$-0.910796\pi$
$307$	−3.46971e8	+	3.46971e8i	−0.684399	+	0.684399i	0.276589	+	0.960988i	$0.410796\pi$
$308$	5.83065e7	+	1.14433e8i	0.113708	+	0.223164i
$309$	67537.3	−	37523.3i	0.000130223	−	7.23514e-5i
$310$	6.64631e7	+	3.01250e8i	0.126711	+	0.574329i
$311$	−4.99844e8	+	6.87976e8i	−0.942264	+	1.29692i	0.0126146	+	0.999920i	$0.495985\pi$
$311$	−4.99844e8	+	6.87976e8i	−0.942264	+	1.29692i	−0.954879	+	0.296995i	$0.904015\pi$
$312$	−5.87043e6	+	2.05488e7i	−0.0109428	+	0.0383041i
$313$	−4.86186e8	−	7.70042e7i	−0.896183	−	0.141941i	−0.308683	−	0.951165i	$-0.599888\pi$
$313$	−4.86186e8	−	7.70042e7i	−0.896183	−	0.141941i	−0.587501	+	0.809224i	$0.699888\pi$
$314$	−4.99027e8	−	3.62564e8i	−0.909642	−	0.660893i
$315$	−7.23703e6	+	2.86721e8i	−0.0130459	+	0.516859i
$316$	1.12792e8	−	8.19484e7i	0.201083	−	0.146095i
$317$	6.50771e8	−	3.31584e8i	1.14741	−	0.584637i	0.226350	−	0.974046i	$-0.427321\pi$
$317$	6.50771e8	−	3.31584e8i	1.14741	−	0.584637i	0.921065	+	0.389409i	$0.127321\pi$
$318$	−7.39086e8	+	5.78607e8i	−1.28884	+	1.00899i
$319$	3.07217e7	+	9.98208e6i	0.0529880	+	0.0172169i
$320$	−1.90853e8	−	4.95657e7i	−0.325592	−	0.0845583i
$321$	1.39605e8	+	7.14457e8i	0.235577	+	1.20562i
$322$	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
$327$	−1.02022e7	−	2.84148e8i	−0.0161352	−	0.449395i
$328$	−1.92485e7	+	3.77773e7i	−0.0301188	+	0.0591115i
$329$	−1.62870e7	−	5.01262e7i	−0.0252148	−	0.0776031i
$330$	−3.74815e8	+	4.54651e8i	−0.574140	+	0.696434i
$331$	1.72045e8	−	5.29501e8i	0.260763	−	0.802545i	−0.731877	−	0.681437i	$-0.761355\pi$
$331$	1.72045e8	−	5.29501e8i	0.260763	−	0.802545i	0.992639	−	0.121108i	$-0.0386446\pi$
$332$	−4.09551e8	−	4.09551e8i	−0.614222	−	0.614222i
$333$	1.13702e9	−	2.64857e8i	1.68739	−	0.393058i
$334$	7.15283e8	+	9.84503e8i	1.05043	+	1.44579i
$335$	6.73083e8	−	7.59220e8i	0.978165	−	1.10334i
$336$	−2.96378e8	+	3.18453e8i	−0.426244	+	0.457992i
$337$	1.93475e8	−	1.22155e9i	0.275373	−	1.73863i	−0.331159	−	0.943575i	$-0.607440\pi$
$337$	1.93475e8	−	1.22155e9i	0.275373	−	1.73863i	0.606531	−	0.795060i	$-0.292560\pi$
$338$	−1.43288e8	+	9.04688e8i	−0.201838	+	1.27435i
$339$	1.57329e8	−	1.69047e8i	0.219336	−	0.235673i
$340$	−1.62977e8	−	7.10622e7i	−0.224880	−	0.0980534i
$341$	1.34414e8	+	1.85005e8i	0.183571	+	0.252664i
$342$	1.31649e8	−	3.06662e7i	0.177962	−	0.0414541i
$343$	−4.73418e8	−	4.73418e8i	−0.633454	−	0.633454i
$344$	−1.14572e8	+	3.52617e8i	−0.151749	+	0.467034i
$345$	−2.06351e7	+	3.37171e8i	−0.0270545	+	0.442063i
$346$	1.57861e8	+	4.85846e8i	0.204884	+	0.630568i
$347$	1.02439e8	−	2.01048e8i	0.131617	−	0.258313i	−0.815787	−	0.578352i	$-0.803696\pi$
$347$	1.02439e8	−	2.01048e8i	0.131617	−	0.258313i	0.947404	+	0.320039i	$0.103696\pi$
$348$	−1.58857e6	−	4.42445e7i	−0.00202059	−	0.0562771i
$349$			6.21336e7i			0.0782416i	0.999234	+	0.0391208i	$0.0124557\pi$
$349$			6.21336e7i			0.0782416i	−0.999234	+	0.0391208i	$0.987544\pi$
$350$	−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	$-0.425841\pi$
$353$	−3.47583e8	−	1.77102e8i	−0.420579	−	0.214296i	−0.651455	+	0.758688i	$0.725841\pi$
$354$	−3.05357e8	−	1.56273e9i	−0.365844	−	1.87228i
$355$	4.53991e8	+	5.51881e8i	0.538577	+	0.654706i
$356$	8.27305e8	+	2.68808e8i	0.971831	+	0.315767i
$357$	−1.22703e8	+	9.60606e7i	−0.142731	+	0.111739i
$358$	1.71041e9	−	8.71498e8i	1.97020	−	1.00387i
$359$	−1.25747e9	+	9.13609e8i	−1.43439	+	1.04215i	−0.445217	+	0.895423i	$0.646874\pi$
$359$	−1.25747e9	+	9.13609e8i	−1.43439	+	1.04215i	−0.989177	+	0.146726i	$0.953126\pi$
$360$	−3.26768e8	−	1.15367e8i	−0.369131	−	0.130324i
$361$	−7.08952e8	−	5.15084e8i	−0.793125	−	0.576239i
$362$	−2.09692e9	−	3.32120e8i	−2.32328	−	0.367972i
$363$	1.30353e8	−	4.56288e8i	0.143037	−	0.500686i
$364$	1.99119e7	−	2.74063e7i	0.0216400	−	0.0297849i
$365$	3.04152e8	−	1.78741e8i	0.327390	−	0.192398i
$366$	−1.92232e9	+	1.06803e9i	−2.04948	+	1.13868i
$367$	−7.27723e8	−	1.42824e9i	−0.768484	−	1.50823i	−0.858794	−	0.512320i	$-0.828786\pi$
$367$	−7.27723e8	−	1.42824e9i	−0.768484	−	1.50823i	0.0903107	−	0.995914i	$-0.471214\pi$
$368$	−3.62302e8	+	3.62302e8i	−0.378969	+	0.378969i
$369$	8.64043e7	−	1.38882e8i	0.0895248	−	0.143898i
$370$	8.04517e8	+	2.04851e9i	0.825713	+	2.10248i
$371$	−6.07205e8	+	1.97293e8i	−0.617343	+	0.200587i
$372$	1.75007e8	−	2.60009e8i	0.176261	−	0.261872i
$373$	−3.67596e7	−	2.32091e8i	−0.0366767	−	0.231567i	0.962540	−	0.271140i	$-0.0874005\pi$
$373$	−3.67596e7	−	2.32091e8i	−0.0366767	−	0.231567i	−0.999217	+	0.0395722i	$0.987401\pi$
$374$	−3.20145e8			−0.316444
$375$	−5.16467e8	−	8.80968e8i	−0.505747	−	0.862682i
$376$	6.36809e7			0.0617806
$377$	−1.33289e6	−	8.41554e6i	−0.00128115	−	0.00808886i
$378$	5.24614e8	−	4.75172e8i	0.499596	−	0.452511i
$379$	5.27313e8	−	1.71334e8i	0.497544	−	0.161662i	−0.0494862	−	0.998775i	$-0.515758\pi$
$379$	5.27313e8	−	1.71334e8i	0.497544	−	0.161662i	0.547030	+	0.837113i	$0.315758\pi$
$380$	3.83475e7	+	9.76429e7i	0.0358505	+	0.0912847i
$381$	−3.61183e8	−	1.67991e8i	−0.334573	−	0.155614i
$382$	−6.10393e8	+	6.10393e8i	−0.560258	+	0.560258i
$383$	−1.02201e7	−	2.00581e7i	−0.00929525	−	0.0182429i	0.886312	−	0.463088i	$-0.153259\pi$
$383$	−1.02201e7	−	2.00581e7i	−0.00929525	−	0.0182429i	−0.895607	+	0.444845i	$0.853259\pi$
$384$	−4.02890e8	−	7.25152e8i	−0.363101	−	0.653536i
$385$	−3.45541e8	+	2.03065e8i	−0.308594	+	0.181352i
$386$	−6.29997e8	+	8.67116e8i	−0.557549	+	0.767400i
$387$	5.56294e8	−	1.31774e9i	0.487883	−	1.15569i
$388$	−3.05308e8	−	4.83560e7i	−0.265355	−	0.0420281i
$389$	7.34333e8	+	5.33524e8i	0.632513	+	0.459548i	0.857270	−	0.514867i	$-0.172159\pi$
$389$	7.34333e8	+	5.33524e8i	0.632513	+	0.459548i	−0.224757	+	0.974415i	$0.572159\pi$
$390$	1.51736e8	+	3.36450e7i	0.129527	+	0.0287206i
$391$	−1.48484e8	+	1.07880e8i	−0.125621	+	0.0912690i
$392$	3.04782e8	−	1.55294e8i	0.255557	−	0.130213i
$393$	−7.19359e8	−	9.18876e8i	−0.597822	−	0.763630i
$394$	1.55758e9	+	5.06088e8i	1.28296	+	0.416859i
$395$	2.76403e8	+	3.36002e8i	0.225659	+	0.274316i
$396$	5.97098e8	−	4.29322e7i	0.483184	−	0.0347416i
$397$	9.22687e8	+	4.70132e8i	0.740095	+	0.377097i	0.783033	−	0.621980i	$-0.213672\pi$
$397$	9.22687e8	+	4.70132e8i	0.740095	+	0.377097i	−0.0429376	+	0.999078i	$0.513672\pi$
$398$	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	$-0.0182535\pi$
$402$	−2.50236e9	+	8.98456e7i	−1.92114	+	0.0689772i
$403$	2.73840e7	−	5.37441e7i	0.0208415	−	0.0409037i
$404$	2.16950e7	+	6.67703e7i	0.0163691	+	0.0503789i
$405$	1.21812e9	+	5.50854e8i	0.911164	+	0.412044i
$406$	2.26048e7	−	6.95704e7i	0.0167633	−	0.0515921i
$407$	1.15359e9	+	1.15359e9i	0.848145	+	0.848145i
$408$	−6.45700e7	−	1.76864e8i	−0.0470674	−	0.128922i
$409$	4.52660e8	+	6.23033e8i	0.327145	+	0.450276i	0.940632	−	0.339429i	$-0.110234\pi$
$409$	4.52660e8	+	6.23033e8i	0.327145	+	0.450276i	−0.613487	+	0.789705i	$0.710234\pi$
$410$	2.82645e8	+	1.23241e8i	0.202534	+	0.0883101i
$411$	−4.73632e8	−	4.40800e8i	−0.336507	−	0.313181i
$412$	23148.1	−	146152.i	1.63071e−5	−	0.000102959i
$413$	1.69428e8	−	1.06972e9i	0.118348	−	0.747217i
$414$	6.37565e8	−	5.37119e8i	0.441594	−	0.372022i
$415$	1.19905e9	−	1.35250e9i	0.823509	−	0.928897i
$416$	1.04183e8	+	1.43395e8i	0.0709527	+	0.0976580i
$417$	1.29155e9	−	4.71522e8i	0.872237	−	0.318439i
$418$	1.33567e8	+	1.33567e8i	0.0894502	+	0.0894502i
$419$	1.21056e7	−	3.72572e7i	0.00803965	−	0.0247435i	−0.946956	−	0.321363i	$-0.895859\pi$
$419$	1.21056e7	−	3.72572e7i	0.00803965	−	0.0247435i	0.954996	+	0.296619i	$0.0958592\pi$
$420$	4.23849e8	+	3.49421e8i	0.279151	+	0.230132i
$421$	6.70341e8	+	2.06310e9i	0.437833	+	1.34751i	0.890156	+	0.455656i	$0.150595\pi$
$421$	6.70341e8	+	2.06310e9i	0.437833	+	1.34751i	−0.452323	+	0.891854i	$0.649405\pi$
$422$	−1.17265e9	+	2.30145e9i	−0.759579	+	1.49076i
$423$	−2.44778e8	−	2.09308e7i	−0.157246	−	0.0134460i
$424$		−	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
$429$	1.13071e8	−	2.20941e7i	0.0691435	−	0.0135106i
$430$	2.60982e9	+	6.77787e8i	1.58296	+	0.411106i
$431$	−1.78525e9	−	5.80062e8i	−1.07406	−	0.348983i	−0.281991	−	0.959417i	$-0.590995\pi$
$431$	−1.78525e9	−	5.80062e8i	−1.07406	−	0.348983i	−0.792067	+	0.610434i	$0.790995\pi$
$432$	8.30219e8	+	1.85001e9i	0.495449	+	1.10403i
$433$	−4.90994e8	+	2.50174e8i	−0.290649	+	0.148093i	−0.593236	−	0.805029i	$-0.702150\pi$
$433$	−4.90994e8	+	2.50174e8i	−0.290649	+	0.148093i	0.302587	+	0.953122i	$0.402150\pi$
$434$	4.18951e8	−	3.04386e8i	0.246008	−	0.178735i
$435$	1.37526e8	−	1.32370e7i	0.0801075	−	0.00771042i
$436$	−4.40559e8	−	3.20085e8i	−0.254567	−	0.184954i
$437$	1.06957e8	+	1.69403e7i	0.0613091	+	0.00971040i
$438$	−8.37141e8	−	2.39157e8i	−0.476035	−	0.135995i
$439$	−2.07966e8	+	2.86241e8i	−0.117319	+	0.161475i	−0.863638	−	0.504113i	$-0.831819\pi$
$439$	−2.07966e8	+	2.86241e8i	−0.117319	+	0.161475i	0.746319	+	0.665589i	$0.231819\pi$
$440$	−1.04329e8	−	4.72878e8i	−0.0583874	−	0.264646i
$441$	−1.22257e9	+	4.96747e8i	−0.678795	+	0.275803i
$442$	3.83369e7	+	7.52404e7i	0.0211173	+	0.0414451i
$443$	3.39333e8	−	3.39333e8i	0.185444	−	0.185444i	−0.608279	−	0.793723i	$-0.708140\pi$
$443$	3.39333e8	−	3.39333e8i	0.185444	−	0.185444i	0.793723	+	0.608279i	$0.208140\pi$
$444$	9.42970e8	−	2.02740e9i	0.511278	−	1.09926i
$445$	−6.82365e8	+	2.62745e9i	−0.367077	+	1.41343i
$446$	4.55773e9	−	1.48090e9i	2.43263	−	0.790410i
$447$	1.44369e9	+	9.71720e8i	0.764536	+	0.514594i
$448$	5.17801e7	+	3.26927e8i	0.0272076	+	0.171782i
$449$	−1.19146e9			−0.621178			−0.310589	−	0.950544i	$-0.600526\pi$
$449$	−1.19146e9			−0.621178			−0.310589	+	0.950544i	$0.600526\pi$
$450$	−6.94844e8	+	2.42252e9i	−0.359454	+	1.25321i
$451$	2.28568e8			0.117327
$452$	−6.91891e7	−	4.36843e8i	−0.0352414	−	0.222506i
$453$	−2.27957e9	−	1.53433e9i	−1.15215	−	0.775488i
$454$	4.66879e9	−	1.51698e9i	2.34158	−	0.760825i
$455$	8.91023e7	+	5.68923e7i	0.0443454	+	0.0283148i
$456$	−4.68498e7	+	1.00728e8i	−0.0231383	+	0.0497477i
$457$	−1.25931e9	+	1.25931e9i	−0.617200	+	0.617200i	−0.944812	−	0.327612i	$-0.893756\pi$
$457$	−1.25931e9	+	1.25931e9i	−0.617200	+	0.617200i	0.327612	+	0.944812i	$0.393756\pi$
$458$	−3.26065e8	−	6.39939e8i	−0.158590	−	0.311250i
$459$	1.90063e8	+	7.01055e8i	0.0917390	+	0.338382i
$460$	4.84115e8	+	4.29190e8i	0.231897	+	0.205588i
$461$	2.11798e9	−	2.91515e9i	1.00686	−	1.38582i	0.0858372	−	0.996309i	$-0.472643\pi$
$461$	2.11798e9	−	2.91515e9i	1.00686	−	1.38582i	0.921021	−	0.389513i	$-0.127357\pi$
$462$	9.51060e8	+	2.71701e8i	0.448705	+	0.128187i
$463$	−1.30891e9	−	2.07310e8i	−0.612879	−	0.0970705i	−0.157725	−	0.987483i	$-0.550416\pi$
$463$	−1.30891e9	−	2.07310e8i	−0.612879	−	0.0970705i	−0.455154	+	0.890413i	$0.650416\pi$
$464$	1.69539e8	+	1.23177e8i	0.0787872	+	0.0572423i
$465$	8.42726e8	+	4.96446e8i	0.388688	+	0.228974i
$466$	−3.50135e9	+	2.54388e9i	−1.60282	+	1.16452i
$467$	−3.62054e9	+	1.84476e9i	−1.64499	+	0.838166i	−0.647920	+	0.761708i	$0.724361\pi$
$467$	−3.62054e9	+	1.84476e9i	−1.64499	+	0.838166i	−0.997073	+	0.0764578i	$0.975639\pi$
$468$	−8.15915e7	−	1.35189e8i	−0.0367947	−	0.0609649i
$469$	−1.61983e9	−	5.26314e8i	−0.725043	−	0.235581i
$470$	−2.78014e7	−	4.62288e8i	−0.0123516	−	0.205385i
$471$	−1.91937e9	+	3.75044e8i	−0.846418	+	0.165390i
$472$	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
$477$	−2.53545e8	+	2.96512e9i	−0.106965	+	1.25092i
$478$	1.85972e9	−	3.64990e9i	0.778842	−	1.52856i
$479$	8.29859e8	+	2.55404e9i	0.345009	+	1.06183i	0.961579	+	0.274528i	$0.0885216\pi$
$479$	8.29859e8	+	2.55404e9i	0.345009	+	1.06183i	−0.616570	+	0.787300i	$0.711478\pi$
$480$	−2.42405e9	+	1.54416e9i	−1.00046	+	0.637307i
$481$	1.32975e8	−	4.09256e8i	0.0544833	−	0.167682i
$482$	8.59169e7	+	8.59169e7i	0.0349473	+	0.0349473i
$483$	5.32661e8	−	1.94466e8i	0.215098	−	0.0785286i
$484$	−5.34214e8	−	7.35283e8i	−0.214169	−	0.294779i
$485$	9.34365e7	−	9.60108e8i	0.0371895	−	0.382141i
$486$	−1.08945e9	−	3.11421e9i	−0.430506	−	1.23061i
$487$	6.42820e8	−	4.05860e9i	0.252196	−	1.59230i	−0.458430	−	0.888731i	$-0.651588\pi$
$487$	6.42820e8	−	4.05860e9i	0.252196	−	1.59230i	0.710625	−	0.703571i	$-0.248412\pi$
$488$	2.82722e8	−	1.78504e9i	0.110126	−	0.695310i
$489$	2.12013e9	+	1.97316e9i	0.819938	+	0.763100i
$490$	−1.26041e9	−	2.14475e9i	−0.483978	−	0.823551i
$491$	1.59241e9	+	2.19176e9i	0.607112	+	0.835618i	0.996336	−	0.0855253i	$-0.0272569\pi$
$491$	1.59241e9	+	2.19176e9i	0.607112	+	0.835618i	−0.389224	+	0.921143i	$0.627257\pi$
$492$	−1.07433e8	−	2.94270e8i	−0.0406687	−	0.111396i
$493$	5.30803e7	+	5.30803e7i	0.0199512	+	0.0199512i
$494$	1.53964e7	−	4.73853e7i	0.00574612	−	0.0176847i
$495$	2.45593e8	+	1.85195e9i	0.0910119	+	0.686294i
$496$	4.58439e8	+	1.41093e9i	0.168692	+	0.519182i
$497$	5.44603e8	−	1.06884e9i	0.198991	−	0.390541i
$498$	−4.45777e9	+	1.60053e8i	−1.61739	+	0.0580714i
$499$			6.57247e7i			0.0236797i	0.999930	+	0.0118399i	$0.00376883\pi$
$499$			6.57247e7i			0.0236797i	−0.999930	+	0.0118399i	$0.996231\pi$
$500$	−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	$-0.561553\pi$
$503$	−3.13698e9	−	1.59837e9i	−1.09906	−	0.560001i	−0.906893	+	0.421360i	$0.861553\pi$
$504$	4.17180e7	+	5.80212e8i	0.0145150	+	0.201874i
$505$	−2.03928e8	+	8.00893e7i	−0.0704624	+	0.0276729i
$506$	1.10794e9	+	3.59991e8i	0.380180	+	0.123528i
$507$	1.79017e9	+	2.28668e9i	0.610052	+	0.779251i
$508$	−6.79761e8	+	3.46356e8i	−0.230056	+	0.117219i
$509$	8.82697e8	−	6.41317e8i	0.296688	−	0.215556i	−0.429476	−	0.903078i	$-0.641302\pi$
$509$	8.82697e8	−	6.41317e8i	0.296688	−	0.215556i	0.726163	+	0.687522i	$0.241302\pi$
$510$	−1.25574e9	+	5.45956e8i	−0.419184	+	0.182248i
$511$	−4.79099e8	−	3.48086e8i	−0.158837	−	0.115402i
$512$	−2.88477e9	−	4.56903e8i	−0.949876	−	0.150446i
$513$	2.13189e8	−	3.71781e8i	0.0697196	−	0.121584i
$514$	7.23352e8	−	9.95609e8i	0.234952	−	0.323384i
$515$	459605.	+	44728.2i	0.000148272	+	1.44297e-5i
$516$	−1.33047e9	−	2.39467e9i	−0.426314	−	0.767312i
$517$	−1.55856e8	−	3.05884e8i	−0.0496027	−	0.0973508i
$518$	2.61234e9	−	2.61234e9i	0.825801	−	0.825801i
$519$	1.46857e9	+	6.83050e8i	0.461115	+	0.214470i
$520$	−9.86425e7	+	8.11457e7i	−0.0307647	+	0.0253078i
$521$	−2.41642e9	+	7.85142e8i	−0.748584	+	0.243230i	−0.658372	−	0.752693i	$-0.728754\pi$
$521$	−2.41642e9	+	7.85142e8i	−0.748584	+	0.243230i	−0.0902121	+	0.995923i	$0.528754\pi$
$522$	−2.57771e8	−	2.23189e8i	−0.0793207	−	0.0686793i
$523$	−4.25978e8	−	2.68952e9i	−0.130206	−	0.822088i	−0.963196	−	0.268800i	$-0.913373\pi$
$523$	−4.25978e8	−	2.68952e9i	−0.130206	−	0.822088i	0.832990	−	0.553288i	$-0.186627\pi$
$524$	−2.23501e9			−0.678611
$525$	−1.00906e9	+	1.38577e9i	−0.304341	+	0.417959i
$526$	−1.64965e9			−0.494243
$527$	8.31321e7	+	5.24876e8i	0.0247418	+	0.156214i
$528$	−1.58222e9	+	2.35071e9i	−0.467786	+	0.694993i
$529$	−2.60301e9	+	8.45769e8i	−0.764506	+	0.248403i
$530$	−5.59994e9	+	3.36773e8i	−1.63387	+	0.0982590i
$531$	−4.28647e9	−	2.66679e9i	−1.24242	−	0.772962i
$532$	1.24518e8	−	1.24518e8i	0.0358543	−	0.0358543i
$533$	−2.73707e7	−	5.37180e7i	−0.00782962	−	0.0153665i
$534$	5.85620e9	−	3.25367e9i	1.66426	−	0.924654i
$535$	−1.73900e9	+	3.98831e9i	−0.490979	+	1.12603i
$536$	1.20957e9	−	1.66483e9i	0.339278	−	0.466976i
$537$	1.67184e9	−	5.85210e9i	0.465892	−	1.63080i
$538$	4.57925e9	+	7.25282e8i	1.26782	+	0.200802i
$539$	−1.49188e9	−	1.08391e9i	−0.410367	−	0.298149i
$540$	2.26886e9	−	1.18665e9i	0.620053	−	0.324299i
$541$	1.08056e8	−	7.85071e7i	0.0293398	−	0.0213166i	−0.573019	−	0.819542i	$-0.694228\pi$
$541$	1.08056e8	−	7.85071e7i	0.0293398	−	0.0213166i	0.602359	+	0.798226i	$0.294228\pi$
$542$	−1.33317e9	+	6.79284e8i	−0.359656	+	0.183254i
$543$	−5.30016e9	+	4.14933e9i	−1.42066	+	1.11219i
$544$	−1.48515e9	−	4.82554e8i	−0.395524	−	0.128514i
$545$	9.14548e8	−	1.43233e9i	0.242002	−	0.379013i
$546$	−5.00329e7	−	2.56054e8i	−0.0131547	−	0.0673220i
$547$	4.30848e9	+	2.19528e9i	1.12556	+	0.573501i	0.914747	−	0.404026i	$-0.132390\pi$
$547$	4.30848e9	+	2.19528e9i	1.12556	+	0.573501i	0.210811	+	0.977527i	$0.432390\pi$
$548$	−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
$552$	2.45832e7	+	6.84687e8i	0.00622088	+	0.173263i
$553$	3.31570e8	−	6.50743e8i	0.0833753	−	0.163633i
$554$	2.32817e9	+	7.16538e9i	0.581742	+	1.79042i
$555$	6.49211e9	+	2.55759e9i	1.61198	+	0.635047i
$556$	8.13738e8	−	2.50443e9i	0.200781	−	0.617941i
$557$	−3.14880e9	−	3.14880e9i	−0.772061	−	0.772061i	0.206406	−	0.978467i	$-0.433823\pi$
$557$	−3.14880e9	−	3.14880e9i	−0.772061	−	0.772061i	−0.978467	+	0.206406i	$0.933823\pi$
$558$	−5.47606e8	−	2.35086e9i	−0.133429	−	0.572806i
$559$	−3.09888e8	−	4.26525e8i	−0.0750350	−	0.103277i
$560$	−2.53905e9	+	5.60176e8i	−0.610959	+	0.134793i
$561$	−6.91513e8	+	7.43019e8i	−0.165360	+	0.177677i
$562$	9.04822e8	−	5.71282e9i	0.215024	−	1.35761i
$563$	−1.39380e8	+	8.80012e8i	−0.0329171	+	0.207830i	−0.998665	−	0.0516511i	$-0.983552\pi$
$563$	−1.39380e8	+	8.80012e8i	−0.0329171	+	0.207830i	0.965748	+	0.259481i	$0.0835516\pi$
$564$	−3.20554e8	+	3.44430e8i	−0.0752358	+	0.0808395i
$565$	1.34783e9	−	2.97364e8i	0.314387	−	0.0693614i
$566$	4.96565e9	+	6.83463e9i	1.15111	+	1.58437i
$567$	3.03487e7	−	2.24394e9i	0.00699196	−	0.516976i
$568$	1.02487e9	+	1.02487e9i	0.234666	+	0.234666i
$569$	1.72288e9	−	5.30248e9i	0.392069	−	1.20666i	−0.539152	−	0.842208i	$-0.681255\pi$
$569$	1.72288e9	−	5.30248e9i	0.392069	−	1.20666i	0.931221	−	0.364455i	$-0.118745\pi$
$570$	7.51682e8	+	2.96128e8i	0.170009	+	0.0669757i
$571$	1.77701e9	+	5.46907e9i	0.399451	+	1.22938i	0.925441	+	0.378892i	$0.123695\pi$
$571$	1.77701e9	+	5.46907e9i	0.399451	+	1.22938i	−0.525990	+	0.850491i	$0.676305\pi$
$572$	1.00175e8	−	1.96604e8i	0.0223806	−	0.0439244i
$573$	9.82020e7	+	2.73510e9i	0.0218062	+	0.607340i
$574$		−	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	−0.777102	−	0.629375i	$-0.783311\pi$
$577$	−6.09877e9	+	9.65950e8i	−1.32168	+	0.209334i	−0.544580	+	0.838709i	$0.683311\pi$
$578$	4.72998e9	+	2.41005e9i	1.01885	+	0.519132i
$579$	6.51682e8	+	3.33512e9i	0.139528	+	0.714063i
$580$	1.42404e8	−	2.23026e8i	0.0303056	−	0.0474634i
$581$	−2.88560e9	−	9.37589e8i	−0.610408	−	0.198334i
$582$	−1.87452e9	+	1.46751e9i	−0.394149	+	0.308567i
$583$	−3.70533e9	+	1.88796e9i	−0.774439	+	0.394596i
$584$	5.78864e8	−	4.20569e8i	0.120263	−	0.0873760i
$585$	4.05835e8	−	2.79487e8i	0.0838115	−	0.0577187i
$586$	−3.63518e9	−	2.64111e9i	−0.746249	−	0.542182i
$587$	1.61531e8	+	2.55839e7i	0.0329626	+	0.00522077i	0.172894	−	0.984940i	$-0.444688\pi$
$587$	1.61531e8	+	2.55839e7i	0.0329626	+	0.00522077i	−0.139931	+	0.990161i	$0.544688\pi$
$588$	−6.94261e8	+	2.43018e9i	−0.140832	+	0.492968i
$589$	1.84298e8	−	2.53665e8i	0.0371636	−	0.0511514i
$590$	3.80371e9	−	8.72359e9i	0.762474	−	1.74869i
$591$	4.53894e9	−	2.52181e9i	0.904478	−	0.502522i
$592$	4.80490e9	+	9.43015e9i	0.951828	+	1.86807i
$593$	−1.12540e9	+	1.12540e9i	−0.221624	+	0.221624i	−0.809182	−	0.587558i	$-0.800089\pi$
$593$	−1.12540e9	+	1.12540e9i	−0.221624	+	0.221624i	0.587558	+	0.809182i	$0.300089\pi$
$594$	2.89085e9	−	3.59150e9i	0.565944	−	0.703110i
$595$	−9.29704e8	+	5.59113e7i	−0.180940	+	0.0108815i
$596$	3.16987e9	−	1.02995e9i	0.613309	−	0.199276i
$597$	2.96232e9	−	4.40113e9i	0.569798	−	0.846553i
$598$	−4.80690e7	−	3.03496e8i	−0.00919202	−	0.0580362i
$599$	−8.59373e9			−1.63376			−0.816879	−	0.576809i	$-0.804298\pi$
$599$	−8.59373e9			−1.63376			−0.816879	+	0.576809i	$0.804298\pi$
$600$	−1.21564e9	−	1.67691e9i	−0.229760	−	0.316942i
$601$	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
$603$	−5.19658e9	+	6.00175e9i	−0.965176	+	1.11472i
$604$	−5.00517e9	+	1.62628e9i	−0.924250	+	0.300307i
$605$	2.19036e9	−	1.80185e9i	0.402136	−	0.330807i
$606$	4.90259e8	+	2.28025e8i	0.0894893	+	0.0416226i
$607$	−3.18214e9	+	3.18214e9i	−0.577510	+	0.577510i	−0.934216	−	0.356707i	$-0.883900\pi$
$607$	−3.18214e9	+	3.18214e9i	−0.577510	+	0.577510i	0.356707	+	0.934216i	$0.383900\pi$
$608$	4.18289e8	+	8.20939e8i	0.0754769	+	0.148132i
$609$	−1.12638e8	−	2.02735e8i	−0.0202081	−	0.0363721i
$610$	−1.30818e10	−	1.27310e9i	−2.33353	−	0.227096i
$611$	−5.32252e7	+	7.32582e7i	−0.00944003	+	0.0129931i
$612$	1.28163e9	+	5.41051e8i	0.226013	+	0.0954131i
$613$	−1.49080e9	−	2.36119e8i	−0.261401	−	0.0414018i	0.0243584	−	0.999703i	$-0.492246\pi$
$613$	−1.49080e9	−	2.36119e8i	−0.261401	−	0.0414018i	−0.285759	+	0.958301i	$0.592246\pi$
$614$	5.85548e9	+	4.25426e9i	1.02088	+	0.741710i
$615$	8.96540e8	−	3.89787e8i	0.155420	−	0.0675716i
$616$	−6.57636e8	+	4.77801e8i	−0.113358	+	0.0823596i
$617$	3.72950e9	−	1.90028e9i	0.639223	−	0.325701i	−0.104166	−	0.994560i	$-0.533217\pi$
$617$	3.72950e9	−	1.90028e9i	0.639223	−	0.325701i	0.743389	+	0.668859i	$0.233217\pi$
$618$	−702498.	−	897338.i	−0.000119725	−	0.000152931i
$619$	−4.41500e9	−	1.43452e9i	−0.748193	−	0.243103i	−0.0899897	−	0.995943i	$-0.528683\pi$
$619$	−4.41500e9	−	1.43452e9i	−0.748193	−	0.243103i	−0.658204	+	0.752840i	$0.728683\pi$
$620$	1.74361e9	−	6.84773e8i	0.293818	−	0.115392i
$621$	1.30551e8	−	2.63989e9i	0.0218755	−	0.442349i
$622$	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
$627$	5.98497e8	−	2.14886e7i	0.0969674	−	0.00348155i
$628$	−1.70045e9	+	3.33732e9i	−0.273971	+	0.537699i
$629$	1.17154e9	+	3.60563e9i	0.187707	+	0.577703i
$630$	4.19380e9	−	5.56155e8i	0.668214	−	0.0886143i
$631$	1.16141e9	−	3.57444e9i	0.184027	−	0.566376i	−0.815903	−	0.578188i	$-0.803760\pi$
$631$	1.16141e9	−	3.57444e9i	0.184027	−	0.566376i	0.999930	+	0.0118118i	$0.00375990\pi$
$632$	6.23972e8	+	6.23972e8i	0.0983230	+	0.0983230i
$633$	2.80847e9	+	7.69269e9i	0.440106	+	1.20550i
$634$	−6.33231e9	−	8.71567e9i	−0.986846	−	1.35828i
$635$	−1.20626e9	−	2.05260e9i	−0.186953	−	0.318125i
$636$	4.17226e9	+	3.88304e9i	0.643090	+	0.598511i
$637$	−7.60906e7	+	4.80417e8i	−0.0116639	+	0.0736428i
$638$	7.45362e7	−	4.70603e8i	0.0113631	−	0.0717435i
$639$	−3.60256e9	−	4.27627e9i	−0.546208	−	0.648354i
$640$	4.80249e8	−	4.93481e9i	0.0724163	−	0.744115i
$641$	5.34541e9	+	7.35733e9i	0.801638	+	1.10336i	0.992560	+	0.121754i	$0.0388520\pi$
$641$	5.34541e9	+	7.35733e9i	0.801638	+	1.10336i	−0.190923	+	0.981605i	$0.561148\pi$
$642$	1.00865e10	−	3.68240e9i	1.50441	−	0.549235i
$643$	3.60886e9	+	3.60886e9i	0.535342	+	0.535342i	0.922157	−	0.386815i	$-0.126425\pi$
$643$	3.60886e9	+	3.60886e9i	0.535342	+	0.535342i	−0.386815	+	0.922157i	$0.626425\pi$
$644$	3.35602e8	−	1.03288e9i	0.0495136	−	0.152387i
$645$	7.21028e9	−	4.59307e9i	1.05802	−	0.673975i
$646$	1.35646e8	+	4.17474e8i	0.0197967	+	0.0609279i
$647$	−2.94139e8	+	5.77281e8i	−0.0426961	+	0.0837958i	−0.911369	−	0.411590i	$-0.864973\pi$
$647$	−2.94139e8	+	5.77281e8i	−0.0426961	+	0.0837958i	0.868673	+	0.495386i	$0.164973\pi$
$648$	2.56718e9	+	8.72682e8i	0.370632	+	0.125992i
$649$		−	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	$-0.143940\pi$
$653$	7.64684e9	+	3.89626e9i	1.07470	+	0.547585i	0.175208	+	0.984531i	$0.443940\pi$
$654$	−4.11609e9	+	8.04283e8i	−0.575390	+	0.112431i
$655$	−4.18697e8	−	6.96218e9i	−0.0582177	−	0.968056i
$656$	1.41024e9	+	4.58216e8i	0.195043	+	0.0633734i
$657$	−2.36328e9	+	1.42633e9i	−0.325114	+	0.196219i
$658$	−6.92684e8	+	3.52940e8i	−0.0947861	+	0.0482959i
$659$	−5.67650e9	+	4.12422e9i	−0.772648	+	0.561362i	−0.902764	−	0.430137i	$-0.858465\pi$
$659$	−5.67650e9	+	4.12422e9i	−0.772648	+	0.561362i	0.130115	+	0.991499i	$0.458465\pi$
$660$	3.08281e9	+	1.81607e9i	0.417391	+	0.245883i
$661$	−6.55167e9	−	4.76007e9i	−0.882363	−	0.641074i	0.0515128	−	0.998672i	$-0.483596\pi$
$661$	−6.55167e9	−	4.76007e9i	−0.882363	−	0.641074i	−0.933876	+	0.357598i	$0.883596\pi$
$662$	−8.11105e9	−	1.28466e9i	−1.08661	−	0.172102i
$663$	2.57432e8	+	7.35438e7i	0.0343056	+	0.00980051i
$664$	2.15477e9	−	2.96578e9i	0.285635	−	0.393143i
$665$	4.11206e8	+	3.64552e8i	0.0542230	+	0.0480711i
$666$	−6.48218e9	−	1.59536e10i	−0.850279	−	2.09267i
$667$	−1.24010e8	−	2.43384e8i	−0.0161815	−	0.0317579i
$668$	5.22510e9	−	5.22510e9i	0.678230	−	0.678230i
$669$	6.40770e9	−	1.37767e10i	0.827391	−	1.77891i
$670$	−1.26138e10	−	8.05399e9i	−1.62026	−	1.03455i
$671$	−9.26617e9	+	3.01076e9i	−1.18405	+	0.384722i
$672$	4.00242e9	+	2.69395e9i	0.508780	+	0.342450i
$673$	−1.06649e9	−	6.73357e9i	−0.134867	−	0.851515i	−0.958645	−	0.284603i	$-0.908138\pi$
$673$	−1.06649e9	−	6.73357e9i	−0.134867	−	0.851515i	0.823779	−	0.566912i	$-0.191862\pi$
$674$	−1.82427e10			−2.29498
$675$	4.12152e9	+	6.84529e9i	0.515815	+	0.856700i
$676$	5.56197e9			0.692493
$677$	−1.85053e9	−	1.16838e10i	−0.229211	−	1.44718i	−0.786875	−	0.617113i	$-0.788302\pi$
$677$	−1.85053e9	−	1.16838e10i	−0.229211	−	1.44718i	0.557664	−	0.830067i	$-0.311698\pi$
$678$	−2.82580e9	−	1.90199e9i	−0.348207	−	0.234371i
$679$	−1.54004e9	+	5.00389e8i	−0.188794	+	0.0613428i
$680$	2.82871e8	−	1.08920e9i	0.0344991	−	0.132839i
$681$	6.56384e9	−	1.41124e10i	0.796422	−	1.71232i
$682$	2.38511e9	−	2.38511e9i	0.287914	−	0.287914i
$683$	4.71317e9	+	9.25011e9i	0.566031	+	1.11090i	0.979700	+	0.200471i	$0.0642472\pi$
$683$	4.71317e9	+	9.25011e9i	0.566031	+	1.11090i	−0.413669	+	0.910428i	$0.635753\pi$
$684$	−3.08975e8	−	7.60435e8i	−0.0369171	−	0.0908586i
$685$	−8.33144e8	−	3.77630e9i	−0.0990383	−	0.448900i
$686$	−5.80463e9	+	7.98939e9i	−0.686499	+	0.944885i
$687$	−2.18953e9	−	6.25509e8i	−0.257633	−	0.0736012i
$688$	1.28072e10	+	2.02847e9i	1.49933	+	0.237470i
$689$	8.87416e8	+	6.44745e8i	0.103362	+	0.0750967i
$690$	4.95971e9	−	4.77377e8i	0.574757	−	0.0553209i
$691$	−5.71021e9	+	4.14871e9i	−0.658384	+	0.478344i	−0.866117	−	0.499842i	$-0.833391\pi$
$691$	−5.71021e9	+	4.14871e9i	−0.658384	+	0.478344i	0.207733	+	0.978186i	$0.433391\pi$
$692$	2.76391e9	−	1.40828e9i	0.317068	−	0.161554i
$693$	2.68488e9	−	1.62042e9i	0.306449	−	0.184953i
$694$	−3.16534e9	−	1.02848e9i	−0.359470	−	0.116799i
$695$	7.95386e9	+	2.06567e9i	0.898733	+	0.233407i
$696$	2.75018e8	−	5.37384e7i	0.0309192	−	0.00604161i
$697$	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	$0.958637\pi$
$702$	−1.19025e9	−	2.49331e8i	−0.129855	−	0.0272017i
$703$	1.01552e9	−	1.99307e9i	0.110241	−	0.216361i
$704$	6.66239e8	+	2.05047e9i	0.0719657	+	0.221488i
$705$	−1.13297e9	−	9.34017e8i	−0.121774	−	0.100391i
$706$	−1.77810e9	+	5.47243e9i	−0.190169	+	0.585280i
$707$	2.60057e8	+	2.60057e8i	0.0276758	+	0.0276758i
$708$	−9.08239e9	+	3.31583e9i	−0.961797	+	0.351136i
$709$	5.39092e9	+	7.41996e9i	0.568069	+	0.781879i	0.992324	−	0.123663i	$-0.0394642\pi$
$709$	5.39092e9	+	7.41996e9i	0.568069	+	0.781879i	−0.424256	+	0.905542i	$0.639464\pi$
$710$	6.99255e9	−	7.88741e9i	0.733215	−	0.827047i
$711$	−2.19334e9	−	2.60352e9i	−0.228856	−	0.271655i
$712$	−8.61290e8	+	5.43797e9i	−0.0894272	+	0.564621i
$713$	3.02504e8	−	1.90994e9i	0.0312549	−	0.197336i
$714$	1.68259e9	+	1.56596e9i	0.172996	+	0.161004i
$715$	6.31196e8	+	2.75218e8i	0.0645792	+	0.0281582i
$716$	−6.85155e9	−	9.43034e9i	−0.697578	−	0.960134i
$717$	−4.45400e9	−	1.22000e10i	−0.451267	−	1.23607i
$718$	1.62115e10	+	1.62115e10i	1.63451	+	1.63451i
$719$	−1.72827e9	+	5.31907e9i	−0.173405	+	0.533685i	−0.999557	−	0.0297622i	$-0.990525\pi$
$719$	−1.72827e9	+	5.31907e9i	−0.173405	+	0.533685i	0.826152	+	0.563447i	$0.190525\pi$
$720$	−2.19736e9	+	1.19187e10i	−0.219400	+	1.19005i
$721$	−239537.	−	737219.i	−2.38012e−5	−	7.32526e-5i
$722$	−5.86816e9	+	1.15169e10i	−0.580259	+	1.13882i
$723$	3.84983e8	−	1.38226e7i	0.0378842	−	0.00136021i
$724$			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	0.215812	−	0.976435i	$-0.430760\pi$
$727$	7.48836e9	−	1.18604e9i	0.722797	−	0.114480i	0.506985	+	0.861955i	$0.330760\pi$
$728$	1.91043e8	+	9.73415e7i	0.0183515	+	0.00935057i
$729$	−9.58092e9	−	4.19821e9i	−0.915927	−	0.401345i
$730$	−3.30581e9	−	4.01861e9i	−0.314520	−	0.382337i
$731$	4.41753e9	+	1.43534e9i	0.418282	+	0.135908i
$732$	8.23155e9	+	1.05146e10i	0.775699	+	0.990841i
$733$	−1.41949e10	+	7.23264e9i	−1.33127	+	0.678318i	−0.967429	−	0.253142i	$-0.918536\pi$
$733$	−1.41949e10	+	7.23264e9i	−1.33127	+	0.678318i	−0.363844	+	0.931460i	$0.618536\pi$
$734$	−1.91281e10	+	1.38974e10i	−1.78540	+	1.29717i
$735$	−7.70020e9	−	1.70740e9i	−0.715313	−	0.158609i
$736$	4.59710e9	+	3.33999e9i	0.425022	+	0.308796i
$737$	−1.09572e10	−	1.73545e9i	−1.00824	−	0.159689i
$738$	−2.22268e9	−	9.38324e8i	−0.203554	−	0.0859321i
$739$	−9.19296e9	+	1.26530e10i	−0.837915	+	1.15329i	0.148483	+	0.988915i	$0.452561\pi$
$739$	−9.19296e9	+	1.26530e10i	−0.837915	+	1.15329i	−0.986398	+	0.164376i	$0.947439\pi$
$740$	1.15217e10	−	6.77099e9i	1.04522	−	0.614244i
$741$	−7.67194e7	−	1.38085e8i	−0.00692694	−	0.0124676i
$742$	4.27535e9	+	8.39085e9i	0.384201	+	0.754037i
$743$	4.14332e9	−	4.14332e9i	0.370584	−	0.370584i	−0.497106	−	0.867690i	$-0.665604\pi$
$743$	4.14332e9	−	4.14332e9i	0.370584	−	0.370584i	0.867690	+	0.497106i	$0.165604\pi$
$744$	1.79870e9	+	8.36598e8i	0.160123	+	0.0744752i
$745$	3.80218e9	+	9.68134e9i	0.336888	+	0.857805i
$746$	−3.29641e9	+	1.07107e9i	−0.290707	+	0.0944563i
$747$	−9.25732e9	+	1.06917e10i	−0.812574	+	0.938477i
$748$	3.04109e8	+	1.92007e9i	0.0265689	+	0.167750i
$749$	7.30368e9			0.635120
$750$	−1.16427e10	+	9.55694e9i	−1.00772	+	0.827189i
$751$	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
$753$	−3.33314e9	+	4.95206e9i	−0.284492	+	0.422672i
$754$	−1.19527e8	+	3.88366e7i	−0.0101547	+	0.00329945i
$755$	−6.00358e9	−	1.52867e10i	−0.507687	−	1.29270i
$756$	−3.34818e9	−	2.69500e9i	−0.281827	−	0.226847i
$757$	8.31009e9	−	8.31009e9i	0.696258	−	0.696258i	−0.267344	−	0.963601i	$-0.586146\pi$
$757$	8.31009e9	−	8.31009e9i	0.696258	−	0.696258i	0.963601	+	0.267344i	$0.0861459\pi$
$758$	−3.71283e9	−	7.28684e9i	−0.309644	−	0.607711i
$759$	3.22864e9	−	1.79382e9i	0.268024	−	0.148913i
$760$	−5.72436e8	+	3.36405e8i	−0.0473020	+	0.0277981i
$761$	3.22472e9	−	4.43845e9i	0.265244	−	0.365077i	−0.655533	−	0.755167i	$-0.727556\pi$
$761$	3.22472e9	−	4.43845e9i	0.265244	−	0.365077i	0.920777	+	0.390089i	$0.127556\pi$
$762$	−1.61398e9	+	5.64954e9i	−0.132146	+	0.462563i
$763$	−2.81756e9	−	4.46258e8i	−0.229635	−	0.0363706i
$764$	4.24065e9	+	3.08101e9i	0.344038	+	0.249958i
$765$	−1.44530e9	+	4.09370e9i	−0.116720	+	0.330598i
$766$	−2.68636e8	+	1.95175e8i	−0.0215955	+	0.0156900i
$767$	−1.65796e9	+	8.44772e8i	−0.132675	+	0.0676014i
$768$	−1.29599e10	+	1.01459e10i	−1.03238	+	0.808214i
$769$	−5.77156e9	−	1.87529e9i	−0.457669	−	0.148706i	0.0711042	−	0.997469i	$-0.477348\pi$
$769$	−5.77156e9	−	1.87529e9i	−0.457669	−	0.148706i	−0.528773	+	0.848763i	$0.677348\pi$
$770$	3.75567e9	+	4.56547e9i	0.296463	+	0.360386i
$771$	−7.48251e8	−	3.82933e9i	−0.0587973	−	0.300907i
$772$	5.79897e9	+	2.95472e9i	0.453618	+	0.231130i
$773$	−2.16964e9	+	3.43638e8i	−0.168951	+	0.0267592i	−0.240337	−	0.970690i	$-0.577258\pi$
$773$	−2.16964e9	+	3.43638e8i	−0.168951	+	0.0267592i	0.0713858	+	0.997449i	$0.477258\pi$
$774$	−2.04811e10	−	5.06380e9i	−1.58767	−	0.392539i
$775$	2.45974e9	+	5.30315e9i	0.189816	+	0.409240i
$776$		−	1.95648e9i		−	0.150300i
$777$	−4.20281e8	−	1.17056e10i	−0.0321415	−	0.895198i
$778$	6.07825e9	−	1.19292e10i	0.462754	−	0.908205i
$779$	−9.68445e7	−	2.98057e8i	−0.00733996	−	0.0225901i
$780$	5.76505e7	−	9.41993e8i	0.00434982	−	0.0710750i
$781$	2.41453e9	−	7.43116e9i	0.181365	−	0.558185i
$782$	1.91428e9	+	1.91428e9i	0.143147	+	0.143147i
$783$	−1.07478e9	+	1.16167e8i	−0.0800117	+	0.00864804i
$784$	−7.03179e9	−	9.67843e9i	−0.521147	−	0.717297i
$785$	−1.07145e10	−	4.67178e9i	−0.790545	−	0.344698i
$786$	−1.17268e10	+	1.26003e10i	−0.861392	+	0.925551i
$787$	4.93153e8	−	3.11364e9i	0.0360637	−	0.227697i	−0.963073	−	0.269240i	$-0.913227\pi$
$787$	4.93153e8	−	3.11364e9i	0.0360637	−	0.227697i	0.999137	+	0.0415433i	$0.0132274\pi$
$788$	1.55570e9	−	9.82231e9i	0.113262	−	0.715108i
$789$	−3.56323e9	+	3.82863e9i	−0.258270	+	0.277507i
$790$	4.25727e9	−	4.80209e9i	0.307211	−	0.346526i
$791$	−1.36186e9	−	1.87443e9i	−0.0978393	−	0.134664i
$792$	8.59589e8	+	3.69020e9i	0.0614827	+	0.263944i
$793$	1.81720e9	+	1.81720e9i	0.129404	+	0.129404i
$794$	4.72011e9	−	1.45270e10i	0.334642	−	1.02992i
$795$	−1.13142e10	+	1.37242e10i	−0.798621	+	0.968730i
$796$	−3.13984e9	−	9.66343e9i	−0.220654	−	0.679103i
$797$	−3.57165e9	+	7.00976e9i	−0.249899	+	0.490455i	−0.981545	−	0.191230i	$-0.938752\pi$
$797$	−3.57165e9	+	7.00976e9i	−0.249899	+	0.490455i	0.731646	+	0.681685i	$0.238752\pi$
$798$	−4.86618e7	−	1.35532e9i	−0.00338983	−	0.0944128i
$799$		−	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
$804$	2.91587e9	+	1.49226e10i	0.197866	+	1.01262i
$805$	3.28033e9	+	8.51923e8i	0.221632	+	0.0575592i
$806$	−8.46160e8	−	2.74934e8i	−0.0569219	−	0.0184951i
$807$	1.15745e10	−	9.06129e9i	0.775254	−	0.606922i
$808$	−3.95927e8	+	2.01735e8i	−0.0264044	+	0.0134537i
$809$	2.04496e10	−	1.48575e10i	1.35789	−	0.986568i	0.359318	−	0.933215i	$-0.383009\pi$
$809$	2.04496e10	−	1.48575e10i	1.35789	−	0.986568i	0.998576	−	0.0533526i	$-0.0169907\pi$
$810$	5.21442e9	−	1.90172e10i	0.344753	−	1.25733i
$811$	1.86113e10	+	1.35219e10i	1.22519	+	0.890153i	0.996520	−	0.0833513i	$-0.0265624\pi$
$811$	1.86113e10	+	1.35219e10i	1.22519	+	0.890153i	0.228670	+	0.973504i	$0.426562\pi$
$812$	−4.38721e8	−	6.94865e7i	−0.0287569	−	0.00455464i
$813$	−1.30311e9	+	4.56138e9i	−0.0850478	+	0.297700i
$814$	1.41443e10	−	1.94679e10i	0.919168	−	1.26513i
$815$	3.72942e9	+	1.69039e10i	0.241318	+	1.09379i
$816$	−5.75612e9	+	3.19807e9i	−0.370864	+	0.206050i
$817$	−1.24419e9	−	2.44186e9i	−0.0798196	−	0.156655i
$818$	8.03220e9	−	8.03220e9i	0.513095	−	0.513095i
$819$	−7.02341e8	−	4.36955e8i	−0.0446740	−	0.0277935i
$820$	4.70648e8	−	1.81223e9i	0.0298090	−	0.114780i
$821$	1.98668e10	−	6.45510e9i	1.25293	−	0.407101i	0.393959	−	0.919128i	$-0.371105\pi$
$821$	1.98668e10	−	6.45510e9i	1.25293	−	0.407101i	0.858969	+	0.512027i	$0.171105\pi$
$822$	−5.32894e9	+	7.91724e9i	−0.334649	+	0.497190i
$823$	−3.69060e9	−	2.33015e10i	−0.230780	−	1.45709i	−0.782288	−	0.622917i	$-0.785947\pi$
$823$	−3.69060e9	−	2.33015e10i	−0.230780	−	1.45709i	0.551508	−	0.834170i	$-0.314053\pi$
$824$	936572.			5.83171e−5
$825$	−5.07963e9	+	9.94332e9i	−0.314951	+	0.616513i
$826$	−1.59753e10			−0.986321
$827$	4.36116e8	+	2.75353e9i	0.0268122	+	0.169286i	0.997461	−	0.0712161i	$-0.0226880\pi$
$827$	4.36116e8	+	2.75353e9i	0.0268122	+	0.169286i	−0.970649	+	0.240502i	$0.922688\pi$
$828$	−3.82700e9	−	3.31358e9i	−0.234289	−	0.202858i
$829$	5.13617e9	−	1.66884e9i	0.313111	−	0.101736i	−0.148246	−	0.988951i	$-0.547363\pi$
$829$	5.13617e9	−	1.66884e9i	0.313111	−	0.101736i	0.461357	+	0.887215i	$0.347363\pi$
$830$	−2.24706e10	−	1.43476e10i	−1.36409	−	0.870976i
$831$	2.16588e10	+	1.00738e10i	1.30928	+	0.608961i
$832$	4.02120e8	−	4.02120e8i	0.0242061	−	0.0242061i
$833$	−1.94550e9	−	3.81826e9i	−0.116620	−	0.228880i
$834$	−9.84955e9	−	1.77280e10i	−0.587943	−	1.05822i
$835$	1.72553e10	+	1.52976e10i	1.02570	+	0.909328i
$836$	6.74190e8	−	9.27943e8i	0.0399080	−	0.0549287i
$837$	−6.63890e9	−	3.80693e9i	−0.391343	−	0.224407i
$838$	−5.70716e8	−	9.03925e7i	−0.0335016	−	0.00530614i
$839$	1.57010e10	+	1.14074e10i	0.917826	+	0.666840i	0.942982	−	0.332844i	$-0.108008\pi$
$839$	1.57010e10	+	1.14074e10i	0.917826	+	0.666840i	−0.0251557	+	0.999684i	$0.508008\pi$
$840$	−1.76471e9	+	2.99563e9i	−0.102730	+	0.174385i
$841$	1.38651e10	−	1.00736e10i	0.803777	−	0.583978i
$842$	2.85095e10	−	1.45263e10i	1.64588	−	0.838617i
$843$	−1.13044e10	−	1.44397e10i	−0.649905	−	0.830159i
$844$	1.49168e10	+	4.84677e9i	0.854039	+	0.277494i
$845$	1.04195e9	+	1.73258e10i	0.0594087	+	0.987859i
$846$	2.59877e8	+	3.61435e9i	0.0147561	+	0.205227i
$847$	−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
$852$	−1.07021e10	+	3.84253e8i	−0.592833	+	0.0212853i
$853$	−4.28852e9	+	8.41669e9i	−0.236584	+	0.464323i	−0.978521	−	0.206147i	$-0.933907\pi$
$853$	−4.28852e9	+	8.41669e9i	−0.236584	+	0.464323i	0.741937	+	0.670470i	$0.233907\pi$
$854$	6.81797e9	+	2.09836e10i	0.374587	+	1.15286i
$855$	2.31091e9	−	1.10493e9i	0.126445	−	0.0604579i
$856$	−2.72694e9	+	8.39265e9i	−0.148599	+	0.457342i
$857$	1.41252e10	+	1.41252e10i	0.766588	+	0.766588i	0.977504	−	0.210916i	$-0.0676447\pi$
$857$	1.41252e10	+	1.41252e10i	0.766588	+	0.766588i	−0.210916	+	0.977504i	$0.567645\pi$
$858$	−5.82783e8	−	1.59630e9i	−0.0314993	−	0.0862799i
$859$	−5.12384e9	−	7.05236e9i	−0.275816	−	0.379628i	0.648526	−	0.761192i	$-0.275386\pi$
$859$	−5.12384e9	−	7.05236e9i	−0.275816	−	0.379628i	−0.924342	+	0.381564i	$0.875386\pi$
$860$	1.58593e9	−	1.62962e10i	0.0850235	−	0.873661i
$861$	−1.20129e9	−	1.11802e9i	−0.0641412	−	0.0596949i
$862$	−4.33132e9	+	2.73469e10i	−0.230327	+	1.45423i
$863$	−1.09309e9	+	6.90148e9i	−0.0578918	+	0.365514i	0.941687	+	0.336490i	$0.109240\pi$
$863$	−1.09309e9	+	6.90148e9i	−0.0578918	+	0.365514i	−0.999579	+	0.0290241i	$0.990760\pi$
$864$	1.88241e10	−	1.23035e10i	0.992923	−	0.648980i
$865$	4.90464e9	+	8.34588e9i	0.257662	+	0.438445i
$866$	4.77760e9	+	6.57580e9i	0.249975	+	0.344062i
$867$	1.58102e10	−	5.77203e9i	0.823892	−	0.300789i
$868$	−2.22352e9	−	2.22352e9i	−0.115404	−	0.115404i
$869$	1.47004e9	−	4.52431e9i	0.0759905	−	0.233875i
$870$	−5.10176e8	−	1.97301e9i	−0.0262665	−	0.101581i
$871$	9.04243e8	+	2.78297e9i	0.0463683	+	0.142707i
$872$	1.56477e9	−	3.07104e9i	0.0799178	−	0.156848i
$873$	−6.43061e8	+	7.52036e9i	−0.0327116	+	0.382551i
$874$		−	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	−0.00771012	−	0.999970i	$-0.502454\pi$
$877$	5.87211e9	−	9.30051e8i	0.293965	−	0.0465595i	0.301675	+	0.953411i	$0.402454\pi$
$878$	4.64999e9	+	2.36929e9i	0.231857	+	0.118137i
$879$	−1.39817e10	+	2.73202e9i	−0.694382	+	0.135682i
$880$	−1.57638e10	+	6.19095e9i	−0.779778	+	0.306244i
$881$	2.18908e10	+	7.11275e9i	1.07856	+	0.350447i	0.793817	−	0.608156i	$-0.208091\pi$
$881$	2.18908e10	+	7.11275e9i	1.07856	+	0.350447i	0.284746	+	0.958603i	$0.408091\pi$
$882$	1.00579e10	+	1.66649e10i	0.493589	+	0.817827i
$883$	−1.46832e10	+	7.48147e9i	−0.717725	+	0.365699i	−0.774403	−	0.632693i	$-0.781949\pi$
$883$	−1.46832e10	+	7.48147e9i	−0.717725	+	0.365699i	0.0566771	+	0.998393i	$0.481949\pi$
$884$	4.14838e8	−	3.01397e8i	0.0201974	−	0.0146743i
$885$	−1.20304e10	−	2.76709e10i	−0.583417	−	1.34191i
$886$	−5.72657e9	−	4.16060e9i	−0.276616	−	0.200973i
$887$	−2.34506e10	−	3.71421e9i	−1.12829	−	0.178704i	−0.435740	−	0.900072i	$-0.643513\pi$
$887$	−2.34506e10	−	3.71421e9i	−1.12829	−	0.178704i	−0.692551	+	0.721369i	$0.743513\pi$
$888$	1.36078e10	+	3.88751e9i	0.652142	+	0.186306i
$889$	−2.34910e9	+	3.23326e9i	−0.112136	+	0.154342i
$890$	3.98526e10	+	3.87841e9i	1.89493	+	0.184412i
$891$	−2.09120e9	−	1.44670e10i	−0.0990430	−	0.685181i
$892$	−1.32111e10	−	2.59282e10i	−0.623250	−	1.22320i
$893$	−3.32841e8	+	3.32841e8i	−0.0156407	+	0.0156407i
$894$	1.08253e10	−	2.32747e10i	0.506710	−	1.08944i
$895$	2.80924e10	−	2.31095e10i	1.30981	−	1.07748i
$896$	−7.91556e9	+	2.57192e9i	−0.367624	+	0.119448i
$897$	−8.08207e8	−	5.43988e8i	−0.0373895	−	0.0251661i
$898$	2.74921e9	+	1.73578e10i	0.126689	+	0.799885i
$899$	−7.90905e8			−0.0363049
$900$	1.51891e10	+	1.86615e9i	0.694517	+	0.0853292i
$901$	−9.66398e9			−0.440169
$902$	−5.27405e8	−	3.32991e9i	−0.0239288	−	0.151081i
$903$	−1.19051e10	−	8.01307e9i	−0.538053	−	0.362153i
$904$	2.66238e9	−	8.65059e8i	0.119862	−	0.0389454i
$905$	−4.01585e10	+	2.41508e9i	−1.80097	+	0.108308i
$906$	−1.70930e10	+	3.67503e10i	−0.763607	+	1.64177i
$907$	−6.97627e9	+	6.97627e9i	−0.310455	+	0.310455i	−0.845086	−	0.534631i	$-0.820451\pi$
$907$	−6.97627e9	+	6.97627e9i	−0.310455	+	0.310455i	0.534631	+	0.845086i	$0.320451\pi$
$908$	−1.35330e10	−	2.65600e10i	−0.599921	−	1.17741i
$909$	1.58818e9	−	6.45298e8i	0.0701335	−	0.0284962i
$910$	6.23240e8	−	1.42936e9i	0.0274164	−	0.0628779i
$911$	1.87030e10	−	2.57425e10i	0.819593	−	1.12807i	−0.170179	−	0.985413i	$-0.554435\pi$
$911$	1.87030e10	−	2.57425e10i	0.819593	−	1.12807i	0.989772	−	0.142659i	$-0.0455653\pi$
$912$	3.73575e9	+	1.06724e9i	0.163078	+	0.0465886i
$913$	−1.95194e10	−	3.09158e9i	−0.848828	−	0.134441i
$914$	2.12521e10	+	1.54405e10i	0.920640	+	0.668884i
$915$	−3.12114e10	+	2.76114e10i	−1.34691	+	1.19156i
$916$	−3.52830e9	+	2.56346e9i	−0.151681	+	0.110203i
$917$	−1.04320e10	+	5.31538e9i	−0.446761	+	0.227636i
$918$	9.77480e9	−	4.38658e9i	0.417021	−	0.187144i
$919$	1.70491e10	+	5.53959e9i	0.724598	+	0.235436i	0.648016	−	0.761627i	$-0.275599\pi$
$919$	1.70491e10	+	5.53959e9i	0.724598	+	0.235436i	0.0765827	+	0.997063i	$0.475599\pi$
$920$	−2.20370e9	+	3.45135e9i	−0.0933031	+	0.146127i
$921$	2.25215e10	−	4.40069e9i	0.949922	−	0.185615i
$922$	−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
$927$	−3.60001e6	−	307834.i	−0.000148431	−	1.26922e-5i
$928$	1.05511e9	−	2.07077e9i	0.0433391	−	0.0850578i
$929$	7.58780e8	+	2.33528e9i	0.0310499	+	0.0955619i	0.965380	−	0.260846i	$-0.0840014\pi$
$929$	7.58780e8	+	2.33528e9i	0.0310499	+	0.0955619i	−0.934331	+	0.356408i	$0.884001\pi$
$930$	5.28797e9	−	1.34228e10i	0.215575	−	0.547208i
$931$	−7.81329e8	+	2.40468e9i	−0.0317329	+	0.0976639i
$932$	1.85829e10	+	1.85829e10i	0.751896	+	0.751896i
$933$	3.73568e10	−	1.36384e10i	1.50586	−	0.549764i
$934$	3.52296e10	+	4.84893e10i	1.41479	+	1.94730i
$935$	−5.92414e9	+	1.30701e9i	−0.237020	+	0.0522924i
$936$	7.64334e8	−	6.43916e8i	0.0304662	−	0.0256663i
$937$	−3.54225e9	+	2.23649e10i	−0.140667	+	0.888134i	0.811898	+	0.583799i	$0.198434\pi$
$937$	−3.54225e9	+	2.23649e10i	−0.140667	+	0.888134i	−0.952565	+	0.304335i	$0.901566\pi$
$938$	−3.92999e9	+	2.48129e10i	−0.155482	+	0.981677i
$939$	1.68512e10	+	1.56831e10i	0.664204	+	0.618162i
$940$	−2.74616e9	+	6.05871e8i	−0.107840	+	0.0237921i
$941$	2.31483e10	+	3.18609e10i	0.905639	+	1.24651i	0.968634	+	0.248492i	$0.0799350\pi$
$941$	2.31483e10	+	3.18609e10i	0.905639	+	1.24651i	−0.0629945	+	0.998014i	$0.520065\pi$
$942$	9.89266e9	+	2.70970e10i	0.385598	+	1.05619i
$943$	−1.36670e9	−	1.36670e9i	−0.0530741	−	0.0530741i
$944$	1.41424e10	−	4.35259e10i	0.547170	−	1.68401i
$945$	7.76783e9	−	1.09346e10i	0.299425	−	0.421494i
$946$	−9.11049e9	−	2.80392e10i	−0.349883	−	1.07683i
$947$	−1.78382e10	+	3.50094e10i	−0.682536	+	1.33955i	0.246347	+	0.969182i	$0.420770\pi$
$947$	−1.78382e10	+	3.50094e10i	−0.682536	+	1.33955i	−0.928884	+	0.370371i	$0.879230\pi$
$948$	−6.51578e9	+	2.33945e8i	−0.248392	+	0.00891835i
$949$			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	$-0.182011\pi$
$953$	2.39782e10	+	1.22175e10i	0.897410	+	0.457253i	0.0564841	+	0.998403i	$0.482011\pi$
$954$	4.37826e10	−	3.14803e9i	1.63261	−	0.117387i
$955$	−8.80308e9	+	1.37870e10i	−0.327057	+	0.512222i
$956$	−2.36568e10	−	7.68657e9i	−0.875697	−	0.284531i
$957$	−9.31217e8	−	1.18949e9i	−0.0343446	−	0.0438702i
$958$	3.52939e10	−	1.79831e10i	1.29694	−	0.660824i
$959$	−5.25173e9	+	3.81561e9i	−0.192282	+	0.139701i
$960$	6.11002e9	+	6.90664e9i	0.222891	+	0.251952i
$961$	1.77285e10	+	1.28805e10i	0.644376	+	0.468167i
$962$	−6.26909e9	−	9.92927e8i	−0.227035	−	0.0359587i
$963$	1.32404e10	−	3.13635e10i	0.477758	−	1.13170i
$964$	4.33673e8	−	5.96900e8i	0.0155917	−	0.0214601i
$965$	−8.11775e9	+	1.86176e10i	−0.290797	+	0.666926i
$966$	−4.06216e9	−	7.31138e9i	−0.144990	−	0.260963i
$967$	−2.31873e10	−	4.55077e10i	−0.824629	−	1.61842i	−0.785233	−	0.619201i	$-0.787457\pi$
$967$	−2.31873e10	−	4.55077e10i	−0.824629	−	1.61842i	−0.0393959	−	0.999224i	$-0.512543\pi$
$968$	4.06761e9	−	4.06761e9i	0.144137	−	0.144137i
$969$	1.26190e9	+	5.86927e8i	0.0445546	+	0.0207229i
$970$	−1.42030e10	+	8.54149e8i	−0.499664	+	0.0300492i
$971$	−2.60145e10	+	8.45263e9i	−0.911902	+	0.296295i	−0.727141	−	0.686488i	$-0.759151\pi$
$971$	−2.60145e10	+	8.45263e9i	−0.911902	+	0.296295i	−0.184762	+	0.982783i	$0.559151\pi$
$972$	−1.76426e10	+	9.49218e9i	−0.616212	+	0.331538i
$973$	−2.15795e9	−	1.36248e10i	−0.0751012	−	0.474170i
$974$	−6.06112e10			−2.10183
$975$	2.94515e9	+	3.11548e6i	0.101763	+	0.000107649i
$976$	−6.32072e10			−2.17617
$977$	−6.64852e9	−	4.19771e10i	−0.228084	−	1.44006i	−0.790121	−	0.612951i	$-0.789982\pi$
$977$	−6.64852e9	−	4.19771e10i	−0.228084	−	1.44006i	0.562037	−	0.827112i	$-0.310018\pi$
$978$	2.38540e10	−	3.54401e10i	0.815410	−	1.21146i
$979$	2.82286e10	−	9.17203e9i	0.961502	−	0.312411i
$980$	−1.16659e10	+	9.59663e9i	−0.395937	+	0.325707i
$981$	−7.02410e9	+	1.12902e10i	−0.237547	+	0.381821i
$982$	2.82564e10	−	2.82564e10i	0.952196	−	0.952196i
$983$	−1.33017e10	−	2.61061e10i	−0.446653	−	0.876605i	−0.999073	−	0.0430398i	$-0.986296\pi$
$983$	−1.33017e10	−	2.61061e10i	−0.446653	−	0.876605i	0.552421	−	0.833565i	$-0.313704\pi$
$984$	1.73323e9	−	9.62973e8i	0.0579928	−	0.0322204i
$985$	3.08884e10	+	3.00602e9i	1.02984	+	0.100222i
$986$	6.50824e8	−	8.95782e8i	0.0216219	−	0.0297600i
$987$	−6.77065e8	+	2.36999e9i	−0.0224140	+	0.0784578i
$988$	−2.98818e8	−	4.73281e7i	−0.00985729	−	0.00156124i
$989$	−1.36739e10	−	9.93469e9i	−0.449476	−	0.326563i
$990$	2.64135e10	−	7.85118e9i	0.865172	−	0.257165i
$991$	1.45040e10	−	1.05378e10i	0.473402	−	0.343947i	−0.325364	−	0.945589i	$-0.605487\pi$
$991$	1.45040e10	−	1.05378e10i	0.473402	−	0.343947i	0.798766	+	0.601642i	$0.205487\pi$
$992$	1.46595e10	−	7.46940e9i	0.476792	−	0.242938i
$993$	−2.05014e10	+	1.60499e10i	−0.664448	+	0.520176i
$994$	−1.68281e10	−	5.46779e9i	−0.543479	−	0.176587i
$995$	2.95138e10	−	1.15910e10i	0.949828	−	0.373028i
$996$	5.19440e9	+	2.65834e10i	0.166582	+	0.852518i
$997$	−4.53994e10	−	2.31321e10i	−1.45083	−	0.739236i	−0.461806	−	0.886981i	$-0.652798\pi$
$997$	−4.53994e10	−	2.31321e10i	−1.45083	−	0.739236i	−0.989025	+	0.147745i	$0.952798\pi$
$998$	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.38.14	yes	544
3.2	odd	2	inner	75.8.l.a.38.55	yes	544
25.2	odd	20	inner	75.8.l.a.2.55	yes	544
75.2	even	20	inner	75.8.l.a.2.14	✓	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.8.l.a.2.14	✓	544	75.2	even	20	inner
75.8.l.a.2.55	yes	544	25.2	odd	20	inner
75.8.l.a.38.14	yes	544	1.1	even	1	trivial
75.8.l.a.38.55	yes	544	3.2	odd	2	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} +(-38.7959 - 26.1128i) q^{3} +(-85.1830 + 27.6776i) q^{4} +(-102.175 - 260.164i) q^{5} +(-290.906 + 625.453i) q^{6} +(-331.771 + 331.771i) q^{7} +(-257.366 - 505.109i) q^{8} +(823.247 + 2026.14i) q^{9} +(-3554.45 + 2088.85i) q^{10} +(-1796.34 + 2472.45i) q^{11} +(4027.49 + 1150.58i) q^{12} +(796.184 + 126.103i) q^{13} +(5598.96 + 4067.88i) q^{14} +(-2829.63 + 12761.4i) q^{15} +(-16039.9 + 11653.6i) q^{16} +(-6327.92 + 3224.24i) q^{17} +(27618.3 - 16668.7i) q^{18} +(3985.23 + 1294.88i) q^{19} +(15904.3 + 19333.6i) q^{20} +(21534.8 - 4207.90i) 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} +(20969.4 - 100103. i) q^{27} +(19078.6 - 37443.9i) q^{28} +(-3266.26 - 10052.5i) q^{29} +(192444. + 11777.7i) q^{30} +(23122.7 - 71164.3i) q^{31} +(155478. + 155478. i) q^{32} +(134253. - 49013.6i) q^{33} +(61573.7 + 84748.9i) q^{34} +(120213. + 52416.2i) q^{35} +(-126205. - 149807. i) q^{36} +(83507.9 - 527248. i) q^{37} +(9668.87 - 61046.8i) q^{38} +(-27595.8 - 25682.9i) q^{39} +(-105115. + 118567. i) q^{40} +(-43960.7 - 60506.7i) q^{41} +(-110993. - 304021. i) q^{42} +(-462464. - 462464. i) q^{43} +(84586.1 - 260329. i) q^{44} +(443013. - 421200. i) q^{45} +(-117794. - 362531. i) q^{46} +(-50997.8 + 100089. i) q^{47} +(926589. - 33268.6i) 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} +(-1.50674e6 - 74513.1i) q^{54} +(826784. + 214721. i) q^{55} +(252967. + 82194.0i) q^{56} +(-120798. - 154301. i) q^{57} +(-138914. + 70780.1i) q^{58} +(-1.86748e6 + 1.35681e6i) q^{59} +(-112168. - 1.16537e6i) q^{60} +(2.57918e6 + 1.87388e6i) q^{61} +(-1.09011e6 - 172657. i) q^{62} +(-945343. - 399084. i) q^{63} +(414663. - 570735. i) q^{64} +(-48542.5 - 220023. i) q^{65} +(-1.02384e6 - 1.84278e6i) q^{66} +(1.64799e6 + 3.23437e6i) q^{67} +(449792. - 449792. i) q^{68} +(-1.09583e6 - 509682. i) q^{69} +(486243. - 1.87228e6i) q^{70} +(-2.43157e6 + 790064. i) q^{71} +(811545. - 937288. i) q^{72} +(197445. + 1.24662e6i) q^{73} -7.87392e6 q^{74} +(3.60917e6 - 567723. i) q^{75} -375313. q^{76} +(-224314. - 1.41626e6i) q^{77} +(-310487. + 461292. i) q^{78} +(-1.48041e6 + 481014. i) q^{79} +(4.67073e6 + 2.98228e6i) q^{80} +(-3.42750e6 + 3.33602e6i) q^{81} +(-780058. + 780058. i) q^{82} +(2.93578e6 + 5.76180e6i) q^{83} +(-1.71793e6 + 954474. i) q^{84} +(1.48539e6 + 1.31686e6i) q^{85} +(-5.67032e6 + 7.80453e6i) q^{86} +(-135781. + 475288. i) q^{87} +(1.71118e6 + 271024. i) q^{88} +(-7.85725e6 - 5.70863e6i) q^{89} +(-7.15848e6 - 5.48216e6i) q^{90} +(-305988. + 222313. i) q^{91} +(-2.06239e6 + 1.05084e6i) q^{92} +(-2.75536e6 + 2.15709e6i) q^{93} +(1.57582e6 + 512016. i) q^{94} +(-70309.3 - 1.16912e6i) q^{95} +(-1.97195e6 - 1.00918e7i) 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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