LMFDB - Embedded newform 69.7.h.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(2,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 2]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.h (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	69.2
Dual form			69.7.h.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.20003 + 12.7595i) q^{2} +(2.39070 - 26.8939i) q^{3} +(-68.9776 - 151.040i) q^{4} +(54.2696 - 184.825i) q^{5} +(323.549 + 251.035i) q^{6} +(122.578 - 141.462i) q^{7} +(1531.99 + 220.266i) q^{8} +(-717.569 - 128.591i) q^{9} +O(q^{10})$	\(q+(-8.20003 + 12.7595i) q^{2} +(2.39070 - 26.8939i) q^{3} +(-68.9776 - 151.040i) q^{4} +(54.2696 - 184.825i) q^{5} +(323.549 + 251.035i) q^{6} +(122.578 - 141.462i) q^{7} +(1531.99 + 220.266i) q^{8} +(-717.569 - 128.591i) q^{9} +(1913.26 + 2208.02i) q^{10} +(-553.536 - 861.320i) q^{11} +(-4226.96 + 1493.99i) q^{12} +(-2272.78 - 2622.93i) q^{13} +(799.844 + 2724.02i) q^{14} +(-4840.94 - 1901.38i) q^{15} +(-8413.70 + 9709.92i) q^{16} +(4209.00 + 1922.19i) q^{17} +(7524.84 - 8101.37i) q^{18} +(2079.04 + 4552.45i) q^{19} +(-31659.3 + 4551.93i) q^{20} +(-3511.43 - 3634.79i) q^{21} +15529.0 q^{22} +(-2445.18 + 11918.8i) q^{23} +(9586.36 - 40674.6i) q^{24} +(-18070.6 - 11613.2i) q^{25} +(52104.1 - 7491.44i) q^{26} +(-5173.81 + 18990.8i) q^{27} +(-29821.5 - 8756.38i) q^{28} +(16582.8 + 7573.11i) q^{29} +(63956.5 - 46176.5i) q^{30} +(5634.57 - 39189.3i) q^{31} +(-26994.0 - 91933.1i) q^{32} +(-24487.6 + 12827.6i) q^{33} +(-59040.0 + 37942.7i) q^{34} +(-19493.5 - 30332.5i) q^{35} +(30073.8 + 117251. i) q^{36} +(-49118.8 + 14422.6i) q^{37} +(-75135.1 - 10802.8i) q^{38} +(-75974.5 + 54853.5i) q^{39} +(123851. - 271196. i) q^{40} +(28442.0 - 96864.7i) q^{41} +(75171.8 - 14998.6i) q^{42} +(3082.19 + 21437.1i) q^{43} +(-91912.0 + 143018. i) q^{44} +(-62709.0 + 125646. i) q^{45} +(-132027. - 128933. i) q^{46} +17862.3i q^{47} +(241024. + 249491. i) q^{48} +(11757.0 + 81771.4i) q^{49} +(296358. - 135342. i) q^{50} +(61757.6 - 108601. i) q^{51} +(-239396. + 524204. i) q^{52} +(69130.5 + 59901.9i) q^{53} +(-199888. - 221741. i) q^{54} +(-189234. + 55564.0i) q^{55} +(218947. - 189718. i) q^{56} +(127404. - 45029.9i) q^{57} +(-232608. + 149488. i) q^{58} +(-81135.4 + 70304.2i) q^{59} +(46731.2 + 862327. i) q^{60} +(33600.4 - 233696. i) q^{61} +(453832. + 393248. i) q^{62} +(-106149. + 85746.4i) q^{63} +(605403. + 177762. i) q^{64} +(-608127. + 277722. i) q^{65} +(37125.3 - 417636. i) q^{66} +(-272994. - 175443. i) q^{67} -768315. i q^{68} +(314697. + 94254.7i) q^{69} +546874. q^{70} +(-73166.7 + 113850. i) q^{71} +(-1.07098e6 - 355056. i) q^{72} +(-224273. - 491089. i) q^{73} +(218751. - 744997. i) q^{74} +(-355527. + 458225. i) q^{75} +(544195. - 628035. i) q^{76} +(-189695. - 27274.0i) q^{77} +(-76909.0 - 1.41920e6i) q^{78} +(120340. + 138879. i) q^{79} +(1.33803e6 + 2.08202e6i) q^{80} +(498370. + 184546. i) q^{81} +(1.00272e6 + 1.15720e6i) q^{82} +(144692. + 492777. i) q^{83} +(-306788. + 781084. i) q^{84} +(583689. - 673613. i) q^{85} +(-298801. - 136458. i) q^{86} +(243315. - 427872. i) q^{87} +(-658291. - 1.44146e6i) q^{88} +(-811560. + 116685. i) q^{89} +(-1.08897e6 - 1.83044e6i) q^{90} -649637. q^{91} +(1.96887e6 - 452809. i) q^{92} +(-1.04048e6 - 245226. i) q^{93} +(-227914. - 146471. i) q^{94} +(954236. - 137198. i) q^{95} +(-2.53698e6 + 506190. i) q^{96} +(590735. + 173455. i) q^{97} +(-1.13977e6 - 520515. i) q^{98} +(286443. + 689236. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) $ 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$-1$

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 $

$2$	−8.20003	+	12.7595i	−1.02500	+	1.59494i	−0.244636	+	0.969615i	$0.578668\pi$
$2$	−8.20003	+	12.7595i	−1.02500	+	1.59494i	−0.780367	+	0.625321i	$0.784968\pi$
$3$	2.39070	−	26.8939i	0.0885446	−	0.996072i
$3$	2.39070	−	26.8939i	0.0885446	−	0.996072i
$4$	−68.9776	−	151.040i	−1.07777	−	2.36000i
$5$	54.2696	−	184.825i	0.434156	−	1.47860i	−0.394527	−	0.918884i	$-0.629092\pi$
$5$	54.2696	−	184.825i	0.434156	−	1.47860i	0.828684	−	0.559717i	$-0.189090\pi$
$6$	323.549	+	251.035i	1.49791	+	1.16220i
$7$	122.578	−	141.462i	0.357369	−	0.412426i	−0.548388	−	0.836224i	$-0.684758\pi$
$7$	122.578	−	141.462i	0.357369	−	0.412426i	0.905756	+	0.423799i	$0.139304\pi$
$8$	1531.99	+	220.266i	2.99216	+	0.430208i
$9$	−717.569	−	128.591i	−0.984320	−	0.176394i
$10$	1913.26	+	2208.02i	1.91326	+	2.20802i
$11$	−553.536	−	861.320i	−0.415880	−	0.647122i	0.568601	−	0.822614i	$-0.307485\pi$
$11$	−553.536	−	861.320i	−0.415880	−	0.647122i	−0.984481	+	0.175491i	$0.943849\pi$
$12$	−4226.96	+	1493.99i	−2.44616	+	0.864577i
$13$	−2272.78	−	2622.93i	−1.03449	−	1.19387i	−0.980741	−	0.195315i	$-0.937427\pi$
$13$	−2272.78	−	2622.93i	−1.03449	−	1.19387i	−0.0537531	−	0.998554i	$-0.517118\pi$
$14$	799.844	+	2724.02i	0.291488	+	0.992718i
$15$	−4840.94	−	1901.38i	−1.43435	−	0.563373i
$16$	−8413.70	+	9709.92i	−2.05412	+	2.37059i
$17$	4209.00	+	1922.19i	0.856707	+	0.391245i	0.794825	−	0.606839i	$-0.207563\pi$
$17$	4209.00	+	1922.19i	0.856707	+	0.391245i	0.0618817	+	0.998083i	$0.480290\pi$
$18$	7524.84	−	8101.37i	1.29027	−	1.38912i
$19$	2079.04	+	4552.45i	0.303111	+	0.663720i	0.998491	−	0.0549225i	$-0.0174912\pi$
$19$	2079.04	+	4552.45i	0.303111	+	0.663720i	−0.695380	+	0.718642i	$0.744764\pi$
$20$	−31659.3	+	4551.93i	−3.95742	+	0.568991i
$21$	−3511.43	−	3634.79i	−0.379163	−	0.392483i
$22$	15529.0			1.45840
$23$	−2445.18	+	11918.8i	−0.200968	+	0.979598i
$23$	−2445.18	+	11918.8i	−0.200968	+	0.979598i
$24$	9586.36	−	40674.6i	0.693458	−	2.94232i
$25$	−18070.6	−	11613.2i	−1.15652	−	0.743248i
$26$	52104.1	−	7491.44i	2.96450	−	0.426231i
$27$	−5173.81	+	18990.8i	−0.262857	+	0.964835i
$28$	−29821.5	−	8756.38i	−1.35849	−	0.398888i
$29$	16582.8	+	7573.11i	0.679929	+	0.310513i	0.725276	−	0.688458i	$-0.241712\pi$
$29$	16582.8	+	7573.11i	0.679929	+	0.310513i	−0.0453469	+	0.998971i	$0.514439\pi$
$30$	63956.5	−	46176.5i	2.36876	−	1.71024i
$31$	5634.57	−	39189.3i	0.189137	−	1.31547i	−0.645113	−	0.764087i	$-0.723190\pi$
$31$	5634.57	−	39189.3i	0.189137	−	1.31547i	0.834249	−	0.551387i	$-0.185901\pi$
$32$	−26994.0	−	91933.1i	−0.823791	−	2.80558i
$33$	−24487.6	+	12827.6i	−0.681404	+	0.356947i
$34$	−59040.0	+	37942.7i	−1.50214	+	0.965365i
$35$	−19493.5	−	30332.5i	−0.454659	−	0.707463i
$36$	30073.8	+	117251.i	0.644587	+	2.51311i
$37$	−49118.8	+	14422.6i	−0.969712	+	0.284733i	−0.727971	−	0.685608i	$-0.759537\pi$
$37$	−49118.8	+	14422.6i	−0.969712	+	0.284733i	−0.241741	+	0.970341i	$0.577718\pi$
$38$	−75135.1	−	10802.8i	−1.36928	−	0.196873i
$39$	−75974.5	+	54853.5i	−1.28078	+	0.924720i
$40$	123851.	−	271196.i	1.93517	−	4.23744i
$41$	28442.0	−	96864.7i	0.412676	−	1.40545i	−0.446967	−	0.894550i	$-0.647496\pi$
$41$	28442.0	−	96864.7i	0.412676	−	1.40545i	0.859643	−	0.510895i	$-0.170686\pi$
$42$	75171.8	−	14998.6i	1.01463	−	0.202444i
$43$	3082.19	+	21437.1i	0.0387663	+	0.269625i	0.999981	−	0.00617597i	$-0.00196589\pi$
$43$	3082.19	+	21437.1i	0.0387663	+	0.269625i	−0.961215	+	0.275801i	$0.911057\pi$
$44$	−91912.0	+	143018.i	−1.07898	+	1.67893i
$45$	−62709.0	+	125646.i	−0.688165	+	1.37883i
$46$	−132027.	−	128933.i	−1.35640	−	1.32462i
$47$			17862.3i			0.172046i	0.996293	+	0.0860228i	$0.0274158\pi$
$47$			17862.3i			0.172046i	−0.996293	+	0.0860228i	$0.972584\pi$
$48$	241024.	+	249491.i	2.17939	+	2.25596i
$49$	11757.0	+	81771.4i	0.0999324	+	0.695045i
$50$	296358.	−	135342.i	2.37087	−	1.08274i
$51$	61757.6	−	108601.i	0.465565	−	0.818699i
$52$	−239396.	+	524204.i	−1.70258	+	3.72813i
$53$	69130.5	+	59901.9i	0.464346	+	0.402359i	0.855366	−	0.518024i	$-0.173332\pi$
$53$	69130.5	+	59901.9i	0.464346	+	0.402359i	−0.391020	+	0.920382i	$0.627878\pi$
$54$	−199888.	−	221741.i	−1.26942	−	1.40820i
$55$	−189234.	+	55564.0i	−1.13739	+	0.333969i
$56$	218947.	−	189718.i	1.24673	−	1.08030i
$57$	127404.	−	45029.9i	0.687952	−	0.243151i
$58$	−232608.	+	149488.i	−1.19218	+	0.766167i
$59$	−81135.4	+	70304.2i	−0.395052	+	0.342315i	−0.829624	−	0.558323i	$-0.811445\pi$
$59$	−81135.4	+	70304.2i	−0.395052	+	0.342315i	0.434572	+	0.900637i	$0.356900\pi$
$60$	46731.2	+	862327.i	0.216348	+	3.99226i
$61$	33600.4	−	233696.i	0.148032	−	1.02958i	−0.771405	−	0.636345i	$-0.780446\pi$
$61$	33600.4	−	233696.i	0.148032	−	1.02958i	0.919437	−	0.393238i	$-0.128645\pi$
$62$	453832.	+	393248.i	1.90423	+	1.65003i
$63$	−106149.	+	85746.4i	−0.424514	+	0.342921i
$64$	605403.	+	177762.i	2.30943	+	0.678109i
$65$	−608127.	+	277722.i	−2.21439	+	1.01128i
$66$	37125.3	−	417636.i	0.129133	−	1.45267i
$67$	−272994.	−	175443.i	−0.907673	−	0.583326i	0.00138356	−	0.999999i	$-0.499560\pi$
$67$	−272994.	−	175443.i	−0.907673	−	0.583326i	−0.909056	+	0.416673i	$0.863196\pi$
$68$		−	768315.i		−	2.44350i
$69$	314697.	+	94254.7i	0.957956	+	0.286917i
$70$	546874.			1.59439
$71$	−73166.7	+	113850.i	−0.204427	+	0.318095i	−0.928295	−	0.371843i	$-0.878726\pi$
$71$	−73166.7	+	113850.i	−0.204427	+	0.318095i	0.723868	+	0.689938i	$0.242362\pi$
$72$	−1.07098e6	−	355056.i	−2.86936	−	0.951260i
$73$	−224273.	−	491089.i	−0.576511	−	1.26238i	−0.943257	−	0.332063i	$-0.892255\pi$
$73$	−224273.	−	491089.i	−0.576511	−	1.26238i	0.366746	−	0.930321i	$-0.380472\pi$
$74$	218751.	−	744997.i	0.539827	−	1.83848i
$75$	−355527.	+	458225.i	−0.842732	+	1.08616i
$76$	544195.	−	628035.i	1.23969	−	1.43068i
$77$	−189695.	−	27274.0i	−0.415512	−	0.0597417i
$78$	−76909.0	−	1.41920e6i	−0.162066	−	2.99060i
$79$	120340.	+	138879.i	0.244077	+	0.281680i	0.864549	−	0.502549i	$-0.167604\pi$
$79$	120340.	+	138879.i	0.244077	+	0.281680i	−0.620472	+	0.784229i	$0.713059\pi$
$80$	1.33803e6	+	2.08202e6i	2.61334	+	4.06644i
$81$	498370.	+	184546.i	0.937771	+	0.347255i
$82$	1.00272e6	+	1.15720e6i	1.81860	+	2.09878i
$83$	144692.	+	492777.i	0.253053	+	0.861819i	0.983815	+	0.179187i	$0.0573468\pi$
$83$	144692.	+	492777.i	0.253053	+	0.861819i	−0.730762	+	0.682632i	$0.760835\pi$
$84$	−306788.	+	781084.i	−0.517608	+	1.31783i
$85$	583689.	−	673613.i	0.950440	−	1.09687i
$86$	−298801.	−	136458.i	−0.469771	−	0.214537i
$87$	243315.	−	427872.i	0.369498	−	0.649765i
$88$	−658291.	−	1.44146e6i	−0.965984	−	2.11521i
$89$	−811560.	+	116685.i	−1.15120	+	0.165517i	−0.691378	−	0.722494i	$-0.742996\pi$
$89$	−811560.	+	116685.i	−1.15120	+	0.165517i	−0.459822	+	0.888011i	$0.652087\pi$
$90$	−1.08897e6	−	1.83044e6i	−1.49378	−	2.51089i
$91$	−649637.			−0.862078
$92$	1.96887e6	−	452809.i	2.52845	−	0.581502i
$93$	−1.04048e6	−	245226.i	−1.29356	−	0.304872i
$94$	−227914.	−	146471.i	−0.274402	−	0.176347i
$95$	954236.	−	137198.i	1.11297	−	0.160022i
$96$	−2.53698e6	+	506190.i	−2.86750	+	0.572137i
$97$	590735.	+	173455.i	0.647258	+	0.190052i	0.588852	−	0.808241i	$-0.299580\pi$
$97$	590735.	+	173455.i	0.647258	+	0.190052i	0.0584058	+	0.998293i	$0.481398\pi$
$98$	−1.13977e6	−	520515.i	−1.21098	−	0.553038i
$99$	286443.	+	689236.i	0.295211	+	0.710334i
$100$	−507599.	+	3.53043e6i	−0.507599	+	3.53043i
$101$	242513.	+	825924.i	0.235381	+	0.801634i	0.989455	+	0.144844i	$0.0462680\pi$
$101$	242513.	+	825924.i	0.235381	+	0.801634i	−0.754074	+	0.656790i	$0.771914\pi$
$102$	879282.	+	1.67853e6i	0.828567	+	1.58172i
$103$	958826.	−	616200.i	0.877462	−	0.563910i	−0.0225649	−	0.999745i	$-0.507183\pi$
$103$	958826.	−	616200.i	0.877462	−	0.563910i	0.900027	+	0.435835i	$0.143547\pi$
$104$	−2.90413e6	−	4.51891e6i	−2.58176	−	4.01730i
$105$	−862364.	+	451741.i	−0.744942	+	0.390231i
$106$	−1.33119e6	+	390873.i	−1.11769	+	0.328184i
$107$	273281.	+	39291.8i	0.223078	+	0.0320738i	0.252948	−	0.967480i	$-0.418600\pi$
$107$	273281.	+	39291.8i	0.223078	+	0.0320738i	−0.0298692	+	0.999554i	$0.509509\pi$
$108$	3.22525e6	−	528491.i	2.56031	−	0.419533i
$109$	−598744.	+	1.31107e6i	−0.462340	+	1.01238i	0.524608	+	0.851344i	$0.324212\pi$
$109$	−598744.	+	1.31107e6i	−0.462340	+	1.01238i	−0.986948	+	0.161040i	$0.948515\pi$
$110$	842753.	−	2.87015e6i	0.633173	−	2.15639i
$111$	270452.	+	1.35548e6i	0.197752	+	0.991115i
$112$	342255.	+	2.38044e6i	0.243610	+	1.69435i
$113$	−533087.	+	829499.i	−0.369456	+	0.574885i	−0.975351	−	0.220660i	$-0.929179\pi$
$113$	−533087.	+	829499.i	−0.369456	+	0.574885i	0.605895	+	0.795545i	$0.292815\pi$
$114$	−470156.	+	1.99485e6i	−0.317342	+	1.34647i
$115$	2.07019e6	+	1.09876e6i	1.36118	+	0.722450i
$116$		−	3.02704e6i		−	1.93930i
$117$	1.29359e6	+	2.17439e6i	0.807682	+	1.35763i
$118$	−231734.	−	1.61174e6i	−0.141040	−	0.980956i
$119$	787845.	−	359797.i	0.467520	−	0.213509i
$120$	−6.99744e6	−	3.97919e6i	−4.04944	−	2.30277i
$121$	300464.	−	657925.i	0.169604	−	0.371382i
$122$	2.70631e6	+	2.34503e6i	1.49039	+	1.29143i
$123$	−2.53708e6	−	996493.i	−1.36338	−	0.535500i
$124$	−6.30781e6	+	1.85214e6i	−3.30836	+	0.971423i
$125$	−852438.	+	738641.i	−0.436448	+	0.378184i
$126$	−223659.	−	2.05752e6i	−0.111809	−	1.02857i
$127$	1.25884e6	−	809006.i	0.614552	−	0.394948i	−0.196010	−	0.980602i	$-0.562798\pi$
$127$	1.25884e6	−	809006.i	0.614552	−	0.394948i	0.810562	+	0.585653i	$0.199162\pi$
$128$	−2.59813e6	+	2.25129e6i	−1.23889	+	1.07350i
$129$	583897.	−	31642.5i	0.271999	−	0.0147401i
$130$	1.44306e6	−	1.00367e7i	0.656833	−	4.56837i
$131$	−964006.	−	835316.i	−0.428811	−	0.371567i	0.413549	−	0.910482i	$-0.364289\pi$
$131$	−964006.	−	835316.i	−0.428811	−	0.371567i	−0.842360	+	0.538915i	$0.818834\pi$
$132$	3.62658e6	+	2.81379e6i	1.57680	+	1.22340i
$133$	898842.	+	263924.i	0.382057	+	0.112182i
$134$	4.47712e6	−	2.04463e6i	1.86074	−	0.849769i
$135$	3.22920e6	+	1.98688e6i	1.31248	+	0.807550i
$136$	6.02474e6	+	3.87187e6i	2.39509	+	1.53923i
$137$		−	3.15159e6i		−	1.22565i	−0.790218	−	0.612826i	$-0.790032\pi$
$137$		−	3.15159e6i		−	1.22565i	0.790218	−	0.612826i	$-0.209968\pi$
$138$	−3.78317e6	+	3.24248e6i	−1.43952	+	1.23379i
$139$	−319718.			−0.119048			−0.0595240	−	0.998227i	$-0.518958\pi$
$139$	−319718.			−0.119048			−0.0595240	+	0.998227i	$0.518958\pi$
$140$	−3.23680e6	+	5.03656e6i	−1.17959	+	1.83548i
$141$	480387.	+	42703.4i	0.171370	+	0.0152337i
$142$	−852694.	−	1.86714e6i	−0.297802	−	0.652096i
$143$	−1.00111e6	+	3.40948e6i	−0.342354	+	1.16595i
$144$	7.28602e6	−	5.88562e6i	2.44007	−	1.97108i
$145$	2.29964e6	−	2.65393e6i	0.754321	−	0.870533i
$146$	8.10508e6	+	1.16534e6i	2.60435	+	0.374449i
$147$	2.22726e6	−	120700.i	0.701164	−	0.0379974i
$148$	5.56649e6	+	6.42407e6i	1.71710	+	1.98164i
$149$	−2.58588e6	−	4.02371e6i	−0.781718	−	1.21638i	−0.972077	−	0.234662i	$-0.924602\pi$
$149$	−2.58588e6	−	4.02371e6i	−0.781718	−	1.21638i	0.190359	−	0.981715i	$-0.439035\pi$
$150$	−2.93138e6	−	8.29381e6i	−0.868558	−	2.45742i
$151$	−2.10988e6	−	2.43493e6i	−0.612811	−	0.707222i	0.361514	−	0.932367i	$-0.382260\pi$
$151$	−2.10988e6	−	2.43493e6i	−0.612811	−	0.707222i	−0.974325	+	0.225145i	$0.927715\pi$
$152$	2.18230e6	+	7.43224e6i	0.621419	+	2.11636i
$153$	−2.77307e6	−	1.92054e6i	−0.774260	−	0.536228i
$154$	1.90351e6	−	2.19676e6i	0.521186	−	0.601480i
$155$	−6.93738e6	−	3.16820e6i	−1.86295	−	0.850780i
$156$	1.35256e7	+	7.69152e6i	3.56273	+	2.02600i
$157$	−1.43803e6	−	3.14885e6i	−0.371595	−	0.813679i	−0.999377	−	0.0352900i	$-0.988764\pi$
$157$	−1.43803e6	−	3.14885e6i	−0.371595	−	0.813679i	0.627782	−	0.778389i	$-0.283963\pi$
$158$	−2.75882e6	+	396658.i	−0.699441	+	0.100564i
$159$	1.77627e6	−	1.71598e6i	0.441893	−	0.426896i
$160$	−1.84565e7			−4.50598
$161$	1.38633e6	+	1.80687e6i	0.332192	+	0.432962i
$162$	−6.44135e6	+	4.84566e6i	−1.51507	+	1.13975i
$163$	−2.92073e6	−	1.87704e6i	−0.674418	−	0.433422i	0.158098	−	0.987423i	$-0.449464\pi$
$163$	−2.92073e6	−	1.87704e6i	−0.674418	−	0.433422i	−0.832516	+	0.554001i	$0.813100\pi$
$164$	−1.65923e7	+	2.38561e6i	−3.76162	+	0.540839i
$165$	1.04193e6	+	5.22208e6i	0.231947	+	1.16250i
$166$	−7.47407e6	−	2.19458e6i	−1.63393	−	0.479764i
$167$	6.43252e6	+	2.93763e6i	1.38112	+	0.630737i	0.960954	−	0.276710i	$-0.0892440\pi$
$167$	6.43252e6	+	2.93763e6i	1.38112	+	0.630737i	0.420168	+	0.907447i	$0.361971\pi$
$168$	−4.57884e6	−	6.34190e6i	−0.965667	−	1.33749i
$169$	−1.02730e6	+	7.14502e6i	−0.212832	+	1.48028i
$170$	3.80869e6	+	1.29712e7i	0.775228	+	2.64018i
$171$	−906448.	−	3.53405e6i	−0.181282	−	0.706779i
$172$	3.02526e6	−	1.94421e6i	0.594534	−	0.382084i
$173$	2.04887e6	+	3.18811e6i	0.395709	+	0.615736i	0.980750	−	0.195268i	$-0.0625577\pi$
$173$	2.04887e6	+	3.18811e6i	0.395709	+	0.615736i	−0.585040	+	0.811004i	$0.698921\pi$
$174$	3.46423e6	+	6.61314e6i	0.657597	+	1.25534i
$175$	−3.85788e6	+	1.13277e6i	−0.719837	+	0.211363i
$176$	1.30206e7	+	1.87208e6i	2.38833	+	0.343390i
$177$	1.69679e6	+	2.35013e6i	0.305990	+	0.423810i
$178$	5.16598e6	−	1.13119e7i	0.915993	−	2.00575i
$179$	1.40810e6	−	4.79553e6i	0.245512	−	0.836137i	−0.740867	−	0.671651i	$-0.765585\pi$
$179$	1.40810e6	−	4.79553e6i	0.245512	−	0.836137i	0.986379	−	0.164486i	$-0.0525965\pi$
$180$	2.33031e7	+	804783.i	3.99573	+	0.137994i
$181$	1.10073e6	+	7.65572e6i	0.185628	+	1.29107i	0.843167	+	0.537651i	$0.180688\pi$
$181$	1.10073e6	+	7.65572e6i	0.185628	+	1.29107i	−0.657539	+	0.753420i	$0.728403\pi$
$182$	5.32704e6	−	8.28904e6i	0.883633	−	1.37496i
$183$	−6.20467e6	−	1.46234e6i	−1.01243	−	0.238614i
$184$	−6.37128e6	+	1.77208e7i	−1.02276	+	2.84466i
$185$			9.86111e6i			1.55744i
$186$	1.16610e7	−	1.12652e7i	1.81216	−	1.75065i
$187$	−674219.	−	4.68929e6i	−0.103104	−	0.717105i
$188$	2.69792e6	−	1.23210e6i	0.406027	−	0.185426i
$189$	2.05229e6	+	3.05975e6i	0.303986	+	0.453211i
$190$	−6.07418e6	+	1.33006e7i	−0.885578	+	1.93915i
$191$	−6.24112e6	−	5.40796e6i	−0.895700	−	0.776128i	0.0796430	−	0.996823i	$-0.474622\pi$
$191$	−6.24112e6	−	5.40796e6i	−0.895700	−	0.776128i	−0.975343	+	0.220695i	$0.929167\pi$
$192$	6.22807e6	−	1.58567e7i	0.879933	−	2.24031i
$193$	2.96917e6	−	871827.i	0.413012	−	0.121271i	−0.0686239	−	0.997643i	$-0.521861\pi$
$193$	2.96917e6	−	871827.i	0.413012	−	0.121271i	0.481636	+	0.876371i	$0.340043\pi$
$194$	−7.05724e6	+	6.11514e6i	−0.966562	+	0.837531i
$195$	6.01519e6	+	1.70189e7i	0.811233	+	2.29523i
$196$	1.15398e7	−	7.41616e6i	1.53260	−	0.984943i
$197$	−4.54864e6	+	3.94142e6i	−0.594953	+	0.515530i	−0.899473	−	0.436976i	$-0.856049\pi$
$197$	−4.54864e6	+	3.94142e6i	−0.594953	+	0.515530i	0.304520	+	0.952506i	$0.401504\pi$
$198$	−1.11431e7	−	1.99689e6i	−1.43553	−	0.257252i
$199$	2.14160e6	−	1.48951e7i	0.271756	−	1.89010i	−0.158445	−	0.987368i	$-0.550648\pi$
$199$	2.14160e6	−	1.48951e7i	0.271756	−	1.89010i	0.430201	−	0.902733i	$-0.358443\pi$
$200$	−2.51259e7	−	2.17717e7i	−3.14073	−	2.72146i
$201$	−5.37100e6	+	6.92247e6i	−0.661404	+	0.852457i
$202$	−1.25270e7	−	3.67825e6i	−1.51982	−	0.446260i
$203$	3.10399e6	−	1.41754e6i	0.371049	−	0.169453i
$204$	−2.06630e7	−	1.83681e6i	−2.43390	−	0.216359i
$205$	−1.63595e7	−	1.05136e7i	−1.89893	−	1.22037i
$206$			1.72870e7i			1.97751i
$207$	3.28723e6	−	8.23811e6i	0.370611	−	0.928788i
$208$	4.45910e7			4.95515
$209$	2.77030e6	−	4.31066e6i	0.303450	−	0.472177i
$210$	1.30741e6	−	1.47076e7i	0.141174	−	1.58812i
$211$	4.76926e6	+	1.04432e7i	0.507696	+	1.11170i	0.973891	+	0.227016i	$0.0728971\pi$
$211$	4.76926e6	+	1.04432e7i	0.507696	+	1.11170i	−0.466195	+	0.884682i	$0.654376\pi$
$212$	4.27912e6	−	1.45734e7i	0.449104	−	1.52951i
$213$	2.88694e6	+	2.23992e6i	0.298744	+	0.231790i
$214$	−2.74225e6	+	3.16473e6i	−0.279812	+	0.322920i
$215$	4.12939e6	+	593716.i	0.415499	+	0.0597397i
$216$	−1.21093e7	+	2.79541e7i	−1.20159	+	2.77386i
$217$	−4.85313e6	−	5.60081e6i	−0.474944	−	0.548114i
$218$	−1.18188e7	−	1.83904e7i	−1.14079	−	1.77510i
$219$	−1.37435e7	+	4.85753e6i	−1.30847	+	0.462470i
$220$	2.14453e7	+	2.47492e7i	2.01402	+	2.32430i
$221$	−4.52438e6	−	1.54086e7i	−0.419162	−	1.42754i
$222$	−1.95129e7	−	7.66414e6i	−1.78346	−	0.700494i
$223$	1.00442e7	−	1.15916e7i	0.905734	−	1.04527i	−0.0930348	−	0.995663i	$-0.529657\pi$
$223$	1.00442e7	−	1.15916e7i	0.905734	−	1.04527i	0.998769	−	0.0496097i	$-0.0157977\pi$
$224$	−1.63139e7	−	7.45031e6i	−1.45149	−	0.662873i
$225$	1.14735e7	+	1.06570e7i	1.00728	+	0.935595i
$226$	−6.21266e6	−	1.36038e7i	−0.538211	−	1.17852i
$227$	5.72368e6	−	822941.i	0.489326	−	0.0703544i	0.106764	−	0.994284i	$-0.465951\pi$
$227$	5.72368e6	−	822941.i	0.489326	−	0.0703544i	0.382562	+	0.923930i	$0.375042\pi$
$228$	−1.55893e7	−	1.61370e7i	−1.31529	−	1.36150i
$229$	−3.94923e6			−0.328856			−0.164428	−	0.986389i	$-0.552578\pi$
$229$	−3.94923e6			−0.328856			−0.164428	+	0.986389i	$0.552578\pi$
$230$	−3.09952e7	+	1.74047e7i	−2.54748	+	1.43049i
$231$	−1.18701e6	+	5.03645e6i	−0.0962984	+	0.408590i
$232$	2.37365e7	+	1.52545e7i	1.90087	+	1.22162i
$233$	−2.17010e6	+	312013.i	−0.171558	+	0.0246664i	−0.227559	−	0.973764i	$-0.573074\pi$
$233$	−2.17010e6	+	312013.i	−0.171558	+	0.0246664i	0.0560002	+	0.998431i	$0.482165\pi$
$234$	−3.83517e7	−	1.32449e6i	−2.99321	−	0.103372i
$235$	3.30140e6	+	969378.i	0.254387	+	0.0746947i
$236$	1.62153e7	+	7.40526e6i	1.23364	+	0.563384i
$237$	4.02271e6	−	2.90439e6i	0.302185	−	0.218177i
$238$	−1.86953e6	+	1.30028e7i	−0.138676	+	0.964512i
$239$	−3.66609e6	−	1.24856e7i	−0.268540	−	0.914564i	−0.977786	−	0.209603i	$-0.932783\pi$
$239$	−3.66609e6	−	1.24856e7i	−0.268540	−	0.914564i	0.709246	−	0.704961i	$-0.249035\pi$
$240$	5.91925e7	−	3.10074e7i	4.28186	−	2.24301i
$241$	−1.62177e7	+	1.04225e7i	−1.15861	+	0.744594i	−0.971335	−	0.237713i	$-0.923602\pi$
$241$	−1.62177e7	+	1.04225e7i	−1.15861	+	0.744594i	−0.187276	+	0.982307i	$0.559966\pi$
$242$	5.93097e6	+	9.22877e6i	0.418485	+	0.651175i
$243$	6.15462e6	−	1.29619e7i	0.428926	−	0.903340i
$244$	−3.76150e7	+	1.10448e7i	−2.58936	+	0.760304i
$245$	1.57515e7	+	2.26472e6i	1.07108	+	0.153998i
$246$	3.35189e7	−	2.42005e7i	2.25156	−	1.62562i
$247$	7.21558e6	−	1.57999e7i	0.478829	−	1.04849i
$248$	1.72642e7	−	5.87964e7i	1.13186	−	3.85475i
$249$	1.35986e7	−	2.71327e6i	0.880841	−	0.175750i
$250$	−2.43468e6	−	1.69335e7i	−0.155819	−	1.08375i
$251$	−7.86832e6	+	1.22434e7i	−0.497578	+	0.774246i	−0.995678	−	0.0928733i	$-0.970395\pi$
$251$	−7.86832e6	+	1.22434e7i	−0.497578	+	0.774246i	0.498100	+	0.867120i	$0.334031\pi$
$252$	2.02730e7	+	1.01181e7i	1.26682	+	0.632261i
$253$	1.16194e7	−	4.49139e6i	0.717498	−	0.277344i
$254$			2.26960e7i			1.38499i
$255$	−1.67207e7	−	1.73081e7i	−1.00840	−	1.04383i
$256$	−1.67373e6	−	1.16410e7i	−0.0997620	−	0.693860i
$257$	−7.80733e6	+	3.56549e6i	−0.459942	+	0.210048i	−0.631891	−	0.775057i	$-0.717721\pi$
$257$	−7.80733e6	+	3.56549e6i	−0.459942	+	0.210048i	0.171949	+	0.985106i	$0.444994\pi$
$258$	−4.38423e6	+	7.70970e6i	−0.255290	+	0.448930i
$259$	−3.98062e6	+	8.71634e6i	−0.229114	+	0.501689i
$260$	8.38942e7	+	7.26947e7i	4.77323	+	4.13602i
$261$	−1.09255e7	−	7.56663e6i	−0.614495	−	0.425580i
$262$	1.85631e7	−	5.45061e6i	1.03216	−	0.303069i
$263$	1.06922e7	−	9.26489e6i	0.587762	−	0.509299i	−0.309440	−	0.950919i	$-0.600142\pi$
$263$	1.06922e7	−	9.26489e6i	0.587762	−	0.509299i	0.897202	+	0.441620i	$0.145596\pi$
$264$	−4.03402e7	+	1.42579e7i	−2.19243	+	0.774899i
$265$	1.48231e7	−	9.52621e6i	0.796527	−	0.511897i
$266$	−1.07381e7	+	9.30459e6i	−0.570533	+	0.494370i
$267$	1.19791e6	+	2.21050e7i	0.0629349	+	1.16133i
$268$	−7.66837e6	+	5.33347e7i	−0.398381	+	2.77080i
$269$	2.97177e6	+	2.57506e6i	0.152672	+	0.132291i	0.727847	−	0.685739i	$-0.240521\pi$
$269$	2.97177e6	+	2.57506e6i	0.152672	+	0.132291i	−0.575176	+	0.818030i	$0.695066\pi$
$270$	−5.18311e7	+	2.49106e7i	−2.63329	+	1.26559i
$271$	5.53176e6	+	1.62427e6i	0.277943	+	0.0816114i	0.417733	−	0.908570i	$-0.362825\pi$
$271$	5.53176e6	+	1.62427e6i	0.277943	+	0.0816114i	−0.139790	+	0.990181i	$0.544643\pi$
$272$	−5.40775e7	+	2.46964e7i	−2.68726	+	1.22723i
$273$	−1.55309e6	+	1.74713e7i	−0.0763323	+	0.858692i
$274$	4.02126e7	+	2.58431e7i	1.95484	+	1.25630i
$275$			2.19929e7i			1.05751i
$276$	−7.47082e6	−	5.40333e7i	−0.355338	−	2.57000i
$277$	−3.06941e7			−1.44416			−0.722080	−	0.691809i	$-0.756814\pi$
$277$	−3.06941e7			−1.44416			−0.722080	+	0.691809i	$0.756814\pi$
$278$	2.62169e6	−	4.07943e6i	0.122025	−	0.189874i
$279$	−9.08258e6	+	2.73965e7i	−0.418212	+	1.26149i
$280$	−2.31826e7	−	5.07627e7i	−1.05606	−	2.31244i
$281$	6.65936e6	−	2.26797e7i	0.300133	−	1.02216i	−0.661983	−	0.749518i	$-0.730285\pi$
$281$	6.65936e6	−	2.26797e7i	0.300133	−	1.02216i	0.962116	−	0.272640i	$-0.0878967\pi$
$282$	−4.48406e6	+	5.77933e6i	−0.199951	+	0.257709i
$283$	6.02731e6	−	6.95588e6i	0.265928	−	0.306897i	−0.607043	−	0.794669i	$-0.707645\pi$
$283$	6.02731e6	−	6.95588e6i	0.265928	−	0.306897i	0.872971	+	0.487771i	$0.162190\pi$
$284$	2.22427e7	+	3.19802e6i	0.971029	+	0.139613i
$285$	−1.40851e6	−	2.59912e7i	−0.0608452	−	1.12277i
$286$	−3.52941e7	−	4.07315e7i	−1.50870	−	1.74114i
$287$	−1.02163e7	−	1.58969e7i	−0.432164	−	0.672460i
$288$	7.54829e6	+	6.94395e7i	0.315989	+	2.90690i
$289$	−1.78586e6	−	2.06099e6i	−0.0739868	−	0.0853853i
$290$	1.50056e7	+	5.11045e7i	0.615263	+	2.09539i
$291$	6.07717e6	−	1.54725e7i	0.246617	−	0.627887i
$292$	−5.87042e7	+	6.77482e7i	−2.35787	+	2.72113i
$293$	−2.84944e7	−	1.30130e7i	−1.13281	−	0.517337i	−0.241351	−	0.970438i	$-0.577590\pi$
$293$	−2.84944e7	−	1.30130e7i	−1.13281	−	0.517337i	−0.891459	+	0.453101i	$0.850318\pi$
$294$	−1.67235e7	+	2.94085e7i	−0.658092	+	1.15726i
$295$	8.59081e6	+	1.88112e7i	0.334632	+	0.732743i
$296$	−7.84263e7	+	1.12760e7i	−3.02403	+	0.434790i
$297$	1.92211e7	−	6.05582e6i	0.733683	−	0.231155i
$298$	7.25448e7			2.74131
$299$	3.68195e7	−	2.06752e7i	1.37741	−	0.773458i
$300$	9.37337e7	+	2.20916e7i	3.47162	+	0.818206i
$301$	3.41034e6	+	2.19169e6i	0.125054	+	0.0803675i
$302$	4.83695e7	−	6.95449e6i	1.75611	−	0.252490i
$303$	2.27921e7	−	4.54760e6i	0.819327	−	0.163476i
$304$	−6.16964e7	−	1.81157e7i	−2.19603	−	0.644813i
$305$	−4.13694e7	−	1.88928e7i	−1.45807	−	0.665880i
$306$	4.72444e7	−	1.96345e7i	1.64887	−	0.685261i
$307$	−2.21368e6	+	1.53965e7i	−0.0765069	+	0.532117i	0.915140	+	0.403136i	$0.132080\pi$
$307$	−2.21368e6	+	1.53965e7i	−0.0765069	+	0.532117i	−0.991647	+	0.128981i	$0.958829\pi$
$308$	8.96524e6	+	3.05328e7i	0.306839	+	1.04500i
$309$	−1.42798e7	−	2.72598e7i	−0.484001	−	0.923946i
$310$	9.73113e7	−	6.25382e7i	3.26647	−	2.09923i
$311$	−2.47737e6	−	3.85486e6i	−0.0823586	−	0.128153i	0.797630	−	0.603147i	$-0.206087\pi$
$311$	−2.47737e6	−	3.85486e6i	−0.0823586	−	0.128153i	−0.879989	+	0.474994i	$0.842450\pi$
$312$	−1.28474e8	+	6.73001e7i	−4.23012	+	2.21591i
$313$	−2.32159e7	+	6.81681e6i	−0.757100	+	0.222305i	−0.637429	−	0.770509i	$-0.720002\pi$
$313$	−2.32159e7	+	6.81681e6i	−0.757100	+	0.222305i	−0.119671	+	0.992814i	$0.538184\pi$
$314$	5.19696e7	+	7.47210e6i	1.67865	+	0.241354i
$315$	1.00875e7	+	2.42723e7i	0.322738	+	0.776569i
$316$	1.26756e7	−	2.77556e7i	0.401704	−	0.879609i
$317$	1.16082e7	−	3.95340e7i	0.364408	−	1.24106i	−0.549622	−	0.835413i	$-0.685228\pi$
$317$	1.16082e7	−	3.95340e7i	0.364408	−	1.24106i	0.914030	−	0.405646i	$-0.132953\pi$
$318$	7.32963e6	+	3.67354e7i	0.227930	+	1.14236i
$319$	−2.65632e6	−	1.84751e7i	−0.0818291	−	0.569134i
$320$	6.57099e7	−	1.02247e8i	2.00531	−	3.12032i
$321$	1.71005e6	−	7.25566e6i	0.0517002	−	0.219362i
$322$	−3.44227e7	+	2.87245e6i	−1.03104	+	0.0860368i
$323$			2.31576e7i			0.687204i
$324$	−6.50258e6	−	8.80032e7i	−0.191184	−	2.58740i
$325$	1.06097e7	+	7.37922e7i	0.309068	+	2.14961i
$326$	4.79002e7	−	2.18753e7i	1.38256	−	0.631394i
$327$	3.38283e7	+	1.92370e7i	0.967470	+	0.550165i
$328$	6.49089e7	−	1.42131e8i	1.83943	−	4.02778i
$329$	2.52683e6	+	2.18951e6i	0.0709560	+	0.0614837i
$330$	−7.51749e7	−	2.95266e7i	−2.09185	−	0.821622i
$331$	3.20575e7	−	9.41294e6i	0.883987	−	0.259562i	0.191933	−	0.981408i	$-0.438524\pi$
$331$	3.20575e7	−	9.41294e6i	0.883987	−	0.259562i	0.692054	+	0.721846i	$0.256706\pi$
$332$	6.44485e7	−	5.58449e7i	1.76116	−	1.52605i
$333$	3.71008e7	−	4.03297e6i	1.00473	−	0.109218i
$334$	−9.02296e7	+	5.79870e7i	−2.42164	+	1.55629i
$335$	−4.72415e7	+	4.09350e7i	−1.25658	+	1.08883i
$336$	6.48376e7	−	3.51367e6i	1.70926	−	0.0926283i
$337$	5.02644e6	−	3.49597e7i	0.131332	−	0.913435i	−0.812489	−	0.582977i	$-0.801888\pi$
$337$	5.02644e6	−	3.49597e7i	0.131332	−	0.913435i	0.943821	−	0.330458i	$-0.107203\pi$
$338$	−8.27430e7	−	7.16972e7i	−2.14280	−	1.85674i
$339$	2.10341e7	+	1.63199e7i	0.539913	+	0.418908i
$340$	−1.42004e8	−	4.16961e7i	−3.61296	−	1.06086i
$341$	−3.68735e7	+	1.68395e7i	−0.929931	+	0.424685i
$342$	5.25255e7	+	1.74135e7i	1.31308	+	0.435318i
$343$	3.15345e7	+	2.02660e7i	0.781454	+	0.502210i
$344$			3.35203e7i			0.823441i
$345$	3.44991e7	−	5.30488e7i	0.840138	−	1.29187i
$346$	−5.74794e7			−1.38766
$347$	7.54740e6	−	1.17440e7i	0.180638	−	0.281078i	−0.739112	−	0.673582i	$-0.764755\pi$
$347$	7.54740e6	−	1.17440e7i	0.180638	−	0.281078i	0.919750	+	0.392504i	$0.128391\pi$
$348$	−8.14090e7	−	7.23675e6i	−1.93168	−	0.171714i
$349$	−3.41334e6	−	7.47418e6i	−0.0802978	−	0.175828i	0.865225	−	0.501384i	$-0.167176\pi$
$349$	−3.41334e6	−	7.47418e6i	−0.0802978	−	0.175828i	−0.945523	+	0.325557i	$0.894448\pi$
$350$	1.71811e7	−	5.85133e7i	0.400725	−	1.36474i
$351$	6.15706e7	−	2.95915e7i	1.42381	−	0.684299i
$352$	−6.42416e7	+	7.41388e7i	−1.47295	+	1.69988i
$353$	3.66998e7	+	5.27663e6i	0.834332	+	0.119959i	0.546224	−	0.837639i	$-0.316065\pi$
$353$	3.66998e7	+	5.27663e6i	0.834332	+	0.119959i	0.288108	+	0.957598i	$0.406974\pi$
$354$	−4.39001e7	+	2.37903e6i	−0.989592	+	0.0536279i
$355$	1.70715e7	+	1.97016e7i	0.381582	+	0.440369i
$356$	7.36035e7	+	1.14529e8i	1.63135	+	2.53844i
$357$	−7.79285e6	−	2.20484e7i	−0.171274	−	0.484588i
$358$	4.96421e7	+	5.72901e7i	1.08194	+	1.24862i
$359$	59663.7	+	203196.i	0.00128952	+	0.00439169i	0.960135	−	0.279536i	$-0.0901806\pi$
$359$	59663.7	+	203196.i	0.00128952	+	0.00439169i	−0.958846	+	0.283928i	$0.908362\pi$
$360$	−1.23745e8	+	1.78676e8i	−2.65229	+	3.82964i
$361$	1.44061e7	−	1.66255e7i	0.306213	−	0.353388i
$362$	−1.06709e8	−	4.87324e7i	−2.24945	−	1.02729i
$363$	−1.69759e7	−	9.65358e6i	−0.354905	−	0.201822i
$364$	4.48104e7	+	9.81211e7i	0.929126	+	2.03450i
$365$	−1.02937e8	+	1.48001e7i	−2.11686	+	0.304358i
$366$	6.95372e7	−	6.71772e7i	1.41832	−	1.37018i
$367$	9.60933e7			1.94399			0.971997	−	0.234994i	$-0.0755071\pi$
$367$	9.60933e7			1.94399			0.971997	+	0.234994i	$0.0755071\pi$
$368$	−9.51573e7	−	1.24023e8i	−1.90941	−	2.48863i
$369$	−3.28650e7	+	6.58497e7i	−0.654117	+	1.31061i
$370$	−1.25823e8	−	8.08613e7i	−2.48401	−	1.59638i
$371$	1.69477e7	−	2.43671e6i	0.331886	−	0.0477180i
$372$	3.47312e7	+	1.74070e8i	0.674670	+	3.38138i
$373$	1.89815e7	+	5.57348e6i	0.365767	+	0.107399i	0.459451	−	0.888203i	$-0.348046\pi$
$373$	1.89815e7	+	5.57348e6i	0.365767	+	0.107399i	−0.0936841	+	0.995602i	$0.529864\pi$
$374$	6.53616e7	+	2.98496e7i	1.24942	+	0.570590i
$375$	1.78271e7	+	2.46913e7i	0.338054	+	0.468220i
$376$	−3.93446e6	+	2.73648e7i	−0.0740154	+	0.514788i
$377$	−1.78253e7	−	6.07076e7i	−0.332670	−	1.13297i
$378$	−5.58697e7	+	1.09615e6i	−1.03443	+	0.0202953i
$379$	−7.88338e7	+	5.06634e7i	−1.44809	+	0.930629i	−0.448772	+	0.893646i	$0.648138\pi$
$379$	−7.88338e7	+	5.06634e7i	−1.44809	+	0.930629i	−0.999316	+	0.0369829i	$0.988225\pi$
$380$	−8.65434e7	−	1.34664e8i	−1.57719	−	2.45415i
$381$	−1.87479e7	−	3.57892e7i	−0.338982	−	0.647109i
$382$	1.20180e8	−	3.52881e7i	2.15597	−	0.633050i
$383$	5.75510e7	+	8.27458e6i	1.02437	+	0.147282i	0.633965	−	0.773362i	$-0.281426\pi$
$383$	5.75510e7	+	8.27458e6i	1.02437	+	0.147282i	0.390404	+	0.920644i	$0.372335\pi$
$384$	5.43348e7	+	7.52562e7i	0.959588	+	1.32907i
$385$	−1.53356e7	+	3.35803e7i	−0.268731	+	0.588440i
$386$	−1.32232e7	+	4.50341e7i	−0.229919	+	0.783032i
$387$	544933.	−	1.57789e7i	0.00940178	−	0.272236i
$388$	−1.45488e7	−	1.01189e8i	−0.249076	−	1.73236i
$389$	−3.39427e7	+	5.28158e7i	−0.576630	+	0.897254i	−0.999962	−	0.00872076i	$-0.997224\pi$
$389$	−3.39427e7	+	5.28158e7i	−0.576630	+	0.897254i	0.423332	+	0.905975i	$0.360860\pi$
$390$	−2.66477e8	−	6.28044e7i	−4.49227	−	1.05876i
$391$	−3.32018e7	+	4.54660e7i	−0.555433	+	0.760600i
$392$			1.27862e8i			2.12268i
$393$	−2.47696e7	+	2.39289e7i	−0.408076	+	0.394227i
$394$	−1.29915e7	−	9.03581e7i	−0.212408	−	1.47733i
$395$	3.21991e7	−	1.47049e7i	0.522460	−	0.238599i
$396$	8.43440e7	−	9.08061e7i	1.35822	−	1.46228i
$397$	−2.27046e6	+	4.97161e6i	−0.0362863	+	0.0794558i	−0.926907	−	0.375291i	$-0.877543\pi$
$397$	−2.27046e6	+	4.97161e6i	−0.0362863	+	0.0794558i	0.890621	+	0.454747i	$0.150270\pi$
$398$	1.72493e8	+	1.49466e8i	2.73604	+	2.37079i
$399$	9.24682e6	−	2.35425e7i	0.145571	−	0.370624i
$400$	2.64804e8	−	7.77534e7i	4.13756	−	1.21490i
$401$	−1.81890e7	+	1.57609e7i	−0.282083	+	0.244426i	−0.784397	−	0.620259i	$-0.787028\pi$
$401$	−1.81890e7	+	1.57609e7i	−0.282083	+	0.244426i	0.502314	+	0.864685i	$0.332482\pi$
$402$	−4.42848e7	−	1.25296e8i	−0.681674	−	1.92867i
$403$	−1.15597e8	+	7.42897e7i	−1.76617	+	1.13505i
$404$	1.08019e8	−	9.35994e7i	1.63817	−	1.41948i
$405$	6.11550e7	−	8.20960e7i	0.920591	−	1.23583i
$406$	−7.36564e6	+	5.12292e7i	−0.110061	+	0.765489i
$407$	3.96115e7	+	3.43236e7i	0.587541	+	0.509107i
$408$	1.18533e8	−	1.52773e8i	1.74526	−	2.24939i
$409$	−9.54115e7	−	2.80153e7i	−1.39454	−	0.409474i	−0.503734	−	0.863859i	$-0.668041\pi$
$409$	−9.54115e7	−	2.80153e7i	−1.39454	−	0.409474i	−0.890805	+	0.454385i	$0.849859\pi$
$410$	2.68297e8	−	1.22527e8i	3.89281	−	1.77779i
$411$	−8.47586e7	−	7.53451e6i	−1.22084	−	0.108525i
$412$	−1.59208e8	−	1.02317e8i	−2.27653	−	1.46304i
$413$			2.00953e7i			0.285262i
$414$	7.81587e7	+	1.09496e8i	1.10148	+	1.54311i
$415$	9.89300e7			1.38415
$416$	−1.79783e8	+	2.79747e8i	−2.49728	+	3.88585i
$417$	−764350.	+	8.59847e6i	−0.0105411	+	0.118580i
$418$	3.22854e7	+	7.06951e7i	0.442056	+	0.967967i
$419$	−2.17280e7	+	7.39988e7i	−0.295378	+	1.00596i	0.669401	+	0.742901i	$0.266551\pi$
$419$	−2.17280e7	+	7.39988e7i	−0.295378	+	1.00596i	−0.964779	+	0.263063i	$0.915267\pi$
$420$	1.27715e8	+	9.90912e7i	1.72382	+	1.33748i
$421$	−1.12996e7	+	1.30404e7i	−0.151432	+	0.174761i	−0.826397	−	0.563088i	$-0.809613\pi$
$421$	−1.12996e7	+	1.30404e7i	−0.151432	+	0.174761i	0.674965	+	0.737850i	$0.264159\pi$
$422$	−1.72358e8	−	2.47814e7i	−2.29348	−	0.329752i
$423$	2.29693e6	−	1.28174e7i	0.0303477	−	0.169348i
$424$	9.27127e7	+	1.06996e8i	1.21630	+	1.40369i
$425$	−5.37362e7	−	8.36151e7i	−0.700003	−	1.08923i
$426$	−5.22533e7	+	1.84685e7i	−0.675904	+	0.238893i
$427$	−2.89404e7	−	3.33990e7i	−0.371724	−	0.428993i
$428$	−1.29156e7	−	4.39865e7i	−0.164734	−	0.561033i
$429$	8.93010e7	+	3.50750e7i	1.13106	+	0.444248i
$430$	−4.14366e7	+	4.78204e7i	−0.521169	+	0.601461i
$431$	−1.52651e7	−	6.97133e6i	−0.190663	−	0.0870731i	0.317796	−	0.948159i	$-0.397057\pi$
$431$	−1.52651e7	−	6.97133e6i	−0.190663	−	0.0870731i	−0.508459	+	0.861086i	$0.669785\pi$
$432$	−1.40869e8	−	2.10020e8i	−1.74728	−	2.60502i
$433$	−3.55957e7	−	7.79438e7i	−0.438464	−	0.960103i	−0.991878	−	0.127196i	$-0.959402\pi$
$433$	−3.55957e7	−	7.79438e7i	−0.438464	−	0.960103i	0.553413	−	0.832907i	$-0.313325\pi$
$434$	1.11259e8	−	1.59967e7i	1.36103	−	0.195686i
$435$	−6.58769e7	−	6.81912e7i	−0.800323	−	0.828439i
$436$	2.39323e8			2.88752
$437$	−5.93433e7	+	1.36480e7i	−0.711094	+	0.163540i
$438$	5.07173e7	−	2.15192e8i	0.603579	−	2.56096i
$439$	1.01453e8	+	6.52002e7i	1.19915	+	0.770646i	0.978809	−	0.204777i	$-0.0656468\pi$
$439$	1.01453e8	+	6.52002e7i	1.19915	+	0.770646i	0.220341	+	0.975423i	$0.429283\pi$
$440$	−3.02142e8	+	4.34415e7i	−3.54694	+	0.509973i
$441$	2.07863e6	−	6.01885e7i	0.0242361	−	0.701774i
$442$	2.33706e8	+	6.86224e7i	2.70647	+	0.794692i
$443$	9.26109e7	+	4.22940e7i	1.06525	+	0.486482i	0.869378	−	0.494147i	$-0.164520\pi$
$443$	9.26109e7	+	4.22940e7i	1.06525	+	0.486482i	0.195870	+	0.980630i	$0.437247\pi$
$444$	1.86076e8	−	1.34347e8i	2.12590	−	1.53489i
$445$	−2.24767e7	+	1.56329e8i	−0.255066	+	1.77403i
$446$	6.55405e7	+	2.23210e8i	0.738763	+	2.51600i
$447$	−1.14396e8	+	5.99251e7i	−1.28082	+	0.670944i
$448$	9.93554e7	−	6.38518e7i	1.10499	−	0.710132i
$449$	−3.52363e7	−	5.48287e7i	−0.389270	−	0.605716i	0.590212	−	0.807249i	$-0.299044\pi$
$449$	−3.52363e7	−	5.48287e7i	−0.389270	−	0.605716i	−0.979482	+	0.201532i	$0.935408\pi$
$450$	−2.30061e8	+	5.90084e7i	−2.52468	+	0.647555i
$451$	−9.91751e7	+	2.91205e7i	−1.08112	+	0.317445i
$452$	1.62059e8	+	2.33005e7i	1.75492	+	0.252319i
$453$	−7.05290e7	+	5.09218e7i	−0.758705	+	0.547784i
$454$	−3.64340e7	+	7.97794e7i	−0.389350	+	0.852557i
$455$	−3.52555e7	+	1.20069e8i	−0.374277	+	1.27467i
$456$	2.05100e8	−	4.09225e7i	2.16307	−	0.431586i
$457$	2.92329e6	+	2.03319e7i	0.0306283	+	0.213025i	0.999388	−	0.0349762i	$-0.0111355\pi$
$457$	2.92329e6	+	2.03319e7i	0.0306283	+	0.213025i	−0.968760	+	0.248001i	$0.920226\pi$
$458$	3.23838e7	−	5.03901e7i	0.337078	−	0.524504i
$459$	−5.82805e7	+	6.99874e7i	−0.602678	+	0.723739i
$460$	2.31594e7	−	3.88471e8i	0.237932	−	3.99103i
$461$			2.41124e7i			0.246115i	0.992400	+	0.123057i	$0.0392699\pi$
$461$			2.41124e7i			0.246115i	−0.992400	+	0.123057i	$0.960730\pi$
$462$	−5.45290e7	−	5.64446e7i	−0.552970	−	0.572396i
$463$	−2.45727e7	−	1.70907e8i	−0.247577	−	1.72194i	−0.612133	−	0.790755i	$-0.709688\pi$
$463$	−2.45727e7	−	1.70907e8i	−0.247577	−	1.72194i	0.364555	−	0.931182i	$-0.381221\pi$
$464$	−2.13057e8	+	9.72998e7i	−2.13276	+	0.973998i
$465$	−1.01791e8	+	1.78999e8i	−1.01239	+	1.78030i
$466$	1.38137e7	−	3.02479e7i	0.136507	−	0.298908i
$467$	−8.56289e7	−	7.41978e7i	−0.840755	−	0.728518i	0.123826	−	0.992304i	$-0.460483\pi$
$467$	−8.56289e7	−	7.41978e7i	−0.840755	−	0.728518i	−0.964581	+	0.263786i	$0.915029\pi$
$468$	2.39191e8	−	3.45369e8i	2.33350	−	3.36934i
$469$	−5.82815e7	+	1.71130e7i	−0.564953	+	0.165885i
$470$	−3.94403e7	+	3.41752e7i	−0.379881	+	0.329168i
$471$	−8.81229e7	+	3.11464e7i	−0.843386	+	0.298088i
$472$	−1.39784e8	+	8.98338e7i	−1.32933	+	0.854306i
$473$	1.67581e7	−	1.45210e7i	0.158358	−	0.137218i
$474$	4.07218e6	+	7.51437e7i	0.0382378	+	0.705599i
$475$	1.52994e7	−	1.06410e8i	0.142756	−	0.992889i
$476$	−1.08687e8	−	9.41781e7i	−1.00776	−	0.873231i
$477$	−4.19031e7	−	5.18733e7i	−0.386092	−	0.477957i
$478$	1.89371e8	+	5.56045e7i	1.73393	+	0.509127i
$479$	6.54816e7	−	2.99044e7i	0.595816	−	0.272100i	−0.0945965	−	0.995516i	$-0.530156\pi$
$479$	6.54816e7	−	2.99044e7i	0.595816	−	0.272100i	0.690413	+	0.723415i	$0.257429\pi$
$480$	−4.41240e7	+	4.96368e8i	−0.398980	+	4.48828i
$481$	1.49466e8	+	9.60559e7i	1.34310	+	0.863155i
$482$		−	2.92394e8i		−	2.61112i
$483$	5.19082e7	−	3.29642e7i	0.460675	−	0.292550i
$484$	−1.20098e8			−1.05925
$485$	6.41178e7	−	9.97693e7i	0.562022	−	0.874524i
$486$	1.14920e8	+	1.84818e8i	1.00112	+	1.61004i
$487$	−5.80748e7	−	1.27166e8i	−0.502807	−	1.10099i	−0.975547	−	0.219791i	$-0.929462\pi$
$487$	−5.80748e7	−	1.27166e8i	−0.502807	−	1.10099i	0.472740	−	0.881202i	$-0.343265\pi$
$488$	1.02951e8	−	3.50618e8i	0.885869	−	3.01699i
$489$	−5.74636e7	+	7.40626e7i	−0.491436	+	0.633392i
$490$	−1.58059e8	+	1.82410e8i	−1.34348	+	1.55046i
$491$	1.52584e7	+	2.19382e6i	0.128903	+	0.0185335i	0.206464	−	0.978454i	$-0.433804\pi$
$491$	1.52584e7	+	2.19382e6i	0.128903	+	0.0185335i	−0.0775612	+	0.996988i	$0.524713\pi$
$492$	2.44913e7	+	4.51936e8i	0.205644	+	3.79473i
$493$	5.52401e7	+	6.37504e7i	0.461013	+	0.532038i
$494$	1.42431e8	+	2.21627e8i	1.18147	+	1.83841i
$495$	1.42933e8	−	1.55373e7i	1.17847	−	0.128103i
$496$	3.33118e8	+	3.84438e8i	2.72994	+	3.15051i
$497$	7.13680e6	+	2.43057e7i	0.0581345	+	0.197988i
$498$	−7.68893e7	+	1.95761e8i	−0.622555	+	1.58503i
$499$	−1.55873e7	+	1.79887e7i	−0.125450	+	0.144777i	−0.815000	−	0.579461i	$-0.803263\pi$
$499$	−1.55873e7	+	1.79887e7i	−0.125450	+	0.144777i	0.689550	+	0.724238i	$0.257808\pi$
$500$	1.70363e8	+	7.78024e7i	1.36291	+	0.622419i
$501$	9.43828e7	−	1.65973e8i	0.750550	−	1.31985i
$502$	−9.16985e7	−	2.00792e8i	−0.724855	−	1.58721i
$503$	1.02032e8	−	1.46700e7i	0.801737	−	0.115272i	0.270747	−	0.962650i	$-0.412729\pi$
$503$	1.02032e8	−	1.46700e7i	0.801737	−	0.115272i	0.530990	+	0.847378i	$0.321820\pi$
$504$	−1.81505e8	+	1.07981e8i	−1.41774	+	0.843446i
$505$	1.65813e8			1.28749
$506$	−3.79712e7	+	1.85087e8i	−0.293091	+	1.42864i
$507$	1.89702e8	+	4.47098e7i	1.45562	+	0.343067i
$508$	−2.09024e8	−	1.34331e8i	−1.59443	−	1.02468i
$509$	−2.51088e8	+	3.61011e7i	−1.90403	+	0.273758i	−0.990971	−	0.134074i	$-0.957194\pi$
$509$	−2.51088e8	+	3.61011e7i	−1.90403	+	0.273758i	−0.913057	+	0.407832i	$0.866285\pi$
$510$	3.57953e8	−	7.14205e7i	2.69845	−	0.538409i
$511$	−9.69612e7	−	2.84704e7i	−0.726667	−	0.213369i
$512$	−3.78794e7	−	1.72990e7i	−0.282224	−	0.128887i
$513$	−9.72115e7	+	1.59291e7i	−0.720055	+	0.117988i
$514$	1.85265e7	−	1.28855e8i	0.136428	−	0.948879i
$515$	−6.18542e7	−	2.10656e8i	−0.452843	−	1.54224i
$516$	−4.50551e7	−	8.60091e7i	−0.327940	−	0.626030i
$517$	1.53851e7	−	9.88743e6i	0.111334	−	0.0715503i
$518$	−7.85748e7	−	1.22265e8i	−0.565320	−	0.879655i
$519$	9.06390e7	−	4.74804e7i	0.648355	−	0.339635i
$520$	−9.92815e8	+	2.91517e8i	−7.06087	+	2.07326i
$521$	−5.19140e6	−	746410.i	−0.0367089	−	0.00527794i	0.123936	−	0.992290i	$-0.460448\pi$
$521$	−5.19140e6	−	746410.i	−0.0367089	−	0.00527794i	−0.160645	+	0.987012i	$0.551357\pi$
$522$	1.86135e8	−	7.73569e7i	1.30863	−	0.543860i
$523$	−1.01790e7	+	2.22889e7i	−0.0711540	+	0.155806i	−0.941867	−	0.335986i	$-0.890931\pi$
$523$	−1.01790e7	+	2.22889e7i	−0.0711540	+	0.155806i	0.870713	+	0.491792i	$0.163658\pi$
$524$	−5.96712e7	+	2.03221e8i	−0.414735	+	1.41246i
$525$	2.12418e7	+	1.06462e8i	0.146795	+	0.735725i
$526$	3.05385e7	+	2.12400e8i	0.209841	+	1.45948i
$527$	9.90451e7	−	1.54117e8i	0.676707	−	1.05298i
$528$	8.14762e7	−	3.45701e8i	0.553515	−	2.34854i
$529$	−1.36078e8	−	5.82870e7i	−0.919224	−	0.393736i
$530$			2.67250e8i			1.79511i
$531$	6.72607e7	−	4.00149e7i	0.449240	−	0.267262i
$532$	−2.21369e7	−	1.53966e8i	−0.147022	−	1.02256i
$533$	−3.18712e8	+	1.45551e8i	−2.10483	+	0.961243i
$534$	−2.91872e8	−	1.65977e8i	−1.91676	−	1.08999i
$535$	2.20929e7	−	4.83768e7i	0.144275	−	0.315919i
$536$	−3.79580e8	−	3.28908e8i	−2.46495	−	2.13589i
$537$	−1.25604e8	−	4.93339e7i	−0.811115	−	0.318583i
$538$	−5.72250e7	+	1.68028e7i	−0.367485	+	0.107903i
$539$	6.39234e7	−	5.53899e7i	0.408219	−	0.353724i
$540$	7.73546e7	−	6.24789e8i	0.491253	−	3.96782i
$541$	3.10117e7	−	1.99300e7i	0.195854	−	0.125868i	−0.439038	−	0.898468i	$-0.644681\pi$
$541$	3.10117e7	−	1.99300e7i	0.195854	−	0.125868i	0.634893	+	0.772600i	$0.281044\pi$
$542$	−6.60855e7	+	5.72634e7i	−0.415057	+	0.359649i
$543$	2.08524e8	−	1.13003e7i	1.30244	−	0.0705816i
$544$	6.30948e7	−	4.38834e8i	0.391919	−	2.72586i
$545$	2.09824e8	+	1.81814e8i	1.29618	+	1.12315i
$546$	−2.10190e8	−	1.63082e8i	−1.29132	−	1.00191i
$547$	1.02597e8	+	3.01251e7i	0.626862	+	0.184063i	0.579708	−	0.814824i	$-0.303167\pi$
$547$	1.02597e8	+	3.01251e7i	0.626862	+	0.184063i	0.0471540	+	0.998888i	$0.484985\pi$
$548$	−4.76015e8	+	2.17389e8i	−2.89254	+	1.32098i
$549$	−5.41617e7	+	1.63372e8i	−0.327322	+	0.987327i
$550$	−2.80618e8	−	1.80342e8i	−1.68666	−	1.08395i
$551$			9.12372e7i			0.545403i
$552$	4.61351e8	+	2.13714e8i	2.74292	+	1.27062i
$553$	3.43970e7			0.203398
$554$	2.51692e8	−	3.91641e8i	1.48027	−	2.30334i
$555$	2.65204e8	+	2.35750e7i	1.55132	+	0.137903i
$556$	2.20534e7	+	4.82901e7i	0.128307	+	0.280953i
$557$	−8.18104e7	+	2.78620e8i	−0.473416	+	1.61231i	0.283623	+	0.958936i	$0.408464\pi$
$557$	−8.18104e7	+	2.78620e8i	−0.473416	+	1.61231i	−0.757039	+	0.653370i	$0.773355\pi$
$558$	−2.75088e8	−	3.40541e8i	−1.58332	−	1.96005i
$559$	4.92229e7	−	5.68063e7i	0.281794	−	0.325208i
$560$	4.58538e8	+	6.59279e7i	2.61103	+	0.375409i
$561$	−1.27725e8	+	6.92169e6i	−0.723418	+	0.0392034i
$562$	2.34774e8	+	2.70944e8i	1.32264	+	1.52641i
$563$	2.25660e7	+	3.51134e7i	0.126453	+	0.196765i	0.898708	−	0.438548i	$-0.144507\pi$
$563$	2.25660e7	+	3.51134e7i	0.126453	+	0.196765i	−0.772254	+	0.635314i	$0.780871\pi$
$564$	−2.66860e7	−	7.55032e7i	−0.148747	−	0.420851i
$565$	1.24382e8	+	1.43544e8i	0.689623	+	0.795868i
$566$	3.93294e7	+	1.33944e8i	0.216904	+	0.738709i
$567$	8.71951e7	−	4.78792e7i	0.478347	−	0.262662i
$568$	−1.37168e8	+	1.58300e8i	−0.748526	+	0.863845i
$569$	9.44990e7	+	4.31563e7i	0.512968	+	0.234265i	0.655044	−	0.755591i	$-0.272650\pi$
$569$	9.44990e7	+	4.31563e7i	0.512968	+	0.234265i	−0.142075	+	0.989856i	$0.545378\pi$
$570$	3.43184e8	+	1.95157e8i	1.85312	+	1.05380i
$571$	−9.02960e7	−	1.97721e8i	−0.485021	−	1.06205i	−0.981052	−	0.193743i	$-0.937937\pi$
$571$	−9.02960e7	−	1.97721e8i	−0.485021	−	1.06205i	0.496032	−	0.868304i	$-0.334790\pi$
$572$	5.84022e8	−	8.39697e7i	3.12062	−	0.448678i
$573$	−1.60362e8	+	1.54920e8i	−0.852389	+	0.823460i
$574$	2.86610e8			1.51550
$575$	1.82601e8	−	1.86982e8i	0.960506	−	0.983552i
$576$	−4.11560e8	−	2.05406e8i	−2.15360	−	1.07484i
$577$	1.13825e8	+	7.31507e7i	0.592528	+	0.380795i	0.802269	−	0.596962i	$-0.203626\pi$
$577$	1.13825e8	+	7.31507e7i	0.592528	+	0.380795i	−0.209741	+	0.977757i	$0.567262\pi$
$578$	4.09414e7	−	5.88648e6i	0.212021	−	0.0304840i
$579$	−1.63485e7	−	8.19370e7i	−0.0842250	−	0.422128i
$580$	−5.59473e8	−	1.64276e8i	−2.86744	−	0.841958i
$581$	8.74453e7	+	3.99349e7i	0.445870	+	0.203622i
$582$	1.47588e8	+	2.04417e8i	0.748658	+	1.03692i
$583$	1.33284e7	−	9.27014e7i	0.0672626	−	0.467822i
$584$	−2.35412e8	−	8.01741e8i	−1.18193	−	4.02528i
$585$	4.72085e8	−	1.21085e8i	2.35805	−	0.604816i
$586$	3.99694e8	−	2.56868e8i	1.98625	−	1.27649i
$587$	−4.22963e7	−	6.58143e7i	−0.209116	−	0.325392i	0.720813	−	0.693130i	$-0.243769\pi$
$587$	−4.22963e7	−	6.58143e7i	−0.209116	−	0.325392i	−0.929929	+	0.367738i	$0.880132\pi$
$588$	−1.71862e8	−	3.28080e8i	−0.845371	−	1.61379i
$589$	1.90122e8	−	5.58249e7i	0.930436	−	0.273201i
$590$	−3.10467e8	−	4.46384e7i	−1.51168	−	0.217346i
$591$	9.51259e7	+	1.31754e8i	0.460825	+	0.638264i
$592$	2.73229e8	−	5.98288e8i	1.31693	−	2.88367i
$593$	2.38548e7	−	8.12421e7i	0.114396	−	0.389598i	−0.882312	−	0.470664i	$-0.844014\pi$
$593$	2.38548e7	−	8.12421e7i	0.114396	−	0.389598i	0.996709	+	0.0810660i	$0.0258325\pi$
$594$	−8.03442e7	+	2.94909e8i	−0.383350	+	1.40711i
$595$	−2.37435e7	−	1.65140e8i	−0.112718	−	0.783972i
$596$	−4.29373e8	+	6.68118e8i	−2.02813	+	3.15583i
$597$	−3.95469e8	−	9.32058e7i	−1.85861	−	0.438046i
$598$	−3.81151e7	+	6.39335e8i	−0.178235	+	2.98968i
$599$			5.83021e7i			0.271271i	0.990759	+	0.135636i	$0.0433077\pi$
$599$			5.83021e7i			0.271271i	−0.990759	+	0.135636i	$0.956692\pi$
$600$	−6.45595e8	+	6.23684e8i	−2.98887	+	2.88743i
$601$	−5.20102e7	−	3.61739e8i	−0.239588	−	1.66637i	−0.654162	−	0.756355i	$-0.726978\pi$
$601$	−5.20102e7	−	3.61739e8i	−0.239588	−	1.66637i	0.414574	−	0.910016i	$-0.363931\pi$
$602$	−5.59298e7	+	2.55423e7i	−0.256362	+	0.117077i
$603$	1.73332e8	+	1.60997e8i	0.790545	+	0.734287i
$604$	−2.22237e8	+	4.86632e8i	−1.00857	+	2.20846i
$605$	−1.05295e8	−	9.12387e7i	−0.475490	−	0.412015i
$606$	−1.28871e8	+	3.28106e8i	−0.579079	+	1.47434i
$607$	−1.36529e8	+	4.00886e7i	−0.610464	+	0.179248i	−0.572329	−	0.820024i	$-0.693960\pi$
$607$	−1.36529e8	+	4.00886e7i	−0.610464	+	0.179248i	−0.0381350	+	0.999273i	$0.512142\pi$
$608$	3.62400e8	−	3.14021e8i	1.61242	−	1.39717i
$609$	−3.07026e7	−	8.68673e7i	−0.135933	−	0.384596i
$610$	5.80292e8	−	3.72931e8i	2.55657	−	1.64301i
$611$	4.68515e7	−	4.05971e7i	0.205400	−	0.177980i
$612$	−9.87983e7	+	5.51319e8i	−0.431018	+	2.40519i
$613$	−2.81616e7	+	1.95869e8i	−0.122258	+	0.850322i	0.832731	+	0.553678i	$0.186776\pi$
$613$	−2.81616e7	+	1.95869e8i	−0.122258	+	0.850322i	−0.954988	+	0.296643i	$0.904133\pi$
$614$	−1.78299e8	−	1.54497e8i	−0.770273	−	0.667445i
$615$	−3.21863e8	+	4.14836e8i	−1.38371	+	1.78341i
$616$	−2.84603e8	−	8.35669e7i	−1.21758	−	0.357513i
$617$	3.61768e8	−	1.65214e8i	1.54019	−	0.703381i	0.548999	−	0.835823i	$-0.315009\pi$
$617$	3.61768e8	−	1.65214e8i	1.54019	−	0.703381i	0.991191	+	0.132442i	$0.0422818\pi$
$618$	4.64915e8	+	4.13281e7i	1.96974	+	0.175097i
$619$	2.28278e8	+	1.46706e8i	0.962482	+	0.618550i	0.924684	−	0.380736i	$-0.124329\pi$
$619$	2.28278e8	+	1.46706e8i	0.962482	+	0.618550i	0.0377982	+	0.999285i	$0.487966\pi$
$620$			1.26636e9i			5.31350i
$621$	−2.13697e8	−	1.08101e8i	−0.892324	−	0.451395i
$622$	6.95005e7			0.288813
$623$	−8.29725e7	+	1.29108e8i	−0.343139	+	0.533935i
$624$	1.06604e8	−	1.19923e9i	0.438752	−	4.93569i
$625$	−4.91690e7	−	1.07665e8i	−0.201396	−	0.440996i
$626$	1.03392e8	−	3.52122e8i	0.421468	−	1.43539i
$627$	−1.09308e8	−	8.48097e7i	−0.443454	−	0.344067i
$628$	−3.76410e8	+	4.34400e8i	−1.51979	+	1.75393i
$629$	−2.34464e8	−	3.37109e7i	−0.942160	−	0.135462i
$630$	−3.92420e8	−	7.03231e7i	−1.56939	−	0.281239i
$631$	4.48265e7	+	5.17326e7i	0.178421	+	0.205909i	0.837915	−	0.545801i	$-0.183775\pi$
$631$	4.48265e7	+	5.17326e7i	0.178421	+	0.205909i	−0.659493	+	0.751710i	$0.729229\pi$
$632$	1.53768e8	+	2.39268e8i	0.609137	+	0.947836i
$633$	2.92261e8	−	1.03298e8i	1.15229	−	0.407267i
$634$	4.09245e8	+	4.72294e8i	1.60589	+	1.85330i
$635$	−8.12081e7	−	2.76569e8i	−0.317160	−	1.08015i
$636$	−3.81705e8	−	1.49923e8i	−1.48374	−	0.582770i
$637$	1.87760e8	−	2.16686e8i	0.726414	−	0.838326i
$638$	2.57514e8	+	1.17603e8i	0.991607	+	0.452852i
$639$	6.71422e7	−	7.22864e7i	0.257331	−	0.277047i
$640$	2.75096e8	+	6.02377e8i	1.04941	+	2.29789i
$641$	−3.14819e6	+	452641.i	−0.0119533	+	0.00171862i	−0.148289	−	0.988944i	$-0.547377\pi$
$641$	−3.14819e6	+	452641.i	−0.0119533	+	0.00171862i	0.136336	+	0.990663i	$0.456467\pi$
$642$	7.85561e7	+	8.13159e7i	0.296876	+	0.307306i
$643$	−3.47527e8			−1.30724			−0.653620	−	0.756823i	$-0.726750\pi$
$643$	−3.47527e8			−1.30724			−0.653620	+	0.756823i	$0.726750\pi$
$644$	1.77284e8	−	3.34025e8i	0.663762	−	1.25061i
$645$	2.58395e7	−	1.09636e8i	0.0962953	−	0.408577i
$646$	−2.95479e8	−	1.89893e8i	−1.09605	−	0.704386i
$647$	5.03149e8	−	7.23420e7i	1.85774	−	0.267102i	0.879699	−	0.475531i	$-0.157744\pi$
$647$	5.03149e8	−	7.23420e7i	1.85774	−	0.267102i	0.978038	+	0.208429i	$0.0668350\pi$
$648$	7.22847e8	+	3.92496e8i	2.65657	+	1.44248i
$649$	1.05466e8	+	3.09676e7i	0.385814	+	0.113285i
$650$	−1.02855e9	−	4.69724e8i	−3.74529	−	1.71042i
$651$	−1.62230e8	+	1.17130e8i	−0.588015	+	0.424546i
$652$	−8.20429e7	+	5.70621e8i	−0.296004	+	2.05876i
$653$	−1.87408e6	−	6.38253e6i	−0.00673052	−	0.0229221i	0.956059	−	0.293173i	$-0.0947114\pi$
$653$	−1.87408e6	−	6.38253e6i	−0.00673052	−	0.0229221i	−0.962790	+	0.270251i	$0.912893\pi$
$654$	−5.22847e8	+	2.73889e8i	−1.86914	+	0.979131i
$655$	−2.06704e8	+	1.32840e8i	−0.735570	+	0.472722i
$656$	7.01246e8	+	1.09116e9i	2.48404	+	3.86524i
$657$	9.77816e7	+	3.81229e8i	0.344795	+	1.34428i
$658$	−4.86572e7	+	1.42870e7i	−0.170793	+	0.0501493i
$659$	2.16102e8	+	3.10708e7i	0.755098	+	0.108567i	0.509104	−	0.860705i	$-0.329977\pi$
$659$	2.16102e8	+	3.10708e7i	0.755098	+	0.108567i	0.245994	+	0.969271i	$0.420886\pi$
$660$	7.16872e8	−	5.17580e8i	2.49350	−	1.80030i
$661$	1.08158e8	−	2.36832e8i	0.374501	−	0.820043i	−0.624730	−	0.780841i	$-0.714791\pi$
$661$	1.08158e8	−	2.36832e8i	0.374501	−	0.820043i	0.999231	−	0.0392022i	$-0.0124817\pi$
$662$	−1.42768e8	+	4.86224e8i	−0.492105	+	1.67595i
$663$	−4.25215e8	+	8.48410e7i	−1.45904	+	0.291115i
$664$	1.13125e8	+	7.86799e8i	0.386414	+	2.68757i
$665$	9.75595e7	−	1.51806e8i	0.331745	−	0.516206i
$666$	−2.52769e8	+	5.06458e8i	−0.855659	+	1.71443i
$667$	−1.30810e8	+	1.79129e8i	−0.440822	+	0.603654i
$668$		−	1.17420e9i		−	3.93924i
$669$	−2.87732e8	−	2.97840e8i	−0.960969	−	0.994730i
$670$	−1.34928e8	−	9.38446e8i	−0.448620	−	3.12022i
$671$	−2.19886e8	+	1.00418e8i	−0.727829	+	0.332388i
$672$	−2.39370e8	+	4.20934e8i	−0.788791	+	1.38709i
$673$	−3.51490e7	+	7.69656e7i	−0.115310	+	0.252494i	−0.958484	−	0.285147i	$-0.907957\pi$
$673$	−3.51490e7	+	7.69656e7i	−0.115310	+	0.252494i	0.843173	+	0.537642i	$0.180685\pi$
$674$	4.04851e8	+	3.50805e8i	1.32226	+	1.14574i
$675$	3.14039e8	−	2.83090e8i	1.02111	−	0.920479i
$676$	1.15004e9	−	3.37683e8i	3.72284	−	1.09312i
$677$	−5.59989e7	+	4.85233e7i	−0.180474	+	0.156381i	−0.740413	−	0.672152i	$-0.765370\pi$
$677$	−5.59989e7	+	4.85233e7i	−0.180474	+	0.156381i	0.559939	+	0.828534i	$0.310824\pi$
$678$	−3.80713e8	+	1.34560e8i	−1.22154	+	0.431746i
$679$	9.69481e7	−	6.23048e7i	0.309692	−	0.199027i
$680$	1.04258e9	−	9.03399e8i	3.31575	−	2.87311i
$681$	−8.44852e6	−	1.55900e8i	−0.0267509	−	0.493633i
$682$	8.74993e7	−	6.08571e8i	0.275836	−	1.91848i
$683$	−1.00394e8	−	8.69919e7i	−0.315098	−	0.273034i	0.482924	−	0.875662i	$-0.339575\pi$
$683$	−1.00394e8	−	8.69919e7i	−0.315098	−	0.273034i	−0.798022	+	0.602628i	$0.794120\pi$
$684$	−4.71257e8	+	3.80680e8i	−1.47262	+	1.18957i
$685$	−5.82492e8	−	1.71035e8i	−1.81225	−	0.532125i
$686$	−5.17167e8	+	2.36182e8i	−1.60199	+	0.731602i
$687$	−9.44143e6	+	1.06210e8i	−0.0291184	+	0.327564i
$688$	−2.34085e8	−	1.50437e8i	−0.718801	−	0.461945i
$689$		−	3.17469e8i		−	0.970606i
$690$	3.93982e8	+	8.75192e8i	1.19930	+	2.66413i
$691$	−3.26749e8			−0.990329			−0.495165	−	0.868799i	$-0.664892\pi$
$691$	−3.26749e8			−0.990329			−0.495165	+	0.868799i	$0.664892\pi$
$692$	3.40205e8	−	5.29369e8i	1.02665	−	1.59750i
$693$	1.32612e8	+	4.39641e7i	0.398459	+	0.132099i
$694$	8.79584e7	+	1.92602e8i	0.263147	+	0.576212i
$695$	−1.73509e7	+	5.90919e7i	−0.0516855	+	0.176025i
$696$	4.67002e8	−	6.01900e8i	1.38513	−	1.78524i
$697$	3.05904e8	−	3.53033e8i	0.903415	−	1.04260i
$698$	1.23356e8	+	1.77359e7i	0.362739	+	0.0521540i
$699$	3.20320e6	+	5.91085e7i	0.00937892	+	0.173069i
$700$	4.37201e8	+	5.04557e8i	1.27464	+	1.47101i
$701$	1.81196e8	+	2.81947e8i	0.526012	+	0.818490i	0.998007	−	0.0631110i	$-0.0201022\pi$
$701$	1.81196e8	+	2.81947e8i	0.526012	+	0.818490i	−0.471995	+	0.881601i	$0.656466\pi$
$702$	−1.27308e8	+	1.02826e9i	−0.367998	+	2.97230i
$703$	−1.67778e8	−	1.93626e8i	−0.482913	−	0.557312i
$704$	−1.82002e8	−	6.19843e8i	−0.521626	−	1.77649i
$705$	3.39631e7	−	8.64702e7i	0.0969259	−	0.246774i
$706$	−3.68266e8	+	4.25002e8i	−1.04652	+	1.20775i
$707$	1.46564e8	+	6.69333e7i	0.414732	+	0.189402i
$708$	2.37923e8	−	4.18389e8i	0.670403	−	1.17891i
$709$	1.76980e8	+	3.87533e8i	0.496577	+	1.08735i	0.977567	+	0.210625i	$0.0675500\pi$
$709$	1.76980e8	+	3.87533e8i	0.496577	+	1.08735i	−0.480990	+	0.876726i	$0.659723\pi$
$710$	−3.91370e8	+	5.62704e7i	−1.09348	+	0.157219i
$711$	−6.84933e7	−	1.15130e8i	−0.190563	−	0.320317i
$712$	−1.26900e9			−3.51578
$713$	4.53311e8	+	1.62982e8i	1.25063	+	0.449646i
$714$	3.45228e8	+	8.13649e7i	0.948444	+	0.223533i
$715$	5.75828e8	+	3.70062e8i	1.57534	+	1.01241i
$716$	−8.21443e8	+	1.18106e8i	−2.23789	+	0.321760i
$717$	−3.44551e8	+	6.87464e7i	−0.934750	+	0.186506i
$718$	−3.08192e6	−	904934.i	−0.00832623	−	0.00244480i
$719$	9.49274e7	+	4.33519e7i	0.255391	+	0.116633i	0.538997	−	0.842308i	$-0.318804\pi$
$719$	9.49274e7	+	4.33519e7i	0.255391	+	0.116633i	−0.283606	+	0.958941i	$0.591531\pi$
$720$	−6.92401e8	−	1.66605e9i	−1.85507	−	4.46365i
$721$	3.03616e7	−	2.11170e8i	0.0810064	−	0.563412i
$722$	9.40025e7	+	3.20143e8i	0.249763	+	0.850614i
$723$	2.41530e8	+	4.61075e8i	0.639081	+	1.21999i
$724$	1.08039e9	−	6.94327e8i	2.84686	−	1.82957i
$725$	−2.11712e8	−	3.29430e8i	−0.555561	−	0.864470i
$726$	2.62377e8	−	1.37444e8i	0.685672	−	0.359183i
$727$	−2.47121e8	+	7.25612e7i	−0.643141	+	0.188843i	−0.587009	−	0.809580i	$-0.699695\pi$
$727$	−2.47121e8	+	7.25612e7i	−0.643141	+	0.188843i	−0.0561315	+	0.998423i	$0.517877\pi$
$728$	−9.95236e8	−	1.43093e8i	−2.57948	−	0.370873i
$729$	−3.33884e8	−	1.96510e8i	−0.861812	−	0.507227i
$730$	6.55243e8	−	1.43478e9i	1.68435	−	3.68822i
$731$	−2.82332e7	+	9.61533e7i	−0.0722782	+	0.246157i
$732$	2.07111e8	+	1.03802e9i	0.528044	+	2.64651i
$733$	−6.44138e7	−	4.48008e8i	−0.163556	−	1.13756i	−0.891862	−	0.452307i	$-0.850601\pi$
$733$	−6.44138e7	−	4.48008e8i	−0.163556	−	1.13756i	0.728306	−	0.685252i	$-0.240308\pi$
$734$	−7.87967e8	+	1.22610e9i	−1.99260	+	3.10055i
$735$	9.85642e7	−	4.18205e8i	0.248232	−	1.05324i
$736$	1.16173e9	−	9.69424e7i	2.91389	−	0.243153i
$737$			3.32249e8i			0.829969i
$738$	−5.70715e8	−	9.59311e8i	−1.41987	−	2.38666i
$739$	46728.6	+	325005.i	0.000115784	+	0.000805297i	0.989879	−	0.141912i	$-0.0453251\pi$
$739$	46728.6	+	325005.i	0.000115784	+	0.000805297i	−0.989763	+	0.142717i	$0.954416\pi$
$740$	1.48942e9	−	6.80195e8i	3.67555	−	1.67857i
$741$	−4.07672e8	−	2.31828e8i	−1.00197	−	0.569786i
$742$	−1.07880e8	+	2.36225e8i	−0.264077	+	0.578248i
$743$	4.10975e6	+	3.56112e6i	0.0100196	+	0.00868201i	0.659856	−	0.751392i	$-0.270617\pi$
$743$	4.10975e6	+	3.56112e6i	0.0100196	+	0.00868201i	−0.649837	+	0.760074i	$0.725163\pi$
$744$	−1.53999e9	−	6.04867e8i	−3.73939	−	1.46873i
$745$	−8.84018e8	+	2.59571e8i	−2.13792	+	0.627751i
$746$	−2.26764e8	+	1.96492e8i	−0.546207	+	0.473291i
$747$	−4.04601e7	−	3.72208e8i	−0.0970657	−	0.892943i
$748$	−6.61764e8	+	4.25290e8i	−1.58124	+	1.01620i
$749$	3.90564e7	−	3.38425e7i	0.0929494	−	0.0805411i
$750$	−4.61231e8	+	2.49950e7i	−1.09329	+	0.0592474i
$751$	−5.31364e6	+	3.69572e7i	−0.0125451	+	0.0872528i	−0.995132	−	0.0985502i	$-0.968580\pi$
$751$	−5.31364e6	+	3.69572e7i	−0.0125451	+	0.0872528i	0.982587	+	0.185803i	$0.0594886\pi$
$752$	−1.73441e8	−	1.50288e8i	−0.407849	−	0.353403i
$753$	3.10461e8	+	2.40881e8i	0.727147	+	0.564179i
$754$	9.20766e8	+	2.70361e8i	2.14800	+	0.630711i
$755$	−5.64539e8	+	2.57816e8i	−1.31176	+	0.599059i
$756$	3.20582e8	−	5.21032e8i	0.741948	−	1.20586i
$757$	3.85657e8	+	2.47846e8i	0.889023	+	0.571341i	0.903516	−	0.428554i	$-0.140977\pi$
$757$	3.85657e8	+	2.47846e8i	0.889023	+	0.571341i	−0.0144927	+	0.999895i	$0.504613\pi$
$758$		−	1.42132e9i		−	3.26351i
$759$	−9.30128e7	−	3.23228e8i	−0.212725	−	0.739237i
$760$	1.49210e9			3.39904
$761$	−3.60892e8	+	5.61559e8i	−0.818886	+	1.27421i	0.139924	+	0.990162i	$0.455314\pi$
$761$	−3.60892e8	+	5.61559e8i	−0.818886	+	1.27421i	−0.958810	+	0.284049i	$0.908322\pi$
$762$	6.10385e8	+	5.42594e7i	1.37955	+	0.122634i
$763$	1.12074e8	+	2.45407e8i	0.252307	+	0.552475i
$764$	−3.86320e8	+	1.31569e9i	−0.866298	+	2.95034i
$765$	−5.05458e8	+	4.08307e8i	−1.12902	+	0.912015i
$766$	−5.77499e8	+	6.66470e8i	−1.28489	+	1.48284i
$767$	3.68806e8	+	5.30263e7i	0.817358	+	0.117518i
$768$	−3.17075e8	+	1.71829e7i	−0.699968	+	0.0379326i
$769$	−3.78879e8	−	4.37250e8i	−0.833147	−	0.961503i	0.166552	−	0.986033i	$-0.446737\pi$
$769$	−3.78879e8	−	4.37250e8i	−0.833147	−	0.961503i	−0.999699	+	0.0245298i	$0.992191\pi$
$770$	−3.02715e8	−	4.71034e8i	−0.663073	−	1.03176i
$771$	7.72250e7	+	2.18494e8i	0.168498	+	0.476734i
$772$	−3.36487e8	−	3.88326e8i	−0.731334	−	0.844005i
$773$	−6.65251e7	−	2.26564e8i	−0.144028	−	0.490514i	0.855604	−	0.517631i	$-0.173186\pi$
$773$	−6.65251e7	−	2.26564e8i	−0.144028	−	0.490514i	−0.999632	+	0.0271161i	$0.991368\pi$
$774$	1.96863e8	+	1.36341e8i	0.424562	+	0.294038i
$775$	−5.56935e8	+	6.42737e8i	−1.19646	+	1.38079i
$776$	8.66792e8	+	3.95850e8i	1.85494	+	0.847122i
$777$	2.24900e8	+	1.27893e8i	0.479432	+	0.272636i
$778$	−3.95572e8	−	8.66183e8i	−0.840015	−	1.83938i
$779$	5.00104e8	−	7.19041e7i	1.05791	−	0.152104i
$780$	2.15562e9	−	2.08246e9i	4.54242	−	4.38825i
$781$	1.38561e8			0.290863
$782$	−3.07867e8	−	7.96461e8i	−0.643788	−	1.66550i
$783$	−2.29616e8	+	2.75739e8i	−0.478318	+	0.574399i
$784$	−8.92913e8	−	5.73840e8i	−1.85294	−	1.19081i
$785$	−6.60028e8	+	9.48977e7i	−1.36444	+	0.196176i
$786$	−1.02210e8	−	5.12266e8i	−0.210487	−	1.05494i
$787$	8.23070e7	+	2.41675e7i	0.168854	+	0.0495801i	0.365067	−	0.930981i	$-0.381046\pi$
$787$	8.23070e7	+	2.41675e7i	0.168854	+	0.0495801i	−0.196213	+	0.980561i	$0.562864\pi$
$788$	9.09066e8	+	4.15156e8i	1.85788	+	0.848463i
$789$	−2.23607e8	−	3.09706e8i	−0.455255	−	0.630549i
$790$	−7.64074e7	+	5.31425e8i	−0.154972	+	1.07786i
$791$	5.19982e7	+	1.77090e8i	0.105065	+	0.357819i
$792$	2.87011e8	+	1.11899e9i	0.577727	+	2.25244i
$793$	−6.89334e8	+	4.43008e8i	−1.38233	+	0.888366i
$794$	−4.48174e7	−	6.97373e7i	−0.0895334	−	0.139317i
$795$	−2.20760e8	−	4.21425e8i	−0.439358	−	0.838724i
$796$	−2.39748e9	+	7.03964e8i	−4.75353	+	1.39576i
$797$	7.67210e8	+	1.10308e8i	1.51544	+	0.217888i	0.849290	−	0.527927i	$-0.177031\pi$
$797$	7.67210e8	+	1.10308e8i	1.51544	+	0.217888i	0.666153	+	0.745815i	$0.267940\pi$
$798$	2.24566e8	+	3.11033e8i	0.441911	+	0.612066i
$799$	−3.43346e7	+	7.51824e7i	−0.0673119	+	0.147393i
$800$	−5.79845e8	+	1.97477e9i	−1.13251	+	3.85697i
$801$	5.97355e8	+	2.06299e7i	1.16234	+	0.0401421i
$802$	−5.19504e7	−	3.61323e8i	−0.100708	−	0.700442i
$803$	−2.98841e8	+	4.65006e8i	−0.577157	+	0.898073i
$804$	1.41605e9	+	3.33740e8i	2.72464	+	0.642155i
$805$	4.09191e8	−	1.58170e8i	0.784401	−	0.303206i
$806$		−	2.08414e9i		−	3.98035i
$807$	7.63580e7	−	7.37665e7i	0.145289	−	0.140358i
$808$	1.89604e8	+	1.31872e9i	0.359429	+	2.49988i
$809$	4.49160e7	−	2.05124e7i	0.0848311	−	0.0387411i	−0.372548	−	0.928013i	$-0.621516\pi$
$809$	4.49160e7	−	2.05124e7i	0.0848311	−	0.0387411i	0.457379	+	0.889272i	$0.348788\pi$
$810$	5.46031e8	+	1.45350e9i	1.02745	+	2.73501i
$811$	4.04547e8	−	8.85835e8i	0.758414	−	1.66070i	0.00778720	−	0.999970i	$-0.497521\pi$
$811$	4.04547e8	−	8.85835e8i	0.758414	−	1.66070i	0.750627	−	0.660726i	$-0.229751\pi$
$812$	−4.28211e8	−	3.71047e8i	−0.799815	−	0.693044i
$813$	5.69079e7	−	1.44888e8i	0.105901	−	0.269625i
$814$	−7.62767e8	+	2.23969e8i	−1.41423	+	0.415254i
$815$	−5.05431e8	+	4.37959e8i	−0.933661	+	0.809022i
$816$	5.34900e8	+	1.51340e9i	0.984469	+	2.78537i
$817$	−9.11835e7	+	5.86001e7i	−0.167205	+	0.107456i
$818$	1.13984e9	−	9.87675e8i	2.08249	−	1.80449i
$819$	4.66159e8	+	8.35374e7i	0.848560	+	0.152065i
$820$	−4.59535e8	+	3.19614e9i	−0.833446	+	5.79674i
$821$	−1.95283e8	−	1.69214e8i	−0.352887	−	0.305779i	0.460320	−	0.887753i	$-0.347735\pi$
$821$	−1.95283e8	−	1.69214e8i	−0.352887	−	0.305779i	−0.813207	+	0.581975i	$0.802280\pi$
$822$	7.91159e8	−	1.01969e9i	1.42445	−	1.83592i
$823$	6.53019e7	+	1.91744e7i	0.117146	+	0.0343971i	0.339780	−	0.940505i	$-0.389647\pi$
$823$	6.53019e7	+	1.91744e7i	0.117146	+	0.0343971i	−0.222634	+	0.974902i	$0.571466\pi$
$824$	1.60464e9	−	7.32813e8i	2.86811	−	1.30982i
$825$	5.91475e8	+	5.25785e7i	1.05336	+	0.0936367i
$826$	−2.56406e8	−	1.64782e8i	−0.454975	−	0.292395i
$827$		−	8.23512e7i		−	0.145597i	−0.997347	−	0.0727987i	$-0.976807\pi$
$827$		−	8.23512e7i		−	0.145597i	0.997347	−	0.0727987i	$-0.0231931\pi$
$828$	−1.47103e9	+	7.17425e7i	−2.59137	+	0.126382i
$829$	−4.37336e8			−0.767630			−0.383815	−	0.923410i	$-0.625390\pi$
$829$	−4.37336e8			−0.767630			−0.383815	+	0.923410i	$0.625390\pi$
$830$	−8.11229e8	+	1.26230e9i	−1.41876	+	2.20763i
$831$	−7.33805e7	+	8.25485e8i	−0.127873	+	1.43849i
$832$	−9.09691e8	−	1.99194e9i	−1.57951	−	3.45865i
$833$	−1.07695e8	+	3.66775e8i	−0.186320	+	0.634548i
$834$	−1.03444e8	−	8.02604e7i	−0.178324	−	0.138358i
$835$	8.92039e8	−	1.02947e9i	1.53223	−	1.76829i
$836$	−8.42170e8	−	1.21086e8i	−1.44139	−	0.207240i
$837$	7.15086e8	+	3.09763e8i	1.21950	+	0.528267i
$838$	−7.66017e8	−	8.84030e8i	−1.30169	−	1.50223i
$839$	−4.98595e8	−	7.75828e8i	−0.844232	−	1.31365i	−0.947747	−	0.319022i	$-0.896646\pi$
$839$	−4.98595e8	−	7.75828e8i	−0.844232	−	1.31365i	0.103516	−	0.994628i	$-0.466991\pi$
$840$	−1.42063e9	+	5.02112e8i	−2.39687	+	0.847155i
$841$	−1.71889e8	−	1.98371e8i	−0.288975	−	0.333495i
$842$	−7.37322e7	−	2.51109e8i	−0.123515	−	0.420655i
$843$	−5.94026e8	−	2.33317e8i	−0.991568	−	0.389460i
$844$	1.24837e9	−	1.44070e9i	2.07642	−	2.39632i
$845$	1.26483e9	+	5.77628e8i	2.09634	+	0.957366i
$846$	1.44709e8	+	1.34411e8i	0.238992	+	0.221985i
$847$	−5.62412e7	−	1.23151e8i	−0.0925560	−	0.202669i
$848$	−1.16329e9	+	1.67255e8i	−1.90765	+	0.274279i
$849$	−1.72662e8	−	1.78728e8i	−0.282145	−	0.292057i
$850$	1.50752e9			2.45475
$851$	−5.17953e7	−	6.20702e8i	−0.0840429	−	1.00715i
$852$	1.39183e8	−	5.90548e8i	0.225044	−	0.954853i
$853$	5.22843e8	+	3.36011e8i	0.842411	+	0.541385i	0.889199	−	0.457520i	$-0.151262\pi$
$853$	5.22843e8	+	3.36011e8i	0.842411	+	0.541385i	−0.0467884	+	0.998905i	$0.514899\pi$
$854$	6.63467e8	−	9.53921e7i	1.06523	−	0.153158i
$855$	−7.02373e8	−	2.42567e7i	−1.12375	−	0.0388092i
$856$	4.10008e8	+	1.20389e8i	0.653689	+	0.191940i
$857$	−8.39862e8	−	3.83552e8i	−1.33434	−	0.609371i	−0.384792	−	0.923003i	$-0.625727\pi$
$857$	−8.39862e8	−	3.83552e8i	−1.33434	−	0.609371i	−0.949545	+	0.313632i	$0.898454\pi$
$858$	−1.17981e9	+	8.51820e8i	−1.86788	+	1.34861i
$859$	1.12473e7	−	7.82269e7i	0.0177448	−	0.123417i	−0.979024	−	0.203747i	$-0.934688\pi$
$859$	1.12473e7	−	7.82269e7i	0.0177448	−	0.123417i	0.996768	+	0.0803293i	$0.0255972\pi$
$860$	−1.95160e8	−	6.64655e8i	−0.306829	−	1.04496i
$861$	−4.51955e8	+	2.36752e8i	−0.708085	+	0.370924i
$862$	2.14125e8	−	1.37610e8i	0.334307	−	0.214846i
$863$	4.54515e7	+	7.07239e7i	0.0707157	+	0.110036i	0.874810	−	0.484465i	$-0.160986\pi$
$863$	4.54515e7	+	7.07239e7i	0.0707157	+	0.110036i	−0.804095	+	0.594501i	$0.797350\pi$
$864$	1.88555e9	−	3.69941e7i	2.92346	−	0.0573576i
$865$	7.00434e8	−	2.05666e8i	1.08223	−	0.317771i
$866$	1.28641e9	+	1.84958e8i	1.98073	+	0.284786i
$867$	−5.96978e7	+	4.31017e7i	−0.0916011	+	0.0661358i
$868$	−5.11188e8	+	1.11935e9i	−0.781666	+	1.71161i
$869$	5.30071e7	−	1.80525e8i	0.0807745	−	0.275093i
$870$	1.41028e9	−	2.81385e8i	2.14164	−	0.427311i
$871$	1.60282e8	+	1.11479e9i	0.242567	+	1.68709i
$872$	−1.20605e9	+	1.87665e9i	−1.81893	+	2.83031i
$873$	−4.01588e8	−	2.00429e8i	−0.603585	−	0.301244i
$874$	3.12475e8	−	8.69103e8i	0.468038	−	1.30178i
$875$			2.11128e8i			0.315154i
$876$	1.68167e9	+	1.74075e9i	2.50167	+	2.58955i
$877$	9.49279e7	+	6.60238e8i	0.140733	+	0.978817i	0.930730	+	0.365707i	$0.119173\pi$
$877$	9.49279e7	+	6.60238e8i	0.140733	+	0.978817i	−0.789997	+	0.613110i	$0.789918\pi$
$878$	−1.66384e9	+	7.59851e8i	−2.45826	+	1.12265i
$879$	−4.18092e8	+	7.35218e8i	−0.615609	+	1.08255i
$880$	1.05263e9	−	2.30494e9i	1.54464	−	3.38230i
$881$	8.73145e8	+	7.56584e8i	1.27690	+	1.10644i	0.988863	+	0.148826i	$0.0475496\pi$
$881$	8.73145e8	+	7.56584e8i	1.27690	+	1.10644i	0.288041	+	0.957618i	$0.406996\pi$
$882$	7.50929e8	+	5.20069e8i	1.09444	+	0.757976i
$883$	1.26605e9	−	3.71745e8i	1.83894	−	0.539961i	0.838949	−	0.544210i	$-0.183171\pi$
$883$	1.26605e9	−	3.71745e8i	1.83894	−	0.539961i	0.999991	+	0.00424908i	$0.00135253\pi$
$884$	−2.01524e9	+	1.74621e9i	−2.91722	+	2.52779i
$885$	5.26447e8	−	1.86069e8i	0.759494	−	0.268438i
$886$	−1.29906e9	+	8.34856e8i	−1.86779	+	1.20036i
$887$	−2.19684e8	+	1.90358e8i	−0.314795	+	0.272772i	−0.797899	−	0.602792i	$-0.794055\pi$
$887$	−2.19684e8	+	1.90358e8i	−0.314795	+	0.272772i	0.483103	+	0.875563i	$0.339510\pi$
$888$	1.15762e8	+	2.13615e9i	0.165321	+	3.05065i
$889$	3.98616e7	−	2.77244e8i	0.0567348	−	0.394599i
$890$	−1.81037e9	−	1.56869e9i	−2.56801	−	2.22520i
$891$	−1.16913e8	−	5.31408e8i	−0.165284	−	0.751269i
$892$	−2.44362e9	−	7.17512e8i	−3.44302	−	1.01096i
$893$	−8.13172e7	+	3.71363e7i	−0.114190	+	0.0521488i
$894$	1.73433e8	−	1.95102e9i	0.242728	−	2.73054i
$895$	−8.09918e8	−	5.20503e8i	−1.12972	−	0.726029i
$896$			6.43495e8i			0.894584i
$897$	−4.68014e8	−	1.03965e9i	−0.648458	−	1.44049i
$898$	9.88525e8			1.36508
$899$	3.90222e8	−	6.07197e8i	0.537072	−	0.835700i
$900$	8.18219e8	−	2.46805e9i	1.12238	−	3.38553i
$901$	1.75828e8	+	3.85009e8i	0.240388	+	0.526376i
$902$	4.41677e8	−	1.50421e9i	0.601845	−	2.04970i
$903$	6.70964e7	−	8.64779e7i	0.0911247	−	0.117447i
$904$	−9.99393e8	+	1.15336e9i	−1.35279	+	1.56121i
$905$	1.47471e9	+	2.12031e8i	1.98957	+	0.286057i
$906$	−7.13965e7	−	1.31747e9i	−0.0960046	−	1.77157i
$907$	3.89270e8	+	4.49242e8i	0.521710	+	0.602086i	0.954058	−	0.299621i	$-0.0968603\pi$
$907$	3.89270e8	+	4.49242e8i	0.521710	+	0.602086i	−0.432348	+	0.901707i	$0.642315\pi$
$908$	−5.19103e8	−	8.07740e8i	−0.693419	−	1.07898i
$909$	−6.78136e7	−	6.23842e8i	−0.0902870	−	0.830584i
$910$	−1.24293e9	−	1.43441e9i	−1.64938	−	1.90349i
$911$	1.37568e8	+	4.68513e8i	0.181954	+	0.619679i	0.999066	+	0.0432001i	$0.0137553\pi$
$911$	1.37568e8	+	4.68513e8i	0.181954	+	0.619679i	−0.817112	+	0.576478i	$0.804427\pi$
$912$	−6.34700e8	+	1.61595e9i	−0.836727	+	2.13031i
$913$	3.44346e8	−	3.97397e8i	0.452463	−	0.522170i
$914$	−2.83396e8	−	1.29423e8i	−0.371155	−	0.169501i
$915$	−6.07003e8	+	1.06742e9i	−0.792369	+	1.39339i
$916$	2.72408e8	+	5.96491e8i	0.354433	+	0.776099i
$917$	−2.36331e8	+	3.39793e7i	−0.306487	+	0.0440662i
$918$	−4.15102e8	−	1.31753e9i	−0.536571	−	1.70307i
$919$	8.06144e8			1.03864			0.519322	−	0.854579i	$-0.326185\pi$
$919$	8.06144e8			1.03864			0.519322	+	0.854579i	$0.326185\pi$
$920$	2.92948e9	+	2.13927e9i	3.76208	+	2.74728i
$921$	4.08781e8	+	9.63432e7i	0.523253	+	0.123322i
$922$	−3.07662e8	−	1.97722e8i	−0.392537	−	0.252268i
$923$	4.64911e8	−	6.68442e7i	0.591242	−	0.0850077i
$924$	8.42581e8	−	1.68116e8i	1.06806	−	0.213105i
$925$	1.05510e9	+	3.09805e8i	1.33312	+	0.391438i
$926$	2.38218e9	+	1.08791e9i	3.00015	+	1.37012i
$927$	−7.67262e8	+	3.18870e8i	−0.963173	+	0.400290i
$928$	2.48584e8	−	1.72894e9i	0.311049	−	2.16339i
$929$	−4.27259e7	−	1.45511e8i	−0.0532898	−	0.181488i	0.928547	−	0.371214i	$-0.121058\pi$
$929$	−4.27259e7	−	1.45511e8i	−0.0532898	−	0.181488i	−0.981837	+	0.189726i	$0.939240\pi$
$930$	−1.44926e9	−	2.76660e9i	−1.80176	−	3.43951i
$931$	−3.47817e8	+	2.23529e8i	−0.431025	+	0.277003i
$932$	1.96815e8	+	3.06250e8i	0.243114	+	0.378293i
$933$	−1.09595e8	+	5.74103e7i	−0.134942	+	0.0706879i
$934$	1.64889e9	−	4.84156e8i	2.02372	−	0.594217i
$935$	−9.03289e8	−	1.29873e8i	−1.10508	−	0.158886i
$936$	1.50282e9	+	3.61608e9i	1.83265	+	4.40971i
$937$	1.15972e8	−	2.53944e8i	0.140973	−	0.308687i	−0.825956	−	0.563735i	$-0.809364\pi$
$937$	1.15972e8	−	2.53944e8i	0.140973	−	0.308687i	0.966928	+	0.255048i	$0.0820912\pi$
$938$	2.59557e8	−	8.83969e8i	0.314502	−	1.07110i
$939$	1.27829e8	+	6.40665e8i	0.154394	+	0.773810i
$940$	−8.13078e7	−	5.65508e8i	−0.0978924	−	0.680856i
$941$	6.31220e8	−	9.82197e8i	0.757551	−	1.17877i	−0.221501	−	0.975160i	$-0.571096\pi$
$941$	6.31220e8	−	9.82197e8i	0.757551	−	1.17877i	0.979052	−	0.203612i	$-0.0652680\pi$
$942$	3.25198e8	−	1.37980e9i	0.389041	−	1.65069i
$943$	1.08496e9	+	5.75845e8i	1.29384	+	0.686706i
$944$		−	1.37934e9i		−	1.63966i
$945$	6.76895e8	−	2.13264e8i	0.802095	−	0.252709i
$946$	4.78634e7	+	3.32897e8i	0.0565366	+	0.393221i
$947$	−5.55711e8	+	2.53784e8i	−0.654333	+	0.298824i	−0.714782	−	0.699348i	$-0.753474\pi$
$947$	−5.55711e8	+	2.53784e8i	−0.654333	+	0.298824i	0.0604490	+	0.998171i	$0.480747\pi$
$948$	−7.16155e8	−	4.07252e8i	−0.840585	−	0.478011i
$949$	−7.78369e8	+	1.70439e9i	−0.910724	+	1.99421i
$950$	1.23228e9	+	1.06778e9i	1.43727	+	1.24540i
$951$	−1.03547e9	−	4.06705e8i	−1.20392	−	0.472866i
$952$	1.28622e9	−	3.77668e8i	1.49075	−	0.437723i
$953$	1.32506e8	−	1.14817e8i	0.153093	−	0.132656i	−0.574947	−	0.818191i	$-0.694977\pi$
$953$	1.32506e8	−	1.14817e8i	0.153093	−	0.132656i	0.728040	+	0.685535i	$0.240432\pi$
$954$	1.00548e9	−	1.09299e8i	1.15806	−	0.125884i
$955$	−1.33823e9	+	8.60028e8i	−1.53646	+	0.987422i
$956$	−1.63294e9	+	1.41495e9i	−1.86894	+	1.61945i
$957$	−5.03218e8	+	2.72704e7i	−0.574144	+	0.0311140i
$958$	−1.55385e8	+	1.08073e9i	−0.176731	+	1.22919i
$959$	−4.45830e8	−	3.86314e8i	−0.505491	−	0.438010i
$960$	−2.59272e9	−	2.01164e9i	−2.93050	−	2.27372i
$961$	−6.52500e8	−	1.91591e8i	−0.735208	−	0.215877i
$962$	−2.45125e9	+	1.11945e9i	−2.75336	+	1.25742i
$963$	−1.91045e8	−	6.33360e7i	−0.213923	−	0.0709205i
$964$	2.69287e9	+	1.73060e9i	3.00596	+	1.93182i
$965$		−	5.96091e8i		−	0.663331i
$966$	−5.04306e6	+	9.32630e8i	−0.00559451	+	1.03461i
$967$	−7.27922e8			−0.805018			−0.402509	−	0.915416i	$-0.631862\pi$
$967$	−7.27922e8			−0.805018			−0.402509	+	0.915416i	$0.631862\pi$
$968$	6.05226e8	−	9.41751e8i	0.667255	−	1.03827i
$969$	6.22799e8	+	5.53629e7i	0.684505	+	0.0608482i
$970$	7.47237e8	+	1.63622e9i	0.818735	+	1.79278i
$971$	1.22339e8	−	4.16648e8i	0.133631	−	0.455105i	−0.865304	−	0.501248i	$-0.832875\pi$
$971$	1.22339e8	−	4.16648e8i	0.133631	−	0.455105i	0.998935	+	0.0461424i	$0.0146928\pi$
$972$	−2.38230e9	−	3.55094e7i	−2.59417	−	0.0386674i
$973$	−3.91902e7	+	4.52279e7i	−0.0425441	+	0.0490985i
$974$	2.09879e9	+	3.01760e8i	2.27139	+	0.326577i
$975$	2.00993e9	−	1.08922e8i	2.16854	−	0.117517i
$976$	1.98646e9	+	2.29250e9i	2.13664	+	2.46581i
$977$	6.10808e8	+	9.50436e8i	0.654970	+	1.01915i	0.996842	+	0.0794067i	$0.0253026\pi$
$977$	6.10808e8	+	9.50436e8i	0.654970	+	1.01915i	−0.341872	+	0.939746i	$0.611061\pi$
$978$	−4.73797e8	−	1.34052e9i	−0.506496	−	1.43304i
$979$	5.49731e8	+	6.34423e8i	0.585871	+	0.676131i
$980$	−7.44435e8	−	2.53531e9i	−0.790949	−	2.69372i
$981$	5.98231e8	−	8.63788e8i	0.633669	−	0.914956i
$982$	−1.53111e8	+	1.76700e8i	−0.161686	+	0.186596i
$983$	1.45679e9	+	6.65293e8i	1.53368	+	0.700410i	0.990283	−	0.139064i	$-0.0444094\pi$
$983$	1.45679e9	+	6.65293e8i	1.53368	+	0.700410i	0.543400	+	0.839474i	$0.317137\pi$
$984$	−3.66728e9	−	2.08545e9i	−3.84909	−	2.18884i
$985$	4.81621e8	+	1.05460e9i	0.503960	+	1.10352i
$986$	−1.26639e9	+	1.82080e8i	−1.32111	+	0.189946i
$987$	6.49256e7	−	6.27221e7i	0.0675250	−	0.0652332i
$988$	−2.88413e9			−2.99050
$989$	−2.63040e8	−	1.56816e7i	−0.271915	−	0.0162107i
$990$	−9.73809e8	+	1.95116e9i	−1.00362	+	2.01089i
$991$	−1.55402e9	−	9.98707e8i	−1.59674	−	1.02616i	−0.968780	−	0.247921i	$-0.920253\pi$
$991$	−1.55402e9	−	9.98707e8i	−1.59674	−	1.02616i	−0.627963	−	0.778243i	$-0.716111\pi$
$992$	−3.75489e9	+	5.39872e8i	−3.84647	+	0.553039i
$993$	−1.76511e8	−	8.84657e8i	−0.180270	−	0.903498i
$994$	−3.68650e8	−	1.08245e8i	−0.375366	−	0.110218i
$995$	−2.63677e9	−	1.20417e9i	−2.67672	−	1.22242i
$996$	−1.34781e9	−	1.86678e9i	−1.36412	−	1.88936i
$997$	−1.78760e8	+	1.24330e9i	−0.180379	+	1.25456i	0.675491	+	0.737369i	$0.263932\pi$
$997$	−1.78760e8	+	1.24330e9i	−0.180379	+	1.25456i	−0.855869	+	0.517192i	$0.826977\pi$
$998$	−1.01711e8	−	3.46394e8i	−0.102323	−	0.348481i
$999$	−1.97655e7	−	1.00743e9i	−0.0198250	−	1.01046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.h.a.2.2	✓	460
3.2	odd	2	inner	69.7.h.a.2.45	yes	460
23.12	even	11	inner	69.7.h.a.35.45	yes	460
69.35	odd	22	inner	69.7.h.a.35.2	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.h.a.2.2	✓	460	1.1	even	1	trivial
69.7.h.a.2.45	yes	460	3.2	odd	2	inner
69.7.h.a.35.2	yes	460	69.35	odd	22	inner
69.7.h.a.35.45	yes	460	23.12	even	11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.20003 + 12.7595i) q^{2} +(2.39070 - 26.8939i) q^{3} +(-68.9776 - 151.040i) q^{4} +(54.2696 - 184.825i) q^{5} +(323.549 + 251.035i) q^{6} +(122.578 - 141.462i) q^{7} +(1531.99 + 220.266i) q^{8} +(-717.569 - 128.591i) q^{9} +O(q^{10})\)	\(q+(-8.20003 + 12.7595i) q^{2} +(2.39070 - 26.8939i) q^{3} +(-68.9776 - 151.040i) q^{4} +(54.2696 - 184.825i) q^{5} +(323.549 + 251.035i) q^{6} +(122.578 - 141.462i) q^{7} +(1531.99 + 220.266i) q^{8} +(-717.569 - 128.591i) q^{9} +(1913.26 + 2208.02i) q^{10} +(-553.536 - 861.320i) q^{11} +(-4226.96 + 1493.99i) q^{12} +(-2272.78 - 2622.93i) q^{13} +(799.844 + 2724.02i) q^{14} +(-4840.94 - 1901.38i) q^{15} +(-8413.70 + 9709.92i) q^{16} +(4209.00 + 1922.19i) q^{17} +(7524.84 - 8101.37i) q^{18} +(2079.04 + 4552.45i) q^{19} +(-31659.3 + 4551.93i) q^{20} +(-3511.43 - 3634.79i) q^{21} +15529.0 q^{22} +(-2445.18 + 11918.8i) q^{23} +(9586.36 - 40674.6i) q^{24} +(-18070.6 - 11613.2i) q^{25} +(52104.1 - 7491.44i) q^{26} +(-5173.81 + 18990.8i) q^{27} +(-29821.5 - 8756.38i) q^{28} +(16582.8 + 7573.11i) q^{29} +(63956.5 - 46176.5i) q^{30} +(5634.57 - 39189.3i) q^{31} +(-26994.0 - 91933.1i) q^{32} +(-24487.6 + 12827.6i) q^{33} +(-59040.0 + 37942.7i) q^{34} +(-19493.5 - 30332.5i) q^{35} +(30073.8 + 117251. i) q^{36} +(-49118.8 + 14422.6i) q^{37} +(-75135.1 - 10802.8i) q^{38} +(-75974.5 + 54853.5i) q^{39} +(123851. - 271196. i) q^{40} +(28442.0 - 96864.7i) q^{41} +(75171.8 - 14998.6i) q^{42} +(3082.19 + 21437.1i) q^{43} +(-91912.0 + 143018. i) q^{44} +(-62709.0 + 125646. i) q^{45} +(-132027. - 128933. i) q^{46} +17862.3i q^{47} +(241024. + 249491. i) q^{48} +(11757.0 + 81771.4i) q^{49} +(296358. - 135342. i) q^{50} +(61757.6 - 108601. i) q^{51} +(-239396. + 524204. i) q^{52} +(69130.5 + 59901.9i) q^{53} +(-199888. - 221741. i) q^{54} +(-189234. + 55564.0i) q^{55} +(218947. - 189718. i) q^{56} +(127404. - 45029.9i) q^{57} +(-232608. + 149488. i) q^{58} +(-81135.4 + 70304.2i) q^{59} +(46731.2 + 862327. i) q^{60} +(33600.4 - 233696. i) q^{61} +(453832. + 393248. i) q^{62} +(-106149. + 85746.4i) q^{63} +(605403. + 177762. i) q^{64} +(-608127. + 277722. i) q^{65} +(37125.3 - 417636. i) q^{66} +(-272994. - 175443. i) q^{67} -768315. i q^{68} +(314697. + 94254.7i) q^{69} +546874. q^{70} +(-73166.7 + 113850. i) q^{71} +(-1.07098e6 - 355056. i) q^{72} +(-224273. - 491089. i) q^{73} +(218751. - 744997. i) q^{74} +(-355527. + 458225. i) q^{75} +(544195. - 628035. i) q^{76} +(-189695. - 27274.0i) q^{77} +(-76909.0 - 1.41920e6i) q^{78} +(120340. + 138879. i) q^{79} +(1.33803e6 + 2.08202e6i) q^{80} +(498370. + 184546. i) q^{81} +(1.00272e6 + 1.15720e6i) q^{82} +(144692. + 492777. i) q^{83} +(-306788. + 781084. i) q^{84} +(583689. - 673613. i) q^{85} +(-298801. - 136458. i) q^{86} +(243315. - 427872. i) q^{87} +(-658291. - 1.44146e6i) q^{88} +(-811560. + 116685. i) q^{89} +(-1.08897e6 - 1.83044e6i) q^{90} -649637. q^{91} +(1.96887e6 - 452809. i) q^{92} +(-1.04048e6 - 245226. i) q^{93} +(-227914. - 146471. i) q^{94} +(954236. - 137198. i) q^{95} +(-2.53698e6 + 506190. i) q^{96} +(590735. + 173455. i) q^{97} +(-1.13977e6 - 520515. i) q^{98} +(286443. + 689236. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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