LMFDB - Embedded newform 32.8.g.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,8,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, 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:	$9.99632081549$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	32.13
Dual form			32.8.g.a.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.13171 - 8.78286i) q^{2} +(15.6913 - 37.8822i) q^{3} +(-26.2773 + 125.274i) q^{4} +(221.433 - 91.7205i) q^{5} +(-444.620 + 132.350i) q^{6} +(1084.35 - 1084.35i) q^{7} +(1287.66 - 662.626i) q^{8} +(357.601 + 357.601i) q^{9} +O(q^{10})$	\(q+(-7.13171 - 8.78286i) q^{2} +(15.6913 - 37.8822i) q^{3} +(-26.2773 + 125.274i) q^{4} +(221.433 - 91.7205i) q^{5} +(-444.620 + 132.350i) q^{6} +(1084.35 - 1084.35i) q^{7} +(1287.66 - 662.626i) q^{8} +(357.601 + 357.601i) q^{9} +(-2384.77 - 1290.69i) q^{10} +(368.136 + 888.758i) q^{11} +(4333.31 + 2961.15i) q^{12} +(-6392.96 - 2648.05i) q^{13} +(-17257.0 - 1790.42i) q^{14} -9827.57i q^{15} +(-15003.0 - 6583.71i) q^{16} -5314.69i q^{17} +(590.453 - 5691.07i) q^{18} +(-1568.95 - 649.881i) q^{19} +(5671.51 + 30149.9i) q^{20} +(-24062.7 - 58092.4i) q^{21} +(5180.40 - 9571.65i) q^{22} +(-43662.3 - 43662.3i) q^{23} +(-4896.58 - 59177.0i) q^{24} +(-14622.8 + 14622.8i) q^{25} +(22335.3 + 75033.6i) q^{26} +(102006. - 42252.4i) q^{27} +(107347. + 164334. i) q^{28} +(-41215.8 + 99503.8i) q^{29} +(-86314.2 + 70087.4i) q^{30} +107133. q^{31} +(49173.3 + 178722. i) q^{32} +39444.6 q^{33} +(-46678.1 + 37902.8i) q^{34} +(140654. - 339568. i) q^{35} +(-54194.9 + 35401.2i) q^{36} +(487984. - 202130. i) q^{37} +(5481.49 + 18414.6i) q^{38} +(-200628. + 200628. i) q^{39} +(224355. - 264832. i) q^{40} +(-566671. - 566671. i) q^{41} +(-338610. + 625637. i) q^{42} +(207365. + 500624. i) q^{43} +(-121012. + 22763.5i) q^{44} +(111984. + 46385.3i) q^{45} +(-72092.9 + 694867. i) q^{46} +1.04551e6i q^{47} +(-484822. + 465039. i) q^{48} -1.52809e6i q^{49} +(232716. + 24144.4i) q^{50} +(-201332. - 83394.4i) q^{51} +(499721. - 731286. i) q^{52} +(-307777. - 743039. i) q^{53} +(-1.09858e6 - 594575. i) q^{54} +(163035. + 163035. i) q^{55} +(677760. - 2.11480e6i) q^{56} +(-49237.8 + 49237.8i) q^{57} +(1.16787e6 - 347640. i) q^{58} +(-404521. + 167558. i) q^{59} +(1.23114e6 + 258242. i) q^{60} +(-577434. + 1.39405e6i) q^{61} +(-764044. - 940937. i) q^{62} +775530. q^{63} +(1.21901e6 - 1.70648e6i) q^{64} -1.65849e6 q^{65} +(-281308. - 346437. i) q^{66} +(-1.44606e6 + 3.49109e6i) q^{67} +(665790. + 139656. i) q^{68} +(-2.33914e6 + 968904. i) q^{69} +(-3.98548e6 + 1.18636e6i) q^{70} +(3.66079e6 - 3.66079e6i) q^{71} +(697426. + 223514. i) q^{72} +(767133. + 767133. i) q^{73} +(-5.25544e6 - 2.84437e6i) q^{74} +(324493. + 783395. i) q^{75} +(122641. - 179471. i) q^{76} +(1.36291e6 + 564537. i) q^{77} +(3.19291e6 + 331266. i) q^{78} +6.71053e6i q^{79} +(-3.92602e6 - 81767.9i) q^{80} -3.42119e6i q^{81} +(-935658. + 9.01833e6i) q^{82} +(6.38141e6 + 2.64327e6i) q^{83} +(7.90975e6 - 1.48791e6i) q^{84} +(-487466. - 1.17685e6i) q^{85} +(2.91804e6 - 5.39157e6i) q^{86} +(3.12269e6 + 3.12269e6i) q^{87} +(1.06295e6 + 900486. i) q^{88} +(-2.32270e6 + 2.32270e6i) q^{89} +(-391243. - 1.31435e6i) q^{90} +(-9.80362e6 + 4.06079e6i) q^{91} +(6.61706e6 - 4.32241e6i) q^{92} +(1.68106e6 - 4.05844e6i) q^{93} +(9.18253e6 - 7.45625e6i) q^{94} -407025. q^{95} +(7.54199e6 + 941599. i) q^{96} +1.71081e6 q^{97} +(-1.34210e7 + 1.08979e7i) q^{98} +(-186175. + 449467. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−7.13171	−	8.78286i	−0.630360	−	0.776303i
$2$	−7.13171	−	8.78286i	−0.630360	−	0.776303i
$3$	15.6913	−	37.8822i	0.335533	−	0.810047i	−0.662601	−	0.748973i	$-0.730547\pi$
$3$	15.6913	−	37.8822i	0.335533	−	0.810047i	0.998133	−	0.0610744i	$-0.0194527\pi$
$4$	−26.2773	+	125.274i	−0.205292	+	0.978701i
$5$	221.433	−	91.7205i	0.792223	−	0.328149i	0.0503858	−	0.998730i	$-0.483955\pi$
$5$	221.433	−	91.7205i	0.792223	−	0.328149i	0.741837	+	0.670580i	$0.233955\pi$
$6$	−444.620	+	132.350i	−0.840348	+	0.250147i
$7$	1084.35	−	1084.35i	1.19489	−	1.19489i	0.219208	−	0.975678i	$-0.429653\pi$
$7$	1084.35	−	1084.35i	1.19489	−	1.19489i	0.975678	−	0.219208i	$-0.0703472\pi$
$8$	1287.66	−	662.626i	0.889176	−	0.457566i
$9$	357.601	+	357.601i	0.163512	+	0.163512i
$10$	−2384.77	−	1290.69i	−0.754129	−	0.408152i
$11$	368.136	+	888.758i	0.0833938	+	0.201330i	0.960076	−	0.279740i	$-0.0902482\pi$
$11$	368.136	+	888.758i	0.0833938	+	0.201330i	−0.876682	+	0.481070i	$0.840248\pi$
$12$	4333.31	+	2961.15i	0.723912	+	0.494682i
$13$	−6392.96	−	2648.05i	−0.807049	−	0.334291i	−0.0592734	−	0.998242i	$-0.518878\pi$
$13$	−6392.96	−	2648.05i	−0.807049	−	0.334291i	−0.747776	+	0.663951i	$0.768878\pi$
$14$	−17257.0	−	1790.42i	−1.68080	−	0.174384i
$15$		−	9827.57i		−	0.751843i
$16$	−15003.0	−	6583.71i	−0.915711	−	0.401838i
$17$		−	5314.69i		−	0.262365i	−0.991358	−	0.131183i	$-0.958123\pi$
$17$		−	5314.69i		−	0.262365i	0.991358	−	0.131183i	$-0.0418774\pi$
$18$	590.453	−	5691.07i	0.0238634	−	0.230007i
$19$	−1568.95	−	649.881i	−0.0524773	−	0.0217368i	0.356290	−	0.934375i	$-0.384041\pi$
$19$	−1568.95	−	649.881i	−0.0524773	−	0.0217368i	−0.408768	+	0.912638i	$0.634041\pi$
$20$	5671.51	+	30149.9i	0.158523	+	0.842715i
$21$	−24062.7	−	58092.4i	−0.566991	−	1.36884i
$22$	5180.40	−	9571.65i	0.103725	−	0.191649i
$23$	−43662.3	−	43662.3i	−0.748271	−	0.748271i	0.225883	−	0.974154i	$-0.427473\pi$
$23$	−43662.3	−	43662.3i	−0.748271	−	0.748271i	−0.974154	+	0.225883i	$0.927473\pi$
$24$	−4896.58	−	59177.0i	−0.0723026	−	0.873803i
$25$	−14622.8	+	14622.8i	−0.187172	+	0.187172i
$26$	22335.3	+	75033.6i	0.249221	+	0.837238i
$27$	102006.	−	42252.4i	0.997364	−	0.413122i
$28$	107347.	+	164334.i	0.924136	+	1.41474i
$29$	−41215.8	+	99503.8i	−0.313813	+	0.757612i	0.685744	+	0.727843i	$0.259477\pi$
$29$	−41215.8	+	99503.8i	−0.313813	+	0.757612i	−0.999557	+	0.0297687i	$0.990523\pi$
$30$	−86314.2	+	70087.4i	−0.583657	+	0.473932i
$31$	107133.			0.645890			0.322945	−	0.946418i	$-0.395327\pi$
$31$	107133.			0.645890			0.322945	+	0.946418i	$0.395327\pi$
$32$	49173.3	+	178722.i	0.265280	+	0.964171i
$33$	39444.6			0.191068
$34$	−46678.1	+	37902.8i	−0.203675	+	0.165385i
$35$	140654.	−	339568.i	0.554515	−	1.33872i
$36$	−54194.9	+	35401.2i	−0.193597	+	0.126462i
$37$	487984.	−	202130.i	1.58380	−	0.656031i	0.594789	−	0.803882i	$-0.297236\pi$
$37$	487984.	−	202130.i	1.58380	−	0.656031i	0.989010	+	0.147851i	$0.0472357\pi$
$38$	5481.49	+	18414.6i	0.0162053	+	0.0544403i
$39$	−200628.	+	200628.i	−0.541583	+	0.541583i
$40$	224355.	−	264832.i	0.554275	−	0.654276i
$41$	−566671.	−	566671.i	−1.28407	−	1.28407i	−0.938332	−	0.345735i	$-0.887630\pi$
$41$	−566671.	−	566671.i	−1.28407	−	1.28407i	−0.345735	−	0.938332i	$-0.612370\pi$
$42$	−338610.	+	625637.i	−0.705223	+	1.30302i
$43$	207365.	+	500624.i	0.397737	+	0.960223i	0.988202	+	0.153159i	$0.0489447\pi$
$43$	207365.	+	500624.i	0.397737	+	0.960223i	−0.590464	+	0.807064i	$0.701055\pi$
$44$	−121012.	+	22763.5i	−0.214162	+	0.0402861i
$45$	111984.	+	46385.3i	0.183195	+	0.0758817i
$46$	−72092.9	+	694867.i	−0.109204	+	1.05257i
$47$			1.04551e6i			1.46887i	0.678678	+	0.734436i	$0.262553\pi$
$47$			1.04551e6i			1.46887i	−0.678678	+	0.734436i	$0.737447\pi$
$48$	−484822.	+	465039.i	−0.632759	+	0.606939i
$49$		−	1.52809e6i		−	1.85550i
$50$	232716.	+	24144.4i	0.263288	+	0.0273163i
$51$	−201332.	−	83394.4i	−0.212528	−	0.0880321i
$52$	499721.	−	731286.i	0.492851	−	0.721233i
$53$	−307777.	−	743039.i	−0.283969	−	0.685561i	0.715952	−	0.698150i	$-0.245993\pi$
$53$	−307777.	−	743039.i	−0.283969	−	0.685561i	−0.999921	+	0.0125882i	$0.995993\pi$
$54$	−1.09858e6	−	594575.i	−0.949406	−	0.513841i
$55$	163035.	+	163035.i	0.132133	+	0.132133i
$56$	677760.	−	2.11480e6i	0.515725	−	1.60920i
$57$	−49237.8	+	49237.8i	−0.0352157	+	0.0352157i
$58$	1.16787e6	−	347640.i	0.785951	−	0.233955i
$59$	−404521.	+	167558.i	−0.256425	+	0.106215i	−0.507193	−	0.861833i	$-0.669317\pi$
$59$	−404521.	+	167558.i	−0.256425	+	0.106215i	0.250768	+	0.968047i	$0.419317\pi$
$60$	1.23114e6	+	258242.i	0.735829	+	0.154347i
$61$	−577434.	+	1.39405e6i	−0.325723	+	0.786365i	0.673177	+	0.739481i	$0.264929\pi$
$61$	−577434.	+	1.39405e6i	−0.325723	+	0.786365i	−0.998900	+	0.0468837i	$0.985071\pi$
$62$	−764044.	−	940937.i	−0.407143	−	0.501406i
$63$	775530.			0.390757
$64$	1.21901e6	−	1.70648e6i	0.581267	−	0.813713i
$65$	−1.65849e6			−0.749060
$66$	−281308.	−	346437.i	−0.120442	−	0.148327i
$67$	−1.44606e6	+	3.49109e6i	−0.587385	+	1.41807i	0.298608	+	0.954376i	$0.403478\pi$
$67$	−1.44606e6	+	3.49109e6i	−0.587385	+	1.41807i	−0.885993	+	0.463698i	$0.846522\pi$
$68$	665790.	+	139656.i	0.256777	+	0.0538614i
$69$	−2.33914e6	+	968904.i	−0.857204	+	0.355066i
$70$	−3.98548e6	+	1.18636e6i	−1.38879	+	0.413403i
$71$	3.66079e6	−	3.66079e6i	1.21386	−	1.21386i	0.244119	−	0.969745i	$-0.421501\pi$
$71$	3.66079e6	−	3.66079e6i	1.21386	−	1.21386i	0.969745	−	0.244119i	$-0.0784987\pi$
$72$	697426.	+	223514.i	0.220209	+	0.0705735i
$73$	767133.	+	767133.i	0.230803	+	0.230803i	0.813028	−	0.582225i	$-0.197818\pi$
$73$	767133.	+	767133.i	0.230803	+	0.230803i	−0.582225	+	0.813028i	$0.697818\pi$
$74$	−5.25544e6	−	2.84437e6i	−1.50764	−	0.815971i
$75$	324493.	+	783395.i	0.0888159	+	0.214421i
$76$	122641.	−	179471.i	0.0320470	−	0.0468972i
$77$	1.36291e6	+	564537.i	0.340213	+	0.140921i
$78$	3.19291e6	+	331266.i	0.761824	+	0.0790398i
$79$			6.71053e6i			1.53131i	0.643253	+	0.765653i	$0.277584\pi$
$79$			6.71053e6i			1.53131i	−0.643253	+	0.765653i	$0.722416\pi$
$80$	−3.92602e6	−	81767.9i	−0.857310	−	0.0178553i
$81$		−	3.42119e6i		−	0.715286i
$82$	−935658.	+	9.01833e6i	−0.187400	+	1.80625i
$83$	6.38141e6	+	2.64327e6i	1.22502	+	0.507420i	0.899002	−	0.437944i	$-0.144293\pi$
$83$	6.38141e6	+	2.64327e6i	1.22502	+	0.507420i	0.326018	+	0.945364i	$0.394293\pi$
$84$	7.90975e6	−	1.48791e6i	1.45608	−	0.273904i
$85$	−487466.	−	1.17685e6i	−0.0860950	−	0.207852i
$86$	2.91804e6	−	5.39157e6i	0.494706	−	0.914051i
$87$	3.12269e6	+	3.12269e6i	0.508407	+	0.508407i
$88$	1.06295e6	+	900486.i	0.166274	+	0.140860i
$89$	−2.32270e6	+	2.32270e6i	−0.349244	+	0.349244i	−0.859828	−	0.510584i	$-0.829429\pi$
$89$	−2.32270e6	+	2.32270e6i	−0.349244	+	0.349244i	0.510584	+	0.859828i	$0.329429\pi$
$90$	−391243.	−	1.31435e6i	−0.0565715	−	0.190047i
$91$	−9.80362e6	+	4.06079e6i	−1.36377	+	0.564893i
$92$	6.61706e6	−	4.32241e6i	0.885947	−	0.578720i
$93$	1.68106e6	−	4.05844e6i	0.216717	−	0.523201i
$94$	9.18253e6	−	7.45625e6i	1.14029	−	0.925918i
$95$	−407025.			−0.0487066
$96$	7.54199e6	+	941599.i	0.870035	+	0.108622i
$97$	1.71081e6			0.190327			0.0951636	−	0.995462i	$-0.469663\pi$
$97$	1.71081e6			0.190327			0.0951636	+	0.995462i	$0.469663\pi$
$98$	−1.34210e7	+	1.08979e7i	−1.44043	+	1.16964i
$99$	−186175.	+	449467.i	−0.0192841	+	0.0465559i
$100$	−1.44761e6	−	2.21610e6i	−0.144761	−	0.221610i
$101$	−3.81763e6	+	1.58132e6i	−0.368697	+	0.152719i	−0.559336	−	0.828941i	$-0.688944\pi$
$101$	−3.81763e6	+	1.58132e6i	−0.368697	+	0.152719i	0.190639	+	0.981660i	$0.438944\pi$
$102$	703399.	+	2.36301e6i	0.0656299	+	0.220478i
$103$	7.20543e6	−	7.20543e6i	0.649725	−	0.649725i	−0.303202	−	0.952926i	$-0.598056\pi$
$103$	7.20543e6	−	7.20543e6i	0.649725	−	0.649725i	0.952926	+	0.303202i	$0.0980555\pi$
$104$	−9.98665e6	+	826343.i	−0.870569	+	0.0720350i
$105$	−1.06565e7	−	1.06565e7i	−0.898366	−	0.898366i
$106$	−4.33103e6	+	8.00231e6i	−0.353200	+	0.652596i
$107$	−2.89741e6	−	6.99497e6i	−0.228648	−	0.552004i	0.767366	−	0.641210i	$-0.221567\pi$
$107$	−2.89741e6	−	6.99497e6i	−0.228648	−	0.552004i	−0.996013	+	0.0892056i	$0.971567\pi$
$108$	2.61266e6	+	1.38890e7i	0.199572	+	1.06093i
$109$	1.58648e7	+	6.57142e6i	1.17339	+	0.486034i	0.882312	−	0.470666i	$-0.155986\pi$
$109$	1.58648e7	+	6.57142e6i	1.17339	+	0.486034i	0.291078	+	0.956699i	$0.405986\pi$
$110$	269195.	−	2.59463e6i	0.0192838	−	0.185866i
$111$		−	2.16576e7i		−	1.50307i
$112$	−2.34076e7	+	9.12946e6i	−1.57432	+	0.614019i
$113$		−	8.33979e6i		−	0.543727i	−0.962336	−	0.271863i	$-0.912360\pi$
$113$		−	8.33979e6i		−	0.543727i	0.962336	−	0.271863i	$-0.0876399\pi$
$114$	783598.	+	81298.8i	0.0495366	+	0.00513946i
$115$	−1.36730e7	−	5.66354e6i	−0.838342	−	0.347253i
$116$	−1.13822e7	−	7.77795e6i	−0.677052	−	0.462660i
$117$	−1.33918e6	−	3.23308e6i	−0.0773018	−	0.186623i
$118$	4.35657e6	+	2.35788e6i	0.244094	+	0.132110i
$119$	−5.76298e6	−	5.76298e6i	−0.313497	−	0.313497i
$120$	−6.51201e6	−	1.26546e7i	−0.344018	−	0.668520i
$121$	1.31251e7	−	1.31251e7i	0.673527	−	0.673527i
$122$	1.63618e7	−	4.87044e6i	0.815780	−	0.242834i
$123$	−3.03586e7	+	1.25749e7i	−1.47100	+	0.609309i
$124$	−2.81518e6	+	1.34210e7i	−0.132596	+	0.632133i
$125$	−9.06243e6	+	2.18786e7i	−0.415011	+	1.00192i
$126$	−5.53086e6	−	6.81137e6i	−0.246318	−	0.303346i
$127$	2.84926e7			1.23429			0.617147	−	0.786848i	$-0.288289\pi$
$127$	2.84926e7			1.23429			0.617147	+	0.786848i	$0.288289\pi$
$128$	−2.36814e7	+	1.46377e6i	−0.998095	+	0.0616933i
$129$	2.22186e7			0.911280
$130$	1.18279e7	+	1.45663e7i	0.472178	+	0.581497i
$131$	5.56165e6	−	1.34270e7i	0.216149	−	0.521831i	−0.778196	−	0.628021i	$-0.783865\pi$
$131$	5.56165e6	−	1.34270e7i	0.216149	−	0.521831i	0.994346	+	0.106190i	$0.0338652\pi$
$132$	−1.03650e6	+	4.94137e6i	−0.0392247	+	0.186999i
$133$	−2.40599e6	+	996594.i	−0.0886774	+	0.0367314i
$134$	4.09746e7	−	1.21969e7i	1.47112	−	0.437909i
$135$	1.87121e7	−	1.87121e7i	0.654568	−	0.654568i
$136$	−3.52165e6	−	6.84353e6i	−0.120049	−	0.233289i
$137$	−2.00789e7	−	2.00789e7i	−0.667141	−	0.667141i	0.289912	−	0.957053i	$-0.406374\pi$
$137$	−2.00789e7	−	2.00789e7i	−0.667141	−	0.667141i	−0.957053	+	0.289912i	$0.906374\pi$
$138$	2.51918e7	+	1.36344e7i	0.815986	+	0.441631i
$139$	9.67736e6	+	2.33632e7i	0.305637	+	0.737872i	0.999836	+	0.0180896i	$0.00575840\pi$
$139$	9.67736e6	+	2.33632e7i	0.305637	+	0.737872i	−0.694200	+	0.719782i	$0.744242\pi$
$140$	3.88429e7	+	2.65431e7i	1.19637	+	0.817531i
$141$	3.96060e7	+	1.64053e7i	1.18986	+	0.492854i
$142$	−5.82599e7	−	6.04450e6i	−1.70750	−	0.177154i
$143$		−	6.65664e6i		−	0.190361i
$144$	−3.01075e6	−	7.71944e6i	−0.0840245	−	0.215435i
$145$			2.58138e7i			0.703175i
$146$	1.26665e6	−	1.22086e7i	0.0336839	−	0.324661i
$147$	−5.78873e7	−	2.39777e7i	−1.50305	−	0.622582i
$148$	1.24986e7	+	6.64430e7i	0.316917	+	1.68474i
$149$	2.64709e7	+	6.39064e7i	0.655566	+	1.58268i	0.804582	+	0.593842i	$0.202390\pi$
$149$	2.64709e7	+	6.39064e7i	0.655566	+	1.58268i	−0.149015	+	0.988835i	$0.547610\pi$
$150$	4.56626e6	−	8.43693e6i	0.110469	−	0.204110i
$151$	8.90642e6	+	8.90642e6i	0.210515	+	0.210515i	0.804486	−	0.593971i	$-0.202441\pi$
$151$	8.90642e6	+	8.90642e6i	0.210515	+	0.210515i	−0.593971	+	0.804486i	$0.702441\pi$
$152$	−2.45091e6	+	202800.i	−0.0566076	+	0.00468398i
$153$	1.90054e6	−	1.90054e6i	0.0428999	−	0.0428999i
$154$	−4.76165e6	−	1.59964e7i	−0.105060	−	0.352939i
$155$	2.37228e7	−	9.82632e6i	0.511689	−	0.211948i
$156$	−1.98614e7	−	3.04053e7i	−0.418865	−	0.641230i
$157$	−3.38756e7	+	8.17829e7i	−0.698615	+	1.68661i	0.0280420	+	0.999607i	$0.491073\pi$
$157$	−3.38756e7	+	8.17829e7i	−0.698615	+	1.68661i	−0.726657	+	0.687000i	$0.758927\pi$
$158$	5.89377e7	−	4.78576e7i	1.18876	−	0.965275i
$159$	−3.29774e7			−0.650618
$160$	2.72811e7	+	3.50648e7i	0.526553	+	0.676787i
$161$	−9.46904e7			−1.78820
$162$	−3.00479e7	+	2.43990e7i	−0.555279	+	0.450888i
$163$	6.61600e6	−	1.59724e7i	0.119657	−	0.288878i	−0.852690	−	0.522417i	$-0.825031\pi$
$163$	6.61600e6	−	1.59724e7i	0.119657	−	0.288878i	0.972348	+	0.233539i	$0.0750305\pi$
$164$	8.58796e7	−	5.60984e7i	1.52033	−	0.993110i
$165$	8.73434e6	−	3.61788e6i	0.151369	−	0.0626990i
$166$	−2.22949e7	−	7.48980e7i	−0.378293	−	1.27084i
$167$	1.12101e6	−	1.12101e6i	0.0186253	−	0.0186253i	−0.697733	−	0.716358i	$-0.745808\pi$
$167$	1.12101e6	−	1.12101e6i	0.0186253	−	0.0186253i	0.716358	+	0.697733i	$0.245808\pi$
$168$	−6.94782e7	−	5.88589e7i	−1.13049	−	0.957701i
$169$	−1.05121e7	−	1.05121e7i	−0.167528	−	0.167528i
$170$	−6.85961e6	+	1.26743e7i	−0.107085	+	0.197857i
$171$	−328661.	−	793457.i	−0.00502645	−	0.0121349i
$172$	−6.81640e7	+	1.28224e7i	−1.02142	+	0.192140i
$173$	7.74573e7	+	3.20838e7i	1.13737	+	0.471113i	0.870279	−	0.492559i	$-0.163938\pi$
$173$	7.74573e7	+	3.20838e7i	1.13737	+	0.471113i	0.267088	+	0.963672i	$0.413938\pi$
$174$	5.15602e6	−	4.96963e7i	0.0741980	−	0.715157i
$175$			3.17125e7i			0.447299i
$176$	328189.	−	1.57577e7i	0.00453764	−	0.217871i
$177$			1.79534e7i			0.243354i
$178$	3.69648e7	+	3.83513e6i	0.491268	+	0.0509694i
$179$	−2.27005e7	−	9.40286e6i	−0.295835	−	0.122539i	0.229829	−	0.973231i	$-0.426183\pi$
$179$	−2.27005e7	−	9.40286e6i	−0.295835	−	0.122539i	−0.525664	+	0.850692i	$0.676183\pi$
$180$	−8.75351e6	+	1.28098e7i	−0.111874	+	0.163715i
$181$	1.01039e7	+	2.43930e7i	0.126653	+	0.305767i	0.974469	−	0.224524i	$-0.0720827\pi$
$181$	1.01039e7	+	2.43930e7i	0.126653	+	0.305767i	−0.847816	+	0.530291i	$0.822083\pi$
$182$	1.05582e8	+	5.71434e7i	1.29820	+	0.702613i
$183$	4.37489e7	+	4.37489e7i	0.527702	+	0.527702i
$184$	−8.51541e7	−	2.72906e7i	−1.00773	−	0.322961i
$185$	8.95164e7	−	8.95164e7i	1.03944	−	1.03944i
$186$	−4.76336e7	+	1.41791e7i	−0.542773	+	0.161567i
$187$	4.72347e6	−	1.95653e6i	0.0528221	−	0.0218796i
$188$	−1.30974e8	−	2.74731e7i	−1.43759	−	0.301547i
$189$	6.47941e7	−	1.56427e8i	0.698103	−	1.68537i
$190$	2.90278e6	+	3.57484e6i	0.0307027	+	0.0378111i
$191$	−1.50637e8			−1.56428			−0.782142	−	0.623100i	$-0.785873\pi$
$191$	−1.50637e8			−1.56428			−0.782142	+	0.623100i	$0.785873\pi$
$192$	−4.55174e7	−	7.29554e7i	−0.464112	−	0.743881i
$193$	−9.08129e7			−0.909279			−0.454639	−	0.890676i	$-0.650232\pi$
$193$	−9.08129e7			−0.909279			−0.454639	+	0.890676i	$0.650232\pi$
$194$	−1.22010e7	−	1.50258e7i	−0.119975	−	0.147751i
$195$	−2.60239e7	+	6.28273e7i	−0.251334	+	0.606774i
$196$	1.91429e8	+	4.01541e7i	1.81598	+	0.380919i
$197$	−7.28850e7	+	3.01900e7i	−0.679214	+	0.281340i	−0.695498	−	0.718528i	$-0.744816\pi$
$197$	−7.28850e7	+	3.01900e7i	−0.679214	+	0.281340i	0.0162843	+	0.999867i	$0.494816\pi$
$198$	5.27535e6	−	1.57032e6i	0.0482974	−	0.0143767i
$199$	1.17470e8	−	1.17470e8i	1.05667	−	1.05667i	0.0583784	−	0.998295i	$-0.481407\pi$
$199$	1.17470e8	−	1.17470e8i	1.05667	−	1.05667i	0.998295	−	0.0583784i	$-0.0185930\pi$
$200$	−9.13982e6	+	2.85187e7i	−0.0807853	+	0.252072i
$201$	1.09559e8	+	1.09559e8i	0.951620	+	0.951620i
$202$	4.11147e7	+	2.22523e7i	0.350968	+	0.189952i
$203$	6.32046e7	+	1.52589e8i	0.530289	+	1.28023i
$204$	1.57376e7	−	2.30302e7i	0.129787	−	0.189929i
$205$	−1.77455e8	−	7.35043e7i	−1.43863	−	0.595901i
$206$	−1.14671e8	−	1.18972e7i	−0.913944	−	0.0948223i
$207$		−	3.12274e7i		−	0.244703i
$208$	7.84796e7	+	8.18181e7i	0.604693	+	0.630417i
$209$		−	1.63366e6i		−	0.0123780i
$210$	−1.75955e7	+	1.69594e8i	−0.131110	+	1.26370i
$211$	−1.39402e8	−	5.77424e7i	−1.02160	−	0.423162i	−0.191928	−	0.981409i	$-0.561474\pi$
$211$	−1.39402e8	−	5.77424e7i	−1.02160	−	0.423162i	−0.829675	+	0.558247i	$0.811474\pi$
$212$	1.01171e8	−	1.90313e7i	0.729256	−	0.137181i
$213$	−8.12360e7	−	1.96121e8i	−0.575996	−	1.39058i
$214$	−4.07723e7	+	7.53336e7i	−0.284392	+	0.525461i
$215$	9.18350e7	+	9.18350e7i	0.630193	+	0.630193i
$216$	1.03352e8	−	1.21999e8i	0.697801	−	0.823697i
$217$	1.16170e8	−	1.16170e8i	0.771765	−	0.771765i
$218$	−5.54274e7	−	1.86204e8i	−0.362349	−	1.21728i
$219$	4.10980e7	−	1.70233e7i	0.264403	−	0.109519i
$220$	−2.47081e7	+	1.61399e7i	−0.156444	+	0.102193i
$221$	−1.40736e7	+	3.39766e7i	−0.0877063	+	0.211742i
$222$	−1.90216e8	+	1.54456e8i	−1.16684	+	0.947477i
$223$	8.42303e7			0.508629			0.254315	−	0.967122i	$-0.418150\pi$
$223$	8.42303e7			0.508629			0.254315	+	0.967122i	$0.418150\pi$
$224$	2.47119e8	+	1.40477e8i	1.46905	+	0.835096i
$225$	−1.04583e7			−0.0612099
$226$	−7.32472e7	+	5.94770e7i	−0.422097	+	0.342744i
$227$	1.55186e6	−	3.74653e6i	0.00880568	−	0.0212588i	−0.919416	−	0.393287i	$-0.871338\pi$
$227$	1.55186e6	−	3.74653e6i	0.00880568	−	0.0212588i	0.928221	+	0.372029i	$0.121338\pi$
$228$	−4.87436e6	−	7.46203e6i	−0.0272362	−	0.0416951i
$229$	−6.77764e7	+	2.80739e7i	−0.372953	+	0.154482i	−0.561284	−	0.827623i	$-0.689692\pi$
$229$	−6.77764e7	+	2.80739e7i	−0.372953	+	0.154482i	0.188331	+	0.982106i	$0.439692\pi$
$230$	4.77698e7	+	1.60479e8i	0.258884	+	0.869702i
$231$	4.27718e7	−	4.27718e7i	0.228305	−	0.228305i
$232$	1.28617e7	+	1.55438e8i	0.0676223	+	0.817240i
$233$	−2.02829e8	−	2.02829e8i	−1.05047	−	1.05047i	−0.998657	−	0.0518161i	$-0.983499\pi$
$233$	−2.02829e8	−	2.02829e8i	−1.05047	−	1.05047i	−0.0518161	−	0.998657i	$-0.516501\pi$
$234$	−1.88450e7	+	3.48193e7i	−0.0961480	+	0.177649i
$235$	9.58943e7	+	2.31509e8i	0.482009	+	1.16367i
$236$	−1.03609e7	−	5.50789e7i	−0.0513104	−	0.272768i
$237$	2.54210e8	+	1.05297e8i	1.24043	+	0.513803i
$238$	−9.51553e6	+	9.17154e7i	−0.0457524	+	0.440984i
$239$			3.17135e7i			0.150263i	0.997174	+	0.0751314i	$0.0239376\pi$
$239$			3.17135e7i			0.150263i	−0.997174	+	0.0751314i	$0.976062\pi$
$240$	−6.47019e7	+	1.47443e8i	−0.302119	+	0.688470i
$241$			3.17565e8i			1.46141i	0.682691	+	0.730707i	$0.260809\pi$
$241$			3.17565e8i			1.46141i	−0.682691	+	0.730707i	$0.739191\pi$
$242$	−2.08881e8	−	2.16716e7i	−0.947426	−	0.0982961i
$243$	9.34855e7	+	3.87230e7i	0.417948	+	0.173120i
$244$	−1.59464e8	−	1.08969e8i	−0.702748	−	0.480219i
$245$	−1.40157e8	−	3.38369e8i	−0.608883	−	1.46997i
$246$	3.26952e8	+	1.76954e8i	1.40027	+	0.757858i
$247$	8.30932e6	+	8.30932e6i	0.0350854	+	0.0350854i
$248$	1.37952e8	−	7.09893e7i	0.574310	−	0.295537i
$249$	2.00265e8	−	2.00265e8i	0.822068	−	0.822068i
$250$	2.56788e8	−	7.64381e7i	1.03940	−	0.309400i
$251$	3.29747e7	−	1.36586e7i	0.131620	−	0.0545190i	−0.315901	−	0.948792i	$-0.602307\pi$
$251$	3.29747e7	−	1.36586e7i	0.131620	−	0.0545190i	0.447522	+	0.894273i	$0.352307\pi$
$252$	−2.03789e7	+	9.71535e7i	−0.0802191	+	0.382434i
$253$	2.27316e7	−	5.48789e7i	0.0882485	−	0.213051i
$254$	−2.03201e8	−	2.50246e8i	−0.778050	−	0.958185i
$255$	−5.22305e7			−0.197257
$256$	1.81745e8	+	1.97551e8i	0.677052	+	0.735935i
$257$	9.08522e6			0.0333864			0.0166932	−	0.999861i	$-0.494686\pi$
$257$	9.08522e6			0.0333864			0.0166932	+	0.999861i	$0.494686\pi$
$258$	−1.58456e8	−	1.95142e8i	−0.574435	−	0.707429i
$259$	3.09967e8	−	7.48325e8i	1.10858	−	2.67634i
$260$	4.35807e7	−	2.07765e8i	0.153776	−	0.733106i
$261$	−5.03215e7	+	2.08439e7i	−0.175191	+	0.0725665i
$262$	−1.57592e8	+	4.69104e7i	−0.541351	+	0.161144i
$263$	−1.42586e8	+	1.42586e8i	−0.483317	+	0.483317i	−0.906189	−	0.422873i	$-0.861022\pi$
$263$	−1.42586e8	+	1.42586e8i	−0.483317	+	0.483317i	0.422873	+	0.906189i	$0.361022\pi$
$264$	5.07914e7	−	2.61370e7i	0.169893	−	0.0874264i
$265$	−1.36304e8	−	1.36304e8i	−0.449933	−	0.449933i
$266$	2.59118e7	+	1.40241e7i	0.0844134	+	0.0456865i
$267$	5.15428e7	+	1.24435e8i	0.165721	+	0.400087i
$268$	−3.99343e8	−	2.72889e8i	−1.26728	−	0.865993i
$269$	−2.21502e7	−	9.17490e6i	−0.0693816	−	0.0287388i	0.347723	−	0.937597i	$-0.386955\pi$
$269$	−2.21502e7	−	9.17490e6i	−0.0693816	−	0.0287388i	−0.417104	+	0.908859i	$0.636955\pi$
$270$	−2.97796e8	−	3.08965e7i	−0.920757	−	0.0955292i
$271$			2.98073e8i			0.909768i	0.890551	+	0.454884i	$0.150319\pi$
$271$			2.98073e8i			0.909768i	−0.890551	+	0.454884i	$0.849681\pi$
$272$	−3.49904e7	+	7.97362e7i	−0.105428	+	0.240251i
$273$			4.35101e8i			1.29426i
$274$	−3.31532e7	+	3.19547e8i	−0.0973641	+	0.938443i
$275$	−1.83793e7	−	7.61297e6i	−0.0532924	−	0.0220744i
$276$	−5.99118e7	−	3.18493e8i	−0.171526	−	0.911839i
$277$	−1.23455e8	−	2.98047e8i	−0.349004	−	0.842569i	−0.996738	−	0.0807032i	$-0.974283\pi$
$277$	−1.23455e8	−	2.98047e8i	−0.349004	−	0.842569i	0.647735	−	0.761866i	$-0.275717\pi$
$278$	1.36180e8	−	2.51615e8i	0.380151	−	0.702392i
$279$	3.83110e7	+	3.83110e7i	0.105611	+	0.105611i
$280$	−4.38920e7	−	5.30450e8i	−0.119490	−	1.44408i
$281$	−5.07472e8	+	5.07472e8i	−1.36440	+	1.36440i	−0.496169	+	0.868226i	$0.665261\pi$
$281$	−5.07472e8	+	5.07472e8i	−1.36440	+	1.36440i	−0.868226	+	0.496169i	$0.834739\pi$
$282$	−1.38373e8	−	4.64852e8i	−0.367434	−	1.23436i
$283$	−6.36078e7	+	2.63472e7i	−0.166824	+	0.0691007i	−0.464532	−	0.885556i	$-0.653778\pi$
$283$	−6.36078e7	+	2.63472e7i	−0.166824	+	0.0691007i	0.297709	+	0.954657i	$0.403778\pi$
$284$	3.62405e8	+	5.54796e8i	0.938814	+	1.43721i
$285$	−6.38675e6	+	1.54190e7i	−0.0163427	+	0.0394547i
$286$	−5.84643e7	+	4.74732e7i	−0.147778	+	0.119996i
$287$	−1.22894e9			−3.06863
$288$	−4.63270e7	+	8.14958e7i	−0.114277	+	0.201030i
$289$	3.82093e8			0.931164
$290$	2.26719e8	−	1.84096e8i	0.545876	−	0.443254i
$291$	2.68448e7	−	6.48092e7i	0.0638609	−	0.154174i
$292$	−1.16260e8	+	7.59434e7i	−0.273269	+	0.178505i
$293$	−5.33872e8	+	2.21137e8i	−1.23994	+	0.513600i	−0.903696	−	0.428175i	$-0.859157\pi$
$293$	−5.33872e8	+	2.21137e8i	−1.23994	+	0.513600i	−0.336244	+	0.941775i	$0.609157\pi$
$294$	2.02243e8	+	6.79418e8i	0.464149	+	1.55927i
$295$	−7.42059e7	+	7.42059e7i	−0.168291	+	0.168291i
$296$	4.94423e8	−	5.83626e8i	1.10810	−	1.30802i
$297$	7.51043e7	+	7.51043e7i	0.166348	+	0.166348i
$298$	3.72498e8	−	6.88252e8i	0.815393	−	1.50657i
$299$	1.63511e8	+	3.94751e8i	0.353752	+	0.854032i
$300$	−1.06666e8	+	2.00649e7i	−0.228087	+	0.0429055i
$301$	7.67708e8	+	3.17995e8i	1.62261	+	0.672106i
$302$	1.47058e7	−	1.41742e8i	0.0307231	−	0.296124i
$303$			1.69433e8i			0.349904i
$304$	1.92603e7	+	2.00797e7i	0.0393194	+	0.0409920i
$305$			3.61651e8i			0.729862i
$306$	−3.02463e7	−	3.13807e6i	−0.0603458	−	0.00626091i
$307$	4.79225e8	+	1.98501e8i	0.945268	+	0.391543i	0.801450	−	0.598061i	$-0.204062\pi$
$307$	4.79225e8	+	1.98501e8i	0.945268	+	0.391543i	0.143818	+	0.989604i	$0.454062\pi$
$308$	−1.06535e8	+	1.55903e8i	−0.207762	+	0.304037i
$309$	−1.59895e8	−	3.86020e8i	−0.308304	−	0.744312i
$310$	−2.55488e8	−	1.38276e8i	−0.487084	−	0.263621i
$311$	2.54748e7	+	2.54748e7i	0.0480230	+	0.0480230i	0.730710	−	0.682687i	$-0.239189\pi$
$311$	2.54748e7	+	2.54748e7i	0.0480230	+	0.0480230i	−0.682687	+	0.730710i	$0.739189\pi$
$312$	−1.25400e8	+	3.91282e8i	−0.233752	+	0.729372i
$313$	7.11469e8	−	7.11469e8i	1.31145	−	1.31145i	0.391098	−	0.920349i	$-0.372095\pi$
$313$	7.11469e8	−	7.11469e8i	1.31145	−	1.31145i	0.920349	−	0.391098i	$-0.127905\pi$
$314$	9.59879e8	−	2.85728e8i	1.74970	−	0.520833i
$315$	1.71728e8	−	7.11320e7i	0.309567	−	0.128227i
$316$	−8.40653e8	−	1.76335e8i	−1.49869	−	0.314364i
$317$	1.42189e8	−	3.43274e8i	0.250702	−	0.605249i	−0.747559	−	0.664196i	$-0.768774\pi$
$317$	1.42189e8	−	3.43274e8i	0.250702	−	0.605249i	0.998261	+	0.0589466i	$0.0187742\pi$
$318$	2.35185e8	+	2.89636e8i	0.410124	+	0.505076i
$319$	−1.03608e8			−0.178700
$320$	1.13409e8	−	4.89679e8i	0.193473	−	0.835384i
$321$	−3.10449e8			−0.523868
$322$	6.75305e8	+	8.31653e8i	1.12721	+	1.38818i
$323$	−3.45391e6	+	8.33848e6i	−0.00570299	+	0.0137682i
$324$	4.28585e8	+	8.98998e7i	0.700051	+	0.146842i
$325$	1.32205e8	−	5.47611e7i	0.213627	−	0.0884872i
$326$	−1.87467e8	+	5.58035e7i	−0.299684	+	0.0892071i
$327$	4.97879e8	−	4.97879e8i	0.787421	−	0.787421i
$328$	−1.10517e9	−	3.54191e8i	−1.72931	−	0.554216i
$329$	1.13369e9	+	1.13369e9i	1.75513	+	1.75513i
$330$	−9.40661e7	−	5.09108e7i	−0.144090	−	0.0779850i
$331$	−2.22659e8	−	5.37546e8i	−0.337475	−	0.814737i	−0.997957	−	0.0638945i	$-0.979648\pi$
$331$	−2.22659e8	−	5.37546e8i	−0.337475	−	0.814737i	0.660482	−	0.750842i	$-0.270352\pi$
$332$	−4.98818e8	+	7.29965e8i	−0.748098	+	1.09476i
$333$	2.46786e8	+	1.02222e8i	0.366240	+	0.151701i
$334$	−1.78405e7	−	1.85096e6i	−0.0261995	−	0.00271822i
$335$			9.05675e8i			1.31618i
$336$	−2.14516e7	+	1.02998e9i	−0.0308512	+	1.48130i
$337$			2.99085e8i			0.425686i	0.977086	+	0.212843i	$0.0682723\pi$
$337$			2.99085e8i			0.425686i	−0.977086	+	0.212843i	$0.931728\pi$
$338$	−1.73571e7	+	1.67296e8i	−0.0244495	+	0.235656i
$339$	−3.15929e8	−	1.30862e8i	−0.440444	−	0.182438i
$340$	1.60237e8	−	3.01423e7i	0.221099	−	0.0415910i
$341$	3.94396e7	+	9.52156e7i	0.0538632	+	0.130037i
$342$	−4.62491e6	+	8.54529e6i	−0.00625190	+	0.0115514i
$343$	−7.63973e8	−	7.63973e8i	−1.02223	−	1.02223i
$344$	5.98743e8	+	5.07230e8i	0.793024	+	0.671816i
$345$	−4.29094e8	+	4.29094e8i	−0.562582	+	0.562582i
$346$	−2.70615e8	−	9.09109e8i	−0.351225	−	1.17991i
$347$	1.10061e8	−	4.55887e7i	0.141410	−	0.0585739i	−0.310856	−	0.950457i	$-0.600616\pi$
$347$	1.10061e8	−	4.55887e7i	0.141410	−	0.0585739i	0.452266	+	0.891883i	$0.350616\pi$
$348$	−4.73247e8	+	3.09135e8i	−0.601950	+	0.393207i
$349$	−4.63075e8	+	1.11796e9i	−0.583126	+	1.40779i	0.306840	+	0.951761i	$0.400728\pi$
$349$	−4.63075e8	+	1.11796e9i	−0.583126	+	1.40779i	−0.889965	+	0.456028i	$0.849272\pi$
$350$	2.78527e8	−	2.26165e8i	0.347239	−	0.281959i
$351$	−7.64008e8			−0.943025
$352$	−1.40739e8	+	1.09497e8i	−0.171994	+	0.133815i
$353$	−7.37692e8			−0.892614			−0.446307	−	0.894880i	$-0.647261\pi$
$353$	−7.37692e8			−0.892614			−0.446307	+	0.894880i	$0.647261\pi$
$354$	1.57682e8	−	1.28038e8i	0.188917	−	0.153401i
$355$	4.74849e8	−	1.14639e9i	0.563322	−	1.35998i
$356$	−2.29939e8	−	3.52008e8i	−0.270108	−	0.413502i
$357$	−3.08743e8	+	1.27885e8i	−0.359135	+	0.148759i
$358$	7.93095e7	+	2.66434e8i	0.0913555	+	0.306901i
$359$	1.03050e9	−	1.03050e9i	1.17548	−	1.17548i	0.194599	−	0.980883i	$-0.437659\pi$
$359$	1.03050e9	−	1.03050e9i	1.17548	−	1.17548i	0.980883	−	0.194599i	$-0.0623407\pi$
$360$	1.74934e8	−	1.44749e7i	0.197613	−	0.0163514i
$361$	−6.30024e8	−	6.30024e8i	−0.704825	−	0.704825i
$362$	1.42182e8	−	2.62705e8i	0.157531	−	0.291064i
$363$	−2.91258e8	−	7.03159e8i	−0.319599	−	0.771579i
$364$	−2.51098e8	−	1.33484e9i	−0.272890	−	1.45069i
$365$	2.40230e8	+	9.95067e7i	0.258585	+	0.107109i
$366$	7.22360e7	−	6.96246e8i	0.0770140	−	0.742299i
$367$		−	1.23380e9i		−	1.30291i	−0.758687	−	0.651455i	$-0.774159\pi$
$367$		−	1.23380e9i		−	1.30291i	0.758687	−	0.651455i	$-0.225841\pi$
$368$	3.67605e8	+	9.42526e8i	0.384516	+	0.985884i
$369$		−	4.05285e8i		−	0.419922i
$370$	−1.42462e9	−	1.47805e8i	−1.46215	−	0.151699i
$371$	−1.13945e9	−	4.71977e8i	−1.15848	−	0.479857i
$372$	4.64242e8	+	3.17238e8i	0.467568	+	0.319510i
$373$	5.80157e7	+	1.40062e8i	0.0578848	+	0.139746i	0.950176	−	0.311714i	$-0.100903\pi$
$373$	5.80157e7	+	1.40062e8i	0.0578848	+	0.139746i	−0.892291	+	0.451461i	$0.850903\pi$
$374$	−5.08703e7	−	2.75322e7i	−0.0502822	−	0.0272139i
$375$	6.86609e8	+	6.86609e8i	0.672357	+	0.672357i
$376$	6.92779e8	+	1.34626e9i	0.672105	+	1.30608i
$377$	5.26982e8	−	5.26982e8i	0.506525	−	0.506525i
$378$	−1.83597e9	+	5.46514e8i	−1.74841	+	0.520451i
$379$	2.05898e8	−	8.52858e7i	0.194274	−	0.0804710i	−0.283425	−	0.958994i	$-0.591471\pi$
$379$	2.05898e8	−	8.52858e7i	0.194274	−	0.0804710i	0.477699	+	0.878523i	$0.341471\pi$
$380$	1.06955e7	−	5.09895e7i	0.00999906	−	0.0476692i
$381$	4.47085e8	−	1.07936e9i	0.414146	−	0.999836i
$382$	1.07430e9	+	1.32303e9i	0.986063	+	1.21436i
$383$	3.05603e8			0.277947			0.138974	−	0.990296i	$-0.455620\pi$
$383$	3.05603e8			0.277947			0.138974	+	0.990296i	$0.455620\pi$
$384$	−3.16141e8	+	9.20070e8i	−0.284919	+	0.829204i
$385$	3.53574e8			0.315767
$386$	6.47652e8	+	7.97597e8i	0.573173	+	0.705876i
$387$	−1.04870e8	+	2.53178e8i	−0.0919733	+	0.222043i
$388$	−4.49555e7	+	2.14319e8i	−0.0390726	+	0.186273i
$389$	3.99807e8	−	1.65605e8i	0.344371	−	0.142643i	−0.203793	−	0.979014i	$-0.565327\pi$
$389$	3.99807e8	−	1.65605e8i	0.344371	−	0.142643i	0.548164	+	0.836371i	$0.315327\pi$
$390$	7.37398e8	−	2.19502e8i	0.629471	−	0.187375i
$391$	−2.32051e8	+	2.32051e8i	−0.196320	+	0.196320i
$392$	−1.01255e9	−	1.96766e9i	−0.849015	−	1.64987i
$393$	−4.21375e8	−	4.21375e8i	−0.350182	−	0.350182i
$394$	7.84950e8	+	4.24833e8i	0.646554	+	0.349930i
$395$	6.15494e8	+	1.48593e9i	0.502497	+	1.21314i
$396$	−5.14142e7	−	3.51337e7i	−0.0416054	−	0.0284309i
$397$	−7.34807e8	−	3.04367e8i	−0.589395	−	0.244135i	0.0679953	−	0.997686i	$-0.478340\pi$
$397$	−7.34807e8	−	3.04367e8i	−0.589395	−	0.244135i	−0.657390	+	0.753550i	$0.728340\pi$
$398$	−1.86948e9	−	1.93960e8i	−1.48638	−	0.154213i
$399$			1.06782e8i			0.0841575i
$400$	3.15659e8	−	1.23114e8i	0.246608	−	0.0961826i
$401$		−	6.76700e8i		−	0.524072i	−0.965058	−	0.262036i	$-0.915606\pi$
$401$		−	6.76700e8i		−	0.524072i	0.965058	−	0.262036i	$-0.0843939\pi$
$402$	1.80899e8	−	1.74359e9i	0.138882	−	1.33861i
$403$	−6.84899e8	−	2.83694e8i	−0.521265	−	0.215915i
$404$	−9.77801e7	−	5.19802e8i	−0.0737761	−	0.392196i
$405$	−3.13794e8	−	7.57565e8i	−0.234721	−	0.566666i
$406$	8.89414e8	−	1.64334e9i	0.659573	−	1.21867i
$407$	3.59289e8	+	3.59289e8i	0.264158	+	0.264158i
$408$	−3.14507e8	+	2.60238e7i	−0.229255	+	0.0189697i
$409$	1.86411e8	−	1.86411e8i	0.134722	−	0.134722i	−0.636530	−	0.771252i	$-0.719631\pi$
$409$	1.86411e8	−	1.86411e8i	0.134722	−	0.134722i	0.771252	+	0.636530i	$0.219631\pi$
$410$	6.19981e8	+	2.08278e9i	0.444257	+	1.49245i
$411$	−1.07570e9	+	4.45568e8i	−0.764263	+	0.316568i
$412$	7.13311e8	+	1.09199e9i	0.502503	+	0.769269i
$413$	−2.56951e8	+	6.20335e8i	−0.179484	+	0.433312i
$414$	−2.74266e8	+	2.22705e8i	−0.189964	+	0.154251i
$415$	1.65550e9			1.13700
$416$	1.58903e8	−	1.27278e9i	0.108220	−	0.866815i
$417$	1.03690e9			0.700262
$418$	−1.43482e7	+	1.16508e7i	−0.00960907	+	0.00780260i
$419$	−1.03262e9	+	2.49297e9i	−0.685791	+	1.65564i	0.0673039	+	0.997733i	$0.478560\pi$
$419$	−1.03262e9	+	2.49297e9i	−0.685791	+	1.65564i	−0.753094	+	0.657912i	$0.771440\pi$
$420$	1.61501e9	−	1.05496e9i	1.06366	−	0.694805i
$421$	2.26020e8	−	9.36205e7i	0.147625	−	0.0611482i	−0.307648	−	0.951500i	$-0.599542\pi$
$421$	2.26020e8	−	9.36205e7i	0.147625	−	0.0611482i	0.455273	+	0.890352i	$0.349542\pi$
$422$	4.87035e8	+	1.63616e9i	0.315476	+	1.05982i
$423$	−3.73874e8	+	3.73874e8i	−0.240179	+	0.240179i
$424$	−8.88671e8	−	7.52844e8i	−0.566188	−	0.479650i
$425$	7.77157e7	+	7.77157e7i	0.0491075	+	0.0491075i
$426$	−1.14315e9	+	2.11216e9i	−0.716424	+	1.32371i
$427$	8.85497e8	+	2.13778e9i	0.550414	+	1.32882i
$428$	9.52421e8	−	1.79160e8i	0.587186	−	0.110456i
$429$	−2.52168e8	−	1.04451e8i	−0.154202	−	0.0638724i
$430$	1.51633e8	−	1.46152e9i	0.0919718	−	0.886469i
$431$		−	7.97384e8i		−	0.479730i	−0.970806	−	0.239865i	$-0.922897\pi$
$431$		−	7.97384e8i		−	0.479730i	0.970806	−	0.239865i	$-0.0771032\pi$
$432$	−1.80858e9	−	3.76675e7i	−1.07930	−	0.0224788i
$433$			1.91680e9i			1.13467i	0.823488	+	0.567334i	$0.192025\pi$
$433$			1.91680e9i			1.13467i	−0.823488	+	0.567334i	$0.807975\pi$
$434$	−1.84880e9	−	1.91814e8i	−1.08561	−	0.112633i
$435$	9.77881e8	+	4.05052e8i	0.569605	+	0.235938i
$436$	−1.24011e9	+	1.81476e9i	−0.716569	+	1.04862i
$437$	4.01287e7	+	9.68792e7i	0.0230022	+	0.0555323i
$438$	−4.42613e8	−	2.39552e8i	−0.251689	−	0.136220i
$439$	−4.60692e8	−	4.60692e8i	−0.259887	−	0.259887i	0.565121	−	0.825008i	$-0.308829\pi$
$439$	−4.60692e8	−	4.60692e8i	−0.259887	−	0.259887i	−0.825008	+	0.565121i	$0.808829\pi$
$440$	3.17965e8	+	1.01903e8i	0.177949	+	0.0570298i
$441$	5.46446e8	−	5.46446e8i	0.303398	−	0.303398i
$442$	3.98780e8	−	1.18705e8i	0.219662	−	0.0653870i
$443$	−2.37171e8	+	9.82395e7i	−0.129613	+	0.0536875i	−0.446547	−	0.894760i	$-0.647347\pi$
$443$	−2.37171e8	+	9.82395e7i	−0.129613	+	0.0536875i	0.316934	+	0.948448i	$0.397347\pi$
$444$	2.71313e9	+	5.69103e8i	1.47106	+	0.308568i
$445$	−3.01283e8	+	7.27363e8i	−0.162075	+	0.391283i
$446$	−6.00706e8	−	7.39783e8i	−0.320620	−	0.394850i
$447$	2.83627e9			1.50201
$448$	−5.28593e8	−	3.17225e9i	−0.277746	−	1.66684i
$449$	−6.51328e8			−0.339577			−0.169788	−	0.985481i	$-0.554308\pi$
$449$	−6.51328e8			−0.339577			−0.169788	+	0.985481i	$0.554308\pi$
$450$	7.45855e7	+	9.18536e7i	0.0385843	+	0.0475174i
$451$	2.95022e8	−	7.12246e8i	0.151438	−	0.365605i
$452$	1.04476e9	+	2.19147e8i	0.532146	+	0.111623i
$453$	4.77148e8	−	1.97641e8i	0.241162	−	0.0998927i
$454$	−4.39727e7	+	1.30894e7i	−0.0220540	+	0.00656482i
$455$	−1.79839e9	+	1.79839e9i	−0.895041	+	0.895041i
$456$	−3.07755e7	+	9.60279e7i	−0.0151994	+	0.0474265i
$457$	−2.16213e9	−	2.16213e9i	−1.05968	−	1.05968i	−0.998102	−	0.0615779i	$-0.980387\pi$
$457$	−2.16213e9	−	2.16213e9i	−1.05968	−	1.05968i	−0.0615779	−	0.998102i	$-0.519613\pi$
$458$	7.29931e8	+	3.95056e8i	0.355020	+	0.192145i
$459$	−2.24558e8	−	5.42131e8i	−0.108389	−	0.261674i
$460$	1.06878e9	−	1.56404e9i	0.511961	−	0.749198i
$461$	−1.22000e9	−	5.05341e8i	−0.579971	−	0.240232i	0.0733581	−	0.997306i	$-0.476628\pi$
$461$	−1.22000e9	−	5.05341e8i	−0.579971	−	0.240232i	−0.653330	+	0.757074i	$0.726628\pi$
$462$	−6.80695e8	−	7.06225e7i	−0.321148	−	0.0333193i
$463$		−	6.52050e8i		−	0.305314i	−0.988279	−	0.152657i	$-0.951217\pi$
$463$		−	6.52050e8i		−	0.305314i	0.988279	−	0.152657i	$-0.0487830\pi$
$464$	1.27347e9	−	1.22150e9i	0.591799	−	0.567651i
$465$		−	1.05286e9i		−	0.485608i
$466$	−3.34901e8	+	3.22794e9i	−0.153308	+	1.47766i
$467$	−1.17953e9	−	4.88576e8i	−0.535918	−	0.221985i	0.0982749	−	0.995159i	$-0.468668\pi$
$467$	−1.17953e9	−	4.88576e8i	−0.535918	−	0.221985i	−0.634193	+	0.773175i	$0.718668\pi$
$468$	4.40210e8	−	8.28080e7i	0.198518	−	0.0373432i
$469$	2.21753e9	+	5.35359e9i	0.992578	+	2.39629i
$470$	1.34942e9	−	2.49329e9i	0.599523	−	1.10772i
$471$	2.56656e9	+	2.56656e9i	1.13182	+	1.13182i
$472$	−4.09859e8	+	4.83805e8i	−0.179406	+	0.211774i
$473$	−3.68595e8	+	3.68595e8i	−0.160153	+	0.160153i
$474$	−8.88140e8	−	2.98364e9i	−0.383052	−	1.28683i
$475$	3.24456e7	−	1.34394e7i	0.0138908	−	0.00575376i
$476$	8.73386e8	−	5.70514e8i	0.371178	−	0.242461i
$477$	1.55650e8	−	3.75773e8i	0.0656653	−	0.158530i
$478$	2.78535e8	−	2.26172e8i	0.116649	−	0.0947197i
$479$	−6.36797e8			−0.264744			−0.132372	−	0.991200i	$-0.542259\pi$
$479$	−6.36797e8			−0.264744			−0.132372	+	0.991200i	$0.542259\pi$
$480$	1.75641e9	−	4.83254e8i	0.724905	−	0.199449i
$481$	−3.65491e9			−1.49751
$482$	2.78913e9	−	2.26478e9i	1.13450	−	0.921217i
$483$	−1.48582e9	+	3.58708e9i	−0.599998	+	1.44852i
$484$	1.29934e9	+	1.98913e9i	0.520912	+	0.797451i
$485$	3.78830e8	−	1.56916e8i	0.150781	−	0.0624557i
$486$	−3.26613e8	−	1.09723e9i	−0.129065	−	0.433582i
$487$	−1.11825e9	+	1.11825e9i	−0.438721	+	0.438721i	−0.891581	−	0.452861i	$-0.850404\pi$
$487$	−1.11825e9	+	1.11825e9i	−0.438721	+	0.438721i	0.452861	+	0.891581i	$0.350404\pi$
$488$	1.80192e8	+	2.17769e9i	0.0701887	+	0.848256i
$489$	−5.01257e8	−	5.01257e8i	−0.193856	−	0.193856i
$490$	−1.97229e9	+	3.64413e9i	−0.757328	+	1.39929i
$491$	−1.06001e9	−	2.55908e9i	−0.404132	−	0.975662i	−0.986652	−	0.162845i	$-0.947933\pi$
$491$	−1.06001e9	−	2.55908e9i	−0.404132	−	0.975662i	0.582519	−	0.812817i	$-0.302067\pi$
$492$	−7.77566e8	−	4.13356e9i	−0.294347	−	1.56476i
$493$	5.28831e8	+	2.19049e8i	0.198771	+	0.0823336i
$494$	1.37199e7	−	1.32239e8i	0.00512044	−	0.0493533i
$495$			1.16603e8i			0.0432107i
$496$	−1.60732e9	−	7.05335e8i	−0.591448	−	0.259543i
$497$		−	7.93915e9i		−	2.90086i
$498$	−3.18714e9	−	3.30668e8i	−1.15637	−	0.119974i
$499$	3.02270e9	+	1.25204e9i	1.08904	+	0.451094i	0.853671	−	0.520812i	$-0.174371\pi$
$499$	3.02270e9	+	1.25204e9i	1.08904	+	0.451094i	0.235367	+	0.971907i	$0.424371\pi$
$500$	−2.50268e9	−	1.71020e9i	−0.895387	−	0.611858i
$501$	−2.48763e7	−	6.00566e7i	−0.00883798	−	0.0213368i
$502$	−3.55128e8	−	1.92203e8i	−0.125292	−	0.0678107i
$503$	7.93479e7	+	7.93479e7i	0.0278002	+	0.0278002i	0.720870	−	0.693070i	$-0.243742\pi$
$503$	7.93479e7	+	7.93479e7i	0.0278002	+	0.0278002i	−0.693070	+	0.720870i	$0.743742\pi$
$504$	9.98622e8	−	5.13887e8i	0.347452	−	0.178797i
$505$	−7.00311e8	+	7.00311e8i	−0.241975	+	0.241975i
$506$	−6.44108e8	+	1.91732e8i	−0.221020	+	0.0657912i
$507$	−5.63172e8	+	2.33274e8i	−0.191917	+	0.0794946i
$508$	−7.48708e8	+	3.56937e9i	−0.253390	+	1.20800i
$509$	5.85772e8	−	1.41418e9i	0.196887	−	0.475327i	−0.794344	−	0.607468i	$-0.792185\pi$
$509$	5.85772e8	−	1.41418e9i	0.196887	−	0.475327i	0.991231	+	0.132141i	$0.0421852\pi$
$510$	3.72493e8	+	4.58733e8i	0.124343	+	0.153131i
$511$	1.66368e9			0.551566
$512$	4.38911e8	−	3.00512e9i	0.144521	−	0.989502i
$513$	−1.87502e8			−0.0613189
$514$	−6.47932e7	−	7.97942e7i	−0.0210455	−	0.0259179i
$515$	9.34634e8	−	2.25641e9i	0.301520	−	0.727934i
$516$	−5.83844e8	+	2.78340e9i	−0.187078	+	0.891870i
$517$	−9.29202e8	+	3.84888e8i	−0.295728	+	0.122495i
$518$	−8.78303e9	+	2.61445e9i	−2.77645	+	0.826468i
$519$	2.43081e9	−	2.43081e9i	0.763248	−	0.763248i
$520$	−2.13558e9	+	1.09896e9i	−0.666046	+	0.342744i
$521$	−1.81456e9	−	1.81456e9i	−0.562132	−	0.562132i	0.367780	−	0.929913i	$-0.380118\pi$
$521$	−1.81456e9	−	1.81456e9i	−0.562132	−	0.562132i	−0.929913	+	0.367780i	$0.880118\pi$
$522$	5.41948e8	+	2.93315e8i	0.166767	+	0.0902583i
$523$	−2.12255e9	−	5.12428e9i	−0.648786	−	1.56631i	−0.814519	−	0.580137i	$-0.802999\pi$
$523$	−2.12255e9	−	5.12428e9i	−0.648786	−	1.56631i	0.165733	−	0.986171i	$-0.447001\pi$
$524$	1.53591e9	+	1.04955e9i	0.466343	+	0.318673i
$525$	1.20134e9	+	4.97611e8i	0.362333	+	0.150083i
$526$	2.26920e9	+	2.35431e8i	0.679864	+	0.0705363i
$527$		−	5.69380e8i		−	0.169459i
$528$	−5.91788e8	−	2.59692e8i	−0.174963	−	0.0767786i
$529$			4.07965e8i			0.119820i
$530$	−2.25058e8	+	2.16922e9i	−0.0656642	+	0.632904i
$531$	−2.04577e8	−	8.47384e7i	−0.0592959	−	0.0245612i
$532$	−6.16240e7	−	3.27595e8i	−0.0177443	−	0.0943293i
$533$	2.12213e9	+	5.12328e9i	0.607054	+	1.46556i
$534$	7.25309e8	−	1.34013e9i	0.206124	−	0.380849i
$535$	−1.28316e9	−	1.28316e9i	−0.362280	−	0.362280i
$536$	4.51252e8	+	5.45354e9i	0.126573	+	1.52968i
$537$	−7.12401e8	+	7.12401e8i	−0.198525	+	0.198525i
$538$	7.73868e7	+	2.59975e8i	0.0214254	+	0.0719769i
$539$	1.35810e9	−	5.62544e8i	0.373569	−	0.154737i
$540$	1.85243e9	+	2.83584e9i	0.506249	+	0.775004i
$541$	6.89947e8	−	1.66568e9i	0.187338	−	0.452273i	−0.802108	−	0.597179i	$-0.796288\pi$
$541$	6.89947e8	−	1.66568e9i	0.187338	−	0.452273i	0.989445	+	0.144906i	$0.0462880\pi$
$542$	2.61794e9	−	2.12577e9i	0.706255	−	0.573482i
$543$	1.08260e9			0.290182
$544$	9.49854e8	−	2.61340e8i	0.252965	−	0.0696002i
$545$	4.11573e9			1.08908
$546$	3.82144e9	−	3.10302e9i	1.00474	−	0.815850i
$547$	−1.57488e9	+	3.80210e9i	−0.411426	+	0.993270i	0.573329	+	0.819325i	$0.305652\pi$
$547$	−1.57488e9	+	3.80210e9i	−0.411426	+	0.993270i	−0.984755	+	0.173945i	$0.944348\pi$
$548$	3.04298e9	−	1.98774e9i	0.789890	−	0.515973i
$549$	−7.05006e8	+	2.92023e8i	−0.181840	+	0.0753206i
$550$	6.42125e7	+	2.15717e8i	0.0164570	+	0.0552859i
$551$	1.29331e8	−	1.29331e8i	0.0329361	−	0.0329361i
$552$	−2.37001e9	+	2.79760e9i	−0.599739	+	0.707943i
$553$	7.27657e9	+	7.27657e9i	1.82974	+	1.82974i
$554$	−1.73726e9	+	3.20988e9i	−0.434091	+	0.802055i
$555$	−1.98645e9	−	4.79570e9i	−0.493232	−	1.19077i
$556$	−3.18109e9	+	5.98396e8i	−0.784900	+	0.147648i
$557$	−4.67663e9	−	1.93712e9i	−1.14667	−	0.474968i	−0.273257	−	0.961941i	$-0.588101\pi$
$557$	−4.67663e9	−	1.93712e9i	−1.14667	−	0.474968i	−0.873417	+	0.486973i	$0.838101\pi$
$558$	6.32572e7	−	6.09704e8i	0.0154131	−	0.148559i
$559$		−	3.74958e9i		−	0.907908i
$560$	−4.34585e9	+	4.16852e9i	−1.04572	+	1.00305i
$561$		−	2.09636e8i		−	0.0501297i
$562$	8.07621e9	+	8.37912e8i	1.91924	+	0.199123i
$563$	2.16163e9	+	8.95378e8i	0.510508	+	0.211459i	0.623042	−	0.782188i	$-0.285897\pi$
$563$	2.16163e9	+	8.95378e8i	0.510508	+	0.211459i	−0.112534	+	0.993648i	$0.535897\pi$
$564$	−3.09590e9	+	4.53050e9i	−0.726624	+	1.06333i
$565$	−7.64930e8	−	1.84670e9i	−0.178424	−	0.430753i
$566$	6.85037e8	+	3.70758e8i	0.158802	+	0.0859474i
$567$	−3.70977e9	−	3.70977e9i	−0.854685	−	0.854685i
$568$	2.28813e9	−	7.13959e9i	0.523916	−	1.63476i
$569$	−1.29037e9	+	1.29037e9i	−0.293644	+	0.293644i	−0.838518	−	0.544874i	$-0.816578\pi$
$569$	−1.29037e9	+	1.29037e9i	−0.293644	+	0.293644i	0.544874	+	0.838518i	$0.316578\pi$
$570$	1.80971e8	−	5.38698e7i	0.0409305	−	0.0121838i
$571$	−2.13541e9	+	8.84516e8i	−0.480015	+	0.198829i	−0.609552	−	0.792746i	$-0.708651\pi$
$571$	−2.13541e9	+	8.84516e8i	−0.480015	+	0.198829i	0.129537	+	0.991575i	$0.458651\pi$
$572$	8.33901e8	+	1.74919e8i	0.186307	+	0.0390796i
$573$	−2.36370e9	+	5.70647e9i	−0.524868	+	1.26714i
$574$	8.76445e9	+	1.07936e10i	1.93434	+	2.38218i
$575$	1.27693e9			0.280111
$576$	1.04616e9	−	1.74322e8i	0.228096	−	0.0380078i
$577$	4.16177e9			0.901910			0.450955	−	0.892547i	$-0.351084\pi$
$577$	4.16177e9			0.901910			0.450955	+	0.892547i	$0.351084\pi$
$578$	−2.72498e9	−	3.35587e9i	−0.586969	−	0.722865i
$579$	−1.42497e9	+	3.44019e9i	−0.305093	+	0.736559i
$580$	−3.23379e9	−	6.78316e8i	−0.688198	−	0.144356i
$581$	9.78591e9	−	4.05345e9i	2.07007	−	0.857450i
$582$	−7.60660e8	+	2.26426e8i	−0.159941	+	0.0476097i
$583$	5.47079e8	−	5.47079e8i	0.114343	−	0.114343i
$584$	1.49613e9	+	4.79487e8i	0.310831	+	0.0996167i
$585$	−5.93079e8	−	5.93079e8i	−0.122481	−	0.122481i
$586$	5.74964e9	+	3.11184e9i	1.18032	+	0.638816i
$587$	2.71084e9	+	6.54455e9i	0.553185	+	1.33551i	0.915074	+	0.403286i	$0.132132\pi$
$587$	2.71084e9	+	6.54455e9i	0.553185	+	1.33551i	−0.361889	+	0.932221i	$0.617868\pi$
$588$	4.52490e9	−	6.62168e9i	0.917884	−	1.34322i
$589$	−1.68087e8	−	6.96239e7i	−0.0338946	−	0.0140396i
$590$	1.18095e9	+	1.22525e8i	0.236729	+	0.0245608i
$591$			3.23476e9i			0.644594i
$592$	−8.65200e9	−	1.80196e8i	−1.71392	−	0.0356961i
$593$		−	1.81498e9i		−	0.357421i	−0.983902	−	0.178711i	$-0.942807\pi$
$593$		−	1.81498e9i		−	0.357421i	0.983902	−	0.178711i	$-0.0571926\pi$
$594$	1.24008e8	−	1.19525e9i	0.0242772	−	0.233995i
$595$	−1.80470e9	−	7.47530e8i	−0.351233	−	0.145485i
$596$	−8.70137e9	+	1.63682e9i	−1.68355	+	0.316693i
$597$	−2.60676e9	−	6.29327e9i	−0.501407	−	1.21050i
$598$	2.30093e9	−	4.25135e9i	0.439996	−	0.812966i
$599$	−5.74784e9	−	5.74784e9i	−1.09272	−	1.09272i	−0.995237	−	0.0974876i	$-0.968919\pi$
$599$	−5.74784e9	−	5.74784e9i	−1.09272	−	1.09272i	−0.0974876	−	0.995237i	$-0.531081\pi$
$600$	9.36936e8	+	7.93732e8i	0.177084	+	0.150018i
$601$	−7.06884e9	+	7.06884e9i	−1.32827	+	1.32827i	−0.421398	+	0.906876i	$0.638460\pi$
$601$	−7.06884e9	+	7.06884e9i	−1.32827	+	1.32827i	−0.906876	+	0.421398i	$0.861540\pi$
$602$	−2.68217e9	−	9.01053e9i	−0.501070	−	1.68330i
$603$	−1.76553e9	+	7.31306e8i	−0.327917	+	0.135828i
$604$	−1.34978e9	+	8.81704e8i	−0.249249	+	0.162815i
$605$	1.70249e9	−	4.11018e9i	0.312566	−	0.754601i
$606$	1.48811e9	−	1.20835e9i	0.271632	−	0.220566i
$607$	1.53677e9			0.278900			0.139450	−	0.990229i	$-0.455467\pi$
$607$	1.53677e9			0.278900			0.139450	+	0.990229i	$0.455467\pi$
$608$	3.89978e7	−	3.12364e8i	0.00703685	−	0.0563635i
$609$	6.77218e9			1.21498
$610$	3.17633e9	−	2.57919e9i	0.566594	−	0.460076i
$611$	2.76855e9	−	6.68387e9i	0.491030	−	1.18545i
$612$	1.88146e8	+	2.88029e8i	0.0331792	+	0.0507932i
$613$	−2.76595e9	+	1.14569e9i	−0.484990	+	0.200890i	−0.611761	−	0.791042i	$-0.709539\pi$
$613$	−2.76595e9	+	1.14569e9i	−0.484990	+	0.200890i	0.126771	+	0.991932i	$0.459539\pi$
$614$	−1.67428e9	−	5.62462e9i	−0.291904	−	0.980627i
$615$	−5.56900e9	+	5.56900e9i	−0.965416	+	0.965416i
$616$	2.12905e9	−	1.76168e8i	0.366989	−	0.0303664i
$617$	4.79872e9	+	4.79872e9i	0.822483	+	0.822483i	0.986464	−	0.163980i	$-0.0524334\pi$
$617$	4.79872e9	+	4.79872e9i	0.822483	+	0.822483i	−0.163980	+	0.986464i	$0.552433\pi$
$618$	−2.25004e9	+	4.15732e9i	−0.383469	+	0.708522i
$619$	−1.85815e9	−	4.48598e9i	−0.314894	−	0.760221i	−0.999510	−	0.0313168i	$-0.990030\pi$
$619$	−1.85815e9	−	4.48598e9i	−0.314894	−	0.760221i	0.684616	−	0.728904i	$-0.259970\pi$
$620$	6.07607e8	+	3.23006e9i	0.102389	+	0.544301i
$621$	−6.29866e9	−	2.60899e9i	−1.05543	−	0.437172i
$622$	4.20626e7	−	4.05420e8i	0.00700858	−	0.0675522i
$623$			5.03725e9i			0.834613i
$624$	4.33089e9	−	1.68914e9i	0.713562	−	0.278305i
$625$			4.06025e9i			0.665232i
$626$	−1.13227e10	−	1.17474e9i	−1.84476	−	0.191396i
$627$	−6.18866e7	−	2.56343e7i	−0.0100268	−	0.00415322i
$628$	−9.35509e9	−	6.39276e9i	−1.50726	−	1.02998i
$629$	−1.07426e9	−	2.59348e9i	−0.172120	−	0.415534i
$630$	−1.84946e9	−	1.00097e9i	−0.294681	−	0.159488i
$631$	−2.64735e9	−	2.64735e9i	−0.419478	−	0.419478i	0.465546	−	0.885024i	$-0.345858\pi$
$631$	−2.64735e9	−	2.64735e9i	−0.419478	−	0.419478i	−0.885024	+	0.465546i	$0.845858\pi$
$632$	4.44657e9	+	8.64091e9i	0.700674	+	1.36160i
$633$	−4.37481e9	+	4.37481e9i	−0.685562	+	0.685562i
$634$	−4.02898e9	+	1.19931e9i	−0.627889	+	0.186904i
$635$	6.30919e9	−	2.61335e9i	0.977835	−	0.405033i
$636$	8.66557e8	−	4.13120e9i	0.133566	−	0.636760i
$637$	−4.04645e9	+	9.76900e9i	−0.620278	+	1.49748i
$638$	7.38901e8	+	9.09973e8i	0.112646	+	0.138725i
$639$	2.61820e9			0.396963
$640$	−5.10958e9	+	2.49620e9i	−0.770469	+	0.376399i
$641$	5.59680e8			0.0839337			0.0419669	−	0.999119i	$-0.486638\pi$
$641$	5.59680e8			0.0839337			0.0419669	+	0.999119i	$0.486638\pi$
$642$	2.21403e9	+	2.72663e9i	0.330226	+	0.406680i
$643$	6.27666e8	−	1.51532e9i	0.0931087	−	0.224784i	−0.870463	−	0.492233i	$-0.836181\pi$
$643$	6.27666e8	−	1.51532e9i	0.0931087	−	0.224784i	0.963572	+	0.267449i	$0.0861807\pi$
$644$	2.48821e9	−	1.18622e10i	0.367102	−	1.75011i
$645$	4.91992e9	−	2.03790e9i	0.721937	−	0.299036i
$646$	9.78680e7	−	2.91324e7i	0.0142832	−	0.00425170i
$647$	−6.88139e9	+	6.88139e9i	−0.998876	+	0.998876i	−0.999999	−	0.00112385i	$-0.999642\pi$
$647$	−6.88139e9	+	6.88139e9i	−0.998876	+	0.998876i	0.00112385	+	0.999999i	$0.499642\pi$
$648$	−2.26697e9	−	4.40535e9i	−0.327291	−	0.636015i
$649$	−2.97838e8	−	2.97838e8i	−0.0427684	−	0.0427684i
$650$	−1.42381e9	−	7.70598e8i	−0.203355	−	0.110060i
$651$	−2.57791e9	−	6.22363e9i	−0.366214	−	0.884118i
$652$	1.82708e9	+	1.24852e9i	0.258161	+	0.176413i
$653$	3.16400e9	+	1.31057e9i	0.444672	+	0.184189i	0.593773	−	0.804633i	$-0.297638\pi$
$653$	3.16400e9	+	1.31057e9i	0.444672	+	0.184189i	−0.149101	+	0.988822i	$0.547638\pi$
$654$	−7.92354e9	−	8.22072e8i	−1.10764	−	0.114918i
$655$		−	3.48330e9i		−	0.484335i
$656$	4.77097e9	+	1.22326e10i	0.659847	+	1.69182i
$657$			5.48656e8i			0.0754781i
$658$	1.87190e9	−	1.80423e10i	0.256148	−	2.46888i
$659$	1.21540e10	+	5.03434e9i	1.65432	+	0.685241i	0.997623	−	0.0689146i	$-0.0219536\pi$
$659$	1.21540e10	+	5.03434e9i	1.65432	+	0.685241i	0.656696	+	0.754156i	$0.271954\pi$
$660$	2.23710e8	+	1.18925e9i	0.0302888	+	0.161016i
$661$	2.50164e9	+	6.03950e9i	0.336915	+	0.813385i	0.998008	+	0.0630812i	$0.0200927\pi$
$661$	2.50164e9	+	6.03950e9i	0.336915	+	0.813385i	−0.661093	+	0.750304i	$0.729907\pi$
$662$	−3.13325e9	+	5.78920e9i	−0.419751	+	0.775560i
$663$	1.06627e9	+	1.06627e9i	0.142093	+	0.142093i
$664$	9.96860e9	−	8.24850e8i	1.32144	−	0.109342i
$665$	−4.41357e8	+	4.41357e8i	−0.0581989	+	0.0581989i
$666$	−8.62204e8	−	2.89650e9i	−0.113097	−	0.379939i
$667$	6.14414e9	−	2.54499e9i	0.801716	−	0.332082i
$668$	1.10976e8	+	1.69891e8i	0.0144050	+	0.0220522i
$669$	1.32168e9	−	3.19083e9i	0.170662	−	0.412014i
$670$	7.95442e9	−	6.45901e9i	1.02175	−	0.829668i
$671$	−1.45155e9			−0.185482
$672$	9.19918e9	−	7.15713e9i	1.16938	−	0.909801i
$673$	−5.74890e9			−0.726996			−0.363498	−	0.931595i	$-0.618418\pi$
$673$	−5.74890e9			−0.726996			−0.363498	+	0.931595i	$0.618418\pi$
$674$	2.62682e9	−	2.13299e9i	0.330461	−	0.268336i
$675$	−8.73770e8	+	2.10947e9i	−0.109354	+	0.264003i
$676$	1.59313e9	−	1.04066e9i	0.198352	−	0.129568i
$677$	−3.14777e9	+	1.30385e9i	−0.389890	+	0.161498i	−0.569012	−	0.822329i	$-0.692674\pi$
$677$	−3.14777e9	+	1.30385e9i	−0.389890	+	0.161498i	0.179122	+	0.983827i	$0.442674\pi$
$678$	1.10377e9	+	3.70804e9i	0.136012	+	0.456920i
$679$	1.85512e9	−	1.85512e9i	0.227419	−	0.227419i
$680$	−1.40750e9	−	1.19238e9i	−0.171659	−	0.145423i
$681$	−1.17576e8	−	1.17576e8i	−0.0142660	−	0.0142660i
$682$	5.54994e8	−	1.02544e9i	0.0669950	−	0.123784i
$683$	1.08584e9	+	2.62144e9i	0.130404	+	0.314824i	0.975573	−	0.219676i	$-0.0705000\pi$
$683$	1.08584e9	+	2.62144e9i	0.130404	+	0.314824i	−0.845168	+	0.534500i	$0.820500\pi$
$684$	1.08036e8	−	2.03226e7i	0.0129083	−	0.00242819i
$685$	−6.28777e9	−	2.60448e9i	−0.747446	−	0.309602i
$686$	−1.26143e9	+	1.21583e10i	−0.149187	+	1.43793i
$687$			3.00803e9i			0.353944i
$688$	1.84864e8	−	8.87610e9i	0.0216418	−	1.03911i
$689$			5.56523e9i			0.648210i
$690$	6.82885e9	+	7.08498e8i	0.791364	+	0.0821045i
$691$	−2.22501e9	−	9.21629e8i	−0.256542	−	0.106263i	0.250706	−	0.968063i	$-0.419337\pi$
$691$	−2.22501e9	−	9.21629e8i	−0.256542	−	0.106263i	−0.507248	+	0.861800i	$0.669337\pi$
$692$	−6.05463e9	+	8.86028e9i	−0.694571	+	1.01643i
$693$	2.85500e8	+	6.89259e8i	0.0325867	+	0.0786712i
$694$	−1.18532e9	−	6.41524e8i	−0.134610	−	0.0728542i
$695$	4.28577e9	+	4.28577e9i	0.484264	+	0.484264i
$696$	6.09015e9	+	1.95180e9i	0.684693	+	0.219433i
$697$	−3.01168e9	+	3.01168e9i	−0.336895	+	0.336895i
$698$	1.31214e10	−	3.90586e9i	1.46045	−	0.434733i
$699$	−1.08663e10	+	4.50095e9i	−1.20340	+	0.498465i
$700$	−3.97274e9	−	8.33320e8i	−0.437771	−	0.0918266i
$701$	4.77973e9	−	1.15393e10i	0.524071	−	1.26522i	−0.411284	−	0.911507i	$-0.634919\pi$
$701$	4.77973e9	−	1.15393e10i	0.524071	−	1.26522i	0.935355	−	0.353712i	$-0.115081\pi$
$702$	5.44869e9	+	6.71018e9i	0.594445	+	0.732072i
$703$	−8.96984e8			−0.0973735
$704$	1.96541e9	+	4.55185e8i	0.212299	+	0.0491681i
$705$	1.02748e10			1.10436
$706$	5.26101e9	+	6.47905e9i	0.562668	+	0.692938i
$707$	−2.42495e9	+	5.85435e9i	−0.258069	+	0.623033i
$708$	−2.24908e9	−	4.71766e8i	−0.238171	−	0.0499586i
$709$	−1.01735e10	+	4.21400e9i	−1.07203	+	0.444051i	−0.847708	−	0.530463i	$-0.822018\pi$
$709$	−1.01735e10	+	4.21400e9i	−1.07203	+	0.444051i	−0.224326	+	0.974514i	$0.572018\pi$
$710$	−1.34551e10	+	4.00517e9i	−1.41085	+	0.419969i
$711$	−2.39970e9	+	2.39970e9i	−0.250387	+	0.250387i
$712$	−1.45178e9	+	4.52994e9i	−0.150737	+	0.470341i
$713$	−4.67769e9	−	4.67769e9i	−0.483301	−	0.483301i
$714$	3.32507e9	+	1.79960e9i	0.341866	+	0.185026i
$715$	−6.10550e8	−	1.47400e9i	−0.0624669	−	0.150809i
$716$	1.77444e9	−	2.59669e9i	0.180661	−	0.264378i
$717$	1.20138e9	+	4.97626e8i	0.121720	+	0.0504181i
$718$	−1.63999e10	−	1.70150e9i	−1.65351	−	0.171553i
$719$		−	1.99542e9i		−	0.200209i	−0.994977	−	0.100104i	$-0.968082\pi$
$719$		−	1.99542e9i		−	0.200209i	0.994977	−	0.100104i	$-0.0319177\pi$
$720$	−1.37471e9	−	1.43319e9i	−0.137261	−	0.143100i
$721$		−	1.56264e10i		−	1.55269i
$722$	−1.04026e9	+	1.00266e10i	−0.102864	+	0.991452i
$723$	1.20301e10	+	4.98301e9i	1.18381	+	0.490352i
$724$	−3.32131e9	+	6.24772e8i	−0.325255	+	0.0611838i
$725$	−8.52335e8	−	2.05772e9i	−0.0830667	−	0.200541i
$726$	−4.09858e9	+	7.57281e9i	−0.397517	+	0.734478i
$727$	9.72258e9	+	9.72258e9i	0.938450	+	0.938450i	0.998213	−	0.0597626i	$-0.0190344\pi$
$727$	9.72258e9	+	9.72258e9i	0.938450	+	0.938450i	−0.0597626	+	0.998213i	$0.519034\pi$
$728$	−9.93298e9	+	1.17251e10i	−0.954157	+	1.12630i
$729$	8.22450e9	−	8.22450e9i	0.786254	−	0.786254i
$730$	−8.39301e8	−	2.81956e9i	−0.0798523	−	0.268258i
$731$	2.66066e9	−	1.10208e9i	0.251929	−	0.104352i
$732$	−6.63020e9	+	4.33099e9i	−0.624795	+	0.408130i
$733$	5.79613e9	−	1.39931e10i	0.543594	−	1.31235i	−0.378577	−	0.925570i	$-0.623587\pi$
$733$	5.79613e9	−	1.39931e10i	0.543594	−	1.31235i	0.922171	−	0.386782i	$-0.126413\pi$
$734$	−1.08363e10	+	8.79913e9i	−1.01145	+	0.821303i
$735$	−1.50174e10			−1.39505
$736$	5.65641e9	−	9.95045e9i	0.522961	−	0.919963i
$737$	−3.63508e9			−0.334486
$738$	−3.55956e9	+	2.89038e9i	−0.325986	+	0.264702i
$739$	2.66059e9	−	6.42324e9i	0.242506	−	0.585462i	−0.755024	−	0.655697i	$-0.772375\pi$
$739$	2.66059e9	−	6.42324e9i	0.242506	−	0.585462i	0.997530	+	0.0702352i	$0.0223750\pi$
$740$	8.86180e9	+	1.35663e10i	0.803916	+	1.23069i
$741$	4.45159e8	−	1.84391e8i	0.0401931	−	0.0166485i
$742$	3.98094e9	+	1.33737e10i	0.357744	+	1.20181i
$743$	−1.45605e9	+	1.45605e9i	−0.130231	+	0.130231i	−0.769218	−	0.638987i	$-0.779354\pi$
$743$	−1.45605e9	+	1.45605e9i	−0.130231	+	0.130231i	0.638987	+	0.769218i	$0.279354\pi$
$744$	−5.24587e8	−	6.33982e9i	−0.0466995	−	0.564380i
$745$	1.17231e10	+	1.17231e10i	1.03871	+	1.03871i
$746$	8.16396e8	−	1.50843e9i	0.0719971	−	0.133027i
$747$	1.33676e9	+	3.22724e9i	0.117336	+	0.283275i
$748$	1.20981e8	+	6.43139e8i	0.0105697	+	0.0561887i
$749$	−1.07268e10	−	4.44319e9i	−0.932790	−	0.386374i
$750$	1.13369e9	−	1.09271e10i	0.0981253	−	0.945780i
$751$		−	3.88025e9i		−	0.334288i	−0.985933	−	0.167144i	$-0.946546\pi$
$751$		−	3.88025e9i		−	0.334288i	0.985933	−	0.167144i	$-0.0534544\pi$
$752$	6.88331e9	−	1.56857e10i	0.590249	−	1.34506i
$753$		−	1.46348e9i		−	0.124912i
$754$	−8.38670e9	−	8.70126e8i	−0.712511	−	0.0739235i
$755$	2.78908e9	+	1.15527e9i	0.235856	+	0.0976946i
$756$	1.78936e10	+	1.22275e10i	1.50616	+	1.02923i
$757$	−3.71888e9	−	8.97818e9i	−0.311585	−	0.752234i	−0.999647	−	0.0265811i	$-0.991538\pi$
$757$	−3.71888e9	−	8.97818e9i	−0.311585	−	0.752234i	0.688061	−	0.725653i	$-0.258462\pi$
$758$	−2.21746e9	−	1.20014e9i	−0.184933	−	0.100090i
$759$	−1.72224e9	−	1.72224e9i	−0.142971	−	0.142971i
$760$	−5.24111e8	+	2.69705e8i	−0.0433088	+	0.0222865i
$761$	1.10472e10	−	1.10472e10i	0.908672	−	0.908672i	−0.0874931	−	0.996165i	$-0.527886\pi$
$761$	1.10472e10	−	1.10472e10i	0.908672	−	0.908672i	0.996165	+	0.0874931i	$0.0278856\pi$
$762$	−1.26684e10	+	3.77099e9i	−1.03724	+	0.308755i
$763$	2.43287e10	−	1.00773e10i	1.98282	−	0.821312i
$764$	3.95834e9	−	1.88709e10i	0.321134	−	1.53097i
$765$	2.46523e8	−	5.95160e8i	0.0199087	−	0.0480639i
$766$	−2.17948e9	−	2.68407e9i	−0.175207	−	0.215771i
$767$	3.02979e9			0.242454
$768$	1.03355e10	−	3.78505e9i	0.823315	−	0.301514i
$769$	−2.32206e10			−1.84133			−0.920665	−	0.390354i	$-0.872353\pi$
$769$	−2.32206e10			−1.84133			−0.920665	+	0.390354i	$0.872353\pi$
$770$	−2.52159e9	−	3.10539e9i	−0.199047	−	0.245131i
$771$	1.42559e8	−	3.44168e8i	0.0112022	−	0.0270446i
$772$	2.38632e9	−	1.13765e10i	0.186667	−	0.889912i
$773$	1.63570e10	−	6.77530e9i	1.27373	−	0.527595i	0.359631	−	0.933094i	$-0.382902\pi$
$773$	1.63570e10	−	6.77530e9i	1.27373	−	0.527595i	0.914095	+	0.405500i	$0.132902\pi$
$774$	2.97153e9	−	8.84536e8i	0.230349	−	0.0685681i
$775$	−1.56659e9	+	1.56659e9i	−0.120893	+	0.120893i
$776$	2.20295e9	−	1.13363e9i	0.169234	−	0.0870872i
$777$	−2.34844e10	−	2.34844e10i	−1.79600	−	1.79600i
$778$	−4.30580e9	−	2.33040e9i	−0.327812	−	0.177420i
$779$	5.20811e8	+	1.25735e9i	0.0394729	+	0.0952960i
$780$	−7.18677e9	−	4.91104e9i	−0.542254	−	0.370547i
$781$	4.60122e9	+	1.90589e9i	0.345616	+	0.143159i
$782$	3.69300e9	+	3.83151e8i	0.276157	+	0.0286514i
$783$			1.18915e10i			0.885257i
$784$	−1.00605e10	+	2.29259e10i	−0.745612	+	1.69911i
$785$			2.12165e10i			1.56542i
$786$	−6.95752e8	+	6.70600e9i	−0.0511064	+	0.492589i
$787$	−1.64072e10	−	6.79609e9i	−1.19984	−	0.496990i	−0.308892	−	0.951097i	$-0.599958\pi$
$787$	−1.64072e10	−	6.79609e9i	−1.19984	−	0.496990i	−0.890947	+	0.454107i	$0.849958\pi$
$788$	−1.86679e9	−	9.92389e9i	−0.135910	−	0.722504i
$789$	3.16411e9	+	7.63883e9i	0.229341	+	0.553678i
$790$	8.66122e9	−	1.60030e10i	0.625006	−	1.15480i
$791$	−9.04326e9	−	9.04326e9i	−0.649691	−	0.649691i
$792$	5.80973e7	+	7.02127e8i	0.00415545	+	0.0502201i
$793$	7.38303e9	−	7.38303e9i	0.525749	−	0.525749i
$794$	2.56722e9	+	8.62437e9i	0.182008	+	0.611442i
$795$	−7.30227e9	+	3.02470e9i	−0.515434	+	0.213500i
$796$	1.16291e10	+	1.78027e10i	0.817241	+	1.25109i
$797$	3.05374e9	−	7.37239e9i	0.213663	−	0.515827i	−0.780318	−	0.625383i	$-0.784943\pi$
$797$	3.05374e9	−	7.37239e9i	0.213663	−	0.515827i	0.993981	+	0.109556i	$0.0349428\pi$
$798$	9.37851e8	−	7.61538e8i	0.0653317	−	0.0530495i
$799$	5.55653e9			0.385381
$800$	−3.33248e9	−	1.89437e9i	−0.230119	−	0.130813i
$801$	−1.66120e9			−0.114211
$802$	−5.94336e9	+	4.82603e9i	−0.406838	+	0.330354i
$803$	−3.99387e8	+	9.64205e8i	−0.0272201	+	0.0657151i
$804$	−1.66038e10	+	1.08460e10i	−1.12671	+	0.735992i
$805$	−2.09676e10	+	8.68506e9i	−1.41665	+	0.586796i
$806$	2.39285e9	+	8.03860e9i	0.160969	+	0.540764i
$807$	−6.95130e8	+	6.95130e8i	−0.0465596	+	0.0465596i
$808$	−3.86801e9	+	4.56587e9i	−0.257957	+	0.304497i
$809$	6.89923e9	+	6.89923e9i	0.458122	+	0.458122i	0.898039	−	0.439917i	$-0.144992\pi$
$809$	6.89923e9	+	6.89923e9i	0.458122	+	0.458122i	−0.439917	+	0.898039i	$0.644992\pi$
$810$	−4.41570e9	+	8.15874e9i	−0.291946	+	0.539418i
$811$	−3.44169e8	−	8.30898e8i	−0.0226568	−	0.0546984i	0.912146	−	0.409865i	$-0.134424\pi$
$811$	−3.44169e8	−	8.30898e8i	−0.0226568	−	0.0546984i	−0.934803	+	0.355167i	$0.884424\pi$
$812$	−2.07763e10	+	3.90823e9i	−1.36183	+	0.256174i
$813$	1.12917e10	+	4.67716e9i	0.736955	+	0.305257i
$814$	5.93239e8	−	5.71793e9i	0.0385518	−	0.371581i
$815$		−	4.14365e9i		−	0.268121i
$816$	2.47154e9	+	2.57668e9i	0.159240	+	0.166014i
$817$		−	9.20217e8i		−	0.0590355i
$818$	−2.96665e9	−	3.07792e8i	−0.189509	−	0.0196617i
$819$	−4.95793e9	−	2.05364e9i	−0.315360	−	0.130626i
$820$	1.38712e10	−	2.02990e10i	0.878548	−	1.28566i
$821$	−5.66762e9	−	1.36828e10i	−0.357437	−	0.862929i	−0.995659	−	0.0930770i	$-0.970330\pi$
$821$	−5.66762e9	−	1.36828e10i	−0.357437	−	0.862929i	0.638222	−	0.769853i	$-0.279670\pi$
$822$	1.15849e10	+	6.27002e9i	0.727514	+	0.393748i
$823$	1.65885e10	+	1.65885e10i	1.03731	+	1.03731i	0.999277	+	0.0380313i	$0.0121086\pi$
$823$	1.65885e10	+	1.65885e10i	1.03731	+	1.03731i	0.0380313	+	0.999277i	$0.487891\pi$
$824$	4.50367e9	−	1.40527e10i	0.280428	−	0.875012i
$825$	−5.76791e8	+	5.76791e8i	−0.0357627	+	0.0357627i
$826$	7.28082e9	−	2.16728e9i	0.449521	−	0.133809i
$827$	1.63855e8	−	6.78711e7i	0.0100737	−	0.00417268i	−0.377641	−	0.925952i	$-0.623265\pi$
$827$	1.63855e8	−	6.78711e7i	0.0100737	−	0.00417268i	0.387715	+	0.921779i	$0.373265\pi$
$828$	3.91197e9	+	8.20572e8i	0.239491	+	0.0502355i
$829$	−5.28016e9	+	1.27474e10i	−0.321889	+	0.777109i	0.677255	+	0.735748i	$0.263169\pi$
$829$	−5.28016e9	+	1.27474e10i	−0.321889	+	0.777109i	−0.999144	+	0.0413607i	$0.986831\pi$
$830$	−1.18065e10	−	1.45400e10i	−0.716718	−	0.882654i
$831$	−1.32278e10			−0.799623
$832$	−1.23119e10	+	7.68147e9i	−0.741128	+	0.462394i
$833$	−8.12131e9			−0.486820
$834$	−7.39487e9	−	9.10695e9i	−0.441418	−	0.543615i
$835$	1.45409e8	−	3.51049e8i	0.00864351	−	0.0208673i
$836$	2.04655e8	+	4.29283e7i	0.0121144	+	0.00254110i
$837$	1.09283e10	−	4.52664e9i	0.644187	−	0.266831i
$838$	2.92597e10	−	8.70976e9i	1.71758	−	0.511272i
$839$	9.02898e9	−	9.02898e9i	0.527803	−	0.527803i	−0.392114	−	0.919917i	$-0.628256\pi$
$839$	9.02898e9	−	9.02898e9i	0.527803	−	0.527803i	0.919917	+	0.392114i	$0.128256\pi$
$840$	−2.07833e10	−	6.66074e9i	−1.20987	−	0.387744i
$841$	3.99524e9	+	3.99524e9i	0.231610	+	0.231610i
$842$	−2.43417e9	−	1.31743e9i	−0.140526	−	0.0760562i
$843$	1.12612e10	+	2.71870e10i	0.647426	+	1.56302i
$844$	1.08967e10	−	1.59462e10i	0.623875	−	0.912972i
$845$	−3.29192e9	−	1.36356e9i	−0.187694	−	0.0777454i
$846$	5.95005e9	+	6.17322e8i	0.337850	+	0.0350522i
$847$		−	2.84645e10i		−	1.60958i
$848$	−2.74380e8	+	1.31741e10i	−0.0154514	+	0.741885i
$849$			2.82302e9i			0.158321i
$850$	1.28320e8	−	1.23681e9i	0.00716685	−	0.0690776i
$851$	−3.01320e10	−	1.24811e10i	−1.67600	−	0.694222i
$852$	2.67035e10	−	5.02320e9i	1.47921	−	0.278254i
$853$	9.15327e9	+	2.20980e10i	0.504957	+	1.21908i	0.946753	+	0.321960i	$0.104342\pi$
$853$	9.15327e9	+	2.20980e10i	0.504957	+	1.21908i	−0.441796	+	0.897116i	$0.645658\pi$
$854$	1.24607e10	−	2.30232e10i	0.684605	−	1.26492i
$855$	−1.45553e8	−	1.45553e8i	−0.00796413	−	0.00796413i
$856$	−8.36594e9	−	7.08727e9i	−0.455886	−	0.386207i
$857$	−2.27817e10	+	2.27817e10i	−1.23638	+	1.23638i	−0.274912	+	0.961469i	$0.588649\pi$
$857$	−2.27817e10	+	2.27817e10i	−1.23638	+	1.23638i	−0.961469	+	0.274912i	$0.911351\pi$
$858$	8.81007e8	+	2.95967e9i	0.0476183	+	0.159970i
$859$	−2.39974e10	+	9.94005e9i	−1.29178	+	0.535072i	−0.919515	−	0.393055i	$-0.871418\pi$
$859$	−2.39974e10	+	9.94005e9i	−1.29178	+	0.535072i	−0.372264	+	0.928127i	$0.621418\pi$
$860$	−1.39177e10	+	9.09133e9i	−0.746144	+	0.487397i
$861$	−1.92837e10	+	4.65549e10i	−1.02962	+	2.48573i
$862$	−7.00331e9	+	5.68671e9i	−0.372416	+	0.302403i
$863$	2.43528e10			1.28977			0.644883	−	0.764281i	$-0.276906\pi$
$863$	2.43528e10			1.28977			0.644883	+	0.764281i	$0.276906\pi$
$864$	1.25674e10	+	1.61531e10i	0.662900	+	0.852037i
$865$	2.00943e10			1.05564
$866$	1.68350e10	−	1.36701e10i	0.880845	−	0.715249i
$867$	5.99553e9	−	1.44745e10i	0.312436	−	0.754287i
$868$	1.15004e10	+	1.76057e10i	0.596890	+	0.913764i
$869$	−5.96404e9	+	2.47039e9i	−0.308299	+	0.127701i
$870$	−3.41646e9	−	1.14773e10i	−0.175897	−	0.590912i
$871$	1.84891e10	−	1.84891e10i	0.948098	−	0.948098i
$872$	2.47829e10	−	2.05066e9i	1.26574	−	0.104733i
$873$	6.11788e8	+	6.11788e8i	0.0311208	+	0.0311208i
$874$	5.64691e8	−	1.04336e9i	0.0286102	−	0.0528621i
$875$	1.38973e10	+	3.35509e10i	0.701295	+	1.69308i
$876$	1.05263e9	+	5.59582e9i	0.0529069	+	0.281255i
$877$	2.54989e10	+	1.05620e10i	1.27651	+	0.528747i	0.914936	−	0.403598i	$-0.132241\pi$
$877$	2.54989e10	+	1.05620e10i	1.27651	+	0.528747i	0.361571	+	0.932345i	$0.382241\pi$
$878$	−7.60670e8	+	7.33171e9i	−0.0379285	+	0.365574i
$879$			2.36942e10i			1.17674i
$880$	−1.37264e9	−	3.51939e9i	−0.0678995	−	0.174091i
$881$			2.34404e10i			1.15491i	0.816422	+	0.577456i	$0.195955\pi$
$881$			2.34404e10i			1.15491i	−0.816422	+	0.577456i	$0.804045\pi$
$882$	−8.69646e9	−	9.02264e8i	−0.426778	−	0.0442786i
$883$	−2.44672e10	−	1.01346e10i	−1.19597	−	0.495388i	−0.306277	−	0.951942i	$-0.599084\pi$
$883$	−2.44672e10	−	1.01346e10i	−1.19597	−	0.495388i	−0.889696	+	0.456554i	$0.849084\pi$
$884$	−3.88655e9	−	2.65586e9i	−0.189226	−	0.129307i
$885$	1.64669e9	+	3.97547e9i	0.0798566	+	0.192791i
$886$	2.55426e9	+	1.38243e9i	0.123381	+	0.0667765i
$887$	−1.53654e9	−	1.53654e9i	−0.0739285	−	0.0739285i	0.669176	−	0.743104i	$-0.266647\pi$
$887$	−1.53654e9	−	1.53654e9i	−0.0739285	−	0.0739285i	−0.743104	+	0.669176i	$0.766647\pi$
$888$	−1.43509e10	−	2.78877e10i	−0.687754	−	1.33649i
$889$	3.08959e10	−	3.08959e10i	1.47484	−	1.47484i
$890$	8.53699e9	−	2.54121e9i	0.405919	−	0.120830i
$891$	3.04061e9	−	1.25946e9i	0.144009	−	0.0596504i
$892$	−2.21335e9	+	1.05518e10i	−0.104417	+	0.497796i
$893$	6.79454e8	−	1.64035e9i	0.0319286	−	0.0770824i
$894$	−2.02275e10	−	2.49106e10i	−0.946806	−	1.16601i
$895$	−5.88908e9			−0.274578
$896$	−2.40917e10	+	2.72661e10i	−1.11889	+	1.26633i
$897$	1.75197e10			0.810502
$898$	4.64509e9	+	5.72053e9i	0.214056	+	0.263614i
$899$	−4.41559e9	+	1.06602e10i	−0.202689	+	0.489334i
$900$	2.74816e8	−	1.31015e9i	0.0125659	−	0.0599062i
$901$	−3.94902e9	+	1.63574e9i	−0.179867	+	0.0745035i
$902$	−8.35957e9	+	2.48840e9i	−0.379281	+	0.112901i
$903$	2.40927e10	−	2.40927e10i	1.08888	−	1.08888i
$904$	−5.52616e9	−	1.07389e10i	−0.248791	−	0.483469i
$905$	4.47468e9	+	4.47468e9i	0.200674	+	0.200674i
$906$	−5.13874e9	−	2.78120e9i	−0.229566	−	0.124247i
$907$	−2.25475e9	−	5.44345e9i	−0.100340	−	0.242242i	0.865736	−	0.500501i	$-0.166851\pi$
$907$	−2.25475e9	−	5.44345e9i	−0.100340	−	0.242242i	−0.966076	+	0.258260i	$0.916851\pi$
$908$	4.28563e8	+	2.92856e8i	0.0189983	+	0.0129824i
$909$	−1.93067e9	−	7.99710e8i	−0.0852579	−	0.0353150i
$910$	2.86206e10	+	2.96940e9i	1.25902	+	0.130624i
$911$		−	2.88864e10i		−	1.26584i	−0.774216	−	0.632921i	$-0.781856\pi$
$911$		−	2.88864e10i		−	1.26584i	0.774216	−	0.632921i	$-0.218144\pi$
$912$	1.06288e9	−	4.14547e8i	0.0463984	−	0.0180964i
$913$			6.64461e9i			0.288949i
$914$	−3.56999e9	+	3.44094e10i	−0.154652	+	1.49061i
$915$	1.37001e10	+	5.67478e9i	0.591222	+	0.244892i
$916$	−1.73594e9	−	9.22831e9i	−0.0746278	−	0.396724i
$917$	−8.52880e9	−	2.05904e10i	−0.365254	−	0.881802i
$918$	−3.15998e9	+	5.83859e9i	−0.134814	+	0.249091i
$919$	−1.49593e9	−	1.49593e9i	−0.0635780	−	0.0635780i	0.674603	−	0.738181i	$-0.264315\pi$
$919$	−1.49593e9	−	1.49593e9i	−0.0635780	−	0.0635780i	−0.738181	+	0.674603i	$0.764315\pi$
$920$	−2.13590e10	+	1.76735e9i	−0.904324	+	0.0748281i
$921$	1.50393e10	−	1.50393e10i	0.634337	−	0.634337i
$922$	4.26235e9	+	1.43190e10i	0.179098	+	0.601666i
$923$	−3.30972e10	+	1.37093e10i	−1.38543	+	0.573865i
$924$	4.23425e9	+	6.48211e9i	0.176573	+	0.270311i
$925$	−4.18000e9	+	1.00914e10i	−0.173652	+	0.419233i
$926$	−5.72686e9	+	4.65023e9i	−0.237016	+	0.192458i
$927$	5.15334e9			0.212476
$928$	−1.98103e10	−	2.47327e9i	−0.813716	−	0.101590i
$929$	−3.21390e10			−1.31516			−0.657579	−	0.753386i	$-0.728419\pi$
$929$	−3.21390e10			−1.31516			−0.657579	+	0.753386i	$0.728419\pi$
$930$	−9.24713e9	+	7.50870e9i	−0.376978	+	0.306108i
$931$	−9.93075e8	+	2.39749e9i	−0.0403328	+	0.0973719i
$932$	3.07390e10	−	2.00794e10i	1.24375	−	0.812445i
$933$	1.36477e9	−	5.65307e8i	0.0550142	−	0.0227876i
$934$	4.12095e9	+	1.38440e10i	0.165494	+	0.555965i
$935$	8.66478e8	−	8.66478e8i	0.0346671	−	0.0346671i
$936$	−3.86674e9	−	3.27574e9i	−0.154127	−	0.130570i
$937$	−2.59572e10	−	2.59572e10i	−1.03079	−	1.03079i	−0.999511	−	0.0312758i	$-0.990043\pi$
$937$	−2.59572e10	−	2.59572e10i	−1.03079	−	1.03079i	−0.0312758	−	0.999511i	$-0.509957\pi$
$938$	3.12051e10	−	5.76565e10i	1.23457	−	2.28107i
$939$	−1.57881e10	−	3.81159e10i	−0.622301	−	1.50237i
$940$	−3.15219e10	+	5.92959e9i	−1.23784	+	0.232851i
$941$	3.67475e10	+	1.52213e10i	1.43768	+	0.595508i	0.959236	−	0.282607i	$-0.0911993\pi$
$941$	3.67475e10	+	1.52213e10i	1.43768	+	0.595508i	0.478449	+	0.878116i	$0.341199\pi$
$942$	4.23777e9	−	4.08457e10i	0.165181	−	1.59209i
$943$			4.94843e10i			1.92166i
$944$	7.17219e9	+	1.49376e8i	0.277492	+	0.00577936i
$945$		−	4.05810e10i		−	1.56427i
$946$	5.86604e9	+	6.08605e8i	0.225282	+	0.0233731i
$947$	−1.91175e10	−	7.91873e9i	−0.731487	−	0.302992i	−0.0143239	−	0.999897i	$-0.504560\pi$
$947$	−1.91175e10	−	7.91873e9i	−0.731487	−	0.302992i	−0.717163	+	0.696906i	$0.754560\pi$
$948$	−1.98709e10	+	2.90788e10i	−0.757510	+	1.10853i
$949$	−2.87284e9	−	6.93566e9i	−0.109114	−	0.263424i
$950$	−3.49429e8	−	1.89119e8i	−0.0132229	−	0.00715653i
$951$	−1.07729e10	−	1.07729e10i	−0.406162	−	0.406162i
$952$	−1.12395e10	−	3.60208e9i	−0.422199	−	0.135308i
$953$	7.76327e9	−	7.76327e9i	0.290549	−	0.290549i	−0.546748	−	0.837297i	$-0.684134\pi$
$953$	7.76327e9	−	7.76327e9i	0.290549	−	0.290549i	0.837297	+	0.546748i	$0.184134\pi$
$954$	−4.41042e9	+	1.31285e9i	−0.164460	+	0.0489549i
$955$	−3.33561e10	+	1.38165e10i	−1.23926	+	0.513319i
$956$	−3.97287e9	−	8.33346e8i	−0.147062	−	0.0308477i
$957$	−1.62574e9	+	3.92489e9i	−0.0599598	+	0.144756i
$958$	4.54146e9	+	5.59290e9i	0.166884	+	0.205522i
$959$	−4.35451e10			−1.59431
$960$	−1.67706e10	−	1.19799e10i	−0.611784	−	0.437021i
$961$	−1.60351e10			−0.582826
$962$	2.60658e10	+	3.21006e10i	0.943970	+	1.16252i
$963$	1.46529e9	−	3.53753e9i	0.0528728	−	0.127646i
$964$	−3.97826e10	−	8.34476e9i	−1.43029	−	0.300016i
$965$	−2.01090e10	+	8.32941e9i	−0.720351	+	0.298379i
$966$	4.21012e10	−	1.25323e10i	1.50271	−	0.447312i
$967$	7.31788e9	−	7.31788e9i	0.260251	−	0.260251i	−0.564905	−	0.825156i	$-0.691087\pi$
$967$	7.31788e9	−	7.31788e9i	0.260251	−	0.260251i	0.825156	+	0.564905i	$0.191087\pi$
$968$	8.20371e9	−	2.55978e10i	0.290701	−	0.907067i
$969$	2.61683e8	+	2.61683e8i	0.00923938	+	0.00923938i
$970$	−4.07988e9	−	2.20813e9i	−0.143531	−	0.0776824i
$971$	8.62112e8	+	2.08132e9i	0.0302201	+	0.0729578i	0.938269	−	0.345906i	$-0.112428\pi$
$971$	8.62112e8	+	2.08132e9i	0.0302201	+	0.0729578i	−0.908049	+	0.418864i	$0.862428\pi$
$972$	−7.30752e9	+	1.06937e10i	−0.255234	+	0.373506i
$973$	3.58276e10	+	1.48403e10i	1.24687	+	0.516472i
$974$	1.77965e10	+	1.84640e9i	0.617132	+	0.0640279i
$975$		−	5.86749e9i		−	0.202738i
$976$	1.78413e10	−	1.71133e10i	0.614259	−	0.589195i
$977$			1.00669e10i			0.345353i	0.984979	+	0.172676i	$0.0552415\pi$
$977$			1.00669e10i			0.345353i	−0.984979	+	0.172676i	$0.944759\pi$
$978$	−8.27650e8	+	7.97729e9i	−0.0282918	+	0.272690i
$979$	−2.91939e9	−	1.20925e9i	−0.0994381	−	0.0411886i
$980$	4.60717e10	−	8.66656e9i	1.56366	−	0.294141i
$981$	3.32333e9	+	8.02323e9i	0.112391	+	0.271336i
$982$	−1.49164e10	+	2.75606e10i	−0.502660	+	0.928748i
$983$	−2.78268e9	−	2.78268e9i	−0.0934385	−	0.0934385i	0.658842	−	0.752281i	$-0.271046\pi$
$983$	−2.78268e9	−	2.78268e9i	−0.0934385	−	0.0934385i	−0.752281	+	0.658842i	$0.771046\pi$
$984$	−3.07591e10	+	3.63086e10i	−1.02918	+	1.21486i
$985$	−1.33701e10	+	1.33701e10i	−0.445767	+	0.445767i
$986$	−1.84760e9	−	6.20685e9i	−0.0613815	−	0.206206i
$987$	6.07359e10	−	2.51576e10i	2.01065	−	0.832837i
$988$	−1.25929e9	+	8.22593e8i	−0.0415408	+	0.0271354i
$989$	1.28043e10	−	3.09124e10i	0.420892	−	1.01612i
$990$	1.02411e9	−	8.31578e8i	0.0335446	−	0.0272383i
$991$	−3.30428e10			−1.07850			−0.539248	−	0.842147i	$-0.681292\pi$
$991$	−3.30428e10			−1.07850			−0.539248	+	0.842147i	$0.681292\pi$
$992$	5.26810e9	+	1.91471e10i	0.171342	+	0.622749i
$993$	−2.38572e10			−0.773209
$994$	−6.97284e10	+	5.66197e10i	−2.25194	+	1.82859i
$995$	1.52373e10	−	3.67861e10i	0.490374	−	1.18387i
$996$	1.98255e10	+	3.03504e10i	0.635795	+	0.973322i
$997$	−1.22894e8	+	5.09042e7i	−0.00392732	+	0.00162675i	−0.384646	−	0.923064i	$-0.625677\pi$
$997$	−1.22894e8	+	5.09042e7i	−0.00392732	+	0.00162675i	0.380719	+	0.924691i	$0.375677\pi$
$998$	−1.05605e10	−	3.54772e10i	−0.336301	−	1.12977i
$999$	4.12370e10	−	4.12370e10i	1.30860	−	1.30860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.13.8	yes	108
32.5	even	8	inner	32.8.g.a.5.8	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.5.8	✓	108	32.5	even	8	inner
32.8.g.a.13.8	yes	108	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.13171 - 8.78286i) q^{2} +(15.6913 - 37.8822i) q^{3} +(-26.2773 + 125.274i) q^{4} +(221.433 - 91.7205i) q^{5} +(-444.620 + 132.350i) q^{6} +(1084.35 - 1084.35i) q^{7} +(1287.66 - 662.626i) q^{8} +(357.601 + 357.601i) q^{9} +O(q^{10})\)	\(q+(-7.13171 - 8.78286i) q^{2} +(15.6913 - 37.8822i) q^{3} +(-26.2773 + 125.274i) q^{4} +(221.433 - 91.7205i) q^{5} +(-444.620 + 132.350i) q^{6} +(1084.35 - 1084.35i) q^{7} +(1287.66 - 662.626i) q^{8} +(357.601 + 357.601i) q^{9} +(-2384.77 - 1290.69i) q^{10} +(368.136 + 888.758i) q^{11} +(4333.31 + 2961.15i) q^{12} +(-6392.96 - 2648.05i) q^{13} +(-17257.0 - 1790.42i) q^{14} -9827.57i q^{15} +(-15003.0 - 6583.71i) q^{16} -5314.69i q^{17} +(590.453 - 5691.07i) q^{18} +(-1568.95 - 649.881i) q^{19} +(5671.51 + 30149.9i) q^{20} +(-24062.7 - 58092.4i) q^{21} +(5180.40 - 9571.65i) q^{22} +(-43662.3 - 43662.3i) q^{23} +(-4896.58 - 59177.0i) q^{24} +(-14622.8 + 14622.8i) q^{25} +(22335.3 + 75033.6i) q^{26} +(102006. - 42252.4i) q^{27} +(107347. + 164334. i) q^{28} +(-41215.8 + 99503.8i) q^{29} +(-86314.2 + 70087.4i) q^{30} +107133. q^{31} +(49173.3 + 178722. i) q^{32} +39444.6 q^{33} +(-46678.1 + 37902.8i) q^{34} +(140654. - 339568. i) q^{35} +(-54194.9 + 35401.2i) q^{36} +(487984. - 202130. i) q^{37} +(5481.49 + 18414.6i) q^{38} +(-200628. + 200628. i) q^{39} +(224355. - 264832. i) q^{40} +(-566671. - 566671. i) q^{41} +(-338610. + 625637. i) q^{42} +(207365. + 500624. i) q^{43} +(-121012. + 22763.5i) q^{44} +(111984. + 46385.3i) q^{45} +(-72092.9 + 694867. i) q^{46} +1.04551e6i q^{47} +(-484822. + 465039. i) q^{48} -1.52809e6i q^{49} +(232716. + 24144.4i) q^{50} +(-201332. - 83394.4i) q^{51} +(499721. - 731286. i) q^{52} +(-307777. - 743039. i) q^{53} +(-1.09858e6 - 594575. i) q^{54} +(163035. + 163035. i) q^{55} +(677760. - 2.11480e6i) q^{56} +(-49237.8 + 49237.8i) q^{57} +(1.16787e6 - 347640. i) q^{58} +(-404521. + 167558. i) q^{59} +(1.23114e6 + 258242. i) q^{60} +(-577434. + 1.39405e6i) q^{61} +(-764044. - 940937. i) q^{62} +775530. q^{63} +(1.21901e6 - 1.70648e6i) q^{64} -1.65849e6 q^{65} +(-281308. - 346437. i) q^{66} +(-1.44606e6 + 3.49109e6i) q^{67} +(665790. + 139656. i) q^{68} +(-2.33914e6 + 968904. i) q^{69} +(-3.98548e6 + 1.18636e6i) q^{70} +(3.66079e6 - 3.66079e6i) q^{71} +(697426. + 223514. i) q^{72} +(767133. + 767133. i) q^{73} +(-5.25544e6 - 2.84437e6i) q^{74} +(324493. + 783395. i) q^{75} +(122641. - 179471. i) q^{76} +(1.36291e6 + 564537. i) q^{77} +(3.19291e6 + 331266. i) q^{78} +6.71053e6i q^{79} +(-3.92602e6 - 81767.9i) q^{80} -3.42119e6i q^{81} +(-935658. + 9.01833e6i) q^{82} +(6.38141e6 + 2.64327e6i) q^{83} +(7.90975e6 - 1.48791e6i) q^{84} +(-487466. - 1.17685e6i) q^{85} +(2.91804e6 - 5.39157e6i) q^{86} +(3.12269e6 + 3.12269e6i) q^{87} +(1.06295e6 + 900486. i) q^{88} +(-2.32270e6 + 2.32270e6i) q^{89} +(-391243. - 1.31435e6i) q^{90} +(-9.80362e6 + 4.06079e6i) q^{91} +(6.61706e6 - 4.32241e6i) q^{92} +(1.68106e6 - 4.05844e6i) q^{93} +(9.18253e6 - 7.45625e6i) q^{94} -407025. q^{95} +(7.54199e6 + 941599. i) q^{96} +1.71081e6 q^{97} +(-1.34210e7 + 1.08979e7i) q^{98} +(-186175. + 449467. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Introduction

L-functions

Modular forms

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