LMFDB - Embedded newform 32.8.g.a.21.7

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			21.7
Character	$\chi$	$=$	32.21
Dual form			32.8.g.a.29.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.35242 - 8.59895i) q^{2} +(-46.0630 + 19.0799i) q^{3} +(-19.8839 + 126.446i) q^{4} +(-76.0972 + 183.715i) q^{5} +(502.742 + 255.810i) q^{6} +(60.8852 + 60.8852i) q^{7} +(1233.50 - 758.705i) q^{8} +(211.316 - 211.316i) q^{9} +O(q^{10})$	\(q+(-7.35242 - 8.59895i) q^{2} +(-46.0630 + 19.0799i) q^{3} +(-19.8839 + 126.446i) q^{4} +(-76.0972 + 183.715i) q^{5} +(502.742 + 255.810i) q^{6} +(60.8852 + 60.8852i) q^{7} +(1233.50 - 758.705i) q^{8} +(211.316 - 211.316i) q^{9} +(2139.25 - 696.393i) q^{10} +(-2108.05 - 873.183i) q^{11} +(-1496.67 - 6203.88i) q^{12} +(-817.758 - 1974.24i) q^{13} +(75.8952 - 971.202i) q^{14} -9914.40i q^{15} +(-15593.3 - 5028.48i) q^{16} -4840.34i q^{17} +(-3370.78 - 263.412i) q^{18} +(-10480.9 - 25303.0i) q^{19} +(-21716.9 - 13275.2i) q^{20} +(-3966.24 - 1642.87i) q^{21} +(7990.81 + 24547.0i) q^{22} +(66736.0 - 66736.0i) q^{23} +(-42342.7 + 58483.3i) q^{24} +(27282.3 + 27282.3i) q^{25} +(-10963.9 + 21547.3i) q^{26} +(36025.8 - 86974.1i) q^{27} +(-8909.33 + 6488.06i) q^{28} +(12021.5 - 4979.49i) q^{29} +(-85253.4 + 72894.8i) q^{30} +138399. q^{31} +(71408.6 + 171057. i) q^{32} +113763. q^{33} +(-41621.8 + 35588.2i) q^{34} +(-15818.7 + 6552.32i) q^{35} +(22518.3 + 30921.9i) q^{36} +(-119289. + 287989. i) q^{37} +(-140520. + 276163. i) q^{38} +(75336.9 + 75336.9i) q^{39} +(45519.6 + 284347. i) q^{40} +(170926. - 170926. i) q^{41} +(15034.5 + 46184.6i) q^{42} +(-631406. - 261537. i) q^{43} +(152327. - 249192. i) q^{44} +(22741.4 + 54902.5i) q^{45} +(-1.06453e6 - 83188.5i) q^{46} -384434. i q^{47} +(814216. - 65891.4i) q^{48} -816129. i q^{49} +(34008.3 - 435190. i) q^{50} +(92353.4 + 222961. i) q^{51} +(265896. - 64146.8i) q^{52} +(790705. + 327521. i) q^{53} +(-1.01276e6 + 329685. i) q^{54} +(320833. - 320833. i) q^{55} +(121296. + 28907.9i) q^{56} +(965560. + 965560. i) q^{57} +(-131206. - 66761.4i) q^{58} +(743905. - 1.79595e6i) q^{59} +(1.25364e6 + 197137. i) q^{60} +(-2.02208e6 + 837574. i) q^{61} +(-1.01756e6 - 1.19008e6i) q^{62} +25732.0 q^{63} +(945886. - 1.87172e6i) q^{64} +424927. q^{65} +(-836436. - 978246. i) q^{66} +(-799191. + 331036. i) q^{67} +(612042. + 96244.7i) q^{68} +(-1.80074e6 + 4.34738e6i) q^{69} +(172649. + 87848.8i) q^{70} +(-2.25324e6 - 2.25324e6i) q^{71} +(100332. - 420985. i) q^{72} +(-3.58020e6 + 3.58020e6i) q^{73} +(3.35347e6 - 1.09166e6i) q^{74} +(-1.77725e6 - 736162. i) q^{75} +(3.40787e6 - 822142. i) q^{76} +(-75185.0 - 181513. i) q^{77} +(93909.7 - 1.20173e6i) q^{78} -5.44176e6i q^{79} +(2.11041e6 - 2.48206e6i) q^{80} +5.34724e6i q^{81} +(-2.72651e6 - 213065. i) q^{82} +(2.73615e6 + 6.60566e6i) q^{83} +(286599. - 468849. i) q^{84} +(889243. + 368336. i) q^{85} +(2.39342e6 + 7.35236e6i) q^{86} +(-458741. + 458741. i) q^{87} +(-3.26276e6 + 522317. i) q^{88} +(4.81222e6 + 4.81222e6i) q^{89} +(304900. - 599218. i) q^{90} +(70412.8 - 169991. i) q^{91} +(7.11154e6 + 9.76548e6i) q^{92} +(-6.37506e6 + 2.64064e6i) q^{93} +(-3.30573e6 + 2.82652e6i) q^{94} +5.44611e6 q^{95} +(-6.55305e6 - 6.51694e6i) q^{96} +1.22252e7 q^{97} +(-7.01785e6 + 6.00052e6i) q^{98} +(-629983. + 260947. 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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

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

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 $

$2$	−7.35242	−	8.59895i	−0.649868	−	0.760047i
$2$	−7.35242	−	8.59895i	−0.649868	−	0.760047i
$3$	−46.0630	+	19.0799i	−0.984982	+	0.407993i	−0.816269	−	0.577673i	$-0.803961\pi$
$3$	−46.0630	+	19.0799i	−0.984982	+	0.407993i	−0.168713	+	0.985665i	$0.553961\pi$
$4$	−19.8839	+	126.446i	−0.155343	+	0.987861i
$5$	−76.0972	+	183.715i	−0.272254	+	0.657279i	−0.999579	−	0.0290143i	$-0.990763\pi$
$5$	−76.0972	+	183.715i	−0.272254	+	0.657279i	0.727325	+	0.686293i	$0.240763\pi$
$6$	502.742	+	255.810i	0.950202	+	0.483491i
$7$	60.8852	+	60.8852i	0.0670916	+	0.0670916i	0.739856	−	0.672765i	$-0.234893\pi$
$7$	60.8852	+	60.8852i	0.0670916	+	0.0670916i	−0.672765	+	0.739856i	$0.734893\pi$
$8$	1233.50	−	758.705i	0.851773	−	0.523911i
$9$	211.316	−	211.316i	0.0966238	−	0.0966238i
$10$	2139.25	−	696.393i	0.676492	−	0.220219i
$11$	−2108.05	−	873.183i	−0.477536	−	0.197802i	0.130914	−	0.991394i	$-0.458209\pi$
$11$	−2108.05	−	873.183i	−0.477536	−	0.197802i	−0.608451	+	0.793592i	$0.708209\pi$
$12$	−1496.67	−	6203.88i	−0.250030	−	1.03640i
$13$	−817.758	−	1974.24i	−0.103234	−	0.249229i	0.863820	−	0.503801i	$-0.168066\pi$
$13$	−817.758	−	1974.24i	−0.103234	−	0.249229i	−0.967054	+	0.254572i	$0.918066\pi$
$14$	75.8952	−	971.202i	0.00739208	−	0.0945935i
$15$		−	9914.40i		−	0.758485i
$16$	−15593.3	−	5028.48i	−0.951737	−	0.306914i
$17$		−	4840.34i		−	0.238949i	−0.992837	−	0.119474i	$-0.961879\pi$
$17$		−	4840.34i		−	0.238949i	0.992837	−	0.119474i	$-0.0381209\pi$
$18$	−3370.78	−	263.412i	−0.136231	−	0.0106459i
$19$	−10480.9	−	25303.0i	−0.350557	−	0.846320i	−0.996551	−	0.0829779i	$-0.973557\pi$
$19$	−10480.9	−	25303.0i	−0.350557	−	0.846320i	0.645994	−	0.763342i	$-0.276443\pi$
$20$	−21716.9	−	13275.2i	−0.607007	−	0.371052i
$21$	−3966.24	−	1642.87i	−0.0934569	−	0.0387111i
$22$	7990.81	+	24547.0i	0.159997	+	0.491495i
$23$	66736.0	−	66736.0i	1.14370	−	1.14370i	0.155934	−	0.987768i	$-0.450161\pi$
$23$	66736.0	−	66736.0i	1.14370	−	1.14370i	0.987768	−	0.155934i	$-0.0498386\pi$
$24$	−42342.7	+	58483.3i	−0.625228	+	0.863560i
$25$	27282.3	+	27282.3i	0.349214	+	0.349214i
$26$	−10963.9	+	21547.3i	−0.122337	+	0.240429i
$27$	36025.8	−	86974.1i	0.352242	−	0.850387i
$28$	−8909.33	+	6488.06i	−0.0766994	+	0.0558550i
$29$	12021.5	−	4979.49i	0.0915308	−	0.0379133i	−0.336448	−	0.941702i	$-0.609226\pi$
$29$	12021.5	−	4979.49i	0.0915308	−	0.0379133i	0.427979	+	0.903789i	$0.359226\pi$
$30$	−85253.4	+	72894.8i	−0.576484	+	0.492915i
$31$	138399.			0.834384			0.417192	−	0.908818i	$-0.363014\pi$
$31$	138399.			0.834384			0.417192	+	0.908818i	$0.363014\pi$
$32$	71408.6	+	171057.i	0.385235	+	0.922819i
$33$	113763.			0.551066
$34$	−41621.8	+	35588.2i	−0.181612	+	0.155285i
$35$	−15818.7	+	6552.32i	−0.0623638	+	0.0258319i
$36$	22518.3	+	30921.9i	0.0804410	+	0.110461i
$37$	−119289.	+	287989.i	−0.387163	+	0.934695i	0.603375	+	0.797458i	$0.293822\pi$
$37$	−119289.	+	287989.i	−0.387163	+	0.934695i	−0.990538	+	0.137237i	$0.956178\pi$
$38$	−140520.	+	276163.i	−0.415427	+	0.816437i
$39$	75336.9	+	75336.9i	0.203367	+	0.203367i
$40$	45519.6	+	284347.i	0.112457	+	0.702489i
$41$	170926.	−	170926.i	0.387316	−	0.387316i	−0.486413	−	0.873729i	$-0.661695\pi$
$41$	170926.	−	170926.i	0.387316	−	0.387316i	0.873729	+	0.486413i	$0.161695\pi$
$42$	15034.5	+	46184.6i	0.0313124	+	0.0961888i
$43$	−631406.	−	261537.i	−1.21107	−	0.501642i	−0.316510	−	0.948589i	$-0.602511\pi$
$43$	−631406.	−	261537.i	−1.21107	−	0.501642i	−0.894560	+	0.446948i	$0.852511\pi$
$44$	152327.	−	249192.i	0.269583	−	0.441012i
$45$	22741.4	+	54902.5i	0.0372026	+	0.0898149i
$46$	−1.06453e6	−	83188.5i	−1.61252	−	0.126012i
$47$		−	384434.i		−	0.540107i	−0.962845	−	0.270053i	$-0.912959\pi$
$47$		−	384434.i		−	0.540107i	0.962845	−	0.270053i	$-0.0870413\pi$
$48$	814216.	−	65891.4i	1.06266	−	0.0859972i
$49$		−	816129.i		−	0.990997i
$50$	34008.3	−	435190.i	0.0384760	−	0.492362i
$51$	92353.4	+	222961.i	0.0974893	+	0.235360i
$52$	265896.	−	64146.8i	0.262240	−	0.0632650i
$53$	790705.	+	327521.i	0.729540	+	0.302185i	0.716363	−	0.697728i	$-0.245806\pi$
$53$	790705.	+	327521.i	0.729540	+	0.302185i	0.0131769	+	0.999913i	$0.495806\pi$
$54$	−1.01276e6	+	329685.i	−0.875245	+	0.284919i
$55$	320833.	−	320833.i	0.260022	−	0.260022i
$56$	121296.	+	28907.9i	0.0922969	+	0.0219968i
$57$	965560.	+	965560.i	0.690585	+	0.690585i
$58$	−131206.	−	66761.4i	−0.0882989	−	0.0449291i
$59$	743905.	−	1.79595e6i	0.471558	−	1.13844i	−0.491916	−	0.870643i	$-0.663703\pi$
$59$	743905.	−	1.79595e6i	0.471558	−	1.13844i	0.963475	−	0.267800i	$-0.0862967\pi$
$60$	1.25364e6	+	197137.i	0.749277	+	0.117825i
$61$	−2.02208e6	+	837574.i	−1.14063	+	0.472464i	−0.871381	−	0.490607i	$-0.836775\pi$
$61$	−2.02208e6	+	837574.i	−1.14063	+	0.472464i	−0.269248	+	0.963071i	$0.586775\pi$
$62$	−1.01756e6	−	1.19008e6i	−0.542239	−	0.634171i
$63$	25732.0			0.0129653
$64$	945886.	−	1.87172e6i	0.451034	−	0.892507i
$65$	424927.			0.191919
$66$	−836436.	−	978246.i	−0.358120	−	0.418836i
$67$	−799191.	+	331036.i	−0.324630	+	0.134466i	−0.539046	−	0.842276i	$-0.681215\pi$
$67$	−799191.	+	331036.i	−0.324630	+	0.134466i	0.214416	+	0.976742i	$0.431215\pi$
$68$	612042.	+	96244.7i	0.236048	+	0.0371190i
$69$	−1.80074e6	+	4.34738e6i	−0.659903	+	1.59315i
$70$	172649.	+	87848.8i	0.0601617	+	0.0306121i
$71$	−2.25324e6	−	2.25324e6i	−0.747143	−	0.747143i	0.226799	−	0.973942i	$-0.427174\pi$
$71$	−2.25324e6	−	2.25324e6i	−0.747143	−	0.747143i	−0.973942	+	0.226799i	$0.927174\pi$
$72$	100332.	−	420985.i	0.0316792	−	0.132924i
$73$	−3.58020e6	+	3.58020e6i	−1.07715	+	1.07715i	−0.0803899	+	0.996763i	$0.525617\pi$
$73$	−3.58020e6	+	3.58020e6i	−1.07715	+	1.07715i	−0.996763	+	0.0803899i	$0.974383\pi$
$74$	3.35347e6	−	1.09166e6i	0.962017	−	0.313166i
$75$	−1.77725e6	−	736162.i	−0.486446	−	0.201492i
$76$	3.40787e6	−	822142.i	0.890503	−	0.214832i
$77$	−75185.0	−	181513.i	−0.0187678	−	0.0453095i
$78$	93909.7	−	1.20173e6i	0.0224068	−	0.286731i
$79$		−	5.44176e6i		−	1.24178i	−0.783898	−	0.620890i	$-0.786771\pi$
$79$		−	5.44176e6i		−	1.24178i	0.783898	−	0.620890i	$-0.213229\pi$
$80$	2.11041e6	−	2.48206e6i	0.460842	−	0.541998i
$81$			5.34724e6i			1.11797i
$82$	−2.72651e6	−	213065.i	−0.546082	−	0.0426740i
$83$	2.73615e6	+	6.60566e6i	0.525251	+	1.26807i	0.934603	+	0.355692i	$0.115755\pi$
$83$	2.73615e6	+	6.60566e6i	0.525251	+	1.26807i	−0.409352	+	0.912377i	$0.634245\pi$
$84$	286599.	−	468849.i	0.0527590	−	0.0863089i
$85$	889243.	+	368336.i	0.157056	+	0.0650547i
$86$	2.39342e6	+	7.35236e6i	0.405765	+	1.24647i
$87$	−458741.	+	458741.i	−0.0746878	+	0.0746878i
$88$	−3.26276e6	+	522317.i	−0.510383	+	0.0817043i
$89$	4.81222e6	+	4.81222e6i	0.723570	+	0.723570i	0.969331	−	0.245761i	$-0.0790378\pi$
$89$	4.81222e6	+	4.81222e6i	0.723570	+	0.723570i	−0.245761	+	0.969331i	$0.579038\pi$
$90$	304900.	−	599218.i	0.0440868	−	0.0866435i
$91$	70412.8	−	169991.i	0.00979505	−	0.0236473i
$92$	7.11154e6	+	9.76548e6i	0.952152	+	1.30748i
$93$	−6.37506e6	+	2.64064e6i	−0.821853	+	0.340423i
$94$	−3.30573e6	+	2.82652e6i	−0.410506	+	0.350998i
$95$	5.44611e6			0.651709
$96$	−6.55305e6	−	6.51694e6i	−0.755952	−	0.751786i
$97$	1.22252e7			1.36005			0.680025	−	0.733189i	$-0.261969\pi$
$97$	1.22252e7			1.36005			0.680025	+	0.733189i	$0.261969\pi$
$98$	−7.01785e6	+	6.00052e6i	−0.753205	+	0.644018i
$99$	−629983.	+	260947.i	−0.0652537	+	0.0270290i
$100$	−3.99222e6	+	2.90727e6i	−0.399222	+	0.290727i
$101$	5.74294e6	−	1.38647e7i	0.554638	−	1.33902i	−0.359323	−	0.933213i	$-0.616992\pi$
$101$	5.74294e6	−	1.38647e7i	0.554638	−	1.33902i	0.913961	−	0.405802i	$-0.133008\pi$
$102$	1.23821e6	−	2.43344e6i	0.115529	−	0.227049i
$103$	−9.68858e6	−	9.68858e6i	−0.873635	−	0.873635i	0.119232	−	0.992866i	$-0.461957\pi$
$103$	−9.68858e6	−	9.68858e6i	−0.873635	−	0.873635i	−0.992866	+	0.119232i	$0.961957\pi$
$104$	−2.50657e6	−	1.81479e6i	−0.218506	−	0.158201i
$105$	603639.	−	603639.i	0.0508880	−	0.0508880i
$106$	−2.99726e6	−	9.20730e6i	−0.244430	−	0.750865i
$107$	6.62961e6	+	2.74607e6i	0.523172	+	0.216705i	0.628610	−	0.777721i	$-0.283624\pi$
$107$	6.62961e6	+	2.74607e6i	0.523172	+	0.216705i	−0.105437	+	0.994426i	$0.533624\pi$
$108$	1.02812e7	+	6.28471e6i	0.785346	+	0.480067i
$109$	−8.08689e6	−	1.95235e7i	−0.598121	−	1.44399i	−0.875494	−	0.483229i	$-0.839464\pi$
$109$	−8.08689e6	−	1.95235e7i	−0.598121	−	1.44399i	0.277373	−	0.960762i	$-0.410536\pi$
$110$	−5.11773e6	−	399929.i	−0.366609	−	0.0286489i
$111$		−	1.55417e7i		−	1.07862i
$112$	−643238.	−	1.25556e6i	−0.0432622	−	0.0844450i
$113$		−	1.58523e7i		−	1.03352i	−0.856130	−	0.516760i	$-0.827138\pi$
$113$		−	1.58523e7i		−	1.03352i	0.856130	−	0.516760i	$-0.172862\pi$
$114$	1.20360e6	−	1.54020e7i	0.0760878	−	0.973666i
$115$	7.18197e6	+	1.73388e7i	0.440353	+	1.06311i
$116$	390602.	+	1.61909e6i	0.0232344	+	0.0963093i
$117$	−589995.	−	244384.i	−0.0340563	−	0.0141066i
$118$	−2.09127e7	+	6.80774e6i	−1.17172	+	0.381431i
$119$	294705.	−	294705.i	0.0160315	−	0.0160315i
$120$	−7.52210e6	−	1.22294e7i	−0.397379	−	0.646057i
$121$	−1.00981e7	−	1.00981e7i	−0.518192	−	0.518192i
$122$	2.20694e7	+	1.12296e7i	1.10035	+	0.559892i
$123$	−4.61212e6	+	1.11346e7i	−0.223477	+	0.539521i
$124$	−2.75190e6	+	1.75000e7i	−0.129616	+	0.824255i
$125$	−2.14410e7	+	8.88116e6i	−0.981884	+	0.406710i
$126$	−189193.	−	221269.i	−0.00842573	−	0.00985423i
$127$	2.27727e6			0.0986511			0.0493255	−	0.998783i	$-0.484293\pi$
$127$	2.27727e6			0.0986511			0.0493255	+	0.998783i	$0.484293\pi$
$128$	−2.30494e7	+	5.62806e6i	−0.971460	+	0.237205i
$129$	3.40746e7			1.39755
$130$	−3.12424e6	−	3.65393e6i	−0.124722	−	0.145867i
$131$	−1.03055e7	+	4.26869e6i	−0.400517	+	0.165900i	−0.573844	−	0.818965i	$-0.694548\pi$
$131$	−1.03055e7	+	4.26869e6i	−0.400517	+	0.165900i	0.173327	+	0.984864i	$0.444548\pi$
$132$	−2.26206e6	+	1.43849e7i	−0.0856041	+	0.544377i
$133$	902450.	−	2.17871e6i	0.0332615	−	0.0803005i
$134$	8.72255e6	+	4.43829e6i	0.313167	+	0.159349i
$135$	1.32370e7	+	1.32370e7i	0.463042	+	0.463042i
$136$	−3.67239e6	−	5.97055e6i	−0.125188	−	0.203530i
$137$	2.57297e7	−	2.57297e7i	0.854896	−	0.854896i	−0.135836	−	0.990731i	$-0.543372\pi$
$137$	2.57297e7	−	2.57297e7i	0.854896	−	0.854896i	0.990731	+	0.135836i	$0.0433719\pi$
$138$	5.06227e7	−	1.64792e7i	1.63972	−	0.533778i
$139$	2.98402e6	+	1.23602e6i	0.0942433	+	0.0390368i	0.429307	−	0.903159i	$-0.358758\pi$
$139$	2.98402e6	+	1.23602e6i	0.0942433	+	0.0390368i	−0.335064	+	0.942195i	$0.608758\pi$
$140$	−513979.	−	2.13050e6i	−0.0158306	−	0.0656196i
$141$	7.33498e6	+	1.77082e7i	0.220360	+	0.531995i
$142$	−2.80874e6	+	3.59423e7i	−0.0823193	+	1.05341i
$143$			4.87586e6i			0.139436i
$144$	−4.35771e6	+	2.23251e6i	−0.121616	+	0.0623053i
$145$			2.58746e6i			0.0704833i
$146$	5.71091e7	+	4.46283e6i	1.51869	+	0.118679i
$147$	1.55717e7	+	3.75934e7i	0.404320	+	0.976114i
$148$	−3.40432e7	−	2.08100e7i	−0.863205	−	0.527662i
$149$	−3.06032e7	−	1.26763e7i	−0.757906	−	0.313935i	−0.0299431	−	0.999552i	$-0.509533\pi$
$149$	−3.06032e7	−	1.26763e7i	−0.757906	−	0.313935i	−0.727963	+	0.685617i	$0.759533\pi$
$150$	6.73688e6	+	2.06951e7i	0.162982	+	0.500665i
$151$	2.52754e7	−	2.52754e7i	0.597418	−	0.597418i	−0.342207	−	0.939625i	$-0.611174\pi$
$151$	2.52754e7	−	2.52754e7i	0.597418	−	0.597418i	0.939625	+	0.342207i	$0.111174\pi$
$152$	−3.21256e7	−	2.32594e7i	−0.741992	−	0.537212i
$153$	−1.02284e6	−	1.02284e6i	−0.0230881	−	0.0230881i
$154$	−1.00803e6	+	1.98107e6i	−0.0222408	+	0.0437097i
$155$	−1.05318e7	+	2.54259e7i	−0.227164	+	0.548423i
$156$	−1.10240e7	+	8.02807e6i	−0.232490	+	0.169307i
$157$	−5.31163e7	+	2.20015e7i	−1.09542	+	0.453736i	−0.855892	−	0.517154i	$-0.826991\pi$
$157$	−5.31163e7	+	2.20015e7i	−1.09542	+	0.453736i	−0.239524	+	0.970890i	$0.576991\pi$
$158$	−4.67934e7	+	4.00101e7i	−0.943811	+	0.806993i
$159$	−4.26713e7			−0.841873
$160$	−3.68597e7	+	101844.i	−0.711430	+	0.00196569i
$161$	8.12646e6			0.153466
$162$	4.59806e7	−	3.93151e7i	0.849713	−	0.726536i
$163$	−6.44563e7	+	2.66987e7i	−1.16576	+	0.482873i	−0.879788	−	0.475365i	$-0.842316\pi$
$163$	−6.44563e7	+	2.66987e7i	−1.16576	+	0.482873i	−0.285970	+	0.958239i	$0.592316\pi$
$164$	1.82143e7	+	2.50116e7i	0.322447	+	0.442780i
$165$	−8.65708e6	+	2.09000e7i	−0.150030	+	0.362204i
$166$	3.66844e7	−	7.20956e7i	0.622448	−	1.22329i
$167$	3.70164e7	+	3.70164e7i	0.615016	+	0.615016i	0.944249	−	0.329232i	$-0.106790\pi$
$167$	3.70164e7	+	3.70164e7i	0.615016	+	0.615016i	−0.329232	+	0.944249i	$0.606790\pi$
$168$	−6.13880e6	+	982726.i	−0.0998852	+	0.0159901i
$169$	4.11410e7	−	4.11410e7i	0.655649	−	0.655649i
$170$	−3.37078e6	−	1.03547e7i	−0.0526210	−	0.161647i
$171$	−7.56171e6	−	3.13216e6i	−0.115647	−	0.0479025i
$172$	4.56252e7	−	7.46385e7i	0.683683	−	1.11844i
$173$	−3.58811e6	−	8.66245e6i	−0.0526871	−	0.127198i	0.895344	−	0.445375i	$-0.146929\pi$
$173$	−3.58811e6	−	8.66245e6i	−0.0526871	−	0.127198i	−0.948031	+	0.318177i	$0.896929\pi$
$174$	7.31754e6	+	571834.i	0.105303	+	0.00822902i
$175$			3.32218e6i			0.0468586i
$176$	2.84806e7	+	2.42160e7i	0.393781	+	0.334818i
$177$			9.69204e7i			1.31374i
$178$	5.99858e6	−	7.67615e7i	0.0797221	−	1.02017i
$179$	1.01428e7	+	2.44868e7i	0.132182	+	0.319115i	0.976088	−	0.217376i	$-0.0697497\pi$
$179$	1.01428e7	+	2.44868e7i	0.132182	+	0.319115i	−0.843906	+	0.536491i	$0.819750\pi$
$180$	−7.39440e6	+	1.78388e6i	−0.0945038	+	0.0227988i
$181$	−8.06784e7	−	3.34181e7i	−1.01131	−	0.418897i	−0.185375	−	0.982668i	$-0.559350\pi$
$181$	−8.06784e7	−	3.34181e7i	−1.01131	−	0.418897i	−0.825931	+	0.563771i	$0.809350\pi$
$182$	−1.97945e6	+	644373.i	−0.0243386	+	0.00792296i
$183$	7.71624e7	−	7.71624e7i	0.930736	−	0.930736i
$184$	3.16858e7	−	1.32952e8i	0.374975	−	1.57337i
$185$	−4.38303e7	−	4.38303e7i	−0.508948	−	0.508948i
$186$	6.95788e7	+	3.54038e7i	0.792833	+	0.403417i
$187$	−4.22650e6	+	1.02037e7i	−0.0472645	+	0.114107i
$188$	4.86102e7	+	7.64404e6i	0.533550	+	0.0839017i
$189$	7.48887e6	−	3.10199e6i	0.0806863	−	0.0334214i
$190$	−4.00421e7	−	4.68308e7i	−0.423525	−	0.495329i
$191$	−1.46433e8			−1.52062			−0.760310	−	0.649560i	$-0.774953\pi$
$191$	−1.46433e8			−1.52062			−0.760310	+	0.649560i	$0.774953\pi$
$192$	−7.85805e6	+	1.04265e8i	−0.0801237	+	1.06312i
$193$	1.91842e7			0.192085			0.0960423	−	0.995377i	$-0.469382\pi$
$193$	1.91842e7			0.192085			0.0960423	+	0.995377i	$0.469382\pi$
$194$	−8.98848e7	−	1.05124e8i	−0.883853	−	1.03370i
$195$	−1.95734e7	+	8.10758e6i	−0.189037	+	0.0783015i
$196$	1.03196e8	+	1.62278e7i	0.978967	+	0.153944i
$197$	4.11509e7	−	9.93472e7i	0.383485	−	0.925814i	−0.607802	−	0.794089i	$-0.707948\pi$
$197$	4.11509e7	−	9.93472e7i	0.383485	−	0.925814i	0.991286	−	0.131725i	$-0.0420516\pi$
$198$	6.87577e6	+	3.49859e6i	0.0629496	+	0.0320306i
$199$	3.42196e7	+	3.42196e7i	0.307815	+	0.307815i	0.844061	−	0.536247i	$-0.180158\pi$
$199$	3.42196e7	+	3.42196e7i	0.307815	+	0.307815i	−0.536247	+	0.844061i	$0.680158\pi$
$200$	5.43519e7	+	1.29535e7i	0.480408	+	0.114494i
$201$	3.04970e7	−	3.04970e7i	0.264893	−	0.264893i
$202$	−1.61446e8	+	5.25557e7i	−1.37816	+	0.448632i
$203$	1.03511e6	+	428757.i	0.00868462	+	0.00359729i
$204$	−3.00289e7	+	7.24440e6i	−0.247647	+	0.0597444i
$205$	1.83947e7	+	4.44087e7i	0.149126	+	0.360022i
$206$	−1.20771e7	+	1.54546e8i	−0.0962560	+	1.23175i
$207$		−	2.82048e7i		−	0.221017i
$208$	2.82408e6	+	3.48970e7i	0.0217598	+	0.268885i
$209$			6.24917e7i			0.473490i
$210$	−9.62888e6	−	752455.i	−0.0717477	−	0.00560678i
$211$	1.73679e7	+	4.19298e7i	0.127279	+	0.307280i	0.974655	−	0.223715i	$-0.0718185\pi$
$211$	1.73679e7	+	4.19298e7i	0.127279	+	0.307280i	−0.847375	+	0.530995i	$0.821818\pi$
$212$	−5.71360e7	+	9.34692e7i	−0.411846	+	0.673741i
$213$	1.46783e8	+	6.07995e7i	1.04075	+	0.431093i
$214$	−2.51303e7	−	7.71980e7i	−0.175287	−	0.538465i
$215$	9.60965e7	−	9.60965e7i	0.659437	−	0.659437i
$216$	−2.15498e7	−	1.34615e8i	−0.145497	−	0.908880i
$217$	8.42642e6	+	8.42642e6i	0.0559802	+	0.0559802i
$218$	−1.08423e8	+	2.13084e8i	−0.708802	+	1.39300i
$219$	9.66049e7	−	2.33225e8i	0.621505	−	1.50045i
$220$	3.41887e7	+	4.69476e7i	0.216473	+	0.297258i
$221$	−9.55601e6	+	3.95823e6i	−0.0595530	+	0.0246677i
$222$	−1.33642e8	+	1.14269e8i	−0.819800	+	0.700959i
$223$	−2.05066e8			−1.23830			−0.619152	−	0.785271i	$-0.712523\pi$
$223$	−2.05066e8			−1.23830			−0.619152	+	0.785271i	$0.712523\pi$
$224$	−6.06712e6	+	1.47626e7i	−0.0360674	+	0.0877594i
$225$	1.15304e7			0.0674847
$226$	−1.36314e8	+	1.16553e8i	−0.785524	+	0.671652i
$227$	1.44293e8	−	5.97679e7i	0.818754	−	0.339139i	0.0663132	−	0.997799i	$-0.478876\pi$
$227$	1.44293e8	−	5.97679e7i	0.818754	−	0.339139i	0.752441	+	0.658660i	$0.228876\pi$
$228$	−1.41290e8	+	1.02892e8i	−0.789479	+	0.574924i
$229$	6.72767e7	−	1.62420e8i	0.370203	−	0.893750i	−0.623512	−	0.781814i	$-0.714295\pi$
$229$	6.72767e7	−	1.62420e8i	0.370203	−	0.893750i	0.993715	−	0.111936i	$-0.0357052\pi$
$230$	9.62907e7	−	1.89240e8i	0.521840	−	1.02557i
$231$	6.92650e6	+	6.92650e6i	0.0369719	+	0.0369719i
$232$	1.10506e7	−	1.52630e7i	0.0581003	−	0.0802476i
$233$	−9.82543e7	+	9.82543e7i	−0.508869	+	0.508869i	−0.914179	−	0.405310i	$-0.867163\pi$
$233$	−9.82543e7	+	9.82543e7i	−0.508869	+	0.508869i	0.405310	+	0.914179i	$0.367163\pi$
$234$	2.23645e6	+	6.87015e6i	0.0114105	+	0.0350518i
$235$	7.06263e7	+	2.92544e7i	0.355000	+	0.147046i
$236$	2.12299e8	+	1.29774e8i	1.05137	+	0.642683i
$237$	1.03828e8	+	2.50664e8i	0.506637	+	1.22313i
$238$	−4.70095e6	−	367359.i	−0.0226030	−	0.00176633i
$239$		−	1.84008e8i		−	0.871857i	−0.899981	−	0.435928i	$-0.856420\pi$
$239$		−	1.84008e8i		−	0.871857i	0.899981	−	0.435928i	$-0.143580\pi$
$240$	−4.98543e7	+	1.54598e8i	−0.232790	+	0.721878i
$241$			4.13091e8i			1.90102i	0.310699	+	0.950508i	$0.399437\pi$
$241$			4.13091e8i			1.90102i	−0.310699	+	0.950508i	$0.600563\pi$
$242$	−1.25876e7	+	1.61078e8i	−0.0570937	+	0.730606i
$243$	−2.32364e7	−	5.60976e7i	−0.103884	−	0.250797i
$244$	−6.57012e7	−	2.72339e8i	−0.289540	−	1.20018i
$245$	1.49935e8	+	6.21051e7i	0.651361	+	0.269803i
$246$	1.29656e8	−	4.22071e7i	0.555291	−	0.180764i
$247$	−4.13835e7	+	4.13835e7i	−0.174738	+	0.174738i
$248$	1.70715e8	−	1.05004e8i	0.710705	−	0.437143i
$249$	−2.52071e8	−	2.52071e8i	−1.03473	−	1.03473i
$250$	2.34012e8	+	1.19072e8i	0.947214	+	0.481970i
$251$	1.61089e8	−	3.88903e8i	0.642995	−	1.55233i	−0.179625	−	0.983735i	$-0.557489\pi$
$251$	1.61089e8	−	3.88903e8i	0.642995	−	1.55233i	0.822620	−	0.568591i	$-0.192511\pi$
$252$	−511653.	+	3.25372e6i	−0.00201406	+	0.0128079i
$253$	−1.98955e8	+	8.24100e7i	−0.772385	+	0.319932i
$254$	−1.67435e7	−	1.95821e7i	−0.0641102	−	0.0749795i
$255$	−4.79890e7			−0.181239
$256$	2.17864e8	+	1.56821e8i	0.811608	+	0.584203i
$257$	1.18304e7			0.0434746			0.0217373	−	0.999764i	$-0.493080\pi$
$257$	1.18304e7			0.0434746			0.0217373	+	0.999764i	$0.493080\pi$
$258$	−2.50531e8	−	2.93006e8i	−0.908222	−	1.06220i
$259$	−2.47972e7	+	1.02713e7i	−0.0886856	+	0.0367348i
$260$	−8.44920e6	+	5.37304e7i	−0.0298132	+	0.189589i
$261$	1.48810e6	−	3.59259e6i	0.00518073	−	0.0125074i
$262$	1.12477e8	+	5.72316e7i	0.386375	+	0.196599i
$263$	1.61096e8	+	1.61096e8i	0.546059	+	0.546059i	0.925298	−	0.379240i	$-0.123814\pi$
$263$	1.61096e8	+	1.61096e8i	0.546059	+	0.546059i	−0.379240	+	0.925298i	$0.623814\pi$
$264$	1.40327e8	−	8.63128e7i	0.469383	−	0.288710i
$265$	−1.20341e8	+	1.20341e8i	−0.397240	+	0.397240i
$266$	−2.53698e7	+	8.25864e6i	−0.0826477	+	0.0269044i
$267$	−3.13482e8	−	1.29849e8i	−1.00791	−	0.417492i
$268$	−2.59672e7	−	1.07637e8i	−0.0824049	−	0.341578i
$269$	−8.74758e6	−	2.11185e7i	−0.0274003	−	0.0661501i	0.909587	−	0.415513i	$-0.136398\pi$
$269$	−8.74758e6	−	2.11185e7i	−0.0274003	−	0.0661501i	−0.936987	+	0.349363i	$0.886398\pi$
$270$	1.65003e7	−	2.11148e8i	0.0510174	−	0.652850i
$271$			2.07110e8i			0.632134i	0.948737	+	0.316067i	$0.102363\pi$
$271$			2.07110e8i			0.632134i	−0.948737	+	0.316067i	$0.897637\pi$
$272$	−2.43396e7	+	7.54767e7i	−0.0733367	+	0.227416i
$273$			9.17379e6i			0.0272885i
$274$	−4.10424e8	−	3.20729e7i	−1.20533	−	0.0941914i
$275$	−3.36900e7	−	8.13349e7i	−0.0976871	−	0.235837i
$276$	−5.13904e8	−	3.14140e8i	−1.47130	−	0.899376i
$277$	3.78283e8	+	1.56690e8i	1.06939	+	0.442957i	0.846776	−	0.531949i	$-0.178540\pi$
$277$	3.78283e8	+	1.56690e8i	1.06939	+	0.442957i	0.222617	+	0.974906i	$0.428540\pi$
$278$	−1.13113e7	−	3.47472e7i	−0.0315759	−	0.0969981i
$279$	2.92459e7	−	2.92459e7i	0.0806213	−	0.0806213i
$280$	−1.45411e7	+	2.00840e7i	−0.0395862	+	0.0546761i
$281$	−4.60843e8	−	4.60843e8i	−1.23903	−	1.23903i	−0.960399	−	0.278629i	$-0.910120\pi$
$281$	−4.60843e8	−	4.60843e8i	−1.23903	−	1.23903i	−0.278629	−	0.960399i	$-0.589880\pi$
$282$	9.83421e7	−	1.93271e8i	0.261137	−	0.513210i
$283$	1.11276e8	−	2.68645e8i	0.291843	−	0.704572i	−0.708155	−	0.706057i	$-0.750472\pi$
$283$	1.11276e8	−	2.68645e8i	0.291843	−	0.704572i	0.999999	+	0.00148409i	$0.000472402\pi$
$284$	3.29717e8	−	2.40111e8i	0.854136	−	0.622010i
$285$	−2.50864e8	+	1.03911e8i	−0.641921	+	0.265892i
$286$	4.19272e7	−	3.58493e7i	0.105978	−	0.0906150i
$287$	2.08137e7			0.0519713
$288$	5.12369e7	+	2.10574e7i	0.126389	+	0.0519434i
$289$	3.86910e8			0.942904
$290$	2.22495e7	−	1.90241e7i	0.0535706	−	0.0458048i
$291$	−5.63130e8	+	2.33256e8i	−1.33962	+	0.554891i
$292$	−3.81515e8	−	5.23891e8i	−0.896749	−	1.23141i
$293$	2.44576e8	−	5.90459e8i	0.568038	−	1.37137i	−0.335168	−	0.942158i	$-0.608793\pi$
$293$	2.44576e8	−	5.90459e8i	0.568038	−	1.37137i	0.903206	−	0.429207i	$-0.141207\pi$
$294$	2.08774e8	−	4.10302e8i	0.479138	−	0.941647i
$295$	2.73333e8	+	2.73333e8i	0.619890	+	0.619890i
$296$	7.13558e7	+	4.45739e8i	0.159922	+	0.998987i
$297$	−1.51888e8	+	1.51888e8i	−0.336417	+	0.336417i
$298$	1.16005e8	+	3.56357e8i	0.253934	+	0.780060i
$299$	−1.86327e8	−	7.71792e7i	−0.403113	−	0.166975i
$300$	1.28423e8	−	2.10089e8i	0.274612	−	0.449240i
$301$	−2.25195e7	−	5.43670e7i	−0.0475967	−	0.114909i
$302$	−4.03177e8	−	3.15065e7i	−0.842308	−	0.0658228i
$303$			7.48225e8i			1.54519i
$304$	3.61950e7	+	4.47259e8i	0.0738909	+	0.913066i
$305$		−	4.35224e8i		−	0.878341i
$306$	−1.27500e6	+	1.63157e7i	−0.00254382	+	0.0325523i
$307$	2.72031e8	+	6.56740e8i	0.536579	+	1.29542i	0.927097	+	0.374821i	$0.122296\pi$
$307$	2.72031e8	+	6.56740e8i	0.536579	+	1.29542i	−0.390518	+	0.920595i	$0.627704\pi$
$308$	2.44466e7	−	5.89768e6i	0.0476750	−	0.0115015i
$309$	6.31143e8	+	2.61428e8i	1.21695	+	0.504077i
$310$	2.96070e8	−	9.63798e7i	0.564454	−	0.183747i
$311$	−5.47635e8	+	5.47635e8i	−1.03236	+	1.03236i	−0.0328974	+	0.999459i	$0.510473\pi$
$311$	−5.47635e8	+	5.47635e8i	−1.03236	+	1.03236i	−0.999459	+	0.0328974i	$0.989527\pi$
$312$	1.50086e8	+	3.57695e7i	0.279769	+	0.0666763i
$313$	7.81949e7	+	7.81949e7i	0.144136	+	0.144136i	0.775493	−	0.631356i	$-0.217502\pi$
$313$	7.81949e7	+	7.81949e7i	0.144136	+	0.144136i	−0.631356	+	0.775493i	$0.717502\pi$
$314$	5.79723e8	+	2.94980e8i	1.05674	+	0.537699i
$315$	−1.95814e6	+	4.72736e6i	−0.00352985	+	0.00852181i
$316$	6.88090e8	+	1.08203e8i	1.22671	+	0.192902i
$317$	−5.28350e8	+	2.18850e8i	−0.931567	+	0.385868i	−0.796273	−	0.604938i	$-0.793198\pi$
$317$	−5.28350e8	+	2.18850e8i	−0.931567	+	0.385868i	−0.135295	+	0.990805i	$0.543198\pi$
$318$	3.13738e8	+	3.66929e8i	0.547106	+	0.639863i
$319$	−2.96900e7			−0.0512086
$320$	2.71884e8	+	3.16206e8i	0.463830	+	0.539443i
$321$	−3.57775e8			−0.603729
$322$	−5.97491e7	−	6.98790e7i	−0.0997323	−	0.116641i
$323$	−1.22475e8	+	5.07309e7i	−0.202227	+	0.0837652i
$324$	−6.76138e8	−	1.06324e8i	−1.10440	−	0.173669i
$325$	3.15516e7	−	7.61723e7i	0.0509835	−	0.123085i
$326$	7.03490e8	+	3.57957e8i	1.12460	+	0.572228i
$327$	7.45014e8	+	7.45014e8i	1.17828	+	1.17828i
$328$	8.11547e7	−	3.40520e8i	0.126986	−	0.532824i
$329$	2.34063e7	−	2.34063e7i	0.0362366	−	0.0362366i
$330$	2.43369e8	−	7.92240e7i	0.372792	−	0.121355i
$331$	−7.18195e8	−	2.97486e8i	−1.08854	−	0.450888i	−0.235043	−	0.971985i	$-0.575523\pi$
$331$	−7.18195e8	−	2.97486e8i	−1.08854	−	0.450888i	−0.853498	+	0.521097i	$0.825523\pi$
$332$	−8.89666e8	+	2.14630e8i	−1.33427	+	0.321890i
$333$	3.56491e7	+	8.60644e7i	0.0529046	+	0.127723i
$334$	4.61421e7	−	5.90462e8i	0.0677618	−	0.867121i
$335$		−	1.72014e8i		−	0.249981i
$336$	5.35855e7	+	4.55619e7i	0.0770654	+	0.0655260i
$337$		−	2.13823e7i		−	0.0304334i	−0.999884	−	0.0152167i	$-0.995156\pi$
$337$		−	2.13823e7i		−	0.0304334i	0.999884	−	0.0152167i	$-0.00484381\pi$
$338$	−6.56255e8	−	5.12835e7i	−0.924409	−	0.0722386i
$339$	3.02462e8	+	7.30207e8i	0.421669	+	1.01800i
$340$	−6.42563e7	+	1.05117e8i	−0.0886624	+	0.145044i
$341$	−2.91751e8	−	1.20847e8i	−0.398449	−	0.165043i
$342$	2.86636e7	+	8.80518e7i	0.0387471	+	0.119027i
$343$	9.98317e7	−	9.98317e7i	0.133579	−	0.133579i
$344$	−9.77268e8	+	1.56445e8i	−1.29437	+	0.207209i
$345$	−6.61647e8	−	6.61647e8i	−0.867480	−	0.867480i
$346$	−4.81068e7	+	9.45439e7i	−0.0624367	+	0.122706i
$347$	5.27812e8	−	1.27425e9i	0.678151	−	1.63720i	−0.0892316	−	0.996011i	$-0.528441\pi$
$347$	5.27812e8	−	1.27425e9i	0.678151	−	1.63720i	0.767382	−	0.641190i	$-0.221559\pi$
$348$	−4.88844e7	−	6.71275e7i	−0.0621789	−	0.0853834i
$349$	6.68790e8	−	2.77022e8i	0.842172	−	0.348839i	0.0804627	−	0.996758i	$-0.474360\pi$
$349$	6.68790e8	−	2.77022e8i	0.842172	−	0.348839i	0.761710	+	0.647918i	$0.224360\pi$
$350$	2.85672e7	−	2.44260e7i	0.0356148	−	0.0304519i
$351$	−2.01168e8			−0.248305
$352$	−1.16861e6	−	4.22950e8i	−0.00142814	−	0.516880i
$353$	2.79755e8			0.338506			0.169253	−	0.985573i	$-0.445864\pi$
$353$	2.79755e8			0.338506			0.169253	+	0.985573i	$0.445864\pi$
$354$	8.33413e8	−	7.12599e8i	0.998502	−	0.853756i
$355$	5.85420e8	−	2.42489e8i	0.694493	−	0.287669i
$356$	−7.04172e8	+	5.12801e8i	−0.827187	+	0.602385i
$357$	−7.95205e6	+	1.91979e7i	−0.00924997	+	0.0223314i
$358$	1.35987e8	−	2.67255e8i	0.156642	−	0.307847i
$359$	−4.37394e8	−	4.37394e8i	−0.498933	−	0.498933i	0.412173	−	0.911106i	$-0.364770\pi$
$359$	−4.37394e8	−	4.37394e8i	−0.498933	−	0.498933i	−0.911106	+	0.412173i	$0.864770\pi$
$360$	6.97062e7	+	5.04682e7i	0.0787432	+	0.0570111i
$361$	1.01668e8	−	1.01668e8i	0.113739	−	0.113739i
$362$	3.05821e8	+	9.39454e8i	0.338834	+	1.04087i
$363$	6.57819e8	+	2.72478e8i	0.721827	+	0.298991i
$364$	2.00947e7	+	1.22835e7i	0.0218387	+	0.0133496i
$365$	−3.85293e8	−	9.30180e8i	−0.414731	−	1.00125i
$366$	−1.23085e9	−	9.61853e7i	−1.31226	−	0.102547i
$367$		−	4.02029e8i		−	0.424547i	−0.977210	−	0.212274i	$-0.931913\pi$
$367$		−	4.02029e8i		−	0.424547i	0.977210	−	0.212274i	$-0.0680868\pi$
$368$	−1.37621e9	+	7.05051e8i	−1.43952	+	0.737485i
$369$		−	7.22389e7i		−	0.0748478i
$370$	−5.46359e7	+	6.99154e8i	−0.0560753	+	0.717574i
$371$	2.82011e7	+	6.80834e7i	0.0286719	+	0.0692201i
$372$	−2.07137e8	−	8.58608e8i	−0.208621	−	0.864758i
$373$	6.58320e8	+	2.72685e8i	0.656834	+	0.272070i	0.686106	−	0.727502i	$-0.259319\pi$
$373$	6.58320e8	+	2.72685e8i	0.656834	+	0.272070i	−0.0292713	+	0.999572i	$0.509319\pi$
$374$	1.18816e8	−	3.86782e7i	0.117442	−	0.0382310i
$375$	8.18186e8	−	8.18186e8i	0.801203	−	0.801203i
$376$	−2.91672e8	−	4.74199e8i	−0.282968	−	0.460048i
$377$	−1.96614e7	−	1.96614e7i	−0.0188982	−	0.0188982i
$378$	−8.17352e7	−	4.15893e7i	−0.0778373	−	0.0396059i
$379$	1.03943e8	−	2.50940e8i	0.0980748	−	0.236774i	−0.867226	−	0.497915i	$-0.834099\pi$
$379$	1.03943e8	−	2.50940e8i	0.0980748	−	0.236774i	0.965300	+	0.261142i	$0.0840990\pi$
$380$	−1.08290e8	+	6.88639e8i	−0.101238	+	0.643797i
$381$	−1.04898e8	+	4.34502e7i	−0.0971695	+	0.0402489i
$382$	1.07663e9	+	1.25917e9i	0.988203	+	1.15574i
$383$	−8.90648e8			−0.810047			−0.405023	−	0.914306i	$-0.632737\pi$
$383$	−8.90648e8			−0.810047			−0.405023	+	0.914306i	$0.632737\pi$
$384$	9.54342e8	−	6.99026e8i	0.860092	−	0.629991i
$385$	3.90680e7			0.0348906
$386$	−1.41050e8	−	1.64964e8i	−0.124830	−	0.145993i
$387$	−1.88693e8	+	7.81594e7i	−0.165489	+	0.0685476i
$388$	−2.43084e8	+	1.54583e9i	−0.211274	+	1.34354i
$389$	5.15183e8	−	1.24376e9i	0.443749	−	1.07131i	−0.530873	−	0.847451i	$-0.678136\pi$
$389$	5.15183e8	−	1.24376e9i	0.443749	−	1.07131i	0.974623	−	0.223855i	$-0.0718641\pi$
$390$	2.13629e8	+	1.08701e8i	0.182362	+	0.0927910i
$391$	−3.23025e8	−	3.23025e8i	−0.273286	−	0.273286i
$392$	−6.19201e8	−	1.00669e9i	−0.519195	−	0.844105i
$393$	3.93258e8	−	3.93258e8i	0.326816	−	0.326816i
$394$	−1.15684e9	+	3.76587e8i	−0.952877	+	0.310191i
$395$	9.99733e8	+	4.14103e8i	0.816195	+	0.338079i
$396$	−2.04693e7	−	8.48475e7i	−0.0165642	−	0.0686603i
$397$	2.46969e8	+	5.96235e8i	0.198096	+	0.478245i	0.991446	−	0.130521i	$-0.0416649\pi$
$397$	2.46969e8	+	5.96235e8i	0.198096	+	0.478245i	−0.793350	+	0.608766i	$0.791665\pi$
$398$	4.26558e7	−	5.45849e8i	0.0339146	−	0.433992i
$399$			1.17577e8i			0.0926649i
$400$	−2.88232e8	−	5.62609e8i	−0.225181	−	0.439538i
$401$			3.56244e8i			0.275894i	0.990440	+	0.137947i	$0.0440504\pi$
$401$			3.56244e8i			0.275894i	−0.990440	+	0.137947i	$0.955950\pi$
$402$	−4.86469e8	−	3.80155e7i	−0.373477	−	0.0291857i
$403$	−1.13177e8	−	2.73233e8i	−0.0861369	−	0.207953i
$404$	1.63895e9	+	1.00186e9i	1.23660	+	0.755912i
$405$	−9.82367e8	−	4.06910e8i	−0.734821	−	0.304373i
$406$	−3.92371e6	−	1.20533e7i	−0.00290975	−	0.00893848i
$407$	5.02934e8	−	5.02934e8i	0.369769	−	0.369769i
$408$	2.83079e8	+	2.04953e8i	0.206347	+	0.149398i
$409$	1.29171e9	+	1.29171e9i	0.933542	+	0.933542i	0.997925	−	0.0643831i	$-0.0205080\pi$
$409$	1.29171e9	+	1.29171e9i	0.933542	+	0.933542i	−0.0643831	+	0.997925i	$0.520508\pi$
$410$	2.46623e8	−	4.84686e8i	0.176722	−	0.347310i
$411$	−6.94268e8	+	1.67611e9i	−0.493265	+	1.19085i
$412$	1.41773e9	−	1.03244e9i	0.998742	−	0.727316i
$413$	1.54639e8	−	6.40537e7i	0.108018	−	0.0447423i
$414$	−2.42531e8	+	2.07373e8i	−0.167984	+	0.143632i
$415$	−1.42177e9			−0.976476
$416$	2.79314e8	−	2.80861e8i	0.190224	−	0.191278i
$417$	−1.61036e8			−0.108755
$418$	5.37363e8	−	4.59465e8i	0.359874	−	0.307706i
$419$	−1.33687e8	+	5.53748e7i	−0.0887848	+	0.0367759i	−0.426634	−	0.904424i	$-0.640301\pi$
$419$	−1.33687e8	+	5.53748e7i	−0.0887848	+	0.0367759i	0.337849	+	0.941200i	$0.390301\pi$
$420$	6.43252e7	+	8.83306e7i	0.0423651	+	0.0581753i
$421$	−4.41059e8	+	1.06481e9i	−0.288077	+	0.695480i	−0.999977	−	0.00680099i	$-0.997835\pi$
$421$	−4.41059e8	+	1.06481e9i	−0.288077	+	0.695480i	0.711899	+	0.702281i	$0.247835\pi$
$422$	2.32856e8	−	4.57631e8i	0.150832	−	0.296430i
$423$	−8.12372e7	−	8.12372e7i	−0.0521871	−	0.0521871i
$424$	1.22383e9	−	1.95915e8i	0.779720	−	0.124821i
$425$	1.32056e8	−	1.32056e8i	0.0834442	−	0.0834442i
$426$	−5.56398e8	−	1.70920e9i	−0.348700	−	1.07117i
$427$	−1.74111e8	−	7.21190e7i	−0.108225	−	0.0448283i
$428$	−4.79053e8	+	7.83686e8i	−0.295345	+	0.483158i
$429$	−9.30310e7	−	2.24597e8i	−0.0568888	−	0.137342i
$430$	−1.53287e9	−	1.19787e8i	−0.929750	−	0.0726559i
$431$		−	1.16498e9i		−	0.700886i	−0.936584	−	0.350443i	$-0.886031\pi$
$431$		−	1.16498e9i		−	0.700886i	0.936584	−	0.350443i	$-0.113969\pi$
$432$	−9.99108e8	+	1.17505e9i	−0.596237	+	0.701237i
$433$			3.28503e9i			1.94460i	0.233728	+	0.972302i	$0.424908\pi$
$433$			3.28503e9i			1.94460i	−0.233728	+	0.972302i	$0.575092\pi$
$434$	1.05038e7	−	1.34413e8i	0.00616783	−	0.0789273i
$435$	−4.93686e7	−	1.19186e8i	−0.0287567	−	0.0694247i
$436$	2.62947e9	−	6.34354e8i	1.51938	−	0.366546i
$437$	−2.38807e9	−	9.89172e8i	−1.36887	−	0.567005i
$438$	−2.71577e9	+	8.84067e8i	−1.54431	+	0.502719i
$439$	−5.00965e8	+	5.00965e8i	−0.282606	+	0.282606i	−0.834148	−	0.551541i	$-0.814040\pi$
$439$	−5.00965e8	+	5.00965e8i	−0.282606	+	0.282606i	0.551541	+	0.834148i	$0.314040\pi$
$440$	1.52330e8	−	6.39165e8i	0.0852512	−	0.357708i
$441$	−1.72461e8	−	1.72461e8i	−0.0957539	−	0.0957539i
$442$	1.04296e8	+	5.30691e7i	0.0574502	+	0.0292324i
$443$	−1.29509e9	+	3.12664e9i	−0.707764	+	1.70869i	−0.00224998	+	0.999997i	$0.500716\pi$
$443$	−1.29509e9	+	3.12664e9i	−0.707764	+	1.70869i	−0.705514	+	0.708696i	$0.749284\pi$
$444$	1.96518e9	+	3.09029e8i	1.06552	+	0.167555i
$445$	−1.25027e9	+	5.17880e8i	−0.672581	+	0.278592i
$446$	1.50773e9	+	1.76335e9i	0.804734	+	0.941169i
$447$	1.65154e9			0.874606
$448$	1.71551e8	−	5.63697e7i	0.0901403	−	0.0296191i
$449$	1.13549e9			0.592000			0.296000	−	0.955188i	$-0.404347\pi$
$449$	1.13549e9			0.592000			0.296000	+	0.955188i	$0.404347\pi$
$450$	−8.47763e7	−	9.91493e7i	−0.0438562	−	0.0512916i
$451$	−5.09570e8	+	2.11071e8i	−0.261569	+	0.108345i
$452$	2.00447e9	+	3.15206e8i	1.02097	+	0.160550i
$453$	−6.82008e8	+	1.64651e9i	−0.344703	+	0.832187i
$454$	−1.57484e9	−	8.01326e8i	−0.789844	−	0.401896i
$455$	2.58718e7	+	2.58718e7i	0.0128761	+	0.0128761i
$456$	1.92359e9	+	4.58442e8i	0.950027	+	0.226416i
$457$	−3.06009e8	+	3.06009e8i	−0.149978	+	0.149978i	−0.778108	−	0.628130i	$-0.783820\pi$
$457$	−3.06009e8	+	3.06009e8i	−0.149978	+	0.149978i	0.628130	+	0.778108i	$0.283820\pi$
$458$	−1.89129e9	+	6.15673e8i	−0.919875	+	0.299448i
$459$	−4.20984e8	−	1.74377e8i	−0.203199	−	0.0841677i
$460$	−2.33523e9	+	5.63370e8i	−1.11861	+	0.269862i
$461$	1.03087e9	+	2.48875e9i	0.490063	+	1.18312i	0.954688	+	0.297610i	$0.0961894\pi$
$461$	1.03087e9	+	2.48875e9i	0.490063	+	1.18312i	−0.464624	+	0.885508i	$0.653811\pi$
$462$	8.63410e6	−	1.10487e8i	0.00407352	−	0.0521273i
$463$		−	1.52278e9i		−	0.713025i	−0.934291	−	0.356513i	$-0.883966\pi$
$463$		−	1.52278e9i		−	0.713025i	0.934291	−	0.356513i	$-0.116034\pi$
$464$	−2.12494e8	+	1.71964e7i	−0.0987494	+	0.00799141i
$465$		−	1.37214e9i		−	0.632867i
$466$	1.56729e9	+	1.22477e8i	0.717462	+	0.0560665i
$467$	−5.23468e8	−	1.26376e9i	−0.237838	−	0.574192i	0.759221	−	0.650833i	$-0.225580\pi$
$467$	−5.23468e8	−	1.26376e9i	−0.237838	−	0.574192i	−0.997059	+	0.0766415i	$0.975580\pi$
$468$	4.26328e7	−	6.97433e7i	0.0192258	−	0.0314516i
$469$	−6.88140e7	−	2.85037e7i	−0.0308015	−	0.0127584i
$470$	−2.67717e8	−	8.22402e8i	−0.118942	−	0.365377i
$471$	2.02691e9	−	2.02691e9i	0.893844	−	0.893844i
$472$	−4.44986e8	−	2.77970e9i	−0.194782	−	1.21675i
$473$	1.10267e9	+	1.10267e9i	0.479104	+	0.479104i
$474$	1.39206e9	−	2.73580e9i	0.600389	−	1.17994i
$475$	4.04383e8	−	9.76267e8i	0.173127	−	0.417966i
$476$	3.14044e7	+	4.31242e7i	0.0133465	+	0.0183272i
$477$	2.36299e8	−	9.78784e7i	0.0996892	−	0.0412926i
$478$	−1.58228e9	+	1.35291e9i	−0.662652	+	0.566592i
$479$	2.19823e9			0.913901			0.456951	−	0.889492i	$-0.348942\pi$
$479$	2.19823e9			0.913901			0.456951	+	0.889492i	$0.348942\pi$
$480$	1.69593e9	−	7.07973e8i	0.699944	−	0.292195i
$481$	6.66110e8			0.272922
$482$	3.55215e9	−	3.03722e9i	1.44486	−	1.23541i
$483$	−3.74329e8	+	1.55052e8i	−0.151161	+	0.0626128i
$484$	1.47765e9	−	1.07608e9i	0.592398	−	0.431404i
$485$	−9.30304e8	+	2.24595e9i	−0.370279	+	0.893932i
$486$	−3.11537e8	+	6.12262e8i	−0.123107	+	0.241941i
$487$	−3.04663e9	−	3.04663e9i	−1.19528	−	1.19528i	−0.975565	−	0.219711i	$-0.929489\pi$
$487$	−3.04663e9	−	3.04663e9i	−1.19528	−	1.19528i	−0.219711	−	0.975565i	$-0.570511\pi$
$488$	−1.85876e9	+	2.56731e9i	−0.724027	+	1.00002i
$489$	2.45964e9	−	2.45964e9i	0.951242	−	0.951242i
$490$	−5.68346e8	−	1.74591e9i	−0.218236	−	0.670401i
$491$	2.45618e9	+	1.01738e9i	0.936429	+	0.387881i	0.798114	−	0.602507i	$-0.205831\pi$
$491$	2.45618e9	+	1.01738e9i	0.936429	+	0.387881i	0.138315	+	0.990388i	$0.455831\pi$
$492$	−1.31622e9	−	8.04584e8i	−0.498256	−	0.304575i
$493$	−2.41024e7	−	5.81884e7i	−0.00905934	−	0.0218712i
$494$	6.60124e8	+	5.15858e7i	0.246366	+	0.0192525i
$495$		−	1.35595e8i		−	0.0502486i
$496$	−2.15809e9	−	6.95935e8i	−0.794114	−	0.256084i
$497$		−	2.74378e8i		−	0.100254i
$498$	−3.14214e8	+	4.02088e9i	−0.114005	+	1.45888i
$499$	−1.66547e9	−	4.02079e9i	−0.600045	−	1.44864i	−0.873535	−	0.486761i	$-0.838178\pi$
$499$	−1.66547e9	−	4.02079e9i	−0.600045	−	1.44864i	0.273490	−	0.961875i	$-0.411822\pi$
$500$	−6.96658e8	−	2.88773e9i	−0.249244	−	1.03314i
$501$	−2.41136e9	−	9.98817e8i	−0.856702	−	0.354858i
$502$	−4.52855e9	+	1.47418e9i	−1.59770	+	0.520101i
$503$	−1.03882e9	+	1.03882e9i	−0.363959	+	0.363959i	−0.865268	−	0.501309i	$-0.832852\pi$
$503$	−1.03882e9	+	1.03882e9i	−0.363959	+	0.363959i	0.501309	+	0.865268i	$0.332852\pi$
$504$	3.17404e7	−	1.95230e7i	0.0110435	−	0.00679266i
$505$	2.11013e9	+	2.11013e9i	0.729104	+	0.729104i
$506$	2.17144e9	+	1.10489e9i	0.745112	+	0.379135i
$507$	−1.11011e9	+	2.68005e9i	−0.378302	+	0.913302i
$508$	−4.52810e7	+	2.87952e8i	−0.0153247	+	0.0974535i
$509$	−1.67288e9	+	6.92928e8i	−0.562279	+	0.232903i	−0.645674	−	0.763613i	$-0.723424\pi$
$509$	−1.67288e9	+	6.92928e8i	−0.562279	+	0.232903i	0.0833954	+	0.996517i	$0.473424\pi$
$510$	3.52836e8	+	4.12655e8i	0.117781	+	0.137750i
$511$	−4.35962e8			−0.144536
$512$	−2.53335e8	−	3.02642e9i	−0.0834162	−	0.996515i
$513$	−2.57829e9			−0.843181
$514$	−8.69824e7	−	1.01729e8i	−0.0282527	−	0.0330427i
$515$	2.51721e9	−	1.04266e9i	0.812071	−	0.336371i
$516$	−6.77535e8	+	4.30860e9i	−0.217099	+	1.38058i
$517$	−3.35681e8	+	8.10406e8i	−0.106834	+	0.257920i
$518$	2.70642e8	+	1.37711e8i	0.0855541	+	0.0435325i
$519$	3.30558e8	+	3.30558e8i	0.103792	+	0.103792i
$520$	5.24147e8	−	3.22394e8i	0.163471	−	0.100548i
$521$	−8.88634e8	+	8.88634e8i	−0.275290	+	0.275290i	−0.831226	−	0.555935i	$-0.812360\pi$
$521$	−8.88634e8	+	8.88634e8i	−0.275290	+	0.275290i	0.555935	+	0.831226i	$0.312360\pi$
$522$	−4.18337e7	+	1.36181e7i	−0.0128730	+	0.00419055i
$523$	−2.61918e9	−	1.08490e9i	−0.800590	−	0.331615i	−0.0553970	−	0.998464i	$-0.517642\pi$
$523$	−2.61918e9	−	1.08490e9i	−0.800590	−	0.331615i	−0.745193	+	0.666849i	$0.767642\pi$
$524$	−3.34846e8	−	1.38797e9i	−0.101668	−	0.421426i
$525$	−6.33869e7	−	1.53030e8i	−0.0191180	−	0.0461549i
$526$	2.00811e8	−	2.56970e9i	0.0601641	−	0.769896i
$527$		−	6.69896e8i		−	0.199375i
$528$	−1.77394e9	−	5.72057e8i	−0.524470	−	0.169130i
$529$		−	5.50255e9i		−	1.61610i
$530$	1.91960e9	+	1.50009e8i	0.560074	+	0.0437674i
$531$	−2.22313e8	−	5.36712e8i	−0.0644369	−	0.155564i
$532$	2.57545e8	+	1.57432e8i	0.0741587	+	0.0453319i
$533$	−4.77226e8	−	1.97674e8i	−0.136515	−	0.0565462i
$534$	1.18829e9	+	3.65032e9i	0.337698	+	1.03738i
$535$	−1.00899e9	+	1.00899e9i	−0.284871	+	0.284871i
$536$	−7.34643e8	+	1.01468e9i	−0.206063	+	0.284612i
$537$	−9.34414e8	−	9.34414e8i	−0.260393	−	0.260393i
$538$	−1.17281e8	+	2.30492e8i	−0.0324706	+	0.0638143i
$539$	−7.12630e8	+	1.72044e9i	−0.196021	+	0.473237i
$540$	−1.93697e9	+	1.41056e9i	−0.529351	+	0.385491i
$541$	3.83656e9	−	1.58915e9i	1.04172	−	0.431495i	0.204792	−	0.978806i	$-0.434348\pi$
$541$	3.83656e9	−	1.58915e9i	1.04172	−	0.431495i	0.836930	+	0.547311i	$0.184348\pi$
$542$	1.78093e9	−	1.52276e9i	0.480452	−	0.410804i
$543$	4.35391e9			1.16702
$544$	8.27975e8	−	3.45642e8i	0.220506	−	0.0920513i
$545$	4.20215e9			1.11195
$546$	7.88850e7	−	6.74496e7i	0.0207405	−	0.0177339i
$547$	9.63723e8	−	3.99187e8i	0.251766	−	0.104285i	−0.253232	−	0.967406i	$-0.581493\pi$
$547$	9.63723e8	−	3.99187e8i	0.251766	−	0.104285i	0.504997	+	0.863121i	$0.331493\pi$
$548$	2.74182e9	+	3.76503e9i	0.711716	+	0.977320i
$549$	−2.50306e8	+	6.04291e8i	−0.0645606	+	0.155863i
$550$	−4.51692e8	+	8.87708e8i	−0.115764	+	0.227510i
$551$	−2.51992e8	−	2.51992e8i	−0.0641736	−	0.0641736i
$552$	1.07716e9	+	6.72872e9i	0.272580	+	1.70273i
$553$	3.31322e8	−	3.31322e8i	0.0833130	−	0.0833130i
$554$	−1.43393e9	−	4.40488e9i	−0.358296	−	1.10065i
$555$	2.85524e9	+	1.18268e9i	0.708952	+	0.293657i
$556$	−2.15624e8	+	3.52741e8i	−0.0532030	+	0.0870351i
$557$	−2.20609e9	−	5.32597e9i	−0.540916	−	1.30589i	−0.924077	−	0.382205i	$-0.875165\pi$
$557$	−2.20609e9	−	5.32597e9i	−0.540916	−	1.30589i	0.383161	−	0.923681i	$-0.374835\pi$
$558$	−4.66512e8	−	3.64559e7i	−0.113669	−	0.00888276i
$559$			1.46042e9i			0.353621i
$560$	2.79613e8	−	2.26280e7i	0.0672822	−	0.00544489i
$561$		−	5.50654e8i		−	0.131677i
$562$	−5.74455e8	+	7.35108e9i	−0.136515	+	1.74692i
$563$	2.53665e9	+	6.12402e9i	0.599076	+	1.44630i	0.874525	+	0.484981i	$0.161173\pi$
$563$	2.53665e9	+	6.12402e9i	0.599076	+	1.44630i	−0.275449	+	0.961316i	$0.588827\pi$
$564$	−2.38498e9	+	5.75372e8i	−0.559768	+	0.135043i
$565$	2.91231e9	+	1.20632e9i	0.679311	+	0.281380i
$566$	−3.12821e9	+	1.01833e9i	−0.725168	+	0.236064i
$567$	−3.25567e8	+	3.25567e8i	−0.0750067	+	0.0750067i
$568$	−4.48892e9	−	1.06983e9i	−1.02783	−	0.244959i
$569$	1.99831e9	+	1.99831e9i	0.454748	+	0.454748i	0.896927	−	0.442179i	$-0.145794\pi$
$569$	1.99831e9	+	1.99831e9i	0.454748	+	0.454748i	−0.442179	+	0.896927i	$0.645794\pi$
$570$	2.73799e9	+	1.39317e9i	0.619255	+	0.315095i
$571$	−1.20267e8	+	2.90350e8i	−0.0270346	+	0.0652673i	−0.936820	−	0.349811i	$-0.886246\pi$
$571$	−1.20267e8	+	2.90350e8i	−0.0270346	+	0.0652673i	0.909786	+	0.415078i	$0.136246\pi$
$572$	−6.16533e8	−	9.69509e7i	−0.137743	−	0.0216604i
$573$	6.74513e9	−	2.79392e9i	1.49778	−	0.620402i
$574$	−1.53031e8	−	1.78976e8i	−0.0337745	−	0.0395006i
$575$	3.64143e9			0.798792
$576$	−1.95644e8	−	5.95406e8i	−0.0426568	−	0.129818i
$577$	−7.46758e9			−1.61832			−0.809160	−	0.587588i	$-0.800078\pi$
$577$	−7.46758e9			−1.61832			−0.809160	+	0.587588i	$0.800078\pi$
$578$	−2.84472e9	−	3.32702e9i	−0.612763	−	0.716651i
$579$	−8.83681e8	+	3.66033e8i	−0.189200	+	0.0783691i
$580$	−3.27175e8	−	5.14488e7i	−0.0696277	−	0.0109491i
$581$	−2.35595e8	+	5.68778e8i	−0.0498368	+	0.120317i
$582$	6.14612e9	+	3.12733e9i	1.29232	+	0.657572i
$583$	−1.38086e9	−	1.38086e9i	−0.288609	−	0.288609i
$584$	−1.69986e9	+	7.13249e9i	−0.353157	+	1.48182i
$585$	8.97940e7	−	8.97940e7i	0.0185439	−	0.0185439i
$586$	−6.87555e9	+	2.23820e9i	−1.41145	+	0.459471i
$587$	2.86515e9	+	1.18678e9i	0.584674	+	0.242180i	0.655357	−	0.755319i	$-0.272518\pi$
$587$	2.86515e9	+	1.18678e9i	0.584674	+	0.242180i	−0.0706834	+	0.997499i	$0.522518\pi$
$588$	−5.06316e9	+	1.22148e9i	−1.02707	+	0.247779i
$589$	−1.45054e9	−	3.50190e9i	−0.292499	−	0.706156i
$590$	3.40718e8	−	4.36003e9i	0.0682988	−	0.873993i
$591$			5.36139e9i			1.06837i
$592$	3.30825e9	−	3.89085e9i	0.655349	−	0.770758i
$593$		−	7.57898e9i		−	1.49252i	−0.665656	−	0.746259i	$-0.731848\pi$
$593$		−	7.57898e9i		−	1.49252i	0.665656	−	0.746259i	$-0.268152\pi$
$594$	2.42283e9	+	1.89334e8i	0.474319	+	0.0370660i
$595$	3.17155e7	+	7.65679e7i	0.00617251	+	0.0149018i
$596$	2.21138e9	−	3.61761e9i	0.427859	−	0.699938i
$597$	−2.22917e9	−	9.23351e8i	−0.428778	−	0.177606i
$598$	7.06294e8	+	2.16967e9i	0.135061	+	0.414896i
$599$	−6.35413e9	+	6.35413e9i	−1.20799	+	1.20799i	−0.236309	+	0.971678i	$0.575938\pi$
$599$	−6.35413e9	+	6.35413e9i	−1.20799	+	1.20799i	−0.971678	+	0.236309i	$0.924062\pi$
$600$	−2.75077e9	+	4.40355e8i	−0.519906	+	0.0832287i
$601$	4.32032e9	+	4.32032e9i	0.811812	+	0.811812i	0.984905	−	0.173093i	$-0.0553761\pi$
$601$	4.32032e9	+	4.32032e9i	0.811812	+	0.811812i	−0.173093	+	0.984905i	$0.555376\pi$
$602$	−3.01926e8	+	5.93373e8i	−0.0564044	+	0.110851i
$603$	−9.89288e7	+	2.38835e8i	−0.0183744	+	0.0443596i
$604$	2.69340e9	+	3.69854e9i	0.497361	+	0.682970i
$605$	2.62361e9	−	1.08673e9i	0.481676	−	0.199517i
$606$	6.43395e9	−	5.50126e9i	1.17442	−	1.00417i
$607$	6.26761e8			0.113747			0.0568737	−	0.998381i	$-0.481887\pi$
$607$	6.26761e8			0.113747			0.0568737	+	0.998381i	$0.481887\pi$
$608$	3.57984e9	−	3.59968e9i	0.645953	−	0.649533i
$609$	−5.58610e7			−0.0100219
$610$	−3.74247e9	+	3.19995e9i	−0.667580	+	0.570806i
$611$	−7.58967e8	+	3.14374e8i	−0.134610	+	0.0557574i
$612$	1.49673e8	−	1.08996e8i	0.0263944	−	0.0192213i
$613$	1.65265e9	−	3.98985e9i	0.289781	−	0.699592i	−0.710210	−	0.703990i	$-0.751400\pi$
$613$	1.65265e9	−	3.98985e9i	0.289781	−	0.699592i	0.999990	+	0.00439779i	$0.00139987\pi$
$614$	3.64719e9	−	7.16781e9i	0.635872	−	1.24968i
$615$	−1.69463e9	−	1.69463e9i	−0.293773	−	0.293773i
$616$	−2.30455e8	−	1.66853e8i	−0.0397241	−	0.0287608i
$617$	−6.54348e9	+	6.54348e9i	−1.12153	+	1.12153i	−0.130019	+	0.991512i	$0.541504\pi$
$617$	−6.54348e9	+	6.54348e9i	−1.12153	+	1.12153i	−0.991512	+	0.130019i	$0.958496\pi$
$618$	−2.39242e9	−	7.34929e9i	−0.407735	−	1.25252i
$619$	−7.12476e9	−	2.95117e9i	−1.20740	−	0.500123i	−0.314020	−	0.949416i	$-0.601676\pi$
$619$	−7.12476e9	−	2.95117e9i	−1.20740	−	0.500123i	−0.893384	+	0.449293i	$0.851676\pi$
$620$	−3.00559e9	−	1.83726e9i	−0.506477	−	0.309600i
$621$	−3.40008e9	−	8.20852e9i	−0.569729	−	1.37545i
$622$	8.73552e9	+	6.82644e8i	1.45553	+	0.113744i
$623$			5.85985e8i			0.0970909i
$624$	−7.95918e8	−	1.55358e9i	−0.131136	−	0.255969i
$625$		−	1.60056e9i		−	0.262237i
$626$	9.74724e7	−	1.24732e9i	0.0158808	−	0.203220i
$627$	−1.19234e9	−	2.87856e9i	−0.193180	−	0.466378i
$628$	−1.72585e9	−	7.15383e9i	−0.278063	−	1.15260i
$629$	1.39396e9	+	5.77399e8i	0.223344	+	0.0925122i
$630$	5.50474e7	−	1.79196e7i	0.00877091	−	0.00285520i
$631$	−5.59322e9	+	5.59322e9i	−0.886256	+	0.886256i	−0.994161	−	0.107905i	$-0.965586\pi$
$631$	−5.59322e9	+	5.59322e9i	−0.886256	+	0.886256i	0.107905	+	0.994161i	$0.465586\pi$
$632$	−4.12869e9	−	6.71240e9i	−0.650583	−	1.05771i
$633$	−1.60003e9	−	1.60003e9i	−0.250736	−	0.250736i
$634$	5.76653e9	+	2.93418e9i	0.898674	+	0.457272i
$635$	−1.73294e8	+	4.18369e8i	−0.0268581	+	0.0648412i
$636$	8.48472e8	−	5.39563e9i	0.130779	−	0.831653i
$637$	−1.61124e9	+	6.67396e8i	−0.246986	+	0.102305i
$638$	2.18293e8	+	2.55303e8i	0.0332789	+	0.0389210i
$639$	−9.52293e8			−0.144384
$640$	7.20037e8	−	4.66280e9i	0.108574	−	0.703099i
$641$	−1.10426e10			−1.65604			−0.828018	−	0.560702i	$-0.810531\pi$
$641$	−1.10426e10			−1.65604			−0.828018	+	0.560702i	$0.810531\pi$
$642$	2.63051e9	+	3.07649e9i	0.392344	+	0.458863i
$643$	5.70000e9	−	2.36102e9i	0.845545	−	0.350236i	0.0825074	−	0.996590i	$-0.473707\pi$
$643$	5.70000e9	−	2.36102e9i	0.845545	−	0.350236i	0.763037	+	0.646354i	$0.223707\pi$
$644$	−1.61586e8	+	1.02756e9i	−0.0238398	+	0.151603i
$645$	−2.59298e9	+	6.26001e9i	−0.380487	+	0.918578i
$646$	1.33672e9	+	6.80164e8i	0.195086	+	0.0992658i
$647$	4.40192e8	+	4.40192e8i	0.0638965	+	0.0638965i	0.738333	−	0.674436i	$-0.235613\pi$
$647$	4.40192e8	+	4.40192e8i	0.0638965	+	0.0638965i	−0.674436	+	0.738333i	$0.735613\pi$
$648$	4.05697e9	+	6.59581e9i	0.585719	+	0.952260i
$649$	−3.13638e9	+	3.13638e9i	−0.450372	+	0.450372i
$650$	−8.86983e8	+	2.88740e8i	−0.126683	+	0.0412392i
$651$	−5.48922e8	−	2.27371e8i	−0.0779789	−	0.0322999i
$652$	−2.09430e9	−	8.68112e9i	−0.295919	−	1.22662i
$653$	3.35888e9	+	8.10906e9i	0.472061	+	1.13966i	0.963251	+	0.268604i	$0.0865624\pi$
$653$	3.35888e9	+	8.10906e9i	0.472061	+	1.13966i	−0.491189	+	0.871053i	$0.663438\pi$
$654$	9.28683e8	−	1.18840e10i	0.129821	−	1.66127i
$655$		−	2.21812e9i		−	0.308418i
$656$	−3.52479e9	+	1.80580e9i	−0.487495	+	0.249750i
$657$			1.51311e9i			0.208157i
$658$	−3.73363e8	−	2.91767e7i	−0.0510906	−	0.00399251i
$659$	1.67647e8	+	4.04735e8i	0.0228190	+	0.0550899i	0.934878	−	0.354968i	$-0.115508\pi$
$659$	1.67647e8	+	4.04735e8i	0.0228190	+	0.0550899i	−0.912059	+	0.410058i	$0.865508\pi$
$660$	−2.47059e9	−	1.51023e9i	−0.334501	−	0.204474i
$661$	7.53540e9	+	3.12127e9i	1.01485	+	0.420364i	0.827221	−	0.561876i	$-0.189920\pi$
$661$	7.53540e9	+	3.12127e9i	1.01485	+	0.420364i	0.187627	+	0.982240i	$0.439920\pi$
$662$	2.72240e9	+	8.36297e9i	0.364712	+	1.12036i
$663$	3.64656e8	−	3.64656e8i	0.0485944	−	0.0485944i
$664$	8.38679e9	+	6.07214e9i	1.11175	+	0.804922i
$665$	3.31587e8	+	3.31587e8i	0.0437242	+	0.0437242i
$666$	4.77957e8	−	9.39326e8i	0.0626944	−	0.123213i
$667$	4.69959e8	−	1.13458e9i	0.0613224	−	0.148045i
$668$	−5.41661e9	+	3.94455e9i	−0.703089	+	0.512012i
$669$	9.44597e9	−	3.91265e9i	1.21971	−	0.505219i
$670$	−1.47914e9	+	1.26472e9i	−0.189998	+	0.162455i
$671$	4.99400e9			0.638146
$672$	−2.19871e6	−	7.95769e8i	−0.000279496	−	0.101157i
$673$	3.95399e9			0.500014			0.250007	−	0.968244i	$-0.419567\pi$
$673$	3.95399e9			0.500014			0.250007	+	0.968244i	$0.419567\pi$
$674$	−1.83865e8	+	1.57212e8i	−0.0231308	+	0.0197777i
$675$	3.35572e9	−	1.38999e9i	0.419975	−	0.173959i
$676$	4.38408e9	+	6.02016e9i	0.545839	+	0.749540i
$677$	−1.56672e9	+	3.78239e9i	−0.194057	+	0.468496i	−0.990718	−	0.135931i	$-0.956598\pi$
$677$	−1.56672e9	+	3.78239e9i	−0.194057	+	0.468496i	0.796661	+	0.604426i	$0.206598\pi$
$678$	4.05519e9	−	7.96964e9i	0.499698	−	0.982053i
$679$	7.44333e8	+	7.44333e8i	0.0912480	+	0.0912480i
$680$	1.37634e9	−	2.20330e8i	0.167859	−	0.0268715i
$681$	−5.50618e9	+	5.50618e9i	−0.668091	+	0.668091i
$682$	1.10592e9	+	3.39727e9i	0.133499	+	0.410096i
$683$	2.93603e9	+	1.21614e9i	0.352605	+	0.146054i	0.551953	−	0.833875i	$-0.313883\pi$
$683$	2.93603e9	+	1.21614e9i	0.352605	+	0.146054i	−0.199349	+	0.979929i	$0.563883\pi$
$684$	5.46406e8	−	8.93870e8i	0.0652859	−	0.106802i
$685$	2.76897e9	+	6.68490e9i	0.329156	+	0.794653i
$686$	−1.59245e9	−	1.24443e8i	−0.188335	−	0.0147176i
$687$			8.76520e9i			1.03137i
$688$	8.53055e9	+	7.25323e9i	0.998660	+	0.849125i
$689$		−	1.82888e9i		−	0.213019i
$690$	−8.24763e8	+	1.05542e10i	−0.0955779	+	1.22307i
$691$	−4.96318e9	−	1.19822e10i	−0.572252	−	1.38154i	−0.899633	−	0.436646i	$-0.856166\pi$
$691$	−4.96318e9	−	1.19822e10i	−0.572252	−	1.38154i	0.327382	−	0.944892i	$-0.393834\pi$
$692$	1.16668e9	−	2.81459e8i	0.133838	−	0.0322882i
$693$	−5.42444e7	−	2.24688e7i	−0.00619140	−	0.00256456i
$694$	−1.48379e10	+	4.83020e9i	−1.68506	+	0.548538i
$695$	−4.54152e8	+	4.54152e8i	−0.0513162	+	0.0513162i
$696$	−2.17807e8	+	9.13905e8i	−0.0244873	+	0.102747i
$697$	−8.27341e8	−	8.27341e8i	−0.0925486	−	0.0925486i
$698$	−7.29933e9	−	3.71411e9i	−0.812435	−	0.413391i
$699$	2.65120e9	−	6.40057e9i	0.293612	−	0.708841i
$700$	−4.20077e8	−	6.60578e7i	−0.0462898	−	0.00727915i
$701$	−1.51833e10	+	6.28914e9i	−1.66477	+	0.689570i	−0.998426	−	0.0560767i	$-0.982141\pi$
$701$	−1.51833e10	+	6.28914e9i	−1.66477	+	0.689570i	−0.666342	+	0.745646i	$0.732141\pi$
$702$	1.47907e9	+	1.72984e9i	0.161365	+	0.188723i
$703$	8.53724e9			0.926774
$704$	−3.62833e9	+	3.11975e9i	−0.391925	+	0.336989i
$705$	−3.81143e9			−0.409663
$706$	−2.05688e9	−	2.40560e9i	−0.219985	−	0.257281i
$707$	1.19381e9	−	4.94494e8i	0.127048	−	0.0526251i
$708$	−1.22552e10	−	1.92715e9i	−1.29779	−	0.204080i
$709$	−7.80353e8	+	1.88394e9i	−0.0822299	+	0.198520i	−0.959647	−	0.281208i	$-0.909265\pi$
$709$	−7.80353e8	+	1.88394e9i	−0.0822299	+	0.198520i	0.877417	+	0.479729i	$0.159265\pi$
$710$	−6.38940e9	−	3.25112e9i	−0.669971	−	0.340901i
$711$	−1.14993e9	−	1.14993e9i	−0.119985	−	0.119985i
$712$	9.58692e9	+	2.28481e9i	0.995403	+	0.237231i
$713$	9.23617e9	−	9.23617e9i	0.954286	−	0.954286i
$714$	2.23549e8	−	7.27721e7i	0.0229842	−	0.00748206i
$715$	−8.95767e8	−	3.71039e8i	−0.0916482	−	0.0379619i
$716$	−3.29794e9	+	7.95622e8i	−0.335775	+	0.0810049i
$717$	3.51087e9	+	8.47599e9i	0.355711	+	0.858763i
$718$	−5.45225e8	+	6.97703e9i	−0.0549718	+	0.703453i
$719$			4.21305e9i			0.422713i	0.977409	+	0.211356i	$0.0677881\pi$
$719$			4.21305e9i			0.422713i	−0.977409	+	0.211356i	$0.932212\pi$
$720$	−7.85359e7	−	9.70464e8i	−0.00784160	−	0.0968982i
$721$		−	1.17978e9i		−	0.117227i
$722$	−1.62175e9	−	1.26733e8i	−0.160362	−	0.0125316i
$723$	−7.88174e9	−	1.90282e10i	−0.775601	−	1.87247i
$724$	5.82979e9	−	9.53700e9i	0.570910	−	0.933957i
$725$	4.63828e8	+	1.92124e8i	0.0452037	+	0.0187240i
$726$	−2.49354e9	−	7.65992e9i	−0.241846	−	0.742927i
$727$	1.42053e9	−	1.42053e9i	0.137113	−	0.137113i	−0.635219	−	0.772332i	$-0.719090\pi$
$727$	1.42053e9	−	1.42053e9i	0.137113	−	0.137113i	0.772332	+	0.635219i	$0.219090\pi$
$728$	−4.21193e7	−	2.63107e8i	−0.00404595	−	0.0252739i
$729$	−6.12852e9	−	6.12852e9i	−0.585881	−	0.585881i
$730$	−5.16573e9	+	1.01522e10i	−0.491476	+	0.965895i
$731$	−1.26593e9	+	3.05622e9i	−0.119867	+	0.289384i
$732$	8.22260e9	+	1.12912e10i	0.774855	+	1.06402i
$733$	1.65280e10	−	6.84612e9i	1.55009	−	0.642067i	0.566755	−	0.823887i	$-0.308199\pi$
$733$	1.65280e10	−	6.84612e9i	1.55009	−	0.642067i	0.983332	+	0.181820i	$0.0581987\pi$
$734$	−3.45702e9	+	2.95588e9i	−0.322676	+	0.275900i
$735$	−8.09143e9			−0.751656
$736$	1.61812e10	+	6.65015e9i	1.49602	+	0.614835i
$737$	1.97379e9			0.181620
$738$	−6.21179e8	+	5.31131e8i	−0.0568878	+	0.0486412i
$739$	−6.33976e9	+	2.62601e9i	−0.577853	+	0.239355i	−0.652415	−	0.757862i	$-0.726244\pi$
$739$	−6.33976e9	+	2.62601e9i	−0.577853	+	0.239355i	0.0745621	+	0.997216i	$0.476244\pi$
$740$	6.41369e9	−	4.67066e9i	0.581831	−	0.423709i
$741$	1.11666e9	−	2.69584e9i	0.100822	−	0.243406i
$742$	3.78099e8	−	7.43077e8i	0.0339776	−	0.0667759i
$743$	3.48041e9	+	3.48041e9i	0.311293	+	0.311293i	0.845410	−	0.534117i	$-0.179356\pi$
$743$	3.48041e9	+	3.48041e9i	0.311293	+	0.311293i	−0.534117	+	0.845410i	$0.679356\pi$
$744$	−5.86017e9	+	8.09401e9i	−0.521681	+	0.720541i
$745$	4.65764e9	−	4.65764e9i	0.412685	−	0.412685i
$746$	−2.49544e9	−	7.66575e9i	−0.220070	−	0.676035i
$747$	1.97408e9	+	8.17689e8i	0.173277	+	0.0717738i
$748$	−1.20618e9	−	7.37313e8i	−0.105379	−	0.0644164i
$749$	2.36450e8	+	5.70840e8i	0.0205614	+	0.0496396i
$750$	−1.30512e10	−	1.01989e9i	−1.12963	−	0.0882756i
$751$		−	1.03319e10i		−	0.890102i	−0.895505	−	0.445051i	$-0.853185\pi$
$751$		−	1.03319e10i		−	0.890102i	0.895505	−	0.445051i	$-0.146815\pi$
$752$	−1.93312e9	+	5.99458e9i	−0.165766	+	0.514040i
$753$			2.09876e10i			1.79135i
$754$	−2.45086e7	+	3.13627e8i	−0.00208218	+	0.0266449i
$755$	2.72008e9	+	6.56685e9i	0.230021	+	0.555319i
$756$	2.43327e8	+	1.00862e9i	0.0204816	+	0.0848986i
$757$	−5.09693e6	−	2.11122e6i	−0.000427044	−	0.000176888i	0.382470	−	0.923968i	$-0.375074\pi$
$757$	−5.09693e6	−	2.11122e6i	−0.000427044	−	0.000176888i	−0.382897	+	0.923791i	$0.625074\pi$
$758$	−2.92205e9	+	9.51219e8i	−0.243695	+	0.0793301i
$759$	7.59211e9	−	7.59211e9i	0.630255	−	0.630255i
$760$	6.71777e9	−	4.13199e9i	0.555108	−	0.341438i
$761$	−4.05652e9	−	4.05652e9i	−0.333662	−	0.333662i	0.520313	−	0.853975i	$-0.325815\pi$
$761$	−4.05652e9	−	4.05652e9i	−0.333662	−	0.333662i	−0.853975	+	0.520313i	$0.825815\pi$
$762$	1.14488e9	+	5.82549e8i	0.0937384	+	0.0476969i
$763$	6.96319e8	−	1.68106e9i	0.0567508	−	0.137009i
$764$	2.91165e9	−	1.85158e10i	0.236217	−	1.50216i
$765$	2.65747e8	−	1.10076e8i	0.0214612	−	0.00888950i
$766$	6.54841e9	+	7.65863e9i	0.526424	+	0.615674i
$767$	−4.15397e9			−0.332414
$768$	−1.30276e10	−	3.06681e9i	−1.03777	−	0.244299i
$769$	5.87375e9			0.465772			0.232886	−	0.972504i	$-0.425183\pi$
$769$	5.87375e9			0.465772			0.232886	+	0.972504i	$0.425183\pi$
$770$	−2.87244e8	−	3.35944e8i	−0.0226743	−	0.0265185i
$771$	−5.44946e8	+	2.25724e8i	−0.0428216	+	0.0177373i
$772$	−3.81456e8	+	2.42576e9i	−0.0298389	+	0.189753i
$773$	4.20656e9	−	1.01555e10i	0.327566	−	0.790814i	−0.671206	−	0.741271i	$-0.734224\pi$
$773$	4.20656e9	−	1.01555e10i	0.327566	−	0.790814i	0.998772	−	0.0495429i	$-0.0157765\pi$
$774$	2.05944e9	+	1.04790e9i	0.159645	+	0.0812322i
$775$	3.77584e9	+	3.77584e9i	0.291378	+	0.291378i
$776$	1.50798e10	−	9.27532e9i	1.15845	−	0.712546i
$777$	9.46257e8	−	9.46257e8i	0.0723662	−	0.0723662i
$778$	−1.44829e10	+	4.71462e9i	−1.10262	+	0.358937i
$779$	−6.11640e9	−	2.53350e9i	−0.463569	−	0.192017i
$780$	−6.35977e8	−	2.63620e9i	−0.0479855	−	0.198905i
$781$	2.78245e9	+	6.71744e9i	0.209001	+	0.504574i
$782$	−4.02660e8	+	5.15269e9i	−0.0301103	+	0.385310i
$783$		−	1.22495e9i		−	0.0911913i
$784$	−4.10389e9	+	1.27261e10i	−0.304151	+	0.943169i
$785$		−	1.14325e10i		−	0.843525i
$786$	−6.27300e9	−	4.90208e8i	−0.460783	−	0.0360082i
$787$	−5.54108e8	−	1.33774e9i	−0.0405213	−	0.0978270i	0.902323	−	0.431060i	$-0.141860\pi$
$787$	−5.54108e8	−	1.33774e9i	−0.0405213	−	0.0978270i	−0.942844	+	0.333233i	$0.891860\pi$
$788$	1.17438e10	+	7.17879e9i	0.855004	+	0.522648i
$789$	−1.04943e10	−	4.34687e9i	−0.760646	−	0.315070i
$790$	−3.78960e9	−	1.16413e10i	−0.273463	−	0.840053i
$791$	9.65173e8	−	9.65173e8i	0.0693405	−	0.0693405i
$792$	−5.79101e8	+	7.99849e8i	−0.0414206	+	0.0572097i
$793$	3.30715e9	+	3.30715e9i	0.235504	+	0.235504i
$794$	3.31118e9	−	6.50744e9i	0.234753	−	0.461358i
$795$	3.24717e9	−	7.83936e9i	0.229203	−	0.553345i
$796$	−5.00735e9	+	3.64652e9i	−0.351895	+	0.256261i
$797$	−3.93742e9	+	1.63093e9i	−0.275491	+	0.114112i	−0.516152	−	0.856497i	$-0.672636\pi$
$797$	−3.93742e9	+	1.63093e9i	−0.275491	+	0.114112i	0.240660	+	0.970609i	$0.422636\pi$
$798$	1.01103e9	−	8.64472e8i	0.0704297	−	0.0602200i
$799$	−1.86079e9			−0.129058
$800$	−2.71865e9	+	6.61503e9i	−0.187732	+	0.456790i
$801$	2.03380e9			0.139828
$802$	3.06333e9	−	2.61926e9i	0.209693	−	0.179295i
$803$	1.06734e10	−	4.42107e9i	0.727443	−	0.301317i
$804$	3.24983e9	+	4.46263e9i	0.220529	+	0.302827i
$805$	−6.18401e8	+	1.49295e9i	−0.0417815	+	0.100870i
$806$	−1.51739e9	+	2.98212e9i	−0.102076	+	0.200610i
$807$	8.05880e8	+	8.05880e8i	0.0539775	+	0.0539775i
$808$	−3.43529e9	−	2.14593e10i	−0.229099	−	1.43112i
$809$	6.30667e9	−	6.30667e9i	0.418774	−	0.418774i	−0.466007	−	0.884781i	$-0.654308\pi$
$809$	6.30667e9	−	6.30667e9i	0.418774	−	0.418774i	0.884781	+	0.466007i	$0.154308\pi$
$810$	3.72378e9	+	1.14391e10i	0.246199	+	0.756300i
$811$	−7.64715e9	−	3.16755e9i	−0.503415	−	0.208521i	0.116499	−	0.993191i	$-0.462833\pi$
$811$	−7.64715e9	−	3.16755e9i	−0.503415	−	0.208521i	−0.619915	+	0.784669i	$0.712833\pi$
$812$	−7.47967e7	+	1.22360e8i	−0.00490271	+	0.00802038i
$813$	−3.95165e9	−	9.54013e9i	−0.257906	−	0.622641i
$814$	−8.02249e9	−	6.26923e8i	−0.521343	−	0.0407407i
$815$		−	1.38733e10i		−	0.897692i
$816$	−3.18937e8	−	3.94108e9i	−0.0205489	−	0.253922i
$817$			1.87176e10i			1.20081i
$818$	1.61016e9	−	2.06046e10i	0.102857	−	1.31622i
$819$	−2.10426e7	−	5.08013e7i	−0.00133846	−	0.00323133i
$820$	−5.98107e9	+	1.44292e9i	−0.378818	+	0.0913890i
$821$	−5.80941e9	−	2.40634e9i	−0.366379	−	0.151759i	0.191895	−	0.981415i	$-0.438537\pi$
$821$	−5.80941e9	−	2.40634e9i	−0.366379	−	0.151759i	−0.558275	+	0.829656i	$0.688537\pi$
$822$	1.95173e10	−	6.35349e9i	1.22566	−	0.398989i
$823$	1.76146e10	−	1.76146e10i	1.10147	−	1.10147i	0.107242	−	0.994233i	$-0.465798\pi$
$823$	1.76146e10	−	1.76146e10i	1.10147	−	1.10147i	0.994233	−	0.107242i	$-0.0342018\pi$
$824$	−1.93016e10	−	4.60008e9i	−1.20185	−	0.286431i
$825$	3.10373e9	+	3.10373e9i	0.192440	+	0.192440i
$826$	−1.68777e9	−	8.58785e8i	−0.104203	−	0.0530218i
$827$	−2.42173e9	+	5.84656e9i	−0.148887	+	0.359444i	−0.980674	−	0.195651i	$-0.937318\pi$
$827$	−2.42173e9	+	5.84656e9i	−0.148887	+	0.359444i	0.831787	+	0.555095i	$0.187318\pi$
$828$	3.56639e9	+	5.60820e8i	0.218334	+	0.0343335i
$829$	−2.21353e10	+	9.16874e9i	−1.34941	+	0.558945i	−0.936129	−	0.351658i	$-0.885618\pi$
$829$	−2.21353e10	+	9.16874e9i	−1.34941	+	0.558945i	−0.413283	+	0.910603i	$0.635618\pi$
$830$	1.04535e10	+	1.22257e10i	0.634581	+	0.742168i
$831$	−2.04145e10			−1.23406
$832$	−4.46874e9	−	3.36793e8i	−0.269001	−	0.0202736i
$833$	−3.95034e9			−0.236798
$834$	1.18401e9	+	1.38474e9i	0.0706762	+	0.0826586i
$835$	−9.61731e9	+	3.98362e9i	−0.571678	+	0.236797i
$836$	−7.90184e9	−	1.24258e9i	−0.467742	−	0.0735532i
$837$	4.98593e9	−	1.20371e10i	0.293905	−	0.709549i
$838$	1.45908e9	+	7.42425e8i	0.0856498	+	0.0435811i
$839$	2.07510e9	+	2.07510e9i	0.121303	+	0.121303i	0.765152	−	0.643849i	$-0.222664\pi$
$839$	2.07510e9	+	2.07510e9i	0.121303	+	0.121303i	−0.643849	+	0.765152i	$0.722664\pi$
$840$	2.86604e8	−	1.20257e9i	0.0166842	−	0.0700058i
$841$	−1.20778e10	+	1.20778e10i	−0.700166	+	0.700166i
$842$	1.23991e10	−	4.03629e9i	0.715810	−	0.233018i
$843$	3.00207e10	+	1.24350e10i	1.72593	+	0.714905i
$844$	−5.64720e9	+	1.36237e9i	−0.323321	+	0.0780006i
$845$	4.42750e9	+	1.06889e10i	0.252441	+	0.609447i
$846$	−1.01265e8	+	1.29584e9i	−0.00574992	+	0.0735794i
$847$		−	1.22965e9i		−	0.0695326i
$848$	−1.06827e10	−	9.08316e9i	−0.601585	−	0.511507i
$849$			1.44977e10i			0.813061i
$850$	−2.10647e9	−	1.64612e8i	−0.117649	−	0.00919378i
$851$	1.12584e10	+	2.71801e10i	0.626213	+	1.51181i
$852$	−1.06065e10	+	1.73512e10i	−0.587533	+	0.961149i
$853$	1.44981e10	+	6.00532e9i	0.799817	+	0.331295i	0.744883	−	0.667195i	$-0.232505\pi$
$853$	1.44981e10	+	6.00532e9i	0.799817	+	0.331295i	0.0549336	+	0.998490i	$0.482505\pi$
$854$	6.59986e8	+	2.02742e9i	0.0362604	+	0.111389i
$855$	1.15085e9	−	1.15085e9i	0.0629706	−	0.0629706i
$856$	1.02611e10	−	1.64264e9i	0.559158	−	0.0895124i
$857$	−1.33601e9	−	1.33601e9i	−0.0725065	−	0.0725065i	0.669924	−	0.742430i	$-0.266327\pi$
$857$	−1.33601e9	−	1.33601e9i	−0.0725065	−	0.0725065i	−0.742430	+	0.669924i	$0.766327\pi$
$858$	−1.24729e9	+	2.45130e9i	−0.0674160	+	0.132492i
$859$	−5.59783e9	+	1.35143e10i	−0.301331	+	0.727477i	0.698598	+	0.715515i	$0.253808\pi$
$859$	−5.59783e9	+	1.35143e10i	−0.301331	+	0.727477i	−0.999928	+	0.0119620i	$0.996192\pi$
$860$	1.02403e10	+	1.40618e10i	0.548993	+	0.753870i
$861$	−9.58743e8	+	3.97124e8i	−0.0511907	+	0.0212039i
$862$	−1.00176e10	+	8.56541e9i	−0.532706	+	0.455483i
$863$	−2.78365e10			−1.47427			−0.737135	−	0.675746i	$-0.763822\pi$
$863$	−2.78365e10			−1.47427			−0.737135	+	0.675746i	$0.763822\pi$
$864$	1.74501e10	−	4.82147e7i	0.920449	−	0.00254320i
$865$	1.86447e9			0.0979486
$866$	2.82478e10	−	2.41529e10i	1.47799	−	1.26374i
$867$	−1.78222e10	+	7.38221e9i	−0.928743	+	0.384698i
$868$	−1.23304e9	+	8.97939e8i	−0.0639967	+	0.0466045i
$869$	−4.75165e9	+	1.14715e10i	−0.245627	+	0.592995i
$870$	−6.61899e8	+	1.30083e9i	−0.0340780	+	0.0669733i
$871$	1.30709e9	+	1.30709e9i	0.0670258	+	0.0670258i
$872$	−2.47877e10	−	1.79466e10i	−1.26599	−	0.916591i
$873$	2.58338e9	−	2.58338e9i	0.131413	−	0.131413i
$874$	9.05227e9	+	2.78077e10i	0.458635	+	1.40888i
$875$	−1.84617e9	−	7.64709e8i	−0.0931630	−	0.0385894i
$876$	2.75695e10	+	1.68527e10i	1.38569	+	0.847044i
$877$	−7.38854e9	−	1.78375e10i	−0.369879	−	0.892968i	−0.993769	−	0.111456i	$-0.964449\pi$
$877$	−7.38854e9	−	1.78375e10i	−0.369879	−	0.892968i	0.623890	−	0.781512i	$-0.285551\pi$
$878$	7.99108e9	+	6.24468e8i	0.398451	+	0.0311372i
$879$			3.18648e10i			1.58252i
$880$	−6.61614e9	+	3.38953e9i	−0.327277	+	0.167668i
$881$			5.66943e9i			0.279334i	0.990199	+	0.139667i	$0.0446032\pi$
$881$			5.66943e9i			0.279334i	−0.990199	+	0.139667i	$0.955397\pi$
$882$	−2.14978e8	+	2.75099e9i	−0.0105501	+	0.135005i
$883$	1.52015e10	+	3.66997e10i	0.743061	+	1.79391i	0.592953	+	0.805237i	$0.297962\pi$
$883$	1.52015e10	+	3.66997e10i	0.743061	+	1.79391i	0.150108	+	0.988670i	$0.452038\pi$
$884$	−3.10492e8	−	1.28703e9i	−0.0151171	−	0.0626620i
$885$	−1.78057e10	−	7.37537e9i	−0.863491	−	0.357670i
$886$	3.64079e10	−	1.18519e10i	1.75864	−	0.572492i
$887$	3.56456e9	−	3.56456e9i	0.171504	−	0.171504i	−0.616136	−	0.787640i	$-0.711303\pi$
$887$	3.56456e9	−	3.56456e9i	0.171504	−	0.171504i	0.787640	+	0.616136i	$0.211303\pi$
$888$	−1.17915e10	−	1.91706e10i	−0.565100	−	0.918737i
$889$	1.38652e8	+	1.38652e8i	0.00661866	+	0.00661866i
$890$	1.36458e10	+	6.94336e9i	0.648832	+	0.330145i
$891$	4.66911e9	−	1.12722e10i	0.221138	−	0.533873i
$892$	4.07751e9	−	2.59298e10i	0.192361	−	1.22327i
$893$	−9.72735e9	+	4.02920e9i	−0.457103	+	0.189338i
$894$	−1.21428e10	−	1.42015e10i	−0.568379	−	0.664742i
$895$	−5.27043e9			−0.245734
$896$	−1.74603e9	−	1.06070e9i	−0.0810913	−	0.0492623i
$897$	1.00554e10			0.465183
$898$	−8.34861e9	−	9.76403e9i	−0.384722	−	0.449948i
$899$	1.66377e9	−	6.89154e8i	0.0763718	−	0.0316343i
$900$	−2.29269e8	+	1.45797e9i	−0.0104833	+	0.0666655i
$901$	1.58531e9	−	3.82728e9i	0.0722068	−	0.174323i
$902$	5.56156e9	+	2.82989e9i	0.252333	+	0.128394i
$903$	2.07464e9	+	2.07464e9i	0.0937637	+	0.0937637i
$904$	−1.20272e10	−	1.95539e10i	−0.541473	−	0.880324i
$905$	1.22788e10	−	1.22788e10i	0.550663	−	0.550663i
$906$	1.91727e10	−	6.24130e9i	0.856513	−	0.278821i
$907$	−9.60929e9	−	3.98030e9i	−0.427628	−	0.177129i	0.158480	−	0.987362i	$-0.449341\pi$
$907$	−9.60929e9	−	3.98030e9i	−0.427628	−	0.177129i	−0.586108	+	0.810233i	$0.699341\pi$
$908$	4.68833e9	+	1.94337e10i	0.207835	+	0.861498i
$909$	−1.71626e9	−	4.14341e9i	−0.0757895	−	0.182972i
$910$	3.22499e7	−	4.12690e8i	0.00141868	−	0.0181543i
$911$		−	2.14598e10i		−	0.940396i	−0.882561	−	0.470198i	$-0.844182\pi$
$911$		−	2.14598e10i		−	0.940396i	0.882561	−	0.470198i	$-0.155818\pi$
$912$	−1.02009e10	−	1.99115e10i	−0.445305	−	0.869206i
$913$		−	1.63142e10i		−	0.709445i
$914$	4.88126e9	+	3.81449e8i	0.211456	+	0.0165244i
$915$	8.30404e9	+	2.00477e10i	0.358357	+	0.865149i
$916$	1.91997e10	+	1.17364e10i	0.825392	+	0.504547i
$917$	−8.87354e8	−	3.67554e8i	−0.0380018	−	0.0157409i
$918$	1.59579e9	+	4.90212e9i	0.0680811	+	0.209139i
$919$	−2.45286e10	+	2.45286e10i	−1.04248	+	1.04248i	−0.0434235	+	0.999057i	$0.513826\pi$
$919$	−2.45286e10	+	2.45286e10i	−1.04248	+	1.04248i	−0.999057	+	0.0434235i	$0.986174\pi$
$920$	2.20140e10	+	1.59384e10i	0.932055	+	0.674819i
$921$	−2.50611e10	−	2.50611e10i	−1.05704	−	1.05704i
$922$	1.38212e10	−	2.71628e10i	0.580748	−	1.14134i
$923$	−2.60584e9	+	6.29106e9i	−0.109079	+	0.263340i
$924$	−1.01356e9	+	7.38104e8i	−0.0422664	+	0.0307798i
$925$	−1.11115e10	+	4.60253e9i	−0.461611	+	0.191206i
$926$	−1.30943e10	+	1.11961e10i	−0.541933	+	0.463372i
$927$	−4.09471e9			−0.168828
$928$	1.71022e9	+	1.70079e9i	0.0702480	+	0.0698608i
$929$	4.75743e10			1.94678			0.973390	−	0.229154i	$-0.0735959\pi$
$929$	4.75743e10			1.94678			0.973390	+	0.229154i	$0.0735959\pi$
$930$	−1.17990e10	+	1.00885e10i	−0.481009	+	0.411280i
$931$	−2.06505e10	+	8.55373e9i	−0.838701	+	0.347401i
$932$	−1.04702e10	−	1.43775e10i	−0.423642	−	0.581740i
$933$	1.47769e10	−	3.56745e10i	0.595658	−	1.43805i
$934$	−7.01829e9	+	1.37930e10i	−0.281849	+	0.553917i
$935$	−1.55294e9	−	1.55294e9i	−0.0621319	−	0.0621319i
$936$	−9.13174e8	+	1.46185e8i	−0.0363989	+	0.00582689i
$937$	1.38669e10	−	1.38669e10i	0.550668	−	0.550668i	−0.375966	−	0.926634i	$-0.622689\pi$
$937$	1.38669e10	−	1.38669e10i	0.550668	−	0.550668i	0.926634	+	0.375966i	$0.122689\pi$
$938$	2.60848e8	+	8.01300e8i	0.0103199	+	0.0317019i
$939$	−5.09385e9	−	2.10994e9i	−0.200778	−	0.0831650i
$940$	−5.10343e9	+	8.34873e9i	−0.200408	+	0.327848i
$941$	−8.52746e9	−	2.05871e10i	−0.333623	−	0.805438i	−0.998299	−	0.0583055i	$-0.981430\pi$
$941$	−8.52746e9	−	2.05871e10i	−0.333623	−	0.805438i	0.664676	−	0.747132i	$-0.268570\pi$
$942$	−3.23320e10	−	2.52661e9i	−1.26024	−	0.0984827i
$943$		−	2.28138e10i		−	0.885946i
$944$	−2.06308e10	+	2.42639e10i	−0.798204	+	0.938770i
$945$			1.61187e9i			0.0621325i
$946$	1.37451e9	−	1.75890e10i	0.0527871	−	0.675496i
$947$	1.30554e10	+	3.15186e10i	0.499535	+	1.20598i	0.949735	+	0.313056i	$0.101353\pi$
$947$	1.30554e10	+	3.15186e10i	0.499535	+	1.20598i	−0.450199	+	0.892928i	$0.648647\pi$
$948$	−3.37600e10	+	8.14453e9i	−1.28698	+	0.310482i
$949$	9.99593e9	+	4.14045e9i	0.379657	+	0.157259i
$950$	−1.13681e10	+	3.70066e9i	−0.430184	+	0.140038i
$951$	2.01618e10	−	2.01618e10i	0.760145	−	0.760145i
$952$	1.39924e8	−	5.87112e8i	0.00525610	−	0.0220542i
$953$	−8.85597e9	−	8.85597e9i	−0.331445	−	0.331445i	0.521690	−	0.853135i	$-0.325302\pi$
$953$	−8.85597e9	−	8.85597e9i	−0.331445	−	0.331445i	−0.853135	+	0.521690i	$0.825302\pi$
$954$	−2.57902e9	−	1.31228e9i	−0.0961691	−	0.0489337i
$955$	1.11431e10	−	2.69019e10i	0.413995	−	0.999471i
$956$	2.32672e10	+	3.65880e9i	0.861273	+	0.135437i
$957$	1.36761e9	−	5.66483e8i	0.0504395	−	0.0208927i
$958$	−1.61623e10	−	1.89025e10i	−0.593915	−	0.694608i
$959$	3.13312e9			0.114713
$960$	−1.85570e10	−	9.37789e9i	−0.676953	−	0.342102i
$961$	−8.35843e9			−0.303804
$962$	−4.89752e9	−	5.72785e9i	−0.177363	−	0.207433i
$963$	1.98123e9	−	8.20654e8i	0.0714898	−	0.0296120i
$964$	−5.22337e10	−	8.21385e9i	−1.87794	−	0.295309i
$965$	−1.45986e9	+	3.52442e9i	−0.0522957	+	0.126253i
$966$	4.08551e9	+	2.07883e9i	0.145823	+	0.0741992i
$967$	1.38025e10	+	1.38025e10i	0.490869	+	0.490869i	0.908580	−	0.417711i	$-0.137168\pi$
$967$	1.38025e10	+	1.38025e10i	0.490869	+	0.490869i	−0.417711	+	0.908580i	$0.637168\pi$
$968$	−2.01174e10	−	4.79451e9i	−0.712868	−	0.169895i
$969$	4.67364e9	−	4.67364e9i	0.165014	−	0.165014i
$970$	2.61528e10	−	8.51354e9i	0.920062	−	0.299509i
$971$	−1.38973e10	−	5.75646e9i	−0.487151	−	0.201785i	0.125568	−	0.992085i	$-0.459925\pi$
$971$	−1.38973e10	−	5.75646e9i	−0.487151	−	0.201785i	−0.612720	+	0.790300i	$0.709925\pi$
$972$	7.55536e9	−	1.82271e9i	0.263890	−	0.0636629i
$973$	1.06427e8	+	2.56938e8i	0.00370389	+	0.00894198i
$974$	−3.79772e9	+	4.85979e10i	−0.131694	+	1.68524i
$975$			4.11073e9i			0.142037i
$976$	3.57426e10	−	2.89251e9i	1.23058	−	0.0995865i
$977$		−	4.15130e10i		−	1.42414i	−0.702107	−	0.712071i	$-0.747757\pi$
$977$		−	4.15130e10i		−	1.42414i	0.702107	−	0.712071i	$-0.252243\pi$
$978$	−3.92347e10	−	3.06602e9i	−1.34117	−	0.104807i
$979$	−5.94245e9	−	1.43463e10i	−0.202407	−	0.488654i
$980$	−1.08342e10	+	1.77238e10i	−0.367712	+	0.601542i
$981$	−5.83452e9	−	2.41674e9i	−0.197317	−	0.0817312i
$982$	−9.31043e9	−	2.86008e10i	−0.313747	−	0.963801i
$983$	2.39634e10	−	2.39634e10i	0.804658	−	0.804658i	−0.179162	−	0.983820i	$-0.557339\pi$
$983$	2.39634e10	−	2.39634e10i	0.804658	−	0.804658i	0.983820	+	0.179162i	$0.0573386\pi$
$984$	2.75886e9	+	1.72338e10i	0.0923096	+	0.576631i
$985$	1.51201e10	+	1.51201e10i	0.504113	+	0.504113i
$986$	−3.23148e8	+	6.35081e8i	−0.0107357	+	0.0210989i
$987$	−6.31575e8	+	1.52476e9i	−0.0209081	+	0.0504767i
$988$	−4.40992e9	−	6.05565e9i	−0.145473	−	0.199761i
$989$	−5.95914e10	+	2.46836e10i	−1.95883	+	0.811374i
$990$	−1.16597e9	+	9.96948e8i	−0.0381913	+	0.0326550i
$991$	3.91133e10			1.27664			0.638318	−	0.769773i	$-0.279631\pi$
$991$	3.91133e10			1.27664			0.638318	+	0.769773i	$0.279631\pi$
$992$	9.88285e9	+	2.36741e10i	0.321434	+	0.769985i
$993$	3.87583e10			1.25615
$994$	−2.35936e9	+	2.01734e9i	−0.0761978	+	0.0651519i
$995$	−8.89067e9	+	3.68263e9i	−0.286124	+	0.118516i
$996$	3.68856e10	−	2.68613e10i	1.18290	−	0.861428i
$997$	8.93788e9	−	2.15780e10i	0.285629	−	0.689568i	−0.714319	−	0.699820i	$-0.753263\pi$
$997$	8.93788e9	−	2.15780e10i	0.285629	−	0.689568i	0.999947	+	0.0102520i	$0.00326337\pi$
$998$	−2.23294e10	+	4.38838e10i	−0.711082	+	1.39748i
$999$	2.07501e10	+	2.07501e10i	0.658477	+	0.658477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.21.7	✓	108
32.29	even	8	inner	32.8.g.a.29.7	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.21.7	✓	108	1.1	even	1	trivial
32.8.g.a.29.7	yes	108	32.29	even	8	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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.35242 - 8.59895i) q^{2} +(-46.0630 + 19.0799i) q^{3} +(-19.8839 + 126.446i) q^{4} +(-76.0972 + 183.715i) q^{5} +(502.742 + 255.810i) q^{6} +(60.8852 + 60.8852i) q^{7} +(1233.50 - 758.705i) q^{8} +(211.316 - 211.316i) q^{9} +O(q^{10})\)	\(q+(-7.35242 - 8.59895i) q^{2} +(-46.0630 + 19.0799i) q^{3} +(-19.8839 + 126.446i) q^{4} +(-76.0972 + 183.715i) q^{5} +(502.742 + 255.810i) q^{6} +(60.8852 + 60.8852i) q^{7} +(1233.50 - 758.705i) q^{8} +(211.316 - 211.316i) q^{9} +(2139.25 - 696.393i) q^{10} +(-2108.05 - 873.183i) q^{11} +(-1496.67 - 6203.88i) q^{12} +(-817.758 - 1974.24i) q^{13} +(75.8952 - 971.202i) q^{14} -9914.40i q^{15} +(-15593.3 - 5028.48i) q^{16} -4840.34i q^{17} +(-3370.78 - 263.412i) q^{18} +(-10480.9 - 25303.0i) q^{19} +(-21716.9 - 13275.2i) q^{20} +(-3966.24 - 1642.87i) q^{21} +(7990.81 + 24547.0i) q^{22} +(66736.0 - 66736.0i) q^{23} +(-42342.7 + 58483.3i) q^{24} +(27282.3 + 27282.3i) q^{25} +(-10963.9 + 21547.3i) q^{26} +(36025.8 - 86974.1i) q^{27} +(-8909.33 + 6488.06i) q^{28} +(12021.5 - 4979.49i) q^{29} +(-85253.4 + 72894.8i) q^{30} +138399. q^{31} +(71408.6 + 171057. i) q^{32} +113763. q^{33} +(-41621.8 + 35588.2i) q^{34} +(-15818.7 + 6552.32i) q^{35} +(22518.3 + 30921.9i) q^{36} +(-119289. + 287989. i) q^{37} +(-140520. + 276163. i) q^{38} +(75336.9 + 75336.9i) q^{39} +(45519.6 + 284347. i) q^{40} +(170926. - 170926. i) q^{41} +(15034.5 + 46184.6i) q^{42} +(-631406. - 261537. i) q^{43} +(152327. - 249192. i) q^{44} +(22741.4 + 54902.5i) q^{45} +(-1.06453e6 - 83188.5i) q^{46} -384434. i q^{47} +(814216. - 65891.4i) q^{48} -816129. i q^{49} +(34008.3 - 435190. i) q^{50} +(92353.4 + 222961. i) q^{51} +(265896. - 64146.8i) q^{52} +(790705. + 327521. i) q^{53} +(-1.01276e6 + 329685. i) q^{54} +(320833. - 320833. i) q^{55} +(121296. + 28907.9i) q^{56} +(965560. + 965560. i) q^{57} +(-131206. - 66761.4i) q^{58} +(743905. - 1.79595e6i) q^{59} +(1.25364e6 + 197137. i) q^{60} +(-2.02208e6 + 837574. i) q^{61} +(-1.01756e6 - 1.19008e6i) q^{62} +25732.0 q^{63} +(945886. - 1.87172e6i) q^{64} +424927. q^{65} +(-836436. - 978246. i) q^{66} +(-799191. + 331036. i) q^{67} +(612042. + 96244.7i) q^{68} +(-1.80074e6 + 4.34738e6i) q^{69} +(172649. + 87848.8i) q^{70} +(-2.25324e6 - 2.25324e6i) q^{71} +(100332. - 420985. i) q^{72} +(-3.58020e6 + 3.58020e6i) q^{73} +(3.35347e6 - 1.09166e6i) q^{74} +(-1.77725e6 - 736162. i) q^{75} +(3.40787e6 - 822142. i) q^{76} +(-75185.0 - 181513. i) q^{77} +(93909.7 - 1.20173e6i) q^{78} -5.44176e6i q^{79} +(2.11041e6 - 2.48206e6i) q^{80} +5.34724e6i q^{81} +(-2.72651e6 - 213065. i) q^{82} +(2.73615e6 + 6.60566e6i) q^{83} +(286599. - 468849. i) q^{84} +(889243. + 368336. i) q^{85} +(2.39342e6 + 7.35236e6i) q^{86} +(-458741. + 458741. i) q^{87} +(-3.26276e6 + 522317. i) q^{88} +(4.81222e6 + 4.81222e6i) q^{89} +(304900. - 599218. i) q^{90} +(70412.8 - 169991. i) q^{91} +(7.11154e6 + 9.76548e6i) q^{92} +(-6.37506e6 + 2.64064e6i) q^{93} +(-3.30573e6 + 2.82652e6i) q^{94} +5.44611e6 q^{95} +(-6.55305e6 - 6.51694e6i) q^{96} +1.22252e7 q^{97} +(-7.01785e6 + 6.00052e6i) q^{98} +(-629983. + 260947. 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

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