LMFDB - Embedded newform 27.7.f.a.2.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.87880 - 0.683936i) q^{2} +(-3.37914 + 26.7877i) q^{3} +(-45.5630 - 16.5836i) q^{4} +(-43.1394 - 51.4115i) q^{5} +(31.4281 - 101.593i) q^{6} +(424.254 - 154.416i) q^{7} +(383.689 + 221.523i) q^{8} +(-706.163 - 181.039i) q^{9} +O(q^{10})$	\(q+(-3.87880 - 0.683936i) q^{2} +(-3.37914 + 26.7877i) q^{3} +(-45.5630 - 16.5836i) q^{4} +(-43.1394 - 51.4115i) q^{5} +(31.4281 - 101.593i) q^{6} +(424.254 - 154.416i) q^{7} +(383.689 + 221.523i) q^{8} +(-706.163 - 181.039i) q^{9} +(132.167 + 228.919i) q^{10} +(1154.19 - 1375.51i) q^{11} +(598.200 - 1164.49i) q^{12} +(-488.827 - 2772.27i) q^{13} +(-1751.20 + 308.785i) q^{14} +(1522.97 - 981.879i) q^{15} +(1040.43 + 873.024i) q^{16} +(-5946.51 + 3433.22i) q^{17} +(2615.24 + 1185.18i) q^{18} +(4951.44 - 8576.15i) q^{19} +(1112.97 + 3057.87i) q^{20} +(2702.83 + 11886.6i) q^{21} +(-5417.64 + 4545.94i) q^{22} +(-4137.47 + 11367.6i) q^{23} +(-7230.63 + 9529.59i) q^{24} +(1931.12 - 10951.9i) q^{25} +11087.4i q^{26} +(7235.83 - 18304.7i) q^{27} -21891.1 q^{28} +(-9212.78 - 1624.46i) q^{29} +(-6578.84 + 2766.89i) q^{30} +(17964.5 + 6538.56i) q^{31} +(-21664.7 - 25819.0i) q^{32} +(32946.7 + 35566.2i) q^{33} +(25413.4 - 9249.72i) q^{34} +(-26240.8 - 15150.1i) q^{35} +(29172.7 + 19959.4i) q^{36} +(-26288.7 - 45533.4i) q^{37} +(-25071.2 + 29878.7i) q^{38} +(75914.7 - 3726.66i) q^{39} +(-5163.27 - 29282.4i) q^{40} +(72041.3 - 12702.8i) q^{41} +(-2354.07 - 47954.2i) q^{42} +(-31061.0 - 26063.2i) q^{43} +(-75399.5 + 43531.9i) q^{44} +(21156.0 + 44114.8i) q^{45} +(23823.1 - 41262.8i) q^{46} +(-29328.7 - 80579.8i) q^{47} +(-26902.1 + 24920.7i) q^{48} +(66022.7 - 55399.6i) q^{49} +(-14980.8 + 41159.4i) q^{50} +(-71874.0 - 170895. i) q^{51} +(-23701.8 + 134420. i) q^{52} +44983.7i q^{53} +(-40585.6 + 66051.5i) q^{54} -120508. q^{55} +(196988. + 34734.3i) q^{56} +(213004. + 161618. i) q^{57} +(34623.5 + 12601.9i) q^{58} +(-17011.3 - 20273.3i) q^{59} +(-85674.3 + 19481.1i) q^{60} +(110077. - 40064.7i) q^{61} +(-65208.9 - 37648.4i) q^{62} +(-327547. + 32236.3i) q^{63} +(22912.6 + 39685.7i) q^{64} +(-121439. + 144726. i) q^{65} +(-103468. - 160488. i) q^{66} +(77205.6 + 437855. i) q^{67} +(327876. - 57813.4i) q^{68} +(-290531. - 149246. i) q^{69} +(91421.0 + 76711.3i) q^{70} +(-31019.4 + 17909.1i) q^{71} +(-230843. - 225894. i) q^{72} +(-132848. + 230100. i) q^{73} +(70826.7 + 194595. i) q^{74} +(286851. + 88738.1i) q^{75} +(-367826. + 308643. i) q^{76} +(277270. - 761792. i) q^{77} +(-297006. - 37465.9i) q^{78} +(68546.7 - 388748. i) q^{79} -91151.8i q^{80} +(465891. + 255686. i) q^{81} -288121. q^{82} +(769521. + 135687. i) q^{83} +(73972.9 - 586411. i) q^{84} +(433036. + 157612. i) q^{85} +(102654. + 122338. i) q^{86} +(74646.8 - 241300. i) q^{87} +(747558. - 272089. i) q^{88} +(-746055. - 430735. i) q^{89} +(-51888.0 - 185582. i) q^{90} +(-635469. - 1.10067e6i) q^{91} +(377031. - 449328. i) q^{92} +(-235858. + 459134. i) q^{93} +(58648.4 + 332612. i) q^{94} +(-654515. + 115409. i) q^{95} +(764840. - 493102. i) q^{96} +(417556. + 350371. i) q^{97} +(-293978. + 169728. i) q^{98} +(-1.06407e6 + 762383. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	−3.87880	−	0.683936i	−0.484850	−	0.0854921i	−0.0741201	−	0.997249i	$-0.523615\pi$
$2$	−3.87880	−	0.683936i	−0.484850	−	0.0854921i	−0.410729	+	0.911757i	$0.634726\pi$
$3$	−3.37914	+	26.7877i	−0.125153	+	0.992137i
$3$	−3.37914	+	26.7877i	−0.125153	+	0.992137i
$4$	−45.5630	−	16.5836i	−0.711922	−	0.259119i
$5$	−43.1394	−	51.4115i	−0.345115	−	0.411292i	0.565368	−	0.824839i	$-0.308734\pi$
$5$	−43.1394	−	51.4115i	−0.345115	−	0.411292i	−0.910483	+	0.413547i	$0.864290\pi$
$6$	31.4281	−	101.593i	0.145500	−	0.470338i
$7$	424.254	−	154.416i	1.23689	−	0.450192i	0.360939	−	0.932589i	$-0.382456\pi$
$7$	424.254	−	154.416i	1.23689	−	0.450192i	0.875952	+	0.482398i	$0.160234\pi$
$8$	383.689	+	221.523i	0.749392	+	0.432662i
$9$	−706.163	−	181.039i	−0.968673	−	0.248338i
$10$	132.167	+	228.919i	0.132167	+	0.228919i
$11$	1154.19	−	1375.51i	0.867162	−	1.03344i	−0.131948	−	0.991257i	$-0.542123\pi$
$11$	1154.19	−	1375.51i	0.867162	−	1.03344i	0.999110	−	0.0421867i	$-0.0134324\pi$
$12$	598.200	−	1164.49i	0.346181	−	0.673895i
$13$	−488.827	−	2772.27i	−0.222497	−	1.26185i	−0.867412	−	0.497591i	$-0.834218\pi$
$13$	−488.827	−	2772.27i	−0.222497	−	1.26185i	0.644915	−	0.764255i	$-0.276893\pi$
$14$	−1751.20	+	308.785i	−0.638194	+	0.112531i
$15$	1522.97	−	981.879i	0.451251	−	0.290927i
$16$	1040.43	+	873.024i	0.254011	+	0.213141i
$17$	−5946.51	+	3433.22i	−1.21036	+	0.698803i	−0.962838	−	0.270079i	$-0.912950\pi$
$17$	−5946.51	+	3433.22i	−1.21036	+	0.698803i	−0.247524	+	0.968882i	$0.579617\pi$
$18$	2615.24	+	1185.18i	0.448430	+	0.203221i
$19$	4951.44	−	8576.15i	0.721890	−	1.25035i	−0.238352	−	0.971179i	$-0.576607\pi$
$19$	4951.44	−	8576.15i	0.721890	−	1.25035i	0.960241	−	0.279171i	$-0.0900596\pi$
$20$	1112.97	+	3057.87i	0.139122	+	0.382234i
$21$	2702.83	+	11886.6i	0.291851	+	1.28351i
$22$	−5417.64	+	4545.94i	−0.508794	+	0.426929i
$23$	−4137.47	+	11367.6i	−0.340057	+	0.934298i	0.645321	+	0.763912i	$0.276724\pi$
$23$	−4137.47	+	11367.6i	−0.340057	+	0.934298i	−0.985377	+	0.170386i	$0.945499\pi$
$24$	−7230.63	+	9529.59i	−0.523049	+	0.689351i
$25$	1931.12	−	10951.9i	0.123591	−	0.700921i
$26$			11087.4i			0.630827i
$27$	7235.83	−	18304.7i	0.367618	−	0.929977i
$28$	−21891.1			−0.997224
$29$	−9212.78	−	1624.46i	−0.377743	−	0.0666063i	−0.0184468	−	0.999830i	$-0.505872\pi$
$29$	−9212.78	−	1624.46i	−0.377743	−	0.0666063i	−0.359296	+	0.933224i	$0.616983\pi$
$30$	−6578.84	+	2766.89i	−0.243661	+	0.102478i
$31$	17964.5	+	6538.56i	0.603019	+	0.219481i	0.625446	−	0.780267i	$-0.284917\pi$
$31$	17964.5	+	6538.56i	0.603019	+	0.219481i	−0.0224267	+	0.999748i	$0.507139\pi$
$32$	−21664.7	−	25819.0i	−0.661155	−	0.787933i
$33$	32946.7	+	35566.2i	0.916790	+	0.989683i
$34$	25413.4	−	9249.72i	0.646585	−	0.235338i
$35$	−26240.8	−	15150.1i	−0.612030	−	0.353356i
$36$	29172.7	+	19959.4i	0.625271	+	0.427799i
$37$	−26288.7	−	45533.4i	−0.518997	−	0.898929i	−0.999756	−	0.0220763i	$-0.992972\pi$
$37$	−26288.7	−	45533.4i	−0.518997	−	0.898929i	0.480759	−	0.876853i	$-0.340361\pi$
$38$	−25071.2	+	29878.7i	−0.456903	+	0.544516i
$39$	75914.7	−	3726.66i	1.27977	−	0.0628240i
$40$	−5163.27	−	29282.4i	−0.0806762	−	0.457537i
$41$	72041.3	−	12702.8i	1.04527	−	0.184310i	0.375459	−	0.926839i	$-0.377485\pi$
$41$	72041.3	−	12702.8i	1.04527	−	0.184310i	0.669814	+	0.742529i	$0.266374\pi$
$42$	−2354.07	−	47954.2i	−0.0317740	−	0.647260i
$43$	−31061.0	−	26063.2i	−0.390670	−	0.327811i	0.426204	−	0.904627i	$-0.359850\pi$
$43$	−31061.0	−	26063.2i	−0.390670	−	0.327811i	−0.816874	+	0.576816i	$0.804295\pi$
$44$	−75399.5	+	43531.9i	−0.885136	+	0.511034i
$45$	21156.0	+	44114.8i	0.232164	+	0.484113i
$46$	23823.1	−	41262.8i	0.244751	−	0.423922i
$47$	−29328.7	−	80579.8i	−0.282487	−	0.776127i	−0.997064	−	0.0765703i	$-0.975603\pi$
$47$	−29328.7	−	80579.8i	−0.282487	−	0.776127i	0.714577	−	0.699557i	$-0.246619\pi$
$48$	−26902.1	+	24920.7i	−0.243255	+	0.225339i
$49$	66022.7	−	55399.6i	0.561184	−	0.470889i
$50$	−14980.8	+	41159.4i	−0.119846	+	0.329275i
$51$	−71874.0	−	170895.i	−0.541828	−	1.28830i
$52$	−23701.8	+	134420.i	−0.168567	+	0.955989i
$53$			44983.7i			0.302153i	0.988522	+	0.151077i	$0.0482740\pi$
$53$			44983.7i			0.302153i	−0.988522	+	0.151077i	$0.951726\pi$
$54$	−40585.6	+	66051.5i	−0.257745	+	0.419470i
$55$	−120508.			−0.724318
$56$	196988.	+	34734.3i	1.12170	+	0.197786i
$57$	213004.	+	161618.i	1.15017	+	0.872699i
$58$	34623.5	+	12601.9i	0.177454	+	0.0645881i
$59$	−17011.3	−	20273.3i	−0.0828287	−	0.0987115i	0.723038	−	0.690808i	$-0.242745\pi$
$59$	−17011.3	−	20273.3i	−0.0828287	−	0.0987115i	−0.805867	+	0.592096i	$0.798300\pi$
$60$	−85674.3	+	19481.1i	−0.396640	+	0.0901901i
$61$	110077.	−	40064.7i	0.484961	−	0.176511i	−0.0879569	−	0.996124i	$-0.528034\pi$
$61$	110077.	−	40064.7i	0.484961	−	0.176511i	0.572917	+	0.819613i	$0.305812\pi$
$62$	−65208.9	−	37648.4i	−0.273610	−	0.157969i
$63$	−327547.	+	32236.3i	−1.30994	+	0.128921i
$64$	22912.6	+	39685.7i	0.0874045	+	0.151389i
$65$	−121439.	+	144726.i	−0.442200	+	0.526993i
$66$	−103468.	−	160488.i	−0.359895	−	0.558225i
$67$	77205.6	+	437855.i	0.256699	+	1.45581i	0.791674	+	0.610944i	$0.209210\pi$
$67$	77205.6	+	437855.i	0.256699	+	1.45581i	−0.534974	+	0.844868i	$0.679679\pi$
$68$	327876.	−	57813.4i	1.04276	−	0.183866i
$69$	−290531.	−	149246.i	−0.884393	−	0.454313i
$70$	91421.0	+	76711.3i	0.266533	+	0.223648i
$71$	−31019.4	+	17909.1i	−0.0866679	+	0.0500377i	−0.542708	−	0.839922i	$-0.682601\pi$
$71$	−31019.4	+	17909.1i	−0.0866679	+	0.0500377i	0.456040	+	0.889959i	$0.349267\pi$
$72$	−230843.	−	225894.i	−0.618470	−	0.605211i
$73$	−132848.	+	230100.i	−0.341497	+	0.591491i	−0.984711	−	0.174196i	$-0.944267\pi$
$73$	−132848.	+	230100.i	−0.341497	+	0.591491i	0.643214	+	0.765687i	$0.277601\pi$
$74$	70826.7	+	194595.i	0.174784	+	0.480215i
$75$	286851.	+	88738.1i	0.679943	+	0.210342i
$76$	−367826.	+	308643.i	−0.837918	+	0.703097i
$77$	277270.	−	761792.i	0.607338	−	1.66865i
$78$	−297006.	−	37465.9i	−0.625867	−	0.0789500i
$79$	68546.7	−	388748.i	0.139029	−	0.788473i	−0.832940	−	0.553363i	$-0.813344\pi$
$79$	68546.7	−	388748.i	0.139029	−	0.788473i	0.971969	−	0.235109i	$-0.0755448\pi$
$80$		−	91151.8i		−	0.178031i
$81$	465891.	+	255686.i	0.876656	+	0.481117i
$82$	−288121.			−0.522557
$83$	769521.	+	135687.i	1.34582	+	0.237304i	0.799698	−	0.600403i	$-0.204993\pi$
$83$	769521.	+	135687.i	1.34582	+	0.237304i	0.546120	+	0.837707i	$0.316104\pi$
$84$	73972.9	−	586411.i	0.124806	−	0.989383i
$85$	433036.	+	157612.i	0.705126	+	0.256645i
$86$	102654.	+	122338.i	0.161391	+	0.192338i
$87$	74646.8	−	241300.i	0.113358	−	0.366437i
$88$	747558.	−	272089.i	1.09698	−	0.399267i
$89$	−746055.	−	430735.i	−1.05828	−	0.610999i	−0.133325	−	0.991072i	$-0.542565\pi$
$89$	−746055.	−	430735.i	−1.05828	−	0.610999i	−0.924956	+	0.380074i	$0.875899\pi$
$90$	−51888.0	−	185582.i	−0.0711769	−	0.254570i
$91$	−635469.	−	1.10067e6i	−0.843277	−	1.46060i
$92$	377031.	−	449328.i	0.484188	−	0.577033i
$93$	−235858.	+	459134.i	−0.293225	+	0.570809i
$94$	58648.4	+	332612.i	0.0706111	+	0.400455i
$95$	−654515.	+	115409.i	−0.763394	+	0.134607i
$96$	764840.	−	493102.i	0.864484	−	0.557344i
$97$	417556.	+	350371.i	0.457509	+	0.383896i	0.842213	−	0.539144i	$-0.181252\pi$
$97$	417556.	+	350371.i	0.457509	+	0.383896i	−0.384705	+	0.923040i	$0.625697\pi$
$98$	−293978.	+	169728.i	−0.312347	+	0.180334i
$99$	−1.06407e6	+	762383.i	−1.09664	+	0.785720i
$100$	−269609.	+	466977.i	−0.269609	+	0.466977i
$101$	222386.	+	611000.i	0.215846	+	0.593031i	0.999607	−	0.0280312i	$-0.00892377\pi$
$101$	222386.	+	611000.i	0.215846	+	0.593031i	−0.783762	+	0.621062i	$0.786702\pi$
$102$	161904.	+	712023.i	0.152565	+	0.670955i
$103$	−1.51776e6	+	1.27355e6i	−1.38896	+	1.16548i	−0.423207	+	0.906033i	$0.639096\pi$
$103$	−1.51776e6	+	1.27355e6i	−1.38896	+	1.16548i	−0.965757	+	0.259447i	$0.916460\pi$
$104$	426565.	−	1.17198e6i	0.379214	−	1.04188i
$105$	494509.	−	651737.i	0.427175	−	0.562995i
$106$	30766.0	−	174483.i	0.0258317	−	0.146499i
$107$			1.35872e6i			1.10912i	0.832143	+	0.554561i	$0.187114\pi$
$107$			1.35872e6i			1.10912i	−0.832143	+	0.554561i	$0.812886\pi$
$108$	−633245.	+	714023.i	−0.502690	+	0.566815i
$109$	55580.7			0.0429185			0.0214592	−	0.999770i	$-0.493169\pi$
$109$	55580.7			0.0429185			0.0214592	+	0.999770i	$0.493169\pi$
$110$	467427.	+	82420.1i	0.351185	+	0.0619234i
$111$	1.30857e6	−	550352.i	0.956815	−	0.402412i
$112$	576215.	+	209725.i	0.410138	+	0.149278i
$113$	−1.07412e6	−	1.28009e6i	−0.744419	−	0.887164i	0.252338	−	0.967639i	$-0.418801\pi$
$113$	−1.07412e6	−	1.28009e6i	−0.744419	−	0.887164i	−0.996757	+	0.0804756i	$0.974356\pi$
$114$	−715662.	−	772564.i	−0.483052	−	0.521458i
$115$	762913.	−	277678.i	0.501628	−	0.182578i
$116$	392823.	+	226796.i	0.251665	+	0.145299i
$117$	−156697.	+	2.04617e6i	−0.0978372	+	1.27757i
$118$	52117.7	+	90270.5i	0.0317204	+	0.0549414i
$119$	−1.99269e6	+	2.37479e6i	−1.18249	+	1.40924i
$120$	801856.	−	39363.2i	0.464037	−	0.0227796i
$121$	−252248.	−	1.43057e6i	−0.142387	−	0.807518i
$122$	−454367.	+	80117.2i	−0.250223	+	0.0441211i
$123$	96842.2	+	1.97274e6i	0.0520414	+	1.06012i
$124$	−710087.	−	595833.i	−0.372431	−	0.312507i
$125$	−1.55451e6	+	897497.i	−0.795909	+	0.459518i
$126$	1.29254e6	+	98983.4i	0.646147	+	0.0494824i
$127$	1.64400e6	−	2.84749e6i	0.802584	−	1.39012i	−0.115327	−	0.993328i	$-0.536791\pi$
$127$	1.64400e6	−	2.84749e6i	0.802584	−	1.39012i	0.917910	−	0.396788i	$-0.129875\pi$
$128$	676033.	+	1.85738e6i	0.322358	+	0.885670i
$129$	803134.	−	743981.i	0.374127	−	0.346571i
$130$	570021.	−	478304.i	0.259454	−	0.217708i
$131$	−210837.	+	579269.i	−0.0937847	+	0.257671i	−0.977711	−	0.209955i	$-0.932668\pi$
$131$	−210837.	+	579269.i	−0.0937847	+	0.257671i	0.883926	+	0.467626i	$0.154891\pi$
$132$	−911335.	−	2.16688e6i	−0.396238	−	0.942134i
$133$	776376.	−	4.40305e6i	0.330002	−	1.87154i
$134$		−	1.75115e6i		−	0.727796i
$135$	−1.25322e6	+	417650.i	−0.509363	+	0.169751i
$136$	−3.04214e6			−1.20938
$137$	147487.	+	26005.9i	0.0573576	+	0.0101137i	0.202253	−	0.979333i	$-0.435174\pi$
$137$	147487.	+	26005.9i	0.0573576	+	0.0101137i	−0.144896	+	0.989447i	$0.546285\pi$
$138$	1.02484e6	+	777599.i	0.389957	+	0.295882i
$139$	1.26552e6	+	460612.i	0.471222	+	0.171511i	0.566706	−	0.823920i	$-0.308218\pi$
$139$	1.26552e6	+	460612.i	0.471222	+	0.171511i	−0.0954839	+	0.995431i	$0.530440\pi$
$140$	944367.	+	1.12545e6i	0.344157	+	0.410150i
$141$	2.25765e6	−	513358.i	0.805379	−	0.183131i
$142$	132567.	−	48250.3i	0.0462987	−	0.0168514i
$143$	−4.37750e6	−	2.52735e6i	−1.49699	−	0.864286i
$144$	−576662.	−	804855.i	−0.193123	−	0.269544i
$145$	313918.	+	543721.i	0.102970	+	0.178350i
$146$	672665.	−	801651.i	0.216143	−	0.257589i
$147$	1.26093e6	+	1.95580e6i	0.396953	+	0.615704i
$148$	442687.	+	2.51060e6i	0.136556	+	0.774449i
$149$	3.06311e6	−	540110.i	0.925986	−	0.163276i	0.309732	−	0.950824i	$-0.399761\pi$
$149$	3.06311e6	−	540110.i	0.925986	−	0.163276i	0.616254	+	0.787548i	$0.288650\pi$
$150$	−1.05194e6	−	540385.i	−0.311687	−	0.160114i
$151$	910877.	+	764317.i	0.264563	+	0.221995i	0.765413	−	0.643539i	$-0.222535\pi$
$151$	910877.	+	764317.i	0.264563	+	0.221995i	−0.500850	+	0.865534i	$0.666979\pi$
$152$	3.79963e6	−	2.19372e6i	1.08196	−	0.624668i
$153$	4.82075e6	−	1.34786e6i	1.34598	−	0.376332i
$154$	−1.59649e6	+	2.76520e6i	−0.437123	+	0.757120i
$155$	−438822.	−	1.20565e6i	−0.117840	−	0.323763i
$156$	−3.52070e6	−	1.08914e6i	−0.927376	−	0.286886i
$157$	323333.	−	271309.i	0.0835509	−	0.0701075i	−0.600056	−	0.799958i	$-0.704855\pi$
$157$	323333.	−	271309.i	0.0835509	−	0.0701075i	0.683607	+	0.729851i	$0.260410\pi$
$158$	−531757.	+	1.46099e6i	−0.134816	+	0.370405i
$159$	−1.20501e6	−	152006.i	−0.299778	−	0.0378155i
$160$	−392792.	+	2.22763e6i	−0.0958964	+	0.543855i
$161$			5.46164e6i			1.30872i
$162$	−1.63222e6	−	1.31039e6i	−0.383915	−	0.308217i
$163$	2.12411e6			0.490472			0.245236	−	0.969463i	$-0.421135\pi$
$163$	2.12411e6			0.490472			0.245236	+	0.969463i	$0.421135\pi$
$164$	−3.49308e6	−	615924.i	−0.791911	−	0.139635i
$165$	407214.	−	3.22814e6i	0.0906507	−	0.718623i
$166$	−2.89201e6	−	1.05261e6i	−0.632231	−	0.230113i
$167$	−1.60815e6	−	1.91651e6i	−0.345284	−	0.411493i	0.565256	−	0.824916i	$-0.308778\pi$
$167$	−1.60815e6	−	1.91651e6i	−0.345284	−	0.411493i	−0.910539	+	0.413423i	$0.864333\pi$
$168$	−1.59610e6	+	5.15949e6i	−0.336614	+	1.08812i
$169$	−2.91083e6	+	1.05946e6i	−0.603055	+	0.219494i
$170$	−1.57186e6	−	907514.i	−0.319939	−	0.184717i
$171$	−5.04914e6	+	5.15976e6i	−1.00979	+	1.03191i
$172$	983010.	+	1.70262e6i	0.193185	+	0.334606i
$173$	5.96450e6	−	7.10821e6i	1.15196	−	1.37285i	0.235909	−	0.971775i	$-0.424193\pi$
$173$	5.96450e6	−	7.10821e6i	1.15196	−	1.37285i	0.916047	−	0.401072i	$-0.131362\pi$
$174$	−454574.	+	884900.i	−0.0862892	+	0.167976i
$175$	−871863.	−	4.94458e6i	−0.162680	−	0.922604i
$176$	2.40171e6	−	423487.i	0.440538	−	0.0776787i
$177$	600558.	−	387187.i	0.108302	−	0.0698234i
$178$	2.59920e6	+	2.18099e6i	0.460872	+	0.386717i
$179$	3.60143e6	−	2.07929e6i	0.627936	−	0.362539i	−0.152016	−	0.988378i	$-0.548577\pi$
$179$	3.60143e6	−	2.07929e6i	0.627936	−	0.362539i	0.779952	+	0.625839i	$0.215243\pi$
$180$	−232348.	−	2.36085e6i	−0.0398402	−	0.404809i
$181$	−928040.	+	1.60741e6i	−0.156506	+	0.271076i	−0.933606	−	0.358300i	$-0.883356\pi$
$181$	−928040.	+	1.60741e6i	−0.156506	+	0.271076i	0.777100	+	0.629377i	$0.216690\pi$
$182$	1.71207e6	+	4.70388e6i	0.283993	+	0.780264i
$183$	701277.	+	3.08409e6i	0.114429	+	0.503238i
$184$	−4.10568e6	+	3.44508e6i	−0.659071	+	0.553026i
$185$	−1.20686e6	+	3.31583e6i	−0.190609	+	0.523693i
$186$	1.22886e6	−	1.61958e6i	0.190970	−	0.251688i
$187$	−2.14098e6	+	1.21421e7i	−0.327407	+	1.85682i
$188$			4.15784e6i			0.625740i
$189$	243289.	−	8.88318e6i	0.0360361	−	1.31578i
$190$	2.61766e6			0.381639
$191$	−3.22352e6	−	568394.i	−0.462627	−	0.0815736i	−0.0625233	−	0.998044i	$-0.519915\pi$
$191$	−3.22352e6	−	568394.i	−0.462627	−	0.0815736i	−0.400104	+	0.916470i	$0.631026\pi$
$192$	−1.14051e6	+	479672.i	−0.161138	+	0.0677705i
$193$	8.31341e6	+	3.02583e6i	1.15640	+	0.420894i	0.847809	−	0.530301i	$-0.177921\pi$
$193$	8.31341e6	+	3.02583e6i	1.15640	+	0.420894i	0.308589	+	0.951196i	$0.400143\pi$
$194$	−1.37998e6	−	1.64460e6i	−0.189003	−	0.225245i
$195$	−3.46651e6	−	3.74212e6i	−0.467507	−	0.504678i
$196$	−3.92692e6	+	1.42928e6i	−0.521535	+	0.189823i
$197$	8.83663e6	+	5.10183e6i	1.15581	+	0.667310i	0.950297	−	0.311344i	$-0.100779\pi$
$197$	8.83663e6	+	5.10183e6i	1.15581	+	0.667310i	0.205517	+	0.978653i	$0.434112\pi$
$198$	4.64873e6	−	2.22937e6i	0.598878	−	0.287202i
$199$	−2.37677e6	−	4.11668e6i	−0.301597	−	0.522381i	0.674901	−	0.737908i	$-0.264186\pi$
$199$	−2.37677e6	−	4.11668e6i	−0.301597	−	0.522381i	−0.976498	+	0.215527i	$0.930853\pi$
$200$	3.16704e6	−	3.77433e6i	0.395880	−	0.471792i
$201$	−1.19900e7	+	588591.i	−1.47649	+	0.0724812i
$202$	−444704.	−	2.52204e6i	−0.0539532	−	0.305984i
$203$	−4.15940e6	+	733414.i	−0.497213	+	0.0876720i
$204$	440751.	+	8.97841e6i	0.0519162	+	1.05757i
$205$	−3.76089e6	−	3.15576e6i	−0.436545	−	0.366304i
$206$	6.75811e6	−	3.90179e6i	0.773078	−	0.446337i
$207$	4.97970e6	−	7.27834e6i	0.561426	−	0.820580i
$208$	1.91167e6	−	3.31111e6i	0.212434	−	0.367946i
$209$	−6.08169e6	−	1.67093e7i	−0.666170	−	1.83029i
$210$	−2.36384e6	+	2.18974e6i	−0.255247	+	0.236448i
$211$	2.76626e6	−	2.32117e6i	0.294474	−	0.247093i	−0.483566	−	0.875308i	$-0.660659\pi$
$211$	2.76626e6	−	2.32117e6i	0.294474	−	0.247093i	0.778040	+	0.628215i	$0.216214\pi$
$212$	745991.	−	2.04959e6i	0.0782936	−	0.215110i
$213$	−374924.	−	891456.i	−0.0387975	−	0.0922489i
$214$	929280.	−	5.27021e6i	0.0948212	−	0.537758i
$215$			2.72124e6i			0.273812i
$216$	6.83122e6	−	5.42042e6i	0.677856	−	0.537863i
$217$	8.63118e6			0.844678
$218$	−215586.	−	38013.6i	−0.0208090	−	0.00366919i
$219$	−5.71494e6	−	4.33624e6i	−0.544101	−	0.412839i
$220$	5.49073e6	+	1.99846e6i	0.515658	+	0.187684i
$221$	1.24246e7	+	1.48071e7i	1.15108	+	1.37181i
$222$	−5.45208e6	+	1.23972e6i	−0.498314	+	0.113309i
$223$	−1.21843e6	+	443472.i	−0.109872	+	0.0399900i	−0.396371	−	0.918090i	$-0.629731\pi$
$223$	−1.21843e6	+	443472.i	−0.109872	+	0.0399900i	0.286499	+	0.958080i	$0.407508\pi$
$224$	−1.31782e7	−	7.60844e6i	−1.17250	−	0.676942i
$225$	−3.34640e6	+	7.38422e6i	−0.293785	+	0.648271i
$226$	3.29079e6	+	5.69982e6i	0.285086	+	0.493783i
$227$	−1.00948e7	+	1.20305e7i	−0.863015	+	1.02850i	0.136269	+	0.990672i	$0.456489\pi$
$227$	−1.00948e7	+	1.20305e7i	−0.863015	+	1.02850i	−0.999284	+	0.0378292i	$0.987956\pi$
$228$	−7.02490e6	−	1.08962e7i	−0.592701	−	0.919325i
$229$	−2.44736e6	−	1.38797e7i	−0.203794	−	1.15577i	−0.899327	−	0.437278i	$-0.855943\pi$
$229$	−2.44736e6	−	1.38797e7i	−0.203794	−	1.15577i	0.695533	−	0.718494i	$-0.255168\pi$
$230$	−3.14910e6	+	555271.i	−0.258823	+	0.0456375i
$231$	1.94697e7	+	1.00016e7i	1.57952	+	0.811399i
$232$	−3.17498e6	−	2.66413e6i	−0.254260	−	0.213349i
$233$	1.65724e7	−	9.56807e6i	1.31014	−	0.756409i	0.328020	−	0.944671i	$-0.393619\pi$
$233$	1.65724e7	−	9.56807e6i	1.31014	−	0.756409i	0.982119	+	0.188262i	$0.0602854\pi$
$234$	2.00725e6	−	7.82952e6i	0.156658	−	0.611065i
$235$	−2.87751e6	+	4.98400e6i	−0.221724	+	0.384038i
$236$	438882.	+	1.20582e6i	0.0333897	+	0.0917374i
$237$	1.01820e7	+	3.14984e6i	0.764873	+	0.236616i
$238$	9.35343e6	−	7.84846e6i	0.693809	−	0.582175i
$239$	−1.81898e6	+	4.99760e6i	−0.133240	+	0.366073i	−0.988314	−	0.152433i	$-0.951289\pi$
$239$	−1.81898e6	+	4.99760e6i	−0.133240	+	0.366073i	0.855074	+	0.518506i	$0.173511\pi$
$240$	2.44175e6	+	308014.i	0.176631	+	0.0222811i
$241$	−2.66610e6	+	1.51202e7i	−0.190469	+	1.08020i	0.728255	+	0.685306i	$0.240331\pi$
$241$	−2.66610e6	+	1.51202e7i	−0.190469	+	1.08020i	−0.918725	+	0.394899i	$0.870780\pi$
$242$			5.72140e6i			0.403698i
$243$	−8.42354e6	+	1.16162e7i	−0.587051	+	0.809550i
$244$	−5.67985e6			−0.390992
$245$	−5.69636e6	−	1.00442e6i	−0.387346	−	0.0682995i
$246$	973601.	−	7.71811e6i	0.0653997	−	0.518449i
$247$	−2.61958e7	−	9.53450e6i	−1.73837	−	0.632714i
$248$	5.44436e6	+	6.48833e6i	0.356937	+	0.425381i
$249$	−6.23507e6	+	2.01552e7i	−0.403871	+	1.30554i
$250$	6.64346e6	−	2.41802e6i	0.425181	−	0.154753i
$251$	−1.31947e7	−	7.61795e6i	−0.834406	−	0.481745i	0.0209527	−	0.999780i	$-0.493330\pi$
$251$	−1.31947e7	−	7.61795e6i	−0.834406	−	0.481745i	−0.855359	+	0.518036i	$0.826663\pi$
$252$	1.54587e7	+	3.96313e6i	0.965984	+	0.247649i
$253$	1.08608e7	+	1.88115e7i	0.670660	+	1.16162i
$254$	−8.32424e6	+	9.92044e6i	−0.507976	+	0.605382i
$255$	−5.68535e6	+	1.10674e7i	−0.342876	+	0.667462i
$256$	−1.86114e6	−	1.05550e7i	−0.110932	−	0.629129i
$257$	−2.88893e7	+	5.09397e6i	−1.70192	+	0.300094i	−0.938363	−	0.345652i	$-0.887658\pi$
$257$	−2.88893e7	+	5.09397e6i	−1.70192	+	0.300094i	−0.763553	+	0.645745i	$0.776547\pi$
$258$	−3.62403e6	+	2.33646e6i	−0.211024	+	0.136050i
$259$	−1.81842e7	−	1.52583e7i	−1.04663	−	0.878229i
$260$	7.93320e6	−	4.58024e6i	0.451366	−	0.260596i
$261$	6.21163e6	+	2.81500e6i	0.349369	+	0.158328i
$262$	1.21398e6	−	2.10267e6i	0.0675004	−	0.116914i
$263$	−3.50932e6	−	9.64177e6i	−0.192910	−	0.530017i	0.805095	−	0.593146i	$-0.202114\pi$
$263$	−3.50932e6	−	9.64177e6i	−0.192910	−	0.530017i	−0.998005	+	0.0631291i	$0.979892\pi$
$264$	4.76254e6	+	2.09448e7i	0.258837	+	1.13832i
$265$	2.31268e6	−	1.94057e6i	0.124273	−	0.104278i
$266$	−6.02281e6	+	1.65475e7i	−0.320003	+	0.879201i
$267$	1.40594e7	−	1.85296e7i	0.738642	−	0.973492i
$268$	3.74348e6	−	2.12303e7i	0.194478	−	1.10294i
$269$			3.16390e7i			1.62542i	0.582668	+	0.812710i	$0.302009\pi$
$269$			3.16390e7i			1.62542i	−0.582668	+	0.812710i	$0.697991\pi$
$270$	5.14664e6	−	762854.i	0.261477	−	0.0387570i
$271$	2.64272e7			1.32783			0.663917	−	0.747806i	$-0.268893\pi$
$271$	2.64272e7			1.32783			0.663917	+	0.747806i	$0.268893\pi$
$272$	−9.18420e6	−	1.61942e6i	−0.456389	−	0.0804736i
$273$	3.16316e7	−	1.33035e7i	1.55465	−	0.653848i
$274$	−554284.	−	201743.i	−0.0269452	−	0.00980723i
$275$	−1.28356e7	−	1.52969e7i	−0.617189	−	0.735537i
$276$	1.07624e7	+	1.16181e7i	0.511898	+	0.552598i
$277$	−2.86155e7	+	1.04152e7i	−1.34636	+	0.490037i	−0.911811	−	0.410610i	$-0.865316\pi$
$277$	−2.86155e7	+	1.04152e7i	−1.34636	+	0.490037i	−0.434553	+	0.900646i	$0.643094\pi$
$278$	−4.59367e6	−	2.65216e6i	−0.213809	−	0.123443i
$279$	−1.15022e7	−	7.86957e6i	−0.529623	−	0.362358i
$280$	−6.71220e6	−	1.16259e7i	−0.305767	−	0.529604i
$281$	1.52140e7	−	1.81313e7i	0.685685	−	0.817167i	−0.305142	−	0.952307i	$-0.598704\pi$
$281$	1.52140e7	−	1.81313e7i	0.685685	−	0.817167i	0.990827	+	0.135140i	$0.0431484\pi$
$282$	−9.10809e6	+	447117.i	−0.406144	+	0.0199376i
$283$	4.69742e6	+	2.66404e7i	0.207252	+	1.17539i	0.893856	+	0.448355i	$0.147990\pi$
$283$	4.69742e6	+	2.66404e7i	0.207252	+	1.17539i	−0.686603	+	0.727032i	$0.740899\pi$
$284$	1.71033e6	−	301578.i	0.0746665	−	0.0131657i
$285$	−879839.	−	1.79229e7i	−0.0380074	−	0.774239i
$286$	1.52509e7	+	1.27970e7i	0.651924	+	0.547029i
$287$	2.86023e7	−	1.65135e7i	1.20991	−	0.698544i
$288$	1.06246e7	+	2.21546e7i	0.444769	+	0.927440i
$289$	1.15052e7	−	1.99276e7i	0.476651	−	0.825583i
$290$	−845751.	−	2.32368e6i	−0.0346776	−	0.0952759i
$291$	−1.07966e7	+	1.00014e7i	−0.438136	+	0.405866i
$292$	9.86885e6	−	8.28095e6i	0.396386	−	0.332607i
$293$	5.11571e6	−	1.40553e7i	0.203377	−	0.558775i	−0.795510	−	0.605941i	$-0.792797\pi$
$293$	5.11571e6	−	1.40553e7i	0.203377	−	0.558775i	0.998887	+	0.0471661i	$0.0150190\pi$
$294$	−3.55324e6	−	8.44854e6i	−0.139824	−	0.332460i
$295$	−308423.	+	1.74915e6i	−0.0120138	+	0.0681336i
$296$		−	2.32942e7i		−	0.898200i
$297$	−1.68269e7	−	3.10802e7i	−0.642294	−	1.18635i
$298$	−1.22506e7			−0.462923
$299$	3.35366e7	+	5.91341e6i	1.25460	+	0.221220i
$300$	−1.15982e7	−	8.80019e6i	−0.429563	−	0.325933i
$301$	−1.72023e7	−	6.26113e6i	−0.630794	−	0.229590i
$302$	−3.01036e6	−	3.58761e6i	−0.109294	−	0.130252i
$303$	−1.71188e7	+	3.89256e6i	−0.615382	+	0.139929i
$304$	1.26388e7	−	4.60015e6i	0.449868	−	0.163739i
$305$	−6.80843e6	−	3.93085e6i	−0.239965	−	0.138544i
$306$	−1.96206e7	+	1.93100e6i	−0.684774	+	0.0673936i
$307$	410508.	+	711020.i	0.0141875	+	0.0245735i	0.873032	−	0.487663i	$-0.162150\pi$
$307$	410508.	+	711020.i	0.0141875	+	0.0245735i	−0.858844	+	0.512236i	$0.828817\pi$
$308$	−2.52665e7	+	3.01114e7i	−0.864755	+	1.03057i
$309$	−2.89868e7	−	4.49608e7i	−0.982483	−	1.52391i
$310$	877511.	+	4.97661e6i	0.0294556	+	0.167051i
$311$	4.51301e7	−	7.95765e6i	1.50032	−	0.264548i	0.637657	−	0.770320i	$-0.279904\pi$
$311$	4.51301e7	−	7.95765e6i	1.50032	−	0.264548i	0.862667	+	0.505773i	$0.168793\pi$
$312$	2.99532e7	+	1.53870e7i	0.986231	+	0.506628i
$313$	2.16810e7	+	1.81925e7i	0.707044	+	0.593280i	0.923768	−	0.382953i	$-0.125093\pi$
$313$	2.16810e7	+	1.81925e7i	0.707044	+	0.593280i	−0.216724	+	0.976233i	$0.569537\pi$
$314$	−1.43970e6	+	831211.i	−0.0465032	+	0.0268487i
$315$	1.57875e7	+	1.54491e7i	0.505106	+	0.494277i
$316$	−9.57003e6	+	1.65758e7i	−0.303286	+	0.525306i
$317$	1.06993e7	+	2.93961e7i	0.335875	+	0.922809i	0.986551	+	0.163453i	$0.0522633\pi$
$317$	1.06993e7	+	2.93961e7i	0.335875	+	0.922809i	−0.650676	+	0.759355i	$0.725514\pi$
$318$	4.57003e6	+	1.41375e6i	0.142114	+	0.0439634i
$319$	−1.28678e7	+	1.07974e7i	−0.396398	+	0.332618i
$320$	1.05187e6	−	2.88999e6i	0.0321005	−	0.0881954i
$321$	−3.63971e7	−	4.59131e6i	−1.10040	−	0.138810i
$322$	3.73541e6	−	2.11846e7i	0.111885	−	0.634530i
$323$			6.79975e7i			2.01783i
$324$	−1.69872e7	−	1.93760e7i	−0.499445	−	0.569676i
$325$	−3.13056e7			−0.911953
$326$	−8.23899e6	−	1.45276e6i	−0.237805	−	0.0419314i
$327$	−187815.	+	1.48888e6i	−0.00537138	+	0.0425810i
$328$	3.04554e7	+	1.10849e7i	0.863063	+	0.314129i
$329$	−2.48856e7	−	2.96575e7i	−0.698812	−	0.832812i
$330$	−3.78735e6	+	1.22428e7i	−0.105388	+	0.340674i
$331$	4.81216e7	−	1.75148e7i	1.32695	−	0.482972i	0.421274	−	0.906933i	$-0.361583\pi$
$331$	4.81216e7	−	1.75148e7i	1.32695	−	0.482972i	0.905680	+	0.423962i	$0.139361\pi$
$332$	−3.28115e7	−	1.89437e7i	−0.896628	−	0.517668i
$333$	1.03208e7	+	3.69133e7i	0.279500	+	0.999655i
$334$	4.92689e6	+	8.53363e6i	0.132231	+	0.229031i
$335$	1.91802e7	−	2.28580e7i	0.510174	−	0.608001i
$336$	−7.56516e6	+	1.47268e7i	−0.199435	+	0.388231i
$337$	6.56839e6	+	3.72512e7i	0.171621	+	0.973308i	0.941973	+	0.335690i	$0.108969\pi$
$337$	6.56839e6	+	3.72512e7i	0.171621	+	0.973308i	−0.770352	+	0.637619i	$0.779920\pi$
$338$	1.20151e7	−	2.11859e6i	0.311156	−	0.0548652i
$339$	3.79202e7	−	2.44476e7i	0.973355	−	0.627534i
$340$	−1.71166e7	−	1.43626e7i	−0.435494	−	0.365423i
$341$	2.97284e7	−	1.71637e7i	0.749737	−	0.432861i
$342$	2.31135e7	−	1.65604e7i	0.577814	−	0.413991i
$343$	−7.10237e6	+	1.23017e7i	−0.176003	+	0.304847i
$344$	−6.14414e6	−	1.68809e7i	−0.150934	−	0.414687i
$345$	4.86036e6	+	2.13750e7i	0.118362	+	0.520534i
$346$	−2.79966e7	+	2.34920e7i	−0.675893	+	0.567141i
$347$	376062.	−	1.03322e6i	0.00900059	−	0.0247289i	−0.935111	−	0.354355i	$-0.884700\pi$
$347$	376062.	−	1.03322e6i	0.00900059	−	0.0247289i	0.944112	+	0.329626i	$0.106923\pi$
$348$	−7.40275e6	+	9.75644e6i	−0.175653	+	0.231501i
$349$	−8.00251e6	+	4.53845e7i	−0.188257	+	1.06766i	0.733443	+	0.679751i	$0.237912\pi$
$349$	−8.00251e6	+	4.53845e7i	−0.188257	+	1.06766i	−0.921699	+	0.387905i	$0.873199\pi$
$350$			1.97753e7i			0.461232i
$351$	−5.42828e7	−	1.11119e7i	−1.25528	−	0.256960i
$352$	−6.05196e7			−1.38761
$353$	4.64591e7	+	8.19199e6i	1.05620	+	0.186237i	0.674670	−	0.738119i	$-0.264286\pi$
$353$	4.64591e7	+	8.19199e6i	1.05620	+	0.186237i	0.381531	+	0.924356i	$0.375397\pi$
$354$	−2.59425e6	+	1.09108e6i	−0.0584793	+	0.0245949i
$355$	2.25889e6	+	822169.i	0.0504905	+	0.0183771i
$356$	2.68494e7	+	3.19979e7i	0.595093	+	0.709204i
$357$	−5.68816e7	−	6.14042e7i	−1.25017	−	1.34956i
$358$	−1.53913e7	+	5.60198e6i	−0.335449	+	0.122093i
$359$	−5.51182e7	−	3.18225e7i	−1.19127	−	0.687783i	−0.232679	−	0.972554i	$-0.574749\pi$
$359$	−5.51182e7	−	3.18225e7i	−1.19127	−	0.687783i	−0.958596	+	0.284771i	$0.908082\pi$
$360$	−1.65513e6	+	2.16129e7i	−0.0354752	+	0.463239i
$361$	−2.55106e7	−	4.41857e7i	−0.542250	−	0.939205i
$362$	4.69905e6	−	5.60011e6i	0.0990568	−	0.118051i
$363$	3.91740e7	−	1.92305e6i	0.818989	−	0.0402042i
$364$	1.07009e7	+	6.06880e7i	0.221880	+	1.25834i
$365$	1.75608e7	−	3.09644e6i	0.361131	−	0.0636772i
$366$	−610788.	−	1.24422e7i	−0.0124580	−	0.253778i
$367$	4.94634e7	+	4.15047e7i	1.00066	+	0.839652i	0.987076	−	0.160255i	$-0.0512318\pi$
$367$	4.94634e7	+	4.15047e7i	1.00066	+	0.839652i	0.0135831	+	0.999908i	$0.495676\pi$
$368$	−1.42289e7	+	8.21508e6i	−0.285515	+	0.164842i
$369$	−5.31726e7	−	4.07199e6i	−1.05830	−	0.0810453i
$370$	6.94899e6	−	1.20360e7i	0.137188	−	0.237617i
$371$	6.94619e6	+	1.90845e7i	0.136027	+	0.373731i
$372$	1.83605e7	−	1.70082e7i	0.356661	−	0.330392i
$373$	1.48537e7	−	1.24637e7i	0.286225	−	0.240171i	−0.488358	−	0.872643i	$-0.662404\pi$
$373$	1.48537e7	−	1.24637e7i	0.286225	−	0.240171i	0.774583	+	0.632472i	$0.217960\pi$
$374$	1.66088e7	−	4.56324e7i	0.317486	−	0.872286i
$375$	−1.87890e7	−	4.46745e7i	−0.356295	−	0.847161i
$376$	6.59719e6	−	3.74146e7i	0.124107	−	0.703845i
$377$			2.63344e7i			0.491473i
$378$	−7.01920e6	+	3.42896e7i	−0.129961	+	0.634874i
$379$	8.02692e7			1.47445			0.737227	−	0.675645i	$-0.236135\pi$
$379$	8.02692e7			1.47445			0.737227	+	0.675645i	$0.236135\pi$
$380$	3.17356e7	+	5.59584e6i	0.578357	+	0.101980i
$381$	7.07224e7	+	5.36610e7i	1.27874	+	0.970251i
$382$	1.21147e7	+	4.40937e6i	0.217331	+	0.0791019i
$383$	−3.40490e7	−	4.05780e7i	−0.606050	−	0.722262i	0.372555	−	0.928010i	$-0.378482\pi$
$383$	−3.40490e7	−	4.05780e7i	−0.606050	−	0.722262i	−0.978605	+	0.205748i	$0.934037\pi$
$384$	−5.20395e7	+	1.18330e7i	−0.919051	+	0.208979i
$385$	−5.11261e7	+	1.86084e7i	−0.895903	+	0.326082i
$386$	−3.01765e7	−	1.74224e7i	−0.524696	−	0.302933i
$387$	1.72156e7	+	2.40281e7i	0.297023	+	0.414560i
$388$	−1.32147e7	−	2.28886e7i	−0.226236	−	0.391853i
$389$	2.18877e7	−	2.60847e7i	0.371835	−	0.443136i	−0.547384	−	0.836881i	$-0.684376\pi$
$389$	2.18877e7	−	2.60847e7i	0.371835	−	0.443136i	0.919220	+	0.393745i	$0.128821\pi$
$390$	1.08865e7	+	1.68858e7i	0.183525	+	0.284661i
$391$	−1.44240e7	−	8.18024e7i	−0.241298	−	1.36847i
$392$	3.76044e7	−	6.63068e6i	0.624282	−	0.110078i
$393$	−1.48048e7	−	7.60526e6i	−0.243908	−	0.125296i
$394$	−3.07862e7	−	2.58327e7i	−0.503347	−	0.422358i
$395$	−2.29432e7	+	1.32462e7i	−0.372274	+	0.214932i
$396$	6.11253e7	−	1.70904e7i	0.984317	−	0.275211i
$397$	−2.05147e7	+	3.55326e7i	−0.327865	+	0.567878i	−0.982088	−	0.188423i	$-0.939662\pi$
$397$	−2.05147e7	+	3.55326e7i	−0.327865	+	0.567878i	0.654223	+	0.756301i	$0.272996\pi$
$398$	6.40344e6	+	1.75933e7i	0.101570	+	0.279061i
$399$	1.15324e8	+	3.56758e7i	1.81552	+	0.561636i
$400$	1.15705e7	−	9.70877e6i	0.180788	−	0.151700i
$401$	4.14061e6	−	1.13762e7i	0.0642143	−	0.176427i	−0.903436	−	0.428723i	$-0.858963\pi$
$401$	4.14061e6	−	1.13762e7i	0.0642143	−	0.176427i	0.967650	+	0.252296i	$0.0811857\pi$
$402$	4.69094e7	+	5.91738e6i	0.722073	+	0.0910860i
$403$	9.34513e6	−	5.29989e7i	0.142781	−	0.809751i
$404$		−	3.15270e7i		−	0.478121i
$405$	−6.95307e6	−	3.49823e7i	−0.104667	−	0.526603i
$406$	1.66351e7			0.248569
$407$	−9.29741e7	−	1.63938e7i	−1.37905	−	0.243163i
$408$	1.02798e7	−	8.14921e7i	0.151358	−	1.19987i
$409$	−4.34861e7	−	1.58276e7i	−0.635595	−	0.231338i	0.00406974	−	0.999992i	$-0.498705\pi$
$409$	−4.34861e7	−	1.58276e7i	−0.635595	−	0.231338i	−0.639665	+	0.768654i	$0.720927\pi$
$410$	1.24294e7	+	1.48128e7i	0.180342	+	0.214924i
$411$	−1.19501e6	+	3.86295e6i	−0.0172127	+	0.0556408i
$412$	9.02738e7	−	3.28570e7i	1.29083	−	0.469825i
$413$	−1.03476e7	−	5.97420e6i	−0.146889	−	0.0848065i
$414$	−2.42932e7	+	2.48254e7i	−0.342360	+	0.349861i
$415$	−2.62208e7	−	4.54157e7i	−0.366861	−	0.635421i
$416$	−6.09871e7	+	7.26815e7i	−0.847145	+	1.00959i
$417$	−1.66151e7	+	3.23440e7i	−0.229137	+	0.446052i
$418$	1.21615e7	+	6.89715e7i	0.166517	+	0.944367i
$419$	−9.65974e7	+	1.70327e7i	−1.31318	+	0.231548i	−0.786010	−	0.618214i	$-0.787857\pi$
$419$	−9.65974e7	+	1.70327e7i	−1.31318	+	0.231548i	−0.527167	+	0.849762i	$0.676746\pi$
$420$	−3.33394e7	+	2.14944e7i	−0.449998	+	0.290119i
$421$	−9.03926e6	−	7.58484e6i	−0.121140	−	0.101648i	0.580205	−	0.814470i	$-0.302972\pi$
$421$	−9.03926e6	−	7.58484e6i	−0.121140	−	0.101648i	−0.701345	+	0.712822i	$0.747417\pi$
$422$	−1.23173e7	+	7.11140e6i	−0.163900	+	0.0946276i
$423$	6.12275e6	+	6.22121e7i	0.0808957	+	0.821966i
$424$	−9.96492e6	+	1.72597e7i	−0.130730	+	0.226431i
$425$	2.61169e7	+	7.17555e7i	0.340216	+	0.934735i
$426$	844554.	+	3.71420e6i	0.0109244	+	0.0480437i
$427$	4.05139e7	−	3.39952e7i	0.520380	−	0.436650i
$428$	2.25325e7	−	6.19075e7i	0.287394	−	0.789609i
$429$	8.24941e7	−	1.08723e8i	1.04484	−	1.37705i
$430$	1.86116e6	−	1.05552e7i	0.0234087	−	0.132758i
$431$			6.17645e7i			0.771449i	0.922614	+	0.385724i	$0.126048\pi$
$431$			6.17645e7i			0.771449i	−0.922614	+	0.385724i	$0.873952\pi$
$432$	2.35088e7	−	1.27277e7i	0.291595	−	0.157870i
$433$	−1.33143e8			−1.64004			−0.820018	−	0.572338i	$-0.806037\pi$
$433$	−1.33143e8			−1.64004			−0.820018	+	0.572338i	$0.806037\pi$
$434$	−3.34786e7	−	5.90318e6i	−0.409542	−	0.0722133i
$435$	−1.56258e7	+	6.57182e6i	−0.189834	+	0.0798396i
$436$	−2.53242e6	−	921727.i	−0.0305546	−	0.0111210i
$437$	7.70038e7	+	9.17696e7i	0.922716	+	1.09965i
$438$	1.92014e7	+	2.07280e7i	0.228512	+	0.246681i
$439$	7.21789e7	−	2.62710e7i	0.853133	−	0.310515i	0.121816	−	0.992553i	$-0.461128\pi$
$439$	7.21789e7	−	2.62710e7i	0.853133	−	0.310515i	0.731317	+	0.682038i	$0.238906\pi$
$440$	−4.62377e7	−	2.66954e7i	−0.542798	−	0.313385i
$441$	−5.66522e7	+	2.71685e7i	−0.660543	+	0.316774i
$442$	−3.80655e7	−	6.59314e7i	−0.440823	−	0.763529i
$443$	5.64634e7	−	6.72904e7i	0.649465	−	0.774002i	−0.336369	−	0.941730i	$-0.609199\pi$
$443$	5.64634e7	−	6.72904e7i	0.649465	−	0.774002i	0.985833	+	0.167729i	$0.0536432\pi$
$444$	−6.87492e7	+	3.37490e6i	−0.785451	+	0.0385578i
$445$	1.00396e7	+	5.69375e7i	0.113930	+	0.646128i
$446$	5.02935e6	−	886810.i	0.0566901	−	0.00999599i
$447$	4.11762e6	+	8.38789e7i	0.0461025	+	0.939140i
$448$	1.58488e7	+	1.32988e7i	0.176264	+	0.147903i
$449$	−8.18063e7	+	4.72309e7i	−0.903749	+	0.521780i	−0.878415	−	0.477899i	$-0.841398\pi$
$449$	−8.18063e7	+	4.72309e7i	−0.903749	+	0.521780i	−0.0253345	+	0.999679i	$0.508065\pi$
$450$	1.80303e7	−	2.63532e7i	0.197864	−	0.289198i
$451$	6.56766e7	−	1.13755e8i	0.715947	−	1.24006i
$452$	2.77117e7	+	7.61373e7i	0.300088	+	0.824484i
$453$	−2.35523e7	+	2.18176e7i	−0.253360	+	0.234699i
$454$	4.73836e7	−	3.97595e7i	0.506361	−	0.424887i
$455$	−2.91731e7	+	8.01525e7i	−0.309705	+	0.850908i
$456$	4.59252e7	+	1.09196e8i	0.484346	+	1.15163i
$457$	−4.16248e6	+	2.36066e7i	−0.0436117	+	0.247334i	−0.998818	−	0.0486064i	$-0.984522\pi$
$457$	−4.16248e6	+	2.36066e7i	−0.0436117	+	0.247334i	0.955206	+	0.295941i	$0.0956331\pi$
$458$			5.55102e7i			0.577798i
$459$	1.98162e7	+	1.33691e8i	0.204919	+	1.38250i
$460$	−3.93655e7			−0.404429
$461$	−3.40998e7	−	6.01272e6i	−0.348056	−	0.0613717i	−0.00311260	−	0.999995i	$-0.500991\pi$
$461$	−3.40998e7	−	6.01272e6i	−0.348056	−	0.0613717i	−0.344943	+	0.938623i	$0.612102\pi$
$462$	−6.86787e7	−	5.21103e7i	−0.696460	−	0.528442i
$463$	3.29939e7	+	1.20088e7i	0.332423	+	0.120992i	0.502839	−	0.864380i	$-0.332289\pi$
$463$	3.29939e7	+	1.20088e7i	0.332423	+	0.120992i	−0.170416	+	0.985372i	$0.554511\pi$
$464$	−8.16705e6	−	9.73311e6i	−0.0817544	−	0.0974311i
$465$	3.37796e7	−	7.68098e6i	0.335966	−	0.0763937i
$466$	−7.08249e7	+	2.57781e7i	−0.699887	+	0.254738i
$467$	2.98265e6	+	1.72203e6i	0.0292854	+	0.0169080i	0.514571	−	0.857448i	$-0.327951\pi$
$467$	2.98265e6	+	1.72203e6i	0.0292854	+	0.0169080i	−0.485286	+	0.874356i	$0.661284\pi$
$468$	4.10725e7	−	9.06313e7i	0.400695	−	0.884180i
$469$	1.00366e8	+	1.73840e8i	0.972904	+	1.68512i
$470$	1.45700e7	−	1.73639e7i	0.140335	−	0.167245i
$471$	6.17515e6	+	9.57814e6i	0.0590996	+	0.0916681i
$472$	−2.03605e6	−	1.15470e7i	−0.0193625	−	0.109810i
$473$	−7.17007e7	+	1.26428e7i	−0.677548	+	0.119470i
$474$	−3.73397e7	−	1.91815e7i	−0.350620	−	0.180114i
$475$	−8.43633e7	−	7.07892e7i	−0.787178	−	0.660521i
$476$	1.30175e8	−	7.51568e7i	1.20700	−	0.696863i
$477$	8.14379e6	−	3.17658e7i	0.0750363	−	0.292688i
$478$	1.04735e7	−	1.81406e7i	0.0958975	−	0.166099i
$479$	−2.35519e7	−	6.47082e7i	−0.214298	−	0.588780i	0.785239	−	0.619193i	$-0.212540\pi$
$479$	−2.35519e7	−	6.47082e7i	−0.214298	−	0.588780i	−0.999537	+	0.0304127i	$0.990318\pi$
$480$	−5.83459e7	−	1.80495e7i	−0.527578	−	0.163208i
$481$	−1.13381e8	+	9.51376e7i	−1.01883	+	0.854903i
$482$	2.06825e7	−	5.68247e7i	0.184698	−	0.507453i
$483$	−1.46305e8	−	1.84556e7i	−1.29843	−	0.163790i
$484$	−1.22308e7	+	6.93641e7i	−0.107874	+	0.611785i
$485$		−	3.65820e7i		−	0.320658i
$486$	4.06179e7	−	3.92955e7i	0.353841	−	0.342322i
$487$	8.78437e7			0.760543			0.380272	−	0.924875i	$-0.375830\pi$
$487$	8.78437e7			0.760543			0.380272	+	0.924875i	$0.375830\pi$
$488$	5.11105e7	+	9.01216e6i	0.439795	+	0.0775478i
$489$	−7.17765e6	+	5.69000e7i	−0.0613841	+	0.486615i
$490$	2.14080e7	+	7.79189e6i	0.181965	+	0.0662300i
$491$	−1.43986e8	−	1.71596e8i	−1.21640	−	1.44965i	−0.856099	−	0.516811i	$-0.827119\pi$
$491$	−1.43986e8	−	1.71596e8i	−1.21640	−	1.44965i	−0.360300	−	0.932837i	$-0.617326\pi$
$492$	2.83028e7	−	9.14902e7i	0.237648	−	0.768209i
$493$	6.03610e7	−	2.19696e7i	0.503750	−	0.183350i
$494$	9.50873e7	+	5.48987e7i	0.788754	+	0.455387i
$495$	8.50985e7	+	2.18167e7i	0.701627	+	0.179876i
$496$	1.29825e7	+	2.24864e7i	0.106393	+	0.184279i
$497$	−1.03947e7	+	1.23879e7i	−0.0846722	+	0.100908i
$498$	3.79694e7	−	7.39135e7i	0.307430	−	0.598461i
$499$	−3.85848e7	−	2.18825e8i	−0.310538	−	1.76115i	−0.596217	−	0.802823i	$-0.703330\pi$
$499$	−3.85848e7	−	2.18825e8i	−0.310538	−	1.76115i	0.285679	−	0.958325i	$-0.407781\pi$
$500$	8.57119e7	−	1.51133e7i	0.685695	−	0.120907i
$501$	5.67731e7	−	3.66024e7i	0.451471	−	0.291069i
$502$	4.59693e7	+	3.85728e7i	0.363376	+	0.304909i
$503$	1.19086e8	−	6.87546e7i	0.935747	−	0.540254i	0.0471225	−	0.998889i	$-0.484995\pi$
$503$	1.19086e8	−	6.87546e7i	0.935747	−	0.540254i	0.888625	+	0.458635i	$0.151662\pi$
$504$	−1.32817e8	−	6.01905e7i	−1.03744	−	0.470150i
$505$	2.18189e7	−	3.77914e7i	0.169417	−	0.293439i
$506$	−2.92611e7	−	8.03943e7i	−0.225860	−	0.620545i
$507$	−1.85443e7	−	8.15546e7i	−0.142294	−	0.625784i
$508$	−1.22127e8	+	1.02477e8i	−0.931582	+	0.781690i
$509$	−2.67628e6	+	7.35302e6i	−0.0202945	+	0.0557587i	−0.949426	−	0.313990i	$-0.898334\pi$
$509$	−2.67628e6	+	7.35302e6i	−0.0202945	+	0.0557587i	0.929132	+	0.369749i	$0.120556\pi$
$510$	2.96218e7	−	3.90399e7i	0.223306	−	0.294306i
$511$	−2.08303e7	+	1.18135e8i	−0.156111	+	0.885349i
$512$		−	8.42879e7i		−	0.627994i
$513$	−1.21156e8	−	1.52690e8i	−0.897417	−	1.13099i
$514$	1.15540e8			0.850829
$515$	1.30950e8	+	2.30901e7i	0.958705	+	0.169046i
$516$	−4.89311e7	+	2.05792e7i	−0.356152	+	0.149789i
$517$	−1.44690e8	−	5.26627e7i	−1.04705	−	0.381093i
$518$	6.00970e7	+	7.16208e7i	0.432378	+	0.515288i
$519$	1.70258e8	+	1.83795e8i	1.21788	+	1.31471i
$520$	−7.86548e7	+	2.86280e7i	−0.559391	+	0.203602i
$521$	1.77976e8	+	1.02754e8i	1.25849	+	0.726587i	0.972780	−	0.231731i	$-0.0744388\pi$
$521$	1.77976e8	+	1.02754e8i	1.25849	+	0.726587i	0.285705	+	0.958317i	$0.407772\pi$
$522$	−2.21684e7	−	1.51672e7i	−0.155856	−	0.106633i
$523$	4.42256e7	+	7.66010e7i	0.309149	+	0.535463i	0.978177	−	0.207775i	$-0.0666223\pi$
$523$	4.42256e7	+	7.66010e7i	0.309149	+	0.535463i	−0.669027	+	0.743238i	$0.733289\pi$
$524$	1.92127e7	−	2.28968e7i	0.133535	−	0.159141i
$525$	1.35400e8	−	6.64680e6i	0.935709	−	0.0459341i
$526$	7.01757e6	+	3.97986e7i	0.0482203	+	0.273471i
$527$	−1.29275e8	+	2.27946e7i	−0.883246	+	0.155740i
$528$	3.22853e6	+	6.57674e7i	0.0219332	+	0.446796i
$529$	1.29838e6	+	1.08947e6i	0.00877073	+	0.00735952i
$530$	−1.02976e7	+	5.94535e6i	−0.0691688	+	0.0399346i
$531$	8.34250e6	+	1.73959e7i	0.0557202	+	0.116189i
$532$	−1.08392e8	+	1.87741e8i	−0.719886	+	1.24688i
$533$	−7.04314e7	−	1.93509e8i	−0.465141	−	1.27796i
$534$	−6.72068e7	+	6.22568e7i	−0.441356	+	0.408849i
$535$	6.98540e7	−	5.86145e7i	0.456173	−	0.382775i
$536$	−6.73719e7	+	1.85103e8i	−0.437506	+	1.20204i
$537$	4.35296e7	+	1.03500e8i	0.281101	+	0.668372i
$538$	2.16391e7	−	1.22721e8i	0.138961	−	0.788084i
$539$		−	1.54757e8i		−	0.988288i
$540$	6.40268e7	+	1.75354e6i	0.406612	+	0.0111362i
$541$	1.06399e8			0.671967			0.335983	−	0.941868i	$-0.390931\pi$
$541$	1.06399e8			0.671967			0.335983	+	0.941868i	$0.390931\pi$
$542$	−1.02506e8	−	1.80746e7i	−0.643800	−	0.113519i
$543$	−3.99229e7	−	3.02917e7i	−0.249358	−	0.189202i
$544$	2.17472e8	+	7.91532e7i	1.35085	+	0.491668i
$545$	−2.39772e6	−	2.85749e6i	−0.0148118	−	0.0176520i
$546$	−1.31791e8	+	2.99674e7i	−0.809672	+	0.184108i
$547$	−1.89944e8	+	6.91338e7i	−1.16055	+	0.422405i	−0.849293	−	0.527922i	$-0.822971\pi$
$547$	−1.89944e8	+	6.91338e7i	−1.16055	+	0.422405i	−0.311254	+	0.950327i	$0.600749\pi$
$548$	−6.28867e6	−	3.63076e6i	−0.0382135	−	0.0220626i
$549$	−8.49854e7	+	8.36404e6i	−0.513603	+	0.0505474i
$550$	3.93246e7	+	6.81122e7i	0.236361	+	0.409390i
$551$	−5.95482e7	+	7.09667e7i	−0.355970	+	0.424229i
$552$	−7.84121e7	−	1.21623e8i	−0.466193	−	0.723102i
$553$	−3.09476e7	−	1.75512e8i	−0.183000	−	1.03784i
$554$	1.18117e8	−	2.08272e7i	0.694678	−	0.122491i
$555$	−8.47453e7	−	4.35337e7i	−0.495720	−	0.254652i
$556$	−5.00224e7	−	4.19738e7i	−0.291032	−	0.244205i
$557$	−1.89012e7	+	1.09126e7i	−0.109377	+	0.0631486i	−0.553690	−	0.832723i	$-0.686781\pi$
$557$	−1.89012e7	+	1.09126e7i	−0.109377	+	0.0631486i	0.444314	+	0.895871i	$0.353448\pi$
$558$	3.92323e7	+	3.83912e7i	0.225809	+	0.220968i
$559$	−5.70710e7	+	9.88499e7i	−0.326723	+	0.565902i
$560$	−1.40753e7	−	3.86715e7i	−0.0801480	−	0.220205i
$561$	−3.18024e8	−	9.83817e7i	−1.80124	−	0.557219i
$562$	−7.14127e7	+	5.99224e7i	−0.402315	+	0.337583i
$563$	−6.86151e7	+	1.88518e8i	−0.384498	+	1.05640i	0.584942	+	0.811075i	$0.301117\pi$
$563$	−6.86151e7	+	1.88518e8i	−0.384498	+	1.05640i	−0.969441	+	0.245326i	$0.921105\pi$
$564$	−1.11379e8	−	1.40499e7i	−0.620820	−	0.0783133i
$565$	−1.94743e7	+	1.10444e8i	−0.107973	+	0.612347i
$566$		−	1.06545e8i		−	0.587604i
$567$	2.37138e8	+	3.65346e7i	1.30092	+	0.200427i
$568$	−1.58691e7			−0.0865977
$569$	1.01564e8	+	1.79084e7i	0.551318	+	0.0972122i	0.442366	−	0.896835i	$-0.354139\pi$
$569$	1.01564e8	+	1.79084e7i	0.551318	+	0.0972122i	0.108952	+	0.994047i	$0.465251\pi$
$570$	−8.84544e6	+	7.01212e7i	−0.0477634	+	0.378639i
$571$	7.69357e7	+	2.80023e7i	0.413257	+	0.150413i	0.540277	−	0.841487i	$-0.318319\pi$
$571$	7.69357e7	+	2.80023e7i	0.413257	+	0.150413i	−0.127021	+	0.991900i	$0.540542\pi$
$572$	1.57540e8	+	1.87748e8i	0.841786	+	1.00320i
$573$	2.61187e7	−	8.44302e7i	0.138831	−	0.448780i
$574$	−1.22237e8	+	4.44905e7i	−0.646347	+	0.235251i
$575$	1.16507e8	+	6.72653e7i	0.612841	+	0.353824i
$576$	−8.99535e6	−	3.21726e7i	−0.0470707	−	0.168352i
$577$	3.17101e7	+	5.49235e7i	0.165071	+	0.285911i	0.936680	−	0.350185i	$-0.113881\pi$
$577$	3.17101e7	+	5.49235e7i	0.165071	+	0.285911i	−0.771610	+	0.636096i	$0.780548\pi$
$578$	−5.82555e7	+	6.94262e7i	−0.301685	+	0.359534i
$579$	−1.09147e8	+	2.12473e8i	−0.562312	+	1.09463i
$580$	−5.28619e6	−	2.99795e7i	−0.0270931	−	0.153653i
$581$	3.47424e8	−	6.12603e7i	1.77146	−	0.312357i
$582$	4.87182e7	−	3.14093e7i	0.247128	−	0.159327i
$583$	6.18757e7	+	5.19198e7i	0.312258	+	0.262016i
$584$	−1.01945e8	+	5.88579e7i	−0.511831	+	0.295506i
$585$	1.11957e8	−	8.02146e7i	0.559220	−	0.400669i
$586$	−2.94557e7	+	5.10188e7i	−0.146378	+	0.253535i
$587$	−4.19548e6	−	1.15270e7i	−0.0207428	−	0.0569904i	0.928889	−	0.370358i	$-0.120765\pi$
$587$	−4.19548e6	−	1.15270e7i	−0.0207428	−	0.0569904i	−0.949632	+	0.313368i	$0.898543\pi$
$588$	−2.50176e7	−	1.10023e8i	−0.123059	−	0.541192i
$589$	1.45026e8	−	1.21691e8i	0.709742	−	0.595544i
$590$	2.39262e6	−	6.57366e6i	0.0116498	−	0.0320075i
$591$	−1.66527e8	+	2.19473e8i	−0.806717	+	1.06321i
$592$	1.24002e7	−	7.03250e7i	0.0597673	−	0.338957i
$593$		−	2.79956e8i		−	1.34253i	−0.741216	−	0.671267i	$-0.765750\pi$
$593$		−	2.79956e8i		−	1.34253i	0.741216	−	0.671267i	$-0.234250\pi$
$594$	4.40111e7	+	1.32062e8i	0.209992	+	0.630114i
$595$	2.08055e8			0.987704
$596$	−1.48522e8	−	2.61884e7i	−0.701538	−	0.123700i
$597$	1.18308e8	−	4.97573e7i	0.556020	−	0.233848i
$598$	−1.26037e8	−	4.58738e7i	−0.589380	−	0.214517i
$599$	−6.26399e7	−	7.46513e7i	−0.291454	−	0.347342i	0.600371	−	0.799722i	$-0.295020\pi$
$599$	−6.26399e7	−	7.46513e7i	−0.291454	−	0.347342i	−0.891825	+	0.452380i	$0.850575\pi$
$600$	9.04039e7	+	9.75918e7i	0.418537	+	0.451814i
$601$	1.63040e7	−	5.93418e6i	0.0751054	−	0.0273361i	−0.304194	−	0.952610i	$-0.598387\pi$
$601$	1.63040e7	−	5.93418e6i	0.0751054	−	0.0273361i	0.379300	+	0.925274i	$0.376165\pi$
$602$	6.24420e7	+	3.60509e7i	0.286212	+	0.165245i
$603$	2.47489e7	−	3.23174e8i	0.112877	−	1.47396i
$604$	−2.88272e7	−	4.99302e7i	−0.130825	−	0.226596i
$605$	−6.26658e7	+	7.46822e7i	−0.282986	+	0.337249i
$606$	6.90625e7	−	3.39028e6i	0.310330	−	0.0152341i
$607$	−1.59291e7	−	9.03383e7i	−0.0712237	−	0.403930i	−0.999488	−	0.0320076i	$-0.989810\pi$
$607$	−1.59291e7	−	9.03383e7i	−0.0712237	−	0.403930i	0.928264	−	0.371922i	$-0.121301\pi$
$608$	−3.28699e8	+	5.79585e7i	−1.46247	+	0.257874i
$609$	−5.59131e6	−	1.13899e8i	−0.0247549	−	0.504276i
$610$	2.37201e7	+	1.99035e7i	0.104502	+	0.0876880i
$611$	−2.09053e8	+	1.20697e8i	−0.916499	+	0.529141i
$612$	−2.42000e8	−	1.85326e7i	−1.05575	−	0.0808502i
$613$	1.53233e8	−	2.65408e8i	0.665231	−	1.15221i	−0.313992	−	0.949426i	$-0.601667\pi$
$613$	1.53233e8	−	2.65408e8i	0.665231	−	1.15221i	0.979223	−	0.202788i	$-0.0650001\pi$
$614$	−1.10598e6	−	3.03866e6i	−0.00477797	−	0.0131274i
$615$	9.72441e7	−	9.00818e7i	0.418059	−	0.387268i
$616$	2.75140e8	−	2.30870e8i	1.17709	−	0.987699i
$617$	−5.22391e7	+	1.43526e8i	−0.222403	+	0.611047i	−0.999840	−	0.0179144i	$-0.994297\pi$
$617$	−5.22391e7	+	1.43526e8i	−0.222403	+	0.611047i	0.777437	+	0.628961i	$0.216520\pi$
$618$	8.16836e7	+	1.94219e8i	0.346074	+	0.822860i
$619$	−1.91607e7	+	1.08666e8i	−0.0807865	+	0.458163i	0.917400	+	0.397966i	$0.130284\pi$
$619$	−1.91607e7	+	1.08666e8i	−0.0807865	+	0.458163i	−0.998187	+	0.0601968i	$0.980827\pi$
$620$			6.22105e7i			0.261029i
$621$	1.78143e8	+	1.57989e8i	0.743864	+	0.659710i
$622$	−1.80493e8			−0.750048
$623$	−3.83029e8	−	6.75384e7i	−1.58405	−	0.279310i
$624$	8.22373e7	+	6.23980e7i	0.338466	+	0.256813i
$625$	−5.00818e7	−	1.82283e7i	−0.205135	−	0.0746630i
$626$	−7.16537e7	−	8.53935e7i	−0.292089	−	0.348098i
$627$	4.68155e8	−	1.06452e8i	1.89927	−	0.431866i
$628$	−1.92313e7	+	6.99962e6i	−0.0776479	+	0.0282615i
$629$	3.12652e8	+	1.80510e8i	1.25635	+	0.725353i
$630$	−5.06704e7	−	7.07214e7i	−0.202643	−	0.282832i
$631$	−1.80099e8	−	3.11941e8i	−0.716842	−	1.24161i	−0.962245	−	0.272186i	$-0.912253\pi$
$631$	−1.80099e8	−	3.11941e8i	−0.716842	−	1.24161i	0.245402	−	0.969421i	$-0.421080\pi$
$632$	1.12417e8	−	1.33973e8i	0.445329	−	0.530723i
$633$	5.28313e7	+	8.19454e7i	0.208296	+	0.323083i
$634$	−2.13953e7	−	1.21339e8i	−0.0839560	−	0.476138i
$635$	−2.17315e8	+	3.83185e7i	−0.848727	+	0.149654i
$636$	5.23831e7	+	2.69092e7i	0.203620	+	0.104600i
$637$	−1.85857e8	−	1.55952e8i	−0.719051	−	0.603355i
$638$	5.72962e7	−	3.30800e7i	0.220630	−	0.127381i
$639$	2.51470e7	−	7.03100e6i	0.0963792	−	0.0269473i
$640$	6.63273e7	−	1.14882e8i	0.253019	−	0.438241i
$641$	−5.42957e7	−	1.49176e8i	−0.206154	−	0.566403i	0.792925	−	0.609320i	$-0.208557\pi$
$641$	−5.42957e7	−	1.49176e8i	−0.206154	−	0.566403i	−0.999079	+	0.0429163i	$0.986335\pi$
$642$	1.38037e8	+	4.27020e7i	0.521662	+	0.161378i
$643$	−6.84535e7	+	5.74393e7i	−0.257491	+	0.216061i	−0.762390	−	0.647118i	$-0.775974\pi$
$643$	−6.84535e7	+	5.74393e7i	−0.257491	+	0.216061i	0.504899	+	0.863179i	$0.331530\pi$
$644$	9.05735e7	−	2.48849e8i	0.339112	−	0.931704i
$645$	−7.28959e7	−	9.19545e6i	−0.271659	−	0.0342684i
$646$	4.65060e7	−	2.63749e8i	0.172509	−	0.978346i
$647$			3.61143e8i			1.33342i	0.745318	+	0.666709i	$0.232298\pi$
$647$			3.61143e8i			1.33342i	−0.745318	+	0.666709i	$0.767702\pi$
$648$	1.22117e8	+	2.01309e8i	0.448798	+	0.739841i
$649$	−4.75204e7			−0.173839
$650$	1.21428e8	+	2.14111e7i	0.442160	+	0.0779647i
$651$	−2.91659e7	+	2.31210e8i	−0.105714	+	0.838037i
$652$	−9.67808e7	−	3.52253e7i	−0.349178	−	0.127090i
$653$	2.15546e7	+	2.56878e7i	0.0774105	+	0.0922543i	0.803360	−	0.595494i	$-0.203044\pi$
$653$	2.15546e7	+	2.56878e7i	0.0774105	+	0.0922543i	−0.725949	+	0.687748i	$0.758599\pi$
$654$	1.74679e6	−	5.64660e6i	0.00624465	−	0.0201862i
$655$	3.88765e7	−	1.41499e7i	0.138345	−	0.0503534i
$656$	8.60437e7	+	4.96774e7i	0.304795	+	0.175973i
$657$	1.35470e8	−	1.38437e8i	0.477689	−	0.488154i
$658$	7.62423e7	+	1.32056e8i	0.267620	+	0.463531i
$659$	6.04191e7	−	7.20047e7i	0.211115	−	0.251597i	−0.650087	−	0.759859i	$-0.725268\pi$
$659$	6.04191e7	−	7.20047e7i	0.211115	−	0.251597i	0.861202	+	0.508263i	$0.169712\pi$
$660$	−7.20881e7	+	1.40331e8i	−0.250745	+	0.488114i
$661$	2.71957e7	+	1.54234e8i	0.0941662	+	0.534043i	0.995000	+	0.0998784i	$0.0318454\pi$
$661$	2.71957e7	+	1.54234e8i	0.0941662	+	0.534043i	−0.900833	+	0.434165i	$0.857044\pi$
$662$	−1.98633e8	+	3.50243e7i	−0.684663	+	0.120725i
$663$	−4.38633e8	+	2.82792e8i	−1.50508	+	0.970347i
$664$	2.65199e8	+	2.22528e8i	0.905873	+	0.760118i
$665$	−2.59860e8	+	1.50030e8i	−0.883637	+	0.510168i
$666$	−1.47860e7	−	1.50238e8i	−0.0500528	−	0.508577i
$667$	5.65838e7	−	9.80060e7i	0.190684	−	0.330275i
$668$	4.14893e7	+	1.13991e8i	0.139190	+	0.382420i
$669$	−7.76236e6	−	3.41375e7i	−0.0259248	−	0.114013i
$670$	−9.00294e7	+	7.55436e7i	−0.299337	+	0.251173i
$671$	7.19404e7	−	1.97654e8i	0.238125	−	0.654243i
$672$	2.48344e8	−	3.27304e8i	0.818361	−	1.07856i
$673$	−3.60256e7	+	2.04311e8i	−0.118186	+	0.670266i	0.866937	+	0.498417i	$0.166085\pi$
$673$	−3.60256e7	+	2.04311e8i	−0.118186	+	0.670266i	−0.985123	+	0.171849i	$0.945026\pi$
$674$		−	1.48982e8i		−	0.486580i
$675$	−1.86498e8	−	1.14595e8i	−0.606406	−	0.372609i
$676$	1.50196e8			0.486204
$677$	3.28427e8	+	5.79105e7i	1.05846	+	0.186634i	0.675671	−	0.737203i	$-0.263854\pi$
$677$	3.28427e8	+	5.79105e7i	1.05846	+	0.186634i	0.382785	+	0.923837i	$0.374965\pi$
$678$	−1.63805e8	+	6.88924e7i	−0.525580	+	0.221046i
$679$	2.31253e8	+	8.41691e7i	0.738716	+	0.268870i
$680$	1.31236e8	+	1.56401e8i	0.417376	+	0.497409i
$681$	−2.88157e8	−	3.11068e8i	−0.912405	−	0.984950i
$682$	−1.27049e8	+	4.62422e7i	−0.400516	+	0.145776i
$683$	−3.42978e8	−	1.98018e8i	−1.07647	−	0.621503i	−0.146531	−	0.989206i	$-0.546811\pi$
$683$	−3.42978e8	−	1.98018e8i	−1.07647	−	0.621503i	−0.929943	+	0.367703i	$0.880144\pi$
$684$	3.15621e8	−	1.51361e8i	0.986275	−	0.472984i
$685$	−5.02548e6	−	8.70439e6i	−0.0156353	−	0.0270811i
$686$	3.59622e7	−	4.28581e7i	0.111397	−	0.132758i
$687$	3.80074e8	−	1.86579e7i	1.17219	−	0.0575429i
$688$	−9.56291e6	−	5.42339e7i	−0.0293646	−	0.166535i
$689$	1.24707e8	−	2.19892e7i	0.381271	−	0.0672283i
$690$	−4.23321e6	−	8.62335e7i	−0.0128861	−	0.262500i
$691$	−9.13237e7	−	7.66297e7i	−0.276789	−	0.232254i	0.493816	−	0.869566i	$-0.335602\pi$
$691$	−9.13237e7	−	7.66297e7i	−0.276789	−	0.232254i	−0.770605	+	0.637312i	$0.780046\pi$
$692$	−3.89640e8	+	2.24959e8i	−1.17583	+	0.678867i
$693$	−3.33711e8	+	4.87753e8i	−1.00270	+	1.46555i
$694$	−2.16532e6	+	3.75045e6i	−0.00647806	+	0.0112203i
$695$	−3.09131e7	−	8.49330e7i	−0.0920848	−	0.253001i
$696$	8.20946e7	−	7.60481e7i	0.243493	−	0.225559i
$697$	−3.84782e8	+	3.22871e8i	−1.13636	+	0.953521i
$698$	6.20802e7	−	1.70564e8i	0.182552	−	0.501558i
$699$	2.00306e8	+	4.76268e8i	0.586494	+	1.39450i
$700$	−4.22741e7	+	2.39749e8i	−0.123248	+	0.698976i
$701$		−	4.73491e8i		−	1.37454i	−0.726401	−	0.687271i	$-0.758808\pi$
$701$		−	4.73491e8i		−	1.37454i	0.726401	−	0.687271i	$-0.241192\pi$
$702$	2.02952e8	+	8.02266e7i	0.586654	+	0.231903i
$703$	−5.20669e8			−1.49863
$704$	8.10337e7	+	1.42884e7i	0.232246	+	0.0409512i
$705$	−1.23786e8	−	9.39235e7i	−0.353269	−	0.268045i
$706$	−1.74603e8	−	6.35501e7i	−0.496177	−	0.180594i
$707$	1.88696e8	+	2.24879e8i	0.533955	+	0.636343i
$708$	−3.37842e7	+	7.68203e6i	−0.0951949	+	0.0216459i
$709$	4.33283e8	−	1.57702e8i	1.21572	−	0.442485i	0.347035	−	0.937852i	$-0.387189\pi$
$709$	4.33283e8	−	1.57702e8i	1.21572	−	0.442485i	0.868684	+	0.495367i	$0.164966\pi$
$710$	−8.19946e6	−	4.73396e6i	−0.0229092	−	0.0132266i
$711$	−1.18783e8	+	2.62110e8i	−0.330482	+	0.729246i
$712$	−1.90835e8	−	3.30537e8i	−0.528712	−	0.915756i
$713$	−1.48655e8	+	1.77161e8i	−0.410121	+	0.488764i
$714$	1.78636e8	+	2.77078e8i	0.490765	+	0.761215i
$715$	5.89077e7	+	3.34082e8i	0.161159	+	0.913977i
$716$	−1.98574e8	+	3.50140e7i	−0.540983	+	0.0953898i
$717$	−1.27728e8	−	6.56138e7i	−0.346519	−	0.178007i
$718$	1.92028e8	+	1.61130e8i	0.518789	+	0.435316i
$719$	−4.06220e8	+	2.34531e8i	−1.09288	+	0.630977i	−0.934343	−	0.356375i	$-0.884012\pi$
$719$	−4.06220e8	+	2.34531e8i	−1.09288	+	0.630977i	−0.158541	+	0.987352i	$0.550679\pi$
$720$	−1.65020e7	+	6.43680e7i	−0.0442119	+	0.172454i
$721$	−4.47259e8	+	7.74675e8i	−1.19331	+	2.06687i
$722$	6.87303e7	+	1.88835e8i	0.182615	+	0.501731i
$723$	−3.96026e8	−	1.22512e8i	−1.04787	−	0.324163i
$724$	6.89410e7	−	5.78484e7i	0.181661	−	0.152432i
$725$	−3.55819e7	+	9.77604e7i	−0.0933716	+	0.256536i
$726$	−1.53263e8	−	1.93334e7i	−0.400523	−	0.0505240i
$727$	9.74259e7	−	5.52530e8i	0.253554	−	1.43798i	−0.546202	−	0.837653i	$-0.683927\pi$
$727$	9.74259e7	−	5.52530e8i	0.253554	−	1.43798i	0.799756	−	0.600325i	$-0.204962\pi$
$728$		−	5.63084e8i		−	1.45942i
$729$	−2.82706e8	−	2.64900e8i	−0.729714	−	0.683753i
$730$	−7.02325e7			−0.180538
$731$	2.74185e8	+	4.83462e7i	0.701927	+	0.123769i
$732$	1.91930e7	−	1.52150e8i	0.0489338	−	0.387917i
$733$	6.65828e8	+	2.42341e8i	1.69064	+	0.615341i	0.994705	−	0.102769i	$-0.0327703\pi$
$733$	6.65828e8	+	2.42341e8i	1.69064	+	0.615341i	0.695930	+	0.718110i	$0.254992\pi$
$734$	−1.63472e8	−	1.94818e8i	−0.413385	−	0.492653i
$735$	4.61549e7	−	1.49198e8i	0.116240	−	0.375752i
$736$	3.83137e8	−	1.39451e8i	0.960994	−	0.349773i
$737$	6.91385e8	+	3.99171e8i	1.72710	+	0.997141i
$738$	2.03461e8	+	5.21611e7i	0.506187	+	0.129771i
$739$	2.14535e8	+	3.71586e8i	0.531575	+	0.920716i	0.999321	+	0.0368524i	$0.0117331\pi$
$739$	2.14535e8	+	3.71586e8i	0.531575	+	0.920716i	−0.467745	+	0.883863i	$0.654934\pi$
$740$	1.09977e8	−	1.31065e8i	0.271397	−	0.323439i
$741$	3.43927e8	−	6.69508e8i	0.845301	−	1.64551i
$742$	−1.38903e7	−	7.87756e7i	−0.0340016	−	0.192833i
$743$	7.96046e8	−	1.40364e8i	1.94076	−	0.342208i	0.940764	−	0.339062i	$-0.110110\pi$
$743$	7.96046e8	−	1.40364e8i	1.94076	−	0.342208i	0.999995	−	0.00314626i	$-0.00100149\pi$
$744$	−1.92205e8	+	1.23917e8i	−0.466708	+	0.300893i
$745$	−1.59909e8	−	1.34179e8i	−0.386726	−	0.324502i
$746$	−6.61387e7	+	3.81852e7i	−0.159309	+	0.0919769i
$747$	−5.18843e8	−	2.35130e8i	−1.24473	−	0.564088i
$748$	2.98909e8	−	5.17726e8i	0.714224	−	1.23707i
$749$	2.09808e8	+	5.76443e8i	0.499318	+	1.37186i
$750$	4.23241e7	+	1.86134e8i	0.100324	+	0.441206i
$751$	−9.41515e7	+	7.90025e7i	−0.222284	+	0.186518i	−0.747128	−	0.664680i	$-0.768568\pi$
$751$	−9.41515e7	+	7.90025e7i	−0.222284	+	0.186518i	0.524845	+	0.851198i	$0.324123\pi$
$752$	3.98337e7	−	1.09442e8i	0.0936693	−	0.257354i
$753$	2.48654e8	−	3.27713e8i	0.582386	−	0.767554i
$754$	1.80111e7	−	1.02146e8i	0.0420170	−	0.238290i
$755$		−	7.98017e7i		−	0.185426i
$756$	−1.58400e8	+	4.00710e8i	−0.366598	+	0.927395i
$757$	−1.13610e8			−0.261895			−0.130948	−	0.991389i	$-0.541802\pi$
$757$	−1.13610e8			−0.261895			−0.130948	+	0.991389i	$0.541802\pi$
$758$	−3.11348e8	−	5.48990e7i	−0.714888	−	0.126054i
$759$	−5.40618e8	+	2.27370e8i	−1.23642

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.87880 - 0.683936i) q^{2} +(-3.37914 + 26.7877i) q^{3} +(-45.5630 - 16.5836i) q^{4} +(-43.1394 - 51.4115i) q^{5} +(31.4281 - 101.593i) q^{6} +(424.254 - 154.416i) q^{7} +(383.689 + 221.523i) q^{8} +(-706.163 - 181.039i) q^{9} +O(q^{10})\)	\(q+(-3.87880 - 0.683936i) q^{2} +(-3.37914 + 26.7877i) q^{3} +(-45.5630 - 16.5836i) q^{4} +(-43.1394 - 51.4115i) q^{5} +(31.4281 - 101.593i) q^{6} +(424.254 - 154.416i) q^{7} +(383.689 + 221.523i) q^{8} +(-706.163 - 181.039i) q^{9} +(132.167 + 228.919i) q^{10} +(1154.19 - 1375.51i) q^{11} +(598.200 - 1164.49i) q^{12} +(-488.827 - 2772.27i) q^{13} +(-1751.20 + 308.785i) q^{14} +(1522.97 - 981.879i) q^{15} +(1040.43 + 873.024i) q^{16} +(-5946.51 + 3433.22i) q^{17} +(2615.24 + 1185.18i) q^{18} +(4951.44 - 8576.15i) q^{19} +(1112.97 + 3057.87i) q^{20} +(2702.83 + 11886.6i) q^{21} +(-5417.64 + 4545.94i) q^{22} +(-4137.47 + 11367.6i) q^{23} +(-7230.63 + 9529.59i) q^{24} +(1931.12 - 10951.9i) q^{25} +11087.4i q^{26} +(7235.83 - 18304.7i) q^{27} -21891.1 q^{28} +(-9212.78 - 1624.46i) q^{29} +(-6578.84 + 2766.89i) q^{30} +(17964.5 + 6538.56i) q^{31} +(-21664.7 - 25819.0i) q^{32} +(32946.7 + 35566.2i) q^{33} +(25413.4 - 9249.72i) q^{34} +(-26240.8 - 15150.1i) q^{35} +(29172.7 + 19959.4i) q^{36} +(-26288.7 - 45533.4i) q^{37} +(-25071.2 + 29878.7i) q^{38} +(75914.7 - 3726.66i) q^{39} +(-5163.27 - 29282.4i) q^{40} +(72041.3 - 12702.8i) q^{41} +(-2354.07 - 47954.2i) q^{42} +(-31061.0 - 26063.2i) q^{43} +(-75399.5 + 43531.9i) q^{44} +(21156.0 + 44114.8i) q^{45} +(23823.1 - 41262.8i) q^{46} +(-29328.7 - 80579.8i) q^{47} +(-26902.1 + 24920.7i) q^{48} +(66022.7 - 55399.6i) q^{49} +(-14980.8 + 41159.4i) q^{50} +(-71874.0 - 170895. i) q^{51} +(-23701.8 + 134420. i) q^{52} +44983.7i q^{53} +(-40585.6 + 66051.5i) q^{54} -120508. q^{55} +(196988. + 34734.3i) q^{56} +(213004. + 161618. i) q^{57} +(34623.5 + 12601.9i) q^{58} +(-17011.3 - 20273.3i) q^{59} +(-85674.3 + 19481.1i) q^{60} +(110077. - 40064.7i) q^{61} +(-65208.9 - 37648.4i) q^{62} +(-327547. + 32236.3i) q^{63} +(22912.6 + 39685.7i) q^{64} +(-121439. + 144726. i) q^{65} +(-103468. - 160488. i) q^{66} +(77205.6 + 437855. i) q^{67} +(327876. - 57813.4i) q^{68} +(-290531. - 149246. i) q^{69} +(91421.0 + 76711.3i) q^{70} +(-31019.4 + 17909.1i) q^{71} +(-230843. - 225894. i) q^{72} +(-132848. + 230100. i) q^{73} +(70826.7 + 194595. i) q^{74} +(286851. + 88738.1i) q^{75} +(-367826. + 308643. i) q^{76} +(277270. - 761792. i) q^{77} +(-297006. - 37465.9i) q^{78} +(68546.7 - 388748. i) q^{79} -91151.8i q^{80} +(465891. + 255686. i) q^{81} -288121. q^{82} +(769521. + 135687. i) q^{83} +(73972.9 - 586411. i) q^{84} +(433036. + 157612. i) q^{85} +(102654. + 122338. i) q^{86} +(74646.8 - 241300. i) q^{87} +(747558. - 272089. i) q^{88} +(-746055. - 430735. i) q^{89} +(-51888.0 - 185582. i) q^{90} +(-635469. - 1.10067e6i) q^{91} +(377031. - 449328. i) q^{92} +(-235858. + 459134. i) q^{93} +(58648.4 + 332612. i) q^{94} +(-654515. + 115409. i) q^{95} +(764840. - 493102. i) q^{96} +(417556. + 350371. i) q^{97} +(-293978. + 169728. i) q^{98} +(-1.06407e6 + 762383. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Introduction

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