LMFDB - Embedded newform 43.6.c.a.36.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, 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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.13
Character	$\chi$	$=$	43.36
Dual form			43.6.c.a.6.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.50187 q^{2} +(14.9934 + 25.9693i) q^{3} -11.7331 q^{4} +(16.1936 + 28.0482i) q^{5} +(67.4982 + 116.910i) q^{6} +(70.7811 - 122.596i) q^{7} -196.881 q^{8} +(-328.101 + 568.288i) q^{9} +O(q^{10})$	\(q+4.50187 q^{2} +(14.9934 + 25.9693i) q^{3} -11.7331 q^{4} +(16.1936 + 28.0482i) q^{5} +(67.4982 + 116.910i) q^{6} +(70.7811 - 122.596i) q^{7} -196.881 q^{8} +(-328.101 + 568.288i) q^{9} +(72.9017 + 126.269i) q^{10} +210.154 q^{11} +(-175.919 - 304.701i) q^{12} +(55.4098 - 95.9727i) q^{13} +(318.647 - 551.914i) q^{14} +(-485.594 + 841.073i) q^{15} -510.873 q^{16} +(856.791 - 1484.01i) q^{17} +(-1477.07 + 2558.36i) q^{18} +(1234.85 + 2138.82i) q^{19} +(-190.002 - 329.093i) q^{20} +4244.98 q^{21} +946.087 q^{22} +(1245.82 + 2157.82i) q^{23} +(-2951.91 - 5112.85i) q^{24} +(1038.03 - 1797.92i) q^{25} +(249.448 - 432.057i) q^{26} -12390.6 q^{27} +(-830.483 + 1438.44i) q^{28} +(2343.61 - 4059.25i) q^{29} +(-2186.08 + 3786.41i) q^{30} +(-3511.19 - 6081.57i) q^{31} +4000.31 q^{32} +(3150.92 + 5457.55i) q^{33} +(3857.16 - 6680.80i) q^{34} +4584.81 q^{35} +(3849.66 - 6667.80i) q^{36} +(-3163.28 - 5478.96i) q^{37} +(5559.14 + 9628.70i) q^{38} +3323.12 q^{39} +(-3188.22 - 5522.16i) q^{40} -6712.78 q^{41} +19110.4 q^{42} +(-7752.06 + 9322.77i) q^{43} -2465.77 q^{44} -21252.6 q^{45} +(5608.52 + 9714.24i) q^{46} -387.683 q^{47} +(-7659.71 - 13267.0i) q^{48} +(-1616.42 - 2799.72i) q^{49} +(4673.09 - 8094.03i) q^{50} +51384.7 q^{51} +(-650.131 + 1126.06i) q^{52} +(-2288.98 - 3964.63i) q^{53} -55780.9 q^{54} +(3403.16 + 5894.45i) q^{55} +(-13935.4 + 24136.9i) q^{56} +(-37029.1 + 64136.2i) q^{57} +(10550.6 - 18274.2i) q^{58} -4215.23 q^{59} +(5697.54 - 9868.42i) q^{60} +(7571.41 - 13114.1i) q^{61} +(-15806.9 - 27378.4i) q^{62} +(46446.7 + 80448.1i) q^{63} +34356.8 q^{64} +3589.15 q^{65} +(14185.0 + 24569.2i) q^{66} +(-10931.4 - 18933.8i) q^{67} +(-10052.8 + 17412.0i) q^{68} +(-37358.0 + 64705.9i) q^{69} +20640.2 q^{70} +(17902.9 - 31008.7i) q^{71} +(64596.9 - 111885. i) q^{72} +(-33982.9 + 58860.1i) q^{73} +(-14240.7 - 24665.6i) q^{74} +62254.3 q^{75} +(-14488.6 - 25095.1i) q^{76} +(14874.9 - 25764.1i) q^{77} +14960.3 q^{78} +(-27601.2 + 47806.7i) q^{79} +(-8272.90 - 14329.1i) q^{80} +(-106048. - 183680. i) q^{81} -30220.1 q^{82} +(-47576.4 - 82404.8i) q^{83} -49806.9 q^{84} +55498.2 q^{85} +(-34898.8 + 41969.9i) q^{86} +140554. q^{87} -41375.4 q^{88} +(12679.5 + 21961.6i) q^{89} -95676.6 q^{90} +(-7843.94 - 13586.1i) q^{91} +(-14617.3 - 25318.0i) q^{92} +(105289. - 182366. i) q^{93} -1745.30 q^{94} +(-39993.4 + 69270.6i) q^{95} +(59978.0 + 103885. i) q^{96} +46119.0 q^{97} +(-7276.91 - 12604.0i) q^{98} +(-68951.9 + 119428. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) $ 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	4.50187			0.795826			0.397913	−	0.917423i	$-0.369735\pi$
$2$	4.50187			0.795826			0.397913	+	0.917423i	$0.369735\pi$
$3$	14.9934	+	25.9693i	0.961824	+	1.66593i	0.717916	+	0.696130i	$0.245096\pi$
$3$	14.9934	+	25.9693i	0.961824	+	1.66593i	0.243908	+	0.969798i	$0.421570\pi$
$4$	−11.7331			−0.366660
$5$	16.1936	+	28.0482i	0.289681	+	0.501741i	0.973733	−	0.227691i	$-0.0731176\pi$
$5$	16.1936	+	28.0482i	0.289681	+	0.501741i	−0.684053	+	0.729432i	$0.739784\pi$
$6$	67.4982	+	116.910i	0.765445	+	1.32579i
$7$	70.7811	−	122.596i	0.545974	−	0.945655i	−0.452571	−	0.891728i	$-0.649493\pi$
$7$	70.7811	−	122.596i	0.545974	−	0.945655i	0.998545	−	0.0539263i	$-0.0171736\pi$
$8$	−196.881			−1.08762
$9$	−328.101	+	568.288i	−1.35021	+	2.33863i
$10$	72.9017	+	126.269i	0.230535	+	0.399299i
$11$	210.154			0.523668			0.261834	−	0.965113i	$-0.415673\pi$
$11$	210.154			0.523668			0.261834	+	0.965113i	$0.415673\pi$
$12$	−175.919	−	304.701i	−0.352663	−	0.610830i
$13$	55.4098	−	95.9727i	0.0909345	−	0.157503i	−0.816970	−	0.576680i	$-0.804348\pi$
$13$	55.4098	−	95.9727i	0.0909345	−	0.157503i	0.907905	+	0.419177i	$0.137681\pi$
$14$	318.647	−	551.914i	0.434501	−	0.752577i
$15$	−485.594	+	841.073i	−0.557243	+	0.965174i
$16$	−510.873			−0.498900
$17$	856.791	−	1484.01i	0.719039	−	1.24541i	−0.242342	−	0.970191i	$-0.577916\pi$
$17$	856.791	−	1484.01i	0.719039	−	1.24541i	0.961381	−	0.275221i	$-0.0887511\pi$
$18$	−1477.07	+	2558.36i	−1.07453	+	1.86115i
$19$	1234.85	+	2138.82i	0.784747	+	1.35922i	0.929150	+	0.369703i	$0.120541\pi$
$19$	1234.85	+	2138.82i	0.784747	+	1.35922i	−0.144402	+	0.989519i	$0.546126\pi$
$20$	−190.002	−	329.093i	−0.106214	−	0.183969i
$21$	4244.98			2.10052
$22$	946.087			0.416749
$23$	1245.82	+	2157.82i	0.491061	+	0.850542i	0.999947	−	0.0102917i	$-0.00327600\pi$
$23$	1245.82	+	2157.82i	0.491061	+	0.850542i	−0.508886	+	0.860834i	$0.669943\pi$
$24$	−2951.91	−	5112.85i	−1.04610	−	1.81190i
$25$	1038.03	−	1797.92i	0.332170	−	0.575336i
$26$	249.448	−	432.057i	0.0723681	−	0.125345i
$27$	−12390.6			−3.27101
$28$	−830.483	+	1438.44i	−0.200187	+	0.346734i
$29$	2343.61	−	4059.25i	0.517476	−	0.896295i	−0.482318	−	0.875996i	$-0.660205\pi$
$29$	2343.61	−	4059.25i	0.517476	−	0.896295i	0.999794	−	0.0202989i	$-0.00646178\pi$
$30$	−2186.08	+	3786.41i	−0.443469	+	0.768111i
$31$	−3511.19	−	6081.57i	−0.656222	−	1.13661i	−0.981586	−	0.191020i	$-0.938820\pi$
$31$	−3511.19	−	6081.57i	−0.656222	−	1.13661i	0.325364	−	0.945589i	$-0.394513\pi$
$32$	4000.31			0.690587
$33$	3150.92	+	5457.55i	0.503677	+	0.872394i
$34$	3857.16	−	6680.80i	0.572230	−	0.991132i
$35$	4584.81			0.632632
$36$	3849.66	−	6667.80i	0.495069	−	0.857484i
$37$	−3163.28	−	5478.96i	−0.379868	−	0.657951i	0.611174	−	0.791496i	$-0.290697\pi$
$37$	−3163.28	−	5478.96i	−0.379868	−	0.657951i	−0.991043	+	0.133545i	$0.957364\pi$
$38$	5559.14	+	9628.70i	0.624523	+	1.08171i
$39$	3323.12			0.349852
$40$	−3188.22	−	5522.16i	−0.315064	−	0.545706i
$41$	−6712.78			−0.623652			−0.311826	−	0.950139i	$-0.600941\pi$
$41$	−6712.78			−0.623652			−0.311826	+	0.950139i	$0.600941\pi$
$42$	19110.4			1.67165
$43$	−7752.06	+	9322.77i	−0.639361	+	0.768907i
$43$	−7752.06	+	9322.77i	−0.639361	+	0.768907i
$44$	−2465.77			−0.192008
$45$	−21252.6			−1.56452
$46$	5608.52	+	9714.24i	0.390799	+	0.676884i
$47$	−387.683			−0.0255995			−0.0127998	−	0.999918i	$-0.504074\pi$
$47$	−387.683			−0.0255995			−0.0127998	+	0.999918i	$0.504074\pi$
$48$	−7659.71	−	13267.0i	−0.479854	−	0.831131i
$49$	−1616.42	−	2799.72i	−0.0961753	−	0.166580i
$50$	4673.09	−	8094.03i	0.264350	−	0.457868i
$51$	51384.7			2.76636
$52$	−650.131	+	1126.06i	−0.0333421	+	0.0577502i
$53$	−2288.98	−	3964.63i	−0.111931	−	0.193871i	0.804617	−	0.593793i	$-0.202370\pi$
$53$	−2288.98	−	3964.63i	−0.111931	−	0.193871i	−0.916549	+	0.399922i	$0.869037\pi$
$54$	−55780.9			−2.60316
$55$	3403.16	+	5894.45i	0.151697	+	0.262746i
$56$	−13935.4	+	24136.9i	−0.593815	+	1.02852i
$57$	−37029.1	+	64136.2i	−1.50958	+	2.61467i
$58$	10550.6	−	18274.2i	0.411821	−	0.713295i
$59$	−4215.23			−0.157649			−0.0788246	−	0.996889i	$-0.525117\pi$
$59$	−4215.23			−0.157649			−0.0788246	+	0.996889i	$0.525117\pi$
$60$	5697.54	−	9868.42i	0.204319	−	0.353891i
$61$	7571.41	−	13114.1i	0.260527	−	0.451246i	−0.705855	−	0.708356i	$-0.749437\pi$
$61$	7571.41	−	13114.1i	0.260527	−	0.451246i	0.966382	+	0.257110i	$0.0827704\pi$
$62$	−15806.9	−	27378.4i	−0.522238	−	0.904544i
$63$	46446.7	+	80448.1i	1.47436	+	2.55367i
$64$	34356.8			1.04849
$65$	3589.15			0.105368
$66$	14185.0	+	24569.2i	0.400839	+	0.694274i
$67$	−10931.4	−	18933.8i	−0.297502	−	0.515288i	0.678062	−	0.735005i	$-0.262820\pi$
$67$	−10931.4	−	18933.8i	−0.297502	−	0.515288i	−0.975564	+	0.219717i	$0.929487\pi$
$68$	−10052.8	+	17412.0i	−0.263643	+	0.456643i
$69$	−37358.0	+	64705.9i	−0.944628	+	1.63614i
$70$	20640.2			0.503465
$71$	17902.9	−	31008.7i	0.421480	−	0.730024i	−0.574605	−	0.818431i	$-0.694844\pi$
$71$	17902.9	−	31008.7i	0.421480	−	0.730024i	0.996084	+	0.0884069i	$0.0281776\pi$
$72$	64596.9	−	111885.i	1.46852	−	2.54356i
$73$	−33982.9	+	58860.1i	−0.746368	+	1.29275i	0.203185	+	0.979140i	$0.434871\pi$
$73$	−33982.9	+	58860.1i	−0.746368	+	1.29275i	−0.949553	+	0.313607i	$0.898463\pi$
$74$	−14240.7	−	24665.6i	−0.302309	−	0.523615i
$75$	62254.3			1.27796
$76$	−14488.6	−	25095.1i	−0.287736	−	0.498373i
$77$	14874.9	−	25764.1i	0.285909	−	0.495209i
$78$	14960.3			0.278421
$79$	−27601.2	+	47806.7i	−0.497577	+	0.861828i	−0.999996	−	0.00279596i	$-0.999110\pi$
$79$	−27601.2	+	47806.7i	−0.497577	+	0.861828i	0.502419	+	0.864624i	$0.332443\pi$
$80$	−8272.90	−	14329.1i	−0.144522	−	0.250319i
$81$	−106048.	−	183680.i	−1.79593	−	3.11064i
$82$	−30220.1			−0.496319
$83$	−47576.4	−	82404.8i	−0.758048	−	1.31298i	−0.943845	−	0.330389i	$-0.892820\pi$
$83$	−47576.4	−	82404.8i	−0.758048	−	1.31298i	0.185797	−	0.982588i	$-0.440513\pi$
$84$	−49806.9			−0.770179
$85$	55498.2			0.833167
$86$	−34898.8	+	41969.9i	−0.508820	+	0.611916i
$87$	140554.			1.99088
$88$	−41375.4			−0.569554
$89$	12679.5	+	21961.6i	0.169679	+	0.293893i	0.938307	−	0.345803i	$-0.112394\pi$
$89$	12679.5	+	21961.6i	0.169679	+	0.293893i	−0.768628	+	0.639696i	$0.779060\pi$
$90$	−95676.6			−1.24509
$91$	−7843.94	−	13586.1i	−0.0992957	−	0.171985i
$92$	−14617.3	−	25318.0i	−0.180052	−	0.311860i
$93$	105289.	−	182366.i	1.26234	−	2.18644i
$94$	−1745.30			−0.0203728
$95$	−39993.4	+	69270.6i	−0.454652	+	0.787481i
$96$	59978.0	+	103885.i	0.664223	+	1.15047i
$97$	46119.0			0.497681			0.248840	−	0.968545i	$-0.419951\pi$
$97$	46119.0			0.497681			0.248840	+	0.968545i	$0.419951\pi$
$98$	−7276.91	−	12604.0i	−0.0765388	−	0.132569i
$99$	−68951.9	+	119428.i	−0.707063	+	1.22467i
$100$	−12179.4	+	21095.3i	−0.121794	+	0.210953i
$101$	−40509.8	+	70165.1i	−0.395145	+	0.684412i	−0.993120	−	0.117103i	$-0.962639\pi$
$101$	−40509.8	+	70165.1i	−0.395145	+	0.684412i	0.597974	+	0.801515i	$0.295972\pi$
$102$	231327.			2.20154
$103$	−12319.0	+	21337.2i	−0.114415	+	0.198173i	−0.917546	−	0.397630i	$-0.869833\pi$
$103$	−12319.0	+	21337.2i	−0.114415	+	0.198173i	0.803131	+	0.595803i	$0.203166\pi$
$104$	−10909.1	+	18895.2i	−0.0989026	+	0.171304i
$105$	68741.7	+	119064.i	0.608481	+	1.05392i
$106$	−10304.7	−	17848.3i	−0.0890780	−	0.154288i
$107$	−26768.6			−0.226030			−0.113015	−	0.993593i	$-0.536051\pi$
$107$	−26768.6			−0.226030			−0.113015	+	0.993593i	$0.536051\pi$
$108$	145380.			1.19935
$109$	−32214.4	−	55797.0i	−0.259707	−	0.449826i	0.706456	−	0.707757i	$-0.250293\pi$
$109$	−32214.4	−	55797.0i	−0.259707	−	0.449826i	−0.966163	+	0.257931i	$0.916959\pi$
$110$	15320.6	+	26536.1i	0.120724	+	0.209100i
$111$	94856.3	−	164296.i	0.730733	−	1.26567i
$112$	−36160.2	+	62631.2i	−0.272386	+	0.471787i
$113$	−231849.			−1.70808			−0.854040	−	0.520207i	$-0.825855\pi$
$113$	−231849.			−1.70808			−0.854040	+	0.520207i	$0.825855\pi$
$114$	−166700.	+	288733.i	−1.20136	+	2.08082i
$115$	−40348.7	+	69885.9i	−0.284501	+	0.492771i
$116$	−27497.9	+	47627.7i	−0.189738	+	0.328636i
$117$	36360.1	+	62977.5i	0.245562	+	0.425325i
$118$	−18976.5			−0.125461
$119$	−121289.	−	210079.i	−0.785153	−	1.35993i
$120$	95604.2	−	165591.i	0.606072	−	1.04975i
$121$	−116886.			−0.725772
$122$	34085.6	−	59037.9i	0.207334	−	0.359113i
$123$	−100647.	−	174326.i	−0.599844	−	1.03896i
$124$	41197.3	+	71355.8i	0.240610	+	0.416749i
$125$	168448.			0.964254
$126$	209097.	+	362167.i	1.17334	+	2.03228i
$127$	294993.			1.62294			0.811470	−	0.584395i	$-0.198668\pi$
$127$	294993.			1.62294			0.811470	+	0.584395i	$0.198668\pi$
$128$	26660.3			0.143827
$129$	−358335.	−	61535.6i	−1.89590	−	0.325576i
$130$	16157.9			0.0838545
$131$	−249024.			−1.26783			−0.633917	−	0.773401i	$-0.718554\pi$
$131$	−249024.			−1.26783			−0.633917	+	0.773401i	$0.718554\pi$
$132$	−36970.1	−	64034.1i	−0.184678	−	0.319872i
$133$	349616.			1.71381
$134$	−49211.8	−	85237.4i	−0.236760	−	0.410080i
$135$	−200649.	−	347534.i	−0.947549	−	1.64120i
$136$	−168686.	+	292172.i	−0.782044	+	1.35454i
$137$	42854.8			0.195073			0.0975366	−	0.995232i	$-0.468904\pi$
$137$	42854.8			0.195073			0.0975366	+	0.995232i	$0.468904\pi$
$138$	−168181.	+	291298.i	−0.751760	+	1.30209i
$139$	45377.5	+	78596.2i	0.199207	+	0.345036i	0.948271	−	0.317461i	$-0.102830\pi$
$139$	45377.5	+	78596.2i	0.199207	+	0.345036i	−0.749065	+	0.662497i	$0.769497\pi$
$140$	−53794.2			−0.231961
$141$	−5812.67	−	10067.8i	−0.0246223	−	0.0426470i
$142$	80596.4	−	139597.i	0.335425	−	0.580972i
$143$	11644.6	−	20169.1i	0.0476195	−	0.0824794i
$144$	167618.	−	290323.i	0.673620	−	1.16674i
$145$	151806.			0.599611
$146$	−152987.	+	264981.i	−0.593979	+	1.02880i
$147$	48471.1	−	83954.3i	0.185007	−	0.320442i
$148$	37115.2	+	64285.4i	0.139283	+	0.241245i
$149$	−198480.	−	343777.i	−0.732403	−	1.26856i	−0.955853	−	0.293844i	$-0.905065\pi$
$149$	−198480.	−	343777.i	−0.732403	−	1.26856i	0.223450	−	0.974715i	$-0.428268\pi$
$150$	280261.			1.01703
$151$	439517.			1.56867			0.784337	−	0.620334i	$-0.213003\pi$
$151$	439517.			1.56867			0.784337	+	0.620334i	$0.213003\pi$
$152$	−243118.	−	421093.i	−0.853510	−	1.47832i
$153$	562228.	+	973808.i	1.94171	+	3.36314i
$154$	66965.1	−	115987.i	0.227534	−	0.394101i
$155$	113718.	−	196965.i	0.380189	−	0.658507i
$156$	−38990.6			−0.128277
$157$	−136893.	+	237106.i	−0.443234	+	0.767704i	−0.997927	−	0.0643508i	$-0.979502\pi$
$157$	−136893.	+	237106.i	−0.443234	+	0.767704i	0.554693	+	0.832055i	$0.312836\pi$
$158$	−124257.	+	215220.i	−0.395985	+	0.685866i
$159$	68639.0	−	118886.i	0.215317	−	0.372940i
$160$	64779.5	+	112201.i	0.200050	+	0.346496i
$161$	352721.			1.07243
$162$	−477414.	−	826905.i	−1.42925	−	2.47553i
$163$	23534.1	−	40762.2i	0.0693790	−	0.120168i	−0.829249	−	0.558879i	$-0.811232\pi$
$163$	23534.1	−	40762.2i	0.0693790	−	0.120168i	0.898628	+	0.438711i	$0.144565\pi$
$164$	78761.9			0.228669
$165$	−102050.	+	176755.i	−0.291811	+	0.505431i
$166$	−214183.	−	370976.i	−0.603274	−	1.04490i
$167$	−29585.2	−	51243.1i	−0.0820887	−	0.142182i	0.822058	−	0.569403i	$-0.192826\pi$
$167$	−29585.2	−	51243.1i	−0.0820887	−	0.142182i	−0.904147	+	0.427222i	$0.859492\pi$
$168$	−835757.			−2.28458
$169$	179506.	+	310914.i	0.483462	+	0.837380i
$170$	249846.			0.663056
$171$	−1.62062e6			−4.23830
$172$	90955.9	−	109385.i	0.234428	−	0.281928i
$173$	−127692.			−0.324377			−0.162188	−	0.986760i	$-0.551855\pi$
$173$	−127692.			−0.324377			−0.162188	+	0.986760i	$0.551855\pi$
$174$	632758.			1.58440
$175$	−146946.	−	254518.i	−0.362713	−	0.628237i
$176$	−107362.			−0.261258
$177$	−63200.5	−	109466.i	−0.151631	−	0.262632i
$178$	57081.6	+	98868.3i	0.135035	+	0.233888i
$179$	370148.	−	641116.i	0.863462	−	1.49556i	−0.00510484	−	0.999987i	$-0.501625\pi$
$179$	370148.	−	641116.i	0.863462	−	1.49556i	0.868567	−	0.495573i	$-0.165042\pi$
$180$	249360.			0.573647
$181$	66917.0	−	115904.i	0.151824	−	0.262966i	−0.780074	−	0.625687i	$-0.784819\pi$
$181$	66917.0	−	115904.i	0.151824	−	0.262966i	0.931898	+	0.362721i	$0.118152\pi$
$182$	−35312.4	−	61162.9i	−0.0790222	−	0.136870i
$183$	454084.			1.00232
$184$	−245278.	−	424834.i	−0.534090	−	0.925070i
$185$	102450.	−	177449.i	0.220081	−	0.381191i
$186$	473998.	−	820989.i	1.00460	−	1.74002i
$187$	180058.	−	311870.i	0.376538	−	0.652183i
$188$	4548.74			0.00938634
$189$	−877019.	+	1.51904e6i	−1.78589	+	3.09325i
$190$	−180045.	+	311847.i	−0.361824	+	0.626698i
$191$	422070.	+	731047.i	0.837147	+	1.44998i	0.892271	+	0.451501i	$0.149111\pi$
$191$	422070.	+	731047.i	0.837147	+	1.44998i	−0.0551241	+	0.998480i	$0.517555\pi$
$192$	515124.	+	892221.i	1.00846	+	1.74670i
$193$	917747.			1.77349			0.886747	−	0.462256i	$-0.152960\pi$
$193$	917747.			1.77349			0.886747	+	0.462256i	$0.152960\pi$
$194$	207622.			0.396067
$195$	53813.4	+	93207.5i	0.101345	+	0.175535i
$196$	18965.6	+	32849.5i	0.0352637	+	0.0610785i
$197$	−211802.	+	366852.i	−0.388835	+	0.673482i	−0.992293	−	0.123913i	$-0.960456\pi$
$197$	−211802.	+	366852.i	−0.388835	+	0.673482i	0.603458	+	0.797395i	$0.293789\pi$
$198$	−310413.	+	537650.i	−0.562699	+	0.974624i
$199$	823770.			1.47460			0.737298	−	0.675568i	$-0.236101\pi$
$199$	823770.			1.47460			0.737298	+	0.675568i	$0.236101\pi$
$200$	−204369.	+	353977.i	−0.361277	+	0.625749i
$201$	327797.	−	567761.i	0.572288	−	0.991233i
$202$	−182370.	+	315874.i	−0.314467	+	0.544673i
$203$	−331767.	−	574636.i	−0.565057	−	0.978708i
$204$	−602903.			−1.01431
$205$	−108704.	−	188281.i	−0.180660	−	0.312912i
$206$	−55458.7	+	96057.4i	−0.0910546	+	0.157711i
$207$	−1.63502e6			−2.65214
$208$	−28307.4	+	49029.9i	−0.0453672	+	0.0785783i
$209$	259509.	+	449482.i	0.410947	+	0.711782i
$210$	309466.	+	536012.i	0.484245	+	0.838737i
$211$	−156088.			−0.241358			−0.120679	−	0.992692i	$-0.538507\pi$
$211$	−156088.			−0.241358			−0.120679	+	0.992692i	$0.538507\pi$
$212$	26856.9	+	46517.5i	0.0410408	+	0.0710848i
$213$	1.07370e6			1.62156
$214$	−120509.			−0.179881
$215$	−387021.	−	66461.8i	−0.571003	−	0.0980564i
$216$	2.43947e6			3.55764
$217$	−994104.			−1.43312
$218$	−145025.	−	251191.i	−0.206682	−	0.357983i
$219$	−2.03807e6			−2.87150
$220$	−39929.7	−	69160.3i	−0.0556211	−	0.0963386i
$221$	−94949.3	−	164457.i	−0.130771	−	0.226502i
$222$	427031.	−	739640.i	0.581537	−	1.00725i
$223$	−488086.			−0.657256			−0.328628	−	0.944459i	$-0.606586\pi$
$223$	−488086.			−0.657256			−0.328628	+	0.944459i	$0.606586\pi$
$224$	283146.	−	490423.i	0.377042	−	0.653057i
$225$	681160.	+	1.17980e6i	0.897000	+	1.55365i
$226$	−1.04375e6			−1.35934
$227$	102520.	+	177570.i	0.132052	+	0.228720i	0.924467	−	0.381261i	$-0.124510\pi$
$227$	102520.	+	177570.i	0.132052	+	0.228720i	−0.792416	+	0.609982i	$0.791177\pi$
$228$	434467.	−	752519.i	0.553502	−	0.958694i
$229$	−287489.	+	497946.i	−0.362271	+	0.627471i	−0.988334	−	0.152301i	$-0.951332\pi$
$229$	−287489.	+	497946.i	−0.362271	+	0.627471i	0.626063	+	0.779772i	$0.284665\pi$
$230$	−181645.	+	314618.i	−0.226414	+	0.392160i
$231$	892101.			1.09998
$232$	−461413.	+	799190.i	−0.562820	+	0.974833i
$233$	−375407.	+	650224.i	−0.453015	+	0.784645i	−0.998572	−	0.0534287i	$-0.982985\pi$
$233$	−375407.	+	650224.i	−0.453015	+	0.784645i	0.545556	+	0.838074i	$0.316318\pi$
$234$	163689.	+	283517.i	0.195424	+	0.338485i
$235$	−6278.00	−	10873.8i	−0.00741569	−	0.0128444i
$236$	49457.9			0.0578037
$237$	−1.65534e6			−1.91432
$238$	−546028.	−	945749.i	−0.624846	−	1.08226i
$239$	687748.	+	1.19121e6i	0.778815	+	1.34895i	0.932625	+	0.360847i	$0.117512\pi$
$239$	687748.	+	1.19121e6i	0.778815	+	1.34895i	−0.153810	+	0.988100i	$0.549154\pi$
$240$	248077.	−	429682.i	0.278009	−	0.481525i
$241$	267091.	−	462615.i	0.296222	−	0.513071i	−0.679047	−	0.734095i	$-0.737607\pi$
$241$	267091.	−	462615.i	0.296222	−	0.513071i	0.975268	+	0.221024i	$0.0709400\pi$
$242$	−526207.			−0.577588
$243$	1.67457e6	−	2.90044e6i	1.81923	−	3.15100i
$244$	−88836.4	+	153869.i	−0.0955248	+	0.165454i
$245$	52351.4	−	90675.2i	0.0557202	−	0.0965103i
$246$	−453100.	−	784793.i	−0.477372	−	0.826832i
$247$	273691.			0.285442
$248$	691287.	+	1.19734e6i	0.713723	+	1.23620i
$249$	1.42666e6	−	2.47105e6i	1.45822	−	2.52571i
$250$	758333.			0.767379
$251$	631904.	−	1.09449e6i	0.633092	−	1.09655i	−0.353824	−	0.935312i	$-0.615119\pi$
$251$	631904.	−	1.09449e6i	0.633092	−	1.09655i	0.986916	−	0.161236i	$-0.0515479\pi$
$252$	−544965.	−	943908.i	−0.540590	−	0.936329i
$253$	261814.	+	453475.i	0.257153	+	0.445402i
$254$	1.32802e6			1.29158
$255$	832105.	+	1.44125e6i	0.801360	+	1.38800i
$256$	−979397.			−0.934026
$257$	−452785.			−0.427621			−0.213810	−	0.976875i	$-0.568587\pi$
$257$	−452785.			−0.427621			−0.213810	+	0.976875i	$0.568587\pi$
$258$	−1.61318e6	−	277026.i	−1.50880	−	0.259102i
$259$	−895601.			−0.829593
$260$	−42111.9			−0.0386342
$261$	1.53788e6	+	2.66369e6i	1.39740	+	2.42038i
$262$	−1.12107e6			−1.00898
$263$	−353630.	−	612506.i	−0.315254	−	0.546035i	0.664238	−	0.747521i	$-0.268756\pi$
$263$	−353630.	−	612506.i	−0.315254	−	0.546035i	−0.979491	+	0.201486i	$0.935423\pi$
$264$	−620356.	−	1.07449e6i	−0.547811	−	0.948837i
$265$	74133.8	−	128404.i	0.0648487	−	0.112321i
$266$	1.57393e6			1.36389
$267$	−380217.	+	658556.i	−0.326403	+	0.565346i
$268$	128260.	+	222152.i	0.109082	+	0.188936i
$269$	−1.55694e6			−1.31188			−0.655938	−	0.754815i	$-0.727727\pi$
$269$	−1.55694e6			−1.31188			−0.655938	+	0.754815i	$0.727727\pi$
$270$	−903295.	−	1.56455e6i	−0.754085	−	1.30611i
$271$	−876.913	+	1518.86i	−0.000725326	+	0.00125630i	−0.866388	−	0.499372i	$-0.833564\pi$
$271$	−876.913	+	1518.86i	−0.000725326	+	0.00125630i	0.865663	+	0.500628i	$0.166898\pi$
$272$	−437712.	+	758139.i	−0.358729	+	0.621336i
$273$	235214.	−	407402.i	0.191010	−	0.330839i
$274$	192927.			0.155244
$275$	218147.	−	377841.i	0.173947	−	0.301285i
$276$	438326.	−	759203.i	0.346358	−	0.599909i
$277$	−825896.	−	1.43049e6i	−0.646734	−	1.12018i	−0.983898	−	0.178731i	$-0.942801\pi$
$277$	−825896.	−	1.43049e6i	−0.646734	−	1.12018i	0.337164	−	0.941446i	$-0.390532\pi$
$278$	204284.	+	353830.i	0.158534	+	0.274589i
$279$	4.60811e6			3.54415
$280$	−902662.			−0.688066
$281$	207535.	+	359461.i	0.156793	+	0.271573i	0.933710	−	0.358029i	$-0.116551\pi$
$281$	207535.	+	359461.i	0.156793	+	0.271573i	−0.776918	+	0.629602i	$0.783218\pi$
$282$	−26167.9	−	45324.1i	−0.0195950	−	0.0339396i
$283$	−71948.6	+	124619.i	−0.0534018	+	0.0924947i	−0.891491	−	0.453039i	$-0.850340\pi$
$283$	−71948.6	+	124619.i	−0.0534018	+	0.0924947i	0.838089	+	0.545534i	$0.183673\pi$
$284$	−210057.	+	363829.i	−0.154540	+	0.267671i
$285$	−2.39854e6			−1.74918
$286$	52422.6	−	90798.5i	0.0378969	−	0.0656393i
$287$	−475137.	+	822962.i	−0.340498	+	0.589760i
$288$	−1.31251e6	+	2.27333e6i	−0.932438	+	1.61503i
$289$	−758252.	−	1.31333e6i	−0.534034	−	0.924975i
$290$	683413.			0.477187
$291$	691479.	+	1.19768e6i	0.478681	+	0.829100i
$292$	398725.	−	690613.i	0.273663	−	0.473999i
$293$	−264184.			−0.179778			−0.0898891	−	0.995952i	$-0.528651\pi$
$293$	−264184.			−0.179778			−0.0898891	+	0.995952i	$0.528651\pi$
$294$	218211.	−	377952.i	0.147234	−	0.255016i
$295$	−68260.0	−	118230.i	−0.0456679	−	0.0790991i
$296$	622790.	+	1.07870e6i	0.413154	+	0.715604i
$297$	−2.60393e6			−1.71293
$298$	−893530.	−	1.54764e6i	−0.582866	−	1.00955i
$299$	276122.			0.178617
$300$	−730438.			−0.468576
$301$	594239.	+	1.61025e6i	0.378046	+	1.02442i
$302$	1.97865e6			1.24839
$303$	−2.42951e6			−1.52024
$304$	−630852.	−	1.09267e6i	−0.391510	−	0.678116i
$305$	490435.			0.301878
$306$	2.53108e6	+	4.38396e6i	1.54526	+	2.67647i
$307$	1.31865e6	+	2.28397e6i	0.798515	+	1.38307i	0.920583	+	0.390547i	$0.127714\pi$
$307$	1.31865e6	+	2.28397e6i	0.798515	+	1.38307i	−0.122067	+	0.992522i	$0.538952\pi$
$308$	−174530.	+	302294.i	−0.104832	+	0.181574i
$309$	−738815.			−0.440189
$310$	511944.	−	886713.i	0.302565	−	0.524057i
$311$	−548242.	−	949583.i	−0.321419	−	0.556714i	0.659362	−	0.751825i	$-0.270826\pi$
$311$	−548242.	−	949583.i	−0.321419	−	0.556714i	−0.980781	+	0.195112i	$0.937493\pi$
$312$	−654259.			−0.380507
$313$	249547.	+	432229.i	0.143977	+	0.249375i	0.928991	−	0.370103i	$-0.120678\pi$
$313$	249547.	+	432229.i	0.143977	+	0.249375i	−0.785014	+	0.619478i	$0.787344\pi$
$314$	−616277.	+	1.06742e6i	−0.352738	+	0.610959i
$315$	−1.50428e6	+	2.60549e6i	−0.854187	+	1.47950i
$316$	323848.	−	560922.i	0.182442	−	0.315998i
$317$	127005.			0.0709858			0.0354929	−	0.999370i	$-0.488700\pi$
$317$	127005.			0.0709858			0.0354929	+	0.999370i	$0.488700\pi$
$318$	309004.	−	535211.i	0.171355	−	0.296795i
$319$	492520.	−	853069.i	0.270986	−	0.469361i
$320$	556362.	+	963647.i	0.303726	+	0.526069i
$321$	−401352.	−	695162.i	−0.217402	−	0.376551i
$322$	1.58791e6			0.853465
$323$	4.23203e6			2.25706
$324$	1.24427e6	+	2.15514e6i	0.658496	+	1.14055i
$325$	−115034.	−	199245.i	−0.0604115	−	0.104636i
$326$	105947.	−	183506.i	0.0552136	−	0.0956328i
$327$	966004.	−	1.67317e6i	0.499585	−	0.865307i
$328$	1.32162e6			0.678299
$329$	−27440.6	+	47528.5i	−0.0139767	+	0.0242083i
$330$	−459414.	+	795729.i	−0.232231	+	0.402235i
$331$	−384809.	+	666509.i	−0.193052	+	0.334376i	−0.946260	−	0.323406i	$-0.895172\pi$
$331$	−384809.	+	666509.i	−0.193052	+	0.334376i	0.753208	+	0.657782i	$0.228505\pi$
$332$	558220.	+	966866.i	0.277946	+	0.481417i
$333$	4.15150e6			2.05161
$334$	−133189.	−	230690.i	−0.0653283	−	0.113152i
$335$	354039.	−	613213.i	0.172361	−	0.298538i
$336$	−2.16865e6			−1.04795
$337$	−1.48812e6	+	2.57750e6i	−0.713777	+	1.23630i	0.249652	+	0.968336i	$0.419684\pi$
$337$	−1.48812e6	+	2.57750e6i	−0.713777	+	1.23630i	−0.963429	+	0.267963i	$0.913650\pi$
$338$	808113.	+	1.39969e6i	0.384752	+	0.666409i
$339$	−3.47619e6	−	6.02093e6i	−1.64287	−	2.84554i
$340$	−651168.			−0.305489
$341$	−737892.	−	1.27807e6i	−0.343642	−	0.595206i
$342$	−7.29584e6			−3.37295
$343$	1.92159e6			0.881911
$344$	1.52623e6	−	1.83548e6i	0.695384	−	0.836282i
$345$	−2.41985e6			−1.09456
$346$	−574855.			−0.258147
$347$	−1.12629e6	−	1.95079e6i	−0.502141	−	0.869734i	−0.999997	−	0.00247401i	$-0.999212\pi$
$347$	−1.12629e6	−	1.95079e6i	−0.502141	−	0.869734i	0.497856	−	0.867260i	$-0.334121\pi$
$348$	−1.64914e6			−0.729978
$349$	−1.12608e6	−	1.95043e6i	−0.494888	−	0.857171i	0.505095	−	0.863064i	$-0.331458\pi$
$349$	−1.12608e6	−	1.95043e6i	−0.494888	−	0.857171i	−0.999983	+	0.00589279i	$0.998124\pi$
$350$	−661533.	−	1.14581e6i	−0.288656	−	0.499968i
$351$	−686561.	+	1.18916e6i	−0.297448	+	0.515195i
$352$	840681.			0.361638
$353$	−657037.	+	1.13802e6i	−0.280642	+	0.486087i	−0.971543	−	0.236863i	$-0.923881\pi$
$353$	−657037.	+	1.13802e6i	−0.280642	+	0.486087i	0.690901	+	0.722950i	$0.257214\pi$
$354$	−284521.	−	492804.i	−0.120672	−	0.209010i
$355$	1.15965e6			0.488378
$356$	−148771.	−	257678.i	−0.0622146	−	0.107759i
$357$	3.63706e6	−	6.29958e6i	1.51036	−	2.61602i
$358$	1.66636e6	−	2.88622e6i	0.687166	−	1.19021i
$359$	−1.62892e6	+	2.82137e6i	−0.667057	+	1.15538i	0.311666	+	0.950192i	$0.399113\pi$
$359$	−1.62892e6	+	2.82137e6i	−0.667057	+	1.15538i	−0.978723	+	0.205185i	$0.934220\pi$
$360$	4.18424e6			1.70161
$361$	−1.81166e6	+	3.13788e6i	−0.731657	+	1.26727i
$362$	301252.	−	521783.i	0.120825	−	0.209276i
$363$	−1.75252e6	−	3.03545e6i	−0.698065	−	1.20908i
$364$	92033.9	+	159407.i	0.0364078	+	0.0630602i
$365$	−2.20123e6			−0.864833
$366$	2.04423e6			0.797676
$367$	746594.	+	1.29314e6i	0.289347	+	0.501164i	0.973654	−	0.228030i	$-0.0732284\pi$
$367$	746594.	+	1.29314e6i	0.289347	+	0.501164i	−0.684307	+	0.729194i	$0.739895\pi$
$368$	−636456.	−	1.10237e6i	−0.244990	−	0.424335i
$369$	2.20247e6	−	3.81479e6i	0.842062	−	1.45849i
$370$	461217.	−	798851.i	0.175146	−	0.303362i
$371$	−648066.			−0.244447
$372$	−1.23537e6	+	2.13973e6i	−0.462850	+	0.801679i
$373$	1.00052e6	−	1.73295e6i	0.372351	−	0.644930i	−0.617576	−	0.786511i	$-0.711885\pi$
$373$	1.00052e6	−	1.73295e6i	0.372351	−	0.644930i	0.989927	+	0.141581i	$0.0452185\pi$
$374$	810599.	−	1.40400e6i	0.299659	−	0.519024i
$375$	2.52560e6	+	4.37448e6i	0.927443	+	1.60638i
$376$	76327.4			0.0278427
$377$	−259718.	−	449845.i	−0.0941129	−	0.163008i
$378$	−3.94823e6	+	6.83853e6i	−1.42126	+	2.46169i
$379$	−2.97080e6			−1.06237			−0.531185	−	0.847256i	$-0.678253\pi$
$379$	−2.97080e6			−1.06237			−0.531185	+	0.847256i	$0.678253\pi$
$380$	469248.	−	812761.i	0.166703	−	0.288738i
$381$	4.42293e6	+	7.66074e6i	1.56098	+	2.70370i
$382$	1.90011e6	+	3.29108e6i	0.666223	+	1.15393i
$383$	−5.20130e6			−1.81182			−0.905909	−	0.423472i	$-0.860811\pi$
$383$	−5.20130e6			−1.81182			−0.905909	+	0.423472i	$0.860811\pi$
$384$	399728.	+	692348.i	0.138336	+	0.239605i
$385$	963517.			0.331289
$386$	4.13158e6			1.41139
$387$	−2.75456e6	−	7.46422e6i	−0.934920	−	2.53342i
$388$	−541120.			−0.182480
$389$	4.14019e6			1.38722			0.693611	−	0.720349i	$-0.256019\pi$
$389$	4.14019e6			1.38722			0.693611	+	0.720349i	$0.256019\pi$
$390$	242261.	+	419608.i	0.0806533	+	0.139696i
$391$	4.26962e6			1.41237
$392$	318242.	+	551211.i	0.104603	+	0.181177i
$393$	−3.73370e6	−	6.46696e6i	−1.21943	−	2.11212i
$394$	−953508.	+	1.65152e6i	−0.309445	+	0.535975i
$395$	−1.78785e6			−0.576553
$396$	809021.	−	1.40127e6i	0.259252	−	0.449037i
$397$	101940.	+	176566.i	0.0324615	+	0.0562250i	0.881800	−	0.471624i	$-0.156332\pi$
$397$	101940.	+	176566.i	0.0324615	+	0.0562250i	−0.849338	+	0.527849i	$0.822999\pi$
$398$	3.70851e6			1.17352
$399$	5.24191e6	+	9.07926e6i	1.64838	+	2.85508i
$400$	−530303.	+	918512.i	−0.165720	+	0.287035i
$401$	−281928.	+	488313.i	−0.0875542	+	0.151648i	−0.906477	−	0.422256i	$-0.861238\pi$
$401$	−281928.	+	488313.i	−0.0875542	+	0.151648i	0.818923	+	0.573904i	$0.194572\pi$
$402$	1.47570e6	−	2.55599e6i	0.455442	−	0.788849i
$403$	−778219.			−0.238693
$404$	475307.	−	823256.i	0.144884	−	0.250947i
$405$	3.43460e6	−	5.94890e6i	1.04049	−	1.80218i
$406$	−1.49357e6	−	2.58694e6i	−0.449688	−	0.778882i
$407$	−664776.	−	1.15143e6i	−0.198925	−	0.344548i
$408$	−1.01167e7			−3.00876
$409$	1.34992e6			0.399024			0.199512	−	0.979895i	$-0.436064\pi$
$409$	1.34992e6			0.399024			0.199512	+	0.979895i	$0.436064\pi$
$410$	−489373.	−	847619.i	−0.143774	−	0.249024i
$411$	642537.	+	1.11291e6i	0.187626	+	0.324978i
$412$	144541.	−	250352.i	0.0419515	−	0.0726621i
$413$	−298359.	+	516773.i	−0.0860723	+	0.149082i
$414$	−7.36065e6			−2.11065
$415$	1.54087e6	−	2.66887e6i	0.439183	−	0.760688i
$416$	221656.	−	383920.i	0.0627981	−	0.108770i
$417$	−1.36072e6	+	2.35684e6i	−0.383204	+	0.663728i
$418$	1.16828e6	+	2.02351e6i	0.327043	+	0.566455i
$419$	−1.87823e6			−0.522654			−0.261327	−	0.965250i	$-0.584160\pi$
$419$	−1.87823e6			−0.522654			−0.261327	+	0.965250i	$0.584160\pi$
$420$	−806555.	−	1.39699e6i	−0.223106	−	0.386431i
$421$	−2.02916e6	+	3.51461e6i	−0.557970	+	0.966433i	0.439695	+	0.898147i	$0.355086\pi$
$421$	−2.02916e6	+	3.51461e6i	−0.557970	+	0.966433i	−0.997666	+	0.0682860i	$0.978247\pi$
$422$	−702686.			−0.192079
$423$	127199.	−	220316.i	0.0345648	−	0.0598680i
$424$	450657.	+	780560.i	0.121739	+	0.210859i
$425$	−1.77875e6	−	3.08089e6i	−0.477687	−	0.827378i
$426$	4.83364e6			1.29048
$427$	−1.07183e6	−	1.85646e6i	−0.284482	−	0.492737i
$428$	314080.			0.0828764
$429$	698367.			0.183206
$430$	−1.74232e6	−	299203.i	−0.454419	−	0.0780359i
$431$	−429481.			−0.111366			−0.0556828	−	0.998449i	$-0.517734\pi$
$431$	−429481.			−0.111366			−0.0556828	+	0.998449i	$0.517734\pi$
$432$	6.33002e6			1.63191
$433$	1.81463e6	+	3.14303e6i	0.465123	+	0.805616i	0.999207	−	0.0398149i	$-0.0126768\pi$
$433$	1.81463e6	+	3.14303e6i	0.465123	+	0.805616i	−0.534084	+	0.845431i	$0.679344\pi$
$434$	−4.47533e6			−1.14051
$435$	2.27609e6	+	3.94230e6i	0.576721	+	0.998909i
$436$	377976.	+	654673.i	0.0952243	+	0.164933i
$437$	−3.07680e6	+	5.32917e6i	−0.770717	+	1.33492i
$438$	−9.17513e6			−2.28521
$439$	−952359.	+	1.64954e6i	−0.235852	+	0.408508i	−0.959520	−	0.281641i	$-0.909121\pi$
$439$	−952359.	+	1.64954e6i	−0.235852	+	0.408508i	0.723668	+	0.690148i	$0.242455\pi$
$440$	−670018.	−	1.16050e6i	−0.164989	−	0.285769i
$441$	2.12140e6			0.519428
$442$	−427450.	−	740365.i	−0.104071	−	0.180256i
$443$	1.40962e6	−	2.44153e6i	0.341265	−	0.591088i	−0.643403	−	0.765528i	$-0.722478\pi$
$443$	1.40962e6	−	2.44153e6i	0.341265	−	0.591088i	0.984668	+	0.174440i	$0.0558114\pi$
$444$	−1.11296e6	+	1.92771e6i	−0.267931	+	0.464070i
$445$	−410655.	+	711276.i	−0.0983054	+	0.170270i
$446$	−2.19730e6			−0.523062
$447$	5.95175e6	−	1.03087e7i	1.40889	−	2.44026i
$448$	2.43181e6	−	4.21202e6i	0.572447	−	0.991507i
$449$	17293.3	+	29952.8i	0.00404819	+	0.00701167i	0.868042	−	0.496490i	$-0.165378\pi$
$449$	17293.3	+	29952.8i	0.00404819	+	0.00701167i	−0.863994	+	0.503502i	$0.832045\pi$
$450$	3.06649e6	+	5.31132e6i	0.713857	+	1.23644i
$451$	−1.41072e6			−0.326587
$452$	2.72031e6			0.626285
$453$	6.58983e6	+	1.14139e7i	1.50879	+	2.61330i
$454$	461533.	+	799398.i	0.105090	+	0.182022i
$455$	254044.	−	440017.i	0.0575281	−	0.0996416i
$456$	7.29032e6	−	1.26272e7i	1.64185	−	2.84377i
$457$	758865.			0.169971			0.0849853	−	0.996382i	$-0.472916\pi$
$457$	758865.			0.169971			0.0849853	+	0.996382i	$0.472916\pi$
$458$	−1.29424e6	+	2.24169e6i	−0.288305	+	0.499358i
$459$	−1.06161e7	+	1.83877e7i	−2.35199	+	4.07376i
$460$	473416.	−	819981.i	0.104315	−	0.180680i
$461$	−546759.	−	947015.i	−0.119824	−	0.207541i	0.799874	−	0.600168i	$-0.204900\pi$
$461$	−546759.	−	947015.i	−0.119824	−	0.207541i	−0.919698	+	0.392627i	$0.871566\pi$
$462$	4.01612e6			0.875391
$463$	−2.02307e6	−	3.50405e6i	−0.438589	−	0.759658i	0.558992	−	0.829173i	$-0.311188\pi$
$463$	−2.02307e6	−	3.50405e6i	−0.438589	−	0.759658i	−0.997581	+	0.0695150i	$0.977855\pi$
$464$	−1.19729e6	+	2.07376e6i	−0.258169	+	0.447162i
$465$	6.82006e6			1.46270
$466$	−1.69004e6	+	2.92723e6i	−0.360521	+	0.624441i
$467$	−1.82627e6	−	3.16319e6i	−0.387501	−	0.671171i	0.604612	−	0.796520i	$-0.293328\pi$
$467$	−1.82627e6	−	3.16319e6i	−0.387501	−	0.671171i	−0.992113	+	0.125349i	$0.959995\pi$
$468$	−426618.	−	738923.i	−0.0900377	−	0.155950i
$469$	−3.09495e6			−0.649713
$470$	−28262.8	−	48952.5i	−0.00590160	−	0.0102219i
$471$	−8.20996e6			−1.70525
$472$	829900.			0.171463
$473$	−1.62913e6	+	1.95922e6i	−0.334813	+	0.402652i
$474$	−7.45212e6			−1.52347
$475$	5.12725e6			1.04268
$476$	1.42310e6	+	2.46488e6i	0.287885	+	0.498631i
$477$	3.00407e6			0.604525
$478$	3.09615e6	+	5.36269e6i	0.619802	+	1.07353i
$479$	−55147.4	−	95518.1i	−0.0109821	−	0.0190216i	0.860482	−	0.509481i	$-0.170162\pi$
$479$	−55147.4	−	95518.1i	−0.0109821	−	0.0190216i	−0.871464	+	0.490459i	$0.836829\pi$
$480$	−1.94252e6	+	3.36455e6i	−0.384825	+	0.666536i
$481$	−701107.			−0.138173
$482$	1.20241e6	−	2.08264e6i	0.235741	−	0.408315i
$483$	5.28848e6	+	9.15991e6i	1.03148	+	1.78658i
$484$	1.37144e6			0.266112
$485$	746835.	+	1.29356e6i	0.144168	+	0.249707i
$486$	7.53870e6	−	1.30574e7i	1.44779	−	2.50765i
$487$	−518118.	+	897407.i	−0.0989934	+	0.171462i	−0.911268	−	0.411813i	$-0.864896\pi$
$487$	−518118.	+	897407.i	−0.0989934	+	0.171462i	0.812275	+	0.583275i	$0.198229\pi$
$488$	−1.49067e6	+	2.58191e6i	−0.283355	+	0.490786i
$489$	1.41142e6			0.266922
$490$	235679.	−	408208.i	0.0443436	−	0.0768054i
$491$	−751775.	+	1.30211e6i	−0.140729	+	0.243750i	−0.927771	−	0.373149i	$-0.878278\pi$
$491$	−751775.	+	1.30211e6i	−0.140729	+	0.243750i	0.787042	+	0.616899i	$0.211611\pi$
$492$	1.18090e6	+	2.04539e6i	0.219939	+	0.380945i
$493$	−4.01597e6	−	6.95586e6i	−0.744171	−	1.28894i
$494$	1.23212e6			0.227163
$495$	−4.46632e6			−0.819289
$496$	1.79378e6	+	3.10691e6i	0.327389	+	0.567054i
$497$	−2.53437e6	−	4.38965e6i	−0.460234	−	0.797148i
$498$	6.42264e6	−	1.11243e7i	1.16049	−	2.01002i
$499$	4.01702e6	−	6.95768e6i	0.722192	−	1.25087i	−0.237927	−	0.971283i	$-0.576468\pi$
$499$	4.01702e6	−	6.95768e6i	0.722192	−	1.25087i	0.960119	−	0.279590i	$-0.0901986\pi$
$500$	−1.97643e6			−0.353554
$501$	887163.	−	1.53661e6i	0.157910	−	0.273508i
$502$	2.84475e6	−	4.92726e6i	0.503831	−	0.872662i
$503$	1.27805e6	−	2.21364e6i	0.225230	−	0.390110i	−0.731158	−	0.682208i	$-0.761020\pi$
$503$	1.27805e6	−	2.21364e6i	0.225230	−	0.390110i	0.956388	+	0.292098i	$0.0943533\pi$
$504$	−9.14448e6	−	1.58387e7i	−1.60355	−	2.77743i
$505$	−2.62400e6			−0.457864
$506$	1.17865e6	+	2.04149e6i	0.204649	+	0.354463i
$507$	−5.38279e6	+	9.32327e6i	−0.930011	+	1.61083i
$508$	−3.46119e6			−0.595067
$509$	514010.	−	890291.i	0.0879381	−	0.152313i	−0.818701	−	0.574220i	$-0.805306\pi$
$509$	514010.	−	890291.i	0.0879381	−	0.152313i	0.906639	+	0.421906i	$0.138639\pi$
$510$	3.74603e6	+	6.48831e6i	0.637743	+	1.10460i
$511$	4.81069e6	+	8.33236e6i	0.814995	+	1.41161i
$512$	−5.26225e6			−0.887149
$513$	−1.53005e7	−	2.65013e7i	−2.56692	−	4.44604i
$514$	−2.03838e6			−0.340312
$515$	−797960.			−0.132575
$516$	4.20439e6	+	722005.i	0.695150	+	0.119376i
$517$	−81473.2			−0.0134057
$518$	−4.03188e6			−0.660212
$519$	−1.91454e6	−	3.31607e6i	−0.311993	−	0.540388i
$520$	−706635.			−0.114601
$521$	−1.03132e6	−	1.78631e6i	−0.166457	−	0.288311i	0.770715	−	0.637180i	$-0.219899\pi$
$521$	−1.03132e6	−	1.78631e6i	−0.166457	−	0.288311i	−0.937172	+	0.348869i	$0.886566\pi$
$522$	6.92336e6	+	1.19916e7i	1.11209	+	1.92620i
$523$	−1.83339e6	+	3.17552e6i	−0.293089	+	0.507645i	−0.974539	−	0.224220i	$-0.928017\pi$
$523$	−1.83339e6	+	3.17552e6i	−0.293089	+	0.507645i	0.681449	+	0.731865i	$0.261350\pi$
$524$	2.92183e6			0.464865
$525$	4.40643e6	−	7.63216e6i	0.697732	−	1.20851i
$526$	−1.59200e6	−	2.75742e6i	−0.250887	−	0.434549i
$527$	−1.20334e7			−1.88740
$528$	−1.60972e6	−	2.78812e6i	−0.251284	−	0.435237i
$529$	114045.	−	197531.i	0.0177189	−	0.0306900i
$530$	333741.	−	578056.i	0.0516083	−	0.0893883i
$531$	1.38302e6	−	2.39547e6i	0.212860	−	0.368684i
$532$	−4.10209e6			−0.628385
$533$	−371954.	+	644243.i	−0.0567115	+	0.0982272i
$534$	−1.71169e6	+	2.96473e6i	−0.259760	+	0.449917i
$535$	−433482.	−	750812.i	−0.0654766	−	0.113409i
$536$	2.15219e6	+	3.72770e6i	0.323570	+	0.560440i
$537$	2.21991e7			3.32199
$538$	−7.00917e6			−1.04402
$539$	−339697.	−	588372.i	−0.0503639	−	0.0872329i
$540$	2.35424e6	+	4.07766e6i	0.347429	+	0.601764i
$541$	−6.03703e6	+	1.04564e7i	−0.886809	+	1.53600i	−0.0431826	+	0.999067i	$0.513750\pi$
$541$	−6.03703e6	+	1.04564e7i	−0.886809	+	1.53600i	−0.843626	+	0.536931i	$0.819584\pi$
$542$	−3947.75	+	6837.70i	−0.000577233	+	0.000999798i
$543$	4.01324e6			0.584111
$544$	3.42742e6	−	5.93647e6i	0.496559	−	0.860065i
$545$	1.04334e6	−	1.80711e6i	0.150464	−	0.260612i
$546$	1.05890e6	−	1.83407e6i	0.152011	−	0.263291i
$547$	2.83747e6	+	4.91463e6i	0.405473	+	0.702300i	0.994376	−	0.105903i	$-0.0337734\pi$
$547$	2.83747e6	+	4.91463e6i	0.405473	+	0.702300i	−0.588903	+	0.808204i	$0.700440\pi$
$548$	−502820.			−0.0715256
$549$	4.96838e6	+	8.60549e6i	0.703532	+	1.21855i
$550$	982069.	−	1.70099e6i	0.138432	−	0.239771i
$551$	1.15760e7			1.62435
$552$	7.35508e6	−	1.27394e7i	1.02740	−	1.77951i
$553$	3.90728e6	+	6.76761e6i	0.543328	+	0.941072i
$554$	−3.71808e6	−	6.43990e6i	−0.514688	−	0.891466i
$555$	6.14428e6			0.846717
$556$	−532421.	−	922179.i	−0.0730412	−	0.126511i
$557$	−3.95353e6			−0.539942			−0.269971	−	0.962869i	$-0.587014\pi$
$557$	−3.95353e6			−0.539942			−0.269971	+	0.962869i	$0.587014\pi$
$558$	2.07451e7			2.82053
$559$	465191.	+	1.26056e6i	0.0629653	+	0.170621i
$560$	−2.34226e6			−0.315620
$561$	1.07987e7			1.44865
$562$	934297.	+	1.61825e6i	0.124780	+	0.216125i
$563$	−1.08927e6			−0.144832			−0.0724158	−	0.997375i	$-0.523071\pi$
$563$	−1.08927e6			−0.144832			−0.0724158	+	0.997375i	$0.523071\pi$
$564$	68200.8	+	118127.i	0.00902800	+	0.0156370i
$565$	−3.75447e6	−	6.50293e6i	−0.494798	−	0.857015i
$566$	−323903.	+	561017.i	−0.0424986	+	0.0736097i
$567$	−3.00247e7			−3.92212
$568$	−3.52473e6	+	6.10502e6i	−0.458412	+	0.793992i
$569$	−1.80004e6	−	3.11777e6i	−0.233078	−	0.403704i	0.725634	−	0.688081i	$-0.241547\pi$
$569$	−1.80004e6	−	3.11777e6i	−0.233078	−	0.403704i	−0.958713	+	0.284377i	$0.908213\pi$
$570$	−1.07979e7			−1.39204
$571$	−800294.	−	1.38615e6i	−0.102721	−	0.177918i	0.810084	−	0.586314i	$-0.199422\pi$
$571$	−800294.	−	1.38615e6i	−0.102721	−	0.177918i	−0.912805	+	0.408396i	$0.866088\pi$
$572$	−136628.	+	236646.i	−0.0174602	+	0.0302419i
$573$	−1.26565e7	+	2.19217e7i	−1.61038	+	2.78925i
$574$	−2.13901e6	+	3.70487e6i	−0.270977	+	0.469346i
$575$	5.17280e6			0.652463
$576$	−1.12725e7	+	1.95246e7i	−1.41568	+	2.45203i
$577$	−313362.	+	542760.i	−0.0391839	+	0.0678685i	−0.884952	−	0.465682i	$-0.845809\pi$
$577$	−313362.	+	542760.i	−0.0391839	+	0.0678685i	0.845768	+	0.533550i	$0.179142\pi$
$578$	−3.41356e6	−	5.91245e6i	−0.424999	−	0.736119i
$579$	1.37601e7	+	2.38332e7i	1.70579	+	2.95451i
$580$	−1.78116e6			−0.219854
$581$	−1.34700e7			−1.65550
$582$	3.11295e6	+	5.39179e6i	0.380947	+	0.659820i
$583$	−481039.	−	833183.i	−0.0586150	−	0.101524i
$584$	6.69058e6	−	1.15884e7i	0.811768	−	1.40602i
$585$	−1.17760e6	+	2.03967e6i	−0.142269	+	0.246417i
$586$	−1.18932e6			−0.143072
$587$	6.38144e6	−	1.10530e7i	0.764405	−	1.32399i	−0.176155	−	0.984362i	$-0.556366\pi$
$587$	6.38144e6	−	1.10530e7i	0.764405	−	1.32399i	0.940560	−	0.339626i	$-0.110301\pi$
$588$	−568717.	+	985047.i	−0.0678349	+	0.117493i
$589$	8.67159e6	−	1.50196e7i	1.02994	−	1.78390i
$590$	−307298.	−	532255.i	−0.0363437	−	0.0629492i
$591$	−1.27025e7			−1.49596
$592$	1.61604e6	+	2.79906e6i	0.189516	+	0.328252i
$593$	2.24669e6	−	3.89139e6i	0.262366	−	0.454431i	−0.704504	−	0.709700i	$-0.748831\pi$
$593$	2.24669e6	−	3.89139e6i	0.262366	−	0.454431i	0.966870	+	0.255269i	$0.0821640\pi$
$594$	−1.17226e7			−1.36319
$595$	3.92822e6	−	6.80388e6i	0.454887	−	0.787888i
$596$	2.32879e6	+	4.03358e6i	0.268543	+	0.465130i
$597$	1.23511e7	+	2.13927e7i	1.41830	+	2.45657i
$598$	1.24307e6			0.142148
$599$	4.90505e6	+	8.49580e6i	0.558568	+	0.967469i	0.997616	+	0.0690052i	$0.0219825\pi$
$599$	4.90505e6	+	8.49580e6i	0.558568	+	0.967469i	−0.439048	+	0.898464i	$0.644684\pi$
$600$	−1.22567e7			−1.38994
$601$	−3.88842e6			−0.439123			−0.219562	−	0.975599i	$-0.570463\pi$
$601$	−3.88842e6			−0.439123			−0.219562	+	0.975599i	$0.570463\pi$
$602$	2.67519e6	+	7.24914e6i	0.300859	+	0.815259i
$603$	1.43464e7			1.60676
$604$	−5.15691e6			−0.575171
$605$	−1.89281e6	−	3.27845e6i	−0.210242	−	0.364150i
$606$	−1.09374e7			−1.20985
$607$	1.54809e6	+	2.68137e6i	0.170539	+	0.295382i	0.938608	−	0.344984i	$-0.112116\pi$
$607$	1.54809e6	+	2.68137e6i	0.170539	+	0.295382i	−0.768069	+	0.640367i	$0.778782\pi$
$608$	4.93977e6	+	8.55594e6i	0.541936	+	0.938661i
$609$	9.94859e6	−	1.72315e7i	1.08697	−	1.88269i
$610$	2.20788e6			0.240243
$611$	−21481.5	+	37207.0i	−0.00232788	+	0.00403201i
$612$	−6.59670e6	−	1.14258e7i	−0.711948	−	1.23313i
$613$	2.93469e6			0.315436			0.157718	−	0.987484i	$-0.449586\pi$
$613$	2.93469e6			0.315436			0.157718	+	0.987484i	$0.449586\pi$
$614$	5.93639e6	+	1.02821e7i	0.635480	+	1.10068i
$615$	3.25968e6	−	5.64594e6i	0.347526	−	0.601933i
$616$	−2.92859e6	+	5.07247e6i	−0.310962	+	0.538602i
$617$	1.41770e6	−	2.45553e6i	0.149924	−	0.259676i	−0.781275	−	0.624187i	$-0.785430\pi$
$617$	1.41770e6	−	2.45553e6i	0.149924	−	0.259676i	0.931199	+	0.364511i	$0.118764\pi$
$618$	−3.32605e6			−0.350314
$619$	2.43317e6	−	4.21437e6i	0.255238	−	0.442086i	−0.709722	−	0.704482i	$-0.751179\pi$
$619$	2.43317e6	−	4.21437e6i	0.255238	−	0.442086i	0.964960	+	0.262396i	$0.0845128\pi$
$620$	−1.33427e6	+	2.31102e6i	−0.139400	+	0.241448i
$621$	−1.54364e7	−	2.67367e7i	−1.60627	−	2.78214i
$622$	−2.46812e6	−	4.27490e6i	−0.255794	−	0.443048i
$623$	3.58988e6			0.370561
$624$	−1.69769e6			−0.174541
$625$	−516061.	−	893844.i	−0.0528446	−	0.0915296i
$626$	1.12343e6	+	1.94584e6i	0.114580	+	0.198459i
$627$	−7.78181e6	+	1.34785e7i	−0.790518	+	1.36922i
$628$	1.60619e6	−	2.78200e6i	0.162516	−	0.281487i
$629$	−1.08411e7			−1.09256
$630$	−6.77209e6	+	1.17296e7i	−0.679785	+	1.17742i
$631$	4.58232e6	−	7.93682e6i	0.458155	−	0.793548i	−0.540709	−	0.841210i	$-0.681844\pi$
$631$	4.58232e6	−	7.93682e6i	0.458155	−	0.793548i	0.998864	+	0.0476624i	$0.0151771\pi$
$632$	5.43415e6	−	9.41222e6i	0.541177	−	0.937345i
$633$	−2.34028e6	−	4.05348e6i	−0.232144	−	0.402085i
$634$	571759.			0.0564924
$635$	4.77701e6	+	8.27402e6i	0.470134	+	0.814296i
$636$	−805350.	+	1.39491e6i	−0.0789481	+	0.136742i
$637$	−358262.			−0.0349826
$638$	2.21726e6	−	3.84041e6i	0.215658	−	0.373530i
$639$	1.17479e7	+	2.03480e7i	1.13817	+	1.97137i
$640$	431727.	+	747774.i	0.0416639	+	0.0721639i
$641$	−1.54253e7			−1.48282			−0.741410	−	0.671052i	$-0.765843\pi$
$641$	−1.54253e7			−1.48282			−0.741410	+	0.671052i	$0.765843\pi$
$642$	−1.80684e6	−	3.12953e6i	−0.173014	−	0.299669i
$643$	5.30616e6			0.506119			0.253060	−	0.967451i	$-0.418563\pi$
$643$	5.30616e6			0.506119			0.253060	+	0.967451i	$0.418563\pi$
$644$	−4.13853e6			−0.393216
$645$	−4.07678e6	−	1.10471e7i	−0.385849	−	1.04556i
$646$	1.90521e7			1.79622
$647$	1.50038e7			1.40909			0.704547	−	0.709657i	$-0.251150\pi$
$647$	1.50038e7			1.40909			0.704547	+	0.709657i	$0.251150\pi$
$648$	2.08788e7	+	3.61632e7i	1.95330	+	3.38321i
$649$	−885849.			−0.0825559
$650$	−517871.	−	896978.i	−0.0480770	−	0.0832719i
$651$	−1.49050e7	−	2.58161e7i	−1.37841	−	2.38747i
$652$	−276128.	+	478268.i	−0.0254385	+	0.0440608i
$653$	1.01911e7			0.935276			0.467638	−	0.883920i	$-0.345105\pi$
$653$	1.01911e7			0.935276			0.467638	+	0.883920i	$0.345105\pi$
$654$	4.34883e6	−	7.53239e6i	0.397583	−	0.688634i
$655$	−4.03260e6	−	6.98467e6i	−0.367267	−	0.636125i
$656$	3.42938e6			0.311140
$657$	−2.22997e7	−	3.86241e7i	−2.01551	−	3.49096i
$658$	−123534.	+	213968.i	−0.0111230	+	0.0192656i
$659$	6.22457e6	−	1.07813e7i	0.558337	−	0.967067i	−0.439299	−	0.898341i	$-0.644773\pi$
$659$	6.22457e6	−	1.07813e7i	0.558337	−	0.967067i	0.997636	−	0.0687264i	$-0.0218935\pi$
$660$	1.19736e6	−	2.07389e6i	0.106995	−	0.185321i
$661$	438191.			0.0390085			0.0195043	−	0.999810i	$-0.493791\pi$
$661$	438191.			0.0390085			0.0195043	+	0.999810i	$0.493791\pi$
$662$	−1.73236e6	+	3.00054e6i	−0.153636	+	0.266106i
$663$	2.84722e6	−	4.93152e6i	0.251557	−	0.435710i
$664$	9.36689e6	+	1.62239e7i	0.824471	+	1.42803i
$665$	5.66155e6	+	9.80609e6i	0.496457	+	0.859888i
$666$	1.86896e7			1.63273
$667$	1.16789e7			1.01645
$668$	347127.	+	601242.i	0.0300987	+	0.0521324i
$669$	−7.31805e6	−	1.26752e7i	−0.632164	−	1.09494i
$670$	1.59384e6	−	2.76061e6i	0.137169	−	0.237584i
$671$	1.59116e6	−	2.75598e6i	0.136430	−	0.236303i
$672$	1.69812e7			1.45059
$673$	−7.36179e6	+	1.27510e7i	−0.626536	+	1.08519i	0.361706	+	0.932292i	$0.382194\pi$
$673$	−7.36179e6	+	1.27510e7i	−0.626536	+	1.08519i	−0.988242	+	0.152900i	$0.951139\pi$
$674$	−6.69932e6	+	1.16036e7i	−0.568043	+	0.983879i
$675$	−1.28618e7	+	2.22773e7i	−1.08653	+	1.88193i
$676$	−2.10617e6	−	3.64799e6i	−0.177266	−	0.307034i
$677$	−1.16558e7			−0.977394			−0.488697	−	0.872454i	$-0.662528\pi$
$677$	−1.16558e7			−0.977394			−0.488697	+	0.872454i	$0.662528\pi$
$678$	−1.56494e7	−	2.71055e7i	−1.30744	−	2.26456i
$679$	3.26435e6	−	5.65403e6i	0.271721	−	0.470634i
$680$	−1.09265e7			−0.906172
$681$	−3.07424e6	+	5.32474e6i	−0.254021	+	0.439978i
$682$	−3.32190e6	−	5.75369e6i	−0.273480	−	0.473681i
$683$	−8.40764e6	−	1.45625e7i	−0.689640	−	1.19449i	−0.971954	−	0.235169i	$-0.924436\pi$
$683$	−8.40764e6	−	1.45625e7i	−0.689640	−	1.19449i	0.282315	−	0.959322i	$-0.408898\pi$
$684$	1.90150e7			1.55402
$685$	693974.	+	1.20200e6i	0.0565089	+	0.0978763i
$686$	8.65074e6			0.701848
$687$	−1.72417e7			−1.39376
$688$	3.96032e6	−	4.76276e6i	0.318977	−	0.383608i
$689$	−507328.			−0.0407137
$690$	−1.08938e7			−0.871081
$691$	4.87549e6	+	8.44460e6i	0.388440	+	0.672797i	0.992240	−	0.124339i	$-0.0396809\pi$
$691$	4.87549e6	+	8.44460e6i	0.388440	+	0.672797i	−0.603800	+	0.797136i	$0.706348\pi$
$692$	1.49823e6			0.118936
$693$	9.76097e6	+	1.69065e7i	0.772076	+	1.33727i
$694$	−5.07041e6	−	8.78220e6i	−0.399617	−	0.692157i
$695$	−1.46965e6	+	2.54552e6i	−0.115413	+	0.199900i
$696$	−2.76725e7			−2.16533
$697$	−5.75144e6	+	9.96179e6i	−0.448430	+	0.776704i
$698$	−5.06948e6	−	8.78061e6i	−0.393845	−	0.682159i
$699$	−2.25145e7			−1.74288
$700$	1.72414e6	+	2.98629e6i	0.132992	+	0.230350i
$701$	−658975.	+	1.14138e6i	−0.0506493	+	0.0877272i	−0.890239	−	0.455495i	$-0.849462\pi$
$701$	−658975.	+	1.14138e6i	−0.0506493	+	0.0877272i	0.839589	+	0.543222i	$0.182796\pi$
$702$	−3.09081e6	+	5.35344e6i	−0.236717	+	0.410006i
$703$	7.81235e6	−	1.35314e7i	0.596202	−	1.03265i
$704$	7.22023e6			0.549059
$705$	188256.	−	326070.i	0.0142652	−	0.0247080i
$706$	−2.95790e6	+	5.12323e6i	−0.223343	+	0.386841i
$707$	5.73466e6	+	9.93272e6i	0.431478	+	0.747342i
$708$	741540.	+	1.28438e6i	0.0555970	+	0.0962968i
$709$	2.10656e7			1.57383			0.786915	−	0.617062i	$-0.211677\pi$
$709$	2.10656e7			1.57383			0.786915	+	0.617062i	$0.211677\pi$
$710$	5.22060e6			0.388664
$711$	−1.81120e7	−	3.13709e7i	−1.34367	−	2.32730i
$712$	−2.49636e6	−	4.32382e6i	−0.184547	−	0.319645i
$713$	8.74862e6	−	1.51531e7i	0.644489	−	1.11629i
$714$	1.63736e7	−	2.83599e7i	1.20198	−	2.08190i
$715$	754274.			0.0551778
$716$	−4.34300e6	+	7.52229e6i	−0.316597	+	0.548362i
$717$	−2.06233e7	+	3.57206e7i	−1.49817	+	2.59490i
$718$	−7.33318e6	+	1.27014e7i	−0.530862	+	0.919479i
$719$	4.85807e6	+	8.41443e6i	0.350463	+	0.607019i	0.986331	−	0.164779i	$-0.0526910\pi$
$719$	4.85807e6	+	8.41443e6i	0.350463	+	0.607019i	−0.635868	+	0.771798i	$0.719358\pi$
$720$	1.08574e7			0.780539
$721$	1.74391e6	+	3.02054e6i	0.124935	+	0.216395i
$722$	−8.15584e6	+	1.41263e7i	−0.582272	+	1.00852i
$723$	1.60184e7			1.13965
$724$	−785145.	+	1.35991e6i	−0.0556677	+	0.0964194i
$725$	−4.86549e6	−	8.42727e6i	−0.343781	−	0.595445i
$726$	−7.88961e6	−	1.36652e7i	−0.555538	−	0.962220i
$727$	−1.67144e7			−1.17289			−0.586443	−	0.809991i	$-0.699472\pi$
$727$	−1.67144e7			−1.17289			−0.586443	+	0.809991i	$0.699472\pi$
$728$	1.54432e6	+	2.67484e6i	0.107996	+	0.187055i
$729$	4.88904e7			3.40726
$730$	−9.90964e6			−0.688257
$731$	7.19314e6	+	1.94918e7i	0.497881	+	1.34914i
$732$	−5.32782e6			−0.367512
$733$	−1.23889e7			−0.851675			−0.425837	−	0.904800i	$-0.640020\pi$
$733$	−1.23889e7			−0.851675			−0.425837	+	0.904800i	$0.640020\pi$
$734$	3.36107e6	+	5.82155e6i	0.230270	+	0.398840i
$735$	3.13969e6			0.214372
$736$	4.98365e6	+	8.63194e6i	0.339120	+	0.587373i
$737$	−2.29728e6	−	3.97901e6i	−0.155792	−	0.269840i
$738$	9.91525e6	−	1.71737e7i	0.670135	−	1.16071i
$739$	−1.77669e7			−1.19674			−0.598370	−	0.801220i	$-0.704185\pi$
$739$	−1.77669e7			−1.19674			−0.598370	+	0.801220i	$0.704185\pi$
$740$	−1.20206e6	+	2.08203e6i	−0.0806950	+	0.139768i
$741$	4.10355e6	+	7.10756e6i	0.274545	+	0.475527i
$742$	−2.91751e6			−0.194537
$743$	3.33508e6	+	5.77652e6i	0.221633	+	0.383879i	0.955304	−	0.295626i	$-0.0955281\pi$
$743$	3.33508e6	+	5.77652e6i	0.221633	+	0.383879i	−0.733671	+	0.679505i	$0.762195\pi$
$744$	−2.07294e7	+	3.59044e7i	−1.37295	+	2.37802i
$745$	6.42821e6	−	1.11340e7i	0.424326	−	0.734954i
$746$	4.50420e6	−	7.80150e6i	0.296327	−	0.513253i
$747$	6.24395e7			4.09410
$748$	−2.11265e6	+	3.65921e6i	−0.138062	+	0.239130i
$749$	−1.89471e6	+	3.28174e6i	−0.123407	+	0.213747i
$750$	1.13700e7	+	1.96933e7i	0.738084	+	1.27840i
$751$	−1.11318e7	−	1.92808e7i	−0.720220	−	1.24746i	−0.960911	−	0.276856i	$-0.910707\pi$
$751$	−1.11318e7	−	1.92808e7i	−0.720220	−	1.24746i	0.240691	−	0.970602i	$-0.422626\pi$
$752$	198057.			0.0127716
$753$	3.78974e7			2.43569
$754$	−1.16922e6	−	2.02515e6i	−0.0748975	−	0.129726i
$755$	7.11737e6	+	1.23277e7i	0.454415	+	0.787069i
$756$	1.02902e7	−	1.78231e7i	0.654815	−	1.13417i
$757$	−1.39106e7	+	2.40938e7i	−0.882278	+	1.52815i	−0.0334768	+	0.999439i	$0.510658\pi$
$757$	−1.39106e7	+	2.40938e7i	−0.882278	+	1.52815i	−0.848802	+	0.528712i	$0.822675\pi$
$758$	−1.33742e7			−0.845462
$759$	−7.85094e6	+	1.35982e7i	−0.494672	+	0.856796i
$760$	7.87394e6	−	1.36381e7i	0.494491	−	0.856483i
$761$	2.04069e6	−	3.53457e6i	0.127736	−	0.221246i	−0.795063	−	0.606527i	$-0.792562\pi$
$761$	2.04069e6	−	3.53457e6i	0.127736	−	0.221246i	0.922799	+	0.385281i	$0.125896\pi$
$762$	1.99115e7	+	3.44877e7i	1.24227	+	2.15168i
$763$	−9.12068e6			−0.567173
$764$	−4.95221e6	−	8.57747e6i	−0.306948	−	0.531650i
$765$	−1.82090e7	+	3.15390e7i	−1.12495	+	1.94847i
$766$	−2.34156e7			−1.44189
$767$	−233565.	+	404547.i	−0.0143357	+	0.0248302i
$768$	−1.46844e7	−	2.54342e7i	−0.898368	−	1.55602i
$769$	1.18867e7	+	2.05884e7i	0.724846	+	1.25547i	0.959037	+	0.283280i	$0.0914226\pi$
$769$	1.18867e7	+	2.05884e7i	0.724846	+	1.25547i	−0.234191	+	0.972191i	$0.575244\pi$
$770$	4.33763e6			0.263649
$771$	−6.78876e6	−	1.17585e7i	−0.411296	−	0.712386i
$772$	−1.07680e7			−0.650270
$773$	2.29871e7			1.38368			0.691840	−	0.722051i	$-0.256800\pi$
$773$	2.29871e7			1.38368			0.691840	+	0.722051i	$0.256800\pi$
$774$	−1.24007e7	−	3.36030e7i	−0.744034	−	2.01616i
$775$	−1.45789e7			−0.871909
$776$	−9.07996e6			−0.541290
$777$	−1.34281e7	−	2.32581e7i	−0.797923	−	1.38204i
$778$	1.86386e7			1.10399
$779$	−8.28927e6	−	1.43574e7i	−0.489410	−	0.847682i
$780$	−631399.	−	1.09362e6i	−0.0371593	−	0.0643618i
$781$	3.76236e6	−	6.51660e6i	0.220716	−	0.382290i
$782$	1.92213e7			1.12400
$783$	−2.90387e7	+	5.02965e7i	−1.69267	+	2.93180i
$784$	825785.	+	1.43030e6i	0.0479818	+	0.0831070i
$785$	−8.86721e6			−0.513585
$786$	−1.68087e7	−	2.91135e7i	−0.970458	−	1.68088i
$787$	2.23108e6	−	3.86434e6i	0.128404	−	0.222402i	−0.794655	−	0.607062i	$-0.792348\pi$
$787$	2.23108e6	−	3.86434e6i	0.128404	−	0.222402i	0.923058	+	0.384660i	$0.125681\pi$
$788$	2.48510e6	−	4.30433e6i	0.142570	−	0.246939i
$789$	1.06042e7	−	1.83670e7i	0.606437	−	1.05038i
$790$	−8.04869e6			−0.458836
$791$	−1.64105e7	+	2.84238e7i	−0.932567	+	1.61525i
$792$	1.35753e7	−	2.35131e7i	0.769019	−	1.33198i
$793$	−839062.	−	1.45330e6i	−0.0473817	−	0.0820676i
$794$	458922.	+	794876.i	0.0258337	+	0.0447454i
$795$	4.44606e6			0.249492
$796$	−9.66540e6			−0.540676
$797$	−3.67031e6	−	6.35716e6i	−0.204671	−	0.354501i	0.745357	−	0.666666i	$-0.232279\pi$
$797$	−3.67031e6	−	6.35716e6i	−0.204671	−	0.354501i	−0.950028	+	0.312165i	$0.898946\pi$
$798$	2.35984e7	+	4.08737e7i	1.31182	+	2.27215i
$799$	−332163.	+	575324.i	−0.0184071	+	0.0318820i
$800$	4.15245e6	−	7.19225e6i	0.229392	−	0.397319i
$801$	−1.66407e7			−0.916410
$802$	−1.26920e6	+	2.19833e6i	−0.0696780	+	0.120686i
$803$	−7.14164e6	+	1.23697e7i	−0.390849	+	0.676971i
$804$	−3.84609e6	+	6.66162e6i	−0.209835	+	0.363446i
$805$	5.71184e6	+	9.89320e6i	0.310661	+	0.538080i
$806$	−3.50344e6			−0.189958
$807$	−2.33438e7	−	4.04327e7i	−1.26179	−	2.18549i
$808$	7.97561e6	−	1.38142e7i	0.429770	−	0.744383i
$809$	−2.13058e7			−1.14453			−0.572264	−	0.820070i	$-0.693935\pi$
$809$	−2.13058e7			−1.14453			−0.572264	+	0.820070i	$0.693935\pi$
$810$	1.54621e7	−	2.67812e7i	0.828051	−	1.43423i
$811$	1.40970e7	+	2.44167e7i	0.752619	+	1.30357i	0.946550	+	0.322558i	$0.104543\pi$
$811$	1.40970e7	+	2.44167e7i	0.752619	+	1.30357i	−0.193931	+	0.981015i	$0.562124\pi$
$812$	3.89266e6	+	6.74228e6i	0.207184	+	0.358853i
$813$	−52591.5			−0.00279054
$814$	−2.99274e6	−	5.18358e6i	−0.158310	−	0.274201i
$815$	1.52441e6			0.0803910
$816$	−2.62511e7			−1.38013
$817$	−2.95124e7	−	5.06806e6i	−1.54685	−	0.265636i
$818$	6.07716e6			0.317554
$819$	1.02944e7			0.536281
$820$	1.27544e6	+	2.20913e6i	0.0662408	+	0.114732i
$821$	3.26367e7			1.68985			0.844926	−	0.534884i	$-0.179645\pi$
$821$	3.26367e7			1.68985			0.844926	+	0.534884i	$0.179645\pi$
$822$	2.89262e6	+	5.01016e6i	0.149318	+	0.258626i
$823$	−3.96239e6	−	6.86306e6i	−0.203919	−	0.353198i	0.745869	−	0.666093i	$-0.232035\pi$
$823$	−3.96239e6	−	6.86306e6i	−0.203919	−	0.353198i	−0.949788	+	0.312895i	$0.898701\pi$
$824$	2.42538e6	−	4.20089e6i	0.124441	−	0.215538i
$825$	1.30830e7			0.669226
$826$	−1.34317e6	+	2.32644e6i	−0.0684986	+	0.118643i
$827$	2.75165e6	+	4.76599e6i	0.139904	+	0.242320i	0.927460	−	0.373923i	$-0.121987\pi$
$827$	2.75165e6	+	4.76599e6i	0.139904	+	0.242320i	−0.787556	+	0.616243i	$0.788654\pi$
$828$	1.91839e7			0.972435
$829$	1.50672e7	+	2.60972e7i	0.761460	+	1.31889i	0.942098	+	0.335338i	$0.108851\pi$
$829$	1.50672e7	+	2.60972e7i	0.761460	+	1.31889i	−0.180638	+	0.983550i	$0.557816\pi$
$830$	6.93680e6	−	1.20149e7i	0.349514	−	0.605375i
$831$	2.47659e7	−	4.28958e7i	1.24409	−	2.15483i
$832$	1.90371e6	−	3.29732e6i	0.0953436	−	0.165140i
$833$	−5.53973e6			−0.276615
$834$	−6.12580e6	+	1.06102e7i	−0.304964	+	0.528212i
$835$	958184.	−	1.65962e6i	0.0475590	−	0.0823746i
$836$	−3.04485e6	−	5.27383e6i	−0.150678	−	0.260982i
$837$	4.35058e7	+	7.53542e7i	2.14651	+	3.71787i
$838$	−8.45556e6			−0.415942
$839$	1.45025e7			0.711275			0.355638	−	0.934624i	$-0.384264\pi$
$839$	1.45025e7			0.711275			0.355638	+	0.934624i	$0.384264\pi$
$840$	−1.35339e7	−	2.34415e7i	−0.661799	−	1.14627i
$841$	−729448.	−	1.26344e6i	−0.0355635	−	0.0615978i
$842$	−9.13502e6	+	1.58223e7i	−0.444048	+	0.769113i
$843$	−6.22330e6	+	1.07791e7i	−0.301614	+	0.522411i
$844$	1.83140e6			0.0884965
$845$	−5.81371e6	+	1.00696e7i	−0.280099	+	0.485146i
$846$	572635.	−	991834.i	0.0275076	−	0.0476445i
$847$	−8.27333e6	+	1.43298e7i	−0.396252	+	0.686329i
$848$	1.16938e6	+	2.02542e6i	0.0558426	+	0.0967222i
$849$	−4.31500e6			−0.205453
$850$	−8.00772e6	−	1.38698e7i	−0.380156	−	0.658449i
$851$	7.88174e6	−	1.36516e7i	0.373077	−	0.646188i
$852$	−1.25978e7			−0.594561
$853$	1.29860e7	−	2.24924e7i	0.611087	−	1.05843i	−0.379971	−	0.924998i	$-0.624066\pi$
$853$	1.29860e7	−	2.24924e7i	0.611087	−	1.05843i	0.991058	−	0.133435i	$-0.0426007\pi$
$854$	−4.82522e6	−	8.35753e6i	−0.226398	−	0.392133i
$855$	−2.62438e7	−	4.54555e7i	−1.22775	−	2.12653i
$856$	5.27024e6			0.245836
$857$	7.88094e6	+	1.36502e7i	0.366544	+	0.634873i	0.989023	−	0.147764i	$-0.0472076\pi$
$857$	7.88094e6	+	1.36502e7i	0.366544	+	0.634873i	−0.622479	+	0.782637i	$0.713874\pi$
$858$	3.14396e6			0.145800
$859$	2.93204e7			1.35577			0.677886	−	0.735167i	$-0.262896\pi$
$859$	2.93204e7			1.35577			0.677886	+	0.735167i	$0.262896\pi$
$860$	4.54097e6	+	779805.i	0.209364	+	0.0359534i
$861$	−2.84956e7			−1.31000
$862$	−1.93347e6			−0.0886277
$863$	−1.04399e7	−	1.80824e7i	−0.477164	−	0.826472i	0.522493	−	0.852643i	$-0.325002\pi$
$863$	−1.04399e7	−	1.80824e7i	−0.477164	−	0.826472i	−0.999657	+	0.0261709i	$0.991669\pi$
$864$	−4.95661e7			−2.25892
$865$	−2.06780e6	−	3.58154e6i	−0.0939656	−	0.162753i
$866$	8.16922e6	+	1.41495e7i	0.370157	+	0.641131i
$867$	2.27375e7	−	3.93825e7i	1.02729	−	1.77933i
$868$	1.16640e7			0.525468
$869$	−5.80050e6	+	1.00468e7i	−0.260565	+	0.451312i
$870$	1.02467e7	+	1.77477e7i	0.458970	+	0.794959i
$871$	−2.42283e6			−0.108213
$872$	6.34241e6	+	1.09854e7i	0.282464	+	0.489242i
$873$	−1.51317e7	+	2.62089e7i	−0.671974	+	1.16389i
$874$	−1.38513e7	+	2.39912e7i	−0.613357	+	1.06237i
$875$	1.19229e7	−	2.06512e7i	0.526458	−	0.911852i
$876$	2.39129e7			1.05286
$877$	3.80423e6	−	6.58912e6i	0.167020	−	0.289287i	−0.770351	−	0.637620i	$-0.779919\pi$
$877$	3.80423e6	−	6.58912e6i	0.167020	−	0.289287i	0.937371	+	0.348333i	$0.113252\pi$
$878$	−4.28740e6	+	7.42600e6i	−0.187697	+	0.325101i
$879$	−3.96100e6	−	6.86066e6i	−0.172915	−	0.299498i
$880$	−1.73858e6	−	3.01132e6i	−0.0756814	−	0.131084i
$881$	5.90609e6			0.256366			0.128183	−	0.991751i	$-0.459086\pi$
$881$	5.90609e6			0.256366			0.128183	+	0.991751i	$0.459086\pi$
$882$	9.55026e6			0.413374
$883$	−2.14923e7	−	3.72257e7i	−0.927642	−	1.60672i	−0.787256	−	0.616627i	$-0.788499\pi$
$883$	−2.14923e7	−	3.72257e7i	−0.927642	−	1.60672i	−0.140387	−	0.990097i	$-0.544835\pi$
$884$	1.11405e6	+	1.92960e6i	0.0479485	+	0.0830492i
$885$	2.04689e6	−	3.54532e6i	0.0878490	−	0.152159i
$886$	6.34591e6	−	1.09914e7i	0.271587	−	0.470403i
$887$	2.15654e7			0.920342			0.460171	−	0.887830i	$-0.347788\pi$
$887$	2.15654e7			0.920342			0.460171	+	0.887830i	$0.347788\pi$
$888$	−1.86754e7	+	3.23468e7i	−0.794763	+	1.37657i
$889$	2.08799e7	−	3.61651e7i	0.886083	−	1.53474i
$890$	−1.84872e6	+	3.20207e6i	−0.0782340	+	0.135505i
$891$	−2.22864e7	−	3.86012e7i	−0.940471	−	1.62894i
$892$	5.72678e6			0.240990
$893$	−478730.	−	829185.i	−0.0200892	−	0.0347955i
$894$	2.67940e7	−	4.64086e7i	1.12123	−	1.94202i
$895$	2.39762e7			1.00051
$896$	1.88705e6	−	3.26846e6i	0.0785258	−	0.136011i
$897$	4.14000e6	+	7.17069e6i	0.171799	+	0.297564i
$898$	77852.1	+	134844.i	0.00322166	+	0.00558007i
$899$	−3.29155e7			−1.35832
$900$	−7.99213e6	−	1.38428e7i	−0.328894	−	0.569662i
$901$	−7.84471e6			−0.321932
$902$	−6.35087e6			−0.259906
$903$	−3.29074e7	+	3.95750e7i	−1.34299	+	1.61511i
$904$	4.56466e7			1.85775
$905$	4.33451e6			0.175922
$906$	2.96666e7	+	5.13840e7i	1.20073	+	2.07973i
$907$	−841320.			−0.0339581			−0.0169790	−	0.999856i	$-0.505405\pi$
$907$	−841320.			−0.0339581			−0.0169790	+	0.999856i	$0.505405\pi$
$908$	−1.20288e6	−	2.08345e6i	−0.0484182	−	0.0838627i
$909$	−2.65826e7	−	4.60425e7i	−1.06706	−	1.84820i
$910$	1.14367e6	−	1.98090e6i	0.0457824	−	0.0792974i
$911$	1.75168e7			0.699294			0.349647	−	0.936882i	$-0.386302\pi$
$911$	1.75168e7			0.699294			0.349647	+	0.936882i	$0.386302\pi$
$912$	1.89172e7	−	3.27655e7i	0.753128	−	1.30446i
$913$	−9.99838e6	−	1.73177e7i	−0.396965	−	0.687564i
$914$	3.41631e6			0.135267
$915$	7.35326e6	+	1.27362e7i	0.290354	+	0.502907i
$916$	3.37315e6	−	5.84247e6i	0.132830	−	0.230069i
$917$	−1.76262e7	+	3.05294e7i	−0.692205	+	1.19893i
$918$	−4.77925e7	+	8.27791e7i	−1.87177	+	3.24201i
$919$	−3.88460e7			−1.51725			−0.758625	−	0.651528i	$-0.774128\pi$
$919$	−3.88460e7			−1.51725			−0.758625	+	0.651528i	$0.774128\pi$
$920$	7.94389e6	−	1.37592e7i	0.309431	−	0.535950i
$921$	−3.95419e7	+	6.84887e7i	−1.53606	+	2.66054i
$922$	−2.46144e6	−	4.26334e6i	−0.0953591	−	0.165167i
$923$	−1.98399e6	−	3.43637e6i	−0.0766541	−	0.132769i
$924$	−1.04671e7			−0.403318
$925$	−1.31343e7			−0.504724
$926$	−9.10759e6	−	1.57748e7i	−0.349040	−	0.604556i
$927$	−8.08378e6	−	1.40015e7i	−0.308969	−	0.535151i
$928$	9.37516e6	−	1.62383e7i	0.357362	−	0.618970i
$929$	−4.40217e6	+	7.62478e6i	−0.167351	+	0.289860i	−0.937488	−	0.348019i	$-0.886855\pi$
$929$	−4.40217e6	+	7.62478e6i	−0.167351	+	0.289860i	0.770137	+	0.637879i	$0.220188\pi$
$930$	3.07030e7			1.16406
$931$	3.99206e6	−	6.91446e6i	0.150947	−	0.261447i
$932$	4.40470e6	−	7.62917e6i	0.166103	−	0.287698i
$933$	1.64400e7	−	2.84749e7i	0.618297	−	1.07092i
$934$	−8.22163e6	−	1.42403e7i	−0.308383	−	0.534136i
$935$	1.16632e7			0.436303
$936$	−7.15861e6	−	1.23991e7i	−0.267079	−	0.462594i
$937$	−8.61983e6	+	1.49300e7i	−0.320738	+	0.555534i	−0.980640	−	0.195817i	$-0.937264\pi$
$937$	−8.61983e6	+	1.49300e7i	−0.320738	+	0.555534i	0.659903	+	0.751351i	$0.270597\pi$
$938$	−1.39331e7			−0.517058
$939$	−7.48311e6	+	1.29611e7i	−0.276961	+	0.479710i
$940$	73660.6	+	127584.i	0.00271904	+	0.00470951i
$941$	1.51335e7	+	2.62120e7i	0.557141	+	0.964997i	0.997733	+	0.0672899i	$0.0214352\pi$
$941$	1.51335e7	+	2.62120e7i	0.557141	+	0.964997i	−0.440592	+	0.897707i	$0.645231\pi$
$942$	−3.69602e7			−1.35709
$943$	−8.36290e6	−	1.44850e7i	−0.306251	−	0.530442i
$944$	2.15345e6			0.0786511
$945$	−5.68085e7			−2.06935
$946$	−7.33413e6	+	8.82015e6i	−0.266453	+	0.320441i
$947$	3.02266e7			1.09525			0.547627	−	0.836723i	$-0.315531\pi$
$947$	3.02266e7			1.09525			0.547627	+	0.836723i	$0.315531\pi$
$948$	1.94223e7			0.701907
$949$	3.76597e6	+	6.52285e6i	0.135741	+	0.235111i
$950$	2.30822e7			0.829792
$951$	1.90423e6	+	3.29821e6i	0.0682758	+	0.118257i
$952$	2.38795e7	+	4.13606e7i	0.853952	+	1.47909i
$953$	1.79860e7	−	3.11527e7i	0.641509	−	1.11113i	−0.343587	−	0.939121i	$-0.611642\pi$
$953$	1.79860e7	−	3.11527e7i	0.641509	−	1.11113i	0.985096	−	0.172005i	$-0.0550245\pi$
$954$	1.35239e7			0.481097
$955$	−1.36697e7	+	2.36766e7i	−0.485010	+	0.840062i
$956$	−8.06943e6	−	1.39767e7i	−0.285561	−	0.494605i
$957$	2.95381e7			1.04256
$958$	−248267.	−	430011.i	−0.00873987	−	0.0151379i
$959$	3.03331e6	−	5.25384e6i	0.106505	−	0.184472i
$960$	−1.66835e7	+	2.88966e7i	−0.584263	+	1.01197i
$961$	−1.03424e7	+	1.79135e7i	−0.361254	+	0.625709i
$962$	−3.15630e6			−0.109961
$963$	8.78283e6	−	1.52123e7i	0.305189	−	0.528603i
$964$	−3.13381e6	+	5.42792e6i	−0.108613	+	0.188123i
$965$	1.48617e7	+	2.57411e7i	0.513746	+	0.889835i
$966$	2.38081e7	+	4.12368e7i	0.820883	+	1.42181i
$967$	3.36935e7			1.15872			0.579361	−	0.815071i	$-0.303302\pi$
$967$	3.36935e7			1.15872			0.579361	+	0.815071i	$0.303302\pi$
$968$	2.30127e7			0.789367
$969$	6.34523e7	+	1.09903e8i	2.17089	+	3.76009i
$970$	3.36216e6	+	5.82342e6i	0.114733	+	0.198723i
$971$	1.15444e7	−	1.99955e7i	0.392938	−	0.680589i	−0.599898	−	0.800077i	$-0.704792\pi$
$971$	1.15444e7	−	1.99955e7i	0.392938	−	0.680589i	0.992836	+	0.119488i	$0.0381254\pi$
$972$	−1.96479e7	+	3.40312e7i	−0.667039	+	1.15535i
$973$	1.28475e7			0.435047
$974$	−2.33250e6	+	4.04001e6i	−0.0787816	+	0.136454i
$975$	3.44950e6	−	5.97472e6i	0.116210	−	0.201282i
$976$	−3.86803e6	+	6.69963e6i	−0.129977	+	0.225126i
$977$	−1.25909e7	−	2.18080e7i	−0.422007	−	0.730938i	0.574129	−	0.818765i	$-0.305341\pi$
$977$	−1.25909e7	−	2.18080e7i	−0.422007	−	0.730938i	−0.996136	+	0.0878274i	$0.972008\pi$
$978$	6.35403e6			0.212423
$979$	2.66466e6	+	4.61532e6i	0.0888555	+	0.153902i
$980$	−614245.	+	1.06390e6i	−0.0204304	+	0.0353865i
$981$	4.22784e7			1.40264
$982$	−3.38440e6	+	5.86195e6i	−0.111996	+	0.193983i
$983$	6.17053e6	+	1.06877e7i	0.203675	+	0.352776i	0.949710	−	0.313131i	$-0.101378\pi$
$983$	6.17053e6	+	1.06877e7i	0.203675	+	0.352776i	−0.746035	+	0.665907i	$0.768045\pi$
$984$	1.98155e7	+	3.43214e7i	0.652405	+	1.13000i
$985$	−1.37194e7			−0.450552
$986$	−1.80794e7	−	3.13144e7i	−0.592231	−	1.02577i
$987$	−1.64571e6			−0.0537724
$988$	−3.21125e6			−0.104660
$989$	−2.97745e7	−	5.11308e6i	−0.967953	−	0.166223i
$990$	−2.01068e7			−0.652012
$991$	−2.65917e7			−0.860124			−0.430062	−	0.902799i	$-0.641508\pi$
$991$	−2.65917e7			−0.860124			−0.430062	+	0.902799i	$0.641508\pi$
$992$	−1.40458e7	−	2.43281e7i	−0.453178	−	0.784927i
$993$	−2.30783e7			−0.742730
$994$	−1.14094e7	−	1.97617e7i	−0.366266	−	0.634392i
$995$	1.33398e7	+	2.31053e7i	0.427162	+	0.739866i
$996$	−1.67392e7	+	2.89931e7i	−0.534670	+	0.926076i
$997$	2.82114e7			0.898849			0.449425	−	0.893318i	$-0.351629\pi$
$997$	2.82114e7			0.898849			0.449425	+	0.893318i	$0.351629\pi$
$998$	1.80841e7	−	3.13226e7i	0.574739	−	0.995478i
$999$	3.91949e7	+	6.78875e7i	1.24256	+	2.15217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.36.13	yes	34
43.6	even	3	inner	43.6.c.a.6.13	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.13	✓	34	43.6	even	3	inner
43.6.c.a.36.13	yes	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+4.50187 q^{2} +(14.9934 + 25.9693i) q^{3} -11.7331 q^{4} +(16.1936 + 28.0482i) q^{5} +(67.4982 + 116.910i) q^{6} +(70.7811 - 122.596i) q^{7} -196.881 q^{8} +(-328.101 + 568.288i) q^{9} +O(q^{10})\)	\(q+4.50187 q^{2} +(14.9934 + 25.9693i) q^{3} -11.7331 q^{4} +(16.1936 + 28.0482i) q^{5} +(67.4982 + 116.910i) q^{6} +(70.7811 - 122.596i) q^{7} -196.881 q^{8} +(-328.101 + 568.288i) q^{9} +(72.9017 + 126.269i) q^{10} +210.154 q^{11} +(-175.919 - 304.701i) q^{12} +(55.4098 - 95.9727i) q^{13} +(318.647 - 551.914i) q^{14} +(-485.594 + 841.073i) q^{15} -510.873 q^{16} +(856.791 - 1484.01i) q^{17} +(-1477.07 + 2558.36i) q^{18} +(1234.85 + 2138.82i) q^{19} +(-190.002 - 329.093i) q^{20} +4244.98 q^{21} +946.087 q^{22} +(1245.82 + 2157.82i) q^{23} +(-2951.91 - 5112.85i) q^{24} +(1038.03 - 1797.92i) q^{25} +(249.448 - 432.057i) q^{26} -12390.6 q^{27} +(-830.483 + 1438.44i) q^{28} +(2343.61 - 4059.25i) q^{29} +(-2186.08 + 3786.41i) q^{30} +(-3511.19 - 6081.57i) q^{31} +4000.31 q^{32} +(3150.92 + 5457.55i) q^{33} +(3857.16 - 6680.80i) q^{34} +4584.81 q^{35} +(3849.66 - 6667.80i) q^{36} +(-3163.28 - 5478.96i) q^{37} +(5559.14 + 9628.70i) q^{38} +3323.12 q^{39} +(-3188.22 - 5522.16i) q^{40} -6712.78 q^{41} +19110.4 q^{42} +(-7752.06 + 9322.77i) q^{43} -2465.77 q^{44} -21252.6 q^{45} +(5608.52 + 9714.24i) q^{46} -387.683 q^{47} +(-7659.71 - 13267.0i) q^{48} +(-1616.42 - 2799.72i) q^{49} +(4673.09 - 8094.03i) q^{50} +51384.7 q^{51} +(-650.131 + 1126.06i) q^{52} +(-2288.98 - 3964.63i) q^{53} -55780.9 q^{54} +(3403.16 + 5894.45i) q^{55} +(-13935.4 + 24136.9i) q^{56} +(-37029.1 + 64136.2i) q^{57} +(10550.6 - 18274.2i) q^{58} -4215.23 q^{59} +(5697.54 - 9868.42i) q^{60} +(7571.41 - 13114.1i) q^{61} +(-15806.9 - 27378.4i) q^{62} +(46446.7 + 80448.1i) q^{63} +34356.8 q^{64} +3589.15 q^{65} +(14185.0 + 24569.2i) q^{66} +(-10931.4 - 18933.8i) q^{67} +(-10052.8 + 17412.0i) q^{68} +(-37358.0 + 64705.9i) q^{69} +20640.2 q^{70} +(17902.9 - 31008.7i) q^{71} +(64596.9 - 111885. i) q^{72} +(-33982.9 + 58860.1i) q^{73} +(-14240.7 - 24665.6i) q^{74} +62254.3 q^{75} +(-14488.6 - 25095.1i) q^{76} +(14874.9 - 25764.1i) q^{77} +14960.3 q^{78} +(-27601.2 + 47806.7i) q^{79} +(-8272.90 - 14329.1i) q^{80} +(-106048. - 183680. i) q^{81} -30220.1 q^{82} +(-47576.4 - 82404.8i) q^{83} -49806.9 q^{84} +55498.2 q^{85} +(-34898.8 + 41969.9i) q^{86} +140554. q^{87} -41375.4 q^{88} +(12679.5 + 21961.6i) q^{89} -95676.6 q^{90} +(-7843.94 - 13586.1i) q^{91} +(-14617.3 - 25318.0i) q^{92} +(105289. - 182366. i) q^{93} -1745.30 q^{94} +(-39993.4 + 69270.6i) q^{95} +(59978.0 + 103885. i) q^{96} +46119.0 q^{97} +(-7276.91 - 12604.0i) q^{98} +(-68951.9 + 119428. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

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