LMFDB - Embedded newform 18.6.c.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,6,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, 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("18.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	18.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:	$2.88690875663$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	18.7
Dual form			18.6.c.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 3.46410i) q^{2} +(-14.6969 - 5.19615i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-28.1969 - 48.8385i) q^{5} +(-47.3939 + 40.5194i) q^{6} +(11.1515 - 19.3150i) q^{7} -64.0000 q^{8} +(189.000 + 152.735i) q^{9} -225.576 q^{10} +(296.484 - 513.526i) q^{11} +(45.5755 + 245.216i) q^{12} +(129.531 + 224.354i) q^{13} +(-44.6061 - 77.2601i) q^{14} +(160.636 + 864.292i) q^{15} +(-128.000 + 221.703i) q^{16} +1627.51 q^{17} +(907.090 - 349.245i) q^{18} -2642.42 q^{19} +(-451.151 + 781.416i) q^{20} +(-264.257 + 225.927i) q^{21} +(-1185.94 - 2054.10i) q^{22} +(-1568.21 - 2716.22i) q^{23} +(940.604 + 332.554i) q^{24} +(-27.6347 + 47.8647i) q^{25} +1036.24 q^{26} +(-1984.09 - 3226.81i) q^{27} -356.849 q^{28} +(-62.2898 + 107.889i) q^{29} +(3315.27 + 1172.12i) q^{30} +(4376.08 + 7579.60i) q^{31} +(512.000 + 886.810i) q^{32} +(-7025.77 + 6006.68i) q^{33} +(3255.02 - 5637.87i) q^{34} -1257.76 q^{35} +(604.359 - 3840.74i) q^{36} +9741.67 q^{37} +(-5284.84 + 9153.61i) q^{38} +(-737.928 - 3970.37i) q^{39} +(1804.60 + 3125.67i) q^{40} +(3735.62 + 6470.29i) q^{41} +(254.118 + 1367.27i) q^{42} +(6252.46 - 10829.6i) q^{43} -9487.49 q^{44} +(2130.13 - 13537.1i) q^{45} -12545.7 q^{46} +(4408.73 - 7636.15i) q^{47} +(3033.21 - 2593.24i) q^{48} +(8154.79 + 14124.5i) q^{49} +(110.539 + 191.459i) q^{50} +(-23919.4 - 8456.80i) q^{51} +(2072.49 - 3589.66i) q^{52} -10782.1 q^{53} +(-15146.2 + 419.457i) q^{54} -33439.8 q^{55} +(-713.698 + 1236.16i) q^{56} +(38835.5 + 13730.4i) q^{57} +(249.159 + 431.557i) q^{58} +(7776.87 + 13469.9i) q^{59} +(10690.9 - 9140.18i) q^{60} +(5965.22 - 10332.1i) q^{61} +35008.7 q^{62} +(5057.72 - 1947.31i) q^{63} +4096.00 q^{64} +(7304.73 - 12652.2i) q^{65} +(6756.21 + 36351.3i) q^{66} +(-3089.79 - 5351.68i) q^{67} +(-13020.1 - 22551.5i) q^{68} +(8934.01 + 48068.8i) q^{69} +(-2515.51 + 4356.99i) q^{70} -10498.9 q^{71} +(-12096.0 - 9775.04i) q^{72} -38380.3 q^{73} +(19483.3 - 33746.1i) q^{74} +(654.857 - 559.870i) q^{75} +(21139.4 + 36614.5i) q^{76} +(-6612.50 - 11453.2i) q^{77} +(-15229.6 - 5384.49i) q^{78} +(-8926.87 + 15461.8i) q^{79} +14436.8 q^{80} +(12393.0 + 57733.9i) q^{81} +29885.0 q^{82} +(21610.3 - 37430.1i) q^{83} +(5244.59 + 1854.24i) q^{84} +(-45890.9 - 79485.3i) q^{85} +(-25009.8 - 43318.3i) q^{86} +(1476.08 - 1261.97i) q^{87} +(-18975.0 + 32865.6i) q^{88} -94095.6 q^{89} +(-42633.8 - 34453.3i) q^{90} +5777.86 q^{91} +(-25091.4 + 43459.6i) q^{92} +(-24930.3 - 134136. i) q^{93} +(-17634.9 - 30544.6i) q^{94} +(74508.2 + 129052. i) q^{95} +(-2916.83 - 15693.8i) q^{96} +(40743.3 - 70569.5i) q^{97} +65238.3 q^{98} +(134469. - 51772.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9} - 432 q^{10} - 78 q^{11} - 288 q^{12} + 1106 q^{13} - 296 q^{14} + 378 q^{15} - 512 q^{16} + 984 q^{17} + 1512 q^{18} - 3280 q^{19}+ \cdots + 319626 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9 - 432 * q^10 - 78 * q^11 - 288 * q^12 + 1106 * q^13 - 296 * q^14 + 378 * q^15 - 512 * q^16 + 984 * q^17 + 1512 * q^18 - 3280 * q^19 - 864 * q^20 - 234 * q^21 + 312 * q^22 - 5538 * q^23 + 3064 * q^25 + 8848 * q^26 - 2368 * q^28 - 3894 * q^29 + 6912 * q^30 + 4718 * q^31 + 2048 * q^32 - 17874 * q^33 + 1968 * q^34 - 2268 * q^35 - 6048 * q^36 - 9592 * q^37 - 6560 * q^38 + 18594 * q^39 + 3456 * q^40 + 15354 * q^41 - 4392 * q^42 + 32858 * q^43 + 2496 * q^44 + 5346 * q^45 - 44304 * q^46 + 24954 * q^47 + 4608 * q^48 + 30444 * q^49 - 12256 * q^50 - 81216 * q^51 + 17696 * q^52 - 32664 * q^53 - 44712 * q^54 - 70092 * q^55 - 4736 * q^56 + 107136 * q^57 + 15576 * q^58 + 21966 * q^59 + 21600 * q^60 + 3050 * q^61 + 37744 * q^62 + 6210 * q^63 + 16384 * q^64 + 12582 * q^65 + 77112 * q^66 + 36758 * q^67 - 7872 * q^68 - 39042 * q^69 - 4536 * q^70 - 147696 * q^71 - 48384 * q^72 - 102376 * q^73 - 19184 * q^74 + 19080 * q^75 + 26240 * q^76 + 21462 * q^77 + 69120 * q^78 - 14926 * q^79 + 27648 * q^80 + 49572 * q^81 + 122832 * q^82 + 90762 * q^83 - 13824 * q^84 - 94500 * q^85 - 131432 * q^86 - 18522 * q^87 + 4992 * q^88 - 18600 * q^89 - 81648 * q^90 + 99124 * q^91 - 88608 * q^92 - 145458 * q^93 - 99816 * q^94 + 151416 * q^95 + 18432 * q^96 - 30262 * q^97 + 243552 * q^98 + 319626 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	−14.6969	−	5.19615i	−0.942809	−	0.333333i
$3$	−14.6969	−	5.19615i	−0.942809	−	0.333333i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−28.1969	−	48.8385i	−0.504402	−	0.873650i	−0.999987	−	0.00509067i	$-0.998380\pi$
$5$	−28.1969	−	48.8385i	−0.504402	−	0.873650i	0.495585	−	0.868560i	$-0.334954\pi$
$6$	−47.3939	+	40.5194i	−0.537457	+	0.459499i
$7$	11.1515	−	19.3150i	0.0860180	−	0.148988i	−0.819807	−	0.572641i	$-0.805919\pi$
$7$	11.1515	−	19.3150i	0.0860180	−	0.148988i	0.905825	+	0.423653i	$0.139252\pi$
$8$	−64.0000			−0.353553
$9$	189.000	+	152.735i	0.777778	+	0.628539i
$10$	−225.576			−0.713332
$11$	296.484	−	513.526i	0.738788	−	1.27962i	−0.214253	−	0.976778i	$-0.568732\pi$
$11$	296.484	−	513.526i	0.738788	−	1.27962i	0.953041	−	0.302840i	$-0.0979348\pi$
$12$	45.5755	+	245.216i	0.0913647	+	0.491582i
$13$	129.531	+	224.354i	0.212576	+	0.368192i	0.952520	−	0.304476i	$-0.0984814\pi$
$13$	129.531	+	224.354i	0.212576	+	0.368192i	−0.739944	+	0.672668i	$0.765148\pi$
$14$	−44.6061	−	77.2601i	−0.0608239	−	0.105350i
$15$	160.636	+	864.292i	0.184338	+	0.991819i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	1627.51			1.36585			0.682923	−	0.730490i	$-0.260708\pi$
$17$	1627.51			1.36585			0.682923	+	0.730490i	$0.260708\pi$
$18$	907.090	−	349.245i	0.659886	−	0.254067i
$19$	−2642.42			−1.67926			−0.839630	−	0.543159i	$-0.817228\pi$
$19$	−2642.42			−1.67926			−0.839630	+	0.543159i	$0.817228\pi$
$20$	−451.151	+	781.416i	−0.252201	+	0.436825i
$21$	−264.257	+	225.927i	−0.130761	+	0.111794i
$22$	−1185.94	−	2054.10i	−0.522402	−	0.904827i
$23$	−1568.21	−	2716.22i	−0.618138	−	1.07065i	−0.989825	−	0.142288i	$-0.954554\pi$
$23$	−1568.21	−	2716.22i	−0.618138	−	1.07065i	0.371688	−	0.928358i	$-0.378779\pi$
$24$	940.604	+	332.554i	0.333333	+	0.117851i
$25$	−27.6347	+	47.8647i	−0.00884310	+	0.0153167i
$26$	1036.24			0.300628
$27$	−1984.09	−	3226.81i	−0.523783	−	0.851852i
$28$	−356.849			−0.0860180
$29$	−62.2898	+	107.889i	−0.0137538	+	0.0238222i	−0.872820	−	0.488042i	$-0.837711\pi$
$29$	−62.2898	+	107.889i	−0.0137538	+	0.0238222i	0.859067	+	0.511864i	$0.171045\pi$
$30$	3315.27	+	1172.12i	0.672536	+	0.237777i
$31$	4376.08	+	7579.60i	0.817865	+	1.41658i	0.907253	+	0.420586i	$0.138176\pi$
$31$	4376.08	+	7579.60i	0.817865	+	1.41658i	−0.0893879	+	0.995997i	$0.528491\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	−7025.77	+	6006.68i	−1.12308	+	0.960173i
$34$	3255.02	−	5637.87i	0.482900	−	0.836407i
$35$	−1257.76			−0.173551
$36$	604.359	−	3840.74i	0.0777211	−	0.493922i
$37$	9741.67			1.16985			0.584924	−	0.811088i	$-0.301124\pi$
$37$	9741.67			1.16985			0.584924	+	0.811088i	$0.301124\pi$
$38$	−5284.84	+	9153.61i	−0.593708	+	1.02833i
$39$	−737.928	−	3970.37i	−0.0776877	−	0.417994i
$40$	1804.60	+	3125.67i	0.178333	+	0.308882i
$41$	3735.62	+	6470.29i	0.347059	+	0.601124i	0.985726	−	0.168360i	$-0.0538471\pi$
$41$	3735.62	+	6470.29i	0.347059	+	0.601124i	−0.638667	+	0.769484i	$0.720514\pi$
$42$	254.118	+	1367.27i	0.0222286	+	0.119600i
$43$	6252.46	−	10829.6i	0.515679	−	0.893183i	−0.484155	−	0.874982i	$-0.660873\pi$
$43$	6252.46	−	10829.6i	0.515679	−	0.893183i	0.999834	−	0.0182005i	$-0.00579373\pi$
$44$	−9487.49			−0.738788
$45$	2130.13	−	13537.1i	0.156811	−	0.996542i
$46$	−12545.7			−0.874178
$47$	4408.73	−	7636.15i	0.291118	−	0.504231i	−0.682956	−	0.730459i	$-0.739306\pi$
$47$	4408.73	−	7636.15i	0.291118	−	0.504231i	0.974074	+	0.226228i	$0.0726395\pi$
$48$	3033.21	−	2593.24i	0.190020	−	0.162457i
$49$	8154.79	+	14124.5i	0.485202	+	0.840394i
$50$	110.539	+	191.459i	0.00625301	+	0.0108305i
$51$	−23919.4	−	8456.80i	−1.28773	−	0.455282i
$52$	2072.49	−	3589.66i	0.106288	−	0.184096i
$53$	−10782.1			−0.527244			−0.263622	−	0.964626i	$-0.584917\pi$
$53$	−10782.1			−0.527244			−0.263622	+	0.964626i	$0.584917\pi$
$54$	−15146.2	+	419.457i	−0.706836	+	0.0195750i
$55$	−33439.8			−1.49058
$56$	−713.698	+	1236.16i	−0.0304120	+	0.0526751i
$57$	38835.5	+	13730.4i	1.58322	+	0.559753i
$58$	249.159	+	431.557i	0.00972539	+	0.0168449i
$59$	7776.87	+	13469.9i	0.290854	+	0.503774i	0.974012	−	0.226497i	$-0.0727273\pi$
$59$	7776.87	+	13469.9i	0.290854	+	0.503774i	−0.683158	+	0.730271i	$0.739394\pi$
$60$	10690.9	−	9140.18i	0.383386	−	0.327776i
$61$	5965.22	−	10332.1i	0.205259	−	0.355519i	−0.744956	−	0.667113i	$-0.767530\pi$
$61$	5965.22	−	10332.1i	0.205259	−	0.355519i	0.950215	+	0.311595i	$0.100863\pi$
$62$	35008.7			1.15664
$63$	5057.72	−	1947.31i	0.160547	−	0.0618135i
$64$	4096.00			0.125000
$65$	7304.73	−	12652.2i	0.214448	−	0.371434i
$66$	6756.21	+	36351.3i	0.190916	+	1.02721i
$67$	−3089.79	−	5351.68i	−0.0840896	−	0.145647i	0.820913	−	0.571053i	$-0.193465\pi$
$67$	−3089.79	−	5351.68i	−0.0840896	−	0.145647i	−0.905003	+	0.425405i	$0.860132\pi$
$68$	−13020.1	−	22551.5i	−0.341462	−	0.591429i
$69$	8934.01	+	48068.8i	0.225904	+	1.21546i
$70$	−2515.51	+	4356.99i	−0.0613594	+	0.106278i
$71$	−10498.9			−0.247171			−0.123586	−	0.992334i	$-0.539439\pi$
$71$	−10498.9			−0.247171			−0.123586	+	0.992334i	$0.539439\pi$
$72$	−12096.0	−	9775.04i	−0.274986	−	0.222222i
$73$	−38380.3			−0.842950			−0.421475	−	0.906840i	$-0.638487\pi$
$73$	−38380.3			−0.842950			−0.421475	+	0.906840i	$0.638487\pi$
$74$	19483.3	−	33746.1i	0.413603	−	0.716382i
$75$	654.857	−	559.870i	0.0134429	−	0.0114930i
$76$	21139.4	+	36614.5i	0.419815	+	0.727141i
$77$	−6612.50	−	11453.2i	−0.127098	−	0.220140i
$78$	−15229.6	−	5384.49i	−0.283435	−	0.100209i
$79$	−8926.87	+	15461.8i	−0.160928	+	0.278735i	−0.935202	−	0.354115i	$-0.884782\pi$
$79$	−8926.87	+	15461.8i	−0.160928	+	0.278735i	0.774274	+	0.632851i	$0.218115\pi$
$80$	14436.8			0.252201
$81$	12393.0	+	57733.9i	0.209877	+	0.977728i
$82$	29885.0			0.490815
$83$	21610.3	−	37430.1i	0.344322	−	0.596384i	−0.640908	−	0.767618i	$-0.721442\pi$
$83$	21610.3	−	37430.1i	0.344322	−	0.596384i	0.985230	+	0.171234i	$0.0547754\pi$
$84$	5244.59	+	1854.24i	0.0810986	+	0.0286727i
$85$	−45890.9	−	79485.3i	−0.688936	−	1.19327i
$86$	−25009.8	−	43318.3i	−0.364640	−	0.631576i
$87$	1476.08	−	1261.97i	0.0209079	−	0.0178752i
$88$	−18975.0	+	32865.6i	−0.261201	+	0.452413i
$89$	−94095.6			−1.25920			−0.629599	−	0.776920i	$-0.716781\pi$
$89$	−94095.6			−1.25920			−0.629599	+	0.776920i	$0.716781\pi$
$90$	−42633.8	−	34453.3i	−0.554814	−	0.448357i
$91$	5777.86			0.0731414
$92$	−25091.4	+	43459.6i	−0.309069	+	0.535323i
$93$	−24930.3	−	134136.i	−0.298896	−	1.60819i
$94$	−17634.9	−	30544.6i	−0.205851	−	0.356545i
$95$	74508.2	+	129052.i	0.847022	+	1.46709i
$96$	−2916.83	−	15693.8i	−0.0323023	−	0.173800i
$97$	40743.3	−	70569.5i	0.439670	−	0.761532i	−0.557993	−	0.829845i	$-0.688429\pi$
$97$	40743.3	−	70569.5i	0.439670	−	0.761532i	0.997664	+	0.0683138i	$0.0217619\pi$
$98$	65238.3			0.686179
$99$	134469.	−	51772.8i	1.37890	−	0.530901i
$100$	884.310			0.00884310
$101$	−66434.0	+	115067.i	−0.648017	+	1.12240i	0.335578	+	0.942012i	$0.391068\pi$
$101$	−66434.0	+	115067.i	−0.648017	+	1.12240i	−0.983596	+	0.180387i	$0.942265\pi$
$102$	−77134.1	+	65945.8i	−0.734085	+	0.627605i
$103$	62055.5	+	107483.i	0.576352	+	0.998270i	0.995893	+	0.0905343i	$0.0288575\pi$
$103$	62055.5	+	107483.i	0.576352	+	0.998270i	−0.419542	+	0.907736i	$0.637809\pi$
$104$	−8289.96	−	14358.6i	−0.0751569	−	0.130176i
$105$	18485.2	+	6535.49i	0.163625	+	0.0578502i
$106$	−21564.1	+	37350.1i	−0.186409	+	0.322870i
$107$	102868.			0.868605			0.434303	−	0.900767i	$-0.356995\pi$
$107$	102868.			0.868605			0.434303	+	0.900767i	$0.356995\pi$
$108$	−28839.3	+	53306.8i	−0.237917	+	0.439768i
$109$	229354.			1.84901			0.924506	−	0.381167i	$-0.124478\pi$
$109$	229354.			1.84901			0.924506	+	0.381167i	$0.124478\pi$
$110$	−66879.6	+	115839.i	−0.527001	+	0.912793i
$111$	−143173.	−	50619.2i	−1.10294	−	0.389949i
$112$	2854.79	+	4944.64i	0.0215045	+	0.0372469i
$113$	−37466.9	−	64894.5i	−0.276027	−	0.478092i	0.694367	−	0.719621i	$-0.255685\pi$
$113$	−37466.9	−	64894.5i	−0.276027	−	0.478092i	−0.970394	+	0.241529i	$0.922351\pi$
$114$	125235.	−	107069.i	0.902531	−	0.771618i
$115$	−88437.5	+	153178.i	−0.623580	+	1.08007i
$116$	1993.27			0.0137538
$117$	−9785.38	+	62186.7i	−0.0660865	+	0.419984i
$118$	62215.0			0.411330
$119$	18149.3	−	31435.4i	0.117487	−	0.203494i
$120$	−10280.7	−	55314.7i	−0.0651734	−	0.350661i
$121$	−95280.2	−	165030.i	−0.591615	−	1.02471i
$122$	−23860.9	−	41328.2i	−0.145140	−	0.251390i
$123$	−21281.6	−	114504.i	−0.126836	−	0.682431i
$124$	70017.3	−	121274.i	0.408932	−	0.708292i
$125$	−173114.			−0.990962
$126$	3369.76	−	21415.1i	0.0189092	−	0.120169i
$127$	34578.3			0.190237			0.0951184	−	0.995466i	$-0.469677\pi$
$127$	34578.3			0.190237			0.0951184	+	0.995466i	$0.469677\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	−148164.	+	126673.i	−0.783915	+	0.670208i
$130$	−29218.9	−	50608.7i	−0.151637	−	0.262643i
$131$	−39811.8	−	68956.1i	−0.202691	−	0.351071i	0.746704	−	0.665157i	$-0.231635\pi$
$131$	−39811.8	−	68956.1i	−0.202691	−	0.351071i	−0.949395	+	0.314086i	$0.898302\pi$
$132$	139437.	+	49298.5i	0.696536	+	0.246263i
$133$	−29467.0	+	51038.4i	−0.144447	+	0.250189i
$134$	−24718.3			−0.118921
$135$	−101648.	+	187886.i	−0.480023	+	0.887279i
$136$	−104161.			−0.482900
$137$	135520.	−	234728.i	0.616883	−	1.06847i	−0.373168	−	0.927764i	$-0.621728\pi$
$137$	135520.	−	234728.i	0.616883	−	1.06847i	0.990051	−	0.140709i	$-0.0449383\pi$
$138$	184383.	+	65189.3i	0.824183	+	0.291393i
$139$	−16584.4	−	28725.0i	−0.0728053	−	0.126102i	0.827324	−	0.561724i	$-0.189862\pi$
$139$	−16584.4	−	28725.0i	−0.0728053	−	0.126102i	−0.900130	+	0.435622i	$0.856528\pi$
$140$	10062.0	+	17428.0i	0.0433877	+	0.0751496i
$141$	−104473.	+	89319.5i	−0.442546	+	0.378354i
$142$	−20997.8	+	36369.3i	−0.0873883	+	0.151361i
$143$	153615.			0.628194
$144$	−58053.7	+	22351.7i	−0.233305	+	0.0898264i
$145$	7025.53			0.0277497
$146$	−76760.7	+	132953.i	−0.298028	+	0.516199i
$147$	−46457.3	−	249960.i	−0.177321	−	0.954065i
$148$	−77933.4	−	134985.i	−0.292462	−	0.506559i
$149$	18317.4	+	31726.7i	0.0675925	+	0.117074i	0.897841	−	0.440320i	$-0.145135\pi$
$149$	18317.4	+	31726.7i	0.0675925	+	0.117074i	−0.830249	+	0.557393i	$0.811802\pi$
$150$	−629.732	−	3388.23i	−0.00228522	−	0.0122955i
$151$	−247485.	+	428657.i	−0.883297	+	1.52992i	−0.0356448	+	0.999365i	$0.511349\pi$
$151$	−247485.	+	428657.i	−0.883297	+	1.52992i	−0.847653	+	0.530552i	$0.821985\pi$
$152$	169115.			0.593708
$153$	307600.	+	248578.i	1.06233	+	0.858488i
$154$	−52900.0			−0.179744
$155$	246784.	−	427443.i	0.825065	−	1.42906i
$156$	−49111.7	+	41988.0i	−0.161575	+	0.138138i
$157$	28915.9	+	50083.7i	0.0936239	+	0.162161i	0.909033	−	0.416723i	$-0.136822\pi$
$157$	28915.9	+	50083.7i	0.0936239	+	0.162161i	−0.815410	+	0.578885i	$0.803488\pi$
$158$	35707.5	+	61847.2i	0.113793	+	0.197096i
$159$	158463.	+	56025.2i	0.497091	+	0.175748i
$160$	28873.7	−	50010.7i	0.0891665	−	0.154441i
$161$	−69951.8			−0.212684
$162$	224782.	+	72537.1i	0.672936	+	0.217156i
$163$	−135023.			−0.398050			−0.199025	−	0.979994i	$-0.563777\pi$
$163$	−135023.			−0.398050			−0.199025	+	0.979994i	$0.563777\pi$
$164$	59769.9	−	103525.i	0.173529	−	0.300562i
$165$	491462.	+	173758.i	1.40534	+	0.496862i
$166$	−86441.1	−	149720.i	−0.243473	−	0.421707i
$167$	203014.	+	351631.i	0.563294	+	0.975655i	0.997206	+	0.0746992i	$0.0237997\pi$
$167$	203014.	+	351631.i	0.563294	+	0.975655i	−0.433912	+	0.900955i	$0.642867\pi$
$168$	16912.5	−	14459.3i	0.0462310	−	0.0395252i
$169$	152090.	−	263428.i	0.409623	−	0.709488i
$170$	−367127.			−0.974303
$171$	−499417.	−	403590.i	−1.30609	−	1.05548i
$172$	−200079.			−0.515679
$173$	−114121.	+	197663.i	−0.289901	+	0.502123i	−0.973786	−	0.227467i	$-0.926956\pi$
$173$	−114121.	+	197663.i	−0.289901	+	0.502123i	0.683885	+	0.729590i	$0.260289\pi$
$174$	−1419.44	−	7637.23i	−0.00355423	−	0.0191233i
$175$	616.338	+	1067.53i	0.00152133	+	0.00263502i
$176$	75899.9	+	131463.i	0.184697	+	0.319905i
$177$	−44304.4	−	238377.i	−0.106295	−	0.571914i
$178$	−188191.	+	325957.i	−0.445194	+	0.771098i
$179$	−19370.0			−0.0451853			−0.0225927	−	0.999745i	$-0.507192\pi$
$179$	−19370.0			−0.0451853			−0.0225927	+	0.999745i	$0.507192\pi$
$180$	−204617.	+	78781.1i	−0.470718	+	0.181235i
$181$	−137790.			−0.312623			−0.156311	−	0.987708i	$-0.549960\pi$
$181$	−137790.			−0.312623			−0.156311	+	0.987708i	$0.549960\pi$
$182$	11555.7	−	20015.1i	0.0258594	−	0.0447898i
$183$	−141357.	+	120853.i	−0.312026	+	0.266767i
$184$	100366.	+	173838.i	0.218545	+	0.378530i
$185$	−274685.	−	475769.i	−0.590073	−	1.02204i
$186$	−514520.	−	181910.i	−1.09049	−	0.385545i
$187$	482532.	−	835769.i	1.00907	−	1.74776i
$188$	−141079.			−0.291118
$189$	−84451.5	+	2338.79i	−0.171970	+	0.00476252i
$190$	596065.			1.19787
$191$	−168262.	+	291438.i	−0.333735	+	0.578046i	−0.983241	−	0.182311i	$-0.941642\pi$
$191$	−168262.	+	291438.i	−0.333735	+	0.578046i	0.649506	+	0.760356i	$0.274976\pi$
$192$	−60198.7	−	21283.4i	−0.117851	−	0.0416667i
$193$	370436.	+	641615.i	0.715847	+	1.23988i	0.962632	+	0.270813i	$0.0872926\pi$
$193$	370436.	+	641615.i	0.715847	+	1.23988i	−0.246785	+	0.969070i	$0.579374\pi$
$194$	−162973.	−	282278.i	−0.310894	−	0.538484i
$195$	−173100.	+	147992.i	−0.325994	+	0.278709i
$196$	130477.	−	225992.i	0.242601	−	0.420197i
$197$	219128.			0.402284			0.201142	−	0.979562i	$-0.435535\pi$
$197$	219128.			0.402284			0.201142	+	0.979562i	$0.435535\pi$
$198$	89591.5	−	569360.i	0.162407	−	1.03210i
$199$	−215378.			−0.385540			−0.192770	−	0.981244i	$-0.561747\pi$
$199$	−215378.			−0.385540			−0.192770	+	0.981244i	$0.561747\pi$
$200$	1768.62	−	3063.34i	0.00312651	−	0.00541527i
$201$	17602.4	+	94708.3i	0.0307313	+	0.165348i
$202$	265736.	+	460268.i	0.458218	+	0.793656i
$203$	1389.25	+	2406.26i	0.00236615	+	0.00409828i
$204$	74174.7	+	399092.i	0.124790	+	0.671425i
$205$	210666.	−	364885.i	0.350115	−	0.606416i
$206$	496444.			0.815084
$207$	118470.	−	752887.i	0.192169	−	1.22125i
$208$	−66319.7			−0.106288
$209$	−783436.	+	1.35695e6i	−1.24062	+	2.14881i
$210$	59609.9	−	50963.5i	0.0932761	−	0.0797464i
$211$	−2285.57	−	3958.73i	−0.00353419	−	0.00612139i	0.864253	−	0.503058i	$-0.167792\pi$
$211$	−2285.57	−	3958.73i	−0.00353419	−	0.00612139i	−0.867787	+	0.496936i	$0.834458\pi$
$212$	86256.4	+	149401.i	0.131811	+	0.228303i
$213$	154302.	+	54553.9i	0.233035	+	0.0823904i
$214$	205737.	−	356347.i	0.307098	−	0.531910i
$215$	−705201.			−1.04044
$216$	126982.	+	206516.i	0.185185	+	0.301175i
$217$	195200.			0.281404
$218$	458708.	−	794505.i	0.653725	−	1.13228i
$219$	564073.	+	199430.i	0.794741	+	0.280983i
$220$	267518.	+	463355.i	0.372646	+	0.645442i
$221$	210813.	+	365138.i	0.290346	+	0.502894i
$222$	−461696.	+	394727.i	−0.628743	+	0.537544i
$223$	−472764.	+	818852.i	−0.636623	+	1.10266i	0.349546	+	0.936919i	$0.386336\pi$
$223$	−472764.	+	818852.i	−0.636623	+	1.10266i	−0.986169	+	0.165744i	$0.946997\pi$
$224$	22838.3			0.0304120
$225$	−12533.6	+	4825.64i	−0.0165051	+	0.00635475i
$226$	−299735.			−0.390361
$227$	−91944.9	+	159253.i	−0.118430	+	0.205127i	−0.919146	−	0.393917i	$-0.871120\pi$
$227$	−91944.9	+	159253.i	−0.118430	+	0.205127i	0.800715	+	0.599045i	$0.204453\pi$
$228$	−120430.	−	647964.i	−0.153425	−	0.825493i
$229$	−279217.	−	483618.i	−0.351846	−	0.609416i	0.634727	−	0.772737i	$-0.281113\pi$
$229$	−279217.	−	483618.i	−0.351846	−	0.609416i	−0.986573	+	0.163321i	$0.947779\pi$
$230$	353750.	+	612713.i	0.440938	+	0.763726i
$231$	37671.0	+	202686.i	0.0464491	+	0.249916i
$232$	3986.55	−	6904.90i	0.00486270	−	0.00842244i
$233$	1.04850e6			1.26526			0.632630	−	0.774454i	$-0.281975\pi$
$233$	1.04850e6			1.26526			0.632630	+	0.774454i	$0.281975\pi$
$234$	195850.	+	158271.i	0.233822	+	0.188956i
$235$	−497251.			−0.587362
$236$	124430.	−	215519.i	0.145427	−	0.251887i
$237$	211539.	−	180856.i	0.244636	−	0.209152i
$238$	−72597.0	−	125742.i	−0.0830761	−	0.143892i
$239$	−356902.	−	618172.i	−0.404160	−	0.700026i	0.590063	−	0.807357i	$-0.299103\pi$
$239$	−356902.	−	618172.i	−0.404160	−	0.700026i	−0.994223	+	0.107331i	$0.965770\pi$
$240$	−212177.	−	75016.0i	−0.237777	−	0.0840670i
$241$	385469.	−	667651.i	0.427510	−	0.740469i	−0.569141	−	0.822240i	$-0.692724\pi$
$241$	385469.	−	667651.i	0.427510	−	0.740469i	0.996651	+	0.0817707i	$0.0260575\pi$
$242$	−762242.			−0.836670
$243$	117855.	−	912907.i	0.128036	−	0.991770i
$244$	−190887.			−0.205259
$245$	459880.	−	796536.i	0.489474	−	0.847793i
$246$	−439218.	−	155287.i	−0.462745	−	0.163605i
$247$	−342274.	−	592837.i	−0.356970	−	0.618291i
$248$	−280069.	−	485094.i	−0.289159	−	0.500838i
$249$	−512097.	+	437818.i	−0.523425	+	0.447502i
$250$	−346228.	+	599685.i	−0.350358	+	0.606838i
$251$	450848.			0.451696			0.225848	−	0.974163i	$-0.427485\pi$
$251$	450848.			0.451696			0.225848	+	0.974163i	$0.427485\pi$
$252$	−67444.5	−	54503.4i	−0.0669029	−	0.0540657i
$253$	−1.85980e6			−1.82669
$254$	69156.6	−	119783.i	0.0672589	−	0.116496i
$255$	261437.	+	1.40665e6i	0.251778	+	1.35467i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−442803.	−	766958.i	−0.418194	−	0.724334i	0.577564	−	0.816346i	$-0.304004\pi$
$257$	−442803.	−	766958.i	−0.418194	−	0.724334i	−0.995758	+	0.0920119i	$0.970670\pi$
$258$	142479.	+	766601.i	0.133261	+	0.717002i
$259$	108635.	−	188161.i	0.100628	−	0.174293i
$260$	−233751.			−0.214448
$261$	−28251.2	+	10877.2i	−0.0256706	+	0.00988362i
$262$	−318495.			−0.286648
$263$	143984.	−	249388.i	0.128359	−	0.222324i	−0.794682	−	0.607026i	$-0.792362\pi$
$263$	143984.	−	249388.i	0.128359	−	0.222324i	0.923041	+	0.384702i	$0.125696\pi$
$264$	449649.	−	384427.i	0.397067	−	0.339472i
$265$	304021.	+	526580.i	0.265943	+	0.460627i
$266$	117868.	+	204154.i	0.102139	+	0.176910i
$267$	1.38292e6	+	488935.i	1.18718	+	0.419733i
$268$	−49436.7	+	85626.8i	−0.0420448	+	0.0728237i
$269$	898860.			0.757376			0.378688	−	0.925524i	$-0.376375\pi$
$269$	898860.			0.757376			0.378688	+	0.925524i	$0.376375\pi$
$270$	447561.	+	727889.i	0.373631	+	0.607654i
$271$	1.89319e6			1.56592			0.782962	−	0.622069i	$-0.213708\pi$
$271$	1.89319e6			1.56592			0.782962	+	0.622069i	$0.213708\pi$
$272$	−208322.	+	360824.i	−0.170731	+	0.295714i
$273$	−84916.8	−	30022.6i	−0.0689584	−	0.0243805i
$274$	−542081.	−	938913.i	−0.436202	−	0.755525i
$275$	16386.5	+	28382.2i	0.0130663	+	0.0226316i
$276$	594589.	−	508344.i	0.469834	−	0.401684i
$277$	−866062.	+	1.50006e6i	−0.678187	+	1.17465i	0.297340	+	0.954772i	$0.403901\pi$
$277$	−866062.	+	1.50006e6i	−0.678187	+	1.17465i	−0.975526	+	0.219882i	$0.929433\pi$
$278$	−132675.			−0.102962
$279$	−330591.	+	2.10093e6i	−0.254261	+	1.61585i
$280$	80496.4			0.0613594
$281$	146629.	−	253968.i	0.110778	−	0.191873i	−0.805306	−	0.592859i	$-0.797999\pi$
$281$	146629.	−	253968.i	0.110778	−	0.191873i	0.916084	+	0.400986i	$0.131332\pi$
$282$	100465.	+	540546.i	0.0752302	+	0.404771i
$283$	399082.	+	691230.i	0.296208	+	0.513046i	0.975265	−	0.221039i	$-0.0709447\pi$
$283$	399082.	+	691230.i	0.296208	+	0.513046i	−0.679058	+	0.734085i	$0.737611\pi$
$284$	83991.2	+	145477.i	0.0617928	+	0.107028i
$285$	−424468.	−	2.28382e6i	−0.309552	−	1.66552i
$286$	307230.	−	532138.i	0.222100	−	0.384689i
$287$	166632.			0.119413
$288$	−38679.0	+	245807.i	−0.0274786	+	0.174628i
$289$	1.22894e6			0.865537
$290$	14051.1	−	24337.1i	0.00981102	−	0.0169932i
$291$	−965492.	+	825447.i	−0.668369	+	0.571422i
$292$	307043.	+	531814.i	0.210737	+	0.365008i
$293$	−695365.	−	1.20441e6i	−0.473199	−	0.819605i	0.526330	−	0.850280i	$-0.323568\pi$
$293$	−695365.	−	1.20441e6i	−0.473199	−	0.819605i	−0.999529	+	0.0306753i	$0.990234\pi$
$294$	−958803.	−	338988.i	−0.646936	−	0.228726i
$295$	438568.	−	759622.i	0.293415	−	0.508209i
$296$	−623467.			−0.413603
$297$	−2.24530e6	+	62181.1i	−1.47701	+	0.0409042i
$298$	146539.			0.0955902
$299$	406263.	−	703668.i	0.262802	−	0.455187i
$300$	−12996.6	−	4595.01i	−0.00833735	−	0.00294770i
$301$	−139449.	−	241533.i	−0.0887154	−	0.153660i
$302$	989941.	+	1.71463e6i	0.624586	+	1.08181i
$303$	1.57428e6	−	1.34593e6i	0.985090	−	0.842202i
$304$	338230.	−	585831.i	0.209907	−	0.363570i
$305$	−672803.			−0.414132
$306$	1.47630e6	−	568401.i	0.901303	−	0.347017i
$307$	598019.			0.362134			0.181067	−	0.983471i	$-0.442045\pi$
$307$	598019.			0.362134			0.181067	+	0.983471i	$0.442045\pi$
$308$	−105800.	+	183251.i	−0.0635491	+	0.110070i
$309$	−353527.	−	1.90213e6i	−0.210633	−	1.13330i
$310$	−987137.	−	1.70977e6i	−0.583409	−	1.01049i
$311$	1.48902e6	+	2.57905e6i	0.872968	+	1.51203i	0.858912	+	0.512124i	$0.171141\pi$
$311$	1.48902e6	+	2.57905e6i	0.872968	+	1.51203i	0.0140565	+	0.999901i	$0.495526\pi$
$312$	47227.4	+	254104.i	0.0274668	+	0.147783i
$313$	−1.25187e6	+	2.16830e6i	−0.722266	+	1.25100i	0.237823	+	0.971309i	$0.423566\pi$
$313$	−1.25187e6	+	2.16830e6i	−0.722266	+	1.25100i	−0.960089	+	0.279694i	$0.909767\pi$
$314$	231327.			0.132404
$315$	−237716.	−	192103.i	−0.134984	−	0.109083i
$316$	285660.			0.160928
$317$	−1.04317e6	+	1.80683e6i	−0.583053	+	1.00988i	0.412062	+	0.911156i	$0.364809\pi$
$317$	−1.04317e6	+	1.80683e6i	−0.583053	+	1.00988i	−0.995115	+	0.0987220i	$0.968525\pi$
$318$	511003.	−	436882.i	0.283371	−	0.242268i
$319$	36935.9	+	63974.8i	0.0203223	+	0.0351992i
$320$	−115495.	−	200043.i	−0.0630503	−	0.109206i
$321$	−1.51185e6	−	534520.i	−0.818929	−	0.289535i
$322$	−139904.	+	242320.i	−0.0751951	+	0.130242i
$323$	−4.30057e6			−2.29361
$324$	700840.	−	633593.i	0.370899	−	0.335311i
$325$	−14318.1			−0.00751932
$326$	−270045.	+	467732.i	−0.140732	+	0.243755i
$327$	−3.37080e6	−	1.19176e6i	−1.74327	−	0.616338i
$328$	−239080.	−	414098.i	−0.122704	−	0.212529i
$329$	−98328.2	−	170309.i	−0.0500828	−	0.0867459i
$330$	1.58484e6	−	1.35496e6i	0.801126	−	0.684923i
$331$	947564.	−	1.64123e6i	0.475378	−	0.823378i	−0.524225	−	0.851580i	$-0.675645\pi$
$331$	947564.	−	1.64123e6i	0.475378	−	0.823378i	0.999602	+	0.0282018i	$0.00897810\pi$
$332$	−691529.			−0.344322
$333$	1.84118e6	+	1.48789e6i	0.909881	+	0.735295i
$334$	1.62411e6			0.796619
$335$	−174245.	+	301802.i	−0.0848299	+	0.146930i
$336$	−16263.6	−	87505.1i	−0.00785901	−	0.0422849i
$337$	−666562.	−	1.15452e6i	−0.319717	−	0.553766i	0.660712	−	0.750639i	$-0.270254\pi$
$337$	−666562.	−	1.15452e6i	−0.319717	−	0.553766i	−0.980429	+	0.196874i	$0.936921\pi$
$338$	−608361.	−	1.05371e6i	−0.289647	−	0.501684i
$339$	213446.	+	1.14843e6i	0.100876	+	0.542759i
$340$	−734254.	+	1.27176e6i	−0.344468	+	0.596636i
$341$	5.18976e6			2.41691
$342$	−2.39691e6	+	922852.i	−1.10812	+	0.426645i
$343$	738601.			0.338980
$344$	−400157.	+	693093.i	−0.182320	+	0.315788i
$345$	2.09570e6	−	1.79172e6i	0.947941	−	0.810442i
$346$	456483.	+	790652.i	0.204991	+	0.355055i
$347$	−184376.	−	319349.i	−0.0822018	−	0.142378i	0.821994	−	0.569497i	$-0.192862\pi$
$347$	−184376.	−	319349.i	−0.0822018	−	0.142378i	−0.904195	+	0.427119i	$0.859529\pi$
$348$	−29295.0	−	10357.4i	−0.0129672	−	0.00458459i
$349$	−1.36770e6	+	2.36892e6i	−0.601071	+	1.04109i	0.391588	+	0.920141i	$0.371926\pi$
$349$	−1.36770e6	+	2.36892e6i	−0.601071	+	1.04109i	−0.992659	+	0.120945i	$0.961407\pi$
$350$	4930.70			0.00215149
$351$	466947.	−	863108.i	0.202302	−	0.373936i
$352$	607200.			0.261201
$353$	1.64512e6	−	2.84944e6i	0.702687	−	1.21709i	−0.264833	−	0.964294i	$-0.585317\pi$
$353$	1.64512e6	−	2.84944e6i	0.702687	−	1.21709i	0.967520	−	0.252795i	$-0.0813500\pi$
$354$	−914370.	−	323279.i	−0.387805	−	0.137110i
$355$	296037.	+	512751.i	0.124674	+	0.215941i
$356$	752765.	+	1.30383e6i	0.314800	+	0.545249i
$357$	−430082.	+	367698.i	−0.178600	+	0.152694i
$358$	−38740.0	+	67099.7i	−0.0159754	+	0.0276702i
$359$	−1.85769e6			−0.760740			−0.380370	−	0.924834i	$-0.624203\pi$
$359$	−1.85769e6			−0.760740			−0.380370	+	0.924834i	$0.624203\pi$
$360$	−136329.	+	866377.i	−0.0554410	+	0.352331i
$361$	4.50629e6			1.81991
$362$	−275580.	+	477318.i	−0.110529	+	0.191442i
$363$	542806.	+	2.92053e6i	0.216211	+	1.16331i
$364$	−46222.9	−	80060.4i	−0.0182854	−	0.0316712i
$365$	1.08221e6	+	1.87444e6i	0.425186	+	0.736443i
$366$	135934.	+	731383.i	0.0530426	+	0.285392i
$367$	1.13820e6	−	1.97141e6i	0.441115	−	0.764034i	−0.556657	−	0.830742i	$-0.687916\pi$
$367$	1.13820e6	−	1.97141e6i	0.441115	−	0.764034i	0.997773	+	0.0667081i	$0.0212496\pi$
$368$	802924.			0.309069
$369$	−282207.	+	1.79344e6i	−0.107895	+	0.685681i
$370$	−2.19748e6			−0.834490
$371$	−120236.	+	208256.i	−0.0453525	+	0.0785528i
$372$	−1.65920e6	+	1.41853e6i	−0.621642	+	0.531473i
$373$	−264482.	−	458096.i	−0.0984292	−	0.170484i	0.812605	−	0.582814i	$-0.198048\pi$
$373$	−264482.	−	458096.i	−0.0984292	−	0.170484i	−0.911035	+	0.412330i	$0.864715\pi$
$374$	−1.93013e6	−	3.34308e6i	−0.713521	−	1.23585i
$375$	2.54425e6	+	899527.i	0.934288	+	0.330321i
$376$	−282159.	+	488713.i	−0.102926	+	0.178273i
$377$	−32273.8			−0.0116949
$378$	−160801.	+	297226.i	−0.0578842	+	0.106994i
$379$	−3.23027e6			−1.15516			−0.577578	−	0.816336i	$-0.696002\pi$
$379$	−3.23027e6			−1.15516			−0.577578	+	0.816336i	$0.696002\pi$
$380$	1.19213e6	−	2.06483e6i	0.423511	−	0.733543i
$381$	−508195.	−	179674.i	−0.179357	−	0.0634123i
$382$	673046.	+	1.16575e6i	0.235986	+	0.408740i
$383$	−1.96451e6	−	3.40264e6i	−0.684319	−	1.18527i	−0.973650	−	0.228046i	$-0.926766\pi$
$383$	−1.96451e6	−	3.40264e6i	−0.684319	−	1.18527i	0.289332	−	0.957229i	$-0.406567\pi$
$384$	−194125.	+	165967.i	−0.0671822	+	0.0574374i
$385$	−372905.	+	645890.i	−0.128217	+	0.222079i
$386$	2.96349e6			1.01236
$387$	2.83577e6	−	1.09182e6i	0.962484	−	0.370573i
$388$	−1.30379e6			−0.439670
$389$	−2.34603e6	+	4.06344e6i	−0.786066	+	1.36151i	0.142294	+	0.989825i	$0.454552\pi$
$389$	−2.34603e6	+	4.06344e6i	−0.786066	+	1.36151i	−0.928360	+	0.371682i	$0.878781\pi$
$390$	166458.	+	895619.i	0.0554172	+	0.298168i
$391$	−2.55228e6	−	4.42069e6i	−0.844281	−	1.46234i
$392$	−521906.	−	903968.i	−0.171545	−	0.297124i
$393$	226806.	+	1.22031e6i	0.0740751	+	0.398556i
$394$	438257.	−	759083.i	0.142229	−	0.246348i
$395$	1.00684e6			0.324690
$396$	−1.79314e6	−	1.44907e6i	−0.574613	−	0.464357i
$397$	−4.97999e6			−1.58581			−0.792907	−	0.609343i	$-0.791433\pi$
$397$	−4.97999e6			−1.58581			−0.792907	+	0.609343i	$0.791433\pi$
$398$	−430757.	+	746092.i	−0.136309	+	0.236094i
$399$	698278.	−	596993.i	0.219582	−	0.187731i
$400$	−7074.48	−	12253.4i	−0.00221077	−	0.00382917i
$401$	−1.74213e6	−	3.01746e6i	−0.541027	−	0.937087i	−0.998845	−	0.0480411i	$-0.984702\pi$
$401$	−1.74213e6	−	3.01746e6i	−0.541027	−	0.937087i	0.457818	−	0.889046i	$-0.348631\pi$
$402$	363284.	+	128440.i	0.112119	+	0.0396402i
$403$	−1.13367e6	+	1.96358e6i	−0.347717	+	0.602263i
$404$	2.12589e6			0.648017
$405$	2.47019e6	−	2.23317e6i	0.748330	−	0.676527i
$406$	11114.0			0.00334623
$407$	2.88825e6	−	5.00260e6i	0.864269	−	1.49696i
$408$	1.53084e6	+	541235.i	0.455282	+	0.160967i
$409$	647421.	+	1.12137e6i	0.191372	+	0.331466i	0.945705	−	0.325026i	$-0.105373\pi$
$409$	647421.	+	1.12137e6i	0.191372	+	0.331466i	−0.754333	+	0.656492i	$0.772040\pi$
$410$	−842665.	−	1.45954e6i	−0.247568	−	0.428801i
$411$	−3.21142e6	+	2.74560e6i	−0.937761	+	0.801739i
$412$	992889.	−	1.71973e6i	0.288176	−	0.499135i
$413$	346896.			0.100075
$414$	−2.37114e6	−	1.91617e6i	−0.679917	−	0.549456i
$415$	−2.43737e6			−0.694708
$416$	−132639.	+	229738.i	−0.0375785	+	0.0650878i
$417$	94480.3	+	508345.i	0.0266073	+	0.143159i
$418$	3.13374e6	+	5.42780e6i	0.877249	+	1.51944i
$419$	3.18739e6	+	5.52073e6i	0.886953	+	1.53625i	0.843459	+	0.537194i	$0.180516\pi$
$419$	3.18739e6	+	5.52073e6i	0.886953	+	1.53625i	0.0434947	+	0.999054i	$0.486151\pi$
$420$	−57322.9	−	308422.i	−0.0158564	−	0.0853143i
$421$	2.20802e6	−	3.82440e6i	0.607152	−	1.05162i	−0.384555	−	0.923102i	$-0.625645\pi$
$421$	2.20802e6	−	3.82440e6i	0.607152	−	1.05162i	0.991707	−	0.128516i	$-0.0410214\pi$
$422$	−18284.6			−0.00499809
$423$	1.99956e6	−	769864.i	0.543354	−	0.209201i
$424$	690052.			0.186409
$425$	−44975.8	+	77900.3i	−0.0120783	+	0.0209203i
$426$	497584.	−	425409.i	0.132844	−	0.113575i
$427$	−133043.	−	230437.i	−0.0353119	−	0.0611620i
$428$	−822947.	−	1.42539e6i	−0.217151	−	0.376117i
$429$	−2.25767e6	−	798208.i	−0.592267	−	0.209398i
$430$	−1.41040e6	+	2.44289e6i	−0.367851	+	0.637136i
$431$	−6.65197e6			−1.72487			−0.862436	−	0.506166i	$-0.831062\pi$
$431$	−6.65197e6			−1.72487			−0.862436	+	0.506166i	$0.831062\pi$
$432$	969355.	−	26845.2i	0.249904	−	0.00692082i
$433$	−3.41878e6			−0.876297			−0.438149	−	0.898903i	$-0.644366\pi$
$433$	−3.41878e6			−0.876297			−0.438149	+	0.898903i	$0.644366\pi$
$434$	390400.	−	676193.i	0.0994915	−	0.172324i
$435$	−103254.	−	36505.7i	−0.0261627	−	0.00924991i
$436$	−1.83483e6	−	3.17802e6i	−0.462253	−	0.800646i
$437$	4.14387e6	+	7.17740e6i	1.03801	+	1.79789i
$438$	1.81899e6	−	1.55515e6i	0.453050	−	0.387335i
$439$	−1982.34	+	3433.51i	−0.000490927	+	0.000850310i	−0.866271	−	0.499575i	$-0.833490\pi$
$439$	−1982.34	+	3433.51i	−0.000490927	+	0.000850310i	0.865780	+	0.500425i	$0.166823\pi$
$440$	2.14015e6			0.527001
$441$	−616052.	+	3.91505e6i	−0.150842	+	0.958608i
$442$	1.68650e6			0.410611
$443$	−1.91417e6	+	3.31544e6i	−0.463417	+	0.802661i	−0.999129	−	0.0417398i	$-0.986710\pi$
$443$	−1.91417e6	+	3.31544e6i	−0.463417	+	0.802661i	0.535712	+	0.844401i	$0.320043\pi$
$444$	443982.	+	2.38881e6i	0.106883	+	0.575075i
$445$	2.65321e6	+	4.59549e6i	0.635142	+	1.10010i
$446$	1.89106e6	+	3.27541e6i	0.450160	+	0.779701i
$447$	−104353.	−	561465.i	−0.0247023	−	0.132909i
$448$	45676.7	−	79114.3i	0.0107523	−	0.0186234i
$449$	1.62273e6			0.379866			0.189933	−	0.981797i	$-0.439173\pi$
$449$	1.62273e6			0.379866			0.189933	+	0.981797i	$0.439173\pi$
$450$	−8350.63	+	53068.8i	−0.00194396	+	0.0123540i
$451$	4.43021e6			1.02561
$452$	−599470.	+	1.03831e6i	−0.138013	+	0.239046i
$453$	5.86464e6	−	5.01398e6i	1.34275	−	1.14799i
$454$	367780.	+	637013.i	0.0837429	+	0.145047i
$455$	−162918.	−	282182.i	−0.0368927	−	0.0639000i
$456$	−2.48547e6	−	878747.i	−0.559753	−	0.197903i
$457$	3.76377e6	−	6.51904e6i	0.843010	−	1.46014i	−0.0443285	−	0.999017i	$-0.514115\pi$
$457$	3.76377e6	−	6.51904e6i	0.843010	−	1.46014i	0.887338	−	0.461119i	$-0.152552\pi$
$458$	−2.23374e6			−0.497586
$459$	−3.22913e6	−	5.25167e6i	−0.715407	−	1.16350i
$460$	2.83000e6			0.623580
$461$	−360297.	+	624052.i	−0.0789602	+	0.136763i	−0.902802	−	0.430057i	$-0.858493\pi$
$461$	−360297.	+	624052.i	−0.0789602	+	0.136763i	0.823841	+	0.566820i	$0.191827\pi$
$462$	777469.	+	274877.i	0.169464	+	0.0599146i
$463$	2.72788e6	+	4.72483e6i	0.591389	+	1.02432i	0.994046	+	0.108965i	$0.0347536\pi$
$463$	2.72788e6	+	4.72483e6i	0.591389	+	1.02432i	−0.402656	+	0.915351i	$0.631913\pi$
$464$	−15946.2	−	27619.6i	−0.00343844	−	0.00595556i
$465$	−5.84803e6	+	4.99977e6i	−1.25423	+	1.07230i
$466$	2.09701e6	−	3.63212e6i	0.447337	−	0.774810i
$467$	−3.70082e6			−0.785245			−0.392623	−	0.919700i	$-0.628432\pi$
$467$	−3.70082e6			−0.785245			−0.392623	+	0.919700i	$0.628432\pi$
$468$	939967.	−	361903.i	0.198380	−	0.0763797i
$469$	−137824.			−0.0289329
$470$	−994502.	+	1.72253e6i	−0.207664	+	0.359684i
$471$	−164732.	−	886329.i	−0.0342157	−	0.184095i
$472$	−497720.	−	862076.i	−0.102832	−	0.178111i
$473$	−3.70751e6	−	6.42160e6i	−0.761955	−	1.31975i
$474$	−203423.	−	1.09451e6i	−0.0415867	−	0.223755i
$475$	73022.4	−	126479.i	0.0148499	−	0.0257207i
$476$	−580776.			−0.117487
$477$	−2.03781e6	−	1.64680e6i	−0.410079	−	0.331394i
$478$	−2.85521e6			−0.571569
$479$	3.00801e6	−	5.21003e6i	0.599020	−	1.03753i	−0.393946	−	0.919133i	$-0.628890\pi$
$479$	3.00801e6	−	5.21003e6i	0.599020	−	1.03753i	0.992966	−	0.118399i	$-0.0377762\pi$
$480$	−684217.	+	584972.i	−0.135547	+	0.115886i
$481$	1.26184e6	+	2.18558e6i	0.248681	+	0.430729i
$482$	−1.54187e6	−	2.67060e6i	−0.302295	−	0.523591i
$483$	1.02808e6	+	363480.i	0.200520	+	0.0708946i
$484$	−1.52448e6	+	2.64048e6i	−0.295808	+	0.512354i
$485$	−4.59535e6			−0.887083
$486$	−2.92669e6	−	2.23407e6i	−0.562065	−	0.429049i
$487$	1.27159e6			0.242954			0.121477	−	0.992594i	$-0.461237\pi$
$487$	1.27159e6			0.242954			0.121477	+	0.992594i	$0.461237\pi$
$488$	−381774.	+	661252.i	−0.0725699	+	0.125695i
$489$	1.98442e6	+	701598.i	0.375285	+	0.132683i
$490$	−1.83952e6	−	3.18614e6i	−0.346110	−	0.599480i
$491$	1.96015e6	+	3.39507e6i	0.366931	+	0.635544i	0.989084	−	0.147352i	$-0.0470751\pi$
$491$	1.96015e6	+	3.39507e6i	0.366931	+	0.635544i	−0.622153	+	0.782896i	$0.713742\pi$
$492$	−1.41636e6	+	1.21092e6i	−0.263792	+	0.225529i
$493$	−101377.	+	175591.i	−0.0187856	+	0.0325375i
$494$	−2.73819e6			−0.504832
$495$	−6.32012e6	−	5.10743e6i	−1.15934	−	0.936891i
$496$	−2.24056e6			−0.408932
$497$	−117079.	+	202787.i	−0.0212612	+	0.0368255i
$498$	492450.	+	2.64959e6i	0.0889792	+	0.478747i
$499$	2.19781e6	+	3.80672e6i	0.395129	+	0.684383i	0.993118	−	0.117122i	$-0.0373667\pi$
$499$	2.19781e6	+	3.80672e6i	0.395129	+	0.684383i	−0.597989	+	0.801504i	$0.704033\pi$
$500$	1.38491e6	+	2.39874e6i	0.247741	+	0.429099i
$501$	−1.15656e6	−	6.22279e6i	−0.205861	−	1.10762i
$502$	901696.	−	1.56178e6i	0.159698	−	0.276606i
$503$	6.81583e6			1.20115			0.600577	−	0.799567i	$-0.294938\pi$
$503$	6.81583e6			1.20115			0.600577	+	0.799567i	$0.294938\pi$
$504$	−323694.	+	124628.i	−0.0567621	+	0.0218544i
$505$	7.49294e6			1.30745
$506$	−3.71960e6	+	6.44254e6i	−0.645833	+	1.11861i
$507$	−3.60407e6	+	3.08130e6i	−0.622692	+	0.532371i
$508$	−276626.	−	479131.i	−0.0475592	−	0.0823749i
$509$	−2.33301e6	−	4.04089e6i	−0.399137	−	0.691325i	0.594483	−	0.804108i	$-0.297357\pi$
$509$	−2.33301e6	−	4.04089e6i	−0.399137	−	0.691325i	−0.993620	+	0.112783i	$0.964023\pi$
$510$	5.39564e6	+	1.90765e6i	0.918581	+	0.324768i
$511$	−428000.	+	741317.i	−0.0725088	+	0.125589i
$512$	−262144.			−0.0441942
$513$	5.24279e6	+	8.52659e6i	0.879567	+	1.43048i
$514$	−3.54243e6			−0.591416
$515$	3.49955e6	−	6.06140e6i	0.581426	−	1.00706i
$516$	2.94054e6	+	1.03964e6i	0.486187	+	0.171893i
$517$	−2.61424e6	−	4.52799e6i	−0.430149	−	0.745040i
$518$	−434538.	−	752642.i	−0.0711547	−	0.123244i
$519$	2.70431e6	−	2.31205e6i	0.440696	−	0.376773i
$520$	−467503.	+	809739.i	−0.0758186	+	0.131322i
$521$	−619313.			−0.0999576			−0.0499788	−	0.998750i	$-0.515915\pi$
$521$	−619313.			−0.0999576			−0.0499788	+	0.998750i	$0.515915\pi$
$522$	−18822.7	+	119620.i	−0.00302347	+	0.0192144i
$523$	−4.63344e6			−0.740713			−0.370356	−	0.928890i	$-0.620764\pi$
$523$	−4.63344e6			−0.740713			−0.370356	+	0.928890i	$0.620764\pi$
$524$	−636989.	+	1.10330e6i	−0.101345	+	0.175535i
$525$	−3511.24	−	18892.0i	−0.000555984	−	0.00299143i
$526$	−575937.	−	997552.i	−0.0907634	−	0.157207i
$527$	7.12213e6	+	1.23359e7i	1.11708	+	1.93484i
$528$	−432397.	−	2.32648e6i	−0.0674991	−	0.363175i
$529$	−1.70040e6	+	2.94519e6i	−0.264188	+	0.457587i
$530$	2.43217e6			0.376100
$531$	−587503.	+	3.73362e6i	−0.0904219	+	0.574637i
$532$	942945.			0.144447
$533$	−967755.	+	1.67620e6i	−0.147553	+	0.255569i
$534$	4.45955e6	−	3.81269e6i	0.676766	−	0.578601i
$535$	−2.90057e6	−	5.02394e6i	−0.438126	−	0.758857i
$536$	197747.	+	342507.i	0.0297302	+	0.0514941i
$537$	284680.	+	100650.i	0.0426011	+	0.0150618i
$538$	1.79772e6	−	3.11374e6i	0.267773	−	0.463796i
$539$	9.67106e6			1.43384
$540$	3.41661e6	−	94619.1i	0.504209	−	0.0139635i
$541$	−9.72857e6			−1.42908			−0.714539	−	0.699596i	$-0.753364\pi$
$541$	−9.72857e6			−1.42908			−0.714539	+	0.699596i	$0.753364\pi$
$542$	3.78638e6	−	6.55820e6i	0.553638	−	0.958929i
$543$	2.02509e6	+	715977.i	0.294744	+	0.104208i
$544$	833286.	+	1.44329e6i	0.120725	+	0.209102i
$545$	−6.46708e6	−	1.12013e7i	−0.932646	−	1.61539i
$546$	−273835.	+	234115.i	−0.0393104	+	0.0336084i
$547$	−4.63898e6	+	8.03494e6i	−0.662909	+	1.14819i	0.316939	+	0.948446i	$0.397345\pi$
$547$	−4.63898e6	+	8.03494e6i	−0.662909	+	1.14819i	−0.979848	+	0.199746i	$0.935988\pi$
$548$	−4.33665e6			−0.616883
$549$	2.70549e6	−	1.04166e6i	0.383103	−	0.147501i
$550$	131092.			0.0184786
$551$	164596.	−	285088.i	0.0230962	−	0.0400037i
$552$	−571776.	−	3.07640e6i	−0.0798690	−	0.429730i
$553$	199096.	+	344845.i	0.0276854	+	0.0479525i
$554$	3.46425e6	+	6.00025e6i	0.479551	+	0.830606i
$555$	1.56487e6	+	8.41965e6i	0.215648	+	1.16028i
$556$	−265350.	+	459600.i	−0.0364026	+	0.0630512i
$557$	2.83520e6			0.387209			0.193604	−	0.981080i	$-0.437982\pi$
$557$	2.83520e6			0.387209			0.193604	+	0.981080i	$0.437982\pi$
$558$	6.61664e6	+	5.34705e6i	0.899605	+	0.726991i
$559$	3.23954e6			0.438484
$560$	160993.	−	278848.i	0.0216938	−	0.0375748i
$561$	−1.14345e7	+	9.77594e6i	−1.53395	+	1.31145i
$562$	−586514.	−	1.01587e6i	−0.0783317	−	0.135675i
$563$	−4.85708e6	−	8.41271e6i	−0.645809	−	1.11857i	−0.984114	−	0.177538i	$-0.943187\pi$
$563$	−4.85708e6	−	8.41271e6i	−0.645809	−	1.11857i	0.338305	−	0.941037i	$-0.390147\pi$
$564$	2.07344e6	+	733070.i	0.274469	+	0.0970393i
$565$	−2.11290e6	+	3.65965e6i	−0.278457	+	0.482302i
$566$	3.19266e6			0.418901
$567$	1.25333e6	+	404450.i	0.163722	+	0.0528332i
$568$	671930.			0.0873883
$569$	901486.	−	1.56142e6i	0.116729	−	0.202180i	−0.801741	−	0.597672i	$-0.796092\pi$
$569$	901486.	−	1.56142e6i	0.116729	−	0.202180i	0.918470	+	0.395492i	$0.129426\pi$
$570$	−8.76034e6	−	3.09725e6i	−1.12936	−	0.399290i
$571$	3.24846e6	+	5.62649e6i	0.416953	+	0.722183i	0.995631	−	0.0933726i	$-0.0297648\pi$
$571$	3.24846e6	+	5.62649e6i	0.416953	+	0.722183i	−0.578679	+	0.815556i	$0.696431\pi$
$572$	−1.22892e6	−	2.12855e6i	−0.157049	−	0.272016i
$573$	3.98728e6	−	3.40893e6i	0.507330	−	0.433742i
$574$	333263.	−	577229.i	0.0422190	−	0.0731254i
$575$	173348.			0.0218650
$576$	774144.	+	625603.i	0.0972222	+	0.0785674i
$577$	3.93067e6			0.491504			0.245752	−	0.969333i	$-0.420965\pi$
$577$	3.93067e6			0.491504			0.245752	+	0.969333i	$0.420965\pi$
$578$	2.45788e6	−	4.25717e6i	0.306014	−	0.530031i
$579$	−2.11035e6	−	1.13546e7i	−0.261613	−	1.40759i
$580$	−56204.2	−	97348.6i	−0.00693744	−	0.0120160i
$581$	−481975.	−	834806.i	−0.0592358	−	0.102599i
$582$	928449.	+	4.99546e6i	0.113619	+	0.611319i
$583$	−3.19671e6	+	5.53686e6i	−0.389522	+	0.674671i
$584$	2.45634e6			0.298028
$585$	3.31302e6	−	1.27557e6i	0.400253	−	0.154104i
$586$	−5.56292e6			−0.669205
$587$	−1.07731e6	+	1.86595e6i	−0.129046	+	0.223514i	−0.923307	−	0.384062i	$-0.874525\pi$
$587$	−1.07731e6	+	1.86595e6i	−0.129046	+	0.223514i	0.794261	+	0.607576i	$0.207858\pi$
$588$	−3.09190e6	+	2.64342e6i	−0.368792	+	0.315299i
$589$	−1.15635e7	−	2.00285e7i	−1.37341	−	2.37881i
$590$	−1.75427e6	−	3.03849e6i	−0.207476	−	0.359358i
$591$	−3.22052e6	−	1.13862e6i	−0.379277	−	0.134095i
$592$	−1.24693e6	+	2.15975e6i	−0.146231	+	0.253279i
$593$	−1.38401e7			−1.61623			−0.808113	−	0.589027i	$-0.799511\pi$
$593$	−1.38401e7			−1.61623			−0.808113	+	0.589027i	$0.799511\pi$
$594$	−4.27520e6	+	7.90231e6i	−0.497153	+	0.918942i
$595$	−2.04701e6			−0.237044
$596$	293079.	−	507627.i	0.0337962	−	0.0585368i
$597$	3.16540e6	+	1.11914e6i	0.363490	+	0.128513i
$598$	−1.62505e6	−	2.81467e6i	−0.185829	−	0.321866i
$599$	83012.3	+	143782.i	0.00945313	+	0.0163733i	0.870713	−	0.491791i	$-0.163658\pi$
$599$	83012.3	+	143782.i	0.00945313	+	0.0163733i	−0.861260	+	0.508164i	$0.830324\pi$
$600$	−41910.9	+	35831.7i	−0.00475279	+	0.00406340i
$601$	7.32908e6	−	1.26943e7i	0.827682	−	1.43359i	−0.0721708	−	0.997392i	$-0.522993\pi$
$601$	7.32908e6	−	1.26943e7i	0.827682	−	1.43359i	0.899852	−	0.436194i	$-0.143674\pi$
$602$	−1.11559e6			−0.125463
$603$	233418.	−	1.48339e6i	0.0261421	−	0.166135i
$604$	7.91953e6			0.883297
$605$	−5.37322e6	+	9.30669e6i	−0.596824	+	1.03373i
$606$	−1.51388e6	−	8.14533e6i	−0.167460	−	0.901005i
$607$	1.45547e6	+	2.52096e6i	0.160337	+	0.277711i	0.934989	−	0.354676i	$-0.115409\pi$
$607$	1.45547e6	+	2.52096e6i	0.160337	+	0.277711i	−0.774653	+	0.632387i	$0.782075\pi$
$608$	−1.35292e6	−	2.34332e6i	−0.148427	−	0.257083i
$609$	−7914.49	−	42583.4i	−0.000864729	−	0.00465261i
$610$	−1.34561e6	+	2.33066e6i	−0.146418	+	0.253603i
$611$	2.28426e6			0.247539
$612$	983602.	−	6.25085e6i	0.106155	−	0.674622i
$613$	1.46967e7			1.57968			0.789838	−	0.613315i	$-0.210164\pi$
$613$	1.46967e7			1.57968			0.789838	+	0.613315i	$0.210164\pi$
$614$	1.19604e6	−	2.07160e6i	0.128034	−	0.221761i
$615$	−4.99214e6	+	4.26803e6i	−0.532230	+	0.455030i
$616$	423200.	+	733004.i	0.0449360	+	0.0778314i
$617$	1.49092e6	+	2.58235e6i	0.157668	+	0.273088i	0.934027	−	0.357202i	$-0.116269\pi$
$617$	1.49092e6	+	2.58235e6i	0.157668	+	0.273088i	−0.776360	+	0.630290i	$0.782936\pi$
$618$	−7.29621e6	−	2.57960e6i	−0.768469	−	0.271695i
$619$	−879493.	+	1.52333e6i	−0.0922583	+	0.159796i	−0.908461	−	0.417969i	$-0.862742\pi$
$619$	−879493.	+	1.52333e6i	−0.0922583	+	0.159796i	0.816203	+	0.577766i	$0.196075\pi$
$620$	−7.89710e6			−0.825065
$621$	−5.65327e6	+	1.04495e7i	−0.588262	+	1.08735i
$622$	1.19121e7			1.23456
$623$	−1.04931e6	+	1.81746e6i	−0.108314	+	0.187605i
$624$	974696.	+	344607.i	0.100209	+	0.0354293i
$625$	4.96764e6	+	8.60421e6i	0.508687	+	0.881071i
$626$	5.00747e6	+	8.67319e6i	0.510720	+	0.884592i
$627$	1.85650e7	−	1.58722e7i	1.88594	−	1.61238i
$628$	462654.	−	801340.i	0.0468120	−	0.0810807i
$629$	1.58547e7			1.59783
$630$	−1.14090e6	+	439265.i	−0.114524	+	0.0440936i
$631$	4.55795e6			0.455718			0.227859	−	0.973694i	$-0.426827\pi$
$631$	4.55795e6			0.455718			0.227859	+	0.973694i	$0.426827\pi$
$632$	571320.	−	989554.i	0.0568966	−	0.0985478i
$633$	13020.8	+	70057.4i	0.00129160	+	0.00694936i
$634$	4.17269e6	+	7.22732e6i	0.412281	+	0.714092i
$635$	−975003.	−	1.68875e6i	−0.0959558	−	0.166200i
$636$	−491398.	−	2.64393e6i	−0.0481715	−	0.259184i
$637$	−2.11259e6	+	3.65911e6i	−0.206284	+	0.357295i
$638$	295487.			0.0287400
$639$	−1.98429e6	−	1.60355e6i	−0.192244	−	0.155357i
$640$	−923957.			−0.0891665
$641$	−8.62721e6	+	1.49428e7i	−0.829326	+	1.43643i	0.0692419	+	0.997600i	$0.477942\pi$
$641$	−8.62721e6	+	1.49428e7i	−0.829326	+	1.43643i	−0.898568	+	0.438835i	$0.855391\pi$
$642$	−4.87533e6	+	4.16816e6i	−0.466838	+	0.399123i
$643$	−6.68107e6	−	1.15719e7i	−0.637263	−	1.10377i	−0.986031	−	0.166562i	$-0.946733\pi$
$643$	−6.68107e6	−	1.15719e7i	−0.637263	−	1.10377i	0.348768	−	0.937209i	$-0.386600\pi$
$644$	559615.	+	969281.i	0.0531710	+	0.0920948i
$645$	1.03643e7	+	3.66433e6i	0.980935	+	0.346813i
$646$	−8.60114e6	+	1.48976e7i	−0.810914	+	1.40454i
$647$	357748.			0.0335982			0.0167991	−	0.999859i	$-0.494652\pi$
$647$	357748.			0.0335982			0.0167991	+	0.999859i	$0.494652\pi$
$648$	−793152.	−	3.69497e6i	−0.0742026	−	0.345679i
$649$	9.22288e6			0.859518
$650$	−28636.3	+	49599.5i	−0.00265848	+	0.00460462i
$651$	−2.86884e6	−	1.01429e6i	−0.265311	−	0.0938014i
$652$	1.08018e6	+	1.87093e6i	0.0995125	+	0.172361i
$653$	6.12091e6	+	1.06017e7i	0.561737	+	0.972957i	0.997345	+	0.0728208i	$0.0232001\pi$
$653$	6.12091e6	+	1.06017e7i	0.561737	+	0.972957i	−0.435608	+	0.900137i	$0.643467\pi$
$654$	−1.08700e7	+	9.29328e6i	−0.993766	+	0.849620i
$655$	−2.24514e6	+	3.88870e6i	−0.204475	+	0.354162i
$656$	−1.91264e6			−0.173529
$657$	−7.25388e6	−	5.86202e6i	−0.655627	−	0.529827i
$658$	−786626.			−0.0708277
$659$	−5.25518e6	+	9.10224e6i	−0.471383	+	0.816460i	−0.999464	−	0.0327344i	$-0.989578\pi$
$659$	−5.25518e6	+	9.10224e6i	−0.471383	+	0.816460i	0.528081	+	0.849194i	$0.322912\pi$
$660$	−1.52404e6	−	8.19997e6i	−0.136187	−	0.732744i
$661$	−1.51211e6	−	2.61905e6i	−0.134611	−	0.233153i	0.790838	−	0.612026i	$-0.209645\pi$
$661$	−1.51211e6	−	2.61905e6i	−0.134611	−	0.233153i	−0.925449	+	0.378873i	$0.876312\pi$
$662$	−3.79026e6	−	6.56492e6i	−0.336143	−	0.582216i
$663$	−1.20099e6	−	6.46183e6i	−0.106110	−	0.570915i
$664$	−1.38306e6	+	2.39553e6i	−0.121736	+	0.210853i
$665$	3.32352e6			0.291437
$666$	8.83657e6	−	3.40223e6i	0.771966	−	0.297220i
$667$	390734.			0.0340069
$668$	3.24823e6	−	5.62610e6i	0.281647	−	0.487827i
$669$	1.12031e7	−	9.57806e6i	0.967769	−	0.827393i
$670$	696981.	+	1.20721e6i	0.0599838	+	0.103895i
$671$	−3.53718e6	−	6.12658e6i	−0.303285	−	0.525306i
$672$	−335654.	−	118671.i	−0.0286727	−	0.0101373i
$673$	6.14813e6	−	1.06489e7i	0.523245	−	0.906287i	−0.476389	−	0.879235i	$-0.658055\pi$
$673$	6.14813e6	−	1.06489e7i	0.523245	−	0.906287i	0.999634	−	0.0270524i	$-0.00861210\pi$
$674$	−5.33249e6			−0.452148
$675$	209280.	−	5795.77i	0.0176794	−	0.000489612i
$676$	−4.86688e6			−0.409623
$677$	−605609.	+	1.04895e6i	−0.0507833	+	0.0879592i	−0.890300	−	0.455375i	$-0.849505\pi$
$677$	−605609.	+	1.04895e6i	−0.0507833	+	0.0879592i	0.839516	+	0.543334i	$0.182838\pi$
$678$	4.40519e6	+	1.55747e6i	0.368036	+	0.130120i
$679$	−908701.	−	1.57392e6i	−0.0756392	−	0.131011i
$680$	2.93702e6	+	5.08706e6i	0.243576	+	0.421885i
$681$	2.17881e6	−	1.86278e6i	0.180033	−	0.153919i
$682$	1.03795e7	−	1.79779e7i	0.854508	−	1.48005i
$683$	−5.89207e6			−0.483299			−0.241650	−	0.970364i	$-0.577688\pi$
$683$	−5.89207e6			−0.483299			−0.241650	+	0.970364i	$0.577688\pi$
$684$	−1.59697e6	+	1.01489e7i	−0.130514	+	0.829424i
$685$	−1.52850e7			−1.24463
$686$	1.47720e6	−	2.55859e6i	0.119848	−	0.207582i
$687$	1.59068e6	+	8.55856e6i	0.128585	+	0.691845i
$688$	1.60063e6	+	2.77237e6i	0.128920	+	0.223296i
$689$	−1.39661e6	−	2.41899e6i	−0.112079	−	0.194127i
$690$	−2.01529e6	−	1.08431e7i	−0.161144	−	0.867027i
$691$	6.20006e6	−	1.07388e7i	0.493970	−	0.855581i	−0.506006	−	0.862530i	$-0.668879\pi$
$691$	6.20006e6	−	1.07388e7i	0.493970	−	0.855581i	0.999976	+	0.00694867i	$0.00221185\pi$
$692$	3.65187e6			0.289901
$693$	499541.	−	3.17462e6i	0.0395128	−	0.251107i
$694$	−1.47501e6			−0.116251
$695$	−935259.	+	1.61992e6i	−0.0734463	+	0.127213i
$696$	−94469.0	+	80766.2i	−0.00739207	+	0.00631985i
$697$	6.07977e6	+	1.05305e7i	0.474029	+	0.821043i
$698$	5.47079e6	+	9.47568e6i	0.425022	+	0.736159i
$699$	−1.54098e7	−	5.44818e6i	−1.19290	−	0.421753i
$700$	9861.41	−	17080.5i	0.000760666	−	0.00131751i
$701$	−1.29116e7			−0.992396			−0.496198	−	0.868209i	$-0.665271\pi$
$701$	−1.29116e7			−0.992396			−0.496198	+	0.868209i	$0.665271\pi$
$702$	−2.05600e6	−	3.34377e6i	−0.157464	−	0.256090i
$703$	−2.57416e7			−1.96448
$704$	1.21440e6	−	2.10340e6i	0.0923485	−	0.159952i
$705$	7.30807e6	+	2.58379e6i	0.553770	+	0.195787i
$706$	−6.58050e6	−	1.13978e7i	−0.496875	−	0.860612i
$707$	1.48168e6	+	2.56635e6i	0.111482	+	0.193093i
$708$	−2.94861e6	+	2.52091e6i	−0.221072	+	0.189006i
$709$	−9.36762e6	+	1.62252e7i	−0.699864	+	1.21220i	0.268650	+	0.963238i	$0.413423\pi$
$709$	−9.36762e6	+	1.62252e7i	−0.699864	+	1.21220i	−0.968513	+	0.248962i	$0.919911\pi$
$710$	2.36830e6			0.176315
$711$	−4.04874e6	+	1.55883e6i	−0.300362	+	0.115645i
$712$	6.02212e6			0.445194
$713$	1.37253e7	−	2.37728e7i	1.01111	−	1.75129i
$714$	413581.	+	2.22524e6i	0.0303609	+	0.163355i
$715$	−4.33148e6	−	7.50234e6i	−0.316862	−	0.548822i
$716$	154960.	+	268399.i	0.0112963	+	0.0195658i
$717$	2.03325e6	+	1.09397e7i	0.147704	+	0.794711i
$718$	−3.71537e6	+	6.43522e6i	−0.268962	+	0.465856i
$719$	−1.08129e7			−0.780044			−0.390022	−	0.920806i	$-0.627533\pi$
$719$	−1.08129e7			−0.780044			−0.390022	+	0.920806i	$0.627533\pi$
$720$	2.72856e6	+	2.20501e6i	0.196156	+	0.158518i
$721$	2.76806e6			0.198306
$722$	9.01257e6	−	1.56102e7i	0.643437	−	1.11446i
$723$	−9.13442e6	+	7.80947e6i	−0.649883	+	0.555618i
$724$	1.10232e6	+	1.90927e6i	0.0781557	+	0.135370i
$725$	−3442.72	−	5962.96i	−0.000243252	−	0.000421325i
$726$	1.12026e7	+	3.96072e6i	0.788820	+	0.278890i
$727$	2.80710e6	−	4.86205e6i	0.196980	−	0.341180i	−0.750568	−	0.660794i	$-0.770220\pi$
$727$	2.80710e6	−	4.86205e6i	0.196980	−	0.341180i	0.947548	+	0.319614i	$0.103553\pi$
$728$	−369783.			−0.0258594
$729$	−6.47571e6	+	1.28045e7i	−0.451303	+	0.892371i
$730$	8.65766e6			0.601303
$731$	1.01760e7	−	1.76253e7i	0.704339	−	1.21995i
$732$	2.80545e6	+	991878.i	0.193520	+	0.0684196i
$733$	8.84117e6	+	1.53133e7i	0.607785	+	1.05271i	0.991605	+	0.129306i	$0.0412749\pi$
$733$	8.84117e6	+	1.53133e7i	0.607785	+	1.05271i	−0.383820	+	0.923408i	$0.625392\pi$
$734$	−4.55279e6	−	7.88566e6i	−0.311916	−	0.540254i
$735$	−1.08977e7	+	9.31703e6i	−0.744078	+	0.636149i
$736$	1.60585e6	−	2.78141e6i	0.109272	−	0.189265i
$737$	−3.66430e6			−0.248498
$738$	5.64826e6	+	4.56448e6i	0.381745	+	0.308497i
$739$	9.10643e6			0.613390			0.306695	−	0.951808i	$-0.400777\pi$
$739$	9.10643e6			0.613390			0.306695	+	0.951808i	$0.400777\pi$
$740$	−4.39496e6	+	7.61230e6i	−0.295037	+	0.511019i
$741$	1.94992e6	+	1.04914e7i	0.130458	+	0.701920i
$742$	480946.	+	833022.i	0.0320691	+	0.0555452i
$743$	165517.	+	286683.i	0.0109994	+	0.0190515i	0.871473	−	0.490444i	$-0.163165\pi$
$743$	165517.	+	286683.i	0.0109994	+	0.0190515i	−0.860473	+	0.509496i	$0.829832\pi$
$744$	1.59554e6	+	8.58469e6i	0.105676	+	0.568581i
$745$	1.03299e6	−	1.78919e6i	0.0681876	−	0.118104i
$746$	−2.11585e6			−0.139200
$747$	9.80123e6	−	3.77364e6i	0.642657	−	0.247434i
$748$	−1.54410e7			−1.00907
$749$	1.14714e6	−	1.98690e6i	0.0747157	−	0.129411i
$750$	8.20454e6	−	7.01447e6i	0.532600	−	0.455346i
$751$	1.40412e7	+	2.43202e7i	0.908460	+	1.57350i	0.816204	+	0.577764i	$0.196074\pi$
$751$	1.40412e7	+	2.43202e7i	0.908460	+	1.57350i	0.0922561	+	0.995735i	$0.470592\pi$
$752$	1.12864e6	+	1.95485e6i	0.0727795	+	0.126058i
$753$	−6.62608e6	−	2.34267e6i	−0.425863	−	0.150565i
$754$	−64547.5	+	111800.i	−0.00413477	+	0.00716163i
$755$	2.79133e7			1.78215
$756$	708019.	+	1.15148e6i	0.0450548	+	0.0732746i
$757$	−1.85991e7			−1.17965			−0.589824	−	0.807532i	$-0.700803\pi$
$757$	−1.85991e7			−1.17965			−0.589824	+	0.807532i	$0.700803\pi$
$758$	−6.46054e6	+	1.11900e7i	−0.408409	+	0.707385i
$759$	2.73334e7	+	9.66380e6i	1.72222	+	0.608897i
$760$	−4.76852e6	−	8.25932e6i	−0.299468	−	0.518693i
$761$	−5.16614e6	−	8.94802e6i	−0.323374	−	0.560099i	0.657808	−	0.753185i	$-0.271484\pi$
$761$	−5.16614e6	−	8.94802e6i	−0.323374	−	0.560099i	−0.981182	+	0.193086i	$0.938150\pi$
$762$	−1.63880e6	+	1.40109e6i	−0.102244	+	0.0874136i
$763$	2.55765e6	−	4.42997e6i	0.159048	−	0.275480i
$764$	5.38437e6			0.333735
$765$	3.46682e6	−	2.20319e7i	0.214179	−	1.36112i
$766$	−1.57161e7			−0.967773
$767$	−2.01469e6	+	3.48954e6i	−0.123657	+	0.214180i
$768$	186677.	+	1.00440e6i	0.0114206	+	0.0614477i
$769$	−1.00261e7	−	1.73658e7i	−0.611388	−	1.05896i	−0.991007	−	0.133813i	$-0.957278\pi$
$769$	−1.00261e7	−	1.73658e7i	−0.611388	−	1.05896i	0.379618	−	0.925143i	$-0.376055\pi$
$770$	1.49162e6	+	2.58356e6i	0.0906632	+	0.157033i
$771$	2.52262e6	+	1.35728e7i	0.152833	+	0.822306i
$772$	5.92698e6	−	1.02658e7i	0.357924	−	0.619942i
$773$	2.68448e7			1.61589			0.807943	−	0.589260i	$-0.200581\pi$
$773$	2.68448e7			1.61589			0.807943	+	0.589260i	$0.200581\pi$
$774$	1.88937e6	−	1.20070e7i	0.113361	−	0.720416i
$775$	−483727.			−0.0289298
$776$	−2.60757e6	+	4.51645e6i	−0.155447	+	0.269242i
$777$	−2.57431e6	+	2.20090e6i	−0.152970	+	0.130782i
$778$	9.38411e6	+	1.62538e7i	0.555833	+	0.962731i
$779$	−9.87108e6	−	1.70972e7i	−0.582802	−	1.00944i
$780$	3.43543e6	+	1.21461e6i	0.202183	+	0.0714825i
$781$	−3.11276e6	+	5.39146e6i	−0.182607	+	0.316285i
$782$	−2.04183e7			−1.19399
$783$	471726.	−	13063.9i	0.0274970	−	0.000761500i
$784$	−4.17525e6			−0.242601
$785$	1.63068e6	−	2.82442e6i	0.0944482	−	0.163589i
$786$	4.68090e6	+	1.65495e6i	0.270254	+	0.0955494i
$787$	−3.83561e6	−	6.64347e6i	−0.220748	−	0.382347i	0.734287	−	0.678839i	$-0.237517\pi$
$787$	−3.83561e6	−	6.64347e6i	−0.220748	−	0.382347i	−0.955035	+	0.296492i	$0.904183\pi$
$788$	−1.75303e6	−	3.03633e6i	−0.100571	−	0.174194i
$789$	−3.41199e6	+	2.91708e6i	−0.195126	+	0.166823i
$790$	2.01368e6	−	3.48780e6i	0.114795	−	0.198831i
$791$	−1.67125e6			−0.0949731
$792$	−8.60601e6	+	3.31346e6i	−0.487516	+	0.187702i
$793$	3.09071e6			0.174532
$794$	−9.95998e6	+	1.72512e7i	−0.560670	+	0.971109i
$795$	−1.73199e6	−	9.31885e6i	−0.0971913	−	0.522931i
$796$	1.72303e6	+	2.98437e6i	0.0963850	+	0.166944i
$797$	4.41643e6	+	7.64949e6i	0.246278	+	0.426566i	0.962490	−	0.271316i	$-0.0874590\pi$
$797$	4.41643e6	+	7.64949e6i	0.246278	+	0.426566i	−0.716212	+	0.697883i	$0.754126\pi$
$798$	−671487.	−	3.61289e6i	−0.0373277	−	0.200839i
$799$	7.17526e6	−	1.24279e7i	0.397622	−	0.688702i
$800$	−56595.8			−0.00312651
$801$	−1.77841e7	−	1.43717e7i	−0.979377	−	0.791456i
$802$	−1.39370e7			−0.765128
$803$	−1.13792e7	+	1.97093e7i	−0.622761	+	1.07865i
$804$	1.17150e6	−	1.00157e6i	0.0639148	−	0.0546439i
$805$	1.97243e6	+	3.41635e6i	0.107278	+	0.185811i
$806$	4.53469e6	+	7.85432e6i	0.245873	+	0.425864i
$807$	−1.32105e7	−	4.67061e6i	−0.714061	−	0.252459i
$808$	4.25177e6	−	7.36429e6i	0.229109	−	0.396828i
$809$	−2.96255e6			−0.159146			−0.0795729	−	0.996829i	$-0.525356\pi$
$809$	−2.96255e6			−0.159146			−0.0795729	+	0.996829i	$0.525356\pi$
$810$	−2.79556e6	−	1.30233e7i	−0.149712	−	0.697445i
$811$	1.86775e7			0.997161			0.498581	−	0.866843i	$-0.333855\pi$
$811$	1.86775e7			0.997161			0.498581	+	0.866843i	$0.333855\pi$
$812$	22228.1	−	38500.1i	0.00118307	−	0.00204914i
$813$	−2.78241e7	−	9.83730e6i	−1.47637	−	0.521975i
$814$	−1.15530e7	−	2.00104e7i	−0.611131	−	1.05851i
$815$	3.80722e6	+	6.59431e6i	0.200777	+	0.347756i
$816$	4.93658e6	−	4.22053e6i	0.259538	−	0.221892i
$817$	−1.65216e7	+	2.86163e7i	−0.865960	+	1.49989i
$818$	5.17937e6			0.270641
$819$	1.09202e6	+	882482.i	0.0568878	+	0.0459723i
$820$	−6.74132e6			−0.350115
$821$	1.36264e7	−	2.36015e7i	0.705540	−	1.22203i	−0.260956	−	0.965351i	$-0.584038\pi$
$821$	1.36264e7	−	2.36015e7i	0.705540	−	1.22203i	0.966496	−	0.256681i	$-0.0826290\pi$
$822$	3.08820e6	+	1.66159e7i	0.159414	+	0.857716i
$823$	8.78359e6	+	1.52136e7i	0.452035	+	0.782948i	0.998512	−	0.0545260i	$-0.0173648\pi$
$823$	8.78359e6	+	1.52136e7i	0.452035	+	0.782948i	−0.546477	+	0.837474i	$0.684031\pi$
$824$	−3.97156e6	−	6.87894e6i	−0.203771	−	0.352942i
$825$	−93352.8	−	502279.i	−0.00477521	−	0.0256927i
$826$	693792.	−	1.20168e6i	0.0353818	−	0.0612830i
$827$	−1.92954e7			−0.981046			−0.490523	−	0.871428i	$-0.663194\pi$
$827$	−1.92954e7			−0.981046			−0.490523	+	0.871428i	$0.663194\pi$
$828$	−1.13801e7	+	4.38152e6i	−0.576858	+	0.222100i
$829$	4.98059e6			0.251707			0.125853	−	0.992049i	$-0.459833\pi$
$829$	4.98059e6			0.251707			0.125853	+	0.992049i	$0.459833\pi$
$830$	−4.87475e6	+	8.44331e6i	−0.245616	+	0.425420i
$831$	2.05230e7	−	1.75461e7i	1.03095	−	0.881412i
$832$	530557.	+	918952.i	0.0265720	+	0.0460240i
$833$	1.32720e7	+	2.29878e7i	0.662711	+	1.14785i
$834$	1.94992e6	+	689401.i	0.0970737	+	0.0343207i
$835$	1.14488e7	−	1.98298e7i	0.568254	−	0.984245i
$836$	2.50699e7			1.24062
$837$	1.57754e7	−	2.91594e7i	0.778336	−	1.43868i
$838$	2.54992e7			1.25434
$839$	−1.47355e7	+	2.55226e7i	−0.722703	+	1.25176i	0.237210	+	0.971458i	$0.423767\pi$
$839$	−1.47355e7	+	2.55226e7i	−0.722703	+	1.25176i	−0.959913	+	0.280300i	$0.909566\pi$
$840$	−1.18305e6	−	418272.i	−0.0578502	−	0.0204531i
$841$	1.02478e7	+	1.77497e7i	0.499622	+	0.865370i
$842$	−8.83207e6	−	1.52976e7i	−0.429321	−	0.743606i
$843$	−3.47465e6	+	2.97065e6i	−0.168400	+	0.143973i
$844$	−36569.2	+	63339.7i	−0.00176709	+	0.00306069i
$845$	−1.71539e7			−0.826459
$846$	1.33223e6	−	8.46640e6i	0.0639960	−	0.406699i
$847$	−4.25008e6			−0.203558
$848$	1.38010e6	−	2.39041e6i	0.0659055	−	0.114152i
$849$	−2.27355e6	−	1.22327e7i	−0.108252	−	0.582441i
$850$	179903.	+	311601.i	0.00854066	+	0.0147929i
$851$	−1.52770e7	−	2.64605e7i	−0.723126	−	1.25249i
$852$	−478493.	−	2.57450e6i	−0.0225827	−	0.121505i
$853$	1.36546e7	−	2.36505e7i	0.642551	−	1.11293i	−0.342310	−	0.939587i	$-0.611209\pi$
$853$	1.36546e7	−	2.36505e7i	0.642551	−	1.11293i	0.984861	−	0.173344i	$-0.0554572\pi$
$854$	−1.06434e6			−0.0499386
$855$	−5.62871e6	+	3.57708e7i	−0.263326	+	1.67345i
$856$	−6.58358e6			−0.307098
$857$	1.54427e6	−	2.67476e6i	0.0718244	−	0.124404i	−0.827876	−	0.560910i	$-0.810451\pi$
$857$	1.54427e6	−	2.67476e6i	0.0718244	−	0.124404i	0.899701	+	0.436507i	$0.143785\pi$
$858$	−7.28042e6	+	6.22439e6i	−0.337628	+	0.288655i
$859$	1.24557e6	+	2.15740e6i	0.0575952	+	0.0997578i	0.893385	−	0.449291i	$-0.148323\pi$
$859$	1.24557e6	+	2.15740e6i	0.0575952	+	0.0997578i	−0.835790	+	0.549049i	$0.814990\pi$
$860$	5.64161e6	+	9.77155e6i	0.260110	+	0.450523i
$861$	−2.44897e6	−	865843.i	−0.112584	−	0.0398044i
$862$	−1.33039e7	+	2.30431e7i	−0.609834	+	1.05626i
$863$	6.26889e6			0.286526			0.143263	−	0.989685i	$-0.454241\pi$
$863$	6.26889e6			0.286526			0.143263	+	0.989685i	$0.454241\pi$
$864$	1.84572e6	−	3.41164e6i	0.0841164	−	0.155481i
$865$	1.28714e7			0.584907
$866$	−6.83756e6	+	1.18430e7i	−0.309818	+	0.536620i
$867$	−1.80616e7	−	6.38575e6i	−0.816036	−	0.288512i
$868$	−1.56160e6	−	2.70477e6i	−0.0703511	−	0.121852i
$869$	5.29335e6	+	9.16835e6i	0.237783	+	0.411853i
$870$	−332967.	+	284670.i	−0.0149143	+	0.0127510i
$871$	800445.	−	1.38641e6i	0.0357508	−	0.0619223i
$872$	−1.46786e7			−0.653725
$873$	1.84789e7	−	7.11470e6i	0.820618	−	0.315952i
$874$	3.31510e7			1.46797
$875$	−1.93049e6	+	3.34370e6i	−0.0852406	+	0.147641i
$876$	−1.74920e6	−	9.41147e6i	−0.0770158	−	0.414379i
$877$	−1.30800e6	−	2.26553e6i	−0.0574261	−	0.0994650i	0.835883	−	0.548907i	$-0.184956\pi$
$877$	−1.30800e6	−	2.26553e6i	−0.0574261	−	0.0994650i	−0.893309	+	0.449442i	$0.851623\pi$
$878$	7929.36	+	13734.1i	0.000347138	+	0.000601260i
$879$	3.96145e6	+	2.13143e7i	0.172935	+	0.930464i
$880$	4.28029e6	−	7.41368e6i	0.186323	−	0.322721i
$881$	−1.63208e7			−0.708436			−0.354218	−	0.935163i	$-0.615253\pi$
$881$	−1.63208e7			−0.708436			−0.354218	+	0.935163i	$0.615253\pi$
$882$	1.23300e7	+	9.96418e6i	0.533695	+	0.431290i
$883$	−2.80814e6			−0.121204			−0.0606020	−	0.998162i	$-0.519302\pi$
$883$	−2.80814e6			−0.121204			−0.0606020	+	0.998162i	$0.519302\pi$
$884$	3.37300e6	−	5.84221e6i	0.145173	−	0.251447i
$885$	−1.03927e7	+	8.88525e6i	−0.446037	+	0.381339i
$886$	7.65669e6	+	1.32618e7i	0.327685	+	0.567567i
$887$	1.30991e7	+	2.26883e7i	0.559027	+	0.968263i	0.997578	+	0.0695566i	$0.0221584\pi$
$887$	1.30991e7	+	2.26883e7i	0.559027	+	0.968263i	−0.438551	+	0.898706i	$0.644508\pi$
$888$	9.16306e6	+	3.23963e6i	0.389949	+	0.137868i
$889$	385601.	−	667881.i	0.0163638	−	0.0283429i
$890$	2.12257e7			0.898227
$891$	3.33221e7	+	1.07531e7i	1.40617	+	0.453772i
$892$	1.51285e7			0.636623
$893$	−1.16497e7	+	2.01779e7i	−0.488863	+	0.846735i
$894$	−2.15368e6	−	761441.i	−0.0901233	−	0.0318634i
$895$	546175.	+	946003.i	0.0227916	+	0.0394762i
$896$	−182707.	−	316457.i	−0.00760299	−	0.0131688i
$897$	−9.62719e6	+	8.23076e6i	−0.399501	+	0.341554i
$898$	3.24546e6	−	5.62131e6i	0.134303	−	0.232620i
$899$	−1.09034e6			−0.0449949
$900$	167135.	+	135065.i	0.00687796	+	0.00555823i
$901$	−1.75479e7			−0.720135
$902$	8.86042e6	−	1.53467e7i	0.362609	−	0.628056i
$903$	794432.	+	4.27439e6i	0.0324218	+	0.174443i
$904$	2.39788e6	+	4.15325e6i	0.0975902	+	0.169031i
$905$	3.88525e6	+	6.72945e6i	0.157688	+	0.273123i
$906$	−5.63963e6	−	3.03437e7i	−0.228260	−	1.22814i
$907$	−1.39621e7	+	2.41831e7i	−0.563550	+	0.976097i	0.433633	+	0.901090i	$0.357231\pi$
$907$	−1.39621e7	+	2.41831e7i	−0.563550	+	0.976097i	−0.997183	+	0.0750075i	$0.976102\pi$
$908$	2.94224e6			0.118430
$909$	−3.01308e7	+	1.16009e7i	−1.20949	+	0.465673i
$910$	−1.30334e6			−0.0521741
$911$	2.28045e7	−	3.94986e7i	0.910384	−	1.57683i	0.0968626	−	0.995298i	$-0.469119\pi$
$911$	2.28045e7	−	3.94986e7i	0.910384	−	1.57683i	0.813522	−	0.581534i	$-0.197547\pi$
$912$	−8.01501e6	+	6.85243e6i	−0.319093	+	0.272808i
$913$	−1.28142e7	−	2.21949e7i	−0.508762	−	0.881202i
$914$	−1.50551e7	−	2.60762e7i	−0.596098	−	1.03247i
$915$	9.88815e6	+	3.49599e6i	0.390447	+	0.138044i
$916$	−4.46747e6	+	7.73789e6i	−0.175923	+	0.304708i
$917$	−1.77585e6			−0.0697402
$918$	−2.46506e7	+	682671.i	−0.965429	+	0.0267365i
$919$	6.63615e6			0.259196			0.129598	−	0.991567i	$-0.458631\pi$
$919$	6.63615e6			0.259196			0.129598	+	0.991567i	$0.458631\pi$
$920$	5.66000e6	−	9.80341e6i	0.220469	−	0.381863i
$921$	−8.78904e6	−	3.10740e6i	−0.341423	−	0.120711i
$922$	1.44119e6	+	2.49621e6i	0.0558333	+	0.0967061i
$923$	−1.35993e6	−	2.35547e6i	−0.0525427	−	0.0910066i
$924$	2.50714e6	−	2.14348e6i	0.0966047	−	0.0825922i
$925$	−269208.	+	466282.i	−0.0103451	+	0.0179182i
$926$	2.18231e7			0.836351
$927$	−4.68798e6	+	2.97924e7i	−0.179179	+	1.13869i
$928$	−127570.			−0.00486270
$929$	1.02667e7	−	1.77825e7i	0.390295	−	0.676011i	−0.602193	−	0.798350i	$-0.705706\pi$
$929$	1.02667e7	−	1.77825e7i	0.390295	−	0.676011i	0.992488	+	0.122339i	$0.0390396\pi$
$930$	5.62366e6	+	3.02577e7i	0.213212	+	1.14717i
$931$	−2.15484e7	−	3.73229e7i	−0.814780	−	1.41124i
$932$	−8.38802e6	−	1.45285e7i	−0.316315	−	0.547874i
$933$	−8.48283e6	−	4.56413e7i	−0.319034	−	1.71654i
$934$	−7.40163e6	+	1.28200e7i	−0.277626	+	0.480863i
$935$	−5.44237e7			−2.03591
$936$	626264.	−	3.97995e6i	0.0233651	−	0.148487i
$937$	−3.95168e7			−1.47039			−0.735196	−	0.677855i	$-0.762910\pi$
$937$	−3.95168e7			−1.47039			−0.735196	+	0.677855i	$0.762910\pi$
$938$	−275647.	+	477435.i	−0.0102293	+	0.0177177i
$939$	2.96654e7	−	2.53624e7i	1.09796	−	0.938701i
$940$	3.97801e6	+	6.89011e6i	0.146841	+	0.254335i
$941$	4.91319e6	+	8.50989e6i	0.180879	+	0.313292i	0.942180	−	0.335106i	$-0.108772\pi$
$941$	4.91319e6	+	8.50989e6i	0.180879	+	0.313292i	−0.761301	+	0.648399i	$0.775439\pi$
$942$	−3.39980e6	−	1.20201e6i	−0.124832	−	0.0441348i
$943$	1.17165e7	−	2.02936e7i	0.429060	−	0.743154i
$944$	−3.98176e6			−0.145427
$945$	2.49550e6	+	4.05854e6i	0.0909029	+	0.147839i
$946$	−2.96601e7			−1.07757
$947$	−9.54088e6	+	1.65253e7i	−0.345711	+	0.598789i	−0.985483	−	0.169776i	$-0.945696\pi$
$947$	−9.54088e6	+	1.65253e7i	−0.345711	+	0.598789i	0.639772	+	0.768565i	$0.279029\pi$
$948$	−4.19832e6	−	1.48433e6i	−0.151724	−	0.0536426i
$949$	−4.97143e6	−	8.61077e6i	−0.179191	−	0.310368i
$950$	−292090.	−	505914.i	−0.0105004	−	0.0181873i
$951$	2.47200e7	−	2.11344e7i	0.886334	−	0.757771i
$952$	−1.16155e6	+	2.01187e6i	−0.0415381	+	0.0719461i
$953$	3.72070e7			1.32707			0.663533	−	0.748147i	$-0.269056\pi$
$953$	3.72070e7			1.32707			0.663533	+	0.748147i	$0.269056\pi$
$954$	−9.78029e6	+	3.76558e6i	−0.347921	+	0.133956i
$955$	1.89778e7			0.673346
$956$	−5.71043e6	+	9.89075e6i	−0.202080	+	0.350013i
$957$	−210421.	−	1.13216e6i	−0.00742695	−	0.0399602i
$958$	−1.20321e7	−	2.08401e7i	−0.423571	−	0.733646i
$959$	−3.02252e6	−	5.23516e6i	−0.106126	−	0.183816i
$960$	657966.	+	3.54014e6i	0.0230423	+	0.123977i
$961$	−2.39856e7	+	4.15444e7i	−0.837805	+	1.45112i
$962$	1.00948e7			0.351689
$963$	1.94421e7	+	1.57116e7i	0.675582	+	0.545953i
$964$	−1.23350e7			−0.427510
$965$	2.08903e7	−	3.61831e7i	0.722150	−	1.25080i
$966$	3.31529e6	−	2.83441e6i	0.114309	−	0.0977280i
$967$	−2.69082e7	−	4.66064e7i	−0.925377	−	1.60280i	−0.790954	−	0.611876i	$-0.790415\pi$
$967$	−2.69082e7	−	4.66064e7i	−0.925377	−	1.60280i	−0.134423	−	0.990924i	$-0.542918\pi$
$968$	6.09793e6	+	1.05619e7i	0.209168	+	0.362289i
$969$	6.32052e7	+	2.23464e7i	2.16244	+	0.764537i
$970$	−9.19070e6	+	1.59188e7i	−0.313631	+	0.543225i
$971$	3.16679e7			1.07788			0.538940	−	0.842344i	$-0.318825\pi$
$971$	3.16679e7			1.07788			0.538940	+	0.842344i	$0.318825\pi$
$972$	−1.35924e7	+	5.67021e6i	−0.461458	+	0.192501i
$973$	−739766.			−0.0250503
$974$	2.54318e6	−	4.40491e6i	0.0858972	−	0.148778i
$975$	210433.	+	74399.3i	0.00708928	+	0.00250644i
$976$	1.52710e6	+	2.64501e6i	0.0513147	+	0.0888796i
$977$	3.03115e6	+	5.25011e6i	0.101595	+	0.175967i	0.912342	−	0.409429i	$-0.134272\pi$
$977$	3.03115e6	+	5.25011e6i	0.101595	+	0.175967i	−0.810747	+	0.585397i	$0.800939\pi$
$978$	6.39924e6	−	5.47103e6i	0.213935	−	0.182904i
$979$	−2.78978e7	+	4.83205e7i	−0.930281	+	1.61129i
$980$	−1.47162e7			−0.489474
$981$	4.33479e7	+	3.50304e7i	1.43812	+	1.16218i
$982$	1.56812e7			0.518919
$983$	−1.13501e7	+	1.96590e7i	−0.374642	+	0.648898i	−0.990273	−	0.139136i	$-0.955568\pi$
$983$	−1.13501e7	+	1.96590e7i	−0.374642	+	0.648898i	0.615632	+	0.788034i	$0.288901\pi$
$984$	1.36202e6	+	7.32827e6i	0.0448432	+	0.241276i
$985$	−6.17875e6	−	1.07019e7i	−0.202913	−	0.351456i
$986$	405510.	+	702363.i	0.0132834	+	0.0230075i
$987$	560170.	+	3.01396e6i	0.0183032	+	0.0984791i
$988$	−5.47639e6	+	9.48538e6i	−0.178485	+	0.309145i
$989$	−3.92207e7			−1.27504
$990$	−3.03329e7	+	1.16787e7i	−0.983616	+	0.378709i
$991$	4.31783e7			1.39663			0.698315	−	0.715790i	$-0.253933\pi$
$991$	4.31783e7			1.39663			0.698315	+	0.715790i	$0.253933\pi$
$992$	−4.48111e6	+	7.76151e6i	−0.144579	+	0.250419i
$993$	−2.24544e7	+	1.91974e7i	−0.722650	+	0.617829i
$994$	468315.	+	811146.i	0.0150339	+	0.0260395i
$995$	6.07301e6	+	1.05188e7i	0.194467	+	0.336827i
$996$	1.01634e7	+	3.59329e6i	0.324630	+	0.114774i
$997$	1.32803e7	−	2.30021e7i	0.423125	−	0.732874i	−0.573118	−	0.819473i	$-0.694266\pi$
$997$	1.32803e7	−	2.30021e7i	0.423125	−	0.732874i	0.996243	+	0.0865984i	$0.0275997\pi$
$998$	1.75825e7			0.558796
$999$	−1.93283e7	−	3.14345e7i	−0.612746	−	0.996537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.6.c.a.7.1	✓	4
3.2	odd	2		54.6.c.a.19.2		4
4.3	odd	2		144.6.i.a.97.2		4
9.2	odd	6		162.6.a.f.1.1		2
9.4	even	3	inner	18.6.c.a.13.1	yes	4
9.5	odd	6		54.6.c.a.37.2		4
9.7	even	3		162.6.a.e.1.2		2
12.11	even	2		432.6.i.a.289.2		4
36.23	even	6		432.6.i.a.145.2		4
36.31	odd	6		144.6.i.a.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.a.7.1	✓	4	1.1	even	1	trivial
18.6.c.a.13.1	yes	4	9.4	even	3	inner
54.6.c.a.19.2		4	3.2	odd	2
54.6.c.a.37.2		4	9.5	odd	6
144.6.i.a.49.2		4	36.31	odd	6
144.6.i.a.97.2		4	4.3	odd	2
162.6.a.e.1.2		2	9.7	even	3
162.6.a.f.1.1		2	9.2	odd	6
432.6.i.a.145.2		4	36.23	even	6
432.6.i.a.289.2		4	12.11	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-14.6969 - 5.19615i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-28.1969 - 48.8385i) q^{5} +(-47.3939 + 40.5194i) q^{6} +(11.1515 - 19.3150i) q^{7} -64.0000 q^{8} +(189.000 + 152.735i) q^{9} -225.576 q^{10} +(296.484 - 513.526i) q^{11} +(45.5755 + 245.216i) q^{12} +(129.531 + 224.354i) q^{13} +(-44.6061 - 77.2601i) q^{14} +(160.636 + 864.292i) q^{15} +(-128.000 + 221.703i) q^{16} +1627.51 q^{17} +(907.090 - 349.245i) q^{18} -2642.42 q^{19} +(-451.151 + 781.416i) q^{20} +(-264.257 + 225.927i) q^{21} +(-1185.94 - 2054.10i) q^{22} +(-1568.21 - 2716.22i) q^{23} +(940.604 + 332.554i) q^{24} +(-27.6347 + 47.8647i) q^{25} +1036.24 q^{26} +(-1984.09 - 3226.81i) q^{27} -356.849 q^{28} +(-62.2898 + 107.889i) q^{29} +(3315.27 + 1172.12i) q^{30} +(4376.08 + 7579.60i) q^{31} +(512.000 + 886.810i) q^{32} +(-7025.77 + 6006.68i) q^{33} +(3255.02 - 5637.87i) q^{34} -1257.76 q^{35} +(604.359 - 3840.74i) q^{36} +9741.67 q^{37} +(-5284.84 + 9153.61i) q^{38} +(-737.928 - 3970.37i) q^{39} +(1804.60 + 3125.67i) q^{40} +(3735.62 + 6470.29i) q^{41} +(254.118 + 1367.27i) q^{42} +(6252.46 - 10829.6i) q^{43} -9487.49 q^{44} +(2130.13 - 13537.1i) q^{45} -12545.7 q^{46} +(4408.73 - 7636.15i) q^{47} +(3033.21 - 2593.24i) q^{48} +(8154.79 + 14124.5i) q^{49} +(110.539 + 191.459i) q^{50} +(-23919.4 - 8456.80i) q^{51} +(2072.49 - 3589.66i) q^{52} -10782.1 q^{53} +(-15146.2 + 419.457i) q^{54} -33439.8 q^{55} +(-713.698 + 1236.16i) q^{56} +(38835.5 + 13730.4i) q^{57} +(249.159 + 431.557i) q^{58} +(7776.87 + 13469.9i) q^{59} +(10690.9 - 9140.18i) q^{60} +(5965.22 - 10332.1i) q^{61} +35008.7 q^{62} +(5057.72 - 1947.31i) q^{63} +4096.00 q^{64} +(7304.73 - 12652.2i) q^{65} +(6756.21 + 36351.3i) q^{66} +(-3089.79 - 5351.68i) q^{67} +(-13020.1 - 22551.5i) q^{68} +(8934.01 + 48068.8i) q^{69} +(-2515.51 + 4356.99i) q^{70} -10498.9 q^{71} +(-12096.0 - 9775.04i) q^{72} -38380.3 q^{73} +(19483.3 - 33746.1i) q^{74} +(654.857 - 559.870i) q^{75} +(21139.4 + 36614.5i) q^{76} +(-6612.50 - 11453.2i) q^{77} +(-15229.6 - 5384.49i) q^{78} +(-8926.87 + 15461.8i) q^{79} +14436.8 q^{80} +(12393.0 + 57733.9i) q^{81} +29885.0 q^{82} +(21610.3 - 37430.1i) q^{83} +(5244.59 + 1854.24i) q^{84} +(-45890.9 - 79485.3i) q^{85} +(-25009.8 - 43318.3i) q^{86} +(1476.08 - 1261.97i) q^{87} +(-18975.0 + 32865.6i) q^{88} -94095.6 q^{89} +(-42633.8 - 34453.3i) q^{90} +5777.86 q^{91} +(-25091.4 + 43459.6i) q^{92} +(-24930.3 - 134136. i) q^{93} +(-17634.9 - 30544.6i) q^{94} +(74508.2 + 129052. i) q^{95} +(-2916.83 - 15693.8i) q^{96} +(40743.3 - 70569.5i) q^{97} +65238.3 q^{98} +(134469. - 51772.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9} - 432 q^{10} - 78 q^{11} - 288 q^{12} + 1106 q^{13} - 296 q^{14} + 378 q^{15} - 512 q^{16} + 984 q^{17} + 1512 q^{18} - 3280 q^{19}+ \cdots + 319626 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9 - 432 * q^10 - 78 * q^11 - 288 * q^12 + 1106 * q^13 - 296 * q^14 + 378 * q^15 - 512 * q^16 + 984 * q^17 + 1512 * q^18 - 3280 * q^19 - 864 * q^20 - 234 * q^21 + 312 * q^22 - 5538 * q^23 + 3064 * q^25 + 8848 * q^26 - 2368 * q^28 - 3894 * q^29 + 6912 * q^30 + 4718 * q^31 + 2048 * q^32 - 17874 * q^33 + 1968 * q^34 - 2268 * q^35 - 6048 * q^36 - 9592 * q^37 - 6560 * q^38 + 18594 * q^39 + 3456 * q^40 + 15354 * q^41 - 4392 * q^42 + 32858 * q^43 + 2496 * q^44 + 5346 * q^45 - 44304 * q^46 + 24954 * q^47 + 4608 * q^48 + 30444 * q^49 - 12256 * q^50 - 81216 * q^51 + 17696 * q^52 - 32664 * q^53 - 44712 * q^54 - 70092 * q^55 - 4736 * q^56 + 107136 * q^57 + 15576 * q^58 + 21966 * q^59 + 21600 * q^60 + 3050 * q^61 + 37744 * q^62 + 6210 * q^63 + 16384 * q^64 + 12582 * q^65 + 77112 * q^66 + 36758 * q^67 - 7872 * q^68 - 39042 * q^69 - 4536 * q^70 - 147696 * q^71 - 48384 * q^72 - 102376 * q^73 - 19184 * q^74 + 19080 * q^75 + 26240 * q^76 + 21462 * q^77 + 69120 * q^78 - 14926 * q^79 + 27648 * q^80 + 49572 * q^81 + 122832 * q^82 + 90762 * q^83 - 13824 * q^84 - 94500 * q^85 - 131432 * q^86 - 18522 * q^87 + 4992 * q^88 - 18600 * q^89 - 81648 * q^90 + 99124 * q^91 - 88608 * q^92 - 145458 * q^93 - 99816 * q^94 + 151416 * q^95 + 18432 * q^96 - 30262 * q^97 + 243552 * q^98 + 319626 * q^99

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