LMFDB - Embedded newform 27.9.f.a.14.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,9,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.9992224717$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.15
Character	$\chi$	$=$	27.14
Dual form			27.9.f.a.2.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(13.3375 - 2.35175i) q^{2} +(34.9288 - 73.0820i) q^{3} +(-68.2042 + 24.8243i) q^{4} +(-636.805 + 758.914i) q^{5} +(293.990 - 1056.87i) q^{6} +(-2502.00 - 910.653i) q^{7} +(-3853.85 + 2225.02i) q^{8} +(-4120.96 - 5105.33i) q^{9} +(-6708.58 + 11619.6i) q^{10} +(15349.9 + 18293.3i) q^{11} +(-568.081 + 5851.58i) q^{12} +(4780.28 - 27110.3i) q^{13} +(-35511.9 - 6261.71i) q^{14} +(33220.2 + 73046.9i) q^{15} +(-31934.2 + 26796.0i) q^{16} +(-105956. - 61173.5i) q^{17} +(-66969.6 - 58400.7i) q^{18} +(-547.495 - 948.289i) q^{19} +(24593.2 - 67569.4i) q^{20} +(-153944. + 151043. i) q^{21} +(247750. + 207887. i) q^{22} +(50471.0 + 138668. i) q^{23} +(27998.7 + 359365. i) q^{24} +(-102599. - 581870. i) q^{25} -372825. i q^{26} +(-517048. + 122845. i) q^{27} +193253. q^{28} +(-924074. + 162939. i) q^{29} +(614861. + 896135. i) q^{30} +(131238. - 47766.6i) q^{31} +(369368. - 440196. i) q^{32} +(1.87306e6 - 482838. i) q^{33} +(-1.55704e6 - 566717. i) q^{34} +(2.28439e6 - 1.31889e6i) q^{35} +(407803. + 245905. i) q^{36} +(-379045. + 656525. i) q^{37} +(-9532.34 - 11360.2i) q^{38} +(-1.81431e6 - 1.29628e6i) q^{39} +(765550. - 4.34165e6i) q^{40} +(4.60079e6 + 811243. i) q^{41} +(-1.69801e6 + 2.37657e6i) q^{42} +(-1.82392e6 + 1.53045e6i) q^{43} +(-1.50104e6 - 866629. i) q^{44} +(6.49876e6 + 123645. i) q^{45} +(999268. + 1.73078e6i) q^{46} +(425686. - 1.16956e6i) q^{47} +(842880. + 3.26976e6i) q^{48} +(1.01461e6 + 851361. i) q^{49} +(-2.73683e6 - 7.51938e6i) q^{50} +(-8.17158e6 + 5.60673e6i) q^{51} +(346960. + 1.96771e6i) q^{52} +6.96711e6i q^{53} +(-6.60721e6 + 2.85441e6i) q^{54} -2.36579e7 q^{55} +(1.16686e7 - 2.05748e6i) q^{56} +(-88426.2 + 6889.44i) q^{57} +(-1.19416e7 + 4.34639e6i) q^{58} +(4.48304e6 - 5.34268e6i) q^{59} +(-4.07909e6 - 4.15744e6i) q^{60} +(-2.36882e7 - 8.62179e6i) q^{61} +(1.63804e6 - 945725. i) q^{62} +(5.66145e6 + 1.65263e7i) q^{63} +(9.22715e6 - 1.59819e7i) q^{64} +(1.75303e7 + 2.08918e7i) q^{65} +(2.38464e7 - 1.08448e7i) q^{66} +(-3.60777e6 + 2.04607e7i) q^{67} +(8.74520e6 + 1.54201e6i) q^{68} +(1.18970e7 + 1.15498e6i) q^{69} +(2.73663e7 - 2.29630e7i) q^{70} +(-1.06620e7 - 6.15572e6i) q^{71} +(2.72411e7 + 1.05060e7i) q^{72} +(3.50114e6 + 6.06416e6i) q^{73} +(-3.51151e6 + 9.64780e6i) q^{74} +(-4.61079e7 - 1.28258e7i) q^{75} +(60882.1 + 51086.1i) q^{76} +(-2.17466e7 - 5.97482e7i) q^{77} +(-2.72468e7 - 1.30223e7i) q^{78} +(2.79249e6 + 1.58370e7i) q^{79} -4.12991e7i q^{80} +(-9.08211e6 + 4.20777e7i) q^{81} +6.32706e7 q^{82} +(4.48356e6 - 790573. i) q^{83} +(6.75010e6 - 1.41233e7i) q^{84} +(1.13898e8 - 4.14556e7i) q^{85} +(-2.07272e7 + 2.47018e7i) q^{86} +(-2.03689e7 + 7.32244e7i) q^{87} +(-9.98592e7 - 3.63458e7i) q^{88} +(-3.86601e7 + 2.23204e7i) q^{89} +(8.69677e7 - 1.36344e7i) q^{90} +(-3.66484e7 + 6.34768e7i) q^{91} +(-6.88467e6 - 8.20483e6i) q^{92} +(1.09309e6 - 1.12595e7i) q^{93} +(2.92705e6 - 1.66001e7i) q^{94} +(1.06832e6 + 188373. i) q^{95} +(-1.92688e7 - 4.23697e7i) q^{96} +(1.19186e7 - 1.00009e7i) q^{97} +(1.55345e7 + 8.96887e6i) q^{98} +(3.01370e7 - 1.53752e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) $ 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	13.3375	−	2.35175i	0.833591	−	0.146985i	0.259466	−	0.965752i	$-0.416453\pi$
$2$	13.3375	−	2.35175i	0.833591	−	0.146985i	0.574125	+	0.818768i	$0.305342\pi$
$3$	34.9288	−	73.0820i	0.431220	−	0.902247i
$3$	34.9288	−	73.0820i	0.431220	−	0.902247i
$4$	−68.2042	+	24.8243i	−0.266423	+	0.0969699i
$5$	−636.805	+	758.914i	−1.01889	+	1.21426i	−0.0423083	+	0.999105i	$0.513471\pi$
$5$	−636.805	+	758.914i	−1.01889	+	1.21426i	−0.976579	+	0.215158i	$0.930973\pi$
$6$	293.990	−	1056.87i	0.226844	−	0.815488i
$7$	−2502.00	−	910.653i	−1.04207	−	0.379281i	−0.236402	−	0.971655i	$-0.575968\pi$
$7$	−2502.00	−	910.653i	−1.04207	−	0.379281i	−0.805663	+	0.592375i	$0.798191\pi$
$8$	−3853.85	+	2225.02i	−0.940882	+	0.543219i
$9$	−4120.96	−	5105.33i	−0.628099	−	0.778133i
$10$	−6708.58	+	11619.6i	−0.670858	+	1.16196i
$11$	15349.9	+	18293.3i	1.04842	+	1.24946i	0.967536	+	0.252732i	$0.0813290\pi$
$11$	15349.9	+	18293.3i	1.04842	+	1.24946i	0.0808814	+	0.996724i	$0.474227\pi$
$12$	−568.081	+	5851.58i	−0.0273959	+	0.282194i
$13$	4780.28	−	27110.3i	0.167371	−	0.949208i	−0.779215	−	0.626757i	$-0.784382\pi$
$13$	4780.28	−	27110.3i	0.167371	−	0.949208i	0.946586	−	0.322451i	$-0.104507\pi$
$14$	−35511.9	−	6261.71i	−0.924405	−	0.162997i
$15$	33220.2	+	73046.9i	0.656201	+	1.44290i
$16$	−31934.2	+	26796.0i	−0.487277	+	0.408874i
$17$	−105956.	−	61173.5i	−1.26861	−	0.732432i	−0.293885	−	0.955841i	$-0.594948\pi$
$17$	−105956.	−	61173.5i	−1.26861	−	0.732432i	−0.974725	+	0.223409i	$0.928281\pi$
$18$	−66969.6	−	58400.7i	−0.637952	−	0.556324i
$19$	−547.495	−	948.289i	−0.00420113	−	0.00727656i	0.863917	−	0.503634i	$-0.168004\pi$
$19$	−547.495	−	948.289i	−0.00420113	−	0.00727656i	−0.868118	+	0.496357i	$0.834671\pi$
$20$	24593.2	−	67569.4i	0.153708	−	0.422309i
$21$	−153944.	+	151043.i	−0.791564	+	0.776647i
$22$	247750.	+	207887.i	1.05760	+	0.887434i
$23$	50471.0	+	138668.i	0.180356	+	0.495524i	0.996619	−	0.0821558i	$-0.0261805\pi$
$23$	50471.0	+	138668.i	0.180356	+	0.495524i	−0.816264	+	0.577680i	$0.803958\pi$
$24$	27998.7	+	359365.i	0.0843905	+	1.08315i
$25$	−102599.	−	581870.i	−0.262654	−	1.48959i
$26$		−	372825.i		−	0.815853i
$27$	−517048.	+	122845.i	−0.972917	+	0.231154i
$28$	193253.			0.314409
$29$	−924074.	+	162939.i	−1.30652	+	0.230374i	−0.783203	−	0.621766i	$-0.786415\pi$
$29$	−924074.	+	162939.i	−1.30652	+	0.230374i	−0.523313	+	0.852140i	$0.675304\pi$
$30$	614861.	+	896135.i	0.759088	+	1.10634i
$31$	131238.	−	47766.6i	0.142106	−	0.0517223i	−0.269988	−	0.962864i	$-0.587020\pi$
$31$	131238.	−	47766.6i	0.142106	−	0.0517223i	0.412094	+	0.911141i	$0.364798\pi$
$32$	369368.	−	440196.i	0.352257	−	0.419804i
$33$	1.87306e6	−	482838.i	1.57942	−	0.407142i
$34$	−1.55704e6	−	566717.i	−1.16516	−	0.424083i
$35$	2.28439e6	−	1.31889e6i	1.52229	−	0.878897i
$36$	407803.	+	245905.i	0.242795	+	0.146406i
$37$	−379045.	+	656525.i	−0.202248	+	0.350303i	−0.949252	−	0.314515i	$-0.898158\pi$
$37$	−379045.	+	656525.i	−0.202248	+	0.350303i	0.747005	+	0.664819i	$0.231491\pi$
$38$	−9532.34	−	11360.2i	−0.00457157	−	0.00544818i
$39$	−1.81431e6	−	1.29628e6i	−0.784247	−	0.560327i
$40$	765550.	−	4.34165e6i	0.299043	−	1.69596i
$41$	4.60079e6	+	811243.i	1.62816	+	0.287088i	0.911797	−	0.410641i	$-0.134695\pi$
$41$	4.60079e6	+	811243.i	1.62816	+	0.287088i	0.716361	+	0.697730i	$0.245806\pi$
$42$	−1.69801e6	+	2.37657e6i	−0.545685	+	0.763754i
$43$	−1.82392e6	+	1.53045e6i	−0.533498	+	0.447658i	−0.869307	−	0.494272i	$-0.835435\pi$
$43$	−1.82392e6	+	1.53045e6i	−0.533498	+	0.447658i	0.335810	+	0.941930i	$0.390990\pi$
$44$	−1.50104e6	−	866629.i	−0.400482	−	0.231218i
$45$	6.49876e6	+	123645.i	1.58482	+	0.0301527i
$46$	999268.	+	1.73078e6i	0.223178	+	0.386555i
$47$	425686.	−	1.16956e6i	0.0872365	−	0.239680i	−0.888401	−	0.459068i	$-0.848184\pi$
$47$	425686.	−	1.16956e6i	0.0872365	−	0.239680i	0.975638	+	0.219387i	$0.0704058\pi$
$48$	842880.	+	3.26976e6i	0.158782	+	0.615958i
$49$	1.01461e6	+	851361.i	0.176001	+	0.147683i
$50$	−2.73683e6	−	7.51938e6i	−0.437893	−	1.20310i
$51$	−8.17158e6	+	5.60673e6i	−1.20788	+	0.828760i
$52$	346960.	+	1.96771e6i	0.0474532	+	0.269121i
$53$			6.96711e6i			0.882977i	0.897267	+	0.441489i	$0.145549\pi$
$53$			6.96711e6i			0.882977i	−0.897267	+	0.441489i	$0.854451\pi$
$54$	−6.60721e6	+	2.85441e6i	−0.777039	+	0.335692i
$55$	−2.36579e7			−2.58539
$56$	1.16686e7	−	2.05748e6i	1.18649	−	0.209211i
$57$	−88426.2	+	6889.44i	−0.00837687	+	0.000652656i
$58$	−1.19416e7	+	4.34639e6i	−1.05524	+	0.384076i
$59$	4.48304e6	−	5.34268e6i	0.369968	−	0.440911i	−0.548653	−	0.836050i	$-0.684859\pi$
$59$	4.48304e6	−	5.34268e6i	0.369968	−	0.440911i	0.918621	+	0.395139i	$0.129304\pi$
$60$	−4.07909e6	−	4.15744e6i	−0.314745	−	0.320790i
$61$	−2.36882e7	−	8.62179e6i	−1.71085	−	0.622699i	−0.713865	−	0.700284i	$-0.753057\pi$
$61$	−2.36882e7	−	8.62179e6i	−1.71085	−	0.622699i	−0.996986	+	0.0775852i	$0.975279\pi$
$62$	1.63804e6	−	945725.i	0.110856	−	0.0640026i
$63$	5.66145e6	+	1.65263e7i	0.359389	+	1.04909i
$64$	9.22715e6	−	1.59819e7i	0.549981	−	0.952595i
$65$	1.75303e7	+	2.08918e7i	0.982056	+	1.17037i
$66$	2.38464e7	−	1.08448e7i	1.25674	−	0.571540i
$67$	−3.60777e6	+	2.04607e7i	−0.179036	+	1.01536i	0.754346	+	0.656477i	$0.227954\pi$
$67$	−3.60777e6	+	2.04607e7i	−0.179036	+	1.01536i	−0.933382	+	0.358885i	$0.883157\pi$
$68$	8.74520e6	+	1.54201e6i	0.409010	+	0.0721195i
$69$	1.18970e7	+	1.15498e6i	0.524858	+	0.0509540i
$70$	2.73663e7	−	2.29630e7i	1.13979	−	0.956394i
$71$	−1.06620e7	−	6.15572e6i	−0.419571	−	0.242240i	0.275323	−	0.961352i	$-0.411215\pi$
$71$	−1.06620e7	−	6.15572e6i	−0.419571	−	0.242240i	−0.694894	+	0.719112i	$0.744549\pi$
$72$	2.72411e7	+	1.05060e7i	1.01366	+	0.390937i
$73$	3.50114e6	+	6.06416e6i	0.123287	+	0.213540i	0.921062	−	0.389415i	$-0.127323\pi$
$73$	3.50114e6	+	6.06416e6i	0.123287	+	0.213540i	−0.797775	+	0.602956i	$0.793990\pi$
$74$	−3.51151e6	+	9.64780e6i	−0.117103	+	0.321737i
$75$	−4.61079e7	−	1.28258e7i	−1.45724	−	0.405360i
$76$	60882.1	+	51086.1i	0.00182488	+	0.00153126i
$77$	−2.17466e7	−	5.97482e7i	−0.618625	−	1.69966i
$78$	−2.72468e7	−	1.30223e7i	−0.736101	−	0.351812i
$79$	2.79249e6	+	1.58370e7i	0.0716941	+	0.406598i	0.999442	+	0.0333910i	$0.0106306\pi$
$79$	2.79249e6	+	1.58370e7i	0.0716941	+	0.406598i	−0.927748	+	0.373207i	$0.878258\pi$
$80$		−	4.12991e7i		−	1.00828i
$81$	−9.08211e6	+	4.20777e7i	−0.210983	+	0.977490i
$82$	6.32706e7			1.39942
$83$	4.48356e6	−	790573.i	0.0944737	−	0.0166583i	−0.126211	−	0.992003i	$-0.540282\pi$
$83$	4.48356e6	−	790573.i	0.0944737	−	0.0166583i	0.220685	+	0.975345i	$0.429171\pi$
$84$	6.75010e6	−	1.41233e7i	0.135579	−	0.283674i
$85$	1.13898e8	−	4.14556e7i	2.18194	−	0.794159i
$86$	−2.07272e7	+	2.47018e7i	−0.378920	+	0.451579i
$87$	−2.03689e7	+	7.32244e7i	−0.355541	+	1.27814i
$88$	−9.98592e7	−	3.63458e7i	−1.66517	−	0.606071i
$89$	−3.86601e7	+	2.23204e7i	−0.616174	+	0.355748i	−0.775378	−	0.631497i	$-0.782441\pi$
$89$	−3.86601e7	+	2.23204e7i	−0.616174	+	0.355748i	0.159204	+	0.987246i	$0.449107\pi$
$90$	8.69677e7	−	1.36344e7i	1.32552	−	0.207809i
$91$	−3.66484e7	+	6.34768e7i	−0.534428	+	0.925656i
$92$	−6.88467e6	−	8.20483e6i	−0.0961018	−	0.114530i
$93$	1.09309e6	−	1.12595e7i	0.0146125	−	0.150518i
$94$	2.92705e6	−	1.66001e7i	0.0374903	−	0.212618i
$95$	1.06832e6	+	188373.i	0.0131161	+	0.00231273i
$96$	−1.92688e7	−	4.23697e7i	−0.226866	−	0.498850i
$97$	1.19186e7	−	1.00009e7i	0.134629	−	0.112967i	−0.572987	−	0.819565i	$-0.694215\pi$
$97$	1.19186e7	−	1.00009e7i	0.134629	−	0.112967i	0.707616	+	0.706598i	$0.249771\pi$
$98$	1.55345e7	+	8.96887e6i	0.168420	+	0.0972374i
$99$	3.01370e7	−	1.53752e8i	0.313733	−	1.60059i
$100$	2.14422e7	+	3.71390e7i	0.214422	+	0.371390i
$101$	−5.97338e7	+	1.64117e8i	−0.574030	+	1.57714i	0.224046	+	0.974579i	$0.428073\pi$
$101$	−5.97338e7	+	1.64117e8i	−0.574030	+	1.57714i	−0.798076	+	0.602557i	$0.794149\pi$
$102$	−9.58024e7	+	9.39970e7i	−0.885066	+	0.868387i
$103$	6.03092e7	+	5.06054e7i	0.535839	+	0.449623i	0.870112	−	0.492854i	$-0.164046\pi$
$103$	6.03092e7	+	5.06054e7i	0.535839	+	0.449623i	−0.334273	+	0.942476i	$0.608491\pi$
$104$	4.18986e7	+	1.15116e8i	0.358151	+	0.984012i
$105$	−1.65964e7	−	2.13015e8i	−0.136539	−	1.75248i
$106$	1.63849e7	+	9.29236e7i	0.129784	+	0.736042i
$107$		−	6.15134e7i		−	0.469283i	−0.972082	−	0.234641i	$-0.924608\pi$
$107$		−	6.15134e7i		−	0.469283i	0.972082	−	0.234641i	$-0.0753916\pi$
$108$	3.22153e7	−	2.12139e7i	0.236792	−	0.155928i
$109$	−2.02005e7			−0.143105			−0.0715526	−	0.997437i	$-0.522795\pi$
$109$	−2.02005e7			−0.143105			−0.0715526	+	0.997437i	$0.522795\pi$
$110$	−3.15536e8	+	5.56376e7i	−2.15516	+	0.380012i
$111$	3.47406e7	+	5.06330e7i	0.228847	+	0.333535i
$112$	1.04301e8	−	3.79625e7i	0.662852	−	0.241258i
$113$	7.22019e7	−	8.60469e7i	0.442828	−	0.527742i	−0.497750	−	0.867321i	$-0.665840\pi$
$113$	7.22019e7	−	8.60469e7i	0.442828	−	0.527742i	0.940578	+	0.339579i	$0.110285\pi$
$114$	−1.16318e6	+	299844.i	−0.00688695	+	0.00177532i
$115$	−1.37377e8	−	5.00012e7i	−0.785459	−	0.285884i
$116$	5.89809e7	−	3.40526e7i	0.325746	−	0.188070i
$117$	−1.58107e8	+	8.73156e7i	−0.843736	+	0.465960i
$118$	4.72277e7	−	8.18007e7i	0.243595	−	0.421919i
$119$	2.09393e8	+	2.49545e8i	1.04418	+	1.24440i
$120$	−2.90557e8	−	2.07597e8i	−1.40122	−	1.00114i
$121$	−6.18021e7	+	3.50497e8i	−0.288311	+	1.63510i
$122$	−3.36216e8	−	5.92840e7i	−1.51768	−	0.267607i
$123$	2.19987e8	−	3.07899e8i	0.961118	−	1.34520i
$124$	−7.76519e6	+	6.51577e6i	−0.0328447	+	0.0275600i
$125$	1.71783e8	+	9.91787e7i	0.703622	+	0.406236i
$126$	1.14375e8	+	2.07104e8i	0.453784	+	0.821689i
$127$	−1.22668e8	−	2.12467e8i	−0.471536	−	0.816725i	0.527934	−	0.849286i	$-0.322967\pi$
$127$	−1.22668e8	−	2.12467e8i	−0.471536	−	0.816725i	−0.999470	+	0.0325610i	$0.989634\pi$
$128$	3.51679e7	−	9.66229e7i	0.131011	−	0.359948i
$129$	4.81411e7	+	1.86753e8i	0.173843	+	0.674385i
$130$	2.82942e8	+	2.37417e8i	0.990660	+	0.831262i
$131$	−1.43812e8	−	3.95121e8i	−0.488327	−	1.34167i	−0.902194	−	0.431330i	$-0.858045\pi$
$131$	−1.43812e8	−	3.95121e8i	−0.488327	−	1.34167i	0.413867	−	0.910337i	$-0.364178\pi$
$132$	−1.15765e8	+	7.94291e7i	−0.381312	+	0.261628i
$133$	506269.	+	2.87120e6i	0.00161799	+	0.00917606i
$134$			2.81378e8i			0.872713i
$135$	2.36030e8	−	4.70623e8i	0.710611	−	1.41690i
$136$	5.44450e8			1.59148
$137$	3.65675e8	−	6.44783e7i	1.03804	−	0.183034i	0.371444	−	0.928456i	$-0.378863\pi$
$137$	3.65675e8	−	6.44783e7i	1.03804	−	0.183034i	0.666593	+	0.745422i	$0.267752\pi$
$138$	1.61392e8	−	1.25743e7i	0.445006	−	0.0346712i
$139$	−3.96654e8	+	1.44370e8i	−1.06256	+	0.386739i	−0.813389	−	0.581721i	$-0.802380\pi$
$139$	−3.96654e8	+	1.44370e8i	−1.06256	+	0.386739i	−0.249169	+	0.968460i	$0.580158\pi$
$140$	−1.23064e8	+	1.46663e8i	−0.320347	+	0.381775i
$141$	−7.06054e7	−	7.19615e7i	−0.178633	−	0.182064i
$142$	−1.56681e8	−	5.70272e7i	−0.385357	−	0.140258i
$143$	5.69314e8	−	3.28693e8i	1.36147	−	0.786044i
$144$	2.68402e8	+	5.26095e7i	0.624216	+	0.122353i
$145$	4.64798e8	−	8.05053e8i	1.05146	−	1.82118i
$146$	6.09578e7	+	7.26467e7i	0.134158	+	0.159884i
$147$	9.76583e7	−	4.44129e7i	0.209141	−	0.0951129i
$148$	9.55468e6	−	5.41873e7i	0.0199145	−	0.112941i
$149$	−4.73599e8	−	8.35083e7i	−0.960873	−	0.169428i	−0.328854	−	0.944381i	$-0.606662\pi$
$149$	−4.73599e8	−	8.35083e7i	−0.960873	−	0.169428i	−0.632019	+	0.774953i	$0.717773\pi$
$150$	−6.45125e8	−	6.26298e7i	−1.27432	−	0.123713i
$151$	−3.88229e8	+	3.25763e8i	−0.746758	+	0.626605i	−0.934643	−	0.355586i	$-0.884281\pi$
$151$	−3.88229e8	+	3.25763e8i	−0.746758	+	0.626605i	0.187885	+	0.982191i	$0.439837\pi$
$152$	4.21993e6	+	2.43638e6i	0.00790553	+	0.00456426i
$153$	1.24328e8	+	7.93031e8i	0.226883	+	1.44719i
$154$	−4.30557e8	−	7.45746e8i	−0.765504	−	1.32589i
$155$	−4.73220e7	+	1.30016e8i	−0.0819854	+	0.225253i
$156$	1.55923e8	+	4.33731e7i	0.263276	+	0.0732356i
$157$	−3.53896e8	−	2.96954e8i	−0.582475	−	0.488755i	0.303284	−	0.952900i	$-0.401917\pi$
$157$	−3.53896e8	−	2.96954e8i	−0.582475	−	0.488755i	−0.885759	+	0.464146i	$0.846361\pi$
$158$	7.44895e7	+	2.04658e8i	0.119527	+	0.328398i
$159$	5.09171e8	+	2.43353e8i	0.796663	+	0.380757i
$160$	9.88555e7	+	5.60638e8i	0.150842	+	0.855465i
$161$		−	3.92908e8i		−	0.584774i
$162$	−2.21759e7	+	5.82569e8i	−0.0321974	+	0.845838i
$163$	−4.56114e8			−0.646134			−0.323067	−	0.946376i	$-0.604714\pi$
$163$	−4.56114e8			−0.646134			−0.323067	+	0.946376i	$0.604714\pi$
$164$	−3.33932e8	+	5.88811e7i	−0.461617	+	0.0813956i
$165$	−8.26342e8	+	1.72897e9i	−1.11487	+	2.33266i
$166$	5.79401e7	−	2.10885e7i	0.0763040	−	0.0277724i
$167$	1.61471e8	−	1.92434e8i	0.207601	−	0.247409i	−0.652190	−	0.758056i	$-0.726150\pi$
$167$	1.61471e8	−	1.92434e8i	0.207601	−	0.247409i	0.859791	+	0.510647i	$0.170594\pi$
$168$	2.57204e8	−	9.24627e8i	0.322879	−	1.16073i
$169$	5.44170e7	+	1.98062e7i	0.0667095	+	0.0242803i
$170$	1.42162e9	−	8.20774e8i	1.70211	−	0.982715i
$171$	−2.58513e6	+	6.70300e6i	−0.00302341	+	0.00783944i
$172$	8.64068e7	−	1.49661e8i	0.0987265	−	0.170999i
$173$	−7.42345e8	−	8.84693e8i	−0.828746	−	0.987661i	−0.999997	−	0.00243395i	$-0.999225\pi$
$173$	−7.42345e8	−	8.84693e8i	−0.828746	−	0.987661i	0.171251	−	0.985227i	$-0.445219\pi$
$174$	−9.94630e7	+	1.02453e9i	−0.108509	+	1.11771i
$175$	−2.73178e8	+	1.54927e9i	−0.291269	+	1.65187i
$176$	−9.80372e8	−	1.72866e8i	−1.02174	−	0.180160i
$177$	−2.33866e8	−	5.14243e8i	−0.238273	−	0.523932i
$178$	−4.63136e8	+	3.88617e8i	−0.461348	+	0.387117i
$179$	6.53835e8	+	3.77492e8i	0.636878	+	0.367702i	0.783411	−	0.621504i	$-0.213478\pi$
$179$	6.53835e8	+	3.77492e8i	0.636878	+	0.367702i	−0.146533	+	0.989206i	$0.546811\pi$
$180$	−4.46312e8	+	1.52894e8i	−0.425156	+	0.145647i
$181$	1.14593e8	+	1.98480e8i	0.106768	+	0.184928i	0.914459	−	0.404678i	$-0.132616\pi$
$181$	1.14593e8	+	1.98480e8i	0.106768	+	0.184928i	−0.807691	+	0.589606i	$0.799283\pi$
$182$	−3.39514e8	+	9.32808e8i	−0.309437	+	0.850171i
$183$	−1.45750e9	+	1.43003e9i	−1.29958	+	1.27509i
$184$	−5.03047e8	−	4.22107e8i	−0.438872	−	0.368257i
$185$	−2.56869e8	−	7.05741e8i	−0.219293	−	0.602502i
$186$	−1.19006e7	−	1.52744e8i	−0.00994298	−	0.127619i
$187$	−5.07342e8	−	2.87728e9i	−0.414891	−	2.35297i
$188$			9.03366e7i			0.0723156i
$189$	1.40552e9	+	1.63494e8i	1.10152	+	0.128131i
$190$	1.46916e7			0.0112734
$191$	−9.71028e7	+	1.71218e7i	−0.0729623	+	0.0128652i	−0.210010	−	0.977699i	$-0.567350\pi$
$191$	−9.71028e7	+	1.71218e7i	−0.0729623	+	0.0128652i	0.137048	+	0.990564i	$0.456239\pi$
$192$	−8.45696e8	−	1.23257e9i	−0.622313	−	0.906996i
$193$	2.38182e9	−	8.66911e8i	1.71664	−	0.624806i	0.719102	−	0.694905i	$-0.244554\pi$
$193$	2.38182e9	−	8.66911e8i	1.71664	−	0.624806i	0.997540	+	0.0700985i	$0.0223314\pi$
$194$	1.35444e8	−	1.61416e8i	0.0956211	−	0.113957i
$195$	2.13913e9	−	5.51425e8i	1.47944	−	0.381371i
$196$	−9.03352e7	−	3.28793e7i	−0.0612115	−	0.0222792i
$197$	3.70754e8	−	2.14055e8i	0.246162	−	0.142122i	−0.371843	−	0.928295i	$-0.621274\pi$
$197$	3.70754e8	−	2.14055e8i	0.246162	−	0.142122i	0.618006	+	0.786174i	$0.287941\pi$
$198$	4.03642e7	−	2.12154e9i	0.0262625	−	1.38035i
$199$	4.87197e8	−	8.43850e8i	0.310665	−	0.538088i	−0.667842	−	0.744303i	$-0.732782\pi$
$199$	4.87197e8	−	8.43850e8i	0.310665	−	0.538088i	0.978507	+	0.206216i	$0.0661149\pi$
$200$	1.69008e9	+	2.01416e9i	1.05630	+	1.25885i
$201$	1.36929e9	+	9.78331e8i	0.838904	+	0.599379i
$202$	−4.10734e8	+	2.32939e9i	−0.246692	+	1.39906i
$203$	2.46041e9	+	4.33837e8i	1.44885	+	0.255472i
$204$	4.18153e8	−	5.85256e8i	0.241443	−	0.337929i
$205$	−3.54547e9	+	2.97500e9i	−2.00751	+	1.68450i
$206$	9.23383e8	+	5.33115e8i	0.512759	+	0.296041i
$207$	4.99957e8	−	8.29116e8i	0.272302	−	0.451579i
$208$	5.73793e8	+	9.93838e8i	0.306550	+	0.530961i
$209$	8.94333e6	−	2.45716e7i	0.00468721	−	0.0128780i
$210$	−7.22313e8	−	2.80205e9i	−0.371406	−	1.44078i
$211$	−1.10978e9	−	9.31219e8i	−0.559897	−	0.469809i	0.318379	−	0.947964i	$-0.396862\pi$
$211$	−1.10978e9	−	9.31219e8i	−0.559897	−	0.469809i	−0.878276	+	0.478154i	$0.841306\pi$
$212$	−1.72954e8	−	4.75187e8i	−0.0856222	−	0.235245i
$213$	−8.22283e8	+	5.64190e8i	−0.399487	+	0.274099i
$214$	−1.44664e8	−	8.20432e8i	−0.0689773	−	0.391190i
$215$		−	2.35880e9i		−	1.10392i
$216$	1.71930e9	−	1.62387e9i	0.789833	−	0.745996i
$217$	−3.71855e8			−0.167701
$218$	−2.69423e8	+	4.75066e7i	−0.119291	+	0.0210343i
$219$	5.65472e8	−	4.40569e7i	0.245830	−	0.0191530i
$220$	1.61357e9	−	5.87291e8i	0.688806	−	0.250705i
$221$	−2.16493e9	+	2.58006e9i	−0.907559	+	1.08159i
$222$	5.82427e8	+	5.93614e8i	0.239789	+	0.244395i
$223$	9.28127e8	+	3.37811e8i	0.375308	+	0.136601i	0.522785	−	0.852464i	$-0.324893\pi$
$223$	9.28127e8	+	3.37811e8i	0.375308	+	0.136601i	−0.147477	+	0.989065i	$0.547115\pi$
$224$	−1.32502e9	+	7.65003e8i	−0.526298	+	0.303858i
$225$	−2.54783e9	+	2.92167e9i	−0.994124	+	1.13999i
$226$	7.60629e8	−	1.31745e9i	0.291568	−	0.505010i
$227$	4.10560e8	+	4.89286e8i	0.154623	+	0.184272i	0.837795	−	0.545985i	$-0.183845\pi$
$227$	4.10560e8	+	4.89286e8i	0.154623	+	0.184272i	−0.683172	+	0.730257i	$0.739400\pi$
$228$	5.86001e6	−	2.66501e6i	0.00216850	−	0.000986187i
$229$	1.06279e8	−	6.02738e8i	0.0386460	−	0.219173i	−0.959369	−	0.282156i	$-0.908950\pi$
$229$	1.06279e8	−	6.02738e8i	0.0386460	−	0.219173i	0.998015	+	0.0629834i	$0.0200615\pi$
$230$	−1.94985e9	−	3.43812e8i	−0.696772	−	0.122860i
$231$	−5.12610e9	−	4.97649e8i	−1.80028	−	0.174774i
$232$	3.19870e9	−	2.68403e9i	1.10413	−	0.926479i
$233$	−3.04859e9	−	1.76010e9i	−1.03437	−	0.597192i	−0.116134	−	0.993234i	$-0.537050\pi$
$233$	−3.04859e9	−	1.76010e9i	−1.03437	−	0.597192i	−0.918233	+	0.396041i	$0.870384\pi$
$234$	−1.90340e9	+	1.53640e9i	−0.634842	+	0.512436i
$235$	6.16520e8	+	1.06784e9i	0.202151	+	0.350135i
$236$	−1.73134e8	+	4.75681e8i	−0.0558128	+	0.153344i
$237$	1.25494e9	+	3.49087e8i	0.397767	+	0.110647i
$238$	3.37963e9	+	2.83585e9i	1.05332	+	0.883844i
$239$	−1.07538e9	−	2.95458e9i	−0.329587	−	0.905533i	−0.988216	−	0.153065i	$-0.951086\pi$
$239$	−1.07538e9	−	2.95458e9i	−0.329587	−	0.905533i	0.658629	−	0.752468i	$-0.271137\pi$
$240$	−3.01822e9	−	1.44253e9i	−0.909716	−	0.434789i
$241$	6.25199e8	+	3.54568e9i	0.185332	+	1.05107i	0.925528	+	0.378679i	$0.123622\pi$
$241$	6.25199e8	+	3.54568e9i	0.185332	+	1.05107i	−0.740196	+	0.672391i	$0.765267\pi$
$242$			4.82009e9i			1.40538i
$243$	2.75790e9	+	2.13346e9i	0.790957	+	0.611871i
$244$	1.82966e9			0.516192
$245$	−1.29222e9	+	2.27853e8i	−0.358651	+	0.0632398i
$246$	2.20997e9	−	4.62395e9i	0.603456	−	1.26262i
$247$	−2.83256e7	+	1.03097e7i	−0.00761012	+	0.00276986i
$248$	−3.99489e8	+	4.76093e8i	−0.105608	+	0.125859i
$249$	9.88288e7	−	3.55282e8i	0.0257091	−	0.0924220i
$250$	2.52439e9	+	9.18802e8i	0.646243	+	0.235213i
$251$	−1.40741e9	+	8.12567e8i	−0.354589	+	0.204722i	−0.666705	−	0.745322i	$-0.732296\pi$
$251$	−1.40741e9	+	8.12567e8i	−0.354589	+	0.204722i	0.312116	+	0.950044i	$0.398962\pi$
$252$	−7.96388e8	−	9.86621e8i	−0.197480	−	0.244652i
$253$	−1.76197e9	+	3.05182e9i	−0.430047	+	0.744863i
$254$	−2.13574e9	−	2.54528e9i	−0.513114	−	0.611506i
$255$	9.48673e8	−	9.77192e9i	0.224365	−	2.31110i
$256$	−5.78550e8	+	3.28112e9i	−0.134704	+	0.763945i
$257$	5.64879e8	+	9.96034e7i	0.129486	+	0.0228319i	0.238016	−	0.971261i	$-0.423503\pi$
$257$	5.64879e8	+	9.96034e7i	0.129486	+	0.0228319i	−0.108530	+	0.994093i	$0.534614\pi$
$258$	1.08128e9	+	2.37759e9i	0.244038	+	0.536609i
$259$	1.54624e9	−	1.29745e9i	0.343619	−	0.288330i
$260$	−1.71427e9	−	9.89732e8i	−0.375133	−	0.216583i
$261$	4.63993e9	+	4.04624e9i	0.999883	+	0.871946i
$262$	−2.84732e9	−	4.93170e9i	−0.604269	−	1.04663i
$263$	−2.40422e9	+	6.60554e9i	−0.502517	+	1.38065i	0.386292	+	0.922377i	$0.373756\pi$
$263$	−2.40422e9	+	6.60554e9i	−0.502517	+	1.38065i	−0.888809	+	0.458278i	$0.848466\pi$
$264$	−6.14418e9	+	6.02840e9i	−1.26488	+	1.24104i
$265$	−5.28744e9	−	4.43669e9i	−1.07217	−	0.899654i
$266$	1.35047e7	+	3.71038e7i	0.00269748	+	0.00741126i
$267$	2.80871e8	+	3.60499e9i	0.0552664	+	0.709347i
$268$	−2.61857e8	−	1.48507e9i	−0.0507604	−	0.287877i
$269$			8.50405e9i			1.62411i	0.583578	+	0.812057i	$0.301652\pi$
$269$			8.50405e9i			1.62411i	−0.583578	+	0.812057i	$0.698348\pi$
$270$	2.04125e9	−	6.83200e9i	0.384097	−	1.28556i
$271$	3.66496e9			0.679504			0.339752	−	0.940515i	$-0.389657\pi$
$271$	3.66496e9			0.679504			0.339752	+	0.940515i	$0.389657\pi$
$272$	5.02280e9	−	8.85656e8i	0.917636	−	0.161804i
$273$	3.35893e9	+	4.89550e9i	0.604715	+	0.881347i
$274$	4.72554e9	−	1.71995e9i	0.838395	−	0.305151i
$275$	9.06942e9	−	1.08085e10i	1.58580	−	1.88988i
$276$	−8.40098e8	+	2.16561e8i	−0.144775	+	0.0373201i
$277$	−7.34026e9	−	2.67163e9i	−1.24679	−	0.453793i	−0.367472	−	0.930035i	$-0.619777\pi$
$277$	−7.34026e9	−	2.67163e9i	−1.24679	−	0.453793i	−0.879315	+	0.476241i	$0.841999\pi$
$278$	−4.95083e9	+	2.85836e9i	−0.828894	+	0.478562i
$279$	−7.84690e8	−	4.73168e8i	−0.129503	−	0.0780906i
$280$	−5.86914e9	+	1.01657e10i	−0.954866	+	1.65388i
$281$	−1.00634e9	−	1.19931e9i	−0.161405	−	0.192356i	0.679280	−	0.733879i	$-0.262292\pi$
$281$	−1.00634e9	−	1.19931e9i	−0.161405	−	0.192356i	−0.840686	+	0.541524i	$0.817848\pi$
$282$	−1.11093e9	−	7.93737e8i	−0.175667	−	0.125511i
$283$	1.38681e9	−	7.86497e9i	0.216207	−	1.22617i	−0.662592	−	0.748980i	$-0.730544\pi$
$283$	1.38681e9	−	7.86497e9i	0.216207	−	1.22617i	0.878799	−	0.477192i	$-0.158345\pi$
$284$	8.80006e8	+	1.55169e8i	0.135273	+	0.0238523i
$285$	5.10817e7	−	7.14951e7i	0.00774259	−	0.0108367i
$286$	6.82019e9	−	5.72282e9i	1.01937	−	0.855354i
$287$	−1.07724e10	−	6.21945e9i	−1.58776	−	0.916693i
$288$	−3.76950e9	−	7.17182e7i	−0.547915	−	0.0104246i
$289$	3.99650e9	+	6.92215e9i	0.572913	+	0.992315i
$290$	4.30593e9	−	1.18305e10i	0.608801	−	1.67267i
$291$	−3.14583e8	−	1.22036e9i	−0.0438696	−	0.170182i
$292$	−3.89331e8	−	3.26688e8i	−0.0535535	−	0.0449367i
$293$	3.64627e9	+	1.00180e10i	0.494741	+	1.35929i	0.896296	+	0.443456i	$0.146248\pi$
$293$	3.64627e9	+	1.00180e10i	0.494741	+	1.35929i	−0.401555	+	0.915835i	$0.631530\pi$
$294$	1.19807e9	−	8.22023e8i	0.160358	−	0.110026i
$295$	1.19981e9	+	6.80448e9i	0.158426	+	0.898477i
$296$		−	3.37354e9i		−	0.439459i
$297$	−1.01839e10	−	7.57285e9i	−1.30884	−	0.973270i
$298$	−6.51300e9			−0.825878
$299$	4.00060e9	−	7.05414e8i	0.500542	−	0.0882590i
$300$	3.46314e9	−	2.69820e8i	0.427549	−	0.0333111i
$301$	5.95716e9	−	2.16823e9i	0.725727	−	0.264143i
$302$	−4.41187e9	+	5.25787e9i	−0.530390	+	0.632094i
$303$	9.90759e9	+	1.00979e10i	1.17543	+	1.19801i
$304$	4.28941e7	+	1.56122e7i	0.00502231	+	0.00182797i
$305$	2.16279e10	−	1.24869e10i	2.49928	−	1.44296i
$306$	3.52323e9	+	1.02846e10i	0.401842	+	1.17301i
$307$	−1.42521e9	+	2.46854e9i	−0.160445	+	0.277899i	−0.935028	−	0.354573i	$-0.884626\pi$
$307$	−1.42521e9	+	2.46854e9i	−0.160445	+	0.277899i	0.774583	+	0.632472i	$0.217960\pi$
$308$	2.96641e9	+	3.53523e9i	0.329632	+	0.392840i
$309$	5.80487e9	−	2.63993e9i	0.636735	−	0.289573i
$310$	−3.25390e8	+	1.84538e9i	−0.0352336	+	0.199820i
$311$	1.12462e10	+	1.98300e9i	1.20216	+	0.211974i	0.738633	−	0.674108i	$-0.235472\pi$
$311$	1.12462e10	+	1.98300e9i	1.20216	+	0.211974i	0.463529	+	0.886082i	$0.346583\pi$
$312$	9.87634e9	+	9.58811e8i	1.04226	+	0.101185i
$313$	3.45161e9	−	2.89625e9i	0.359621	−	0.301758i	−0.445019	−	0.895521i	$-0.646803\pi$
$313$	3.45161e9	−	2.89625e9i	0.359621	−	0.301758i	0.804639	+	0.593764i	$0.202359\pi$
$314$	−5.41844e9	−	3.12834e9i	−0.557386	−	0.321807i
$315$	−1.61473e10	−	6.22747e9i	−1.64005	−	0.632513i
$316$	−5.83602e8	−	1.01083e9i	−0.0585287	−	0.101375i
$317$	1.83180e9	−	5.03284e9i	0.181402	−	0.498398i	−0.815347	−	0.578973i	$-0.803454\pi$
$317$	1.83180e9	−	5.03284e9i	0.181402	−	0.498398i	0.996749	+	0.0805754i	$0.0256758\pi$
$318$	7.36335e9	+	2.04827e9i	0.720057	+	0.200298i
$319$	−1.71651e10	−	1.44032e10i	−1.65762	−	1.39091i
$320$	6.25299e9	+	1.71800e10i	0.596332	+	1.63841i
$321$	−4.49552e9	−	2.14859e9i	−0.423409	−	0.202364i
$322$	−9.24024e8	−	5.24040e9i	−0.0859527	−	0.487462i
$323$			1.33969e8i			0.0123082i
$324$	−4.25112e8	−	3.09534e9i	−0.0385765	−	0.280884i
$325$	−1.62651e10			−1.45789
$326$	−6.08340e9	+	1.07267e9i	−0.538612	+	0.0949718i
$327$	−7.05578e8	+	1.47629e9i	−0.0617098	+	0.129116i
$328$	−1.95358e10	+	7.11045e9i	−1.68786	+	0.614330i
$329$	−2.13013e9	+	2.53859e9i	−0.181812	+	0.216675i
$330$	−6.95520e9	+	2.50034e10i	−0.586481	+	2.10835i
$331$	−3.90947e9	−	1.42293e9i	−0.325691	−	0.118542i	0.174000	−	0.984746i	$-0.444331\pi$
$331$	−3.90947e9	−	1.42293e9i	−0.325691	−	0.118542i	−0.499691	+	0.866204i	$0.666553\pi$
$332$	−2.86173e8	+	1.65222e8i	−0.0235546	+	0.0135992i
$333$	4.91381e9	−	7.70362e8i	0.399614	−	0.0626496i
$334$	1.70106e9	−	2.94632e9i	0.136689	−	0.236752i
$335$	−1.32305e10	−	1.57675e10i	−1.05050	−	1.25194i
$336$	8.68736e8	−	8.94851e9i	0.0681601	−	0.702092i
$337$	−1.67135e9	+	9.47871e9i	−0.129583	+	0.734902i	0.848897	+	0.528559i	$0.177267\pi$
$337$	−1.67135e9	+	9.47871e9i	−0.129583	+	0.734902i	−0.978480	+	0.206343i	$0.933844\pi$
$338$	7.72364e8	+	1.36189e8i	0.0591773	+	0.0104346i
$339$	−3.76656e9	−	8.28218e9i	−0.285197	−	0.627113i
$340$	−6.73924e9	+	5.65490e9i	−0.504307	+	0.423164i
$341$	2.88829e9	+	1.66756e9i	0.213611	+	0.123328i
$342$	−1.87152e7	+	9.54806e7i	−0.00136801	+	0.00697928i
$343$	5.91133e9	+	1.02387e10i	0.427080	+	0.739724i
$344$	3.62384e9	−	9.95641e9i	0.258782	−	0.710999i
$345$	−8.45261e9	+	8.29332e9i	−0.596643	+	0.585399i
$346$	−1.19816e10	−	1.00537e10i	−0.836007	−	0.701493i
$347$	−6.87957e7	−	1.89015e8i	−0.00474508	−	0.0130370i	0.937297	−	0.348530i	$-0.113319\pi$
$347$	−6.87957e7	−	1.89015e8i	−0.00474508	−	0.0130370i	−0.942043	+	0.335493i	$0.891097\pi$
$348$	−4.28503e8	−	5.49986e9i	−0.0292171	−	0.375003i
$349$	2.82255e9	+	1.60075e10i	0.190257	+	1.07900i	0.919013	+	0.394227i	$0.128988\pi$
$349$	2.82255e9	+	1.60075e10i	0.190257	+	1.07900i	−0.728756	+	0.684773i	$0.759901\pi$
$350$			2.13058e10i			1.41979i
$351$	8.58729e8	+	1.46046e10i	0.0565754	+	0.962189i
$352$	1.37224e10			0.893838
$353$	5.10574e9	−	9.00279e8i	0.328821	−	0.0579800i	−0.00680064	−	0.999977i	$-0.502165\pi$
$353$	5.10574e9	−	9.00279e8i	0.328821	−	0.0579800i	0.335622	+	0.941997i	$0.391054\pi$
$354$	−4.32856e9	−	6.30869e9i	−0.275632	−	0.401723i
$355$	1.14613e10	−	4.17157e9i	0.721639	−	0.262655i
$356$	2.08270e9	−	2.48206e9i	0.129666	−	0.154530i
$357$	2.55511e10	−	6.58655e9i	1.57303	−	0.405495i
$358$	9.60827e9	+	3.49712e9i	0.584942	+	0.212902i
$359$	−2.29627e10	+	1.32575e10i	−1.38244	+	0.798151i	−0.992448	−	0.122668i	$-0.960855\pi$
$359$	−2.29627e10	+	1.32575e10i	−1.38244	+	0.798151i	−0.389991	+	0.920819i	$0.627522\pi$
$360$	−2.53204e10	+	1.39834e10i	−1.50751	+	0.832534i
$361$	8.49118e9	−	1.47072e10i	0.499965	−	0.865964i
$362$	1.99515e9	+	2.37773e9i	0.116183	+	0.138461i
$363$	2.34564e10	+	1.67591e10i	1.35093	+	0.965213i
$364$	9.23805e8	−	5.23916e9i	0.0526229	−	0.298439i
$365$	−6.83172e9	−	1.20462e9i	−0.384910	−	0.0678700i
$366$	−1.60762e10	+	2.25006e10i	−0.895900	+	1.25392i
$367$	2.18128e10	−	1.83031e10i	1.20239	−	1.00893i	0.202834	−	0.979213i	$-0.434985\pi$
$367$	2.18128e10	−	1.83031e10i	1.20239	−	1.00893i	0.999558	−	0.0297143i	$-0.00945975\pi$
$368$	−5.32749e9	−	3.07583e9i	−0.290490	−	0.167714i
$369$	−1.48180e10	−	2.68316e10i	−0.799252	−	1.44724i
$370$	−5.08570e9	−	8.80870e9i	−0.271359	−	0.470007i
$371$	6.34462e9	−	1.74317e10i	0.334896	−	0.920120i
$372$	2.04957e8	+	7.95084e8i	0.0107026	+	0.0415185i
$373$	2.43295e9	+	2.04149e9i	0.125689	+	0.105466i	0.703465	−	0.710729i	$-0.251635\pi$
$373$	2.43295e9	+	2.04149e9i	0.125689	+	0.105466i	−0.577776	+	0.816195i	$0.696079\pi$
$374$	−1.35333e10	−	3.71825e10i	−0.691700	−	1.90043i
$375$	1.32483e10	−	9.09002e9i	0.669941	−	0.459663i
$376$	9.61774e8	+	5.45449e9i	0.0481196	+	0.272900i
$377$			2.58308e10i			1.27871i
$378$	1.91306e10	−	1.12485e9i	0.937047	−	0.0550971i
$379$	−2.63613e10			−1.27764			−0.638822	−	0.769354i	$-0.720578\pi$
$379$	−2.63613e10			−1.27764			−0.638822	+	0.769354i	$0.720578\pi$
$380$	−7.75400e7	+	1.36724e7i	−0.00371870	+	0.000655707i
$381$	−1.98121e10	+	1.54360e9i	−0.940223	+	0.0732544i
$382$	−1.25484e9	+	4.56724e8i	−0.0589297	+	0.0214487i
$383$	5.71089e9	−	6.80598e9i	0.265405	−	0.316297i	−0.616839	−	0.787089i	$-0.711587\pi$
$383$	5.71089e9	−	6.80598e9i	0.265405	−	0.316297i	0.882244	+	0.470792i	$0.156032\pi$
$384$	−5.83303e9	−	5.94506e9i	−0.268268	−	0.273421i
$385$	5.91920e10	+	2.15441e10i	2.69414	+	0.980587i
$386$	2.97287e10	−	1.71639e10i	1.33914	−	0.773153i
$387$	1.53298e10	+	3.00480e9i	0.683427	+	0.133959i
$388$	−5.64634e8	+	9.77975e8i	−0.0249138	+	0.0431520i
$389$	3.83291e9	+	4.56788e9i	0.167390	+	0.199488i	0.843218	−	0.537572i	$-0.180658\pi$
$389$	3.83291e9	+	4.56788e9i	0.167390	+	0.199488i	−0.675828	+	0.737059i	$0.736214\pi$
$390$	2.72337e10	−	1.23853e10i	1.17720	−	0.535363i
$391$	3.13511e9	−	1.77801e10i	0.134136	−	0.760725i
$392$	−5.80446e9	−	1.02348e9i	−0.245820	−	0.0433448i
$393$	−3.38994e10	−	3.29101e9i	−1.42109	−	0.137962i
$394$	4.44152e9	−	3.72688e9i	0.184309	−	0.154654i
$395$	−1.37972e10	−	7.96582e9i	−0.566765	−	0.327222i
$396$	1.76132e9	+	1.12347e10i	0.0716237	+	0.456856i
$397$	−1.60190e9	−	2.77457e9i	−0.0644871	−	0.111695i	0.831979	−	0.554807i	$-0.187208\pi$
$397$	−1.60190e9	−	2.77457e9i	−0.0644871	−	0.111695i	−0.896466	+	0.443112i	$0.853874\pi$
$398$	4.51344e9	−	1.24006e10i	0.179877	−	0.494208i
$399$	2.27516e8	+	6.32882e7i	0.00897678	+	0.00249707i
$400$	1.88682e10	+	1.58323e10i	0.737038	+	0.618449i
$401$	1.33575e10	+	3.66996e10i	0.516594	+	1.41933i	0.874250	+	0.485477i	$0.161354\pi$
$401$	1.33575e10	+	3.66996e10i	0.516594	+	1.41933i	−0.357656	+	0.933853i	$0.616424\pi$
$402$	2.05637e10	+	9.82820e9i	0.787403	+	0.376331i
$403$	−6.67616e8	−	3.78624e9i	−0.0253108	−	0.143545i
$404$		−	1.26763e10i		−	0.475848i
$405$	−2.61499e10	−	3.36878e10i	−0.971962	−	1.25214i
$406$	3.38359e10			1.24530
$407$	−1.78283e10	+	3.14361e9i	−0.649729	+	0.114565i
$408$	1.90170e10	−	3.97895e10i	0.686279	−	1.43591i
$409$	−3.94804e10	+	1.43697e10i	−1.41087	+	0.513516i	−0.931386	−	0.364032i	$-0.881400\pi$
$409$	−3.94804e10	+	1.43697e10i	−1.41087	+	0.513516i	−0.479488	+	0.877548i	$0.659178\pi$
$410$	−4.02910e10	+	4.80170e10i	−1.42585	+	1.69926i
$411$	8.06037e9	−	2.89764e10i	0.282480	−	1.01549i
$412$	−5.36959e9	−	1.95437e9i	−0.186360	−	0.0678294i
$413$	−1.60819e10	+	9.28487e9i	−0.552760	+	0.319136i
$414$	4.71828e9	−	1.22341e10i	0.160614	−	0.416457i
$415$	−2.25518e9	+	3.90608e9i	−0.0760306	+	0.131689i
$416$	−1.01682e10	−	1.21180e10i	−0.339523	−	0.404628i
$417$	−3.30378e9	+	3.40309e10i	−0.109261	+	1.12546i
$418$	6.14950e7	−	3.48755e8i	0.00201435	−	0.0114239i
$419$	2.44273e10	+	4.30720e9i	0.792538	+	0.139746i	0.555239	−	0.831691i	$-0.312627\pi$
$419$	2.44273e10	+	4.30720e9i	0.792538	+	0.139746i	0.237299	+	0.971437i	$0.423738\pi$
$420$	6.41990e9	+	1.41165e10i	0.206315	+	0.453661i
$421$	−4.34557e10	+	3.64636e10i	−1.38331	+	1.16073i	−0.415335	+	0.909669i	$0.636335\pi$
$421$	−4.34557e10	+	3.64636e10i	−1.38331	+	1.16073i	−0.967971	+	0.251062i	$0.919220\pi$
$422$	−1.69917e10	−	9.81015e9i	−0.535780	−	0.309333i
$423$	−7.72525e9	+	2.64645e9i	−0.241297	+	0.0826614i
$424$	−1.55020e10	−	2.68502e10i	−0.479650	−	0.830778i
$425$	−2.47240e10	+	6.79287e10i	−0.757815	+	2.08208i
$426$	−9.64034e9	+	9.45867e9i	−0.292721	+	0.287205i
$427$	5.14163e10	+	4.31434e10i	1.54664	+	1.29778i
$428$	1.52703e9	+	4.19547e9i	0.0455063	+	0.125028i
$429$	−4.13613e9	−	5.30875e10i	−0.122114	−	1.56734i
$430$	−5.54732e9	−	3.14604e10i	−0.162259	−	0.920217i
$431$			6.46311e10i			1.87298i	0.350698	+	0.936489i	$0.385945\pi$
$431$			6.46311e10i			1.87298i	−0.350698	+	0.936489i	$0.614055\pi$
$432$	1.32198e10	−	1.77777e10i	0.379567	−	0.510436i
$433$	2.65628e10			0.755653			0.377826	−	0.925876i	$-0.376672\pi$
$433$	2.65628e10			0.755653			0.377826	+	0.925876i	$0.376672\pi$
$434$	−4.95961e9	+	8.74513e8i	−0.139794	+	0.0246494i
$435$	−4.26001e10	−	6.20879e10i	−1.18974	−	1.73400i
$436$	1.37776e9	−	5.01463e8i	0.0381265	−	0.0138769i
$437$	1.03865e8	−	1.23781e8i	0.00284801	−	0.00339413i
$438$	7.43835e9	−	1.91746e9i	0.202106	−	0.0520990i
$439$	−5.28937e10	−	1.92517e10i	−1.42412	−	0.518337i	−0.488878	−	0.872352i	$-0.662594\pi$
$439$	−5.28937e10	−	1.92517e10i	−1.42412	−	0.518337i	−0.935240	+	0.354015i	$0.884816\pi$
$440$	9.11741e10	−	5.26394e10i	2.43255	−	1.40443i
$441$	1.65304e8	−	8.68835e9i	0.00437048	−	0.229712i
$442$	−2.28070e10	+	3.95029e10i	−0.597557	+	1.03500i
$443$	2.12742e10	+	2.53536e10i	0.552381	+	0.658302i	0.967916	−	0.251275i	$-0.0808498\pi$
$443$	2.12742e10	+	2.53536e10i	0.552381	+	0.658302i	−0.415534	+	0.909577i	$0.636405\pi$
$444$	−3.62638e9	−	2.59097e9i	−0.0933129	−	0.0666701i
$445$	7.67966e9	−	4.35535e10i	0.195840	−	1.11066i
$446$	1.31733e10	+	2.32281e9i	0.332932	+	0.0587049i
$447$	−2.26452e10	+	3.16947e10i	−0.567213	+	0.793884i
$448$	−3.76403e10	+	3.15839e10i	−0.934417	+	0.784069i
$449$	−6.27975e10	−	3.62562e10i	−1.54510	−	0.892065i	−0.998505	−	0.0546691i	$-0.982590\pi$
$449$	−6.27975e10	−	3.62562e10i	−1.54510	−	0.892065i	−0.546597	−	0.837396i	$-0.684077\pi$
$450$	−2.71106e10	+	4.49595e10i	−0.661132	+	1.09641i
$451$	5.57812e10	+	9.66159e10i	1.34829	+	2.33530i
$452$	−2.78842e9	+	7.66113e9i	−0.0668043	+	0.183543i
$453$	1.02470e10	+	3.97510e10i	0.243335	+	0.943965i
$454$	6.62650e9	+	5.56030e9i	0.155977	+	0.130880i
$455$	−2.48356e10	−	6.82353e10i	−0.579468	−	1.59208i
$456$	3.25453e8	−	2.23301e8i	0.00752711	−	0.00516454i
$457$	−9.23518e9	−	5.23753e10i	−0.211729	−	1.20078i	−0.886493	−	0.462742i	$-0.846866\pi$
$457$	−9.23518e9	−	5.23753e10i	−0.211729	−	1.20078i	0.674764	−	0.738033i	$-0.264245\pi$
$458$		−	8.28893e9i		−	0.188381i
$459$	6.22989e10	+	1.86135e10i	1.40356	+	0.419351i
$460$	1.06110e10			0.236986
$461$	−3.01751e10	+	5.32068e9i	−0.668104	+	0.117805i	−0.497405	−	0.867518i	$-0.665714\pi$
$461$	−3.01751e10	+	5.32068e9i	−0.668104	+	0.117805i	−0.170699	+	0.985323i	$0.554603\pi$
$462$	−6.95395e10	+	5.41794e9i	−1.52638	+	0.118923i
$463$	3.02920e10	−	1.10254e10i	0.659181	−	0.239922i	0.00929829	−	0.999957i	$-0.497040\pi$
$463$	3.02920e10	−	1.10254e10i	0.659181	−	0.239922i	0.649883	+	0.760035i	$0.274818\pi$
$464$	2.51434e10	−	2.99648e10i	0.542441	−	0.646456i
$465$	7.84895e9	+	7.99970e9i	0.167880	+	0.171105i
$466$	−4.47997e10	−	1.63058e10i	−0.950017	−	0.345778i
$467$	4.49907e10	−	2.59754e10i	0.945922	−	0.546129i	0.0541106	−	0.998535i	$-0.482768\pi$
$467$	4.49907e10	−	2.59754e10i	0.945922	−	0.546129i	0.891812	+	0.452406i	$0.149434\pi$
$468$	8.61599e9	−	9.88018e9i	0.179606	−	0.205959i
$469$	2.76592e10	−	4.79072e10i	0.571674	−	0.990169i
$470$	1.07341e10	+	1.27924e10i	0.219976	+	0.262157i
$471$	−3.40632e10	+	1.54912e10i	−0.692152	+	0.314776i
$472$	−5.38939e9	+	3.05648e10i	−0.108585	+	0.615819i
$473$	−5.59940e10	−	9.87325e9i	−1.11866	−	0.197249i
$474$	1.75587e10	+	1.70462e9i	0.347839	+	0.0337687i
$475$	−4.95608e8	+	4.15865e8i	−0.00973563	+	0.00816916i
$476$	−2.04762e10	−	1.18220e10i	−0.398862	−	0.230283i
$477$	3.55694e10	−	2.87112e10i	0.687074	−	0.554597i
$478$	−2.12913e10	−	3.68776e10i	−0.407840	−	0.706400i
$479$	−7.77313e9	+	2.13565e10i	−0.147657	+	0.405684i	−0.991367	−	0.131115i	$-0.958144\pi$
$479$	−7.77313e9	+	2.13565e10i	−0.147657	+	0.405684i	0.843710	+	0.536799i	$0.180367\pi$
$480$	4.44254e10	+	1.23578e10i	0.836887	+	0.232797i
$481$	1.59867e10	+	1.34144e10i	0.298660	+	0.250606i
$482$	1.66771e10	+	4.58201e10i	0.308982	+	0.848922i
$483$	−2.87145e10	−	1.37238e10i	−0.527610	−	0.252166i
$484$	−4.48568e9	−	2.54396e10i	−0.0817424	−	0.463584i
$485$			1.54138e10i			0.278576i
$486$	4.18007e10	+	2.19691e10i	0.749271	+	0.393792i
$487$	−6.87683e10			−1.22257			−0.611283	−	0.791412i	$-0.709346\pi$
$487$	−6.87683e10			−1.22257			−0.611283	+	0.791412i	$0.709346\pi$
$488$	1.10474e11	−	1.94796e10i	1.94797	−	0.343480i
$489$	−1.59315e10	+	3.33337e10i	−0.278626	+	0.582973i
$490$	−1.66991e10	+	6.07796e9i	−0.289673	+	0.105432i
$491$	4.69265e10	−	5.59248e10i	0.807406	−	0.962229i	−0.192412	−	0.981314i	$-0.561631\pi$
$491$	4.69265e10	−	5.59248e10i	0.807406	−	0.962229i	0.999818	+	0.0190855i	$0.00607549\pi$
$492$	−7.36067e9	+	2.64610e10i	−0.125620	+	0.451592i
$493$	1.07878e11	+	3.92645e10i	1.82619	+	0.664679i
$494$	−3.53546e8	+	2.04120e8i	−0.00593660	+	0.00342750i
$495$	9.74933e10	+	1.20781e11i	1.62388	+	2.01178i
$496$	−2.91102e9	+	5.04203e9i	−0.0480970	+	0.0833064i
$497$	2.10706e10	+	2.51110e10i	0.345344	+	0.411565i
$498$	4.82590e8	−	4.97098e9i	0.00784623	−	0.0808210i
$499$	6.66714e9	−	3.78112e10i	0.107532	−	0.609844i	−0.882647	−	0.470037i	$-0.844241\pi$
$499$	6.66714e9	−	3.78112e10i	0.107532	−	0.609844i	0.990179	−	0.139807i	$-0.0446482\pi$
$500$	−1.41783e10	−	2.50002e9i	−0.226853	−	0.0400004i
$501$	−8.42345e9	−	1.85221e10i	−0.133702	−	0.293995i
$502$	−1.68603e10	+	1.41475e10i	−0.265491	+	0.222774i
$503$	1.37684e9	+	7.94918e8i	0.0215085	+	0.0124180i	0.510716	−	0.859750i	$-0.329380\pi$
$503$	1.37684e9	+	7.94918e8i	0.0215085	+	0.0124180i	−0.489207	+	0.872168i	$0.662714\pi$
$504$	−5.85898e10	−	5.10931e10i	−0.908029	−	0.791845i
$505$	−8.65122e10	−	1.49844e11i	−1.33018	−	2.30395i
$506$	−1.63230e10	+	4.48472e10i	−0.249000	+	0.684121i
$507$	3.34820e9	−	3.28510e9i	0.0506733	−	0.0497183i
$508$	1.36408e10	+	1.14460e10i	0.204826	+	0.171869i
$509$	−2.97231e10	−	8.16637e10i	−0.442816	−	1.21663i	−0.937632	−	0.347630i	$-0.886987\pi$
$509$	−2.97231e10	−	8.16637e10i	−0.442816	−	1.21663i	0.494816	−	0.868998i	$-0.335236\pi$
$510$	−1.03283e10	−	1.32564e11i	−0.152667	−	1.95949i
$511$	−3.23751e9	−	1.83608e10i	−0.0474819	−	0.269283i
$512$			7.14453e10i			1.03967i
$513$	3.99574e8	+	4.23054e8i	0.00576936	+	0.00610839i
$514$	7.76829e9			0.111294
$515$	−7.68104e10	+	1.35437e10i	−1.09192	+	0.192535i
$516$	−7.91943e9	−	1.15423e10i	−0.111711	−	0.162814i
$517$	2.79294e10	−	1.01655e10i	0.390930	−	0.142287i
$518$	1.75716e10	−	2.09410e10i	0.244057	−	0.290856i
$519$	−9.05844e10	+	2.33508e10i	−1.24849	+	0.321835i
$520$	−1.14044e11	−	4.15086e10i	−1.55977	−	0.567708i
$521$	1.18023e11	−	6.81406e10i	1.60183	−	0.924815i	0.610704	−	0.791859i	$-0.290886\pi$
$521$	1.18023e11	−	6.81406e10i	1.60183	−	0.924815i	0.991122	−	0.132956i	$-0.0424470\pi$
$522$	7.14006e10	+	4.30546e10i	0.961657	+	0.579879i
$523$	−1.68568e10	+	2.91969e10i	−0.225304	+	0.390238i	−0.956411	−	0.292025i	$-0.905671\pi$
$523$	−1.68568e10	+	2.91969e10i	−0.225304	+	0.390238i	0.731107	+	0.682263i	$0.239004\pi$
$524$	1.96172e10	+	2.33789e10i	0.260203	+	0.310098i
$525$	1.03682e11	+	7.40785e10i	1.36479	+	0.975113i
$526$	−1.65316e10	+	9.37552e10i	−0.215959	+	1.22476i
$527$	−1.68274e10	−	2.96713e9i	−0.218160	−	0.0384675i
$528$	−4.68766e10	+	6.56095e10i	−0.603143	+	0.844173i
$529$	4.33082e10	−	3.63399e10i	0.553029	−	0.464046i
$530$	−8.09551e10	−	4.67394e10i	−1.02598	−	0.592352i
$531$	−4.57505e10	−	8.70447e8i	−0.575464	−	0.0109487i
$532$	−1.05805e8	−	1.83260e8i	−0.00132087	−	0.00228781i
$533$	4.39861e10	−	1.20851e11i	0.545013	−	1.49741i
$534$	1.22241e10	+	4.74208e10i	0.150333	+	0.583182i
$535$	4.66834e10	+	3.91720e10i	0.569832	+	0.478146i
$536$	−3.16217e10	−	8.68799e10i	−0.383112	−	1.05259i
$537$	5.04255e10	−	3.45982e10i	0.606392	−	0.416061i
$538$	1.99994e10	+	1.13422e11i	0.238720	+	1.35385i
$539$			3.16289e10i			0.374739i
$540$	−4.41534e9	+	3.79578e10i	−0.0519265	+	0.446402i
$541$	1.02849e11			1.20064			0.600319	−	0.799760i	$-0.295040\pi$
$541$	1.02849e11			1.20064			0.600319	+	0.799760i	$0.295040\pi$
$542$	4.88813e10	−	8.61908e9i	0.566429	−	0.0998767i
$543$	1.85079e10	−	1.44198e9i	0.212892	−	0.0165868i
$544$	−6.60649e10	+	2.40457e10i	−0.754354	+	0.274562i
$545$	1.28638e10	−	1.53304e10i	0.145808	−	0.173767i
$546$	5.63126e10	+	5.73942e10i	0.633629	+	0.645799i
$547$	−1.29316e11	−	4.70673e10i	−1.44446	−	0.525739i	−0.503418	−	0.864043i	$-0.667925\pi$
$547$	−1.29316e11	−	4.70673e10i	−1.44446	−	0.525739i	−0.941037	+	0.338304i	$0.890147\pi$
$548$	−2.33399e10	+	1.34753e10i	−0.258808	+	0.149423i
$549$	5.36009e10	+	1.56466e11i	0.590041	+	1.72239i
$550$	9.55441e10	−	1.65487e11i	1.04413	−	1.80848i
$551$	6.60439e8	+	7.87081e8i	0.00716517	+	0.00853912i
$552$	−4.84192e10	+	2.20200e10i	−0.521509	+	0.237171i
$553$	7.43521e9	−	4.21672e10i	0.0795047	−	0.450893i
$554$	−1.04183e11	−	1.83703e10i	−1.10601	−	0.195020i
$555$	−6.05491e10	−	5.87820e9i	−0.638169	−	0.0619544i
$556$	2.34696e10	−	1.96933e10i	0.245587	−	0.206072i
$557$	1.34913e11	+	7.78922e10i	1.40163	+	0.809232i	0.994560	−	0.104165i	$-0.0332169\pi$
$557$	1.34913e11	+	7.78922e10i	1.40163	+	0.809232i	0.407071	+	0.913397i	$0.366550\pi$
$558$	−1.15785e10	−	4.46546e9i	−0.119431	−	0.0460606i
$559$	3.27722e10	+	5.67631e10i	0.335628	+	0.581325i
$560$	−3.76091e10	+	1.03330e11i	−0.382421	+	1.05069i
$561$	−2.27998e11	−	6.34223e10i	−2.30187	−	0.640311i
$562$	−1.62425e10	−	1.36290e10i	−0.162820	−	0.136622i
$563$	3.49849e10	+	9.61202e10i	0.348214	+	0.956711i	0.982932	+	0.183967i	$0.0588941\pi$
$563$	3.49849e10	+	9.61202e10i	0.348214	+	0.956711i	−0.634718	+	0.772744i	$0.718884\pi$
$564$	6.60198e9	+	3.15535e9i	0.0652466	+	0.0311839i
$565$	1.93237e10	+	1.09590e11i	0.189625	+	1.07542i
$566$		−	1.08160e11i		−	1.05391i
$567$	6.10416e10	−	9.70077e10i	0.590601	−	0.938586i
$568$	5.47865e10			0.526356
$569$	−8.94456e10	+	1.57717e10i	−0.853316	+	0.150463i	−0.583163	−	0.812355i	$-0.698185\pi$
$569$	−8.94456e10	+	1.57717e10i	−0.853316	+	0.150463i	−0.270152	+	0.962818i	$0.587074\pi$
$570$	5.13162e8	−	1.07370e9i	0.00486133	−	0.0101714i
$571$	−1.14927e11	+	4.18298e10i	−1.08113	+	0.393497i	−0.820326	−	0.571896i	$-0.806208\pi$
$571$	−1.14927e11	+	4.18298e10i	−1.08113	+	0.393497i	−0.260799	+	0.965393i	$0.583986\pi$
$572$	−3.06700e10	+	3.65511e10i	−0.286503	+	0.341441i
$573$	−2.14039e9	+	7.69451e9i	−0.0198552	+	0.0713777i
$574$	−1.58303e11	−	5.76176e10i	−1.45828	−	0.530771i
$575$	7.55084e10	−	4.35948e10i	0.690755	−	0.398807i
$576$	−1.19618e11	+	1.87531e10i	−1.08669	+	0.170366i
$577$	−1.35572e9	+	2.34817e9i	−0.0122311	+	0.0211849i	−0.872076	−	0.489370i	$-0.837227\pi$
$577$	−1.35572e9	+	2.34817e9i	−0.0122311	+	0.0211849i	0.859845	+	0.510555i	$0.170560\pi$
$578$	6.95824e10	+	8.29251e10i	0.623431	+	0.742976i
$579$	1.98385e10	−	2.04348e11i	0.176520	−	1.81826i
$580$	−1.17163e10	+	6.64463e10i	−0.103533	+	0.587163i
$581$	−1.19378e10	−	2.10496e9i	−0.104766	−	0.0184731i
$582$	−7.06572e9	−	1.55366e10i	−0.0615835	−	0.135414i
$583$	−1.27451e11	+	1.06944e11i	−1.10324	+	0.925729i
$584$	−2.69858e10	−	1.55803e10i	−0.231998	−	0.133944i
$585$	3.44179e10	−	1.75592e11i	0.293874	−	1.49928i
$586$	7.21919e10	+	1.25040e11i	0.612207	+	1.06037i
$587$	−4.01800e10	+	1.10394e11i	−0.338421	+	0.929805i	0.647421	+	0.762132i	$0.275847\pi$
$587$	−4.01800e10	+	1.10394e11i	−0.338421	+	0.929805i	−0.985843	+	0.167673i	$0.946375\pi$
$588$	−5.55819e9	+	5.45345e9i	−0.0464969	+	0.0456207i
$589$	−1.17149e8	−	9.82993e7i	−0.000973365	−	0.000816751i
$590$	3.20049e10	+	8.79328e10i	0.264125	+	0.725677i
$591$	−2.69358e9	−	3.45722e10i	−0.0220790	−	0.283385i
$592$	−5.48773e9	−	3.11224e10i	−0.0446792	−	0.253389i
$593$			1.69673e11i			1.37212i	0.727544	+	0.686061i	$0.240662\pi$
$593$			1.69673e11i			1.37212i	−0.727544	+	0.686061i	$0.759338\pi$
$594$	−1.53636e11	−	7.70526e10i	−1.23409	−	0.618930i
$595$	−3.22725e11			−2.57493
$596$	3.43745e10	−	6.06115e9i	0.272428	−	0.0480364i
$597$	−4.46530e10	−	6.50800e10i	−0.351523	−	0.512330i
$598$	5.16989e10	−	1.88168e10i	0.404274	−	0.147144i
$599$	−1.03440e11	+	1.23275e11i	−0.803493	+	0.957566i	−0.999736	−	0.0229897i	$-0.992681\pi$
$599$	−1.03440e11	+	1.23275e11i	−0.803493	+	0.957566i	0.196243	+	0.980555i	$0.437126\pi$
$600$	2.06231e11	−	5.31622e10i	1.59129	−	0.410202i
$601$	1.59242e11	+	5.79593e10i	1.22056	+	0.444248i	0.870355	−	0.492425i	$-0.163889\pi$
$601$	1.59242e11	+	5.79593e10i	1.22056	+	0.444248i	0.350206	+	0.936673i	$0.386112\pi$
$602$	7.43542e10	−	4.29284e10i	0.566135	−	0.326858i
$603$	1.19326e11	−	6.58988e10i	0.902540	−	0.498435i
$604$	1.83920e10	−	3.18559e10i	0.138192	−	0.239355i
$605$	−2.26641e11	−	2.70101e11i	−1.69168	−	2.01606i
$606$	1.55890e11	+	1.11380e11i	1.15592	+	0.825879i
$607$	3.08833e10	−	1.75148e11i	0.227494	−	1.29018i	−0.630366	−	0.776298i	$-0.717095\pi$
$607$	3.08833e10	−	1.75148e11i	0.227494	−	1.29018i	0.857860	−	0.513883i	$-0.171794\pi$
$608$	−6.19660e8	−	1.09263e8i	−0.00453460	−	0.000799573i
$609$	1.17645e11	−	1.64658e11i	0.855271	−	1.19706i
$610$	2.59096e11	−	2.17407e11i	1.87129	−	1.57020i
$611$	−2.96724e10	−	1.71314e10i	−0.212906	−	0.122921i
$612$	−2.81661e10	−	5.10017e10i	−0.200780	−	0.363563i
$613$	−2.91010e10	−	5.04044e10i	−0.206094	−	0.356966i	0.744387	−	0.667749i	$-0.232742\pi$
$613$	−2.91010e10	−	5.04044e10i	−0.206094	−	0.356966i	−0.950481	+	0.310783i	$0.899409\pi$
$614$	−1.32033e10	+	3.62758e10i	−0.0928987	+	0.255237i
$615$	9.35801e10	+	3.63023e11i	0.654158	+	2.53766i
$616$	2.16749e11	+	1.81874e11i	1.50534	+	1.26313i
$617$	4.57298e10	+	1.25641e11i	0.315543	+	0.866947i	0.991512	+	0.130017i	$0.0415031\pi$
$617$	4.57298e10	+	1.25641e11i	0.315543	+	0.866947i	−0.675969	+	0.736930i	$0.736275\pi$
$618$	7.12138e10	−	4.88616e10i	0.488214	−	0.334976i
$619$	2.33487e10	+	1.32417e11i	0.159038	+	0.901948i	0.955001	+	0.296603i	$0.0958538\pi$
$619$	2.33487e10	+	1.32417e11i	0.159038	+	0.901948i	−0.795963	+	0.605345i	$0.793035\pi$
$620$		−	1.00424e10i		−	0.0679627i
$621$	−4.31306e10	−	6.54979e10i	−0.290014	−	0.440414i
$622$	1.54659e11			1.03327
$623$	1.17054e11	−	2.06397e10i	0.777022	−	0.137010i
$624$	9.26736e10	−	7.22036e9i	0.611248	−	0.0476234i
$625$	3.22202e10	−	1.17272e10i	0.211158	−	0.0768554i
$626$	3.92245e10	−	4.67459e10i	0.255423	−	0.304401i
$627$	−1.48336e9	−	1.51185e9i	−0.00959792	−	0.00978227i
$628$	3.15089e10	+	1.14683e10i	0.202579	+	0.0737328i
$629$	8.03238e10	−	4.63750e10i	0.513147	−	0.296265i
$630$	−2.30009e11	−	4.50842e10i	−1.46010	−	0.286195i
$631$	−1.52481e10	+	2.64105e10i	−0.0961831	+	0.166594i	−0.910102	−	0.414385i	$-0.863997\pi$
$631$	−1.52481e10	+	2.64105e10i	−0.0961831	+	0.166594i	0.813919	+	0.580979i	$0.197330\pi$
$632$	−4.59996e10	−	5.48202e10i	−0.288327	−	0.343615i
$633$	−1.06819e11	+	4.85788e10i	−0.665323	+	0.302574i
$634$	1.25956e10	−	7.14333e10i	0.0779583	−	0.442123i
$635$	2.39359e11	+	4.22055e10i	1.47216	+	0.259582i
$636$	−4.07686e10	−	3.95788e9i	−0.249171	−	0.0241899i
$637$	2.79308e10	−	2.34367e10i	0.169639	−	0.142344i
$638$	−2.62812e11	−	1.51735e11i	−1.58622	−	0.915802i
$639$	1.25107e10	+	7.98006e10i	0.0750377	+	0.478633i
$640$	5.09334e10	+	8.82193e10i	0.303587	+	0.525828i
$641$	7.45477e10	−	2.04818e11i	0.441572	−	1.21321i	−0.496885	−	0.867816i	$-0.665523\pi$
$641$	7.45477e10	−	2.04818e11i	0.441572	−	1.21321i	0.938458	−	0.345394i	$-0.112255\pi$
$642$	−6.50118e10	−	1.80843e10i	−0.382694	−	0.106454i
$643$	−1.17314e11	−	9.84380e10i	−0.686286	−	0.575863i	0.231549	−	0.972823i	$-0.425621\pi$
$643$	−1.17314e11	−	9.84380e10i	−0.686286	−	0.575863i	−0.917836	+	0.396961i	$0.870065\pi$
$644$	9.75368e9	+	2.67980e10i	0.0567055	+	0.155797i
$645$	−1.72386e11	−	8.23900e10i	−0.996008	−	0.476032i
$646$	3.15061e8	+	1.78680e9i	0.00180911	+	0.0102600i
$647$			1.23404e11i			0.704226i	0.935957	+	0.352113i	$0.114537\pi$
$647$			1.23404e11i			0.704226i	−0.935957	+	0.352113i	$0.885463\pi$
$648$	−5.86228e10	−	1.82369e11i	−0.332481	−	1.03431i
$649$	1.66549e11			0.938780
$650$	−2.16936e11	+	3.82516e10i	−1.21528	+	0.214287i
$651$	−1.29885e10	+	2.71759e10i	−0.0723159	+	0.151308i
$652$	3.11089e10	−	1.13227e10i	0.172145	−	0.0626556i
$653$	−4.83237e10	+	5.75899e10i	−0.265771	+	0.316733i	−0.882381	−	0.470535i	$-0.844061\pi$
$653$	−4.83237e10	+	5.75899e10i	−0.265771	+	0.316733i	0.616610	+	0.787268i	$0.288505\pi$
$654$	−5.93875e9	+	2.13493e10i	−0.0324626	+	0.116701i
$655$	3.91443e11	+	1.42474e11i	2.12669	+	0.774051i
$656$	−1.68660e11	+	9.73761e10i	−0.910747	+	0.525820i
$657$	1.65315e10	−	4.28647e10i	0.0887259	−	0.230058i
$658$	−2.24404e10	+	3.88680e10i	−0.119709	+	0.207342i
$659$	4.53931e10	+	5.40973e10i	0.240684	+	0.286836i	0.872842	−	0.488004i	$-0.162275\pi$
$659$	4.53931e10	+	5.40973e10i	0.240684	+	0.286836i	−0.632157	+	0.774840i	$0.717830\pi$
$660$	1.34396e10	−	1.38436e11i	0.0708289	−	0.729582i
$661$	−2.47641e10	+	1.40444e11i	−0.129723	+	0.735696i	0.848667	+	0.528928i	$0.177406\pi$
$661$	−2.47641e10	+	1.40444e11i	−0.129723	+	0.735696i	−0.978390	+	0.206768i	$0.933705\pi$
$662$	−5.54888e10	−	9.78418e9i	−0.288917	−	0.0509439i
$663$	1.12938e11	+	2.48336e11i	0.584501	+	1.28524i
$664$	−1.55200e10	+	1.30228e10i	−0.0798396	+	0.0669934i
$665$	−2.50139e9	−	1.44418e9i	−0.0127907	−	0.00738471i
$666$	6.37260e10	−	2.18307e10i	0.323907	−	0.110961i
$667$	−6.92334e10	−	1.19916e11i	−0.349794	−	0.605861i
$668$	−6.23597e9	+	1.71332e10i	−0.0313183	+	0.0860464i
$669$	5.71062e10	−	5.60301e10i	0.285088	−	0.279716i
$670$	−2.13542e11	−	1.79183e11i	−1.05970	−	0.889196i
$671$	−2.05890e11	−	5.65678e11i	−1.01565	−	2.79048i
$672$	9.62647e9	+	1.23556e11i	0.0472052	+	0.605881i
$673$	−1.33595e10	−	7.57657e10i	−0.0651225	−	0.369328i	−0.999901	−	0.0140960i	$-0.995513\pi$
$673$	−1.33595e10	−	7.57657e10i	−0.0651225	−	0.369328i	0.934778	−	0.355232i	$-0.115598\pi$
$674$			1.30353e11i			0.631655i
$675$	1.24529e11	+	2.88251e11i	0.599865	+	1.38853i
$676$	−4.20314e9			−0.0201274
$677$	−2.24167e11	+	3.95267e10i	−1.06713	+	0.188164i	−0.679518	−	0.733659i	$-0.737811\pi$
$677$	−2.24167e11	+	3.95267e10i	−1.06713	+	0.188164i	−0.387612	+	0.921823i	$0.626700\pi$
$678$	−6.97139e10	−	1.01605e11i	−0.329914	−	0.480836i
$679$	−3.89277e10	+	1.41685e10i	−0.183138	+	0.0666569i
$680$	−3.46708e11	+	4.13191e11i	−1.62154	+	1.93248i
$681$	5.00984e10	−	1.29144e10i	0.232935	−	0.0600460i
$682$	4.24442e10	+	1.54484e10i	0.196192	+	0.0714079i
$683$	−6.00315e10	+	3.46592e10i	−0.275865	+	0.159271i	−0.631550	−	0.775335i	$-0.717581\pi$
$683$	−6.00315e10	+	3.46592e10i	−0.275865	+	0.159271i	0.355685	+	0.934606i	$0.384248\pi$
$684$	9.91912e6	−	5.21347e8i	4.53157e−5	−	0.00238178i
$685$	−1.83930e11	+	3.18576e11i	−0.835392	+	1.44694i
$686$	1.02921e11	+	1.22657e11i	0.464738	+	0.553853i
$687$	−4.03371e10	−	2.88200e10i	−0.181083	−	0.129380i
$688$	1.72355e10	−	9.77475e10i	0.0769255	−	0.436266i
$689$	1.88881e11	+	3.33048e10i	0.838129	+	0.147785i
$690$	−9.32325e10	+	1.30490e11i	−0.411312	+	0.575681i
$691$	−6.29010e10	+	5.27802e10i	−0.275896	+	0.231504i	−0.770228	−	0.637769i	$-0.779857\pi$
$691$	−6.29010e10	+	5.27802e10i	−0.275896	+	0.231504i	0.494331	+	0.869274i	$0.335413\pi$
$692$	7.25930e10	+	4.19116e10i	0.316570	+	0.182772i
$693$	−2.15418e11	+	3.57243e11i	−0.934003	+	1.54893i
$694$	−1.36208e9	−	2.35919e9i	−0.00587170	−	0.0101701i
$695$	1.43026e11	−	3.92962e11i	0.613024	−	1.68427i
$696$	−8.44275e10	−	3.27518e11i	−0.359788	−	1.39572i
$697$	−4.37852e11	−	3.67402e11i	−1.85522	−	1.55672i
$698$	7.52914e10	+	2.06861e11i	0.317193	+	0.871480i
$699$	−2.35115e11	+	1.61319e11i	−0.984854	+	0.675734i
$700$	−1.98276e10	−	1.12448e11i	−0.0825808	−	0.468339i
$701$			3.67111e11i			1.52029i	0.649755	+	0.760144i	$0.274871\pi$
$701$			3.67111e11i			1.52029i	−0.649755	+	0.760144i	$0.725129\pi$
$702$	4.57996e10	+	1.92768e11i	0.188588	+	0.793757i
$703$	8.30101e8			0.00339867
$704$	4.33997e11	−	7.65254e10i	1.76684	−	0.311541i
$705$	9.95744e10	−	7.75801e9i	0.403080	−	0.0314047i
$706$	6.59803e10	−	2.40149e10i	0.265580	−	0.0966633i
$707$	2.98908e11	−	3.56224e11i	1.19635	−	1.42576i
$708$	2.87164e10	+	2.92679e10i	0.114287	+	0.116482i
$709$	−2.03327e10	−	7.40048e9i	−0.0804654	−	0.0292870i	0.301474	−	0.953474i	$-0.402521\pi$
$709$	−2.03327e10	−	7.40048e9i	−0.0804654	−	0.0292870i	−0.381939	+	0.924187i	$0.624744\pi$
$710$	1.43054e11	−	8.25922e10i	0.562945	−	0.325017i
$711$	6.93455e10	−	7.95203e10i	0.271356	−	0.311171i
$712$	9.93270e10	−	1.72039e11i	0.386498	−	0.669435i
$713$	1.32474e10	+	1.57876e10i	0.0512593	+	0.0610884i
$714$	3.25296e11	−	1.47938e11i	1.25166	−	0.569228i
$715$	−1.13092e11	+	6.41374e11i	−0.432719	+	2.45407i
$716$	−5.39653e10	−	9.51553e9i	−0.205335	−	0.0362060i
$717$	−2.53488e11	−	2.46090e10i	−0.959138	−	0.0931147i
$718$	−2.75086e11	+	2.30825e11i	−1.03507	+	0.868529i
$719$	−2.85002e11	−	1.64546e11i	−1.06643	−	0.615703i	−0.139226	−	0.990261i	$-0.544461\pi$
$719$	−2.85002e11	−	1.64546e11i	−1.06643	−	0.615703i	−0.927204	+	0.374557i	$0.877795\pi$
$720$	−2.10846e11	+	1.70192e11i	−0.784575	+	0.633299i
$721$	−1.04810e11	−	1.81535e11i	−0.387846	−	0.671770i
$722$	7.86632e10	−	2.16125e11i	0.289483	−	0.795347i
$723$	2.80963e11	+	7.81556e10i	1.02824	+	0.286027i
$724$	−1.27428e10	−	1.06925e10i	−0.0463780	−	0.0389158i
$725$	1.89619e11	+	5.20973e11i	0.686324	+	1.88566i
$726$	3.52261e11	+	1.68360e11i	1.26800	+	0.606027i
$727$	−6.75215e10	−	3.82933e11i	−0.241715	−	1.37084i	−0.827999	−	0.560730i	$-0.810521\pi$
$727$	−6.75215e10	−	3.82933e11i	−0.241715	−	1.37084i	0.586283	−	0.810106i	$-0.300590\pi$
$728$		−	3.26174e11i		−	1.16124i
$729$	2.52248e11	−	1.27033e11i	0.893135	−	0.449788i
$730$	−9.39508e10			−0.330833
$731$	2.86878e11	−	5.05843e10i	1.00468	−	0.177152i
$732$	6.39079e10	−	1.33715e11i	0.222592	−	0.465733i
$733$	2.34914e11	−	8.55016e10i	0.813753	−	0.296182i	0.0985795	−	0.995129i	$-0.468570\pi$
$733$	2.34914e11	−	8.55016e10i	0.813753	−	0.296182i	0.715173	+	0.698947i	$0.246348\pi$
$734$	2.47882e11	−	2.95415e11i	0.854007	−	1.01777i
$735$	−2.84837e10	+	1.02397e11i	−0.0975994	+	0.350862i
$736$	7.96834e10	+	2.90024e10i	0.271554	+	0.0988377i
$737$	−4.29672e11	+	2.48071e11i	−1.45635	+	0.840827i
$738$	−2.60736e11	−	3.23018e11i	−0.878972	−	1.08893i
$739$	−2.59650e11	+	4.49726e11i	−0.870582	+	1.50789i	−0.00918707	+	0.999958i	$0.502924\pi$
$739$	−2.59650e11	+	4.49726e11i	−0.870582	+	1.50789i	−0.861395	+	0.507935i	$0.830409\pi$
$740$	3.50390e10	+	4.17579e10i	0.116849	+	0.139255i
$741$	−2.35927e8	+	2.43020e9i	−0.000782538	+	0.00806063i
$742$	4.36261e10	−	2.47416e11i	0.143923	−	0.816228i
$743$	−1.13404e11	−	1.99962e10i	−0.372112	−	0.0656133i	−0.0155348	−	0.999879i	$-0.504945\pi$
$743$	−1.13404e11	−	1.99962e10i	−0.372112	−	0.0656133i	−0.356577	+	0.934266i	$0.616056\pi$
$744$	2.08401e10	+	4.58248e10i	0.0680157	+	0.149558i
$745$	3.64966e11	−	3.06243e11i	1.18475	−	0.994124i
$746$	3.72504e10	+	2.15065e10i	0.120275	+	0.0694409i
$747$	−2.25127e10	−	1.96322e10i	−0.0723012	−	0.0630501i
$748$	1.06029e11	+	1.83648e11i	0.338703	+	0.586652i
$749$	−5.60173e10	+	1.53906e11i	−0.177990	+	0.489023i
$750$	1.55322e11	−	1.52395e11i	0.490893	−	0.481642i
$751$	−2.06886e11	−	1.73598e11i	−0.650387	−	0.545740i	0.256801	−	0.966464i	$-0.417331\pi$
$751$	−2.06886e11	−	1.73598e11i	−0.650387	−	0.545740i	−0.907188	+	0.420725i	$0.861776\pi$
$752$	1.77456e10	+	4.87557e10i	0.0554907	+	0.152459i
$753$	1.02250e10	+	1.31238e11i	0.0318041	+	0.408207i
$754$	6.07478e10	+	3.44518e11i	0.187951	+	1.06592i
$755$		−	5.02080e11i		−	1.54520i
$756$	−9.99212e10	+	2.37402e10i	−0.305893	+	0.0726769i
$757$	−3.18441e11			−0.969719			−0.484859	−	0.874592i	$-0.661129\pi$
$757$	−3.18441e11			−0.969719			−0.484859	+	0.874592i	$0.661129\pi$
$758$	−3.51593e11	+	6.19953e10i	−1.06503	+	0.187794i
$759$	1.61489e11	+	2.35364e11i	0.486606	+	0.709208i
$760$	−4.53627e9	+	1.65107e9i	−0.0135971	+	0.00494892i
$761$	2.11330e11	−	2.51853e11i	0.630118	−	0.750946i	−0.352656	−	0.935753i	$-0.614722\pi$
$761$	2.11330e11	−	2.51853e11i	0.630118	−	0.750946i	0.982775	+	0.184807i	$0.0591660\pi$
$762$	−2.60613e11	+	6.71809e10i	−0.772995	+	0.199263i
$763$	5.05416e10	+	1.83956e10i	0.149125	+	0.0542771i
$764$	6.19778e9	−	3.57829e9i	0.0181913	−	0.0105027i
$765$	−6.81015e11	−	4.10652e11i	−1.98843	−	1.19903i
$766$	6.01628e10	−	1.04205e11i	0.174748	−	0.302673i
$767$	−1.23412e11	−	1.47076e11i	−0.356594	−	0.424972i
$768$	2.19583e11	+	1.56887e11i	0.631180	+	0.450964i
$769$	5.37175e10	−	3.04647e11i	0.153607	−	0.871148i	−0.806442	−	0.591314i	$-0.798609\pi$
$769$	5.37175e10	−	3.04647e11i	0.153607	−	0.871148i	0.960048	−	0.279834i	$-0.0902794\pi$
$770$	8.40138e11	+	1.48139e11i	2.38994	+	0.421412i
$771$	2.70098e10	−	3.78035e10i	0.0764369	−	0.106983i
$772$	−1.40930e11	+	1.18254e11i	−0.396765	+	0.332925i
$773$	4.97453e11	+	2.87205e11i	1.39327	+	0.804403i	0.993675	−	0.112291i	$-0.0358189\pi$
$773$	4.97453e11	+	2.87205e11i	1.39327	+	0.804403i	0.399591	+	0.916694i	$0.369152\pi$
$774$	2.11527e11	+	4.02450e9i	0.589388	+	0.0112137i
$775$	−4.12589e10	−	7.14625e10i	−0.114370	−	0.198094i
$776$	−2.36803e10	+	6.50612e10i	−0.0653042	+	0.179422i
$777$	−4.08118e10	−	1.58320e11i	−0.111970	−	0.434363i
$778$	6.18638e10	+	5.19099e10i	0.168857	+	0.141688i
$779$	−1.74961e9	−	4.80703e9i	−0.00475108	−	0.0130535i
$780$	−1.32209e11	+	9.07119e10i	−0.357176	+	0.245067i
$781$	−5.10524e10	−	2.89533e11i	−0.137218	−	0.778204i
$782$		−	2.44515e11i		−	0.653849i
$783$	4.57774e11	−	1.97765e11i	1.21788	−	0.526142i
$784$	−5.52138e10			−0.146145
$785$	4.50726e11	−	7.94751e10i	1.18695	−	0.209292i
$786$	−4.59872e11	+	3.58294e10i	−1.20489	+	0.0938749i
$787$	4.88907e11	−	1.77948e11i	1.27446	−	0.463867i	0.385867	−	0.922555i	$-0.373902\pi$
$787$	4.88907e11	−	1.77948e11i	1.27446	−	0.463867i	0.888598	+	0.458687i	$0.151680\pi$
$788$	−1.99732e10	+	2.38032e10i	−0.0518017	+	0.0617348i
$789$	3.98769e11	+	4.06428e11i	1.02900	+	1.04876i
$790$	−2.02753e11	−	7.37962e10i	−0.520547	−	0.189463i
$791$	−2.59008e11	+	1.49538e11i	−0.661618	+	0.381985i
$792$	2.25958e11	+	6.59594e11i	0.574285	+	1.67639i
$793$	−3.46976e11	+	6.00979e11i	−0.877417	+	1.51973i
$794$	−2.78904e10	−	3.32384e10i	−0.0701733	−	0.0836293i
$795$	−5.08926e11	+	2.31449e11i	−1.27405	+	0.579410i
$796$	−1.22809e10	+	6.96484e10i	−0.0305899	+	0.173484i
$797$	−2.25157e11	−	3.97012e10i	−0.558023	−	0.0983945i	−0.112478	−	0.993654i	$-0.535879\pi$
$797$	−2.25157e11	−	3.97012e10i	−0.558023	−	0.0983945i	−0.445545	+	0.895260i	$0.646990\pi$
$798$	3.18333e9	+	3.09042e8i	0.00785000	+	0.000762090i
$799$	−1.16650e11	+	9.78811e10i	−0.286219	+	0.240166i
$800$	−2.94034e11	−	1.69760e11i	−0.717856	−	0.414454i
$801$	2.73270e11	+	1.05391e11i	0.663838	+	0.256020i
$802$	2.64464e11	+	4.58065e11i	0.639248	+	1.10721i
$803$	−5.71912e10	+	1.57132e11i	−0.137552	+	0.377921i
$804$	−1.17678e11	−	3.27345e10i	−0.281625	−	0.0783397i
$805$	2.98184e11	+	2.50206e11i	0.710069	+	0.595819i
$806$	−1.78086e10	−	4.89287e10i	−0.0421978	−	0.115937i
$807$	6.21493e11	+	2.97036e11i	1.46535	+	0.700350i
$808$	−1.34960e11	−	7.65393e11i	−0.316634	−	1.79572i
$809$			2.80231e11i			0.654218i	0.944987	+	0.327109i	$0.106074\pi$
$809$			2.80231e11i			0.654218i	−0.944987	+	0.327109i	$0.893926\pi$
$810$	−4.27998e11	−	3.87812e11i	−0.994264	−	0.900910i
$811$	−6.94464e11			−1.60534			−0.802668	−	0.596426i	$-0.796587\pi$
$811$	−6.94464e11			−1.60534			−0.802668	+	0.596426i	$0.796587\pi$
$812$	−1.78580e11	+	3.14885e10i	−0.410780	+	0.0724316i
$813$	1.28013e11	−	2.67843e11i	0.293015	−	0.613080i
$814$	−2.30391e11	+	8.38555e10i	−0.524769	+	0.191000i
$815$	2.90455e11	−	3.46151e11i	0.658338	−	0.784577i
$816$	1.10715e11	−	3.98011e11i	0.249716	−	0.897707i
$817$	2.44990e9	+	8.91690e8i	0.00549870	+	0.00200136i
$818$	−4.92774e11	+	2.84503e11i	−1.10061	+	0.635440i
$819$	4.75097e11	−	7.44833e10i	1.05596	−	0.165548i
$820$	1.67963e11	−	2.90921e11i	0.371500	−	0.643458i
$821$	9.00287e10	+	1.07292e11i	0.198157	+	0.236154i	0.855968	−	0.517029i	$-0.172962\pi$
$821$	9.00287e10	+	1.07292e11i	0.198157	+	0.236154i	−0.657811	+	0.753183i	$0.728518\pi$
$822$	3.93595e10	−	4.05428e11i	0.0862110	−	0.888027i
$823$	1.32353e11	−	7.50609e11i	0.288492	−	1.63612i	−0.404048	−	0.914738i	$-0.632397\pi$
$823$	1.32353e11	−	7.50609e11i	0.288492	−	1.63612i	0.692540	−	0.721379i	$-0.256492\pi$
$824$	−3.45021e11	−	6.08365e10i	−0.748405	−	0.131964i
$825$	−4.73124e11	−	1.04034e12i	−1.02131	−	2.24574i
$826$	−1.92656e11	+	1.61657e11i	−0.413868	+	0.347276i
$827$	1.73429e11	+	1.00129e11i	0.370765	+	0.214061i	0.673793	−	0.738921i	$-0.264664\pi$
$827$	1.73429e11	+	1.00129e11i	0.370765	+	0.214061i	−0.303028	+	0.952982i	$0.597997\pi$
$828$	−1.35169e10	+	6.89603e10i	−0.0287579	+	0.146716i
$829$	3.02214e11	+	5.23449e11i	0.639876	+	1.10830i	0.985460	+	0.169910i	$0.0543476\pi$
$829$	3.02214e11	+	5.23449e11i	0.639876	+	1.10830i	−0.345584	+	0.938388i	$0.612319\pi$
$830$	−2.08922e10	+	5.74008e10i	−0.0440222	+	0.120950i
$831$	−4.51635e11	+	4.43124e11i	−0.947072	+	0.929225i
$832$	−3.89166e11	−	3.26549e11i	−0.812160	−	0.681483i
$833$	−5.54231e10	−	1.52274e11i	−0.115109	−	0.316260i
$834$	3.59684e10	+	4.61656e11i	0.0743459	+	0.954233i
$835$	4.32152e10	+	2.45085e11i	0.0888976	+	0.504164i
$836$			1.89790e9i			0.00388551i
$837$	−6.19883e10	+	4.08195e10i	−0.126301	+	0.0831699i
$838$	3.35928e11			0.681193
$839$	−8.98602e11	+	1.58448e11i	−1.81351	+	0.319771i	−0.974507	−	0.224358i	$-0.927972\pi$
$839$	−8.98602e11	+	1.58448e11i	−1.81351	+	0.319771i	−0.839002	+	0.544129i	$0.816860\pi$
$840$	5.37924e11	+	7.84003e11i	1.08045	+	1.57471i
$841$	3.57286e11	−	1.30041e11i	0.714219	−	0.259955i
$842$	−4.93835e11	+	5.88529e11i	−0.982502	+	1.17090i
$843$	−1.22798e11	+	3.16548e10i	−0.243153	+	0.0626801i
$844$	9.88087e10	+	3.59634e10i	0.194727	+	0.0708747i
$845$	−4.96842e10	+	2.86852e10i	−0.0974521	+	0.0562640i
$846$	−9.68114e10	+	5.34649e10i	−0.188993	+	0.104373i
$847$	4.73810e11	−	8.20663e11i	0.920599	−	1.59452i
$848$	−1.86690e11	−	2.22489e11i	−0.361026	−	0.430254i
$849$	−5.26348e11	−	3.76065e11i	−1.01308	−	0.723822i
$850$	−1.70004e11	+	9.64141e11i	−0.325674	+	1.84699i
$851$	−1.10170e11	−	1.94259e10i	−0.210060	−	0.0370393i
$852$	4.20776e10	−	5.88927e10i	0.0798532	−	0.111764i
$853$	4.59900e10	−	3.85902e10i	0.0868695	−	0.0728922i	−0.598319	−	0.801258i	$-0.704164\pi$
$853$	4.59900e10	−	3.85902e10i	0.0868695	−	0.0728922i	0.685188	+	0.728366i	$0.259720\pi$
$854$	7.87225e11	+	4.54505e11i	1.48002	+	0.854490i
$855$	−3.44078e9	−	6.23039e9i	−0.00643862	−	0.0116587i
$856$	1.36869e11	+	2.37064e11i	0.254923	+	0.441540i
$857$	−1.56719e11	+	4.30581e11i	−0.290535	+	0.798237i	0.705454	+	0.708756i	$0.250743\pi$
$857$	−1.56719e11	+	4.30581e11i	−0.290535	+	0.798237i	−0.995988	+	0.0894815i	$0.971479\pi$
$858$	−1.80014e11	−	6.98325e11i	−0.332168	−	1.28857i
$859$	2.76176e11	+	2.31740e11i	0.507241	+	0.425625i	0.860157	−	0.510030i	$-0.170366\pi$
$859$	2.76176e11	+	2.31740e11i	0.507241	+	0.425625i	−0.352916	+	0.935655i	$0.614810\pi$
$860$	5.85556e10	+	1.60880e11i	0.107047	+	0.294109i
$861$	−8.30796e11	+	5.70031e11i	−1.51176	+	1.03726i
$862$	1.51996e11	+	8.62015e11i	0.275299	+	1.56130i
$863$		−	8.65609e11i		−	1.56055i	−0.625435	−	0.780276i	$-0.715078\pi$
$863$		−	8.65609e11i		−	1.56055i	0.625435	−	0.780276i	$-0.284922\pi$
$864$	−1.36905e11	+	2.72977e11i	−0.245677	+	0.489860i
$865$	1.14414e12			2.04368
$866$	3.54280e11	−	6.24692e10i	0.629906	−	0.111069i
$867$	6.45477e11	−	5.02903e10i	1.14236	−	0.0890036i
$868$	2.53621e10	−	9.23105e9i	0.0446793	−	0.0162619i
$869$	−2.46846e11	+	2.94180e11i	−0.432860	+	0.515863i
$870$	−7.14192e11	−	7.27910e11i	−1.24663	−	1.27058i
$871$	5.37450e11	+	1.95616e11i	0.933825	+	0.339885i
$872$	7.78497e10	−	4.49465e10i	0.134645	−	0.0777375i
$873$	−1.00174e11	−	1.96352e10i	−0.172464	−	0.0338047i
$874$	1.09419e9	−	1.89519e9i	0.00187519	−	0.00324793i
$875$	−3.39482e11	−	4.04579e11i	−0.579142	−	0.690195i
$876$	−3.74739e10	+	1.70423e10i	−0.0636374	+	0.0289409i
$877$	−5.54872e10	+	3.14683e11i	−0.0937981	+	0.531956i	0.901311	+	0.433173i	$0.142606\pi$
$877$	−5.54872e10	+	3.14683e11i	−0.0937981	+	0.531956i	−0.995109	+	0.0987829i	$0.968505\pi$
$878$	−7.50743e11	−	1.32376e11i	−1.26332	−	0.222757i
$879$	8.59498e11	+	8.34414e10i	1.43976	+	0.139774i
$880$	7.55496e11	−	6.33936e11i	1.25980	−	1.05710i
$881$	−7.29538e11	−	4.21199e11i	−1.21100	−	0.699172i	−0.248024	−	0.968754i	$-0.579781\pi$
$881$	−7.29538e11	−	4.21199e11i	−1.21100	−	0.699172i	−0.962977	+	0.269582i	$0.913114\pi$
$882$	−1.82281e10	−	1.16269e11i	−0.0301209	−	0.192128i
$883$	−5.44619e11	−	9.43307e11i	−0.895880	−	1.55171i	−0.832712	−	0.553706i	$-0.813213\pi$
$883$	−5.44619e11	−	9.43307e11i	−0.895880	−	1.55171i	−0.0631678	−	0.998003i	$-0.520120\pi$
$884$	8.36091e10	−	2.29714e11i	0.136913	−	0.376165i
$885$	5.39193e11	+	1.49988e11i	0.878965	+	0.244502i
$886$	3.43370e11	+	2.88121e11i	0.557221	+	0.467564i
$887$	1.25823e11	+	3.45697e11i	0.203267	+	0.558471i	0.998879	−	0.0473352i	$-0.0150729\pi$
$887$	1.25823e11	+	3.45697e11i	0.203267	+	0.558471i	−0.795612	+	0.605806i	$0.792851\pi$
$888$	−2.46545e11	−	1.17834e11i	−0.396501	−	0.189503i
$889$	1.13431e11	+	6.43299e11i	0.181604	+	1.02992i
$890$		−	5.98954e11i		−	0.954626i
$891$	−9.09149e11	+	4.79747e11i	−1.44253	+	0.761204i
$892$	−7.16881e10			−0.113237
$893$	−1.34215e9	+	2.36657e8i	−0.00211054	+	0.000372145i
$894$	−2.27491e11	+	4.75983e11i	−0.356135	+	0.745146i
$895$	−7.02849e11	+	2.55816e11i	−1.09539	+	0.398690i
$896$	−1.75980e11	+	2.09725e11i	−0.273043	+	0.325400i
$897$	8.81831e10	−	3.17011e11i	0.136212	−	0.489671i
$898$	−9.22825e11	−	3.35881e11i	−1.41910	−	0.516511i
$899$	−1.13490e11	+	6.55237e10i	−0.173748	+	0.100314i
$900$	1.01245e11	−	2.62518e11i	0.154313	−	0.400119i
$901$	4.26202e11	−	7.38204e11i	0.646721	−	1.12015i
$902$	9.71197e11	+	1.15743e12i	1.46717	+	1.74851i
$903$	4.96179e10	−	5.11095e11i	0.0746255	−	0.768689i
$904$	−8.67993e10	+	4.92263e11i	−0.129970	+	0.737096i
$905$	−2.23603e11	−	3.94272e10i	−0.333337	−	0.0587762i
$906$	2.30154e11	+	5.06079e11i	0.341590	+	0.751114i
$907$	−1.47819e11	+	1.24035e11i	−0.218425	+	0.183280i	−0.745434	−	0.666579i	$-0.767758\pi$
$907$	−1.47819e11	+	1.24035e11i	−0.218425	+	0.183280i	0.527009	+	0.849860i	$0.323313\pi$
$908$	−4.01481e10	−	2.31795e10i	−0.0590638	−	0.0341005i
$909$	1.08403e12	−	3.71360e11i	1.58777	−	0.543925i
$910$	−4.91717e11	−	8.51678e11i	−0.717050	−	1.24197i
$911$	3.85785e10	−	1.05994e11i	0.0560109	−	0.153889i	−0.908532	−	0.417816i	$-0.862796\pi$
$911$	3.85785e10	−	1.05994e11i	0.0560109	−	0.153889i	0.964543	+	0.263927i	$0.0850179\pi$
$912$	2.63921e9	−	2.58947e9i	0.00381500	−	0.00374310i
$913$	8.32844e10	+	6.98839e10i	0.119862	+	0.100576i
$914$	−2.46348e11	−	6.76834e11i	−0.352991	−	0.969835i
$915$	−1.57130e11	−	2.01676e12i	−0.224168	−	2.87720i
$916$	7.71387e9	+	4.37475e10i	0.0109570	+	0.0621401i
$917$			1.11955e12i			1.58332i
$918$	8.74684e11	+	1.01745e11i	1.23163	+	0.143266i
$919$	3.60073e11			0.504811			0.252405	−	0.967622i	$-0.418778\pi$
$919$	3.60073e11			0.504811			0.252405	+	0.967622i	$0.418778\pi$
$920$	6.40686e11	−	1.12970e11i	0.894322	−	0.157693i
$921$	1.30625e11	+	1.90381e11i	0.181546	+	0.264597i
$922$	−3.89946e11	+	1.41929e11i	−0.539610	+	0.196402i
$923$	−2.17851e11	+	2.59625e11i	−0.300160	+	0.357717i
$924$	3.61975e11	−	9.33100e10i	0.496582	−	0.128009i
$925$	4.20902e11	+	1.53196e11i	0.574929	+	0.209257i
$926$	3.78090e11	−	2.18290e11i	0.514223	−	0.296887i
$927$	9.82578e9	−	5.16441e11i	0.0133060	−	0.699362i
$928$	−2.69598e11	+	4.66958e11i	−0.363518	+	0.629631i
$929$	−4.96330e10	−	5.91503e10i	−0.0666358	−	0.0794135i	0.731697	−	0.681630i	$-0.238729\pi$
$929$	−4.96330e10	−	5.91503e10i	−0.0666358	−	0.0794135i	−0.798333	+	0.602217i	$0.794284\pi$
$930$	1.23498e11	+	8.82369e10i	0.165093	+	0.117956i
$931$	2.51841e8	−	1.42826e9i	0.000335218	−	0.00190112i
$932$	2.51620e11	+	4.43673e10i	0.333489	+	0.0588030i
$933$	5.37737e11	−	7.52629e11i	0.709649	−	0.993240i
$934$	5.38974e11	−	4.52253e11i	0.708240	−	0.594284i
$935$	2.50669e12	+	1.44724e12i	3.27985	+	1.89362i
$936$	4.15040e11	−	6.88293e11i	0.540738	−	0.896747i
$937$	−5.46345e10	−	9.46298e10i	−0.0708776	−	0.122764i	0.828409	−	0.560124i	$-0.189247\pi$
$937$	−5.46345e10	−	9.46298e10i	−0.0708776	−	0.122764i	−0.899286	+	0.437361i	$0.855913\pi$
$938$	2.56238e11	−	7.04008e11i	0.331003	−	0.909424i
$939$	−9.11028e10	−	3.53413e11i	−0.117184	−	0.454590i
$940$	−6.85577e10	−	5.75267e10i	−0.0878102	−	0.0736815i
$941$	−1.51783e11	−	4.17019e11i	−0.193581	−	0.531860i	0.804488	−	0.593969i	$-0.202440\pi$
$941$	−1.51783e11	−	4.17019e11i	−0.193581	−	0.531860i	−0.998069	+	0.0621085i	$0.980218\pi$
$942$	−4.17885e11	+	2.86721e11i	−0.530705	+	0.364130i
$943$	1.19713e11	+	6.78926e11i	0.151389	+	0.858569i
$944$			2.90741e11i			0.366116i
$945$	−1.01912e12	+	9.62557e11i	−1.27790	+	1.20698i
$946$	−7.70037e11			−0.961495
$947$	5.80418e11	−	1.02343e11i	0.721673	−	0.127250i	0.199265	−	0.979946i	$-0.436145\pi$
$947$	5.80418e11	−	1.02343e11i	0.721673	−	0.127250i	0.522409	+	0.852695i	$0.325034\pi$
$948$	−9.42580e10	+	7.34380e9i	−0.116704	+	0.00909259i
$949$	1.81138e11	−	6.59288e10i	0.223329	−	0.0812850i
$950$	−5.63214e9	+	6.71213e9i	−0.00691479	+	0.00824073i
$951$	−3.03827e11	−	3.09663e11i	−0.371454	−	0.378588i
$952$	−1.36221e12	−	4.95805e11i	−1.65843	−	0.603619i
$953$	1.23865e10	−	7.15133e9i	0.0150168	−	0.00866992i	−0.492473	−	0.870328i	$-0.663907\pi$
$953$	1.23865e10	−	7.15133e9i	0.0150168	−	0.00866992i	0.507490	+	0.861658i	$0.330574\pi$
$954$	4.06884e11	−	4.66585e11i	0.491221	−	0.563297i
$955$	4.88415e10	−	8.45960e10i	0.0587186	−	0.101704i
$956$	1.46691e11	+	1.74819e11i	0.175619	+	0.209294i
$957$	−1.65217e12	+	7.51373e11i	−1.96974	+	0.895794i
$958$	−5.34486e10	+	3.03122e11i	−0.0634562	+	0.359878i
$959$	−9.73635e11	−	1.71678e11i	−1.15112	−	0.202974i
$960$	1.47396e12	+	1.43094e11i	1.73540	+	0.168475i
$961$	−6.38411e11	+	5.35690e11i	−0.748526	+	0.628088i
$962$	2.44769e11	+	1.41317e11i	0.285796	+	0.165004i
$963$	−3.14046e11	+	2.53494e11i	−0.365164	+	0.294756i
$964$	−1.30660e11	−	2.26310e11i	−0.151299	−	0.262057i
$965$	−8.58842e11	+	2.35965e12i	−0.990385	+	2.72106i
$966$	−4.15254e11	−	1.15511e11i	−0.476876	−	0.132653i
$967$	−1.09840e11	−	9.21663e10i	−0.125618	−	0.105406i	0.577814	−	0.816168i	$-0.303906\pi$
$967$	−1.09840e11	−	9.21663e10i	−0.125618	−	0.105406i	−0.703433	+	0.710762i	$0.748350\pi$
$968$	−5.41688e11	−	1.48828e12i	−0.616947	−	1.69505i
$969$	9.79070e9	+	4.67936e9i	0.0111050	+	0.00530752i
$970$	3.62495e10	+	2.05581e11i	0.0409464	+	0.232218i
$971$		−	1.68081e12i		−	1.89078i	−0.325944	−	0.945389i	$-0.605682\pi$
$971$		−	1.68081e12i		−	1.89078i	0.325944	−	0.945389i	$-0.394318\pi$
$972$	−2.41062e11	−	7.70483e10i	−0.270062	−	0.0863173i
$973$	1.12390e12			1.25394
$974$	−9.17194e11	+	1.61726e11i	−1.01912	+	0.179698i
$975$	−5.68122e11	+	1.18869e12i	−0.628670	+	1.31538i
$976$	9.87491e11	−	3.59417e11i	1.08826	−	0.396095i
$977$	3.78131e11	−	4.50639e11i	0.415015	−	0.494596i	−0.517522	−	0.855670i	$-0.673145\pi$
$977$	3.78131e11	−	4.50639e11i	0.415015	−	0.494596i	0.932537	+	0.361074i	$0.117590\pi$
$978$	−1.34093e11	+	4.82054e11i	−0.146572	+	0.526915i
$979$	−1.00174e12	−	3.64605e11i	−1.09050	−	0.396909i
$980$	8.24785e10	−	4.76190e10i	0.0894204	−	0.0516269i
$981$	8.32453e10	+	1.03130e11i	0.0898843	+	0.111355i
$982$	4.94358e11	−	8.56254e11i	0.531614	−	0.920782i
$983$	−5.44055e11	−	6.48380e11i	−0.582678	−	0.694409i	0.391503	−	0.920177i	$-0.371955\pi$
$983$	−5.44055e11	−	6.48380e11i	−0.582678	−	0.694409i	−0.974181	+	0.225768i	$0.927511\pi$
$984$	−1.62716e11	+	1.67607e12i	−0.173560	+	1.78778i
$985$	−7.36486e10	+	4.17682e11i	−0.0782384	+	0.443712i
$986$	1.53116e12	+	2.69985e11i	1.62000	+	0.285649i
$987$	1.11123e11	+	2.44344e11i	0.117094	+	0.257474i
$988$	1.67600e9	−	1.40633e9i	0.00175892	−	0.00147591i
$989$	−3.04280e11	−	1.75676e11i	−0.318045	−	0.183623i
$990$	1.58436e12	+	1.38164e12i	1.64935	+	1.43831i
$991$	4.81519e11	+	8.34015e11i	0.499251	+	0.864728i	1.00000		0.000864758i	$-0.000275261\pi$
$991$	4.81519e11	+	8.34015e11i	0.499251	+	0.864728i	−0.500749	+	0.865593i	$0.666942\pi$
$992$	2.74484e10	−	7.54138e10i	0.0283446	−	0.0778761i
$993$	−2.40544e11	+	2.36011e11i	−0.247399	+	0.242736i
$994$	3.40083e11	+	2.85364e11i	0.348369	+	0.292317i
$995$	3.30160e11	+	9.07108e11i	0.336847	+	0.925480i
$996$	2.07908e9	+	2.66851e10i	0.00211268	+	0.0271163i
$997$	−1.22891e11	−	6.96951e11i	−0.124377	−	0.705378i	−0.981676	−	0.190559i	$-0.938970\pi$
$997$	−1.22891e11	−	6.96951e11i	−0.124377	−	0.705378i	0.857299	−	0.514819i	$-0.172141\pi$
$998$		−	5.19985e11i		−	0.524166i
$999$	1.15334e11	−	3.86019e11i	0.115796	−	0.387567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.f.a.14.15	yes	138
3.2	odd	2		81.9.f.a.71.9		138
27.2	odd	18	inner	27.9.f.a.2.15	✓	138
27.25	even	9		81.9.f.a.8.9		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.15	✓	138	27.2	odd	18	inner
27.9.f.a.14.15	yes	138	1.1	even	1	trivial
81.9.f.a.8.9		138	27.25	even	9
81.9.f.a.71.9		138	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(13.3375 - 2.35175i) q^{2} +(34.9288 - 73.0820i) q^{3} +(-68.2042 + 24.8243i) q^{4} +(-636.805 + 758.914i) q^{5} +(293.990 - 1056.87i) q^{6} +(-2502.00 - 910.653i) q^{7} +(-3853.85 + 2225.02i) q^{8} +(-4120.96 - 5105.33i) q^{9} +(-6708.58 + 11619.6i) q^{10} +(15349.9 + 18293.3i) q^{11} +(-568.081 + 5851.58i) q^{12} +(4780.28 - 27110.3i) q^{13} +(-35511.9 - 6261.71i) q^{14} +(33220.2 + 73046.9i) q^{15} +(-31934.2 + 26796.0i) q^{16} +(-105956. - 61173.5i) q^{17} +(-66969.6 - 58400.7i) q^{18} +(-547.495 - 948.289i) q^{19} +(24593.2 - 67569.4i) q^{20} +(-153944. + 151043. i) q^{21} +(247750. + 207887. i) q^{22} +(50471.0 + 138668. i) q^{23} +(27998.7 + 359365. i) q^{24} +(-102599. - 581870. i) q^{25} -372825. i q^{26} +(-517048. + 122845. i) q^{27} +193253. q^{28} +(-924074. + 162939. i) q^{29} +(614861. + 896135. i) q^{30} +(131238. - 47766.6i) q^{31} +(369368. - 440196. i) q^{32} +(1.87306e6 - 482838. i) q^{33} +(-1.55704e6 - 566717. i) q^{34} +(2.28439e6 - 1.31889e6i) q^{35} +(407803. + 245905. i) q^{36} +(-379045. + 656525. i) q^{37} +(-9532.34 - 11360.2i) q^{38} +(-1.81431e6 - 1.29628e6i) q^{39} +(765550. - 4.34165e6i) q^{40} +(4.60079e6 + 811243. i) q^{41} +(-1.69801e6 + 2.37657e6i) q^{42} +(-1.82392e6 + 1.53045e6i) q^{43} +(-1.50104e6 - 866629. i) q^{44} +(6.49876e6 + 123645. i) q^{45} +(999268. + 1.73078e6i) q^{46} +(425686. - 1.16956e6i) q^{47} +(842880. + 3.26976e6i) q^{48} +(1.01461e6 + 851361. i) q^{49} +(-2.73683e6 - 7.51938e6i) q^{50} +(-8.17158e6 + 5.60673e6i) q^{51} +(346960. + 1.96771e6i) q^{52} +6.96711e6i q^{53} +(-6.60721e6 + 2.85441e6i) q^{54} -2.36579e7 q^{55} +(1.16686e7 - 2.05748e6i) q^{56} +(-88426.2 + 6889.44i) q^{57} +(-1.19416e7 + 4.34639e6i) q^{58} +(4.48304e6 - 5.34268e6i) q^{59} +(-4.07909e6 - 4.15744e6i) q^{60} +(-2.36882e7 - 8.62179e6i) q^{61} +(1.63804e6 - 945725. i) q^{62} +(5.66145e6 + 1.65263e7i) q^{63} +(9.22715e6 - 1.59819e7i) q^{64} +(1.75303e7 + 2.08918e7i) q^{65} +(2.38464e7 - 1.08448e7i) q^{66} +(-3.60777e6 + 2.04607e7i) q^{67} +(8.74520e6 + 1.54201e6i) q^{68} +(1.18970e7 + 1.15498e6i) q^{69} +(2.73663e7 - 2.29630e7i) q^{70} +(-1.06620e7 - 6.15572e6i) q^{71} +(2.72411e7 + 1.05060e7i) q^{72} +(3.50114e6 + 6.06416e6i) q^{73} +(-3.51151e6 + 9.64780e6i) q^{74} +(-4.61079e7 - 1.28258e7i) q^{75} +(60882.1 + 51086.1i) q^{76} +(-2.17466e7 - 5.97482e7i) q^{77} +(-2.72468e7 - 1.30223e7i) q^{78} +(2.79249e6 + 1.58370e7i) q^{79} -4.12991e7i q^{80} +(-9.08211e6 + 4.20777e7i) q^{81} +6.32706e7 q^{82} +(4.48356e6 - 790573. i) q^{83} +(6.75010e6 - 1.41233e7i) q^{84} +(1.13898e8 - 4.14556e7i) q^{85} +(-2.07272e7 + 2.47018e7i) q^{86} +(-2.03689e7 + 7.32244e7i) q^{87} +(-9.98592e7 - 3.63458e7i) q^{88} +(-3.86601e7 + 2.23204e7i) q^{89} +(8.69677e7 - 1.36344e7i) q^{90} +(-3.66484e7 + 6.34768e7i) q^{91} +(-6.88467e6 - 8.20483e6i) q^{92} +(1.09309e6 - 1.12595e7i) q^{93} +(2.92705e6 - 1.66001e7i) q^{94} +(1.06832e6 + 188373. i) q^{95} +(-1.92688e7 - 4.23697e7i) q^{96} +(1.19186e7 - 1.00009e7i) q^{97} +(1.55345e7 + 8.96887e6i) q^{98} +(3.01370e7 - 1.53752e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) \) 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

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