LMFDB - Embedded newform 27.9.f.a.2.15

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			2.15
Character	$\chi$	$=$	27.2
Dual form			27.9.f.a.14.15

$q$-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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	13.3375	+	2.35175i	0.833591	+	0.146985i	0.574125	−	0.818768i	$-0.305342\pi$
$2$	13.3375	+	2.35175i	0.833591	+	0.146985i	0.259466	+	0.965752i	$0.416453\pi$
$3$	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	−0.976579	−	0.215158i	$-0.930973\pi$
$5$	−636.805	−	758.914i	−1.01889	−	1.21426i	−0.0423083	−	0.999105i	$-0.513471\pi$
$6$	293.990	+	1056.87i	0.226844	+	0.815488i
$7$	−2502.00	+	910.653i	−1.04207	+	0.379281i	−0.805663	−	0.592375i	$-0.798191\pi$
$7$	−2502.00	+	910.653i	−1.04207	+	0.379281i	−0.236402	+	0.971655i	$0.575968\pi$
$8$	−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	0.0808814	−	0.996724i	$-0.474227\pi$
$11$	15349.9	−	18293.3i	1.04842	−	1.24946i	0.967536	−	0.252732i	$-0.0813290\pi$
$12$	−568.081	−	5851.58i	−0.0273959	−	0.282194i
$13$	4780.28	+	27110.3i	0.167371	+	0.949208i	0.946586	+	0.322451i	$0.104507\pi$
$13$	4780.28	+	27110.3i	0.167371	+	0.949208i	−0.779215	+	0.626757i	$0.784382\pi$
$14$	−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	−0.974725	−	0.223409i	$-0.928281\pi$
$17$	−105956.	+	61173.5i	−1.26861	+	0.732432i	−0.293885	+	0.955841i	$0.594948\pi$
$18$	−66969.6	+	58400.7i	−0.637952	+	0.556324i
$19$	−547.495	+	948.289i	−0.00420113	+	0.00727656i	−0.868118	−	0.496357i	$-0.834671\pi$
$19$	−547.495	+	948.289i	−0.00420113	+	0.00727656i	0.863917	+	0.503634i	$0.168004\pi$
$20$	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	−0.816264	−	0.577680i	$-0.803958\pi$
$23$	50471.0	−	138668.i	0.180356	−	0.495524i	0.996619	+	0.0821558i	$0.0261805\pi$
$24$	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	−0.523313	−	0.852140i	$-0.675304\pi$
$29$	−924074.	−	162939.i	−1.30652	−	0.230374i	−0.783203	+	0.621766i	$0.786415\pi$
$30$	614861.	−	896135.i	0.759088	−	1.10634i
$31$	131238.	+	47766.6i	0.142106	+	0.0517223i	0.412094	−	0.911141i	$-0.364798\pi$
$31$	131238.	+	47766.6i	0.142106	+	0.0517223i	−0.269988	+	0.962864i	$0.587020\pi$
$32$	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	0.747005	−	0.664819i	$-0.231491\pi$
$37$	−379045.	−	656525.i	−0.202248	−	0.350303i	−0.949252	+	0.314515i	$0.898158\pi$
$38$	−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	0.716361	−	0.697730i	$-0.245806\pi$
$41$	4.60079e6	−	811243.i	1.62816	−	0.287088i	0.911797	+	0.410641i	$0.134695\pi$
$42$	−1.69801e6	−	2.37657e6i	−0.545685	−	0.763754i
$43$	−1.82392e6	−	1.53045e6i	−0.533498	−	0.447658i	0.335810	−	0.941930i	$-0.390990\pi$
$43$	−1.82392e6	−	1.53045e6i	−0.533498	−	0.447658i	−0.869307	+	0.494272i	$0.835435\pi$
$44$	−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	0.975638	−	0.219387i	$-0.0704058\pi$
$47$	425686.	+	1.16956e6i	0.0872365	+	0.239680i	−0.888401	+	0.459068i	$0.848184\pi$
$48$	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	$-0.854451\pi$
$53$		−	6.96711e6i		−	0.882977i	0.897267	−	0.441489i	$-0.145549\pi$
$54$	−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	0.918621	−	0.395139i	$-0.129304\pi$
$59$	4.48304e6	+	5.34268e6i	0.369968	+	0.440911i	−0.548653	+	0.836050i	$0.684859\pi$
$60$	−4.07909e6	+	4.15744e6i	−0.314745	+	0.320790i
$61$	−2.36882e7	+	8.62179e6i	−1.71085	+	0.622699i	−0.996986	−	0.0775852i	$-0.975279\pi$
$61$	−2.36882e7	+	8.62179e6i	−1.71085	+	0.622699i	−0.713865	+	0.700284i	$0.753057\pi$
$62$	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	−0.933382	−	0.358885i	$-0.883157\pi$
$67$	−3.60777e6	−	2.04607e7i	−0.179036	−	1.01536i	0.754346	−	0.656477i	$-0.227954\pi$
$68$	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	−0.694894	−	0.719112i	$-0.744549\pi$
$71$	−1.06620e7	+	6.15572e6i	−0.419571	+	0.242240i	0.275323	+	0.961352i	$0.411215\pi$
$72$	2.72411e7	−	1.05060e7i	1.01366	−	0.390937i
$73$	3.50114e6	−	6.06416e6i	0.123287	−	0.213540i	−0.797775	−	0.602956i	$-0.793990\pi$
$73$	3.50114e6	−	6.06416e6i	0.123287	−	0.213540i	0.921062	+	0.389415i	$0.127323\pi$
$74$	−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	−0.927748	−	0.373207i	$-0.878258\pi$
$79$	2.79249e6	−	1.58370e7i	0.0716941	−	0.406598i	0.999442	−	0.0333910i	$-0.0106306\pi$
$80$			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	0.220685	−	0.975345i	$-0.429171\pi$
$83$	4.48356e6	+	790573.i	0.0944737	+	0.0166583i	−0.126211	+	0.992003i	$0.540282\pi$
$84$	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	0.159204	−	0.987246i	$-0.449107\pi$
$89$	−3.86601e7	−	2.23204e7i	−0.616174	−	0.355748i	−0.775378	+	0.631497i	$0.782441\pi$
$90$	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	0.707616	−	0.706598i	$-0.249771\pi$
$97$	1.19186e7	+	1.00009e7i	0.134629	+	0.112967i	−0.572987	+	0.819565i	$0.694215\pi$
$98$	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	−0.798076	−	0.602557i	$-0.794149\pi$
$101$	−5.97338e7	−	1.64117e8i	−0.574030	−	1.57714i	0.224046	−	0.974579i	$-0.428073\pi$
$102$	−9.58024e7	−	9.39970e7i	−0.885066	−	0.868387i
$103$	6.03092e7	−	5.06054e7i	0.535839	−	0.449623i	−0.334273	−	0.942476i	$-0.608491\pi$
$103$	6.03092e7	−	5.06054e7i	0.535839	−	0.449623i	0.870112	+	0.492854i	$0.164046\pi$
$104$	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	$0.0753916\pi$
$107$			6.15134e7i			0.469283i	−0.972082	+	0.234641i	$0.924608\pi$
$108$	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	0.940578	−	0.339579i	$-0.110285\pi$
$113$	7.22019e7	+	8.60469e7i	0.442828	+	0.527742i	−0.497750	+	0.867321i	$0.665840\pi$
$114$	−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	−0.999470	−	0.0325610i	$-0.989634\pi$
$127$	−1.22668e8	+	2.12467e8i	−0.471536	+	0.816725i	0.527934	+	0.849286i	$0.322967\pi$
$128$	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	0.413867	+	0.910337i	$0.364178\pi$
$131$	−1.43812e8	+	3.95121e8i	−0.488327	+	1.34167i	−0.902194	+	0.431330i	$0.858045\pi$
$132$	−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	0.666593	−	0.745422i	$-0.267752\pi$
$137$	3.65675e8	+	6.44783e7i	1.03804	+	0.183034i	0.371444	+	0.928456i	$0.378863\pi$
$138$	1.61392e8	+	1.25743e7i	0.445006	+	0.0346712i
$139$	−3.96654e8	−	1.44370e8i	−1.06256	−	0.386739i	−0.249169	−	0.968460i	$-0.580158\pi$
$139$	−3.96654e8	−	1.44370e8i	−1.06256	−	0.386739i	−0.813389	+	0.581721i	$0.802380\pi$
$140$	−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	−0.632019	−	0.774953i	$-0.717773\pi$
$149$	−4.73599e8	+	8.35083e7i	−0.960873	+	0.169428i	−0.328854	+	0.944381i	$0.606662\pi$
$150$	−6.45125e8	+	6.26298e7i	−1.27432	+	0.123713i
$151$	−3.88229e8	−	3.25763e8i	−0.746758	−	0.626605i	0.187885	−	0.982191i	$-0.439837\pi$
$151$	−3.88229e8	−	3.25763e8i	−0.746758	−	0.626605i	−0.934643	+	0.355586i	$0.884281\pi$
$152$	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	−0.885759	−	0.464146i	$-0.846361\pi$
$157$	−3.53896e8	+	2.96954e8i	−0.582475	+	0.488755i	0.303284	+	0.952900i	$0.401917\pi$
$158$	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	0.859791	−	0.510647i	$-0.170594\pi$
$167$	1.61471e8	+	1.92434e8i	0.207601	+	0.247409i	−0.652190	+	0.758056i	$0.726150\pi$
$168$	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	0.171251	+	0.985227i	$0.445219\pi$
$173$	−7.42345e8	+	8.84693e8i	−0.828746	+	0.987661i	−0.999997	+	0.00243395i	$0.999225\pi$
$174$	−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	−0.146533	−	0.989206i	$-0.546811\pi$
$179$	6.53835e8	−	3.77492e8i	0.636878	−	0.367702i	0.783411	+	0.621504i	$0.213478\pi$
$180$	−4.46312e8	−	1.52894e8i	−0.425156	−	0.145647i
$181$	1.14593e8	−	1.98480e8i	0.106768	−	0.184928i	−0.807691	−	0.589606i	$-0.799283\pi$
$181$	1.14593e8	−	1.98480e8i	0.106768	−	0.184928i	0.914459	+	0.404678i	$0.132616\pi$
$182$	−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	0.137048	−	0.990564i	$-0.456239\pi$
$191$	−9.71028e7	−	1.71218e7i	−0.0729623	−	0.0128652i	−0.210010	+	0.977699i	$0.567350\pi$
$192$	−8.45696e8	+	1.23257e9i	−0.622313	+	0.906996i
$193$	2.38182e9	+	8.66911e8i	1.71664	+	0.624806i	0.997540	−	0.0700985i	$-0.0223314\pi$
$193$	2.38182e9	+	8.66911e8i	1.71664	+	0.624806i	0.719102	+	0.694905i	$0.244554\pi$
$194$	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	0.618006	−	0.786174i	$-0.287941\pi$
$197$	3.70754e8	+	2.14055e8i	0.246162	+	0.142122i	−0.371843	+	0.928295i	$0.621274\pi$
$198$	4.03642e7	+	2.12154e9i	0.0262625	+	1.38035i
$199$	4.87197e8	+	8.43850e8i	0.310665	+	0.538088i	0.978507	−	0.206216i	$-0.0661149\pi$
$199$	4.87197e8	+	8.43850e8i	0.310665	+	0.538088i	−0.667842	+	0.744303i	$0.732782\pi$
$200$	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	−0.878276	−	0.478154i	$-0.841306\pi$
$211$	−1.10978e9	+	9.31219e8i	−0.559897	+	0.469809i	0.318379	+	0.947964i	$0.396862\pi$
$212$	−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	−0.147477	−	0.989065i	$-0.547115\pi$
$223$	9.28127e8	−	3.37811e8i	0.375308	−	0.136601i	0.522785	+	0.852464i	$0.324893\pi$
$224$	−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	−0.683172	−	0.730257i	$-0.739400\pi$
$227$	4.10560e8	−	4.89286e8i	0.154623	−	0.184272i	0.837795	+	0.545985i	$0.183845\pi$
$228$	5.86001e6	+	2.66501e6i	0.00216850	+	0.000986187i
$229$	1.06279e8	+	6.02738e8i	0.0386460	+	0.219173i	0.998015	−	0.0629834i	$-0.0200615\pi$
$229$	1.06279e8	+	6.02738e8i	0.0386460	+	0.219173i	−0.959369	+	0.282156i	$0.908950\pi$
$230$	−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	−0.918233	−	0.396041i	$-0.870384\pi$
$233$	−3.04859e9	+	1.76010e9i	−1.03437	+	0.597192i	−0.116134	+	0.993234i	$0.537050\pi$
$234$	−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	0.658629	+	0.752468i	$0.271137\pi$
$239$	−1.07538e9	+	2.95458e9i	−0.329587	+	0.905533i	−0.988216	+	0.153065i	$0.951086\pi$
$240$	−3.01822e9	+	1.44253e9i	−0.909716	+	0.434789i
$241$	6.25199e8	−	3.54568e9i	0.185332	−	1.05107i	−0.740196	−	0.672391i	$-0.765267\pi$
$241$	6.25199e8	−	3.54568e9i	0.185332	−	1.05107i	0.925528	−	0.378679i	$-0.123622\pi$
$242$		−	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	0.312116	−	0.950044i	$-0.398962\pi$
$251$	−1.40741e9	−	8.12567e8i	−0.354589	−	0.204722i	−0.666705	+	0.745322i	$0.732296\pi$
$252$	−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	−0.108530	−	0.994093i	$-0.534614\pi$
$257$	5.64879e8	−	9.96034e7i	0.129486	−	0.0228319i	0.238016	+	0.971261i	$0.423503\pi$
$258$	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	−0.888809	−	0.458278i	$-0.848466\pi$
$263$	−2.40422e9	−	6.60554e9i	−0.502517	−	1.38065i	0.386292	−	0.922377i	$-0.373756\pi$
$264$	−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	$-0.698348\pi$
$269$		−	8.50405e9i		−	1.62411i	0.583578	−	0.812057i	$-0.301652\pi$
$270$	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	−0.879315	−	0.476241i	$-0.841999\pi$
$277$	−7.34026e9	+	2.67163e9i	−1.24679	+	0.453793i	−0.367472	+	0.930035i	$0.619777\pi$
$278$	−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	−0.840686	−	0.541524i	$-0.817848\pi$
$281$	−1.00634e9	+	1.19931e9i	−0.161405	+	0.192356i	0.679280	+	0.733879i	$0.262292\pi$
$282$	−1.11093e9	+	7.93737e8i	−0.175667	+	0.125511i
$283$	1.38681e9	+	7.86497e9i	0.216207	+	1.22617i	0.878799	+	0.477192i	$0.158345\pi$
$283$	1.38681e9	+	7.86497e9i	0.216207	+	1.22617i	−0.662592	+	0.748980i	$0.730544\pi$
$284$	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	−0.401555	−	0.915835i	$-0.631530\pi$
$293$	3.64627e9	−	1.00180e10i	0.494741	−	1.35929i	0.896296	−	0.443456i	$-0.146248\pi$
$294$	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	0.774583	−	0.632472i	$-0.217960\pi$
$307$	−1.42521e9	−	2.46854e9i	−0.160445	−	0.277899i	−0.935028	+	0.354573i	$0.884626\pi$
$308$	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	0.463529	−	0.886082i	$-0.346583\pi$
$311$	1.12462e10	−	1.98300e9i	1.20216	−	0.211974i	0.738633	+	0.674108i	$0.235472\pi$
$312$	9.87634e9	−	9.58811e8i	1.04226	−	0.101185i
$313$	3.45161e9	+	2.89625e9i	0.359621	+	0.301758i	0.804639	−	0.593764i	$-0.202359\pi$
$313$	3.45161e9	+	2.89625e9i	0.359621	+	0.301758i	−0.445019	+	0.895521i	$0.646803\pi$
$314$	−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	0.996749	−	0.0805754i	$-0.0256758\pi$
$317$	1.83180e9	+	5.03284e9i	0.181402	+	0.498398i	−0.815347	+	0.578973i	$0.803454\pi$
$318$	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	−0.499691	−	0.866204i	$-0.666553\pi$
$331$	−3.90947e9	+	1.42293e9i	−0.325691	+	0.118542i	0.174000	+	0.984746i	$0.444331\pi$
$332$	−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	−0.978480	−	0.206343i	$-0.933844\pi$
$337$	−1.67135e9	−	9.47871e9i	−0.129583	−	0.734902i	0.848897	−	0.528559i	$-0.177267\pi$
$338$	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	−0.942043	−	0.335493i	$-0.891097\pi$
$347$	−6.87957e7	+	1.89015e8i	−0.00474508	+	0.0130370i	0.937297	+	0.348530i	$0.113319\pi$
$348$	−4.28503e8	+	5.49986e9i	−0.0292171	+	0.375003i
$349$	2.82255e9	−	1.60075e10i	0.190257	−	1.07900i	−0.728756	−	0.684773i	$-0.759901\pi$
$349$	2.82255e9	−	1.60075e10i	0.190257	−	1.07900i	0.919013	−	0.394227i	$-0.128988\pi$
$350$		−	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	0.335622	−	0.941997i	$-0.391054\pi$
$353$	5.10574e9	+	9.00279e8i	0.328821	+	0.0579800i	−0.00680064	+	0.999977i	$0.502165\pi$
$354$	−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	−0.389991	−	0.920819i	$-0.627522\pi$
$359$	−2.29627e10	−	1.32575e10i	−1.38244	−	0.798151i	−0.992448	+	0.122668i	$0.960855\pi$
$360$	−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	0.999558	+	0.0297143i	$0.00945975\pi$
$367$	2.18128e10	+	1.83031e10i	1.20239	+	1.00893i	0.202834	+	0.979213i	$0.434985\pi$
$368$	−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	−0.577776	−	0.816195i	$-0.696079\pi$
$373$	2.43295e9	−	2.04149e9i	0.125689	−	0.105466i	0.703465	+	0.710729i	$0.251635\pi$
$374$	−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	0.882244	−	0.470792i	$-0.156032\pi$
$383$	5.71089e9	+	6.80598e9i	0.265405	+	0.316297i	−0.616839	+	0.787089i	$0.711587\pi$
$384$	−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	−0.675828	−	0.737059i	$-0.736214\pi$
$389$	3.83291e9	−	4.56788e9i	0.167390	−	0.199488i	0.843218	+	0.537572i	$0.180658\pi$
$390$	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	−0.896466	−	0.443112i	$-0.853874\pi$
$397$	−1.60190e9	+	2.77457e9i	−0.0644871	+	0.111695i	0.831979	+	0.554807i	$0.187208\pi$
$398$	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	−0.357656	−	0.933853i	$-0.616424\pi$
$401$	1.33575e10	−	3.66996e10i	0.516594	−	1.41933i	0.874250	−	0.485477i	$-0.161354\pi$
$402$	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	−0.479488	−	0.877548i	$-0.659178\pi$
$409$	−3.94804e10	−	1.43697e10i	−1.41087	−	0.513516i	−0.931386	+	0.364032i	$0.881400\pi$
$410$	−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	0.237299	−	0.971437i	$-0.423738\pi$
$419$	2.44273e10	−	4.30720e9i	0.792538	−	0.139746i	0.555239	+	0.831691i	$0.312627\pi$
$420$	6.41990e9	−	1.41165e10i	0.206315	−	0.453661i
$421$	−4.34557e10	−	3.64636e10i	−1.38331	−	1.16073i	−0.967971	−	0.251062i	$-0.919220\pi$
$421$	−4.34557e10	−	3.64636e10i	−1.38331	−	1.16073i	−0.415335	−	0.909669i	$-0.636335\pi$
$422$	−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	$-0.614055\pi$
$431$		−	6.46311e10i		−	1.87298i	0.350698	−	0.936489i	$-0.385945\pi$
$432$	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	−0.935240	−	0.354015i	$-0.884816\pi$
$439$	−5.28937e10	+	1.92517e10i	−1.42412	+	0.518337i	−0.488878	+	0.872352i	$0.662594\pi$
$440$	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	−0.415534	−	0.909577i	$-0.636405\pi$
$443$	2.12742e10	−	2.53536e10i	0.552381	−	0.658302i	0.967916	+	0.251275i	$0.0808498\pi$
$444$	−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	−0.546597	+	0.837396i	$0.684077\pi$
$449$	−6.27975e10	+	3.62562e10i	−1.54510	+	0.892065i	−0.998505	+	0.0546691i	$0.982590\pi$
$450$	−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	0.674764	+	0.738033i	$0.264245\pi$
$457$	−9.23518e9	+	5.23753e10i	−0.211729	+	1.20078i	−0.886493	+	0.462742i	$0.846866\pi$
$458$			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	−0.170699	−	0.985323i	$-0.554603\pi$
$461$	−3.01751e10	−	5.32068e9i	−0.668104	−	0.117805i	−0.497405	+	0.867518i	$0.665714\pi$
$462$	−6.95395e10	−	5.41794e9i	−1.52638	−	0.118923i
$463$	3.02920e10	+	1.10254e10i	0.659181	+	0.239922i	0.649883	−	0.760035i	$-0.274818\pi$
$463$	3.02920e10	+	1.10254e10i	0.659181	+	0.239922i	0.00929829	+	0.999957i	$0.497040\pi$
$464$	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	0.891812	−	0.452406i	$-0.149434\pi$
$467$	4.49907e10	+	2.59754e10i	0.945922	+	0.546129i	0.0541106	+	0.998535i	$0.482768\pi$
$468$	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	0.843710	−	0.536799i	$-0.180367\pi$
$479$	−7.77313e9	−	2.13565e10i	−0.147657	−	0.405684i	−0.991367	+	0.131115i	$0.958144\pi$
$480$	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	0.999818	−	0.0190855i	$-0.00607549\pi$
$491$	4.69265e10	+	5.59248e10i	0.807406	+	0.962229i	−0.192412	+	0.981314i	$0.561631\pi$
$492$	−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	0.990179	+	0.139807i	$0.0446482\pi$
$499$	6.66714e9	+	3.78112e10i	0.107532	+	0.609844i	−0.882647	+	0.470037i	$0.844241\pi$
$500$	−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	−0.489207	−	0.872168i	$-0.662714\pi$
$503$	1.37684e9	−	7.94918e8i	0.0215085	−	0.0124180i	0.510716	+	0.859750i	$0.329380\pi$
$504$	−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	0.494816	+	0.868998i	$0.335236\pi$
$509$	−2.97231e10	+	8.16637e10i	−0.442816	+	1.21663i	−0.937632	+	0.347630i	$0.886987\pi$
$510$	−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	0.991122	+	0.132956i	$0.0424470\pi$
$521$	1.18023e11	+	6.81406e10i	1.60183	+	0.924815i	0.610704	+	0.791859i	$0.290886\pi$
$522$	7.14006e10	−	4.30546e10i	0.961657	−	0.579879i
$523$	−1.68568e10	−	2.91969e10i	−0.225304	−	0.390238i	0.731107	−	0.682263i	$-0.239004\pi$
$523$	−1.68568e10	−	2.91969e10i	−0.225304	−	0.390238i	−0.956411	+	0.292025i	$0.905671\pi$
$524$	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	−0.941037	−	0.338304i	$-0.890147\pi$
$547$	−1.29316e11	+	4.70673e10i	−1.44446	+	0.525739i	−0.503418	+	0.864043i	$0.667925\pi$
$548$	−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	0.407071	−	0.913397i	$-0.366550\pi$
$557$	1.34913e11	−	7.78922e10i	1.40163	−	0.809232i	0.994560	+	0.104165i	$0.0332169\pi$
$558$	−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	−0.634718	−	0.772744i	$-0.718884\pi$
$563$	3.49849e10	−	9.61202e10i	0.348214	−	0.956711i	0.982932	−	0.183967i	$-0.0588941\pi$
$564$	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	−0.270152	−	0.962818i	$-0.587074\pi$
$569$	−8.94456e10	−	1.57717e10i	−0.853316	−	0.150463i	−0.583163	+	0.812355i	$0.698185\pi$
$570$	5.13162e8	+	1.07370e9i	0.00486133	+	0.0101714i
$571$	−1.14927e11	−	4.18298e10i	−1.08113	−	0.393497i	−0.260799	−	0.965393i	$-0.583986\pi$
$571$	−1.14927e11	−	4.18298e10i	−1.08113	−	0.393497i	−0.820326	+	0.571896i	$0.806208\pi$
$572$	−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	0.859845	−	0.510555i	$-0.170560\pi$
$577$	−1.35572e9	−	2.34817e9i	−0.0122311	−	0.0211849i	−0.872076	+	0.489370i	$0.837227\pi$
$578$	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	−0.985843	−	0.167673i	$-0.946375\pi$
$587$	−4.01800e10	−	1.10394e11i	−0.338421	−	0.929805i	0.647421	−	0.762132i	$-0.275847\pi$
$588$	−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	$-0.759338\pi$
$593$		−	1.69673e11i		−	1.37212i	0.727544	−	0.686061i	$-0.240662\pi$
$594$	−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	0.196243	−	0.980555i	$-0.437126\pi$
$599$	−1.03440e11	−	1.23275e11i	−0.803493	−	0.957566i	−0.999736	+	0.0229897i	$0.992681\pi$
$600$	2.06231e11	+	5.31622e10i	1.59129	+	0.410202i
$601$	1.59242e11	−	5.79593e10i	1.22056	−	0.444248i	0.350206	−	0.936673i	$-0.386112\pi$
$601$	1.59242e11	−	5.79593e10i	1.22056	−	0.444248i	0.870355	+	0.492425i	$0.163889\pi$
$602$	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	0.857860	+	0.513883i	$0.171794\pi$
$607$	3.08833e10	+	1.75148e11i	0.227494	+	1.29018i	−0.630366	+	0.776298i	$0.717095\pi$
$608$	−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	−0.950481	−	0.310783i	$-0.899409\pi$
$613$	−2.91010e10	+	5.04044e10i	−0.206094	+	0.356966i	0.744387	+	0.667749i	$0.232742\pi$
$614$	−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	−0.675969	−	0.736930i	$-0.736275\pi$
$617$	4.57298e10	−	1.25641e11i	0.315543	−	0.866947i	0.991512	−	0.130017i	$-0.0415031\pi$
$618$	7.12138e10	+	4.88616e10i	0.488214	+	0.334976i
$619$	2.33487e10	−	1.32417e11i	0.159038	−	0.901948i	−0.795963	−	0.605345i	$-0.793035\pi$
$619$	2.33487e10	−	1.32417e11i	0.159038	−	0.901948i	0.955001	−	0.296603i	$-0.0958538\pi$
$620$			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	0.813919	−	0.580979i	$-0.197330\pi$
$631$	−1.52481e10	−	2.64105e10i	−0.0961831	−	0.166594i	−0.910102	+	0.414385i	$0.863997\pi$
$632$	−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	0.938458	+	0.345394i	$0.112255\pi$
$641$	7.45477e10	+	2.04818e11i	0.441572	+	1.21321i	−0.496885	+	0.867816i	$0.665523\pi$
$642$	−6.50118e10	+	1.80843e10i	−0.382694	+	0.106454i
$643$	−1.17314e11	+	9.84380e10i	−0.686286	+	0.575863i	−0.917836	−	0.396961i	$-0.870065\pi$
$643$	−1.17314e11	+	9.84380e10i	−0.686286	+	0.575863i	0.231549	+	0.972823i	$0.425621\pi$
$644$	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	$-0.885463\pi$
$647$		−	1.23404e11i		−	0.704226i	0.935957	−	0.352113i	$-0.114537\pi$
$648$	−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	0.616610	−	0.787268i	$-0.288505\pi$
$653$	−4.83237e10	−	5.75899e10i	−0.265771	−	0.316733i	−0.882381	+	0.470535i	$0.844061\pi$
$654$	−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	−0.632157	−	0.774840i	$-0.717830\pi$
$659$	4.53931e10	−	5.40973e10i	0.240684	−	0.286836i	0.872842	+	0.488004i	$0.162275\pi$
$660$	1.34396e10	+	1.38436e11i	0.0708289	+	0.729582i
$661$	−2.47641e10	−	1.40444e11i	−0.129723	−	0.735696i	−0.978390	−	0.206768i	$-0.933705\pi$
$661$	−2.47641e10	−	1.40444e11i	−0.129723	−	0.735696i	0.848667	−	0.528928i	$-0.177406\pi$
$662$	−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	0.934778	+	0.355232i	$0.115598\pi$
$673$	−1.33595e10	+	7.57657e10i	−0.0651225	+	0.369328i	−0.999901	+	0.0140960i	$0.995513\pi$
$674$		−	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	−0.387612	−	0.921823i	$-0.626700\pi$
$677$	−2.24167e11	−	3.95267e10i	−1.06713	−	0.188164i	−0.679518	+	0.733659i	$0.737811\pi$
$678$	−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	0.355685	−	0.934606i	$-0.384248\pi$
$683$	−6.00315e10	−	3.46592e10i	−0.275865	−	0.159271i	−0.631550	+	0.775335i	$0.717581\pi$
$684$	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	0.494331	−	0.869274i	$-0.335413\pi$
$691$	−6.29010e10	−	5.27802e10i	−0.275896	−	0.231504i	−0.770228	+	0.637769i	$0.779857\pi$
$692$	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	$-0.725129\pi$
$701$		−	3.67111e11i		−	1.52029i	0.649755	−	0.760144i	$-0.274871\pi$
$702$	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	−0.381939	−	0.924187i	$-0.624744\pi$
$709$	−2.03327e10	+	7.40048e9i	−0.0804654	+	0.0292870i	0.301474	+	0.953474i	$0.402521\pi$
$710$	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	−0.927204	−	0.374557i	$-0.877795\pi$
$719$	−2.85002e11	+	1.64546e11i	−1.06643	+	0.615703i	−0.139226	+	0.990261i	$0.544461\pi$
$720$	−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	0.586283	+	0.810106i	$0.300590\pi$
$727$	−6.75215e10	+	3.82933e11i	−0.241715	+	1.37084i	−0.827999	+	0.560730i	$0.810521\pi$
$728$			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	0.715173	−	0.698947i	$-0.246348\pi$
$733$	2.34914e11	+	8.55016e10i	0.813753	+	0.296182i	0.0985795	+	0.995129i	$0.468570\pi$
$734$	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	−0.861395	−	0.507935i	$-0.830409\pi$
$739$	−2.59650e11	−	4.49726e11i	−0.870582	−	1.50789i	−0.00918707	−	0.999958i	$-0.502924\pi$
$740$	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	−0.356577	−	0.934266i	$-0.616056\pi$
$743$	−1.13404e11	+	1.99962e10i	−0.372112	+	0.0656133i	−0.0155348	+	0.999879i	$0.504945\pi$
$744$	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	−0.907188	−	0.420725i	$-0.861776\pi$
$751$	−2.06886e11	+	1.73598e11i	−0.650387	+	0.545740i	0.256801	+	0.966464i	$0.417331\pi$
$752$	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	0.982775	−	0.184807i	$-0.0591660\pi$
$761$	2.11330e11	+	2.51853e11i	0.630118	+	0.750946i	−0.352656	+	0.935753i	$0.614722\pi$
$762$	−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	0.960048	+	0.279834i	$0.0902794\pi$
$769$	5.37175e10	+	3.04647e11i	0.153607	+	0.871148i	−0.806442	+	0.591314i	$0.798609\pi$
$770$	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	0.399591	−	0.916694i	$-0.369152\pi$
$773$	4.97453e11	−	2.87205e11i	1.39327	−	0.804403i	0.993675	+	0.112291i	$0.0358189\pi$
$774$	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	0.888598	−	0.458687i	$-0.151680\pi$
$787$	4.88907e11	+	1.77948e11i	1.27446	+	0.463867i	0.385867	+	0.922555i	$0.373902\pi$
$788$	−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	−0.445545	−	0.895260i	$-0.646990\pi$
$797$	−2.25157e11	+	3.97012e10i	−0.558023	+	0.0983945i	−0.112478	+	0.993654i	$0.535879\pi$
$798$	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	$-0.893926\pi$
$809$		−	2.80231e11i		−	0.654218i	0.944987	−	0.327109i	$-0.106074\pi$
$810$	−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	−0.657811	−	0.753183i	$-0.728518\pi$
$821$	9.00287e10	−	1.07292e11i	0.198157	−	0.236154i	0.855968	+	0.517029i	$0.172962\pi$
$822$	3.93595e10	+	4.05428e11i	0.0862110	+	0.888027i
$823$	1.32353e11	+	7.50609e11i	0.288492	+	1.63612i	0.692540	+	0.721379i	$0.256492\pi$
$823$	1.32353e11	+	7.50609e11i	0.288492	+	1.63612i	−0.404048	+	0.914738i	$0.632397\pi$
$824$	−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	−0.303028	−	0.952982i	$-0.597997\pi$
$827$	1.73429e11	−	1.00129e11i	0.370765	−	0.214061i	0.673793	+	0.738921i	$0.264664\pi$
$828$	−1.35169e10	−	6.89603e10i	−0.0287579	−	0.146716i
$829$	3.02214e11	−	5.23449e11i	0.639876	−	1.10830i	−0.345584	−	0.938388i	$-0.612319\pi$
$829$	3.02214e11	−	5.23449e11i	0.639876	−	1.10830i	0.985460	−	0.169910i	$-0.0543476\pi$
$830$	−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	−0.839002	−	0.544129i	$-0.816860\pi$
$839$	−8.98602e11	−	1.58448e11i	−1.81351	−	0.319771i	−0.974507	+	0.224358i	$0.927972\pi$
$840$	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	0.685188	−	0.728366i	$-0.259720\pi$
$853$	4.59900e10	+	3.85902e10i	0.0868695	+	0.0728922i	−0.598319	+	0.801258i	$0.704164\pi$
$854$	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	−0.995988	−	0.0894815i	$-0.971479\pi$
$857$	−1.56719e11	−	4.30581e11i	−0.290535	−	0.798237i	0.705454	−	0.708756i	$-0.250743\pi$
$858$	−1.80014e11	+	6.98325e11i	−0.332168	+	1.28857i
$859$	2.76176e11	−	2.31740e11i	0.507241	−	0.425625i	−0.352916	−	0.935655i	$-0.614810\pi$
$859$	2.76176e11	−	2.31740e11i	0.507241	−	0.425625i	0.860157	+	0.510030i	$0.170366\pi$
$860$	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	$0.284922\pi$
$863$			8.65609e11i			1.56055i	−0.625435	+	0.780276i	$0.715078\pi$
$864$	−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	−0.995109	−	0.0987829i	$-0.968505\pi$
$877$	−5.54872e10	−	3.14683e11i	−0.0937981	−	0.531956i	0.901311	−	0.433173i	$-0.142606\pi$
$878$	−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	−0.962977	−	0.269582i	$-0.913114\pi$
$881$	−7.29538e11	+	4.21199e11i	−1.21100	+	0.699172i	−0.248024	+	0.968754i	$0.579781\pi$
$882$	−1.82281e10	+	1.16269e11i	−0.0301209	+	0.192128i
$883$	−5.44619e11	+	9.43307e11i	−0.895880	+	1.55171i	−0.0631678	+	0.998003i	$0.520120\pi$
$883$	−5.44619e11	+	9.43307e11i	−0.895880	+	1.55171i	−0.832712	+	0.553706i	$0.813213\pi$
$884$	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	−0.795612	−	0.605806i	$-0.792851\pi$
$887$	1.25823e11	−	3.45697e11i	0.203267	−	0.558471i	0.998879	+	0.0473352i	$0.0150729\pi$
$888$	−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	0.527009	−	0.849860i	$-0.323313\pi$
$907$	−1.47819e11	−	1.24035e11i	−0.218425	−	0.183280i	−0.745434	+	0.666579i	$0.767758\pi$
$908$	−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	0.964543	−	0.263927i	$-0.0850179\pi$
$911$	3.85785e10	+	1.05994e11i	0.0560109	+	0.153889i	−0.908532	+	0.417816i	$0.862796\pi$
$912$	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	−0.798333	−	0.602217i	$-0.794284\pi$
$929$	−4.96330e10	+	5.91503e10i	−0.0666358	+	0.0794135i	0.731697	+	0.681630i	$0.238729\pi$
$930$	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	−0.899286	−	0.437361i	$-0.855913\pi$
$937$	−5.46345e10	+	9.46298e10i	−0.0708776	+	0.122764i	0.828409	+	0.560124i	$0.189247\pi$
$938$	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	−0.998069	−	0.0621085i	$-0.980218\pi$
$941$	−1.51783e11	+	4.17019e11i	−0.193581	+	0.531860i	0.804488	+	0.593969i	$0.202440\pi$
$942$	−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	0.522409	−	0.852695i	$-0.325034\pi$
$947$	5.80418e11	+	1.02343e11i	0.721673	+	0.127250i	0.199265	+	0.979946i	$0.436145\pi$
$948$	−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	0.507490	−	0.861658i	$-0.330574\pi$
$953$	1.23865e10	+	7.15133e9i	0.0150168	+	0.00866992i	−0.492473	+	0.870328i	$0.663907\pi$
$954$	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	−0.703433	−	0.710762i	$-0.748350\pi$
$967$	−1.09840e11	+	9.21663e10i	−0.125618	+	0.105406i	0.577814	+	0.816168i	$0.303906\pi$
$968$	−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	$0.394318\pi$
$971$			1.68081e12i			1.89078i	−0.325944	+	0.945389i	$0.605682\pi$
$972$	−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	0.932537	−	0.361074i	$-0.117590\pi$
$977$	3.78131e11	+	4.50639e11i	0.415015	+	0.494596i	−0.517522	+	0.855670i	$0.673145\pi$
$978$	−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	−0.974181	−	0.225768i	$-0.927511\pi$
$983$	−5.44055e11	+	6.48380e11i	−0.582678	+	0.694409i	0.391503	+	0.920177i	$0.371955\pi$
$984$	−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	−0.500749	−	0.865593i	$-0.666942\pi$
$991$	4.81519e11	−	8.34015e11i	0.499251	−	0.864728i	1.00000		0.000864758i	$0.000275261\pi$
$992$	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	0.857299	+	0.514819i	$0.172141\pi$
$997$	−1.22891e11	+	6.96951e11i	−0.124377	+	0.705378i	−0.981676	+	0.190559i	$0.938970\pi$
$998$			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.2.15	✓	138
3.2	odd	2		81.9.f.a.8.9		138
27.13	even	9		81.9.f.a.71.9		138
27.14	odd	18	inner	27.9.f.a.14.15	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.15	✓	138	1.1	even	1	trivial
27.9.f.a.14.15	yes	138	27.14	odd	18	inner
81.9.f.a.8.9		138	3.2	odd	2
81.9.f.a.71.9		138	27.13	even	9

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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