LMFDB - Embedded newform 27.9.f.a.2.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,9,Mod(2,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			2.11
Character	$\chi$	$=$	27.2
Dual form			27.9.f.a.14.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.24198 - 0.571649i) q^{2} +(-71.7460 + 37.5966i) q^{3} +(-230.378 - 83.8506i) q^{4} +(387.667 + 462.003i) q^{5} +(254.092 - 80.8741i) q^{6} +(-3862.15 + 1405.71i) q^{7} +(1428.79 + 824.913i) q^{8} +(3733.99 - 5394.82i) q^{9} +(-992.706 - 1719.42i) q^{10} +(11423.3 - 13613.8i) q^{11} +(19681.2 - 2645.47i) q^{12} +(-882.859 - 5006.94i) q^{13} +(13324.6 - 2349.49i) q^{14} +(-45183.3 - 18571.9i) q^{15} +(43917.7 + 36851.3i) q^{16} +(23746.9 - 13710.3i) q^{17} +(-15189.5 + 15355.4i) q^{18} +(92857.3 - 160834. i) q^{19} +(-50570.5 - 138941. i) q^{20} +(224244. - 246058. i) q^{21} +(-44816.5 + 37605.5i) q^{22} +(-88410.2 + 242905. i) q^{23} +(-133524. - 5466.51i) q^{24} +(4669.78 - 26483.6i) q^{25} +16737.1i q^{26} +(-65071.9 + 527442. i) q^{27} +1.00762e6 q^{28} +(-234351. - 41322.5i) q^{29} +(135867. + 86039.0i) q^{30} +(-618503. - 225117. i) q^{31} +(-392799. - 468120. i) q^{32} +(-307745. + 1.40621e6i) q^{33} +(-84824.4 + 30873.6i) q^{34} +(-2.14667e6 - 1.23938e6i) q^{35} +(-1.31259e6 + 929748. i) q^{36} +(779022. + 1.34931e6i) q^{37} +(-392982. + 468338. i) q^{38} +(251586. + 326036. i) q^{39} +(172782. + 979898. i) q^{40} +(3.82274e6 - 674052. i) q^{41} +(-867655. + 669527. i) q^{42} +(-1.19676e6 - 1.00420e6i) q^{43} +(-3.77320e6 + 2.17846e6i) q^{44} +(3.93997e6 - 366277. i) q^{45} +(425481. - 736954. i) q^{46} +(407155. + 1.11865e6i) q^{47} +(-4.53640e6 - 992779. i) q^{48} +(8.52411e6 - 7.15258e6i) q^{49} +(-30278.7 + 83190.0i) q^{50} +(-1.18828e6 + 1.87646e6i) q^{51} +(-216444. + 1.22752e6i) q^{52} -1.29944e7i q^{53} +(512474. - 1.67276e6i) q^{54} +1.07180e7 q^{55} +(-6.67780e6 - 1.17748e6i) q^{56} +(-615344. + 1.50303e7i) q^{57} +(736141. + 267934. i) q^{58} +(-1.38268e7 - 1.64782e7i) q^{59} +(8.85196e6 + 8.06721e6i) q^{60} +(1.39731e7 - 5.08578e6i) q^{61} +(1.87649e6 + 1.08339e6i) q^{62} +(-6.83769e6 + 2.60845e7i) q^{63} +(-6.33245e6 - 1.09681e7i) q^{64} +(1.97097e6 - 2.34891e6i) q^{65} +(1.80156e6 - 4.38299e6i) q^{66} +(-1.06177e6 - 6.02157e6i) q^{67} +(-6.62036e6 + 1.16735e6i) q^{68} +(-2.78933e6 - 2.07514e7i) q^{69} +(6.25098e6 + 5.24520e6i) q^{70} +(3.07395e7 - 1.77475e7i) q^{71} +(9.78534e6 - 4.62785e6i) q^{72} +(6.89919e6 - 1.19498e7i) q^{73} +(-1.75425e6 - 4.81975e6i) q^{74} +(660657. + 2.07566e6i) q^{75} +(-3.48782e7 + 2.92663e7i) q^{76} +(-2.49816e7 + 6.86363e7i) q^{77} +(-629259. - 1.20082e6i) q^{78} +(-7.76297e6 + 4.40260e7i) q^{79} +3.45761e7i q^{80} +(-1.51614e7 - 4.02884e7i) q^{81} -1.27786e7 q^{82} +(-4.57442e7 - 8.06593e6i) q^{83} +(-7.22930e7 + 3.78832e7i) q^{84} +(1.55401e7 + 5.65612e6i) q^{85} +(3.30581e6 + 3.93971e6i) q^{86} +(1.83674e7 - 5.84610e6i) q^{87} +(2.75517e7 - 1.00280e7i) q^{88} +(-3.60126e6 - 2.07919e6i) q^{89} +(-1.29827e7 - 1.06481e6i) q^{90} +(1.04480e7 + 1.80965e7i) q^{91} +(4.07355e7 - 4.85466e7i) q^{92} +(5.28388e7 - 7.10240e6i) q^{93} +(-680516. - 3.85940e6i) q^{94} +(1.10303e8 - 1.94495e7i) q^{95} +(4.57815e7 + 1.88178e7i) q^{96} +(-1.08572e8 - 9.11031e7i) q^{97} +(-3.17238e7 + 1.83157e7i) q^{98} +(-3.07893e7 - 1.12460e8i) 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 $

$2$	−3.24198	−	0.571649i	−0.202624	−	0.0357281i	0.0714149	−	0.997447i	$-0.477249\pi$
$2$	−3.24198	−	0.571649i	−0.202624	−	0.0357281i	−0.274039	+	0.961719i	$0.588360\pi$
$3$	−71.7460	+	37.5966i	−0.885754	+	0.464156i
$3$	−71.7460	+	37.5966i	−0.885754	+	0.464156i
$4$	−230.378	−	83.8506i	−0.899913	−	0.327541i
$5$	387.667	+	462.003i	0.620267	+	0.739206i	0.981116	−	0.193419i	$-0.0619576\pi$
$5$	387.667	+	462.003i	0.620267	+	0.739206i	−0.360849	+	0.932624i	$0.617513\pi$
$6$	254.092	−	80.8741i	0.196058	−	0.0624028i
$7$	−3862.15	+	1405.71i	−1.60856	+	0.585468i	−0.981155	−	0.193225i	$-0.938105\pi$
$7$	−3862.15	+	1405.71i	−1.60856	+	0.585468i	−0.627405	+	0.778693i	$0.715883\pi$
$8$	1428.79	+	824.913i	0.348826	+	0.201395i
$9$	3733.99	−	5394.82i	0.569119	−	0.822255i
$10$	−992.706	−	1719.42i	−0.0992706	−	0.171942i
$11$	11423.3	−	13613.8i	0.780227	−	0.929839i	−0.218716	−	0.975788i	$-0.570187\pi$
$11$	11423.3	−	13613.8i	0.780227	−	0.929839i	0.998944	+	0.0459497i	$0.0146314\pi$
$12$	19681.2	−	2645.47i	0.949131	−	0.127579i
$13$	−882.859	−	5006.94i	−0.0309113	−	0.175307i	0.965443	−	0.260612i	$-0.0839245\pi$
$13$	−882.859	−	5006.94i	−0.0309113	−	0.175307i	−0.996355	+	0.0853055i	$0.972813\pi$
$14$	13324.6	−	2349.49i	0.346850	−	0.0611591i
$15$	−45183.3	−	18571.9i	−0.892510	−	0.366853i
$16$	43917.7	+	36851.3i	0.670130	+	0.562306i
$17$	23746.9	−	13710.3i	0.284322	−	0.164153i	−0.351056	−	0.936354i	$-0.614177\pi$
$17$	23746.9	−	13710.3i	0.284322	−	0.164153i	0.635378	+	0.772201i	$0.280844\pi$
$18$	−15189.5	+	15355.4i	−0.144695	+	0.146275i
$19$	92857.3	−	160834.i	0.712528	−	1.23413i	−0.251378	−	0.967889i	$-0.580884\pi$
$19$	92857.3	−	160834.i	0.712528	−	1.23413i	0.963905	−	0.266245i	$-0.0857831\pi$
$20$	−50570.5	−	138941.i	−0.316066	−	0.868384i
$21$	224244.	−	246058.i	1.15304	−	1.26520i
$22$	−44816.5	+	37605.5i	−0.191314	+	0.160532i
$23$	−88410.2	+	242905.i	−0.315930	+	0.868011i	0.675498	+	0.737361i	$0.263928\pi$
$23$	−88410.2	+	242905.i	−0.315930	+	0.868011i	−0.991429	+	0.130650i	$0.958294\pi$
$24$	−133524.	−	5466.51i	−0.402452	−	0.0164765i
$25$	4669.78	−	26483.6i	0.0119546	−	0.0677981i
$26$			16737.1i			0.0366258i
$27$	−65071.9	+	527442.i	−0.122444	+	0.992475i
$28$	1.00762e6			1.63933
$29$	−234351.	−	41322.5i	−0.331341	−	0.0584244i	0.00550273	−	0.999985i	$-0.498248\pi$
$29$	−234351.	−	41322.5i	−0.331341	−	0.0584244i	−0.336844	+	0.941560i	$0.609360\pi$
$30$	135867.	+	86039.0i	0.167737	+	0.106221i
$31$	−618503.	−	225117.i	−0.669723	−	0.243759i	−0.0152945	−	0.999883i	$-0.504869\pi$
$31$	−618503.	−	225117.i	−0.669723	−	0.243759i	−0.654429	+	0.756124i	$0.727091\pi$
$32$	−392799.	−	468120.i	−0.374602	−	0.446434i
$33$	−307745.	+	1.40621e6i	−0.259499	+	1.18576i
$34$	−84824.4	+	30873.6i	−0.0634754	+	0.0231031i
$35$	−2.14667e6	−	1.23938e6i	−1.43052	−	0.825910i
$36$	−1.31259e6	+	929748.i	−0.781480	+	0.553548i
$37$	779022.	+	1.34931e6i	0.415664	+	0.719952i	0.995498	−	0.0947831i	$-0.0302158\pi$
$37$	779022.	+	1.34931e6i	0.415664	+	0.719952i	−0.579834	+	0.814735i	$0.696882\pi$
$38$	−392982.	+	468338.i	−0.188468	+	0.224608i
$39$	251586.	+	326036.i	0.108750	+	0.140931i
$40$	172782.	+	979898.i	0.0674931	+	0.382773i
$41$	3.82274e6	−	674052.i	1.35282	−	0.238538i	0.550201	−	0.835033i	$-0.314551\pi$
$41$	3.82274e6	−	674052.i	1.35282	−	0.238538i	0.802617	+	0.596494i	$0.203440\pi$
$42$	−867655.	+	669527.i	−0.278837	+	0.215165i
$43$	−1.19676e6	−	1.00420e6i	−0.350051	−	0.293728i	0.450759	−	0.892645i	$-0.351153\pi$
$43$	−1.19676e6	−	1.00420e6i	−0.350051	−	0.293728i	−0.800811	+	0.598918i	$0.795598\pi$
$44$	−3.77320e6	+	2.17846e6i	−1.00670	+	0.581217i
$45$	3.93997e6	−	366277.i	0.960821	−	0.0893223i
$46$	425481.	−	736954.i	0.0950274	−	0.164592i
$47$	407155.	+	1.11865e6i	0.0834390	+	0.229247i	0.974395	−	0.224843i	$-0.0721869\pi$
$47$	407155.	+	1.11865e6i	0.0834390	+	0.229247i	−0.890956	+	0.454089i	$0.849965\pi$
$48$	−4.53640e6	−	992779.i	−0.854568	−	0.187020i
$49$	8.52411e6	−	7.15258e6i	1.47865	−	1.24073i
$50$	−30278.7	+	83190.0i	−0.00484459	+	0.0133104i
$51$	−1.18828e6	+	1.87646e6i	−0.175647	+	0.277369i
$52$	−216444.	+	1.22752e6i	−0.0296028	+	0.167886i
$53$		−	1.29944e7i		−	1.64684i	−0.567432	−	0.823420i	$-0.692063\pi$
$53$		−	1.29944e7i		−	1.64684i	0.567432	−	0.823420i	$-0.307937\pi$
$54$	512474.	−	1.67276e6i	0.0602694	−	0.196725i
$55$	1.07180e7			1.17129
$56$	−6.67780e6	−	1.17748e6i	−0.679018	−	0.119729i
$57$	−615344.	+	1.50303e7i	−0.0582933	+	1.42386i
$58$	736141.	+	267934.i	0.0650503	+	0.0236764i
$59$	−1.38268e7	−	1.64782e7i	−1.14107	−	1.35988i	−0.923391	−	0.383861i	$-0.874594\pi$
$59$	−1.38268e7	−	1.64782e7i	−1.14107	−	1.35988i	−0.217684	−	0.976019i	$-0.569850\pi$
$60$	8.85196e6	+	8.06721e6i	0.683022	+	0.622470i
$61$	1.39731e7	−	5.08578e6i	1.00919	−	0.367315i	0.216068	−	0.976378i	$-0.430677\pi$
$61$	1.39731e7	−	5.08578e6i	1.00919	−	0.367315i	0.793121	+	0.609064i	$0.208455\pi$
$62$	1.87649e6	+	1.08339e6i	0.126993	+	0.0733194i
$63$	−6.83769e6	+	2.60845e7i	−0.434057	+	1.65585i
$64$	−6.33245e6	−	1.09681e7i	−0.377443	−	0.653751i
$65$	1.97097e6	−	2.34891e6i	0.110415	−	0.131587i
$66$	1.80156e6	−	4.38299e6i	0.0949455	−	0.230991i
$67$	−1.06177e6	−	6.02157e6i	−0.0526901	−	0.298821i	0.947063	−	0.321048i	$-0.104035\pi$
$67$	−1.06177e6	−	6.02157e6i	−0.0526901	−	0.298821i	−0.999753	+	0.0222278i	$0.992924\pi$
$68$	−6.62036e6	+	1.16735e6i	−0.309632	+	0.0545965i
$69$	−2.78933e6	−	2.07514e7i	−0.123056	−	0.915485i
$70$	6.25098e6	+	5.24520e6i	0.260349	+	0.218459i
$71$	3.07395e7	−	1.77475e7i	1.20966	−	0.698398i	0.246975	−	0.969022i	$-0.420563\pi$
$71$	3.07395e7	−	1.77475e7i	1.20966	−	0.698398i	0.962685	+	0.270624i	$0.0872300\pi$
$72$	9.78534e6	−	4.62785e6i	0.364121	−	0.172207i
$73$	6.89919e6	−	1.19498e7i	0.242944	−	0.420792i	−0.718607	−	0.695416i	$-0.755220\pi$
$73$	6.89919e6	−	1.19498e7i	0.242944	−	0.420792i	0.961552	+	0.274624i	$0.0885534\pi$
$74$	−1.75425e6	−	4.81975e6i	−0.0585011	−	0.160730i
$75$	660657.	+	2.07566e6i	0.0208800	+	0.0656012i
$76$	−3.48782e7	+	2.92663e7i	−1.04544	+	0.877231i
$77$	−2.49816e7	+	6.86363e7i	−0.710652	+	1.95250i
$78$	−629259.	−	1.20082e6i	−0.0170001	−	0.0324414i
$79$	−7.76297e6	+	4.40260e7i	−0.199306	+	1.13032i	0.706846	+	0.707367i	$0.250117\pi$
$79$	−7.76297e6	+	4.40260e7i	−0.199306	+	1.13032i	−0.906152	+	0.422952i	$0.860994\pi$
$80$			3.45761e7i			0.844144i
$81$	−1.51614e7	−	4.02884e7i	−0.352208	−	0.935922i
$82$	−1.27786e7			−0.282636
$83$	−4.57442e7	−	8.06593e6i	−0.963881	−	0.169958i	−0.330506	−	0.943804i	$-0.607220\pi$
$83$	−4.57442e7	−	8.06593e6i	−0.963881	−	0.169958i	−0.633374	+	0.773846i	$0.718331\pi$
$84$	−7.22930e7	+	3.78832e7i	−1.45204	+	0.760904i
$85$	1.55401e7	+	5.65612e6i	0.297699	+	0.108354i
$86$	3.30581e6	+	3.93971e6i	0.0604344	+	0.0720230i
$87$	1.83674e7	−	5.84610e6i	0.320605	−	0.102044i
$88$	2.75517e7	−	1.00280e7i	0.459428	−	0.167218i
$89$	−3.60126e6	−	2.07919e6i	−0.0573977	−	0.0331386i	0.471027	−	0.882119i	$-0.343884\pi$
$89$	−3.60126e6	−	2.07919e6i	−0.0573977	−	0.0331386i	−0.528424	+	0.848980i	$0.677217\pi$
$90$	−1.29827e7	−	1.06481e6i	−0.197877	−	0.0162295i
$91$	1.04480e7	+	1.80965e7i	0.152359	+	0.263894i
$92$	4.07355e7	−	4.85466e7i	0.568619	−	0.677654i
$93$	5.28388e7	−	7.10240e6i	0.706352	−	0.0949453i
$94$	−680516.	−	3.85940e6i	−0.00871619	−	0.0494320i
$95$	1.10303e8	−	1.94495e7i	1.35424	−	0.238788i
$96$	4.57815e7	+	1.88178e7i	0.539020	+	0.221556i
$97$	−1.08572e8	−	9.11031e7i	−1.22640	−	1.02907i	−0.998464	−	0.0553970i	$-0.982358\pi$
$97$	−1.08572e8	−	9.11031e7i	−1.22640	−	1.02907i	−0.227937	−	0.973676i	$-0.573198\pi$
$98$	−3.17238e7	+	1.83157e7i	−0.343938	+	0.198573i
$99$	−3.07893e7	−	1.12460e8i	−0.320523	−	1.17073i
$100$	−3.29648e6	+	5.70967e6i	−0.0329648	+	0.0570967i
$101$	4.07022e7	+	1.11828e8i	0.391140	+	1.07465i	0.966482	+	0.256735i	$0.0826467\pi$
$101$	4.07022e7	+	1.11828e8i	0.391140	+	1.07465i	−0.575342	+	0.817913i	$0.695131\pi$
$102$	4.92507e6	−	5.40417e6i	0.0455001	−	0.0499262i
$103$	−2.77608e7	+	2.32941e7i	−0.246651	+	0.206965i	−0.757729	−	0.652570i	$-0.773691\pi$
$103$	−2.77608e7	+	2.32941e7i	−0.246651	+	0.206965i	0.511077	+	0.859535i	$0.329247\pi$
$104$	2.86887e6	−	7.88216e6i	0.0245232	−	0.0673770i
$105$	2.00612e8	+	8.21309e6i	1.65044	+	0.0675693i
$106$	−7.42821e6	+	4.21275e7i	−0.0588384	+	0.333689i
$107$		−	1.86649e8i		−	1.42394i	−0.702212	−	0.711968i	$-0.747804\pi$
$107$		−	1.86649e8i		−	1.42394i	0.702212	−	0.711968i	$-0.252196\pi$
$108$	5.92174e7	−	1.16055e8i	0.435266	−	0.853036i
$109$	1.05606e8			0.748138			0.374069	−	0.927401i	$-0.377962\pi$
$109$	1.05606e8			0.748138			0.374069	+	0.927401i	$0.377962\pi$
$110$	−3.47477e7	−	6.12696e6i	−0.237332	−	0.0418480i
$111$	−1.06621e8	−	6.75187e7i	−0.702346	−	0.444767i
$112$	−2.21419e8	−	8.05899e7i	−1.40716	−	0.512163i
$113$	1.87685e8	+	2.23674e8i	1.15110	+	1.37183i	0.916643	+	0.399708i	$0.130888\pi$
$113$	1.87685e8	+	2.23674e8i	1.15110	+	1.37183i	0.234462	+	0.972125i	$0.424667\pi$
$114$	1.05870e7	−	4.83762e7i	0.0626835	−	0.286426i
$115$	−1.46497e8	+	5.33204e7i	−0.837599	+	0.304861i
$116$	5.05244e7	+	2.91703e7i	0.279042	+	0.161105i
$117$	−3.03081e7	−	1.39330e7i	−0.161739	−	0.0743534i
$118$	3.54066e7	+	6.13260e7i	0.182623	+	0.316313i
$119$	−7.24414e7	+	8.63323e7i	−0.361243	+	0.430512i
$120$	−4.92373e7	−	6.38077e7i	−0.237448	−	0.307715i
$121$	−1.76197e7	−	9.99263e7i	−0.0821972	−	0.466164i
$122$	−4.82078e7	+	8.50033e6i	−0.217609	+	0.0383704i
$123$	−2.48924e8	+	1.92083e8i	−1.08754	+	0.839205i
$124$	1.23613e8	+	1.03724e8i	0.522851	+	0.438724i
$125$	2.18070e8	−	1.25903e8i	0.893215	−	0.515698i
$126$	3.70789e7	−	8.06568e7i	0.147111	−	0.320006i
$127$	1.44951e8	−	2.51062e8i	0.557192	−	0.965085i	−0.440537	−	0.897734i	$-0.645212\pi$
$127$	1.44951e8	−	2.51062e8i	0.557192	−	0.965085i	0.997729	−	0.0673506i	$-0.0214546\pi$
$128$	6.77648e7	+	1.86182e8i	0.252444	+	0.693583i
$129$	1.23617e8	+	2.70532e7i	0.446395	+	0.0976922i
$130$	−7.73260e6	+	6.48842e6i	−0.0270740	+	0.0227178i
$131$	5.14222e7	−	1.41281e8i	0.174609	−	0.479733i	−0.821258	−	0.570556i	$-0.806728\pi$
$131$	5.14222e7	−	1.41281e8i	0.174609	−	0.479733i	0.995867	+	0.0908232i	$0.0289498\pi$
$132$	1.88809e8	−	2.98155e8i	0.621910	−	0.982079i
$133$	−1.32544e8	+	7.51694e8i	−0.423598	+	2.40234i
$134$			2.01288e7i			0.0624307i
$135$	−2.68906e8	+	1.74408e8i	−0.809591	+	0.525088i
$136$	4.52391e7			0.132239
$137$	−6.49465e8	−	1.14518e8i	−1.84363	−	0.325082i	−0.860707	−	0.509101i	$-0.829978\pi$
$137$	−6.49465e8	−	1.14518e8i	−1.84363	−	0.325082i	−0.982923	+	0.184020i	$0.941089\pi$
$138$	−2.81956e6	+	6.88702e7i	−0.00777438	+	0.189896i
$139$	−4.91164e8	−	1.78769e8i	−1.31573	−	0.478887i	−0.413643	−	0.910439i	$-0.635744\pi$
$139$	−4.91164e8	−	1.78769e8i	−1.31573	−	0.478887i	−0.902088	+	0.431552i	$0.857966\pi$
$140$	3.90622e8	+	4.65525e8i	1.01682	+	1.21180i
$141$	−7.12693e7	−	6.49511e7i	−0.180313	−	0.164327i
$142$	−1.09802e8	+	3.99648e7i	−0.270059	+	0.0982933i
$143$	−7.82485e7	−	4.51768e7i	−0.187125	−	0.108037i
$144$	3.62794e8	−	9.93255e7i	0.843743	−	0.230999i
$145$	−7.17592e7	−	1.24291e8i	−0.162332	−	0.281168i
$146$	−2.91981e7	+	3.47970e7i	−0.0642604	+	0.0765826i
$147$	−3.42658e8	+	8.33647e8i	−0.733824	+	1.78531i
$148$	−6.63292e7	−	3.76171e8i	−0.138248	−	0.784041i
$149$	−5.15210e8	+	9.08454e7i	−1.04530	+	0.184314i	−0.669824	−	0.742520i	$-0.733630\pi$
$149$	−5.15210e8	+	9.08454e7i	−1.04530	+	0.184314i	−0.375472	+	0.926834i	$0.622519\pi$
$150$	−955287.	−	7.10693e6i	−0.00188699	−	0.0140384i
$151$	5.15851e8	+	4.32850e8i	0.992239	+	0.832588i	0.985890	−	0.167392i	$-0.0535346\pi$
$151$	5.15851e8	+	4.32850e8i	0.992239	+	0.832588i	0.00634899	+	0.999980i	$0.497979\pi$
$152$	2.65347e8	−	1.53198e8i	0.497096	−	0.286999i
$153$	1.47062e7	−	1.79304e8i	0.0268370	−	0.327208i
$154$	1.20226e8	−	2.08237e8i	0.213754	−	0.370233i
$155$	−1.35769e8	−	3.73021e8i	−0.235219	−	0.646259i
$156$	−3.06214e7	−	9.62070e7i	−0.0517044	−	0.162446i
$157$	4.46343e8	−	3.74526e8i	0.734633	−	0.616430i	−0.196758	−	0.980452i	$-0.563041\pi$
$157$	4.46343e8	−	3.74526e8i	0.734633	−	0.616430i	0.931390	+	0.364022i	$0.118597\pi$
$158$	5.03349e7	−	1.38294e8i	0.0807682	−	0.221909i
$159$	4.88544e8	+	9.32294e8i	0.764390	+	1.45869i
$160$	6.39977e7	−	3.62949e8i	0.0976528	−	0.553816i
$161$		−	1.06242e9i		−	1.58121i
$162$	2.61222e7	+	1.39281e8i	0.0379271	+	0.202224i
$163$	1.04960e9			1.48687			0.743437	−	0.668806i	$-0.233194\pi$
$163$	1.04960e9			1.48687			0.743437	+	0.668806i	$0.233194\pi$
$164$	−9.37194e8	−	1.65253e8i	−1.29555	−	0.228440i
$165$	−7.68977e8	+	4.02962e8i	−1.03748	+	0.543662i
$166$	1.43691e8	+	5.22992e7i	0.189233	+	0.0688752i
$167$	−1.58207e8	−	1.88544e8i	−0.203404	−	0.242407i	0.654693	−	0.755895i	$-0.272798\pi$
$167$	−1.58207e8	−	1.88544e8i	−0.203404	−	0.242407i	−0.858097	+	0.513487i	$0.828353\pi$
$168$	5.23375e8	−	1.66583e8i	0.657015	−	0.209120i
$169$	7.42246e8	−	2.70155e8i	0.909916	−	0.331182i
$170$	−4.71473e7	−	2.72205e7i	−0.0564496	−	0.0325912i
$171$	−5.20940e8	−	1.10150e9i	−0.609261	−	1.28825i
$172$	1.91503e8	+	3.31693e8i	0.218808	+	0.378986i
$173$	−2.45942e8	+	2.93102e8i	−0.274567	+	0.327216i	−0.885653	−	0.464348i	$-0.846289\pi$
$173$	−2.45942e8	+	2.93102e8i	−0.274567	+	0.327216i	0.611086	+	0.791564i	$0.290733\pi$
$174$	−6.28886e7	+	8.45326e6i	−0.0686081	+	0.00922205i
$175$	1.91929e7	+	1.08848e8i	0.0204639	+	0.116056i
$176$	1.00337e9	−	1.76921e8i	1.04571	−	0.184387i
$177$	1.61154e9	+	6.62401e8i	1.64191	+	0.674882i
$178$	1.04867e7	+	8.79935e6i	0.0104462	+	0.00876538i
$179$	−1.76049e8	+	1.01642e8i	−0.171483	+	0.0990057i	−0.583285	−	0.812268i	$-0.698233\pi$
$179$	−1.76049e8	+	1.01642e8i	−0.171483	+	0.0990057i	0.411802	+	0.911273i	$0.364900\pi$
$180$	−9.38393e8	−	2.45987e8i	−0.893912	−	0.234327i
$181$	3.05406e8	−	5.28979e8i	0.284553	−	0.492861i	−0.687948	−	0.725760i	$-0.741488\pi$
$181$	3.05406e8	−	5.28979e8i	0.284553	−	0.492861i	0.972501	+	0.232900i	$0.0748214\pi$
$182$	−2.35275e7	−	6.46413e7i	−0.0214432	−	0.0589148i
$183$	−8.11304e8	+	8.90225e8i	−0.723402	+	0.793772i
$184$	−3.26695e8	+	2.74130e8i	−0.285017	+	0.239158i
$185$	−3.21383e8	+	8.82992e8i	−0.274369	+	0.753824i
$186$	−1.75363e8	−	7.17939e6i	−0.146516	−	0.00599841i
$187$	8.46195e7	−	4.79901e8i	0.0691997	−	0.392451i
$188$		−	2.91852e8i		−	0.233632i
$189$	−4.90112e8	−	2.12853e9i	−0.384104	−	1.66814i
$190$	−3.68720e8			−0.282932
$191$	1.58410e8	+	2.79319e7i	0.119028	+	0.0209878i	0.232845	−	0.972514i	$-0.425197\pi$
$191$	1.58410e8	+	2.79319e7i	0.119028	+	0.0209878i	−0.113817	+	0.993502i	$0.536308\pi$
$192$	8.66693e8	+	5.48841e8i	0.637764	+	0.403870i
$193$	−1.24511e8	−	4.53181e7i	−0.0897381	−	0.0326620i	0.296761	−	0.954952i	$-0.404094\pi$
$193$	−1.24511e8	−	4.53181e7i	−0.0897381	−	0.0326620i	−0.386499	+	0.922290i	$0.626316\pi$
$194$	2.99911e8	+	3.57420e8i	0.211731	+	0.252332i
$195$	−5.30982e7	+	2.42627e8i	−0.0367232	+	0.167803i
$196$	−2.56351e9	+	9.33042e8i	−1.73705	+	0.632233i
$197$	−5.26529e7	−	3.03991e7i	−0.0349588	−	0.0201835i	0.482419	−	0.875941i	$-0.339758\pi$
$197$	−5.26529e7	−	3.03991e7i	−0.0349588	−	0.0201835i	−0.517378	+	0.855757i	$0.673092\pi$
$198$	3.55306e7	+	3.82195e8i	0.0231175	+	0.248671i
$199$	−3.16579e8	−	5.48332e8i	−0.201869	−	0.349648i	0.747261	−	0.664530i	$-0.231368\pi$
$199$	−3.16579e8	−	5.48332e8i	−0.201869	−	0.349648i	−0.949131	+	0.314882i	$0.898035\pi$
$200$	2.85188e7	−	3.39874e7i	0.0178243	−	0.0212421i
$201$	3.02568e8	+	3.92105e8i	0.185370	+	0.240225i
$202$	−6.80292e7	−	3.85813e8i	−0.0408592	−	0.231724i
$203$	9.63188e8	−	1.69836e8i	0.567188	−	0.100011i
$204$	4.31096e8	−	3.32656e8i	0.248916	−	0.192077i
$205$	1.79336e9	+	1.50481e9i	1.01544	+	0.852053i
$206$	1.03316e8	−	5.96496e7i	0.0573719	−	0.0331237i
$207$	9.80306e8	+	1.38396e9i	0.533925	+	0.753776i
$208$	1.45739e8	−	2.52428e8i	0.0778616	−	0.134860i
$209$	−1.12881e9	−	3.10139e9i	−0.591612	−	1.62544i
$210$	−6.45685e8	−	1.41306e8i	−0.332004	−	0.0726581i
$211$	−1.27463e9	+	1.06955e9i	−0.643067	+	0.539597i	−0.904958	−	0.425500i	$-0.860098\pi$
$211$	−1.27463e9	+	1.06955e9i	−0.643067	+	0.539597i	0.261892	+	0.965097i	$0.415654\pi$
$212$	−1.08958e9	+	2.99361e9i	−0.539408	+	1.48201i
$213$	−1.53819e9	+	2.42901e9i	−0.747296	+	1.18008i
$214$	−1.06698e8	+	6.05112e8i	−0.0508745	+	0.288523i
$215$		−	9.42199e8i		−	0.440950i
$216$	−5.28068e8	+	6.99926e8i	−0.242591	+	0.321542i
$217$	2.70520e9			1.22000
$218$	−3.42372e8	−	6.03695e7i	−0.151591	−	0.0267295i
$219$	−4.57194e7	+	1.11673e9i	−0.0198758	+	0.485482i
$220$	−2.46920e9	−	8.98715e8i	−1.05406	−	0.383646i
$221$	−8.96116e7	−	1.06795e8i	−0.0375660	−	0.0447695i
$222$	3.07067e8	+	2.79844e8i	0.126421	+	0.115214i
$223$	−9.28099e7	+	3.37800e7i	−0.0375297	+	0.0136597i	−0.360717	−	0.932675i	$-0.617468\pi$
$223$	−9.28099e7	+	3.37800e7i	−0.0375297	+	0.0136597i	0.323187	+	0.946335i	$0.395246\pi$
$224$	2.17509e9	+	1.25579e9i	0.863943	+	0.498798i
$225$	−1.25437e8	−	1.24082e8i	−0.0489437	−	0.0484149i
$226$	−4.80607e8	−	8.32436e8i	−0.184228	−	0.319093i
$227$	−2.09551e9	+	2.49733e9i	−0.789198	+	0.940529i	−0.999310	−	0.0371480i	$-0.988173\pi$
$227$	−2.09551e9	+	2.49733e9i	−0.789198	+	0.940529i	0.210112	+	0.977677i	$0.432617\pi$
$228$	1.40206e9	−	3.41105e9i	0.518833	−	1.26226i
$229$	−2.35578e8	−	1.33603e9i	−0.0856630	−	0.485819i	−0.997212	−	0.0746264i	$-0.976224\pi$
$229$	−2.35578e8	−	1.33603e9i	−0.0856630	−	0.485819i	0.911549	−	0.411192i	$-0.134888\pi$
$230$	5.05420e8	−	8.91192e7i	0.180610	−	0.0318464i
$231$	−7.88165e8	−	5.86360e9i	−0.276802	−	2.05929i
$232$	−3.00752e8	−	2.52361e8i	−0.103814	−	0.0871104i
$233$	6.27753e8	−	3.62433e8i	0.212993	−	0.122972i	−0.389709	−	0.920938i	$-0.627424\pi$
$233$	6.27753e8	−	3.62433e8i	0.212993	−	0.122972i	0.602702	+	0.797967i	$0.294091\pi$
$234$	9.02936e7	+	6.24962e7i	0.0301158	+	0.0208444i
$235$	−3.58980e8	+	6.21771e8i	−0.117706	+	0.203873i
$236$	1.80369e9	+	4.95559e9i	0.581451	+	1.59752i
$237$	−1.09827e9	−	3.45055e9i	−0.348108	−	1.09369i
$238$	2.84206e8	−	2.38477e8i	0.0885778	−	0.0743256i
$239$	7.45604e8	−	2.04853e9i	0.228516	−	0.627842i	−0.771448	−	0.636292i	$-0.780467\pi$
$239$	7.45604e8	−	2.04853e9i	0.228516	−	0.627842i	0.999964	+	0.00844956i	$0.00268961\pi$
$240$	−1.29995e9	−	2.48070e9i	−0.391814	−	0.747704i
$241$	−2.83147e8	+	1.60581e9i	−0.0839352	+	0.476020i	0.913646	+	0.406511i	$0.133255\pi$
$241$	−2.83147e8	+	1.60581e9i	−0.0839352	+	0.476020i	−0.997581	+	0.0695097i	$0.977857\pi$
$242$			3.34032e8i			0.0973927i
$243$	2.60248e9	+	2.32051e9i	0.746383	+	0.665517i
$244$	−3.64553e9			−1.02849
$245$	6.60903e9	+	1.16535e9i	1.83431	+	0.323439i
$246$	9.16813e8	−	4.80432e8i	0.250346	−	0.131187i
$247$	−8.87265e8	−	3.22938e8i	−0.238378	−	0.0867623i
$248$	−6.98010e8	−	8.31856e8i	−0.184525	−	0.219908i
$249$	3.58521e9	−	1.14113e9i	0.932648	−	0.296850i
$250$	−7.78952e8	+	2.83515e8i	−0.199412	+	0.0725799i
$251$	−5.80211e8	−	3.34985e8i	−0.146181	−	0.0843977i	0.425126	−	0.905134i	$-0.360230\pi$
$251$	−5.80211e8	−	3.34985e8i	−0.146181	−	0.0843977i	−0.571307	+	0.820737i	$0.693563\pi$
$252$	3.76245e9	−	5.43594e9i	0.932972	−	1.34795i
$253$	2.29692e9	+	3.97838e9i	0.560613	+	0.971010i
$254$	−6.13446e8	+	7.31077e8i	−0.147381	+	0.175642i
$255$	−1.32759e9	+	1.78450e8i	−0.313981	+	0.0422042i
$256$	4.49743e8	+	2.55062e9i	0.104714	+	0.593862i
$257$	3.70746e9	−	6.53725e8i	0.849853	−	0.149852i	0.268275	−	0.963343i	$-0.413547\pi$
$257$	3.70746e9	−	6.53725e8i	0.849853	−	0.149852i	0.581578	+	0.813491i	$0.302435\pi$
$258$	−3.85299e8	−	1.58371e8i	−0.0869599	−	0.0357436i
$259$	−4.90543e9	−	4.11615e9i	−1.09013	−	0.914728i
$260$	−6.51025e8	+	3.75869e8i	−0.142464	+	0.0822514i
$261$	−1.09799e9	+	1.10999e9i	−0.236612	+	0.239197i
$262$	−2.47473e8	+	4.28636e8i	−0.0525198	+	0.0909670i
$263$	−8.27508e8	−	2.27356e9i	−0.172961	−	0.475207i	0.822676	−	0.568510i	$-0.192480\pi$
$263$	−8.27508e8	−	2.27356e9i	−0.172961	−	0.475207i	−0.995638	+	0.0933024i	$0.970258\pi$
$264$	−1.59971e9	+	1.75532e9i	−0.329325	+	0.361360i
$265$	6.00344e9	−	5.03748e9i	1.21735	−	1.02148i
$266$	8.59411e8	−	2.36121e9i	0.171662	−	0.471638i
$267$	3.36547e8	+	1.37783e7i	0.0662217	+	0.00271113i
$268$	−2.60305e8	+	1.47626e9i	−0.0504596	+	0.286171i
$269$		−	2.83899e9i		−	0.542195i	−0.962552	−	0.271097i	$-0.912613\pi$
$269$		−	2.83899e9i		−	0.542195i	0.962552	−	0.271097i	$-0.0873865\pi$
$270$	9.71490e8	−	4.11709e8i	0.182803	−	0.0774703i
$271$	−4.82586e9			−0.894741			−0.447370	−	0.894349i	$-0.647639\pi$
$271$	−4.82586e9			−0.894741			−0.447370	+	0.894349i	$0.647639\pi$
$272$	1.54815e9	+	2.72980e8i	0.282837	+	0.0498719i
$273$	−1.42997e9	−	9.05544e8i	−0.257441	−	0.163027i
$274$	2.04009e9	+	7.42532e8i	0.361949	+	0.131739i
$275$	−3.07198e8	−	3.66104e8i	−0.0537139	−	0.0640138i
$276$	−1.09742e9	+	5.01455e9i	−0.189119	+	0.864162i
$277$	1.86396e9	−	6.78426e8i	0.316605	−	0.115235i	−0.178830	−	0.983880i	$-0.557231\pi$
$277$	1.86396e9	−	6.78426e8i	0.316605	−	0.115235i	0.495434	+	0.868645i	$0.335009\pi$
$278$	1.49015e9	+	8.60339e8i	0.249489	+	0.144043i
$279$	−3.52395e9	+	2.49613e9i	−0.581584	+	0.411956i
$280$	−2.04476e9	−	3.54163e9i	−0.332668	−	0.576198i
$281$	−7.81636e8	+	9.31518e8i	−0.125366	+	0.149405i	−0.825076	−	0.565021i	$-0.808868\pi$
$281$	−7.81636e8	+	9.31518e8i	−0.125366	+	0.149405i	0.699710	+	0.714427i	$0.253312\pi$
$282$	1.93925e8	+	2.51311e8i	0.0306645	+	0.0397389i
$283$	1.67891e9	+	9.52155e9i	0.261746	+	1.48444i	0.778143	+	0.628087i	$0.216162\pi$
$283$	1.67891e9	+	9.52155e9i	0.261746	+	1.48444i	−0.516396	+	0.856350i	$0.672727\pi$
$284$	−8.56983e9	+	1.51109e9i	−1.31734	+	0.232283i
$285$	−7.18260e9	+	5.54246e9i	−1.08868	+	0.840084i
$286$	2.27855e8	+	1.91193e8i	0.0340561	+	0.0285764i
$287$	−1.38165e10	+	7.97695e9i	−2.03643	+	1.17573i
$288$	−3.99213e9	+	3.71126e8i	−0.580276	+	0.0539451i
$289$	−3.11194e9	+	5.39003e9i	−0.446107	+	0.772680i
$290$	1.61591e8	+	4.43969e8i	0.0228469	+	0.0627712i
$291$	1.12148e10	+	2.45433e9i	1.56394	+	0.342264i
$292$	−2.59141e9	+	2.17445e9i	−0.356456	+	0.299102i
$293$	1.75048e8	−	4.80940e8i	0.0237512	−	0.0652560i	−0.927250	−	0.374442i	$-0.877834\pi$
$293$	1.75048e8	−	4.80940e8i	0.0237512	−	0.0652560i	0.951002	+	0.309186i	$0.100057\pi$
$294$	1.58745e9	−	2.50679e9i	0.212476	−	0.335528i
$295$	2.25277e9	−	1.27761e10i	0.297460	−	1.68698i
$296$			2.57050e9i			0.334850i
$297$	6.43714e9	+	6.91101e9i	0.827308	+	0.888210i
$298$	1.72223e9			0.218387
$299$	1.29427e9	+	2.28214e8i	0.161934	+	0.0285534i
$300$	2.18450e7	−	5.33583e8i	0.00269692	−	0.0658744i
$301$	6.03366e9	+	2.19607e9i	0.735047	+	0.267535i
$302$	−1.42494e9	−	1.69818e9i	−0.171305	−	0.204153i
$303$	−7.12458e9	−	6.49297e9i	−0.845257	−	0.770323i
$304$	1.00050e10	−	3.64152e9i	1.17145	−	0.426372i
$305$	7.76655e9	+	4.48402e9i	0.897488	+	0.518165i
$306$	−1.50176e8	+	5.72894e8i	−0.0171283	+	0.0653414i
$307$	3.72843e8	+	6.45783e8i	0.0419733	+	0.0726998i	0.886249	−	0.463209i	$-0.153302\pi$
$307$	3.72843e8	+	6.45783e8i	0.0419733	+	0.0726998i	−0.844276	+	0.535909i	$0.819969\pi$
$308$	1.15104e10	−	1.37175e10i	1.27905	−	1.52431i
$309$	1.11595e9	−	2.71497e9i	0.122408	−	0.297805i
$310$	2.26922e8	+	1.28694e9i	0.0245714	+	0.139351i
$311$	−1.43070e10	+	2.52271e9i	−1.52935	+	0.269666i	−0.874101	−	0.485745i	$-0.838548\pi$
$311$	−1.43070e10	+	2.52271e9i	−1.52935	+	0.269666i	−0.655252	+	0.755411i	$0.727437\pi$
$312$	9.05124e7	+	6.73373e8i	0.00955190	+	0.0710620i
$313$	−4.83723e9	−	4.05892e9i	−0.503988	−	0.422896i	0.355020	−	0.934859i	$-0.384474\pi$
$313$	−4.83723e9	−	4.05892e9i	−0.503988	−	0.422896i	−0.859008	+	0.511963i	$0.828919\pi$
$314$	−1.66113e9	+	9.59056e8i	−0.170878	+	0.0986565i
$315$	−1.47019e10	+	6.95307e9i	−1.49324	+	0.706210i
$316$	5.48002e9	−	9.49168e9i	0.549584	−	0.951907i
$317$	−3.91673e9	−	1.07611e10i	−0.387870	−	1.06566i	−0.967958	−	0.251110i	$-0.919204\pi$
$317$	−3.91673e9	−	1.07611e10i	−0.387870	−	1.06566i	0.580089	−	0.814553i	$-0.303018\pi$
$318$	−1.05091e9	−	3.30176e9i	−0.102767	−	0.322877i
$319$	−3.23962e9	+	2.71837e9i	−0.312847	+	0.262510i
$320$	2.61243e9	−	7.17759e9i	0.249141	−	0.684509i
$321$	7.01737e9	+	1.33913e10i	0.660928	+	1.26126i
$322$	−6.07329e8	+	3.44433e9i	−0.0564937	+	0.320392i
$323$		−	5.09239e9i		−	0.467856i
$324$	1.14643e8	+	1.05528e10i	0.0104032	+	0.957611i
$325$	−1.36725e8			−0.0122550
$326$	−3.40279e9	−	6.00004e8i	−0.301276	−	0.0531232i
$327$	−7.57680e9	+	3.97042e9i	−0.662666	+	0.347253i
$328$	6.01793e9	+	2.19035e9i	0.519938	+	0.189242i
$329$	−3.14499e9	−	3.74806e9i	−0.268433	−	0.319906i
$330$	2.72336e9	−	8.66812e8i	0.229641	−	0.0730919i
$331$	1.41536e10	−	5.15148e9i	1.17911	−	0.429161i	0.323223	−	0.946323i	$-0.395234\pi$
$331$	1.41536e10	−	5.15148e9i	1.17911	−	0.429161i	0.855888	+	0.517162i	$0.173011\pi$
$332$	9.86210e9	+	5.69389e9i	0.811740	+	0.468658i
$333$	1.01881e10	+	8.35609e8i	0.828547	+	0.0679557i
$334$	4.05123e8	+	7.01694e8i	0.0325538	+	0.0563848i
$335$	2.37038e9	−	2.82490e9i	0.188208	−	0.224297i
$336$	1.89158e10	−	2.54260e9i	1.48412	−	0.199490i
$337$	−9.05604e8	−	5.13594e9i	−0.0702132	−	0.398199i	−0.999578	−	0.0290371i	$-0.990756\pi$
$337$	−9.05604e8	−	5.13594e9i	−0.0702132	−	0.398199i	0.929365	−	0.369162i	$-0.120355\pi$
$338$	−2.56078e9	+	4.51535e8i	−0.196203	+	0.0345959i
$339$	−2.18750e10	−	8.99140e9i	−1.65634	−	0.680814i
$340$	−3.10581e9	−	2.60609e9i	−0.232413	−	0.195017i
$341$	−1.01300e10	+	5.84858e9i	−0.749193	+	0.432547i
$342$	1.05921e9	+	3.86884e9i	0.0774242	+	0.282798i
$343$	−1.10203e10	+	1.90877e10i	−0.796188	+	1.37904i
$344$	−8.81538e8	−	2.42201e9i	−0.0629517	−	0.172958i
$345$	8.50589e9	−	9.33331e9i	0.600404	−	0.658809i
$346$	9.64890e8	−	8.09639e8i	0.0673246	−	0.0564920i
$347$	5.88556e9	−	1.61705e10i	0.405948	−	1.11533i	−0.553353	−	0.832947i	$-0.686652\pi$
$347$	5.88556e9	−	1.61705e10i	0.405948	−	1.11533i	0.959301	−	0.282386i	$-0.0911257\pi$
$348$	−4.72163e9	−	1.93305e8i	−0.321940	−	0.0131803i
$349$	1.33644e9	−	7.57932e9i	0.0900840	−	0.510891i	−0.906059	−	0.423151i	$-0.860924\pi$
$349$	1.33644e9	−	7.57932e9i	0.0900840	−	0.510891i	0.996143	−	0.0877409i	$-0.0279648\pi$
$350$		−	3.63855e8i		−	0.0242469i
$351$	2.69832e9	−	1.39846e8i	0.177773	−	0.00921343i
$352$	−1.08599e10			−0.707387
$353$	1.16353e10	+	2.05161e9i	0.749337	+	0.132128i	0.535259	−	0.844688i	$-0.320214\pi$
$353$	1.16353e10	+	2.05161e9i	0.749337	+	0.132128i	0.214078	+	0.976817i	$0.431325\pi$
$354$	−4.84593e9	−	3.06873e9i	−0.308578	−	0.195409i
$355$	2.01161e10	+	7.32165e9i	1.26657	+	0.460995i
$356$	6.55309e8	+	7.80966e8i	0.0407987	+	0.0486219i
$357$	1.95158e9	−	8.91755e9i	0.120147	−	0.549001i
$358$	6.28850e8	−	2.28883e8i	0.0382838	−	0.0139342i
$359$	−7.89075e9	−	4.55572e9i	−0.475051	−	0.274271i	0.243301	−	0.969951i	$-0.421770\pi$
$359$	−7.89075e9	−	4.55572e9i	−0.475051	−	0.274271i	−0.718352	+	0.695680i	$0.755103\pi$
$360$	5.93154e9	+	2.72680e9i	0.353148	+	0.162346i
$361$	−8.75319e9	−	1.51610e10i	−0.515392	−	0.892684i
$362$	−1.29251e9	+	1.54036e9i	−0.0752662	+	0.0896988i
$363$	5.02104e9	+	6.50687e9i	0.289179	+	0.374754i
$364$	−8.89589e8	−	5.04511e9i	−0.0506739	−	0.287386i
$365$	8.19542e9	−	1.44507e9i	0.461742	−	0.0814176i
$366$	3.13913e9	−	2.42231e9i	0.174938	−	0.134991i
$367$	4.80686e9	+	4.03344e9i	0.264971	+	0.222337i	0.765587	−	0.643333i	$-0.222449\pi$
$367$	4.80686e9	+	4.03344e9i	0.264971	+	0.222337i	−0.500616	+	0.865669i	$0.666893\pi$
$368$	−1.28341e10	+	7.40979e9i	−0.699802	+	0.404031i
$369$	1.06377e10	−	2.31399e10i	0.573775	−	1.24812i
$370$	1.54668e9	−	2.67893e9i	0.0825265	−	0.142940i
$371$	1.82663e10	+	5.01862e10i	0.964172	+	2.64904i
$372$	−1.27684e10	−	2.79433e9i	−0.666754	−	0.145917i
$373$	1.92922e10	−	1.61881e10i	0.996660	−	0.836297i	0.0101421	−	0.999949i	$-0.496772\pi$
$373$	1.92922e10	−	1.61881e10i	0.996660	−	0.836297i	0.986518	+	0.163651i	$0.0523272\pi$
$374$	−5.48670e8	+	1.50746e9i	−0.0280430	+	0.0770476i
$375$	−1.09121e10	+	1.72317e10i	−0.551804	+	0.871373i
$376$	−3.41049e8	+	1.93419e9i	−0.0170634	+	0.0967713i
$377$			1.20987e9i			0.0598924i
$378$	3.72162e8	+	7.18084e9i	0.0182291	+	0.351729i
$379$	−4.03794e9			−0.195705			−0.0978527	−	0.995201i	$-0.531197\pi$
$379$	−4.03794e9			−0.195705			−0.0978527	+	0.995201i	$0.531197\pi$
$380$	−2.70423e10	−	4.76828e9i	−1.29691	−	0.228680i
$381$	−9.60554e8	+	2.34623e10i	−0.0455850	+	1.11345i
$382$	−4.97594e8	−	1.81109e8i	−0.0233680	−	0.00850526i
$383$	−1.68071e10	−	2.00299e10i	−0.781082	−	0.930857i	0.217900	−	0.975971i	$-0.430079\pi$
$383$	−1.68071e10	−	2.00299e10i	−0.781082	−	0.930857i	−0.998982	+	0.0451138i	$0.985635\pi$
$384$	−1.18617e10	−	1.08101e10i	−0.545533	−	0.497171i
$385$	−4.13947e10	+	1.50665e10i	−1.88409	+	0.685754i
$386$	3.77755e8	+	2.18097e8i	0.0170161	+	0.00982427i
$387$	−9.88613e9	+	2.70662e9i	−0.440740	+	0.120666i
$388$	1.73736e10	+	3.00920e10i	0.766590	+	1.32777i
$389$	5.81049e8	−	6.92467e8i	0.0253755	−	0.0302413i	−0.753207	−	0.657783i	$-0.771494\pi$
$389$	5.81049e8	−	6.92467e8i	0.0253755	−	0.0302413i	0.778583	+	0.627542i	$0.215939\pi$
$390$	3.10841e8	−	7.56238e8i	0.0134363	−	0.0326889i
$391$	1.23083e9	+	6.98036e9i	0.0526611	+	0.298656i
$392$	1.80794e10	−	3.18789e9i	0.765668	−	0.135008i
$393$	1.62236e9	+	1.20697e10i	0.0680108	+	0.505971i
$394$	1.53322e8	+	1.28652e8i	0.00636238	+	0.00533867i
$395$	−2.33496e10	+	1.34809e10i	−0.959161	+	0.553772i
$396$	−2.33670e9	+	2.84900e10i	−0.0950214	+	1.15854i
$397$	−1.45975e10	+	2.52837e10i	−0.587648	+	1.01784i	0.406892	+	0.913476i	$0.366613\pi$
$397$	−1.45975e10	+	2.52837e10i	−0.587648	+	1.01784i	−0.994540	+	0.104360i	$0.966721\pi$
$398$	7.12892e8	+	1.95865e9i	0.0284113	+	0.0780594i
$399$	−1.87517e10	−	5.89143e10i	−0.739858	−	2.32450i
$400$	1.18104e9	−	9.91012e8i	0.0461344	−	0.0387114i
$401$	−7.29919e9	+	2.00544e10i	−0.282291	+	0.775589i	0.714797	+	0.699332i	$0.246519\pi$
$401$	−7.29919e9	+	2.00544e10i	−0.282291	+	0.775589i	−0.997088	+	0.0762567i	$0.975703\pi$
$402$	−7.56774e8	−	1.44416e9i	−0.0289776	−	0.0552982i
$403$	−5.81096e8	+	3.29556e9i	−0.0220307	+	0.124942i
$404$		−	2.91756e10i		−	1.09520i
$405$	1.27358e10	−	2.26231e10i	0.473376	−	0.840875i
$406$	−3.21973e9			−0.118499
$407$	2.72681e10	+	4.80811e9i	0.993752	+	0.175225i
$408$	−3.24573e9	+	1.70084e9i	−0.117131	+	0.0613793i
$409$	−4.86243e10	−	1.76978e10i	−1.73764	−	0.632450i	−0.738516	−	0.674236i	$-0.764473\pi$
$409$	−4.86243e10	−	1.76978e10i	−1.73764	−	0.632450i	−0.999127	+	0.0417856i	$0.986695\pi$
$410$	−4.95383e9	−	5.90375e9i	−0.175310	−	0.208926i
$411$	5.09021e10	−	1.62015e10i	1.78389	−	0.567789i
$412$	8.34869e9	−	3.03868e9i	0.289754	−	0.105462i
$413$	7.65648e10	+	4.42047e10i	2.63165	+	1.51939i
$414$	−2.38699e9	−	5.04717e9i	−0.0812550	−	0.171809i
$415$	−1.40070e10	−	2.42609e10i	−0.472229	−	0.817925i
$416$	−1.99706e9	+	2.38001e9i	−0.0666835	+	0.0794703i
$417$	4.19602e10	−	5.64013e9i	1.38769	−	0.186529i
$418$	1.88669e9	+	1.06999e10i	0.0618009	+	0.350490i
$419$	3.61100e10	−	6.36717e9i	1.17158	−	0.206581i	0.446202	−	0.894932i	$-0.352776\pi$
$419$	3.61100e10	−	6.36717e9i	1.17158	−	0.206581i	0.725378	+	0.688351i	$0.241665\pi$
$420$	−4.55278e10	−	1.87135e10i	−1.46312	−	0.601393i
$421$	−6.06361e9	−	5.08797e9i	−0.193020	−	0.161963i	0.541156	−	0.840922i	$-0.317987\pi$
$421$	−6.06361e9	−	5.08797e9i	−0.193020	−	0.161963i	−0.734176	+	0.678959i	$0.762431\pi$
$422$	4.74375e9	−	2.73881e9i	0.149579	−	0.0863597i
$423$	7.55523e9	+	1.98050e9i	0.235986	+	0.0618604i
$424$	1.07192e10	−	1.85662e10i	0.331665	−	0.574460i
$425$	−2.52205e8	−	6.92927e8i	−0.00773032	−	0.0212389i
$426$	6.37534e9	−	6.99551e9i	0.193582	−	0.212413i
$427$	−4.68170e10	+	3.92841e10i	−1.40829	+	1.18170i
$428$	−1.56506e10	+	4.29997e10i	−0.466398	+	1.28142i
$429$	7.31252e9	+	2.99376e8i	0.215893	+	0.00883870i
$430$	−5.38607e8	+	3.05459e9i	−0.0157543	+	0.0893469i
$431$		−	5.13707e10i		−	1.48870i	−0.667791	−	0.744349i	$-0.732760\pi$
$431$		−	5.13707e10i		−	1.48870i	0.667791	−	0.744349i	$-0.267240\pi$
$432$	−2.22947e10	+	2.07660e10i	−0.640129	+	0.596237i
$433$	−1.87525e9			−0.0533468			−0.0266734	−	0.999644i	$-0.508491\pi$
$433$	−1.87525e9			−0.0533468			−0.0266734	+	0.999644i	$0.508491\pi$
$434$	−8.77022e9	−	1.54643e9i	−0.247202	−	0.0435884i
$435$	9.82134e9	+	6.21945e9i	0.274292	+	0.173698i
$436$	−2.43292e10	−	8.85511e9i	−0.673259	−	0.245046i
$437$	3.08578e10	+	3.67748e10i	0.846133	+	1.00838i
$438$	7.86601e8	−	3.59430e9i	0.0213726	−	0.0976602i
$439$	−1.43069e10	+	5.20730e9i	−0.385202	+	0.140202i	−0.527360	−	0.849642i	$-0.676818\pi$
$439$	−1.43069e10	+	5.20730e9i	−0.385202	+	0.140202i	0.142158	+	0.989844i	$0.454596\pi$
$440$	1.53139e10	+	8.84146e9i	0.408577	+	0.235892i
$441$	−6.75793e9	−	7.26937e10i	−0.178673	−	1.92195i
$442$	2.29470e8	+	3.97454e8i	0.00601225	+	0.0104135i
$443$	2.80078e10	−	3.33784e10i	0.727217	−	0.866663i	−0.268094	−	0.963393i	$-0.586394\pi$
$443$	2.80078e10	−	3.33784e10i	0.727217	−	0.866663i	0.995311	+	0.0967298i	$0.0308383\pi$
$444$	1.89016e10	+	2.44950e10i	0.486371	+	0.630299i
$445$	−4.35497e8	−	2.46983e9i	−0.0111057	−	0.0629835i
$446$	3.20198e8	−	5.64596e7i	0.00809245	−	0.00142692i
$447$	3.35488e10	−	2.58880e10i	0.840324	−	0.648437i
$448$	3.98749e10	+	3.34590e10i	0.989891	+	0.830617i
$449$	−4.37682e10	+	2.52696e10i	−1.07690	+	0.621746i	−0.930057	−	0.367415i	$-0.880243\pi$
$449$	−4.37682e10	+	2.52696e10i	−1.07690	+	0.621746i	−0.146838	+	0.989161i	$0.546910\pi$
$450$	3.35735e8	+	4.73978e8i	0.00818740	+	0.0115587i
$451$	3.44920e10	−	5.97418e10i	0.833703	−	1.44402i
$452$	−2.44832e10	−	6.72669e10i	−0.586562	−	1.61156i
$453$	−5.32840e10	−	1.16610e10i	−1.26533	−	0.276914i
$454$	8.22120e9	−	6.89840e9i	0.193514	−	0.162377i
$455$	−4.31030e9	+	1.18425e10i	−0.100569	+	0.276310i
$456$	−1.32779e10	+	2.09675e10i	−0.307093	+	0.484940i
$457$	6.63960e9	−	3.76550e10i	0.152222	−	0.863293i	−0.809060	−	0.587726i	$-0.800023\pi$
$457$	6.63960e9	−	3.76550e10i	0.152222	−	0.863293i	0.961282	−	0.275567i	$-0.0888656\pi$
$458$			4.46605e9i			0.101499i
$459$	5.68612e9	+	1.34173e10i	0.128105	+	0.302282i
$460$	3.82205e10			0.853621
$461$	−5.77035e10	−	1.01747e10i	−1.27761	−	0.225277i	−0.506646	−	0.862154i	$-0.669115\pi$
$461$	−5.77035e10	−	1.01747e10i	−1.27761	−	0.225277i	−0.770965	+	0.636877i	$0.780226\pi$
$462$	−7.96708e8	+	1.94603e10i	−0.0174876	+	0.427150i
$463$	6.30183e10	+	2.29368e10i	1.37133	+	0.499124i	0.919539	−	0.392999i	$-0.128562\pi$
$463$	6.30183e10	+	2.29368e10i	1.37133	+	0.499124i	0.451793	+	0.892123i	$0.350785\pi$
$464$	−8.76938e9	−	1.04509e10i	−0.189190	−	0.225467i
$465$	2.37652e10	+	2.16583e10i	0.508311	+	0.463248i
$466$	−2.24235e9	+	8.16148e8i	−0.0475510	+	0.0173071i
$467$	−7.50725e9	−	4.33431e9i	−0.157839	−	0.0911281i	0.419000	−	0.907986i	$-0.362381\pi$
$467$	−7.50725e9	−	4.33431e9i	−0.157839	−	0.0911281i	−0.576839	+	0.816858i	$0.695714\pi$
$468$	5.81402e9	+	5.75121e9i	0.121197	+	0.119888i
$469$	1.25653e10	+	2.17637e10i	0.259705	+	0.449823i
$470$	1.51924e9	−	1.81056e9i	0.0311340	−	0.0371041i
$471$	−1.79424e10	+	4.36518e10i	−0.364584	+	0.886989i
$472$	−6.16259e9	−	3.49498e10i	−0.124164	−	0.704168i
$473$	−2.73418e10	+	4.82110e9i	−0.546239	+	0.0963167i
$474$	1.58806e9	+	1.18145e10i	0.0314596	+	0.234046i
$475$	−3.82583e9	−	3.21026e9i	−0.0751539	−	0.0630616i
$476$	2.39279e10	−	1.38148e10i	0.466097	−	0.269101i
$477$	−7.01022e10	−	4.85208e10i	−1.35412	−	0.937247i
$478$	−3.58827e9	+	6.21507e9i	−0.0687344	+	0.119051i
$479$	1.03071e10	+	2.83185e10i	0.195792	+	0.537933i	0.998273	−	0.0587442i	$-0.0187096\pi$
$479$	1.03071e10	+	2.83185e10i	0.195792	+	0.537933i	−0.802482	+	0.596677i	$0.796487\pi$
$480$	9.05408e9	+	2.84463e10i	0.170561	+	0.535871i
$481$	6.06813e9	−	5.09176e9i	0.113364	−	0.0951235i
$482$	1.83592e9	−	5.04414e9i	0.0340146	−	0.0934543i
$483$	3.99432e10	+	7.62241e10i	0.733930	+	1.40057i
$484$	−4.31970e9	+	2.44982e10i	−0.0787176	+	0.446429i
$485$		−	8.54785e10i		−	1.54486i
$486$	−7.11067e9	−	9.01077e9i	−0.127457	−	0.161516i
$487$	2.41067e10			0.428570			0.214285	−	0.976771i	$-0.431258\pi$
$487$	2.41067e10			0.428570			0.214285	+	0.976771i	$0.431258\pi$
$488$	2.41599e10	+	4.26005e9i	0.426007	+	0.0751165i
$489$	−7.53048e10	+	3.94615e10i	−1.31700	+	0.690141i
$490$	−2.07602e10	−	7.55609e9i	−0.360120	−	0.131073i
$491$	3.30867e10	+	3.94312e10i	0.569282	+	0.678444i	0.971483	−	0.237108i	$-0.0761994\pi$
$491$	3.30867e10	+	3.94312e10i	0.569282	+	0.678444i	−0.402202	+	0.915551i	$0.631755\pi$
$492$	7.34529e10	−	2.33791e10i	1.25357	−	0.398995i
$493$	−6.13166e9	+	2.23174e9i	−0.103798	+	0.0377795i
$494$	2.69189e9	+	1.55416e9i	0.0452011	+	0.0260969i
$495$	4.00211e10	−	5.78219e10i	0.666604	−	0.963101i
$496$	−1.88674e10	−	3.26793e10i	−0.311735	−	0.539940i
$497$	−9.37729e10	+	1.11754e11i	−1.53692	+	1.83163i
$498$	−1.22755e10	+	1.65003e9i	−0.199583	+	0.0268272i
$499$	−5.22963e9	−	2.96587e10i	−0.0843468	−	0.478355i	−0.997496	−	0.0707282i	$-0.977468\pi$
$499$	−5.22963e9	−	2.96587e10i	−0.0843468	−	0.478355i	0.913149	−	0.407626i	$-0.133643\pi$
$500$	−6.07955e10	+	1.07199e10i	−0.972728	+	0.171518i
$501$	1.84393e10	+	7.57921e9i	0.292681	+	0.120302i
$502$	1.68954e9	+	1.41769e9i	0.0266044	+	0.0223238i
$503$	−1.24574e10	+	7.19230e9i	−0.194606	+	0.112356i	−0.594137	−	0.804364i	$-0.702506\pi$
$503$	−1.24574e10	+	7.19230e9i	−0.194606	+	0.112356i	0.399531	+	0.916720i	$0.369173\pi$
$504$	−3.12871e10	+	3.16288e10i	−0.484890	+	0.490186i
$505$	−3.58862e10	+	6.21567e10i	−0.551774	+	0.955701i
$506$	−5.17233e9	−	1.42109e10i	−0.0789013	−	0.216779i
$507$	−4.30963e10	+	4.72885e10i	−0.652241	+	0.715688i
$508$	−5.44450e10	+	4.56848e10i	−0.817529	+	0.685989i
$509$	2.93880e10	−	8.07429e10i	0.437824	−	1.20291i	−0.503081	−	0.864239i	$-0.667800\pi$
$509$	2.93880e10	−	8.07429e10i	0.437824	−	1.20291i	0.940905	−	0.338671i	$-0.109977\pi$
$510$	4.40603e9	+	1.80384e8i	0.0651279	+	0.00266635i
$511$	−9.84787e9	+	5.58500e10i	−0.144430	+	0.819105i
$512$		−	5.92477e10i		−	0.862168i
$513$	7.87880e10	+	5.94426e10i	1.13760	+	0.858279i
$514$	−1.23932e10			−0.177554
$515$	−2.15239e10	−	3.79524e9i	−0.305979	−	0.0539524i
$516$	−2.62101e10	−	1.65978e10i	−0.369718	−	0.234127i
$517$	1.98801e10	+	7.23577e9i	0.278264	+	0.101280i
$518$	1.35503e10	+	1.61487e10i	0.188205	+	0.224294i
$519$	6.62570e9	−	3.02755e10i	0.0913192	−	0.417274i
$520$	4.75375e9	−	1.73022e9i	0.0650164	−	0.0236640i
$521$	3.91268e8	+	2.25899e8i	0.00531036	+	0.00306594i	0.502653	−	0.864488i	$-0.332357\pi$
$521$	3.91268e8	+	2.25899e8i	0.00531036	+	0.00306594i	−0.497342	+	0.867554i	$0.665691\pi$
$522$	4.19420e9	−	2.97089e9i	0.0564894	−	0.0400133i
$523$	3.63173e10	+	6.29034e10i	0.485408	+	0.840751i	0.999859	−	0.0167684i	$-0.00533780\pi$
$523$	3.63173e10	+	6.29034e10i	0.485408	+	0.840751i	−0.514452	+	0.857519i	$0.672004\pi$
$524$	−2.36931e10	+	2.82363e10i	−0.314265	+	0.374526i
$525$	−5.46933e9	−	7.08783e9i	−0.0719942	−	0.0932989i
$526$	1.38309e9	+	7.84388e9i	0.0180679	+	0.102468i
$527$	−1.77739e10	+	3.13402e9i	−0.230431	+	0.0406312i
$528$	−6.53362e10	+	5.04167e10i	−0.840656	+	0.648693i
$529$	8.80320e9	+	7.38676e9i	0.112413	+	0.0943260i
$530$	−2.23427e10	+	1.28996e10i	−0.283160	+	0.163483i
$531$	−1.40526e11	+	1.30639e10i	−1.76758	+	0.164322i
$532$	9.35652e10	−	1.62060e11i	1.16807	−	2.02315i
$533$	−6.74988e9	−	1.85451e10i	−0.0836349	−	0.229785i
$534$	−1.08320e9	−	2.37056e8i	−0.0133212	−	0.00291531i
$535$	8.62324e10	−	7.23576e10i	1.05258	−	0.883220i
$536$	3.45023e9	−	9.47943e9i	0.0418012	−	0.114848i
$537$	8.80941e9	−	1.39112e10i	0.105937	−	0.167289i
$538$	−1.62291e9	+	9.20397e9i	−0.0193716	+	0.109862i
$539$		−	1.97751e11i		−	2.34296i
$540$	7.65742e10	−	1.76318e10i	0.900550	−	0.207359i
$541$	1.03907e11			1.21298			0.606491	−	0.795091i	$-0.292577\pi$
$541$	1.03907e11			1.21298			0.606491	+	0.795091i	$0.292577\pi$
$542$	1.56453e10	+	2.75870e9i	0.181296	+	0.0319674i
$543$	−2.02386e9	+	4.94344e10i	−0.0232799	+	0.568630i
$544$	−1.57458e10	−	5.73100e9i	−0.179791	−	0.0654387i
$545$	4.09399e10	+	4.87902e10i	0.464045	+	0.553028i
$546$	4.11830e9	+	3.75320e9i	0.0463391	+	0.0422310i
$547$	2.07308e10	−	7.54538e9i	0.231561	−	0.0842814i	−0.223633	−	0.974673i	$-0.571792\pi$
$547$	2.07308e10	−	7.54538e9i	0.231561	−	0.0842814i	0.455195	+	0.890392i	$0.349570\pi$
$548$	1.40020e11	+	8.08405e10i	1.55263	+	0.896410i
$549$	2.47384e10	−	9.43724e10i	0.272322	−	1.03886i
$550$	7.86646e8	+	1.36251e9i	0.00859664	+	0.0148898i
$551$	−2.84073e10	+	3.38545e10i	−0.308193	+	0.367291i
$552$	1.31327e10	−	3.19504e10i	0.141449	−	0.344128i
$553$	−3.19060e10	−	1.80948e11i	−0.341170	−	1.93487i
$554$	−6.43075e9	+	1.13391e9i	−0.0682688	+	0.0120376i
$555$	−1.01396e10	−	7.54341e10i	−0.106868	−	0.795052i
$556$	9.81633e10	+	8.23688e10i	1.02719	+	0.861913i
$557$	−1.00807e11	+	5.82008e10i	−1.04729	+	0.604656i	−0.921891	−	0.387450i	$-0.873356\pi$
$557$	−1.00807e11	+	5.82008e10i	−1.04729	+	0.604656i	−0.125404	+	0.992106i	$0.540023\pi$
$558$	1.28515e10	−	6.07795e9i	0.132561	−	0.0626932i
$559$	−3.97139e9	+	6.87865e9i	−0.0406720	+	0.0704459i
$560$	−4.86040e10	−	1.33538e11i	−0.494219	−	1.35786i
$561$	1.19715e10	+	3.76124e10i	0.120864	+	0.379734i
$562$	3.06655e9	−	2.57314e9i	0.0307401	−	0.0257940i
$563$	−1.04359e10	+	2.86725e10i	−0.103872	+	0.285386i	−0.980731	−	0.195361i	$-0.937412\pi$
$563$	−1.04359e10	+	2.86725e10i	−0.103872	+	0.285386i	0.876860	+	0.480747i	$0.159634\pi$
$564$	1.09727e10	+	2.09392e10i	0.108442	+	0.206940i
$565$	−3.05790e10	+	1.73422e11i	−0.300074	+	1.70181i
$566$		−	3.18284e10i		−	0.310134i
$567$	1.15189e11	+	1.34287e11i	1.11450	+	1.29928i
$568$	5.85604e10			0.562615
$569$	−7.50849e10	−	1.32395e10i	−0.716314	−	0.126305i	−0.196400	−	0.980524i	$-0.562925\pi$
$569$	−7.50849e10	−	1.32395e10i	−0.716314	−	0.126305i	−0.519914	+	0.854219i	$0.674036\pi$
$570$	2.64542e10	−	1.38626e10i	0.250608	−	0.131325i
$571$	−1.53807e11	−	5.59810e10i	−1.44687	−	0.526619i	−0.505157	−	0.863027i	$-0.668566\pi$
$571$	−1.53807e11	−	5.59810e10i	−1.44687	−	0.526619i	−0.941716	+	0.336408i	$0.890788\pi$
$572$	1.42386e10	+	1.69689e10i	0.133010	+	0.158515i
$573$	−1.24154e10	+	3.95166e9i	−0.115171	+	0.0366574i
$574$	4.93528e10	−	1.79630e10i	0.454637	−	0.165474i
$575$	6.02015e9	+	3.47573e9i	0.0550726	+	0.0317962i
$576$	−8.28163e10	−	6.79243e9i	−0.752360	−	0.0617071i
$577$	−3.03217e10	−	5.25187e10i	−0.273559	−	0.473818i	0.696212	−	0.717836i	$-0.254867\pi$
$577$	−3.03217e10	−	5.25187e10i	−0.273559	−	0.473818i	−0.969770	+	0.244019i	$0.921534\pi$
$578$	1.31701e10	−	1.56955e10i	0.117998	−	0.140625i
$579$	1.06369e10	−	1.42978e9i	0.0946461	−	0.0127220i
$580$	6.10987e9	+	3.46508e10i	0.0539909	+	0.306197i
$581$	1.88009e11	−	3.31511e10i	1.64996	−	0.290933i
$582$	−3.49552e10	−	1.43678e10i	−0.304663	−	0.125227i
$583$	−1.76902e11	−	1.48439e11i	−1.53130	−	1.28491i
$584$	1.97150e10	−	1.13825e10i	0.169491	−	0.0978554i
$585$	−5.31237e9	−	1.94038e10i	−0.0453591	−	0.165678i
$586$	−8.42431e8	+	1.45913e9i	−0.00714404	+	0.0123738i
$587$	2.20481e10	+	6.05765e10i	0.185703	+	0.510214i	0.997253	−	0.0740686i	$-0.0235984\pi$
$587$	2.20481e10	+	6.05765e10i	0.185703	+	0.510214i	−0.811551	+	0.584282i	$0.801376\pi$
$588$	1.48843e11	−	1.63322e11i	1.24514	−	1.36626i
$589$	−9.36389e10	+	7.85724e10i	−0.778028	+	0.652843i
$590$	−1.46069e10	+	4.01320e10i	−0.120545	+	0.331194i
$591$	4.92054e9	+	2.01448e8i	0.0403332	+	0.00165125i
$592$	−1.55108e10	+	8.79663e10i	−0.126284	+	0.716192i
$593$			8.45828e10i			0.684011i	0.939698	+	0.342006i	$0.111106\pi$
$593$			8.45828e10i			0.684011i	−0.939698	+	0.342006i	$0.888894\pi$
$594$	−1.69184e10	−	2.60852e10i	−0.135898	−	0.209531i
$595$	−6.79690e10			−0.542304
$596$	1.26310e11	+	2.22719e10i	1.00105	+	0.176511i
$597$	4.33287e10	+	2.74383e10i	0.341098	+	0.216003i
$598$	−4.06553e9	−	1.47973e9i	−0.0317916	−	0.0115712i
$599$	1.36255e10	+	1.62383e10i	0.105839	+	0.126134i	0.816364	−	0.577538i	$-0.195987\pi$
$599$	1.36255e10	+	1.62383e10i	0.105839	+	0.126134i	−0.710524	+	0.703673i	$0.751542\pi$
$600$	−7.68300e8	+	3.51067e9i	−0.00592824	+	0.0270885i
$601$	8.36696e9	−	3.04533e9i	0.0641313	−	0.0233419i	−0.309755	−	0.950816i	$-0.600247\pi$
$601$	8.36696e9	−	3.04533e9i	0.0641313	−	0.0233419i	0.373887	+	0.927474i	$0.378025\pi$
$602$	−1.83056e10	−	1.05688e10i	−0.139380	−	0.0804708i
$603$	−3.64499e10	−	1.67564e10i	−0.275694	−	0.126740i
$604$	−8.25458e10	−	1.42973e11i	−0.620222	−	1.07426i
$605$	3.93357e10	−	4.68785e10i	0.293606	−	0.349907i
$606$	1.93861e10	+	2.51229e10i	0.143747	+	0.186285i
$607$	3.13171e10	+	1.77608e11i	0.230689	+	1.30830i	0.851506	+	0.524345i	$0.175690\pi$
$607$	3.13171e10	+	1.77608e11i	0.230689	+	1.30830i	−0.620817	+	0.783955i	$0.713199\pi$
$608$	−1.11764e11	+	1.97070e10i	−0.817874	+	0.144213i
$609$	−6.27197e10	+	4.83977e10i	−0.455968	+	0.351848i
$610$	−2.26157e10	−	1.89769e10i	−0.163340	−	0.137058i
$611$	5.24156e9	−	3.02621e9i	0.0376093	−	0.0217138i
$612$	−1.84227e10	+	4.00745e10i	−0.131325	+	0.285669i
$613$	−9.37926e10	+	1.62454e11i	−0.664243	+	1.15050i	0.315248	+	0.949009i	$0.397912\pi$
$613$	−9.37926e10	+	1.62454e11i	−0.664243	+	1.15050i	−0.979490	+	0.201492i	$0.935421\pi$
$614$	−8.39590e8	−	2.30675e9i	−0.00590736	−	0.0162303i
$615$	−1.85243e11	−	4.05398e10i	−1.29491	−	0.283388i
$616$	−9.23124e10	+	7.74593e10i	−0.641117	+	0.537961i
$617$	6.58893e9	−	1.81029e10i	0.0454647	−	0.124913i	−0.914882	−	0.403720i	$-0.867717\pi$
$617$	6.58893e9	−	1.81029e10i	0.0454647	−	0.124913i	0.960347	+	0.278807i	$0.0899391\pi$
$618$	−5.16990e9	+	8.16396e9i	−0.0354428	+	0.0559689i
$619$	3.75319e10	−	2.12854e11i	0.255646	−	1.44984i	−0.538764	−	0.842457i	$-0.681109\pi$
$619$	3.75319e10	−	2.12854e11i	0.255646	−	1.44984i	0.794410	−	0.607382i	$-0.207780\pi$
$620$			9.73200e10i			0.658621i
$621$	−1.22365e11	−	6.24375e10i	−0.822796	−	0.419836i
$622$	4.78252e10			0.319518
$623$	1.68313e10	+	2.96782e9i	0.111729	+	0.0197009i
$624$	−9.65781e8	+	2.35900e10i	−0.00637001	+	0.155593i
$625$	1.32835e11	+	4.83479e10i	0.870547	+	0.316853i
$626$	1.33620e10	+	1.59242e10i	0.0870107	+	0.103695i
$627$	1.97590e11	+	1.80073e11i	1.27848	+	1.16514i
$628$	−1.34232e11	+	4.88563e10i	−0.863011	+	0.314110i
$629$	3.69987e10	+	2.13612e10i	0.236365	+	0.136466i
$630$	5.16380e10	−	1.41374e10i	0.327798	−	0.0897444i
$631$	1.52109e11	+	2.63460e11i	0.959482	+	1.66187i	0.723760	+	0.690052i	$0.242412\pi$
$631$	1.52109e11	+	2.63460e11i	0.959482	+	1.66187i	0.235722	+	0.971820i	$0.424254\pi$
$632$	−4.74093e10	+	5.65002e10i	−0.297163	+	0.354145i
$633$	5.12387e10	−	1.24658e11i	0.319141	−	0.776433i
$634$	6.54638e9	+	3.71263e10i	0.0405176	+	0.229787i
$635$	1.72184e11	−	3.03607e10i	1.05900	−	0.186731i
$636$	−3.43762e10	−	2.55744e11i	−0.210102	−	1.56307i
$637$	−4.33381e10	−	3.63650e10i	−0.263216	−	0.220865i
$638$	1.20568e10	−	6.96097e9i	0.0727692	−	0.0420133i
$639$	1.90366e10	−	2.32103e11i	0.114179	−	1.39212i
$640$	−5.97467e10	+	1.03484e11i	−0.356118	+	0.616814i
$641$	7.60783e10	+	2.09023e11i	0.450639	+	1.23812i	0.932276	+	0.361749i	$0.117820\pi$
$641$	7.60783e10	+	2.09023e11i	0.450639	+	1.23812i	−0.481637	+	0.876371i	$0.659958\pi$
$642$	−1.50951e10	−	4.74259e10i	−0.0888576	−	0.279174i
$643$	2.07474e11	−	1.74091e11i	1.21372	−	1.01844i	0.214595	−	0.976703i	$-0.431157\pi$
$643$	2.07474e11	−	1.74091e11i	1.21372	−	1.01844i	0.999129	−	0.0417321i	$-0.0132876\pi$
$644$	−8.90842e10	+	2.44757e11i	−0.517913	+	1.42295i
$645$	3.54235e10	+	6.75991e10i	0.204669	+	0.390573i
$646$	−2.91106e9	+	1.65095e10i	−0.0167156	+	0.0947988i
$647$		−	2.00279e9i		−	0.0114293i	−0.999984	−	0.00571463i	$-0.998181\pi$
$647$		−	2.00279e9i		−	0.0114293i	0.999984	−	0.00571463i	$-0.00181903\pi$
$648$	1.15719e10	−	7.00705e10i	0.0656305	−	0.397407i
$649$	−3.82278e11			−2.15477
$650$	4.43259e8	+	7.81586e7i	0.00248316	+	0.000437848i
$651$	−1.94088e11	+	1.01707e11i	−1.08062	+	0.566272i
$652$	−2.41805e11	−	8.80098e10i	−1.33806	−	0.487013i
$653$	−1.92647e11	−	2.29588e11i	−1.05952	−	1.26269i	−0.963614	−	0.267299i	$-0.913869\pi$
$653$	−1.92647e11	−	2.29588e11i	−1.05952	−	1.26269i	−0.0959083	−	0.995390i	$-0.530576\pi$
$654$	2.68335e10	−	8.54077e9i	0.146679	−	0.0466859i
$655$	8.52072e10	−	3.10129e10i	0.462925	−	0.168491i
$656$	1.92726e11	+	1.11270e11i	1.04070	+	0.600846i
$657$	−3.87052e10	−	8.18401e10i	−0.207734	−	0.439243i
$658$	8.05344e9	+	1.39490e10i	0.0429614	+	0.0744112i
$659$	1.37639e11	−	1.64032e11i	0.729794	−	0.869734i	−0.265749	−	0.964042i	$-0.585619\pi$
$659$	1.37639e11	−	1.64032e11i	0.729794	−	0.869734i	0.995543	+	0.0943079i	$0.0300638\pi$
$660$	2.10944e11	−	2.83543e10i	1.11171	−	0.149432i
$661$	3.06780e10	+	1.73984e11i	0.160702	+	0.911386i	0.953386	+	0.301753i	$0.0975719\pi$
$661$	3.06780e10	+	1.73984e11i	0.160702	+	0.911386i	−0.792684	+	0.609633i	$0.791317\pi$
$662$	−4.88305e10	+	8.61014e9i	−0.254249	+	0.0448310i
$663$	1.04444e10	+	4.29302e9i	0.0540542	+	0.0222182i
$664$	−5.87052e10	−	4.92595e10i	−0.301998	−	0.253406i
$665$	−3.98668e11	+	2.30171e11i	−2.03857	+	1.17697i
$666$	−3.25520e10	−	8.53306e9i	−0.165455	−	0.0433718i
$667$	3.07565e10	−	5.32718e10i	0.155394	−	0.269150i
$668$	2.06378e10	+	5.67020e10i	0.103647	+	0.284769i
$669$	5.38873e9	−	5.91292e9i	0.0269018	−	0.0295187i
$670$	−9.29957e9	+	7.80327e9i	−0.0461491	+	0.0387237i
$671$	9.03821e10	−	2.48323e11i	0.445853	−	1.22497i
$672$	−2.03268e11	−	8.32183e9i	−0.996761	−	0.0408076i
$673$	5.10778e10	−	2.89676e11i	0.248984	−	1.41206i	−0.562071	−	0.827089i	$-0.689995\pi$
$673$	5.10778e10	−	2.89676e11i	0.248984	−	1.41206i	0.811055	−	0.584970i	$-0.198894\pi$
$674$			1.71683e10i			0.0831932i
$675$	1.36647e10	+	4.18638e9i	0.0658241	+	0.0201662i
$676$	−1.93650e11			−0.927320
$677$	1.66165e11	+	2.92994e10i	0.791015	+	0.139477i	0.554537	−	0.832159i	$-0.312896\pi$
$677$	1.66165e11	+	2.92994e10i	0.791015	+	0.139477i	0.236479	+	0.971637i	$0.424007\pi$
$678$	6.57785e10	+	4.16548e10i	0.311290	+	0.197127i
$679$	5.47388e11	+	1.99233e11i	2.57523	+	0.937307i
$680$	1.75377e10	+	2.09006e10i	0.0820232	+	0.0977515i
$681$	5.64532e10	−	2.57957e11i	0.262483	−	1.19939i
$682$	3.61848e10	−	1.31702e10i	0.167259	−	0.0608771i
$683$	5.30164e10	+	3.06090e10i	0.243628	+	0.140659i	0.616843	−	0.787086i	$-0.288411\pi$
$683$	5.30164e10	+	3.06090e10i	0.243628	+	0.140659i	−0.373215	+	0.927745i	$0.621745\pi$
$684$	2.76515e10	+	2.97442e11i	0.126327	+	1.35887i
$685$	−1.98868e11	−	3.44450e11i	−0.903240	−	1.56446i
$686$	4.66389e10	−	5.55821e10i	0.210597	−	0.250980i
$687$	6.71320e10	+	8.69979e10i	0.301372	+	0.390555i
$688$	−1.55527e10	−	8.82040e10i	−0.0694150	−	0.393672i
$689$	−6.50620e10	+	1.14722e10i	−0.288703	+	0.0509060i
$690$	−3.29113e10	+	2.53961e10i	−0.145194	+	0.112039i
$691$	2.97075e11	+	2.49275e11i	1.30303	+	1.09337i	0.989613	+	0.143754i	$0.0459173\pi$
$691$	2.97075e11	+	2.49275e11i	1.30303	+	1.09337i	0.313414	+	0.949616i	$0.398527\pi$
$692$	8.12362e10	−	4.69018e10i	0.354263	−	0.204534i
$693$	2.76999e11	+	3.91058e11i	1.20101	+	1.69554i
$694$	−2.83247e10	+	4.90599e10i	−0.122103	+	0.211489i
$695$	−1.07816e11	−	2.96222e11i	−0.462109	−	1.26963i
$696$	3.10657e10	+	6.79863e9i	0.132386	+	0.0289724i
$697$	8.15367e10	−	6.84174e10i	0.345479	−	0.289892i
$698$	−8.66543e9	+	2.38081e10i	−0.0365063	+	0.100300i
$699$	−3.14125e10	+	4.96046e10i	−0.131581	+	0.207784i
$700$	4.70537e9	−	2.66855e10i	0.0195976	−	0.111143i
$701$		−	5.50796e10i		−	0.228096i	−0.993475	−	0.114048i	$-0.963618\pi$
$701$		−	5.50796e10i		−	0.228096i	0.993475	−	0.114048i	$-0.0363818\pi$
$702$	−8.82786e9	−	1.08911e9i	−0.0363502	−	0.00448462i
$703$	2.89352e11			1.18469
$704$	−2.21655e11	−	3.90838e10i	−0.902375	−	0.159113i
$705$	2.37888e9	−	5.81060e10i	0.00962976	−	0.235215i
$706$	−3.65485e10	−	1.33026e10i	−0.147113	−	0.0535447i
$707$	−3.14396e11	−	3.74682e11i	−1.25834	−	1.49964i
$708$	−3.15721e11	−	2.87731e11i	−1.25652	−	1.14513i
$709$	9.30404e10	−	3.38639e10i	0.368202	−	0.134015i	−0.151291	−	0.988489i	$-0.548343\pi$
$709$	9.30404e10	−	3.38639e10i	0.368202	−	0.134015i	0.519493	+	0.854475i	$0.326121\pi$
$710$	−6.10306e10	−	3.52360e10i	−0.240167	−	0.138661i
$711$	2.08525e11	+	2.06272e11i	0.815982	+	0.807166i
$712$	−3.43030e9	−	5.94145e9i	−0.0133479	−	0.0231192i
$713$	1.09364e11	−	1.30335e11i	0.423171	−	0.504316i
$714$	−1.14247e10	+	2.77949e10i	−0.0439594	+	0.106948i
$715$	−9.46253e9	−	5.36646e10i	−0.0362062	−	0.205336i
$716$	4.90804e10	−	8.65420e9i	0.186748	−	0.0329287i
$717$	2.35237e10	+	1.75006e11i	0.0890079	+	0.662181i
$718$	2.29774e10	+	1.92803e10i	0.0864576	+	0.0725465i
$719$	2.21541e11	−	1.27907e11i	0.828968	−	0.478605i	−0.0245313	−	0.999699i	$-0.507809\pi$
$719$	2.21541e11	−	1.27907e11i	0.828968	−	0.478605i	0.853499	+	0.521094i	$0.174476\pi$
$720$	1.86532e11	+	1.29107e11i	0.694102	+	0.480418i
$721$	7.44718e10	−	1.28989e11i	0.275582	−	0.477322i
$722$	1.97109e10	+	5.41553e10i	0.0725368	+	0.199293i
$723$	−4.00583e10	−	1.25856e11i	−0.146602	−	0.460596i
$724$	−1.14714e11	+	9.62564e10i	−0.417505	+	0.350329i
$725$	−2.18874e9	+	6.01351e9i	−0.00792213	+	0.0217659i
$726$	−1.25585e10	−	2.39654e10i	−0.0452054	−	0.0862659i
$727$	1.05428e10	−	5.97912e10i	0.0377414	−	0.214042i	−0.960105	−	0.279641i	$-0.909785\pi$
$727$	1.05428e10	−	5.97912e10i	0.0377414	−	0.214042i	0.997846	+	0.0655987i	$0.0208957\pi$
$728$			3.44749e10i			0.122738i
$729$	−2.73961e11	−	6.86433e10i	−0.970015	−	0.243046i
$730$	−2.73955e10			−0.0964689
$731$	−4.21870e10	−	7.43871e9i	−0.147744	−	0.0260512i
$732$	2.61552e11	−	1.37060e11i	0.910991	−	0.477381i
$733$	−4.73428e10	−	1.72314e10i	−0.163998	−	0.0596903i	0.258717	−	0.965953i	$-0.416700\pi$
$733$	−4.73428e10	−	1.72314e10i	−0.163998	−	0.0596903i	−0.422714	+	0.906263i	$0.638923\pi$
$734$	−1.32781e10	−	1.58242e10i	−0.0457457	−	0.0545176i
$735$	−5.17985e11	+	1.64868e11i	−1.77488	+	0.564920i
$736$	1.48436e11	−	5.40263e10i	0.505858	−	0.184117i
$737$	−9.41051e10	−	5.43316e10i	−0.318965	−	0.184155i
$738$	−4.77151e10	+	6.89381e10i	−0.160853	+	0.232399i
$739$	2.34907e11	+	4.06871e11i	0.787624	+	1.36420i	0.927419	+	0.374024i	$0.122022\pi$
$739$	2.34907e11	+	4.06871e11i	0.787624	+	1.36420i	−0.139796	+	0.990180i	$0.544645\pi$
$740$	1.48079e11	−	1.76473e11i	0.493817	−	0.588508i
$741$	7.57991e10	−	1.01886e10i	0.251415	−	0.0337943i
$742$	−3.05301e10	−	1.73145e11i	−0.100719	−	0.571207i
$743$	−5.04740e11	+	8.89993e10i	−1.65620	+	0.292033i	−0.922083	−	0.386991i	$-0.873514\pi$
$743$	−5.04740e11	+	8.89993e10i	−1.65620	+	0.292033i	−0.734116	+	0.679024i	$0.762403\pi$
$744$	8.13545e10	+	3.34396e10i	0.265515	+	0.109136i
$745$	−2.41701e11	−	2.02811e11i	−0.784608	−	0.658364i
$746$	−7.17990e10	+	4.14532e10i	−0.231827	+	0.133845i
$747$	−2.14322e11	+	2.16663e11i	−0.688311	+	0.695830i
$748$	−5.97344e10	+	1.03463e11i	−0.190818	+	0.330506i
$749$	2.62374e11	+	7.20866e11i	0.833668	+	2.29049i
$750$	4.52275e10	−	4.96271e10i	0.142941	−	0.156846i
$751$	2.12965e10	−	1.78699e10i	0.0669498	−	0.0561776i	−0.608699	−	0.793401i	$-0.708308\pi$
$751$	2.12965e10	−	1.78699e10i	0.0669498	−	0.0561776i	0.675649	+	0.737224i	$0.263864\pi$
$752$	−2.33424e10	+	6.41327e10i	−0.0729918	+	0.200543i
$753$	5.42222e10	+	2.21987e9i	0.168654	+	0.00690475i
$754$	6.91619e8	−	3.92237e9i	0.00213984	−	0.0121356i
$755$			4.06127e11i			1.24990i
$756$	−6.55679e10	+	5.31463e11i	−0.200726	+	1.62699i
$757$	−3.59044e11			−1.09336			−0.546681	−	0.837341i	$-0.684109\pi$
$757$	−3.59044e11			−1.09336			−0.546681	+	0.837341i	$0.684109\pi$
$758$	1.30909e10	+	2.30828e9i	0.0396546	+	0.00699218i
$759$	−3.14368e11	−	1.99076e11i	−0.947265	−	0.599864i
$760$	1.73645e11	+	6.32015e10i	0.520484	+	0.189441i
$761$	4.75589e10	+	5.66785e10i	0.141806	+	0.168997i	0.832273	−	0.554367i	$-0.187039\pi$
$761$	4.75589e10	+	5.66785e10i	0.141806	+	0.168997i	−0.690467	+	0.723364i	$0.742595\pi$
$762$	1.65263e10	−	7.55154e10i	0.0490181	−	0.223983i
$763$	−4.07866e11	+	1.48451e11i	−1.20343	+	0.438011i
$764$	−3.41519e10	−	1.97176e10i	−0.100240	−	0.0578737i
$765$	8.85401e10	−	6.27159e10i	0.258520	−	0.183118i
$766$	4.30381e10	+	7.45443e10i	0.125008	+	0.216521i
$767$	−7.02981e10	+	8.37780e10i	−0.203124	+	0.242074i
$768$	−1.28162e11	−	1.66088e11i	−0.368396	−	0.477412i
$769$	6.71441e10	+	3.80793e11i	0.192000	+	1.08889i	0.916626	+	0.399746i	$0.130902\pi$
$769$	6.71441e10	+	3.80793e11i	0.192000	+	1.08889i	−0.724626	+	0.689143i	$0.757987\pi$
$770$	1.42814e11	−	2.51819e10i	0.406263	−	0.0716351i
$771$	−2.41418e11	+	1.86290e11i	−0.683205	+	0.527196i
$772$	2.48845e10	+	2.08806e10i	0.0700583	+	0.0587859i
$773$	−3.24557e11	+	1.87383e11i	−0.909020	+	0.524823i	−0.880116	−	0.474759i	$-0.842535\pi$
$773$	−3.24557e11	+	1.87383e11i	−0.909020	+	0.524823i	−0.0289045	+	0.999582i	$0.509202\pi$
$774$	3.35979e10	−	3.12341e9i	0.0936156	−	0.00870293i
$775$	−8.85018e9	+	1.53290e10i	−0.0245327	+	0.0424919i
$776$	−7.99752e10	−	2.19730e11i	−0.220551	−	0.605958i
$777$	5.06699e11	+	1.10889e11i	1.39016	+	0.304233i
$778$	−2.27960e9	+	1.91281e9i	−0.00622214	+	0.00522100i
$779$	2.46559e11	−	6.77416e11i	0.669532	−	1.83952i
$780$	3.25770e10	−	5.14435e10i	0.0880102	−	0.138980i
$781$	1.09537e11	−	6.21215e11i	0.294413	−	1.66970i
$782$		−	2.33338e10i		−	0.0623963i
$783$	3.70449e10	−	1.20918e11i	0.0985556	−	0.321694i
$784$	6.37941e11			1.68856
$785$	3.46065e11	+	6.10206e10i	0.911337	+	0.160693i
$786$	1.63995e9	−	4.00571e10i	0.00429675	−	0.104952i
$787$	1.64892e11	+	6.00158e10i	0.429834	+	0.156447i	0.547872	−	0.836562i	$-0.315438\pi$
$787$	1.64892e11	+	6.00158e10i	0.429834	+	0.156447i	−0.118038	+	0.993009i	$0.537660\pi$
$788$	9.58105e9	+	1.14183e10i	0.0248490	+	0.0296139i
$789$	1.44849e11	+	1.32007e11i	0.373771	+	0.340636i
$790$	8.34054e10	−	3.03571e10i	0.214134	−	0.0779384i
$791$	−1.03929e12	−	6.00032e11i	−2.65479	−	1.53274i
$792$	4.87785e10	−	1.86081e11i	0.123973	−	0.472934i
$793$	−3.78005e10	−	6.54723e10i	−0.0955883	−	0.165564i
$794$	6.17783e10	−	7.36245e10i	0.155437	−	0.185242i
$795$	−2.41331e11	+	5.87128e11i	−0.604149	+	1.46982i
$796$	2.69549e10	+	1.52869e11i	0.0671406	+	0.380773i
$797$	1.75652e10	−	3.09722e9i	0.0435331	−	0.00767606i	−0.151839	−	0.988405i	$-0.548520\pi$
$797$	1.75652e10	−	3.09722e9i	0.0435331	−	0.00767606i	0.195372	+	0.980729i	$0.437408\pi$
$798$	2.71143e10	+	2.01719e11i	0.0668631	+	0.497433i
$799$	2.50057e10	+	2.09822e10i	0.0613552	+	0.0514831i
$800$	−1.42318e10	+	8.21673e9i	−0.0347456	+	0.0200604i
$801$	−2.46639e10	+	1.16645e10i	−0.0599145	+	0.0283358i
$802$	3.51279e10	−	6.08433e10i	0.0849092	−	0.147067i
$803$	−8.38696e10	−	2.30430e11i	−0.201717	−	0.554213i
$804$	−3.68267e10	−	1.15703e11i	−0.0881330	−	0.276898i
$805$	4.90840e11	−	4.11863e11i	1.16884	−	0.980775i
$806$	3.76781e9	−	1.03520e10i	0.00892788	−	0.0245291i
$807$	1.06737e11	+	2.03686e11i	0.251663	+	0.480251i
$808$	−3.40937e10	+	1.93355e11i	−0.0799887	+	0.453638i
$809$		−	1.94607e11i		−	0.454323i	−0.973857	−	0.227161i	$-0.927056\pi$
$809$		−	1.94607e11i		−	0.454323i	0.973857	−	0.227161i	$-0.0729445\pi$
$810$	−5.42217e10	+	6.60632e10i	−0.125960	+	0.153469i
$811$	−8.64952e10			−0.199944			−0.0999720	−	0.994990i	$-0.531875\pi$
$811$	−8.64952e10			−0.199944			−0.0999720	+	0.994990i	$0.531875\pi$
$812$	−2.36138e11	−	4.16375e10i	−0.543177	−	0.0957768i
$813$	3.46236e11	−	1.81436e11i	0.792520	−	0.415299i
$814$	−8.56543e10	−	3.11756e10i	−0.195097	−	0.0710097i
$815$	4.06896e11	+	4.84920e11i	0.922259	+	1.09911i
$816$	−1.21337e11	+	3.86199e10i	−0.273673	+	0.0871065i
$817$	−2.72636e11	+	9.92315e10i	−0.611921	+	0.222721i
$818$	1.47522e11	+	8.51721e10i	0.329492	+	0.190232i
$819$	1.36640e11	+	1.12070e10i	0.303699	+	0.0249088i
$820$	−2.86972e11	−	4.97050e11i	−0.634722	−	1.09937i
$821$	−1.63679e11	+	1.95065e11i	−0.360264	+	0.429346i	−0.915482	−	0.402359i	$-0.868190\pi$
$821$	−1.63679e11	+	1.95065e11i	−0.360264	+	0.429346i	0.555218	+	0.831705i	$0.312635\pi$
$822$	−1.74285e11	+	2.34268e10i	−0.381745	+	0.0513128i
$823$	4.26800e10	+	2.42050e11i	0.0930304	+	0.527602i	0.995333	+	0.0964986i	$0.0307643\pi$
$823$	4.26800e10	+	2.42050e11i	0.0930304	+	0.527602i	−0.902303	+	0.431103i	$0.858125\pi$
$824$	−5.88800e10	+	1.03821e10i	−0.127720	+	0.0225205i
$825$	3.58045e10	+	1.47169e10i	0.0772897	+	0.0317688i
$826$	−2.22952e11	−	1.87079e11i	−0.478951	−	0.401888i
$827$	5.42919e11	−	3.13454e11i	1.16068	−	0.670120i	0.209214	−	0.977870i	$-0.432909\pi$
$827$	5.42919e11	−	3.13454e11i	1.16068	−	0.670120i	0.951467	+	0.307750i	$0.0995760\pi$
$828$	−1.09795e11	−	4.01033e11i	−0.233593	−	0.853215i
$829$	−3.00938e11	+	5.21239e11i	−0.637174	+	1.10362i	0.348876	+	0.937169i	$0.386564\pi$
$829$	−3.00938e11	+	5.21239e11i	−0.637174	+	1.10362i	−0.986050	+	0.166449i	$0.946770\pi$
$830$	3.15418e10	+	8.66604e10i	0.0664621	+	0.182603i
$831$	−1.08225e11	+	1.18753e11i	−0.226947	+	0.249023i
$832$	−4.93261e10	+	4.13895e10i	−0.102940	+	0.0863768i
$833$	1.04357e11	−	2.86719e11i	0.216742	−	0.595493i
$834$	−1.39258e11	−	5.70127e9i	−0.287844	−	0.0117844i
$835$	2.57762e10	−	1.46184e11i	0.0530241	−	0.300715i
$836$			8.09143e11i			1.65653i
$837$	1.58983e11	−	3.11576e11i	0.323929	−	0.634837i
$838$	−1.20708e11			−0.244771
$839$	2.19890e11	+	3.87726e10i	0.443770	+	0.0782486i	0.391068	−	0.920362i	$-0.372106\pi$
$839$	2.19890e11	+	3.87726e10i	0.443770	+	0.0782486i	0.0527018	+	0.998610i	$0.483217\pi$
$840$	2.79857e11	+	1.77222e11i	0.562107	+	0.355959i
$841$	−4.16865e11	−	1.51726e11i	−0.833319	−	0.303303i
$842$	1.67496e10	+	1.99614e10i	0.0333239	+	0.0397138i
$843$	2.10574e10	−	9.62196e10i	0.0416960	−	0.190526i
$844$	3.83329e11	−	1.39520e11i	0.755444	−	0.274959i
$845$	4.12557e11	+	2.38190e11i	0.809202	+	0.467193i
$846$	−2.33618e10	−	1.07397e10i	−0.0456063	−	0.0209657i
$847$	2.08517e11	+	3.61162e11i	0.405143	+	0.701728i
$848$	4.78859e11	−	5.70682e11i	0.926028	−	1.10360i
$849$	−4.78433e11	−	6.20012e11i	−0.920853	−	1.19335i
$850$	4.21533e8	+	2.39063e9i	0.000807524	+	0.00457970i
$851$	−3.96627e11	+	6.99360e10i	−0.756247	+	0.133347i
$852$	5.58039e11	−	4.30612e11i	1.05903	−	0.817198i
$853$	1.07390e10	+	9.01105e9i	0.0202846	+	0.0170208i	0.652874	−	0.757467i	$-0.273563\pi$
$853$	1.07390e10	+	9.01105e9i	0.0202846	+	0.0170208i	−0.632589	+	0.774488i	$0.718008\pi$
$854$	1.74237e11	−	1.00596e11i	0.327573	−	0.189124i
$855$	3.06945e11	−	6.67691e11i	0.574376	−	1.24943i
$856$	1.53969e11	−	2.66682e11i	0.286773	−	0.496706i
$857$	−3.56164e10	−	9.78554e10i	−0.0660279	−	0.181410i	0.902291	−	0.431128i	$-0.141884\pi$
$857$	−3.56164e10	−	9.78554e10i	−0.0660279	−	0.181410i	−0.968319	+	0.249718i	$0.919662\pi$
$858$	−2.35359e10	−	5.15077e9i	−0.0434292	−	0.00950436i
$859$	−2.94212e11	+	2.46873e11i	−0.540365	+	0.453420i	−0.871663	−	0.490106i	$-0.836958\pi$
$859$	−2.94212e11	+	2.46873e11i	−0.540365	+	0.453420i	0.331298	+	0.943526i	$0.392514\pi$
$860$	−7.90040e10	+	2.17062e11i	−0.144429	+	0.396816i
$861$	6.91372e11	−	1.09177e12i	1.25805	−	1.98663i
$862$	−2.93660e10	+	1.66543e11i	−0.0531883	+	0.301646i
$863$			2.17241e11i			0.391650i	0.980639	+	0.195825i	$0.0627384\pi$
$863$			2.17241e11i			0.391650i	−0.980639	+	0.195825i	$0.937262\pi$
$864$	2.72466e11	−	1.76717e11i	0.488942	−	0.317120i
$865$	−2.30758e11			−0.412184
$866$	6.07954e9	+	1.07199e9i	0.0108093	+	0.00190598i
$867$	2.06221e10	−	5.03712e11i	0.0364969	−	0.891468i
$868$	−6.23218e11	−	2.26833e11i	−1.09790	−	0.399602i
$869$	5.10681e11	+	6.08606e11i	0.895511	+	1.06723i
$870$	−2.82853e10	−	2.57777e10i	−0.0493723	−	0.0449953i
$871$	−2.92123e10	+	1.06324e10i	−0.0507566	+	0.0184739i
$872$	1.50889e11	+	8.71156e10i	0.260970	+	0.150671i
$873$	−8.96893e11	+	2.45551e11i	−1.54413	+	0.422751i
$874$	−7.90180e10	−	1.36863e11i	−0.135419	−	0.234553i
$875$	−6.65237e11	+	7.92799e11i	−1.13487	+	1.35248i
$876$	1.04172e11	−	2.53437e11i	0.176902	−	0.430381i
$877$	−2.14413e10	−	1.21600e11i	−0.0362454	−	0.205558i	0.961307	−	0.275479i	$-0.0888364\pi$
$877$	−2.14413e10	−	1.21600e11i	−0.0362454	−	0.205558i	−0.997553	+	0.0699210i	$0.977725\pi$
$878$	4.93596e10	−	8.70343e9i	0.0830603	−	0.0146458i
$879$	5.52273e9	+	4.10868e10i	0.00925121	+	0.0688250i
$880$	4.70712e11	+	3.94974e11i	0.784918	+	0.658624i
$881$	7.64992e11	−	4.41668e11i	1.26985	−	0.733150i	0.294893	−	0.955530i	$-0.404716\pi$
$881$	7.64992e11	−	4.41668e11i	1.26985	−	0.733150i	0.974960	+	0.222381i	$0.0713828\pi$
$882$	−1.96462e10	+	2.39535e11i	−0.0324641	+	0.395817i
$883$	8.16461e10	−	1.41415e11i	0.134305	−	0.232623i	−0.791027	−	0.611782i	$-0.790453\pi$
$883$	8.16461e10	−	1.41415e11i	0.134305	−	0.232623i	0.925332	+	0.379158i	$0.123786\pi$
$884$	1.16897e10	+	3.21172e10i	0.0191423	+	0.0525930i
$885$	3.18710e11	+	1.00133e12i	0.519545	+	1.63231i
$886$	−1.09881e11	+	9.22015e10i	−0.178316	+	0.149625i
$887$	−3.73853e11	+	1.02715e12i	−0.603957	+	1.65936i	0.139218	+	0.990262i	$0.455541\pi$
$887$	−3.73853e11	+	1.02715e12i	−0.603957	+	1.65936i	−0.743175	+	0.669097i	$0.766681\pi$
$888$	−9.66422e10	−	1.84423e11i	−0.155423	−	0.296595i
$889$	−2.06901e11	+	1.17340e12i	−0.331251	+	1.87862i
$890$			8.25609e9i			0.0131587i
$891$	−7.21670e11	−	2.53823e11i	−1.14506	−	0.402735i
$892$	2.42138e10			0.0382475
$893$	2.17724e11	+	3.83906e10i	0.342374	+	0.0603697i
$894$	−1.23563e11	+	6.47502e10i	−0.193437	+	0.101366i
$895$	−1.15207e11	−	4.19320e10i	−0.179551	−	0.0653511i
$896$	−5.23436e11	−	6.23807e11i	−0.812141	−	0.967872i
$897$	−1.01438e11	+	3.22866e10i	−0.156687	+	0.0498715i
$898$	1.56341e11	−	5.69035e10i	0.240419	−	0.0875052i
$899$	1.35645e11	+	7.83146e10i	0.207665	+	0.119896i
$900$	1.84936e10	+	3.91037e10i	0.0281872	+	0.0596003i
$901$	−1.78156e11	−	3.08575e11i	−0.270334	−	0.468233i
$902$	−1.45974e11	+	1.73965e11i	−0.220520	+	0.262806i
$903$	−5.15456e11	+	6.92858e10i	−0.775248	+	0.104206i
$904$	8.36507e10	+	4.74407e11i	0.125255	+	0.710357i
$905$	3.62786e11	−	6.39690e10i	0.540824	−	0.0953619i
$906$	1.66080e11	+	6.82646e10i	0.246493	+	0.101317i
$907$	−2.36599e11	−	1.98531e11i	−0.349611	−	0.293358i	0.451023	−	0.892512i	$-0.351059\pi$
$907$	−2.36599e11	−	1.98531e11i	−0.349611	−	0.293358i	−0.800634	+	0.599154i	$0.795504\pi$
$908$	6.92161e11	−	3.99619e11i	1.01827	−	0.587899i
$909$	7.55274e11	+	1.97985e11i	1.10624	+	0.289985i
$910$	2.07437e10	−	3.59291e10i	0.0302496	−	0.0523939i
$911$	−2.99551e11	−	8.23009e11i	−0.434907	−	1.19490i	−0.942765	−	0.333457i	$-0.891785\pi$
$911$	−2.99551e11	−	8.23009e11i	−0.434907	−	1.19490i	0.507858	−	0.861441i	$-0.330437\pi$
$912$	−5.80910e11	+	6.37419e11i	−0.839711	+	0.921395i
$913$	−6.32357e11	+	5.30611e11i	−0.910080	+	0.763648i
$914$	−4.30509e10	+	1.18282e11i	−0.0616876	+	0.169485i
$915$	−7.25803e11	−	2.97146e10i	−1.03546	−	0.0423921i
$916$	−5.77550e10	+	3.27545e11i	−0.0820366	+	0.465253i
$917$			6.17935e11i			0.873907i
$918$	−1.07643e10	−	4.67490e10i	−0.0151571	−	0.0658266i
$919$	−5.59623e11			−0.784574			−0.392287	−	0.919843i	$-0.628316\pi$
$919$	−5.59623e11			−0.784574			−0.392287	+	0.919843i	$0.628316\pi$
$920$	−2.53298e11	−	4.46632e10i	−0.353574	−	0.0623446i
$921$	−5.10293e10	−	3.23147e10i	−0.0709220	−	0.0449120i
$922$	1.81258e11	+	6.59723e10i	0.250826	+	0.0912932i
$923$	−1.15999e11	−	1.38242e11i	−0.159826	−	0.190474i
$924$	−3.10091e11	+	1.41693e12i	−0.425404	+	1.94384i
$925$	3.93724e10	−	1.43304e10i	0.0537805	−	0.0195745i
$926$	−1.91192e11	−	1.10385e11i	−0.260032	−	0.150130i
$927$	2.20088e10	+	2.36744e11i	0.0298042	+	0.320598i
$928$	7.27092e10	+	1.25936e11i	0.0980386	+	0.169808i
$929$	−4.11643e11	+	4.90577e11i	−0.552660	+	0.658634i	−0.967976	−	0.251043i	$-0.919226\pi$
$929$	−4.11643e11	+	4.90577e11i	−0.552660	+	0.658634i	0.415316	+	0.909677i	$0.363671\pi$
$930$	−6.46654e10	−	8.38013e10i	−0.0864450	−	0.112026i
$931$	−3.58849e11	−	2.03513e12i	−0.477653	−	2.70891i
$932$	−1.75011e11	+	3.08591e10i	−0.231953	+	0.0408996i
$933$	9.31626e11	−	7.18890e11i	1.22946	−	0.948716i
$934$	2.18607e10	+	1.83433e10i	0.0287260	+	0.0241040i
$935$	2.54520e11	−	1.46947e11i	0.333024	−	0.192272i
$936$	−3.18105e10	−	4.49089e10i	−0.0414445	−	0.0585099i
$937$	1.69447e11	−	2.93491e11i	0.219824	−	0.380747i	−0.734930	−	0.678143i	$-0.762785\pi$
$937$	1.69447e11	−	2.93491e11i	0.219824	−	0.380747i	0.954754	+	0.297396i	$0.0961182\pi$
$938$	−2.82952e10	−	7.77404e10i	−0.0365512	−	0.100424i
$939$	4.99654e11	+	1.09348e11i	0.642698	+	0.140653i
$940$	1.34837e11	−	1.13141e11i	0.172702	−	0.144914i
$941$	−2.45934e11	+	6.75699e11i	−0.313661	+	0.861777i	0.678249	+	0.734833i	$0.262739\pi$
$941$	−2.45934e11	+	6.75699e11i	−0.313661	+	0.861777i	−0.991910	+	0.126945i	$0.959483\pi$
$942$	8.31225e10	−	1.31262e11i	0.105564	−	0.166699i
$943$	−1.74239e11	+	9.88156e11i	−0.220342	+	1.24962i
$944$		−	1.23322e12i		−	1.55293i
$945$	7.93390e11	−	1.05160e12i	0.994854	−	1.31863i
$946$	9.13977e10			0.114122
$947$	−4.79075e11	−	8.44739e10i	−0.595667	−	0.105032i	−0.132317	−	0.991207i	$-0.542242\pi$
$947$	−4.79075e11	−	8.44739e10i	−0.595667	−	0.105032i	−0.463350	+	0.886175i	$0.653353\pi$
$948$	−3.63149e10	+	8.87021e11i	−0.0449626	+	1.09825i
$949$	−6.59227e10	−	2.39939e10i	−0.0812775	−	0.0295826i
$950$	1.05681e10	+	1.25946e10i	0.0129749	+	0.0154629i
$951$	6.85591e11	+	6.24812e11i	0.838191	+	0.763883i
$952$	−1.74720e11	+	6.35930e10i	−0.212714	+	0.0774215i
$953$	−7.27038e11	−	4.19755e11i	−0.881425	−	0.508891i	−0.0102969	−	0.999947i	$-0.503278\pi$
$953$	−7.27038e11	−	4.19755e11i	−0.881425	−	0.508891i	−0.871128	+	0.491056i	$0.836611\pi$
$954$	1.99533e11	+	1.97377e11i	0.240892	+	0.238289i
$955$	4.85055e10	+	8.40140e10i	0.0583147	+	0.101004i
$956$	−3.43541e11	+	4.09416e11i	−0.411289	+	0.490155i
$957$	1.30229e11	−	3.16831e11i	0.155260	−	0.377729i
$958$	−1.72272e10	−	9.77001e10i	−0.0204527	−	0.115993i
$959$	2.66931e12	−	4.70672e11i	3.15591	−	0.556473i
$960$	8.24218e10	+	6.13182e11i	0.0970414	+	0.721946i
$961$	−3.21484e11	−	2.69757e11i	−0.376934	−	0.316285i
$962$	−2.25835e10	+	1.30386e10i	−0.0263688	+	0.0152240i
$963$	−1.00694e12	−	6.96944e11i	−1.17084	−	0.810388i
$964$	1.99879e11	−	3.46200e11i	0.231451	−	0.400884i
$965$	−2.73315e10	−	7.50926e10i	−0.0315177	−	0.0865940i
$966$	−8.59218e10	−	2.69951e11i	−0.0986723	−	0.310010i
$967$	3.58024e11	−	3.00417e11i	0.409455	−	0.343573i	−0.414680	−	0.909967i	$-0.636106\pi$
$967$	3.58024e11	−	3.00417e11i	0.409455	−	0.343573i	0.824135	+	0.566394i	$0.191662\pi$
$968$	5.72556e10	−	1.57309e11i	0.0652104	−	0.179164i
$969$	1.91457e11	+	3.65359e11i	0.217158	+	0.414405i
$970$	−4.88637e10	+	2.77120e11i	−0.0551950	+	0.313026i
$971$			9.07616e11i			1.02100i	0.859878	+	0.510500i	$0.170539\pi$
$971$			9.07616e11i			1.02100i	−0.859878	+	0.510500i	$0.829461\pi$
$972$	−4.04976e11	−	7.52814e11i	−0.453695	−	0.843378i
$973$	2.14825e12			2.39681
$974$	−7.81535e10	−	1.37806e10i	−0.0868386	−	0.0153120i
$975$	9.80946e9	−	5.14039e9i	0.0108549	−	0.00568823i
$976$	8.01083e11	+	2.91570e11i	0.882832	+	0.321325i
$977$	1.09047e11	+	1.29957e11i	0.119684	+	0.142634i	0.822559	−	0.568679i	$-0.192545\pi$
$977$	1.09047e11	+	1.29957e11i	0.119684	+	0.142634i	−0.702876	+	0.711313i	$0.748101\pi$
$978$	2.66695e11	−	8.48856e10i	0.291514	−	0.0927852i
$979$	−6.94439e10	+	2.52755e10i	−0.0755968	+	0.0275150i
$980$	−1.42486e12	−	8.22642e11i	−1.54478	−	0.891880i
$981$	3.94331e11	−	5.69724e11i	0.425779	−	0.615161i
$982$	−8.47257e10	−	1.46749e11i	−0.0911106	−	0.157808i
$983$	−2.30885e11	+	2.75158e11i	−0.247276	+	0.294692i	−0.875378	−	0.483439i	$-0.839387\pi$
$983$	−2.30885e11	+	2.75158e11i	−0.247276	+	0.294692i	0.628102	+	0.778131i	$0.283832\pi$
$984$	−5.14112e11	+	6.91051e10i	−0.548375	+	0.0737106i
$985$	−6.36726e9	−	3.61105e10i	−0.00676407	−	0.0383609i
$986$	2.11545e10	−	3.73011e9i	0.0223818	−	0.00394652i
$987$	3.66555e11	+	1.50667e11i	0.386252	+	0.158763i
$988$	1.77327e11	+	1.48795e11i	0.186101	+	0.156157i
$989$	3.49730e11	−	2.01917e11i	0.365551	−	0.211051i
$990$	−1.62801e11	+	1.64580e11i	−0.169480	+	0.171331i
$991$	1.75783e11	−	3.04465e11i	0.182256	−	0.315677i	−0.760392	−	0.649464i	$-0.774993\pi$
$991$	1.75783e11	−	3.04465e11i	0.182256	−	0.315677i	0.942648	+	0.333787i	$0.108327\pi$
$992$	1.37566e11	+	3.77959e11i	0.142058	+	0.390300i
$993$	−8.21785e11	+	9.01725e11i	−0.845203	+	0.927422i
$994$	3.67894e11	−	3.08700e11i	0.376858	−	0.316221i
$995$	1.30604e11	−	3.58831e11i	0.133249	−	0.366098i
$996$	−9.21637e11	−	3.77321e10i	−0.936532	−	0.0383419i
$997$	2.09430e11	−	1.18774e12i	0.211962	−	1.20210i	−0.674139	−	0.738604i	$-0.735485\pi$
$997$	2.09430e11	−	1.18774e12i	0.211962	−	1.20210i	0.886101	−	0.463492i	$-0.153404\pi$
$998$			9.91425e10i			0.0999397i
$999$	−7.62373e11	+	3.23087e11i	−0.765430	+	0.324383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.f.a.2.11	✓	138
3.2	odd	2		81.9.f.a.8.13		138
27.13	even	9		81.9.f.a.71.13		138
27.14	odd	18	inner	27.9.f.a.14.11	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.11	✓	138	1.1	even	1	trivial
27.9.f.a.14.11	yes	138	27.14	odd	18	inner
81.9.f.a.8.13		138	3.2	odd	2
81.9.f.a.71.13		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-3.24198 - 0.571649i) q^{2} +(-71.7460 + 37.5966i) q^{3} +(-230.378 - 83.8506i) q^{4} +(387.667 + 462.003i) q^{5} +(254.092 - 80.8741i) q^{6} +(-3862.15 + 1405.71i) q^{7} +(1428.79 + 824.913i) q^{8} +(3733.99 - 5394.82i) q^{9} +(-992.706 - 1719.42i) q^{10} +(11423.3 - 13613.8i) q^{11} +(19681.2 - 2645.47i) q^{12} +(-882.859 - 5006.94i) q^{13} +(13324.6 - 2349.49i) q^{14} +(-45183.3 - 18571.9i) q^{15} +(43917.7 + 36851.3i) q^{16} +(23746.9 - 13710.3i) q^{17} +(-15189.5 + 15355.4i) q^{18} +(92857.3 - 160834. i) q^{19} +(-50570.5 - 138941. i) q^{20} +(224244. - 246058. i) q^{21} +(-44816.5 + 37605.5i) q^{22} +(-88410.2 + 242905. i) q^{23} +(-133524. - 5466.51i) q^{24} +(4669.78 - 26483.6i) q^{25} +16737.1i q^{26} +(-65071.9 + 527442. i) q^{27} +1.00762e6 q^{28} +(-234351. - 41322.5i) q^{29} +(135867. + 86039.0i) q^{30} +(-618503. - 225117. i) q^{31} +(-392799. - 468120. i) q^{32} +(-307745. + 1.40621e6i) q^{33} +(-84824.4 + 30873.6i) q^{34} +(-2.14667e6 - 1.23938e6i) q^{35} +(-1.31259e6 + 929748. i) q^{36} +(779022. + 1.34931e6i) q^{37} +(-392982. + 468338. i) q^{38} +(251586. + 326036. i) q^{39} +(172782. + 979898. i) q^{40} +(3.82274e6 - 674052. i) q^{41} +(-867655. + 669527. i) q^{42} +(-1.19676e6 - 1.00420e6i) q^{43} +(-3.77320e6 + 2.17846e6i) q^{44} +(3.93997e6 - 366277. i) q^{45} +(425481. - 736954. i) q^{46} +(407155. + 1.11865e6i) q^{47} +(-4.53640e6 - 992779. i) q^{48} +(8.52411e6 - 7.15258e6i) q^{49} +(-30278.7 + 83190.0i) q^{50} +(-1.18828e6 + 1.87646e6i) q^{51} +(-216444. + 1.22752e6i) q^{52} -1.29944e7i q^{53} +(512474. - 1.67276e6i) q^{54} +1.07180e7 q^{55} +(-6.67780e6 - 1.17748e6i) q^{56} +(-615344. + 1.50303e7i) q^{57} +(736141. + 267934. i) q^{58} +(-1.38268e7 - 1.64782e7i) q^{59} +(8.85196e6 + 8.06721e6i) q^{60} +(1.39731e7 - 5.08578e6i) q^{61} +(1.87649e6 + 1.08339e6i) q^{62} +(-6.83769e6 + 2.60845e7i) q^{63} +(-6.33245e6 - 1.09681e7i) q^{64} +(1.97097e6 - 2.34891e6i) q^{65} +(1.80156e6 - 4.38299e6i) q^{66} +(-1.06177e6 - 6.02157e6i) q^{67} +(-6.62036e6 + 1.16735e6i) q^{68} +(-2.78933e6 - 2.07514e7i) q^{69} +(6.25098e6 + 5.24520e6i) q^{70} +(3.07395e7 - 1.77475e7i) q^{71} +(9.78534e6 - 4.62785e6i) q^{72} +(6.89919e6 - 1.19498e7i) q^{73} +(-1.75425e6 - 4.81975e6i) q^{74} +(660657. + 2.07566e6i) q^{75} +(-3.48782e7 + 2.92663e7i) q^{76} +(-2.49816e7 + 6.86363e7i) q^{77} +(-629259. - 1.20082e6i) q^{78} +(-7.76297e6 + 4.40260e7i) q^{79} +3.45761e7i q^{80} +(-1.51614e7 - 4.02884e7i) q^{81} -1.27786e7 q^{82} +(-4.57442e7 - 8.06593e6i) q^{83} +(-7.22930e7 + 3.78832e7i) q^{84} +(1.55401e7 + 5.65612e6i) q^{85} +(3.30581e6 + 3.93971e6i) q^{86} +(1.83674e7 - 5.84610e6i) q^{87} +(2.75517e7 - 1.00280e7i) q^{88} +(-3.60126e6 - 2.07919e6i) q^{89} +(-1.29827e7 - 1.06481e6i) q^{90} +(1.04480e7 + 1.80965e7i) q^{91} +(4.07355e7 - 4.85466e7i) q^{92} +(5.28388e7 - 7.10240e6i) q^{93} +(-680516. - 3.85940e6i) q^{94} +(1.10303e8 - 1.94495e7i) q^{95} +(4.57815e7 + 1.88178e7i) q^{96} +(-1.08572e8 - 9.11031e7i) q^{97} +(-3.17238e7 + 1.83157e7i) q^{98} +(-3.07893e7 - 1.12460e8i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more