LMFDB - Embedded newform 27.9.f.a.2.12

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			2.12
Character	$\chi$	$=$	27.2
Dual form			27.9.f.a.14.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.46646 - 0.434904i) q^{2} +(-52.6972 - 61.5143i) q^{3} +(-234.667 - 85.4118i) q^{4} +(-411.949 - 490.942i) q^{5} +(103.223 + 174.641i) q^{6} +(243.334 - 88.5664i) q^{7} +(1096.91 + 633.301i) q^{8} +(-1007.01 + 6483.26i) q^{9} +(802.546 + 1390.05i) q^{10} +(4355.96 - 5191.23i) q^{11} +(7112.24 + 18936.3i) q^{12} +(-733.507 - 4159.93i) q^{13} +(-638.693 + 112.619i) q^{14} +(-8491.39 + 51212.1i) q^{15} +(46543.3 + 39054.5i) q^{16} +(-27580.9 + 15923.8i) q^{17} +(5303.36 - 15552.8i) q^{18} +(-31761.5 + 55012.5i) q^{19} +(54738.7 + 150393. i) q^{20} +(-18271.1 - 10301.3i) q^{21} +(-13001.5 + 10909.6i) q^{22} +(-67576.8 + 185666. i) q^{23} +(-18847.0 - 100849. i) q^{24} +(-3490.62 + 19796.3i) q^{25} +10579.3i q^{26} +(451880. - 279704. i) q^{27} -64667.1 q^{28} +(1.01674e6 + 179279. i) q^{29} +(43216.0 - 122620. i) q^{30} +(-1.67239e6 - 608702. i) q^{31} +(-306236. - 364958. i) q^{32} +(-548882. + 5609.45i) q^{33} +(74952.5 - 27280.5i) q^{34} +(-143722. - 82978.2i) q^{35} +(790060. - 1.43540e6i) q^{36} +(-711454. - 1.23227e6i) q^{37} +(102264. - 121873. i) q^{38} +(-217241. + 264338. i) q^{39} +(-140957. - 799407. i) q^{40} +(47826.5 - 8433.11i) q^{41} +(40585.0 + 33354.1i) q^{42} +(670492. + 562610. i) q^{43} +(-1.46559e6 + 846160. i) q^{44} +(3.59774e6 - 2.17639e6i) q^{45} +(247423. - 428549. i) q^{46} +(2.11724e6 + 5.81707e6i) q^{47} +(-50293.0 - 4.92114e6i) q^{48} +(-4.36473e6 + 3.66244e6i) q^{49} +(17219.0 - 47308.8i) q^{50} +(2.43298e6 + 857477. i) q^{51} +(-183177. + 1.03885e6i) q^{52} +9.95902e6i q^{53} +(-1.23619e6 + 493355. i) q^{54} -4.34303e6 q^{55} +(323005. + 56954.4i) q^{56} +(5.05780e6 - 945219. i) q^{57} +(-2.42979e6 - 884370. i) q^{58} +(9.92151e6 + 1.18240e7i) q^{59} +(6.36676e6 - 1.12925e7i) q^{60} +(-2.00776e7 + 7.30764e6i) q^{61} +(3.86018e6 + 2.22867e6i) q^{62} +(329158. + 1.66679e6i) q^{63} +(-7.18042e6 - 1.24369e7i) q^{64} +(-1.74012e6 + 2.07379e6i) q^{65} +(1.35624e6 + 224875. i) q^{66} +(2.15182e6 + 1.22036e7i) q^{67} +(7.83240e6 - 1.38106e6i) q^{68} +(1.49822e7 - 5.62712e6i) q^{69} +(318399. + 267168. i) q^{70} +(-2.36946e6 + 1.36801e6i) q^{71} +(-5.21046e6 + 6.47380e6i) q^{72} +(874977. - 1.51550e6i) q^{73} +(1.21886e6 + 3.34878e6i) q^{74} +(1.40170e6 - 828486. i) q^{75} +(1.21521e7 - 1.01968e7i) q^{76} +(600185. - 1.64900e6i) q^{77} +(650779. - 557500. i) q^{78} +(7.53737e6 - 4.27466e7i) q^{79} -3.89386e7i q^{80} +(-4.10186e7 - 1.30575e7i) q^{81} -121630. q^{82} +(-5.86063e7 - 1.03339e7i) q^{83} +(3.40778e6 + 3.97795e6i) q^{84} +(1.91796e7 + 6.98080e6i) q^{85} +(-1.40906e6 - 1.67926e6i) q^{86} +(-4.25512e7 - 7.19916e7i) q^{87} +(8.06570e6 - 2.93568e6i) q^{88} +(-3.32007e7 - 1.91684e7i) q^{89} +(-9.82023e6 + 3.80331e6i) q^{90} +(-546917. - 947288. i) q^{91} +(3.17161e7 - 3.77978e7i) q^{92} +(5.06866e7 + 1.34953e8i) q^{93} +(-2.69223e6 - 1.52684e7i) q^{94} +(4.00921e7 - 7.06932e6i) q^{95} +(-6.31236e6 + 3.80702e7i) q^{96} +(1.06250e8 + 8.91546e7i) q^{97} +(1.23583e7 - 7.13504e6i) q^{98} +(2.92696e7 + 3.34685e7i) 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 $

$2$	−2.46646	−	0.434904i	−0.154154	−	0.0271815i	0.0960385	−	0.995378i	$-0.469383\pi$
$2$	−2.46646	−	0.434904i	−0.154154	−	0.0271815i	−0.250193	+	0.968196i	$0.580494\pi$
$3$	−52.6972	−	61.5143i	−0.650582	−	0.759436i
$3$	−52.6972	−	61.5143i	−0.650582	−	0.759436i
$4$	−234.667	−	85.4118i	−0.916668	−	0.333640i
$5$	−411.949	−	490.942i	−0.659119	−	0.785508i	0.328140	−	0.944629i	$-0.393578\pi$
$5$	−411.949	−	490.942i	−0.659119	−	0.785508i	−0.987259	+	0.159122i	$0.949134\pi$
$6$	103.223	+	174.641i	0.0796473	+	0.134754i
$7$	243.334	−	88.5664i	0.101347	−	0.0368873i	−0.290849	−	0.956769i	$-0.593938\pi$
$7$	243.334	−	88.5664i	0.101347	−	0.0368873i	0.392196	+	0.919882i	$0.371715\pi$
$8$	1096.91	+	633.301i	0.267800	+	0.154614i
$9$	−1007.01	+	6483.26i	−0.153485	+	0.988151i
$10$	802.546	+	1390.05i	0.0802546	+	0.139005i
$11$	4355.96	−	5191.23i	0.297518	−	0.354568i	−0.596489	−	0.802621i	$-0.703438\pi$
$11$	4355.96	−	5191.23i	0.297518	−	0.354568i	0.894007	+	0.448053i	$0.147882\pi$
$12$	7112.24	+	18936.3i	0.342990	+	0.913211i
$13$	−733.507	−	4159.93i	−0.0256821	−	0.145651i	0.969270	−	0.245998i	$-0.0791157\pi$
$13$	−733.507	−	4159.93i	−0.0256821	−	0.145651i	−0.994952	+	0.100347i	$0.968005\pi$
$14$	−638.693	+	112.619i	−0.0166257	+	0.00293156i
$15$	−8491.39	+	51212.1i	−0.167731	+	1.01160i
$16$	46543.3	+	39054.5i	0.710195	+	0.595924i
$17$	−27580.9	+	15923.8i	−0.330227	+	0.190656i	−0.655942	−	0.754812i	$-0.727728\pi$
$17$	−27580.9	+	15923.8i	−0.330227	+	0.190656i	0.325715	+	0.945468i	$0.394395\pi$
$18$	5303.36	−	15552.8i	0.0505198	−	0.148156i
$19$	−31761.5	+	55012.5i	−0.243717	+	0.422131i	−0.961770	−	0.273858i	$-0.911700\pi$
$19$	−31761.5	+	55012.5i	−0.243717	+	0.422131i	0.718053	+	0.695989i	$0.245034\pi$
$20$	54738.7	+	150393.i	0.342117	+	0.939958i
$21$	−18271.1	−	10301.3i	−0.0939481	−	0.0529683i
$22$	−13001.5	+	10909.6i	−0.0555013	+	0.0465711i
$23$	−67576.8	+	185666.i	−0.241483	+	0.663469i	0.758448	+	0.651733i	$0.225958\pi$
$23$	−67576.8	+	185666.i	−0.241483	+	0.663469i	−0.999931	+	0.0117355i	$0.996264\pi$
$24$	−18847.0	−	100849.i	−0.0568063	−	0.303966i
$25$	−3490.62	+	19796.3i	−0.00893599	+	0.0506785i
$26$			10579.3i			0.0231507i
$27$	451880.	−	279704.i	0.850292	−	0.526312i
$28$	−64667.1			−0.105209
$29$	1.01674e6	+	179279.i	1.43753	+	0.253476i	0.837474	−	0.546478i	$-0.184032\pi$
$29$	1.01674e6	+	179279.i	1.43753	+	0.253476i	0.600061	+	0.799954i	$0.295143\pi$
$30$	43216.0	−	122620.i	0.0533531	−	0.151382i
$31$	−1.67239e6	−	608702.i	−1.81089	−	0.659110i	−0.996940	−	0.0781752i	$-0.975091\pi$
$31$	−1.67239e6	−	608702.i	−1.81089	−	0.659110i	−0.813950	−	0.580935i	$-0.802687\pi$
$32$	−306236.	−	364958.i	−0.292050	−	0.348051i
$33$	−548882.	+	5609.45i	−0.462832	+	0.00473004i
$34$	74952.5	−	27280.5i	0.0560881	−	0.0204144i
$35$	−143722.	−	82978.2i	−0.0957750	−	0.0552957i
$36$	790060.	−	1.43540e6i	0.470381	−	0.854598i
$37$	−711454.	−	1.23227e6i	−0.379612	−	0.657507i	0.611394	−	0.791327i	$-0.290609\pi$
$37$	−711454.	−	1.23227e6i	−0.379612	−	0.657507i	−0.991006	+	0.133819i	$0.957276\pi$
$38$	102264.	−	121873.i	0.0490442	−	0.0584486i
$39$	−217241.	+	264338.i	−0.0939039	+	0.114262i
$40$	−140957.	−	799407.i	−0.0550613	−	0.312268i
$41$	47826.5	−	8433.11i	0.0169252	−	0.00298437i	−0.165179	−	0.986264i	$-0.552820\pi$
$41$	47826.5	−	8433.11i	0.0169252	−	0.00298437i	0.182104	+	0.983279i	$0.441709\pi$
$42$	40585.0	+	33354.1i	0.0130427	+	0.0107189i
$43$	670492.	+	562610.i	0.196119	+	0.164564i	0.735559	−	0.677461i	$-0.236920\pi$
$43$	670492.	+	562610.i	0.196119	+	0.164564i	−0.539440	+	0.842024i	$0.681364\pi$
$44$	−1.46559e6	+	846160.i	−0.391023	+	0.225757i
$45$	3.59774e6	−	2.17639e6i	0.877365	−	0.530746i
$46$	247423.	−	428549.i	0.0552597	−	0.0957125i
$47$	2.11724e6	+	5.81707e6i	0.433889	+	1.19210i	0.943406	+	0.331639i	$0.107602\pi$
$47$	2.11724e6	+	5.81707e6i	0.433889	+	1.19210i	−0.509517	+	0.860460i	$0.670176\pi$
$48$	−50293.0	−	4.92114e6i	−0.00947420	−	0.927045i
$49$	−4.36473e6	+	3.66244e6i	−0.757134	+	0.635311i
$50$	17219.0	−	47308.8i	0.00275504	−	0.00756941i
$51$	2.43298e6	+	857477.i	0.359631	+	0.126748i
$52$	−183177.	+	1.03885e6i	−0.0250529	+	0.142082i
$53$			9.95902e6i			1.26216i	0.775719	+	0.631078i	$0.217387\pi$
$53$			9.95902e6i			1.26216i	−0.775719	+	0.631078i	$0.782613\pi$
$54$	−1.23619e6	+	493355.i	−0.145382	+	0.0580209i
$55$	−4.34303e6			−0.474616
$56$	323005.	+	56954.4i	0.0328440	+	0.00579129i
$57$	5.05780e6	−	945219.i	0.479140	−	0.0895433i
$58$	−2.42979e6	−	884370.i	−0.214712	−	0.0781487i
$59$	9.92151e6	+	1.18240e7i	0.818785	+	0.975790i	0.999971	−	0.00765928i	$-0.00243805\pi$
$59$	9.92151e6	+	1.18240e7i	0.818785	+	0.975790i	−0.181186	+	0.983449i	$0.557994\pi$
$60$	6.36676e6	−	1.12925e7i	0.491263	−	0.871336i
$61$	−2.00776e7	+	7.30764e6i	−1.45008	+	0.527786i	−0.942613	−	0.333886i	$-0.891640\pi$
$61$	−2.00776e7	+	7.30764e6i	−1.45008	+	0.527786i	−0.507466	+	0.861672i	$0.669418\pi$
$62$	3.86018e6	+	2.22867e6i	0.261240	+	0.150827i
$63$	329158.	+	1.66679e6i	0.0208950	+	0.105808i
$64$	−7.18042e6	−	1.24369e7i	−0.427987	−	0.741295i
$65$	−1.74012e6	+	2.07379e6i	−0.0974821	+	0.116175i
$66$	1.35624e6	+	224875.i	0.0714759	+	0.0118513i
$67$	2.15182e6	+	1.22036e7i	0.106784	+	0.605602i	0.990493	+	0.137565i	$0.0439276\pi$
$67$	2.15182e6	+	1.22036e7i	0.106784	+	0.605602i	−0.883709	+	0.468037i	$0.844961\pi$
$68$	7.83240e6	−	1.38106e6i	0.366319	−	0.0645919i
$69$	1.49822e7	−	5.62712e6i	0.660966	−	0.248250i
$70$	318399.	+	267168.i	0.0132611	+	0.0111274i
$71$	−2.36946e6	+	1.36801e6i	−0.0932429	+	0.0538338i	−0.545896	−	0.837853i	$-0.683811\pi$
$71$	−2.36946e6	+	1.36801e6i	−0.0932429	+	0.0538338i	0.452654	+	0.891686i	$0.350477\pi$
$72$	−5.21046e6	+	6.47380e6i	−0.193886	+	0.240896i
$73$	874977.	−	1.51550e6i	0.0308109	−	0.0533661i	−0.850209	−	0.526446i	$-0.823524\pi$
$73$	874977.	−	1.51550e6i	0.0308109	−	0.0533661i	0.881020	+	0.473080i	$0.156858\pi$
$74$	1.21886e6	+	3.34878e6i	0.0406467	+	0.111676i
$75$	1.40170e6	−	828486.i	0.0443007	−	0.0261843i
$76$	1.21521e7	−	1.01968e7i	0.364248	−	0.305640i
$77$	600185.	−	1.64900e6i	0.0170735	−	0.0469091i
$78$	650779.	−	557500.i	0.0175815	−	0.0150614i
$79$	7.53737e6	−	4.27466e7i	0.193514	−	1.09747i	−0.721006	−	0.692929i	$-0.756320\pi$
$79$	7.53737e6	−	4.27466e7i	0.193514	−	1.09747i	0.914520	−	0.404542i	$-0.132569\pi$
$80$		−	3.89386e7i		−	0.950648i
$81$	−4.10186e7	−	1.30575e7i	−0.952885	−	0.303333i
$82$	−121630.			−0.00269020
$83$	−5.86063e7	−	1.03339e7i	−1.23490	−	0.217746i	−0.482172	−	0.876077i	$-0.660152\pi$
$83$	−5.86063e7	−	1.03339e7i	−1.23490	−	0.217746i	−0.752729	+	0.658330i	$0.771263\pi$
$84$	3.40778e6	+	3.97795e6i	0.0684469	+	0.0798992i
$85$	1.91796e7	+	6.98080e6i	0.367421	+	0.133730i
$86$	−1.40906e6	−	1.67926e6i	−0.0257595	−	0.0306990i
$87$	−4.25512e7	−	7.19916e7i	−0.742736	−	1.25662i
$88$	8.06570e6	−	2.93568e6i	0.134497	−	0.0489528i
$89$	−3.32007e7	−	1.91684e7i	−0.529161	−	0.305511i	0.211514	−	0.977375i	$-0.432161\pi$
$89$	−3.32007e7	−	1.91684e7i	−0.529161	−	0.305511i	−0.740675	+	0.671864i	$0.765494\pi$
$90$	−9.82023e6	+	3.80331e6i	−0.149676	+	0.0579685i
$91$	−546917.	−	947288.i	−0.00797547	−	0.0138139i
$92$	3.17161e7	−	3.77978e7i	0.442719	−	0.527612i
$93$	5.06866e7	+	1.34953e8i	0.677581	+	1.80406i
$94$	−2.69223e6	−	1.52684e7i	−0.0344826	−	0.195561i
$95$	4.00921e7	−	7.06932e6i	0.492226	−	0.0867927i
$96$	−6.31236e6	+	3.80702e7i	−0.0743201	+	0.448229i
$97$	1.06250e8	+	8.91546e7i	1.20017	+	1.00706i	0.999625	+	0.0273787i	$0.00871601\pi$
$97$	1.06250e8	+	8.91546e7i	1.20017	+	1.00706i	0.200546	+	0.979684i	$0.435728\pi$
$98$	1.23583e7	−	7.13504e6i	0.133984	−	0.0773557i
$99$	2.92696e7	+	3.34685e7i	0.304702	+	0.348413i
$100$	2.50997e6	−	4.34740e6i	0.0250997	−	0.0434740i
$101$	4.55685e7	+	1.25198e8i	0.437904	+	1.20313i	0.940853	+	0.338816i	$0.110026\pi$
$101$	4.55685e7	+	1.25198e8i	0.437904	+	1.20313i	−0.502949	+	0.864316i	$0.667751\pi$
$102$	−5.62793e6	−	3.17305e6i	−0.0519933	−	0.0293140i
$103$	−9.13908e7	+	7.66860e7i	−0.811995	+	0.681345i	−0.951083	−	0.308935i	$-0.900027\pi$
$103$	−9.13908e7	+	7.66860e7i	−0.811995	+	0.681345i	0.139088	+	0.990280i	$0.455583\pi$
$104$	1.82989e6	−	5.02759e6i	0.0156420	−	0.0429761i
$105$	2.46942e6	+	1.32137e7i	0.0203160	+	0.108709i
$106$	4.33122e6	−	2.45636e7i	0.0343073	−	0.194567i
$107$		−	1.15116e8i		−	0.878216i	−0.898434	−	0.439108i	$-0.855295\pi$
$107$		−	1.15116e8i		−	0.878216i	0.898434	−	0.439108i	$-0.144705\pi$
$108$	−1.29931e8	+	2.70413e7i	−0.955034	+	0.198762i
$109$	3.18734e7			0.225799			0.112900	−	0.993606i	$-0.463986\pi$
$109$	3.18734e7			0.225799			0.112900	+	0.993606i	$0.463986\pi$
$110$	1.07119e7	+	1.88880e6i	0.0731639	+	0.0129008i
$111$	−3.83109e7	+	1.08702e8i	−0.252366	+	0.716054i
$112$	1.47845e7	+	5.38112e6i	0.0939582	+	0.0341980i
$113$	−4.45785e7	−	5.31266e7i	−0.273408	−	0.325835i	0.611816	−	0.791000i	$-0.290439\pi$
$113$	−4.45785e7	−	5.31266e7i	−0.273408	−	0.325835i	−0.885224	+	0.465165i	$0.845995\pi$
$114$	−1.28860e7	+	131692.i	−0.0762952	+	0.000779721i
$115$	1.18989e8	−	4.33086e7i	0.680326	−	0.247618i
$116$	−2.23283e8	−	1.28913e8i	−1.23317	−	0.711972i
$117$	2.77085e7	−	566410.i	0.147867	−	0.00302264i
$118$	−1.93287e7	−	3.34784e7i	−0.0996955	−	0.172678i
$119$	−5.30105e6	+	6.31755e6i	−0.0264347	+	0.0315036i
$120$	−4.17469e7	+	5.07974e7i	−0.201326	+	0.244972i
$121$	2.92485e7	+	1.65877e8i	0.136447	+	0.773827i
$122$	5.26987e7	−	9.29221e6i	0.237882	−	0.0419449i
$123$	−3.03908e6	−	2.49761e6i	−0.0132777	−	0.0109120i
$124$	3.40466e8	+	2.85685e8i	1.44008	+	1.20837i
$125$	−2.05647e8	+	1.18730e8i	−0.842331	+	0.486320i
$126$	−86963.5	−	4.25422e6i	−0.000345029	−	0.0168787i
$127$	2.33645e8	−	4.04684e8i	0.898133	−	1.55561i	0.0682548	−	0.997668i	$-0.478257\pi$
$127$	2.33645e8	−	4.04684e8i	0.898133	−	1.55561i	0.829878	−	0.557944i	$-0.188410\pi$
$128$	5.40153e7	+	1.48406e8i	0.201223	+	0.552855i
$129$	−724509.	−	7.08928e7i	−0.00261629	−	0.256002i
$130$	5.19383e6	−	4.35814e6i	0.0181851	−	0.0152591i
$131$	1.80234e8	−	4.95187e8i	0.611998	−	1.68145i	−0.113765	−	0.993508i	$-0.536291\pi$
$131$	1.80234e8	−	4.95187e8i	0.611998	−	1.68145i	0.725763	−	0.687944i	$-0.241487\pi$
$132$	1.29284e8	+	4.55646e7i	0.425841	+	0.150083i
$133$	−2.85640e6	+	1.61994e7i	−0.00912876	+	0.0517718i
$134$		−	3.10355e7i		−	0.0962586i
$135$	−3.23470e8	−	1.06623e8i	−0.973865	−	0.321008i
$136$	−4.03382e7			−0.117913
$137$	−3.13130e8	−	5.52133e7i	−0.888879	−	0.156733i	−0.289480	−	0.957184i	$-0.593482\pi$
$137$	−3.13130e8	−	5.52133e7i	−0.888879	−	0.156733i	−0.599399	+	0.800451i	$0.704594\pi$
$138$	−3.94003e7	+	7.36327e6i	−0.108638	+	0.0203027i
$139$	−5.17739e8	−	1.88442e8i	−1.38692	−	0.504798i	−0.462652	−	0.886540i	$-0.653102\pi$
$139$	−5.17739e8	−	1.88442e8i	−1.38692	−	0.504798i	−0.924269	+	0.381742i	$0.875324\pi$
$140$	2.66396e7	+	3.17478e7i	0.0693450	+	0.0826422i
$141$	2.46260e8	−	4.36783e8i	0.623043	−	1.10507i
$142$	6.43914e6	−	2.34365e6i	0.0158370	−	0.00576421i
$143$	−2.47903e7	−	1.43127e7i	−0.0592839	−	0.0342276i
$144$	−3.00070e8	+	2.62424e8i	−0.697867	+	0.610314i
$145$	−3.30830e8	−	5.73015e8i	−0.748399	−	1.29627i
$146$	−2.81720e6	+	3.35741e6i	−0.00620020	+	0.00738912i
$147$	4.55301e8	+	7.54928e7i	0.975056	+	0.161672i
$148$	6.17040e7	+	3.49941e8i	0.128608	+	0.729370i
$149$	6.98309e8	−	1.23131e8i	1.41678	−	0.249817i	0.587761	−	0.809035i	$-0.300010\pi$
$149$	6.98309e8	−	1.23131e8i	1.41678	−	0.249817i	0.829021	+	0.559218i	$0.188899\pi$
$150$	−3.81756e6	+	1.43383e6i	−0.00754086	+	0.00283225i
$151$	−2.61562e8	−	2.19476e8i	−0.503114	−	0.422163i	0.355584	−	0.934644i	$-0.384282\pi$
$151$	−2.61562e8	−	2.19476e8i	−0.503114	−	0.422163i	−0.858698	+	0.512481i	$0.828726\pi$
$152$	−6.96789e7	+	4.02291e7i	−0.130535	+	0.0753644i
$153$	−7.54639e7	−	1.94849e8i	−0.137712	−	0.355577i
$154$	−2.19749e6	+	3.80617e6i	−0.00390701	+	0.00676714i
$155$	3.90105e8	+	1.07180e9i	0.675856	+	1.85690i
$156$	7.35569e7	−	4.34763e7i	0.124201	−	0.0734099i
$157$	−6.89517e8	+	5.78573e8i	−1.13487	+	0.952269i	−0.999259	−	0.0384927i	$-0.987744\pi$
$157$	−6.89517e8	+	5.78573e8i	−1.13487	+	0.952269i	−0.135612	+	0.990762i	$0.543300\pi$
$158$	−3.71813e7	+	1.02155e8i	−0.0596618	+	0.163920i
$159$	6.12622e8	−	5.24812e8i	0.958527	−	0.821137i
$160$	−5.30195e7	+	3.00689e8i	−0.0809014	+	0.458815i
$161$			5.11639e7i			0.0761483i
$162$	9.54921e7	+	5.00449e7i	0.138646	+	0.0726608i
$163$	−5.07912e8			−0.719512			−0.359756	−	0.933046i	$-0.617140\pi$
$163$	−5.07912e8			−0.719512			−0.359756	+	0.933046i	$0.617140\pi$
$164$	−1.19436e7	−	2.10598e6i	−0.0165105	−	0.00291124i
$165$	2.28865e8	+	2.67158e8i	0.308777	+	0.360440i
$166$	1.40056e8	+	5.09763e7i	0.184446	+	0.0671330i
$167$	5.64103e8	+	6.72272e8i	0.725258	+	0.864329i	0.995130	−	0.0985671i	$-0.0314259\pi$
$167$	5.64103e8	+	6.72272e8i	0.725258	+	0.864329i	−0.269872	+	0.962896i	$0.586981\pi$
$168$	−1.35179e7	−	2.28707e7i	−0.0169696	−	0.0287107i
$169$	7.49769e8	−	2.72894e8i	0.919138	−	0.334539i
$170$	−4.42698e7	−	2.55592e7i	−0.0530044	−	0.0306021i
$171$	−3.24676e8	−	2.61316e8i	−0.379722	−	0.305620i
$172$	−1.09289e8	−	1.89294e8i	−0.124871	−	0.216283i
$173$	−9.08559e8	+	1.08278e9i	−1.01430	+	1.20880i	−0.0364893	+	0.999334i	$0.511617\pi$
$173$	−9.08559e8	+	1.08278e9i	−1.01430	+	1.20880i	−0.977816	+	0.209467i	$0.932827\pi$
$174$	7.36415e7	+	1.96070e8i	0.0803389	+	0.213902i
$175$	903900.	+	5.12627e6i	0.000963758	+	0.00546574i
$176$	4.05482e8	−	7.14974e7i	0.422591	−	0.0745143i
$177$	2.04509e8	−	1.23341e9i	0.208362	−	1.25665i
$178$	7.35520e7	+	6.17174e7i	0.0732680	+	0.0614792i
$179$	−1.09594e8	+	6.32741e7i	−0.106752	+	0.0616330i	−0.552425	−	0.833562i	$-0.686298\pi$
$179$	−1.09594e8	+	6.32741e7i	−0.106752	+	0.0616330i	0.445674	+	0.895196i	$0.352964\pi$
$180$	−1.03016e9	+	2.03437e8i	−0.981330	+	0.193794i
$181$	−2.30450e8	+	3.99152e8i	−0.214715	+	0.371898i	−0.953185	−	0.302389i	$-0.902216\pi$
$181$	−2.30450e8	+	3.99152e8i	−0.214715	+	0.371898i	0.738469	+	0.674287i	$0.235549\pi$
$182$	936972.	+	2.57431e6i	0.000853967	+	0.00234626i
$183$	1.50755e9	+	8.49965e8i	1.34422	+	0.757874i
$184$	−1.91708e8	+	1.60862e8i	−0.167251	+	0.140340i
$185$	−3.11893e8	+	8.56918e8i	−0.266268	+	0.731564i
$186$	−6.63251e7	−	3.54901e8i	−0.0554148	−	0.296521i
$187$	−3.74769e7	+	2.12542e8i	−0.0306477	+	0.173811i
$188$		−	1.54591e9i		−	1.23752i
$189$	8.51855e7	−	1.08083e8i	0.0667603	−	0.0847051i
$190$	−1.01960e8			−0.0782378
$191$	7.37923e8	+	1.30116e8i	0.554469	+	0.0977679i	0.443860	−	0.896096i	$-0.353609\pi$
$191$	7.37923e8	+	1.30116e8i	0.554469	+	0.0977679i	0.110609	+	0.993864i	$0.464720\pi$
$192$	−3.86656e8	+	1.09709e9i	−0.284525	+	0.807302i
$193$	−1.25557e9	−	4.56992e8i	−0.904927	−	0.329366i	−0.152701	−	0.988272i	$-0.548797\pi$
$193$	−1.25557e9	−	4.56992e8i	−0.904927	−	0.329366i	−0.752225	+	0.658906i	$0.771019\pi$
$194$	−2.23289e8	−	2.66105e8i	−0.157638	−	0.187865i
$195$	2.19267e8	−	2.24086e6i	0.151647	−	0.00154980i
$196$	1.33707e9	−	4.86655e8i	0.906005	−	0.329759i
$197$	−8.27317e8	−	4.77652e8i	−0.549297	−	0.317137i	0.199541	−	0.979889i	$-0.436055\pi$
$197$	−8.27317e8	−	4.77652e8i	−0.549297	−	0.317137i	−0.748838	+	0.662753i	$0.769388\pi$
$198$	−5.76368e7	−	9.52782e7i	−0.0375007	−	0.0619916i
$199$	−4.23487e8	−	7.33501e8i	−0.270040	−	0.467723i	0.698832	−	0.715286i	$-0.253704\pi$
$199$	−4.23487e8	−	7.33501e8i	−0.270040	−	0.467723i	−0.968872	+	0.247563i	$0.920370\pi$
$200$	−1.63659e7	+	1.95041e7i	−0.0102287	+	0.0121901i
$201$	6.37299e8	−	7.75461e8i	0.390444	−	0.475090i
$202$	−5.79438e7	−	3.28615e8i	−0.0348018	−	0.197371i
$203$	2.63286e8	−	4.64244e7i	0.155040	−	0.0273377i
$204$	−4.97700e8	−	4.09026e8i	−0.287374	−	0.236173i
$205$	−2.38423e7	−	2.00060e7i	−0.0135000	−	0.0113278i
$206$	2.58763e8	−	1.49397e8i	0.143692	−	0.0829608i
$207$	−1.13567e9	−	6.25086e8i	−0.618543	−	0.340454i
$208$	1.28324e8	−	2.22264e8i	0.0685574	−	0.118745i
$209$	1.47231e8	+	4.04514e8i	0.0771638	+	0.212006i
$210$	−344050.	−	3.36651e7i	−0.000176907	−	0.0173102i
$211$	−1.74069e8	+	1.46061e8i	−0.0878195	+	0.0736893i	−0.685641	−	0.727940i	$-0.740478\pi$
$211$	−1.74069e8	+	1.46061e8i	−0.0878195	+	0.0736893i	0.597821	+	0.801630i	$0.296033\pi$
$212$	8.50618e8	−	2.33705e9i	0.421106	−	1.15698i
$213$	2.09016e8	+	7.36654e7i	0.101545	+	0.0357886i
$214$	−5.00645e7	+	2.83930e8i	−0.0238712	+	0.135381i
$215$		−	5.60940e8i		−	0.262520i
$216$	6.72808e8	−	2.06336e7i	0.309084	−	0.00947894i
$217$	−4.60861e8			−0.207841
$218$	−7.86146e7	−	1.38619e7i	−0.0348079	−	0.00613757i
$219$	−1.39334e8	+	2.60392e7i	−0.0605732	+	0.0113201i
$220$	1.01917e9	+	3.70946e8i	0.435065	+	0.158351i
$221$	8.64727e7	+	1.03054e8i	0.0362501	+	0.0432012i
$222$	1.41767e8	−	2.51448e8i	0.0583666	−	0.103523i
$223$	6.09381e8	−	2.21796e8i	0.246416	−	0.0896882i	−0.215859	−	0.976424i	$-0.569255\pi$
$223$	6.09381e8	−	2.21796e8i	0.246416	−	0.0896882i	0.462276	+	0.886736i	$0.347033\pi$
$224$	−1.06841e8	−	6.16846e7i	−0.0424371	−	0.0245010i
$225$	−1.24829e8	−	4.25658e7i	−0.0487065	−	0.0166085i
$226$	8.68463e7	+	1.50422e8i	0.0332903	+	0.0576605i
$227$	−6.84046e8	+	8.15215e8i	−0.257622	+	0.307021i	−0.879316	−	0.476238i	$-0.842000\pi$
$227$	−6.84046e8	+	8.15215e8i	−0.257622	+	0.307021i	0.621695	+	0.783260i	$0.286444\pi$
$228$	−1.26763e9	−	2.10184e8i	−0.469087	−	0.0777786i
$229$	3.42445e8	+	1.94210e9i	0.124523	+	0.706205i	0.981590	+	0.191000i	$0.0611731\pi$
$229$	3.42445e8	+	1.94210e9i	0.124523	+	0.706205i	−0.857067	+	0.515205i	$0.827716\pi$
$230$	−3.12318e8	+	5.50701e7i	−0.111606	+	0.0196791i
$231$	−1.33065e8	+	4.99775e7i	−0.0467321	+	0.0175520i
$232$	1.00173e9	+	8.40555e8i	0.345781	+	0.290145i
$233$	−3.99283e9	+	2.30526e9i	−1.35474	+	0.782161i	−0.988910	−	0.148519i	$-0.952549\pi$
$233$	−3.99283e9	+	2.30526e9i	−1.35474	+	0.782161i	−0.365833	+	0.930680i	$0.619216\pi$
$234$	−6.85884e7	−	1.06535e7i	−0.0228764	−	0.00355329i
$235$	1.98365e9	−	3.43578e9i	0.650419	−	1.12656i
$236$	−1.31834e9	−	3.62212e9i	−0.424991	−	1.16765i
$237$	−3.02672e9	+	1.78897e9i	−0.959355	+	0.567034i
$238$	1.58224e7	−	1.32766e7i	0.00493133	−	0.00413788i
$239$	4.79266e8	−	1.31677e9i	0.146888	−	0.403570i	−0.844328	−	0.535827i	$-0.820000\pi$
$239$	4.79266e8	−	1.31677e9i	0.146888	−	0.403570i	0.991216	+	0.132256i	$0.0422222\pi$
$240$	−2.39528e9	+	2.05195e9i	−0.721956	+	0.618475i
$241$	−5.55644e8	+	3.15122e9i	−0.164713	+	0.934136i	0.784646	+	0.619944i	$0.212845\pi$
$241$	−5.55644e8	+	3.15122e9i	−0.164713	+	0.934136i	−0.949359	+	0.314192i	$0.898266\pi$
$242$		−	4.21849e8i		−	0.122997i
$243$	1.35834e9	+	3.21132e9i	0.389568	+	0.920998i
$244$	5.33570e9			1.50533
$245$	3.59609e9	+	6.34088e8i	0.998083	+	0.175989i
$246$	6.40956e6	+	7.48198e6i	0.00175020	+	0.00204304i
$247$	2.52145e8	+	9.17734e7i	0.0677428	+	0.0246564i
$248$	−1.44897e9	−	1.72682e9i	−0.383048	−	0.456499i
$249$	2.45271e9	+	4.14969e9i	0.638041	+	1.07949i
$250$	5.58858e8	−	2.03408e8i	0.143068	−	0.0520723i
$251$	2.82883e9	+	1.63323e9i	0.712709	+	0.411483i	0.812063	−	0.583569i	$-0.198344\pi$
$251$	2.82883e9	+	1.63323e9i	0.712709	+	0.411483i	−0.0993540	+	0.995052i	$0.531678\pi$
$252$	6.51208e7	−	4.19254e8i	0.0161479	−	0.103962i
$253$	6.69472e8	+	1.15956e9i	0.163399	+	0.283016i
$254$	−7.52275e8	+	8.96526e8i	−0.180735	+	0.215391i
$255$	−5.81291e8	−	1.54769e9i	−0.137478	−	0.366035i
$256$	5.69712e8	+	3.23100e9i	0.132646	+	0.752275i
$257$	−1.01335e9	+	1.78680e8i	−0.232287	+	0.0409585i	−0.288580	−	0.957456i	$-0.593183\pi$
$257$	−1.01335e9	+	1.78680e8i	−0.232287	+	0.0409585i	0.0562927	+	0.998414i	$0.482072\pi$
$258$	−2.90446e7	+	1.75170e8i	−0.00655521	+	0.0395349i
$259$	−2.82259e8	−	2.36844e8i	−0.0627262	−	0.0526336i
$260$	5.85474e8	−	3.38023e8i	0.128119	−	0.0739696i
$261$	−2.18618e9	+	6.41126e9i	−0.471113	+	1.38160i
$262$	−6.59899e8	+	1.14298e9i	−0.140046	+	0.242568i
$263$	−1.69620e9	−	4.66027e9i	−0.354531	−	0.974066i	−0.980895	−	0.194536i	$-0.937680\pi$
$263$	−1.69620e9	−	4.66027e9i	−0.354531	−	0.974066i	0.626364	−	0.779530i	$-0.284542\pi$
$264$	−6.05626e8	−	3.41454e8i	−0.124678	−	0.0702937i
$265$	4.88931e9	−	4.10261e9i	0.991434	−	0.831912i
$266$	1.40904e7	−	3.87131e7i	0.00281447	−	0.00773270i
$267$	5.70451e8	+	3.05244e9i	0.112247	+	0.600624i
$268$	5.37368e8	−	3.04756e9i	0.104168	−	0.590764i
$269$		−	1.08134e9i		−	0.206516i	−0.994655	−	0.103258i	$-0.967073\pi$
$269$		−	1.08134e9i		−	0.206516i	0.994655	−	0.103258i	$-0.0329267\pi$
$270$	7.51456e8	+	4.03661e8i	0.141400	+	0.0759559i
$271$	−4.66467e9			−0.864855			−0.432428	−	0.901669i	$-0.642343\pi$
$271$	−4.66467e9			−0.864855			−0.432428	+	0.901669i	$0.642343\pi$
$272$	−1.90560e9	−	3.36009e8i	−0.348142	−	0.0613868i
$273$	−2.94508e7	+	8.35627e7i	−0.00530208	+	0.0150439i
$274$	7.48312e8	+	2.72363e8i	0.132764	+	0.0483221i
$275$	8.75622e7	+	1.04353e8i	0.0153104	+	0.0182462i
$276$	−3.99645e9	+	4.08429e7i	−0.688713	+	0.00703850i
$277$	−8.24991e9	+	3.00272e9i	−1.40130	+	0.510030i	−0.928563	−	0.371175i	$-0.878955\pi$
$277$	−8.24991e9	+	3.00272e9i	−1.40130	+	0.510030i	−0.472734	+	0.881205i	$0.656733\pi$
$278$	1.19503e9	+	6.89951e8i	0.200078	+	0.115515i
$279$	5.63050e9	−	1.02296e10i	0.929245	−	1.68827i
$280$	−1.05100e8	−	1.82039e8i	−0.0170990	−	0.0296164i
$281$	3.27244e9	−	3.89994e9i	0.524864	−	0.625508i	−0.436860	−	0.899530i	$-0.643909\pi$
$281$	3.27244e9	−	3.89994e9i	0.524864	−	0.625508i	0.961724	+	0.274021i	$0.0883539\pi$
$282$	−7.97351e8	+	9.70211e8i	−0.126082	+	0.153416i
$283$	−1.36212e9	−	7.72497e9i	−0.212359	−	1.20435i	−0.885432	−	0.464770i	$-0.846137\pi$
$283$	−1.36212e9	−	7.72497e9i	−0.212359	−	1.20435i	0.673073	−	0.739576i	$-0.264974\pi$
$284$	6.72878e8	−	1.18646e8i	0.103434	−	0.0182382i
$285$	−2.54760e9	−	2.09370e9i	−0.386147	−	0.317348i
$286$	5.49197e7	+	4.60831e7i	0.00820850	+	0.00688775i
$287$	1.08909e7	−	6.28789e6i	0.00160523	−	0.000926781i
$288$	2.67450e9	−	1.61789e9i	0.388752	−	0.235169i
$289$	−2.98074e9	+	5.16280e9i	−0.427300	+	0.740106i
$290$	5.66775e8	+	1.55720e9i	0.0801343	+	0.220167i
$291$	−1.14810e8	−	1.12341e10i	−0.0160106	−	1.56663i
$292$	−3.34770e8	+	2.80905e8i	−0.0460485	+	0.0386393i
$293$	−4.13715e9	+	1.13667e10i	−0.561347	+	1.54229i	0.256318	+	0.966592i	$0.417490\pi$
$293$	−4.13715e9	+	1.13667e10i	−0.561347	+	1.54229i	−0.817665	+	0.575695i	$0.804732\pi$
$294$	−1.09015e9	−	3.84213e8i	−0.145914	−	0.0514259i
$295$	1.71774e9	−	9.74178e9i	0.226813	−	1.28632i
$296$		−	1.80226e9i		−	0.234774i
$297$	5.16364e8	−	3.56419e9i	0.0663637	−	0.458073i
$298$	−1.77591e9			−0.225193
$299$	8.21924e8	+	1.44927e8i	0.102836	+	0.0181328i
$300$	−3.99696e8	+	7.46965e7i	−0.0493451	+	0.00922179i
$301$	2.12982e8	+	7.75192e7i	0.0259464	+	0.00944372i
$302$	5.49682e8	+	6.55085e8i	0.0660820	+	0.0787535i
$303$	5.30016e9	−	9.40072e9i	0.628809	−	1.11530i
$304$	−3.62677e9	+	1.32004e9i	−0.424645	+	0.154558i
$305$	1.18586e10	+	6.84655e9i	1.37035	+	0.791175i
$306$	1.01388e8	+	5.13409e8i	0.0115638	+	0.0585568i
$307$	6.47222e9	+	1.12102e10i	0.728618	+	1.26200i	0.957467	+	0.288542i	$0.0931705\pi$
$307$	6.47222e9	+	1.12102e10i	0.728618	+	1.26200i	−0.228849	+	0.973462i	$0.573496\pi$
$308$	−2.81687e8	+	3.35702e8i	−0.0313015	+	0.0373036i
$309$	9.53332e9	+	1.58070e9i	1.04571	+	0.173387i
$310$	−4.96047e8	−	2.81322e9i	−0.0537126	−	0.304619i
$311$	−1.24197e10	+	2.18993e9i	−1.32761	+	0.234093i	−0.792076	−	0.610423i	$-0.791000\pi$
$311$	−1.24197e10	+	2.18993e9i	−1.32761	+	0.234093i	−0.535531	+	0.844516i	$0.679888\pi$
$312$	−4.05699e8	+	1.52375e8i	−0.0428140	+	0.0160804i
$313$	−6.91530e9	−	5.80262e9i	−0.720499	−	0.604571i	0.207024	−	0.978336i	$-0.433622\pi$
$313$	−6.91530e9	−	5.80262e9i	−0.720499	−	0.604571i	−0.927523	+	0.373765i	$0.878067\pi$
$314$	1.95229e9	−	1.12716e9i	0.200829	−	0.115949i
$315$	6.82700e8	−	8.48229e8i	0.0693406	−	0.0861531i
$316$	−5.41983e9	+	9.38743e9i	−0.543548	+	0.941452i
$317$	−8.52565e8	−	2.34240e9i	−0.0844287	−	0.231966i	0.890293	−	0.455388i	$-0.150499\pi$
$317$	−8.52565e8	−	2.34240e9i	−0.0844287	−	0.231966i	−0.974722	+	0.223422i	$0.928277\pi$
$318$	−1.73925e9	+	1.02800e9i	−0.170081	+	0.100527i
$319$	5.35956e9	−	4.49721e9i	0.517567	−	0.434290i
$320$	−3.14781e9	+	8.64853e9i	−0.300198	+	0.824788i
$321$	−7.08129e9	+	6.06630e9i	−0.666949	+	0.571352i
$322$	2.22514e7	−	1.26194e8i	0.00206983	−	0.0117386i
$323$		−	2.02306e9i		−	0.185865i
$324$	8.51044e9	+	6.56763e9i	0.772275	+	0.595976i
$325$	8.49116e7			0.00761085
$326$	1.25275e9	+	2.20893e8i	0.110916	+	0.0195574i
$327$	−1.67964e9	−	1.96067e9i	−0.146901	−	0.171480i
$328$	5.78020e7	+	2.10382e7i	0.00499399	+	0.00181766i
$329$	1.03039e9	+	1.22798e9i	0.0879467	+	0.104811i
$330$	−4.48300e8	−	7.58471e8i	−0.0378019	−	0.0639563i
$331$	−1.23169e10	+	4.48300e9i	−1.02610	+	0.373471i	−0.799596	−	0.600539i	$-0.794953\pi$
$331$	−1.23169e10	+	4.48300e9i	−1.02610	+	0.373471i	−0.226507	+	0.974010i	$0.572731\pi$
$332$	1.28703e10	+	7.43069e9i	1.05935	+	0.611614i
$333$	8.70560e9	−	3.37162e9i	0.707981	−	0.274197i
$334$	−1.09897e9	−	1.90347e9i	−0.0883077	−	0.152953i
$335$	5.10481e9	−	6.08367e9i	0.405322	−	0.483044i
$336$	−4.48086e8	−	1.19303e9i	−0.0351564	−	0.0936038i
$337$	−2.91787e8	−	1.65481e9i	−0.0226228	−	0.128300i	0.971405	−	0.237430i	$-0.0763049\pi$
$337$	−2.91787e8	−	1.65481e9i	−0.0226228	−	0.128300i	−0.994028	+	0.109129i	$0.965194\pi$
$338$	−1.96796e9	+	3.47005e8i	−0.150782	+	0.0265870i
$339$	−9.18883e8	+	5.54183e9i	−0.0695763	+	0.419619i
$340$	−3.90457e9	−	3.27633e9i	−0.292185	−	0.245172i
$341$	−1.04448e10	+	6.03031e9i	−0.772472	+	0.445987i
$342$	6.87155e8	+	7.85731e8i	0.0502285	+	0.0574340i
$343$	−1.48412e9	+	2.57057e9i	−0.107224	+	0.185717i
$344$	3.79168e8	+	1.04176e9i	0.0270768	+	0.0743930i
$345$	−8.93450e9	−	5.03731e9i	−0.630658	−	0.355568i
$346$	2.71183e9	−	2.27550e9i	0.189216	−	0.158771i
$347$	2.77675e9	−	7.62907e9i	0.191522	−	0.526203i	−0.806347	−	0.591442i	$-0.798559\pi$
$347$	2.77675e9	−	7.62907e9i	0.191522	−	0.526203i	0.997870	+	0.0652390i	$0.0207810\pi$
$348$	3.83642e9	+	2.05284e10i	0.261583	+	1.39971i
$349$	1.80498e7	−	1.02366e8i	0.00121667	−	0.00690006i	−0.984193	−	0.177097i	$-0.943329\pi$
$349$	1.80498e7	−	1.02366e8i	0.00121667	−	0.00690006i	0.985410	+	0.170197i	$0.0544404\pi$
$350$		−	1.30369e7i		−	0.000868763i
$351$	−1.49500e9	−	1.67462e9i	−0.0984949	−	0.110329i
$352$	−3.22854e9			−0.210298
$353$	−9.42955e9	−	1.66268e9i	−0.607285	−	0.107081i	−0.138454	−	0.990369i	$-0.544213\pi$
$353$	−9.42955e9	−	1.66268e9i	−0.607285	−	0.107081i	−0.468830	+	0.883288i	$0.655324\pi$
$354$	−1.04083e9	+	2.95321e9i	−0.0662774	+	0.188053i
$355$	1.64771e9	+	5.99717e8i	0.103745	+	0.0377601i
$356$	6.15390e9	+	7.33394e9i	0.383134	+	0.456601i
$357$	6.67970e8	−	6.82651e6i	0.0411229	−	0.000420267i
$358$	2.97828e8	−	1.08400e8i	0.0181315	−	0.00659931i
$359$	2.20697e10	+	1.27419e10i	1.32867	+	0.767109i	0.985094	−	0.172015i	$-0.0550276\pi$
$359$	2.20697e10	+	1.27419e10i	1.32867	+	0.767109i	0.343578	+	0.939124i	$0.388361\pi$
$360$	5.32471e9	−	1.08846e8i	0.317019	−	0.00648041i
$361$	6.47420e9	+	1.12136e10i	0.381204	+	0.660264i
$362$	7.41991e8	−	8.84270e8i	0.0432080	−	0.0514933i
$363$	8.66247e9	−	1.05404e10i	0.498902	−	0.607061i
$364$	4.74338e7	+	2.69011e8i	0.00270198	+	0.0153237i
$365$	−1.10447e9	+	1.94748e8i	−0.0622276	+	0.0109724i
$366$	−3.34868e9	−	2.75205e9i	−0.186616	−	0.153367i
$367$	−4.98172e8	−	4.18016e8i	−0.0274609	−	0.0230424i	0.628954	−	0.777443i	$-0.283483\pi$
$367$	−4.98172e8	−	4.18016e8i	−0.0274609	−	0.0230424i	−0.656415	+	0.754400i	$0.727928\pi$
$368$	−1.03963e10	+	6.00232e9i	−0.566877	+	0.327287i
$369$	6.51199e6	+	3.18564e8i	0.000351243	+	0.0171827i
$370$	1.14195e9	−	1.97791e9i	0.0609312	−	0.105536i
$371$	8.82035e8	+	2.42337e9i	0.0465576	+	0.127916i
$372$	−3.67894e8	−	3.59983e10i	−0.0192111	−	1.87979i
$373$	9.77422e8	−	8.20154e8i	0.0504948	−	0.0423702i	−0.617191	−	0.786813i	$-0.711729\pi$
$373$	9.77422e8	−	8.20154e8i	0.0504948	−	0.0423702i	0.667686	+	0.744443i	$0.267285\pi$
$374$	1.84871e8	−	5.07929e8i	0.00944892	−	0.0259607i
$375$	1.81406e10	+	6.39348e9i	0.917334	+	0.323305i
$376$	−1.36153e9	+	7.72164e9i	−0.0681204	+	0.386330i
$377$		−	4.36107e9i		−	0.215888i
$378$	−2.57113e8	+	2.29535e8i	−0.0125938	+	0.0112430i
$379$	2.22343e10			1.07762			0.538811	−	0.842427i	$-0.318874\pi$
$379$	2.22343e10			1.07762			0.538811	+	0.842427i	$0.318874\pi$
$380$	−1.00121e10	−	1.76540e9i	−0.480165	−	0.0846661i
$381$	−3.72063e10	+	6.95324e9i	−1.76570	+	0.329980i
$382$	−1.76347e9	−	6.41851e8i	−0.0828162	−	0.0301426i
$383$	−2.13080e10	−	2.53939e10i	−0.990258	−	1.18014i	−0.983636	−	0.180166i	$-0.942337\pi$
$383$	−2.13080e10	−	2.53939e10i	−0.990258	−	1.18014i	−0.00662182	−	0.999978i	$-0.502108\pi$
$384$	6.28263e9	−	1.11433e10i	0.288946	−	0.512494i
$385$	−1.05681e9	+	3.84647e8i	−0.0481009	+	0.0175073i
$386$	2.89808e9	+	1.67321e9i	0.130545	+	0.0753704i
$387$	−4.32274e9	+	3.78042e9i	−0.192715	+	0.168537i
$388$	−1.73186e10	−	2.99967e10i	−0.764162	−	1.32357i
$389$	2.54213e10	−	3.02959e10i	1.11019	−	1.32308i	0.168845	−	0.985643i	$-0.445996\pi$
$389$	2.54213e10	−	3.02959e10i	1.11019	−	1.32308i	0.941349	−	0.337435i	$-0.109559\pi$
$390$	−5.41789e8	−	8.98331e7i	−0.0234192	−	0.00388309i
$391$	−1.09268e9	−	6.19690e9i	−0.0467505	−	0.265135i
$392$	−7.10713e9	+	1.25318e9i	−0.300989	+	0.0530724i
$393$	−3.99589e10	+	1.50080e10i	−1.67511	+	0.629150i
$394$	1.83282e9	+	1.53792e9i	0.0760561	+	0.0638186i
$395$	−2.40911e10	+	1.39090e10i	−0.989620	+	0.571357i
$396$	−4.01000e9	−	1.03539e10i	−0.163066	−	0.421040i
$397$	1.01278e10	−	1.75419e10i	0.407712	−	0.706179i	−0.586921	−	0.809645i	$-0.699660\pi$
$397$	1.01278e10	−	1.75419e10i	0.407712	−	0.706179i	0.994633	+	0.103466i	$0.0329932\pi$
$398$	7.25513e8	+	1.99333e9i	0.0289143	+	0.0794414i
$399$	1.14702e9	−	6.77955e8i	0.0452564	−	0.0267491i
$400$	−9.35600e8	+	7.85061e8i	−0.0365469	+	0.0306665i
$401$	9.60582e9	−	2.63918e10i	0.371498	−	1.02068i	−0.603284	−	0.797526i	$-0.706142\pi$
$401$	9.60582e9	−	2.63918e10i	0.371498	−	1.02068i	0.974783	−	0.223157i	$-0.0716363\pi$
$402$	−1.90913e9	+	1.63548e9i	−0.0731022	+	0.0626242i
$403$	−1.30544e9	+	7.40353e9i	−0.0494923	+	0.280685i
$404$		−	3.32720e10i		−	1.24897i
$405$	1.04871e10	+	2.55168e10i	0.389794	+	0.948431i
$406$	−6.69576e8			−0.0246431
$407$	−9.49609e9	−	1.67442e9i	−0.346073	−	0.0610219i
$408$	2.12571e9	+	2.48138e9i	0.0767121	+	0.0895473i
$409$	2.22849e10	+	8.11103e9i	0.796374	+	0.289856i	0.707983	−	0.706229i	$-0.249605\pi$
$409$	2.22849e10	+	8.11103e9i	0.796374	+	0.289856i	0.0883910	+	0.996086i	$0.471828\pi$
$410$	5.01054e7	+	5.97133e7i	0.00177317	+	0.00211318i
$411$	1.31047e10	+	2.21716e10i	0.459260	+	0.777014i
$412$	2.79963e10	−	1.01898e10i	0.971654	−	0.353653i
$413$	3.46145e9	+	1.99847e9i	0.118976	+	0.0686906i
$414$	2.52923e9	+	2.03566e9i	0.0860969	+	0.0692953i
$415$	1.90695e10	+	3.30294e10i	0.642906	+	1.11355i
$416$	−1.29357e9	+	1.54162e9i	−0.0431934	+	0.0514759i
$417$	1.56915e10	+	4.17787e10i	0.518945	+	1.38169i
$418$	−1.87215e8	−	1.06175e9i	−0.00613248	−	0.0347790i
$419$	1.55067e10	−	2.73425e9i	0.503111	−	0.0887120i	0.0836677	−	0.996494i	$-0.473337\pi$
$419$	1.55067e10	−	2.73425e9i	0.503111	−	0.0887120i	0.419443	+	0.907782i	$0.362225\pi$
$420$	5.49114e8	−	3.31174e9i	0.0176468	−	0.106429i
$421$	3.24333e9	+	2.72148e9i	0.103244	+	0.0866316i	0.692948	−	0.720987i	$-0.256311\pi$
$421$	3.24333e9	+	2.72148e9i	0.103244	+	0.0866316i	−0.589705	+	0.807619i	$0.700756\pi$
$422$	4.92857e8	−	2.84551e8i	0.0155407	−	0.00897244i
$423$	−3.98456e10	+	7.86873e9i	−1.24457	+	0.245778i
$424$	−6.30706e9	+	1.09241e10i	−0.195148	+	0.338006i
$425$	−2.18958e8	−	6.01583e8i	−0.00671128	−	0.0184391i
$426$	−4.83492e8	−	2.72595e8i	−0.0146809	−	0.00827712i
$427$	−4.23835e9	+	3.55640e9i	−0.127493	+	0.106979i
$428$	−9.83228e9	+	2.70140e10i	−0.293008	+	0.805033i
$429$	4.25944e8	+	2.27919e9i	0.0125754	+	0.0672902i
$430$	−2.43955e8	+	1.38354e9i	−0.00713569	+	0.0404685i
$431$		−	5.43801e10i		−	1.57591i	−0.615734	−	0.787954i	$-0.711140\pi$
$431$		−	5.43801e10i		−	1.57591i	0.615734	−	0.787954i	$-0.288860\pi$
$432$	3.19557e10	+	4.62960e9i	0.917515	+	0.132926i
$433$	1.01330e10			0.288261			0.144130	−	0.989559i	$-0.453962\pi$
$433$	1.01330e10			0.288261			0.144130	+	0.989559i	$0.453962\pi$
$434$	1.13670e9	+	2.00431e8i	0.0320395	+	0.00564944i
$435$	−1.78148e10	+	5.05471e10i	−0.497535	+	1.41169i
$436$	−7.47964e9	−	2.72237e9i	−0.206983	−	0.0753356i
$437$	−8.06760e9	−	9.61459e9i	−0.221217	−	0.263636i
$438$	3.54987e8	−	3.62789e6i	0.00964530	−	9.85729e-5i
$439$	4.09720e10	−	1.49126e10i	1.10314	−	0.401509i	0.274665	−	0.961540i	$-0.411433\pi$
$439$	4.09720e10	−	1.49126e10i	1.10314	−	0.401509i	0.828471	+	0.560031i	$0.189211\pi$
$440$	−4.76391e9	−	2.75044e9i	−0.127102	−	0.0733824i
$441$	−1.93492e10	−	3.19858e10i	−0.511574	−	0.845673i
$442$	−1.68463e8	−	2.91787e8i	−0.00441383	−	0.00764498i
$443$	−2.87742e10	+	3.42918e10i	−0.747117	+	0.890379i	−0.996961	−	0.0779071i	$-0.975176\pi$
$443$	−2.87742e10	+	3.42918e10i	−0.747117	+	0.890379i	0.249844	+	0.968286i	$0.419621\pi$
$444$	1.82747e10	−	2.22366e10i	0.470240	−	0.572184i
$445$	4.26642e9	+	2.41961e10i	0.108799	+	0.617028i
$446$	−1.59948e9	+	2.82031e8i	−0.0404239	+	0.00712783i
$447$	−4.43732e10	−	3.64674e10i	−1.11145	−	0.913428i
$448$	−2.84873e9	−	2.39037e9i	−0.0707195	−	0.0593407i
$449$	−3.94571e10	+	2.27806e10i	−0.970823	+	0.560505i	−0.899487	−	0.436947i	$-0.856060\pi$
$449$	−3.94571e10	+	2.27806e10i	−0.970823	+	0.560505i	−0.0713360	+	0.997452i	$0.522726\pi$
$450$	2.89375e8	+	1.59276e8i	0.00705686	+	0.00388418i
$451$	1.64552e8	−	2.85013e8i	0.00397738	−	0.00688903i
$452$	5.92346e9	+	1.62746e10i	0.141913	+	0.389903i
$453$	2.82634e8	+	2.76556e10i	0.00671168	+	0.656734i
$454$	2.04172e9	−	1.71320e9i	0.0480587	−	0.0403260i
$455$	−2.39762e8	+	6.58740e8i	−0.00559415	+	0.0153698i
$456$	6.14655e9	+	2.16629e9i	0.142158	+	0.0501022i
$457$	−7.31714e9	+	4.14976e10i	−0.167755	+	0.951388i	0.778422	+	0.627741i	$0.216020\pi$
$457$	−7.31714e9	+	4.14976e10i	−0.167755	+	0.951388i	−0.946178	+	0.323647i	$0.895091\pi$
$458$		−	4.93906e9i		−	0.112249i
$459$	−8.00928e9	+	1.49101e10i	−0.180444	+	0.335916i
$460$	−3.16220e10			−0.706248
$461$	1.81731e10	+	3.20440e9i	0.402369	+	0.0709484i	0.371170	−	0.928565i	$-0.378957\pi$
$461$	1.81731e10	+	3.20440e9i	0.402369	+	0.0709484i	0.0311982	+	0.999513i	$0.490068\pi$
$462$	3.49935e8	−	6.53971e7i	0.00768104	−	0.00143546i
$463$	−2.73595e10	−	9.95805e9i	−0.595367	−	0.216696i	0.0267215	−	0.999643i	$-0.491493\pi$
$463$	−2.73595e10	−	9.95805e9i	−0.595367	−	0.216696i	−0.622088	+	0.782947i	$0.713715\pi$
$464$	4.03209e10	+	4.80525e10i	0.869877	+	1.03668i
$465$	4.53738e10	−	8.04780e10i	0.970496	−	1.72134i
$466$	1.08507e10	−	3.94934e9i	0.230099	−	0.0837493i
$467$	4.63413e10	+	2.67552e10i	0.974319	+	0.562523i	0.900550	−	0.434752i	$-0.143164\pi$
$467$	4.63413e10	+	2.67552e10i	0.974319	+	0.562523i	0.0737688	+	0.997275i	$0.476497\pi$
$468$	−6.55066e9	−	2.23372e9i	−0.136553	−	0.0465634i
$469$	1.60444e9	+	2.77897e9i	0.0331613	+	0.0574370i
$470$	−6.38683e9	+	7.61153e9i	−0.130886	+	0.155984i
$471$	7.19261e10	+	1.19260e10i	1.46151	+	0.242331i
$472$	3.39485e9	+	1.92531e10i	0.0683994	+	0.387912i
$473$	5.84128e9	−	1.02997e9i	0.116698	−	0.0205770i
$474$	8.24334e9	−	3.09609e9i	0.163301	−	0.0613339i
$475$	−9.78177e8	−	8.20788e8i	−0.0192151	−	0.0161234i
$476$	1.78357e9	−	1.02975e9i	0.0347427	−	0.0200587i
$477$	−6.45669e10	−	1.00289e10i	−1.24720	−	0.193722i
$478$	−1.75476e9	+	3.03934e9i	−0.0336130	+	0.0582194i
$479$	9.54151e9	+	2.62151e10i	0.181249	+	0.497977i	0.996730	−	0.0808069i	$-0.0257497\pi$
$479$	9.54151e9	+	2.62151e10i	0.181249	+	0.497977i	−0.815481	+	0.578784i	$0.803527\pi$
$480$	2.12906e10	−	1.25840e10i	0.401073	−	0.237057i
$481$	−4.60432e9	+	3.86348e9i	−0.0860171	+	0.0721769i
$482$	2.74095e9	−	7.53071e9i	0.0507825	−	0.139524i
$483$	3.14731e9	−	2.69619e9i	0.0578297	−	0.0495407i
$484$	7.30416e9	−	4.14240e10i	0.133103	−	0.754867i
$485$		−	8.88899e10i		−	1.60652i
$486$	−1.95368e9	−	8.51135e9i	−0.0350194	−	0.152565i
$487$	−5.43062e10			−0.965458			−0.482729	−	0.875770i	$-0.660354\pi$
$487$	−5.43062e10			−0.965458			−0.482729	+	0.875770i	$0.660354\pi$
$488$	−2.66512e10	−	4.69932e9i	−0.469934	−	0.0828621i
$489$	2.67655e10	+	3.12438e10i	0.468102	+	0.546423i
$490$	−8.59387e9	−	3.12791e9i	−0.149075	−	0.0542588i
$491$	2.12598e10	+	2.53364e10i	0.365791	+	0.435933i	0.917276	−	0.398252i	$-0.130383\pi$
$491$	2.12598e10	+	2.53364e10i	0.365791	+	0.435933i	−0.551485	+	0.834185i	$0.685939\pi$
$492$	4.99846e8	+	8.45681e8i	0.00853052	+	0.0144326i
$493$	−3.08974e10	+	1.12457e10i	−0.523039	+	0.190371i
$494$	−5.81995e8	−	3.36015e8i	−0.00977263	−	0.00564223i
$495$	4.37350e9	−	2.81570e10i	0.0728464	−	0.468992i
$496$	−5.40663e10	−	9.36455e10i	−0.893305	−	1.54725i
$497$	−4.55411e8	+	5.42737e8i	−0.00746410	+	0.00889537i
$498$	−4.24480e9	−	1.13018e10i	−0.0690144	−	0.183751i
$499$	−7.01014e9	−	3.97565e10i	−0.113064	−	0.641218i	−0.987691	−	0.156421i	$-0.950004\pi$
$499$	−7.01014e9	−	3.97565e10i	−0.113064	−	0.641218i	0.874626	−	0.484798i	$-0.161107\pi$
$500$	5.83996e10	−	1.02974e10i	0.934393	−	0.164759i
$501$	1.16277e10	−	7.01272e10i	0.184562	−	1.11310i
$502$	−6.26692e9	−	5.25857e9i	−0.0986823	−	0.0828043i
$503$	−1.03883e11	+	5.99768e10i	−1.62283	+	0.936940i	−0.636668	+	0.771138i	$0.719688\pi$
$503$	−1.03883e11	+	5.99768e10i	−1.62283	+	0.936940i	−0.986159	+	0.165801i	$0.946979\pi$
$504$	−6.94521e8	+	2.03677e9i	−0.0107637	+	0.0315660i
$505$	4.26933e10	−	7.39469e10i	0.656438	−	1.13698i
$506$	−1.14693e9	−	3.15117e9i	−0.0174959	−	0.0480695i
$507$	−5.62976e10	−	3.17408e10i	−0.852036	−	0.480381i
$508$	−8.93935e10	+	7.50100e10i	−1.34230	+	1.12633i
$509$	1.99802e10	−	5.48952e10i	0.297666	−	0.817830i	−0.697223	−	0.716854i	$-0.745581\pi$
$509$	1.99802e10	−	5.48952e10i	0.297666	−	0.817830i	0.994889	−	0.100976i	$-0.0321966\pi$
$510$	7.60639e8	+	4.07012e9i	0.0112434	+	0.0601626i
$511$	7.86890e7	−	4.46268e8i	0.00115407	−	0.00654503i
$512$		−	4.86471e10i		−	0.707908i
$513$	1.03482e9	+	3.37429e10i	0.0149416	+	0.487206i
$514$	2.57709e9			0.0369213
$515$	7.52968e10	+	1.32768e10i	1.07040	+	0.188741i
$516$	−5.88507e9	+	1.66981e10i	−0.0830142	+	0.235542i
$517$	3.94203e10	+	1.43478e10i	0.551770	+	0.200828i
$518$	5.93178e8	+	7.06922e8i	0.00823884	+	0.00981867i
$519$	1.14485e11	−	1.17001e9i	1.57790	−	0.0161258i
$520$	−3.22208e9	+	1.17274e9i	−0.0440680	+	0.0160394i
$521$	6.93877e9	+	4.00610e9i	0.0941741	+	0.0543715i	0.546347	−	0.837559i	$-0.316018\pi$
$521$	6.93877e9	+	4.00610e9i	0.0941741	+	0.0543715i	−0.452173	+	0.891930i	$0.649351\pi$
$522$	8.18043e9	−	1.48624e10i	0.110178	−	0.200173i
$523$	−2.54192e10	−	4.40273e10i	−0.339746	−	0.588457i	0.644639	−	0.764487i	$-0.277008\pi$
$523$	−2.54192e10	−	4.40273e10i	−0.339746	−	0.588457i	−0.984385	+	0.176030i	$0.943674\pi$
$524$	−8.45897e10	+	1.00810e11i	−1.12200	+	1.33715i
$525$	2.67706e8	−	3.25743e8i	0.00352388	−	0.00428783i
$526$	2.15685e9	+	1.22321e10i	0.0281758	+	0.159793i
$527$	5.58189e10	−	9.84238e9i	0.723667	−	0.127602i
$528$	−2.57659e10	−	2.11752e10i	−0.331519	−	0.272453i
$529$	3.00845e10	+	2.52439e10i	0.384168	+	0.322355i
$530$	−1.38435e10	+	7.99257e9i	−0.175446	+	0.101294i
$531$	−8.66491e10	+	5.24168e10i	−1.08990	+	0.659314i
$532$	2.05392e9	−	3.55750e9i	0.0256412	−	0.0444118i
$533$	−7.01622e7	−	1.92769e8i	−0.000869349	−	0.00238852i
$534$	−7.94775e7	−	7.77683e9i	−0.000977416	−	0.0956396i
$535$	−5.65154e10	+	4.74221e10i	−0.689845	+	0.578849i
$536$	−5.36818e9	+	1.47489e10i	−0.0650381	+	0.178691i
$537$	9.66755e9	+	3.40723e9i	0.116257	+	0.0409736i
$538$	−4.70280e8	+	2.66709e9i	−0.00561342	+	0.0318353i
$539$			3.86117e10i			0.457472i
$540$	6.68009e10	+	5.26491e10i	0.785610	+	0.619179i
$541$	4.99438e10			0.583032			0.291516	−	0.956566i	$-0.405840\pi$
$541$	4.99438e10			0.583032			0.291516	+	0.956566i	$0.405840\pi$
$542$	1.15052e10	+	2.02868e9i	0.133321	+	0.0235081i
$543$	3.66976e10	−	6.85818e9i	0.422123	−	0.0788878i
$544$	1.42578e10	+	5.18941e9i	0.162801	+	0.0592546i
$545$	−1.31302e10	−	1.56480e10i	−0.148829	−	0.177367i
$546$	1.08981e8	−	1.93296e8i	0.00122625	−	0.00217497i
$547$	−2.21042e10	+	8.04528e9i	−0.246903	+	0.0898653i	−0.462507	−	0.886616i	$-0.653050\pi$
$547$	−2.21042e10	+	8.04528e9i	−0.246903	+	0.0898653i	0.215604	+	0.976481i	$0.430828\pi$
$548$	6.87654e10	+	3.97017e10i	0.762514	+	0.440238i
$549$	−2.71589e10	−	1.37527e11i	−0.298967	−	1.51390i
$550$	−1.70586e8	−	2.95463e8i	−0.00186420	−	0.00322888i
$551$	−4.21558e10	+	5.02393e10i	−0.457352	+	0.545051i
$552$	1.99978e10	+	3.31580e9i	0.215390	+	0.0357135i
$553$	−1.95181e9	−	1.10693e10i	−0.0208707	−	0.118364i
$554$	2.16540e10	−	3.81819e9i	0.229879	−	0.0405339i
$555$	6.91486e10	−	2.59713e10i	0.728805	−	0.273730i
$556$	1.05401e11	+	8.84420e10i	1.10293	+	0.925464i
$557$	−1.24286e11	+	7.17563e10i	−1.29122	+	0.745486i	−0.978870	−	0.204482i	$-0.934449\pi$
$557$	−1.24286e11	+	7.17563e10i	−1.29122	+	0.745486i	−0.312349	+	0.949968i	$0.601116\pi$
$558$	−1.83363e10	+	2.27822e10i	−0.189137	+	0.234995i
$559$	1.84861e9	−	3.20188e9i	0.0189320	−	0.0327912i
$560$	−3.44865e9	−	9.47509e9i	−0.0350669	−	0.0963454i
$561$	1.50493e10	−	8.89500e9i	0.151937	−	0.0898038i
$562$	−9.76746e9	+	8.19588e9i	−0.0979121	+	0.0821580i
$563$	1.27931e10	−	3.51488e10i	0.127334	−	0.349846i	−0.859601	−	0.510965i	$-0.829288\pi$
$563$	1.27931e10	−	3.51488e10i	0.127334	−	0.349846i	0.986935	+	0.161119i	$0.0515103\pi$
$564$	−9.50956e10	+	8.14651e10i	−0.939818	+	0.805110i
$565$	−7.71799e9	+	4.37709e10i	−0.0757375	+	0.429528i
$566$			1.96458e10i			0.191427i
$567$	−1.11377e10	+	4.55536e8i	−0.107761	+	0.00440749i
$568$	−3.46544e9			−0.0332939
$569$	1.61367e11	+	2.84534e10i	1.53945	+	0.271447i	0.878043	−	0.478581i	$-0.158849\pi$
$569$	1.61367e11	+	2.84534e10i	1.53945	+	0.271447i	0.661407	+	0.750028i	$0.269960\pi$
$570$	5.37302e9	+	6.27201e9i	0.0509001	+	0.0594165i
$571$	−1.72062e11	−	6.26253e10i	−1.61860	−	0.589122i	−0.635486	−	0.772112i	$-0.719200\pi$
$571$	−1.72062e11	−	6.26253e10i	−1.61860	−	0.589122i	−0.983115	+	0.182990i	$0.941422\pi$
$572$	4.59499e9	+	5.47609e9i	0.0429240	+	0.0511548i
$573$	−3.08825e10	−	5.22495e10i	−0.286479	−	0.484690i
$574$	−2.95967e7	+	1.07723e7i	−0.000272644	+	9.92344e-5i
$575$	−3.43961e9	−	1.98586e9i	−0.0314657	−	0.0181668i
$576$	8.78622e10	−	3.40284e10i	0.798201	−	0.309138i
$577$	−1.38743e10	−	2.40309e10i	−0.125172	−	0.216804i	0.796628	−	0.604470i	$-0.206615\pi$
$577$	−1.38743e10	−	2.40309e10i	−0.125172	−	0.216804i	−0.921800	+	0.387665i	$0.873282\pi$
$578$	9.59722e9	−	1.14375e10i	0.0859873	−	0.102476i
$579$	3.80537e10	+	1.01318e11i	0.338597	+	0.901513i
$580$	2.86927e10	+	1.62725e11i	0.253548	+	1.43794i
$581$	−1.51762e10	+	2.67597e9i	−0.133186	+	0.0234842i
$582$	−4.60258e9	+	2.77585e10i	−0.0401153	+	0.241938i
$583$	5.16996e10	+	4.33811e10i	0.447520	+	0.375514i
$584$	1.91954e9	−	1.10825e9i	0.0165023	−	0.00952763i
$585$	−1.16926e10	−	1.33700e10i	−0.0998360	−	0.114158i
$586$	1.51476e10	−	2.62364e10i	0.128456	−	0.222492i
$587$	1.84410e10	+	5.06662e10i	0.155322	+	0.426743i	0.992808	−	0.119715i	$-0.0381981\pi$
$587$	1.84410e10	+	5.06662e10i	0.155322	+	0.426743i	−0.837487	+	0.546458i	$0.815976\pi$
$588$	−1.00396e11	−	5.66038e10i	−0.839862	−	0.473517i
$589$	8.66040e10	−	7.26694e10i	0.719576	−	0.603796i
$590$	−8.47348e9	+	2.32807e10i	−0.0699284	+	0.192127i
$591$	1.42149e10	+	7.60627e10i	0.116518	+	0.623479i
$592$	1.50124e10	−	8.51396e10i	0.122226	−	0.693178i
$593$		−	1.98579e11i		−	1.60589i	−0.596054	−	0.802945i	$-0.703265\pi$
$593$		−	1.98579e11i		−	1.60589i	0.596054	−	0.802945i	$-0.296735\pi$
$594$	−2.82368e9	+	8.56638e9i	−0.0226814	+	0.0688100i
$595$	5.28532e9			0.0421700
$596$	−1.74387e11	−	3.07491e10i	−1.38207	−	0.243696i
$597$	−2.28042e10	+	6.47039e10i	−0.179522	+	0.509370i
$598$	−1.96422e9	−	7.14917e8i	−0.0153598	−	0.00559050i
$599$	−1.00906e11	−	1.20255e11i	−0.783808	−	0.934105i	0.215291	−	0.976550i	$-0.430930\pi$
$599$	−1.00906e11	−	1.20255e11i	−0.783808	−	0.934105i	−0.999099	+	0.0424444i	$0.986485\pi$
$600$	2.06222e9	−	2.10754e7i	0.0159122	−	0.000162619i
$601$	1.23406e10	−	4.49162e9i	0.0945887	−	0.0344275i	−0.294292	−	0.955715i	$-0.595084\pi$
$601$	1.23406e10	−	4.49162e9i	0.0945887	−	0.0344275i	0.388881	+	0.921288i	$0.372862\pi$
$602$	−4.91599e8	−	2.83825e8i	−0.00374305	−	0.00216105i
$603$	−8.12858e10	+	1.66162e9i	−0.614816	+	0.0125679i
$604$	4.26340e10	+	7.38443e10i	0.320338	+	0.554842i
$605$	6.93870e10	−	8.26922e10i	0.517912	−	0.617224i
$606$	−1.71611e10	+	2.08815e10i	−0.127249	+	0.154836i
$607$	−2.69000e10	−	1.52558e11i	−0.198152	−	1.12377i	−0.907858	−	0.419277i	$-0.862284\pi$
$607$	−2.69000e10	−	1.52558e11i	−0.198152	−	1.12377i	0.709706	−	0.704497i	$-0.248828\pi$
$608$	2.98038e10	−	5.25521e9i	0.218101	−	0.0384571i
$609$	−1.67302e10	−	1.37494e10i	−0.121628	−	0.0999574i
$610$	−2.62711e10	−	2.20441e10i	−0.189740	−	0.159211i
$611$	2.26456e10	−	1.30744e10i	0.162487	−	0.0938118i
$612$	1.06645e9	+	5.21702e10i	0.00760211	+	0.371892i
$613$	−6.82522e10	+	1.18216e11i	−0.483364	+	0.837212i	−0.999818	−	0.0191038i	$-0.993919\pi$
$613$	−6.82522e10	+	1.18216e11i	−0.483364	+	0.837212i	0.516453	+	0.856315i	$0.327252\pi$
$614$	−1.10881e10	−	3.04644e10i	−0.0780163	−	0.214348i
$615$	2.57631e7	+	2.52090e9i	0.000180093	+	0.0176220i
$616$	1.70266e9	−	1.42870e9i	0.0118251	−	0.00992244i
$617$	1.05167e10	−	2.88945e10i	0.0725672	−	0.199377i	−0.898106	−	0.439778i	$-0.855057\pi$
$617$	1.05167e10	−	2.88945e10i	0.0725672	−	0.199377i	0.970673	+	0.240402i	$0.0772792\pi$
$618$	−2.28261e10	−	8.04483e9i	−0.156487	−	0.0551522i
$619$	2.29396e10	−	1.30097e11i	0.156251	−	0.886143i	−0.801382	−	0.598152i	$-0.795902\pi$
$619$	2.29396e10	−	1.30097e11i	0.156251	−	0.886143i	0.957633	−	0.287991i	$-0.0929872\pi$
$620$		−	2.84837e11i		−	1.92765i
$621$	2.13948e10	+	1.02800e11i	0.143861	+	0.691237i
$622$	3.15852e10			0.211019
$623$	−9.77655e9	−	1.72387e9i	−0.0648983	−	0.0114433i
$624$	−2.04347e10	+	3.81891e9i	−0.134781	+	0.0251884i
$625$	1.50385e11	+	5.47355e10i	0.985561	+	0.358715i
$626$	1.45327e10	+	1.73195e10i	0.0946347	+	0.112781i
$627$	1.71247e10	−	3.03735e10i	0.110803	−	0.196528i
$628$	2.11224e11	−	7.68792e10i	1.35801	−	0.494277i
$629$	3.92450e10	+	2.26581e10i	0.250716	+	0.144751i
$630$	−2.05275e9	+	1.79522e9i	−0.0130309	+	0.0113961i
$631$	6.47545e10	+	1.12158e11i	0.408463	+	0.707478i	0.994718	−	0.102648i	$-0.0327316\pi$
$631$	6.47545e10	+	1.12158e11i	0.408463	+	0.707478i	−0.586255	+	0.810127i	$0.699398\pi$
$632$	3.53392e10	−	4.21157e10i	0.221508	−	0.263983i
$633$	1.81578e10	+	3.01071e9i	0.113096	+	0.0187523i
$634$	1.08410e9	+	6.14824e9i	0.00670984	+	0.0380534i
$635$	−2.94926e11	+	5.20035e10i	−1.81392	+	0.319843i
$636$	−1.88587e11	+	7.08310e10i	−1.15261	+	0.432907i
$637$	1.84370e10	+	1.54705e10i	0.111978	+	0.0939609i
$638$	−1.51750e10	+	8.76130e9i	−0.0915897	+	0.0528793i
$639$	−6.48306e9	−	1.67394e10i	−0.0388845	−	0.100401i
$640$	5.06071e10	−	8.76541e10i	0.301642	−	0.522459i
$641$	−5.46839e10	−	1.50243e11i	−0.323912	−	0.889941i	−0.989617	−	0.143726i	$-0.954092\pi$
$641$	−5.46839e10	−	1.50243e11i	−0.323912	−	0.889941i	0.665706	−	0.746215i	$-0.268131\pi$
$642$	2.01040e10	−	1.18826e10i	0.118343	−	0.0699475i
$643$	1.61080e11	−	1.35162e11i	0.942318	−	0.790699i	−0.0356691	−	0.999364i	$-0.511356\pi$
$643$	1.61080e11	−	1.35162e11i	0.942318	−	0.790699i	0.977987	+	0.208665i	$0.0669118\pi$
$644$	4.37000e9	−	1.20065e10i	0.0254061	−	0.0698027i
$645$	−3.45058e10	+	2.95600e10i	−0.199367	+	0.170791i
$646$	−8.79836e8	+	4.98980e9i	−0.00505210	+	0.0286519i
$647$			1.78264e11i			1.01730i	0.860974	+	0.508648i	$0.169855\pi$
$647$			1.78264e11i			1.01730i	−0.860974	+	0.508648i	$0.830145\pi$
$648$	−3.67243e10	−	4.02999e10i	−0.208283	−	0.228562i
$649$	1.04599e11			0.589587
$650$	−2.09431e8	−	3.69284e7i	−0.00117324	−	0.000206875i
$651$	2.42861e10	+	2.83496e10i	0.135218	+	0.157842i
$652$	1.19190e11	+	4.33817e10i	0.659554	+	0.240058i
$653$	6.49968e10	+	7.74602e10i	0.357470	+	0.426016i	0.914569	−	0.404430i	$-0.132530\pi$
$653$	6.49968e10	+	7.74602e10i	0.357470	+	0.426016i	−0.557099	+	0.830446i	$0.688086\pi$
$654$	3.29007e9	+	5.56641e9i	0.0179843	+	0.0304273i
$655$	−3.17356e11	+	1.15508e11i	−1.72417	+	0.627548i
$656$	2.55536e9	+	1.47534e9i	0.0137986	+	0.00796664i
$657$	8.94429e9	+	7.19884e9i	0.0480048	+	0.0386368i
$658$	−2.00738e9	−	3.47688e9i	−0.0107084	−	0.0185475i
$659$	−1.04978e9	+	1.25108e9i	−0.00556616	+	0.00663349i	−0.768820	−	0.639465i	$-0.779156\pi$
$659$	−1.04978e9	+	1.25108e9i	−0.00556616	+	0.00663349i	0.763254	+	0.646098i	$0.223600\pi$
$660$	−3.08887e10	−	8.22411e10i	−0.162788	−	0.433424i
$661$	−1.54225e10	−	8.74653e10i	−0.0807884	−	0.458174i	−0.998186	−	0.0602023i	$-0.980825\pi$
$661$	−1.54225e10	−	8.74653e10i	−0.0807884	−	0.458174i	0.917398	−	0.397971i	$-0.130286\pi$
$662$	3.23290e10	−	5.70047e9i	0.168329	−	0.0296810i
$663$	1.78243e9	−	1.07500e10i	0.00922485	−	0.0556356i
$664$	−5.77414e10	−	4.84508e10i	−0.297040	−	0.249246i
$665$	9.12968e9	−	5.27102e9i	0.0466841	−	0.0269531i
$666$	−2.29384e10	+	4.52988e9i	−0.116591	+	0.0230245i
$667$	−1.01994e11	+	1.76659e11i	−0.515314	+	0.892549i
$668$	−7.49564e10	−	2.05941e11i	−0.376446	−	1.03428i
$669$	−4.57563e10	−	2.57976e10i	−0.228426	−	0.128788i
$670$	−1.52366e10	+	1.27851e10i	−0.0756119	+	0.0634459i
$671$	−4.95214e10	+	1.36059e11i	−0.244289	+	0.671177i
$672$	1.83573e9	+	9.82284e9i	0.00900184	+	0.0481682i
$673$	−1.34793e10	+	7.64450e10i	−0.0657064	+	0.372640i	0.934169	+	0.356832i	$0.116143\pi$
$673$	−1.34793e10	+	7.64450e10i	−0.0657064	+	0.372640i	−0.999875	+	0.0158078i	$0.994968\pi$
$674$			4.20842e9i			0.0203929i
$675$	3.95976e9	+	9.92189e9i	0.0190745	+	0.0477947i
$676$	−1.99254e11			−0.954160
$677$	−1.68693e11	−	2.97451e10i	−0.803050	−	0.141599i	−0.242965	−	0.970035i	$-0.578120\pi$
$677$	−1.68693e11	−	2.97451e10i	−0.803050	−	0.141599i	−0.560084	+	0.828436i	$0.689231\pi$
$678$	4.67656e9	−	1.32691e10i	0.0221313	−	0.0627947i
$679$	3.37504e10	+	1.22842e10i	0.158782	+	0.0577918i
$680$	1.66173e10	+	1.98037e10i	0.0777187	+	0.0926215i
$681$	8.61947e10	−	8.80891e8i	0.400767	−	0.00409575i
$682$	2.83843e10	−	1.03311e10i	0.131202	−	0.0477537i
$683$	3.58504e11	+	2.06982e11i	1.64744	+	0.951153i	0.978083	+	0.208216i	$0.0667657\pi$
$683$	3.58504e11	+	2.06982e11i	1.64744	+	0.951153i	0.669362	+	0.742937i	$0.266568\pi$
$684$	5.38713e10	+	8.90535e10i	0.246112	+	0.406843i
$685$	1.01887e11	+	1.76474e11i	0.462762	+	0.801527i
$686$	4.77848e9	−	5.69477e9i	0.0215771	−	0.0257146i
$687$	1.01421e11	−	1.23409e11i	0.455305	−	0.554012i
$688$	9.23450e9	+	5.23715e10i	0.0412154	+	0.233744i
$689$	4.14288e10	−	7.30502e9i	0.183834	−	0.0324149i
$690$	1.98459e10	+	1.63100e10i	0.0875536	+	0.0719544i
$691$	−3.19102e11	−	2.67758e11i	−1.39964	−	1.17444i	−0.961258	−	0.275650i	$-0.911107\pi$
$691$	−3.19102e11	−	2.67758e11i	−1.39964	−	1.17444i	−0.438383	−	0.898788i	$-0.644449\pi$
$692$	3.05691e11	−	1.76491e11i	1.33309	−	0.769657i
$693$	1.00865e10	+	5.55172e9i	0.0437327	+	0.0240710i
$694$	−1.01667e10	+	1.76092e10i	−0.0438269	+	0.0759105i
$695$	1.20768e11	+	3.31808e11i	0.517623	+	1.42216i
$696$	−1.08244e9	−	1.05916e11i	−0.00461281	−	0.451361i
$697$	−1.18481e9	+	9.94173e8i	−0.00502016	+	0.00421241i
$698$	−8.90386e7	+	2.44632e8i	−0.000375108	+	0.00103060i
$699$	3.52217e11	+	1.24135e11i	1.47537	+	0.519980i
$700$	2.25729e8	−	1.28017e9i	0.000940144	−	0.00533182i
$701$			4.23591e11i			1.75418i	0.480326	+	0.877090i	$0.340518\pi$
$701$			4.23591e11i			1.75418i	−0.480326	+	0.877090i	$0.659482\pi$
$702$	2.95907e9	+	4.78058e9i	0.0121845	+	0.0196849i
$703$	9.03874e10			0.370072
$704$	−9.58403e10	−	1.68992e10i	−0.390173	−	0.0687980i
$705$	−3.15882e11	+	5.90332e10i	−1.27870	+	0.238968i
$706$	2.25345e10	+	8.20191e9i	0.0907048	+	0.0330138i
$707$	2.21767e10	+	2.64292e10i	0.0887606	+	0.105781i
$708$	−1.53339e11	+	2.71972e11i	−0.610266	+	1.08241i
$709$	−1.98886e11	+	7.23886e10i	−0.787081	+	0.286474i	−0.704122	−	0.710079i	$-0.748659\pi$
$709$	−1.98886e11	+	7.23886e10i	−0.787081	+	0.286474i	−0.0829588	+	0.996553i	$0.526437\pi$
$710$	−3.80320e9	−	2.19578e9i	−0.0149663	−	0.00864082i
$711$	2.69547e11	+	9.19132e10i	1.05477	+	0.359666i
$712$	−2.42788e10	−	4.20521e10i	−0.0944728	−	0.163632i
$713$	2.26030e11	−	2.69372e11i	0.874598	−	1.04231i
$714$	−1.65049e9	−	2.73666e8i	−0.00635069	−	0.00105300i
$715$	3.18564e9	+	1.80667e10i	0.0121891	+	0.0691281i
$716$	3.11224e10	−	5.48772e9i	0.118419	−	0.0208805i
$717$	−1.06256e11	+	3.99085e10i	−0.402048	+	0.151004i
$718$	−4.88925e10	−	4.10257e10i	−0.183969	−	0.154368i
$719$	−3.55351e11	+	2.05162e11i	−1.32966	+	0.767681i	−0.985247	−	0.171137i	$-0.945256\pi$
$719$	−3.55351e11	+	2.05162e11i	−1.32966	+	0.767681i	−0.344415	+	0.938817i	$0.611923\pi$
$720$	2.52449e11	+	3.92117e10i	0.939384	+	0.145910i
$721$	−1.54467e10	+	2.67545e10i	−0.0571603	+	0.0990046i
$722$	−1.10915e10	−	3.04737e10i	−0.0408171	−	0.112144i
$723$	2.23126e11	−	1.31880e11i	0.816576	−	0.482643i
$724$	8.81714e10	−	7.39846e10i	0.320903	−	0.269269i
$725$	−7.09812e9	+	1.95019e10i	−0.0256916	+	0.0705871i
$726$	−2.59498e10	+	2.22303e10i	−0.0934086	+	0.0800199i
$727$	−5.40742e10	+	3.06670e11i	−0.193576	+	1.09783i	0.720855	+	0.693086i	$0.243749\pi$
$727$	−5.40742e10	+	3.06670e11i	−0.193576	+	1.09783i	−0.914432	+	0.404741i	$0.867362\pi$
$728$		−	1.38545e9i		−	0.00493249i
$729$	1.25961e11	−	2.52785e11i	0.445992	−	0.895037i
$730$	2.80884e9			0.00989088
$731$	−2.74517e10	−	4.84047e9i	−0.0961389	−	0.0169519i
$732$	−2.81176e11	−	3.28222e11i	−0.979342	−	1.14320i
$733$	−1.43090e11	−	5.20803e10i	−0.495669	−	0.180409i	0.0820759	−	0.996626i	$-0.473845\pi$
$733$	−1.43090e11	−	5.20803e10i	−0.495669	−	0.180409i	−0.577745	+	0.816217i	$0.696067\pi$
$734$	1.04693e9	+	1.24768e9i	0.00360688	+	0.00429851i
$735$	−1.50498e11	−	2.54626e11i	−0.515683	−	0.872475i
$736$	8.84547e10	−	3.21949e10i	0.301446	−	0.109717i
$737$	7.27248e10	+	4.19877e10i	0.246497	+	0.142315i
$738$	1.22483e8	−	7.88559e8i	0.000412906	−	0.00265833i
$739$	−3.62658e10	−	6.28143e10i	−0.121596	−	0.210611i	0.798801	−	0.601595i	$-0.205468\pi$
$739$	−3.62658e10	−	6.28143e10i	−0.121596	−	0.210611i	−0.920397	+	0.390984i	$0.872135\pi$
$740$	1.46382e11	−	1.74451e11i	0.488158	−	0.581764i
$741$	−7.64197e9	−	2.03467e10i	−0.0253474	−	0.0674873i
$742$	−1.12157e9	−	6.36076e9i	−0.00370009	−	0.0209842i
$743$	−2.97391e11	+	5.24380e10i	−0.975826	+	0.172064i	−0.638751	−	0.769413i	$-0.720549\pi$
$743$	−2.97391e11	+	5.24380e10i	−0.975826	+	0.172064i	−0.337075	+	0.941478i	$0.609438\pi$
$744$	−2.98672e10	+	1.80131e11i	−0.0974773	+	0.587891i
$745$	−3.48118e11	−	2.92106e11i	−1.13006	−	0.948234i
$746$	−2.76746e9	+	1.59780e9i	−0.00893566	+	0.00515901i
$747$	1.26015e11	−	3.69554e11i	0.404705	−	1.18685i
$748$	2.69482e10	−	4.66756e10i	0.0860842	−	0.149102i
$749$	−1.01954e10	−	2.80117e10i	−0.0323950	−	0.0890046i
$750$	−4.19627e10	−	2.36587e10i	−0.132623	−	0.0747733i
$751$	1.35125e11	−	1.13384e11i	0.424793	−	0.356443i	−0.405190	−	0.914232i	$-0.632795\pi$
$751$	1.35125e11	−	1.13384e11i	0.424793	−	0.356443i	0.829983	+	0.557789i	$0.188350\pi$
$752$	−1.28639e11	+	3.53433e11i	−0.402255	+	1.10519i
$753$	−4.86047e10	−	2.60080e11i	−0.151181	−	0.808961i
$754$	−1.89665e9	+	1.07564e10i	−0.00586815	+	0.0332799i
$755$			2.18825e11i			0.673455i
$756$	−2.92218e10	+	1.80876e10i	−0.0894581	+	0.0553726i
$757$	1.08704e11			0.331025			0.165513	−	0.986208i	$-0.447072\pi$
$757$	1.08704e11			0.331025			0.165513	+	0.986208i	$0.447072\pi$
$758$	−5.48401e10	−	9.66979e9i	−0.166120	−	0.0292914i
$759$	3.60502e10	−	1.02288e11i	0.108628	−	0.308217i
$760$	4.84544e10	+	1.76360e10i	0.145237	+	0.0528621i
$761$	−3.21895e11	−	3.83619e11i	−0.959788	−	1.14383i	−0.989538	−	0.144273i	$-0.953916\pi$
$761$	−3.21895e11	−	3.83619e11i	−0.959788	−	1.14383i	0.0297499	−	0.999557i	$-0.490529\pi$
$762$	9.47919e10	−	9.68753e8i	0.281159	−	0.00287338i
$763$	7.75589e9	−	2.82291e9i	0.0228841	−	0.00832913i
$764$	−1.62053e11	−	9.35612e10i	−0.475645	−	0.274614i
$765$	−6.45725e10	+	1.17316e11i	−0.188539	+	0.342542i
$766$	4.15116e10	+	7.19002e10i	0.120574	+	0.208841i
$767$	4.19094e10	−	4.99457e10i	0.121096	−	0.144317i
$768$	1.68730e11	−	2.05310e11i	0.485007	−	0.590153i
$769$	−7.36249e10	−	4.17547e11i	−0.210533	−	1.19399i	−0.888493	−	0.458891i	$-0.848247\pi$
$769$	−7.36249e10	−	4.17547e11i	−0.210533	−	1.19399i	0.677960	−	0.735099i	$-0.262864\pi$
$770$	2.77386e9	−	4.89107e8i	0.00789082	−	0.00139136i
$771$	6.43919e10	+	5.29193e10i	0.182227	+	0.149760i
$772$	2.55609e11	+	2.14482e11i	0.719627	+	0.603839i
$773$	2.87823e11	−	1.66175e11i	0.806134	−	0.465422i	−0.0394773	−	0.999220i	$-0.512569\pi$
$773$	2.87823e11	−	1.66175e11i	0.806134	−	0.465422i	0.845612	+	0.533799i	$0.179236\pi$
$774$	1.23060e10	−	7.44429e9i	0.0342889	−	0.0207424i
$775$	1.78877e10	−	3.09825e10i	0.0495848	−	0.0858834i
$776$	6.00852e10	+	1.65083e11i	0.165699	+	0.455255i
$777$	3.04999e8	+	2.98440e10i	0.000836786	+	0.0818790i
$778$	−7.58765e10	+	6.36679e10i	−0.207104	+	0.173781i
$779$	−1.05512e9	+	2.89891e9i	−0.00286517	+	0.00787198i
$780$	−5.16461e10	−	1.82021e10i	−0.139527	−	0.0491749i
$781$	−3.21962e9	+	1.82594e10i	−0.00865368	+	0.0490775i
$782$			1.57596e10i			0.0421424i
$783$	5.09590e11	−	2.03374e11i	1.35573	−	0.541063i
$784$	−3.46184e11			−0.916310
$785$	5.68092e11	+	1.00170e11i	1.49603	+	0.263790i
$786$	1.05084e11	−	1.96385e10i	0.275326	−	0.0514539i
$787$	−4.41598e11	−	1.60728e11i	−1.15114	−	0.418980i	−0.305215	−	0.952283i	$-0.598728\pi$
$787$	−4.41598e11	−	1.60728e11i	−1.15114	−	0.418980i	−0.845924	+	0.533303i	$0.820951\pi$
$788$	1.53347e11	+	1.82752e11i	0.397714	+	0.473977i
$789$	−1.97288e11	+	3.49924e11i	−0.509089	+	0.902954i
$790$	6.54690e10	−	2.38288e10i	0.168084	−	0.0611777i
$791$	−1.55527e10	−	8.97936e9i	−0.0397283	−	0.0229371i
$792$	1.09105e10	+	5.52483e10i	0.0277295	+	0.140417i
$793$	4.51263e10	+	7.81610e10i	0.114113	+	0.197650i
$794$	−3.26090e10	+	3.88618e10i	−0.0820455	+	0.0977781i
$795$	−5.10022e11	−	8.45659e10i	−1.27679	−	0.211703i
$796$	3.67288e10	+	2.08299e11i	0.0914859	+	0.518842i
$797$	−4.55285e10	+	8.02790e9i	−0.112837	+	0.0198961i	−0.229781	−	0.973242i	$-0.573801\pi$
$797$	−4.55285e10	+	8.02790e9i	−0.112837	+	0.0198961i	0.116945	+	0.993138i	$0.462690\pi$
$798$	−3.12393e9	+	1.17331e9i	−0.00770353	+	0.00289335i
$799$	−1.51025e11	−	1.26725e11i	−0.370563	−	0.310939i
$800$	8.29378e9	−	4.78842e9i	0.0202485	−	0.0116905i
$801$	1.57708e11	−	1.95946e11i	0.383109	−	0.475999i
$802$	−3.51703e10	+	6.09168e10i	−0.0850117	+	0.147245i
$803$	−4.05597e9	−	1.11437e10i	−0.00975512	−	0.0268020i
$804$	−2.15787e11	+	1.27542e11i	−0.516417	+	0.305232i
$805$	2.51185e10	−	2.10769e10i	0.0598150	−	0.0501908i
$806$	6.43965e9	−	1.76928e10i	0.0152589	−	0.0419234i
$807$	−6.65180e10	+	5.69837e10i	−0.156836	+	0.134356i
$808$	−2.93037e10	+	1.66190e11i	−0.0687508	+	0.389905i
$809$			1.18357e11i			0.276312i	0.990410	+	0.138156i	$0.0441175\pi$
$809$			1.18357e11i			0.276312i	−0.990410	+	0.138156i	$0.955882\pi$
$810$	−1.47687e10	−	6.74971e10i	−0.0343086	−	0.156800i
$811$	9.39449e10			0.217165			0.108582	−	0.994087i	$-0.465369\pi$
$811$	9.39449e10			0.217165			0.108582	+	0.994087i	$0.465369\pi$
$812$	−6.57497e10	−	1.15935e10i	−0.151241	−	0.0266679i
$813$	2.45815e11	+	2.86944e11i	0.562660	+	0.656802i
$814$	2.26936e10	+	8.25978e9i	0.0516898	+	0.0188136i
$815$	2.09234e11	+	2.49355e11i	0.474244	+	0.565182i
$816$	7.97505e10	+	1.34928e11i	0.179876	+	0.304329i
$817$	−5.22464e10	+	1.90161e10i	−0.117265	+	0.0426810i
$818$	−5.14373e10	−	2.96974e10i	−0.114886	−	0.0663292i
$819$	6.69227e9	−	2.59187e9i	0.0148743	−	0.00576074i
$820$	3.88624e9	+	6.73117e9i	0.00859557	+	0.0148880i
$821$	1.46122e11	−	1.74141e11i	0.321619	−	0.383291i	−0.580875	−	0.813993i	$-0.697290\pi$
$821$	1.46122e11	−	1.74141e11i	0.321619	−	0.383291i	0.902494	+	0.430702i	$0.141734\pi$
$822$	−2.26797e10	−	6.03846e10i	−0.0496764	−	0.132263i
$823$	6.39160e9	+	3.62485e10i	0.0139319	+	0.0790117i	0.990981	−	0.134003i	$-0.0427830\pi$
$823$	6.39160e9	+	3.62485e10i	0.0139319	+	0.0790117i	−0.977049	+	0.213014i	$0.931672\pi$
$824$	−1.48813e11	+	2.62397e10i	−0.322798	+	0.0569180i
$825$	1.80489e9	−	1.08854e10i	0.00389615	−	0.0234979i
$826$	−7.66841e9	−	6.43456e9i	−0.0164735	−	0.0138229i
$827$	3.00935e11	−	1.73745e11i	0.643354	−	0.371441i	−0.142551	−	0.989787i	$-0.545531\pi$
$827$	3.00935e11	−	1.73745e11i	0.643354	−	0.371441i	0.785906	+	0.618347i	$0.212197\pi$
$828$	2.13114e11	+	2.43687e11i	0.453410	+	0.518454i
$829$	−2.97922e11	+	5.16016e11i	−0.630790	+	1.09256i	0.356601	+	0.934257i	$0.383936\pi$
$829$	−2.97922e11	+	5.16016e11i	−0.630790	+	1.09256i	−0.987391	+	0.158303i	$0.949398\pi$
$830$	−3.26697e10	−	8.97592e10i	−0.0688387	−	0.189133i
$831$	6.19457e11	+	3.49252e11i	1.29899	+	0.732378i
$832$	−4.64695e10	+	3.89926e10i	−0.0969784	+	0.0813745i
$833$	6.20629e10	−	1.70516e11i	0.128900	−	0.354149i
$834$	−2.05329e10	−	1.09870e11i	−0.0424410	−	0.227099i
$835$	9.76647e10	−	5.53884e11i	0.200905	−	1.13939i
$836$		−	1.07501e11i		−	0.220084i
$837$	−9.25978e11	+	1.92715e11i	−1.88668	+	0.392657i
$838$	−3.94359e10			−0.0799678
$839$	−3.77521e11	−	6.65672e10i	−0.761892	−	0.134342i	−0.220816	−	0.975316i	$-0.570872\pi$
$839$	−3.77521e11	−	6.65672e10i	−0.761892	−	0.134342i	−0.541077	+	0.840973i	$0.681983\pi$
$840$	−5.65951e9	+	1.60581e10i	−0.0113674	+	0.0322535i
$841$	5.31543e11	+	1.93466e11i	1.06256	+	0.386741i
$842$	−6.81598e9	−	8.12297e9i	−0.0135606	−	0.0161609i
$843$	−4.12351e11	+	4.21414e9i	−0.816501	+	0.00834446i
$844$	5.33235e10	−	1.94082e10i	0.105087	−	0.0382486i
$845$	−4.42842e11	−	2.55675e11i	−0.868604	−	0.501489i
$846$	1.01700e11	−	2.07892e9i	0.198536	−	0.00405842i
$847$	2.18083e10	+	3.77730e10i	0.0423729	+	0.0733919i
$848$	−3.88945e11	+	4.63526e11i	−0.752150	+	0.896377i
$849$	−4.03416e11	+	4.90874e11i	−0.776466	+	0.944799i
$850$	2.78422e8	+	1.57901e9i	0.000533369	+	0.00302489i
$851$	2.76869e11	−	4.88195e10i	0.527906	−	0.0930840i
$852$	−4.27572e10	−	3.51392e10i	−0.0811430	−	0.0666859i
$853$	6.58027e11	+	5.52150e11i	1.24293	+	1.04294i	0.997289	+	0.0735846i	$0.0234439\pi$
$853$	6.58027e11	+	5.52150e11i	1.24293	+	1.04294i	0.245644	+	0.969360i	$0.421001\pi$
$854$	1.20004e10	−	6.92845e9i	0.0225614	−	0.0130258i
$855$	5.45888e9	+	2.67046e11i	0.0102150	+	0.499715i
$856$	7.29032e10	−	1.26272e11i	0.135785	−	0.235186i
$857$	−1.21489e11	−	3.33788e11i	−0.225223	−	0.618795i	0.774685	−	0.632347i	$-0.217908\pi$
$857$	−1.21489e11	−	3.33788e11i	−0.225223	−	0.618795i	−0.999908	+	0.0135519i	$0.995686\pi$
$858$	−5.93442e7	−	5.80679e9i	−0.000109504	−	0.0107149i
$859$	3.20921e11	−	2.69285e11i	0.589421	−	0.494583i	−0.298605	−	0.954377i	$-0.596521\pi$
$859$	3.20921e11	−	2.69285e11i	0.589421	−	0.494583i	0.888026	+	0.459794i	$0.152077\pi$
$860$	−4.79109e10	+	1.31634e11i	−0.0875872	+	0.240644i
$861$	−9.60717e8	−	3.38594e8i	−0.00174817	−	0.000616123i
$862$	−2.36501e10	+	1.34127e11i	−0.0428356	+	0.242933i
$863$			3.69630e11i			0.666383i	0.942859	+	0.333191i	$0.108125\pi$
$863$			3.69630e11i			0.666383i	−0.942859	+	0.333191i	$0.891875\pi$
$864$	−2.40462e11	−	7.92619e10i	−0.431511	−	0.142236i
$865$	9.05862e11			1.61807
$866$	−2.49926e10	−	4.40687e9i	−0.0444365	−	0.00783536i
$867$	4.74663e11	−	8.87066e10i	0.840057	−	0.156993i
$868$	1.08149e11	+	3.93630e10i	0.190521	+	0.0693441i
$869$	−1.89075e11	−	2.25331e11i	−0.331554	−	0.395131i
$870$	6.59227e10	−	1.16925e11i	0.115069	−	0.204094i
$871$	4.91876e10	−	1.79028e10i	0.0854639	−	0.0311063i
$872$	3.49622e10	+	2.01855e10i	0.0604691	+	0.0349118i
$873$	−6.85008e11	+	5.99068e11i	−1.17934	+	1.03138i
$874$	1.57170e10	+	2.72227e10i	0.0269355	+	0.0466536i
$875$	−3.95255e10	+	4.71046e10i	−0.0674287	+	0.0803584i
$876$	3.49211e10	+	5.79022e9i	0.0593024	+	0.00983283i
$877$	1.45845e11	+	8.27127e11i	0.246543	+	1.39821i	0.816882	+	0.576805i	$0.195701\pi$
$877$	1.45845e11	+	8.27127e11i	0.246543	+	1.39821i	−0.570339	+	0.821409i	$0.693188\pi$
$878$	−1.07542e11	+	1.89625e10i	−0.180967	+	0.0319093i
$879$	9.17233e11	−	3.44501e11i	1.53647	−	0.577078i
$880$	−2.02139e11	−	1.69615e11i	−0.337070	−	0.282835i
$881$	6.57619e11	−	3.79677e11i	1.09162	−	0.630246i	0.157612	−	0.987501i	$-0.449621\pi$
$881$	6.57619e11	−	3.79677e11i	1.09162	−	0.630246i	0.934007	+	0.357255i	$0.116287\pi$
$882$	3.38134e10	+	8.73068e10i	0.0558746	+	0.144269i
$883$	5.00897e11	−	8.67579e11i	0.823959	−	1.42714i	−0.0787530	−	0.996894i	$-0.525094\pi$
$883$	5.00897e11	−	8.67579e11i	0.823959	−	1.42714i	0.902712	−	0.430245i	$-0.141573\pi$
$884$	−1.14902e10	−	3.15692e10i	−0.0188157	−	0.0516957i
$885$	−6.89778e11	+	4.07699e11i	−1.12444	+	0.664609i
$886$	8.58842e10	−	7.20654e10i	0.139373	−	0.116948i
$887$	2.56509e11	−	7.04753e11i	0.414389	−	1.13853i	−0.540443	−	0.841380i	$-0.681743\pi$
$887$	2.56509e11	−	7.04753e11i	0.414389	−	1.13853i	0.954832	−	0.297145i	$-0.0960344\pi$
$888$	−1.10865e11	+	9.49739e10i	−0.178296	+	0.152740i
$889$	2.10123e10	−	1.19167e11i	0.0336408	−	0.190786i
$890$		−	6.15342e10i		−	0.0980747i
$891$	−2.46460e11	+	1.56059e11i	−0.391052	+	0.247616i
$892$	−1.61946e11			−0.255805
$893$	−3.87258e11	−	6.82841e10i	−0.608968	−	0.107378i
$894$	9.35852e10	+	1.09244e11i	0.146507	+	0.171020i
$895$	7.62111e10	+	2.77386e10i	0.118775	+	0.0432306i
$896$	2.62876e10	+	3.13283e10i	0.0407867	+	0.0486077i
$897$	−3.43980e10	−	5.81973e10i	−0.0531328	−	0.0898945i
$898$	1.07227e11	−	3.90274e10i	0.164892	−	0.0600157i
$899$	−1.59126e12	−	9.18717e11i	−2.43615	−	1.40651i
$900$	2.56577e10	+	2.06507e10i	0.0391064	+	0.0314749i
$901$	−1.58586e11	−	2.74678e11i	−0.240638	−	0.416798i
$902$	−5.29815e8	+	6.31409e8i	−0.000800384	+	0.000953861i
$903$	−6.45502e9	−	1.71865e10i	−0.00970838	−	0.0258485i
$904$	−1.52534e10	−	8.65066e10i	−0.0228399	−	0.129532i
$905$	2.90895e11	−	5.12925e10i	0.433652	−	0.0764645i
$906$	1.13304e10	−	6.83344e10i	0.0168164	−	0.101421i
$907$	1.50108e11	+	1.25956e11i	0.221807	+	0.186118i	0.746919	−	0.664915i	$-0.231532\pi$
$907$	1.50108e11	+	1.25956e11i	0.221807	+	0.186118i	−0.525112	+	0.851033i	$0.675977\pi$
$908$	2.30152e11	−	1.32878e11i	0.338588	−	0.195484i
$909$	−8.57582e11	+	1.69356e11i	−1.25609	+	0.248053i
$910$	8.77852e8	−	1.52049e9i	0.00128014	−	0.00221726i
$911$	−2.20777e11	−	6.06578e11i	−0.320538	−	0.880671i	−0.990406	−	0.138190i	$-0.955871\pi$
$911$	−2.20777e11	−	6.06578e11i	−0.320538	−	0.880671i	0.669868	−	0.742480i	$-0.266351\pi$
$912$	2.72322e11	+	1.53536e11i	0.393643	+	0.221938i
$913$	−3.08932e11	+	2.59225e11i	−0.444611	+	0.373073i
$914$	3.60949e10	−	9.91700e10i	0.0517204	−	0.142101i
$915$	−2.03753e11	−	1.09027e12i	−0.290682	−	1.55542i
$916$	8.55180e10	−	4.84997e11i	0.121472	−	0.688901i
$917$		−	1.36459e11i		−	0.192985i
$918$	2.62391e10	−	3.32920e10i	0.0369469	−	0.0468780i
$919$	−6.41781e11			−0.899756			−0.449878	−	0.893090i	$-0.648532\pi$
$919$	−6.41781e11			−0.899756			−0.449878	+	0.893090i	$0.648532\pi$
$920$	1.57948e11	+	2.78505e10i	0.220477	+	0.0388760i
$921$	3.48521e11	−	9.88881e11i	0.484384	−	1.37438i
$922$	−4.34296e10	−	1.58071e10i	−0.0600983	−	0.0218740i
$923$	7.42882e9	+	8.85333e9i	0.0102356	+	0.0121983i
$924$	3.54946e10	−	3.62747e8i	0.0486939	−	0.000497641i
$925$	2.68779e10	−	9.78276e9i	0.0367137	−	0.0133627i
$926$	6.31505e10	+	3.64600e10i	0.0858881	+	0.0495875i
$927$	−4.05143e11	−	6.69734e11i	−0.548642	−	0.906950i
$928$	−2.45934e11	−	4.25970e11i	−0.331609	−	0.574363i
$929$	−8.58049e11	+	1.02258e12i	−1.15199	+	1.37289i	−0.235970	+	0.971760i	$0.575827\pi$
$929$	−8.58049e11	+	1.02258e12i	−1.15199	+	1.37289i	−0.916021	+	0.401129i	$0.868618\pi$
$930$	−1.46913e11	+	1.78763e11i	−0.196394	+	0.238971i
$931$	−6.28498e10	−	3.56439e11i	−0.0836576	−	0.474446i
$932$	1.13388e12	−	1.99934e11i	1.50281	−	0.264986i
$933$	7.89195e11	+	6.48586e11i	1.04150	+	0.855935i
$934$	−1.02663e11	−	8.61448e10i	−0.134905	−	0.113199i
$935$	1.19784e11	−	6.91576e10i	0.156731	−	0.0904885i
$936$	3.07524e10	+	1.69265e10i	0.0400660	+	0.0220528i
$937$	−2.84345e11	+	4.92500e11i	−0.368882	+	0.638922i	−0.989391	−	0.145277i	$-0.953593\pi$
$937$	−2.84345e11	+	4.92500e11i	−0.368882	+	0.638922i	0.620509	+	0.784199i	$0.286926\pi$
$938$	−2.74870e9	−	7.55200e9i	−0.00355072	−	0.00975552i
$939$	7.47241e9	+	7.31171e11i	0.00961166	+	0.940496i
$940$	−7.58953e11	+	6.36837e11i	−0.972083	+	0.815675i
$941$	1.33808e11	−	3.67635e11i	0.170657	−	0.468876i	−0.824650	−	0.565643i	$-0.808628\pi$
$941$	1.33808e11	−	3.67635e11i	0.170657	−	0.468876i	0.995307	+	0.0967671i	$0.0308502\pi$
$942$	−1.72217e11	−	6.06959e10i	−0.218711	−	0.0770825i
$943$	−1.66622e9	+	9.44963e9i	−0.00210711	+	0.0119500i
$944$			9.37807e11i			1.18093i
$945$	−8.81546e10	+	2.70351e9i	−0.110540	+	0.00339001i
$946$	−1.48552e10			−0.0185488
$947$	1.36936e12	+	2.41455e11i	1.70262	+	0.300218i	0.938608	−	0.344986i	$-0.112116\pi$
$947$	1.36936e12	+	2.41455e11i	1.70262	+	0.300218i	0.764011	+	0.645203i	$0.223227\pi$
$948$	8.63071e11	−	1.61294e11i	1.06860	−	0.199703i
$949$	−6.94619e9	−	2.52821e9i	−0.00856410	−	0.00311708i
$950$	2.05568e9	+	2.44986e9i	0.00252383	+	0.00300778i
$951$	−9.91635e10	+	1.75883e11i	−0.121235	+	0.215031i
$952$	−9.81568e9	+	3.57261e9i	−0.0119501	+	0.00434949i
$953$	−2.09625e11	−	1.21027e11i	−0.254139	−	0.146727i	0.367519	−	0.930016i	$-0.380207\pi$
$953$	−2.09625e11	−	1.21027e11i	−0.254139	−	0.146727i	−0.621658	+	0.783289i	$0.713541\pi$
$954$	1.54890e11	+	5.28163e10i	0.186995	+	0.0637639i
$955$	−2.40108e11	−	4.15879e11i	−0.288664	−	0.499980i
$956$	−2.24936e11	+	2.68068e11i	−0.269294	+	0.320932i
$957$	−5.59076e11	−	9.26995e10i	−0.666535	−	0.110517i
$958$	−1.21327e10	−	6.88082e10i	−0.0144045	−	0.0816918i
$959$	−8.10853e10	+	1.42975e10i	−0.0958667	+	0.0169039i
$960$	6.97889e11	−	2.62118e11i	0.821677	−	0.308611i
$961$	1.77303e12	+	1.48775e12i	2.07885	+	1.74436i
$962$	1.30366e10	−	7.52670e9i	0.0152218	−	0.00878829i
$963$	7.46328e11	+	1.15924e11i	0.867810	+	0.134793i
$964$	3.99542e11	−	6.92028e11i	0.462652	−	0.801337i
$965$	2.92877e11	+	8.04672e11i	0.337735	+	0.927918i
$966$	−8.93531e9	+	5.28128e9i	−0.0102613	+	0.00606500i
$967$	−2.96716e11	+	2.48974e11i	−0.339340	+	0.284740i	−0.796492	−	0.604648i	$-0.793314\pi$
$967$	−2.96716e11	+	2.48974e11i	−0.339340	+	0.284740i	0.457153	+	0.889388i	$0.348869\pi$
$968$	−7.29668e10	+	2.00475e11i	−0.0831044	+	0.228328i
$969$	−1.24447e11	+	1.06609e11i	−0.141153	+	0.120921i
$970$	−3.86586e10	+	2.19244e11i	−0.0436676	+	0.247651i
$971$			4.12689e11i			0.464243i	0.972687	+	0.232122i	$0.0745668\pi$
$971$			4.12689e11i			0.464243i	−0.972687	+	0.232122i	$0.925433\pi$
$972$	−4.44732e10	−	8.69609e11i	−0.0498235	−	0.974225i
$973$	−1.42673e11			−0.159181
$974$	1.33944e11	+	2.36180e10i	0.148829	+	0.0262426i
$975$	−4.47460e9	−	5.22327e9i	−0.00495149	−	0.00577995i
$976$	−1.21987e12	−	4.43997e11i	−1.34436	−	0.489307i
$977$	2.63596e11	+	3.14142e11i	0.289308	+	0.344784i	0.891049	−	0.453907i	$-0.149970\pi$
$977$	2.63596e11	+	3.14142e11i	0.289308	+	0.344784i	−0.601741	+	0.798692i	$0.705526\pi$
$978$	−5.24281e10	−	8.87023e10i	−0.0573072	−	0.0969570i
$979$	−2.44129e11	+	8.88556e10i	−0.265759	+	0.0967285i
$980$	−7.89726e11	−	4.55948e11i	−0.856194	−	0.494324i
$981$	−3.20970e10	+	2.06644e11i	−0.0346568	+	0.223124i
$982$	−4.14176e10	−	7.17374e10i	−0.0445389	−	0.0771436i
$983$	−1.47538e11	+	1.75829e11i	−0.158012	+	0.188311i	−0.839242	−	0.543758i	$-0.817001\pi$
$983$	−1.47538e11	+	1.75829e11i	−0.158012	+	0.188311i	0.681230	+	0.732069i	$0.261445\pi$
$984$	−1.75185e9	−	4.66430e9i	−0.00186860	−	0.00497515i
$985$	1.06313e11	+	6.02934e11i	0.112939	+	0.640508i
$986$	8.10981e10	−	1.42998e10i	0.0858031	−	0.0151294i
$987$	2.12392e10	−	1.28095e11i	0.0223805	−	0.134978i
$988$	−5.13317e10	−	4.30724e10i	−0.0538713	−	0.0452034i
$989$	−1.49767e11	+	8.64681e10i	−0.156542	+	0.0903797i
$990$	−2.30327e10	+	6.75462e10i	−0.0239775	+	0.0703169i
$991$	2.92488e11	−	5.06604e11i	0.303259	−	0.525260i	−0.673613	−	0.739084i	$-0.735259\pi$
$991$	2.92488e11	−	5.06604e11i	0.303259	−	0.525260i	0.976872	+	0.213824i	$0.0685920\pi$
$992$	2.89997e11	+	7.96761e11i	0.299466	+	0.822775i
$993$	9.24836e11	+	5.21426e11i	0.951191	+	0.536285i
$994$	1.35929e9	−	1.14058e9i	0.00139241	−	0.00116837i
$995$	−1.85651e11	+	5.10073e11i	−0.189411	+	0.520403i
$996$	−2.21137e11	−	1.18329e12i	−0.224711	−	1.20241i
$997$	−5.61372e10	+	3.18370e11i	−0.0568160	+	0.322219i	−0.999948	−	0.0101990i	$-0.996753\pi$
$997$	−5.61372e10	+	3.18370e11i	−0.0568160	+	0.322219i	0.943132	+	0.332418i	$0.107865\pi$
$998$			1.01107e11i			0.101920i
$999$	−6.66164e11	−	3.57844e11i	−0.668835	−	0.359279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.f.a.2.12	✓	138
3.2	odd	2		81.9.f.a.8.12		138
27.13	even	9		81.9.f.a.71.12		138
27.14	odd	18	inner	27.9.f.a.14.12	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.12	✓	138	1.1	even	1	trivial
27.9.f.a.14.12	yes	138	27.14	odd	18	inner
81.9.f.a.8.12		138	3.2	odd	2
81.9.f.a.71.12		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+(-2.46646 - 0.434904i) q^{2} +(-52.6972 - 61.5143i) q^{3} +(-234.667 - 85.4118i) q^{4} +(-411.949 - 490.942i) q^{5} +(103.223 + 174.641i) q^{6} +(243.334 - 88.5664i) q^{7} +(1096.91 + 633.301i) q^{8} +(-1007.01 + 6483.26i) q^{9} +(802.546 + 1390.05i) q^{10} +(4355.96 - 5191.23i) q^{11} +(7112.24 + 18936.3i) q^{12} +(-733.507 - 4159.93i) q^{13} +(-638.693 + 112.619i) q^{14} +(-8491.39 + 51212.1i) q^{15} +(46543.3 + 39054.5i) q^{16} +(-27580.9 + 15923.8i) q^{17} +(5303.36 - 15552.8i) q^{18} +(-31761.5 + 55012.5i) q^{19} +(54738.7 + 150393. i) q^{20} +(-18271.1 - 10301.3i) q^{21} +(-13001.5 + 10909.6i) q^{22} +(-67576.8 + 185666. i) q^{23} +(-18847.0 - 100849. i) q^{24} +(-3490.62 + 19796.3i) q^{25} +10579.3i q^{26} +(451880. - 279704. i) q^{27} -64667.1 q^{28} +(1.01674e6 + 179279. i) q^{29} +(43216.0 - 122620. i) q^{30} +(-1.67239e6 - 608702. i) q^{31} +(-306236. - 364958. i) q^{32} +(-548882. + 5609.45i) q^{33} +(74952.5 - 27280.5i) q^{34} +(-143722. - 82978.2i) q^{35} +(790060. - 1.43540e6i) q^{36} +(-711454. - 1.23227e6i) q^{37} +(102264. - 121873. i) q^{38} +(-217241. + 264338. i) q^{39} +(-140957. - 799407. i) q^{40} +(47826.5 - 8433.11i) q^{41} +(40585.0 + 33354.1i) q^{42} +(670492. + 562610. i) q^{43} +(-1.46559e6 + 846160. i) q^{44} +(3.59774e6 - 2.17639e6i) q^{45} +(247423. - 428549. i) q^{46} +(2.11724e6 + 5.81707e6i) q^{47} +(-50293.0 - 4.92114e6i) q^{48} +(-4.36473e6 + 3.66244e6i) q^{49} +(17219.0 - 47308.8i) q^{50} +(2.43298e6 + 857477. i) q^{51} +(-183177. + 1.03885e6i) q^{52} +9.95902e6i q^{53} +(-1.23619e6 + 493355. i) q^{54} -4.34303e6 q^{55} +(323005. + 56954.4i) q^{56} +(5.05780e6 - 945219. i) q^{57} +(-2.42979e6 - 884370. i) q^{58} +(9.92151e6 + 1.18240e7i) q^{59} +(6.36676e6 - 1.12925e7i) q^{60} +(-2.00776e7 + 7.30764e6i) q^{61} +(3.86018e6 + 2.22867e6i) q^{62} +(329158. + 1.66679e6i) q^{63} +(-7.18042e6 - 1.24369e7i) q^{64} +(-1.74012e6 + 2.07379e6i) q^{65} +(1.35624e6 + 224875. i) q^{66} +(2.15182e6 + 1.22036e7i) q^{67} +(7.83240e6 - 1.38106e6i) q^{68} +(1.49822e7 - 5.62712e6i) q^{69} +(318399. + 267168. i) q^{70} +(-2.36946e6 + 1.36801e6i) q^{71} +(-5.21046e6 + 6.47380e6i) q^{72} +(874977. - 1.51550e6i) q^{73} +(1.21886e6 + 3.34878e6i) q^{74} +(1.40170e6 - 828486. i) q^{75} +(1.21521e7 - 1.01968e7i) q^{76} +(600185. - 1.64900e6i) q^{77} +(650779. - 557500. i) q^{78} +(7.53737e6 - 4.27466e7i) q^{79} -3.89386e7i q^{80} +(-4.10186e7 - 1.30575e7i) q^{81} -121630. q^{82} +(-5.86063e7 - 1.03339e7i) q^{83} +(3.40778e6 + 3.97795e6i) q^{84} +(1.91796e7 + 6.98080e6i) q^{85} +(-1.40906e6 - 1.67926e6i) q^{86} +(-4.25512e7 - 7.19916e7i) q^{87} +(8.06570e6 - 2.93568e6i) q^{88} +(-3.32007e7 - 1.91684e7i) q^{89} +(-9.82023e6 + 3.80331e6i) q^{90} +(-546917. - 947288. i) q^{91} +(3.17161e7 - 3.77978e7i) q^{92} +(5.06866e7 + 1.34953e8i) q^{93} +(-2.69223e6 - 1.52684e7i) q^{94} +(4.00921e7 - 7.06932e6i) q^{95} +(-6.31236e6 + 3.80702e7i) q^{96} +(1.06250e8 + 8.91546e7i) q^{97} +(1.23583e7 - 7.13504e6i) q^{98} +(2.92696e7 + 3.34685e7i) 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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