LMFDB - Embedded newform 54.8.e.b.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,8,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, 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:	$16.8687913761$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	54.13
Dual form			54.8.e.b.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38919 - 7.87846i) q^{2} +(-7.96623 - 46.0819i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-406.101 - 340.759i) q^{5} +(-351.988 + 126.778i) q^{6} +(-407.930 - 148.474i) q^{7} +(256.000 + 443.405i) q^{8} +(-2060.08 + 734.197i) q^{9} +O(q^{10})$	\(q+(-1.38919 - 7.87846i) q^{2} +(-7.96623 - 46.0819i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-406.101 - 340.759i) q^{5} +(-351.988 + 126.778i) q^{6} +(-407.930 - 148.474i) q^{7} +(256.000 + 443.405i) q^{8} +(-2060.08 + 734.197i) q^{9} +(-2120.51 + 3672.83i) q^{10} +(4080.13 - 3423.64i) q^{11} +(1487.79 + 2597.00i) q^{12} +(372.856 - 2114.57i) q^{13} +(-603.059 + 3420.12i) q^{14} +(-12467.7 + 21428.5i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-43.7315 + 75.7452i) q^{17} +(8646.18 + 15210.3i) q^{18} +(-20454.2 - 35427.7i) q^{19} +(31882.0 + 11604.1i) q^{20} +(-3592.31 + 19980.9i) q^{21} +(-32641.1 - 27389.1i) q^{22} +(77181.3 - 28091.7i) q^{23} +(18393.6 - 15329.2i) q^{24} +(35234.9 + 199827. i) q^{25} -17177.5 q^{26} +(50244.2 + 89083.5i) q^{27} +27783.0 q^{28} +(402.156 + 2280.74i) q^{29} +(186143. + 68458.4i) q^{30} +(67734.9 - 24653.5i) q^{31} +(-25101.7 - 21062.9i) q^{32} +(-190271. - 160747. i) q^{33} +(657.507 + 239.313i) q^{34} +(115067. + 199301. i) q^{35} +(107823. - 89248.5i) q^{36} +(-262356. + 454415. i) q^{37} +(-250701. + 210363. i) q^{38} +(-100414. - 336.749i) q^{39} +(47132.5 - 267302. i) q^{40} +(2721.58 - 15434.8i) q^{41} +(162409. + 544.660i) q^{42} +(148773. - 124835. i) q^{43} +(-170439. + 295210. i) q^{44} +(1.08678e6 + 403832. i) q^{45} +(-328539. - 569045. i) q^{46} +(-998719. - 363504. i) q^{47} +(-146323. - 123618. i) q^{48} +(-486509. - 408229. i) q^{49} +(1.52538e6 - 555194. i) q^{50} +(3838.85 + 1411.83i) q^{51} +(23862.8 + 135333. i) q^{52} +1.21611e6 q^{53} +(632042. - 519601. i) q^{54} -2.82358e6 q^{55} +(-38595.8 - 218887. i) q^{56} +(-1.46963e6 + 1.22479e6i) q^{57} +(17410.1 - 6336.74i) q^{58} +(573687. + 481381. i) q^{59} +(280760. - 1.56162e6i) q^{60} +(-3.03922e6 - 1.10619e6i) q^{61} +(-288328. - 499399. i) q^{62} +(949376. + 6367.77i) q^{63} +(-131072. + 227023. i) q^{64} +(-871976. + 731675. i) q^{65} +(-1.00211e6 + 1.72235e6i) q^{66} +(632318. - 3.58605e6i) q^{67} +(972.019 - 5512.59i) q^{68} +(-1.90936e6 - 3.33287e6i) q^{69} +(1.41034e6 - 1.18341e6i) q^{70} +(-1.57972e6 + 2.73615e6i) q^{71} +(-852927. - 725495. i) q^{72} +(-184500. - 319563. i) q^{73} +(3.94455e6 + 1.43570e6i) q^{74} +(8.92772e6 - 3.21556e6i) q^{75} +(2.00561e6 + 1.68291e6i) q^{76} +(-2.17273e6 + 790808. i) q^{77} +(136840. + 791573. i) q^{78} +(489615. + 2.77674e6i) q^{79} -2.17140e6 q^{80} +(3.70488e6 - 3.02501e6i) q^{81} -125384. q^{82} +(1.03418e6 + 5.86511e6i) q^{83} +(-221326. - 1.28029e6i) q^{84} +(43570.3 - 15858.3i) q^{85} +(-1.19018e6 - 998681. i) q^{86} +(101897. - 36701.0i) q^{87} +(2.56257e6 + 932700. i) q^{88} +(-2.40728e6 - 4.16954e6i) q^{89} +(1.67183e6 - 9.12319e6i) q^{90} +(-466058. + 807237. i) q^{91} +(-4.02680e6 + 3.37889e6i) q^{92} +(-1.67567e6 - 2.92496e6i) q^{93} +(-1.47645e6 + 8.37334e6i) q^{94} +(-3.76584e6 + 2.13572e7i) q^{95} +(-770650. + 1.32453e6i) q^{96} +(-8.03676e6 + 6.74364e6i) q^{97} +(-2.54037e6 + 4.40005e6i) q^{98} +(-5.89177e6 + 1.00486e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9}+O(q^{10}) $ 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9} - 3000 q^{10} - 2523 q^{11} - 5376 q^{12} - 9924 q^{13} + 13416 q^{14} - 15084 q^{15} + 29478 q^{17} + 22848 q^{18} - 61731 q^{19} - 27264 q^{20} - 36372 q^{21} + 20184 q^{22} + 255234 q^{23} + 558999 q^{25} - 316368 q^{26} - 51597 q^{27} + 263424 q^{28} + 132153 q^{29} + 610632 q^{30} + 776898 q^{31} + 645795 q^{33} + 387840 q^{34} - 321081 q^{35} - 314688 q^{36} - 759795 q^{37} + 174504 q^{38} - 84012 q^{39} - 109056 q^{40} + 349287 q^{41} + 313752 q^{42} - 1043622 q^{43} + 255552 q^{44} + 845496 q^{45} - 524472 q^{46} + 1280709 q^{47} - 872448 q^{48} + 1011003 q^{49} - 1537704 q^{50} - 7812153 q^{51} - 635136 q^{52} - 2951976 q^{53} - 1256832 q^{54} + 2539854 q^{55} + 858624 q^{56} - 3973923 q^{57} - 47496 q^{58} + 639426 q^{59} - 94464 q^{60} + 1639350 q^{61} + 2859936 q^{62} + 6955635 q^{63} - 8650752 q^{64} - 4119567 q^{65} + 712512 q^{66} - 6408441 q^{67} - 1634496 q^{68} - 1007298 q^{69} + 2380872 q^{70} + 3531612 q^{71} + 6623232 q^{72} - 6666213 q^{73} + 7873368 q^{74} + 16535910 q^{75} - 1396032 q^{76} - 8256489 q^{77} - 4117104 q^{78} - 22540695 q^{79} - 3072000 q^{80} - 13134636 q^{81} + 3798096 q^{82} + 8663238 q^{83} + 8570304 q^{84} - 15143175 q^{85} + 8348976 q^{86} + 45908613 q^{87} + 11028480 q^{88} + 21718137 q^{89} - 27904392 q^{90} - 8606796 q^{91} - 8332800 q^{92} - 20412249 q^{93} - 10358784 q^{94} - 21603363 q^{95} - 5505024 q^{96} - 17397492 q^{97} + 44171448 q^{98} + 103927383 q^{99}+O(q^{100}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9 - 3000 * q^10 - 2523 * q^11 - 5376 * q^12 - 9924 * q^13 + 13416 * q^14 - 15084 * q^15 + 29478 * q^17 + 22848 * q^18 - 61731 * q^19 - 27264 * q^20 - 36372 * q^21 + 20184 * q^22 + 255234 * q^23 + 558999 * q^25 - 316368 * q^26 - 51597 * q^27 + 263424 * q^28 + 132153 * q^29 + 610632 * q^30 + 776898 * q^31 + 645795 * q^33 + 387840 * q^34 - 321081 * q^35 - 314688 * q^36 - 759795 * q^37 + 174504 * q^38 - 84012 * q^39 - 109056 * q^40 + 349287 * q^41 + 313752 * q^42 - 1043622 * q^43 + 255552 * q^44 + 845496 * q^45 - 524472 * q^46 + 1280709 * q^47 - 872448 * q^48 + 1011003 * q^49 - 1537704 * q^50 - 7812153 * q^51 - 635136 * q^52 - 2951976 * q^53 - 1256832 * q^54 + 2539854 * q^55 + 858624 * q^56 - 3973923 * q^57 - 47496 * q^58 + 639426 * q^59 - 94464 * q^60 + 1639350 * q^61 + 2859936 * q^62 + 6955635 * q^63 - 8650752 * q^64 - 4119567 * q^65 + 712512 * q^66 - 6408441 * q^67 - 1634496 * q^68 - 1007298 * q^69 + 2380872 * q^70 + 3531612 * q^71 + 6623232 * q^72 - 6666213 * q^73 + 7873368 * q^74 + 16535910 * q^75 - 1396032 * q^76 - 8256489 * q^77 - 4117104 * q^78 - 22540695 * q^79 - 3072000 * q^80 - 13134636 * q^81 + 3798096 * q^82 + 8663238 * q^83 + 8570304 * q^84 - 15143175 * q^85 + 8348976 * q^86 + 45908613 * q^87 + 11028480 * q^88 + 21718137 * q^89 - 27904392 * q^90 - 8606796 * q^91 - 8332800 * q^92 - 20412249 * q^93 - 10358784 * q^94 - 21603363 * q^95 - 5505024 * q^96 - 17397492 * q^97 + 44171448 * q^98 + 103927383 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−1.38919	−	7.87846i	−0.122788	−	0.696364i
$2$	−1.38919	−	7.87846i	−0.122788	−	0.696364i
$3$	−7.96623	−	46.0819i	−0.170345	−	0.985385i
$3$	−7.96623	−	46.0819i	−0.170345	−	0.985385i
$4$	−60.1403	+	21.8893i	−0.469846	+	0.171010i
$5$	−406.101	−	340.759i	−1.45291	−	1.21914i	−0.930422	−	0.366491i	$-0.880559\pi$
$5$	−406.101	−	340.759i	−1.45291	−	1.21914i	−0.522489	−	0.852646i	$-0.674997\pi$
$6$	−351.988	+	126.778i	−0.665270	+	0.239615i
$7$	−407.930	−	148.474i	−0.449513	−	0.163609i	0.107337	−	0.994223i	$-0.465768\pi$
$7$	−407.930	−	148.474i	−0.449513	−	0.163609i	−0.556849	+	0.830613i	$0.687990\pi$
$8$	256.000	+	443.405i	0.176777	+	0.306186i
$9$	−2060.08	+	734.197i	−0.941965	+	0.335710i
$10$	−2120.51	+	3672.83i	−0.670564	+	1.16145i
$11$	4080.13	−	3423.64i	0.924272	−	0.775556i	−0.0505082	−	0.998724i	$-0.516084\pi$
$11$	4080.13	−	3423.64i	0.924272	−	0.775556i	0.974780	+	0.223167i	$0.0716397\pi$
$12$	1487.79	+	2597.00i	0.248546	+	0.433849i
$13$	372.856	−	2114.57i	0.0470695	−	0.266944i	−0.952186	−	0.305518i	$-0.901170\pi$
$13$	372.856	−	2114.57i	0.0470695	−	0.266944i	0.999256	+	0.0385738i	$0.0122815\pi$
$14$	−603.059	+	3420.12i	−0.0587370	+	0.333114i
$15$	−12467.7	+	21428.5i	−0.953823	+	1.63935i
$16$	3137.72	−	2632.86i	0.191511	−	0.160697i
$17$	−43.7315	+	75.7452i	−0.00215885	+	0.00373924i	−0.867103	−	0.498129i	$-0.834021\pi$
$17$	−43.7315	+	75.7452i	−0.00215885	+	0.00373924i	0.864944	+	0.501868i	$0.167354\pi$
$18$	8646.18	+	15210.3i	0.349438	+	0.614730i
$19$	−20454.2	−	35427.7i	−0.684139	−	1.18496i	−0.973706	−	0.227806i	$-0.926845\pi$
$19$	−20454.2	−	35427.7i	−0.684139	−	1.18496i	0.289567	−	0.957158i	$-0.406489\pi$
$20$	31882.0	+	11604.1i	0.891129	+	0.324345i
$21$	−3592.31	+	19980.9i	−0.0846460	+	0.470813i
$22$	−32641.1	−	27389.1i	−0.653559	−	0.548401i
$23$	77181.3	−	28091.7i	1.32271	−	0.481427i	0.418384	−	0.908270i	$-0.362597\pi$
$23$	77181.3	−	28091.7i	1.32271	−	0.481427i	0.904326	+	0.426843i	$0.140374\pi$
$24$	18393.6	−	15329.2i	0.271598	−	0.226350i
$25$	35234.9	+	199827.i	0.451007	+	2.55779i
$26$	−17177.5			−0.191670
$27$	50244.2	+	89083.5i	0.491262	+	0.871012i
$28$	27783.0			0.239181
$29$	402.156	+	2280.74i	0.00306198	+	0.0173653i	0.986300	−	0.164959i	$-0.0527491\pi$
$29$	402.156	+	2280.74i	0.00306198	+	0.0173653i	−0.983238	+	0.182324i	$0.941638\pi$
$30$	186143.	+	68458.4i	1.25870	+	0.462916i
$31$	67734.9	−	24653.5i	0.408363	−	0.148632i	−0.129667	−	0.991558i	$-0.541391\pi$
$31$	67734.9	−	24653.5i	0.408363	−	0.148632i	0.538030	+	0.842926i	$0.319169\pi$
$32$	−25101.7	−	21062.9i	−0.135419	−	0.113630i
$33$	−190271.	−	160747.i	−0.921666	−	0.778652i
$34$	657.507	+	239.313i	0.00286896	+	0.00104421i
$35$	115067.	+	199301.i	0.453640	+	0.785727i
$36$	107823.	−	89248.5i	0.385169	−	0.318818i
$37$	−262356.	+	454415.i	−0.851502	+	1.47485i	0.0283502	+	0.999598i	$0.490975\pi$
$37$	−262356.	+	454415.i	−0.851502	+	1.47485i	−0.879852	+	0.475247i	$0.842359\pi$
$38$	−250701.	+	210363.i	−0.741163	+	0.621909i
$39$	−100414.	−	336.749i	−0.271061	−	0.000909035i
$40$	47132.5	−	267302.i	0.116442	−	0.660376i
$41$	2721.58	−	15434.8i	0.00616705	−	0.0349751i	−0.981569	−	0.191108i	$-0.938792\pi$
$41$	2721.58	−	15434.8i	0.00616705	−	0.0349751i	0.987736	+	0.156133i	$0.0499029\pi$
$42$	162409.	+	544.660i	0.338251	+	0.00113436i
$43$	148773.	−	124835.i	0.285354	−	0.239440i	−0.488863	−	0.872360i	$-0.662588\pi$
$43$	148773.	−	124835.i	0.285354	−	0.239440i	0.774217	+	0.632920i	$0.218144\pi$
$44$	−170439.	+	295210.i	−0.301638	+	0.522452i
$45$	1.08678e6	+	403832.i	1.77787	+	0.660629i
$46$	−328539.	−	569045.i	−0.497661	−	0.861975i
$47$	−998719.	−	363504.i	−1.40314	−	0.510701i	−0.474030	−	0.880508i	$-0.657201\pi$
$47$	−998719.	−	363504.i	−1.40314	−	0.510701i	−0.929108	+	0.369808i	$0.879424\pi$
$48$	−146323.	−	123618.i	−0.190971	−	0.161338i
$49$	−486509.	−	408229.i	−0.590751	−	0.495699i
$50$	1.52538e6	−	555194.i	1.72577	−	0.628130i
$51$	3838.85	+	1411.83i	0.00405234	+	0.00149034i
$52$	23862.8	+	135333.i	0.0235347	+	0.133472i
$53$	1.21611e6			1.12204			0.561019	−	0.827803i	$-0.310409\pi$
$53$	1.21611e6			1.12204			0.561019	+	0.827803i	$0.310409\pi$
$54$	632042.	−	519601.i	0.546221	−	0.449047i
$55$	−2.82358e6			−2.28839
$56$	−38595.8	−	218887.i	−0.0293685	−	0.166557i
$57$	−1.46963e6	+	1.22479e6i	−1.05111	+	0.875992i
$58$	17410.1	−	6336.74i	0.0117166	−	0.00426450i
$59$	573687.	+	481381.i	0.363658	+	0.305145i	0.806247	−	0.591579i	$-0.201495\pi$
$59$	573687.	+	481381.i	0.363658	+	0.305145i	−0.442589	+	0.896725i	$0.645940\pi$
$60$	280760.	−	1.56162e6i	0.167805	−	0.933356i
$61$	−3.03922e6	−	1.10619e6i	−1.71438	−	0.623984i	−0.717053	−	0.697019i	$-0.754509\pi$
$61$	−3.03922e6	−	1.10619e6i	−1.71438	−	0.623984i	−0.997329	+	0.0730347i	$0.976732\pi$
$62$	−288328.	−	499399.i	−0.153644	−	0.266119i
$63$	949376.	+	6367.77i	0.478351	+	0.00320845i
$64$	−131072.	+	227023.i	−0.0625000	+	0.108253i
$65$	−871976.	+	731675.i	−0.393829	+	0.330462i
$66$	−1.00211e6	+	1.72235e6i	−0.429056	+	0.737424i
$67$	632318.	−	3.58605e6i	0.256846	−	1.45665i	−0.534442	−	0.845205i	$-0.679478\pi$
$67$	632318.	−	3.58605e6i	0.256846	−	1.45665i	0.791288	−	0.611443i	$-0.209411\pi$
$68$	972.019	−	5512.59i	0.000374881	−	0.00212606i
$69$	−1.90936e6	−	3.33287e6i	−0.699707	−	1.22137i
$70$	1.41034e6	−	1.18341e6i	0.491451	−	0.412376i
$71$	−1.57972e6	+	2.73615e6i	−0.523811	+	0.907268i	0.475804	+	0.879551i	$0.342157\pi$
$71$	−1.57972e6	+	2.73615e6i	−0.523811	+	0.907268i	−0.999616	+	0.0277168i	$0.991176\pi$
$72$	−852927.	−	725495.i	−0.269307	−	0.229071i
$73$	−184500.	−	319563.i	−0.0555093	−	0.0961450i	0.836935	−	0.547302i	$-0.184345\pi$
$73$	−184500.	−	319563.i	−0.0555093	−	0.0961450i	−0.892445	+	0.451157i	$0.851012\pi$
$74$	3.94455e6	+	1.43570e6i	1.13158	+	0.411863i
$75$	8.92772e6	−	3.21556e6i	2.44358	−	0.880120i
$76$	2.00561e6	+	1.68291e6i	0.524081	+	0.439756i
$77$	−2.17273e6	+	790808.i	−0.542360	+	0.197403i
$78$	136840.	+	791573.i	0.0326499	+	0.188869i
$79$	489615.	+	2.77674e6i	0.111727	+	0.633637i	0.988319	+	0.152402i	$0.0487008\pi$
$79$	489615.	+	2.77674e6i	0.111727	+	0.633637i	−0.876591	+	0.481236i	$0.840188\pi$
$80$	−2.17140e6			−0.474160
$81$	3.70488e6	−	3.02501e6i	0.774598	−	0.632454i
$82$	−125384.			−0.0251126
$83$	1.03418e6	+	5.86511e6i	0.198528	+	1.12591i	0.907304	+	0.420474i	$0.138136\pi$
$83$	1.03418e6	+	5.86511e6i	0.198528	+	1.12591i	−0.708776	+	0.705433i	$0.750753\pi$
$84$	−221326.	−	1.28029e6i	−0.0407431	−	0.235685i
$85$	43570.3	−	15858.3i	0.00769527	−	0.00280085i
$86$	−1.19018e6	−	998681.i	−0.201776	−	0.169310i
$87$	101897.	−	36701.0i	0.0165899	−	0.00597531i
$88$	2.56257e6	+	932700.i	0.400854	+	0.145899i
$89$	−2.40728e6	−	4.16954e6i	−0.361962	−	0.626936i	0.626322	−	0.779564i	$-0.284560\pi$
$89$	−2.40728e6	−	4.16954e6i	−0.361962	−	0.626936i	−0.988284	+	0.152629i	$0.951226\pi$
$90$	1.67183e6	−	9.12319e6i	0.241738	−	1.31916i
$91$	−466058.	+	807237.i	−0.0648329	+	0.112294i
$92$	−4.02680e6	+	3.37889e6i	−0.539142	+	0.452394i
$93$	−1.67567e6	−	2.92496e6i	−0.216022	−	0.377076i
$94$	−1.47645e6	+	8.37334e6i	−0.183345	+	1.03980i
$95$	−3.76584e6	+	2.13572e7i	−0.450640	+	2.55571i
$96$	−770650.	+	1.32453e6i	−0.0889013	+	0.152796i
$97$	−8.03676e6	+	6.74364e6i	−0.894088	+	0.750229i	−0.969026	−	0.246960i	$-0.920569\pi$
$97$	−8.03676e6	+	6.74364e6i	−0.894088	+	0.750229i	0.0749382	+	0.997188i	$0.476124\pi$
$98$	−2.54037e6	+	4.40005e6i	−0.272650	+	0.472243i
$99$	−5.89177e6	+	1.00486e7i	−0.610270	+	1.04083i
$100$	−6.49311e6	−	1.12464e7i	−0.649311	−	1.12464i
$101$	1.21610e7	+	4.42625e6i	1.17448	+	0.427475i	0.854249	−	0.519864i	$-0.174018\pi$
$101$	1.21610e7	+	4.42625e6i	1.17448	+	0.427475i	0.320230	+	0.947340i	$0.396240\pi$
$102$	5790.14	−	32205.6i	0.000540242	−	0.00300490i
$103$	−262552.	−	220307.i	−0.0236747	−	0.0198655i	0.630873	−	0.775886i	$-0.282697\pi$
$103$	−262552.	−	220307.i	−0.0236747	−	0.0198655i	−0.654548	+	0.756020i	$0.727141\pi$
$104$	1.03306e6	−	376004.i	0.0900554	−	0.0327775i
$105$	8.26753e6	−	6.89017e6i	0.696969	−	0.580854i
$106$	−1.68940e6	−	9.58109e6i	−0.137773	−	0.781348i
$107$	1.35566e7			1.06981			0.534907	−	0.844911i	$-0.320347\pi$
$107$	1.35566e7			1.06981			0.534907	+	0.844911i	$0.320347\pi$
$108$	−4.97168e6	−	4.25770e6i	−0.379769	−	0.325231i
$109$	1.83424e7			1.35664			0.678319	−	0.734767i	$-0.262709\pi$
$109$	1.83424e7			1.35664			0.678319	+	0.734767i	$0.262709\pi$
$110$	3.92248e6	+	2.22455e7i	0.280987	+	1.59356i
$111$	2.30303e7	+	8.46991e6i	1.59834	+	0.587825i
$112$	−1.67088e6	+	608150.i	−0.112378	+	0.0409023i
$113$	−1.41282e7	−	1.18550e7i	−0.921112	−	0.772905i	0.0530883	−	0.998590i	$-0.483094\pi$
$113$	−1.41282e7	−	1.18550e7i	−0.921112	−	0.772905i	−0.974200	+	0.225685i	$0.927538\pi$
$114$	1.16911e7	+	9.87697e6i	0.739073	+	0.624391i
$115$	−4.09159e7	−	1.48922e7i	−2.50871	−	0.913094i
$116$	−74109.6	−	128362.i	−0.00440830	−	0.00763541i
$117$	784400.	+	4.62993e6i	0.0452780	+	0.267254i
$118$	2.99558e6	−	5.18850e6i	0.167840	−	0.290707i
$119$	29085.6	−	24405.7i	0.00158221	−	0.00132763i
$120$	−1.26932e7	−	42568.3i	−0.670560	−	0.00224880i
$121$	1.54227e6	−	8.74666e6i	0.0791429	−	0.448842i
$122$	−4.49300e6	+	2.54811e7i	−0.224015	+	1.27045i
$123$	−732947.	−	2458.03i	−0.0355144	−	0.000119102i
$124$	−3.53395e6	+	2.96534e6i	−0.166450	+	0.139668i
$125$	3.30759e7	−	5.72891e7i	1.51470	−	2.62354i
$126$	−1.26869e6	−	7.48847e6i	−0.0565014	−	0.333500i
$127$	567222.	+	982458.i	0.0245720	+	0.0425599i	0.878050	−	0.478569i	$-0.158844\pi$
$127$	567222.	+	982458.i	0.0245720	+	0.0425599i	−0.853478	+	0.521129i	$0.825511\pi$
$128$	1.97068e6	+	717268.i	0.0830579	+	0.0302306i
$129$	−6.93779e6	−	5.86126e6i	−0.284549	−	0.240396i
$130$	6.97581e6	+	5.85340e6i	0.278479	+	0.233672i
$131$	1.73426e7	−	6.31220e6i	0.674009	−	0.245319i	0.0177358	−	0.999843i	$-0.494354\pi$
$131$	1.73426e7	−	6.31220e6i	0.674009	−	0.245319i	0.656273	+	0.754524i	$0.272132\pi$
$132$	1.49616e7	+	5.50246e6i	0.566199	+	0.208232i
$133$	3.08377e6	+	1.74889e7i	0.113658	+	0.644588i
$134$	−2.91310e7			−1.04590
$135$	9.95178e6	−	5.32981e7i	0.348123	−	1.86442i
$136$	−44781.1			−0.00152654
$137$	−6.84553e6	−	3.88230e7i	−0.227450	−	1.28993i	−0.857946	−	0.513739i	$-0.828260\pi$
$137$	−6.84553e6	−	3.88230e7i	−0.227450	−	1.28993i	0.630497	−	0.776192i	$-0.282851\pi$
$138$	−2.36055e7	+	1.96728e7i	−0.764603	+	0.637220i
$139$	1.23210e7	−	4.48447e6i	0.389129	−	0.141631i	−0.140044	−	0.990145i	$-0.544725\pi$
$139$	1.23210e7	−	4.48447e6i	0.389129	−	0.141631i	0.529173	+	0.848514i	$0.322502\pi$
$140$	−1.12827e7	−	9.46732e6i	−0.347508	−	0.291594i
$141$	−8.79492e6	+	4.89186e7i	−0.264220	+	1.46963i
$142$	2.37512e7	+	8.64472e6i	0.696107	+	0.253362i
$143$	−5.71822e6	−	9.90425e6i	−0.163525	−	0.283234i
$144$	−4.53091e6	+	7.72760e6i	−0.126449	+	0.215663i
$145$	613867.	−	1.06325e6i	0.0167219	−	0.0289632i
$146$	−2.26136e6	+	1.89751e6i	−0.0601361	+	0.0504602i
$147$	−1.49363e7	+	2.56713e7i	−0.387823	+	0.666556i
$148$	5.83139e6	−	3.30714e7i	0.147862	−	0.838566i
$149$	−4.32241e6	+	2.45136e7i	−0.107047	+	0.607093i	0.883336	+	0.468740i	$0.155292\pi$
$149$	−4.32241e6	+	2.45136e7i	−0.107047	+	0.607093i	−0.990383	+	0.138353i	$0.955819\pi$
$150$	−3.77359e7	−	6.58697e7i	−0.912926	−	1.59355i
$151$	−3.61069e7	+	3.02973e7i	−0.853436	+	0.716118i	−0.960544	−	0.278129i	$-0.910286\pi$
$151$	−3.61069e7	+	3.02973e7i	−0.853436	+	0.716118i	0.107107	+	0.994247i	$0.465841\pi$
$152$	1.04725e7	−	1.81390e7i	0.241880	−	0.418948i
$153$	34478.4	−	188149.i	0.000778265	−	0.00424699i
$154$	9.24868e6	+	1.60192e7i	0.204060	+	0.353442i
$155$	−3.59081e7	−	1.30695e7i	−0.774518	−	0.281901i
$156$	6.04628e6	−	2.17773e6i	0.127512	−	0.0459270i
$157$	5.32003e6	+	4.46404e6i	0.109715	+	0.0920617i	0.695995	−	0.718047i	$-0.254964\pi$
$157$	5.32003e6	+	4.46404e6i	0.109715	+	0.0920617i	−0.586280	+	0.810109i	$0.699408\pi$
$158$	2.11963e7	−	7.71482e6i	0.427524	−	0.155606i
$159$	−9.68782e6	−	5.60407e7i	−0.191133	−	1.10564i
$160$	3.01648e6	+	1.71073e7i	0.0582211	+	0.330188i
$161$	−3.56554e7			−0.673341
$162$	−2.89792e7	−	2.49864e7i	−0.535530	−	0.461745i
$163$	−7.48752e7			−1.35420			−0.677098	−	0.735893i	$-0.736763\pi$
$163$	−7.48752e7			−1.35420			−0.677098	+	0.735893i	$0.736763\pi$
$164$	174181.	+	987830.i	0.00308352	+	0.0174875i
$165$	2.24933e7	+	1.30116e8i	0.389815	+	2.25495i
$166$	4.47714e7	−	1.62954e7i	0.759665	−	0.276495i
$167$	−6.28395e7	−	5.27286e7i	−1.04406	−	0.876070i	−0.0516033	−	0.998668i	$-0.516433\pi$
$167$	−6.28395e7	−	5.27286e7i	−1.04406	−	0.876070i	−0.992456	+	0.122597i	$0.960878\pi$
$168$	−9.77928e6	+	3.52227e6i	−0.159120	+	0.0573113i
$169$	5.46319e7	+	1.98844e7i	0.870649	+	0.316890i
$170$	−185466.	−	321237.i	−0.00289530	−	0.00501480i
$171$	6.81481e7	+	5.79664e7i	1.04224	+	0.886523i
$172$	−6.21469e6	+	1.07642e7i	−0.0931257	+	0.161298i
$173$	2.92264e6	−	2.45239e6i	0.0429155	−	0.0360104i	−0.621078	−	0.783749i	$-0.713305\pi$
$173$	2.92264e6	−	2.45239e6i	0.0429155	−	0.0360104i	0.663993	+	0.747739i	$0.268860\pi$
$174$	−430702.	−	751808.i	−0.00619804	−	0.0108189i
$175$	1.52958e7	−	8.67469e7i	0.215744	−	1.22355i
$176$	3.78835e6	−	2.14848e7i	0.0523789	−	0.297055i
$177$	1.76128e7	−	3.02714e7i	0.238738	−	0.410323i
$178$	−2.95054e7	+	2.47580e7i	−0.392131	+	0.329037i
$179$	1.45913e6	−	2.52728e6i	0.0190155	−	0.0329358i	−0.856361	−	0.516378i	$-0.827280\pi$
$179$	1.45913e6	−	2.52728e6i	0.0190155	−	0.0329358i	0.875377	+	0.483442i	$0.160613\pi$
$180$	−7.41992e7	−	497677.i	−0.948299	−	0.00636054i
$181$	3.19475e7	+	5.53347e7i	0.400462	+	0.693621i	0.993782	−	0.111346i	$-0.0355162\pi$
$181$	3.19475e7	+	5.53347e7i	0.400462	+	0.693621i	−0.593319	+	0.804967i	$0.702183\pi$
$182$	7.00722e6	+	2.55042e6i	0.0861581	+	0.0313590i
$183$	−2.67640e7	+	1.48865e8i	−0.322829	+	1.79562i
$184$	3.22144e7	+	2.70311e7i	0.381231	+	0.319891i
$185$	2.61389e8	−	9.51379e7i	3.03519	−	1.10472i
$186$	−2.07163e7	+	1.72650e7i	−0.236057	+	0.196730i
$187$	80893.7	+	458771.i	0.000904626	+	0.00513039i
$188$	6.80201e7			0.746594
$189$	−7.26951e6	−	4.37998e7i	−0.0783229	−	0.471906i
$190$	1.73493e8			1.83504
$191$	1.80588e7	+	1.02417e8i	0.187531	+	1.06354i	0.922661	+	0.385613i	$0.126010\pi$
$191$	1.80588e7	+	1.02417e8i	0.187531	+	1.06354i	−0.735130	+	0.677926i	$0.762879\pi$
$192$	1.15058e7	+	4.23152e6i	0.117318	+	0.0431462i
$193$	4.82942e6	−	1.75777e6i	0.0483553	−	0.0175999i	−0.317729	−	0.948181i	$-0.602920\pi$
$193$	4.82942e6	−	1.75777e6i	0.0483553	−	0.0175999i	0.366085	+	0.930582i	$0.380698\pi$
$194$	6.42941e7	+	5.39492e7i	0.632215	+	0.530492i
$195$	4.06633e7	+	3.43536e7i	0.392719	+	0.331781i
$196$	3.81946e7	+	1.39017e7i	0.362331	+	0.131878i
$197$	−4.00797e7	−	6.94201e7i	−0.373502	−	0.646924i	0.616600	−	0.787277i	$-0.288510\pi$
$197$	−4.00797e7	−	6.94201e7i	−0.373502	−	0.646924i	−0.990102	+	0.140353i	$0.955176\pi$
$198$	8.73521e7	+	3.24587e7i	0.799734	+	0.297169i
$199$	−5.91462e7	+	1.02444e8i	−0.532036	+	0.921514i	0.467264	+	0.884118i	$0.345240\pi$
$199$	−5.91462e7	+	1.02444e8i	−0.532036	+	0.921514i	−0.999301	+	0.0373960i	$0.988094\pi$
$200$	−7.95842e7	+	6.67791e7i	−0.703432	+	0.590249i
$201$	−1.70289e8	−	571085.i	−1.47911	−	0.00496038i
$202$	1.79781e7	−	1.01959e8i	0.153467	−	0.870354i
$203$	174580.	−	990092.i	0.00146473	−	0.00830691i
$204$	−261774.	−	877.890i	−0.00215884	−	7.23993e-6i
$205$	−6.36480e6	+	5.34070e6i	−0.0515996	+	0.0432972i
$206$	−1.37095e6	+	2.37455e6i	−0.0109266	+	0.0189255i
$207$	−1.38375e8	+	1.14537e8i	−1.08433	+	0.897534i
$208$	−4.39745e6	−	7.61660e6i	−0.0338828	−	0.0586867i
$209$	−2.04747e8	−	7.45219e7i	−1.55134	−	0.564641i
$210$	−6.57690e7	−	5.55637e7i	−0.490065	−	0.414022i
$211$	1.40153e8	+	1.17602e8i	1.02710	+	0.861841i	0.990503	−	0.137489i	$-0.0439033\pi$
$211$	1.40153e8	+	1.17602e8i	1.02710	+	0.861841i	0.0365985	+	0.999330i	$0.488348\pi$
$212$	−7.31373e7	+	2.66198e7i	−0.527186	+	0.191880i
$213$	1.38671e8	+	5.09995e7i	0.983236	+	0.361607i
$214$	−1.88327e7	−	1.06805e8i	−0.131360	−	0.744981i
$215$	−1.02955e8			−0.706504
$216$	−2.66375e7	+	4.50839e7i	−0.179848	+	0.304392i
$217$	−3.12915e7			−0.207882
$218$	−2.54810e7	−	1.44510e8i	−0.166579	−	0.944715i
$219$	−1.32563e7	+	1.10478e7i	−0.0852841	+	0.0710758i
$220$	1.69811e8	−	6.18062e7i	1.07519	−	0.391338i
$221$	143863.	+	120715.i	0.000896553	+	0.000752298i
$222$	3.47365e7	−	1.93209e8i	0.213084	−	1.18520i
$223$	−1.48807e8	−	5.41614e7i	−0.898581	−	0.327057i	−0.148897	−	0.988853i	$-0.547572\pi$
$223$	−1.48807e8	−	5.41614e7i	−0.898581	−	0.327057i	−0.749684	+	0.661796i	$0.769794\pi$
$224$	7.11245e6	+	1.23191e7i	0.0422816	+	0.0732339i
$225$	−2.19299e8	−	3.85790e8i	−1.28351	−	2.25794i
$226$	−7.37722e7	+	1.27777e8i	−0.425122	+	0.736333i
$227$	−1.52239e8	+	1.27744e8i	−0.863844	+	0.724852i	−0.962793	−	0.270241i	$-0.912897\pi$
$227$	−1.52239e8	+	1.27744e8i	−0.863844	+	0.724852i	0.0989483	+	0.995093i	$0.468452\pi$
$228$	6.15743e7	−	1.05829e8i	0.344055	−	0.591332i
$229$	1.33624e6	−	7.57820e6i	0.00735293	−	0.0417005i	−0.980911	−	0.194460i	$-0.937705\pi$
$229$	1.33624e6	−	7.57820e6i	0.00735293	−	0.0417005i	0.988263	+	0.152759i	$0.0488158\pi$
$230$	−6.04876e7	+	3.43042e8i	−0.327808	+	1.85909i
$231$	5.37504e7	+	9.38236e7i	0.286906	+	0.500807i
$232$	−908340.	+	762188.i	−0.00477574	+	0.00400732i
$233$	1.60660e8	−	2.78272e8i	0.832077	−	1.44120i	−0.0643120	−	0.997930i	$-0.520485\pi$
$233$	1.60660e8	−	2.78272e8i	0.832077	−	1.44120i	0.896389	−	0.443269i	$-0.146181\pi$
$234$	3.53871e7	−	1.26117e7i	0.180546	−	0.0643455i
$235$	2.81713e8	+	4.87942e8i	1.41602	+	2.45262i
$236$	−4.50388e7	−	1.63928e7i	−0.223046	−	0.0811822i
$237$	1.24057e8	−	4.46825e7i	0.605344	−	0.218031i
$238$	−232685.	−	195246.i	−0.00111879	−	0.000938776i
$239$	1.01121e8	−	3.68050e7i	0.479125	−	0.174387i	−0.0911565	−	0.995837i	$-0.529056\pi$
$239$	1.01121e8	−	3.68050e7i	0.479125	−	0.174387i	0.570281	+	0.821449i	$0.306834\pi$
$240$	1.72979e7	+	1.00062e8i	0.0807706	+	0.467230i
$241$	−1.09168e7	−	6.19125e7i	−0.0502386	−	0.284917i	0.949330	−	0.314280i	$-0.101763\pi$
$241$	−1.09168e7	−	6.19125e7i	−0.0502386	−	0.284917i	−0.999569	+	0.0293632i	$0.990652\pi$
$242$	−7.10527e7			−0.322275
$243$	−1.68912e8	−	1.46630e8i	−0.755159	−	0.655542i
$244$	2.06993e8			0.912204
$245$	5.84638e7	+	3.31564e8i	0.253983	+	1.44041i
$246$	998834.	+	5.77791e6i	0.00427780	+	0.0247456i
$247$	−8.25408e7	+	3.00424e7i	−0.348521	+	0.126851i
$248$	2.82716e7	+	2.37227e7i	0.117698	+	0.0987605i
$249$	2.62037e8	−	9.43796e7i	1.07563	−	0.387419i
$250$	−4.97299e8	−	1.81002e8i	−2.01292	−	0.732644i
$251$	−2.42029e8	−	4.19206e8i	−0.966070	−	1.67328i	−0.706711	−	0.707502i	$-0.749822\pi$
$251$	−2.42029e8	−	4.19206e8i	−0.966070	−	1.67328i	−0.259359	−	0.965781i	$-0.583511\pi$
$252$	−5.72352e7	+	2.03982e7i	−0.225300	+	0.0802953i
$253$	2.18734e8	−	3.78859e8i	0.849170	−	1.47081i
$254$	6.95228e6	−	5.83366e6i	0.0266201	−	0.0223369i
$255$	−1.07787e6	−	1.88147e6i	−0.00407076	−	0.00710569i
$256$	2.91333e6	−	1.65223e7i	0.0108530	−	0.0615505i
$257$	4.55027e7	−	2.58059e8i	0.167214	−	0.948315i	−0.779539	−	0.626353i	$-0.784547\pi$
$257$	4.55027e7	−	2.58059e8i	0.167214	−	0.948315i	0.946753	−	0.321962i	$-0.104342\pi$
$258$	−3.65398e7	+	6.28015e7i	−0.132464	+	0.227668i
$259$	1.74492e8	−	1.46416e8i	0.624060	−	0.523648i
$260$	3.64251e7	−	6.30901e7i	0.128527	−	0.222615i
$261$	−2.50299e6	−	4.40324e6i	−0.00871399	−	0.0153296i
$262$	−7.38226e7	−	1.27864e8i	−0.253591	−	0.439233i
$263$	2.19718e8	+	7.99710e7i	0.744769	+	0.271074i	0.686403	−	0.727222i	$-0.259189\pi$
$263$	2.19718e8	+	7.99710e7i	0.744769	+	0.271074i	0.0583659	+	0.998295i	$0.481411\pi$
$264$	2.25665e7	−	1.25518e8i	0.0754833	−	0.419849i
$265$	−4.93864e8	−	4.14401e8i	−1.63022	−	1.36792i
$266$	1.33502e8	−	4.85907e7i	0.434912	−	0.158295i
$267$	−1.72963e8	+	1.44148e8i	−0.556115	+	0.463466i
$268$	4.04683e7	+	2.29507e8i	0.128423	+	0.728324i
$269$	−6.79945e7			−0.212981			−0.106490	−	0.994314i	$-0.533961\pi$
$269$	−6.79945e7			−0.212981			−0.106490	+	0.994314i	$0.533961\pi$
$270$	−4.33732e8	−	4.36385e6i	−1.34106	−	0.0134926i
$271$	−3.39199e8			−1.03529			−0.517646	−	0.855595i	$-0.673191\pi$
$271$	−3.39199e8			−1.03529			−0.517646	+	0.855595i	$0.673191\pi$
$272$	62209.2	+	352806.i	0.000187440	+	0.00106303i
$273$	4.09117e7	+	1.50462e7i	0.121697	+	0.0447567i
$274$	−2.96355e8	+	1.07865e8i	−0.870334	+	0.316776i
$275$	8.27898e8	+	6.94689e8i	2.40056	+	2.01431i
$276$	1.87784e8	+	1.58646e8i	0.537621	+	0.454199i
$277$	−6.32121e8	−	2.30073e8i	−1.78698	−	0.650409i	−0.999416	−	0.0341827i	$-0.989117\pi$
$277$	−6.32121e8	−	2.30073e8i	−1.78698	−	0.650409i	−0.787569	−	0.616227i	$-0.788661\pi$
$278$	−5.24468e7	−	9.08405e7i	−0.146407	−	0.253585i
$279$	−1.21439e8	+	1.00519e8i	−0.334767	+	0.277098i
$280$	−5.89141e7	+	1.02042e8i	−0.160386	+	0.277797i
$281$	−8.79139e7	+	7.37685e7i	−0.236366	+	0.198335i	−0.753275	−	0.657706i	$-0.771527\pi$
$281$	−8.79139e7	+	7.37685e7i	−0.236366	+	0.198335i	0.516909	+	0.856040i	$0.327083\pi$
$282$	3.97621e8	+	1.33347e6i	1.05584	+	0.00354088i
$283$	6.40139e7	−	3.63041e8i	0.167889	−	0.952145i	−0.778147	−	0.628083i	$-0.783840\pi$
$283$	6.40139e7	−	3.63041e8i	0.167889	−	0.952145i	0.946036	−	0.324063i	$-0.105049\pi$
$284$	3.51123e7	−	1.99132e8i	0.0909589	−	0.515853i
$285$	1.01418e9	+	3.40117e6i	2.59512	+	0.00870304i
$286$	−7.00866e7	+	5.88096e7i	−0.177155	+	0.148651i
$287$	−3.40189e6	+	5.89224e6i	−0.00849441	+	0.0147128i
$288$	6.71759e7	+	2.49615e7i	0.165706	+	0.0615740i
$289$	2.05166e8	+	3.55357e8i	0.499991	+	0.866009i
$290$	−9.22955e6	−	3.35928e6i	−0.0222222	−	0.00808822i
$291$	3.74782e8	+	3.16628e8i	0.891567	+	0.753223i
$292$	1.80909e7	+	1.51801e7i	0.0425226	+	0.0356807i
$293$	−6.47598e8	+	2.35707e8i	−1.50407	+	0.547438i	−0.957112	−	0.289720i	$-0.906438\pi$
$293$	−6.47598e8	+	2.35707e8i	−1.50407	+	0.547438i	−0.546962	+	0.837158i	$0.684216\pi$
$294$	2.22999e8	+	8.20131e7i	0.511786	+	0.188221i
$295$	−6.89401e7	−	3.90978e8i	−0.156349	−	0.886698i
$296$	−2.68653e8			−0.602103
$297$	5.09993e8	+	1.91454e8i	1.12958	+	0.424051i
$298$	1.99134e8			0.435902
$299$	−3.06244e7	−	1.73679e8i	−0.0662549	−	0.375750i
$300$	−4.66530e8	+	3.88806e8i	−0.997596	+	0.831397i
$301$	−7.92236e7	+	2.88350e7i	−0.167445	+	0.0609449i
$302$	2.88855e8	+	2.42378e8i	0.603470	+	0.506372i
$303$	1.07092e8	−	5.95663e8i	0.221162	−	1.23013i
$304$	−1.57456e8	−	5.73091e7i	−0.321440	−	0.116995i
$305$	8.57287e8	+	1.48486e9i	1.73012	+	2.99666i
$306$	−1.53022e6	−	10263.7i	−0.00305301	−	2.04775e-5i
$307$	−2.78626e8	+	4.82595e8i	−0.549589	+	0.951916i	0.448714	+	0.893676i	$0.351882\pi$
$307$	−2.78626e8	+	4.82595e8i	−0.549589	+	0.951916i	−0.998303	+	0.0582403i	$0.981451\pi$
$308$	1.13358e8	−	9.51190e7i	0.221068	−	0.185498i
$309$	−8.06063e6	+	1.38539e7i	−0.0155423	+	0.0267127i
$310$	−5.30844e7	+	3.01057e8i	−0.101205	+	0.573961i
$311$	6.67729e7	−	3.78688e8i	0.125875	−	0.713872i	−0.854910	−	0.518777i	$-0.826387\pi$
$311$	6.67729e7	−	3.78688e8i	0.125875	−	0.713872i	0.980784	−	0.195095i	$-0.0625014\pi$
$312$	−2.55566e7	−	4.46101e7i	−0.0476389	−	0.0831558i
$313$	−1.75486e8	+	1.47250e8i	−0.323473	+	0.271426i	−0.790034	−	0.613063i	$-0.789937\pi$
$313$	−1.75486e8	+	1.47250e8i	−0.323473	+	0.271426i	0.466561	+	0.884489i	$0.345493\pi$
$314$	2.77792e7	−	4.81151e7i	0.0506368	−	0.0877056i
$315$	−3.83373e8	−	3.26095e8i	−0.691090	−	0.587837i
$316$	−9.02265e7	−	1.56277e8i	−0.160853	−	0.278606i
$317$	−7.31781e8	−	2.66346e8i	−1.29025	−	0.469612i	−0.396440	−	0.918061i	$-0.629755\pi$
$317$	−7.31781e8	−	2.66346e8i	−1.29025	−	0.469612i	−0.893809	+	0.448448i	$0.851977\pi$
$318$	−4.28056e8	+	1.54176e8i	−0.746459	+	0.268857i
$319$	9.44928e6	+	7.92889e6i	0.0162979	+	0.0136756i
$320$	1.30589e8	−	4.75304e7i	0.222782	−	0.0810862i
$321$	−1.07995e8	−	6.24715e8i	−0.182237	−	1.05418i
$322$	4.95320e7	+	2.80910e8i	0.0826781	+	0.468891i
$323$	3.57797e6			0.00590783
$324$	−1.56597e8	+	2.63022e8i	−0.255786	+	0.429620i
$325$	4.35686e8			0.704015
$326$	1.04016e8	+	5.89902e8i	0.166279	+	0.943014i
$327$	−1.46120e8	−	8.45254e8i	−0.231096	−	1.33681i
$328$	7.54061e6	−	2.74456e6i	0.0117991	−	0.00429451i
$329$	3.53436e8	+	2.96568e8i	0.547173	+	0.459133i
$330$	9.93866e8	−	3.57968e8i	1.52240	−	0.548334i
$331$	4.75014e8	+	1.72891e8i	0.719960	+	0.262044i	0.675909	−	0.736985i	$-0.263751\pi$
$331$	4.75014e8	+	1.72891e8i	0.719960	+	0.262044i	0.0440512	+	0.999029i	$0.485974\pi$
$332$	−1.90579e8	−	3.30092e8i	−0.285819	−	0.495053i
$333$	2.06845e8	−	1.12875e9i	0.306966	−	1.67511i
$334$	−3.28125e8	+	5.68329e8i	−0.481866	+	0.834617i
$335$	−1.47876e9	+	1.24083e9i	−2.14903	+	1.80325i
$336$	4.13353e7	+	7.21526e7i	0.0594475	+	0.103768i
$337$	1.81701e8	−	1.03048e9i	0.258615	−	1.46668i	−0.528005	−	0.849241i	$-0.677060\pi$
$337$	1.81701e8	−	1.03048e9i	0.258615	−	1.46668i	0.786620	−	0.617437i	$-0.211829\pi$
$338$	8.07646e7	−	4.58039e8i	0.113766	−	0.645199i
$339$	−4.33751e8	+	7.45494e8i	−0.604702	+	1.03931i
$340$	−2.27320e6	+	1.90744e6i	−0.00313662	+	0.00263194i
$341$	1.91963e8	−	3.32489e8i	0.262166	−	0.454085i
$342$	3.62016e8	−	6.17429e8i	0.489369	−	0.834633i
$343$	3.16604e8	+	5.48374e8i	0.423630	+	0.733748i
$344$	9.34383e7	+	3.40088e7i	0.123757	+	0.0450439i
$345$	−3.60314e8	+	2.00412e9i	−0.472405	+	2.62758i
$346$	−2.33811e7	−	1.96191e7i	−0.0303458	−	0.0254632i
$347$	4.17940e8	−	1.52118e8i	0.536984	−	0.195446i	−0.0592703	−	0.998242i	$-0.518877\pi$
$347$	4.17940e8	−	1.52118e8i	0.536984	−	0.195446i	0.596254	+	0.802796i	$0.296655\pi$
$348$	−5.32477e6	+	4.43767e6i	−0.00677288	+	0.00564452i
$349$	1.07989e8	+	6.12438e8i	0.135985	+	0.771211i	0.974169	+	0.225822i	$0.0725069\pi$
$349$	1.07989e8	+	6.12438e8i	0.135985	+	0.771211i	−0.838183	+	0.545389i	$0.816382\pi$
$350$	−7.04681e8			−0.878525
$351$	2.07107e8	−	7.30297e7i	0.255635	−	0.0901415i
$352$	−1.74530e8			−0.213290
$353$	−1.42778e8	−	8.09737e8i	−0.172763	−	0.979789i	−0.940694	−	0.339256i	$-0.889825\pi$
$353$	−1.42778e8	−	8.09737e8i	−0.172763	−	0.979789i	0.767931	−	0.640533i	$-0.221286\pi$
$354$	−2.62959e8	−	9.67093e7i	−0.315048	−	0.115866i
$355$	1.57389e9	−	5.72850e8i	1.86713	−	0.679582i
$356$	2.36043e8	+	1.98064e8i	0.277279	+	0.232664i
$357$	−1.35636e6	−	1.14590e6i	−0.00157775	−	0.00133293i
$358$	−2.19381e7	−	7.98482e6i	−0.0252702	−	0.00919760i
$359$	2.54526e8	+	4.40851e8i	0.290336	+	0.502877i	0.973889	−	0.227024i	$-0.0728996\pi$
$359$	2.54526e8	+	4.40851e8i	0.290336	+	0.502877i	−0.683553	+	0.729901i	$0.739566\pi$
$360$	9.91555e7	+	5.85267e8i	0.112010	+	0.661142i
$361$	−3.89811e8	+	6.75173e8i	−0.436093	+	0.755336i
$362$	3.91571e8	−	3.28567e8i	0.433841	−	0.364036i
$363$	−4.15349e8	−	1.39292e6i	−0.455763	−	0.00152846i
$364$	1.03591e7	−	5.87492e7i	0.0112581	−	0.0638479i
$365$	−3.39685e7	+	1.92645e8i	−0.0365638	+	0.207364i
$366$	1.21001e9	+	4.05791e6i	1.29004	+	0.00432632i
$367$	1.88414e7	−	1.58098e7i	0.0198968	−	0.0166954i	−0.632785	−	0.774328i	$-0.718088\pi$
$367$	1.88414e7	−	1.58098e7i	0.0198968	−	0.0166954i	0.652682	+	0.757632i	$0.273644\pi$
$368$	1.68212e8	−	2.91351e8i	0.175950	−	0.304754i
$369$	5.72555e6	+	3.37952e7i	0.00593233	+	0.0350156i
$370$	−1.11266e9	−	1.92718e9i	−1.14197	−	1.97795i
$371$	−4.96088e8	−	1.80561e8i	−0.504371	−	0.183576i
$372$	1.64801e8	+	1.39229e8i	0.165981	+	0.140226i
$373$	−8.47439e8	−	7.11086e8i	−0.845527	−	0.709482i	0.113273	−	0.993564i	$-0.463867\pi$
$373$	−8.47439e8	−	7.11086e8i	−0.845527	−	0.709482i	−0.958800	+	0.284082i	$0.908311\pi$
$374$	3.50203e6	−	1.27464e6i	0.00346154	−	0.00125990i
$375$	−2.90348e9	−	1.06782e9i	−2.84321	−	1.04566i
$376$	−9.44925e7	−	5.35894e8i	−0.0916727	−	0.519902i
$377$	4.97274e6			0.00477970
$378$	−3.34976e8	+	1.18119e8i	−0.319001	+	0.112486i
$379$	−4.20959e8			−0.397194			−0.198597	−	0.980081i	$-0.563638\pi$
$379$	−4.20959e8			−0.397194			−0.198597	+	0.980081i	$0.563638\pi$
$380$	−2.41014e8	−	1.36686e9i	−0.225320	−	1.27785i
$381$	4.07549e7	−	3.39652e7i	0.0377522	−	0.0314627i
$382$	7.81798e8	−	2.84551e8i	0.717584	−	0.261179i
$383$	−9.70448e7	−	8.14302e7i	−0.0882625	−	0.0740611i	0.597589	−	0.801803i	$-0.296126\pi$
$383$	−9.70448e7	−	8.14302e7i	−0.0882625	−	0.0740611i	−0.685851	+	0.727742i	$0.740570\pi$
$384$	1.73542e7	−	9.65265e7i	0.0156403	−	0.0869936i
$385$	1.15182e9	+	4.19229e8i	1.02866	+	0.374403i
$386$	−2.05575e7	−	3.56066e7i	−0.0181934	−	0.0315119i
$387$	−2.14830e8	+	3.66399e8i	−0.188411	+	0.321341i
$388$	3.35720e8	−	5.81484e8i	0.291787	−	0.505390i
$389$	1.11992e9	−	9.39723e8i	0.964634	−	0.809424i	−0.0170664	−	0.999854i	$-0.505433\pi$
$389$	1.11992e9	−	9.39723e8i	0.964634	−	0.809424i	0.981701	+	0.190430i	$0.0609882\pi$
$390$	2.14165e8	−	3.68088e8i	0.182819	−	0.314214i
$391$	−1.24744e6	+	7.07460e6i	−0.00105536	+	0.00598527i
$392$	5.64647e7	−	3.20227e8i	0.0473451	−	0.268508i
$393$	−4.29033e8	−	7.48897e8i	−0.356547	−	0.622369i
$394$	−4.91245e8	+	4.12204e8i	−0.404633	+	0.339528i
$395$	7.47367e8	−	1.29448e9i	0.610161	−	1.05683i
$396$	1.34376e8	−	7.33292e8i	0.108740	−	0.593395i
$397$	7.70508e8	+	1.33456e9i	0.618031	+	1.07046i	0.989845	+	0.142154i	$0.0454028\pi$
$397$	7.70508e8	+	1.33456e9i	0.618031	+	1.07046i	−0.371813	+	0.928308i	$0.621264\pi$
$398$	8.89268e8	+	3.23667e8i	0.707037	+	0.257340i
$399$	7.81356e8	−	2.81427e8i	0.615806	−	0.221799i
$400$	6.36674e8	+	5.34233e8i	0.497401	+	0.417369i
$401$	−1.41971e9	+	5.16732e8i	−1.09950	+	0.400184i	−0.827131	−	0.562009i	$-0.810028\pi$
$401$	−1.41971e9	+	5.16732e8i	−1.09950	+	0.400184i	−0.272366	+	0.962194i	$0.587806\pi$
$402$	2.32064e8	+	1.34241e9i	0.178163	+	1.03061i
$403$	−2.68762e7	−	1.52422e8i	−0.0204550	−	0.116006i
$404$	−8.28255e8			−0.624927
$405$	−2.53535e9	−	3.40124e7i	−1.89647	−	0.0254416i
$406$	−8.04292e6			−0.00596448
$407$	4.85302e8	+	2.75229e9i	0.356806	+	2.02355i
$408$	356736.	+	2.06359e6i	0.000260038	+	0.00150423i
$409$	−5.65786e8	+	2.05929e8i	−0.408903	+	0.148829i	−0.538278	−	0.842767i	$-0.680925\pi$
$409$	−5.65786e8	+	2.05929e8i	−0.408903	+	0.148829i	0.129375	+	0.991596i	$0.458703\pi$
$410$	5.09184e7	+	4.27256e7i	0.0364864	+	0.0306157i
$411$	−1.73450e9	+	6.24728e8i	−1.23233	+	0.443858i
$412$	2.06123e7	+	7.50228e6i	0.0145207	+	0.00528510i
$413$	−1.62551e8	−	2.81547e8i	−0.113544	−	0.196665i
$414$	1.09461e9	+	9.31066e8i	0.758153	+	0.644881i
$415$	1.57861e9	−	2.73423e9i	1.08419	−	1.87788i
$416$	−5.38983e7	+	4.52260e7i	−0.0367069	+	0.0308008i
$417$	−3.04804e8	−	5.32049e8i	−0.205847	−	0.359315i
$418$	−3.02686e8	+	1.71662e9i	−0.202710	+	1.14963i
$419$	1.26231e8	−	7.15890e8i	0.0838332	−	0.475442i	−0.913769	−	0.406234i	$-0.866842\pi$
$419$	1.26231e8	−	7.15890e8i	0.0838332	−	0.475442i	0.997602	−	0.0692076i	$-0.0220471\pi$
$420$	−3.46391e8	+	5.95347e8i	−0.228136	+	0.392101i
$421$	4.07233e8	−	3.41709e8i	0.265984	−	0.223187i	−0.500035	−	0.866005i	$-0.666679\pi$
$421$	4.07233e8	−	3.41709e8i	0.265984	−	0.223187i	0.766019	+	0.642818i	$0.222235\pi$
$422$	7.31826e8	−	1.26756e9i	0.474039	−	0.821060i
$423$	2.32432e9	+	1.55900e7i	1.49316	+	0.0100151i
$424$	3.11325e8	+	5.39230e8i	0.198350	+	0.343553i
$425$	−1.66768e7	−	6.06986e6i	−0.0105378	−	0.00383546i
$426$	2.09158e8	−	1.16336e9i	0.131081	−	0.729092i
$427$	1.07555e9	+	9.02492e8i	0.668547	+	0.560978i
$428$	−8.15300e8	+	2.96745e8i	−0.502648	+	0.182949i
$429$	−4.10854e8	+	3.42406e8i	−0.251239	+	0.209383i
$430$	1.43024e8	+	8.11130e8i	0.0867501	+	0.491984i
$431$	−2.04700e9			−1.23154			−0.615768	−	0.787928i	$-0.711154\pi$
$431$	−2.04700e9			−1.23154			−0.615768	+	0.787928i	$0.711154\pi$
$432$	3.92196e8	+	1.47233e8i	0.234051	+	0.0878642i
$433$	1.08482e9			0.642167			0.321084	−	0.947051i	$-0.395953\pi$
$433$	1.08482e9			0.642167			0.321084	+	0.947051i	$0.395953\pi$
$434$	4.34697e7	+	2.46529e8i	0.0255254	+	0.144762i
$435$	−5.38867e7	−	1.98181e7i	−0.0313884	−	0.0115438i
$436$	−1.10312e9	+	4.01503e8i	−0.637412	+	0.231999i
$437$	−2.57390e9	−	2.15976e9i	−1.47539	−	1.23800i
$438$	1.05455e8	+	8.90918e7i	0.0599665	+	0.0506615i
$439$	−2.18519e9	−	7.95344e8i	−1.23272	−	0.448672i	−0.358190	−	0.933649i	$-0.616606\pi$
$439$	−2.18519e9	−	7.95344e8i	−1.23272	−	0.448672i	−0.874527	+	0.484976i	$0.838828\pi$
$440$	−7.22837e8	−	1.25199e9i	−0.404535	−	0.700675i
$441$	1.30197e9	+	4.83791e8i	0.722878	+	0.268610i
$442$	751199.	−	1.30112e6i	0.000413787	−	0.000716701i
$443$	−6.40864e8	+	5.37749e8i	−0.350230	+	0.293877i	−0.800882	−	0.598822i	$-0.795636\pi$
$443$	−6.40864e8	+	5.37749e8i	−0.350230	+	0.293877i	0.450653	+	0.892699i	$0.351191\pi$
$444$	−1.57045e9	−	5.26669e6i	−0.851497	−	0.00285560i
$445$	−4.43208e8	+	2.51356e9i	−0.238423	+	1.35216i
$446$	−2.19988e8	+	1.24761e9i	−0.117416	+	0.665898i
$447$	1.16407e9	+	3.90383e6i	0.616455	+	0.00206736i
$448$	8.71753e7	−	7.31487e7i	0.0458058	−	0.0384356i
$449$	1.11620e8	−	1.93331e8i	0.0581941	−	0.100795i	−0.835461	−	0.549550i	$-0.814799\pi$
$449$	1.11620e8	−	1.93331e8i	0.0581941	−	0.100795i	0.893655	+	0.448755i	$0.148132\pi$
$450$	−2.73479e9	+	2.26367e9i	−1.41475	+	1.17104i
$451$	−4.17389e7	−	7.22939e7i	−0.0214251	−	0.0371094i
$452$	1.10917e9	+	4.03706e8i	0.564956	+	0.205627i
$453$	1.68379e9	+	1.42252e9i	0.851030	+	0.718976i
$454$	1.21791e9	+	1.02195e9i	0.610830	+	0.512547i
$455$	4.64340e8	−	1.69006e8i	0.231098	−	0.0841128i
$456$	−9.19305e8	−	3.38095e8i	−0.454028	−	0.166979i
$457$	6.40331e8	+	3.63150e9i	0.313832	+	1.77983i	0.578693	+	0.815546i	$0.303563\pi$
$457$	6.40331e8	+	3.63150e9i	0.313832	+	1.77983i	−0.264860	+	0.964287i	$0.585326\pi$
$458$	−6.15608e7			−0.0299416
$459$	−8.94490e6	−	89996.1i	−0.00431749	−	4.34390e-5i
$460$	2.78667e9			1.33485
$461$	−1.43777e8	−	8.15403e8i	−0.0683499	−	0.387631i	−0.999722	−	0.0235636i	$-0.992499\pi$
$461$	−1.43777e8	−	8.15403e8i	−0.0683499	−	0.387631i	0.931372	−	0.364068i	$-0.118612\pi$
$462$	6.64517e8	−	5.53809e8i	0.313515	−	0.261284i
$463$	5.30500e8	−	1.93086e8i	0.248400	−	0.0904103i	−0.214819	−	0.976654i	$-0.568916\pi$
$463$	5.30500e8	−	1.93086e8i	0.248400	−	0.0904103i	0.463220	+	0.886243i	$0.346694\pi$
$464$	7.26672e6	+	6.09750e6i	0.00337696	+	0.00283360i
$465$	−3.16214e8	+	1.75883e9i	−0.145846	+	0.811218i
$466$	−2.41554e9	−	8.79186e8i	−1.10577	−	0.402467i
$467$	2.61297e8	+	4.52579e8i	0.118720	+	0.205629i	0.919261	−	0.393649i	$-0.128788\pi$
$467$	2.61297e8	+	4.52579e8i	0.118720	+	0.205629i	−0.800541	+	0.599279i	$0.795454\pi$
$468$	−1.48520e8	−	2.61276e8i	−0.0669768	−	0.117825i
$469$	−7.90377e8	+	1.36897e9i	−0.353777	+	0.612760i
$470$	3.45288e9	−	2.89731e9i	1.53405	−	1.28722i
$471$	1.63331e8	−	2.80719e8i	0.0720269	−	0.123794i
$472$	−6.65827e7	+	3.77609e8i	−0.0291450	+	0.165290i
$473$	1.79622e8	−	1.01869e9i	0.0780451	−	0.442616i
$474$	−5.24368e8	−	9.15307e8i	−0.226158	−	0.394769i
$475$	6.35871e9	−	5.33559e9i	2.72233	−	2.28431i
$476$	−1.21499e6	+	2.10443e6i	−0.000516356	+	0.000894355i
$477$	−2.50528e9	+	8.92866e8i	−1.05692	+	0.376679i
$478$	−4.30443e8	−	7.45549e8i	−0.180268	−	0.312233i
$479$	4.13091e9	+	1.50353e9i	1.71740	+	0.625083i	0.997609	−	0.0691072i	$-0.0220150\pi$
$479$	4.13091e9	+	1.50353e9i	1.71740	+	0.625083i	0.719792	+	0.694190i	$0.244237\pi$
$480$	7.64306e8	−	2.75286e8i	0.315445	−	0.113616i
$481$	8.63071e8	+	7.24203e8i	0.353622	+	0.296724i
$482$	−4.72610e8	+	1.72016e8i	−0.192237	+	0.0699687i
$483$	2.84039e8	+	1.64307e9i	0.114700	+	0.663500i
$484$	9.87054e7	+	5.59786e8i	0.0395715	+	0.224421i
$485$	5.56170e9			2.21366
$486$	−9.20567e8	+	1.53446e9i	−0.363771	+	0.606358i
$487$	−4.16593e9			−1.63441			−0.817204	−	0.576349i	$-0.804477\pi$
$487$	−4.16593e9			−1.63441			−0.817204	+	0.576349i	$0.804477\pi$
$488$	−2.87552e8	−	1.63079e9i	−0.112007	−	0.635226i
$489$	5.96473e8	+	3.45039e9i	0.230680	+	1.33440i
$490$	2.53100e9	−	9.21209e8i	0.971865	−	0.353730i
$491$	−1.24411e9	−	1.04393e9i	−0.474321	−	0.398003i	0.374047	−	0.927410i	$-0.377970\pi$
$491$	−1.24411e9	−	1.04393e9i	−0.474321	−	0.398003i	−0.848368	+	0.529407i	$0.822414\pi$
$492$	4.41335e7	−	1.58959e7i	0.0167067	−	0.00601736i
$493$	−190342.	−	69278.8i	−7.15436e−5	−	2.60397e-5i
$494$	3.51352e8	+	6.08560e8i	0.131129	+	0.227122i
$495$	5.81680e9	−	2.07307e9i	2.15559	−	0.768236i
$496$	1.47624e8	−	2.55692e8i	0.0543214	−	0.0940874i
$497$	1.05066e9	−	8.81609e8i	0.383897	−	0.322128i
$498$	−1.10758e9	−	1.93334e9i	−0.401859	−	0.701463i
$499$	−2.59915e8	+	1.47405e9i	−0.0936440	+	0.531082i	0.901510	+	0.432757i	$0.142459\pi$
$499$	−2.59915e8	+	1.47405e9i	−0.0936440	+	0.531082i	−0.995154	+	0.0983242i	$0.968652\pi$
$500$	−7.35177e8	+	4.16939e9i	−0.263025	+	1.49169i
$501$	−1.92924e9	+	3.31581e9i	−0.685416	+	1.17803i
$502$	−2.96648e9	+	2.48917e9i	−1.04659	+	0.878196i
$503$	5.04469e8	−	8.73766e8i	0.176745	−	0.306131i	−0.764019	−	0.645194i	$-0.776777\pi$
$503$	5.04469e8	−	8.73766e8i	0.176745	−	0.306131i	0.940764	+	0.339063i	$0.110110\pi$
$504$	2.40217e8	+	4.22588e8i	0.0835789	+	0.147032i
$505$	−3.43032e9	−	5.94148e9i	−1.18526	−	2.05293i
$506$	−3.28869e9	−	1.19698e9i	−1.12848	−	0.410735i
$507$	4.81100e8	−	2.67595e9i	0.163949	−	0.911905i
$508$	−5.56182e7	−	4.66693e7i	−0.0188232	−	0.0157946i
$509$	2.25498e8	−	8.20747e7i	0.0757934	−	0.0275865i	−0.303845	−	0.952721i	$-0.598271\pi$
$509$	2.25498e8	−	8.20747e7i	0.0757934	−	0.0275865i	0.379639	+	0.925135i	$0.376048\pi$
$510$	−1.33257e7	+	1.11057e7i	−0.00444831	+	0.00370723i
$511$	2.78161e7	+	1.57753e8i	0.00922195	+	0.0523003i
$512$	−1.34218e8			−0.0441942
$513$	2.12832e9	−	3.60217e9i	0.696026	−	1.17802i
$514$	−2.09632e9			−0.680905
$515$	3.15509e7	+	1.78934e8i	0.0101786	+	0.0577255i
$516$	5.45540e8	+	2.00635e8i	0.174805	+	0.0642883i
$517$	−5.31941e9	+	1.93611e9i	−1.69296	+	0.616187i
$518$	−1.39593e9	−	1.17133e9i	−0.441277	−	0.370275i
$519$	−1.36293e8	−	1.15145e8i	−0.0427945	−	0.0361541i
$520$	−5.47654e8	−	1.99330e8i	−0.170803	−	0.0621671i
$521$	4.12860e8	+	7.15095e8i	0.127900	+	0.221530i	0.922863	−	0.385129i	$-0.125843\pi$
$521$	4.12860e8	+	7.15095e8i	0.127900	+	0.221530i	−0.794963	+	0.606658i	$0.792510\pi$
$522$	−3.12137e7	+	2.58366e7i	−0.00960502	+	0.00795040i
$523$	−1.42251e9	+	2.46386e9i	−0.434809	+	0.753112i	−0.997280	−	0.0737053i	$-0.976518\pi$
$523$	−1.42251e9	+	2.46386e9i	−0.434809	+	0.753112i	0.562471	+	0.826817i	$0.309851\pi$
$524$	−9.04822e8	+	7.59236e8i	−0.274728	+	0.230525i
$525$	−4.11931e9	−	1.38146e7i	−1.24242	−	0.00416659i
$526$	3.24819e8	−	1.84214e9i	0.0973175	−	0.551915i
$527$	−1.09477e6	+	6.20873e6i	−0.000325825	+	0.00184784i
$528$	−1.02024e9	−	3.42150e6i	−0.301636	−	0.00101157i
$529$	2.55956e9	−	2.14773e9i	0.751746	−	0.630789i
$530$	−2.57877e9	+	4.46657e9i	−0.752398	+	1.30319i
$531$	−1.53527e9	−	5.70483e8i	−0.444994	−	0.165353i
$532$	−5.68279e8	−	9.84288e8i	−0.163633	−	0.283421i
$533$	−3.16233e7	−	1.15099e7i	−0.00904611	−	0.00329252i
$534$	1.37594e9	+	1.16244e9i	0.391026	+	0.330350i
$535$	−5.50536e9	−	4.61955e9i	−1.55435	−	1.30425i
$536$	1.75195e9	−	6.37656e8i	0.491410	−	0.178859i
$537$	−1.28086e8	−	4.71064e7i	−0.0356936	−	0.0131271i
$538$	9.44570e7	+	5.35692e8i	0.0261515	+	0.148312i
$539$	−3.38265e9			−0.930456
$540$	5.68153e8	+	3.42320e9i	0.155270	+	0.935523i
$541$	−2.40672e9			−0.653486			−0.326743	−	0.945113i	$-0.605951\pi$
$541$	−2.40672e9			−0.653486			−0.326743	+	0.945113i	$0.605951\pi$
$542$	4.71211e8	+	2.67237e9i	0.127121	+	0.720940i
$543$	2.29543e9	−	1.91301e9i	0.615267	−	0.512764i
$544$	2.69315e6	−	980225.i	0.000717239	−	0.000261054i
$545$	−7.44888e9	−	6.25035e9i	−1.97107	−	1.65393i
$546$	6.17071e7	−	3.43223e8i	0.0162241	−	0.0902407i
$547$	4.72089e9	+	1.71826e9i	1.23330	+	0.448884i	0.874726	−	0.484618i	$-0.161041\pi$
$547$	4.72089e9	+	1.71826e9i	1.23330	+	0.448884i	0.358572	+	0.933502i	$0.383264\pi$
$548$	1.26150e9	+	2.18498e9i	0.327458	+	0.567173i
$549$	7.07319e9	+	4.74421e7i	1.82437	+	0.0122366i
$550$	4.32298e9	−	7.48762e9i	1.10793	−	1.91900i
$551$	7.25756e7	−	6.08982e7i	0.0184825	−	0.0155086i
$552$	9.89017e8	−	1.69984e9i	0.250275	−	0.430150i
$553$	2.12546e8	−	1.20541e9i	0.0534461	−	0.303108i
$554$	−9.34489e8	+	5.29975e9i	−0.233502	+	1.32425i
$555$	−6.46642e9	−	1.12874e10i	−1.60560	−	2.80265i
$556$	−6.42825e8	+	5.39395e8i	−0.158610	+	0.133090i
$557$	−3.55924e9	+	6.16478e9i	−0.872698	+	1.51156i	−0.0135027	+	0.999909i	$0.504298\pi$
$557$	−3.55924e9	+	6.16478e9i	−0.872698	+	1.51156i	−0.859195	+	0.511648i	$0.829035\pi$
$558$	9.60635e8	+	8.17111e8i	0.234066	+	0.199095i
$559$	−2.08502e8	−	3.61136e8i	−0.0504857	−	0.0874439i
$560$	8.85779e8	+	3.22397e8i	0.213141	+	0.0775770i
$561$	2.04966e7	−	7.38241e6i	0.00490131	−	0.00176534i
$562$	7.03311e8	+	5.90148e8i	0.167136	+	0.140244i
$563$	5.83128e9	−	2.12241e9i	1.37716	−	0.501245i	0.455844	−	0.890060i	$-0.349338\pi$
$563$	5.83128e9	−	2.12241e9i	1.37716	−	0.501245i	0.921316	+	0.388814i	$0.127115\pi$
$564$	−5.41863e8	−	3.13449e9i	−0.127178	−	0.735683i
$565$	1.69779e9	+	9.62863e9i	0.396017	+	2.24592i
$566$	−2.94913e9			−0.683655
$567$	−1.96047e9	+	6.83911e8i	−0.451667	+	0.157565i
$568$	−1.61763e9			−0.370391
$569$	−8.44417e8	−	4.78893e9i	−0.192161	−	1.08980i	−0.916405	−	0.400253i	$-0.868922\pi$
$569$	−8.44417e8	−	4.78893e9i	−0.192161	−	1.08980i	0.724244	−	0.689544i	$-0.242189\pi$
$570$	−1.38209e9	−	7.99489e9i	−0.312588	−	1.80822i
$571$	5.48220e8	−	1.99536e8i	0.123233	−	0.0448533i	−0.279667	−	0.960097i	$-0.590224\pi$
$571$	5.48220e8	−	1.99536e8i	0.123233	−	0.0448533i	0.402901	+	0.915244i	$0.368002\pi$
$572$	5.60693e8	+	4.70477e8i	0.125268	+	0.105112i
$573$	4.57569e9	−	1.64806e9i	1.01605	−	0.365958i
$574$	5.11477e7	+	1.86162e7i	0.0112884	+	0.00410866i
$575$	8.33296e9	+	1.44331e10i	1.82794	+	3.16608i
$576$	1.03339e8	−	5.63919e8i	0.0225312	−	0.122953i
$577$	−6.49955e8	+	1.12576e9i	−0.140854	+	0.243966i	−0.927818	−	0.373032i	$-0.878318\pi$
$577$	−6.49955e8	+	1.12576e9i	−0.140854	+	0.243966i	0.786965	+	0.616998i	$0.211651\pi$
$578$	2.51465e9	−	2.11005e9i	0.541665	−	0.454511i
$579$	−1.19473e8	−	2.08546e8i	−0.0255797	−	0.0446506i
$580$	−1.36444e7	+	7.73813e7i	−0.00290373	+	0.0164679i
$581$	4.48946e8	−	2.54610e9i	0.0949681	−	0.538591i
$582$	1.97390e9	−	3.39256e9i	0.415044	−	0.713342i
$583$	4.96189e9	−	4.16352e9i	1.03707	−	0.870204i
$584$	9.44639e7	−	1.63616e8i	0.0196255	−	0.0339924i
$585$	1.25915e9	−	2.14751e9i	0.260034	−	0.443496i
$586$	2.75664e9	+	4.77464e9i	0.565898	+	0.980164i
$587$	−5.79116e9	−	2.10781e9i	−1.18177	−	0.430128i	−0.324941	−	0.945734i	$-0.605345\pi$
$587$	−5.79116e9	−	2.10781e9i	−1.18177	−	0.430128i	−0.856826	+	0.515606i	$0.827567\pi$
$588$	3.36350e8	−	1.87082e9i	0.0682292	−	0.379501i
$589$	−2.25888e9	−	1.89542e9i	−0.455501	−	0.382211i
$590$	−2.98454e9	+	1.08628e9i	−0.598267	+	0.217751i
$591$	−2.87972e9	+	2.39996e9i	−0.573845	+	0.478243i
$592$	3.73209e8	+	2.11657e9i	0.0739309	+	0.419283i
$593$	−7.13175e8			−0.140444			−0.0702222	−	0.997531i	$-0.522371\pi$
$593$	−7.13175e8			−0.140444			−0.0702222	+	0.997531i	$0.522371\pi$
$594$	7.99892e8	−	4.28392e9i	0.156595	−	0.838666i
$595$	−2.01281e7			−0.00391737
$596$	−2.76634e8	−	1.56887e9i	−0.0535234	−	0.303546i
$597$	5.19199e9	+	1.90947e9i	0.998675	+	0.367285i
$598$	−1.32578e9	+	4.82546e8i	−0.253524	+	0.0922751i
$599$	8.91582e8	+	7.48126e8i	0.169499	+	0.142227i	0.723591	−	0.690229i	$-0.242490\pi$
$599$	8.91582e8	+	7.48126e8i	0.169499	+	0.142227i	−0.554092	+	0.832455i	$0.686934\pi$
$600$	3.71129e9	+	3.13541e9i	0.701448	+	0.592605i
$601$	−4.66636e9	−	1.69841e9i	−0.876834	−	0.319141i	−0.135902	−	0.990722i	$-0.543393\pi$
$601$	−4.66636e9	−	1.69841e9i	−0.876834	−	0.319141i	−0.740931	+	0.671581i	$0.765616\pi$
$602$	3.37232e8	+	5.84103e8i	0.0630001	+	0.109119i
$603$	1.33025e9	+	7.85179e9i	0.247071	+	1.45834i
$604$	1.50830e9	−	2.61244e9i	0.278520	−	0.482412i
$605$	−3.60682e9	+	3.02648e9i	−0.662187	+	0.555641i
$606$	−4.84168e9	−	1.62372e7i	−0.883776	−	0.00296385i
$607$	−3.61227e8	+	2.04862e9i	−0.0655572	+	0.371793i	0.934325	+	0.356423i	$0.116004\pi$
$607$	−3.61227e8	+	2.04862e9i	−0.0655572	+	0.371793i	−0.999882	+	0.0153702i	$0.995107\pi$
$608$	−2.32773e8	+	1.32012e9i	−0.0420020	+	0.238205i
$609$	−4.70160e7	−	157674.i	−0.00843501	−	2.82878e-5i
$610$	1.05075e10	−	8.81686e9i	1.87433	−	1.57275i
$611$	−1.14103e9	+	1.97633e9i	−0.202374	+	0.350521i
$612$	2.04489e6	+	1.20700e7i	0.000360613	+	0.00212852i
$613$	−5.07837e8	−	8.79599e8i	−0.0890456	−	0.154232i	0.818062	−	0.575130i	$-0.195048\pi$
$613$	−5.07837e8	−	8.79599e8i	−0.0890456	−	0.154232i	−0.907108	+	0.420898i	$0.861715\pi$
$614$	4.18917e9	+	1.52473e9i	0.730363	+	0.265830i
$615$	2.96813e8	+	2.50757e8i	0.0514541	+	0.0434700i
$616$	−9.06867e8	−	7.60952e8i	−0.156319	−	0.131167i
$617$	1.04341e9	−	3.79769e8i	0.178836	−	0.0650911i	−0.251050	−	0.967974i	$-0.580776\pi$
$617$	1.04341e9	−	3.79769e8i	0.178836	−	0.0650911i	0.429886	+	0.902883i	$0.358554\pi$
$618$	1.20345e8	+	4.42597e7i	0.0205102	+	0.00754308i
$619$	−1.20763e8	−	6.84879e8i	−0.0204652	−	0.116064i	0.972864	−	0.231378i	$-0.0743235\pi$
$619$	−1.20763e8	−	6.84879e8i	−0.0204652	−	0.116064i	−0.993329	+	0.115315i	$0.963212\pi$
$620$	2.44561e9			0.412112
$621$	6.38042e9	+	5.46413e9i	1.06913	+	0.915589i
$622$	−3.07624e9			−0.512571
$623$	3.62934e8	+	2.05830e9i	0.0601338	+	0.341036i
$624$	−3.15956e8	+	2.63318e8i	−0.0520572	+	0.0433845i
$625$	−1.80576e10	+	6.57244e9i	−2.95856	+	1.07683i
$626$	1.40389e9	+	1.17800e9i	0.228730	+	0.191927i
$627$	−1.80305e9	+	1.00288e10i	−0.292126	+	1.62485i
$628$	−4.17663e8	−	1.52017e8i	−0.0672926	−	0.0244925i
$629$	−2.29465e7	−	3.97445e7i	−0.00367654	−	0.00636795i
$630$	−2.03655e9	+	3.47339e9i	−0.324491	+	0.553429i
$631$	−1.27920e9	+	2.21564e9i	−0.202692	+	0.351072i	−0.949395	−	0.314085i	$-0.898302\pi$
$631$	−1.27920e9	+	2.21564e9i	−0.202692	+	0.351072i	0.746703	+	0.665157i	$0.231636\pi$
$632$	−1.10588e9	+	9.27944e8i	−0.174260	+	0.146222i
$633$	4.30284e9	−	7.39535e9i	0.674283	−	1.15890i
$634$	−1.08182e9	+	6.13531e9i	−0.168594	+	0.956146i
$635$	1.04432e8	−	5.92263e8i	0.0161855	−	0.0917924i
$636$	1.80932e9	+	3.15825e9i	0.278879	+	0.486795i
$637$	−1.04463e9	+	8.76546e8i	−0.160130	+	0.134365i
$638$	4.93406e7	−	8.54605e7i	0.00752198	−	0.0130285i
$639$	1.24547e9	−	6.79651e9i	0.188834	−	1.03046i
$640$	−5.55879e8	−	9.62810e8i	−0.0838205	−	0.145181i
$641$	3.78081e9	+	1.37610e9i	0.566999	+	0.206371i	0.609583	−	0.792722i	$-0.291337\pi$
$641$	3.78081e9	+	1.37610e9i	0.566999	+	0.206371i	−0.0425842	+	0.999093i	$0.513559\pi$
$642$	−4.77177e9	+	1.71868e9i	−0.711716	+	0.256344i
$643$	2.06867e9	+	1.73582e9i	0.306869	+	0.257493i	0.783196	−	0.621774i	$-0.213588\pi$
$643$	2.06867e9	+	1.73582e9i	0.306869	+	0.257493i	−0.476328	+	0.879268i	$0.658032\pi$
$644$	2.14433e9	−	7.80472e8i	0.316367	−	0.115148i
$645$	8.20166e8	+	4.74438e9i	0.120349	+	0.696178i
$646$	−4.97046e6	−	2.81889e7i	−0.000725409	−	0.00411400i
$647$	6.27632e9			0.911045			0.455523	−	0.890224i	$-0.349452\pi$
$647$	6.27632e9			0.911045			0.455523	+	0.890224i	$0.349452\pi$
$648$	2.28975e9	+	8.68359e8i	0.330580	+	0.125368i
$649$	3.98879e9			0.572776
$650$	−6.05249e8	−	3.43254e9i	−0.0864445	−	0.490251i
$651$	2.49275e8	+	1.44197e9i	0.0354116	+	0.204844i
$652$	4.50302e9	−	1.63897e9i	0.636264	−	0.231581i
$653$	7.09608e9	+	5.95432e9i	0.997292	+	0.836828i	0.986607	−	0.163115i	$-0.0521543\pi$
$653$	7.09608e9	+	5.95432e9i	0.997292	+	0.836828i	0.0106853	+	0.999943i	$0.496599\pi$
$654$	−6.45631e9	+	2.32541e9i	−0.902531	+	0.325071i
$655$	−9.19380e9	−	3.34627e9i	−1.27835	−	0.465282i
$656$	−3.20982e7	−	5.55957e7i	−0.00443933	−	0.00768914i
$657$	6.14707e8	+	5.22866e8i	0.0845647	+	0.0719302i
$658$	1.84551e9	−	3.19652e9i	0.252538	−	0.437408i
$659$	4.34111e9	−	3.64262e9i	0.590883	−	0.495810i	−0.297618	−	0.954685i	$-0.596192\pi$
$659$	4.34111e9	−	3.64262e9i	0.590883	−	0.495810i	0.888501	+	0.458876i	$0.151748\pi$
$660$	−4.20090e9	−	7.33285e9i	−0.568772	−	0.992817i
$661$	1.25107e9	−	7.09520e9i	0.168492	−	0.955563i	−0.776899	−	0.629625i	$-0.783209\pi$
$661$	1.25107e9	−	7.09520e9i	0.168492	−	0.955563i	0.945391	−	0.325938i	$-0.105680\pi$
$662$	7.02232e8	−	3.98256e9i	0.0940758	−	0.533530i
$663$	4.41675e6	−	7.59112e6i	0.000588579	−	0.00101160i
$664$	−2.33587e9	+	1.96003e9i	−0.309642	+	0.259821i
$665$	4.70719e9	−	8.15309e9i	0.620706	−	1.07509i
$666$	−9.18017e9	−	6.15743e7i	−1.20418	−	0.00807681i
$667$	9.51088e7	+	1.64733e8i	0.0124102	+	0.0214952i
$668$	4.93338e9	+	1.79560e9i	0.640364	+	0.233074i
$669$	−1.31043e9	+	7.28878e9i	−0.169208	+	0.941160i
$670$	1.18301e10	+	9.92665e9i	1.51959	+	1.27509i
$671$	−1.61876e10	+	5.89180e9i	−2.06849	+	0.752869i
$672$	5.11029e8	−	4.25892e8i	0.0649611	−	0.0541386i
$673$	−1.65485e9	−	9.38511e9i	−0.209269	−	1.18682i	−0.890579	−	0.454829i	$-0.849700\pi$
$673$	−1.65485e9	−	9.38511e9i	−0.209269	−	1.18682i	0.681309	−	0.731996i	$-0.261411\pi$
$674$	−8.37101e9			−1.05310
$675$	−1.60309e10	+	1.31790e10i	−2.00630	+	1.64938i
$676$	−3.72084e9			−0.463263
$677$	−3.52580e8	−	1.99958e9i	−0.0436714	−	0.247673i	0.955155	−	0.296106i	$-0.0956883\pi$
$677$	−3.52580e8	−	1.99958e9i	−0.0436714	−	0.247673i	−0.998826	+	0.0484334i	$0.984577\pi$
$678$	6.47590e9	+	2.38166e9i	0.797988	+	0.293478i
$679$	4.27969e9	−	1.55768e9i	0.524648	−	0.190956i
$680$	1.81856e7	+	1.52596e7i	0.00221793	+	0.00186106i
$681$	7.09944e9	+	5.99782e9i	0.861409	+	0.727744i
$682$	−2.88617e9	−	1.05048e9i	−0.348399	−	0.126807i
$683$	−5.18192e9	−	8.97535e9i	−0.622327	−	1.07790i	−0.989051	−	0.147572i	$-0.952854\pi$
$683$	−5.18192e9	−	8.97535e9i	−0.622327	−	1.07790i	0.366725	−	0.930330i	$-0.380479\pi$
$684$	−5.36729e9	−	1.99440e9i	−0.641297	−	0.238296i
$685$	−1.04493e10	+	1.80987e10i	−1.24214	+	2.15145i
$686$	3.88052e9	−	3.25614e9i	0.458940	−	0.385096i
$687$	−3.59862e8	−	1.20684e6i	−0.0423436	−	0.000142004i
$688$	1.38134e8	−	7.83395e8i	0.0161711	−	0.0917109i
$689$	4.53434e8	−	2.57155e9i	0.0528138	−	0.299522i
$690$	1.62899e10	+	5.46301e7i	1.88776	+	0.00633083i
$691$	3.57754e9	−	3.00191e9i	0.412488	−	0.346119i	−0.412809	−	0.910818i	$-0.635452\pi$
$691$	3.57754e9	−	3.00191e9i	0.412488	−	0.346119i	0.825297	+	0.564699i	$0.191008\pi$
$692$	−1.22088e8	+	2.11462e8i	−0.0140056	+	0.0242583i
$693$	3.89538e9	−	3.22434e9i	0.444615	−	0.368022i
$694$	−1.77905e9	−	3.08141e9i	−0.202037	−	0.349938i
$695$	−6.53168e9	−	2.37734e9i	−0.738037	−	0.268623i
$696$	4.23591e7	+	3.57863e7i	0.00476227	+	0.00402331i
$697$	1.05010e6	+	881135.i	0.000117467	+	9.85661e-5i
$698$	4.67505e9	−	1.70158e9i	0.520346	−	0.189391i
$699$	−1.41032e10	−	5.18676e9i	−1.56187	−	0.574415i
$700$	9.78932e8	+	5.55180e9i	0.107872	+	0.611773i
$701$	−9.05695e7			−0.00993045			−0.00496523	−	0.999988i	$-0.501580\pi$
$701$	−9.05695e7			−0.00993045			−0.00496523	+	0.999988i	$0.501580\pi$
$702$	−8.63072e8	−	1.53023e9i	−0.0941602	−	0.166947i
$703$	2.14652e10			2.33018
$704$	2.42455e8	+	1.37503e9i	0.0261894	+	0.148528i
$705$	2.02411e10	−	1.68689e10i	2.17556	−	1.81312i
$706$	−6.18114e9	+	2.24975e9i	−0.661077	+	0.240612i
$707$	−4.30366e9	−	3.61120e9i	−0.458004	−	0.384311i
$708$	−3.96621e8	+	2.20606e9i	−0.0420010	+	0.233615i
$709$	9.27996e8	+	3.37763e8i	0.0977878	+	0.0355918i	0.390451	−	0.920624i	$-0.372319\pi$
$709$	9.27996e8	+	3.37763e8i	0.0977878	+	0.0355918i	−0.292663	+	0.956216i	$0.594541\pi$
$710$	−6.69960e9	−	1.16041e10i	−0.702498	−	1.21676i
$711$	−3.04732e9	−	5.36083e9i	−0.317962	−	0.559357i
$712$	1.23253e9	−	2.13480e9i	0.127973	−	0.221655i
$713$	4.53531e9	−	3.80558e9i	0.468591	−	0.393194i
$714$	−7.14367e6	+	1.22779e7i	−0.000734476	+	0.00126235i
$715$	−1.05279e9	+	5.97066e9i	−0.107713	+	0.610874i
$716$	−3.24320e7	+	1.83931e8i	−0.00330201	+	0.0187266i
$717$	−2.50160e9	−	4.36665e9i	−0.253455	−	0.442416i
$718$	3.11965e9	−	2.61769e9i	0.314536	−	0.263927i
$719$	−4.85186e9	+	8.40368e9i	−0.486808	+	0.843176i	−0.999885	−	0.0151666i	$-0.995172\pi$
$719$	−4.85186e9	+	8.40368e9i	−0.486808	+	0.843176i	0.513077	+	0.858342i	$0.328505\pi$
$720$	4.47326e9	−	1.59424e9i	0.446642	−	0.159180i
$721$	7.43928e7	+	1.28852e8i	0.00739192	+	0.0128032i
$722$	5.86085e9	+	2.13317e9i	0.579536	+	0.210934i
$723$	−2.76608e9	+	9.96277e8i	−0.272195	+	0.0980384i
$724$	−3.13257e9	−	2.62854e9i	−0.306772	−	0.257412i
$725$	−4.41584e8	+	1.60723e8i	−0.0430358	+	0.0156638i
$726$	5.66022e8	+	3.27424e9i	0.0548978	+	0.317565i
$727$	1.33080e9	+	7.54734e9i	0.128452	+	0.728490i	0.979197	+	0.202911i	$0.0650401\pi$
$727$	1.33080e9	+	7.54734e9i	0.128452	+	0.728490i	−0.850745	+	0.525579i	$0.823849\pi$
$728$	−4.77244e8			−0.0458438
$729$	−5.41139e9	+	8.95187e9i	−0.517323	+	0.855790i
$730$	1.56493e9			0.148890
$731$	2.94960e6	+	1.67280e7i	0.000279288	+	0.00158392i
$732$	−1.64896e9	−	9.53864e9i	−0.155389	−	0.898871i
$733$	1.05648e10	−	3.84528e9i	0.990829	−	0.360632i	0.204788	−	0.978806i	$-0.434350\pi$
$733$	1.05648e10	−	3.84528e9i	0.990829	−	0.360632i	0.786041	+	0.618174i	$0.212127\pi$
$734$	−1.50732e8	−	1.26479e8i	−0.0140691	−	0.0118054i
$735$	1.48134e10	−	5.33544e9i	1.37609	−	0.495638i
$736$	−2.52908e9	−	9.20509e8i	−0.233824	−	0.0851051i
$737$	−9.69740e9	−	1.67964e10i	−0.892317	−	1.54554i
$738$	2.58300e8	−	9.20563e7i	0.0236552	−	0.00843055i
$739$	8.16284e9	−	1.41385e10i	0.744022	−	1.28868i	−0.206628	−	0.978420i	$-0.566249\pi$
$739$	8.16284e9	−	1.41385e10i	0.744022	−	1.28868i	0.950650	−	0.310265i	$-0.100418\pi$
$740$	−1.36375e10	+	1.14432e10i	−1.23716	+	1.03810i
$741$	2.04195e9	+	3.56431e9i	0.184366	+	0.321819i
$742$	−7.33387e8	+	4.15924e9i	−0.0659051	+	0.373767i
$743$	3.01399e9	−	1.70932e10i	0.269576	−	1.52884i	−0.486105	−	0.873900i	$-0.661583\pi$
$743$	3.01399e9	−	1.70932e10i	0.269576	−	1.52884i	0.755681	−	0.654940i	$-0.227306\pi$
$744$	8.67968e8	−	1.49179e9i	0.0772678	−	0.132801i
$745$	1.01086e10	−	8.48209e9i	0.895659	−	0.751547i
$746$	−4.42501e9	+	7.66435e9i	−0.390237	+	0.675911i
$747$	−6.43663e9	−	1.13233e10i	−0.564985	−	0.993918i
$748$	−1.49071e7	−	2.58199e7i	−0.00130238	−	0.00225579i
$749$	−5.53015e9	−	2.01281e9i	−0.480895	−	0.175032i
$750$	−4.37931e9	+	2.43584e10i	−0.379046	+	2.10831i
$751$	1.00479e9	+	8.43122e8i	0.0865639	+	0.0726357i	0.685043	−	0.728503i	$-0.259784\pi$
$751$	1.00479e9	+	8.43122e8i	0.0865639	+	0.0726357i	−0.598479	+	0.801139i	$0.704228\pi$
$752$	−4.09075e9	+	1.48891e9i	−0.350785	+	0.127675i
$753$	−1.73897e10	+	1.44926e10i	−1.48426	+	1.23699i
$754$	−6.90805e6	−	3.91775e7i	−0.000586889	−	0.00332841i
$755$	2.49871e10			2.11301
$756$	1.39594e9	+	2.47501e9i	0.117500	+	0.208329i
$757$	−8.02196e9			−0.672117			−0.336058	−	0.941841i	$-0.609094\pi$
$757$	−8.02196e9			−0.672117			−0.336058	+	0.941841i	$0.609094\pi$
$758$	5.84790e8	+	3.31651e9i	0.0487706	+	0.276592i
$759$	−1.92010e10	−	7.06160e9i	−1.59396	−	0.586215i
$760$	−1.04339e10	+	3.79764e9i	−0.862185	+	0.313810i
$761$	4.69427e9	+	3.93896e9i	0.386119	+	0.323992i	0.815099	−	0.579322i	$-0.196682\pi$
$761$	4.69427e9	+	3.93896e9i	0.386119	+	0.323992i	−0.428980	+	0.903314i	$0.641127\pi$
$762$	−3.24209e8	−	2.73902e8i	−0.0265450	−	0.0224260i
$763$	−7.48242e9	−	2.72338e9i	−0.609826	−	0.221959i
$764$	−3.32789e9	−	5.76407e9i	−0.269987	−	0.467631i
$765$	−7.81151e7	+	6.46585e7i	−0.00630841	+	0.00522168i
$766$	−5.06732e8	+	8.77685e8i	−0.0407359	+	0.0705567i
$767$	1.23182e9	−	1.03362e9i	0.0985740	−	0.0827134i
$768$	−7.84588e8	−	2.63121e6i	−0.0624996	−	0.000209600i
$769$	1.39259e9	−	7.89776e9i	0.110428	−	0.626271i	−0.878484	−	0.477771i	$-0.841445\pi$
$769$	1.39259e9	−	7.89776e9i	0.110428	−	0.626271i	0.988913	−	0.148499i	$-0.0474442\pi$
$770$	1.70279e9	−	9.65697e9i	0.134413	−	0.762296i
$771$	−1.22543e10	−	4.10963e7i	−0.962939	−	0.00322933i
$772$	−2.51967e8	+	2.11425e8i	−0.0197098	+	0.0165385i
$773$	3.90232e9	−	6.75901e9i	0.303875	−	0.526326i	−0.673135	−	0.739519i	$-0.735053\pi$
$773$	3.90232e9	−	6.75901e9i	0.303875	−	0.526326i	0.977010	+	0.213193i	$0.0683863\pi$
$774$	3.18510e9	+	1.18353e9i	0.246905	+	0.0917460i
$775$	7.31307e9	+	1.26666e10i	0.564344	+	0.977472i
$776$	−5.04758e9	−	1.83717e9i	−0.387764	−	0.141134i
$777$	−8.13717e9	−	6.87453e9i	−0.622300	−	0.525738i
$778$	−8.95935e9	−	7.51778e9i	−0.682100	−	0.572349i
$779$	−6.02488e8	+	2.19288e8i	−0.0456633	+	0.0166201i
$780$	−3.19748e9	−	1.17595e9i	−0.241255	−	0.0887272i
$781$	2.92213e9	+	1.65722e10i	0.219493	+	1.24481i
$782$	5.74699e7			0.00429751
$783$	−1.82970e8	+	1.50420e8i	−0.0136212	+	0.0111979i
$784$	−2.60134e9			−0.192793
$785$	−6.39309e8	−	3.62570e9i	−0.0471701	−	0.267515i
$786$	−5.30415e9	+	4.42048e9i	−0.389616	+	0.324706i
$787$	1.58038e10	−	5.75210e9i	1.15571	−	0.420644i	0.308147	−	0.951339i	$-0.400291\pi$
$787$	1.58038e10	−	5.75210e9i	1.15571	−	0.420644i	0.847563	+	0.530694i	$0.178069\pi$
$788$	3.92996e9	+	3.29763e9i	0.286119	+	0.240082i
$789$	1.93489e9	−	1.07621e10i	0.140244	−	0.780059i
$790$	−1.12367e10	−	4.08984e9i	−0.810859	−	0.295128i
$791$	4.00316e9	+	6.93367e9i	0.287597	+	0.498133i
$792$	−5.96388e9	−	4.00017e7i	−0.426571	−	0.00286115i
$793$	−3.47230e9	+	6.01420e9i	−0.247264	+	0.428274i
$794$	9.44390e9	−	7.92437e9i	0.669544	−	0.561814i
$795$	−1.51621e10	+	2.60594e10i	−1.07023	+	1.83941i
$796$	1.31464e9	−	7.45570e9i	0.0923871	−	0.523953i
$797$	3.24430e9	−	1.83993e10i	0.226995	−	1.28735i	−0.631839	−	0.775099i	$-0.717700\pi$
$797$	3.24430e9	−	1.83993e10i	0.226995	−	1.28735i	0.858834	−	0.512253i	$-0.171189\pi$
$798$	−3.30266e9	−	5.76493e9i	−0.230066	−	0.401591i
$799$	7.12091e7	−	5.97515e7i	0.00493880	−	0.00414415i
$800$	3.32447e9	−	5.75816e9i	0.229566	−	0.397620i
$801$	8.02046e9	+	6.82216e9i	0.551424	+	0.469038i
$802$	6.04329e9	+	1.04673e10i	0.413679	+	0.716513i
$803$	−1.84685e9	−	6.72199e8i	−0.125872	−	0.0458135i
$804$	1.02537e10	−	3.69316e9i	0.695803	−	0.250612i
$805$	1.44797e10	+	1.21499e10i	0.978305	+	0.820895i
$806$	−1.16352e9	+	4.23486e8i	−0.0782709	+	0.0284883i
$807$	5.41659e8	+	3.13331e9i	0.0362801	+	0.209868i
$808$	1.15060e9	+	6.52538e9i	0.0767334	+	0.435177i
$809$	2.75298e8			0.0182803			0.00914014	−	0.999958i	$-0.497091\pi$
$809$	2.75298e8			0.0182803			0.00914014	+	0.999958i	$0.497091\pi$
$810$	3.25411e9	+	2.00219e10i	0.215147	+	1.32376i
$811$	9.03174e9			0.594564			0.297282	−	0.954790i	$-0.403920\pi$
$811$	9.03174e9			0.594564			0.297282	+	0.954790i	$0.403920\pi$
$812$	1.11731e7	+	6.33659e7i	0.000732366	+	0.00415345i
$813$	2.70214e9	+	1.56309e10i	0.176356	+	1.02016i
$814$	2.10096e10	−	7.64687e9i	1.36531	−	0.496933i
$815$	3.04069e10	+	2.55144e10i	1.96753	+	1.65095i
$816$	1.57624e7	−	5.67725e6i	0.00101556	−	0.000365782i
$817$	−7.46564e9	−	2.71727e9i	−0.478950	−	0.174323i
$818$	2.40839e9	+	4.17145e9i	0.153847	+	0.266471i
$819$	3.67446e8	−	2.00515e9i	0.0233722	−	0.127542i
$820$	2.65877e8	−	4.60512e8i	0.0168396	−	0.0291671i
$821$	−2.14338e10	+	1.79851e10i	−1.35175	+	1.13426i	−0.373317	+	0.927704i	$0.621780\pi$
$821$	−2.14338e10	+	1.79851e10i	−1.35175	+	1.13426i	−0.978436	+	0.206551i	$0.933776\pi$
$822$	7.33144e9	+	1.27973e10i	0.460403	+	0.803653i
$823$	2.71689e9	−	1.54082e10i	0.169892	−	0.963505i	−0.773984	−	0.633205i	$-0.781739\pi$
$823$	2.71689e9	−	1.54082e10i	0.169892	−	0.963505i	0.943876	−	0.330300i	$-0.107150\pi$
$824$	3.04720e7	−	1.72816e8i	0.00189739	−	0.0107606i
$825$	2.54174e10	−	4.36852e10i	1.57595	−	2.70860i
$826$	−1.99235e9	+	1.67178e9i	−0.123008	+	0.103216i
$827$	−1.06680e10	+	1.84775e10i	−0.655863	+	1.13599i	0.325813	+	0.945434i	$0.394362\pi$
$827$	−1.06680e10	+	1.84775e10i	−0.655863	+	1.13599i	−0.981677	+	0.190554i	$0.938971\pi$
$828$	5.81476e9	−	9.91724e9i	0.355980	−	0.607134i
$829$	−1.54620e9	−	2.67809e9i	−0.0942592	−	0.163262i	0.815040	−	0.579405i	$-0.196715\pi$
$829$	−1.54620e9	−	2.67809e9i	−0.0942592	−	0.163262i	−0.909299	+	0.416143i	$0.863382\pi$
$830$	−2.37345e10	−	8.63866e9i	−1.44081	−	0.524412i
$831$	−5.56658e9	+	3.09621e10i	−0.336500	+	1.87166i
$832$	4.31186e8	+	3.61808e8i	0.0259557	+	0.0217794i
$833$	5.21971e7	−	1.89982e7i	0.00312888	−	0.00113882i
$834$	−3.76830e9	+	3.14050e9i	−0.224939	+	0.187464i
$835$	7.55143e9	+	4.28263e10i	0.448876	+	2.54570i
$836$	1.39448e10			0.825449
$837$	5.59951e9	+	4.79537e9i	0.330074	+	0.282672i
$838$	−5.81547e9			−0.341374
$839$	1.74708e9	+	9.90818e9i	0.102128	+	0.579198i	0.992329	+	0.123629i	$0.0394532\pi$
$839$	1.74708e9	+	9.90818e9i	0.102128	+	0.579198i	−0.890200	+	0.455569i	$0.849436\pi$
$840$	5.17162e9	+	1.90198e9i	0.301057	+	0.110721i
$841$	1.62045e10	−	5.89797e9i	0.939400	−	0.341914i
$842$	−3.25787e9	−	2.73367e9i	−0.188079	−	0.157817i
$843$	4.09973e9	+	3.46358e9i	0.235700	+	0.199126i
$844$	−1.10031e10	−	4.00479e9i	−0.629963	−	0.229288i
$845$	−1.54103e10	−	2.66914e10i	−0.878643	−	1.52185i
$846$	−3.10609e9	−	1.83337e10i	−0.176367	−	1.04101i
$847$	−1.92779e9	+	3.33903e9i	−0.109010	+	0.188812i
$848$	3.81581e9	−	3.20185e9i	0.214883	−	0.180308i
$849$	−1.72396e10	−	5.78150e7i	−0.966828	−	0.00324238i
$850$	−2.46540e7	+	1.39820e8i	−0.00137696	+	0.00780913i
$851$	−7.48373e9	+	4.24424e10i	−0.416260	+	2.36073i
$852$	−9.45608e9	−	3.17121e7i	−0.523808	−	0.00175665i
$853$	1.75585e10	−	1.47333e10i	0.968648	−	0.812792i	−0.0136902	−	0.999906i	$-0.504358\pi$
$853$	1.75585e10	−	1.47333e10i	0.968648	−	0.812792i	0.982338	+	0.187114i	$0.0599134\pi$
$854$	5.61611e9	−	9.72739e9i	0.308555	−	0.534434i
$855$	−7.92244e9	−	4.67623e10i	−0.433488	−	2.55867i
$856$	3.47050e9	+	6.01108e9i	0.189118	+	0.327562i
$857$	2.44051e9	+	8.88273e8i	0.132449	+	0.0482074i	0.407394	−	0.913252i	$-0.366438\pi$
$857$	2.44051e9	+	8.88273e8i	0.132449	+	0.0482074i	−0.274945	+	0.961460i	$0.588660\pi$
$858$	3.26838e9	+	2.76123e9i	0.176656	+	0.149244i
$859$	−2.12419e10	−	1.78241e10i	−1.14345	−	0.959470i	−0.143905	−	0.989591i	$-0.545966\pi$
$859$	−2.12419e10	−	1.78241e10i	−1.14345	−	0.959470i	−0.999546	+	0.0301218i	$0.990410\pi$
$860$	6.19177e9	−	2.25362e9i	0.331948	−	0.120819i
$861$	2.98626e8	+	1.09826e8i	0.0159447	+	0.00586403i
$862$	2.84366e9	+	1.61272e10i	0.151218	+	0.857597i
$863$	−2.20142e10			−1.16591			−0.582954	−	0.812505i	$-0.698103\pi$
$863$	−2.20142e10			−1.16591			−0.582954	+	0.812505i	$0.698103\pi$
$864$	6.15136e8	−	3.29444e9i	0.0324469	−	0.173773i
$865$	−2.02256e9			−0.106254
$866$	−1.50701e9	−	8.54668e9i	−0.0788503	−	0.447182i
$867$	1.47411e10	−	1.22853e10i	0.768181	−	0.640203i
$868$	1.88188e9	−	6.84948e8i	0.0976726	−	0.0355499i
$869$	1.15043e10	+	9.65321e9i	0.594688	+	0.499002i
$870$	−8.12773e7	+	4.52076e8i	−0.00418458	+	0.0232752i
$871$	−7.34720e9	−	2.67416e9i	−0.376754	−	0.137127i
$872$	4.69566e9	+	8.13313e9i	0.239822	+	0.415384i
$873$	1.16052e10	−	1.97930e10i	0.590341	−	1.00684i
$874$	−1.34400e10	+	2.32787e10i	−0.680939	+	1.17942i
$875$	−2.19986e10	+	1.84590e10i	−1.11011	+	0.931494i
$876$	5.55410e8	−	9.54590e8i	0.0279157	−	0.0479792i
$877$	3.39944e9	−	1.92792e10i	0.170180	−	0.965138i	−0.773381	−	0.633941i	$-0.781436\pi$
$877$	3.39944e9	−	1.92792e10i	0.170180	−	0.965138i	0.943561	−	0.331198i	$-0.107453\pi$
$878$	−3.23046e9	+	1.83208e10i	−0.161077	+	0.913512i
$879$	1.60207e10	+	2.79649e10i	0.795648	+	1.38884i
$880$	−8.85960e9	+	7.43409e9i	−0.438253	+	0.367738i
$881$	4.51380e9	−	7.81814e9i	0.222396	−	0.385201i	−0.733139	−	0.680079i	$-0.761946\pi$
$881$	4.51380e9	−	7.81814e9i	0.222396	−	0.385201i	0.955535	+	0.294878i	$0.0952789\pi$
$882$	2.00285e9	−	1.09296e10i	0.0982900	−	0.536368i
$883$	−1.00189e10	−	1.73533e10i	−0.489733	−	0.848242i	0.510198	−	0.860057i	$-0.329572\pi$
$883$	−1.00189e10	−	1.73533e10i	−0.489733	−	0.848242i	−0.999930	+	0.0118155i	$0.996239\pi$
$884$	−1.12943e7	−	4.11080e6i	−0.000549893	−	0.000200145i
$885$	−1.74678e10	+	6.29151e9i	−0.847105	+	0.305108i
$886$	5.12691e9	+	4.30199e9i	0.247650	+	0.207803i
$887$	−3.30005e10	+	1.20112e10i	−1.58777	+	0.577901i	−0.976875	−	0.213809i	$-0.931413\pi$
$887$	−3.30005e10	+	1.20112e10i	−1.58777	+	0.577901i	−0.610896	+	0.791711i	$0.709191\pi$
$888$	2.14015e9	+	1.23800e10i	0.102565	+	0.593303i
$889$	−8.55171e7	−	4.84992e8i	−0.00408222	−	0.0231514i
$890$	2.04187e10			0.970873
$891$	4.75986e9	−	2.50266e10i	0.225435	−	1.18530i
$892$	1.01349e10			0.478125
$893$	7.54987e9	+	4.28175e10i	0.354780	+	2.01206i
$894$	−1.58635e9	−	9.17647e9i	−0.0742535	−	0.429531i
$895$	−1.45375e9	+	5.29121e8i	−0.0677811	+	0.0246703i
$896$	−6.97402e8	−	5.85190e8i	−0.0323896	−	0.0271781i
$897$	−7.75952e9	+	2.79480e9i	−0.358972	+	0.129294i
$898$	−1.67821e9	−	6.10819e8i	−0.0773356	−	0.0281479i
$899$	8.34682e7	+	1.44571e8i	0.00383144	+	0.00663625i
$900$	2.16334e10	+	1.84012e10i	0.989181	+	0.841392i
$901$	−5.31824e7	+	9.21146e7i	−0.00242232	+	0.00419558i
$902$	−5.11581e8	+	4.29268e8i	−0.0232109	+	0.0194763i
$903$	1.95989e9	+	3.42107e9i	0.0885775	+	0.154616i
$904$	1.63973e9	−	9.29939e9i	0.0738216	−	0.418663i
$905$	5.88189e9	−	3.33579e10i	0.263783	−	1.49599i
$906$	8.86816e9	−	1.52418e10i	0.396173	−	0.680908i
$907$	3.57836e9	−	3.00260e9i	0.159242	−	0.133620i	−0.559685	−	0.828705i	$-0.689078\pi$
$907$	3.57836e9	−	3.00260e9i	0.159242	−	0.133620i	0.718927	+	0.695085i	$0.244633\pi$
$908$	6.35949e9	−	1.10150e10i	0.281917	−	0.488295i
$909$	−2.83024e10	−	1.89833e8i	−1.24983	−	0.00838298i
$910$	−1.97656e9	−	3.42350e9i	−0.0869491	−	0.150600i
$911$	2.13681e10	+	7.77737e9i	0.936381	+	0.340815i	0.764736	−	0.644344i	$-0.222870\pi$
$911$	2.13681e10	+	7.77737e9i	0.936381	+	0.340815i	0.171645	+	0.985159i	$0.445092\pi$
$912$	−1.38659e9	+	7.71238e9i	−0.0605292	+	0.336672i
$913$	2.42996e10	+	2.03898e10i	1.05670	+	0.886675i
$914$	2.77211e10	−	1.00896e10i	1.20088	−	0.437083i
$915$	6.15960e10	−	5.13342e10i	2.65815	−	2.21530i
$916$	8.55194e7	+	4.85005e8i	0.00367647	+	0.0208503i
$917$	−8.01177e9			−0.343112
$918$	1.17171e7	+	7.05971e7i	0.000499886	+	0.00301188i
$919$	−1.79683e10			−0.763664			−0.381832	−	0.924232i	$-0.624707\pi$
$919$	−1.79683e10			−0.763664			−0.381832	+	0.924232i	$0.624707\pi$
$920$	−3.87121e9	−	2.19547e10i	−0.163904	−	0.929545i
$921$	2.44585e10	+	8.99517e9i	1.03162	+	0.379403i
$922$	−6.22438e9	+	2.26549e9i	−0.261540	+	0.0951928i
$923$	5.19677e9	+	4.36061e9i	0.217534	+	0.182533i
$924$	−5.28630e9	−	4.46603e9i	−0.220445	−	0.186238i
$925$	−1.00048e11	−	3.64147e10i	−4.15637	−	1.51280i
$926$	−2.25819e9	−	3.91129e9i	−0.0934590	−	0.161876i
$927$	7.02627e8	+	2.61085e8i	0.0289698	+	0.0107647i
$928$	3.79441e7	−	6.57211e7i	0.00155857	−	0.00269952i
$929$	1.83469e10	−	1.53949e10i	0.750771	−	0.629972i	−0.184936	−	0.982751i	$-0.559208\pi$
$929$	1.83469e10	−	1.53949e10i	0.750771	−	0.629972i	0.935707	+	0.352779i	$0.114763\pi$
$930$	1.42961e10	+	4.79438e7i	0.582812	+	0.00195453i
$931$	−4.51148e9	+	2.55859e10i	−0.183229	+	1.03915i
$932$	−3.57099e9	+	2.02521e10i	−0.144489	+	0.819435i
$933$	−1.79826e10	−	6.03068e7i	−0.724880	−	0.00243097i
$934$	3.20264e9	−	2.68733e9i	0.128616	−	0.107921i
$935$	1.23479e8	−	2.13873e8i	0.00494031	−	0.00855686i
$936$	−1.85213e9	+	1.53307e9i	−0.0738254	+	0.0611078i
$937$	2.74051e9	+	4.74670e9i	0.108829	+	0.188497i	0.915296	−	0.402782i	$-0.131957\pi$
$937$	2.74051e9	+	4.74670e9i	0.108829	+	0.188497i	−0.806467	+	0.591279i	$0.798623\pi$
$938$	1.18834e10	+	4.32520e9i	0.470143	+	0.171118i
$939$	8.18354e9	+	6.91371e9i	0.322561	+	0.272509i
$940$	−2.76230e10	−	2.31785e10i	−1.08474	−	0.910201i
$941$	9.32215e9	−	3.39298e9i	0.364714	−	0.132745i	−0.153161	−	0.988201i	$-0.548945\pi$
$941$	9.32215e9	−	3.39298e9i	0.364714	−	0.132745i	0.517875	+	0.855456i	$0.326723\pi$
$942$	−2.43853e9	−	8.96824e8i	−0.0950494	−	0.0349566i
$943$	−2.23536e8	−	1.26773e9i	−0.00868073	−	0.0492309i
$944$	3.06748e9			0.118680
$945$	−1.19730e10	+	2.02643e10i	−0.461522	+	0.781124i
$946$	−8.27522e9			−0.317805
$947$	2.58224e9	+	1.46446e10i	0.0988034	+	0.560342i	0.993515	+	0.113698i	$0.0362697\pi$
$947$	2.58224e9	+	1.46446e10i	0.0988034	+	0.560342i	−0.894712	+	0.446644i	$0.852619\pi$
$948$	−6.48277e9	+	5.40274e9i	−0.247133	+	0.205961i
$949$	−7.44531e8	+	2.70987e8i	−0.0282781	+	0.0102924i
$950$	−5.08697e10	−	4.26847e10i	−1.92498	−	1.61525i
$951$	−6.44421e9	+	3.58436e10i	−0.242962	+	1.35139i
$952$	1.82675e7	+	6.64883e6i	0.000686199	+	0.000249756i
$953$	−8.47209e8	−	1.46741e9i	−0.0317077	−	0.0549194i	0.849736	−	0.527208i	$-0.176761\pi$
$953$	−8.47209e8	−	1.46741e9i	−0.0317077	−	0.0549194i	−0.881444	+	0.472289i	$0.843428\pi$
$954$	1.05147e10	+	1.84974e10i	0.392083	+	0.689751i
$955$	2.75657e10	−	4.77452e10i	1.02413	−	1.77385i
$956$	−5.27581e9	+	4.42693e9i	−0.195293	+	0.163870i
$957$	2.90103e8	−	4.98604e8i	0.0106994	−	0.0183892i
$958$	6.10689e9	−	3.46339e10i	0.224409	−	1.27269i
$959$	−2.97171e9	+	1.68534e10i	−0.108803	+	0.617054i
$960$	−3.23059e9	−	5.63914e9i	−0.117851	−	0.205714i
$961$	−1.70957e10	+	1.43450e10i	−0.621375	+	0.521396i
$962$	4.50664e9	−	7.80572e9i	0.163207	−	0.282683i
$963$	−2.79277e10	+	9.95324e9i	−1.00773	+	0.359147i
$964$	2.01176e9	+	3.48447e9i	0.0723281	+	0.125276i
$965$	−2.56021e9	−	9.31839e8i	−0.0917127	−	0.0333807i
$966$	1.25503e10	−	4.52032e9i	0.447954	−	0.161343i
$967$	−3.01435e10	−	2.52934e10i	−1.07202	−	0.899529i	−0.0767834	−	0.997048i	$-0.524465\pi$
$967$	−3.01435e10	−	2.52934e10i	−1.07202	−	0.899529i	−0.995234	+	0.0975187i	$0.968909\pi$
$968$	4.27313e9	−	1.55529e9i	0.151420	−	0.0551123i
$969$	−2.85029e7	−	1.64879e8i	−0.00100637	−	0.00582148i
$970$	−7.72623e9	−	4.38176e10i	−0.271811	−	1.54151i
$971$	−1.43977e10			−0.504691			−0.252345	−	0.967637i	$-0.581202\pi$
$971$	−1.43977e10			−0.504691			−0.252345	+	0.967637i	$0.581202\pi$
$972$	1.33680e10	+	5.12100e9i	0.466913	+	0.178864i
$973$	−5.69192e9			−0.198090
$974$	5.78725e9	+	3.28211e10i	0.200685	+	1.13814i
$975$	−3.47077e9	−	2.00772e10i	−0.119925	−	0.693726i
$976$	−1.24486e10	+	4.53094e9i	−0.428596	+	0.155996i
$977$	−3.11271e9	−	2.61187e9i	−0.106784	−	0.0896027i	0.587832	−	0.808983i	$-0.299982\pi$
$977$	−3.11271e9	−	2.61187e9i	−0.106784	−	0.0896027i	−0.694617	+	0.719380i	$0.744426\pi$
$978$	2.63552e10	−	9.49252e9i	0.900906	−	0.324486i
$979$	−2.40970e10	−	8.77060e9i	−0.820775	−	0.298738i
$980$	−1.07737e10	−	1.86607e10i	−0.365658	−	0.633338i
$981$	−3.77868e10	+	1.34670e10i	−1.27791	+	0.455437i
$982$	−6.49627e9	+	1.12519e10i	−0.218914	+	0.379170i
$983$	1.34711e10	−	1.13036e10i	0.452342	−	0.379560i	−0.387962	−	0.921675i	$-0.626821\pi$
$983$	1.34711e10	−	1.13036e10i	0.452342	−	0.379560i	0.840304	+	0.542115i	$0.182376\pi$
$984$	−1.86545e8	−	3.25622e8i	−0.00624165	−	0.0108951i
$985$	−7.37912e9	+	4.18491e10i	−0.246024	+	1.39527i
$986$	−281390.	+	1.59584e6i	−9.34846e−6	+	5.30177e-5i
$987$	1.08509e10	−	1.86495e10i	0.359215	−	0.617387i
$988$	4.30642e9	−	3.61352e9i	0.142059	−	0.119201i
$989$	7.97564e9	−	1.38142e10i	0.262167	−	0.454087i
$990$	−2.44132e10	−	4.29475e10i	−0.799652	−	1.40674i
$991$	−5.79646e8	−	1.00398e9i	−0.0189193	−	0.0327692i	0.856411	−	0.516295i	$-0.172689\pi$
$991$	−5.79646e8	−	1.00398e9i	−0.0189193	−	0.0327692i	−0.875330	+	0.483526i	$0.839356\pi$
$992$	−2.21954e9	−	8.07845e8i	−0.0721891	−	0.0262747i
$993$	4.18307e9	−	2.32668e10i	0.135573	−	0.754075i
$994$	−8.40529e9	−	7.05287e9i	−0.271456	−	0.227779i
$995$	5.89281e10	−	2.14481e10i	1.89645	−	0.690252i
$996$	−1.36931e10	+	1.14118e10i	−0.439130	+	0.365971i
$997$	2.77199e9	+	1.57207e10i	0.0885846	+	0.502388i	0.996525	+	0.0832898i	$0.0265427\pi$
$997$	2.77199e9	+	1.57207e10i	0.0885846	+	0.502388i	−0.907941	+	0.419099i	$0.862346\pi$
$998$	1.19743e10			0.381325
$999$	−5.36628e10	−	5.39910e8i	−1.70292	−	0.0171333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.e.b.13.5	✓	66
27.25	even	9	inner	54.8.e.b.25.5	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.e.b.13.5	✓	66	1.1	even	1	trivial
54.8.e.b.25.5	yes	66	27.25	even	9	inner

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38919 - 7.87846i) q^{2} +(-7.96623 - 46.0819i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-406.101 - 340.759i) q^{5} +(-351.988 + 126.778i) q^{6} +(-407.930 - 148.474i) q^{7} +(256.000 + 443.405i) q^{8} +(-2060.08 + 734.197i) q^{9} +O(q^{10})\)	\(q+(-1.38919 - 7.87846i) q^{2} +(-7.96623 - 46.0819i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-406.101 - 340.759i) q^{5} +(-351.988 + 126.778i) q^{6} +(-407.930 - 148.474i) q^{7} +(256.000 + 443.405i) q^{8} +(-2060.08 + 734.197i) q^{9} +(-2120.51 + 3672.83i) q^{10} +(4080.13 - 3423.64i) q^{11} +(1487.79 + 2597.00i) q^{12} +(372.856 - 2114.57i) q^{13} +(-603.059 + 3420.12i) q^{14} +(-12467.7 + 21428.5i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-43.7315 + 75.7452i) q^{17} +(8646.18 + 15210.3i) q^{18} +(-20454.2 - 35427.7i) q^{19} +(31882.0 + 11604.1i) q^{20} +(-3592.31 + 19980.9i) q^{21} +(-32641.1 - 27389.1i) q^{22} +(77181.3 - 28091.7i) q^{23} +(18393.6 - 15329.2i) q^{24} +(35234.9 + 199827. i) q^{25} -17177.5 q^{26} +(50244.2 + 89083.5i) q^{27} +27783.0 q^{28} +(402.156 + 2280.74i) q^{29} +(186143. + 68458.4i) q^{30} +(67734.9 - 24653.5i) q^{31} +(-25101.7 - 21062.9i) q^{32} +(-190271. - 160747. i) q^{33} +(657.507 + 239.313i) q^{34} +(115067. + 199301. i) q^{35} +(107823. - 89248.5i) q^{36} +(-262356. + 454415. i) q^{37} +(-250701. + 210363. i) q^{38} +(-100414. - 336.749i) q^{39} +(47132.5 - 267302. i) q^{40} +(2721.58 - 15434.8i) q^{41} +(162409. + 544.660i) q^{42} +(148773. - 124835. i) q^{43} +(-170439. + 295210. i) q^{44} +(1.08678e6 + 403832. i) q^{45} +(-328539. - 569045. i) q^{46} +(-998719. - 363504. i) q^{47} +(-146323. - 123618. i) q^{48} +(-486509. - 408229. i) q^{49} +(1.52538e6 - 555194. i) q^{50} +(3838.85 + 1411.83i) q^{51} +(23862.8 + 135333. i) q^{52} +1.21611e6 q^{53} +(632042. - 519601. i) q^{54} -2.82358e6 q^{55} +(-38595.8 - 218887. i) q^{56} +(-1.46963e6 + 1.22479e6i) q^{57} +(17410.1 - 6336.74i) q^{58} +(573687. + 481381. i) q^{59} +(280760. - 1.56162e6i) q^{60} +(-3.03922e6 - 1.10619e6i) q^{61} +(-288328. - 499399. i) q^{62} +(949376. + 6367.77i) q^{63} +(-131072. + 227023. i) q^{64} +(-871976. + 731675. i) q^{65} +(-1.00211e6 + 1.72235e6i) q^{66} +(632318. - 3.58605e6i) q^{67} +(972.019 - 5512.59i) q^{68} +(-1.90936e6 - 3.33287e6i) q^{69} +(1.41034e6 - 1.18341e6i) q^{70} +(-1.57972e6 + 2.73615e6i) q^{71} +(-852927. - 725495. i) q^{72} +(-184500. - 319563. i) q^{73} +(3.94455e6 + 1.43570e6i) q^{74} +(8.92772e6 - 3.21556e6i) q^{75} +(2.00561e6 + 1.68291e6i) q^{76} +(-2.17273e6 + 790808. i) q^{77} +(136840. + 791573. i) q^{78} +(489615. + 2.77674e6i) q^{79} -2.17140e6 q^{80} +(3.70488e6 - 3.02501e6i) q^{81} -125384. q^{82} +(1.03418e6 + 5.86511e6i) q^{83} +(-221326. - 1.28029e6i) q^{84} +(43570.3 - 15858.3i) q^{85} +(-1.19018e6 - 998681. i) q^{86} +(101897. - 36701.0i) q^{87} +(2.56257e6 + 932700. i) q^{88} +(-2.40728e6 - 4.16954e6i) q^{89} +(1.67183e6 - 9.12319e6i) q^{90} +(-466058. + 807237. i) q^{91} +(-4.02680e6 + 3.37889e6i) q^{92} +(-1.67567e6 - 2.92496e6i) q^{93} +(-1.47645e6 + 8.37334e6i) q^{94} +(-3.76584e6 + 2.13572e7i) q^{95} +(-770650. + 1.32453e6i) q^{96} +(-8.03676e6 + 6.74364e6i) q^{97} +(-2.54037e6 + 4.40005e6i) q^{98} +(-5.89177e6 + 1.00486e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9}+O(q^{10}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9	\( 66 q + 213 q^{5} - 1320 q^{6} - 1677 q^{7} + 16896 q^{8} + 6468 q^{9} - 3000 q^{10} - 2523 q^{11} - 5376 q^{12} - 9924 q^{13} + 13416 q^{14} - 15084 q^{15} + 29478 q^{17} + 22848 q^{18} - 61731 q^{19} - 27264 q^{20} - 36372 q^{21} + 20184 q^{22} + 255234 q^{23} + 558999 q^{25} - 316368 q^{26} - 51597 q^{27} + 263424 q^{28} + 132153 q^{29} + 610632 q^{30} + 776898 q^{31} + 645795 q^{33} + 387840 q^{34} - 321081 q^{35} - 314688 q^{36} - 759795 q^{37} + 174504 q^{38} - 84012 q^{39} - 109056 q^{40} + 349287 q^{41} + 313752 q^{42} - 1043622 q^{43} + 255552 q^{44} + 845496 q^{45} - 524472 q^{46} + 1280709 q^{47} - 872448 q^{48} + 1011003 q^{49} - 1537704 q^{50} - 7812153 q^{51} - 635136 q^{52} - 2951976 q^{53} - 1256832 q^{54} + 2539854 q^{55} + 858624 q^{56} - 3973923 q^{57} - 47496 q^{58} + 639426 q^{59} - 94464 q^{60} + 1639350 q^{61} + 2859936 q^{62} + 6955635 q^{63} - 8650752 q^{64} - 4119567 q^{65} + 712512 q^{66} - 6408441 q^{67} - 1634496 q^{68} - 1007298 q^{69} + 2380872 q^{70} + 3531612 q^{71} + 6623232 q^{72} - 6666213 q^{73} + 7873368 q^{74} + 16535910 q^{75} - 1396032 q^{76} - 8256489 q^{77} - 4117104 q^{78} - 22540695 q^{79} - 3072000 q^{80} - 13134636 q^{81} + 3798096 q^{82} + 8663238 q^{83} + 8570304 q^{84} - 15143175 q^{85} + 8348976 q^{86} + 45908613 q^{87} + 11028480 q^{88} + 21718137 q^{89} - 27904392 q^{90} - 8606796 q^{91} - 8332800 q^{92} - 20412249 q^{93} - 10358784 q^{94} - 21603363 q^{95} - 5505024 q^{96} - 17397492 q^{97} + 44171448 q^{98} + 103927383 q^{99}+O(q^{100}) \) 66 * q + 213 * q^5 - 1320 * q^6 - 1677 * q^7 + 16896 * q^8 + 6468 * q^9 - 3000 * q^10 - 2523 * q^11 - 5376 * q^12 - 9924 * q^13 + 13416 * q^14 - 15084 * q^15 + 29478 * q^17 + 22848 * q^18 - 61731 * q^19 - 27264 * q^20 - 36372 * q^21 + 20184 * q^22 + 255234 * q^23 + 558999 * q^25 - 316368 * q^26 - 51597 * q^27 + 263424 * q^28 + 132153 * q^29 + 610632 * q^30 + 776898 * q^31 + 645795 * q^33 + 387840 * q^34 - 321081 * q^35 - 314688 * q^36 - 759795 * q^37 + 174504 * q^38 - 84012 * q^39 - 109056 * q^40 + 349287 * q^41 + 313752 * q^42 - 1043622 * q^43 + 255552 * q^44 + 845496 * q^45 - 524472 * q^46 + 1280709 * q^47 - 872448 * q^48 + 1011003 * q^49 - 1537704 * q^50 - 7812153 * q^51 - 635136 * q^52 - 2951976 * q^53 - 1256832 * q^54 + 2539854 * q^55 + 858624 * q^56 - 3973923 * q^57 - 47496 * q^58 + 639426 * q^59 - 94464 * q^60 + 1639350 * q^61 + 2859936 * q^62 + 6955635 * q^63 - 8650752 * q^64 - 4119567 * q^65 + 712512 * q^66 - 6408441 * q^67 - 1634496 * q^68 - 1007298 * q^69 + 2380872 * q^70 + 3531612 * q^71 + 6623232 * q^72 - 6666213 * q^73 + 7873368 * q^74 + 16535910 * q^75 - 1396032 * q^76 - 8256489 * q^77 - 4117104 * q^78 - 22540695 * q^79 - 3072000 * q^80 - 13134636 * q^81 + 3798096 * q^82 + 8663238 * q^83 + 8570304 * q^84 - 15143175 * q^85 + 8348976 * q^86 + 45908613 * q^87 + 11028480 * q^88 + 21718137 * q^89 - 27904392 * q^90 - 8606796 * q^91 - 8332800 * q^92 - 20412249 * q^93 - 10358784 * q^94 - 21603363 * q^95 - 5505024 * q^96 - 17397492 * q^97 + 44171448 * q^98 + 103927383 * q^99

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