LMFDB - Embedded newform 69.8.e.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,8,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, 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:	$21.5545667584$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$14$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	69.4
Dual form			69.8.e.a.52.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.02622 - 11.0059i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(-12.0443 + 13.8999i) q^{4} +(97.9555 + 62.9522i) q^{5} +(213.930 + 246.888i) q^{6} +(-58.9625 - 410.093i) q^{7} +(-1272.45 - 373.626i) q^{8} +(613.274 - 394.127i) q^{9} +O(q^{10})$	\(q+(-5.02622 - 11.0059i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(-12.0443 + 13.8999i) q^{4} +(97.9555 + 62.9522i) q^{5} +(213.930 + 246.888i) q^{6} +(-58.9625 - 410.093i) q^{7} +(-1272.45 - 373.626i) q^{8} +(613.274 - 394.127i) q^{9} +(200.498 - 1394.50i) q^{10} +(-1286.52 + 2817.08i) q^{11} +(206.291 - 451.714i) q^{12} +(-1394.02 + 9695.65i) q^{13} +(-4217.08 + 2710.15i) q^{14} +(-3016.53 - 885.732i) q^{15} +(2618.58 + 18212.6i) q^{16} +(5639.29 + 6508.08i) q^{17} +(-7420.16 - 4768.65i) q^{18} +(5523.96 - 6374.99i) q^{19} +(-2054.84 + 603.355i) q^{20} +(4646.99 + 10175.5i) q^{21} +37470.8 q^{22} +(50000.8 + 30079.0i) q^{23} +35806.7 q^{24} +(-26822.0 - 58732.0i) q^{25} +(113716. - 33390.0i) q^{26} +(-12889.6 + 14875.4i) q^{27} +(6410.42 + 4119.73i) q^{28} +(11678.1 + 13477.3i) q^{29} +(5413.46 + 37651.4i) q^{30} +(36107.8 + 10602.2i) q^{31} +(44481.6 - 28586.6i) q^{32} +(11900.0 - 82766.4i) q^{33} +(43282.9 - 94776.3i) q^{34} +(20040.6 - 43882.7i) q^{35} +(-1908.15 + 13271.4i) q^{36} +(441757. - 283900. i) q^{37} +(-97926.9 - 28753.9i) q^{38} +(-37638.6 - 261782. i) q^{39} +(-101123. - 116702. i) q^{40} +(419339. + 269493. i) q^{41} +(88633.4 - 102288. i) q^{42} +(121790. - 35760.7i) q^{43} +(-23661.9 - 51812.3i) q^{44} +84884.7 q^{45} +(79730.6 - 701486. i) q^{46} +194296. q^{47} +(-206377. - 451903. i) q^{48} +(625484. - 183659. i) q^{49} +(-511584. + 590399. i) q^{50} +(-195599. - 125704. i) q^{51} +(-117978. - 136154. i) q^{52} +(227988. + 1.58569e6i) q^{53} +(228503. + 67094.6i) q^{54} +(-303363. + 194959. i) q^{55} +(-78194.5 + 543855. i) q^{56} +(-94612.2 + 207172. i) q^{57} +(89632.6 - 196268. i) q^{58} +(-143123. + 995439. i) q^{59} +(48643.7 - 31261.4i) q^{60} +(407839. + 119752. i) q^{61} +(-64799.0 - 450687. i) q^{62} +(-197789. - 228261. i) q^{63} +(1.44312e6 + 927436. i) q^{64} +(-746914. + 861985. i) q^{65} +(-970729. + 285032. i) q^{66} +(-501260. - 1.09761e6i) q^{67} -158383. q^{68} +(-1.52414e6 - 398890. i) q^{69} -583696. q^{70} +(1.12187e6 + 2.45655e6i) q^{71} +(-927619. + 272374. i) q^{72} +(-2.63180e6 + 3.03726e6i) q^{73} +(-5.34493e6 - 3.43498e6i) q^{74} +(1.14162e6 + 1.31750e6i) q^{75} +(22079.3 + 153565. i) q^{76} +(1.23112e6 + 361490. i) q^{77} +(-2.69197e6 + 1.73002e6i) q^{78} +(537925. - 3.74135e6i) q^{79} +(-890021. + 1.94887e6i) q^{80} +(220769. - 483416. i) q^{81} +(858316. - 5.96972e6i) q^{82} +(-5.88751e6 + 3.78367e6i) q^{83} +(-197408. - 57964.3i) q^{84} +(142701. + 992508. i) q^{85} +(-1.00572e6 - 1.16066e6i) q^{86} +(-405056. - 260314. i) q^{87} +(2.68957e6 - 3.10393e6i) q^{88} +(1.73580e6 - 509676. i) q^{89} +(-426649. - 934230. i) q^{90} +4.05831e6 q^{91} +(-1.02032e6 + 332725. i) q^{92} -1.01607e6 q^{93} +(-976572. - 2.13839e6i) q^{94} +(942421. - 276720. i) q^{95} +(-934902. + 1.07893e6i) q^{96} +(-4.56782e6 - 2.93556e6i) q^{97} +(-5.16514e6 - 5.96089e6i) q^{98} +(321300. + 2.23469e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9}+O(q^{10}) $ 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9	\( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9} + 1322 q^{10} + 7892 q^{11} - 19980 q^{12} + 39810 q^{13} - 26296 q^{14} + 135 q^{15} - 142164 q^{16} - 97081 q^{17} - 11664 q^{18} + 120905 q^{19} + 124755 q^{20} + 26406 q^{21} - 837266 q^{22} - 224688 q^{23} - 60264 q^{24} - 180624 q^{25} + 385108 q^{26} - 275562 q^{27} + 1121760 q^{28} - 375654 q^{29} + 35694 q^{30} + 505029 q^{31} - 661528 q^{32} - 360423 q^{33} - 1872759 q^{34} - 964610 q^{35} - 1269189 q^{36} - 28802 q^{37} - 1459868 q^{38} + 1074870 q^{39} + 5371901 q^{40} - 1557480 q^{41} + 883116 q^{42} + 1160786 q^{43} - 4521825 q^{44} - 2009124 q^{45} - 4123580 q^{46} + 811422 q^{47} - 1563111 q^{48} - 10960262 q^{49} + 16636695 q^{50} + 4413852 q^{51} - 4843791 q^{52} + 4291672 q^{53} - 98415 q^{54} + 2093539 q^{55} - 12548382 q^{56} - 4007907 q^{57} - 7414367 q^{58} + 2955424 q^{59} + 7289973 q^{60} + 4919292 q^{61} + 16083211 q^{62} + 712962 q^{63} - 1673596 q^{64} - 13246221 q^{65} + 7219449 q^{66} + 148565 q^{67} - 23039568 q^{68} - 657018 q^{69} + 12781104 q^{70} - 7247645 q^{71} - 600696 q^{72} + 32596055 q^{73} + 32550658 q^{74} - 10061874 q^{75} + 12150569 q^{76} - 43349150 q^{77} - 17201700 q^{78} + 4815410 q^{79} + 36529590 q^{80} - 7440174 q^{81} + 20862470 q^{82} + 35160800 q^{83} - 5346540 q^{84} + 48578363 q^{85} + 76972708 q^{86} + 1505088 q^{87} - 35912212 q^{88} + 1401264 q^{89} + 963738 q^{90} - 91970208 q^{91} - 74293537 q^{92} + 555606 q^{93} - 32520253 q^{94} + 79436789 q^{95} + 41519736 q^{96} + 18296816 q^{97} - 38956823 q^{98} - 9731421 q^{99}+O(q^{100}) \) 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9 + 1322 * q^10 + 7892 * q^11 - 19980 * q^12 + 39810 * q^13 - 26296 * q^14 + 135 * q^15 - 142164 * q^16 - 97081 * q^17 - 11664 * q^18 + 120905 * q^19 + 124755 * q^20 + 26406 * q^21 - 837266 * q^22 - 224688 * q^23 - 60264 * q^24 - 180624 * q^25 + 385108 * q^26 - 275562 * q^27 + 1121760 * q^28 - 375654 * q^29 + 35694 * q^30 + 505029 * q^31 - 661528 * q^32 - 360423 * q^33 - 1872759 * q^34 - 964610 * q^35 - 1269189 * q^36 - 28802 * q^37 - 1459868 * q^38 + 1074870 * q^39 + 5371901 * q^40 - 1557480 * q^41 + 883116 * q^42 + 1160786 * q^43 - 4521825 * q^44 - 2009124 * q^45 - 4123580 * q^46 + 811422 * q^47 - 1563111 * q^48 - 10960262 * q^49 + 16636695 * q^50 + 4413852 * q^51 - 4843791 * q^52 + 4291672 * q^53 - 98415 * q^54 + 2093539 * q^55 - 12548382 * q^56 - 4007907 * q^57 - 7414367 * q^58 + 2955424 * q^59 + 7289973 * q^60 + 4919292 * q^61 + 16083211 * q^62 + 712962 * q^63 - 1673596 * q^64 - 13246221 * q^65 + 7219449 * q^66 + 148565 * q^67 - 23039568 * q^68 - 657018 * q^69 + 12781104 * q^70 - 7247645 * q^71 - 600696 * q^72 + 32596055 * q^73 + 32550658 * q^74 - 10061874 * q^75 + 12150569 * q^76 - 43349150 * q^77 - 17201700 * q^78 + 4815410 * q^79 + 36529590 * q^80 - 7440174 * q^81 + 20862470 * q^82 + 35160800 * q^83 - 5346540 * q^84 + 48578363 * q^85 + 76972708 * q^86 + 1505088 * q^87 - 35912212 * q^88 + 1401264 * q^89 + 963738 * q^90 - 91970208 * q^91 - 74293537 * q^92 + 555606 * q^93 - 32520253 * q^94 + 79436789 * q^95 + 41519736 * q^96 + 18296816 * q^97 - 38956823 * q^98 - 9731421 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

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 $

$2$	−5.02622	−	11.0059i	−0.444259	−	0.972791i	−0.990797	−	0.135357i	$-0.956782\pi$
$2$	−5.02622	−	11.0059i	−0.444259	−	0.972791i	0.546538	−	0.837434i	$-0.315945\pi$
$3$	−25.9063	+	7.60678i	−0.553964	+	0.162658i
$3$	−25.9063	+	7.60678i	−0.553964	+	0.162658i
$4$	−12.0443	+	13.8999i	−0.0940963	+	0.108593i
$5$	97.9555	+	62.9522i	0.350456	+	0.225224i	0.704011	−	0.710189i	$-0.251391\pi$
$5$	97.9555	+	62.9522i	0.350456	+	0.225224i	−0.353554	+	0.935414i	$0.615027\pi$
$6$	213.930	+	246.888i	0.404336	+	0.466629i
$7$	−58.9625	−	410.093i	−0.0649730	−	0.451897i	−0.996174	−	0.0873912i	$-0.972147\pi$
$7$	−58.9625	−	410.093i	−0.0649730	−	0.451897i	0.931201	−	0.364506i	$-0.118762\pi$
$8$	−1272.45	−	373.626i	−0.878673	−	0.258002i
$9$	613.274	−	394.127i	0.280418	−	0.180214i
$10$	200.498	−	1394.50i	0.0634032	−	0.440979i
$11$	−1286.52	+	2817.08i	−0.291435	+	0.638153i	−0.997551	−	0.0699428i	$-0.977718\pi$
$11$	−1286.52	+	2817.08i	−0.291435	+	0.638153i	0.706116	+	0.708096i	$0.250446\pi$
$12$	206.291	−	451.714i	0.0344624	−	0.0754621i
$13$	−1394.02	+	9695.65i	−0.175982	+	1.22398i	0.689964	+	0.723844i	$0.257626\pi$
$13$	−1394.02	+	9695.65i	−0.175982	+	1.22398i	−0.865946	+	0.500138i	$0.833283\pi$
$14$	−4217.08	+	2710.15i	−0.410737	+	0.263965i
$15$	−3016.53	−	885.732i	−0.230775	−	0.0677615i
$16$	2618.58	+	18212.6i	0.159826	+	1.11161i
$17$	5639.29	+	6508.08i	0.278390	+	0.321279i	0.877675	−	0.479257i	$-0.159094\pi$
$17$	5639.29	+	6508.08i	0.278390	+	0.321279i	−0.599285	+	0.800536i	$0.704548\pi$
$18$	−7420.16	−	4768.65i	−0.299888	−	0.192727i
$19$	5523.96	−	6374.99i	0.184762	−	0.213227i	−0.655811	−	0.754925i	$-0.727673\pi$
$19$	5523.96	−	6374.99i	0.184762	−	0.213227i	0.840573	+	0.541699i	$0.182219\pi$
$20$	−2054.84	+	603.355i	−0.0574344	+	0.0168643i
$21$	4646.99	+	10175.5i	0.109498	+	0.239766i
$22$	37470.8			0.750262
$23$	50000.8	+	30079.0i	0.856899	+	0.515484i
$23$	50000.8	+	30079.0i	0.856899	+	0.515484i
$24$	35806.7			0.528719
$25$	−26822.0	−	58732.0i	−0.343322	−	0.751769i
$26$	113716.	−	33390.0i	1.26886	−	0.372571i
$27$	−12889.6	+	14875.4i	−0.126028	+	0.145444i
$28$	6410.42	+	4119.73i	0.0551866	+	0.0354663i
$29$	11678.1	+	13477.3i	0.0889162	+	0.102615i	0.798464	−	0.602042i	$-0.205646\pi$
$29$	11678.1	+	13477.3i	0.0889162	+	0.102615i	−0.709548	+	0.704657i	$0.751101\pi$
$30$	5413.46	+	37651.4i	0.0366058	+	0.254599i
$31$	36107.8	+	10602.2i	0.217688	+	0.0639191i	0.388758	−	0.921340i	$-0.372904\pi$
$31$	36107.8	+	10602.2i	0.217688	+	0.0639191i	−0.171070	+	0.985259i	$0.554722\pi$
$32$	44481.6	−	28586.6i	0.239969	−	0.154219i
$33$	11900.0	−	82766.4i	0.0576433	−	0.400918i
$34$	43282.9	−	94776.3i	0.188860	−	0.413546i
$35$	20040.6	−	43882.7i	0.0790081	−	0.173004i
$36$	−1908.15	+	13271.4i	−0.00681636	+	0.0474088i
$37$	441757.	−	283900.i	1.43376	−	0.921423i	0.433972	−	0.900926i	$-0.357112\pi$
$37$	441757.	−	283900.i	1.43376	−	0.921423i	0.999790	−	0.0204964i	$-0.00652467\pi$
$38$	−97926.9	−	28753.9i	−0.289507	−	0.0850070i
$39$	−37638.6	−	261782.i	−0.101603	−	0.706666i
$40$	−101123.	−	116702.i	−0.249828	−	0.288317i
$41$	419339.	+	269493.i	0.950214	+	0.610666i	0.921273	−	0.388916i	$-0.127150\pi$
$41$	419339.	+	269493.i	0.950214	+	0.610666i	0.0289408	+	0.999581i	$0.490787\pi$
$42$	88633.4	−	102288.i	0.184597	−	0.213036i
$43$	121790.	−	35760.7i	0.233599	−	0.0685909i	−0.162838	−	0.986653i	$-0.552065\pi$
$43$	121790.	−	35760.7i	0.233599	−	0.0685909i	0.396437	+	0.918062i	$0.370247\pi$
$44$	−23661.9	−	51812.3i	−0.0418760	−	0.0916956i
$45$	84884.7			0.138863
$46$	79730.6	−	701486.i	0.120774	−	1.06259i
$47$	194296.			0.272974			0.136487	−	0.990642i	$-0.456419\pi$
$47$	194296.			0.272974			0.136487	+	0.990642i	$0.456419\pi$
$48$	−206377.	−	451903.i	−0.269350	−	0.589795i
$49$	625484.	−	183659.i	0.759503	−	0.223010i
$50$	−511584.	+	590399.i	−0.578791	+	0.667961i
$51$	−195599.	−	125704.i	−0.206476	−	0.132694i
$52$	−117978.	−	136154.i	−0.116357	−	0.134283i
$53$	227988.	+	1.58569e6i	0.210352	+	1.46303i	0.771984	+	0.635642i	$0.219265\pi$
$53$	227988.	+	1.58569e6i	0.210352	+	1.46303i	−0.561632	+	0.827387i	$0.689826\pi$
$54$	228503.	+	67094.6i	0.197476	+	0.0579841i
$55$	−303363.	+	194959.i	−0.245863	+	0.158006i
$56$	−78194.5	+	543855.i	−0.0595002	+	0.413833i
$57$	−94612.2	+	207172.i	−0.0676683	+	0.148173i
$58$	89632.6	−	196268.i	0.0603209	−	0.132084i
$59$	−143123.	+	995439.i	−0.0907248	+	0.631005i	0.892830	+	0.450394i	$0.148717\pi$
$59$	−143123.	+	995439.i	−0.0907248	+	0.631005i	−0.983555	+	0.180611i	$0.942193\pi$
$60$	48643.7	−	31261.4i	0.0290735	−	0.0186844i
$61$	407839.	+	119752.i	0.230056	+	0.0675507i	0.394729	−	0.918798i	$-0.370839\pi$
$61$	407839.	+	119752.i	0.230056	+	0.0675507i	−0.164672	+	0.986348i	$0.552657\pi$
$62$	−64799.0	−	450687.i	−0.0345301	−	0.240162i
$63$	−197789.	−	228261.i	−0.0996576	−	0.115011i
$64$	1.44312e6	+	927436.i	0.688132	+	0.442236i
$65$	−746914.	+	861985.i	−0.337345	+	0.389316i
$66$	−970729.	+	285032.i	−0.415618	+	0.122036i
$67$	−501260.	−	1.09761e6i	−0.203611	−	0.445846i	0.780088	−	0.625670i	$-0.215174\pi$
$67$	−501260.	−	1.09761e6i	−0.203611	−	0.445846i	−0.983699	+	0.179824i	$0.942447\pi$
$68$	−158383.			−0.0610840
$69$	−1.52414e6	−	398890.i	−0.558539	−	0.146178i
$70$	−583696.			−0.203396
$71$	1.12187e6	+	2.45655e6i	0.371996	+	0.814558i	0.999358	+	0.0358303i	$0.0114076\pi$
$71$	1.12187e6	+	2.45655e6i	0.371996	+	0.814558i	−0.627362	+	0.778728i	$0.715865\pi$
$72$	−927619.	+	272374.i	−0.292891	+	0.0860006i
$73$	−2.63180e6	+	3.03726e6i	−0.791813	+	0.913800i	−0.997903	−	0.0647326i	$-0.979381\pi$
$73$	−2.63180e6	+	3.03726e6i	−0.791813	+	0.913800i	0.206090	+	0.978533i	$0.433926\pi$
$74$	−5.34493e6	−	3.43498e6i	−1.53331	−	0.985401i
$75$	1.14162e6	+	1.31750e6i	0.312469	+	0.360609i
$76$	22079.3	+	153565.i	0.00576949	+	0.0401277i
$77$	1.23112e6	+	361490.i	0.307315	+	0.0902358i
$78$	−2.69197e6	+	1.73002e6i	−0.642301	+	0.412782i
$79$	537925.	−	3.74135e6i	0.122751	−	0.853755i	−0.831665	−	0.555277i	$-0.812612\pi$
$79$	537925.	−	3.74135e6i	0.122751	−	0.853755i	0.954417	−	0.298478i	$-0.0964788\pi$
$80$	−890021.	+	1.94887e6i	−0.194350	+	0.425568i
$81$	220769.	−	483416.i	0.0461572	−	0.101070i
$82$	858316.	−	5.96972e6i	0.171909	−	1.19565i
$83$	−5.88751e6	+	3.78367e6i	−1.13021	+	0.726341i	−0.965603	−	0.260019i	$-0.916271\pi$
$83$	−5.88751e6	+	3.78367e6i	−1.13021	+	0.726341i	−0.164604	+	0.986360i	$0.552635\pi$
$84$	−197408.	−	57964.3i	−0.0363402	−	0.0106705i
$85$	142701.	+	992508.i	0.0252035	+	0.175294i
$86$	−1.00572e6	−	1.16066e6i	−0.170503	−	0.196771i
$87$	−405056.	−	260314.i	−0.0659475	−	0.0423819i
$88$	2.68957e6	−	3.10393e6i	0.420720	−	0.485537i
$89$	1.73580e6	−	509676.i	0.260996	−	0.0766353i	−0.148617	−	0.988895i	$-0.547482\pi$
$89$	1.73580e6	−	509676.i	0.260996	−	0.0766353i	0.409613	+	0.912260i	$0.365664\pi$
$90$	−426649.	−	934230.i	−0.0616910	−	0.135084i
$91$	4.05831e6			0.564548
$92$	−1.02032e6	+	332725.i	−0.136609	+	0.0445480i
$93$	−1.01607e6			−0.130988
$94$	−976572.	−	2.13839e6i	−0.121271	−	0.265546i
$95$	942421.	−	276720.i	0.112775	−	0.0331137i
$96$	−934902.	+	1.07893e6i	−0.107849	+	0.124465i
$97$	−4.56782e6	−	2.93556e6i	−0.508169	−	0.326580i	0.261308	−	0.965256i	$-0.415846\pi$
$97$	−4.56782e6	−	2.93556e6i	−0.508169	−	0.326580i	−0.769476	+	0.638675i	$0.779483\pi$
$98$	−5.16514e6	−	5.96089e6i	−0.554359	−	0.639764i
$99$	321300.	+	2.23469e6i	0.0332804	+	0.231470i
$100$	1.13942e6	+	334564.i	0.113942	+	0.0334564i
$101$	−2.36896e6	+	1.52244e6i	−0.228788	+	0.147033i	−0.650013	−	0.759923i	$-0.725237\pi$
$101$	−2.36896e6	+	1.52244e6i	−0.228788	+	0.147033i	0.421225	+	0.906956i	$0.361600\pi$
$102$	−400358.	+	2.78455e6i	−0.0373549	+	0.259809i
$103$	1.21427e6	−	2.65888e6i	0.109493	−	0.239756i	−0.846952	−	0.531670i	$-0.821565\pi$
$103$	1.21427e6	−	2.65888e6i	0.109493	−	0.239756i	0.956445	+	0.291914i	$0.0942921\pi$
$104$	5.39638e6	−	1.18164e7i	0.470420	−	1.03008i
$105$	−185371.	+	1.28928e6i	−0.0156271	+	0.108689i
$106$	1.63060e7	−	1.04792e7i	1.32977	−	0.854592i
$107$	−1.06808e7	−	3.13616e6i	−0.842867	−	0.247488i	−0.168332	−	0.985730i	$-0.553838\pi$
$107$	−1.06808e7	−	3.13616e6i	−0.842867	−	0.247488i	−0.674536	+	0.738242i	$0.735656\pi$
$108$	−51519.9	−	358329.i	−0.00393543	−	0.0273715i
$109$	1.65922e7	+	1.91484e7i	1.22719	+	1.41625i	0.877634	+	0.479331i	$0.159121\pi$
$109$	1.65922e7	+	1.91484e7i	1.22719	+	1.41625i	0.349552	+	0.936917i	$0.386334\pi$
$110$	3.67047e6	+	2.35887e6i	0.262934	+	0.168977i
$111$	−9.28472e6	+	1.07151e7i	−0.644375	+	0.743648i
$112$	7.31449e6	−	2.14773e6i	0.491950	−	0.144449i
$113$	6.08491e6	+	1.33241e7i	0.396716	+	0.868687i	0.997593	+	0.0693454i	$0.0220911\pi$
$113$	6.08491e6	+	1.33241e7i	0.396716	+	0.868687i	−0.600877	+	0.799342i	$0.705182\pi$
$114$	2.75565e6			0.174204
$115$	3.00432e6	+	6.09406e6i	0.184206	+	0.373649i
$116$	−327989.			−0.0195099
$117$	2.96640e6	+	6.49551e6i	0.171230	+	0.374941i
$118$	1.16750e7	−	3.42810e6i	0.654141	−	0.192073i
$119$	2.33642e6	−	2.69637e6i	0.127097	−	0.146678i
$120$	3.50746e6	+	2.25411e6i	0.185293	+	0.119080i
$121$	6.48057e6	+	7.47897e6i	0.332556	+	0.383790i
$122$	−731908.	−	5.09053e6i	−0.0364919	−	0.253807i
$123$	−1.29135e7	−	3.79174e6i	−0.625714	−	0.183726i
$124$	−582264.	+	374198.i	−0.0274248	+	0.0176249i
$125$	2.36456e6	−	1.64459e7i	0.108284	−	0.753134i
$126$	−1.51808e6	+	3.32413e6i	−0.0676079	+	0.148041i
$127$	1.48014e6	−	3.24105e6i	0.0641194	−	0.140402i	−0.874859	−	0.484377i	$-0.839046\pi$
$127$	1.48014e6	−	3.24105e6i	0.0641194	−	0.140402i	0.938979	+	0.343975i	$0.111774\pi$
$128$	3.91701e6	−	2.72434e7i	0.165090	−	1.14822i
$129$	−2.88310e6	+	1.85286e6i	−0.118249	+	0.0759938i
$130$	1.32410e7	+	3.88792e6i	0.528592	+	0.155209i
$131$	4.83583e6	+	3.36339e7i	0.187941	+	1.30716i	0.837328	+	0.546700i	$0.184116\pi$
$131$	4.83583e6	+	3.36339e7i	0.187941	+	1.30716i	−0.649387	+	0.760458i	$0.724975\pi$
$132$	1.00712e6	+	1.16228e6i	0.0381128	+	0.0439846i
$133$	−2.94005e6	−	1.88945e6i	−0.108361	−	0.0696394i
$134$	−9.56068e6	+	1.10336e7i	−0.343259	+	0.396142i
$135$	−2.19905e6	+	645699.i	−0.0769249	+	0.0225872i
$136$	−4.74414e6	−	1.03882e7i	−0.161723	−	0.354124i
$137$	−9.57343e6			−0.318087			−0.159043	−	0.987272i	$-0.550841\pi$
$137$	−9.57343e6			−0.318087			−0.159043	+	0.987272i	$0.550841\pi$
$138$	3.27053e6	+	1.87794e7i	0.105935	+	0.608282i
$139$	3.82694e6			0.120865			0.0604324	−	0.998172i	$-0.480752\pi$
$139$	3.82694e6			0.120865			0.0604324	+	0.998172i	$0.480752\pi$
$140$	368590.	+	807100.i	0.0113526	+	0.0248587i
$141$	−5.03348e6	+	1.47796e6i	−0.151217	+	0.0444014i
$142$	2.13978e7	−	2.46944e7i	0.627133	−	0.723750i
$143$	−2.55200e7	−	1.64007e7i	−0.729801	−	0.469014i
$144$	8.78401e6	+	1.01373e7i	0.245145	+	0.282913i
$145$	295513.	+	2.05534e6i	0.00804987	+	0.0559881i
$146$	4.66556e7	+	1.36993e7i	1.24071	+	0.364304i
$147$	−1.48069e7	+	9.51583e6i	−0.384463	+	0.247079i
$148$	−1.37449e6	+	9.55976e6i	−0.0348517	+	0.242399i
$149$	1.08141e7	−	2.36796e7i	0.267817	−	0.586438i	−0.727168	−	0.686460i	$-0.759164\pi$
$149$	1.08141e7	−	2.36796e7i	0.267817	−	0.586438i	0.994985	+	0.100021i	$0.0318912\pi$
$150$	8.76221e6	−	1.91866e7i	0.211980	−	0.464171i
$151$	9.94408e6	−	6.91626e7i	0.235042	−	1.63475i	−0.440729	−	0.897640i	$-0.645280\pi$
$151$	9.94408e6	−	6.91626e7i	0.235042	−	1.63475i	0.675771	−	0.737112i	$-0.263811\pi$
$152$	−9.41085e6	+	6.04798e6i	−0.217358	+	0.139688i
$153$	6.02344e6	+	1.76864e6i	0.135964	+	0.0399227i
$154$	−2.20937e6	−	1.53665e7i	−0.0487468	−	0.339041i
$155$	2.86952e6	+	3.31161e6i	0.0618941	+	0.0714296i
$156$	4.09208e6	+	2.62982e6i	0.0862995	+	0.0554613i
$157$	−2.28306e7	+	2.63479e7i	−0.470835	+	0.543373i	−0.940644	−	0.339395i	$-0.889778\pi$
$157$	−2.28306e7	+	2.63479e7i	−0.470835	+	0.543373i	0.469808	+	0.882768i	$0.344323\pi$
$158$	−4.38805e7	+	1.28845e7i	−0.885059	+	0.259877i
$159$	−1.79683e7	−	3.93452e7i	−0.354501	−	0.776250i
$160$	6.15680e6			0.118833
$161$	9.38701e6	−	2.22785e7i	0.177271	−	0.420723i
$162$	−6.43005e6			−0.118826
$163$	1.35588e6	+	2.96896e6i	0.0245225	+	0.0536968i	0.921497	−	0.388386i	$-0.126967\pi$
$163$	1.35588e6	+	2.96896e6i	0.0245225	+	0.0536968i	−0.896974	+	0.442082i	$0.854240\pi$
$164$	−8.79658e6	+	2.58291e6i	−0.155726	+	0.0457252i
$165$	6.37600e6	−	7.35829e6i	0.110498	−	0.127521i
$166$	7.12345e7	+	4.57797e7i	1.20868	+	0.776773i
$167$	−7.19078e6	−	8.29861e6i	−0.119473	−	0.137879i	0.692862	−	0.721070i	$-0.256349\pi$
$167$	−7.19078e6	−	8.29861e6i	−0.119473	−	0.137879i	−0.812335	+	0.583191i	$0.801804\pi$
$168$	−2.11125e6	−	1.46841e7i	−0.0343525	−	0.238927i
$169$	−3.18555e7	−	9.35361e6i	−0.507669	−	0.149065i
$170$	1.02062e7	−	6.55911e6i	0.159328	−	0.102394i
$171$	875143.	−	6.08675e6i	0.0133842	−	0.0930892i
$172$	−969807.	+	2.12358e6i	−0.0145323	+	0.0318214i
$173$	−3.53713e7	+	7.74523e7i	−0.519385	+	1.13729i	0.450287	+	0.892884i	$0.351322\pi$
$173$	−3.53713e7	+	7.74523e7i	−0.519385	+	1.13729i	−0.969672	+	0.244410i	$0.921406\pi$
$174$	−829083.	+	5.76640e6i	−0.0119310	+	0.0829817i
$175$	−2.25041e7	+	1.44625e7i	−0.317416	+	0.203991i
$176$	−5.46753e7	−	1.60541e7i	−0.755957	−	0.221969i
$177$	−3.86431e6	−	2.68769e7i	−0.0523800	−	0.364311i
$178$	−1.43339e7	−	1.65422e7i	−0.190500	−	0.219849i
$179$	4.14281e7	+	2.66242e7i	0.539895	+	0.346969i	0.781998	−	0.623281i	$-0.214201\pi$
$179$	4.14281e7	+	2.66242e7i	0.539895	+	0.346969i	−0.242103	+	0.970251i	$0.577837\pi$
$180$	−1.02238e6	+	1.17989e6i	−0.0130665	+	0.0150795i
$181$	−9.60379e7	+	2.81993e7i	−1.20384	+	0.353479i	−0.821319	−	0.570469i	$-0.806761\pi$
$181$	−9.60379e7	+	2.81993e7i	−1.20384	+	0.353479i	−0.382518	+	0.923948i	$0.624943\pi$
$182$	−2.03980e7	−	4.46653e7i	−0.250805	−	0.549187i
$183$	−1.14765e7			−0.138431
$184$	−5.23855e7	−	5.69557e7i	−0.619938	−	0.674024i
$185$	6.11446e7			0.709998
$186$	5.10698e6	+	1.11827e7i	0.0581928	+	0.127424i
$187$	−2.55888e7	+	7.51356e6i	−0.286157	+	0.0840234i
$188$	−2.34016e6	+	2.70069e6i	−0.0256858	+	0.0296430i
$189$	6.86032e6	+	4.40886e6i	0.0739142	+	0.0475018i
$190$	−7.78235e6	−	8.98132e6i	−0.0823139	−	0.0949954i
$191$	1.36532e7	+	9.49599e7i	0.141781	+	0.986106i	0.929171	+	0.369651i	$0.120523\pi$
$191$	1.36532e7	+	9.49599e7i	0.141781	+	0.986106i	−0.787390	+	0.616455i	$0.788568\pi$
$192$	−4.44407e7	−	1.30490e7i	−0.453134	−	0.133052i
$193$	−9.38288e7	+	6.03001e7i	−0.939476	+	0.603764i	−0.918246	−	0.396010i	$-0.870394\pi$
$193$	−9.38288e7	+	6.03001e7i	−0.939476	+	0.603764i	−0.0212297	+	0.999775i	$0.506758\pi$
$194$	−9.34956e6	+	6.50276e7i	−0.0919359	+	0.639428i
$195$	1.27929e7	−	2.80125e7i	0.123551	−	0.270539i
$196$	−4.98070e6	+	1.09062e7i	−0.0472491	+	0.103461i
$197$	−2.15258e7	+	1.49715e8i	−0.200598	+	1.39519i	0.601916	+	0.798560i	$0.294404\pi$
$197$	−2.15258e7	+	1.49715e8i	−0.200598	+	1.39519i	−0.802514	+	0.596633i	$0.796505\pi$
$198$	2.29798e7	−	1.47682e7i	0.210387	−	0.135207i
$199$	−8.78839e7	−	2.58051e7i	−0.790540	−	0.232123i	−0.138554	−	0.990355i	$-0.544246\pi$
$199$	−8.78839e7	−	2.58051e7i	−0.790540	−	0.232123i	−0.651986	+	0.758231i	$0.726064\pi$
$200$	1.21860e7	+	8.47552e7i	0.107710	+	0.749137i
$201$	2.13351e7	+	2.46220e7i	0.185314	+	0.213863i
$202$	2.86627e7	+	1.84204e7i	0.244673	+	0.157242i
$203$	4.83838e6	−	5.58379e6i	0.0405942	−	0.0468482i
$204$	4.10312e6	−	1.20479e6i	0.0338383	−	0.00993583i
$205$	2.41114e7	+	5.27966e7i	0.195472	+	0.428023i
$206$	−3.53665e7			−0.281876
$207$	4.25191e7	−	1.26003e6i	0.333187	−	0.00987383i
$208$	−1.80234e8			−1.38872
$209$	1.08522e7	+	2.37630e7i	0.0822252	+	0.180048i
$210$	1.51214e7	−	4.44005e6i	0.112674	−	0.0330841i
$211$	2.98438e7	−	3.44415e7i	0.218708	−	0.252403i	−0.635784	−	0.771867i	$-0.719323\pi$
$211$	2.98438e7	−	3.44415e7i	0.218708	−	0.252403i	0.854492	+	0.519464i	$0.173869\pi$
$212$	−2.47869e7	−	1.59296e7i	−0.178668	−	0.114823i
$213$	−4.77500e7	−	5.51064e7i	−0.338567	−	0.390727i
$214$	1.91677e7	+	1.33314e8i	0.133697	+	0.929883i
$215$	1.41812e7	+	4.16397e6i	0.0973147	+	0.0285742i
$216$	2.19593e7	−	1.41124e7i	0.148262	−	0.0952823i
$217$	2.21889e6	−	1.54327e7i	0.0147410	−	0.102526i
$218$	1.27349e8	−	2.78855e8i	0.832526	−	1.82298i
$219$	4.50764e7	−	9.87036e7i	0.289998	−	0.635007i
$220$	943885.	−	6.56487e6i	0.00597640	−	0.0415668i
$221$	−7.09614e7	+	4.56041e7i	−0.442231	+	0.284204i
$222$	1.64597e8	+	4.83299e7i	1.00968	+	0.296470i
$223$	5.13399e6	+	3.57077e7i	0.0310019	+	0.215623i	0.999433	−	0.0336568i	$-0.0107153\pi$
$223$	5.13399e6	+	3.57077e7i	0.0310019	+	0.215623i	−0.968432	+	0.249279i	$0.919806\pi$
$224$	−1.43459e7	−	1.65561e7i	−0.0852826	−	0.0984213i
$225$	−3.95971e7	−	2.54475e7i	−0.231753	−	0.148938i
$226$	1.16059e8	−	1.33940e8i	0.668807	−	0.771844i
$227$	−4.66992e7	+	1.37121e7i	−0.264984	+	0.0778063i	−0.411526	−	0.911398i	$-0.635004\pi$
$227$	−4.66992e7	+	1.37121e7i	−0.264984	+	0.0778063i	0.146542	+	0.989204i	$0.453186\pi$
$228$	−1.74013e6	−	3.81035e6i	−0.00972320	−	0.0212908i
$229$	2.35703e8			1.29700			0.648501	−	0.761214i	$-0.275396\pi$
$229$	2.35703e8			1.29700			0.648501	+	0.761214i	$0.275396\pi$
$230$	5.19701e7	−	6.36952e7i	0.281648	−	0.345191i
$231$	−3.46436e7			−0.184919
$232$	−9.82443e6	−	2.15125e7i	−0.0516535	−	0.113105i
$233$	2.40342e8	−	7.05708e7i	1.24476	−	0.365493i	0.407956	−	0.913002i	$-0.366242\pi$
$233$	2.40342e8	−	7.05708e7i	1.24476	−	0.365493i	0.836800	+	0.547508i	$0.184424\pi$
$234$	5.65790e7	−	6.52957e7i	0.288669	−	0.333142i
$235$	1.90323e7	+	1.22313e7i	0.0956653	+	0.0614803i
$236$	−1.21127e7	−	1.39788e7i	−0.0599858	−	0.0692273i
$237$	1.45240e7	+	1.01016e8i	0.0708706	+	0.492916i
$238$	−4.14192e7	−	1.21618e7i	−0.199151	−	0.0584760i
$239$	3.17115e8	−	2.03798e8i	1.50254	−	0.965621i	0.507984	−	0.861366i	$-0.330391\pi$
$239$	3.17115e8	−	2.03798e8i	1.50254	−	0.965621i	0.994551	−	0.104254i	$-0.0332456\pi$
$240$	8.23250e6	−	5.72583e7i	0.0384408	−	0.267362i
$241$	−8.97154e7	+	1.96449e8i	−0.412864	+	0.904047i	0.582938	+	0.812517i	$0.301903\pi$
$241$	−8.97154e7	+	1.96449e8i	−0.412864	+	0.904047i	−0.995802	+	0.0915300i	$0.970824\pi$
$242$	4.97399e7	−	1.08915e8i	0.225606	−	0.494009i
$243$	−2.04206e6	+	1.42029e7i	−0.00912950	+	0.0634971i
$244$	−6.57670e6	+	4.22659e6i	−0.0289830	+	0.0186262i
$245$	7.28313e7	+	2.13852e7i	0.316400	+	0.0929034i
$246$	2.31745e7	+	1.61182e8i	0.0992517	+	0.690311i
$247$	5.41091e7	+	6.24452e7i	0.228471	+	0.263669i
$248$	−4.19843e7	−	2.69817e7i	−0.174786	−	0.112328i
$249$	1.23742e8	−	1.42806e8i	0.507949	−	0.586204i
$250$	−1.92886e8	+	5.66365e7i	−0.780749	+	0.229249i
$251$	−4.25060e7	−	9.30751e7i	−0.169665	−	0.371514i	0.805631	−	0.592418i	$-0.201827\pi$
$251$	−4.25060e7	−	9.30751e7i	−0.169665	−	0.371514i	−0.975296	+	0.220904i	$0.929099\pi$
$252$	5.55504e6			0.0218668
$253$	−1.49062e8	+	1.02159e8i	−0.578688	+	0.396603i
$254$	−4.31101e7			−0.165067
$255$	−1.12466e7	−	2.46267e7i	−0.0424749	−	0.0930070i
$256$	−1.08844e8	+	3.19595e7i	−0.405476	+	0.119058i
$257$	2.05455e8	−	2.37108e8i	0.755007	−	0.871325i	−0.240036	−	0.970764i	$-0.577159\pi$
$257$	2.05455e8	−	2.37108e8i	0.755007	−	0.871325i	0.995044	+	0.0994390i	$0.0317048\pi$
$258$	3.48834e7	+	2.24182e7i	0.126459	+	0.0812703i
$259$	−1.42472e8	−	1.64422e8i	−0.509544	−	0.588045i
$260$	−2.98542e6	−	2.07641e7i	−0.0105341	−	0.0732665i
$261$	1.24737e7	+	3.66260e6i	0.0434263	+	0.0127511i
$262$	3.45865e8	−	2.22274e8i	1.18810	−	0.763544i
$263$	4.00091e7	−	2.78269e8i	0.135617	−	0.943235i	−0.802435	−	0.596740i	$-0.796463\pi$
$263$	4.00091e7	−	2.78269e8i	0.135617	−	0.943235i	0.938052	−	0.346495i	$-0.112628\pi$
$264$	−4.60659e7	+	1.00870e8i	−0.154087	+	0.337404i
$265$	−7.74900e7	+	1.69679e8i	−0.255791	+	0.560104i
$266$	−6.01778e6	+	4.18546e7i	−0.0196043	+	0.136351i
$267$	−4.10911e7	+	2.64076e7i	−0.132117	+	0.0849063i
$268$	2.12940e7	+	6.25247e6i	0.0675748	+	0.0198418i
$269$	−2.18577e7	−	1.52023e8i	−0.0684653	−	0.476187i	−0.994992	−	0.0999571i	$-0.968129\pi$
$269$	−2.18577e7	−	1.52023e8i	−0.0684653	−	0.476187i	0.926526	−	0.376230i	$-0.122780\pi$
$270$	1.81594e7	+	2.09570e7i	0.0561472	+	0.0647973i
$271$	−1.11510e8	−	7.16629e7i	−0.340345	−	0.218727i	0.359291	−	0.933225i	$-0.383018\pi$
$271$	−1.11510e8	−	7.16629e7i	−0.340345	−	0.218727i	−0.699637	+	0.714499i	$0.746655\pi$
$272$	−1.03762e8	+	1.19748e8i	−0.312643	+	0.360810i
$273$	−1.05136e8	+	3.08707e7i	−0.312739	+	0.0918285i
$274$	4.81181e7	+	1.05364e8i	0.141313	+	0.309432i
$275$	1.99960e8			0.579800
$276$	2.39018e7	−	1.63810e7i	0.0684303	−	0.0468986i
$277$	8.24240e7			0.233010			0.116505	−	0.993190i	$-0.462831\pi$
$277$	8.24240e7			0.233010			0.116505	+	0.993190i	$0.462831\pi$
$278$	−1.92350e7	−	4.21189e7i	−0.0536953	−	0.117576i
$279$	2.63226e7	−	7.72901e6i	0.0725628	−	0.0213064i
$280$	−4.18964e7	+	4.83511e7i	−0.114058	+	0.131629i
$281$	−2.20834e8	−	1.41921e8i	−0.593736	−	0.381571i	0.208991	−	0.977918i	$-0.432982\pi$
$281$	−2.20834e8	−	1.41921e8i	−0.593736	−	0.381571i	−0.802727	+	0.596347i	$0.796618\pi$
$282$	4.15657e7	+	4.79694e7i	0.110373	+	0.127377i
$283$	1.05617e8	+	7.34581e8i	0.277001	+	1.92658i	0.366136	+	0.930561i	$0.380680\pi$
$283$	1.05617e8	+	7.34581e8i	0.277001	+	1.92658i	−0.0891355	+	0.996020i	$0.528410\pi$
$284$	−4.76581e7	−	1.39937e7i	−0.123459	−	0.0362508i
$285$	−2.23097e7	+	1.43376e7i	−0.0570869	+	0.0366875i
$286$	−5.22351e7	+	3.63303e8i	−0.132033	+	0.918308i
$287$	8.57919e7	−	1.87858e8i	0.214220	−	0.469076i
$288$	1.60126e7	−	3.50628e7i	0.0394993	−	0.0864914i
$289$	4.78437e7	−	3.32760e8i	0.116596	−	0.810940i
$290$	2.11355e7	−	1.35830e7i	0.0508885	−	0.0327040i
$291$	1.40665e8	+	4.13031e7i	0.334628	+	0.0982556i
$292$	−1.05193e7	−	7.31634e7i	−0.0247256	−	0.171971i
$293$	3.36053e8	+	3.87826e8i	0.780497	+	0.900741i	0.997145	−	0.0755085i	$-0.0240580\pi$
$293$	3.36053e8	+	3.87826e8i	0.780497	+	0.900741i	−0.216648	+	0.976250i	$0.569513\pi$
$294$	1.79153e8	+	1.15135e8i	0.411157	+	0.264235i
$295$	−7.66847e7	+	8.84988e7i	−0.173913	+	0.200706i
$296$	−6.68188e8	+	1.96198e8i	−1.49754	+	0.439716i
$297$	−2.53225e7	−	5.54486e7i	−0.0560866	−	0.122813i
$298$	−3.14969e8			−0.689462
$299$	−3.61337e8	+	4.42859e8i	−0.781742	+	0.958113i
$300$	−3.20632e7			−0.0685618
$301$	−2.18463e7	−	4.78367e7i	−0.0461737	−	0.101106i
$302$	−8.11176e8	+	2.38183e8i	−1.69469	+	0.497606i
$303$	4.97901e7	−	5.74609e7i	0.102824	−	0.118665i
$304$	1.30570e8	+	8.39124e7i	0.266555	+	0.171305i
$305$	3.24114e7	+	3.74048e7i	0.0654106	+	0.0754879i
$306$	−1.08097e7	−	7.51828e7i	−0.0215669	−	0.150001i
$307$	−5.91780e8	−	1.73762e8i	−1.16728	−	0.342745i	−0.360024	−	0.932943i	$-0.617231\pi$
$307$	−5.91780e8	−	1.73762e8i	−1.16728	−	0.342745i	−0.807258	+	0.590198i	$0.799050\pi$
$308$	−1.98527e7	+	1.27586e7i	−0.0387162	+	0.0248814i
$309$	−1.12318e7	+	7.81186e7i	−0.0216567	+	0.150626i
$310$	2.20243e7	−	4.82265e7i	0.0419891	−	0.0919432i
$311$	285404.	−	624947.i	0.000538020	−	0.00117810i	−0.909363	−	0.416004i	$-0.863430\pi$
$311$	285404.	−	624947.i	0.000538020	−	0.00117810i	0.909901	+	0.414826i	$0.136158\pi$
$312$	−4.99154e7	+	3.47169e8i	−0.0930450	+	0.647142i
$313$	2.01487e8	−	1.29488e8i	0.371400	−	0.238684i	−0.341604	−	0.939844i	$-0.610970\pi$
$313$	2.01487e8	−	1.29488e8i	0.371400	−	0.238684i	0.713004	+	0.701159i	$0.247334\pi$
$314$	4.04734e8	+	1.18841e8i	0.737761	+	0.216626i
$315$	−5.00501e6	−	3.48106e7i	−0.00902232	−	0.0627516i
$316$	4.55254e7	+	5.25391e7i	0.0811613	+	0.0936652i
$317$	9.77098e7	+	6.27943e7i	0.172278	+	0.110717i	0.623938	−	0.781474i	$-0.285532\pi$
$317$	9.77098e7	+	6.27943e7i	0.172278	+	0.110717i	−0.451660	+	0.892190i	$0.649168\pi$
$318$	−3.42715e8	+	3.95515e8i	−0.597638	+	0.689712i
$319$	−5.29908e7	+	1.55595e7i	−0.0913972	+	0.0268366i
$320$	8.29772e7	+	1.81695e8i	0.141558	+	0.309968i
$321$	3.00555e8			0.507174
$322$	−2.92376e8	+	8.66442e6i	−0.488030	+	0.0144625i
$323$	7.26401e7			0.119941
$324$	4.06042e6	+	8.89108e6i	0.00663229	+	0.0145227i
$325$	6.06835e8	−	1.78183e8i	0.980571	−	0.287922i
$326$	2.58611e7	−	2.98453e7i	0.0413414	−	0.0477105i
$327$	−5.75499e8	−	3.69851e8i	−0.910181	−	0.584938i
$328$	−4.32900e8	−	4.99593e8i	−0.677375	−	0.781732i
$329$	−1.14562e7	−	7.96794e7i	−0.0177359	−	0.123356i
$330$	−1.13032e8	−	3.31891e7i	−0.173141	−	0.0508389i
$331$	4.23188e8	−	2.71966e8i	0.641409	−	0.412209i	−0.179109	−	0.983829i	$-0.557321\pi$
$331$	4.23188e8	−	2.71966e8i	0.641409	−	0.412209i	0.820518	+	0.571621i	$0.193685\pi$
$332$	1.83185e7	−	1.27408e8i	0.0274730	−	0.191079i
$333$	1.59025e8	−	3.48217e8i	0.235999	−	0.516767i
$334$	−5.51910e7	+	1.20851e8i	−0.0810505	+	0.177476i
$335$	1.99955e7	−	1.39072e8i	0.0290587	−	0.202108i
$336$	−1.73154e8	+	1.11279e8i	−0.249026	+	0.160039i
$337$	−8.65281e7	−	2.54070e7i	−0.123155	−	0.0361616i	0.219574	−	0.975596i	$-0.429533\pi$
$337$	−8.65281e7	−	2.54070e7i	−0.123155	−	0.0361616i	−0.342729	+	0.939434i	$0.611351\pi$
$338$	5.71678e7	+	3.97611e8i	0.0805273	+	0.560080i
$339$	−2.58991e8	−	2.98892e8i	−0.361066	−	0.416692i
$340$	−1.55145e7	−	9.97056e6i	−0.0214073	−	0.0137576i
$341$	−7.63206e7	+	8.80787e7i	−0.104232	+	0.120290i
$342$	−7.13887e7	+	2.09616e7i	−0.0965024	+	0.0283357i
$343$	−2.53938e8	−	5.56046e8i	−0.339780	−	0.744015i
$344$	−1.68333e8			−0.222954
$345$	−1.24187e8	−	1.35021e8i	−0.162820	−	0.177025i
$346$	1.03021e9			1.33709
$347$	−5.71152e8	−	1.25065e9i	−0.733836	−	1.60688i	−0.793436	−	0.608653i	$-0.791710\pi$
$347$	−5.71152e8	−	1.25065e9i	−0.733836	−	1.60688i	0.0596008	−	0.998222i	$-0.481017\pi$
$348$	8.49697e6	−	2.49494e6i	0.0108078	−	0.00317345i
$349$	1.82815e8	−	2.10979e8i	0.230209	−	0.265675i	−0.628879	−	0.777503i	$-0.716486\pi$
$349$	1.82815e8	−	2.10979e8i	0.230209	−	0.265675i	0.859088	+	0.511828i	$0.171031\pi$
$350$	2.72283e8	+	1.74986e8i	0.339455	+	0.218155i
$351$	−1.26258e8	−	1.45710e8i	−0.155842	−	0.179852i
$352$	2.33044e7	+	1.62085e8i	0.0284799	+	0.198082i
$353$	−1.31166e9	−	3.85137e8i	−1.58712	−	0.466020i	−0.635193	−	0.772354i	$-0.719079\pi$
$353$	−1.31166e9	−	3.85137e8i	−1.58712	−	0.466020i	−0.951924	+	0.306334i	$0.900898\pi$
$354$	−2.76381e8	+	1.77619e8i	−0.331128	+	0.212803i
$355$	−4.47520e7	+	3.11257e8i	−0.0530901	+	0.369250i
$356$	−1.38221e7	+	3.02661e7i	−0.0162367	+	0.0355534i
$357$	−4.00172e7	+	8.76255e7i	−0.0465488	+	0.101928i
$358$	8.47963e7	−	5.89771e8i	0.0976757	−	0.679349i
$359$	2.50972e8	−	1.61290e8i	0.286283	−	0.183983i	−0.389616	−	0.920978i	$-0.627392\pi$
$359$	2.50972e8	−	1.61290e8i	0.286283	−	0.183983i	0.675899	+	0.736995i	$0.263756\pi$
$360$	−1.08012e8	−	3.17151e7i	−0.122015	−	0.0358268i
$361$	1.17085e8	+	8.14343e8i	0.130986	+	0.911029i
$362$	7.93065e8	+	9.15246e8i	0.878676	+	1.01405i
$363$	−2.24778e8	−	1.44456e8i	−0.246650	−	0.158512i
$364$	−4.88797e7	+	5.64102e7i	−0.0531219	+	0.0613059i
$365$	−4.49001e8	+	1.31838e8i	−0.483306	+	0.141911i
$366$	5.76836e7	+	1.26309e8i	0.0614990	+	0.134664i
$367$	8.07920e8			0.853173			0.426587	−	0.904447i	$-0.359716\pi$
$367$	8.07920e8			0.853173			0.426587	+	0.904447i	$0.359716\pi$
$368$	−4.16886e8	+	9.89411e8i	−0.436064	+	1.03493i
$369$	3.63384e8			0.376507
$370$	−3.07326e8	−	6.72950e8i	−0.315423	−	0.690680i
$371$	6.36839e8	−	1.86993e8i	0.647472	−	0.190115i
$372$	1.22379e7	−	1.41233e7i	0.0123255	−	0.0142244i
$373$	−2.71665e8	−	1.74588e8i	−0.271052	−	0.174194i	0.398053	−	0.917362i	$-0.369686\pi$
$373$	−2.71665e8	−	1.74588e8i	−0.271052	−	0.174194i	−0.669105	+	0.743168i	$0.733322\pi$
$374$	2.11308e8	+	2.43863e8i	0.208865	+	0.241043i
$375$	6.38432e7	+	4.44039e8i	0.0625180	+	0.434822i
$376$	−2.47232e8	−	7.25940e7i	−0.239855	−	0.0704277i
$377$	−1.46951e8	+	9.44395e7i	−0.141246	+	0.0907735i
$378$	1.40419e7	−	9.76637e7i	0.0133723	−	0.0930062i
$379$	7.64031e8	−	1.67299e9i	0.720898	−	1.57855i	−0.0917448	−	0.995783i	$-0.529244\pi$
$379$	7.64031e8	−	1.67299e9i	0.720898	−	1.57855i	0.812642	−	0.582763i	$-0.198028\pi$
$380$	−7.50445e6	+	1.64325e7i	−0.00701579	+	0.0153624i
$381$	−1.36910e7	+	9.52228e7i	−0.0126823	+	0.0882071i
$382$	9.76493e8	−	6.27554e8i	0.896288	−	0.576009i
$383$	1.14527e8	+	3.36281e7i	0.104162	+	0.0305849i	0.333398	−	0.942786i	$-0.391805\pi$
$383$	1.14527e8	+	3.36281e7i	0.104162	+	0.0305849i	−0.229236	+	0.973371i	$0.573623\pi$
$384$	1.05759e8	+	7.35573e8i	0.0953146	+	0.662928i
$385$	9.78386e7	+	1.12912e8i	0.0873771	+	0.100839i
$386$	1.13526e9	+	7.29587e8i	1.00471	+	0.645686i
$387$	6.05963e7	−	6.99318e7i	0.0531444	−	0.0613319i
$388$	9.58203e7	−	2.81354e7i	0.0832811	−	0.0244535i
$389$	2.67526e8	+	5.85801e8i	0.230432	+	0.504576i	0.989162	−	0.146830i	$-0.0469069\pi$
$389$	2.67526e8	+	5.85801e8i	0.230432	+	0.504576i	−0.758730	+	0.651406i	$0.774180\pi$
$390$	−3.72601e8			−0.318067
$391$	8.62125e7	+	4.95033e8i	0.0729376	+	0.418809i
$392$	−8.64519e8			−0.724892
$393$	−3.81124e8	−	8.34546e8i	−0.316733	−	0.693548i
$394$	1.75594e9	−	5.15591e8i	1.44635	−	0.424686i
$395$	2.88219e8	−	3.32622e8i	0.235306	−	0.271557i
$396$	−3.49319e7	−	2.24493e7i	−0.0282676	−	0.0181665i
$397$	−8.71462e8	−	1.00572e9i	−0.699008	−	0.806698i	0.289610	−	0.957145i	$-0.406474\pi$
$397$	−8.71462e8	−	1.00572e9i	−0.699008	−	0.806698i	−0.988618	+	0.150447i	$0.951929\pi$
$398$	1.57716e8	+	1.09694e9i	0.125397	+	0.872153i
$399$	9.05384e7	+	2.65845e7i	0.0713555	+	0.0209519i
$400$	9.99429e8	−	6.42294e8i	0.780804	−	0.501792i
$401$	−1.09249e8	+	7.59845e8i	−0.0846083	+	0.588464i	0.902775	+	0.430114i	$0.141527\pi$
$401$	−1.09249e8	+	7.59845e8i	−0.0846083	+	0.588464i	−0.987383	+	0.158350i	$0.949383\pi$
$402$	1.63752e8	−	3.58566e8i	0.125717	−	0.275282i
$403$	−1.53130e8	+	3.35309e8i	−0.116545	+	0.255198i
$404$	7.37080e6	−	5.12650e7i	0.00556134	−	0.0386800i
$405$	5.20575e7	−	3.34554e7i	0.0389396	−	0.0250249i
$406$	−8.57732e7	−	2.51853e7i	−0.0636078	−	0.0186769i
$407$	2.31441e8	+	1.60971e9i	0.170161	+	1.18349i
$408$	2.01924e8	+	2.33033e8i	0.147190	+	0.169866i
$409$	2.31010e9	+	1.48461e9i	1.66955	+	1.07296i	0.901738	+	0.432282i	$0.142292\pi$
$409$	2.31010e9	+	1.48461e9i	1.66955	+	1.07296i	0.767814	+	0.640673i	$0.221345\pi$
$410$	4.59883e8	−	5.30734e8i	0.329537	−	0.380306i
$411$	2.48012e8	−	7.28229e7i	0.176208	−	0.0517394i
$412$	2.23331e7	+	4.89027e7i	0.0157329	+	0.0344503i
$413$	4.16662e8			0.291044
$414$	−2.27578e8	−	4.61627e8i	−0.157627	−	0.319735i
$415$	−8.14904e8			−0.559678
$416$	2.15157e8	+	4.71128e8i	0.146531	+	0.320858i
$417$	−9.91420e7	+	2.91107e7i	−0.0669547	+	0.0196597i
$418$	2.06987e8	−	2.38876e8i	0.138620	−	0.159976i
$419$	−8.58842e8	−	5.51944e8i	−0.570380	−	0.366561i	0.223437	−	0.974718i	$-0.428272\pi$
$419$	−8.58842e8	−	5.51944e8i	−0.570380	−	0.366561i	−0.793816	+	0.608158i	$0.791909\pi$
$420$	−1.56882e7	−	1.81052e7i	−0.0103324	−	0.0119242i
$421$	2.98146e8	+	2.07365e9i	0.194734	+	1.35440i	0.819270	+	0.573408i	$0.194379\pi$
$421$	2.98146e8	+	2.07365e9i	0.194734	+	1.35440i	−0.624536	+	0.780996i	$0.714712\pi$
$422$	−5.29061e8	−	1.55346e8i	−0.342698	−	0.100625i
$423$	1.19156e8	−	7.65772e7i	0.0765467	−	0.0491936i
$424$	3.02352e8	−	2.10290e9i	0.192634	−	1.33980i
$425$	2.30976e8	−	5.05766e8i	0.145950	−	0.319587i
$426$	−3.66493e8	+	8.02508e8i	−0.229685	+	0.502939i
$427$	2.50624e7	−	1.74313e8i	0.0155785	−	0.108351i
$428$	1.72235e8	−	1.10689e8i	0.106186	−	0.0682417i
$429$	7.85885e8	+	2.30757e8i	0.480572	+	0.141109i
$430$	−2.54496e7	−	1.77006e8i	−0.0154362	−	0.107361i
$431$	−6.26048e8	−	7.22498e8i	−0.376649	−	0.434677i	0.535500	−	0.844536i	$-0.320123\pi$
$431$	−6.26048e8	−	7.22498e8i	−0.376649	−	0.434677i	−0.912149	+	0.409859i	$0.865578\pi$
$432$	−3.04673e8	−	1.95802e8i	−0.181820	−	0.116849i
$433$	−1.06258e9	+	1.22628e9i	−0.629005	+	0.725910i	−0.977391	−	0.211441i	$-0.932184\pi$
$433$	−1.06258e9	+	1.22628e9i	−0.629005	+	0.725910i	0.348386	+	0.937351i	$0.386730\pi$
$434$	−1.81003e8	+	5.31473e7i	−0.106285	+	0.0312081i
$435$	−2.32902e7	−	5.09984e7i	−0.0135663	−	0.0297060i
$436$	−4.66002e8			−0.269268
$437$	4.67955e8	−	1.52600e8i	0.268237	−	0.0874718i
$438$	−1.31288e9			−0.746564
$439$	9.64906e7	+	2.11285e8i	0.0544326	+	0.119191i	0.934894	−	0.354927i	$-0.115494\pi$
$439$	9.64906e7	+	2.11285e8i	0.0544326	+	0.119191i	−0.880461	+	0.474118i	$0.842767\pi$
$440$	4.58857e8	−	1.34733e8i	0.256799	−	0.0754030i
$441$	3.11208e8	−	3.59153e8i	0.172789	−	0.199409i
$442$	8.58580e8	+	5.51776e8i	0.472937	+	0.303938i
$443$	−1.06351e9	−	1.22735e9i	−0.581202	−	0.670743i	0.386661	−	0.922222i	$-0.373628\pi$
$443$	−1.06351e9	−	1.22735e9i	−0.581202	−	0.670743i	−0.967863	+	0.251479i	$0.919083\pi$
$444$	−3.71111e7	−	2.58113e8i	−0.0201216	−	0.139949i
$445$	2.02116e8	+	5.93466e7i	0.108728	+	0.0319253i
$446$	3.67190e8	−	2.35979e8i	0.195983	−	0.125951i
$447$	−1.00028e8	+	6.95711e8i	−0.0529720	+	0.368428i
$448$	2.95245e8	−	6.46497e8i	0.155135	−	0.339698i
$449$	7.45353e8	−	1.63210e9i	0.388597	−	0.850910i	−0.609703	−	0.792630i	$-0.708711\pi$
$449$	7.45353e8	−	1.63210e9i	0.388597	−	0.850910i	0.998300	−	0.0582797i	$-0.0185615\pi$
$450$	−8.10486e7	+	5.63706e8i	−0.0419278	+	0.291614i
$451$	−1.29867e9	+	8.34604e8i	−0.666624	+	0.428413i
$452$	−2.58492e8	−	7.59002e7i	−0.131663	−	0.0386597i
$453$	2.68490e8	+	1.86739e9i	0.135701	+	0.943824i
$454$	3.85635e8	+	4.45046e8i	0.193411	+	0.223208i
$455$	3.97534e8	+	2.55480e8i	0.197849	+	0.127150i
$456$	1.97795e8	−	2.28267e8i	0.0976872	−	0.112737i
$457$	−1.02771e9	+	3.01763e8i	−0.503691	+	0.147897i	−0.523700	−	0.851903i	$-0.675449\pi$
$457$	−1.02771e9	+	3.01763e8i	−0.503691	+	0.147897i	0.0200092	+	0.999800i	$0.493630\pi$
$458$	−1.18469e9	−	2.59412e9i	−0.576205	−	1.26171i
$459$	−1.69499e8			−0.0818130
$460$	−1.20892e8	−	3.16392e7i	−0.0579088	−	0.0151556i
$461$	−2.70429e9			−1.28558			−0.642792	−	0.766041i	$-0.722224\pi$
$461$	−2.70429e9			−1.28558			−0.642792	+	0.766041i	$0.722224\pi$
$462$	1.74126e8	+	3.81283e8i	0.0821519	+	0.179888i
$463$	−7.03863e8	+	2.06673e8i	−0.329575	+	0.0967720i	−0.442334	−	0.896850i	$-0.645849\pi$
$463$	−7.03863e8	+	2.06673e8i	−0.329575	+	0.0967720i	0.112759	+	0.993622i	$0.464031\pi$
$464$	−2.14877e8	+	2.47981e8i	−0.0998567	+	0.115241i
$465$	−9.95295e7	−	6.39637e7i	−0.0459057	−	0.0295018i
$466$	−1.98471e9	−	2.29047e9i	−0.908543	−	1.04851i
$467$	2.42473e6	+	1.68644e7i	0.00110168	+	0.00766233i	0.990365	−	0.138483i	$-0.0442225\pi$
$467$	2.42473e6	+	1.68644e7i	0.00110168	+	0.00766233i	−0.989263	+	0.146145i	$0.953313\pi$
$468$	−1.26015e8	−	3.70014e7i	−0.0568280	−	0.0166862i
$469$	−4.20566e8	+	2.70281e8i	−0.188247	+	0.120979i
$470$	3.89560e7	−	2.70945e8i	0.0173074	−	0.120376i
$471$	3.91034e8	−	8.56246e8i	0.172441	−	0.377594i
$472$	5.54039e8	−	1.21318e9i	0.242518	−	0.531040i
$473$	−5.59439e7	+	3.89099e8i	−0.0243074	+	0.169062i
$474$	1.03877e9	−	6.67579e8i	0.448019	−	0.287925i
$475$	−5.22579e8	−	1.53443e8i	−0.223730	−	0.0656931i
$476$	9.33867e6	+	6.49519e7i	0.00396881	+	0.0276037i
$477$	7.64783e8	+	8.82607e8i	0.322644	+	0.372351i
$478$	−3.83686e9	−	2.46580e9i	−1.60686	−	1.03267i
$479$	1.94427e9	−	2.24381e9i	0.808320	−	0.932851i	−0.190487	−	0.981690i	$-0.561007\pi$
$479$	1.94427e9	−	2.24381e9i	0.808320	−	0.932851i	0.998807	+	0.0488392i	$0.0155522\pi$
$480$	−1.59500e8	+	4.68334e7i	−0.0658289	+	0.0193291i
$481$	2.13677e9	+	4.67888e9i	0.875489	+	1.91705i
$482$	2.61303e9			1.06287
$483$	−7.37150e7	+	6.48559e8i	−0.0297674	+	0.261900i
$484$	−1.82011e8			−0.0729691
$485$	−2.62643e8	−	5.75108e8i	−0.104537	−	0.228904i
$486$	1.66579e8	−	4.89119e7i	0.0658253	−	0.0193280i
$487$	−1.23732e9	+	1.42794e9i	−0.485433	+	0.560220i	−0.944640	−	0.328110i	$-0.893588\pi$
$487$	−1.23732e9	+	1.42794e9i	−0.485433	+	0.560220i	0.459206	+	0.888330i	$0.348134\pi$
$488$	−4.74214e8	−	3.04759e8i	−0.184716	−	0.118710i
$489$	−5.77101e7	−	6.66010e7i	−0.0223188	−	0.0257573i
$490$	−1.30703e8	−	9.09058e8i	−0.0501879	−	0.349064i
$491$	−3.95930e9	−	1.16255e9i	−1.50950	−	0.443229i	−0.580795	−	0.814050i	$-0.697258\pi$
$491$	−3.95930e9	−	1.16255e9i	−1.50950	−	0.443229i	−0.928704	+	0.370821i	$0.879076\pi$
$492$	2.08239e8	−	1.33827e8i	0.0788288	−	0.0506602i
$493$	−2.18550e7	+	1.52005e8i	−0.00821459	+	0.0571338i
$494$	4.15300e8	−	9.09381e8i	0.154995	−	0.339392i
$495$	−1.09206e8	+	2.39127e8i	−0.0404694	+	0.0886156i
$496$	−9.85430e7	+	6.85381e8i	−0.0362610	+	0.252201i
$497$	9.41268e8	−	6.04916e8i	0.343927	−	0.221028i
$498$	−2.19366e9	−	6.44117e8i	−0.795915	−	0.233702i
$499$	6.72543e8	+	4.67764e9i	0.242308	+	1.68529i	0.640477	+	0.767977i	$0.278737\pi$
$499$	6.72543e8	+	4.67764e9i	0.242308	+	1.68529i	−0.398169	+	0.917312i	$0.630354\pi$
$500$	2.00117e8	+	2.30947e8i	0.0715959	+	0.0826261i
$501$	2.49412e8	+	1.60288e8i	0.0886106	+	0.0569466i
$502$	−8.10729e8	+	9.35631e8i	−0.286031	+	0.330097i
$503$	−4.23509e9	+	1.24353e9i	−1.48380	+	0.435682i	−0.920556	−	0.390611i	$-0.872264\pi$
$503$	−4.23509e9	+	1.24353e9i	−1.48380	+	0.435682i	−0.563241	+	0.826293i	$0.690446\pi$
$504$	1.66393e8	+	3.64351e8i	0.0578934	+	0.126769i
$505$	−3.27893e8			−0.113295
$506$	1.87357e9	+	1.12708e9i	0.642899	+	0.386749i
$507$	8.96409e8			0.305477
$508$	2.72230e7	+	5.96101e7i	0.00921326	+	0.0201742i
$509$	5.50327e9	−	1.61591e9i	1.84973	−	0.543130i	0.849861	−	0.527006i	$-0.176686\pi$
$509$	5.50327e9	−	1.61591e9i	1.84973	−	0.543130i	0.999870	−	0.0161237i	$-0.00513255\pi$
$510$	−2.14511e8	+	2.47558e8i	−0.0716066	+	0.0826384i
$511$	1.40074e9	+	9.00198e8i	0.464390	+	0.298445i
$512$	−1.40827e9	−	1.62523e9i	−0.463705	−	0.535144i
$513$	2.36289e7	+	1.64342e8i	0.00772738	+	0.0537451i
$514$	−3.64224e9	−	1.06946e9i	−1.18304	−	0.347371i
$515$	2.86327e8	−	1.84011e8i	0.0923713	−	0.0593634i
$516$	8.97051e6	−	6.23913e7i	0.00287437	−	0.0199917i
$517$	−2.49965e8	+	5.47347e8i	−0.0795540	+	0.174199i
$518$	−1.09351e9	+	2.39446e9i	−0.345676	+	0.756925i
$519$	3.27177e8	−	2.27556e9i	0.102730	−	0.714502i
$520$	1.27247e9	−	8.17769e8i	0.396860	−	0.255046i
$521$	−2.02418e9	−	5.94354e8i	−0.627073	−	0.184125i	−0.0472701	−	0.998882i	$-0.515052\pi$
$521$	−2.02418e9	−	5.94354e8i	−0.627073	−	0.184125i	−0.579803	+	0.814757i	$0.696870\pi$
$522$	−2.23852e7	−	1.55693e8i	−0.00688834	−	0.0479095i
$523$	1.10121e8	+	1.27087e8i	0.0336602	+	0.0388459i	0.772330	−	0.635221i	$-0.219091\pi$
$523$	1.10121e8	+	1.27087e8i	0.0336602	+	0.0388459i	−0.738670	+	0.674067i	$0.764546\pi$
$524$	−5.25753e8	−	3.37881e8i	−0.159633	−	0.102590i
$525$	4.72985e8	−	5.45854e8i	0.142656	−	0.164634i
$526$	−3.26369e9	+	9.58306e8i	−0.977820	+	0.287114i
$527$	1.34622e8	+	2.94781e8i	0.0400663	+	0.0877330i
$528$	1.53856e9			0.454878
$529$	1.59534e9	+	3.00795e9i	0.468552	+	0.883436i
$530$	2.25695e9			0.658502
$531$	3.04556e8	+	6.66885e8i	0.0882748	+	0.193295i
$532$	6.16741e7	−	1.81091e7i	0.0177587	−	0.00521444i
$533$	−3.19747e9	+	3.69008e9i	−0.914664	+	1.05558i
$534$	4.97172e8	+	3.19513e8i	0.141290	+	0.0908017i
$535$	−8.48812e8	−	9.79581e8i	−0.239648	−	0.276568i
$536$	2.27736e8	+	1.58394e9i	0.0638785	+	0.444285i
$537$	−1.27577e9	−	3.74601e8i	−0.355519	−	0.104390i
$538$	−1.56329e9	+	1.00467e9i	−0.432814	+	0.278153i
$539$	−2.87315e8	+	1.99832e9i	−0.0790310	+	0.549672i
$540$	1.75109e7	−	3.83436e7i	0.00478554	−	0.0104789i
$541$	−2.34781e8	+	5.14099e8i	−0.0637489	+	0.139591i	−0.938825	−	0.344395i	$-0.888084\pi$
$541$	−2.34781e8	+	5.14099e8i	−0.0637489	+	0.139591i	0.875076	+	0.483986i	$0.160811\pi$
$542$	−2.28241e8	+	1.58745e9i	−0.0615739	+	0.428256i
$543$	2.27348e9	−	1.46108e9i	0.609386	−	0.391628i
$544$	4.36888e8	+	1.28282e8i	0.116352	+	0.0341641i
$545$	4.19862e8	+	2.92020e9i	0.111101	+	0.772725i
$546$	8.68195e8	+	1.00195e9i	0.228267	+	0.263434i
$547$	−3.19486e8	−	2.05321e8i	−0.0834633	−	0.0536386i	0.498244	−	0.867037i	$-0.333979\pi$
$547$	−3.19486e8	−	2.05321e8i	−0.0834633	−	0.0536386i	−0.581707	+	0.813398i	$0.697615\pi$
$548$	1.15306e8	−	1.33070e8i	0.0299308	−	0.0345420i
$549$	2.97315e8	−	8.72995e7i	0.0766855	−	0.0225169i
$550$	−1.00504e9	−	2.20073e9i	−0.257581	−	0.564024i
$551$	1.50427e8			0.0383085
$552$	1.79036e9	+	1.07703e9i	0.453059	+	0.272546i
$553$	−1.56602e9			−0.393785
$554$	−4.14281e8	−	9.07148e8i	−0.103517	−	0.226670i
$555$	−1.58403e9	+	4.65113e8i	−0.393313	+	0.115487i
$556$	−4.60930e7	+	5.31941e7i	−0.0113729	+	0.0131251i
$557$	1.64680e9	+	1.05833e9i	0.403783	+	0.259495i	0.726732	−	0.686921i	$-0.241038\pi$
$557$	1.64680e9	+	1.05833e9i	0.403783	+	0.259495i	−0.322950	+	0.946416i	$0.604674\pi$
$558$	−2.17368e8	−	2.50856e8i	−0.0529633	−	0.0611229i
$559$	1.76945e8	+	1.23068e9i	0.0428448	+	0.297992i
$560$	8.51698e8	+	2.50081e8i	0.204940	+	0.0601759i
$561$	6.05758e8	−	3.89297e8i	0.144854	−	0.0930918i
$562$	−4.52010e8	+	3.14380e9i	−0.107416	+	0.747098i
$563$	2.72629e9	−	5.96974e9i	0.643862	−	1.40986i	−0.252964	−	0.967476i	$-0.581405\pi$
$563$	2.72629e9	−	5.96974e9i	0.643862	−	1.40986i	0.896825	−	0.442385i	$-0.145867\pi$
$564$	4.00814e7	−	8.77660e7i	0.00940732	−	0.0205992i
$565$	−2.42730e8	+	1.68823e9i	−0.0566180	+	0.393787i
$566$	7.55386e9	−	4.85457e9i	1.75110	−	1.12536i
$567$	−2.11263e8	−	6.20323e7i	−0.0486723	−	0.0142915i
$568$	−5.09696e8	−	3.54501e9i	−0.116706	−	0.811706i
$569$	3.01187e9	+	3.47588e9i	0.685399	+	0.790992i	0.986703	−	0.162536i	$-0.0519673\pi$
$569$	3.01187e9	+	3.47588e9i	0.685399	+	0.790992i	−0.301304	+	0.953528i	$0.597422\pi$
$570$	2.69931e8	+	1.73474e8i	0.0610507	+	0.0392349i
$571$	1.67128e9	−	1.92876e9i	0.375684	−	0.433563i	−0.536149	−	0.844123i	$-0.680121\pi$
$571$	1.67128e9	−	1.92876e9i	0.375684	−	0.433563i	0.911833	+	0.410560i	$0.134667\pi$
$572$	5.35339e8	−	1.57190e8i	0.119603	−	0.0351187i
$573$	−1.07604e9	−	2.35620e9i	−0.238940	−	0.523205i
$574$	−2.49875e9			−0.551482
$575$	4.25476e8	−	3.74342e9i	0.0933335	−	0.821167i
$576$	1.25055e9			0.272661
$577$	−1.65189e9	−	3.61714e9i	−0.357987	−	0.783882i	−0.999854	−	0.0170661i	$-0.994567\pi$
$577$	−1.65189e9	−	3.61714e9i	−0.357987	−	0.783882i	0.641868	−	0.766815i	$-0.278160\pi$
$578$	−3.90279e9	+	1.14596e9i	−0.840674	+	0.246844i
$579$	1.97207e9	−	2.27589e9i	0.422228	−	0.487277i
$580$	−3.21283e7	−	2.06476e7i	−0.00683737	−	0.00439411i
$581$	1.89880e9	+	2.19133e9i	0.401664	+	0.463545i
$582$	−2.52438e8	−	1.75575e9i	−0.0530792	−	0.369174i
$583$	−4.76033e9	−	1.39776e9i	−0.994941	−	0.292141i
$584$	4.48364e9	−	2.88146e9i	0.931506	−	0.598643i
$585$	−1.18331e8	+	8.23012e8i	−0.0244373	+	0.169965i
$586$	2.57929e9	−	5.64785e9i	0.529491	−	1.15942i
$587$	−2.66640e8	+	5.83860e8i	−0.0544116	+	0.119145i	−0.934885	−	0.354951i	$-0.884498\pi$
$587$	−2.66640e8	+	5.83860e8i	−0.0544116	+	0.119145i	0.880473	+	0.474096i	$0.157225\pi$
$588$	4.60704e7	−	3.20427e8i	0.00934547	−	0.0649992i
$589$	2.67047e8	−	1.71621e8i	0.0538498	−	0.0346072i
$590$	1.35944e9	+	3.99168e8i	0.272507	+	0.0800154i
$591$	−5.81197e8	−	4.04231e9i	−0.115816	−	0.805515i
$592$	6.32734e9	+	7.30214e9i	1.25342	+	1.44652i
$593$	−2.23489e9	−	1.43627e9i	−0.440113	−	0.282843i	0.301760	−	0.953384i	$-0.402426\pi$
$593$	−2.23489e9	−	1.43627e9i	−0.440113	−	0.282843i	−0.741873	+	0.670541i	$0.766062\pi$
$594$	−4.82984e8	+	5.57393e8i	−0.0945541	+	0.109121i
$595$	3.98607e8	−	1.17041e8i	0.0775774	−	0.0227788i
$596$	1.98895e8	+	4.35520e8i	0.0384824	+	0.0842648i
$597$	2.47304e9			0.475687
$598$	6.69022e9	+	1.75093e9i	1.27934	+	0.334822i
$599$	−1.45010e9			−0.275679			−0.137839	−	0.990455i	$-0.544016\pi$
$599$	−1.45010e9			−0.275679			−0.137839	+	0.990455i	$0.544016\pi$
$600$	−9.60407e8	−	2.10300e9i	−0.181521	−	0.397475i
$601$	−1.21684e9	+	3.57296e8i	−0.228651	+	0.0671379i	−0.394051	−	0.919089i	$-0.628927\pi$
$601$	−1.21684e9	+	3.57296e8i	−0.228651	+	0.0671379i	0.165400	+	0.986227i	$0.447108\pi$
$602$	−4.16680e8	+	4.80875e8i	−0.0778423	+	0.0898347i
$603$	−7.40006e8	−	4.75573e8i	−0.137444	−	0.0883297i
$604$	8.41583e8	+	9.71239e8i	0.155406	+	0.179348i
$605$	1.63989e8	+	1.14057e9i	0.0301073	+	0.209401i
$606$	−8.82664e8	−	2.59173e8i	−0.161117	−	0.0473082i
$607$	4.11289e9	−	2.64319e9i	0.746426	−	0.479699i	−0.111312	−	0.993785i	$-0.535505\pi$
$607$	4.11289e9	−	2.64319e9i	0.746426	−	0.479699i	0.857738	+	0.514087i	$0.171869\pi$
$608$	6.34753e7	−	4.41481e8i	0.0114536	−	0.0796616i
$609$	−8.28699e7	+	1.81460e8i	−0.0148674	+	0.0325552i
$610$	2.48765e8	−	5.44720e8i	0.0443747	−	0.0971671i
$611$	−2.70853e8	+	1.88382e9i	−0.0480385	+	0.334115i
$612$	−9.71322e7	+	6.24231e7i	−0.0171291	+	0.0110082i
$613$	5.13640e8	+	1.50818e8i	0.0900632	+	0.0264449i	0.326454	−	0.945213i	$-0.394146\pi$
$613$	5.13640e8	+	1.50818e8i	0.0900632	+	0.0264449i	−0.236390	+	0.971658i	$0.575964\pi$
$614$	1.06201e9	+	7.38642e9i	0.185156	+	1.28779i
$615$	−1.02625e9	−	1.18435e9i	−0.177906	−	0.205314i
$616$	−1.43148e9	−	9.19959e8i	−0.246748	−	0.158576i
$617$	1.90615e9	−	2.19982e9i	0.326708	−	0.377041i	−0.568505	−	0.822680i	$-0.692478\pi$
$617$	1.90615e9	−	2.19982e9i	0.326708	−	0.377041i	0.895213	+	0.445639i	$0.147023\pi$
$618$	9.16217e8	−	2.69025e8i	0.156149	−	0.0458494i
$619$	−2.01119e9	−	4.40389e9i	−0.340828	−	0.746310i	0.659156	−	0.752007i	$-0.270914\pi$
$619$	−2.01119e9	−	4.40389e9i	−0.340828	−	0.746310i	−0.999984	+	0.00569694i	$0.998187\pi$
$620$	−8.05925e7			−0.0135808
$621$	−1.09193e9	+	3.56076e8i	−0.182967	+	0.0596654i
$622$	−8.31259e6			−0.00138506
$623$	−3.11361e8	−	6.81786e8i	−0.0515889	−	0.112964i
$624$	4.66919e9	−	1.37100e9i	0.769300	−	0.225887i
$625$	−2.03637e9	+	2.35010e9i	−0.333639	+	0.385040i
$626$	−2.43785e9	−	1.56671e9i	−0.397188	−	0.255257i
$627$	−4.61900e8	−	5.33061e8i	−0.0748361	−	0.0863655i
$628$	−9.12542e7	−	6.34687e8i	−0.0147026	−	0.102259i
$629$	4.33884e9	+	1.27400e9i	0.695178	+	0.204123i
$630$	−3.57965e8	+	2.30050e8i	−0.0570360	+	0.0366548i
$631$	1.67434e9	−	1.16453e10i	0.265301	−	1.84521i	−0.225880	−	0.974155i	$-0.572526\pi$
$631$	1.67434e9	−	1.16453e10i	0.265301	−	1.84521i	0.491182	−	0.871057i	$-0.336565\pi$
$632$	−2.08235e9	+	4.55971e9i	−0.328129	+	0.718501i
$633$	−5.11153e8	+	1.11927e9i	−0.0801009	+	0.175397i
$634$	1.99996e8	−	1.39100e9i	0.0311679	−	0.216778i
$635$	3.49019e8	−	2.24301e8i	0.0540930	−	0.0347635i
$636$	7.63310e8	+	2.24128e8i	0.117653	+	0.0345459i
$637$	9.08750e8	+	6.32049e9i	0.139302	+	0.968864i
$638$	4.37589e8	+	5.05005e8i	0.0667105	+	0.0769880i
$639$	1.65621e9	+	1.06438e9i	0.251109	+	0.161378i
$640$	2.09873e9	−	2.42206e9i	0.316465	−	0.365220i
$641$	5.78690e9	−	1.69919e9i	0.867846	−	0.254823i	0.182647	−	0.983179i	$-0.441533\pi$
$641$	5.78690e9	−	1.69919e9i	0.867846	−	0.254823i	0.685199	+	0.728356i	$0.259715\pi$
$642$	−1.51066e9	−	3.30787e9i	−0.225316	−	0.493374i
$643$	−9.73483e9			−1.44408			−0.722038	−	0.691853i	$-0.756794\pi$
$643$	−9.73483e9			−1.44408			−0.722038	+	0.691853i	$0.756794\pi$
$644$	1.96609e8	+	3.98809e8i	0.0290070	+	0.0588388i
$645$	−3.99057e8			−0.0585566
$646$	−3.65105e8	−	7.99468e8i	−0.0532849	−	0.116678i
$647$	7.25293e9	−	2.12965e9i	1.05281	−	0.309132i	0.290856	−	0.956767i	$-0.406060\pi$
$647$	7.25293e9	−	2.12965e9i	1.05281	−	0.309132i	0.761951	+	0.647635i	$0.224242\pi$
$648$	−4.61535e8	+	5.32640e8i	−0.0666334	+	0.0768990i
$649$	−2.62010e9	−	1.68384e9i	−0.376237	−	0.241793i
$650$	−5.01114e9	−	5.78317e9i	−0.715715	−	0.825979i
$651$	5.99100e7	+	4.16683e8i	0.00851071	+	0.0591933i
$652$	−5.75990e7	−	1.69126e7i	−0.00813857	−	0.00238970i
$653$	−4.35283e9	+	2.79739e9i	−0.611752	+	0.393149i	−0.809514	−	0.587101i	$-0.800269\pi$
$653$	−4.35283e9	+	2.79739e9i	−0.611752	+	0.393149i	0.197762	+	0.980250i	$0.436633\pi$
$654$	−1.17795e9	+	8.19283e9i	−0.164666	+	1.14528i
$655$	−1.64363e9	+	3.59905e9i	−0.228539	+	0.500430i
$656$	−3.81010e9	+	8.34296e9i	−0.526954	+	1.15387i
$657$	−4.16947e8	+	2.89993e9i	−0.0573591	+	0.398941i
$658$	−8.19360e8	+	5.26571e8i	−0.112120	+	0.0720554i
$659$	−4.02803e9	−	1.18274e9i	−0.548269	−	0.160986i	−0.00414532	−	0.999991i	$-0.501319\pi$
$659$	−4.02803e9	−	1.18274e9i	−0.548269	−	0.160986i	−0.544123	+	0.839005i	$0.683138\pi$
$660$	2.54849e7	+	1.77251e8i	0.00345048	+	0.0239986i
$661$	5.48543e9	+	6.33052e9i	0.738763	+	0.852578i	0.993429	−	0.114451i	$-0.0365108\pi$
$661$	5.48543e9	+	6.33052e9i	0.738763	+	0.852578i	−0.254666	+	0.967029i	$0.581965\pi$
$662$	−5.12026e9	−	3.29059e9i	−0.685945	−	0.440830i
$663$	1.49145e9	−	1.72122e9i	0.198752	−	0.229371i
$664$	8.90527e9	−	2.61482e9i	1.18048	−	0.346620i
$665$	−1.69048e8	−	3.70164e8i	−0.0222913	−	0.0488111i
$666$	−4.63172e9			−0.607551
$667$	1.78533e8	+	1.02514e9i	0.0232959	+	0.133765i
$668$	2.01958e8			0.0262146
$669$	−4.04623e8	−	8.86001e8i	−0.0522467	−	0.114404i
$670$	−1.63111e9	+	4.78937e8i	−0.209518	+	0.0615201i
$671$	−8.62044e8	+	9.94852e8i	−0.110154	+	0.127125i
$672$	4.97588e8	+	3.19780e8i	0.0632525	+	0.0406499i
$673$	−2.51130e9	−	2.89819e9i	−0.317575	−	0.366501i	0.574409	−	0.818569i	$-0.305232\pi$
$673$	−2.51130e9	−	2.89819e9i	−0.317575	−	0.366501i	−0.891984	+	0.452068i	$0.850687\pi$
$674$	1.55283e8	+	1.08002e9i	0.0195351	+	0.135869i
$675$	1.21939e9	+	3.58045e8i	0.152609	+	0.0448099i
$676$	5.13692e8	−	3.30130e8i	0.0639572	−	0.0411028i
$677$	−1.51777e9	+	1.05563e10i	−0.187995	+	1.30754i	0.649194	+	0.760623i	$0.275106\pi$
$677$	−1.51777e9	+	1.05563e10i	−0.187995	+	1.30754i	−0.837190	+	0.546913i	$0.815803\pi$
$678$	−1.98782e9	+	4.35272e9i	−0.244948	+	0.536361i
$679$	−9.34523e8	+	2.04632e9i	−0.114563	+	0.250859i
$680$	1.89246e8	−	1.31624e9i	0.0230806	−	0.160529i
$681$	1.10550e9	−	7.10462e8i	0.134136	−	0.0862037i
$682$	1.35299e9	+	3.97273e8i	0.163323	+	0.0479561i
$683$	−8.66071e8	−	6.02366e9i	−0.104011	−	0.723416i	−0.973371	−	0.229236i	$-0.926377\pi$
$683$	−8.66071e8	−	6.02366e9i	−0.104011	−	0.723416i	0.869360	−	0.494180i	$-0.164532\pi$
$684$	7.40648e7	+	8.54753e7i	0.00884943	+	0.0102128i
$685$	−9.37769e8	−	6.02668e8i	−0.111475	−	0.0716409i
$686$	−4.84343e9	+	5.58962e9i	−0.572821	+	0.661071i
$687$	−6.10619e9	+	1.79294e9i	−0.718492	+	0.210968i
$688$	9.70214e8	+	2.12447e9i	0.113582	+	0.248709i
$689$	−1.56921e10			−1.82774
$690$	−8.61839e8	+	2.04543e9i	−0.0998744	+	0.237035i
$691$	−5.55498e9			−0.640486			−0.320243	−	0.947336i	$-0.603764\pi$
$691$	−5.55498e9			−0.640486			−0.320243	+	0.947336i	$0.603764\pi$
$692$	−6.50556e8	−	1.42452e9i	−0.0746299	−	0.163417i
$693$	8.97488e8	−	2.63526e8i	0.102438	−	0.0300786i
$694$	−1.08938e10	+	1.25721e10i	−1.23714	+	1.42774i
$695$	3.74870e8	+	2.40914e8i	0.0423578	+	0.0272217i
$696$	4.18156e8	+	4.82577e8i	0.0470117	+	0.0542544i
$697$	6.10891e8	+	4.24884e9i	0.0683359	+	0.475286i
$698$	−3.24088e9	−	9.51608e8i	−0.360719	−	0.105917i
$699$	−5.68956e9	+	3.65646e9i	−0.630099	+	0.404940i
$700$	7.00195e7	−	4.86996e8i	0.00771571	−	0.0536639i
$701$	1.08832e9	−	2.38309e9i	0.119328	−	0.261292i	−0.840537	−	0.541754i	$-0.817760\pi$
$701$	1.08832e9	−	2.38309e9i	0.119328	−	0.261292i	0.959865	+	0.280462i	$0.0904876\pi$
$702$	−9.69064e8	+	2.12195e9i	−0.105724	+	0.231503i
$703$	6.30388e8	−	4.38444e9i	0.0684328	−	0.475960i
$704$	−4.46926e9	+	2.87222e9i	−0.482760	+	0.310251i
$705$	−5.86098e8	−	1.72094e8i	−0.0629954	−	0.0184971i
$706$	2.35390e9	+	1.63717e10i	0.251751	+	1.75097i
$707$	7.64021e8	+	8.81728e8i	0.0813088	+	0.0938353i
$708$	4.20129e8	+	2.70000e8i	0.0444904	+	0.0285922i
$709$	1.13997e10	−	1.31560e10i	1.20125	−	1.38631i	0.299474	−	0.954104i	$-0.403189\pi$
$709$	1.13997e10	−	1.31560e10i	1.20125	−	1.38631i	0.901773	−	0.432209i	$-0.142266\pi$
$710$	3.65059e9	−	1.07191e9i	0.382789	−	0.112397i
$711$	−1.14467e9	−	2.50648e9i	−0.119437	−	0.261530i
$712$	−2.39915e9			−0.249102
$713$	1.48652e9	+	1.61620e9i	0.153588	+	0.166987i
$714$	1.16553e9			0.119834
$715$	−1.46736e9	−	3.21308e9i	−0.150130	−	0.328738i
$716$	−8.69047e8	+	2.55175e8i	−0.0884805	+	0.0259802i
$717$	−6.66504e9	+	7.69187e9i	−0.675283	+	0.779319i
$718$	−3.03658e9	−	1.95149e9i	−0.306161	−	0.196758i
$719$	−5.61205e9	−	6.47665e9i	−0.563080	−	0.649829i	0.400800	−	0.916166i	$-0.368732\pi$
$719$	−5.61205e9	−	6.47665e9i	−0.563080	−	0.649829i	−0.963880	+	0.266336i	$0.914187\pi$
$720$	2.22278e8	+	1.54597e9i	0.0221938	+	0.154361i
$721$	−1.16199e9	−	3.41190e8i	−0.115459	−	0.0339018i
$722$	8.37407e9	−	5.38169e9i	0.828049	−	0.532155i
$723$	8.29848e8	−	5.77172e9i	0.0816610	−	0.567965i
$724$	7.64746e8	−	1.67456e9i	0.0748914	−	0.163989i
$725$	4.78317e8	−	1.04737e9i	0.0466158	−	0.102074i
$726$	−4.60084e8	+	3.19995e9i	−0.0446230	+	0.310360i
$727$	−9.34103e8	+	6.00311e8i	−0.0901622	+	0.0579437i	−0.584945	−	0.811073i	$-0.698884\pi$
$727$	−9.34103e8	+	6.00311e8i	−0.0901622	+	0.0579437i	0.494783	+	0.869017i	$0.335248\pi$
$728$	−5.16402e9	−	1.51629e9i	−0.496053	−	0.145654i
$729$	−5.51357e7	−	3.83477e8i	−0.00527092	−	0.0366601i
$730$	3.70777e9	+	4.27900e9i	0.352763	+	0.407110i
$731$	9.19542e8	+	5.90954e8i	0.0870684	+	0.0559555i
$732$	1.38227e8	−	1.59523e8i	0.0130258	−	0.0150326i
$733$	1.82492e10	−	5.35846e9i	1.71152	−	0.502546i	0.728341	−	0.685215i	$-0.240292\pi$
$733$	1.82492e10	−	5.35846e9i	1.71152	−	0.502546i	0.983175	+	0.182668i	$0.0584735\pi$
$734$	−4.06078e9	−	8.89187e9i	−0.379030	−	0.829960i
$735$	−2.04946e9			−0.190386
$736$	3.08397e9	−	9.13919e7i	0.285127	−	0.00844959i
$737$	3.73693e9			0.343857
$738$	−1.82645e9	−	3.99936e9i	−0.167267	−	0.366263i
$739$	8.77703e9	−	2.57717e9i	0.800004	−	0.234902i	0.143919	−	0.989589i	$-0.454030\pi$
$739$	8.77703e9	−	2.57717e9i	0.800004	−	0.234902i	0.656085	+	0.754687i	$0.272211\pi$
$740$	−7.36446e8	+	8.49903e8i	−0.0668082	+	0.0771007i
$741$	−1.87677e9	−	1.20613e9i	−0.169453	−	0.108901i
$742$	−5.25891e9	−	6.06910e9i	−0.472587	−	0.545395i
$743$	−1.80508e9	−	1.25546e10i	−0.161449	−	1.12290i	−0.895905	−	0.444246i	$-0.853471\pi$
$743$	−1.80508e9	−	1.25546e10i	−0.161449	−	1.12290i	0.734456	−	0.678657i	$-0.237438\pi$
$744$	1.29290e9	+	3.79630e8i	0.115096	+	0.0337952i
$745$	2.54998e9	−	1.63877e9i	0.225938	−	0.145202i
$746$	−5.56052e8	+	3.86743e9i	−0.0490376	+	0.341064i
$747$	−2.11941e9	+	4.64086e9i	−0.186034	+	0.407358i
$748$	2.03763e8	−	4.46178e8i	0.0178020	−	0.0389810i
$749$	−6.56352e8	+	4.56503e9i	−0.0570756	+	0.396969i
$750$	4.56615e9	−	2.93449e9i	0.395217	−	0.253991i
$751$	1.40150e10	+	4.11519e9i	1.20741	+	0.354528i	0.822682	−	0.568502i	$-0.192477\pi$
$751$	1.40150e10	+	4.11519e9i	1.20741	+	0.354528i	0.384728	+	0.923030i	$0.374295\pi$
$752$	5.08779e8	+	3.53864e9i	0.0436282	+	0.303441i
$753$	1.80917e9	+	2.08790e9i	0.154418	+	0.178208i
$754$	1.77800e9	+	1.14265e9i	0.151054	+	0.0970762i
$755$	5.32801e9	−	6.14885e9i	0.450558	−	0.519972i
$756$	−1.43911e8	+	4.22560e7i	−0.0121134	+	0.00355682i
$757$	−3.07284e9	−	6.72858e9i	−0.257457	−	0.563751i	0.736128	−	0.676842i	$-0.236652\pi$
$757$	−3.07284e9	−	6.72858e9i	−0.257457	−	0.563751i	−0.993585	+	0.113091i	$0.963925\pi$
$758$	−2.22529e10			−1.85586
$759$	3.08454e9	−	3.78045e9i	0.256061	−	0.313832i
$760$	−1.30258e9			−0.107636
$761$	4.15849e9	+	9.10581e9i	0.342049	+	0.748984i	0.999992	−	0.00408465i	$-0.00130019\pi$
$761$	4.15849e9	+	9.10581e9i	0.342049	+	0.748984i	−0.657942	+	0.753068i	$0.728573\pi$
$762$	1.11682e9	−	3.27929e8i	0.0914413	−	0.0268496i
$763$	6.87431e9	−	7.93338e9i	0.560265	−	0.646580i
$764$	−1.48438e9	−	9.53951e8i	−0.120425	−	0.0773926i
$765$	4.78689e8	+	5.52437e8i	0.0386579	+	0.0446136i
$766$	−2.05530e8	−	1.42949e9i	−0.0165224	−	0.114916i
$767$	−9.45191e9	−	2.77533e9i	−0.756373	−	0.222091i
$768$	2.57664e9	−	1.65590e9i	0.205253	−	0.131908i
$769$	1.30673e9	−	9.08848e9i	0.103620	−	0.720691i	−0.870089	−	0.492894i	$-0.835939\pi$
$769$	1.30673e9	−	9.08848e9i	0.103620	−	0.720691i	0.973709	−	0.227796i	$-0.0731520\pi$
$770$	7.50935e8	−	1.64432e9i	0.0592768	−	0.129798i
$771$	−3.51896e9	+	7.70544e9i	−0.276518	+	0.605490i
$772$	2.91940e8	−	2.03049e9i	0.0228367	−	0.158833i
$773$	2.06726e10	−	1.32855e10i	1.60978	−	1.03454i	0.647657	−	0.761932i	$-0.275749\pi$
$773$	2.06726e10	−	1.32855e10i	1.60978	−	1.03454i	0.962124	−	0.272611i	$-0.0878873\pi$
$774$	−1.07423e9	−	3.15423e8i	−0.0832730	−	0.0244512i
$775$	−3.45795e8	−	2.40506e9i	−0.0266847	−	0.185596i
$776$	4.71554e9	+	5.44202e9i	0.362256	+	0.418065i
$777$	4.94166e9	+	3.17581e9i	0.377919	+	0.242874i
$778$	5.10261e9	−	5.88873e9i	0.388476	−	0.448325i
$779$	4.03442e9	−	1.18461e9i	0.305774	−	0.0897833i
$780$	2.35289e8	+	5.15211e8i	0.0177529	+	0.0388735i
$781$	−8.36362e9			−0.628226
$782$	5.01495e9	−	3.43699e9i	0.375010	−	0.257013i
$783$	−3.51007e8			−0.0261306
$784$	4.98279e9	+	1.09108e10i	0.369289	+	0.808630i
$785$	−3.89504e9	+	1.14369e9i	−0.287388	+	0.0843847i
$786$	−7.26930e9	+	8.38922e9i	−0.533966	+	0.616230i
$787$	−4.36067e9	−	2.80244e9i	−0.318891	−	0.204939i	0.371396	−	0.928475i	$-0.378879\pi$
$787$	−4.36067e9	−	2.80244e9i	−0.318891	−	0.204939i	−0.690287	+	0.723536i	$0.742516\pi$
$788$	−1.82176e9	−	2.10243e9i	−0.132633	−	0.153066i
$789$	1.08024e9	+	7.51327e9i	0.0782984	+	0.544577i
$790$	−5.10945e9	−	1.50027e9i	−0.368705	−	0.108262i
$791$	5.10534e9	−	3.28101e9i	0.366781	−	0.235716i
$792$	4.26100e8	−	2.96359e9i	0.0304771	−	0.211973i
$793$	−1.72961e9	+	3.78733e9i	−0.123167	+	0.269697i
$794$	−6.68869e9	+	1.46462e10i	−0.474208	+	1.03837i
$795$	7.16766e8	−	4.98522e9i	0.0505932	−	0.351884i
$796$	1.41719e9	−	9.10773e8i	0.0995939	−	0.0640051i
$797$	2.08865e10	+	6.13284e9i	1.46138	+	0.429099i	0.913286	−	0.407319i	$-0.133536\pi$
$797$	2.08865e10	+	6.13284e9i	1.46138	+	0.429099i	0.548092	+	0.836418i	$0.315354\pi$
$798$	−1.62480e8	−	1.13007e9i	−0.0113185	−	0.0787221i
$799$	1.09569e9	+	1.26449e9i	0.0759930	+	0.0877006i
$800$	−2.87203e9	−	1.84574e9i	−0.198324	−	0.127455i
$801$	8.63641e8	−	9.96695e8i	0.0593772	−	0.0685249i
$802$	8.91187e9	−	2.61676e9i	0.610040	−	0.179124i
$803$	−5.17034e9	−	1.13215e10i	−0.352383	−	0.771611i
$804$	−5.99209e8			−0.0406614
$805$	2.32199e9	−	1.59137e9i	0.156883	−	0.107519i
$806$	4.46003e9			0.300031
$807$	1.72266e9	+	3.77210e9i	0.115383	+	0.252654i
$808$	3.58321e9	−	1.05213e9i	0.238964	−	0.0701663i
$809$	−9.17163e9	+	1.05846e10i	−0.609013	+	0.702838i	−0.973582	−	0.228338i	$-0.926671\pi$
$809$	−9.17163e9	+	1.05846e10i	−0.609013	+	0.702838i	0.364569	+	0.931176i	$0.381216\pi$
$810$	−6.29858e8	−	4.04785e8i	−0.0416433	−	0.0267625i
$811$	1.39389e10	+	1.60863e10i	0.917604	+	1.05897i	0.998063	+	0.0622138i	$0.0198161\pi$
$811$	1.39389e10	+	1.60863e10i	0.917604	+	1.05897i	−0.0804586	+	0.996758i	$0.525638\pi$
$812$	1.93390e7	+	1.34506e8i	0.00126762	+	0.00881648i
$813$	3.43393e9	+	1.00829e9i	0.224117	+	0.0658066i
$814$	1.65530e10	−	1.06379e10i	1.07570	−	0.691309i
$815$	−5.40868e7	+	3.76182e8i	−0.00349977	+	0.0243414i
$816$	1.77720e9	−	3.89153e9i	0.114504	−	0.250729i
$817$	4.44788e8	−	9.73949e8i	0.0285349	−	0.0624826i
$818$	4.72839e9	−	3.28867e10i	0.302049	−	2.10080i
$819$	2.48886e9	−	1.59949e9i	0.158309	−	0.101739i
$820$	−1.02427e9	−	3.00753e8i	−0.0648734	−	0.0190486i
$821$	2.64404e9	+	1.83897e10i	0.166751	+	1.15978i	0.885545	+	0.464553i	$0.153785\pi$
$821$	2.64404e9	+	1.83897e10i	0.166751	+	1.15978i	−0.718795	+	0.695222i	$0.755306\pi$
$822$	−2.04804e9	−	2.36357e9i	−0.128614	−	0.148428i
$823$	−1.57492e10	−	1.01214e10i	−0.984824	−	0.632908i	−0.0540634	−	0.998538i	$-0.517217\pi$
$823$	−1.57492e10	−	1.01214e10i	−0.984824	−	0.632908i	−0.930760	+	0.365630i	$0.880854\pi$
$824$	−2.53853e9	+	2.92962e9i	−0.158066	+	0.182418i
$825$	−5.18022e9	+	1.52105e9i	−0.321188	+	0.0943093i
$826$	−2.09423e9	−	4.58573e9i	−0.129299	−	0.283125i
$827$	−5.29729e9			−0.325675			−0.162837	−	0.986653i	$-0.552065\pi$
$827$	−5.29729e9			−0.325675			−0.162837	+	0.986653i	$0.552065\pi$
$828$	−4.94600e8	+	6.06188e8i	−0.0302795	+	0.0371109i
$829$	−1.23640e10			−0.753732			−0.376866	−	0.926268i	$-0.622998\pi$
$829$	−1.23640e10			−0.753732			−0.376866	+	0.926268i	$0.622998\pi$
$830$	4.09588e9	+	8.96874e9i	0.248642	+	0.544450i
$831$	−2.13530e9	+	6.26981e8i	−0.129079	+	0.0379010i
$832$	−1.10038e10	+	1.26991e10i	−0.662388	+	0.764436i
$833$	4.72255e9	+	3.03500e9i	0.283086	+	0.181929i
$834$	8.18698e8	+	9.44828e8i	0.0488700	+	0.0563990i
$835$	−1.81961e8	−	1.26557e9i	−0.0108162	−	0.0752286i
$836$	−4.61010e8	−	1.35365e8i	−0.0272891	−	0.00801279i
$837$	−6.23128e8	+	4.00460e8i	−0.0367315	+	0.0236059i
$838$	−1.75790e9	+	1.22265e10i	−0.103191	+	0.717708i
$839$	−6.56369e9	+	1.43725e10i	−0.383691	+	0.840166i	0.614976	+	0.788546i	$0.289166\pi$
$839$	−6.56369e9	+	1.43725e10i	−0.383691	+	0.840166i	−0.998667	+	0.0516198i	$0.983562\pi$
$840$	7.17586e8	−	1.57129e9i	0.0417731	−	0.0914703i
$841$	2.40965e9	−	1.67595e10i	0.139691	−	0.971573i
$842$	2.13238e10	−	1.37040e10i	1.23104	−	0.791141i
$843$	6.80055e9	+	1.99682e9i	0.390974	+	0.114800i
$844$	1.19286e8	+	8.29651e8i	0.00682952	+	0.0475003i
$845$	−2.53159e9	−	2.92161e9i	−0.144343	−	0.166580i
$846$	−1.44171e9	−	9.26528e8i	−0.0818616	−	0.0526093i
$847$	2.68497e9	−	3.09862e9i	0.151826	−	0.175217i
$848$	−2.82826e10	+	8.30453e9i	−1.59270	+	0.467659i
$849$	−8.32394e9	−	1.82269e10i	−0.466823	−	1.02220i
$850$	−6.72734e9			−0.375731
$851$	3.06276e10	−	9.07634e8i	1.70357	−	0.0504844i
$852$	1.34109e9			0.0742882
$853$	9.48240e9	+	2.07636e10i	0.523114	+	1.14546i	0.968247	+	0.249996i	$0.0804292\pi$
$853$	9.48240e9	+	2.07636e10i	0.523114	+	1.14546i	−0.445133	+	0.895465i	$0.646843\pi$
$854$	−2.04444e9	+	6.00301e8i	−0.112324	+	0.0329812i
$855$	4.68899e8	−	5.41139e8i	0.0256565	−	0.0296092i
$856$	1.24190e10	+	7.98123e9i	0.676752	+	0.434922i
$857$	1.98571e10	+	2.29163e10i	1.07766	+	1.24369i	0.968327	+	0.249684i	$0.0803268\pi$
$857$	1.98571e10	+	2.29163e10i	1.07766	+	1.24369i	0.109336	+	0.994005i	$0.465128\pi$
$858$	−1.41035e9	−	9.80919e9i	−0.0762291	−	0.530185i
$859$	6.02891e9	+	1.77025e9i	0.324536	+	0.0952924i	0.439942	−	0.898026i	$-0.354999\pi$
$859$	6.02891e9	+	1.77025e9i	0.324536	+	0.0952924i	−0.115406	+	0.993318i	$0.536817\pi$
$860$	−2.28682e8	+	1.46965e8i	−0.0122599	+	0.00787896i
$861$	−7.93557e8	+	5.51931e9i	−0.0423708	+	0.294696i
$862$	−4.80507e9	+	1.05216e10i	−0.255520	+	0.559510i
$863$	−1.31627e10	+	2.88223e10i	−0.697119	+	1.52648i	0.146311	+	0.989239i	$0.453260\pi$
$863$	−1.31627e10	+	2.88223e10i	−0.697119	+	1.52648i	−0.843430	+	0.537239i	$0.819467\pi$
$864$	−1.48114e8	+	1.03015e9i	−0.00781262	+	0.0543380i
$865$	−8.34060e9	+	5.36018e9i	−0.438168	+	0.281593i
$866$	1.88371e10	+	5.53106e9i	0.985600	+	0.289398i
$867$	1.29178e9	+	8.98452e9i	0.0673165	+	0.468197i
$868$	1.87788e8	+	2.16719e8i	0.00974650	+	0.0112481i
$869$	9.84763e9	+	6.32869e9i	0.509052	+	0.327148i
$870$	−4.44220e8	+	5.12658e8i	−0.0228708	+	0.0263943i
$871$	1.13408e10	−	3.32995e9i	0.581539	−	0.170755i
$872$	−1.39584e10	−	3.05647e10i	−0.712901	−	1.56104i
$873$	−3.95831e9			−0.201354
$874$	−4.03154e9	−	4.38326e9i	−0.204259	−	0.222079i
$875$	−6.88377e9			−0.347375
$876$	8.29055e8	+	1.81538e9i	0.0416695	+	0.0912436i
$877$	−2.92867e10	+	8.59934e9i	−1.46613	+	0.430493i	−0.914838	−	0.403822i	$-0.867682\pi$
$877$	−2.92867e10	+	8.59934e9i	−1.46613	+	0.430493i	−0.551288	+	0.834315i	$0.685863\pi$
$878$	1.84039e9	−	2.12393e9i	0.0917656	−	0.105903i
$879$	−1.16560e10	−	7.49085e9i	−0.578880	−	0.372023i
$880$	−4.34511e9	−	5.01452e9i	−0.214937	−	0.248050i
$881$	−2.20632e9	−	1.53453e10i	−0.108706	−	0.756066i	−0.969141	−	0.246506i	$-0.920717\pi$
$881$	−2.20632e9	−	1.53453e10i	−0.108706	−	0.756066i	0.860435	−	0.509560i	$-0.170192\pi$
$882$	−5.51699e9	−	1.61994e9i	−0.270746	−	0.0794983i
$883$	1.95303e10	−	1.25514e10i	0.954657	−	0.613521i	0.0321428	−	0.999483i	$-0.489767\pi$
$883$	1.95303e10	−	1.25514e10i	0.954657	−	0.613521i	0.922515	+	0.385962i	$0.126130\pi$
$884$	2.20790e8	−	1.53563e9i	0.0107497	−	0.0747658i
$885$	1.31343e9	−	2.87600e9i	0.0636948	−	0.139472i
$886$	−8.16267e9	+	1.78738e10i	−0.394289	+	0.863372i
$887$	−3.15226e9	+	2.19244e10i	−0.151666	+	1.05486i	0.761761	+	0.647859i	$0.224335\pi$
$887$	−3.15226e9	+	2.19244e10i	−0.151666	+	1.05486i	−0.913427	+	0.407003i	$0.866574\pi$
$888$	1.58178e10	−	1.01655e10i	0.758057	−	0.487174i
$889$	−1.41641e9	−	4.15895e8i	−0.0676133	−	0.0198530i
$890$	−3.62717e8	−	2.52275e9i	−0.0172466	−	0.119952i
$891$	1.07780e9	+	1.24385e9i	0.0510465	+	0.0589108i
$892$	−5.58168e8	−	3.58713e8i	−0.0263323	−	0.0169227i
$893$	1.07328e9	−	1.23863e9i	0.0504352	−	0.0582053i
$894$	8.15968e9	−	2.39590e9i	0.381937	−	0.112147i
$895$	2.38205e9	+	5.21597e9i	0.111063	+	0.243195i
$896$	−1.14033e10			−0.529606
$897$	5.99218e9	−	1.42215e10i	0.277212	−	0.657917i
$898$	−2.17090e10			−1.00040
$899$	2.78783e8	+	6.10450e8i	0.0127970	+	0.0280215i
$900$	8.30638e8	−	2.43897e8i	0.0379807	−	0.0111521i
$901$	−9.03412e9	+	1.04259e10i	−0.411480	+	0.474874i
$902$	1.57129e10	+	1.00981e10i	0.712910	+	0.458159i
$903$	9.29839e8	+	1.07309e9i	0.0420243	+	0.0484987i
$904$	−2.76454e9	−	1.92278e10i	−0.124461	−	0.865645i
$905$	−1.11826e10	−	3.28352e9i	−0.501504	−	0.147255i
$906$	1.92028e10	−	1.23409e10i	0.857858	−	0.551312i
$907$	5.05618e9	−	3.51665e10i	0.225008	−	1.56496i	−0.493689	−	0.869638i	$-0.664352\pi$
$907$	5.05618e9	−	3.51665e10i	0.225008	−	1.56496i	0.718697	−	0.695324i	$-0.244739\pi$
$908$	3.71864e8	−	8.14268e8i	0.0164848	−	0.0360967i
$909$	−8.52787e8	+	1.86734e9i	−0.0376588	+	0.0824613i
$910$	8.13686e8	−	5.65931e9i	0.0357941	−	0.248954i
$911$	3.03205e9	−	1.94858e9i	0.132868	−	0.0853893i	−0.472518	−	0.881321i	$-0.656655\pi$
$911$	3.03205e9	−	1.94858e9i	0.132868	−	0.0853893i	0.605387	+	0.795932i	$0.293019\pi$
$912$	−4.02090e9	−	1.18064e9i	−0.175526	−	0.0515390i
$913$	−3.08453e9	−	2.14534e10i	−0.134135	−	0.932927i
$914$	8.48666e9	+	9.79412e9i	0.367642	+	0.424281i
$915$	−1.12419e9	−	7.22473e8i	−0.0485138	−	0.0311780i
$916$	−2.83888e9	+	3.27625e9i	−0.122043	+	0.140845i
$917$	1.35079e10	−	3.96628e9i	0.578490	−	0.169860i
$918$	8.51937e8	+	1.86548e9i	0.0363461	+	0.0795869i
$919$	−3.20533e10			−1.36229			−0.681143	−	0.732150i	$-0.738517\pi$
$919$	−3.20533e10			−1.36229			−0.681143	+	0.732150i	$0.738517\pi$
$920$	−1.54596e9	−	8.87690e9i	−0.0654545	−	0.375841i
$921$	1.66526e10			0.702382
$922$	1.35924e10	+	2.97631e10i	0.571132	+	1.25060i
$923$	−2.53818e10	+	7.45277e9i	−1.06247	+	0.311969i
$924$	4.17259e8	−	4.81543e8i	0.0174002	−	0.0200809i
$925$	−2.85228e10	−	1.83305e10i	−1.18494	−	0.761514i
$926$	5.81238e9	+	6.70785e9i	0.240556	+	0.277616i
$927$	−3.03257e8	−	2.10920e9i	−0.0125035	−	0.0869639i
$928$	9.04732e8	+	2.65653e8i	0.0371623	+	0.0109118i
$929$	−3.35788e10	+	2.15798e10i	−1.37407	+	0.883064i	−0.999034	−	0.0439452i	$-0.986007\pi$
$929$	−3.35788e10	+	2.15798e10i	−1.37407	+	0.883064i	−0.375040	+	0.927009i	$0.622371\pi$
$930$	−2.03720e8	+	1.41690e9i	−0.00830508	+	0.0577631i
$931$	2.28432e9	−	5.00197e9i	0.0927756	−	0.203150i
$932$	−1.91383e9	+	4.19071e9i	−0.0774370	+	0.169563i
$933$	−2.63992e6	+	1.83611e7i	−0.000106416	+	0.000740137i
$934$	1.73420e8	−	1.11450e8i	0.00696442	−	0.00447576i
$935$	−2.97956e9	−	8.74878e8i	−0.119210	−	0.0350031i
$936$	−1.34771e9	−	9.37356e9i	−0.0537196	−	0.373628i
$937$	2.23275e10	+	2.57673e10i	0.886650	+	1.02325i	0.999561	+	0.0296433i	$0.00943713\pi$
$937$	2.23275e10	+	2.57673e10i	0.886650	+	1.02325i	−0.112911	+	0.993605i	$0.536017\pi$
$938$	5.08853e9	+	3.27020e9i	0.201318	+	0.129379i
$939$	−4.23480e9	+	4.88722e9i	−0.166918	+	0.192634i
$940$	−3.99246e8	+	1.17229e8i	−0.0156781	+	0.00460350i
$941$	−1.62941e10	−	3.56791e10i	−0.637481	−	1.39589i	−0.902097	−	0.431534i	$-0.857972\pi$
$941$	−1.62941e10	−	3.56791e10i	−0.637481	−	1.39589i	0.264616	−	0.964354i	$-0.414755\pi$
$942$	−1.13892e10			−0.443929
$943$	1.28612e10	+	2.60881e10i	0.499449	+	1.01310i
$944$	−1.85044e10			−0.715933
$945$	3.94458e8	+	8.63743e8i	0.0152051	+	0.0332946i
$946$	4.56356e9	−	1.33998e9i	0.175261	−	0.0514612i
$947$	−1.86287e10	+	2.14987e10i	−0.712784	+	0.822597i	−0.990420	−	0.138090i	$-0.955904\pi$
$947$	−1.86287e10	+	2.14987e10i	−0.712784	+	0.822597i	0.277635	+	0.960687i	$0.410449\pi$
$948$	−1.57905e9	−	1.01479e9i	−0.0601958	−	0.0386855i
$949$	−2.57794e10	−	2.97510e10i	−0.979130	−	1.12998i
$950$	9.37820e8	+	6.52268e9i	0.0354884	+	0.246827i
$951$	−3.00896e9	−	8.83511e8i	−0.113445	−	0.0333104i
$952$	−3.98042e9	+	2.55806e9i	−0.149520	+	0.0960906i
$953$	2.46548e9	−	1.71478e10i	0.0922732	−	0.641774i	−0.890228	−	0.455516i	$-0.849455\pi$
$953$	2.46548e9	−	1.71478e10i	0.0922732	−	0.641774i	0.982501	−	0.186258i	$-0.0596361\pi$
$954$	5.86990e9	−	1.28533e10i	0.218883	−	0.479286i
$955$	−4.64053e9	+	1.01613e10i	−0.172407	+	0.377519i
$956$	−9.86675e8	+	6.86248e9i	−0.0365234	+	0.254026i
$957$	1.25444e9	−	8.06178e8i	0.0462655	−	0.0297330i
$958$	−3.44675e10	−	1.01206e10i	−1.26657	−	0.371899i
$959$	5.64473e8	+	3.92600e9i	0.0206670	+	0.143742i
$960$	−3.53175e9	−	4.07585e9i	−0.128837	−	0.148686i
$961$	−2.19537e10	−	1.41088e10i	−0.797951	−	0.512812i
$962$	4.07553e10	−	4.70341e10i	1.47595	−	1.70334i
$963$	−7.78628e9	+	2.28626e9i	−0.280956	+	0.0824960i
$964$	−1.65006e9	−	3.61314e9i	−0.0593241	−	0.129902i
$965$	−1.29871e10			−0.465228
$966$	7.50847e9	−	2.44850e9i	0.267998	−	0.0873938i
$967$	−5.19096e10			−1.84610			−0.923049	−	0.384683i	$-0.874311\pi$
$967$	−5.19096e10			−1.84610			−0.923049	+	0.384683i	$0.874311\pi$
$968$	−5.45188e9	−	1.19380e10i	−0.193189	−	0.423025i
$969$	−1.88184e9	+	5.52557e8i	−0.0664429	+	0.0195094i
$970$	−5.00947e9	+	5.78123e9i	−0.176234	+	0.203385i
$971$	2.27150e10	+	1.45980e10i	0.796241	+	0.511713i	0.874387	−	0.485229i	$-0.161264\pi$
$971$	2.27150e10	+	1.45980e10i	0.796241	+	0.511713i	−0.0781461	+	0.996942i	$0.524900\pi$
$972$	−1.72823e8	−	1.99448e8i	−0.00603628	−	0.00696624i
$973$	−2.25646e8	−	1.56940e9i	−0.00785295	−	0.0546185i
$974$	2.19348e10	+	6.44063e9i	0.760635	+	0.223343i
$975$	−1.43655e10	+	9.23212e9i	−0.496367	+	0.318996i
$976$	−1.11305e9	+	7.74141e9i	−0.0383212	+	0.266530i
$977$	9.28266e9	−	2.03262e10i	0.318450	−	0.697308i	−0.680936	−	0.732343i	$-0.738427\pi$
$977$	9.28266e9	−	2.03262e10i	0.318450	−	0.697308i	0.999386	+	0.0350345i	$0.0111541\pi$
$978$	−4.42939e8	+	9.69901e8i	−0.0151411	+	0.0331544i
$979$	−7.97334e8	+	5.54558e9i	−0.0271582	+	0.188889i
$980$	−1.17446e9	+	7.54777e8i	−0.0398607	+	0.0256169i
$981$	1.77224e10	+	5.20378e9i	0.599352	+	0.175986i
$982$	7.10535e9	+	4.94188e10i	0.239439	+	1.66534i
$983$	−1.65840e10	−	1.91390e10i	−0.556869	−	0.642661i	0.405601	−	0.914050i	$-0.367062\pi$
$983$	−1.65840e10	−	1.91390e10i	−0.556869	−	0.642661i	−0.962470	+	0.271389i	$0.912517\pi$
$984$	1.50151e10	+	9.64964e9i	0.502396	+	0.322870i
$985$	−1.15335e10	+	1.33103e10i	−0.384532	+	0.443774i
$986$	1.78279e9	−	5.23475e8i	0.0592286	−	0.0173911i
$987$	9.02890e8	+	1.97705e9i	0.0298899	+	0.0654498i
$988$	−1.51969e9			−0.0501309
$989$	7.16524e9	+	1.87525e9i	0.235529	+	0.0616413i
$990$	3.18069e9			0.104183
$991$	1.85283e10	+	4.05713e10i	0.604752	+	1.32422i	0.926106	+	0.377263i	$0.123135\pi$
$991$	1.85283e10	+	4.05713e10i	0.604752	+	1.32422i	−0.321354	+	0.946959i	$0.604138\pi$
$992$	1.90921e9	−	5.60596e8i	0.0620960	−	0.0182330i
$993$	−8.89444e9	+	1.02647e10i	−0.288268	+	0.332679i
$994$	−1.13887e10	−	7.31904e9i	−0.367807	−	0.236375i
$995$	−6.98423e9	−	8.06023e9i	−0.224770	−	0.259398i
$996$	4.94598e8	+	3.44001e9i	0.0158615	+	0.110319i
$997$	1.99819e10	+	5.86723e9i	0.638564	+	0.187499i	0.584959	−	0.811063i	$-0.301111\pi$
$997$	1.99819e10	+	5.86723e9i	0.638564	+	0.187499i	0.0536052	+	0.998562i	$0.482929\pi$
$998$	4.81011e10	−	3.09127e10i	1.53179	−	0.984420i
$999$	−1.47095e9	+	1.02307e10i	−0.0466787	+	0.324657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.8.e.a.4.4	✓	140
23.6	even	11	inner	69.8.e.a.52.4	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.e.a.4.4	✓	140	1.1	even	1	trivial
69.8.e.a.52.4	yes	140	23.6	even	11	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.02622 - 11.0059i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(-12.0443 + 13.8999i) q^{4} +(97.9555 + 62.9522i) q^{5} +(213.930 + 246.888i) q^{6} +(-58.9625 - 410.093i) q^{7} +(-1272.45 - 373.626i) q^{8} +(613.274 - 394.127i) q^{9} +O(q^{10})\)	\(q+(-5.02622 - 11.0059i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(-12.0443 + 13.8999i) q^{4} +(97.9555 + 62.9522i) q^{5} +(213.930 + 246.888i) q^{6} +(-58.9625 - 410.093i) q^{7} +(-1272.45 - 373.626i) q^{8} +(613.274 - 394.127i) q^{9} +(200.498 - 1394.50i) q^{10} +(-1286.52 + 2817.08i) q^{11} +(206.291 - 451.714i) q^{12} +(-1394.02 + 9695.65i) q^{13} +(-4217.08 + 2710.15i) q^{14} +(-3016.53 - 885.732i) q^{15} +(2618.58 + 18212.6i) q^{16} +(5639.29 + 6508.08i) q^{17} +(-7420.16 - 4768.65i) q^{18} +(5523.96 - 6374.99i) q^{19} +(-2054.84 + 603.355i) q^{20} +(4646.99 + 10175.5i) q^{21} +37470.8 q^{22} +(50000.8 + 30079.0i) q^{23} +35806.7 q^{24} +(-26822.0 - 58732.0i) q^{25} +(113716. - 33390.0i) q^{26} +(-12889.6 + 14875.4i) q^{27} +(6410.42 + 4119.73i) q^{28} +(11678.1 + 13477.3i) q^{29} +(5413.46 + 37651.4i) q^{30} +(36107.8 + 10602.2i) q^{31} +(44481.6 - 28586.6i) q^{32} +(11900.0 - 82766.4i) q^{33} +(43282.9 - 94776.3i) q^{34} +(20040.6 - 43882.7i) q^{35} +(-1908.15 + 13271.4i) q^{36} +(441757. - 283900. i) q^{37} +(-97926.9 - 28753.9i) q^{38} +(-37638.6 - 261782. i) q^{39} +(-101123. - 116702. i) q^{40} +(419339. + 269493. i) q^{41} +(88633.4 - 102288. i) q^{42} +(121790. - 35760.7i) q^{43} +(-23661.9 - 51812.3i) q^{44} +84884.7 q^{45} +(79730.6 - 701486. i) q^{46} +194296. q^{47} +(-206377. - 451903. i) q^{48} +(625484. - 183659. i) q^{49} +(-511584. + 590399. i) q^{50} +(-195599. - 125704. i) q^{51} +(-117978. - 136154. i) q^{52} +(227988. + 1.58569e6i) q^{53} +(228503. + 67094.6i) q^{54} +(-303363. + 194959. i) q^{55} +(-78194.5 + 543855. i) q^{56} +(-94612.2 + 207172. i) q^{57} +(89632.6 - 196268. i) q^{58} +(-143123. + 995439. i) q^{59} +(48643.7 - 31261.4i) q^{60} +(407839. + 119752. i) q^{61} +(-64799.0 - 450687. i) q^{62} +(-197789. - 228261. i) q^{63} +(1.44312e6 + 927436. i) q^{64} +(-746914. + 861985. i) q^{65} +(-970729. + 285032. i) q^{66} +(-501260. - 1.09761e6i) q^{67} -158383. q^{68} +(-1.52414e6 - 398890. i) q^{69} -583696. q^{70} +(1.12187e6 + 2.45655e6i) q^{71} +(-927619. + 272374. i) q^{72} +(-2.63180e6 + 3.03726e6i) q^{73} +(-5.34493e6 - 3.43498e6i) q^{74} +(1.14162e6 + 1.31750e6i) q^{75} +(22079.3 + 153565. i) q^{76} +(1.23112e6 + 361490. i) q^{77} +(-2.69197e6 + 1.73002e6i) q^{78} +(537925. - 3.74135e6i) q^{79} +(-890021. + 1.94887e6i) q^{80} +(220769. - 483416. i) q^{81} +(858316. - 5.96972e6i) q^{82} +(-5.88751e6 + 3.78367e6i) q^{83} +(-197408. - 57964.3i) q^{84} +(142701. + 992508. i) q^{85} +(-1.00572e6 - 1.16066e6i) q^{86} +(-405056. - 260314. i) q^{87} +(2.68957e6 - 3.10393e6i) q^{88} +(1.73580e6 - 509676. i) q^{89} +(-426649. - 934230. i) q^{90} +4.05831e6 q^{91} +(-1.02032e6 + 332725. i) q^{92} -1.01607e6 q^{93} +(-976572. - 2.13839e6i) q^{94} +(942421. - 276720. i) q^{95} +(-934902. + 1.07893e6i) q^{96} +(-4.56782e6 - 2.93556e6i) q^{97} +(-5.16514e6 - 5.96089e6i) q^{98} +(321300. + 2.23469e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9}+O(q^{10}) \) 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9	\( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9} + 1322 q^{10} + 7892 q^{11} - 19980 q^{12} + 39810 q^{13} - 26296 q^{14} + 135 q^{15} - 142164 q^{16} - 97081 q^{17} - 11664 q^{18} + 120905 q^{19} + 124755 q^{20} + 26406 q^{21} - 837266 q^{22} - 224688 q^{23} - 60264 q^{24} - 180624 q^{25} + 385108 q^{26} - 275562 q^{27} + 1121760 q^{28} - 375654 q^{29} + 35694 q^{30} + 505029 q^{31} - 661528 q^{32} - 360423 q^{33} - 1872759 q^{34} - 964610 q^{35} - 1269189 q^{36} - 28802 q^{37} - 1459868 q^{38} + 1074870 q^{39} + 5371901 q^{40} - 1557480 q^{41} + 883116 q^{42} + 1160786 q^{43} - 4521825 q^{44} - 2009124 q^{45} - 4123580 q^{46} + 811422 q^{47} - 1563111 q^{48} - 10960262 q^{49} + 16636695 q^{50} + 4413852 q^{51} - 4843791 q^{52} + 4291672 q^{53} - 98415 q^{54} + 2093539 q^{55} - 12548382 q^{56} - 4007907 q^{57} - 7414367 q^{58} + 2955424 q^{59} + 7289973 q^{60} + 4919292 q^{61} + 16083211 q^{62} + 712962 q^{63} - 1673596 q^{64} - 13246221 q^{65} + 7219449 q^{66} + 148565 q^{67} - 23039568 q^{68} - 657018 q^{69} + 12781104 q^{70} - 7247645 q^{71} - 600696 q^{72} + 32596055 q^{73} + 32550658 q^{74} - 10061874 q^{75} + 12150569 q^{76} - 43349150 q^{77} - 17201700 q^{78} + 4815410 q^{79} + 36529590 q^{80} - 7440174 q^{81} + 20862470 q^{82} + 35160800 q^{83} - 5346540 q^{84} + 48578363 q^{85} + 76972708 q^{86} + 1505088 q^{87} - 35912212 q^{88} + 1401264 q^{89} + 963738 q^{90} - 91970208 q^{91} - 74293537 q^{92} + 555606 q^{93} - 32520253 q^{94} + 79436789 q^{95} + 41519736 q^{96} + 18296816 q^{97} - 38956823 q^{98} - 9731421 q^{99}+O(q^{100}) \) 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9 + 1322 * q^10 + 7892 * q^11 - 19980 * q^12 + 39810 * q^13 - 26296 * q^14 + 135 * q^15 - 142164 * q^16 - 97081 * q^17 - 11664 * q^18 + 120905 * q^19 + 124755 * q^20 + 26406 * q^21 - 837266 * q^22 - 224688 * q^23 - 60264 * q^24 - 180624 * q^25 + 385108 * q^26 - 275562 * q^27 + 1121760 * q^28 - 375654 * q^29 + 35694 * q^30 + 505029 * q^31 - 661528 * q^32 - 360423 * q^33 - 1872759 * q^34 - 964610 * q^35 - 1269189 * q^36 - 28802 * q^37 - 1459868 * q^38 + 1074870 * q^39 + 5371901 * q^40 - 1557480 * q^41 + 883116 * q^42 + 1160786 * q^43 - 4521825 * q^44 - 2009124 * q^45 - 4123580 * q^46 + 811422 * q^47 - 1563111 * q^48 - 10960262 * q^49 + 16636695 * q^50 + 4413852 * q^51 - 4843791 * q^52 + 4291672 * q^53 - 98415 * q^54 + 2093539 * q^55 - 12548382 * q^56 - 4007907 * q^57 - 7414367 * q^58 + 2955424 * q^59 + 7289973 * q^60 + 4919292 * q^61 + 16083211 * q^62 + 712962 * q^63 - 1673596 * q^64 - 13246221 * q^65 + 7219449 * q^66 + 148565 * q^67 - 23039568 * q^68 - 657018 * q^69 + 12781104 * q^70 - 7247645 * q^71 - 600696 * q^72 + 32596055 * q^73 + 32550658 * q^74 - 10061874 * q^75 + 12150569 * q^76 - 43349150 * q^77 - 17201700 * q^78 + 4815410 * q^79 + 36529590 * q^80 - 7440174 * q^81 + 20862470 * q^82 + 35160800 * q^83 - 5346540 * q^84 + 48578363 * q^85 + 76972708 * q^86 + 1505088 * q^87 - 35912212 * q^88 + 1401264 * q^89 + 963738 * q^90 - 91970208 * q^91 - 74293537 * q^92 + 555606 * q^93 - 32520253 * q^94 + 79436789 * q^95 + 41519736 * q^96 + 18296816 * q^97 - 38956823 * q^98 - 9731421 * q^99

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