LMFDB - Embedded newform 69.7.h.a.2.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(2,69)]

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([11, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("69.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.h (of order $22$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			2.15
Character	$\chi$	$=$	69.2
Dual form			69.7.h.a.35.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.42615 + 5.33119i) q^{2} +(-15.7384 - 21.9386i) q^{3} +(9.90347 + 21.6856i) q^{4} +(55.1132 - 187.698i) q^{5} +(170.881 - 8.73922i) q^{6} +(168.523 - 194.486i) q^{7} +(-550.993 - 79.2208i) q^{8} +(-233.608 + 690.557i) q^{9} +O(q^{10})$	\(q+(-3.42615 + 5.33119i) q^{2} +(-15.7384 - 21.9386i) q^{3} +(9.90347 + 21.6856i) q^{4} +(55.1132 - 187.698i) q^{5} +(170.881 - 8.73922i) q^{6} +(168.523 - 194.486i) q^{7} +(-550.993 - 79.2208i) q^{8} +(-233.608 + 690.557i) q^{9} +(811.829 + 936.900i) q^{10} +(-388.967 - 605.245i) q^{11} +(319.888 - 558.564i) q^{12} +(2606.90 + 3008.52i) q^{13} +(459.456 + 1564.76i) q^{14} +(-4985.24 + 1744.96i) q^{15} +(1310.97 - 1512.93i) q^{16} +(-4897.84 - 2236.77i) q^{17} +(-2881.11 - 3611.35i) q^{18} +(-4127.31 - 9037.55i) q^{19} +(4616.16 - 663.703i) q^{20} +(-6919.03 - 636.274i) q^{21} +4559.33 q^{22} +(-11283.2 + 4552.57i) q^{23} +(6933.73 + 13334.8i) q^{24} +(-19048.6 - 12241.8i) q^{25} +(-24970.6 + 3590.23i) q^{26} +(18826.5 - 5743.20i) q^{27} +(5886.50 + 1728.43i) q^{28} +(-11292.1 - 5156.92i) q^{29} +(7777.46 - 32555.7i) q^{30} +(647.426 - 4502.95i) q^{31} +(-6462.87 - 22010.5i) q^{32} +(-7156.54 + 18059.0i) q^{33} +(28705.3 - 18447.8i) q^{34} +(-27216.8 - 42350.2i) q^{35} +(-17288.7 + 1772.99i) q^{36} +(-78726.4 + 23116.2i) q^{37} +(62321.7 + 8960.50i) q^{38} +(24974.5 - 104541. i) q^{39} +(-45236.6 + 99054.3i) q^{40} +(-2791.89 + 9508.32i) q^{41} +(27097.7 - 34706.7i) q^{42} +(-6504.19 - 45237.7i) q^{43} +(9272.96 - 14429.0i) q^{44} +(116741. + 81906.5i) q^{45} +(14387.2 - 75750.5i) q^{46} +25049.3i q^{47} +(-53824.2 - 4949.67i) q^{48} +(7318.43 + 50900.8i) q^{49} +(130526. - 59609.5i) q^{50} +(28012.3 + 142655. i) q^{51} +(-39424.2 + 86327.0i) q^{52} +(-85338.8 - 73946.5i) q^{53} +(-33884.2 + 120045. i) q^{54} +(-135041. + 39651.5i) q^{55} +(-108262. + 93809.8i) q^{56} +(-133314. + 232784. i) q^{57} +(66180.9 - 42531.9i) q^{58} +(-62111.4 + 53819.8i) q^{59} +(-87211.5 - 90826.6i) q^{60} +(-32345.1 + 224965. i) q^{61} +(21787.9 + 18879.3i) q^{62} +(94935.3 + 161808. i) q^{63} +(262417. + 77052.5i) q^{64} +(708369. - 323501. i) q^{65} +(-71756.5 - 100026. i) q^{66} +(168861. + 108520. i) q^{67} -128364. i q^{68} +(277456. + 175887. i) q^{69} +319026. q^{70} +(-119410. + 185805. i) q^{71} +(183423. - 361985. i) q^{72} +(-266212. - 582923. i) q^{73} +(146492. - 498905. i) q^{74} +(31225.6 + 610566. i) q^{75} +(155110. - 179006. i) q^{76} +(-183262. - 26349.0i) q^{77} +(471762. + 491317. i) q^{78} +(-250512. - 289107. i) q^{79} +(-211724. - 329449. i) q^{80} +(-422296. - 322638. i) q^{81} +(-41125.2 - 47461.0i) q^{82} +(-99794.4 - 339869. i) q^{83} +(-54724.5 - 156345. i) q^{84} +(-689772. + 796040. i) q^{85} +(263455. + 120316. i) q^{86} +(64583.1 + 328895. i) q^{87} +(166370. + 364300. i) q^{88} +(1.04357e6 - 150042. i) q^{89} +(-836632. + 341747. i) q^{90} +1.02444e6 q^{91} +(-210468. - 199596. i) q^{92} +(-108978. + 56665.4i) q^{93} +(-133543. - 85822.6i) q^{94} +(-1.92380e6 + 276601. i) q^{95} +(-381166. + 488196. i) q^{96} +(-1.43642e6 - 421772. i) q^{97} +(-296436. - 135378. i) q^{98} +(508822. - 127214. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) $ 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−3.42615	+	5.33119i	−0.428268	+	0.666399i	−0.986589	−	0.163227i	$-0.947810\pi$
$2$	−3.42615	+	5.33119i	−0.428268	+	0.666399i	0.558320	+	0.829626i	$0.311446\pi$
$3$	−15.7384	−	21.9386i	−0.582903	−	0.812542i
$3$	−15.7384	−	21.9386i	−0.582903	−	0.812542i
$4$	9.90347	+	21.6856i	0.154742	+	0.338837i
$5$	55.1132	−	187.698i	0.440905	−	1.50159i	−0.376989	−	0.926218i	$-0.623041\pi$
$5$	55.1132	−	187.698i	0.440905	−	1.50159i	0.817894	−	0.575368i	$-0.195141\pi$
$6$	170.881	−	8.73922i	0.791116	−	0.0404593i
$7$	168.523	−	194.486i	0.491321	−	0.567014i	−0.454897	−	0.890544i	$-0.650324\pi$
$7$	168.523	−	194.486i	0.491321	−	0.567014i	0.946218	+	0.323530i	$0.104870\pi$
$8$	−550.993	−	79.2208i	−1.07616	−	0.154728i
$9$	−233.608	+	690.557i	−0.320449	+	0.947266i
$10$	811.829	+	936.900i	0.811829	+	0.936900i
$11$	−388.967	−	605.245i	−0.292237	−	0.454729i	0.663828	−	0.747886i	$-0.268931\pi$
$11$	−388.967	−	605.245i	−0.292237	−	0.454729i	−0.956065	+	0.293156i	$0.905294\pi$
$12$	319.888	−	558.564i	0.185120	−	0.323243i
$13$	2606.90	+	3008.52i	1.18657	+	1.36938i	0.913221	+	0.407464i	$0.133587\pi$
$13$	2606.90	+	3008.52i	1.18657	+	1.36938i	0.273351	+	0.961914i	$0.411868\pi$
$14$	459.456	+	1564.76i	0.167440	+	0.570250i
$15$	−4985.24	+	1744.96i	−1.47711	+	0.517024i
$16$	1310.97	−	1512.93i	0.320060	−	0.369369i
$17$	−4897.84	−	2236.77i	−0.996913	−	0.455275i	−0.150965	−	0.988539i	$-0.548238\pi$
$17$	−4897.84	−	2236.77i	−0.996913	−	0.455275i	−0.845949	+	0.533264i	$0.820965\pi$
$18$	−2881.11	−	3611.35i	−0.494018	−	0.619231i
$19$	−4127.31	−	9037.55i	−0.601737	−	1.31762i	−0.928084	−	0.372370i	$-0.878545\pi$
$19$	−4127.31	−	9037.55i	−0.601737	−	1.31762i	0.326348	−	0.945250i	$-0.394182\pi$
$20$	4616.16	−	663.703i	0.577020	−	0.0829629i
$21$	−6919.03	−	636.274i	−0.747115	−	0.0687047i
$22$	4559.33			0.428187
$23$	−11283.2	+	4552.57i	−0.927359	+	0.374174i
$23$	−11283.2	+	4552.57i	−0.927359	+	0.374174i
$24$	6933.73	+	13334.8i	0.501572	+	0.964615i
$25$	−19048.6	−	12241.8i	−1.21911	−	0.783474i
$26$	−24970.6	+	3590.23i	−1.42072	+	0.204269i
$27$	18826.5	−	5743.20i	0.956484	−	0.291785i
$28$	5886.50	+	1728.43i	0.268153	+	0.0787369i
$29$	−11292.1	−	5156.92i	−0.462999	−	0.211445i	0.170237	−	0.985403i	$-0.445547\pi$
$29$	−11292.1	−	5156.92i	−0.462999	−	0.211445i	−0.633236	+	0.773958i	$0.718274\pi$
$30$	7777.46	−	32555.7i	0.288054	−	1.20577i
$31$	647.426	−	4502.95i	0.0217323	−	0.151151i	−0.976066	−	0.217475i	$-0.930218\pi$
$31$	647.426	−	4502.95i	0.0217323	−	0.151151i	0.997798	+	0.0663238i	$0.0211270\pi$
$32$	−6462.87	−	22010.5i	−0.197231	−	0.671708i
$33$	−7156.54	+	18059.0i	−0.199141	+	0.502518i
$34$	28705.3	−	18447.8i	0.730341	−	0.469362i
$35$	−27216.8	−	42350.2i	−0.634795	−	0.987760i
$36$	−17288.7	+	1772.99i	−0.370556	+	0.0380014i
$37$	−78726.4	+	23116.2i	−1.55423	+	0.456363i	−0.942361	−	0.334597i	$-0.891400\pi$
$37$	−78726.4	+	23116.2i	−1.55423	+	0.456363i	−0.611868	+	0.790960i	$0.709582\pi$
$38$	62321.7	+	8960.50i	1.13576	+	0.163298i
$39$	24974.5	−	104541.i	0.421021	−	1.76235i
$40$	−45236.6	+	99054.3i	−0.706822	+	1.54772i
$41$	−2791.89	+	9508.32i	−0.0405086	+	0.137960i	−0.977265	−	0.212024i	$-0.931995\pi$
$41$	−2791.89	+	9508.32i	−0.0405086	+	0.137960i	0.936756	+	0.349983i	$0.113813\pi$
$42$	27097.7	−	34706.7i	0.365750	−	0.468452i
$43$	−6504.19	−	45237.7i	−0.0818065	−	0.568977i	−0.988961	−	0.148178i	$-0.952659\pi$
$43$	−6504.19	−	45237.7i	−0.0818065	−	0.568977i	0.907154	−	0.420799i	$-0.138250\pi$
$44$	9272.96	−	14429.0i	0.108858	−	0.169386i
$45$	116741.	+	81906.5i	1.28111	+	0.898837i
$46$	14387.2	−	75750.5i	0.147809	−	0.778237i
$47$			25049.3i			0.241269i	0.992697	+	0.120635i	$0.0384930\pi$
$47$			25049.3i			0.241269i	−0.992697	+	0.120635i	$0.961507\pi$
$48$	−53824.2	−	4949.67i	−0.486691	−	0.0447561i
$49$	7318.43	+	50900.8i	0.0622056	+	0.432650i
$50$	130526.	−	59609.5i	1.04421	−	0.476876i
$51$	28012.3	+	142655.i	0.211173	+	1.07541i
$52$	−39424.2	+	86327.0i	−0.280384	+	0.613955i
$53$	−85338.8	−	73946.5i	−0.573217	−	0.496695i	0.319334	−	0.947642i	$-0.396541\pi$
$53$	−85338.8	−	73946.5i	−0.573217	−	0.496695i	−0.892551	+	0.450947i	$0.851086\pi$
$54$	−33884.2	+	120045.i	−0.215187	+	0.762362i
$55$	−135041.	+	39651.5i	−0.811664	+	0.238326i
$56$	−108262.	+	93809.8i	−0.616472	+	0.534176i
$57$	−133314.	+	232784.i	−0.719868	+	1.25698i
$58$	66180.9	−	42531.9i	0.339194	−	0.217987i
$59$	−62111.4	+	53819.8i	−0.302423	+	0.262051i	−0.792831	−	0.609442i	$-0.791393\pi$
$59$	−62111.4	+	53819.8i	−0.302423	+	0.262051i	0.490407	+	0.871493i	$0.336848\pi$
$60$	−87211.5	−	90826.6i	−0.403757	−	0.420494i
$61$	−32345.1	+	224965.i	−0.142501	+	0.991119i	0.785585	+	0.618754i	$0.212362\pi$
$61$	−32345.1	+	224965.i	−0.142501	+	0.991119i	−0.928086	+	0.372365i	$0.878547\pi$
$62$	21787.9	+	18879.3i	0.0914197	+	0.0792157i
$63$	94935.3	+	161808.i	0.379670	+	0.647111i
$64$	262417.	+	77052.5i	1.00104	+	0.293932i
$65$	708369.	−	323501.i	2.57940	−	1.17797i
$66$	−71756.5	−	100026.i	−0.249591	−	0.347920i
$67$	168861.	+	108520.i	0.561442	+	0.360817i	0.790373	−	0.612626i	$-0.209887\pi$
$67$	168861.	+	108520.i	0.561442	+	0.360817i	−0.228931	+	0.973443i	$0.573523\pi$
$68$		−	128364.i		−	0.408241i
$69$	277456.	+	175887.i	0.844592	+	0.535411i
$70$	319026.			0.930104
$71$	−119410.	+	185805.i	−0.333629	+	0.519137i	−0.967022	−	0.254693i	$-0.918025\pi$
$71$	−119410.	+	185805.i	−0.333629	+	0.519137i	0.633393	+	0.773831i	$0.281662\pi$
$72$	183423.	−	361985.i	0.491423	−	0.969825i
$73$	−266212.	−	582923.i	−0.684320	−	1.49845i	−0.858000	−	0.513649i	$-0.828293\pi$
$73$	−266212.	−	582923.i	−0.684320	−	1.49845i	0.173681	−	0.984802i	$-0.444434\pi$
$74$	146492.	−	498905.i	0.361508	−	1.23118i
$75$	31225.6	+	610566.i	0.0740163	+	1.44727i
$76$	155110.	−	179006.i	0.353345	−	0.407782i
$77$	−183262.	−	26349.0i	−0.401420	−	0.0577155i
$78$	471762.	+	491317.i	0.994120	+	1.03533i
$79$	−250512.	−	289107.i	−0.508099	−	0.586377i	0.442512	−	0.896762i	$-0.354087\pi$
$79$	−250512.	−	289107.i	−0.508099	−	0.586377i	−0.950611	+	0.310385i	$0.899542\pi$
$80$	−211724.	−	329449.i	−0.413523	−	0.643454i
$81$	−422296.	−	322638.i	−0.794624	−	0.607101i
$82$	−41125.2	−	47461.0i	−0.0745875	−	0.0860786i
$83$	−99794.4	−	339869.i	−0.174531	−	0.594397i	−0.999570	−	0.0293217i	$-0.990665\pi$
$83$	−99794.4	−	339869.i	−0.174531	−	0.594397i	0.825039	−	0.565075i	$-0.191153\pi$
$84$	−54724.5	−	156345.i	−0.0923302	−	0.263782i
$85$	−689772.	+	796040.i	−1.12318	+	1.29622i
$86$	263455.	+	120316.i	0.414201	+	0.189159i
$87$	64583.1	+	328895.i	0.0980757	+	0.499458i
$88$	166370.	+	364300.i	0.244134	+	0.534578i
$89$	1.04357e6	−	150042.i	1.48030	−	0.212835i	0.645659	−	0.763626i	$-0.276583\pi$
$89$	1.04357e6	−	150042.i	1.48030	−	0.212835i	0.834644	+	0.550790i	$0.185674\pi$
$90$	−836632.	+	341747.i	−1.14764	+	0.468789i
$91$	1.02444e6			1.35944
$92$	−210468.	−	199596.i	−0.270285	−	0.256323i
$93$	−108978.	+	56665.4i	−0.135485	+	0.0704481i
$94$	−133543.	−	85822.6i	−0.160782	−	0.103328i
$95$	−1.92380e6	+	276601.i	−2.24383	+	0.322614i
$96$	−381166.	+	488196.i	−0.430824	+	0.551799i
$97$	−1.43642e6	−	421772.i	−1.57386	−	0.462128i	−0.625741	−	0.780031i	$-0.715203\pi$
$97$	−1.43642e6	−	421772.i	−1.57386	−	0.462128i	−0.948123	+	0.317902i	$0.897022\pi$
$98$	−296436.	−	135378.i	−0.314958	−	0.143836i
$99$	508822.	−	127214.i	0.524397	−	0.131108i
$100$	76823.0	−	534316.i	0.0768230	−	0.534316i
$101$	274405.	+	934537.i	0.266335	+	0.907052i	0.978709	+	0.205253i	$0.0658016\pi$
$101$	274405.	+	934537.i	0.266335	+	0.907052i	−0.712375	+	0.701800i	$0.752380\pi$
$102$	−856494.	−	339418.i	−0.807094	−	0.319841i
$103$	291415.	−	187281.i	0.266686	−	0.171389i	−0.400463	−	0.916313i	$-0.631151\pi$
$103$	291415.	−	187281.i	0.266686	−	0.171389i	0.667149	+	0.744924i	$0.267514\pi$
$104$	−1.19805e6	−	1.86420e6i	−1.06506	−	1.65726i
$105$	−500757.	+	1.26362e6i	−0.432573	+	1.09157i
$106$	686606.	−	201606.i	0.576488	−	0.169272i
$107$	548830.	+	78909.8i	0.448009	+	0.0644139i	0.362627	−	0.931934i	$-0.381880\pi$
$107$	548830.	+	78909.8i	0.448009	+	0.0644139i	0.0853817	+	0.996348i	$0.472789\pi$
$108$	310992.	+	351385.i	0.246876	+	0.278941i
$109$	688038.	−	1.50659e6i	0.531292	−	1.16337i	−0.433693	−	0.901061i	$-0.642790\pi$
$109$	688038.	−	1.50659e6i	0.531292	−	1.16337i	0.964985	−	0.262306i	$-0.0844828\pi$
$110$	251279.	−	855779.i	0.188790	−	0.642959i
$111$	1.74616e6	+	1.36334e6i	1.27678	+	0.996862i
$112$	−73316.7	−	509929.i	−0.0521854	−	0.362957i
$113$	336644.	−	523828.i	0.233311	−	0.363039i	−0.704781	−	0.709425i	$-0.748955\pi$
$113$	336644.	−	523828.i	0.233311	−	0.363039i	0.938092	+	0.346386i	$0.112591\pi$
$114$	−784260.	−	1.50828e6i	−0.529353	−	1.01804i
$115$	232658.	+	2.36874e6i	0.152977	+	1.55748i
$116$		−	295947.i		−	0.189601i
$117$	−2.68655e6	+	1.09740e6i	−1.67740	+	0.685183i
$118$	−74120.9	−	515522.i	−0.0451123	−	0.313763i
$119$	−1.26042e6	+	575613.i	−0.747952	+	0.341578i
$120$	2.88507e6	−	566524.i	1.66960	−	0.327850i
$121$	520907.	−	1.14063e6i	0.294039	−	0.643855i
$122$	−1.08851e6	−	943202.i	−0.599451	−	0.519428i
$123$	252539.	−	88395.0i	0.135711	−	0.0475021i
$124$	104061.	−	30555.0i	0.0545786	−	0.0160257i
$125$	−1.03757e6	+	899056.i	−0.531234	+	0.460317i
$126$	−1.18789e6	−	48260.2i	−0.593834	−	0.0241256i
$127$	3.01837e6	−	1.93979e6i	1.47354	−	0.946984i	0.475813	−	0.879546i	$-0.342154\pi$
$127$	3.01837e6	−	1.93979e6i	1.47354	−	0.946984i	0.997723	−	0.0674380i	$-0.0214825\pi$
$128$	−200311.	+	173570.i	−0.0955156	+	0.0827647i
$129$	−890087.	+	854660.i	−0.414633	+	0.398129i
$130$	−702330.	+	4.88481e6i	−0.319677	+	2.22340i
$131$	2.58173e6	+	2.23708e6i	1.14841	+	0.995104i	0.999981	+	0.00618072i	$0.00196740\pi$
$131$	2.58173e6	+	2.23708e6i	1.14841	+	0.995104i	0.148430	+	0.988923i	$0.452578\pi$
$132$	−462494.	+	23652.9i	−0.201087	+	0.0102840i
$133$	−2.45322e6	−	720331.i	−1.04275	−	0.306180i
$134$	−1.15709e6	+	528423.i	−0.480896	+	0.219618i
$135$	−40402.6	−	3.85022e6i	−0.0164213	−	1.56489i
$136$	2.52147e6	+	1.62045e6i	1.00239	+	0.644199i
$137$		−	2.28818e6i		−	0.889874i	−0.895562	−	0.444937i	$-0.853226\pi$
$137$		−	2.28818e6i		−	0.889874i	0.895562	−	0.444937i	$-0.146774\pi$
$138$	−1.88829e6	+	876554.i	−0.718509	+	0.333535i
$139$	−771.009			−0.000287088			−0.000143544	−	1.00000i	$-0.500046\pi$
$139$	−771.009			−0.000287088			−0.000143544		1.00000i	$0.500046\pi$
$140$	648848.	−	1.00963e6i	0.236461	−	0.367940i
$141$	549548.	−	394235.i	0.196042	−	0.140637i
$142$	−581446.	−	1.27319e6i	−0.203069	−	0.444660i
$143$	806894.	−	2.74803e6i	0.275936	−	0.939752i
$144$	738516.	+	1.25873e6i	0.247327	+	0.421546i
$145$	−1.59029e6	+	1.83529e6i	−0.521641	+	0.602006i
$146$	4.01975e6	+	577953.i	1.29164	+	0.185710i
$147$	1.00151e6	−	961652.i	0.315286	−	0.302737i
$148$	−1.28095e6	−	1.47830e6i	−0.395137	−	0.456012i
$149$	2.77642e6	+	4.32019e6i	0.839317	+	1.30600i	0.950033	+	0.312150i	$0.101049\pi$
$149$	2.77642e6	+	4.32019e6i	0.839317	+	1.30600i	−0.110716	+	0.993852i	$0.535314\pi$
$150$	−3.36202e6	−	1.92542e6i	−0.996155	−	0.570494i
$151$	−3.74210e6	−	4.31862e6i	−1.08689	−	1.25434i	−0.965128	−	0.261777i	$-0.915692\pi$
$151$	−3.74210e6	−	4.31862e6i	−1.08689	−	1.25434i	−0.121760	−	0.992560i	$-0.538854\pi$
$152$	1.55816e6	+	5.30660e6i	0.443691	+	1.51107i
$153$	2.68879e6	−	2.85971e6i	0.750727	−	0.798449i
$154$	768352.	−	886726.i	0.210377	−	0.242788i
$155$	−809514.	−	369693.i	−0.217385	−	0.0992763i
$156$	2.51437e6	−	493732.i	0.662301	−	0.130052i
$157$	581440.	+	1.27318e6i	0.150247	+	0.328995i	0.969758	−	0.244068i	$-0.0784821\pi$
$157$	581440.	+	1.27318e6i	0.150247	+	0.328995i	−0.819511	+	0.573064i	$0.805755\pi$
$158$	2.39957e6	−	345007.i	0.608363	−	0.0874694i
$159$	−279192.	+	3.03601e6i	−0.0694562	+	0.755288i
$160$	−4.48753e6			−1.09559
$161$	−1.01606e6	+	2.96163e6i	−0.243469	+	0.709665i
$162$	3.16689e6	−	1.14593e6i	0.744884	−	0.269534i
$163$	−324836.	−	208760.i	−0.0750070	−	0.0482041i	0.502600	−	0.864519i	$-0.332377\pi$
$163$	−324836.	−	208760.i	−0.0750070	−	0.0482041i	−0.577607	+	0.816315i	$0.696013\pi$
$164$	−233843.	+	33621.5i	−0.0530142	+	0.00762230i
$165$	2.99522e6	+	2.33856e6i	0.666771	+	0.520590i
$166$	2.15381e6	+	632417.i	0.470851	+	0.138254i
$167$	2.78879e6	+	1.27360e6i	0.598778	+	0.273453i	0.691659	−	0.722224i	$-0.256880\pi$
$167$	2.78879e6	+	1.27360e6i	0.598778	+	0.273453i	−0.0928805	+	0.995677i	$0.529607\pi$
$168$	3.76193e6	+	898714.i	0.793383	+	0.189537i
$169$	−1.56836e6	+	1.09082e7i	−0.324926	+	2.25991i
$170$	−1.88058e6	−	6.40466e6i	−0.382776	−	1.30361i
$171$	7.20511e6	−	738902.i	1.44096	−	0.147774i
$172$	916591.	−	589057.i	0.180132	−	0.115764i
$173$	−5.13961e6	−	7.99739e6i	−0.992640	−	1.54458i	−0.829903	−	0.557908i	$-0.811604\pi$
$173$	−5.13961e6	−	7.99739e6i	−0.992640	−	1.54458i	−0.162737	−	0.986669i	$-0.552032\pi$
$174$	−1.97467e6	−	782536.i	−0.374841	−	0.148544i
$175$	−5.59098e6	+	1.64166e6i	−1.04321	+	0.306315i
$176$	−1.42562e6	−	204973.i	−0.261496	−	0.0375975i
$177$	2.15827e6	+	515603.i	0.389211	+	0.0929813i
$178$	−2.77551e6	+	6.07752e6i	−0.492134	+	1.07762i
$179$	−63117.5	+	214958.i	−0.0110050	+	0.0374796i	−0.964812	−	0.262939i	$-0.915308\pi$
$179$	−63117.5	+	214958.i	−0.0110050	+	0.0374796i	0.953807	+	0.300419i	$0.0971264\pi$
$180$	−620045.	+	3.34277e6i	−0.106318	+	0.573176i
$181$	395663.	+	2.75190e6i	0.0667252	+	0.464084i	0.995601	+	0.0936929i	$0.0298672\pi$
$181$	395663.	+	2.75190e6i	0.0667252	+	0.464084i	−0.928876	+	0.370391i	$0.879224\pi$
$182$	−3.50987e6	+	5.46147e6i	−0.582207	+	0.905932i
$183$	5.44449e6	−	2.83098e6i	0.888390	−	0.461937i
$184$	6.57761e6	−	1.61457e6i	1.05588	−	0.259182i
$185$			1.60508e7i			2.53502i
$186$	71280.6	−	775126.i	0.0110773	−	0.120457i
$187$	551306.	+	3.83442e6i	0.0843078	+	0.586374i
$188$	−543209.	+	248075.i	−0.0817511	+	0.0373345i
$189$	2.05572e6	−	4.62935e6i	0.304494	−	0.685700i
$190$	5.11662e6	−	1.12038e7i	0.745971	−	1.63345i
$191$	1.04832e6	+	908373.i	0.150450	+	0.130366i	0.726834	−	0.686813i	$-0.240991\pi$
$191$	1.04832e6	+	908373.i	0.150450	+	0.130366i	−0.576383	+	0.817179i	$0.695537\pi$
$192$	−2.43958e6	−	6.96975e6i	−0.344677	−	0.984721i
$193$	2.46016e6	−	722368.i	0.342209	−	0.100482i	−0.106112	−	0.994354i	$-0.533840\pi$
$193$	2.46016e6	−	722368.i	0.342209	−	0.100482i	0.448321	+	0.893872i	$0.352022\pi$
$194$	7.16994e6	−	6.21279e6i	0.981998	−	0.850906i
$195$	−1.82458e7	−	1.04493e7i	−2.46070	−	1.40923i
$196$	−1.03134e6	+	662799.i	−0.136972	+	0.0880266i
$197$	−6.34470e6	+	5.49772e6i	−0.829875	+	0.719091i	−0.962267	−	0.272107i	$-0.912280\pi$
$197$	−6.34470e6	+	5.49772e6i	−0.829875	+	0.719091i	0.132392	+	0.991197i	$0.457734\pi$
$198$	−1.06509e6	+	3.14848e6i	−0.137212	+	0.405607i
$199$	828160.	−	5.75998e6i	0.105088	−	0.730906i	−0.867342	−	0.497713i	$-0.834173\pi$
$199$	828160.	−	5.75998e6i	0.105088	−	0.730906i	0.972430	−	0.233194i	$-0.0749176\pi$
$200$	9.52583e6	+	8.25418e6i	1.19073	+	1.03177i
$201$	−276808.	−	5.41251e6i	−0.0340871	−	0.666516i
$202$	−5.92234e6	−	1.73896e6i	−0.718521	−	0.210977i
$203$	−2.90592e6	+	1.32709e6i	−0.347373	+	0.158640i
$204$	−2.81614e6	+	2.02024e6i	−0.331713	+	0.237965i
$205$	1.63082e6	+	1.04807e6i	0.189298	+	0.121654i
$206$			2.19524e6i			0.251120i
$207$	−507975.	−	8.85519e6i	−0.0572705	−	0.998359i
$208$	7.96926e6			0.885580
$209$	−3.86454e6	+	6.01335e6i	−0.423311	+	0.658684i
$210$	−5.02094e6	−	6.99899e6i	−0.542160	−	0.755749i
$211$	−4.24709e6	−	9.29982e6i	−0.452109	−	0.989982i	−0.989216	−	0.146467i	$-0.953210\pi$
$211$	−4.24709e6	−	9.29982e6i	−0.452109	−	0.989982i	0.537106	−	0.843515i	$-0.319517\pi$
$212$	758422.	−	2.58295e6i	0.0795982	−	0.271087i
$213$	5.95562e6	−	304583.i	0.616294	−	0.0315186i
$214$	−2.30105e6	+	2.65556e6i	−0.234793	+	0.270966i
$215$	−8.84950e6	−	1.27237e6i	−0.890437	−	0.128025i
$216$	−1.08282e7	+	1.67302e6i	−1.07448	+	0.166012i
$217$	−766654.	−	884765.i	−0.0750274	−	0.0865863i
$218$	5.67461e6	+	8.82987e6i	0.547730	+	0.852285i
$219$	−8.59879e6	+	1.50146e7i	−0.818663	+	1.42949i
$220$	−2.19724e6	−	2.53575e6i	−0.206352	−	0.238143i
$221$	−6.03880e6	−	2.05663e7i	−0.559467	−	1.90537i
$222$	−1.32508e7	+	4.63812e6i	−1.21111	+	0.423919i
$223$	7.10849e6	−	8.20364e6i	0.641007	−	0.739762i	−0.338545	−	0.940950i	$-0.609935\pi$
$223$	7.10849e6	−	8.20364e6i	0.641007	−	0.739762i	0.979553	+	0.201188i	$0.0644803\pi$
$224$	−5.36988e6	−	2.45234e6i	−0.477772	−	0.218191i
$225$	1.29035e7	−	1.02944e7i	1.13282	−	0.903757i
$226$	1.63923e6	+	3.58942e6i	0.142009	+	0.310956i
$227$	1.64618e6	−	236684.i	0.140734	−	0.0202345i	−0.0715878	−	0.997434i	$-0.522807\pi$
$227$	1.64618e6	−	236684.i	0.140734	−	0.0202345i	0.212322	+	0.977200i	$0.431898\pi$
$228$	−6.36833e6	−	585632.i	−0.537305	−	0.0494106i
$229$	−3.53318e6			−0.294211			−0.147106	−	0.989121i	$-0.546996\pi$
$229$	−3.53318e6			−0.294211			−0.147106	+	0.989121i	$0.546996\pi$
$230$	−1.34253e7	−	6.87530e6i	−1.10342	−	0.565078i
$231$	2.30618e6	+	4.43520e6i	0.187093	+	0.359813i
$232$	5.81332e6	+	3.73600e6i	0.465544	+	0.299187i
$233$	−8.60632e6	+	1.23740e6i	−0.680377	+	0.0978234i	−0.473834	−	0.880614i	$-0.657130\pi$
$233$	−8.60632e6	+	1.23740e6i	−0.680377	+	0.0978234i	−0.206543	+	0.978438i	$0.566221\pi$
$234$	3.35407e6	−	1.80823e7i	0.261773	−	1.41126i
$235$	4.70171e6	+	1.38055e6i	0.362287	+	0.106377i
$236$	−1.78223e6	−	813918.i	−0.135590	−	0.0619220i
$237$	−2.39995e6	+	1.00460e7i	−0.180284	+	0.754652i
$238$	1.24967e6	−	8.69166e6i	0.0926969	−	0.644721i
$239$	1.74456e6	+	5.94144e6i	0.127789	+	0.435209i	0.998386	−	0.0567871i	$-0.0180856\pi$
$239$	1.74456e6	+	5.94144e6i	0.127789	+	0.435209i	−0.870597	+	0.491996i	$0.836267\pi$
$240$	−3.89547e6	+	9.82991e6i	−0.281790	+	0.711076i
$241$	7.26293e6	−	4.66760e6i	0.518873	−	0.333459i	−0.254853	−	0.966980i	$-0.582027\pi$
$241$	7.26293e6	−	4.66760e6i	0.518873	−	0.333459i	0.773726	+	0.633520i	$0.218391\pi$
$242$	4.29620e6	+	6.68501e6i	0.303136	+	0.471689i
$243$	−431998.	+	1.43424e7i	−0.0301067	+	0.999547i
$244$	−5.19883e6	+	1.52651e6i	−0.357879	+	0.105083i
$245$	9.95733e6	+	1.43165e6i	0.677088	+	0.0973505i
$246$	−393986.	+	1.64919e6i	−0.0264652	+	0.110781i
$247$	1.64302e7	−	3.59771e7i	1.09031	−	2.38746i
$248$	−713454.	+	2.42980e6i	−0.0467747	+	0.159300i
$249$	−5.88565e6	+	7.53833e6i	−0.381238	+	0.488289i
$250$	−1.23818e6	−	8.61176e6i	−0.0792438	−	0.551152i
$251$	1.18697e7	−	1.84696e7i	0.750615	−	1.16798i	−0.230220	−	0.973139i	$-0.573944\pi$
$251$	1.18697e7	−	1.84696e7i	0.750615	−	1.16798i	0.980835	−	0.194841i	$-0.0624192\pi$
$252$	−2.56871e6	+	3.66119e6i	−0.160514	+	0.228781i
$253$	7.14421e6	+	5.05828e6i	0.441156	+	0.312350i
$254$			2.27375e7i			1.38753i
$255$	2.83199e7	+	2.60430e6i	1.70794	+	0.157062i
$256$	2.25199e6	+	1.56630e7i	0.134229	+	0.933585i
$257$	170693.	−	77953.0i	0.0100558	−	0.00459233i	−0.410381	−	0.911914i	$-0.634604\pi$
$257$	170693.	−	77953.0i	0.0100558	−	0.00459233i	0.420437	+	0.907322i	$0.361877\pi$
$258$	−1.50678e6	−	7.67341e6i	−0.0877389	−	0.446817i
$259$	−8.77144e6	+	1.92068e7i	−0.504861	+	1.10549i
$260$	1.40306e7	+	1.21576e7i	0.798284	+	0.691717i
$261$	6.19906e6	−	6.59313e6i	0.348662	−	0.370826i
$262$	−2.07717e7	+	6.09912e6i	−1.15496	+	0.339128i
$263$	2.04313e7	−	1.77038e7i	1.12312	−	0.973193i	0.123308	−	0.992368i	$-0.460650\pi$
$263$	2.04313e7	−	1.77038e7i	1.12312	−	0.973193i	0.999816	+	0.0191754i	$0.00610410\pi$
$264$	5.37385e6	−	9.38342e6i	0.292061	−	0.509976i
$265$	−1.85829e7	+	1.19425e7i	−0.998565	+	0.641739i
$266$	1.22453e7	−	1.06106e7i	0.650617	−	0.563763i
$267$	−1.97158e7	−	2.05330e7i	−1.03581	−	1.07875i
$268$	−681017.	+	4.73658e6i	−0.0353797	+	0.246071i
$269$	−2.61959e7	−	2.26989e7i	−1.34579	−	1.16613i	−0.971016	−	0.239014i	$-0.923176\pi$
$269$	−2.61959e7	−	2.26989e7i	−1.34579	−	1.16613i	−0.374772	−	0.927117i	$-0.622279\pi$
$270$	2.06647e7	+	1.29760e7i	1.04987	+	0.659251i
$271$	4.93912e6	+	1.45026e6i	0.248166	+	0.0728681i	0.403450	−	0.915002i	$-0.367811\pi$
$271$	4.93912e6	+	1.45026e6i	0.248166	+	0.0728681i	−0.155284	+	0.987870i	$0.549629\pi$
$272$	−9.80497e6	+	4.47778e6i	−0.487236	+	0.222513i
$273$	−1.61230e7	−	2.24748e7i	−0.792424	−	1.10461i
$274$	1.21987e7	+	7.83964e6i	0.593011	+	0.381105i
$275$			1.62907e7i			0.783325i
$276$	−1.06644e6	+	7.75869e6i	−0.0507236	+	0.369030i
$277$	−2.44918e7			−1.15234			−0.576171	−	0.817329i	$-0.695454\pi$
$277$	−2.44918e7			−1.15234			−0.576171	+	0.817329i	$0.695454\pi$
$278$	2641.59	−	4110.39i	0.000122951	−	0.000191315i
$279$	2.95830e6	+	1.49901e6i	0.136216	+	0.0690226i
$280$	1.16413e7	+	2.54908e7i	0.530305	+	1.16121i
$281$	−6.10795e6	+	2.08018e7i	−0.275281	+	0.937522i	0.699551	+	0.714583i	$0.253383\pi$
$281$	−6.10795e6	+	2.08018e7i	−0.275281	+	0.937522i	−0.974832	+	0.222939i	$0.928435\pi$
$282$	218911.	+	4.28045e6i	0.00976160	+	0.190872i
$283$	1.68590e6	−	1.94564e6i	0.0743829	−	0.0858425i	−0.717338	−	0.696725i	$-0.754640\pi$
$283$	1.68590e6	−	1.94564e6i	0.0743829	−	0.0858425i	0.791721	+	0.610883i	$0.209185\pi$
$284$	−5.21186e6	−	749352.i	−0.227529	−	0.0327138i
$285$	3.63458e7	+	3.78523e7i	1.57007	+	1.63515i
$286$	1.18857e7	+	1.37169e7i	0.508075	+	0.586350i
$287$	1.37874e6	+	2.14535e6i	0.0583224	+	0.0907514i
$288$	1.67093e7	+	678844.i	0.699488	+	0.0284179i
$289$	3.17892e6	+	3.66867e6i	0.131700	+	0.151990i
$290$	−4.33572e6	−	1.47661e7i	−0.177773	−	0.605441i
$291$	1.33539e7	+	3.81512e7i	0.541911	+	1.54821i
$292$	1.00046e7	−	1.15459e7i	0.401838	−	0.463746i
$293$	−1.55277e7	−	7.09128e6i	−0.617312	−	0.281917i	0.0821126	−	0.996623i	$-0.473833\pi$
$293$	−1.55277e7	−	7.09128e6i	−0.617312	−	0.281917i	−0.699425	+	0.714706i	$0.746561\pi$
$294$	1.69541e6	+	8.63402e6i	0.0667166	+	0.339759i
$295$	6.67873e6	+	1.46244e7i	0.260152	+	0.569654i
$296$	4.52090e7	−	6.50007e6i	1.74321	−	0.250636i
$297$	−1.07989e7	−	9.16071e6i	−0.412203	−	0.349671i
$298$	−3.25441e7			−1.22977
$299$	−4.31106e7	−	2.20776e7i	−1.61276	−	0.825920i
$300$	−1.29312e7	+	6.72387e6i	−0.478934	+	0.249032i
$301$	−9.89419e6	−	6.35861e6i	−0.362811	−	0.233165i
$302$	3.58444e7	−	5.15364e6i	1.30137	−	0.187108i
$303$	1.61838e7	−	2.07281e7i	0.581771	−	0.745131i
$304$	−1.90840e7	−	5.60357e6i	−0.679279	−	0.199454i
$305$	4.04429e7	+	1.84697e7i	1.42542	+	0.650968i
$306$	6.03347e6	+	2.41322e7i	0.210573	+	0.842234i
$307$	−2.40225e6	+	1.67080e7i	−0.0830240	+	0.577445i	0.905265	+	0.424848i	$0.139673\pi$
$307$	−2.40225e6	+	1.67080e7i	−0.0830240	+	0.577445i	−0.988289	+	0.152596i	$0.951237\pi$
$308$	−1.24353e6	−	4.23508e6i	−0.0425603	−	0.144947i
$309$	−8.69510e6	−	3.44575e6i	−0.294713	−	0.116791i
$310$	4.74441e6	−	3.04905e6i	0.159257	−	0.102348i
$311$	−2.06526e7	−	3.21361e7i	−0.686584	−	1.06834i	−0.993190	−	0.116508i	$-0.962830\pi$
$311$	−2.06526e7	−	3.21361e7i	−0.686584	−	1.06834i	0.306606	−	0.951836i	$-0.400807\pi$
$312$	−2.20426e7	+	5.56229e7i	−0.725771	+	1.83143i
$313$	8.80828e6	−	2.58635e6i	0.287249	−	0.0843439i	−0.134934	−	0.990855i	$-0.543082\pi$
$313$	8.80828e6	−	2.58635e6i	0.287249	−	0.0843439i	0.422183	+	0.906511i	$0.361264\pi$
$314$	−8.77964e6	−	1.26232e6i	−0.283588	−	0.0407738i
$315$	3.56033e7	−	8.90143e6i	1.13909	−	0.284792i
$316$	3.78851e6	−	8.29567e6i	0.120062	−	0.262900i
$317$	3.87197e6	−	1.31867e7i	0.121550	−	0.413961i	−0.876127	−	0.482080i	$-0.839882\pi$
$317$	3.87197e6	−	1.31867e7i	0.121550	−	0.413961i	0.997677	+	0.0681189i	$0.0216997\pi$
$318$	−1.52290e7	−	1.18903e7i	−0.473577	−	0.369751i
$319$	1.27105e6	+	8.84035e6i	0.0391553	+	0.272331i
$320$	2.89252e7	−	4.50086e7i	0.882728	−	1.37355i
$321$	−6.90651e6	−	1.32825e7i	−0.208806	−	0.401573i
$322$	−1.23078e7	−	1.55638e7i	−0.368650	−	0.466174i
$323$			5.34963e7i			1.58751i
$324$	2.81441e6	−	1.23530e7i	0.0827469	−	0.363192i
$325$	−1.28281e7	−	8.92212e7i	−0.373690	−	2.59907i
$326$	2.22587e6	−	1.01652e6i	0.0642462	−	0.0293403i
$327$	−4.38812e7	+	8.61670e6i	−1.25498	+	0.246432i
$328$	2.29157e6	−	5.01784e6i	0.0649399	−	0.142199i
$329$	4.87174e6	+	4.22139e6i	0.136803	+	0.118541i
$330$	−2.27293e7	+	7.95584e6i	−0.632478	+	0.221383i
$331$	2.56414e7	−	7.52900e6i	0.707062	−	0.207612i	0.0916200	−	0.995794i	$-0.470796\pi$
$331$	2.56414e7	−	7.52900e6i	0.707062	−	0.207612i	0.615443	+	0.788182i	$0.288977\pi$
$332$	6.38194e6	−	5.52998e6i	0.174397	−	0.151116i
$333$	2.42806e6	−	5.97651e7i	0.0657548	−	1.61851i
$334$	−1.63446e7	+	1.05040e7i	−0.438666	+	0.281914i
$335$	2.96756e7	−	2.57140e7i	0.789341	−	0.683967i
$336$	−1.00333e7	+	9.63391e6i	−0.264499	+	0.253971i
$337$	3.52091e6	−	2.44885e7i	0.0919952	−	0.639841i	−0.890697	−	0.454597i	$-0.849783\pi$
$337$	3.52091e6	−	2.44885e7i	0.0919952	−	0.639841i	0.982693	−	0.185244i	$-0.0593076\pi$
$338$	−5.27800e7	−	4.57342e7i	−1.36685	−	1.18438i
$339$	−1.67903e7	+	858691.i	−0.430982	+	0.0220413i
$340$	−2.40937e7	−	7.07456e6i	−0.613010	−	0.179996i
$341$	−2.97721e6	+	1.35965e6i	−0.0750839	+	0.0342897i
$342$	−2.07465e7	+	4.09434e7i	−0.518642	+	1.02354i
$343$	3.66026e7	+	2.35231e7i	0.907047	+	0.582923i
$344$			2.54409e7i			0.624967i
$345$	4.83052e7	−	4.23843e7i	1.17635	−	1.03216i
$346$	6.02446e7			1.45442
$347$	5.32759e6	−	8.28989e6i	0.127509	−	0.198408i	−0.771629	−	0.636073i	$-0.780558\pi$
$347$	5.32759e6	−	8.28989e6i	0.127509	−	0.198408i	0.899138	+	0.437664i	$0.144194\pi$
$348$	−6.49267e6	+	4.65772e6i	−0.154059	+	0.110519i
$349$	1.97568e7	+	4.32614e7i	0.464773	+	1.01771i	0.986374	+	0.164521i	$0.0526078\pi$
$349$	1.97568e7	+	4.32614e7i	0.464773	+	1.01771i	−0.521601	+	0.853190i	$0.674665\pi$
$350$	1.04035e7	−	3.54311e7i	0.242648	−	0.826382i
$351$	6.63573e7	+	4.16679e7i	1.53450	+	0.963564i
$352$	−1.08079e7	+	1.24730e7i	−0.247807	+	0.285985i
$353$	−2.49936e7	−	3.59354e6i	−0.568205	−	0.0816956i	−0.147776	−	0.989021i	$-0.547211\pi$
$353$	−2.49936e7	−	3.59354e6i	−0.568205	−	0.0816956i	−0.420429	+	0.907325i	$0.638121\pi$
$354$	−1.01433e7	+	9.73959e6i	−0.228649	+	0.219549i
$355$	2.82942e7	+	3.26533e7i	0.632430	+	0.729864i
$356$	1.35887e7	+	2.11444e7i	0.301181	+	0.468647i
$357$	3.24651e7	+	1.85926e7i	0.713529	+	0.408635i
$358$	−929734.	−	1.07297e6i	−0.0202633	−	0.0233851i
$359$	7.99571e6	+	2.72309e7i	0.172812	+	0.588543i	0.999659	+	0.0261162i	$0.00831399\pi$
$359$	7.99571e6	+	2.72309e7i	0.172812	+	0.588543i	−0.826847	+	0.562427i	$0.809868\pi$
$360$	−5.78350e7	−	5.43783e7i	−1.23960	−	1.16551i
$361$	−3.38342e7	+	3.90467e7i	−0.719174	+	0.829971i
$362$	−1.60265e7	−	7.31905e6i	−0.337841	−	0.154287i
$363$	−3.32220e7	+	6.52362e6i	−0.694555	+	0.136386i
$364$	1.01455e7	+	2.22155e7i	0.210363	+	0.460630i
$365$	−1.24085e8	+	1.78408e7i	−2.55177	+	0.366890i
$366$	−3.56114e6	+	3.87249e7i	−0.0726351	+	0.789855i
$367$	−3.85183e7			−0.779235			−0.389618	−	0.920977i	$-0.627393\pi$
$367$	−3.85183e7			−0.779235			−0.389618	+	0.920977i	$0.627393\pi$
$368$	−7.90410e6	+	2.30390e7i	−0.158602	+	0.462295i
$369$	−5.91382e6	−	4.14918e6i	−0.117703	−	0.0825815i
$370$	−8.55699e7	−	5.49924e7i	−1.68934	−	1.08567i
$371$	−2.87631e7	+	4.13551e6i	−0.563267	+	0.0809855i
$372$	−2.30808e6	−	1.80207e6i	−0.0448356	−	0.0350060i
$373$	−1.11619e7	−	3.27742e6i	−0.215085	−	0.0631546i	0.172415	−	0.985024i	$-0.444843\pi$
$373$	−1.11619e7	−	3.27742e6i	−0.215085	−	0.0631546i	−0.387500	+	0.921870i	$0.626661\pi$
$374$	−2.23309e7	−	1.01982e7i	−0.426865	−	0.194943i
$375$	3.60537e7	+	8.61311e6i	0.683684	+	0.163330i
$376$	1.98443e6	−	1.38020e7i	0.0373312	−	0.259644i
$377$	−1.39226e7	−	4.74161e7i	−0.259835	−	0.884915i
$378$	1.76367e7	+	2.68203e7i	0.326544	+	0.496578i
$379$	−8.93297e6	+	5.74087e6i	−0.164088	+	0.105453i	−0.620108	−	0.784517i	$-0.712911\pi$
$379$	−8.93297e6	+	5.74087e6i	−0.164088	+	0.105453i	0.456019	+	0.889970i	$0.349275\pi$
$380$	−2.50506e7	−	3.89795e7i	−0.456528	−	0.710371i
$381$	−9.00605e7	−	3.56898e7i	−1.62839	−	0.645311i
$382$	−8.43440e6	+	2.47656e6i	−0.151309	+	0.0444282i
$383$	8.29812e7	+	1.19309e7i	1.47701	+	0.212362i	0.833263	−	0.552877i	$-0.186470\pi$
$383$	8.29812e7	+	1.19309e7i	1.47701	+	0.212362i	0.643747	+	0.765239i	$0.277379\pi$
$384$	6.96046e6	+	1.66283e6i	0.122926	+	0.0293667i
$385$	−1.50458e7	+	3.29457e7i	−0.263653	+	0.577320i
$386$	−4.57779e6	+	1.55905e7i	−0.0795965	+	0.271081i
$387$	3.27586e7	+	6.07634e6i	0.565187	+	0.104836i
$388$	−5.07921e6	−	3.53267e7i	−0.0869563	−	0.604795i
$389$	2.10642e7	−	3.27765e7i	0.357846	−	0.556819i	−0.614926	−	0.788585i	$-0.710814\pi$
$389$	2.10642e7	−	3.27765e7i	0.357846	−	0.556819i	0.972772	+	0.231766i	$0.0744504\pi$
$390$	1.18220e8	−	6.14708e7i	1.99295	−	1.03628i
$391$	6.54462e7	+	2.94007e6i	1.09485	+	0.0491844i
$392$		−	2.86258e7i		−	0.475224i
$393$	8.44631e6	−	9.18477e7i	0.139152	−	1.51318i
$394$	−7.57148e6	−	5.26608e7i	−0.123792	−	0.860991i
$395$	−6.80714e7	+	3.10872e7i	−1.10452	+	0.504417i
$396$	7.79781e6	+	9.77423e6i	0.125570	+	0.157397i
$397$	9.19434e6	−	2.01328e7i	0.146943	−	0.321760i	−0.821821	−	0.569746i	$-0.807041\pi$
$397$	9.19434e6	−	2.01328e7i	0.146943	−	0.321760i	0.968764	+	0.247986i	$0.0797687\pi$
$398$	2.78701e7	+	2.41496e7i	0.442069	+	0.383055i
$399$	2.28066e7	+	6.51572e7i	0.359040	+	1.02576i
$400$	−4.34931e7	+	1.27707e7i	−0.679579	+	0.199542i
$401$	−7.79593e7	+	6.75521e7i	−1.20902	+	1.04762i	−0.211494	+	0.977379i	$0.567833\pi$
$401$	−7.79593e7	+	6.75521e7i	−1.20902	+	1.04762i	−0.997530	+	0.0702457i	$0.977622\pi$
$402$	2.98035e7	+	1.70684e7i	0.458764	+	0.262732i
$403$	1.52350e7	−	9.79094e6i	0.232770	−	0.149592i
$404$	−1.75484e7	+	1.52058e7i	−0.266130	+	0.230603i
$405$	−8.38328e7	+	6.14826e7i	−1.26197	+	0.925523i
$406$	2.88115e6	−	2.00388e7i	0.0430515	−	0.299429i
$407$	4.46129e7	+	3.86573e7i	0.661725	+	0.573388i
$408$	−4.13336e6	−	8.08210e7i	−0.0608587	−	1.18999i
$409$	9.24636e7	+	2.71498e7i	1.35145	+	0.396822i	0.875742	−	0.482779i	$-0.160373\pi$
$409$	9.24636e7	+	2.71498e7i	1.35145	+	0.396822i	0.475711	+	0.879602i	$0.342191\pi$
$410$	−1.11749e7	+	5.10340e6i	−0.162141	+	0.0740471i
$411$	−5.01996e7	+	3.60122e7i	−0.723060	+	0.518710i
$412$	6.94733e6	+	4.46478e6i	0.0993405	+	0.0638423i
$413$			2.11497e7i			0.300229i
$414$	4.89491e7	+	2.76311e7i	0.689832	+	0.389400i
$415$	−6.92927e7			−0.969490
$416$	4.93711e7	−	7.68229e7i	0.685793	−	1.06711i
$417$	12134.4	+	16914.9i	0.000167344	+	0.000233271i
$418$	−1.88178e7	−	4.12052e7i	−0.257656	−	0.564187i
$419$	2.54850e7	−	8.67940e7i	0.346452	−	1.17991i	−0.583465	−	0.812138i	$-0.698304\pi$
$419$	2.54850e7	−	8.67940e7i	0.346452	−	1.17991i	0.929917	−	0.367769i	$-0.119878\pi$
$420$	−3.23616e7	+	1.65504e6i	−0.436800	+	0.0223389i
$421$	−5.33777e7	+	6.16012e7i	−0.715342	+	0.825549i	−0.990739	−	0.135782i	$-0.956645\pi$
$421$	−5.33777e7	+	6.16012e7i	−0.715342	+	0.825549i	0.275397	+	0.961331i	$0.411191\pi$
$422$	6.41302e7	+	9.22053e6i	0.853346	+	0.122693i
$423$	−1.72980e7	−	5.85171e6i	−0.228546	−	0.0773146i
$424$	4.11630e7	+	4.75046e7i	0.540019	+	0.623215i
$425$	6.59148e7	+	1.02565e8i	0.858650	+	1.33609i
$426$	−1.87810e7	+	3.27941e7i	−0.242935	+	0.424196i
$427$	3.83017e7	+	4.42025e7i	0.491965	+	0.567758i
$428$	3.72412e6	+	1.26832e7i	0.0474998	+	0.161770i
$429$	−7.29872e7	+	2.55473e7i	−0.924432	+	0.323574i
$430$	3.71029e7	−	4.28190e7i	0.466662	−	0.538557i
$431$	8.73267e6	+	3.98808e6i	0.109073	+	0.0498117i	0.469204	−	0.883090i	$-0.344541\pi$
$431$	8.73267e6	+	3.98808e6i	0.109073	+	0.0498117i	−0.360131	+	0.932902i	$0.617268\pi$
$432$	1.59918e7	−	3.60124e7i	0.198356	−	0.446684i
$433$	2.06159e7	+	4.51426e7i	0.253945	+	0.556061i	0.993072	−	0.117504i	$-0.0374893\pi$
$433$	2.06159e7	+	4.51426e7i	0.253945	+	0.556061i	−0.739128	+	0.673565i	$0.764762\pi$
$434$	7.34352e6	−	1.05584e6i	0.0898328	−	0.0129160i
$435$	6.52923e7	+	6.00428e6i	0.793221	+	0.0729446i
$436$	3.94853e7			0.476405
$437$	8.77133e7	+	8.31824e7i	1.05104	+	0.996752i
$438$	−5.05848e7	−	9.72839e7i	−0.602002	−	1.15776i
$439$	−7.38156e7	−	4.74384e7i	−0.872478	−	0.560707i	0.0260319	−	0.999661i	$-0.491713\pi$
$439$	−7.38156e7	−	4.74384e7i	−0.872478	−	0.560707i	−0.898510	+	0.438954i	$0.855349\pi$
$440$	7.75477e7	−	1.11497e7i	0.910355	−	0.130889i
$441$	−3.68595e7	−	6.83702e6i	−0.429768	−	0.0797170i
$442$	1.30333e8	+	3.82691e7i	1.50934	+	0.443181i
$443$	−2.11495e7	−	9.65866e6i	−0.243270	−	0.111098i	0.290049	−	0.957012i	$-0.406328\pi$
$443$	−2.11495e7	−	9.65866e6i	−0.243270	−	0.111098i	−0.533320	+	0.845914i	$0.679056\pi$
$444$	−1.22717e7	+	5.13683e7i	−0.140203	+	0.586876i
$445$	2.93516e7	−	2.04145e8i	0.333083	−	2.31664i
$446$	1.93804e7	+	6.60036e7i	0.218453	+	0.743983i
$447$	5.10828e7	−	1.28904e8i	0.571942	−	1.44325i
$448$	5.92089e7	−	3.80512e7i	0.658496	−	0.423189i
$449$	−3.59852e7	−	5.59940e7i	−0.397543	−	0.618589i	0.583561	−	0.812069i	$-0.301659\pi$
$449$	−3.59852e7	−	5.59940e7i	−0.397543	−	0.618589i	−0.981104	+	0.193480i	$0.938023\pi$
$450$	1.06717e7	+	1.04061e8i	0.117111	+	1.14196i
$451$	6.84081e6	−	2.00864e6i	0.0745724	−	0.0218964i
$452$	1.46934e7	+	2.11260e6i	0.159114	+	0.0228771i
$453$	−3.58500e7	+	1.50065e8i	−0.385651	+	1.61430i
$454$	−4.37823e6	+	9.58699e6i	−0.0467876	+	0.102451i
$455$	5.64600e7	−	1.92285e8i	0.599386	−	2.04132i
$456$	9.18966e7	−	1.17701e8i	0.969182	−	1.24133i
$457$	1.99614e7	+	1.38835e8i	0.209143	+	1.45462i	0.775963	+	0.630778i	$0.217264\pi$
$457$	1.99614e7	+	1.38835e8i	0.209143	+	1.45462i	−0.566820	+	0.823842i	$0.691827\pi$
$458$	1.21052e7	−	1.88361e7i	0.126001	−	0.196062i
$459$	−1.05055e8	−	1.39812e7i	−1.08637	−	0.144579i
$460$	−4.90634e7	+	2.85041e7i	−0.504062	+	0.292842i
$461$			1.67954e8i			1.71430i	0.515068	+	0.857150i	$0.327767\pi$
$461$			1.67954e8i			1.71430i	−0.515068	+	0.857150i	$0.672233\pi$
$462$	−3.15462e7	−	2.90098e6i	−0.319905	−	0.0294184i
$463$	−1.52979e7	−	1.06399e8i	−0.154130	−	1.07200i	−0.909202	−	0.416356i	$-0.863307\pi$
$463$	−1.52979e7	−	1.06399e8i	−0.154130	−	1.07200i	0.755071	−	0.655643i	$-0.227602\pi$
$464$	−2.26056e7	+	1.03236e7i	−0.226289	+	0.103343i
$465$	4.62987e6	+	2.35780e7i	0.0460480	+	0.234503i
$466$	2.28897e7	−	5.01214e7i	0.226194	−	0.495297i
$467$	8.71745e6	+	7.55372e6i	0.0855931	+	0.0741669i	0.696606	−	0.717453i	$-0.254692\pi$
$467$	8.71745e6	+	7.55372e6i	0.0855931	+	0.0741669i	−0.611013	+	0.791620i	$0.709238\pi$
$468$	−5.04039e7	−	4.73913e7i	−0.491730	−	0.462339i
$469$	4.95627e7	−	1.45529e7i	0.480436	−	0.141069i
$470$	−2.34687e7	+	2.03358e7i	−0.226045	+	0.195869i
$471$	1.87808e7	−	3.27937e7i	0.179743	−	0.313854i
$472$	3.84866e7	−	2.47338e7i	0.366002	−	0.235215i
$473$	−2.48499e7	+	2.15326e7i	−0.234824	+	0.203476i
$474$	−4.53344e7	−	4.72136e7i	−0.425689	−	0.443335i
$475$	−3.20163e7	+	2.22678e8i	−0.298738	+	2.07777i
$476$	−2.49650e7	−	2.16323e7i	−0.231479	−	0.200577i
$477$	7.10000e7	−	4.16568e7i	0.654189	−	0.383823i
$478$	−3.76520e7	−	1.10556e7i	−0.344750	−	0.101228i
$479$	−7.27308e7	+	3.32150e7i	−0.661777	+	0.302223i	−0.717844	−	0.696204i	$-0.754871\pi$
$479$	−7.27308e7	+	3.32150e7i	−0.661777	+	0.302223i	0.0560674	+	0.998427i	$0.482144\pi$
$480$	7.06263e7	+	9.84502e7i	0.638621	+	0.890211i
$481$	−2.74777e8	−	1.76589e8i	−2.46914	−	1.58682i
$482$			5.47120e7i			0.488586i
$483$	8.09653e7	−	2.43202e7i	0.718551	−	0.215837i
$484$	2.98940e7			0.263662
$485$	−1.58332e8	+	2.46369e8i	−1.38785	+	2.15954i
$486$	−7.49820e7	−	5.14422e7i	−0.653203	−	0.448137i
$487$	3.93565e7	+	8.61787e7i	0.340745	+	0.746128i	0.999983	−	0.00580652i	$-0.00184828\pi$
$487$	3.93565e7	+	8.61787e7i	0.340745	+	0.746128i	−0.659238	+	0.751934i	$0.729121\pi$
$488$	3.56439e7	−	1.21392e8i	0.306708	−	1.04455i
$489$	532492.	+	1.04120e7i	0.00455393	+	0.0890446i
$490$	−4.17477e7	+	4.81794e7i	−0.354849	+	0.409518i
$491$	2.23671e8	+	3.21590e7i	1.88958	+	0.271681i	0.987227	−	0.159317i	$-0.0509292\pi$
$491$	2.23671e8	+	3.21590e7i	1.88958	+	0.271681i	0.902353	+	0.430998i	$0.141838\pi$
$492$	4.41792e6	+	4.60105e6i	0.0370956	+	0.0386332i
$493$	4.37719e7	+	5.05155e7i	0.365305	+	0.421584i
$494$	1.35508e8	+	2.10855e8i	1.12405	+	1.74906i
$495$	4.16490e6	−	1.02516e8i	0.0343391	−	0.845233i
$496$	−5.96391e6	−	6.88272e6i	−0.0488749	−	0.0564047i
$497$	1.60132e7	+	5.45359e7i	0.130439	+	0.444235i
$498$	−2.00231e7	−	5.72049e7i	−0.162123	−	0.463175i
$499$	−7.42505e7	+	8.56897e7i	−0.597583	+	0.689647i	−0.971290	−	0.237900i	$-0.923541\pi$
$499$	−7.42505e7	+	8.56897e7i	−0.597583	+	0.689647i	0.373707	+	0.927547i	$0.378087\pi$
$500$	−2.97721e7	−	1.35964e7i	−0.238177	−	0.108772i
$501$	−1.59500e7	−	8.12265e7i	−0.126837	−	0.645929i
$502$	5.77975e7	+	1.26559e8i	0.456875	+	1.00042i
$503$	−1.97161e8	+	2.83475e7i	−1.54924	+	0.222746i	−0.863215	−	0.504836i	$-0.831553\pi$
$503$	−1.97161e8	+	2.83475e7i	−1.54924	+	0.222746i	−0.686020	+	0.727583i	$0.740644\pi$
$504$	−3.94901e7	−	9.66760e7i	−0.308459	−	0.755139i
$505$	1.90534e8			1.47945
$506$	−5.14437e7	+	2.07567e7i	−0.397083	+	0.160216i
$507$	2.63994e8	−	1.37269e8i	2.02567	−	1.05329i
$508$	7.19577e7	+	4.62444e7i	0.548891	+	0.352751i
$509$	−4.37837e7	+	6.29515e6i	−0.332016	+	0.0477367i	−0.306307	−	0.951933i	$-0.599093\pi$
$509$	−4.37837e7	+	6.29515e6i	−0.332016	+	0.0477367i	−0.0257091	+	0.999669i	$0.508184\pi$
$510$	−1.10912e8	+	1.42056e8i	−0.836120	+	1.07090i
$511$	−1.58233e8	−	4.64614e7i	−1.18586	−	0.348201i
$512$	−1.06648e8	−	4.87045e7i	−0.794590	−	0.362877i
$513$	−1.29607e8	−	1.46441e8i	−0.960013	−	1.08470i
$514$	−169238.	+	1.17708e6i	−0.00124626	+	0.00866793i
$515$	−1.90915e7	−	6.50198e7i	−0.139772	−	0.476019i
$516$	−2.73488e7	−	1.08380e7i	−0.199062	−	0.0788857i
$517$	1.51610e7	−	9.74336e6i	0.109712	−	0.0705078i
$518$	−7.23427e7	−	1.12567e8i	−0.520482	−	0.809885i
$519$	−9.45627e7	+	2.38622e8i	−0.676422	+	1.70690i
$520$	−4.15934e8	+	1.22129e8i	−2.95811	+	0.868581i
$521$	2.34596e8	+	3.37299e7i	1.65885	+	0.238507i	0.907093	−	0.420930i	$-0.138296\pi$
$521$	2.34596e8	+	3.37299e7i	1.65885	+	0.238507i	0.751760	+	0.659437i	$0.229205\pi$
$522$	1.39103e7	+	5.56374e7i	0.0977969	+	0.391161i
$523$	1.03146e8	−	2.25858e8i	0.721021	−	1.57881i	−0.0914481	−	0.995810i	$-0.529150\pi$
$523$	1.03146e8	−	2.25858e8i	0.721021	−	1.57881i	0.812469	−	0.583005i	$-0.198123\pi$
$524$	−2.29443e7	+	7.81413e7i	−0.159471	+	0.543109i
$525$	1.24009e8	+	9.68214e7i	0.856987	+	0.669104i
$526$	2.43817e7	+	1.69579e8i	0.167536	+	1.16524i
$527$	−1.32430e7	+	2.06066e7i	−0.0904806	+	0.140791i
$528$	1.79401e7	+	3.45021e7i	0.121877	+	0.234392i
$529$	1.06584e8	−	1.02735e8i	0.719988	−	0.693987i
$530$		−	1.39986e8i		−	0.940279i
$531$	−2.26559e7	−	5.54641e7i	−0.151321	−	0.370449i
$532$	−8.67463e6	−	6.03334e7i	−0.0576124	−	0.400703i
$533$	−3.58842e7	+	1.63878e7i	−0.236985	+	0.108228i
$534$	1.77015e8	−	3.47594e7i	1.16248	−	0.228270i
$535$	4.50590e7	−	9.86654e7i	0.294252	−	0.644323i
$536$	−8.44442e7	−	7.31713e7i	−0.548372	−	0.475167i
$537$	5.70926e6	−	1.99838e6i	0.0368686	−	0.0129049i
$538$	2.10763e8	−	6.18856e7i	1.35347	−	0.397414i
$539$	2.79608e7	−	2.42282e7i	0.178560	−	0.154723i
$540$	8.30942e7	−	3.90067e7i	0.527703	−	0.247718i
$541$	−9.58429e7	+	6.15945e7i	−0.605296	+	0.389000i	−0.807091	−	0.590428i	$-0.798959\pi$
$541$	−9.58429e7	+	6.15945e7i	−0.605296	+	0.389000i	0.201794	+	0.979428i	$0.435323\pi$
$542$	−2.46538e7	+	2.13626e7i	−0.154841	+	0.134170i
$543$	5.41458e7	−	5.19907e7i	0.338193	−	0.324733i
$544$	−1.75783e7	+	1.22260e8i	−0.109189	+	0.759429i
$545$	−2.44865e8	−	2.12177e8i	−1.51265	−	1.31071i
$546$	1.75057e8	−	8.95279e6i	1.07548	−	0.0550022i
$547$	−1.27015e8	−	3.72949e7i	−0.776054	−	0.227870i	−0.130361	−	0.991467i	$-0.541614\pi$
$547$	−1.27015e8	−	3.72949e7i	−0.776054	−	0.227870i	−0.645694	+	0.763596i	$0.723432\pi$
$548$	4.96205e7	−	2.26609e7i	0.301522	−	0.137701i
$549$	−1.47795e8	−	7.48897e7i	−0.893189	−	0.452590i
$550$	−8.68488e7	−	5.58144e7i	−0.522007	−	0.335473i
$551$			1.23337e8i			0.737291i
$552$	−1.38942e8	−	1.18893e8i	−0.826071	−	0.706869i
$553$	−9.84443e7			−0.582124
$554$	8.39125e7	−	1.30570e8i	0.493512	−	0.767919i
$555$	3.52133e8	−	2.52614e8i	2.05981	−	1.47767i
$556$	−7635.67	−	16719.8i	−4.44245e−5	−	9.72761e-5i
$557$	−3.85963e7	+	1.31447e8i	−0.223347	+	0.760649i	0.769224	+	0.638979i	$0.220643\pi$
$557$	−3.85963e7	+	1.31447e8i	−0.223347	+	0.760649i	−0.992571	+	0.121670i	$0.961175\pi$
$558$	−1.81270e7	+	1.06354e7i	−0.104334	+	0.0612142i
$559$	1.19143e8	−	1.37498e8i	0.682075	−	0.787157i
$560$	−9.97534e7	−	1.43424e7i	−0.568020	−	0.0816690i
$561$	7.54453e7	−	7.24424e7i	0.427310	−	0.410303i
$562$	−8.99714e7	−	1.03833e8i	−0.506869	−	0.584958i
$563$	−1.56902e8	−	2.44145e8i	−0.879233	−	1.36811i	−0.929284	−	0.369366i	$-0.879575\pi$
$563$	−1.56902e8	−	2.44145e8i	−0.879233	−	1.36811i	0.0500509	−	0.998747i	$-0.484062\pi$
$564$	1.39917e7	+	8.01297e6i	0.0779887	+	0.0446638i
$565$	−7.97680e7	−	9.20572e7i	−0.442266	−	0.510402i
$566$	4.59640e6	+	1.56539e7i	0.0253494	+	0.0863323i
$567$	−1.33915e8	+	2.77586e7i	−0.734651	+	0.152282i
$568$	8.05135e7	−	9.29175e7i	0.439363	−	0.507052i
$569$	1.24817e8	+	5.70022e7i	0.677545	+	0.309425i	0.724303	−	0.689482i	$-0.242162\pi$
$569$	1.24817e8	+	5.70022e7i	0.677545	+	0.309425i	−0.0467579	+	0.998906i	$0.514889\pi$
$570$	−3.26324e8	+	6.40784e7i	−1.76207	+	0.346009i
$571$	3.04944e7	+	6.67733e7i	0.163799	+	0.358670i	0.973678	−	0.227927i	$-0.0731947\pi$
$571$	3.04944e7	+	6.67733e7i	0.163799	+	0.358670i	−0.809879	+	0.586597i	$0.800467\pi$
$572$	6.75837e7	−	9.71707e6i	0.361122	−	0.0519215i
$573$	3.42964e6	−	3.72950e7i	0.0182299	−	0.198238i
$574$	−1.61610e7			−0.0854542
$575$	2.70660e8	+	5.14061e7i	1.42371	+	0.270403i
$576$	−1.14512e8	+	1.63214e8i	−0.599214	+	0.854061i
$577$	−8.68020e7	−	5.57843e7i	−0.451858	−	0.290392i	0.294850	−	0.955544i	$-0.404730\pi$
$577$	−8.68020e7	−	5.57843e7i	−0.451858	−	0.290392i	−0.746708	+	0.665152i	$0.768367\pi$
$578$	−3.04498e7	+	4.37802e6i	−0.157689	+	0.0226722i
$579$	−5.45667e7	−	4.26037e7i	−0.281120	−	0.219488i
$580$	−5.55487e7	−	1.63106e7i	−0.284702	−	0.0835960i
$581$	−8.29173e7	−	3.78671e7i	−0.422782	−	0.193078i
$582$	−2.49143e8	−	5.95196e7i	−1.26381	−	0.301919i
$583$	−1.15617e7	+	8.04136e7i	−0.0583468	+	0.405811i
$584$	1.00501e8	+	3.42276e8i	0.504584	+	1.71845i
$585$	5.79156e7	+	5.64741e8i	0.289287	+	2.82086i
$586$	9.10052e7	−	5.84855e7i	0.452245	−	0.290640i
$587$	3.58736e7	+	5.58204e7i	0.177362	+	0.275981i	0.918540	−	0.395328i	$-0.129369\pi$
$587$	3.58736e7	+	5.58204e7i	0.177362	+	0.275981i	−0.741178	+	0.671308i	$0.765733\pi$
$588$	3.07725e7	+	1.21947e7i	0.151367	+	0.0599846i
$589$	−4.33678e7	+	1.27339e7i	−0.212237	+	0.0623184i
$590$	−1.00848e8	−	1.44997e7i	−0.491032	−	0.0705997i
$591$	2.20468e8	+	5.26691e7i	1.06803	+	0.255149i
$592$	−6.82343e7	+	1.49412e8i	−0.328880	+	0.720147i
$593$	4.09919e7	−	1.39606e8i	0.196578	−	0.669482i	−0.800919	−	0.598772i	$-0.795655\pi$
$593$	4.09919e7	−	1.39606e8i	0.196578	−	0.669482i	0.997497	−	0.0707098i	$-0.0225264\pi$
$594$	8.58362e7	−	2.61852e7i	0.409554	−	0.124938i
$595$	3.85760e7	+	2.68302e8i	0.183133	+	1.27372i
$596$	−6.61896e7	+	1.02993e8i	−0.312645	+	0.486485i
$597$	−1.39400e8	+	7.24840e7i	−0.655149	+	0.340658i
$598$	2.65403e8	−	1.54190e8i	1.24109	−	0.721028i
$599$		−	2.09175e8i		−	0.973263i	−0.873607	−	0.486631i	$-0.838226\pi$
$599$		−	2.09175e8i		−	0.973263i	0.873607	−	0.486631i	$-0.161774\pi$
$600$	3.11644e7	−	3.38891e8i	0.144280	−	1.56894i
$601$	3.44273e6	+	2.39447e7i	0.0158591	+	0.110303i	0.996213	−	0.0869425i	$-0.0277096\pi$
$601$	3.44273e6	+	2.39447e7i	0.0158591	+	0.110303i	−0.980354	+	0.197245i	$0.936801\pi$
$602$	6.77979e7	−	3.09623e7i	0.310761	−	0.141920i
$603$	−1.14387e8	+	9.12569e7i	−0.521703	+	0.416211i
$604$	5.65919e7	−	1.23919e8i	0.256829	−	0.562377i
$605$	−1.85385e8	−	1.60637e8i	−0.837160	−	0.725403i
$606$	5.50577e7	+	1.57296e8i	0.247400	+	0.706807i
$607$	−2.06957e8	+	6.07680e7i	−0.925366	+	0.271712i	−0.709495	−	0.704710i	$-0.751077\pi$
$607$	−2.06957e8	+	6.07680e7i	−0.925366	+	0.271712i	−0.215871	+	0.976422i	$0.569259\pi$
$608$	−1.72247e8	+	1.49253e8i	−0.766374	+	0.664067i
$609$	7.48491e7	+	4.28658e7i	0.331386	+	0.189784i
$610$	−2.37029e8	+	1.52329e8i	−1.04427	+	0.671109i
$611$	−7.53614e7	+	6.53011e7i	−0.330389	+	0.286284i
$612$	8.86427e7	+	2.99868e7i	0.386713	+	0.130821i
$613$	1.81020e7	−	1.25902e8i	0.0785861	−	0.546578i	−0.912053	−	0.410072i	$-0.865504\pi$
$613$	1.81020e7	−	1.25902e8i	0.0785861	−	0.546578i	0.990639	−	0.136506i	$-0.0435873\pi$
$614$	−8.08432e7	−	7.00510e7i	−0.349252	−	0.302628i
$615$	−2.67335e6	−	5.22729e7i	−0.0114929	−	0.224725i
$616$	9.88884e7	+	2.90363e7i	0.423061	+	0.124222i
$617$	6.42912e6	−	2.93608e6i	0.0273713	−	0.0125001i	−0.401682	−	0.915779i	$-0.631574\pi$
$617$	6.42912e6	−	2.93608e6i	0.0273713	−	0.0125001i	0.429054	+	0.903279i	$0.358847\pi$
$618$	4.81607e7	−	3.45496e7i	0.204045	−	0.146378i
$619$	2.37077e8	+	1.52360e8i	0.999581	+	0.642392i	0.934676	−	0.355499i	$-0.115689\pi$
$619$	2.37077e8	+	1.52360e8i	0.999581	+	0.642392i	0.0649049	+	0.997891i	$0.479326\pi$
$620$		−	2.12160e7i		−	0.0890202i
$621$	−1.86276e8	+	1.50510e8i	−0.777825	+	0.628481i
$622$	2.42082e8			1.00599
$623$	1.46684e8	−	2.28245e8i	0.606623	−	0.943923i
$624$	−1.25423e8	−	1.74835e8i	−0.516207	−	0.719571i
$625$	−3.54055e7	−	7.75272e7i	−0.145021	−	0.317551i
$626$	−1.63902e7	+	5.58198e7i	−0.0668129	+	0.227544i
$627$	1.92746e8	−	9.85745e6i	0.781958	−	0.0399910i
$628$	−2.18513e7	+	2.52177e7i	−0.0882264	+	0.101819i
$629$	4.37294e8	+	6.28734e7i	1.75720	+	0.252648i
$630$	−7.45268e7	+	2.20305e8i	−0.298051	+	0.881056i
$631$	1.57919e8	+	1.82249e8i	0.628561	+	0.725398i	0.977309	−	0.211819i	$-0.0679387\pi$
$631$	1.57919e8	+	1.82249e8i	0.628561	+	0.725398i	−0.348748	+	0.937216i	$0.613393\pi$
$632$	1.15127e8	+	1.79142e8i	0.456065	+	0.709652i
$633$	−1.37183e8	+	2.39539e8i	−0.540866	+	0.944421i
$634$	5.70350e7	+	6.58219e7i	0.223807	+	0.258287i
$635$	−1.97743e8	−	6.73450e8i	−0.772288	−	2.63017i
$636$	−6.86027e7	+	2.40127e7i	−0.266667	+	0.0933402i
$637$	−1.34058e8	+	1.54711e8i	−0.518649	+	0.598553i
$638$	−5.14844e7	−	2.35121e7i	−0.198250	−	0.0905378i
$639$	−1.00414e8	−	1.25865e8i	−0.384850	−	0.482393i
$640$	2.15391e7	+	4.71640e7i	0.0821650	+	0.179916i
$641$	2.07655e8	−	2.98563e7i	0.788440	−	0.113361i	0.263679	−	0.964610i	$-0.415064\pi$
$641$	2.07655e8	−	2.98563e7i	0.788440	−	0.113361i	0.524761	+	0.851250i	$0.324155\pi$
$642$	9.44742e7	+	8.68784e6i	0.357033	+	0.0328327i
$643$	1.48539e8			0.558738			0.279369	−	0.960184i	$-0.409875\pi$
$643$	1.48539e8			0.558738			0.279369	+	0.960184i	$0.409875\pi$
$644$	−7.42873e7	+	7.29652e6i	−0.278136	+	0.0273186i
$645$	1.11363e8	+	2.14171e8i	0.415012	+	0.798144i
$646$	−2.85199e8	−	1.83286e8i	−1.05791	−	0.679879i
$647$	3.27277e8	−	4.70554e7i	1.20838	−	0.173739i	0.491463	−	0.870899i	$-0.336462\pi$
$647$	3.27277e8	−	4.70554e7i	1.20838	−	0.173739i	0.716916	+	0.697160i	$0.245553\pi$
$648$	2.07122e8	+	2.11226e8i	0.761206	+	0.776288i
$649$	5.67335e7	+	1.66584e7i	0.207542	+	0.0609397i
$650$	5.19606e8	+	2.37296e8i	1.89206	+	0.864073i
$651$	−7.34467e6	+	3.07441e7i	−0.0266213	+	0.111434i
$652$	1.31007e6	−	9.11171e6i	0.00472662	−	0.0328743i
$653$	−1.07366e8	−	3.65656e8i	−0.385592	−	1.31321i	−0.892438	−	0.451170i	$-0.851007\pi$
$653$	−1.07366e8	−	3.65656e8i	−0.385592	−	1.31321i	0.506845	−	0.862037i	$-0.330812\pi$
$654$	1.04406e8	−	2.63461e8i	0.373244	−	0.941853i
$655$	5.62184e8	−	3.61294e8i	2.00057	−	1.28569i
$656$	1.07254e7	+	1.66890e7i	0.0379928	+	0.0591180i
$657$	4.64730e8	−	4.76593e7i	1.63872	−	0.168055i
$658$	−3.91963e7	+	1.15091e7i	−0.137584	+	0.0403982i
$659$	3.74268e7	+	5.38116e6i	0.130775	+	0.0188027i	0.207392	−	0.978258i	$-0.433503\pi$
$659$	3.74268e7	+	5.38116e6i	0.130775	+	0.0188027i	−0.0766163	+	0.997061i	$0.524412\pi$
$660$	−2.10499e7	+	8.81129e7i	−0.0732181	+	0.306484i
$661$	6.67290e6	−	1.46116e7i	0.0231052	−	0.0505934i	−0.897728	−	0.440551i	$-0.854783\pi$
$661$	6.67290e6	−	1.46116e7i	0.0231052	−	0.0505934i	0.920833	+	0.389958i	$0.127510\pi$
$662$	−4.77127e7	+	1.62495e8i	−0.164460	+	0.560099i
$663$	−3.56155e8	+	4.56163e8i	−1.22208	+	1.56523i
$664$	2.80613e7	+	1.95171e8i	0.0958527	+	0.666670i
$665$	−2.70410e8	+	4.20766e8i	−0.919513	+	1.43079i
$666$	3.10300e8	+	2.17709e8i	1.05041	+	0.736975i
$667$	1.50888e8	+	6.77841e6i	0.508483	+	0.0228429i
$668$			7.30895e7i			0.245203i
$669$	−2.91853e8	−	2.68388e7i	−0.974732	−	0.0896363i
$670$	3.54134e7	+	2.46306e8i	0.117745	+	0.818937i
$671$	1.48740e8	−	6.79274e7i	0.492335	−	0.224842i
$672$	3.07121e7	+	1.56404e8i	0.101205	+	0.515394i
$673$	1.09495e8	−	2.39761e8i	0.359211	−	0.786563i	−0.640614	−	0.767863i	$-0.721320\pi$
$673$	1.09495e8	−	2.39761e8i	0.359211	−	0.786563i	0.999825	−	0.0186996i	$-0.00595261\pi$
$674$	1.18489e8	+	1.02672e8i	0.386990	+	0.335329i
$675$	−4.28925e8	−	1.21070e8i	−1.39466	−	0.393663i
$676$	−2.52082e8	+	7.40180e7i	−0.816022	+	0.239606i
$677$	−1.09908e8	+	9.52356e7i	−0.354211	+	0.306926i	−0.813731	−	0.581242i	$-0.802567\pi$
$677$	−1.09908e8	+	9.52356e7i	−0.354211	+	0.306926i	0.459520	+	0.888168i	$0.348022\pi$
$678$	5.29481e7	−	9.24542e7i	0.169888	−	0.296645i
$679$	−3.24099e8	+	2.08286e8i	−1.03531	+	0.665351i
$680$	4.43123e8	−	3.83968e8i	1.40928	−	1.22115i
$681$	−3.11007e7	−	3.23898e7i	−0.0984755	−	0.102557i
$682$	2.95183e6	−	2.05304e7i	0.00930547	−	0.0647210i
$683$	−1.35492e8	−	1.17405e8i	−0.425258	−	0.368488i	0.415779	−	0.909466i	$-0.363509\pi$
$683$	−1.35492e8	−	1.17405e8i	−0.425258	−	0.368488i	−0.841037	+	0.540978i	$0.818054\pi$
$684$	8.73792e7	+	1.48929e8i	0.273048	+	0.465385i
$685$	−4.29487e8	−	1.26109e8i	−1.33622	−	0.392350i
$686$	−2.50812e8	+	1.14542e8i	−0.776919	+	0.354807i
$687$	5.56065e7	+	7.75132e7i	0.171497	+	0.239059i
$688$	−7.69684e7	−	4.94646e7i	−0.236345	−	0.151890i
$689$		−	4.49515e8i		−	1.37432i
$690$	6.04578e7	+	4.02739e8i	0.184037	+	1.22596i
$691$	4.26219e7			0.129181			0.0645905	−	0.997912i	$-0.479426\pi$
$691$	4.26219e7			0.129181			0.0645905	+	0.997912i	$0.479426\pi$
$692$	1.22528e8	−	1.90657e8i	0.369758	−	0.575354i
$693$	6.10068e7	−	1.20397e8i	0.183307	−	0.361757i
$694$	2.59419e7	+	5.68047e7i	0.0776109	+	0.169944i
$695$	−42492.7	+	144717.i	−0.000126579	+	0.000431087i
$696$	−9.52956e6	−	1.86335e8i	−0.0282648	−	0.552671i
$697$	3.49421e7	−	4.03254e7i	0.103193	−	0.119091i
$698$	−2.98324e8	−	4.28926e7i	−0.877248	−	0.126129i
$699$	1.62596e8	+	1.69336e8i	0.476079	+	0.495813i
$700$	−9.09705e7	−	1.04986e8i	−0.265220	−	0.306080i
$701$	8.63662e6	+	1.34388e7i	0.0250720	+	0.0390129i	0.853563	−	0.520989i	$-0.174437\pi$
$701$	8.63662e6	+	1.34388e7i	0.0250720	+	0.0390129i	−0.828491	+	0.560002i	$0.810800\pi$
$702$	−4.49489e8	+	2.11003e8i	−1.29930	+	0.609926i
$703$	5.33842e8	+	6.16086e8i	1.53655	+	1.77327i
$704$	−5.54359e7	−	1.88797e8i	−0.158881	−	0.541100i
$705$	−4.37100e7	−	1.24877e8i	−0.124742	−	0.356381i
$706$	1.04790e8	−	1.20934e8i	0.297786	−	0.343663i
$707$	2.27998e8	+	1.04123e8i	0.645167	+	0.294638i
$708$	1.01932e7	+	5.19095e7i	0.0287217	+	0.146267i
$709$	−1.58394e8	−	3.46835e8i	−0.444427	−	0.973160i	−0.990764	−	0.135595i	$-0.956705\pi$
$709$	−1.58394e8	−	3.46835e8i	−0.444427	−	0.973160i	0.546337	−	0.837566i	$-0.316022\pi$
$710$	−2.71021e8	+	3.89669e7i	−0.757230	+	0.108873i
$711$	2.58166e8	−	1.05456e8i	0.718275	−	0.293400i
$712$	−5.86885e8			−1.62597
$713$	1.31950e7	+	5.37550e7i	0.0364032	+	0.148303i
$714$	−2.10351e8	+	1.09376e8i	−0.577896	+	0.300489i
$715$	−4.71330e8	−	3.02905e8i	−1.28946	−	0.828684i
$716$	−5.28658e6	+	760095.i	−0.0144024	+	0.00207076i
$717$	1.02890e8	−	1.31782e8i	0.279137	−	0.357518i
$718$	−1.72567e8	−	5.06703e7i	−0.466214	−	0.136893i
$719$	−3.39960e7	−	1.55255e7i	−0.0914621	−	0.0417693i	0.369159	−	0.929366i	$-0.379646\pi$
$719$	−3.39960e7	−	1.55255e7i	−0.0914621	−	0.0417693i	−0.460621	+	0.887597i	$0.652373\pi$
$720$	2.76963e8	−	6.92456e7i	0.742035	−	0.185522i
$721$	1.26866e7	−	8.82374e7i	0.0338486	−	0.235422i
$722$	−9.22445e7	−	3.14156e8i	−0.245092	−	0.834706i
$723$	−2.16708e8	−	8.58784e7i	−0.573402	−	0.227232i
$724$	−5.57580e7	+	3.58335e7i	−0.146924	+	0.0944221i
$725$	1.51968e8	+	2.36467e8i	0.398785	+	0.620522i
$726$	7.90449e7	−	1.99464e8i	0.206569	−	0.521260i
$727$	−3.49755e8	+	1.02697e8i	−0.910249	+	0.267273i	−0.703146	−	0.711046i	$-0.748222\pi$
$727$	−3.49755e8	+	1.02697e8i	−0.910249	+	0.267273i	−0.207104	+	0.978319i	$0.566404\pi$
$728$	−5.64458e8	−	8.11568e7i	−1.46298	−	0.210344i
$729$	3.21452e8	−	2.16249e8i	0.829723	−	0.558175i
$730$	3.30022e8	−	7.22648e8i	0.848349	−	1.85763i
$731$	−6.93296e7	+	2.36115e8i	−0.177487	+	0.604465i
$732$	1.15311e8	+	9.00304e7i	0.293993	+	0.229539i
$733$	9.35972e6	+	6.50983e7i	0.0237657	+	0.165294i	0.998248	−	0.0591708i	$-0.0188457\pi$
$733$	9.35972e6	+	6.50983e7i	0.0237657	+	0.165294i	−0.974482	+	0.224465i	$0.927937\pi$
$734$	1.31969e8	−	2.05348e8i	0.333722	−	0.519281i
$735$	−1.25304e8	−	2.40982e8i	−0.315575	−	0.606908i
$736$	1.73126e8	+	2.18926e8i	0.434240	+	0.549115i
$737$		−	1.44413e8i		−	0.360748i
$738$	4.23817e7	−	1.73120e7i	0.105441	−	0.0430704i
$739$	−8.17611e7	−	5.68661e8i	−0.202588	−	1.40903i	−0.796568	−	0.604549i	$-0.793353\pi$
$739$	−8.17611e7	−	5.68661e8i	−0.202588	−	1.40903i	0.593980	−	0.804480i	$-0.297556\pi$
$740$	−3.48071e8	+	1.58959e8i	−0.858960	+	0.392274i
$741$	−1.04787e9	+	2.05765e8i	−2.57546	+	0.505728i
$742$	7.64994e7	−	1.67510e8i	0.187261	−	0.410044i
$743$	4.14511e8	+	3.59176e8i	1.01058	+	0.875670i	0.992262	−	0.124162i	$-0.0396244\pi$
$743$	4.14511e8	+	3.59176e8i	1.01058	+	0.875670i	0.0183150	+	0.999832i	$0.494170\pi$
$744$	6.45352e7	−	2.25889e7i	0.156703	−	0.0548500i
$745$	9.63909e8	−	2.83029e8i	2.33113	−	0.684483i
$746$	5.57147e7	−	4.82770e7i	0.134200	−	0.116285i
$747$	2.58011e8	+	1.04822e7i	0.618980	+	0.0251472i
$748$	−7.76918e7	+	4.99295e7i	−0.185639	+	0.119303i
$749$	1.07837e8	−	9.34415e7i	0.256639	−	0.222379i
$750$	−1.69443e8	+	1.62699e8i	−0.401643	+	0.385657i
$751$	−1.04759e8	+	7.28612e8i	−0.247326	+	1.72019i	0.366217	+	0.930529i	$0.380653\pi$
$751$	−1.04759e8	+	7.28612e8i	−0.247326	+	1.72019i	−0.613543	+	0.789661i	$0.710256\pi$
$752$	3.78980e7	+	3.28388e7i	0.0891174	+	0.0772207i
$753$	−5.92006e8	+	3.02765e7i	−1.38657	+	0.0709121i
$754$	3.00485e8	+	8.82304e7i	0.700985	+	0.205828i
$755$	−1.01684e9	+	4.64374e8i	−2.36271	+	1.07901i
$756$	1.20749e8	−	1.26709e6i	0.279459	−	0.00293252i
$757$	−1.86289e8	−	1.19721e8i	−0.429437	−	0.275982i	0.308016	−	0.951381i	$-0.400335\pi$
$757$	−1.86289e8	−	1.19721e8i	−0.429437	−	0.275982i	−0.737453	+	0.675399i	$0.763971\pi$
$758$		−	6.72924e7i		−	0.154511i
$759$	−1.46636e6	−	2.36343e8i	−0.00335363	−	0.540527i
$760$	1.08191e9			2.46463
$761$	1.36413e8	−	2.12262e8i	0.309529	−	0.481636i	−0.651284	−	0.758834i	$-0.725769\pi$
$761$	1.36413e8	−	2.12262e8i	0.309529	−	0.481636i	0.960813	+	0.277198i	$0.0894058\pi$
$762$	4.98829e8	−	3.57851e8i	1.12742	−	0.808792i
$763$	−1.77061e8	−	3.87709e8i	−0.398611	−	0.872836i
$764$	−9.31660e6	+	3.17294e7i	−0.0208919	+	0.0711512i
$765$	−3.88575e8	−	6.62288e8i	−0.867941	−	1.47932i
$766$	−3.47912e8	+	4.01511e8i	−0.774074	+	0.893329i
$767$	−3.23836e8	−	4.65606e7i	−0.717694	−	0.103189i
$768$	3.08181e8	−	2.95915e8i	0.680335	−	0.653256i
$769$	3.04610e8	+	3.51539e8i	0.669831	+	0.773026i	0.984350	−	0.176225i	$-0.0563886\pi$
$769$	3.04610e8	+	3.51539e8i	0.669831	+	0.773026i	−0.314519	+	0.949251i	$0.601843\pi$
$770$	−1.24091e8	−	1.93089e8i	−0.271811	−	0.422946i
$771$	−4.39662e6	−	2.51792e6i	−0.00959302	−	0.00549389i
$772$	4.00291e7	+	4.61961e7i	0.0870010	+	0.100405i
$773$	−1.62657e8	−	5.53958e8i	−0.352155	−	1.19933i	−0.925096	−	0.379733i	$-0.876016\pi$
$773$	−1.62657e8	−	5.53958e8i	−0.352155	−	1.19933i	0.572941	−	0.819596i	$-0.305802\pi$
$774$	−1.44630e8	+	1.53824e8i	−0.311914	+	0.331742i
$775$	−6.74567e7	+	7.78491e7i	−0.144917	+	0.167243i
$776$	7.58046e8	+	3.46188e8i	1.62222	+	0.740844i
$777$	5.59419e8	−	1.09850e8i	1.19254	−	0.234173i
$778$	1.02569e8	+	2.24594e8i	0.217809	+	0.476936i
$779$	9.74549e7	−	1.40119e7i	0.206154	−	0.0296404i
$780$	4.59022e7	−	4.99154e8i	0.0967274	−	1.05184i
$781$	1.58904e8			0.333566
$782$	−2.39902e8	+	3.38833e8i	−0.501665	+	0.708541i
$783$	−2.42207e8	−	3.22339e7i	−0.504548	−	0.0671472i
$784$	8.66038e7	+	5.56569e7i	0.179717	+	0.115497i
$785$	2.71018e8	−	3.89665e7i	0.560260	−	0.0805532i
$786$	4.60719e8	+	3.59713e8i	0.948787	+	0.740778i
$787$	−2.30171e8	−	6.75842e7i	−0.472200	−	0.138650i	0.0369700	−	0.999316i	$-0.488229\pi$
$787$	−2.30171e8	−	6.75842e7i	−0.472200	−	0.138650i	−0.509170	+	0.860666i	$0.670048\pi$
$788$	−1.82056e8	−	8.31421e7i	−0.372071	−	0.169919i
$789$	−7.09952e8	−	1.69605e8i	−1.44543	−	0.345309i
$790$	6.74910e7	−	4.69410e8i	0.136888	−	0.952076i
$791$	−4.51449e7	−	1.53749e8i	−0.0912177	−	0.310659i
$792$	−2.90435e8	+	2.97848e7i	−0.584620	+	0.0599542i
$793$	−7.61133e8	+	4.89151e8i	−1.52630	+	0.980896i
$794$	7.58306e7	+	1.17995e8i	0.151490	+	0.235722i
$795$	5.54467e8	+	2.19728e8i	1.10351	+	0.437305i
$796$	1.33110e8	−	3.90847e7i	0.263920	−	0.0774939i
$797$	−7.20834e8	−	1.03640e8i	−1.42384	−	0.204717i	−0.613044	−	0.790049i	$-0.710055\pi$
$797$	−7.20834e8	−	1.03640e8i	−1.42384	−	0.204717i	−0.810794	+	0.585332i	$0.800964\pi$
$798$	−4.25504e8	−	1.01652e8i	−0.837327	−	0.200035i
$799$	5.60295e7	−	1.22687e8i	0.109844	−	0.240525i
$800$	−1.46339e8	+	4.98386e8i	−0.285819	+	0.973411i
$801$	−1.40173e8	+	7.55694e8i	−0.272750	+	1.47044i
$802$	−9.30331e7	−	6.47059e8i	−0.180349	−	1.25436i
$803$	−2.49263e8	+	3.87861e8i	−0.481406	+	0.749083i
$804$	1.14632e8	−	5.96054e7i	0.220566	−	0.114688i
$805$	4.99895e8	+	3.53938e8i	0.958276	+	0.678484i
$806$			1.14766e8i			0.219183i
$807$	−8.57017e7	+	9.31946e8i	−0.163068	+	1.77325i
$808$	−7.71603e7	−	5.36662e8i	−0.146272	−	1.01734i
$809$	4.09537e8	−	1.87030e8i	0.773478	−	0.353236i	0.0107394	−	0.999942i	$-0.496581\pi$
$809$	4.09537e8	−	1.87030e8i	0.773478	−	0.353236i	0.762739	+	0.646707i	$0.223854\pi$
$810$	−4.05520e7	−	6.57577e8i	−0.0763057	−	1.23735i
$811$	−3.26802e8	+	7.15597e8i	−0.612664	+	1.34155i	0.308073	+	0.951363i	$0.400316\pi$
$811$	−3.26802e8	+	7.15597e8i	−0.612664	+	1.34155i	−0.920737	+	0.390184i	$0.872411\pi$
$812$	−5.75575e7	−	4.98739e7i	−0.107506	−	0.0931547i
$813$	−4.59171e7	−	1.31182e8i	−0.0854481	−	0.244120i
$814$	−3.58940e8	+	1.05394e8i	−0.665501	+	0.195409i
$815$	−5.70866e7	+	4.94658e7i	−0.105454	+	0.0913760i
$816$	2.52551e8	+	1.44635e8i	0.464813	+	0.266196i
$817$	−3.81993e8	+	2.45492e8i	−0.700469	+	0.450164i
$818$	−4.61534e8	+	3.99922e8i	−0.843226	+	0.730660i
$819$	−2.39316e8	+	7.07432e8i	−0.435633	+	1.28776i
$820$	−6.57712e6	+	4.57449e7i	−0.0119287	+	0.0829662i
$821$	4.78363e8	+	4.14504e8i	0.864427	+	0.749030i	0.969411	−	0.245444i	$-0.0789337\pi$
$821$	4.78363e8	+	4.14504e8i	0.864427	+	0.749030i	−0.104984	+	0.994474i	$0.533479\pi$
$822$	−1.99969e7	−	3.91006e8i	−0.0360037	−	0.703993i
$823$	−1.02180e9	−	3.00027e8i	−1.83301	−	0.538221i	−0.833123	−	0.553088i	$-0.813449\pi$
$823$	−1.02180e9	−	3.00027e8i	−1.83301	−	0.538221i	−0.999889	+	0.0148676i	$0.995267\pi$
$824$	−1.75404e8	+	8.01045e7i	−0.313515	+	0.143178i
$825$	3.57396e8	−	2.56389e8i	0.636484	−	0.456602i
$826$	−1.12753e8	−	7.24619e7i	−0.200072	−	0.128579i
$827$			5.07299e8i			0.896908i	0.893806	+	0.448454i	$0.148025\pi$
$827$			5.07299e8i			0.896908i	−0.893806	+	0.448454i	$0.851975\pi$
$828$	1.86999e8	−	9.87128e7i	0.329419	−	0.173893i
$829$	6.13473e8			1.07679			0.538396	−	0.842692i	$-0.319030\pi$
$829$	6.13473e8			1.07679			0.538396	+	0.842692i	$0.319030\pi$
$830$	2.37407e8	−	3.69412e8i	0.415202	−	0.646067i
$831$	3.85461e8	+	5.37317e8i	0.671703	+	0.936327i
$832$	4.52280e8	+	9.90355e8i	0.785303	+	1.71957i
$833$	7.80087e7	−	2.65673e8i	0.134961	−	0.459635i
$834$	−131751.	+	6738.01i	−0.000227120	+	1.16154e-5i
$835$	3.92751e8	−	4.53259e8i	0.674618	−	0.778550i
$836$	−1.68675e8	−	2.42519e7i	−0.288691	−	0.0415075i
$837$	−1.36726e7	−	8.84929e7i	−0.0233171	−	0.150915i
$838$	3.75400e8	+	4.33234e8i	0.637914	+	0.736192i
$839$	1.67883e8	+	2.61232e8i	0.284264	+	0.442323i	0.953794	−	0.300462i	$-0.0971408\pi$
$839$	1.67883e8	+	2.61232e8i	0.284264	+	0.442323i	−0.669530	+	0.742785i	$0.733504\pi$
$840$	3.76019e8	−	6.56577e8i	0.634413	−	1.10777i
$841$	−2.88609e8	−	3.33073e8i	−0.485201	−	0.559952i
$842$	−1.45528e8	−	4.95621e8i	−0.243786	−	0.830259i
$843$	5.52492e8	−	1.93386e8i	0.922238	−	0.322806i
$844$	1.59611e8	−	1.84201e8i	0.265482	−	0.306383i
$845$	1.96101e9	+	8.95561e8i	3.25019	+	1.48431i
$846$	9.04619e7	−	7.21699e7i	0.149401	−	0.119191i
$847$	−1.34051e8	−	2.93531e8i	−0.220608	−	0.483063i
$848$	−2.23752e8	+	3.21707e7i	−0.366927	+	0.0527562i
$849$	−6.92180e7	−	6.36528e6i	−0.113109	−	0.0104015i
$850$	−7.72630e8			−1.25810
$851$	7.83045e8	−	6.19231e8i	1.27057	−	1.00476i
$852$	6.55864e7	+	1.26135e8i	0.106046	+	0.203946i
$853$	7.03283e8	+	4.51972e8i	1.13314	+	0.728224i	0.966213	−	0.257746i	$-0.0829798\pi$
$853$	7.03283e8	+	4.51972e8i	1.13314	+	0.728224i	0.166925	+	0.985970i	$0.446616\pi$
$854$	−3.66879e8	+	5.27492e7i	−0.589046	+	0.0846920i
$855$	2.58406e8	−	1.39311e9i	0.413432	−	2.22888i
$856$	−2.96150e8	−	8.69575e7i	−0.472161	−	0.138639i
$857$	4.48314e8	+	2.04738e8i	0.712262	+	0.325279i	0.738385	−	0.674380i	$-0.235589\pi$
$857$	4.48314e8	+	2.04738e8i	0.712262	+	0.325279i	−0.0261228	+	0.999659i	$0.508316\pi$
$858$	1.13867e8	−	4.76638e8i	0.180276	−	0.754617i
$859$	4.92678e7	−	3.42665e8i	0.0777291	−	0.540618i	−0.913333	−	0.407214i	$-0.866500\pi$
$859$	4.92678e7	−	3.42665e8i	0.0777291	−	0.540618i	0.991062	−	0.133404i	$-0.0425907\pi$
$860$	−6.00488e7	−	2.04507e8i	−0.0944080	−	0.321524i
$861$	2.53671e7	−	6.40119e7i	0.0397431	−	0.100289i
$862$	−5.11806e7	+	3.28918e7i	−0.0799068	+	0.0513530i
$863$	−2.38634e8	−	3.71322e8i	−0.371278	−	0.577720i	0.604467	−	0.796630i	$-0.293386\pi$
$863$	−2.38634e8	−	3.71322e8i	−0.371278	−	0.577720i	−0.975745	+	0.218910i	$0.929750\pi$
$864$	−2.48084e8	−	3.77263e8i	−0.384643	−	0.584929i
$865$	−1.78436e9	+	5.23934e8i	−2.75698	+	0.809521i
$866$	−3.11297e8	−	4.47577e7i	−0.479315	−	0.0689150i
$867$	3.04546e7	−	1.27480e8i	0.0467299	−	0.195607i
$868$	1.15941e7	−	2.53876e7i	0.0177288	−	0.0388206i
$869$	−7.75392e7	+	2.64074e8i	−0.118158	+	0.402408i
$870$	−2.55711e8	+	3.27514e8i	−0.388322	+	0.497361i
$871$	1.13718e8	+	7.90924e8i	0.172097	+	1.19696i
$872$	−4.98458e8	+	7.75615e8i	−0.751759	+	1.16976i
$873$	6.26817e8	−	8.93403e8i	0.942102	−	1.34278i
$874$	−7.43979e8	+	1.82621e8i	−1.11436	+	0.273537i
$875$			3.53304e8i			0.527380i
$876$	−4.10758e8	−	3.77733e7i	−0.611046	−	0.0561917i
$877$	−3.09907e7	−	2.15545e8i	−0.0459444	−	0.319550i	−0.999813	−	0.0193266i	$-0.993848\pi$
$877$	−3.09907e7	−	2.15545e8i	−0.0459444	−	0.319550i	0.953869	−	0.300224i	$-0.0970613\pi$
$878$	5.05806e8	−	2.30994e8i	0.747309	−	0.341285i
$879$	8.88082e7	+	4.52262e8i	0.130763	+	0.665923i
$880$	−1.17043e8	+	2.56289e8i	−0.171751	+	0.376082i
$881$	2.45299e8	+	2.12553e8i	0.358731	+	0.310842i	0.815515	−	0.578735i	$-0.196454\pi$
$881$	2.45299e8	+	2.12553e8i	0.358731	+	0.310842i	−0.456785	+	0.889577i	$0.650999\pi$
$882$	1.62736e8	−	1.73080e8i	0.237179	−	0.252256i
$883$	1.54558e8	−	4.53823e7i	0.224496	−	0.0659180i	−0.167550	−	0.985864i	$-0.553586\pi$
$883$	1.54558e8	−	4.53823e7i	0.224496	−	0.0659180i	0.392046	+	0.919946i	$0.371767\pi$
$884$	3.86187e8	−	3.34633e8i	0.559037	−	0.484408i
$885$	2.15727e8	−	3.76686e8i	0.311225	−	0.543438i
$886$	1.23954e8	−	7.96601e7i	0.178221	−	0.114535i
$887$	−5.10282e8	+	4.42162e8i	−0.731206	+	0.633594i	−0.938737	−	0.344635i	$-0.888003\pi$
$887$	−5.10282e8	+	4.42162e8i	−0.731206	+	0.633594i	0.207531	+	0.978228i	$0.433457\pi$
$888$	−8.54118e8	−	8.89523e8i	−1.21977	−	1.27033i
$889$	1.31403e8	−	9.13929e8i	0.187025	−	1.30079i
$890$	9.87773e8	+	8.55910e8i	1.40116	+	1.21411i
$891$	−3.10160e7	+	3.81088e8i	−0.0438482	+	0.538756i
$892$	2.48299e8	+	7.29073e7i	0.349849	+	0.102725i
$893$	2.26384e8	−	1.03386e8i	0.317901	−	0.145181i
$894$	5.12192e8	+	7.13974e8i	0.716836	+	0.999240i
$895$	3.68687e7	+	2.36941e7i	0.0514267	+	0.0330499i
$896$			6.82082e7i			0.0948227i
$897$	1.94139e8	+	1.29325e9i	0.268989	+	1.79187i
$898$	4.21805e8			0.582482
$899$	−3.05321e7	+	4.75089e7i	−0.0420221	+	0.0653877i
$900$	3.51029e8	+	1.77871e8i	0.481521	+	0.243993i
$901$	2.52574e8	+	5.53061e8i	0.345315	+	0.756133i
$902$	−1.27292e7	+	4.33516e7i	−0.0173453	+	0.0590725i
$903$	1.62192e7	+	3.17139e8i	0.0220275	+	0.430712i
$904$	−2.26986e8	+	2.61956e8i	−0.307252	+	0.354587i
$905$	5.38332e8	+	7.74005e7i	0.726281	+	0.104423i
$906$	−6.77196e8	−	7.05267e8i	−0.910604	−	0.948350i
$907$	−6.32747e8	−	7.30229e8i	−0.848024	−	0.978672i	0.151929	−	0.988391i	$-0.451452\pi$
$907$	−6.32747e8	−	7.30229e8i	−0.848024	−	0.978672i	−0.999953	+	0.00971961i	$0.996906\pi$
$908$	2.14355e7	+	3.33543e7i	0.0286336	+	0.0445548i
$909$	−7.09454e8	−	2.88228e7i	−0.944566	−	0.0383747i
$910$	8.31668e8	+	9.59796e8i	1.10364	+	1.27366i
$911$	5.04557e7	+	1.71836e8i	0.0667352	+	0.227279i	0.986107	−	0.166110i	$-0.0531207\pi$
$911$	5.04557e7	+	1.71836e8i	0.0667352	+	0.227279i	−0.919372	+	0.393389i	$0.871302\pi$
$912$	1.77416e8	+	5.06868e8i	0.233889	+	0.668206i
$913$	−1.66887e8	+	1.92598e8i	−0.219286	+	0.253069i
$914$	−8.08545e8	−	3.69250e8i	−1.05893	−	0.483595i
$915$	−2.31306e8	−	1.17795e9i	−0.301943	−	1.53767i
$916$	−3.49908e7	−	7.66191e7i	−0.0455268	−	0.0996898i
$917$	8.70162e8	−	1.25110e8i	1.12848	−	0.162250i
$918$	4.34471e8	−	5.12167e8i	0.561607	−	0.662039i
$919$	1.45754e8			0.187791			0.0938953	−	0.995582i	$-0.470068\pi$
$919$	1.45754e8			0.187791			0.0938953	+	0.995582i	$0.470068\pi$
$920$	5.94603e7	−	1.32359e9i	0.0763596	−	1.69977i
$921$	4.04359e8	−	2.10255e8i	0.517593	−	0.269133i
$922$	−8.95392e8	−	5.75434e8i	−1.14241	−	0.734180i
$923$	−8.70287e8	+	1.25128e8i	−1.10677	+	0.159130i
$924$	−7.33407e7	+	9.39346e7i	−0.0929671	+	0.119072i
$925$	1.78261e9	+	5.23421e8i	2.25232	+	0.661342i
$926$	6.19645e8	+	2.82983e8i	0.780387	+	0.356391i
$927$	6.12515e7	+	2.44989e8i	0.0768914	+	0.307544i
$928$	−4.05273e7	+	2.81873e8i	−0.0507111	+	0.352704i
$929$	2.22236e8	+	7.56867e8i	0.277184	+	0.944001i	0.973961	+	0.226714i	$0.0727982\pi$
$929$	2.22236e8	+	7.56867e8i	0.277184	+	0.944001i	−0.696778	+	0.717287i	$0.745384\pi$
$930$	−1.41561e8	−	5.60989e7i	−0.175993	−	0.0697438i
$931$	4.29813e8	−	2.76224e8i	0.532636	−	0.342305i
$932$	−1.12066e8	−	1.74378e8i	−0.138429	−	0.215400i
$933$	−3.79983e8	+	9.58859e8i	−0.467864	+	1.18062i
$934$	−7.01376e7	+	2.05942e7i	−0.0860815	+	0.0252758i
$935$	7.50098e8	+	1.07848e8i	0.917663	+	0.131940i
$936$	1.56721e9	−	3.91828e8i	1.91117	−	0.477824i
$937$	−6.37449e7	+	1.39582e8i	−0.0774867	+	0.169672i	−0.944411	−	0.328768i	$-0.893366\pi$
$937$	−6.37449e7	+	1.39582e8i	−0.0774867	+	0.169672i	0.866924	+	0.498440i	$0.166094\pi$
$938$	−9.22246e7	+	3.14088e8i	−0.111748	+	0.380577i
$939$	−1.95369e8	−	1.52537e8i	−0.235971	−	0.184238i
$940$	1.66253e7	+	1.15632e8i	0.0200164	+	0.139217i
$941$	−4.41395e8	+	6.86823e8i	−0.529734	+	0.824283i	−0.998248	−	0.0591737i	$-0.981153\pi$
$941$	−4.41395e8	+	6.86823e8i	−0.529734	+	0.824283i	0.468513	+	0.883456i	$0.344790\pi$
$942$	1.10484e8	+	2.12480e8i	0.132174	+	0.254194i
$943$	−1.17859e7	−	1.19994e8i	−0.0140549	−	0.143095i
$944$			1.64526e8i			0.195578i
$945$	−7.55623e8	−	6.40993e8i	−0.895385	−	0.759553i
$946$	−2.96548e7	−	2.06254e8i	−0.0350285	−	0.243628i
$947$	−1.00294e9	+	4.58029e8i	−1.18094	+	0.539315i	−0.906465	−	0.422280i	$-0.861230\pi$
$947$	−1.00294e9	+	4.58029e8i	−1.18094	+	0.539315i	−0.274470	+	0.961596i	$0.588503\pi$
$948$	−2.41621e8	+	4.74457e7i	−0.283602	+	0.0556893i
$949$	1.05975e9	−	2.32053e9i	1.23995	−	2.71511i
$950$	−1.07745e9	−	9.33613e8i	−1.25668	−	1.08892i
$951$	−3.50237e8	+	1.22592e8i	−0.407212	+	0.142534i
$952$	7.40082e8	−	2.17308e8i	0.857766	−	0.251863i
$953$	−1.06644e9	+	9.24078e8i	−1.23214	+	1.06765i	−0.236764	+	0.971567i	$0.576087\pi$
$953$	−1.06644e9	+	9.24078e8i	−1.23214	+	1.06765i	−0.995373	+	0.0960858i	$0.969368\pi$
$954$	−2.11762e7	+	5.21237e8i	−0.0243895	+	0.600330i
$955$	2.28276e8	−	1.46704e8i	0.262090	−	0.168435i
$956$	−1.11566e8	+	9.66727e7i	−0.127691	+	0.110645i
$957$	1.73941e8	−	1.67018e8i	0.198457	−	0.190558i
$958$	7.21107e7	−	5.01541e8i	0.0820169	−	0.570440i
$959$	−4.45019e8	−	3.85611e8i	−0.504571	−	0.437213i
$960$	−1.44266e9	+	7.37808e7i	−1.63061	+	0.0833931i
$961$	8.31696e8	+	2.44208e8i	0.937119	+	0.275163i
$962$	1.88285e9	−	8.59871e8i	2.11491	−	0.965846i
$963$	−1.82702e8	+	3.60564e8i	−0.204581	+	0.403742i
$964$	1.73148e8	+	1.11275e8i	0.193280	+	0.124213i
$965$		−	5.01580e8i		−	0.558159i
$966$	−1.47743e8	+	5.14966e8i	−0.163899	+	0.571277i
$967$	−4.46098e8			−0.493345			−0.246673	−	0.969099i	$-0.579337\pi$
$967$	−4.46098e8			−0.493345			−0.246673	+	0.969099i	$0.579337\pi$
$968$	−3.77378e8	+	5.87211e8i	−0.416054	+	0.647393i
$969$	1.17364e9	−	8.41944e8i	1.28992	−	0.925363i
$970$	−7.70972e8	−	1.68819e9i	−0.844740	−	1.84972i
$971$	3.50702e8	−	1.19438e9i	0.383072	−	1.30462i	−0.512109	−	0.858921i	$-0.671136\pi$
$971$	3.50702e8	−	1.19438e9i	0.383072	−	1.30462i	0.895181	−	0.445703i	$-0.147046\pi$
$972$	−3.15302e8	+	1.32671e8i	−0.343342	+	0.144470i
$973$	−129933.	+	149950.i	−0.000141052	+	0.000162783i
$974$	−5.94276e8	−	8.54440e7i	−0.643149	−	0.0924708i
$975$	−1.75550e9	+	1.68563e9i	−1.89403	+	1.81864i
$976$	2.97954e8	+	3.43858e8i	0.320479	+	0.369853i
$977$	−5.03774e8	−	7.83887e8i	−0.540197	−	0.840562i	0.458648	−	0.888618i	$-0.348334\pi$
$977$	−5.03774e8	−	7.83887e8i	−0.540197	−	0.840562i	−0.998845	+	0.0480557i	$0.984697\pi$
$978$	−5.73327e7	−	3.28342e7i	−0.0612895	−	0.0351002i
$979$	−4.96726e8	−	5.73252e8i	−0.529382	−	0.610939i
$980$	6.75661e7	+	2.30109e8i	0.0717878	+	0.244487i
$981$	8.79657e8	+	8.27081e8i	0.931765	+	0.876074i
$982$	−9.37776e8	+	1.08225e9i	−0.990295	+	1.14286i
$983$	−5.51832e8	−	2.52013e8i	−0.580960	−	0.265316i	0.103184	−	0.994662i	$-0.467097\pi$
$983$	−5.51832e8	−	2.52013e8i	−0.580960	−	0.265316i	−0.684144	+	0.729347i	$0.739824\pi$
$984$	−1.46150e8	+	2.86987e7i	−0.153396	+	0.0301215i
$985$	6.82235e8	+	1.49389e9i	0.713880	+	1.56318i
$986$	−4.19277e8	+	6.02829e7i	−0.437391	+	0.0628874i
$987$	1.59382e7	−	1.73317e8i	0.0165763	−	0.180256i
$988$	9.42901e8			0.977676
$989$	2.79336e8	+	4.80813e8i	0.288760	+	0.497036i
$990$	5.32263e8	+	3.73439e8i	0.548556	+	0.384870i
$991$	−5.34802e8	−	3.43696e8i	−0.549506	−	0.353146i	0.236241	−	0.971695i	$-0.424085\pi$
$991$	−5.34802e8	−	3.43696e8i	−0.549506	−	0.353146i	−0.785746	+	0.618549i	$0.787721\pi$
$992$	−1.03296e8	+	1.48518e7i	−0.105816	+	0.0152140i
$993$	−5.68730e8	−	4.44043e8i	−0.580842	−	0.453500i
$994$	−3.45605e8	−	1.01479e8i	−0.351901	−	0.103327i
$995$	−1.03550e9	−	4.72895e8i	−1.05118	−	0.480060i
$996$	−2.21761e8	−	5.29781e7i	−0.224444	−	0.0536190i
$997$	−2.14879e8	+	1.49451e9i	−0.216824	+	1.50805i	0.532833	+	0.846220i	$0.321127\pi$
$997$	−2.14879e8	+	1.49451e9i	−0.216824	+	1.50805i	−0.749658	+	0.661826i	$0.769782\pi$
$998$	−2.02435e8	−	6.89429e8i	−0.203654	−	0.693582i
$999$	−1.34938e9	+	8.87337e8i	−1.35344	+	0.890005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.h.a.2.15	✓	460
3.2	odd	2	inner	69.7.h.a.2.32	yes	460
23.12	even	11	inner	69.7.h.a.35.32	yes	460
69.35	odd	22	inner	69.7.h.a.35.15	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.h.a.2.15	✓	460	1.1	even	1	trivial
69.7.h.a.2.32	yes	460	3.2	odd	2	inner
69.7.h.a.35.15	yes	460	69.35	odd	22	inner
69.7.h.a.35.32	yes	460	23.12	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.42615 + 5.33119i) q^{2} +(-15.7384 - 21.9386i) q^{3} +(9.90347 + 21.6856i) q^{4} +(55.1132 - 187.698i) q^{5} +(170.881 - 8.73922i) q^{6} +(168.523 - 194.486i) q^{7} +(-550.993 - 79.2208i) q^{8} +(-233.608 + 690.557i) q^{9} +O(q^{10})\)	\(q+(-3.42615 + 5.33119i) q^{2} +(-15.7384 - 21.9386i) q^{3} +(9.90347 + 21.6856i) q^{4} +(55.1132 - 187.698i) q^{5} +(170.881 - 8.73922i) q^{6} +(168.523 - 194.486i) q^{7} +(-550.993 - 79.2208i) q^{8} +(-233.608 + 690.557i) q^{9} +(811.829 + 936.900i) q^{10} +(-388.967 - 605.245i) q^{11} +(319.888 - 558.564i) q^{12} +(2606.90 + 3008.52i) q^{13} +(459.456 + 1564.76i) q^{14} +(-4985.24 + 1744.96i) q^{15} +(1310.97 - 1512.93i) q^{16} +(-4897.84 - 2236.77i) q^{17} +(-2881.11 - 3611.35i) q^{18} +(-4127.31 - 9037.55i) q^{19} +(4616.16 - 663.703i) q^{20} +(-6919.03 - 636.274i) q^{21} +4559.33 q^{22} +(-11283.2 + 4552.57i) q^{23} +(6933.73 + 13334.8i) q^{24} +(-19048.6 - 12241.8i) q^{25} +(-24970.6 + 3590.23i) q^{26} +(18826.5 - 5743.20i) q^{27} +(5886.50 + 1728.43i) q^{28} +(-11292.1 - 5156.92i) q^{29} +(7777.46 - 32555.7i) q^{30} +(647.426 - 4502.95i) q^{31} +(-6462.87 - 22010.5i) q^{32} +(-7156.54 + 18059.0i) q^{33} +(28705.3 - 18447.8i) q^{34} +(-27216.8 - 42350.2i) q^{35} +(-17288.7 + 1772.99i) q^{36} +(-78726.4 + 23116.2i) q^{37} +(62321.7 + 8960.50i) q^{38} +(24974.5 - 104541. i) q^{39} +(-45236.6 + 99054.3i) q^{40} +(-2791.89 + 9508.32i) q^{41} +(27097.7 - 34706.7i) q^{42} +(-6504.19 - 45237.7i) q^{43} +(9272.96 - 14429.0i) q^{44} +(116741. + 81906.5i) q^{45} +(14387.2 - 75750.5i) q^{46} +25049.3i q^{47} +(-53824.2 - 4949.67i) q^{48} +(7318.43 + 50900.8i) q^{49} +(130526. - 59609.5i) q^{50} +(28012.3 + 142655. i) q^{51} +(-39424.2 + 86327.0i) q^{52} +(-85338.8 - 73946.5i) q^{53} +(-33884.2 + 120045. i) q^{54} +(-135041. + 39651.5i) q^{55} +(-108262. + 93809.8i) q^{56} +(-133314. + 232784. i) q^{57} +(66180.9 - 42531.9i) q^{58} +(-62111.4 + 53819.8i) q^{59} +(-87211.5 - 90826.6i) q^{60} +(-32345.1 + 224965. i) q^{61} +(21787.9 + 18879.3i) q^{62} +(94935.3 + 161808. i) q^{63} +(262417. + 77052.5i) q^{64} +(708369. - 323501. i) q^{65} +(-71756.5 - 100026. i) q^{66} +(168861. + 108520. i) q^{67} -128364. i q^{68} +(277456. + 175887. i) q^{69} +319026. q^{70} +(-119410. + 185805. i) q^{71} +(183423. - 361985. i) q^{72} +(-266212. - 582923. i) q^{73} +(146492. - 498905. i) q^{74} +(31225.6 + 610566. i) q^{75} +(155110. - 179006. i) q^{76} +(-183262. - 26349.0i) q^{77} +(471762. + 491317. i) q^{78} +(-250512. - 289107. i) q^{79} +(-211724. - 329449. i) q^{80} +(-422296. - 322638. i) q^{81} +(-41125.2 - 47461.0i) q^{82} +(-99794.4 - 339869. i) q^{83} +(-54724.5 - 156345. i) q^{84} +(-689772. + 796040. i) q^{85} +(263455. + 120316. i) q^{86} +(64583.1 + 328895. i) q^{87} +(166370. + 364300. i) q^{88} +(1.04357e6 - 150042. i) q^{89} +(-836632. + 341747. i) q^{90} +1.02444e6 q^{91} +(-210468. - 199596. i) q^{92} +(-108978. + 56665.4i) q^{93} +(-133543. - 85822.6i) q^{94} +(-1.92380e6 + 276601. i) q^{95} +(-381166. + 488196. i) q^{96} +(-1.43642e6 - 421772. i) q^{97} +(-296436. - 135378. i) q^{98} +(508822. - 127214. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

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