LMFDB - Embedded newform 69.7.h.a.2.11

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			2.11
Character	$\chi$	$=$	69.2
Dual form			69.7.h.a.35.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.28963 + 8.23082i) q^{2} +(16.8611 - 21.0880i) q^{3} +(-13.1797 - 28.8596i) q^{4} +(16.1556 - 55.0211i) q^{5} +(84.3823 + 250.328i) q^{6} +(-182.035 + 210.080i) q^{7} +(-312.548 - 44.9377i) q^{8} +(-160.405 - 711.134i) q^{9} +O(q^{10})$	\(q+(-5.28963 + 8.23082i) q^{2} +(16.8611 - 21.0880i) q^{3} +(-13.1797 - 28.8596i) q^{4} +(16.1556 - 55.0211i) q^{5} +(84.3823 + 250.328i) q^{6} +(-182.035 + 210.080i) q^{7} +(-312.548 - 44.9377i) q^{8} +(-160.405 - 711.134i) q^{9} +(367.412 + 424.016i) q^{10} +(150.224 + 233.754i) q^{11} +(-830.815 - 208.671i) q^{12} +(2176.86 + 2512.22i) q^{13} +(-766.232 - 2609.55i) q^{14} +(-887.881 - 1268.41i) q^{15} +(3352.84 - 3869.38i) q^{16} +(7527.50 + 3437.69i) q^{17} +(6701.70 + 2441.37i) q^{18} +(2357.99 + 5163.29i) q^{19} +(-1800.81 + 258.918i) q^{20} +(1360.84 + 7380.94i) q^{21} -2718.62 q^{22} +(-10710.8 - 5771.81i) q^{23} +(-6217.56 + 5833.31i) q^{24} +(10378.3 + 6669.71i) q^{25} +(-32192.4 + 4628.57i) q^{26} +(-17701.0 - 8607.89i) q^{27} +(8462.00 + 2484.67i) q^{28} +(13635.9 + 6227.29i) q^{29} +(15136.6 - 598.588i) q^{30} +(-5352.17 + 37225.1i) q^{31} +(8419.45 + 28674.0i) q^{32} +(7462.34 + 773.422i) q^{33} +(-68112.8 + 43773.4i) q^{34} +(8617.94 + 13409.8i) q^{35} +(-18408.9 + 14001.8i) q^{36} +(13189.5 - 3872.80i) q^{37} +(-54971.0 - 7903.64i) q^{38} +(89682.0 - 3546.54i) q^{39} +(-7521.94 + 16470.8i) q^{40} +(-16537.5 + 56321.7i) q^{41} +(-67949.6 - 27841.6i) q^{42} +(16941.4 + 117830. i) q^{43} +(4766.12 - 7416.22i) q^{44} +(-41718.8 - 2663.15i) q^{45} +(104163. - 57628.4i) q^{46} -201598. i q^{47} +(-25064.8 - 135947. i) q^{48} +(5746.45 + 39967.4i) q^{49} +(-109794. + 50141.4i) q^{50} +(199416. - 100776. i) q^{51} +(43811.4 - 95933.6i) q^{52} +(16027.5 + 13887.9i) q^{53} +(164482. - 100161. i) q^{54} +(15288.4 - 4489.07i) q^{55} +(66335.4 - 57479.9i) q^{56} +(148642. + 37333.5i) q^{57} +(-123384. + 79294.4i) q^{58} +(167488. - 145129. i) q^{59} +(-24903.7 + 42341.1i) q^{60} +(6179.89 - 42982.0i) q^{61} +(-278083. - 240960. i) q^{62} +(178594. + 95753.6i) q^{63} +(33855.4 + 9940.85i) q^{64} +(173394. - 79186.3i) q^{65} +(-45838.9 + 57330.1i) q^{66} +(-434122. - 278994. i) q^{67} -262548. i q^{68} +(-302312. + 128551. i) q^{69} -155959. q^{70} +(-71415.1 + 111124. i) q^{71} +(18177.7 + 229472. i) q^{72} +(-16139.2 - 35339.8i) q^{73} +(-37891.4 + 129046. i) q^{74} +(315640. - 106398. i) q^{75} +(117933. - 136101. i) q^{76} +(-76453.2 - 10992.3i) q^{77} +(-445193. + 756916. i) q^{78} +(172335. + 198885. i) q^{79} +(-158730. - 246989. i) q^{80} +(-479981. + 228139. i) q^{81} +(-376097. - 434039. i) q^{82} +(187082. + 637143. i) q^{83} +(195075. - 136552. i) q^{84} +(310757. - 358633. i) q^{85} +(-1.05945e6 - 483837. i) q^{86} +(361237. - 182554. i) q^{87} +(-36448.0 - 79810.1i) q^{88} +(144983. - 20845.5i) q^{89} +(242597. - 329293. i) q^{90} -924033. q^{91} +(-25405.9 + 385181. i) q^{92} +(694759. + 740524. i) q^{93} +(1.65932e6 + 1.06638e6i) q^{94} +(322185. - 46323.1i) q^{95} +(746638. + 305927. i) q^{96} +(-464503. - 136390. i) q^{97} +(-359362. - 164115. i) q^{98} +(142133. - 144325. 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 $

$2$	−5.28963	+	8.23082i	−0.661204	+	1.02885i	0.335035	+	0.942206i	$0.391252\pi$
$2$	−5.28963	+	8.23082i	−0.661204	+	1.02885i	−0.996239	+	0.0866475i	$0.972385\pi$
$3$	16.8611	−	21.0880i	0.624486	−	0.781036i
$3$	16.8611	−	21.0880i	0.624486	−	0.781036i
$4$	−13.1797	−	28.8596i	−0.205933	−	0.450931i
$5$	16.1556	−	55.0211i	0.129245	−	0.440169i	−0.869288	−	0.494305i	$-0.835422\pi$
$5$	16.1556	−	55.0211i	0.129245	−	0.440169i	0.998534	+	0.0541366i	$0.0172407\pi$
$6$	84.3823	+	250.328i	0.390659	+	1.15893i
$7$	−182.035	+	210.080i	−0.530716	+	0.612478i	−0.956281	−	0.292449i	$-0.905530\pi$
$7$	−182.035	+	210.080i	−0.530716	+	0.612478i	0.425565	+	0.904928i	$0.360075\pi$
$8$	−312.548	−	44.9377i	−0.610446	−	0.0877689i
$9$	−160.405	−	711.134i	−0.220035	−	0.975492i
$10$	367.412	+	424.016i	0.367412	+	0.424016i
$11$	150.224	+	233.754i	0.112866	+	0.175623i	0.893091	−	0.449876i	$-0.148532\pi$
$11$	150.224	+	233.754i	0.112866	+	0.175623i	−0.780225	+	0.625499i	$0.784896\pi$
$12$	−830.815	−	208.671i	−0.480796	−	0.120759i
$13$	2176.86	+	2512.22i	0.990831	+	1.14348i	0.989653	+	0.143480i	$0.0458294\pi$
$13$	2176.86	+	2512.22i	0.990831	+	1.14348i	0.00117764	+	0.999999i	$0.499625\pi$
$14$	−766.232	−	2609.55i	−0.279239	−	0.951001i
$15$	−887.881	−	1268.41i	−0.263076	−	0.375824i
$16$	3352.84	−	3869.38i	0.818564	−	0.944673i
$17$	7527.50	+	3437.69i	1.53216	+	0.699714i	0.990066	−	0.140604i	$-0.0449044\pi$
$17$	7527.50	+	3437.69i	1.53216	+	0.699714i	0.542094	+	0.840318i	$0.317632\pi$
$18$	6701.70	+	2441.37i	1.14913	+	0.418616i
$19$	2357.99	+	5163.29i	0.343781	+	0.752775i	0.999998	−	0.00179657i	$-0.000571865\pi$
$19$	2357.99	+	5163.29i	0.343781	+	0.752775i	−0.656217	+	0.754572i	$0.727845\pi$
$20$	−1800.81	+	258.918i	−0.225102	+	0.0323647i
$21$	1360.84	+	7380.94i	0.146943	+	0.796992i
$22$	−2718.62			−0.255317
$23$	−10710.8	−	5771.81i	−0.880319	−	0.474382i
$23$	−10710.8	−	5771.81i	−0.880319	−	0.474382i
$24$	−6217.56	+	5833.31i	−0.449766	+	0.421970i
$25$	10378.3	+	6669.71i	0.664209	+	0.426861i
$26$	−32192.4	+	4628.57i	−1.83161	+	0.263346i
$27$	−17701.0	−	8607.89i	−0.899303	−	0.437326i
$28$	8462.00	+	2484.67i	0.385478	+	0.113186i
$29$	13635.9	+	6227.29i	0.559099	+	0.255332i	0.674861	−	0.737945i	$-0.264204\pi$
$29$	13635.9	+	6227.29i	0.559099	+	0.255332i	−0.115762	+	0.993277i	$0.536931\pi$
$30$	15136.6	−	598.588i	0.560615	−	0.0221699i
$31$	−5352.17	+	37225.1i	−0.179657	+	1.24954i	0.677900	+	0.735154i	$0.262890\pi$
$31$	−5352.17	+	37225.1i	−0.179657	+	1.24954i	−0.857557	+	0.514389i	$0.828019\pi$
$32$	8419.45	+	28674.0i	0.256941	+	0.875062i
$33$	7462.34	+	773.422i	0.207651	+	0.0215216i
$34$	−68112.8	+	43773.4i	−1.73297	+	1.11371i
$35$	8617.94	+	13409.8i	0.201001	+	0.312764i
$36$	−18408.9	+	14001.8i	−0.394567	+	0.300107i
$37$	13189.5	−	3872.80i	0.260390	−	0.0764574i	−0.148932	−	0.988847i	$-0.547584\pi$
$37$	13189.5	−	3872.80i	0.260390	−	0.0764574i	0.409322	+	0.912390i	$0.365765\pi$
$38$	−54971.0	−	7903.64i	−1.00180	−	0.144038i
$39$	89682.0	−	3546.54i	1.51186	−	0.0597876i
$40$	−7521.94	+	16470.8i	−0.117530	+	0.257356i
$41$	−16537.5	+	56321.7i	−0.239949	+	0.817192i	0.748171	+	0.663506i	$0.230932\pi$
$41$	−16537.5	+	56321.7i	−0.239949	+	0.817192i	−0.988120	+	0.153686i	$0.950886\pi$
$42$	−67949.6	−	27841.6i	−0.917147	−	0.375791i
$43$	16941.4	+	117830.i	0.213081	+	1.48201i	0.762785	+	0.646652i	$0.223831\pi$
$43$	16941.4	+	117830.i	0.213081	+	1.48201i	−0.549704	+	0.835359i	$0.685260\pi$
$44$	4766.12	−	7416.22i	0.0559509	−	0.0870612i
$45$	−41718.8	−	2663.15i	−0.457820	−	0.0292253i
$46$	104163.	−	57628.4i	1.07014	−	0.592056i
$47$		−	201598.i		−	1.94175i	−0.239587	−	0.970875i	$-0.577012\pi$
$47$		−	201598.i		−	1.94175i	0.239587	−	0.970875i	$-0.422988\pi$
$48$	−25064.8	−	135947.i	−0.226642	−	1.22926i
$49$	5746.45	+	39967.4i	0.0488440	+	0.339718i
$50$	−109794.	+	50141.4i	−0.878355	+	0.401131i
$51$	199416.	−	100776.i	1.50331	−	0.759711i
$52$	43811.4	−	95933.6i	0.311585	−	0.682277i
$53$	16027.5	+	13887.9i	0.107656	+	0.0932842i	0.707025	−	0.707188i	$-0.250037\pi$
$53$	16027.5	+	13887.9i	0.107656	+	0.0932842i	−0.599370	+	0.800472i	$0.704582\pi$
$54$	164482.	−	100161.i	1.04457	−	0.636089i
$55$	15288.4	−	4489.07i	0.0918910	−	0.0269816i
$56$	66335.4	−	57479.9i	0.377730	−	0.327305i
$57$	148642.	+	37333.5i	0.802631	+	0.201592i
$58$	−123384.	+	79294.4i	−0.632378	+	0.406404i
$59$	167488.	−	145129.i	0.815506	−	0.706640i	−0.143616	−	0.989634i	$-0.545873\pi$
$59$	167488.	−	145129.i	0.815506	−	0.706640i	0.959122	+	0.282994i	$0.0913275\pi$
$60$	−24903.7	+	42341.1i	−0.115295	+	0.196024i
$61$	6179.89	−	42982.0i	0.0272264	−	0.189364i	−0.971669	−	0.236344i	$-0.924051\pi$
$61$	6179.89	−	42982.0i	0.0272264	−	0.189364i	0.998896	+	0.0469802i	$0.0149598\pi$
$62$	−278083.	−	240960.i	−1.16681	−	1.01104i
$63$	178594.	+	95753.6i	0.714244	+	0.382942i
$64$	33855.4	+	9940.85i	0.129148	+	0.0379213i
$65$	173394.	−	79186.3i	0.631384	−	0.288343i
$66$	−45838.9	+	57330.1i	−0.159442	+	0.199412i
$67$	−434122.	−	278994.i	−1.44340	−	0.927619i	−0.999502	−	0.0315438i	$-0.989958\pi$
$67$	−434122.	−	278994.i	−1.44340	−	0.927619i	−0.443902	−	0.896076i	$-0.646406\pi$
$68$		−	262548.i		−	0.834993i
$69$	−302312.	+	128551.i	−0.920256	+	0.391316i
$70$	−155959.			−0.454691
$71$	−71415.1	+	111124.i	−0.199533	+	0.310479i	−0.926572	−	0.376116i	$-0.877259\pi$
$71$	−71415.1	+	111124.i	−0.199533	+	0.310479i	0.727039	+	0.686596i	$0.240896\pi$
$72$	18177.7	+	229472.i	0.0487014	+	0.614797i
$73$	−16139.2	−	35339.8i	−0.0414870	−	0.0908439i	0.887754	−	0.460319i	$-0.152265\pi$
$73$	−16139.2	−	35339.8i	−0.0414870	−	0.0908439i	−0.929241	+	0.369475i	$0.879538\pi$
$74$	−37891.4	+	129046.i	−0.0935074	+	0.318457i
$75$	315640.	−	106398.i	0.748184	−	0.252203i
$76$	117933.	−	136101.i	0.268654	−	0.310043i
$77$	−76453.2	−	10992.3i	−0.167465	−	0.0240778i
$78$	−445193.	+	756916.i	−0.938134	+	1.59501i
$79$	172335.	+	198885.i	0.349537	+	0.403387i	0.903107	−	0.429416i	$-0.141280\pi$
$79$	172335.	+	198885.i	0.349537	+	0.403387i	−0.553570	+	0.832802i	$0.686735\pi$
$80$	−158730.	−	246989.i	−0.310020	−	0.482401i
$81$	−479981.	+	228139.i	−0.903170	+	0.429284i
$82$	−376097.	−	434039.i	−0.682115	−	0.787203i
$83$	187082.	+	637143.i	0.327188	+	1.11430i	0.944754	+	0.327781i	$0.106301\pi$
$83$	187082.	+	637143.i	0.327188	+	1.11430i	−0.617565	+	0.786520i	$0.711881\pi$
$84$	195075.	−	136552.i	0.329128	−	0.230389i
$85$	310757.	−	358633.i	0.506017	−	0.583974i
$86$	−1.05945e6	−	483837.i	−1.66566	−	0.760682i
$87$	361237.	−	182554.i	0.548573	−	0.277225i
$88$	−36448.0	−	79810.1i	−0.0534843	−	0.117114i
$89$	144983.	−	20845.5i	0.205659	−	0.0295693i	−0.0387152	−	0.999250i	$-0.512327\pi$
$89$	144983.	−	20845.5i	0.205659	−	0.0295693i	0.244374	+	0.969681i	$0.421417\pi$
$90$	242597.	−	329293.i	0.332780	−	0.451705i
$91$	−924033.			−1.22621
$92$	−25405.9	+	385181.i	−0.0326265	+	0.494654i
$93$	694759.	+	740524.i	0.863745	+	0.920641i
$94$	1.65932e6	+	1.06638e6i	1.99778	+	1.28389i
$95$	322185.	−	46323.1i	0.375780	−	0.0540290i
$96$	746638.	+	305927.i	0.843911	+	0.345783i
$97$	−464503.	−	136390.i	−0.508948	−	0.149441i	0.0171694	−	0.999853i	$-0.494535\pi$
$97$	−464503.	−	136390.i	−0.508948	−	0.149441i	−0.526117	+	0.850412i	$0.676353\pi$
$98$	−359362.	−	164115.i	−0.381815	−	0.174369i
$99$	142133.	−	144325.i	0.146484	−	0.148743i
$100$	55702.2	−	387418.i	0.0557022	−	0.387418i
$101$	−164234.	−	559330.i	−0.159404	−	0.542880i	−0.999999	−	0.00121640i	$-0.999613\pi$
$101$	−164234.	−	559330.i	−0.159404	−	0.542880i	0.840595	−	0.541664i	$-0.182205\pi$
$102$	−225365.	+	2.17443e6i	−0.212366	+	2.04901i
$103$	1.50190e6	−	965211.i	1.37445	−	0.883305i	0.375398	−	0.926864i	$-0.377506\pi$
$103$	1.50190e6	−	965211.i	1.37445	−	0.883305i	0.999051	+	0.0435586i	$0.0138695\pi$
$104$	−567479.	−	883015.i	−0.504487	−	0.784997i
$105$	428093.	+	44368.9i	0.369803	+	0.0383276i
$106$	−199088.	+	58457.5i	−0.167158	+	0.0490820i
$107$	−657900.	−	94591.7i	−0.537042	−	0.0772150i	−0.131543	−	0.991310i	$-0.541993\pi$
$107$	−657900.	−	94591.7i	−0.537042	−	0.0772150i	−0.405499	+	0.914095i	$0.632902\pi$
$108$	−15125.9	+	624293.i	−0.0120074	+	0.495584i
$109$	484901.	−	1.06178e6i	0.374432	−	0.819893i	−0.624803	−	0.780783i	$-0.714821\pi$
$109$	484901.	−	1.06178e6i	0.374432	−	0.819893i	0.999235	−	0.0391098i	$-0.0124522\pi$
$110$	−43921.0	+	149581.i	−0.0329985	+	0.112383i
$111$	140721.	−	343440.i	0.102894	−	0.251121i
$112$	202545.	+	1.40873e6i	0.144167	+	1.00271i
$113$	−397304.	+	618217.i	−0.275352	+	0.428455i	−0.951195	−	0.308590i	$-0.900143\pi$
$113$	−397304.	+	618217.i	−0.275352	+	0.428455i	0.675844	+	0.737045i	$0.263779\pi$
$114$	−1.09354e6	+	1.02596e6i	−0.738111	+	0.692496i
$115$	−490612.	+	496075.i	−0.322585	+	0.326177i
$116$		−	475599.i		−	0.304696i
$117$	1.43735e6	−	1.95101e6i	0.897438	−	1.21815i
$118$	308583.	+	2.14624e6i	0.187813	+	1.30627i
$119$	−2.09246e6	+	955596.i	−1.24170	+	0.567066i
$120$	220506.	+	436338.i	0.127608	+	0.252510i
$121$	703860.	−	1.54124e6i	0.397310	−	0.869988i
$122$	321088.	+	278225.i	0.176826	+	0.153220i
$123$	908869.	+	1.29839e6i	0.488412	+	0.697734i
$124$	1.14484e6	−	336156.i	0.600455	−	0.176310i
$125$	1.21179e6	−	1.05002e6i	0.620438	−	0.537613i
$126$	−1.73283e6	+	963479.i	−0.866252	+	0.481649i
$127$	−47504.4	+	30529.2i	−0.0231912	+	0.0149041i	−0.552185	−	0.833722i	$-0.686206\pi$
$127$	−47504.4	+	30529.2i	−0.0231912	+	0.0149041i	0.528994	+	0.848626i	$0.322569\pi$
$128$	−1.70636e6	+	1.47857e6i	−0.813656	+	0.705037i
$129$	2.77045e6	+	1.62949e6i	1.29057	+	0.759071i
$130$	−265421.	+	1.84604e6i	−0.120810	+	0.840255i
$131$	−1.73996e6	−	1.50768e6i	−0.773972	−	0.670650i	0.175508	−	0.984478i	$-0.443843\pi$
$131$	−1.73996e6	−	1.50768e6i	−0.773972	−	0.670650i	−0.949480	+	0.313828i	$0.898389\pi$
$132$	−76031.1	−	225554.i	−0.0330574	−	0.0980682i
$133$	−1.51394e6	−	444533.i	−0.643509	−	0.188951i
$134$	4.59269e6	−	2.09741e6i	1.90877	−	0.871705i
$135$	−759586.	+	834861.i	−0.308728	+	0.339323i
$136$	−2.19823e6	−	1.41271e6i	−0.873888	−	0.561614i
$137$			2.37092e6i			0.922050i	0.887387	+	0.461025i	$0.152518\pi$
$137$			2.37092e6i			0.922050i	−0.887387	+	0.461025i	$0.847482\pi$
$138$	541041.	−	3.16827e6i	0.205870	−	1.20555i
$139$	−3.50055e6			−1.30344			−0.651722	−	0.758458i	$-0.725953\pi$
$139$	−3.50055e6			−1.30344			−0.651722	+	0.758458i	$0.725953\pi$
$140$	273418.	−	425447.i	0.0996422	−	0.155046i
$141$	−4.25130e6	−	3.39917e6i	−1.51658	−	1.21260i
$142$	−536883.	−	1.17561e6i	−0.187506	−	0.410580i
$143$	−260225.	+	886246.i	−0.0889900	+	0.303072i
$144$	−3.28946e6	−	1.76365e6i	−1.10163	−	0.590642i
$145$	562929.	−	649654.i	0.184650	−	0.213097i
$146$	376246.	+	54096.0i	0.120896	+	0.0173823i
$147$	939724.	+	552715.i	0.295834	+	0.174000i
$148$	−285602.	−	329602.i	−0.0881000	−	0.101673i
$149$	1.58364e6	+	2.46420e6i	0.478739	+	0.744933i	0.993675	−	0.112296i	$-0.0358206\pi$
$149$	1.58364e6	+	2.46420e6i	0.478739	+	0.744933i	−0.514936	+	0.857229i	$0.672184\pi$
$150$	−793876.	+	3.16078e6i	−0.235222	+	0.936528i
$151$	4.16848e6	+	4.81069e6i	1.21073	+	1.39726i	0.893594	+	0.448877i	$0.148176\pi$
$151$	4.16848e6	+	4.81069e6i	1.21073	+	1.39726i	0.317136	+	0.948380i	$0.397279\pi$
$152$	−504961.	−	1.71974e6i	−0.143789	−	0.489702i
$153$	1.23721e6	−	5.90448e6i	0.345437	−	1.64857i
$154$	494885.	−	571127.i	0.135501	−	0.156376i
$155$	1.96170e6	+	895878.i	0.526790	+	0.240577i
$156$	−1.28434e6	−	2.54144e6i	−0.338302	−	0.669432i
$157$	−1.50903e6	−	3.30432e6i	−0.389941	−	0.853853i	−0.998192	−	0.0601074i	$-0.980856\pi$
$157$	−1.50903e6	−	3.30432e6i	−0.389941	−	0.853853i	0.608251	−	0.793745i	$-0.291872\pi$
$158$	−2.54858e6	+	366430.i	−0.646141	+	0.0929010i
$159$	563108.	−	103822.i	0.140088	−	0.0258283i
$160$	1.71370e6			0.418383
$161$	3.16229e6	−	1.19946e6i	0.757748	−	0.287415i
$162$	661150.	−	5.15741e6i	0.155509	−	1.21307i
$163$	−171873.	−	110456.i	−0.0396868	−	0.0255052i	0.520647	−	0.853772i	$-0.325691\pi$
$163$	−171873.	−	110456.i	−0.0396868	−	0.0255052i	−0.560334	+	0.828267i	$0.689327\pi$
$164$	1.84338e6	−	265038.i	0.417911	−	0.0600865i
$165$	163114.	−	398091.i	0.0363110	−	0.0886198i
$166$	−6.23380e6	−	1.83041e6i	−1.36279	−	0.400151i
$167$	3.97070e6	+	1.81336e6i	0.852545	+	0.389344i	0.793250	−	0.608896i	$-0.208387\pi$
$167$	3.97070e6	+	1.81336e6i	0.852545	+	0.389344i	0.0592950	+	0.998241i	$0.481115\pi$
$168$	−93646.6	−	2.36806e6i	−0.0197499	−	0.499418i
$169$	−885649.	+	6.15982e6i	−0.183485	+	1.27617i
$170$	1.30806e6	+	4.45483e6i	0.266244	+	0.906743i
$171$	3.29355e6	−	2.50507e6i	0.658683	−	0.500992i
$172$	3.17725e6	−	2.04189e6i	0.624404	−	0.401280i
$173$	−974683.	−	1.51664e6i	−0.188246	−	0.292916i	0.734284	−	0.678843i	$-0.237518\pi$
$173$	−974683.	−	1.51664e6i	−0.188246	−	0.292916i	−0.922529	+	0.385927i	$0.873882\pi$
$174$	−408242.	+	3.93892e6i	−0.0774944	+	0.747703i
$175$	−3.29039e6	+	966145.i	−0.613950	+	0.180272i
$176$	1.40816e6	+	202463.i	0.258294	+	0.0371371i
$177$	−236445.	−	5.97902e6i	−0.0426393	−	1.07823i
$178$	−595333.	+	1.30360e6i	−0.105560	+	0.231144i
$179$	1.58292e6	−	5.39095e6i	0.275995	−	0.939953i	−0.698513	−	0.715598i	$-0.746154\pi$
$179$	1.58292e6	−	5.39095e6i	0.275995	−	0.939953i	0.974508	−	0.224355i	$-0.0720274\pi$
$180$	472985.	+	1.23909e6i	0.0811017	+	0.212463i
$181$	388830.	+	2.70437e6i	0.0655728	+	0.456069i	0.995983	+	0.0895478i	$0.0285422\pi$
$181$	388830.	+	2.70437e6i	0.0655728	+	0.456069i	−0.930410	+	0.366521i	$0.880549\pi$
$182$	4.88779e6	−	7.60556e6i	0.810772	−	1.26159i
$183$	−802205.	−	855047.i	−0.130898	−	0.139520i
$184$	3.08829e6	+	2.28529e6i	0.495751	+	0.366849i
$185$		−	788270.i		−	0.124497i
$186$	−9.77014e6	+	1.80134e6i	−1.51832	+	0.279935i
$187$	327240.	+	2.27601e6i	0.0500429	+	0.348056i
$188$	−5.81804e6	+	2.65701e6i	−0.875595	+	0.399871i
$189$	5.03055e6	−	2.15168e6i	0.745127	−	0.318708i
$190$	−1.32296e6	+	2.89688e6i	−0.192879	+	0.422347i
$191$	2.79146e6	+	2.41881e6i	0.400618	+	0.347138i	0.831749	−	0.555152i	$-0.187340\pi$
$191$	2.79146e6	+	2.41881e6i	0.400618	+	0.347138i	−0.431131	+	0.902289i	$0.641885\pi$
$192$	780473.	−	546329.i	0.110269	−	0.0771881i
$193$	−4.76901e6	+	1.40031e6i	−0.663371	+	0.194783i	−0.596049	−	0.802948i	$-0.703264\pi$
$193$	−4.76901e6	+	1.40031e6i	−0.663371	+	0.194783i	−0.0673220	+	0.997731i	$0.521445\pi$
$194$	3.57965e6	−	3.10179e6i	0.490271	−	0.424822i
$195$	1.25374e6	−	4.99170e6i	0.169084	−	0.673200i
$196$	1.07771e6	−	692600.i	0.143131	−	0.0919845i
$197$	−777009.	+	673282.i	−0.101631	+	0.0880640i	−0.704194	−	0.710007i	$-0.748692\pi$
$197$	−777009.	+	673282.i	−0.101631	+	0.0880640i	0.602563	+	0.798071i	$0.294146\pi$
$198$	436081.	+	1.93330e6i	0.0561786	+	0.249060i
$199$	856576.	−	5.95762e6i	0.108694	−	0.755985i	−0.860458	−	0.509522i	$-0.829822\pi$
$199$	856576.	−	5.95762e6i	0.108694	−	0.755985i	0.969152	−	0.246463i	$-0.0792685\pi$
$200$	−2.94399e6	−	2.55098e6i	−0.367999	−	0.318873i
$201$	−1.32032e7	+	4.45062e6i	−1.62589	+	0.548065i
$202$	5.47248e6	+	1.60687e6i	0.663942	+	0.194951i
$203$	−3.79044e6	+	1.73104e6i	−0.453108	+	0.206927i
$204$	−5.53661e6	−	4.42686e6i	−0.652159	−	0.521441i
$205$	2.83171e6	+	1.81983e6i	0.328690	+	0.211236i
$206$			1.74675e7i			1.99815i
$207$	−2.38645e6	+	8.54267e6i	−0.269055	+	0.963125i
$208$	1.70194e7			1.89127
$209$	−852709.	+	1.32684e6i	−0.0934033	+	0.145338i
$210$	−2.62965e6	+	3.28886e6i	−0.283948	+	0.355130i
$211$	−1.54685e6	−	3.38712e6i	−0.164664	−	0.360565i	0.809256	−	0.587457i	$-0.199871\pi$
$211$	−1.54685e6	−	3.38712e6i	−0.164664	−	0.360565i	−0.973920	+	0.226892i	$0.927144\pi$
$212$	189561.	−	645584.i	0.0198948	−	0.0677556i
$213$	1.13924e6	+	3.37967e6i	0.117890	+	0.349732i
$214$	4.25861e6	−	4.91470e6i	0.434537	−	0.501483i
$215$	6.75685e6	+	971488.i	0.679875	+	0.0977512i
$216$	5.14559e6	+	3.48582e6i	0.510592	+	0.345895i
$217$	−6.84598e6	−	7.90068e6i	−0.669971	−	0.773188i
$218$	6.17442e6	+	9.60758e6i	0.595973	+	0.927352i
$219$	−1.01737e6	−	255527.i	−0.0968604	−	0.0243279i
$220$	−331049.	−	382051.i	−0.0310903	−	0.0358801i
$221$	7.75002e6	+	2.63941e7i	0.718002	+	2.44529i
$222$	2.08244e6	+	2.97492e6i	0.190332	+	0.271905i
$223$	−8.06246e6	+	9.30457e6i	−0.727031	+	0.839038i	−0.992134	−	0.125182i	$-0.960049\pi$
$223$	−8.06246e6	+	9.30457e6i	−0.727031	+	0.839038i	0.265103	+	0.964220i	$0.414594\pi$
$224$	−7.55648e6	−	3.45093e6i	−0.672319	−	0.307038i
$225$	3.07833e6	−	8.45020e6i	0.270251	−	0.741855i
$226$	−2.98685e6	−	6.54028e6i	−0.258754	−	0.566593i
$227$	−1.96540e7	+	2.82581e6i	−1.68024	+	0.241583i	−0.915375	−	0.402603i	$-0.868106\pi$
$227$	−1.96540e7	+	2.82581e6i	−1.68024	+	0.241583i	−0.764869	+	0.644186i	$0.777196\pi$
$228$	−881628.	−	4.78178e6i	−0.0743842	−	0.403446i
$229$	2.03365e7			1.69344			0.846719	−	0.532040i	$-0.178575\pi$
$229$	2.03365e7			1.69344			0.846719	+	0.532040i	$0.178575\pi$
$230$	−1.48795e6	−	6.66219e6i	−0.122294	−	0.547562i
$231$	−1.52089e6	+	1.42690e6i	−0.123385	+	0.115760i
$232$	−3.98203e6	−	2.55909e6i	−0.318890	−	0.204938i
$233$	−7.99491e6	+	1.14949e6i	−0.632042	+	0.0908739i	−0.450887	−	0.892581i	$-0.648892\pi$
$233$	−7.99491e6	+	1.14949e6i	−0.632042	+	0.0908739i	−0.181154	+	0.983455i	$0.557983\pi$
$234$	8.45537e6	+	2.21507e7i	0.659911	+	1.72878i
$235$	−1.10922e7	−	3.25695e6i	−0.854698	−	0.250962i
$236$	−6.39581e6	−	2.92087e6i	−0.486586	−	0.222216i
$237$	7.09985e6	−	280769.i	0.533340	−	0.0210913i
$238$	3.20301e6	−	2.22774e7i	0.237590	−	1.65247i
$239$	−1.28766e6	−	4.38536e6i	−0.0943205	−	0.321226i	0.898794	−	0.438370i	$-0.144444\pi$
$239$	−1.28766e6	−	4.38536e6i	−0.0943205	−	0.321226i	−0.993115	+	0.117144i	$0.962626\pi$
$240$	−7.88487e6	−	817214.i	−0.570376	−	0.0591156i
$241$	−1.06128e7	+	6.82044e6i	−0.758193	+	0.487261i	−0.861731	−	0.507365i	$-0.830620\pi$
$241$	−1.06128e7	+	6.82044e6i	−0.758193	+	0.487261i	0.103539	+	0.994625i	$0.466983\pi$
$242$	8.96250e6	+	1.39459e7i	0.632387	+	0.984014i
$243$	−3.28203e6	+	1.39685e7i	−0.228730	+	0.973490i
$244$	−1.32189e6	+	388143.i	−0.0909970	+	0.0267191i
$245$	2.29189e6	+	329524.i	0.155846	+	0.0224073i
$246$	−1.54944e7	+	612738.i	−1.04081	+	0.0411594i
$247$	−7.83832e6	+	1.71635e7i	−0.520154	+	1.13898i
$248$	3.34562e6	−	1.13941e7i	0.219342	−	0.747010i
$249$	1.65905e7	+	6.79776e6i	1.07463	+	0.440319i
$250$	2.23263e6	+	1.55283e7i	0.142888	+	0.993811i
$251$	1.09683e7	−	1.70670e7i	0.693614	−	1.07928i	−0.298556	−	0.954392i	$-0.596505\pi$
$251$	1.09683e7	−	1.70670e7i	0.693614	−	1.07928i	0.992170	−	0.124893i	$-0.0398586\pi$
$252$	409582.	−	6.41617e6i	0.0255940	−	0.400935i
$253$	−259849.	−	3.37077e6i	−0.0160457	−	0.208145i
$254$		−	552489.i		−	0.0337150i
$255$	−2.32313e6	−	1.26002e7i	−0.140105	−	0.759901i
$256$	−2.82245e6	−	1.96306e7i	−0.168231	−	1.17007i
$257$	−1.05001e7	+	4.79522e6i	−0.618575	+	0.282494i	−0.699952	−	0.714190i	$-0.746795\pi$
$257$	−1.05001e7	+	4.79522e6i	−0.618575	+	0.282494i	0.0813773	+	0.996683i	$0.474068\pi$
$258$	−2.80667e7	+	1.41837e7i	−1.63430	+	0.825907i
$259$	−1.58737e6	+	3.47585e6i	−0.0913645	+	0.200060i
$260$	−4.57057e6	−	3.96042e6i	−0.260046	−	0.225331i
$261$	2.24117e6	−	1.06958e7i	0.126053	−	0.601579i
$262$	2.16132e7	−	6.34621e6i	1.20175	−	0.352867i
$263$	−1.73886e6	+	1.50673e6i	−0.0955869	+	0.0828266i	−0.701343	−	0.712824i	$-0.747416\pi$
$263$	−1.73886e6	+	1.50673e6i	−0.0955869	+	0.0828266i	0.605756	+	0.795650i	$0.292871\pi$
$264$	−2.29759e6	−	577072.i	−0.124871	−	0.0313630i
$265$	1.02306e6	−	657481.i	0.0549748	−	0.0353301i
$266$	1.16671e7	−	1.01096e7i	0.619893	−	0.537141i
$267$	2.00499e6	−	3.40888e6i	0.105337	−	0.179093i
$268$	−2.33002e6	+	1.62057e7i	−0.121047	+	0.841903i
$269$	1.29959e6	+	1.12610e6i	0.0667651	+	0.0578523i	0.687604	−	0.726086i	$-0.258662\pi$
$269$	1.29959e6	+	1.12610e6i	0.0667651	+	0.0578523i	−0.620839	+	0.783938i	$0.713208\pi$
$270$	−2.85367e6	−	1.06681e7i	−0.144981	−	0.541997i
$271$	−2.43604e7	−	7.15287e6i	−1.22399	−	0.359395i	−0.395010	−	0.918677i	$-0.629259\pi$
$271$	−2.43604e7	−	7.15287e6i	−1.22399	−	0.359395i	−0.828978	+	0.559282i	$0.811077\pi$
$272$	3.85402e7	−	1.76007e7i	1.91517	−	0.874630i
$273$	−1.55802e7	+	1.94860e7i	−0.765748	+	0.957711i
$274$	−1.95146e7	−	1.25413e7i	−0.948654	−	0.609663i
$275$			3.42791e6i			0.164828i
$276$	7.69432e6	+	7.03035e6i	0.365968	+	0.334387i
$277$	4.05979e7			1.91014			0.955068	−	0.296386i	$-0.0957814\pi$
$277$	4.05979e7			1.91014			0.955068	+	0.296386i	$0.0957814\pi$
$278$	1.85166e7	−	2.88124e7i	0.861841	−	1.34105i
$279$	2.73306e7	−	2.16500e6i	1.25845	−	0.0996886i
$280$	−2.09092e6	−	4.57847e6i	−0.0952495	−	0.208567i
$281$	−111643.	+	380222.i	−0.00503169	+	0.0171364i	−0.961971	−	0.273153i	$-0.911933\pi$
$281$	−111643.	+	380222.i	−0.00503169	+	0.0171364i	0.956939	+	0.290289i	$0.0937516\pi$
$282$	5.04658e7	−	1.70113e7i	2.25035	−	0.758562i
$283$	1.69228e7	−	1.95300e7i	0.746644	−	0.861673i	−0.247595	−	0.968864i	$-0.579640\pi$
$283$	1.69228e7	−	1.95300e7i	0.746644	−	0.861673i	0.994238	+	0.107191i	$0.0341855\pi$
$284$	4.14822e6	+	596424.i	0.181095	+	0.0260376i
$285$	4.45553e6	−	7.57528e6i	0.192471	−	0.327238i
$286$	−5.91804e6	−	6.82978e6i	−0.252976	−	0.291950i
$287$	−8.82165e6	−	1.37268e7i	−0.373168	−	0.580660i
$288$	1.90405e7	−	1.05868e7i	0.797080	−	0.443188i
$289$	2.90388e7	+	3.35126e7i	1.20305	+	1.38840i
$290$	2.36951e6	+	8.06980e6i	0.0971547	+	0.330879i
$291$	−1.07082e7	+	7.49573e6i	−0.434549	+	0.304183i
$292$	−807183.	+	931539.i	−0.0324208	+	0.0374156i
$293$	−3.17453e7	−	1.44976e7i	−1.26205	−	0.576359i	−0.331823	−	0.943342i	$-0.607664\pi$
$293$	−3.17453e7	−	1.44976e7i	−1.26205	−	0.576359i	−0.930228	+	0.366982i	$0.880391\pi$
$294$	−9.52009e6	+	4.81105e6i	−0.374627	+	0.189320i
$295$	−5.27928e6	−	1.15600e7i	−0.205641	−	0.450290i
$296$	−4.29640e6	+	617729.i	−0.165665	+	0.0238190i
$297$	−646993.	−	5.43079e6i	−0.0246962	−	0.207297i
$298$	−2.86593e7			−1.08297
$299$	−8.81588e6	−	3.94724e7i	−0.329801	−	1.47666i
$300$	−7.23065e6	−	7.70694e6i	−0.267802	−	0.285442i
$301$	−2.78377e7	−	1.78902e7i	−1.02079	−	0.656019i
$302$	−6.16457e7	+	8.86331e6i	−2.23811	+	0.321792i
$303$	−1.45643e7	−	5.96756e6i	−0.523554	−	0.214521i
$304$	2.78847e7	+	8.18768e6i	0.992533	+	0.291434i
$305$	−2.26508e6	−	1.03443e6i	−0.0798333	−	0.0364586i
$306$	4.20544e7	+	4.14158e7i	1.46773	+	1.44545i
$307$	675943.	−	4.70129e6i	0.0233612	−	0.162481i	−0.974801	−	0.223075i	$-0.928391\pi$
$307$	675943.	−	4.70129e6i	0.0233612	−	0.162481i	0.998162	+	0.0605943i	$0.0192996\pi$
$308$	690399.	+	2.35128e6i	0.0236291	+	0.0804735i
$309$	4.96933e6	−	4.79465e7i	0.168431	−	1.62511i
$310$	−1.77505e7	+	1.14075e7i	−0.595834	+	0.382919i
$311$	−1.02737e7	−	1.59862e7i	−0.341543	−	0.531451i	0.627413	−	0.778687i	$-0.284114\pi$
$311$	−1.02737e7	−	1.59862e7i	−0.341543	−	0.531451i	−0.968955	+	0.247236i	$0.920478\pi$
$312$	−2.81893e7	−	2.92163e6i	−0.928156	−	0.0961971i
$313$	−2.67256e7	+	7.84736e6i	−0.871556	+	0.255912i	−0.686777	−	0.726868i	$-0.740975\pi$
$313$	−2.67256e7	+	7.84736e6i	−0.871556	+	0.255912i	−0.184779	+	0.982780i	$0.559157\pi$
$314$	3.51795e7	+	5.05805e6i	1.13632	+	0.163378i
$315$	8.15378e6	−	8.27950e6i	0.260872	−	0.264894i
$316$	3.46842e6	−	7.59478e6i	0.109918	−	0.240688i
$317$	−1.35288e7	+	4.60750e7i	−0.424700	+	1.44640i	0.418214	+	0.908349i	$0.362656\pi$
$317$	−1.35288e7	+	4.60750e7i	−0.424700	+	1.44640i	−0.842914	+	0.538048i	$0.819162\pi$
$318$	−2.12410e6	+	5.18402e6i	−0.0660530	+	0.161208i
$319$	592787.	+	4.12293e6i	0.0182611	+	0.127009i
$320$	1.09391e6	−	1.70216e6i	0.0333836	−	0.0519459i
$321$	−1.30877e7	+	1.22789e7i	−0.395683	+	0.371230i
$322$	−6.85481e6	+	3.23730e7i	−0.205318	+	0.969651i
$323$			4.69727e7i			1.39392i
$324$	1.29100e7	+	1.08452e7i	0.379570	+	0.318863i
$325$	5.83618e6	+	4.05915e7i	0.170012	+	1.18246i
$326$	1.81829e6	−	830387.i	0.0524821	−	0.0239678i
$327$	−1.42149e7	−	2.81285e7i	−0.406538	−	0.804457i
$328$	7.69975e6	−	1.68601e7i	0.218200	−	0.477792i
$329$	4.23518e7	+	3.66980e7i	1.18928	+	1.03052i
$330$	2.41381e6	+	3.44831e6i	0.0671678	+	0.0959544i
$331$	−1.46594e7	+	4.30437e6i	−0.404232	+	0.118693i	−0.477527	−	0.878617i	$-0.658467\pi$
$331$	−1.46594e7	+	4.30437e6i	−0.404232	+	0.118693i	0.0732950	+	0.997310i	$0.476649\pi$
$332$	1.59220e7	−	1.37965e7i	0.435094	−	0.377011i
$333$	−4.86975e6	−	8.75831e6i	−0.131878	−	0.237185i
$334$	−3.59289e7	+	2.30901e7i	−0.964284	+	0.619708i
$335$	−2.23641e7	+	1.93786e7i	−0.594862	+	0.515451i
$336$	3.31224e7	+	1.94815e7i	0.873180	+	0.513576i
$337$	4.38001e6	−	3.04636e7i	0.114442	−	0.795961i	−0.849067	−	0.528285i	$-0.822835\pi$
$337$	4.38001e6	−	3.04636e7i	0.114442	−	0.795961i	0.963509	−	0.267676i	$-0.0862556\pi$
$338$	−4.60157e7	−	3.98728e7i	−1.19167	−	1.03259i
$339$	6.33796e6	+	1.88022e7i	0.162686	+	0.482624i
$340$	−1.44457e7	−	4.24164e6i	−0.367538	−	0.107919i
$341$	−9.50554e6	+	4.34103e6i	−0.239725	+	0.109479i
$342$	3.19710e6	+	4.03595e7i	0.0799240	+	1.00895i
$343$	−3.69544e7	−	2.37492e7i	−0.915765	−	0.588526i
$344$		−	3.75890e7i		−	0.923390i
$345$	2.18895e6	+	1.87104e7i	0.0533064	+	0.455644i
$346$	1.76389e7			0.425836
$347$	−1.97087e7	+	3.06673e7i	−0.471704	+	0.733985i	−0.992835	−	0.119491i	$-0.961874\pi$
$347$	−1.97087e7	+	3.06673e7i	−0.471704	+	0.733985i	0.521132	+	0.853476i	$0.325510\pi$
$348$	−1.00294e7	−	8.01914e6i	−0.237979	−	0.190279i
$349$	2.02179e7	+	4.42711e7i	0.475620	+	1.04146i	0.983645	+	0.180120i	$0.0576487\pi$
$349$	2.02179e7	+	4.42711e7i	0.475620	+	1.04146i	−0.508024	+	0.861343i	$0.669624\pi$
$350$	9.45276e6	−	3.21931e7i	0.220473	−	0.750860i
$351$	−1.69075e7	−	6.32070e7i	−0.390984	−	1.46165i
$352$	−5.43785e6	+	6.27562e6i	−0.124681	+	0.143889i
$353$	−3.56779e7	−	5.12971e6i	−0.811102	−	0.116619i	−0.275730	−	0.961235i	$-0.588920\pi$
$353$	−3.56779e7	−	5.12971e6i	−0.811102	−	0.116619i	−0.535372	+	0.844616i	$0.679829\pi$
$354$	5.04629e7	+	2.96806e7i	1.13753	+	0.669058i
$355$	4.96041e6	+	5.72461e6i	0.110875	+	0.127956i
$356$	−2.51243e6	−	3.90942e6i	−0.0556858	−	0.0866488i
$357$	−1.51297e7	+	6.02382e7i	−0.332526	+	1.32394i
$358$	3.59988e7	+	4.15449e7i	0.784584	+	0.905458i
$359$	−3.39692e6	−	1.15688e7i	−0.0734178	−	0.250038i	0.914604	−	0.404350i	$-0.132502\pi$
$359$	−3.39692e6	−	1.15688e7i	−0.0734178	−	0.250038i	−0.988022	+	0.154312i	$0.950684\pi$
$360$	1.29195e7	+	2.70711e6i	0.276909	+	0.0580228i
$361$	9.70911e6	−	1.12049e7i	0.206375	−	0.238170i
$362$	−2.43160e7	−	1.11047e7i	−0.512585	−	0.234090i
$363$	−2.06337e7	−	4.08300e7i	−0.431378	−	0.853609i
$364$	1.21785e7	+	2.66672e7i	0.252517	+	0.552934i
$365$	−2.20517e6	+	317056.i	−0.0453486	+	0.00652015i
$366$	1.12811e7	−	2.07992e6i	0.230096	−	0.0424233i
$367$	9.05473e7			1.83180			0.915899	−	0.401409i	$-0.131479\pi$
$367$	9.05473e7			1.83180			0.915899	+	0.401409i	$0.131479\pi$
$368$	−5.82450e7	+	2.20924e7i	−1.16873	+	0.443302i
$369$	4.27050e7	+	2.72611e6i	0.849962	+	0.0542580i
$370$	6.48811e6	+	4.16966e6i	0.128089	+	0.0823181i
$371$	−5.83513e6	+	838965.i	−0.114269	+	0.0164294i
$372$	1.22145e7	−	2.98104e7i	0.237272	−	0.579080i
$373$	7.36578e7	+	2.16279e7i	1.41936	+	0.416761i	0.899286	−	0.437361i	$-0.144087\pi$
$373$	7.36578e7	+	2.16279e7i	1.41936	+	0.416761i	0.520072	+	0.854122i	$0.325905\pi$
$374$	−2.04644e7	−	9.34578e6i	−0.391187	−	0.178649i
$375$	−1.71070e6	−	4.32589e7i	−0.0324400	−	0.820316i
$376$	−9.05936e6	+	6.30092e7i	−0.170425	+	1.18533i
$377$	1.40390e7	+	4.78123e7i	0.262006	+	0.892309i
$378$	−8.89963e6	+	5.27872e7i	−0.164777	+	0.977357i
$379$	6.88871e7	−	4.42711e7i	1.26538	−	0.813209i	0.276367	−	0.961052i	$-0.410869\pi$
$379$	6.88871e7	−	4.42711e7i	1.26538	−	0.813209i	0.989011	+	0.147843i	$0.0472330\pi$
$380$	−5.58317e6	−	8.68758e6i	−0.101749	−	0.158325i
$381$	−157178.	+	1.51653e6i	−0.00284195	+	0.0274205i
$382$	−3.46746e7	+	1.01814e7i	−0.622044	+	0.182649i
$383$	2.26426e7	+	3.25551e6i	0.403022	+	0.0579459i	0.340846	−	0.940119i	$-0.389287\pi$
$383$	2.26426e7	+	3.25551e6i	0.403022	+	0.0579459i	0.0621768	+	0.998065i	$0.480196\pi$
$384$	2.40889e6	+	6.09140e7i	0.0425425	+	1.07578i
$385$	−1.83996e6	+	4.02895e6i	−0.0322423	+	0.0706008i
$386$	1.37006e7	−	4.66600e7i	0.238220	−	0.811303i
$387$	8.10756e7	−	3.09482e7i	1.39881	−	0.533953i
$388$	2.18585e6	+	1.52029e7i	0.0374219	+	0.260275i
$389$	4.62084e7	−	7.19016e7i	0.785004	−	1.22149i	−0.186029	−	0.982544i	$-0.559562\pi$
$389$	4.62084e7	−	7.19016e7i	0.785004	−	1.22149i	0.971033	−	0.238946i	$-0.0768018\pi$
$390$	3.44540e7	+	3.67235e7i	0.580825	+	0.619085i
$391$	−6.07842e7	−	8.02679e7i	−1.01686	−	1.34280i
$392$		−	1.27500e7i		−	0.211666i
$393$	−6.11316e7	+	1.12710e7i	−1.00714	+	0.185688i
$394$	−1.43158e6	−	9.95683e6i	−0.0234059	−	0.162792i
$395$	1.37271e7	−	6.26895e6i	0.222734	−	0.101719i
$396$	−6.03844e6	−	2.19975e6i	−0.0972387	−	0.0354231i
$397$	2.17881e7	−	4.77092e7i	0.348215	−	0.762484i	−0.651777	−	0.758411i	$-0.725976\pi$
$397$	2.17881e7	−	4.77092e7i	0.348215	−	0.762484i	0.999992	−	0.00407306i	$-0.00129650\pi$
$398$	4.45051e7	+	3.85639e7i	0.705929	+	0.611691i
$399$	−3.49011e7	+	2.44306e7i	−0.549440	+	0.384606i
$400$	6.06043e7	−	1.77950e7i	0.946942	−	0.278047i
$401$	4.67842e7	−	4.05387e7i	0.725548	−	0.628691i	−0.211708	−	0.977333i	$-0.567903\pi$
$401$	4.67842e7	−	4.05387e7i	0.725548	−	0.628691i	0.937256	+	0.348642i	$0.113357\pi$
$402$	3.32078e7	−	1.32215e8i	0.511166	−	2.03518i
$403$	−1.05169e8	+	6.75879e7i	−1.60684	+	1.03265i
$404$	−1.39775e7	+	1.21115e7i	−0.211975	+	0.183677i
$405$	4.79806e6	+	3.00948e7i	0.0722271	+	0.453030i
$406$	5.80217e6	−	4.03550e7i	0.0866987	−	0.603003i
$407$	2.88667e6	+	2.50131e6i	0.0428168	+	0.0371010i
$408$	−6.68558e7	+	2.25362e7i	−0.984371	+	0.331818i
$409$	−6.74595e7	−	1.98079e7i	−0.985992	−	0.289513i	−0.251296	−	0.967910i	$-0.580857\pi$
$409$	−6.74595e7	−	1.98079e7i	−0.985992	−	0.289513i	−0.734696	+	0.678397i	$0.762675\pi$
$410$	−2.99574e7	+	1.36811e7i	−0.434662	+	0.198504i
$411$	4.99978e7	+	3.99763e7i	0.720154	+	0.575807i
$412$	−4.76502e7	−	3.06229e7i	−0.681354	−	0.437880i
$413$			6.16045e7i			0.874505i
$414$	−5.76898e7	−	6.48300e7i	−0.813014	−	0.913640i
$415$	3.80787e7			0.532768
$416$	−5.37077e7	+	8.35708e7i	−0.746030	+	1.16085i
$417$	−5.90232e7	+	7.38195e7i	−0.813982	+	1.01804i
$418$	−6.41048e6	−	1.40370e7i	−0.0877732	−	0.192196i
$419$	1.61977e7	−	5.51644e7i	0.220198	−	0.749924i	−0.773094	−	0.634291i	$-0.781292\pi$
$419$	1.61977e7	−	5.51644e7i	0.220198	−	0.749924i	0.993292	−	0.115633i	$-0.0368896\pi$
$420$	−4.36168e6	−	1.29394e7i	−0.0588716	−	0.174648i
$421$	5.97056e7	−	6.89039e7i	0.800145	−	0.923416i	−0.198244	−	0.980153i	$-0.563524\pi$
$421$	5.97056e7	−	6.89039e7i	0.800145	−	0.923416i	0.998389	+	0.0567362i	$0.0180694\pi$
$422$	3.60610e7	+	5.18479e6i	0.479845	+	0.0689913i
$423$	−1.43363e8	+	3.23374e7i	−1.89416	+	0.427252i
$424$	−4.38527e6	−	5.06087e6i	−0.0575305	−	0.0663938i
$425$	5.51940e7	+	8.58836e7i	0.718994	+	1.11878i
$426$	−3.38437e7	−	8.50032e6i	−0.437773	−	0.109953i
$427$	7.90472e6	+	9.12253e6i	0.101532	+	0.117174i
$428$	5.94107e6	+	2.02334e7i	0.0757762	+	0.258070i
$429$	1.43014e7	+	2.04307e7i	0.181137	+	0.258769i
$430$	−4.37374e7	+	5.04756e7i	−0.550107	+	0.634858i
$431$	−3.86923e7	−	1.76702e7i	−0.483273	−	0.220704i	0.158853	−	0.987302i	$-0.449220\pi$
$431$	−3.86923e7	−	1.76702e7i	−0.483273	−	0.220704i	−0.642127	+	0.766599i	$0.721948\pi$
$432$	−9.26557e7	+	3.96310e7i	−1.14927	+	0.491568i
$433$	−1.31917e7	−	2.88859e7i	−0.162494	−	0.355813i	0.810818	−	0.585299i	$-0.199023\pi$
$433$	−1.31917e7	−	2.88859e7i	−0.162494	−	0.355813i	−0.973312	+	0.229486i	$0.926296\pi$
$434$	1.01242e8	−	1.45564e7i	1.23848	−	0.178067i
$435$	−4.20829e6	−	2.28249e7i	−0.0511255	−	0.277295i
$436$	−3.70335e7			−0.446823
$437$	4.54538e6	−	6.89130e7i	0.0544661	−	0.825766i
$438$	7.48471e6	−	7.02215e6i	0.0890743	−	0.0835695i
$439$	1.64471e7	+	1.05699e7i	0.194400	+	0.124933i	0.634220	−	0.773153i	$-0.281321\pi$
$439$	1.64471e7	+	1.05699e7i	0.194400	+	0.124933i	−0.439820	+	0.898086i	$0.644958\pi$
$440$	−4.98008e6	+	716027.i	−0.0584626	+	0.00840566i
$441$	2.75004e7	−	1.04975e7i	0.320645	−	0.122397i
$442$	−2.58240e8	−	7.58262e7i	−2.99059	−	0.878117i
$443$	9.19791e7	+	4.20055e7i	1.05798	+	0.483164i	0.866937	−	0.498417i	$-0.166085\pi$
$443$	9.19791e7	+	4.20055e7i	1.05798	+	0.483164i	0.191044	+	0.981581i	$0.438813\pi$
$444$	−1.17662e7	+	465304.i	−0.134427	+	0.00531603i
$445$	1.19536e6	−	8.31391e6i	0.0135650	−	0.0943464i
$446$	−3.39369e7	−	1.15578e8i	−0.382532	−	1.30278i
$447$	7.86670e7	+	8.15330e6i	0.880785	+	0.0912874i
$448$	−8.25126e6	+	5.30277e6i	−0.0917670	+	0.0589751i
$449$	1.08571e7	+	1.68940e7i	0.119943	+	0.186635i	0.896033	−	0.443987i	$-0.146436\pi$
$449$	1.08571e7	+	1.68940e7i	0.119943	+	0.186635i	−0.776090	+	0.630622i	$0.782800\pi$
$450$	5.32689e7	+	7.00356e7i	0.584569	+	0.768566i
$451$	−1.56498e7	+	4.59518e6i	−0.170600	+	0.0500925i
$452$	2.30778e7	+	3.31809e6i	0.249908	+	0.0359313i
$453$	1.71733e8	−	6.79131e6i	1.84739	−	0.0730565i
$454$	8.07034e7	−	1.76716e8i	0.862431	−	1.88846i
$455$	−1.49284e7	+	5.08413e7i	−0.158481	+	0.539738i
$456$	−4.47800e7	−	1.83481e7i	−0.472269	−	0.193507i
$457$	7.10592e6	+	4.94228e7i	0.0744512	+	0.517819i	0.992585	+	0.121550i	$0.0387864\pi$
$457$	7.10592e6	+	4.94228e7i	0.0744512	+	0.517819i	−0.918134	+	0.396270i	$0.870305\pi$
$458$	−1.07572e8	+	1.67386e8i	−1.11971	+	1.74230i
$459$	−1.03653e8	−	1.25646e8i	−1.07187	−	1.29931i
$460$	2.07826e7	+	7.62071e6i	0.213514	+	0.0782928i
$461$			1.00746e8i			1.02832i	0.857696	+	0.514158i	$0.171895\pi$
$461$			1.00746e8i			1.02832i	−0.857696	+	0.514158i	$0.828105\pi$
$462$	−3.69961e6	−	2.00660e7i	−0.0375172	−	0.203486i
$463$	−2.02785e7	−	1.41040e8i	−0.204311	−	1.42102i	−0.791303	−	0.611424i	$-0.790597\pi$
$463$	−2.02785e7	−	1.41040e8i	−0.204311	−	1.42102i	0.586992	−	0.809593i	$-0.300312\pi$
$464$	6.98146e7	−	3.18833e7i	0.698864	−	0.319160i
$465$	5.19687e7	−	2.62628e7i	0.516872	−	0.261205i
$466$	3.28288e7	−	7.18851e7i	0.324412	−	0.710364i
$467$	3.57840e7	+	3.10070e7i	0.351348	+	0.304445i	0.812597	−	0.582826i	$-0.198053\pi$
$467$	3.57840e7	+	3.10070e7i	0.351348	+	0.304445i	−0.461249	+	0.887271i	$0.652598\pi$
$468$	−7.52492e7	−	1.57675e7i	−0.734115	−	0.153825i
$469$	1.37637e8	−	4.04138e7i	1.33418	−	0.391752i
$470$	8.54808e7	−	7.40695e7i	0.823332	−	0.713421i
$471$	−9.51253e7	−	2.38921e7i	−0.910402	−	0.228661i
$472$	−5.88698e7	+	3.78333e7i	−0.559843	+	0.359789i
$473$	−2.49983e7	+	2.16611e7i	−0.236225	+	0.204690i
$474$	−3.52446e7	+	5.99228e7i	−0.330947	+	0.562674i
$475$	−9.96572e6	+	6.93131e7i	−0.0929882	+	0.646747i
$476$	5.51562e7	+	4.77931e7i	0.511415	+	0.443144i
$477$	7.30524e6	−	1.36254e7i	0.0673100	−	0.125543i
$478$	4.29063e7	+	1.25984e7i	0.392860	+	0.115354i
$479$	7.97688e7	−	3.64292e7i	0.725816	−	0.331469i	−0.0180142	−	0.999838i	$-0.505734\pi$
$479$	7.97688e7	−	3.64292e7i	0.725816	−	0.331469i	0.743830	+	0.668369i	$0.233007\pi$
$480$	2.88949e7	−	3.61384e7i	0.261274	−	0.326772i
$481$	3.84410e7	+	2.47046e7i	0.345430	+	0.221994i
$482$		−	1.23430e8i		−	1.10225i
$483$	2.80256e7	−	8.69107e7i	0.248722	−	0.771315i
$484$	−5.37562e7			−0.474124
$485$	−1.50087e7	+	2.33540e7i	−0.131558	+	0.204708i
$486$	−9.76117e7	−	1.00902e8i	−0.850341	−	0.879005i
$487$	−3.78562e7	−	8.28936e7i	−0.327756	−	0.717685i	0.671982	−	0.740567i	$-0.265443\pi$
$487$	−3.78562e7	−	8.28936e7i	−0.327756	−	0.717685i	−0.999738	+	0.0228821i	$0.992716\pi$
$488$	−3.86303e6	+	1.31563e7i	−0.0332406	+	0.113207i
$489$	−5.22728e6	+	1.76205e6i	−0.0447043	+	0.0150692i
$490$	−1.48355e7	+	1.71211e7i	−0.126100	+	0.145527i
$491$	−2.39086e7	−	3.43754e6i	−0.201981	−	0.0290405i	0.0405816	−	0.999176i	$-0.487079\pi$
$491$	−2.39086e7	−	3.43754e6i	−0.201981	−	0.0290405i	−0.242563	+	0.970136i	$0.577988\pi$
$492$	2.54924e7	−	4.33420e7i	0.214050	−	0.363927i
$493$	8.12365e7	+	9.37519e7i	0.677970	+	0.782419i
$494$	−9.98082e7	−	1.55305e8i	−0.827914	−	1.28826i
$495$	−5.64466e6	−	1.01520e7i	−0.0465396	−	0.0837020i
$496$	1.26093e8	+	1.45519e8i	1.03335	+	1.19255i
$497$	−1.03449e7	−	3.52314e7i	−0.0842667	−	0.286986i
$498$	−1.43709e8	+	1.00596e8i	−1.16358	+	0.814499i
$499$	3.03575e6	−	3.50344e6i	0.0244323	−	0.0281964i	−0.743402	−	0.668845i	$-0.766789\pi$
$499$	3.03575e6	−	3.50344e6i	0.0244323	−	0.0281964i	0.767834	+	0.640649i	$0.221334\pi$
$500$	−4.62744e7	−	2.11328e7i	−0.370195	−	0.169062i
$501$	1.05190e8	−	5.31587e7i	0.836494	−	0.422728i
$502$	8.24573e7	+	1.80556e8i	0.651805	+	1.42725i
$503$	1.24533e8	−	1.79051e7i	0.978541	−	0.140693i	0.365558	−	0.930789i	$-0.380878\pi$
$503$	1.24533e8	−	1.79051e7i	0.978541	−	0.140693i	0.612984	+	0.790096i	$0.289969\pi$
$504$	−5.15165e7	−	3.79533e7i	−0.402397	−	0.296454i
$505$	−3.34283e7			−0.259561
$506$	2.91187e7	+	1.56913e7i	0.224761	+	0.121118i
$507$	1.14965e8	+	1.22538e8i	0.882150	+	0.940258i
$508$	1.50716e6	+	968591.i	0.0114965	+	0.00738838i
$509$	−9.85026e7	+	1.41625e7i	−0.746955	+	0.107396i	−0.505273	−	0.862960i	$-0.668608\pi$
$509$	−9.85026e7	+	1.41625e7i	−0.746955	+	0.107396i	−0.241682	+	0.970356i	$0.577699\pi$
$510$	1.15999e8	+	4.75291e7i	0.874464	+	0.358302i
$511$	1.03621e7	+	3.04258e6i	0.0776577	+	0.0228024i
$512$	4.50624e7	+	2.05793e7i	0.335741	+	0.153328i
$513$	2.70619e6	−	1.11693e8i	0.0200450	−	0.827317i
$514$	1.60728e7	−	1.11789e8i	0.118360	−	0.823209i
$515$	−2.88428e7	−	9.82297e7i	−0.211162	−	0.719153i
$516$	1.05126e7	−	1.01430e8i	0.0765173	−	0.738276i
$517$	4.71244e7	−	3.02850e7i	0.341015	−	0.219157i
$518$	−2.02125e7	−	3.14513e7i	−0.145422	−	0.226281i
$519$	−4.84170e7	−	5.01810e6i	−0.346335	−	0.0358952i
$520$	−5.77524e7	+	1.69576e7i	−0.410734	+	0.120602i
$521$	2.38778e8	+	3.43311e7i	1.68842	+	0.242759i	0.918512	−	0.395392i	$-0.129391\pi$
$521$	2.38778e8	+	3.43311e7i	1.68842	+	0.242759i	0.769911	+	0.638151i	$0.220300\pi$
$522$	7.61804e7	+	7.50236e7i	0.535589	+	0.527456i
$523$	−7.95595e7	+	1.74211e8i	−0.556143	+	1.21778i	0.397710	+	0.917511i	$0.369805\pi$
$523$	−7.95595e7	+	1.74211e8i	−0.556143	+	1.21778i	−0.953853	+	0.300273i	$0.902922\pi$
$524$	−2.05789e7	+	7.00853e7i	−0.143030	+	0.487117i
$525$	−3.51056e7	+	8.56779e7i	−0.242604	+	0.592094i
$526$	−3.20372e6	−	2.22824e7i	−0.0220139	−	0.153110i
$527$	−1.68257e8	+	2.61813e8i	−1.14959	+	1.78879i
$528$	2.80127e7	−	2.62815e7i	0.190306	−	0.178545i
$529$	8.14084e7	+	1.23642e8i	0.549924	+	0.835215i
$530$			1.18985e7i			0.0799214i
$531$	−1.30072e8	−	9.58268e7i	−0.868761	−	0.640034i
$532$	7.12430e6	+	4.95506e7i	0.0473159	+	0.329089i
$533$	−1.77493e8	+	8.10582e7i	−1.17219	+	0.535322i
$534$	1.74522e7	+	3.45345e7i	0.114611	+	0.226793i
$535$	−1.58333e7	+	3.46702e7i	−0.103398	+	0.226410i
$536$	1.23147e8	+	1.06707e8i	0.799704	+	0.692948i
$537$	−8.69943e7	−	1.24278e8i	−0.561782	−	0.802549i
$538$	−1.61431e7	+	4.74004e6i	−0.103667	+	0.0304393i
$539$	−8.47928e6	+	7.34734e6i	−0.0541493	+	0.0469206i
$540$	3.41049e7	+	1.09181e7i	0.216588	+	0.0693371i
$541$	1.17067e8	−	7.52346e7i	0.739340	−	0.475145i	−0.115976	−	0.993252i	$-0.537000\pi$
$541$	1.17067e8	−	7.52346e7i	0.739340	−	0.475145i	0.855316	+	0.518107i	$0.173363\pi$
$542$	1.87732e8	−	1.62670e8i	1.17907	−	1.02167i
$543$	6.35858e7	+	3.73991e7i	0.397156	+	0.233594i
$544$	−3.51951e7	+	2.44787e8i	−0.218618	+	1.52052i
$545$	−5.05867e7	−	4.38336e7i	−0.312497	−	0.270781i
$546$	−7.79721e7	−	2.31312e8i	−0.479028	−	1.42108i
$547$	−8.84979e7	−	2.59853e7i	−0.540718	−	0.158769i	−4.21291e−5	−	1.00000i	$-0.500013\pi$
$547$	−8.84979e7	−	2.59853e7i	−0.540718	−	0.158769i	−0.540676	+	0.841231i	$0.681832\pi$
$548$	6.84236e7	−	3.12480e7i	0.415781	−	0.189881i
$549$	−3.15573e7	+	2.49982e6i	−0.190714	+	0.0151075i
$550$	−2.82146e7	−	1.81324e7i	−0.169584	−	0.108985i
$551$			8.50898e7i			0.508654i
$552$	1.00264e8	−	2.65931e7i	0.596112	−	0.158108i
$553$	−7.31530e7			−0.432570
$554$	−2.14748e8	+	3.34154e8i	−1.26299	+	1.96525i
$555$	−1.66230e7	−	1.32911e7i	−0.0972369	−	0.0777468i
$556$	4.61363e7	+	1.01024e8i	0.268422	+	0.587763i
$557$	−2.80857e7	+	9.56510e7i	−0.162525	+	0.553508i	0.837451	+	0.546513i	$0.184045\pi$
$557$	−2.80857e7	+	9.56510e7i	−0.162525	+	0.553508i	−0.999976	+	0.00699552i	$0.997773\pi$
$558$	−1.26749e8	+	2.36405e8i	−0.729527	+	1.36067i
$559$	−2.59137e8	+	2.99060e8i	−1.48352	+	1.71208i
$560$	8.07821e7	+	1.16147e7i	0.459993	+	0.0661369i
$561$	5.35140e7	+	3.14752e7i	0.303095	+	0.178271i
$562$	−2.53899e6	−	2.93015e6i	−0.0143038	−	0.0165075i
$563$	−1.79897e8	−	2.79925e8i	−1.00809	−	1.56862i	−0.808294	−	0.588779i	$-0.799609\pi$
$563$	−1.79897e8	−	2.79925e8i	−1.00809	−	1.56862i	−0.199795	−	0.979838i	$-0.564028\pi$
$564$	−4.20677e7	+	1.67491e8i	−0.234483	+	0.933585i
$565$	2.75963e7	+	3.18478e7i	0.153005	+	0.176577i
$566$	7.12324e7	+	2.42595e8i	0.392851	+	1.33793i
$567$	3.94461e7	−	1.42364e8i	0.216399	−	0.781000i
$568$	2.73143e7	−	3.15224e7i	0.149055	−	0.172018i
$569$	1.58806e8	+	7.25243e7i	0.862046	+	0.393683i	0.796841	−	0.604189i	$-0.206503\pi$
$569$	1.58806e8	+	7.25243e7i	0.862046	+	0.393683i	0.0652044	+	0.997872i	$0.479230\pi$
$570$	3.87827e7	+	7.67431e7i	0.209418	+	0.414395i
$571$	−4.88597e7	−	1.06988e8i	−0.262448	−	0.574680i	0.731832	−	0.681485i	$-0.238665\pi$
$571$	−4.88597e7	−	1.06988e8i	−0.262448	−	0.574680i	−0.994280	+	0.106804i	$0.965938\pi$
$572$	2.90064e7	−	4.17049e6i	0.154991	−	0.0222843i
$573$	9.80749e7	−	1.80823e7i	0.521307	−	0.0961147i
$574$	1.59646e8			0.844154
$575$	−7.26638e7	−	1.31340e8i	−0.382221	−	0.690863i
$576$	1.63869e6	−	2.56703e7i	0.00857488	−	0.134327i
$577$	−2.12467e8	−	1.36544e8i	−1.10602	−	0.710798i	−0.145600	−	0.989344i	$-0.546511\pi$
$577$	−2.12467e8	−	1.36544e8i	−1.10602	−	0.710798i	−0.960423	+	0.278545i	$0.910148\pi$
$578$	−4.29440e8	+	6.17442e7i	−2.22392	+	0.319752i
$579$	−5.08812e7	+	1.24180e8i	−0.262133	+	0.639756i
$580$	−2.61680e7	−	7.68362e6i	−0.134118	−	0.0393806i
$581$	−1.67907e8	−	7.66804e7i	−0.856129	−	0.390981i
$582$	−5.05344e6	−	1.27787e8i	−0.0256341	−	0.648214i
$583$	−838627.	+	5.83278e6i	−0.00423217	+	0.0294354i
$584$	3.45618e6	+	1.17707e7i	0.0173523	+	0.0590966i
$585$	−8.41254e7	−	1.10604e8i	−0.420203	−	0.552465i
$586$	2.87248e8	−	1.84603e8i	1.42746	−	0.917374i
$587$	−1.79681e7	−	2.79590e7i	−0.0888359	−	0.138231i	0.793992	−	0.607929i	$-0.207999\pi$
$587$	−1.79681e7	−	2.79590e7i	−0.0888359	−	0.138231i	−0.882827	+	0.469697i	$0.844363\pi$
$588$	3.56581e6	−	3.44047e7i	0.0175399	−	0.169233i
$589$	−2.04824e8	+	6.01419e7i	−1.00239	+	0.294328i
$590$	1.23074e8	+	1.76954e7i	0.599253	+	0.0861595i
$591$	1.09691e6	+	2.77378e7i	0.00531386	+	0.134372i
$592$	2.92370e7	−	6.40202e7i	0.140919	−	0.308569i
$593$	−3.61472e7	+	1.23106e8i	−0.173345	+	0.590358i	0.826288	+	0.563248i	$0.190449\pi$
$593$	−3.61472e7	+	1.23106e8i	−0.173345	+	0.590358i	−0.999632	+	0.0271097i	$0.991370\pi$
$594$	4.81222e7	+	2.34016e7i	0.229608	+	0.111657i
$595$	1.87728e7	+	1.30568e8i	0.0891208	+	0.619848i
$596$	5.02437e7	−	7.81808e7i	0.237325	−	0.369285i
$597$	−1.11191e8	−	1.18516e8i	−0.522574	−	0.556996i
$598$	3.71523e8	+	1.36233e8i	1.73733	+	0.637056i
$599$		−	3.11603e8i		−	1.44984i	−0.688831	−	0.724922i	$-0.741876\pi$
$599$		−	3.11603e8i		−	1.44984i	0.688831	−	0.724922i	$-0.258124\pi$
$600$	−1.03434e8	+	1.90704e7i	−0.478861	+	0.0882888i
$601$	−4.33088e7	−	3.01219e8i	−0.199505	−	1.38759i	−0.805726	−	0.592289i	$-0.798224\pi$
$601$	−4.33088e7	−	3.01219e8i	−0.199505	−	1.38759i	0.606221	−	0.795296i	$-0.292685\pi$
$602$	2.94503e8	−	1.34495e8i	1.34989	−	0.616476i
$603$	−1.28766e8	+	3.53471e8i	−0.587286	+	1.61214i
$604$	8.38949e7	−	1.83704e8i	0.380737	−	0.833697i
$605$	−7.34293e7	−	6.36268e7i	−0.331591	−	0.287325i
$606$	1.26158e8	−	8.83100e7i	0.566886	−	0.396819i
$607$	−2.26260e8	+	6.64360e7i	−1.01168	+	0.297055i	−0.745240	−	0.666797i	$-0.767665\pi$
$607$	−2.26260e8	+	6.64360e7i	−1.01168	+	0.297055i	−0.266438	+	0.963852i	$0.585847\pi$
$608$	−1.28199e8	+	1.11085e8i	−0.570393	+	0.494249i
$609$	−2.74070e7	+	1.09120e8i	−0.121342	+	0.483117i
$610$	2.04956e7	−	1.31717e7i	0.0902966	−	0.0580301i
$611$	5.06460e8	−	4.38850e8i	2.22035	−	1.92395i
$612$	−1.86707e8	+	4.21142e7i	−0.814529	+	0.183727i
$613$	5.01633e7	−	3.48893e8i	0.217773	−	1.51465i	−0.528458	−	0.848960i	$-0.677229\pi$
$613$	5.01633e7	−	3.48893e8i	0.217773	−	1.51465i	0.746231	−	0.665687i	$-0.231861\pi$
$614$	3.51200e7	+	3.04317e7i	0.151722	+	0.131468i
$615$	8.61222e7	−	2.90306e7i	0.370246	−	0.124805i
$616$	2.34013e7	+	6.87126e6i	0.100115	+	0.0293964i
$617$	−3.83814e8	+	1.75282e8i	−1.63405	+	0.746246i	−0.999642	−	0.0267522i	$-0.991483\pi$
$617$	−3.83814e8	+	1.75282e8i	−1.63405	+	0.746246i	−0.634408	+	0.772998i	$0.718756\pi$
$618$	3.68354e8	+	2.94521e8i	1.56063	+	1.24782i
$619$	1.57203e8	+	1.01028e8i	0.662810	+	0.425962i	0.828327	−	0.560245i	$-0.189293\pi$
$619$	1.57203e8	+	1.01028e8i	0.662810	+	0.425962i	−0.165517	+	0.986207i	$0.552929\pi$
$620$		−	6.84213e7i		−	0.287089i
$621$	1.39909e8	+	1.94364e8i	0.584214	+	0.811600i
$622$	1.85923e8			0.772614
$623$	−2.20129e7	+	3.42527e7i	−0.0910359	+	0.141655i
$624$	2.86966e8	−	3.58905e8i	1.18107	−	1.47715i
$625$	4.18794e7	+	9.17031e7i	0.171538	+	0.375616i
$626$	7.67785e7	−	2.61484e8i	0.312980	−	1.06591i
$627$	1.36028e7	+	4.03539e7i	0.0551854	+	0.163713i
$628$	−7.54726e7	+	8.71000e7i	−0.304727	+	0.351673i
$629$	1.12598e8	+	1.61891e7i	0.452457	+	0.0650536i
$630$	2.50167e7	+	1.10908e8i	0.100048	+	0.443548i
$631$	1.62019e8	+	1.86980e8i	0.644880	+	0.744231i	0.980230	−	0.197863i	$-0.0634000\pi$
$631$	1.62019e8	+	1.86980e8i	0.644880	+	0.744231i	−0.335350	+	0.942094i	$0.608855\pi$
$632$	−4.49256e7	−	6.99056e7i	−0.177968	−	0.276924i
$633$	−9.75090e7	−	2.44908e7i	−0.384445	−	0.0965587i
$634$	−3.07673e8	−	3.55073e8i	−1.20732	−	1.39332i
$635$	912287.	+	3.10697e6i	0.00356296	+	0.0121343i
$636$	−1.04179e7	−	1.48827e7i	−0.0404955	−	0.0578510i
$637$	−8.78980e7	+	1.01440e8i	−0.340064	+	0.392455i
$638$	−3.70707e7	−	1.69296e7i	−0.142748	−	0.0651907i
$639$	9.04794e7	+	3.29608e7i	0.346774	+	0.126327i
$640$	5.37851e7	+	1.17773e8i	0.205174	+	0.449268i
$641$	3.47712e8	−	4.99934e7i	1.32022	−	0.189819i	0.554063	−	0.832475i	$-0.313077\pi$
$641$	3.47712e8	−	4.99934e7i	1.32022	−	0.189819i	0.766155	+	0.642656i	$0.222168\pi$
$642$	−3.18361e7	−	1.72673e8i	−0.120314	−	0.652558i
$643$	−3.03048e7			−0.113993			−0.0569965	−	0.998374i	$-0.518152\pi$
$643$	−3.03048e7			−0.113993			−0.0569965	+	0.998374i	$0.518152\pi$
$644$	−7.62942e7	−	7.54539e7i	−0.285650	−	0.282504i
$645$	1.34415e8	−	1.26108e8i	0.500919	−	0.469962i
$646$	−3.86624e8	−	2.48468e8i	−1.43414	−	0.921665i
$647$	−2.48865e8	+	3.57814e7i	−0.918864	+	0.132113i	−0.585488	−	0.810681i	$-0.699097\pi$
$647$	−2.48865e8	+	3.57814e7i	−0.918864	+	0.132113i	−0.333376	+	0.942794i	$0.608188\pi$
$648$	1.60269e8	−	4.97353e7i	0.589014	−	0.182785i
$649$	5.90852e7	+	1.73490e7i	0.216145	+	0.0634658i
$650$	−3.64973e8	−	1.66678e8i	−1.32899	−	0.606928i
$651$	−2.82040e8	+	1.11535e7i	−1.02228	+	0.0404267i
$652$	−922479.	+	6.41598e6i	−0.00332823	+	0.0231484i
$653$	−5.39410e7	−	1.83706e8i	−0.193722	−	0.659757i	−0.997864	−	0.0653203i	$-0.979193\pi$
$653$	−5.39410e7	−	1.83706e8i	−0.193722	−	0.659757i	0.804142	−	0.594437i	$-0.202625\pi$
$654$	3.06712e8	+	3.17886e7i	1.09647	+	0.113642i
$655$	−1.11064e8	+	7.13768e7i	−0.395231	+	0.254000i
$656$	1.62482e8	+	2.52828e8i	0.575566	+	0.895598i
$657$	−2.25425e7	+	1.71458e7i	−0.0794889	+	0.0604591i
$658$	−5.26080e8	+	1.54471e8i	−1.84661	+	0.542213i
$659$	−5.52985e8	−	7.95072e7i	−1.93222	−	0.277811i	−0.935147	−	0.354259i	$-0.884733\pi$
$659$	−5.52985e8	−	7.95072e7i	−1.93222	−	0.277811i	−0.997074	+	0.0764473i	$0.975642\pi$
$660$	−1.36385e7	+	539346.i	−0.0474391	+	0.00187601i
$661$	1.13175e8	−	2.47820e8i	0.391875	−	0.858087i	−0.606155	−	0.795347i	$-0.707289\pi$
$661$	1.13175e8	−	2.47820e8i	0.391875	−	0.858087i	0.998030	−	0.0627402i	$-0.0199840\pi$
$662$	4.21140e7	−	1.43427e8i	0.145162	−	0.494376i
$663$	6.87273e8	+	2.81603e8i	2.35824	+	0.966265i
$664$	−2.98405e7	−	2.07545e8i	−0.101930	−	0.708938i
$665$	−4.89174e7	+	7.61170e7i	−0.166341	+	0.258831i
$666$	9.78472e7	+	6.24616e6i	0.331227	+	0.0211442i
$667$	−1.10109e8	−	1.45403e8i	−0.371061	−	0.490000i
$668$		−	1.38492e8i		−	0.464618i
$669$	6.02725e7	+	3.26906e8i	0.201299	+	1.09181i
$670$	−4.12040e7	−	2.86580e8i	−0.136998	−	0.952844i
$671$	1.09756e7	−	5.01238e6i	0.0363296	−	0.0165912i
$672$	−2.00184e8	+	1.01164e8i	−0.659662	+	0.333365i
$673$	6.48655e7	−	1.42036e8i	0.212799	−	0.465964i	−0.772890	−	0.634540i	$-0.781190\pi$
$673$	6.48655e7	−	1.42036e8i	0.212799	−	0.465964i	0.985689	+	0.168576i	$0.0539169\pi$
$674$	2.27572e8	+	1.97192e8i	0.743257	+	0.644036i
$675$	−1.26293e8	−	2.07395e8i	−0.410648	−	0.674354i
$676$	1.89442e8	−	5.56253e7i	0.613250	−	0.180066i
$677$	3.37560e8	−	2.92497e8i	1.08789	−	0.942662i	0.0893132	−	0.996004i	$-0.471533\pi$
$677$	3.37560e8	−	2.92497e8i	1.08789	−	0.942662i	0.998576	+	0.0533420i	$0.0169874\pi$
$678$	−1.88283e8	−	4.72899e7i	−0.604118	−	0.151733i
$679$	1.13209e8	−	7.27549e7i	0.361636	−	0.232409i
$680$	−1.13243e8	+	9.81255e7i	−0.360151	+	0.312072i
$681$	−2.71797e8	+	4.62108e8i	−0.860604	+	1.46320i
$682$	1.45505e7	−	1.01201e8i	0.0458696	−	0.319030i
$683$	−1.53370e8	−	1.32896e8i	−0.481370	−	0.417110i	0.380078	−	0.924954i	$-0.375897\pi$
$683$	−1.53370e8	−	1.32896e8i	−0.481370	−	0.417110i	−0.861449	+	0.507844i	$0.830442\pi$
$684$	−1.15703e8	−	6.20344e7i	−0.361558	−	0.193849i
$685$	1.30450e8	+	3.83037e7i	0.405858	+	0.119171i
$686$	3.90950e8	−	1.78541e8i	1.21101	−	0.553052i
$687$	3.42896e8	−	4.28855e8i	1.05753	−	1.32264i
$688$	5.12732e8	+	3.29513e8i	1.57444	+	1.01183i
$689$			7.04965e7i			0.215531i
$690$	−1.65581e8	−	8.09541e7i	−0.504037	−	0.246429i
$691$	−5.33767e7			−0.161777			−0.0808887	−	0.996723i	$-0.525776\pi$
$691$	−5.33767e7			−0.161777			−0.0808887	+	0.996723i	$0.525776\pi$
$692$	−3.09234e7	+	4.81178e7i	−0.0933188	+	0.145207i
$693$	4.44649e6	+	5.61317e7i	0.0133603	+	0.168658i
$694$	−1.48166e8	−	3.24438e8i	−0.443271	−	0.970628i
$695$	−5.65537e7	+	1.92604e8i	−0.168464	+	0.573735i
$696$	−1.21108e8	+	4.08237e7i	−0.359206	+	0.121083i
$697$	−3.18103e8	+	3.67111e8i	−0.939441	+	1.08417i
$698$	−4.71333e8	−	6.77674e7i	−1.38599	−	0.199276i
$699$	−1.10563e8	+	1.87978e8i	−0.323725	+	0.550397i
$700$	7.12489e7	+	8.22257e7i	0.207723	+	0.239725i
$701$	7.60916e7	+	1.18401e8i	0.220893	+	0.343717i	0.933959	−	0.357381i	$-0.116330\pi$
$701$	7.60916e7	+	1.18401e8i	0.220893	+	0.343717i	−0.713065	+	0.701097i	$0.752694\pi$
$702$	6.09680e8	+	1.95179e8i	1.76234	+	0.564184i
$703$	5.10972e7	+	5.89693e7i	0.147072	+	0.169731i
$704$	2.76220e6	+	9.40719e6i	0.00791657	+	0.0269614i
$705$	−2.55709e8	+	1.78995e8i	−0.729757	+	0.510827i
$706$	2.30945e8	−	2.66524e8i	0.656287	−	0.757396i
$707$	1.47401e8	+	6.73156e7i	0.417101	+	0.190483i
$708$	−1.69436e8	+	8.56255e7i	−0.477425	+	0.241270i
$709$	−9.48920e7	−	2.07785e8i	−0.266251	−	0.583008i	0.728533	−	0.685010i	$-0.240202\pi$
$709$	−9.48920e7	−	2.07785e8i	−0.266251	−	0.583008i	−0.994784	+	0.102002i	$0.967475\pi$
$710$	−7.33570e7	+	1.05471e7i	−0.204959	+	0.0294686i
$711$	1.13791e8	−	1.54456e8i	0.316590	−	0.429729i
$712$	−4.62510e7			−0.128139
$713$	2.72182e8	−	3.67821e8i	0.750916	−	1.01477i
$714$	−4.15780e8	−	4.43168e8i	−1.14227	−	1.21751i
$715$	4.45581e7	+	2.86357e7i	0.121901	+	0.0783412i
$716$	−1.76443e8	+	2.53687e7i	−0.480690	+	0.0691128i
$717$	−1.14190e8	−	4.67879e7i	−0.309791	−	0.126934i
$718$	1.13189e8	+	3.32354e7i	0.305797	+	0.0897900i
$719$	−6.38826e7	−	2.91742e7i	−0.171868	−	0.0784896i	0.327623	−	0.944809i	$-0.393752\pi$
$719$	−6.38826e7	−	2.91742e7i	−0.171868	−	0.0784896i	−0.499491	+	0.866319i	$0.666480\pi$
$720$	−1.50181e8	+	1.52497e8i	−0.402363	+	0.408567i
$721$	−7.06270e7	+	4.91222e8i	−0.188436	+	1.31060i
$722$	4.08681e7	+	1.39184e8i	0.108586	+	0.369809i
$723$	−3.51147e7	+	3.38803e8i	−0.0929124	+	0.896463i
$724$	7.29223e7	−	4.68643e7i	0.192152	−	0.123489i
$725$	9.99825e7	+	1.55576e8i	0.262367	+	0.408252i
$726$	4.45209e8	+	4.61429e7i	1.16347	+	0.120585i
$727$	−6.66361e7	+	1.95661e7i	−0.173423	+	0.0509215i	−0.367291	−	0.930106i	$-0.619715\pi$
$727$	−6.66361e7	+	1.95661e7i	−0.173423	+	0.0509215i	0.193868	+	0.981028i	$0.437897\pi$
$728$	2.88805e8	+	4.15239e7i	0.748533	+	0.107623i
$729$	2.39229e8	+	3.04736e8i	0.617492	+	0.786577i
$730$	9.05492e6	−	1.98275e7i	0.0232764	−	0.0509682i
$731$	−2.77538e8	+	9.45207e8i	−0.710510	+	2.41977i
$732$	−1.41035e7	+	3.44206e7i	−0.0359577	+	0.0877576i
$733$	6.33769e7	+	4.40796e8i	0.160923	+	1.11925i	0.896898	+	0.442237i	$0.145815\pi$
$733$	6.33769e7	+	4.40796e8i	0.160923	+	1.11925i	−0.735975	+	0.677009i	$0.763276\pi$
$734$	−4.78962e8	+	7.45279e8i	−1.21119	+	1.88465i
$735$	4.55928e7	−	4.27752e7i	0.114824	−	0.107728i
$736$	7.53214e7	−	3.55718e8i	0.188923	−	0.892222i
$737$		−	1.43389e8i		−	0.358191i
$738$	−2.48332e8	+	3.37077e8i	−0.617821	+	0.838610i
$739$	−7.92738e7	−	5.51361e8i	−0.196425	−	1.36616i	−0.814554	−	0.580088i	$-0.803018\pi$
$739$	−7.92738e7	−	5.51361e8i	−0.196425	−	1.36616i	0.618129	−	0.786076i	$-0.287891\pi$
$740$	−2.27491e7	+	1.03892e7i	−0.0561397	+	0.0256381i
$741$	2.29781e8	+	4.54691e8i	0.564755	+	1.11754i
$742$	2.39603e7	−	5.24658e7i	0.0586517	−	0.128429i
$743$	−5.57718e8	−	4.83265e8i	−1.35971	−	1.17820i	−0.965871	−	0.259022i	$-0.916600\pi$
$743$	−5.57718e8	−	4.83265e8i	−1.35971	−	1.17820i	−0.393844	−	0.919177i	$-0.628855\pi$
$744$	−1.83868e8	−	2.62670e8i	−0.446466	−	0.637811i
$745$	1.61168e8	−	4.73231e7i	0.389771	−	0.114447i
$746$	−5.67637e8	+	4.91861e8i	−1.36727	+	1.18475i
$747$	4.23085e8	−	2.35241e8i	1.01500	−	0.564354i
$748$	6.13717e7	−	3.94412e7i	0.146644	−	0.0942421i
$749$	1.39633e8	−	1.20993e8i	0.332309	−	0.287948i
$750$	3.65105e8	+	2.14743e8i	0.865434	+	0.509020i
$751$	−6.21294e7	+	4.32120e8i	−0.146682	+	1.02020i	0.774919	+	0.632060i	$0.217790\pi$
$751$	−6.21294e7	+	4.32120e8i	−0.146682	+	1.02020i	−0.921602	+	0.388137i	$0.873119\pi$
$752$	−7.80061e8	−	6.75926e8i	−1.83432	−	1.58945i
$753$	−1.74971e8	−	5.19068e8i	−0.409808	−	1.21574i
$754$	−4.67795e8	−	1.37357e8i	−1.09129	−	0.320433i
$755$	3.32034e8	−	1.51635e8i	0.771510	−	0.352337i
$756$	−1.28398e8	−	1.16821e8i	−0.297162	−	0.270368i
$757$	−1.95144e8	−	1.25411e8i	−0.449850	−	0.289101i	0.296034	−	0.955178i	$-0.404336\pi$
$757$	−1.95144e8	−	1.25411e8i	−0.449850	−	0.289101i	−0.745883	+	0.666077i	$0.767972\pi$
$758$			8.01175e8i			1.83958i
$759$	−7.54640e7	−	5.13552e7i	−0.172589	−	0.117452i
$760$	−1.02780e8			−0.234136
$761$	4.62008e8	−	7.18899e8i	1.04832	−	1.63122i	0.318046	−	0.948075i	$-0.396973\pi$
$761$	4.62008e8	−	7.18899e8i	1.04832	−	1.63122i	0.730279	−	0.683149i	$-0.239390\pi$
$762$	−1.16509e7	−	9.31558e6i	−0.0263326	−	0.0210545i
$763$	1.34791e8	+	2.95150e8i	0.303449	+	0.664462i
$764$	3.30152e7	−	1.12439e8i	0.0740345	−	0.252138i
$765$	−3.04883e8	−	1.63463e8i	−0.681003	−	0.365121i
$766$	−1.46566e8	+	1.69147e8i	−0.326098	+	0.376337i
$767$	7.29193e8	+	1.04842e8i	1.61606	+	0.232354i
$768$	−4.61559e8	−	2.71474e8i	−1.01893	−	0.599300i
$769$	3.71137e8	+	4.28315e8i	0.816123	+	0.941856i	0.999149	−	0.0412522i	$-0.0131347\pi$
$769$	3.71137e8	+	4.28315e8i	0.816123	+	0.941856i	−0.183026	+	0.983108i	$0.558589\pi$
$770$	−2.34289e7	−	3.64560e7i	−0.0513191	−	0.0798541i
$771$	−7.59214e7	+	3.02278e8i	−0.165654	+	0.659543i
$772$	1.03267e8	+	1.19176e8i	0.224444	+	0.259022i
$773$	−3.96197e7	−	1.34932e8i	−0.0857773	−	0.292131i	0.905421	−	0.424514i	$-0.139555\pi$
$773$	−3.96197e7	−	1.34932e8i	−0.0857773	−	0.292131i	−0.991199	+	0.132384i	$0.957737\pi$
$774$	−1.74130e8	+	8.31024e8i	−0.375536	+	1.79222i
$775$	−3.03827e8	+	3.50635e8i	−0.652712	+	0.753269i
$776$	1.39051e8	+	6.35023e7i	0.297569	+	0.135895i
$777$	4.65338e7	+	9.20810e7i	0.0991985	+	0.196294i
$778$	3.47384e8	+	7.60666e8i	0.737686	+	1.61531i
$779$	−3.29800e8	+	4.74181e7i	−0.697652	+	0.100307i
$780$	−1.60582e8	+	2.96069e7i	−0.338387	+	0.0623892i
$781$	−3.67039e7			−0.0770477
$782$	9.82197e8	−	7.57166e7i	2.05389	−	0.158333i
$783$	−1.87764e8	−	2.27605e8i	−0.391136	−	0.474129i
$784$	1.73916e8	+	1.11769e8i	0.360904	+	0.231939i
$785$	−2.06187e8	+	2.96452e7i	−0.426237	+	0.0612837i
$786$	2.30594e8	−	5.62783e8i	0.474876	−	1.15897i
$787$	5.77512e8	+	1.69573e8i	1.18478	+	0.347882i	0.814014	−	0.580845i	$-0.197278\pi$
$787$	5.77512e8	+	1.69573e8i	1.18478	+	0.347882i	0.370763	+	0.928727i	$0.379096\pi$
$788$	2.96714e7	+	1.35505e7i	0.0606400	+	0.0276934i
$789$	2.45478e6	+	6.20744e7i	0.00499783	+	0.126381i
$790$	−2.10126e7	+	1.46146e8i	−0.0426185	+	0.296418i
$791$	−5.75517e7	−	1.96003e8i	−0.116286	−	0.396035i
$792$	−5.09092e7	+	3.87214e7i	−0.102476	+	0.0779427i
$793$	1.21433e8	−	7.80404e7i	0.243511	−	0.156495i
$794$	2.77435e8	+	4.31698e8i	0.554243	+	0.862419i
$795$	3.38500e6	−	3.26601e7i	0.00673686	−	0.0650004i
$796$	−1.83224e8	+	5.37993e7i	−0.363281	+	0.106669i
$797$	6.87652e8	+	9.88695e7i	1.35829	+	0.195293i	0.782678	−	0.622427i	$-0.213853\pi$
$797$	6.87652e8	+	9.88695e7i	1.35829	+	0.195293i	0.575616	+	0.817720i	$0.304762\pi$
$798$	−1.64706e7	−	4.16494e8i	−0.0324115	−	0.819596i
$799$	6.93033e8	−	1.51753e9i	1.35867	−	2.97507i
$800$	−1.03868e8	+	3.53742e8i	−0.202867	+	0.690903i
$801$	−3.80800e7	−	9.97588e7i	−0.0740968	−	0.194113i
$802$	8.61961e7	+	5.99507e8i	0.167095	+	1.16217i
$803$	5.83632e6	−	9.08149e6i	0.0112718	−	0.0175392i
$804$	3.02458e8	+	3.22381e8i	0.581964	+	0.620299i
$805$	−1.49068e7	−	1.93371e8i	−0.0285756	−	0.370684i
$806$		−	1.22314e9i		−	2.33599i
$807$	4.56597e7	−	8.41839e6i	0.0868785	−	0.0160180i
$808$	2.61961e7	+	1.82198e8i	0.0496595	+	0.345390i
$809$	−4.45229e8	+	2.03329e8i	−0.840887	+	0.384020i	−0.788821	−	0.614623i	$-0.789308\pi$
$809$	−4.45229e8	+	2.03329e8i	−0.840887	+	0.384020i	−0.0520664	+	0.998644i	$0.516581\pi$
$810$	−2.73085e8	−	1.19699e8i	−0.513858	−	0.225234i
$811$	−2.37558e8	+	5.20181e8i	−0.445357	+	0.975195i	0.545227	+	0.838288i	$0.316443\pi$
$811$	−2.37558e8	+	5.20181e8i	−0.445357	+	0.975195i	−0.990584	+	0.136907i	$0.956284\pi$
$812$	9.99140e7	+	8.65760e7i	0.186620	+	0.161707i
$813$	−5.61583e8	+	3.93107e8i	−1.04506	+	0.731541i
$814$	−3.58573e7	+	1.05287e7i	−0.0664820	+	0.0195209i
$815$	−8.85416e6	+	7.67217e6i	−0.0163559	+	0.0141725i
$816$	2.78668e8	−	1.10950e9i	0.512881	−	2.04201i
$817$	−5.68444e8	+	3.65317e8i	−1.04237	+	0.669889i
$818$	5.19871e8	−	4.50471e8i	0.949808	−	0.823013i
$819$	1.48220e8	+	6.57111e8i	0.269808	+	1.19615i
$820$	1.51983e7	−	1.05707e8i	0.0275648	−	0.191717i
$821$	59814.1	+	51829.2i	0.000108087	+	9.36581e-5i	0.654915	−	0.755703i	$-0.272705\pi$
$821$	59814.1	+	51829.2i	0.000108087	+	9.36581e-5i	−0.654807	+	0.755796i	$0.727250\pi$
$822$	−5.93508e8	+	2.00063e8i	−1.06859	+	0.360207i
$823$	2.54201e8	+	7.46400e7i	0.456013	+	0.133897i	0.501669	−	0.865060i	$-0.332720\pi$
$823$	2.54201e8	+	7.46400e7i	0.456013	+	0.133897i	−0.0456560	+	0.998957i	$0.514538\pi$
$824$	−5.12790e8	+	2.34183e8i	−0.916554	+	0.418576i
$825$	7.22877e7	+	5.77985e7i	0.128737	+	0.102933i
$826$	−5.07056e8	−	3.25865e8i	−0.899737	−	0.578226i
$827$		−	6.00451e8i		−	1.06160i	−0.847497	−	0.530800i	$-0.821891\pi$
$827$		−	6.00451e8i		−	1.06160i	0.847497	−	0.530800i	$-0.178109\pi$
$828$	2.77991e8	−	4.37181e7i	0.489710	−	0.0770142i
$829$	−3.00401e8			−0.527275			−0.263638	−	0.964622i	$-0.584922\pi$
$829$	−3.00401e8			−0.527275			−0.263638	+	0.964622i	$0.584922\pi$
$830$	−2.01422e8	+	3.13419e8i	−0.352268	+	0.548140i
$831$	6.84526e8	−	8.56128e8i	1.19285	−	1.49189i
$832$	4.87247e7	+	1.06692e8i	0.0846018	+	0.185252i
$833$	−9.41395e7	+	3.20610e8i	−0.162868	+	0.554679i
$834$	−2.95385e8	−	8.76288e8i	−0.509202	−	1.51060i
$835$	1.63922e8	−	1.89176e8i	0.281564	−	0.324943i
$836$	4.95306e7	+	7.12142e6i	0.0847724	+	0.0121884i
$837$	4.15168e8	−	6.12851e8i	0.708024	−	1.04515i
$838$	3.68369e8	+	4.25120e8i	0.625966	+	0.722403i
$839$	3.54503e8	+	5.51617e8i	0.600252	+	0.934010i	0.999850	+	0.0173196i	$0.00551327\pi$
$839$	3.54503e8	+	5.51617e8i	0.600252	+	0.934010i	−0.399598	+	0.916690i	$0.630850\pi$
$840$	−1.31806e8	−	3.31049e7i	−0.222381	−	0.0558541i
$841$	−2.42369e8	−	2.79708e8i	−0.407463	−	0.470238i
$842$	2.51316e8	+	8.55902e8i	0.421001	+	1.43380i
$843$	6.13568e6	+	8.76530e6i	0.0102419	+	0.0146313i
$844$	−7.73638e7	+	8.92826e7i	−0.128680	+	0.148505i
$845$	3.24612e8	+	1.48245e8i	0.538015	+	0.245703i
$846$	4.92175e8	−	1.35105e9i	0.812847	−	2.23131i
$847$	1.95656e8	+	4.28427e8i	0.321990	+	0.705060i
$848$	1.07475e8	−	1.54526e7i	0.176246	−	0.0253404i
$849$	−1.26510e8	−	6.86165e8i	−0.206729	−	1.12126i
$850$	−9.98849e8			−1.62646
$851$	−1.63624e8	−	3.46465e7i	−0.265496	−	0.0562174i
$852$	8.25211e7	−	7.74212e7i	0.133428	−	0.125182i
$853$	6.32924e6	+	4.06755e6i	0.0101977	+	0.00655369i	0.545730	−	0.837961i	$-0.316253\pi$
$853$	6.32924e6	+	4.06755e6i	0.0101977	+	0.00655369i	−0.535532	+	0.844515i	$0.679889\pi$
$854$	−1.16899e8	+	1.68075e7i	−0.187688	+	0.0269855i
$855$	−8.46220e7	−	2.21686e8i	−0.135390	−	0.354682i
$856$	2.01375e8	+	5.91290e7i	0.321058	+	0.0942712i
$857$	−9.23088e8	−	4.21560e8i	−1.46656	−	0.669757i	−0.487465	−	0.873143i	$-0.662078\pi$
$857$	−9.23088e8	−	4.21560e8i	−1.46656	−	0.669757i	−0.979099	+	0.203386i	$0.934805\pi$
$858$	−2.43811e8	+	9.64169e6i	−0.386004	+	0.0152648i
$859$	1.44703e8	−	1.00643e9i	0.228296	−	1.58783i	−0.476988	−	0.878910i	$-0.658272\pi$
$859$	1.44703e8	−	1.00643e9i	0.228296	−	1.58783i	0.705285	−	0.708924i	$-0.250819\pi$
$860$	−6.10167e7	−	2.07804e8i	−0.0959298	−	0.326707i
$861$	−4.38212e8	−	4.54177e7i	−0.686555	−	0.0711567i
$862$	3.50108e8	−	2.25001e8i	0.546614	−	0.351287i
$863$	3.87148e8	+	6.02414e8i	0.602344	+	0.937266i	0.999807	+	0.0196479i	$0.00625452\pi$
$863$	3.87148e8	+	6.02414e8i	0.602344	+	0.937266i	−0.397462	+	0.917618i	$0.630109\pi$
$864$	9.77902e7	−	5.80032e8i	0.151619	−	0.899313i
$865$	−9.91936e7	+	2.91259e7i	−0.153262	+	0.0450019i
$866$	3.07534e8	+	4.42167e7i	0.473521	+	0.0680820i
$867$	1.19634e9	−	4.73101e7i	1.83568	−	0.0725933i
$868$	−1.37782e8	+	3.01701e8i	−0.210685	+	0.461336i
$869$	−2.06013e7	+	7.01614e7i	−0.0313931	+	0.106915i
$870$	2.10128e8	+	8.60977e7i	0.319100	+	0.130748i
$871$	−2.44127e8	−	1.69794e9i	−0.369455	−	2.56962i
$872$	−1.99269e8	+	3.10069e8i	−0.300532	+	0.467637i
$873$	−2.24831e7	+	3.52201e8i	−0.0337919	+	0.529357i
$874$	5.43168e8	+	4.01937e8i	0.813579	+	0.602037i
$875$			4.45715e8i			0.665324i
$876$	6.03426e6	+	3.27286e7i	0.00897659	+	0.0486873i
$877$	4.85101e7	+	3.37395e8i	0.0719174	+	0.500196i	0.993663	+	0.112401i	$0.0358541\pi$
$877$	4.85101e7	+	3.37395e8i	0.0719174	+	0.500196i	−0.921746	+	0.387795i	$0.873237\pi$
$878$	−1.73998e8	+	7.94623e7i	−0.257076	+	0.117403i
$879$	−8.40987e8	+	4.24999e8i	−1.23829	+	0.625779i
$880$	3.38895e7	−	7.42076e7i	0.0497298	−	0.108893i
$881$	7.60732e8	+	6.59178e8i	1.11251	+	0.963996i	0.999562	−	0.0296047i	$-0.00942486\pi$
$881$	7.60732e8	+	6.59178e8i	1.11251	+	0.963996i	0.112949	+	0.993601i	$0.463970\pi$
$882$	−5.90642e7	+	2.81879e8i	−0.0860832	+	0.410825i
$883$	−4.96701e8	+	1.45845e8i	−0.721461	+	0.211840i	−0.621794	−	0.783181i	$-0.713596\pi$
$883$	−4.96701e8	+	1.45845e8i	−0.721461	+	0.211840i	−0.0996671	+	0.995021i	$0.531778\pi$
$884$	6.59581e8	−	5.71530e8i	0.954797	−	0.827337i
$885$	−3.32792e8	−	8.35854e7i	−0.480112	−	0.120587i
$886$	−8.32275e8	+	5.34871e8i	−1.19665	+	0.769038i
$887$	1.50459e8	−	1.30374e8i	0.215599	−	0.186818i	−0.540365	−	0.841431i	$-0.681714\pi$
$887$	1.50459e8	−	1.30374e8i	0.215599	−	0.186818i	0.755964	+	0.654613i	$0.227168\pi$
$888$	−5.94155e7	+	1.01018e8i	−0.0848518	+	0.144265i
$889$	2.23390e6	−	1.55371e7i	0.00317950	−	0.0221139i
$890$	6.21073e7	+	5.38163e7i	0.0880994	+	0.0763385i
$891$	−1.25433e8	−	7.79254e7i	−0.177329	−	0.110166i
$892$	3.74787e8	+	1.10047e8i	0.528068	+	0.155055i
$893$	1.04091e9	−	4.75368e8i	1.46170	−	0.667537i
$894$	−4.83228e8	+	6.04366e8i	−0.676300	+	0.845839i
$895$	−2.71043e8	−	1.74188e8i	−0.378067	−	0.242969i
$896$		−	6.27624e8i		−	0.872520i
$897$	−9.81039e8	−	4.79640e8i	−1.35928	−	0.664566i
$898$	−1.96481e8			−0.271327
$899$	−3.04793e8	+	4.74267e8i	−0.419494	+	0.652746i
$900$	−2.84441e8	+	2.25321e7i	−0.390179	+	0.0309082i
$901$	7.29045e7	+	1.59638e8i	0.0996735	+	0.218255i
$902$	4.49593e7	−	1.53117e8i	0.0612632	−	0.208643i
$903$	−8.46644e8	+	2.85392e8i	−1.14984	+	0.387596i
$904$	1.51958e8	−	1.75369e8i	0.205692	−	0.237382i
$905$	1.55079e8	+	2.22970e7i	0.209222	+	0.0300816i
$906$	−8.52506e8	+	1.44943e9i	−1.14634	+	1.94900i
$907$	6.35757e7	+	7.33703e7i	0.0852059	+	0.0983328i	0.796752	−	0.604307i	$-0.206550\pi$
$907$	6.35757e7	+	7.33703e7i	0.0852059	+	0.0983328i	−0.711546	+	0.702640i	$0.752005\pi$
$908$	3.40586e8	+	5.29961e8i	0.454955	+	0.707924i
$909$	−3.71414e8	+	2.06512e8i	−0.494501	+	0.274950i
$910$	−3.39500e8	−	3.91804e8i	−0.450522	−	0.519930i
$911$	−1.95384e8	−	6.65416e8i	−0.258424	−	0.880112i	−0.981842	−	0.189701i	$-0.939248\pi$
$911$	−1.95384e8	−	6.65416e8i	−0.258424	−	0.880112i	0.723418	−	0.690411i	$-0.242570\pi$
$912$	6.42829e8	−	4.49978e8i	0.847444	−	0.593208i
$913$	−1.20830e8	+	1.39446e8i	−0.158768	+	0.183228i
$914$	−4.44378e8	−	2.02940e8i	−0.581987	−	0.265785i
$915$	−6.00057e7	+	3.03243e7i	−0.0783302	+	0.0395848i
$916$	−2.68029e8	−	5.86902e8i	−0.348735	−	0.763624i
$917$	6.33468e8	−	9.10790e7i	0.821518	−	0.118116i
$918$	1.58246e9	−	1.88525e8i	2.04552	−	0.243692i
$919$	3.81241e7			0.0491194			0.0245597	−	0.999698i	$-0.492182\pi$
$919$	3.81241e7			0.0491194			0.0245597	+	0.999698i	$0.492182\pi$
$920$	1.75632e8	−	1.33000e8i	0.225549	−	0.170801i
$921$	−8.77435e7	−	9.35233e7i	−0.112315	−	0.119713i
$922$	−8.29225e8	−	5.32911e8i	−1.05799	−	0.679926i
$923$	−4.34629e8	+	6.24902e7i	−0.552730	+	0.0794706i
$924$	6.12247e7	+	2.50861e7i	0.0776087	+	0.0317993i
$925$	1.62715e8	+	4.77774e7i	0.205590	+	0.0603667i
$926$	1.26814e9	+	5.79140e8i	1.59711	+	0.729375i
$927$	−9.27307e8	−	9.13225e8i	−1.16408	−	1.14641i
$928$	−6.37550e7	+	4.43426e8i	−0.0797756	+	0.554852i
$929$	−3.70857e8	−	1.26302e9i	−0.462550	−	1.57530i	−0.779211	−	0.626762i	$-0.784380\pi$
$929$	−3.70857e8	−	1.26302e9i	−0.462550	−	1.57530i	0.316660	−	0.948539i	$-0.397438\pi$
$930$	−5.87311e7	+	5.66666e8i	−0.0730162	+	0.704495i
$931$	−1.92813e8	+	1.23914e8i	−0.238939	+	0.153557i
$932$	1.38545e8	+	2.15580e8i	0.171136	+	0.266293i
$933$	−5.10341e8	−	5.28934e7i	−0.628371	−	0.0651264i
$934$	−4.44497e8	+	1.30516e8i	−0.545542	+	0.160186i
$935$	1.30515e8	+	1.87653e7i	0.159671	+	0.0229572i
$936$	−5.36915e8	+	5.45194e8i	−0.654754	+	0.664849i
$937$	2.82895e8	−	6.19453e8i	0.343879	−	0.752990i	−0.656120	−	0.754657i	$-0.727803\pi$
$937$	2.82895e8	−	6.19453e8i	0.343879	−	0.752990i	0.999999	+	0.00166679i	$0.000530557\pi$
$938$	−3.95408e8	+	1.34664e9i	−0.479112	+	1.63171i
$939$	−2.85139e8	+	6.95905e8i	−0.344398	+	0.840530i
$940$	5.21974e7	+	3.63041e8i	0.0628442	+	0.437091i
$941$	−2.40145e8	+	3.73673e8i	−0.288207	+	0.448459i	−0.954923	−	0.296853i	$-0.904063\pi$
$941$	−2.40145e8	+	3.73673e8i	−0.288207	+	0.448459i	0.666716	+	0.745312i	$0.267699\pi$
$942$	6.99829e8	−	6.56580e8i	0.837220	−	0.785479i
$943$	5.02209e8	−	5.07801e8i	0.598893	−	0.605562i
$944$		−	1.13467e9i		−	1.34882i
$945$	−3.71161e7	−	3.11548e8i	−0.0439812	−	0.369173i
$946$	−4.60573e7	−	3.20335e8i	−0.0544033	−	0.378383i
$947$	−1.00628e9	+	4.59551e8i	−1.18486	+	0.541108i	−0.907661	−	0.419705i	$-0.862134\pi$
$947$	−1.00628e9	+	4.59551e8i	−1.18486	+	0.541108i	−0.277200	+	0.960812i	$0.589406\pi$
$948$	−1.01677e8	−	2.01198e8i	−0.119343	−	0.236156i
$949$	5.36490e7	−	1.17475e8i	0.0627715	−	0.137451i
$950$	−5.17789e8	−	4.48667e8i	−0.603924	−	0.523303i
$951$	7.43517e8	+	1.06217e9i	0.864468	+	1.23496i
$952$	6.96938e8	−	2.04640e8i	0.807762	−	0.237180i
$953$	5.96895e8	−	5.17213e8i	0.689635	−	0.597572i	−0.237908	−	0.971288i	$-0.576462\pi$
$953$	5.96895e8	−	5.17213e8i	0.689635	−	0.597572i	0.927543	+	0.373715i	$0.121916\pi$
$954$	7.35059e7	+	1.32201e8i	0.0846597	+	0.152262i
$955$	1.78183e8	−	1.14511e8i	0.204577	−	0.131474i
$956$	−1.09589e8	+	9.49590e7i	−0.125427	+	0.108683i
$957$	9.69392e7	+	5.70165e7i	0.110602	+	0.0650526i
$958$	−1.22105e8	+	8.49260e8i	−0.138879	+	0.965926i
$959$	−4.98082e8	−	4.31591e8i	−0.564736	−	0.489346i
$960$	−1.74505e7	−	5.17688e7i	−0.0197240	−	0.0585132i
$961$	−5.05511e8	−	1.48432e8i	−0.569588	−	0.167246i
$962$	−4.06678e8	+	1.85724e8i	−0.456799	+	0.208613i
$963$	3.82632e7	+	4.83028e8i	0.0428453	+	0.540870i
$964$	3.36709e8	+	2.16390e8i	0.375858	+	0.241549i
$965$			2.85019e8i			0.317170i
$966$	5.67101e8	+	6.90399e8i	0.629114	+	0.765894i
$967$	8.65434e8			0.957094			0.478547	−	0.878062i	$-0.341164\pi$
$967$	8.65434e8			0.957094			0.478547	+	0.878062i	$0.341164\pi$
$968$	−2.89250e8	+	4.50081e8i	−0.318894	+	0.496209i
$969$	9.90559e8	+	7.92012e8i	1.08870	+	0.870484i
$970$	−1.12832e8	−	2.47068e8i	−0.123628	−	0.270708i
$971$	−4.56432e7	+	1.55447e8i	−0.0498561	+	0.169794i	−0.980658	−	0.195730i	$-0.937292\pi$
$971$	−4.56432e7	+	1.55447e8i	−0.0498561	+	0.169794i	0.930802	+	0.365525i	$0.119110\pi$
$972$	4.46382e8	−	8.93833e7i	0.486080	−	0.0973324i
$973$	6.37224e8	−	7.35396e8i	0.691758	−	0.798331i
$974$	8.82528e8	+	1.26888e8i	0.955106	+	0.137323i
$975$	9.54398e8	+	5.61346e8i	1.02971	+	0.605643i
$976$	−1.45594e8	−	1.68024e8i	−0.156601	−	0.180727i
$977$	−8.54524e7	−	1.32966e8i	−0.0916306	−	0.142580i	0.792412	−	0.609986i	$-0.208825\pi$
$977$	−8.54524e7	−	1.32966e8i	−0.0916306	−	0.142580i	−0.884043	+	0.467406i	$0.845189\pi$
$978$	1.31473e7	−	5.23454e7i	0.0140546	−	0.0559580i
$979$	2.66527e7	+	3.07589e7i	0.0284049	+	0.0327810i
$980$	−2.06966e7	−	7.04860e7i	−0.0219897	−	0.0748902i
$981$	−8.32851e8	−	1.74513e8i	−0.882187	−	0.184851i
$982$	1.54762e8	−	1.78605e8i	0.163429	−	0.188607i
$983$	9.65736e8	+	4.41037e8i	1.01671	+	0.464317i	0.852844	−	0.522166i	$-0.174876\pi$
$983$	9.65736e8	+	4.41037e8i	1.01671	+	0.464317i	0.163868	+	0.986482i	$0.447603\pi$
$984$	−2.25719e8	−	4.46652e8i	−0.236910	−	0.468796i
$985$	2.44916e7	+	5.36292e7i	0.0256277	+	0.0561167i
$986$	−1.20137e9	+	1.72730e8i	−1.25327	+	0.180193i
$987$	1.48799e9	−	2.74343e8i	1.54756	−	0.285327i
$988$	5.98639e8			0.620718
$989$	4.98636e8	−	1.35984e9i	0.515460	−	1.40572i
$990$	1.13417e8	+	7.24010e6i	0.116889	+	0.00746172i
$991$	4.81536e8	+	3.09464e8i	0.494775	+	0.317972i	0.764123	−	0.645070i	$-0.223172\pi$
$991$	4.81536e8	+	3.09464e8i	0.494775	+	0.317972i	−0.269349	+	0.963043i	$0.586808\pi$
$992$	−1.11246e9	+	1.59947e8i	−1.13959	+	0.163848i
$993$	−1.56403e8	+	3.81713e8i	−0.159734	+	0.389842i
$994$	3.44704e8	+	1.01214e8i	0.350984	+	0.103058i
$995$	−3.13956e8	−	1.43379e8i	−0.318713	−	0.145551i
$996$	−2.24773e7	−	5.68386e8i	−0.0227492	−	0.575262i
$997$	2.22213e8	−	1.54552e9i	0.224225	−	1.55952i	−0.497579	−	0.867419i	$-0.665778\pi$
$997$	2.22213e8	−	1.54552e9i	0.224225	−	1.55952i	0.721804	−	0.692098i	$-0.243313\pi$
$998$	1.27782e7	+	4.35186e7i	0.0128552	+	0.0437808i
$999$	−2.66804e8	−	4.49817e7i	−0.267606	−	0.0451170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.h.a.2.11	✓	460
3.2	odd	2	inner	69.7.h.a.2.36	yes	460
23.12	even	11	inner	69.7.h.a.35.36	yes	460
69.35	odd	22	inner	69.7.h.a.35.11	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.h.a.2.11	✓	460	1.1	even	1	trivial
69.7.h.a.2.36	yes	460	3.2	odd	2	inner
69.7.h.a.35.11	yes	460	69.35	odd	22	inner
69.7.h.a.35.36	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)

\(f(q)\)	\(=\)	\(q+(-5.28963 + 8.23082i) q^{2} +(16.8611 - 21.0880i) q^{3} +(-13.1797 - 28.8596i) q^{4} +(16.1556 - 55.0211i) q^{5} +(84.3823 + 250.328i) q^{6} +(-182.035 + 210.080i) q^{7} +(-312.548 - 44.9377i) q^{8} +(-160.405 - 711.134i) q^{9} +O(q^{10})\)	\(q+(-5.28963 + 8.23082i) q^{2} +(16.8611 - 21.0880i) q^{3} +(-13.1797 - 28.8596i) q^{4} +(16.1556 - 55.0211i) q^{5} +(84.3823 + 250.328i) q^{6} +(-182.035 + 210.080i) q^{7} +(-312.548 - 44.9377i) q^{8} +(-160.405 - 711.134i) q^{9} +(367.412 + 424.016i) q^{10} +(150.224 + 233.754i) q^{11} +(-830.815 - 208.671i) q^{12} +(2176.86 + 2512.22i) q^{13} +(-766.232 - 2609.55i) q^{14} +(-887.881 - 1268.41i) q^{15} +(3352.84 - 3869.38i) q^{16} +(7527.50 + 3437.69i) q^{17} +(6701.70 + 2441.37i) q^{18} +(2357.99 + 5163.29i) q^{19} +(-1800.81 + 258.918i) q^{20} +(1360.84 + 7380.94i) q^{21} -2718.62 q^{22} +(-10710.8 - 5771.81i) q^{23} +(-6217.56 + 5833.31i) q^{24} +(10378.3 + 6669.71i) q^{25} +(-32192.4 + 4628.57i) q^{26} +(-17701.0 - 8607.89i) q^{27} +(8462.00 + 2484.67i) q^{28} +(13635.9 + 6227.29i) q^{29} +(15136.6 - 598.588i) q^{30} +(-5352.17 + 37225.1i) q^{31} +(8419.45 + 28674.0i) q^{32} +(7462.34 + 773.422i) q^{33} +(-68112.8 + 43773.4i) q^{34} +(8617.94 + 13409.8i) q^{35} +(-18408.9 + 14001.8i) q^{36} +(13189.5 - 3872.80i) q^{37} +(-54971.0 - 7903.64i) q^{38} +(89682.0 - 3546.54i) q^{39} +(-7521.94 + 16470.8i) q^{40} +(-16537.5 + 56321.7i) q^{41} +(-67949.6 - 27841.6i) q^{42} +(16941.4 + 117830. i) q^{43} +(4766.12 - 7416.22i) q^{44} +(-41718.8 - 2663.15i) q^{45} +(104163. - 57628.4i) q^{46} -201598. i q^{47} +(-25064.8 - 135947. i) q^{48} +(5746.45 + 39967.4i) q^{49} +(-109794. + 50141.4i) q^{50} +(199416. - 100776. i) q^{51} +(43811.4 - 95933.6i) q^{52} +(16027.5 + 13887.9i) q^{53} +(164482. - 100161. i) q^{54} +(15288.4 - 4489.07i) q^{55} +(66335.4 - 57479.9i) q^{56} +(148642. + 37333.5i) q^{57} +(-123384. + 79294.4i) q^{58} +(167488. - 145129. i) q^{59} +(-24903.7 + 42341.1i) q^{60} +(6179.89 - 42982.0i) q^{61} +(-278083. - 240960. i) q^{62} +(178594. + 95753.6i) q^{63} +(33855.4 + 9940.85i) q^{64} +(173394. - 79186.3i) q^{65} +(-45838.9 + 57330.1i) q^{66} +(-434122. - 278994. i) q^{67} -262548. i q^{68} +(-302312. + 128551. i) q^{69} -155959. q^{70} +(-71415.1 + 111124. i) q^{71} +(18177.7 + 229472. i) q^{72} +(-16139.2 - 35339.8i) q^{73} +(-37891.4 + 129046. i) q^{74} +(315640. - 106398. i) q^{75} +(117933. - 136101. i) q^{76} +(-76453.2 - 10992.3i) q^{77} +(-445193. + 756916. i) q^{78} +(172335. + 198885. i) q^{79} +(-158730. - 246989. i) q^{80} +(-479981. + 228139. i) q^{81} +(-376097. - 434039. i) q^{82} +(187082. + 637143. i) q^{83} +(195075. - 136552. i) q^{84} +(310757. - 358633. i) q^{85} +(-1.05945e6 - 483837. i) q^{86} +(361237. - 182554. i) q^{87} +(-36448.0 - 79810.1i) q^{88} +(144983. - 20845.5i) q^{89} +(242597. - 329293. i) q^{90} -924033. q^{91} +(-25405.9 + 385181. i) q^{92} +(694759. + 740524. i) q^{93} +(1.65932e6 + 1.06638e6i) q^{94} +(322185. - 46323.1i) q^{95} +(746638. + 305927. i) q^{96} +(-464503. - 136390. i) q^{97} +(-359362. - 164115. i) q^{98} +(142133. - 144325. 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

Introduction

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