Properties

Label 162.9.d.d.107.2
Level $162$
Weight $9$
Character 162.107
Analytic conductor $65.995$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,9,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not 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: \(65.9953348299\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.2
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.9.d.d.53.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(9.79796 + 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(-202.083 + 116.673i) q^{5} +(1766.00 - 3058.80i) q^{7} +1448.15i q^{8} +O(q^{10})\) \(q+(9.79796 + 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(-202.083 + 116.673i) q^{5} +(1766.00 - 3058.80i) q^{7} +1448.15i q^{8} -2640.00 q^{10} +(-17474.7 - 10089.0i) q^{11} +(20912.0 + 36220.6i) q^{13} +(34606.4 - 19980.0i) q^{14} +(-8192.00 + 14189.0i) q^{16} -94784.8i q^{17} -36304.0 q^{19} +(-25866.6 - 14934.1i) q^{20} +(-114144. - 197703. i) q^{22} +(-358208. + 206812. i) q^{23} +(-168088. + 291136. i) q^{25} +473185. i q^{26} +452096. q^{28} +(233127. + 134596. i) q^{29} +(235598. + 408068. i) q^{31} +(-160530. + 92681.9i) q^{32} +(536184. - 928698. i) q^{34} +824175. i q^{35} -3.00740e6 q^{37} +(-355705. - 205366. i) q^{38} +(-168960. - 292647. i) q^{40} +(1.48553e6 - 857669. i) q^{41} +(-1.81186e6 + 3.13823e6i) q^{43} -2.58278e6i q^{44} -4.67962e6 q^{46} +(-5.20882e6 - 3.00731e6i) q^{47} +(-3.35511e6 - 5.81122e6i) q^{49} +(-3.29383e6 + 1.90169e6i) q^{50} +(-2.67674e6 + 4.63624e6i) q^{52} -1.02767e7i q^{53} +4.70844e6 q^{55} +(4.42962e6 + 2.55744e6i) q^{56} +(1.52278e6 + 2.63753e6i) q^{58} +(-2.32797e6 + 1.34405e6i) q^{59} +(2.72032e6 - 4.71172e6i) q^{61} +5.33097e6i q^{62} -2.09715e6 q^{64} +(-8.45192e6 - 4.87972e6i) q^{65} +(3.06079e6 + 5.30144e6i) q^{67} +(1.05070e7 - 6.06623e6i) q^{68} +(-4.66224e6 + 8.07524e6i) q^{70} +2.11941e7i q^{71} -4.90312e7 q^{73} +(-2.94664e7 - 1.70124e7i) q^{74} +(-2.32346e6 - 4.02434e6i) q^{76} +(-6.17205e7 + 3.56343e7i) q^{77} +(-4.17888e6 + 7.23803e6i) q^{79} -3.82313e6i q^{80} +1.94068e7 q^{82} +(-4.45066e7 - 2.56959e7i) q^{83} +(1.10588e7 + 1.91544e7i) q^{85} +(-3.55051e7 + 2.04989e7i) q^{86} +(1.46104e7 - 2.53060e7i) q^{88} -1.07337e8i q^{89} +1.47722e8 q^{91} +(-4.58507e7 - 2.64719e7i) q^{92} +(-3.40238e7 - 5.89310e7i) q^{94} +(7.33642e6 - 4.23568e6i) q^{95} +(-1.02157e7 + 1.76940e7i) q^{97} -7.59175e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 256 q^{4} + 7064 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 256 q^{4} + 7064 q^{7} - 10560 q^{10} + 83648 q^{13} - 32768 q^{16} - 145216 q^{19} - 456576 q^{22} - 672350 q^{25} + 1808384 q^{28} + 942392 q^{31} + 2144736 q^{34} - 12029608 q^{37} - 675840 q^{40} - 7247440 q^{43} - 18718464 q^{46} - 13420446 q^{49} - 10706944 q^{52} + 18833760 q^{55} + 6091104 q^{58} + 10881260 q^{61} - 8388608 q^{64} + 12243152 q^{67} - 18648960 q^{70} - 196124608 q^{73} - 9293824 q^{76} - 16715512 q^{79} + 77627328 q^{82} + 44235180 q^{85} + 58441728 q^{88} + 590889472 q^{91} - 136095360 q^{94} - 40862656 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.79796 + 5.65685i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 64.0000 + 110.851i 0.250000 + 0.433013i
\(5\) −202.083 + 116.673i −0.323333 + 0.186676i −0.652877 0.757464i \(-0.726438\pi\)
0.329544 + 0.944140i \(0.393105\pi\)
\(6\) 0 0
\(7\) 1766.00 3058.80i 0.735527 1.27397i −0.218965 0.975733i \(-0.570268\pi\)
0.954492 0.298237i \(-0.0963986\pi\)
\(8\) 1448.15i 0.353553i
\(9\) 0 0
\(10\) −2640.00 −0.264000
\(11\) −17474.7 10089.0i −1.19354 0.689092i −0.234435 0.972132i \(-0.575324\pi\)
−0.959108 + 0.283040i \(0.908657\pi\)
\(12\) 0 0
\(13\) 20912.0 + 36220.6i 0.732187 + 1.26819i 0.955946 + 0.293541i \(0.0948337\pi\)
−0.223759 + 0.974644i \(0.571833\pi\)
\(14\) 34606.4 19980.0i 0.900833 0.520096i
\(15\) 0 0
\(16\) −8192.00 + 14189.0i −0.125000 + 0.216506i
\(17\) 94784.8i 1.13486i −0.823421 0.567431i \(-0.807937\pi\)
0.823421 0.567431i \(-0.192063\pi\)
\(18\) 0 0
\(19\) −36304.0 −0.278574 −0.139287 0.990252i \(-0.544481\pi\)
−0.139287 + 0.990252i \(0.544481\pi\)
\(20\) −25866.6 14934.1i −0.161666 0.0933381i
\(21\) 0 0
\(22\) −114144. 197703.i −0.487262 0.843962i
\(23\) −358208. + 206812.i −1.28004 + 0.739033i −0.976856 0.213898i \(-0.931384\pi\)
−0.303187 + 0.952931i \(0.598051\pi\)
\(24\) 0 0
\(25\) −168088. + 291136.i −0.430304 + 0.745308i
\(26\) 473185.i 1.03547i
\(27\) 0 0
\(28\) 452096. 0.735527
\(29\) 233127. + 134596.i 0.329609 + 0.190300i 0.655668 0.755050i \(-0.272387\pi\)
−0.326058 + 0.945350i \(0.605721\pi\)
\(30\) 0 0
\(31\) 235598. + 408068.i 0.255108 + 0.441861i 0.964925 0.262526i \(-0.0845555\pi\)
−0.709817 + 0.704387i \(0.751222\pi\)
\(32\) −160530. + 92681.9i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 536184. 928698.i 0.401234 0.694958i
\(35\) 824175.i 0.549221i
\(36\) 0 0
\(37\) −3.00740e6 −1.60467 −0.802333 0.596877i \(-0.796408\pi\)
−0.802333 + 0.596877i \(0.796408\pi\)
\(38\) −355705. 205366.i −0.170591 0.0984907i
\(39\) 0 0
\(40\) −168960. 292647.i −0.0660000 0.114315i
\(41\) 1.48553e6 857669.i 0.525708 0.303518i −0.213559 0.976930i \(-0.568505\pi\)
0.739267 + 0.673412i \(0.235172\pi\)
\(42\) 0 0
\(43\) −1.81186e6 + 3.13823e6i −0.529969 + 0.917934i 0.469419 + 0.882975i \(0.344463\pi\)
−0.999389 + 0.0349586i \(0.988870\pi\)
\(44\) 2.58278e6i 0.689092i
\(45\) 0 0
\(46\) −4.67962e6 −1.04515
\(47\) −5.20882e6 3.00731e6i −1.06745 0.616293i −0.139966 0.990156i \(-0.544699\pi\)
−0.927484 + 0.373864i \(0.878033\pi\)
\(48\) 0 0
\(49\) −3.35511e6 5.81122e6i −0.582000 1.00805i
\(50\) −3.29383e6 + 1.90169e6i −0.527013 + 0.304271i
\(51\) 0 0
\(52\) −2.67674e6 + 4.63624e6i −0.366094 + 0.634093i
\(53\) 1.02767e7i 1.30241i −0.758901 0.651206i \(-0.774263\pi\)
0.758901 0.651206i \(-0.225737\pi\)
\(54\) 0 0
\(55\) 4.70844e6 0.514548
\(56\) 4.42962e6 + 2.55744e6i 0.450416 + 0.260048i
\(57\) 0 0
\(58\) 1.52278e6 + 2.63753e6i 0.134563 + 0.233069i
\(59\) −2.32797e6 + 1.34405e6i −0.192118 + 0.110919i −0.592974 0.805222i \(-0.702046\pi\)
0.400856 + 0.916141i \(0.368713\pi\)
\(60\) 0 0
\(61\) 2.72032e6 4.71172e6i 0.196472 0.340299i −0.750910 0.660404i \(-0.770385\pi\)
0.947382 + 0.320105i \(0.103718\pi\)
\(62\) 5.33097e6i 0.360778i
\(63\) 0 0
\(64\) −2.09715e6 −0.125000
\(65\) −8.45192e6 4.87972e6i −0.473480 0.273364i
\(66\) 0 0
\(67\) 3.06079e6 + 5.30144e6i 0.151892 + 0.263084i 0.931923 0.362657i \(-0.118130\pi\)
−0.780031 + 0.625741i \(0.784797\pi\)
\(68\) 1.05070e7 6.06623e6i 0.491410 0.283716i
\(69\) 0 0
\(70\) −4.66224e6 + 8.07524e6i −0.194179 + 0.336328i
\(71\) 2.11941e7i 0.834029i 0.908900 + 0.417014i \(0.136924\pi\)
−0.908900 + 0.417014i \(0.863076\pi\)
\(72\) 0 0
\(73\) −4.90312e7 −1.72656 −0.863278 0.504729i \(-0.831593\pi\)
−0.863278 + 0.504729i \(0.831593\pi\)
\(74\) −2.94664e7 1.70124e7i −0.982653 0.567335i
\(75\) 0 0
\(76\) −2.32346e6 4.02434e6i −0.0696434 0.120626i
\(77\) −6.17205e7 + 3.56343e7i −1.75577 + 1.01369i
\(78\) 0 0
\(79\) −4.17888e6 + 7.23803e6i −0.107288 + 0.185828i −0.914671 0.404200i \(-0.867550\pi\)
0.807383 + 0.590028i \(0.200883\pi\)
\(80\) 3.82313e6i 0.0933381i
\(81\) 0 0
\(82\) 1.94068e7 0.429239
\(83\) −4.45066e7 2.56959e7i −0.937804 0.541441i −0.0485328 0.998822i \(-0.515455\pi\)
−0.889271 + 0.457380i \(0.848788\pi\)
\(84\) 0 0
\(85\) 1.10588e7 + 1.91544e7i 0.211852 + 0.366938i
\(86\) −3.55051e7 + 2.04989e7i −0.649077 + 0.374745i
\(87\) 0 0
\(88\) 1.46104e7 2.53060e7i 0.243631 0.421981i
\(89\) 1.07337e8i 1.71076i −0.517997 0.855382i \(-0.673322\pi\)
0.517997 0.855382i \(-0.326678\pi\)
\(90\) 0 0
\(91\) 1.47722e8 2.15417
\(92\) −4.58507e7 2.64719e7i −0.640021 0.369517i
\(93\) 0 0
\(94\) −3.40238e7 5.89310e7i −0.435785 0.754801i
\(95\) 7.33642e6 4.23568e6i 0.0900720 0.0520031i
\(96\) 0 0
\(97\) −1.02157e7 + 1.76940e7i −0.115393 + 0.199867i −0.917937 0.396727i \(-0.870146\pi\)
0.802544 + 0.596593i \(0.203479\pi\)
\(98\) 7.59175e7i 0.823072i
\(99\) 0 0
\(100\) −4.30304e7 −0.430304
\(101\) −1.46863e8 8.47915e7i −1.41133 0.814830i −0.415813 0.909450i \(-0.636503\pi\)
−0.995513 + 0.0946199i \(0.969836\pi\)
\(102\) 0 0
\(103\) 1.49126e7 + 2.58294e7i 0.132497 + 0.229491i 0.924638 0.380846i \(-0.124367\pi\)
−0.792142 + 0.610337i \(0.791034\pi\)
\(104\) −5.24531e7 + 3.02838e7i −0.448371 + 0.258867i
\(105\) 0 0
\(106\) 5.81336e7 1.00690e8i 0.460472 0.797562i
\(107\) 1.22823e8i 0.937014i 0.883460 + 0.468507i \(0.155208\pi\)
−0.883460 + 0.468507i \(0.844792\pi\)
\(108\) 0 0
\(109\) −4.88844e7 −0.346310 −0.173155 0.984895i \(-0.555396\pi\)
−0.173155 + 0.984895i \(0.555396\pi\)
\(110\) 4.61331e7 + 2.66350e7i 0.315095 + 0.181920i
\(111\) 0 0
\(112\) 2.89341e7 + 5.01154e7i 0.183882 + 0.318492i
\(113\) −1.63891e8 + 9.46226e7i −1.00518 + 0.580338i −0.909775 0.415101i \(-0.863746\pi\)
−0.0953999 + 0.995439i \(0.530413\pi\)
\(114\) 0 0
\(115\) 4.82585e7 8.35862e7i 0.275920 0.477907i
\(116\) 3.44565e7i 0.190300i
\(117\) 0 0
\(118\) −3.04124e7 −0.156864
\(119\) −2.89928e8 1.67390e8i −1.44578 0.834722i
\(120\) 0 0
\(121\) 9.63964e7 + 1.66963e8i 0.449696 + 0.778897i
\(122\) 5.33071e7 3.07769e7i 0.240628 0.138926i
\(123\) 0 0
\(124\) −3.01565e7 + 5.22327e7i −0.127554 + 0.220930i
\(125\) 1.69595e8i 0.694662i
\(126\) 0 0
\(127\) 3.39908e8 1.30661 0.653306 0.757094i \(-0.273381\pi\)
0.653306 + 0.757094i \(0.273381\pi\)
\(128\) −2.05478e7 1.18633e7i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −5.52077e7 9.56225e7i −0.193297 0.334801i
\(131\) −6.66178e7 + 3.84618e7i −0.226207 + 0.130600i −0.608821 0.793308i \(-0.708357\pi\)
0.382614 + 0.923908i \(0.375024\pi\)
\(132\) 0 0
\(133\) −6.41129e7 + 1.11047e8i −0.204898 + 0.354894i
\(134\) 6.92577e7i 0.214807i
\(135\) 0 0
\(136\) 1.37263e8 0.401234
\(137\) 1.10729e8 + 6.39295e7i 0.314326 + 0.181476i 0.648860 0.760907i \(-0.275246\pi\)
−0.334535 + 0.942383i \(0.608579\pi\)
\(138\) 0 0
\(139\) −4.54464e6 7.87155e6i −0.0121742 0.0210863i 0.859874 0.510506i \(-0.170542\pi\)
−0.872048 + 0.489420i \(0.837209\pi\)
\(140\) −9.13609e7 + 5.27472e7i −0.237820 + 0.137305i
\(141\) 0 0
\(142\) −1.19892e8 + 2.07659e8i −0.294874 + 0.510736i
\(143\) 8.43925e8i 2.01818i
\(144\) 0 0
\(145\) −6.28145e7 −0.142098
\(146\) −4.80405e8 2.77362e8i −1.05730 0.610430i
\(147\) 0 0
\(148\) −1.92474e8 3.33374e8i −0.401166 0.694841i
\(149\) −1.60391e8 + 9.26018e7i −0.325413 + 0.187877i −0.653803 0.756665i \(-0.726827\pi\)
0.328390 + 0.944542i \(0.393494\pi\)
\(150\) 0 0
\(151\) 1.67801e8 2.90639e8i 0.322764 0.559044i −0.658293 0.752762i \(-0.728721\pi\)
0.981057 + 0.193717i \(0.0620545\pi\)
\(152\) 5.25738e7i 0.0984907i
\(153\) 0 0
\(154\) −8.06313e8 −1.43358
\(155\) −9.52207e7 5.49757e7i −0.164970 0.0952453i
\(156\) 0 0
\(157\) 1.00815e8 + 1.74617e8i 0.165931 + 0.287401i 0.936986 0.349368i \(-0.113604\pi\)
−0.771054 + 0.636769i \(0.780270\pi\)
\(158\) −8.18890e7 + 4.72786e7i −0.131400 + 0.0758641i
\(159\) 0 0
\(160\) 2.16269e7 3.74589e7i 0.0330000 0.0571577i
\(161\) 1.46092e9i 2.17431i
\(162\) 0 0
\(163\) −5.27661e8 −0.747488 −0.373744 0.927532i \(-0.621926\pi\)
−0.373744 + 0.927532i \(0.621926\pi\)
\(164\) 1.90147e8 + 1.09782e8i 0.262854 + 0.151759i
\(165\) 0 0
\(166\) −2.90716e8 5.03535e8i −0.382857 0.663128i
\(167\) 1.57284e8 9.08077e7i 0.202217 0.116750i −0.395472 0.918478i \(-0.629419\pi\)
0.597689 + 0.801728i \(0.296086\pi\)
\(168\) 0 0
\(169\) −4.66758e8 + 8.08449e8i −0.572196 + 0.991073i
\(170\) 2.50232e8i 0.299604i
\(171\) 0 0
\(172\) −4.63836e8 −0.529969
\(173\) −6.11812e7 3.53230e7i −0.0683020 0.0394342i 0.465460 0.885069i \(-0.345889\pi\)
−0.533762 + 0.845635i \(0.679222\pi\)
\(174\) 0 0
\(175\) 5.93685e8 + 1.02829e9i 0.633000 + 1.09639i
\(176\) 2.86305e8 1.65298e8i 0.298386 0.172273i
\(177\) 0 0
\(178\) 6.07191e8 1.05169e9i 0.604847 1.04763i
\(179\) 7.90371e7i 0.0769873i 0.999259 + 0.0384936i \(0.0122559\pi\)
−0.999259 + 0.0384936i \(0.987744\pi\)
\(180\) 0 0
\(181\) 5.48168e8 0.510739 0.255370 0.966844i \(-0.417803\pi\)
0.255370 + 0.966844i \(0.417803\pi\)
\(182\) 1.44738e9 + 8.35644e8i 1.31916 + 0.761615i
\(183\) 0 0
\(184\) −2.99495e8 5.18741e8i −0.261288 0.452564i
\(185\) 6.07745e8 3.50881e8i 0.518841 0.299553i
\(186\) 0 0
\(187\) −9.56284e8 + 1.65633e9i −0.782025 + 1.35451i
\(188\) 7.69872e8i 0.616293i
\(189\) 0 0
\(190\) 9.58426e7 0.0735435
\(191\) 1.94507e9 + 1.12299e9i 1.46151 + 0.843803i 0.999081 0.0428538i \(-0.0136450\pi\)
0.462428 + 0.886657i \(0.346978\pi\)
\(192\) 0 0
\(193\) −3.27788e8 5.67745e8i −0.236245 0.409189i 0.723389 0.690441i \(-0.242584\pi\)
−0.959634 + 0.281252i \(0.909250\pi\)
\(194\) −2.00185e8 + 1.15577e8i −0.141327 + 0.0815952i
\(195\) 0 0
\(196\) 4.29454e8 7.43837e8i 0.291000 0.504026i
\(197\) 4.48231e8i 0.297603i 0.988867 + 0.148801i \(0.0475415\pi\)
−0.988867 + 0.148801i \(0.952458\pi\)
\(198\) 0 0
\(199\) 7.34930e8 0.468634 0.234317 0.972160i \(-0.424715\pi\)
0.234317 + 0.972160i \(0.424715\pi\)
\(200\) −4.21610e8 2.43417e8i −0.263506 0.152135i
\(201\) 0 0
\(202\) −9.59307e8 1.66157e9i −0.576172 0.997959i
\(203\) 8.23403e8 4.75392e8i 0.484873 0.279942i
\(204\) 0 0
\(205\) −2.00133e8 + 3.46640e8i −0.113319 + 0.196274i
\(206\) 3.37434e8i 0.187379i
\(207\) 0 0
\(208\) −6.85244e8 −0.366094
\(209\) 6.34400e8 + 3.66271e8i 0.332490 + 0.191963i
\(210\) 0 0
\(211\) 1.63400e9 + 2.83017e9i 0.824370 + 1.42785i 0.902400 + 0.430900i \(0.141804\pi\)
−0.0780291 + 0.996951i \(0.524863\pi\)
\(212\) 1.13918e9 6.57707e8i 0.563961 0.325603i
\(213\) 0 0
\(214\) −6.94794e8 + 1.20342e9i −0.331284 + 0.573802i
\(215\) 8.45578e8i 0.395731i
\(216\) 0 0
\(217\) 1.66426e9 0.750556
\(218\) −4.78968e8 2.76532e8i −0.212070 0.122439i
\(219\) 0 0
\(220\) 3.01340e8 + 5.21936e8i 0.128637 + 0.222806i
\(221\) 3.43317e9 1.98214e9i 1.43922 0.830932i
\(222\) 0 0
\(223\) 1.90420e9 3.29818e9i 0.770005 1.33369i −0.167554 0.985863i \(-0.553587\pi\)
0.937559 0.347825i \(-0.113080\pi\)
\(224\) 6.54705e8i 0.260048i
\(225\) 0 0
\(226\) −2.14107e9 −0.820722
\(227\) 3.76419e9 + 2.17325e9i 1.41765 + 0.818478i 0.996092 0.0883248i \(-0.0281513\pi\)
0.421554 + 0.906803i \(0.361485\pi\)
\(228\) 0 0
\(229\) 1.43198e9 + 2.48027e9i 0.520711 + 0.901897i 0.999710 + 0.0240820i \(0.00766629\pi\)
−0.478999 + 0.877815i \(0.659000\pi\)
\(230\) 9.45670e8 5.45983e8i 0.337931 0.195105i
\(231\) 0 0
\(232\) −1.94915e8 + 3.37603e8i −0.0672813 + 0.116535i
\(233\) 5.57102e8i 0.189022i −0.995524 0.0945108i \(-0.969871\pi\)
0.995524 0.0945108i \(-0.0301287\pi\)
\(234\) 0 0
\(235\) 1.40348e9 0.460189
\(236\) −2.97980e8 1.72039e8i −0.0960591 0.0554597i
\(237\) 0 0
\(238\) −1.89380e9 3.28016e9i −0.590237 1.02232i
\(239\) −1.13303e9 + 6.54155e8i −0.347256 + 0.200488i −0.663476 0.748198i \(-0.730920\pi\)
0.316220 + 0.948686i \(0.397586\pi\)
\(240\) 0 0
\(241\) 2.42091e9 4.19314e9i 0.717647 1.24300i −0.244283 0.969704i \(-0.578553\pi\)
0.961930 0.273297i \(-0.0881140\pi\)
\(242\) 2.18120e9i 0.635967i
\(243\) 0 0
\(244\) 6.96401e8 0.196472
\(245\) 1.35602e9 + 7.82899e8i 0.376359 + 0.217291i
\(246\) 0 0
\(247\) −7.59189e8 1.31495e9i −0.203968 0.353283i
\(248\) −5.90945e8 + 3.41182e8i −0.156221 + 0.0901945i
\(249\) 0 0
\(250\) 9.59376e8 1.66169e9i 0.245600 0.425392i
\(251\) 7.77711e9i 1.95940i 0.200466 + 0.979701i \(0.435754\pi\)
−0.200466 + 0.979701i \(0.564246\pi\)
\(252\) 0 0
\(253\) 8.34610e9 2.03705
\(254\) 3.33041e9 + 1.92281e9i 0.800134 + 0.461957i
\(255\) 0 0
\(256\) −1.34218e8 2.32472e8i −0.0312500 0.0541266i
\(257\) −4.92074e9 + 2.84099e9i −1.12797 + 0.651234i −0.943424 0.331589i \(-0.892415\pi\)
−0.184547 + 0.982824i \(0.559082\pi\)
\(258\) 0 0
\(259\) −5.31107e9 + 9.19905e9i −1.18027 + 2.04430i
\(260\) 1.24921e9i 0.273364i
\(261\) 0 0
\(262\) −8.70292e8 −0.184697
\(263\) −9.05270e8 5.22658e8i −0.189215 0.109243i 0.402400 0.915464i \(-0.368176\pi\)
−0.591615 + 0.806221i \(0.701509\pi\)
\(264\) 0 0
\(265\) 1.19901e9 + 2.07674e9i 0.243129 + 0.421113i
\(266\) −1.25635e9 + 7.25354e8i −0.250948 + 0.144885i
\(267\) 0 0
\(268\) −3.91781e8 + 6.78584e8i −0.0759458 + 0.131542i
\(269\) 4.92684e9i 0.940935i −0.882417 0.470467i \(-0.844085\pi\)
0.882417 0.470467i \(-0.155915\pi\)
\(270\) 0 0
\(271\) −6.59224e9 −1.22224 −0.611119 0.791539i \(-0.709280\pi\)
−0.611119 + 0.791539i \(0.709280\pi\)
\(272\) 1.34490e9 + 7.76477e8i 0.245705 + 0.141858i
\(273\) 0 0
\(274\) 7.23280e8 + 1.25276e9i 0.128323 + 0.222262i
\(275\) 5.87454e9 3.39167e9i 1.02717 0.593038i
\(276\) 0 0
\(277\) 6.07949e7 1.05300e8i 0.0103264 0.0178858i −0.860816 0.508916i \(-0.830046\pi\)
0.871142 + 0.491030i \(0.163380\pi\)
\(278\) 1.02834e8i 0.0172169i
\(279\) 0 0
\(280\) −1.19353e9 −0.194179
\(281\) −4.85527e9 2.80319e9i −0.778732 0.449601i 0.0572486 0.998360i \(-0.481767\pi\)
−0.835981 + 0.548759i \(0.815101\pi\)
\(282\) 0 0
\(283\) −8.12798e8 1.40781e9i −0.126718 0.219481i 0.795685 0.605710i \(-0.207111\pi\)
−0.922403 + 0.386229i \(0.873778\pi\)
\(284\) −2.34939e9 + 1.35642e9i −0.361145 + 0.208507i
\(285\) 0 0
\(286\) 4.77396e9 8.26874e9i 0.713534 1.23588i
\(287\) 6.05857e9i 0.892982i
\(288\) 0 0
\(289\) −2.00841e9 −0.287912
\(290\) −6.15454e8 3.55333e8i −0.0870169 0.0502392i
\(291\) 0 0
\(292\) −3.13799e9 5.43516e9i −0.431639 0.747621i
\(293\) 3.64813e9 2.10625e9i 0.494993 0.285784i −0.231650 0.972799i \(-0.574413\pi\)
0.726644 + 0.687015i \(0.241079\pi\)
\(294\) 0 0
\(295\) 3.13628e8 5.43220e8i 0.0414121 0.0717278i
\(296\) 4.35518e9i 0.567335i
\(297\) 0 0
\(298\) −2.09534e9 −0.265699
\(299\) −1.49817e10 8.64970e9i −1.87446 1.08222i
\(300\) 0 0
\(301\) 6.39949e9 + 1.10842e10i 0.779613 + 1.35033i
\(302\) 3.28821e9 1.89845e9i 0.395304 0.228229i
\(303\) 0 0
\(304\) 2.97402e8 5.15116e8i 0.0348217 0.0603130i
\(305\) 1.26955e9i 0.146706i
\(306\) 0 0
\(307\) 5.88475e9 0.662483 0.331241 0.943546i \(-0.392533\pi\)
0.331241 + 0.943546i \(0.392533\pi\)
\(308\) −7.90022e9 4.56120e9i −0.877883 0.506846i
\(309\) 0 0
\(310\) −6.21979e8 1.07730e9i −0.0673486 0.116651i
\(311\) −8.48710e9 + 4.90003e9i −0.907231 + 0.523790i −0.879539 0.475827i \(-0.842149\pi\)
−0.0276917 + 0.999617i \(0.508816\pi\)
\(312\) 0 0
\(313\) −1.88081e9 + 3.25766e9i −0.195960 + 0.339413i −0.947215 0.320599i \(-0.896116\pi\)
0.751255 + 0.660012i \(0.229449\pi\)
\(314\) 2.28119e9i 0.234662i
\(315\) 0 0
\(316\) −1.06979e9 −0.107288
\(317\) 1.46660e10 + 8.46743e9i 1.45236 + 0.838522i 0.998615 0.0526083i \(-0.0167535\pi\)
0.453748 + 0.891130i \(0.350087\pi\)
\(318\) 0 0
\(319\) −2.71587e9 4.70403e9i −0.262269 0.454263i
\(320\) 4.23799e8 2.44680e8i 0.0404166 0.0233345i
\(321\) 0 0
\(322\) −8.26420e9 + 1.43140e10i −0.768736 + 1.33149i
\(323\) 3.44107e9i 0.316143i
\(324\) 0 0
\(325\) −1.40602e10 −1.26025
\(326\) −5.17000e9 2.98490e9i −0.457741 0.264277i
\(327\) 0 0
\(328\) 1.24204e9 + 2.15127e9i 0.107310 + 0.185866i
\(329\) −1.83975e10 + 1.06218e10i −1.57028 + 0.906599i
\(330\) 0 0
\(331\) −1.59499e9 + 2.76261e9i −0.132876 + 0.230148i −0.924784 0.380492i \(-0.875755\pi\)
0.791908 + 0.610640i \(0.209088\pi\)
\(332\) 6.57815e9i 0.541441i
\(333\) 0 0
\(334\) 2.05474e9 0.165109
\(335\) −1.23707e9 7.14220e8i −0.0982231 0.0567091i
\(336\) 0 0
\(337\) −8.31888e9 1.44087e10i −0.644978 1.11714i −0.984307 0.176467i \(-0.943533\pi\)
0.339328 0.940668i \(-0.389800\pi\)
\(338\) −9.14655e9 + 5.28077e9i −0.700795 + 0.404604i
\(339\) 0 0
\(340\) −1.41553e9 + 2.45176e9i −0.105926 + 0.183469i
\(341\) 9.50779e9i 0.703173i
\(342\) 0 0
\(343\) −3.33923e9 −0.241251
\(344\) −4.54465e9 2.62385e9i −0.324539 0.187372i
\(345\) 0 0
\(346\) −3.99634e8 6.92186e8i −0.0278842 0.0482968i
\(347\) −9.28877e8 + 5.36287e8i −0.0640678 + 0.0369896i −0.531692 0.846938i \(-0.678444\pi\)
0.467624 + 0.883928i \(0.345110\pi\)
\(348\) 0 0
\(349\) 1.16151e9 2.01180e9i 0.0782928 0.135607i −0.824221 0.566269i \(-0.808386\pi\)
0.902513 + 0.430662i \(0.141720\pi\)
\(350\) 1.34336e10i 0.895198i
\(351\) 0 0
\(352\) 3.74027e9 0.243631
\(353\) −1.71912e10 9.92532e9i −1.10715 0.639213i −0.169060 0.985606i \(-0.554073\pi\)
−0.938090 + 0.346393i \(0.887406\pi\)
\(354\) 0 0
\(355\) −2.47277e9 4.28296e9i −0.155693 0.269669i
\(356\) 1.18985e10 6.86958e9i 0.740783 0.427691i
\(357\) 0 0
\(358\) −4.47102e8 + 7.74403e8i −0.0272191 + 0.0471449i
\(359\) 1.03679e10i 0.624187i −0.950051 0.312094i \(-0.898970\pi\)
0.950051 0.312094i \(-0.101030\pi\)
\(360\) 0 0
\(361\) −1.56656e10 −0.922397
\(362\) 5.37093e9 + 3.10091e9i 0.312763 + 0.180574i
\(363\) 0 0
\(364\) 9.45423e9 + 1.63752e10i 0.538543 + 0.932785i
\(365\) 9.90836e9 5.72059e9i 0.558252 0.322307i
\(366\) 0 0
\(367\) 1.01440e10 1.75699e10i 0.559171 0.968512i −0.438395 0.898782i \(-0.644453\pi\)
0.997566 0.0697299i \(-0.0222137\pi\)
\(368\) 6.77681e9i 0.369517i
\(369\) 0 0
\(370\) 7.93954e9 0.423632
\(371\) −3.14343e10 1.81486e10i −1.65923 0.957960i
\(372\) 0 0
\(373\) −1.11055e10 1.92354e10i −0.573726 0.993723i −0.996179 0.0873379i \(-0.972164\pi\)
0.422453 0.906385i \(-0.361169\pi\)
\(374\) −1.87393e10 + 1.08191e10i −0.957781 + 0.552975i
\(375\) 0 0
\(376\) 4.35505e9 7.54317e9i 0.217892 0.377401i
\(377\) 1.12587e10i 0.557341i
\(378\) 0 0
\(379\) 1.23790e10 0.599967 0.299983 0.953944i \(-0.403019\pi\)
0.299983 + 0.953944i \(0.403019\pi\)
\(380\) 9.39061e8 + 5.42167e8i 0.0450360 + 0.0260015i
\(381\) 0 0
\(382\) 1.27051e10 + 2.20059e10i 0.596659 + 1.03344i
\(383\) −2.51466e10 + 1.45184e10i −1.16865 + 0.674720i −0.953361 0.301831i \(-0.902402\pi\)
−0.215287 + 0.976551i \(0.569069\pi\)
\(384\) 0 0
\(385\) 8.31511e9 1.44022e10i 0.378464 0.655519i
\(386\) 7.41699e9i 0.334101i
\(387\) 0 0
\(388\) −2.61521e9 −0.115393
\(389\) −2.54384e10 1.46869e10i −1.11094 0.641404i −0.171870 0.985120i \(-0.554981\pi\)
−0.939074 + 0.343716i \(0.888314\pi\)
\(390\) 0 0
\(391\) 1.96026e10 + 3.39527e10i 0.838701 + 1.45267i
\(392\) 8.41555e9 4.85872e9i 0.356400 0.205768i
\(393\) 0 0
\(394\) −2.53558e9 + 4.39175e9i −0.105219 + 0.182244i
\(395\) 1.95024e9i 0.0801125i
\(396\) 0 0
\(397\) 2.58158e10 1.03926 0.519630 0.854391i \(-0.326070\pi\)
0.519630 + 0.854391i \(0.326070\pi\)
\(398\) 7.20082e9 + 4.15739e9i 0.286979 + 0.165687i
\(399\) 0 0
\(400\) −2.75395e9 4.76997e9i −0.107576 0.186327i
\(401\) 5.67198e9 3.27472e9i 0.219360 0.126647i −0.386294 0.922376i \(-0.626245\pi\)
0.605654 + 0.795728i \(0.292912\pi\)
\(402\) 0 0
\(403\) −9.85365e9 + 1.70670e10i −0.373574 + 0.647050i
\(404\) 2.17066e10i 0.814830i
\(405\) 0 0
\(406\) 1.07569e10 0.395897
\(407\) 5.25533e10 + 3.03417e10i 1.91524 + 1.10576i
\(408\) 0 0
\(409\) −2.20907e10 3.82622e10i −0.789433 1.36734i −0.926314 0.376751i \(-0.877041\pi\)
0.136881 0.990588i \(-0.456292\pi\)
\(410\) −3.92179e9 + 2.26425e9i −0.138787 + 0.0801287i
\(411\) 0 0
\(412\) −1.90882e9 + 3.30616e9i −0.0662483 + 0.114745i
\(413\) 9.49438e9i 0.326337i
\(414\) 0 0
\(415\) 1.19920e10 0.404297
\(416\) −6.71400e9 3.87633e9i −0.224186 0.129434i
\(417\) 0 0
\(418\) 4.14388e9 + 7.17742e9i 0.135738 + 0.235106i
\(419\) 3.91899e10 2.26263e10i 1.27150 0.734103i 0.296233 0.955116i \(-0.404270\pi\)
0.975271 + 0.221013i \(0.0709363\pi\)
\(420\) 0 0
\(421\) −1.09596e10 + 1.89826e10i −0.348873 + 0.604266i −0.986050 0.166452i \(-0.946769\pi\)
0.637176 + 0.770718i \(0.280102\pi\)
\(422\) 3.69732e10i 1.16584i
\(423\) 0 0
\(424\) 1.48822e10 0.460472
\(425\) 2.75953e10 + 1.59321e10i 0.845822 + 0.488336i
\(426\) 0 0
\(427\) −9.60815e9 1.66418e10i −0.289020 0.500598i
\(428\) −1.36151e10 + 7.86070e9i −0.405739 + 0.234254i
\(429\) 0 0
\(430\) 4.78331e9 8.28494e9i 0.139912 0.242335i
\(431\) 9.62022e9i 0.278789i −0.990237 0.139395i \(-0.955484\pi\)
0.990237 0.139395i \(-0.0445157\pi\)
\(432\) 0 0
\(433\) −4.64805e10 −1.32227 −0.661134 0.750268i \(-0.729924\pi\)
−0.661134 + 0.750268i \(0.729924\pi\)
\(434\) 1.63064e10 + 9.41450e9i 0.459620 + 0.265362i
\(435\) 0 0
\(436\) −3.12860e9 5.41890e9i −0.0865774 0.149956i
\(437\) 1.30044e10 7.50809e9i 0.356586 0.205875i
\(438\) 0 0
\(439\) 1.86137e10 3.22398e10i 0.501158 0.868030i −0.498842 0.866693i \(-0.666241\pi\)
0.999999 0.00133709i \(-0.000425610\pi\)
\(440\) 6.81855e9i 0.181920i
\(441\) 0 0
\(442\) 4.48507e10 1.17511
\(443\) 4.62286e10 + 2.66901e10i 1.20032 + 0.693003i 0.960626 0.277846i \(-0.0896206\pi\)
0.239691 + 0.970849i \(0.422954\pi\)
\(444\) 0 0
\(445\) 1.25233e10 + 2.16910e10i 0.319359 + 0.553146i
\(446\) 3.73146e10 2.15436e10i 0.943060 0.544476i
\(447\) 0 0
\(448\) −3.70357e9 + 6.41477e9i −0.0919409 + 0.159246i
\(449\) 4.16287e9i 0.102425i 0.998688 + 0.0512126i \(0.0163086\pi\)
−0.998688 + 0.0512126i \(0.983691\pi\)
\(450\) 0 0
\(451\) −3.46121e10 −0.836607
\(452\) −2.09781e10 1.21117e10i −0.502588 0.290169i
\(453\) 0 0
\(454\) 2.45876e10 + 4.25869e10i 0.578752 + 1.00243i
\(455\) −2.98522e10 + 1.72352e10i −0.696515 + 0.402133i
\(456\) 0 0
\(457\) 1.45988e10 2.52858e10i 0.334697 0.579712i −0.648730 0.761019i \(-0.724699\pi\)
0.983427 + 0.181307i \(0.0580328\pi\)
\(458\) 3.24021e10i 0.736396i
\(459\) 0 0
\(460\) 1.23542e10 0.275920
\(461\) −1.43559e10 8.28837e9i −0.317853 0.183512i 0.332582 0.943074i \(-0.392080\pi\)
−0.650435 + 0.759562i \(0.725413\pi\)
\(462\) 0 0
\(463\) 1.83424e10 + 3.17699e10i 0.399146 + 0.691341i 0.993621 0.112773i \(-0.0359734\pi\)
−0.594475 + 0.804114i \(0.702640\pi\)
\(464\) −3.81954e9 + 2.20522e9i −0.0824024 + 0.0475750i
\(465\) 0 0
\(466\) 3.15145e9 5.45847e9i 0.0668292 0.115752i
\(467\) 1.80368e10i 0.379220i 0.981860 + 0.189610i \(0.0607223\pi\)
−0.981860 + 0.189610i \(0.939278\pi\)
\(468\) 0 0
\(469\) 2.16214e10 0.446882
\(470\) 1.37513e10 + 7.93930e9i 0.281807 + 0.162701i
\(471\) 0 0
\(472\) −1.94639e9 3.37125e9i −0.0392160 0.0679240i
\(473\) 6.33233e10 3.65597e10i 1.26508 0.730396i
\(474\) 0 0
\(475\) 6.10225e9 1.05694e10i 0.119871 0.207623i
\(476\) 4.28518e10i 0.834722i
\(477\) 0 0
\(478\) −1.48018e10 −0.283533
\(479\) 2.46920e9 + 1.42559e9i 0.0469045 + 0.0270803i 0.523269 0.852168i \(-0.324712\pi\)
−0.476364 + 0.879248i \(0.658046\pi\)
\(480\) 0 0
\(481\) −6.28908e10 1.08930e11i −1.17492 2.03501i
\(482\) 4.74400e10 2.73895e10i 0.878934 0.507453i
\(483\) 0 0
\(484\) −1.23387e10 + 2.13713e10i −0.224848 + 0.389448i
\(485\) 4.76755e9i 0.0861645i
\(486\) 0 0
\(487\) −1.01307e11 −1.80104 −0.900522 0.434810i \(-0.856816\pi\)
−0.900522 + 0.434810i \(0.856816\pi\)
\(488\) 6.82330e9 + 3.93944e9i 0.120314 + 0.0694632i
\(489\) 0 0
\(490\) 8.85749e9 + 1.53416e10i 0.153648 + 0.266126i
\(491\) 1.01731e10 5.87345e9i 0.175036 0.101057i −0.409922 0.912120i \(-0.634444\pi\)
0.584958 + 0.811063i \(0.301111\pi\)
\(492\) 0 0
\(493\) 1.27576e10 2.20969e10i 0.215964 0.374061i
\(494\) 1.71785e10i 0.288454i
\(495\) 0 0
\(496\) −7.72008e9 −0.127554
\(497\) 6.48285e10 + 3.74287e10i 1.06253 + 0.613451i
\(498\) 0 0
\(499\) −5.73333e10 9.93042e10i −0.924708 1.60164i −0.792029 0.610483i \(-0.790975\pi\)
−0.132679 0.991159i \(-0.542358\pi\)
\(500\) 1.87999e10 1.08541e10i 0.300798 0.173666i
\(501\) 0 0
\(502\) −4.39940e10 + 7.61998e10i −0.692753 + 1.19988i
\(503\) 1.63604e10i 0.255577i 0.991801 + 0.127789i \(0.0407879\pi\)
−0.991801 + 0.127789i \(0.959212\pi\)
\(504\) 0 0
\(505\) 3.95714e10 0.608437
\(506\) 8.17747e10 + 4.72126e10i 1.24743 + 0.720205i
\(507\) 0 0
\(508\) 2.17541e10 + 3.76793e10i 0.326653 + 0.565780i
\(509\) −3.40097e10 + 1.96355e10i −0.506678 + 0.292531i −0.731467 0.681877i \(-0.761164\pi\)
0.224789 + 0.974407i \(0.427831\pi\)
\(510\) 0 0
\(511\) −8.65890e10 + 1.49977e11i −1.26993 + 2.19958i
\(512\) 3.03700e9i 0.0441942i
\(513\) 0 0
\(514\) −6.42843e10 −0.920984
\(515\) −6.02717e9 3.47979e9i −0.0856810 0.0494680i
\(516\) 0 0
\(517\) 6.06815e10 + 1.05103e11i 0.849365 + 1.47114i
\(518\) −1.04075e11 + 6.00879e10i −1.44554 + 0.834580i
\(519\) 0 0
\(520\) 7.06658e9 1.22397e10i 0.0966487 0.167400i
\(521\) 3.71996e10i 0.504879i 0.967613 + 0.252439i \(0.0812328\pi\)
−0.967613 + 0.252439i \(0.918767\pi\)
\(522\) 0 0
\(523\) 3.03301e10 0.405385 0.202692 0.979242i \(-0.435031\pi\)
0.202692 + 0.979242i \(0.435031\pi\)
\(524\) −8.52708e9 4.92311e9i −0.113103 0.0653002i
\(525\) 0 0
\(526\) −5.91320e9 1.02420e10i −0.0772466 0.133795i
\(527\) 3.86786e10 2.23311e10i 0.501451 0.289513i
\(528\) 0 0
\(529\) 4.63867e10 8.03442e10i 0.592340 1.02596i
\(530\) 2.71304e10i 0.343837i
\(531\) 0 0
\(532\) −1.64129e10 −0.204898
\(533\) 6.21306e10 + 3.58711e10i 0.769834 + 0.444464i
\(534\) 0 0
\(535\) −1.43301e10 2.48205e10i −0.174918 0.302967i
\(536\) −7.67731e9 + 4.43249e9i −0.0930143 + 0.0537018i
\(537\) 0 0
\(538\) 2.78704e10 4.82730e10i 0.332671 0.576203i
\(539\) 1.35399e11i 1.60421i
\(540\) 0 0
\(541\) 7.54262e10 0.880508 0.440254 0.897873i \(-0.354888\pi\)
0.440254 + 0.897873i \(0.354888\pi\)
\(542\) −6.45905e10 3.72913e10i −0.748465 0.432126i
\(543\) 0 0
\(544\) 8.78484e9 + 1.52158e10i 0.100309 + 0.173740i
\(545\) 9.87870e9 5.70347e9i 0.111973 0.0646477i
\(546\) 0 0
\(547\) 1.02110e10 1.76860e10i 0.114057 0.197552i −0.803346 0.595513i \(-0.796949\pi\)
0.917402 + 0.397961i \(0.130282\pi\)
\(548\) 1.63660e10i 0.181476i
\(549\) 0 0
\(550\) 7.67447e10 0.838683
\(551\) −8.46342e9 4.88636e9i −0.0918205 0.0530126i
\(552\) 0 0
\(553\) 1.47598e10 + 2.55647e10i 0.157826 + 0.273363i
\(554\) 1.19133e9 6.87816e8i 0.0126472 0.00730185i
\(555\) 0 0
\(556\) 5.81714e8 1.00756e9i 0.00608710 0.0105432i
\(557\) 2.53750e10i 0.263625i −0.991275 0.131812i \(-0.957920\pi\)
0.991275 0.131812i \(-0.0420796\pi\)
\(558\) 0 0
\(559\) −1.51558e11 −1.55215
\(560\) −1.16942e10 6.75164e9i −0.118910 0.0686527i
\(561\) 0 0
\(562\) −3.17145e10 5.49311e10i −0.317916 0.550647i
\(563\) 8.95847e10 5.17218e10i 0.891662 0.514802i 0.0171765 0.999852i \(-0.494532\pi\)
0.874486 + 0.485051i \(0.161199\pi\)
\(564\) 0 0
\(565\) 2.20797e10 3.82432e10i 0.216671 0.375285i
\(566\) 1.83915e10i 0.179206i
\(567\) 0 0
\(568\) −3.06923e10 −0.294874
\(569\) −8.23428e10 4.75406e10i −0.785555 0.453540i 0.0528406 0.998603i \(-0.483172\pi\)
−0.838395 + 0.545063i \(0.816506\pi\)
\(570\) 0 0
\(571\) 5.15232e10 + 8.92409e10i 0.484684 + 0.839498i 0.999845 0.0175958i \(-0.00560122\pi\)
−0.515161 + 0.857093i \(0.672268\pi\)
\(572\) 9.35501e10 5.40112e10i 0.873897 0.504545i
\(573\) 0 0
\(574\) 3.42725e10 5.93617e10i 0.315717 0.546838i
\(575\) 1.39050e11i 1.27204i
\(576\) 0 0
\(577\) −8.28869e10 −0.747795 −0.373898 0.927470i \(-0.621979\pi\)
−0.373898 + 0.927470i \(0.621979\pi\)
\(578\) −1.96783e10 1.13613e10i −0.176310 0.101792i
\(579\) 0 0
\(580\) −4.02013e9 6.96307e9i −0.0355245 0.0615302i
\(581\) −1.57197e11 + 9.07579e10i −1.37956 + 0.796489i
\(582\) 0 0
\(583\) −1.03681e11 + 1.79581e11i −0.897483 + 1.55449i
\(584\) 7.10047e10i 0.610430i
\(585\) 0 0
\(586\) 4.76589e10 0.404160
\(587\) −9.74307e9 5.62516e9i −0.0820622 0.0473787i 0.458407 0.888742i \(-0.348420\pi\)
−0.540470 + 0.841364i \(0.681753\pi\)
\(588\) 0 0
\(589\) −8.55315e9 1.48145e10i −0.0710665 0.123091i
\(590\) 6.14583e9 3.54830e9i 0.0507192 0.0292827i
\(591\) 0 0
\(592\) 2.46366e10 4.26719e10i 0.200583 0.347420i
\(593\) 1.94961e11i 1.57663i −0.615272 0.788315i \(-0.710954\pi\)
0.615272 0.788315i \(-0.289046\pi\)
\(594\) 0 0
\(595\) 7.81193e10 0.623291
\(596\) −2.05300e10 1.18530e10i −0.162707 0.0939387i
\(597\) 0 0
\(598\) −9.78601e10 1.69499e11i −0.765246 1.32544i
\(599\) 2.63203e10 1.51960e10i 0.204448 0.118038i −0.394281 0.918990i \(-0.629006\pi\)
0.598729 + 0.800952i \(0.295673\pi\)
\(600\) 0 0
\(601\) 5.95074e10 1.03070e11i 0.456114 0.790012i −0.542638 0.839967i \(-0.682574\pi\)
0.998751 + 0.0499547i \(0.0159077\pi\)
\(602\) 1.44804e11i 1.10254i
\(603\) 0 0
\(604\) 4.29569e10 0.322764
\(605\) −3.89601e10 2.24936e10i −0.290803 0.167895i
\(606\) 0 0
\(607\) 5.65400e10 + 9.79301e10i 0.416486 + 0.721376i 0.995583 0.0938832i \(-0.0299280\pi\)
−0.579097 + 0.815259i \(0.696595\pi\)
\(608\) 5.82787e9 3.36472e9i 0.0426477 0.0246227i
\(609\) 0 0
\(610\) −7.18163e9 + 1.24390e10i −0.0518685 + 0.0898389i
\(611\) 2.51556e11i 1.80497i
\(612\) 0 0
\(613\) 1.93018e11 1.36696 0.683481 0.729968i \(-0.260465\pi\)
0.683481 + 0.729968i \(0.260465\pi\)
\(614\) 5.76585e10 + 3.32892e10i 0.405686 + 0.234223i
\(615\) 0 0
\(616\) −5.16040e10 8.93808e10i −0.358394 0.620757i
\(617\) −1.97593e11 + 1.14080e11i −1.36342 + 0.787172i −0.990078 0.140521i \(-0.955122\pi\)
−0.373344 + 0.927693i \(0.621789\pi\)
\(618\) 0 0
\(619\) −6.07372e10 + 1.05200e11i −0.413706 + 0.716560i −0.995292 0.0969250i \(-0.969099\pi\)
0.581585 + 0.813485i \(0.302433\pi\)
\(620\) 1.40738e10i 0.0952453i
\(621\) 0 0
\(622\) −1.10875e11 −0.740751
\(623\) −3.28323e11 1.89558e11i −2.17946 1.25831i
\(624\) 0 0
\(625\) −4.58720e10 7.94527e10i −0.300627 0.520701i
\(626\) −3.68562e10 + 2.12789e10i −0.240001 + 0.138565i
\(627\) 0 0
\(628\) −1.29044e10 + 2.23510e10i −0.0829657 + 0.143701i
\(629\) 2.85056e11i 1.82107i
\(630\) 0 0
\(631\) 3.03109e11 1.91197 0.955986 0.293412i \(-0.0947908\pi\)
0.955986 + 0.293412i \(0.0947908\pi\)
\(632\) −1.04818e10 6.05166e9i −0.0657002 0.0379321i
\(633\) 0 0
\(634\) 9.57980e10 + 1.65927e11i 0.592925 + 1.02698i
\(635\) −6.86897e10 + 3.96580e10i −0.422471 + 0.243913i
\(636\) 0 0
\(637\) 1.40324e11 2.43049e11i 0.852265 1.47617i
\(638\) 6.14531e10i 0.370904i
\(639\) 0 0
\(640\) 5.53648e9 0.0330000
\(641\) 2.45984e10 + 1.42019e10i 0.145705 + 0.0841228i 0.571080 0.820894i \(-0.306525\pi\)
−0.425375 + 0.905017i \(0.639858\pi\)
\(642\) 0 0
\(643\) 1.69442e11 + 2.93481e11i 0.991234 + 1.71687i 0.610035 + 0.792375i \(0.291155\pi\)
0.381199 + 0.924493i \(0.375511\pi\)
\(644\) −1.61945e11 + 9.34988e10i −0.941506 + 0.543579i
\(645\) 0 0
\(646\) −1.94656e10 + 3.37154e10i −0.111773 + 0.193597i
\(647\) 1.91011e11i 1.09004i 0.838424 + 0.545019i \(0.183477\pi\)
−0.838424 + 0.545019i \(0.816523\pi\)
\(648\) 0 0
\(649\) 5.42405e10 0.305735
\(650\) −1.37761e11 7.95364e10i −0.771744 0.445567i
\(651\) 0 0
\(652\) −3.37703e10 5.84919e10i −0.186872 0.323672i
\(653\) 4.12673e10 2.38257e10i 0.226962 0.131037i −0.382208 0.924076i \(-0.624836\pi\)
0.609170 + 0.793040i \(0.291503\pi\)
\(654\) 0 0
\(655\) 8.97488e9 1.55450e10i 0.0487600 0.0844548i
\(656\) 2.81041e10i 0.151759i
\(657\) 0 0
\(658\) −2.40344e11 −1.28213
\(659\) 7.06817e10 + 4.08081e10i 0.374770 + 0.216374i 0.675540 0.737323i \(-0.263910\pi\)
−0.300770 + 0.953697i \(0.597244\pi\)
\(660\) 0 0
\(661\) −2.94428e10 5.09965e10i −0.154232 0.267137i 0.778547 0.627586i \(-0.215957\pi\)
−0.932779 + 0.360449i \(0.882624\pi\)
\(662\) −3.12553e10 + 1.80453e10i −0.162739 + 0.0939575i
\(663\) 0 0
\(664\) 3.72116e10 6.44525e10i 0.191428 0.331564i
\(665\) 2.99209e10i 0.152999i
\(666\) 0 0
\(667\) −1.11344e11 −0.562552
\(668\) 2.01323e10 + 1.16234e10i 0.101108 + 0.0583750i
\(669\) 0 0
\(670\) −8.08048e9 1.39958e10i −0.0400994 0.0694542i
\(671\) −9.50732e10 + 5.48905e10i −0.468995 + 0.270774i
\(672\) 0 0
\(673\) −8.28169e7 + 1.43443e8i −0.000403700 + 0.000699229i −0.866227 0.499650i \(-0.833462\pi\)
0.865823 + 0.500350i \(0.166795\pi\)
\(674\) 1.88235e11i 0.912137i
\(675\) 0 0
\(676\) −1.19490e11 −0.572196
\(677\) −2.24109e11 1.29390e11i −1.06685 0.615949i −0.139534 0.990217i \(-0.544561\pi\)
−0.927320 + 0.374268i \(0.877894\pi\)
\(678\) 0 0
\(679\) 3.60817e10 + 6.24954e10i 0.169749 + 0.294015i
\(680\) −2.77385e10 + 1.60148e10i −0.129732 + 0.0749009i
\(681\) 0 0
\(682\) 5.37842e10 9.31570e10i 0.248609 0.430604i
\(683\) 1.24132e11i 0.570428i 0.958464 + 0.285214i \(0.0920647\pi\)
−0.958464 + 0.285214i \(0.907935\pi\)
\(684\) 0 0
\(685\) −2.98353e10 −0.135509
\(686\) −3.27176e10 1.88895e10i −0.147736 0.0852953i
\(687\) 0 0
\(688\) −2.96855e10 5.14168e10i −0.132492 0.229483i
\(689\) 3.72227e11 2.14906e11i 1.65170 0.953610i
\(690\) 0 0
\(691\) −5.98669e10 + 1.03692e11i −0.262588 + 0.454815i −0.966929 0.255047i \(-0.917909\pi\)
0.704341 + 0.709862i \(0.251243\pi\)
\(692\) 9.04269e9i 0.0394342i
\(693\) 0 0
\(694\) −1.21348e10 −0.0523112
\(695\) 1.83679e9 + 1.06047e9i 0.00787264 + 0.00454527i
\(696\) 0 0
\(697\) −8.12940e10 1.40805e11i −0.344451 0.596607i
\(698\) 2.27609e10 1.31410e10i 0.0958887 0.0553614i
\(699\) 0 0
\(700\) −7.59917e10 + 1.31621e11i −0.316500 + 0.548194i
\(701\) 1.43654e11i 0.594902i −0.954737 0.297451i \(-0.903864\pi\)
0.954737 0.297451i \(-0.0961365\pi\)
\(702\) 0 0
\(703\) 1.09181e11 0.447018
\(704\) 3.66470e10 + 2.11582e10i 0.149193 + 0.0861365i
\(705\) 0 0
\(706\) −1.12292e11 1.94496e11i −0.451992 0.782873i
\(707\) −5.18721e11 + 2.99484e11i −2.07614 + 1.19866i
\(708\) 0 0
\(709\) −2.07121e11 + 3.58743e11i −0.819669 + 1.41971i 0.0862581 + 0.996273i \(0.472509\pi\)
−0.905927 + 0.423435i \(0.860824\pi\)
\(710\) 5.59524e10i 0.220184i
\(711\) 0 0
\(712\) 1.55441e11 0.604847
\(713\) −1.68786e11 9.74489e10i −0.653099 0.377067i
\(714\) 0 0
\(715\) 9.84629e10 + 1.70543e11i 0.376746 + 0.652543i
\(716\) −8.76137e9 + 5.05838e9i −0.0333365 + 0.0192468i
\(717\) 0 0
\(718\) 5.86500e10 1.01585e11i 0.220684 0.382235i
\(719\) 3.07755e11i 1.15157i −0.817602 0.575784i \(-0.804697\pi\)
0.817602 0.575784i \(-0.195303\pi\)
\(720\) 0 0
\(721\) 1.05343e11 0.389819
\(722\) −1.53491e11 8.86179e10i −0.564850 0.326116i
\(723\) 0 0
\(724\) 3.50827e10 + 6.07651e10i 0.127685 + 0.221157i
\(725\) −7.83713e10 + 4.52477e10i −0.283665 + 0.163774i
\(726\) 0 0
\(727\) 7.96979e9 1.38041e10i 0.0285305 0.0494163i −0.851408 0.524505i \(-0.824251\pi\)
0.879938 + 0.475088i \(0.157584\pi\)
\(728\) 2.13925e11i 0.761615i
\(729\) 0 0
\(730\) 1.29442e11 0.455811
\(731\) 2.97457e11 + 1.71737e11i 1.04173 + 0.601442i
\(732\) 0 0
\(733\) −8.39154e9 1.45346e10i −0.0290687 0.0503485i 0.851125 0.524963i \(-0.175921\pi\)
−0.880194 + 0.474614i \(0.842587\pi\)
\(734\) 1.98781e11 1.14766e11i 0.684842 0.395393i
\(735\) 0 0
\(736\) 3.83354e10 6.63989e10i 0.130644 0.226282i
\(737\) 1.23521e11i 0.418670i
\(738\) 0 0
\(739\) −3.67552e11 −1.23237 −0.616185 0.787601i \(-0.711323\pi\)
−0.616185 + 0.787601i \(0.711323\pi\)
\(740\) 7.77913e10 + 4.49128e10i 0.259420 + 0.149776i
\(741\) 0 0
\(742\) −2.05328e11 3.55638e11i −0.677380 1.17326i
\(743\) 2.89546e11 1.67169e11i 0.950084 0.548531i 0.0569771 0.998375i \(-0.481854\pi\)
0.893107 + 0.449844i \(0.148520\pi\)
\(744\) 0 0
\(745\) 2.16082e10 3.74265e10i 0.0701444 0.121494i
\(746\) 2.51290e11i 0.811371i
\(747\) 0 0
\(748\) −2.44809e11 −0.782025
\(749\) 3.75693e11 + 2.16906e11i 1.19373 + 0.689199i
\(750\) 0 0
\(751\) 8.96862e10 + 1.55341e11i 0.281946 + 0.488345i 0.971864 0.235543i \(-0.0756868\pi\)
−0.689918 + 0.723888i \(0.742353\pi\)
\(752\) 8.53412e10 4.92718e10i 0.266862 0.154073i
\(753\) 0 0
\(754\) −6.36886e10 + 1.10312e11i −0.197050 + 0.341300i
\(755\) 7.83109e10i 0.241010i
\(756\) 0 0
\(757\) −1.95683e11 −0.595894 −0.297947 0.954582i \(-0.596302\pi\)
−0.297947 + 0.954582i \(0.596302\pi\)
\(758\) 1.21288e11 + 7.00259e10i 0.367403 + 0.212120i
\(759\) 0 0
\(760\) 6.13392e9 + 1.06243e10i 0.0183859 + 0.0318452i
\(761\) 2.85175e11 1.64646e11i 0.850301 0.490922i −0.0104512 0.999945i \(-0.503327\pi\)
0.860752 + 0.509024i \(0.169993\pi\)
\(762\) 0 0
\(763\) −8.63299e10 + 1.49528e11i −0.254720 + 0.441188i
\(764\) 2.87485e11i 0.843803i
\(765\) 0 0
\(766\) −3.28514e11 −0.954198
\(767\) −9.73648e10 5.62136e10i −0.281333 0.162428i
\(768\) 0 0
\(769\) 4.33600e10 + 7.51018e10i 0.123989 + 0.214756i 0.921337 0.388764i \(-0.127098\pi\)
−0.797348 + 0.603520i \(0.793764\pi\)