Properties

Label 48.13.e.d.17.2
Level $48$
Weight $13$
Character 48.17
Analytic conductor $43.872$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,13,Mod(17,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.17");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\), degree \(1\), 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: \(43.8717032293\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 4105x^{2} + 385000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{7} \)
Twist minimal: no (minimal twist has level 12)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 17.2
Root \(63.3164i\) of defining polynomial
Character \(\chi\) \(=\) 48.17
Dual form 48.13.e.d.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-596.724 + 418.762i) q^{3} +23907.4i q^{5} -32123.1 q^{7} +(180718. - 499770. i) q^{9} +O(q^{10})\) \(q+(-596.724 + 418.762i) q^{3} +23907.4i q^{5} -32123.1 q^{7} +(180718. - 499770. i) q^{9} -2.66781e6i q^{11} +7.50690e6 q^{13} +(-1.00115e7 - 1.42661e7i) q^{15} +1.32887e6i q^{17} -3.25909e7 q^{19} +(1.91686e7 - 1.34519e7i) q^{21} -8.48263e7i q^{23} -3.27423e8 q^{25} +(1.01446e8 + 3.73903e8i) q^{27} -8.40937e8i q^{29} +1.20660e9 q^{31} +(1.11718e9 + 1.59195e9i) q^{33} -7.67979e8i q^{35} +1.09905e9 q^{37} +(-4.47955e9 + 3.14360e9i) q^{39} +5.50833e9i q^{41} +6.27668e9 q^{43} +(1.19482e10 + 4.32050e9i) q^{45} +4.76723e9i q^{47} -1.28094e10 q^{49} +(-5.56479e8 - 7.92968e8i) q^{51} -2.32344e10i q^{53} +6.37804e10 q^{55} +(1.94478e10 - 1.36478e10i) q^{57} +1.03316e10i q^{59} +4.64493e10 q^{61} +(-5.80523e9 + 1.60542e10i) q^{63} +1.79470e11i q^{65} -3.54165e10 q^{67} +(3.55220e10 + 5.06179e10i) q^{69} +2.45268e11i q^{71} +2.38881e11 q^{73} +(1.95381e11 - 1.37112e11i) q^{75} +8.56984e10i q^{77} +3.79121e10 q^{79} +(-2.17111e11 - 1.80635e11i) q^{81} -2.26620e11i q^{83} -3.17698e10 q^{85} +(3.52152e11 + 5.01807e11i) q^{87} -8.22422e11i q^{89} -2.41145e11 q^{91} +(-7.20005e11 + 5.05276e11i) q^{93} -7.79163e11i q^{95} +3.60606e11 q^{97} +(-1.33329e12 - 4.82122e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 300 q^{3} - 15800 q^{7} + 96804 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 300 q^{3} - 15800 q^{7} + 96804 q^{9} + 3432200 q^{13} - 6613920 q^{15} + 2050024 q^{19} + 59979336 q^{21} - 437451260 q^{25} - 508358700 q^{27} + 2519008264 q^{31} + 3795184800 q^{33} - 7466711800 q^{37} - 14132878296 q^{39} + 26119930600 q^{43} + 35876727360 q^{45} - 52127844660 q^{49} - 54522702720 q^{51} + 96029271360 q^{55} + 68929593000 q^{57} - 9307235704 q^{61} - 18020676600 q^{63} - 89055584600 q^{67} - 143365584960 q^{69} + 464142475400 q^{73} + 487877005140 q^{75} - 567022026488 q^{79} - 929051518716 q^{81} + 1015432485120 q^{85} + 976838637600 q^{87} - 762832207984 q^{91} - 1392739649400 q^{93} + 862958525000 q^{97} - 1272066016320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −596.724 + 418.762i −0.818552 + 0.574433i
\(4\) 0 0
\(5\) 23907.4i 1.53007i 0.643987 + 0.765036i \(0.277279\pi\)
−0.643987 + 0.765036i \(0.722721\pi\)
\(6\) 0 0
\(7\) −32123.1 −0.273042 −0.136521 0.990637i \(-0.543592\pi\)
−0.136521 + 0.990637i \(0.543592\pi\)
\(8\) 0 0
\(9\) 180718. 499770.i 0.340053 0.940406i
\(10\) 0 0
\(11\) 2.66781e6i 1.50591i −0.658072 0.752955i \(-0.728628\pi\)
0.658072 0.752955i \(-0.271372\pi\)
\(12\) 0 0
\(13\) 7.50690e6 1.55525 0.777626 0.628727i \(-0.216424\pi\)
0.777626 + 0.628727i \(0.216424\pi\)
\(14\) 0 0
\(15\) −1.00115e7 1.42661e7i −0.878925 1.25244i
\(16\) 0 0
\(17\) 1.32887e6i 0.0550540i 0.999621 + 0.0275270i \(0.00876322\pi\)
−0.999621 + 0.0275270i \(0.991237\pi\)
\(18\) 0 0
\(19\) −3.25909e7 −0.692747 −0.346373 0.938097i \(-0.612587\pi\)
−0.346373 + 0.938097i \(0.612587\pi\)
\(20\) 0 0
\(21\) 1.91686e7 1.34519e7i 0.223499 0.156844i
\(22\) 0 0
\(23\) 8.48263e7i 0.573012i −0.958079 0.286506i \(-0.907506\pi\)
0.958079 0.286506i \(-0.0924938\pi\)
\(24\) 0 0
\(25\) −3.27423e8 −1.34112
\(26\) 0 0
\(27\) 1.01446e8 + 3.73903e8i 0.261849 + 0.965109i
\(28\) 0 0
\(29\) 8.40937e8i 1.41376i −0.707334 0.706880i \(-0.750102\pi\)
0.707334 0.706880i \(-0.249898\pi\)
\(30\) 0 0
\(31\) 1.20660e9 1.35954 0.679770 0.733426i \(-0.262080\pi\)
0.679770 + 0.733426i \(0.262080\pi\)
\(32\) 0 0
\(33\) 1.11718e9 + 1.59195e9i 0.865045 + 1.23267i
\(34\) 0 0
\(35\) 7.67979e8i 0.417774i
\(36\) 0 0
\(37\) 1.09905e9 0.428357 0.214179 0.976794i \(-0.431293\pi\)
0.214179 + 0.976794i \(0.431293\pi\)
\(38\) 0 0
\(39\) −4.47955e9 + 3.14360e9i −1.27305 + 0.893388i
\(40\) 0 0
\(41\) 5.50833e9i 1.15962i 0.814751 + 0.579811i \(0.196874\pi\)
−0.814751 + 0.579811i \(0.803126\pi\)
\(42\) 0 0
\(43\) 6.27668e9 0.992931 0.496466 0.868056i \(-0.334631\pi\)
0.496466 + 0.868056i \(0.334631\pi\)
\(44\) 0 0
\(45\) 1.19482e10 + 4.32050e9i 1.43889 + 0.520306i
\(46\) 0 0
\(47\) 4.76723e9i 0.442261i 0.975244 + 0.221131i \(0.0709747\pi\)
−0.975244 + 0.221131i \(0.929025\pi\)
\(48\) 0 0
\(49\) −1.28094e10 −0.925448
\(50\) 0 0
\(51\) −5.56479e8 7.92968e8i −0.0316248 0.0450645i
\(52\) 0 0
\(53\) 2.32344e10i 1.04828i −0.851633 0.524138i \(-0.824388\pi\)
0.851633 0.524138i \(-0.175612\pi\)
\(54\) 0 0
\(55\) 6.37804e10 2.30415
\(56\) 0 0
\(57\) 1.94478e10 1.36478e10i 0.567049 0.397937i
\(58\) 0 0
\(59\) 1.03316e10i 0.244938i 0.992472 + 0.122469i \(0.0390812\pi\)
−0.992472 + 0.122469i \(0.960919\pi\)
\(60\) 0 0
\(61\) 4.64493e10 0.901571 0.450786 0.892632i \(-0.351144\pi\)
0.450786 + 0.892632i \(0.351144\pi\)
\(62\) 0 0
\(63\) −5.80523e9 + 1.60542e10i −0.0928488 + 0.256770i
\(64\) 0 0
\(65\) 1.79470e11i 2.37965i
\(66\) 0 0
\(67\) −3.54165e10 −0.391523 −0.195761 0.980652i \(-0.562718\pi\)
−0.195761 + 0.980652i \(0.562718\pi\)
\(68\) 0 0
\(69\) 3.55220e10 + 5.06179e10i 0.329157 + 0.469040i
\(70\) 0 0
\(71\) 2.45268e11i 1.91466i 0.289005 + 0.957328i \(0.406676\pi\)
−0.289005 + 0.957328i \(0.593324\pi\)
\(72\) 0 0
\(73\) 2.38881e11 1.57850 0.789249 0.614074i \(-0.210470\pi\)
0.789249 + 0.614074i \(0.210470\pi\)
\(74\) 0 0
\(75\) 1.95381e11 1.37112e11i 1.09778 0.770385i
\(76\) 0 0
\(77\) 8.56984e10i 0.411176i
\(78\) 0 0
\(79\) 3.79121e10 0.155961 0.0779804 0.996955i \(-0.475153\pi\)
0.0779804 + 0.996955i \(0.475153\pi\)
\(80\) 0 0
\(81\) −2.17111e11 1.80635e11i −0.768728 0.639576i
\(82\) 0 0
\(83\) 2.26620e11i 0.693155i −0.938021 0.346577i \(-0.887344\pi\)
0.938021 0.346577i \(-0.112656\pi\)
\(84\) 0 0
\(85\) −3.17698e10 −0.0842366
\(86\) 0 0
\(87\) 3.52152e11 + 5.01807e11i 0.812110 + 1.15723i
\(88\) 0 0
\(89\) 8.22422e11i 1.65483i −0.561587 0.827417i \(-0.689809\pi\)
0.561587 0.827417i \(-0.310191\pi\)
\(90\) 0 0
\(91\) −2.41145e11 −0.424649
\(92\) 0 0
\(93\) −7.20005e11 + 5.05276e11i −1.11285 + 0.780964i
\(94\) 0 0
\(95\) 7.79163e11i 1.05995i
\(96\) 0 0
\(97\) 3.60606e11 0.432914 0.216457 0.976292i \(-0.430550\pi\)
0.216457 + 0.976292i \(0.430550\pi\)
\(98\) 0 0
\(99\) −1.33329e12 4.82122e11i −1.41617 0.512090i
\(100\) 0 0
\(101\) 4.74841e10i 0.0447322i −0.999750 0.0223661i \(-0.992880\pi\)
0.999750 0.0223661i \(-0.00711994\pi\)
\(102\) 0 0
\(103\) −1.10858e12 −0.928421 −0.464210 0.885725i \(-0.653662\pi\)
−0.464210 + 0.885725i \(0.653662\pi\)
\(104\) 0 0
\(105\) 3.21600e11 + 4.58272e11i 0.239983 + 0.341969i
\(106\) 0 0
\(107\) 3.12780e11i 0.208418i −0.994555 0.104209i \(-0.966769\pi\)
0.994555 0.104209i \(-0.0332311\pi\)
\(108\) 0 0
\(109\) −1.39013e12 −0.828889 −0.414445 0.910075i \(-0.636024\pi\)
−0.414445 + 0.910075i \(0.636024\pi\)
\(110\) 0 0
\(111\) −6.55828e11 + 4.60239e11i −0.350633 + 0.246063i
\(112\) 0 0
\(113\) 4.49822e11i 0.216058i 0.994148 + 0.108029i \(0.0344539\pi\)
−0.994148 + 0.108029i \(0.965546\pi\)
\(114\) 0 0
\(115\) 2.02798e12 0.876750
\(116\) 0 0
\(117\) 1.35663e12 3.75173e12i 0.528868 1.46257i
\(118\) 0 0
\(119\) 4.26874e10i 0.0150320i
\(120\) 0 0
\(121\) −3.97879e12 −1.26777
\(122\) 0 0
\(123\) −2.30668e12 3.28695e12i −0.666125 0.949210i
\(124\) 0 0
\(125\) 1.99105e12i 0.521943i
\(126\) 0 0
\(127\) 4.33023e12 1.03202 0.516011 0.856582i \(-0.327416\pi\)
0.516011 + 0.856582i \(0.327416\pi\)
\(128\) 0 0
\(129\) −3.74544e12 + 2.62843e12i −0.812765 + 0.570373i
\(130\) 0 0
\(131\) 7.15100e12i 1.41494i 0.706742 + 0.707472i \(0.250164\pi\)
−0.706742 + 0.707472i \(0.749836\pi\)
\(132\) 0 0
\(133\) 1.04692e12 0.189149
\(134\) 0 0
\(135\) −8.93904e12 + 2.42530e12i −1.47669 + 0.400649i
\(136\) 0 0
\(137\) 3.47005e12i 0.524822i 0.964956 + 0.262411i \(0.0845176\pi\)
−0.964956 + 0.262411i \(0.915482\pi\)
\(138\) 0 0
\(139\) −1.88664e12 −0.261577 −0.130788 0.991410i \(-0.541751\pi\)
−0.130788 + 0.991410i \(0.541751\pi\)
\(140\) 0 0
\(141\) −1.99633e12 2.84472e12i −0.254049 0.362014i
\(142\) 0 0
\(143\) 2.00270e13i 2.34207i
\(144\) 0 0
\(145\) 2.01046e13 2.16315
\(146\) 0 0
\(147\) 7.64367e12 5.36408e12i 0.757527 0.531608i
\(148\) 0 0
\(149\) 2.92256e12i 0.267083i 0.991043 + 0.133541i \(0.0426349\pi\)
−0.991043 + 0.133541i \(0.957365\pi\)
\(150\) 0 0
\(151\) 4.68828e12 0.395505 0.197753 0.980252i \(-0.436636\pi\)
0.197753 + 0.980252i \(0.436636\pi\)
\(152\) 0 0
\(153\) 6.64129e11 + 2.40151e11i 0.0517731 + 0.0187213i
\(154\) 0 0
\(155\) 2.88466e13i 2.08019i
\(156\) 0 0
\(157\) 1.18879e13 0.793791 0.396895 0.917864i \(-0.370088\pi\)
0.396895 + 0.917864i \(0.370088\pi\)
\(158\) 0 0
\(159\) 9.72967e12 + 1.38645e13i 0.602165 + 0.858068i
\(160\) 0 0
\(161\) 2.72488e12i 0.156456i
\(162\) 0 0
\(163\) 2.49183e13 1.32860 0.664299 0.747467i \(-0.268730\pi\)
0.664299 + 0.747467i \(0.268730\pi\)
\(164\) 0 0
\(165\) −3.80593e13 + 2.67088e13i −1.88607 + 1.32358i
\(166\) 0 0
\(167\) 5.63556e12i 0.259799i 0.991527 + 0.129900i \(0.0414655\pi\)
−0.991527 + 0.129900i \(0.958534\pi\)
\(168\) 0 0
\(169\) 3.30555e13 1.41881
\(170\) 0 0
\(171\) −5.88977e12 + 1.62880e13i −0.235571 + 0.651463i
\(172\) 0 0
\(173\) 9.19932e12i 0.343146i −0.985171 0.171573i \(-0.945115\pi\)
0.985171 0.171573i \(-0.0548850\pi\)
\(174\) 0 0
\(175\) 1.05178e13 0.366183
\(176\) 0 0
\(177\) −4.32648e12 6.16512e12i −0.140700 0.200494i
\(178\) 0 0
\(179\) 2.22903e13i 0.677639i −0.940851 0.338819i \(-0.889972\pi\)
0.940851 0.338819i \(-0.110028\pi\)
\(180\) 0 0
\(181\) 5.76657e12 0.164001 0.0820004 0.996632i \(-0.473869\pi\)
0.0820004 + 0.996632i \(0.473869\pi\)
\(182\) 0 0
\(183\) −2.77174e13 + 1.94512e13i −0.737982 + 0.517892i
\(184\) 0 0
\(185\) 2.62754e13i 0.655418i
\(186\) 0 0
\(187\) 3.54517e12 0.0829063
\(188\) 0 0
\(189\) −3.25875e12 1.20109e13i −0.0714958 0.263515i
\(190\) 0 0
\(191\) 3.86757e13i 0.796595i −0.917256 0.398298i \(-0.869601\pi\)
0.917256 0.398298i \(-0.130399\pi\)
\(192\) 0 0
\(193\) 4.81541e13 0.931728 0.465864 0.884856i \(-0.345744\pi\)
0.465864 + 0.884856i \(0.345744\pi\)
\(194\) 0 0
\(195\) −7.51553e13 1.07094e14i −1.36695 1.94786i
\(196\) 0 0
\(197\) 7.39066e13i 1.26440i −0.774804 0.632202i \(-0.782151\pi\)
0.774804 0.632202i \(-0.217849\pi\)
\(198\) 0 0
\(199\) 2.72647e13 0.439017 0.219509 0.975611i \(-0.429555\pi\)
0.219509 + 0.975611i \(0.429555\pi\)
\(200\) 0 0
\(201\) 2.11339e13 1.48311e13i 0.320482 0.224904i
\(202\) 0 0
\(203\) 2.70135e13i 0.386015i
\(204\) 0 0
\(205\) −1.31690e14 −1.77431
\(206\) 0 0
\(207\) −4.23937e13 1.53297e13i −0.538864 0.194854i
\(208\) 0 0
\(209\) 8.69463e13i 1.04321i
\(210\) 0 0
\(211\) 7.65024e13 0.866923 0.433462 0.901172i \(-0.357292\pi\)
0.433462 + 0.901172i \(0.357292\pi\)
\(212\) 0 0
\(213\) −1.02709e14 1.46357e14i −1.09984 1.56724i
\(214\) 0 0
\(215\) 1.50059e14i 1.51926i
\(216\) 0 0
\(217\) −3.87596e13 −0.371211
\(218\) 0 0
\(219\) −1.42546e14 + 1.00034e14i −1.29208 + 0.906741i
\(220\) 0 0
\(221\) 9.97569e12i 0.0856227i
\(222\) 0 0
\(223\) 8.20519e13 0.667205 0.333602 0.942714i \(-0.391736\pi\)
0.333602 + 0.942714i \(0.391736\pi\)
\(224\) 0 0
\(225\) −5.91712e13 + 1.63636e14i −0.456053 + 1.26120i
\(226\) 0 0
\(227\) 1.95268e14i 1.42717i −0.700568 0.713585i \(-0.747070\pi\)
0.700568 0.713585i \(-0.252930\pi\)
\(228\) 0 0
\(229\) 6.05545e13 0.419888 0.209944 0.977713i \(-0.432672\pi\)
0.209944 + 0.977713i \(0.432672\pi\)
\(230\) 0 0
\(231\) −3.58872e13 5.11383e13i −0.236193 0.336569i
\(232\) 0 0
\(233\) 1.02896e14i 0.643078i −0.946896 0.321539i \(-0.895800\pi\)
0.946896 0.321539i \(-0.104200\pi\)
\(234\) 0 0
\(235\) −1.13972e14 −0.676692
\(236\) 0 0
\(237\) −2.26231e13 + 1.58761e13i −0.127662 + 0.0895890i
\(238\) 0 0
\(239\) 6.67575e13i 0.358189i −0.983832 0.179095i \(-0.942683\pi\)
0.983832 0.179095i \(-0.0573169\pi\)
\(240\) 0 0
\(241\) 3.32285e14 1.69593 0.847966 0.530050i \(-0.177827\pi\)
0.847966 + 0.530050i \(0.177827\pi\)
\(242\) 0 0
\(243\) 2.05199e14 + 1.68715e13i 0.996637 + 0.0819436i
\(244\) 0 0
\(245\) 3.06239e14i 1.41600i
\(246\) 0 0
\(247\) −2.44657e14 −1.07740
\(248\) 0 0
\(249\) 9.48999e13 + 1.35230e14i 0.398171 + 0.567383i
\(250\) 0 0
\(251\) 2.95929e14i 1.18344i −0.806144 0.591719i \(-0.798449\pi\)
0.806144 0.591719i \(-0.201551\pi\)
\(252\) 0 0
\(253\) −2.26301e14 −0.862904
\(254\) 0 0
\(255\) 1.89578e13 1.33040e13i 0.0689520 0.0483883i
\(256\) 0 0
\(257\) 3.56383e14i 1.23685i 0.785842 + 0.618427i \(0.212230\pi\)
−0.785842 + 0.618427i \(0.787770\pi\)
\(258\) 0 0
\(259\) −3.53048e13 −0.116959
\(260\) 0 0
\(261\) −4.20275e14 1.51973e14i −1.32951 0.480753i
\(262\) 0 0
\(263\) 3.05992e14i 0.924647i 0.886711 + 0.462324i \(0.152984\pi\)
−0.886711 + 0.462324i \(0.847016\pi\)
\(264\) 0 0
\(265\) 5.55473e14 1.60394
\(266\) 0 0
\(267\) 3.44399e14 + 4.90759e14i 0.950592 + 1.35457i
\(268\) 0 0
\(269\) 1.68860e14i 0.445669i 0.974856 + 0.222835i \(0.0715310\pi\)
−0.974856 + 0.222835i \(0.928469\pi\)
\(270\) 0 0
\(271\) 5.29221e14 1.33605 0.668023 0.744141i \(-0.267141\pi\)
0.668023 + 0.744141i \(0.267141\pi\)
\(272\) 0 0
\(273\) 1.43897e14 1.00982e14i 0.347597 0.243932i
\(274\) 0 0
\(275\) 8.73502e14i 2.01961i
\(276\) 0 0
\(277\) −4.62727e14 −1.02434 −0.512172 0.858883i \(-0.671159\pi\)
−0.512172 + 0.858883i \(0.671159\pi\)
\(278\) 0 0
\(279\) 2.18054e14 6.03021e14i 0.462316 1.27852i
\(280\) 0 0
\(281\) 4.12927e13i 0.0838756i −0.999120 0.0419378i \(-0.986647\pi\)
0.999120 0.0419378i \(-0.0133531\pi\)
\(282\) 0 0
\(283\) 1.04587e14 0.203590 0.101795 0.994805i \(-0.467541\pi\)
0.101795 + 0.994805i \(0.467541\pi\)
\(284\) 0 0
\(285\) 3.26284e14 + 4.64945e14i 0.608872 + 0.867626i
\(286\) 0 0
\(287\) 1.76944e14i 0.316625i
\(288\) 0 0
\(289\) 5.80856e14 0.996969
\(290\) 0 0
\(291\) −2.15182e14 + 1.51008e14i −0.354363 + 0.248680i
\(292\) 0 0
\(293\) 2.45106e14i 0.387389i 0.981062 + 0.193695i \(0.0620471\pi\)
−0.981062 + 0.193695i \(0.937953\pi\)
\(294\) 0 0
\(295\) −2.47002e14 −0.374773
\(296\) 0 0
\(297\) 9.97503e14 2.70638e14i 1.45337 0.394322i
\(298\) 0 0
\(299\) 6.36783e14i 0.891177i
\(300\) 0 0
\(301\) −2.01626e14 −0.271112
\(302\) 0 0
\(303\) 1.98845e13 + 2.83349e13i 0.0256956 + 0.0366156i
\(304\) 0 0
\(305\) 1.11048e15i 1.37947i
\(306\) 0 0
\(307\) 4.26340e14 0.509244 0.254622 0.967041i \(-0.418049\pi\)
0.254622 + 0.967041i \(0.418049\pi\)
\(308\) 0 0
\(309\) 6.61518e14 4.64232e14i 0.759960 0.533316i
\(310\) 0 0
\(311\) 5.14727e14i 0.568872i 0.958695 + 0.284436i \(0.0918063\pi\)
−0.958695 + 0.284436i \(0.908194\pi\)
\(312\) 0 0
\(313\) −1.72353e15 −1.83296 −0.916479 0.400083i \(-0.868981\pi\)
−0.916479 + 0.400083i \(0.868981\pi\)
\(314\) 0 0
\(315\) −3.83813e14 1.38788e14i −0.392877 0.142065i
\(316\) 0 0
\(317\) 1.32460e15i 1.30536i −0.757635 0.652678i \(-0.773645\pi\)
0.757635 0.652678i \(-0.226355\pi\)
\(318\) 0 0
\(319\) −2.24346e15 −2.12899
\(320\) 0 0
\(321\) 1.30980e14 + 1.86643e14i 0.119722 + 0.170601i
\(322\) 0 0
\(323\) 4.33090e13i 0.0381385i
\(324\) 0 0
\(325\) −2.45793e15 −2.08578
\(326\) 0 0
\(327\) 8.29524e14 5.82133e14i 0.678489 0.476141i
\(328\) 0 0
\(329\) 1.53138e14i 0.120756i
\(330\) 0 0
\(331\) 7.89498e14 0.600320 0.300160 0.953889i \(-0.402960\pi\)
0.300160 + 0.953889i \(0.402960\pi\)
\(332\) 0 0
\(333\) 1.98618e14 5.49272e14i 0.145664 0.402830i
\(334\) 0 0
\(335\) 8.46717e14i 0.599059i
\(336\) 0 0
\(337\) −2.01522e14 −0.137576 −0.0687882 0.997631i \(-0.521913\pi\)
−0.0687882 + 0.997631i \(0.521913\pi\)
\(338\) 0 0
\(339\) −1.88368e14 2.68420e14i −0.124111 0.176855i
\(340\) 0 0
\(341\) 3.21897e15i 2.04734i
\(342\) 0 0
\(343\) 8.56102e14 0.525728
\(344\) 0 0
\(345\) −1.21014e15 + 8.49238e14i −0.717665 + 0.503634i
\(346\) 0 0
\(347\) 5.82827e14i 0.333859i −0.985969 0.166929i \(-0.946615\pi\)
0.985969 0.166929i \(-0.0533852\pi\)
\(348\) 0 0
\(349\) 1.34356e15 0.743541 0.371771 0.928325i \(-0.378751\pi\)
0.371771 + 0.928325i \(0.378751\pi\)
\(350\) 0 0
\(351\) 7.61544e14 + 2.80685e15i 0.407242 + 1.50099i
\(352\) 0 0
\(353\) 2.93492e14i 0.151687i 0.997120 + 0.0758435i \(0.0241650\pi\)
−0.997120 + 0.0758435i \(0.975835\pi\)
\(354\) 0 0
\(355\) −5.86371e15 −2.92956
\(356\) 0 0
\(357\) 1.78758e13 + 2.54726e13i 0.00863490 + 0.0123045i
\(358\) 0 0
\(359\) 3.00435e15i 1.40341i −0.712470 0.701703i \(-0.752423\pi\)
0.712470 0.701703i \(-0.247577\pi\)
\(360\) 0 0
\(361\) −1.15115e15 −0.520102
\(362\) 0 0
\(363\) 2.37424e15 1.66617e15i 1.03773 0.728246i
\(364\) 0 0
\(365\) 5.71101e15i 2.41522i
\(366\) 0 0
\(367\) −1.36037e15 −0.556750 −0.278375 0.960473i \(-0.589796\pi\)
−0.278375 + 0.960473i \(0.589796\pi\)
\(368\) 0 0
\(369\) 2.75290e15 + 9.95455e14i 1.09052 + 0.394333i
\(370\) 0 0
\(371\) 7.46360e14i 0.286223i
\(372\) 0 0
\(373\) 3.28428e15 1.21951 0.609757 0.792589i \(-0.291267\pi\)
0.609757 + 0.792589i \(0.291267\pi\)
\(374\) 0 0
\(375\) 8.33778e14 + 1.18811e15i 0.299821 + 0.427237i
\(376\) 0 0
\(377\) 6.31283e15i 2.19875i
\(378\) 0 0
\(379\) −5.77798e14 −0.194958 −0.0974789 0.995238i \(-0.531078\pi\)
−0.0974789 + 0.995238i \(0.531078\pi\)
\(380\) 0 0
\(381\) −2.58395e15 + 1.81333e15i −0.844763 + 0.592827i
\(382\) 0 0
\(383\) 6.08079e15i 1.92649i 0.268619 + 0.963246i \(0.413433\pi\)
−0.268619 + 0.963246i \(0.586567\pi\)
\(384\) 0 0
\(385\) −2.04882e15 −0.629130
\(386\) 0 0
\(387\) 1.13431e15 3.13690e15i 0.337649 0.933759i
\(388\) 0 0
\(389\) 4.63647e15i 1.33810i 0.743215 + 0.669052i \(0.233300\pi\)
−0.743215 + 0.669052i \(0.766700\pi\)
\(390\) 0 0
\(391\) 1.12723e14 0.0315466
\(392\) 0 0
\(393\) −2.99457e15 4.26718e15i −0.812790 1.15820i
\(394\) 0 0
\(395\) 9.06379e14i 0.238631i
\(396\) 0 0
\(397\) −2.01737e15 −0.515278 −0.257639 0.966241i \(-0.582945\pi\)
−0.257639 + 0.966241i \(0.582945\pi\)
\(398\) 0 0
\(399\) −6.24723e14 + 4.38410e14i −0.154828 + 0.108653i
\(400\) 0 0
\(401\) 1.56671e15i 0.376811i 0.982091 + 0.188405i \(0.0603319\pi\)
−0.982091 + 0.188405i \(0.939668\pi\)
\(402\) 0 0
\(403\) 9.05780e15 2.11443
\(404\) 0 0
\(405\) 4.31852e15 5.19057e15i 0.978598 1.17621i
\(406\) 0 0
\(407\) 2.93205e15i 0.645068i
\(408\) 0 0
\(409\) 6.76025e15 1.44418 0.722092 0.691797i \(-0.243181\pi\)
0.722092 + 0.691797i \(0.243181\pi\)
\(410\) 0 0
\(411\) −1.45312e15 2.07066e15i −0.301475 0.429594i
\(412\) 0 0
\(413\) 3.31883e14i 0.0668783i
\(414\) 0 0
\(415\) 5.41790e15 1.06058
\(416\) 0 0
\(417\) 1.12580e15 7.90051e14i 0.214114 0.150258i
\(418\) 0 0
\(419\) 4.15053e15i 0.767042i 0.923532 + 0.383521i \(0.125289\pi\)
−0.923532 + 0.383521i \(0.874711\pi\)
\(420\) 0 0
\(421\) 9.35263e14 0.167974 0.0839868 0.996467i \(-0.473235\pi\)
0.0839868 + 0.996467i \(0.473235\pi\)
\(422\) 0 0
\(423\) 2.38252e15 + 8.61525e14i 0.415905 + 0.150392i
\(424\) 0 0
\(425\) 4.35102e14i 0.0738341i
\(426\) 0 0
\(427\) −1.49209e15 −0.246167
\(428\) 0 0
\(429\) 8.38654e15 + 1.19506e16i 1.34536 + 1.91710i
\(430\) 0 0
\(431\) 5.12689e15i 0.799817i −0.916555 0.399908i \(-0.869042\pi\)
0.916555 0.399908i \(-0.130958\pi\)
\(432\) 0 0
\(433\) −1.14255e16 −1.73359 −0.866795 0.498664i \(-0.833824\pi\)
−0.866795 + 0.498664i \(0.833824\pi\)
\(434\) 0 0
\(435\) −1.19969e16 + 8.41904e15i −1.77065 + 1.24259i
\(436\) 0 0
\(437\) 2.76456e15i 0.396952i
\(438\) 0 0
\(439\) −5.29408e15 −0.739611 −0.369805 0.929109i \(-0.620576\pi\)
−0.369805 + 0.929109i \(0.620576\pi\)
\(440\) 0 0
\(441\) −2.31489e15 + 6.40176e15i −0.314702 + 0.870297i
\(442\) 0 0
\(443\) 8.75315e15i 1.15809i 0.815296 + 0.579045i \(0.196574\pi\)
−0.815296 + 0.579045i \(0.803426\pi\)
\(444\) 0 0
\(445\) 1.96620e16 2.53202
\(446\) 0 0
\(447\) −1.22386e15 1.74396e15i −0.153421 0.218621i
\(448\) 0 0
\(449\) 8.80832e15i 1.07502i 0.843259 + 0.537508i \(0.180634\pi\)
−0.843259 + 0.537508i \(0.819366\pi\)
\(450\) 0 0
\(451\) 1.46952e16 1.74629
\(452\) 0 0
\(453\) −2.79761e15 + 1.96327e15i −0.323741 + 0.227191i
\(454\) 0 0
\(455\) 5.76515e15i 0.649743i
\(456\) 0 0
\(457\) −1.05517e16 −1.15831 −0.579154 0.815218i \(-0.696617\pi\)
−0.579154 + 0.815218i \(0.696617\pi\)
\(458\) 0 0
\(459\) −4.96868e14 + 1.34808e14i −0.0531331 + 0.0144158i
\(460\) 0 0
\(461\) 1.46940e16i 1.53086i −0.643520 0.765430i \(-0.722527\pi\)
0.643520 0.765430i \(-0.277473\pi\)
\(462\) 0 0
\(463\) −2.69625e14 −0.0273700 −0.0136850 0.999906i \(-0.504356\pi\)
−0.0136850 + 0.999906i \(0.504356\pi\)
\(464\) 0 0
\(465\) −1.20798e16 1.72134e16i −1.19493 1.70275i
\(466\) 0 0
\(467\) 1.09367e16i 1.05435i −0.849757 0.527175i \(-0.823251\pi\)
0.849757 0.527175i \(-0.176749\pi\)
\(468\) 0 0
\(469\) 1.13769e15 0.106902
\(470\) 0 0
\(471\) −7.09378e15 + 4.97818e15i −0.649759 + 0.455980i
\(472\) 0 0
\(473\) 1.67450e16i 1.49527i
\(474\) 0 0
\(475\) 1.06710e16 0.929059
\(476\) 0 0
\(477\) −1.16119e16 4.19888e15i −0.985806 0.356470i
\(478\) 0 0
\(479\) 9.92011e14i 0.0821303i 0.999156 + 0.0410651i \(0.0130751\pi\)
−0.999156 + 0.0410651i \(0.986925\pi\)
\(480\) 0 0
\(481\) 8.25044e15 0.666203
\(482\) 0 0
\(483\) −1.14108e15 1.62600e15i −0.0898736 0.128067i
\(484\) 0 0
\(485\) 8.62114e15i 0.662391i
\(486\) 0 0
\(487\) −1.19610e16 −0.896587 −0.448294 0.893886i \(-0.647968\pi\)
−0.448294 + 0.893886i \(0.647968\pi\)
\(488\) 0 0
\(489\) −1.48694e16 + 1.04348e16i −1.08753 + 0.763190i
\(490\) 0 0
\(491\) 7.43241e15i 0.530446i −0.964187 0.265223i \(-0.914554\pi\)
0.964187 0.265223i \(-0.0854455\pi\)
\(492\) 0 0
\(493\) 1.11749e15 0.0778330
\(494\) 0 0
\(495\) 1.15263e16 3.18756e16i 0.783534 2.16684i
\(496\) 0 0
\(497\) 7.87876e15i 0.522781i
\(498\) 0 0
\(499\) −3.01777e16 −1.95471 −0.977356 0.211601i \(-0.932132\pi\)
−0.977356 + 0.211601i \(0.932132\pi\)
\(500\) 0 0
\(501\) −2.35996e15 3.36287e15i −0.149237 0.212659i
\(502\) 0 0
\(503\) 2.10960e16i 1.30254i 0.758844 + 0.651272i \(0.225764\pi\)
−0.758844 + 0.651272i \(0.774236\pi\)
\(504\) 0 0
\(505\) 1.13522e15 0.0684435
\(506\) 0 0
\(507\) −1.97250e16 + 1.38424e16i −1.16137 + 0.815010i
\(508\) 0 0
\(509\) 8.44753e15i 0.485761i 0.970056 + 0.242881i \(0.0780923\pi\)
−0.970056 + 0.242881i \(0.921908\pi\)
\(510\) 0 0
\(511\) −7.67359e15 −0.430996
\(512\) 0 0
\(513\) −3.30621e15 1.21858e16i −0.181395 0.668576i
\(514\) 0 0
\(515\) 2.65033e16i 1.42055i
\(516\) 0 0
\(517\) 1.27181e16 0.666006
\(518\) 0 0
\(519\) 3.85233e15 + 5.48946e15i 0.197115 + 0.280883i
\(520\) 0 0
\(521\) 8.89514e15i 0.444761i 0.974960 + 0.222380i \(0.0713827\pi\)
−0.974960 + 0.222380i \(0.928617\pi\)
\(522\) 0 0
\(523\) 1.11232e16 0.543525 0.271763 0.962364i \(-0.412393\pi\)
0.271763 + 0.962364i \(0.412393\pi\)
\(524\) 0 0
\(525\) −6.27624e15 + 4.40446e15i −0.299739 + 0.210347i
\(526\) 0 0
\(527\) 1.60341e15i 0.0748480i
\(528\) 0 0
\(529\) 1.47191e16 0.671658
\(530\) 0 0
\(531\) 5.16343e15 + 1.86711e15i 0.230341 + 0.0832919i
\(532\) 0 0
\(533\) 4.13505e16i 1.80350i
\(534\) 0 0
\(535\) 7.47775e15 0.318895
\(536\) 0 0
\(537\) 9.33434e15 + 1.33012e16i 0.389258 + 0.554682i
\(538\) 0 0
\(539\) 3.41730e16i 1.39364i
\(540\) 0 0
\(541\) −1.38450e16 −0.552217 −0.276108 0.961127i \(-0.589045\pi\)
−0.276108 + 0.961127i \(0.589045\pi\)
\(542\) 0 0
\(543\) −3.44105e15 + 2.41482e15i −0.134243 + 0.0942075i
\(544\) 0 0
\(545\) 3.32344e16i 1.26826i
\(546\) 0 0
\(547\) 4.75107e16 1.77365 0.886824 0.462108i \(-0.152907\pi\)
0.886824 + 0.462108i \(0.152907\pi\)
\(548\) 0 0
\(549\) 8.39423e15 2.32140e16i 0.306582 0.847843i
\(550\) 0 0
\(551\) 2.74069e16i 0.979377i
\(552\) 0 0
\(553\) −1.21785e15 −0.0425838
\(554\) 0 0
\(555\) −1.10031e16 1.56791e16i −0.376494 0.536493i
\(556\) 0 0
\(557\) 3.48584e16i 1.16728i −0.812011 0.583642i \(-0.801627\pi\)
0.812011 0.583642i \(-0.198373\pi\)
\(558\) 0 0
\(559\) 4.71184e16 1.54426
\(560\) 0 0
\(561\) −2.11549e15 + 1.48458e15i −0.0678631 + 0.0476241i
\(562\) 0 0
\(563\) 4.07548e16i 1.27976i −0.768475 0.639880i \(-0.778984\pi\)
0.768475 0.639880i \(-0.221016\pi\)
\(564\) 0 0
\(565\) −1.07541e16 −0.330585
\(566\) 0 0
\(567\) 6.97429e15 + 5.80256e15i 0.209895 + 0.174631i
\(568\) 0 0
\(569\) 1.81151e16i 0.533787i 0.963726 + 0.266893i \(0.0859972\pi\)
−0.963726 + 0.266893i \(0.914003\pi\)
\(570\) 0 0
\(571\) 4.01906e15 0.115960 0.0579799 0.998318i \(-0.481534\pi\)
0.0579799 + 0.998318i \(0.481534\pi\)
\(572\) 0 0
\(573\) 1.61959e16 + 2.30787e16i 0.457591 + 0.652054i
\(574\) 0 0
\(575\) 2.77740e16i 0.768479i
\(576\) 0 0
\(577\) 2.16773e15 0.0587423 0.0293711 0.999569i \(-0.490650\pi\)
0.0293711 + 0.999569i \(0.490650\pi\)
\(578\) 0 0
\(579\) −2.87347e16 + 2.01651e16i −0.762668 + 0.535216i
\(580\) 0 0
\(581\) 7.27975e15i 0.189260i
\(582\) 0 0
\(583\) −6.19849e16 −1.57861
\(584\) 0 0
\(585\) 8.96940e16 + 3.24336e16i 2.23784 + 0.809207i
\(586\) 0 0
\(587\) 2.89892e16i 0.708611i −0.935130 0.354306i \(-0.884717\pi\)
0.935130 0.354306i \(-0.115283\pi\)
\(588\) 0 0
\(589\) −3.93240e16 −0.941817
\(590\) 0 0
\(591\) 3.09492e16 + 4.41018e16i 0.726315 + 1.03498i
\(592\) 0 0
\(593\) 8.16887e16i 1.87860i 0.343099 + 0.939299i \(0.388523\pi\)
−0.343099 + 0.939299i \(0.611477\pi\)
\(594\) 0 0
\(595\) 1.02054e15 0.0230001
\(596\) 0 0
\(597\) −1.62695e16 + 1.14174e16i −0.359358 + 0.252186i
\(598\) 0 0
\(599\) 6.71654e16i 1.45407i −0.686602 0.727034i \(-0.740898\pi\)
0.686602 0.727034i \(-0.259102\pi\)
\(600\) 0 0
\(601\) 2.08203e16 0.441815 0.220907 0.975295i \(-0.429098\pi\)
0.220907 + 0.975295i \(0.429098\pi\)
\(602\) 0 0
\(603\) −6.40041e15 + 1.77001e16i −0.133139 + 0.368191i
\(604\) 0 0
\(605\) 9.51225e16i 1.93977i
\(606\) 0 0
\(607\) −3.19708e16 −0.639177 −0.319589 0.947556i \(-0.603545\pi\)
−0.319589 + 0.947556i \(0.603545\pi\)
\(608\) 0 0
\(609\) −1.13122e16 1.61196e16i −0.221740 0.315973i
\(610\) 0 0
\(611\) 3.57871e16i 0.687827i
\(612\) 0 0
\(613\) 5.53934e16 1.04399 0.521993 0.852950i \(-0.325189\pi\)
0.521993 + 0.852950i \(0.325189\pi\)
\(614\) 0 0
\(615\) 7.85824e16 5.51466e16i 1.45236 1.01922i
\(616\) 0 0
\(617\) 3.00264e16i 0.544242i −0.962263 0.272121i \(-0.912275\pi\)
0.962263 0.272121i \(-0.0877251\pi\)
\(618\) 0 0
\(619\) 6.72566e16 1.19561 0.597807 0.801640i \(-0.296039\pi\)
0.597807 + 0.801640i \(0.296039\pi\)
\(620\) 0 0
\(621\) 3.17168e16 8.60527e15i 0.553019 0.150043i
\(622\) 0 0
\(623\) 2.64187e16i 0.451839i
\(624\) 0 0
\(625\) −3.23362e16 −0.542512
\(626\) 0 0
\(627\) −3.64098e16 5.18830e16i −0.599257 0.853925i
\(628\) 0 0
\(629\) 1.46049e15i 0.0235828i
\(630\) 0 0
\(631\) −9.48541e16 −1.50273 −0.751363 0.659889i \(-0.770603\pi\)
−0.751363 + 0.659889i \(0.770603\pi\)
\(632\) 0 0
\(633\) −4.56509e16 + 3.20363e16i −0.709621 + 0.497989i
\(634\) 0 0
\(635\) 1.03524e17i 1.57907i
\(636\) 0 0
\(637\) −9.61589e16 −1.43930
\(638\) 0 0
\(639\) 1.22578e17 + 4.43244e16i 1.80055 + 0.651085i
\(640\) 0 0
\(641\) 1.21087e17i 1.74561i 0.488068 + 0.872806i \(0.337702\pi\)
−0.488068 + 0.872806i \(0.662298\pi\)
\(642\) 0 0
\(643\) −4.15025e12 −5.87230e−5 −2.93615e−5 1.00000i \(-0.500009\pi\)
−2.93615e−5 1.00000i \(0.500009\pi\)
\(644\) 0 0
\(645\) −6.28390e16 8.95438e16i −0.872712 1.24359i
\(646\) 0 0
\(647\) 8.78508e16i 1.19762i −0.800890 0.598811i \(-0.795640\pi\)
0.800890 0.598811i \(-0.204360\pi\)
\(648\) 0 0
\(649\) 2.75628e16 0.368855
\(650\) 0 0
\(651\) 2.31288e16 1.62310e16i 0.303855 0.213236i
\(652\) 0 0
\(653\) 4.91168e16i 0.633507i −0.948508 0.316753i \(-0.897407\pi\)
0.948508 0.316753i \(-0.102593\pi\)
\(654\) 0 0
\(655\) −1.70962e17 −2.16497
\(656\) 0 0
\(657\) 4.31701e16 1.19386e17i 0.536773 1.48443i
\(658\) 0 0
\(659\) 1.34814e17i 1.64598i 0.568058 + 0.822989i \(0.307695\pi\)
−0.568058 + 0.822989i \(0.692305\pi\)
\(660\) 0 0
\(661\) −1.12334e17 −1.34680 −0.673398 0.739280i \(-0.735166\pi\)
−0.673398 + 0.739280i \(0.735166\pi\)
\(662\) 0 0
\(663\) −4.17744e15 5.95273e15i −0.0491845 0.0700866i
\(664\) 0 0
\(665\) 2.50291e16i 0.289412i
\(666\) 0 0
\(667\) −7.13336e16 −0.810100
\(668\) 0 0
\(669\) −4.89623e16 + 3.43602e16i −0.546142 + 0.383265i
\(670\) 0 0
\(671\) 1.23918e17i 1.35768i
\(672\) 0 0
\(673\) 8.85555e16 0.953071 0.476535 0.879155i \(-0.341892\pi\)
0.476535 + 0.879155i \(0.341892\pi\)
\(674\) 0 0
\(675\) −3.32157e16 1.22424e17i −0.351172 1.29433i
\(676\) 0 0
\(677\) 3.15610e16i 0.327808i 0.986476 + 0.163904i \(0.0524087\pi\)
−0.986476 + 0.163904i \(0.947591\pi\)
\(678\) 0 0
\(679\) −1.15838e16 −0.118204
\(680\) 0 0
\(681\) 8.17708e16 + 1.16521e17i 0.819814 + 1.16821i
\(682\) 0 0
\(683\) 1.62687e17i 1.60262i −0.598251 0.801309i \(-0.704138\pi\)
0.598251 0.801309i \(-0.295862\pi\)
\(684\) 0 0
\(685\) −8.29598e16 −0.803016
\(686\) 0 0
\(687\) −3.61343e16 + 2.53579e16i −0.343700 + 0.241198i
\(688\) 0 0
\(689\) 1.74418e17i 1.63033i
\(690\) 0 0
\(691\) −1.26552e17 −1.16252 −0.581262 0.813717i \(-0.697441\pi\)
−0.581262 + 0.813717i \(0.697441\pi\)
\(692\) 0 0
\(693\) 4.28295e16 + 1.54873e16i 0.386673 + 0.139822i
\(694\) 0 0
\(695\) 4.51045e16i 0.400232i
\(696\) 0 0
\(697\) −7.31984e15 −0.0638418
\(698\) 0 0
\(699\) 4.30889e16 + 6.14006e16i 0.369405 + 0.526392i
\(700\) 0 0
\(701\) 1.06212e17i 0.895087i −0.894262 0.447544i \(-0.852299\pi\)
0.894262 0.447544i \(-0.147701\pi\)
\(702\) 0 0
\(703\) −3.58189e16 −0.296743
\(704\) 0 0
\(705\) 6.80098e16 4.77271e16i 0.553907 0.388714i
\(706\) 0 0
\(707\) 1.52534e15i 0.0122138i
\(708\) 0 0
\(709\) −1.00372e17 −0.790198 −0.395099 0.918638i \(-0.629290\pi\)
−0.395099 + 0.918638i \(0.629290\pi\)
\(710\) 0 0
\(711\) 6.85141e15 1.89473e16i 0.0530349 0.146666i
\(712\) 0 0
\(713\) 1.02351e17i 0.779032i
\(714\) 0 0
\(715\) 4.78793e17 3.58354
\(716\) 0 0
\(717\) 2.79555e16 + 3.98358e16i 0.205756 + 0.293196i
\(718\) 0 0
\(719\) 1.14056e17i 0.825553i 0.910832 + 0.412777i \(0.135441\pi\)
−0.910832 + 0.412777i \(0.864559\pi\)
\(720\) 0 0
\(721\) 3.56111e16 0.253498
\(722\) 0 0
\(723\) −1.98282e17 + 1.39148e17i −1.38821 + 0.974200i
\(724\) 0 0
\(725\) 2.75342e17i 1.89602i
\(726\) 0 0
\(727\) 8.50991e16 0.576393 0.288196 0.957571i \(-0.406944\pi\)
0.288196 + 0.957571i \(0.406944\pi\)
\(728\) 0 0
\(729\) −1.29512e17 + 7.58618e16i −0.862870 + 0.505426i
\(730\) 0 0
\(731\) 8.34088e15i 0.0546648i
\(732\) 0 0
\(733\) −1.21654e15 −0.00784338 −0.00392169 0.999992i \(-0.501248\pi\)
−0.00392169 + 0.999992i \(0.501248\pi\)
\(734\) 0 0
\(735\) 1.28241e17 + 1.82740e17i 0.813399 + 1.15907i
\(736\) 0 0
\(737\) 9.44846e16i 0.589598i
\(738\) 0 0
\(739\) −5.96546e16 −0.366250 −0.183125 0.983090i \(-0.558621\pi\)
−0.183125 + 0.983090i \(0.558621\pi\)
\(740\) 0 0
\(741\) 1.45992e17 1.02453e17i 0.881904 0.618892i
\(742\) 0 0
\(743\) 1.50758e17i 0.896081i 0.894013 + 0.448041i \(0.147878\pi\)
−0.894013 + 0.448041i \(0.852122\pi\)
\(744\) 0 0
\(745\) −6.98708e16 −0.408656
\(746\) 0 0
\(747\) −1.13258e17 4.09544e16i −0.651847 0.235710i
\(748\) 0 0
\(749\) 1.00475e16i 0.0569069i
\(750\) 0 0
\(751\) 1.59484e17 0.888949 0.444474 0.895792i \(-0.353390\pi\)
0.444474 + 0.895792i \(0.353390\pi\)
\(752\) 0 0
\(753\) 1.23924e17 + 1.76588e17i 0.679806 + 0.968706i
\(754\) 0 0
\(755\) 1.12085e17i 0.605152i
\(756\) 0 0
\(757\) 1.38985e17 0.738569 0.369285 0.929316i \(-0.379603\pi\)
0.369285 + 0.929316i \(0.379603\pi\)
\(758\) 0 0
\(759\) 1.35039e17 9.47660e16i 0.706331 0.495681i
\(760\) 0 0
\(761\) 1.06699e17i 0.549354i 0.961537 + 0.274677i \(0.0885710\pi\)
−0.961537 + 0.274677i \(0.911429\pi\)
\(762\) 0 0
\(763\) 4.46553e16 0.226321
\(764\) 0 0
\(765\) −5.74138e15 + 1.58776e16i −0.0286449 + 0.0792166i
\(766\) 0 0
\(767\) 7.75584e16i 0.380940i
\(768\) 0 0
\(769\) −1.33329e17 −0.644712 −0.322356 0.946619i \(-0.604475\pi\)
−0.322356 + 0.946619i \(0.604475\pi\)
\(770\) 0 0
\(771\) −1.49240e17 2.12662e17i −0.710490 1.01243i
\(772\) 0 0
\(773\) 2.55517e17i 1.19768i −0.800867 0.598842i \(-0.795628\pi\)
0.800867 0.598842i \(-0.204372\pi\)
\(774\) 0 0
\(775\) −3.95067e17 −1.82331
\(776\) 0 0