Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,8,Mod(19,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.19");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.b (of order \(2\), degree \(1\), 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: | \(14.0573261468\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-29}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 29 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(5.38516i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.19 |
Dual form | 45.8.b.a.19.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.7703i | 0.951972i | 0.879453 | + | 0.475986i | \(0.157909\pi\) | ||||
−0.879453 | + | 0.475986i | \(0.842091\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.0000 | 0.0937500 | ||||||||
\(5\) | −75.0000 | − | 269.258i | −0.268328 | − | 0.963328i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 420.043i | 0.462861i | 0.972851 | + | 0.231430i | \(0.0743406\pi\) | ||||
−0.972851 | + | 0.231430i | \(0.925659\pi\) | |||||||
\(8\) | 1507.85i | 1.04122i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2900.00 | − | 807.775i | 0.917061 | − | 0.255441i | ||||
\(11\) | 6828.00 | 1.54675 | 0.773373 | − | 0.633951i | \(-0.218568\pi\) | ||||
0.773373 | + | 0.633951i | \(0.218568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10145.7i | 1.28079i | 0.768045 | + | 0.640395i | \(0.221229\pi\) | ||||
−0.768045 | + | 0.640395i | \(0.778771\pi\) | |||||||
\(14\) | −4524.00 | −0.440630 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14704.0 | −0.897461 | ||||||||
\(17\) | 15681.6i | 0.774139i | 0.922050 | + | 0.387070i | \(0.126513\pi\) | ||||
−0.922050 | + | 0.387070i | \(0.873487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6860.00 | 0.229449 | 0.114725 | − | 0.993397i | \(-0.463401\pi\) | ||||
0.114725 | + | 0.993397i | \(0.463401\pi\) | |||||||
\(20\) | −900.000 | − | 3231.10i | −0.0251558 | − | 0.0903120i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 73539.8i | 1.47246i | ||||||||
\(23\) | 29219.9i | 0.500762i | 0.968147 | + | 0.250381i | \(0.0805559\pi\) | ||||
−0.968147 | + | 0.250381i | \(0.919444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −66875.0 | + | 40388.7i | −0.856000 | + | 0.516976i | ||||
\(26\) | −109272. | −1.21928 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5040.51i | 0.0433932i | ||||||||
\(29\) | −25590.0 | −0.194840 | −0.0974198 | − | 0.995243i | \(-0.531059\pi\) | ||||
−0.0974198 | + | 0.995243i | \(0.531059\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 82112.0 | 0.495040 | 0.247520 | − | 0.968883i | \(-0.420384\pi\) | ||||
0.247520 | + | 0.968883i | \(0.420384\pi\) | |||||||
\(32\) | 34637.4i | 0.186862i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −168896. | −0.736959 | ||||||||
\(35\) | 113100. | − | 31503.2i | 0.445887 | − | 0.124199i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 223527.i | 0.725479i | 0.931891 | + | 0.362739i | \(0.118158\pi\) | ||||
−0.931891 | + | 0.362739i | \(0.881842\pi\) | |||||||
\(38\) | 73884.5i | 0.218429i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 406000. | − | 113088.i | 1.00303 | − | 0.279388i | ||||
\(41\) | 533118. | 1.20804 | 0.604018 | − | 0.796971i | \(-0.293566\pi\) | ||||
0.604018 | + | 0.796971i | \(0.293566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 708935.i | − | 1.35978i | −0.733316 | − | 0.679888i | \(-0.762029\pi\) | ||
0.733316 | − | 0.679888i | \(-0.237971\pi\) | |||||||
\(44\) | 81936.0 | 0.145007 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −314708. | −0.476711 | ||||||||
\(47\) | 5826.75i | 0.00818623i | 0.999992 | + | 0.00409311i | \(0.00130288\pi\) | ||||
−0.999992 | + | 0.00409311i | \(0.998697\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 647107. | 0.785760 | ||||||||
\(50\) | −435000. | − | 720266.i | −0.492146 | − | 0.814888i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 121748.i | 0.120074i | ||||||||
\(53\) | − | 589374.i | − | 0.543783i | −0.962328 | − | 0.271891i | \(-0.912351\pi\) | ||
0.962328 | − | 0.271891i | \(-0.0876491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −512100. | − | 1.83850e6i | −0.415036 | − | 1.49002i | ||||
\(56\) | −633360. | −0.481940 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 275613.i | − | 0.185482i | ||||||
\(59\) | −1.43898e6 | −0.912164 | −0.456082 | − | 0.889938i | \(-0.650748\pi\) | ||||
−0.456082 | + | 0.889938i | \(0.650748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.38102e6 | 0.779016 | 0.389508 | − | 0.921023i | \(-0.372645\pi\) | ||||
0.389508 | + | 0.921023i | \(0.372645\pi\) | |||||||
\(62\) | 884373.i | 0.471264i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.25517e6 | −1.07535 | ||||||||
\(65\) | 2.73180e6 | − | 760924.i | 1.23382 | − | 0.343672i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.71487e6i | 1.10277i | 0.834250 | + | 0.551387i | \(0.185901\pi\) | ||||
−0.834250 | + | 0.551387i | \(0.814099\pi\) | |||||||
\(68\) | 188179.i | 0.0725756i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 339300. | + | 1.21812e6i | 0.118234 | + | 0.424471i | ||||
\(71\) | 481608. | 0.159694 | 0.0798472 | − | 0.996807i | \(-0.474557\pi\) | ||||
0.0798472 | + | 0.996807i | \(0.474557\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.48618e6i | − | 0.447137i | −0.974688 | − | 0.223568i | \(-0.928229\pi\) | ||
0.974688 | − | 0.223568i | \(-0.0717706\pi\) | |||||||
\(74\) | −2.40746e6 | −0.690635 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 82320.0 | 0.0215109 | ||||||||
\(77\) | 2.86805e6i | 0.715928i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.05976e6 | −0.241831 | −0.120916 | − | 0.992663i | \(-0.538583\pi\) | ||||
−0.120916 | + | 0.992663i | \(0.538583\pi\) | |||||||
\(80\) | 1.10280e6 | + | 3.95917e6i | 0.240814 | + | 0.864549i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.74186e6i | 1.15002i | ||||||||
\(83\) | − | 2.60380e6i | − | 0.499844i | −0.968266 | − | 0.249922i | \(-0.919595\pi\) | ||
0.968266 | − | 0.249922i | \(-0.0804050\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.22240e6 | − | 1.17612e6i | 0.745750 | − | 0.207723i | ||||
\(86\) | 7.63547e6 | 1.29447 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.02956e7i | 1.61050i | ||||||||
\(89\) | −5.64417e6 | −0.848663 | −0.424331 | − | 0.905507i | \(-0.639491\pi\) | ||||
−0.424331 | + | 0.905507i | \(0.639491\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.26161e6 | −0.592828 | ||||||||
\(92\) | 350639.i | 0.0469464i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −62756.0 | −0.00779306 | ||||||||
\(95\) | −514500. | − | 1.84711e6i | −0.0615677 | − | 0.221035i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.20091e7i | − | 1.33601i | −0.744158 | − | 0.668004i | \(-0.767149\pi\) | ||
0.744158 | − | 0.668004i | \(-0.232851\pi\) | |||||||
\(98\) | 6.96956e6i | 0.748021i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −802500. | + | 484665.i | −0.0802500 | + | 0.0484665i | ||||
\(101\) | −5.14270e6 | −0.496668 | −0.248334 | − | 0.968674i | \(-0.579883\pi\) | ||||
−0.248334 | + | 0.968674i | \(0.579883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.48477e6i | − | 0.314227i | −0.987581 | − | 0.157114i | \(-0.949781\pi\) | ||
0.987581 | − | 0.157114i | \(-0.0502189\pi\) | |||||||
\(104\) | −1.52981e7 | −1.33358 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.34775e6 | 0.517666 | ||||||||
\(107\) | − | 1.48640e7i | − | 1.17299i | −0.809954 | − | 0.586493i | \(-0.800508\pi\) | ||
0.809954 | − | 0.586493i | \(-0.199492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.01124e7 | −1.48755 | −0.743773 | − | 0.668432i | \(-0.766966\pi\) | ||||
−0.743773 | + | 0.668432i | \(0.766966\pi\) | |||||||
\(110\) | 1.98012e7 | − | 5.51549e6i | 1.41846 | − | 0.395102i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 6.17631e6i | − | 0.415400i | ||||||
\(113\) | − | 5.62633e6i | − | 0.366818i | −0.983037 | − | 0.183409i | \(-0.941287\pi\) | ||
0.983037 | − | 0.183409i | \(-0.0587133\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.86770e6 | − | 2.19149e6i | 0.482398 | − | 0.134369i | ||||
\(116\) | −307080. | −0.0182662 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.54983e7i | − | 0.868354i | ||||||
\(119\) | −6.58694e6 | −0.358319 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.71344e7 | 1.39242 | ||||||||
\(122\) | 1.48741e7i | 0.741601i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 985344. | 0.0464100 | ||||||||
\(125\) | 1.58906e7 | + | 1.49775e7i | 0.727706 | + | 0.685889i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.85360e7i | − | 1.23618i | −0.786109 | − | 0.618088i | \(-0.787908\pi\) | ||
0.786109 | − | 0.618088i | \(-0.212092\pi\) | |||||||
\(128\) | − | 1.98553e7i | − | 0.836839i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.19540e6 | + | 2.94224e7i | 0.327166 | + | 1.17456i | ||||
\(131\) | 3.33132e7 | 1.29469 | 0.647346 | − | 0.762196i | \(-0.275879\pi\) | ||||
0.647346 | + | 0.762196i | \(0.275879\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.88149e6i | 0.106203i | ||||||||
\(134\) | −2.92400e7 | −1.04981 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.36454e7 | −0.806049 | ||||||||
\(137\) | − | 4.28099e7i | − | 1.42240i | −0.702988 | − | 0.711202i | \(-0.748151\pi\) | ||
0.702988 | − | 0.711202i | \(-0.251849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.13808e7 | 0.359436 | 0.179718 | − | 0.983718i | \(-0.442481\pi\) | ||||
0.179718 | + | 0.983718i | \(0.442481\pi\) | |||||||
\(140\) | 1.35720e6 | − | 378039.i | 0.0418019 | − | 0.0116436i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.18708e6i | 0.152024i | ||||||||
\(143\) | 6.92745e7i | 1.98106i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.91925e6 | + | 6.89032e6i | 0.0522810 | + | 0.187694i | ||||
\(146\) | 1.60066e7 | 0.425661 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.68233e6i | 0.0680136i | ||||||||
\(149\) | −4.00070e7 | −0.990794 | −0.495397 | − | 0.868667i | \(-0.664977\pi\) | ||||
−0.495397 | + | 0.868667i | \(0.664977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.86594e7 | −0.677405 | −0.338703 | − | 0.940893i | \(-0.609988\pi\) | ||||
−0.338703 | + | 0.940893i | \(0.609988\pi\) | |||||||
\(152\) | 1.03438e7i | 0.238907i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.08899e7 | −0.681544 | ||||||||
\(155\) | −6.15840e6 | − | 2.21093e7i | −0.132833 | − | 0.476886i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.01958e7i | 0.622728i | 0.950291 | + | 0.311364i | \(0.100786\pi\) | ||||
−0.950291 | + | 0.311364i | \(0.899214\pi\) | |||||||
\(158\) | − | 1.14140e7i | − | 0.230217i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.32640e6 | − | 2.59780e6i | 0.180009 | − | 0.0501402i | ||||
\(161\) | −1.22736e7 | −0.231783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.35416e7i | 1.69180i | 0.533345 | + | 0.845898i | \(0.320935\pi\) | ||||
−0.533345 | + | 0.845898i | \(0.679065\pi\) | |||||||
\(164\) | 6.39742e6 | 0.113253 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.80438e7 | 0.475838 | ||||||||
\(167\) | 5.73507e7i | 0.952865i | 0.879211 | + | 0.476432i | \(0.158070\pi\) | ||||
−0.879211 | + | 0.476432i | \(0.841930\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.01857e7 | −0.640425 | ||||||||
\(170\) | 1.26672e7 | + | 4.54766e7i | 0.197747 | + | 0.709933i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 8.50722e6i | − | 0.127479i | ||||||
\(173\) | − | 4.87192e7i | − | 0.715383i | −0.933840 | − | 0.357691i | \(-0.883564\pi\) | ||
0.933840 | − | 0.357691i | \(-0.116436\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.69650e7 | − | 2.80904e7i | −0.239288 | − | 0.396209i | ||||
\(176\) | −1.00399e8 | −1.38814 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 6.07896e7i | − | 0.807903i | ||||||
\(179\) | −1.93505e7 | −0.252178 | −0.126089 | − | 0.992019i | \(-0.540243\pi\) | ||||
−0.126089 | + | 0.992019i | \(0.540243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.82617e7 | 0.981011 | 0.490506 | − | 0.871438i | \(-0.336812\pi\) | ||||
0.490506 | + | 0.871438i | \(0.336812\pi\) | |||||||
\(182\) | − | 4.58989e7i | − | 0.564355i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.40591e7 | −0.521403 | ||||||||
\(185\) | 6.01866e7 | − | 1.67646e7i | 0.698874 | − | 0.194666i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.07074e8i | 1.19740i | ||||||||
\(188\) | 69921.0i | 0.000767459i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.98940e7 | − | 5.54133e6i | 0.210419 | − | 0.0586107i | ||||
\(191\) | 1.19454e8 | 1.24046 | 0.620229 | − | 0.784420i | \(-0.287040\pi\) | ||||
0.620229 | + | 0.784420i | \(0.287040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.98469e7i | − | 0.599227i | −0.954061 | − | 0.299613i | \(-0.903142\pi\) | ||
0.954061 | − | 0.299613i | \(-0.0968577\pi\) | |||||||
\(194\) | 1.29342e8 | 1.27184 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.76528e6 | 0.0736650 | ||||||||
\(197\) | 1.22964e8i | 1.14590i | 0.819589 | + | 0.572952i | \(0.194202\pi\) | ||||
−0.819589 | + | 0.572952i | \(0.805798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.69053e8 | 1.52067 | 0.760337 | − | 0.649529i | \(-0.225034\pi\) | ||||
0.760337 | + | 0.649529i | \(0.225034\pi\) | |||||||
\(200\) | −6.09000e7 | − | 1.00837e8i | −0.538285 | − | 0.891283i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 5.53886e7i | − | 0.472814i | ||||||
\(203\) | − | 1.07489e7i | − | 0.0901836i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.99838e7 | − | 1.43546e8i | −0.324150 | − | 1.16373i | ||||
\(206\) | 3.75321e7 | 0.299136 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.49182e8i | − | 1.14946i | ||||||
\(209\) | 4.68401e7 | 0.354900 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.67605e8 | −1.96113 | −0.980565 | − | 0.196195i | \(-0.937141\pi\) | ||||
−0.980565 | + | 0.196195i | \(0.937141\pi\) | |||||||
\(212\) | − | 7.07249e6i | − | 0.0509796i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.60090e8 | 1.11665 | ||||||||
\(215\) | −1.90887e8 | + | 5.31702e7i | −1.30991 | + | 0.364866i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.44906e7i | 0.229135i | ||||||||
\(218\) | − | 2.16617e8i | − | 1.41610i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.14520e6 | − | 2.20619e7i | −0.0389096 | − | 0.139690i | ||||
\(221\) | −1.59100e8 | −0.991510 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.49333e8i | 0.901753i | 0.892586 | + | 0.450877i | \(0.148889\pi\) | ||||
−0.892586 | + | 0.450877i | \(0.851111\pi\) | |||||||
\(224\) | −1.45492e7 | −0.0864909 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.05975e7 | 0.349201 | ||||||||
\(227\) | − | 2.34185e8i | − | 1.32883i | −0.747365 | − | 0.664414i | \(-0.768681\pi\) | ||
0.747365 | − | 0.664414i | \(-0.231319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.31882e8 | −0.725706 | −0.362853 | − | 0.931846i | \(-0.618197\pi\) | ||||
−0.362853 | + | 0.931846i | \(0.618197\pi\) | |||||||
\(230\) | 2.36031e7 | + | 8.47377e7i | 0.127915 | + | 0.459229i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 3.85858e7i | − | 0.202871i | ||||||
\(233\) | 1.83419e8i | 0.949948i | 0.880000 | + | 0.474974i | \(0.157542\pi\) | ||||
−0.880000 | + | 0.474974i | \(0.842458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.56890e6 | − | 437006.i | 0.00788602 | − | 0.00219660i | ||||
\(236\) | −1.72678e7 | −0.0855153 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 7.09436e7i | − | 0.341109i | ||||||
\(239\) | 1.05117e8 | 0.498058 | 0.249029 | − | 0.968496i | \(-0.419889\pi\) | ||||
0.249029 | + | 0.968496i | \(0.419889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.94216e8 | 0.893770 | 0.446885 | − | 0.894591i | \(-0.352533\pi\) | ||||
0.446885 | + | 0.894591i | \(0.352533\pi\) | |||||||
\(242\) | 2.92247e8i | 1.32555i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.65723e7 | 0.0730327 | ||||||||
\(245\) | −4.85330e7 | − | 1.74239e8i | −0.210841 | − | 0.756944i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.95992e7i | 0.293876i | ||||||||
\(248\) | 1.23812e8i | 0.515446i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.61312e8 | + | 1.71147e8i | −0.652947 | + | 0.692755i | ||||
\(251\) | −2.02689e8 | −0.809045 | −0.404523 | − | 0.914528i | \(-0.632562\pi\) | ||||
−0.404523 | + | 0.914528i | \(0.632562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.99514e8i | 0.774552i | ||||||||
\(254\) | 3.07342e8 | 1.17680 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.48132e7 | −0.278701 | ||||||||
\(257\) | − | 1.34593e7i | − | 0.0494603i | −0.999694 | − | 0.0247301i | \(-0.992127\pi\) | ||
0.999694 | − | 0.0247301i | \(-0.00787265\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.38911e7 | −0.335796 | ||||||||
\(260\) | 3.27816e7 | − | 9.13109e6i | 0.115671 | − | 0.0322193i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.58794e8i | 1.23251i | ||||||||
\(263\) | 1.42205e8i | 0.482026i | 0.970522 | + | 0.241013i | \(0.0774797\pi\) | ||||
−0.970522 | + | 0.241013i | \(0.922520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.58694e8 | + | 4.42030e7i | −0.523841 | + | 0.145912i | ||||
\(266\) | −3.10346e7 | −0.101102 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.25784e7i | 0.103385i | ||||||||
\(269\) | 5.07548e8 | 1.58981 | 0.794903 | − | 0.606737i | \(-0.207522\pi\) | ||||
0.794903 | + | 0.606737i | \(0.207522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.12836e8 | 0.344393 | 0.172197 | − | 0.985063i | \(-0.444914\pi\) | ||||
0.172197 | + | 0.985063i | \(0.444914\pi\) | |||||||
\(272\) | − | 2.30582e8i | − | 0.694760i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.61077e8 | 1.35409 | ||||||||
\(275\) | −4.56622e8 | + | 2.75774e8i | −1.32401 | + | 0.799630i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.10728e8i | − | 1.44381i | −0.691991 | − | 0.721906i | \(-0.743266\pi\) | ||
0.691991 | − | 0.721906i | \(-0.256734\pi\) | |||||||
\(278\) | 1.22575e8i | 0.342173i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.75020e7 | + | 1.70537e8i | 0.129318 | + | 0.464266i | ||||
\(281\) | 1.70459e8 | 0.458297 | 0.229148 | − | 0.973391i | \(-0.426406\pi\) | ||||
0.229148 | + | 0.973391i | \(0.426406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.62144e8i | 0.425253i | 0.977134 | + | 0.212626i | \(0.0682017\pi\) | ||||
−0.977134 | + | 0.212626i | \(0.931798\pi\) | |||||||
\(284\) | 5.77930e6 | 0.0149713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.46109e8 | −1.88591 | ||||||||
\(287\) | 2.23932e8i | 0.559153i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.64426e8 | 0.400708 | ||||||||
\(290\) | −7.42110e7 | + | 2.06710e7i | −0.178680 | + | 0.0497700i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 1.78341e7i | − | 0.0419191i | ||||||
\(293\) | − | 3.85845e8i | − | 0.896141i | −0.893998 | − | 0.448070i | \(-0.852111\pi\) | ||
0.893998 | − | 0.448070i | \(-0.147889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.07924e8 | + | 3.87457e8i | 0.244759 | + | 0.878712i | ||||
\(296\) | −3.37045e8 | −0.755382 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 4.30888e8i | − | 0.943208i | ||||||
\(299\) | −2.96455e8 | −0.641371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.97783e8 | 0.629387 | ||||||||
\(302\) | − | 3.08672e8i | − | 0.644871i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00869e8 | −0.205922 | ||||||||
\(305\) | −1.03577e8 | − | 3.71852e8i | −0.209032 | − | 0.750447i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.37817e8i | − | 1.25809i | −0.777369 | − | 0.629045i | \(-0.783446\pi\) | ||
0.777369 | − | 0.629045i | \(-0.216554\pi\) | |||||||
\(308\) | 3.44166e7i | 0.0671183i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.38125e8 | − | 6.63280e7i | 0.453982 | − | 0.126454i | ||||
\(311\) | 7.27817e8 | 1.37202 | 0.686010 | − | 0.727592i | \(-0.259360\pi\) | ||||
0.686010 | + | 0.727592i | \(0.259360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.46869e8i | − | 0.823711i | −0.911249 | − | 0.411855i | \(-0.864881\pi\) | ||
0.911249 | − | 0.411855i | \(-0.135119\pi\) | |||||||
\(314\) | −3.25219e8 | −0.592819 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.27171e7 | −0.0226717 | ||||||||
\(317\) | − | 5.91083e8i | − | 1.04218i | −0.853503 | − | 0.521088i | \(-0.825526\pi\) | ||
0.853503 | − | 0.521088i | \(-0.174474\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.74729e8 | −0.301367 | ||||||||
\(320\) | 1.69138e8 | + | 6.07223e8i | 0.288546 | + | 1.03591i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 1.32191e8i | − | 0.220651i | ||||||
\(323\) | 1.07576e8i | 0.177626i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.09770e8 | − | 6.78490e8i | −0.662138 | − | 1.09636i | ||||
\(326\) | −1.00747e9 | −1.61054 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.03860e8i | 1.25783i | ||||||||
\(329\) | −2.44748e6 | −0.00378908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.84868e8 | 0.886462 | 0.443231 | − | 0.896407i | \(-0.353832\pi\) | ||||
0.443231 | + | 0.896407i | \(0.353832\pi\) | |||||||
\(332\) | − | 3.12456e7i | − | 0.0468604i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.17686e8 | −0.907100 | ||||||||
\(335\) | 7.31000e8 | − | 2.03615e8i | 1.06233 | − | 0.295905i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.39373e8i | − | 1.05235i | −0.850377 | − | 0.526174i | \(-0.823626\pi\) | ||
0.850377 | − | 0.526174i | \(-0.176374\pi\) | |||||||
\(338\) | − | 4.32813e8i | − | 0.609666i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.06688e7 | − | 1.41134e7i | 0.0699140 | − | 0.0194741i | ||||
\(341\) | 5.60661e8 | 0.765702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.17736e8i | 0.826558i | ||||||||
\(344\) | 1.06897e9 | 1.41582 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.24722e8 | 0.681024 | ||||||||
\(347\) | 3.70870e8i | 0.476506i | 0.971203 | + | 0.238253i | \(0.0765747\pi\) | ||||
−0.971203 | + | 0.238253i | \(0.923425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.13274e9 | 1.42640 | 0.713199 | − | 0.700962i | \(-0.247246\pi\) | ||||
0.713199 | + | 0.700962i | \(0.247246\pi\) | |||||||
\(350\) | 3.02542e8 | − | 1.82719e8i | 0.377180 | − | 0.227795i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.36504e8i | 0.289028i | ||||||||
\(353\) | 8.32858e8i | 1.00777i | 0.863772 | + | 0.503883i | \(0.168096\pi\) | ||||
−0.863772 | + | 0.503883i | \(0.831904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.61206e7 | − | 1.29677e8i | −0.0428505 | − | 0.153838i | ||||
\(356\) | −6.77300e7 | −0.0795621 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2.08412e8i | − | 0.240066i | ||||||
\(359\) | −6.75318e8 | −0.770332 | −0.385166 | − | 0.922847i | \(-0.625856\pi\) | ||||
−0.385166 | + | 0.922847i | \(0.625856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.46812e8 | −0.947353 | ||||||||
\(362\) | 8.42904e8i | 0.933895i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.11393e7 | −0.0555776 | ||||||||
\(365\) | −4.00165e8 | + | 1.11463e8i | −0.430739 | + | 0.119979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.80237e9i | 1.90333i | 0.307141 | + | 0.951664i | \(0.400628\pi\) | ||||
−0.307141 | + | 0.951664i | \(0.599372\pi\) | |||||||
\(368\) | − | 4.29649e8i | − | 0.449414i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.80560e8 | + | 6.48230e8i | 0.185317 | + | 0.665308i | ||||
\(371\) | 2.47562e8 | 0.251696 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.29928e8i | − | 0.927830i | −0.885880 | − | 0.463915i | \(-0.846444\pi\) | ||
0.885880 | − | 0.463915i | \(-0.153556\pi\) | |||||||
\(374\) | −1.15322e9 | −1.13989 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.78584e6 | −0.00852365 | ||||||||
\(377\) | − | 2.59627e8i | − | 0.249549i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.43545e9 | −1.35441 | −0.677206 | − | 0.735794i | \(-0.736809\pi\) | ||||
−0.677206 | + | 0.735794i | \(0.736809\pi\) | |||||||
\(380\) | −6.17400e6 | − | 2.21653e7i | −0.00577197 | − | 0.0207220i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.28655e9i | 1.18088i | ||||||||
\(383\) | − | 1.57707e9i | − | 1.43435i | −0.696894 | − | 0.717174i | \(-0.745435\pi\) | ||
0.696894 | − | 0.717174i | \(-0.254565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.72247e8 | − | 2.15104e8i | 0.689674 | − | 0.192104i | ||||
\(386\) | 6.44571e8 | 0.570447 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.44109e8i | − | 0.125251i | ||||||
\(389\) | −2.24425e9 | −1.93307 | −0.966537 | − | 0.256528i | \(-0.917421\pi\) | ||||
−0.966537 | + | 0.256528i | \(0.917421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.58215e8 | −0.387660 | ||||||||
\(392\) | 9.75738e8i | 0.818148i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.32437e9 | −1.09087 | ||||||||
\(395\) | 7.94820e7 | + | 2.85349e8i | 0.0648902 | + | 0.232963i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.26641e8i | 0.181791i | 0.995860 | + | 0.0908956i | \(0.0289729\pi\) | ||||
−0.995860 | + | 0.0908956i | \(0.971027\pi\) | |||||||
\(398\) | 1.82075e9i | 1.44764i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.83330e8 | − | 5.93876e8i | 0.768227 | − | 0.463966i | ||||
\(401\) | 9.11721e8 | 0.706085 | 0.353042 | − | 0.935607i | \(-0.385147\pi\) | ||||
0.353042 | + | 0.935607i | \(0.385147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.33080e8i | 0.634043i | ||||||||
\(404\) | −6.17124e7 | −0.0465627 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.15769e8 | 0.0858523 | ||||||||
\(407\) | 1.52625e9i | 1.12213i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.55215e8 | −0.184449 | −0.0922243 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922243 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(410\) | 1.54604e9 | − | 4.30639e8i | 1.10784 | − | 0.308582i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 4.18173e7i | − | 0.0294588i | ||||||
\(413\) | − | 6.04433e8i | − | 0.422205i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.01095e8 | + | 1.95285e8i | −0.481514 | + | 0.134122i | ||||
\(416\) | −3.51419e8 | −0.239331 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.04483e8i | 0.337854i | ||||||||
\(419\) | −2.96316e8 | −0.196791 | −0.0983957 | − | 0.995147i | \(-0.531371\pi\) | ||||
−0.0983957 | + | 0.995147i | \(0.531371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.06676e9 | 0.696754 | 0.348377 | − | 0.937354i | \(-0.386733\pi\) | ||||
0.348377 | + | 0.937354i | \(0.386733\pi\) | |||||||
\(422\) | − | 2.88220e9i | − | 1.86694i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.88685e8 | 0.566197 | ||||||||
\(425\) | −6.33360e8 | − | 1.04871e9i | −0.400211 | − | 0.662663i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.80088e8i | 0.360576i | ||||||||
\(428\) | − | 1.78368e8i | − | 0.109967i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.72660e8 | − | 2.05591e9i | −0.347342 | − | 1.24700i | ||||
\(431\) | −9.53169e7 | −0.0573455 | −0.0286728 | − | 0.999589i | \(-0.509128\pi\) | ||||
−0.0286728 | + | 0.999589i | \(0.509128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.89973e9i | − | 1.12456i | −0.826946 | − | 0.562281i | \(-0.809924\pi\) | ||
0.826946 | − | 0.562281i | \(-0.190076\pi\) | |||||||
\(434\) | −3.71475e8 | −0.218130 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.41348e8 | −0.139457 | ||||||||
\(437\) | 2.00449e8i | 0.114899i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.11226e9 | −0.627450 | −0.313725 | − | 0.949514i | \(-0.601577\pi\) | ||||
−0.313725 | + | 0.949514i | \(0.601577\pi\) | |||||||
\(440\) | 2.77217e9 | − | 7.72168e8i | 1.55144 | − | 0.432143i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.71356e9i | − | 0.943890i | ||||||
\(443\) | 3.22249e9i | 1.76108i | 0.473972 | + | 0.880540i | \(0.342820\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.23313e8 | + | 1.51974e9i | 0.227720 | + | 0.817540i | ||||
\(446\) | −1.60836e9 | −0.858443 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 9.47267e8i | − | 0.497736i | ||||||
\(449\) | 7.29482e7 | 0.0380323 | 0.0190161 | − | 0.999819i | \(-0.493947\pi\) | ||||
0.0190161 | + | 0.999819i | \(0.493947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.64013e9 | 1.86853 | ||||||||
\(452\) | − | 6.75160e7i | − | 0.0343892i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.52225e9 | 1.26501 | ||||||||
\(455\) | 3.19621e8 | + | 1.14747e9i | 0.159072 | + | 0.571087i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.45286e8i | − | 0.120217i | −0.998192 | − | 0.0601085i | \(-0.980855\pi\) | ||
0.998192 | − | 0.0601085i | \(-0.0191447\pi\) | |||||||
\(458\) | − | 1.42041e9i | − | 0.690852i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.44124e7 | − | 2.62979e7i | 0.0452248 | − | 0.0125971i | ||||
\(461\) | 3.25654e9 | 1.54812 | 0.774058 | − | 0.633115i | \(-0.218224\pi\) | ||||
0.774058 | + | 0.633115i | \(0.218224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.48463e8i | − | 0.256811i | −0.991722 | − | 0.128406i | \(-0.959014\pi\) | ||
0.991722 | − | 0.128406i | \(-0.0409859\pi\) | |||||||
\(464\) | 3.76275e8 | 0.174861 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.97549e9 | −0.904323 | ||||||||
\(467\) | − | 1.31891e9i | − | 0.599245i | −0.954058 | − | 0.299623i | \(-0.903139\pi\) | ||
0.954058 | − | 0.299623i | \(-0.0968607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.14036e9 | −0.510431 | ||||||||
\(470\) | 4.70670e6 | + | 1.68976e7i | 0.00209110 | + | 0.00750727i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 2.16976e9i | − | 0.949762i | ||||||
\(473\) | − | 4.84061e9i | − | 2.10323i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.58762e8 | + | 2.77067e8i | −0.196408 | + | 0.118620i | ||||
\(476\) | −7.90433e7 | −0.0335924 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.13214e9i | 0.474137i | ||||||||
\(479\) | −1.59989e9 | −0.665144 | −0.332572 | − | 0.943078i | \(-0.607916\pi\) | ||||
−0.332572 | + | 0.943078i | \(0.607916\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.26783e9 | −0.929187 | ||||||||
\(482\) | 2.09177e9i | 0.850844i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.25613e8 | 0.130540 | ||||||||
\(485\) | −3.23355e9 | + | 9.00682e8i | −1.28701 | + | 0.358489i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.95948e9i | 0.768759i | 0.923175 | + | 0.384380i | \(0.125585\pi\) | ||||
−0.923175 | + | 0.384380i | \(0.874415\pi\) | |||||||
\(488\) | 2.08237e9i | 0.811126i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.87661e9 | − | 5.22717e8i | 0.720589 | − | 0.200715i | ||||
\(491\) | −2.38785e8 | −0.0910376 | −0.0455188 | − | 0.998963i | \(-0.514494\pi\) | ||||
−0.0455188 | + | 0.998963i | \(0.514494\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.01292e8i | − | 0.150833i | ||||||
\(494\) | −7.49606e8 | −0.279762 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.20737e9 | −0.444279 | ||||||||
\(497\) | 2.02296e8i | 0.0739163i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.06642e9 | −1.10479 | −0.552394 | − | 0.833583i | \(-0.686286\pi\) | ||||
−0.552394 | + | 0.833583i | \(0.686286\pi\) | |||||||
\(500\) | 1.90688e8 | + | 1.79730e8i | 0.0682224 | + | 0.0643021i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 2.18303e9i | − | 0.770188i | ||||||
\(503\) | 1.60348e9i | 0.561793i | 0.959738 | + | 0.280897i | \(0.0906318\pi\) | ||||
−0.959738 | + | 0.280897i | \(0.909368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.85703e8 | + | 1.38471e9i | 0.133270 | + | 0.478454i | ||||
\(506\) | −2.14883e9 | −0.737351 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 3.42432e8i | − | 0.115891i | ||||||
\(509\) | 1.21742e9 | 0.409192 | 0.204596 | − | 0.978847i | \(-0.434412\pi\) | ||||
0.204596 | + | 0.978847i | \(0.434412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.24258e8 | 0.206962 | ||||||||
\(512\) | − | 3.34724e9i | − | 1.10215i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.44961e8 | 0.0470848 | ||||||||
\(515\) | −9.38304e8 | + | 2.61358e8i | −0.302704 | + | 0.0843161i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.97850e7i | 0.0126620i | ||||||||
\(518\) | − | 1.01124e9i | − | 0.319668i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.14736e9 | + | 4.11913e9i | 0.357838 | + | 1.28468i | ||||
\(521\) | 2.08635e9 | 0.646331 | 0.323166 | − | 0.946342i | \(-0.395253\pi\) | ||||
0.323166 | + | 0.946342i | \(0.395253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.28922e9i | 1.31106i | 0.755169 | + | 0.655531i | \(0.227555\pi\) | ||||
−0.755169 | + | 0.655531i | \(0.772445\pi\) | |||||||
\(524\) | 3.99758e8 | 0.121377 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.53160e9 | −0.458875 | ||||||||
\(527\) | 1.28765e9i | 0.383230i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.55102e9 | 0.749237 | ||||||||
\(530\) | −4.76081e8 | − | 1.70918e9i | −0.138904 | − | 0.498682i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.45779e7i | 0.00995654i | ||||||||
\(533\) | 5.40883e9i | 1.54724i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00226e9 | + | 1.11480e9i | −1.12997 | + | 0.314745i | ||||
\(536\) | −4.09360e9 | −1.14823 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.46646e9i | 1.51345i | ||||||||
\(539\) | 4.41845e9 | 1.21537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.91116e9 | 1.33350 | 0.666751 | − | 0.745280i | \(-0.267684\pi\) | ||||
0.666751 | + | 0.745280i | \(0.267684\pi\) | |||||||
\(542\) | 1.21528e9i | 0.327852i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.43170e8 | −0.144657 | ||||||||
\(545\) | 1.50843e9 | + | 5.41542e9i | 0.399151 | + | 1.43299i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.76451e9i | − | 0.460965i | −0.973077 | − | 0.230482i | \(-0.925970\pi\) | ||
0.973077 | − | 0.230482i | \(-0.0740304\pi\) | |||||||
\(548\) | − | 5.13719e8i | − | 0.133350i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.97018e9 | − | 4.91797e9i | −0.761226 | − | 1.26042i | ||||
\(551\) | −1.75547e8 | −0.0447058 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.45145e8i | − | 0.111934i | ||||||
\(554\) | 5.50071e9 | 1.37447 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.36570e8 | 0.0336971 | ||||||||
\(557\) | − | 4.13406e8i | − | 0.101364i | −0.998715 | − | 0.0506820i | \(-0.983860\pi\) | ||
0.998715 | − | 0.0506820i | \(-0.0161395\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.19261e9 | 1.74159 | ||||||||
\(560\) | −1.66302e9 | + | 4.63223e8i | −0.400166 | + | 0.111463i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.83590e9i | 0.436286i | ||||||||
\(563\) | − | 7.57073e9i | − | 1.78796i | −0.448104 | − | 0.893982i | \(-0.647900\pi\) | ||
0.448104 | − | 0.893982i | \(-0.352100\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.51494e9 | + | 4.21975e8i | −0.353366 | + | 0.0984277i | ||||
\(566\) | −1.74634e9 | −0.404829 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.26191e8i | 0.166277i | ||||||||
\(569\) | 8.90287e8 | 0.202599 | 0.101299 | − | 0.994856i | \(-0.467700\pi\) | ||||
0.101299 | + | 0.994856i | \(0.467700\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.96089e9 | −1.11515 | −0.557575 | − | 0.830126i | \(-0.688268\pi\) | ||||
−0.557575 | + | 0.830126i | \(0.688268\pi\) | |||||||
\(572\) | 8.31294e8i | 0.185724i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.41183e9 | −0.532297 | ||||||||
\(575\) | −1.18016e9 | − | 1.95408e9i | −0.258882 | − | 0.428652i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.53066e9i | − | 0.331713i | −0.986150 | − | 0.165856i | \(-0.946961\pi\) | ||
0.986150 | − | 0.165856i | \(-0.0530388\pi\) | |||||||
\(578\) | 1.77092e9i | 0.381463i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.30310e7 | + | 8.26838e7i | 0.00490134 | + | 0.0175963i | ||||
\(581\) | 1.09371e9 | 0.231358 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.02425e9i | − | 0.841094i | ||||||
\(584\) | 2.24093e9 | 0.465567 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.15568e9 | 0.853100 | ||||||||
\(587\) | − | 4.39564e9i | − | 0.896992i | −0.893785 | − | 0.448496i | \(-0.851960\pi\) | ||
0.893785 | − | 0.448496i | \(-0.148040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.63288e8 | 0.113587 | ||||||||
\(590\) | −4.17304e9 | + | 1.16237e9i | −0.836509 | + | 0.233004i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 3.28675e9i | − | 0.651089i | ||||||
\(593\) | 3.32990e9i | 0.655753i | 0.944721 | + | 0.327877i | \(0.106333\pi\) | ||||
−0.944721 | + | 0.327877i | \(0.893667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.94021e8 | + | 1.77359e9i | 0.0961470 | + | 0.345178i | ||||
\(596\) | −4.80083e8 | −0.0928870 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 3.19292e9i | − | 0.610567i | ||||||
\(599\) | −4.53030e9 | −0.861258 | −0.430629 | − | 0.902529i | \(-0.641708\pi\) | ||||
−0.430629 | + | 0.902529i | \(0.641708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.70479e9 | −0.884056 | −0.442028 | − | 0.897001i | \(-0.645741\pi\) | ||||
−0.442028 | + | 0.897001i | \(0.645741\pi\) | |||||||
\(602\) | 3.20722e9i | 0.599158i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.43913e8 | −0.0635067 | ||||||||
\(605\) | −2.03508e9 | − | 7.30616e9i | −0.373627 | − | 1.34136i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.24429e9i | − | 0.407303i | −0.979043 | − | 0.203652i | \(-0.934719\pi\) | ||
0.979043 | − | 0.203652i | \(-0.0652810\pi\) | |||||||
\(608\) | 2.37612e8i | 0.0428752i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00496e9 | − | 1.11555e9i | 0.714404 | − | 0.198992i | ||||
\(611\) | −5.91162e7 | −0.0104848 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.74415e9i | − | 1.53323i | −0.642109 | − | 0.766613i | \(-0.721941\pi\) | ||
0.642109 | − | 0.766613i | \(-0.278059\pi\) | |||||||
\(614\) | 6.86950e9 | 1.19767 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.32458e9 | −0.745438 | ||||||||
\(617\) | − | 4.49031e9i | − | 0.769623i | −0.922995 | − | 0.384812i | \(-0.874266\pi\) | ||
0.922995 | − | 0.384812i | \(-0.125734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.74101e9 | 0.633974 | 0.316987 | − | 0.948430i | \(-0.397329\pi\) | ||||
0.316987 | + | 0.948430i | \(0.397329\pi\) | |||||||
\(620\) | −7.39008e7 | − | 2.65312e8i | −0.0124531 | − | 0.0447081i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.83883e9i | 1.30612i | ||||||||
\(623\) | − | 2.37079e9i | − | 0.392813i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.84102e9 | − | 5.40199e9i | 0.465472 | − | 0.885063i | ||||
\(626\) | 4.81292e9 | 0.784149 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.62350e8i | 0.0583808i | ||||||||
\(629\) | −3.50527e9 | −0.561622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.93545e9 | 0.306675 | 0.153337 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153337 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(632\) | − | 1.59796e9i | − | 0.251799i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.36616e9 | 0.992122 | ||||||||
\(635\) | −7.68355e9 | + | 2.14020e9i | −1.19084 | + | 0.331701i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.56532e9i | 1.00639i | ||||||||
\(638\) | − | 1.88188e9i | − | 0.286893i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.34621e9 | + | 1.48915e9i | −0.806150 | + | 0.224547i | ||||
\(641\) | −5.89076e9 | −0.883422 | −0.441711 | − | 0.897157i | \(-0.645628\pi\) | ||||
−0.441711 | + | 0.897157i | \(0.645628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.16008e9i | − | 0.468770i | −0.972144 | − | 0.234385i | \(-0.924692\pi\) | ||
0.972144 | − | 0.234385i | \(-0.0753076\pi\) | |||||||
\(644\) | −1.47283e8 | −0.0217297 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.15863e9 | −0.169095 | ||||||||
\(647\) | 1.27557e10i | 1.85157i | 0.378054 | + | 0.925783i | \(0.376593\pi\) | ||||
−0.378054 | + | 0.925783i | \(0.623407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.82536e9 | −1.41089 | ||||||||
\(650\) | 7.30756e9 | − | 4.41336e9i | 1.04370 | − | 0.630336i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.12250e9i | 0.158606i | ||||||||
\(653\) | − | 4.43892e9i | − | 0.623852i | −0.950106 | − | 0.311926i | \(-0.899026\pi\) | ||
0.950106 | − | 0.311926i | \(-0.100974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.49849e9 | − | 8.96985e9i | −0.347402 | − | 1.24721i | ||||
\(656\) | −7.83897e9 | −1.08417 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 2.63602e7i | − | 0.00360710i | ||||||
\(659\) | 1.08526e10 | 1.47719 | 0.738595 | − | 0.674149i | \(-0.235489\pi\) | ||||
0.738595 | + | 0.674149i | \(0.235489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.49307e9 | 1.14382 | 0.571912 | − | 0.820315i | \(-0.306202\pi\) | ||||
0.571912 | + | 0.820315i | \(0.306202\pi\) | |||||||
\(662\) | 6.29922e9i | 0.843887i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.92613e9 | 0.520447 | ||||||||
\(665\) | 7.75866e8 | − | 2.16112e8i | 0.102308 | − | 0.0284973i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.47737e8i | − | 0.0975683i | ||||||
\(668\) | 6.88209e8i | 0.0893311i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.19300e9 | + | 7.87311e9i | 0.281694 | + | 1.01131i | ||||
\(671\) | 9.42962e9 | 1.20494 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.20188e9i | 0.531362i | 0.964061 | + | 0.265681i | \(0.0855969\pi\) | ||||
−0.964061 | + | 0.265681i | \(0.914403\pi\) | |||||||
\(674\) | 7.96330e9 | 1.00180 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.82228e8 | −0.0600398 | ||||||||
\(677\) | − | 6.56755e9i | − | 0.813472i | −0.913546 | − | 0.406736i | \(-0.866667\pi\) | ||
0.913546 | − | 0.406736i | \(-0.133333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.04433e9 | 0.618386 | ||||||||
\(680\) | 1.77341e9 | + | 6.36673e9i | 0.216286 | + | 0.776489i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.03850e9i | 0.728927i | ||||||||
\(683\) | 6.31484e9i | 0.758386i | 0.925318 | + | 0.379193i | \(0.123798\pi\) | ||||
−0.925318 | + | 0.379193i | \(0.876202\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.15269e10 | + | 3.21075e9i | −1.37024 | + | 0.381671i | ||||
\(686\) | −6.65322e9 | −0.786860 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.04242e10i | 1.22035i | ||||||||
\(689\) | 5.97958e9 | 0.696472 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.76447e9 | 0.434041 | 0.217020 | − | 0.976167i | \(-0.430366\pi\) | ||||
0.217020 | + | 0.976167i | \(0.430366\pi\) | |||||||
\(692\) | − | 5.84630e8i | − | 0.0670672i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.99439e9 | −0.453620 | ||||||||
\(695\) | −8.53562e8 | − | 3.06438e9i | −0.0964468 | − | 0.346255i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.36014e9i | 0.935188i | ||||||||
\(698\) | 1.22000e10i | 1.35789i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.03580e8 | − | 3.37084e8i | −0.0224332 | − | 0.0371446i | ||||
\(701\) | −1.97083e9 | −0.216090 | −0.108045 | − | 0.994146i | \(-0.534459\pi\) | ||||
−0.108045 | + | 0.994146i | \(0.534459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.53340e9i | 0.166461i | ||||||||
\(704\) | −1.53983e10 | −1.66329 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.97016e9 | −0.959364 | ||||||||
\(707\) | − | 2.16016e9i | − | 0.229888i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.62853e9 | −1.01461 | −0.507304 | − | 0.861767i | \(-0.669358\pi\) | ||||
−0.507304 | + | 0.861767i | \(0.669358\pi\) | |||||||
\(710\) | 1.39666e9 | − | 3.89031e8i | 0.146449 | − | 0.0407924i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 8.51054e9i | − | 0.883644i | ||||||
\(713\) | 2.39930e9i | 0.247897i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.86527e10 | − | 5.19559e9i | 1.90841 | − | 0.531574i | ||||
\(716\) | −2.32206e8 | −0.0236417 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 7.27340e9i | − | 0.733334i | ||||||
\(719\) | −1.89490e10 | −1.90123 | −0.950614 | − | 0.310376i | \(-0.899545\pi\) | ||||
−0.950614 | + | 0.310376i | \(0.899545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.46375e9 | 0.145444 | ||||||||
\(722\) | − | 9.12045e9i | − | 0.901853i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.39140e8 | 0.0919698 | ||||||||
\(725\) | 1.71133e9 | − | 1.03355e9i | 0.166783 | − | 0.100727i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44446e9i | 0.139423i | 0.997567 | + | 0.0697116i | \(0.0222079\pi\) | ||||
−0.997567 | + | 0.0697116i | \(0.977792\pi\) | |||||||
\(728\) | − | 6.42585e9i | − | 0.617264i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.20050e9 | − | 4.30991e9i | −0.114217 | − | 0.410051i | ||||
\(731\) | 1.11172e10 | 1.05266 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.38939e10i | 1.30305i | 0.758627 | + | 0.651525i | \(0.225871\pi\) | ||||
−0.758627 | + | 0.651525i | \(0.774129\pi\) | |||||||
\(734\) | −1.94122e10 | −1.81191 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.01210e9 | −0.0935732 | ||||||||
\(737\) | 1.85371e10i | 1.70571i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.19008e10 | −1.08473 | −0.542366 | − | 0.840142i | \(-0.682471\pi\) | ||||
−0.542366 | + | 0.840142i | \(0.682471\pi\) | |||||||
\(740\) | 7.22239e8 | − | 2.01175e8i | 0.0655194 | − | 0.0182500i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.66633e9i | 0.239607i | ||||||||
\(743\) | − | 1.57512e10i | − | 1.40882i | −0.709796 | − | 0.704408i | \(-0.751213\pi\) | ||
0.709796 | − | 0.704408i | \(-0.248787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00052e9 | + | 1.07722e10i | 0.265858 | + | 0.954459i | ||||
\(746\) | 1.00156e10 | 0.883268 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.28489e9i | 0.112256i | ||||||||
\(749\) | 6.24352e9 | 0.542929 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.60645e10 | −1.38397 | −0.691984 | − | 0.721912i | \(-0.743263\pi\) | ||||
−0.691984 | + | 0.721912i | \(0.743263\pi\) | |||||||
\(752\) | − | 8.56765e7i | − | 0.00734682i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.79627e9 | 0.237563 | ||||||||
\(755\) | 2.14946e9 | + | 7.71679e9i | 0.181767 | + | 0.652563i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.88969e10i | − | 1.58327i | −0.610993 | − | 0.791636i | \(-0.709229\pi\) | ||
0.610993 | − | 0.791636i | \(-0.290771\pi\) | |||||||
\(758\) | − | 1.54603e10i | − | 1.28936i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.78516e9 | − | 7.75787e8i | 0.230146 | − | 0.0641054i | ||||
\(761\) | −1.01100e10 | −0.831584 | −0.415792 | − | 0.909460i | \(-0.636496\pi\) | ||||
−0.415792 | + | 0.909460i | \(0.636496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.44806e9i | − | 0.688527i | ||||||
\(764\) | 1.43344e9 | 0.116293 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.69855e10 | 1.36546 | ||||||||
\(767\) | − | 1.45994e10i | − | 1.16829i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00677e10 | 1.59132 | 0.795658 | − | 0.605746i | \(-0.207125\pi\) | ||||
0.795658 | + | 0.605746i | \(0.207125\pi\) | |||||||
\(770\) | 2.31674e9 | + | 8.31735e9i | 0.182877 | + | 0.656550i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 7.18163e8i | − | 0.0561775i | ||||||
\(773\) | 2.15770e10i | 1.68020i | 0.542428 | + | 0.840102i | \(0.317505\pi\) | ||||
−0.542428 | + | 0.840102i | \(0.682495\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.49124e9 | + | 3.31640e9i | −0.423755 | + | 0.255924i | ||||
\(776\) | 1.81079e10 | 1.39108 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 2.41714e10i | − | 1.84023i | ||||||
\(779\) | 3.65719e9 | 0.277183 |