Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (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: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.14 | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.7.c.a.31.13 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59351 | + | 7.56794i | 0.324189 | + | 0.945992i | ||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | −50.5474 | + | 39.2551i | −0.789803 | + | 0.613361i | ||||
\(5\) | −55.9017 | −0.447214 | ||||||||
\(6\) | −117.972 | + | 40.4289i | −0.546169 | + | 0.187171i | ||||
\(7\) | − | 671.100i | − | 1.95656i | −0.207288 | − | 0.978280i | \(-0.566464\pi\) | ||
0.207288 | − | 0.978280i | \(-0.433536\pi\) | |||||||
\(8\) | −428.176 | − | 280.731i | −0.836281 | − | 0.548302i | ||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | −144.982 | − | 423.061i | −0.144982 | − | 0.423061i | ||||
\(11\) | 199.628i | 0.149983i | 0.997184 | + | 0.0749917i | \(0.0238930\pi\) | ||||
−0.997184 | + | 0.0749917i | \(0.976107\pi\) | |||||||
\(12\) | −611.927 | − | 787.955i | −0.354124 | − | 0.455993i | ||||
\(13\) | 2041.73 | 0.929328 | 0.464664 | − | 0.885487i | \(-0.346175\pi\) | ||||
0.464664 | + | 0.885487i | \(0.346175\pi\) | |||||||
\(14\) | 5078.84 | − | 1740.51i | 1.85089 | − | 0.634296i | ||||
\(15\) | − | 871.421i | − | 0.258199i | ||||||
\(16\) | 1014.07 | − | 3968.49i | 0.247576 | − | 0.968868i | ||||
\(17\) | −8219.18 | −1.67294 | −0.836472 | − | 0.548009i | \(-0.815386\pi\) | ||||
−0.836472 | + | 0.548009i | \(0.815386\pi\) | |||||||
\(18\) | −630.224 | − | 1839.01i | −0.108063 | − | 0.315331i | ||||
\(19\) | 5147.13i | 0.750420i | 0.926940 | + | 0.375210i | \(0.122429\pi\) | ||||
−0.926940 | + | 0.375210i | \(0.877571\pi\) | |||||||
\(20\) | 2825.68 | − | 2194.43i | 0.353210 | − | 0.274303i | ||||
\(21\) | 10461.4 | 1.12962 | ||||||||
\(22\) | −1510.77 | + | 517.738i | −0.141883 | + | 0.0486230i | ||||
\(23\) | − | 14631.4i | − | 1.20255i | −0.799044 | − | 0.601273i | \(-0.794660\pi\) | ||
0.799044 | − | 0.601273i | \(-0.205340\pi\) | |||||||
\(24\) | 4376.16 | − | 6674.60i | 0.316562 | − | 0.482827i | ||||
\(25\) | 3125.00 | 0.200000 | ||||||||
\(26\) | 5295.27 | + | 15451.7i | 0.301278 | + | 0.879137i | ||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | 26344.1 | + | 33922.3i | 1.20008 | + | 1.54530i | ||||
\(29\) | −12573.4 | −0.515534 | −0.257767 | − | 0.966207i | \(-0.582987\pi\) | ||||
−0.257767 | + | 0.966207i | \(0.582987\pi\) | |||||||
\(30\) | 6594.86 | − | 2260.04i | 0.244254 | − | 0.0837053i | ||||
\(31\) | − | 54422.8i | − | 1.82682i | −0.407041 | − | 0.913410i | \(-0.633439\pi\) | ||
0.407041 | − | 0.913410i | \(-0.366561\pi\) | |||||||
\(32\) | 32663.3 | − | 2617.90i | 0.996804 | − | 0.0798919i | ||||
\(33\) | −3111.89 | −0.0865930 | ||||||||
\(34\) | −21316.6 | − | 62202.2i | −0.542351 | − | 1.58259i | ||||
\(35\) | 37515.6i | 0.875000i | ||||||||
\(36\) | 12283.0 | − | 9538.99i | 0.263268 | − | 0.204454i | ||||
\(37\) | −11.6361 | −0.000229721 | −0.000114861 | − | 1.00000i | \(-0.500037\pi\) | ||||
−0.000114861 | 1.00000i | \(0.500037\pi\) | ||||||||
\(38\) | −38953.1 | + | 13349.2i | −0.709891 | + | 0.243278i | ||||
\(39\) | 31827.5i | 0.536548i | ||||||||
\(40\) | 23935.7 | + | 15693.3i | 0.373996 | + | 0.245208i | ||||
\(41\) | −67862.4 | −0.984640 | −0.492320 | − | 0.870414i | \(-0.663851\pi\) | ||||
−0.492320 | + | 0.870414i | \(0.663851\pi\) | |||||||
\(42\) | 27131.8 | + | 79171.3i | 0.366211 | + | 1.06861i | ||||
\(43\) | − | 105037.i | − | 1.32111i | −0.750778 | − | 0.660554i | \(-0.770321\pi\) | ||
0.750778 | − | 0.660554i | \(-0.229679\pi\) | |||||||
\(44\) | −7836.42 | − | 10090.7i | −0.0919940 | − | 0.118457i | ||||
\(45\) | 13584.1 | 0.149071 | ||||||||
\(46\) | 110729. | − | 37946.7i | 1.13760 | − | 0.389853i | ||||
\(47\) | 89660.8i | 0.863592i | 0.901971 | + | 0.431796i | \(0.142120\pi\) | ||||
−0.901971 | + | 0.431796i | \(0.857880\pi\) | |||||||
\(48\) | 61862.6 | + | 15807.8i | 0.559376 | + | 0.142938i | ||||
\(49\) | −332726. | −2.82813 | ||||||||
\(50\) | 8104.73 | + | 23649.8i | 0.0648379 | + | 0.189198i | ||||
\(51\) | − | 128124.i | − | 0.965875i | ||||||
\(52\) | −103204. | + | 80148.5i | −0.733985 | + | 0.570014i | ||||
\(53\) | −1369.17 | −0.00919668 | −0.00459834 | − | 0.999989i | \(-0.501464\pi\) | ||||
−0.00459834 | + | 0.999989i | \(0.501464\pi\) | |||||||
\(54\) | 28667.3 | − | 9824.22i | 0.182056 | − | 0.0623903i | ||||
\(55\) | − | 11159.5i | − | 0.0670746i | ||||||
\(56\) | −188398. | + | 287349.i | −1.07279 | + | 1.63623i | ||||
\(57\) | −80235.8 | −0.433255 | ||||||||
\(58\) | −32609.2 | − | 95154.5i | −0.167131 | − | 0.487691i | ||||
\(59\) | − | 5601.86i | − | 0.0272757i | −0.999907 | − | 0.0136379i | \(-0.995659\pi\) | ||
0.999907 | − | 0.0136379i | \(-0.00434120\pi\) | |||||||
\(60\) | 34207.7 | + | 44048.0i | 0.158369 | + | 0.203926i | ||||
\(61\) | −132681. | −0.584548 | −0.292274 | − | 0.956335i | \(-0.594412\pi\) | ||||
−0.292274 | + | 0.956335i | \(0.594412\pi\) | |||||||
\(62\) | 411868. | − | 141146.i | 1.72816 | − | 0.592235i | ||||
\(63\) | 163077.i | 0.652187i | ||||||||
\(64\) | 104525. | + | 240404.i | 0.398730 | + | 0.917068i | ||||
\(65\) | −114136. | −0.415608 | ||||||||
\(66\) | −8070.74 | − | 23550.6i | −0.0280725 | − | 0.0819163i | ||||
\(67\) | 325492.i | 1.08222i | 0.840951 | + | 0.541111i | \(0.181996\pi\) | ||||
−0.840951 | + | 0.541111i | \(0.818004\pi\) | |||||||
\(68\) | 415458. | − | 322645.i | 1.32130 | − | 1.02612i | ||||
\(69\) | 228081. | 0.694290 | ||||||||
\(70\) | −283916. | + | 97297.4i | −0.827743 | + | 0.283666i | ||||
\(71\) | 303340.i | 0.847529i | 0.905772 | + | 0.423764i | \(0.139292\pi\) | ||||
−0.905772 | + | 0.423764i | \(0.860708\pi\) | |||||||
\(72\) | 104047. | + | 68217.5i | 0.278760 | + | 0.182767i | ||||
\(73\) | −247561. | −0.636376 | −0.318188 | − | 0.948028i | \(-0.603074\pi\) | ||||
−0.318188 | + | 0.948028i | \(0.603074\pi\) | |||||||
\(74\) | −30.1783 | − | 88.0611i | −7.44732e−5 | − | 0.000217315i | ||||
\(75\) | 48713.9i | 0.115470i | ||||||||
\(76\) | −202051. | − | 260174.i | −0.460278 | − | 0.592683i | ||||
\(77\) | 133970. | 0.293452 | ||||||||
\(78\) | −240868. | + | 82545.0i | −0.507570 | + | 0.173943i | ||||
\(79\) | − | 389964.i | − | 0.790939i | −0.918479 | − | 0.395470i | \(-0.870582\pi\) | ||
0.918479 | − | 0.395470i | \(-0.129418\pi\) | |||||||
\(80\) | −56688.3 | + | 221845.i | −0.110719 | + | 0.433291i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −176002. | − | 513578.i | −0.319210 | − | 0.931462i | ||||
\(83\) | − | 215366.i | − | 0.376654i | −0.982106 | − | 0.188327i | \(-0.939694\pi\) | ||
0.982106 | − | 0.188327i | \(-0.0603065\pi\) | |||||||
\(84\) | −528797. | + | 410664.i | −0.892177 | + | 0.692865i | ||||
\(85\) | 459466. | 0.748164 | ||||||||
\(86\) | 794916. | − | 272416.i | 1.24976 | − | 0.428289i | ||||
\(87\) | − | 195999.i | − | 0.297644i | ||||||
\(88\) | 56041.7 | − | 85475.8i | 0.0822362 | − | 0.125428i | ||||
\(89\) | 46200.5 | 0.0655355 | 0.0327677 | − | 0.999463i | \(-0.489568\pi\) | ||||
0.0327677 | + | 0.999463i | \(0.489568\pi\) | |||||||
\(90\) | 35230.6 | + | 102804.i | 0.0483273 | + | 0.141020i | ||||
\(91\) | − | 1.37021e6i | − | 1.81829i | ||||||
\(92\) | 574357. | + | 739578.i | 0.737595 | + | 0.949774i | ||||
\(93\) | 848367. | 1.05471 | ||||||||
\(94\) | −678547. | + | 232537.i | −0.816952 | + | 0.279968i | ||||
\(95\) | − | 287733.i | − | 0.335598i | ||||||
\(96\) | 40809.0 | + | 509170.i | 0.0461256 | + | 0.575505i | ||||
\(97\) | 800223. | 0.876791 | 0.438396 | − | 0.898782i | \(-0.355547\pi\) | ||||
0.438396 | + | 0.898782i | \(0.355547\pi\) | |||||||
\(98\) | −862931. | − | 2.51805e6i | −0.916849 | − | 2.67539i | ||||
\(99\) | − | 48509.6i | − | 0.0499945i | ||||||
\(100\) | −157961. | + | 122672.i | −0.157961 | + | 0.122672i | ||||
\(101\) | 850500. | 0.825487 | 0.412743 | − | 0.910847i | \(-0.364571\pi\) | ||||
0.412743 | + | 0.910847i | \(0.364571\pi\) | |||||||
\(102\) | 969637. | − | 332292.i | 0.913710 | − | 0.313126i | ||||
\(103\) | − | 591093.i | − | 0.540934i | −0.962729 | − | 0.270467i | \(-0.912822\pi\) | ||
0.962729 | − | 0.270467i | \(-0.0871781\pi\) | |||||||
\(104\) | −874220. | − | 573177.i | −0.777179 | − | 0.509552i | ||||
\(105\) | −584811. | −0.505182 | ||||||||
\(106\) | −3550.97 | − | 10361.8i | −0.00298147 | − | 0.00869999i | ||||
\(107\) | 1.02379e6i | 0.835718i | 0.908512 | + | 0.417859i | \(0.137219\pi\) | ||||
−0.908512 | + | 0.417859i | \(0.862781\pi\) | |||||||
\(108\) | 148698. | + | 191473.i | 0.118041 | + | 0.151998i | ||||
\(109\) | −1.78875e6 | −1.38125 | −0.690623 | − | 0.723215i | \(-0.742663\pi\) | ||||
−0.690623 | + | 0.723215i | \(0.742663\pi\) | |||||||
\(110\) | 84454.7 | − | 28942.4i | 0.0634521 | − | 0.0217449i | ||||
\(111\) | − | 181.389i | − | 0.000132630i | ||||||
\(112\) | −2.66325e6 | − | 680543.i | −1.89565 | − | 0.484397i | ||||
\(113\) | 2.22824e6 | 1.54428 | 0.772142 | − | 0.635450i | \(-0.219186\pi\) | ||||
0.772142 | + | 0.635450i | \(0.219186\pi\) | |||||||
\(114\) | −208093. | − | 607219.i | −0.140457 | − | 0.409856i | ||||
\(115\) | 817919.i | 0.537795i | ||||||||
\(116\) | 635551. | − | 493569.i | 0.407170 | − | 0.316209i | ||||
\(117\) | −496141. | −0.309776 | ||||||||
\(118\) | 42394.5 | − | 14528.5i | 0.0258026 | − | 0.00884250i | ||||
\(119\) | 5.51589e6i | 3.27322i | ||||||||
\(120\) | −244635. | + | 373121.i | −0.141571 | + | 0.215927i | ||||
\(121\) | 1.73171e6 | 0.977505 | ||||||||
\(122\) | −344111. | − | 1.00412e6i | −0.189504 | − | 0.552978i | ||||
\(123\) | − | 1.05787e6i | − | 0.568482i | ||||||
\(124\) | 2.13637e6 | + | 2.75093e6i | 1.12050 | + | 1.44283i | ||||
\(125\) | −174693. | −0.0894427 | ||||||||
\(126\) | −1.23416e6 | + | 422943.i | −0.616964 | + | 0.211432i | ||||
\(127\) | − | 1.20836e6i | − | 0.589908i | −0.955511 | − | 0.294954i | \(-0.904696\pi\) | ||
0.955511 | − | 0.294954i | \(-0.0953043\pi\) | |||||||
\(128\) | −1.54828e6 | + | 1.41453e6i | −0.738275 | + | 0.674499i | ||||
\(129\) | 1.63737e6 | 0.762742 | ||||||||
\(130\) | −296014. | − | 863777.i | −0.134736 | − | 0.393162i | ||||
\(131\) | 283537.i | 0.126123i | 0.998010 | + | 0.0630616i | \(0.0200865\pi\) | ||||
−0.998010 | + | 0.0630616i | \(0.979914\pi\) | |||||||
\(132\) | 157298. | − | 122158.i | 0.0683914 | − | 0.0531128i | ||||
\(133\) | 3.45424e6 | 1.46824 | ||||||||
\(134\) | −2.46331e6 | + | 844169.i | −1.02377 | + | 0.350845i | ||||
\(135\) | 211755.i | 0.0860663i | ||||||||
\(136\) | 3.51925e6 | + | 2.30737e6i | 1.39905 | + | 0.917279i | ||||
\(137\) | −4.15204e6 | −1.61473 | −0.807364 | − | 0.590053i | \(-0.799107\pi\) | ||||
−0.807364 | + | 0.590053i | \(0.799107\pi\) | |||||||
\(138\) | 591531. | + | 1.72610e6i | 0.225082 | + | 0.656793i | ||||
\(139\) | 3.85092e6i | 1.43391i | 0.697122 | + | 0.716953i | \(0.254464\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(140\) | −1.47268e6 | − | 1.89632e6i | −0.536691 | − | 0.691077i | ||||
\(141\) | −1.39767e6 | −0.498595 | ||||||||
\(142\) | −2.29566e6 | + | 786716.i | −0.801756 | + | 0.274760i | ||||
\(143\) | 407587.i | 0.139384i | ||||||||
\(144\) | −246419. | + | 964342.i | −0.0825253 | + | 0.322956i | ||||
\(145\) | 702873. | 0.230554 | ||||||||
\(146\) | −642054. | − | 1.87353e6i | −0.206306 | − | 0.602007i | ||||
\(147\) | − | 5.18669e6i | − | 1.63282i | ||||||
\(148\) | 588.173 | − | 456.776i | 0.000181435 | − | 0.000140902i | ||||
\(149\) | −3.30508e6 | −0.999132 | −0.499566 | − | 0.866276i | \(-0.666507\pi\) | ||||
−0.499566 | + | 0.866276i | \(0.666507\pi\) | |||||||
\(150\) | −368664. | + | 126340.i | −0.109234 | + | 0.0374342i | ||||
\(151\) | − | 2.96350e6i | − | 0.860743i | −0.902652 | − | 0.430371i | \(-0.858383\pi\) | ||
0.902652 | − | 0.430371i | \(-0.141617\pi\) | |||||||
\(152\) | 1.44496e6 | − | 2.20387e6i | 0.411456 | − | 0.627561i | ||||
\(153\) | 1.99726e6 | 0.557648 | ||||||||
\(154\) | 347454. | + | 1.01388e6i | 0.0951339 | + | 0.277603i | ||||
\(155\) | 3.04233e6i | 0.816979i | ||||||||
\(156\) | −1.24939e6 | − | 1.60879e6i | −0.329098 | − | 0.423767i | ||||
\(157\) | 3010.29 | 0.000777874 | 0.000388937 | − | 1.00000i | \(-0.499876\pi\) | ||||
0.000388937 | 1.00000i | \(0.499876\pi\) | ||||||||
\(158\) | 2.95122e6 | − | 1.01138e6i | 0.748222 | − | 0.256414i | ||||
\(159\) | − | 21343.3i | − | 0.00530971i | ||||||
\(160\) | −1.82593e6 | + | 146345.i | −0.445784 | + | 0.0357287i | ||||
\(161\) | −9.81912e6 | −2.35285 | ||||||||
\(162\) | 153144. | + | 446879.i | 0.0360210 | + | 0.105110i | ||||
\(163\) | 1.03461e6i | 0.238899i | 0.992840 | + | 0.119449i | \(0.0381129\pi\) | ||||
−0.992840 | + | 0.119449i | \(0.961887\pi\) | |||||||
\(164\) | 3.43026e6 | − | 2.66395e6i | 0.777671 | − | 0.603940i | ||||
\(165\) | 173960. | 0.0387256 | ||||||||
\(166\) | 1.62988e6 | − | 558555.i | 0.356312 | − | 0.122107i | ||||
\(167\) | − | 593738.i | − | 0.127481i | −0.997967 | − | 0.0637405i | \(-0.979697\pi\) | ||
0.997967 | − | 0.0637405i | \(-0.0203030\pi\) | |||||||
\(168\) | −4.47932e6 | − | 2.93684e6i | −0.944680 | − | 0.619373i | ||||
\(169\) | −658135. | −0.136350 | ||||||||
\(170\) | 1.19163e6 | + | 3.47721e6i | 0.242547 | + | 0.707757i | ||||
\(171\) | − | 1.25075e6i | − | 0.250140i | ||||||
\(172\) | 4.12325e6 | + | 5.30936e6i | 0.810317 | + | 1.04341i | ||||
\(173\) | 1.01324e6 | 0.195692 | 0.0978458 | − | 0.995202i | \(-0.468805\pi\) | ||||
0.0978458 | + | 0.995202i | \(0.468805\pi\) | |||||||
\(174\) | 1.48331e6 | − | 508327.i | 0.281569 | − | 0.0964930i | ||||
\(175\) | − | 2.09719e6i | − | 0.391312i | ||||||
\(176\) | 792221. | + | 202437.i | 0.145314 | + | 0.0371323i | ||||
\(177\) | 87324.3 | 0.0157476 | ||||||||
\(178\) | 119822. | + | 349642.i | 0.0212459 | + | 0.0619960i | ||||
\(179\) | − | 1.05856e7i | − | 1.84569i | −0.385176 | − | 0.922843i | \(-0.625859\pi\) | ||
0.385176 | − | 0.922843i | \(-0.374141\pi\) | |||||||
\(180\) | −686641. | + | 533246.i | −0.117737 | + | 0.0914345i | ||||
\(181\) | −2.44921e6 | −0.413038 | −0.206519 | − | 0.978443i | \(-0.566214\pi\) | ||||
−0.206519 | + | 0.978443i | \(0.566214\pi\) | |||||||
\(182\) | 1.03696e7 | − | 3.55365e6i | 1.72008 | − | 0.589469i | ||||
\(183\) | − | 2.06830e6i | − | 0.337489i | ||||||
\(184\) | −4.10748e6 | + | 6.26480e6i | −0.659358 | + | 1.00567i | ||||
\(185\) | 650.477 | 0.000102735 | ||||||||
\(186\) | 2.20025e6 | + | 6.42039e6i | 0.341927 | + | 0.997752i | ||||
\(187\) | − | 1.64078e6i | − | 0.250914i | ||||||
\(188\) | −3.51964e6 | − | 4.53212e6i | −0.529694 | − | 0.682068i | ||||
\(189\) | −2.54212e6 | −0.376540 | ||||||||
\(190\) | 2.17755e6 | − | 746240.i | 0.317473 | − | 0.108797i | ||||
\(191\) | 5.41860e6i | 0.777655i | 0.921311 | + | 0.388827i | \(0.127120\pi\) | ||||
−0.921311 | + | 0.388827i | \(0.872880\pi\) | |||||||
\(192\) | −3.74753e6 | + | 1.62938e6i | −0.529470 | + | 0.230207i | ||||
\(193\) | 9.97092e6 | 1.38696 | 0.693479 | − | 0.720477i | \(-0.256077\pi\) | ||||
0.693479 | + | 0.720477i | \(0.256077\pi\) | |||||||
\(194\) | 2.07539e6 | + | 6.05604e6i | 0.284246 | + | 0.829437i | ||||
\(195\) | − | 1.77921e6i | − | 0.239951i | ||||||
\(196\) | 1.68184e7 | − | 1.30612e7i | 2.23366 | − | 1.73466i | ||||
\(197\) | 1.33406e7 | 1.74492 | 0.872459 | − | 0.488687i | \(-0.162524\pi\) | ||||
0.872459 | + | 0.488687i | \(0.162524\pi\) | |||||||
\(198\) | 367118. | − | 125810.i | 0.0472944 | − | 0.0162077i | ||||
\(199\) | − | 6.57996e6i | − | 0.834957i | −0.908687 | − | 0.417479i | \(-0.862914\pi\) | ||
0.908687 | − | 0.417479i | \(-0.137086\pi\) | |||||||
\(200\) | −1.33805e6 | − | 877283.i | −0.167256 | − | 0.109660i | ||||
\(201\) | −5.07392e6 | −0.624821 | ||||||||
\(202\) | 2.20578e6 | + | 6.43653e6i | 0.267614 | + | 0.780904i | ||||
\(203\) | 8.43799e6i | 1.00867i | ||||||||
\(204\) | 5.02953e6 | + | 6.47634e6i | 0.592430 | + | 0.762851i | ||||
\(205\) | 3.79362e6 | 0.440344 | ||||||||
\(206\) | 4.47336e6 | − | 1.53301e6i | 0.511719 | − | 0.175365i | ||||
\(207\) | 3.55543e6i | 0.400849i | ||||||||
\(208\) | 2.07046e6 | − | 8.10259e6i | 0.230079 | − | 0.900396i | ||||
\(209\) | −1.02751e6 | −0.112551 | ||||||||
\(210\) | −1.51672e6 | − | 4.42581e6i | −0.163775 | − | 0.477898i | ||||
\(211\) | 870512.i | 0.0926675i | 0.998926 | + | 0.0463337i | \(0.0147538\pi\) | ||||
−0.998926 | + | 0.0463337i | \(0.985246\pi\) | |||||||
\(212\) | 69208.1 | − | 53747.1i | 0.00726356 | − | 0.00564089i | ||||
\(213\) | −4.72860e6 | −0.489321 | ||||||||
\(214\) | −7.74798e6 | + | 2.65521e6i | −0.790582 | + | 0.270931i | ||||
\(215\) | 5.87177e6i | 0.590818i | ||||||||
\(216\) | −1.06341e6 | + | 1.62193e6i | −0.105521 | + | 0.160942i | ||||
\(217\) | −3.65231e7 | −3.57428 | ||||||||
\(218\) | −4.63916e6 | − | 1.35372e7i | −0.447785 | − | 1.30665i | ||||
\(219\) | − | 3.85910e6i | − | 0.367412i | ||||||
\(220\) | 438069. | + | 564086.i | 0.0411410 | + | 0.0529757i | ||||
\(221\) | −1.67814e7 | −1.55471 | ||||||||
\(222\) | 1372.74 | − | 470.434i | 0.000125467 | − | 4.29971e-5i | ||||
\(223\) | 5.16242e6i | 0.465521i | 0.972534 | + | 0.232760i | \(0.0747758\pi\) | ||||
−0.972534 | + | 0.232760i | \(0.925224\pi\) | |||||||
\(224\) | −1.75687e6 | − | 2.19203e7i | −0.156313 | − | 1.95031i | ||||
\(225\) | −759375. | −0.0666667 | ||||||||
\(226\) | 5.77898e6 | + | 1.68632e7i | 0.500640 | + | 1.46088i | ||||
\(227\) | − | 3.88936e6i | − | 0.332506i | −0.986083 | − | 0.166253i | \(-0.946833\pi\) | ||
0.986083 | − | 0.166253i | \(-0.0531669\pi\) | |||||||
\(228\) | 4.05571e6 | − | 3.14967e6i | 0.342186 | − | 0.265742i | ||||
\(229\) | 1.00633e7 | 0.837978 | 0.418989 | − | 0.907991i | \(-0.362385\pi\) | ||||
0.418989 | + | 0.907991i | \(0.362385\pi\) | |||||||
\(230\) | −6.18996e6 | + | 2.12129e6i | −0.508750 | + | 0.174347i | ||||
\(231\) | 2.08839e6i | 0.169424i | ||||||||
\(232\) | 5.38361e6 | + | 3.52973e6i | 0.431131 | + | 0.282668i | ||||
\(233\) | 6.03617e6 | 0.477192 | 0.238596 | − | 0.971119i | \(-0.423313\pi\) | ||||
0.238596 | + | 0.971119i | \(0.423313\pi\) | |||||||
\(234\) | −1.28675e6 | − | 3.75477e6i | −0.100426 | − | 0.293046i | ||||
\(235\) | − | 5.01219e6i | − | 0.386210i | ||||||
\(236\) | 219902. | + | 283159.i | 0.0167299 | + | 0.0215424i | ||||
\(237\) | 6.07894e6 | 0.456649 | ||||||||
\(238\) | −4.17439e7 | + | 1.43055e7i | −3.09644 | + | 1.06114i | ||||
\(239\) | − | 1.34966e6i | − | 0.0988621i | −0.998778 | − | 0.0494311i | \(-0.984259\pi\) | ||
0.998778 | − | 0.0494311i | \(-0.0157408\pi\) | |||||||
\(240\) | −3.45822e6 | − | 883683.i | −0.250161 | − | 0.0639239i | ||||
\(241\) | 7.74261e6 | 0.553141 | 0.276571 | − | 0.960994i | \(-0.410802\pi\) | ||||
0.276571 | + | 0.960994i | \(0.410802\pi\) | |||||||
\(242\) | 4.49121e6 | + | 1.31055e7i | 0.316897 | + | 0.924712i | ||||
\(243\) | 920483.i | 0.0641500i | ||||||||
\(244\) | 6.70669e6 | − | 5.20842e6i | 0.461677 | − | 0.358539i | ||||
\(245\) | 1.86000e7 | 1.26478 | ||||||||
\(246\) | 8.00589e6 | − | 2.74360e6i | 0.537780 | − | 0.184296i | ||||
\(247\) | 1.05091e7i | 0.697386i | ||||||||
\(248\) | −1.52781e7 | + | 2.33025e7i | −1.00165 | + | 1.52773i | ||||
\(249\) | 3.35722e6 | 0.217461 | ||||||||
\(250\) | −453068. | − | 1.32206e6i | −0.0289964 | − | 0.0846121i | ||||
\(251\) | − | 1.64750e7i | − | 1.04185i | −0.853603 | − | 0.520924i | \(-0.825587\pi\) | ||
0.853603 | − | 0.520924i | \(-0.174413\pi\) | |||||||
\(252\) | −6.40162e6 | − | 8.24313e6i | −0.400026 | − | 0.515099i | ||||
\(253\) | 2.92083e6 | 0.180362 | ||||||||
\(254\) | 9.14477e6 | − | 3.13389e6i | 0.558048 | − | 0.191242i | ||||
\(255\) | 7.16237e6i | 0.431952i | ||||||||
\(256\) | −1.47205e7 | − | 8.04865e6i | −0.877412 | − | 0.479737i | ||||
\(257\) | 1.38542e7 | 0.816175 | 0.408088 | − | 0.912943i | \(-0.366196\pi\) | ||||
0.408088 | + | 0.912943i | \(0.366196\pi\) | |||||||
\(258\) | 4.24655e6 | + | 1.23915e7i | 0.247273 | + | 0.721548i | ||||
\(259\) | 7808.97i | 0.000449464i | ||||||||
\(260\) | 5.76929e6 | − | 4.48044e6i | 0.328248 | − | 0.254918i | ||||
\(261\) | 3.05533e6 | 0.171845 | ||||||||
\(262\) | −2.14579e6 | + | 735356.i | −0.119312 | + | 0.0408878i | ||||
\(263\) | 7.65702e6i | 0.420913i | 0.977603 | + | 0.210457i | \(0.0674950\pi\) | ||||
−0.977603 | + | 0.210457i | \(0.932505\pi\) | |||||||
\(264\) | 1.33244e6 | + | 873603.i | 0.0724160 | + | 0.0474791i | ||||
\(265\) | 76539.2 | 0.00411288 | ||||||||
\(266\) | 8.95862e6 | + | 2.61415e7i | 0.475988 | + | 1.38894i | ||||
\(267\) | 720194.i | 0.0378369i | ||||||||
\(268\) | −1.27772e7 | − | 1.64528e7i | −0.663793 | − | 0.854742i | ||||
\(269\) | −3.63062e7 | −1.86520 | −0.932598 | − | 0.360917i | \(-0.882464\pi\) | ||||
−0.932598 | + | 0.360917i | \(0.882464\pi\) | |||||||
\(270\) | −1.60255e6 | + | 549191.i | −0.0814180 | + | 0.0279018i | ||||
\(271\) | − | 144294.i | − | 0.00725002i | −0.999993 | − | 0.00362501i | \(-0.998846\pi\) | ||
0.999993 | − | 0.00362501i | \(-0.00115388\pi\) | |||||||
\(272\) | −8.33483e6 | + | 3.26177e7i | −0.414181 | + | 1.62086i | ||||
\(273\) | 2.13594e7 | 1.04979 | ||||||||
\(274\) | −1.07684e7 | − | 3.14224e7i | −0.523478 | − | 1.52752i | ||||
\(275\) | 623838.i | 0.0299967i | ||||||||
\(276\) | −1.15289e7 | + | 8.95333e6i | −0.548352 | + | 0.425851i | ||||
\(277\) | 4.74727e6 | 0.223360 | 0.111680 | − | 0.993744i | \(-0.464377\pi\) | ||||
0.111680 | + | 0.993744i | \(0.464377\pi\) | |||||||
\(278\) | −2.91436e7 | + | 9.98743e6i | −1.35646 | + | 0.464857i | ||||
\(279\) | 1.32247e7i | 0.608940i | ||||||||
\(280\) | 1.05318e7 | − | 1.60633e7i | 0.479764 | − | 0.731746i | ||||
\(281\) | 4.52651e6 | 0.204007 | 0.102003 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102003 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(282\) | −3.62489e6 | − | 1.05775e7i | −0.161639 | − | 0.471667i | ||||
\(283\) | 1.07319e7i | 0.473497i | 0.971571 | + | 0.236749i | \(0.0760818\pi\) | ||||
−0.971571 | + | 0.236749i | \(0.923918\pi\) | |||||||
\(284\) | −1.19076e7 | − | 1.53330e7i | −0.519841 | − | 0.669380i | ||||
\(285\) | 4.48532e6 | 0.193758 | ||||||||
\(286\) | −3.08459e6 | + | 1.05708e6i | −0.131856 | + | 0.0451867i | ||||
\(287\) | 4.55424e7i | 1.92651i | ||||||||
\(288\) | −7.93717e6 | + | 636149.i | −0.332268 | + | 0.0266306i | ||||
\(289\) | 4.34173e7 | 1.79874 | ||||||||
\(290\) | 1.82291e6 | + | 5.31930e6i | 0.0747431 | + | 0.218102i | ||||
\(291\) | 1.24742e7i | 0.506216i | ||||||||
\(292\) | 1.25136e7 | − | 9.71804e6i | 0.502612 | − | 0.390328i | ||||
\(293\) | 2.88844e7 | 1.14831 | 0.574157 | − | 0.818745i | \(-0.305330\pi\) | ||||
0.574157 | + | 0.818745i | \(0.305330\pi\) | |||||||
\(294\) | 3.92525e7 | − | 1.34518e7i | 1.54463 | − | 0.529343i | ||||
\(295\) | 313153.i | 0.0121981i | ||||||||
\(296\) | 4982.29 | + | 3266.60i | 0.000192112 | + | 0.000125957i | ||||
\(297\) | 756190. | 0.0288643 | ||||||||
\(298\) | −8.57177e6 | − | 2.50126e7i | −0.323908 | − | 0.945171i | ||||
\(299\) | − | 2.98734e7i | − | 1.11756i | ||||||
\(300\) | −1.91227e6 | − | 2.46236e6i | −0.0708249 | − | 0.0911985i | ||||
\(301\) | −7.04906e7 | −2.58483 | ||||||||
\(302\) | 2.24275e7 | − | 7.68587e6i | 0.814256 | − | 0.279044i | ||||
\(303\) | 1.32580e7i | 0.476595i | ||||||||
\(304\) | 2.04263e7 | + | 5.21956e6i | 0.727058 | + | 0.185786i | ||||
\(305\) | 7.41711e6 | 0.261418 | ||||||||
\(306\) | 5.17992e6 | + | 1.51151e7i | 0.180784 | + | 0.527531i | ||||
\(307\) | − | 4.55936e7i | − | 1.57575i | −0.615833 | − | 0.787877i | \(-0.711180\pi\) | ||
0.615833 | − | 0.787877i | \(-0.288820\pi\) | |||||||
\(308\) | −6.77185e6 | + | 5.25902e6i | −0.231769 | + | 0.179992i | ||||
\(309\) | 9.21423e6 | 0.312308 | ||||||||
\(310\) | −2.30241e7 | + | 7.89032e6i | −0.772855 | + | 0.264856i | ||||
\(311\) | − | 2.33624e7i | − | 0.776670i | −0.921518 | − | 0.388335i | \(-0.873050\pi\) | ||
0.921518 | − | 0.388335i | \(-0.126950\pi\) | |||||||
\(312\) | 8.93494e6 | − | 1.36277e7i | 0.294190 | − | 0.448704i | ||||
\(313\) | 2.77900e7 | 0.906266 | 0.453133 | − | 0.891443i | \(-0.350306\pi\) | ||||
0.453133 | + | 0.891443i | \(0.350306\pi\) | |||||||
\(314\) | 7807.23 | + | 22781.7i | 0.000252179 | + | 0.000735863i | ||||
\(315\) | − | 9.11630e6i | − | 0.291667i | ||||||
\(316\) | 1.53081e7 | + | 1.97116e7i | 0.485131 | + | 0.624686i | ||||
\(317\) | 7.68469e6 | 0.241239 | 0.120620 | − | 0.992699i | \(-0.461512\pi\) | ||||
0.120620 | + | 0.992699i | \(0.461512\pi\) | |||||||
\(318\) | 161525. | − | 55354.2i | 0.00502294 | − | 0.00172135i | ||||
\(319\) | − | 2.51000e6i | − | 0.0773216i | ||||||
\(320\) | −5.84311e6 | − | 1.34390e7i | −0.178318 | − | 0.410125i | ||||
\(321\) | −1.59593e7 | −0.482502 | ||||||||
\(322\) | −2.54660e7 | − | 7.43105e7i | −0.762770 | − | 2.22578i | ||||
\(323\) | − | 4.23052e7i | − | 1.25541i | ||||||
\(324\) | −2.98477e6 | + | 2.31798e6i | −0.0877558 | + | 0.0681512i | ||||
\(325\) | 6.38042e6 | 0.185866 | ||||||||
\(326\) | −7.82987e6 | + | 2.68328e6i | −0.225996 | + | 0.0774484i | ||||
\(327\) | − | 2.78839e7i | − | 0.797462i | ||||||
\(328\) | 2.90570e7 | + | 1.90510e7i | 0.823435 | + | 0.539880i | ||||
\(329\) | 6.01713e7 | 1.68967 | ||||||||
\(330\) | 451168. | + | 1.31652e6i | 0.0125544 | + | 0.0366341i | ||||
\(331\) | − | 2.26621e7i | − | 0.624907i | −0.949933 | − | 0.312453i | \(-0.898849\pi\) | ||
0.949933 | − | 0.312453i | \(-0.101151\pi\) | |||||||
\(332\) | 8.45421e6 | + | 1.08862e7i | 0.231025 | + | 0.297482i | ||||
\(333\) | 2827.57 | 7.65738e−5 | ||||||||
\(334\) | 4.49338e6 | − | 1.53987e6i | 0.120596 | − | 0.0413280i | ||||
\(335\) | − | 1.81956e7i | − | 0.483984i | ||||||
\(336\) | 1.06086e7 | − | 4.15160e7i | 0.279667 | − | 1.09445i | ||||
\(337\) | −5.15429e7 | −1.34673 | −0.673363 | − | 0.739312i | \(-0.735151\pi\) | ||||
−0.673363 | + | 0.739312i | \(0.735151\pi\) | |||||||
\(338\) | −1.70688e6 | − | 4.98073e6i | −0.0442032 | − | 0.128986i | ||||
\(339\) | 3.47349e7i | 0.891593i | ||||||||
\(340\) | −2.32248e7 | + | 1.80364e7i | −0.590901 | + | 0.458895i | ||||
\(341\) | 1.08643e7 | 0.273993 | ||||||||
\(342\) | 9.46561e6 | − | 3.24384e6i | 0.236630 | − | 0.0810927i | ||||
\(343\) | 1.44338e8i | 3.57684i | ||||||||
\(344\) | −2.94872e7 | + | 4.49744e7i | −0.724366 | + | 1.10482i | ||||
\(345\) | −1.27501e7 | −0.310496 | ||||||||
\(346\) | 2.62784e6 | + | 7.66811e6i | 0.0634411 | + | 0.185123i | ||||
\(347\) | − | 2.69989e7i | − | 0.646186i | −0.946367 | − | 0.323093i | \(-0.895277\pi\) | ||
0.946367 | − | 0.323093i | \(-0.104723\pi\) | |||||||
\(348\) | 7.69398e6 | + | 9.90725e6i | 0.182563 | + | 0.235080i | ||||
\(349\) | −3.98391e7 | −0.937201 | −0.468601 | − | 0.883410i | \(-0.655242\pi\) | ||||
−0.468601 | + | 0.883410i | \(0.655242\pi\) | |||||||
\(350\) | 1.58714e7 | − | 5.43909e6i | 0.370178 | − | 0.126859i | ||||
\(351\) | − | 7.73407e6i | − | 0.178849i | ||||||
\(352\) | 522605. | + | 6.52050e6i | 0.0119825 | + | 0.149504i | ||||
\(353\) | −3.70984e7 | −0.843395 | −0.421697 | − | 0.906737i | \(-0.638566\pi\) | ||||
−0.421697 | + | 0.906737i | \(0.638566\pi\) | |||||||
\(354\) | 226477. | + | 660865.i | 0.00510522 | + | 0.0148971i | ||||
\(355\) | − | 1.69572e7i | − | 0.379026i | ||||||
\(356\) | −2.33531e6 | + | 1.81360e6i | −0.0517601 | + | 0.0401969i | ||||
\(357\) | −8.59842e7 | −1.88979 | ||||||||
\(358\) | 8.01114e7 | − | 2.74540e7i | 1.74600 | − | 0.598352i | ||||
\(359\) | − | 3.23502e7i | − | 0.699186i | −0.936902 | − | 0.349593i | \(-0.886320\pi\) | ||
0.936902 | − | 0.349593i | \(-0.113680\pi\) | |||||||
\(360\) | −5.81639e6 | − | 3.81348e6i | −0.124665 | − | 0.0817360i | ||||
\(361\) | 2.05530e7 | 0.436870 | ||||||||
\(362\) | −6.35206e6 | − | 1.85355e7i | −0.133903 | − | 0.390731i | ||||
\(363\) | 2.69947e7i | 0.564363i | ||||||||
\(364\) | 5.37876e7 | + | 6.92604e7i | 1.11527 | + | 1.43609i | ||||
\(365\) | 1.38391e7 | 0.284596 | ||||||||
\(366\) | 1.56527e7 | − | 5.36416e6i | 0.319262 | − | 0.109410i | ||||
\(367\) | 5.83482e6i | 0.118040i | 0.998257 | + | 0.0590200i | \(0.0187976\pi\) | ||||
−0.998257 | + | 0.0590200i | \(0.981202\pi\) | |||||||
\(368\) | −5.80644e7 | − | 1.48373e7i | −1.16511 | − | 0.297722i | ||||
\(369\) | 1.64906e7 | 0.328213 | ||||||||
\(370\) | 1687.02 | + | 4922.77i | 3.33054e−5 | + | 9.71861e-5i | ||||
\(371\) | 918853.i | 0.0179939i | ||||||||
\(372\) | −4.28827e7 | + | 3.33028e7i | −0.833016 | + | 0.646921i | ||||
\(373\) | −1.63274e7 | −0.314623 | −0.157311 | − | 0.987549i | \(-0.550283\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(374\) | 1.24173e7 | − | 4.25538e6i | 0.237363 | − | 0.0813437i | ||||
\(375\) | − | 2.72319e6i | − | 0.0516398i | ||||||
\(376\) | 2.51705e7 | − | 3.83906e7i | 0.473509 | − | 0.722206i | ||||
\(377\) | −2.56715e7 | −0.479100 | ||||||||
\(378\) | −6.59304e6 | − | 1.92386e7i | −0.122070 | − | 0.356204i | ||||
\(379\) | − | 6.49860e7i | − | 1.19372i | −0.802346 | − | 0.596859i | \(-0.796415\pi\) | ||
0.802346 | − | 0.596859i | \(-0.203585\pi\) | |||||||
\(380\) | 1.12950e7 | + | 1.45442e7i | 0.205843 | + | 0.265056i | ||||
\(381\) | 1.88364e7 | 0.340583 | ||||||||
\(382\) | −4.10076e7 | + | 1.40532e7i | −0.735656 | + | 0.252107i | ||||
\(383\) | − | 5.64474e7i | − | 1.00473i | −0.864657 | − | 0.502363i | \(-0.832464\pi\) | ||
0.864657 | − | 0.502363i | \(-0.167536\pi\) | |||||||
\(384\) | −2.20503e7 | − | 2.41352e7i | −0.389422 | − | 0.426243i | ||||
\(385\) | −7.48917e6 | −0.131236 | ||||||||
\(386\) | 2.58597e7 | + | 7.54593e7i | 0.449637 | + | 1.31205i | ||||
\(387\) | 2.55241e7i | 0.440370i | ||||||||
\(388\) | −4.04492e7 | + | 3.14129e7i | −0.692492 | + | 0.537790i | ||||
\(389\) | −8.66539e7 | −1.47211 | −0.736053 | − | 0.676924i | \(-0.763313\pi\) | ||||
−0.736053 | + | 0.676924i | \(0.763313\pi\) | |||||||
\(390\) | 1.34649e7 | − | 4.61441e6i | 0.226992 | − | 0.0777897i | ||||
\(391\) | 1.20258e8i | 2.01179i | ||||||||
\(392\) | 1.42465e8 | + | 9.34064e7i | 2.36511 | + | 1.55067i | ||||
\(393\) | −4.41990e6 | −0.0728173 | ||||||||
\(394\) | 3.45989e7 | + | 1.00960e8i | 0.565684 | + | 1.65068i | ||||
\(395\) | 2.17996e7i | 0.353719i | ||||||||
\(396\) | 1.90425e6 | + | 2.45203e6i | 0.0306647 | + | 0.0394858i | ||||
\(397\) | 1.11044e8 | 1.77469 | 0.887346 | − | 0.461105i | \(-0.152547\pi\) | ||||
0.887346 | + | 0.461105i | \(0.152547\pi\) | |||||||
\(398\) | 4.97968e7 | − | 1.70652e7i | 0.789863 | − | 0.270684i | ||||
\(399\) | 5.38462e7i | 0.847689i | ||||||||
\(400\) | 3.16897e6 | − | 1.24015e7i | 0.0495152 | − | 0.193774i | ||||
\(401\) | −5.61325e7 | −0.870525 | −0.435262 | − | 0.900304i | \(-0.643344\pi\) | ||||
−0.435262 | + | 0.900304i | \(0.643344\pi\) | |||||||
\(402\) | −1.31593e7 | − | 3.83991e7i | −0.202560 | − | 0.591076i | ||||
\(403\) | − | 1.11117e8i | − | 1.69771i | ||||||
\(404\) | −4.29905e7 | + | 3.33865e7i | −0.651971 | + | 0.506321i | ||||
\(405\) | −3.30094e6 | −0.0496904 | ||||||||
\(406\) | −6.38582e7 | + | 2.18840e7i | −0.954198 | + | 0.327001i | ||||
\(407\) | − | 2322.89i | − | 3.44544e-5i | ||||||
\(408\) | −3.59684e7 | + | 5.48597e7i | −0.529591 | + | 0.807742i | ||||
\(409\) | −5.17276e7 | −0.756053 | −0.378026 | − | 0.925795i | \(-0.623397\pi\) | ||||
−0.378026 | + | 0.925795i | \(0.623397\pi\) | |||||||
\(410\) | 9.83881e6 | + | 2.87099e7i | 0.142755 | + | 0.416562i | ||||
\(411\) | − | 6.47238e7i | − | 0.932264i | ||||||
\(412\) | 2.32034e7 | + | 2.98782e7i | 0.331788 | + | 0.427231i | ||||
\(413\) | −3.75941e6 | −0.0533666 | ||||||||
\(414\) | −2.69072e7 | + | 9.22105e6i | −0.379200 | + | 0.129951i | ||||
\(415\) | 1.20393e7i | 0.168445i | ||||||||
\(416\) | 6.66897e7 | − | 5.34505e6i | 0.926357 | − | 0.0742457i | ||||
\(417\) | −6.00300e7 | −0.827866 | ||||||||
\(418\) | −2.66486e6 | − | 7.77614e6i | −0.0364877 | − | 0.106472i | ||||
\(419\) | 2.85658e7i | 0.388333i | 0.980969 | + | 0.194167i | \(0.0622002\pi\) | ||||
−0.980969 | + | 0.194167i | \(0.937800\pi\) | |||||||
\(420\) | 2.95606e7 | − | 2.29568e7i | 0.398994 | − | 0.309859i | ||||
\(421\) | −1.03346e7 | −0.138499 | −0.0692496 | − | 0.997599i | \(-0.522060\pi\) | ||||
−0.0692496 | + | 0.997599i | \(0.522060\pi\) | |||||||
\(422\) | −6.58798e6 | + | 2.25769e6i | −0.0876627 | + | 0.0300418i | ||||
\(423\) | − | 2.17876e7i | − | 0.287864i | ||||||
\(424\) | 586247. | + | 384369.i | 0.00769101 | + | 0.00504256i | ||||
\(425\) | −2.56849e7 | −0.334589 | ||||||||
\(426\) | −1.22637e7 | − | 3.57858e7i | −0.158633 | − | 0.462894i | ||||
\(427\) | 8.90424e7i | 1.14370i | ||||||||
\(428\) | −4.01890e7 | − | 5.17499e7i | −0.512597 | − | 0.660052i | ||||
\(429\) | −6.35365e6 | −0.0804733 | ||||||||
\(430\) | −4.44372e7 | + | 1.52285e7i | −0.558909 | + | 0.191537i | ||||
\(431\) | − | 3.74717e7i | − | 0.468027i | −0.972233 | − | 0.234014i | \(-0.924814\pi\) | ||
0.972233 | − | 0.234014i | \(-0.0751860\pi\) | |||||||
\(432\) | −1.50326e7 | − | 3.84130e6i | −0.186459 | − | 0.0476460i | ||||
\(433\) | −7.74967e7 | −0.954595 | −0.477298 | − | 0.878742i | \(-0.658384\pi\) | ||||
−0.477298 | + | 0.878742i | \(0.658384\pi\) | |||||||
\(434\) | −9.47233e7 | − | 2.76405e8i | −1.15874 | − | 3.38124i | ||||
\(435\) | 1.09567e7i | 0.133110i | ||||||||
\(436\) | 9.04167e7 | − | 7.02177e7i | 1.09091 | − | 0.847202i | ||||
\(437\) | 7.53096e7 | 0.902414 | ||||||||
\(438\) | 2.92054e7 | − | 1.00086e7i | 0.347569 | − | 0.119111i | ||||
\(439\) | 1.06961e8i | 1.26425i | 0.774868 | + | 0.632124i | \(0.217817\pi\) | ||||
−0.774868 | + | 0.632124i | \(0.782183\pi\) | |||||||
\(440\) | −3.13283e6 | + | 4.77824e6i | −0.0367772 | + | 0.0560932i | ||||
\(441\) | 8.08525e7 | 0.942709 | ||||||||
\(442\) | −4.35227e7 | − | 1.27000e8i | −0.504022 | − | 1.47075i | ||||
\(443\) | − | 6.93528e7i | − | 0.797724i | −0.917011 | − | 0.398862i | \(-0.869405\pi\) | ||
0.917011 | − | 0.398862i | \(-0.130595\pi\) | |||||||
\(444\) | 7120.43 | + | 9168.71i | 8.13499e−5 | + | 0.000104751i | ||||
\(445\) | −2.58268e6 | −0.0293083 | ||||||||
\(446\) | −3.90689e7 | + | 1.33888e7i | −0.440379 | + | 0.150917i | ||||
\(447\) | − | 5.15211e7i | − | 0.576849i | ||||||
\(448\) | 1.61335e8 | − | 7.01466e7i | 1.79430 | − | 0.780140i | ||||
\(449\) | −1.10854e8 | −1.22465 | −0.612327 | − | 0.790605i | \(-0.709766\pi\) | ||||
−0.612327 | + | 0.790605i | \(0.709766\pi\) | |||||||
\(450\) | −1.96945e6 | − | 5.74690e6i | −0.0216126 | − | 0.0630661i | ||||
\(451\) | − | 1.35472e7i | − | 0.147680i | ||||||
\(452\) | −1.12632e8 | + | 8.74699e7i | −1.21968 | + | 0.947204i | ||||
\(453\) | 4.61963e7 | 0.496950 | ||||||||
\(454\) | 2.94344e7 | − | 1.00871e7i | 0.314548 | − | 0.107795i | ||||
\(455\) | 7.65969e7i | 0.813162i | ||||||||
\(456\) | 3.43550e7 | + | 2.25246e7i | 0.362323 | + | 0.237554i | ||||
\(457\) | 1.12207e8 | 1.17564 | 0.587818 | − | 0.808993i | \(-0.299987\pi\) | ||||
0.587818 | + | 0.808993i | \(0.299987\pi\) | |||||||
\(458\) | 2.60992e7 | + | 7.61582e7i | 0.271664 | + | 0.792721i | ||||
\(459\) | 3.11342e7i | 0.321958i | ||||||||
\(460\) | −3.21075e7 | − | 4.13436e7i | −0.329863 | − | 0.424752i | ||||
\(461\) | 1.44607e8 | 1.47600 | 0.737998 | − | 0.674803i | \(-0.235771\pi\) | ||||
0.737998 | + | 0.674803i | \(0.235771\pi\) | |||||||
\(462\) | −1.58048e7 | + | 5.41627e6i | −0.160274 | + | 0.0549256i | ||||
\(463\) | − | 9.36261e7i | − | 0.943309i | −0.881783 | − | 0.471655i | \(-0.843657\pi\) | ||
0.881783 | − | 0.471655i | \(-0.156343\pi\) | |||||||
\(464\) | −1.27503e7 | + | 4.98972e7i | −0.127634 | + | 0.499485i | ||||
\(465\) | −4.74252e7 | −0.471683 | ||||||||
\(466\) | 1.56549e7 | + | 4.56813e7i | 0.154701 | + | 0.451420i | ||||
\(467\) | − | 5.11897e7i | − | 0.502611i | −0.967908 | − | 0.251305i | \(-0.919140\pi\) | ||
0.967908 | − | 0.251305i | \(-0.0808598\pi\) | |||||||
\(468\) | 2.50786e7 | − | 1.94761e7i | 0.244662 | − | 0.190005i | ||||
\(469\) | 2.18438e8 | 2.11743 | ||||||||
\(470\) | 3.79319e7 | − | 1.29992e7i | 0.365352 | − | 0.125205i | ||||
\(471\) | 46925.8i | 0.000449106i | ||||||||
\(472\) | −1.57261e6 | + | 2.39858e6i | −0.0149553 | + | 0.0228101i | ||||
\(473\) | 2.09684e7 | 0.198144 | ||||||||
\(474\) | 1.57658e7 | + | 4.60050e7i | 0.148041 | + | 0.431986i | ||||
\(475\) | 1.60848e7i | 0.150084i | ||||||||
\(476\) | −2.16527e8 | − | 2.78814e8i | −2.00766 | − | 2.58519i | ||||
\(477\) | 332709. | 0.00306556 | ||||||||
\(478\) | 1.02141e7 | − | 3.50036e6i | 0.0935228 | − | 0.0320500i | ||||
\(479\) | 1.88871e8i | 1.71854i | 0.511525 | + | 0.859269i | \(0.329081\pi\) | ||||
−0.511525 | + | 0.859269i | \(0.670919\pi\) | |||||||
\(480\) | −2.28129e6 | − | 2.84635e7i | −0.0206280 | − | 0.257374i | ||||
\(481\) | −23757.8 | −0.000213487 | ||||||||
\(482\) | 2.00806e7 | + | 5.85956e7i | 0.179323 | + | 0.523267i | ||||
\(483\) | − | 1.53065e8i | − | 1.35842i | ||||||
\(484\) | −8.75334e7 | + | 6.79785e7i | −0.772036 | + | 0.599564i | ||||
\(485\) | −4.47339e7 | −0.392113 | ||||||||
\(486\) | −6.96616e6 | + | 2.38729e6i | −0.0606854 | + | 0.0207968i | ||||
\(487\) | − | 1.41791e8i | − | 1.22761i | −0.789456 | − | 0.613807i | \(-0.789637\pi\) | ||
0.789456 | − | 0.613807i | \(-0.210363\pi\) | |||||||
\(488\) | 5.68109e7 | + | 3.72477e7i | 0.488846 | + | 0.320509i | ||||
\(489\) | −1.61280e7 | −0.137928 | ||||||||
\(490\) | 4.82393e7 | + | 1.40763e8i | 0.410027 | + | 1.19647i | ||||
\(491\) | 1.73081e7i | 0.146219i | 0.997324 | + | 0.0731095i | \(0.0232923\pi\) | ||||
−0.997324 | + | 0.0731095i | \(0.976708\pi\) | |||||||
\(492\) | 4.15268e7 | + | 5.34725e7i | 0.348685 | + | 0.448989i | ||||
\(493\) | 1.03343e8 | 0.862460 | ||||||||
\(494\) | −7.95319e7 | + | 2.72554e7i | −0.659721 | + | 0.226085i | ||||
\(495\) | 2.71177e6i | 0.0223582i | ||||||||
\(496\) | −2.15976e8 | − | 5.51886e7i | −1.76995 | − | 0.452277i | ||||
\(497\) | 2.03571e8 | 1.65824 | ||||||||
\(498\) | 8.70701e6 | + | 2.54073e7i | 0.0704987 | + | 0.205717i | ||||
\(499\) | − | 2.37084e8i | − | 1.90810i | −0.299655 | − | 0.954048i | \(-0.596872\pi\) | ||
0.299655 | − | 0.954048i | \(-0.403128\pi\) | |||||||
\(500\) | 8.83026e6 | − | 6.85759e6i | 0.0706421 | − | 0.0548607i | ||||
\(501\) | 9.25547e6 | 0.0736012 | ||||||||
\(502\) | 1.24682e8 | − | 4.27282e7i | 0.985580 | − | 0.337756i | ||||
\(503\) | − | 2.25165e7i | − | 0.176928i | −0.996079 | − | 0.0884640i | \(-0.971804\pi\) | ||
0.996079 | − | 0.0884640i | \(-0.0281958\pi\) | |||||||
\(504\) | 4.57808e7 | − | 6.98257e7i | 0.357595 | − | 0.545411i | ||||
\(505\) | −4.75444e7 | −0.369169 | ||||||||
\(506\) | 7.57522e6 | + | 2.21047e7i | 0.0584715 | + | 0.170621i | ||||
\(507\) | − | 1.02593e7i | − | 0.0787217i | ||||||
\(508\) | 4.74342e7 | + | 6.10793e7i | 0.361827 | + | 0.465911i | ||||
\(509\) | −9.38014e7 | −0.711305 | −0.355653 | − | 0.934618i | \(-0.615741\pi\) | ||||
−0.355653 | + | 0.934618i | \(0.615741\pi\) | |||||||
\(510\) | −5.42043e7 | + | 1.85757e7i | −0.408624 | + | 0.140034i | ||||
\(511\) | 1.66138e8i | 1.24511i | ||||||||
\(512\) | 2.27338e7 | − | 1.32278e8i | 0.169380 | − | 0.985551i | ||||
\(513\) | 1.94973e7 | 0.144418 | ||||||||
\(514\) | 3.59312e7 | + | 1.04848e8i | 0.264595 | + | 0.772095i | ||||
\(515\) | 3.30431e7i | 0.241913i | ||||||||
\(516\) | −8.27648e7 | + | 6.42752e7i | −0.602416 | + | 0.467837i | ||||
\(517\) | −1.78988e7 | −0.129525 | ||||||||
\(518\) | −59097.8 | + | 20252.7i | −0.000425189 | + | 0.000145711i | ||||
\(519\) | 1.57948e7i | 0.112983i | ||||||||
\(520\) | 4.88704e7 | + | 3.20416e7i | 0.347565 | + | 0.227879i | ||||
\(521\) | 1.78407e8 | 1.26153 | 0.630765 | − | 0.775974i | \(-0.282741\pi\) | ||||
0.630765 | + | 0.775974i | \(0.282741\pi\) | |||||||
\(522\) | 7.92404e6 | + | 2.31225e7i | 0.0557102 | + | 0.162564i | ||||
\(523\) | 2.26348e8i | 1.58224i | 0.611662 | + | 0.791119i | \(0.290501\pi\) | ||||
−0.611662 | + | 0.791119i | \(0.709499\pi\) | |||||||
\(524\) | −1.11303e7 | − | 1.43320e7i | −0.0773591 | − | 0.0996125i | ||||
\(525\) | 3.26919e7 | 0.225924 | ||||||||
\(526\) | −5.79478e7 | + | 1.98586e7i | −0.398180 | + | 0.136456i | ||||
\(527\) | 4.47310e8i | 3.05617i | ||||||||
\(528\) | −3.15568e6 | + | 1.23495e7i | −0.0214384 | + | 0.0838972i | ||||
\(529\) | −6.60414e7 | −0.446118 | ||||||||
\(530\) | 198505. | + | 579244.i | 0.00133335 | + | 0.00389075i | ||||
\(531\) | 1.36125e6i | 0.00909190i | ||||||||
\(532\) | −1.74603e8 | + | 1.35597e8i | −1.15962 | + | 0.900562i | ||||
\(533\) | −1.38557e8 | −0.915053 | ||||||||
\(534\) | −5.45038e6 | + | 1.86783e6i | −0.0357934 | + | 0.0122663i | ||||
\(535\) | − | 5.72316e7i | − | 0.373744i | ||||||
\(536\) | 9.13757e7 | − | 1.39368e8i | 0.593384 | − | 0.905041i | ||||
\(537\) | 1.65014e8 | 1.06561 | ||||||||
\(538\) | −9.41608e7 | − | 2.74763e8i | −0.604677 | − | 1.76446i | ||||
\(539\) | − | 6.64215e7i | − | 0.424172i | ||||||
\(540\) | −8.31248e6 | − | 1.07037e7i | −0.0527897 | − | 0.0679754i | ||||
\(541\) | 5.52591e7 | 0.348990 | 0.174495 | − | 0.984658i | \(-0.444171\pi\) | ||||
0.174495 | + | 0.984658i | \(0.444171\pi\) | |||||||
\(542\) | 1.09201e6 | − | 374228.i | 0.00685847 | − | 0.00235038i | ||||
\(543\) | − | 3.81794e7i | − | 0.238468i | ||||||
\(544\) | −2.68465e8 | + | 2.15170e7i | −1.66760 | + | 0.133655i | ||||
\(545\) | 9.99943e7 | 0.617712 | ||||||||
\(546\) | 5.53960e7 | + | 1.61647e8i | 0.340330 | + | 0.993091i | ||||
\(547\) | − | 5.20328e7i | − | 0.317918i | −0.987285 | − | 0.158959i | \(-0.949186\pi\) | ||
0.987285 | − | 0.158959i | \(-0.0508137\pi\) | |||||||
\(548\) | 2.09875e8 | − | 1.62989e8i | 1.27532 | − | 0.990412i | ||||
\(549\) | 3.22416e7 | 0.194849 | ||||||||
\(550\) | −4.72116e6 | + | 1.61793e6i | −0.0283766 | + | 0.00972461i | ||||
\(551\) | − | 6.47167e7i | − | 0.386867i | ||||||
\(552\) | −9.76586e7 | − | 6.40292e7i | −0.580622 | − | 0.380681i | ||||
\(553\) | −2.61705e8 | −1.54752 | ||||||||
\(554\) | 1.23121e7 | + | 3.59271e7i | 0.0724109 | + | 0.211297i | ||||
\(555\) | 10139.9i | 5.93138e-5i | ||||||||
\(556\) | −1.51168e8 | − | 1.94654e8i | −0.879502 | − | 1.13250i | ||||
\(557\) | −2.24751e8 | −1.30058 | −0.650289 | − | 0.759687i | \(-0.725352\pi\) | ||||
−0.650289 | + | 0.759687i | \(0.725352\pi\) | |||||||
\(558\) | −1.00084e8 | + | 3.42986e7i | −0.576052 | + | 0.197412i | ||||
\(559\) | − | 2.14458e8i | − | 1.22774i | ||||||
\(560\) | 1.48880e8 | + | 3.80435e7i | 0.847760 | + | 0.216629i | ||||
\(561\) | 2.55772e7 | 0.144865 | ||||||||
\(562\) | 1.17396e7 | + | 3.42563e7i | 0.0661367 | + | 0.192989i | ||||
\(563\) | 1.16024e8i | 0.650165i | 0.945686 | + | 0.325083i | \(0.105392\pi\) | ||||
−0.945686 | + | 0.325083i | \(0.894608\pi\) | |||||||
\(564\) | 7.06487e7 | − | 5.48658e7i | 0.393792 | − | 0.305819i | ||||
\(565\) | −1.24563e8 | −0.690625 | ||||||||
\(566\) | −8.12184e7 | + | 2.78334e7i | −0.447925 | + | 0.153503i | ||||
\(567\) | − | 3.96278e7i | − | 0.217396i | ||||||
\(568\) | 8.51568e7 | − | 1.29883e8i | 0.464702 | − | 0.708772i | ||||
\(569\) | 6.45365e7 | 0.350323 | 0.175161 | − | 0.984540i | \(-0.443955\pi\) | ||||
0.175161 | + | 0.984540i | \(0.443955\pi\) | |||||||
\(570\) | 1.16327e7 | + | 3.39446e7i | 0.0628141 | + | 0.183293i | ||||
\(571\) | − | 5.29903e7i | − | 0.284635i | −0.989821 | − | 0.142317i | \(-0.954545\pi\) | ||
0.989821 | − | 0.142317i | \(-0.0454553\pi\) | |||||||
\(572\) | −1.59999e7 | − | 2.06025e7i | −0.0854926 | − | 0.110086i | ||||
\(573\) | −8.44676e7 | −0.448979 | ||||||||
\(574\) | −3.44662e8 | + | 1.18115e8i | −1.82246 | + | 0.624553i | ||||
\(575\) | − | 4.57231e7i | − | 0.240509i | ||||||
\(576\) | −2.53995e7 | − | 5.84182e7i | −0.132910 | − | 0.305689i | ||||
\(577\) | −1.97923e8 | −1.03031 | −0.515155 | − | 0.857097i | \(-0.672266\pi\) | ||||
−0.515155 | + | 0.857097i | \(0.672266\pi\) | |||||||
\(578\) | 1.12603e8 | + | 3.28579e8i | 0.583134 | + | 1.70160i | ||||
\(579\) | 1.55431e8i | 0.800760i | ||||||||
\(580\) | −3.55284e7 | + | 2.75913e7i | −0.182092 | + | 0.141413i | ||||
\(581\) | −1.44532e8 | −0.736946 | ||||||||
\(582\) | −9.44043e7 | + | 3.23522e7i | −0.478876 | + | 0.164110i | ||||
\(583\) | − | 273326.i | − | 0.00137935i | ||||||
\(584\) | 1.06000e8 | + | 6.94980e7i | 0.532189 | + | 0.348926i | ||||
\(585\) | 2.77351e7 | 0.138536 | ||||||||
\(586\) | 7.49122e7 | + | 2.18596e8i | 0.372271 | + | 1.08630i | ||||
\(587\) | − | 6.20004e7i | − | 0.306535i | −0.988185 | − | 0.153268i | \(-0.951020\pi\) | ||
0.988185 | − | 0.153268i | \(-0.0489796\pi\) | |||||||
\(588\) | 2.03604e8 | + | 2.62174e8i | 1.00151 | + | 1.28961i | ||||
\(589\) | 2.80121e8 | 1.37088 | ||||||||
\(590\) | −2.36993e6 | + | 812168.i | −0.0115393 | + | 0.00395448i | ||||
\(591\) | 2.07959e8i | 1.00743i | ||||||||
\(592\) | −11799.8 | + | 46177.6i | −5.68735e−5 | + | 0.000222570i | ||||
\(593\) | −3.48324e8 | −1.67039 | −0.835197 | − | 0.549950i | \(-0.814647\pi\) | ||||
−0.835197 | + | 0.549950i | \(0.814647\pi\) | |||||||
\(594\) | 1.96119e6 | + | 5.72280e6i | 0.00935751 | + | 0.0273054i | ||||
\(595\) | − | 3.08348e8i | − | 1.46383i | ||||||
\(596\) | 1.67063e8 | − | 1.29741e8i | 0.789117 | − | 0.612829i | ||||
\(597\) | 1.02571e8 | 0.482063 | ||||||||
\(598\) | 2.26080e8 | − | 7.74770e7i | 1.05720 | − | 0.362301i | ||||
\(599\) | 2.16010e8i | 1.00506i | 0.864559 | + | 0.502531i | \(0.167598\pi\) | ||||
−0.864559 | + | 0.502531i | \(0.832402\pi\) | |||||||
\(600\) | 1.36755e7 | − | 2.08581e7i | 0.0633124 | − | 0.0965654i | ||||
\(601\) | 2.07109e8 | 0.954058 | 0.477029 | − | 0.878888i | \(-0.341714\pi\) | ||||
0.477029 | + | 0.878888i | \(0.341714\pi\) | |||||||
\(602\) | −1.82818e8 | − | 5.33468e8i | −0.837974 | − | 2.44523i | ||||
\(603\) | − | 7.90946e7i | − | 0.360741i | ||||||
\(604\) | 1.16332e8 | + | 1.49797e8i | 0.527946 | + | 0.679817i | ||||
\(605\) | −9.68055e7 | −0.437154 | ||||||||
\(606\) | −1.00336e8 | + | 3.43848e7i | −0.450855 | + | 0.154507i | ||||
\(607\) | − | 7.87805e7i | − | 0.352251i | −0.984368 | − | 0.176126i | \(-0.943644\pi\) | ||
0.984368 | − | 0.176126i | \(-0.0563565\pi\) | |||||||
\(608\) | 1.34746e7 | + | 1.68122e8i | 0.0599524 | + | 0.748021i | ||||
\(609\) | −1.31535e8 | −0.582358 | ||||||||
\(610\) | 1.92364e7 | + | 5.61322e7i | 0.0847489 | + | 0.247299i | ||||
\(611\) | 1.83063e8i | 0.802560i | ||||||||
\(612\) | −1.00956e8 | + | 7.84027e7i | −0.440432 | + | 0.342040i | ||||
\(613\) | −2.49628e8 | −1.08371 | −0.541853 | − | 0.840473i | \(-0.682277\pi\) | ||||
−0.541853 | + | 0.840473i | \(0.682277\pi\) | |||||||
\(614\) | 3.45049e8 | − | 1.18248e8i | 1.49065 | − | 0.510843i | ||||
\(615\) | 5.91367e7i | 0.254233i | ||||||||
\(616\) | −5.73628e7 | − | 3.76096e7i | −0.245408 | − | 0.160900i | ||||
\(617\) | 2.37350e8 | 1.01049 | 0.505247 | − | 0.862975i | \(-0.331401\pi\) | ||||
0.505247 | + | 0.862975i | \(0.331401\pi\) | |||||||
\(618\) | 2.38972e7 | + | 6.97327e7i | 0.101247 | + | 0.295441i | ||||
\(619\) | 5.81494e7i | 0.245173i | 0.992458 | + | 0.122587i | \(0.0391190\pi\) | ||||
−0.992458 | + | 0.122587i | \(0.960881\pi\) | |||||||
\(620\) | −1.19427e8 | − | 1.53782e8i | −0.501103 | − | 0.645252i | ||||
\(621\) | −5.54236e7 | −0.231430 | ||||||||
\(622\) | 1.76805e8 | − | 6.05908e7i | 0.734724 | − | 0.251788i | ||||
\(623\) | − | 3.10051e7i | − | 0.128224i | ||||||
\(624\) | 1.26307e8 | + | 3.22753e7i | 0.519844 | + | 0.132836i | ||||
\(625\) | 9.76562e6 | 0.0400000 | ||||||||
\(626\) | 7.20738e7 | + | 2.10313e8i | 0.293802 | + | 0.857320i | ||||
\(627\) | − | 1.60173e7i | − | 0.0649811i | ||||||
\(628\) | −152162. | + | 118169.i | −0.000614367 | + | 0.000477118i | ||||
\(629\) | 95639.0 | 0.000384311 | ||||||||
\(630\) | 6.89916e7 | − | 2.36433e7i | 0.275914 | − | 0.0945553i | ||||
\(631\) | − | 1.07588e8i | − | 0.428227i | −0.976809 | − | 0.214114i | \(-0.931314\pi\) | ||
0.976809 | − | 0.214114i | \(-0.0686863\pi\) | |||||||
\(632\) | −1.09475e8 | + | 1.66973e8i | −0.433673 | + | 0.661447i | ||||
\(633\) | −1.35699e7 | −0.0535016 | ||||||||
\(634\) | 1.99304e7 | + | 5.81572e7i | 0.0782073 | + | 0.228211i | ||||
\(635\) | 6.75492e7i | 0.263815i | ||||||||
\(636\) | 837834. | + | 1.07885e6i | 0.00325677 | + | 0.00419362i | ||||
\(637\) | −6.79338e8 | −2.62826 | ||||||||
\(638\) | 1.89955e7 | − | 6.50971e6i | 0.0731457 | − | 0.0250668i | ||||
\(639\) | − | 7.37116e7i | − | 0.282510i | ||||||
\(640\) | 8.65512e7 | − | 7.90745e7i | 0.330167 | − | 0.301645i | ||||
\(641\) | 2.45332e8 | 0.931492 | 0.465746 | − | 0.884918i | \(-0.345786\pi\) | ||||
0.465746 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(642\) | −4.13907e7 | − | 1.20779e8i | −0.156422 | − | 0.456443i | ||||
\(643\) | 3.42151e8i | 1.28702i | 0.765439 | + | 0.643509i | \(0.222522\pi\) | ||||
−0.765439 | + | 0.643509i | \(0.777478\pi\) | |||||||
\(644\) | 4.96331e8 | − | 3.85451e8i | 1.85829 | − | 1.44315i | ||||
\(645\) | −9.15318e7 | −0.341109 | ||||||||
\(646\) | 3.20163e8 | − | 1.09719e8i | 1.18761 | − | 0.406991i | ||||
\(647\) | − | 2.08510e8i | − | 0.769862i | −0.922945 | − | 0.384931i | \(-0.874225\pi\) | ||
0.922945 | − | 0.384931i | \(-0.125775\pi\) | |||||||
\(648\) | −2.52833e7 | − | 1.65769e7i | −0.0929201 | − | 0.0609224i | ||||
\(649\) | 1.11829e6 | 0.00409091 | ||||||||
\(650\) | 1.65477e7 | + | 4.82866e7i | 0.0602556 | + | 0.175827i | ||||
\(651\) | − | 5.69339e8i | − | 2.06361i | ||||||
\(652\) | −4.06137e7 | − | 5.22968e7i | −0.146531 | − | 0.188683i | ||||
\(653\) | 4.76031e8 | 1.70960 | 0.854802 | − | 0.518954i | \(-0.173678\pi\) | ||||
0.854802 | + | 0.518954i | \(0.173678\pi\) | |||||||
\(654\) | 2.11024e8 | − | 7.23173e7i | 0.754393 | − | 0.258529i | ||||
\(655\) | − | 1.58502e7i | − | 0.0564040i | ||||||
\(656\) | −6.88173e7 | + | 2.69311e8i | −0.243773 | + | 0.953987i | ||||
\(657\) | 6.01574e7 | 0.212125 | ||||||||
\(658\) | 1.56055e8 | + | 4.55373e8i | 0.547773 | + | 1.59842i | ||||
\(659\) | 1.75876e8i | 0.614540i | 0.951622 | + | 0.307270i | \(0.0994155\pi\) | ||||
−0.951622 | + | 0.307270i | \(0.900584\pi\) | |||||||
\(660\) | −8.79322e6 | + | 6.82882e6i | −0.0305855 | + | 0.0237528i | ||||
\(661\) | 3.80396e8 | 1.31714 | 0.658570 | − | 0.752520i | \(-0.271162\pi\) | ||||
0.658570 | + | 0.752520i | \(0.271162\pi\) | |||||||
\(662\) | 1.71505e8 | − | 5.87744e7i | 0.591157 | − | 0.202588i | ||||
\(663\) | − | 2.61596e8i | − | 0.897614i | ||||||
\(664\) | −6.04598e7 | + | 9.22144e7i | −0.206520 | + | 0.314988i | ||||
\(665\) | −1.93098e8 | −0.656617 | ||||||||
\(666\) | 7333.34 | + | 21398.9i | 2.48244e−5 | + | 7.24382e-5i | ||||
\(667\) | 1.83966e8i | 0.619954i | ||||||||
\(668\) | 2.33073e7 | + | 3.00119e7i | 0.0781920 | + | 0.100685i | ||||
\(669\) | −8.04742e7 | −0.268769 | ||||||||
\(670\) | 1.37703e8 | − | 4.71905e7i | 0.457846 | − | 0.156903i | ||||
\(671\) | − | 2.64869e7i | − | 0.0876725i | ||||||
\(672\) | 3.41704e8 | − | 2.73869e7i | 1.12601 | − | 0.0902475i | ||||
\(673\) | −3.67932e8 | −1.20704 | −0.603521 | − | 0.797347i | \(-0.706236\pi\) | ||||
−0.603521 | + | 0.797347i | \(0.706236\pi\) | |||||||
\(674\) | −1.33677e8 | − | 3.90074e8i | −0.436594 | − | 1.27399i | ||||
\(675\) | − | 1.18375e7i | − | 0.0384900i | ||||||
\(676\) | 3.32670e7 | − | 2.58352e7i | 0.107690 | − | 0.0836318i | ||||
\(677\) | 4.64821e7 | 0.149803 | 0.0749014 | − | 0.997191i | \(-0.476136\pi\) | ||||
0.0749014 | + | 0.997191i | \(0.476136\pi\) | |||||||
\(678\) | −2.62871e8 | + | 9.00854e7i | −0.843440 | + | 0.289045i | ||||
\(679\) | − | 5.37030e8i | − | 1.71549i | ||||||
\(680\) | −1.96732e8 | − | 1.28986e8i | −0.625675 | − | 0.410219i | ||||
\(681\) | 6.06290e7 | 0.191973 | ||||||||
\(682\) | 2.81768e7 | + | 8.22204e7i | 0.0888255 | + | 0.259195i | ||||
\(683\) | − | 6.18385e8i | − | 1.94087i | −0.241361 | − | 0.970435i | \(-0.577594\pi\) | ||
0.241361 | − | 0.970435i | \(-0.422406\pi\) | |||||||
\(684\) | 4.90984e7 | + | 6.32222e7i | 0.153426 | + | 0.197561i | ||||
\(685\) | 2.32106e8 | 0.722129 | ||||||||
\(686\) | −1.09234e9 | + | 3.74344e8i | −3.38366 | + | 1.15957i | ||||
\(687\) | 1.56871e8i | 0.483807i | ||||||||
\(688\) | −4.16839e8 | − | 1.06515e8i | −1.27998 | − | 0.327075i | ||||
\(689\) | −2.79549e6 | −0.00854673 | ||||||||
\(690\) | −3.30676e7 | − | 9.64919e7i | −0.100660 | − | 0.293727i | ||||
\(691\) | 5.57874e7i | 0.169084i | 0.996420 | + | 0.0845419i | \(0.0269427\pi\) | ||||
−0.996420 | + | 0.0845419i | \(0.973057\pi\) | |||||||
\(692\) | −5.12164e7 | + | 3.97747e7i | −0.154558 | + | 0.120030i | ||||
\(693\) | −3.25548e7 | −0.0978172 | ||||||||
\(694\) | 2.04326e8 | − | 7.00221e7i | 0.611287 | − | 0.209487i | ||||
\(695\) | − | 2.15273e8i | − | 0.641262i | ||||||
\(696\) | −5.50230e7 | + | 8.39222e7i | −0.163199 | + | 0.248914i | ||||
\(697\) | 5.57773e8 | 1.64725 | ||||||||
\(698\) | −1.03323e8 | − | 3.01500e8i | −0.303831 | − | 0.886585i | ||||
\(699\) | 9.40946e7i | 0.275507i | ||||||||
\(700\) | 8.23254e7 | + | 1.06007e8i | 0.240016 | + | 0.309059i | ||||
\(701\) | −5.45837e8 | −1.58456 | −0.792280 | − | 0.610158i | \(-0.791106\pi\) | ||||
−0.792280 | + | 0.610158i | \(0.791106\pi\) | |||||||
\(702\) | 5.85310e7 | − | 2.00584e7i | 0.169190 | − | 0.0579810i | ||||
\(703\) | − | 59892.4i | − | 0.000172387i | ||||||
\(704\) | −4.79914e7 | + | 2.08661e7i | −0.137545 | + | 0.0598029i | ||||
\(705\) | 7.81323e7 | 0.222979 | ||||||||
\(706\) | −9.62152e7 | − | 2.80758e8i | −0.273420 | − | 0.797845i | ||||
\(707\) | − | 5.70770e8i | − | 1.61511i | ||||||
\(708\) | −4.41401e6 | + | 3.42793e6i | −0.0124375 | + | 0.00965899i | ||||
\(709\) | 2.11110e8 | 0.592339 | 0.296170 | − | 0.955135i | \(-0.404291\pi\) | ||||
0.296170 | + | 0.955135i | \(0.404291\pi\) | |||||||
\(710\) | 1.28331e8 | − | 4.39788e7i | 0.358556 | − | 0.122876i | ||||
\(711\) | 9.47612e7i | 0.263646i | ||||||||
\(712\) | −1.97819e7 | − | 1.29699e7i | −0.0548060 | − | 0.0359332i | ||||
\(713\) | −7.96280e8 | −2.19684 | ||||||||
\(714\) | −2.23001e8 | − | 6.50723e8i | −0.612651 | − | 1.78773i | ||||
\(715\) | − | 2.27848e7i | − | 0.0623343i | ||||||
\(716\) | 4.15540e8 | + | 5.35076e8i | 1.13207 | + | 1.45773i | ||||
\(717\) | 2.10391e7 | 0.0570781 | ||||||||
\(718\) | 2.44824e8 | − | 8.39006e7i | 0.661425 | − | 0.226669i | ||||
\(719\) | 2.73670e8i | 0.736276i | 0.929771 | + | 0.368138i | \(0.120005\pi\) | ||||
−0.929771 | + | 0.368138i | \(0.879995\pi\) | |||||||
\(720\) | 1.37753e7 | − | 5.39084e7i | 0.0369065 | − | 0.144430i | ||||
\(721\) | −3.96683e8 | −1.05837 | ||||||||
\(722\) | 5.33044e7 | + | 1.55543e8i | 0.141629 | + | 0.413276i | ||||
\(723\) | 1.20695e8i | 0.319356i | ||||||||
\(724\) | 1.23801e8 | − | 9.61440e7i | 0.326219 | − | 0.253342i | ||||
\(725\) | −3.92918e7 | −0.103107 | ||||||||
\(726\) | −2.04294e8 | + | 7.00111e7i | −0.533883 | + | 0.182960i | ||||
\(727\) | 6.77998e8i | 1.76451i | 0.470768 | + | 0.882257i | \(0.343977\pi\) | ||||
−0.470768 | + | 0.882257i | \(0.656023\pi\) | |||||||
\(728\) | −3.84659e8 | + | 5.86689e8i | −0.996969 | + | 1.52060i | ||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 3.58919e7 | + | 1.04733e8i | 0.0922630 | + | 0.269226i | ||||
\(731\) | 8.63321e8i | 2.21014i | ||||||||
\(732\) | 8.11912e7 | + | 1.04547e8i | 0.207003 | + | 0.266550i | ||||
\(733\) | 4.75863e8 | 1.20829 | 0.604143 | − | 0.796876i | \(-0.293516\pi\) | ||||
0.604143 | + | 0.796876i | \(0.293516\pi\) | |||||||
\(734\) | −4.41575e7 | + | 1.51327e7i | −0.111665 | + | 0.0382673i | ||||
\(735\) | 2.89945e8i | 0.730219i | ||||||||
\(736\) | −3.83034e7 | − | 4.77909e8i | −0.0960737 | − | 1.19870i | ||||
\(737\) | −6.49774e7 | −0.162315 | ||||||||
\(738\) | 4.27685e7 | + | 1.24800e8i | 0.106403 | + | 0.310487i | ||||
\(739\) | − | 4.04862e8i | − | 1.00317i | −0.865109 | − | 0.501584i | \(-0.832751\pi\) | ||
0.865109 | − | 0.501584i | \(-0.167249\pi\) | |||||||
\(740\) | −32879.9 | + | 25534.5i | −8.11400e−5 | + | 6.30134e-5i | ||||
\(741\) | −1.63820e8 | −0.402636 | ||||||||
\(742\) | −6.95382e6 | + | 2.38306e6i | −0.0170221 | + | 0.00583342i | ||||
\(743\) | 3.57127e8i | 0.870676i | 0.900267 | + | 0.435338i | \(0.143371\pi\) | ||||
−0.900267 | + | 0.435338i | \(0.856629\pi\) | |||||||
\(744\) | −3.63250e8 | − | 2.38163e8i | −0.882037 | − | 0.578302i | ||||
\(745\) | 1.84759e8 | 0.446825 | ||||||||
\(746\) | −4.23453e7 | − | 1.23565e8i | −0.101997 | − | 0.297631i | ||||
\(747\) | 5.23339e7i | 0.125551i | ||||||||
\(748\) | 6.44089e7 | + | 8.29370e7i | 0.153901 | + | 0.198173i | ||||
\(749\) | 6.87066e8 | 1.63513 | ||||||||
\(750\) | 2.06089e7 | − | 7.06264e6i | 0.0488508 | − | 0.0167411i | ||||
\(751\) | 1.02196e8i | 0.241275i | 0.992697 | + | 0.120637i | \(0.0384938\pi\) | ||||
−0.992697 | + | 0.120637i | \(0.961506\pi\) | |||||||
\(752\) | 3.55817e8 | + | 9.09224e7i | 0.836708 | + | 0.213805i | ||||
\(753\) | 2.56820e8 | 0.601511 | ||||||||
\(754\) | −6.65793e7 | − | 1.94280e8i | −0.155319 | − | 0.453225i | ||||
\(755\) | 1.65664e8i | 0.384936i | ||||||||
\(756\) | 1.28498e8 | − | 9.97914e7i | 0.297392 | − | 0.230955i | ||||
\(757\) | 4.38046e8 | 1.00979 | 0.504896 | − | 0.863180i | \(-0.331531\pi\) | ||||
0.504896 | + | 0.863180i | \(0.331531\pi\) | |||||||
\(758\) | 4.91810e8 | − | 1.68542e8i | 1.12925 | − | 0.386991i | ||||
\(759\) | 4.55313e7i | 0.104132i | ||||||||
\(760\) | −8.07755e7 | + | 1.23200e8i | −0.184009 | + | 0.280654i | ||||
\(761\) | 1.40458e8 | 0.318708 | 0.159354 | − | 0.987222i | \(-0.449059\pi\) | ||||
0.159354 | + | 0.987222i | \(0.449059\pi\) | |||||||
\(762\) | 4.88525e7 | + | 1.42553e8i | 0.110414 | + | 0.322189i | ||||
\(763\) | 1.20043e9i | 2.70249i | ||||||||
\(764\) | −2.12708e8 | − | 2.73896e8i | −0.476983 | − | 0.614194i | ||||
\(765\) | −1.11650e8 | −0.249388 | ||||||||
\(766\) | 4.27191e8 | − | 1.46397e8i | 0.950464 | − | 0.325722i | ||||
\(767\) | − | 1.14375e7i | − | 0.0253481i | ||||||
\(768\) | 1.25466e8 | − | 2.29470e8i | 0.276976 | − | 0.506574i | ||||
\(769\) | 2.32792e7 | 0.0511905 | 0.0255952 | − | 0.999672i | \(-0.491852\pi\) | ||||
0.0255952 | + | 0.999672i | \(0.491852\pi\) | |||||||
\(770\) | −1.94233e7 | − | 5.66776e7i | −0.0425452 | − | 0.124148i | ||||
\(771\) | 2.15966e8i | 0.471219i | ||||||||
\(772\) | −5.04004e8 | + | 3.91410e8i | −1.09542 | + | 0.850706i | ||||
\(773\) | 1.98042e8 | 0.428763 | 0.214382 | − | 0.976750i | \(-0.431226\pi\) | ||||
0.214382 | + | 0.976750i | \(0.431226\pi\) | |||||||
\(774\) | −1.93165e8 | + | 6.61971e7i | −0.416586 | + | 0.142763i | ||||
\(775\) | − | 1.70071e8i | − | 0.365364i | ||||||
\(776\) | −3.42636e8 | − | 2.24647e8i | −0.733243 | − | 0.480746i | ||||
\(777\) | −121730. | −0.000259498 | ||||||||
\(778\) | −2.24738e8 | − | 6.55791e8i | −0.477241 | − | 1.39260i | ||||
\(779\) | − | 3.49296e8i | − | 0.738893i | ||||||
\(780\) | 6.98431e7 | + | 8.99343e7i | 0.147177 | + | 0.189514i | ||||
\(781\) | −6.05551e7 | −0.127115 | ||||||||
\(782\) | −9.10104e8 | + | 3.11891e8i | −1.90314 | + | 0.652202i | ||||
\(783\) | 4.76279e7i | 0.0992146i | ||||||||
\(784\) | −3.37408e8 | + | 1.32042e9i | −0.700176 | + | 2.74008i | ||||
\(785\) | −168280. | −0.000347876 | ||||||||
\(786\) | −1.14631e7 | − | 3.34495e7i | −0.0236066 | − | 0.0688846i | ||||
\(787\) | 8.67740e8i | 1.78019i | 0.455778 | + | 0.890093i | \(0.349361\pi\) | ||||
−0.455778 | + | 0.890093i | \(0.650639\pi\) | |||||||
\(788\) | −6.74330e8 | + | 5.23685e8i | −1.37814 | + | 1.07027i | ||||
\(789\) | −1.19361e8 | −0.243014 | ||||||||
\(790\) | −1.64978e8 | + | 5.65377e7i | −0.334615 | + | 0.114672i | ||||
\(791\) | − | 1.49537e9i | − | 3.02148i | ||||||
\(792\) | −1.36181e7 | + | 2.07706e7i | −0.0274121 | + | 0.0418094i | ||||
\(793\) | −2.70900e8 | −0.543237 | ||||||||
\(794\) | 2.87994e8 | + | 8.40372e8i | 0.575336 | + | 1.67884i | ||||
\(795\) | 1.19313e6i | 0.00237457i | ||||||||
\(796\) | 2.58297e8 | + | 3.32600e8i | 0.512130 | + | 0.659451i | ||||
\(797\) | −9.81006e8 | −1.93775 | −0.968873 | − | 0.247558i | \(-0.920372\pi\) | ||||
−0.968873 | + | 0.247558i | \(0.920372\pi\) | |||||||
\(798\) | −4.07505e8 | + | 1.39651e8i | −0.801908 | + | 0.274812i | ||||
\(799\) | − | 7.36938e8i | − | 1.44474i | ||||||
\(800\) | 1.02073e8 | − | 8.18093e6i | 0.199361 | − | 0.0159784i | ||||
\(801\) | −1.12267e7 | −0.0218452 | ||||||||
\(802\) | −1.45580e8 | − | 4.24807e8i | −0.282215 | − | 0.823509i | ||||
\(803\) | − | 4.94201e7i | − | 0.0954459i | ||||||
\(804\) | 2.56473e8 | − | 1.99177e8i | 0.493485 | − | 0.383241i | ||||
\(805\) | 5.48906e8 | 1.05223 | ||||||||
\(806\) | 8.40925e8 | − | 2.88183e8i | 1.60602 | − | 0.550381i | ||||
\(807\) | − | 5.65958e8i | − | 1.07687i | ||||||
\(808\) | −3.64163e8 | − | 2.38761e8i | −0.690338 | − | 0.452616i | ||||
\(809\) | 1.28177e8 | 0.242084 | 0.121042 | − | 0.992647i | \(-0.461376\pi\) | ||||
0.121042 | + | 0.992647i | \(0.461376\pi\) | |||||||
\(810\) | −8.56104e6 | − | 2.49813e7i | −0.0161091 | − | 0.0470067i | ||||
\(811\) | 7.64793e8i | 1.43378i | 0.697189 | + | 0.716888i | \(0.254434\pi\) | ||||
−0.697189 | + | 0.716888i | \(0.745566\pi\) | |||||||
\(812\) | −3.31234e8 | − | 4.26518e8i | −0.618681 | − | 0.796653i | ||||
\(813\) | 2.24932e6 | 0.00418580 | ||||||||
\(814\) | 17579.5 | − | 6024.44i | 3.25936e−5 | − | 1.11698e-5i | ||||
\(815\) | − | 5.78365e7i | − | 0.106839i | ||||||
\(816\) | −5.08459e8 | − | 1.29927e8i | −0.935806 | − | 0.239128i | ||||
\(817\) | 5.40641e8 | 0.991386 | ||||||||
\(818\) | −1.34156e8 | − | 3.91471e8i | −0.245104 | − | 0.715220i | ||||
\(819\) | 3.32960e8i | 0.606095i | ||||||||
\(820\) | −1.91758e8 | + | 1.48919e8i | −0.347785 | + | 0.270090i | ||||
\(821\) | 5.85652e8 | 1.05830 | 0.529152 | − | 0.848527i | \(-0.322510\pi\) | ||||
0.529152 | + | 0.848527i | \(0.322510\pi\) | |||||||
\(822\) | 4.89826e8 | − | 1.67862e8i | 0.881914 | − | 0.302230i | ||||
\(823\) | 2.85566e8i | 0.512280i | 0.966640 | + | 0.256140i | \(0.0824508\pi\) | ||||
−0.966640 | + | 0.256140i | \(0.917549\pi\) | |||||||
\(824\) | −1.65938e8 | + | 2.53092e8i | −0.296595 | + | 0.452372i | ||||
\(825\) | −9.72466e6 | −0.0173186 | ||||||||
\(826\) | −9.75008e6 | − | 2.84510e7i | −0.0173009 | − | 0.0504844i | ||||
\(827\) | 8.74738e7i | 0.154654i | 0.997006 | + | 0.0773271i | \(0.0246386\pi\) | ||||
−0.997006 | + | 0.0773271i | \(0.975361\pi\) | |||||||
\(828\) | −1.39569e8 | − | 1.79717e8i | −0.245865 | − | 0.316591i | ||||
\(829\) | −6.72359e8 | −1.18015 | −0.590076 | − | 0.807348i | \(-0.700902\pi\) | ||||
−0.590076 | + | 0.807348i | \(0.700902\pi\) | |||||||
\(830\) | −9.11128e7 | + | 3.12242e7i | −0.159348 | + | 0.0546080i | ||||
\(831\) | 7.40027e7i | 0.128957i | ||||||||
\(832\) | 2.13412e8 | + | 4.90841e8i | 0.370551 | + | 0.852257i | ||||
\(833\) | 2.73474e9 | 4.73130 | ||||||||
\(834\) | −1.55689e8 | − | 4.54303e8i | −0.268385 | − | 0.783155i | ||||
\(835\) | 3.31910e7i | 0.0570113i | ||||||||
\(836\) | 5.19380e7 | − | 4.03351e7i | 0.0888927 | − | 0.0690341i | ||||
\(837\) | −2.06153e8 | −0.351572 | ||||||||
\(838\) | −2.16184e8 | + | 7.40859e7i | −0.367360 | + | 0.125893i | ||||
\(839\) | − | 1.71003e8i | − | 0.289547i | −0.989465 | − | 0.144773i | \(-0.953755\pi\) | ||
0.989465 | − | 0.144773i | \(-0.0462453\pi\) | |||||||
\(840\) | 2.50402e8 | + | 1.64174e8i | 0.422474 | + | 0.276992i | ||||
\(841\) | −4.36734e8 | −0.734224 | ||||||||
\(842\) | −2.68029e7 | − | 7.82116e7i | −0.0449000 | − | 0.131019i | ||||
\(843\) | 7.05612e7i | 0.117783i | ||||||||
\(844\) | −3.41720e7 | − | 4.40021e7i | −0.0568386 | − | 0.0731890i | ||||
\(845\) | 3.67909e7 | 0.0609775 | ||||||||
\(846\) | 1.64887e8 | − | 5.65064e7i | 0.272317 | − | 0.0933225i | ||||
\(847\) | − | 1.16215e9i | − | 1.91255i | ||||||
\(848\) | −1.38844e6 | + | 5.43355e6i | −0.00227688 | + | 0.00891037i | ||||
\(849\) | −1.67294e8 | −0.273374 | ||||||||
\(850\) | −6.66142e7 | − | 1.94382e8i | −0.108470 | − | 0.316519i | ||||
\(851\) | 170252.i | 0.000276251i | ||||||||
\(852\) | 2.39018e8 | − | 1.85622e8i | 0.386467 | − | 0.300130i | ||||
\(853\) | −4.85282e8 | −0.781892 | −0.390946 | − | 0.920414i | \(-0.627852\pi\) | ||||
−0.390946 | + | 0.920414i | \(0.627852\pi\) | |||||||
\(854\) | −6.73867e8 | + | 2.30933e8i | −1.08193 | + | 0.370776i | ||||
\(855\) | 6.99192e7i | 0.111866i | ||||||||
\(856\) | 2.87409e8 | − | 4.38362e8i | 0.458226 | − | 0.698894i | ||||
\(857\) | −3.49086e8 | −0.554612 | −0.277306 | − | 0.960782i | \(-0.589442\pi\) | ||||
−0.277306 | + | 0.960782i | \(0.589442\pi\) | |||||||
\(858\) | −1.64783e7 | − | 4.80841e7i | −0.0260886 | − | 0.0761271i | ||||
\(859\) | − | 7.34854e8i | − | 1.15937i | −0.814841 | − | 0.579684i | \(-0.803176\pi\) | ||
0.814841 | − | 0.579684i | \(-0.196824\pi\) | |||||||
\(860\) | −2.30497e8 | − | 2.96802e8i | −0.362385 | − | 0.466629i | ||||
\(861\) | −7.09936e8 | −1.11227 | ||||||||
\(862\) | 2.83583e8 | − | 9.71833e7i | 0.442750 | − | 0.151729i | ||||
\(863\) | − | 8.76714e8i | − | 1.36403i | −0.731336 | − | 0.682017i | \(-0.761103\pi\) | ||
0.731336 | − | 0.682017i | \(-0.238897\pi\) | |||||||
\(864\) | −9.91658e6 | − | 1.23728e8i | −0.0153752 | − | 0.191835i | ||||
\(865\) | −5.66416e7 | −0.0875160 | ||||||||
\(866\) | −2.00989e8 | − | 5.86490e8i | −0.309470 | − | 0.903040i | ||||
\(867\) | 6.76809e8i | 1.03851i | ||||||||
\(868\) | 1.84615e9 | − | 1.43372e9i | 2.82298 | − | 2.19233i | ||||
\(869\) | 7.78477e7 | 0.118628 | ||||||||
\(870\) | −8.29196e7 | + | 2.84164e7i | −0.125921 | + | 0.0431530i | ||||
\(871\) | 6.64569e8i | 1.00574i | ||||||||
\(872\) | 7.65900e8 | + | 5.02158e8i | 1.15511 | + | 0.757339i | ||||
\(873\) | −1.94454e8 | −0.292264 | ||||||||
\(874\) | 1.95317e8 | + | 5.69938e8i | 0.292553 | + | 0.853677i | ||||
\(875\) | 1.17236e8i | 0.175000i | ||||||||
\(876\) | 1.51489e8 | + | 1.95067e8i | 0.225356 | + | 0.290183i | ||||
\(877\) | 4.38615e8 | 0.650256 | 0.325128 | − | 0.945670i | \(-0.394593\pi\) | ||||
0.325128 | + | 0.945670i | \(0.394593\pi\) | |||||||
\(878\) | −8.09474e8 | + | 2.77405e8i | −1.19597 | + | 0.409856i | ||||
\(879\) | 4.50264e8i | 0.662980i | ||||||||
\(880\) | −4.42865e7 | − | 1.13166e7i | −0.0649865 | − | 0.0166061i | ||||
\(881\) | −9.05059e7 | −0.132358 | −0.0661788 | − | 0.997808i | \(-0.521081\pi\) | ||||
−0.0661788 | + | 0.997808i | \(0.521081\pi\) | |||||||
\(882\) | 2.09692e8 | + | 6.11887e8i | 0.305616 | + | 0.891795i | ||||
\(883\) | − | 8.35267e8i | − | 1.21323i | −0.794995 | − | 0.606615i | \(-0.792527\pi\) | ||
0.794995 | − | 0.606615i | \(-0.207473\pi\) | |||||||
\(884\) | 8.48254e8 | − | 6.58754e8i | 1.22792 | − | 0.953601i | ||||
\(885\) | −4.88158e6 | −0.00704256 | ||||||||
\(886\) | 5.24858e8 | − | 1.79868e8i | 0.754641 | − | 0.258614i | ||||
\(887\) | − | 9.00078e8i | − | 1.28976i | −0.764283 | − | 0.644881i | \(-0.776907\pi\) | ||
0.764283 | − | 0.644881i | \(-0.223093\pi\) | |||||||
\(888\) | −50921.3 | + | 77666.2i | −7.27211e−5 | + | 0.000110916i | ||||
\(889\) | −8.10928e8 | −1.15419 | ||||||||
\(890\) | −6.69823e6 | − | 1.95456e7i | −0.00950145 | − | 0.0277255i | ||||
\(891\) | 1.17878e7i | 0.0166648i | ||||||||
\(892\) | −2.02652e8 | − | 2.60947e8i | −0.285532 | − | 0.367669i | ||||
\(893\) | −4.61495e8 | −0.648057 | ||||||||
\(894\) | 3.89908e8 | − | 1.33621e8i | 0.545695 | − | 0.187008i | ||||
\(895\) | 5.91755e8i | 0.825416i | ||||||||
\(896\) | 9.49290e8 | + | 1.03905e9i | 1.31970 | + | 1.44448i | ||||
\(897\) | 4.65680e8 | 0.645223 | ||||||||
\(898\) | −2.87502e8 | − | 8.38938e8i | −0.397020 | − | 1.15851i | ||||
\(899\) | 6.84278e8i | 0.941788i | ||||||||
\(900\) | 3.83844e7 | − | 2.98094e7i | 0.0526535 | − | 0.0408907i | ||||
\(901\) | 1.12535e7 | 0.0153855 | ||||||||
\(902\) | 1.02525e8 | − | 3.51349e7i | 0.139704 | − | 0.0478762i | ||||
\(903\) | − | 1.09884e9i | − | 1.49235i | ||||||
\(904\) | −9.54079e8 | − | 6.25536e8i | −1.29145 | − | 0.846733i | ||||
\(905\) | 1.36915e8 | 0.184716 | ||||||||
\(906\) | 1.19811e8 | + | 3.49611e8i | 0.161106 | + | 0.470111i | ||||
\(907\) | 5.63841e8i | 0.755675i | 0.925872 | + | 0.377838i | \(0.123332\pi\) | ||||
−0.925872 | + | 0.377838i | \(0.876668\pi\) | |||||||
\(908\) | 1.52677e8 | + | 1.96597e8i | 0.203947 | + | 0.262614i | ||||
\(909\) | −2.06671e8 | −0.275162 | ||||||||
\(910\) | −5.79681e8 | + | 1.98655e8i | −0.769245 | + | 0.263618i | ||||
\(911\) | − | 1.25733e9i | − | 1.66301i | −0.555517 | − | 0.831505i | \(-0.687480\pi\) | ||
0.555517 | − | 0.831505i | \(-0.312520\pi\) | |||||||
\(912\) | −8.13648e7 | + | 3.18415e8i | −0.107264 | + | 0.419767i | ||||
\(913\) | 4.29931e7 | 0.0564919 | ||||||||
\(914\) | 2.91012e8 | + | 8.49178e8i | 0.381129 | + | 1.11214i | ||||
\(915\) | 1.15621e8i | 0.150930i | ||||||||
\(916\) | −5.08672e8 | + | 3.95035e8i | −0.661837 | + | 0.513983i | ||||
\(917\) | 1.90281e8 | 0.246768 | ||||||||
\(918\) | −2.35622e8 | + | 8.07470e7i | −0.304570 | + | 0.104375i | ||||
\(919\) | 6.09120e8i | 0.784796i | 0.919796 | + | 0.392398i | \(0.128354\pi\) | ||||
−0.919796 | + | 0.392398i | \(0.871646\pi\) | |||||||
\(920\) | 2.29615e8 | − | 3.50213e8i | 0.294874 | − | 0.449748i | ||||
\(921\) | 7.10733e8 | 0.909762 | ||||||||
\(922\) | 3.75039e8 | + | 1.09437e9i | 0.478502 | + | 1.39628i | ||||
\(923\) | 6.19339e8i | 0.787632i | ||||||||
\(924\) | −8.19801e7 | − | 1.05563e8i | −0.103918 | − | 0.133812i | ||||
\(925\) | −36362.8 | −4.59443e−5 | ||||||||
\(926\) | 7.08557e8 | − | 2.42821e8i | 0.892363 | − | 0.305811i | ||||
\(927\) | 1.43636e8i | 0.180311i | ||||||||
\(928\) | −4.10687e8 | + | 3.29158e7i | −0.513886 | + | 0.0411870i | ||||
\(929\) | 1.98668e8 | 0.247788 | 0.123894 | − | 0.992295i | \(-0.460462\pi\) | ||||
0.123894 | + | 0.992295i | \(0.460462\pi\) | |||||||
\(930\) | −1.22998e8 | − | 3.58911e8i | −0.152915 | − | 0.446208i | ||||
\(931\) | − | 1.71259e9i | − | 2.12228i | ||||||
\(932\) | −3.05112e8 | + | 2.36951e8i | −0.376888 | + | 0.292691i | ||||
\(933\) | 3.64184e8 | 0.448411 | ||||||||
\(934\) | 3.87400e8 | − | 1.32761e8i | 0.475466 | − | 0.162941i | ||||
\(935\) | 9.17223e7i | 0.112212i | ||||||||
\(936\) | 2.12436e8 | + | 1.39282e8i | 0.259060 | + | 0.169851i | ||||
\(937\) | −1.36957e9 | −1.66481 | −0.832404 | − | 0.554169i | \(-0.813036\pi\) | ||||
−0.832404 | + | 0.554169i | \(0.813036\pi\) | |||||||
\(938\) | 5.66522e8 | + | 1.65312e9i | 0.686449 | + | 2.00307i | ||||
\(939\) | 4.33203e8i | 0.523233i | ||||||||
\(940\) | 1.96754e8 | + | 2.53353e8i | 0.236886 | + | 0.305030i | ||||
\(941\) | −1.54960e9 | −1.85974 | −0.929869 | − | 0.367890i | \(-0.880080\pi\) | ||||
−0.929869 | + | 0.367890i | \(0.880080\pi\) | |||||||
\(942\) | −355131. | + | 121703.i | −0.000424851 | + | 0.000145595i | ||||
\(943\) | 9.92920e8i | 1.18408i | ||||||||
\(944\) | −2.22309e7 | − | 5.68068e6i | −0.0264266 | − | 0.00675281i | ||||
\(945\) | 1.42109e8 | 0.168394 | ||||||||
\(946\) | 5.43819e7 | + | 1.58688e8i | 0.0642363 | + | 0.187443i | ||||
\(947\) | − | 1.24286e9i | − | 1.46343i | −0.681613 | − | 0.731713i | \(-0.738721\pi\) | ||
0.681613 | − | 0.731713i | \(-0.261279\pi\) | |||||||
\(948\) | −3.07274e8 | + | 2.38629e8i | −0.360663 | + | 0.280091i | ||||
\(949\) | −5.05454e8 | −0.591402 | ||||||||
\(950\) | −1.21729e8 | + | 4.17161e7i | −0.141978 | + | 0.0486556i | ||||
\(951\) | 1.19792e8i | 0.139280i | ||||||||
\(952\) | 1.54848e9 | − | 2.36177e9i | 1.79471 | − | 2.73733i | ||||
\(953\) | 1.19499e8 | 0.138066 | 0.0690331 | − | 0.997614i | \(-0.478009\pi\) | ||||
0.0690331 | + | 0.997614i | \(0.478009\pi\) | |||||||
\(954\) | 862887. | + | 2.51792e6i | 0.000993822 | + | 0.00290000i | ||||
\(955\) | − | 3.02909e8i | − | 0.347778i | ||||||
\(956\) | 5.29810e7 | + | 6.82216e7i | 0.0606382 | + | 0.0780815i | ||||
\(957\) | 3.91270e7 | 0.0446417 | ||||||||
\(958\) | −1.42936e9 | + | 4.89840e8i | −1.62572 | + | 0.557131i | ||||
\(959\) | 2.78643e9i | 3.15931i | ||||||||
\(960\) | 2.09493e8 | − | 9.10851e7i | 0.236786 | − | 0.102952i | ||||
\(961\) | −2.07434e9 | −2.33727 | ||||||||
\(962\) | −61616.1 | − | 179797.i | −6.92101e−5 | − | 0.000201957i | ||||
\(963\) | − | 2.48781e8i | − | 0.278573i | ||||||
\(964\) | −3.91368e8 | + | 3.03937e8i | −0.436872 | + | 0.339276i | ||||
\(965\) | −5.57391e8 | −0.620266 | ||||||||
\(966\) | 1.15839e9 | − | 3.96976e8i | 1.28506 | − | 0.440386i | ||||
\(967\) | − | 5.80070e8i | − | 0.641506i | −0.947163 | − | 0.320753i | \(-0.896064\pi\) | ||
0.947163 | − | 0.320753i | \(-0.103936\pi\) | |||||||
\(968\) | −7.41476e8 | − | 4.86144e8i | −0.817468 | − | 0.535968i | ||||
\(969\) | 6.59472e8 | 0.724812 | ||||||||
\(970\) | −1.16018e8 | − | 3.38543e8i | −0.127119 | − | 0.370936i | ||||
\(971\) | 1.33064e9i | 1.45346i | 0.686925 | + | 0.726729i | \(0.258960\pi\) | ||||
−0.686925 | + | 0.726729i | \(0.741040\pi\) | |||||||
\(972\) | −3.61337e7 | − | 4.65280e7i | −0.0393471 | − | 0.0506659i | ||||
\(973\) | 2.58436e9 | 2.80552 | ||||||||
\(974\) | 1.07306e9 | − | 3.67737e8i | 1.16131 | − | 0.397979i | ||||
\(975\) | 9.94608e7i | 0.107310i | ||||||||
\(976\) | −1.34548e8 | + | 5.26544e8i | −0.144720 | + | 0.566350i | ||||
\(977\) | −1.81751e9 | −1.94891 | −0.974456 | − | 0.224577i | \(-0.927900\pi\) | ||||
−0.974456 | + | 0.224577i | \(0.927900\pi\) | |||||||
\(978\) | −4.18281e7 | − | 1.22056e8i | −0.0447149 | − | 0.130479i | ||||
\(979\) | 9.22291e6i | 0.00982923i | ||||||||
\(980\) | −9.40179e8 | + | 7.30144e8i | −0.998924 | + | 0.775765i | ||||
\(981\) | 4.34667e8 | 0.460415 | ||||||||
\(982\) | −1.30986e8 | + | 4.48887e7i | −0.138322 | + | 0.0474027i | ||||
\(983\) | − | 9.05360e8i | − | 0.953149i | −0.879134 | − | 0.476575i | \(-0.841878\pi\) | ||
0.879134 | − | 0.476575i | \(-0.158122\pi\) | |||||||
\(984\) | −2.96976e8 | + | 4.52954e8i | −0.311700 | + | 0.475411i | ||||
\(985\) | −7.45760e8 | −0.780351 | ||||||||
\(986\) | 2.68021e8 | + | 7.82091e8i | 0.279600 | + | 0.815881i | ||||
\(987\) | 9.37978e8i | 0.975532i | ||||||||
\(988\) | −4.12534e8 | − | 5.31205e8i | −0.427749 | − | 0.550797i | ||||
\(989\) | −1.53684e9 | −1.58869 | ||||||||
\(990\) | −2.05225e7 | + | 7.03301e6i | −0.0211507 | + | 0.00724830i | ||||
\(991\) | 1.75428e6i | 0.00180251i | 1.00000 | 0.000901257i | \(0.000286879\pi\) | |||||
−1.00000 | 0.000901257i | \(0.999713\pi\) | ||||||||
\(992\) | −1.42473e8 | − | 1.77763e9i | −0.145948 | − | 1.82098i | ||||
\(993\) | 3.53266e8 | 0.360790 | ||||||||
\(994\) | 5.27965e8 | + | 1.54062e9i | 0.537584 | + | 1.56868i | ||||
\(995\) | 3.67831e8i | 0.373404i | ||||||||
\(996\) | −1.69699e8 | + | 1.31788e8i | −0.171752 | + | 0.133382i | ||||
\(997\) | 2.07639e8 | 0.209519 | 0.104759 | − | 0.994498i | \(-0.466593\pi\) | ||||
0.104759 | + | 0.994498i | \(0.466593\pi\) | |||||||
\(998\) | 1.79423e9 | − | 6.14880e8i | 1.80504 | − | 0.618584i | ||||
\(999\) | 44077.4i | 4.42099e-5i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 60.7.c.a.31.14 | yes | 24 | |
3.2 | odd | 2 | 180.7.c.b.91.11 | 24 | |||
4.3 | odd | 2 | inner | 60.7.c.a.31.13 | ✓ | 24 | |
12.11 | even | 2 | 180.7.c.b.91.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.c.a.31.13 | ✓ | 24 | 4.3 | odd | 2 | inner | |
60.7.c.a.31.14 | yes | 24 | 1.1 | even | 1 | trivial | |
180.7.c.b.91.11 | 24 | 3.2 | odd | 2 | |||
180.7.c.b.91.12 | 24 | 12.11 | even | 2 |