Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.7 | ||
Character | \(\chi\) | \(=\) | 76.29 |
Dual form | 76.7.j.a.21.7 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 15.2868 | + | 18.2181i | 0.566178 | + | 0.674744i | 0.970842 | − | 0.239721i | \(-0.0770560\pi\) |
−0.404664 | + | 0.914465i | \(0.632612\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −90.7408 | − | 33.0269i | −0.725926 | − | 0.264216i | −0.0474868 | − | 0.998872i | \(-0.515121\pi\) |
−0.678439 | + | 0.734656i | \(0.737343\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −57.6521 | + | 99.8564i | −0.168082 | + | 0.291126i | −0.937745 | − | 0.347323i | \(-0.887091\pi\) |
0.769664 | + | 0.638450i | \(0.220424\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 28.3767 | − | 160.932i | 0.0389255 | − | 0.220758i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −847.329 | − | 1467.62i | −0.636611 | − | 1.10264i | −0.986171 | − | 0.165729i | \(-0.947002\pi\) |
0.349561 | − | 0.936914i | \(-0.386331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −294.417 | + | 350.872i | −0.134009 | + | 0.159705i | −0.828875 | − | 0.559433i | \(-0.811019\pi\) |
0.694867 | + | 0.719138i | \(0.255463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −785.448 | − | 2158.00i | −0.232725 | − | 0.639407i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1213.76 | − | 6883.60i | −0.247052 | − | 1.40110i | −0.815679 | − | 0.578504i | \(-0.803637\pi\) |
0.568628 | − | 0.822595i | \(-0.307474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 168.439 | + | 6856.93i | 0.0245573 | + | 0.999698i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2700.51 | + | 476.172i | −0.291600 | + | 0.0514170i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22166.1 | − | 8067.82i | 1.82182 | − | 0.663090i | 0.826914 | − | 0.562328i | \(-0.190094\pi\) |
0.994911 | − | 0.100761i | \(-0.0321279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4826.34 | − | 4049.78i | −0.308885 | − | 0.259186i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18380.0 | − | 10611.7i | 0.933803 | − | 0.539131i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28103.1 | − | 4955.34i | −1.15229 | − | 0.203179i | −0.435313 | − | 0.900279i | \(-0.643362\pi\) |
−0.716974 | + | 0.697100i | \(0.754473\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35500.7 | − | 20496.4i | −1.19166 | − | 0.688005i | −0.232977 | − | 0.972482i | \(-0.574847\pi\) |
−0.958683 | + | 0.284477i | \(0.908180\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13784.2 | − | 37871.9i | 0.383567 | − | 1.05384i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8529.35 | − | 7156.97i | 0.198935 | − | 0.166926i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 46331.5i | − | 0.914684i | −0.889291 | − | 0.457342i | \(-0.848801\pi\) | ||
0.889291 | − | 0.457342i | \(-0.151199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10892.9 | −0.183633 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −41265.7 | − | 49178.5i | −0.598738 | − | 0.713549i | 0.378522 | − | 0.925592i | \(-0.376433\pi\) |
−0.977260 | + | 0.212044i | \(0.931988\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −38251.3 | − | 13922.4i | −0.481107 | − | 0.175109i | 0.0900704 | − | 0.995935i | \(-0.471291\pi\) |
−0.571177 | + | 0.820827i | \(0.693513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7890.03 | + | 13665.9i | −0.0865847 | + | 0.149969i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1995.19 | − | 11315.3i | 0.0192172 | − | 0.108986i | −0.973690 | − | 0.227875i | \(-0.926822\pi\) |
0.992908 | + | 0.118889i | \(0.0379332\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 52177.0 | + | 90373.2i | 0.443497 | + | 0.768159i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 106852. | − | 127341.i | 0.805508 | − | 0.959968i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55354.8 | + | 152086.i | 0.371816 | + | 1.02156i | 0.974659 | + | 0.223696i | \(0.0718122\pi\) |
−0.602843 | + | 0.797860i | \(0.705966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 28416.4 | + | 161157.i | 0.170797 | + | 0.968639i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −122345. | + | 107889.i | −0.660637 | + | 0.582577i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 91587.5 | − | 16149.3i | 0.445944 | − | 0.0786319i | 0.0538331 | − | 0.998550i | \(-0.482856\pi\) |
0.392111 | + | 0.919918i | \(0.371745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40171.8 | + | 14621.3i | −0.176983 | + | 0.0644166i | −0.428992 | − | 0.903308i | \(-0.641131\pi\) |
0.252009 | + | 0.967725i | \(0.418909\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14434.1 | + | 12111.7i | 0.0577257 | + | 0.0484376i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 38303.8 | − | 22114.7i | 0.139477 | − | 0.0805270i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −187695. | − | 33095.8i | −0.624064 | − | 0.110039i | −0.147331 | − | 0.989087i | \(-0.547068\pi\) |
−0.476733 | + | 0.879048i | \(0.658179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 485829. | + | 280494.i | 1.47889 | + | 0.853839i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −121287. | + | 333234.i | −0.338876 | + | 0.931053i | 0.646839 | + | 0.762627i | \(0.276091\pi\) |
−0.985714 | + | 0.168426i | \(0.946132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −325378. | + | 273024.i | −0.836410 | + | 0.701832i | −0.956753 | − | 0.290901i | \(-0.906045\pi\) |
0.120343 | + | 0.992732i | \(0.461601\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 149835.i | − | 0.355164i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 195401. | 0.428011 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −149619. | − | 178309.i | −0.303463 | − | 0.361654i | 0.592665 | − | 0.805449i | \(-0.298076\pi\) |
−0.896128 | + | 0.443796i | \(0.853632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 362352. | + | 131885.i | 0.681829 | + | 0.248166i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −285527. | + | 494547.i | −0.499358 | + | 0.864914i | −1.00000 | 0.000740745i | \(-0.999764\pi\) | |
0.500641 | + | 0.865655i | \(0.333098\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −117206. | + | 664710.i | −0.190851 | + | 1.08237i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −339330. | − | 587737.i | −0.515305 | − | 0.892535i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −227531. | + | 271161.i | −0.322753 | + | 0.384642i | −0.902886 | − | 0.429880i | \(-0.858556\pi\) |
0.580133 | + | 0.814522i | \(0.303000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18063.1 | − | 49627.9i | −0.0239700 | − | 0.0658570i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −169288. | − | 960079.i | −0.210464 | − | 1.19360i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 211179. | − | 627766.i | 0.246309 | − | 0.732196i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 507984. | − | 89571.2i | 0.556589 | − | 0.0981417i | 0.111724 | − | 0.993739i | \(-0.464363\pi\) |
0.444865 | + | 0.895598i | \(0.353252\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −260231. | + | 94716.5i | −0.268197 | + | 0.0976158i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.15765e6 | + | 971380.i | 1.12360 | + | 0.942812i | 0.998781 | − | 0.0493674i | \(-0.0157205\pi\) |
0.124819 | + | 0.992180i | \(0.460165\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 683342. | − | 394528.i | 0.625355 | − | 0.361049i | −0.153596 | − | 0.988134i | \(-0.549085\pi\) |
0.778951 | + | 0.627085i | \(0.215752\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 260773. | + | 45981.3i | 0.225265 | + | 0.0397204i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.43252e6 | − | 827064.i | −1.16936 | − | 0.675131i | −0.215831 | − | 0.976431i | \(-0.569246\pi\) |
−0.953529 | + | 0.301300i | \(0.902579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22261.0 | − | 61161.7i | 0.0171896 | − | 0.0472281i | −0.930801 | − | 0.365526i | \(-0.880889\pi\) |
0.947991 | + | 0.318298i | \(0.103111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 844072. | − | 708260.i | 0.617178 | − | 0.517874i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.58959e6i | − | 1.10167i | −0.834615 | − | 0.550834i | \(-0.814310\pi\) | ||
0.834615 | − | 0.550834i | \(-0.185690\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.27783e6 | −1.49771 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 48112.1 | + | 57337.8i | 0.0300398 | + | 0.0358000i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 757347. | + | 275652.i | 0.449422 | + | 0.163576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −550153. | + | 952892.i | −0.310547 | + | 0.537883i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 265119. | − | 1.50356e6i | 0.142471 | − | 0.807991i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.05860e6 | + | 1.83355e6i | 0.542004 | + | 0.938779i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.49325e6 | − | 1.77958e6i | 0.728988 | − | 0.868775i | −0.266483 | − | 0.963840i | \(-0.585862\pi\) |
0.995471 | + | 0.0950652i | \(0.0303060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −331102. | − | 909695.i | −0.154238 | − | 0.423766i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −601568. | − | 3.41166e6i | −0.267591 | − | 1.51758i | −0.761555 | − | 0.648100i | \(-0.775564\pi\) |
0.493964 | − | 0.869482i | \(-0.335547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −694419. | − | 378497.i | −0.295166 | − | 0.160882i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.01829e6 | + | 355879.i | −0.820319 | + | 0.144644i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.84327e6 | + | 670896.i | −0.716849 | + | 0.260912i | −0.674588 | − | 0.738195i | \(-0.735678\pi\) |
−0.0422615 | + | 0.999107i | \(0.513456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.28329e6 | − | 1.91591e6i | −0.850193 | − | 0.713397i | 0.109639 | − | 0.993971i | \(-0.465030\pi\) |
−0.959832 | + | 0.280575i | \(0.909475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 236643. | − | 136626.i | 0.0844183 | − | 0.0487389i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 764414. | + | 134787.i | 0.261409 | + | 0.0460935i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.38644e6 | + | 1.37781e6i | 0.782793 | + | 0.451945i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −848808. | + | 2.33208e6i | −0.267213 | + | 0.734162i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −77742.0 | + | 65233.2i | −0.0235016 | + | 0.0197201i | −0.654463 | − | 0.756094i | \(-0.727105\pi\) |
0.630961 | + | 0.775814i | \(0.282661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.14513e6i | − | 1.49440i | −0.664601 | − | 0.747198i | \(-0.731399\pi\) | ||
0.664601 | − | 0.747198i | \(-0.268601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.14224e6 | −0.318920 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.54443e6 | + | 3.03234e6i | 0.683275 | + | 0.814296i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.81262e6 | + | 2.11562e6i | 1.50201 | + | 0.546687i | 0.956580 | − | 0.291469i | \(-0.0941439\pi\) |
0.545431 | + | 0.838156i | \(0.316366\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.92452e6 | + | 3.33337e6i | −0.478775 | + | 0.829262i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −472302. | + | 2.67856e6i | −0.113173 | + | 0.641835i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.08174e6 | + | 3.60569e6i | 0.480689 | + | 0.832578i | 0.999755 | − | 0.0221563i | \(-0.00705313\pi\) |
−0.519065 | + | 0.854735i | \(0.673720\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.50158e6 | + | 2.98127e6i | −0.556882 | + | 0.663666i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 883755. | + | 2.42810e6i | 0.189750 | + | 0.521335i | 0.997690 | − | 0.0679303i | \(-0.0216396\pi\) |
−0.807940 | + | 0.589265i | \(0.799417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 801736. | + | 4.54687e6i | 0.166101 | + | 0.942004i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.10828e6 | + | 167470.i | 0.221647 | + | 0.0334926i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.35854e6 | − | 415875.i | 0.455518 | − | 0.0803201i | 0.0588187 | − | 0.998269i | \(-0.481267\pi\) |
0.396699 | + | 0.917949i | \(0.370156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 682644. | − | 248462.i | 0.127374 | − | 0.0463603i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.69429e6 | + | 1.42168e6i | 0.305540 | + | 0.256378i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.63996e6 | − | 4.41093e6i | 1.33209 | − | 0.769080i | 0.346466 | − | 0.938062i | \(-0.387381\pi\) |
0.985619 | + | 0.168982i | \(0.0540481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.37586e6 | − | 1.47689e6i | −1.41252 | − | 0.249065i | −0.585241 | − | 0.810860i | \(-0.699000\pi\) |
−0.827277 | + | 0.561795i | \(0.810111\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −880471. | − | 508340.i | −0.143669 | − | 0.0829471i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.53019e6 | + | 4.20416e6i | −0.241674 | + | 0.663993i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.07403e6 | + | 7.61402e6i | −1.38764 | + | 1.16436i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.44715e6i | 0.362473i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.55762e6 | 0.941123 | 0.470561 | − | 0.882367i | \(-0.344051\pi\) | ||||
0.470561 | + | 0.882367i | \(0.344051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.56021e6 | − | 9.00991e6i | −1.05163 | − | 1.25328i | −0.966433 | − | 0.256917i | \(-0.917293\pi\) |
−0.0851946 | − | 0.996364i | \(-0.527151\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 988431. | + | 359760.i | 0.133304 | + | 0.0485186i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.88732e6 | − | 5.00098e6i | 0.377655 | − | 0.654118i | −0.613065 | − | 0.790032i | \(-0.710064\pi\) |
0.990721 | + | 0.135914i | \(0.0433971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −690779. | + | 3.91760e6i | −0.0876556 | + | 0.497120i | 0.909096 | + | 0.416586i | \(0.136774\pi\) |
−0.996752 | + | 0.0805336i | \(0.974338\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.26632e6 | − | 3.92538e6i | −0.279083 | − | 0.483385i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.11503e6 | − | 2.52059e6i | 0.252830 | − | 0.301311i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.12026e6 | + | 5.82537e6i | 0.246109 | + | 0.676180i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −669370. | − | 3.79619e6i | −0.0754667 | − | 0.427993i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.92063e6 | − | 6.05728e6i | 1.08668 | − | 0.663497i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.57725e7 | + | 2.78112e6i | −1.67901 | + | 0.296055i | −0.930289 | − | 0.366827i | \(-0.880444\pi\) |
−0.748723 | + | 0.662883i | \(0.769333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.92498e6 | + | 2.88446e6i | −0.820086 | + | 0.298487i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.01114e6 | + | 2.52665e6i | 0.302982 | + | 0.254232i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.09338e6 | − | 2.36332e6i | 0.400593 | − | 0.231282i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.94797e6 | − | 1.75410e6i | −0.947114 | − | 0.167002i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.77262e6 | + | 1.60077e6i | 0.256870 | + | 0.148304i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.01317e6 | − | 1.10261e7i | 0.361887 | − | 0.994277i | −0.616474 | − | 0.787375i | \(-0.711440\pi\) |
0.978362 | − | 0.206902i | \(-0.0663382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −788695. | + | 661794.i | −0.0692407 | + | 0.0580999i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.02426e7i | − | 0.875657i | −0.899059 | − | 0.437828i | \(-0.855748\pi\) | ||
0.899059 | − | 0.437828i | \(-0.144252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.05134e7 | 0.875462 | 0.437731 | − | 0.899106i | \(-0.355782\pi\) | ||||
0.437731 | + | 0.899106i | \(0.355782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.98706e6 | + | 3.55984e6i | 0.242330 | + | 0.288798i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.03076e7 | + | 3.75164e6i | 0.814869 | + | 0.296588i | 0.715634 | − | 0.698476i | \(-0.246138\pi\) |
0.0992356 | + | 0.995064i | \(0.468360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −554755. | + | 960864.i | −0.0427462 | + | 0.0740386i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 961256. | − | 5.45156e6i | 0.0722095 | − | 0.409520i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.35095e6 | + | 1.10002e7i | 0.465205 | + | 0.805759i | 0.999211 | − | 0.0397218i | \(-0.0126472\pi\) |
−0.534005 | + | 0.845481i | \(0.679314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.05230e7 | − | 1.25409e7i | 0.751779 | − | 0.895935i | −0.245519 | − | 0.969392i | \(-0.578959\pi\) |
0.997298 | + | 0.0734564i | \(0.0234030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.15520e6 | − | 5.92135e6i | −0.150199 | − | 0.412669i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.74983e6 | − | 9.92378e6i | −0.118986 | − | 0.674806i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.45550e6 | − | 1.95970e6i | −0.162948 | − | 0.130046i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.33745e7 | + | 2.35828e6i | −0.866321 | + | 0.152756i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.07248e7 | − | 3.90350e6i | 0.678215 | − | 0.246850i | 0.0201340 | − | 0.999797i | \(-0.493591\pi\) |
0.658081 | + | 0.752947i | \(0.271368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.06225e7 | − | 2.56953e7i | −1.89094 | − | 1.58669i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.39015e7 | + | 8.02601e6i | −0.838378 | + | 0.484038i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.03192e7 | − | 1.81955e6i | −0.607918 | − | 0.107192i | −0.138789 | − | 0.990322i | \(-0.544321\pi\) |
−0.469129 | + | 0.883130i | \(0.655432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.62650e6 | + | 2.67111e6i | 0.266289 | + | 0.153742i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.59495e6 | + | 4.38209e6i | −0.0897068 | + | 0.246467i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.07497e7 | − | 1.74110e7i | 1.14063 | − | 0.957100i | 0.141168 | − | 0.989986i | \(-0.454914\pi\) |
0.999459 | + | 0.0328860i | \(0.0104698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.56286e7i | − | 0.839813i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.41825e6 | −0.442270 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.87872e7 | + | 2.23898e7i | 0.965176 | + | 1.15025i | 0.988606 | + | 0.150526i | \(0.0480967\pi\) |
−0.0234304 | + | 0.999725i | \(0.507459\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.37618e6 | − | 2.68471e6i | −0.370616 | − | 0.134893i | 0.149996 | − | 0.988687i | \(-0.452074\pi\) |
−0.520612 | + | 0.853794i | \(0.674296\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 627999. | − | 1.08773e6i | 0.0308654 | − | 0.0534604i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.85403e6 | + | 1.05147e7i | −0.0891493 | + | 0.505591i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 654860. | + | 1.13425e6i | 0.0308112 | + | 0.0533666i | 0.881020 | − | 0.473079i | \(-0.156858\pi\) |
−0.850209 | + | 0.526446i | \(0.823524\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.30592e6 | + | 5.13160e6i | −0.198268 | + | 0.236287i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.25235e6 | − | 6.18829e6i | −0.101512 | − | 0.278902i | 0.878532 | − | 0.477684i | \(-0.158524\pi\) |
−0.980044 | + | 0.198782i | \(0.936301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.08221e6 | + | 2.31514e7i | 0.180109 | + | 1.02145i | 0.932080 | + | 0.362254i | \(0.117993\pi\) |
−0.751970 | + | 0.659197i | \(0.770896\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.46650e7 | − | 5.74925e6i | 0.633499 | − | 0.248357i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.28984e6 | − | 1.28539e6i | 0.308370 | − | 0.0543740i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.32288e7 | + | 8.45460e6i | −0.962352 | + | 0.350267i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.39726e6 | + | 7.88524e6i | 0.381349 | + | 0.319990i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.34000e6 | − | 2.50570e6i | 0.172539 | − | 0.0996153i | −0.411244 | − | 0.911525i | \(-0.634905\pi\) |
0.583782 | + | 0.811910i | \(0.301572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.84408e6 | − | 1.55945e6i | −0.344498 | − | 0.0607443i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.11479e7 | − | 1.79832e7i | −1.18894 | − | 0.686434i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.69531e6 | + | 1.01528e7i | −0.138241 | + | 0.379815i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.59551e6 | − | 3.01699e6i | 0.131844 | − | 0.110630i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.59394e7i | 1.29194i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.12812e6 | 0.145497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.45137e7 | + | 2.92143e7i | 0.847217 | + | 1.00967i | 0.999771 | + | 0.0213783i | \(0.00680546\pi\) |
−0.152555 | + | 0.988295i | \(0.548750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.76337e7 | + | 6.41813e6i | 0.597678 | + | 0.217537i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.07750e6 | + | 5.33039e6i | −0.102310 | + | 0.177206i | −0.912636 | − | 0.408773i | \(-0.865957\pi\) |
0.810326 | + | 0.585979i | \(0.199290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.83026e6 | + | 1.60512e7i | −0.0922982 | + | 0.523449i | 0.903244 | + | 0.429128i | \(0.141179\pi\) |
−0.995542 | + | 0.0943209i | \(0.969932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −909753. | − | 1.57574e6i | −0.0291066 | − | 0.0504142i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.11651e7 | + | 1.33061e7i | −0.350498 | + | 0.417708i | −0.912273 | − | 0.409583i | \(-0.865674\pi\) |
0.561775 | + | 0.827290i | \(0.310119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.65401e7 | + | 4.54434e7i | 0.509525 | + | 1.39991i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.83106e6 | − | 3.87409e7i | −0.206525 | − | 1.17126i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.69959e7 | − | 9.48216e6i | 1.39461 | − | 0.281384i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.84191e6 | − | 501105.i | 0.0827866 | − | 0.0145975i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.45455e6 | − | 529413.i | 0.0415992 | − | 0.0151409i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.01488e6 | + | 851583.i | 0.0284988 | + | 0.0239133i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.41999e7 | + | 8.19833e6i | −0.391563 | + | 0.226069i | −0.682837 | − | 0.730571i | \(-0.739254\pi\) |
0.291274 | + | 0.956640i | \(0.405921\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.45624e6 | − | 1.31474e6i | −0.201924 | − | 0.0356046i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.59386e7 | + | 9.20214e6i | 0.423950 | + | 0.244768i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.62486e7 | + | 4.46427e7i | −0.424548 | + | 1.16644i | 0.524529 | + | 0.851392i | \(0.324241\pi\) |
−0.949077 | + | 0.315043i | \(0.897981\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.89594e7 | − | 2.42998e7i | 0.743344 | − | 0.623740i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.94686e7i | 1.75197i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.55979e7 | −0.634339 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.48207e7 | − | 4.14977e7i | −0.847969 | − | 1.01057i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.92224e7 | + | 1.42758e7i | 0.938740 | + | 0.341673i | 0.765668 | − | 0.643236i | \(-0.222409\pi\) |
0.173072 | + | 0.984909i | \(0.444631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.50024e7 | − | 2.59850e7i | 0.352927 | − | 0.611288i | −0.633834 | − | 0.773469i | \(-0.718520\pi\) |
0.986761 | + | 0.162181i | \(0.0518530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.68803e6 | + | 9.57331e6i | −0.0390355 | + | 0.221381i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.55658e7 | − | 4.42813e7i | −0.581214 | − | 1.00669i | −0.995336 | − | 0.0964702i | \(-0.969245\pi\) |
0.414122 | − | 0.910221i | \(-0.364089\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.20114e7 | − | 2.62322e7i | 0.491997 | − | 0.586340i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.55556e6 | + | 1.80113e7i | 0.144081 | + | 0.395858i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.38354e6 | + | 1.91890e7i | 0.0731288 | + | 0.414734i | 0.999292 | + | 0.0376120i | \(0.0119751\pi\) |
−0.926164 | + | 0.377122i | \(0.876914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.69891e7 | + | 2.30994e6i | −0.998794 | + | 0.0490998i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.57699e7 | + | 4.54394e6i | −0.538758 | + | 0.0949976i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.85422e7 | − | 1.40282e7i | 0.792607 | − | 0.288485i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.73682e7 | − | 2.29646e7i | −0.553666 | − | 0.464581i | 0.322514 | − | 0.946565i | \(-0.395472\pi\) |
−0.876180 | + | 0.481984i | \(0.839916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.08539e6 | + | 5.24545e6i | −0.180828 | + | 0.104401i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.83781e7 | − | 3.24055e6i | −0.359897 | − | 0.0634596i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.61645e7 | − | 9.33259e6i | −0.311484 | − | 0.179836i | 0.336106 | − | 0.941824i | \(-0.390890\pi\) |
−0.647591 | + | 0.761989i | \(0.724223\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.72212e7 | + | 4.73149e7i | −0.326565 | + | 0.897230i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00127e7 | − | 8.40168e6i | 0.186865 | − | 0.156798i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.97856e7i | − | 1.46557i | −0.680460 | − | 0.732785i | \(-0.738220\pi\) | ||
0.680460 | − | 0.732785i | \(-0.261780\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.52476e7 | 0.998937 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.09883e7 | − | 4.88479e7i | −0.729563 | − | 0.869460i | 0.265959 | − | 0.963984i | \(-0.414311\pi\) |
−0.995523 | + | 0.0945244i | \(0.969867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.77309e7 | − | 6.45350e6i | −0.310704 | − | 0.113087i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.32600e6 | + | 5.76081e6i | −0.0573839 | + | 0.0993918i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.32867e6 | − | 5.29055e7i | 0.158479 | − | 0.898778i | −0.797057 | − | 0.603904i | \(-0.793611\pi\) |
0.955536 | − | 0.294874i | \(-0.0952777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.24401e7 | − | 1.42790e8i | −1.37914 | − | 2.38874i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.29580e7 | − | 6.31128e7i | 0.872476 | − | 1.03978i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.68756e6 | + | 2.11214e7i | 0.124738 | + | 0.342713i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.09325e7 | + | 1.18714e8i | 0.334542 | + | 1.89728i | 0.431709 | + | 0.902013i | \(0.357911\pi\) |
−0.0971669 | + | 0.995268i | \(0.530978\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.71995e6 | − | 1.84370e7i | −0.0585624 | − | 0.290249i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.37463e7 | − | 1.12402e7i | 0.988603 | − | 0.174317i | 0.344111 | − | 0.938929i | \(-0.388180\pi\) |
0.644492 | + | 0.764611i | \(0.277069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.76436e7 | − | 6.42175e6i | 0.269571 | − | 0.0981157i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.85243e7 | − | 2.39348e7i | −0.429389 | − | 0.360300i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.79969e7 | + | 3.92580e7i | −1.00857 | + | 0.582298i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.05426e7 | + | 3.62221e6i | 0.300251 | + | 0.0529424i | 0.321744 | − | 0.946827i | \(-0.395731\pi\) |
−0.0214932 | + | 0.999769i | \(0.506842\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.04002e7 | − | 2.33250e7i | −0.581912 | − | 0.335967i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.66760e6 | + | 1.00766e7i | −0.0520633 | + | 0.143043i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.22423e7 | − | 3.54455e7i | 0.591021 | − | 0.495926i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 7.08854e7i | − | 0.977572i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.09917e7 | 0.285368 | 0.142684 | − | 0.989768i | \(-0.454427\pi\) | ||||
0.142684 | + | 0.989768i | \(0.454427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.26378e7 | + | 7.46488e7i | 0.839441 | + | 1.00041i | 0.999911 | + | 0.0133657i | \(0.00425455\pi\) |
−0.160470 | + | 0.987041i | \(0.551301\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.76438e6 | − | 642182.i | −0.0233115 | − | 0.00848471i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.20190e7 | + | 3.81380e7i | −0.286834 | + | 0.496811i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 855955. | − | 4.85436e6i | 0.0109943 | − | 0.0623517i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.22988e6 | + | 1.59866e7i | 0.116903 | + | 0.202481i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.79044e7 | − | 1.04760e8i | 1.09794 | − | 1.30847i | 0.150476 | − | 0.988614i | \(-0.451919\pi\) |
0.947465 | − | 0.319861i | \(-0.103636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.68775e6 | + | 1.01320e7i | 0.0454253 | + | 0.124805i | 0.960331 | − | 0.278863i | \(-0.0899574\pi\) |
−0.914906 | + | 0.403668i | \(0.867735\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.13799e7 | + | 6.45387e7i | 0.138252 | + | 0.784066i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.90541e7 | + | 1.50633e8i | 0.707629 | + | 1.80499i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.77786e7 | + | 1.01879e7i | −0.682926 | + | 0.120418i | −0.504339 | − | 0.863506i | \(-0.668264\pi\) |
−0.178587 | + | 0.983924i | \(0.557153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.60246e7 | − | 5.83247e6i | 0.186840 | − | 0.0680043i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.69378e6 | − | 8.13404e6i | −0.111502 | − | 0.0935611i | 0.585332 | − | 0.810794i | \(-0.300964\pi\) |
−0.696834 | + | 0.717232i | \(0.745409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.96019e7 | − | 1.70907e7i | 0.335923 | − | 0.193945i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.37685e6 | − | 419103.i | −0.0266121 | − | 0.00469243i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.45455e8 | − | 8.39786e7i | −1.60690 | − | 0.927747i | −0.990057 | − | 0.140664i | \(-0.955076\pi\) |
−0.616847 | − | 0.787083i | \(-0.711590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.72096e7 | + | 1.02233e8i | −0.405626 | + | 1.11445i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.37345e7 | − | 7.86526e7i | 1.00834 | − | 0.846094i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.09984e6i | 0.0541406i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.61713e8 | −1.69432 | −0.847161 | − | 0.531336i | \(-0.821690\pi\) | ||||
−0.847161 | + | 0.531336i | \(0.821690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.53559e7 | − | 1.13641e8i | −0.986074 | − | 1.17516i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.03740e8 | + | 3.77581e7i | 1.05887 | + | 0.385396i | 0.812003 | − | 0.583654i | \(-0.198377\pi\) |
0.246865 | + | 0.969050i | \(0.420600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.75922e6 | + | 4.77911e6i | −0.0277999 | + | 0.0481508i | −0.879591 | − | 0.475731i | \(-0.842183\pi\) |
0.851791 | + | 0.523882i | \(0.175517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.63472e7 | + | 9.27094e7i | −0.162586 | + | 0.922072i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.28931e7 | − | 1.08934e8i | −0.617522 | − | 1.06958i | −0.989936 | − | 0.141513i | \(-0.954803\pi\) |
0.372415 | − | 0.928066i | \(-0.378530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.41259e7 | − | 1.68345e7i | 0.136929 | − | 0.163186i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.03138e7 | + | 1.38236e8i | 0.481531 | + | 1.32300i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.19788e7 | + | 6.79351e7i | 0.113196 | + | 0.641965i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.69561e7 | − | 3.37760e7i | 0.251522 | − | 0.315157i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.60464e7 | − | 4.59267e6i | 0.239989 | − | 0.0423166i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.34035e7 | − | 2.67167e7i | 0.667898 | − | 0.243095i | 0.0142552 | − | 0.999898i | \(-0.495462\pi\) |
0.653642 | + | 0.756804i | \(0.273240\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.62564e7 | + | 1.36408e7i | 0.146080 | + | 0.122576i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.60182e7 | + | 3.23421e7i | −0.497150 | + | 0.287030i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.90531e7 | − | 8.64939e6i | −0.429973 | − | 0.0758159i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.75110e7 | − | 1.58835e7i | −0.238188 | − | 0.137518i | 0.376156 | − | 0.926556i | \(-0.377246\pi\) |
−0.614344 | + | 0.789039i | \(0.710579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.38655e7 | + | 9.30448e7i | −0.289622 | + | 0.795730i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.75811e7 | − | 3.15343e7i | 0.317486 | − | 0.266403i | −0.470092 | − | 0.882618i | \(-0.655779\pi\) |
0.787578 | + | 0.616215i | \(0.211335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.99465e8i | 1.66466i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.67418e7 | 0.220483 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.62831e7 | − | 3.13230e7i | −0.214095 | − | 0.255149i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.23803e8 | + | 4.50606e7i | 0.996390 | + | 0.362656i | 0.788191 | − | 0.615430i | \(-0.211018\pi\) |
0.208198 | + | 0.978087i | \(0.433240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.07255e7 | + | 5.32182e7i | −0.244335 | + | 0.423201i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.07105e6 | − | 2.30881e7i | 0.0319891 | − | 0.181419i | −0.964627 | − | 0.263620i | \(-0.915084\pi\) |
0.996616 | + | 0.0822003i | \(0.0261947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.29640e7 | − | 1.26377e8i | −0.566545 | − | 0.981285i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.05794e7 | + | 8.41132e7i | −0.541569 | + | 0.645417i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.34134e7 | + | 1.19277e8i | 0.329208 | + | 0.904491i | 0.988313 | + | 0.152440i | \(0.0487131\pi\) |
−0.659105 | + | 0.752051i | \(0.729065\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.50451e6 | − | 4.82315e7i | −0.0637363 | − | 0.361466i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.58597e7 | + | 1.24243e8i | 0.561900 | + | 0.920281i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.50370e7 | + | 1.32311e7i | −0.549356 | + | 0.0968663i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.82971e7 | + | 6.65960e6i | −0.132407 | + | 0.0481922i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.36310e7 | + | 3.66108e7i | 0.312100 | + | 0.261883i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.63751e8 | + | 9.45414e7i | −1.15790 | + | 0.668511i | −0.950799 | − | 0.309809i | \(-0.899735\pi\) |
−0.207097 | + | 0.978320i | \(0.566402\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.62562e8 | + | 2.86641e7i | 1.13636 | + | 0.200370i | 0.710011 | − | 0.704191i | \(-0.248690\pi\) |
0.426345 | + | 0.904561i | \(0.359801\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.49620e7 | + | 8.63829e6i | 0.103398 | + | 0.0596966i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.79992e7 | + | 2.69251e8i | −0.669562 | + | 1.83961i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.12846e8 | − | 2.62509e8i | 2.11331 | − | 1.77328i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.51977e7i | − | 0.101506i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.94047e7 | 0.194193 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.02672e8 | + | 1.22360e8i | 0.670489 | + | 0.799058i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.97149e8 | + | 7.17565e7i | 1.27313 | + | 0.463381i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.84221e7 | − | 1.53152e8i | 0.564670 | − | 0.978037i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.98707e7 | + | 1.12692e8i | −0.125493 | + | 0.711708i | 0.855520 | + | 0.517769i | \(0.173237\pi\) |
−0.981014 | + | 0.193939i | \(0.937874\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.01134e8 | − | 1.75169e8i | −0.631681 | − | 1.09410i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.03997e6 | + | 4.81465e6i | −0.0249568 | + | 0.0297423i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.53910e6 | + | 6.97612e6i | 0.0155138 | + | 0.0426238i | 0.947208 | − | 0.320620i | \(-0.103891\pi\) |
−0.931694 | + | 0.363244i | \(0.881669\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.21310e6 | + | 6.87985e6i | 0.00733129 | + | 0.0415778i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.92448e7 | − | 1.93536e8i | 0.174821 | − | 1.15693i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.64312e7 | − | 4.66053e6i | 0.156294 | − | 0.0275588i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.99834e7 | + | 3.63910e7i | −0.584856 | + | 0.212870i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.36145e8 | − | 1.98149e8i | −1.36651 | − | 1.14664i | −0.973912 | − | 0.226927i | \(-0.927132\pi\) |
−0.392597 | − | 0.919711i | \(-0.628423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.61468e7 | − | 9.32236e6i | 0.0924381 | − | 0.0533692i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.77426e8 | − | 4.89176e7i | −1.57130 | − | 0.277062i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.12163e7 | − | 1.80228e7i | −0.174927 | − | 0.100994i | 0.409980 | − | 0.912094i | \(-0.365536\pi\) |
−0.584907 | + | 0.811100i | \(0.698869\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.24994e7 | + | 1.44241e8i | −0.291078 | + | 0.799730i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.40600e7 | + | 2.85797e7i | −0.186851 | + | 0.156786i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.33183e8i | − | 1.26579i | −0.774239 | − | 0.632893i | \(-0.781867\pi\) | ||
0.774239 | − | 0.632893i | \(-0.218133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.79249e7 | −0.472285 | −0.236142 | − | 0.971718i | \(-0.575883\pi\) | ||||
−0.236142 | + | 0.971718i | \(0.575883\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.00245e8 | + | 1.19467e8i | 0.532843 | + | 0.635017i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.39654e8 | − | 5.08299e7i | −0.734599 | − | 0.267372i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.83129e7 | − | 1.35642e8i | 0.407667 | − | 0.706100i | −0.586961 | − | 0.809615i | \(-0.699676\pi\) |
0.994628 | + | 0.103515i | \(0.0330090\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.85720e7 | − | 2.75465e8i | 0.250236 | − | 1.41916i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.29224e7 | − | 5.70233e7i | −0.167866 | − | 0.290753i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.76300e8 | − | 2.10107e8i | 0.889708 | − | 1.06031i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.47204e6 | − | 6.79187e6i | −0.0123477 | − | 0.0339252i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.85452e7 | + | 2.18601e8i | 0.190571 | + | 1.08078i | 0.918587 | + | 0.395219i | \(0.129331\pi\) |
−0.728016 | + | 0.685560i | \(0.759557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.34562e8 | − | 2.46878e8i | 0.658534 | − | 1.20820i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.35246e8 | − | 2.38475e7i | 0.655183 | − | 0.115526i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.03523e8 | + | 7.40762e7i | −0.975998 | + | 0.355234i | −0.780283 | − | 0.625426i | \(-0.784925\pi\) |
−0.195715 | + | 0.980661i | \(0.562703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.96183e7 | − | 5.00257e7i | −0.283028 | − | 0.237488i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.19310e7 | + | 4.73029e7i | −0.385057 | + | 0.222313i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.72334e8 | − | 4.80199e7i | −1.26713 | − | 0.223430i | −0.500624 | − | 0.865665i | \(-0.666896\pi\) |
−0.766508 | + | 0.642235i | \(0.778007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.91895e8 | − | 1.10791e8i | −0.883975 | − | 0.510363i | −0.0120082 | − | 0.999928i | \(-0.503822\pi\) |
−0.871967 | + | 0.489565i | \(0.837156\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.06524e7 | + | 2.92671e7i | −0.0485841 | + | 0.133484i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.13924e7 | − | 6.82963e7i | 0.367551 | − | 0.308412i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.12539e7i | 0.273885i | 0.990579 | + | 0.136942i | \(0.0437275\pi\) | ||||
−0.990579 | + | 0.136942i | \(0.956273\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.82524e7 | 0.346454 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.38281e6 | + | 4.03147e6i | 0.0148304 | + | 0.0176742i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.04083e8 | + | 1.10677e8i | 1.32011 | + | 0.480481i | 0.903494 | − | 0.428602i | \(-0.140994\pi\) |
0.416617 | + | 0.909082i | \(0.363216\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.37152e7 | + | 1.27678e8i | −0.316907 | + | 0.548899i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.04446e7 | + | 2.29373e8i | −0.172189 | + | 0.976531i | 0.769150 | + | 0.639068i | \(0.220680\pi\) |
−0.941339 | + | 0.337463i | \(0.890431\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.95043e7 | − | 1.55026e8i | −0.377374 | − | 0.653631i | 0.613305 | − | 0.789846i | \(-0.289840\pi\) |
−0.990679 | + | 0.136215i | \(0.956506\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.21801e8 | − | 3.83508e8i | 1.34373 | − | 1.60140i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.39595e7 | − | 3.83534e7i | −0.0577305 | − | 0.158613i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.84074e7 | − | 1.04393e8i | −0.0753965 | − | 0.427595i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.62007e8 | + | 8.81385e7i | 1.06294 | + | 0.357572i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.18928e8 | + | 5.62355e7i | −1.28156 | + | 0.225974i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.69856e8 | − | 9.82197e7i | 1.07410 | − | 0.390940i | 0.256391 | − | 0.966573i | \(-0.417466\pi\) |
0.817708 | + | 0.575633i | \(0.195244\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.91778e8 | − | 2.44831e8i | −1.15038 | − | 0.965284i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.94273e8 | + | 1.12163e8i | −0.758735 | + | 0.438056i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.70712e7 | − | 8.29992e6i | −0.182111 | − | 0.0321111i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.01864e7 | + | 2.89751e7i | 0.192346 | + | 0.111051i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04249e7 | − | 2.86423e7i | 0.0395821 | − | 0.108751i | −0.918327 | − | 0.395823i | \(-0.870460\pi\) |
0.957909 | + | 0.287072i | \(0.0926818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.89205e7 | − | 3.26582e7i | 0.146402 | − | 0.122846i | −0.566645 | − | 0.823962i | \(-0.691759\pi\) |
0.713047 | + | 0.701116i | \(0.247315\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.34817e7i | 0.348375i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.21372e8 | 0.817355 | 0.408678 | − | 0.912679i | \(-0.365990\pi\) | ||||
0.408678 | + | 0.912679i | \(0.365990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.01306e8 | − | 1.20732e8i | −0.370596 | − | 0.441659i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.05630e8 | + | 3.84461e7i | 0.382863 | + | 0.139351i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.69577e6 | − | 4.66921e6i | 0.00968152 | − | 0.0167689i | −0.861144 | − | 0.508361i | \(-0.830252\pi\) |
0.870826 | + | 0.491592i | \(0.163585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.80900e7 | + | 3.29445e8i | −0.206718 | + | 1.17235i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.47053e7 | + | 6.01114e7i | 0.122377 | + | 0.211963i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.60674e8 | − | 1.91484e8i | 0.561422 | − | 0.669077i | −0.408425 | − | 0.912792i | \(-0.633922\pi\) |
0.969847 | + | 0.243715i | \(0.0783661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.93223e8 | + | 5.30875e8i | 0.669042 | + | 1.83818i | 0.530217 | + | 0.847862i | \(0.322110\pi\) |
0.138825 | + | 0.990317i | \(0.455667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.32214e7 | + | 7.49825e7i | 0.0453668 | + | 0.257288i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.05115e7 | + | 5.72796e7i | 0.171761 | + | 0.194776i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.62917e8 | + | 1.16890e8i | −2.23399 | + | 0.393913i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.62223e8 | − | 9.54414e7i | 0.875775 | − | 0.318756i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.54973e7 | + | 4.65677e7i | 0.183698 | + | 0.154141i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.50243e8 | − | 2.59948e8i | 1.47707 | − | 0.852788i | 0.477407 | − | 0.878682i | \(-0.341577\pi\) |
0.999665 | + | 0.0258943i | \(0.00824332\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.31683e8 | − | 2.32193e7i | −0.428173 | − | 0.0754985i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.65163e8 | − | 1.53092e8i | −0.854570 | − | 0.493386i | 0.00762015 | − | 0.999971i | \(-0.497574\pi\) |
−0.862190 | + | 0.506585i | \(0.830908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.03421e7 | + | 5.58894e7i | −0.0649809 | + | 0.178534i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.86601e8 | − | 1.56577e8i | 0.590844 | − | 0.495777i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.00148e8i | 0.314326i | 0.987573 | + | 0.157163i | \(0.0502348\pi\) | ||||
−0.987573 | + | 0.157163i | \(0.949765\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.89418e8 | 0.589316 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.60716e8 | + | 1.91534e8i | 0.495667 | + | 0.590713i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.96602e7 | − | 2.53542e7i | −0.212974 | − | 0.0775162i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.86469e8 | + | 4.96179e8i | −0.868247 | + | 1.50385i | −0.00446097 | + | 0.999990i | \(0.501420\pi\) |
−0.863786 | + | 0.503858i | \(0.831913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.54484e6 | − | 3.14464e7i | 0.0166606 | − | 0.0944867i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.43911e8 | + | 2.49262e8i | 0.428687 | + | 0.742508i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.88438e8 | + | 3.43747e8i | −0.851833 | + | 1.01518i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.92217e7 | + | 2.45135e8i | 0.261240 | + | 0.717750i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.06437e7 | − | 6.03631e7i | −0.0308984 | − | 0.175234i | 0.965453 | − | 0.260576i | \(-0.0839126\pi\) |
−0.996352 | + | 0.0853427i | \(0.972801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.17692e8 | − | 7.80402e6i | 0.914408 | − | 0.0224622i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.59855e7 | + | 4.58195e6i | −0.0741591 | + | 0.0130762i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.63739e8 | + | 5.95962e7i | −0.463334 | + | 0.168640i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.54526e8 | − | 2.13573e8i | −0.714158 | − | 0.599250i | 0.211605 | − | 0.977355i | \(-0.432131\pi\) |
−0.925762 | + | 0.378106i | \(0.876576\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.29414e7 | + | 1.90187e7i | −0.0916503 | + | 0.0529143i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.52275e8 | − | 1.67912e8i | −2.62720 | − | 0.463247i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.49119e7 | − | 3.74769e7i | −0.177585 | − | 0.102529i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.03316e8 | + | 2.83859e8i | −0.280293 | + | 0.770097i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.36026e8 | − | 1.14139e8i | 0.365961 | − | 0.307078i | −0.441200 | − | 0.897409i | \(-0.645447\pi\) |
0.807161 | + | 0.590331i | \(0.201003\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.09814e7i | 0.242743i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.89334e8 | 1.03017 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.15567e8 | + | 1.37728e8i | 0.303264 | + | 0.361416i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.61796e8 | + | 2.04477e8i | 1.46209 | + | 0.532159i | 0.945941 | − | 0.324338i | \(-0.105142\pi\) |
0.516152 | + | 0.856497i | \(0.327364\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.15483e8 | − | 3.73228e8i | 0.556200 | − | 0.963367i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.94078e7 | + | 2.80205e8i | −0.126486 | + | 0.717339i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.76101e7 | − | 4.78221e7i | −0.0701061 | − | 0.121427i | 0.828842 | − | 0.559483i | \(-0.189000\pi\) |
−0.898948 | + | 0.438056i | \(0.855667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.54043e8 | − | 1.83581e8i | 0.387954 | − | 0.462345i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.10468e8 | + | 3.03508e8i | 0.275952 | + | 0.758172i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.38780e7 | + | 1.92131e8i | 0.0839429 | + | 0.476064i | 0.997580 | + | 0.0695324i | \(0.0221507\pi\) |
−0.913637 | + | 0.406531i | \(0.866738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.83479e6 | − | 7.46920e7i | −0.00450953 | − | 0.183577i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.17117e8 | + | 3.82836e7i | −0.529331 | + | 0.0933354i | −0.431925 | − | 0.901909i | \(-0.642166\pi\) |
−0.0974059 | + | 0.995245i | \(0.531054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.20882e6 | − | 3.35174e6i | 0.0222708 | − | 0.00810590i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.14862e7 | + | 5.99841e7i | 0.171499 | + | 0.143904i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.65175e8 | − | 9.53639e7i | 0.393097 | − | 0.226954i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.78970e8 | − | 8.44554e7i | −1.13081 | − | 0.199392i | −0.423226 | − | 0.906024i | \(-0.639103\pi\) |
−0.707581 | + | 0.706632i | \(0.750214\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.35062e8 | + | 1.35713e8i | 0.550551 | + | 0.317861i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.69928e8 | + | 4.66873e8i | −0.394843 | + | 1.08482i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.89281e8 | + | 4.94466e8i | −1.35842 | + | 1.13985i | −0.381957 | + | 0.924180i | \(0.624750\pi\) |
−0.976466 | + | 0.215672i | \(0.930806\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 9.50682e8i | − | 2.17425i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.45772e8 | −0.557672 | −0.278836 | − | 0.960339i | \(-0.589949\pi\) | ||||
−0.278836 | + | 0.960339i | \(0.589949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.82399e6 | + | 5.74901e6i | 0.0108601 | + | 0.0129425i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.03647e8 | + | 3.77246e7i | 0.231512 | + | 0.0842636i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.12985e7 | + | 3.68901e7i | −0.0472024 | + | 0.0817569i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.14708e7 | − | 5.18757e8i | 0.201142 | − | 1.14073i | −0.702253 | − | 0.711927i | \(-0.747823\pi\) |
0.903396 | − | 0.428808i | \(-0.141066\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.24598e8 | − | 2.15810e8i | −0.271862 | − | 0.470879i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.66904e7 | − | 9.13961e7i | 0.166036 | − | 0.197874i | −0.676611 | − | 0.736341i | \(-0.736552\pi\) |
0.842647 | + | 0.538467i | \(0.180996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.83328e7 | + | 2.42692e8i | 0.189765 | + | 0.521376i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.20618e7 | + | 1.25119e8i | 0.0470303 | + | 0.266722i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.30263e8 | − | 2.91239e8i | 0.698630 | − | 0.616081i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.91830e8 | − | 1.04356e8i | 1.24235 | − | 0.219060i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.69121e8 | + | 2.07143e8i | −1.18555 | + | 0.431505i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.57569e8 | − | 3.83946e8i | −0.945906 | − | 0.793709i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.44638e8 | + | 8.35070e7i | −0.296729 | + | 0.171316i | −0.640972 | − | 0.767564i | \(-0.721469\pi\) |
0.344244 | + | 0.938880i | \(0.388135\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.34391e8 | + | 1.11860e8i | 1.29159 | + | 0.227743i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.58731e8 | + | 9.16434e7i | 0.320725 | + | 0.185171i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.69703e6 | − | 1.83999e7i | 0.0134296 | − | 0.0368975i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.84723e8 | − | 2.38911e8i | 0.566659 | − | 0.475483i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.86518e6i | − | 0.00565949i | −0.999996 | − | 0.00282974i | \(-0.999099\pi\) | ||
0.999996 | − | 0.00282974i | \(-0.000900737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.03117e7 | −0.157448 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.71819e7 | + | 4.43117e7i | 0.0723493 | + | 0.0862226i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.76398e8 | + | 2.46189e8i | 1.30634 | + | 0.475468i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.31322e8 | − | 2.27456e8i | 0.251738 | − | 0.436023i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.20702e8 | + | 6.84536e8i | −0.229665 | + | 1.30249i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 798305. | + | 1.38270e6i | 0.00150773 | + | 0.00261146i | 0.866778 | − | 0.498694i | \(-0.166187\pi\) |
−0.865271 | + | 0.501305i | \(0.832853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.63328e8 | − | 5.52173e8i | 0.868613 | − | 1.03517i | −0.130431 | − | 0.991457i | \(-0.541636\pi\) |
0.999044 | − | 0.0437149i | \(-0.0139193\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.38479e7 | − | 1.75421e8i | −0.118816 | − | 0.326444i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.98143e7 | − | 3.95936e8i | −0.128965 | − | 0.731396i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.90216e7 | − | 2.64632e8i | 0.163241 | − | 0.485262i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.49931e6 | + | 1.49866e6i | −0.0154715 | + | 0.00272804i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.50145e8 | + | 2.73031e8i | −1.35555 | + | 0.493380i | −0.914676 | − | 0.404188i | \(-0.867554\pi\) |
−0.440875 | + | 0.897568i | \(0.645332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.70445e8 | − | 1.43020e8i | −0.305763 | − | 0.256565i | 0.476975 | − | 0.878917i | \(-0.341733\pi\) |
−0.782738 | + | 0.622351i | \(0.786178\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.19900e8 | + | 1.26959e8i | −0.391619 | + | 0.226101i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.83717e7 | + | 1.73456e7i | 0.173922 | + | 0.0306671i | 0.259931 | − | 0.965627i | \(-0.416300\pi\) |
−0.0860090 | + | 0.996294i | \(0.527411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.31946e8 | − | 7.61793e7i | −0.231598 | − | 0.133713i | 0.379711 | − | 0.925105i | \(-0.376023\pi\) |
−0.611309 | + | 0.791392i | \(0.709357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.06532e7 | + | 2.92694e7i | −0.0185642 | + | 0.0510047i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.58762e8 | − | 4.68857e8i | 0.966701 | − | 0.811158i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.49515e8i | − | 0.428586i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.70007e8 | −1.48370 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.16877e8 | − | 1.39289e8i | −0.197899 | − | 0.235847i | 0.657964 | − | 0.753049i | \(-0.271418\pi\) |
−0.855863 | + | 0.517203i | \(0.826973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.06280e8 | + | 7.50797e7i | 0.346792 | + | 0.126222i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.83075e7 | − | 1.35633e8i | 0.130714 | − | 0.226403i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.74191e7 | − | 4.39066e8i | 0.128315 | − | 0.727712i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.34349e7 | − | 1.09872e8i | −0.104395 | − | 0.180817i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.59370e8 | + | 4.28280e8i | −0.587244 | + | 0.699850i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.73794e8 | − | 1.02699e9i | −0.606518 | − | 1.66639i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.10108e7 | − | 4.02722e8i | −0.114413 | − | 0.648871i | −0.987039 | − | 0.160481i | \(-0.948695\pi\) |
0.872625 | − | 0.488390i | \(-0.162416\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.50353e7 | − | 5.17995e7i | −0.152050 | − | 0.0828757i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.00405e8 | + | 7.06023e7i | −0.636147 | + | 0.112170i | −0.482415 | − | 0.875943i | \(-0.660240\pi\) |
−0.153732 | + | 0.988113i | \(0.549129\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.38167e8 | − | 2.32274e8i | 1.00683 | − | 0.366455i | 0.214613 | − | 0.976699i | \(-0.431151\pi\) |
0.792213 | + | 0.610244i | \(0.208929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.34856e8 | + | 1.13157e8i | 0.211281 | + | 0.177286i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.33321e7 | + | 3.65648e7i | −0.0985353 | + | 0.0568894i | −0.548458 | − | 0.836178i | \(-0.684785\pi\) |
0.449923 | + | 0.893068i | \(0.351452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.27751e8 | − | 4.01587e7i | −0.351894 | − | 0.0620485i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.09121e8 | − | 2.93941e8i | −0.781203 | − | 0.451028i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.34913e8 | + | 3.70670e8i | −0.205586 | + | 0.564844i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.68731e7 | − | 5.61132e7i | 0.101204 | − | 0.0849201i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.42927e7i | − | 0.126691i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.44123e8 | −0.364405 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.98187e8 | − | 3.55366e8i | −0.442069 | − | 0.526838i | 0.498295 | − | 0.867008i | \(-0.333960\pi\) |
−0.940364 | + | 0.340170i | \(0.889515\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.11994e8 | + | 4.07624e7i | 0.164902 | + | 0.0600195i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.39198e7 | − | 2.41097e7i | 0.0203565 | − | 0.0352586i | −0.855668 | − | 0.517526i | \(-0.826853\pi\) |
0.876024 | + | 0.482267i | \(0.160187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.10127e7 | − | 1.75882e8i | 0.0450462 | − | 0.255470i | −0.953966 | − | 0.299916i | \(-0.903041\pi\) |
0.999012 | + | 0.0444465i | \(0.0141524\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.06787e8 | − | 1.84961e8i | −0.154060 | − | 0.266840i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.54692e8 | − | 1.84355e8i | 0.221665 | − | 0.264170i | −0.643739 | − | 0.765245i | \(-0.722618\pi\) |
0.865404 | + | 0.501075i | \(0.167062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.16138e7 | + | 2.51707e8i | 0.130393 | + | 0.358253i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.13474e8 | − | 6.43544e8i | −0.160422 | − | 0.909799i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.79243e7 | + | 1.17750e7i | 0.109425 | + | 0.0165350i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.38936e8 | + | 1.47927e8i | −1.17020 | + | 0.206338i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.41454e8 | + | 8.78820e7i | −0.334547 | + | 0.121765i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.96116e8 | + | 7.51930e8i | 1.23335 | + | 1.03490i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.79712e8 | − | 5.65637e8i | 1.33944 | − | 0.773327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.09928e8 | + | 1.93832e7i | 0.149294 | + | 0.0263246i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.11255e8 | + | 4.10643e8i | 0.959577 | + | 0.554012i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.73479e8 | + | 7.51377e8i | −0.366524 | + | 1.00702i | 0.610150 | + | 0.792286i | \(0.291109\pi\) |
−0.976674 | + | 0.214729i | \(0.931113\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.89177e8 | − | 1.58738e8i | 0.251870 | − | 0.211344i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.24537e7i | 0.0296984i | 0.999890 | + | 0.0148492i | \(0.00472682\pi\) | ||||
−0.999890 | + | 0.0148492i | \(0.995273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.67740e8 | 1.27159 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.31057e7 | + | 7.52064e7i | 0.0823769 | + | 0.0981729i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.75358e8 | + | 1.36619e8i | 0.486786 | + | 0.177175i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.66337e8 | + | 1.15413e9i | −0.858514 | + | 1.48699i | 0.0148320 | + | 0.999890i | \(0.495279\pi\) |
−0.873346 | + | 0.487100i | \(0.838055\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.57493e8 | + | 8.93187e8i | −0.201596 | + | 1.14331i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.12136e7 | − | 1.40666e8i | −0.103282 | − | 0.178889i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.87632e8 | + | 2.23611e8i | −0.237073 | + | 0.282533i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.41013e7 | − | 1.21167e8i | −0.0553620 | − | 0.152106i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.66796e7 | + | 4.91585e8i | 0.108111 | + | 0.613128i | 0.989932 | + | 0.141544i | \(0.0452066\pi\) |
−0.881821 | + | 0.471584i | \(0.843682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.10894e8 | + | 3.72996e8i | −0.757036 | + | 0.462227i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.44155e8 | + | 2.54184e7i | −0.177494 | + | 0.0312970i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.07485e9 | − | 3.91214e8i | 1.31496 | − | 0.478608i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.68059e8 | + | 6.44478e8i | 0.933632 | + | 0.783410i | 0.976466 | − | 0.215672i | \(-0.0691941\pi\) |
−0.0428337 | + | 0.999082i | \(0.513639\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.35688e8 | + | 1.93809e8i | −0.405451 | + | 0.234087i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.48682e8 | + | 6.14820e7i | 0.418466 | + | 0.0737869i | 0.378917 | − | 0.925431i | \(-0.376297\pi\) |
0.0395494 | + | 0.999218i | \(0.487408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.31146e9 | − | 7.57174e8i | −1.56394 | − | 0.902943i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.08219e7 | − | 2.22056e8i | 0.0957710 | − | 0.263129i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.53489e7 | + | 1.28792e7i | −0.0180728 | + | 0.0151649i | −0.651779 | − | 0.758409i | \(-0.725977\pi\) |
0.633706 | + | 0.773574i | \(0.281533\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.94549e8i | − | 0.227631i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.13090e8 | −0.480290 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.82972e8 | + | 9.33110e8i | 0.904623 | + | 1.07809i | 0.996605 | + | 0.0823273i | \(0.0262353\pi\) |
−0.0919821 | + | 0.995761i | \(0.529320\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.95044e8 | − | 2.16578e8i | −0.683186 | − | 0.248659i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.75048e8 | + | 9.96013e8i | −0.656098 | + | 1.13639i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.92752e7 | − | 2.22741e8i | 0.0445311 | − | 0.252548i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.96450e8 | + | 6.86671e8i | 0.446702 | + | 0.773711i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.73751e8 | + | 2.07069e8i | −0.194558 | + | 0.231865i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.88450e8 | + | 1.06726e9i | 0.432268 | + | 1.18765i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.18280e8 | + | 1.23792e9i | 0.241398 | + | 1.36904i | 0.828711 | + | 0.559676i | \(0.189075\pi\) |
−0.587313 | + | 0.809360i | \(0.699814\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.91164e8 | + | 7.11224e8i | 0.979459 | + | 0.781691i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.37951e9 | − | 2.43244e8i | 1.50684 | − | 0.265696i | 0.641592 | − | 0.767046i | \(-0.278274\pi\) |
0.865244 | + | 0.501350i | \(0.167163\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.22953e8 | − | 1.17545e8i | 0.350591 | − | 0.127605i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.25728e7 | + | 4.41139e7i | 0.0567215 | + | 0.0475950i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.24980e8 | + | 4.18567e8i | −0.777396 | + | 0.448830i | −0.835507 | − | 0.549480i | \(-0.814826\pi\) |
0.0581106 | + | 0.998310i | \(0.481492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.90753e8 | + | 1.04166e8i | 0.629590 | + | 0.111014i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.21120e6 | − | 5.31809e6i | −0.00975684 | − | 0.00563311i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.85083e8 | − | 1.60750e9i | 0.615966 | − | 1.69235i | −0.100681 | − | 0.994919i | \(-0.532102\pi\) |
0.716648 | − | 0.697435i | \(-0.245676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.27164e8 | + | 3.58433e8i | −0.446978 | + | 0.375059i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.15071e7i | 0.0327685i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.60208e8 | −0.992605 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.11008e8 | − | 8.47346e8i | −0.730556 | − | 0.870642i | 0.265055 | − | 0.964233i | \(-0.414610\pi\) |
−0.995611 | + | 0.0935909i | \(0.970165\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.66429e8 | − | 1.33369e8i | −0.374233 | − | 0.136210i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.92068e8 | − | 3.32672e8i | 0.194978 | − | 0.337712i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.12678e8 | − | 1.20616e9i | 0.214604 | − | 1.21708i | −0.666989 | − | 0.745068i | \(-0.732417\pi\) |
0.881592 | − | 0.472011i | \(-0.156472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.91657e8 | − | 8.51575e8i | −0.493135 | − | 0.854135i |
(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 | 76.7.j.a.29.7 | yes | 60 | |
19.2 | odd | 18 | inner | 76.7.j.a.21.7 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.21.7 | ✓ | 60 | 19.2 | odd | 18 | inner | |
76.7.j.a.29.7 | yes | 60 | 1.1 | even | 1 | trivial |