Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,12,Mod(32,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.32");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.e (of order \(4\), degree \(2\), 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: | \(57.6257385420\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 68.5 | ||
Character | \(\chi\) | \(=\) | 75.68 |
Dual form | 75.12.e.d.32.5 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −37.4902 | − | 37.4902i | −0.828424 | − | 0.828424i | 0.158874 | − | 0.987299i | \(-0.449213\pi\) |
−0.987299 | + | 0.158874i | \(0.949213\pi\) | |||||||
\(3\) | −201.005 | − | 369.789i | −0.477572 | − | 0.878593i | ||||
\(4\) | 763.031i | 0.372574i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6327.78 | + | 21399.2i | −0.332215 | + | 1.12348i | ||||
\(7\) | 46363.7 | − | 46363.7i | 1.04265 | − | 1.04265i | 0.0436027 | − | 0.999049i | \(-0.486116\pi\) |
0.999049 | − | 0.0436027i | \(-0.0138836\pi\) | |||||||
\(8\) | −48173.8 | + | 48173.8i | −0.519775 | + | 0.519775i | ||||
\(9\) | −96341.3 | + | 148659.i | −0.543850 | + | 0.839183i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 55617.1i | 0.104123i | 0.998644 | + | 0.0520617i | \(0.0165793\pi\) | ||||
−0.998644 | + | 0.0520617i | \(0.983421\pi\) | |||||||
\(12\) | 282161. | − | 153373.i | 0.327341 | − | 0.177931i | ||||
\(13\) | −631358. | − | 631358.i | −0.471615 | − | 0.471615i | 0.430822 | − | 0.902437i | \(-0.358224\pi\) |
−0.902437 | + | 0.430822i | \(0.858224\pi\) | |||||||
\(14\) | −3.47637e6 | −1.72752 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.17478e6 | 1.23376 | ||||||||
\(17\) | 2.79681e6 | + | 2.79681e6i | 0.477743 | + | 0.477743i | 0.904409 | − | 0.426666i | \(-0.140312\pi\) |
−0.426666 | + | 0.904409i | \(0.640312\pi\) | |||||||
\(18\) | 9.18510e6 | − | 1.96139e6i | 1.14574 | − | 0.244661i | ||||
\(19\) | 1.01926e7i | 0.944368i | 0.881500 | + | 0.472184i | \(0.156534\pi\) | ||||
−0.881500 | + | 0.472184i | \(0.843466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64641e7 | − | 7.82549e6i | −1.41401 | − | 0.418125i | ||||
\(22\) | 2.08510e6 | − | 2.08510e6i | 0.0862584 | − | 0.0862584i | ||||
\(23\) | 1.26689e7 | − | 1.26689e7i | 0.410426 | − | 0.410426i | −0.471461 | − | 0.881887i | \(-0.656273\pi\) |
0.881887 | + | 0.471461i | \(0.156273\pi\) | |||||||
\(24\) | 2.74973e7 | + | 8.13100e6i | 0.704901 | + | 0.208440i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.73395e7i | 0.781394i | ||||||||
\(27\) | 7.43374e7 | + | 5.74493e6i | 0.997027 | + | 0.0770520i | ||||
\(28\) | 3.53770e7 | + | 3.53770e7i | 0.388465 | + | 0.388465i | ||||
\(29\) | 1.48130e8 | 1.34108 | 0.670539 | − | 0.741874i | \(-0.266063\pi\) | ||||
0.670539 | + | 0.741874i | \(0.266063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.61818e8 | 1.64252 | 0.821258 | − | 0.570557i | \(-0.193273\pi\) | ||||
0.821258 | + | 0.570557i | \(0.193273\pi\) | |||||||
\(32\) | −9.53435e7 | − | 9.53435e7i | −0.502304 | − | 0.502304i | ||||
\(33\) | 2.05666e7 | − | 1.11793e7i | 0.0914821 | − | 0.0497265i | ||||
\(34\) | − | 2.09706e8i | − | 0.791548i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.13431e8 | − | 7.35114e7i | −0.312657 | − | 0.202624i | ||||
\(37\) | 3.41740e8 | − | 3.41740e8i | 0.810189 | − | 0.810189i | −0.174473 | − | 0.984662i | \(-0.555822\pi\) |
0.984662 | + | 0.174473i | \(0.0558222\pi\) | |||||||
\(38\) | 3.82124e8 | − | 3.82124e8i | 0.782337 | − | 0.782337i | ||||
\(39\) | −1.06564e8 | + | 3.60375e8i | −0.189127 | + | 0.639587i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.32229e9i | 1.78244i | 0.453567 | + | 0.891222i | \(0.350151\pi\) | ||||
−0.453567 | + | 0.891222i | \(0.649849\pi\) | |||||||
\(42\) | 6.98767e8 | + | 1.28553e9i | 0.825014 | + | 1.51778i | ||||
\(43\) | 6.29639e7 | + | 6.29639e7i | 0.0653153 | + | 0.0653153i | 0.739010 | − | 0.673695i | \(-0.235294\pi\) |
−0.673695 | + | 0.739010i | \(0.735294\pi\) | |||||||
\(44\) | −4.24376e7 | −0.0387937 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.49916e8 | −0.680013 | ||||||||
\(47\) | 1.38825e9 | + | 1.38825e9i | 0.882939 | + | 0.882939i | 0.993832 | − | 0.110894i | \(-0.0353713\pi\) |
−0.110894 | + | 0.993832i | \(0.535371\pi\) | |||||||
\(48\) | −1.04015e9 | − | 1.91358e9i | −0.589211 | − | 1.08397i | ||||
\(49\) | − | 2.32187e9i | − | 1.17425i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.72059e8 | − | 1.59640e9i | 0.191585 | − | 0.647898i | ||||
\(52\) | 4.81746e8 | − | 4.81746e8i | 0.175711 | − | 0.175711i | ||||
\(53\) | −4.62211e8 | + | 4.62211e8i | −0.151818 | + | 0.151818i | −0.778929 | − | 0.627112i | \(-0.784237\pi\) |
0.627112 | + | 0.778929i | \(0.284237\pi\) | |||||||
\(54\) | −2.57155e9 | − | 3.00230e9i | −0.762130 | − | 0.889793i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.46703e9i | 1.08389i | ||||||||
\(57\) | 3.76912e9 | − | 2.04876e9i | 0.829715 | − | 0.451004i | ||||
\(58\) | −5.55343e9 | − | 5.55343e9i | −1.11098 | − | 1.11098i | ||||
\(59\) | 6.47821e9 | 1.17969 | 0.589847 | − | 0.807515i | \(-0.299188\pi\) | ||||
0.589847 | + | 0.807515i | \(0.299188\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68237e9 | −1.01302 | −0.506508 | − | 0.862235i | \(-0.669064\pi\) | ||||
−0.506508 | + | 0.862235i | \(0.669064\pi\) | |||||||
\(62\) | −9.81560e9 | − | 9.81560e9i | −1.36070 | − | 1.36070i | ||||
\(63\) | 2.42563e9 | + | 1.13591e10i | 0.307929 | + | 1.44202i | ||||
\(64\) | − | 3.44904e9i | − | 0.401521i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.19016e9 | − | 3.51933e8i | −0.116981 | − | 0.0345914i | ||||
\(67\) | −3.32538e9 | + | 3.32538e9i | −0.300905 | + | 0.300905i | −0.841368 | − | 0.540463i | \(-0.818249\pi\) |
0.540463 | + | 0.841368i | \(0.318249\pi\) | |||||||
\(68\) | −2.13405e9 | + | 2.13405e9i | −0.177994 | + | 0.177994i | ||||
\(69\) | −7.23131e9 | − | 2.13831e9i | −0.556605 | − | 0.164589i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.73190e9i | − | 0.508587i | −0.967127 | − | 0.254293i | \(-0.918157\pi\) | ||
0.967127 | − | 0.254293i | \(-0.0818429\pi\) | |||||||
\(72\) | −2.52032e9 | − | 1.18026e10i | −0.153507 | − | 0.718866i | ||||
\(73\) | −1.89044e9 | − | 1.89044e9i | −0.106730 | − | 0.106730i | 0.651725 | − | 0.758455i | \(-0.274046\pi\) |
−0.758455 | + | 0.651725i | \(0.774046\pi\) | |||||||
\(74\) | −2.56238e10 | −1.34236 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.77729e9 | −0.351847 | ||||||||
\(77\) | 2.57862e9 | + | 2.57862e9i | 0.108564 | + | 0.108564i | ||||
\(78\) | 1.75056e10 | − | 9.51545e9i | 0.686527 | − | 0.373172i | ||||
\(79\) | − | 2.39607e10i | − | 0.876094i | −0.898952 | − | 0.438047i | \(-0.855670\pi\) | ||
0.898952 | − | 0.438047i | \(-0.144330\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.28178e10 | − | 2.86440e10i | −0.408455 | − | 0.912778i | ||||
\(82\) | 4.95730e10 | − | 4.95730e10i | 1.47662 | − | 1.47662i | ||||
\(83\) | −2.08763e10 | + | 2.08763e10i | −0.581733 | + | 0.581733i | −0.935379 | − | 0.353647i | \(-0.884942\pi\) |
0.353647 | + | 0.935379i | \(0.384942\pi\) | |||||||
\(84\) | 5.97110e9 | − | 2.01930e10i | 0.155782 | − | 0.526822i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 4.72106e9i | − | 0.108218i | ||||||
\(87\) | −2.97748e10 | − | 5.47769e10i | −0.640462 | − | 1.17826i | ||||
\(88\) | −2.67928e9 | − | 2.67928e9i | −0.0541208 | − | 0.0541208i | ||||
\(89\) | −1.75952e10 | −0.334001 | −0.167001 | − | 0.985957i | \(-0.553408\pi\) | ||||
−0.167001 | + | 0.985957i | \(0.553408\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.85443e10 | −0.983460 | ||||||||
\(92\) | 9.66673e9 | + | 9.66673e9i | 0.152914 | + | 0.152914i | ||||
\(93\) | −5.26266e10 | − | 9.68174e10i | −0.784420 | − | 1.44310i | ||||
\(94\) | − | 1.04092e11i | − | 1.46290i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.60925e10 | + | 5.44215e10i | −0.201434 | + | 0.681207i | ||||
\(97\) | −4.63107e10 | + | 4.63107e10i | −0.547566 | + | 0.547566i | −0.925736 | − | 0.378170i | \(-0.876553\pi\) |
0.378170 | + | 0.925736i | \(0.376553\pi\) | |||||||
\(98\) | −8.70472e10 | + | 8.70472e10i | −0.972773 | + | 0.972773i | ||||
\(99\) | −8.26796e9 | − | 5.35823e9i | −0.0873786 | − | 0.0566275i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.36284e11i | 1.29026i | 0.764073 | + | 0.645129i | \(0.223197\pi\) | ||||
−0.764073 | + | 0.645129i | \(0.776803\pi\) | |||||||
\(102\) | −7.75471e10 | + | 4.21519e10i | −0.695448 | + | 0.378021i | ||||
\(103\) | 4.19193e9 | + | 4.19193e9i | 0.0356295 | + | 0.0356295i | 0.724697 | − | 0.689068i | \(-0.241980\pi\) |
−0.689068 | + | 0.724697i | \(0.741980\pi\) | |||||||
\(104\) | 6.08298e10 | 0.490267 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.46568e10 | 0.251539 | ||||||||
\(107\) | 1.14858e11 | + | 1.14858e11i | 0.791681 | + | 0.791681i | 0.981767 | − | 0.190086i | \(-0.0608767\pi\) |
−0.190086 | + | 0.981767i | \(0.560877\pi\) | |||||||
\(108\) | −4.38356e9 | + | 5.67218e10i | −0.0287075 | + | 0.371466i | ||||
\(109\) | − | 7.06110e10i | − | 0.439568i | −0.975549 | − | 0.219784i | \(-0.929465\pi\) | ||
0.975549 | − | 0.219784i | \(-0.0705353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.95063e11 | − | 5.76805e10i | −1.09875 | − | 0.324902i | ||||
\(112\) | 2.39922e11 | − | 2.39922e11i | 1.28638 | − | 1.28638i | ||||
\(113\) | 1.87895e11 | − | 1.87895e11i | 0.959366 | − | 0.959366i | −0.0398404 | − | 0.999206i | \(-0.512685\pi\) |
0.999206 | + | 0.0398404i | \(0.0126850\pi\) | |||||||
\(114\) | −2.18114e11 | − | 6.44967e10i | −1.06098 | − | 0.313733i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.13028e11i | 0.499651i | ||||||||
\(117\) | 1.54683e11 | − | 3.30310e10i | 0.652258 | − | 0.139283i | ||||
\(118\) | −2.42870e11 | − | 2.42870e11i | −0.977287 | − | 0.977287i | ||||
\(119\) | 2.59341e11 | 0.996239 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.82218e11 | 0.989158 | ||||||||
\(122\) | 2.50524e11 | + | 2.50524e11i | 0.839208 | + | 0.839208i | ||||
\(123\) | 4.88969e11 | − | 2.65787e11i | 1.56604 | − | 0.851246i | ||||
\(124\) | 1.99775e11i | 0.611959i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.34918e11 | − | 5.16793e11i | 0.939509 | − | 1.44970i | ||||
\(127\) | −2.27468e11 | + | 2.27468e11i | −0.610941 | + | 0.610941i | −0.943191 | − | 0.332250i | \(-0.892192\pi\) |
0.332250 | + | 0.943191i | \(0.392192\pi\) | |||||||
\(128\) | −3.24569e11 | + | 3.24569e11i | −0.834934 | + | 0.834934i | ||||
\(129\) | 1.06274e10 | − | 3.59394e10i | 0.0261928 | − | 0.0885784i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.52427e11i | 1.47754i | 0.673957 | + | 0.738771i | \(0.264593\pi\) | ||||
−0.673957 | + | 0.738771i | \(0.735407\pi\) | |||||||
\(132\) | 8.53014e9 | + | 1.56930e10i | 0.0185268 | + | 0.0340838i | ||||
\(133\) | 4.72568e11 | + | 4.72568e11i | 0.984647 | + | 0.984647i | ||||
\(134\) | 2.49338e11 | 0.498555 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.69466e11 | −0.496638 | ||||||||
\(137\) | −6.39965e11 | − | 6.39965e11i | −1.13290 | − | 1.13290i | −0.989692 | − | 0.143212i | \(-0.954257\pi\) |
−0.143212 | − | 0.989692i | \(-0.545743\pi\) | |||||||
\(138\) | 1.90937e11 | + | 3.51269e11i | 0.324755 | + | 0.597454i | ||||
\(139\) | 9.51431e11i | 1.55523i | 0.628738 | + | 0.777617i | \(0.283572\pi\) | ||||
−0.628738 | + | 0.777617i | \(0.716428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.34316e11 | − | 7.92407e11i | 0.354076 | − | 1.19741i | ||||
\(142\) | −2.89870e11 | + | 2.89870e11i | −0.421326 | + | 0.421326i | ||||
\(143\) | 3.51143e10 | − | 3.51143e10i | 0.0491061 | − | 0.0491061i | ||||
\(144\) | −4.98545e11 | + | 7.69275e11i | −0.670981 | + | 1.03535i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.41746e11i | 0.176836i | ||||||||
\(147\) | −8.58601e11 | + | 4.66706e11i | −1.03168 | + | 0.560787i | ||||
\(148\) | 2.60758e11 | + | 2.60758e11i | 0.301855 | + | 0.301855i | ||||
\(149\) | 7.48036e11 | 0.834446 | 0.417223 | − | 0.908804i | \(-0.363003\pi\) | ||||
0.417223 | + | 0.908804i | \(0.363003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.28642e11 | 0.444346 | 0.222173 | − | 0.975007i | \(-0.428685\pi\) | ||||
0.222173 | + | 0.975007i | \(0.428685\pi\) | |||||||
\(152\) | −4.91017e11 | − | 4.91017e11i | −0.490859 | − | 0.490859i | ||||
\(153\) | −6.85219e11 | + | 1.46322e11i | −0.660734 | + | 0.141093i | ||||
\(154\) | − | 1.93346e11i | − | 0.179875i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.74978e11 | − | 8.13114e10i | −0.238293 | − | 0.0704638i | ||||
\(157\) | 1.71815e11 | − | 1.71815e11i | 0.143752 | − | 0.143752i | −0.631568 | − | 0.775320i | \(-0.717589\pi\) |
0.775320 | + | 0.631568i | \(0.217589\pi\) | |||||||
\(158\) | −8.98292e11 | + | 8.98292e11i | −0.725778 | + | 0.725778i | ||||
\(159\) | 2.63827e11 | + | 7.80142e10i | 0.205890 | + | 0.0608821i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.17475e12i | − | 0.855862i | ||||||
\(162\) | −5.93328e11 | + | 1.55441e12i | −0.417794 | + | 1.09454i | ||||
\(163\) | −1.17074e12 | − | 1.17074e12i | −0.796947 | − | 0.796947i | 0.185666 | − | 0.982613i | \(-0.440556\pi\) |
−0.982613 | + | 0.185666i | \(0.940556\pi\) | |||||||
\(164\) | −1.00895e12 | −0.664092 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.56531e12 | 0.963843 | ||||||||
\(167\) | 1.53598e12 | + | 1.53598e12i | 0.915051 | + | 0.915051i | 0.996664 | − | 0.0816127i | \(-0.0260071\pi\) |
−0.0816127 | + | 0.996664i | \(0.526007\pi\) | |||||||
\(168\) | 1.65186e12 | − | 8.97893e11i | 0.952297 | − | 0.517635i | ||||
\(169\) | − | 9.94934e11i | − | 0.555159i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.51522e12 | − | 9.81971e11i | −0.792497 | − | 0.513594i | ||||
\(172\) | −4.80434e10 | + | 4.80434e10i | −0.0243348 | + | 0.0243348i | ||||
\(173\) | 6.87025e11 | − | 6.87025e11i | 0.337069 | − | 0.337069i | −0.518194 | − | 0.855263i | \(-0.673395\pi\) |
0.855263 | + | 0.518194i | \(0.173395\pi\) | |||||||
\(174\) | −9.37334e11 | + | 3.16986e12i | −0.445527 | + | 1.50668i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.87806e11i | 0.128464i | ||||||||
\(177\) | −1.30215e12 | − | 2.39557e12i | −0.563389 | − | 1.03647i | ||||
\(178\) | 6.59647e11 | + | 6.59647e11i | 0.276695 | + | 0.276695i | ||||
\(179\) | −1.31234e12 | −0.533769 | −0.266884 | − | 0.963729i | \(-0.585994\pi\) | ||||
−0.266884 | + | 0.963729i | \(0.585994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.03204e12 | 0.777498 | 0.388749 | − | 0.921344i | \(-0.372907\pi\) | ||||
0.388749 | + | 0.921344i | \(0.372907\pi\) | |||||||
\(182\) | 2.19484e12 | + | 2.19484e12i | 0.814722 | + | 0.814722i | ||||
\(183\) | 1.34319e12 | + | 2.47107e12i | 0.483789 | + | 0.890029i | ||||
\(184\) | 1.22061e12i | 0.426658i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.65672e12 | + | 5.60268e12i | −0.545669 | + | 1.84533i | ||||
\(187\) | −1.55551e11 | + | 1.55551e11i | −0.0497442 | + | 0.0497442i | ||||
\(188\) | −1.05928e12 | + | 1.05928e12i | −0.328960 | + | 0.328960i | ||||
\(189\) | 3.71292e12 | − | 3.18021e12i | 1.11989 | − | 0.959214i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.22025e12i | − | 0.347350i | −0.984803 | − | 0.173675i | \(-0.944436\pi\) | ||
0.984803 | − | 0.173675i | \(-0.0555642\pi\) | |||||||
\(192\) | −1.27542e12 | + | 6.93273e11i | −0.352774 | + | 0.191755i | ||||
\(193\) | −1.22556e12 | − | 1.22556e12i | −0.329435 | − | 0.329435i | 0.522936 | − | 0.852372i | \(-0.324837\pi\) |
−0.852372 | + | 0.522936i | \(0.824837\pi\) | |||||||
\(194\) | 3.47239e12 | 0.907234 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.77166e12 | 0.437493 | ||||||||
\(197\) | −1.43636e12 | − | 1.43636e12i | −0.344904 | − | 0.344904i | 0.513304 | − | 0.858207i | \(-0.328421\pi\) |
−0.858207 | + | 0.513304i | \(0.828421\pi\) | |||||||
\(198\) | 1.09087e11 | + | 5.10849e11i | 0.0254750 | + | 0.119298i | ||||
\(199\) | − | 1.44198e12i | − | 0.327543i | −0.986498 | − | 0.163771i | \(-0.947634\pi\) | ||
0.986498 | − | 0.163771i | \(-0.0523660\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.89811e12 | + | 5.61274e11i | 0.408077 | + | 0.120669i | ||||
\(202\) | 5.10931e12 | − | 5.10931e12i | 1.06888 | − | 1.06888i | ||||
\(203\) | 6.86787e12 | − | 6.86787e12i | 1.39828 | − | 1.39828i | ||||
\(204\) | 1.21811e12 | + | 3.60196e11i | 0.241390 | + | 0.0713794i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 3.14313e11i | − | 0.0590327i | ||||||
\(207\) | 6.62801e11 | + | 3.10387e12i | 0.121212 | + | 0.567632i | ||||
\(208\) | −3.26714e12 | − | 3.26714e12i | −0.581861 | − | 0.581861i | ||||
\(209\) | −5.66884e11 | −0.0983309 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.21613e12 | −0.529395 | −0.264698 | − | 0.964331i | \(-0.585272\pi\) | ||||
−0.264698 | + | 0.964331i | \(0.585272\pi\) | |||||||
\(212\) | −3.52682e11 | − | 3.52682e11i | −0.0565634 | − | 0.0565634i | ||||
\(213\) | −2.85917e12 | + | 1.55415e12i | −0.446841 | + | 0.242887i | ||||
\(214\) | − | 8.61210e12i | − | 1.31170i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.85787e12 | + | 3.30436e12i | −0.558280 | + | 0.478180i | ||||
\(217\) | 1.21388e13 | − | 1.21388e13i | 1.71257 | − | 1.71257i | ||||
\(218\) | −2.64722e12 | + | 2.64722e12i | −0.364149 | + | 0.364149i | ||||
\(219\) | −3.19077e11 | + | 1.07905e12i | −0.0428009 | + | 0.144744i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.53158e12i | − | 0.450621i | ||||||
\(222\) | 5.15050e12 | + | 9.47541e12i | 0.641074 | + | 1.17939i | ||||
\(223\) | −9.25140e11 | − | 9.25140e11i | −0.112339 | − | 0.112339i | 0.648703 | − | 0.761042i | \(-0.275312\pi\) |
−0.761042 | + | 0.648703i | \(0.775312\pi\) | |||||||
\(224\) | −8.84097e12 | −1.04746 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.40885e13 | −1.58952 | ||||||||
\(227\) | −4.50902e12 | − | 4.50902e12i | −0.496523 | − | 0.496523i | 0.413830 | − | 0.910354i | \(-0.364191\pi\) |
−0.910354 | + | 0.413830i | \(0.864191\pi\) | |||||||
\(228\) | 1.56327e12 | + | 2.87596e12i | 0.168032 | + | 0.309130i | ||||
\(229\) | − | 4.57505e12i | − | 0.480066i | −0.970765 | − | 0.240033i | \(-0.922842\pi\) | ||
0.970765 | − | 0.240033i | \(-0.0771582\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.35231e11 | − | 1.47186e12i | 0.0435366 | − | 0.147231i | ||||
\(232\) | −7.13598e12 | + | 7.13598e12i | −0.697060 | + | 0.697060i | ||||
\(233\) | 2.74585e12 | − | 2.74585e12i | 0.261950 | − | 0.261950i | −0.563896 | − | 0.825846i | \(-0.690698\pi\) |
0.825846 | + | 0.563896i | \(0.190698\pi\) | |||||||
\(234\) | −7.03743e12 | − | 4.56075e12i | −0.655732 | − | 0.424961i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.94308e12i | 0.439523i | ||||||||
\(237\) | −8.86042e12 | + | 4.81621e12i | −0.769730 | + | 0.418398i | ||||
\(238\) | −9.72276e12 | − | 9.72276e12i | −0.825308 | − | 0.825308i | ||||
\(239\) | −1.86895e13 | −1.55028 | −0.775138 | − | 0.631792i | \(-0.782320\pi\) | ||||
−0.775138 | + | 0.631792i | \(0.782320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.13946e13 | 1.69516 | 0.847579 | − | 0.530669i | \(-0.178059\pi\) | ||||
0.847579 | + | 0.530669i | \(0.178059\pi\) | |||||||
\(242\) | −1.05804e13 | − | 1.05804e13i | −0.819443 | − | 0.819443i | ||||
\(243\) | −8.01580e12 | + | 1.04974e13i | −0.606894 | + | 0.794783i | ||||
\(244\) | − | 5.09886e12i | − | 0.377423i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.82959e13 | − | 8.36716e12i | −2.00254 | − | 0.592155i | ||||
\(247\) | 6.43520e12 | − | 6.43520e12i | 0.445378 | − | 0.445378i | ||||
\(248\) | −1.26127e13 | + | 1.26127e13i | −0.853739 | + | 0.853739i | ||||
\(249\) | 1.19160e13 | + | 3.52360e12i | 0.788925 | + | 0.233287i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.63600e12i | − | 0.230366i | −0.993344 | − | 0.115183i | \(-0.963255\pi\) | ||
0.993344 | − | 0.115183i | \(-0.0367454\pi\) | |||||||
\(252\) | −8.66736e12 | + | 1.85083e12i | −0.537259 | + | 0.114726i | ||||
\(253\) | 7.04605e11 | + | 7.04605e11i | 0.0427349 | + | 0.0427349i | ||||
\(254\) | 1.70556e13 | 1.01224 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.72727e13 | 0.981838 | ||||||||
\(257\) | −1.95072e13 | − | 1.95072e13i | −1.08533 | − | 1.08533i | −0.996002 | − | 0.0893287i | \(-0.971528\pi\) |
−0.0893287 | − | 0.996002i | \(-0.528472\pi\) | |||||||
\(258\) | −1.74580e12 | + | 9.48955e11i | −0.0950792 | + | 0.0516817i | ||||
\(259\) | − | 3.16887e13i | − | 1.68949i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.42711e13 | + | 2.20208e13i | −0.729345 | + | 1.12541i | ||||
\(262\) | 2.44596e13 | − | 2.44596e13i | 1.22403 | − | 1.22403i | ||||
\(263\) | 5.04148e12 | − | 5.04148e12i | 0.247059 | − | 0.247059i | −0.572703 | − | 0.819763i | \(-0.694105\pi\) |
0.819763 | + | 0.572703i | \(0.194105\pi\) | |||||||
\(264\) | −4.52222e11 | + | 1.52932e12i | −0.0217035 | + | 0.0733967i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 3.54334e13i | − | 1.63141i | ||||||
\(267\) | 3.53671e12 | + | 6.50651e12i | 0.159510 | + | 0.293451i | ||||
\(268\) | −2.53737e12 | − | 2.53737e12i | −0.112109 | − | 0.112109i | ||||
\(269\) | 8.15175e12 | 0.352869 | 0.176434 | − | 0.984312i | \(-0.443544\pi\) | ||||
0.176434 | + | 0.984312i | \(0.443544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.26813e13 | 0.527027 | 0.263513 | − | 0.964656i | \(-0.415119\pi\) | ||||
0.263513 | + | 0.964656i | \(0.415119\pi\) | |||||||
\(272\) | 1.44729e13 | + | 1.44729e13i | 0.589421 | + | 0.589421i | ||||
\(273\) | 1.17677e13 | + | 2.16490e13i | 0.469673 | + | 0.864060i | ||||
\(274\) | 4.79849e13i | 1.87705i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.63160e12 | − | 5.51771e12i | 0.0613215 | − | 0.207376i | ||||
\(277\) | −1.01118e13 | + | 1.01118e13i | −0.372554 | + | 0.372554i | −0.868407 | − | 0.495853i | \(-0.834856\pi\) |
0.495853 | + | 0.868407i | \(0.334856\pi\) | |||||||
\(278\) | 3.56693e13 | − | 3.56693e13i | 1.28839 | − | 1.28839i | ||||
\(279\) | −2.52239e13 | + | 3.89215e13i | −0.893282 | + | 1.37837i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.28758e13i | 0.438418i | 0.975678 | + | 0.219209i | \(0.0703477\pi\) | ||||
−0.975678 | + | 0.219209i | \(0.929652\pi\) | |||||||
\(282\) | −3.84920e13 | + | 2.09229e13i | −1.28529 | + | 0.698638i | ||||
\(283\) | 1.06470e13 | + | 1.06470e13i | 0.348661 | + | 0.348661i | 0.859611 | − | 0.510950i | \(-0.170706\pi\) |
−0.510950 | + | 0.859611i | \(0.670706\pi\) | |||||||
\(284\) | 5.89968e12 | 0.189486 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.63289e12 | −0.0813615 | ||||||||
\(287\) | 6.13064e13 | + | 6.13064e13i | 1.85847 | + | 1.85847i | ||||
\(288\) | 2.33592e13 | − | 4.98812e12i | 0.694702 | − | 0.148347i | ||||
\(289\) | − | 1.86276e13i | − | 0.543524i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.64338e13 | + | 7.81654e12i | 0.742590 | + | 0.219585i | ||||
\(292\) | 1.44246e12 | − | 1.44246e12i | 0.0397648 | − | 0.0397648i | ||||
\(293\) | −2.44636e13 | + | 2.44636e13i | −0.661834 | + | 0.661834i | −0.955812 | − | 0.293978i | \(-0.905021\pi\) |
0.293978 | + | 0.955812i | \(0.405021\pi\) | |||||||
\(294\) | 4.96860e13 | + | 1.46923e13i | 1.31924 | + | 0.390102i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.29258e13i | 0.842232i | ||||||||
\(297\) | −3.19516e11 | + | 4.13443e12i | −0.00802292 | + | 0.103814i | ||||
\(298\) | −2.80440e13 | − | 2.80440e13i | −0.691275 | − | 0.691275i | ||||
\(299\) | −1.59972e13 | −0.387125 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.83848e12 | 0.136202 | ||||||||
\(302\) | −1.60699e13 | − | 1.60699e13i | −0.368107 | − | 0.368107i | ||||
\(303\) | 5.03963e13 | − | 2.73937e13i | 1.13361 | − | 0.616192i | ||||
\(304\) | 5.27445e13i | 1.16513i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.11746e13 | + | 2.02034e13i | 0.664253 | + | 0.430483i | ||||
\(307\) | 2.31565e13 | − | 2.31565e13i | 0.484632 | − | 0.484632i | −0.421976 | − | 0.906607i | \(-0.638663\pi\) |
0.906607 | + | 0.421976i | \(0.138663\pi\) | |||||||
\(308\) | −1.96756e12 | + | 1.96756e12i | −0.0404483 | + | 0.0404483i | ||||
\(309\) | 7.07534e11 | − | 2.39273e12i | 0.0142881 | − | 0.0483194i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.95317e13i | − | 0.575581i | −0.957693 | − | 0.287790i | \(-0.907079\pi\) | ||
0.957693 | − | 0.287790i | \(-0.0929206\pi\) | |||||||
\(312\) | −1.22271e13 | − | 2.24942e13i | −0.234138 | − | 0.430745i | ||||
\(313\) | 3.21868e13 | + | 3.21868e13i | 0.605597 | + | 0.605597i | 0.941792 | − | 0.336195i | \(-0.109140\pi\) |
−0.336195 | + | 0.941792i | \(0.609140\pi\) | |||||||
\(314\) | −1.28828e13 | −0.238175 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.82828e13 | 0.326410 | ||||||||
\(317\) | 3.70619e13 | + | 3.70619e13i | 0.650282 | + | 0.650282i | 0.953061 | − | 0.302779i | \(-0.0979143\pi\) |
−0.302779 | + | 0.953061i | \(0.597914\pi\) | |||||||
\(318\) | −6.96617e12 | − | 1.28157e13i | −0.120128 | − | 0.221001i | ||||
\(319\) | 8.23857e12i | 0.139638i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.93863e13 | − | 6.55602e13i | 0.317480 | − | 1.07365i | ||||
\(322\) | −4.40417e13 | + | 4.40417e13i | −0.709017 | + | 0.709017i | ||||
\(323\) | −2.85069e13 | + | 2.85069e13i | −0.451165 | + | 0.451165i | ||||
\(324\) | 2.18562e13 | − | 9.78034e12i | 0.340077 | − | 0.152180i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.77827e13i | 1.32042i | ||||||||
\(327\) | −2.61112e13 | + | 1.41931e13i | −0.386201 | + | 0.209926i | ||||
\(328\) | −6.36997e13 | − | 6.36997e13i | −0.926470 | − | 0.926470i | ||||
\(329\) | 1.28729e14 | 1.84120 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.26878e13 | 1.28224 | 0.641119 | − | 0.767441i | \(-0.278470\pi\) | ||||
0.641119 | + | 0.767441i | \(0.278470\pi\) | |||||||
\(332\) | −1.59292e13 | − | 1.59292e13i | −0.216738 | − | 0.216738i | ||||
\(333\) | 1.78789e13 | + | 8.37263e13i | 0.239276 | + | 1.12052i | ||||
\(334\) | − | 1.15169e14i | − | 1.51610i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.36946e14 | − | 4.04952e13i | −1.74455 | − | 0.515866i | ||||
\(337\) | −3.00431e13 | + | 3.00431e13i | −0.376513 | + | 0.376513i | −0.869842 | − | 0.493330i | \(-0.835780\pi\) |
0.493330 | + | 0.869842i | \(0.335780\pi\) | |||||||
\(338\) | −3.73003e13 | + | 3.73003e13i | −0.459907 | + | 0.459907i | ||||
\(339\) | −1.07249e14 | − | 3.17138e13i | −1.30106 | − | 0.384725i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.45615e13i | 0.171024i | ||||||||
\(342\) | 1.99917e13 | + | 9.36203e13i | 0.231050 | + | 1.08200i | ||||
\(343\) | −1.59741e13 | − | 1.59741e13i | −0.181677 | − | 0.181677i | ||||
\(344\) | −6.06642e12 | −0.0678986 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.15134e13 | −0.558473 | ||||||||
\(347\) | −2.84539e13 | − | 2.84539e13i | −0.303619 | − | 0.303619i | 0.538809 | − | 0.842428i | \(-0.318874\pi\) |
−0.842428 | + | 0.538809i | \(0.818874\pi\) | |||||||
\(348\) | 4.17965e13 | − | 2.27191e13i | 0.438989 | − | 0.238619i | ||||
\(349\) | 1.78493e14i | 1.84536i | 0.385571 | + | 0.922678i | \(0.374004\pi\) | ||||
−0.385571 | + | 0.922678i | \(0.625996\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.33064e13 | − | 5.05607e13i | −0.433874 | − | 0.506551i | ||||
\(352\) | 5.30273e12 | − | 5.30273e12i | 0.0523016 | − | 0.0523016i | ||||
\(353\) | 9.49048e12 | − | 9.49048e12i | 0.0921568 | − | 0.0921568i | −0.659525 | − | 0.751682i | \(-0.729243\pi\) |
0.751682 | + | 0.659525i | \(0.229243\pi\) | |||||||
\(354\) | −4.09927e13 | + | 1.38628e14i | −0.391912 | + | 1.32536i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.34257e13i | − | 0.124440i | ||||||
\(357\) | −5.21288e13 | − | 9.59017e13i | −0.475776 | − | 0.875288i | ||||
\(358\) | 4.91997e13 | + | 4.91997e13i | 0.442187 | + | 0.442187i | ||||
\(359\) | −7.78654e13 | −0.689168 | −0.344584 | − | 0.938756i | \(-0.611980\pi\) | ||||
−0.344584 | + | 0.938756i | \(0.611980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.26006e13 | 0.108169 | ||||||||
\(362\) | −7.61814e13 | − | 7.61814e13i | −0.644098 | − | 0.644098i | ||||
\(363\) | −5.67272e13 | − | 1.04361e14i | −0.472394 | − | 0.869067i | ||||
\(364\) | − | 4.46711e13i | − | 0.366411i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.22846e13 | − | 1.42997e14i | 0.336539 | − | 1.13810i | ||||
\(367\) | 1.49313e14 | − | 1.49313e14i | 1.17067 | − | 1.17067i | 0.188622 | − | 0.982050i | \(-0.439598\pi\) |
0.982050 | − | 0.188622i | \(-0.0604021\pi\) | |||||||
\(368\) | 6.55585e13 | − | 6.55585e13i | 0.506368 | − | 0.506368i | ||||
\(369\) | −1.96570e14 | − | 1.27391e14i | −1.49580 | − | 0.969382i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.28597e13i | 0.316587i | ||||||||
\(372\) | 7.38747e13 | − | 4.01557e13i | 0.537662 | − | 0.292254i | ||||
\(373\) | 1.72842e14 | + | 1.72842e14i | 1.23951 | + | 1.23951i | 0.960201 | + | 0.279308i | \(0.0901052\pi\) |
0.279308 | + | 0.960201i | \(0.409895\pi\) | |||||||
\(374\) | 1.16632e13 | 0.0824187 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.33755e14 | −0.917859 | ||||||||
\(377\) | −9.35232e13 | − | 9.35232e13i | −0.632473 | − | 0.632473i | ||||
\(378\) | −2.58425e14 | − | 1.99715e13i | −1.72238 | − | 0.133109i | ||||
\(379\) | − | 2.55919e14i | − | 1.68107i | −0.541754 | − | 0.840537i | \(-0.682240\pi\) | ||
0.541754 | − | 0.840537i | \(-0.317760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.29837e14 | + | 3.83931e13i | 0.828537 | + | 0.245000i | ||||
\(382\) | −4.57476e13 | + | 4.57476e13i | −0.287753 | + | 0.287753i | ||||
\(383\) | −1.56911e14 | + | 1.56911e14i | −0.972883 | + | 0.972883i | −0.999642 | − | 0.0267587i | \(-0.991481\pi\) |
0.0267587 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(384\) | 1.85262e14 | + | 5.47823e13i | 1.13231 | + | 0.334825i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.18932e13i | 0.545825i | ||||||||
\(387\) | −1.54262e13 | + | 3.29411e12i | −0.0903332 | + | 0.0192898i | ||||
\(388\) | −3.53365e13 | − | 3.53365e13i | −0.204009 | − | 0.204009i | ||||
\(389\) | 1.06415e14 | 0.605730 | 0.302865 | − | 0.953033i | \(-0.402057\pi\) | ||||
0.302865 | + | 0.953033i | \(0.402057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.08648e13 | 0.392156 | ||||||||
\(392\) | 1.11853e14 | + | 1.11853e14i | 0.610343 | + | 0.610343i | ||||
\(393\) | 2.41260e14 | − | 1.31141e14i | 1.29816 | − | 0.705633i | ||||
\(394\) | 1.07699e14i | 0.571453i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.08849e12 | − | 6.30871e12i | 0.0210979 | − | 0.0325550i | ||||
\(397\) | 4.67234e13 | − | 4.67234e13i | 0.237786 | − | 0.237786i | −0.578147 | − | 0.815933i | \(-0.696224\pi\) |
0.815933 | + | 0.578147i | \(0.196224\pi\) | |||||||
\(398\) | −5.40603e13 | + | 5.40603e13i | −0.271345 | + | 0.271345i | ||||
\(399\) | 7.97623e13 | − | 2.69739e14i | 0.394863 | − | 1.33534i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.16339e14i | − | 0.560313i | −0.959954 | − | 0.280157i | \(-0.909614\pi\) | ||
0.959954 | − | 0.280157i | \(-0.0903864\pi\) | |||||||
\(402\) | −5.01181e13 | − | 9.22027e13i | −0.238096 | − | 0.438026i | ||||
\(403\) | −1.65301e14 | − | 1.65301e14i | −0.774635 | − | 0.774635i | ||||
\(404\) | −1.03989e14 | −0.480717 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.14955e14 | −2.31674 | ||||||||
\(407\) | 1.90066e13 | + | 1.90066e13i | 0.0843597 | + | 0.0843597i | ||||
\(408\) | 5.41639e13 | + | 9.96456e13i | 0.237180 | + | 0.436342i | ||||
\(409\) | − | 1.31811e14i | − | 0.569472i | −0.958606 | − | 0.284736i | \(-0.908094\pi\) | ||
0.958606 | − | 0.284736i | \(-0.0919059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.08016e14 | + | 3.65288e14i | −0.454318 | + | 1.53640i | ||||
\(412\) | −3.19857e12 | + | 3.19857e12i | −0.0132746 | + | 0.0132746i | ||||
\(413\) | 3.00354e14 | − | 3.00354e14i | 1.23001 | − | 1.23001i | ||||
\(414\) | 9.15162e13 | − | 1.41213e14i | 0.369825 | − | 0.570655i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.20392e14i | 0.473788i | ||||||||
\(417\) | 3.51829e14 | − | 1.91242e14i | 1.36642 | − | 0.742737i | ||||
\(418\) | 2.12526e13 | + | 2.12526e13i | 0.0814597 | + | 0.0814597i | ||||
\(419\) | 2.41692e14 | 0.914293 | 0.457146 | − | 0.889391i | \(-0.348872\pi\) | ||||
0.457146 | + | 0.889391i | \(0.348872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.15430e14 | 0.425372 | 0.212686 | − | 0.977121i | \(-0.431779\pi\) | ||||
0.212686 | + | 0.977121i | \(0.431779\pi\) | |||||||
\(422\) | 1.20573e14 | + | 1.20573e14i | 0.438564 | + | 0.438564i | ||||
\(423\) | −3.40122e14 | + | 7.26297e13i | −1.22113 | + | 0.260761i | ||||
\(424\) | − | 4.45329e13i | − | 0.157822i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.65456e14 | + | 4.89257e13i | 0.571387 | + | 0.168960i | ||||
\(427\) | −3.09820e14 | + | 3.09820e14i | −1.05622 | + | 1.05622i | ||||
\(428\) | −8.76402e13 | + | 8.76402e13i | −0.294960 | + | 0.294960i | ||||
\(429\) | −2.00430e13 | − | 5.92676e12i | −0.0665960 | − | 0.0196926i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.25269e14i | − | 0.729587i | −0.931089 | − | 0.364793i | \(-0.881140\pi\) | ||
0.931089 | − | 0.364793i | \(-0.118860\pi\) | |||||||
\(432\) | 3.84680e14 | + | 2.97287e13i | 1.23009 | + | 0.0950638i | ||||
\(433\) | −1.67103e14 | − | 1.67103e14i | −0.527597 | − | 0.527597i | 0.392258 | − | 0.919855i | \(-0.371694\pi\) |
−0.919855 | + | 0.392258i | \(0.871694\pi\) | |||||||
\(434\) | −9.10176e14 | −2.83747 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.38784e13 | 0.163772 | ||||||||
\(437\) | 1.29129e14 | + | 1.29129e14i | 0.387593 | + | 0.387593i | ||||
\(438\) | 5.24161e13 | − | 2.84916e13i | 0.155366 | − | 0.0844518i | ||||
\(439\) | 1.10282e14i | 0.322812i | 0.986888 | + | 0.161406i | \(0.0516029\pi\) | ||||
−0.986888 | + | 0.161406i | \(0.948397\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.45166e14 | + | 2.23692e14i | 0.985406 | + | 0.638613i | ||||
\(442\) | −1.32400e14 | + | 1.32400e14i | −0.373306 | + | 0.373306i | ||||
\(443\) | 2.12623e14 | − | 2.12623e14i | 0.592093 | − | 0.592093i | −0.346104 | − | 0.938196i | \(-0.612495\pi\) |
0.938196 | + | 0.346104i | \(0.112495\pi\) | |||||||
\(444\) | 4.40120e13 | − | 1.48839e14i | 0.121050 | − | 0.409365i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.93674e13i | 0.186129i | ||||||||
\(447\) | −1.50359e14 | − | 2.76616e14i | −0.398508 | − | 0.733138i | ||||
\(448\) | −1.59910e14 | − | 1.59910e14i | −0.418647 | − | 0.418647i | ||||
\(449\) | −2.09893e14 | −0.542803 | −0.271402 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271402 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.35420e13 | −0.185594 | ||||||||
\(452\) | 1.43370e14 | + | 1.43370e14i | 0.357434 | + | 0.357434i | ||||
\(453\) | −8.61589e13 | − | 1.58507e14i | −0.212207 | − | 0.390399i | ||||
\(454\) | 3.38088e14i | 0.822664i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.28762e13 | + | 2.80270e14i | −0.196844 | + | 0.665686i | ||||
\(457\) | 3.40714e13 | − | 3.40714e13i | 0.0799561 | − | 0.0799561i | −0.665998 | − | 0.745954i | \(-0.731994\pi\) |
0.745954 | + | 0.665998i | \(0.231994\pi\) | |||||||
\(458\) | −1.71520e14 | + | 1.71520e14i | −0.397698 | + | 0.397698i | ||||
\(459\) | 1.91840e14 | + | 2.23975e14i | 0.439512 | + | 0.513134i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.31120e14i | − | 1.85913i | −0.368663 | − | 0.929563i | \(-0.620184\pi\) | ||
0.368663 | − | 0.929563i | \(-0.379816\pi\) | |||||||
\(462\) | −7.14972e13 | + | 3.88634e13i | −0.158037 | + | 0.0859033i | ||||
\(463\) | 5.49396e14 | + | 5.49396e14i | 1.20002 | + | 1.20002i | 0.974159 | + | 0.225865i | \(0.0725208\pi\) |
0.225865 | + | 0.974159i | \(0.427479\pi\) | |||||||
\(464\) | 7.66540e14 | 1.65457 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.05885e14 | −0.434012 | ||||||||
\(467\) | −1.39727e14 | − | 1.39727e14i | −0.291097 | − | 0.291097i | 0.546416 | − | 0.837514i | \(-0.315992\pi\) |
−0.837514 | + | 0.546416i | \(0.815992\pi\) | |||||||
\(468\) | 2.52037e13 | + | 1.18028e14i | 0.0518933 | + | 0.243014i | ||||
\(469\) | 3.08354e14i | 0.627479i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.80709e13 | − | 2.89997e13i | −0.194951 | − | 0.0576473i | ||||
\(472\) | −3.12080e14 | + | 3.12080e14i | −0.613175 | + | 0.613175i | ||||
\(473\) | −3.50187e12 | + | 3.50187e12i | −0.00680086 | + | 0.00680086i | ||||
\(474\) | 5.12740e14 | + | 1.51618e14i | 0.984274 | + | 0.291052i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.97885e14i | 0.371172i | ||||||||
\(477\) | −2.41817e13 | − | 1.13242e14i | −0.0448369 | − | 0.209969i | ||||
\(478\) | 7.00673e14 | + | 7.00673e14i | 1.28429 | + | 1.28429i | ||||
\(479\) | 4.58603e14 | 0.830981 | 0.415491 | − | 0.909597i | \(-0.363610\pi\) | ||||
0.415491 | + | 0.909597i | \(0.363610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.31521e14 | −0.764194 | ||||||||
\(482\) | −8.02088e14 | − | 8.02088e14i | −1.40431 | − | 1.40431i | ||||
\(483\) | −4.34410e14 | + | 2.36130e14i | −0.751954 | + | 0.408736i | ||||
\(484\) | 2.15341e14i | 0.368534i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.94065e14 | − | 9.30369e13i | 1.16118 | − | 0.155652i | ||||
\(487\) | −3.32018e14 | + | 3.32018e14i | −0.549228 | + | 0.549228i | −0.926217 | − | 0.376990i | \(-0.876959\pi\) |
0.376990 | + | 0.926217i | \(0.376959\pi\) | |||||||
\(488\) | 3.21915e14 | − | 3.21915e14i | 0.526541 | − | 0.526541i | ||||
\(489\) | −1.97603e14 | + | 6.68252e14i | −0.319592 | + | 1.08079i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.44188e14i | − | 1.01874i | −0.860547 | − | 0.509372i | \(-0.829878\pi\) | ||
0.860547 | − | 0.509372i | \(-0.170122\pi\) | |||||||
\(492\) | 2.02803e14 | + | 3.73099e14i | 0.317152 | + | 0.583466i | ||||
\(493\) | 4.14292e14 | + | 4.14292e14i | 0.640691 | + | 0.640691i | ||||
\(494\) | −4.82514e14 | −0.737924 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.35485e15 | 2.02648 | ||||||||
\(497\) | −3.58480e14 | − | 3.58480e14i | −0.530279 | − | 0.530279i | ||||
\(498\) | −3.14635e14 | − | 5.78835e14i | −0.460304 | − | 0.846825i | ||||
\(499\) | − | 3.35306e14i | − | 0.485164i | −0.970131 | − | 0.242582i | \(-0.922006\pi\) | ||
0.970131 | − | 0.242582i | \(-0.0779944\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.59250e14 | − | 8.76729e14i | 0.366954 | − | 1.24096i | ||||
\(502\) | −1.36314e14 | + | 1.36314e14i | −0.190841 | + | 0.190841i | ||||
\(503\) | 4.24232e14 | − | 4.24232e14i | 0.587461 | − | 0.587461i | −0.349482 | − | 0.936943i | \(-0.613642\pi\) |
0.936943 | + | 0.349482i | \(0.113642\pi\) | |||||||
\(504\) | −6.64063e14 | − | 4.30360e14i | −0.909581 | − | 0.589473i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 5.28316e13i | − | 0.0708053i | ||||||
\(507\) | −3.67916e14 | + | 1.99986e14i | −0.487759 | + | 0.265129i | ||||
\(508\) | −1.73565e14 | − | 1.73565e14i | −0.227621 | − | 0.227621i | ||||
\(509\) | 1.01770e14 | 0.132030 | 0.0660149 | − | 0.997819i | \(-0.478971\pi\) | ||||
0.0660149 | + | 0.997819i | \(0.478971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.75296e14 | −0.222565 | ||||||||
\(512\) | 1.71611e13 | + | 1.71611e13i | 0.0215556 | + | 0.0215556i | ||||
\(513\) | −5.85559e13 | + | 7.57694e14i | −0.0727654 | + | 0.941560i | ||||
\(514\) | 1.46266e15i | 1.79823i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.74229e13 | + | 8.10900e12i | 0.0330020 | + | 0.00975874i | ||||
\(517\) | −7.72106e13 | + | 7.72106e13i | −0.0919346 | + | 0.0919346i | ||||
\(518\) | −1.18802e15 | + | 1.18802e15i | −1.39961 | + | 1.39961i | ||||
\(519\) | −3.92150e14 | − | 1.15959e14i | −0.457121 | − | 0.135172i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.19954e15i | 1.36901i | 0.729008 | + | 0.684505i | \(0.239981\pi\) | ||||
−0.729008 | + | 0.684505i | \(0.760019\pi\) | |||||||
\(522\) | 1.36059e15 | − | 2.90541e14i | 1.53652 | − | 0.328110i | ||||
\(523\) | −1.65527e14 | − | 1.65527e14i | −0.184973 | − | 0.184973i | 0.608546 | − | 0.793519i | \(-0.291753\pi\) |
−0.793519 | + | 0.608546i | \(0.791753\pi\) | |||||||
\(524\) | −4.97822e14 | −0.550493 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.78012e14 | −0.409340 | ||||||||
\(527\) | 7.32255e14 | + | 7.32255e14i | 0.784700 | + | 0.784700i | ||||
\(528\) | 1.06428e14 | − | 5.78503e13i | 0.112867 | − | 0.0613506i | ||||
\(529\) | 6.31810e14i | 0.663102i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.24120e14 | + | 9.63043e14i | −0.641576 | + | 0.989978i | ||||
\(532\) | −3.60584e14 | + | 3.60584e14i | −0.366854 | + | 0.366854i | ||||
\(533\) | 8.34839e14 | − | 8.34839e14i | 0.840627 | − | 0.840627i | ||||
\(534\) | 1.11338e14 | − | 3.76522e14i | 0.110960 | − | 0.375244i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3.20392e14i | − | 0.312806i | ||||||
\(537\) | 2.63785e14 | + | 4.85288e14i | 0.254913 | + | 0.468965i | ||||
\(538\) | −3.05611e14 | − | 3.05611e14i | −0.292325 | − | 0.292325i | ||||
\(539\) | 1.29135e14 | 0.122266 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.90173e14 | −0.454742 | −0.227371 | − | 0.973808i | \(-0.573013\pi\) | ||||
−0.227371 | + | 0.973808i | \(0.573013\pi\) | |||||||
\(542\) | −4.75425e14 | − | 4.75425e14i | −0.436602 | − | 0.436602i | ||||
\(543\) | −4.08448e14 | − | 7.51425e14i | −0.371311 | − | 0.683104i | ||||
\(544\) | − | 5.33316e14i | − | 0.479944i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.70455e14 | − | 1.25280e15i | 0.326720 | − | 1.10490i | ||||
\(547\) | −7.74424e14 | + | 7.74424e14i | −0.676159 | + | 0.676159i | −0.959129 | − | 0.282970i | \(-0.908680\pi\) |
0.282970 | + | 0.959129i | \(0.408680\pi\) | |||||||
\(548\) | 4.88313e14 | − | 4.88313e14i | 0.422090 | − | 0.422090i | ||||
\(549\) | 6.43789e14 | − | 9.93393e14i | 0.550929 | − | 0.850106i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.50983e15i | 1.26647i | ||||||||
\(552\) | 4.51370e14 | − | 2.45349e14i | 0.374859 | − | 0.203760i | ||||
\(553\) | −1.11091e15 | − | 1.11091e15i | −0.913461 | − | 0.913461i | ||||
\(554\) | 7.58186e14 | 0.617266 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.25971e14 | −0.579440 | ||||||||
\(557\) | 1.65220e15 | + | 1.65220e15i | 1.30575 | + | 1.30575i | 0.924454 | + | 0.381293i | \(0.124521\pi\) |
0.381293 | + | 0.924454i | \(0.375479\pi\) | |||||||
\(558\) | 2.40482e15 | − | 5.13526e14i | 1.88189 | − | 0.401860i | ||||
\(559\) | − | 7.95056e13i | − | 0.0616074i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.87873e13 | + | 2.62546e13i | 0.0674614 | + | 0.0199485i | ||||
\(562\) | 4.82715e14 | − | 4.82715e14i | 0.363196 | − | 0.363196i | ||||
\(563\) | −1.34187e15 | + | 1.34187e15i | −0.999803 | + | 0.999803i | −1.00000 | 0.000197220i | \(-0.999937\pi\) | |
0.000197220 | 1.00000i | \(0.499937\pi\) | ||||||||
\(564\) | 6.04631e14 | + | 1.78790e14i | 0.446124 | + | 0.131920i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 7.98319e14i | − | 0.577678i | ||||||
\(567\) | −1.92232e15 | − | 7.33762e14i | −1.37759 | − | 0.525834i | ||||
\(568\) | 3.72474e14 | + | 3.72474e14i | 0.264351 | + | 0.264351i | ||||
\(569\) | 7.18460e14 | 0.504993 | 0.252496 | − | 0.967598i | \(-0.418748\pi\) | ||||
0.252496 | + | 0.967598i | \(0.418748\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.57104e14 | −0.246205 | −0.123102 | − | 0.992394i | \(-0.539284\pi\) | ||||
−0.123102 | + | 0.992394i | \(0.539284\pi\) | |||||||
\(572\) | 2.67933e13 | + | 2.67933e13i | 0.0182957 | + | 0.0182957i | ||||
\(573\) | −4.51237e14 | + | 2.45277e14i | −0.305179 | + | 0.165885i | ||||
\(574\) | − | 4.59678e15i | − | 3.07920i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.12730e14 | + | 3.32285e14i | 0.336950 | + | 0.218367i | ||||
\(577\) | 1.43625e15 | − | 1.43625e15i | 0.934899 | − | 0.934899i | −0.0631080 | − | 0.998007i | \(-0.520101\pi\) |
0.998007 | + | 0.0631080i | \(0.0201013\pi\) | |||||||
\(578\) | −6.98352e14 | + | 6.98352e14i | −0.450268 | + | 0.450268i | ||||
\(579\) | −2.06856e14 | + | 6.99544e14i | −0.132110 | + | 0.446769i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.93580e15i | 1.21309i | ||||||||
\(582\) | −6.97967e14 | − | 1.28405e15i | −0.433270 | − | 0.797089i | ||||
\(583\) | −2.57068e13 | − | 2.57068e13i | −0.0158078 | − | 0.0158078i | ||||
\(584\) | 1.82139e14 | 0.110951 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.83429e15 | 1.09656 | ||||||||
\(587\) | 8.41064e14 | + | 8.41064e14i | 0.498103 | + | 0.498103i | 0.910847 | − | 0.412744i | \(-0.135430\pi\) |
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(588\) | −3.56111e14 | − | 6.55140e14i | −0.208934 | − | 0.384378i | ||||
\(589\) | 2.66861e15i | 1.55114i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.42435e14 | + | 8.19863e14i | −0.138313 | + | 0.467746i | ||||
\(592\) | 1.76843e15 | − | 1.76843e15i | 0.999581 | − | 0.999581i | ||||
\(593\) | 2.40054e14 | − | 2.40054e14i | 0.134434 | − | 0.134434i | −0.636688 | − | 0.771122i | \(-0.719696\pi\) |
0.771122 | + | 0.636688i | \(0.219696\pi\) | |||||||
\(594\) | 1.66979e14 | − | 1.43022e14i | 0.0926483 | − | 0.0793556i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.70775e14i | 0.310893i | ||||||||
\(597\) | −5.33230e14 | + | 2.89845e14i | −0.287777 | + | 0.156425i | ||||
\(598\) | 5.99737e14 | + | 5.99737e14i | 0.320704 | + | 0.320704i | ||||
\(599\) | −7.78763e14 | −0.412627 | −0.206314 | − | 0.978486i | \(-0.566147\pi\) | ||||
−0.206314 | + | 0.978486i | \(0.566147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50292e14 | −0.442342 | −0.221171 | − | 0.975235i | \(-0.570988\pi\) | ||||
−0.221171 | + | 0.975235i | \(0.570988\pi\) | |||||||
\(602\) | −2.18886e14 | − | 2.18886e14i | −0.112833 | − | 0.112833i | ||||
\(603\) | −1.73975e14 | − | 8.14718e14i | −0.0888673 | − | 0.416162i | ||||
\(604\) | 3.27067e14i | 0.165552i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.91636e15 | − | 8.62374e14i | −1.44958 | − | 0.428643i | ||||
\(607\) | 1.93561e15 | − | 1.93561e15i | 0.953409 | − | 0.953409i | −0.0455530 | − | 0.998962i | \(-0.514505\pi\) |
0.998962 | + | 0.0455530i | \(0.0145050\pi\) | |||||||
\(608\) | 9.71801e14 | − | 9.71801e14i | 0.474360 | − | 0.474360i | ||||
\(609\) | −3.92014e15 | − | 1.15919e15i | −1.89630 | − | 0.560738i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.75297e15i | − | 0.832814i | ||||||
\(612\) | −1.11648e14 | − | 5.22843e14i | −0.0525676 | − | 0.246172i | ||||
\(613\) | 2.12061e14 | + | 2.12061e14i | 0.0989527 | + | 0.0989527i | 0.754850 | − | 0.655897i | \(-0.227710\pi\) |
−0.655897 | + | 0.754850i | \(0.727710\pi\) | |||||||
\(614\) | −1.73628e15 | −0.802961 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.48443e14 | −0.112858 | ||||||||
\(617\) | −1.80161e15 | − | 1.80161e15i | −0.811134 | − | 0.811134i | 0.173670 | − | 0.984804i | \(-0.444437\pi\) |
−0.984804 | + | 0.173670i | \(0.944437\pi\) | |||||||
\(618\) | −1.16230e14 | + | 6.31783e13i | −0.0518656 | + | 0.0281924i | ||||
\(619\) | − | 2.75526e15i | − | 1.21861i | −0.792937 | − | 0.609303i | \(-0.791449\pi\) | ||
0.792937 | − | 0.609303i | \(-0.208551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.01455e15 | − | 8.68989e14i | 0.440829 | − | 0.377581i | ||||
\(622\) | −1.10715e15 | + | 1.10715e15i | −0.476825 | + | 0.476825i | ||||
\(623\) | −8.15778e14 | + | 8.15778e14i | −0.348247 | + | 0.348247i | ||||
\(624\) | −5.51443e14 | + | 1.86486e15i | −0.233338 | + | 0.789099i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 2.41338e15i | − | 1.00338i | ||||||
\(627\) | 1.13946e14 | + | 2.09628e14i | 0.0469601 | + | 0.0863928i | ||||
\(628\) | 1.31100e14 | + | 1.31100e14i | 0.0535581 | + | 0.0535581i | ||||
\(629\) | 1.91156e15 | 0.774124 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.08725e13 | −0.0282043 | −0.0141022 | − | 0.999901i | \(-0.504489\pi\) | ||||
−0.0141022 | + | 0.999901i | \(0.504489\pi\) | |||||||
\(632\) | 1.15428e15 | + | 1.15428e15i | 0.455372 | + | 0.455372i | ||||
\(633\) | 6.46457e14 | + | 1.18929e15i | 0.252824 | + | 0.465123i | ||||
\(634\) | − | 2.77892e15i | − | 1.07742i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.95273e13 | + | 2.01308e14i | −0.0226831 | + | 0.0767093i | ||||
\(637\) | −1.46593e15 | + | 1.46593e15i | −0.553791 | + | 0.553791i | ||||
\(638\) | 3.08866e14 | − | 3.08866e14i | 0.115679 | − | 0.115679i | ||||
\(639\) | 1.14941e15 | + | 7.44901e14i | 0.426797 | + | 0.276595i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.19967e14i | − | 0.153284i | −0.997059 | − | 0.0766418i | \(-0.975580\pi\) | ||
0.997059 | − | 0.0766418i | \(-0.0244198\pi\) | |||||||
\(642\) | −3.18466e15 | + | 1.73107e15i | −1.15245 | + | 0.626430i | ||||
\(643\) | −1.15949e15 | − | 1.15949e15i | −0.416013 | − | 0.416013i | 0.467814 | − | 0.883827i | \(-0.345042\pi\) |
−0.883827 | + | 0.467814i | \(0.845042\pi\) | |||||||
\(644\) | 8.96372e14 | 0.318872 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.13746e15 | 0.747512 | ||||||||
\(647\) | 3.26531e14 | + | 3.26531e14i | 0.113227 | + | 0.113227i | 0.761450 | − | 0.648223i | \(-0.224488\pi\) |
−0.648223 | + | 0.761450i | \(0.724488\pi\) | |||||||
\(648\) | 1.99737e15 | + | 7.62407e14i | 0.686744 | + | 0.262135i | ||||
\(649\) | 3.60299e14i | 0.122834i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.92878e15 | − | 2.04885e15i | −2.32253 | − | 0.686776i | ||||
\(652\) | 8.93312e14 | − | 8.93312e14i | 0.296921 | − | 0.296921i | ||||
\(653\) | −3.10191e15 | + | 3.10191e15i | −1.02237 | + | 1.02237i | −0.0226233 | + | 0.999744i | \(0.507202\pi\) |
−0.999744 | + | 0.0226233i | \(0.992798\pi\) | |||||||
\(654\) | 1.51102e15 | + | 4.46810e14i | 0.493846 | + | 0.146031i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.84256e15i | 2.19911i | ||||||||
\(657\) | 4.63157e14 | − | 9.89027e13i | 0.147611 | − | 0.0315209i | ||||
\(658\) | −4.82609e15 | − | 4.82609e15i | −1.52529 | − | 1.52529i | ||||
\(659\) | −3.56536e15 | −1.11747 | −0.558733 | − | 0.829348i | \(-0.688712\pi\) | ||||
−0.558733 | + | 0.829348i | \(0.688712\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.39665e15 | −0.430507 | −0.215254 | − | 0.976558i | \(-0.569058\pi\) | ||||
−0.215254 | + | 0.976558i | \(0.569058\pi\) | |||||||
\(662\) | −3.47489e15 | − | 3.47489e15i | −1.06224 | − | 1.06224i | ||||
\(663\) | −1.30594e15 | + | 7.09864e14i | −0.395912 | + | 0.215204i | ||||
\(664\) | − | 2.01138e15i | − | 0.604740i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.46863e15 | − | 3.80920e15i | 0.730042 | − | 1.12649i | ||||
\(667\) | 1.87664e15 | − | 1.87664e15i | 0.550413 | − | 0.550413i | ||||
\(668\) | −1.17200e15 | + | 1.17200e15i | −0.340924 | + | 0.340924i | ||||
\(669\) | −1.56150e14 | + | 5.28064e14i | −0.0450502 | + | 0.152350i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.71654e14i | − | 0.105479i | ||||||
\(672\) | 1.77707e15 | + | 3.26930e15i | 0.500236 | + | 0.920287i | ||||
\(673\) | −1.04662e15 | − | 1.04662e15i | −0.292216 | − | 0.292216i | 0.545739 | − | 0.837955i | \(-0.316249\pi\) |
−0.837955 | + | 0.545739i | \(0.816249\pi\) | |||||||
\(674\) | 2.25264e15 | 0.623825 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.59166e14 | 0.206838 | ||||||||
\(677\) | −2.97438e15 | − | 2.97438e15i | −0.803820 | − | 0.803820i | 0.179871 | − | 0.983690i | \(-0.442432\pi\) |
−0.983690 | + | 0.179871i | \(0.942432\pi\) | |||||||
\(678\) | 2.83184e15 | + | 5.20976e15i | 0.759112 | + | 1.39654i | ||||
\(679\) | 4.29427e15i | 1.14184i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.61054e14 | + | 2.57372e15i | −0.199116 | + | 0.673368i | ||||
\(682\) | 5.45915e14 | − | 5.45915e14i | 0.141681 | − | 0.141681i | ||||
\(683\) | −8.63475e14 | + | 8.63475e14i | −0.222298 | + | 0.222298i | −0.809466 | − | 0.587167i | \(-0.800243\pi\) |
0.587167 | + | 0.809466i | \(0.300243\pi\) | |||||||
\(684\) | 7.49275e14 | − | 1.15616e15i | 0.191352 | − | 0.295264i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.19775e15i | 0.301011i | ||||||||
\(687\) | −1.69180e15 | + | 9.19606e14i | −0.421782 | + | 0.229266i | ||||
\(688\) | 3.25824e14 | + | 3.25824e14i | 0.0805836 | + | 0.0805836i | ||||
\(689\) | 5.83642e14 | 0.143199 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.92420e15 | 1.67201 | 0.836007 | − | 0.548718i | \(-0.184884\pi\) | ||||
0.836007 | + | 0.548718i | \(0.184884\pi\) | |||||||
\(692\) | 5.24221e14 | + | 5.24221e14i | 0.125583 | + | 0.125583i | ||||
\(693\) | −6.31761e14 | + | 1.34906e14i | −0.150148 | + | 0.0320627i | ||||
\(694\) | 2.13348e15i | 0.503051i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.07318e15 | + | 1.20445e15i | 0.945328 | + | 0.279535i | ||||
\(697\) | −3.69820e15 | + | 3.69820e15i | −0.851550 | + | 0.851550i | ||||
\(698\) | 6.69172e15 | − | 6.69172e15i | 1.52874 | − | 1.52874i | ||||
\(699\) | −1.56731e15 | − | 4.63458e14i | −0.355248 | − | 0.105047i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.35981e15i | − | 1.19591i | −0.801528 | − | 0.597957i | \(-0.795979\pi\) | ||
0.801528 | − | 0.597957i | \(-0.204021\pi\) | |||||||
\(702\) | −2.71962e14 | + | 3.51910e15i | −0.0602080 | + | 0.779071i | ||||
\(703\) | 3.48323e15 | + | 3.48323e15i | 0.765117 | + | 0.765117i | ||||
\(704\) | 1.91826e14 | 0.0418078 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.11600e14 | −0.152690 | ||||||||
\(707\) | 6.31863e15 | + | 6.31863e15i | 1.34529 | + | 1.34529i | ||||
\(708\) | 1.82790e15 | − | 9.93581e14i | 0.386161 | − | 0.209904i | ||||
\(709\) | 2.97820e15i | 0.624310i | 0.950031 | + | 0.312155i | \(0.101051\pi\) | ||||
−0.950031 | + | 0.312155i | \(0.898949\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.56197e15 | + | 2.30841e15i | 0.735203 | + | 0.476464i | ||||
\(712\) | 8.47625e14 | − | 8.47625e14i | 0.173606 | − | 0.173606i | ||||
\(713\) | 3.31693e15 | − | 3.31693e15i | 0.674131 | − | 0.674131i | ||||
\(714\) | −1.64105e15 | + | 5.54969e15i | −0.330966 | + | 1.11925i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1.00135e15i | − | 0.198868i | ||||||
\(717\) | 3.75667e15 | + | 6.91117e15i | 0.740369 | + | 1.36206i | ||||
\(718\) | 2.91919e15 | + | 2.91919e15i | 0.570923 | + | 0.570923i | ||||
\(719\) | 5.08231e15 | 0.986398 | 0.493199 | − | 0.869916i | \(-0.335827\pi\) | ||||
0.493199 | + | 0.869916i | \(0.335827\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.88707e14 | 0.0742983 | ||||||||
\(722\) | −4.72401e14 | − | 4.72401e14i | −0.0896099 | − | 0.0896099i | ||||
\(723\) | −4.30041e15 | − | 7.91149e15i | −0.809561 | − | 1.48935i | ||||
\(724\) | 1.55051e15i | 0.289675i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.78582e15 | + | 6.03924e15i | −0.328613 | + | 1.11130i | ||||
\(727\) | 5.23725e15 | − | 5.23725e15i | 0.956454 | − | 0.956454i | −0.0426365 | − | 0.999091i | \(-0.513576\pi\) |
0.999091 | + | 0.0426365i | \(0.0135757\pi\) | |||||||
\(728\) | 2.82030e15 | − | 2.82030e15i | 0.511178 | − | 0.511178i | ||||
\(729\) | 5.49305e15 | + | 8.54126e14i | 0.988126 | + | 0.153646i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.52196e14i | 0.0624079i | ||||||||
\(732\) | −1.88550e15 | + | 1.02489e15i | −0.331601 | + | 0.180247i | ||||
\(733\) | 1.65063e15 | + | 1.65063e15i | 0.288123 | + | 0.288123i | 0.836337 | − | 0.548215i | \(-0.184692\pi\) |
−0.548215 | + | 0.836337i | \(0.684692\pi\) | |||||||
\(734\) | −1.11956e16 | −1.93963 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.41579e15 | −0.412317 | ||||||||
\(737\) | −1.84948e14 | − | 1.84948e14i | −0.0313313 | − | 0.0313313i | ||||
\(738\) | 2.59353e15 | + | 1.21454e16i | 0.436095 | + | 2.04221i | ||||
\(739\) | − | 1.89093e14i | − | 0.0315596i | −0.999875 | − | 0.0157798i | \(-0.994977\pi\) | ||
0.999875 | − | 0.0157798i | \(-0.00502308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.67317e15 | − | 1.08616e15i | −0.604006 | − | 0.178606i | ||||
\(742\) | 1.60682e15 | − | 1.60682e15i | 0.262268 | − | 0.262268i | ||||
\(743\) | 6.46972e15 | − | 6.46972e15i | 1.04821 | − | 1.04821i | 0.0494294 | − | 0.998778i | \(-0.484260\pi\) |
0.998778 | − | 0.0494294i | \(-0.0157403\pi\) | |||||||
\(744\) | 7.19928e15 | + | 2.12884e15i | 1.15781 | + | 0.342367i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 1.29597e16i | − | 2.05368i | ||||||
\(747\) | −1.09219e15 | − | 5.11469e15i | −0.171805 | − | 0.804555i | ||||
\(748\) | −1.18690e14 | − | 1.18690e14i | −0.0185334 | − | 0.0185334i | ||||
\(749\) | 1.06505e16 | 1.65090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.99169e15 | 0.762479 | 0.381239 | − | 0.924476i | \(-0.375497\pi\) | ||||
0.381239 | + | 0.924476i | \(0.375497\pi\) | |||||||
\(752\) | 7.18390e15 | + | 7.18390e15i | 1.08934 | + | 1.08934i | ||||
\(753\) | −1.34455e15 | + | 7.30852e14i | −0.202398 | + | 0.110016i | ||||
\(754\) | 7.01240e15i | 1.04791i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.42660e15 | + | 2.83307e15i | 0.357378 | + | 0.417242i | ||||
\(757\) | −2.11962e15 | + | 2.11962e15i | −0.309907 | + | 0.309907i | −0.844873 | − | 0.534967i | \(-0.820324\pi\) |
0.534967 | + | 0.844873i | \(0.320324\pi\) | |||||||
\(758\) | −9.59446e15 | + | 9.59446e15i | −1.39264 | + | 1.39264i | ||||
\(759\) | 1.18927e14 | − | 4.02184e14i | 0.0171376 | − | 0.0579556i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.13233e15i | 1.29708i | 0.761182 | + | 0.648539i | \(0.224620\pi\) | ||||
−0.761182 | + | 0.648539i | \(0.775380\pi\) | |||||||
\(762\) | −3.42826e15 | − | 6.30699e15i | −0.483416 | − | 0.889344i | ||||
\(763\) | −3.27379e15 | − | 3.27379e15i | −0.458317 | − | 0.458317i | ||||
\(764\) | 9.31092e14 | 0.129413 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.17653e16 | 1.61192 | ||||||||
\(767\) | −4.09007e15 | − | 4.09007e15i | −0.556361 | − | 0.556361i | ||||
\(768\) | −3.47189e15 | − | 6.38725e15i | −0.468898 | − | 0.862635i | ||||
\(769\) | − | 8.83397e15i | − | 1.18457i | −0.805728 | − | 0.592285i | \(-0.798226\pi\) | ||
0.805728 | − | 0.592285i | \(-0.201774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.29251e15 | + | 1.11346e16i | −0.435240 | + | 1.47189i | ||||
\(772\) | 9.35142e14 | − | 9.35142e14i | 0.122739 | − | 0.122739i | ||||
\(773\) | −5.04041e15 | + | 5.04041e15i | −0.656869 | + | 0.656869i | −0.954638 | − | 0.297769i | \(-0.903758\pi\) |
0.297769 | + | 0.954638i | \(0.403758\pi\) | |||||||
\(774\) | 7.01827e14 | + | 4.54833e14i | 0.0908144 | + | 0.0588541i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 4.46192e15i | − | 0.569222i | ||||||
\(777\) | −1.17181e16 | + | 6.36957e15i | −1.48437 | + | 0.806853i | ||||
\(778\) | −3.98951e15 | − | 3.98951e15i | −0.501802 | − | 0.501802i | ||||
\(779\) | −1.34776e16 | −1.68328 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.30026e14 | 0.0529558 | ||||||||
\(782\) | −2.65674e15 | − | 2.65674e15i | −0.324871 | − | 0.324871i | ||||
\(783\) | 1.10116e16 | + | 8.50997e14i | 1.33709 | + | 0.103333i | ||||
\(784\) | − | 1.20151e16i | − | 1.44874i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.39614e16 | − | 4.12841e15i | −1.65999 | − | 0.490861i | ||||
\(787\) | −2.36821e15 | + | 2.36821e15i | −0.279614 | + | 0.279614i | −0.832955 | − | 0.553341i | \(-0.813353\pi\) |
0.553341 | + | 0.832955i | \(0.313353\pi\) | |||||||
\(788\) | 1.09598e15 | − | 1.09598e15i | 0.128502 | − | 0.128502i | ||||
\(789\) | −2.87764e15 | − | 8.50925e14i | −0.335053 | − | 0.0990758i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.74230e16i | − | 2.00057i | ||||||
\(792\) | 6.56425e14 | − | 1.40173e14i | 0.0748508 | − | 0.0159837i | ||||
\(793\) | 4.21897e15 | + | 4.21897e15i | 0.477754 | + | 0.477754i | ||||
\(794\) | −3.50334e15 | −0.393975 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.10028e15 | 0.122034 | ||||||||
\(797\) | −8.64980e15 | − | 8.64980e15i | −0.952764 | − | 0.952764i | 0.0461696 | − | 0.998934i | \(-0.485299\pi\) |
−0.998934 | + | 0.0461696i | \(0.985299\pi\) | |||||||
\(798\) | −1.31029e16 | + | 7.12227e15i | −1.43335 | + | 0.779116i | ||||
\(799\) | 7.76537e15i | 0.843635i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.69514e15 | − | 2.61567e15i | 0.181647 | − | 0.280288i | ||||
\(802\) | −4.36157e15 | + | 4.36157e15i | −0.464177 | + | 0.464177i | ||||
\(803\) | 1.05141e14 | − | 1.05141e14i | 0.0111131 | − | 0.0111131i | ||||
\(804\) | −4.28269e14 | + | 1.44831e15i | −0.0449582 | + | 0.152039i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.23943e16i | 1.28345i | ||||||||
\(807\) | −1.63854e15 | − | 3.01443e15i | −0.168520 | − | 0.310028i | ||||
\(808\) | −6.56530e15 | − | 6.56530e15i | −0.670645 | − | 0.670645i | ||||
\(809\) | −3.82178e15 | −0.387747 | −0.193874 | − | 0.981027i | \(-0.562105\pi\) | ||||
−0.193874 | + | 0.981027i | \(0.562105\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.93944e16 | −1.94116 | −0.970581 | − | 0.240776i | \(-0.922598\pi\) | ||||
−0.970581 | + | 0.240776i | \(0.922598\pi\) | |||||||
\(812\) | 5.24040e15 | + | 5.24040e15i | 0.520962 | + | 0.520962i | ||||
\(813\) | −2.54900e15 | − | 4.68941e15i | −0.251693 | − | 0.463042i | ||||
\(814\) | − | 1.42512e15i | − | 0.139771i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.44280e15 | − | 8.26103e15i | 0.236370 | − | 0.799352i | ||||
\(817\) | −6.41768e14 | + | 6.41768e14i | −0.0616817 | + | 0.0616817i | ||||
\(818\) | −4.94161e15 | + | 4.94161e15i | −0.471764 | + | 0.471764i | ||||
\(819\) | 5.64023e15 | − | 8.70311e15i | 0.534854 | − | 0.825302i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.91983e15i | 0.647453i | 0.946151 | + | 0.323727i | \(0.104936\pi\) | ||||
−0.946151 | + | 0.323727i | \(0.895064\pi\) | |||||||
\(822\) | 1.77443e16 | − | 9.64517e15i | 1.64916 | − | 0.896427i | ||||
\(823\) | 9.24390e15 | + | 9.24390e15i | 0.853407 | + | 0.853407i | 0.990551 | − | 0.137144i | \(-0.0437923\pi\) |
−0.137144 | + | 0.990551i | \(0.543792\pi\) | |||||||
\(824\) | −4.03882e14 | −0.0370386 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.25207e16 | −2.03794 | ||||||||
\(827\) | 1.10814e14 | + | 1.10814e14i | 0.00996130 | + | 0.00996130i | 0.712070 | − | 0.702109i | \(-0.247758\pi\) |
−0.702109 | + | 0.712070i | \(0.747758\pi\) | |||||||
\(828\) | −2.36835e15 | + | 5.05738e14i | −0.211485 | + | 0.0451605i | ||||
\(829\) | − | 6.85619e14i | − | 0.0608181i | −0.999538 | − | 0.0304091i | \(-0.990319\pi\) | ||
0.999538 | − | 0.0304091i | \(-0.00968100\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.77175e15 | + | 1.70672e15i | 0.505245 | + | 0.149402i | ||||
\(832\) | −2.17758e15 | + | 2.17758e15i | −0.189363 | + | 0.189363i | ||||
\(833\) | 6.49382e15 | − | 6.49382e15i | 0.560987 | − | 0.560987i | ||||
\(834\) | −2.03598e16 | − | 6.02044e15i | −1.74727 | − | 0.516672i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 4.32550e14i | − | 0.0366355i | ||||||
\(837\) | 1.94629e16 | + | 1.50412e15i | 1.63763 | + | 0.126559i | ||||
\(838\) | −9.06108e15 | − | 9.06108e15i | −0.757422 | − | 0.757422i | ||||
\(839\) | −9.59629e15 | −0.796916 | −0.398458 | − | 0.917187i | \(-0.630454\pi\) | ||||
−0.398458 | + | 0.917187i | \(0.630454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.74202e15 | 0.798493 | ||||||||
\(842\) | −4.32751e15 | − | 4.32751e15i | −0.352388 | − | 0.352388i | ||||
\(843\) | 4.76132e15 | − | 2.58809e15i | 0.385191 | − | 0.209376i | ||||
\(844\) | − | 2.45401e15i | − | 0.197239i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.54742e16 | + | 1.00283e16i | 1.22764 | + | 0.795595i | ||||
\(847\) | 1.30847e16 | − | 1.30847e16i | 1.03135 | − | 1.03135i | ||||
\(848\) | −2.39184e15 | + | 2.39184e15i | −0.187307 | + | 0.187307i | ||||
\(849\) | 1.79706e15 | − | 6.07726e15i | 0.139820 | − | 0.472842i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.65891e15i | − | 0.665044i | ||||||
\(852\) | −1.18586e15 | − | 2.18164e15i | −0.0904933 | − | 0.166481i | ||||
\(853\) | −5.31904e15 | − | 5.31904e15i | −0.403286 | − | 0.403286i | 0.476103 | − | 0.879389i | \(-0.342049\pi\) |
−0.879389 | + | 0.476103i | \(0.842049\pi\) | |||||||
\(854\) | 2.32304e16 | 1.75000 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.10663e16 | −0.822993 | ||||||||
\(857\) | −9.41959e15 | − | 9.41959e15i | −0.696045 | − | 0.696045i | 0.267510 | − | 0.963555i | \(-0.413799\pi\) |
−0.963555 | + | 0.267510i | \(0.913799\pi\) | |||||||
\(858\) | 5.29222e14 | + | 9.73613e14i | 0.0388560 | + | 0.0714836i | ||||
\(859\) | − | 1.25705e16i | − | 0.917045i | −0.888683 | − | 0.458523i | \(-0.848379\pi\) | ||
0.888683 | − | 0.458523i | \(-0.151621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.03476e16 | − | 3.49933e16i | 0.745284 | − | 2.52039i | ||||
\(862\) | −8.44539e15 | + | 8.44539e15i | −0.604407 | + | 0.604407i | ||||
\(863\) | 3.67056e14 | − | 3.67056e14i | 0.0261019 | − | 0.0261019i | −0.693935 | − | 0.720037i | \(-0.744125\pi\) |
0.720037 | + | 0.693935i | \(0.244125\pi\) | |||||||
\(864\) | −6.53985e15 | − | 7.63534e15i | −0.462107 | − | 0.539514i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.25295e16i | 0.874148i | ||||||||
\(867\) | −6.88828e15 | + | 3.74423e15i | −0.477536 | + | 0.259572i | ||||
\(868\) | 9.26232e15 | + | 9.26232e15i | 0.638060 | + | 0.638060i | ||||
\(869\) | 1.33263e15 | 0.0912220 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.19901e15 | 0.283823 | ||||||||
\(872\) | 3.40160e15 | + | 3.40160e15i | 0.228477 | + | 0.228477i | ||||
\(873\) | −2.42285e15 | − | 1.13461e16i | −0.161714 | − | 0.757302i | ||||
\(874\) | − | 9.68214e15i | − | 0.642182i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.23349e14 | − | 2.43466e14i | −0.0539277 | − | 0.0159465i | ||||
\(877\) | 7.08696e15 | − | 7.08696e15i | 0.461278 | − | 0.461278i | −0.437797 | − | 0.899074i | \(-0.644241\pi\) |
0.899074 | + | 0.437797i | \(0.144241\pi\) | |||||||
\(878\) | 4.13450e15 | − | 4.13450e15i | 0.267426 | − | 0.267426i | ||||
\(879\) | 1.39637e16 | + | 4.12909e15i | 0.897556 | + | 0.265409i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.86234e16i | 1.81700i | 0.417887 | + | 0.908499i | \(0.362771\pi\) | ||||
−0.417887 | + | 0.908499i | \(0.637229\pi\) | |||||||
\(882\) | −4.55408e15 | − | 2.13266e16i | −0.287292 | − | 1.34538i | ||||
\(883\) | 5.81145e15 | + | 5.81145e15i | 0.364335 | + | 0.364335i | 0.865406 | − | 0.501071i | \(-0.167061\pi\) |
−0.501071 | + | 0.865406i | \(0.667061\pi\) | |||||||
\(884\) | 2.69471e15 | 0.167890 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.59426e16 | −0.981008 | ||||||||
\(887\) | 1.32618e15 | + | 1.32618e15i | 0.0811005 | + | 0.0811005i | 0.746493 | − | 0.665393i | \(-0.231736\pi\) |
−0.665393 | + | 0.746493i | \(0.731736\pi\) | |||||||
\(888\) | 1.21756e16 | − | 6.61823e15i | 0.739979 | − | 0.402227i | ||||
\(889\) | 2.10925e16i | 1.27400i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.59309e15 | − | 7.12886e14i | 0.0950416 | − | 0.0425297i | ||||
\(892\) | 7.05910e14 | − | 7.05910e14i | 0.0418546 | − | 0.0418546i | ||||
\(893\) | −1.41499e16 | + | 1.41499e16i | −0.833819 | + | 0.833819i | ||||
\(894\) | −4.73341e15 | + | 1.60074e16i | −0.277215 | + | 0.937483i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.00965e16i | 1.74109i | ||||||||
\(897\) | 3.21550e15 | + | 5.91558e15i | 0.184880 | + | 0.340125i | ||||
\(898\) | 7.86892e15 | + | 7.86892e15i | 0.449671 | + | 0.449671i | ||||
\(899\) | 3.87831e16 | 2.20274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.58544e15 | −0.145060 | ||||||||
\(902\) | 2.75710e15 | + | 2.75710e15i | 0.153751 | + | 0.153751i | ||||
\(903\) | −1.17356e15 | − | 2.15901e15i | −0.0650464 | − | 0.119666i | ||||
\(904\) | 1.81032e16i | 0.997309i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.71235e15 | + | 9.17258e15i | −0.147618 | + | 0.499214i | ||||
\(907\) | −7.63881e15 | + | 7.63881e15i | −0.413224 | + | 0.413224i | −0.882860 | − | 0.469636i | \(-0.844385\pi\) |
0.469636 | + | 0.882860i | \(0.344385\pi\) | |||||||
\(908\) | 3.44052e15 | − | 3.44052e15i | 0.184992 | − | 0.184992i | ||||
\(909\) | −2.02598e16 | − | 1.31298e16i | −1.08276 | − | 0.701707i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.10415e16i | 0.583009i | 0.956569 | + | 0.291504i | \(0.0941558\pi\) | ||||
−0.956569 | + | 0.291504i | \(0.905844\pi\) | |||||||
\(912\) | 1.95044e16 | − | 1.06019e16i | 1.02367 | − | 0.556432i | ||||
\(913\) | −1.16108e15 | − | 1.16108e15i | −0.0605720 | − | 0.0605720i | ||||
\(914\) | −2.55469e15 | −0.132475 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.49090e15 | 0.178860 | ||||||||
\(917\) | 3.02489e16 | + | 3.02489e16i | 1.54056 | + | 1.54056i | ||||
\(918\) | 1.20475e15 | − | 1.55890e16i | 0.0609903 | − | 0.789194i | ||||
\(919\) | − | 1.55832e16i | − | 0.784192i | −0.919924 | − | 0.392096i | \(-0.871750\pi\) | ||
0.919924 | − | 0.392096i | \(-0.128250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.32176e16 | − | 3.90846e15i | −0.657240 | − | 0.194347i | ||||
\(922\) | −3.11589e16 | + | 3.11589e16i | −1.54015 | + | 1.54015i | ||||
\(923\) | −4.88160e15 | + | 4.88160e15i | −0.239857 | + | 0.239857i | ||||
\(924\) | 1.12307e15 | + | 3.32095e14i | 0.0548545 | + | 0.0162206i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 4.11939e16i | − | 1.98826i | ||||||
\(927\) | −1.02702e15 | + | 2.19311e14i | −0.0492767 | + | 0.0105226i | ||||
\(928\) | −1.41233e16 | − | 1.41233e16i | −0.673629 | − | 0.673629i | ||||
\(929\) | −3.49192e16 | −1.65569 | −0.827843 | − | 0.560961i | \(-0.810432\pi\) | ||||
−0.827843 | + | 0.560961i | \(0.810432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.36659e16 | 1.10892 | ||||||||
\(932\) | 2.09517e15 | + | 2.09517e15i | 0.0975959 | + | 0.0975959i | ||||
\(933\) | −1.09205e16 | + | 5.93601e15i | −0.505701 | + | 0.274881i | ||||
\(934\) | 1.04768e16i | 0.482304i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.86042e15 | + | 9.04288e15i | −0.266632 | + | 0.411424i | ||||
\(937\) | 7.08661e15 | − | 7.08661e15i | 0.320532 | − | 0.320532i | −0.528439 | − | 0.848971i | \(-0.677223\pi\) |
0.848971 | + | 0.528439i | \(0.177223\pi\) | |||||||
\(938\) | 1.15603e16 | − | 1.15603e16i | 0.519819 | − | 0.519819i | ||||
\(939\) | 5.43264e15 | − | 1.83720e16i | 0.242857 | − | 0.821289i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.27144e15i | − | 0.409642i | −0.978799 | − | 0.204821i | \(-0.934339\pi\) | ||
0.978799 | − | 0.204821i | \(-0.0656612\pi\) | |||||||
\(942\) | 2.58949e15 | + | 4.76390e15i | 0.113746 | + | 0.209258i | ||||
\(943\) | 1.67519e16 | + | 1.67519e16i | 0.731560 | + | 0.731560i | ||||
\(944\) | 3.35233e16 | 1.45546 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.62572e14 | 0.0112680 | ||||||||
\(947\) | −2.29673e15 | − | 2.29673e15i | −0.0979906 | − | 0.0979906i | 0.656412 | − | 0.754403i | \(-0.272073\pi\) |
−0.754403 | + | 0.656412i | \(0.772073\pi\) | |||||||
\(948\) | −3.67492e15 | − | 6.76078e15i | −0.155884 | − | 0.286781i | ||||
\(949\) | 2.38709e15i | 0.100671i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.25549e15 | − | 2.11547e16i | 0.260776 | − | 0.881890i | ||||
\(952\) | −1.24934e16 | + | 1.24934e16i | −0.517820 | + | 0.517820i | ||||
\(953\) | 1.33125e16 | − | 1.33125e16i | 0.548590 | − | 0.548590i | −0.377443 | − | 0.926033i | \(-0.623196\pi\) |
0.926033 | + | 0.377443i | \(0.123196\pi\) | |||||||
\(954\) | −3.33888e15 | + | 5.15203e15i | −0.136800 | + | 0.211088i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.42607e16i | − | 0.577592i | ||||||
\(957\) | 3.04653e15 | − | 1.65599e15i | 0.122685 | − | 0.0666871i | ||||
\(958\) | −1.71931e16 | − | 1.71931e16i | −0.688405 | − | 0.688405i | ||||
\(959\) | −5.93424e16 | −2.36245 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.31400e16 | 1.69786 | ||||||||
\(962\) | 1.61778e16 | + | 1.61778e16i | 0.633077 | + | 0.633077i | ||||
\(963\) | −2.81402e16 | + | 6.00907e15i | −1.09492 | + | 0.233810i | ||||
\(964\) | 1.63247e16i | 0.631572i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.51387e16 | + | 7.43356e15i | 0.961543 | + | 0.284330i | ||||
\(967\) | 1.60974e16 | − | 1.60974e16i | 0.612225 | − | 0.612225i | −0.331300 | − | 0.943525i | \(-0.607487\pi\) |
0.943525 | + | 0.331300i | \(0.107487\pi\) | |||||||
\(968\) | −1.35955e16 | + | 1.35955e16i | −0.514140 | + | 0.514140i | ||||
\(969\) | 1.62715e16 | + | 4.81152e15i | 0.611854 | + | 0.180926i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.94286e16i | 0.722330i | 0.932502 | + | 0.361165i | \(0.117621\pi\) | ||||
−0.932502 | + | 0.361165i | \(0.882379\pi\) | |||||||
\(972\) | −8.00987e15 | − | 6.11631e15i | −0.296115 | − | 0.226113i | ||||
\(973\) | 4.41119e16 | + | 4.41119e16i | 1.62157 | + | 1.62157i | ||||
\(974\) | 2.48949e16 | 0.909987 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.45798e16 | −1.24982 | ||||||||
\(977\) | −1.62065e16 | − | 1.62065e16i | −0.582464 | − | 0.582464i | 0.353116 | − | 0.935580i | \(-0.385122\pi\) |
−0.935580 | + | 0.353116i | \(0.885122\pi\) | |||||||
\(978\) | 3.24611e16 | − | 1.76447e16i | 1.16011 | − | 0.630596i | ||||
\(979\) | − | 9.78592e14i | − | 0.0347774i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.04969e16 | + | 6.80276e15i | 0.368878 | + | 0.239059i | ||||
\(982\) | −2.41508e16 | + | 2.41508e16i | −0.843952 | + | 0.843952i | ||||
\(983\) | −2.73690e16 | + | 2.73690e16i | −0.951074 | + | 0.951074i | −0.998858 | − | 0.0477837i | \(-0.984784\pi\) |
0.0477837 | + | 0.998858i | \(0.484784\pi\) | |||||||
\(984\) | −1.07515e16 | + | 3.63594e16i | −0.371533 | + | 1.25645i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 3.10638e16i | − | 1.06153i | ||||||
\(987\) | −2.58752e16 | − | 4.76027e16i | −0.879303 | − | 1.61766i | ||||
\(988\) | 4.91026e15 | + | 4.91026e15i | 0.165936 | + | 0.165936i | ||||
\(989\) | 1.59536e15 | 0.0536142 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.79251e16 | −1.26044 | −0.630219 | − | 0.776417i | \(-0.717035\pi\) | ||||
−0.630219 | + | 0.776417i | \(0.717035\pi\) | |||||||
\(992\) | −2.49626e16 | − | 2.49626e16i | −0.825042 | − | 0.825042i | ||||
\(993\) | −1.86307e16 | − | 3.42750e16i | −0.612361 | − | 1.12656i | ||||
\(994\) | 2.68790e16i | 0.878592i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.68861e15 | + | 9.09231e15i | −0.0869165 | + | 0.293933i | ||||
\(997\) | −2.46526e16 | + | 2.46526e16i | −0.792574 | + | 0.792574i | −0.981912 | − | 0.189338i | \(-0.939366\pi\) |
0.189338 | + | 0.981912i | \(0.439366\pi\) | |||||||
\(998\) | −1.25707e16 | + | 1.25707e16i | −0.401922 | + | 0.401922i | ||||
\(999\) | 2.73674e16 | − | 2.34408e16i | 0.870207 | − | 0.745354i |
(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 | 75.12.e.d.68.5 | 40 | ||
3.2 | odd | 2 | inner | 75.12.e.d.68.16 | 40 | ||
5.2 | odd | 4 | inner | 75.12.e.d.32.16 | 40 | ||
5.3 | odd | 4 | 15.12.e.a.2.5 | ✓ | 40 | ||
5.4 | even | 2 | 15.12.e.a.8.16 | yes | 40 | ||
15.2 | even | 4 | inner | 75.12.e.d.32.5 | 40 | ||
15.8 | even | 4 | 15.12.e.a.2.16 | yes | 40 | ||
15.14 | odd | 2 | 15.12.e.a.8.5 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.12.e.a.2.5 | ✓ | 40 | 5.3 | odd | 4 | ||
15.12.e.a.2.16 | yes | 40 | 15.8 | even | 4 | ||
15.12.e.a.8.5 | yes | 40 | 15.14 | odd | 2 | ||
15.12.e.a.8.16 | yes | 40 | 5.4 | even | 2 | ||
75.12.e.d.32.5 | 40 | 15.2 | even | 4 | inner | ||
75.12.e.d.32.16 | 40 | 5.2 | odd | 4 | inner | ||
75.12.e.d.68.5 | 40 | 1.1 | even | 1 | trivial | ||
75.12.e.d.68.16 | 40 | 3.2 | odd | 2 | inner |