Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,8,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.4917218349\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.14 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.8.f.a.35.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.319783 | + | 11.3092i | −0.0282651 | + | 0.999600i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −127.795 | − | 7.23297i | −0.998402 | − | 0.0565076i | ||||
\(5\) | 412.177 | 1.47465 | 0.737324 | − | 0.675539i | \(-0.236089\pi\) | ||||
0.737324 | + | 0.675539i | \(0.236089\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 359.164i | 0.395776i | 0.980225 | + | 0.197888i | \(0.0634082\pi\) | ||||
−0.980225 | + | 0.197888i | \(0.936592\pi\) | |||||||
\(8\) | 122.666 | − | 1442.95i | 0.0847049 | − | 0.996406i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −131.807 | + | 4661.38i | −0.0416810 | + | 1.47406i | ||||
\(11\) | − | 3819.02i | − | 0.865123i | −0.901604 | − | 0.432561i | \(-0.857610\pi\) | ||
0.901604 | − | 0.432561i | \(-0.142390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14141.7i | − | 1.78526i | −0.450791 | − | 0.892630i | \(-0.648858\pi\) | ||
0.450791 | − | 0.892630i | \(-0.351142\pi\) | |||||||
\(14\) | −4061.85 | − | 114.854i | −0.395618 | − | 0.0111866i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16279.4 | + | 1848.68i | 0.993614 | + | 0.112835i | ||||
\(17\) | − | 3331.48i | − | 0.164462i | −0.996613 | − | 0.0822312i | \(-0.973795\pi\) | ||
0.996613 | − | 0.0822312i | \(-0.0262046\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34327.6 | 1.14817 | 0.574084 | − | 0.818796i | \(-0.305358\pi\) | ||||
0.574084 | + | 0.818796i | \(0.305358\pi\) | |||||||
\(20\) | −52674.3 | − | 2981.26i | −1.47229 | − | 0.0833288i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 43190.0 | + | 1221.26i | 0.864777 | + | 0.0244528i | ||||
\(23\) | 69918.3 | 1.19824 | 0.599120 | − | 0.800659i | \(-0.295517\pi\) | ||||
0.599120 | + | 0.800659i | \(0.295517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 91764.7 | 1.17459 | ||||||||
\(26\) | 159932. | + | 4522.29i | 1.78455 | + | 0.0504605i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2597.82 | − | 45899.5i | 0.0223643 | − | 0.395144i | ||||
\(29\) | −186332. | −1.41872 | −0.709358 | − | 0.704848i | \(-0.751015\pi\) | ||||
−0.709358 | + | 0.704848i | \(0.751015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 189759.i | 1.14403i | 0.820245 | + | 0.572013i | \(0.193837\pi\) | ||||
−0.820245 | + | 0.572013i | \(0.806163\pi\) | |||||||
\(32\) | −26112.9 | + | 183515.i | −0.140874 | + | 0.990028i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 37676.4 | + | 1065.35i | 0.164397 | + | 0.00464854i | ||||
\(35\) | 148039.i | 0.583630i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 190024.i | − | 0.616739i | −0.951267 | − | 0.308369i | \(-0.900217\pi\) | ||
0.951267 | − | 0.308369i | \(-0.0997833\pi\) | |||||||
\(38\) | −10977.4 | + | 388217.i | −0.0324530 | + | 1.14771i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 50560.0 | − | 594751.i | 0.124910 | − | 1.46935i | ||||
\(41\) | 159461.i | 0.361335i | 0.983544 | + | 0.180668i | \(0.0578258\pi\) | ||||
−0.983544 | + | 0.180668i | \(0.942174\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 757231. | 1.45241 | 0.726205 | − | 0.687478i | \(-0.241282\pi\) | ||||
0.726205 | + | 0.687478i | \(0.241282\pi\) | |||||||
\(44\) | −27622.9 | + | 488054.i | −0.0488860 | + | 0.863741i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22358.7 | + | 790720.i | −0.0338683 | + | 1.19776i | ||||
\(47\) | 235539. | 0.330918 | 0.165459 | − | 0.986217i | \(-0.447089\pi\) | ||||
0.165459 | + | 0.986217i | \(0.447089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 694544. | 0.843361 | ||||||||
\(50\) | −29344.8 | + | 1.03778e6i | −0.0331998 | + | 1.17412i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −102287. | + | 1.80725e6i | −0.100881 | + | 1.78241i | ||||
\(53\) | 732030. | 0.675404 | 0.337702 | − | 0.941253i | \(-0.390350\pi\) | ||||
0.337702 | + | 0.941253i | \(0.390350\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.57411e6i | − | 1.27575i | ||||||
\(56\) | 518255. | + | 44057.1i | 0.394354 | + | 0.0335242i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 59585.9 | − | 2.10727e6i | 0.0401001 | − | 1.41815i | ||||
\(59\) | − | 1.98198e6i | − | 1.25637i | −0.778064 | − | 0.628185i | \(-0.783798\pi\) | ||
0.778064 | − | 0.628185i | \(-0.216202\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.37932e6i | 0.778055i | 0.921226 | + | 0.389028i | \(0.127189\pi\) | ||||
−0.921226 | + | 0.389028i | \(0.872811\pi\) | |||||||
\(62\) | −2.14602e6 | − | 60681.5i | −1.14357 | − | 0.0323360i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.06706e6 | − | 354001.i | −0.985650 | − | 0.168801i | ||||
\(65\) | − | 5.82890e6i | − | 2.63263i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.28147e6 | 0.926731 | 0.463366 | − | 0.886167i | \(-0.346642\pi\) | ||||
0.463366 | + | 0.886167i | \(0.346642\pi\) | |||||||
\(68\) | −24096.5 | + | 425749.i | −0.00929337 | + | 0.164200i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.67420e6 | − | 47340.3i | −0.583397 | − | 0.0164964i | ||||
\(71\) | −5.12011e6 | −1.69776 | −0.848878 | − | 0.528589i | \(-0.822721\pi\) | ||||
−0.848878 | + | 0.528589i | \(0.822721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −521725. | −0.156968 | −0.0784841 | − | 0.996915i | \(-0.525008\pi\) | ||||
−0.0784841 | + | 0.996915i | \(0.525008\pi\) | |||||||
\(74\) | 2.14901e6 | + | 60766.2i | 0.616493 | + | 0.0174322i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.38691e6 | − | 248290.i | −1.14633 | − | 0.0648801i | ||||
\(77\) | 1.37165e6 | 0.342395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.85831e6i | 0.880446i | 0.897888 | + | 0.440223i | \(0.145101\pi\) | ||||
−0.897888 | + | 0.440223i | \(0.854899\pi\) | |||||||
\(80\) | 6.70998e6 | + | 761983.i | 1.46523 | + | 0.166391i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.80337e6 | − | 50992.8i | −0.361191 | − | 0.0102132i | ||||
\(83\) | − | 4.75271e6i | − | 0.912363i | −0.889887 | − | 0.456182i | \(-0.849217\pi\) | ||
0.889887 | − | 0.456182i | \(-0.150783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.37316e6i | − | 0.242524i | ||||||
\(86\) | −242150. | + | 8.56367e6i | −0.0410525 | + | 1.45183i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.51066e6 | − | 468463.i | −0.862014 | − | 0.0732801i | ||||
\(89\) | − | 7.08773e6i | − | 1.06572i | −0.846204 | − | 0.532859i | \(-0.821118\pi\) | ||
0.846204 | − | 0.532859i | \(-0.178882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.07920e6 | 0.706563 | ||||||||
\(92\) | −8.93525e6 | − | 505717.i | −1.19632 | − | 0.0677096i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −75321.4 | + | 2.66376e6i | −0.00935343 | + | 0.330786i | ||||
\(95\) | 1.41490e7 | 1.69314 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.34983e7 | −1.50169 | −0.750844 | − | 0.660480i | \(-0.770353\pi\) | ||||
−0.750844 | + | 0.660480i | \(0.770353\pi\) | |||||||
\(98\) | −222103. | + | 7.85473e6i | −0.0238377 | + | 0.843024i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.17271e7 | − | 663731.i | −1.17271 | − | 0.0663731i | ||||
\(101\) | −1.25843e7 | −1.21535 | −0.607677 | − | 0.794184i | \(-0.707899\pi\) | ||||
−0.607677 | + | 0.794184i | \(0.707899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.44045e6i | − | 0.761089i | −0.924763 | − | 0.380544i | \(-0.875737\pi\) | ||
0.924763 | − | 0.380544i | \(-0.124263\pi\) | |||||||
\(104\) | −2.04058e7 | − | 1.73471e6i | −1.77884 | − | 0.151220i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −234091. | + | 8.27867e6i | −0.0190903 | + | 0.675134i | ||||
\(107\) | 1.12718e7i | 0.889505i | 0.895654 | + | 0.444752i | \(0.146708\pi\) | ||||
−0.895654 | + | 0.444752i | \(0.853292\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.83959e6i | − | 0.579830i | −0.957052 | − | 0.289915i | \(-0.906373\pi\) | ||
0.957052 | − | 0.289915i | \(-0.0936270\pi\) | |||||||
\(110\) | 1.78019e7 | + | 503374.i | 1.27524 | + | 0.0360592i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −663979. | + | 5.84696e6i | −0.0446572 | + | 0.393248i | ||||
\(113\) | − | 1.34305e7i | − | 0.875623i | −0.899067 | − | 0.437811i | \(-0.855754\pi\) | ||
0.899067 | − | 0.437811i | \(-0.144246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.88187e7 | 1.76698 | ||||||||
\(116\) | 2.38125e7 | + | 1.34774e6i | 1.41645 | + | 0.0801682i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.24146e7 | + | 633804.i | 1.25587 | + | 0.0355114i | ||||
\(119\) | 1.19655e6 | 0.0650903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.90224e6 | 0.251562 | ||||||||
\(122\) | −1.55990e7 | − | 441083.i | −0.777744 | − | 0.0219918i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.37252e6 | − | 2.42503e7i | 0.0646461 | − | 1.14220i | ||||
\(125\) | 5.62197e6 | 0.257456 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.93022e7i | 1.26937i | 0.772771 | + | 0.634684i | \(0.218870\pi\) | ||||
−0.772771 | + | 0.634684i | \(0.781130\pi\) | |||||||
\(128\) | 4.66448e6 | − | 2.32635e7i | 0.196593 | − | 0.980485i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.59201e7 | + | 1.86398e6i | 2.63158 | + | 0.0744115i | ||||
\(131\) | 4.27923e7i | 1.66309i | 0.555457 | + | 0.831546i | \(0.312544\pi\) | ||||
−0.555457 | + | 0.831546i | \(0.687456\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.23292e7i | 0.454417i | ||||||||
\(134\) | −729576. | + | 2.58016e7i | −0.0261941 | + | 0.926361i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.80717e6 | − | 408659.i | −0.163871 | − | 0.0139308i | ||||
\(137\) | 3.57159e6i | 0.118670i | 0.998238 | + | 0.0593348i | \(0.0188979\pi\) | ||||
−0.998238 | + | 0.0593348i | \(0.981102\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.65242e7 | 1.46936 | 0.734678 | − | 0.678417i | \(-0.237333\pi\) | ||||
0.734678 | + | 0.678417i | \(0.237333\pi\) | |||||||
\(140\) | 1.07076e6 | − | 1.89187e7i | 0.0329795 | − | 0.582698i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.63732e6 | − | 5.79043e7i | 0.0479872 | − | 1.69708i | ||||
\(143\) | −5.40076e7 | −1.54447 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.68019e7 | −2.09211 | ||||||||
\(146\) | 166839. | − | 5.90029e6i | 0.00443672 | − | 0.156906i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.37443e6 | + | 2.42841e7i | −0.0348504 | + | 0.615753i | ||||
\(149\) | 3.43823e7 | 0.851496 | 0.425748 | − | 0.904842i | \(-0.360011\pi\) | ||||
0.425748 | + | 0.904842i | \(0.360011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.33709e7i | − | 1.73422i | −0.498116 | − | 0.867110i | \(-0.665975\pi\) | ||
0.498116 | − | 0.867110i | \(-0.334025\pi\) | |||||||
\(152\) | 4.21082e6 | − | 4.95330e7i | 0.0972554 | − | 1.14404i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −438631. | + | 1.55123e7i | −0.00967781 | + | 0.342258i | ||||
\(155\) | 7.82141e7i | 1.68704i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.78154e7i | 0.779867i | 0.920843 | + | 0.389933i | \(0.127502\pi\) | ||||
−0.920843 | + | 0.389933i | \(0.872498\pi\) | |||||||
\(158\) | −4.36344e7 | − | 1.23382e6i | −0.880094 | − | 0.0248859i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.07631e7 | + | 7.56407e7i | −0.207740 | + | 1.45994i | ||||
\(161\) | 2.51121e7i | 0.474234i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.97142e7 | −0.356552 | −0.178276 | − | 0.983981i | \(-0.557052\pi\) | ||||
−0.178276 | + | 0.983981i | \(0.557052\pi\) | |||||||
\(164\) | 1.15337e6 | − | 2.03784e7i | 0.0204182 | − | 0.360758i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.37493e7 | + | 1.51983e6i | 0.911999 | + | 0.0257880i | ||||
\(167\) | 8.21858e7 | 1.36549 | 0.682746 | − | 0.730656i | \(-0.260786\pi\) | ||||
0.682746 | + | 0.730656i | \(0.260786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.37240e8 | −2.18715 | ||||||||
\(170\) | 1.55293e7 | + | 439113.i | 0.242427 | + | 0.00685496i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.67708e7 | − | 5.47703e6i | −1.45009 | − | 0.0820721i | ||||
\(173\) | 2.64838e7 | 0.388883 | 0.194441 | − | 0.980914i | \(-0.437711\pi\) | ||||
0.194441 | + | 0.980914i | \(0.437711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.29586e7i | 0.464874i | ||||||||
\(176\) | 7.06015e6 | − | 6.21713e7i | 0.0976157 | − | 0.859598i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.01565e7 | + | 2.26653e6i | 1.06529 | + | 0.0301226i | ||||
\(179\) | 9.25036e7i | 1.20552i | 0.797924 | + | 0.602758i | \(0.205932\pi\) | ||||
−0.797924 | + | 0.602758i | \(0.794068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.91658e7i | − | 0.992344i | −0.868224 | − | 0.496172i | \(-0.834738\pi\) | ||
0.868224 | − | 0.496172i | \(-0.165262\pi\) | |||||||
\(182\) | −1.62424e6 | + | 5.74417e7i | −0.0199710 | + | 0.706280i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.57659e6 | − | 1.00889e8i | 0.101497 | − | 1.19393i | ||||
\(185\) | − | 7.83233e7i | − | 0.909473i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.27230e7 | −0.142280 | ||||||||
\(188\) | −3.01008e7 | − | 1.70365e6i | −0.330390 | − | 0.0186994i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.52461e6 | + | 1.60014e8i | −0.0478568 | + | 1.69247i | ||||
\(191\) | −1.02924e8 | −1.06881 | −0.534403 | − | 0.845230i | \(-0.679464\pi\) | ||||
−0.534403 | + | 0.845230i | \(0.679464\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.98055e7 | −0.598812 | −0.299406 | − | 0.954126i | \(-0.596789\pi\) | ||||
−0.299406 | + | 0.954126i | \(0.596789\pi\) | |||||||
\(194\) | 4.31654e6 | − | 1.52655e8i | 0.0424453 | − | 1.50109i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.87596e7 | − | 5.02362e6i | −0.842014 | − | 0.0476563i | ||||
\(197\) | −1.68356e8 | −1.56890 | −0.784452 | − | 0.620190i | \(-0.787055\pi\) | ||||
−0.784452 | + | 0.620190i | \(0.787055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.24295e7i | 0.831428i | 0.909495 | + | 0.415714i | \(0.136468\pi\) | ||||
−0.909495 | + | 0.415714i | \(0.863532\pi\) | |||||||
\(200\) | 1.12564e7 | − | 1.32412e8i | 0.0994934 | − | 1.17037i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.02423e6 | − | 1.42318e8i | 0.0343521 | − | 1.21487i | ||||
\(203\) | − | 6.69239e7i | − | 0.561494i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.57260e7i | 0.532842i | ||||||||
\(206\) | 9.54546e7 | + | 2.69911e6i | 0.760785 | + | 0.0215122i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.61436e7 | − | 2.30219e8i | 0.201439 | − | 1.77386i | ||||
\(209\) | − | 1.31098e8i | − | 0.993306i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.21026e8 | 0.886928 | 0.443464 | − | 0.896292i | \(-0.353749\pi\) | ||||
0.443464 | + | 0.896292i | \(0.353749\pi\) | |||||||
\(212\) | −9.35502e7 | − | 5.29475e6i | −0.674325 | − | 0.0381654i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.27474e8 | − | 3.60451e6i | −0.889150 | − | 0.0251419i | ||||
\(215\) | 3.12113e8 | 2.14179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.81544e7 | −0.452778 | ||||||||
\(218\) | 8.86594e7 | + | 2.50696e6i | 0.579598 | + | 0.0163889i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.13855e7 | + | 2.01164e8i | −0.0720896 | + | 1.27371i | ||||
\(221\) | −4.71130e7 | −0.293608 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.34758e7i | 0.383302i | 0.981463 | + | 0.191651i | \(0.0613842\pi\) | ||||
−0.981463 | + | 0.191651i | \(0.938616\pi\) | |||||||
\(224\) | −6.59120e7 | − | 9.37882e6i | −0.391829 | − | 0.0557545i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.51888e8 | + | 4.29484e6i | 0.875273 | + | 0.0247495i | ||||
\(227\) | − | 1.62893e8i | − | 0.924296i | −0.886803 | − | 0.462148i | \(-0.847079\pi\) | ||
0.886803 | − | 0.462148i | \(-0.152921\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.85285e7i | − | 0.156984i | −0.996915 | − | 0.0784918i | \(-0.974990\pi\) | ||
0.996915 | − | 0.0784918i | \(-0.0250105\pi\) | |||||||
\(230\) | −9.21573e6 | + | 3.25916e8i | −0.0499439 | + | 1.76628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.28566e7 | + | 2.68869e8i | −0.120172 | + | 1.41362i | ||||
\(233\) | 8.67347e7i | 0.449207i | 0.974450 | + | 0.224604i | \(0.0721088\pi\) | ||||
−0.974450 | + | 0.224604i | \(0.927891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.70838e7 | 0.487988 | ||||||||
\(236\) | −1.43356e7 | + | 2.53288e8i | −0.0709944 | + | 1.25436i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −382636. | + | 1.35320e7i | −0.00183978 | + | 0.0650642i | ||||
\(239\) | −3.35437e8 | −1.58935 | −0.794673 | − | 0.607038i | \(-0.792358\pi\) | ||||
−0.794673 | + | 0.607038i | \(0.792358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.29134e8 | 1.97484 | 0.987422 | − | 0.158107i | \(-0.0505391\pi\) | ||||
0.987422 | + | 0.158107i | \(0.0505391\pi\) | |||||||
\(242\) | −1.56765e6 | + | 5.54403e7i | −0.00711043 | + | 0.251462i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.97657e6 | − | 1.76271e8i | 0.0439660 | − | 0.776812i | ||||
\(245\) | 2.86275e8 | 1.24366 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.85452e8i | − | 2.04978i | ||||||
\(248\) | 2.73812e8 | + | 2.32769e7i | 1.13991 | + | 0.0969045i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.79781e6 | + | 6.35799e7i | −0.00727702 | + | 0.257354i | ||||
\(251\) | 1.57080e8i | 0.626992i | 0.949590 | + | 0.313496i | \(0.101500\pi\) | ||||
−0.949590 | + | 0.313496i | \(0.898500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.67020e8i | − | 1.03662i | ||||||
\(254\) | −3.31385e8 | − | 9.37035e6i | −1.26886 | − | 0.0358788i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.61600e8 | + | 6.01907e7i | 0.974537 | + | 0.224228i | ||||
\(257\) | 4.69735e7i | 0.172618i | 0.996268 | + | 0.0863092i | \(0.0275073\pi\) | ||||
−0.996268 | + | 0.0863092i | \(0.972493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.82496e7 | 0.244090 | ||||||||
\(260\) | −4.21602e7 | + | 7.44907e8i | −0.148763 | + | 2.62842i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.83946e8 | − | 1.36842e7i | −1.66243 | − | 0.0470074i | ||||
\(263\) | −1.00330e8 | −0.340082 | −0.170041 | − | 0.985437i | \(-0.554390\pi\) | ||||
−0.170041 | + | 0.985437i | \(0.554390\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.01726e8 | 0.995983 | ||||||||
\(266\) | −1.39433e8 | − | 3.94267e6i | −0.454236 | − | 0.0128441i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.91562e8 | − | 1.65018e7i | −0.925250 | − | 0.0523673i | ||||
\(269\) | 2.70778e8 | 0.848164 | 0.424082 | − | 0.905624i | \(-0.360597\pi\) | ||||
0.424082 | + | 0.905624i | \(0.360597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.20621e8i | 1.89424i | 0.320885 | + | 0.947118i | \(0.396020\pi\) | ||||
−0.320885 | + | 0.947118i | \(0.603980\pi\) | |||||||
\(272\) | 6.15885e6 | − | 5.42345e7i | 0.0185570 | − | 0.163412i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.03918e7 | − | 1.14213e6i | −0.118622 | − | 0.00335420i | ||||
\(275\) | − | 3.50452e8i | − | 1.01616i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.93506e8i | 1.67782i | 0.544268 | + | 0.838911i | \(0.316807\pi\) | ||||
−0.544268 | + | 0.838911i | \(0.683193\pi\) | |||||||
\(278\) | −1.48776e7 | + | 5.26150e8i | −0.0415314 | + | 1.46877i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.13613e8 | + | 1.81593e7i | 0.581533 | + | 0.0494363i | ||||
\(281\) | − | 2.49386e8i | − | 0.670503i | −0.942129 | − | 0.335251i | \(-0.891179\pi\) | ||
0.942129 | − | 0.335251i | \(-0.108821\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.41236e8 | −0.632688 | −0.316344 | − | 0.948645i | \(-0.602455\pi\) | ||||
−0.316344 | + | 0.948645i | \(0.602455\pi\) | |||||||
\(284\) | 6.54327e8 | + | 3.70336e7i | 1.69504 | + | 0.0959360i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.72707e7 | − | 6.10783e8i | 0.0436545 | − | 1.54385i | ||||
\(287\) | −5.72725e7 | −0.143008 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.99240e8 | 0.972952 | ||||||||
\(290\) | 2.45599e7 | − | 8.68567e8i | 0.0591336 | − | 2.09127i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.66741e7 | + | 3.77362e6i | 0.156717 | + | 0.00886989i | ||||
\(293\) | −4.41368e8 | −1.02509 | −0.512547 | − | 0.858659i | \(-0.671298\pi\) | ||||
−0.512547 | + | 0.858659i | \(0.671298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.16927e8i | − | 1.85271i | ||||||
\(296\) | −2.74194e8 | − | 2.33094e7i | −0.614522 | − | 0.0522408i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.09949e7 | + | 3.88836e8i | −0.0240676 | + | 0.851156i | ||||
\(299\) | − | 9.88767e8i | − | 2.13917i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.71970e8i | 0.574829i | ||||||||
\(302\) | 8.29765e8 | + | 2.34627e7i | 1.73353 | + | 0.0490179i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.58831e8 | + | 6.34607e7i | 1.14084 | + | 0.129553i | ||||
\(305\) | 5.68523e8i | 1.14736i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.02987e8 | −0.794889 | −0.397445 | − | 0.917626i | \(-0.630103\pi\) | ||||
−0.397445 | + | 0.917626i | \(0.630103\pi\) | |||||||
\(308\) | −1.75291e8 | − | 9.92113e6i | −0.341848 | − | 0.0193479i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.84538e8 | − | 2.50115e7i | −1.68636 | − | 0.0476842i | ||||
\(311\) | 1.04195e8 | 0.196420 | 0.0982099 | − | 0.995166i | \(-0.468688\pi\) | ||||
0.0982099 | + | 0.995166i | \(0.468688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.28900e8 | 1.15925 | 0.579624 | − | 0.814884i | \(-0.303200\pi\) | ||||
0.579624 | + | 0.814884i | \(0.303200\pi\) | |||||||
\(314\) | −4.27662e8 | − | 1.20927e7i | −0.779555 | − | 0.0220430i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.79071e7 | − | 4.93075e8i | 0.0497519 | − | 0.879039i | ||||
\(317\) | −5.51759e8 | −0.972841 | −0.486421 | − | 0.873725i | \(-0.661698\pi\) | ||||
−0.486421 | + | 0.873725i | \(0.661698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.11608e8i | 1.22736i | ||||||||
\(320\) | −8.51993e8 | − | 1.45911e8i | −1.45349 | − | 0.248922i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.83998e8 | − | 8.03043e6i | −0.474045 | − | 0.0134043i | ||||
\(323\) | − | 1.14362e8i | − | 0.188830i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.29771e9i | − | 2.09694i | ||||||
\(326\) | 6.30426e6 | − | 2.22952e8i | 0.0100780 | − | 0.356409i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.30094e8 | + | 1.95604e7i | 0.360037 | + | 0.0306068i | ||||
\(329\) | 8.45972e7i | 0.130969i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.03548e8 | −1.21791 | −0.608953 | − | 0.793206i | \(-0.708410\pi\) | ||||
−0.608953 | + | 0.793206i | \(0.708410\pi\) | |||||||
\(332\) | −3.43762e7 | + | 6.07375e8i | −0.0515554 | + | 0.910906i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.62816e7 | + | 9.29455e8i | −0.0385957 | + | 1.36495i | ||||
\(335\) | 9.40371e8 | 1.36660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.74822e8 | −1.24513 | −0.622565 | − | 0.782568i | \(-0.713910\pi\) | ||||
−0.622565 | + | 0.782568i | \(0.713910\pi\) | |||||||
\(338\) | 4.38871e7 | − | 1.55208e9i | 0.0618199 | − | 2.18628i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.93202e6 | + | 1.75484e8i | −0.0137044 | + | 0.242137i | ||||
\(341\) | 7.24693e8 | 0.989723 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.45242e8i | 0.729558i | ||||||||
\(344\) | 9.28864e7 | − | 1.09265e9i | 0.123026 | − | 1.44719i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.46905e6 | + | 2.99510e8i | −0.0109918 | + | 0.388727i | ||||
\(347\) | 3.16428e8i | 0.406557i | 0.979121 | + | 0.203279i | \(0.0651597\pi\) | ||||
−0.979121 | + | 0.203279i | \(0.934840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.41239e8i | − | 0.555629i | −0.960635 | − | 0.277814i | \(-0.910390\pi\) | ||
0.960635 | − | 0.277814i | \(-0.0896101\pi\) | |||||||
\(350\) | −3.72735e8 | − | 1.05396e7i | −0.464688 | − | 0.0131397i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.00849e8 | + | 9.97259e7i | 0.856496 | + | 0.121873i | ||||
\(353\) | 3.79064e8i | 0.458670i | 0.973348 | + | 0.229335i | \(0.0736552\pi\) | ||||
−0.973348 | + | 0.229335i | \(0.926345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.11039e9 | −2.50359 | ||||||||
\(356\) | −5.12653e7 | + | 9.05780e8i | −0.0602211 | + | 1.06402i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.04614e9 | − | 2.95811e7i | −1.20503 | − | 0.0340740i | ||||
\(359\) | −4.43347e8 | −0.505723 | −0.252862 | − | 0.967502i | \(-0.581372\pi\) | ||||
−0.252862 | + | 0.967502i | \(0.581372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.84510e8 | 0.318289 | ||||||||
\(362\) | 8.95300e8 | + | 2.53158e7i | 0.991948 | + | 0.0280487i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.49099e8 | − | 3.67377e7i | −0.705434 | − | 0.0399261i | ||||
\(365\) | −2.15043e8 | −0.231473 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.76323e8i | − | 0.291800i | −0.989299 | − | 0.145900i | \(-0.953392\pi\) | ||
0.989299 | − | 0.145900i | \(-0.0466078\pi\) | |||||||
\(368\) | 1.13823e9 | + | 1.29257e8i | 1.19059 | + | 0.135203i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.85773e8 | + | 2.50464e7i | 0.909110 | + | 0.0257063i | ||||
\(371\) | 2.62919e8i | 0.267309i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.23995e9i | 1.23715i | 0.785726 | + | 0.618575i | \(0.212290\pi\) | ||||
−0.785726 | + | 0.618575i | \(0.787710\pi\) | |||||||
\(374\) | 4.06860e6 | − | 1.43887e8i | 0.00402156 | − | 0.142223i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.88926e7 | − | 3.39871e8i | 0.0280304 | − | 0.329729i | ||||
\(377\) | 2.63507e9i | 2.53278i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00434e8 | −0.472183 | −0.236091 | − | 0.971731i | \(-0.575866\pi\) | ||||
−0.236091 | + | 0.971731i | \(0.575866\pi\) | |||||||
\(380\) | −1.80818e9 | − | 1.02339e8i | −1.69044 | − | 0.0956754i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.29133e7 | − | 1.16398e9i | 0.0302099 | − | 1.06838i | ||||
\(383\) | −4.63975e8 | −0.421987 | −0.210993 | − | 0.977487i | \(-0.567670\pi\) | ||||
−0.210993 | + | 0.977487i | \(0.567670\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.65364e8 | 0.504912 | ||||||||
\(386\) | 1.91248e7 | − | 6.76352e8i | 0.0169255 | − | 0.598573i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.72503e9 | + | 9.76331e7i | 1.49929 | + | 0.0848567i | ||||
\(389\) | −2.74898e8 | −0.236781 | −0.118391 | − | 0.992967i | \(-0.537774\pi\) | ||||
−0.118391 | + | 0.992967i | \(0.537774\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.32932e8i | − | 0.197065i | ||||||
\(392\) | 8.51968e7 | − | 1.00219e9i | 0.0714368 | − | 0.840330i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.38373e7 | − | 1.90397e9i | 0.0443452 | − | 1.56828i | ||||
\(395\) | 1.59031e9i | 1.29835i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.28191e9i | 1.02823i | 0.857721 | + | 0.514116i | \(0.171880\pi\) | ||||
−0.857721 | + | 0.514116i | \(0.828120\pi\) | |||||||
\(398\) | −1.04530e9 | − | 2.95573e7i | −0.831096 | − | 0.0235004i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.49387e9 | + | 1.69644e8i | 1.16709 | + | 0.132534i | ||||
\(401\) | − | 2.19451e8i | − | 0.169954i | −0.996383 | − | 0.0849772i | \(-0.972918\pi\) | ||
0.996383 | − | 0.0849772i | \(-0.0270817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.68352e9 | 2.04238 | ||||||||
\(404\) | 1.60821e9 | + | 9.10216e7i | 1.21341 | + | 0.0686767i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.56855e8 | + | 2.14011e7i | 0.561269 | + | 0.0158707i | ||||
\(407\) | −7.25704e8 | −0.533555 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.87644e8 | −0.135614 | −0.0678068 | − | 0.997698i | \(-0.521600\pi\) | ||||
−0.0678068 | + | 0.997698i | \(0.521600\pi\) | |||||||
\(410\) | −7.43308e8 | − | 2.10180e7i | −0.532629 | − | 0.0150608i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.10495e7 | + | 1.07865e9i | −0.0430073 | + | 0.759873i | ||||
\(413\) | 7.11856e8 | 0.497241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.95896e9i | − | 1.34542i | ||||||
\(416\) | 2.59523e9 | + | 3.69283e8i | 1.76746 | + | 0.251497i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.48261e9 | + | 4.19228e7i | 0.992909 | + | 0.0280759i | ||||
\(419\) | − | 7.92192e8i | − | 0.526116i | −0.964780 | − | 0.263058i | \(-0.915269\pi\) | ||
0.964780 | − | 0.263058i | \(-0.0847310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.56076e7i | 0.0363201i | 0.999835 | + | 0.0181601i | \(0.00578084\pi\) | ||||
−0.999835 | + | 0.0181601i | \(0.994219\pi\) | |||||||
\(422\) | −3.87019e7 | + | 1.36870e9i | −0.0250691 | + | 0.886574i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.97951e7 | − | 1.05628e9i | 0.0572100 | − | 0.672977i | ||||
\(425\) | − | 3.05713e8i | − | 0.193176i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.95402e8 | −0.307936 | ||||||||
\(428\) | 8.15282e7 | − | 1.44048e9i | 0.0502637 | − | 0.888084i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.98084e7 | + | 3.52975e9i | −0.0605379 | + | 2.14094i | ||||
\(431\) | −8.21789e8 | −0.494413 | −0.247206 | − | 0.968963i | \(-0.579513\pi\) | ||||
−0.247206 | + | 0.968963i | \(0.579513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.34831e8 | 0.139011 | 0.0695054 | − | 0.997582i | \(-0.477858\pi\) | ||||
0.0695054 | + | 0.997582i | \(0.477858\pi\) | |||||||
\(434\) | 2.17946e7 | − | 7.70771e8i | 0.0127978 | − | 0.452597i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.67035e7 | + | 1.00186e9i | −0.0327648 | + | 0.578903i | ||||
\(437\) | 2.40013e9 | 1.37578 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.08919e9i | 1.17856i | 0.807928 | + | 0.589281i | \(0.200589\pi\) | ||||
−0.807928 | + | 0.589281i | \(0.799411\pi\) | |||||||
\(440\) | −2.27137e9 | − | 1.93090e8i | −1.27117 | − | 0.108062i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.50659e7 | − | 5.32810e8i | 0.00829885 | − | 0.293491i | ||||
\(443\) | 4.20790e8i | 0.229960i | 0.993368 | + | 0.114980i | \(0.0366804\pi\) | ||||
−0.993368 | + | 0.114980i | \(0.963320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.92140e9i | − | 1.57156i | ||||||
\(446\) | −7.17860e8 | − | 2.02985e7i | −0.383149 | − | 0.0108341i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.27144e8 | − | 7.42412e8i | 0.0668073 | − | 0.390097i | ||||
\(449\) | − | 1.20517e9i | − | 0.628329i | −0.949369 | − | 0.314164i | \(-0.898276\pi\) | ||
0.949369 | − | 0.314164i | \(-0.101724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.08984e8 | 0.312599 | ||||||||
\(452\) | −9.71422e7 | + | 1.71635e9i | −0.0494793 | + | 0.874224i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.84218e9 | + | 5.20902e7i | 0.923926 | + | 0.0261253i | ||||
\(455\) | 2.09353e9 | 1.04193 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.17565e8 | 0.0576198 | 0.0288099 | − | 0.999585i | \(-0.490828\pi\) | ||||
0.0288099 | + | 0.999585i | \(0.490828\pi\) | |||||||
\(458\) | 3.22634e8 | + | 9.12292e6i | 0.156921 | + | 0.00443715i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.68290e9 | − | 2.08445e8i | −1.76416 | − | 0.0998478i | ||||
\(461\) | −1.15104e9 | −0.547190 | −0.273595 | − | 0.961845i | \(-0.588213\pi\) | ||||
−0.273595 | + | 0.961845i | \(0.588213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.00264e9i | − | 0.937712i | −0.883275 | − | 0.468856i | \(-0.844666\pi\) | ||
0.883275 | − | 0.468856i | \(-0.155334\pi\) | |||||||
\(464\) | −3.03338e9 | − | 3.44469e8i | −1.40966 | − | 0.160080i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.80899e8 | − | 2.77362e7i | −0.449028 | − | 0.0126969i | ||||
\(467\) | 1.12001e9i | 0.508876i | 0.967089 | + | 0.254438i | \(0.0818905\pi\) | ||||
−0.967089 | + | 0.254438i | \(0.918110\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.19423e8i | 0.366778i | ||||||||
\(470\) | −3.10457e7 | + | 1.09794e9i | −0.0137930 | + | 0.487793i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.85990e9 | − | 2.43121e8i | −1.25186 | − | 0.106421i | ||||
\(473\) | − | 2.89188e9i | − | 1.25651i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.15006e9 | 1.34862 | ||||||||
\(476\) | −1.52913e8 | − | 8.65460e6i | −0.0649862 | − | 0.00367809i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.07267e8 | − | 3.79352e9i | 0.0449230 | − | 1.58871i | ||||
\(479\) | 1.11855e9 | 0.465031 | 0.232515 | − | 0.972593i | \(-0.425304\pi\) | ||||
0.232515 | + | 0.972593i | \(0.425304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.68726e9 | −1.10104 | ||||||||
\(482\) | −1.37229e8 | + | 4.85315e9i | −0.0558191 | + | 1.97405i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.26484e8 | − | 3.54577e7i | −0.251160 | − | 0.0142152i | ||||
\(485\) | −5.56371e9 | −2.21446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.33703e9i | 1.30921i | 0.755972 | + | 0.654604i | \(0.227165\pi\) | ||||
−0.755972 | + | 0.654604i | \(0.772835\pi\) | |||||||
\(488\) | 1.99029e9 | + | 1.69195e8i | 0.775259 | + | 0.0659051i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.15458e7 | + | 3.23754e9i | −0.0351522 | + | 1.24316i | ||||
\(491\) | 4.90001e8i | 0.186815i | 0.995628 | + | 0.0934075i | \(0.0297759\pi\) | ||||
−0.995628 | + | 0.0934075i | \(0.970224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.20764e8i | 0.233325i | ||||||||
\(494\) | 5.49006e9 | + | 1.55239e8i | 2.04896 | + | 0.0579371i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.50803e8 | + | 3.08915e9i | −0.129086 | + | 1.13672i | ||||
\(497\) | − | 1.83896e9i | − | 0.671931i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.65302e9 | 0.595563 | 0.297781 | − | 0.954634i | \(-0.403753\pi\) | ||||
0.297781 | + | 0.954634i | \(0.403753\pi\) | |||||||
\(500\) | −7.18463e8 | − | 4.06635e7i | −0.257045 | − | 0.0145482i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.77644e9 | − | 5.02314e7i | −0.626741 | − | 0.0177220i | ||||
\(503\) | 1.28708e7 | 0.00450938 | 0.00225469 | − | 0.999997i | \(-0.499282\pi\) | ||||
0.00225469 | + | 0.999997i | \(0.499282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.18694e9 | −1.79222 | ||||||||
\(506\) | 3.01978e9 | + | 8.53883e7i | 1.03621 | + | 0.0293003i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.11942e8 | − | 3.74469e9i | 0.0717289 | − | 1.26734i | ||||
\(509\) | 5.13852e8 | 0.172713 | 0.0863567 | − | 0.996264i | \(-0.472478\pi\) | ||||
0.0863567 | + | 0.996264i | \(0.472478\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.87385e8i | − | 0.0621243i | ||||||
\(512\) | −7.64363e8 | + | 2.93924e9i | −0.251684 | + | 0.967810i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.31232e8 | − | 1.50213e7i | −0.172549 | − | 0.00487907i | ||||
\(515\) | − | 3.47896e9i | − | 1.12234i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.99530e8i | − | 0.286285i | ||||||
\(518\) | −2.18250e7 | + | 7.71847e8i | −0.00689923 | + | 0.243993i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.41081e9 | − | 7.15006e8i | −2.62317 | − | 0.222997i | ||||
\(521\) | − | 4.90297e9i | − | 1.51889i | −0.650570 | − | 0.759446i | \(-0.725470\pi\) | ||
0.650570 | − | 0.759446i | \(-0.274530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.66052e8 | 0.0813224 | 0.0406612 | − | 0.999173i | \(-0.487054\pi\) | ||||
0.0406612 | + | 0.999173i | \(0.487054\pi\) | |||||||
\(524\) | 3.09515e8 | − | 5.46866e9i | 0.0939772 | − | 1.66043i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.20836e7 | − | 1.13465e9i | 0.00961244 | − | 0.339946i | ||||
\(527\) | 6.32178e8 | 0.188149 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.48375e9 | 0.435778 | ||||||||
\(530\) | −9.64868e7 | + | 3.41228e9i | −0.0281515 | + | 0.995586i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.91768e7 | − | 1.57562e9i | 0.0256780 | − | 0.453691i | ||||
\(533\) | 2.25505e9 | 0.645077 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.64596e9i | 1.31171i | ||||||||
\(536\) | 2.79859e8 | − | 3.29205e9i | 0.0784986 | − | 0.923400i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.65900e7 | + | 3.06227e9i | −0.0239734 | + | 0.847825i | ||||
\(539\) | − | 2.65248e9i | − | 0.729611i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.26607e9i | 0.615295i | 0.951500 | + | 0.307647i | \(0.0995417\pi\) | ||||
−0.951500 | + | 0.307647i | \(0.900458\pi\) | |||||||
\(542\) | −7.01872e9 | − | 1.98464e8i | −1.89348 | − | 0.0535407i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.11378e8 | + | 8.69949e7i | 0.162822 | + | 0.0231685i | ||||
\(545\) | − | 3.23130e9i | − | 0.855045i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.06164e9 | 1.58356 | 0.791780 | − | 0.610806i | \(-0.209155\pi\) | ||||
0.791780 | + | 0.610806i | \(0.209155\pi\) | |||||||
\(548\) | 2.58332e7 | − | 4.56433e8i | 0.00670573 | − | 0.118480i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.96332e9 | + | 1.12068e8i | 1.01576 | + | 0.0287219i | ||||
\(551\) | −6.39634e9 | −1.62892 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.38577e9 | −0.348459 | ||||||||
\(554\) | −6.71207e9 | − | 1.89793e8i | −1.67715 | − | 0.0474238i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.94558e9 | − | 3.36508e8i | −1.46701 | − | 0.0830297i | ||||
\(557\) | 2.14513e9 | 0.525968 | 0.262984 | − | 0.964800i | \(-0.415293\pi\) | ||||
0.262984 | + | 0.964800i | \(0.415293\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.07086e10i | − | 2.59293i | ||||||
\(560\) | −2.73677e8 | + | 2.40998e9i | −0.0658537 | + | 0.579903i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.82036e9 | + | 7.97494e7i | 0.670235 | + | 0.0189518i | ||||
\(563\) | 3.66627e9i | 0.865855i | 0.901429 | + | 0.432927i | \(0.142519\pi\) | ||||
−0.901429 | + | 0.432927i | \(0.857481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 5.53573e9i | − | 1.29124i | ||||||
\(566\) | 7.71431e7 | − | 2.72818e9i | 0.0178830 | − | 0.632435i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.28063e8 | + | 7.38807e9i | −0.143808 | + | 1.69165i | ||||
\(569\) | − | 4.28882e9i | − | 0.975989i | −0.872847 | − | 0.487994i | \(-0.837729\pi\) | ||
0.872847 | − | 0.487994i | \(-0.162271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.79269e9 | 0.627763 | 0.313881 | − | 0.949462i | \(-0.398371\pi\) | ||||
0.313881 | + | 0.949462i | \(0.398371\pi\) | |||||||
\(572\) | 6.90193e9 | + | 3.90635e8i | 1.54200 | + | 0.0872741i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.83148e7 | − | 6.47706e8i | 0.00404212 | − | 0.142951i | ||||
\(575\) | 6.41604e9 | 1.40744 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.42684e9 | −0.309214 | −0.154607 | − | 0.987976i | \(-0.549411\pi\) | ||||
−0.154607 | + | 0.987976i | \(0.549411\pi\) | |||||||
\(578\) | −1.27670e8 | + | 4.51508e9i | −0.0275006 | + | 0.972563i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.81494e9 | + | 5.55506e8i | 2.08877 | + | 0.118220i | ||||
\(581\) | 1.70700e9 | 0.361092 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.79564e9i | − | 0.584307i | ||||||
\(584\) | −6.39978e7 | + | 7.52824e8i | −0.0132960 | + | 0.156404i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.41142e8 | − | 4.99151e9i | 0.0289744 | − | 1.02469i | ||||
\(587\) | 8.26290e9i | 1.68616i | 0.537787 | + | 0.843081i | \(0.319260\pi\) | ||||
−0.537787 | + | 0.843081i | \(0.680740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.51395e9i | 1.31353i | ||||||||
\(590\) | 9.23878e9 | + | 2.61239e8i | 1.85196 | + | 0.0523668i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.51293e8 | − | 3.09346e9i | 0.0695894 | − | 0.612800i | ||||
\(593\) | 4.44985e9i | 0.876302i | 0.898901 | + | 0.438151i | \(0.144366\pi\) | ||||
−0.898901 | + | 0.438151i | \(0.855634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.93190e8 | 0.0959852 | ||||||||
\(596\) | −4.39390e9 | − | 2.48686e8i | −0.850136 | − | 0.0481160i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.11822e10 | + | 3.16191e8i | 2.13831 | + | 0.0604637i | ||||
\(599\) | −5.97431e9 | −1.13578 | −0.567890 | − | 0.823105i | \(-0.692240\pi\) | ||||
−0.567890 | + | 0.823105i | \(0.692240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.81457e9 | 1.09259 | 0.546295 | − | 0.837593i | \(-0.316038\pi\) | ||||
0.546295 | + | 0.837593i | \(0.316038\pi\) | |||||||
\(602\) | −3.07576e9 | − | 8.69713e7i | −0.574599 | − | 0.0162476i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.30689e8 | + | 9.37646e9i | −0.0979965 | + | 1.73145i | ||||
\(605\) | 2.02059e9 | 0.370966 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.54687e9i | 0.643703i | 0.946790 | + | 0.321851i | \(0.104305\pi\) | ||||
−0.946790 | + | 0.321851i | \(0.895695\pi\) | |||||||
\(608\) | −8.96394e8 | + | 6.29963e9i | −0.161747 | + | 1.13672i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.42954e9 | − | 1.81804e8i | −1.14690 | − | 0.0324302i | ||||
\(611\) | − | 3.33094e9i | − | 0.590775i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.92550e9i | 1.56502i | 0.622635 | + | 0.782512i | \(0.286062\pi\) | ||||
−0.622635 | + | 0.782512i | \(0.713938\pi\) | |||||||
\(614\) | 1.28868e8 | − | 4.55746e9i | 0.0224676 | − | 0.794572i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.68255e8 | − | 1.97923e9i | 0.0290025 | − | 0.341164i | ||||
\(617\) | 6.93844e9i | 1.18923i | 0.804012 | + | 0.594613i | \(0.202695\pi\) | ||||
−0.804012 | + | 0.594613i | \(0.797305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.41395e9 | −0.239617 | −0.119808 | − | 0.992797i | \(-0.538228\pi\) | ||||
−0.119808 | + | 0.992797i | \(0.538228\pi\) | |||||||
\(620\) | 5.65720e8 | − | 9.99541e9i | 0.0953302 | − | 1.68434i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.33197e7 | + | 1.17836e9i | −0.00555182 | + | 0.196341i | ||||
\(623\) | 2.54566e9 | 0.421786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.85187e9 | −0.794931 | ||||||||
\(626\) | −2.01111e8 | + | 7.11234e9i | −0.0327662 | + | 1.15878i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.73518e8 | − | 4.83264e9i | 0.0440683 | − | 0.778620i | ||||
\(629\) | −6.33060e8 | −0.101430 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.00062e8i | − | 0.110926i | −0.998461 | − | 0.0554631i | \(-0.982336\pi\) | ||
0.998461 | − | 0.0554631i | \(-0.0176635\pi\) | |||||||
\(632\) | 5.56736e9 | + | 4.73283e8i | 0.877282 | + | 0.0745781i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.76443e8 | − | 6.23995e9i | 0.0274974 | − | 0.972453i | ||||
\(635\) | 1.20777e10i | 1.87187i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 9.82207e9i | − | 1.50562i | ||||||
\(638\) | −8.04771e9 | − | 2.27560e8i | −1.22687 | − | 0.0346915i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.92259e9 | − | 9.58869e9i | 0.289905 | − | 1.44587i | ||||
\(641\) | 1.19021e10i | 1.78493i | 0.451117 | + | 0.892465i | \(0.351026\pi\) | ||||
−0.451117 | + | 0.892465i | \(0.648974\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.57955e9 | −0.382653 | −0.191326 | − | 0.981526i | \(-0.561279\pi\) | ||||
−0.191326 | + | 0.981526i | \(0.561279\pi\) | |||||||
\(644\) | 1.81635e8 | − | 3.20922e9i | 0.0267978 | − | 0.473477i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.29334e9 | + | 3.65709e7i | 0.188755 | + | 0.00533730i | ||||
\(647\) | −5.01688e9 | −0.728230 | −0.364115 | − | 0.931354i | \(-0.618629\pi\) | ||||
−0.364115 | + | 0.931354i | \(0.618629\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.56924e9 | −1.08692 | ||||||||
\(650\) | 1.46761e10 | + | 4.14986e8i | 2.09611 | + | 0.0592703i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.51939e9 | + | 1.42592e8i | 0.355982 | + | 0.0201479i | ||||
\(653\) | −9.90200e9 | −1.39164 | −0.695820 | − | 0.718216i | \(-0.744959\pi\) | ||||
−0.695820 | + | 0.718216i | \(0.744959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.76380e10i | 2.45247i | ||||||||
\(656\) | −2.94792e8 | + | 2.59592e9i | −0.0407711 | + | 0.359028i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.56725e8 | − | 2.70527e7i | −0.130917 | − | 0.00370186i | ||||
\(659\) | − | 3.56641e9i | − | 0.485437i | −0.970097 | − | 0.242719i | \(-0.921961\pi\) | ||
0.970097 | − | 0.242719i | \(-0.0780391\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.03477e10i | − | 1.39360i | −0.717265 | − | 0.696800i | \(-0.754606\pi\) | ||
0.717265 | − | 0.696800i | \(-0.245394\pi\) | |||||||
\(662\) | 2.56961e8 | − | 9.08748e9i | 0.0344242 | − | 1.21742i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.85792e9 | − | 5.82995e8i | −0.909085 | − | 0.0772816i | ||||
\(665\) | 5.08182e9i | 0.670106i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.30281e10 | −1.69996 | ||||||||
\(668\) | −1.05030e10 | − | 5.94447e8i | −1.36331 | − | 0.0771606i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.00714e8 | + | 1.06348e10i | −0.0386271 | + | 1.36606i | ||||
\(671\) | 5.26765e9 | 0.673113 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.52836e9 | 1.20494 | 0.602470 | − | 0.798142i | \(-0.294183\pi\) | ||||
0.602470 | + | 0.798142i | \(0.294183\pi\) | |||||||
\(674\) | 2.79753e8 | − | 9.89352e9i | 0.0351937 | − | 1.24463i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.75387e10 | + | 9.92655e8i | 2.18366 | + | 0.123590i | ||||
\(677\) | 1.90058e8 | 0.0235411 | 0.0117705 | − | 0.999931i | \(-0.496253\pi\) | ||||
0.0117705 | + | 0.999931i | \(0.496253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.84812e9i | − | 0.594332i | ||||||
\(680\) | −1.98140e9 | − | 1.68440e8i | −0.241653 | − | 0.0205430i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.31744e8 | + | 8.19569e9i | −0.0279746 | + | 0.989327i | ||||
\(683\) | − | 3.28062e9i | − | 0.393988i | −0.980405 | − | 0.196994i | \(-0.936882\pi\) | ||
0.980405 | − | 0.196994i | \(-0.0631180\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.47213e9i | 0.174996i | ||||||||
\(686\) | −6.16624e9 | − | 1.74359e8i | −0.729267 | − | 0.0206210i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.23273e10 | + | 1.39988e9i | 1.44313 | + | 0.163882i | ||||
\(689\) | − | 1.03522e10i | − | 1.20577i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.49476e9 | 0.402944 | 0.201472 | − | 0.979494i | \(-0.435428\pi\) | ||||
0.201472 | + | 0.979494i | \(0.435428\pi\) | |||||||
\(692\) | −3.38451e9 | − | 1.91556e8i | −0.388261 | − | 0.0219748i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.57854e9 | − | 1.01188e8i | −0.406395 | − | 0.0114914i | ||||
\(695\) | 1.91762e10 | 2.16678 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.31241e8 | 0.0594260 | ||||||||
\(698\) | 4.99005e9 | + | 1.41101e8i | 0.555407 | + | 0.0157049i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.38388e8 | − | 4.21195e9i | 0.0262689 | − | 0.464131i | ||||
\(701\) | 1.22907e10 | 1.34761 | 0.673805 | − | 0.738909i | \(-0.264659\pi\) | ||||
0.673805 | + | 0.738909i | \(0.264659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.52304e9i | − | 0.708120i | ||||||
\(704\) | −1.35194e9 | + | 7.89414e9i | −0.146034 | + | 0.852709i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.28690e9 | − | 1.21218e8i | −0.458487 | − | 0.0129643i | ||||
\(707\) | − | 4.51981e9i | − | 0.481008i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.80574e9i | 0.927906i | 0.885860 | + | 0.463953i | \(0.153569\pi\) | ||||
−0.885860 | + | 0.463953i | \(0.846431\pi\) | |||||||
\(710\) | 6.74867e8 | − | 2.38668e10i | 0.0707642 | − | 2.50259i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.02272e10 | − | 8.69422e8i | −1.06189 | − | 0.0902715i | ||||
\(713\) | 1.32676e10i | 1.37082i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.22607e10 | −2.27755 | ||||||||
\(716\) | 6.69075e8 | − | 1.18215e10i | 0.0681208 | − | 1.20359i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.41775e8 | − | 5.01389e9i | 0.0142943 | − | 0.505521i | ||||
\(719\) | −6.43721e9 | −0.645872 | −0.322936 | − | 0.946421i | \(-0.604670\pi\) | ||||
−0.322936 | + | 0.946421i | \(0.604670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.03150e9 | 0.301221 | ||||||||
\(722\) | −9.09813e7 | + | 3.21757e9i | −0.00899647 | + | 0.318162i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.72603e8 | + | 1.01170e10i | −0.0560749 | + | 0.990759i | ||||
\(725\) | −1.70987e10 | −1.66641 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.15462e10i | − | 1.11447i | −0.830354 | − | 0.557236i | \(-0.811862\pi\) | ||
0.830354 | − | 0.557236i | \(-0.188138\pi\) | |||||||
\(728\) | 6.23044e8 | − | 7.32904e9i | 0.0598493 | − | 0.704023i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.87671e7 | − | 2.43196e9i | 0.00654260 | − | 0.231381i | ||||
\(731\) | − | 2.52270e9i | − | 0.238867i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.00798e9i | − | 0.375890i | −0.982180 | − | 0.187945i | \(-0.939817\pi\) | ||
0.982180 | − | 0.187945i | \(-0.0601828\pi\) | |||||||
\(734\) | 3.12499e9 | + | 8.83633e7i | 0.291684 | + | 0.00824775i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.82577e9 | + | 1.28311e10i | −0.168801 | + | 1.18629i | ||||
\(737\) | − | 8.71300e9i | − | 0.801736i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.11260e10 | −1.01411 | −0.507055 | − | 0.861914i | \(-0.669266\pi\) | ||||
−0.507055 | + | 0.861914i | \(0.669266\pi\) | |||||||
\(740\) | −5.66510e8 | + | 1.00094e10i | −0.0513921 | + | 0.908020i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.97340e9 | − | 8.40769e7i | −0.267202 | − | 0.00755550i | ||||
\(743\) | −3.41895e9 | −0.305796 | −0.152898 | − | 0.988242i | \(-0.548861\pi\) | ||||
−0.152898 | + | 0.988242i | \(0.548861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.41716e10 | 1.25566 | ||||||||
\(746\) | −1.40228e10 | − | 3.96514e8i | −1.23666 | − | 0.0349681i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.62594e9 | + | 9.20251e7i | 0.142053 | + | 0.00803990i | ||||
\(749\) | −4.04841e9 | −0.352045 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.35287e9i | 0.202702i | 0.994851 | + | 0.101351i | \(0.0323165\pi\) | ||||
−0.994851 | + | 0.101351i | \(0.967683\pi\) | |||||||
\(752\) | 3.83443e9 | + | 4.35437e8i | 0.328805 | + | 0.0373390i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.98005e10 | − | 8.42649e8i | −2.53176 | − | 0.0715891i | ||||
\(755\) | − | 3.02418e10i | − | 2.55737i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.65364e9i | − | 0.222334i | −0.993802 | − | 0.111167i | \(-0.964541\pi\) | ||
0.993802 | − | 0.111167i | \(-0.0354589\pi\) | |||||||
\(758\) | 1.60030e8 | − | 5.65951e9i | 0.0133463 | − | 0.471994i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.73560e9 | − | 2.04163e10i | 0.143418 | − | 1.68706i | ||||
\(761\) | 4.75292e9i | 0.390944i | 0.980709 | + | 0.195472i | \(0.0626238\pi\) | ||||
−0.980709 | + | 0.195472i | \(0.937376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.81570e9 | 0.229483 | ||||||||
\(764\) | 1.31532e10 | + | 7.44445e8i | 1.06710 | + | 0.0603956i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.48371e8 | − | 5.24718e9i | 0.0119275 | − | 0.421818i | ||||
\(767\) | −2.80287e10 | −2.24295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.27901e10 | −1.01422 | −0.507108 | − | 0.861883i | \(-0.669285\pi\) | ||||
−0.507108 | + | 0.861883i | \(0.669285\pi\) | |||||||
\(770\) | −1.80794e8 | + | 6.39381e9i | −0.0142714 | + | 0.504710i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.64287e9 | + | 4.32571e8i | 0.597855 | + | 0.0338374i | ||||
\(773\) | 1.92520e10 | 1.49916 | 0.749579 | − | 0.661915i | \(-0.230256\pi\) | ||||
0.749579 | + | 0.661915i | \(0.230256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.74131e10i | 1.34376i | ||||||||
\(776\) | −1.65579e9 | + | 1.94774e10i | −0.127200 | + | 1.49629i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.79075e7 | − | 3.10887e9i | 0.00669264 | − | 0.236687i | ||||
\(779\) | 5.47390e9i | 0.414873i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.95538e10i | 1.46877i | ||||||||
\(782\) | 2.63427e9 | + | 7.44876e7i | 0.196987 | + | 0.00557006i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.13067e10 | + | 1.28399e9i | 0.837976 | + | 0.0951603i | ||||
\(785\) | 1.55866e10i | 1.15003i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.18441e9 | −0.525388 | −0.262694 | − | 0.964879i | \(-0.584611\pi\) | ||||
−0.262694 | + | 0.964879i | \(0.584611\pi\) | |||||||
\(788\) | 2.15151e10 | + | 1.21771e9i | 1.56640 | + | 0.0886549i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.79851e10 | − | 5.08553e8i | −1.29783 | − | 0.0366979i | ||||
\(791\) | 4.82374e9 | 0.346550 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.95060e10 | 1.38903 | ||||||||
\(794\) | −1.44974e10 | − | 4.09933e8i | −1.02782 | − | 0.0290630i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.68539e8 | − | 1.18121e10i | 0.0469820 | − | 0.830100i | ||||
\(797\) | 2.37227e10 | 1.65981 | 0.829907 | − | 0.557901i | \(-0.188393\pi\) | ||||
0.829907 | + | 0.557901i | \(0.188393\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.84695e8i | − | 0.0544236i | ||||||
\(800\) | −2.39625e9 | + | 1.68402e10i | −0.165469 | + | 1.16287i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.48181e9 | + | 7.01767e7i | 0.169887 | + | 0.00480377i | ||||
\(803\) | 1.99248e9i | 0.135797i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.03506e10i | 0.699329i | ||||||||
\(806\) | −8.58143e8 | + | 3.03484e10i | −0.0577281 | + | 2.04157i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.54366e9 | + | 1.81585e10i | −0.102946 | + | 1.21099i | ||||
\(809\) | − | 5.26128e9i | − | 0.349359i | −0.984625 | − | 0.174679i | \(-0.944111\pi\) | ||
0.984625 | − | 0.174679i | \(-0.0558889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.25968e9 | 0.412078 | 0.206039 | − | 0.978544i | \(-0.433943\pi\) | ||||
0.206039 | + | 0.978544i | \(0.433943\pi\) | |||||||
\(812\) | −4.84058e8 | + | 8.55257e9i | −0.0317286 | + | 0.560597i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.32068e8 | − | 8.20713e9i | 0.0150810 | − | 0.533342i | ||||
\(815\) | −8.12574e9 | −0.525789 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.59939e10 | 1.66761 | ||||||||
\(818\) | 6.00054e7 | − | 2.12210e9i | 0.00383313 | − | 0.135559i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.75394e8 | − | 8.39949e9i | 0.0301096 | − | 0.531991i | ||||
\(821\) | 4.64242e9 | 0.292781 | 0.146391 | − | 0.989227i | \(-0.453234\pi\) | ||||
0.146391 | + | 0.989227i | \(0.453234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.47371e10i | − | 0.921540i | −0.887520 | − | 0.460770i | \(-0.847573\pi\) | ||
0.887520 | − | 0.460770i | \(-0.152427\pi\) | |||||||
\(824\) | −1.21791e10 | − | 1.03535e9i | −0.758354 | − | 0.0644679i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.27639e8 | + | 8.05052e9i | −0.0140546 | + | 0.497043i | ||||
\(827\) | − | 5.88827e9i | − | 0.362008i | −0.983482 | − | 0.181004i | \(-0.942065\pi\) | ||
0.983482 | − | 0.181004i | \(-0.0579348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.00855e10i | − | 1.83407i | −0.398807 | − | 0.917035i | \(-0.630576\pi\) | ||
0.398807 | − | 0.917035i | \(-0.369424\pi\) | |||||||
\(830\) | 2.21542e10 | + | 6.26440e8i | 1.34488 | + | 0.0380283i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.00619e9 | + | 2.92318e10i | −0.301353 | + | 1.75964i | ||||
\(833\) | − | 2.31386e9i | − | 0.138701i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.38751e10 | 2.01362 | ||||||||
\(836\) | −9.48226e8 | + | 1.67537e10i | −0.0561293 | + | 0.991719i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.95905e9 | + | 2.53329e8i | 0.525906 | + | 0.0148707i | ||||
\(839\) | 2.18944e10 | 1.27987 | 0.639937 | − | 0.768428i | \(-0.278961\pi\) | ||||
0.639937 | + | 0.768428i | \(0.278961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.74699e10 | 1.01276 | ||||||||
\(842\) | −6.28877e8 | − | 1.77824e7i | −0.0363056 | − | 0.00102659i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.54665e10 | − | 8.75374e8i | −0.885511 | − | 0.0501182i | ||||
\(845\) | −5.65673e10 | −3.22528 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.76071e9i | 0.0995623i | ||||||||
\(848\) | 1.19170e10 | + | 1.35329e9i | 0.671091 | + | 0.0762089i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.45736e9 | + | 9.77617e7i | 0.193098 | + | 0.00546012i | ||||
\(851\) | − | 1.32861e10i | − | 0.739001i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.74899e10i | − | 0.964862i | −0.875934 | − | 0.482431i | \(-0.839754\pi\) | ||
0.875934 | − | 0.482431i | \(-0.160246\pi\) | |||||||
\(854\) | 1.58421e8 | − | 5.60259e9i | 0.00870382 | − | 0.307812i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.62646e10 | + | 1.38266e9i | 0.886308 | + | 0.0753454i | ||||
\(857\) | − | 1.86981e10i | − | 1.01476i | −0.861721 | − | 0.507382i | \(-0.830613\pi\) | ||
0.861721 | − | 0.507382i | \(-0.169387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.23322e10 | −1.74044 | −0.870221 | − | 0.492662i | \(-0.836024\pi\) | ||||
−0.870221 | + | 0.492662i | \(0.836024\pi\) | |||||||
\(860\) | −3.98867e10 | − | 2.25750e9i | −2.13837 | − | 0.121028i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.62794e8 | − | 9.29376e9i | 0.0139746 | − | 0.494215i | ||||
\(863\) | 1.19116e9 | 0.0630859 | 0.0315429 | − | 0.999502i | \(-0.489958\pi\) | ||||
0.0315429 | + | 0.999502i | \(0.489958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.09160e10 | 0.573465 | ||||||||
\(866\) | −7.50950e7 | + | 2.65575e9i | −0.00392915 | + | 0.138955i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.70983e9 | + | 4.92959e8i | 0.452054 | + | 0.0255854i | ||||
\(869\) | 1.47350e10 | 0.761694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.22640e10i | − | 1.65445i | ||||||
\(872\) | −1.13121e10 | − | 9.61649e8i | −0.577746 | − | 0.0491144i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.67519e8 | + | 2.71435e10i | −0.0388865 | + | 1.37523i | ||||
\(875\) | 2.01921e9i | 0.101895i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.08862e10i | 1.04559i | 0.852459 | + | 0.522794i | \(0.175110\pi\) | ||||
−0.852459 | + | 0.522794i | \(0.824890\pi\) | |||||||
\(878\) | −2.36271e10 | − | 6.68088e8i | −1.17809 | − | 0.0333122i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.91003e9 | − | 2.56256e10i | 0.143949 | − | 1.26761i | ||||
\(881\) | 4.96861e9i | 0.244804i | 0.992481 | + | 0.122402i | \(0.0390598\pi\) | ||||
−0.992481 | + | 0.122402i | \(0.960940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.57384e10 | 1.25811 | 0.629056 | − | 0.777360i | \(-0.283442\pi\) | ||||
0.629056 | + | 0.777360i | \(0.283442\pi\) | |||||||
\(884\) | 6.02083e9 | + | 3.40767e8i | 0.293139 | + | 0.0165911i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.75879e9 | − | 1.34561e8i | −0.229868 | − | 0.00649984i | ||||
\(887\) | 3.14294e10 | 1.51218 | 0.756089 | − | 0.654468i | \(-0.227108\pi\) | ||||
0.756089 | + | 0.654468i | \(0.227108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.05243e10 | −0.502386 | ||||||||
\(890\) | 3.30387e10 | + | 9.34213e8i | 1.57093 | + | 0.0444202i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.59118e8 | − | 8.11192e9i | 0.0216595 | − | 0.382690i | ||||
\(893\) | 8.08549e9 | 0.379950 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.81278e10i | 1.77771i | ||||||||
\(896\) | 8.35542e9 | + | 1.67531e9i | 0.388052 | + | 0.0778068i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.36295e10 | + | 3.85393e8i | 0.628078 | + | 0.0177598i | ||||
\(899\) | − | 3.53582e10i | − | 1.62305i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.43875e9i | − | 0.111079i | ||||||
\(902\) | −1.94743e8 | + | 6.88712e9i | −0.00883564 | + | 0.312474i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.93795e10 | − | 1.64746e9i | −0.872476 | − | 0.0741695i | ||||
\(905\) | − | 3.26303e10i | − | 1.46336i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.28352e10 | 1.01620 | 0.508099 | − | 0.861299i | \(-0.330348\pi\) | ||||
0.508099 | + | 0.861299i | \(0.330348\pi\) | |||||||
\(908\) | −1.17820e9 | + | 2.08169e10i | −0.0522297 | + | 0.922819i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.69475e8 | + | 2.36761e10i | −0.0294503 | + | 1.04152i | ||||
\(911\) | −1.67176e10 | −0.732589 | −0.366295 | − | 0.930499i | \(-0.619374\pi\) | ||||
−0.366295 | + | 0.930499i | \(0.619374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.81507e10 | −0.789307 | ||||||||
\(914\) | −3.75953e7 | + | 1.32957e9i | −0.00162863 | + | 0.0575968i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.06346e8 | + | 3.64581e9i | −0.00887076 | + | 0.156733i | ||||
\(917\) | −1.53694e10 | −0.658211 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.46269e10i | 1.47167i | 0.677162 | + | 0.735834i | \(0.263210\pi\) | ||||
−0.677162 | + | 0.735834i | \(0.736790\pi\) | |||||||
\(920\) | 3.53507e9 | − | 4.15840e10i | 0.149672 | − | 1.76063i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.68084e8 | − | 1.30174e10i | 0.0154664 | − | 0.546972i | ||||
\(923\) | 7.24073e10i | 3.03093i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.74375e10i | − | 0.724414i | ||||||
\(926\) | 2.26482e10 | + | 6.40410e8i | 0.937338 | + | 0.0265045i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.86569e9 | − | 3.41949e10i | 0.199860 | − | 1.40457i | ||||
\(929\) | 1.05754e10i | 0.432753i | 0.976310 | + | 0.216377i | \(0.0694239\pi\) | ||||
−0.976310 | + | 0.216377i | \(0.930576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.38420e10 | 0.968320 | ||||||||
\(932\) | 6.27349e8 | − | 1.10843e10i | 0.0253836 | − | 0.448490i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.26664e10 | − | 3.58159e8i | −0.508673 | − | 0.0143834i | ||||
\(935\) | −5.24413e9 | −0.209813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.29022e10 | −1.30658 | −0.653290 | − | 0.757107i | \(-0.726612\pi\) | ||||
−0.653290 | + | 0.757107i | \(0.726612\pi\) | |||||||
\(938\) | −9.26701e9 | − | 2.62037e8i | −0.366631 | − | 0.0103670i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.24069e10 | − | 7.02204e8i | −0.487208 | − | 0.0275750i | ||||
\(941\) | −3.87420e9 | −0.151572 | −0.0757859 | − | 0.997124i | \(-0.524147\pi\) | ||||
−0.0757859 | + | 0.997124i | \(0.524147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.11492e10i | 0.432966i | ||||||||
\(944\) | 3.66405e9 | − | 3.22654e10i | 0.141762 | − | 1.24835i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.27049e10 | + | 9.24775e8i | 1.25601 | + | 0.0355154i | ||||
\(947\) | − | 3.64475e10i | − | 1.39458i | −0.716791 | − | 0.697288i | \(-0.754390\pi\) | ||
0.716791 | − | 0.697288i | \(-0.245610\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.37811e9i | 0.280229i | ||||||||
\(950\) | −1.00733e9 | + | 3.56246e10i | −0.0381190 | + | 1.34809i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.46776e8 | − | 1.72656e9i | 0.00551346 | − | 0.0648563i | ||||
\(953\) | 4.75252e10i | 1.77868i | 0.457242 | + | 0.889342i | \(0.348837\pi\) | ||||
−0.457242 | + | 0.889342i | \(0.651163\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.24228e10 | −1.57611 | ||||||||
\(956\) | 4.28673e10 | + | 2.42620e9i | 1.58681 | + | 0.0898100i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.57693e8 | + | 1.26499e10i | −0.0131441 | + | 0.464845i | ||||
\(959\) | −1.28278e9 | −0.0469666 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.49574e9 | −0.308794 | ||||||||
\(962\) | 8.59341e8 | − | 3.03908e10i | 0.0311209 | − | 1.10060i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.48413e10 | − | 3.10391e9i | −1.97169 | − | 0.111594i | ||||
\(965\) | −2.46504e10 | −0.883037 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.17956e10i | − | 1.84205i | −0.389508 | − | 0.921023i | \(-0.627355\pi\) | ||
0.389508 | − | 0.921023i | \(-0.372645\pi\) | |||||||
\(968\) | 6.01337e8 | − | 7.07368e9i | 0.0213086 | − | 0.250658i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.77918e9 | − | 6.29210e10i | 0.0625919 | − | 2.21358i | ||||
\(971\) | 4.27726e10i | 1.49933i | 0.661816 | + | 0.749667i | \(0.269786\pi\) | ||||
−0.661816 | + | 0.749667i | \(0.730214\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.67098e10i | 0.581535i | ||||||||
\(974\) | −3.77391e10 | − | 1.06712e9i | −1.30868 | − | 0.0370048i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.54992e9 | + | 2.24544e10i | −0.0877915 | + | 0.773086i | ||||
\(977\) | − | 4.75207e10i | − | 1.63024i | −0.579291 | − | 0.815121i | \(-0.696670\pi\) | ||
0.579291 | − | 0.815121i | \(-0.303330\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.70682e10 | −0.921977 | ||||||||
\(980\) | −3.65847e10 | − | 2.07062e9i | −1.24167 | − | 0.0702763i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.54151e9 | − | 1.56694e8i | −0.186740 | − | 0.00528034i | ||||
\(983\) | −3.39823e10 | −1.14108 | −0.570540 | − | 0.821270i | \(-0.693266\pi\) | ||||
−0.570540 | + | 0.821270i | \(0.693266\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.93923e10 | −2.31358 | ||||||||
\(986\) | −7.02033e9 | − | 1.98510e8i | −0.233232 | − | 0.00659496i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.51126e9 | + | 6.20385e10i | −0.115828 | + | 2.04650i | ||||
\(989\) | 5.29444e10 | 1.74033 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6.63551e9i | − | 0.216579i | −0.994119 | − | 0.108289i | \(-0.965463\pi\) | ||
0.994119 | − | 0.108289i | \(-0.0345373\pi\) | |||||||
\(992\) | −3.48236e10 | − | 4.95516e9i | −1.13262 | − | 0.161163i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.07971e10 | + | 5.88067e8i | 0.671662 | + | 0.0189922i | ||||
\(995\) | 3.80973e10i | 1.22606i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.33996e10i | 1.70650i | 0.521506 | + | 0.853248i | \(0.325370\pi\) | ||||
−0.521506 | + | 0.853248i | \(0.674630\pi\) | |||||||
\(998\) | −5.28609e8 | + | 1.86944e10i | −0.0168336 | + | 0.595325i | ||||
\(999\) | 0 | 0 |
(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 | 72.8.f.a.35.14 | yes | 28 | |
3.2 | odd | 2 | inner | 72.8.f.a.35.15 | yes | 28 | |
4.3 | odd | 2 | 288.8.f.a.143.26 | 28 | |||
8.3 | odd | 2 | inner | 72.8.f.a.35.16 | yes | 28 | |
8.5 | even | 2 | 288.8.f.a.143.3 | 28 | |||
12.11 | even | 2 | 288.8.f.a.143.4 | 28 | |||
24.5 | odd | 2 | 288.8.f.a.143.25 | 28 | |||
24.11 | even | 2 | inner | 72.8.f.a.35.13 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.8.f.a.35.13 | ✓ | 28 | 24.11 | even | 2 | inner | |
72.8.f.a.35.14 | yes | 28 | 1.1 | even | 1 | trivial | |
72.8.f.a.35.15 | yes | 28 | 3.2 | odd | 2 | inner | |
72.8.f.a.35.16 | yes | 28 | 8.3 | odd | 2 | inner | |
288.8.f.a.143.3 | 28 | 8.5 | even | 2 | |||
288.8.f.a.143.4 | 28 | 12.11 | even | 2 | |||
288.8.f.a.143.25 | 28 | 24.5 | odd | 2 | |||
288.8.f.a.143.26 | 28 | 4.3 | odd | 2 |