Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,7,Mod(47,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.47");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.8737317698\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.28 | ||
Character | \(\chi\) | \(=\) | 69.47 |
Dual form | 69.7.b.a.47.17 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.53332i | 0.566665i | 0.959022 | + | 0.283332i | \(0.0914400\pi\) | ||||
−0.959022 | + | 0.283332i | \(0.908560\pi\) | |||||||
\(3\) | −0.406897 | + | 26.9969i | −0.0150703 | + | 0.999886i | ||||
\(4\) | 43.4490 | 0.678891 | ||||||||
\(5\) | − | 169.748i | − | 1.35798i | −0.734146 | − | 0.678992i | \(-0.762417\pi\) | ||
0.734146 | − | 0.678992i | \(-0.237583\pi\) | |||||||
\(6\) | −122.386 | − | 1.84460i | −0.566601 | − | 0.00853980i | ||||
\(7\) | −134.238 | −0.391363 | −0.195682 | − | 0.980667i | \(-0.562692\pi\) | ||||
−0.195682 | + | 0.980667i | \(0.562692\pi\) | |||||||
\(8\) | 487.101i | 0.951369i | ||||||||
\(9\) | −728.669 | − | 21.9700i | −0.999546 | − | 0.0301371i | ||||
\(10\) | 769.522 | 0.769522 | ||||||||
\(11\) | 2613.65i | 1.96368i | 0.189724 | + | 0.981838i | \(0.439241\pi\) | ||||
−0.189724 | + | 0.981838i | \(0.560759\pi\) | |||||||
\(12\) | −17.6793 | + | 1172.99i | −0.0102311 | + | 0.678814i | ||||
\(13\) | −3449.14 | −1.56993 | −0.784966 | − | 0.619539i | \(-0.787319\pi\) | ||||
−0.784966 | + | 0.619539i | \(0.787319\pi\) | |||||||
\(14\) | − | 608.542i | − | 0.221772i | ||||||
\(15\) | 4582.67 | + | 69.0700i | 1.35783 | + | 0.0204652i | ||||
\(16\) | 572.554 | 0.139784 | ||||||||
\(17\) | 3824.51i | 0.778447i | 0.921143 | + | 0.389224i | \(0.127257\pi\) | ||||
−0.921143 | + | 0.389224i | \(0.872743\pi\) | |||||||
\(18\) | 99.5969 | − | 3303.29i | 0.0170777 | − | 0.566408i | ||||
\(19\) | −6532.99 | −0.952470 | −0.476235 | − | 0.879318i | \(-0.657999\pi\) | ||||
−0.476235 | + | 0.879318i | \(0.657999\pi\) | |||||||
\(20\) | − | 7375.38i | − | 0.921923i | ||||||
\(21\) | 54.6209 | − | 3624.01i | 0.00589795 | − | 0.391319i | ||||
\(22\) | −11848.5 | −1.11275 | ||||||||
\(23\) | − | 2536.99i | − | 0.208514i | ||||||
\(24\) | −13150.2 | − | 198.200i | −0.951261 | − | 0.0143374i | ||||
\(25\) | −13189.4 | −0.844120 | ||||||||
\(26\) | − | 15636.1i | − | 0.889625i | ||||||
\(27\) | 889.615 | − | 19662.9i | 0.0451971 | − | 0.998978i | ||||
\(28\) | −5832.49 | −0.265693 | ||||||||
\(29\) | 29638.9i | 1.21526i | 0.794221 | + | 0.607628i | \(0.207879\pi\) | ||||
−0.794221 | + | 0.607628i | \(0.792121\pi\) | |||||||
\(30\) | −313.116 | + | 20774.7i | −0.0115969 | + | 0.769434i | ||||
\(31\) | 17438.5 | 0.585362 | 0.292681 | − | 0.956210i | \(-0.405453\pi\) | ||||
0.292681 | + | 0.956210i | \(0.405453\pi\) | |||||||
\(32\) | 33770.0i | 1.03058i | ||||||||
\(33\) | −70560.6 | − | 1063.49i | −1.96345 | − | 0.0295931i | ||||
\(34\) | −17337.7 | −0.441119 | ||||||||
\(35\) | 22786.6i | 0.531465i | ||||||||
\(36\) | −31659.9 | − | 954.573i | −0.678582 | − | 0.0204598i | ||||
\(37\) | 25117.8 | 0.495879 | 0.247940 | − | 0.968776i | \(-0.420247\pi\) | ||||
0.247940 | + | 0.968776i | \(0.420247\pi\) | |||||||
\(38\) | − | 29616.2i | − | 0.539732i | ||||||
\(39\) | 1403.45 | − | 93116.2i | 0.0236593 | − | 1.56975i | ||||
\(40\) | 82684.3 | 1.29194 | ||||||||
\(41\) | − | 44919.6i | − | 0.651755i | −0.945412 | − | 0.325878i | \(-0.894340\pi\) | ||
0.945412 | − | 0.325878i | \(-0.105660\pi\) | |||||||
\(42\) | 16428.8 | + | 247.614i | 0.221747 | + | 0.00334216i | ||||
\(43\) | 346.138 | 0.00435355 | 0.00217677 | − | 0.999998i | \(-0.499307\pi\) | ||||
0.00217677 | + | 0.999998i | \(0.499307\pi\) | |||||||
\(44\) | 113561.i | 1.33312i | ||||||||
\(45\) | −3729.36 | + | 123690.i | −0.0409257 | + | 1.35737i | ||||
\(46\) | 11501.0 | 0.118158 | ||||||||
\(47\) | − | 163614.i | − | 1.57589i | −0.615743 | − | 0.787947i | \(-0.711144\pi\) | ||
0.615743 | − | 0.787947i | \(-0.288856\pi\) | |||||||
\(48\) | −232.971 | + | 15457.2i | −0.00210658 | + | 0.139768i | ||||
\(49\) | −99629.3 | −0.846835 | ||||||||
\(50\) | − | 59791.6i | − | 0.478333i | ||||||
\(51\) | −103250. | − | 1556.18i | −0.778359 | − | 0.0117314i | ||||
\(52\) | −149862. | −1.06581 | ||||||||
\(53\) | 190996.i | 1.28291i | 0.767160 | + | 0.641456i | \(0.221669\pi\) | ||||
−0.767160 | + | 0.641456i | \(0.778331\pi\) | |||||||
\(54\) | 89138.1 | + | 4032.91i | 0.566086 | + | 0.0256116i | ||||
\(55\) | 443662. | 2.66664 | ||||||||
\(56\) | − | 65387.3i | − | 0.372331i | ||||||
\(57\) | 2658.26 | − | 176371.i | 0.0143540 | − | 0.952362i | ||||
\(58\) | −134363. | −0.688643 | ||||||||
\(59\) | 17156.5i | 0.0835357i | 0.999127 | + | 0.0417678i | \(0.0132990\pi\) | ||||
−0.999127 | + | 0.0417678i | \(0.986701\pi\) | |||||||
\(60\) | 199113. | + | 3001.02i | 0.921818 | + | 0.0138936i | ||||
\(61\) | 301351. | 1.32765 | 0.663824 | − | 0.747889i | \(-0.268932\pi\) | ||||
0.663824 | + | 0.747889i | \(0.268932\pi\) | |||||||
\(62\) | 79054.4i | 0.331704i | ||||||||
\(63\) | 97814.8 | + | 2949.20i | 0.391186 | + | 0.0117946i | ||||
\(64\) | −116447. | −0.444209 | ||||||||
\(65\) | 585484.i | 2.13194i | ||||||||
\(66\) | 4821.13 | − | 319874.i | 0.0167694 | − | 1.11262i | ||||
\(67\) | 23407.9 | 0.0778284 | 0.0389142 | − | 0.999243i | \(-0.487610\pi\) | ||||
0.0389142 | + | 0.999243i | \(0.487610\pi\) | |||||||
\(68\) | 166171.i | 0.528481i | ||||||||
\(69\) | 68491.1 | + | 1032.30i | 0.208491 | + | 0.00314237i | ||||
\(70\) | −103299. | −0.301163 | ||||||||
\(71\) | 147413.i | 0.411870i | 0.978566 | + | 0.205935i | \(0.0660235\pi\) | ||||
−0.978566 | + | 0.205935i | \(0.933976\pi\) | |||||||
\(72\) | 10701.6 | − | 354935.i | 0.0286715 | − | 0.950936i | ||||
\(73\) | 546480. | 1.40477 | 0.702385 | − | 0.711797i | \(-0.252118\pi\) | ||||
0.702385 | + | 0.711797i | \(0.252118\pi\) | |||||||
\(74\) | 113867.i | 0.280997i | ||||||||
\(75\) | 5366.72 | − | 356073.i | 0.0127211 | − | 0.844024i | ||||
\(76\) | −283852. | −0.646623 | ||||||||
\(77\) | − | 350850.i | − | 0.768511i | ||||||
\(78\) | 422125. | + | 6362.27i | 0.889524 | + | 0.0134069i | ||||
\(79\) | −540217. | −1.09569 | −0.547844 | − | 0.836581i | \(-0.684551\pi\) | ||||
−0.547844 | + | 0.836581i | \(0.684551\pi\) | |||||||
\(80\) | − | 97189.8i | − | 0.189824i | ||||||
\(81\) | 530476. | + | 32017.7i | 0.998184 | + | 0.0602469i | ||||
\(82\) | 203635. | 0.369327 | ||||||||
\(83\) | 11319.8i | 0.0197972i | 0.999951 | + | 0.00989858i | \(0.00315087\pi\) | ||||
−0.999951 | + | 0.00989858i | \(0.996849\pi\) | |||||||
\(84\) | 2373.23 | − | 157459.i | 0.00400407 | − | 0.265663i | ||||
\(85\) | 649203. | 1.05712 | ||||||||
\(86\) | 1569.15i | 0.00246700i | ||||||||
\(87\) | −800159. | − | 12060.0i | −1.21512 | − | 0.0183143i | ||||
\(88\) | −1.27311e6 | −1.86818 | ||||||||
\(89\) | 530896.i | 0.753077i | 0.926401 | + | 0.376539i | \(0.122886\pi\) | ||||
−0.926401 | + | 0.376539i | \(0.877114\pi\) | |||||||
\(90\) | −560727. | − | 16906.4i | −0.769172 | − | 0.0231912i | ||||
\(91\) | 463004. | 0.614414 | ||||||||
\(92\) | − | 110230.i | − | 0.141559i | ||||||
\(93\) | −7095.69 | + | 470787.i | −0.00882156 | + | 0.585295i | ||||
\(94\) | 741715. | 0.893004 | ||||||||
\(95\) | 1.10896e6i | 1.29344i | ||||||||
\(96\) | −911687. | − | 13740.9i | −1.03046 | − | 0.0155311i | ||||
\(97\) | −424344. | −0.464946 | −0.232473 | − | 0.972603i | \(-0.574682\pi\) | ||||
−0.232473 | + | 0.972603i | \(0.574682\pi\) | |||||||
\(98\) | − | 451651.i | − | 0.479872i | ||||||
\(99\) | 57421.8 | − | 1.90449e6i | 0.0591795 | − | 1.96278i | ||||
\(100\) | −573065. | −0.573065 | ||||||||
\(101\) | 1.40686e6i | 1.36548i | 0.730661 | + | 0.682740i | \(0.239212\pi\) | ||||
−0.730661 | + | 0.682740i | \(0.760788\pi\) | |||||||
\(102\) | 7054.68 | − | 468066.i | 0.00664778 | − | 0.441069i | ||||
\(103\) | −142007. | −0.129956 | −0.0649781 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649781 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(104\) | − | 1.68008e6i | − | 1.49358i | ||||||
\(105\) | −615167. | − | 9271.79i | −0.531405 | − | 0.00800932i | ||||
\(106\) | −865846. | −0.726981 | ||||||||
\(107\) | − | 433519.i | − | 0.353881i | −0.984222 | − | 0.176940i | \(-0.943380\pi\) | ||
0.984222 | − | 0.176940i | \(-0.0566200\pi\) | |||||||
\(108\) | 38652.9 | − | 854333.i | 0.0306839 | − | 0.678197i | ||||
\(109\) | −306091. | −0.236359 | −0.118179 | − | 0.992992i | \(-0.537706\pi\) | ||||
−0.118179 | + | 0.992992i | \(0.537706\pi\) | |||||||
\(110\) | 2.01126e6i | 1.51109i | ||||||||
\(111\) | −10220.4 | + | 678103.i | −0.00747303 | + | 0.495823i | ||||
\(112\) | −76858.3 | −0.0547062 | ||||||||
\(113\) | − | 568260.i | − | 0.393832i | −0.980420 | − | 0.196916i | \(-0.936907\pi\) | ||
0.980420 | − | 0.196916i | \(-0.0630927\pi\) | |||||||
\(114\) | 799545. | + | 12050.7i | 0.539670 | + | 0.00813390i | ||||
\(115\) | −430650. | −0.283159 | ||||||||
\(116\) | 1.28778e6i | 0.825027i | ||||||||
\(117\) | 2.51328e6 | + | 75777.5i | 1.56922 | + | 0.0473132i | ||||
\(118\) | −77775.8 | −0.0473367 | ||||||||
\(119\) | − | 513394.i | − | 0.304656i | ||||||
\(120\) | −33644.0 | + | 2.23222e6i | −0.0194699 | + | 1.29180i | ||||
\(121\) | −5.05961e6 | −2.85602 | ||||||||
\(122\) | 1.36612e6i | 0.752332i | ||||||||
\(123\) | 1.21269e6 | + | 18277.7i | 0.651681 | + | 0.00982213i | ||||
\(124\) | 757686. | 0.397397 | ||||||||
\(125\) | − | 413444.i | − | 0.211683i | ||||||
\(126\) | −13369.6 | + | 443426.i | −0.00668357 | + | 0.221671i | ||||
\(127\) | 3.48368e6 | 1.70070 | 0.850349 | − | 0.526219i | \(-0.176391\pi\) | ||||
0.850349 | + | 0.526219i | \(0.176391\pi\) | |||||||
\(128\) | 1.63339e6i | 0.778861i | ||||||||
\(129\) | −140.842 | + | 9344.65i | −6.56092e−5 | + | 0.00435305i | ||||
\(130\) | −2.65419e6 | −1.20810 | ||||||||
\(131\) | − | 844991.i | − | 0.375871i | −0.982181 | − | 0.187935i | \(-0.939820\pi\) | ||
0.982181 | − | 0.187935i | \(-0.0601795\pi\) | |||||||
\(132\) | −3.06579e6 | − | 46207.5i | −1.33297 | − | 0.0200905i | ||||
\(133\) | 876974. | 0.372762 | ||||||||
\(134\) | 106116.i | 0.0441026i | ||||||||
\(135\) | −3.33773e6 | − | 151010.i | −1.35660 | − | 0.0613770i | ||||
\(136\) | −1.86292e6 | −0.740590 | ||||||||
\(137\) | − | 2.49550e6i | − | 0.970499i | −0.874376 | − | 0.485250i | \(-0.838729\pi\) | ||
0.874376 | − | 0.485250i | \(-0.161271\pi\) | |||||||
\(138\) | −4679.73 | + | 310492.i | −0.00178067 | + | 0.118144i | ||||
\(139\) | 4.10229e6 | 1.52750 | 0.763752 | − | 0.645510i | \(-0.223355\pi\) | ||||
0.763752 | + | 0.645510i | \(0.223355\pi\) | |||||||
\(140\) | 990054.i | 0.360807i | ||||||||
\(141\) | 4.41708e6 | + | 66574.1i | 1.57571 | + | 0.0237491i | ||||
\(142\) | −668269. | −0.233392 | ||||||||
\(143\) | − | 9.01485e6i | − | 3.08283i | ||||||
\(144\) | −417202. | − | 12579.0i | −0.139720 | − | 0.00421268i | ||||
\(145\) | 5.03114e6 | 1.65030 | ||||||||
\(146\) | 2.47737e6i | 0.796034i | ||||||||
\(147\) | 40538.9 | − | 2.68968e6i | 0.0127620 | − | 0.846738i | ||||
\(148\) | 1.09134e6 | 0.336648 | ||||||||
\(149\) | 5.78549e6i | 1.74897i | 0.485056 | + | 0.874483i | \(0.338799\pi\) | ||||
−0.485056 | + | 0.874483i | \(0.661201\pi\) | |||||||
\(150\) | 1.61419e6 | + | 24329.1i | 0.478279 | + | 0.00720861i | ||||
\(151\) | 2.16429e6 | 0.628615 | 0.314308 | − | 0.949321i | \(-0.398228\pi\) | ||||
0.314308 | + | 0.949321i | \(0.398228\pi\) | |||||||
\(152\) | − | 3.18223e6i | − | 0.906150i | ||||||
\(153\) | 84024.4 | − | 2.78680e6i | 0.0234602 | − | 0.778094i | ||||
\(154\) | 1.59052e6 | 0.435488 | ||||||||
\(155\) | − | 2.96015e6i | − | 0.794912i | ||||||
\(156\) | 60978.3 | − | 4.04581e6i | 0.0160621 | − | 1.06569i | ||||
\(157\) | −6.88868e6 | −1.78007 | −0.890034 | − | 0.455894i | \(-0.849320\pi\) | ||||
−0.890034 | + | 0.455894i | \(0.849320\pi\) | |||||||
\(158\) | − | 2.44897e6i | − | 0.620888i | ||||||
\(159\) | −5.15631e6 | − | 77715.8i | −1.28277 | − | 0.0193338i | ||||
\(160\) | 5.73239e6 | 1.39951 | ||||||||
\(161\) | 340560.i | 0.0816049i | ||||||||
\(162\) | −145146. | + | 2.40482e6i | −0.0341398 | + | 0.565636i | ||||
\(163\) | 2.62152e6 | 0.605328 | 0.302664 | − | 0.953097i | \(-0.402124\pi\) | ||||
0.302664 | + | 0.953097i | \(0.402124\pi\) | |||||||
\(164\) | − | 1.95171e6i | − | 0.442471i | ||||||
\(165\) | −180525. | + | 1.19775e7i | −0.0401870 | + | 2.66634i | ||||
\(166\) | −51316.1 | −0.0112184 | ||||||||
\(167\) | 1.87915e6i | 0.403471i | 0.979440 | + | 0.201736i | \(0.0646582\pi\) | ||||
−0.979440 | + | 0.201736i | \(0.935342\pi\) | |||||||
\(168\) | 1.76526e6 | + | 26605.9i | 0.372289 | + | 0.00561113i | ||||
\(169\) | 7.06975e6 | 1.46468 | ||||||||
\(170\) | 2.94304e6i | 0.599032i | ||||||||
\(171\) | 4.76039e6 | + | 143530.i | 0.952038 | + | 0.0287047i | ||||
\(172\) | 15039.3 | 0.00295558 | ||||||||
\(173\) | 3.00075e6i | 0.579551i | 0.957095 | + | 0.289775i | \(0.0935806\pi\) | ||||
−0.957095 | + | 0.289775i | \(0.906419\pi\) | |||||||
\(174\) | 54671.8 | − | 3.62738e6i | 0.0103780 | − | 0.688565i | ||||
\(175\) | 1.77051e6 | 0.330358 | ||||||||
\(176\) | 1.49646e6i | 0.274490i | ||||||||
\(177\) | −463172. | − | 6980.92i | −0.0835262 | − | 0.00125891i | ||||
\(178\) | −2.40672e6 | −0.426742 | ||||||||
\(179\) | 1.92332e6i | 0.335345i | 0.985843 | + | 0.167672i | \(0.0536251\pi\) | ||||
−0.985843 | + | 0.167672i | \(0.946375\pi\) | |||||||
\(180\) | −162037. | + | 5.37421e6i | −0.0277841 | + | 0.921504i | ||||
\(181\) | 5.12632e6 | 0.864510 | 0.432255 | − | 0.901751i | \(-0.357718\pi\) | ||||
0.432255 | + | 0.901751i | \(0.357718\pi\) | |||||||
\(182\) | 2.09895e6i | 0.348167i | ||||||||
\(183\) | −122619. | + | 8.13555e6i | −0.0200080 | + | 1.32750i | ||||
\(184\) | 1.23577e6 | 0.198374 | ||||||||
\(185\) | − | 4.26369e6i | − | 0.673396i | ||||||
\(186\) | −2.13423e6 | − | 32167.0i | −0.331666 | − | 0.00499887i | ||||
\(187\) | −9.99594e6 | −1.52862 | ||||||||
\(188\) | − | 7.10887e6i | − | 1.06986i | ||||||
\(189\) | −119420. | + | 2.63950e6i | −0.0176885 | + | 0.390963i | ||||
\(190\) | −5.02728e6 | −0.732947 | ||||||||
\(191\) | 8.23738e6i | 1.18220i | 0.806600 | + | 0.591098i | \(0.201305\pi\) | ||||
−0.806600 | + | 0.591098i | \(0.798695\pi\) | |||||||
\(192\) | 47381.9 | − | 3.14371e6i | 0.00669436 | − | 0.444159i | ||||
\(193\) | 2.14568e6 | 0.298465 | 0.149232 | − | 0.988802i | \(-0.452320\pi\) | ||||
0.149232 | + | 0.988802i | \(0.452320\pi\) | |||||||
\(194\) | − | 1.92369e6i | − | 0.263469i | ||||||
\(195\) | −1.58063e7 | − | 238232.i | −2.13170 | − | 0.0321289i | ||||
\(196\) | −4.32879e6 | −0.574908 | ||||||||
\(197\) | − | 4.11516e6i | − | 0.538255i | −0.963105 | − | 0.269127i | \(-0.913265\pi\) | ||
0.963105 | − | 0.269127i | \(-0.0867352\pi\) | |||||||
\(198\) | 8.63365e6 | + | 260311.i | 1.11224 | + | 0.0335350i | ||||
\(199\) | 3.87330e6 | 0.491498 | 0.245749 | − | 0.969334i | \(-0.420966\pi\) | ||||
0.245749 | + | 0.969334i | \(0.420966\pi\) | |||||||
\(200\) | − | 6.42455e6i | − | 0.803069i | ||||||
\(201\) | −9524.62 | + | 631942.i | −0.00117290 | + | 0.0778196i | ||||
\(202\) | −6.37773e6 | −0.773770 | ||||||||
\(203\) | − | 3.97866e6i | − | 0.475607i | ||||||
\(204\) | −4.48611e6 | − | 67614.7i | −0.528421 | − | 0.00796435i | ||||
\(205\) | −7.62502e6 | −0.885073 | ||||||||
\(206\) | − | 643762.i | − | 0.0736417i | ||||||
\(207\) | −55737.7 | + | 1.84863e6i | −0.00628402 | + | 0.208420i | ||||
\(208\) | −1.97482e6 | −0.219451 | ||||||||
\(209\) | − | 1.70750e7i | − | 1.87034i | ||||||
\(210\) | 42032.0 | − | 2.78875e6i | 0.00453860 | − | 0.301128i | ||||
\(211\) | 6.78113e6 | 0.721863 | 0.360931 | − | 0.932592i | \(-0.382459\pi\) | ||||
0.360931 | + | 0.932592i | \(0.382459\pi\) | |||||||
\(212\) | 8.29859e6i | 0.870957i | ||||||||
\(213\) | −3.97969e6 | − | 59981.9i | −0.411823 | − | 0.00620699i | ||||
\(214\) | 1.96528e6 | 0.200532 | ||||||||
\(215\) | − | 58756.1i | − | 0.00591205i | ||||||
\(216\) | 9.57781e6 | + | 433332.i | 0.950396 | + | 0.0429991i | ||||
\(217\) | −2.34091e6 | −0.229089 | ||||||||
\(218\) | − | 1.38761e6i | − | 0.133936i | ||||||
\(219\) | −222361. | + | 1.47533e7i | −0.0211703 | + | 1.40461i | ||||
\(220\) | 1.92767e7 | 1.81036 | ||||||||
\(221\) | − | 1.31913e7i | − | 1.22211i | ||||||
\(222\) | −3.07406e6 | − | 46332.1i | −0.280965 | − | 0.00423471i | ||||
\(223\) | −2.10690e7 | −1.89989 | −0.949947 | − | 0.312411i | \(-0.898864\pi\) | ||||
−0.949947 | + | 0.312411i | \(0.898864\pi\) | |||||||
\(224\) | − | 4.53321e6i | − | 0.403331i | ||||||
\(225\) | 9.61068e6 | + | 289770.i | 0.843736 | + | 0.0254393i | ||||
\(226\) | 2.57610e6 | 0.223171 | ||||||||
\(227\) | − | 6.90559e6i | − | 0.590369i | −0.955440 | − | 0.295184i | \(-0.904619\pi\) | ||
0.955440 | − | 0.295184i | \(-0.0953811\pi\) | |||||||
\(228\) | 115499. | − | 7.66314e6i | 0.00974479 | − | 0.646550i | ||||
\(229\) | −1.43017e7 | −1.19091 | −0.595457 | − | 0.803387i | \(-0.703029\pi\) | ||||
−0.595457 | + | 0.803387i | \(0.703029\pi\) | |||||||
\(230\) | − | 1.95227e6i | − | 0.160456i | ||||||
\(231\) | 9.47189e6 | + | 142760.i | 0.768423 | + | 0.0115817i | ||||
\(232\) | −1.44371e7 | −1.15616 | ||||||||
\(233\) | 1.36973e7i | 1.08285i | 0.840749 | + | 0.541425i | \(0.182115\pi\) | ||||
−0.840749 | + | 0.541425i | \(0.817885\pi\) | |||||||
\(234\) | −343523. | + | 1.13935e7i | −0.0268107 | + | 0.889221i | ||||
\(235\) | −2.77731e7 | −2.14004 | ||||||||
\(236\) | 745432.i | 0.0567116i | ||||||||
\(237\) | 219813. | − | 1.45842e7i | 0.0165123 | − | 1.09556i | ||||
\(238\) | 2.32738e6 | 0.172638 | ||||||||
\(239\) | 5.06271e6i | 0.370842i | 0.982659 | + | 0.185421i | \(0.0593649\pi\) | ||||
−0.982659 | + | 0.185421i | \(0.940635\pi\) | |||||||
\(240\) | 2.62383e6 | + | 39546.3i | 0.189802 | + | 0.00286070i | ||||
\(241\) | −2.58963e7 | −1.85006 | −0.925032 | − | 0.379889i | \(-0.875962\pi\) | ||||
−0.925032 | + | 0.379889i | \(0.875962\pi\) | |||||||
\(242\) | − | 2.29368e7i | − | 1.61841i | ||||||
\(243\) | −1.08023e6 | + | 1.43082e7i | −0.0752829 | + | 0.997162i | ||||
\(244\) | 1.30934e7 | 0.901328 | ||||||||
\(245\) | 1.69119e7i | 1.14999i | ||||||||
\(246\) | −82858.6 | + | 5.49752e6i | −0.00556586 | + | 0.369285i | ||||
\(247\) | 2.25332e7 | 1.49531 | ||||||||
\(248\) | 8.49431e6i | 0.556895i | ||||||||
\(249\) | −305599. | − | 4605.98i | −0.0197949 | − | 0.000298349i | ||||
\(250\) | 1.87427e6 | 0.119953 | ||||||||
\(251\) | 8.69995e6i | 0.550168i | 0.961420 | + | 0.275084i | \(0.0887057\pi\) | ||||
−0.961420 | + | 0.275084i | \(0.911294\pi\) | |||||||
\(252\) | 4.24996e6 | + | 128140.i | 0.265572 | + | 0.00800722i | ||||
\(253\) | 6.63082e6 | 0.409455 | ||||||||
\(254\) | 1.57926e7i | 0.963726i | ||||||||
\(255\) | −264159. | + | 1.75265e7i | −0.0159311 | + | 1.05700i | ||||
\(256\) | −1.48573e7 | −0.885563 | ||||||||
\(257\) | − | 1.92474e7i | − | 1.13389i | −0.823754 | − | 0.566947i | \(-0.808124\pi\) | ||
0.823754 | − | 0.566947i | \(-0.191876\pi\) | |||||||
\(258\) | −42362.3 | − | 638.484i | −0.00246672 | − | 3.71784e-5i | ||||
\(259\) | −3.37175e6 | −0.194069 | ||||||||
\(260\) | 2.54387e7i | 1.44736i | ||||||||
\(261\) | 651165. | − | 2.15969e7i | 0.0366243 | − | 1.21470i | ||||
\(262\) | 3.83062e6 | 0.212993 | ||||||||
\(263\) | − | 2.62596e7i | − | 1.44351i | −0.692146 | − | 0.721757i | \(-0.743335\pi\) | ||
0.692146 | − | 0.721757i | \(-0.256665\pi\) | |||||||
\(264\) | 518026. | − | 3.43701e7i | 0.0281540 | − | 1.86797i | ||||
\(265\) | 3.24212e7 | 1.74217 | ||||||||
\(266\) | 3.97560e6i | 0.211231i | ||||||||
\(267\) | −1.43326e7 | − | 216020.i | −0.752992 | − | 0.0113491i | ||||
\(268\) | 1.01705e6 | 0.0528370 | ||||||||
\(269\) | 2.58401e7i | 1.32751i | 0.747950 | + | 0.663755i | \(0.231038\pi\) | ||||
−0.747950 | + | 0.663755i | \(0.768962\pi\) | |||||||
\(270\) | 684578. | − | 1.51310e7i | 0.0347802 | − | 0.768735i | ||||
\(271\) | 2.59722e7 | 1.30497 | 0.652485 | − | 0.757802i | \(-0.273727\pi\) | ||||
0.652485 | + | 0.757802i | \(0.273727\pi\) | |||||||
\(272\) | 2.18974e6i | 0.108814i | ||||||||
\(273\) | −188395. | + | 1.24997e7i | −0.00925938 | + | 0.614344i | ||||
\(274\) | 1.13129e7 | 0.549948 | ||||||||
\(275\) | − | 3.44724e7i | − | 1.65758i | ||||||
\(276\) | 2.97587e6 | + | 44852.3i | 0.141542 | + | 0.00213333i | ||||
\(277\) | 2.33029e7 | 1.09640 | 0.548201 | − | 0.836346i | \(-0.315313\pi\) | ||||
0.548201 | + | 0.836346i | \(0.315313\pi\) | |||||||
\(278\) | 1.85970e7i | 0.865583i | ||||||||
\(279\) | −1.27069e7 | − | 383124.i | −0.585096 | − | 0.0176411i | ||||
\(280\) | −1.10994e7 | −0.505619 | ||||||||
\(281\) | 2.38846e7i | 1.07646i | 0.842797 | + | 0.538232i | \(0.180907\pi\) | ||||
−0.842797 | + | 0.538232i | \(0.819093\pi\) | |||||||
\(282\) | −301802. | + | 2.00240e7i | −0.0134578 | + | 0.892902i | ||||
\(283\) | −1.16364e6 | −0.0513403 | −0.0256701 | − | 0.999670i | \(-0.508172\pi\) | ||||
−0.0256701 | + | 0.999670i | \(0.508172\pi\) | |||||||
\(284\) | 6.40494e6i | 0.279615i | ||||||||
\(285\) | −2.99386e7 | − | 451234.i | −1.29329 | − | 0.0194925i | ||||
\(286\) | 4.08672e7 | 1.74693 | ||||||||
\(287\) | 6.02991e6i | 0.255073i | ||||||||
\(288\) | 741926. | − | 2.46072e7i | 0.0310587 | − | 1.03011i | ||||
\(289\) | 9.51068e6 | 0.394020 | ||||||||
\(290\) | 2.28078e7i | 0.935167i | ||||||||
\(291\) | 172664. | − | 1.14560e7i | 0.00700686 | − | 0.464893i | ||||
\(292\) | 2.37440e7 | 0.953686 | ||||||||
\(293\) | 1.03655e6i | 0.0412087i | 0.999788 | + | 0.0206043i | \(0.00655903\pi\) | ||||
−0.999788 | + | 0.0206043i | \(0.993441\pi\) | |||||||
\(294\) | 1.21932e7 | + | 183776.i | 0.479817 | + | 0.00723179i | ||||
\(295\) | 2.91228e6 | 0.113440 | ||||||||
\(296\) | 1.22349e7i | 0.471764i | ||||||||
\(297\) | 5.13919e7 | + | 2.32514e6i | 1.96167 | + | 0.0887525i | ||||
\(298\) | −2.62275e7 | −0.991078 | ||||||||
\(299\) | 8.75045e6i | 0.327353i | ||||||||
\(300\) | 233179. | − | 1.54710e7i | 0.00863625 | − | 0.573000i | ||||
\(301\) | −46464.7 | −0.00170382 | ||||||||
\(302\) | 9.81143e6i | 0.356214i | ||||||||
\(303\) | −3.79808e7 | − | 572446.i | −1.36533 | − | 0.0205782i | ||||
\(304\) | −3.74049e6 | −0.133140 | ||||||||
\(305\) | − | 5.11537e7i | − | 1.80292i | ||||||
\(306\) | 1.26335e7 | + | 380909.i | 0.440918 | + | 0.0132941i | ||||
\(307\) | −2.16038e7 | −0.746647 | −0.373324 | − | 0.927701i | \(-0.621782\pi\) | ||||
−0.373324 | + | 0.927701i | \(0.621782\pi\) | |||||||
\(308\) | − | 1.52441e7i | − | 0.521735i | ||||||
\(309\) | 57782.2 | − | 3.83375e6i | 0.00195848 | − | 0.129942i | ||||
\(310\) | 1.34193e7 | 0.450449 | ||||||||
\(311\) | 2.23224e7i | 0.742095i | 0.928614 | + | 0.371048i | \(0.121001\pi\) | ||||
−0.928614 | + | 0.371048i | \(0.878999\pi\) | |||||||
\(312\) | 4.53570e7 | + | 683619.i | 1.49341 | + | 0.0225087i | ||||
\(313\) | −2.11620e6 | −0.0690119 | −0.0345059 | − | 0.999404i | \(-0.510986\pi\) | ||||
−0.0345059 | + | 0.999404i | \(0.510986\pi\) | |||||||
\(314\) | − | 3.12286e7i | − | 1.00870i | ||||||
\(315\) | 500620. | − | 1.66039e7i | 0.0160168 | − | 0.531224i | ||||
\(316\) | −2.34719e7 | −0.743852 | ||||||||
\(317\) | − | 2.18386e7i | − | 0.685562i | −0.939415 | − | 0.342781i | \(-0.888631\pi\) | ||
0.939415 | − | 0.342781i | \(-0.111369\pi\) | |||||||
\(318\) | 352311. | − | 2.33752e7i | 0.0109558 | − | 0.726899i | ||||
\(319\) | −7.74657e7 | −2.38637 | ||||||||
\(320\) | 1.97666e7i | 0.603229i | ||||||||
\(321\) | 1.17037e7 | + | 176398.i | 0.353841 | + | 0.00533308i | ||||
\(322\) | −1.54387e6 | −0.0462426 | ||||||||
\(323\) | − | 2.49855e7i | − | 0.741448i | ||||||
\(324\) | 2.30486e7 | + | 1.39114e6i | 0.677658 | + | 0.0409010i | ||||
\(325\) | 4.54920e7 | 1.32521 | ||||||||
\(326\) | 1.18842e7i | 0.343018i | ||||||||
\(327\) | 124548. | − | 8.26353e6i | 0.00356199 | − | 0.236332i | ||||
\(328\) | 2.18804e7 | 0.620060 | ||||||||
\(329\) | 2.19632e7i | 0.616747i | ||||||||
\(330\) | −5.42979e7 | − | 818377.i | −1.51092 | − | 0.0227725i | ||||
\(331\) | −5.82897e7 | −1.60734 | −0.803670 | − | 0.595075i | \(-0.797122\pi\) | ||||
−0.803670 | + | 0.595075i | \(0.797122\pi\) | |||||||
\(332\) | 491833.i | 0.0134401i | ||||||||
\(333\) | −1.83025e7 | − | 551836.i | −0.495654 | − | 0.0149444i | ||||
\(334\) | −8.51880e6 | −0.228633 | ||||||||
\(335\) | − | 3.97344e6i | − | 0.105690i | ||||||
\(336\) | 31273.4 | − | 2.07494e6i | 0.000824437 | − | 0.0547000i | ||||
\(337\) | 1.58693e7 | 0.414636 | 0.207318 | − | 0.978274i | \(-0.433527\pi\) | ||||
0.207318 | + | 0.978274i | \(0.433527\pi\) | |||||||
\(338\) | 3.20494e7i | 0.829985i | ||||||||
\(339\) | 1.53413e7 | + | 231223.i | 0.393788 | + | 0.00593516i | ||||
\(340\) | 2.82072e7 | 0.717668 | ||||||||
\(341\) | 4.55782e7i | 1.14946i | ||||||||
\(342\) | −650666. | + | 2.15804e7i | −0.0162660 | + | 0.539486i | ||||
\(343\) | 2.91669e7 | 0.722784 | ||||||||
\(344\) | 168604.i | 0.00414183i | ||||||||
\(345\) | 175230. | − | 1.16262e7i | 0.00426729 | − | 0.283127i | ||||
\(346\) | −1.36034e7 | −0.328411 | ||||||||
\(347\) | − | 1.73415e7i | − | 0.415048i | −0.978230 | − | 0.207524i | \(-0.933459\pi\) | ||
0.978230 | − | 0.207524i | \(-0.0665406\pi\) | |||||||
\(348\) | −3.47661e7 | − | 523995.i | −0.824933 | − | 0.0124334i | ||||
\(349\) | 3.76317e6 | 0.0885274 | 0.0442637 | − | 0.999020i | \(-0.485906\pi\) | ||||
0.0442637 | + | 0.999020i | \(0.485906\pi\) | |||||||
\(350\) | 8.02629e6i | 0.187202i | ||||||||
\(351\) | −3.06841e6 | + | 6.78200e7i | −0.0709564 | + | 1.56833i | ||||
\(352\) | −8.82630e7 | −2.02372 | ||||||||
\(353\) | 4.89432e7i | 1.11267i | 0.830957 | + | 0.556337i | \(0.187794\pi\) | ||||
−0.830957 | + | 0.556337i | \(0.812206\pi\) | |||||||
\(354\) | 31646.8 | − | 2.09971e6i | 0.000713378 | − | 0.0473314i | ||||
\(355\) | 2.50230e7 | 0.559313 | ||||||||
\(356\) | 2.30669e7i | 0.511257i | ||||||||
\(357\) | 1.38601e7 | + | 208898.i | 0.304621 | + | 0.00459125i | ||||
\(358\) | −8.71901e6 | −0.190028 | ||||||||
\(359\) | 5.79027e7i | 1.25146i | 0.780041 | + | 0.625728i | \(0.215198\pi\) | ||||
−0.780041 | + | 0.625728i | \(0.784802\pi\) | |||||||
\(360\) | −6.02495e7 | − | 1.81657e6i | −1.29136 | − | 0.0389354i | ||||
\(361\) | −4.36586e6 | −0.0928000 | ||||||||
\(362\) | 2.32393e7i | 0.489888i | ||||||||
\(363\) | 2.05874e6 | − | 1.36594e8i | 0.0430410 | − | 2.85570i | ||||
\(364\) | 2.01171e7 | 0.417120 | ||||||||
\(365\) | − | 9.27638e7i | − | 1.90766i | ||||||
\(366\) | −3.68810e7 | − | 555871.i | −0.752246 | − | 0.0113378i | ||||
\(367\) | 4.02106e7 | 0.813471 | 0.406736 | − | 0.913546i | \(-0.366667\pi\) | ||||
0.406736 | + | 0.913546i | \(0.366667\pi\) | |||||||
\(368\) | − | 1.45257e6i | − | 0.0291469i | ||||||
\(369\) | −986883. | + | 3.27315e7i | −0.0196420 | + | 0.651459i | ||||
\(370\) | 1.93287e7 | 0.381590 | ||||||||
\(371\) | − | 2.56389e7i | − | 0.502085i | ||||||
\(372\) | −308301. | + | 2.04552e7i | −0.00598888 | + | 0.397352i | ||||
\(373\) | −7.28534e7 | −1.40386 | −0.701929 | − | 0.712247i | \(-0.747678\pi\) | ||||
−0.701929 | + | 0.712247i | \(0.747678\pi\) | |||||||
\(374\) | − | 4.53148e7i | − | 0.866214i | ||||||
\(375\) | 1.11617e7 | + | 168229.i | 0.211659 | + | 0.00319012i | ||||
\(376\) | 7.96965e7 | 1.49926 | ||||||||
\(377\) | − | 1.02229e8i | − | 1.90787i | ||||||
\(378\) | −1.19657e7 | − | 541368.i | −0.221545 | − | 0.0100235i | ||||
\(379\) | −2.42618e7 | −0.445662 | −0.222831 | − | 0.974857i | \(-0.571530\pi\) | ||||
−0.222831 | + | 0.974857i | \(0.571530\pi\) | |||||||
\(380\) | 4.81833e7i | 0.878104i | ||||||||
\(381\) | −1.41750e6 | + | 9.40487e7i | −0.0256300 | + | 1.70050i | ||||
\(382\) | −3.73427e7 | −0.669909 | ||||||||
\(383\) | − | 2.36613e6i | − | 0.0421155i | −0.999778 | − | 0.0210577i | \(-0.993297\pi\) | ||
0.999778 | − | 0.0210577i | \(-0.00670338\pi\) | |||||||
\(384\) | −4.40965e7 | − | 664622.i | −0.778773 | − | 0.0117377i | ||||
\(385\) | −5.95561e7 | −1.04362 | ||||||||
\(386\) | 9.72706e6i | 0.169130i | ||||||||
\(387\) | −252220. | − | 7604.63i | −0.00435157 | − | 0.000131203i | ||||
\(388\) | −1.84373e7 | −0.315648 | ||||||||
\(389\) | 4.52137e7i | 0.768105i | 0.923311 | + | 0.384053i | \(0.125472\pi\) | ||||
−0.923311 | + | 0.384053i | \(0.874528\pi\) | |||||||
\(390\) | 1.07998e6 | − | 7.16549e7i | 0.0182063 | − | 1.20796i | ||||
\(391\) | 9.70277e6 | 0.162317 | ||||||||
\(392\) | − | 4.85295e7i | − | 0.805652i | ||||||
\(393\) | 2.28122e7 | + | 343825.i | 0.375828 | + | 0.00566447i | ||||
\(394\) | 1.86553e7 | 0.305010 | ||||||||
\(395\) | 9.17006e7i | 1.48793i | ||||||||
\(396\) | 2.49492e6 | − | 8.27481e7i | 0.0401764 | − | 1.33252i | ||||
\(397\) | 5.99525e7 | 0.958156 | 0.479078 | − | 0.877772i | \(-0.340971\pi\) | ||||
0.479078 | + | 0.877772i | \(0.340971\pi\) | |||||||
\(398\) | 1.75589e7i | 0.278514i | ||||||||
\(399\) | −356838. | + | 2.36756e7i | −0.00561763 | + | 0.372720i | ||||
\(400\) | −7.55162e6 | −0.117994 | ||||||||
\(401\) | − | 7.63325e6i | − | 0.118379i | −0.998247 | − | 0.0591897i | \(-0.981148\pi\) | ||
0.998247 | − | 0.0591897i | \(-0.0188517\pi\) | |||||||
\(402\) | −2.86479e6 | − | 43178.1i | −0.0440976 | − | 0.000664639i | ||||
\(403\) | −6.01479e7 | −0.918978 | ||||||||
\(404\) | 6.11265e7i | 0.927012i | ||||||||
\(405\) | 5.43493e6 | − | 9.00472e7i | 0.0818143 | − | 1.35552i | ||||
\(406\) | 1.80365e7 | 0.269510 | ||||||||
\(407\) | 6.56491e7i | 0.973745i | ||||||||
\(408\) | 758018. | − | 5.02932e7i | 0.0111609 | − | 0.740506i | ||||
\(409\) | −8.30683e6 | −0.121413 | −0.0607066 | − | 0.998156i | \(-0.519335\pi\) | ||||
−0.0607066 | + | 0.998156i | \(0.519335\pi\) | |||||||
\(410\) | − | 3.45666e7i | − | 0.501540i | ||||||
\(411\) | 6.73707e7 | + | 1.01541e6i | 0.970389 | + | 0.0146257i | ||||
\(412\) | −6.17005e6 | −0.0882261 | ||||||||
\(413\) | − | 2.30304e6i | − | 0.0326928i | ||||||
\(414\) | −8.38043e6 | − | 252677.i | −0.118104 | − | 0.00356094i | ||||
\(415\) | 1.92151e6 | 0.0268842 | ||||||||
\(416\) | − | 1.16477e8i | − | 1.61794i | ||||||
\(417\) | −1.66921e6 | + | 1.10749e8i | −0.0230199 | + | 1.52733i | ||||
\(418\) | 7.74063e7 | 1.05986 | ||||||||
\(419\) | 430161.i | 0.00584775i | 0.999996 | + | 0.00292388i | \(0.000930700\pi\) | ||||
−0.999996 | + | 0.00292388i | \(0.999069\pi\) | |||||||
\(420\) | −2.67284e7 | − | 402850.i | −0.360766 | − | 0.00543746i | ||||
\(421\) | 7.34160e7 | 0.983885 | 0.491943 | − | 0.870628i | \(-0.336287\pi\) | ||||
0.491943 | + | 0.870628i | \(0.336287\pi\) | |||||||
\(422\) | 3.07410e7i | 0.409054i | ||||||||
\(423\) | −3.59459e6 | + | 1.19220e8i | −0.0474929 | + | 1.57518i | ||||
\(424\) | −9.30343e7 | −1.22052 | ||||||||
\(425\) | − | 5.04429e7i | − | 0.657103i | ||||||
\(426\) | 271917. | − | 1.80412e7i | 0.00351729 | − | 0.233366i | ||||
\(427\) | −4.04526e7 | −0.519593 | ||||||||
\(428\) | − | 1.88360e7i | − | 0.240246i | ||||||
\(429\) | 2.43373e8 | + | 3.66812e6i | 3.08248 | + | 0.0464592i | ||||
\(430\) | 266360. | 0.00335015 | ||||||||
\(431\) | 4.77108e7i | 0.595915i | 0.954579 | + | 0.297958i | \(0.0963054\pi\) | ||||
−0.954579 | + | 0.297958i | \(0.903695\pi\) | |||||||
\(432\) | 509352. | − | 1.12581e7i | 0.00631782 | − | 0.139641i | ||||
\(433\) | −1.04269e8 | −1.28437 | −0.642185 | − | 0.766550i | \(-0.721972\pi\) | ||||
−0.642185 | + | 0.766550i | \(0.721972\pi\) | |||||||
\(434\) | − | 1.06121e7i | − | 0.129817i | ||||||
\(435\) | −2.04716e6 | + | 1.35825e8i | −0.0248705 | + | 1.65011i | ||||
\(436\) | −1.32994e7 | −0.160462 | ||||||||
\(437\) | 1.65742e7i | 0.198604i | ||||||||
\(438\) | −6.68813e7 | − | 1.00803e6i | −0.795944 | − | 0.0119965i | ||||
\(439\) | −1.16395e7 | −0.137575 | −0.0687875 | − | 0.997631i | \(-0.521913\pi\) | ||||
−0.0687875 | + | 0.997631i | \(0.521913\pi\) | |||||||
\(440\) | 2.16108e8i | 2.53696i | ||||||||
\(441\) | 7.25967e7 | + | 2.18885e6i | 0.846450 | + | 0.0255212i | ||||
\(442\) | 5.98003e7 | 0.692526 | ||||||||
\(443\) | − | 1.63171e8i | − | 1.87687i | −0.345462 | − | 0.938433i | \(-0.612278\pi\) | ||
0.345462 | − | 0.938433i | \(-0.387722\pi\) | |||||||
\(444\) | −444064. | + | 2.94629e7i | −0.00507337 | + | 0.336610i | ||||
\(445\) | 9.01185e7 | 1.02267 | ||||||||
\(446\) | − | 9.55125e7i | − | 1.07660i | ||||||
\(447\) | −1.56191e8 | − | 2.35410e6i | −1.74877 | − | 0.0263574i | ||||
\(448\) | 1.56315e7 | 0.173847 | ||||||||
\(449\) | − | 1.36644e8i | − | 1.50957i | −0.655974 | − | 0.754784i | \(-0.727742\pi\) | ||
0.655974 | − | 0.754784i | \(-0.272258\pi\) | |||||||
\(450\) | −1.31362e6 | + | 4.35683e7i | −0.0144156 | + | 0.478116i | ||||
\(451\) | 1.17404e8 | 1.27984 | ||||||||
\(452\) | − | 2.46903e7i | − | 0.267369i | ||||||
\(453\) | −880645. | + | 5.84293e7i | −0.00947341 | + | 0.628544i | ||||
\(454\) | 3.13053e7 | 0.334541 | ||||||||
\(455\) | − | 7.85940e7i | − | 0.834364i | ||||||
\(456\) | 8.59104e7 | + | 1.29484e6i | 0.906048 | + | 0.0136559i | ||||
\(457\) | 1.13481e8 | 1.18898 | 0.594489 | − | 0.804104i | \(-0.297354\pi\) | ||||
0.594489 | + | 0.804104i | \(0.297354\pi\) | |||||||
\(458\) | − | 6.48341e7i | − | 0.674849i | ||||||
\(459\) | 7.52009e7 | + | 3.40234e6i | 0.777652 | + | 0.0351836i | ||||
\(460\) | −1.87113e7 | −0.192234 | ||||||||
\(461\) | − | 9.62347e7i | − | 0.982266i | −0.871085 | − | 0.491133i | \(-0.836583\pi\) | ||
0.871085 | − | 0.491133i | \(-0.163417\pi\) | |||||||
\(462\) | −647177. | + | 4.29391e7i | −0.00656292 | + | 0.435439i | ||||
\(463\) | 2.85176e7 | 0.287323 | 0.143662 | − | 0.989627i | \(-0.454112\pi\) | ||||
0.143662 | + | 0.989627i | \(0.454112\pi\) | |||||||
\(464\) | 1.69699e7i | 0.169873i | ||||||||
\(465\) | 7.99150e7 | + | 1.20448e6i | 0.794822 | + | 0.0119795i | ||||
\(466\) | −6.20944e7 | −0.613613 | ||||||||
\(467\) | 9.20520e7i | 0.903821i | 0.892063 | + | 0.451911i | \(0.149257\pi\) | ||||
−0.892063 | + | 0.451911i | \(0.850743\pi\) | |||||||
\(468\) | 1.09200e8 | + | 3.29246e6i | 1.06533 | + | 0.0321205i | ||||
\(469\) | −3.14222e6 | −0.0304592 | ||||||||
\(470\) | − | 1.25905e8i | − | 1.21268i | ||||||
\(471\) | 2.80298e6 | − | 1.85973e8i | 0.0268261 | − | 1.77987i | ||||
\(472\) | −8.35693e6 | −0.0794732 | ||||||||
\(473\) | 904683.i | 0.00854895i | ||||||||
\(474\) | 6.61148e7 | + | 996481.i | 0.620817 | + | 0.00935694i | ||||
\(475\) | 8.61661e7 | 0.803999 | ||||||||
\(476\) | − | 2.23064e7i | − | 0.206828i | ||||||
\(477\) | 4.19618e6 | − | 1.39173e8i | 0.0386633 | − | 1.28233i | ||||
\(478\) | −2.29509e7 | −0.210143 | ||||||||
\(479\) | 9.65232e7i | 0.878265i | 0.898422 | + | 0.439132i | \(0.144714\pi\) | ||||
−0.898422 | + | 0.439132i | \(0.855286\pi\) | |||||||
\(480\) | −2.33249e6 | + | 1.54757e8i | −0.0210910 | + | 1.39935i | ||||
\(481\) | −8.66347e7 | −0.778496 | ||||||||
\(482\) | − | 1.17396e8i | − | 1.04837i | ||||||
\(483\) | −9.19408e6 | − | 138573.i | −0.0815957 | − | 0.00122981i | ||||
\(484\) | −2.19835e8 | −1.93893 | ||||||||
\(485\) | 7.20315e7i | 0.631389i | ||||||||
\(486\) | −6.48636e7 | − | 4.89702e6i | −0.565057 | − | 0.0426602i | ||||
\(487\) | −2.04861e7 | −0.177367 | −0.0886833 | − | 0.996060i | \(-0.528266\pi\) | ||||
−0.0886833 | + | 0.996060i | \(0.528266\pi\) | |||||||
\(488\) | 1.46788e8i | 1.26308i | ||||||||
\(489\) | −1.06669e6 | + | 7.07731e7i | −0.00912246 | + | 0.605260i | ||||
\(490\) | −7.66669e7 | −0.651658 | ||||||||
\(491\) | − | 1.99701e8i | − | 1.68708i | −0.537063 | − | 0.843542i | \(-0.680466\pi\) | ||
0.537063 | − | 0.843542i | \(-0.319534\pi\) | |||||||
\(492\) | 5.26903e7 | + | 794147.i | 0.442420 | + | 0.00666815i | ||||
\(493\) | −1.13354e8 | −0.946013 | ||||||||
\(494\) | 1.02150e8i | 0.847342i | ||||||||
\(495\) | −3.23283e8 | − | 9.74724e6i | −2.66543 | − | 0.0803648i | ||||
\(496\) | 9.98449e6 | 0.0818240 | ||||||||
\(497\) | − | 1.97884e7i | − | 0.161191i | ||||||
\(498\) | 20880.4 | − | 1.38538e6i | 0.000169064 | − | 0.0112171i | ||||
\(499\) | −6.46534e6 | −0.0520343 | −0.0260171 | − | 0.999661i | \(-0.508282\pi\) | ||||
−0.0260171 | + | 0.999661i | \(0.508282\pi\) | |||||||
\(500\) | − | 1.79637e7i | − | 0.143710i | ||||||
\(501\) | −5.07313e7 | − | 764622.i | −0.403425 | − | 0.00608042i | ||||
\(502\) | −3.94396e7 | −0.311761 | ||||||||
\(503\) | − | 3.27665e7i | − | 0.257470i | −0.991679 | − | 0.128735i | \(-0.958908\pi\) | ||
0.991679 | − | 0.128735i | \(-0.0410916\pi\) | |||||||
\(504\) | −1.43656e6 | + | 4.76457e7i | −0.0112210 | + | 0.372162i | ||||
\(505\) | 2.38811e8 | 1.85430 | ||||||||
\(506\) | 3.00596e7i | 0.232024i | ||||||||
\(507\) | −2.87666e6 | + | 1.90862e8i | −0.0220732 | + | 1.46452i | ||||
\(508\) | 1.51363e8 | 1.15459 | ||||||||
\(509\) | 5.02033e7i | 0.380696i | 0.981717 | + | 0.190348i | \(0.0609617\pi\) | ||||
−0.981717 | + | 0.190348i | \(0.939038\pi\) | |||||||
\(510\) | −7.94532e7 | − | 1.19752e6i | −0.598964 | − | 0.00902758i | ||||
\(511\) | −7.33582e7 | −0.549776 | ||||||||
\(512\) | 3.71842e7i | 0.277044i | ||||||||
\(513\) | −5.81185e6 | + | 1.28458e8i | −0.0430489 | + | 0.951497i | ||||
\(514\) | 8.72546e7 | 0.642539 | ||||||||
\(515\) | 2.41054e7i | 0.176479i | ||||||||
\(516\) | −6119.47 | + | 406016.i | −4.45415e−5 | + | 0.00295525i | ||||
\(517\) | 4.27630e8 | 3.09454 | ||||||||
\(518\) | − | 1.52852e7i | − | 0.109972i | ||||||
\(519\) | −8.10110e7 | − | 1.22100e6i | −0.579485 | − | 0.00873399i | ||||
\(520\) | −2.85190e8 | −2.02826 | ||||||||
\(521\) | − | 1.80370e8i | − | 1.27541i | −0.770280 | − | 0.637706i | \(-0.779883\pi\) | ||
0.770280 | − | 0.637706i | \(-0.220117\pi\) | |||||||
\(522\) | 9.79058e7 | + | 2.95194e6i | 0.688331 | + | 0.0207537i | ||||
\(523\) | −1.62459e8 | −1.13564 | −0.567818 | − | 0.823154i | \(-0.692212\pi\) | ||||
−0.567818 | + | 0.823154i | \(0.692212\pi\) | |||||||
\(524\) | − | 3.67140e7i | − | 0.255175i | ||||||
\(525\) | −720416. | + | 4.77983e7i | −0.00497858 | + | 0.330320i | ||||
\(526\) | 1.19043e8 | 0.817989 | ||||||||
\(527\) | 6.66938e7i | 0.455673i | ||||||||
\(528\) | −4.03997e7 | − | 608904.i | −0.274458 | − | 0.00413663i | ||||
\(529\) | −6.43634e6 | −0.0434783 | ||||||||
\(530\) | 1.46976e8i | 0.987228i | ||||||||
\(531\) | 376927. | − | 1.25014e7i | 0.00251752 | − | 0.0834977i | ||||
\(532\) | 3.81037e7 | 0.253065 | ||||||||
\(533\) | 1.54934e8i | 1.02321i | ||||||||
\(534\) | 979289. | − | 6.49741e7i | 0.00643113 | − | 0.426694i | ||||
\(535\) | −7.35890e7 | −0.480564 | ||||||||
\(536\) | 1.14020e7i | 0.0740435i | ||||||||
\(537\) | −5.19237e7 | − | 782593.i | −0.335307 | − | 0.00505374i | ||||
\(538\) | −1.17142e8 | −0.752253 | ||||||||
\(539\) | − | 2.60396e8i | − | 1.66291i | ||||||
\(540\) | −1.45021e8 | − | 6.56125e6i | −0.920981 | − | 0.0416683i | ||||
\(541\) | 6.12842e7 | 0.387041 | 0.193520 | − | 0.981096i | \(-0.438009\pi\) | ||||
0.193520 | + | 0.981096i | \(0.438009\pi\) | |||||||
\(542\) | 1.17740e8i | 0.739481i | ||||||||
\(543\) | −2.08589e6 | + | 1.38395e8i | −0.0130284 | + | 0.864412i | ||||
\(544\) | −1.29154e8 | −0.802252 | ||||||||
\(545\) | 5.19584e7i | 0.320971i | ||||||||
\(546\) | −5.66651e7 | − | 854056.i | −0.348127 | − | 0.00524697i | ||||
\(547\) | −1.06218e8 | −0.648989 | −0.324495 | − | 0.945888i | \(-0.605194\pi\) | ||||
−0.324495 | + | 0.945888i | \(0.605194\pi\) | |||||||
\(548\) | − | 1.08427e8i | − | 0.658863i | ||||||
\(549\) | −2.19585e8 | − | 6.62067e6i | −1.32704 | − | 0.0400115i | ||||
\(550\) | 1.56274e8 | 0.939290 | ||||||||
\(551\) | − | 1.93631e8i | − | 1.15750i | ||||||
\(552\) | −502832. | + | 3.33621e7i | −0.00298955 | + | 0.198352i | ||||
\(553\) | 7.25174e7 | 0.428812 | ||||||||
\(554\) | 1.05639e8i | 0.621293i | ||||||||
\(555\) | 1.15107e8 | + | 1.73488e6i | 0.673319 | + | 0.0101483i | ||||
\(556\) | 1.78241e8 | 1.03701 | ||||||||
\(557\) | 2.33514e8i | 1.35128i | 0.737230 | + | 0.675642i | \(0.236133\pi\) | ||||
−0.737230 | + | 0.675642i | \(0.763867\pi\) | |||||||
\(558\) | 1.73682e6 | − | 5.76045e7i | 0.00999661 | − | 0.331553i | ||||
\(559\) | −1.19388e6 | −0.00683477 | ||||||||
\(560\) | 1.30465e7i | 0.0742901i | ||||||||
\(561\) | 4.06732e6 | − | 2.69860e8i | 0.0230367 | − | 1.52844i | ||||
\(562\) | −1.08277e8 | −0.609994 | ||||||||
\(563\) | − | 9.60018e7i | − | 0.537965i | −0.963145 | − | 0.268983i | \(-0.913313\pi\) | ||
0.963145 | − | 0.268983i | \(-0.0866874\pi\) | |||||||
\(564\) | 1.91918e8 | + | 2.89258e6i | 1.06974 | + | 0.0161231i | ||||
\(565\) | −9.64609e7 | −0.534818 | ||||||||
\(566\) | − | 5.27514e6i | − | 0.0290927i | ||||||
\(567\) | −7.12098e7 | − | 4.29798e6i | −0.390653 | − | 0.0235784i | ||||
\(568\) | −7.18049e7 | −0.391840 | ||||||||
\(569\) | − | 1.54770e8i | − | 0.840136i | −0.907493 | − | 0.420068i | \(-0.862006\pi\) | ||
0.907493 | − | 0.420068i | \(-0.137994\pi\) | |||||||
\(570\) | 2.04559e6 | − | 1.35721e8i | 0.0110457 | − | 0.732863i | ||||
\(571\) | −1.85555e8 | −0.996700 | −0.498350 | − | 0.866976i | \(-0.666060\pi\) | ||||
−0.498350 | + | 0.866976i | \(0.666060\pi\) | |||||||
\(572\) | − | 3.91686e8i | − | 2.09291i | ||||||
\(573\) | −2.22384e8 | − | 3.35177e6i | −1.18206 | − | 0.0178160i | ||||
\(574\) | −2.73355e7 | −0.144541 | ||||||||
\(575\) | 3.34614e7i | 0.176011i | ||||||||
\(576\) | 8.48512e7 | + | 2.55833e6i | 0.444008 | + | 0.0133872i | ||||
\(577\) | 1.55843e6 | 0.00811257 | 0.00405629 | − | 0.999992i | \(-0.498709\pi\) | ||||
0.00405629 | + | 0.999992i | \(0.498709\pi\) | |||||||
\(578\) | 4.31149e7i | 0.223277i | ||||||||
\(579\) | −873072. | + | 5.79268e7i | −0.00449795 | + | 0.298431i | ||||
\(580\) | 2.18598e8 | 1.12037 | ||||||||
\(581\) | − | 1.51954e6i | − | 0.00774789i | ||||||
\(582\) | 5.19336e7 | + | 782743.i | 0.263439 | + | 0.00397054i | ||||
\(583\) | −4.99197e8 | −2.51922 | ||||||||
\(584\) | 2.66191e8i | 1.33645i | ||||||||
\(585\) | 1.28631e7 | − | 4.26624e8i | 0.0642506 | − | 2.13097i | ||||
\(586\) | −4.69903e6 | −0.0233515 | ||||||||
\(587\) | − | 6.08182e7i | − | 0.300690i | −0.988634 | − | 0.150345i | \(-0.951962\pi\) | ||
0.988634 | − | 0.150345i | \(-0.0480384\pi\) | |||||||
\(588\) | 1.76137e6 | − | 1.16864e8i | 0.00866402 | − | 0.574843i | ||||
\(589\) | −1.13926e8 | −0.557540 | ||||||||
\(590\) | 1.32023e7i | 0.0642825i | ||||||||
\(591\) | 1.11097e8 | + | 1.67445e6i | 0.538193 | + | 0.00811164i | ||||
\(592\) | 1.43813e7 | 0.0693158 | ||||||||
\(593\) | − | 8.57497e7i | − | 0.411214i | −0.978635 | − | 0.205607i | \(-0.934083\pi\) | ||
0.978635 | − | 0.205607i | \(-0.0659169\pi\) | |||||||
\(594\) | −1.05406e7 | + | 2.32976e8i | −0.0502929 | + | 1.11161i | ||||
\(595\) | −8.71475e7 | −0.413718 | ||||||||
\(596\) | 2.51374e8i | 1.18736i | ||||||||
\(597\) | −1.57603e6 | + | 1.04567e8i | −0.00740700 | + | 0.491442i | ||||
\(598\) | −3.96686e7 | −0.185500 | ||||||||
\(599\) | − | 2.05419e8i | − | 0.955783i | −0.878419 | − | 0.477891i | \(-0.841401\pi\) | ||
0.878419 | − | 0.477891i | \(-0.158599\pi\) | |||||||
\(600\) | 1.73443e8 | + | 2.61413e6i | 0.802978 | + | 0.0121025i | ||||
\(601\) | 1.49556e8 | 0.688938 | 0.344469 | − | 0.938798i | \(-0.388059\pi\) | ||||
0.344469 | + | 0.938798i | \(0.388059\pi\) | |||||||
\(602\) | − | 210639.i | − | 0.000965495i | ||||||
\(603\) | −1.70566e7 | − | 514271.i | −0.0777931 | − | 0.00234552i | ||||
\(604\) | 9.40364e7 | 0.426761 | ||||||||
\(605\) | 8.58859e8i | 3.87843i | ||||||||
\(606\) | 2.59508e6 | − | 1.72179e8i | 0.0116609 | − | 0.773682i | ||||
\(607\) | −7.54118e7 | −0.337189 | −0.168594 | − | 0.985686i | \(-0.553923\pi\) | ||||
−0.168594 | + | 0.985686i | \(0.553923\pi\) | |||||||
\(608\) | − | 2.20619e8i | − | 0.981596i | ||||||
\(609\) | 1.07412e8 | + | 1.61890e6i | 0.475553 | + | 0.00716753i | ||||
\(610\) | 2.31896e8 | 1.02165 | ||||||||
\(611\) | 5.64328e8i | 2.47405i | ||||||||
\(612\) | 3.65078e6 | − | 1.21084e8i | 0.0159269 | − | 0.528241i | ||||
\(613\) | 1.11658e8 | 0.484739 | 0.242369 | − | 0.970184i | \(-0.422075\pi\) | ||||
0.242369 | + | 0.970184i | \(0.422075\pi\) | |||||||
\(614\) | − | 9.79370e7i | − | 0.423099i | ||||||
\(615\) | 3.10260e6 | − | 2.05852e8i | 0.0133383 | − | 0.884973i | ||||
\(616\) | 1.70900e8 | 0.731137 | ||||||||
\(617\) | 2.95889e8i | 1.25972i | 0.776710 | + | 0.629858i | \(0.216887\pi\) | ||||
−0.776710 | + | 0.629858i | \(0.783113\pi\) | |||||||
\(618\) | 1.73796e7 | + | 261945.i | 0.0736333 | + | 0.00110980i | ||||
\(619\) | 3.60810e8 | 1.52127 | 0.760636 | − | 0.649179i | \(-0.224887\pi\) | ||||
0.760636 | + | 0.649179i | \(0.224887\pi\) | |||||||
\(620\) | − | 1.28616e8i | − | 0.539658i | ||||||
\(621\) | −4.98846e7 | − | 2.25695e6i | −0.208301 | − | 0.00942425i | ||||
\(622\) | −1.01195e8 | −0.420519 | ||||||||
\(623\) | − | 7.12663e7i | − | 0.294727i | ||||||
\(624\) | 803548. | − | 5.33140e7i | 0.00330718 | − | 0.219426i | ||||
\(625\) | −2.76265e8 | −1.13158 | ||||||||
\(626\) | − | 9.59342e6i | − | 0.0391066i | ||||||
\(627\) | 4.60972e8 | + | 6.94776e6i | 1.87013 | + | 0.0281866i | ||||
\(628\) | −2.99306e8 | −1.20847 | ||||||||
\(629\) | 9.60632e7i | 0.386016i | ||||||||
\(630\) | 7.52706e7 | + | 2.26947e6i | 0.301026 | + | 0.00907618i | ||||
\(631\) | 3.89749e8 | 1.55130 | 0.775652 | − | 0.631161i | \(-0.217421\pi\) | ||||
0.775652 | + | 0.631161i | \(0.217421\pi\) | |||||||
\(632\) | − | 2.63140e8i | − | 1.04240i | ||||||
\(633\) | −2.75922e6 | + | 1.83070e8i | −0.0108787 | + | 0.721781i | ||||
\(634\) | 9.90013e7 | 0.388484 | ||||||||
\(635\) | − | 5.91348e8i | − | 2.30952i | ||||||
\(636\) | −2.24036e8 | − | 3.37667e6i | −0.870858 | − | 0.0131256i | ||||
\(637\) | 3.43635e8 | 1.32947 | ||||||||
\(638\) | − | 3.51177e8i | − | 1.35227i | ||||||
\(639\) | 3.23865e6 | − | 1.07415e8i | 0.0124126 | − | 0.411683i | ||||
\(640\) | 2.77265e8 | 1.05768 | ||||||||
\(641\) | 3.87378e7i | 0.147083i | 0.997292 | + | 0.0735413i | \(0.0234301\pi\) | ||||
−0.997292 | + | 0.0735413i | \(0.976570\pi\) | |||||||
\(642\) | −799668. | + | 5.30566e7i | −0.00302207 | + | 0.200509i | ||||
\(643\) | −3.51846e8 | −1.32349 | −0.661743 | − | 0.749731i | \(-0.730183\pi\) | ||||
−0.661743 | + | 0.749731i | \(0.730183\pi\) | |||||||
\(644\) | 1.47970e7i | 0.0554008i | ||||||||
\(645\) | 1.58624e6 | + | 23907.7i | 0.00591138 | + | 8.90962e-5i | ||||
\(646\) | 1.13267e8 | 0.420153 | ||||||||
\(647\) | 2.30514e8i | 0.851108i | 0.904933 | + | 0.425554i | \(0.139921\pi\) | ||||
−0.904933 | + | 0.425554i | \(0.860079\pi\) | |||||||
\(648\) | −1.55958e7 | + | 2.58395e8i | −0.0573170 | + | 0.949640i | ||||
\(649\) | −4.48410e7 | −0.164037 | ||||||||
\(650\) | 2.06230e8i | 0.750950i | ||||||||
\(651\) | 952508. | − | 6.31973e7i | 0.00345244 | − | 0.229063i | ||||
\(652\) | 1.13903e8 | 0.410952 | ||||||||
\(653\) | − | 2.13933e7i | − | 0.0768312i | −0.999262 | − | 0.0384156i | \(-0.987769\pi\) | ||
0.999262 | − | 0.0384156i | \(-0.0122311\pi\) | |||||||
\(654\) | 3.74612e7 | + | 564615.i | 0.133921 | + | 0.00201845i | ||||
\(655\) | −1.43436e8 | −0.510426 | ||||||||
\(656\) | − | 2.57189e7i | − | 0.0911047i | ||||||
\(657\) | −3.98203e8 | − | 1.20061e7i | −1.40413 | − | 0.0423357i | ||||
\(658\) | −9.95660e7 | −0.349489 | ||||||||
\(659\) | 2.82771e8i | 0.988049i | 0.869448 | + | 0.494024i | \(0.164475\pi\) | ||||
−0.869448 | + | 0.494024i | \(0.835525\pi\) | |||||||
\(660\) | −7.84363e6 | + | 5.20411e8i | −0.0272826 | + | 1.81015i | ||||
\(661\) | 1.95209e8 | 0.675920 | 0.337960 | − | 0.941160i | \(-0.390263\pi\) | ||||
0.337960 | + | 0.941160i | \(0.390263\pi\) | |||||||
\(662\) | − | 2.64246e8i | − | 0.910823i | ||||||
\(663\) | 3.56124e8 | + | 5.36749e6i | 1.22197 | + | 0.0184175i | ||||
\(664\) | −5.51386e6 | −0.0188344 | ||||||||
\(665\) | − | 1.48865e8i | − | 0.506205i | ||||||
\(666\) | 2.50165e6 | − | 8.29712e7i | 0.00846845 | − | 0.280870i | ||||
\(667\) | 7.51937e7 | 0.253399 | ||||||||
\(668\) | 8.16473e7i | 0.273913i | ||||||||
\(669\) | 8.57292e6 | − | 5.68799e8i | 0.0286319 | − | 1.89968i | ||||
\(670\) | 1.80129e7 | 0.0598907 | ||||||||
\(671\) | 7.87626e8i | 2.60707i | ||||||||
\(672\) | 1.22383e8 | + | 1.84455e6i | 0.403285 | + | 0.00607831i | ||||
\(673\) | −1.44132e8 | −0.472840 | −0.236420 | − | 0.971651i | \(-0.575974\pi\) | ||||
−0.236420 | + | 0.971651i | \(0.575974\pi\) | |||||||
\(674\) | 7.19404e7i | 0.234960i | ||||||||
\(675\) | −1.17335e7 | + | 2.59341e8i | −0.0381518 | + | 0.843257i | ||||
\(676\) | 3.07174e8 | 0.994361 | ||||||||
\(677\) | 4.66018e8i | 1.50189i | 0.660367 | + | 0.750943i | \(0.270401\pi\) | ||||
−0.660367 | + | 0.750943i | \(0.729599\pi\) | |||||||
\(678\) | −1.04821e6 | + | 6.95469e7i | −0.00336325 | + | 0.223146i | ||||
\(679\) | 5.69629e7 | 0.181963 | ||||||||
\(680\) | 3.16227e8i | 1.00571i | ||||||||
\(681\) | 1.86430e8 | + | 2.80987e6i | 0.590302 | + | 0.00889702i | ||||
\(682\) | −2.06621e8 | −0.651359 | ||||||||
\(683\) | 3.20070e8i | 1.00458i | 0.864700 | + | 0.502288i | \(0.167508\pi\) | ||||
−0.864700 | + | 0.502288i | \(0.832492\pi\) | |||||||
\(684\) | 2.06834e8 | + | 6.23622e6i | 0.646330 | + | 0.0194874i | ||||
\(685\) | −4.23605e8 | −1.31792 | ||||||||
\(686\) | 1.32223e8i | 0.409576i | ||||||||
\(687\) | 5.81932e6 | − | 3.86101e8i | 0.0179474 | − | 1.19078i | ||||
\(688\) | 198182. | 0.000608555 | ||||||||
\(689\) | − | 6.58772e8i | − | 2.01408i | ||||||
\(690\) | 5.27054e7 | + | 794375.i | 0.160438 | + | 0.00241812i | ||||
\(691\) | 4.11499e8 | 1.24720 | 0.623598 | − | 0.781745i | \(-0.285670\pi\) | ||||
0.623598 | + | 0.781745i | \(0.285670\pi\) | |||||||
\(692\) | 1.30380e8i | 0.393452i | ||||||||
\(693\) | −7.70817e6 | + | 2.55654e8i | −0.0231607 | + | 0.768162i | ||||
\(694\) | 7.86147e7 | 0.235193 | ||||||||
\(695\) | − | 6.96356e8i | − | 2.07432i | ||||||
\(696\) | 5.87443e6 | − | 3.89758e8i | 0.0174236 | − | 1.15603i | ||||
\(697\) | 1.71796e8 | 0.507357 | ||||||||
\(698\) | 1.70597e7i | 0.0501654i | ||||||||
\(699\) | −3.69786e8 | − | 5.57341e6i | −1.08273 | − | 0.0163188i | ||||
\(700\) | 7.69269e7 | 0.224277 | ||||||||
\(701\) | 3.16021e8i | 0.917408i | 0.888589 | + | 0.458704i | \(0.151686\pi\) | ||||
−0.888589 | + | 0.458704i | \(0.848314\pi\) | |||||||
\(702\) | −3.07450e8 | − | 1.39101e7i | −0.888716 | − | 0.0402085i | ||||
\(703\) | −1.64094e8 | −0.472310 | ||||||||
\(704\) | − | 3.04351e8i | − | 0.872283i | ||||||
\(705\) | 1.13008e7 | − | 7.49790e8i | 0.0322510 | − | 2.13979i | ||||
\(706\) | −2.21875e8 | −0.630513 | ||||||||
\(707\) | − | 1.88853e8i | − | 0.534399i | ||||||
\(708\) | −2.01244e7 | − | 303314.i | −0.0567052 | − | 0.000854659i | ||||
\(709\) | 1.02656e8 | 0.288034 | 0.144017 | − | 0.989575i | \(-0.453998\pi\) | ||||
0.144017 | + | 0.989575i | \(0.453998\pi\) | |||||||
\(710\) | 1.13437e8i | 0.316943i | ||||||||
\(711\) | 3.93639e8 | + | 1.18685e7i | 1.09519 | + | 0.0330209i | ||||
\(712\) | −2.58600e8 | −0.716454 | ||||||||
\(713\) | − | 4.42414e7i | − | 0.122056i | ||||||
\(714\) | −947004. | + | 6.28320e7i | −0.00260170 | + | 0.172618i | ||||
\(715\) | −1.53025e9 | −4.18644 | ||||||||
\(716\) | 8.35662e7i | 0.227663i | ||||||||
\(717\) | −1.36678e8 | − | 2.06000e6i | −0.370800 | − | 0.00558870i | ||||
\(718\) | −2.62491e8 | −0.709156 | ||||||||
\(719\) | − | 1.53471e8i | − | 0.412894i | −0.978458 | − | 0.206447i | \(-0.933810\pi\) | ||
0.978458 | − | 0.206447i | \(-0.0661902\pi\) | |||||||
\(720\) | −2.13526e6 | + | 7.08192e7i | −0.00572075 | + | 0.189738i | ||||
\(721\) | 1.90627e7 | 0.0508601 | ||||||||
\(722\) | − | 1.97918e7i | − | 0.0525865i | ||||||
\(723\) | 1.05371e7 | − | 6.99121e8i | 0.0278810 | − | 1.84985i | ||||
\(724\) | 2.22734e8 | 0.586908 | ||||||||
\(725\) | − | 3.90918e8i | − | 1.02582i | ||||||
\(726\) | 6.19224e8 | + | 9.33294e6i | 1.61822 | + | 0.0243898i | ||||
\(727\) | 4.14620e8 | 1.07906 | 0.539531 | − | 0.841966i | \(-0.318602\pi\) | ||||
0.539531 | + | 0.841966i | \(0.318602\pi\) | |||||||
\(728\) | 2.25530e8i | 0.584534i | ||||||||
\(729\) | −3.85838e8 | − | 3.49848e7i | −0.995914 | − | 0.0903019i | ||||
\(730\) | 4.20528e8 | 1.08100 | ||||||||
\(731\) | 1.32381e6i | 0.00338901i | ||||||||
\(732\) | −5.32767e6 | + | 3.53482e8i | −0.0135833 | + | 0.901226i | ||||
\(733\) | 2.31612e8 | 0.588098 | 0.294049 | − | 0.955790i | \(-0.404997\pi\) | ||||
0.294049 | + | 0.955790i | \(0.404997\pi\) | |||||||
\(734\) | 1.82287e8i | 0.460966i | ||||||||
\(735\) | −4.56568e8 | − | 6.88139e6i | −1.14986 | − | 0.0173306i | ||||
\(736\) | 8.56744e7 | 0.214891 | ||||||||
\(737\) | 6.11801e7i | 0.152830i | ||||||||
\(738\) | −1.48383e8 | − | 4.47385e6i | −0.369159 | − | 0.0111305i | ||||
\(739\) | −2.21737e8 | −0.549421 | −0.274711 | − | 0.961527i | \(-0.588582\pi\) | ||||
−0.274711 | + | 0.961527i | \(0.588582\pi\) | |||||||
\(740\) | − | 1.85253e8i | − | 0.457162i | ||||||
\(741\) | −9.16870e6 | + | 6.08328e8i | −0.0225348 | + | 1.49514i | ||||
\(742\) | 1.16229e8 | 0.284514 | ||||||||
\(743\) | − | 2.05127e8i | − | 0.500100i | −0.968233 | − | 0.250050i | \(-0.919553\pi\) | ||
0.968233 | − | 0.250050i | \(-0.0804470\pi\) | |||||||
\(744\) | −2.29320e8 | − | 3.45631e6i | −0.556832 | − | 0.00839256i | ||||
\(745\) | 9.82075e8 | 2.37507 | ||||||||
\(746\) | − | 3.30268e8i | − | 0.795517i | ||||||
\(747\) | 248695. | − | 8.24836e6i | 0.000596630 | − | 0.0197882i | ||||
\(748\) | −4.34314e8 | −1.03776 | ||||||||
\(749\) | 5.81946e7i | 0.138496i | ||||||||
\(750\) | −762636. | + | 5.05996e7i | −0.00180773 | + | 0.119940i | ||||
\(751\) | −1.97141e8 | −0.465432 | −0.232716 | − | 0.972545i | \(-0.574761\pi\) | ||||
−0.232716 | + | 0.972545i | \(0.574761\pi\) | |||||||
\(752\) | − | 9.36778e7i | − | 0.220284i | ||||||
\(753\) | −2.34872e8 | − | 3.53999e6i | −0.550106 | − | 0.00829118i | ||||
\(754\) | 4.63435e8 | 1.08112 | ||||||||
\(755\) | − | 3.67384e8i | − | 0.853650i | ||||||
\(756\) | −5.18867e6 | + | 1.14684e8i | −0.0120086 | + | 0.265422i | ||||
\(757\) | −4.96512e8 | −1.14457 | −0.572285 | − | 0.820055i | \(-0.693943\pi\) | ||||
−0.572285 | + | 0.820055i | \(0.693943\pi\) | |||||||
\(758\) | − | 1.09987e8i | − | 0.252541i | ||||||
\(759\) | −2.69806e6 | + | 1.79012e8i | −0.00617059 | + | 0.409408i | ||||
\(760\) | −5.40176e8 | −1.23054 | ||||||||
\(761\) | 2.10266e8i | 0.477107i | 0.971129 | + | 0.238553i | \(0.0766732\pi\) | ||||
−0.971129 | + | 0.238553i | \(0.923327\pi\) | |||||||
\(762\) | −4.26353e8 | − | 6.42598e6i | −0.963616 | − | 0.0145236i | ||||
\(763\) | 4.10890e7 | 0.0925021 | ||||||||
\(764\) | 3.57906e8i | 0.802582i | ||||||||
\(765\) | −4.73054e8 | − | 1.42630e7i | −1.05664 | − | 0.0318585i | ||||
\(766\) | 1.07264e7 | 0.0238654 | ||||||||
\(767\) | − | 5.91751e7i | − | 0.131145i | ||||||
\(768\) | 6.04539e6 | − | 4.01101e8i | 0.0133457 | − | 0.885462i | ||||
\(769\) | 1.21018e7 | 0.0266117 | 0.0133058 | − | 0.999911i | \(-0.495764\pi\) | ||||
0.0133058 | + | 0.999911i | \(0.495764\pi\) | |||||||
\(770\) | − | 2.69987e8i | − | 0.591386i | ||||||
\(771\) | 5.19621e8 | + | 7.83172e6i | 1.13377 | + | 0.0170881i | ||||
\(772\) | 9.32277e7 | 0.202625 | ||||||||
\(773\) | 6.90900e8i | 1.49581i | 0.663806 | + | 0.747905i | \(0.268940\pi\) | ||||
−0.663806 | + | 0.747905i | \(0.731060\pi\) | |||||||
\(774\) | 34474.2 | − | 1.14339e6i | 7.43484e−5 | − | 0.00246588i | ||||
\(775\) | −2.30003e8 | −0.494115 | ||||||||
\(776\) | − | 2.06698e8i | − | 0.442335i | ||||||
\(777\) | 1.37196e6 | − | 9.10269e7i | 0.00292467 | − | 0.194047i | ||||
\(778\) | −2.04968e8 | −0.435258 | ||||||||
\(779\) | 2.93460e8i | 0.620778i | ||||||||
\(780\) | −6.86767e8 | − | 1.03509e7i | −1.44719 | − | 0.0218120i | ||||
\(781\) | −3.85286e8 | −0.808779 | ||||||||
\(782\) | 4.39857e7i | 0.0919796i | ||||||||
\(783\) | 5.82786e8 | + | 2.63672e7i | 1.21401 | + | 0.0549261i | ||||
\(784\) | −5.70431e7 | −0.118374 | ||||||||
\(785\) | 1.16934e9i | 2.41730i | ||||||||
\(786\) | −1.55867e6 | + | 1.03415e8i | −0.00320986 | + | 0.212968i | ||||
\(787\) | 1.19101e8 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(788\) | − | 1.78799e8i | − | 0.365416i | ||||||
\(789\) | 7.08929e8 | + | 1.06850e7i | 1.44335 | + | 0.0217542i | ||||
\(790\) | −4.15708e8 | −0.843155 | ||||||||
\(791\) | 7.62819e7i | 0.154132i | ||||||||
\(792\) | 9.27677e8 | + | 2.79702e7i | 1.86733 | + | 0.0563015i | ||||
\(793\) | −1.03940e9 | −2.08432 | ||||||||
\(794\) | 2.71784e8i | 0.542953i | ||||||||
\(795\) | −1.31921e7 | + | 8.75273e8i | −0.0262550 | + | 1.74198i | ||||
\(796\) | 1.68291e8 | 0.333673 | ||||||||
\(797\) | − | 6.91478e8i | − | 1.36585i | −0.730488 | − | 0.682926i | \(-0.760707\pi\) | ||
0.730488 | − | 0.682926i | \(-0.239293\pi\) | |||||||
\(798\) | −1.07329e8 | − | 1.61766e6i | −0.211207 | − | 0.00318331i | ||||
\(799\) | 6.25744e8 | 1.22675 | ||||||||
\(800\) | − | 4.45405e8i | − | 0.869932i | ||||||
\(801\) | 1.16638e7 | − | 3.86847e8i | 0.0226956 | − | 0.752735i | ||||
\(802\) | 3.46040e7 | 0.0670815 | ||||||||
\(803\) | 1.42831e9i | 2.75851i | ||||||||
\(804\) | −413835. | + | 2.74572e7i | −0.000796268 | + | 0.0528310i | ||||
\(805\) | 5.78094e7 | 0.110818 | ||||||||
\(806\) | − | 2.72670e8i | − | 0.520753i | ||||||
\(807\) | −6.97604e8 | − | 1.05143e7i | −1.32736 | − | 0.0200059i | ||||
\(808\) | −6.85280e8 | −1.29908 | ||||||||
\(809\) | 7.26455e8i | 1.37203i | 0.727588 | + | 0.686014i | \(0.240641\pi\) | ||||
−0.727588 | + | 0.686014i | \(0.759359\pi\) | |||||||
\(810\) | 4.08213e8 | + | 2.46383e7i | 0.768124 | + | 0.0463613i | ||||
\(811\) | 4.54245e8 | 0.851585 | 0.425792 | − | 0.904821i | \(-0.359995\pi\) | ||||
0.425792 | + | 0.904821i | \(0.359995\pi\) | |||||||
\(812\) | − | 1.72869e8i | − | 0.322885i | ||||||
\(813\) | −1.05680e7 | + | 7.01169e8i | −0.0196663 | + | 1.30482i | ||||
\(814\) | −2.97608e8 | −0.551787 | ||||||||
\(815\) | − | 4.44998e8i | − | 0.822026i | ||||||
\(816\) | −5.91162e7 | − | 890999.i | −0.108802 | − | 0.00163986i | ||||
\(817\) | −2.26131e6 | −0.00414663 | ||||||||
\(818\) | − | 3.76575e7i | − | 0.0688006i | ||||||
\(819\) | −3.37377e8 | − | 1.01722e7i | −0.614135 | − | 0.0185167i | ||||
\(820\) | −3.31299e8 | −0.600868 | ||||||||
\(821\) | − | 5.55621e8i | − | 1.00404i | −0.864857 | − | 0.502018i | \(-0.832591\pi\) | ||
0.864857 | − | 0.502018i | \(-0.167409\pi\) | |||||||
\(822\) | −4.60318e6 | + | 3.05413e8i | −0.00828786 | + | 0.549885i | ||||
\(823\) | −1.65277e7 | −0.0296492 | −0.0148246 | − | 0.999890i | \(-0.504719\pi\) | ||||
−0.0148246 | + | 0.999890i | \(0.504719\pi\) | |||||||
\(824\) | − | 6.91716e7i | − | 0.123636i | ||||||
\(825\) | 9.30649e8 | + | 1.40267e7i | 1.65739 | + | 0.0249801i | ||||
\(826\) | 1.04404e7 | 0.0185259 | ||||||||
\(827\) | − | 2.69586e8i | − | 0.476630i | −0.971188 | − | 0.238315i | \(-0.923405\pi\) | ||
0.971188 | − | 0.238315i | \(-0.0765950\pi\) | |||||||
\(828\) | −2.42175e6 | + | 8.03211e7i | −0.00426617 | + | 0.141494i | ||||
\(829\) | 5.44163e8 | 0.955136 | 0.477568 | − | 0.878595i | \(-0.341518\pi\) | ||||
0.477568 | + | 0.878595i | \(0.341518\pi\) | |||||||
\(830\) | 8.71080e6i | 0.0152344i | ||||||||
\(831\) | −9.48187e6 | + | 6.29106e8i | −0.0165231 | + | 1.09628i | ||||
\(832\) | 4.01641e8 | 0.697378 | ||||||||
\(833\) | − | 3.81033e8i | − | 0.659216i | ||||||
\(834\) | −5.02062e8 | − | 7.56707e6i | −0.865484 | − | 0.0130446i | ||||
\(835\) | 3.18982e8 | 0.547907 | ||||||||
\(836\) | − | 7.41891e8i | − | 1.26976i | ||||||
\(837\) | 1.55136e7 | − | 3.42892e8i | 0.0264567 | − | 0.584764i | ||||
\(838\) | −1.95006e6 | −0.00331372 | ||||||||
\(839\) | − | 6.52958e8i | − | 1.10560i | −0.833313 | − | 0.552802i | \(-0.813559\pi\) | ||
0.833313 | − | 0.552802i | \(-0.186441\pi\) | |||||||
\(840\) | 4.51630e6 | − | 2.99649e8i | 0.00761982 | − | 0.505562i | ||||
\(841\) | −2.83641e8 | −0.476849 | ||||||||
\(842\) | 3.32818e8i | 0.557533i | ||||||||
\(843\) | −6.44811e8 | − | 9.71859e6i | −1.07634 | − | 0.0162226i | ||||
\(844\) | 2.94633e8 | 0.490066 | ||||||||
\(845\) | − | 1.20008e9i | − | 1.98902i | ||||||
\(846\) | −5.40464e8 | − | 1.62954e7i | −0.892598 | − | 0.0269126i | ||||
\(847\) | 6.79191e8 | 1.11774 | ||||||||
\(848\) | 1.09356e8i | 0.179330i | ||||||||
\(849\) | 473481. | − | 3.14146e7i | 0.000773712 | − | 0.0513344i | ||||
\(850\) | 2.28674e8 | 0.372357 | ||||||||
\(851\) | − | 6.37236e7i | − | 0.103398i | ||||||
\(852\) | −1.72914e8 | − | 2.60615e6i | −0.279583 | − | 0.00421387i | ||||
\(853\) | 9.08209e8 | 1.46332 | 0.731659 | − | 0.681670i | \(-0.238746\pi\) | ||||
0.731659 | + | 0.681670i | \(0.238746\pi\) | |||||||
\(854\) | − | 1.83385e8i | − | 0.294435i | ||||||
\(855\) | 2.43639e7 | − | 8.08066e8i | 0.0389805 | − | 1.29285i | ||||
\(856\) | 2.11168e8 | 0.336671 | ||||||||
\(857\) | − | 2.10284e8i | − | 0.334091i | −0.985949 | − | 0.167045i | \(-0.946577\pi\) | ||
0.985949 | − | 0.167045i | \(-0.0534227\pi\) | |||||||
\(858\) | −1.66287e7 | + | 1.10329e9i | −0.0263268 | + | 1.74674i | ||||
\(859\) | 9.64448e8 | 1.52160 | 0.760798 | − | 0.648989i | \(-0.224808\pi\) | ||||
0.760798 | + | 0.648989i | \(0.224808\pi\) | |||||||
\(860\) | − | 2.55290e6i | − | 0.00401363i | ||||||
\(861\) | −1.62789e8 | − | 2.45355e6i | −0.255044 | − | 0.00384402i | ||||
\(862\) | −2.16288e8 | −0.337684 | ||||||||
\(863\) | − | 3.46769e8i | − | 0.539521i | −0.962927 | − | 0.269761i | \(-0.913055\pi\) | ||
0.962927 | − | 0.269761i | \(-0.0869446\pi\) | |||||||
\(864\) | 6.64016e8 | + | 3.00423e7i | 1.02953 | + | 0.0465792i | ||||
\(865\) | 5.09371e8 | 0.787020 | ||||||||
\(866\) | − | 4.72683e8i | − | 0.727807i | ||||||
\(867\) | −3.86987e6 | + | 2.56759e8i | −0.00593798 | + | 0.393975i | ||||
\(868\) | −1.01710e8 | −0.155527 | ||||||||
\(869\) | − | 1.41194e9i | − | 2.15157i | ||||||
\(870\) | −6.15740e8 | − | 9.28042e6i | −0.935060 | − | 0.0140932i | ||||
\(871\) | −8.07371e7 | −0.122185 | ||||||||
\(872\) | − | 1.49097e8i | − | 0.224864i | ||||||
\(873\) | 3.09206e8 | + | 9.32281e6i | 0.464735 | + | 0.0140121i | ||||
\(874\) | −7.51360e7 | −0.112542 | ||||||||
\(875\) | 5.54997e7i | 0.0828450i | ||||||||
\(876\) | −9.66137e6 | + | 6.41015e8i | −0.0143723 | + | 0.953578i | ||||
\(877\) | 1.04938e9 | 1.55572 | 0.777862 | − | 0.628435i | \(-0.216304\pi\) | ||||
0.777862 | + | 0.628435i | \(0.216304\pi\) | |||||||
\(878\) | − | 5.27654e7i | − | 0.0779589i | ||||||
\(879\) | −2.79838e7 | − | 421771.i | −0.0412040 | − | 0.000621026i | ||||
\(880\) | 2.54020e8 | 0.372752 | ||||||||
\(881\) | 7.52464e8i | 1.10042i | 0.835027 | + | 0.550209i | \(0.185452\pi\) | ||||
−0.835027 | + | 0.550209i | \(0.814548\pi\) | |||||||
\(882\) | −9.92276e6 | + | 3.29104e8i | −0.0144619 | + | 0.479654i | ||||
\(883\) | 3.22748e8 | 0.468793 | 0.234397 | − | 0.972141i | \(-0.424689\pi\) | ||||
0.234397 | + | 0.972141i | \(0.424689\pi\) | |||||||
\(884\) | − | 5.73148e8i | − | 0.829679i | ||||||
\(885\) | −1.18500e6 | + | 7.86225e7i | −0.00170957 | + | 0.113427i | ||||
\(886\) | 7.39708e8 | 1.06355 | ||||||||
\(887\) | − | 5.15412e6i | − | 0.00738557i | −0.999993 | − | 0.00369278i | \(-0.998825\pi\) | ||
0.999993 | − | 0.00369278i | \(-0.00117545\pi\) | |||||||
\(888\) | −3.30304e8 | − | 4.97834e6i | −0.471710 | − | 0.00710961i | ||||
\(889\) | −4.67641e8 | −0.665591 | ||||||||
\(890\) | 4.08536e8i | 0.579509i | ||||||||
\(891\) | −8.36830e7 | + | 1.38648e9i | −0.118305 | + | 1.96011i | ||||
\(892\) | −9.15428e8 | −1.28982 | ||||||||
\(893\) | 1.06889e9i | 1.50099i | ||||||||
\(894\) | 1.06719e7 | − | 7.08062e8i | 0.0149358 | − | 0.990965i | ||||
\(895\) | 3.26479e8 | 0.455393 | ||||||||
\(896\) | − | 2.19262e8i | − | 0.304818i | ||||||
\(897\) | −2.36235e8 | − | 3.56053e6i | −0.327316 | − | 0.00493330i | ||||
\(898\) | 6.19452e8 | 0.855419 | ||||||||
\(899\) | 5.16858e8i | 0.711365i | ||||||||
\(900\) | 4.17575e8 | + | 1.25902e7i | 0.572805 | + | 0.0172705i | ||||
\(901\) | −7.30467e8 | −0.998679 | ||||||||
\(902\) | 5.32231e8i | 0.725238i | ||||||||
\(903\) | 18906.4 | − | 1.25440e6i | 2.56770e−5 | − | 0.00170363i | ||||
\(904\) | 2.76800e8 | 0.374680 | ||||||||
\(905\) | − | 8.70183e8i | − | 1.17399i | ||||||
\(906\) | −2.64878e8 | − | 3.99224e6i | −0.356174 | − | 0.00536825i | ||||
\(907\) | 7.83830e8 | 1.05051 | 0.525255 | − | 0.850945i | \(-0.323970\pi\) | ||||
0.525255 | + | 0.850945i | \(0.323970\pi\) | |||||||
\(908\) | − | 3.00041e8i | − | 0.400796i | ||||||
\(909\) | 3.09086e7 | − | 1.02513e9i | 0.0411516 | − | 1.36486i | ||||
\(910\) | 3.56292e8 | 0.472805 | ||||||||
\(911\) | 5.30687e8i | 0.701914i | 0.936392 | + | 0.350957i | \(0.114144\pi\) | ||||
−0.936392 | + | 0.350957i | \(0.885856\pi\) | |||||||
\(912\) | 1.52200e6 | − | 1.00982e8i | 0.00200645 | − | 0.133125i | ||||
\(913\) | −2.95859e7 | −0.0388752 | ||||||||
\(914\) | 5.14444e8i | 0.673752i | ||||||||
\(915\) | 1.38099e9 | + | 2.08143e7i | 1.80272 | + | 0.0271706i | ||||
\(916\) | −6.21394e8 | −0.808501 | ||||||||
\(917\) | 1.13430e8i | 0.147102i | ||||||||
\(918\) | −1.54239e7 | + | 3.40910e8i | −0.0199373 | + | 0.440668i | ||||
\(919\) | −4.67057e8 | −0.601760 | −0.300880 | − | 0.953662i | \(-0.597280\pi\) | ||||
−0.300880 | + | 0.953662i | \(0.597280\pi\) | |||||||
\(920\) | − | 2.09770e8i | − | 0.269389i | ||||||
\(921\) | 8.79054e6 | − | 5.83237e8i | 0.0112522 | − | 0.746562i | ||||
\(922\) | 4.36263e8 | 0.556616 | ||||||||
\(923\) | − | 5.08447e8i | − | 0.646608i | ||||||
\(924\) | 4.11544e8 | + | 6.20279e6i | 0.521676 | + | 0.00786269i | ||||
\(925\) | −3.31287e8 | −0.418581 | ||||||||
\(926\) | 1.29280e8i | 0.162816i | ||||||||
\(927\) | 1.03476e8 | + | 3.11988e6i | 0.129897 | + | 0.00391651i | ||||
\(928\) | −1.00091e9 | −1.25242 | ||||||||
\(929\) | − | 7.88359e8i | − | 0.983280i | −0.870799 | − | 0.491640i | \(-0.836398\pi\) | ||
0.870799 | − | 0.491640i | \(-0.163602\pi\) | |||||||
\(930\) | −5.46029e6 | + | 3.62280e8i | −0.00678839 | + | 0.450398i | ||||
\(931\) | 6.50877e8 | 0.806585 | ||||||||
\(932\) | 5.95135e8i | 0.735137i | ||||||||
\(933\) | −6.02636e8 | − | 9.08292e6i | −0.742011 | − | 0.0111836i | ||||
\(934\) | −4.17301e8 | −0.512164 | ||||||||
\(935\) | 1.69679e9i | 2.07584i | ||||||||
\(936\) | −3.69113e7 | + | 1.22422e9i | −0.0450123 | + | 1.49290i | ||||
\(937\) | −1.36672e9 | −1.66135 | −0.830676 | − | 0.556757i | \(-0.812046\pi\) | ||||
−0.830676 | + | 0.556757i | \(0.812046\pi\) | |||||||
\(938\) | − | 1.42447e7i | − | 0.0172602i | ||||||
\(939\) | 861077. | − | 5.71309e7i | 0.00104003 | − | 0.0690041i | ||||
\(940\) | −1.20672e9 | −1.45285 | ||||||||
\(941\) | − | 5.73908e8i | − | 0.688769i | −0.938829 | − | 0.344384i | \(-0.888088\pi\) | ||
0.938829 | − | 0.344384i | \(-0.111912\pi\) | |||||||
\(942\) | 8.43076e8 | + | 1.27068e7i | 1.00859 | + | 0.0152014i | ||||
\(943\) | −1.13961e8 | −0.135900 | ||||||||
\(944\) | 9.82300e6i | 0.0116769i | ||||||||
\(945\) | 4.48050e8 | + | 2.02713e7i | 0.530922 | + | 0.0240207i | ||||
\(946\) | −4.10122e6 | −0.00484439 | ||||||||
\(947\) | 3.56439e8i | 0.419696i | 0.977734 | + | 0.209848i | \(0.0672970\pi\) | ||||
−0.977734 | + | 0.209848i | \(0.932703\pi\) | |||||||
\(948\) | 9.55064e6 | − | 6.33669e8i | 0.0112101 | − | 0.743768i | ||||
\(949\) | −1.88488e9 | −2.20539 | ||||||||
\(950\) | 3.90618e8i | 0.455598i | ||||||||
\(951\) | 5.89575e8 | + | 8.88606e6i | 0.685484 | + | 0.0103316i | ||||
\(952\) | 2.50074e8 | 0.289840 | ||||||||
\(953\) | 1.16121e9i | 1.34162i | 0.741628 | + | 0.670811i | \(0.234054\pi\) | ||||
−0.741628 | + | 0.670811i | \(0.765946\pi\) | |||||||
\(954\) | 6.30915e8 | + | 1.90226e7i | 0.726651 | + | 0.0219091i | ||||
\(955\) | 1.39828e9 | 1.60540 | ||||||||
\(956\) | 2.19970e8i | 0.251762i | ||||||||
\(957\) | 3.15206e7 | − | 2.09134e9i | 0.0359632 | − | 2.38610i | ||||
\(958\) | −4.37571e8 | −0.497682 | ||||||||
\(959\) | 3.34990e8i | 0.379818i | ||||||||
\(960\) | −5.33638e8 | − | 8.04298e6i | −0.603161 | − | 0.00909083i | ||||
\(961\) | −5.83402e8 | −0.657351 | ||||||||
\(962\) | − | 3.92743e8i | − | 0.441146i | ||||||
\(963\) | −9.52440e6 | + | 3.15892e8i | −0.0106650 | + | 0.353720i | ||||
\(964\) | −1.12517e9 | −1.25599 | ||||||||
\(965\) | − | 3.64225e8i | − | 0.405311i | ||||||
\(966\) | 628196. | − | 4.16797e7i | 0.000696889 | − | 0.0462374i | ||||
\(967\) | 3.16833e8 | 0.350389 | 0.175195 | − | 0.984534i | \(-0.443945\pi\) | ||||
0.175195 | + | 0.984534i | \(0.443945\pi\) | |||||||
\(968\) | − | 2.46454e9i | − | 2.71713i | ||||||
\(969\) | 6.74532e8 | + | 1.01665e7i | 0.741364 | + | 0.0111738i | ||||
\(970\) | −3.26542e8 | −0.357786 | ||||||||
\(971\) | 8.62988e7i | 0.0942642i | 0.998889 | + | 0.0471321i | \(0.0150082\pi\) | ||||
−0.998889 | + | 0.0471321i | \(0.984992\pi\) | |||||||
\(972\) | −4.69348e7 | + | 6.21677e8i | −0.0511089 | + | 0.676964i | ||||
\(973\) | −5.50682e8 | −0.597809 | ||||||||
\(974\) | − | 9.28699e7i | − | 0.100507i | ||||||
\(975\) | −1.85106e7 | + | 1.22814e9i | −0.0199713 | + | 1.32506i | ||||
\(976\) | 1.72540e8 | 0.185583 | ||||||||
\(977\) | − | 9.57957e8i | − | 1.02722i | −0.858024 | − | 0.513609i | \(-0.828308\pi\) | ||
0.858024 | − | 0.513609i | \(-0.171692\pi\) | |||||||
\(978\) | −3.20837e8 | − | 4.83565e6i | −0.342979 | − | 0.00516938i | ||||
\(979\) | −1.38758e9 | −1.47880 | ||||||||
\(980\) | 7.34804e8i | 0.780716i | ||||||||
\(981\) | 2.23039e8 | + | 6.72481e6i | 0.236251 | + | 0.00712317i | ||||
\(982\) | 9.05310e8 | 0.956011 | ||||||||
\(983\) | − | 4.65724e7i | − | 0.0490307i | −0.999699 | − | 0.0245153i | \(-0.992196\pi\) | ||
0.999699 | − | 0.0245153i | \(-0.00780425\pi\) | |||||||
\(984\) | −8.90307e6 | + | 5.90703e8i | −0.00934447 | + | 0.619989i | ||||
\(985\) | −6.98539e8 | −0.730941 | ||||||||
\(986\) | − | 5.13871e8i | − | 0.536073i | ||||||
\(987\) | −5.92938e8 | − | 8.93675e6i | −0.616677 | − | 0.00929455i | ||||
\(988\) | 9.79046e8 | 1.01515 | ||||||||
\(989\) | − | 878149.i | − | 0.000907777i | ||||||
\(990\) | 4.41873e7 | − | 1.46554e9i | 0.0455399 | − | 1.51040i | ||||
\(991\) | 1.30464e9 | 1.34051 | 0.670257 | − | 0.742129i | \(-0.266184\pi\) | ||||
0.670257 | + | 0.742129i | \(0.266184\pi\) | |||||||
\(992\) | 5.88899e8i | 0.603262i | ||||||||
\(993\) | 2.37179e7 | − | 1.57364e9i | 0.0242231 | − | 1.60716i | ||||
\(994\) | 8.97069e7 | 0.0913412 | ||||||||
\(995\) | − | 6.57484e8i | − | 0.667446i | ||||||
\(996\) | −1.32780e7 | − | 200125.i | −0.0134386 | − | 0.000202546i | ||||
\(997\) | −2.74891e8 | −0.277380 | −0.138690 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138690 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(998\) | − | 2.93094e7i | − | 0.0294860i | ||||||
\(999\) | 2.23451e7 | − | 4.93888e8i | 0.0224123 | − | 0.495372i |
(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 | 69.7.b.a.47.28 | yes | 44 | |
3.2 | odd | 2 | inner | 69.7.b.a.47.17 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.7.b.a.47.17 | ✓ | 44 | 3.2 | odd | 2 | inner | |
69.7.b.a.47.28 | yes | 44 | 1.1 | even | 1 | trivial |