Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.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: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.14 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.70638 | + | 7.08962i | −0.463298 | + | 0.886203i | ||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | −36.5255 | − | 52.5537i | −0.570710 | − | 0.821152i | ||||
\(5\) | 108.680 | − | 61.7555i | 0.869437 | − | 0.494044i | ||||
\(6\) | −57.7768 | + | 110.516i | −0.267485 | + | 0.511649i | ||||
\(7\) | −629.059 | −1.83399 | −0.916996 | − | 0.398896i | \(-0.869393\pi\) | ||||
−0.916996 | + | 0.398896i | \(0.869393\pi\) | |||||||
\(8\) | 507.963 | − | 64.1675i | 0.992115 | − | 0.125327i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 35.0151 | + | 999.387i | 0.0350151 | + | 0.999387i | ||||
\(11\) | 1255.72i | 0.943444i | 0.881747 | + | 0.471722i | \(0.156367\pi\) | ||||
−0.881747 | + | 0.471722i | \(0.843633\pi\) | |||||||
\(12\) | −569.375 | − | 819.231i | −0.329500 | − | 0.474092i | ||||
\(13\) | 3334.77i | 1.51788i | 0.651163 | + | 0.758938i | \(0.274281\pi\) | ||||
−0.651163 | + | 0.758938i | \(0.725719\pi\) | |||||||
\(14\) | 2331.53 | − | 4459.79i | 0.849685 | − | 1.62529i | ||||
\(15\) | 1694.15 | − | 962.673i | 0.501970 | − | 0.285237i | ||||
\(16\) | −1427.78 | + | 3839.10i | −0.348580 | + | 0.937279i | ||||
\(17\) | 7637.86i | 1.55462i | 0.629117 | + | 0.777311i | \(0.283417\pi\) | ||||
−0.629117 | + | 0.777311i | \(0.716583\pi\) | |||||||
\(18\) | −900.651 | + | 1722.78i | −0.154433 | + | 0.295401i | ||||
\(19\) | − | 1250.64i | − | 0.182335i | −0.995836 | − | 0.0911675i | \(-0.970940\pi\) | ||
0.995836 | − | 0.0911675i | \(-0.0290599\pi\) | |||||||
\(20\) | −7215.05 | − | 3455.87i | −0.901882 | − | 0.431983i | ||||
\(21\) | −9806.06 | −1.05886 | ||||||||
\(22\) | −8902.61 | − | 4654.19i | −0.836083 | − | 0.437096i | ||||
\(23\) | −14407.2 | −1.18412 | −0.592062 | − | 0.805893i | \(-0.701686\pi\) | ||||
−0.592062 | + | 0.805893i | \(0.701686\pi\) | |||||||
\(24\) | 7918.36 | − | 1000.27i | 0.572798 | − | 0.0723577i | ||||
\(25\) | 7997.51 | − | 13423.1i | 0.511841 | − | 0.859080i | ||||
\(26\) | −23642.3 | − | 12359.9i | −1.34515 | − | 0.703228i | ||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 22976.7 | + | 33059.4i | 1.04668 | + | 1.50599i | ||||
\(29\) | −7208.72 | −0.295573 | −0.147786 | − | 0.989019i | \(-0.547215\pi\) | ||||
−0.147786 | + | 0.989019i | \(0.547215\pi\) | |||||||
\(30\) | 545.832 | + | 15578.9i | 0.0202160 | + | 0.576996i | ||||
\(31\) | 3243.73i | 0.108883i | 0.998517 | + | 0.0544414i | \(0.0173378\pi\) | ||||
−0.998517 | + | 0.0544414i | \(0.982662\pi\) | |||||||
\(32\) | −21925.8 | − | 24351.6i | −0.669123 | − | 0.743152i | ||||
\(33\) | 19574.8i | 0.544698i | ||||||||
\(34\) | −54149.5 | − | 28308.8i | −1.37771 | − | 0.720253i | ||||
\(35\) | −68365.9 | + | 38847.9i | −1.59454 | + | 0.906073i | ||||
\(36\) | −8875.69 | − | 12770.5i | −0.190237 | − | 0.273717i | ||||
\(37\) | 54841.3i | 1.08269i | 0.840802 | + | 0.541343i | \(0.182084\pi\) | ||||
−0.840802 | + | 0.541343i | \(0.817916\pi\) | |||||||
\(38\) | 8866.54 | + | 4635.34i | 0.161586 | + | 0.0844755i | ||||
\(39\) | 51984.0i | 0.876346i | ||||||||
\(40\) | 51242.5 | − | 38343.2i | 0.800664 | − | 0.599113i | ||||
\(41\) | 29113.1 | 0.422412 | 0.211206 | − | 0.977442i | \(-0.432261\pi\) | ||||
0.211206 | + | 0.977442i | \(0.432261\pi\) | |||||||
\(42\) | 36345.0 | − | 69521.3i | 0.490566 | − | 0.938361i | ||||
\(43\) | −12739.1 | −0.160226 | −0.0801129 | − | 0.996786i | \(-0.525528\pi\) | ||||
−0.0801129 | + | 0.996786i | \(0.525528\pi\) | |||||||
\(44\) | 65992.9 | − | 45865.9i | 0.774711 | − | 0.538433i | ||||
\(45\) | 26409.1 | − | 15006.6i | 0.289812 | − | 0.164681i | ||||
\(46\) | 53398.7 | − | 102142.i | 0.548602 | − | 1.04937i | ||||
\(47\) | 15012.6 | 0.144598 | 0.0722988 | − | 0.997383i | \(-0.476966\pi\) | ||||
0.0722988 | + | 0.997383i | \(0.476966\pi\) | |||||||
\(48\) | −22256.9 | + | 59845.6i | −0.201253 | + | 0.541138i | ||||
\(49\) | 278067. | 2.36353 | ||||||||
\(50\) | 65523.1 | + | 106451.i | 0.524185 | + | 0.851605i | ||||
\(51\) | 119062.i | 0.897561i | ||||||||
\(52\) | 175255. | − | 121804.i | 1.24641 | − | 0.866267i | ||||
\(53\) | − | 203806.i | − | 1.36895i | −0.729035 | − | 0.684476i | \(-0.760031\pi\) | ||
0.729035 | − | 0.684476i | \(-0.239969\pi\) | |||||||
\(54\) | −14039.8 | + | 26855.4i | −0.0891617 | + | 0.170550i | ||||
\(55\) | 77547.9 | + | 136472.i | 0.466103 | + | 0.820265i | ||||
\(56\) | −319539. | + | 40365.2i | −1.81953 | + | 0.229849i | ||||
\(57\) | − | 19495.5i | − | 0.105271i | ||||||
\(58\) | 26718.3 | − | 51107.1i | 0.136938 | − | 0.261937i | ||||
\(59\) | − | 14568.1i | − | 0.0709328i | −0.999371 | − | 0.0354664i | \(-0.988708\pi\) | ||
0.999371 | − | 0.0354664i | \(-0.0112917\pi\) | |||||||
\(60\) | −112472. | − | 53871.6i | −0.520702 | − | 0.249406i | ||||
\(61\) | −311116. | −1.37067 | −0.685335 | − | 0.728228i | \(-0.740344\pi\) | ||||
−0.685335 | + | 0.728228i | \(0.740344\pi\) | |||||||
\(62\) | −22996.8 | − | 12022.5i | −0.0964922 | − | 0.0504452i | ||||
\(63\) | −152861. | −0.611331 | ||||||||
\(64\) | 253909. | − | 65189.5i | 0.968586 | − | 0.248678i | ||||
\(65\) | 205941. | + | 362422.i | 0.749898 | + | 1.31970i | ||||
\(66\) | −138778. | − | 72551.7i | −0.482712 | − | 0.252357i | ||||
\(67\) | 101935. | 0.338921 | 0.169461 | − | 0.985537i | \(-0.445797\pi\) | ||||
0.169461 | + | 0.985537i | \(0.445797\pi\) | |||||||
\(68\) | 401398. | − | 278976.i | 1.27658 | − | 0.887239i | ||||
\(69\) | −224586. | −0.683654 | ||||||||
\(70\) | −22026.6 | − | 628674.i | −0.0642175 | − | 1.83287i | ||||
\(71\) | 530826.i | 1.48312i | 0.670885 | + | 0.741561i | \(0.265914\pi\) | ||||
−0.670885 | + | 0.741561i | \(0.734086\pi\) | |||||||
\(72\) | 123435. | − | 15592.7i | 0.330705 | − | 0.0417757i | ||||
\(73\) | 224270.i | 0.576504i | 0.957555 | + | 0.288252i | \(0.0930741\pi\) | ||||
−0.957555 | + | 0.288252i | \(0.906926\pi\) | |||||||
\(74\) | −388804. | − | 203263.i | −0.959480 | − | 0.501606i | ||||
\(75\) | 124669. | − | 209246.i | 0.295511 | − | 0.495990i | ||||
\(76\) | −65725.6 | + | 45680.1i | −0.149725 | + | 0.104061i | ||||
\(77\) | − | 789925.i | − | 1.73027i | ||||||
\(78\) | −368547. | − | 192672.i | −0.776620 | − | 0.406009i | ||||
\(79\) | 13747.8i | 0.0278837i | 0.999903 | + | 0.0139419i | \(0.00443797\pi\) | ||||
−0.999903 | + | 0.0139419i | \(0.995562\pi\) | |||||||
\(80\) | 81914.6 | + | 505405.i | 0.159989 | + | 0.987119i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −107904. | + | 206401.i | −0.195703 | + | 0.374343i | ||||
\(83\) | −632021. | −1.10534 | −0.552671 | − | 0.833399i | \(-0.686392\pi\) | ||||
−0.552671 | + | 0.833399i | \(0.686392\pi\) | |||||||
\(84\) | 358171. | + | 515345.i | 0.604300 | + | 0.869481i | ||||
\(85\) | 471680. | + | 830079.i | 0.768052 | + | 1.35165i | ||||
\(86\) | 47215.9 | − | 90315.3i | 0.0742323 | − | 0.141993i | ||||
\(87\) | −112373. | −0.170649 | ||||||||
\(88\) | 80576.7 | + | 637861.i | 0.118239 | + | 0.936005i | ||||
\(89\) | −303793. | −0.430931 | −0.215465 | − | 0.976512i | \(-0.569127\pi\) | ||||
−0.215465 | + | 0.976512i | \(0.569127\pi\) | |||||||
\(90\) | 8508.68 | + | 242851.i | 0.0116717 | + | 0.333129i | ||||
\(91\) | − | 2.09777e6i | − | 2.78377i | ||||||
\(92\) | 526231. | + | 757153.i | 0.675791 | + | 0.972345i | ||||
\(93\) | 50564.7i | 0.0628635i | ||||||||
\(94\) | −55642.3 | + | 106433.i | −0.0669917 | + | 0.128143i | ||||
\(95\) | −77233.7 | − | 135919.i | −0.0900816 | − | 0.158529i | ||||
\(96\) | −341790. | − | 379604.i | −0.386318 | − | 0.429059i | ||||
\(97\) | − | 625514.i | − | 0.685364i | −0.939451 | − | 0.342682i | \(-0.888665\pi\) | ||
0.939451 | − | 0.342682i | \(-0.111335\pi\) | |||||||
\(98\) | −1.03062e6 | + | 1.97139e6i | −1.09502 | + | 2.09456i | ||||
\(99\) | 305141.i | 0.314481i | ||||||||
\(100\) | −997548. | + | 69987.3i | −0.997548 | + | 0.0699873i | ||||
\(101\) | 70748.0 | 0.0686673 | 0.0343336 | − | 0.999410i | \(-0.489069\pi\) | ||||
0.0343336 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(102\) | −844107. | − | 441291.i | −0.795421 | − | 0.415838i | ||||
\(103\) | 1.12706e6 | 1.03142 | 0.515709 | − | 0.856764i | \(-0.327529\pi\) | ||||
0.515709 | + | 0.856764i | \(0.327529\pi\) | |||||||
\(104\) | 213984. | + | 1.69394e6i | 0.190231 | + | 1.50591i | ||||
\(105\) | −1.06572e6 | + | 605579.i | −0.920608 | + | 0.523122i | ||||
\(106\) | 1.44490e6 | + | 755381.i | 1.21317 | + | 0.634233i | ||||
\(107\) | 1.13145e6 | 0.923599 | 0.461800 | − | 0.886984i | \(-0.347204\pi\) | ||||
0.461800 | + | 0.886984i | \(0.347204\pi\) | |||||||
\(108\) | −138358. | − | 199073.i | −0.109833 | − | 0.158031i | ||||
\(109\) | −1.24198e6 | −0.959034 | −0.479517 | − | 0.877533i | \(-0.659188\pi\) | ||||
−0.479517 | + | 0.877533i | \(0.659188\pi\) | |||||||
\(110\) | −1.25495e6 | + | 43969.4i | −0.942865 | + | 0.0330348i | ||||
\(111\) | 854892.i | 0.625089i | ||||||||
\(112\) | 898160. | − | 2.41502e6i | 0.639292 | − | 1.71896i | ||||
\(113\) | − | 439583.i | − | 0.304653i | −0.988330 | − | 0.152327i | \(-0.951323\pi\) | ||
0.988330 | − | 0.152327i | \(-0.0486766\pi\) | |||||||
\(114\) | 138216. | + | 72257.8i | 0.0932916 | + | 0.0487719i | ||||
\(115\) | −1.56577e6 | + | 889726.i | −1.02952 | + | 0.585009i | ||||
\(116\) | 263302. | + | 378845.i | 0.168686 | + | 0.242710i | ||||
\(117\) | 810350.i | 0.505959i | ||||||||
\(118\) | 103282. | + | 53995.0i | 0.0628608 | + | 0.0328630i | ||||
\(119\) | − | 4.80467e6i | − | 2.85116i | ||||||
\(120\) | 798792. | − | 597712.i | 0.462264 | − | 0.345898i | ||||
\(121\) | 194718. | 0.109913 | ||||||||
\(122\) | 1.15311e6 | − | 2.20569e6i | 0.635028 | − | 1.21469i | ||||
\(123\) | 453828. | 0.243880 | ||||||||
\(124\) | 170470. | − | 118479.i | 0.0894092 | − | 0.0621405i | ||||
\(125\) | 40213.3 | − | 1.95271e6i | 0.0205892 | − | 0.999788i | ||||
\(126\) | 566563. | − | 1.08373e6i | 0.283228 | − | 0.541763i | ||||
\(127\) | 2.74141e6 | 1.33833 | 0.669164 | − | 0.743115i | \(-0.266652\pi\) | ||||
0.669164 | + | 0.743115i | \(0.266652\pi\) | |||||||
\(128\) | −478916. | + | 2.04174e6i | −0.228365 | + | 0.973576i | ||||
\(129\) | −198583. | −0.0925065 | ||||||||
\(130\) | −3.33273e6 | + | 116768.i | −1.51694 | + | 0.0531486i | ||||
\(131\) | 1.16176e6i | 0.516777i | 0.966041 | + | 0.258388i | \(0.0831914\pi\) | ||||
−0.966041 | + | 0.258388i | \(0.916809\pi\) | |||||||
\(132\) | 1.02873e6 | − | 714978.i | 0.447279 | − | 0.310865i | ||||
\(133\) | 786725.i | 0.334401i | ||||||||
\(134\) | −377810. | + | 722680.i | −0.157021 | + | 0.300353i | ||||
\(135\) | 411678. | − | 233930.i | 0.167323 | − | 0.0950789i | ||||
\(136\) | 490102. | + | 3.87975e6i | 0.194836 | + | 1.54236i | ||||
\(137\) | − | 4.10213e6i | − | 1.59532i | −0.603108 | − | 0.797660i | \(-0.706071\pi\) | ||
0.603108 | − | 0.797660i | \(-0.293929\pi\) | |||||||
\(138\) | 832403. | − | 1.59223e6i | 0.316735 | − | 0.605856i | ||||
\(139\) | 1.18125e6i | 0.439842i | 0.975518 | + | 0.219921i | \(0.0705799\pi\) | ||||
−0.975518 | + | 0.219921i | \(0.929420\pi\) | |||||||
\(140\) | 4.53870e6 | + | 2.17394e6i | 1.65404 | + | 0.792254i | ||||
\(141\) | 234023. | 0.0834834 | ||||||||
\(142\) | −3.76335e6 | − | 1.96744e6i | −1.31435 | − | 0.687127i | ||||
\(143\) | −4.18755e6 | −1.43203 | ||||||||
\(144\) | −346951. | + | 932900.i | −0.116193 | + | 0.312426i | ||||
\(145\) | −783441. | + | 445178.i | −0.256982 | + | 0.146026i | ||||
\(146\) | −1.58999e6 | − | 831230.i | −0.510899 | − | 0.267093i | ||||
\(147\) | 4.33463e6 | 1.36458 | ||||||||
\(148\) | 2.88211e6 | − | 2.00310e6i | 0.889050 | − | 0.617900i | ||||
\(149\) | 1.36642e6 | 0.413073 | 0.206536 | − | 0.978439i | \(-0.433781\pi\) | ||||
0.206536 | + | 0.978439i | \(0.433781\pi\) | |||||||
\(150\) | 1.02140e6 | + | 1.65940e6i | 0.302638 | + | 0.491674i | ||||
\(151\) | 3.24068e6i | 0.941251i | 0.882333 | + | 0.470626i | \(0.155972\pi\) | ||||
−0.882333 | + | 0.470626i | \(0.844028\pi\) | |||||||
\(152\) | −80250.2 | − | 635277.i | −0.0228515 | − | 0.180897i | ||||
\(153\) | 1.85600e6i | 0.518207i | ||||||||
\(154\) | 5.60027e6 | + | 2.92776e6i | 1.53337 | + | 0.801630i | ||||
\(155\) | 200318. | + | 352527.i | 0.0537929 | + | 0.0946667i | ||||
\(156\) | 2.73195e6 | − | 1.89874e6i | 0.719613 | − | 0.500140i | ||||
\(157\) | 533613.i | 0.137888i | 0.997621 | + | 0.0689442i | \(0.0219630\pi\) | ||||
−0.997621 | + | 0.0689442i | \(0.978037\pi\) | |||||||
\(158\) | −97466.4 | − | 50954.4i | −0.0247106 | − | 0.0129185i | ||||
\(159\) | − | 3.17701e6i | − | 0.790365i | ||||||
\(160\) | −3.88674e6 | − | 1.29248e6i | −0.948910 | − | 0.315547i | ||||
\(161\) | 9.06300e6 | 2.17167 | ||||||||
\(162\) | −218858. | + | 418635.i | −0.0514775 | + | 0.0984670i | ||||
\(163\) | 3.68844e6 | 0.851686 | 0.425843 | − | 0.904797i | \(-0.359978\pi\) | ||||
0.425843 | + | 0.904797i | \(0.359978\pi\) | |||||||
\(164\) | −1.06337e6 | − | 1.53000e6i | −0.241075 | − | 0.346864i | ||||
\(165\) | 1.20885e6 | + | 2.12738e6i | 0.269105 | + | 0.473580i | ||||
\(166\) | 2.34251e6 | − | 4.48079e6i | 0.512103 | − | 0.979558i | ||||
\(167\) | −5.03742e6 | −1.08158 | −0.540790 | − | 0.841157i | \(-0.681875\pi\) | ||||
−0.540790 | + | 0.841157i | \(0.681875\pi\) | |||||||
\(168\) | −4.98112e6 | + | 629231.i | −1.05051 | + | 0.132703i | ||||
\(169\) | −6.29390e6 | −1.30395 | ||||||||
\(170\) | −7.63317e6 | + | 267441.i | −1.55367 | + | 0.0544353i | ||||
\(171\) | − | 303905.i | − | 0.0607784i | ||||||
\(172\) | 465301. | + | 669486.i | 0.0914426 | + | 0.131570i | ||||
\(173\) | − | 3.35046e6i | − | 0.647092i | −0.946212 | − | 0.323546i | \(-0.895125\pi\) | ||
0.946212 | − | 0.323546i | \(-0.104875\pi\) | |||||||
\(174\) | 416497. | − | 796681.i | 0.0790613 | − | 0.151230i | ||||
\(175\) | −5.03091e6 | + | 8.44395e6i | −0.938712 | + | 1.57555i | ||||
\(176\) | −4.82084e6 | − | 1.79290e6i | −0.884270 | − | 0.328865i | ||||
\(177\) | − | 227094.i | − | 0.0409530i | ||||||
\(178\) | 1.12597e6 | − | 2.15377e6i | 0.199649 | − | 0.381892i | ||||
\(179\) | 497081.i | 0.0866699i | 0.999061 | + | 0.0433349i | \(0.0137983\pi\) | ||||
−0.999061 | + | 0.0433349i | \(0.986202\pi\) | |||||||
\(180\) | −1.75326e6 | − | 839775.i | −0.300627 | − | 0.143994i | ||||
\(181\) | −2.46770e6 | −0.416157 | −0.208079 | − | 0.978112i | \(-0.566721\pi\) | ||||
−0.208079 | + | 0.978112i | \(0.566721\pi\) | |||||||
\(182\) | 1.48724e7 | + | 7.77514e6i | 2.46699 | + | 1.28972i | ||||
\(183\) | −4.84982e6 | −0.791356 | ||||||||
\(184\) | −7.31834e6 | + | 924476.i | −1.17479 | + | 0.148403i | ||||
\(185\) | 3.38676e6 | + | 5.96013e6i | 0.534895 | + | 0.941328i | ||||
\(186\) | −358484. | − | 187412.i | −0.0557098 | − | 0.0291245i | ||||
\(187\) | −9.59104e6 | −1.46670 | ||||||||
\(188\) | −548340. | − | 788965.i | −0.0825233 | − | 0.118736i | ||||
\(189\) | −2.38287e6 | −0.352952 | ||||||||
\(190\) | 1.24987e6 | − | 43791.2i | 0.182223 | − | 0.00638449i | ||||
\(191\) | 1.52891e6i | 0.219423i | 0.993963 | + | 0.109711i | \(0.0349926\pi\) | ||||
−0.993963 | + | 0.109711i | \(0.965007\pi\) | |||||||
\(192\) | 3.95805e6 | − | 1.01620e6i | 0.559214 | − | 0.143574i | ||||
\(193\) | 9.85234e6i | 1.37046i | 0.728325 | + | 0.685232i | \(0.240299\pi\) | ||||
−0.728325 | + | 0.685232i | \(0.759701\pi\) | |||||||
\(194\) | 4.43465e6 | + | 2.31839e6i | 0.607372 | + | 0.317528i | ||||
\(195\) | 3.21030e6 | + | 5.64960e6i | 0.432954 | + | 0.761927i | ||||
\(196\) | −1.01565e7 | − | 1.46134e7i | −1.34889 | − | 1.94081i | ||||
\(197\) | − | 2.71648e6i | − | 0.355310i | −0.984093 | − | 0.177655i | \(-0.943149\pi\) | ||
0.984093 | − | 0.177655i | \(-0.0568511\pi\) | |||||||
\(198\) | −2.16333e6 | − | 1.13097e6i | −0.278694 | − | 0.145699i | ||||
\(199\) | − | 1.14524e7i | − | 1.45324i | −0.687042 | − | 0.726618i | \(-0.741091\pi\) | ||
0.687042 | − | 0.726618i | \(-0.258909\pi\) | |||||||
\(200\) | 3.20111e6 | − | 7.33164e6i | 0.400139 | − | 0.916455i | ||||
\(201\) | 1.58901e6 | 0.195676 | ||||||||
\(202\) | −262219. | + | 501576.i | −0.0318134 | + | 0.0608531i | ||||
\(203\) | 4.53471e6 | 0.542078 | ||||||||
\(204\) | 6.25717e6 | − | 4.34881e6i | 0.737034 | − | 0.512247i | ||||
\(205\) | 3.16400e6 | − | 1.79789e6i | 0.367261 | − | 0.208690i | ||||
\(206\) | −4.17731e6 | + | 7.99041e6i | −0.477853 | + | 0.914045i | ||||
\(207\) | −3.50096e6 | −0.394708 | ||||||||
\(208\) | −1.28025e7 | − | 4.76133e6i | −1.42267 | − | 0.529101i | ||||
\(209\) | 1.57045e6 | 0.172023 | ||||||||
\(210\) | −343361. | − | 9.80005e6i | −0.0370760 | − | 1.05821i | ||||
\(211\) | 1.59562e7i | 1.69857i | 0.527936 | + | 0.849284i | \(0.322966\pi\) | ||||
−0.527936 | + | 0.849284i | \(0.677034\pi\) | |||||||
\(212\) | −1.07107e7 | + | 7.44409e6i | −1.12412 | + | 0.781275i | ||||
\(213\) | 8.27475e6i | 0.856281i | ||||||||
\(214\) | −4.19358e6 | + | 8.02154e6i | −0.427901 | + | 0.818496i | ||||
\(215\) | −1.38448e6 | + | 786709.i | −0.139306 | + | 0.0791587i | ||||
\(216\) | 1.92416e6 | − | 243066.i | 0.190933 | − | 0.0241192i | ||||
\(217\) | − | 2.04050e6i | − | 0.199690i | ||||||
\(218\) | 4.60324e6 | − | 8.80515e6i | 0.444318 | − | 0.849899i | ||||
\(219\) | 3.49602e6i | 0.332845i | ||||||||
\(220\) | 4.33961e6 | − | 9.06012e6i | 0.407552 | − | 0.850875i | ||||
\(221\) | −2.54705e7 | −2.35972 | ||||||||
\(222\) | −6.06086e6 | − | 3.16856e6i | −0.553956 | − | 0.289603i | ||||
\(223\) | 4.91870e6 | 0.443543 | 0.221771 | − | 0.975099i | \(-0.428816\pi\) | ||||
0.221771 | + | 0.975099i | \(0.428816\pi\) | |||||||
\(224\) | 1.37926e7 | + | 1.53186e7i | 1.22717 | + | 1.36293i | ||||
\(225\) | 1.94339e6 | − | 3.26182e6i | 0.170614 | − | 0.286360i | ||||
\(226\) | 3.11648e6 | + | 1.62926e6i | 0.269985 | + | 0.141145i | ||||
\(227\) | 9.26812e6 | 0.792344 | 0.396172 | − | 0.918176i | \(-0.370338\pi\) | ||||
0.396172 | + | 0.918176i | \(0.370338\pi\) | |||||||
\(228\) | −1.02456e6 | + | 712082.i | −0.0864436 | + | 0.0600794i | ||||
\(229\) | 4.35025e6 | 0.362249 | 0.181125 | − | 0.983460i | \(-0.442026\pi\) | ||||
0.181125 | + | 0.983460i | \(0.442026\pi\) | |||||||
\(230\) | −504471. | − | 1.43984e7i | −0.0414623 | − | 1.18340i | ||||
\(231\) | − | 1.23137e7i | − | 0.998971i | ||||||
\(232\) | −3.66177e6 | + | 462566.i | −0.293242 | + | 0.0370433i | ||||
\(233\) | − | 151080.i | − | 0.0119437i | −0.999982 | − | 0.00597185i | \(-0.998099\pi\) | ||
0.999982 | − | 0.00597185i | \(-0.00190091\pi\) | |||||||
\(234\) | −5.74507e6 | − | 3.00347e6i | −0.448382 | − | 0.234409i | ||||
\(235\) | 1.63156e6 | − | 927108.i | 0.125718 | − | 0.0714376i | ||||
\(236\) | −765608. | + | 532106.i | −0.0582465 | + | 0.0404821i | ||||
\(237\) | 214306.i | 0.0160987i | ||||||||
\(238\) | 3.40633e7 | + | 1.78079e7i | 2.52671 | + | 1.32094i | ||||
\(239\) | − | 1.10896e7i | − | 0.812313i | −0.913804 | − | 0.406156i | \(-0.866869\pi\) | ||
0.913804 | − | 0.406156i | \(-0.133131\pi\) | |||||||
\(240\) | 1.27692e6 | + | 7.87848e6i | 0.0923699 | + | 0.569913i | ||||
\(241\) | 2.28233e7 | 1.63053 | 0.815264 | − | 0.579090i | \(-0.196592\pi\) | ||||
0.815264 | + | 0.579090i | \(0.196592\pi\) | |||||||
\(242\) | −721700. | + | 1.38048e6i | −0.0509226 | + | 0.0974055i | ||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 1.13636e7 | + | 1.63503e7i | 0.782255 | + | 1.12553i | ||||
\(245\) | 3.02202e7 | − | 1.71722e7i | 2.05494 | − | 1.16769i | ||||
\(246\) | −1.68206e6 | + | 3.21747e6i | −0.112989 | + | 0.216127i | ||||
\(247\) | 4.17059e6 | 0.276762 | ||||||||
\(248\) | 208142. | + | 1.64769e6i | 0.0136460 | + | 0.108024i | ||||
\(249\) | −9.85223e6 | −0.638170 | ||||||||
\(250\) | 1.36949e7 | + | 7.52259e6i | 0.876476 | + | 0.481446i | ||||
\(251\) | 1.40380e7i | 0.887737i | 0.896092 | + | 0.443868i | \(0.146394\pi\) | ||||
−0.896092 | + | 0.443868i | \(0.853606\pi\) | |||||||
\(252\) | 5.58333e6 | + | 8.03343e6i | 0.348893 | + | 0.501995i | ||||
\(253\) | − | 1.80915e7i | − | 1.11715i | ||||||
\(254\) | −1.01607e7 | + | 1.94356e7i | −0.620045 | + | 1.18603i | ||||
\(255\) | 7.35276e6 | + | 1.29397e7i | 0.443435 | + | 0.780373i | ||||
\(256\) | −1.27001e7 | − | 1.09628e7i | −0.756984 | − | 0.653433i | ||||
\(257\) | 1.36204e7i | 0.802401i | 0.915990 | + | 0.401200i | \(0.131407\pi\) | ||||
−0.915990 | + | 0.401200i | \(0.868593\pi\) | |||||||
\(258\) | 736023. | − | 1.40788e6i | 0.0428580 | − | 0.0819795i | ||||
\(259\) | − | 3.44985e7i | − | 1.98564i | ||||||
\(260\) | 1.15245e7 | − | 2.40606e7i | 0.655697 | − | 1.36894i | ||||
\(261\) | −1.75172e6 | −0.0985242 | ||||||||
\(262\) | −8.23644e6 | − | 4.30593e6i | −0.457969 | − | 0.239421i | ||||
\(263\) | −1.24080e7 | −0.682081 | −0.341041 | − | 0.940049i | \(-0.610779\pi\) | ||||
−0.341041 | + | 0.940049i | \(0.610779\pi\) | |||||||
\(264\) | 1.25607e6 | + | 9.94328e6i | 0.0682654 | + | 0.540403i | ||||
\(265\) | −1.25861e7 | − | 2.21495e7i | −0.676323 | − | 1.19022i | ||||
\(266\) | −5.57758e6 | − | 2.91590e6i | −0.296347 | − | 0.154927i | ||||
\(267\) | −4.73566e6 | −0.248798 | ||||||||
\(268\) | −3.72322e6 | − | 5.35706e6i | −0.193426 | − | 0.278306i | ||||
\(269\) | −1.82099e7 | −0.935513 | −0.467756 | − | 0.883857i | \(-0.654938\pi\) | ||||
−0.467756 | + | 0.883857i | \(0.654938\pi\) | |||||||
\(270\) | 132637. | + | 3.78567e6i | 0.00673867 | + | 0.192332i | ||||
\(271\) | − | 2.00391e7i | − | 1.00686i | −0.864036 | − | 0.503430i | \(-0.832071\pi\) | ||
0.864036 | − | 0.503430i | \(-0.167929\pi\) | |||||||
\(272\) | −2.93225e7 | − | 1.09052e7i | −1.45711 | − | 0.541910i | ||||
\(273\) | − | 3.27010e7i | − | 1.60721i | ||||||
\(274\) | 2.90825e7 | + | 1.52041e7i | 1.41378 | + | 0.739108i | ||||
\(275\) | 1.68557e7 | + | 1.00427e7i | 0.810494 | + | 0.482893i | ||||
\(276\) | 8.20312e6 | + | 1.18028e7i | 0.390168 | + | 0.561383i | ||||
\(277\) | 4.03922e7i | 1.90046i | 0.311552 | + | 0.950229i | \(0.399151\pi\) | ||||
−0.311552 | + | 0.950229i | \(0.600849\pi\) | |||||||
\(278\) | −8.37459e6 | − | 4.37815e6i | −0.389789 | − | 0.203778i | ||||
\(279\) | 788226.i | 0.0362943i | ||||||||
\(280\) | −3.22346e7 | + | 2.41202e7i | −1.46841 | + | 1.09877i | ||||
\(281\) | −1.17723e7 | −0.530570 | −0.265285 | − | 0.964170i | \(-0.585466\pi\) | ||||
−0.265285 | + | 0.964170i | \(0.585466\pi\) | |||||||
\(282\) | −867377. | + | 1.65913e6i | −0.0386777 | + | 0.0739832i | ||||
\(283\) | 3.11617e7 | 1.37487 | 0.687435 | − | 0.726246i | \(-0.258737\pi\) | ||||
0.687435 | + | 0.726246i | \(0.258737\pi\) | |||||||
\(284\) | 2.78969e7 | − | 1.93887e7i | 1.21787 | − | 0.846433i | ||||
\(285\) | −1.20395e6 | − | 2.11876e6i | −0.0520086 | − | 0.0915267i | ||||
\(286\) | 1.55207e7 | − | 2.96882e7i | 0.663457 | − | 1.26907i | ||||
\(287\) | −1.83138e7 | −0.774701 | ||||||||
\(288\) | −5.32798e6 | − | 5.91744e6i | −0.223041 | − | 0.247717i | ||||
\(289\) | −3.41993e7 | −1.41685 | ||||||||
\(290\) | −252414. | − | 7.20430e6i | −0.0103495 | − | 0.295391i | ||||
\(291\) | − | 9.75079e6i | − | 0.395695i | ||||||
\(292\) | 1.17862e7 | − | 8.19156e6i | 0.473397 | − | 0.329017i | ||||
\(293\) | 4.74720e6i | 0.188727i | 0.995538 | + | 0.0943637i | \(0.0300817\pi\) | ||||
−0.995538 | + | 0.0943637i | \(0.969918\pi\) | |||||||
\(294\) | −1.60658e7 | + | 3.07309e7i | −0.632209 | + | 1.20930i | ||||
\(295\) | −899661. | − | 1.58326e6i | −0.0350439 | − | 0.0616715i | ||||
\(296\) | 3.51903e6 | + | 2.78574e7i | 0.135690 | + | 1.07415i | ||||
\(297\) | 4.75668e6i | 0.181566i | ||||||||
\(298\) | −5.06449e6 | + | 9.68743e6i | −0.191376 | + | 0.366066i | ||||
\(299\) | − | 4.80448e7i | − | 1.79735i | ||||||
\(300\) | −1.55502e7 | + | 1.09099e6i | −0.575935 | + | 0.0404072i | ||||
\(301\) | 8.01364e6 | 0.293853 | ||||||||
\(302\) | −2.29752e7 | − | 1.20112e7i | −0.834140 | − | 0.436080i | ||||
\(303\) | 1.10285e6 | 0.0396451 | ||||||||
\(304\) | 4.80131e6 | + | 1.78564e6i | 0.170899 | + | 0.0635583i | ||||
\(305\) | −3.38119e7 | + | 1.92131e7i | −1.19171 | + | 0.677171i | ||||
\(306\) | −1.31583e7 | − | 6.87904e6i | −0.459237 | − | 0.240084i | ||||
\(307\) | 1.59064e7 | 0.549739 | 0.274870 | − | 0.961482i | \(-0.411365\pi\) | ||||
0.274870 | + | 0.961482i | \(0.411365\pi\) | |||||||
\(308\) | −4.15135e7 | + | 2.88524e7i | −1.42081 | + | 0.987482i | ||||
\(309\) | 1.75691e7 | 0.595489 | ||||||||
\(310\) | −3.24174e6 | + | 113580.i | −0.108816 | + | 0.00381255i | ||||
\(311\) | 3.14540e7i | 1.04567i | 0.852433 | + | 0.522836i | \(0.175126\pi\) | ||||
−0.852433 | + | 0.522836i | \(0.824874\pi\) | |||||||
\(312\) | 3.33568e6 | + | 2.64059e7i | 0.109830 | + | 0.869436i | ||||
\(313\) | − | 3.36787e7i | − | 1.09830i | −0.835722 | − | 0.549152i | \(-0.814951\pi\) | ||
0.835722 | − | 0.549152i | \(-0.185049\pi\) | |||||||
\(314\) | −3.78311e6 | − | 1.97777e6i | −0.122197 | − | 0.0638834i | ||||
\(315\) | −1.66129e7 | + | 9.44004e6i | −0.531513 | + | 0.302024i | ||||
\(316\) | 722495. | − | 502143.i | 0.0228968 | − | 0.0159135i | ||||
\(317\) | 3.04193e7i | 0.954931i | 0.878650 | + | 0.477466i | \(0.158444\pi\) | ||||
−0.878650 | + | 0.477466i | \(0.841556\pi\) | |||||||
\(318\) | 2.25238e7 | + | 1.17752e7i | 0.700424 | + | 0.366174i | ||||
\(319\) | − | 9.05217e6i | − | 0.278856i | ||||||
\(320\) | 2.35689e7 | − | 2.27651e7i | 0.719267 | − | 0.694734i | ||||
\(321\) | 1.76375e7 | 0.533240 | ||||||||
\(322\) | −3.35910e7 | + | 6.42533e7i | −1.00613 | + | 1.92454i | ||||
\(323\) | 9.55218e6 | 0.283462 | ||||||||
\(324\) | −2.15679e6 | − | 3.10324e6i | −0.0634122 | − | 0.0912391i | ||||
\(325\) | 4.47631e7 | + | 2.66699e7i | 1.30398 | + | 0.776910i | ||||
\(326\) | −1.36708e7 | + | 2.61496e7i | −0.394584 | + | 0.754766i | ||||
\(327\) | −1.93605e7 | −0.553699 | ||||||||
\(328\) | 1.47884e7 | − | 1.86811e6i | 0.419082 | − | 0.0529397i | ||||
\(329\) | −9.44379e6 | −0.265191 | ||||||||
\(330\) | −1.95628e7 | + | 685414.i | −0.544364 | + | 0.0190727i | ||||
\(331\) | − | 632136.i | − | 0.0174312i | −0.999962 | − | 0.00871559i | \(-0.997226\pi\) | ||
0.999962 | − | 0.00871559i | \(-0.00277429\pi\) | |||||||
\(332\) | 2.30848e7 | + | 3.32150e7i | 0.630830 | + | 0.907654i | ||||
\(333\) | 1.33264e7i | 0.360896i | ||||||||
\(334\) | 1.86706e7 | − | 3.57134e7i | 0.501094 | − | 0.958499i | ||||
\(335\) | 1.10783e7 | − | 6.29505e6i | 0.294671 | − | 0.167442i | ||||
\(336\) | 1.40009e7 | − | 3.76464e7i | 0.369096 | − | 0.992444i | ||||
\(337\) | 9.03413e6i | 0.236046i | 0.993011 | + | 0.118023i | \(0.0376557\pi\) | ||||
−0.993011 | + | 0.118023i | \(0.962344\pi\) | |||||||
\(338\) | 2.33276e7 | − | 4.46214e7i | 0.604116 | − | 1.15556i | ||||
\(339\) | − | 6.85243e6i | − | 0.175892i | ||||||
\(340\) | 2.63954e7 | − | 5.51075e7i | 0.671571 | − | 1.40208i | ||||
\(341\) | −4.07323e6 | −0.102725 | ||||||||
\(342\) | 2.15457e6 | + | 1.12639e6i | 0.0538619 | + | 0.0281585i | ||||
\(343\) | −1.00912e8 | −2.50070 | ||||||||
\(344\) | −6.47098e6 | + | 817435.i | −0.158963 | + | 0.0200807i | ||||
\(345\) | −2.44080e7 | + | 1.38695e7i | −0.594394 | + | 0.337755i | ||||
\(346\) | 2.37535e7 | + | 1.24181e7i | 0.573455 | + | 0.299796i | ||||
\(347\) | 2.44261e7 | 0.584610 | 0.292305 | − | 0.956325i | \(-0.405578\pi\) | ||||
0.292305 | + | 0.956325i | \(0.405578\pi\) | |||||||
\(348\) | 4.10447e6 | + | 5.90561e6i | 0.0973911 | + | 0.140129i | ||||
\(349\) | 4.73481e6 | 0.111385 | 0.0556924 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556924 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(350\) | −4.12179e7 | − | 6.69637e7i | −0.961351 | − | 1.56184i | ||||
\(351\) | 1.26321e7i | 0.292115i | ||||||||
\(352\) | 3.05789e7 | − | 2.75328e7i | 0.701122 | − | 0.631280i | ||||
\(353\) | 4.56869e7i | 1.03865i | 0.854578 | + | 0.519323i | \(0.173816\pi\) | ||||
−0.854578 | + | 0.519323i | \(0.826184\pi\) | |||||||
\(354\) | 1.61001e6 | + | 841698.i | 0.0362927 | + | 0.0189735i | ||||
\(355\) | 3.27814e7 | + | 5.76899e7i | 0.732728 | + | 1.28948i | ||||
\(356\) | 1.10962e7 | + | 1.59654e7i | 0.245936 | + | 0.353859i | ||||
\(357\) | − | 7.48973e7i | − | 1.64612i | ||||||
\(358\) | −3.52412e6 | − | 1.84237e6i | −0.0768071 | − | 0.0401540i | ||||
\(359\) | − | 2.01055e7i | − | 0.434542i | −0.976111 | − | 0.217271i | \(-0.930285\pi\) | ||
0.976111 | − | 0.217271i | \(-0.0697155\pi\) | |||||||
\(360\) | 1.24519e7 | − | 9.31741e6i | 0.266888 | − | 0.199704i | ||||
\(361\) | 4.54818e7 | 0.966754 | ||||||||
\(362\) | 9.14626e6 | − | 1.74951e7i | 0.192805 | − | 0.368800i | ||||
\(363\) | 3.03536e6 | 0.0634585 | ||||||||
\(364\) | −1.10246e8 | + | 7.66220e7i | −2.28590 | + | 1.58873i | ||||
\(365\) | 1.38499e7 | + | 2.43736e7i | 0.284818 | + | 0.501234i | ||||
\(366\) | 1.79753e7 | − | 3.43834e7i | 0.366634 | − | 0.701302i | ||||
\(367\) | −6.85183e7 | −1.38614 | −0.693072 | − | 0.720868i | \(-0.743743\pi\) | ||||
−0.693072 | + | 0.720868i | \(0.743743\pi\) | |||||||
\(368\) | 2.05704e7 | − | 5.53107e7i | 0.412761 | − | 1.10985i | ||||
\(369\) | 7.07447e6 | 0.140804 | ||||||||
\(370\) | −5.48077e7 | + | 1.92028e6i | −1.08202 | + | 0.0379104i | ||||
\(371\) | 1.28206e8i | 2.51065i | ||||||||
\(372\) | 2.65736e6 | − | 1.84690e6i | 0.0516205 | − | 0.0358768i | ||||
\(373\) | − | 1.07141e7i | − | 0.206457i | −0.994658 | − | 0.103229i | \(-0.967083\pi\) | ||
0.994658 | − | 0.103229i | \(-0.0329173\pi\) | |||||||
\(374\) | 3.55481e7 | − | 6.79968e7i | 0.679518 | − | 1.29979i | ||||
\(375\) | 626863. | − | 3.04398e7i | 0.0118872 | − | 0.577228i | ||||
\(376\) | 7.62582e6 | − | 963318.i | 0.143457 | − | 0.0181220i | ||||
\(377\) | − | 2.40395e7i | − | 0.448643i | ||||||
\(378\) | 8.83184e6 | − | 1.68937e7i | 0.163522 | − | 0.312787i | ||||
\(379\) | 9.89266e7i | 1.81717i | 0.417701 | + | 0.908585i | \(0.362836\pi\) | ||||
−0.417701 | + | 0.908585i | \(0.637164\pi\) | |||||||
\(380\) | −4.32203e6 | + | 9.02341e6i | −0.0787657 | + | 0.164445i | ||||
\(381\) | 4.27343e7 | 0.772684 | ||||||||
\(382\) | −1.08394e7 | − | 5.66672e6i | −0.194453 | − | 0.101658i | ||||
\(383\) | 9.90039e7 | 1.76220 | 0.881102 | − | 0.472927i | \(-0.156802\pi\) | ||||
0.881102 | + | 0.472927i | \(0.156802\pi\) | |||||||
\(384\) | −7.46556e6 | + | 3.18275e7i | −0.131846 | + | 0.562094i | ||||
\(385\) | −4.87822e7 | − | 8.58487e7i | −0.854829 | − | 1.50436i | ||||
\(386\) | −6.98494e7 | − | 3.65166e7i | −1.21451 | − | 0.634933i | ||||
\(387\) | −3.09560e6 | −0.0534086 | ||||||||
\(388\) | −3.28731e7 | + | 2.28472e7i | −0.562788 | + | 0.391145i | ||||
\(389\) | −1.22554e7 | −0.208199 | −0.104099 | − | 0.994567i | \(-0.533196\pi\) | ||||
−0.104099 | + | 0.994567i | \(0.533196\pi\) | |||||||
\(390\) | −5.19521e7 | + | 1.82023e6i | −0.875808 | + | 0.0306854i | ||||
\(391\) | − | 1.10040e8i | − | 1.84086i | ||||||
\(392\) | 1.41248e8 | − | 1.78428e7i | 2.34489 | − | 0.296214i | ||||
\(393\) | 1.81101e7i | 0.298361i | ||||||||
\(394\) | 1.92588e7 | + | 1.00683e7i | 0.314877 | + | 0.164614i | ||||
\(395\) | 849000. | + | 1.49410e6i | 0.0137758 | + | 0.0242431i | ||||
\(396\) | 1.60363e7 | − | 1.11454e7i | 0.258237 | − | 0.179478i | ||||
\(397\) | − | 7.48415e7i | − | 1.19611i | −0.801455 | − | 0.598055i | \(-0.795940\pi\) | ||
0.801455 | − | 0.598055i | \(-0.204060\pi\) | |||||||
\(398\) | 8.11929e7 | + | 4.24469e7i | 1.28786 | + | 0.673281i | ||||
\(399\) | 1.22638e7i | 0.193067i | ||||||||
\(400\) | 4.01140e7 | + | 4.98685e7i | 0.626781 | + | 0.779195i | ||||
\(401\) | 1.45370e7 | 0.225446 | 0.112723 | − | 0.993626i | \(-0.464043\pi\) | ||||
0.112723 | + | 0.993626i | \(0.464043\pi\) | |||||||
\(402\) | −5.88948e6 | + | 1.12655e7i | −0.0906564 | + | 0.173409i | ||||
\(403\) | −1.08171e7 | −0.165270 | ||||||||
\(404\) | −2.58410e6 | − | 3.71807e6i | −0.0391891 | − | 0.0563862i | ||||
\(405\) | 6.41742e6 | − | 3.64660e6i | 0.0966041 | − | 0.0548938i | ||||
\(406\) | −1.68074e7 | + | 3.21494e7i | −0.251144 | + | 0.480391i | ||||
\(407\) | −6.88656e7 | −1.02145 | ||||||||
\(408\) | 7.63994e6 | + | 6.04793e7i | 0.112489 | + | 0.890485i | ||||
\(409\) | 7.39246e7 | 1.08049 | 0.540243 | − | 0.841509i | \(-0.318332\pi\) | ||||
0.540243 | + | 0.841509i | \(0.318332\pi\) | |||||||
\(410\) | 1.01940e6 | + | 2.90952e7i | 0.0147908 | + | 0.422153i | ||||
\(411\) | − | 6.39459e7i | − | 0.921058i | ||||||
\(412\) | −4.11663e7 | − | 5.92310e7i | −0.588640 | − | 0.846950i | ||||
\(413\) | 9.16420e6i | 0.130090i | ||||||||
\(414\) | 1.29759e7 | − | 2.48205e7i | 0.182867 | − | 0.349791i | ||||
\(415\) | −6.86878e7 | + | 3.90308e7i | −0.961026 | + | 0.546088i | ||||
\(416\) | 8.12070e7 | − | 7.31176e7i | 1.12801 | − | 1.01565i | ||||
\(417\) | 1.84138e7i | 0.253943i | ||||||||
\(418\) | −5.82070e6 | + | 1.11339e7i | −0.0796979 | + | 0.152447i | ||||
\(419\) | 3.43347e7i | 0.466757i | 0.972386 | + | 0.233379i | \(0.0749782\pi\) | ||||
−0.972386 | + | 0.233379i | \(0.925022\pi\) | |||||||
\(420\) | 7.07513e7 | + | 3.38884e7i | 0.954963 | + | 0.457408i | ||||
\(421\) | −5.83664e7 | −0.782198 | −0.391099 | − | 0.920349i | \(-0.627905\pi\) | ||||
−0.391099 | + | 0.920349i | \(0.627905\pi\) | |||||||
\(422\) | −1.13124e8 | − | 5.91399e7i | −1.50528 | − | 0.786943i | ||||
\(423\) | 3.64805e6 | 0.0481992 | ||||||||
\(424\) | −1.30777e7 | − | 1.03526e8i | −0.171567 | − | 1.35816i | ||||
\(425\) | 1.02524e8 | + | 6.10838e7i | 1.33555 | + | 0.795719i | ||||
\(426\) | −5.86649e7 | − | 3.06694e7i | −0.758839 | − | 0.396713i | ||||
\(427\) | 1.95710e8 | 2.51380 | ||||||||
\(428\) | −4.13267e7 | − | 5.94618e7i | −0.527107 | − | 0.758415i | ||||
\(429\) | −6.52775e7 | −0.826783 | ||||||||
\(430\) | −446061. | − | 1.27313e7i | −0.00561033 | − | 0.160128i | ||||
\(431\) | 5.13527e7i | 0.641404i | 0.947180 | + | 0.320702i | \(0.103919\pi\) | ||||
−0.947180 | + | 0.320702i | \(0.896081\pi\) | |||||||
\(432\) | −5.40843e6 | + | 1.45425e7i | −0.0670842 | + | 0.180379i | ||||
\(433\) | 4.34673e7i | 0.535425i | 0.963499 | + | 0.267713i | \(0.0862678\pi\) | ||||
−0.963499 | + | 0.267713i | \(0.913732\pi\) | |||||||
\(434\) | 1.44663e7 | + | 7.56286e6i | 0.176966 | + | 0.0925160i | ||||
\(435\) | −1.22126e7 | + | 6.93965e6i | −0.148368 | + | 0.0843081i | ||||
\(436\) | 4.53638e7 | + | 6.52705e7i | 0.547331 | + | 0.787512i | ||||
\(437\) | 1.80182e7i | 0.215907i | ||||||||
\(438\) | −2.47855e7 | − | 1.29576e7i | −0.294968 | − | 0.154206i | ||||
\(439\) | 5.32902e7i | 0.629875i | 0.949112 | + | 0.314937i | \(0.101984\pi\) | ||||
−0.949112 | + | 0.314937i | \(0.898016\pi\) | |||||||
\(440\) | 4.81485e7 | + | 6.43465e7i | 0.565230 | + | 0.755382i | ||||
\(441\) | 6.75702e7 | 0.787843 | ||||||||
\(442\) | 9.44035e7 | − | 1.80576e8i | 1.09325 | − | 2.09119i | ||||
\(443\) | −1.63589e6 | −0.0188167 | −0.00940834 | − | 0.999956i | \(-0.502995\pi\) | ||||
−0.00940834 | + | 0.999956i | \(0.502995\pi\) | |||||||
\(444\) | 4.49277e7 | − | 3.12253e7i | 0.513293 | − | 0.356745i | ||||
\(445\) | −3.30161e7 | + | 1.87609e7i | −0.374667 | + | 0.212899i | ||||
\(446\) | −1.82306e7 | + | 3.48717e7i | −0.205492 | + | 0.393069i | ||||
\(447\) | 2.13004e7 | 0.238488 | ||||||||
\(448\) | −1.59724e8 | + | 4.10080e7i | −1.77638 | + | 0.456074i | ||||
\(449\) | 3.93808e7 | 0.435056 | 0.217528 | − | 0.976054i | \(-0.430201\pi\) | ||||
0.217528 | + | 0.976054i | \(0.430201\pi\) | |||||||
\(450\) | 1.59221e7 | + | 2.58675e7i | 0.174728 | + | 0.283868i | ||||
\(451\) | 3.65580e7i | 0.398522i | ||||||||
\(452\) | −2.31017e7 | + | 1.60560e7i | −0.250167 | + | 0.173869i | ||||
\(453\) | 5.05172e7i | 0.543432i | ||||||||
\(454\) | −3.43512e7 | + | 6.57074e7i | −0.367091 | + | 0.702178i | ||||
\(455\) | −1.29549e8 | − | 2.27985e8i | −1.37531 | − | 2.42031i | ||||
\(456\) | −1.25098e6 | − | 9.90299e6i | −0.0131933 | − | 0.104441i | ||||
\(457\) | 1.72529e8i | 1.80765i | 0.427901 | + | 0.903826i | \(0.359253\pi\) | ||||
−0.427901 | + | 0.903826i | \(0.640747\pi\) | |||||||
\(458\) | −1.61237e7 | + | 3.08416e7i | −0.167829 | + | 0.321026i | ||||
\(459\) | 2.89322e7i | 0.299187i | ||||||||
\(460\) | 1.03949e8 | + | 4.97895e7i | 1.06794 | + | 0.511521i | ||||
\(461\) | −1.57854e8 | −1.61122 | −0.805608 | − | 0.592449i | \(-0.798161\pi\) | ||||
−0.805608 | + | 0.592449i | \(0.798161\pi\) | |||||||
\(462\) | 8.72995e7 | + | 4.56393e7i | 0.885291 | + | 0.462821i | ||||
\(463\) | −1.65529e8 | −1.66775 | −0.833876 | − | 0.551951i | \(-0.813883\pi\) | ||||
−0.833876 | + | 0.551951i | \(0.813883\pi\) | |||||||
\(464\) | 1.02925e7 | − | 2.76750e7i | 0.103031 | − | 0.277034i | ||||
\(465\) | 3.12265e6 | + | 5.49535e6i | 0.0310573 | + | 0.0546558i | ||||
\(466\) | 1.07110e6 | + | 559960.i | 0.0105845 | + | 0.00553349i | ||||
\(467\) | 6.51048e7 | 0.639238 | 0.319619 | − | 0.947546i | \(-0.396445\pi\) | ||||
0.319619 | + | 0.947546i | \(0.396445\pi\) | |||||||
\(468\) | 4.25869e7 | − | 2.95984e7i | 0.415469 | − | 0.288756i | ||||
\(469\) | −6.41231e7 | −0.621579 | ||||||||
\(470\) | 525667. | + | 1.50033e7i | 0.00506310 | + | 0.144509i | ||||
\(471\) | 8.31820e6i | 0.0796099i | ||||||||
\(472\) | −934799. | − | 7.40006e6i | −0.00888980 | − | 0.0703735i | ||||
\(473\) | − | 1.59968e7i | − | 0.151164i | ||||||
\(474\) | −1.51935e6 | − | 794301.i | −0.0142667 | − | 0.00745848i | ||||
\(475\) | −1.67875e7 | − | 1.00020e7i | −0.156641 | − | 0.0933265i | ||||
\(476\) | −2.52503e8 | + | 1.75493e8i | −2.34124 | + | 1.62719i | ||||
\(477\) | − | 4.95247e7i | − | 0.456317i | ||||||
\(478\) | 7.86212e7 | + | 4.11024e7i | 0.719874 | + | 0.376343i | ||||
\(479\) | − | 7.59285e7i | − | 0.690873i | −0.938442 | − | 0.345436i | \(-0.887731\pi\) | ||
0.938442 | − | 0.345436i | \(-0.112269\pi\) | |||||||
\(480\) | −6.05882e7 | − | 2.01478e7i | −0.547853 | − | 0.182181i | ||||
\(481\) | −1.82883e8 | −1.64338 | ||||||||
\(482\) | −8.45920e7 | + | 1.61809e8i | −0.755420 | + | 1.44498i | ||||
\(483\) | 1.41278e8 | 1.25382 | ||||||||
\(484\) | −7.11217e6 | − | 1.02332e7i | −0.0627287 | − | 0.0902555i | ||||
\(485\) | −3.86289e7 | − | 6.79806e7i | −0.338600 | − | 0.595881i | ||||
\(486\) | −3.41166e6 | + | 6.52587e6i | −0.0297206 | + | 0.0568499i | ||||
\(487\) | 1.07212e8 | 0.928235 | 0.464118 | − | 0.885774i | \(-0.346372\pi\) | ||||
0.464118 | + | 0.885774i | \(0.346372\pi\) | |||||||
\(488\) | −1.58035e8 | + | 1.99635e7i | −1.35986 | + | 0.171782i | ||||
\(489\) | 5.74970e7 | 0.491721 | ||||||||
\(490\) | 9.73654e6 | + | 2.77896e8i | 0.0827593 | + | 2.36208i | ||||
\(491\) | − | 2.26135e8i | − | 1.91040i | −0.295967 | − | 0.955198i | \(-0.595642\pi\) | ||
0.295967 | − | 0.955198i | \(-0.404358\pi\) | |||||||
\(492\) | −1.65763e7 | − | 2.38503e7i | −0.139185 | − | 0.200262i | ||||
\(493\) | − | 5.50592e7i | − | 0.459504i | ||||||
\(494\) | −1.54578e7 | + | 2.95679e7i | −0.128223 | + | 0.245267i | ||||
\(495\) | 1.88441e7 | + | 3.31626e7i | 0.155368 | + | 0.273422i | ||||
\(496\) | −1.24530e7 | − | 4.63134e6i | −0.102054 | − | 0.0379543i | ||||
\(497\) | − | 3.33921e8i | − | 2.72003i | ||||||
\(498\) | 3.65161e7 | − | 6.98486e7i | 0.295663 | − | 0.565548i | ||||
\(499\) | − | 2.26180e7i | − | 0.182034i | −0.995849 | − | 0.0910172i | \(-0.970988\pi\) | ||
0.995849 | − | 0.0910172i | \(-0.0290118\pi\) | |||||||
\(500\) | −1.04091e8 | + | 6.92103e7i | −0.832728 | + | 0.553682i | ||||
\(501\) | −7.85256e7 | −0.624451 | ||||||||
\(502\) | −9.95241e7 | − | 5.20302e7i | −0.786715 | − | 0.411287i | ||||
\(503\) | −8.37768e7 | −0.658294 | −0.329147 | − | 0.944279i | \(-0.606761\pi\) | ||||
−0.329147 | + | 0.944279i | \(0.606761\pi\) | |||||||
\(504\) | −7.76480e7 | + | 9.80874e6i | −0.606511 | + | 0.0766163i | ||||
\(505\) | 7.68886e6 | − | 4.36908e6i | 0.0597019 | − | 0.0339247i | ||||
\(506\) | 1.28262e8 | + | 6.70540e7i | 0.990025 | + | 0.517575i | ||||
\(507\) | −9.81122e7 | −0.752834 | ||||||||
\(508\) | −1.00131e8 | − | 1.44071e8i | −0.763798 | − | 1.09897i | ||||
\(509\) | 2.00831e8 | 1.52292 | 0.761461 | − | 0.648211i | \(-0.224483\pi\) | ||||
0.761461 | + | 0.648211i | \(0.224483\pi\) | |||||||
\(510\) | −1.18989e8 | + | 4.16899e6i | −0.897011 | + | 0.0314282i | ||||
\(511\) | − | 1.41079e8i | − | 1.05730i | ||||||
\(512\) | 1.24793e8 | − | 4.94065e7i | 0.929783 | − | 0.368107i | ||||
\(513\) | − | 4.73740e6i | − | 0.0350904i | ||||||
\(514\) | −9.65636e7 | − | 5.04825e7i | −0.711090 | − | 0.371750i | ||||
\(515\) | 1.22488e8 | − | 6.96020e7i | 0.896752 | − | 0.509566i | ||||
\(516\) | 7.25332e6 | + | 1.04363e7i | 0.0527944 | + | 0.0759618i | ||||
\(517\) | 1.88516e7i | 0.136420i | ||||||||
\(518\) | 2.44581e8 | + | 1.27864e8i | 1.75968 | + | 0.919942i | ||||
\(519\) | − | 5.22285e7i | − | 0.373599i | ||||||
\(520\) | 1.27866e8 | + | 1.70882e8i | 0.909379 | + | 1.21531i | ||||
\(521\) | −1.16604e8 | −0.824518 | −0.412259 | − | 0.911067i | \(-0.635260\pi\) | ||||
−0.412259 | + | 0.911067i | \(0.635260\pi\) | |||||||
\(522\) | 6.49254e6 | − | 1.24190e7i | 0.0456461 | − | 0.0873124i | ||||
\(523\) | 1.50247e8 | 1.05027 | 0.525134 | − | 0.851020i | \(-0.324015\pi\) | ||||
0.525134 | + | 0.851020i | \(0.324015\pi\) | |||||||
\(524\) | 6.10548e7 | − | 4.24338e7i | 0.424352 | − | 0.294930i | ||||
\(525\) | −7.84241e7 | + | 1.31628e8i | −0.541965 | + | 0.909642i | ||||
\(526\) | 4.59889e7 | − | 8.79683e7i | 0.316007 | − | 0.604462i | ||||
\(527\) | −2.47751e7 | −0.169272 | ||||||||
\(528\) | −7.51495e7 | − | 2.79486e7i | −0.510534 | − | 0.189871i | ||||
\(529\) | 5.95324e7 | 0.402148 | ||||||||
\(530\) | 2.03681e8 | − | 7.13628e6i | 1.36811 | − | 0.0479341i | ||||
\(531\) | − | 3.54005e6i | − | 0.0236443i | ||||||
\(532\) | 4.13453e7 | − | 2.87355e7i | 0.274594 | − | 0.190846i | ||||
\(533\) | 9.70855e7i | 0.641169i | ||||||||
\(534\) | 1.75522e7 | − | 3.35740e7i | 0.115268 | − | 0.220485i | ||||
\(535\) | 1.22965e8 | − | 6.98732e7i | 0.803011 | − | 0.456299i | ||||
\(536\) | 5.17792e7 | − | 6.54091e6i | 0.336249 | − | 0.0424760i | ||||
\(537\) | 7.74873e6i | 0.0500389i | ||||||||
\(538\) | 6.74927e7 | − | 1.29101e8i | 0.433421 | − | 0.829054i | ||||
\(539\) | 3.49175e8i | 2.22986i | ||||||||
\(540\) | −2.73306e7 | − | 1.30908e7i | −0.173567 | − | 0.0831352i | ||||
\(541\) | 2.98826e8 | 1.88724 | 0.943618 | − | 0.331036i | \(-0.107398\pi\) | ||||
0.943618 | + | 0.331036i | \(0.107398\pi\) | |||||||
\(542\) | 1.42069e8 | + | 7.42724e7i | 0.892282 | + | 0.466476i | ||||
\(543\) | −3.84677e7 | −0.240268 | ||||||||
\(544\) | 1.85994e8 | − | 1.67466e8i | 1.15532 | − | 1.04023i | ||||
\(545\) | −1.34978e8 | + | 7.66990e7i | −0.833820 | + | 0.473805i | ||||
\(546\) | 2.31838e8 | + | 1.21202e8i | 1.42432 | + | 0.744618i | ||||
\(547\) | −430499. | −0.00263033 | −0.00131517 | − | 0.999999i | \(-0.500419\pi\) | ||||
−0.00131517 | + | 0.999999i | \(0.500419\pi\) | |||||||
\(548\) | −2.15582e8 | + | 1.49832e8i | −1.31000 | + | 0.910465i | ||||
\(549\) | −7.56011e7 | −0.456890 | ||||||||
\(550\) | −1.33673e8 | + | 8.22789e7i | −0.803441 | + | 0.494539i | ||||
\(551\) | 9.01549e6i | 0.0538933i | ||||||||
\(552\) | −1.14082e8 | + | 1.44112e7i | −0.678264 | + | 0.0856804i | ||||
\(553\) | − | 8.64815e6i | − | 0.0511385i | ||||||
\(554\) | −2.86365e8 | − | 1.49709e8i | −1.68419 | − | 0.880478i | ||||
\(555\) | 5.27943e7 | + | 9.29093e7i | 0.308822 | + | 0.543476i | ||||
\(556\) | 6.20789e7 | − | 4.31456e7i | 0.361177 | − | 0.251022i | ||||
\(557\) | − | 2.29944e8i | − | 1.33063i | −0.746563 | − | 0.665314i | \(-0.768298\pi\) | ||
0.746563 | − | 0.665314i | \(-0.231702\pi\) | |||||||
\(558\) | −5.58822e6 | − | 2.92147e6i | −0.0321641 | − | 0.0168151i | ||||
\(559\) | − | 4.24819e7i | − | 0.243203i | ||||||
\(560\) | −5.15291e7 | − | 3.17930e8i | −0.293419 | − | 1.81037i | ||||
\(561\) | −1.49510e8 | −0.846799 | ||||||||
\(562\) | 4.36327e7 | − | 8.34613e7i | 0.245812 | − | 0.470193i | ||||
\(563\) | −1.37064e8 | −0.768068 | −0.384034 | − | 0.923319i | \(-0.625465\pi\) | ||||
−0.384034 | + | 0.923319i | \(0.625465\pi\) | |||||||
\(564\) | −8.54778e6 | − | 1.22987e7i | −0.0476448 | − | 0.0685525i | ||||
\(565\) | −2.71467e7 | − | 4.77737e7i | −0.150512 | − | 0.264877i | ||||
\(566\) | −1.15497e8 | + | 2.20925e8i | −0.636974 | + | 1.21841i | ||||
\(567\) | −3.71453e7 | −0.203777 | ||||||||
\(568\) | 3.40618e7 | + | 2.69640e8i | 0.185875 | + | 1.47143i | ||||
\(569\) | 1.95327e8 | 1.06029 | 0.530147 | − | 0.847906i | \(-0.322137\pi\) | ||||
0.530147 | + | 0.847906i | \(0.322137\pi\) | |||||||
\(570\) | 1.94835e7 | − | 682637.i | 0.105207 | − | 0.00368609i | ||||
\(571\) | 6.46592e7i | 0.347314i | 0.984806 | + | 0.173657i | \(0.0555584\pi\) | ||||
−0.984806 | + | 0.173657i | \(0.944442\pi\) | |||||||
\(572\) | 1.52952e8 | + | 2.20071e8i | 0.817275 | + | 1.17591i | ||||
\(573\) | 2.38333e7i | 0.126684i | ||||||||
\(574\) | 6.78781e7 | − | 1.29838e8i | 0.358917 | − | 0.686542i | ||||
\(575\) | −1.15222e8 | + | 1.93390e8i | −0.606082 | + | 1.01726i | ||||
\(576\) | 6.16999e7 | − | 1.58410e7i | 0.322862 | − | 0.0828927i | ||||
\(577\) | 1.40370e8i | 0.730714i | 0.930867 | + | 0.365357i | \(0.119053\pi\) | ||||
−0.930867 | + | 0.365357i | \(0.880947\pi\) | |||||||
\(578\) | 1.26756e8 | − | 2.42460e8i | 0.656423 | − | 1.25562i | ||||
\(579\) | 1.53583e8i | 0.791238i | ||||||||
\(580\) | 5.20113e7 | + | 2.49124e7i | 0.266572 | + | 0.127682i | ||||
\(581\) | 3.97579e8 | 2.02719 | ||||||||
\(582\) | 6.91294e7 | + | 3.61402e7i | 0.350666 | + | 0.183325i | ||||
\(583\) | 2.55923e8 | 1.29153 | ||||||||
\(584\) | 1.43908e7 | + | 1.13921e8i | 0.0722516 | + | 0.571958i | ||||
\(585\) | 5.00436e7 | + | 8.80685e7i | 0.249966 | + | 0.439899i | ||||
\(586\) | −3.36559e7 | − | 1.75950e7i | −0.167251 | − | 0.0874370i | ||||
\(587\) | −1.73258e7 | −0.0856603 | −0.0428301 | − | 0.999082i | \(-0.513637\pi\) | ||||
−0.0428301 | + | 0.999082i | \(0.513637\pi\) | |||||||
\(588\) | −1.58324e8 | − | 2.27801e8i | −0.778782 | − | 1.12053i | ||||
\(589\) | 4.05672e6 | 0.0198531 | ||||||||
\(590\) | 1.45592e7 | − | 510104.i | 0.0708893 | − | 0.00248372i | ||||
\(591\) | − | 4.23457e7i | − | 0.205138i | ||||||
\(592\) | −2.10541e8 | − | 7.83015e7i | −1.01478 | − | 0.377403i | ||||
\(593\) | − | 1.03223e8i | − | 0.495008i | −0.968887 | − | 0.247504i | \(-0.920390\pi\) | ||
0.968887 | − | 0.247504i | \(-0.0796104\pi\) | |||||||
\(594\) | −3.37230e7 | − | 1.76301e7i | −0.160904 | − | 0.0841191i | ||||
\(595\) | −2.96715e8 | − | 5.22169e8i | −1.40860 | − | 2.47891i | ||||
\(596\) | −4.99093e7 | − | 7.18106e7i | −0.235745 | − | 0.339195i | ||||
\(597\) | − | 1.78525e8i | − | 0.839026i | ||||||
\(598\) | 3.40620e8 | + | 1.78073e8i | 1.59282 | + | 0.832709i | ||||
\(599\) | 2.33746e8i | 1.08759i | 0.839219 | + | 0.543794i | \(0.183013\pi\) | ||||
−0.839219 | + | 0.543794i | \(0.816987\pi\) | |||||||
\(600\) | 4.99004e7 | − | 1.14289e8i | 0.231020 | − | 0.529115i | ||||
\(601\) | −3.82158e7 | −0.176043 | −0.0880216 | − | 0.996119i | \(-0.528054\pi\) | ||||
−0.0880216 | + | 0.996119i | \(0.528054\pi\) | |||||||
\(602\) | −2.97016e7 | + | 5.68137e7i | −0.136141 | + | 0.260413i | ||||
\(603\) | 2.47702e7 | 0.112974 | ||||||||
\(604\) | 1.70310e8 | − | 1.18367e8i | 0.772910 | − | 0.537182i | ||||
\(605\) | 2.11619e7 | − | 1.20249e7i | 0.0955627 | − | 0.0543021i | ||||
\(606\) | −4.08759e6 | + | 7.81880e6i | −0.0183675 | + | 0.0351336i | ||||
\(607\) | −7.16449e6 | −0.0320346 | −0.0160173 | − | 0.999872i | \(-0.505099\pi\) | ||||
−0.0160173 | + | 0.999872i | \(0.505099\pi\) | |||||||
\(608\) | −3.04550e7 | + | 2.74212e7i | −0.135503 | + | 0.122005i | ||||
\(609\) | 7.06892e7 | 0.312969 | ||||||||
\(610\) | −1.08938e7 | − | 3.10925e8i | −0.0479942 | − | 1.36983i | ||||
\(611\) | 5.00634e7i | 0.219481i | ||||||||
\(612\) | 9.75396e7 | − | 6.77912e7i | 0.425527 | − | 0.295746i | ||||
\(613\) | − | 6.22401e6i | − | 0.0270202i | −0.999909 | − | 0.0135101i | \(-0.995699\pi\) | ||
0.999909 | − | 0.0135101i | \(-0.00430053\pi\) | |||||||
\(614\) | −5.89552e7 | + | 1.12770e8i | −0.254693 | + | 0.487180i | ||||
\(615\) | 4.93218e7 | − | 2.80264e7i | 0.212038 | − | 0.120487i | ||||
\(616\) | −5.06875e7 | − | 4.01253e8i | −0.216850 | − | 1.71663i | ||||
\(617\) | − | 5.77344e7i | − | 0.245799i | −0.992419 | − | 0.122899i | \(-0.960781\pi\) | ||
0.992419 | − | 0.122899i | \(-0.0392192\pi\) | |||||||
\(618\) | −6.51178e7 | + | 1.24558e8i | −0.275889 | + | 0.527724i | ||||
\(619\) | 2.83393e8i | 1.19486i | 0.801920 | + | 0.597431i | \(0.203812\pi\) | ||||
−0.801920 | + | 0.597431i | \(0.796188\pi\) | |||||||
\(620\) | 1.12099e7 | − | 2.34037e7i | 0.0470355 | − | 0.0981994i | ||||
\(621\) | −5.45745e7 | −0.227885 | ||||||||
\(622\) | −2.22997e8 | − | 1.16581e8i | −0.926677 | − | 0.484457i | ||||
\(623\) | 1.91104e8 | 0.790323 | ||||||||
\(624\) | −1.99571e8 | − | 7.42218e7i | −0.821381 | − | 0.305476i | ||||
\(625\) | −1.16220e8 | − | 2.14703e8i | −0.476039 | − | 0.879424i | ||||
\(626\) | 2.38769e8 | + | 1.24826e8i | 0.973320 | + | 0.508842i | ||||
\(627\) | 2.44810e7 | 0.0993175 | ||||||||
\(628\) | 2.80433e7 | − | 1.94905e7i | 0.113227 | − | 0.0786943i | ||||
\(629\) | −4.18870e8 | −1.68317 | ||||||||
\(630\) | −5.35246e6 | − | 1.52768e8i | −0.0214058 | − | 0.610956i | ||||
\(631\) | 3.72306e8i | 1.48187i | 0.671574 | + | 0.740937i | \(0.265618\pi\) | ||||
−0.671574 | + | 0.740937i | \(0.734382\pi\) | |||||||
\(632\) | 882159. | + | 6.98335e6i | 0.00349459 | + | 0.0276639i | ||||
\(633\) | 2.48733e8i | 0.980669i | ||||||||
\(634\) | −2.15662e8 | − | 1.12746e8i | −0.846262 | − | 0.442417i | ||||
\(635\) | 2.97935e8 | − | 1.69297e8i | 1.16359 | − | 0.661193i | ||||
\(636\) | −1.66964e8 | + | 1.16042e8i | −0.649009 | + | 0.451069i | ||||
\(637\) | 9.27289e8i | 3.58754i | ||||||||
\(638\) | 6.41764e7 | + | 3.35508e7i | 0.247123 | + | 0.129194i | ||||
\(639\) | 1.28991e8i | 0.494374i | ||||||||
\(640\) | 7.40401e7 | + | 2.51471e8i | 0.282441 | + | 0.959285i | ||||
\(641\) | −1.96445e8 | −0.745876 | −0.372938 | − | 0.927856i | \(-0.621650\pi\) | ||||
−0.372938 | + | 0.927856i | \(0.621650\pi\) | |||||||
\(642\) | −6.53715e7 | + | 1.25043e8i | −0.247049 | + | 0.472559i | ||||
\(643\) | −3.91175e8 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(644\) | −3.31030e8 | − | 4.76294e8i | −1.23940 | − | 1.78327i | ||||
\(645\) | −2.15819e7 | + | 1.22636e7i | −0.0804285 | + | 0.0457023i | ||||
\(646\) | −3.54040e7 | + | 6.77214e7i | −0.131327 | + | 0.251205i | ||||
\(647\) | −5.32848e8 | −1.96739 | −0.983694 | − | 0.179848i | \(-0.942439\pi\) | ||||
−0.983694 | + | 0.179848i | \(0.942439\pi\) | |||||||
\(648\) | 2.99947e7 | − | 3.78903e6i | 0.110235 | − | 0.0139252i | ||||
\(649\) | 1.82935e7 | 0.0669211 | ||||||||
\(650\) | −3.54988e8 | + | 2.18505e8i | −1.29263 | + | 0.795647i | ||||
\(651\) | − | 3.18082e7i | − | 0.115291i | ||||||
\(652\) | −1.34722e8 | − | 1.93841e8i | −0.486066 | − | 0.699363i | ||||
\(653\) | − | 3.49177e8i | − | 1.25402i | −0.779009 | − | 0.627012i | \(-0.784277\pi\) | ||
0.779009 | − | 0.627012i | \(-0.215723\pi\) | |||||||
\(654\) | 7.17574e7 | − | 1.37259e8i | 0.256527 | − | 0.490689i | ||||
\(655\) | 7.17452e7 | + | 1.26260e8i | 0.255311 | + | 0.449305i | ||||
\(656\) | −4.15671e7 | + | 1.11768e8i | −0.147244 | + | 0.395918i | ||||
\(657\) | 5.44976e7i | 0.192168i | ||||||||
\(658\) | 3.50023e7 | − | 6.69529e7i | 0.122862 | − | 0.235013i | ||||
\(659\) | − | 2.26836e8i | − | 0.792602i | −0.918121 | − | 0.396301i | \(-0.870294\pi\) | ||
0.918121 | − | 0.396301i | \(-0.129706\pi\) | |||||||
\(660\) | 6.76479e7 | − | 1.41233e8i | 0.235300 | − | 0.491253i | ||||
\(661\) | 3.94230e8 | 1.36504 | 0.682521 | − | 0.730866i | \(-0.260884\pi\) | ||||
0.682521 | + | 0.730866i | \(0.260884\pi\) | |||||||
\(662\) | 4.48161e6 | + | 2.34294e6i | 0.0154476 | + | 0.00807583i | ||||
\(663\) | −3.97046e8 | −1.36239 | ||||||||
\(664\) | −3.21043e8 | + | 4.05552e7i | −1.09663 | + | 0.138529i | ||||
\(665\) | 4.85846e7 | + | 8.55009e7i | 0.165209 | + | 0.290741i | ||||
\(666\) | −9.44794e7 | − | 4.93929e7i | −0.319827 | − | 0.167202i | ||||
\(667\) | 1.03858e8 | 0.349995 | ||||||||
\(668\) | 1.83994e8 | + | 2.64735e8i | 0.617269 | + | 0.888141i | ||||
\(669\) | 7.66749e7 | 0.256080 | ||||||||
\(670\) | 3.56927e6 | + | 1.01872e8i | 0.0118674 | + | 0.338713i | ||||
\(671\) | − | 3.90676e8i | − | 1.29315i | ||||||
\(672\) | 2.15006e8 | + | 2.38793e8i | 0.708505 | + | 0.786891i | ||||
\(673\) | − | 3.10414e8i | − | 1.01835i | −0.860664 | − | 0.509174i | \(-0.829951\pi\) | ||
0.860664 | − | 0.509174i | \(-0.170049\pi\) | |||||||
\(674\) | −6.40486e7 | − | 3.34839e7i | −0.209185 | − | 0.109360i | ||||
\(675\) | 3.02945e7 | − | 5.08468e7i | 0.0985038 | − | 0.165330i | ||||
\(676\) | 2.29888e8 | + | 3.30768e8i | 0.744176 | + | 1.07074i | ||||
\(677\) | 5.73658e8i | 1.84879i | 0.381439 | + | 0.924394i | \(0.375429\pi\) | ||||
−0.381439 | + | 0.924394i | \(0.624571\pi\) | |||||||
\(678\) | 4.85811e7 | + | 2.53977e7i | 0.155876 | + | 0.0814902i | ||||
\(679\) | 3.93485e8i | 1.25695i | ||||||||
\(680\) | 2.92860e8 | + | 3.91383e8i | 0.931394 | + | 1.24473i | ||||
\(681\) | 1.44476e8 | 0.457460 | ||||||||
\(682\) | 1.50969e7 | − | 2.88776e7i | 0.0475922 | − | 0.0910350i | ||||
\(683\) | −4.50762e8 | −1.41477 | −0.707384 | − | 0.706830i | \(-0.750125\pi\) | ||||
−0.707384 | + | 0.706830i | \(0.750125\pi\) | |||||||
\(684\) | −1.59713e7 | + | 1.11003e7i | −0.0499082 | + | 0.0346868i | ||||
\(685\) | −2.53329e8 | − | 4.45818e8i | −0.788158 | − | 1.38703i | ||||
\(686\) | 3.74019e8 | − | 7.15430e8i | 1.15857 | − | 2.21613i | ||||
\(687\) | 6.78137e7 | 0.209145 | ||||||||
\(688\) | 1.81886e7 | − | 4.89065e7i | 0.0558515 | − | 0.150176i | ||||
\(689\) | 6.79645e8 | 2.07790 | ||||||||
\(690\) | −7.86393e6 | − | 2.24449e8i | −0.0239382 | − | 0.683235i | ||||
\(691\) | 1.07184e8i | 0.324859i | 0.986720 | + | 0.162430i | \(0.0519330\pi\) | ||||
−0.986720 | + | 0.162430i | \(0.948067\pi\) | |||||||
\(692\) | −1.76079e8 | + | 1.22377e8i | −0.531361 | + | 0.369302i | ||||
\(693\) | − | 1.91952e8i | − | 0.576756i | ||||||
\(694\) | −9.05325e7 | + | 1.73172e8i | −0.270848 | + | 0.518083i | ||||
\(695\) | 7.29485e7 | + | 1.28377e8i | 0.217301 | + | 0.382414i | ||||
\(696\) | −5.70813e7 | + | 7.21069e6i | −0.169303 | + | 0.0213870i | ||||
\(697\) | 2.22361e8i | 0.656691i | ||||||||
\(698\) | −1.75490e7 | + | 3.35680e7i | −0.0516044 | + | 0.0987096i | ||||
\(699\) | − | 2.35510e6i | − | 0.00689570i | ||||||
\(700\) | 6.27517e8 | − | 4.40262e7i | 1.82950 | − | 0.128356i | ||||
\(701\) | 1.74408e8 | 0.506305 | 0.253153 | − | 0.967426i | \(-0.418533\pi\) | ||||
0.253153 | + | 0.967426i | \(0.418533\pi\) | |||||||
\(702\) | −8.95568e7 | − | 4.68194e7i | −0.258873 | − | 0.135336i | ||||
\(703\) | 6.85866e7 | 0.197412 | ||||||||
\(704\) | 8.18600e7 | + | 3.18840e8i | 0.234614 | + | 0.913807i | ||||
\(705\) | 2.54335e7 | − | 1.44522e7i | 0.0725836 | − | 0.0412445i | ||||
\(706\) | −3.23903e8 | − | 1.69333e8i | −0.920450 | − | 0.481202i | ||||
\(707\) | −4.45047e7 | −0.125935 | ||||||||
\(708\) | −1.19346e7 | + | 8.29472e6i | −0.0336287 | + | 0.0233723i | ||||
\(709\) | −3.49999e7 | −0.0982038 | −0.0491019 | − | 0.998794i | \(-0.515636\pi\) | ||||
−0.0491019 | + | 0.998794i | \(0.515636\pi\) | |||||||
\(710\) | −5.30500e8 | + | 1.85869e7i | −1.48221 | + | 0.0519317i | ||||
\(711\) | 3.34070e6i | 0.00929457i | ||||||||
\(712\) | −1.54315e8 | + | 1.94936e7i | −0.427533 | + | 0.0540073i | ||||
\(713\) | − | 4.67331e7i | − | 0.128931i | ||||||
\(714\) | 5.30994e8 | + | 2.77598e8i | 1.45880 | + | 0.762644i | ||||
\(715\) | −4.55102e8 | + | 2.58605e8i | −1.24506 | + | 0.707487i | ||||
\(716\) | 2.61235e7 | − | 1.81561e7i | 0.0711691 | − | 0.0494634i | ||||
\(717\) | − | 1.72870e8i | − | 0.468989i | ||||||
\(718\) | 1.42540e8 | + | 7.45187e7i | 0.385092 | + | 0.201322i | ||||
\(719\) | − | 2.53393e6i | − | 0.00681722i | −0.999994 | − | 0.00340861i | \(-0.998915\pi\) | ||
0.999994 | − | 0.00340861i | \(-0.00108500\pi\) | |||||||
\(720\) | 1.99052e7 | + | 1.22813e8i | 0.0533298 | + | 0.329040i | ||||
\(721\) | −7.08986e8 | −1.89161 | ||||||||
\(722\) | −1.68573e8 | + | 3.22449e8i | −0.447895 | + | 0.856740i | ||||
\(723\) | 3.55781e8 | 0.941385 | ||||||||
\(724\) | 9.01340e7 | + | 1.29687e8i | 0.237505 | + | 0.341728i | ||||
\(725\) | −5.76518e7 | + | 9.67636e7i | −0.151286 | + | 0.253921i | ||||
\(726\) | −1.12502e7 | + | 2.15195e7i | −0.0294002 | + | 0.0562371i | ||||
\(727\) | 3.79075e8 | 0.986555 | 0.493278 | − | 0.869872i | \(-0.335799\pi\) | ||||
0.493278 | + | 0.869872i | \(0.335799\pi\) | |||||||
\(728\) | −1.34609e8 | − | 1.06559e9i | −0.348882 | − | 2.76182i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −2.24132e8 | + | 7.85284e6i | −0.576150 | + | 0.0201864i | ||||
\(731\) | − | 9.72993e7i | − | 0.249091i | ||||||
\(732\) | 1.77142e8 | + | 2.54876e8i | 0.451635 | + | 0.649823i | ||||
\(733\) | 5.64609e7i | 0.143363i | 0.997428 | + | 0.0716813i | \(0.0228364\pi\) | ||||
−0.997428 | + | 0.0716813i | \(0.977164\pi\) | |||||||
\(734\) | 2.53955e8 | − | 4.85769e8i | 0.642198 | − | 1.22841i | ||||
\(735\) | 4.71086e8 | − | 2.67687e8i | 1.18642 | − | 0.674165i | ||||
\(736\) | 3.15890e8 | + | 3.50839e8i | 0.792324 | + | 0.879983i | ||||
\(737\) | 1.28002e8i | 0.319753i | ||||||||
\(738\) | −2.62207e7 | + | 5.01553e7i | −0.0652342 | + | 0.124781i | ||||
\(739\) | − | 6.72986e8i | − | 1.66753i | −0.552122 | − | 0.833763i | \(-0.686182\pi\) | ||
0.552122 | − | 0.833763i | \(-0.313818\pi\) | |||||||
\(740\) | 1.89524e8 | − | 3.95683e8i | 0.467703 | − | 0.976455i | ||||
\(741\) | 6.50130e7 | 0.159789 | ||||||||
\(742\) | −9.08930e8 | − | 4.75180e8i | −2.22494 | − | 1.16318i | ||||
\(743\) | 7.85948e8 | 1.91614 | 0.958070 | − | 0.286533i | \(-0.0925027\pi\) | ||||
0.958070 | + | 0.286533i | \(0.0925027\pi\) | |||||||
\(744\) | 3.24461e6 | + | 2.56850e7i | 0.00787850 | + | 0.0623678i | ||||
\(745\) | 1.48502e8 | − | 8.43842e7i | 0.359141 | − | 0.204076i | ||||
\(746\) | 7.59591e7 | + | 3.97107e7i | 0.182963 | + | 0.0956512i | ||||
\(747\) | −1.53581e8 | −0.368448 | ||||||||
\(748\) | 3.50317e8 | + | 5.04045e8i | 0.837060 | + | 1.20438i | ||||
\(749\) | −7.11748e8 | −1.69387 | ||||||||
\(750\) | 2.13483e8 | + | 1.17266e8i | 0.506034 | + | 0.277963i | ||||
\(751\) | − | 5.89245e8i | − | 1.39116i | −0.718451 | − | 0.695578i | \(-0.755148\pi\) | ||
0.718451 | − | 0.695578i | \(-0.244852\pi\) | |||||||
\(752\) | −2.14347e7 | + | 5.76346e7i | −0.0504038 | + | 0.135528i | ||||
\(753\) | 2.18831e8i | 0.512535i | ||||||||
\(754\) | 1.70431e8 | + | 8.90994e7i | 0.397588 | + | 0.207855i | ||||
\(755\) | 2.00130e8 | + | 3.52196e8i | 0.465020 | + | 0.818359i | ||||
\(756\) | 8.70355e7 | + | 1.25229e8i | 0.201433 | + | 0.289827i | ||||
\(757\) | − | 3.30745e8i | − | 0.762440i | −0.924484 | − | 0.381220i | \(-0.875504\pi\) | ||
0.924484 | − | 0.381220i | \(-0.124496\pi\) | |||||||
\(758\) | −7.01352e8 | − | 3.66660e8i | −1.61038 | − | 0.841891i | ||||
\(759\) | − | 2.82019e8i | − | 0.644989i | ||||||
\(760\) | −4.79534e7 | − | 6.40858e7i | −0.109239 | − | 0.145989i | ||||
\(761\) | −5.22089e7 | −0.118465 | −0.0592325 | − | 0.998244i | \(-0.518865\pi\) | ||||
−0.0592325 | + | 0.998244i | \(0.518865\pi\) | |||||||
\(762\) | −1.58390e8 | + | 3.02970e8i | −0.357983 | + | 0.684755i | ||||
\(763\) | 7.81277e8 | 1.75886 | ||||||||
\(764\) | 8.03498e7 | − | 5.58441e7i | 0.180179 | − | 0.125227i | ||||
\(765\) | 1.14618e8 | + | 2.01709e8i | 0.256017 | + | 0.450548i | ||||
\(766\) | −3.66946e8 | + | 7.01900e8i | −0.816425 | + | 1.56167i | ||||
\(767\) | 4.85813e7 | 0.107667 | ||||||||
\(768\) | −1.97975e8 | − | 1.70893e8i | −0.437045 | − | 0.377260i | ||||
\(769\) | 2.35312e8 | 0.517446 | 0.258723 | − | 0.965952i | \(-0.416698\pi\) | ||||
0.258723 | + | 0.965952i | \(0.416698\pi\) | |||||||
\(770\) | 7.89441e8 | − | 2.76593e7i | 1.72921 | − | 0.0605856i | ||||
\(771\) | 2.12321e8i | 0.463266i | ||||||||
\(772\) | 5.17777e8 | − | 3.59861e8i | 1.12536 | − | 0.782138i | ||||
\(773\) | 2.53680e8i | 0.549221i | 0.961556 | + | 0.274611i | \(0.0885489\pi\) | ||||
−0.961556 | + | 0.274611i | \(0.911451\pi\) | |||||||
\(774\) | 1.14735e7 | − | 2.19466e7i | 0.0247441 | − | 0.0473309i | ||||
\(775\) | 4.35410e7 | + | 2.59417e7i | 0.0935391 | + | 0.0557306i | ||||
\(776\) | −4.01377e7 | − | 3.17738e8i | −0.0858948 | − | 0.679961i | ||||
\(777\) | − | 5.37778e8i | − | 1.14641i | ||||||
\(778\) | 4.54231e7 | − | 8.68860e7i | 0.0964580 | − | 0.184506i | ||||
\(779\) | − | 3.64099e7i | − | 0.0770206i | ||||||
\(780\) | 1.79650e8 | − | 3.75067e8i | 0.378567 | − | 0.790360i | ||||
\(781\) | −6.66571e8 | −1.39924 | ||||||||
\(782\) | 7.80144e8 | + | 4.07852e8i | 1.63138 | + | 0.852868i | ||||
\(783\) | −2.73066e7 | −0.0568830 | ||||||||
\(784\) | −3.97019e8 | + | 1.06752e9i | −0.823878 | + | 2.21529i | ||||
\(785\) | 3.29536e7 | + | 5.79928e7i | 0.0681229 | + | 0.119885i | ||||
\(786\) | −1.28393e8 | − | 6.71228e7i | −0.264408 | − | 0.138230i | ||||
\(787\) | −5.60356e8 | −1.14958 | −0.574791 | − | 0.818300i | \(-0.694917\pi\) | ||||
−0.574791 | + | 0.818300i | \(0.694917\pi\) | |||||||
\(788\) | −1.42761e8 | + | 9.92206e7i | −0.291763 | + | 0.202779i | ||||
\(789\) | −1.93422e8 | −0.393800 | ||||||||
\(790\) | −1.37393e7 | + | 481380.i | −0.0278666 | + | 0.000976352i | ||||
\(791\) | 2.76524e8i | 0.558732i | ||||||||
\(792\) | 1.95801e7 | + | 1.55000e8i | 0.0394131 | + | 0.312002i | ||||
\(793\) | − | 1.03750e9i | − | 2.08051i | ||||||
\(794\) | 5.30598e8 | + | 2.77391e8i | 1.06000 | + | 0.554155i | ||||
\(795\) | −1.96198e8 | − | 3.45277e8i | −0.390475 | − | 0.687172i | ||||
\(796\) | −6.01864e8 | + | 4.18303e8i | −1.19333 | + | 0.829376i | ||||
\(797\) | − | 8.17996e8i | − | 1.61576i | −0.589349 | − | 0.807879i | \(-0.700616\pi\) | ||
0.589349 | − | 0.807879i | \(-0.299384\pi\) | |||||||
\(798\) | −8.69458e7 | − | 4.54544e7i | −0.171096 | − | 0.0894473i | ||||
\(799\) | 1.14664e8i | 0.224795i | ||||||||
\(800\) | −5.02227e8 | + | 9.95611e7i | −0.980911 | + | 0.194455i | ||||
\(801\) | −7.38216e7 | −0.143644 | ||||||||
\(802\) | −5.38797e7 | + | 1.03062e8i | −0.104449 | + | 0.199791i | ||||
\(803\) | −2.81621e8 | −0.543899 | ||||||||
\(804\) | −5.80393e7 | − | 8.35083e7i | −0.111674 | − | 0.160680i | ||||
\(805\) | 9.84963e8 | − | 5.59691e8i | 1.88813 | − | 1.07290i | ||||
\(806\) | 4.00923e7 | − | 7.66891e7i | 0.0765695 | − | 0.146463i | ||||
\(807\) | −2.83864e8 | −0.540119 | ||||||||
\(808\) | 3.59374e7 | − | 4.53972e6i | 0.0681259 | − | 0.00860588i | ||||
\(809\) | −8.25351e8 | −1.55881 | −0.779405 | − | 0.626520i | \(-0.784479\pi\) | ||||
−0.779405 | + | 0.626520i | \(0.784479\pi\) | |||||||
\(810\) | 2.06761e6 | + | 5.90128e7i | 0.00389057 | + | 0.111043i | ||||
\(811\) | 4.97694e7i | 0.0933039i | 0.998911 | + | 0.0466520i | \(0.0148552\pi\) | ||||
−0.998911 | + | 0.0466520i | \(0.985145\pi\) | |||||||
\(812\) | −1.65632e8 | − | 2.38316e8i | −0.309369 | − | 0.445128i | ||||
\(813\) | − | 3.12378e8i | − | 0.581311i | ||||||
\(814\) | 2.55242e8 | − | 4.88231e8i | 0.473238 | − | 0.905216i | ||||
\(815\) | 4.00858e8 | − | 2.27781e8i | 0.740487 | − | 0.420771i | ||||
\(816\) | −4.57092e8 | − | 1.69995e8i | −0.841266 | − | 0.312872i | ||||
\(817\) | 1.59320e7i | 0.0292148i | ||||||||
\(818\) | −2.73993e8 | + | 5.24098e8i | −0.500587 | + | 0.957530i | ||||
\(819\) | − | 5.09758e8i | − | 0.927924i | ||||||
\(820\) | −2.10052e8 | − | 1.00611e8i | −0.380966 | − | 0.182475i | ||||
\(821\) | 3.24281e8 | 0.585993 | 0.292997 | − | 0.956113i | \(-0.405348\pi\) | ||||
0.292997 | + | 0.956113i | \(0.405348\pi\) | |||||||
\(822\) | 4.53352e8 | + | 2.37008e8i | 0.816244 | + | 0.426724i | ||||
\(823\) | −5.16871e8 | −0.927219 | −0.463610 | − | 0.886040i | \(-0.653446\pi\) | ||||
−0.463610 | + | 0.886040i | \(0.653446\pi\) | |||||||
\(824\) | 5.72504e8 | − | 7.23205e7i | 1.02328 | − | 0.129265i | ||||
\(825\) | 2.62755e8 | + | 1.56550e8i | 0.467939 | + | 0.278798i | ||||
\(826\) | −6.49707e7 | − | 3.39660e7i | −0.115286 | − | 0.0602705i | ||||
\(827\) | 7.27572e8 | 1.28635 | 0.643175 | − | 0.765719i | \(-0.277617\pi\) | ||||
0.643175 | + | 0.765719i | \(0.277617\pi\) | |||||||
\(828\) | 1.27874e8 | + | 1.83988e8i | 0.225264 | + | 0.324115i | ||||
\(829\) | 9.40548e8 | 1.65089 | 0.825444 | − | 0.564484i | \(-0.190925\pi\) | ||||
0.825444 | + | 0.564484i | \(0.190925\pi\) | |||||||
\(830\) | −2.21303e7 | − | 6.31633e8i | −0.0387037 | − | 1.10467i | ||||
\(831\) | 6.29652e8i | 1.09723i | ||||||||
\(832\) | 2.17392e8 | + | 8.46729e8i | 0.377462 | + | 1.47019i | ||||
\(833\) | 2.12383e9i | 3.67439i | ||||||||
\(834\) | −1.30547e8 | − | 6.82486e7i | −0.225045 | − | 0.117651i | ||||
\(835\) | −5.47465e8 | + | 3.11089e8i | −0.940366 | + | 0.534349i | ||||
\(836\) | −5.73615e7 | − | 8.25332e7i | −0.0981753 | − | 0.141257i | ||||
\(837\) | 1.22872e7i | 0.0209545i | ||||||||
\(838\) | −2.43420e8 | − | 1.27258e8i | −0.413642 | − | 0.216248i | ||||
\(839\) | − | 7.65799e8i | − | 1.29667i | −0.761356 | − | 0.648334i | \(-0.775466\pi\) | ||
0.761356 | − | 0.648334i | \(-0.224534\pi\) | |||||||
\(840\) | −5.02488e8 | + | 3.75996e8i | −0.847788 | + | 0.634374i | ||||
\(841\) | −5.42858e8 | −0.912637 | ||||||||
\(842\) | 2.16328e8 | − | 4.13796e8i | 0.362391 | − | 0.693186i | ||||
\(843\) | −1.83512e8 | −0.306325 | ||||||||
\(844\) | 8.38559e8 | − | 5.82809e8i | 1.39478 | − | 0.969391i | ||||
\(845\) | −6.84018e8 | + | 3.88683e8i | −1.13370 | + | 0.644207i | ||||
\(846\) | −1.35211e7 | + | 2.58633e7i | −0.0223306 | + | 0.0427142i | ||||
\(847\) | −1.22489e8 | −0.201580 | ||||||||
\(848\) | 7.82429e8 | + | 2.90990e8i | 1.28309 | + | 0.477189i | ||||
\(849\) | 4.85763e8 | 0.793782 | ||||||||
\(850\) | −8.13054e8 | + | 5.00456e8i | −1.32392 | + | 0.814909i | ||||
\(851\) | − | 7.90112e8i | − | 1.28203i | ||||||
\(852\) | 4.34869e8 | − | 3.02239e8i | 0.703137 | − | 0.488688i | ||||
\(853\) | 1.03777e9i | 1.67206i | 0.548681 | + | 0.836032i | \(0.315130\pi\) | ||||
−0.548681 | + | 0.836032i | \(0.684870\pi\) | |||||||
\(854\) | −7.25377e8 | + | 1.38751e9i | −1.16464 | + | 2.22773i | ||||
\(855\) | −1.87678e7 | − | 3.30282e7i | −0.0300272 | − | 0.0528429i | ||||
\(856\) | 5.74734e8 | − | 7.26022e7i | 0.916317 | − | 0.115752i | ||||
\(857\) | − | 2.57612e8i | − | 0.409283i | −0.978837 | − | 0.204641i | \(-0.934397\pi\) | ||
0.978837 | − | 0.204641i | \(-0.0656028\pi\) | |||||||
\(858\) | 2.41943e8 | − | 4.62793e8i | 0.383047 | − | 0.732698i | ||||
\(859\) | − | 4.00986e8i | − | 0.632630i | −0.948654 | − | 0.316315i | \(-0.897554\pi\) | ||
0.948654 | − | 0.316315i | \(-0.102446\pi\) | |||||||
\(860\) | 9.19131e7 | + | 4.40246e7i | 0.144505 | + | 0.0692149i | ||||
\(861\) | −2.85485e8 | −0.447274 | ||||||||
\(862\) | −3.64071e8 | − | 1.90333e8i | −0.568414 | − | 0.297161i | ||||
\(863\) | 8.41242e8 | 1.30885 | 0.654423 | − | 0.756129i | \(-0.272912\pi\) | ||||
0.654423 | + | 0.756129i | \(0.272912\pi\) | |||||||
\(864\) | −8.30549e7 | − | 9.22437e7i | −0.128773 | − | 0.143020i | ||||
\(865\) | −2.06909e8 | − | 3.64127e8i | −0.319692 | − | 0.562605i | ||||
\(866\) | −3.08167e8 | − | 1.61106e8i | −0.474495 | − | 0.248061i | ||||
\(867\) | −5.33114e8 | −0.818018 | ||||||||
\(868\) | −1.07236e8 | + | 7.45301e7i | −0.163976 | + | 0.113965i | ||||
\(869\) | −1.72634e7 | −0.0263067 | ||||||||
\(870\) | −3.93475e6 | − | 1.12304e8i | −0.00597530 | − | 0.170544i | ||||
\(871\) | 3.39930e8i | 0.514440i | ||||||||
\(872\) | −6.30879e8 | + | 7.96946e7i | −0.951473 | + | 0.120193i | ||||
\(873\) | − | 1.52000e8i | − | 0.228455i | ||||||
\(874\) | −1.27742e8 | − | 6.67824e7i | −0.191338 | − | 0.100029i | ||||
\(875\) | −2.52966e7 | + | 1.22837e9i | −0.0377605 | + | 1.83360i | ||||
\(876\) | 1.83729e8 | − | 1.27694e8i | 0.273316 | − | 0.189958i | ||||
\(877\) | 1.05281e9i | 1.56081i | 0.625276 | + | 0.780404i | \(0.284986\pi\) | ||||
−0.625276 | + | 0.780404i | \(0.715014\pi\) | |||||||
\(878\) | −3.77808e8 | − | 1.97514e8i | −0.558197 | − | 0.291820i | ||||
\(879\) | 7.40016e7i | 0.108962i | ||||||||
\(880\) | −6.34649e8 | + | 1.02862e8i | −0.931291 | + | 0.150941i | ||||
\(881\) | 7.73565e8 | 1.13128 | 0.565639 | − | 0.824653i | \(-0.308630\pi\) | ||||
0.565639 | + | 0.824653i | \(0.308630\pi\) | |||||||
\(882\) | −2.50441e8 | + | 4.79047e8i | −0.365006 | + | 0.698188i | ||||
\(883\) | −5.23480e8 | −0.760358 | −0.380179 | − | 0.924913i | \(-0.624138\pi\) | ||||
−0.380179 | + | 0.924913i | \(0.624138\pi\) | |||||||
\(884\) | 9.30322e8 | + | 1.33857e9i | 1.34672 | + | 1.93769i | ||||
\(885\) | −1.40243e7 | − | 2.46805e7i | −0.0202326 | − | 0.0356061i | ||||
\(886\) | 6.06324e6 | − | 1.15978e7i | 0.00871773 | − | 0.0166754i | ||||
\(887\) | 3.93574e8 | 0.563969 | 0.281984 | − | 0.959419i | \(-0.409007\pi\) | ||||
0.281984 | + | 0.959419i | \(0.409007\pi\) | |||||||
\(888\) | 5.48563e7 | + | 4.34253e8i | 0.0783407 | + | 0.620161i | ||||
\(889\) | −1.72451e9 | −2.45448 | ||||||||
\(890\) | −1.06373e7 | − | 3.03606e8i | −0.0150891 | − | 0.430666i | ||||
\(891\) | 7.41492e7i | 0.104827i | ||||||||
\(892\) | −1.79658e8 | − | 2.58496e8i | −0.253134 | − | 0.364216i | ||||
\(893\) | − | 1.87752e7i | − | 0.0263652i | ||||||
\(894\) | −7.89476e7 | + | 1.51012e8i | −0.110491 | + | 0.211348i | ||||
\(895\) | 3.06975e7 | + | 5.40226e7i | 0.0428188 | + | 0.0753540i | ||||
\(896\) | 3.01266e8 | − | 1.28437e9i | 0.418819 | − | 1.78553i | ||||
\(897\) | − | 7.48945e8i | − | 1.03770i | ||||||
\(898\) | −1.45960e8 | + | 2.79195e8i | −0.201561 | + | 0.385548i | ||||
\(899\) | − | 2.33831e7i | − | 0.0321828i | ||||||
\(900\) | −2.42404e8 | + | 1.70069e7i | −0.332516 | + | 0.0233291i | ||||
\(901\) | 1.55664e9 | 2.12820 | ||||||||
\(902\) | −2.59182e8 | − | 1.35498e8i | −0.353171 | − | 0.184634i | ||||
\(903\) | 1.24920e8 | 0.169656 | ||||||||
\(904\) | −2.82070e7 | − | 2.23292e8i | −0.0381813 | − | 0.302251i | ||||
\(905\) | −2.68189e8 | + | 1.52394e8i | −0.361822 | + | 0.205600i | ||||
\(906\) | −3.58148e8 | − | 1.87236e8i | −0.481591 | − | 0.251771i | ||||
\(907\) | 1.14062e9 | 1.52868 | 0.764342 | − | 0.644811i | \(-0.223064\pi\) | ||||
0.764342 | + | 0.644811i | \(0.223064\pi\) | |||||||
\(908\) | −3.38522e8 | − | 4.87074e8i | −0.452199 | − | 0.650635i | ||||
\(909\) | 1.71918e7 | 0.0228891 | ||||||||
\(910\) | 2.09648e9 | − | 7.34537e7i | 2.78207 | − | 0.0974742i | ||||
\(911\) | 6.75025e8i | 0.892821i | 0.894828 | + | 0.446411i | \(0.147298\pi\) | ||||
−0.894828 | + | 0.446411i | \(0.852702\pi\) | |||||||
\(912\) | 7.48451e7 | + | 2.78353e7i | 0.0986685 | + | 0.0366954i | ||||
\(913\) | − | 7.93644e8i | − | 1.04283i | ||||||
\(914\) | −1.22317e9 | − | 6.39460e8i | −1.60195 | − | 0.837481i | ||||
\(915\) | −5.27076e8 | + | 2.99503e8i | −0.688034 | + | 0.390965i | ||||
\(916\) | −1.58895e8 | − | 2.28622e8i | −0.206739 | − | 0.297462i | ||||
\(917\) | − | 7.30816e8i | − | 0.947764i | ||||||
\(918\) | −2.05118e8 | − | 1.07234e8i | −0.265140 | − | 0.138613i | ||||
\(919\) | − | 8.33732e8i | − | 1.07419i | −0.843523 | − | 0.537094i | \(-0.819522\pi\) | ||
0.843523 | − | 0.537094i | \(-0.180478\pi\) | |||||||
\(920\) | −7.38263e8 | + | 5.52420e8i | −0.948086 | + | 0.709424i | ||||
\(921\) | 2.47956e8 | 0.317392 | ||||||||
\(922\) | 5.85069e8 | − | 1.11913e9i | 0.746473 | − | 1.42786i | ||||
\(923\) | −1.77018e9 | −2.25120 | ||||||||
\(924\) | −6.47131e8 | + | 4.49764e8i | −0.820307 | + | 0.570123i | ||||
\(925\) | 7.36142e8 | + | 4.38594e8i | 0.930115 | + | 0.554163i | ||||
\(926\) | 6.13514e8 | − | 1.17354e9i | 0.772666 | − | 1.47797i | ||||
\(927\) | 2.73875e8 | 0.343806 | ||||||||
\(928\) | 1.58057e8 | + | 1.75544e8i | 0.197774 | + | 0.219655i | ||||
\(929\) | 1.25073e8 | 0.155997 | 0.0779986 | − | 0.996953i | \(-0.475147\pi\) | ||||
0.0779986 | + | 0.996953i | \(0.475147\pi\) | |||||||
\(930\) | −5.05337e7 | + | 1.77053e6i | −0.0628249 | + | 0.00220117i | ||||
\(931\) | − | 3.47760e8i | − | 0.430954i | ||||||
\(932\) | −7.93980e6 | + | 5.51826e6i | −0.00980759 | + | 0.00681639i | ||||
\(933\) | 4.90320e8i | 0.603719i | ||||||||
\(934\) | −2.41303e8 | + | 4.61569e8i | −0.296158 | + | 0.566494i | ||||
\(935\) | −1.04235e9 | + | 5.92300e8i | −1.27520 | + | 0.724614i | ||||
\(936\) | 5.19981e7 | + | 4.11628e8i | 0.0634103 | + | 0.501969i | ||||
\(937\) | 7.76885e8i | 0.944361i | 0.881502 | + | 0.472181i | \(0.156533\pi\) | ||||
−0.881502 | + | 0.472181i | \(0.843467\pi\) | |||||||
\(938\) | 2.37665e8 | − | 4.54609e8i | 0.287976 | − | 0.550845i | ||||
\(939\) | − | 5.24999e8i | − | 0.634106i | ||||||
\(940\) | −1.08316e8 | − | 5.18814e7i | −0.130410 | − | 0.0624637i | ||||
\(941\) | −1.33114e9 | −1.59756 | −0.798778 | − | 0.601626i | \(-0.794520\pi\) | ||||
−0.798778 | + | 0.601626i | \(0.794520\pi\) | |||||||
\(942\) | −5.89729e7 | − | 3.08304e7i | −0.0705505 | − | 0.0368831i | ||||
\(943\) | −4.19439e8 | −0.500188 | ||||||||
\(944\) | 5.59283e7 | + | 2.08001e7i | 0.0664838 | + | 0.0247257i | ||||
\(945\) | −2.58970e8 | + | 1.47156e8i | −0.306869 | + | 0.174374i | ||||
\(946\) | 1.13411e8 | + | 5.92901e7i | 0.133962 | + | 0.0700340i | ||||
\(947\) | −1.12323e9 | −1.32257 | −0.661284 | − | 0.750136i | \(-0.729988\pi\) | ||||
−0.661284 | + | 0.750136i | \(0.729988\pi\) | |||||||
\(948\) | 1.12626e7 | − | 7.82764e6i | 0.0132194 | − | 0.00918767i | ||||
\(949\) | −7.47889e8 | −0.875061 | ||||||||
\(950\) | 1.33131e8 | − | 8.19456e7i | 0.155277 | − | 0.0955773i | ||||
\(951\) | 4.74191e8i | 0.551330i | ||||||||
\(952\) | −3.08303e8 | − | 2.44059e9i | −0.357328 | − | 2.82868i | ||||
\(953\) | − | 1.15890e9i | − | 1.33895i | −0.742833 | − | 0.669477i | \(-0.766518\pi\) | ||
0.742833 | − | 0.669477i | \(-0.233482\pi\) | |||||||
\(954\) | 3.51112e8 | + | 1.83558e8i | 0.404390 | + | 0.211411i | ||||
\(955\) | 9.44186e7 | + | 1.66161e8i | 0.108404 | + | 0.190774i | ||||
\(956\) | −5.82801e8 | + | 4.05054e8i | −0.667032 | + | 0.463595i | ||||
\(957\) | − | 1.41109e8i | − | 0.160998i | ||||||
\(958\) | 5.38304e8 | + | 2.81420e8i | 0.612253 | + | 0.320080i | ||||
\(959\) | 2.58048e9i | 2.92580i | ||||||||
\(960\) | 3.67403e8 | − | 3.54872e8i | 0.415269 | − | 0.401105i | ||||
\(961\) | 8.76982e8 | 0.988145 | ||||||||
\(962\) | 6.77836e8 | − | 1.29657e9i | 0.761376 | − | 1.45637i | ||||
\(963\) | 2.74942e8 | 0.307866 | ||||||||
\(964\) | −8.33633e8 | − | 1.19945e9i | −0.930559 | − | 1.33891i | ||||
\(965\) | 6.08437e8 | + | 1.07075e9i | 0.677070 | + | 1.19153i | ||||
\(966\) | −5.23631e8 | + | 1.00161e9i | −0.580890 | + | 1.11114i | ||||
\(967\) | 1.31608e9 | 1.45547 | 0.727737 | − | 0.685857i | \(-0.240572\pi\) | ||||
0.727737 | + | 0.685857i | \(0.240572\pi\) | |||||||
\(968\) | 9.89097e7 | − | 1.24946e7i | 0.109047 | − | 0.0137751i | ||||
\(969\) | 1.48904e8 | 0.163657 | ||||||||
\(970\) | 6.25130e8 | − | 2.19025e7i | 0.684944 | − | 0.0239981i | ||||
\(971\) | 3.94143e8i | 0.430523i | 0.976556 | + | 0.215261i | \(0.0690604\pi\) | ||||
−0.976556 | + | 0.215261i | \(0.930940\pi\) | |||||||
\(972\) | −3.36211e7 | − | 4.83748e7i | −0.0366111 | − | 0.0526769i | ||||
\(973\) | − | 7.43074e8i | − | 0.806666i | ||||||
\(974\) | −3.97370e8 | + | 7.60095e8i | −0.430049 | + | 0.822604i | ||||
\(975\) | 6.97788e8 | + | 4.15742e8i | 0.752852 | + | 0.448549i | ||||
\(976\) | 4.44206e8 | − | 1.19440e9i | 0.477787 | − | 1.28470i | ||||
\(977\) | 1.51060e9i | 1.61982i | 0.586553 | + | 0.809911i | \(0.300484\pi\) | ||||
−0.586553 | + | 0.809911i | \(0.699516\pi\) | |||||||
\(978\) | −2.13106e8 | + | 4.07632e8i | −0.227813 | + | 0.435765i | ||||
\(979\) | − | 3.81480e8i | − | 0.406559i | ||||||
\(980\) | −2.00627e9 | − | 9.60961e8i | −2.13162 | − | 1.02100i | ||||
\(981\) | −3.01800e8 | −0.319678 | ||||||||
\(982\) | 1.60321e9 | + | 8.38143e8i | 1.69300 | + | 0.885083i | ||||
\(983\) | 1.64220e9 | 1.72888 | 0.864440 | − | 0.502736i | \(-0.167673\pi\) | ||||
0.864440 | + | 0.502736i | \(0.167673\pi\) | |||||||
\(984\) | 2.30528e8 | − | 2.91210e7i | 0.241957 | − | 0.0305648i | ||||
\(985\) | −1.67757e8 | − | 2.95226e8i | −0.175539 | − | 0.308920i | ||||
\(986\) | 3.90349e8 | + | 2.04070e8i | 0.407213 | + | 0.212887i | ||||
\(987\) | −1.47214e8 | −0.153108 | ||||||||
\(988\) | −1.52333e8 | − | 2.19180e8i | −0.157951 | − | 0.227264i | ||||
\(989\) | 1.83535e8 | 0.189727 | ||||||||
\(990\) | −3.04954e8 | + | 1.06846e7i | −0.314288 | + | 0.0110116i | ||||
\(991\) | 1.90807e9i | 1.96053i | 0.197680 | + | 0.980267i | \(0.436659\pi\) | ||||
−0.197680 | + | 0.980267i | \(0.563341\pi\) | |||||||
\(992\) | 7.89899e7 | − | 7.11214e7i | 0.0809164 | − | 0.0728560i | ||||
\(993\) | − | 9.85403e6i | − | 0.0100639i | ||||||
\(994\) | 2.36737e9 | + | 1.23764e9i | 2.41050 | + | 1.26019i | ||||
\(995\) | −7.07247e8 | − | 1.24464e9i | −0.717963 | − | 1.26350i | ||||
\(996\) | 3.59857e8 | + | 5.17771e8i | 0.364210 | + | 0.524034i | ||||
\(997\) | − | 7.29485e7i | − | 0.0736090i | −0.999322 | − | 0.0368045i | \(-0.988282\pi\) | ||
0.999322 | − | 0.0368045i | \(-0.0117179\pi\) | |||||||
\(998\) | 1.60353e8 | + | 8.38311e7i | 0.161319 | + | 0.0843361i | ||||
\(999\) | 2.07739e8i | 0.208363i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 60.7.f.a.19.14 | yes | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.23 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.24 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.23 | yes | 36 | |
12.11 | even | 2 | 180.7.f.g.19.13 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.14 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.13 | ✓ | 36 | |
60.59 | even | 2 | 180.7.f.g.19.24 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.13 | ✓ | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.14 | yes | 36 | 1.1 | even | 1 | trivial | |
60.7.f.a.19.23 | yes | 36 | 5.4 | even | 2 | inner | |
60.7.f.a.19.24 | yes | 36 | 4.3 | odd | 2 | inner | |
180.7.f.g.19.13 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.14 | 36 | 15.14 | odd | 2 | |||
180.7.f.g.19.23 | 36 | 3.2 | odd | 2 | |||
180.7.f.g.19.24 | 36 | 60.59 | even | 2 |