Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,7,Mod(6,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.6");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.d (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.51200109393\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 6.7 | ||
Character | \(\chi\) | \(=\) | 37.6 |
Dual form | 37.7.d.a.31.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.76006 | + | 3.76006i | −0.470008 | + | 0.470008i | −0.901917 | − | 0.431909i | \(-0.857840\pi\) |
0.431909 | + | 0.901917i | \(0.357840\pi\) | |||||||
\(3\) | 16.7537i | 0.620507i | 0.950654 | + | 0.310253i | \(0.100414\pi\) | ||||
−0.950654 | + | 0.310253i | \(0.899586\pi\) | |||||||
\(4\) | 35.7238i | 0.558185i | ||||||||
\(5\) | 120.059 | + | 120.059i | 0.960469 | + | 0.960469i | 0.999248 | − | 0.0387784i | \(-0.0123466\pi\) |
−0.0387784 | + | 0.999248i | \(0.512347\pi\) | |||||||
\(6\) | −62.9949 | − | 62.9949i | −0.291643 | − | 0.291643i | ||||
\(7\) | 144.567 | 0.421478 | 0.210739 | − | 0.977542i | \(-0.432413\pi\) | ||||
0.210739 | + | 0.977542i | \(0.432413\pi\) | |||||||
\(8\) | −374.968 | − | 374.968i | −0.732359 | − | 0.732359i | ||||
\(9\) | 448.314 | 0.614971 | ||||||||
\(10\) | −902.857 | −0.902857 | ||||||||
\(11\) | 2306.13i | 1.73263i | 0.499500 | + | 0.866314i | \(0.333517\pi\) | ||||
−0.499500 | + | 0.866314i | \(0.666483\pi\) | |||||||
\(12\) | −598.506 | −0.346357 | ||||||||
\(13\) | −2026.98 | − | 2026.98i | −0.922612 | − | 0.922612i | 0.0746017 | − | 0.997213i | \(-0.476231\pi\) |
−0.997213 | + | 0.0746017i | \(0.976231\pi\) | |||||||
\(14\) | −543.581 | + | 543.581i | −0.198098 | + | 0.198098i | ||||
\(15\) | −2011.43 | + | 2011.43i | −0.595978 | + | 0.595978i | ||||
\(16\) | 533.484 | 0.130245 | ||||||||
\(17\) | −4149.30 | − | 4149.30i | −0.844556 | − | 0.844556i | 0.144892 | − | 0.989448i | \(-0.453717\pi\) |
−0.989448 | + | 0.144892i | \(0.953717\pi\) | |||||||
\(18\) | −1685.69 | + | 1685.69i | −0.289042 | + | 0.289042i | ||||
\(19\) | 3772.92 | + | 3772.92i | 0.550068 | + | 0.550068i | 0.926460 | − | 0.376392i | \(-0.122836\pi\) |
−0.376392 | + | 0.926460i | \(0.622836\pi\) | |||||||
\(20\) | −4288.96 | + | 4288.96i | −0.536119 | + | 0.536119i | ||||
\(21\) | 2422.03i | 0.261530i | ||||||||
\(22\) | −8671.19 | − | 8671.19i | −0.814349 | − | 0.814349i | ||||
\(23\) | −2929.51 | − | 2929.51i | −0.240775 | − | 0.240775i | 0.576396 | − | 0.817171i | \(-0.304459\pi\) |
−0.817171 | + | 0.576396i | \(0.804459\pi\) | |||||||
\(24\) | 6282.10 | − | 6282.10i | 0.454434 | − | 0.454434i | ||||
\(25\) | 13203.2i | 0.845003i | ||||||||
\(26\) | 15243.1 | 0.867270 | ||||||||
\(27\) | 19724.3i | 1.00210i | ||||||||
\(28\) | 5164.49i | 0.235263i | ||||||||
\(29\) | 17578.8 | − | 17578.8i | 0.720769 | − | 0.720769i | −0.247993 | − | 0.968762i | \(-0.579771\pi\) |
0.968762 | + | 0.247993i | \(0.0797709\pi\) | |||||||
\(30\) | − | 15126.2i | − | 0.560229i | ||||||
\(31\) | 26695.5 | − | 26695.5i | 0.896091 | − | 0.896091i | −0.0989963 | − | 0.995088i | \(-0.531563\pi\) |
0.995088 | + | 0.0989963i | \(0.0315632\pi\) | |||||||
\(32\) | 21992.0 | − | 21992.0i | 0.671143 | − | 0.671143i | ||||
\(33\) | −38636.1 | −1.07511 | ||||||||
\(34\) | 31203.3 | 0.793896 | ||||||||
\(35\) | 17356.5 | + | 17356.5i | 0.404817 | + | 0.404817i | ||||
\(36\) | 16015.5i | 0.343268i | ||||||||
\(37\) | 23359.1 | + | 44945.3i | 0.461159 | + | 0.887317i | ||||
\(38\) | −28372.8 | −0.517073 | ||||||||
\(39\) | 33959.3 | − | 33959.3i | 0.572487 | − | 0.572487i | ||||
\(40\) | − | 90036.3i | − | 1.40682i | ||||||
\(41\) | 116578.i | 1.69147i | 0.533606 | + | 0.845733i | \(0.320837\pi\) | ||||
−0.533606 | + | 0.845733i | \(0.679163\pi\) | |||||||
\(42\) | −9106.99 | − | 9106.99i | −0.122921 | − | 0.122921i | ||||
\(43\) | −71593.1 | − | 71593.1i | −0.900463 | − | 0.900463i | 0.0950127 | − | 0.995476i | \(-0.469711\pi\) |
−0.995476 | + | 0.0950127i | \(0.969711\pi\) | |||||||
\(44\) | −82383.7 | −0.967126 | ||||||||
\(45\) | 53824.0 | + | 53824.0i | 0.590661 | + | 0.590661i | ||||
\(46\) | 22030.3 | 0.226332 | ||||||||
\(47\) | 45925.3 | 0.442343 | 0.221171 | − | 0.975235i | \(-0.429012\pi\) | ||||
0.221171 | + | 0.975235i | \(0.429012\pi\) | |||||||
\(48\) | 8937.81i | 0.0808179i | ||||||||
\(49\) | −96749.4 | −0.822356 | ||||||||
\(50\) | −49644.8 | − | 49644.8i | −0.397158 | − | 0.397158i | ||||
\(51\) | 69516.1 | − | 69516.1i | 0.524052 | − | 0.524052i | ||||
\(52\) | 72411.4 | − | 72411.4i | 0.514988 | − | 0.514988i | ||||
\(53\) | 128704. | 0.864501 | 0.432250 | − | 0.901754i | \(-0.357720\pi\) | ||||
0.432250 | + | 0.901754i | \(0.357720\pi\) | |||||||
\(54\) | −74164.8 | − | 74164.8i | −0.470995 | − | 0.470995i | ||||
\(55\) | −276871. | + | 276871.i | −1.66414 | + | 1.66414i | ||||
\(56\) | −54208.0 | − | 54208.0i | −0.308674 | − | 0.308674i | ||||
\(57\) | −63210.2 | + | 63210.2i | −0.341321 | + | 0.341321i | ||||
\(58\) | 132195.i | 0.677535i | ||||||||
\(59\) | 97437.8 | + | 97437.8i | 0.474429 | + | 0.474429i | 0.903345 | − | 0.428915i | \(-0.141104\pi\) |
−0.428915 | + | 0.903345i | \(0.641104\pi\) | |||||||
\(60\) | −71855.8 | − | 71855.8i | −0.332666 | − | 0.332666i | ||||
\(61\) | −213867. | + | 213867.i | −0.942222 | + | 0.942222i | −0.998420 | − | 0.0561972i | \(-0.982102\pi\) |
0.0561972 | + | 0.998420i | \(0.482102\pi\) | |||||||
\(62\) | 200753.i | 0.842341i | ||||||||
\(63\) | 64811.4 | 0.259197 | ||||||||
\(64\) | 199526.i | 0.761131i | ||||||||
\(65\) | − | 486713.i | − | 1.77228i | ||||||
\(66\) | 145274. | − | 145274.i | 0.505309 | − | 0.505309i | ||||
\(67\) | − | 27261.1i | − | 0.0906398i | −0.998973 | − | 0.0453199i | \(-0.985569\pi\) | ||
0.998973 | − | 0.0453199i | \(-0.0144307\pi\) | |||||||
\(68\) | 148229. | − | 148229.i | 0.471418 | − | 0.471418i | ||||
\(69\) | 49080.1 | − | 49080.1i | 0.149403 | − | 0.149403i | ||||
\(70\) | −130523. | −0.380535 | ||||||||
\(71\) | 531344. | 1.48457 | 0.742285 | − | 0.670085i | \(-0.233742\pi\) | ||||
0.742285 | + | 0.670085i | \(0.233742\pi\) | |||||||
\(72\) | −168103. | − | 168103.i | −0.450380 | − | 0.450380i | ||||
\(73\) | 113471.i | 0.291686i | 0.989308 | + | 0.145843i | \(0.0465895\pi\) | ||||
−0.989308 | + | 0.145843i | \(0.953411\pi\) | |||||||
\(74\) | −256829. | − | 81165.4i | −0.633795 | − | 0.200298i | ||||
\(75\) | −221202. | −0.524330 | ||||||||
\(76\) | −134783. | + | 134783.i | −0.307040 | + | 0.307040i | ||||
\(77\) | 333390.i | 0.730265i | ||||||||
\(78\) | 255379.i | 0.538147i | ||||||||
\(79\) | −60615.8 | − | 60615.8i | −0.122943 | − | 0.122943i | 0.642958 | − | 0.765901i | \(-0.277707\pi\) |
−0.765901 | + | 0.642958i | \(0.777707\pi\) | |||||||
\(80\) | 64049.3 | + | 64049.3i | 0.125096 | + | 0.125096i | ||||
\(81\) | −3634.42 | −0.00683879 | ||||||||
\(82\) | −438339. | − | 438339.i | −0.795003 | − | 0.795003i | ||||
\(83\) | 851810. | 1.48973 | 0.744867 | − | 0.667213i | \(-0.232513\pi\) | ||||
0.744867 | + | 0.667213i | \(0.232513\pi\) | |||||||
\(84\) | −86524.2 | −0.145982 | ||||||||
\(85\) | − | 996319.i | − | 1.62234i | ||||||
\(86\) | 538390. | 0.846450 | ||||||||
\(87\) | 294510. | + | 294510.i | 0.447242 | + | 0.447242i | ||||
\(88\) | 864724. | − | 864724.i | 1.26891 | − | 1.26891i | ||||
\(89\) | −6133.25 | + | 6133.25i | −0.00870003 | + | 0.00870003i | −0.711443 | − | 0.702743i | \(-0.751958\pi\) |
0.702743 | + | 0.711443i | \(0.251958\pi\) | |||||||
\(90\) | −404764. | −0.555231 | ||||||||
\(91\) | −293034. | − | 293034.i | −0.388861 | − | 0.388861i | ||||
\(92\) | 104653. | − | 104653.i | 0.134397 | − | 0.134397i | ||||
\(93\) | 447247. | + | 447247.i | 0.556031 | + | 0.556031i | ||||
\(94\) | −172682. | + | 172682.i | −0.207905 | + | 0.207905i | ||||
\(95\) | 905943.i | 1.05665i | ||||||||
\(96\) | 368447. | + | 368447.i | 0.416449 | + | 0.416449i | ||||
\(97\) | 316838. | + | 316838.i | 0.347154 | + | 0.347154i | 0.859048 | − | 0.511894i | \(-0.171056\pi\) |
−0.511894 | + | 0.859048i | \(0.671056\pi\) | |||||||
\(98\) | 363784. | − | 363784.i | 0.386514 | − | 0.386514i | ||||
\(99\) | 1.03387e6i | 1.06552i | ||||||||
\(100\) | −471668. | −0.471668 | ||||||||
\(101\) | − | 1.89725e6i | − | 1.84145i | −0.390207 | − | 0.920727i | \(-0.627596\pi\) | ||
0.390207 | − | 0.920727i | \(-0.372404\pi\) | |||||||
\(102\) | 522770.i | 0.492618i | ||||||||
\(103\) | 356839. | − | 356839.i | 0.326558 | − | 0.326558i | −0.524718 | − | 0.851276i | \(-0.675829\pi\) |
0.851276 | + | 0.524718i | \(0.175829\pi\) | |||||||
\(104\) | 1.52010e6i | 1.35137i | ||||||||
\(105\) | −290786. | + | 290786.i | −0.251192 | + | 0.251192i | ||||
\(106\) | −483937. | + | 483937.i | −0.406322 | + | 0.406322i | ||||
\(107\) | 98615.0 | 0.0804992 | 0.0402496 | − | 0.999190i | \(-0.487185\pi\) | ||||
0.0402496 | + | 0.999190i | \(0.487185\pi\) | |||||||
\(108\) | −704629. | −0.559357 | ||||||||
\(109\) | 114405. | + | 114405.i | 0.0883414 | + | 0.0883414i | 0.749897 | − | 0.661555i | \(-0.230103\pi\) |
−0.661555 | + | 0.749897i | \(0.730103\pi\) | |||||||
\(110\) | − | 2.08210e6i | − | 1.56431i | ||||||
\(111\) | −752999. | + | 391351.i | −0.550586 | + | 0.286152i | ||||
\(112\) | 77124.1 | 0.0548954 | ||||||||
\(113\) | −1.85643e6 | + | 1.85643e6i | −1.28660 | + | 1.28660i | −0.349759 | + | 0.936840i | \(0.613736\pi\) |
−0.936840 | + | 0.349759i | \(0.886264\pi\) | |||||||
\(114\) | − | 475349.i | − | 0.320847i | ||||||
\(115\) | − | 703426.i | − | 0.462514i | ||||||
\(116\) | 627983. | + | 627983.i | 0.402322 | + | 0.402322i | ||||
\(117\) | −908723. | − | 908723.i | −0.567380 | − | 0.567380i | ||||
\(118\) | −732745. | −0.445971 | ||||||||
\(119\) | −599852. | − | 599852.i | −0.355962 | − | 0.355962i | ||||
\(120\) | 1.50844e6 | 0.872940 | ||||||||
\(121\) | −3.54666e6 | −2.00200 | ||||||||
\(122\) | − | 1.60830e6i | − | 0.885704i | ||||||
\(123\) | −1.95310e6 | −1.04957 | ||||||||
\(124\) | 953664. | + | 953664.i | 0.500185 | + | 0.500185i | ||||
\(125\) | 290761. | − | 290761.i | 0.148870 | − | 0.148870i | ||||
\(126\) | −243695. | + | 243695.i | −0.121825 | + | 0.121825i | ||||
\(127\) | −713334. | −0.348242 | −0.174121 | − | 0.984724i | \(-0.555708\pi\) | ||||
−0.174121 | + | 0.984724i | \(0.555708\pi\) | |||||||
\(128\) | 657259. | + | 657259.i | 0.313406 | + | 0.313406i | ||||
\(129\) | 1.19945e6 | − | 1.19945e6i | 0.558744 | − | 0.558744i | ||||
\(130\) | 1.83007e6 | + | 1.83007e6i | 0.832986 | + | 0.832986i | ||||
\(131\) | 1.35381e6 | − | 1.35381e6i | 0.602203 | − | 0.602203i | −0.338694 | − | 0.940897i | \(-0.609985\pi\) |
0.940897 | + | 0.338694i | \(0.109985\pi\) | |||||||
\(132\) | − | 1.38023e6i | − | 0.600108i | ||||||
\(133\) | 545439. | + | 545439.i | 0.231842 | + | 0.231842i | ||||
\(134\) | 102504. | + | 102504.i | 0.0426015 | + | 0.0426015i | ||||
\(135\) | −2.36808e6 | + | 2.36808e6i | −0.962487 | + | 0.962487i | ||||
\(136\) | 3.11171e6i | 1.23704i | ||||||||
\(137\) | 685303. | 0.266515 | 0.133257 | − | 0.991081i | \(-0.457456\pi\) | ||||
0.133257 | + | 0.991081i | \(0.457456\pi\) | |||||||
\(138\) | 369089.i | 0.140441i | ||||||||
\(139\) | 1.90869e6i | 0.710709i | 0.934732 | + | 0.355354i | \(0.115640\pi\) | ||||
−0.934732 | + | 0.355354i | \(0.884360\pi\) | |||||||
\(140\) | −620042. | + | 620042.i | −0.225963 | + | 0.225963i | ||||
\(141\) | 769419.i | 0.274477i | ||||||||
\(142\) | −1.99789e6 | + | 1.99789e6i | −0.697760 | + | 0.697760i | ||||
\(143\) | 4.67447e6 | − | 4.67447e6i | 1.59854 | − | 1.59854i | ||||
\(144\) | 239168. | 0.0800970 | ||||||||
\(145\) | 4.22098e6 | 1.38455 | ||||||||
\(146\) | −426658. | − | 426658.i | −0.137095 | − | 0.137095i | ||||
\(147\) | − | 1.62091e6i | − | 0.510277i | ||||||
\(148\) | −1.60562e6 | + | 834477.i | −0.495287 | + | 0.257412i | ||||
\(149\) | 3.47272e6 | 1.04981 | 0.524906 | − | 0.851160i | \(-0.324101\pi\) | ||||
0.524906 | + | 0.851160i | \(0.324101\pi\) | |||||||
\(150\) | 831733. | − | 831733.i | 0.246439 | − | 0.246439i | ||||
\(151\) | − | 4.90755e6i | − | 1.42539i | −0.701473 | − | 0.712696i | \(-0.747474\pi\) | ||
0.701473 | − | 0.712696i | \(-0.252526\pi\) | |||||||
\(152\) | − | 2.82945e6i | − | 0.805695i | ||||||
\(153\) | −1.86019e6 | − | 1.86019e6i | −0.519378 | − | 0.519378i | ||||
\(154\) | −1.25357e6 | − | 1.25357e6i | −0.343230 | − | 0.343230i | ||||
\(155\) | 6.41004e6 | 1.72134 | ||||||||
\(156\) | 1.21316e6 | + | 1.21316e6i | 0.319553 | + | 0.319553i | ||||
\(157\) | −1.90672e6 | −0.492706 | −0.246353 | − | 0.969180i | \(-0.579232\pi\) | ||||
−0.246353 | + | 0.969180i | \(0.579232\pi\) | |||||||
\(158\) | 455838. | 0.115569 | ||||||||
\(159\) | 2.15627e6i | 0.536429i | ||||||||
\(160\) | 5.28067e6 | 1.28923 | ||||||||
\(161\) | −423511. | − | 423511.i | −0.101481 | − | 0.101481i | ||||
\(162\) | 13665.6 | − | 13665.6i | 0.00321429 | − | 0.00321429i | ||||
\(163\) | 26502.1 | − | 26502.1i | 0.00611951 | − | 0.00611951i | −0.704040 | − | 0.710160i | \(-0.748623\pi\) |
0.710160 | + | 0.704040i | \(0.248623\pi\) | |||||||
\(164\) | −4.16460e6 | −0.944151 | ||||||||
\(165\) | −4.63860e6 | − | 4.63860e6i | −1.03261 | − | 1.03261i | ||||
\(166\) | −3.20286e6 | + | 3.20286e6i | −0.700187 | + | 0.700187i | ||||
\(167\) | −1.87078e6 | − | 1.87078e6i | −0.401674 | − | 0.401674i | 0.477149 | − | 0.878823i | \(-0.341670\pi\) |
−0.878823 | + | 0.477149i | \(0.841670\pi\) | |||||||
\(168\) | 908184. | − | 908184.i | 0.191534 | − | 0.191534i | ||||
\(169\) | 3.39047e6i | 0.702425i | ||||||||
\(170\) | 3.74623e6 | + | 3.74623e6i | 0.762513 | + | 0.762513i | ||||
\(171\) | 1.69145e6 | + | 1.69145e6i | 0.338276 | + | 0.338276i | ||||
\(172\) | 2.55758e6 | − | 2.55758e6i | 0.502625 | − | 0.502625i | ||||
\(173\) | 309904.i | 0.0598535i | 0.999552 | + | 0.0299267i | \(0.00952740\pi\) | ||||
−0.999552 | + | 0.0299267i | \(0.990473\pi\) | |||||||
\(174\) | −2.21476e6 | −0.420415 | ||||||||
\(175\) | 1.90874e6i | 0.356150i | ||||||||
\(176\) | 1.23028e6i | 0.225666i | ||||||||
\(177\) | −1.63244e6 | + | 1.63244e6i | −0.294387 | + | 0.294387i | ||||
\(178\) | − | 46122.9i | − | 0.00817817i | ||||||
\(179\) | −690422. | + | 690422.i | −0.120380 | + | 0.120380i | −0.764731 | − | 0.644350i | \(-0.777128\pi\) |
0.644350 | + | 0.764731i | \(0.277128\pi\) | |||||||
\(180\) | −1.92280e6 | + | 1.92280e6i | −0.329698 | + | 0.329698i | ||||
\(181\) | −4.86601e6 | −0.820610 | −0.410305 | − | 0.911948i | \(-0.634578\pi\) | ||||
−0.410305 | + | 0.911948i | \(0.634578\pi\) | |||||||
\(182\) | 2.20366e6 | 0.365535 | ||||||||
\(183\) | −3.58305e6 | − | 3.58305e6i | −0.584655 | − | 0.584655i | ||||
\(184\) | 2.19695e6i | 0.352668i | ||||||||
\(185\) | −2.59161e6 | + | 8.20054e6i | −0.409312 | + | 1.29517i | ||||
\(186\) | −3.36336e6 | −0.522678 | ||||||||
\(187\) | 9.56882e6 | − | 9.56882e6i | 1.46330 | − | 1.46330i | ||||
\(188\) | 1.64063e6i | 0.246909i | ||||||||
\(189\) | 2.85149e6i | 0.422364i | ||||||||
\(190\) | −3.40640e6 | − | 3.40640e6i | −0.496633 | − | 0.496633i | ||||
\(191\) | −3.48538e6 | − | 3.48538e6i | −0.500207 | − | 0.500207i | 0.411295 | − | 0.911502i | \(-0.365077\pi\) |
−0.911502 | + | 0.411295i | \(0.865077\pi\) | |||||||
\(192\) | −3.34279e6 | −0.472287 | ||||||||
\(193\) | −1.75371e6 | − | 1.75371e6i | −0.243941 | − | 0.243941i | 0.574537 | − | 0.818478i | \(-0.305182\pi\) |
−0.818478 | + | 0.574537i | \(0.805182\pi\) | |||||||
\(194\) | −2.38266e6 | −0.326330 | ||||||||
\(195\) | 8.15423e6 | 1.09971 | ||||||||
\(196\) | − | 3.45626e6i | − | 0.459027i | ||||||
\(197\) | −2.30610e6 | −0.301634 | −0.150817 | − | 0.988562i | \(-0.548190\pi\) | ||||
−0.150817 | + | 0.988562i | \(0.548190\pi\) | |||||||
\(198\) | −3.88742e6 | − | 3.88742e6i | −0.500801 | − | 0.500801i | ||||
\(199\) | −4.43639e6 | + | 4.43639e6i | −0.562951 | + | 0.562951i | −0.930145 | − | 0.367193i | \(-0.880319\pi\) |
0.367193 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(200\) | 4.95077e6 | − | 4.95077e6i | 0.618846 | − | 0.618846i | ||||
\(201\) | 456724. | 0.0562426 | ||||||||
\(202\) | 7.13379e6 | + | 7.13379e6i | 0.865499 | + | 0.865499i | ||||
\(203\) | 2.54132e6 | − | 2.54132e6i | 0.303789 | − | 0.303789i | ||||
\(204\) | 2.48338e6 | + | 2.48338e6i | 0.292518 | + | 0.292518i | ||||
\(205\) | −1.39962e7 | + | 1.39962e7i | −1.62460 | + | 1.62460i | ||||
\(206\) | 2.68347e6i | 0.306970i | ||||||||
\(207\) | −1.31334e6 | − | 1.31334e6i | −0.148070 | − | 0.148070i | ||||
\(208\) | −1.08136e6 | − | 1.08136e6i | −0.120166 | − | 0.120166i | ||||
\(209\) | −8.70083e6 | + | 8.70083e6i | −0.953063 | + | 0.953063i | ||||
\(210\) | − | 2.18675e6i | − | 0.236124i | ||||||
\(211\) | 1.03562e7 | 1.10244 | 0.551220 | − | 0.834360i | \(-0.314163\pi\) | ||||
0.551220 | + | 0.834360i | \(0.314163\pi\) | |||||||
\(212\) | 4.59781e6i | 0.482551i | ||||||||
\(213\) | 8.90196e6i | 0.921185i | ||||||||
\(214\) | −370799. | + | 370799.i | −0.0378353 | + | 0.0378353i | ||||
\(215\) | − | 1.71908e7i | − | 1.72974i | ||||||
\(216\) | 7.39600e6 | − | 7.39600e6i | 0.733898 | − | 0.733898i | ||||
\(217\) | 3.85928e6 | − | 3.85928e6i | 0.377683 | − | 0.377683i | ||||
\(218\) | −860338. | −0.0830423 | ||||||||
\(219\) | −1.90106e6 | −0.180993 | ||||||||
\(220\) | −9.89088e6 | − | 9.89088e6i | −0.928895 | − | 0.928895i | ||||
\(221\) | 1.68211e7i | 1.55839i | ||||||||
\(222\) | 1.35982e6 | − | 4.30283e6i | 0.124286 | − | 0.393274i | ||||
\(223\) | −2.29225e6 | −0.206703 | −0.103352 | − | 0.994645i | \(-0.532957\pi\) | ||||
−0.103352 | + | 0.994645i | \(0.532957\pi\) | |||||||
\(224\) | 3.17932e6 | − | 3.17932e6i | 0.282872 | − | 0.282872i | ||||
\(225\) | 5.91917e6i | 0.519653i | ||||||||
\(226\) | − | 1.39606e7i | − | 1.20942i | ||||||
\(227\) | 1.37947e7 | + | 1.37947e7i | 1.17932 | + | 1.17932i | 0.979917 | + | 0.199408i | \(0.0639018\pi\) |
0.199408 | + | 0.979917i | \(0.436098\pi\) | |||||||
\(228\) | −2.25811e6 | − | 2.25811e6i | −0.190520 | − | 0.190520i | ||||
\(229\) | 1.51636e7 | 1.26268 | 0.631342 | − | 0.775504i | \(-0.282504\pi\) | ||||
0.631342 | + | 0.775504i | \(0.282504\pi\) | |||||||
\(230\) | 2.64493e6 | + | 2.64493e6i | 0.217385 | + | 0.217385i | ||||
\(231\) | −5.58551e6 | −0.453134 | ||||||||
\(232\) | −1.31830e7 | −1.05572 | ||||||||
\(233\) | − | 2.21931e7i | − | 1.75449i | −0.480044 | − | 0.877244i | \(-0.659379\pi\) | ||
0.480044 | − | 0.877244i | \(-0.340621\pi\) | |||||||
\(234\) | 6.83371e6 | 0.533346 | ||||||||
\(235\) | 5.51374e6 | + | 5.51374e6i | 0.424857 | + | 0.424857i | ||||
\(236\) | −3.48085e6 | + | 3.48085e6i | −0.264819 | + | 0.264819i | ||||
\(237\) | 1.01554e6 | − | 1.01554e6i | 0.0762870 | − | 0.0762870i | ||||
\(238\) | 4.51097e6 | 0.334610 | ||||||||
\(239\) | 9.02435e6 | + | 9.02435e6i | 0.661032 | + | 0.661032i | 0.955623 | − | 0.294592i | \(-0.0951836\pi\) |
−0.294592 | + | 0.955623i | \(0.595184\pi\) | |||||||
\(240\) | −1.07306e6 | + | 1.07306e6i | −0.0776231 | + | 0.0776231i | ||||
\(241\) | −1.08267e6 | − | 1.08267e6i | −0.0773476 | − | 0.0773476i | 0.667375 | − | 0.744722i | \(-0.267418\pi\) |
−0.744722 | + | 0.667375i | \(0.767418\pi\) | |||||||
\(242\) | 1.33357e7 | − | 1.33357e7i | 0.940956 | − | 0.940956i | ||||
\(243\) | 1.43182e7i | 0.997857i | ||||||||
\(244\) | −7.64013e6 | − | 7.64013e6i | −0.525934 | − | 0.525934i | ||||
\(245\) | −1.16156e7 | − | 1.16156e7i | −0.789848 | − | 0.789848i | ||||
\(246\) | 7.34380e6 | − | 7.34380e6i | 0.493305 | − | 0.493305i | ||||
\(247\) | − | 1.52952e7i | − | 1.01500i | ||||||
\(248\) | −2.00199e7 | −1.31252 | ||||||||
\(249\) | 1.42710e7i | 0.924390i | ||||||||
\(250\) | 2.18656e6i | 0.139940i | ||||||||
\(251\) | 3.49892e6 | − | 3.49892e6i | 0.221265 | − | 0.221265i | −0.587766 | − | 0.809031i | \(-0.699992\pi\) |
0.809031 | + | 0.587766i | \(0.199992\pi\) | |||||||
\(252\) | 2.31531e6i | 0.144680i | ||||||||
\(253\) | 6.75582e6 | − | 6.75582e6i | 0.417173 | − | 0.417173i | ||||
\(254\) | 2.68218e6 | − | 2.68218e6i | 0.163677 | − | 0.163677i | ||||
\(255\) | 1.66920e7 | 1.00667 | ||||||||
\(256\) | −1.77123e7 | −1.05574 | ||||||||
\(257\) | −7.21253e6 | − | 7.21253e6i | −0.424902 | − | 0.424902i | 0.461986 | − | 0.886887i | \(-0.347137\pi\) |
−0.886887 | + | 0.461986i | \(0.847137\pi\) | |||||||
\(258\) | 9.02001e6i | 0.525228i | ||||||||
\(259\) | 3.37696e6 | + | 6.49761e6i | 0.194369 | + | 0.373985i | ||||
\(260\) | 1.73872e7 | 0.989260 | ||||||||
\(261\) | 7.88084e6 | − | 7.88084e6i | 0.443252 | − | 0.443252i | ||||
\(262\) | 1.01808e7i | 0.566081i | ||||||||
\(263\) | 2.03970e7i | 1.12124i | 0.828073 | + | 0.560620i | \(0.189437\pi\) | ||||
−0.828073 | + | 0.560620i | \(0.810563\pi\) | |||||||
\(264\) | 1.44873e7 | + | 1.44873e7i | 0.787365 | + | 0.787365i | ||||
\(265\) | 1.54521e7 | + | 1.54521e7i | 0.830327 | + | 0.830327i | ||||
\(266\) | −4.10177e6 | −0.217935 | ||||||||
\(267\) | −102755. | − | 102755.i | −0.00539843 | − | 0.00539843i | ||||
\(268\) | 973871. | 0.0505938 | ||||||||
\(269\) | −1.16827e7 | −0.600187 | −0.300094 | − | 0.953910i | \(-0.597018\pi\) | ||||
−0.300094 | + | 0.953910i | \(0.597018\pi\) | |||||||
\(270\) | − | 1.78083e7i | − | 0.904753i | ||||||
\(271\) | −2.01512e7 | −1.01249 | −0.506247 | − | 0.862388i | \(-0.668968\pi\) | ||||
−0.506247 | + | 0.862388i | \(0.668968\pi\) | |||||||
\(272\) | −2.21358e6 | − | 2.21358e6i | −0.109999 | − | 0.109999i | ||||
\(273\) | 4.90940e6 | − | 4.90940e6i | 0.241291 | − | 0.241291i | ||||
\(274\) | −2.57678e6 | + | 2.57678e6i | −0.125264 | + | 0.125264i | ||||
\(275\) | −3.04482e7 | −1.46408 | ||||||||
\(276\) | 1.75333e6 | + | 1.75333e6i | 0.0833942 | + | 0.0833942i | ||||
\(277\) | 2.34769e7 | − | 2.34769e7i | 1.10459 | − | 1.10459i | 0.110741 | − | 0.993849i | \(-0.464678\pi\) |
0.993849 | − | 0.110741i | \(-0.0353225\pi\) | |||||||
\(278\) | −7.17681e6 | − | 7.17681e6i | −0.334039 | − | 0.334039i | ||||
\(279\) | 1.19680e7 | − | 1.19680e7i | 0.551071 | − | 0.551071i | ||||
\(280\) | − | 1.30163e7i | − | 0.592943i | ||||||
\(281\) | −6.58871e6 | − | 6.58871e6i | −0.296949 | − | 0.296949i | 0.542869 | − | 0.839818i | \(-0.317338\pi\) |
−0.839818 | + | 0.542869i | \(0.817338\pi\) | |||||||
\(282\) | −2.89306e6 | − | 2.89306e6i | −0.129006 | − | 0.129006i | ||||
\(283\) | 1.95878e6 | − | 1.95878e6i | 0.0864226 | − | 0.0864226i | −0.662574 | − | 0.748997i | \(-0.730536\pi\) |
0.748997 | + | 0.662574i | \(0.230536\pi\) | |||||||
\(284\) | 1.89816e7i | 0.828664i | ||||||||
\(285\) | −1.51779e7 | −0.655657 | ||||||||
\(286\) | 3.51526e7i | 1.50266i | ||||||||
\(287\) | 1.68533e7i | 0.712917i | ||||||||
\(288\) | 9.85933e6 | − | 9.85933e6i | 0.412734 | − | 0.412734i | ||||
\(289\) | 1.02958e7i | 0.426549i | ||||||||
\(290\) | −1.58712e7 | + | 1.58712e7i | −0.650751 | + | 0.650751i | ||||
\(291\) | −5.30820e6 | + | 5.30820e6i | −0.215411 | + | 0.215411i | ||||
\(292\) | −4.05362e6 | −0.162815 | ||||||||
\(293\) | −2.13990e7 | −0.850729 | −0.425365 | − | 0.905022i | \(-0.639854\pi\) | ||||
−0.425365 | + | 0.905022i | \(0.639854\pi\) | |||||||
\(294\) | 6.09472e6 | + | 6.09472e6i | 0.239835 | + | 0.239835i | ||||
\(295\) | 2.33965e7i | 0.911350i | ||||||||
\(296\) | 8.09413e6 | − | 2.56120e7i | 0.312101 | − | 0.987570i | ||||
\(297\) | −4.54869e7 | −1.73627 | ||||||||
\(298\) | −1.30577e7 | + | 1.30577e7i | −0.493420 | + | 0.493420i | ||||
\(299\) | 1.18761e7i | 0.444284i | ||||||||
\(300\) | − | 7.90217e6i | − | 0.292673i | ||||||
\(301\) | −1.03500e7 | − | 1.03500e7i | −0.379526 | − | 0.379526i | ||||
\(302\) | 1.84527e7 | + | 1.84527e7i | 0.669945 | + | 0.669945i | ||||
\(303\) | 3.17860e7 | 1.14263 | ||||||||
\(304\) | 2.01279e6 | + | 2.01279e6i | 0.0716436 | + | 0.0716436i | ||||
\(305\) | −5.13531e7 | −1.80995 | ||||||||
\(306\) | 1.39889e7 | 0.488223 | ||||||||
\(307\) | − | 4.00238e7i | − | 1.38326i | −0.722252 | − | 0.691630i | \(-0.756893\pi\) | ||
0.722252 | − | 0.691630i | \(-0.243107\pi\) | |||||||
\(308\) | −1.19100e7 | −0.407623 | ||||||||
\(309\) | 5.97836e6 | + | 5.97836e6i | 0.202631 | + | 0.202631i | ||||
\(310\) | −2.41022e7 | + | 2.41022e7i | −0.809042 | + | 0.809042i | ||||
\(311\) | 3.71310e7 | − | 3.71310e7i | 1.23440 | − | 1.23440i | 0.272140 | − | 0.962258i | \(-0.412268\pi\) |
0.962258 | − | 0.272140i | \(-0.0877315\pi\) | |||||||
\(312\) | −2.54673e7 | −0.838532 | ||||||||
\(313\) | −2.46636e7 | − | 2.46636e7i | −0.804310 | − | 0.804310i | 0.179456 | − | 0.983766i | \(-0.442566\pi\) |
−0.983766 | + | 0.179456i | \(0.942566\pi\) | |||||||
\(314\) | 7.16939e6 | − | 7.16939e6i | 0.231576 | − | 0.231576i | ||||
\(315\) | 7.78118e6 | + | 7.78118e6i | 0.248951 | + | 0.248951i | ||||
\(316\) | 2.16543e6 | − | 2.16543e6i | 0.0686250 | − | 0.0686250i | ||||
\(317\) | − | 3.48043e6i | − | 0.109258i | −0.998507 | − | 0.0546292i | \(-0.982602\pi\) | ||
0.998507 | − | 0.0546292i | \(-0.0173977\pi\) | |||||||
\(318\) | −8.10772e6 | − | 8.10772e6i | −0.252126 | − | 0.252126i | ||||
\(319\) | 4.05390e7 | + | 4.05390e7i | 1.24882 | + | 1.24882i | ||||
\(320\) | −2.39548e7 | + | 2.39548e7i | −0.731043 | + | 0.731043i | ||||
\(321\) | 1.65216e6i | 0.0499503i | ||||||||
\(322\) | 3.18485e6 | 0.0953942 | ||||||||
\(323\) | − | 3.13099e7i | − | 0.929126i | ||||||
\(324\) | − | 129835.i | − | 0.00381731i | ||||||
\(325\) | 2.67625e7 | − | 2.67625e7i | 0.779610 | − | 0.779610i | ||||
\(326\) | 199299.i | 0.00575244i | ||||||||
\(327\) | −1.91670e6 | + | 1.91670e6i | −0.0548164 | + | 0.0548164i | ||||
\(328\) | 4.37129e7 | − | 4.37129e7i | 1.23876 | − | 1.23876i | ||||
\(329\) | 6.63929e6 | 0.186438 | ||||||||
\(330\) | 3.48829e7 | 0.970668 | ||||||||
\(331\) | −3.20716e7 | − | 3.20716e7i | −0.884375 | − | 0.884375i | 0.109601 | − | 0.993976i | \(-0.465043\pi\) |
−0.993976 | + | 0.109601i | \(0.965043\pi\) | |||||||
\(332\) | 3.04299e7i | 0.831547i | ||||||||
\(333\) | 1.04722e7 | + | 2.01496e7i | 0.283600 | + | 0.545675i | ||||
\(334\) | 1.40685e7 | 0.377580 | ||||||||
\(335\) | 3.27293e6 | − | 3.27293e6i | 0.0870568 | − | 0.0870568i | ||||
\(336\) | 1.29211e6i | 0.0340630i | ||||||||
\(337\) | − | 1.73634e7i | − | 0.453675i | −0.973933 | − | 0.226838i | \(-0.927161\pi\) | ||
0.973933 | − | 0.226838i | \(-0.0728387\pi\) | |||||||
\(338\) | −1.27484e7 | − | 1.27484e7i | −0.330145 | − | 0.330145i | ||||
\(339\) | −3.11020e7 | − | 3.11020e7i | −0.798343 | − | 0.798343i | ||||
\(340\) | 3.55923e7 | 0.905565 | ||||||||
\(341\) | 6.15631e7 | + | 6.15631e7i | 1.55259 | + | 1.55259i | ||||
\(342\) | −1.27199e7 | −0.317985 | ||||||||
\(343\) | −3.09949e7 | −0.768083 | ||||||||
\(344\) | 5.36903e7i | 1.31893i | ||||||||
\(345\) | 1.17850e7 | 0.286993 | ||||||||
\(346\) | −1.16526e6 | − | 1.16526e6i | −0.0281316 | − | 0.0281316i | ||||
\(347\) | 9.33896e6 | − | 9.33896e6i | 0.223517 | − | 0.223517i | −0.586461 | − | 0.809978i | \(-0.699479\pi\) |
0.809978 | + | 0.586461i | \(0.199479\pi\) | |||||||
\(348\) | −1.05210e7 | + | 1.05210e7i | −0.249644 | + | 0.249644i | ||||
\(349\) | 3.42963e6 | 0.0806809 | 0.0403405 | − | 0.999186i | \(-0.487156\pi\) | ||||
0.0403405 | + | 0.999186i | \(0.487156\pi\) | |||||||
\(350\) | −7.17700e6 | − | 7.17700e6i | −0.167394 | − | 0.167394i | ||||
\(351\) | 3.99808e7 | − | 3.99808e7i | 0.924550 | − | 0.924550i | ||||
\(352\) | 5.07164e7 | + | 5.07164e7i | 1.16284 | + | 1.16284i | ||||
\(353\) | −3.09765e7 | + | 3.09765e7i | −0.704221 | + | 0.704221i | −0.965314 | − | 0.261093i | \(-0.915917\pi\) |
0.261093 | + | 0.965314i | \(0.415917\pi\) | |||||||
\(354\) | − | 1.22762e7i | − | 0.276728i | ||||||
\(355\) | 6.37924e7 | + | 6.37924e7i | 1.42588 | + | 1.42588i | ||||
\(356\) | −219103. | − | 219103.i | −0.00485623 | − | 0.00485623i | ||||
\(357\) | 1.00497e7 | − | 1.00497e7i | 0.220877 | − | 0.220877i | ||||
\(358\) | − | 5.19206e6i | − | 0.113159i | ||||||
\(359\) | −5.08783e7 | −1.09964 | −0.549819 | − | 0.835284i | \(-0.685303\pi\) | ||||
−0.549819 | + | 0.835284i | \(0.685303\pi\) | |||||||
\(360\) | − | 4.03646e7i | − | 0.865153i | ||||||
\(361\) | − | 1.85761e7i | − | 0.394850i | ||||||
\(362\) | 1.82965e7 | − | 1.82965e7i | 0.385694 | − | 0.385694i | ||||
\(363\) | − | 5.94197e7i | − | 1.24225i | ||||||
\(364\) | 1.04683e7 | − | 1.04683e7i | 0.217056 | − | 0.217056i | ||||
\(365\) | −1.36232e7 | + | 1.36232e7i | −0.280156 | + | 0.280156i | ||||
\(366\) | 2.69450e7 | 0.549586 | ||||||||
\(367\) | 3.46776e7 | 0.701536 | 0.350768 | − | 0.936462i | \(-0.385920\pi\) | ||||
0.350768 | + | 0.936462i | \(0.385920\pi\) | |||||||
\(368\) | −1.56285e6 | − | 1.56285e6i | −0.0313597 | − | 0.0313597i | ||||
\(369\) | 5.22634e7i | 1.04020i | ||||||||
\(370\) | −2.10899e7 | − | 4.05792e7i | −0.416361 | − | 0.801121i | ||||
\(371\) | 1.86064e7 | 0.364368 | ||||||||
\(372\) | −1.59774e7 | + | 1.59774e7i | −0.310368 | + | 0.310368i | ||||
\(373\) | − | 8.44038e7i | − | 1.62643i | −0.581963 | − | 0.813215i | \(-0.697715\pi\) | ||
0.581963 | − | 0.813215i | \(-0.302285\pi\) | |||||||
\(374\) | 7.19588e7i | 1.37553i | ||||||||
\(375\) | 4.87132e6 | + | 4.87132e6i | 0.0923746 | + | 0.0923746i | ||||
\(376\) | −1.72205e7 | − | 1.72205e7i | −0.323954 | − | 0.323954i | ||||
\(377\) | −7.12638e7 | −1.32998 | ||||||||
\(378\) | −1.07218e7 | − | 1.07218e7i | −0.198514 | − | 0.198514i | ||||
\(379\) | 2.59764e7 | 0.477157 | 0.238578 | − | 0.971123i | \(-0.423319\pi\) | ||||
0.238578 | + | 0.971123i | \(0.423319\pi\) | |||||||
\(380\) | −3.23637e7 | −0.589804 | ||||||||
\(381\) | − | 1.19510e7i | − | 0.216087i | ||||||
\(382\) | 2.62105e7 | 0.470203 | ||||||||
\(383\) | −4.91806e7 | − | 4.91806e7i | −0.875383 | − | 0.875383i | 0.117670 | − | 0.993053i | \(-0.462457\pi\) |
−0.993053 | + | 0.117670i | \(0.962457\pi\) | |||||||
\(384\) | −1.10115e7 | + | 1.10115e7i | −0.194470 | + | 0.194470i | ||||
\(385\) | −4.00264e7 | + | 4.00264e7i | −0.701397 | + | 0.701397i | ||||
\(386\) | 1.31881e7 | 0.229308 | ||||||||
\(387\) | −3.20962e7 | − | 3.20962e7i | −0.553759 | − | 0.553759i | ||||
\(388\) | −1.13187e7 | + | 1.13187e7i | −0.193776 | + | 0.193776i | ||||
\(389\) | −3.51606e7 | − | 3.51606e7i | −0.597321 | − | 0.597321i | 0.342278 | − | 0.939599i | \(-0.388802\pi\) |
−0.939599 | + | 0.342278i | \(0.888802\pi\) | |||||||
\(390\) | −3.06604e7 | + | 3.06604e7i | −0.516874 | + | 0.516874i | ||||
\(391\) | 2.43108e7i | 0.406696i | ||||||||
\(392\) | 3.62779e7 | + | 3.62779e7i | 0.602260 | + | 0.602260i | ||||
\(393\) | 2.26813e7 | + | 2.26813e7i | 0.373671 | + | 0.373671i | ||||
\(394\) | 8.67110e6 | − | 8.67110e6i | 0.141770 | − | 0.141770i | ||||
\(395\) | − | 1.45549e7i | − | 0.236166i | ||||||
\(396\) | −3.69338e7 | −0.594755 | ||||||||
\(397\) | 6.26764e7i | 1.00169i | 0.865538 | + | 0.500844i | \(0.166977\pi\) | ||||
−0.865538 | + | 0.500844i | \(0.833023\pi\) | |||||||
\(398\) | − | 3.33622e7i | − | 0.529183i | ||||||
\(399\) | −9.13812e6 | + | 9.13812e6i | −0.143859 | + | 0.143859i | ||||
\(400\) | 7.04368e6i | 0.110057i | ||||||||
\(401\) | 3.67643e7 | − | 3.67643e7i | 0.570155 | − | 0.570155i | −0.362017 | − | 0.932172i | \(-0.617912\pi\) |
0.932172 | + | 0.362017i | \(0.117912\pi\) | |||||||
\(402\) | −1.71731e6 | + | 1.71731e6i | −0.0264345 | + | 0.0264345i | ||||
\(403\) | −1.08222e8 | −1.65349 | ||||||||
\(404\) | 6.77771e7 | 1.02787 | ||||||||
\(405\) | −436343. | − | 436343.i | −0.00656845 | − | 0.00656845i | ||||
\(406\) | 1.91111e7i | 0.285566i | ||||||||
\(407\) | −1.03650e8 | + | 5.38691e7i | −1.53739 | + | 0.799017i | ||||
\(408\) | −5.21326e7 | −0.767590 | ||||||||
\(409\) | −5.25407e7 | + | 5.25407e7i | −0.767938 | + | 0.767938i | −0.977743 | − | 0.209805i | \(-0.932717\pi\) |
0.209805 | + | 0.977743i | \(0.432717\pi\) | |||||||
\(410\) | − | 1.05253e8i | − | 1.52715i | ||||||
\(411\) | 1.14814e7i | 0.165374i | ||||||||
\(412\) | 1.27476e7 | + | 1.27476e7i | 0.182280 | + | 0.182280i | ||||
\(413\) | 1.40863e7 | + | 1.40863e7i | 0.199962 | + | 0.199962i | ||||
\(414\) | 9.87649e6 | 0.139188 | ||||||||
\(415\) | 1.02267e8 | + | 1.02267e8i | 1.43084 | + | 1.43084i | ||||
\(416\) | −8.91547e7 | −1.23841 | ||||||||
\(417\) | −3.19776e7 | −0.440999 | ||||||||
\(418\) | − | 6.54313e7i | − | 0.895895i | ||||||
\(419\) | 1.16489e8 | 1.58359 | 0.791794 | − | 0.610788i | \(-0.209147\pi\) | ||||
0.791794 | + | 0.610788i | \(0.209147\pi\) | |||||||
\(420\) | −1.03880e7 | − | 1.03880e7i | −0.140211 | − | 0.140211i | ||||
\(421\) | 1.97811e7 | − | 1.97811e7i | 0.265097 | − | 0.265097i | −0.562024 | − | 0.827121i | \(-0.689977\pi\) |
0.827121 | + | 0.562024i | \(0.189977\pi\) | |||||||
\(422\) | −3.89401e7 | + | 3.89401e7i | −0.518156 | + | 0.518156i | ||||
\(423\) | 2.05890e7 | 0.272028 | ||||||||
\(424\) | −4.82600e7 | − | 4.82600e7i | −0.633125 | − | 0.633125i | ||||
\(425\) | 5.47840e7 | − | 5.47840e7i | 0.713652 | − | 0.713652i | ||||
\(426\) | −3.34720e7 | − | 3.34720e7i | −0.432965 | − | 0.432965i | ||||
\(427\) | −3.09181e7 | + | 3.09181e7i | −0.397126 | + | 0.397126i | ||||
\(428\) | 3.52290e6i | 0.0449334i | ||||||||
\(429\) | 7.83146e7 | + | 7.83146e7i | 0.991906 | + | 0.991906i | ||||
\(430\) | 6.46384e7 | + | 6.46384e7i | 0.812990 | + | 0.812990i | ||||
\(431\) | −2.56941e7 | + | 2.56941e7i | −0.320924 | + | 0.320924i | −0.849121 | − | 0.528198i | \(-0.822868\pi\) |
0.528198 | + | 0.849121i | \(0.322868\pi\) | |||||||
\(432\) | 1.05226e7i | 0.130519i | ||||||||
\(433\) | 5.45999e7 | 0.672556 | 0.336278 | − | 0.941763i | \(-0.390832\pi\) | ||||
0.336278 | + | 0.941763i | \(0.390832\pi\) | |||||||
\(434\) | 2.90223e7i | 0.355028i | ||||||||
\(435\) | 7.07170e7i | 0.859125i | ||||||||
\(436\) | −4.08697e6 | + | 4.08697e6i | −0.0493108 | + | 0.0493108i | ||||
\(437\) | − | 2.21056e7i | − | 0.264885i | ||||||
\(438\) | 7.14809e6 | − | 7.14809e6i | 0.0850683 | − | 0.0850683i | ||||
\(439\) | 6.44076e7 | − | 6.44076e7i | 0.761279 | − | 0.761279i | −0.215275 | − | 0.976554i | \(-0.569065\pi\) |
0.976554 | + | 0.215275i | \(0.0690647\pi\) | |||||||
\(440\) | 2.07635e8 | 2.43749 | ||||||||
\(441\) | −4.33741e7 | −0.505725 | ||||||||
\(442\) | −6.32484e7 | − | 6.32484e7i | −0.732458 | − | 0.732458i | ||||
\(443\) | − | 1.17298e8i | − | 1.34921i | −0.738179 | − | 0.674605i | \(-0.764314\pi\) | ||
0.738179 | − | 0.674605i | \(-0.235686\pi\) | |||||||
\(444\) | −1.39806e7 | − | 2.69000e7i | −0.159726 | − | 0.307329i | ||||
\(445\) | −1.47270e6 | −0.0167122 | ||||||||
\(446\) | 8.61900e6 | − | 8.61900e6i | 0.0971521 | − | 0.0971521i | ||||
\(447\) | 5.81809e7i | 0.651415i | ||||||||
\(448\) | 2.88449e7i | 0.320800i | ||||||||
\(449\) | 1.05146e8 | + | 1.05146e8i | 1.16159 | + | 1.16159i | 0.984127 | + | 0.177464i | \(0.0567894\pi\) |
0.177464 | + | 0.984127i | \(0.443211\pi\) | |||||||
\(450\) | −2.22565e7 | − | 2.22565e7i | −0.244241 | − | 0.244241i | ||||
\(451\) | −2.68843e8 | −2.93068 | ||||||||
\(452\) | −6.63188e7 | − | 6.63188e7i | −0.718160 | − | 0.718160i | ||||
\(453\) | 8.22196e7 | 0.884465 | ||||||||
\(454\) | −1.03738e8 | −1.10858 | ||||||||
\(455\) | − | 7.03626e7i | − | 0.746978i | ||||||
\(456\) | 4.74036e7 | 0.499939 | ||||||||
\(457\) | −479406. | − | 479406.i | −0.00502291 | − | 0.00502291i | 0.704591 | − | 0.709614i | \(-0.251131\pi\) |
−0.709614 | + | 0.704591i | \(0.751131\pi\) | |||||||
\(458\) | −5.70160e7 | + | 5.70160e7i | −0.593472 | + | 0.593472i | ||||
\(459\) | 8.18423e7 | − | 8.18423e7i | 0.846330 | − | 0.846330i | ||||
\(460\) | 2.51291e7 | 0.258168 | ||||||||
\(461\) | −1.10731e8 | − | 1.10731e8i | −1.13023 | − | 1.13023i | −0.990138 | − | 0.140096i | \(-0.955259\pi\) |
−0.140096 | − | 0.990138i | \(-0.544741\pi\) | |||||||
\(462\) | 2.10019e7 | − | 2.10019e7i | 0.212977 | − | 0.212977i | ||||
\(463\) | 9.89639e7 | + | 9.89639e7i | 0.997089 | + | 0.997089i | 0.999996 | − | 0.00290704i | \(-0.000925340\pi\) |
−0.00290704 | + | 0.999996i | \(0.500925\pi\) | |||||||
\(464\) | 9.37802e6 | − | 9.37802e6i | 0.0938766 | − | 0.0938766i | ||||
\(465\) | 1.07392e8i | 1.06810i | ||||||||
\(466\) | 8.34476e7 | + | 8.34476e7i | 0.824624 | + | 0.824624i | ||||
\(467\) | 2.65279e7 | + | 2.65279e7i | 0.260467 | + | 0.260467i | 0.825244 | − | 0.564777i | \(-0.191038\pi\) |
−0.564777 | + | 0.825244i | \(0.691038\pi\) | |||||||
\(468\) | 3.24631e7 | − | 3.24631e7i | 0.316703 | − | 0.316703i | ||||
\(469\) | − | 3.94106e6i | − | 0.0382027i | ||||||
\(470\) | −4.14640e7 | −0.399372 | ||||||||
\(471\) | − | 3.19446e7i | − | 0.305727i | ||||||
\(472\) | − | 7.30721e7i | − | 0.694906i | ||||||
\(473\) | 1.65103e8 | − | 1.65103e8i | 1.56017 | − | 1.56017i | ||||
\(474\) | 7.63697e6i | 0.0717111i | ||||||||
\(475\) | −4.98145e7 | + | 4.98145e7i | −0.464809 | + | 0.464809i | ||||
\(476\) | 2.14290e7 | − | 2.14290e7i | 0.198692 | − | 0.198692i | ||||
\(477\) | 5.77000e7 | 0.531643 | ||||||||
\(478\) | −6.78643e7 | −0.621381 | ||||||||
\(479\) | −6.79102e7 | − | 6.79102e7i | −0.617915 | − | 0.617915i | 0.327081 | − | 0.944996i | \(-0.393935\pi\) |
−0.944996 | + | 0.327081i | \(0.893935\pi\) | |||||||
\(480\) | 8.84706e7i | 0.799973i | ||||||||
\(481\) | 4.37547e7 | − | 1.38451e8i | 0.393178 | − | 1.24412i | ||||
\(482\) | 8.14185e6 | 0.0727080 | ||||||||
\(483\) | 7.09536e6 | − | 7.09536e6i | 0.0629699 | − | 0.0629699i | ||||
\(484\) | − | 1.26700e8i | − | 1.11749i | ||||||
\(485\) | 7.60783e7i | 0.666862i | ||||||||
\(486\) | −5.38372e7 | − | 5.38372e7i | −0.469001 | − | 0.469001i | ||||
\(487\) | 7.26355e7 | + | 7.26355e7i | 0.628872 | + | 0.628872i | 0.947784 | − | 0.318912i | \(-0.103318\pi\) |
−0.318912 | + | 0.947784i | \(0.603318\pi\) | |||||||
\(488\) | 1.60386e8 | 1.38009 | ||||||||
\(489\) | 444007. | + | 444007.i | 0.00379720 | + | 0.00379720i | ||||
\(490\) | 8.73508e7 | 0.742470 | ||||||||
\(491\) | −1.23106e8 | −1.04001 | −0.520003 | − | 0.854164i | \(-0.674069\pi\) | ||||
−0.520003 | + | 0.854164i | \(0.674069\pi\) | |||||||
\(492\) | − | 6.97723e7i | − | 0.585852i | ||||||
\(493\) | −1.45880e8 | −1.21746 | ||||||||
\(494\) | 5.75111e7 | + | 5.75111e7i | 0.477057 | + | 0.477057i | ||||
\(495\) | −1.24125e8 | + | 1.24125e8i | −1.02340 | + | 1.02340i | ||||
\(496\) | 1.42416e7 | − | 1.42416e7i | 0.116711 | − | 0.116711i | ||||
\(497\) | 7.68148e7 | 0.625714 | ||||||||
\(498\) | −5.36597e7 | − | 5.36597e7i | −0.434471 | − | 0.434471i | ||||
\(499\) | −1.25627e8 | + | 1.25627e8i | −1.01107 | + | 1.01107i | −0.0111321 | + | 0.999938i | \(0.503544\pi\) |
−0.999938 | + | 0.0111321i | \(0.996456\pi\) | |||||||
\(500\) | 1.03871e7 | + | 1.03871e7i | 0.0830968 | + | 0.0830968i | ||||
\(501\) | 3.13425e7 | − | 3.13425e7i | 0.249242 | − | 0.249242i | ||||
\(502\) | 2.63123e7i | 0.207993i | ||||||||
\(503\) | 1.17901e8 | + | 1.17901e8i | 0.926430 | + | 0.926430i | 0.997473 | − | 0.0710428i | \(-0.0226327\pi\) |
−0.0710428 | + | 0.997473i | \(0.522633\pi\) | |||||||
\(504\) | −2.43022e7 | − | 2.43022e7i | −0.189825 | − | 0.189825i | ||||
\(505\) | 2.27782e8 | − | 2.27782e8i | 1.76866 | − | 1.76866i | ||||
\(506\) | 5.08047e7i | 0.392150i | ||||||||
\(507\) | −5.68029e7 | −0.435859 | ||||||||
\(508\) | − | 2.54830e7i | − | 0.194384i | ||||||
\(509\) | 1.50645e8i | 1.14236i | 0.820826 | + | 0.571178i | \(0.193513\pi\) | ||||
−0.820826 | + | 0.571178i | \(0.806487\pi\) | |||||||
\(510\) | −6.27631e7 | + | 6.27631e7i | −0.473144 | + | 0.473144i | ||||
\(511\) | 1.64042e7i | 0.122939i | ||||||||
\(512\) | 2.45349e7 | − | 2.45349e7i | 0.182799 | − | 0.182799i | ||||
\(513\) | −7.44183e7 | + | 7.44183e7i | −0.551224 | + | 0.551224i | ||||
\(514\) | 5.42392e7 | 0.399414 | ||||||||
\(515\) | 8.56831e7 | 0.627298 | ||||||||
\(516\) | 4.28489e7 | + | 4.28489e7i | 0.311882 | + | 0.311882i | ||||
\(517\) | 1.05910e8i | 0.766415i | ||||||||
\(518\) | −3.71290e7 | − | 1.17338e7i | −0.267131 | − | 0.0844211i | ||||
\(519\) | −5.19204e6 | −0.0371395 | ||||||||
\(520\) | −1.82502e8 | + | 1.82502e8i | −1.29795 | + | 1.29795i | ||||
\(521\) | 1.37423e8i | 0.971731i | 0.874034 | + | 0.485866i | \(0.161496\pi\) | ||||
−0.874034 | + | 0.485866i | \(0.838504\pi\) | |||||||
\(522\) | 5.92650e7i | 0.416664i | ||||||||
\(523\) | −1.43205e8 | − | 1.43205e8i | −1.00104 | − | 1.00104i | −0.999999 | − | 0.00104303i | \(-0.999668\pi\) |
−0.00104303 | − | 0.999999i | \(-0.500332\pi\) | |||||||
\(524\) | 4.83632e7 | + | 4.83632e7i | 0.336141 | + | 0.336141i | ||||
\(525\) | −3.19785e7 | −0.220994 | ||||||||
\(526\) | −7.66940e7 | − | 7.66940e7i | −0.526992 | − | 0.526992i | ||||
\(527\) | −2.21535e8 | −1.51360 | ||||||||
\(528\) | −2.06117e7 | −0.140027 | ||||||||
\(529\) | − | 1.30872e8i | − | 0.884055i | ||||||
\(530\) | −1.16202e8 | −0.780521 | ||||||||
\(531\) | 4.36828e7 | + | 4.36828e7i | 0.291760 | + | 0.291760i | ||||
\(532\) | −1.94852e7 | + | 1.94852e7i | −0.129411 | + | 0.129411i | ||||
\(533\) | 2.36300e8 | − | 2.36300e8i | 1.56057 | − | 1.56057i | ||||
\(534\) | 772728. | 0.00507461 | ||||||||
\(535\) | 1.18396e7 | + | 1.18396e7i | 0.0773170 | + | 0.0773170i | ||||
\(536\) | −1.02220e7 | + | 1.02220e7i | −0.0663809 | + | 0.0663809i | ||||
\(537\) | −1.15671e7 | − | 1.15671e7i | −0.0746968 | − | 0.0746968i | ||||
\(538\) | 4.39278e7 | − | 4.39278e7i | 0.282093 | − | 0.282093i | ||||
\(539\) | − | 2.23116e8i | − | 1.42484i | ||||||
\(540\) | −8.45968e7 | − | 8.45968e7i | −0.537246 | − | 0.537246i | ||||
\(541\) | 3.55962e7 | + | 3.55962e7i | 0.224808 | + | 0.224808i | 0.810520 | − | 0.585712i | \(-0.199185\pi\) |
−0.585712 | + | 0.810520i | \(0.699185\pi\) | |||||||
\(542\) | 7.57698e7 | − | 7.57698e7i | 0.475881 | − | 0.475881i | ||||
\(543\) | − | 8.15235e7i | − | 0.509194i | ||||||
\(544\) | −1.82503e8 | −1.13364 | ||||||||
\(545\) | 2.74705e7i | 0.169698i | ||||||||
\(546\) | 3.69193e7i | 0.226817i | ||||||||
\(547\) | 6.48912e7 | − | 6.48912e7i | 0.396482 | − | 0.396482i | −0.480508 | − | 0.876990i | \(-0.659548\pi\) |
0.876990 | + | 0.480508i | \(0.159548\pi\) | |||||||
\(548\) | 2.44817e7i | 0.148764i | ||||||||
\(549\) | −9.58794e7 | + | 9.58794e7i | −0.579440 | + | 0.579440i | ||||
\(550\) | 1.14487e8 | − | 1.14487e8i | 0.688128 | − | 0.688128i | ||||
\(551\) | 1.32647e8 | 0.792944 | ||||||||
\(552\) | −3.68069e7 | −0.218833 | ||||||||
\(553\) | −8.76304e6 | − | 8.76304e6i | −0.0518179 | − | 0.0518179i | ||||
\(554\) | 1.76549e8i | 1.03833i | ||||||||
\(555\) | −1.37389e8 | − | 4.34190e7i | −0.803662 | − | 0.253981i | ||||
\(556\) | −6.81858e7 | −0.396707 | ||||||||
\(557\) | 6.90202e7 | − | 6.90202e7i | 0.399402 | − | 0.399402i | −0.478620 | − | 0.878022i | \(-0.658863\pi\) |
0.878022 | + | 0.478620i | \(0.158863\pi\) | |||||||
\(558\) | 9.00006e7i | 0.518015i | ||||||||
\(559\) | 2.90235e8i | 1.66156i | ||||||||
\(560\) | 9.25942e6 | + | 9.25942e6i | 0.0527254 | + | 0.0527254i | ||||
\(561\) | 1.60313e8 | + | 1.60313e8i | 0.907988 | + | 0.907988i | ||||
\(562\) | 4.95480e7 | 0.279137 | ||||||||
\(563\) | 1.33390e8 | + | 1.33390e8i | 0.747480 | + | 0.747480i | 0.974005 | − | 0.226525i | \(-0.0727366\pi\) |
−0.226525 | + | 0.974005i | \(0.572737\pi\) | |||||||
\(564\) | −2.74866e7 | −0.153209 | ||||||||
\(565\) | −4.45761e8 | −2.47148 | ||||||||
\(566\) | 1.47303e7i | 0.0812386i | ||||||||
\(567\) | −525417. | −0.00288240 | ||||||||
\(568\) | −1.99237e8 | − | 1.99237e8i | −1.08724 | − | 1.08724i | ||||
\(569\) | −1.87892e8 | + | 1.87892e8i | −1.01993 | + | 1.01993i | −0.0201361 | + | 0.999797i | \(0.506410\pi\) |
−0.999797 | + | 0.0201361i | \(0.993590\pi\) | |||||||
\(570\) | 5.70698e7 | − | 5.70698e7i | 0.308164 | − | 0.308164i | ||||
\(571\) | −1.88315e8 | −1.01152 | −0.505762 | − | 0.862673i | \(-0.668789\pi\) | ||||
−0.505762 | + | 0.862673i | \(0.668789\pi\) | |||||||
\(572\) | 1.66990e8 | + | 1.66990e8i | 0.892282 | + | 0.892282i | ||||
\(573\) | 5.83929e7 | − | 5.83929e7i | 0.310382 | − | 0.310382i | ||||
\(574\) | −6.33694e7 | − | 6.33694e7i | −0.335077 | − | 0.335077i | ||||
\(575\) | 3.86788e7 | − | 3.86788e7i | 0.203456 | − | 0.203456i | ||||
\(576\) | 8.94502e7i | 0.468074i | ||||||||
\(577\) | −4.09177e7 | − | 4.09177e7i | −0.213002 | − | 0.213002i | 0.592540 | − | 0.805541i | \(-0.298125\pi\) |
−0.805541 | + | 0.592540i | \(0.798125\pi\) | |||||||
\(578\) | −3.87130e7 | − | 3.87130e7i | −0.200481 | − | 0.200481i | ||||
\(579\) | 2.93810e7 | − | 2.93810e7i | 0.151367 | − | 0.151367i | ||||
\(580\) | 1.50790e8i | 0.772837i | ||||||||
\(581\) | 1.23144e8 | 0.627890 | ||||||||
\(582\) | − | 3.99184e7i | − | 0.202490i | ||||||
\(583\) | 2.96809e8i | 1.49786i | ||||||||
\(584\) | 4.25480e7 | − | 4.25480e7i | 0.213619 | − | 0.213619i | ||||
\(585\) | − | 2.18200e8i | − | 1.08990i | ||||||
\(586\) | 8.04618e7 | − | 8.04618e7i | 0.399850 | − | 0.399850i | ||||
\(587\) | −2.85429e7 | + | 2.85429e7i | −0.141119 | + | 0.141119i | −0.774137 | − | 0.633018i | \(-0.781816\pi\) |
0.633018 | + | 0.774137i | \(0.281816\pi\) | |||||||
\(588\) | 5.79050e7 | 0.284829 | ||||||||
\(589\) | 2.01439e8 | 0.985823 | ||||||||
\(590\) | −8.79724e7 | − | 8.79724e7i | −0.428342 | − | 0.428342i | ||||
\(591\) | − | 3.86357e7i | − | 0.187166i | ||||||
\(592\) | 1.24617e7 | + | 2.39776e7i | 0.0600637 | + | 0.115569i | ||||
\(593\) | −1.04143e8 | −0.499418 | −0.249709 | − | 0.968321i | \(-0.580335\pi\) | ||||
−0.249709 | + | 0.968321i | \(0.580335\pi\) | |||||||
\(594\) | 1.71034e8 | − | 1.71034e8i | 0.816060 | − | 0.816060i | ||||
\(595\) | − | 1.44035e8i | − | 0.683781i | ||||||
\(596\) | 1.24059e8i | 0.585989i | ||||||||
\(597\) | −7.43259e7 | − | 7.43259e7i | −0.349315 | − | 0.349315i | ||||
\(598\) | −4.46549e7 | − | 4.46549e7i | −0.208817 | − | 0.208817i | ||||
\(599\) | 2.29928e8 | 1.06982 | 0.534910 | − | 0.844909i | \(-0.320345\pi\) | ||||
0.534910 | + | 0.844909i | \(0.320345\pi\) | |||||||
\(600\) | 8.29436e7 | + | 8.29436e7i | 0.383998 | + | 0.383998i | ||||
\(601\) | 2.41273e8 | 1.11144 | 0.555718 | − | 0.831371i | \(-0.312443\pi\) | ||||
0.555718 | + | 0.831371i | \(0.312443\pi\) | |||||||
\(602\) | 7.78334e7 | 0.356760 | ||||||||
\(603\) | − | 1.22215e7i | − | 0.0557409i | ||||||
\(604\) | 1.75317e8 | 0.795632 | ||||||||
\(605\) | −4.25808e8 | − | 4.25808e8i | −1.92286 | − | 1.92286i | ||||
\(606\) | −1.19517e8 | + | 1.19517e8i | −0.537048 | + | 0.537048i | ||||
\(607\) | 1.15529e8 | − | 1.15529e8i | 0.516567 | − | 0.516567i | −0.399964 | − | 0.916531i | \(-0.630977\pi\) |
0.916531 | + | 0.399964i | \(0.130977\pi\) | |||||||
\(608\) | 1.65948e8 | 0.738349 | ||||||||
\(609\) | 4.25765e7 | + | 4.25765e7i | 0.188503 | + | 0.188503i | ||||
\(610\) | 1.93091e8 | − | 1.93091e8i | 0.850692 | − | 0.850692i | ||||
\(611\) | −9.30897e7 | − | 9.30897e7i | −0.408111 | − | 0.408111i | ||||
\(612\) | 6.64531e7 | − | 6.64531e7i | 0.289909 | − | 0.289909i | ||||
\(613\) | 2.89941e8i | 1.25872i | 0.777115 | + | 0.629359i | \(0.216683\pi\) | ||||
−0.777115 | + | 0.629359i | \(0.783317\pi\) | |||||||
\(614\) | 1.50492e8 | + | 1.50492e8i | 0.650143 | + | 0.650143i | ||||
\(615\) | −2.34487e8 | − | 2.34487e8i | −1.00808 | − | 1.00808i | ||||
\(616\) | 1.25011e8 | − | 1.25011e8i | 0.534816 | − | 0.534816i | ||||
\(617\) | − | 4.32007e8i | − | 1.83922i | −0.392827 | − | 0.919612i | \(-0.628503\pi\) | ||
0.392827 | − | 0.919612i | \(-0.371497\pi\) | |||||||
\(618\) | −4.49580e7 | −0.190477 | ||||||||
\(619\) | 2.41010e8i | 1.01616i | 0.861310 | + | 0.508081i | \(0.169645\pi\) | ||||
−0.861310 | + | 0.508081i | \(0.830355\pi\) | |||||||
\(620\) | 2.28991e8i | 0.960824i | ||||||||
\(621\) | 5.77827e7 | − | 5.77827e7i | 0.241281 | − | 0.241281i | ||||
\(622\) | 2.79230e8i | 1.16035i | ||||||||
\(623\) | −886666. | + | 886666.i | −0.00366687 | + | 0.00366687i | ||||
\(624\) | 1.81168e7 | − | 1.81168e7i | 0.0745635 | − | 0.0745635i | ||||
\(625\) | 2.76116e8 | 1.13097 | ||||||||
\(626\) | 1.85474e8 | 0.756065 | ||||||||
\(627\) | −1.45771e8 | − | 1.45771e8i | −0.591382 | − | 0.591382i | ||||
\(628\) | − | 6.81153e7i | − | 0.275021i | ||||||
\(629\) | 8.95676e7 | − | 2.83416e8i | 0.359914 | − | 1.13886i | ||||
\(630\) | −5.85155e7 | −0.234018 | ||||||||
\(631\) | −1.52340e8 | + | 1.52340e8i | −0.606353 | + | 0.606353i | −0.941991 | − | 0.335638i | \(-0.891048\pi\) |
0.335638 | + | 0.941991i | \(0.391048\pi\) | |||||||
\(632\) | 4.54579e7i | 0.180077i | ||||||||
\(633\) | 1.73505e8i | 0.684071i | ||||||||
\(634\) | 1.30866e7 | + | 1.30866e7i | 0.0513523 | + | 0.0513523i | ||||
\(635\) | −8.56419e7 | − | 8.56419e7i | −0.334476 | − | 0.334476i | ||||
\(636\) | −7.70303e7 | −0.299426 | ||||||||
\(637\) | 1.96109e8 | + | 1.96109e8i | 0.758715 | + | 0.758715i | ||||
\(638\) | −3.04859e8 | −1.17392 | ||||||||
\(639\) | 2.38209e8 | 0.912968 | ||||||||
\(640\) | 1.57819e8i | 0.602033i | ||||||||
\(641\) | −4.97303e7 | −0.188820 | −0.0944098 | − | 0.995533i | \(-0.530096\pi\) | ||||
−0.0944098 | + | 0.995533i | \(0.530096\pi\) | |||||||
\(642\) | −6.21224e6 | − | 6.21224e6i | −0.0234770 | − | 0.0234770i | ||||
\(643\) | −1.41496e8 | + | 1.41496e8i | −0.532243 | + | 0.532243i | −0.921239 | − | 0.388996i | \(-0.872822\pi\) |
0.388996 | + | 0.921239i | \(0.372822\pi\) | |||||||
\(644\) | 1.51294e7 | − | 1.51294e7i | 0.0566454 | − | 0.0566454i | ||||
\(645\) | 2.88008e8 | 1.07331 | ||||||||
\(646\) | 1.17727e8 | + | 1.17727e8i | 0.436697 | + | 0.436697i | ||||
\(647\) | −4.77205e7 | + | 4.77205e7i | −0.176195 | + | 0.176195i | −0.789695 | − | 0.613500i | \(-0.789761\pi\) |
0.613500 | + | 0.789695i | \(0.289761\pi\) | |||||||
\(648\) | 1.36279e6 | + | 1.36279e6i | 0.00500846 | + | 0.00500846i | ||||
\(649\) | −2.24704e8 | + | 2.24704e8i | −0.822009 | + | 0.822009i | ||||
\(650\) | 2.01258e8i | 0.732846i | ||||||||
\(651\) | 6.46572e7 | + | 6.46572e7i | 0.234355 | + | 0.234355i | ||||
\(652\) | 946755. | + | 946755.i | 0.00341582 | + | 0.00341582i | ||||
\(653\) | 2.03794e7 | − | 2.03794e7i | 0.0731898 | − | 0.0731898i | −0.669564 | − | 0.742754i | \(-0.733519\pi\) |
0.742754 | + | 0.669564i | \(0.233519\pi\) | |||||||
\(654\) | − | 1.44138e7i | − | 0.0515283i | ||||||
\(655\) | 3.25073e8 | 1.15680 | ||||||||
\(656\) | 6.21922e7i | 0.220305i | ||||||||
\(657\) | 5.08706e7i | 0.179379i | ||||||||
\(658\) | −2.49642e7 | + | 2.49642e7i | −0.0876273 | + | 0.0876273i | ||||
\(659\) | − | 1.10279e8i | − | 0.385334i | −0.981264 | − | 0.192667i | \(-0.938286\pi\) | ||
0.981264 | − | 0.192667i | \(-0.0617138\pi\) | |||||||
\(660\) | 1.65709e8 | − | 1.65709e8i | 0.576386 | − | 0.576386i | ||||
\(661\) | 1.88109e8 | − | 1.88109e8i | 0.651337 | − | 0.651337i | −0.301978 | − | 0.953315i | \(-0.597647\pi\) |
0.953315 | + | 0.301978i | \(0.0976469\pi\) | |||||||
\(662\) | 2.41182e8 | 0.831326 | ||||||||
\(663\) | −2.81815e8 | −0.966994 | ||||||||
\(664\) | −3.19402e8 | − | 3.19402e8i | −1.09102 | − | 1.09102i | ||||
\(665\) | 1.30969e8i | 0.445354i | ||||||||
\(666\) | −1.15140e8 | − | 3.63876e7i | −0.389766 | − | 0.123177i | ||||
\(667\) | −1.02995e8 | −0.347086 | ||||||||
\(668\) | 6.68315e7 | − | 6.68315e7i | 0.224208 | − | 0.224208i | ||||
\(669\) | − | 3.84036e7i | − | 0.128261i | ||||||
\(670\) | 2.46129e7i | 0.0818348i | ||||||||
\(671\) | −4.93204e8 | − | 4.93204e8i | −1.63252 | − | 1.63252i | ||||
\(672\) | 5.32653e7 | + | 5.32653e7i | 0.175524 | + | 0.175524i | ||||
\(673\) | −2.96667e8 | −0.973248 | −0.486624 | − | 0.873612i | \(-0.661772\pi\) | ||||
−0.486624 | + | 0.873612i | \(0.661772\pi\) | |||||||
\(674\) | 6.52875e7 | + | 6.52875e7i | 0.213231 | + | 0.213231i | ||||
\(675\) | −2.60424e8 | −0.846778 | ||||||||
\(676\) | −1.21121e8 | −0.392083 | ||||||||
\(677\) | − | 5.26403e6i | − | 0.0169649i | −0.999964 | − | 0.00848247i | \(-0.997300\pi\) | ||
0.999964 | − | 0.00848247i | \(-0.00270009\pi\) | |||||||
\(678\) | 2.33891e8 | 0.750455 | ||||||||
\(679\) | 4.58043e7 | + | 4.58043e7i | 0.146318 | + | 0.146318i | ||||
\(680\) | −3.73588e8 | + | 3.73588e8i | −1.18814 | + | 1.18814i | ||||
\(681\) | −2.31111e8 | + | 2.31111e8i | −0.731779 | + | 0.731779i | ||||
\(682\) | −4.62963e8 | −1.45946 | ||||||||
\(683\) | 9.90831e7 | + | 9.90831e7i | 0.310983 | + | 0.310983i | 0.845290 | − | 0.534307i | \(-0.179427\pi\) |
−0.534307 | + | 0.845290i | \(0.679427\pi\) | |||||||
\(684\) | −6.04251e7 | + | 6.04251e7i | −0.188821 | + | 0.188821i | ||||
\(685\) | 8.22766e7 | + | 8.22766e7i | 0.255979 | + | 0.255979i | ||||
\(686\) | 1.16543e8 | − | 1.16543e8i | 0.361005 | − | 0.361005i | ||||
\(687\) | 2.54046e8i | 0.783504i | ||||||||
\(688\) | −3.81938e7 | − | 3.81938e7i | −0.117281 | − | 0.117281i | ||||
\(689\) | −2.60881e8 | − | 2.60881e8i | −0.797599 | − | 0.797599i | ||||
\(690\) | −4.43123e7 | + | 4.43123e7i | −0.134889 | + | 0.134889i | ||||
\(691\) | − | 4.06283e8i | − | 1.23139i | −0.787986 | − | 0.615693i | \(-0.788876\pi\) | ||
0.787986 | − | 0.615693i | \(-0.211124\pi\) | |||||||
\(692\) | −1.10710e7 | −0.0334093 | ||||||||
\(693\) | 1.49463e8i | 0.449092i | ||||||||
\(694\) | 7.02302e7i | 0.210109i | ||||||||
\(695\) | −2.29155e8 | + | 2.29155e8i | −0.682614 | + | 0.682614i | ||||
\(696\) | − | 2.20864e8i | − | 0.655084i | ||||||
\(697\) | 4.83716e8 | − | 4.83716e8i | 1.42854 | − | 1.42854i | ||||
\(698\) | −1.28956e7 | + | 1.28956e7i | −0.0379207 | + | 0.0379207i | ||||
\(699\) | 3.71816e8 | 1.08867 | ||||||||
\(700\) | −6.81876e7 | −0.198798 | ||||||||
\(701\) | 3.25174e8 | + | 3.25174e8i | 0.943977 | + | 0.943977i | 0.998512 | − | 0.0545347i | \(-0.0173676\pi\) |
−0.0545347 | + | 0.998512i | \(0.517368\pi\) | |||||||
\(702\) | 3.00661e8i | 0.869092i | ||||||||
\(703\) | −8.14429e7 | + | 2.57707e8i | −0.234416 | + | 0.741754i | ||||
\(704\) | −4.60132e8 | −1.31876 | ||||||||
\(705\) | −9.23754e7 | + | 9.23754e7i | −0.263626 | + | 0.263626i | ||||
\(706\) | − | 2.32948e8i | − | 0.661979i | ||||||
\(707\) | − | 2.74280e8i | − | 0.776133i | ||||||
\(708\) | −5.83171e7 | − | 5.83171e7i | −0.164322 | − | 0.164322i | ||||
\(709\) | −3.03383e8 | − | 3.03383e8i | −0.851241 | − | 0.851241i | 0.139045 | − | 0.990286i | \(-0.455597\pi\) |
−0.990286 | + | 0.139045i | \(0.955597\pi\) | |||||||
\(710\) | −4.79727e8 | −1.34035 | ||||||||
\(711\) | −2.71749e7 | − | 2.71749e7i | −0.0756065 | − | 0.0756065i | ||||
\(712\) | 4.59955e6 | 0.0127431 | ||||||||
\(713\) | −1.56409e8 | −0.431513 | ||||||||
\(714\) | 7.55753e7i | 0.207628i | ||||||||
\(715\) | 1.12242e9 | 3.07070 | ||||||||
\(716\) | −2.46645e7 | − | 2.46645e7i | −0.0671945 | − | 0.0671945i | ||||
\(717\) | −1.51191e8 | + | 1.51191e8i | −0.410175 | + | 0.410175i | ||||
\(718\) | 1.91306e8 | − | 1.91306e8i | 0.516839 | − | 0.516839i | ||||
\(719\) | −5.24884e8 | −1.41214 | −0.706069 | − | 0.708143i | \(-0.749533\pi\) | ||||
−0.706069 | + | 0.708143i | \(0.749533\pi\) | |||||||
\(720\) | 2.87142e7 | + | 2.87142e7i | 0.0769307 | + | 0.0769307i | ||||
\(721\) | 5.15871e7 | − | 5.15871e7i | 0.137637 | − | 0.137637i | ||||
\(722\) | 6.98473e7 | + | 6.98473e7i | 0.185583 | + | 0.185583i | ||||
\(723\) | 1.81388e7 | − | 1.81388e7i | 0.0479947 | − | 0.0479947i | ||||
\(724\) | − | 1.73832e8i | − | 0.458052i | ||||||
\(725\) | 2.32097e8 | + | 2.32097e8i | 0.609052 | + | 0.609052i | ||||
\(726\) | 2.23422e8 | + | 2.23422e8i | 0.583869 | + | 0.583869i | ||||
\(727\) | −1.39935e8 | + | 1.39935e8i | −0.364186 | + | 0.364186i | −0.865351 | − | 0.501166i | \(-0.832905\pi\) |
0.501166 | + | 0.865351i | \(0.332905\pi\) | |||||||
\(728\) | 2.19757e8i | 0.569572i | ||||||||
\(729\) | −2.42531e8 | −0.626016 | ||||||||
\(730\) | − | 1.02448e8i | − | 0.263351i | ||||||
\(731\) | 5.94123e8i | 1.52098i | ||||||||
\(732\) | 1.28000e8 | − | 1.28000e8i | 0.326346 | − | 0.326346i | ||||
\(733\) | 1.98525e7i | 0.0504084i | 0.999682 | + | 0.0252042i | \(0.00802359\pi\) | ||||
−0.999682 | + | 0.0252042i | \(0.991976\pi\) | |||||||
\(734\) | −1.30390e8 | + | 1.30390e8i | −0.329728 | + | 0.329728i | ||||
\(735\) | 1.94604e8 | − | 1.94604e8i | 0.490106 | − | 0.490106i | ||||
\(736\) | −1.28852e8 | −0.323189 | ||||||||
\(737\) | 6.28676e7 | 0.157045 | ||||||||
\(738\) | −1.96514e8 | − | 1.96514e8i | −0.488904 | − | 0.488904i | ||||
\(739\) | − | 1.35098e8i | − | 0.334747i | −0.985894 | − | 0.167374i | \(-0.946471\pi\) | ||
0.985894 | − | 0.167374i | \(-0.0535286\pi\) | |||||||
\(740\) | −2.92954e8 | − | 9.25822e7i | −0.722945 | − | 0.228472i | ||||
\(741\) | 2.56252e8 | 0.629813 | ||||||||
\(742\) | −6.99613e7 | + | 6.99613e7i | −0.171256 | + | 0.171256i | ||||
\(743\) | 6.52884e8i | 1.59173i | 0.605474 | + | 0.795865i | \(0.292984\pi\) | ||||
−0.605474 | + | 0.795865i | \(0.707016\pi\) | |||||||
\(744\) | − | 3.35407e8i | − | 0.814429i | ||||||
\(745\) | 4.16931e8 | + | 4.16931e8i | 1.00831 | + | 1.00831i | ||||
\(746\) | 3.17364e8 | + | 3.17364e8i | 0.764436 | + | 0.764436i | ||||
\(747\) | 3.81879e8 | 0.916144 | ||||||||
\(748\) | 3.41835e8 | + | 3.41835e8i | 0.816792 | + | 0.816792i | ||||
\(749\) | 1.42565e7 | 0.0339287 | ||||||||
\(750\) | −3.66329e7 | −0.0868336 | ||||||||
\(751\) | − | 3.99546e8i | − | 0.943293i | −0.881788 | − | 0.471646i | \(-0.843660\pi\) | ||
0.881788 | − | 0.471646i | \(-0.156340\pi\) | |||||||
\(752\) | 2.45004e7 | 0.0576129 | ||||||||
\(753\) | 5.86197e7 | + | 5.86197e7i | 0.137296 | + | 0.137296i | ||||
\(754\) | 2.67957e8 | − | 2.67957e8i | 0.625101 | − | 0.625101i | ||||
\(755\) | 5.89194e8 | − | 5.89194e8i | 1.36904 | − | 1.36904i | ||||
\(756\) | −1.01866e8 | −0.235757 | ||||||||
\(757\) | −5.68457e8 | − | 5.68457e8i | −1.31042 | − | 1.31042i | −0.921106 | − | 0.389311i | \(-0.872713\pi\) |
−0.389311 | − | 0.921106i | \(-0.627287\pi\) | |||||||
\(758\) | −9.76729e7 | + | 9.76729e7i | −0.224268 | + | 0.224268i | ||||
\(759\) | 1.13185e8 | + | 1.13185e8i | 0.258859 | + | 0.258859i | ||||
\(760\) | 3.39700e8 | − | 3.39700e8i | 0.773846 | − | 0.773846i | ||||
\(761\) | − | 1.97791e8i | − | 0.448799i | −0.974497 | − | 0.224399i | \(-0.927958\pi\) | ||
0.974497 | − | 0.224399i | \(-0.0720420\pi\) | |||||||
\(762\) | 4.49364e7 | + | 4.49364e7i | 0.101563 | + | 0.101563i | ||||
\(763\) | 1.65391e7 | + | 1.65391e7i | 0.0372340 | + | 0.0372340i | ||||
\(764\) | 1.24511e8 | − | 1.24511e8i | 0.279208 | − | 0.279208i | ||||
\(765\) | − | 4.46664e8i | − | 0.997693i | ||||||
\(766\) | 3.69845e8 | 0.822874 | ||||||||
\(767\) | − | 3.95009e8i | − | 0.875428i | ||||||
\(768\) | − | 2.96747e8i | − | 0.655092i | ||||||
\(769\) | −1.40592e8 | + | 1.40592e8i | −0.309160 | + | 0.309160i | −0.844584 | − | 0.535424i | \(-0.820152\pi\) |
0.535424 | + | 0.844584i | \(0.320152\pi\) | |||||||
\(770\) | − | 3.01003e8i | − | 0.659325i | ||||||
\(771\) | 1.20836e8 | − | 1.20836e8i | 0.263654 | − | 0.263654i | ||||
\(772\) | 6.26491e7 | − | 6.26491e7i | 0.136164 | − | 0.136164i | ||||
\(773\) | −4.79575e7 | −0.103829 | −0.0519144 | − | 0.998652i | \(-0.516532\pi\) | ||||
−0.0519144 | + | 0.998652i | \(0.516532\pi\) | |||||||
\(774\) | 2.41368e8 | 0.520543 | ||||||||
\(775\) | 3.52465e8 | + | 3.52465e8i | 0.757200 | + | 0.757200i | ||||
\(776\) | − | 2.37608e8i | − | 0.508483i | ||||||
\(777\) | −1.08859e8 | + | 5.65765e7i | −0.232060 | + | 0.120607i | ||||
\(778\) | 2.64412e8 | 0.561491 | ||||||||
\(779\) | −4.39838e8 | + | 4.39838e8i | −0.930422 | + | 0.930422i | ||||
\(780\) | 2.91300e8i | 0.613843i | ||||||||
\(781\) | 1.22535e9i | 2.57221i | ||||||||
\(782\) | −9.14103e7 | − | 9.14103e7i | −0.191150 | − | 0.191150i | ||||
\(783\) | 3.46731e8 | + | 3.46731e8i | 0.722283 | + | 0.722283i | ||||
\(784\) | −5.16142e7 | −0.107108 | ||||||||
\(785\) | −2.28918e8 | − | 2.28918e8i | −0.473229 | − | 0.473229i | ||||
\(786\) | −1.70566e8 | −0.351257 | ||||||||
\(787\) | −7.71103e8 | −1.58193 | −0.790966 | − | 0.611860i | \(-0.790422\pi\) | ||||
−0.790966 | + | 0.611860i | \(0.790422\pi\) | |||||||
\(788\) | − | 8.23829e7i | − | 0.168367i | ||||||
\(789\) | −3.41725e8 | −0.695737 | ||||||||
\(790\) | 5.47274e7 | + | 5.47274e7i | 0.111000 | + | 0.111000i | ||||
\(791\) | −2.68378e8 | + | 2.68378e8i | −0.542273 | + | 0.542273i | ||||
\(792\) | 3.87668e8 | − | 3.87668e8i | 0.780341 | − | 0.780341i | ||||
\(793\) | 8.67006e8 | 1.73861 | ||||||||
\(794\) | −2.35667e8 | − | 2.35667e8i | −0.470801 | − | 0.470801i | ||||
\(795\) | −2.58879e8 | + | 2.58879e8i | −0.515223 | + | 0.515223i | ||||
\(796\) | −1.58485e8 | − | 1.58485e8i | −0.314231 | − | 0.314231i | ||||
\(797\) | −2.75302e8 | + | 2.75302e8i | −0.543794 | + | 0.543794i | −0.924639 | − | 0.380845i | \(-0.875633\pi\) |
0.380845 | + | 0.924639i | \(0.375633\pi\) | |||||||
\(798\) | − | 6.87198e7i | − | 0.135230i | ||||||
\(799\) | −1.90558e8 | − | 1.90558e8i | −0.373583 | − | 0.373583i | ||||
\(800\) | 2.90365e8 | + | 2.90365e8i | 0.567118 | + | 0.567118i | ||||
\(801\) | −2.74962e6 | + | 2.74962e6i | −0.00535027 | + | 0.00535027i | ||||
\(802\) | 2.76472e8i | 0.535955i | ||||||||
\(803\) | −2.61678e8 | −0.505384 | ||||||||
\(804\) | 1.63159e7i | 0.0313938i | ||||||||
\(805\) | − | 1.01692e8i | − | 0.194940i | ||||||
\(806\) | 4.06923e8 | − | 4.06923e8i | 0.777153 | − | 0.777153i | ||||
\(807\) | − | 1.95728e8i | − | 0.372420i | ||||||
\(808\) | −7.11409e8 | + | 7.11409e8i | −1.34861 | + | 1.34861i | ||||
\(809\) | 2.79042e8 | − | 2.79042e8i | 0.527017 | − | 0.527017i | −0.392665 | − | 0.919682i | \(-0.628447\pi\) |
0.919682 | + | 0.392665i | \(0.128447\pi\) | |||||||
\(810\) | 3.28136e6 | 0.00617445 | ||||||||
\(811\) | 5.51370e8 | 1.03367 | 0.516834 | − | 0.856086i | \(-0.327110\pi\) | ||||
0.516834 | + | 0.856086i | \(0.327110\pi\) | |||||||
\(812\) | 9.07857e7 | + | 9.07857e7i | 0.169570 | + | 0.169570i | ||||
\(813\) | − | 3.37607e8i | − | 0.628260i | ||||||
\(814\) | 1.87178e8 | − | 5.92280e8i | 0.347041 | − | 1.09813i | ||||
\(815\) | 6.36360e6 | 0.0117552 | ||||||||
\(816\) | 3.70857e7 | − | 3.70857e7i | 0.0682552 | − | 0.0682552i | ||||
\(817\) | − | 5.40230e8i | − | 0.990632i | ||||||
\(818\) | − | 3.95113e8i | − | 0.721874i | ||||||
\(819\) | −1.31371e8 | − | 1.31371e8i | −0.239138 | − | 0.239138i | ||||
\(820\) | −4.99996e8 | − | 4.99996e8i | −0.906828 | − | 0.906828i | ||||
\(821\) | −1.52983e8 | −0.276449 | −0.138224 | − | 0.990401i | \(-0.544140\pi\) | ||||
−0.138224 | + | 0.990401i | \(0.544140\pi\) | |||||||
\(822\) | −4.31706e7 | − | 4.31706e7i | −0.0777272 | − | 0.0777272i | ||||
\(823\) | 3.33053e8 | 0.597467 | 0.298734 | − | 0.954337i | \(-0.403436\pi\) | ||||
0.298734 | + | 0.954337i | \(0.403436\pi\) | |||||||
\(824\) | −2.67606e8 | −0.478315 | ||||||||
\(825\) | − | 5.10120e8i | − | 0.908469i | ||||||
\(826\) | −1.05931e8 | −0.187967 | ||||||||
\(827\) | 3.89632e8 | + | 3.89632e8i | 0.688870 | + | 0.688870i | 0.961982 | − | 0.273112i | \(-0.0880529\pi\) |
−0.273112 | + | 0.961982i | \(0.588053\pi\) | |||||||
\(828\) | 4.69176e7 | − | 4.69176e7i | 0.0826503 | − | 0.0826503i | ||||
\(829\) | −6.98489e8 | + | 6.98489e8i | −1.22602 | + | 1.22602i | −0.260557 | + | 0.965458i | \(0.583906\pi\) |
−0.965458 | + | 0.260557i | \(0.916094\pi\) | |||||||
\(830\) | −7.69063e8 | −1.34502 | ||||||||
\(831\) | 3.93324e8 | + | 3.93324e8i | 0.685406 | + | 0.685406i | ||||
\(832\) | 4.04434e8 | − | 4.04434e8i | 0.702228 | − | 0.702228i | ||||
\(833\) | 4.01442e8 | + | 4.01442e8i | 0.694526 | + | 0.694526i | ||||
\(834\) | 1.20238e8 | − | 1.20238e8i | 0.207273 | − | 0.207273i | ||||
\(835\) | − | 4.49207e8i | − | 0.771592i | ||||||
\(836\) | −3.10827e8 | − | 3.10827e8i | −0.531985 | − | 0.531985i | ||||
\(837\) | 5.26551e8 | + | 5.26551e8i | 0.897974 | + | 0.897974i | ||||
\(838\) | −4.38005e8 | + | 4.38005e8i | −0.744299 | + | 0.744299i | ||||
\(839\) | 5.66867e8i | 0.959832i | 0.877315 | + | 0.479916i | \(0.159333\pi\) | ||||
−0.877315 | + | 0.479916i | \(0.840667\pi\) | |||||||
\(840\) | 2.18071e8 | 0.367925 | ||||||||
\(841\) | − | 2.32079e7i | − | 0.0390165i | ||||||
\(842\) | 1.48757e8i | 0.249195i | ||||||||
\(843\) | 1.10385e8 | − | 1.10385e8i | 0.184259 | − | 0.184259i | ||||
\(844\) | 3.69965e8i | 0.615365i | ||||||||
\(845\) | −4.07055e8 | + | 4.07055e8i | −0.674657 | + | 0.674657i | ||||
\(846\) | −7.74159e7 | + | 7.74159e7i | −0.127855 | + | 0.127855i | ||||
\(847\) | −5.12731e8 | −0.843799 | ||||||||
\(848\) | 6.86616e7 | 0.112597 | ||||||||
\(849\) | 3.28168e7 | + | 3.28168e7i | 0.0536258 | + | 0.0536258i | ||||
\(850\) | 4.11983e8i | 0.670845i | ||||||||
\(851\) | 6.32369e7 | − | 2.00098e8i | 0.102608 | − | 0.324680i | ||||
\(852\) | −3.18012e8 | −0.514192 | ||||||||
\(853\) | −2.86979e8 | + | 2.86979e8i | −0.462385 | + | 0.462385i | −0.899436 | − | 0.437052i | \(-0.856023\pi\) |
0.437052 | + | 0.899436i | \(0.356023\pi\) | |||||||
\(854\) | − | 2.32508e8i | − | 0.373305i | ||||||
\(855\) | 4.06147e8i | 0.649808i | ||||||||
\(856\) | −3.69775e7 | − | 3.69775e7i | −0.0589543 | − | 0.0589543i | ||||
\(857\) | 1.86706e8 | + | 1.86706e8i | 0.296631 | + | 0.296631i | 0.839693 | − | 0.543062i | \(-0.182735\pi\) |
−0.543062 | + | 0.839693i | \(0.682735\pi\) | |||||||
\(858\) | −5.88936e8 | −0.932408 | ||||||||
\(859\) | −7.37235e8 | − | 7.37235e8i | −1.16313 | − | 1.16313i | −0.983787 | − | 0.179338i | \(-0.942604\pi\) |
−0.179338 | − | 0.983787i | \(-0.557396\pi\) | |||||||
\(860\) | 6.14120e8 | 0.965512 | ||||||||
\(861\) | −2.82354e8 | −0.442370 | ||||||||
\(862\) | − | 1.93223e8i | − | 0.301673i | ||||||
\(863\) | 5.23818e8 | 0.814982 | 0.407491 | − | 0.913209i | \(-0.366404\pi\) | ||||
0.407491 | + | 0.913209i | \(0.366404\pi\) | |||||||
\(864\) | 4.33778e8 | + | 4.33778e8i | 0.672553 | + | 0.672553i | ||||
\(865\) | −3.72067e7 | + | 3.72067e7i | −0.0574874 | + | 0.0574874i | ||||
\(866\) | −2.05299e8 | + | 2.05299e8i | −0.316107 | + | 0.316107i | ||||
\(867\) | −1.72493e8 | −0.264676 | ||||||||
\(868\) | 1.37868e8 | + | 1.37868e8i | 0.210817 | + | 0.210817i | ||||
\(869\) | 1.39788e8 | − | 1.39788e8i | 0.213015 | − | 0.213015i | ||||
\(870\) | −2.65901e8 | − | 2.65901e8i | −0.403796 | − | 0.403796i | ||||
\(871\) | −5.52577e7 | + | 5.52577e7i | −0.0836254 | + | 0.0836254i | ||||
\(872\) | − | 8.57962e7i | − | 0.129395i | ||||||
\(873\) | 1.42043e8 | + | 1.42043e8i | 0.213490 | + | 0.213490i | ||||
\(874\) | 8.31185e7 | + | 8.31185e7i | 0.124498 | + | 0.124498i | ||||
\(875\) | 4.20345e7 | − | 4.20345e7i | 0.0627453 | − | 0.0627453i | ||||
\(876\) | − | 6.79130e7i | − | 0.101028i | ||||||
\(877\) | −3.25164e8 | −0.482063 | −0.241031 | − | 0.970517i | \(-0.577486\pi\) | ||||
−0.241031 | + | 0.970517i | \(0.577486\pi\) | |||||||
\(878\) | 4.84354e8i | 0.715614i | ||||||||
\(879\) | − | 3.58513e8i | − | 0.527883i | ||||||
\(880\) | −1.47706e8 | + | 1.47706e8i | −0.216745 | + | 0.216745i | ||||
\(881\) | 9.22555e8i | 1.34916i | 0.738200 | + | 0.674582i | \(0.235676\pi\) | ||||
−0.738200 | + | 0.674582i | \(0.764324\pi\) | |||||||
\(882\) | 1.63089e8 | − | 1.63089e8i | 0.237695 | − | 0.237695i | ||||
\(883\) | 6.09846e8 | − | 6.09846e8i | 0.885804 | − | 0.885804i | −0.108313 | − | 0.994117i | \(-0.534545\pi\) |
0.994117 | + | 0.108313i | \(0.0345448\pi\) | |||||||
\(884\) | −6.00914e8 | −0.869872 | ||||||||
\(885\) | −3.91978e8 | −0.565499 | ||||||||
\(886\) | 4.41048e8 | + | 4.41048e8i | 0.634140 | + | 0.634140i | ||||
\(887\) | 1.19456e9i | 1.71173i | 0.517199 | + | 0.855865i | \(0.326975\pi\) | ||||
−0.517199 | + | 0.855865i | \(0.673025\pi\) | |||||||
\(888\) | 4.29095e8 | + | 1.35606e8i | 0.612794 | + | 0.193661i | ||||
\(889\) | −1.03125e8 | −0.146777 | ||||||||
\(890\) | 5.53745e6 | − | 5.53745e6i | 0.00785488 | − | 0.00785488i | ||||
\(891\) | − | 8.38143e6i | − | 0.0118491i | ||||||
\(892\) | − | 8.18879e7i | − | 0.115379i | ||||||
\(893\) | 1.73273e8 | + | 1.73273e8i | 0.243319 | + | 0.243319i | ||||
\(894\) | −2.18764e8 | − | 2.18764e8i | −0.306170 | − | 0.306170i | ||||
\(895\) | −1.65782e8 | −0.231243 | ||||||||
\(896\) | 9.50180e7 | + | 9.50180e7i | 0.132094 | + | 0.132094i | ||||
\(897\) | −1.98968e8 | −0.275681 | ||||||||
\(898\) | −7.90711e8 | −1.09191 | ||||||||
\(899\) | − | 9.38551e8i | − | 1.29175i | ||||||
\(900\) | −2.11455e8 | −0.290062 | ||||||||
\(901\) | −5.34033e8 | − | 5.34033e8i | −0.730119 | − | 0.730119i | ||||
\(902\) | 1.01087e9 | − | 1.01087e9i | 1.37744 | − | 1.37744i | ||||
\(903\) | 1.73401e8 | − | 1.73401e8i | 0.235498 | − | 0.235498i | ||||
\(904\) | 1.39220e9 | 1.88451 | ||||||||
\(905\) | −5.84206e8 | − | 5.84206e8i | −0.788171 | − | 0.788171i | ||||
\(906\) | −3.09151e8 | + | 3.09151e8i | −0.415706 | + | 0.415706i | ||||
\(907\) | −3.72181e8 | − | 3.72181e8i | −0.498807 | − | 0.498807i | 0.412259 | − | 0.911067i | \(-0.364740\pi\) |
−0.911067 | + | 0.412259i | \(0.864740\pi\) | |||||||
\(908\) | −4.92798e8 | + | 4.92798e8i | −0.658281 | + | 0.658281i | ||||
\(909\) | − | 8.50565e8i | − | 1.13244i | ||||||
\(910\) | 2.64568e8 | + | 2.64568e8i | 0.351086 | + | 0.351086i | ||||
\(911\) | −2.03352e8 | − | 2.03352e8i | −0.268964 | − | 0.268964i | 0.559719 | − | 0.828683i | \(-0.310909\pi\) |
−0.828683 | + | 0.559719i | \(0.810909\pi\) | |||||||
\(912\) | −3.37216e7 | + | 3.37216e7i | −0.0444553 | + | 0.0444553i | ||||
\(913\) | 1.96438e9i | 2.58115i | ||||||||
\(914\) | 3.60520e6 | 0.00472162 | ||||||||
\(915\) | − | 8.60353e8i | − | 1.12309i | ||||||
\(916\) | 5.41701e8i | 0.704811i | ||||||||
\(917\) | 1.95716e8 | − | 1.95716e8i | 0.253815 | − | 0.253815i | ||||
\(918\) | 6.15464e8i | 0.795564i | ||||||||
\(919\) | 8.24077e8 | − | 8.24077e8i | 1.06175 | − | 1.06175i | 0.0637835 | − | 0.997964i | \(-0.479683\pi\) |
0.997964 | − | 0.0637835i | \(-0.0203167\pi\) | |||||||
\(920\) | −2.63762e8 | + | 2.63762e8i | −0.338727 | + | 0.338727i | ||||
\(921\) | 6.70547e8 | 0.858322 | ||||||||
\(922\) | 8.32715e8 | 1.06244 | ||||||||
\(923\) | −1.07702e9 | − | 1.07702e9i | −1.36968 | − | 1.36968i | ||||
\(924\) | − | 1.99536e8i | − | 0.252933i | ||||||
\(925\) | −5.93420e8 | + | 3.08414e8i | −0.749786 | + | 0.389681i | ||||
\(926\) | −7.44221e8 | −0.937280 | ||||||||
\(927\) | 1.59976e8 | − | 1.59976e8i | 0.200824 | − | 0.200824i | ||||
\(928\) | − | 7.73189e8i | − | 0.967479i | ||||||
\(929\) | − | 8.70150e8i | − | 1.08529i | −0.839961 | − | 0.542647i | \(-0.817422\pi\) | ||
0.839961 | − | 0.542647i | \(-0.182578\pi\) | |||||||
\(930\) | −4.03800e8 | − | 4.03800e8i | −0.502016 | − | 0.502016i | ||||
\(931\) | −3.65027e8 | − | 3.65027e8i | −0.452352 | − | 0.452352i | ||||
\(932\) | 7.92823e8 | 0.979329 | ||||||||
\(933\) | 6.22081e8 | + | 6.22081e8i | 0.765952 | + | 0.765952i | ||||
\(934\) | −1.99493e8 | −0.244843 | ||||||||
\(935\) | 2.29764e9 | 2.81091 | ||||||||
\(936\) | 6.81484e8i | 0.831052i | ||||||||
\(937\) | −1.51179e9 | −1.83769 | −0.918843 | − | 0.394623i | \(-0.870875\pi\) | ||||
−0.918843 | + | 0.394623i | \(0.870875\pi\) | |||||||
\(938\) | 1.48186e7 | + | 1.48186e7i | 0.0179556 | + | 0.0179556i | ||||
\(939\) | 4.13206e8 | − | 4.13206e8i | 0.499080 | − | 0.499080i | ||||
\(940\) | −1.96972e8 | + | 1.96972e8i | −0.237149 | + | 0.237149i | ||||
\(941\) | −3.28848e7 | −0.0394663 | −0.0197332 | − | 0.999805i | \(-0.506282\pi\) | ||||
−0.0197332 | + | 0.999805i | \(0.506282\pi\) | |||||||
\(942\) | 1.20114e8 | + | 1.20114e8i | 0.143694 | + | 0.143694i | ||||
\(943\) | 3.41515e8 | − | 3.41515e8i | 0.407263 | − | 0.407263i | ||||
\(944\) | 5.19815e7 | + | 5.19815e7i | 0.0617921 | + | 0.0617921i | ||||
\(945\) | −3.42346e8 | + | 3.42346e8i | −0.405667 | + | 0.405667i | ||||
\(946\) | 1.24160e9i | 1.46658i | ||||||||
\(947\) | 2.73705e8 | + | 2.73705e8i | 0.322279 | + | 0.322279i | 0.849641 | − | 0.527362i | \(-0.176819\pi\) |
−0.527362 | + | 0.849641i | \(0.676819\pi\) | |||||||
\(948\) | 3.62789e7 | + | 3.62789e7i | 0.0425823 | + | 0.0425823i | ||||
\(949\) | 2.30003e8 | − | 2.30003e8i | 0.269113 | − | 0.269113i | ||||
\(950\) | − | 3.74611e8i | − | 0.436928i | ||||||
\(951\) | 5.83100e7 | 0.0677956 | ||||||||
\(952\) | 4.49851e8i | 0.521384i | ||||||||
\(953\) | − | 1.63586e9i | − | 1.89002i | −0.327036 | − | 0.945012i | \(-0.606050\pi\) | ||
0.327036 | − | 0.945012i | \(-0.393950\pi\) | |||||||
\(954\) | −2.16956e8 | + | 2.16956e8i | −0.249877 | + | 0.249877i | ||||
\(955\) | − | 8.36900e8i | − | 0.960867i | ||||||
\(956\) | −3.22384e8 | + | 3.22384e8i | −0.368978 | + | 0.368978i | ||||
\(957\) | −6.79178e8 | + | 6.79178e8i | −0.774904 | + | 0.774904i | ||||
\(958\) | 5.10694e8 | 0.580850 | ||||||||
\(959\) | 9.90723e7 | 0.112330 | ||||||||
\(960\) | −4.01331e8 | − | 4.01331e8i | −0.453617 | − | 0.453617i | ||||
\(961\) | − | 5.37792e8i | − | 0.605960i | ||||||
\(962\) | 3.56066e8 | + | 6.85107e8i | 0.399950 | + | 0.769544i | ||||
\(963\) | 4.42105e7 | 0.0495047 | ||||||||
\(964\) | 3.86773e7 | − | 3.86773e7i | 0.0431743 | − | 0.0431743i | ||||
\(965\) | − | 4.21095e8i | − | 0.468596i | ||||||
\(966\) | 5.33580e7i | 0.0591927i | ||||||||
\(967\) | 9.60718e8 | + | 9.60718e8i | 1.06247 | + | 1.06247i | 0.997914 | + | 0.0645558i | \(0.0205631\pi\) |
0.0645558 | + | 0.997914i | \(0.479437\pi\) | |||||||
\(968\) | 1.32989e9 | + | 1.32989e9i | 1.46618 | + | 1.46618i | ||||
\(969\) | 5.24557e8 | 0.576529 | ||||||||
\(970\) | −2.86059e8 | − | 2.86059e8i | −0.313430 | − | 0.313430i | ||||
\(971\) | 7.09528e8 | 0.775018 | 0.387509 | − | 0.921866i | \(-0.373336\pi\) | ||||
0.387509 | + | 0.921866i | \(0.373336\pi\) | |||||||
\(972\) | −5.11499e8 | −0.556989 | ||||||||
\(973\) | 2.75934e8i | 0.299548i | ||||||||
\(974\) | −5.46228e8 | −0.591150 | ||||||||
\(975\) | 4.48371e8 | + | 4.48371e8i | 0.483753 | + | 0.483753i | ||||
\(976\) | −1.14094e8 | + | 1.14094e8i | −0.122720 | + | 0.122720i | ||||
\(977\) | −1.04480e9 | + | 1.04480e9i | −1.12034 | + | 1.12034i | −0.128647 | + | 0.991690i | \(0.541063\pi\) |
−0.991690 | + | 0.128647i | \(0.958937\pi\) | |||||||
\(978\) | −3.33899e6 | −0.00356943 | ||||||||
\(979\) | −1.41441e7 | − | 1.41441e7i | −0.0150739 | − | 0.0150739i | ||||
\(980\) | 4.14954e8 | − | 4.14954e8i | 0.440881 | − | 0.440881i | ||||
\(981\) | 5.12892e7 | + | 5.12892e7i | 0.0543274 | + | 0.0543274i | ||||
\(982\) | 4.62888e8 | − | 4.62888e8i | 0.488811 | − | 0.488811i | ||||
\(983\) | 1.76215e8i | 0.185517i | 0.995689 | + | 0.0927585i | \(0.0295684\pi\) | ||||
−0.995689 | + | 0.0927585i | \(0.970432\pi\) | |||||||
\(984\) | 7.32352e8 | + | 7.32352e8i | 0.768660 | + | 0.768660i | ||||
\(985\) | −2.76868e8 | − | 2.76868e8i | −0.289710 | − | 0.289710i | ||||
\(986\) | 5.48518e8 | − | 5.48518e8i | 0.572216 | − | 0.572216i | ||||
\(987\) | 1.11233e8i | 0.115686i | ||||||||
\(988\) | 5.46404e8 | 0.566557 | ||||||||
\(989\) | 4.19466e8i | 0.433618i | ||||||||
\(990\) | − | 9.33436e8i | − | 0.962009i | ||||||
\(991\) | 7.89136e8 | − | 7.89136e8i | 0.810832 | − | 0.810832i | −0.173927 | − | 0.984759i | \(-0.555646\pi\) |
0.984759 | + | 0.173927i | \(0.0556456\pi\) | |||||||
\(992\) | − | 1.17417e9i | − | 1.20281i | ||||||
\(993\) | 5.37317e8 | − | 5.37317e8i | 0.548760 | − | 0.548760i | ||||
\(994\) | −2.88829e8 | + | 2.88829e8i | −0.294090 | + | 0.294090i | ||||
\(995\) | −1.06525e9 | −1.08139 | ||||||||
\(996\) | −5.09813e8 | −0.515980 | ||||||||
\(997\) | 4.70853e8 | + | 4.70853e8i | 0.475116 | + | 0.475116i | 0.903566 | − | 0.428450i | \(-0.140940\pi\) |
−0.428450 | + | 0.903566i | \(0.640940\pi\) | |||||||
\(998\) | − | 9.44731e8i | − | 0.950422i | ||||||
\(999\) | −8.86516e8 | + | 4.60743e8i | −0.889181 | + | 0.462128i |
(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 | 37.7.d.a.6.7 | ✓ | 36 | |
37.31 | odd | 4 | inner | 37.7.d.a.31.7 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.7.d.a.6.7 | ✓ | 36 | 1.1 | even | 1 | trivial | |
37.7.d.a.31.7 | yes | 36 | 37.31 | odd | 4 | inner |