Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,6,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.a (trivial) |
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: | yes |
Analytic conductor: | \(173.214525398\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.15881.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 29x - 55 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.15876\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 61.7318 | 0.476172 | 0.238086 | − | 0.971244i | \(-0.423480\pi\) | ||||
0.238086 | + | 0.971244i | \(0.423480\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 218.360 | 0.544115 | 0.272058 | − | 0.962281i | \(-0.412296\pi\) | ||||
0.272058 | + | 0.962281i | \(0.412296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −864.360 | −1.41852 | −0.709261 | − | 0.704946i | \(-0.750971\pi\) | ||||
−0.709261 | + | 0.704946i | \(0.750971\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 521.206 | 0.437408 | 0.218704 | − | 0.975791i | \(-0.429817\pi\) | ||||
0.218704 | + | 0.975791i | \(0.429817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1456.28 | −0.925469 | −0.462735 | − | 0.886497i | \(-0.653132\pi\) | ||||
−0.462735 | + | 0.886497i | \(0.653132\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4923.60 | 1.94072 | 0.970360 | − | 0.241663i | \(-0.0776930\pi\) | ||||
0.970360 | + | 0.241663i | \(0.0776930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5664.06 | −1.25064 | −0.625321 | − | 0.780367i | \(-0.715032\pi\) | ||||
−0.625321 | + | 0.780367i | \(0.715032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2982.68 | −0.557446 | −0.278723 | − | 0.960372i | \(-0.589911\pi\) | ||||
−0.278723 | + | 0.960372i | \(0.589911\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1543.30 | 0.212951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −110.503 | −0.0132700 | −0.00663500 | − | 0.999978i | \(-0.502112\pi\) | ||||
−0.00663500 | + | 0.999978i | \(0.502112\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2417.32 | −0.224582 | −0.112291 | − | 0.993675i | \(-0.535819\pi\) | ||||
−0.112291 | + | 0.993675i | \(0.535819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13599.5 | 1.12164 | 0.560818 | − | 0.827939i | \(-0.310487\pi\) | ||||
0.560818 | + | 0.827939i | \(0.310487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −15203.5 | −1.00392 | −0.501959 | − | 0.864891i | \(-0.667387\pi\) | ||||
−0.501959 | + | 0.864891i | \(0.667387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12996.2 | −0.773260 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10499.4 | 0.513424 | 0.256712 | − | 0.966488i | \(-0.417361\pi\) | ||||
0.256712 | + | 0.966488i | \(0.417361\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5459.00 | 0.243336 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −31719.4 | −1.18630 | −0.593150 | − | 0.805092i | \(-0.702116\pi\) | ||||
−0.593150 | + | 0.805092i | \(0.702116\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28090.1 | −0.966561 | −0.483280 | − | 0.875466i | \(-0.660555\pi\) | ||||
−0.483280 | + | 0.875466i | \(0.660555\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21609.0 | −0.634382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −17898.9 | −0.487123 | −0.243561 | − | 0.969886i | \(-0.578316\pi\) | ||||
−0.243561 | + | 0.969886i | \(0.578316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36783.1 | −0.865969 | −0.432984 | − | 0.901401i | \(-0.642540\pi\) | ||||
−0.432984 | + | 0.901401i | \(0.642540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −49779.7 | −1.09332 | −0.546658 | − | 0.837356i | \(-0.684100\pi\) | ||||
−0.546658 | + | 0.837356i | \(0.684100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13479.7 | 0.259093 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 81941.9 | 1.47720 | 0.738598 | − | 0.674146i | \(-0.235488\pi\) | ||||
0.738598 | + | 0.674146i | \(0.235488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 97419.7 | 1.55221 | 0.776107 | − | 0.630602i | \(-0.217192\pi\) | ||||
0.776107 | + | 0.630602i | \(0.217192\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13030.2 | 0.195615 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18128.7 | −0.242601 | −0.121300 | − | 0.992616i | \(-0.538706\pi\) | ||||
−0.121300 | + | 0.992616i | \(0.538706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −53358.5 | −0.675461 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36407.1 | −0.413882 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 45823.0 | 0.494486 | 0.247243 | − | 0.968954i | \(-0.420475\pi\) | ||||
0.247243 | + | 0.968954i | \(0.420475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 62187.5 | 0.606596 | 0.303298 | − | 0.952896i | \(-0.401912\pi\) | ||||
0.303298 | + | 0.952896i | \(0.401912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −43842.8 | −0.407198 | −0.203599 | − | 0.979054i | \(-0.565264\pi\) | ||||
−0.203599 | + | 0.979054i | \(0.565264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 59741.4 | 0.504447 | 0.252224 | − | 0.967669i | \(-0.418838\pi\) | ||||
0.252224 | + | 0.967669i | \(0.418838\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 144322. | 1.16350 | 0.581750 | − | 0.813368i | \(-0.302368\pi\) | ||||
0.581750 | + | 0.813368i | \(0.302368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −41891.8 | −0.308626 | −0.154313 | − | 0.988022i | \(-0.549316\pi\) | ||||
−0.154313 | + | 0.988022i | \(0.549316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 123090. | 0.867916 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32175.0 | 0.208282 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −113370. | −0.703938 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −267112. | −1.46955 | −0.734775 | − | 0.678311i | \(-0.762712\pi\) | ||||
−0.734775 | + | 0.678311i | \(0.762712\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −149202. | −0.759620 | −0.379810 | − | 0.925065i | \(-0.624011\pi\) | ||||
−0.379810 | + | 0.925065i | \(0.624011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −89899.0 | −0.440683 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −238234. | −1.08443 | −0.542215 | − | 0.840240i | \(-0.682414\pi\) | ||||
−0.542215 | + | 0.840240i | \(0.682414\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37079.7 | 0.162779 | 0.0813896 | − | 0.996682i | \(-0.474064\pi\) | ||||
0.0813896 | + | 0.996682i | \(0.474064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −188741. | −0.771840 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −141602. | −0.559304 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 353924. | 1.30600 | 0.653002 | − | 0.757356i | \(-0.273509\pi\) | ||||
0.653002 | + | 0.757356i | \(0.273509\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −312960. | −1.11698 | −0.558491 | − | 0.829511i | \(-0.688619\pi\) | ||||
−0.558491 | + | 0.829511i | \(0.688619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −74567.0 | −0.249297 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 461545. | 1.49439 | 0.747197 | − | 0.664603i | \(-0.231399\pi\) | ||||
0.747197 | + | 0.664603i | \(0.231399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 303943. | 0.924117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 379232. | 1.11799 | 0.558993 | − | 0.829172i | \(-0.311188\pi\) | ||||
0.558993 | + | 0.829172i | \(0.311188\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −412408. | −1.14429 | −0.572144 | − | 0.820153i | \(-0.693888\pi\) | ||||
−0.572144 | + | 0.820153i | \(0.693888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 375825. | 1.01221 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −730459. | −1.85558 | −0.927792 | − | 0.373098i | \(-0.878296\pi\) | ||||
−0.927792 | + | 0.373098i | \(0.878296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 38582.4 | 0.0952344 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −217864. | −0.508221 | −0.254110 | − | 0.967175i | \(-0.581783\pi\) | ||||
−0.254110 | + | 0.967175i | \(0.581783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 541786. | 1.22923 | 0.614613 | − | 0.788829i | \(-0.289312\pi\) | ||||
0.614613 | + | 0.788829i | \(0.289312\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2762.58 | −0.00593453 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 113810. | 0.238001 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −809680. | −1.60594 | −0.802972 | − | 0.596017i | \(-0.796749\pi\) | ||||
−0.802972 | + | 0.596017i | \(0.796749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −711052. | −1.37407 | −0.687033 | − | 0.726626i | \(-0.741087\pi\) | ||||
−0.687033 | + | 0.726626i | \(0.741087\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −135834. | −0.249370 | −0.124685 | − | 0.992196i | \(-0.539792\pi\) | ||||
−0.124685 | + | 0.992196i | \(0.539792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 393307. | 0.704043 | 0.352021 | − | 0.935992i | \(-0.385494\pi\) | ||||
0.352021 | + | 0.935992i | \(0.385494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −349653. | −0.595521 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −60433.1 | −0.100436 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −317994. | −0.503562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −857.535 | −0.00132601 | −0.000663003 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000663003 | 1.00000i | \(0.500211\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 339988. | 0.501611 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −184126. | −0.265440 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −450510. | −0.620474 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −936796. | −1.26149 | −0.630744 | − | 0.775991i | \(-0.717250\pi\) | ||||
−0.630744 | + | 0.775991i | \(0.717250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −308948. | −0.397943 | −0.198971 | − | 0.980005i | \(-0.563760\pi\) | ||||
−0.198971 | + | 0.980005i | \(0.563760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −711701. | −0.896827 | −0.448413 | − | 0.893826i | \(-0.648011\pi\) | ||||
−0.448413 | + | 0.893826i | \(0.648011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12911.2 | −0.0155804 | −0.00779018 | − | 0.999970i | \(-0.502480\pi\) | ||||
−0.00779018 | + | 0.999970i | \(0.502480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −380087. | −0.448966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 965160. | 1.09296 | 0.546481 | − | 0.837472i | \(-0.315967\pi\) | ||||
0.546481 | + | 0.837472i | \(0.315967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −255074. | −0.282894 | −0.141447 | − | 0.989946i | \(-0.545175\pi\) | ||||
−0.141447 | + | 0.989946i | \(0.545175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −324905. | −0.345812 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.25875e6 | 1.31280 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.09535e6 | −1.09741 | −0.548703 | − | 0.836018i | \(-0.684878\pi\) | ||||
−0.548703 | + | 0.836018i | \(0.684878\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.07512e6 | 1.05598 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.41430e6 | −1.33570 | −0.667852 | − | 0.744294i | \(-0.732786\pi\) | ||||
−0.667852 | + | 0.744294i | \(0.732786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6821.57 | −0.00631881 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.61172e6 | 1.43681 | 0.718407 | − | 0.695623i | \(-0.244872\pi\) | ||||
0.718407 | + | 0.695623i | \(0.244872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 262486. | 0.229610 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.03815e6 | −1.71733 | −0.858667 | − | 0.512535i | \(-0.828707\pi\) | ||||
−0.858667 | + | 0.512535i | \(0.828707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.13393e6 | −0.937914 | −0.468957 | − | 0.883221i | \(-0.655370\pi\) | ||||
−0.468957 | + | 0.883221i | \(0.655370\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 136475. | 0.108823 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 596450. | 0.467062 | 0.233531 | − | 0.972349i | \(-0.424972\pi\) | ||||
0.233531 | + | 0.972349i | \(0.424972\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 867713. | 0.655557 | 0.327778 | − | 0.944755i | \(-0.393700\pi\) | ||||
0.327778 | + | 0.944755i | \(0.393700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 125401. | 0.0930756 | 0.0465378 | − | 0.998917i | \(-0.485181\pi\) | ||||
0.0465378 | + | 0.998917i | \(0.485181\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −149226. | −0.106940 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.14820e6 | −0.808674 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −746956. | −0.508307 | −0.254153 | − | 0.967164i | \(-0.581797\pi\) | ||||
−0.254153 | + | 0.967164i | \(0.581797\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −792984. | −0.530529 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.25576e6 | −2.75296 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 839522. | 0.534092 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −702253. | −0.432259 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.84667e6 | −1.72382 | −0.861908 | − | 0.507065i | \(-0.830731\pi\) | ||||
−0.861908 | + | 0.507065i | \(0.830731\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −256851. | −0.150585 | −0.0752924 | − | 0.997162i | \(-0.523989\pi\) | ||||
−0.0752924 | + | 0.997162i | \(0.523989\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.28277e6 | 1.89400 | 0.946998 | − | 0.321240i | \(-0.104100\pi\) | ||||
0.946998 | + | 0.321240i | \(0.104100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −694224. | −0.388018 | −0.194009 | − | 0.981000i | \(-0.562149\pi\) | ||||
−0.194009 | + | 0.981000i | \(0.562149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.23680e6 | −0.680494 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −759024. | −0.404808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −540225. | −0.283704 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −938538. | −0.478038 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −645658. | −0.323916 | −0.161958 | − | 0.986798i | \(-0.551781\pi\) | ||||
−0.161958 | + | 0.986798i | \(0.551781\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −447471. | −0.217848 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19338.3 | 0.00927562 | 0.00463781 | − | 0.999989i | \(-0.498524\pi\) | ||||
0.00463781 | + | 0.999989i | \(0.498524\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −651297. | −0.303315 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.83980e6 | −0.844377 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.21004e6 | −0.539479 | −0.269739 | − | 0.962933i | \(-0.586938\pi\) | ||||
−0.269739 | + | 0.962933i | \(0.586938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −818886. | −0.359882 | −0.179941 | − | 0.983677i | \(-0.557591\pi\) | ||||
−0.179941 | + | 0.983677i | \(0.557591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.12396e6 | −1.76148 | −0.880740 | − | 0.473599i | \(-0.842954\pi\) | ||||
−0.880740 | + | 0.473599i | \(0.842954\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −919577. | −0.387273 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.59734e6 | −1.06363 | −0.531817 | − | 0.846859i | \(-0.678491\pi\) | ||||
−0.531817 | + | 0.846859i | \(0.678491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −355336. | −0.143506 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.24449e6 | −0.488946 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.37067e6 | 0.531212 | 0.265606 | − | 0.964082i | \(-0.414428\pi\) | ||||
0.265606 | + | 0.964082i | \(0.414428\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 648149. | 0.244478 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.95671e6 | 1.84468 | 0.922340 | − | 0.386379i | \(-0.126274\pi\) | ||||
0.922340 | + | 0.386379i | \(0.126274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.89579e6 | 1.77406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.37710e6 | 0.492456 | 0.246228 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246228 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.87817e6 | −0.654241 | −0.327121 | − | 0.944983i | \(-0.606078\pi\) | ||||
−0.327121 | + | 0.944983i | \(0.606078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 336994. | 0.115870 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.59135e6 | 1.20333 | 0.601663 | − | 0.798750i | \(-0.294505\pi\) | ||||
0.601663 | + | 0.798750i | \(0.294505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.56621e6 | 0.848887 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.04855e6 | 0.660622 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −128220. | −0.0408300 | −0.0204150 | − | 0.999792i | \(-0.506499\pi\) | ||||
−0.0204150 | + | 0.999792i | \(0.506499\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.60952e6 | −0.810400 | −0.405200 | − | 0.914228i | \(-0.632798\pi\) | ||||
−0.405200 | + | 0.914228i | \(0.632798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.57811e6 | 0.790749 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24129.5 | −0.00722041 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.00485e6 | 1.18380 | 0.591900 | − | 0.806012i | \(-0.298378\pi\) | ||||
0.591900 | + | 0.806012i | \(0.298378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.95809e6 | −0.564883 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.43549e6 | 0.694171 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 950749. | 0.264564 | 0.132282 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132282 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.46256e6 | −0.402170 | −0.201085 | − | 0.979574i | \(-0.564447\pi\) | ||||
−0.201085 | + | 0.979574i | \(0.564447\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 325754. | 0.0874817 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.73405e6 | −0.460249 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.57304e6 | −1.44510 | −0.722551 | − | 0.691317i | \(-0.757031\pi\) | ||||
−0.722551 | + | 0.691317i | \(0.757031\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.12055e6 | −0.543535 | −0.271768 | − | 0.962363i | \(-0.587608\pi\) | ||||
−0.271768 | + | 0.962363i | \(0.587608\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.17016e6 | −1.79608 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.88072e6 | −1.45636 | −0.728180 | − | 0.685386i | \(-0.759634\pi\) | ||||
−0.728180 | + | 0.685386i | \(0.759634\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.10594e6 | −0.267747 | −0.133873 | − | 0.990998i | \(-0.542742\pi\) | ||||
−0.133873 | + | 0.990998i | \(0.542742\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −453218. | −0.108494 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.18891e6 | −0.746494 | −0.373247 | − | 0.927732i | \(-0.621756\pi\) | ||||
−0.373247 | + | 0.927732i | \(0.621756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −527846. | −0.122199 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.33396e6 | −0.302075 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −107720. | −0.0241272 | −0.0120636 | − | 0.999927i | \(-0.503840\pi\) | ||||
−0.0120636 | + | 0.999927i | \(0.503840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.77462e6 | −1.04637 | −0.523186 | − | 0.852219i | \(-0.675257\pi\) | ||||
−0.523186 | + | 0.852219i | \(0.675257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.90712e6 | −1.28063 | −0.640315 | − | 0.768113i | \(-0.721196\pi\) | ||||
−0.640315 | + | 0.768113i | \(0.721196\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.51853e6 | 0.322204 | 0.161102 | − | 0.986938i | \(-0.448495\pi\) | ||||
0.161102 | + | 0.986938i | \(0.448495\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.10493e6 | −0.231954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.96958e6 | 0.610299 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −910177. | −0.185094 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.09026e6 | 0.217116 | 0.108558 | − | 0.994090i | \(-0.465377\pi\) | ||||
0.108558 | + | 0.994090i | \(0.465377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 95514.6 | 0.0188238 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.14557e6 | 0.221141 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.09380e6 | 0.208986 | 0.104493 | − | 0.994526i | \(-0.466678\pi\) | ||||
0.104493 | + | 0.994526i | \(0.466678\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 403601. | 0.0755524 | 0.0377762 | − | 0.999286i | \(-0.487973\pi\) | ||||
0.0377762 | + | 0.999286i | \(0.487973\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.95214e6 | −0.547042 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.27069e6 | −0.412350 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.05199e7 | 1.89130 | 0.945650 | − | 0.325187i | \(-0.105427\pi\) | ||||
0.945650 | + | 0.325187i | \(0.105427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.40828e6 | −1.65802 | −0.829011 | − | 0.559232i | \(-0.811096\pi\) | ||||
−0.829011 | + | 0.559232i | \(0.811096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.55469e6 | 0.271278 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.79366e6 | 0.306863 | 0.153432 | − | 0.988159i | \(-0.450967\pi\) | ||||
0.153432 | + | 0.988159i | \(0.450967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.07299e6 | −0.520606 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.09607e6 | −0.182104 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.31983e6 | −0.546247 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.62374e6 | −0.907676 | −0.453838 | − | 0.891084i | \(-0.649946\pi\) | ||||
−0.453838 | + | 0.891084i | \(0.649946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.41420e6 | −1.34511 | −0.672556 | − | 0.740046i | \(-0.734804\pi\) | ||||
−0.672556 | + | 0.740046i | \(0.734804\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.55459e6 | −0.243831 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.78055e7 | 2.76640 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.08944e6 | 0.318575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.49353e6 | 0.225596 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.83784e6 | −0.420743 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.46117e6 | 1.38980 | 0.694899 | − | 0.719107i | \(-0.255449\pi\) | ||||
0.694899 | + | 0.719107i | \(0.255449\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.60805e6 | 0.520333 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.14111e7 | −1.63065 | −0.815325 | − | 0.579004i | \(-0.803442\pi\) | ||||
−0.815325 | + | 0.579004i | \(0.803442\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.24849e6 | 1.15743 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.05842e6 | 0.703400 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.49930e6 | −0.751051 | −0.375526 | − | 0.926812i | \(-0.622538\pi\) | ||||
−0.375526 | + | 0.926812i | \(0.622538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.17549e7 | −1.59107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.82754e6 | 0.375957 | 0.187978 | − | 0.982173i | \(-0.439807\pi\) | ||||
0.187978 | + | 0.982173i | \(0.439807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.04730e6 | −0.138022 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.89752e6 | 1.15210 | 0.576048 | − | 0.817416i | \(-0.304594\pi\) | ||||
0.576048 | + | 0.817416i | \(0.304594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −352454. | −0.0452390 | −0.0226195 | − | 0.999744i | \(-0.507201\pi\) | ||||
−0.0226195 | + | 0.999744i | \(0.507201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.07725e6 | 0.388144 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.69637e6 | 0.587250 | 0.293625 | − | 0.955921i | \(-0.405138\pi\) | ||||
0.293625 | + | 0.955921i | \(0.405138\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.01389e6 | 0.739121 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.29265e6 | 0.279362 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.87559e6 | 0.464240 | 0.232120 | − | 0.972687i | \(-0.425434\pi\) | ||||
0.232120 | + | 0.972687i | \(0.425434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.34363e6 | 0.515899 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.43492e7 | 1.67567 | 0.837837 | − | 0.545921i | \(-0.183820\pi\) | ||||
0.837837 | + | 0.545921i | \(0.183820\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 804375. | 0.0931464 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −614144. | −0.0699364 | −0.0349682 | − | 0.999388i | \(-0.511133\pi\) | ||||
−0.0349682 | + | 0.999388i | \(0.511133\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.48024e6 | 0.844752 | 0.422376 | − | 0.906421i | \(-0.361196\pi\) | ||||
0.422376 | + | 0.906421i | \(0.361196\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.83425e6 | −0.314811 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.16923e6 | −0.899932 | −0.449966 | − | 0.893046i | \(-0.648564\pi\) | ||||
−0.449966 | + | 0.893046i | \(0.648564\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.31413e7 | 1.42408 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.59061e6 | −0.708393 | −0.354197 | − | 0.935171i | \(-0.615246\pi\) | ||||
−0.354197 | + | 0.935171i | \(0.615246\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.08486e7 | 1.14726 | 0.573631 | − | 0.819114i | \(-0.305535\pi\) | ||||
0.573631 | + | 0.819114i | \(0.305535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.77057e6 | −0.290631 | −0.145316 | − | 0.989385i | \(-0.546420\pi\) | ||||
−0.145316 | + | 0.989385i | \(0.546420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.11912e6 | −0.115520 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −57595.0 | −0.00580441 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.80075e7 | −1.80045 | −0.900225 | − | 0.435426i | \(-0.856598\pi\) | ||||
−0.900225 | + | 0.435426i | \(0.856598\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.67780e6 | −0.657202 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.12334e7 | 1.09689 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.37062e6 | 0.324015 | 0.162008 | − | 0.986790i | \(-0.448203\pi\) | ||||
0.162008 | + | 0.986790i | \(0.448203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.08376e6 | 0.389523 | 0.194762 | − | 0.980851i | \(-0.437607\pi\) | ||||
0.194762 | + | 0.980851i | \(0.437607\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11635.6 | −0.00109277 | −0.000546386 | − | 1.00000i | \(-0.500174\pi\) | ||||
−0.000546386 | 1.00000i | \(0.500174\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.92623e6 | −0.645484 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.15712e7 | 1.06193 | 0.530966 | − | 0.847393i | \(-0.321829\pi\) | ||||
0.530966 | + | 0.847393i | \(0.321829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.73005e6 | −0.339712 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.48159e6 | −0.581390 | −0.290695 | − | 0.956816i | \(-0.593887\pi\) | ||||
−0.290695 | + | 0.956816i | \(0.593887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.80346e7 | 1.60547 | 0.802734 | − | 0.596337i | \(-0.203378\pi\) | ||||
0.802734 | + | 0.596337i | \(0.203378\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.24748e6 | −0.197079 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.78876e7 | −2.42715 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.13376e6 | −0.525921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.23135e7 | −1.04795 | −0.523977 | − | 0.851732i | \(-0.675552\pi\) | ||||
−0.523977 | + | 0.851732i | \(0.675552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.41788e6 | −0.789735 | −0.394868 | − | 0.918738i | \(-0.629210\pi\) | ||||
−0.394868 | + | 0.918738i | \(0.629210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.82873e6 | 0.235460 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.20155e7 | 0.985575 | 0.492788 | − | 0.870150i | \(-0.335978\pi\) | ||||
0.492788 | + | 0.870150i | \(0.335978\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.95584e6 | −0.484972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.07528e6 | −0.728303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.13020e6 | 0.727420 | 0.363710 | − | 0.931512i | \(-0.381510\pi\) | ||||
0.363710 | + | 0.931512i | \(0.381510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 926992. | 0.0727971 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.25992e6 | −0.0982340 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.86299e6 | 0.373773 | 0.186887 | − | 0.982382i | \(-0.440160\pi\) | ||||
0.186887 | + | 0.982382i | \(0.440160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 160924. | 0.0122810 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.83894e6 | 0.288844 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.40699e7 | 1.79829 | 0.899143 | − | 0.437655i | \(-0.144191\pi\) | ||||
0.899143 | + | 0.437655i | \(0.144191\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.46855e7 | −1.08185 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.71854e6 | −0.345177 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.27412e7 | 0.919155 | 0.459578 | − | 0.888138i | \(-0.348001\pi\) | ||||
0.459578 | + | 0.888138i | \(0.348001\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.70650e6 | −0.193896 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.54004e6 | −0.250129 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.22701e6 | 0.577306 | 0.288653 | − | 0.957434i | \(-0.406793\pi\) | ||||
0.288653 | + | 0.957434i | \(0.406793\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.08814e6 | 0.490613 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.05392e7 | 1.41196 | 0.705981 | − | 0.708230i | \(-0.250506\pi\) | ||||
0.705981 | + | 0.708230i | \(0.250506\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.90839e6 | −0.265051 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −669477. | −0.0450946 | −0.0225473 | − | 0.999746i | \(-0.507178\pi\) | ||||
−0.0225473 | + | 0.999746i | \(0.507178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.32841e6 | 0.0882793 | 0.0441397 | − | 0.999025i | \(-0.485945\pi\) | ||||
0.0441397 | + | 0.999025i | \(0.485945\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.84811e6 | 0.584063 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.68794e6 | 0.240204 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.73731e6 | −0.565298 | −0.282649 | − | 0.959223i | \(-0.591213\pi\) | ||||
−0.282649 | + | 0.959223i | \(0.591213\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.82399e6 | −0.499529 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.14412e7 | −1.35991 | −0.679953 | − | 0.733255i | \(-0.738000\pi\) | ||||
−0.679953 | + | 0.733255i | \(0.738000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.59944e7 | 1.00117 | 0.500583 | − | 0.865689i | \(-0.333119\pi\) | ||||
0.500583 | + | 0.865689i | \(0.333119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.90925e6 | 0.554026 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.74169e7 | 1.68279 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.22642e6 | 0.196746 | 0.0983729 | − | 0.995150i | \(-0.468636\pi\) | ||||
0.0983729 | + | 0.995150i | \(0.468636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.35896e7 | 0.818010 | 0.409005 | − | 0.912532i | \(-0.365876\pi\) | ||||
0.409005 | + | 0.912532i | \(0.365876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.86417e6 | −0.111489 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.52031e6 | 0.207844 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.03195e6 | −0.471187 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.15386e7 | 0.668313 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.13774e6 | 0.353242 | 0.176621 | − | 0.984279i | \(-0.443483\pi\) | ||||
0.176621 | + | 0.984279i | \(0.443483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.58606e6 | −0.146959 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.42800e7 | 1.37109 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.67400e6 | 0.539461 | 0.269731 | − | 0.962936i | \(-0.413065\pi\) | ||||
0.269731 | + | 0.962936i | \(0.413065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.92414e6 | −0.439122 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.08699e7 | −0.594890 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.59856e6 | 0.413278 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.21470e7 | 1.18972 | 0.594859 | − | 0.803830i | \(-0.297208\pi\) | ||||
0.594859 | + | 0.803830i | \(0.297208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.11479e7 | −0.595168 | −0.297584 | − | 0.954696i | \(-0.596181\pi\) | ||||
−0.297584 | + | 0.954696i | \(0.596181\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.48081e6 | 0.499979 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.98047e7 | −1.03804 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.04925e7 | 0.543278 | 0.271639 | − | 0.962399i | \(-0.412434\pi\) | ||||
0.271639 | + | 0.962399i | \(0.412434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.60842e7 | 1.34239 | 0.671195 | − | 0.741281i | \(-0.265781\pi\) | ||||
0.671195 | + | 0.741281i | \(0.265781\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.64602e6 | −0.337908 | −0.168954 | − | 0.985624i | \(-0.554039\pi\) | ||||
−0.168954 | + | 0.985624i | \(0.554039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.03700e6 | −0.355632 | −0.177816 | − | 0.984064i | \(-0.556903\pi\) | ||||
−0.177816 | + | 0.984064i | \(0.556903\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.77369e6 | −0.338231 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.03102e7 | −0.511741 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.15192e7 | 1.54586 | 0.772931 | − | 0.634490i | \(-0.218790\pi\) | ||||
0.772931 | + | 0.634490i | \(0.218790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.15705e7 | 0.564107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.39562e6 | 0.452672 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.99854e6 | −0.335196 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −544074. | −0.0257534 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.10469e7 | 0.990411 | 0.495206 | − | 0.868776i | \(-0.335093\pi\) | ||||
0.495206 | + | 0.868776i | \(0.335093\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.83597e6 | 0.410963 | 0.205481 | − | 0.978661i | \(-0.434124\pi\) | ||||
0.205481 | + | 0.978661i | \(0.434124\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.34325e7 | −0.621117 | −0.310558 | − | 0.950554i | \(-0.600516\pi\) | ||||
−0.310558 | + | 0.950554i | \(0.600516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.38060e7 | 0.631018 | 0.315509 | − | 0.948923i | \(-0.397825\pi\) | ||||
0.315509 | + | 0.948923i | \(0.397825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.82615e7 | −0.829842 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.78928e7 | 0.803765 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.54711e7 | 0.690994 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 964560. | 0.0425901 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.58782e7 | 1.57519 | 0.787593 | − | 0.616196i | \(-0.211327\pi\) | ||||
0.787593 | + | 0.616196i | \(0.211327\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.42379e6 | −0.192024 | −0.0960118 | − | 0.995380i | \(-0.530609\pi\) | ||||
−0.0960118 | + | 0.995380i | \(0.530609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.69958e7 | −0.733566 | −0.366783 | − | 0.930307i | \(-0.619541\pi\) | ||||
−0.366783 | + | 0.930307i | \(0.619541\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.04106e7 | 0.444291 | 0.222146 | − | 0.975013i | \(-0.428694\pi\) | ||||
0.222146 | + | 0.975013i | \(0.428694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.64893e7 | −0.699758 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.21406e7 | 0.929095 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.44659e6 | −0.227283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.68941e7 | 0.697165 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.47236e6 | 0.224576 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.35447e7 | 0.549726 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.49530e7 | −1.00718 | −0.503588 | − | 0.863944i | \(-0.667987\pi\) | ||||
−0.503588 | + | 0.863944i | \(0.667987\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.66692e6 | 0.106467 | 0.0532333 | − | 0.998582i | \(-0.483047\pi\) | ||||
0.0532333 | + | 0.998582i | \(0.483047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.12725e7 | 0.844583 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.21051e6 | −0.361710 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.85809e7 | 0.725735 | 0.362867 | − | 0.931841i | \(-0.381798\pi\) | ||||
0.362867 | + | 0.931841i | \(0.381798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.17938e7 | 1.22840 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −69064.6 | −0.00265400 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.28293e7 | −1.24802 | −0.624011 | − | 0.781415i | \(-0.714498\pi\) | ||||
−0.624011 | + | 0.781415i | \(0.714498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.89261e7 | 0.715629 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.84526e6 | 0.106437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.77296e7 | −1.03180 | −0.515898 | − | 0.856650i | \(-0.672542\pi\) | ||||
−0.515898 | + | 0.856650i | \(0.672542\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.72967e7 | −1.37308 | −0.686542 | − | 0.727090i | \(-0.740872\pi\) | ||||
−0.686542 | + | 0.727090i | \(0.740872\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.19019e7 | −0.435851 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.05019e7 | 0.742882 | 0.371441 | − | 0.928457i | \(-0.378864\pi\) | ||||
0.371441 | + | 0.928457i | \(0.378864\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.30276e7 | 1.55089 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.05113e7 | −0.374907 | −0.187454 | − | 0.982273i | \(-0.560023\pi\) | ||||
−0.187454 | + | 0.982273i | \(0.560023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.02420e7 | −0.718200 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.47066e7 | −0.516375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.97328e7 | −0.689255 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.77763e7 | −0.614501 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.13682e7 | 0.734854 | 0.367427 | − | 0.930052i | \(-0.380239\pi\) | ||||
0.367427 | + | 0.930052i | \(0.380239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 356908. | 0.0121481 | 0.00607405 | − | 0.999982i | \(-0.498067\pi\) | ||||
0.00607405 | + | 0.999982i | \(0.498067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.28900e6 | 0.0775110 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.13784e7 | 1.72204 | 0.861021 | − | 0.508569i | \(-0.169825\pi\) | ||||
0.861021 | + | 0.508569i | \(0.169825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.95858e6 | −0.132003 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.49482e6 | 0.115356 | 0.0576782 | − | 0.998335i | \(-0.481630\pi\) | ||||
0.0576782 | + | 0.998335i | \(0.481630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.39585e6 | −0.111521 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.69585e7 | 2.17678 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.95776e7 | −0.633249 | −0.316624 | − | 0.948551i | \(-0.602549\pi\) | ||||
−0.316624 | + | 0.948551i | \(0.602549\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.83267e6 | 0.314857 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.77382e6 | 0.0565161 | 0.0282580 | − | 0.999601i | \(-0.491004\pi\) | ||||
0.0282580 | + | 0.999601i | \(0.491004\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.6.a.g.1.2 | yes | 3 | |
3.2 | odd | 2 | 1080.6.a.e.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.6.a.e.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
1080.6.a.g.1.2 | yes | 3 | 1.1 | even | 1 | trivial |