Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,6,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, 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("280.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.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: | \(44.9074695476\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 280.1 |
$q$-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 | ||||||||
\(3\) | 4.00000 | 0.256600 | 0.128300 | − | 0.991735i | \(-0.459048\pi\) | ||||
0.128300 | + | 0.991735i | \(0.459048\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −227.000 | −0.934156 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 124.000 | 0.308987 | 0.154493 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154493 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 766.000 | 1.25710 | 0.628551 | − | 0.777769i | \(-0.283648\pi\) | ||||
0.628551 | + | 0.777769i | \(0.283648\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 100.000 | 0.114755 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1102.00 | −0.924824 | −0.462412 | − | 0.886665i | \(-0.653016\pi\) | ||||
−0.462412 | + | 0.886665i | \(0.653016\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −764.000 | −0.485522 | −0.242761 | − | 0.970086i | \(-0.578053\pi\) | ||||
−0.242761 | + | 0.970086i | \(0.578053\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −196.000 | −0.0969857 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 168.000 | 0.0662201 | 0.0331100 | − | 0.999452i | \(-0.489459\pi\) | ||||
0.0331100 | + | 0.999452i | \(0.489459\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1880.00 | −0.496305 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6866.00 | −1.51603 | −0.758017 | − | 0.652235i | \(-0.773832\pi\) | ||||
−0.758017 | + | 0.652235i | \(0.773832\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4096.00 | −0.765519 | −0.382759 | − | 0.923848i | \(-0.625026\pi\) | ||||
−0.382759 | + | 0.923848i | \(0.625026\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 496.000 | 0.0792861 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1225.00 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4682.00 | −0.562247 | −0.281123 | − | 0.959672i | \(-0.590707\pi\) | ||||
−0.281123 | + | 0.959672i | \(0.590707\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3064.00 | 0.322572 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13130.0 | 1.21985 | 0.609923 | − | 0.792461i | \(-0.291200\pi\) | ||||
0.609923 | + | 0.792461i | \(0.291200\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18220.0 | 1.50272 | 0.751359 | − | 0.659894i | \(-0.229399\pi\) | ||||
0.751359 | + | 0.659894i | \(0.229399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5675.00 | −0.417767 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7104.00 | −0.469092 | −0.234546 | − | 0.972105i | \(-0.575360\pi\) | ||||
−0.234546 | + | 0.972105i | \(0.575360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4408.00 | −0.237310 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −20026.0 | −0.979275 | −0.489637 | − | 0.871926i | \(-0.662871\pi\) | ||||
−0.489637 | + | 0.871926i | \(0.662871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3100.00 | 0.138183 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3056.00 | −0.124585 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −38964.0 | −1.45725 | −0.728624 | − | 0.684914i | \(-0.759840\pi\) | ||||
−0.728624 | + | 0.684914i | \(0.759840\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −56274.0 | −1.93635 | −0.968174 | − | 0.250280i | \(-0.919477\pi\) | ||||
−0.968174 | + | 0.250280i | \(0.919477\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11123.0 | 0.353078 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19150.0 | 0.562193 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24060.0 | −0.654800 | −0.327400 | − | 0.944886i | \(-0.606172\pi\) | ||||
−0.327400 | + | 0.944886i | \(0.606172\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 672.000 | 0.0169921 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −31896.0 | −0.750914 | −0.375457 | − | 0.926840i | \(-0.622514\pi\) | ||||
−0.375457 | + | 0.926840i | \(0.622514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −23670.0 | −0.519866 | −0.259933 | − | 0.965627i | \(-0.583700\pi\) | ||||
−0.259933 | + | 0.965627i | \(0.583700\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2500.00 | 0.0513200 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6076.00 | −0.116786 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37744.0 | 0.680425 | 0.340212 | − | 0.940349i | \(-0.389501\pi\) | ||||
0.340212 | + | 0.940349i | \(0.389501\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 47641.0 | 0.806805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −68204.0 | −1.08671 | −0.543356 | − | 0.839502i | \(-0.682847\pi\) | ||||
−0.543356 | + | 0.839502i | \(0.682847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27550.0 | −0.413594 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −27464.0 | −0.389014 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −19078.0 | −0.255304 | −0.127652 | − | 0.991819i | \(-0.540744\pi\) | ||||
−0.127652 | + | 0.991819i | \(0.540744\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −37534.0 | −0.475140 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16384.0 | −0.196432 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19100.0 | −0.217132 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −115646. | −1.24796 | −0.623981 | − | 0.781440i | \(-0.714486\pi\) | ||||
−0.623981 | + | 0.781440i | \(0.714486\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −28148.0 | −0.288642 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 100790. | 0.983137 | 0.491568 | − | 0.870839i | \(-0.336424\pi\) | ||||
0.491568 | + | 0.870839i | \(0.336424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13304.0 | 0.123563 | 0.0617816 | − | 0.998090i | \(-0.480322\pi\) | ||||
0.0617816 | + | 0.998090i | \(0.480322\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4900.00 | −0.0433733 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 128204. | 1.08254 | 0.541268 | − | 0.840850i | \(-0.317945\pi\) | ||||
0.541268 | + | 0.840850i | \(0.317945\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −176450. | −1.42251 | −0.711255 | − | 0.702934i | \(-0.751873\pi\) | ||||
−0.711255 | + | 0.702934i | \(0.751873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18728.0 | −0.144273 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −166734. | −1.22837 | −0.614183 | − | 0.789163i | \(-0.710514\pi\) | ||||
−0.614183 | + | 0.789163i | \(0.710514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4200.00 | 0.0296145 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −173882. | −1.17433 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 53998.0 | 0.349551 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −145675. | −0.904527 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 52520.0 | 0.313013 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 228112. | 1.25499 | 0.627493 | − | 0.778622i | \(-0.284081\pi\) | ||||
0.627493 | + | 0.778622i | \(0.284081\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 72880.0 | 0.385597 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 131796. | 0.671002 | 0.335501 | − | 0.942040i | \(-0.391094\pi\) | ||||
0.335501 | + | 0.942040i | \(0.391094\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 37436.0 | 0.183510 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −47000.0 | −0.221954 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −187862. | −0.855141 | −0.427570 | − | 0.903982i | \(-0.640630\pi\) | ||||
−0.427570 | + | 0.903982i | \(0.640630\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −106404. | −0.467112 | −0.233556 | − | 0.972343i | \(-0.575036\pi\) | ||||
−0.233556 | + | 0.972343i | \(0.575036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28416.0 | −0.120369 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 94984.0 | 0.388428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −171650. | −0.677991 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9604.00 | 0.0366572 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −177466. | −0.654862 | −0.327431 | − | 0.944875i | \(-0.606183\pi\) | ||||
−0.327431 | + | 0.944875i | \(0.606183\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 117048. | 0.417755 | 0.208877 | − | 0.977942i | \(-0.433019\pi\) | ||||
0.208877 | + | 0.977942i | \(0.433019\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 250154. | 0.863931 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −102400. | −0.342350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31986.0 | −0.103564 | −0.0517822 | − | 0.998658i | \(-0.516490\pi\) | ||||
−0.0517822 | + | 0.998658i | \(0.516490\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −80104.0 | −0.251282 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8232.00 | −0.0250288 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 37060.0 | 0.109254 | 0.0546269 | − | 0.998507i | \(-0.482603\pi\) | ||||
0.0546269 | + | 0.998507i | \(0.482603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12400.0 | 0.0354578 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 185880. | 0.515753 | 0.257876 | − | 0.966178i | \(-0.416977\pi\) | ||||
0.257876 | + | 0.966178i | \(0.416977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 215463. | 0.580305 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 173428. | 0.453554 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 464990. | 1.18121 | 0.590607 | − | 0.806960i | \(-0.298888\pi\) | ||||
0.590607 | + | 0.806960i | \(0.298888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −155856. | −0.373930 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 835300. | 1.94854 | 0.974271 | − | 0.225378i | \(-0.0723618\pi\) | ||||
0.974271 | + | 0.225378i | \(0.0723618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −498682. | −1.13143 | −0.565714 | − | 0.824601i | \(-0.691400\pi\) | ||||
−0.565714 | + | 0.824601i | \(0.691400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −225096. | −0.496867 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −117050. | −0.251444 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −136648. | −0.285759 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 92120.0 | 0.187586 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 295168. | 0.585445 | 0.292722 | − | 0.956197i | \(-0.405439\pi\) | ||||
0.292722 | + | 0.956197i | \(0.405439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 77506.0 | 0.149776 | 0.0748880 | − | 0.997192i | \(-0.476140\pi\) | ||||
0.0748880 | + | 0.997192i | \(0.476140\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 76600.0 | 0.144259 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 310486. | 0.570002 | 0.285001 | − | 0.958527i | \(-0.408006\pi\) | ||||
0.285001 | + | 0.958527i | \(0.408006\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 639080. | 1.14399 | 0.571995 | − | 0.820257i | \(-0.306170\pi\) | ||||
0.571995 | + | 0.820257i | \(0.306170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −96240.0 | −0.168022 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 336434. | 0.573007 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 328250. | 0.545532 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −38136.0 | −0.0618599 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −94736.0 | −0.150020 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 985636. | 1.52409 | 0.762045 | − | 0.647524i | \(-0.224196\pi\) | ||||
0.762045 | + | 0.647524i | \(0.224196\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −127584. | −0.192685 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 455500. | 0.672036 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 200704. | 0.289339 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −94680.0 | −0.133398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −844132. | −1.16260 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.26920e6 | 1.70910 | 0.854551 | − | 0.519368i | \(-0.173833\pi\) | ||||
0.854551 | + | 0.519368i | \(0.173833\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −141875. | −0.186831 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.01843e6 | −1.31179 | −0.655897 | − | 0.754850i | \(-0.727709\pi\) | ||||
−0.655897 | + | 0.754850i | \(0.727709\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 442358. | 0.557423 | 0.278712 | − | 0.960375i | \(-0.410093\pi\) | ||||
0.278712 | + | 0.960375i | \(0.410093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24304.0 | −0.0299673 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 396810. | 0.478843 | 0.239421 | − | 0.970916i | \(-0.423042\pi\) | ||||
0.239421 | + | 0.970916i | \(0.423042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −177600. | −0.209784 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 150976. | 0.174597 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 649872. | 0.735924 | 0.367962 | − | 0.929841i | \(-0.380056\pi\) | ||||
0.367962 | + | 0.929841i | \(0.380056\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 716082. | 0.794182 | 0.397091 | − | 0.917779i | \(-0.370020\pi\) | ||||
0.397091 | + | 0.917779i | \(0.370020\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 647404. | 0.703331 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −585224. | −0.610351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −272816. | −0.278851 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −411860. | −0.412634 | −0.206317 | − | 0.978485i | \(-0.566148\pi\) | ||||
−0.206317 | + | 0.978485i | \(0.566148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20832.0 | 0.0204611 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −110200. | −0.106128 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.51856e6 | −1.43416 | −0.717082 | − | 0.696989i | \(-0.754523\pi\) | ||||
−0.717082 | + | 0.696989i | \(0.754523\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 229418. | 0.212509 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.55858e6 | 1.41621 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.77546e6 | −1.58279 | −0.791394 | − | 0.611307i | \(-0.790644\pi\) | ||||
−0.791394 | + | 0.611307i | \(0.790644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −500650. | −0.437945 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −76312.0 | −0.0655111 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 550014. | 0.463439 | 0.231720 | − | 0.972783i | \(-0.425565\pi\) | ||||
0.231720 | + | 0.972783i | \(0.425565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −64144.0 | −0.0530558 | −0.0265279 | − | 0.999648i | \(-0.508445\pi\) | ||||
−0.0265279 | + | 0.999648i | \(0.508445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −150136. | −0.121921 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 77500.0 | 0.0617974 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 112998. | 0.0884853 | 0.0442427 | − | 0.999021i | \(-0.485913\pi\) | ||||
0.0442427 | + | 0.999021i | \(0.485913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 929792. | 0.715114 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 606330. | 0.458082 | 0.229041 | − | 0.973417i | \(-0.426441\pi\) | ||||
0.229041 | + | 0.973417i | \(0.426441\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −565444. | −0.419685 | −0.209843 | − | 0.977735i | \(-0.567295\pi\) | ||||
−0.209843 | + | 0.977735i | \(0.567295\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −76400.0 | −0.0557162 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −643370. | −0.461059 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −205453. | −0.144700 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −462584. | −0.320227 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −726474. | −0.494369 | −0.247184 | − | 0.968968i | \(-0.579505\pi\) | ||||
−0.247184 | + | 0.968968i | \(0.579505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −974100. | −0.651701 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −233120. | −0.153352 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 128688. | 0.0832454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −892780. | −0.567974 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 403160. | 0.252273 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.40685e6 | −0.865961 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.69346e6 | 1.02548 | 0.512742 | − | 0.858543i | \(-0.328630\pi\) | ||||
0.512742 | + | 0.858543i | \(0.328630\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 53216.0 | 0.0317063 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.52684e6 | 1.48142 | 0.740708 | − | 0.671828i | \(-0.234490\pi\) | ||||
0.740708 | + | 0.671828i | \(0.234490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.00966e6 | 0.582523 | 0.291262 | − | 0.956643i | \(-0.405925\pi\) | ||||
0.291262 | + | 0.956643i | \(0.405925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 278075. | 0.157901 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.14792e6 | −0.641600 | −0.320800 | − | 0.947147i | \(-0.603952\pi\) | ||||
−0.320800 | + | 0.947147i | \(0.603952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −851384. | −0.468434 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 512816. | 0.277779 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 841928. | 0.449023 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 478750. | 0.251420 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −705800. | −0.365016 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 348096. | 0.177300 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.02349e6 | −1.51684 | −0.758418 | − | 0.651768i | \(-0.774028\pi\) | ||||
−0.758418 | + | 0.651768i | \(0.774028\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.06281e6 | 0.525227 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −601500. | −0.292835 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −763054. | −0.366000 | −0.183000 | − | 0.983113i | \(-0.558581\pi\) | ||||
−0.183000 | + | 0.983113i | \(0.558581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −666936. | −0.315199 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −507904. | −0.236535 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16800.0 | 0.00759909 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.93575e6 | −1.75470 | −0.877351 | − | 0.479848i | \(-0.840692\pi\) | ||||
−0.877351 | + | 0.479848i | \(0.840692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.28424e6 | 1.88283 | 0.941413 | − | 0.337257i | \(-0.109499\pi\) | ||||
0.941413 | + | 0.337257i | \(0.109499\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.44008e6 | −0.623906 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 603906. | 0.257948 | 0.128974 | − | 0.991648i | \(-0.458832\pi\) | ||||
0.128974 | + | 0.991648i | \(0.458832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −797400. | −0.335819 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 215992. | 0.0896948 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.78858e6 | 1.14195 | 0.570976 | − | 0.820967i | \(-0.306565\pi\) | ||||
0.570976 | + | 0.820967i | \(0.306565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.89240e6 | −0.764268 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −582700. | −0.232102 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −591750. | −0.232491 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.04883e6 | −1.18159 | −0.590797 | − | 0.806820i | \(-0.701187\pi\) | ||||
−0.590797 | + | 0.806820i | \(0.701187\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.98051e6 | −1.13953 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 981274. | 0.370131 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.57465e6 | −0.586019 | −0.293010 | − | 0.956109i | \(-0.594657\pi\) | ||||
−0.293010 | + | 0.956109i | \(0.594657\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 62500.0 | 0.0229510 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.25936e6 | −1.90581 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00929e6 | 1.43374 | 0.716869 | − | 0.697208i | \(-0.245575\pi\) | ||||
0.716869 | + | 0.697208i | \(0.245575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 912448. | 0.322030 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.44590e6 | −1.20035 | −0.600173 | − | 0.799870i | \(-0.704901\pi\) | ||||
−0.600173 | + | 0.799870i | \(0.704901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −151900. | −0.0522283 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.13594e6 | −1.40377 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.09125e6 | 0.365638 | 0.182819 | − | 0.983147i | \(-0.441478\pi\) | ||||
0.182819 | + | 0.983147i | \(0.441478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −185136. | −0.0612419 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 527184. | 0.172179 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 943600. | 0.304295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 68990.0 | 0.0219690 | 0.0109845 | − | 0.999940i | \(-0.496503\pi\) | ||||
0.0109845 | + | 0.999940i | \(0.496503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 149744. | 0.0470888 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 249938. | 0.0776196 | 0.0388098 | − | 0.999247i | \(-0.487643\pi\) | ||||
0.0388098 | + | 0.999247i | \(0.487643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.13754e6 | −0.962335 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.19102e6 | 0.360814 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −580568. | −0.173727 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.21836e6 | 0.360137 | 0.180069 | − | 0.983654i | \(-0.442368\pi\) | ||||
0.180069 | + | 0.983654i | \(0.442368\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −751448. | −0.219429 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.90924e6 | 0.550788 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.70510e6 | −0.485993 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −425616. | −0.119861 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.21502e6 | −0.338102 | −0.169051 | − | 0.985607i | \(-0.554070\pi\) | ||||
−0.169051 | + | 0.985607i | \(0.554070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 882646. | 0.242706 | 0.121353 | − | 0.992609i | \(-0.461277\pi\) | ||||
0.121353 | + | 0.992609i | \(0.461277\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.61261e6 | 0.438206 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −688750. | −0.184965 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.75743e6 | 0.731870 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 379936. | 0.0996706 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.95086e6 | −1.80238 | −0.901188 | − | 0.433427i | \(-0.857304\pi\) | ||||
−0.901188 | + | 0.433427i | \(0.857304\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.09723e6 | 1.81915 | 0.909577 | − | 0.415536i | \(-0.136406\pi\) | ||||
0.909577 | + | 0.415536i | \(0.136406\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −686600. | −0.173973 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −128352. | −0.0321513 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.40444e6 | 1.09076 | 0.545380 | − | 0.838189i | \(-0.316385\pi\) | ||||
0.545380 | + | 0.838189i | \(0.316385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −545027. | −0.133451 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.59066e6 | −0.627193 | −0.313596 | − | 0.949556i | \(-0.601534\pi\) | ||||
−0.313596 | + | 0.949556i | \(0.601534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −476950. | −0.114175 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −709864. | −0.168038 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.61888e6 | 0.378965 | 0.189483 | − | 0.981884i | \(-0.439319\pi\) | ||||
0.189483 | + | 0.981884i | \(0.439319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.62812e6 | 0.376916 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 468192. | 0.107196 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −938350. | −0.212489 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.32412e6 | −1.64046 | −0.820228 | − | 0.572036i | \(-0.806154\pi\) | ||||
−0.820228 | + | 0.572036i | \(0.806154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.07176e6 | 0.458995 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.86086e6 | 1.28443 | 0.642213 | − | 0.766526i | \(-0.278016\pi\) | ||||
0.642213 | + | 0.766526i | \(0.278016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.15974e6 | −0.251426 | −0.125713 | − | 0.992067i | \(-0.540122\pi\) | ||||
−0.125713 | + | 0.992067i | \(0.540122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −409600. | −0.0878471 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.37889e6 | −1.35348 | −0.676742 | − | 0.736220i | \(-0.736609\pi\) | ||||
−0.676742 | + | 0.736220i | \(0.736609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.17894e6 | 0.247491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −127944. | −0.0265747 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.25928e6 | 0.464320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −477500. | −0.0971045 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.54590e6 | 0.914796 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.52893e6 | −0.503614 | −0.251807 | − | 0.967777i | \(-0.581025\pi\) | ||||
−0.251807 | + | 0.967777i | \(0.581025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.58641e6 | −0.706802 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −32928.0 | −0.00642240 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.89115e6 | −0.558105 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −991272. | −0.189396 | −0.0946979 | − | 0.995506i | \(-0.530189\pi\) | ||||
−0.0946979 | + | 0.995506i | \(0.530189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 148240. | 0.0280345 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.58506e6 | −1.23270 | −0.616348 | − | 0.787474i | \(-0.711389\pi\) | ||||
−0.616348 | + | 0.787474i | \(0.711389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.56633e6 | 1.40206 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −703700. | −0.129085 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.56290e6 | 0.283819 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.39831e6 | 1.15031 | 0.575154 | − | 0.818045i | \(-0.304942\pi\) | ||||
0.575154 | + | 0.818045i | \(0.304942\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 743520. | 0.132342 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.91546e6 | 0.337562 | 0.168781 | − | 0.985654i | \(-0.446017\pi\) | ||||
0.168781 | + | 0.985654i | \(0.446017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.51975e6 | 0.439672 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 861852. | 0.148906 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.72437e6 | −0.466092 | −0.233046 | − | 0.972466i | \(-0.574869\pi\) | ||||
−0.233046 | + | 0.972466i | \(0.574869\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.15983e6 | 0.196491 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.43632e6 | 0.240967 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 332600. | 0.0552591 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −880896. | −0.144943 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.85996e6 | 0.303099 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.28260e6 | 0.691215 | 0.345608 | − | 0.938379i | \(-0.387673\pi\) | ||||
0.345608 | + | 0.938379i | \(0.387673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.61035e6 | 0.577158 | 0.288579 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288579 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −122500. | −0.0193971 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.51379e6 | 0.707970 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.40812e6 | −0.995615 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.84483e6 | 1.36130 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.00576e7 | 1.53347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.20510e6 | 0.484125 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.34120e6 | 0.499996 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 297724. | 0.0441410 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.17755e7 | 1.72977 | 0.864883 | − | 0.501973i | \(-0.167392\pi\) | ||||
0.864883 | + | 0.501973i | \(0.167392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.99473e6 | −0.290325 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.41125e6 | −0.636166 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.07968e7 | −1.54286 | −0.771428 | − | 0.636317i | \(-0.780457\pi\) | ||||
−0.771428 | + | 0.636317i | \(0.780457\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.27742e7 | 1.80885 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.24562e6 | 0.736068 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.84946e6 | −0.257176 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −468200. | −0.0645207 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.11383e7 | −1.52118 | −0.760589 | − | 0.649234i | \(-0.775090\pi\) | ||||
−0.760589 | + | 0.649234i | \(0.775090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.39565e7 | 1.88907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −546592. | −0.0733257 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.49836e6 | 0.598112 | 0.299056 | − | 0.954235i | \(-0.403328\pi\) | ||||
0.299056 | + | 0.954235i | \(0.403328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.16835e6 | −0.549342 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.33441e6 | −0.304943 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.14929e6 | −0.666755 | −0.333378 | − | 0.942793i | \(-0.608188\pi\) | ||||
−0.333378 | + | 0.942793i | \(0.608188\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.95544e6 | 0.250988 | 0.125494 | − | 0.992094i | \(-0.459948\pi\) | ||||
0.125494 | + | 0.992094i | \(0.459948\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.18067e6 | 0.150225 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 105000. | 0.0132440 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.50179e6 | 0.312833 | 0.156416 | − | 0.987691i | \(-0.450006\pi\) | ||||
0.156416 | + | 0.987691i | \(0.450006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 310024. | 0.0384325 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.34200e6 | 0.410739 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.48322e6 | −0.302583 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.34705e6 | −0.525176 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.31352e7 | 1.57341 | 0.786703 | − | 0.617332i | \(-0.211786\pi\) | ||||
0.786703 | + | 0.617332i | \(0.211786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.12934e6 | 0.371676 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.24194e6 | 0.146263 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.61671e7 | −1.88797 | −0.943983 | − | 0.329994i | \(-0.892953\pi\) | ||||
−0.943983 | + | 0.329994i | \(0.892953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.34995e6 | 0.156324 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.55632e6 | 0.293548 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.39864e7 | −1.59272 | −0.796359 | − | 0.604824i | \(-0.793244\pi\) | ||||
−0.796359 | + | 0.604824i | \(0.793244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.95609e6 | 0.672628 | 0.336314 | − | 0.941750i | \(-0.390820\pi\) | ||||
0.336314 | + | 0.941750i | \(0.390820\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.46162e6 | 0.611686 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.64188e6 | −0.404517 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.44142e7 | −1.58789 | −0.793943 | − | 0.607992i | \(-0.791975\pi\) | ||||
−0.793943 | + | 0.607992i | \(0.791975\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.34574e6 | 0.147034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.44166e6 | −0.589697 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.08923e6 | −0.117076 | −0.0585379 | − | 0.998285i | \(-0.518644\pi\) | ||||
−0.0585379 | + | 0.998285i | \(0.518644\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.31300e6 | 0.139984 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −983542. | −0.104011 | −0.0520056 | − | 0.998647i | \(-0.516561\pi\) | ||||
−0.0520056 | + | 0.998647i | \(0.516561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.30483e7 | 1.36875 | 0.684377 | − | 0.729128i | \(-0.260074\pi\) | ||||
0.684377 | + | 0.729128i | \(0.260074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −315840. | −0.0328653 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 934822. | 0.0964959 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −378944. | −0.0384952 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.15956e6 | 0.519980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.59951e6 | 0.859806 | 0.429903 | − | 0.902875i | \(-0.358548\pi\) | ||||
0.429903 | + | 0.902875i | \(0.358548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.94254e6 | 0.391082 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.70280e6 | 0.561247 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.83917e6 | 0.179586 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.24039e6 | 0.701471 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.40288e6 | −0.711632 | −0.355816 | − | 0.934556i | \(-0.615797\pi\) | ||||
−0.355816 | + | 0.934556i | \(0.615797\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.68038e6 | −0.732580 | −0.366290 | − | 0.930501i | \(-0.619372\pi\) | ||||
−0.366290 | + | 0.930501i | \(0.619372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.82200e6 | 0.172444 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.00321e6 | −0.188133 | −0.0940666 | − | 0.995566i | \(-0.529987\pi\) | ||||
−0.0940666 | + | 0.995566i | \(0.529987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.83154e6 | −0.450270 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 802816. | 0.0742444 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.64089e6 | 0.334137 | 0.167069 | − | 0.985945i | \(-0.446570\pi\) | ||||
0.167069 | + | 0.985945i | \(0.446570\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.29490e6 | 0.300081 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.37309e6 | 0.485636 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.02720e6 | 0.271536 | 0.135768 | − | 0.990741i | \(-0.456650\pi\) | ||||
0.135768 | + | 0.990741i | \(0.456650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.76758e6 | −0.513440 | −0.256720 | − | 0.966486i | \(-0.582642\pi\) | ||||
−0.256720 | + | 0.966486i | \(0.582642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.37653e6 | −0.298323 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 935900. | 0.0820683 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.15349e6 | −0.100392 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.07680e6 | 0.438556 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.97798e6 | −0.598306 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.43872e7 | 1.22444 | 0.612220 | − | 0.790687i | \(-0.290277\pi\) | ||||
0.612220 | + | 0.790687i | \(0.290277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.17500e6 | −0.0992610 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.13262e6 | −0.346540 | −0.173270 | − | 0.984874i | \(-0.555433\pi\) | ||||
−0.173270 | + | 0.984874i | \(0.555433\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.66665e6 | 0.471685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.07371e6 | −0.336607 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.15356e6 | −0.422722 | −0.211361 | − | 0.977408i | \(-0.567790\pi\) | ||||
−0.211361 | + | 0.977408i | \(0.567790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.69655e6 | −0.382431 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.76943e6 | 0.143035 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53399e7 | −1.23105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.01299e6 | −0.0807066 | −0.0403533 | − | 0.999185i | \(-0.512848\pi\) | ||||
−0.0403533 | + | 0.999185i | \(0.512848\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.37925e6 | 0.109096 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.66010e6 | −0.208899 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.44693e7 | −1.12814 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.58724e6 | 0.122871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.19041e6 | 0.552661 | 0.276331 | − | 0.961063i | \(-0.410882\pi\) | ||||
0.276331 | + | 0.961063i | \(0.410882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.57705e6 | 0.272984 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −710400. | −0.0538307 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.93871e6 | −0.371591 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.41861e7 | −1.80697 | −0.903484 | − | 0.428621i | \(-0.859000\pi\) | ||||
−0.903484 | + | 0.428621i | \(0.859000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.56789e6 | −0.635623 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −688128. | −0.0506927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.37460e6 | 0.173710 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.59949e6 | 0.188838 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.88305e7 | 1.35844 | 0.679218 | − | 0.733937i | \(-0.262319\pi\) | ||||
0.679218 | + | 0.733937i | \(0.262319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −651896. | −0.0467025 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.86433e6 | 0.203787 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.29125e6 | −0.303207 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.42513e7 | 1.00005 | 0.500023 | − | 0.866012i | \(-0.333325\pi\) | ||||
0.500023 | + | 0.866012i | \(0.333325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.98715e6 | −0.626330 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.00784e7 | −1.38975 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −945586. | −0.0650042 | −0.0325021 | − | 0.999472i | \(-0.510348\pi\) | ||||
−0.0325021 | + | 0.999472i | \(0.510348\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 240100. | 0.0163936 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.98344e6 | −0.202325 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.01534e6 | −0.135749 | −0.0678746 | − | 0.997694i | \(-0.521622\pi\) | ||||
−0.0678746 | + | 0.997694i | \(0.521622\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.34090e6 | −0.156616 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.22830e7 | −0.816264 | −0.408132 | − | 0.912923i | \(-0.633820\pi\) | ||||
−0.408132 | + | 0.912923i | \(0.633820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.43665e6 | −0.292863 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.54823e7 | 1.01516 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.28200e6 | −0.409160 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.43979e6 | 0.416651 | 0.208325 | − | 0.978060i | \(-0.433199\pi\) | ||||
0.208325 | + | 0.978060i | \(0.433199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.64744e6 | −0.105882 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.92620e6 | 0.186826 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.08870e7 | 0.690507 | 0.345253 | − | 0.938510i | \(-0.387793\pi\) | ||||
0.345253 | + | 0.938510i | \(0.387793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 83328.0 | 0.00525033 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.57412e7 | −1.61126 | −0.805632 | − | 0.592417i | \(-0.798174\pi\) | ||||
−0.805632 | + | 0.592417i | \(0.798174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.64605e6 | 0.537658 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.25385e6 | 0.386362 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.98464e7 | −1.83191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.38746e7 | −1.45586 | −0.727930 | − | 0.685652i | \(-0.759517\pi\) | ||||
−0.727930 | + | 0.685652i | \(0.759517\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.07423e6 | −0.368006 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.70534e7 | 1.02651 | 0.513254 | − | 0.858237i | \(-0.328440\pi\) | ||||
0.513254 | + | 0.858237i | \(0.328440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.56000e6 | −0.153104 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 917672. | 0.0545299 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.00313e7 | −0.592263 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.95510e6 | −0.232023 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.29081e7 | 0.752415 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −799650. | −0.0463154 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.15326e7 | 1.23925 | 0.619626 | − | 0.784897i | \(-0.287284\pi\) | ||||
0.619626 | + | 0.784897i | \(0.287284\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.10186e6 | −0.406143 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.16997e6 | 0.464279 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.31059e7 | −2.43419 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.00260e6 | −0.112377 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.38450e6 | −0.411789 | −0.205895 | − | 0.978574i | \(-0.566010\pi\) | ||||
−0.205895 | + | 0.978574i | \(0.566010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.82861e6 | 0.433828 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.33071e6 | 0.238494 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.93508e6 | −0.160632 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −205800. | −0.0111932 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.20006e6 | 0.118919 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.80415e7 | −1.50637 | −0.753183 | − | 0.657811i | \(-0.771482\pi\) | ||||
−0.753183 | + | 0.657811i | \(0.771482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.07165e7 | 0.572138 | 0.286069 | − | 0.958209i | \(-0.407651\pi\) | ||||
0.286069 | + | 0.958209i | \(0.407651\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −256576. | −0.0136141 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 926500. | 0.0488598 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.39201e7 | −0.729603 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.52022e6 | 0.443855 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.28481e7 | −1.18302 | −0.591510 | − | 0.806298i | \(-0.701468\pi\) | ||||
−0.591510 | + | 0.806298i | \(0.701468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.36644e7 | −0.703222 | −0.351611 | − | 0.936146i | \(-0.614366\pi\) | ||||
−0.351611 | + | 0.936146i | \(0.614366\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 310000. | 0.0158572 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.59497e7 | −0.810938 | −0.405469 | − | 0.914109i | \(-0.632892\pi\) | ||||
−0.405469 | + | 0.914109i | \(0.632892\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −615250. | −0.0310932 | −0.0155466 | − | 0.999879i | \(-0.504949\pi\) | ||||
−0.0155466 | + | 0.999879i | \(0.504949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 451992. | 0.0227053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.64590e6 | −0.132118 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.64700e6 | 0.230652 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.70048e6 | 0.379930 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.07702e6 | −0.249002 | −0.124501 | − | 0.992219i | \(-0.539733\pi\) | ||||
−0.124501 | + | 0.992219i | \(0.539733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.66308e7 | 1.29836 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.42532e6 | 0.117544 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.38658e6 | 0.259520 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.13808e6 | 0.341879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.26178e6 | −0.107691 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −786576. | −0.0372320 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.28325e7 | 1.07444 | 0.537218 | − | 0.843443i | \(-0.319475\pi\) | ||||
0.537218 | + | 0.843443i | \(0.319475\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.33570e6 | 0.202835 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.03857e7 | 0.483040 | 0.241520 | − | 0.970396i | \(-0.422354\pi\) | ||||
0.241520 | + | 0.970396i | \(0.422354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.66607e6 | −0.446958 | −0.223479 | − | 0.974709i | \(-0.571741\pi\) | ||||
−0.223479 | + | 0.974709i | \(0.571741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.57348e6 | −0.118308 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.47160e7 | −1.12967 | −0.564835 | − | 0.825204i | \(-0.691060\pi\) | ||||
−0.564835 | + | 0.825204i | \(0.691060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.16248e7 | 0.528255 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −821812. | −0.0371300 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.68026e6 | 0.210242 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.84300e7 | −0.823150 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.62516e7 | 1.16579 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −765625. | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.87672e7 | 1.70202 | 0.851012 | − | 0.525147i | \(-0.175990\pi\) | ||||
0.851012 | + | 0.525147i | \(0.175990\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.90590e6 | −0.126855 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.21677e7 | 0.528162 | 0.264081 | − | 0.964500i | \(-0.414931\pi\) | ||||
0.264081 | + | 0.964500i | \(0.414931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.54978e7 | −1.96376 | −0.981881 | − | 0.189497i | \(-0.939314\pi\) | ||||
−0.981881 | + | 0.189497i | \(0.939314\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.89640e6 | −0.167227 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.30952e7 | 0.558860 | 0.279430 | − | 0.960166i | \(-0.409854\pi\) | ||||
0.279430 | + | 0.960166i | \(0.409854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.11775e7 | −0.474340 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.90748e6 | 0.249292 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.42746e6 | 0.227755 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.08825e7 | 0.871415 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 514752. | 0.0213608 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.81231e7 | 1.16055 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.20687e7 | 0.905657 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.57112e6 | −0.145742 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.24670e7 | −0.505990 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.98552e6 | 0.403044 | 0.201522 | − | 0.979484i | \(-0.435411\pi\) | ||||
0.201522 | + | 0.979484i | \(0.435411\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.28793e7 | −0.918404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.58347e7 | −0.632140 | −0.316070 | − | 0.948736i | \(-0.602363\pi\) | ||||
−0.316070 | + | 0.948736i | \(0.602363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.45730e6 | −0.335780 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.62740e6 | −0.222206 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.45800e6 | −0.253615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.40462e7 | 1.72036 | 0.860180 | − | 0.509991i | \(-0.170351\pi\) | ||||
0.860180 | + | 0.509991i | \(0.170351\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.77384e6 | 0.263139 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.44323e7 | −0.943976 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.92625e6 | −0.112449 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.02001e6 | −0.115427 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.33648e7 | −0.508068 | −0.254034 | − | 0.967195i | \(-0.581758\pi\) | ||||
−0.254034 | + | 0.967195i | \(0.581758\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.83436e6 | −0.0693604 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.01074e7 | 0.380131 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.41620e6 | −0.127795 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.72180e7 | −1.01276 | −0.506381 | − | 0.862310i | \(-0.669017\pi\) | ||||
−0.506381 | + | 0.862310i | \(0.669017\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.03863e6 | 0.149476 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.09420e7 | 1.13913 | 0.569566 | − | 0.821946i | \(-0.307111\pi\) | ||||
0.569566 | + | 0.821946i | \(0.307111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.20584e6 | 0.0807783 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.30300e6 | 0.0838908 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.39058e6 | 0.231561 | 0.115780 | − | 0.993275i | \(-0.463063\pi\) | ||||
0.115780 | + | 0.993275i | \(0.463063\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.81312e7 | −0.653524 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.59169e6 | −0.164635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.72447e7 | −1.32841 | −0.664205 | − | 0.747550i | \(-0.731230\pi\) | ||||
−0.664205 | + | 0.747550i | \(0.731230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.37920e6 | 0.261819 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.40554e6 | −0.120200 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.20524e6 | 0.323213 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.18519e7 | −0.413981 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.91023e7 | −1.01126 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.93765e6 | 0.0669818 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.34627e7 | 1.49469 | 0.747344 | − | 0.664437i | \(-0.231329\pi\) | ||||
0.747344 | + | 0.664437i | \(0.231329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.36771e6 | 0.115219 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.88474e7 | −1.66262 | −0.831311 | − | 0.555807i | \(-0.812409\pi\) | ||||
−0.831311 | + | 0.555807i | \(0.812409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.21380e6 | 0.176552 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.91500e6 | 0.0645145 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.46440e7 | 0.490823 | 0.245411 | − | 0.969419i | \(-0.421077\pi\) | ||||
0.245411 | + | 0.969419i | \(0.421077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.36567e6 | −0.0788856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.00542e7 | 1.32885 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.58487e7 | −1.51336 | −0.756681 | − | 0.653784i | \(-0.773180\pi\) | ||||
−0.756681 | + | 0.653784i | \(0.773180\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.76215e6 | 0.254913 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.39238e6 | 0.0454953 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.06096e6 | 0.0995100 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.86037e7 | 0.601748 | 0.300874 | − | 0.953664i | \(-0.402722\pi\) | ||||
0.300874 | + | 0.953664i | \(0.402722\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.20940e7 | −0.389220 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.59770e7 | 0.511608 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.26338e7 | 1.03975 | 0.519876 | − | 0.854242i | \(-0.325978\pi\) | ||||
0.519876 | + | 0.854242i | \(0.325978\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.80216e6 | 0.279046 |
(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 | 280.6.a.b.1.1 | ✓ | 1 | |
4.3 | odd | 2 | 560.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
560.6.a.b.1.1 | 1 | 4.3 | odd | 2 |