Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.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: | \(64.1535279252\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-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 | ||||||||
\(3\) | −14.0000 | −0.898100 | −0.449050 | − | 0.893507i | \(-0.648238\pi\) | ||||
−0.449050 | + | 0.893507i | \(0.648238\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −158.000 | −1.21874 | −0.609371 | − | 0.792885i | \(-0.708578\pi\) | ||||
−0.609371 | + | 0.792885i | \(0.708578\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −47.0000 | −0.193416 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 148.000 | 0.368791 | 0.184395 | − | 0.982852i | \(-0.440967\pi\) | ||||
0.184395 | + | 0.982852i | \(0.440967\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 684.000 | 1.12253 | 0.561265 | − | 0.827636i | \(-0.310315\pi\) | ||||
0.561265 | + | 0.827636i | \(0.310315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2048.00 | 1.71873 | 0.859365 | − | 0.511363i | \(-0.170859\pi\) | ||||
0.859365 | + | 0.511363i | \(0.170859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2220.00 | −1.41081 | −0.705406 | − | 0.708804i | \(-0.749235\pi\) | ||||
−0.705406 | + | 0.708804i | \(0.749235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2212.00 | 1.09455 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1246.00 | 0.491132 | 0.245566 | − | 0.969380i | \(-0.421026\pi\) | ||||
0.245566 | + | 0.969380i | \(0.421026\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4060.00 | 1.07181 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −270.000 | −0.0596168 | −0.0298084 | − | 0.999556i | \(-0.509490\pi\) | ||||
−0.0298084 | + | 0.999556i | \(0.509490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2048.00 | 0.382759 | 0.191380 | − | 0.981516i | \(-0.438704\pi\) | ||||
0.191380 | + | 0.981516i | \(0.438704\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2072.00 | −0.331211 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4372.00 | −0.525020 | −0.262510 | − | 0.964929i | \(-0.584550\pi\) | ||||
−0.262510 | + | 0.964929i | \(0.584550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9576.00 | −1.00814 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2398.00 | −0.222787 | −0.111393 | − | 0.993776i | \(-0.535531\pi\) | ||||
−0.111393 | + | 0.993776i | \(0.535531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2294.00 | −0.189200 | −0.0946002 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0946002 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10682.0 | 0.705355 | 0.352678 | − | 0.935745i | \(-0.385271\pi\) | ||||
0.352678 | + | 0.935745i | \(0.385271\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8157.00 | 0.485333 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28672.0 | −1.54359 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2964.00 | 0.144940 | 0.0724700 | − | 0.997371i | \(-0.476912\pi\) | ||||
0.0724700 | + | 0.997371i | \(0.476912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 31080.0 | 1.26705 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 39740.0 | 1.48627 | 0.743135 | − | 0.669141i | \(-0.233338\pi\) | ||||
0.743135 | + | 0.669141i | \(0.233338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −42298.0 | −1.45544 | −0.727722 | − | 0.685873i | \(-0.759421\pi\) | ||||
−0.727722 | + | 0.685873i | \(0.759421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7426.00 | 0.235724 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −32098.0 | −0.873556 | −0.436778 | − | 0.899569i | \(-0.643881\pi\) | ||||
−0.436778 | + | 0.899569i | \(0.643881\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17444.0 | −0.441086 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4248.00 | 0.100009 | 0.0500044 | − | 0.998749i | \(-0.484076\pi\) | ||||
0.0500044 | + | 0.998749i | \(0.484076\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30104.0 | 0.661176 | 0.330588 | − | 0.943775i | \(-0.392753\pi\) | ||||
0.330588 | + | 0.943775i | \(0.392753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23384.0 | −0.449461 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −35280.0 | −0.636005 | −0.318003 | − | 0.948090i | \(-0.603012\pi\) | ||||
−0.318003 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −45419.0 | −0.769175 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 27826.0 | 0.443359 | 0.221680 | − | 0.975120i | \(-0.428846\pi\) | ||||
0.221680 | + | 0.975120i | \(0.428846\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3780.00 | 0.0535419 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −85210.0 | −1.14029 | −0.570145 | − | 0.821544i | \(-0.693113\pi\) | ||||
−0.570145 | + | 0.821544i | \(0.693113\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −108072. | −1.36807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28672.0 | −0.343756 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −97232.0 | −1.04925 | −0.524626 | − | 0.851333i | \(-0.675795\pi\) | ||||
−0.524626 | + | 0.851333i | \(0.675795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6956.00 | −0.0713299 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4298.00 | −0.0419240 | −0.0209620 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209620 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −124114. | −1.15273 | −0.576365 | − | 0.817192i | \(-0.695529\pi\) | ||||
−0.576365 | + | 0.817192i | \(0.695529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 42342.0 | 0.357530 | 0.178765 | − | 0.983892i | \(-0.442790\pi\) | ||||
0.178765 | + | 0.983892i | \(0.442790\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −35990.0 | −0.290145 | −0.145073 | − | 0.989421i | \(-0.546342\pi\) | ||||
−0.145073 | + | 0.989421i | \(0.546342\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 61208.0 | 0.471521 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −228816. | −1.68574 | −0.842869 | − | 0.538118i | \(-0.819135\pi\) | ||||
−0.842869 | + | 0.538118i | \(0.819135\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −32148.0 | −0.217115 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −323584. | −2.09469 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139147. | −0.863993 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 33572.0 | 0.200085 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −175238. | −0.964093 | −0.482047 | − | 0.876146i | \(-0.660106\pi\) | ||||
−0.482047 | + | 0.876146i | \(0.660106\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 32116.0 | 0.169921 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −299652. | −1.52559 | −0.762797 | − | 0.646638i | \(-0.776174\pi\) | ||||
−0.762797 | + | 0.646638i | \(0.776174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 350760. | 1.71942 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 107928. | 0.491284 | 0.245642 | − | 0.969361i | \(-0.421001\pi\) | ||||
0.245642 | + | 0.969361i | \(0.421001\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 196460. | 0.862456 | 0.431228 | − | 0.902243i | \(-0.358080\pi\) | ||||
0.431228 | + | 0.902243i | \(0.358080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −149548. | −0.633480 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 101232. | 0.413978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −114198. | −0.435878 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 138850. | 0.512366 | 0.256183 | − | 0.966628i | \(-0.417535\pi\) | ||||
0.256183 | + | 0.966628i | \(0.417535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −416152. | −1.48528 | −0.742642 | − | 0.669688i | \(-0.766428\pi\) | ||||
−0.742642 | + | 0.669688i | \(0.766428\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −96256.0 | −0.332429 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 433108. | 1.40232 | 0.701160 | − | 0.713004i | \(-0.252666\pi\) | ||||
0.701160 | + | 0.713004i | \(0.252666\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −41496.0 | −0.130171 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −196868. | −0.598564 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −149134. | −0.439651 | −0.219825 | − | 0.975539i | \(-0.570549\pi\) | ||||
−0.219825 | + | 0.975539i | \(0.570549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 559602. | 1.55270 | 0.776351 | − | 0.630301i | \(-0.217068\pi\) | ||||
0.776351 | + | 0.630301i | \(0.217068\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 96563.0 | 0.260072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 104340. | 0.272873 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 343804. | 0.873365 | 0.436682 | − | 0.899616i | \(-0.356153\pi\) | ||||
0.436682 | + | 0.899616i | \(0.356153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −556360. | −1.33482 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23980.0 | −0.0559392 | −0.0279696 | − | 0.999609i | \(-0.508904\pi\) | ||||
−0.0279696 | + | 0.999609i | \(0.508904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −651898. | −1.47905 | −0.739526 | − | 0.673128i | \(-0.764950\pi\) | ||||
−0.739526 | + | 0.673128i | \(0.764950\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 592172. | 1.30713 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 303104. | 0.633852 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −641480. | −1.30626 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −202752. | −0.402144 | −0.201072 | − | 0.979576i | \(-0.564443\pi\) | ||||
−0.201072 | + | 0.979576i | \(0.564443\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −452656. | −0.874732 | −0.437366 | − | 0.899284i | \(-0.644089\pi\) | ||||
−0.437366 | + | 0.899284i | \(0.644089\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 337468. | 0.619537 | 0.309768 | − | 0.950812i | \(-0.399748\pi\) | ||||
0.309768 | + | 0.950812i | \(0.399748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 561000. | 1.00422 | 0.502112 | − | 0.864803i | \(-0.332557\pi\) | ||||
0.502112 | + | 0.864803i | \(0.332557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 449372. | 0.784541 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 42660.0 | 0.0726576 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −58562.0 | −0.0949927 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −328560. | −0.520294 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 805548. | 1.24562 | 0.622810 | − | 0.782373i | \(-0.285991\pi\) | ||||
0.622810 | + | 0.782373i | \(0.285991\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −59472.0 | −0.0898180 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −323584. | −0.466485 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −421456. | −0.593802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.40083e6 | 1.92932 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.21855e6 | −1.64090 | −0.820451 | − | 0.571717i | \(-0.806278\pi\) | ||||
−0.820451 | + | 0.571717i | \(0.806278\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −564338. | −0.726900 | −0.363450 | − | 0.931614i | \(-0.618401\pi\) | ||||
−0.363450 | + | 0.931614i | \(0.618401\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 560330. | 0.706082 | 0.353041 | − | 0.935608i | \(-0.385148\pi\) | ||||
0.353041 | + | 0.935608i | \(0.385148\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 327376. | 0.403661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −293576. | −0.354267 | −0.177134 | − | 0.984187i | \(-0.556682\pi\) | ||||
−0.177134 | + | 0.984187i | \(0.556682\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 493920. | 0.571197 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −584240. | −0.661602 | −0.330801 | − | 0.943701i | \(-0.607319\pi\) | ||||
−0.330801 | + | 0.943701i | \(0.607319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −563798. | −0.625289 | −0.312645 | − | 0.949870i | \(-0.601215\pi\) | ||||
−0.312645 | + | 0.949870i | \(0.601215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −350714. | −0.381011 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.51848e6 | −1.58368 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −389564. | −0.398181 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.01975e6 | 1.02167 | 0.510833 | − | 0.859680i | \(-0.329337\pi\) | ||||
0.510833 | + | 0.859680i | \(0.329337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 184408. | 0.181125 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 657408. | 0.620872 | 0.310436 | − | 0.950594i | \(-0.399525\pi\) | ||||
0.310436 | + | 0.950594i | \(0.399525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 690776. | 0.639864 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12690.0 | 0.0115308 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 562366. | 0.501337 | 0.250668 | − | 0.968073i | \(-0.419350\pi\) | ||||
0.250668 | + | 0.968073i | \(0.419350\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.19294e6 | 1.02410 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 366570. | 0.308870 | 0.154435 | − | 0.988003i | \(-0.450644\pi\) | ||||
0.154435 | + | 0.988003i | \(0.450644\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.16075e6 | −0.960099 | −0.480050 | − | 0.877241i | \(-0.659381\pi\) | ||||
−0.480050 | + | 0.877241i | \(0.659381\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.51301e6 | 1.22867 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.51501e6 | −1.96943 | −0.984715 | − | 0.174172i | \(-0.944275\pi\) | ||||
−0.984715 | + | 0.174172i | \(0.944275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −96256.0 | −0.0740316 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.08600e6 | 1.57597 | 0.787987 | − | 0.615692i | \(-0.211124\pi\) | ||||
0.787987 | + | 0.615692i | \(0.211124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.23803e6 | 1.66111 | 0.830556 | − | 0.556935i | \(-0.188023\pi\) | ||||
0.830556 | + | 0.556935i | \(0.188023\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 378884. | 0.271520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.77445e6 | 1.95403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.36125e6 | 0.942334 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −975756. | −0.664006 | −0.332003 | − | 0.943278i | \(-0.607724\pi\) | ||||
−0.332003 | + | 0.943278i | \(0.607724\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 600880. | 0.395273 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 852264. | 0.551310 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 362452. | 0.230587 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 60172.0 | 0.0376520 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −87858.0 | −0.0532029 | −0.0266015 | − | 0.999646i | \(-0.508469\pi\) | ||||
−0.0266015 | + | 0.999646i | \(0.508469\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.73760e6 | 1.03527 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −599352. | −0.351383 | −0.175692 | − | 0.984445i | \(-0.556216\pi\) | ||||
−0.175692 | + | 0.984445i | \(0.556216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.09342e6 | −1.20780 | −0.603900 | − | 0.797060i | \(-0.706387\pi\) | ||||
−0.603900 | + | 0.797060i | \(0.706387\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.41625e6 | −1.35050 | −0.675249 | − | 0.737590i | \(-0.735964\pi\) | ||||
−0.675249 | + | 0.737590i | \(0.735964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39960.0 | −0.0219861 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −592788. | −0.321097 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.54656e6 | −2.42480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 503860. | 0.260580 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.68776e6 | −0.859647 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.64095e6 | 0.823237 | 0.411618 | − | 0.911356i | \(-0.364964\pi\) | ||||
0.411618 | + | 0.911356i | \(0.364964\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 205484. | 0.101547 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.18773e6 | 1.04935 | 0.524673 | − | 0.851304i | \(-0.324188\pi\) | ||||
0.524673 | + | 0.851304i | \(0.324188\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.20342e6 | 1.51396 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 303104. | 0.141158 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.36670e6 | 0.627246 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.74502e6 | −1.22383 | −0.611916 | − | 0.790923i | \(-0.709601\pi\) | ||||
−0.611916 | + | 0.790923i | \(0.709601\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.65115e6 | −1.16512 | −0.582560 | − | 0.812788i | \(-0.697949\pi\) | ||||
−0.582560 | + | 0.812788i | \(0.697949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.77704e6 | 1.20313 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.05766e6 | 1.30603 | 0.653015 | − | 0.757345i | \(-0.273504\pi\) | ||||
0.653015 | + | 0.757345i | \(0.273504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.53018e6 | 1.88124 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.79356e6 | −1.55350 | −0.776749 | − | 0.629810i | \(-0.783133\pi\) | ||||
−0.776749 | + | 0.629810i | \(0.783133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.45230e6 | 0.990389 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94806e6 | 0.775953 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.11060e6 | 1.20553 | 0.602767 | − | 0.797917i | \(-0.294065\pi\) | ||||
0.602767 | + | 0.797917i | \(0.294065\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 112706. | 0.0430905 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −468312. | −0.176645 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.41520e6 | −0.526677 | −0.263339 | − | 0.964703i | \(-0.584824\pi\) | ||||
−0.263339 | + | 0.964703i | \(0.584824\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −184680. | −0.0669216 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.90262e6 | 1.39559 | 0.697796 | − | 0.716297i | \(-0.254164\pi\) | ||||
0.697796 | + | 0.716297i | \(0.254164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.45333e6 | 0.865852 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −695674. | −0.242331 | −0.121165 | − | 0.992632i | \(-0.538663\pi\) | ||||
−0.121165 | + | 0.992632i | \(0.538663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 107818. | 0.0365943 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 498290. | 0.166958 | 0.0834792 | − | 0.996510i | \(-0.473397\pi\) | ||||
0.0834792 | + | 0.996510i | \(0.473397\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.55181e6 | 0.844124 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.19513e6 | 1.37014 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.09567e6 | 0.348901 | 0.174451 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174451 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.91064e6 | −1.54421 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.49160e6 | −0.773779 | −0.386890 | − | 0.922126i | \(-0.626451\pi\) | ||||
−0.386890 | + | 0.922126i | \(0.626451\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.40083e6 | 0.429659 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −647056. | −0.193623 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.63349e6 | −1.07403 | −0.537014 | − | 0.843573i | \(-0.680448\pi\) | ||||
−0.537014 | + | 0.843573i | \(0.680448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.51099e6 | −0.441222 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.27892e6 | −1.81138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.75044e6 | −0.774572 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.64378e6 | 1.01395 | 0.506976 | − | 0.861960i | \(-0.330763\pi\) | ||||
0.506976 | + | 0.861960i | \(0.330763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.82530e6 | −0.501913 | −0.250957 | − | 0.967998i | \(-0.580745\pi\) | ||||
−0.250957 | + | 0.967998i | \(0.580745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −502054. | −0.136427 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.68308e6 | 1.77381 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.41725e6 | −0.371794 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.85435e6 | −0.740141 | −0.370070 | − | 0.929004i | \(-0.620666\pi\) | ||||
−0.370070 | + | 0.929004i | \(0.620666\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −587776. | −0.150658 | −0.0753290 | − | 0.997159i | \(-0.524001\pi\) | ||||
−0.0753290 | + | 0.997159i | \(0.524001\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.76612e6 | −0.692895 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.11604e6 | −1.51464 | −0.757319 | − | 0.653045i | \(-0.773491\pi\) | ||||
−0.757319 | + | 0.653045i | \(0.773491\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −383379. | −0.0938711 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.35771e6 | 0.570795 | 0.285398 | − | 0.958409i | \(-0.407874\pi\) | ||||
0.285398 | + | 0.958409i | \(0.407874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.94390e6 | −0.460156 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.49735e6 | 1.28688 | 0.643439 | − | 0.765497i | \(-0.277507\pi\) | ||||
0.643439 | + | 0.765497i | \(0.277507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −354904. | −0.0821617 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.82613e6 | 1.33393 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.16039e6 | −0.259905 | −0.129952 | − | 0.991520i | \(-0.541482\pi\) | ||||
−0.129952 | + | 0.991520i | \(0.541482\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.31488e6 | 1.84215 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.30330e6 | −0.504775 | −0.252387 | − | 0.967626i | \(-0.581216\pi\) | ||||
−0.252387 | + | 0.967626i | \(0.581216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.71343e6 | −0.588257 | −0.294128 | − | 0.955766i | \(-0.595029\pi\) | ||||
−0.294128 | + | 0.955766i | \(0.595029\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.05050e6 | −0.859441 | −0.429721 | − | 0.902962i | \(-0.641388\pi\) | ||||
−0.429721 | + | 0.902962i | \(0.641388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.07148e6 | 1.06464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.06351e6 | −1.25942 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −339512. | −0.0697754 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −139308. | −0.0280337 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.60528e6 | −1.11624 | −0.558121 | − | 0.829759i | \(-0.688478\pi\) | ||||
−0.558121 | + | 0.829759i | \(0.688478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.99045e6 | −0.589350 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.75615e6 | 0.537570 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.13168e6 | −1.36260 | −0.681301 | − | 0.732003i | \(-0.738586\pi\) | ||||
−0.681301 | + | 0.732003i | \(0.738586\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.08788e6 | 0.394850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.88145e6 | −1.10098 | −0.550492 | − | 0.834841i | \(-0.685560\pi\) | ||||
−0.550492 | + | 0.834841i | \(0.685560\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −552960. | −0.102465 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −671184. | −0.121885 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.75710e6 | −0.315897 | −0.157948 | − | 0.987447i | \(-0.550488\pi\) | ||||
−0.157948 | + | 0.987447i | \(0.550488\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.83443e6 | −1.39448 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.91411e6 | −0.866015 | −0.433007 | − | 0.901390i | \(-0.642548\pi\) | ||||
−0.433007 | + | 0.901390i | \(0.642548\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.35188e6 | −0.233571 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.75499e6 | −0.984578 | −0.492289 | − | 0.870432i | \(-0.663840\pi\) | ||||
−0.492289 | + | 0.870432i | \(0.663840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.75643e6 | −0.805803 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.01320e6 | −1.51212 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.58094e6 | 0.260128 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.81326e6 | −0.784369 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.61980e6 | −0.261437 | −0.130718 | − | 0.991420i | \(-0.541728\pi\) | ||||
−0.130718 | + | 0.991420i | \(0.541728\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.19117e7 | −1.90422 | −0.952112 | − | 0.305751i | \(-0.901093\pi\) | ||||
−0.952112 | + | 0.305751i | \(0.901093\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.19430e6 | 0.657860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.88383e6 | −0.758789 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.86778e6 | −0.287468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.64023e6 | −0.250085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 335720. | 0.0502391 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.20724e6 | 0.178986 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.07630e6 | 0.598788 | 0.299394 | − | 0.954130i | \(-0.403215\pi\) | ||||
0.299394 | + | 0.954130i | \(0.403215\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.12657e6 | 1.32834 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.23680e7 | −1.76739 | −0.883694 | − | 0.468065i | \(-0.844951\pi\) | ||||
−0.883694 | + | 0.468065i | \(0.844951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.98801e6 | 0.281505 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 599400. | 0.0841081 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.57424e6 | 0.775127 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 130308. | 0.0177964 | 0.00889822 | − | 0.999960i | \(-0.497168\pi\) | ||||
0.00889822 | + | 0.999960i | \(0.497168\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.56910e6 | −0.212383 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.24346e6 | −0.569262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.91687e6 | 0.786721 | 0.393361 | − | 0.919384i | \(-0.371312\pi\) | ||||
0.393361 | + | 0.919384i | \(0.371312\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.17620e6 | 0.937426 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.03013e6 | −1.16927 | −0.584633 | − | 0.811298i | \(-0.698761\pi\) | ||||
−0.584633 | + | 0.811298i | \(0.698761\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.07093e7 | 1.37459 | 0.687294 | − | 0.726379i | \(-0.258798\pi\) | ||||
0.687294 | + | 0.726379i | \(0.258798\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.83853e6 | 0.361166 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.22051e6 | −0.152617 | −0.0763084 | − | 0.997084i | \(-0.524313\pi\) | ||||
−0.0763084 | + | 0.997084i | \(0.524313\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.33718e6 | 0.785597 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.39651e6 | −0.540341 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 438672. | 0.0534526 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.47104e7 | 1.76210 | 0.881049 | − | 0.473026i | \(-0.156838\pi\) | ||||
0.881049 | + | 0.473026i | \(0.156838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.54656e6 | −0.540001 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.72455e6 | −0.556406 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.52014e6 | 0.994970 | 0.497485 | − | 0.867472i | \(-0.334257\pi\) | ||||
0.497485 | + | 0.867472i | \(0.334257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.85400e6 | −0.901893 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.90100e6 | −0.330355 | −0.165177 | − | 0.986264i | \(-0.552820\pi\) | ||||
−0.165177 | + | 0.986264i | \(0.552820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.72760e6 | 0.646825 | 0.323412 | − | 0.946258i | \(-0.395170\pi\) | ||||
0.323412 | + | 0.946258i | \(0.395170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.50861e6 | 0.168959 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.79924e6 | 0.969334 | 0.484667 | − | 0.874699i | \(-0.338941\pi\) | ||||
0.484667 | + | 0.874699i | \(0.338941\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −597240. | −0.0652538 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.30649e6 | 0.791782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.03408e6 | 0.111149 | 0.0555744 | − | 0.998455i | \(-0.482301\pi\) | ||||
0.0555744 | + | 0.998455i | \(0.482301\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.29854e7 | 1.37323 | 0.686616 | − | 0.727020i | \(-0.259095\pi\) | ||||
0.686616 | + | 0.727020i | \(0.259095\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.92002e6 | −0.830806 | −0.415403 | − | 0.909637i | \(-0.636359\pi\) | ||||
−0.415403 | + | 0.909637i | \(0.636359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.05876e6 | 0.526399 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.34632e7 | 1.38972 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.59984e6 | 0.467276 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.95386e6 | −0.902368 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.68218e7 | −1.68189 | −0.840945 | − | 0.541120i | \(-0.818001\pi\) | ||||
−0.840945 | + | 0.541120i | \(0.818001\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.12777e7 | −1.11869 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.57939e6 | 0.544801 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −199656. | −0.0193433 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.55154e7 | −1.49148 | −0.745741 | − | 0.666236i | \(-0.767904\pi\) | ||||
−0.745741 | + | 0.666236i | \(0.767904\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.05801e7 | −1.00916 | −0.504582 | − | 0.863364i | \(-0.668354\pi\) | ||||
−0.504582 | + | 0.863364i | \(0.668354\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.37883e7 | −1.29494 | −0.647471 | − | 0.762090i | \(-0.724173\pi\) | ||||
−0.647471 | + | 0.762090i | \(0.724173\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.88152e6 | 0.548123 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.53018e6 | 0.418950 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.58924e6 | −0.145850 | −0.0729248 | − | 0.997337i | \(-0.523233\pi\) | ||||
−0.0729248 | + | 0.997337i | \(0.523233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.41489e6 | −0.127882 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.12434e6 | 0.818442 | 0.409221 | − | 0.912435i | \(-0.365801\pi\) | ||||
0.409221 | + | 0.912435i | \(0.365801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.50310e6 | 0.578918 | 0.289459 | − | 0.957190i | \(-0.406525\pi\) | ||||
0.289459 | + | 0.957190i | \(0.406525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.96116e7 | −1.73273 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −336420. | −0.0292797 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.70598e7 | 1.47369 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.26010e6 | −0.536754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.17810e6 | −0.185370 | −0.0926850 | − | 0.995695i | \(-0.529545\pi\) | ||||
−0.0926850 | + | 0.995695i | \(0.529545\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.98419e6 | 0.334094 | 0.167047 | − | 0.985949i | \(-0.446577\pi\) | ||||
0.167047 | + | 0.985949i | \(0.446577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.53627e7 | 1.27877 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.90073e6 | 0.652829 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.91563e6 | 0.485231 | 0.242616 | − | 0.970122i | \(-0.421995\pi\) | ||||
0.242616 | + | 0.970122i | \(0.421995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.84462e6 | −0.634133 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.02738e6 | 0.162700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.55471e7 | 1.23867 | 0.619335 | − | 0.785127i | \(-0.287402\pi\) | ||||
0.619335 | + | 0.785127i | \(0.287402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.09905e6 | 0.0869328 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.91110e6 | −0.382910 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.11006e6 | 0.318167 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.27103e7 | −1.74553 | −0.872766 | − | 0.488139i | \(-0.837676\pi\) | ||||
−0.872766 | + | 0.488139i | \(0.837676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.70584e6 | 0.740704 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 679084. | 0.0510946 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.29841e6 | 0.470560 | 0.235280 | − | 0.971928i | \(-0.424399\pi\) | ||||
0.235280 | + | 0.971928i | \(0.424399\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.65816e6 | 0.123013 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.55181e6 | 0.187985 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.17936e6 | 0.594185 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.11911e7 | −1.52873 | −0.764367 | − | 0.644782i | \(-0.776948\pi\) | ||||
−0.764367 | + | 0.644782i | \(0.776948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.96100e7 | 1.40488 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.89317e6 | 0.561572 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.35610e7 | −0.951605 | −0.475803 | − | 0.879552i | \(-0.657842\pi\) | ||||
−0.475803 | + | 0.879552i | \(0.657842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59468e7 | 1.11136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.69811e6 | −0.325185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.69413e7 | 1.85208 | 0.926038 | − | 0.377429i | \(-0.123192\pi\) | ||||
0.926038 | + | 0.377429i | \(0.123192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.75050e6 | −0.322160 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.77414e6 | −0.186860 | −0.0934302 | − | 0.995626i | \(-0.529783\pi\) | ||||
−0.0934302 | + | 0.995626i | \(0.529783\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.12587e7 | 1.42230 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.85538e7 | −1.23299 | −0.616497 | − | 0.787358i | \(-0.711449\pi\) | ||||
−0.616497 | + | 0.787358i | \(0.711449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.30782e6 | −0.0857526 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.69004e6 | −0.435736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.19285e6 | 0.141876 | 0.0709380 | − | 0.997481i | \(-0.477401\pi\) | ||||
0.0709380 | + | 0.997481i | \(0.477401\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.42765e7 | −0.917558 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.48749e6 | −0.601744 | −0.300872 | − | 0.953665i | \(-0.597278\pi\) | ||||
−0.300872 | + | 0.953665i | \(0.597278\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.58171e6 | −0.162668 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.69580e6 | 0.606907 | 0.303453 | − | 0.952846i | \(-0.401860\pi\) | ||||
0.303453 | + | 0.952846i | \(0.401860\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.68642e6 | 0.353612 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.71822e7 | 1.66838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.32787e6 | 0.568809 | 0.284405 | − | 0.958704i | \(-0.408204\pi\) | ||||
0.284405 | + | 0.958704i | \(0.408204\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.20371e6 | −0.557606 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.68080e6 | −0.582723 | −0.291362 | − | 0.956613i | \(-0.594108\pi\) | ||||
−0.291362 | + | 0.956613i | \(0.594108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.67086e6 | −0.574662 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.32356e6 | 0.314310 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 628704. | 0.0368824 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.09620e6 | −0.0638977 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.52302e6 | 0.317863 | 0.158931 | − | 0.987290i | \(-0.449195\pi\) | ||||
0.158931 | + | 0.987290i | \(0.449195\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.87312e6 | −0.450251 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.61529e7 | 2.05448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.89318e7 | −1.63378 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.71119e7 | −0.954230 | −0.477115 | − | 0.878841i | \(-0.658318\pi\) | ||||
−0.477115 | + | 0.878841i | \(0.658318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.18767e7 | 1.21232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.00487e6 | 0.220550 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.45539e6 | 0.243836 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.13198e6 | −0.277397 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.45309e7 | −0.780586 | −0.390293 | − | 0.920691i | \(-0.627626\pi\) | ||||
−0.390293 | + | 0.920691i | \(0.627626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.13545e7 | 1.14009 | 0.570044 | − | 0.821614i | \(-0.306926\pi\) | ||||
0.570044 | + | 0.821614i | \(0.306926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.62505e7 | 0.862266 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.09268e6 | 0.266926 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.07938e6 | 0.264607 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.67967e7 | 1.90525 | 0.952623 | − | 0.304154i | \(-0.0983737\pi\) | ||||
0.952623 | + | 0.304154i | \(0.0983737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.30668e7 | 1.70174 | 0.850870 | − | 0.525376i | \(-0.176075\pi\) | ||||
0.850870 | + | 0.525376i | \(0.176075\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.77309e7 | −0.901505 | −0.450752 | − | 0.892649i | \(-0.648844\pi\) | ||||
−0.450752 | + | 0.892649i | \(0.648844\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.29375e7 | 0.653830 | 0.326915 | − | 0.945054i | \(-0.393991\pi\) | ||||
0.326915 | + | 0.945054i | \(0.393991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.52102e7 | 1.76875 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.67055e7 | 0.834157 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.31488e6 | 0.410244 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.31812e7 | −1.62738 | −0.813688 | − | 0.581302i | \(-0.802543\pi\) | ||||
−0.813688 | + | 0.581302i | \(0.802543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04382e7 | −0.996446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.92040e7 | −1.41538 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.19852e7 | 1.05299 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.13324e7 | −1.49185 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.44751e6 | −0.257854 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.17224e6 | −0.243392 | −0.121696 | − | 0.992567i | \(-0.538833\pi\) | ||||
−0.121696 | + | 0.992567i | \(0.538833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.05320e7 | −0.489845 | −0.244922 | − | 0.969543i | \(-0.578762\pi\) | ||||
−0.244922 | + | 0.969543i | \(0.578762\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.14741e7 | 0.530563 | 0.265282 | − | 0.964171i | \(-0.414535\pi\) | ||||
0.265282 | + | 0.964171i | \(0.414535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.30438e6 | −0.243852 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.92722e7 | −0.880856 | −0.440428 | − | 0.897788i | \(-0.645173\pi\) | ||||
−0.440428 | + | 0.897788i | \(0.645173\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.88423e7 | −1.75492 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.22144e6 | −0.234553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.19550e7 | −0.980593 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.56990e6 | 0.202942 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.30524e7 | 1.01208 | 0.506042 | − | 0.862509i | \(-0.331108\pi\) | ||||
0.506042 | + | 0.862509i | \(0.331108\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.36606e7 | 0.596344 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.26690e7 | 0.983994 | 0.491997 | − | 0.870597i | \(-0.336267\pi\) | ||||
0.491997 | + | 0.870597i | \(0.336267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.67337e6 | −0.158549 | −0.0792745 | − | 0.996853i | \(-0.525260\pi\) | ||||
−0.0792745 | + | 0.996853i | \(0.525260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.39649e7 | −1.44951 | −0.724755 | − | 0.689007i | \(-0.758047\pi\) | ||||
−0.724755 | + | 0.689007i | \(0.758047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.76876e7 | 1.17498 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.72201e6 | −0.283665 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.37140e7 | −0.995123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.19317e7 | −0.495132 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −552960. | −0.0228189 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.07027e6 | 0.249113 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.07433e6 | −0.207090 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.13327e7 | 0.861050 | 0.430525 | − | 0.902579i | \(-0.358328\pi\) | ||||
0.430525 | + | 0.902579i | \(0.358328\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 202006. | 0.00810876 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.03512e7 | 0.413235 | 0.206617 | − | 0.978422i | \(-0.433754\pi\) | ||||
0.206617 | + | 0.978422i | \(0.433754\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.11825e6 | 0.163507 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.73450e7 | 1.85931 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.59019e7 | 1.01168 | 0.505839 | − | 0.862628i | \(-0.331183\pi\) | ||||
0.505839 | + | 0.862628i | \(0.331183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.23001e6 | 0.0477816 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.90563e6 | 0.112263 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.83336e6 | 0.222956 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.13230e7 | −1.19076 | −0.595379 | − | 0.803445i | \(-0.702998\pi\) | ||||
−0.595379 | + | 0.803445i | \(0.702998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.81085e7 | −0.684714 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.39093e6 | 0.315577 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.08461e7 | −0.775667 | −0.387833 | − | 0.921729i | \(-0.626776\pi\) | ||||
−0.387833 | + | 0.921729i | \(0.626776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.93078e7 | 1.08472 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.82929e7 | −1.40976 | −0.704878 | − | 0.709328i | \(-0.748998\pi\) | ||||
−0.704878 | + | 0.709328i | \(0.748998\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.98791e6 | −0.109418 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.25088e7 | 1.54029 | 0.770147 | − | 0.637866i | \(-0.220183\pi\) | ||||
0.770147 | + | 0.637866i | \(0.220183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.05911e7 | 0.742189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.38275e7 | 1.21288 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.91855e7 | 1.39763 | 0.698816 | − | 0.715302i | \(-0.253711\pi\) | ||||
0.698816 | + | 0.715302i | \(0.253711\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 559440. | 0.0197458 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.70526e7 | −0.598749 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.44348e7 | −0.853495 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.99007e6 | −0.0691518 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.84836e7 | 0.635653 | 0.317827 | − | 0.948149i | \(-0.397047\pi\) | ||||
0.317827 | + | 0.948149i | \(0.397047\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.36518e7 | 2.17772 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.95031e7 | −1.34457 | −0.672284 | − | 0.740294i | \(-0.734686\pi\) | ||||
−0.672284 | + | 0.740294i | \(0.734686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.10407e7 | −1.05111 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.29043e7 | 1.10285 | 0.551425 | − | 0.834225i | \(-0.314084\pi\) | ||||
0.551425 | + | 0.834225i | \(0.314084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.26111e7 | −0.420529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.69153e6 | 0.0561186 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.65797e7 | 0.877338 | 0.438669 | − | 0.898649i | \(-0.355450\pi\) | ||||
0.438669 | + | 0.898649i | \(0.355450\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.36286e7 | 0.772049 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.85832e6 | −0.0929225 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.92964e7 | −0.624153 | −0.312077 | − | 0.950057i | \(-0.601025\pi\) | ||||
−0.312077 | + | 0.950057i | \(0.601025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.29733e7 | −0.739349 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.12017e7 | −1.63135 | −0.815674 | − | 0.578511i | \(-0.803634\pi\) | ||||
−0.815674 | + | 0.578511i | \(0.803634\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.77503e7 | −0.562720 |
(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 | 400.6.a.c.1.1 | 1 | ||
4.3 | odd | 2 | 50.6.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 80.6.c.c.49.2 | 2 | |||
5.3 | odd | 4 | 80.6.c.c.49.1 | 2 | |||
5.4 | even | 2 | 400.6.a.k.1.1 | 1 | |||
12.11 | even | 2 | 450.6.a.w.1.1 | 1 | |||
15.2 | even | 4 | 720.6.f.a.289.2 | 2 | |||
15.8 | even | 4 | 720.6.f.a.289.1 | 2 | |||
20.3 | even | 4 | 10.6.b.a.9.2 | yes | 2 | ||
20.7 | even | 4 | 10.6.b.a.9.1 | ✓ | 2 | ||
20.19 | odd | 2 | 50.6.a.e.1.1 | 1 | |||
40.3 | even | 4 | 320.6.c.b.129.1 | 2 | |||
40.13 | odd | 4 | 320.6.c.a.129.2 | 2 | |||
40.27 | even | 4 | 320.6.c.b.129.2 | 2 | |||
40.37 | odd | 4 | 320.6.c.a.129.1 | 2 | |||
60.23 | odd | 4 | 90.6.c.a.19.1 | 2 | |||
60.47 | odd | 4 | 90.6.c.a.19.2 | 2 | |||
60.59 | even | 2 | 450.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.b.a.9.1 | ✓ | 2 | 20.7 | even | 4 | ||
10.6.b.a.9.2 | yes | 2 | 20.3 | even | 4 | ||
50.6.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
50.6.a.e.1.1 | 1 | 20.19 | odd | 2 | |||
80.6.c.c.49.1 | 2 | 5.3 | odd | 4 | |||
80.6.c.c.49.2 | 2 | 5.2 | odd | 4 | |||
90.6.c.a.19.1 | 2 | 60.23 | odd | 4 | |||
90.6.c.a.19.2 | 2 | 60.47 | odd | 4 | |||
320.6.c.a.129.1 | 2 | 40.37 | odd | 4 | |||
320.6.c.a.129.2 | 2 | 40.13 | odd | 4 | |||
320.6.c.b.129.1 | 2 | 40.3 | even | 4 | |||
320.6.c.b.129.2 | 2 | 40.27 | even | 4 | |||
400.6.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
400.6.a.k.1.1 | 1 | 5.4 | even | 2 | |||
450.6.a.c.1.1 | 1 | 60.59 | even | 2 | |||
450.6.a.w.1.1 | 1 | 12.11 | even | 2 | |||
720.6.f.a.289.1 | 2 | 15.8 | even | 4 | |||
720.6.f.a.289.2 | 2 | 15.2 | even | 4 |