Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,6,Mod(1,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, 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("392.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.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: | \(62.8704573667\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 328x^{4} - 1328x^{3} + 25933x^{2} + 205840x + 390334 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(15.8064\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.1 |
$q$-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 | ||||||||
\(3\) | 17.5252 | 1.12425 | 0.562123 | − | 0.827054i | \(-0.309985\pi\) | ||||
0.562123 | + | 0.827054i | \(0.309985\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −11.0064 | −0.196889 | −0.0984443 | − | 0.995143i | \(-0.531387\pi\) | ||||
−0.0984443 | + | 0.995143i | \(0.531387\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 64.1343 | 0.263927 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −95.0461 | −0.236839 | −0.118419 | − | 0.992964i | \(-0.537783\pi\) | ||||
−0.118419 | + | 0.992964i | \(0.537783\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −157.485 | −0.258452 | −0.129226 | − | 0.991615i | \(-0.541249\pi\) | ||||
−0.129226 | + | 0.991615i | \(0.541249\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −192.890 | −0.221351 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 100.530 | 0.0843669 | 0.0421834 | − | 0.999110i | \(-0.486569\pi\) | ||||
0.0421834 | + | 0.999110i | \(0.486569\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −664.804 | −0.422483 | −0.211242 | − | 0.977434i | \(-0.567751\pi\) | ||||
−0.211242 | + | 0.977434i | \(0.567751\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2141.54 | 0.844125 | 0.422062 | − | 0.906567i | \(-0.361306\pi\) | ||||
0.422062 | + | 0.906567i | \(0.361306\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3003.86 | −0.961235 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3134.67 | −0.827526 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3050.77 | −0.673619 | −0.336809 | − | 0.941573i | \(-0.609348\pi\) | ||||
−0.336809 | + | 0.941573i | \(0.609348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3084.25 | −0.576429 | −0.288215 | − | 0.957566i | \(-0.593062\pi\) | ||||
−0.288215 | + | 0.957566i | \(0.593062\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1665.71 | −0.266265 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11872.7 | 1.42576 | 0.712879 | − | 0.701287i | \(-0.247391\pi\) | ||||
0.712879 | + | 0.701287i | \(0.247391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2759.96 | −0.290564 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4013.50 | −0.372875 | −0.186438 | − | 0.982467i | \(-0.559694\pi\) | ||||
−0.186438 | + | 0.982467i | \(0.559694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10366.6 | −0.854995 | −0.427497 | − | 0.904017i | \(-0.640605\pi\) | ||||
−0.427497 | + | 0.904017i | \(0.640605\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −705.888 | −0.0519642 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22647.4 | −1.49546 | −0.747729 | − | 0.664004i | \(-0.768856\pi\) | ||||
−0.747729 | + | 0.664004i | \(0.768856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1761.81 | 0.0948491 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −27712.6 | −1.35515 | −0.677576 | − | 0.735453i | \(-0.736969\pi\) | ||||
−0.677576 | + | 0.735453i | \(0.736969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1046.12 | 0.0466308 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11650.9 | −0.474975 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −23383.9 | −0.874553 | −0.437276 | − | 0.899327i | \(-0.644057\pi\) | ||||
−0.437276 | + | 0.899327i | \(0.644057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10242.6 | 0.352440 | 0.176220 | − | 0.984351i | \(-0.443613\pi\) | ||||
0.176220 | + | 0.984351i | \(0.443613\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1733.34 | 0.0508863 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6555.18 | 0.178401 | 0.0892006 | − | 0.996014i | \(-0.471569\pi\) | ||||
0.0892006 | + | 0.996014i | \(0.471569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 37531.0 | 0.949003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −21269.5 | −0.500739 | −0.250370 | − | 0.968150i | \(-0.580552\pi\) | ||||
−0.250370 | + | 0.968150i | \(0.580552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −313.509 | −0.00688562 | −0.00344281 | − | 0.999994i | \(-0.501096\pi\) | ||||
−0.00344281 | + | 0.999994i | \(0.501096\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −52643.4 | −1.08066 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −59231.2 | −1.06778 | −0.533891 | − | 0.845553i | \(-0.679271\pi\) | ||||
−0.533891 | + | 0.845553i | \(0.679271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −70520.4 | −1.19427 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 107561. | 1.71380 | 0.856901 | − | 0.515481i | \(-0.172387\pi\) | ||||
0.856901 | + | 0.515481i | \(0.172387\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1106.47 | −0.0166109 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −53465.4 | −0.757312 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 88357.3 | 1.18241 | 0.591204 | − | 0.806522i | \(-0.298653\pi\) | ||||
0.591204 | + | 0.806522i | \(0.298653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −54052.3 | −0.648048 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7317.11 | 0.0831822 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 164187. | 1.77178 | 0.885891 | − | 0.463894i | \(-0.153548\pi\) | ||||
0.885891 | + | 0.463894i | \(0.153548\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6095.71 | −0.0625081 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −29974.5 | −0.292381 | −0.146190 | − | 0.989256i | \(-0.546701\pi\) | ||||
−0.146190 | + | 0.989256i | \(0.546701\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −81692.8 | −0.758736 | −0.379368 | − | 0.925246i | \(-0.623859\pi\) | ||||
−0.379368 | + | 0.925246i | \(0.623859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −56710.6 | −0.478856 | −0.239428 | − | 0.970914i | \(-0.576960\pi\) | ||||
−0.239428 | + | 0.970914i | \(0.576960\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −185773. | −1.49767 | −0.748837 | − | 0.662754i | \(-0.769387\pi\) | ||||
−0.748837 | + | 0.662754i | \(0.769387\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 208072. | 1.60290 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −47906.7 | −0.352940 | −0.176470 | − | 0.984306i | \(-0.556468\pi\) | ||||
−0.176470 | + | 0.984306i | \(0.556468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23570.7 | −0.166199 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10100.2 | −0.0682125 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −152017. | −0.943907 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −70337.5 | −0.419203 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 67456.7 | 0.386145 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −30596.7 | −0.168331 | −0.0841656 | − | 0.996452i | \(-0.526822\pi\) | ||||
−0.0841656 | + | 0.996452i | \(0.526822\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −181676. | −0.961224 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −138321. | −0.704223 | −0.352111 | − | 0.935958i | \(-0.614536\pi\) | ||||
−0.352111 | + | 0.935958i | \(0.614536\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 34501.4 | 0.162931 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −147583. | −0.671793 | −0.335897 | − | 0.941899i | \(-0.609039\pi\) | ||||
−0.335897 | + | 0.941899i | \(0.609039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 167389. | 0.734834 | 0.367417 | − | 0.930056i | \(-0.380242\pi\) | ||||
0.367417 | + | 0.930056i | \(0.380242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −396902. | −1.68126 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14968.3 | 0.0612115 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33578.0 | 0.132628 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 149761. | 0.552627 | 0.276314 | − | 0.961068i | \(-0.410887\pi\) | ||||
0.276314 | + | 0.961068i | \(0.410887\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −320225. | −1.14291 | −0.571456 | − | 0.820633i | \(-0.693621\pi\) | ||||
−0.571456 | + | 0.820633i | \(0.693621\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6447.40 | 0.0222667 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33946.6 | 0.113492 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −335799. | −1.08725 | −0.543626 | − | 0.839328i | \(-0.682949\pi\) | ||||
−0.543626 | + | 0.839328i | \(0.682949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −485670. | −1.52352 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 494956. | 1.45914 | 0.729571 | − | 0.683905i | \(-0.239720\pi\) | ||||
0.729571 | + | 0.683905i | \(0.239720\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18333.4 | 0.0524245 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 162081. | 0.449717 | 0.224859 | − | 0.974391i | \(-0.427808\pi\) | ||||
0.224859 | + | 0.974391i | \(0.427808\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −346492. | −0.933202 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −42636.7 | −0.111505 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −162681. | −0.413257 | −0.206629 | − | 0.978419i | \(-0.566249\pi\) | ||||
−0.206629 | + | 0.978419i | \(0.566249\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −409808. | −0.983212 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −461348. | −1.07621 | −0.538104 | − | 0.842879i | \(-0.680859\pi\) | ||||
−0.538104 | + | 0.842879i | \(0.680859\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −603891. | −1.37013 | −0.685065 | − | 0.728482i | \(-0.740226\pi\) | ||||
−0.685065 | + | 0.728482i | \(0.740226\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 179504. | 0.396229 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −130676. | −0.280716 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9554.95 | −0.0199813 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 560655. | 1.11202 | 0.556010 | − | 0.831176i | \(-0.312332\pi\) | ||||
0.556010 | + | 0.831176i | \(0.312332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 165122. | 0.319089 | 0.159544 | − | 0.987191i | \(-0.448997\pi\) | ||||
0.159544 | + | 0.987191i | \(0.448997\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 30377.2 | 0.0572087 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −678116. | −1.24491 | −0.622456 | − | 0.782655i | \(-0.713865\pi\) | ||||
−0.622456 | + | 0.782655i | \(0.713865\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 370360. | 0.662965 | 0.331483 | − | 0.943461i | \(-0.392451\pi\) | ||||
0.331483 | + | 0.943461i | \(0.392451\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 114881. | 0.200567 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 44174.2 | 0.0734148 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 137346. | 0.222787 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 63187.0 | 0.100060 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 884876. | 1.36828 | 0.684142 | − | 0.729349i | \(-0.260177\pi\) | ||||
0.684142 | + | 0.729349i | \(0.260177\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −372754. | −0.562954 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 114099. | 0.168339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5494.32 | −0.00774112 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15831.9 | −0.0218048 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 307029. | 0.413444 | 0.206722 | − | 0.978400i | \(-0.433720\pi\) | ||||
0.206722 | + | 0.978400i | \(0.433720\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −192650. | −0.253696 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.05427e6 | 1.35797 | 0.678983 | − | 0.734154i | \(-0.262421\pi\) | ||||
0.678983 | + | 0.734154i | \(0.262421\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 768119. | 0.967921 | 0.483960 | − | 0.875090i | \(-0.339198\pi\) | ||||
0.483960 | + | 0.875090i | \(0.339198\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.16012e6 | −1.39995 | −0.699976 | − | 0.714166i | \(-0.746806\pi\) | ||||
−0.699976 | + | 0.714166i | \(0.746806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 249267. | 0.294439 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.03804e6 | −1.20045 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.14943e6 | 1.30163 | 0.650816 | − | 0.759235i | \(-0.274427\pi\) | ||||
0.650816 | + | 0.759235i | \(0.274427\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 112291. | 0.124538 | 0.0622691 | − | 0.998059i | \(-0.480166\pi\) | ||||
0.0622691 | + | 0.998059i | \(0.480166\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −474164. | −0.515125 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 104697. | 0.109192 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.88504e6 | 1.92673 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 214195. | 0.214598 | 0.107299 | − | 0.994227i | \(-0.465780\pi\) | ||||
0.107299 | + | 0.994227i | \(0.465780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −203545. | −0.199921 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19391.2 | −0.0186747 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.03227e6 | 1.91932 | 0.959662 | − | 0.281156i | \(-0.0907177\pi\) | ||||
0.959662 | + | 0.281156i | \(0.0907177\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −195659. | −0.177786 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.09547e6 | 0.976584 | 0.488292 | − | 0.872680i | \(-0.337620\pi\) | ||||
0.488292 | + | 0.872680i | \(0.337620\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 305016. | 0.266814 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.54848e6 | 1.32932 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 311944. | 0.262843 | 0.131421 | − | 0.991327i | \(-0.458046\pi\) | ||||
0.131421 | + | 0.991327i | \(0.458046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 67932.4 | 0.0561893 | 0.0280947 | − | 0.999605i | \(-0.491056\pi\) | ||||
0.0280947 | + | 0.999605i | \(0.491056\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 285505. | 0.227658 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −498271. | −0.390181 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −197807. | −0.152135 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.47068e6 | 1.11110 | 0.555549 | − | 0.831484i | \(-0.312508\pi\) | ||||
0.555549 | + | 0.831484i | \(0.312508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.34284e6 | 0.996682 | 0.498341 | − | 0.866981i | \(-0.333943\pi\) | ||||
0.498341 | + | 0.866981i | \(0.333943\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 128234. | 0.0935172 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.40975e6 | −0.992882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.87742e6 | 1.99192 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.20931e6 | −1.50345 | −0.751724 | − | 0.659478i | \(-0.770777\pi\) | ||||
−0.751724 | + | 0.659478i | \(0.770777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 257372. | 0.172189 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 297938. | 0.195990 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −337260. | −0.218166 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −525311. | −0.328708 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −112734. | −0.0693914 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.47223e6 | −0.891516 | −0.445758 | − | 0.895153i | \(-0.647066\pi\) | ||||
−0.445758 | + | 0.895153i | \(0.647066\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.43169e6 | −0.853005 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 687625. | 0.403135 | 0.201568 | − | 0.979475i | \(-0.435396\pi\) | ||||
0.201568 | + | 0.979475i | \(0.435396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.27656e6 | 1.89041 | 0.945206 | − | 0.326473i | \(-0.105860\pi\) | ||||
0.945206 | + | 0.326473i | \(0.105860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.35932e6 | 1.31868 | 0.659338 | − | 0.751847i | \(-0.270837\pi\) | ||||
0.659338 | + | 0.751847i | \(0.270837\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 289963. | 0.159539 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −993867. | −0.538351 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −66832.6 | −0.0356436 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 473062. | 0.248433 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.25572e6 | −1.68375 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.14714e6 | 0.575502 | 0.287751 | − | 0.957705i | \(-0.407092\pi\) | ||||
0.287751 | + | 0.957705i | \(0.407092\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 761449. | 0.376296 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −72149.0 | −0.0351251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.34477e6 | 0.645020 | 0.322510 | − | 0.946566i | \(-0.395473\pi\) | ||||
0.322510 | + | 0.946566i | \(0.395473\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −839578. | −0.396791 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 293146. | 0.136521 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −413082. | −0.186848 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 769358. | 0.343008 | 0.171504 | − | 0.985183i | \(-0.445137\pi\) | ||||
0.171504 | + | 0.985183i | \(0.445137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.34745e6 | −1.47113 | −0.735564 | − | 0.677455i | \(-0.763083\pi\) | ||||
−0.735564 | + | 0.677455i | \(0.763083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 493662. | 0.213876 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.72600e6 | 0.737231 | 0.368615 | − | 0.929582i | \(-0.379832\pi\) | ||||
0.368615 | + | 0.929582i | \(0.379832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 234101. | 0.0985899 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.25940e6 | 0.925245 | 0.462623 | − | 0.886555i | \(-0.346909\pi\) | ||||
0.462623 | + | 0.886555i | \(0.346909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03413e6 | −0.821508 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.66414e6 | −1.06118 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3450.61 | 0.00135570 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −837273. | −0.324490 | −0.162245 | − | 0.986750i | \(-0.551874\pi\) | ||||
−0.162245 | + | 0.986750i | \(0.551874\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −257403. | −0.0984118 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.69908e6 | 1.37665 | 0.688323 | − | 0.725405i | \(-0.258347\pi\) | ||||
0.688323 | + | 0.725405i | \(0.258347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.18220e6 | 0.434121 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 480449. | 0.174098 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −752171. | −0.268979 | −0.134490 | − | 0.990915i | \(-0.542939\pi\) | ||||
−0.134490 | + | 0.990915i | \(0.542939\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −536214. | −0.189246 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −396510. | −0.138120 | −0.0690601 | − | 0.997613i | \(-0.522000\pi\) | ||||
−0.0690601 | + | 0.997613i | \(0.522000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −664852. | −0.225656 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.46111e6 | −1.15969 | −0.579844 | − | 0.814727i | \(-0.696887\pi\) | ||||
−0.579844 | + | 0.814727i | \(0.696887\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 215288. | 0.0712162 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.42411e6 | −0.791719 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 651923. | 0.210234 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 424548. | 0.135192 | 0.0675959 | − | 0.997713i | \(-0.478467\pi\) | ||||
0.0675959 | + | 0.997713i | \(0.478467\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −520438. | −0.161625 | −0.0808124 | − | 0.996729i | \(-0.525751\pi\) | ||||
−0.0808124 | + | 0.996729i | \(0.525751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 485723. | 0.148979 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 776177. | 0.235138 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.12846e6 | −0.337675 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −964439. | −0.285080 | −0.142540 | − | 0.989789i | \(-0.545527\pi\) | ||||
−0.142540 | + | 0.989789i | \(0.545527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.58643e6 | −0.755260 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.18386e6 | −0.337428 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.93353e6 | 0.826134 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 588781. | 0.163840 | 0.0819198 | − | 0.996639i | \(-0.473895\pi\) | ||||
0.0819198 | + | 0.996639i | \(0.473895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29013.6 | 0.00797804 | 0.00398902 | − | 0.999992i | \(-0.498730\pi\) | ||||
0.00398902 | + | 0.999992i | \(0.498730\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.45248e6 | −0.394692 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −301977. | −0.0810964 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 262323. | 0.0688167 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.08256e6 | −1.31792 | −0.658960 | − | 0.752178i | \(-0.729004\pi\) | ||||
−0.658960 | + | 0.752178i | \(0.729004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.61686e6 | 1.18339 | 0.591694 | − | 0.806163i | \(-0.298460\pi\) | ||||
0.591694 | + | 0.806163i | \(0.298460\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 588462. | 0.149106 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.42370e6 | −0.356629 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.42017e6 | 0.847005 | 0.423503 | − | 0.905895i | \(-0.360800\pi\) | ||||
0.423503 | + | 0.905895i | \(0.360800\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −549597. | −0.133056 | −0.0665281 | − | 0.997785i | \(-0.521192\pi\) | ||||
−0.0665281 | + | 0.997785i | \(0.521192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −972496. | −0.232803 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.62459e6 | 0.621289 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.98225e6 | 0.698116 | 0.349058 | − | 0.937101i | \(-0.386502\pi\) | ||||
0.349058 | + | 0.937101i | \(0.386502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 381467. | 0.0883112 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.61202e6 | −1.28491 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.65175e6 | −1.26588 | −0.632939 | − | 0.774201i | \(-0.718152\pi\) | ||||
−0.632939 | + | 0.774201i | \(0.718152\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −315127. | −0.0698158 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.17668e6 | 0.696179 | 0.348089 | − | 0.937461i | \(-0.386831\pi\) | ||||
0.348089 | + | 0.937461i | \(0.386831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.69966e6 | −1.23565 | −0.617826 | − | 0.786315i | \(-0.711987\pi\) | ||||
−0.617826 | + | 0.786315i | \(0.711987\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 594922. | 0.127593 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.63943e6 | 0.984402 | 0.492201 | − | 0.870481i | \(-0.336192\pi\) | ||||
0.492201 | + | 0.870481i | \(0.336192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.88496e6 | −1.22234 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 985301. | 0.202496 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.99698e6 | 0.406106 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.77733e6 | −0.357661 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.20916e6 | −0.439934 | −0.219967 | − | 0.975507i | \(-0.570595\pi\) | ||||
−0.219967 | + | 0.975507i | \(0.570595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.86977e6 | −0.368490 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.80711e6 | −0.348844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.82289e6 | −1.49467 | −0.747334 | − | 0.664449i | \(-0.768666\pi\) | ||||
−0.747334 | + | 0.664449i | \(0.768666\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.67422e6 | 1.64043 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.08903e6 | 0.765449 | 0.382724 | − | 0.923863i | \(-0.374986\pi\) | ||||
0.382724 | + | 0.923863i | \(0.374986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −306693. | −0.0568311 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 67091.9 | 0.0123071 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −911248. | −0.163827 | −0.0819135 | − | 0.996639i | \(-0.526103\pi\) | ||||
−0.0819135 | + | 0.996639i | \(0.526103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.84050e6 | 0.505593 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.10725e7 | 1.95130 | 0.975649 | − | 0.219336i | \(-0.0703890\pi\) | ||||
0.975649 | + | 0.219336i | \(0.0703890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 329912. | 0.0575664 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.07235e6 | −1.04915 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.80487e6 | −1.16419 | −0.582097 | − | 0.813119i | \(-0.697768\pi\) | ||||
−0.582097 | + | 0.813119i | \(0.697768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.08394e6 | 0.349616 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 899144. | 0.149386 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.15255e6 | 0.354182 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.85102e6 | −0.464603 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.44538e6 | −0.717487 | −0.358744 | − | 0.933436i | \(-0.616795\pi\) | ||||
−0.358744 | + | 0.933436i | \(0.616795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.72959e6 | 1.39553 | 0.697766 | − | 0.716326i | \(-0.254178\pi\) | ||||
0.697766 | + | 0.716326i | \(0.254178\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −310059. | −0.0486315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.85015e6 | −0.287453 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.49971e6 | −0.230818 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 632065. | 0.0963703 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 624180. | 0.0942813 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.08524e6 | −1.20992 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.73878e6 | −0.549208 | −0.274604 | − | 0.961557i | \(-0.588547\pi\) | ||||
−0.274604 | + | 0.961557i | \(0.588547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.05833e7 | −1.54036 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.04470e6 | 0.294875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.95708e6 | −1.27996 | −0.639982 | − | 0.768390i | \(-0.721058\pi\) | ||||
−0.639982 | + | 0.768390i | \(0.721058\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 656901. | 0.0930184 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.02816e6 | 0.284593 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.29013e6 | −0.315593 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.40749e6 | −0.465368 | −0.232684 | − | 0.972552i | \(-0.574751\pi\) | ||||
−0.232684 | + | 0.972552i | \(0.574751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.63257e6 | 0.220975 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −167453. | −0.0224639 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.39433e6 | 0.983169 | 0.491584 | − | 0.870830i | \(-0.336418\pi\) | ||||
0.491584 | + | 0.870830i | \(0.336418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 527281. | 0.0694898 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.39745e6 | 0.569404 | 0.284702 | − | 0.958616i | \(-0.408105\pi\) | ||||
0.284702 | + | 0.958616i | \(0.408105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.11677e6 | −0.528405 | −0.264202 | − | 0.964467i | \(-0.585109\pi\) | ||||
−0.264202 | + | 0.964467i | \(0.585109\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.82562e6 | 1.25018 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.43289e6 | −0.811402 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.12253e6 | −0.640538 | −0.320269 | − | 0.947327i | \(-0.603773\pi\) | ||||
−0.320269 | + | 0.947327i | \(0.603773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.89380e6 | 0.358734 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.63398e6 | 0.320952 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 111167. | 0.0134303 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.04610e7 | −1.25308 | −0.626538 | − | 0.779391i | \(-0.715529\pi\) | ||||
−0.626538 | + | 0.779391i | \(0.715529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.05043e6 | 0.243532 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18842e7 | −1.39959 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.38124e7 | −1.61300 | −0.806498 | − | 0.591237i | \(-0.798640\pi\) | ||||
−0.806498 | + | 0.591237i | \(0.798640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.49064e6 | 0.745336 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.74704e6 | −0.426699 | −0.213349 | − | 0.976976i | \(-0.568437\pi\) | ||||
−0.213349 | + | 0.976976i | \(0.568437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.77914e6 | −1.10437 | −0.552185 | − | 0.833722i | \(-0.686206\pi\) | ||||
−0.552185 | + | 0.833722i | \(0.686206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 420412. | 0.0470849 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.67316e6 | 0.185845 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −334361. | −0.0368336 | −0.0184168 | − | 0.999830i | \(-0.505863\pi\) | ||||
−0.0184168 | + | 0.999830i | \(0.505863\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.56662e6 | 0.386504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.08435e6 | 0.116551 | 0.0582756 | − | 0.998301i | \(-0.481440\pi\) | ||||
0.0582756 | + | 0.998301i | \(0.481440\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 774164. | 0.0825363 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.42021e6 | 0.784699 | 0.392350 | − | 0.919816i | \(-0.371662\pi\) | ||||
0.392350 | + | 0.919816i | \(0.371662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.44590e6 | −0.256574 | −0.128287 | − | 0.991737i | \(-0.540948\pi\) | ||||
−0.128287 | + | 0.991737i | \(0.540948\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.71301e6 | −0.698536 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.64460e6 | 0.885207 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.10737e6 | 0.112492 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.19356e6 | 0.120287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.54761e7 | −1.54735 | −0.773673 | − | 0.633585i | \(-0.781583\pi\) | ||||
−0.773673 | + | 0.633585i | \(0.781583\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.55077e7 | 1.53829 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 336759. | 0.0331425 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.36411e6 | −0.132159 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.75649e6 | −0.841753 | −0.420877 | − | 0.907118i | \(-0.638277\pi\) | ||||
−0.420877 | + | 0.907118i | \(0.638277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.29737e7 | −1.23747 | −0.618736 | − | 0.785599i | \(-0.712355\pi\) | ||||
−0.618736 | + | 0.785599i | \(0.712355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.99961e6 | 0.189254 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.82476e6 | −0.453121 | −0.226561 | − | 0.973997i | \(-0.572748\pi\) | ||||
−0.226561 | + | 0.973997i | \(0.572748\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.22254e6 | 0.207128 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 781133. | 0.0716873 | 0.0358436 | − | 0.999357i | \(-0.488588\pi\) | ||||
0.0358436 | + | 0.999357i | \(0.488588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.52242e6 | 0.138653 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20106.7 | −0.00181730 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.55442e6 | −0.318827 | −0.159414 | − | 0.987212i | \(-0.550960\pi\) | ||||
−0.159414 | + | 0.987212i | \(0.550960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.88767e6 | −0.880219 | −0.440109 | − | 0.897944i | \(-0.645060\pi\) | ||||
−0.440109 | + | 0.897944i | \(0.645060\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −277458. | −0.0245139 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.53334e6 | −0.568618 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.38075e6 | 0.464813 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −973517. | −0.0834713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.64825e6 | −0.821128 | −0.410564 | − | 0.911832i | \(-0.634668\pi\) | ||||
−0.410564 | + | 0.911832i | \(0.634668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.41609e6 | 0.795447 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 434057. | 0.0363978 | 0.0181989 | − | 0.999834i | \(-0.494207\pi\) | ||||
0.0181989 | + | 0.999834i | \(0.494207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.84764e7 | 1.52669 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.20366e7 | 1.80756 | 0.903778 | − | 0.428001i | \(-0.140782\pi\) | ||||
0.903778 | + | 0.428001i | \(0.140782\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.62436e6 | 0.132268 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.34615e7 | 1.08818 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.36431e6 | 0.350242 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.00504e7 | 0.800737 | 0.400369 | − | 0.916354i | \(-0.368882\pi\) | ||||
0.400369 | + | 0.916354i | \(0.368882\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.84235e6 | −0.144680 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −403476. | −0.0314583 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.03314e7 | −1.57389 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.39421e7 | 1.84021 | 0.920106 | − | 0.391668i | \(-0.128102\pi\) | ||||
0.920106 | + | 0.391668i | \(0.128102\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.89303e6 | −0.602359 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.36846e6 | 0.331021 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.05493e7 | −0.788148 | −0.394074 | − | 0.919079i | \(-0.628935\pi\) | ||||
−0.394074 | + | 0.919079i | \(0.628935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.79875e6 | −0.281817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.60506e6 | −0.486578 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −164747. | −0.0120518 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.01441e7 | 1.46335 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.30506e6 | −0.671270 | −0.335635 | − | 0.941992i | \(-0.608951\pi\) | ||||
−0.335635 | + | 0.941992i | \(0.608951\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.96793e6 | 0.140012 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.16407e6 | 0.647506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.88455e6 | 0.272587 | 0.136294 | − | 0.990668i | \(-0.456481\pi\) | ||||
0.136294 | + | 0.990668i | \(0.456481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.82662e6 | 0.615142 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.04215e6 | −0.0721332 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.15755e7 | 1.48320 | 0.741602 | − | 0.670840i | \(-0.234066\pi\) | ||||
0.741602 | + | 0.670840i | \(0.234066\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −623044. | −0.0422523 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.79027e7 | 1.87947 | 0.939733 | − | 0.341909i | \(-0.111074\pi\) | ||||
0.939733 | + | 0.341909i | \(0.111074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.83483e6 | 0.122758 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.11208e7 | −1.40358 | −0.701790 | − | 0.712384i | \(-0.747616\pi\) | ||||
−0.701790 | + | 0.712384i | \(0.747616\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.64833e6 | −0.108806 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.89837e6 | 0.452319 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.86917e7 | −1.85634 | −0.928168 | − | 0.372161i | \(-0.878617\pi\) | ||||
−0.928168 | + | 0.372161i | \(0.878617\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.75382e6 | 0.241261 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.52452e6 | 0.225026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.39601e7 | 0.885421 | 0.442710 | − | 0.896665i | \(-0.354017\pi\) | ||||
0.442710 | + | 0.896665i | \(0.354017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.56718e6 | −0.224761 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.41380e6 | −0.151091 | −0.0755456 | − | 0.997142i | \(-0.524070\pi\) | ||||
−0.0755456 | + | 0.997142i | \(0.524070\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −70962.7 | −0.00438406 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.68260e6 | 0.226030 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00276e7 | −1.22128 | −0.610638 | − | 0.791910i | \(-0.709087\pi\) | ||||
−0.610638 | + | 0.791910i | \(0.709087\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.56160e7 | 2.15779 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.75771e7 | 1.65997 | 0.829983 | − | 0.557789i | \(-0.188350\pi\) | ||||
0.829983 | + | 0.557789i | \(0.188350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.26467e6 | 0.554084 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.66819e6 | 0.157534 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.02158e6 | 0.118594 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.56313e6 | 0.557437 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.69594e6 | 0.214068 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.74369e7 | 1.00354 | 0.501769 | − | 0.865002i | \(-0.332683\pi\) | ||||
0.501769 | + | 0.865002i | \(0.332683\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.91983e7 | 1.09792 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.61305e6 | −0.0910888 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.34549e6 | 0.299964 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.96631e6 | 0.388469 | 0.194235 | − | 0.980955i | \(-0.437778\pi\) | ||||
0.194235 | + | 0.980955i | \(0.437778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.27674e6 | −0.126167 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.66673e6 | 0.312069 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29797.8 | 0.00163078 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.46690e6 | 0.295500 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.66666e6 | 0.519285 | 0.259642 | − | 0.965705i | \(-0.416395\pi\) | ||||
0.259642 | + | 0.965705i | \(0.416395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.47649e7 | −1.85604 | −0.928022 | − | 0.372525i | \(-0.878492\pi\) | ||||
−0.928022 | + | 0.372525i | \(0.878492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.19053e6 | 0.0631706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.44768e6 | −0.287288 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.89173e6 | 0.361221 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.42770e7 | −0.739231 | −0.369616 | − | 0.929185i | \(-0.620511\pi\) | ||||
−0.369616 | + | 0.929185i | \(0.620511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.54227e6 | 0.491080 | 0.245540 | − | 0.969386i | \(-0.421035\pi\) | ||||
0.245540 | + | 0.969386i | \(0.421035\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.00355e6 | 0.255943 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.08484e7 | 1.56844 | 0.784222 | − | 0.620480i | \(-0.213062\pi\) | ||||
0.784222 | + | 0.620480i | \(0.213062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.18676e7 | −0.599757 | −0.299878 | − | 0.953977i | \(-0.596946\pi\) | ||||
−0.299878 | + | 0.953977i | \(0.596946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.73232e6 | −0.438659 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.78392e6 | −0.0885442 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.66811e6 | 0.477010 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.05321e7 | 1.00700 | 0.503499 | − | 0.863996i | \(-0.332046\pi\) | ||||
0.503499 | + | 0.863996i | \(0.332046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.12040e7 | −0.546238 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.57740e7 | 1.24915 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.81363e6 | 0.183737 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.35335e7 | 1.12052 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.54259e7 | 1.20352 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 543335. | 0.0255679 | 0.0127840 | − | 0.999918i | \(-0.495931\pi\) | ||||
0.0127840 | + | 0.999918i | \(0.495931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 469277. | 0.0219540 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.85917e7 | −0.864704 | −0.432352 | − | 0.901705i | \(-0.642316\pi\) | ||||
−0.432352 | + | 0.901705i | \(0.642316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.15483e7 | 0.996394 | 0.498197 | − | 0.867064i | \(-0.333996\pi\) | ||||
0.498197 | + | 0.867064i | \(0.333996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.80274e7 | 0.823958 | 0.411979 | − | 0.911193i | \(-0.364838\pi\) | ||||
0.411979 | + | 0.911193i | \(0.364838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.79053e6 | 0.0813657 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.47062e7 | −1.11624 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.62969e6 | 0.252892 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.03234e6 | −0.0461082 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.05300e7 | 0.467621 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.98502e7 | −1.31053 | −0.655267 | − | 0.755397i | \(-0.727444\pi\) | ||||
−0.655267 | + | 0.755397i | \(0.727444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.87188e7 | −1.69024 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.90709e7 | −1.69595 | −0.847975 | − | 0.530036i | \(-0.822178\pi\) | ||||
−0.847975 | + | 0.530036i | \(0.822178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.74333e7 | −1.61568 | −0.807842 | − | 0.589399i | \(-0.799365\pi\) | ||||
−0.807842 | + | 0.589399i | \(0.799365\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.51051e6 | 0.193583 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.25735e7 | −1.39013 | −0.695064 | − | 0.718948i | \(-0.744624\pi\) | ||||
−0.695064 | + | 0.718948i | \(0.744624\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.70269e6 | 0.282849 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.50561e7 | 0.631806 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.07779e6 | 0.211893 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.91056e6 | −0.245272 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.40934e6 | 0.388293 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.78594e6 | −0.114330 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.64667e6 | 0.269763 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.29342e6 | −0.132932 | −0.0664659 | − | 0.997789i | \(-0.521172\pi\) | ||||
−0.0664659 | + | 0.997789i | \(0.521172\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.92239e6 | −0.0771672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.47725e7 | 0.988950 | 0.494475 | − | 0.869192i | \(-0.335360\pi\) | ||||
0.494475 | + | 0.869192i | \(0.335360\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.02233e7 | −0.405895 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.97569e6 | −0.0780129 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.50473e7 | 0.587718 | 0.293859 | − | 0.955849i | \(-0.405060\pi\) | ||||
0.293859 | + | 0.955849i | \(0.405060\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.58012e7 | −1.00228 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.34962e6 | 0.129417 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.56640e7 | −1.37049 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.23931e6 | −0.200251 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.20341e7 | −1.21779 | −0.608897 | − | 0.793250i | \(-0.708388\pi\) | ||||
−0.608897 | + | 0.793250i | \(0.708388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.20508e7 | 0.453223 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 105166. | 0.00393410 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.28148e7 | −1.22101 | −0.610507 | − | 0.792011i | \(-0.709034\pi\) | ||||
−0.610507 | + | 0.792011i | \(0.709034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.74224e7 | 2.12529 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.23532e7 | −0.822935 | −0.411467 | − | 0.911424i | \(-0.634984\pi\) | ||||
−0.411467 | + | 0.911424i | \(0.634984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.59507e6 | −0.314753 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.84264e7 | 1.75472 | 0.877360 | − | 0.479834i | \(-0.159303\pi\) | ||||
0.877360 | + | 0.479834i | \(0.159303\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49372.9 | 0.00177960 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.13476e7 | 1.48251 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.85648e7 | −1.37549 | −0.687747 | − | 0.725951i | \(-0.741400\pi\) | ||||
−0.687747 | + | 0.725951i | \(0.741400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.17080e6 | −0.218944 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.08168e6 | 0.179361 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.91165e7 | −0.667729 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.63709e6 | −0.126383 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.81740e6 | −0.0628249 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.03667e7 | −1.38821 | −0.694107 | − | 0.719871i | \(-0.744201\pi\) | ||||
−0.694107 | + | 0.719871i | \(0.744201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.17126e6 | −0.0400722 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.51470e6 | −0.255778 | −0.127889 | − | 0.991788i | \(-0.540820\pi\) | ||||
−0.127889 | + | 0.991788i | \(0.540820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.29053e6 | 0.279300 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.57026e6 | −0.153181 | −0.0765904 | − | 0.997063i | \(-0.524403\pi\) | ||||
−0.0765904 | + | 0.997063i | \(0.524403\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.39801e6 | −0.280040 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.19144e7 | −0.395277 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.62539e7 | 1.19666 | 0.598330 | − | 0.801250i | \(-0.295831\pi\) | ||||
0.598330 | + | 0.801250i | \(0.295831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.46362e6 | 0.245109 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.22004e7 | −0.721722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.45804e7 | −1.76544 | −0.882719 | − | 0.469901i | \(-0.844289\pi\) | ||||
−0.882719 | + | 0.469901i | \(0.844289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.01039e7 | 0.647006 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.07633e6 | −0.130530 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.72786e7 | −1.82496 | −0.912482 | − | 0.409116i | \(-0.865837\pi\) | ||||
−0.912482 | + | 0.409116i | \(0.865837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.72170e7 | −1.17985 |
(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 | 392.6.a.m.1.6 | yes | 6 | |
4.3 | odd | 2 | 784.6.a.bn.1.1 | 6 | |||
7.2 | even | 3 | 392.6.i.q.361.1 | 12 | |||
7.3 | odd | 6 | 392.6.i.q.177.6 | 12 | |||
7.4 | even | 3 | 392.6.i.q.177.1 | 12 | |||
7.5 | odd | 6 | 392.6.i.q.361.6 | 12 | |||
7.6 | odd | 2 | inner | 392.6.a.m.1.1 | ✓ | 6 | |
28.27 | even | 2 | 784.6.a.bn.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.6.a.m.1.1 | ✓ | 6 | 7.6 | odd | 2 | inner | |
392.6.a.m.1.6 | yes | 6 | 1.1 | even | 1 | trivial | |
392.6.i.q.177.1 | 12 | 7.4 | even | 3 | |||
392.6.i.q.177.6 | 12 | 7.3 | odd | 6 | |||
392.6.i.q.361.1 | 12 | 7.2 | even | 3 | |||
392.6.i.q.361.6 | 12 | 7.5 | odd | 6 | |||
784.6.a.bn.1.1 | 6 | 4.3 | odd | 2 | |||
784.6.a.bn.1.6 | 6 | 28.27 | even | 2 |