Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,6,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1104.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.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: | \(177.063737074\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4608x^{6} - 3161x^{5} + 6284039x^{4} - 8279002x^{3} - 2677454576x^{2} + 13573192447x + 77901299860 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 552) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(34.5562\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1104.1 |
$q$-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 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 71.1125 | 1.27210 | 0.636050 | − | 0.771648i | \(-0.280567\pi\) | ||||
0.636050 | + | 0.771648i | \(0.280567\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −188.015 | −1.45026 | −0.725131 | − | 0.688611i | \(-0.758221\pi\) | ||||
−0.725131 | + | 0.688611i | \(0.758221\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −133.529 | −0.332731 | −0.166365 | − | 0.986064i | \(-0.553203\pi\) | ||||
−0.166365 | + | 0.986064i | \(0.553203\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 661.881 | 1.08623 | 0.543115 | − | 0.839658i | \(-0.317245\pi\) | ||||
0.543115 | + | 0.839658i | \(0.317245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −640.012 | −0.734447 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2237.24 | 1.87754 | 0.938771 | − | 0.344542i | \(-0.111966\pi\) | ||||
0.938771 | + | 0.344542i | \(0.111966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 979.973 | 0.622773 | 0.311387 | − | 0.950283i | \(-0.399207\pi\) | ||||
0.311387 | + | 0.950283i | \(0.399207\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1692.13 | 0.837309 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1931.99 | 0.618236 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 337.792 | 0.0745854 | 0.0372927 | − | 0.999304i | \(-0.488127\pi\) | ||||
0.0372927 | + | 0.999304i | \(0.488127\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −423.647 | −0.0791771 | −0.0395886 | − | 0.999216i | \(-0.512605\pi\) | ||||
−0.0395886 | + | 0.999216i | \(0.512605\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1201.76 | 0.192102 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13370.2 | −1.84488 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2257.78 | −0.271130 | −0.135565 | − | 0.990768i | \(-0.543285\pi\) | ||||
−0.135565 | + | 0.990768i | \(0.543285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5956.93 | −0.627135 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11014.8 | −1.02333 | −0.511667 | − | 0.859184i | \(-0.670972\pi\) | ||||
−0.511667 | + | 0.859184i | \(0.670972\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8574.44 | −0.707187 | −0.353594 | − | 0.935399i | \(-0.615040\pi\) | ||||
−0.353594 | + | 0.935399i | \(0.615040\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5760.11 | 0.424033 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1416.94 | 0.0935634 | 0.0467817 | − | 0.998905i | \(-0.485103\pi\) | ||||
0.0467817 | + | 0.998905i | \(0.485103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18542.5 | 1.10326 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20135.1 | −1.08400 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1729.01 | 0.0845490 | 0.0422745 | − | 0.999106i | \(-0.486540\pi\) | ||||
0.0422745 | + | 0.999106i | \(0.486540\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9495.55 | −0.423266 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8819.75 | −0.359558 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50385.7 | 1.88442 | 0.942210 | − | 0.335023i | \(-0.108744\pi\) | ||||
0.942210 | + | 0.335023i | \(0.108744\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23301.9 | −0.801800 | −0.400900 | − | 0.916122i | \(-0.631303\pi\) | ||||
−0.400900 | + | 0.916122i | \(0.631303\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15229.2 | −0.483421 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 47068.0 | 1.38179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25758.6 | 0.701029 | 0.350514 | − | 0.936557i | \(-0.386007\pi\) | ||||
0.350514 | + | 0.936557i | \(0.386007\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 19497.0 | 0.459009 | 0.229504 | − | 0.973308i | \(-0.426289\pi\) | ||||
0.229504 | + | 0.973308i | \(0.426289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −54323.1 | −1.19310 | −0.596551 | − | 0.802575i | \(-0.703463\pi\) | ||||
−0.596551 | + | 0.802575i | \(0.703463\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17387.9 | −0.356939 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25105.3 | 0.482547 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4710.12 | 0.0849111 | 0.0424556 | − | 0.999098i | \(-0.486482\pi\) | ||||
0.0424556 | + | 0.999098i | \(0.486482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 31521.3 | 0.502237 | 0.251119 | − | 0.967956i | \(-0.419202\pi\) | ||||
0.251119 | + | 0.967956i | \(0.419202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 159095. | 2.38842 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3040.12 | −0.0430619 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −111714. | −1.49497 | −0.747484 | − | 0.664280i | \(-0.768738\pi\) | ||||
−0.747484 | + | 0.664280i | \(0.768738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −124443. | −1.57532 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3812.82 | 0.0457129 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 69688.3 | 0.792229 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −100692. | −1.08659 | −0.543294 | − | 0.839543i | \(-0.682823\pi\) | ||||
−0.543294 | + | 0.839543i | \(0.682823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10815.8 | −0.110910 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 153987. | 1.50204 | 0.751021 | − | 0.660278i | \(-0.229562\pi\) | ||||
0.751021 | + | 0.660278i | \(0.229562\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 95768.8 | 0.889469 | 0.444735 | − | 0.895662i | \(-0.353298\pi\) | ||||
0.444735 | + | 0.895662i | \(0.353298\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 120332. | 1.06514 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −134430. | −1.13511 | −0.567555 | − | 0.823335i | \(-0.692111\pi\) | ||||
−0.567555 | + | 0.823335i | \(0.692111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 75035.9 | 0.604927 | 0.302463 | − | 0.953161i | \(-0.402191\pi\) | ||||
0.302463 | + | 0.953161i | \(0.402191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20320.0 | 0.156537 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 176475. | 1.30013 | 0.650066 | − | 0.759877i | \(-0.274741\pi\) | ||||
0.650066 | + | 0.759877i | \(0.274741\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 37618.5 | 0.265251 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 53612.4 | 0.362077 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −420633. | −2.72293 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −143221. | −0.889290 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 99133.4 | 0.590823 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −84838.1 | −0.485642 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −35819.0 | −0.197063 | −0.0985314 | − | 0.995134i | \(-0.531414\pi\) | ||||
−0.0985314 | + | 0.995134i | \(0.531414\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 77169.9 | 0.408295 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 306089. | 1.55836 | 0.779182 | − | 0.626798i | \(-0.215635\pi\) | ||||
0.779182 | + | 0.626798i | \(0.215635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −184249. | −0.903185 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −51841.0 | −0.244816 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 144889. | 0.659530 | 0.329765 | − | 0.944063i | \(-0.393031\pi\) | ||||
0.329765 | + | 0.944063i | \(0.393031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 24005.5 | 0.105384 | 0.0526919 | − | 0.998611i | \(-0.483220\pi\) | ||||
0.0526919 | + | 0.998611i | \(0.483220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12752.4 | −0.0540188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −88380.1 | −0.361422 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24021.2 | 0.0948800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −166883. | −0.636968 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 310431. | 1.14551 | 0.572756 | − | 0.819726i | \(-0.305874\pi\) | ||||
0.572756 | + | 0.819726i | \(0.305874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −369009. | −1.31703 | −0.658513 | − | 0.752569i | \(-0.728814\pi\) | ||||
−0.658513 | + | 0.752569i | \(0.728814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 181216. | 0.625847 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30126.6 | −0.100721 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −380929. | −1.23337 | −0.616686 | − | 0.787209i | \(-0.711525\pi\) | ||||
−0.616686 | + | 0.787209i | \(0.711525\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15561.1 | −0.0488144 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −99459.8 | −0.302401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −173657. | −0.511945 | −0.255972 | − | 0.966684i | \(-0.582396\pi\) | ||||
−0.255972 | + | 0.966684i | \(0.582396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 85460.0 | 0.244373 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 69591.8 | 0.193093 | 0.0965466 | − | 0.995328i | \(-0.469220\pi\) | ||||
0.0965466 | + | 0.995328i | \(0.469220\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 66793.9 | 0.179895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 79377.8 | 0.207591 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 680477. | 1.72862 | 0.864308 | − | 0.502963i | \(-0.167757\pi\) | ||||
0.864308 | + | 0.502963i | \(0.167757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −363242. | −0.896604 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −453472. | −1.08797 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 595916. | 1.39012 | 0.695060 | − | 0.718952i | \(-0.255378\pi\) | ||||
0.695060 | + | 0.718952i | \(0.255378\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 529495. | 1.20134 | 0.600670 | − | 0.799497i | \(-0.294901\pi\) | ||||
0.600670 | + | 0.799497i | \(0.294901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 209717. | 0.462920 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −160556. | −0.344904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −298735. | −0.624715 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 137063. | 0.279103 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −51044.2 | −0.101242 | −0.0506212 | − | 0.998718i | \(-0.516120\pi\) | ||||
−0.0506212 | + | 0.998718i | \(0.516120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 662338. | 1.27993 | 0.639965 | − | 0.768404i | \(-0.278949\pi\) | ||||
0.639965 | + | 0.768404i | \(0.278949\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −423612. | −0.797778 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −519040. | −0.952873 | −0.476436 | − | 0.879209i | \(-0.658072\pi\) | ||||
−0.476436 | + | 0.879209i | \(0.658072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −292840. | −0.524202 | −0.262101 | − | 0.965041i | \(-0.584415\pi\) | ||||
−0.262101 | + | 0.965041i | \(0.584415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −231828. | −0.404739 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −63509.8 | −0.108168 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −783291. | −1.30178 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −130854. | −0.207216 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.10357e6 | −1.70646 | −0.853228 | − | 0.521539i | \(-0.825358\pi\) | ||||
−0.853228 | + | 0.521539i | \(0.825358\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −175473. | −0.265009 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −609750. | −0.899612 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 79651.8 | 0.114828 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 488908. | 0.688838 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.48079e6 | 2.03944 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 64393.2 | 0.0867118 | 0.0433559 | − | 0.999060i | \(-0.486195\pi\) | ||||
0.0433559 | + | 0.999060i | \(0.486195\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 156491. | 0.206079 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 659120. | 0.848984 | 0.424492 | − | 0.905432i | \(-0.360453\pi\) | ||||
0.424492 | + | 0.905432i | \(0.360453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 217092. | 0.273561 | 0.136781 | − | 0.990601i | \(-0.456324\pi\) | ||||
0.136781 | + | 0.990601i | \(0.456324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −225948. | −0.278598 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.11565e6 | 1.34629 | 0.673145 | − | 0.739510i | \(-0.264943\pi\) | ||||
0.673145 | + | 0.739510i | \(0.264943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 100762. | 0.119022 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −42391.1 | −0.0490235 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −87775.6 | −0.0993983 | −0.0496992 | − | 0.998764i | \(-0.515826\pi\) | ||||
−0.0496992 | + | 0.998764i | \(0.515826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 586801. | 0.650801 | 0.325401 | − | 0.945576i | \(-0.394501\pi\) | ||||
0.325401 | + | 0.945576i | \(0.394501\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.31860e6 | 1.40346 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 648626. | 0.676475 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −283692. | −0.289967 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.83841e6 | 1.84186 | 0.920932 | − | 0.389723i | \(-0.127429\pi\) | ||||
0.920932 | + | 0.389723i | \(0.127429\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −70636.6 | −0.0693791 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.43186e6 | −1.37895 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.08346e6 | −1.02325 | −0.511623 | − | 0.859210i | \(-0.670956\pi\) | ||||
−0.511623 | + | 0.859210i | \(0.670956\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 424495. | 0.393209 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27361.1 | 0.0248618 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.55245e6 | 1.38397 | 0.691987 | − | 0.721910i | \(-0.256735\pi\) | ||||
0.691987 | + | 0.721910i | \(0.256735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 122954. | 0.107555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.00542e6 | 0.863120 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.47991e6 | 1.24697 | 0.623484 | − | 0.781836i | \(-0.285717\pi\) | ||||
0.623484 | + | 0.781836i | \(0.285717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.76717e6 | −1.46169 | −0.730845 | − | 0.682544i | \(-0.760874\pi\) | ||||
−0.730845 | + | 0.682544i | \(0.760874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.11999e6 | 0.909511 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −257976. | −0.205706 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.32630e6 | 1.03859 | 0.519293 | − | 0.854597i | \(-0.326196\pi\) | ||||
0.519293 | + | 0.854597i | \(0.326196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −34315.4 | −0.0263924 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −250126. | −0.188970 | −0.0944852 | − | 0.995526i | \(-0.530121\pi\) | ||||
−0.0944852 | + | 0.995526i | \(0.530121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 256231. | 0.190181 | 0.0950903 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950903 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −627195. | −0.457394 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.07095e6 | 1.48410 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.58537e6 | 2.52516 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 906226. | 0.627342 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −746625. | −0.508082 | −0.254041 | − | 0.967193i | \(-0.581760\pi\) | ||||
−0.254041 | + | 0.967193i | \(0.581760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58306e6 | 2.39717 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 97342.4 | 0.0640340 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 350135. | 0.226495 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.61212e6 | 1.02561 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.38589e6 | −0.867204 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.65705e6 | −1.01997 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.01926e6 | 1.22278 | 0.611389 | − | 0.791330i | \(-0.290611\pi\) | ||||
0.611389 | + | 0.791330i | \(0.290611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −861919. | −0.513535 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.92994e6 | 1.13147 | 0.565734 | − | 0.824588i | \(-0.308593\pi\) | ||||
0.565734 | + | 0.824588i | \(0.308593\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.26972e6 | 0.732569 | 0.366284 | − | 0.930503i | \(-0.380630\pi\) | ||||
0.366284 | + | 0.930503i | \(0.380630\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.08299e6 | −0.614959 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 557576. | 0.311642 | 0.155821 | − | 0.987785i | \(-0.450198\pi\) | ||||
0.155821 | + | 0.987785i | \(0.450198\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45104.8 | −0.0248168 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.20987e6 | 0.655356 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.19243e6 | 1.16928 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.27875e6 | 0.671546 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −675323. | −0.349255 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −266405. | −0.135691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.03458e6 | −0.519031 | −0.259516 | − | 0.965739i | \(-0.583563\pi\) | ||||
−0.259516 | + | 0.965739i | \(0.583563\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −182880. | −0.0903765 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.83176e6 | 0.891778 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.08776e6 | 1.00140 | 0.500698 | − | 0.865622i | \(-0.333077\pi\) | ||||
0.500698 | + | 0.865622i | \(0.333077\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.58828e6 | −0.750632 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 56569.0 | 0.0263447 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −326302. | −0.149756 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −338567. | −0.153143 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.07258e6 | 1.36987 | 0.684936 | − | 0.728603i | \(-0.259830\pi\) | ||||
0.684936 | + | 0.728603i | \(0.259830\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.06963e6 | 0.470080 | 0.235040 | − | 0.971986i | \(-0.424478\pi\) | ||||
0.235040 | + | 0.971986i | \(0.424478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −482511. | −0.209045 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.83670e6 | −0.784516 | −0.392258 | − | 0.919855i | \(-0.628306\pi\) | ||||
−0.392258 | + | 0.919855i | \(0.628306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.38648e6 | 0.583905 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.78570e6 | 1.57208 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.05922e6 | −0.843272 | −0.421636 | − | 0.906765i | \(-0.638544\pi\) | ||||
−0.421636 | + | 0.906765i | \(0.638544\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.51575e6 | −0.612154 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.28899e6 | 0.513432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.86305e6 | −1.51774 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.01460e6 | 1.55588 | 0.777941 | − | 0.628337i | \(-0.216264\pi\) | ||||
0.777941 | + | 0.628337i | \(0.216264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −892200. | −0.341112 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −325080. | −0.122618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 957150. | 0.356212 | 0.178106 | − | 0.984011i | \(-0.443003\pi\) | ||||
0.178106 | + | 0.984011i | \(0.443003\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 763543. | 0.280385 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 223578. | 0.0810169 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.04565e6 | 0.731534 | 0.365767 | − | 0.930707i | \(-0.380807\pi\) | ||||
0.365767 | + | 0.930707i | \(0.380807\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 322371. | 0.113774 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −262567. | −0.0914627 | −0.0457313 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457313 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.78530e6 | 0.613847 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −694529. | −0.235729 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.57116e6 | −1.86669 | −0.933343 | − | 0.358986i | \(-0.883123\pi\) | ||||
−0.933343 | + | 0.358986i | \(0.883123\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18350e6 | 0.391495 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.75480e6 | −0.899722 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 334949. | 0.108015 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.48102e6 | −0.471611 | −0.235806 | − | 0.971800i | \(-0.575773\pi\) | ||||
−0.235806 | + | 0.971800i | \(0.575773\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.65824e6 | 0.521454 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.69121e6 | −0.525213 | −0.262607 | − | 0.964903i | \(-0.584582\pi\) | ||||
−0.262607 | + | 0.964903i | \(0.584582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −280404. | −0.0860046 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 466569. | 0.141344 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 301478. | 0.0902131 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 784184. | 0.231798 | 0.115899 | − | 0.993261i | \(-0.463025\pi\) | ||||
0.115899 | + | 0.993261i | \(0.463025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.30400e6 | −0.380780 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.47326e6 | −2.73290 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.24156e6 | 0.638896 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −216049. | −0.0608433 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.72033e6 | 0.478713 | 0.239357 | − | 0.970932i | \(-0.423063\pi\) | ||||
0.239357 | + | 0.970932i | \(0.423063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00599e6 | −0.276624 | −0.138312 | − | 0.990389i | \(-0.544168\pi\) | ||||
−0.138312 | + | 0.990389i | \(0.544168\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 114772. | 0.0311878 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.32231e6 | 1.16076 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.38109e6 | 1.16282 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 795421. | 0.208667 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.99734e6 | −0.517914 | −0.258957 | − | 0.965889i | \(-0.583379\pi\) | ||||
−0.258957 | + | 0.965889i | \(0.583379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.49033e6 | 0.894637 | 0.447318 | − | 0.894375i | \(-0.352379\pi\) | ||||
0.447318 | + | 0.894375i | \(0.352379\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −216191. | −0.0547790 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 518405. | 0.129857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.65337e6 | 1.15241 | 0.576205 | − | 0.817306i | \(-0.304533\pi\) | ||||
0.576205 | + | 0.817306i | \(0.304533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50194e6 | 0.367754 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −433031. | −0.104836 | −0.0524179 | − | 0.998625i | \(-0.516693\pi\) | ||||
−0.0524179 | + | 0.998625i | \(0.516693\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.94425e6 | −1.90175 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.79388e6 | −0.661362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.95195e6 | 0.691025 | 0.345513 | − | 0.938414i | \(-0.387705\pi\) | ||||
0.345513 | + | 0.938414i | \(0.387705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.47079e6 | 0.340495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.32108e6 | 0.760386 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.84948e6 | −2.00396 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.37465e6 | −1.65177 | −0.825887 | − | 0.563836i | \(-0.809325\pi\) | ||||
−0.825887 | + | 0.563836i | \(0.809325\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.63095e6 | −0.361333 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.39294e6 | −0.962728 | −0.481364 | − | 0.876521i | \(-0.659858\pi\) | ||||
−0.481364 | + | 0.876521i | \(0.659858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.76781e6 | 0.383252 | 0.191626 | − | 0.981468i | \(-0.438624\pi\) | ||||
0.191626 | + | 0.981468i | \(0.438624\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 271139. | 0.0581514 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.89091e6 | −0.401216 | −0.200608 | − | 0.979672i | \(-0.564292\pi\) | ||||
−0.200608 | + | 0.979672i | \(0.564292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.84300e6 | −1.01668 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.42836e6 | 0.712088 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.14493e6 | 0.235303 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.89329e6 | 0.385021 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 140050. | 0.0281830 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.41395e6 | −0.480717 | −0.240359 | − | 0.970684i | \(-0.577265\pi\) | ||||
−0.240359 | + | 0.970684i | \(0.577265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.49438e6 | −0.294509 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 895138. | 0.174591 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.16045e6 | −1.38225 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.64022e6 | −0.313386 | −0.156693 | − | 0.987647i | \(-0.550083\pi\) | ||||
−0.156693 | + | 0.987647i | \(0.550083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.56291e6 | 0.295571 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −69046.0 | −0.0129251 | −0.00646256 | − | 0.999979i | \(-0.502057\pi\) | ||||
−0.00646256 | + | 0.999979i | \(0.502057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 755720. | 0.140037 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −769140. | −0.141089 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.66572e6 | −0.665684 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.65341e6 | −1.55574 | −0.777868 | − | 0.628427i | \(-0.783699\pi\) | ||||
−0.777868 | + | 0.628427i | \(0.783699\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −626326. | −0.111482 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.85060e6 | 0.854822 | 0.427411 | − | 0.904057i | \(-0.359426\pi\) | ||||
0.427411 | + | 0.904057i | \(0.359426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.09504e7 | 1.91075 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −601145. | −0.103863 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.59169e6 | 1.12772 | 0.563861 | − | 0.825870i | \(-0.309315\pi\) | ||||
0.563861 | + | 0.825870i | \(0.309315\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.02135e7 | 1.73031 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −714400. | −0.119853 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.81036e6 | 1.13149 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −189202. | −0.0311314 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.12430e6 | −0.998017 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.58425e6 | −0.578501 | −0.289250 | − | 0.957253i | \(-0.593406\pi\) | ||||
−0.289250 | + | 0.957253i | \(0.593406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.13368e6 | 0.500958 | 0.250479 | − | 0.968122i | \(-0.419412\pi\) | ||||
0.250479 | + | 0.968122i | \(0.419412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.26918e6 | 0.517655 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −947798. | −0.148658 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.08125e6 | 0.628140 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.29050e6 | −1.11158 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.55968e6 | −1.44397 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.36324e6 | −0.802586 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.47596e6 | −0.367089 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.50065e6 | 0.367333 | 0.183667 | − | 0.982989i | \(-0.441203\pi\) | ||||
0.183667 | + | 0.982989i | \(0.441203\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.76546e6 | −0.693594 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.33599e6 | 0.769527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.06868e7 | −1.52715 | −0.763573 | − | 0.645722i | \(-0.776556\pi\) | ||||
−0.763573 | + | 0.645722i | \(0.776556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.88745e6 | −0.267267 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 331027. | 0.0464498 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −885572. | −0.123143 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.44501e6 | 0.199130 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 604766. | 0.0825942 | 0.0412971 | − | 0.999147i | \(-0.486851\pi\) | ||||
0.0412971 | + | 0.999147i | \(0.486851\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.67526e6 | −0.768168 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.68862e6 | 0.360680 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.03544e6 | 0.802486 | 0.401243 | − | 0.915972i | \(-0.368578\pi\) | ||||
0.401243 | + | 0.915972i | \(0.368578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.25496e7 | 1.65390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.23356e6 | −0.161140 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.01774e7 | 1.31782 | 0.658910 | − | 0.752222i | \(-0.271018\pi\) | ||||
0.658910 | + | 0.752222i | \(0.271018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.47052e6 | −0.702164 | −0.351082 | − | 0.936345i | \(-0.614186\pi\) | ||||
−0.351082 | + | 0.936345i | \(0.614186\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 459398. | 0.0584524 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.02202e6 | 0.128911 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.48524e6 | 0.935979 | 0.467989 | − | 0.883734i | \(-0.344979\pi\) | ||||
0.467989 | + | 0.883734i | \(0.344979\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.96104e6 | −0.738968 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.92647e6 | −0.728376 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −230873. | −0.0281320 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.81251e6 | 0.460597 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.99098e6 | 0.957204 | 0.478602 | − | 0.878032i | \(-0.341144\pi\) | ||||
0.478602 | + | 0.878032i | \(0.341144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −415162. | −0.0493094 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.67136e6 | 0.550141 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.24720e7 | 1.45646 | 0.728231 | − | 0.685331i | \(-0.240343\pi\) | ||||
0.728231 | + | 0.685331i | \(0.240343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.99123e7 | −3.46383 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.63556e6 | 0.302648 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.12914e7 | 1.28582 | 0.642909 | − | 0.765942i | \(-0.277727\pi\) | ||||
0.642909 | + | 0.765942i | \(0.277727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.73885e7 | 1.96371 | 0.981853 | − | 0.189642i | \(-0.0607326\pi\) | ||||
0.981853 | + | 0.189642i | \(0.0607326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.08645e6 | 0.233676 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.01848e7 | −1.13127 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.15433e7 | 1.27162 | 0.635811 | − | 0.771845i | \(-0.280666\pi\) | ||||
0.635811 | + | 0.771845i | \(0.280666\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 571588. | 0.0624511 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 937844. | 0.101631 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.23860e6 | 0.563072 | 0.281536 | − | 0.959551i | \(-0.409156\pi\) | ||||
0.281536 | + | 0.959551i | \(0.409156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.04962e6 | 0.751585 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.57047e6 | 0.483335 | 0.241668 | − | 0.970359i | \(-0.422306\pi\) | ||||
0.241668 | + | 0.970359i | \(0.422306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.60001e6 | 0.797237 | 0.398618 | − | 0.917117i | \(-0.369490\pi\) | ||||
0.398618 | + | 0.917117i | \(0.369490\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.10038e7 | 2.16810 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20705e7 | −1.23602 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.17769e6 | 0.119636 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.05118e6 | −0.509057 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 893207. | 0.0893056 | 0.0446528 | − | 0.999003i | \(-0.485782\pi\) | ||||
0.0446528 | + | 0.999003i | \(0.485782\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.93216e6 | 0.985222 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.54718e6 | −0.250683 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.22729e7 | 1.19840 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.57925e6 | 0.153003 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −169721. | −0.0163152 | −0.00815758 | − | 0.999967i | \(-0.502597\pi\) | ||||
−0.00815758 | + | 0.999967i | \(0.502597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.10025e6 | 0.868012 | 0.434006 | − | 0.900910i | \(-0.357100\pi\) | ||||
0.434006 | + | 0.900910i | \(0.357100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.48775e6 | 0.519391 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.78218e6 | −0.167375 | −0.0836874 | − | 0.996492i | \(-0.526670\pi\) | ||||
−0.0836874 | + | 0.996492i | \(0.526670\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.72794e6 | −0.627004 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −716867. | −0.0662958 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.80884e7 | −1.66003 | −0.830016 | − | 0.557739i | \(-0.811669\pi\) | ||||
−0.830016 | + | 0.557739i | \(0.811669\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.17667e7 | 1.98239 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.40017e6 | −0.397701 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.57392e7 | 1.41179 | 0.705893 | − | 0.708318i | \(-0.250546\pi\) | ||||
0.705893 | + | 0.708318i | \(0.250546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.20994e7 | 1.07711 | 0.538557 | − | 0.842589i | \(-0.318970\pi\) | ||||
0.538557 | + | 0.842589i | \(0.318970\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.33271e7 | −1.17747 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.31024e7 | −1.14894 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 178692. | 0.0155521 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −579539. | −0.0500631 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.11147e6 | 0.266783 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.46404e7 | 1.24599 | 0.622996 | − | 0.782225i | \(-0.285915\pi\) | ||||
0.622996 | + | 0.782225i | \(0.285915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.40842e6 | −0.118980 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.88409e7 | −1.57991 | −0.789953 | − | 0.613168i | \(-0.789895\pi\) | ||||
−0.789953 | + | 0.613168i | \(0.789895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.89315e7 | 1.57584 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.93208e6 | −0.490161 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.26555e7 | −1.85832 | −0.929162 | − | 0.369673i | \(-0.879470\pi\) | ||||
−0.929162 | + | 0.369673i | \(0.879470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.03034e7 | 0.838987 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.95383e6 | −0.157941 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.14440e6 | 0.0918396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.38740e7 | −1.90208 | −0.951041 | − | 0.309065i | \(-0.899984\pi\) | ||||
−0.951041 | + | 0.309065i | \(0.899984\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.03353e6 | 0.160849 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.70709e6 | 0.134059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.46428e7 | −1.92135 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.00409e7 | −0.777281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.66784e7 | −1.28192 | −0.640959 | − | 0.767575i | \(-0.721463\pi\) | ||||
−0.640959 | + | 0.767575i | \(0.721463\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.21256e6 | −0.168852 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −906857. | −0.0687173 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.89519e7 | −2.17835 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.85537e6 | 0.288038 | 0.144019 | − | 0.989575i | \(-0.453997\pi\) | ||||
0.144019 | + | 0.989575i | \(0.453997\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 381520. | 0.0283037 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −224109. | −0.0165096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.28493e6 | −0.459764 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 789980. | 0.0573876 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.14977e7 | 1.55085 | 0.775423 | − | 0.631442i | \(-0.217536\pi\) | ||||
0.775423 | + | 0.631442i | \(0.217536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.80059e7 | −1.28996 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.28121e6 | −0.375740 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 652609. | 0.0461114 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.96974e6 | 0.348737 | 0.174368 | − | 0.984680i | \(-0.444212\pi\) | ||||
0.174368 | + | 0.984680i | \(0.444212\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.91830e7 | −1.32777 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.34633e7 | 1.61298 | 0.806489 | − | 0.591249i | \(-0.201365\pi\) | ||||
0.806489 | + | 0.591249i | \(0.201365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.18674e7 | −0.810287 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.43951e6 | −0.233254 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.29225e7 | −1.54401 | −0.772007 | − | 0.635614i | \(-0.780747\pi\) | ||||
−0.772007 | + | 0.635614i | \(0.780747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.83763e6 | −0.390563 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.55951e7 | −1.03638 | −0.518188 | − | 0.855267i | \(-0.673393\pi\) | ||||
−0.518188 | + | 0.855267i | \(0.673393\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.20755e7 | 1.45720 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.55323e6 | 0.167412 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.52749e7 | 1.64621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.41940e7 | −1.56533 | −0.782667 | − | 0.622440i | \(-0.786141\pi\) | ||||
−0.782667 | + | 0.622440i | \(0.786141\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.65457e7 | −1.06340 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.62412e7 | −1.67539 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.45942e6 | 0.282839 | 0.141419 | − | 0.989950i | \(-0.454833\pi\) | ||||
0.141419 | + | 0.989950i | \(0.454833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 635730. | 0.0400560 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.72756e6 | −0.546300 | −0.273150 | − | 0.961971i | \(-0.588066\pi\) | ||||
−0.273150 | + | 0.961971i | \(0.588066\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.41078e7 | −0.877302 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.28867e7 | 0.796140 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.33494e7 | 2.04691 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.27707e7 | −1.38855 | −0.694275 | − | 0.719710i | \(-0.744275\pi\) | ||||
−0.694275 | + | 0.719710i | \(0.744275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.75115e6 | 0.590772 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.43137e7 | −0.861594 | −0.430797 | − | 0.902449i | \(-0.641767\pi\) | ||||
−0.430797 | + | 0.902449i | \(0.641767\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −818480. | −0.0489502 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.82046e6 | −0.227019 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.07942e7 | −0.637305 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.60340e6 | −0.152726 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −246250. | −0.0143540 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.70888e7 | −1.56897 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.10140e6 | −0.0633885 | −0.0316942 | − | 0.999498i | \(-0.510090\pi\) | ||||
−0.0316942 | + | 0.999498i | \(0.510090\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.39720e7 | −0.799038 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.31799e7 | −1.88553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.54231e7 | −0.870939 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.10659e6 | −0.0620967 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.39183e7 | 0.776142 | 0.388071 | − | 0.921630i | \(-0.373142\pi\) | ||||
0.388071 | + | 0.921630i | \(0.373142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.17002e6 | 0.175669 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.04882e6 | −0.498323 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.25369e6 | 0.396981 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.07283e6 | −0.384684 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.33192e7 | −0.719937 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.39586e7 | 1.28704 | 0.643518 | − | 0.765431i | \(-0.277474\pi\) | ||||
0.643518 | + | 0.765431i | \(0.277474\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.68484e6 | −0.463671 | −0.231835 | − | 0.972755i | \(-0.574473\pi\) | ||||
−0.231835 | + | 0.972755i | \(0.574473\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.59045e7 | 0.843907 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.23492e7 | −0.651245 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.40271e6 | −0.440417 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00799e7 | −0.525106 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.39635e6 | 0.486521 | 0.243260 | − | 0.969961i | \(-0.421783\pi\) | ||||
0.243260 | + | 0.969961i | \(0.421783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.72483e7 | −0.887659 | −0.443829 | − | 0.896111i | \(-0.646380\pi\) | ||||
−0.443829 | + | 0.896111i | \(0.646380\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.32178e6 | 0.118764 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.53805e7 | −1.79887 | −0.899437 | − | 0.437050i | \(-0.856023\pi\) | ||||
−0.899437 | + | 0.437050i | \(0.856023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.54998e7 | 1.79407 | 0.897035 | − | 0.441959i | \(-0.145716\pi\) | ||||
0.897035 | + | 0.441959i | \(0.145716\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.19367e7 | −0.599627 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.14840e7 | 2.07142 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.94885e6 | 0.245634 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 308839. | 0.0152376 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.74841e7 | −1.34796 | −0.673980 | − | 0.738750i | \(-0.735417\pi\) | ||||
−0.673980 | + | 0.738750i | \(0.735417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03970e7 | −0.994437 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.25114e6 | 0.109102 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.74988e6 | 0.228845 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.69277e7 | 1.28970 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.30608e6 | −0.109801 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.19436e6 | −0.0565344 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.40740e7 | −0.662286 | −0.331143 | − | 0.943581i | \(-0.607434\pi\) | ||||
−0.331143 | + | 0.943581i | \(0.607434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.64475e6 | 0.264076 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.01794e7 | −0.938547 | −0.469274 | − | 0.883053i | \(-0.655484\pi\) | ||||
−0.469274 | + | 0.883053i | \(0.655484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.84235e6 | 0.177670 | 0.0888350 | − | 0.996046i | \(-0.471686\pi\) | ||||
0.0888350 | + | 0.996046i | \(0.471686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.86385e7 | −0.856848 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.31172e6 | −0.151366 | −0.0756828 | − | 0.997132i | \(-0.524114\pi\) | ||||
−0.0756828 | + | 0.997132i | \(0.524114\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.83904e7 | 2.19897 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.22683e7 | −1.45790 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −628936. | −0.0282525 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.70492e7 | 0.761478 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.15604e6 | −0.362196 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.59508e7 | 0.704308 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.23996e7 | 1.86150 | 0.930749 | − | 0.365659i | \(-0.119156\pi\) | ||||
0.930749 | + | 0.365659i | \(0.119156\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.71963e6 | 0.293341 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.13977e6 | −0.309916 | −0.154958 | − | 0.987921i | \(-0.549524\pi\) | ||||
−0.154958 | + | 0.987921i | \(0.549524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.36386e7 | −0.588665 | −0.294333 | − | 0.955703i | \(-0.595097\pi\) | ||||
−0.294333 | + | 0.955703i | \(0.595097\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.22475e7 | −1.38401 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.02258e6 | −0.342377 | −0.171189 | − | 0.985238i | \(-0.554761\pi\) | ||||
−0.171189 | + | 0.985238i | \(0.554761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.73451e6 | 0.285793 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −876081. | −0.0369701 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.38856e6 | 0.0582688 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.23771e7 | 1.76837 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.15122e6 | −0.130767 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −143104. | −0.00590546 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.86821e6 | 0.158744 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.45091e7 | −0.592135 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.76537e7 | 1.52822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.74039e6 | 0.191336 | 0.0956678 | − | 0.995413i | \(-0.469501\pi\) | ||||
0.0956678 | + | 0.995413i | \(0.469501\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.24730e7 | 0.500681 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.59416e7 | 1.43483 | 0.717417 | − | 0.696644i | \(-0.245324\pi\) | ||||
0.717417 | + | 0.696644i | \(0.245324\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.20900e6 | −0.167110 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.49135e7 | 0.588880 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.75491e7 | −2.26004 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.99426e7 | 0.778922 | 0.389461 | − | 0.921043i | \(-0.372661\pi\) | ||||
0.389461 | + | 0.921043i | \(0.372661\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.81734e7 | −0.705971 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.29047e7 | 0.498589 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.36200e6 | −0.167622 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.75727e6 | 0.296490 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.68297e6 | −0.178026 | −0.0890128 | − | 0.996030i | \(-0.528371\pi\) | ||||
−0.0890128 | + | 0.996030i | \(0.528371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.81712e7 | 0.687082 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.73694e7 | −0.653253 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.12438e7 | −0.794700 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.40436e7 | −0.894643 | −0.447321 | − | 0.894373i | \(-0.647622\pi\) | ||||
−0.447321 | + | 0.894373i | \(0.647622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.14275e7 | −0.422949 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.66326e7 | 1.34863 | 0.674317 | − | 0.738442i | \(-0.264438\pi\) | ||||
0.674317 | + | 0.738442i | \(0.264438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.82684e6 | −0.213380 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.74687e6 | 0.355047 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.79519e7 | 1.37518 | 0.687588 | − | 0.726101i | \(-0.258670\pi\) | ||||
0.687588 | + | 0.726101i | \(0.258670\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.59554e7 | −1.29598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.01819e6 | −0.179927 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.79717e7 | −1.35434 | −0.677170 | − | 0.735827i | \(-0.736794\pi\) | ||||
−0.677170 | + | 0.735827i | \(0.736794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.62988e6 | −0.128790 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 405944. | 0.0143280 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.72413e7 | −0.956491 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.84497e7 | −0.993731 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.08889e7 | −0.378370 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.71005e7 | 1.62820 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.35414e7 | 1.15349 | 0.576746 | − | 0.816924i | \(-0.304322\pi\) | ||||
0.576746 | + | 0.816924i | \(0.304322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.97319e7 | −0.675086 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.47181e7 | 1.18170 | 0.590851 | − | 0.806781i | \(-0.298792\pi\) | ||||
0.590851 | + | 0.806781i | \(0.298792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.51338e6 | −0.152834 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.15087e7 | −0.387717 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.46519e6 | −0.183176 | −0.0915880 | − | 0.995797i | \(-0.529194\pi\) | ||||
−0.0915880 | + | 0.995797i | \(0.529194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.49170e7 | 0.497422 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.07791e6 | 0.201642 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.47579e7 | 0.817203 | 0.408602 | − | 0.912713i | \(-0.366017\pi\) | ||||
0.408602 | + | 0.912713i | \(0.366017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.69102e7 | −1.21215 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.39764e6 | 0.0783415 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.53588e6 | −0.147459 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.19572e7 | −1.03368 | −0.516839 | − | 0.856083i | \(-0.672891\pi\) | ||||
−0.516839 | + | 0.856083i | \(0.672891\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.31121e6 | 0.299663 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.08246e7 | −0.666836 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.70746e7 | −1.18124 | −0.590621 | − | 0.806949i | \(-0.701117\pi\) | ||||
−0.590621 | + | 0.806949i | \(0.701117\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.64592e6 | 0.0521789 |
(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 | 1104.6.a.ba.1.7 | 8 | ||
4.3 | odd | 2 | 552.6.a.i.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.6.a.i.1.7 | ✓ | 8 | 4.3 | odd | 2 | ||
1104.6.a.ba.1.7 | 8 | 1.1 | even | 1 | trivial |