Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,6,Mod(719,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.719");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.o (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(115.476350265\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 719.28 | ||
Character | \(\chi\) | \(=\) | 720.719 |
Dual form | 720.6.o.d.719.26 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.8892 | + | 49.5454i | 0.463119 | + | 0.886296i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 154.886 | 1.19472 | 0.597362 | − | 0.801971i | \(-0.296215\pi\) | ||||
0.597362 | + | 0.801971i | \(0.296215\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 104.125 | 0.259462 | 0.129731 | − | 0.991549i | \(-0.458589\pi\) | ||||
0.129731 | + | 0.991549i | \(0.458589\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 727.772i | 1.19436i | 0.802106 | + | 0.597182i | \(0.203713\pi\) | ||||
−0.802106 | + | 0.597182i | \(0.796287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 484.801 | 0.406856 | 0.203428 | − | 0.979090i | \(-0.434792\pi\) | ||||
0.203428 | + | 0.979090i | \(0.434792\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 877.159i | 0.557435i | 0.960373 | + | 0.278718i | \(0.0899094\pi\) | ||||
−0.960373 | + | 0.278718i | \(0.910091\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1026.82i | 0.404740i | 0.979309 | + | 0.202370i | \(0.0648644\pi\) | ||||
−0.979309 | + | 0.202370i | \(0.935136\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1784.50 | + | 2565.38i | −0.571041 | + | 0.820922i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6378.27i | 1.40834i | 0.710031 | + | 0.704170i | \(0.248681\pi\) | ||||
−0.710031 | + | 0.704170i | \(0.751319\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7639.78i | − | 1.42783i | −0.700232 | − | 0.713915i | \(-0.746920\pi\) | ||
0.700232 | − | 0.713915i | \(-0.253080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4009.88 | + | 7673.91i | 0.553300 | + | 1.05888i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5549.52i | 0.666425i | 0.942852 | + | 0.333213i | \(0.108133\pi\) | ||||
−0.942852 | + | 0.333213i | \(0.891867\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4746.20i | − | 0.440947i | −0.975393 | − | 0.220473i | \(-0.929240\pi\) | ||
0.975393 | − | 0.220473i | \(-0.0707602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4329.04 | −0.357043 | −0.178521 | − | 0.983936i | \(-0.557131\pi\) | ||||
−0.178521 | + | 0.983936i | \(0.557131\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16288.7i | 1.07557i | 0.843081 | + | 0.537787i | \(0.180740\pi\) | ||||
−0.843081 | + | 0.537787i | \(0.819260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7182.77 | 0.427368 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3180.41 | −0.155523 | −0.0777614 | − | 0.996972i | \(-0.524777\pi\) | ||||
−0.0777614 | + | 0.996972i | \(0.524777\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2695.71 | + | 5158.92i | 0.120162 | + | 0.229960i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13461.7 | 0.503467 | 0.251733 | − | 0.967797i | \(-0.418999\pi\) | ||||
0.251733 | + | 0.967797i | \(0.418999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10129.2 | −0.348539 | −0.174270 | − | 0.984698i | \(-0.555756\pi\) | ||||
−0.174270 | + | 0.984698i | \(0.555756\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −36057.8 | + | 18841.4i | −1.05856 | + | 0.553133i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 40768.3 | 1.10952 | 0.554761 | − | 0.832010i | \(-0.312810\pi\) | ||||
0.554761 | + | 0.832010i | \(0.312810\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29907.5 | 0.704099 | 0.352049 | − | 0.935981i | \(-0.385485\pi\) | ||||
0.352049 | + | 0.935981i | \(0.385485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 42516.5i | − | 0.933793i | −0.884312 | − | 0.466896i | \(-0.845372\pi\) | ||
0.884312 | − | 0.466896i | \(-0.154628\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16127.5 | 0.309985 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27059.7i | 0.487815i | 0.969799 | + | 0.243907i | \(0.0784293\pi\) | ||||
−0.969799 | + | 0.243907i | \(0.921571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 97816.4i | − | 1.55853i | −0.626692 | − | 0.779267i | \(-0.715591\pi\) | ||
0.626692 | − | 0.779267i | \(-0.284409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12551.1 | + | 24019.7i | 0.188423 | + | 0.360595i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 54193.0i | − | 0.725218i | −0.931941 | − | 0.362609i | \(-0.881886\pi\) | ||
0.931941 | − | 0.362609i | \(-0.118114\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 112722.i | 1.42694i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −43459.2 | + | 22708.9i | −0.494053 | + | 0.258159i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 124356.i | − | 1.34195i | −0.741479 | − | 0.670976i | \(-0.765875\pi\) | ||
0.741479 | − | 0.670976i | \(-0.234125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 61508.4i | 0.599972i | 0.953944 | + | 0.299986i | \(0.0969820\pi\) | ||||
−0.953944 | + | 0.299986i | \(0.903018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −207669. | −1.92877 | −0.964383 | − | 0.264510i | \(-0.914790\pi\) | ||||
−0.964383 | + | 0.264510i | \(0.914790\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 83795.7i | 0.707558i | 0.935329 | + | 0.353779i | \(0.115104\pi\) | ||||
−0.935329 | + | 0.353779i | \(0.884896\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −72230.8 | −0.582312 | −0.291156 | − | 0.956676i | \(-0.594040\pi\) | ||||
−0.291156 | + | 0.956676i | \(0.594040\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 43446.5 | 0.320080 | 0.160040 | − | 0.987111i | \(-0.448838\pi\) | ||||
0.160040 | + | 0.987111i | \(0.448838\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −50874.5 | + | 26583.6i | −0.358720 | + | 0.187443i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 75089.0 | 0.486081 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −150209. | −0.932680 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −173302. | − | 21998.4i | −0.992040 | − | 0.125926i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −128198. | −0.705295 | −0.352647 | − | 0.935756i | \(-0.614719\pi\) | ||||
−0.352647 | + | 0.935756i | \(0.614719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11161.1 | 0.0568234 | 0.0284117 | − | 0.999596i | \(-0.490955\pi\) | ||||
0.0284117 | + | 0.999596i | \(0.490955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 135860.i | 0.665982i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 409309. | 1.86316 | 0.931580 | − | 0.363537i | \(-0.118431\pi\) | ||||
0.931580 | + | 0.363537i | \(0.118431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 338018.i | 1.48389i | 0.670459 | + | 0.741947i | \(0.266097\pi\) | ||||
−0.670459 | + | 0.741947i | \(0.733903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 75779.2i | 0.309892i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −316014. | + | 165128.i | −1.24821 | + | 0.652230i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 351713.i | 1.29785i | 0.760854 | + | 0.648923i | \(0.224780\pi\) | ||||
−0.760854 | + | 0.648923i | \(0.775220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 160296.i | 0.572109i | 0.958213 | + | 0.286055i | \(0.0923439\pi\) | ||||
−0.958213 | + | 0.286055i | \(0.907656\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 378516. | − | 197788.i | 1.26548 | − | 0.661256i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 291321.i | − | 0.943240i | −0.881802 | − | 0.471620i | \(-0.843669\pi\) | ||
0.881802 | − | 0.471620i | \(-0.156331\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 159041.i | 0.483554i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 41756.4 | 0.123099 | 0.0615495 | − | 0.998104i | \(-0.480396\pi\) | ||||
0.0615495 | + | 0.998104i | \(0.480396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 661493.i | 1.83541i | 0.397259 | + | 0.917707i | \(0.369962\pi\) | ||||
−0.397259 | + | 0.917707i | \(0.630038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −158358. | −0.426505 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −635477. | −1.61430 | −0.807150 | − | 0.590346i | \(-0.798991\pi\) | ||||
−0.807150 | + | 0.590346i | \(0.798991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −276395. | + | 397342.i | −0.682237 | + | 0.980776i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 564674. | 1.31724 | 0.658621 | − | 0.752475i | \(-0.271140\pi\) | ||||
0.658621 | + | 0.752475i | \(0.271140\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 43204.7 | 0.0980245 | 0.0490122 | − | 0.998798i | \(-0.484393\pi\) | ||||
0.0490122 | + | 0.998798i | \(0.484393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −274954. | + | 143673.i | −0.590650 | + | 0.308634i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 50479.9 | 0.105564 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 689667. | 1.36790 | 0.683952 | − | 0.729527i | \(-0.260260\pi\) | ||||
0.683952 | + | 0.729527i | \(0.260260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 190713.i | − | 0.368542i | −0.982875 | − | 0.184271i | \(-0.941008\pi\) | ||
0.982875 | − | 0.184271i | \(-0.0589924\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −301619. | −0.553724 | −0.276862 | − | 0.960910i | \(-0.589294\pi\) | ||||
−0.276862 | + | 0.960910i | \(0.589294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 422972.i | 0.757145i | 0.925572 | + | 0.378573i | \(0.123585\pi\) | ||||
−0.925572 | + | 0.378573i | \(0.876415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 987906.i | 1.68258i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 235153. | − | 122875.i | 0.390809 | − | 0.204211i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 91334.2i | 0.144633i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 923292.i | 1.42769i | 0.700306 | + | 0.713843i | \(0.253047\pi\) | ||||
−0.700306 | + | 0.713843i | \(0.746953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −112075. | − | 214484.i | −0.165353 | − | 0.316445i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.18330e6i | − | 1.70586i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 352824.i | 0.485934i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 72349.8 | 0.0974261 | 0.0487131 | − | 0.998813i | \(-0.484488\pi\) | ||||
0.0487131 | + | 0.998813i | \(0.484488\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 66534.1i | 0.0856997i | 0.999082 | + | 0.0428499i | \(0.0136437\pi\) | ||||
−0.999082 | + | 0.0428499i | \(0.986356\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −719131. | −0.906191 | −0.453095 | − | 0.891462i | \(-0.649680\pi\) | ||||
−0.453095 | + | 0.891462i | \(0.649680\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.01104e6 | −1.22005 | −0.610023 | − | 0.792383i | \(-0.708840\pi\) | ||||
−0.610023 | + | 0.792383i | \(0.708840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −807029. | + | 421700.i | −0.953277 | + | 0.498120i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.05941e6 | 1.19969 | 0.599844 | − | 0.800117i | \(-0.295229\pi\) | ||||
0.599844 | + | 0.800117i | \(0.295229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34839e6 | −1.49546 | −0.747729 | − | 0.664005i | \(-0.768856\pi\) | ||||
−0.747729 | + | 0.664005i | \(0.768856\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 185956. | + | 355873.i | 0.197922 | + | 0.378774i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −638372. | −0.665781 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 945587. | 0.947364 | 0.473682 | − | 0.880696i | \(-0.342925\pi\) | ||||
0.473682 | + | 0.880696i | \(0.342925\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 106918.i | 0.105015i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.35263e6 | 1.27746 | 0.638728 | − | 0.769433i | \(-0.279461\pi\) | ||||
0.638728 | + | 0.769433i | \(0.279461\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 859545.i | 0.796195i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 239536.i | − | 0.213541i | −0.994284 | − | 0.106771i | \(-0.965949\pi\) | ||
0.994284 | − | 0.106771i | \(-0.0340511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −82338.3 | − | 157575.i | −0.0720256 | − | 0.137839i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 614017.i | 0.517368i | 0.965962 | + | 0.258684i | \(0.0832889\pi\) | ||||
−0.965962 | + | 0.258684i | \(0.916711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.18206e6i | 1.80486i | 0.430839 | + | 0.902429i | \(0.358218\pi\) | ||||
−0.430839 | + | 0.902429i | \(0.641782\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −185811. | + | 267120.i | −0.148163 | + | 0.212998i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.52191e6i | 1.19176i | 0.803073 | + | 0.595881i | \(0.203197\pi\) | ||||
−0.803073 | + | 0.595881i | \(0.796803\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29215.0i | 0.0220719i | 0.999939 | + | 0.0110359i | \(0.00351292\pi\) | ||||
−0.999939 | + | 0.0110359i | \(0.996487\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.74371e6 | −1.29422 | −0.647111 | − | 0.762395i | \(-0.724023\pi\) | ||||
−0.647111 | + | 0.762395i | \(0.724023\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 735121.i | − | 0.526810i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.18483e6 | −0.834468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.46650e6 | 1.67847 | 0.839233 | − | 0.543772i | \(-0.183004\pi\) | ||||
0.839233 | + | 0.543772i | \(0.183004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 348513. | + | 666968.i | 0.233165 | + | 0.446221i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −747294. | −0.483407 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −670508. | −0.426568 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −262237. | − | 501857.i | −0.161415 | − | 0.308909i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00904e6 | −1.21658 | −0.608292 | − | 0.793713i | \(-0.708145\pi\) | ||||
−0.608292 | + | 0.793713i | \(0.708145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −810096. | −0.474937 | −0.237468 | − | 0.971395i | \(-0.576318\pi\) | ||||
−0.237468 | + | 0.971395i | \(0.576318\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 893672.i | − | 0.515605i | −0.966198 | − | 0.257803i | \(-0.917002\pi\) | ||
0.966198 | − | 0.257803i | \(-0.0829985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.79723e6 | −1.56344 | −0.781719 | − | 0.623631i | \(-0.785657\pi\) | ||||
−0.781719 | + | 0.623631i | \(0.785657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 664137.i | 0.365410i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 425247.i | 0.226796i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.86701e6 | − | 1.29871e6i | −0.980479 | − | 0.682030i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.52289e6i | 1.28502i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.87721e6i | − | 0.941766i | −0.882196 | − | 0.470883i | \(-0.843935\pi\) | ||
0.882196 | − | 0.470883i | \(-0.156065\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.05546e6 | + | 2.01989e6i | 0.513841 | + | 0.983365i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 120244.i | − | 0.0576750i | −0.999584 | − | 0.0288375i | \(-0.990819\pi\) | ||
0.999584 | − | 0.0288375i | \(-0.00918054\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 795492.i | − | 0.370467i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.49066e6 | −0.684138 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 108098.i | 0.0481943i | 0.999710 | + | 0.0240971i | \(0.00767110\pi\) | ||||
−0.999710 | + | 0.0240971i | \(0.992329\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.91905e6 | 1.28286 | 0.641429 | − | 0.767183i | \(-0.278342\pi\) | ||||
0.641429 | + | 0.767183i | \(0.278342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −376244. | −0.160706 | −0.0803531 | − | 0.996766i | \(-0.525605\pi\) | ||||
−0.0803531 | + | 0.996766i | \(0.525605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 774279. | + | 1.48178e6i | 0.326082 | + | 0.624040i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.92622e6 | 1.19832 | 0.599158 | − | 0.800631i | \(-0.295502\pi\) | ||||
0.599158 | + | 0.800631i | \(0.295502\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.70669e6 | 0.689266 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.10650e6 | − | 1.10072e6i | 0.827617 | − | 0.432458i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.23268e6 | 1.25284 | 0.626422 | − | 0.779484i | \(-0.284519\pi\) | ||||
0.626422 | + | 0.779484i | \(0.284519\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −492603. | −0.185807 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.17558e6i | − | 0.809662i | −0.914391 | − | 0.404831i | \(-0.867330\pi\) | ||
0.914391 | − | 0.404831i | \(-0.132670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.64192e6 | −1.68207 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.04384e6i | − | 0.373282i | −0.982428 | − | 0.186641i | \(-0.940240\pi\) | ||
0.982428 | − | 0.186641i | \(-0.0597602\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.50276e6i | − | 1.22015i | −0.792343 | − | 0.610076i | \(-0.791139\pi\) | ||
0.792343 | − | 0.610076i | \(-0.208861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 417528. | + | 799046.i | 0.143560 | + | 0.274739i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.67848e6i | − | 1.23252i | −0.787542 | − | 0.616261i | \(-0.788647\pi\) | ||
0.787542 | − | 0.616261i | \(-0.211353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 497805.i | 0.164671i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.34068e6 | + | 700552.i | −0.432348 | + | 0.225916i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.33149e6i | 0.742434i | 0.928546 | + | 0.371217i | \(0.121059\pi\) | ||||
−0.928546 | + | 0.371217i | \(0.878941\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.20669e6i | 0.685300i | 0.939463 | + | 0.342650i | \(0.111324\pi\) | ||||
−0.939463 | + | 0.342650i | \(0.888676\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.56001e6 | 1.70535 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 577844.i | 0.172912i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.32837e6 | −0.392655 | −0.196328 | − | 0.980538i | \(-0.562902\pi\) | ||||
−0.196328 | + | 0.980538i | \(0.562902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.08504e6 | 0.601505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.84636e6 | − | 2.53239e6i | 1.38132 | − | 0.721788i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.51751e6 | 0.978813 | 0.489406 | − | 0.872056i | \(-0.337213\pi\) | ||||
0.489406 | + | 0.872056i | \(0.337213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.95415e6 | 0.537344 | 0.268672 | − | 0.963232i | \(-0.413415\pi\) | ||||
0.268672 | + | 0.963232i | \(0.413415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −865128. | + | 1.24370e6i | −0.232331 | + | 0.333997i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.56888e6 | −0.416408 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.35646e6 | −0.351733 | −0.175866 | − | 0.984414i | \(-0.556273\pi\) | ||||
−0.175866 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 958941.i | 0.245795i | 0.992419 | + | 0.122897i | \(0.0392186\pi\) | ||||
−0.992419 | + | 0.122897i | \(0.960781\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −900689. | −0.225617 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.29425e6i | − | 1.80642i | −0.429196 | − | 0.903211i | \(-0.641203\pi\) | ||
0.429196 | − | 0.903211i | \(-0.358797\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.38040e6i | 0.818387i | 0.912448 | + | 0.409193i | \(0.134190\pi\) | ||||
−0.912448 | + | 0.409193i | \(0.865810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.68502e6 | − | 1.40301e6i | 0.642758 | − | 0.335863i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.83219e6i | 0.428898i | 0.976735 | + | 0.214449i | \(0.0687957\pi\) | ||||
−0.976735 | + | 0.214449i | \(0.931204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 494198.i | − | 0.114409i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.58485e6 | + | 2.91827e6i | −1.26469 | + | 0.660842i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.56773e6i | 1.02308i | 0.859259 | + | 0.511540i | \(0.170925\pi\) | ||||
−0.859259 | + | 0.511540i | \(0.829075\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.30868e6i | − | 0.725107i | −0.931963 | − | 0.362554i | \(-0.881905\pi\) | ||
0.931963 | − | 0.362554i | \(-0.118095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.15559e6 | −0.467320 | −0.233660 | − | 0.972318i | \(-0.575070\pi\) | ||||
−0.233660 | + | 0.972318i | \(0.575070\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 4.77902e6i | − | 1.01402i | −0.861940 | − | 0.507010i | \(-0.830751\pi\) | ||
0.861940 | − | 0.507010i | \(-0.169249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.31446e6 | 1.32557 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −450761. | −0.0926389 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.25025e6 | − | 1.56529e6i | −0.457611 | − | 0.318318i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.43060e6 | −1.08146 | −0.540728 | − | 0.841198i | \(-0.681851\pi\) | ||||
−0.540728 | + | 0.841198i | \(0.681851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.03879e6 | −0.795954 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.16127e6 | − | 3.21947e6i | 1.18937 | − | 0.621484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.90831e6 | −0.937799 | −0.468899 | − | 0.883252i | \(-0.655349\pi\) | ||||
−0.468899 | + | 0.883252i | \(0.655349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.75489e6 | −1.07729 | −0.538645 | − | 0.842533i | \(-0.681064\pi\) | ||||
−0.538645 | + | 0.842533i | \(0.681064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.09219e6i | 0.572992i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.63225e6 | 0.841204 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7.74644e6i | − | 1.39268i | −0.717713 | − | 0.696339i | \(-0.754811\pi\) | ||
0.717713 | − | 0.696339i | \(-0.245189\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.08354e6i | − | 0.190952i | −0.995432 | − | 0.0954760i | \(-0.969563\pi\) | ||
0.995432 | − | 0.0954760i | \(-0.0304373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.04746e6 | + | 1.59240e6i | −0.531753 | + | 0.277859i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.29709e6i | − | 0.221909i | −0.993825 | − | 0.110954i | \(-0.964609\pi\) | ||
0.993825 | − | 0.110954i | \(-0.0353908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.58523e6i | − | 1.11563i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.37639e6 | − | 1.02891e7i | −0.893249 | − | 1.70946i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.69606e6i | 0.279070i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.87108e6i | − | 0.463394i | −0.972788 | − | 0.231697i | \(-0.925572\pi\) | ||
0.972788 | − | 0.231697i | \(-0.0744278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.74611e6 | 1.23831 | 0.619155 | − | 0.785269i | \(-0.287475\pi\) | ||||
0.619155 | + | 0.785269i | \(0.287475\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.70377e6i | − | 0.580922i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.38197e6 | 0.836185 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.45415e6 | 0.526651 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.15170e6 | + | 2.16940e6i | −0.627106 | + | 0.327684i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 747906. | 0.110886 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.15367e6 | 0.610154 | 0.305077 | − | 0.952328i | \(-0.401318\pi\) | ||||
0.305077 | + | 0.952328i | \(0.401318\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.86999e6 | − | 3.57870e6i | −0.269680 | − | 0.516101i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.82428e6 | 1.40389 | 0.701944 | − | 0.712232i | \(-0.252316\pi\) | ||||
0.701944 | + | 0.712232i | \(0.252316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.59476e6 | −0.785059 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.19117e6i | 0.582804i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.24335e6 | 1.12581 | 0.562906 | − | 0.826521i | \(-0.309683\pi\) | ||||
0.562906 | + | 0.826521i | \(0.309683\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.15055e6i | − | 0.426439i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 544090.i | 0.0723436i | 0.999346 | + | 0.0361718i | \(0.0115164\pi\) | ||||
−0.999346 | + | 0.0361718i | \(0.988484\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.12479e6 | + | 2.15258e6i | 0.148235 | + | 0.283686i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.86937e6i | 1.01896i | 0.860481 | + | 0.509482i | \(0.170163\pi\) | ||||
−0.860481 | + | 0.509482i | \(0.829837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.15081e6i | − | 0.532774i | −0.963866 | − | 0.266387i | \(-0.914170\pi\) | ||
0.963866 | − | 0.266387i | \(-0.0858299\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.63420e6 | − | 1.83237e6i | −0.332260 | − | 0.231123i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.35134e7i | − | 1.68977i | −0.534951 | − | 0.844883i | \(-0.679670\pi\) | ||
0.534951 | − | 0.844883i | \(-0.320330\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.51504e7i | − | 1.86202i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −331161. | −0.0403522 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.07517e6i | − | 0.847504i | −0.905778 | − | 0.423752i | \(-0.860713\pi\) | ||
0.905778 | − | 0.423752i | \(-0.139287\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.70130e6 | 0.795923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.43880e6 | −0.635135 | −0.317567 | − | 0.948236i | \(-0.602866\pi\) | ||||
−0.317567 | + | 0.948236i | \(0.602866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.94399e6 | + | 3.72032e6i | 0.225114 | + | 0.430812i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.50637e6 | 0.171539 | 0.0857697 | − | 0.996315i | \(-0.472665\pi\) | ||||
0.0857697 | + | 0.996315i | \(0.472665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.39751e6 | 0.157823 | 0.0789113 | − | 0.996882i | \(-0.474856\pi\) | ||||
0.0789113 | + | 0.996882i | \(0.474856\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.88879e6 | − | 7.44217e6i | −0.431942 | − | 0.826630i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.32808e7 | 1.46302 | 0.731512 | − | 0.681828i | \(-0.238815\pi\) | ||||
0.731512 | + | 0.681828i | \(0.238815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18544e7 | −1.28463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.61279e6i | 0.710778i | 0.934719 | + | 0.355389i | \(0.115652\pi\) | ||||
−0.934719 | + | 0.355389i | \(0.884348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.99579e6 | −0.211058 | −0.105529 | − | 0.994416i | \(-0.533654\pi\) | ||||
−0.105529 | + | 0.994416i | \(0.533654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.25288e7i | − | 1.31427i | −0.753774 | − | 0.657134i | \(-0.771768\pi\) | ||
0.753774 | − | 0.657134i | \(-0.228232\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 8.39376e6i | − | 0.866436i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.39673e6 | − | 9.15585e6i | −0.347825 | − | 0.937559i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.69041e6i | 0.271139i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.38620e6i | − | 0.838479i | −0.907876 | − | 0.419239i | \(-0.862297\pi\) | ||
0.907876 | − | 0.419239i | \(-0.137703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.31893e6 | − | 6.35161e6i | −0.326636 | − | 0.625100i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.22741e6i | 0.510433i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.36686e6i | 0.131395i | 0.997840 | + | 0.0656974i | \(0.0209272\pi\) | ||||
−0.997840 | + | 0.0656974i | \(0.979073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.02175e6 | 0.669758 | 0.334879 | − | 0.942261i | \(-0.391305\pi\) | ||||
0.334879 | + | 0.942261i | \(0.391305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.47870e7i | 1.38873i | 0.719621 | + | 0.694367i | \(0.244316\pi\) | ||||
−0.719621 | + | 0.694367i | \(0.755684\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.40170e6 | 0.130630 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.24519e7 | −1.14275 | −0.571377 | − | 0.820688i | \(-0.693591\pi\) | ||||
−0.571377 | + | 0.820688i | \(0.693591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 288950. | + | 552979.i | 0.0263160 | + | 0.0503623i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.95740e7 | 1.75577 | 0.877884 | − | 0.478874i | \(-0.158955\pi\) | ||||
0.877884 | + | 0.478874i | \(0.158955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.10926e7 | 1.87770 | 0.938851 | − | 0.344324i | \(-0.111892\pi\) | ||||
0.938851 | + | 0.344324i | \(0.111892\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.73124e6 | + | 3.51730e6i | −0.590257 | + | 0.308429i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.54936e6 | −0.570012 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.05471e6 | −0.0904325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.25319e7i | − | 1.06655i | −0.845943 | − | 0.533273i | \(-0.820962\pi\) | ||
0.845943 | − | 0.533273i | \(-0.179038\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.78634e7 | 1.49793 | 0.748967 | − | 0.662607i | \(-0.230550\pi\) | ||||
0.748967 | + | 0.662607i | \(0.230550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.92610e7i | − | 1.60326i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.58838e7i | 1.30287i | 0.758703 | + | 0.651436i | \(0.225833\pi\) | ||||
−0.758703 | + | 0.651436i | \(0.774167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.05967e7 | + | 2.02794e7i | 0.862866 | + | 1.65131i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.31461e6i | − | 0.185751i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.27317e7i | 1.01436i | 0.861841 | + | 0.507179i | \(0.169312\pi\) | ||||
−0.861841 | + | 0.507179i | \(0.830688\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.67472e7 | + | 8.75100e6i | −1.31517 | + | 0.687220i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.30096e6i | − | 0.179402i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.26599e7i | 0.973049i | 0.873667 | + | 0.486525i | \(0.161736\pi\) | ||||
−0.873667 | + | 0.486525i | \(0.838264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.86782e6 | −0.371489 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.52681e6i | 0.716802i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.55798e6 | 0.489953 | 0.244977 | − | 0.969529i | \(-0.421220\pi\) | ||||
0.244977 | + | 0.969529i | \(0.421220\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.84471e6 | 0.577901 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.75451e6 | + | 1.96186e6i | −0.274656 | + | 0.143517i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.18837e7 | 1.57869 | 0.789347 | − | 0.613947i | \(-0.210419\pi\) | ||||
0.789347 | + | 0.613947i | \(0.210419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.21651e7 | −2.30434 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.63627e7 | − | 1.13820e7i | −1.15614 | − | 0.804220i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.39022e6 | 0.658931 | 0.329465 | − | 0.944168i | \(-0.393131\pi\) | ||||
0.329465 | + | 0.944168i | \(0.393131\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.09872e6 | −0.145265 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.13158e7i | 1.46535i | 0.680577 | + | 0.732677i | \(0.261729\pi\) | ||||
−0.680577 | + | 0.732677i | \(0.738271\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.24500e6 | 0.287879 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.72669e7i | − | 1.16307i | −0.813523 | − | 0.581533i | \(-0.802453\pi\) | ||
0.813523 | − | 0.581533i | \(-0.197547\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.69724e7i | − | 1.79245i | −0.443598 | − | 0.896226i | \(-0.646298\pi\) | ||
0.443598 | − | 0.896226i | \(-0.353702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.74258e7 | + | 9.10557e6i | −1.15028 | + | 0.601058i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.29788e7i | 0.845338i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.88255e7i | 1.21800i | 0.793171 | + | 0.608999i | \(0.208428\pi\) | ||||
−0.793171 | + | 0.608999i | \(0.791572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.94191e6 | + | 4.14992e6i | −0.507058 | + | 0.264955i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.35520e6i | − | 0.403079i | −0.979480 | − | 0.201539i | \(-0.935406\pi\) | ||
0.979480 | − | 0.201539i | \(-0.0645944\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.60819e6i | 0.601423i | 0.953715 | + | 0.300711i | \(0.0972241\pi\) | ||||
−0.953715 | + | 0.300711i | \(0.902776\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.11876e7 | −0.695703 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.79707e6i | 0.601323i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.33196e7 | −0.812225 | −0.406113 | − | 0.913823i | \(-0.633116\pi\) | ||||
−0.406113 | + | 0.913823i | \(0.633116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.03053e7 | 0.620317 | 0.310159 | − | 0.950685i | \(-0.399618\pi\) | ||||
0.310159 | + | 0.950685i | \(0.399618\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.95989e7 | + | 1.36332e7i | 1.17214 | + | 0.815349i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.16317e6 | 0.245799 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.11411e6 | 0.182687 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.44336e7 | − | 7.54205e6i | 0.835990 | − | 0.436833i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.64506e6 | −0.0946772 | −0.0473386 | − | 0.998879i | \(-0.515074\pi\) | ||||
−0.0473386 | + | 0.998879i | \(0.515074\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.72927e6 | 0.382408 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.37176e6i | − | 0.416282i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.23277e6 | −0.124508 | −0.0622542 | − | 0.998060i | \(-0.519829\pi\) | ||||
−0.0622542 | + | 0.998060i | \(0.519829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.89675e6i | 0.437604i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 4.42703e6i | − | 0.242283i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.87976e6 | + | 4.11744e6i | −0.428571 | + | 0.223943i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.52749e7i | 1.89494i | 0.319851 | + | 0.947468i | \(0.396367\pi\) | ||||
−0.319851 | + | 0.947468i | \(0.603633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.36982e6i | 0.286687i | 0.989673 | + | 0.143343i | \(0.0457853\pi\) | ||||
−0.989673 | + | 0.143343i | \(0.954215\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.08104e6 | + | 2.06884e6i | 0.0570095 | + | 0.109102i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.79725e6i | − | 0.199028i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.41519e7i | − | 1.76830i | −0.467200 | − | 0.884152i | \(-0.654737\pi\) | ||
0.467200 | − | 0.884152i | \(-0.345263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.29782e7 | −1.18254 | −0.591270 | − | 0.806474i | \(-0.701373\pi\) | ||||
−0.591270 | + | 0.806474i | \(0.701373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.00130e6i | 0.254284i | 0.991885 | + | 0.127142i | \(0.0405804\pi\) | ||||
−0.991885 | + | 0.127142i | \(0.959420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.83727e7 | 1.93926 | 0.969629 | − | 0.244581i | \(-0.0786504\pi\) | ||||
0.969629 | + | 0.244581i | \(0.0786504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.48221e6 | 0.173877 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.27740e7 | + | 1.71255e7i | −1.62672 | + | 0.850016i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.37076e7 | 1.65319 | 0.826596 | − | 0.562795i | \(-0.190274\pi\) | ||||
0.826596 | + | 0.562795i | \(0.190274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.01711e7 | −0.983422 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.09977e6 | − | 7.84594e6i | −0.197523 | − | 0.378010i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.32653e7 | −1.11430 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.69839e6 | −0.269729 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.84619e7i | − | 1.80992i | −0.425500 | − | 0.904959i | \(-0.639902\pi\) | ||
0.425500 | − | 0.904959i | \(-0.360098\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.81377e7 | −1.30869 | −0.654345 | − | 0.756197i | \(-0.727055\pi\) | ||||
−0.654345 | + | 0.756197i | \(0.727055\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.58144e7i | 0.731256i | 0.930761 | + | 0.365628i | \(0.119146\pi\) | ||||
−0.930761 | + | 0.365628i | \(0.880854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 5.22733e6i | − | 0.238920i | −0.992839 | − | 0.119460i | \(-0.961884\pi\) | ||
0.992839 | − | 0.119460i | \(-0.0381164\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.64520e7 | − | 3.14850e7i | −0.747614 | − | 1.43075i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.81759e6i | 0.126569i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.96700e7i | 1.32517i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.68421e7 | − | 3.40725e6i | −1.18521 | − | 0.150447i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 7.13556e6i | − | 0.313278i | −0.987656 | − | 0.156639i | \(-0.949934\pi\) | ||
0.987656 | − | 0.156639i | \(-0.0500658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.90570e6i | − | 0.126128i | −0.998009 | − | 0.0630638i | \(-0.979913\pi\) | ||
0.998009 | − | 0.0630638i | \(-0.0200872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −886730. | −0.0382727 | −0.0191364 | − | 0.999817i | \(-0.506092\pi\) | ||||
−0.0191364 | + | 0.999817i | \(0.506092\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.43504e7i | − | 0.612426i | −0.951963 | − | 0.306213i | \(-0.900938\pi\) | ||
0.951963 | − | 0.306213i | \(-0.0990619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.98561e7 | −0.842633 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.42877e7 | −0.599563 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.46189e7 | + | 2.79770e7i | 0.610040 | + | 1.16747i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.87285e7 | 2.01087 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.54187e6 | −0.0632754 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.11853e6 | + | 2.14060e6i | 0.0453970 | + | 0.0868787i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.28409e7 | −0.921924 | −0.460962 | − | 0.887420i | \(-0.652495\pi\) | ||||
−0.460962 | + | 0.887420i | \(0.652495\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.77827e7 | −1.50833 | −0.754167 | − | 0.656683i | \(-0.771959\pi\) | ||||
−0.754167 | + | 0.656683i | \(0.771959\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.01851e7i | − | 0.404380i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.72869e6 | 0.0678883 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.23668e6i | 0.126419i | 0.998000 | + | 0.0632093i | \(0.0201336\pi\) | ||||
−0.998000 | + | 0.0632093i | \(0.979866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.17658e7i | 0.840950i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42366e7 | − | 9.90314e6i | −0.547083 | − | 0.380556i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.52545e7i | 1.72037i | 0.509980 | + | 0.860186i | \(0.329653\pi\) | ||||
−0.509980 | + | 0.860186i | \(0.670347\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.30043e6i | 0.238230i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.30688e6 | + | 2.50105e6i | 0.0488886 | + | 0.0935606i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.85407e6i | − | 0.292244i | −0.989267 | − | 0.146122i | \(-0.953321\pi\) | ||
0.989267 | − | 0.146122i | \(-0.0466792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 721027.i | 0.0265447i | 0.999912 | + | 0.0132723i | \(0.00422484\pi\) | ||||
−0.999912 | + | 0.0132723i | \(0.995775\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.87351e6 | 0.178469 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.39438e7i | − | 0.505250i | −0.967564 | − | 0.252625i | \(-0.918706\pi\) | ||
0.967564 | − | 0.252625i | \(-0.0812938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.09423e7 | 1.11529 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.37454e7 | −0.490260 | −0.245130 | − | 0.969490i | \(-0.578831\pi\) | ||||
−0.245130 | + | 0.969490i | \(0.578831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.78549e7 | + | 3.41698e7i | 0.633503 | + | 1.21237i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.33964e7 | 2.22596 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.97371e7 | −1.03870 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.44895e6 | − | 4.93740e6i | 0.326637 | − | 0.170679i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.22441e7 | 0.421077 | 0.210539 | − | 0.977586i | \(-0.432478\pi\) | ||||
0.210539 | + | 0.977586i | \(0.432478\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.33008e7 | 1.81420 | 0.907102 | − | 0.420912i | \(-0.138290\pi\) | ||||
0.907102 | + | 0.420912i | \(0.138290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.23543e7i | 1.77284i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.05399e7 | −1.02360 | −0.511802 | − | 0.859104i | \(-0.671022\pi\) | ||||
−0.511802 | + | 0.859104i | \(0.671022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.64285e6i | − | 0.188166i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.17124e7i | 1.37683i | 0.725315 | + | 0.688417i | \(0.241694\pi\) | ||||
−0.725315 | + | 0.688417i | \(0.758306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.80867e6 | − | 1.49439e7i | −0.256440 | − | 0.490763i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.44516e6i | − | 0.144510i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.89827e7i | 0.937464i | 0.883341 | + | 0.468732i | \(0.155289\pi\) | ||||
−0.883341 | + | 0.468732i | \(0.844711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.09564e7 | + | 1.09504e7i | −0.671055 | + | 0.350649i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.17250e7i | 1.32941i | 0.747106 | + | 0.664705i | \(0.231443\pi\) | ||||
−0.747106 | + | 0.664705i | \(0.768557\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.6.o.d.719.28 | yes | 40 | |
3.2 | odd | 2 | inner | 720.6.o.d.719.14 | yes | 40 | |
4.3 | odd | 2 | inner | 720.6.o.d.719.27 | yes | 40 | |
5.4 | even | 2 | inner | 720.6.o.d.719.15 | yes | 40 | |
12.11 | even | 2 | inner | 720.6.o.d.719.13 | ✓ | 40 | |
15.14 | odd | 2 | inner | 720.6.o.d.719.25 | yes | 40 | |
20.19 | odd | 2 | inner | 720.6.o.d.719.16 | yes | 40 | |
60.59 | even | 2 | inner | 720.6.o.d.719.26 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.6.o.d.719.13 | ✓ | 40 | 12.11 | even | 2 | inner | |
720.6.o.d.719.14 | yes | 40 | 3.2 | odd | 2 | inner | |
720.6.o.d.719.15 | yes | 40 | 5.4 | even | 2 | inner | |
720.6.o.d.719.16 | yes | 40 | 20.19 | odd | 2 | inner | |
720.6.o.d.719.25 | yes | 40 | 15.14 | odd | 2 | inner | |
720.6.o.d.719.26 | yes | 40 | 60.59 | even | 2 | inner | |
720.6.o.d.719.27 | yes | 40 | 4.3 | odd | 2 | inner | |
720.6.o.d.719.28 | yes | 40 | 1.1 | even | 1 | trivial |