Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(81,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.81");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.d (of order \(2\), degree \(1\), not 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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} - 109104 x^{12} - 96128 x^{11} + 3580672 x^{10} - 1538048 x^{9} + \cdots + 1099511627776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{90}\cdot 3^{4}\cdot 5^{12} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 81.4 | ||
Root | \(2.93366 + 2.71913i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.81 |
Dual form | 160.6.d.a.81.17 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 18.7876i | − 1.20523i | −0.798033 | − | 0.602614i | \(-0.794126\pi\) | ||||
0.798033 | − | 0.602614i | \(-0.205874\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 107.536 | 0.829487 | 0.414743 | − | 0.909938i | \(-0.363871\pi\) | ||||
0.414743 | + | 0.909938i | \(0.363871\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −109.975 | −0.452573 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 272.206i | − 0.678290i | −0.940734 | − | 0.339145i | \(-0.889862\pi\) | ||||
0.940734 | − | 0.339145i | \(-0.110138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 198.402i | − 0.325602i | −0.986659 | − | 0.162801i | \(-0.947947\pi\) | ||||
0.986659 | − | 0.162801i | \(-0.0520529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 469.691 | 0.538994 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2065.79 | 1.73366 | 0.866829 | − | 0.498606i | \(-0.166154\pi\) | ||||
0.866829 | + | 0.498606i | \(0.166154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1891.04i | 1.20176i | 0.799341 | + | 0.600878i | \(0.205182\pi\) | ||||
−0.799341 | + | 0.600878i | \(0.794818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2020.35i | − 0.999720i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 987.677 | 0.389310 | 0.194655 | − | 0.980872i | \(-0.437641\pi\) | ||||
0.194655 | + | 0.980872i | \(0.437641\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2499.22i | − 0.659774i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8015.26i | − 1.76979i | −0.465788 | − | 0.884896i | \(-0.654229\pi\) | ||||
0.465788 | − | 0.884896i | \(-0.345771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −827.342 | −0.154625 | −0.0773127 | − | 0.997007i | \(-0.524634\pi\) | ||||
−0.0773127 | + | 0.997007i | \(0.524634\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5114.10 | −0.817494 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2688.40i | 0.370958i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9426.30i | − 1.13198i | −0.824414 | − | 0.565988i | \(-0.808495\pi\) | ||||
0.824414 | − | 0.565988i | \(-0.191505\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3727.50 | −0.392425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8221.07 | −0.763780 | −0.381890 | − | 0.924208i | \(-0.624727\pi\) | ||||
−0.381890 | + | 0.924208i | \(0.624727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9301.63i | − 0.767164i | −0.923507 | − | 0.383582i | \(-0.874690\pi\) | ||||
0.923507 | − | 0.383582i | \(-0.125310\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2749.38i | − 0.202397i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13837.9 | −0.913745 | −0.456873 | − | 0.889532i | \(-0.651031\pi\) | ||||
−0.456873 | + | 0.889532i | \(0.651031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5242.97 | −0.311952 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 38811.3i | − 2.08945i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27751.2i | 1.35704i | 0.734582 | + | 0.678520i | \(0.237378\pi\) | ||||
−0.734582 | + | 0.678520i | \(0.762622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6805.14 | 0.303340 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 35528.1 | 1.44839 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 25106.1i | − 0.938965i | −0.882942 | − | 0.469482i | \(-0.844441\pi\) | ||||
0.882942 | − | 0.469482i | \(-0.155559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 26404.6i | − 0.908563i | −0.890858 | − | 0.454282i | \(-0.849896\pi\) | ||||
0.890858 | − | 0.454282i | \(-0.150104\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11826.3 | −0.375404 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4960.05 | 0.145614 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 38563.9i | − 1.04953i | −0.851248 | − | 0.524764i | \(-0.824154\pi\) | ||||
0.851248 | − | 0.524764i | \(-0.175846\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 18556.1i | − 0.469207i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 71073.0 | 1.67324 | 0.836621 | − | 0.547782i | \(-0.184528\pi\) | ||||
0.836621 | + | 0.547782i | \(0.184528\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18622.0 | 0.408996 | 0.204498 | − | 0.978867i | \(-0.434444\pi\) | ||||
0.204498 | + | 0.978867i | \(0.434444\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11742.3i | 0.241045i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 29271.9i | − 0.562632i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 75599.4 | 1.36286 | 0.681429 | − | 0.731884i | \(-0.261359\pi\) | ||||
0.681429 | + | 0.731884i | \(0.261359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73678.4 | −1.24775 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 125298.i | 1.99641i | 0.0599304 | + | 0.998203i | \(0.480912\pi\) | ||||
−0.0599304 | + | 0.998203i | \(0.519088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 51644.7i | 0.775315i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −150588. | −2.13300 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 30341.5 | 0.406034 | 0.203017 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203017 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 21335.4i | − 0.270083i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15543.8i | 0.186359i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −47275.9 | −0.537441 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15635.2 | 0.168723 | 0.0843617 | − | 0.996435i | \(-0.473115\pi\) | ||||
0.0843617 | + | 0.996435i | \(0.473115\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29935.9i | 0.306976i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 102692.i | − 1.00169i | −0.865538 | − | 0.500843i | \(-0.833024\pi\) | ||||
0.865538 | − | 0.500843i | \(-0.166976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 35981.8 | 0.334187 | 0.167093 | − | 0.985941i | \(-0.446562\pi\) | ||||
0.167093 | + | 0.985941i | \(0.446562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 50508.8 | 0.447088 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 94984.6i | 0.802035i | 0.916070 | + | 0.401018i | \(0.131343\pi\) | ||||
−0.916070 | + | 0.401018i | \(0.868657\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 173158.i | 1.39597i | 0.716113 | + | 0.697984i | \(0.245919\pi\) | ||||
−0.716113 | + | 0.697984i | \(0.754081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −177098. | −1.36429 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −237780. | −1.75178 | −0.875891 | − | 0.482510i | \(-0.839725\pi\) | ||||
−0.875891 | + | 0.482510i | \(0.839725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24691.9i | 0.174105i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 21819.3i | 0.147359i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 222147. | 1.43805 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 86955.1 | 0.539923 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 154454.i | 0.920529i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 15625.0i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 63282.9 | 0.348158 | 0.174079 | − | 0.984732i | \(-0.444305\pi\) | ||||
0.174079 | + | 0.984732i | \(0.444305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −174756. | −0.924607 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 180082.i | 0.916835i | 0.888737 | + | 0.458417i | \(0.151584\pi\) | ||||
−0.888737 | + | 0.458417i | \(0.848416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 203355.i | 0.996840i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 62480.5 | 0.295060 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 365739. | 1.66483 | 0.832414 | − | 0.554155i | \(-0.186958\pi\) | ||||
0.832414 | + | 0.554155i | \(0.186958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 111886.i | − 0.491180i | −0.969374 | − | 0.245590i | \(-0.921018\pi\) | ||||
0.969374 | − | 0.245590i | \(-0.0789817\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 259981.i | 1.10127i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −54006.1 | −0.220853 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 200381. | 0.791475 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 98503.1i | 0.375973i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 136480.i | − 0.503621i | −0.967777 | − | 0.251811i | \(-0.918974\pi\) | ||||
0.967777 | − | 0.251811i | \(-0.0810260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −186354. | −0.665115 | −0.332557 | − | 0.943083i | \(-0.607912\pi\) | ||||
−0.332557 | + | 0.943083i | \(0.607912\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −227186. | −0.784607 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 20683.6i | − 0.0691506i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 74689.6i | 0.241830i | 0.992663 | + | 0.120915i | \(0.0385829\pi\) | ||||
−0.992663 | + | 0.120915i | \(0.961417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 521380. | 1.63554 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 106211. | 0.322927 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 548779.i | − 1.61781i | −0.587937 | − | 0.808907i | \(-0.700060\pi\) | ||||
0.587937 | − | 0.808907i | \(-0.299940\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 127852.i | − 0.365594i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −224312. | −0.622387 | −0.311194 | − | 0.950347i | \(-0.600729\pi\) | ||||
−0.311194 | + | 0.950347i | \(0.600729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 331930. | 0.893983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 207967.i | − 0.543882i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 165260.i | − 0.419809i | −0.977722 | − | 0.209905i | \(-0.932685\pi\) | ||||
0.977722 | − | 0.209905i | \(-0.0673154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −67210.1 | −0.165897 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −471684. | −1.13167 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 431975.i | 1.00769i | 0.863795 | + | 0.503844i | \(0.168081\pi\) | ||||
−0.863795 | + | 0.503844i | \(0.831919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 216944.i | 0.492210i | 0.969243 | + | 0.246105i | \(0.0791508\pi\) | ||||
−0.969243 | + | 0.246105i | \(0.920849\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −496080. | −1.09503 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 235658. | 0.506235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 562319.i | − 1.17592i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 268756.i | − 0.547274i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 34566.0 | 0.0685592 | 0.0342796 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342796 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −473601. | −0.915208 | −0.457604 | − | 0.889156i | \(-0.651292\pi\) | ||||
−0.457604 | + | 0.889156i | \(0.651292\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 93187.6i | − 0.175498i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 394784.i | 0.724760i | 0.932030 | + | 0.362380i | \(0.118036\pi\) | ||||
−0.932030 | + | 0.362380i | \(0.881964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 477089. | 0.854017 | 0.427009 | − | 0.904248i | \(-0.359567\pi\) | ||||
0.427009 | + | 0.904248i | \(0.359567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −724524. | −1.26492 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 861930.i | − 1.46802i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 205527.i | − 0.341573i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −108620. | −0.176191 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 514751. | 0.815139 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 435894.i | 0.674023i | 0.941500 | + | 0.337012i | \(0.109416\pi\) | ||||
−0.941500 | + | 0.337012i | \(0.890584\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.33529e6i | − 2.01664i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 232541. | 0.343086 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −88969.2 | −0.128260 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 349863.i | − 0.492933i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 409856.i | − 0.564483i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.14075e6 | −1.53613 | −0.768067 | − | 0.640369i | \(-0.778781\pi\) | ||||
−0.768067 | + | 0.640369i | \(0.778781\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 68734.6 | 0.0905147 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.08895e6i | 1.40262i | 0.712854 | + | 0.701312i | \(0.247402\pi\) | ||||
−0.712854 | + | 0.701312i | \(0.752598\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 474386.i | − 0.597783i | −0.954287 | − | 0.298891i | \(-0.903383\pi\) | ||||
0.954287 | − | 0.298891i | \(-0.0966168\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −549951. | −0.678100 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −271057. | −0.327093 | −0.163547 | − | 0.986536i | \(-0.552293\pi\) | ||||
−0.163547 | + | 0.986536i | \(0.552293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 345947.i | − 0.408639i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.42033e6i | − 1.64255i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 824404. | 0.933567 | 0.466784 | − | 0.884372i | \(-0.345413\pi\) | ||||
0.466784 | + | 0.884372i | \(0.345413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −86717.2 | −0.0961750 | −0.0480875 | − | 0.998843i | \(-0.515313\pi\) | ||||
−0.0480875 | + | 0.998843i | \(0.515313\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 776933.i | 0.844050i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 131074.i | − 0.139509i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 375186. | 0.391294 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.35405e6 | 2.40612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 411977.i | 0.412751i | 0.978473 | + | 0.206376i | \(0.0661669\pi\) | ||||
−0.978473 | + | 0.206376i | \(0.933833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 268851.i | − 0.264065i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 970282. | 0.934431 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −88057.5 | −0.0831637 | −0.0415818 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415818 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.01367e6i | − 0.938958i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 881480.i | 0.800961i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 126284. | 0.112579 | 0.0562896 | − | 0.998414i | \(-0.482073\pi\) | ||||
0.0562896 | + | 0.998414i | \(0.482073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −693781. | −0.606886 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 570045.i | − 0.489363i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.88178e6i | 1.58558i | 0.609495 | + | 0.792790i | \(0.291372\pi\) | ||||
−0.609495 | + | 0.792790i | \(0.708628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17095e6 | 0.968532 | 0.484266 | − | 0.874921i | \(-0.339087\pi\) | ||||
0.484266 | + | 0.874921i | \(0.339087\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −400841. | −0.325511 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 170128.i | 0.135658i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.11420e6i | 0.872496i | 0.899827 | + | 0.436248i | \(0.143693\pi\) | ||||
−0.899827 | + | 0.436248i | \(0.856307\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 90987.2 | 0.0699793 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.87861e6 | −1.41929 | −0.709646 | − | 0.704558i | \(-0.751145\pi\) | ||||
−0.709646 | + | 0.704558i | \(0.751145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3072.89i | − 0.00228077i | −0.999999 | − | 0.00114038i | \(-0.999637\pi\) | ||||
0.999999 | − | 0.00114038i | \(-0.000362996\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 888203.i | 0.647739i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −884062. | −0.633546 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.84762e6 | 2.00557 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 293749.i | − 0.203350i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.45968e6i | 1.67382i | 0.547339 | + | 0.836911i | \(0.315641\pi\) | ||||
−0.547339 | + | 0.836911i | \(0.684359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 627653. | 0.419918 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −680301. | −0.447518 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 195957.i | − 0.126760i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.00026e6i | − 0.636352i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.92933e6 | −1.20726 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 660115. | 0.406322 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 257478.i | − 0.155917i | −0.996957 | − | 0.0779585i | \(-0.975160\pi\) | ||||
0.996957 | − | 0.0779585i | \(-0.0248402\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 676012.i | − 0.402771i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.43192e6 | −1.42576 | −0.712882 | − | 0.701284i | \(-0.752610\pi\) | ||||
−0.712882 | + | 0.701284i | \(0.752610\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.62542e6 | −1.51474 | −0.757369 | − | 0.652987i | \(-0.773515\pi\) | ||||
−0.757369 | + | 0.652987i | \(0.773515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 295658.i | − 0.167886i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.54754e6i | 1.42388i | 0.702240 | + | 0.711940i | \(0.252183\pi\) | ||||
−0.702240 | + | 0.711940i | \(0.747817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.18180e6 | −1.20043 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.78454e6 | 0.966635 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.90648e6i | 2.08343i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 124001.i | 0.0651205i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.25322e6 | 1.68246 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.48807e6 | −0.757940 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.11710e6i | − 1.06211i | −0.847336 | − | 0.531057i | \(-0.821795\pi\) | ||||
0.847336 | − | 0.531057i | \(-0.178205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.03666e6i | 0.512302i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 964097. | 0.469363 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.56954e6 | −0.752832 | −0.376416 | − | 0.926451i | \(-0.622844\pi\) | ||||
−0.376416 | + | 0.926451i | \(0.622844\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.46733e6i | 2.11129i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 225207.i | 0.104881i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.37117e6 | −1.08825 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 463903. | 0.209836 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 428538.i | − 0.191058i | −0.995427 | − | 0.0955292i | \(-0.969546\pi\) | ||||
0.995427 | − | 0.0955292i | \(-0.0304543\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 522898.i | − 0.229802i | −0.993377 | − | 0.114901i | \(-0.963345\pi\) | ||||
0.993377 | − | 0.114901i | \(-0.0366551\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −495850. | −0.214824 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.89389e6 | 0.808943 | 0.404472 | − | 0.914550i | \(-0.367455\pi\) | ||||
0.404472 | + | 0.914550i | \(0.367455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.77682e6i | 0.748297i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.17361e6i | − 1.73317i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.57094e6 | 1.05282 | 0.526412 | − | 0.850229i | \(-0.323537\pi\) | ||||
0.526412 | + | 0.850229i | \(0.323537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.09992e6 | −0.444216 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.63368e6i | − 0.650730i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 465550.i | 0.182909i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.47263e6 | 0.958282 | 0.479141 | − | 0.877738i | \(-0.340948\pi\) | ||||
0.479141 | + | 0.877738i | \(0.340948\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 904114. | 0.345667 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.98426e6i | 1.12565i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.62533e6i | 0.977038i | 0.872553 | + | 0.488519i | \(0.162463\pi\) | ||||
−0.872553 | + | 0.488519i | \(0.837537\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −293557. | −0.107799 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.59024e6 | −0.576249 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 2.14283e6i | − 0.766284i | −0.923689 | − | 0.383142i | \(-0.874842\pi\) | ||||
0.923689 | − | 0.383142i | \(-0.125158\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1.18894e6i | − 0.419610i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 641783. | 0.223559 | 0.111779 | − | 0.993733i | \(-0.464345\pi\) | ||||
0.111779 | + | 0.993733i | \(0.464345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 731799. | 0.251617 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.02295e6i | 0.347198i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.36321e6i | − 0.791823i | −0.918289 | − | 0.395911i | \(-0.870429\pi\) | ||||
0.918289 | − | 0.395911i | \(-0.129571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.04033e6 | 0.674930 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.38331e6 | 1.10499 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.88998e6i | 0.609489i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 403888.i | − 0.128613i | −0.997930 | − | 0.0643065i | \(-0.979516\pi\) | ||||
0.997930 | − | 0.0643065i | \(-0.0204835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.82056e6 | 1.20142 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.28335e6 | 0.709108 | 0.354554 | − | 0.935036i | \(-0.384633\pi\) | ||||
0.354554 | + | 0.935036i | \(0.384633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 164146.i | 0.0503464i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.84196e6i | − 0.558011i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.56589e6 | −0.767807 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.27964e6 | 0.969435 | 0.484717 | − | 0.874671i | \(-0.338922\pi\) | ||||
0.484717 | + | 0.874671i | \(0.338922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 6.87136e6i | − 2.00650i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.69981e6i | − 0.778859i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.13245e6 | −0.892820 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.10208e6 | −0.591983 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 604670.i | − 0.168261i | −0.996455 | − | 0.0841305i | \(-0.973189\pi\) | ||||
0.996455 | − | 0.0841305i | \(-0.0268113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 3.46346e6i | − 0.952367i | −0.879346 | − | 0.476184i | \(-0.842020\pi\) | ||||
0.879346 | − | 0.476184i | \(-0.157980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.52183e6 | 0.413537 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.29112e6 | −0.346732 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.83945e6i | − 0.753641i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.01465e6i | 0.266178i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.00345e6 | −1.29741 | −0.648704 | − | 0.761041i | \(-0.724689\pi\) | ||||
−0.648704 | + | 0.761041i | \(0.724689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.11259e6 | −1.05413 | −0.527067 | − | 0.849824i | \(-0.676708\pi\) | ||||
−0.527067 | + | 0.849824i | \(0.676708\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 3.76469e6i | − 0.953908i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.86773e6i | 0.467855i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.20313e6 | −1.04091 | −0.520454 | − | 0.853890i | \(-0.674237\pi\) | ||||
−0.520454 | + | 0.853890i | \(0.674237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 576598. | 0.141181 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1.32165e6i | − 0.319969i | −0.987120 | − | 0.159984i | \(-0.948856\pi\) | ||||
0.987120 | − | 0.159984i | \(-0.0511443\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 758538.i | 0.181584i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.56414e6 | −0.606978 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.52202e6 | −1.29265 | −0.646327 | − | 0.763061i | \(-0.723696\pi\) | ||||
−0.646327 | + | 0.763061i | \(0.723696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.23782e6i | 0.518064i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.50115e6i | 0.801615i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 533385. | 0.120785 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.46838e6 | 0.776849 | 0.388424 | − | 0.921481i | \(-0.373019\pi\) | ||||
0.388424 | + | 0.921481i | \(0.373019\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 5.16286e6i | − 1.14382i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.42345e6i | 0.531107i | 0.964096 | + | 0.265554i | \(0.0855547\pi\) | ||||
−0.964096 | + | 0.265554i | \(0.914445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.58501e6 | 1.42759 | 0.713796 | − | 0.700354i | \(-0.246974\pi\) | ||||
0.713796 | + | 0.700354i | \(0.246974\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −388595. | −0.0833422 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.15697e6i | 0.245488i | 0.992438 | + | 0.122744i | \(0.0391694\pi\) | ||||
−0.992438 | + | 0.122744i | \(0.960831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 4.14701e6i | − 0.870569i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.40324e6 | 0.291461 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.53196e6 | −0.520359 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.18190e6i | − 0.240351i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.05195e6i | − 0.614160i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 380517. | 0.0757767 | 0.0378883 | − | 0.999282i | \(-0.487937\pi\) | ||||
0.0378883 | + | 0.999282i | \(0.487937\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.87020e6 | −0.368574 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.99545e6i | − 0.389201i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 390881.i | 0.0754554i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.67715e6 | −0.511505 | −0.255753 | − | 0.966742i | \(-0.582323\pi\) | ||||
−0.255753 | + | 0.966742i | \(0.582323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.03103e7 | −1.94983 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.10695e6i | 0.956000i | 0.878360 | + | 0.478000i | \(0.158638\pi\) | ||||
−0.878360 | + | 0.478000i | \(0.841362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.65578e7i | − 3.06822i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −748397. | −0.137284 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.64292e6 | 1.38793 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 259376.i | − 0.0466313i | −0.999728 | − | 0.0233157i | \(-0.992578\pi\) | ||||
0.999728 | − | 0.0233157i | \(-0.00742228\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.21429e6i | 0.750118i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 324388. | 0.0571669 | 0.0285835 | − | 0.999591i | \(-0.490900\pi\) | ||||
0.0285835 | + | 0.999591i | \(0.490900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.56729e6 | 0.447967 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6.23617e6i | − 1.07745i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.13575e7i | 1.94307i | 0.236890 | + | 0.971537i | \(0.423872\pi\) | ||||
−0.236890 | + | 0.971537i | \(0.576128\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00254e6 | 0.339257 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.72612e6 | 0.792887 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 899544.i | 0.149453i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.76675e6i | 0.619784i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.10484e6 | −0.505966 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.15918e6 | 1.47830 | 0.739149 | − | 0.673541i | \(-0.235228\pi\) | ||||
0.739149 | + | 0.673541i | \(0.235228\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.08351e6i | − 1.13238i | −0.824273 | − | 0.566192i | \(-0.808416\pi\) | ||||
0.824273 | − | 0.566192i | \(-0.191584\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.26272e6i | 0.199944i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.70911e6 | −0.268068 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.46084e6 | −0.848438 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.76105e6i | 0.424950i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.63108e6i | 0.248689i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.37461e6 | −0.358681 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.11579e6 | 1.21449 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.42717e6i | 0.211594i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 2.53136e6i | − 0.371843i | −0.982565 | − | 0.185922i | \(-0.940473\pi\) | ||||
0.982565 | − | 0.185922i | \(-0.0595271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.07586e6 | 0.593225 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.32894e6 | −0.624296 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.30020e7i | 1.85798i | 0.370108 | + | 0.928989i | \(0.379321\pi\) | ||||
−0.370108 | + | 0.928989i | \(0.620679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.90386e6i | 0.411192i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.51571e7 | 2.12686 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.12967e6 | 1.13047 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 4.42745e6i | − 0.610128i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.70438e6i | 0.779059i | 0.921014 | + | 0.389530i | \(0.127362\pi\) | ||||
−0.921014 | + | 0.389530i | \(0.872638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.84546e6 | −0.249790 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.05646e7 | −1.41725 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.98939e6i | 0.264514i | 0.991215 | + | 0.132257i | \(0.0422224\pi\) | ||||
−0.991215 | + | 0.132257i | \(0.957778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.94451e6i | − 0.783420i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.92310e6 | −1.03499 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.30277e6 | 0.168689 | 0.0843447 | − | 0.996437i | \(-0.473120\pi\) | ||||
0.0843447 | + | 0.996437i | \(0.473120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.90628e6i | 0.373033i | 0.982452 | + | 0.186517i | \(0.0597199\pi\) | ||||
−0.982452 | + | 0.186517i | \(0.940280\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 649413.i | − 0.0826294i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −617298. | −0.0778619 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.01853e6 | 0.502490 | 0.251245 | − | 0.967923i | \(-0.419160\pi\) | ||||
0.251245 | + | 0.967923i | \(0.419160\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.89785e6i | 1.10303i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.34741e7i | 1.65599i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.55404e6 | 0.920466 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −545483. | −0.0659009 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.29654e7i | 1.55307i | 0.630074 | + | 0.776535i | \(0.283025\pi\) | ||||
−0.630074 | + | 0.776535i | \(0.716975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.56454e6i | − 0.185822i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.41706e6 | 0.873501 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −107000. | −0.0124953 | −0.00624767 | − | 0.999980i | \(-0.501989\pi\) | ||||
−0.00624767 | + | 0.999980i | \(0.501989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.55367e6i | 0.643114i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8.96337e6i | − 1.02928i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.06394e7 | −1.21157 | −0.605785 | − | 0.795629i | \(-0.707141\pi\) | ||||
−0.605785 | + | 0.795629i | \(0.707141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.42705e6 | −0.725814 | −0.362907 | − | 0.931825i | \(-0.618216\pi\) | ||||
−0.362907 | + | 0.931825i | \(0.618216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.24108e6i | 0.474988i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.17388e6i | 0.241461i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.96807e6 | −0.216805 | −0.108403 | − | 0.994107i | \(-0.534574\pi\) | ||||
−0.108403 | + | 0.994107i | \(0.534574\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.61936e7 | −1.76930 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.74546e6i | 0.297518i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.12485e6i | 0.873301i | 0.899631 | + | 0.436651i | \(0.143835\pi\) | ||||
−0.899631 | + | 0.436651i | \(0.856165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.86136e6 | −0.411673 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.40750e6 | 0.148846 | 0.0744229 | − | 0.997227i | \(-0.476289\pi\) | ||||
0.0744229 | + | 0.997227i | \(0.476289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.01827e6i | 0.526414i | 0.964739 | + | 0.263207i | \(0.0847802\pi\) | ||||
−0.964739 | + | 0.263207i | \(0.915220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.46842e6i | − 0.256856i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.26281e6 | 0.336800 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 9.67095e6i | − 0.982427i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.94727e7i | − 1.96246i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.59458e6 | −0.559363 | −0.279682 | − | 0.960093i | \(-0.590229\pi\) | ||||
−0.279682 | + | 0.960093i | \(0.590229\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.18942e6 | 0.812351 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.58207e6i | 0.155701i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.04022e6i | 0.101572i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.81627e6 | −0.757265 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.70806e6 | 0.356453 | 0.178226 | − | 0.983990i | \(-0.442964\pi\) | ||||
0.178226 | + | 0.983990i | \(0.442964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.36989e6i | 0.130665i | 0.997864 | + | 0.0653325i | \(0.0208108\pi\) | ||||
−0.997864 | + | 0.0653325i | \(0.979189\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4.36889e6i | − 0.413497i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.38641e7 | 1.30206 | 0.651028 | − | 0.759053i | \(-0.274338\pi\) | ||||
0.651028 | + | 0.759053i | \(0.274338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.83402e6 | −0.636890 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.67152e6i | 0.154582i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.00652e7i | 0.923714i | 0.886954 | + | 0.461857i | \(0.152817\pi\) | ||||
−0.886954 | + | 0.461857i | \(0.847183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50204e6 | −0.410021 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.04796e6 | −0.185101 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.94962e6i | − 0.264578i | −0.991211 | − | 0.132289i | \(-0.957767\pi\) | ||||
0.991211 | − | 0.132289i | \(-0.0422326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.46213e6i | 0.219184i | 0.993977 | + | 0.109592i | \(0.0349544\pi\) | ||||
−0.993977 | + | 0.109592i | \(0.965046\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.70023e6 | −0.680331 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.08387e6 | −0.445801 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.91648e6i | − 0.688997i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.14320e7i | 1.85139i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.18748e6 | −0.616269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.46100e6 | 0.720085 | 0.360043 | − | 0.932936i | \(-0.382762\pi\) | ||||
0.360043 | + | 0.932936i | \(0.382762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.56201e6i | 0.131955i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.01968e7i | 1.69360i | 0.531913 | + | 0.846799i | \(0.321473\pi\) | ||||
−0.531913 | + | 0.846799i | \(0.678527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.68135e6 | 0.139954 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.04587e7 | 1.69048 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.52541e6i | − 0.453224i | −0.973985 | − | 0.226612i | \(-0.927235\pi\) | ||||
0.973985 | − | 0.226612i | \(-0.0727649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.14346e6i | 0.744534i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.91259e6 | −0.720464 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.50590e6 | 0.441855 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.66737e7i | − 1.32843i | −0.747543 | − | 0.664214i | \(-0.768766\pi\) | ||||
0.747543 | − | 0.664214i | \(-0.231234\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.21919e6i | 0.254632i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.79716e6 | 0.219662 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.69830e7 | −1.32413 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.09253e6i | 0.394222i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.49989e7i | − 1.15283i | −0.817157 | − | 0.576415i | \(-0.804451\pi\) | ||||
0.817157 | − | 0.576415i | \(-0.195549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.78255e7 | 1.36036 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.49953e6 | −0.492503 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.10431e7i | − 0.830884i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.84405e7i | − 1.37771i | −0.724900 | − | 0.688854i | \(-0.758114\pi\) | ||||
0.724900 | − | 0.688854i | \(-0.241886\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.31407e6 | −0.616793 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −817147. | −0.0601972 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.35015e6i | − 0.0987684i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.54886e7i | − 1.12516i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 334083. | 0.0241009 | 0.0120504 | − | 0.999927i | \(-0.496164\pi\) | ||||
0.0120504 | + | 0.999927i | \(0.496164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.86934e6 | 0.277204 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.62921e6i | 0.115913i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.00953e6i | 0.353959i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.11438e7 | 1.48370 | 0.741851 | − | 0.670564i | \(-0.233948\pi\) | ||||
0.741851 | + | 0.670564i | \(0.233948\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.30712e6 | −0.230479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.92152e7i | − 1.33000i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.48236e6i | − 0.101904i | −0.998701 | − | 0.0509521i | \(-0.983774\pi\) | ||||
0.998701 | − | 0.0509521i | \(-0.0162256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.46258e6 | −0.168140 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.04973e7 | −0.711884 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.69772e7i | − 1.14355i | −0.820411 | − | 0.571775i | \(-0.806255\pi\) | ||||
0.820411 | − | 0.571775i | \(-0.193745\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 7.04885e6i | − 0.471599i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.01294e7 | 1.33770 | 0.668849 | − | 0.743399i | \(-0.266787\pi\) | ||||
0.668849 | + | 0.743399i | \(0.266787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.41201e6 | 0.225226 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.37797e7i | − 0.903520i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.02143e7i | 0.665278i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.16155e7 | 0.751514 | 0.375757 | − | 0.926718i | \(-0.377383\pi\) | ||||
0.375757 | + | 0.926718i | \(0.377383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.74007e6 | 0.497459 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.65885e6i | − 0.297448i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.97313e6i | − 0.632545i | −0.948668 | − | 0.316273i | \(-0.897569\pi\) | ||||
0.948668 | − | 0.316273i | \(-0.102431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.05108e6 | −0.318258 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.00566e7 | 1.25544 | 0.627719 | − | 0.778440i | \(-0.283989\pi\) | ||||
0.627719 | + | 0.778440i | \(0.283989\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.86207e7i | 1.15794i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 5.67964e6i | − 0.350887i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.98110e6 | −0.305729 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.63971e7 | 1.60968 | 0.804842 | − | 0.593489i | \(-0.202250\pi\) | ||||
0.804842 | + | 0.593489i | \(0.202250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.65439e6i | 0.100231i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 902367.i | − 0.0543169i | −0.999631 | − | 0.0271584i | \(-0.991354\pi\) | ||||
0.999631 | − | 0.0271584i | \(-0.00864586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 517089. | 0.0309251 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.90444e7 | −1.13166 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.55463e7i | − 0.917877i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.93465e7i | − 1.13494i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00319e7 | −1.16766 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.86724e6 | −0.108150 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.59032e7i | 0.915269i | 0.889140 | + | 0.457635i | \(0.151303\pi\) | ||||
−0.889140 | + | 0.457635i | \(0.848697\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 2.37258e6i | − 0.135684i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.55700e7 | −1.45308 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.23873e6 | −0.295830 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.30345e7i | 0.731436i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.52099e7i | − 1.40580i | −0.711287 | − | 0.702902i | \(-0.751887\pi\) | ||||
0.711287 | − | 0.702902i | \(-0.248113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.85861e7 | −1.58412 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.33682e6 | −0.183760 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 5.06901e6i | − 0.277418i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.65527e6i | 0.144417i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.53542e7 | 1.91099 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.43630e7 | −0.771570 | −0.385785 | − | 0.922589i | \(-0.626069\pi\) | ||||
−0.385785 | + | 0.922589i | \(0.626069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.49512e7i | 0.798222i | 0.916903 | + | 0.399111i | \(0.130681\pi\) | ||||
−0.916903 | + | 0.399111i | \(0.869319\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.19993e7i | − 1.16730i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.37195e7 | 0.723508 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.75897e7 | 0.921943 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.34637e6i | 0.122232i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.49701e7i | − 1.29289i | −0.762960 | − | 0.646446i | \(-0.776254\pi\) | ||||
0.762960 | − | 0.646446i | \(-0.223746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.50946e7 | −1.29146 | −0.645729 | − | 0.763567i | \(-0.723446\pi\) | ||||
−0.645729 | + | 0.763567i | \(0.723446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.19631e6 | 0.163499 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.47367e7i | 1.25770i | 0.777526 | + | 0.628850i | \(0.216474\pi\) | ||||
−0.777526 | + | 0.628850i | \(0.783526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.02078e7i | 0.515878i | 0.966161 | + | 0.257939i | \(0.0830434\pi\) | ||||
−0.966161 | + | 0.257939i | \(0.916957\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.09332e7 | 1.05156 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.08309e7 | −0.540818 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 5.60779e6i | − 0.278340i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.06771e6i | 0.102018i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.64451e7 | −1.29700 | −0.648501 | − | 0.761214i | \(-0.724604\pi\) | ||||
−0.648501 | + | 0.761214i | \(0.724604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.37332e7 | −2.13217 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.52947e7i | 1.71057i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.29824e6i | 0.399801i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.35082e6 | 0.447859 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −57732.4 | −0.00274885 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 9.31014e6i | − 0.440689i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.30070e7i | 1.08265i | 0.840814 | + | 0.541324i | \(0.182077\pi\) | ||||
−0.840814 | + | 0.541324i | \(0.817923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.19919e6 | 0.243232 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.81332e7 | −0.843379 | −0.421689 | − | 0.906740i | \(-0.638563\pi\) | ||||
−0.421689 | + | 0.906740i | \(0.638563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.83891e6i | − 0.0850310i | −0.999096 | − | 0.0425155i | \(-0.986463\pi\) | ||||
0.999096 | − | 0.0425155i | \(-0.0135372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.66094e7i | 0.763567i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.14230e7 | −0.522097 | −0.261049 | − | 0.965326i | \(-0.584068\pi\) | ||||
−0.261049 | + | 0.965326i | \(0.584068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.13150e6 | 0.187744 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 5.35001e7i | − 2.41717i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.05786e7i | − 0.924413i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.65115e6 | −0.341729 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.71949e6 | −0.0763597 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.68025e6i | − 0.0741915i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.12365e7i | 0.932362i | 0.884689 | + | 0.466181i | \(0.154370\pi\) | ||||
−0.884689 | + | 0.466181i | \(0.845630\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.62116e7 | 2.01734 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.35067e7 | 0.586287 | 0.293143 | − | 0.956069i | \(-0.405299\pi\) | ||||
0.293143 | + | 0.956069i | \(0.405299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.44466e7i | − 1.05515i | −0.849507 | − | 0.527577i | \(-0.823100\pi\) | ||||
0.849507 | − | 0.527577i | \(-0.176900\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.17921e7i | − 0.506096i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.02242e6 | −0.342371 | −0.171185 | − | 0.985239i | \(-0.554760\pi\) | ||||
−0.171185 | + | 0.985239i | \(0.554760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.80520e6 | 0.288793 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00557e7i | 0.846337i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.61680e7i | − 1.09810i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.07994e7 | −0.450652 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.68157e6 | −0.152775 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.63136e6i | 0.273655i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.73281e7i | 2.35264i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.87926e7 | −0.766949 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.42359e6 | −0.220123 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.02868e7i | 0.818831i | 0.912348 | + | 0.409416i | \(0.134267\pi\) | ||||
−0.912348 | + | 0.409416i | \(0.865733\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.12935e7i | 0.453336i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.72893e7 | −0.690209 | −0.345104 | − | 0.938564i | \(-0.612156\pi\) | ||||
−0.345104 | + | 0.938564i | \(0.612156\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.41068e7 | 1.35414 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.24020e7i | − 0.489710i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.93653e7i | 0.760502i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.14060e7 | 0.836079 | 0.418039 | − | 0.908429i | \(-0.362717\pi\) | ||||
0.418039 | + | 0.908429i | \(0.362717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.83740e6 | −0.187916 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.41010e7i | − 0.544812i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.89144e6i | 0.226395i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.95710e6 | −0.151244 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.14158e7 | 1.57444 | 0.787221 | − | 0.616670i | \(-0.211519\pi\) | ||||
0.787221 | + | 0.616670i | \(0.211519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 9.91466e6i | − 0.374890i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.56900e7i | 1.71837i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.40580e7 | 0.525889 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.39335e7 | 0.518455 | 0.259228 | − | 0.965816i | \(-0.416532\pi\) | ||||
0.259228 | + | 0.965816i | \(0.416532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.93254e7i | 1.82560i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.51311e7i | 0.557051i | 0.960429 | + | 0.278526i | \(0.0898457\pi\) | ||||
−0.960429 | + | 0.278526i | \(0.910154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.11975e6 | −0.297347 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.71891e6 | 0.244748 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.72196e7i | 0.986296i | 0.869945 | + | 0.493148i | \(0.164154\pi\) | ||||
−0.869945 | + | 0.493148i | \(0.835846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 3.69464e6i | − 0.133170i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.78623e7 | 1.71610 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.79494e7 | −0.996873 | −0.498437 | − | 0.866926i | \(-0.666092\pi\) | ||||
−0.498437 | + | 0.866926i | \(0.666092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 864150.i | 0.0306606i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.09908e7i | 1.44679i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.93301e7 | 1.38095 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.79447e7 | −0.976091 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.04460e7i | − 0.362980i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.18400e7i | − 0.409293i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.73167e7 | −1.28333 | −0.641663 | − | 0.766987i | \(-0.721755\pi\) | ||||
−0.641663 | + | 0.766987i | \(0.721755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.33936e7 | 2.51101 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.77774e7i | 0.605091i | 0.953135 | + | 0.302545i | \(0.0978364\pi\) | ||||
−0.953135 | + | 0.302545i | \(0.902164\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.20318e7i | − 0.407427i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.32969e6 | 0.0784850 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.67378e7 | 0.561000 | 0.280500 | − | 0.959854i | \(-0.409500\pi\) | ||||
0.280500 | + | 0.959854i | \(0.409500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 8.25913e6i | − 0.275409i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.90431e7i | − 0.631778i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.99351e7 | 0.988091 | 0.494045 | − | 0.869436i | \(-0.335518\pi\) | ||||
0.494045 | + | 0.869436i | \(0.335518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.86961e6 | −0.324123 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.79574e7i | 0.913490i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 9.18701e6i | − 0.298664i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.30589e7 | −0.422398 | −0.211199 | − | 0.977443i | \(-0.567737\pi\) | ||||
−0.211199 | + | 0.977443i | \(0.567737\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.97753e7 | −1.28009 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.19272e7i | 0.381928i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.99417e6i | 0.254704i | 0.991858 | + | 0.127352i | \(0.0406477\pi\) | ||||
−0.991858 | + | 0.127352i | \(0.959352\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.35584e7 | −0.746848 |
(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 | 160.6.d.a.81.4 | 20 | ||
4.3 | odd | 2 | 40.6.d.a.21.20 | yes | 20 | ||
5.2 | odd | 4 | 800.6.f.c.49.4 | 20 | |||
5.3 | odd | 4 | 800.6.f.b.49.17 | 20 | |||
5.4 | even | 2 | 800.6.d.c.401.17 | 20 | |||
8.3 | odd | 2 | 40.6.d.a.21.19 | ✓ | 20 | ||
8.5 | even | 2 | inner | 160.6.d.a.81.17 | 20 | ||
12.11 | even | 2 | 360.6.k.b.181.1 | 20 | |||
20.3 | even | 4 | 200.6.f.c.149.9 | 20 | |||
20.7 | even | 4 | 200.6.f.b.149.12 | 20 | |||
20.19 | odd | 2 | 200.6.d.b.101.1 | 20 | |||
24.11 | even | 2 | 360.6.k.b.181.2 | 20 | |||
40.3 | even | 4 | 200.6.f.b.149.11 | 20 | |||
40.13 | odd | 4 | 800.6.f.c.49.3 | 20 | |||
40.19 | odd | 2 | 200.6.d.b.101.2 | 20 | |||
40.27 | even | 4 | 200.6.f.c.149.10 | 20 | |||
40.29 | even | 2 | 800.6.d.c.401.4 | 20 | |||
40.37 | odd | 4 | 800.6.f.b.49.18 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.d.a.21.19 | ✓ | 20 | 8.3 | odd | 2 | ||
40.6.d.a.21.20 | yes | 20 | 4.3 | odd | 2 | ||
160.6.d.a.81.4 | 20 | 1.1 | even | 1 | trivial | ||
160.6.d.a.81.17 | 20 | 8.5 | even | 2 | inner | ||
200.6.d.b.101.1 | 20 | 20.19 | odd | 2 | |||
200.6.d.b.101.2 | 20 | 40.19 | odd | 2 | |||
200.6.f.b.149.11 | 20 | 40.3 | even | 4 | |||
200.6.f.b.149.12 | 20 | 20.7 | even | 4 | |||
200.6.f.c.149.9 | 20 | 20.3 | even | 4 | |||
200.6.f.c.149.10 | 20 | 40.27 | even | 4 | |||
360.6.k.b.181.1 | 20 | 12.11 | even | 2 | |||
360.6.k.b.181.2 | 20 | 24.11 | even | 2 | |||
800.6.d.c.401.4 | 20 | 40.29 | even | 2 | |||
800.6.d.c.401.17 | 20 | 5.4 | even | 2 | |||
800.6.f.b.49.17 | 20 | 5.3 | odd | 4 | |||
800.6.f.b.49.18 | 20 | 40.37 | odd | 4 | |||
800.6.f.c.49.3 | 20 | 40.13 | odd | 4 | |||
800.6.f.c.49.4 | 20 | 5.2 | odd | 4 |