Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.13 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.b.2157.14 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.0797053 | −0.0460179 | −0.0230090 | − | 0.999735i | \(-0.507325\pi\) | ||||
−0.0230090 | + | 0.999735i | \(0.507325\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.579061i | 0.258964i | 0.991582 | + | 0.129482i | \(0.0413314\pi\) | ||||
−0.991582 | + | 0.129482i | \(0.958669\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99365 | −0.997882 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.19435 | + | 3.40199i | −0.331254 | + | 0.943542i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.0461542i | − | 0.0119170i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.63982 | 1.61039 | 0.805196 | − | 0.593008i | \(-0.202060\pi\) | ||||
0.805196 | + | 0.593008i | \(0.202060\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.33399i | − | 0.764870i | −0.923982 | − | 0.382435i | \(-0.875086\pi\) | ||
0.923982 | − | 0.382435i | \(-0.124914\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0797053i | 0.0173931i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.63162 | −1.79982 | −0.899909 | − | 0.436079i | \(-0.856367\pi\) | ||||
−0.899909 | + | 0.436079i | \(0.856367\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.66469 | 0.932938 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.477726 | 0.0919384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.664989 | 0.123485 | 0.0617427 | − | 0.998092i | \(-0.480334\pi\) | ||||
0.0617427 | + | 0.998092i | \(0.480334\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.646758i | 0.116161i | 0.998312 | + | 0.0580806i | \(0.0184980\pi\) | ||||
−0.998312 | + | 0.0580806i | \(0.981502\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0797053i | 0.0138749i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.579061 | 0.0978791 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0692840i | 0.0113902i | 0.999984 | + | 0.00569511i | \(0.00181282\pi\) | ||||
−0.999984 | + | 0.00569511i | \(0.998187\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0951964 | − | 0.271157i | 0.0152436 | − | 0.0434198i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.306795i | − | 0.0479133i | −0.999713 | − | 0.0239567i | \(-0.992374\pi\) | ||
0.999713 | − | 0.0239567i | \(-0.00762637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.52303 | −0.842254 | −0.421127 | − | 0.907002i | \(-0.638365\pi\) | ||||
−0.421127 | + | 0.907002i | \(0.638365\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.73350i | − | 0.258415i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.26906i | 0.330977i | 0.986212 | + | 0.165489i | \(0.0529201\pi\) | ||||
−0.986212 | + | 0.165489i | \(0.947080\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.529229 | −0.0741069 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.29017 | 0.589300 | 0.294650 | − | 0.955605i | \(-0.404797\pi\) | ||||
0.294650 | + | 0.955605i | \(0.404797\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.579061 | 0.0780805 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.265737i | 0.0351977i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.0513i | − | 1.43876i | −0.694615 | − | 0.719381i | \(-0.744425\pi\) | ||
0.694615 | − | 0.719381i | \(-0.255575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.98125 | −0.381710 | −0.190855 | − | 0.981618i | \(-0.561126\pi\) | ||||
−0.190855 | + | 0.981618i | \(0.561126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.99365i | 0.377164i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.96996 | − | 0.691604i | −0.244343 | − | 0.0857829i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.33089i | − | 0.284764i | −0.989812 | − | 0.142382i | \(-0.954524\pi\) | ||
0.989812 | − | 0.142382i | \(-0.0454761\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.687986 | 0.0828238 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.49278i | 0.414517i | 0.978286 | + | 0.207259i | \(0.0664542\pi\) | ||||
−0.978286 | + | 0.207259i | \(0.933546\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.99030i | − | 1.16928i | −0.811294 | − | 0.584638i | \(-0.801236\pi\) | ||
0.811294 | − | 0.584638i | \(-0.198764\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.371801 | −0.0429318 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0953 | −1.36082 | −0.680412 | − | 0.732830i | \(-0.738199\pi\) | ||||
−0.680412 | + | 0.732830i | \(0.738199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94286 | 0.993652 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.43919i | − | 1.03609i | −0.855355 | − | 0.518043i | \(-0.826661\pi\) | ||
0.855355 | − | 0.518043i | \(-0.173339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.84486i | 0.417033i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0530032 | −0.00568254 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.81854i | − | 0.722764i | −0.932418 | − | 0.361382i | \(-0.882305\pi\) | ||
0.932418 | − | 0.361382i | \(-0.117695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.40199 | + | 1.19435i | 0.356625 | + | 0.125202i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.0515501i | − | 0.00534549i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.93058 | 0.198074 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.5484i | − | 1.47716i | −0.674165 | − | 0.738581i | \(-0.735496\pi\) | ||
0.674165 | − | 0.738581i | \(-0.264504\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.99365i | 0.300873i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.3153 | −1.42442 | −0.712211 | − | 0.701966i | \(-0.752306\pi\) | ||||
−0.712211 | + | 0.701966i | \(0.752306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0201 | 0.987311 | 0.493655 | − | 0.869658i | \(-0.335660\pi\) | ||||
0.493655 | + | 0.869658i | \(0.335660\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0461542 | −0.00450419 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.94064 | −0.864325 | −0.432162 | − | 0.901796i | \(-0.642249\pi\) | ||||
−0.432162 | + | 0.901796i | \(0.642249\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.49245i | − | 0.717646i | −0.933406 | − | 0.358823i | \(-0.883178\pi\) | ||
0.933406 | − | 0.358823i | \(-0.116822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.00552231i | − | 0.000524154i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.14873 | 0.202135 | 0.101068 | − | 0.994880i | \(-0.467774\pi\) | ||||
0.101068 | + | 0.994880i | \(0.467774\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.99823i | − | 0.466087i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.57548 | − | 10.1843i | 0.330553 | − | 0.941543i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.63982i | − | 0.608671i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0244532i | 0.00220487i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.59644i | 0.500561i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.92608 | −0.880797 | −0.440398 | − | 0.897802i | \(-0.645163\pi\) | ||||
−0.440398 | + | 0.897802i | \(0.645163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.440215 | 0.0387588 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.26373 | −0.459895 | −0.229947 | − | 0.973203i | \(-0.573855\pi\) | ||||
−0.229947 | + | 0.973203i | \(0.573855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.33399 | −0.289094 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.276632i | 0.0238087i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 11.6164i | − | 0.992456i | −0.868192 | − | 0.496228i | \(-0.834718\pi\) | ||
0.868192 | − | 0.496228i | \(-0.165282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.106286 | −0.00901503 | −0.00450751 | − | 0.999990i | \(-0.501435\pi\) | ||||
−0.00450751 | + | 0.999990i | \(0.501435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.180857i | − | 0.0152309i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.40199 | + | 1.19435i | 0.284488 | + | 0.0998769i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.385069i | 0.0319782i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0797053 | 0.00657399 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 7.90346i | − | 0.647477i | −0.946147 | − | 0.323738i | \(-0.895060\pi\) | ||
0.946147 | − | 0.323738i | \(-0.104940\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.41831i | − | 0.359557i | −0.983707 | − | 0.179779i | \(-0.942462\pi\) | ||
0.983707 | − | 0.179779i | \(-0.0575381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.8773 | −1.60698 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.374512 | −0.0300815 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4175 | 0.831408 | 0.415704 | − | 0.909500i | \(-0.363535\pi\) | ||||
0.415704 | + | 0.909500i | \(0.363535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.341949 | −0.0271183 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.63162i | 0.680267i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.54204i | − | 0.669064i | −0.942384 | − | 0.334532i | \(-0.891422\pi\) | ||
0.942384 | − | 0.334532i | \(-0.108578\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0461542 | −0.00359310 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.88449i | 0.532738i | 0.963871 | + | 0.266369i | \(0.0858239\pi\) | ||||
−0.963871 | + | 0.266369i | \(0.914176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1470 | − | 8.12636i | −0.780541 | − | 0.625104i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.98079i | 0.763250i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1150 | 0.769031 | 0.384516 | − | 0.923118i | \(-0.374368\pi\) | ||||
0.384516 | + | 0.923118i | \(0.374368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.66469i | − | 0.352617i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.880851i | 0.0662088i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.992942 | −0.0742160 | −0.0371080 | − | 0.999311i | \(-0.511815\pi\) | ||||
−0.0371080 | + | 0.999311i | \(0.511815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.14771 | −0.233968 | −0.116984 | − | 0.993134i | \(-0.537323\pi\) | ||||
−0.116984 | + | 0.993134i | \(0.537323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.237621 | 0.0175655 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0401196 | −0.00294965 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.63982i | − | 0.485552i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 0.477726i | − | 0.0347494i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.813925 | −0.0588935 | −0.0294468 | − | 0.999566i | \(-0.509375\pi\) | ||||
−0.0294468 | + | 0.999566i | \(0.509375\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.02413i | − | 0.289663i | −0.989456 | − | 0.144832i | \(-0.953736\pi\) | ||
0.989456 | − | 0.144832i | \(-0.0462640\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.157016 | + | 0.0551245i | 0.0112442 | + | 0.00394755i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.65712i | − | 0.403053i | −0.979483 | − | 0.201526i | \(-0.935410\pi\) | ||
0.979483 | − | 0.201526i | \(-0.0645902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.3745 | −1.72786 | −0.863931 | − | 0.503610i | \(-0.832005\pi\) | ||||
−0.863931 | + | 0.503610i | \(0.832005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.185784i | 0.0131042i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.664989i | − | 0.0466731i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.177653 | 0.0124078 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.8400 | 1.79601 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.33399 | −0.230617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6501 | 1.00856 | 0.504279 | − | 0.863541i | \(-0.331758\pi\) | ||||
0.504279 | + | 0.863541i | \(0.331758\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 0.278394i | − | 0.0190752i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.19817i | − | 0.218113i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.646758 | 0.0439048 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.796281i | 0.0538077i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.93030 | + | 22.5886i | −0.533450 | + | 1.51947i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3616i | 0.760826i | 0.924817 | + | 0.380413i | \(0.124218\pi\) | ||||
−0.924817 | + | 0.380413i | \(0.875782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.9644 | −0.930962 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.28464i | − | 0.417126i | −0.978009 | − | 0.208563i | \(-0.933121\pi\) | ||
0.978009 | − | 0.208563i | \(-0.0668787\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.9984i | − | 0.792876i | −0.918061 | − | 0.396438i | \(-0.870246\pi\) | ||
0.918061 | − | 0.396438i | \(-0.129754\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0797053 | 0.00524423 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.6933 | 1.02810 | 0.514050 | − | 0.857760i | \(-0.328145\pi\) | ||||
0.514050 | + | 0.857760i | \(0.328145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.31393 | −0.0857111 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.964058 | 0.0626223 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.1855i | − | 1.49975i | −0.661582 | − | 0.749873i | \(-0.730115\pi\) | ||
0.661582 | − | 0.749873i | \(-0.269885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2466i | 0.724455i | 0.932090 | + | 0.362228i | \(0.117984\pi\) | ||||
−0.932090 | + | 0.362228i | \(0.882016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.14597 | −0.137664 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 0.579061i | − | 0.0369948i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3422 | + | 3.98197i | 0.721686 | + | 0.253366i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.752354i | 0.0476785i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.75861 | 0.552838 | 0.276419 | − | 0.961037i | \(-0.410852\pi\) | ||||
0.276419 | + | 0.961037i | \(0.410852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.63162i | 0.542665i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 0.306456i | − | 0.0191910i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.7351 | −0.919149 | −0.459575 | − | 0.888139i | \(-0.651998\pi\) | ||||
−0.459575 | + | 0.888139i | \(0.651998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0692840 | 0.00430510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.99074 | −0.123224 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.712037 | −0.0439061 | −0.0219531 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219531 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.48427i | 0.152607i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.543474i | 0.0332601i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.2597 | 0.625547 | 0.312773 | − | 0.949828i | \(-0.398742\pi\) | ||||
0.312773 | + | 0.949828i | \(0.398742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.00483i | − | 0.0610388i | −0.999534 | − | 0.0305194i | \(-0.990284\pi\) | ||
0.999534 | − | 0.0305194i | \(-0.00971614\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.271157 | − | 0.0951964i | −0.0164111 | − | 0.00576155i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 4.66469i | − | 0.281291i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.50150 | 0.450721 | 0.225361 | − | 0.974275i | \(-0.427644\pi\) | ||||
0.225361 | + | 0.974275i | \(0.427644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.93617i | − | 0.115915i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.1260i | 1.31993i | 0.751298 | + | 0.659963i | \(0.229428\pi\) | ||||
−0.751298 | + | 0.659963i | \(0.770572\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.29148 | −0.195658 | −0.0978291 | − | 0.995203i | \(-0.531190\pi\) | ||||
−0.0978291 | + | 0.995203i | \(0.531190\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.153878 | −0.00911493 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.306795 | −0.0181095 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.0872 | 1.59337 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.15958i | 0.0679759i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.03351i | 0.0603782i | 0.999544 | + | 0.0301891i | \(0.00961094\pi\) | ||||
−0.999544 | + | 0.0301891i | \(0.990389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.39940 | 0.372587 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.477726i | − | 0.0277205i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.3092 | − | 29.3647i | 0.596197 | − | 1.69820i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.52303i | 0.318342i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.14100 | 0.0655489 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.72632i | − | 0.0988489i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.3599i | − | 1.04785i | −0.851763 | − | 0.523927i | \(-0.824467\pi\) | ||
0.851763 | − | 0.523927i | \(-0.175533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.798656 | −0.0454340 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.6862 | −1.11630 | −0.558150 | − | 0.829740i | \(-0.688489\pi\) | ||||
−0.558150 | + | 0.829740i | \(0.688489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.65738 | −0.150204 | −0.0751020 | − | 0.997176i | \(-0.523928\pi\) | ||||
−0.0751020 | + | 0.997176i | \(0.523928\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.73350 | −0.0976718 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.83514i | 0.327734i | 0.986482 | + | 0.163867i | \(0.0523968\pi\) | ||||
−0.986482 | + | 0.163867i | \(0.947603\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.664989i | − | 0.0372322i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.712617 | 0.0397744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 22.1371i | − | 1.23174i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.57129 | + | 15.8692i | −0.309040 | + | 0.880266i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.597188i | 0.0330246i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.26906 | 0.125098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 19.6492i | − | 1.08002i | −0.841660 | − | 0.540008i | \(-0.818421\pi\) | ||
0.841660 | − | 0.540008i | \(-0.181579\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.207412i | − | 0.0113661i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.34973 | 0.0737434 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8862 | −0.810902 | −0.405451 | − | 0.914117i | \(-0.632885\pi\) | ||||
−0.405451 | + | 0.914117i | \(0.632885\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.171265 | −0.00930184 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.646758 | 0.0350239 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.398386i | 0.0214484i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.74011 | −0.308145 | −0.154073 | − | 0.988060i | \(-0.549239\pi\) | ||||
−0.154073 | + | 0.988060i | \(0.549239\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.6144i | − | 0.782291i | −0.920329 | − | 0.391146i | \(-0.872079\pi\) | ||
0.920329 | − | 0.391146i | \(-0.127921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.570574 | + | 1.62522i | −0.0304550 | + | 0.0867477i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 21.4683i | − | 1.14264i | −0.820727 | − | 0.571321i | \(-0.806431\pi\) | ||
0.820727 | − | 0.571321i | \(-0.193569\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.02253 | −0.107345 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.529229i | 0.0280098i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 29.5066i | − | 1.55730i | −0.627461 | − | 0.778648i | \(-0.715906\pi\) | ||
0.627461 | − | 0.778648i | \(-0.284094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.88451 | 0.414974 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0797053 | 0.00418345 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.78499 | 0.302800 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.1014 | −0.840488 | −0.420244 | − | 0.907411i | \(-0.638055\pi\) | ||||
−0.420244 | + | 0.907411i | \(0.638055\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.918436i | 0.0478118i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.29017i | − | 0.222734i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.6332 | 1.58613 | 0.793063 | − | 0.609139i | \(-0.208485\pi\) | ||||
0.793063 | + | 0.609139i | \(0.208485\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 0.446066i | − | 0.0230348i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.794232 | + | 2.26228i | −0.0409051 | + | 0.116514i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 34.5219i | − | 1.77327i | −0.462469 | − | 0.886636i | \(-0.653036\pi\) | ||
0.462469 | − | 0.886636i | \(-0.346964\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.791161 | 0.0405324 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.07605i | 0.0549835i | 0.999622 | + | 0.0274918i | \(0.00875200\pi\) | ||||
−0.999622 | + | 0.0274918i | \(0.991248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.579061i | − | 0.0295117i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.5340 | 0.840470 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.3547 | −1.64045 | −0.820224 | − | 0.572043i | \(-0.806151\pi\) | ||||
−0.820224 | + | 0.572043i | \(0.806151\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.3124 | −2.89841 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.419548 | 0.0211634 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 7.00389i | − | 0.352404i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00679i | 0.0505295i | 0.999681 | + | 0.0252648i | \(0.00804288\pi\) | ||||
−0.999681 | + | 0.0252648i | \(0.991957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.265737 | 0.0133035 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.0916i | 1.90220i | 0.308881 | + | 0.951101i | \(0.400046\pi\) | ||||
−0.308881 | + | 0.951101i | \(0.599954\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.20026 | − | 0.772458i | −0.109603 | − | 0.0384789i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.17846i | 0.257320i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0692840 | 0.00343428 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0243i | 0.940693i | 0.882482 | + | 0.470347i | \(0.155871\pi\) | ||||
−0.882482 | + | 0.470347i | \(0.844129\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.925889i | 0.0456707i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.0513 | −0.543801 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.46586 | 0.268309 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.00847153 | 0.000414853 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.5893 | −1.15241 | −0.576207 | − | 0.817304i | \(-0.695468\pi\) | ||||
−0.576207 | + | 0.817304i | \(0.695468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 24.2343i | − | 1.18111i | −0.806998 | − | 0.590554i | \(-0.798909\pi\) | ||
0.806998 | − | 0.590554i | \(-0.201091\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.79278i | − | 0.330276i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.9727 | 1.50240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.98125i | 0.144273i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.271157 | − | 0.0951964i | −0.0130916 | − | 0.00459613i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 26.4305i | − | 1.27311i | −0.771231 | − | 0.636555i | \(-0.780359\pi\) | ||
0.771231 | − | 0.636555i | \(-0.219641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.7615 | −1.57442 | −0.787209 | − | 0.616687i | \(-0.788475\pi\) | ||||
−0.787209 | + | 0.616687i | \(0.788475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.0306920i | − | 0.00147157i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.7777i | 1.37663i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.62244 | 0.411527 | 0.205763 | − | 0.978602i | \(-0.434032\pi\) | ||||
0.205763 | + | 0.978602i | \(0.434032\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.99365 | 0.142555 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.6381 | −1.45566 | −0.727830 | − | 0.685757i | \(-0.759471\pi\) | ||||
−0.727830 | + | 0.685757i | \(0.759471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.94835 | 0.187170 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.629948i | 0.0297955i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.9360i | 0.657681i | 0.944385 | + | 0.328841i | \(0.106658\pi\) | ||||
−0.944385 | + | 0.328841i | \(0.893342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.306795 | −0.0144464 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.352163i | 0.0165461i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.691604 | + | 1.96996i | −0.0324229 | + | 0.0923530i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.64962i | 0.0771660i | 0.999255 | + | 0.0385830i | \(0.0122844\pi\) | ||||
−0.999255 | + | 0.0385830i | \(0.987716\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.17201 | 0.148057 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8520i | 0.552004i | 0.961157 | + | 0.276002i | \(0.0890097\pi\) | ||||
−0.961157 | + | 0.276002i | \(0.910990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.3489i | 1.41043i | 0.708993 | + | 0.705215i | \(0.249150\pi\) | ||||
−0.708993 | + | 0.705215i | \(0.750850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0298506 | 0.00138429 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.8659 | 0.965560 | 0.482780 | − | 0.875742i | \(-0.339627\pi\) | ||||
0.482780 | + | 0.875742i | \(0.339627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.33089 | −0.107631 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.830332 | −0.0382597 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.52303i | 0.253949i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 15.5520i | − | 0.713576i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.8433 | −0.588052 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.9280i | 1.64159i | 0.571221 | + | 0.820796i | \(0.306470\pi\) | ||||
−0.571221 | + | 0.820796i | \(0.693530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.235703 | − | 0.0827496i | −0.0107471 | − | 0.00377306i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.687986i | − | 0.0313045i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.42438 | 0.382531 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 40.7037i | − | 1.84446i | −0.386643 | − | 0.922229i | \(-0.626365\pi\) | ||
0.386643 | − | 0.922229i | \(-0.373635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.680846i | 0.0307889i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.6372 | 1.11186 | 0.555930 | − | 0.831229i | \(-0.312362\pi\) | ||||
0.555930 | + | 0.831229i | \(0.312362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.41541 | 0.198860 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.73350 | −0.0779152 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.49278 | 0.156673 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.5698i | 1.63709i | 0.574444 | + | 0.818544i | \(0.305218\pi\) | ||||
−0.574444 | + | 0.818544i | \(0.694782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 0.548730i | − | 0.0245155i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.91394 | 0.442041 | 0.221020 | − | 0.975269i | \(-0.429061\pi\) | ||||
0.221020 | + | 0.975269i | \(0.429061\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.28940i | − | 0.368874i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.808773 | + | 0.647714i | 0.0359189 | + | 0.0287660i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.6195i | 1.62313i | 0.584263 | + | 0.811564i | \(0.301384\pi\) | ||||
−0.584263 | + | 0.811564i | \(0.698616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.99030 | −0.441945 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.59273i | − | 0.0703209i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.80225i | 0.255678i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.26906 | 0.0997933 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.806222 | −0.0353892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.6635 | −1.34339 | −0.671696 | − | 0.740827i | \(-0.734434\pi\) | ||||
−0.671696 | + | 0.740827i | \(0.734434\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.3525 | −1.15231 | −0.576157 | − | 0.817339i | \(-0.695448\pi\) | ||||
−0.576157 | + | 0.817339i | \(0.695448\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.371801i | 0.0162267i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.29436i | 0.187065i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 51.5049 | 2.23934 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33.0838i | 1.43572i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.04371 | + | 0.366422i | 0.0452082 | + | 0.0158715i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.17717i | − | 0.223829i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0791428 | 0.00341526 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.03422i | 0.302425i | 0.988501 | + | 0.151212i | \(0.0483177\pi\) | ||||
−0.988501 | + | 0.151212i | \(0.951682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.250890 | 0.0107667 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.33858 | 0.185844 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.4911 | −0.619593 | −0.309797 | − | 0.950803i | \(-0.600261\pi\) | ||||
−0.309797 | + | 0.950803i | \(0.600261\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.92480 | 0.380901 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.21707i | − | 0.0944502i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0953i | 0.514343i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.00319775 | 0.000135737 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.0933i | 1.61407i | 0.590507 | + | 0.807033i | \(0.298928\pi\) | ||||
−0.590507 | + | 0.807033i | \(0.701072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.59645 | − | 18.7893i | 0.279000 | − | 0.794702i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.529229i | 0.0223441i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.3241 | 1.15157 | 0.575786 | − | 0.817600i | \(-0.304696\pi\) | ||||
0.575786 | + | 0.817600i | \(0.304696\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.24424i | 0.0523457i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 8.94286i | − | 0.375565i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.1103 | 0.549613 | 0.274807 | − | 0.961499i | \(-0.411386\pi\) | ||||
0.274807 | + | 0.961499i | \(0.411386\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.3561 | 1.31221 | 0.656105 | − | 0.754670i | \(-0.272203\pi\) | ||||
0.656105 | + | 0.754670i | \(0.272203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0648742 | 0.00271016 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −40.2638 | −1.67912 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.2865i | 0.927801i | 0.885887 | + | 0.463901i | \(0.153551\pi\) | ||||
−0.885887 | + | 0.463901i | \(0.846449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.320744i | 0.0133297i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.43919 | −0.391603 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.29017i | − | 0.177681i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.89735 | + | 2.07042i | 0.243826 | + | 0.0856012i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.9582i | 1.48415i | 0.670315 | + | 0.742076i | \(0.266159\pi\) | ||||
−0.670315 | + | 0.742076i | \(0.733841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.15628 | 0.0888482 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.450903i | 0.0185477i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.04896i | 0.0430757i | 0.999768 | + | 0.0215378i | \(0.00685623\pi\) | ||||
−0.999768 | + | 0.0215378i | \(0.993144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.84486 | 0.157624 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.94278 | 0.0795126 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7314 | 0.479334 | 0.239667 | − | 0.970855i | \(-0.422962\pi\) | ||||
0.239667 | + | 0.970855i | \(0.422962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.6460 | −0.556634 | −0.278317 | − | 0.960489i | \(-0.589777\pi\) | ||||
−0.278317 | + | 0.960489i | \(0.589777\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.97786i | 0.284161i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 0.579061i | − | 0.0235422i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4832 | 0.669031 | 0.334516 | − | 0.942390i | \(-0.391427\pi\) | ||||
0.334516 | + | 0.942390i | \(0.391427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0530032i | 0.00214780i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.71933 | − | 2.71007i | −0.312291 | − | 0.109638i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.4322i | − | 1.79460i | −0.441420 | − | 0.897301i | \(-0.645525\pi\) | ||
0.441420 | − | 0.897301i | \(-0.354475\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0141599 | −0.000570981 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.3782i | 1.46453i | 0.681020 | + | 0.732265i | \(0.261537\pi\) | ||||
−0.681020 | + | 0.732265i | \(0.738463\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 37.6940i | − | 1.51505i | −0.652805 | − | 0.757526i | \(-0.726408\pi\) | ||
0.652805 | − | 0.757526i | \(-0.273592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.12355 | −0.165472 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.81854 | −0.273179 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.0828 | 0.803311 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.265737 | 0.0106125 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.460033i | 0.0183427i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 15.6916i | − | 0.624672i | −0.949972 | − | 0.312336i | \(-0.898888\pi\) | ||
0.949972 | − | 0.312336i | \(-0.101112\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.16769 | −0.0464117 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 5.74780i | − | 0.228094i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.19435 | − | 3.40199i | 0.0473220 | − | 0.134792i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 10.4562i | − | 0.413639i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.4218 | 1.08310 | 0.541549 | − | 0.840669i | \(-0.317838\pi\) | ||||
0.541549 | + | 0.840669i | \(0.317838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.69536i | 0.264039i | 0.991247 | + | 0.132020i | \(0.0421462\pi\) | ||||
−0.991247 | + | 0.132020i | \(0.957854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.254911i | 0.0100371i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.5045 | 0.412975 | 0.206487 | − | 0.978449i | \(-0.433797\pi\) | ||||
0.206487 | + | 0.978449i | \(0.433797\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.0513 | −0.433803 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0515501 | −0.00202041 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.0593 | −1.09805 | −0.549023 | − | 0.835807i | \(-0.685000\pi\) | ||||
−0.549023 | + | 0.835807i | \(0.685000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.04802i | − | 0.119096i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.9074i | 1.16680i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.1233 | 0.705984 | 0.352992 | − | 0.935626i | \(-0.385164\pi\) | ||||
0.352992 | + | 0.935626i | \(0.385164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.71799i | 0.0668222i | 0.999442 | + | 0.0334111i | \(0.0106371\pi\) | ||||
−0.999442 | + | 0.0334111i | \(0.989363\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.632087 | − | 1.80043i | 0.0245482 | − | 0.0699229i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.93058i | − | 0.0748648i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.73993 | −0.222251 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 0.905577i | − | 0.0350116i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.98125i | 0.115090i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0413 | 0.541251 | 0.270626 | − | 0.962685i | \(-0.412769\pi\) | ||||
0.270626 | + | 0.962685i | \(0.412769\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.22844 | 0.0857728 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.7943 | 1.49099 | 0.745493 | − | 0.666514i | \(-0.232214\pi\) | ||||
0.745493 | + | 0.666514i | \(0.232214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.5484 | −0.558315 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.500920i | 0.0191953i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.6219i | 1.20998i | 0.796233 | + | 0.604990i | \(0.206823\pi\) | ||||
−0.796233 | + | 0.604990i | \(0.793177\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.72660 | 0.257010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.956336i | 0.0364865i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.12398 | + | 14.5951i | −0.195208 | + | 0.556029i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.8544i | 1.78243i | 0.453585 | + | 0.891213i | \(0.350145\pi\) | ||||
−0.453585 | + | 0.891213i | \(0.649855\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.99365 | 0.113719 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.0615458i | − | 0.00233456i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.03706i | − | 0.0771593i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.25084 | −0.0473110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.20641 | 0.347721 | 0.173861 | − | 0.984770i | \(-0.444376\pi\) | ||||
0.173861 | + | 0.984770i | \(0.444376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.230992 | 0.00871203 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.104727 | 0.00394424 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.3153i | 0.538381i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 34.5805i | − | 1.29870i | −0.760491 | − | 0.649349i | \(-0.775042\pi\) | ||
0.760491 | − | 0.649349i | \(-0.224958\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.2090 | 1.35794 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.58257i | − | 0.209069i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.691604 | + | 1.96996i | −0.0258645 | + | 0.0736722i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.84801i | 0.0690151i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.6023 | 0.842924 | 0.421462 | − | 0.906846i | \(-0.361517\pi\) | ||||
0.421462 | + | 0.906846i | \(0.361517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.0201i | − | 0.373168i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 0.896411i | − | 0.0333379i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.10197 | 0.115204 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.5453 | −0.539454 | −0.269727 | − | 0.962937i | \(-0.586933\pi\) | ||||
−0.269727 | + | 0.962937i | \(0.586933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6575 | −0.987317 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.6719 | −1.35636 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.9364i | − | 1.03185i | −0.856632 | − | 0.515927i | \(-0.827448\pi\) | ||
0.856632 | − | 0.515927i | \(-0.172552\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0461542i | 0.00170242i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.33089 | −0.0858594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.5046i | − | 1.04856i | −0.851547 | − | 0.524279i | \(-0.824335\pi\) | ||
0.851547 | − | 0.524279i | \(-0.175665\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.904033 | − | 0.317384i | −0.0332105 | − | 0.0116594i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.03999i | − | 0.148213i | −0.997250 | − | 0.0741063i | \(-0.976390\pi\) | ||
0.997250 | − | 0.0741063i | \(-0.0236104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.57658 | 0.167673 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.2576i | 1.03389i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.94064i | 0.326684i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.1909 | 1.21115 | 0.605577 | − | 0.795787i | \(-0.292942\pi\) | ||||
0.605577 | + | 0.795787i | \(0.292942\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.698108 | −0.0254405 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.55847 | 0.0931123 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8799 | −0.395436 | −0.197718 | − | 0.980259i | \(-0.563353\pi\) | ||||
−0.197718 | + | 0.980259i | \(0.563353\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 0.687986i | − | 0.0249723i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.4200i | − | 1.17523i | −0.809142 | − | 0.587613i | \(-0.800068\pi\) | ||
0.809142 | − | 0.587613i | \(-0.199932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.49245 | −0.271245 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 11.5101i | − | 0.416150i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.5965 | + | 13.1992i | 1.35753 | + | 0.476596i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.4458i | 1.02578i | 0.858454 | + | 0.512891i | \(0.171426\pi\) | ||||
−0.858454 | + | 0.512891i | \(0.828574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.17446 | 0.0422973 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 38.8523i | − | 1.39742i | −0.715405 | − | 0.698710i | \(-0.753758\pi\) | ||
0.715405 | − | 0.698710i | \(-0.246242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.01693i | 0.108371i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.00552231 | −0.000198112 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.02285 | −0.0366474 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.49278 | 0.124982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.317682 | 0.0113530 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.03237i | 0.215305i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.6429i | 1.37747i | 0.725013 | + | 0.688735i | \(0.241834\pi\) | ||||
−0.725013 | + | 0.688735i | \(0.758166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.0567532 | 0.00202047 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.14873i | − | 0.0763999i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.56067 | − | 10.1422i | 0.126443 | − | 0.360159i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 0.198009i | − | 0.00702267i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.9629 | 1.09676 | 0.548382 | − | 0.836228i | \(-0.315244\pi\) | ||||
0.548382 | + | 0.836228i | \(0.315244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0662i | 0.533003i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.4123i | 0.721234i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.99030 | −0.352550 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.99823 | −0.176164 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.817755 | −0.0287863 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0419 | −1.05622 | −0.528109 | − | 0.849177i | \(-0.677099\pi\) | ||||
−0.528109 | + | 0.849177i | \(0.677099\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 39.6029i | − | 1.39065i | −0.718698 | − | 0.695323i | \(-0.755261\pi\) | ||
0.718698 | − | 0.695323i | \(-0.244739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0800900i | 0.00280888i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.94636 | 0.173263 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.4137i | 0.644215i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.1843 | − | 3.57548i | −0.355870 | − | 0.124937i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.4490i | 0.957977i | 0.877821 | + | 0.478989i | \(0.158997\pi\) | ||||
−0.877821 | + | 0.478989i | \(0.841003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.85219 | 0.0994210 | 0.0497105 | − | 0.998764i | \(-0.484170\pi\) | ||||
0.0497105 | + | 0.998764i | \(0.484170\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.371801i | 0.0129444i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.3734i | 1.29960i | 0.760105 | + | 0.649800i | \(0.225147\pi\) | ||||
−0.760105 | + | 0.649800i | \(0.774853\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.6517 | −1.20350 | −0.601752 | − | 0.798683i | \(-0.705530\pi\) | ||||
−0.601752 | + | 0.798683i | \(0.705530\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.597909 | −0.0207412 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.63982 | −0.230056 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.98654 | −0.137960 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.308973i | 0.0106797i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.6245i | 1.60966i | 0.593507 | + | 0.804829i | \(0.297743\pi\) | ||||
−0.593507 | + | 0.804829i | \(0.702257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5578 | −0.984751 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.76356i | − | 0.0607402i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.70565 | − | 5.87575i | 0.161879 | − | 0.202132i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.262349 | 0.00900378 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.598033i | − | 0.0205003i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21.4187i | − | 0.733364i | −0.930346 | − | 0.366682i | \(-0.880494\pi\) | ||
0.930346 | − | 0.366682i | \(-0.119506\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.77948 | −0.197654 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.58945 | −0.0542945 | −0.0271472 | − | 0.999631i | \(-0.508642\pi\) | ||||
−0.0271472 | + | 0.999631i | \(0.508642\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.3518 | −0.353198 | −0.176599 | − | 0.984283i | \(-0.556510\pi\) | ||||
−0.176599 | + | 0.984283i | \(0.556510\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0244532 | 0.000833363 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 57.0306i | 1.94134i | 0.240406 | + | 0.970672i | \(0.422719\pi\) | ||||
−0.240406 | + | 0.970672i | \(0.577281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.85721i | 0.199151i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.15900 | −0.0733233 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0953i | 0.410304i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.92966 | + | 2.78391i | 0.268686 | + | 0.0943292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.5526i | 1.47403i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.59644 | 0.189194 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.9301i | 1.24704i | 0.781807 | + | 0.623521i | \(0.214298\pi\) | ||||
−0.781807 | + | 0.623521i | \(0.785702\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 0.0823761i | − | 0.00277848i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.3444 | 0.685419 | 0.342710 | − | 0.939441i | \(-0.388655\pi\) | ||||
0.342710 | + | 0.939441i | \(0.388655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4838 | 1.12682 | 0.563410 | − | 0.826177i | \(-0.309489\pi\) | ||||
0.563410 | + | 0.826177i | \(0.309489\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.510066 | −0.0171457 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.1375 | 0.373961 | 0.186980 | − | 0.982364i | \(-0.440130\pi\) | ||||
0.186980 | + | 0.982364i | \(0.440130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.92608i | 0.332910i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 8.94286i | − | 0.299597i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.56504 | 0.253154 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 0.574974i | − | 0.0192192i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.821699 | + | 2.34052i | −0.0274357 | + | 0.0781477i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.430087i | 0.0143442i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.4859 | 0.949005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 0.440215i | − | 0.0146494i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.82272i | − | 0.0605891i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.30368 | 0.275719 | 0.137860 | − | 0.990452i | \(-0.455978\pi\) | ||||
0.137860 | + | 0.990452i | \(0.455978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.8548 | 1.42141 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.8309 | −0.491371 | −0.245685 | − | 0.969350i | \(-0.579013\pi\) | ||||
−0.245685 | + | 0.969350i | \(0.579013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.43919 | −0.312391 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.137597i | 0.00454882i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.26373i | 0.173824i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.8910 | −0.524194 | −0.262097 | − | 0.965042i | \(-0.584414\pi\) | ||||
−0.262097 | + | 0.965042i | \(0.584414\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.46338i | 0.0482200i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.8824 | − | 4.17162i | −0.391114 | − | 0.137311i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.323188i | 0.0106264i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.9967 | −0.985220 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.4001i | 1.71919i | 0.510976 | + | 0.859595i | \(0.329284\pi\) | ||||
−0.510976 | + | 0.859595i | \(0.670716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.33399i | 0.109267i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.56909 | 0.0513698 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.84486 | 0.125740 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.60786 | −0.248538 | −0.124269 | − | 0.992249i | \(-0.539659\pi\) | ||||
−0.124269 | + | 0.992249i | \(0.539659\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.211807 | 0.00691208 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6954i | 0.935445i | 0.883875 | + | 0.467722i | \(0.154925\pi\) | ||||
−0.883875 | + | 0.467722i | \(0.845075\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.64814i | 0.0862352i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.276632 | 0.00899884 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.62856i | − | 0.0854167i | −0.999088 | − | 0.0427083i | \(-0.986401\pi\) | ||
0.999088 | − | 0.0427083i | \(-0.0135986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.9869 | + | 11.9320i | 1.10326 | + | 0.387328i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.465092i | − | 0.0150816i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.1477 | 0.393503 | 0.196752 | − | 0.980453i | \(-0.436961\pi\) | ||||
0.196752 | + | 0.980453i | \(0.436961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.471312i | − | 0.0152513i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0530032i | 0.00171335i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6164 | −0.375113 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.5817 | 0.986507 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.7651 | 0.862494 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.33021 | 0.0750122 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.0783i | − | 0.549202i | −0.961558 | − | 0.274601i | \(-0.911454\pi\) | ||
0.961558 | − | 0.274601i | \(-0.0885457\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.76444i | 0.0566821i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.0583 | −0.836251 | −0.418125 | − | 0.908389i | \(-0.637313\pi\) | ||||
−0.418125 | + | 0.908389i | \(0.637313\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.106286i | 0.00340736i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.444062 | − | 1.26486i | 0.0142214 | − | 0.0405080i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 10.9210i | − | 0.349393i | −0.984622 | − | 0.174697i | \(-0.944106\pi\) | ||
0.984622 | − | 0.174697i | \(-0.0558945\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.81854 | −0.217922 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.4297i | 0.716127i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.882988i | 0.0281630i | 0.999901 | + | 0.0140815i | \(0.00448242\pi\) | ||||
−0.999901 | + | 0.0140815i | \(0.995518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.27581 | 0.104376 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.180857 | −0.00575673 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.6727 | 1.51590 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0996 | 0.765548 | 0.382774 | − | 0.923842i | \(-0.374969\pi\) | ||||
0.382774 | + | 0.923842i | \(0.374969\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.56615i | 0.0497001i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 14.1143i | − | 0.447454i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.2959 | −1.65623 | −0.828113 | − | 0.560560i | \(-0.810586\pi\) | ||||
−0.828113 | + | 0.560560i | \(0.810586\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.0330987i | 0.00104720i |
(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 | 4004.2.m.b.2157.13 | ✓ | 30 | |
13.12 | even | 2 | inner | 4004.2.m.b.2157.14 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.b.2157.13 | ✓ | 30 | 1.1 | even | 1 | trivial | |
4004.2.m.b.2157.14 | yes | 30 | 13.12 | even | 2 | inner |