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: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.20 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.19 |
$q$-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 | ||||||||
\(3\) | −0.189991 | −0.109692 | −0.0548458 | − | 0.998495i | \(-0.517467\pi\) | ||||
−0.0548458 | + | 0.998495i | \(0.517467\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.01340i | 0.453207i | 0.973987 | + | 0.226604i | \(0.0727622\pi\) | ||||
−0.973987 | + | 0.226604i | \(0.927238\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96390 | −0.987968 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.24743 | + | 3.38289i | 0.345976 | + | 0.938244i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.192538i | − | 0.0497130i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.81146 | 0.924416 | 0.462208 | − | 0.886772i | \(-0.347057\pi\) | ||||
0.462208 | + | 0.886772i | \(0.347057\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.826026i | 0.189503i | 0.995501 | + | 0.0947517i | \(0.0302057\pi\) | ||||
−0.995501 | + | 0.0947517i | \(0.969794\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.189991i | − | 0.0414595i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.31508 | 1.10827 | 0.554136 | − | 0.832426i | \(-0.313049\pi\) | ||||
0.554136 | + | 0.832426i | \(0.313049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.97302 | 0.794603 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.13309 | 0.218063 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.80230 | −0.891764 | −0.445882 | − | 0.895092i | \(-0.647110\pi\) | ||||
−0.445882 | + | 0.895092i | \(0.647110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.20033i | 0.395190i | 0.980284 | + | 0.197595i | \(0.0633132\pi\) | ||||
−0.980284 | + | 0.197595i | \(0.936687\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.189991i | 0.0330732i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.01340 | −0.171296 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.485470i | 0.0798108i | 0.999203 | + | 0.0399054i | \(0.0127057\pi\) | ||||
−0.999203 | + | 0.0399054i | \(0.987294\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.237001 | − | 0.642719i | −0.0379506 | − | 0.102917i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.22731i | − | 0.816369i | −0.912900 | − | 0.408184i | \(-0.866162\pi\) | ||
0.912900 | − | 0.408184i | \(-0.133838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.56315 | 0.238378 | 0.119189 | − | 0.992872i | \(-0.461971\pi\) | ||||
0.119189 | + | 0.992872i | \(0.461971\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 3.00362i | − | 0.447754i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.95964i | − | 1.01517i | −0.861603 | − | 0.507584i | \(-0.830539\pi\) | ||
0.861603 | − | 0.507584i | \(-0.169461\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.724145 | −0.101401 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.3254 | −1.55566 | −0.777832 | − | 0.628473i | \(-0.783680\pi\) | ||||
−0.777832 | + | 0.628473i | \(0.783680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.01340 | 0.136647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.156938i | − | 0.0207869i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.884512i | 0.115154i | 0.998341 | + | 0.0575769i | \(0.0183374\pi\) | ||||
−0.998341 | + | 0.0575769i | \(0.981663\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.77019 | 0.226650 | 0.113325 | − | 0.993558i | \(-0.463850\pi\) | ||||
0.113325 | + | 0.993558i | \(0.463850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.96390i | − | 0.373417i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.42822 | + | 1.26415i | −0.425219 | + | 0.156799i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.9710i | 1.82900i | 0.404587 | + | 0.914500i | \(0.367415\pi\) | ||||
−0.404587 | + | 0.914500i | \(0.632585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00982 | −0.121568 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.34192i | 1.10868i | 0.832289 | + | 0.554341i | \(0.187030\pi\) | ||||
−0.832289 | + | 0.554341i | \(0.812970\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.59317i | 0.537590i | 0.963197 | + | 0.268795i | \(0.0866255\pi\) | ||||
−0.963197 | + | 0.268795i | \(0.913375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.754839 | −0.0871613 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.37613 | 0.379844 | 0.189922 | − | 0.981799i | \(-0.439176\pi\) | ||||
0.189922 | + | 0.981799i | \(0.439176\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.67643 | 0.964048 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0825i | 1.43600i | 0.696046 | + | 0.717998i | \(0.254941\pi\) | ||||
−0.696046 | + | 0.717998i | \(0.745059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.86254i | 0.418952i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.912394 | 0.0978190 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.4177i | 1.31627i | 0.752900 | + | 0.658135i | \(0.228654\pi\) | ||||
−0.752900 | + | 0.658135i | \(0.771346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.38289 | + | 1.24743i | −0.354623 | + | 0.130766i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.418043i | − | 0.0433490i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.837096 | −0.0858842 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.93635i | − | 1.00888i | −0.863446 | − | 0.504442i | \(-0.831698\pi\) | ||
0.863446 | − | 0.504442i | \(-0.168302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.96390i | 0.297883i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.85017 | 0.184098 | 0.0920492 | − | 0.995754i | \(-0.470658\pi\) | ||||
0.0920492 | + | 0.995754i | \(0.470658\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.51317 | −0.444696 | −0.222348 | − | 0.974967i | \(-0.571372\pi\) | ||||
−0.222348 | + | 0.974967i | \(0.571372\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.192538 | 0.0187897 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.4364 | −1.87899 | −0.939494 | − | 0.342565i | \(-0.888704\pi\) | ||||
−0.939494 | + | 0.342565i | \(0.888704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.82552i | 0.845331i | 0.906286 | + | 0.422666i | \(0.138906\pi\) | ||||
−0.906286 | + | 0.422666i | \(0.861094\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.0922351i | − | 0.00875457i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.2667 | −1.53024 | −0.765119 | − | 0.643889i | \(-0.777320\pi\) | ||||
−0.765119 | + | 0.643889i | \(0.777320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.38632i | 0.502276i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.69727 | − | 10.0265i | −0.341813 | − | 0.926954i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.81146i | 0.349396i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.993143i | 0.0895487i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.09327i | 0.813327i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6870 | 0.948321 | 0.474161 | − | 0.880438i | \(-0.342752\pi\) | ||||
0.474161 | + | 0.880438i | \(0.342752\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.296984 | −0.0261480 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.68425 | 0.321894 | 0.160947 | − | 0.986963i | \(-0.448545\pi\) | ||||
0.160947 | + | 0.986963i | \(0.448545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.826026 | −0.0716255 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.14828i | 0.0988278i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00305i | 0.512875i | 0.966561 | + | 0.256437i | \(0.0825488\pi\) | ||||
−0.966561 | + | 0.256437i | \(0.917451\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.5839 | −1.49144 | −0.745722 | − | 0.666257i | \(-0.767895\pi\) | ||||
−0.745722 | + | 0.666257i | \(0.767895\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.32227i | 0.111355i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.38289 | − | 1.24743i | 0.282891 | − | 0.104316i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.86666i | − | 0.404154i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.189991 | 0.0156702 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.3455i | 0.929462i | 0.885452 | + | 0.464731i | \(0.153849\pi\) | ||||
−0.885452 | + | 0.464731i | \(0.846151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2793i | 1.32479i | 0.749153 | + | 0.662397i | \(0.230461\pi\) | ||||
−0.749153 | + | 0.662397i | \(0.769539\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.2968 | −0.913293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.22982 | −0.179103 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.684650 | −0.0546410 | −0.0273205 | − | 0.999627i | \(-0.508697\pi\) | ||||
−0.0273205 | + | 0.999627i | \(0.508697\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.15173 | 0.170643 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.31508i | 0.418887i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.92170i | − | 0.307171i | −0.988135 | − | 0.153585i | \(-0.950918\pi\) | ||
0.988135 | − | 0.153585i | \(-0.0490820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.192538 | −0.0149890 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 9.28829i | − | 0.718750i | −0.933193 | − | 0.359375i | \(-0.882990\pi\) | ||
0.933193 | − | 0.359375i | \(-0.117010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88782 | + | 8.43984i | −0.760602 | + | 0.649219i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 2.44826i | − | 0.187223i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.5700 | 1.79199 | 0.895997 | − | 0.444060i | \(-0.146462\pi\) | ||||
0.895997 | + | 0.444060i | \(0.146462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.97302i | 0.300332i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.168050i | − | 0.0126314i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.5364 | 1.68445 | 0.842225 | − | 0.539126i | \(-0.181245\pi\) | ||||
0.842225 | + | 0.539126i | \(0.181245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.38826 | 0.103188 | 0.0515941 | − | 0.998668i | \(-0.483570\pi\) | ||||
0.0515941 | + | 0.998668i | \(0.483570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.336321 | −0.0248616 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.491976 | −0.0361708 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.81146i | − | 0.278722i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.13309i | 0.0824201i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.88487 | −0.570529 | −0.285265 | − | 0.958449i | \(-0.592081\pi\) | ||||
−0.285265 | + | 0.958449i | \(0.592081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 12.7152i | − | 0.915263i | −0.889142 | − | 0.457632i | \(-0.848698\pi\) | ||
0.889142 | − | 0.457632i | \(-0.151302\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.651332 | − | 0.240178i | 0.0466429 | − | 0.0171995i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.3188i | − | 1.23391i | −0.786997 | − | 0.616956i | \(-0.788365\pi\) | ||
0.786997 | − | 0.616956i | \(-0.211635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.38792 | 0.240164 | 0.120082 | − | 0.992764i | \(-0.461684\pi\) | ||||
0.120082 | + | 0.992764i | \(0.461684\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.84436i | − | 0.200626i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.80230i | − | 0.337055i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.29736 | 0.369984 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.7534 | −1.09494 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.826026 | 0.0571374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.25509 | −0.292932 | −0.146466 | − | 0.989216i | \(-0.546790\pi\) | ||||
−0.146466 | + | 0.989216i | \(0.546790\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.77488i | − | 0.121613i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.58410i | 0.108034i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.20033 | −0.149368 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 0.872663i | − | 0.0589691i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.75455 | + | 12.8937i | 0.319825 | + | 0.867327i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.5061i | 1.03836i | 0.854664 | + | 0.519181i | \(0.173763\pi\) | ||||
−0.854664 | + | 0.519181i | \(0.826237\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.7756 | −0.785043 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 0.0576844i | − | 0.00382865i | −0.999998 | − | 0.00191432i | \(-0.999391\pi\) | ||
0.999998 | − | 0.00191432i | \(-0.000609349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.20446i | 0.476084i | 0.971255 | + | 0.238042i | \(0.0765056\pi\) | ||||
−0.971255 | + | 0.238042i | \(0.923494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.189991 | −0.0125005 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.14158 | −0.598885 | −0.299442 | − | 0.954114i | \(-0.596801\pi\) | ||||
−0.299442 | + | 0.954114i | \(0.596801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.05291 | 0.460081 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.641435 | −0.0416657 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.1085i | 0.783231i | 0.920129 | + | 0.391616i | \(0.128084\pi\) | ||||
−0.920129 | + | 0.391616i | \(0.871916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.56170i | 0.422676i | 0.977413 | + | 0.211338i | \(0.0677821\pi\) | ||||
−0.977413 | + | 0.211338i | \(0.932218\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.04772 | −0.323811 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.01340i | − | 0.0647439i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.79435 | + | 1.03041i | −0.177800 | + | 0.0655635i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.48557i | − | 0.157516i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.4185 | −1.85688 | −0.928441 | − | 0.371480i | \(-0.878851\pi\) | ||||
−0.928441 | + | 0.371480i | \(0.878851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.31508i | − | 0.334156i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 0.733850i | − | 0.0459555i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.6795 | 1.78898 | 0.894490 | − | 0.447088i | \(-0.147539\pi\) | ||||
0.894490 | + | 0.447088i | \(0.147539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.485470 | −0.0301656 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.2335 | 0.881034 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4611 | 0.768382 | 0.384191 | − | 0.923254i | \(-0.374480\pi\) | ||||
0.384191 | + | 0.923254i | \(0.374480\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.4772i | − | 0.705038i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.35925i | − | 0.144384i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.0250 | −1.76969 | −0.884843 | − | 0.465889i | \(-0.845735\pi\) | ||||
−0.884843 | + | 0.465889i | \(0.845735\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.0682i | 1.76577i | 0.469594 | + | 0.882883i | \(0.344400\pi\) | ||||
−0.469594 | + | 0.882883i | \(0.655600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.642719 | − | 0.237001i | 0.0388991 | − | 0.0143440i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.97302i | − | 0.239582i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.638994 | 0.0383934 | 0.0191967 | − | 0.999816i | \(-0.493889\pi\) | ||||
0.0191967 | + | 0.999816i | \(0.493889\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 6.52156i | − | 0.390435i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.5484i | − | 1.10650i | −0.833014 | − | 0.553252i | \(-0.813387\pi\) | ||
0.833014 | − | 0.553252i | \(-0.186613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.5214 | −1.69542 | −0.847710 | − | 0.530460i | \(-0.822019\pi\) | ||||
−0.847710 | + | 0.530460i | \(0.822019\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.159041 | 0.00942077 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.22731 | 0.308558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.47274 | −0.145455 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.88782i | 0.110666i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.6740i | 0.974105i | 0.873373 | + | 0.487053i | \(0.161928\pi\) | ||||
−0.873373 | + | 0.487053i | \(0.838072\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.896366 | −0.0521885 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.13309i | − | 0.0657485i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.63021 | + | 17.9803i | 0.383435 | + | 1.03983i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.56315i | 0.0900983i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.351515 | −0.0201940 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.79392i | 0.102719i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.03711i | − | 0.287483i | −0.989615 | − | 0.143741i | \(-0.954087\pi\) | ||
0.989615 | − | 0.143741i | \(-0.0459134\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.857463 | 0.0487793 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.38097 | −0.248422 | −0.124211 | − | 0.992256i | \(-0.539640\pi\) | ||||
−0.124211 | + | 0.992256i | \(0.539640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.18764 | 0.519316 | 0.259658 | − | 0.965701i | \(-0.416390\pi\) | ||||
0.259658 | + | 0.965701i | \(0.416390\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00362 | 0.169235 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.05702i | 0.227865i | 0.993489 | + | 0.113932i | \(0.0363447\pi\) | ||||
−0.993489 | + | 0.113932i | \(0.963655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.80230i | 0.268877i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.69275 | 0.206109 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.14837i | 0.175180i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.95607 | + | 13.4403i | 0.274913 | + | 0.745531i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.67677i | − | 0.0927257i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.95964 | 0.383697 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.5449i | 1.40408i | 0.712139 | + | 0.702039i | \(0.247727\pi\) | ||||
−0.712139 | + | 0.702039i | \(0.752273\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.43889i | − | 0.0788505i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.1716 | −0.828915 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.71536 | −0.311336 | −0.155668 | − | 0.987809i | \(-0.549753\pi\) | ||||
−0.155668 | + | 0.987809i | \(0.549753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.09052 | 0.167854 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.20033 | 0.119154 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 1.02335i | − | 0.0550955i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6658 | 0.626254 | 0.313127 | − | 0.949711i | \(-0.398623\pi\) | ||||
0.313127 | + | 0.949711i | \(0.398623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.69248i | − | 0.358240i | −0.983827 | − | 0.179120i | \(-0.942675\pi\) | ||
0.983827 | − | 0.179120i | \(-0.0573251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41345 | + | 3.83311i | 0.0754445 | + | 0.204596i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.2069i | − | 0.543258i | −0.962402 | − | 0.271629i | \(-0.912438\pi\) | ||
0.962402 | − | 0.271629i | \(-0.0875623\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.46712 | −0.502463 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.724145i | − | 0.0383258i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.62716i | − | 0.455324i | −0.973740 | − | 0.227662i | \(-0.926892\pi\) | ||
0.973740 | − | 0.227662i | \(-0.0731081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3177 | 0.964088 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.189991 | 0.00997196 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.65473 | −0.243640 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.9414 | 0.675536 | 0.337768 | − | 0.941229i | \(-0.390328\pi\) | ||||
0.337768 | + | 0.941229i | \(0.390328\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.4932i | 0.806546i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.3254i | − | 0.587985i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.4202 | 1.26443 | 0.632214 | − | 0.774793i | \(-0.282146\pi\) | ||||
0.632214 | + | 0.774793i | \(0.282146\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.72764i | − | 0.0892151i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.99054 | − | 16.2456i | −0.308529 | − | 0.836692i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.11317i | − | 0.108546i | −0.998526 | − | 0.0542732i | \(-0.982716\pi\) | ||
0.998526 | − | 0.0542732i | \(-0.0172842\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.03044 | −0.104023 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.92826i | 0.405115i | 0.979270 | + | 0.202558i | \(0.0649254\pi\) | ||||
−0.979270 | + | 0.202558i | \(0.935075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.01340i | 0.0516477i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.63302 | −0.235509 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.70958 | 0.340189 | 0.170095 | − | 0.985428i | \(-0.445593\pi\) | ||||
0.170095 | + | 0.985428i | \(0.445593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.2583 | 1.02450 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.699975 | −0.0353091 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.42137i | 0.172148i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 30.7601i | − | 1.54380i | −0.635741 | − | 0.771902i | \(-0.719305\pi\) | ||
0.635741 | − | 0.771902i | \(-0.280695\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.156938 | 0.00785671 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.24795i | 0.0623198i | 0.999514 | + | 0.0311599i | \(0.00992011\pi\) | ||||
−0.999514 | + | 0.0311599i | \(0.990080\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.44345 | + | 2.74476i | −0.370785 | + | 0.136726i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.79271i | 0.436913i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.485470 | 0.0240639 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.2318i | 1.04984i | 0.851150 | + | 0.524922i | \(0.175906\pi\) | ||||
−0.851150 | + | 0.524922i | \(0.824094\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.14053i | − | 0.0562580i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.884512 | −0.0435240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.2579 | −0.650803 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.34078 | 0.163599 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.95797 | −0.193360 | −0.0966798 | − | 0.995316i | \(-0.530822\pi\) | ||||
−0.0966798 | + | 0.995316i | \(0.530822\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.47820i | 0.413202i | 0.978425 | + | 0.206601i | \(0.0662402\pi\) | ||||
−0.978425 | + | 0.206601i | \(0.933760\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.6277i | 1.00295i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.1430 | 0.734544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.77019i | 0.0856656i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.642719 | + | 0.237001i | −0.0310308 | + | 0.0114425i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.9312i | 0.574708i | 0.957825 | + | 0.287354i | \(0.0927755\pi\) | ||||
−0.957825 | + | 0.287354i | \(0.907224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.6003 | −0.941931 | −0.470966 | − | 0.882152i | \(-0.656094\pi\) | ||||
−0.470966 | + | 0.882152i | \(0.656094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.924622i | 0.0443322i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.39040i | 0.210021i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6490 | −0.699159 | −0.349579 | − | 0.936907i | \(-0.613675\pi\) | ||||
−0.349579 | + | 0.936907i | \(0.613675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.96390 | 0.141138 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5646 | 0.882030 | 0.441015 | − | 0.897500i | \(-0.354619\pi\) | ||||
0.441015 | + | 0.897500i | \(0.354619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.5841 | −0.596542 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.15555i | − | 0.101954i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 36.3052i | − | 1.71335i | −0.515860 | − | 0.856673i | \(-0.672527\pi\) | ||
0.515860 | − | 0.856673i | \(-0.327473\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.22731 | −0.246144 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 3.09293i | − | 0.145319i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.26415 | − | 3.42822i | −0.0592643 | − | 0.160718i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.9697i | 1.16803i | 0.811741 | + | 0.584017i | \(0.198520\pi\) | ||||
−0.811741 | + | 0.584017i | \(0.801480\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.31873 | 0.201581 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.4175i | − | 1.55641i | −0.628011 | − | 0.778205i | \(-0.716131\pi\) | ||
0.628011 | − | 0.778205i | \(-0.283869\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.3266i | 1.82766i | 0.406095 | + | 0.913831i | \(0.366890\pi\) | ||||
−0.406095 | + | 0.913831i | \(0.633110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.423645 | 0.0196461 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.479382 | −0.0221831 | −0.0110916 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110916 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.9710 | −0.691297 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.130078 | 0.00599366 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.56315i | − | 0.0718736i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.28181i | 0.150580i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.5674 | 1.53695 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.66956i | 0.213357i | 0.994294 | + | 0.106679i | \(0.0340216\pi\) | ||||
−0.994294 | + | 0.106679i | \(0.965978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.64229 | + | 0.605591i | −0.0748819 | + | 0.0276126i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.00982i | − | 0.0459484i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0695 | 0.457233 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.14144i | − | 0.0517237i | −0.999666 | − | 0.0258619i | \(-0.991767\pi\) | ||
0.999666 | − | 0.0258619i | \(-0.00823300\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.745088i | 0.0336940i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.8880 | 1.30370 | 0.651849 | − | 0.758349i | \(-0.273993\pi\) | ||||
0.651849 | + | 0.758349i | \(0.273993\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.3038 | −0.824361 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00362 | −0.135003 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.34192 | −0.419043 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.9111i | 1.92096i | 0.278340 | + | 0.960482i | \(0.410216\pi\) | ||||
−0.278340 | + | 0.960482i | \(0.589784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.76469i | 0.0788407i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.00138 | −0.401352 | −0.200676 | − | 0.979658i | \(-0.564314\pi\) | ||||
−0.200676 | + | 0.979658i | \(0.564314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.87496i | 0.0834347i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.87860 | − | 1.60350i | 0.0834316 | − | 0.0712138i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 25.7572i | − | 1.14167i | −0.821066 | − | 0.570833i | \(-0.806620\pi\) | ||
0.821066 | − | 0.570833i | \(-0.193380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.59317 | −0.203190 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.935961i | 0.0413237i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.57365i | − | 0.201539i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.95964 | −0.306084 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.47810 | −0.196567 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.6501 | −0.860885 | −0.430442 | − | 0.902618i | \(-0.641642\pi\) | ||||
−0.430442 | + | 0.902618i | \(0.641642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.70868 | −0.205896 | −0.102948 | − | 0.994687i | \(-0.532828\pi\) | ||||
−0.102948 | + | 0.994687i | \(0.532828\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 0.754839i | − | 0.0329439i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.38647i | 0.365320i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.25012 | 0.228266 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.62161i | − | 0.113768i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.6834 | − | 6.52072i | 0.765953 | − | 0.282444i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 19.6969i | − | 0.851571i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.28172 | −0.184770 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 40.9304i | − | 1.75974i | −0.475218 | − | 0.879868i | \(-0.657631\pi\) | ||
0.475218 | − | 0.879868i | \(-0.342369\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.263756 | −0.0113189 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.94379 | −0.383110 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.47268 | 0.362265 | 0.181133 | − | 0.983459i | \(-0.442024\pi\) | ||||
0.181133 | + | 0.983459i | \(0.442024\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.24668 | −0.223923 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.96682i | − | 0.168992i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.37613i | 0.143568i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0934712 | 0.00396763 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14.8845i | − | 0.630677i | −0.948979 | − | 0.315338i | \(-0.897882\pi\) | ||
0.948979 | − | 0.315338i | \(-0.102118\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.94992 | + | 5.28795i | 0.0824729 | + | 0.223656i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.724145i | 0.0305734i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.5493 | −1.49822 | −0.749112 | − | 0.662443i | \(-0.769520\pi\) | ||||
−0.749112 | + | 0.662443i | \(0.769520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 16.4847i | − | 0.693515i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.67643i | 0.364376i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.5267 | 0.734758 | 0.367379 | − | 0.930071i | \(-0.380255\pi\) | ||||
0.367379 | + | 0.930071i | \(0.380255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0904 | 0.422271 | 0.211136 | − | 0.977457i | \(-0.432284\pi\) | ||||
0.211136 | + | 0.977457i | \(0.432284\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.49806 | 0.0625822 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.1169 | 0.880636 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 35.2321i | − | 1.46673i | −0.679834 | − | 0.733366i | \(-0.737948\pi\) | ||
0.679834 | − | 0.733366i | \(-0.262052\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.41579i | 0.100397i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.0825 | −0.542755 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.3254i | 0.469050i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.1609 | − | 3.74682i | 0.420102 | − | 0.154912i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.5996i | 0.602591i | 0.953531 | + | 0.301296i | \(0.0974191\pi\) | ||||
−0.953531 | + | 0.301296i | \(0.902581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.81753 | −0.0748899 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.29042i | 0.135350i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.2006i | − | 0.459952i | −0.973196 | − | 0.229976i | \(-0.926135\pi\) | ||
0.973196 | − | 0.229976i | \(-0.0738648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.86254 | −0.158349 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.643676 | −0.0263439 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.2433 | 1.39914 | 0.699571 | − | 0.714563i | \(-0.253374\pi\) | ||||
0.699571 | + | 0.714563i | \(0.253374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.7394 | 1.25389 | 0.626943 | − | 0.779065i | \(-0.284306\pi\) | ||||
0.626943 | + | 0.779065i | \(0.284306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 44.3726i | − | 1.80699i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1.01340i | − | 0.0412006i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.1938 | −1.71260 | −0.856298 | − | 0.516483i | \(-0.827241\pi\) | ||||
−0.856298 | + | 0.516483i | \(0.827241\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.912394i | 0.0369721i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.5436 | − | 8.68168i | 0.952474 | − | 0.351223i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.7355i | − | 0.837500i | −0.908102 | − | 0.418750i | \(-0.862468\pi\) | ||
0.908102 | − | 0.418750i | \(-0.137532\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.00645 | −0.0405841 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.00510i | − | 0.161239i | −0.996745 | − | 0.0806197i | \(-0.974310\pi\) | ||
0.996745 | − | 0.0806197i | \(-0.0256899\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.6865i | − | 0.550106i | −0.961429 | − | 0.275053i | \(-0.911305\pi\) | ||
0.961429 | − | 0.275053i | \(-0.0886954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.02247 | 0.241673 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.4177 | −0.497503 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.6499 | 0.425998 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.156938 | −0.00626749 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.85035i | 0.0737784i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.19621i | − | 0.366095i | −0.983104 | − | 0.183048i | \(-0.941404\pi\) | ||
0.983104 | − | 0.183048i | \(-0.0585962\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.808429 | 0.0321322 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.8303i | 0.429786i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.24743 | − | 3.38289i | −0.0494251 | − | 0.134035i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 27.6886i | − | 1.09534i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.7227 | 0.700005 | 0.350002 | − | 0.936749i | \(-0.386181\pi\) | ||||
0.350002 | + | 0.936749i | \(0.386181\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 28.1531i | − | 1.11025i | −0.831767 | − | 0.555125i | \(-0.812671\pi\) | ||
0.831767 | − | 0.555125i | \(-0.187329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 0.300964i | − | 0.0118505i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.66981 | 0.262217 | 0.131109 | − | 0.991368i | \(-0.458146\pi\) | ||||
0.131109 | + | 0.991368i | \(0.458146\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.884512 | 0.0347202 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.418043 | 0.0163844 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.7081 | 1.39737 | 0.698683 | − | 0.715432i | \(-0.253770\pi\) | ||||
0.698683 | + | 0.715432i | \(0.253770\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.73362i | 0.145885i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 13.6137i | − | 0.531122i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.4747 | −1.26503 | −0.632517 | − | 0.774546i | \(-0.717978\pi\) | ||||
−0.632517 | + | 0.774546i | \(0.717978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 47.7693i | − | 1.85801i | −0.370068 | − | 0.929005i | \(-0.620666\pi\) | ||
0.370068 | − | 0.929005i | \(-0.379334\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.903322 | − | 2.44970i | −0.0350821 | − | 0.0951384i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 0.837096i | − | 0.0324612i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.5246 | −0.988317 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 2.94602i | − | 0.113900i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.77019i | − | 0.0683375i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.9932 | −1.23325 | −0.616625 | − | 0.787257i | \(-0.711500\pi\) | ||||
−0.616625 | + | 0.787257i | \(0.711500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50178 | 0.173274 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.974841 | −0.0374662 | −0.0187331 | − | 0.999825i | \(-0.505963\pi\) | ||||
−0.0187331 | + | 0.999825i | \(0.505963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.93635 | 0.381322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0109595i | 0.000419970i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.5297i | 0.976865i | 0.872602 | + | 0.488433i | \(0.162431\pi\) | ||||
−0.872602 | + | 0.488433i | \(0.837569\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.08350 | −0.232439 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.36878i | − | 0.0522224i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.1277 | − | 38.3125i | −0.538221 | − | 1.45959i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.7563i | 0.903733i | 0.892086 | + | 0.451866i | \(0.149242\pi\) | ||||
−0.892086 | + | 0.451866i | \(0.850758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.96390 | −0.112589 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17.8195i | − | 0.675933i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.9237i | − | 0.754664i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.73682 | 0.0656926 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.9239 | −0.412589 | −0.206294 | − | 0.978490i | \(-0.566140\pi\) | ||||
−0.206294 | + | 0.978490i | \(0.566140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.401011 | −0.0151244 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.33999 | −0.0504670 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.85017i | 0.0695826i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.2624i | 1.32431i | 0.749367 | + | 0.662154i | \(0.230358\pi\) | ||||
−0.749367 | + | 0.662154i | \(0.769642\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0065 | −0.375274 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6949i | 0.437978i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.26415 | + | 3.42822i | 0.0472765 | + | 0.128208i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 2.30050i | − | 0.0859138i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.8172 | 1.82057 | 0.910287 | − | 0.413978i | \(-0.135861\pi\) | ||||
0.910287 | + | 0.413978i | \(0.135861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.51317i | − | 0.168079i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.24667i | − | 0.0463640i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.0796 | −0.708599 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.1217 | −0.709185 | −0.354592 | − | 0.935021i | \(-0.615380\pi\) | ||||
−0.354592 | + | 0.935021i | \(0.615380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.0703 | −0.928529 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.95788 | 0.220360 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.0576i | 1.33182i | 0.746033 | + | 0.665909i | \(0.231956\pi\) | ||||
−0.746033 | + | 0.665909i | \(0.768044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.192538i | 0.00710185i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.9710 | 0.551464 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 15.3941i | − | 0.566280i | −0.959079 | − | 0.283140i | \(-0.908624\pi\) | ||
0.959079 | − | 0.283140i | \(-0.0913760\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.530902 | − | 0.195769i | 0.0195032 | − | 0.00719176i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.1836i | − | 0.997271i | −0.866812 | − | 0.498635i | \(-0.833835\pi\) | ||
0.866812 | − | 0.498635i | \(-0.166165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.4976 | −0.421239 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 38.7754i | − | 1.41872i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.4364i | − | 0.710191i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.48372 | 0.0906322 | 0.0453161 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453161 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.58927 | 0.203684 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.4975 | −0.600406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.8686 | 0.976555 | 0.488278 | − | 0.872688i | \(-0.337625\pi\) | ||||
0.488278 | + | 0.872688i | \(0.337625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.00982i | 0.0366541i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.6260i | − | 0.566442i | −0.959055 | − | 0.283221i | \(-0.908597\pi\) | ||
0.959055 | − | 0.283221i | \(-0.0914030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.82552 | −0.319505 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 11.4482i | − | 0.413911i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.99220 | + | 1.10337i | −0.108042 | + | 0.0398404i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28.8620i | − | 1.04079i | −0.853926 | − | 0.520395i | \(-0.825785\pi\) | ||
0.853926 | − | 0.520395i | \(-0.174215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.44886 | −0.196236 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.9189i | 1.14804i | 0.818840 | + | 0.574021i | \(0.194617\pi\) | ||||
−0.818840 | + | 0.574021i | \(0.805383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.74194i | 0.314020i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0922351 | 0.00330892 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.31789 | 0.154705 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.34192 | 0.334280 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.44143 | −0.194461 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 0.693826i | − | 0.0247637i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.1458i | 1.21717i | 0.793490 | + | 0.608584i | \(0.208262\pi\) | ||||
−0.793490 | + | 0.608584i | \(0.791738\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.36749 | −0.0842850 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 16.2667i | − | 0.578376i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.20820 | + | 5.98836i | 0.0784153 | + | 0.212653i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.18056i | 0.0773366i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.5475 | 1.22373 | 0.611867 | − | 0.790961i | \(-0.290419\pi\) | ||||
0.611867 | + | 0.790961i | \(0.290419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 26.5264i | − | 0.938437i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 36.8047i | − | 1.30043i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.59317 | 0.162090 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.38632 | −0.189843 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.51450 | 0.194120 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.2273 | 1.44947 | 0.724737 | − | 0.689026i | \(-0.241961\pi\) | ||||
0.724737 | + | 0.689026i | \(0.241961\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.0685i | − | 0.388666i | −0.980936 | − | 0.194333i | \(-0.937746\pi\) | ||
0.980936 | − | 0.194333i | \(-0.0622543\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.52270i | − | 0.193689i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.97425 | 0.139212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29120i | 0.0451734i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.0265 | − | 3.69727i | 0.350356 | − | 0.129193i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.86968i | − | 0.239753i | −0.992789 | − | 0.119877i | \(-0.961750\pi\) | ||
0.992789 | − | 0.119877i | \(-0.0382499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.9521 | 1.67150 | 0.835752 | − | 0.549107i | \(-0.185032\pi\) | ||||
0.835752 | + | 0.549107i | \(0.185032\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.754839i | 0.0262801i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.1982i | 0.980546i | 0.871569 | + | 0.490273i | \(0.163103\pi\) | ||||
−0.871569 | + | 0.490273i | \(0.836897\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6911 | 0.649170 | 0.324585 | − | 0.945857i | \(-0.394775\pi\) | ||||
0.324585 | + | 0.945857i | \(0.394775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.121403 | −0.00421143 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.81146 | −0.132059 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.41277 | 0.325742 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.49317i | 0.0861765i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.3170i | 0.494276i | 0.968980 | + | 0.247138i | \(0.0794901\pi\) | ||||
−0.968980 | + | 0.247138i | \(0.920510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.93795 | −0.204757 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.52403i | 0.121374i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.55295 | − | 10.0203i | −0.294230 | − | 0.344710i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.41882 | 0.185973 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.58031i | 0.0884520i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.39098i | 0.321541i | 0.986992 | + | 0.160770i | \(0.0513979\pi\) | ||||
−0.986992 | + | 0.160770i | \(0.948602\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.48107 | 0.0848509 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.5219 | −1.48668 | −0.743340 | − | 0.668914i | \(-0.766759\pi\) | ||||
−0.743340 | + | 0.668914i | \(0.766759\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.8786 | 1.56536 | 0.782678 | − | 0.622427i | \(-0.213853\pi\) | ||||
0.782678 | + | 0.622427i | \(0.213853\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.993143 | −0.0338462 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.0817i | − | 0.819750i | −0.912142 | − | 0.409875i | \(-0.865572\pi\) | ||
0.912142 | − | 0.409875i | \(-0.134428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.8859i | 0.812144i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.469799 | 0.0159552 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3.37613i | − | 0.114527i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50.6452 | + | 18.6753i | −1.71605 | + | 0.632789i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.4504i | 0.996745i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.09327 | −0.307409 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.2520i | 0.413722i | 0.978370 | + | 0.206861i | \(0.0663248\pi\) | ||||
−0.978370 | + | 0.206861i | \(0.933675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.16791i | − | 0.106851i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.0026 | 1.31403 | 0.657015 | − | 0.753877i | \(-0.271819\pi\) | ||||
0.657015 | + | 0.753877i | \(0.271819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.5069 | −0.925679 | −0.462840 | − | 0.886442i | \(-0.653169\pi\) | ||||
−0.462840 | + | 0.886442i | \(0.653169\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.170302 | 0.00572463 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.5305 | 1.15942 | 0.579711 | − | 0.814822i | \(-0.303166\pi\) | ||||
0.579711 | + | 0.814822i | \(0.303166\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.6870i | 0.358432i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 8.67643i | − | 0.290671i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.74884 | 0.192378 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.8384i | 0.763405i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.25968 | − | 3.41610i | −0.0420596 | − | 0.114060i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 10.5666i | − | 0.352417i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.1664 | −1.43808 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 0.296984i | − | 0.00988302i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.40686i | 0.0467656i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.29910 | 0.142749 | 0.0713747 | − | 0.997450i | \(-0.477261\pi\) | ||||
0.0713747 | + | 0.997450i | \(0.477261\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.48371 | −0.181883 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6529 | −0.352947 | −0.176474 | − | 0.984305i | \(-0.556469\pi\) | ||||
−0.176474 | + | 0.984305i | \(0.556469\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.0825 | 0.432969 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 0.340828i | − | 0.0112674i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.68425i | 0.121665i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.0975 | −0.498021 | −0.249010 | − | 0.968501i | \(-0.580105\pi\) | ||||
−0.249010 | + | 0.968501i | \(0.580105\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.957007i | 0.0315344i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.6027 | + | 11.6534i | −1.04021 | + | 0.383577i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.92878i | 0.0634179i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.3766 | 0.439345 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.52364i | − | 0.0499891i | −0.999688 | − | 0.0249946i | \(-0.992043\pi\) | ||
0.999688 | − | 0.0249946i | \(-0.00795684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.826026i | − | 0.0270719i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.832347 | 0.0272498 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.86254 | 0.126319 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.9431 | −0.912861 | −0.456430 | − | 0.889759i | \(-0.650872\pi\) | ||||
−0.456430 | + | 0.889759i | \(0.650872\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.74557 | −0.0569646 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 23.6567i | − | 0.771185i | −0.922669 | − | 0.385592i | \(-0.873997\pi\) | ||
0.922669 | − | 0.385592i | \(-0.126003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 27.7836i | − | 0.904758i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.14828 | −0.0373534 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 36.4984i | − | 1.18604i | −0.805188 | − | 0.593020i | \(-0.797936\pi\) | ||
0.805188 | − | 0.593020i | \(-0.202064\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.5382 | + | 5.72968i | −0.504391 | + | 0.185993i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.770798i | − | 0.0249948i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.6645 | −1.70597 | −0.852985 | − | 0.521935i | \(-0.825210\pi\) | ||||
−0.852985 | + | 0.521935i | \(0.825210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7.99054i | − | 0.258568i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.912394i | − | 0.0294935i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00305 | −0.193849 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.1586 | 0.843825 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 57.6076 | 1.85638 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.8857 | 0.414804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 21.4116i | − | 0.688550i | −0.938869 | − | 0.344275i | \(-0.888125\pi\) | ||
0.938869 | − | 0.344275i | \(-0.111875\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.598163i | − | 0.0192157i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.07750 | 0.291311 | 0.145655 | − | 0.989335i | \(-0.453471\pi\) | ||||
0.145655 | + | 0.989335i | \(0.453471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 17.5839i | − | 0.563713i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.941610 | − | 2.55353i | −0.0301557 | − | 0.0817785i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.3776i | 0.555959i | 0.960587 | + | 0.277980i | \(0.0896648\pi\) | ||||
−0.960587 | + | 0.277980i | \(0.910335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4177 | 0.396870 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 26.1580i | − | 0.835160i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 59.4756i | − | 1.89698i | −0.316813 | − | 0.948488i | \(-0.602613\pi\) | ||
0.316813 | − | 0.948488i | \(-0.397387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5509 | 0.559218 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.32227 | −0.0420883 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.30826 | 0.264187 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.5589 | 1.79665 | 0.898326 | − | 0.439330i | \(-0.144784\pi\) | ||||
0.898326 | + | 0.439330i | \(0.144784\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 4.85332i | − | 0.154015i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.43333i | 0.108844i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.9826 | −0.822876 | −0.411438 | − | 0.911438i | \(-0.634973\pi\) | ||||
−0.411438 | + | 0.911438i | \(0.634973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.550081i | 0.0174038i |
(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.c.2157.20 | yes | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.19 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.19 | ✓ | 36 | 13.12 | even | 2 | inner | |
4004.2.m.c.2157.20 | yes | 36 | 1.1 | even | 1 | trivial |