Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(4013,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4014.4013");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.d (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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4013.18 | ||
Character | \(\chi\) | \(=\) | 4014.4013 |
Dual form | 4014.2.d.a.4013.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4014\mathbb{Z}\right)^\times\).
\(n\) | \(893\) | \(2233\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.707934 | 0.316598 | 0.158299 | − | 0.987391i | \(-0.449399\pi\) | ||||
0.158299 | + | 0.987391i | \(0.449399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.916361 | 0.346352 | 0.173176 | − | 0.984891i | \(-0.444597\pi\) | ||||
0.173176 | + | 0.984891i | \(0.444597\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.707934i | 0.223868i | ||||||||
\(11\) | 4.30663 | 1.29850 | 0.649249 | − | 0.760576i | \(-0.275083\pi\) | ||||
0.649249 | + | 0.760576i | \(0.275083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.29049i | − | 1.18997i | −0.803738 | − | 0.594984i | \(-0.797159\pi\) | ||
0.803738 | − | 0.594984i | \(-0.202841\pi\) | |||||||
\(14\) | 0.916361i | 0.244908i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.79279i | − | 0.677351i | −0.940903 | − | 0.338676i | \(-0.890021\pi\) | ||
0.940903 | − | 0.338676i | \(-0.109979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.09016 | 1.39718 | 0.698590 | − | 0.715523i | \(-0.253811\pi\) | ||||
0.698590 | + | 0.715523i | \(0.253811\pi\) | |||||||
\(20\) | −0.707934 | −0.158299 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.30663i | 0.918177i | ||||||||
\(23\) | 0.682495 | 0.142310 | 0.0711550 | − | 0.997465i | \(-0.477332\pi\) | ||||
0.0711550 | + | 0.997465i | \(0.477332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.49883 | −0.899766 | ||||||||
\(26\) | 4.29049 | 0.841434 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.916361 | −0.173176 | ||||||||
\(29\) | − | 3.21724i | − | 0.597427i | −0.954343 | − | 0.298714i | \(-0.903443\pi\) | ||
0.954343 | − | 0.298714i | \(-0.0965575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.315439 | −0.0566544 | −0.0283272 | − | 0.999599i | \(-0.509018\pi\) | ||||
−0.0283272 | + | 0.999599i | \(0.509018\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.79279 | 0.478960 | ||||||||
\(35\) | 0.648723 | 0.109654 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.22523 | −0.694623 | −0.347311 | − | 0.937750i | \(-0.612905\pi\) | ||||
−0.347311 | + | 0.937750i | \(0.612905\pi\) | |||||||
\(38\) | 6.09016i | 0.987955i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 0.707934i | − | 0.111934i | ||||||
\(41\) | 0.607558i | 0.0948847i | 0.998874 | + | 0.0474423i | \(0.0151070\pi\) | ||||
−0.998874 | + | 0.0474423i | \(0.984893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.08767 | 0.165869 | 0.0829343 | − | 0.996555i | \(-0.473571\pi\) | ||||
0.0829343 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(44\) | −4.30663 | −0.649249 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.682495i | 0.100628i | ||||||||
\(47\) | − | 2.90784i | − | 0.424152i | −0.977253 | − | 0.212076i | \(-0.931978\pi\) | ||
0.977253 | − | 0.212076i | \(-0.0680224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.16028 | −0.880040 | ||||||||
\(50\) | − | 4.49883i | − | 0.636231i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.29049i | 0.594984i | ||||||||
\(53\) | − | 11.3029i | − | 1.55257i | −0.630380 | − | 0.776287i | \(-0.717101\pi\) | ||
0.630380 | − | 0.776287i | \(-0.282899\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.04881 | 0.411101 | ||||||||
\(56\) | − | 0.916361i | − | 0.122454i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.21724 | 0.422445 | ||||||||
\(59\) | 0.693451 | 0.0902797 | 0.0451398 | − | 0.998981i | \(-0.485627\pi\) | ||||
0.0451398 | + | 0.998981i | \(0.485627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.12711i | − | 1.16861i | −0.811535 | − | 0.584303i | \(-0.801368\pi\) | ||
0.811535 | − | 0.584303i | \(-0.198632\pi\) | |||||||
\(62\) | − | 0.315439i | − | 0.0400607i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 3.03738i | − | 0.376741i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.9662i | − | 1.58407i | −0.610476 | − | 0.792035i | \(-0.709022\pi\) | ||
0.610476 | − | 0.792035i | \(-0.290978\pi\) | |||||||
\(68\) | 2.79279i | 0.338676i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.648723i | 0.0775373i | ||||||||
\(71\) | −7.15131 | −0.848704 | −0.424352 | − | 0.905497i | \(-0.639498\pi\) | ||||
−0.424352 | + | 0.905497i | \(0.639498\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.17812 | −0.254930 | −0.127465 | − | 0.991843i | \(-0.540684\pi\) | ||||
−0.127465 | + | 0.991843i | \(0.540684\pi\) | |||||||
\(74\) | − | 4.22523i | − | 0.491173i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.09016 | −0.698590 | ||||||||
\(77\) | 3.94643 | 0.449737 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.1897i | 1.48396i | 0.670424 | + | 0.741978i | \(0.266112\pi\) | ||||
−0.670424 | + | 0.741978i | \(0.733888\pi\) | |||||||
\(80\) | 0.707934 | 0.0791494 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.607558 | −0.0670936 | ||||||||
\(83\) | 0.529002i | 0.0580655i | 0.999578 | + | 0.0290328i | \(0.00924272\pi\) | ||||
−0.999578 | + | 0.0290328i | \(0.990757\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.97711i | − | 0.214448i | ||||||
\(86\) | 1.08767i | 0.117287i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.30663i | − | 0.459088i | ||||||
\(89\) | − | 5.43684i | − | 0.576304i | −0.957585 | − | 0.288152i | \(-0.906959\pi\) | ||
0.957585 | − | 0.288152i | \(-0.0930408\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.93164i | − | 0.412148i | ||||||
\(92\) | −0.682495 | −0.0711550 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.90784 | 0.299921 | ||||||||
\(95\) | 4.31143 | 0.442344 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.4837i | 1.36906i | 0.728982 | + | 0.684532i | \(0.239994\pi\) | ||||
−0.728982 | + | 0.684532i | \(0.760006\pi\) | |||||||
\(98\) | − | 6.16028i | − | 0.622282i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.49883 | 0.449883 | ||||||||
\(101\) | − | 15.9010i | − | 1.58221i | −0.611680 | − | 0.791106i | \(-0.709506\pi\) | ||
0.611680 | − | 0.791106i | \(-0.290494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.59780i | 0.945699i | 0.881143 | + | 0.472850i | \(0.156775\pi\) | ||||
−0.881143 | + | 0.472850i | \(0.843225\pi\) | |||||||
\(104\) | −4.29049 | −0.420717 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.3029 | 1.09784 | ||||||||
\(107\) | 13.2748 | 1.28333 | 0.641663 | − | 0.766987i | \(-0.278245\pi\) | ||||
0.641663 | + | 0.766987i | \(0.278245\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2315 | 1.36313 | 0.681567 | − | 0.731755i | \(-0.261299\pi\) | ||||
0.681567 | + | 0.731755i | \(0.261299\pi\) | |||||||
\(110\) | 3.04881i | 0.290693i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.916361 | 0.0865880 | ||||||||
\(113\) | −19.8205 | −1.86455 | −0.932277 | − | 0.361745i | \(-0.882181\pi\) | ||||
−0.932277 | + | 0.361745i | \(0.882181\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.483161 | 0.0450550 | ||||||||
\(116\) | 3.21724i | 0.298714i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.693451i | 0.0638374i | ||||||||
\(119\) | − | 2.55921i | − | 0.234602i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.54707 | 0.686097 | ||||||||
\(122\) | 9.12711 | 0.826330 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.315439 | 0.0283272 | ||||||||
\(125\) | −6.72454 | −0.601461 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.123444 | −0.0109539 | −0.00547696 | − | 0.999985i | \(-0.501743\pi\) | ||||
−0.00547696 | + | 0.999985i | \(0.501743\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.03738 | 0.266396 | ||||||||
\(131\) | − | 5.18225i | − | 0.452776i | −0.974037 | − | 0.226388i | \(-0.927308\pi\) | ||
0.974037 | − | 0.226388i | \(-0.0726917\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.58079 | 0.483916 | ||||||||
\(134\) | 12.9662 | 1.12011 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.79279 | −0.239480 | ||||||||
\(137\) | −9.58358 | −0.818780 | −0.409390 | − | 0.912359i | \(-0.634258\pi\) | ||||
−0.409390 | + | 0.912359i | \(0.634258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2856 | −1.29651 | −0.648256 | − | 0.761423i | \(-0.724501\pi\) | ||||
−0.648256 | + | 0.761423i | \(0.724501\pi\) | |||||||
\(140\) | −0.648723 | −0.0548271 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 7.15131i | − | 0.600125i | ||||||
\(143\) | − | 18.4775i | − | 1.54517i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.27760i | − | 0.189144i | ||||||
\(146\) | − | 2.17812i | − | 0.180263i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.22523 | 0.347311 | ||||||||
\(149\) | 21.8677 | 1.79147 | 0.895734 | − | 0.444590i | \(-0.146651\pi\) | ||||
0.895734 | + | 0.444590i | \(0.146651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3956i | 1.00874i | 0.863487 | + | 0.504370i | \(0.168275\pi\) | ||||
−0.863487 | + | 0.504370i | \(0.831725\pi\) | |||||||
\(152\) | − | 6.09016i | − | 0.493977i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.94643i | 0.318012i | ||||||||
\(155\) | −0.223310 | −0.0179367 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.86184i | 0.707252i | 0.935387 | + | 0.353626i | \(0.115051\pi\) | ||||
−0.935387 | + | 0.353626i | \(0.884949\pi\) | |||||||
\(158\) | −13.1897 | −1.04932 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.707934i | 0.0559671i | ||||||||
\(161\) | 0.625412 | 0.0492893 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6089i | 0.909278i | 0.890676 | + | 0.454639i | \(0.150232\pi\) | ||||
−0.890676 | + | 0.454639i | \(0.849768\pi\) | |||||||
\(164\) | − | 0.607558i | − | 0.0474423i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.529002 | −0.0410585 | ||||||||
\(167\) | 20.0127 | 1.54863 | 0.774316 | − | 0.632799i | \(-0.218094\pi\) | ||||
0.774316 | + | 0.632799i | \(0.218094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.40829 | −0.416022 | ||||||||
\(170\) | 1.97711 | 0.151638 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.08767 | −0.0829343 | ||||||||
\(173\) | 6.40756 | 0.487158 | 0.243579 | − | 0.969881i | \(-0.421678\pi\) | ||||
0.243579 | + | 0.969881i | \(0.421678\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.12255 | −0.311636 | ||||||||
\(176\) | 4.30663 | 0.324625 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.43684 | 0.407508 | ||||||||
\(179\) | − | 26.6168i | − | 1.98943i | −0.102677 | − | 0.994715i | \(-0.532741\pi\) | ||
0.102677 | − | 0.994715i | \(-0.467259\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.55228 | −0.487027 | −0.243513 | − | 0.969898i | \(-0.578300\pi\) | ||||
−0.243513 | + | 0.969898i | \(0.578300\pi\) | |||||||
\(182\) | 3.93164 | 0.291432 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 0.682495i | − | 0.0503142i | ||||||
\(185\) | −2.99118 | −0.219916 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 12.0275i | − | 0.879539i | ||||||
\(188\) | 2.90784i | 0.212076i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.31143i | 0.312784i | ||||||||
\(191\) | 18.7825 | 1.35906 | 0.679528 | − | 0.733650i | \(-0.262185\pi\) | ||||
0.679528 | + | 0.733650i | \(0.262185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.23686i | 0.232994i | 0.993191 | + | 0.116497i | \(0.0371666\pi\) | ||||
−0.993191 | + | 0.116497i | \(0.962833\pi\) | |||||||
\(194\) | −13.4837 | −0.968075 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.16028 | 0.440020 | ||||||||
\(197\) | 9.64258i | 0.687005i | 0.939152 | + | 0.343503i | \(0.111613\pi\) | ||||
−0.939152 | + | 0.343503i | \(0.888387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.4561 | 1.87542 | 0.937711 | − | 0.347417i | \(-0.112941\pi\) | ||||
0.937711 | + | 0.347417i | \(0.112941\pi\) | |||||||
\(200\) | 4.49883i | 0.318115i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.9010 | 1.11879 | ||||||||
\(203\) | − | 2.94816i | − | 0.206920i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.430111i | 0.0300403i | ||||||||
\(206\) | −9.59780 | −0.668710 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.29049i | − | 0.297492i | ||||||
\(209\) | 26.2281 | 1.81423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8071 | 0.812832 | 0.406416 | − | 0.913688i | \(-0.366778\pi\) | ||||
0.406416 | + | 0.913688i | \(0.366778\pi\) | |||||||
\(212\) | 11.3029i | 0.776287i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.2748i | 0.907449i | ||||||||
\(215\) | 0.770001 | 0.0525136 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.289056 | −0.0196224 | ||||||||
\(218\) | 14.2315i | 0.963882i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.04881 | −0.205551 | ||||||||
\(221\) | −11.9824 | −0.806026 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0849 | + | 4.96135i | −0.943196 | + | 0.332237i | ||||
\(224\) | 0.916361i | 0.0612270i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 19.8205i | − | 1.31844i | ||||||
\(227\) | − | 5.13389i | − | 0.340748i | −0.985379 | − | 0.170374i | \(-0.945502\pi\) | ||
0.985379 | − | 0.170374i | \(-0.0544976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.67624i | − | 0.242932i | −0.992596 | − | 0.121466i | \(-0.961240\pi\) | ||
0.992596 | − | 0.121466i | \(-0.0387596\pi\) | |||||||
\(230\) | 0.483161i | 0.0318587i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.21724 | −0.211222 | ||||||||
\(233\) | −2.85827 | −0.187252 | −0.0936259 | − | 0.995607i | \(-0.529846\pi\) | ||||
−0.0936259 | + | 0.995607i | \(0.529846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.05856i | − | 0.134285i | ||||||
\(236\) | −0.693451 | −0.0451398 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.55921 | 0.165889 | ||||||||
\(239\) | 22.3971i | 1.44875i | 0.689407 | + | 0.724374i | \(0.257871\pi\) | ||||
−0.689407 | + | 0.724374i | \(0.742129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.8693 | 1.79522 | 0.897609 | − | 0.440792i | \(-0.145302\pi\) | ||||
0.897609 | + | 0.440792i | \(0.145302\pi\) | |||||||
\(242\) | 7.54707i | 0.485144i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.12711i | 0.584303i | ||||||||
\(245\) | −4.36107 | −0.278619 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 26.1298i | − | 1.66260i | ||||||
\(248\) | 0.315439i | 0.0200304i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 6.72454i | − | 0.425297i | ||||||
\(251\) | − | 21.7690i | − | 1.37405i | −0.726636 | − | 0.687023i | \(-0.758917\pi\) | ||
0.726636 | − | 0.687023i | \(-0.241083\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.93925 | 0.184789 | ||||||||
\(254\) | − | 0.123444i | − | 0.00774559i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 29.0480i | − | 1.81196i | −0.423319 | − | 0.905981i | \(-0.639135\pi\) | ||
0.423319 | − | 0.905981i | \(-0.360865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.87183 | −0.240584 | ||||||||
\(260\) | 3.03738i | 0.188370i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.18225 | 0.320161 | ||||||||
\(263\) | −24.8682 | −1.53344 | −0.766720 | − | 0.641981i | \(-0.778113\pi\) | ||||
−0.766720 | + | 0.641981i | \(0.778113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.00171i | − | 0.491541i | ||||||
\(266\) | 5.58079i | 0.342180i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.9662i | 0.792035i | ||||||||
\(269\) | −9.76578 | −0.595430 | −0.297715 | − | 0.954655i | \(-0.596225\pi\) | ||||
−0.297715 | + | 0.954655i | \(0.596225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.60049i | − | 0.461697i | −0.972990 | − | 0.230848i | \(-0.925850\pi\) | ||
0.972990 | − | 0.230848i | \(-0.0741502\pi\) | |||||||
\(272\) | − | 2.79279i | − | 0.169338i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 9.58358i | − | 0.578965i | ||||||
\(275\) | −19.3748 | −1.16834 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1990i | 1.21364i | 0.794839 | + | 0.606820i | \(0.207555\pi\) | ||||
−0.794839 | + | 0.606820i | \(0.792445\pi\) | |||||||
\(278\) | − | 15.2856i | − | 0.916772i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 0.648723i | − | 0.0387686i | ||||||
\(281\) | − | 6.43316i | − | 0.383770i | −0.981417 | − | 0.191885i | \(-0.938540\pi\) | ||
0.981417 | − | 0.191885i | \(-0.0614601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5196 | 0.625323 | 0.312661 | − | 0.949865i | \(-0.398780\pi\) | ||||
0.312661 | + | 0.949865i | \(0.398780\pi\) | |||||||
\(284\) | 7.15131 | 0.424352 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.4775 | 1.09260 | ||||||||
\(287\) | 0.556743i | 0.0328635i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.20032 | 0.541195 | ||||||||
\(290\) | 2.27760 | 0.133745 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.17812 | 0.127465 | ||||||||
\(293\) | 20.0197 | 1.16956 | 0.584781 | − | 0.811191i | \(-0.301180\pi\) | ||||
0.584781 | + | 0.811191i | \(0.301180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.490918 | 0.0285823 | ||||||||
\(296\) | 4.22523i | 0.245586i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.8677i | 1.26676i | ||||||||
\(299\) | − | 2.92823i | − | 0.169344i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.996702 | 0.0574489 | ||||||||
\(302\) | −12.3956 | −0.713287 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.09016 | 0.349295 | ||||||||
\(305\) | − | 6.46139i | − | 0.369978i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.1982i | 1.20985i | 0.796284 | + | 0.604923i | \(0.206796\pi\) | ||||
−0.796284 | + | 0.604923i | \(0.793204\pi\) | |||||||
\(308\) | −3.94643 | −0.224869 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 0.223310i | − | 0.0126831i | ||||||
\(311\) | 27.2673 | 1.54619 | 0.773094 | − | 0.634291i | \(-0.218708\pi\) | ||||
0.773094 | + | 0.634291i | \(0.218708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.28652i | 0.355335i | 0.984091 | + | 0.177668i | \(0.0568552\pi\) | ||||
−0.984091 | + | 0.177668i | \(0.943145\pi\) | |||||||
\(314\) | −8.86184 | −0.500103 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 13.1897i | − | 0.741978i | ||||||
\(317\) | 16.6895i | 0.937378i | 0.883363 | + | 0.468689i | \(0.155273\pi\) | ||||
−0.883363 | + | 0.468689i | \(0.844727\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 13.8555i | − | 0.775758i | ||||||
\(320\) | −0.707934 | −0.0395747 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.625412i | 0.0348528i | ||||||||
\(323\) | − | 17.0085i | − | 0.946381i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.3022i | 1.07069i | ||||||||
\(326\) | −11.6089 | −0.642957 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.607558 | 0.0335468 | ||||||||
\(329\) | − | 2.66463i | − | 0.146906i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.40295i | − | 0.406903i | −0.979085 | − | 0.203452i | \(-0.934784\pi\) | ||
0.979085 | − | 0.203452i | \(-0.0652160\pi\) | |||||||
\(332\) | − | 0.529002i | − | 0.0290328i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0127i | 1.09505i | ||||||||
\(335\) | − | 9.17919i | − | 0.501513i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.32095i | − | 0.180904i | −0.995901 | − | 0.0904519i | \(-0.971169\pi\) | ||
0.995901 | − | 0.0904519i | \(-0.0288311\pi\) | |||||||
\(338\) | − | 5.40829i | − | 0.294172i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.97711i | 0.107224i | ||||||||
\(341\) | −1.35848 | −0.0735657 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0596 | −0.651156 | ||||||||
\(344\) | − | 1.08767i | − | 0.0586434i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.40756i | 0.344473i | ||||||||
\(347\) | − | 2.50543i | − | 0.134498i | −0.997736 | − | 0.0672492i | \(-0.978578\pi\) | ||
0.997736 | − | 0.0672492i | \(-0.0214223\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.2768 | 1.40656 | 0.703282 | − | 0.710911i | \(-0.251717\pi\) | ||||
0.703282 | + | 0.710911i | \(0.251717\pi\) | |||||||
\(350\) | − | 4.12255i | − | 0.220360i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.30663i | 0.229544i | ||||||||
\(353\) | 15.0382i | 0.800402i | 0.916427 | + | 0.400201i | \(0.131060\pi\) | ||||
−0.916427 | + | 0.400201i | \(0.868940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.06266 | −0.268698 | ||||||||
\(356\) | 5.43684i | 0.288152i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.6168 | 1.40674 | ||||||||
\(359\) | − | 8.25711i | − | 0.435794i | −0.975972 | − | 0.217897i | \(-0.930080\pi\) | ||
0.975972 | − | 0.217897i | \(-0.0699196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0901 | 0.952110 | ||||||||
\(362\) | − | 6.55228i | − | 0.344380i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.93164i | 0.206074i | ||||||||
\(365\) | −1.54197 | −0.0807102 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.5620 | 0.916726 | 0.458363 | − | 0.888765i | \(-0.348436\pi\) | ||||
0.458363 | + | 0.888765i | \(0.348436\pi\) | |||||||
\(368\) | 0.682495 | 0.0355775 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 2.99118i | − | 0.155504i | ||||||
\(371\) | − | 10.3575i | − | 0.537737i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.72130i | − | 0.399794i | −0.979817 | − | 0.199897i | \(-0.935939\pi\) | ||
0.979817 | − | 0.199897i | \(-0.0640607\pi\) | |||||||
\(374\) | 12.0275 | 0.621928 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.90784 | −0.149960 | ||||||||
\(377\) | −13.8035 | −0.710919 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.9842 | −0.872419 | −0.436210 | − | 0.899845i | \(-0.643679\pi\) | ||||
−0.436210 | + | 0.899845i | \(0.643679\pi\) | |||||||
\(380\) | −4.31143 | −0.221172 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.7825i | 0.960998i | ||||||||
\(383\) | −9.74547 | −0.497970 | −0.248985 | − | 0.968507i | \(-0.580097\pi\) | ||||
−0.248985 | + | 0.968507i | \(0.580097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.79381 | 0.142386 | ||||||||
\(386\) | −3.23686 | −0.164752 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 13.4837i | − | 0.684532i | ||||||
\(389\) | 24.1878i | 1.22637i | 0.789940 | + | 0.613184i | \(0.210112\pi\) | ||||
−0.789940 | + | 0.613184i | \(0.789888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.90606i | − | 0.0963938i | ||||||
\(392\) | 6.16028i | 0.311141i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.64258 | −0.485786 | ||||||||
\(395\) | 9.33743i | 0.469817i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.72413i | 0.337475i | 0.985661 | + | 0.168737i | \(0.0539689\pi\) | ||||
−0.985661 | + | 0.168737i | \(0.946031\pi\) | |||||||
\(398\) | 26.4561i | 1.32612i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.49883 | −0.224941 | ||||||||
\(401\) | 19.7180i | 0.984669i | 0.870406 | + | 0.492334i | \(0.163856\pi\) | ||||
−0.870406 | + | 0.492334i | \(0.836144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.35339i | 0.0674169i | ||||||||
\(404\) | 15.9010i | 0.791106i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.94816 | 0.146315 | ||||||||
\(407\) | −18.1965 | −0.901967 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.07773i | 0.448865i | 0.974490 | + | 0.224432i | \(0.0720528\pi\) | ||||
−0.974490 | + | 0.224432i | \(0.927947\pi\) | |||||||
\(410\) | −0.430111 | −0.0212417 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 9.59780i | − | 0.472850i | ||||||
\(413\) | 0.635452 | 0.0312686 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.374499i | 0.0183834i | ||||||||
\(416\) | 4.29049 | 0.210358 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.2281i | 1.28286i | ||||||||
\(419\) | 16.4153i | 0.801941i | 0.916091 | + | 0.400971i | \(0.131327\pi\) | ||||
−0.916091 | + | 0.400971i | \(0.868673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 37.0141i | − | 1.80396i | −0.431783 | − | 0.901978i | \(-0.642115\pi\) | ||
0.431783 | − | 0.901978i | \(-0.357885\pi\) | |||||||
\(422\) | 11.8071i | 0.574759i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.3029 | −0.548918 | ||||||||
\(425\) | 12.5643i | 0.609458i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.36373i | − | 0.404749i | ||||||
\(428\) | −13.2748 | −0.641663 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.770001i | 0.0371327i | ||||||||
\(431\) | 27.6342 | 1.33109 | 0.665545 | − | 0.746357i | \(-0.268199\pi\) | ||||
0.665545 | + | 0.746357i | \(0.268199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.2451 | −0.828747 | −0.414374 | − | 0.910107i | \(-0.635999\pi\) | ||||
−0.414374 | + | 0.910107i | \(0.635999\pi\) | |||||||
\(434\) | − | 0.289056i | − | 0.0138751i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.2315 | −0.681567 | ||||||||
\(437\) | 4.15650 | 0.198832 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.9404i | 1.52443i | 0.647323 | + | 0.762216i | \(0.275889\pi\) | ||||
−0.647323 | + | 0.762216i | \(0.724111\pi\) | |||||||
\(440\) | − | 3.04881i | − | 0.145346i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 11.9824i | − | 0.569946i | ||||||
\(443\) | − | 5.99899i | − | 0.285021i | −0.989793 | − | 0.142510i | \(-0.954483\pi\) | ||
0.989793 | − | 0.142510i | \(-0.0455174\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 3.84892i | − | 0.182456i | ||||||
\(446\) | −4.96135 | − | 14.0849i | −0.234927 | − | 0.666940i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.916361 | −0.0432940 | ||||||||
\(449\) | 13.1828 | 0.622134 | 0.311067 | − | 0.950388i | \(-0.399314\pi\) | ||||
0.311067 | + | 0.950388i | \(0.399314\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.61653i | 0.123208i | ||||||||
\(452\) | 19.8205 | 0.932277 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.13389 | 0.240945 | ||||||||
\(455\) | − | 2.78334i | − | 0.130485i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0199i | 0.609046i | 0.952505 | + | 0.304523i | \(0.0984971\pi\) | ||||
−0.952505 | + | 0.304523i | \(0.901503\pi\) | |||||||
\(458\) | 3.67624 | 0.171779 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.483161 | −0.0225275 | ||||||||
\(461\) | 2.85620i | 0.133026i | 0.997786 | + | 0.0665132i | \(0.0211875\pi\) | ||||
−0.997786 | + | 0.0665132i | \(0.978813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.8442 | −0.968712 | −0.484356 | − | 0.874871i | \(-0.660946\pi\) | ||||
−0.484356 | + | 0.874871i | \(0.660946\pi\) | |||||||
\(464\) | − | 3.21724i | − | 0.149357i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 2.85827i | − | 0.132407i | ||||||
\(467\) | 11.5277 | 0.533440 | 0.266720 | − | 0.963774i | \(-0.414060\pi\) | ||||
0.266720 | + | 0.963774i | \(0.414060\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11.8817i | − | 0.548646i | ||||||
\(470\) | 2.05856 | 0.0949541 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 0.693451i | − | 0.0319187i | ||||||
\(473\) | 4.68421 | 0.215380 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.3986 | −1.25713 | ||||||||
\(476\) | 2.55921i | 0.117301i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.3971 | −1.02442 | ||||||||
\(479\) | 1.79824i | 0.0821636i | 0.999156 | + | 0.0410818i | \(0.0130804\pi\) | ||||
−0.999156 | + | 0.0410818i | \(0.986920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1283i | 0.826579i | ||||||||
\(482\) | 27.8693i | 1.26941i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.54707 | −0.343049 | ||||||||
\(485\) | 9.54559i | 0.433443i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.1233 | −1.50096 | −0.750479 | − | 0.660894i | \(-0.770177\pi\) | ||||
−0.750479 | + | 0.660894i | \(0.770177\pi\) | |||||||
\(488\) | −9.12711 | −0.413165 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 4.36107i | − | 0.197013i | ||||||
\(491\) | −11.0600 | −0.499132 | −0.249566 | − | 0.968358i | \(-0.580288\pi\) | ||||
−0.249566 | + | 0.968358i | \(0.580288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.98509 | −0.404668 | ||||||||
\(494\) | 26.1298 | 1.17563 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.315439 | −0.0141636 | ||||||||
\(497\) | −6.55318 | −0.293951 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1514 | −1.03640 | −0.518200 | − | 0.855260i | \(-0.673398\pi\) | ||||
−0.518200 | + | 0.855260i | \(0.673398\pi\) | |||||||
\(500\) | 6.72454 | 0.300731 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.7690 | 0.971597 | ||||||||
\(503\) | 2.50969 | 0.111902 | 0.0559509 | − | 0.998434i | \(-0.482181\pi\) | ||||
0.0559509 | + | 0.998434i | \(0.482181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 11.2569i | − | 0.500924i | ||||||
\(506\) | 2.93925i | 0.130666i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.123444 | 0.00547696 | ||||||||
\(509\) | 0.432553i | 0.0191726i | 0.999954 | + | 0.00958628i | \(0.00305145\pi\) | ||||
−0.999954 | + | 0.00958628i | \(0.996949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.99595 | −0.0882955 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.0480 | 1.28125 | ||||||||
\(515\) | 6.79461i | 0.299406i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.5230i | − | 0.550760i | ||||||
\(518\) | − | 3.87183i | − | 0.170119i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.03738 | −0.133198 | ||||||||
\(521\) | 30.2220 | 1.32405 | 0.662026 | − | 0.749481i | \(-0.269697\pi\) | ||||
0.662026 | + | 0.749481i | \(0.269697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 29.5062i | − | 1.29022i | −0.764091 | − | 0.645108i | \(-0.776812\pi\) | ||
0.764091 | − | 0.645108i | \(-0.223188\pi\) | |||||||
\(524\) | 5.18225i | 0.226388i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 24.8682i | − | 1.08431i | ||||||
\(527\) | 0.880954i | 0.0383750i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5342 | −0.979748 | ||||||||
\(530\) | 8.00171 | 0.347572 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.58079 | −0.241958 | ||||||||
\(533\) | 2.60672 | 0.112910 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.39770 | 0.406298 | ||||||||
\(536\) | −12.9662 | −0.560053 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 9.76578i | − | 0.421033i | ||||||
\(539\) | −26.5301 | −1.14273 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 28.3366i | − | 1.21828i | −0.793061 | − | 0.609142i | \(-0.791514\pi\) | ||
0.793061 | − | 0.609142i | \(-0.208486\pi\) | |||||||
\(542\) | 7.60049 | 0.326469 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.79279 | 0.119740 | ||||||||
\(545\) | 10.0750 | 0.431565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.7429 | 1.35723 | 0.678615 | − | 0.734494i | \(-0.262580\pi\) | ||||
0.678615 | + | 0.734494i | \(0.262580\pi\) | |||||||
\(548\) | 9.58358 | 0.409390 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 19.3748i | − | 0.826144i | ||||||
\(551\) | − | 19.5935i | − | 0.834713i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0865i | 0.513971i | ||||||||
\(554\) | −20.1990 | −0.858173 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.2856 | 0.648256 | ||||||||
\(557\) | −19.9132 | −0.843747 | −0.421874 | − | 0.906655i | \(-0.638627\pi\) | ||||
−0.421874 | + | 0.906655i | \(0.638627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.66665i | − | 0.197378i | ||||||
\(560\) | 0.648723 | 0.0274136 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.43316 | 0.271366 | ||||||||
\(563\) | −21.6663 | −0.913124 | −0.456562 | − | 0.889692i | \(-0.650919\pi\) | ||||
−0.456562 | + | 0.889692i | \(0.650919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0316 | −0.590313 | ||||||||
\(566\) | 10.5196i | 0.442170i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.15131i | 0.300062i | ||||||||
\(569\) | −12.4174 | −0.520564 | −0.260282 | − | 0.965533i | \(-0.583816\pi\) | ||||
−0.260282 | + | 0.965533i | \(0.583816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.56438i | − | 0.0654672i | −0.999464 | − | 0.0327336i | \(-0.989579\pi\) | ||
0.999464 | − | 0.0327336i | \(-0.0104213\pi\) | |||||||
\(572\) | 18.4775i | 0.772585i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.556743 | −0.0232380 | ||||||||
\(575\) | −3.07043 | −0.128046 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.8990 | −0.870037 | −0.435019 | − | 0.900421i | \(-0.643258\pi\) | ||||
−0.435019 | + | 0.900421i | \(0.643258\pi\) | |||||||
\(578\) | 9.20032i | 0.382683i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.27760i | 0.0945720i | ||||||||
\(581\) | 0.484757i | 0.0201111i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 48.6774i | − | 2.01601i | ||||||
\(584\) | 2.17812i | 0.0901314i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.0197i | 0.827005i | ||||||||
\(587\) | 1.75943 | 0.0726195 | 0.0363097 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363097 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.92107 | −0.0791564 | ||||||||
\(590\) | 0.490918i | 0.0202108i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.22523 | −0.173656 | ||||||||
\(593\) | 10.5072 | 0.431479 | 0.215739 | − | 0.976451i | \(-0.430784\pi\) | ||||
0.215739 | + | 0.976451i | \(0.430784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.81175i | − | 0.0742744i | ||||||
\(596\) | −21.8677 | −0.895734 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.92823 | 0.119744 | ||||||||
\(599\) | 19.5031i | 0.796877i | 0.917195 | + | 0.398438i | \(0.130448\pi\) | ||||
−0.917195 | + | 0.398438i | \(0.869552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.6894i | 1.12947i | 0.825271 | + | 0.564736i | \(0.191022\pi\) | ||||
−0.825271 | + | 0.564736i | \(0.808978\pi\) | |||||||
\(602\) | 0.996702i | 0.0406225i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 12.3956i | − | 0.504370i | ||||||
\(605\) | 5.34283 | 0.217217 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.64182i | 0.350761i | 0.984501 | + | 0.175380i | \(0.0561155\pi\) | ||||
−0.984501 | + | 0.175380i | \(0.943884\pi\) | |||||||
\(608\) | 6.09016i | 0.246989i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.46139 | 0.261614 | ||||||||
\(611\) | −12.4760 | −0.504727 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.66647i | 0.269256i | 0.990896 | + | 0.134628i | \(0.0429840\pi\) | ||||
−0.990896 | + | 0.134628i | \(0.957016\pi\) | |||||||
\(614\) | −21.1982 | −0.855490 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 3.94643i | − | 0.159006i | ||||||
\(617\) | 28.1483i | 1.13321i | 0.823990 | + | 0.566604i | \(0.191743\pi\) | ||||
−0.823990 | + | 0.566604i | \(0.808257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.6495i | − | 1.15152i | −0.817619 | − | 0.575760i | \(-0.804706\pi\) | ||
0.817619 | − | 0.575760i | \(-0.195294\pi\) | |||||||
\(620\) | 0.223310 | 0.00896833 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.2673i | 1.09332i | ||||||||
\(623\) | − | 4.98211i | − | 0.199604i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.7336 | 0.709345 | ||||||||
\(626\) | −6.28652 | −0.251260 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 8.86184i | − | 0.353626i | ||||||
\(629\) | 11.8002i | 0.470504i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3640i | 1.28839i | 0.764861 | + | 0.644195i | \(0.222808\pi\) | ||||
−0.764861 | + | 0.644195i | \(0.777192\pi\) | |||||||
\(632\) | 13.1897 | 0.524658 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.6895 | −0.662826 | ||||||||
\(635\) | −0.0873904 | −0.00346798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4306i | 1.04722i | ||||||||
\(638\) | 13.8555 | 0.548544 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 0.707934i | − | 0.0279835i | ||||||
\(641\) | 41.7534 | 1.64916 | 0.824581 | − | 0.565744i | \(-0.191411\pi\) | ||||
0.824581 | + | 0.565744i | \(0.191411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.0838 | −1.38357 | −0.691785 | − | 0.722104i | \(-0.743175\pi\) | ||||
−0.691785 | + | 0.722104i | \(0.743175\pi\) | |||||||
\(644\) | −0.625412 | −0.0246447 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.0085 | 0.669192 | ||||||||
\(647\) | − | 13.9549i | − | 0.548622i | −0.961641 | − | 0.274311i | \(-0.911550\pi\) | ||
0.961641 | − | 0.274311i | \(-0.0884499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.98644 | 0.117228 | ||||||||
\(650\) | −19.3022 | −0.757094 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 11.6089i | − | 0.454639i | ||||||
\(653\) | −6.75889 | −0.264496 | −0.132248 | − | 0.991217i | \(-0.542220\pi\) | ||||
−0.132248 | + | 0.991217i | \(0.542220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.66869i | − | 0.143348i | ||||||
\(656\) | 0.607558i | 0.0237212i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.66463 | 0.103878 | ||||||||
\(659\) | − | 18.0530i | − | 0.703246i | −0.936142 | − | 0.351623i | \(-0.885630\pi\) | ||
0.936142 | − | 0.351623i | \(-0.114370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.8348i | 1.43271i | 0.697738 | + | 0.716353i | \(0.254190\pi\) | ||||
−0.697738 | + | 0.716353i | \(0.745810\pi\) | |||||||
\(662\) | 7.40295 | 0.287724 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.529002 | 0.0205293 | ||||||||
\(665\) | 3.95083 | 0.153207 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.19575i | − | 0.0850198i | ||||||
\(668\) | −20.0127 | −0.774316 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.17919 | 0.354623 | ||||||||
\(671\) | − | 39.3071i | − | 1.51743i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.13676 | 0.275102 | 0.137551 | − | 0.990495i | \(-0.456077\pi\) | ||||
0.137551 | + | 0.990495i | \(0.456077\pi\) | |||||||
\(674\) | 3.32095 | 0.127918 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.40829 | 0.208011 | ||||||||
\(677\) | 19.2900i | 0.741375i | 0.928758 | + | 0.370688i | \(0.120878\pi\) | ||||
−0.928758 | + | 0.370688i | \(0.879122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.3560i | 0.474178i | ||||||||
\(680\) | −1.97711 | −0.0758188 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1.35848i | − | 0.0520188i | ||||||
\(683\) | − | 20.6801i | − | 0.791300i | −0.918401 | − | 0.395650i | \(-0.870519\pi\) | ||
0.918401 | − | 0.395650i | \(-0.129481\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.78454 | −0.259224 | ||||||||
\(686\) | − | 12.0596i | − | 0.460437i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.08767 | 0.0414672 | ||||||||
\(689\) | −48.4950 | −1.84751 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 40.9355i | − | 1.55726i | −0.627484 | − | 0.778629i | \(-0.715915\pi\) | ||
0.627484 | − | 0.778629i | \(-0.284085\pi\) | |||||||
\(692\) | −6.40756 | −0.243579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.50543 | 0.0951047 | ||||||||
\(695\) | −10.8212 | −0.410473 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.69678 | 0.0642703 | ||||||||
\(698\) | 26.2768i | 0.994592i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.12255 | 0.155818 | ||||||||
\(701\) | 25.5815i | 0.966198i | 0.875566 | + | 0.483099i | \(0.160489\pi\) | ||||
−0.875566 | + | 0.483099i | \(0.839511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.7323 | −0.970513 | ||||||||
\(704\) | −4.30663 | −0.162312 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.0382 | −0.565969 | ||||||||
\(707\) | − | 14.5711i | − | 0.548002i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 38.1785i | − | 1.43383i | −0.697163 | − | 0.716913i | \(-0.745555\pi\) | ||
0.697163 | − | 0.716913i | \(-0.254445\pi\) | |||||||
\(710\) | − | 5.06266i | − | 0.189998i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.43684 | −0.203754 | ||||||||
\(713\) | −0.215285 | −0.00806249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 13.0809i | − | 0.489197i | ||||||
\(716\) | 26.6168i | 0.994715i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.25711 | 0.308153 | ||||||||
\(719\) | 35.1730i | 1.31173i | 0.754877 | + | 0.655866i | \(0.227696\pi\) | ||||
−0.754877 | + | 0.655866i | \(0.772304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.79505i | 0.327545i | ||||||||
\(722\) | 18.0901i | 0.673243i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.55228 | 0.243513 | ||||||||
\(725\) | 14.4738i | 0.537544i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.4730 | −0.573861 | −0.286930 | − | 0.957951i | \(-0.592635\pi\) | ||||
−0.286930 | + | 0.957951i | \(0.592635\pi\) | |||||||
\(728\) | −3.93164 | −0.145716 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 1.54197i | − | 0.0570708i | ||||||
\(731\) | − | 3.03764i | − | 0.112351i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.8853 | 0.734478 | 0.367239 | − | 0.930127i | \(-0.380303\pi\) | ||||
0.367239 | + | 0.930127i | \(0.380303\pi\) | |||||||
\(734\) | 17.5620i | 0.648223i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.682495i | 0.0251571i | ||||||||
\(737\) | − | 55.8405i | − | 2.05691i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.58935i | 0.168822i | 0.996431 | + | 0.0844109i | \(0.0269008\pi\) | ||||
−0.996431 | + | 0.0844109i | \(0.973099\pi\) | |||||||
\(740\) | 2.99118 | 0.109958 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.3575 | 0.380238 | ||||||||
\(743\) | 15.1401i | 0.555435i | 0.960663 | + | 0.277718i | \(0.0895780\pi\) | ||||
−0.960663 | + | 0.277718i | \(0.910422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.4809 | 0.567175 | ||||||||
\(746\) | 7.72130 | 0.282697 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.0275i | 0.439770i | ||||||||
\(749\) | 12.1645 | 0.444483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6214 | −0.460561 | −0.230280 | − | 0.973124i | \(-0.573964\pi\) | ||||
−0.230280 | + | 0.973124i | \(0.573964\pi\) | |||||||
\(752\) | − | 2.90784i | − | 0.106038i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 13.8035i | − | 0.502695i | ||||||
\(755\) | 8.77528i | 0.319365i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.4896i | 0.381252i | 0.981663 | + | 0.190626i | \(0.0610518\pi\) | ||||
−0.981663 | + | 0.190626i | \(0.938948\pi\) | |||||||
\(758\) | − | 16.9842i | − | 0.616893i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 4.31143i | − | 0.156392i | ||||||
\(761\) | −39.8663 | −1.44515 | −0.722576 | − | 0.691291i | \(-0.757042\pi\) | ||||
−0.722576 | + | 0.691291i | \(0.757042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0412 | 0.472125 | ||||||||
\(764\) | −18.7825 | −0.679528 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 9.74547i | − | 0.352118i | ||||||
\(767\) | − | 2.97525i | − | 0.107430i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.2287 | −1.66705 | −0.833525 | − | 0.552482i | \(-0.813681\pi\) | ||||
−0.833525 | + | 0.552482i | \(0.813681\pi\) | |||||||
\(770\) | 2.79381i | 0.100682i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 3.23686i | − | 0.116497i | ||||||
\(773\) | 24.9358 | 0.896878 | 0.448439 | − | 0.893813i | \(-0.351980\pi\) | ||||
0.448439 | + | 0.893813i | \(0.351980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.41910 | 0.0509757 | ||||||||
\(776\) | 13.4837 | 0.484037 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.1878 | −0.867173 | ||||||||
\(779\) | 3.70013i | 0.132571i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.7981 | −1.10204 | ||||||||
\(782\) | 1.90606 | 0.0681607 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.16028 | −0.220010 | ||||||||
\(785\) | 6.27360i | 0.223914i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.6326i | 1.30581i | 0.757439 | + | 0.652906i | \(0.226450\pi\) | ||||
−0.757439 | + | 0.652906i | \(0.773550\pi\) | |||||||
\(788\) | − | 9.64258i | − | 0.343503i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.33743 | −0.332211 | ||||||||
\(791\) | −18.1627 | −0.645792 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.1598 | −1.39060 | ||||||||
\(794\) | −6.72413 | −0.238631 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.4561 | −0.937711 | ||||||||
\(797\) | 28.5419i | 1.01101i | 0.862825 | + | 0.505503i | \(0.168693\pi\) | ||||
−0.862825 | + | 0.505503i | \(0.831307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.12098 | −0.287300 | ||||||||
\(800\) | − | 4.49883i | − | 0.159058i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.7180 | −0.696266 | ||||||||
\(803\) | −9.38037 | −0.331026 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.442750 | 0.0156049 | ||||||||
\(806\) | −1.35339 | −0.0476710 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.9010 | −0.559396 | ||||||||
\(809\) | −10.2364 | −0.359893 | −0.179946 | − | 0.983676i | \(-0.557592\pi\) | ||||
−0.179946 | + | 0.983676i | \(0.557592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.4382i | 0.577222i | 0.957446 | + | 0.288611i | \(0.0931934\pi\) | ||||
−0.957446 | + | 0.288611i | \(0.906807\pi\) | |||||||
\(812\) | 2.94816i | 0.103460i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 18.1965i | − | 0.637787i | ||||||
\(815\) | 8.21833i | 0.287875i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.62411 | 0.231748 | ||||||||
\(818\) | −9.07773 | −0.317395 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 0.430111i | − | 0.0150201i | ||||||
\(821\) | − | 18.1557i | − | 0.633640i | −0.948486 | − | 0.316820i | \(-0.897385\pi\) | ||
0.948486 | − | 0.316820i | \(-0.102615\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.0902i | 1.29288i | 0.762963 | + | 0.646442i | \(0.223744\pi\) | ||||
−0.762963 | + | 0.646442i | \(0.776256\pi\) | |||||||
\(824\) | 9.59780 | 0.334355 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.635452i | 0.0221102i | ||||||||
\(827\) | 27.4977 | 0.956188 | 0.478094 | − | 0.878309i | \(-0.341328\pi\) | ||||
0.478094 | + | 0.878309i | \(0.341328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 17.4292i | − | 0.605339i | −0.953096 | − | 0.302670i | \(-0.902122\pi\) | ||
0.953096 | − | 0.302670i | \(-0.0978779\pi\) | |||||||
\(830\) | −0.374499 | −0.0129990 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.29049i | 0.148746i | ||||||||
\(833\) | 17.2044i | 0.596096i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.1677 | 0.490293 | ||||||||
\(836\) | −26.2281 | −0.907117 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.4153 | −0.567058 | ||||||||
\(839\) | −23.2768 | −0.803605 | −0.401802 | − | 0.915726i | \(-0.631616\pi\) | ||||
−0.401802 | + | 0.915726i | \(0.631616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.6493 | 0.643081 | ||||||||
\(842\) | 37.0141 | 1.27559 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.8071 | −0.406416 | ||||||||
\(845\) | −3.82871 | −0.131712 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.91584 | 0.237631 | ||||||||
\(848\) | − | 11.3029i | − | 0.388143i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.5643 | −0.430952 | ||||||||
\(851\) | −2.88369 | −0.0988518 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.628999i | 0.0215365i | 0.999942 | + | 0.0107683i | \(0.00342771\pi\) | ||||
−0.999942 | + | 0.0107683i | \(0.996572\pi\) | |||||||
\(854\) | 8.36373 | 0.286201 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 13.2748i | − | 0.453724i | ||||||
\(857\) | − | 43.0666i | − | 1.47113i | −0.677455 | − | 0.735564i | \(-0.736917\pi\) | ||
0.677455 | − | 0.735564i | \(-0.263083\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.4684i | − | 0.459537i | −0.973245 | − | 0.229769i | \(-0.926203\pi\) | ||
0.973245 | − | 0.229769i | \(-0.0737969\pi\) | |||||||
\(860\) | −0.770001 | −0.0262568 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.6342i | 0.941223i | ||||||||
\(863\) | 51.8700 | 1.76568 | 0.882838 | − | 0.469677i | \(-0.155630\pi\) | ||||
0.882838 | + | 0.469677i | \(0.155630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.53613 | 0.154233 | ||||||||
\(866\) | − | 17.2451i | − | 0.586013i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.289056 | 0.00981119 | ||||||||
\(869\) | 56.8031i | 1.92691i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −55.6312 | −1.88499 | ||||||||
\(872\) | − | 14.2315i | − | 0.481941i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.15650i | 0.140596i | ||||||||
\(875\) | −6.16211 | −0.208317 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 25.2707i | − | 0.853332i | −0.904409 | − | 0.426666i | \(-0.859688\pi\) | ||
0.904409 | − | 0.426666i | \(-0.140312\pi\) | |||||||
\(878\) | −31.9404 | −1.07794 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.04881 | 0.102775 | ||||||||
\(881\) | 0.988956i | 0.0333188i | 0.999861 | + | 0.0166594i | \(0.00530309\pi\) | ||||
−0.999861 | + | 0.0166594i | \(0.994697\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 40.7149i | − | 1.37016i | −0.728466 | − | 0.685082i | \(-0.759766\pi\) | ||
0.728466 | − | 0.685082i | \(-0.240234\pi\) | |||||||
\(884\) | 11.9824 | 0.403013 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.99899 | 0.201540 | ||||||||
\(887\) | 6.62595i | 0.222478i | 0.993794 | + | 0.111239i | \(0.0354819\pi\) | ||||
−0.993794 | + | 0.111239i | \(0.964518\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.113120 | −0.00379391 | ||||||||
\(890\) | 3.84892 | 0.129016 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.0849 | − | 4.96135i | 0.471598 | − | 0.166118i | ||||
\(893\) | − | 17.7092i | − | 0.592616i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18.8429i | − | 0.629849i | ||||||
\(896\) | − | 0.916361i | − | 0.0306135i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.1828i | 0.439915i | ||||||||
\(899\) | 1.01484i | 0.0338469i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.5667 | −1.05164 | ||||||||
\(902\) | −2.61653 | −0.0871209 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.8205i | 0.659219i | ||||||||
\(905\) | −4.63858 | −0.154192 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.8346 | 0.725006 | 0.362503 | − | 0.931983i | \(-0.381922\pi\) | ||||
0.362503 | + | 0.931983i | \(0.381922\pi\) | |||||||
\(908\) | 5.13389i | 0.170374i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.78334 | 0.0922668 | ||||||||
\(911\) | − | 34.2519i | − | 1.13482i | −0.823437 | − | 0.567408i | \(-0.807946\pi\) | ||
0.823437 | − | 0.567408i | \(-0.192054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.27822i | 0.0753980i | ||||||||
\(914\) | −13.0199 | −0.430661 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.67624i | 0.121466i | ||||||||
\(917\) | − | 4.74882i | − | 0.156820i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.6498i | 0.912082i | 0.889959 | + | 0.456041i | \(0.150733\pi\) | ||||
−0.889959 | + | 0.456041i | \(0.849267\pi\) | |||||||
\(920\) | − | 0.483161i | − | 0.0159293i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.85620 | −0.0940639 | ||||||||
\(923\) | 30.6826i | 1.00993i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.0086 | 0.624998 | ||||||||
\(926\) | − | 20.8442i | − | 0.684983i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.21724 | 0.105611 | ||||||||
\(929\) | 42.1029i | 1.38135i | 0.723165 | + | 0.690675i | \(0.242687\pi\) | ||||
−0.723165 | + | 0.690675i | \(0.757313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.5171 | −1.22957 | ||||||||
\(932\) | 2.85827 | 0.0936259 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.5277i | 0.377199i | ||||||||
\(935\) | − | 8.51469i | − | 0.278460i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.7517i | − | 1.65799i | −0.559259 | − | 0.828993i | \(-0.688914\pi\) | ||
0.559259 | − | 0.828993i | \(-0.311086\pi\) | |||||||
\(938\) | 11.8817 | 0.387951 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.05856i | 0.0671427i | ||||||||
\(941\) | 36.8053i | 1.19982i | 0.800069 | + | 0.599909i | \(0.204796\pi\) | ||||
−0.800069 | + | 0.599909i | \(0.795204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.414655i | 0.0135030i | ||||||||
\(944\) | 0.693451 | 0.0225699 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.68421i | 0.152297i | ||||||||
\(947\) | − | 48.5280i | − | 1.57695i | −0.615068 | − | 0.788474i | \(-0.710871\pi\) | ||
0.615068 | − | 0.788474i | \(-0.289129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.34521i | 0.303358i | ||||||||
\(950\) | − | 27.3986i | − | 0.888928i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.55921 | −0.0829443 | ||||||||
\(953\) | 3.03657 | 0.0983642 | 0.0491821 | − | 0.998790i | \(-0.484339\pi\) | ||||
0.0491821 | + | 0.998790i | \(0.484339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.2968 | 0.430274 | ||||||||
\(956\) | − | 22.3971i | − | 0.724374i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.79824 | −0.0580985 | ||||||||
\(959\) | −8.78202 | −0.283586 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9005 | −0.996790 | ||||||||
\(962\) | −18.1283 | −0.584479 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27.8693 | −0.897609 | ||||||||
\(965\) | 2.29148i | 0.0737655i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.2896i | 1.26347i | 0.775186 | + | 0.631734i | \(0.217656\pi\) | ||||
−0.775186 | + | 0.631734i | \(0.782344\pi\) | |||||||
\(968\) | − | 7.54707i | − | 0.242572i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.54559 | −0.306490 | ||||||||
\(971\) | 60.2843 | 1.93461 | 0.967307 | − | 0.253608i | \(-0.0816174\pi\) | ||||
0.967307 | + | 0.253608i | \(0.0816174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0072 | −0.449050 | ||||||||
\(974\) | − | 33.1233i | − | 1.06134i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 9.12711i | − | 0.292152i | ||||||
\(977\) | −30.9667 | −0.990711 | −0.495356 | − | 0.868690i | \(-0.664962\pi\) | ||||
−0.495356 | + | 0.868690i | \(0.664962\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 23.4145i | − | 0.748330i | ||||||
\(980\) | 4.36107 | 0.139309 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 11.0600i | − | 0.352940i | ||||||
\(983\) | −8.84896 | −0.282238 | −0.141119 | − | 0.989993i | \(-0.545070\pi\) | ||||
−0.141119 | + | 0.989993i | \(0.545070\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.82631i | 0.217504i | ||||||||
\(986\) | − | 8.98509i | − | 0.286143i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.1298i | 0.831299i | ||||||||
\(989\) | 0.742331 | 0.0236048 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.1979i | 0.863968i | 0.901881 | + | 0.431984i | \(0.142186\pi\) | ||||
−0.901881 | + | 0.431984i | \(0.857814\pi\) | |||||||
\(992\) | − | 0.315439i | − | 0.0100152i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 6.55318i | − | 0.207854i | ||||||
\(995\) | 18.7292 | 0.593754 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.1564 | 1.65181 | 0.825905 | − | 0.563809i | \(-0.190665\pi\) | ||||
0.825905 | + | 0.563809i | \(0.190665\pi\) | |||||||
\(998\) | − | 23.1514i | − | 0.732845i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4014.2.d.a.4013.18 | yes | 72 | |
3.2 | odd | 2 | inner | 4014.2.d.a.4013.59 | yes | 72 | |
223.222 | odd | 2 | inner | 4014.2.d.a.4013.60 | yes | 72 | |
669.668 | even | 2 | inner | 4014.2.d.a.4013.17 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.d.a.4013.17 | ✓ | 72 | 669.668 | even | 2 | inner | |
4014.2.d.a.4013.18 | yes | 72 | 1.1 | even | 1 | trivial | |
4014.2.d.a.4013.59 | yes | 72 | 3.2 | odd | 2 | inner | |
4014.2.d.a.4013.60 | yes | 72 | 223.222 | odd | 2 | inner |