Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2700,2,Mod(593,2700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2700, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2700.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.j (of order \(4\), degree \(2\), 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: | \(21.5596085457\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.2 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2700.1457 |
Dual form | 2700.2.j.b.593.2 |
$q$-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 \(\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1351\) | \(2377\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000i | 0.904534i | 0.891883 | + | 0.452267i | \(0.149385\pi\) | ||||
−0.891883 | + | 0.452267i | \(0.850615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.22474 | − | 1.22474i | 0.339683 | − | 0.339683i | −0.516565 | − | 0.856248i | \(-0.672790\pi\) |
0.856248 | + | 0.516565i | \(0.172790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.67423 | + | 3.67423i | 0.766131 | + | 0.766131i | 0.977423 | − | 0.211292i | \(-0.0677671\pi\) |
−0.211292 | + | 0.977423i | \(0.567767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.22474 | − | 1.22474i | −0.201347 | − | 0.201347i | 0.599230 | − | 0.800577i | \(-0.295473\pi\) |
−0.800577 | + | 0.599230i | \(0.795473\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.44949 | + | 2.44949i | −0.373544 | + | 0.373544i | −0.868766 | − | 0.495222i | \(-0.835087\pi\) |
0.495222 | + | 0.868766i | \(0.335087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.67423 | − | 3.67423i | 0.535942 | − | 0.535942i | −0.386392 | − | 0.922335i | \(-0.626279\pi\) |
0.922335 | + | 0.386392i | \(0.126279\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.34847 | + | 7.34847i | 1.00939 | + | 1.00939i | 0.999955 | + | 0.00943438i | \(0.00300310\pi\) |
0.00943438 | + | 0.999955i | \(0.496997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | −0.390567 | −0.195283 | − | 0.980747i | \(-0.562563\pi\) | ||||
−0.195283 | + | 0.980747i | \(0.562563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.89898 | + | 4.89898i | 0.598506 | + | 0.598506i | 0.939915 | − | 0.341409i | \(-0.110904\pi\) |
−0.341409 | + | 0.939915i | \(0.610904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0000i | 1.78017i | 0.455792 | + | 0.890086i | \(0.349356\pi\) | ||||
−0.455792 | + | 0.890086i | \(0.650644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.89898 | + | 4.89898i | −0.573382 | + | 0.573382i | −0.933072 | − | 0.359690i | \(-0.882883\pi\) |
0.359690 | + | 0.933072i | \(0.382883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.34847 | + | 7.34847i | 0.806599 | + | 0.806599i | 0.984118 | − | 0.177518i | \(-0.0568069\pi\) |
−0.177518 | + | 0.984118i | \(0.556807\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.67423 | − | 3.67423i | −0.373062 | − | 0.373062i | 0.495529 | − | 0.868591i | \(-0.334974\pi\) |
−0.868591 | + | 0.495529i | \(0.834974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2474 | − | 12.2474i | 1.20678 | − | 1.20678i | 0.234712 | − | 0.972065i | \(-0.424585\pi\) |
0.972065 | − | 0.234712i | \(-0.0754147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.67423 | − | 3.67423i | 0.355202 | − | 0.355202i | −0.506839 | − | 0.862041i | \(-0.669186\pi\) |
0.862041 | + | 0.506839i | \(0.169186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000i | 0.957826i | 0.877862 | + | 0.478913i | \(0.158969\pi\) | ||||
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.34847 | + | 7.34847i | 0.691286 | + | 0.691286i | 0.962515 | − | 0.271229i | \(-0.0874301\pi\) |
−0.271229 | + | 0.962515i | \(0.587430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | − | 7.34847i | −0.652071 | − | 0.652071i | 0.301420 | − | 0.953491i | \(-0.402539\pi\) |
−0.953491 | + | 0.301420i | \(0.902539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0000i | 1.31056i | 0.755388 | + | 0.655278i | \(0.227449\pi\) | ||||
−0.755388 | + | 0.655278i | \(0.772551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.34847 | + | 7.34847i | −0.627822 | + | 0.627822i | −0.947520 | − | 0.319698i | \(-0.896419\pi\) |
0.319698 | + | 0.947520i | \(0.396419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.0000i | − | 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.67423 | + | 3.67423i | 0.307255 | + | 0.307255i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.79796 | + | 9.79796i | 0.781962 | + | 0.781962i | 0.980162 | − | 0.198199i | \(-0.0635094\pi\) |
−0.198199 | + | 0.980162i | \(0.563509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2474 | + | 12.2474i | −0.959294 | + | 0.959294i | −0.999203 | − | 0.0399091i | \(-0.987293\pi\) |
0.0399091 | + | 0.999203i | \(0.487293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0227 | − | 11.0227i | 0.852962 | − | 0.852962i | −0.137535 | − | 0.990497i | \(-0.543918\pi\) |
0.990497 | + | 0.137535i | \(0.0439178\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0000i | 0.769231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.6969 | + | 14.6969i | 1.11739 | + | 1.11739i | 0.992123 | + | 0.125264i | \(0.0399778\pi\) |
0.125264 | + | 0.992123i | \(0.460022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | 0.224231 | 0.112115 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112115 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00000 | 0.0743294 | 0.0371647 | − | 0.999309i | \(-0.488167\pi\) | ||||
0.0371647 | + | 0.999309i | \(0.488167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000i | 0.868290i | 0.900843 | + | 0.434145i | \(0.142949\pi\) | ||||
−0.900843 | + | 0.434145i | \(0.857051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6969 | − | 14.6969i | 1.05791 | − | 1.05791i | 0.0596919 | − | 0.998217i | \(-0.480988\pi\) |
0.998217 | − | 0.0596919i | \(-0.0190118\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000i | 0.708881i | 0.935079 | + | 0.354441i | \(0.115329\pi\) | ||||
−0.935079 | + | 0.354441i | \(0.884671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.2474 | + | 12.2474i | −0.820150 | + | 0.820150i | −0.986129 | − | 0.165979i | \(-0.946921\pi\) |
0.165979 | + | 0.986129i | \(0.446921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0227 | − | 11.0227i | 0.731603 | − | 0.731603i | −0.239335 | − | 0.970937i | \(-0.576929\pi\) |
0.970937 | + | 0.239335i | \(0.0769293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.0000i | − | 1.65205i | −0.563636 | − | 0.826023i | \(-0.690598\pi\) | ||
0.563636 | − | 0.826023i | \(-0.309402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.00000 | 0.582162 | 0.291081 | − | 0.956698i | \(-0.405985\pi\) | ||||
0.291081 | + | 0.956698i | \(0.405985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | −0.837404 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.44949 | + | 2.44949i | 0.155857 | + | 0.155857i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00000i | 0.568075i | 0.958813 | + | 0.284037i | \(0.0916740\pi\) | ||||
−0.958813 | + | 0.284037i | \(0.908326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0227 | + | 11.0227i | −0.692991 | + | 0.692991i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6969 | + | 14.6969i | −0.916770 | + | 0.916770i | −0.996793 | − | 0.0800232i | \(-0.974501\pi\) |
0.0800232 | + | 0.996793i | \(0.474501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.67423 | − | 3.67423i | −0.226563 | − | 0.226563i | 0.584692 | − | 0.811255i | \(-0.301215\pi\) |
−0.811255 | + | 0.584692i | \(0.801215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.79796 | − | 9.79796i | −0.588702 | − | 0.588702i | 0.348578 | − | 0.937280i | \(-0.386665\pi\) |
−0.937280 | + | 0.348578i | \(0.886665\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.1464 | − | 17.1464i | 1.01925 | − | 1.01925i | 0.0194383 | − | 0.999811i | \(-0.493812\pi\) |
0.999811 | − | 0.0194383i | \(-0.00618779\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.00000 | 0.520483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.2474 | − | 12.2474i | −0.698999 | − | 0.698999i | 0.265196 | − | 0.964195i | \(-0.414563\pi\) |
−0.964195 | + | 0.265196i | \(0.914563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000i | 0.170114i | 0.996376 | + | 0.0850572i | \(0.0271073\pi\) | ||||
−0.996376 | + | 0.0850572i | \(0.972893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.89898 | + | 4.89898i | −0.276907 | + | 0.276907i | −0.831873 | − | 0.554966i | \(-0.812731\pi\) |
0.554966 | + | 0.831873i | \(0.312731\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.34847 | + | 7.34847i | −0.412731 | + | 0.412731i | −0.882689 | − | 0.469958i | \(-0.844269\pi\) |
0.469958 | + | 0.882689i | \(0.344269\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 18.0000i | − | 1.00781i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | 0.769510 | 0.384755 | − | 0.923019i | \(-0.374286\pi\) | ||||
0.384755 | + | 0.923019i | \(0.374286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.4949 | + | 24.4949i | 1.33432 | + | 1.33432i | 0.901460 | + | 0.432862i | \(0.142496\pi\) |
0.432862 | + | 0.901460i | \(0.357504\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.00000i | − | 0.324918i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.34847 | − | 7.34847i | 0.394486 | − | 0.394486i | −0.481797 | − | 0.876283i | \(-0.660016\pi\) |
0.876283 | + | 0.481797i | \(0.160016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000i | 0.749403i | 0.927146 | + | 0.374701i | \(0.122255\pi\) | ||||
−0.927146 | + | 0.374701i | \(0.877745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.0454 | − | 22.0454i | −1.17336 | − | 1.17336i | −0.981404 | − | 0.191955i | \(-0.938517\pi\) |
−0.191955 | − | 0.981404i | \(-0.561483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.0000 | 1.10834 | 0.554169 | − | 0.832404i | \(-0.313036\pi\) | ||||
0.554169 | + | 0.832404i | \(0.313036\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.79796 | + | 9.79796i | 0.511449 | + | 0.511449i | 0.914970 | − | 0.403521i | \(-0.132214\pi\) |
−0.403521 | + | 0.914970i | \(0.632214\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6969 | − | 14.6969i | 0.760979 | − | 0.760979i | −0.215521 | − | 0.976499i | \(-0.569145\pi\) |
0.976499 | + | 0.215521i | \(0.0691449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.34847 | + | 7.34847i | −0.378465 | + | 0.378465i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0000i | 1.33553i | 0.744372 | + | 0.667765i | \(0.232749\pi\) | ||||
−0.744372 | + | 0.667765i | \(0.767251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.67423 | − | 3.67423i | −0.187745 | − | 0.187745i | 0.606976 | − | 0.794720i | \(-0.292383\pi\) |
−0.794720 | + | 0.606976i | \(0.792383\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4722 | − | 13.4722i | −0.676150 | − | 0.676150i | 0.282977 | − | 0.959127i | \(-0.408678\pi\) |
−0.959127 | + | 0.282977i | \(0.908678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 36.0000i | − | 1.79775i | −0.438201 | − | 0.898877i | \(-0.644384\pi\) | ||
0.438201 | − | 0.898877i | \(-0.355616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.44949 | + | 2.44949i | −0.122018 | + | 0.122018i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.67423 | − | 3.67423i | 0.182125 | − | 0.182125i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.0000i | − | 1.23617i | −0.786111 | − | 0.618085i | \(-0.787909\pi\) | ||
0.786111 | − | 0.618085i | \(-0.212091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.0000 | 1.75872 | 0.879358 | − | 0.476162i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476162i | \(0.157972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | −0.243685 | −0.121843 | − | 0.992549i | \(-0.538880\pi\) | ||||
−0.121843 | + | 0.992549i | \(0.538880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.0000i | − | 1.01153i | −0.862670 | − | 0.505767i | \(-0.831209\pi\) | ||
0.862670 | − | 0.505767i | \(-0.168791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.9217 | + | 15.9217i | −0.765147 | + | 0.765147i | −0.977248 | − | 0.212101i | \(-0.931970\pi\) |
0.212101 | + | 0.977248i | \(0.431970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.34847 | + | 7.34847i | −0.351525 | + | 0.351525i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000i | 0.190910i | 0.995434 | + | 0.0954548i | \(0.0304305\pi\) | ||||
−0.995434 | + | 0.0954548i | \(0.969569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.3712 | − | 18.3712i | −0.872841 | − | 0.872841i | 0.119940 | − | 0.992781i | \(-0.461730\pi\) |
−0.992781 | + | 0.119940i | \(0.961730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.7196 | − | 25.7196i | −1.20311 | − | 1.20311i | −0.973214 | − | 0.229900i | \(-0.926160\pi\) |
−0.229900 | − | 0.973214i | \(-0.573840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.0000i | − | 0.558896i | −0.960161 | − | 0.279448i | \(-0.909849\pi\) | ||
0.960161 | − | 0.279448i | \(-0.0901514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.1464 | − | 17.1464i | 0.796862 | − | 0.796862i | −0.185737 | − | 0.982599i | \(-0.559467\pi\) |
0.982599 | + | 0.185737i | \(0.0594674\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.0227 | − | 11.0227i | 0.510070 | − | 0.510070i | −0.404478 | − | 0.914548i | \(-0.632547\pi\) |
0.914548 | + | 0.404478i | \(0.132547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.34847 | − | 7.34847i | −0.337883 | − | 0.337883i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | −0.136788 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.89898 | + | 4.89898i | 0.221994 | + | 0.221994i | 0.809338 | − | 0.587344i | \(-0.199826\pi\) |
−0.587344 | + | 0.809338i | \(0.699826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.0000i | − | 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.0000i | − | 0.895323i | −0.894203 | − | 0.447661i | \(-0.852257\pi\) | ||
0.894203 | − | 0.447661i | \(-0.147743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.0454 | − | 22.0454i | −0.982956 | − | 0.982956i | 0.0169010 | − | 0.999857i | \(-0.494620\pi\) |
−0.999857 | + | 0.0169010i | \(0.994620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0227 | + | 11.0227i | 0.484778 | + | 0.484778i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 36.0000i | − | 1.57719i | −0.614914 | − | 0.788594i | \(-0.710809\pi\) | ||
0.614914 | − | 0.788594i | \(-0.289191\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.6969 | + | 14.6969i | −0.642652 | + | 0.642652i | −0.951207 | − | 0.308554i | \(-0.900155\pi\) |
0.308554 | + | 0.951207i | \(0.400155\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.00000i | 0.173913i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.34847 | + | 7.34847i | 0.318298 | + | 0.318298i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.0000 | 0.904534 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0000 | 0.472927 | 0.236463 | − | 0.971640i | \(-0.424012\pi\) | ||||
0.236463 | + | 0.971640i | \(0.424012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5959 | + | 19.5959i | 0.837861 | + | 0.837861i | 0.988577 | − | 0.150716i | \(-0.0481579\pi\) |
−0.150716 | + | 0.988577i | \(0.548158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.3939 | + | 29.3939i | −1.24546 | + | 1.24546i | −0.287754 | + | 0.957704i | \(0.592909\pi\) |
−0.957704 | + | 0.287754i | \(0.907091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.00000i | 0.253773i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.3712 | − | 18.3712i | −0.774253 | − | 0.774253i | 0.204594 | − | 0.978847i | \(-0.434413\pi\) |
−0.978847 | + | 0.204594i | \(0.934413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.67423 | + | 3.67423i | 0.152960 | + | 0.152960i | 0.779439 | − | 0.626478i | \(-0.215504\pi\) |
−0.626478 | + | 0.779439i | \(0.715504\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.0454 | + | 22.0454i | −0.913027 | + | 0.913027i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.34847 | + | 7.34847i | −0.303304 | + | 0.303304i | −0.842305 | − | 0.539001i | \(-0.818802\pi\) |
0.539001 | + | 0.842305i | \(0.318802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.00000i | − | 0.164817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.3939 | − | 29.3939i | −1.20706 | − | 1.20706i | −0.971974 | − | 0.235088i | \(-0.924462\pi\) |
−0.235088 | − | 0.971974i | \(-0.575538\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.00000 | −0.203954 | −0.101977 | − | 0.994787i | \(-0.532517\pi\) | ||||
−0.101977 | + | 0.994787i | \(0.532517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.44949 | + | 2.44949i | 0.0994217 | + | 0.0994217i | 0.755068 | − | 0.655646i | \(-0.227604\pi\) |
−0.655646 | + | 0.755068i | \(0.727604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 9.00000i | − | 0.364101i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.12372 | + | 6.12372i | −0.247335 | + | 0.247335i | −0.819876 | − | 0.572541i | \(-0.805958\pi\) |
0.572541 | + | 0.819876i | \(0.305958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.34847 | + | 7.34847i | −0.295838 | + | 0.295838i | −0.839381 | − | 0.543543i | \(-0.817082\pi\) |
0.543543 | + | 0.839381i | \(0.317082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000i | 0.401934i | 0.979598 | + | 0.200967i | \(0.0644084\pi\) | ||||
−0.979598 | + | 0.200967i | \(0.935592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0000 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.57321 | − | 8.57321i | −0.339683 | − | 0.339683i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 48.0000i | − | 1.89589i | −0.318440 | − | 0.947943i | \(-0.603159\pi\) | ||
0.318440 | − | 0.947943i | \(-0.396841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0454 | − | 22.0454i | 0.869386 | − | 0.869386i | −0.123018 | − | 0.992404i | \(-0.539257\pi\) |
0.992404 | + | 0.123018i | \(0.0392574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.7196 | − | 25.7196i | 1.01114 | − | 1.01114i | 0.0112063 | − | 0.999937i | \(-0.496433\pi\) |
0.999937 | − | 0.0112063i | \(-0.00356714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.00000i | − | 0.353281i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.6969 | − | 14.6969i | −0.575136 | − | 0.575136i | 0.358423 | − | 0.933559i | \(-0.383314\pi\) |
−0.933559 | + | 0.358423i | \(0.883314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.0000 | 0.972387 | 0.486194 | − | 0.873851i | \(-0.338385\pi\) | ||||
0.486194 | + | 0.873851i | \(0.338385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.0454 | − | 22.0454i | −0.853602 | − | 0.853602i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.00000i | − | 0.115814i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.8207 | − | 20.8207i | 0.802578 | − | 0.802578i | −0.180920 | − | 0.983498i | \(-0.557908\pi\) |
0.983498 | + | 0.180920i | \(0.0579076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.34847 | + | 7.34847i | −0.282425 | + | 0.282425i | −0.834075 | − | 0.551651i | \(-0.813998\pi\) |
0.551651 | + | 0.834075i | \(0.313998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.67423 | − | 3.67423i | −0.140591 | − | 0.140591i | 0.633309 | − | 0.773899i | \(-0.281696\pi\) |
−0.773899 | + | 0.633309i | \(0.781696\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | 0.685745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.0000 | 1.74992 | 0.874961 | − | 0.484193i | \(-0.160887\pi\) | ||||
0.874961 | + | 0.484193i | \(0.160887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000i | 0.453234i | 0.973984 | + | 0.226617i | \(0.0727665\pi\) | ||||
−0.973984 | + | 0.226617i | \(0.927233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.44949 | − | 2.44949i | 0.0923843 | − | 0.0923843i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.00000i | − | 0.0375558i | −0.999824 | − | 0.0187779i | \(-0.994022\pi\) | ||
0.999824 | − | 0.0187779i | \(-0.00597754\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.34847 | − | 7.34847i | −0.275202 | − | 0.275202i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | −0.111881 | −0.0559406 | − | 0.998434i | \(-0.517816\pi\) | ||||
−0.0559406 | + | 0.998434i | \(0.517816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.89898 | − | 4.89898i | −0.181693 | − | 0.181693i | 0.610400 | − | 0.792093i | \(-0.291009\pi\) |
−0.792093 | + | 0.610400i | \(0.791009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.67423 | − | 3.67423i | 0.135711 | − | 0.135711i | −0.635988 | − | 0.771699i | \(-0.719407\pi\) |
0.771699 | + | 0.635988i | \(0.219407\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.6969 | + | 14.6969i | −0.541369 | + | 0.541369i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000i | 0.735712i | 0.929883 | + | 0.367856i | \(0.119908\pi\) | ||||
−0.929883 | + | 0.367856i | \(0.880092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.3712 | − | 18.3712i | −0.673973 | − | 0.673973i | 0.284657 | − | 0.958630i | \(-0.408120\pi\) |
−0.958630 | + | 0.284657i | \(0.908120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0000 | −0.729810 | −0.364905 | − | 0.931045i | \(-0.618899\pi\) | ||||
−0.364905 | + | 0.931045i | \(0.618899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3712 | + | 18.3712i | 0.667712 | + | 0.667712i | 0.957186 | − | 0.289474i | \(-0.0934804\pi\) |
−0.289474 | + | 0.957186i | \(0.593480\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 42.0000i | − | 1.52250i | −0.648459 | − | 0.761249i | \(-0.724586\pi\) | ||
0.648459 | − | 0.761249i | \(-0.275414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.67423 | + | 3.67423i | −0.132669 | + | 0.132669i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.00000i | − | 0.0721218i | −0.999350 | − | 0.0360609i | \(-0.988519\pi\) | ||
0.999350 | − | 0.0360609i | \(-0.0114810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.0454 | + | 22.0454i | 0.792918 | + | 0.792918i | 0.981968 | − | 0.189049i | \(-0.0605406\pi\) |
−0.189049 | + | 0.981968i | \(0.560541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0000 | −0.429945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.0000 | −1.61023 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.6969 | − | 14.6969i | −0.523889 | − | 0.523889i | 0.394854 | − | 0.918744i | \(-0.370795\pi\) |
−0.918744 | + | 0.394854i | \(0.870795\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.22474 | + | 1.22474i | −0.0434920 | + | 0.0434920i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0454 | − | 22.0454i | 0.780888 | − | 0.780888i | −0.199092 | − | 0.979981i | \(-0.563799\pi\) |
0.979981 | + | 0.199092i | \(0.0637994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.6969 | − | 14.6969i | −0.518644 | − | 0.518644i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.89898 | − | 4.89898i | −0.171394 | − | 0.171394i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000i | 0.209401i | 0.994504 | + | 0.104701i | \(0.0333885\pi\) | ||||
−0.994504 | + | 0.104701i | \(0.966612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2474 | + | 12.2474i | −0.426919 | + | 0.426919i | −0.887578 | − | 0.460658i | \(-0.847613\pi\) |
0.460658 | + | 0.887578i | \(0.347613\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.0227 | − | 11.0227i | 0.383297 | − | 0.383297i | −0.488992 | − | 0.872289i | \(-0.662635\pi\) |
0.872289 | + | 0.488992i | \(0.162635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0000i | 0.590434i | 0.955430 | + | 0.295217i | \(0.0953920\pi\) | ||||
−0.955430 | + | 0.295217i | \(0.904608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0000 | 0.517858 | 0.258929 | − | 0.965896i | \(-0.416631\pi\) | ||||
0.258929 | + | 0.965896i | \(0.416631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 9.00000i | − | 0.308516i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.22474 | − | 1.22474i | 0.0419345 | − | 0.0419345i | −0.685829 | − | 0.727763i | \(-0.740560\pi\) |
0.727763 | + | 0.685829i | \(0.240560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.6969 | + | 14.6969i | −0.502038 | + | 0.502038i | −0.912071 | − | 0.410033i | \(-0.865517\pi\) |
0.410033 | + | 0.912071i | \(0.365517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.00000i | − | 0.0682391i | −0.999418 | − | 0.0341196i | \(-0.989137\pi\) | ||
0.999418 | − | 0.0341196i | \(-0.0108627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.34847 | + | 7.34847i | 0.250145 | + | 0.250145i | 0.821030 | − | 0.570885i | \(-0.193400\pi\) |
−0.570885 | + | 0.821030i | \(0.693400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | −0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.0681 | + | 33.0681i | 1.11663 | + | 1.11663i | 0.992232 | + | 0.124398i | \(0.0397001\pi\) |
0.124398 | + | 0.992232i | \(0.460300\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24.0000i | − | 0.808581i | −0.914631 | − | 0.404290i | \(-0.867519\pi\) | ||
0.914631 | − | 0.404290i | \(-0.132481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.6969 | − | 14.6969i | 0.494591 | − | 0.494591i | −0.415158 | − | 0.909749i | \(-0.636274\pi\) |
0.909749 | + | 0.415158i | \(0.136274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.0227 | + | 11.0227i | −0.370106 | + | 0.370106i | −0.867516 | − | 0.497410i | \(-0.834285\pi\) |
0.497410 | + | 0.867516i | \(0.334285\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.34847 | + | 7.34847i | 0.245907 | + | 0.245907i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.8434 | + | 31.8434i | 1.05734 | + | 1.05734i | 0.998253 | + | 0.0590889i | \(0.0188195\pi\) |
0.0590889 | + | 0.998253i | \(0.481180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0000i | 0.496972i | 0.968635 | + | 0.248486i | \(0.0799330\pi\) | ||||
−0.968635 | + | 0.248486i | \(0.920067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.0454 | + | 22.0454i | −0.729597 | + | 0.729597i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 46.0000i | − | 1.51740i | −0.651440 | − | 0.758700i | \(-0.725835\pi\) | ||
0.651440 | − | 0.758700i | \(-0.274165\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.3712 | + | 18.3712i | 0.604695 | + | 0.604695i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0000 | 0.458831 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.0227 | − | 11.0227i | −0.360096 | − | 0.360096i | 0.503752 | − | 0.863848i | \(-0.331952\pi\) |
−0.863848 | + | 0.503752i | \(0.831952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.0000i | 1.17357i | 0.809744 | + | 0.586783i | \(0.199606\pi\) | ||||
−0.809744 | + | 0.586783i | \(0.800394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.0454 | + | 22.0454i | −0.717897 | + | 0.717897i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.0454 | − | 22.0454i | 0.716379 | − | 0.716379i | −0.251482 | − | 0.967862i | \(-0.580918\pi\) |
0.967862 | + | 0.251482i | \(0.0809181\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000i | 0.389536i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.3939 | − | 29.3939i | −0.952161 | − | 0.952161i | 0.0467458 | − | 0.998907i | \(-0.485115\pi\) |
−0.998907 | + | 0.0467458i | \(0.985115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.2929 | − | 34.2929i | −1.10278 | − | 1.10278i | −0.994073 | − | 0.108710i | \(-0.965328\pi\) |
−0.108710 | − | 0.994073i | \(-0.534672\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.00000i | 0.0962746i | 0.998841 | + | 0.0481373i | \(0.0153285\pi\) | ||||
−0.998841 | + | 0.0481373i | \(0.984672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.6969 | + | 14.6969i | −0.470197 | + | 0.470197i | −0.901978 | − | 0.431782i | \(-0.857885\pi\) |
0.431782 | + | 0.901978i | \(0.357885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 36.0000i | − | 1.15056i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.67423 | + | 3.67423i | 0.117190 | + | 0.117190i | 0.763270 | − | 0.646080i | \(-0.223593\pi\) |
−0.646080 | + | 0.763270i | \(0.723593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0000 | −0.572367 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.0000 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0681 | − | 33.0681i | −1.04728 | − | 1.04728i | −0.998826 | − | 0.0484521i | \(-0.984571\pi\) |
−0.0484521 | − | 0.998826i | \(-0.515429\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2700.2.j.b.1457.2 | yes | 4 | |
3.2 | odd | 2 | 2700.2.j.h.1457.2 | yes | 4 | ||
5.2 | odd | 4 | 2700.2.j.h.593.1 | yes | 4 | ||
5.3 | odd | 4 | 2700.2.j.h.593.2 | yes | 4 | ||
5.4 | even | 2 | inner | 2700.2.j.b.1457.1 | yes | 4 | |
15.2 | even | 4 | inner | 2700.2.j.b.593.1 | ✓ | 4 | |
15.8 | even | 4 | inner | 2700.2.j.b.593.2 | yes | 4 | |
15.14 | odd | 2 | 2700.2.j.h.1457.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2700.2.j.b.593.1 | ✓ | 4 | 15.2 | even | 4 | inner | |
2700.2.j.b.593.2 | yes | 4 | 15.8 | even | 4 | inner | |
2700.2.j.b.1457.1 | yes | 4 | 5.4 | even | 2 | inner | |
2700.2.j.b.1457.2 | yes | 4 | 1.1 | even | 1 | trivial | |
2700.2.j.h.593.1 | yes | 4 | 5.2 | odd | 4 | ||
2700.2.j.h.593.2 | yes | 4 | 5.3 | odd | 4 | ||
2700.2.j.h.1457.1 | yes | 4 | 15.14 | odd | 2 | ||
2700.2.j.h.1457.2 | yes | 4 | 3.2 | odd | 2 |