Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4680,2,Mod(2809,4680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4680.2809");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4680.l (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: | \(37.3699881460\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2809.2 | ||
Root | \(1.32001 + 1.32001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4680.2809 |
Dual form | 4680.2.l.e.2809.1 |
$q$-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 \(\left(\mathbb{Z}/4680\mathbb{Z}\right)^\times\).
\(n\) | \(937\) | \(1081\) | \(2081\) | \(2341\) | \(3511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.32001 | + | 1.80487i | −0.590327 | + | 0.807164i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.64002 | 1.39902 | 0.699510 | − | 0.714623i | \(-0.253402\pi\) | ||||
0.699510 | + | 0.714623i | \(0.253402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24977i | 1.03072i | 0.856974 | + | 0.515360i | \(0.172342\pi\) | ||||
−0.856974 | + | 0.515360i | \(0.827658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.24977 | 1.43380 | 0.716898 | − | 0.697178i | \(-0.245561\pi\) | ||||
0.716898 | + | 0.697178i | \(0.245561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.24977i | − | 0.469110i | −0.972103 | − | 0.234555i | \(-0.924637\pi\) | ||
0.972103 | − | 0.234555i | \(-0.0753632\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.51514 | − | 4.76491i | −0.303028 | − | 0.952982i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.21949 | −1.71202 | −0.856009 | − | 0.516962i | \(-0.827063\pi\) | ||||
−0.856009 | + | 0.516962i | \(0.827063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.28005 | 1.66675 | 0.833373 | − | 0.552711i | \(-0.186407\pi\) | ||||
0.833373 | + | 0.552711i | \(0.186407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.28005i | − | 1.19683i | −0.801185 | − | 0.598416i | \(-0.795797\pi\) | ||
0.801185 | − | 0.598416i | \(-0.204203\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.67030 | 0.885552 | 0.442776 | − | 0.896632i | \(-0.353994\pi\) | ||||
0.442776 | + | 0.896632i | \(0.353994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.24977i | − | 0.648084i | −0.946043 | − | 0.324042i | \(-0.894958\pi\) | ||
0.946043 | − | 0.324042i | \(-0.105042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.88979i | 0.421520i | 0.977538 | + | 0.210760i | \(0.0675938\pi\) | ||||
−0.977538 | + | 0.210760i | \(0.932406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.21949i | 1.26639i | 0.773990 | + | 0.633197i | \(0.218258\pi\) | ||||
−0.773990 | + | 0.633197i | \(0.781742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.12489 | + | 8.37466i | −0.825879 | + | 1.12924i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.92007 | 0.770728 | 0.385364 | − | 0.922765i | \(-0.374076\pi\) | ||||
0.385364 | + | 0.922765i | \(0.374076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.969724 | 0.124160 | 0.0620802 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620802 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.80487 | − | 1.32001i | −0.223867 | − | 0.163727i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.93945i | 0.236941i | 0.992958 | + | 0.118471i | \(0.0377991\pi\) | ||||
−0.992958 | + | 0.118471i | \(0.962201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.60975 | −0.665755 | −0.332877 | − | 0.942970i | \(-0.608019\pi\) | ||||
−0.332877 | + | 0.942970i | \(0.608019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.5601i | − | 1.47005i | −0.678041 | − | 0.735024i | \(-0.737171\pi\) | ||
0.678041 | − | 0.735024i | \(-0.262829\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.2498 | −1.37821 | −0.689103 | − | 0.724663i | \(-0.741995\pi\) | ||||
−0.689103 | + | 0.724663i | \(0.741995\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.67030i | 0.402868i | 0.979502 | + | 0.201434i | \(0.0645601\pi\) | ||||
−0.979502 | + | 0.201434i | \(0.935440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.67030 | − | 5.60975i | −0.831961 | − | 0.608463i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.67030 | −1.02505 | −0.512525 | − | 0.858672i | \(-0.671290\pi\) | ||||
−0.512525 | + | 0.858672i | \(0.671290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.24977 | + | 11.2800i | −0.846409 | + | 1.15731i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.2800 | 1.52042 | 0.760211 | − | 0.649677i | \(-0.225096\pi\) | ||||
0.760211 | + | 0.649677i | \(0.225096\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21949i | 0.120160i | 0.998194 | + | 0.0600802i | \(0.0191356\pi\) | ||||
−0.998194 | + | 0.0600802i | \(0.980864\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.28005i | − | 0.510441i | −0.966883 | − | 0.255221i | \(-0.917852\pi\) | ||
0.966883 | − | 0.255221i | \(-0.0821481\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1892 | 0.975950 | 0.487975 | − | 0.872858i | \(-0.337736\pi\) | ||||
0.487975 | + | 0.872858i | \(0.337736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.03028i | − | 0.0969202i | −0.998825 | − | 0.0484601i | \(-0.984569\pi\) | ||
0.998825 | − | 0.0484601i | \(-0.0154314\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.06055 | + | 2.96972i | 0.378648 | + | 0.276928i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5298 | 0.957256 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6001 | + | 3.55510i | 0.948098 | + | 0.317978i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0303i | 0.978779i | 0.872065 | + | 0.489389i | \(0.162780\pi\) | ||||
−0.872065 | + | 0.489389i | \(0.837220\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.21949 | −0.630770 | −0.315385 | − | 0.948964i | \(-0.602134\pi\) | ||||
−0.315385 | + | 0.948964i | \(0.602134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.10929i | 0.692823i | 0.938083 | + | 0.346412i | \(0.112600\pi\) | ||||
−0.938083 | + | 0.346412i | \(0.887400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0596 | 1.61662 | 0.808309 | − | 0.588759i | \(-0.200383\pi\) | ||||
0.808309 | + | 0.588759i | \(0.200383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.64002i | 0.388018i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.1698 | − | 16.6400i | 1.01065 | − | 1.38188i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.92007 | 0.321145 | 0.160572 | − | 0.987024i | \(-0.448666\pi\) | ||||
0.160572 | + | 0.987024i | \(0.448666\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.7796 | 1.77240 | 0.886199 | − | 0.463305i | \(-0.153337\pi\) | ||||
0.886199 | + | 0.463305i | \(0.153337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.2498 | + | 16.7493i | −0.983925 | + | 1.34534i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.5904i | 1.72310i | 0.507673 | + | 0.861550i | \(0.330506\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.28005i | 0.100261i | 0.998743 | + | 0.0501305i | \(0.0159637\pi\) | ||||
−0.998743 | + | 0.0501305i | \(0.984036\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.8898i | − | 1.46174i | −0.682519 | − | 0.730868i | \(-0.739115\pi\) | ||
0.682519 | − | 0.730868i | \(-0.260885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.9991i | 1.74859i | 0.485397 | + | 0.874294i | \(0.338675\pi\) | ||||
−0.485397 | + | 0.874294i | \(0.661325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.49954 | −0.336312 | −0.168156 | − | 0.985760i | \(-0.553781\pi\) | ||||
−0.168156 | + | 0.985760i | \(0.553781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0596 | −1.56535 | −0.782675 | − | 0.622430i | \(-0.786145\pi\) | ||||
−0.782675 | + | 0.622430i | \(0.786145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.1396 | + | 9.60975i | 0.966040 | + | 0.706523i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.7190i | 1.44200i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.4390 | 1.04477 | 0.522384 | − | 0.852710i | \(-0.325043\pi\) | ||||
0.522384 | + | 0.852710i | \(0.325043\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7190i | 1.56337i | 0.623673 | + | 0.781685i | \(0.285640\pi\) | ||||
−0.623673 | + | 0.781685i | \(0.714360\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.0109i | − | 0.926988i | −0.886100 | − | 0.463494i | \(-0.846596\pi\) | ||
0.886100 | − | 0.463494i | \(-0.153404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.6888 | −1.32481 | −0.662406 | − | 0.749145i | \(-0.730464\pi\) | ||||
−0.662406 | + | 0.749145i | \(0.730464\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.48486 | + | 10.2342i | −0.522765 | + | 0.714786i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.9991 | 2.00591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.24977 | −0.567938 | −0.283969 | − | 0.958834i | \(-0.591651\pi\) | ||||
−0.283969 | + | 0.958834i | \(0.591651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.67030 | + | 5.60975i | 0.523110 | + | 0.382582i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.24977 | −0.285871 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.77959i | 0.654890i | 0.944870 | + | 0.327445i | \(0.106188\pi\) | ||||
−0.944870 | + | 0.327445i | \(0.893812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.4499i | 1.68917i | 0.535423 | + | 0.844584i | \(0.320152\pi\) | ||||
−0.535423 | + | 0.844584i | \(0.679848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.24977 | 0.545160 | 0.272580 | − | 0.962133i | \(-0.412123\pi\) | ||||
0.272580 | + | 0.962133i | \(0.412123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.5904i | − | 0.759310i | −0.925128 | − | 0.379655i | \(-0.876043\pi\) | ||
0.925128 | − | 0.379655i | \(-0.123957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.21571 | − | 3.81456i | −0.340236 | − | 0.248835i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.88979 | −0.445664 | −0.222832 | − | 0.974857i | \(-0.571530\pi\) | ||||
−0.222832 | + | 0.974857i | \(0.571530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.2195 | 1.36687 | 0.683434 | − | 0.730012i | \(-0.260486\pi\) | ||||
0.683434 | + | 0.730012i | \(0.260486\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.24008 | + | 12.6341i | −0.590327 | + | 0.807164i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.24977i | 0.397663i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.3397 | 1.53631 | 0.768154 | − | 0.640266i | \(-0.221176\pi\) | ||||
0.768154 | + | 0.640266i | \(0.221176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.4390i | − | 0.656294i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 23.4693i | − | 1.46397i | −0.681319 | − | 0.731986i | \(-0.738593\pi\) | ||
0.681319 | − | 0.731986i | \(-0.261407\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.6282i | 1.39532i | 0.716431 | + | 0.697658i | \(0.245774\pi\) | ||||
−0.716431 | + | 0.697658i | \(0.754226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.6400 | − | 12.1698i | −1.02219 | − | 0.747587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.2791 | 0.748672 | 0.374336 | − | 0.927293i | \(-0.377871\pi\) | ||||
0.374336 | + | 0.927293i | \(0.377871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.9385 | −1.39342 | −0.696708 | − | 0.717355i | \(-0.745353\pi\) | ||||
−0.696708 | + | 0.717355i | \(0.745353\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.03028 | − | 22.1093i | −0.423942 | − | 1.33324i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.5298i | − | 0.692760i | −0.938094 | − | 0.346380i | \(-0.887411\pi\) | ||
0.938094 | − | 0.346380i | \(-0.112589\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3288 | 0.675819 | 0.337909 | − | 0.941179i | \(-0.390280\pi\) | ||||
0.337909 | + | 0.941179i | \(0.390280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9991i | 1.24827i | 0.781318 | + | 0.624133i | \(0.214548\pi\) | ||||
−0.781318 | + | 0.624133i | \(0.785452\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06055 | −0.0623854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.26915i | 0.249406i | 0.992194 | + | 0.124703i | \(0.0397979\pi\) | ||||
−0.992194 | + | 0.124703i | \(0.960202\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.81456 | + | 10.6850i | −0.454981 | + | 0.622104i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.24977 | 0.130108 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.28005 | + | 1.75023i | −0.0732953 | + | 0.100218i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.71904 | −0.210887 | −0.105444 | − | 0.994425i | \(-0.533626\pi\) | ||||
−0.105444 | + | 0.994425i | \(0.533626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.52982i | 0.0864704i | 0.999065 | + | 0.0432352i | \(0.0137665\pi\) | ||||
−0.999065 | + | 0.0432352i | \(0.986234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1093i | 0.904788i | 0.891818 | + | 0.452394i | \(0.149430\pi\) | ||||
−0.891818 | + | 0.452394i | \(0.850570\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.7787 | −2.39515 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.5601i | 1.47784i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.76491 | − | 1.51514i | 0.264310 | − | 0.0840447i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5298 | 0.853596 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.50046 | − | 2.56009i | −0.191250 | − | 0.139873i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.4087i | 1.16621i | 0.812398 | + | 0.583103i | \(0.198162\pi\) | ||||
−0.812398 | + | 0.583103i | \(0.801838\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 43.0596 | 2.33181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4.62065i | − | 0.248049i | −0.992279 | − | 0.124025i | \(-0.960420\pi\) | ||
0.992279 | − | 0.124025i | \(-0.0395802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.9688 | −1.28302 | −0.641510 | − | 0.767114i | \(-0.721692\pi\) | ||||
−0.641510 | + | 0.767114i | \(0.721692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.511357i | 0.0272168i | 0.999907 | + | 0.0136084i | \(0.00433182\pi\) | ||||
−0.999907 | + | 0.0136084i | \(0.995668\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.40493 | − | 10.1249i | 0.393013 | − | 0.537373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.6694 | −0.668664 | −0.334332 | − | 0.942455i | \(-0.608511\pi\) | ||||
−0.334332 | + | 0.942455i | \(0.608511\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.0596 | 1.05577 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.6694 | + | 16.5795i | 1.18657 | + | 0.867809i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.841057i | 0.0439028i | 0.999759 | + | 0.0219514i | \(0.00698792\pi\) | ||||
−0.999759 | + | 0.0219514i | \(0.993012\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.0596i | − | 1.50465i | −0.658792 | − | 0.752325i | \(-0.728932\pi\) | ||
0.658792 | − | 0.752325i | \(-0.271068\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9.21949i | − | 0.474828i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.75023 | −0.500836 | −0.250418 | − | 0.968138i | \(-0.580568\pi\) | ||||
−0.250418 | + | 0.968138i | \(0.580568\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.38934i | 0.377577i | 0.982018 | + | 0.188789i | \(0.0604561\pi\) | ||||
−0.982018 | + | 0.188789i | \(0.939544\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0000 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.56101 | 0.483521 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.1698 | − | 22.1093i | 0.813593 | − | 1.11244i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.2186i | − | 1.31587i | −0.753074 | − | 0.657936i | \(-0.771430\pi\) | ||
0.753074 | − | 0.657936i | \(-0.228570\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.2909 | −0.513905 | −0.256953 | − | 0.966424i | \(-0.582718\pi\) | ||||
−0.256953 | + | 0.966424i | \(0.582718\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.28005i | 0.462272i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 33.7796i | − | 1.67439i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.9007 | 0.588451 | 0.294226 | − | 0.955736i | \(-0.404938\pi\) | ||||
0.294226 | + | 0.955736i | \(0.404938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.62443 | − | 4.84484i | −0.325180 | − | 0.237824i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.2791 | 1.28382 | 0.641910 | − | 0.766780i | \(-0.278142\pi\) | ||||
0.641910 | + | 0.766780i | \(0.278142\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3103 | 1.08734 | 0.543669 | − | 0.839300i | \(-0.317035\pi\) | ||||
0.543669 | + | 0.839300i | \(0.317035\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.2498 | − | 6.43899i | 0.982258 | − | 0.312337i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0487 | −0.580367 | −0.290184 | − | 0.956971i | \(-0.593716\pi\) | ||||
−0.290184 | + | 0.956971i | \(0.593716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.5904i | 1.32591i | 0.748660 | + | 0.662954i | \(0.230698\pi\) | ||||
−0.748660 | + | 0.662954i | \(0.769302\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 14.0606i | − | 0.672607i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8789 | −0.948768 | −0.474384 | − | 0.880318i | \(-0.657329\pi\) | ||||
−0.474384 | + | 0.880318i | \(0.657329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 17.9007i | − | 0.850488i | −0.905079 | − | 0.425244i | \(-0.860188\pi\) | ||
0.905079 | − | 0.425244i | \(-0.139812\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7649 | − | 17.4537i | 0.605115 | − | 0.827383i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.2682 | −0.814938 | −0.407469 | − | 0.913219i | \(-0.633589\pi\) | ||||
−0.407469 | + | 0.913219i | \(0.633589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.3103 | 1.23890 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.4995i | 1.42671i | 0.700804 | + | 0.713354i | \(0.252825\pi\) | ||||
−0.700804 | + | 0.713354i | \(0.747175\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.64002 | 0.122958 | 0.0614791 | − | 0.998108i | \(-0.480418\pi\) | ||||
0.0614791 | + | 0.998108i | \(0.480418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 4.78051i | − | 0.221215i | −0.993864 | − | 0.110608i | \(-0.964720\pi\) | ||
0.993864 | − | 0.110608i | \(-0.0352797\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 19.7190i | − | 0.906682i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.46927 | − | 29.7796i | −0.434480 | − | 1.36638i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.11021 | 0.416256 | 0.208128 | − | 0.978102i | \(-0.433263\pi\) | ||||
0.208128 | + | 0.978102i | \(0.433263\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.28005 | 0.331942 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.8292 | − | 7.92007i | −0.491731 | − | 0.359632i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2791i | 1.19082i | 0.803422 | + | 0.595411i | \(0.203011\pi\) | ||||
−0.803422 | + | 0.595411i | \(0.796989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.40115 | −0.243751 | −0.121875 | − | 0.992545i | \(-0.538891\pi\) | ||||
−0.121875 | + | 0.992545i | \(0.538891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 39.1807i | − | 1.76461i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.9092 | −1.02556 | −0.512778 | − | 0.858521i | \(-0.671383\pi\) | ||||
−0.512778 | + | 0.858521i | \(0.671383\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 37.3094i | − | 1.66354i | −0.555117 | − | 0.831772i | \(-0.687327\pi\) | ||
0.555117 | − | 0.831772i | \(-0.312673\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.1698 | + | 27.5786i | −0.897546 | + | 1.22723i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.700576 | −0.0310525 | −0.0155262 | − | 0.999879i | \(-0.504942\pi\) | ||||
−0.0155262 | + | 0.999879i | \(0.504942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.20103 | − | 1.60975i | −0.0969891 | − | 0.0709339i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.4087i | 0.589715i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8401 | −0.606348 | −0.303174 | − | 0.952935i | \(-0.598046\pi\) | ||||
−0.303174 | + | 0.952935i | \(0.598046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 43.6878i | − | 1.91034i | −0.296064 | − | 0.955168i | \(-0.595674\pi\) | ||
0.296064 | − | 0.955168i | \(-0.404326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.4381i | 1.71795i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.9385 | 0.779936 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.67030i | 0.245608i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.52982 | + | 6.96972i | 0.412010 | + | 0.301327i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.4802 | 1.39902 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1892 | 0.610042 | 0.305021 | − | 0.952346i | \(-0.401336\pi\) | ||||
0.305021 | + | 0.952346i | \(0.401336\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.4499 | + | 18.3903i | −0.576130 | + | 0.787752i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 44.3085i | − | 1.89449i | −0.320504 | − | 0.947247i | \(-0.603852\pi\) | ||
0.320504 | − | 0.947247i | \(-0.396148\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −57.6197 | −2.45468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 39.2077i | − | 1.66128i | −0.556808 | − | 0.830641i | \(-0.687974\pi\) | ||
0.556808 | − | 0.830641i | \(-0.312026\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.24977 | 0.179746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0606i | 0.761162i | 0.924748 | + | 0.380581i | \(0.124276\pi\) | ||||
−0.924748 | + | 0.380581i | \(0.875724\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.85952 | + | 1.35998i | 0.0782305 | + | 0.0572146i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.3397 | −1.77497 | −0.887486 | − | 0.460835i | \(-0.847550\pi\) | ||||
−0.887486 | + | 0.460835i | \(0.847550\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.9301 | −1.67102 | −0.835510 | − | 0.549475i | \(-0.814828\pi\) | ||||
−0.835510 | + | 0.549475i | \(0.814828\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.7200 | + | 3.40871i | −0.447053 | + | 0.142153i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.3406i | − | 0.888421i | −0.895923 | − | 0.444210i | \(-0.853484\pi\) | ||
0.895923 | − | 0.444210i | \(-0.146516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.7787i | 1.77171i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.7905i | 1.35341i | 0.736255 | + | 0.676704i | \(0.236592\pi\) | ||||
−0.736255 | + | 0.676704i | \(0.763408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.9982 | 2.38977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.66938i | − | 0.273879i | −0.990579 | − | 0.136939i | \(-0.956273\pi\) | ||
0.990579 | − | 0.136939i | \(-0.0437265\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.40115 | 0.0572495 | 0.0286247 | − | 0.999590i | \(-0.490887\pi\) | ||||
0.0286247 | + | 0.999590i | \(0.490887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.349078 | 0.0142392 | 0.00711959 | − | 0.999975i | \(-0.497734\pi\) | ||||
0.00711959 | + | 0.999975i | \(0.497734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.8995 | + | 19.0050i | −0.565094 | + | 0.772663i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.2800i | 1.10726i | 0.832762 | + | 0.553631i | \(0.186758\pi\) | ||||
−0.832762 | + | 0.553631i | \(0.813242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.88979 | −0.116909 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.34060i | 0.377263i | 0.982048 | + | 0.188632i | \(0.0604052\pi\) | ||||
−0.982048 | + | 0.188632i | \(0.939595\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 34.6694i | − | 1.39574i | −0.716226 | − | 0.697868i | \(-0.754132\pi\) | ||
0.716226 | − | 0.697868i | \(-0.245868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.6509 | −0.789837 | −0.394919 | − | 0.918716i | \(-0.629227\pi\) | ||||
−0.394919 | + | 0.918716i | \(0.629227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.4087 | + | 14.4390i | −0.816349 | + | 0.577560i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.9385 | 1.23360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.3993 | −1.72770 | −0.863850 | − | 0.503749i | \(-0.831953\pi\) | ||||
−0.863850 | + | 0.503749i | \(0.831953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.9083 | − | 14.5601i | −0.790035 | − | 0.577800i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000i | 0.277350i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.56009 | 0.180113 | 0.0900564 | − | 0.995937i | \(-0.471295\pi\) | ||||
0.0900564 | + | 0.995937i | \(0.471295\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.62065i | − | 0.339965i | −0.985447 | − | 0.169983i | \(-0.945629\pi\) | ||
0.985447 | − | 0.169983i | \(-0.0543711\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.40871i | − | 0.291267i | −0.989339 | − | 0.145633i | \(-0.953478\pi\) | ||
0.989339 | − | 0.145633i | \(-0.0465220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.4693 | 1.07826 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.00000i | 0.0782660i | 0.999234 | + | 0.0391330i | \(0.0124596\pi\) | ||||
−0.999234 | + | 0.0391330i | \(0.987540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.52982 | − | 13.0303i | 0.372361 | − | 0.509135i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.3784 | 1.57292 | 0.786460 | − | 0.617641i | \(-0.211911\pi\) | ||||
0.786460 | + | 0.617641i | \(0.211911\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.0284 | 1.51803 | 0.759015 | − | 0.651073i | \(-0.225681\pi\) | ||||
0.759015 | + | 0.651073i | \(0.225681\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.7418i | 0.803124i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.49954 | 0.173703 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.1807i | − | 0.430986i | −0.976505 | − | 0.215493i | \(-0.930864\pi\) | ||
0.976505 | − | 0.215493i | \(-0.0691358\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 33.3406i | − | 1.28138i | −0.767798 | − | 0.640692i | \(-0.778648\pi\) | ||
0.767798 | − | 0.640692i | \(-0.221352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.8889i | 1.22019i | 0.792327 | + | 0.610097i | \(0.208870\pi\) | ||||
−0.792327 | + | 0.610097i | \(0.791130\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.6362 | − | 10.7044i | −0.559222 | − | 0.408992i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.21949 | −0.351235 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0303 | 1.48478 | 0.742391 | − | 0.669967i | \(-0.233692\pi\) | ||||
0.742391 | + | 0.669967i | \(0.233692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.1589 | + | 34.4002i | −0.954333 | + | 1.30488i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0975i | 0.912757i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.5601 | 1.68301 | 0.841506 | − | 0.540248i | \(-0.181670\pi\) | ||||
0.841506 | + | 0.540248i | \(0.181670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 45.4986i | − | 1.71601i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.4305 | −0.879951 | −0.439976 | − | 0.898010i | \(-0.645013\pi\) | ||||
−0.439976 | + | 0.898010i | \(0.645013\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20.8780i | − | 0.781886i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.37466 | − | 6.12489i | −0.313194 | − | 0.229058i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.0984 | −0.563075 | −0.281537 | − | 0.959550i | \(-0.590844\pi\) | ||||
−0.281537 | + | 0.959550i | \(0.590844\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.9688 | + | 43.9301i | 0.518788 | + | 1.63152i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.40871i | − | 0.126422i | −0.998000 | − | 0.0632111i | \(-0.979866\pi\) | ||
0.998000 | − | 0.0632111i | \(-0.0201341\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.0606 | 0.667994 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.4390i | 0.459445i | 0.973256 | + | 0.229722i | \(0.0737818\pi\) | ||||
−0.973256 | + | 0.229722i | \(0.926218\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.99908i | 0.331485i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4693 | 0.495475 | 0.247737 | − | 0.968827i | \(-0.420313\pi\) | ||||
0.247737 | + | 0.968827i | \(0.420313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.4111i | 1.66597i | 0.553293 | + | 0.832986i | \(0.313371\pi\) | ||||
−0.553293 | + | 0.832986i | \(0.686629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.17454 | + | 7.07523i | −0.189580 | + | 0.259216i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.56101 | 0.0569621 | 0.0284810 | − | 0.999594i | \(-0.490933\pi\) | ||||
0.0284810 | + | 0.999594i | \(0.490933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.7493 | + | 39.3094i | −1.04629 | + | 1.43062i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 38.8780i | − | 1.41304i | −0.707691 | − | 0.706522i | \(-0.750263\pi\) | ||
0.707691 | − | 0.706522i | \(-0.249737\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.42809 | −0.196768 | −0.0983841 | − | 0.995149i | \(-0.531367\pi\) | ||||
−0.0983841 | + | 0.995149i | \(0.531367\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.92007i | 0.213761i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.4390 | −0.592805 | −0.296403 | − | 0.955063i | \(-0.595787\pi\) | ||||
−0.296403 | + | 0.955063i | \(0.595787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 42.3884i | − | 1.52461i | −0.647221 | − | 0.762303i | \(-0.724069\pi\) | ||
0.647221 | − | 0.762303i | \(-0.275931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.0606 | − | 44.2186i | −0.505070 | − | 1.58838i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.4381 | 1.26970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.0294 | −0.931404 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.9679 | − | 28.4995i | −1.39082 | − | 1.01719i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5592i | 0.554625i | 0.960780 | + | 0.277312i | \(0.0894437\pi\) | ||||
−0.960780 | + | 0.277312i | \(0.910556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.969724i | 0.0344359i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.4002i | 1.28936i | 0.764452 | + | 0.644681i | \(0.223010\pi\) | ||||
−0.764452 | + | 0.644681i | \(0.776990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.2810 | −0.434469 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 |