Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(101,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 401.7 | ||
Root | \(0.127146 - 2.99730i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.401 |
Dual form | 900.3.p.e.101.7 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 2.53217 | + | 1.60876i | 0.844056 | + | 0.536255i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.69530 | + | 8.13249i | 0.670757 | + | 1.16178i | 0.977690 | + | 0.210053i | \(0.0673638\pi\) |
−0.306933 | + | 0.951731i | \(0.599303\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.82376 | + | 8.14732i | 0.424862 | + | 0.905258i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.4241 | − | 8.90510i | 1.40219 | − | 0.809554i | 0.407572 | − | 0.913173i | \(-0.366376\pi\) |
0.994617 | + | 0.103619i | \(0.0330422\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.92181 | + | 11.9889i | −0.532447 | + | 0.922226i | 0.466835 | + | 0.884344i | \(0.345394\pi\) |
−0.999282 | + | 0.0378812i | \(0.987939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 30.7147i | − | 1.80675i | −0.428856 | − | 0.903373i | \(-0.641083\pi\) | ||
0.428856 | − | 0.903373i | \(-0.358917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.5585 | 1.50308 | 0.751540 | − | 0.659687i | \(-0.229311\pi\) | ||||
0.751540 | + | 0.659687i | \(0.229311\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.19398 | + | 28.1465i | −0.0568560 | + | 1.34031i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.6734 | + | 6.16230i | 0.464062 | + | 0.267926i | 0.713751 | − | 0.700400i | \(-0.246995\pi\) |
−0.249689 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.42472 | + | 26.7819i | −0.126841 | + | 0.991923i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.02918 | + | 2.90360i | −0.173420 | + | 0.100124i | −0.584198 | − | 0.811612i | \(-0.698591\pi\) |
0.410777 | + | 0.911736i | \(0.365257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.25379 | + | 5.63573i | −0.104961 | + | 0.181798i | −0.913722 | − | 0.406339i | \(-0.866805\pi\) |
0.808761 | + | 0.588137i | \(0.200138\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 53.3826 | + | 2.26449i | 1.61765 | + | 0.0686210i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −66.5560 | −1.79881 | −0.899405 | − | 0.437116i | \(-0.856000\pi\) | ||||
−0.899405 | + | 0.437116i | \(0.856000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −36.8146 | + | 19.2224i | −0.943963 | + | 0.492883i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −33.0070 | − | 19.0566i | −0.805049 | − | 0.464795i | 0.0401848 | − | 0.999192i | \(-0.487205\pi\) |
−0.845233 | + | 0.534397i | \(0.820539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.5777 | + | 47.7660i | 0.641342 | + | 1.11084i | 0.985133 | + | 0.171791i | \(0.0549553\pi\) |
−0.343792 | + | 0.939046i | \(0.611711\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −14.2631 | + | 8.23479i | −0.303470 | + | 0.175208i | −0.644001 | − | 0.765025i | \(-0.722727\pi\) |
0.340531 | + | 0.940233i | \(0.389393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.5916 | + | 33.9337i | −0.399829 | + | 0.692523i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 49.4126 | − | 77.7747i | 0.968875 | − | 1.52499i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 69.8669i | 1.31824i | 0.752036 | + | 0.659121i | \(0.229072\pi\) | ||||
−0.752036 | + | 0.659121i | \(0.770928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 72.3150 | + | 45.9439i | 1.26868 | + | 0.806034i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 91.2592 | + | 52.6885i | 1.54677 | + | 0.893026i | 0.998386 | + | 0.0567963i | \(0.0180885\pi\) |
0.548380 | + | 0.836229i | \(0.315245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33.5580 | − | 58.1242i | −0.550131 | − | 0.952855i | −0.998265 | − | 0.0588885i | \(-0.981244\pi\) |
0.448133 | − | 0.893967i | \(-0.352089\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −48.3044 | + | 69.3508i | −0.766736 | + | 1.10081i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 22.9853 | − | 39.8118i | 0.343065 | − | 0.594206i | −0.641935 | − | 0.766759i | \(-0.721868\pi\) |
0.985000 | + | 0.172553i | \(0.0552016\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.1132 | + | 32.7750i | 0.248018 | + | 0.475000i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 31.1942i | − | 0.439354i | −0.975573 | − | 0.219677i | \(-0.929500\pi\) | ||
0.975573 | − | 0.219677i | \(-0.0705004\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 73.5877 | 1.00805 | 0.504026 | − | 0.863689i | \(-0.331852\pi\) | ||||
0.504026 | + | 0.863689i | \(0.331852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 144.841 | + | 83.6241i | 1.88105 | + | 1.08603i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −47.3263 | − | 81.9715i | −0.599067 | − | 1.03761i | −0.992959 | − | 0.118458i | \(-0.962205\pi\) |
0.393892 | − | 0.919157i | \(-0.371128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51.7578 | + | 62.3068i | −0.638985 | + | 0.769220i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4020 | + | 7.73763i | −0.161470 | + | 0.0932245i | −0.578557 | − | 0.815642i | \(-0.696384\pi\) |
0.417088 | + | 0.908866i | \(0.363051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.4059 | − | 0.738362i | −0.200068 | − | 0.00848692i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 52.7229i | 0.592392i | 0.955127 | + | 0.296196i | \(0.0957181\pi\) | ||||
−0.955127 | + | 0.296196i | \(0.904282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −130.000 | −1.42857 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.3057 | + | 9.03604i | −0.186083 | + | 0.0971617i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 38.1126 | + | 66.0130i | 0.392913 | + | 0.680546i | 0.992832 | − | 0.119515i | \(-0.0381338\pi\) |
−0.599919 | + | 0.800061i | \(0.704801\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 131.531 | + | 91.6140i | 1.32859 | + | 0.925394i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 69.5637 | − | 40.1626i | 0.688750 | − | 0.397650i | −0.114394 | − | 0.993435i | \(-0.536493\pi\) |
0.803144 | + | 0.595786i | \(0.203159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0683 | + | 26.0991i | −0.146295 | + | 0.253390i | −0.929855 | − | 0.367926i | \(-0.880068\pi\) |
0.783561 | + | 0.621315i | \(0.213401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4620i | 0.0977760i | 0.998804 | + | 0.0488880i | \(0.0155677\pi\) | ||||
−0.998804 | + | 0.0488880i | \(0.984432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −187.263 | −1.71801 | −0.859006 | − | 0.511965i | \(-0.828918\pi\) | ||||
−0.859006 | + | 0.511965i | \(0.828918\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −168.531 | − | 107.073i | −1.51830 | − | 0.964620i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −80.6035 | − | 46.5365i | −0.713305 | − | 0.411827i | 0.0989784 | − | 0.995090i | \(-0.468443\pi\) |
−0.812284 | + | 0.583263i | \(0.801776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −124.145 | − | 10.5515i | −1.06107 | − | 0.0901836i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 249.787 | − | 144.214i | 2.09905 | − | 1.21189i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 98.1015 | − | 169.917i | 0.810756 | − | 1.40427i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −52.9217 | − | 101.355i | −0.430258 | − | 0.824024i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 48.4899 | 0.381810 | 0.190905 | − | 0.981608i | \(-0.438858\pi\) | ||||
0.190905 | + | 0.981608i | \(0.438858\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.01278 | + | 165.318i | −0.0543627 | + | 1.28153i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −54.0490 | − | 31.2052i | −0.412588 | − | 0.238208i | 0.279313 | − | 0.960200i | \(-0.409893\pi\) |
−0.691901 | + | 0.721992i | \(0.743227\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 134.091 | + | 232.252i | 1.00820 | + | 1.74626i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.85510 | − | 1.07104i | 0.0135409 | − | 0.00781782i | −0.493214 | − | 0.869908i | \(-0.664178\pi\) |
0.506755 | + | 0.862090i | \(0.330845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.40371 | + | 12.8236i | −0.0532641 | + | 0.0922562i | −0.891428 | − | 0.453162i | \(-0.850296\pi\) |
0.838164 | + | 0.545418i | \(0.183629\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −49.3644 | − | 2.09404i | −0.350102 | − | 0.0148514i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 246.558i | 1.72418i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −104.200 | + | 54.4075i | −0.708847 | + | 0.370119i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −177.328 | − | 102.380i | −1.19012 | − | 0.687116i | −0.231785 | − | 0.972767i | \(-0.574457\pi\) |
−0.958334 | + | 0.285651i | \(0.907790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.45266 | + | 12.9084i | 0.0493553 | + | 0.0854860i | 0.889648 | − | 0.456648i | \(-0.150950\pi\) |
−0.840292 | + | 0.542134i | \(0.817617\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 250.242 | − | 117.445i | 1.63557 | − | 0.767617i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.15362 | − | 15.8545i | 0.0583033 | − | 0.100984i | −0.835401 | − | 0.549642i | \(-0.814764\pi\) |
0.893704 | + | 0.448657i | \(0.148098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −112.399 | + | 176.915i | −0.706914 | + | 1.11267i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 115.735i | 0.718853i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 43.2107 | 0.265096 | 0.132548 | − | 0.991177i | \(-0.457684\pi\) | ||||
0.132548 | + | 0.991177i | \(0.457684\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 61.7635 | + | 35.6591i | 0.369841 | + | 0.213528i | 0.673389 | − | 0.739288i | \(-0.264838\pi\) |
−0.303548 | + | 0.952816i | \(0.598171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3230 | − | 19.6120i | −0.0670000 | − | 0.116047i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 109.201 | + | 232.676i | 0.638602 | + | 1.36068i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −145.397 | + | 83.9449i | −0.840444 | + | 0.485230i | −0.857415 | − | 0.514626i | \(-0.827931\pi\) |
0.0169713 | + | 0.999856i | \(0.494598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 146.320 | + | 280.231i | 0.826668 | + | 1.58322i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 117.614i | − | 0.657063i | −0.944493 | − | 0.328531i | \(-0.893446\pi\) | ||
0.944493 | − | 0.328531i | \(-0.106554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 96.5280 | 0.533304 | 0.266652 | − | 0.963793i | \(-0.414083\pi\) | ||||
0.266652 | + | 0.963793i | \(0.414083\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.53353 | − | 201.167i | 0.0466313 | − | 1.09927i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −273.517 | − | 473.746i | −1.46266 | − | 2.53340i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −233.884 | + | 97.8975i | −1.23748 | + | 0.517976i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 51.9090 | − | 29.9697i | 0.271775 | − | 0.156909i | −0.357919 | − | 0.933753i | \(-0.616514\pi\) |
0.629694 | + | 0.776843i | \(0.283180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 30.6963 | − | 53.1675i | 0.159048 | − | 0.275479i | −0.775478 | − | 0.631375i | \(-0.782491\pi\) |
0.934526 | + | 0.355896i | \(0.115824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 289.758i | − | 1.47085i | −0.677604 | − | 0.735427i | \(-0.736982\pi\) | ||
0.677604 | − | 0.735427i | \(-0.263018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −100.347 | −0.504254 | −0.252127 | − | 0.967694i | \(-0.581130\pi\) | ||||
−0.252127 | + | 0.967694i | \(0.581130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 122.251 | − | 63.8322i | 0.608212 | − | 0.317573i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −47.2270 | − | 27.2665i | −0.232645 | − | 0.134318i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.39369 | + | 110.523i | −0.0453801 | + | 0.533927i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 440.489 | − | 254.316i | 2.10760 | − | 1.21683i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −106.282 | + | 184.086i | −0.503706 | + | 0.872444i | 0.496285 | + | 0.868160i | \(0.334697\pi\) |
−0.999991 | + | 0.00428419i | \(0.998636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 50.1840 | − | 78.9889i | 0.235606 | − | 0.370840i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −61.1100 | −0.281613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 186.337 | + | 118.385i | 0.850852 | + | 0.540572i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 368.236 | + | 212.601i | 1.66623 | + | 0.961996i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −111.359 | − | 192.880i | −0.499369 | − | 0.864932i | 0.500631 | − | 0.865661i | \(-0.333101\pi\) |
−1.00000 | 0.000728529i | \(0.999768\pi\) | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 117.812 | − | 68.0187i | 0.518995 | − | 0.299642i | −0.217528 | − | 0.976054i | \(-0.569799\pi\) |
0.736523 | + | 0.676412i | \(0.236466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 197.762 | − | 342.533i | 0.863589 | − | 1.49578i | −0.00485333 | − | 0.999988i | \(-0.501545\pi\) |
0.868442 | − | 0.495791i | \(-0.165122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 232.231 | + | 444.766i | 1.00533 | + | 1.92539i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 403.347i | − | 1.73110i | −0.500821 | − | 0.865551i | \(-0.666969\pi\) | ||
0.500821 | − | 0.865551i | \(-0.333031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0347 | − | 283.703i | 0.0507793 | − | 1.19706i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 370.505 | + | 213.911i | 1.55023 | + | 0.895025i | 0.998122 | + | 0.0612505i | \(0.0195088\pi\) |
0.552106 | + | 0.833774i | \(0.313824\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.4457 | − | 47.5373i | −0.113882 | − | 0.197250i | 0.803450 | − | 0.595372i | \(-0.202995\pi\) |
−0.917332 | + | 0.398122i | \(0.869662\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −231.296 | + | 74.5053i | −0.951836 | + | 0.306606i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −197.677 | + | 342.386i | −0.800311 | + | 1.38618i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −46.3841 | − | 1.96762i | −0.186281 | − | 0.00790208i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 404.670i | − | 1.61223i | −0.591759 | − | 0.806115i | \(-0.701566\pi\) | ||
0.591759 | − | 0.806115i | \(-0.298434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 219.504 | 0.867603 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 77.2834 | + | 44.6196i | 0.300713 | + | 0.173617i | 0.642763 | − | 0.766065i | \(-0.277788\pi\) |
−0.342050 | + | 0.939682i | \(0.611121\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −312.500 | − | 541.266i | −1.20656 | − | 2.08983i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.8869 | − | 29.8717i | −0.164318 | − | 0.114451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −291.278 | + | 168.170i | −1.10752 | + | 0.639428i | −0.938186 | − | 0.346130i | \(-0.887495\pi\) |
−0.169335 | + | 0.985558i | \(0.554162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −84.8186 | + | 133.503i | −0.317673 | + | 0.500012i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 225.504i | 0.838305i | 0.907916 | + | 0.419153i | \(0.137673\pi\) | ||||
−0.907916 | + | 0.419153i | \(0.862327\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −196.656 | −0.725669 | −0.362834 | − | 0.931854i | \(-0.618191\pi\) | ||||
−0.362834 | + | 0.931854i | \(0.618191\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −329.182 | − | 209.139i | −1.20579 | − | 0.766077i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −89.0481 | − | 154.236i | −0.321473 | − | 0.556808i | 0.659319 | − | 0.751863i | \(-0.270845\pi\) |
−0.980792 | + | 0.195055i | \(0.937511\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −58.3578 | − | 4.96001i | −0.209168 | − | 0.0177778i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 74.3930 | − | 42.9508i | 0.264744 | − | 0.152850i | −0.361753 | − | 0.932274i | \(-0.617822\pi\) |
0.626497 | + | 0.779424i | \(0.284488\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −60.9884 | + | 105.635i | −0.215507 | + | 0.373269i | −0.953429 | − | 0.301617i | \(-0.902474\pi\) |
0.737922 | + | 0.674886i | \(0.235807\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 357.905i | − | 1.24706i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −654.391 | −2.26433 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.69173 | + | 228.470i | −0.0333049 | + | 0.785121i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 77.1800 | + | 44.5599i | 0.263413 | + | 0.152081i | 0.625890 | − | 0.779911i | \(-0.284736\pi\) |
−0.362478 | + | 0.931992i | \(0.618069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 185.672 | + | 443.584i | 0.625160 | + | 1.49355i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −147.759 | + | 85.3086i | −0.494177 | + | 0.285313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −258.971 | + | 448.551i | −0.860368 | + | 1.49020i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 240.759 | + | 10.2130i | 0.794585 | + | 0.0337064i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −602.803 | −1.96353 | −0.981764 | − | 0.190105i | \(-0.939117\pi\) | ||||
−0.981764 | + | 0.190105i | \(0.939117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −80.1430 | + | 41.8460i | −0.259362 | + | 0.135424i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 142.632 | + | 82.3487i | 0.458624 | + | 0.264787i | 0.711466 | − | 0.702721i | \(-0.248032\pi\) |
−0.252841 | + | 0.967508i | \(0.581365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.33340 | + | 12.7018i | 0.0234294 | + | 0.0405809i | 0.877502 | − | 0.479572i | \(-0.159208\pi\) |
−0.854073 | + | 0.520153i | \(0.825875\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 408.868 | − | 236.060i | 1.28981 | − | 0.744670i | 0.311186 | − | 0.950349i | \(-0.399274\pi\) |
0.978619 | + | 0.205679i | \(0.0659403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −51.7137 | + | 89.5707i | −0.162112 | + | 0.280786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.8309 | + | 26.4916i | −0.0524328 | + | 0.0825284i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 877.166i | − | 2.71568i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −474.182 | − | 301.263i | −1.45010 | − | 0.921292i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −133.939 | − | 77.3296i | −0.407109 | − | 0.235044i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −241.860 | − | 418.914i | −0.730695 | − | 1.26560i | −0.956587 | − | 0.291448i | \(-0.905863\pi\) |
0.225892 | − | 0.974152i | \(-0.427470\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −254.494 | − | 542.253i | −0.764246 | − | 1.62839i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 181.488 | − | 314.346i | 0.538540 | − | 0.932778i | −0.460443 | − | 0.887689i | \(-0.652310\pi\) |
0.998983 | − | 0.0450890i | \(-0.0143571\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −129.236 | − | 247.510i | −0.381226 | − | 0.730118i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 115.901i | 0.339886i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 92.1855 | 0.268762 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 318.851 | + | 184.089i | 0.918879 | + | 0.530515i | 0.883277 | − | 0.468851i | \(-0.155332\pi\) |
0.0356015 | + | 0.999366i | \(0.488665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −199.861 | − | 346.170i | −0.572668 | − | 0.991890i | −0.996291 | − | 0.0860512i | \(-0.972575\pi\) |
0.423623 | − | 0.905839i | \(-0.360758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −297.381 | − | 226.438i | −0.847240 | − | 0.645123i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −480.996 | + | 277.703i | −1.36259 | + | 0.786694i | −0.989969 | − | 0.141288i | \(-0.954876\pi\) |
−0.372626 | + | 0.927982i | \(0.621542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 864.509 | + | 36.6726i | 2.42159 | + | 0.102724i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 670.647i | − | 1.86810i | −0.357147 | − | 0.934048i | \(-0.616251\pi\) | ||
0.357147 | − | 0.934048i | \(-0.383749\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 454.590 | 1.25925 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 521.766 | − | 272.436i | 1.43737 | − | 0.750512i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 47.1109 | + | 81.5985i | 0.128368 | + | 0.222339i | 0.923044 | − | 0.384694i | \(-0.125693\pi\) |
−0.794677 | + | 0.607033i | \(0.792360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.0495 | − | 341.786i | 0.0787249 | − | 0.926251i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −568.192 | + | 328.046i | −1.53151 | + | 0.884220i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 96.2886 | − | 166.777i | 0.258146 | − | 0.447123i | −0.707599 | − | 0.706614i | \(-0.750222\pi\) |
0.965745 | + | 0.259492i | \(0.0835550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 80.3927i | − | 0.213243i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 184.387 | 0.486510 | 0.243255 | − | 0.969962i | \(-0.421785\pi\) | ||||
0.243255 | + | 0.969962i | \(0.421785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 122.785 | + | 78.0088i | 0.322269 | + | 0.204748i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −575.841 | − | 332.462i | −1.50350 | − | 0.868047i | −0.999992 | − | 0.00405754i | \(-0.998708\pi\) |
−0.503510 | − | 0.863990i | \(-0.667958\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −283.714 | + | 407.330i | −0.733112 | + | 1.05253i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 539.718 | − | 311.606i | 1.38745 | − | 0.801044i | 0.394422 | − | 0.918929i | \(-0.370945\pi\) |
0.993027 | + | 0.117885i | \(0.0376115\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 189.273 | − | 327.830i | 0.484074 | − | 0.838441i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −86.6594 | − | 165.969i | −0.220507 | − | 0.422313i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 247.371 | 0.623100 | 0.311550 | − | 0.950230i | \(-0.399152\pi\) | ||||
0.311550 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.0982 | + | 803.822i | −0.0854591 | + | 2.01459i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 369.248 | + | 213.185i | 0.920818 | + | 0.531635i | 0.883896 | − | 0.467684i | \(-0.154911\pi\) |
0.0369222 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.0443 | − | 78.0189i | −0.111772 | − | 0.193595i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1026.56 | + | 592.687i | −2.52227 | + | 1.45623i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −87.0543 | + | 150.782i | −0.212847 | + | 0.368661i | −0.952604 | − | 0.304212i | \(-0.901607\pi\) |
0.739758 | + | 0.672873i | \(0.234940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.42047 | + | 0.272357i | 0.0156216 | + | 0.000662669i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 989.553i | 2.39601i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −39.3776 | + | 20.5607i | −0.0944307 | + | 0.0493063i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −265.100 | − | 153.055i | −0.632696 | − | 0.365287i | 0.149099 | − | 0.988822i | \(-0.452363\pi\) |
−0.781796 | + | 0.623535i | \(0.785696\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 140.251 | + | 242.922i | 0.333138 | + | 0.577012i | 0.983125 | − | 0.182933i | \(-0.0585591\pi\) |
−0.649987 | + | 0.759945i | \(0.725226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −121.630 | − | 84.7181i | −0.287542 | − | 0.200279i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 315.130 | − | 545.820i | 0.738008 | − | 1.27827i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −396.653 | + | 624.326i | −0.924599 | + | 1.45530i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 675.034i | − | 1.56620i | −0.621893 | − | 0.783102i | \(-0.713636\pi\) | ||
0.621893 | − | 0.783102i | \(-0.286364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −273.497 | −0.631633 | −0.315817 | − | 0.948820i | \(-0.602278\pi\) | ||||
−0.315817 | + | 0.948820i | \(0.602278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 304.817 | + | 175.986i | 0.697522 | + | 0.402715i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 262.426 | + | 454.535i | 0.597781 | + | 1.03539i | 0.993148 | + | 0.116864i | \(0.0372842\pi\) |
−0.395367 | + | 0.918523i | \(0.629382\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −351.382 | − | 29.8651i | −0.796784 | − | 0.0677212i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 76.6862 | − | 44.2748i | 0.173106 | − | 0.0999431i | −0.410943 | − | 0.911661i | \(-0.634801\pi\) |
0.584050 | + | 0.811718i | \(0.301467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −284.318 | − | 544.522i | −0.636059 | − | 1.21817i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 46.0938i | − | 0.102659i | −0.998682 | − | 0.0513294i | \(-0.983654\pi\) | ||
0.998682 | − | 0.0513294i | \(-0.0163458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −678.803 | −1.50511 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.89515 | + | 44.6758i | −0.00418355 | + | 0.0986220i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 94.6301 | + | 163.904i | 0.207068 | + | 0.358652i | 0.950790 | − | 0.309837i | \(-0.100275\pi\) |
−0.743722 | + | 0.668489i | \(0.766941\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 822.598 | + | 105.189i | 1.79215 | + | 0.229170i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −362.663 | + | 209.384i | −0.786689 | + | 0.454195i | −0.838795 | − | 0.544447i | \(-0.816740\pi\) |
0.0521069 | + | 0.998642i | \(0.483406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −156.514 | + | 271.090i | −0.338043 | + | 0.585507i | −0.984064 | − | 0.177812i | \(-0.943098\pi\) |
0.646022 | + | 0.763319i | \(0.276431\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 148.419i | − | 0.317814i | −0.987294 | − | 0.158907i | \(-0.949203\pi\) | ||
0.987294 | − | 0.158907i | \(-0.0507971\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 431.692 | 0.920452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.6847 | − | 25.4203i | 0.103365 | − | 0.0539710i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 850.721 | + | 491.164i | 1.79856 | + | 1.03840i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −569.228 | + | 267.154i | −1.19335 | + | 0.560071i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 273.219 | − | 157.743i | 0.570395 | − | 0.329317i | −0.186912 | − | 0.982377i | \(-0.559848\pi\) |
0.757307 | + | 0.653059i | \(0.226515\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 460.688 | − | 797.935i | 0.957771 | − | 1.65891i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −186.191 | + | 293.061i | −0.385488 | + | 0.606752i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 492.691 | 1.01169 | 0.505843 | − | 0.862626i | \(-0.331182\pi\) | ||||
0.505843 | + | 0.862626i | \(0.331182\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 109.417 | + | 69.5158i | 0.223756 | + | 0.142159i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 719.318 | + | 415.298i | 1.46501 | + | 0.845822i | 0.999236 | − | 0.0390843i | \(-0.0124441\pi\) |
0.465770 | + | 0.884906i | \(0.345777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 89.1831 | + | 154.470i | 0.180899 | + | 0.313326i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 253.686 | − | 146.466i | 0.510435 | − | 0.294700i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.1379 | + | 24.4876i | −0.0283325 | + | 0.0490733i | −0.879844 | − | 0.475263i | \(-0.842353\pi\) |
0.851512 | + | 0.524336i | \(0.175686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 99.0283 | + | 189.658i | 0.197661 | + | 0.378558i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 31.5709i | − | 0.0627652i | −0.999507 | − | 0.0313826i | \(-0.990009\pi\) | ||
0.999507 | − | 0.0313826i | \(-0.00999103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.87935 | − | 67.8769i | 0.00567918 | − | 0.133880i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 204.163 | + | 117.874i | 0.401107 | + | 0.231579i | 0.686961 | − | 0.726694i | \(-0.258944\pi\) |
−0.285855 | + | 0.958273i | \(0.592277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 345.516 | + | 598.452i | 0.676157 | + | 1.17114i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −97.8049 | + | 764.852i | −0.190653 | + | 1.49094i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −146.663 | + | 254.028i | −0.283681 | + | 0.491350i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −503.217 | − | 21.3465i | −0.969589 | − | 0.0411301i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 582.254i | − | 1.11757i | −0.829312 | − | 0.558785i | \(-0.811268\pi\) | ||
0.829312 | − | 0.558785i | \(-0.188732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 201.726 | 0.385709 | 0.192855 | − | 0.981227i | \(-0.438225\pi\) | ||||
0.192855 | + | 0.981227i | \(0.438225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 173.100 | + | 99.9391i | 0.328462 | + | 0.189638i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −188.552 | − | 326.582i | −0.356431 | − | 0.617357i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −80.3173 | + | 944.986i | −0.151257 | + | 1.77963i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 456.937 | − | 263.812i | 0.857292 | − | 0.494958i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 189.213 | − | 297.819i | 0.352353 | − | 0.554598i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 697.860i | 1.29473i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 390.540 | 0.721886 | 0.360943 | − | 0.932588i | \(-0.382455\pi\) | ||||
0.360943 | + | 0.932588i | \(0.382455\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 244.425 | + | 155.291i | 0.450138 | + | 0.285987i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 321.098 | + | 556.158i | 0.587017 | + | 1.01674i | 0.994621 | + | 0.103584i | \(0.0330310\pi\) |
−0.407604 | + | 0.913159i | \(0.633636\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 345.239 | − | 495.661i | 0.628850 | − | 0.902843i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −143.626 | + | 82.9225i | −0.260664 | + | 0.150495i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 444.422 | − | 769.761i | 0.803656 | − | 1.39197i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 145.052i | − | 0.260417i | −0.991487 | − | 0.130208i | \(-0.958435\pi\) | ||
0.991487 | − | 0.130208i | \(-0.0415646\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −763.551 | −1.36592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 69.5532 | − | 1639.63i | 0.123981 | − | 2.92269i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 732.570 | + | 422.949i | 1.30119 | + | 0.751242i | 0.980608 | − | 0.195979i | \(-0.0627885\pi\) |
0.320581 | + | 0.947221i | \(0.396122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −749.727 | − | 128.371i | −1.32227 | − | 0.226403i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −725.474 | + | 418.853i | −1.27500 | + | 0.736121i | −0.975924 | − | 0.218109i | \(-0.930011\pi\) |
−0.299074 | + | 0.954230i | \(0.596678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −348.675 | + | 603.922i | −0.610639 | + | 1.05766i | 0.380494 | + | 0.924783i | \(0.375754\pi\) |
−0.991133 | + | 0.132874i | \(0.957579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 179.656 | + | 7.62104i | 0.313537 | + | 0.0133003i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −713.999 | −1.23743 | −0.618717 | − | 0.785614i | \(-0.712347\pi\) | ||||
−0.618717 | + | 0.785614i | \(0.712347\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 163.262 | − | 85.2460i | 0.281972 | − | 0.147230i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −125.852 | − | 72.6610i | −0.216614 | − | 0.125062i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 622.171 | + | 1077.63i | 1.06719 | + | 1.84843i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −706.988 | + | 408.180i | −1.20441 | + | 0.695366i | −0.961532 | − | 0.274692i | \(-0.911424\pi\) |
−0.242876 | + | 0.970057i | \(0.578091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −92.9235 | + | 160.948i | −0.157765 | + | 0.273257i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 466.152 | − | 733.717i | 0.788752 | − | 1.24148i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 64.6676i | − | 0.109052i | −0.998512 | − | 0.0545258i | \(-0.982635\pi\) | ||
0.998512 | − | 0.0545258i | \(-0.0173647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −254.095 | − | 161.434i | −0.425619 | − | 0.270409i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −204.565 | − | 118.105i | −0.341510 | − | 0.197171i | 0.319430 | − | 0.947610i | \(-0.396509\pi\) |
−0.660940 | + | 0.750439i | \(0.729842\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 84.0789 | + | 145.629i | 0.139898 | + | 0.242311i | 0.927458 | − | 0.373927i | \(-0.121989\pi\) |
−0.787560 | + | 0.616238i | \(0.788656\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 412.250 | + | 35.0384i | 0.683665 | + | 0.0581068i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −55.0163 | + | 95.2911i | −0.0906365 | + | 0.156987i | −0.907779 | − | 0.419449i | \(-0.862223\pi\) |
0.817143 | + | 0.576435i | \(0.195557\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −75.7213 | − | 145.021i | −0.124337 | − | 0.238129i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 227.999i | − | 0.373157i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 387.013 | 0.631343 | 0.315671 | − | 0.948869i | \(-0.397770\pi\) | ||||
0.315671 | + | 0.948869i | \(0.397770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 333.200 | + | 192.373i | 0.540032 | + | 0.311787i | 0.745092 | − | 0.666962i | \(-0.232406\pi\) |
−0.205060 | + | 0.978749i | \(0.565739\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 403.446 | + | 698.789i | 0.651771 | + | 1.12890i | 0.982693 | + | 0.185242i | \(0.0593068\pi\) |
−0.330922 | + | 0.943658i | \(0.607360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −201.592 | + | 264.750i | −0.324624 | + | 0.426329i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −428.768 | + | 247.549i | −0.688232 | + | 0.397351i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1524.53 | + | 64.6706i | 2.43146 | + | 0.103143i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2044.24i | 3.24999i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −753.299 | −1.19382 | −0.596909 | − | 0.802309i | \(-0.703605\pi\) | ||||
−0.596909 | + | 0.802309i | \(0.703605\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −565.274 | + | 295.153i | −0.893008 | + | 0.466277i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −271.219 | − | 469.765i | −0.425775 | − | 0.737464i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 254.149 | − | 119.279i | 0.397729 | − | 0.186665i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −570.820 | + | 329.563i | −0.890515 | + | 0.514139i | −0.874111 | − | 0.485726i | \(-0.838555\pi\) |
−0.0164041 | + | 0.999865i | \(0.505222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −452.382 | + | 783.548i | −0.703549 | + | 1.21858i | 0.263664 | + | 0.964615i | \(0.415069\pi\) |
−0.967213 | + | 0.253968i | \(0.918264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 360.764i | − | 0.557594i | −0.960350 | − | 0.278797i | \(-0.910064\pi\) | ||
0.960350 | − | 0.278797i | \(-0.0899357\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1876.79 | 2.89181 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −154.741 | − | 98.3116i | −0.237697 | − | 0.151016i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −365.501 | − | 211.022i | −0.559726 | − | 0.323158i | 0.193310 | − | 0.981138i | \(-0.438078\pi\) |
−0.753035 | + | 0.657980i | \(0.771411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 281.382 | + | 599.543i | 0.428283 | + | 0.912547i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 520.928 | − | 300.758i | 0.790483 | − | 0.456385i | −0.0496496 | − | 0.998767i | \(-0.515810\pi\) |
0.840133 | + | 0.542381i | \(0.182477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 465.379 | − | 806.060i | 0.704053 | − | 1.21946i | −0.262979 | − | 0.964802i | \(-0.584705\pi\) |
0.967032 | − | 0.254654i | \(-0.0819617\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 590.411 | + | 1130.75i | 0.890514 | + | 1.70550i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −71.5714 | −0.107303 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.3178 | − | 667.555i | 0.0423285 | − | 0.997840i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1035.20 | − | 597.675i | −1.54278 | − | 0.890722i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.2343 | + | 50.6352i | 0.0434387 | + | 0.0752381i | 0.886927 | − | 0.461909i | \(-0.152835\pi\) |
−0.843489 | + | 0.537147i | \(0.819502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −549.689 | + | 317.363i | −0.811948 | + | 0.468778i | −0.847632 | − | 0.530585i | \(-0.821972\pi\) |
0.0356841 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −357.900 | + | 619.901i | −0.527099 | + | 0.912962i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 407.746 | + | 17.2966i | 0.598746 | + | 0.0253988i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 387.682i | − | 0.567617i | −0.958881 | − | 0.283808i | \(-0.908402\pi\) | ||
0.958881 | − | 0.283808i | \(-0.0915980\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1051.82 | − | 549.201i | 1.53104 | − | 0.799419i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −837.629 | − | 483.605i | −1.21572 | − | 0.701895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −483.665 | − | 837.732i | −0.699949 | − | 1.21235i | −0.968484 | − | 0.249077i | \(-0.919873\pi\) |
0.268535 | − | 0.963270i | \(-0.413461\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −127.475 | + | 1499.83i | −0.183947 | + | 2.16425i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −585.317 | + | 1013.80i | −0.839766 | + | 1.45452i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 648.889 | − | 1021.34i | 0.928311 | − | 1.46115i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 895.039i | 1.27680i | 0.769703 | + | 0.638402i | \(0.220404\pi\) | ||||
−0.769703 | + | 0.638402i | \(0.779596\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1900.74 | −2.70376 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 653.245 | + | 377.151i | 0.923967 | + | 0.533453i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 624.531 | + | 1081.72i | 0.880861 | + | 1.52570i | 0.850385 | + | 0.526161i | \(0.176369\pi\) |
0.0304761 | + | 0.999535i | \(0.490298\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 486.884 | − | 699.022i | 0.684788 | − | 0.983153i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −69.4581 | + | 40.1017i | −0.0974167 | + | 0.0562436i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 594.048 | + | 1137.71i | 0.828519 | + | 1.58677i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 418.228i | 0.581681i | 0.956772 | + | 0.290840i | \(0.0939348\pi\) | ||||
−0.956772 | + | 0.290840i | \(0.906065\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −283.001 | −0.392512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.97921 | − | 164.526i | 0.00965312 | − | 0.227560i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 258.116 | + | 447.070i | 0.355043 | + | 0.614952i | 0.987125 | − | 0.159949i | \(-0.0511329\pi\) |
−0.632082 | + | 0.774901i | \(0.717800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −705.543 | − | 183.441i | −0.967823 | − | 0.251634i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1467.12 | − | 847.040i | 2.00700 | − | 1.15874i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.12563 | + | 7.14580i | −0.00562842 | + | 0.00974871i | −0.868826 | − | 0.495118i | \(-0.835125\pi\) |
0.863197 | + | 0.504866i | \(0.168458\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 818.747i | − | 1.11092i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 294.686 | 0.398763 | 0.199381 | − | 0.979922i | \(-0.436107\pi\) | ||||
0.199381 | + | 0.979922i | \(0.436107\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1051.37 | + | 548.965i | −1.41885 | + | 0.740843i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 438.540 | + | 253.191i | 0.590229 | + | 0.340769i | 0.765188 | − | 0.643807i | \(-0.222646\pi\) |
−0.174959 | + | 0.984576i | \(0.555979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −114.287 | − | 79.6034i | −0.152995 | − | 0.106564i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −85.0824 | + | 49.1223i | −0.113595 | + | 0.0655839i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −395.768 | + | 685.491i | −0.526989 | + | 0.912771i | 0.472517 | + | 0.881322i | \(0.343346\pi\) |
−0.999505 | + | 0.0314493i | \(0.989988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 651.018 | − | 1024.69i | 0.864566 | − | 1.36081i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 957.457 | 1.26480 | 0.632402 | − | 0.774640i | \(-0.282069\pi\) | ||||
0.632402 | + | 0.774640i | \(0.282069\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 555.820 | + | 353.129i | 0.732306 | + | 0.465256i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −378.389 | − | 218.463i | −0.497225 | − | 0.287073i | 0.230342 | − | 0.973110i | \(-0.426016\pi\) |
−0.727567 | + | 0.686037i | \(0.759349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −879.257 | − | 1522.92i | −1.15237 | − | 1.99596i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1263.36 | + | 729.400i | −1.64714 | + | 0.950978i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 302.360 | − | 523.703i | 0.393186 | − | 0.681018i | −0.599682 | − | 0.800238i | \(-0.704706\pi\) |
0.992868 | + | 0.119221i | \(0.0380396\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 123.912 | + | 237.315i | 0.160716 | + | 0.307802i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 596.625i | − | 0.771831i | −0.922534 | − | 0.385915i | \(-0.873886\pi\) | ||
0.922534 | − | 0.385915i | \(-0.126114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 79.4662 | − | 1873.32i | 0.102273 | − | 2.41096i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −942.631 | − | 544.228i | −1.21005 | − | 0.698625i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −277.787 | − | 481.141i | −0.355681 | − | 0.616058i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −60.5404 | − | 144.635i | −0.0773186 | − | 0.184719i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 272.220 | − | 471.499i | 0.345896 | − | 0.599109i | −0.639620 | − | 0.768691i | \(-0.720908\pi\) |
0.985516 | + | 0.169582i | \(0.0542418\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1008.11 | − | 42.7642i | −1.27771 | − | 0.0542005i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 874.010i | − | 1.10494i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 929.129 | 1.17166 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −200.065 | − | 115.508i | −0.251023 | − | 0.144928i | 0.369210 | − | 0.929346i | \(-0.379628\pi\) |
−0.620232 | + | 0.784418i | \(0.712962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 252.929 | + | 438.086i | 0.316557 | + | 0.548293i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −429.550 | + | 201.599i | −0.536267 | + | 0.251685i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1135.02 | − | 655.306i | 1.41348 | − | 0.816072i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −362.783 | + | 571.014i | −0.449545 | + | 0.707577i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 75.6693i | − | 0.0935344i | −0.998906 | − | 0.0467672i | \(-0.985108\pi\) | ||
0.998906 | − | 0.0467672i | \(-0.0148919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1184.72 | 1.46081 | 0.730404 | − | 0.683015i | \(-0.239332\pi\) | ||||
0.730404 | + | 0.683015i | \(0.239332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −497.967 | − | 316.373i | −0.612505 | − | 0.389143i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 787.579 | + | 1364.13i | 0.963988 | + | 1.66968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −497.088 | − | 1059.15i | −0.606945 | − | 1.29322i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1282.37 | + | 740.377i | −1.56196 | + | 0.901799i | −0.564904 | + | 0.825157i | \(0.691087\pi\) |
−0.997059 | + | 0.0766424i | \(0.975580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −380.688 | + | 659.371i | −0.462562 | + | 0.801180i | −0.999088 | − | 0.0427034i | \(-0.986403\pi\) |
0.536526 | + | 0.843884i | \(0.319736\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1019.60i | − | 1.23290i | −0.787396 | − | 0.616448i | \(-0.788571\pi\) | ||
0.787396 | − | 0.616448i | \(-0.211429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 58.7988 | 0.0709274 | 0.0354637 | − | 0.999371i | \(-0.488709\pi\) | ||||
0.0354637 | + | 0.999371i | \(0.488709\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.6442 | − | 533.809i | 0.0272494 | − | 0.642369i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1042.26 | + | 601.750i | 1.25121 | + | 0.722388i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −139.792 | − | 106.444i | −0.167016 | − | 0.127173i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1005.77 | + | 580.682i | −1.19877 | + | 0.692112i | −0.960282 | − | 0.279032i | \(-0.909986\pi\) |
−0.238492 | + | 0.971144i | \(0.576653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −403.638 | + | 699.122i | −0.479950 | + | 0.831298i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 257.473 | + | 10.9221i | 0.305425 | + | 0.0129562i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1842.46 | 2.17528 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −324.375 | + | 169.370i | −0.382067 | + | 0.199493i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −710.380 | − | 410.138i | −0.834759 | − | 0.481948i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −695.272 | − | 1204.25i | −0.815090 | − | 1.41178i | −0.909263 | − | 0.416222i | \(-0.863354\pi\) |
0.0941731 | − | 0.995556i | \(-0.469979\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −914.904 | + | 528.220i | −1.06757 | + | 0.616359i | −0.927515 | − | 0.373785i | \(-0.878060\pi\) |
−0.140050 | + | 0.990144i | \(0.544726\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 537.750 | − | 931.410i | 0.626018 | − | 1.08430i | −0.362325 | − | 0.932052i | \(-0.618017\pi\) |
0.988343 | − | 0.152244i | \(-0.0486498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 575.785 | − | 906.277i | 0.668740 | − | 1.05259i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 66.3453i | − | 0.0768776i | −0.999261 | − | 0.0384388i | \(-0.987762\pi\) | ||
0.999261 | − | 0.0384388i | \(-0.0122385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1657.03 | − | 1052.76i | −1.91122 | − | 1.21426i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1459.93 | − | 842.890i | −1.68001 | − | 0.969954i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 318.200 | + | 551.139i | 0.365328 | + | 0.632766i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −392.096 | + | 562.933i | −0.449136 | + | 0.644826i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −211.603 | + | 366.507i | −0.241280 | + | 0.417909i | −0.961079 | − | 0.276273i | \(-0.910901\pi\) |
0.719799 | + | 0.694182i | \(0.244234\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 123.746 | + | 236.997i | 0.140781 | + | 0.269622i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 525.156i | 0.596090i | 0.954552 | + | 0.298045i | \(0.0963346\pi\) | ||||
−0.954552 | + | 0.298045i | \(0.903665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.5609 | −0.0504653 | −0.0252327 | − | 0.999682i | \(-0.508033\pi\) | ||||
−0.0252327 | + | 0.999682i | \(0.508033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1223.72 | + | 706.516i | 1.37962 | + | 0.796523i | 0.992113 | − | 0.125345i | \(-0.0400038\pi\) |
0.387505 | + | 0.921868i | \(0.373337\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 227.674 | + | 394.344i | 0.256102 | + | 0.443581i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −243.468 | + | 1421.93i | −0.273252 | + | 1.59588i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −407.333 | + | 235.174i | −0.456140 | + | 0.263352i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −511.392 | − | 21.6933i | −0.570113 | − | 0.0241843i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 37.7908i | − | 0.0420365i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2145.94 | 2.38173 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1377.37 | + | 719.183i | −1.52533 | + | 0.796438i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −150.861 | − | 261.298i | −0.166329 | − | 0.288090i | 0.770797 | − | 0.637080i | \(-0.219858\pi\) |
−0.937126 | + | 0.348990i | \(0.886525\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 593.213 | + | 413.186i | 0.652599 | + | 0.454550i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 243.600 | − | 140.643i | 0.267399 | − | 0.154383i | −0.360306 | − | 0.932834i | \(-0.617328\pi\) |
0.627705 | + | 0.778451i | \(0.283994\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −137.809 | + | 238.692i | −0.150941 | + | 0.261437i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 586.071i | − | 0.639117i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 309.762 | 0.337064 | 0.168532 | − | 0.985696i | \(-0.446097\pi\) | ||||
0.168532 | + | 0.985696i | \(0.446097\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1526.40 | − | 969.768i | −1.65733 | − | 1.05295i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 373.985 | + | 215.920i | 0.405184 | + | 0.233933i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −270.256 | − | 22.9699i | −0.291538 | − | 0.0247787i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −416.036 | + | 240.198i | −0.447832 | + | 0.258556i | −0.706914 | − | 0.707300i | \(-0.749913\pi\) |
0.259082 | + | 0.965855i | \(0.416580\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −559.507 | + | 969.095i | −0.600975 | + | 1.04092i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 228.689 | + | 437.982i | 0.245112 | + | 0.469435i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −918.055 | −0.979781 | −0.489891 | − | 0.871784i | \(-0.662963\pi\) | ||||
−0.489891 | + | 0.871784i | \(0.662963\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.86482 | + | 43.9609i | −0.00198597 | + | 0.0468167i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1228.87 | + | 709.489i | 1.30592 | + | 0.753973i | 0.981413 | − | 0.191910i | \(-0.0614682\pi\) |
0.324507 | + | 0.945883i | \(0.394802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −234.865 | − | 406.798i | −0.249061 | − | 0.431387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −232.422 | + | 134.189i | −0.245430 | + | 0.141699i | −0.617670 | − | 0.786438i | \(-0.711923\pi\) |
0.372240 | + | 0.928136i | \(0.378590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −509.361 | + | 882.238i | −0.536734 | + | 0.929651i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1415.09 | + | 60.0282i | 1.48800 | + | 0.0631212i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 476.437i | 0.499934i | 0.968254 | + | 0.249967i | \(0.0804198\pi\) | ||||
−0.968254 | + | 0.249967i | \(0.919580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −275.046 | + | 143.613i | −0.287404 | + | 0.150066i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.4205 | + | 10.0577i | 0.0181652 | + | 0.0104877i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 459.326 | + | 795.575i | 0.477966 | + | 0.827862i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −85.2376 | + | 40.0043i | −0.0885125 | + | 0.0415413i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 506.040 | − | 876.486i | 0.523309 | − | 0.906398i | −0.476323 | − | 0.879270i | \(-0.658031\pi\) |
0.999632 | − | 0.0271272i | \(-0.00863592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1411.15 | − | 2221.13i | 1.45630 | − | 2.29219i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 772.488i | 0.795560i | 0.917481 | + | 0.397780i | \(0.130219\pi\) | ||||
−0.917481 | + | 0.397780i | \(0.869781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −139.050 | −0.142909 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1407.33 | − | 812.523i | −1.44046 | − | 0.831651i | −0.442581 | − | 0.896728i | \(-0.645937\pi\) |
−0.997880 | + | 0.0650777i | \(0.979270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 469.502 | + | 813.202i | 0.479573 | + | 0.830645i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −716.050 | − | 1525.70i | −0.729918 | − | 1.55524i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 698.536 | − | 403.300i | 0.710616 | − | 0.410275i | −0.100673 | − | 0.994920i | \(-0.532100\pi\) |
0.811289 | + | 0.584645i | \(0.198766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −214.750 | − | 411.287i | −0.217579 | − | 0.416704i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 679.768i | 0.687329i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 434.414 | 0.438359 | 0.219180 | − | 0.975685i | \(-0.429662\pi\) | ||||
0.219180 | + | 0.975685i | \(0.429662\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.5030 | − | 1449.86i | 0.0619366 | − | 1.46008i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −883.384 | − | 1530.07i | −0.886042 | − | 1.53467i | −0.844514 | − | 0.535533i | \(-0.820111\pi\) |
−0.0415279 | − | 0.999137i | \(-0.513223\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 227.935 | − | 1782.50i | 0.228164 | − | 1.78428i |
(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 | 900.3.p.e.401.7 | yes | 16 | |
3.2 | odd | 2 | 2700.3.p.d.2501.7 | 16 | |||
5.2 | odd | 4 | 900.3.u.d.149.12 | 32 | |||
5.3 | odd | 4 | 900.3.u.d.149.5 | 32 | |||
5.4 | even | 2 | 900.3.p.d.401.2 | yes | 16 | ||
9.2 | odd | 6 | inner | 900.3.p.e.101.7 | yes | 16 | |
9.7 | even | 3 | 2700.3.p.d.1601.7 | 16 | |||
15.2 | even | 4 | 2700.3.u.d.449.3 | 32 | |||
15.8 | even | 4 | 2700.3.u.d.449.14 | 32 | |||
15.14 | odd | 2 | 2700.3.p.e.2501.2 | 16 | |||
45.2 | even | 12 | 900.3.u.d.749.5 | 32 | |||
45.7 | odd | 12 | 2700.3.u.d.2249.14 | 32 | |||
45.29 | odd | 6 | 900.3.p.d.101.2 | ✓ | 16 | ||
45.34 | even | 6 | 2700.3.p.e.1601.2 | 16 | |||
45.38 | even | 12 | 900.3.u.d.749.12 | 32 | |||
45.43 | odd | 12 | 2700.3.u.d.2249.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.p.d.101.2 | ✓ | 16 | 45.29 | odd | 6 | ||
900.3.p.d.401.2 | yes | 16 | 5.4 | even | 2 | ||
900.3.p.e.101.7 | yes | 16 | 9.2 | odd | 6 | inner | |
900.3.p.e.401.7 | yes | 16 | 1.1 | even | 1 | trivial | |
900.3.u.d.149.5 | 32 | 5.3 | odd | 4 | |||
900.3.u.d.149.12 | 32 | 5.2 | odd | 4 | |||
900.3.u.d.749.5 | 32 | 45.2 | even | 12 | |||
900.3.u.d.749.12 | 32 | 45.38 | even | 12 | |||
2700.3.p.d.1601.7 | 16 | 9.7 | even | 3 | |||
2700.3.p.d.2501.7 | 16 | 3.2 | odd | 2 | |||
2700.3.p.e.1601.2 | 16 | 45.34 | even | 6 | |||
2700.3.p.e.2501.2 | 16 | 15.14 | odd | 2 | |||
2700.3.u.d.449.3 | 32 | 15.2 | even | 4 | |||
2700.3.u.d.449.14 | 32 | 15.8 | even | 4 | |||
2700.3.u.d.2249.3 | 32 | 45.43 | odd | 12 | |||
2700.3.u.d.2249.14 | 32 | 45.7 | odd | 12 |