Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
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, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
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.u (of order \(6\), degree \(2\), not 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: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.5 | ||
Character | \(\chi\) | \(=\) | 900.149 |
Dual form | 900.3.u.d.749.5 |
$q$-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 | ||||||||
\(3\) | −1.60876 | + | 2.53217i | −0.536255 | + | 0.844056i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.13249 | − | 4.69530i | 1.16178 | − | 0.670757i | 0.210053 | − | 0.977690i | \(-0.432636\pi\) |
0.951731 | + | 0.306933i | \(0.0993029\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −11.9889 | − | 6.92181i | −0.922226 | − | 0.532447i | −0.0378812 | − | 0.999282i | \(-0.512061\pi\) |
−0.884344 | + | 0.466835i | \(0.845394\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.7147 | −1.80675 | −0.903373 | − | 0.428856i | \(-0.858917\pi\) | ||||
−0.903373 | + | 0.428856i | \(0.858917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.5585 | −1.50308 | −0.751540 | − | 0.659687i | \(-0.770689\pi\) | ||||
−0.751540 | + | 0.659687i | \(0.770689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.19398 | + | 28.1465i | −0.0568560 | + | 1.34031i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.16230 | + | 10.6734i | −0.267926 | + | 0.464062i | −0.968326 | − | 0.249689i | \(-0.919672\pi\) |
0.700400 | + | 0.713751i | \(0.253005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.7819 | + | 3.42472i | 0.991923 | + | 0.126841i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.02918 | − | 2.90360i | 0.173420 | − | 0.100124i | −0.410777 | − | 0.911736i | \(-0.634743\pi\) |
0.584198 | + | 0.811612i | \(0.301409\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | −2.26449 | + | 53.3826i | −0.0686210 | + | 1.61765i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.5560i | 1.79881i | 0.437116 | + | 0.899405i | \(0.356000\pi\) | ||||
−0.437116 | + | 0.899405i | \(0.644000\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −47.7660 | + | 27.5777i | −1.11084 | + | 0.641342i | −0.939046 | − | 0.343792i | \(-0.888289\pi\) |
−0.171791 | + | 0.985133i | \(0.554955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.23479 | + | 14.2631i | 0.175208 | + | 0.303470i | 0.940233 | − | 0.340531i | \(-0.110607\pi\) |
−0.765025 | + | 0.644001i | \(0.777273\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | −69.8669 | −1.31824 | −0.659121 | − | 0.752036i | \(-0.729072\pi\) | ||||
−0.659121 | + | 0.752036i | \(0.729072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 45.9439 | − | 72.3150i | 0.806034 | − | 1.26868i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −91.2592 | − | 52.6885i | −1.54677 | − | 0.893026i | −0.998386 | − | 0.0567963i | \(-0.981911\pi\) |
−0.548380 | − | 0.836229i | \(-0.684755\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −69.3508 | − | 48.3044i | −1.10081 | − | 0.766736i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39.8118 | − | 22.9853i | −0.594206 | − | 0.343065i | 0.172553 | − | 0.985000i | \(-0.444798\pi\) |
−0.766759 | + | 0.641935i | \(0.778132\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 73.5877i | 1.00805i | 0.863689 | + | 0.504026i | \(0.168148\pi\) | ||||
−0.863689 | + | 0.504026i | \(0.831852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 83.6241 | − | 144.841i | 1.08603 | − | 1.88105i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 47.3263 | + | 81.9715i | 0.599067 | + | 1.03761i | 0.992959 | + | 0.118458i | \(0.0377950\pi\) |
−0.393892 | + | 0.919157i | \(0.628872\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51.7578 | + | 62.3068i | −0.638985 | + | 0.769220i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.73763 | − | 13.4020i | −0.0932245 | − | 0.161470i | 0.815642 | − | 0.578557i | \(-0.196384\pi\) |
−0.908866 | + | 0.417088i | \(0.863051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.738362 | + | 17.4059i | −0.00848692 | + | 0.200068i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 52.7229i | − | 0.592392i | −0.955127 | − | 0.296196i | \(-0.904282\pi\) | ||
0.955127 | − | 0.296196i | \(-0.0957181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −130.000 | −1.42857 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.03604 | − | 17.3057i | −0.0971617 | − | 0.186083i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.0130 | − | 38.1126i | 0.680546 | − | 0.392913i | −0.119515 | − | 0.992832i | \(-0.538134\pi\) |
0.800061 | + | 0.599919i | \(0.204801\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −26.0991 | − | 15.0683i | −0.253390 | − | 0.146295i | 0.367926 | − | 0.929855i | \(-0.380068\pi\) |
−0.621315 | + | 0.783561i | \(0.713401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4620 | 0.0977760 | 0.0488880 | − | 0.998804i | \(-0.484432\pi\) | ||||
0.0488880 | + | 0.998804i | \(0.484432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 187.263 | 1.71801 | 0.859006 | − | 0.511965i | \(-0.171082\pi\) | ||||
0.859006 | + | 0.511965i | \(0.171082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −168.531 | − | 107.073i | −1.51830 | − | 0.964620i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 46.5365 | − | 80.6035i | 0.411827 | − | 0.713305i | −0.583263 | − | 0.812284i | \(-0.698224\pi\) |
0.995090 | + | 0.0989784i | \(0.0315575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.5515 | + | 124.145i | −0.0901836 | + | 1.06107i | ||||
\(118\) | 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 | ||||||||
\(123\) | 101.355 | − | 52.9217i | 0.824024 | − | 0.430258i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 48.4899i | − | 0.381810i | −0.981608 | − | 0.190905i | \(-0.938858\pi\) | ||
0.981608 | − | 0.190905i | \(-0.0611423\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | −232.252 | + | 134.091i | −1.74626 | + | 1.00820i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.07104 | − | 1.85510i | −0.00781782 | − | 0.0135409i | 0.862090 | − | 0.506755i | \(-0.169155\pi\) |
−0.869908 | + | 0.493214i | \(0.835822\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.40371 | − | 12.8236i | 0.0532641 | − | 0.0922562i | −0.838164 | − | 0.545418i | \(-0.816371\pi\) |
0.891428 | + | 0.453162i | \(0.149704\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −49.3644 | − | 2.09404i | −0.350102 | − | 0.0148514i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −246.558 | −1.72418 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.4075 | + | 104.200i | 0.370119 | + | 0.708847i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 177.328 | + | 102.380i | 1.19012 | + | 0.687116i | 0.958334 | − | 0.285651i | \(-0.0922099\pi\) |
0.231785 | + | 0.972767i | \(0.425543\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 117.445 | + | 250.242i | 0.767617 | + | 1.63557i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8545 | − | 9.15362i | −0.100984 | − | 0.0583033i | 0.448657 | − | 0.893704i | \(-0.351902\pi\) |
−0.549642 | + | 0.835401i | \(0.685236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 112.399 | − | 176.915i | 0.706914 | − | 1.11267i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 115.735i | 0.718853i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 43.2107i | 0.265096i | 0.991177 | + | 0.132548i | \(0.0423159\pi\) | ||||
−0.991177 | + | 0.132548i | \(0.957684\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 35.6591 | − | 61.7635i | 0.213528 | − | 0.369841i | −0.739288 | − | 0.673389i | \(-0.764838\pi\) |
0.952816 | + | 0.303548i | \(0.0981713\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | −83.9449 | − | 145.397i | −0.485230 | − | 0.840444i | 0.514626 | − | 0.857415i | \(-0.327931\pi\) |
−0.999856 | + | 0.0169713i | \(0.994598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 280.231 | − | 146.320i | 1.58322 | − | 0.826668i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 117.614i | 0.657063i | 0.944493 | + | 0.328531i | \(0.106554\pi\) | ||||
−0.944493 | + | 0.328531i | \(0.893446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 96.5280 | 0.533304 | 0.266652 | − | 0.963793i | \(-0.414083\pi\) | ||||
0.266652 | + | 0.963793i | \(0.414083\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 201.167 | + | 8.53353i | 1.09927 | + | 0.0466313i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −473.746 | + | 273.517i | −2.53340 | + | 1.46266i | ||||
\(188\) | 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 | ||||||||
\(193\) | 53.1675 | + | 30.6963i | 0.275479 | + | 0.159048i | 0.631375 | − | 0.775478i | \(-0.282491\pi\) |
−0.355896 | + | 0.934526i | \(0.615824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −289.758 | −1.47085 | −0.735427 | − | 0.677604i | \(-0.763018\pi\) | ||||
−0.735427 | + | 0.677604i | \(0.763018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 100.347 | 0.504254 | 0.252127 | − | 0.967694i | \(-0.418870\pi\) | ||||
0.252127 | + | 0.967694i | \(0.418870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 122.251 | − | 63.8322i | 0.608212 | − | 0.317573i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.2665 | − | 47.2270i | 0.134318 | − | 0.232645i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 110.523 | + | 9.39369i | 0.533927 | + | 0.0453801i | ||||
\(208\) | 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 | ||||||||
\(213\) | 78.9889 | + | 50.1840i | 0.370840 | + | 0.235606i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 61.1100i | 0.281613i | ||||||||
\(218\) | 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 | ||||||||
\(223\) | 192.880 | − | 111.359i | 0.864932 | − | 0.499369i | −0.000728529 | − | 1.00000i | \(-0.500232\pi\) |
0.865661 | + | 0.500631i | \(0.166899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −68.0187 | − | 117.812i | −0.299642 | − | 0.518995i | 0.676412 | − | 0.736523i | \(-0.263534\pi\) |
−0.976054 | + | 0.217528i | \(0.930201\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −197.762 | + | 342.533i | −0.863589 | + | 1.49578i | 0.00485333 | + | 0.999988i | \(0.498455\pi\) |
−0.868442 | + | 0.495791i | \(0.834878\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 232.231 | + | 444.766i | 1.00533 | + | 1.92539i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 403.347 | 1.73110 | 0.865551 | − | 0.500821i | \(-0.166969\pi\) | ||||
0.865551 | + | 0.500821i | \(0.166969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −283.703 | − | 12.0347i | −1.19706 | − | 0.0507793i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −370.505 | − | 213.911i | −1.55023 | − | 0.895025i | −0.998122 | − | 0.0612505i | \(-0.980491\pi\) |
−0.552106 | − | 0.833774i | \(-0.686176\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −74.5053 | − | 231.296i | −0.306606 | − | 0.951836i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 342.386 | + | 197.677i | 1.38618 | + | 0.800311i | ||||
\(248\) | 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 | ||||||||
\(253\) | 219.504i | 0.867603i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 44.6196 | − | 77.2834i | 0.173617 | − | 0.300713i | −0.766065 | − | 0.642763i | \(-0.777788\pi\) |
0.939682 | + | 0.342050i | \(0.111121\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | −168.170 | − | 291.278i | −0.639428 | − | 1.10752i | −0.985558 | − | 0.169335i | \(-0.945838\pi\) |
0.346130 | − | 0.938186i | \(-0.387495\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 133.503 | + | 84.8186i | 0.500012 | + | 0.317673i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 225.504i | − | 0.838305i | −0.907916 | − | 0.419153i | \(-0.862327\pi\) | ||
0.907916 | − | 0.419153i | \(-0.137673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −196.656 | −0.725669 | −0.362834 | − | 0.931854i | \(-0.618191\pi\) | ||||
−0.362834 | + | 0.931854i | \(0.618191\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 209.139 | − | 329.182i | 0.766077 | − | 1.20579i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −154.236 | + | 89.0481i | −0.556808 | + | 0.321473i | −0.751863 | − | 0.659319i | \(-0.770845\pi\) |
0.195055 | + | 0.980792i | \(0.437511\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −105.635 | − | 60.9884i | −0.373269 | − | 0.215507i | 0.301617 | − | 0.953429i | \(-0.402474\pi\) |
−0.674886 | + | 0.737922i | \(0.735807\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −357.905 | −1.24706 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 654.391 | 2.26433 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.69173 | + | 228.470i | −0.0333049 | + | 0.785121i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −44.5599 | + | 77.1800i | −0.152081 | + | 0.263413i | −0.931992 | − | 0.362478i | \(-0.881931\pi\) |
0.779911 | + | 0.625890i | \(0.215264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 443.584 | − | 185.672i | 1.49355 | − | 0.625160i | ||||
\(298\) | 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 | ||||||||
\(303\) | −10.2130 | + | 240.759i | −0.0337064 | + | 0.794585i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 602.803i | 1.96353i | 0.190105 | + | 0.981764i | \(0.439117\pi\) | ||||
−0.190105 | + | 0.981764i | \(0.560883\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −12.7018 | + | 7.33340i | −0.0405809 | + | 0.0234294i | −0.520153 | − | 0.854073i | \(-0.674125\pi\) |
0.479572 | + | 0.877502i | \(0.340792\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −236.060 | − | 408.868i | −0.744670 | − | 1.28981i | −0.950349 | − | 0.311186i | \(-0.899274\pi\) |
0.205679 | − | 0.978619i | \(-0.434060\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 877.166 | 2.71568 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −301.263 | + | 474.182i | −0.921292 | + | 1.45010i | ||||
\(328\) | 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 | ||||||||
\(333\) | 542.253 | − | 254.494i | 1.62839 | − | 0.764246i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −314.346 | − | 181.488i | −0.932778 | − | 0.538540i | −0.0450890 | − | 0.998983i | \(-0.514357\pi\) |
−0.887689 | + | 0.460443i | \(0.847690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 129.236 | + | 247.510i | 0.381226 | + | 0.730118i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 115.901i | 0.339886i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 92.1855i | 0.268762i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 184.089 | − | 318.851i | 0.530515 | − | 0.918879i | −0.468851 | − | 0.883277i | \(-0.655332\pi\) |
0.999366 | − | 0.0356015i | \(-0.0113347\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 199.861 | + | 346.170i | 0.572668 | + | 0.991890i | 0.996291 | + | 0.0860512i | \(0.0274249\pi\) |
−0.423623 | + | 0.905839i | \(0.639242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −297.381 | − | 226.438i | −0.847240 | − | 0.645123i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −277.703 | − | 480.996i | −0.786694 | − | 1.36259i | −0.927982 | − | 0.372626i | \(-0.878458\pi\) |
0.141288 | − | 0.989969i | \(-0.454876\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 36.6726 | − | 864.509i | 0.102724 | − | 2.42159i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 670.647i | 1.86810i | 0.357147 | + | 0.934048i | \(0.383749\pi\) | ||||
−0.357147 | + | 0.934048i | \(0.616251\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 454.590 | 1.25925 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 272.436 | + | 521.766i | 0.750512 | + | 1.43737i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 81.5985 | − | 47.1109i | 0.222339 | − | 0.128368i | −0.384694 | − | 0.923044i | \(-0.625693\pi\) |
0.607033 | + | 0.794677i | \(0.292360\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 166.777 | + | 96.2886i | 0.447123 | + | 0.258146i | 0.706614 | − | 0.707599i | \(-0.250222\pi\) |
−0.259492 | + | 0.965745i | \(0.583555\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −80.3927 | −0.213243 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −184.387 | −0.486510 | −0.243255 | − | 0.969962i | \(-0.578215\pi\) | ||||
−0.243255 | + | 0.969962i | \(0.578215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 122.785 | + | 78.0088i | 0.322269 | + | 0.204748i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 332.462 | − | 575.841i | 0.868047 | − | 1.50350i | 0.00405754 | − | 0.999992i | \(-0.498708\pi\) |
0.863990 | − | 0.503510i | \(-0.167958\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 407.330 | + | 283.714i | 1.05253 | + | 0.733112i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −539.718 | + | 311.606i | −1.38745 | + | 0.801044i | −0.993027 | − | 0.117885i | \(-0.962388\pi\) |
−0.394422 | + | 0.918929i | \(0.629055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 189.273 | − | 327.830i | 0.484074 | − | 0.838441i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 165.969 | − | 86.6594i | 0.422313 | − | 0.220507i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 247.371i | − | 0.623100i | −0.950230 | − | 0.311550i | \(-0.899152\pi\) | ||
0.950230 | − | 0.311550i | \(-0.100848\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 78.0189 | − | 45.0443i | 0.193595 | − | 0.111772i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 592.687 | + | 1026.56i | 1.45623 | + | 2.52227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 87.0543 | − | 150.782i | 0.212847 | − | 0.368661i | −0.739758 | − | 0.672873i | \(-0.765060\pi\) |
0.952604 | + | 0.304212i | \(0.0983932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.42047 | + | 0.272357i | 0.0156216 | + | 0.000662669i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −989.553 | −2.39601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.5607 | + | 39.3776i | 0.0493063 | + | 0.0944307i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 265.100 | + | 153.055i | 0.632696 | + | 0.365287i | 0.781796 | − | 0.623535i | \(-0.214304\pi\) |
−0.149099 | + | 0.988822i | \(0.547637\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 84.7181 | − | 121.630i | 0.200279 | − | 0.287542i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −545.820 | − | 315.130i | −1.27827 | − | 0.738008i | ||||
\(428\) | 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 | ||||||||
\(433\) | − | 273.497i | − | 0.631633i | −0.948820 | − | 0.315817i | \(-0.897722\pi\) | ||
0.948820 | − | 0.315817i | \(-0.102278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 175.986 | − | 304.817i | 0.402715 | − | 0.697522i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −262.426 | − | 454.535i | −0.597781 | − | 1.03539i | −0.993148 | − | 0.116864i | \(-0.962716\pi\) |
0.395367 | − | 0.918523i | \(-0.370618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −351.382 | − | 29.8651i | −0.796784 | − | 0.0677212i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 44.2748 | + | 76.6862i | 0.0999431 | + | 0.173106i | 0.911661 | − | 0.410943i | \(-0.134801\pi\) |
−0.811718 | + | 0.584050i | \(0.801467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −544.522 | + | 284.318i | −1.21817 | + | 0.636059i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 46.0938i | 0.102659i | 0.998682 | + | 0.0513294i | \(0.0163458\pi\) | ||||
−0.998682 | + | 0.0513294i | \(0.983654\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −678.803 | −1.50511 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −44.6758 | − | 1.89515i | −0.0986220 | − | 0.00418355i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 163.904 | − | 94.6301i | 0.358652 | − | 0.207068i | −0.309837 | − | 0.950790i | \(-0.600275\pi\) |
0.668489 | + | 0.743722i | \(0.266941\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | −271.090 | − | 156.514i | −0.585507 | − | 0.338043i | 0.177812 | − | 0.984064i | \(-0.443098\pi\) |
−0.763319 | + | 0.646022i | \(0.776431\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −148.419 | −0.317814 | −0.158907 | − | 0.987294i | \(-0.550797\pi\) | ||||
−0.158907 | + | 0.987294i | \(0.550797\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −431.692 | −0.920452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.6847 | − | 25.4203i | 0.103365 | − | 0.0539710i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −491.164 | + | 850.721i | −1.03840 | + | 1.79856i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 267.154 | + | 569.228i | 0.560071 | + | 1.19335i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −273.219 | + | 157.743i | −0.570395 | + | 0.329317i | −0.757307 | − | 0.653059i | \(-0.773485\pi\) |
0.186912 | + | 0.982377i | \(0.440152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 460.688 | − | 797.935i | 0.957771 | − | 1.65891i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −293.061 | − | 186.191i | −0.606752 | − | 0.385488i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 492.691i | − | 1.01169i | −0.862626 | − | 0.505843i | \(-0.831182\pi\) | ||
0.862626 | − | 0.505843i | \(-0.168818\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −154.470 | + | 89.1831i | −0.313326 | + | 0.180899i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −146.466 | − | 253.686i | −0.294700 | − | 0.510435i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.1379 | − | 24.4876i | 0.0283325 | − | 0.0490733i | −0.851512 | − | 0.524336i | \(-0.824314\pi\) |
0.879844 | + | 0.475263i | \(0.157647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 99.0283 | + | 189.658i | 0.197661 | + | 0.378558i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.5709 | 0.0627652 | 0.0313826 | − | 0.999507i | \(-0.490009\pi\) | ||||
0.0313826 | + | 0.999507i | \(0.490009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −67.8769 | − | 2.87935i | −0.133880 | − | 0.00567918i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −204.163 | − | 117.874i | −0.401107 | − | 0.231579i | 0.285855 | − | 0.958273i | \(-0.407723\pi\) |
−0.686961 | + | 0.726694i | \(0.741056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 345.516 | + | 598.452i | 0.676157 | + | 1.17114i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −764.852 | − | 97.8049i | −1.49094 | − | 0.190653i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 254.028 | + | 146.663i | 0.491350 | + | 0.283681i | ||||
\(518\) | 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 | ||||||||
\(523\) | 201.726i | 0.385709i | 0.981227 | + | 0.192855i | \(0.0617745\pi\) | ||||
−0.981227 | + | 0.192855i | \(0.938225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 99.9391 | − | 173.100i | 0.189638 | − | 0.328462i | ||||
\(528\) | 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 | ||||||||
\(533\) | 263.812 | + | 456.937i | 0.494958 | + | 0.857292i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −297.819 | − | 189.213i | −0.554598 | − | 0.352353i | ||||
\(538\) | 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 | ||||||||
\(543\) | −155.291 | + | 244.425i | −0.285987 | + | 0.450138i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 556.158 | − | 321.098i | 1.01674 | − | 0.587017i | 0.103584 | − | 0.994621i | \(-0.466969\pi\) |
0.913159 | + | 0.407604i | \(0.133636\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 769.761 | + | 444.422i | 1.39197 | + | 0.803656i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −145.052 | −0.260417 | −0.130208 | − | 0.991487i | \(-0.541565\pi\) | ||||
−0.130208 | + | 0.991487i | \(0.541565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 763.551 | 1.36592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 69.5532 | − | 1639.63i | 0.123981 | − | 2.92269i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −422.949 | + | 732.570i | −0.751242 | + | 1.30119i | 0.195979 | + | 0.980608i | \(0.437212\pi\) |
−0.947221 | + | 0.320581i | \(0.896122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −128.371 | + | 749.727i | −0.226403 | + | 1.32227i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 725.474 | − | 418.853i | 1.27500 | − | 0.736121i | 0.299074 | − | 0.954230i | \(-0.403322\pi\) |
0.975924 | + | 0.218109i | \(0.0699888\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −7.62104 | + | 179.656i | −0.0133003 | + | 0.313537i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 713.999i | 1.23743i | 0.785614 | + | 0.618717i | \(0.212347\pi\) | ||||
−0.785614 | + | 0.618717i | \(0.787653\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −1077.63 | + | 622.171i | −1.84843 | + | 1.06719i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 408.180 | + | 706.988i | 0.695366 | + | 1.20441i | 0.970057 | + | 0.242876i | \(0.0780909\pi\) |
−0.274692 | + | 0.961532i | \(0.588576\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | 64.6676 | 0.109052 | 0.0545258 | − | 0.998512i | \(-0.482635\pi\) | ||||
0.0545258 | + | 0.998512i | \(0.482635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −161.434 | + | 254.095i | −0.270409 | + | 0.425619i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 204.565 | + | 118.105i | 0.341510 | + | 0.197171i | 0.660940 | − | 0.750439i | \(-0.270158\pi\) |
−0.319430 | + | 0.947610i | \(0.603491\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −35.0384 | + | 412.250i | −0.0581068 | + | 0.683665i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 95.2911 | + | 55.0163i | 0.156987 | + | 0.0906365i | 0.576435 | − | 0.817143i | \(-0.304443\pi\) |
−0.419449 | + | 0.907779i | \(0.637777\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 75.7213 | + | 145.021i | 0.124337 | + | 0.238129i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 227.999i | − | 0.373157i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 387.013i | 0.631343i | 0.948869 | + | 0.315671i | \(0.102230\pi\) | ||||
−0.948869 | + | 0.315671i | \(0.897770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 192.373 | − | 333.200i | 0.311787 | − | 0.540032i | −0.666962 | − | 0.745092i | \(-0.732406\pi\) |
0.978749 | + | 0.205060i | \(0.0657390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −403.446 | − | 698.789i | −0.651771 | − | 1.12890i | −0.982693 | − | 0.185242i | \(-0.940693\pi\) |
0.330922 | − | 0.943658i | \(-0.392640\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −201.592 | + | 264.750i | −0.324624 | + | 0.426329i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −247.549 | − | 428.768i | −0.397351 | − | 0.688232i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 64.6706 | − | 1524.53i | 0.103143 | − | 2.43146i | ||||
\(628\) | 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 | ||||||||
\(633\) | −295.153 | − | 565.274i | −0.466277 | − | 0.893008i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −469.765 | + | 271.219i | −0.737464 | + | 0.425775i | ||||
\(638\) | 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 | ||||||||
\(643\) | −783.548 | − | 452.382i | −1.21858 | − | 0.703549i | −0.253968 | − | 0.967213i | \(-0.581736\pi\) |
−0.964615 | + | 0.263664i | \(0.915069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −360.764 | −0.557594 | −0.278797 | − | 0.960350i | \(-0.589936\pi\) | ||||
−0.278797 | + | 0.960350i | \(0.589936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1876.79 | −2.89181 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −154.741 | − | 98.3116i | −0.237697 | − | 0.151016i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 211.022 | − | 365.501i | 0.323158 | − | 0.559726i | −0.657980 | − | 0.753035i | \(-0.728589\pi\) |
0.981138 | + | 0.193310i | \(0.0619222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 599.543 | − | 281.382i | 0.912547 | − | 0.428283i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −520.928 | + | 300.758i | −0.790483 | + | 0.456385i | −0.840133 | − | 0.542381i | \(-0.817523\pi\) |
0.0496496 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −1130.75 | + | 590.411i | −1.70550 | + | 0.890514i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 71.5714i | 0.107303i | ||||||||
\(668\) | 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 | ||||||||
\(673\) | −50.6352 | + | 29.2343i | −0.0752381 | + | 0.0434387i | −0.537147 | − | 0.843489i | \(-0.680498\pi\) |
0.461909 | + | 0.886927i | \(0.347165\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 317.363 | + | 549.689i | 0.468778 | + | 0.811948i | 0.999363 | − | 0.0356841i | \(-0.0113610\pi\) |
−0.530585 | + | 0.847632i | \(0.678028\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 387.682 | 0.567617 | 0.283808 | − | 0.958881i | \(-0.408402\pi\) | ||||
0.283808 | + | 0.958881i | \(0.408402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −549.201 | − | 1051.82i | −0.799419 | − | 1.53104i | ||||
\(688\) | 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 | ||||||||
\(693\) | −1499.83 | − | 127.475i | −2.16425 | − | 0.183947i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1013.80 | + | 585.317i | 1.45452 | + | 0.839766i | ||||
\(698\) | 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 | ||||||||
\(703\) | − | 1900.74i | − | 2.70376i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 377.151 | − | 653.245i | 0.533453 | − | 0.923967i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −624.531 | − | 1081.72i | −0.880861 | − | 1.52570i | −0.850385 | − | 0.526161i | \(-0.823631\pi\) |
−0.0304761 | − | 0.999535i | \(-0.509702\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 486.884 | − | 699.022i | 0.684788 | − | 0.983153i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.1017 | − | 69.4581i | −0.0562436 | − | 0.0974167i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1137.71 | − | 594.048i | 1.58677 | − | 0.828519i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 418.228i | − | 0.581681i | −0.956772 | − | 0.290840i | \(-0.906065\pi\) | ||
0.956772 | − | 0.290840i | \(-0.0939348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −283.001 | −0.392512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 164.526 | + | 6.97921i | 0.227560 | + | 0.00965312i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 447.070 | − | 258.116i | 0.614952 | − | 0.355043i | −0.159949 | − | 0.987125i | \(-0.551133\pi\) |
0.774901 | + | 0.632082i | \(0.217800\pi\) | |||||||
\(728\) | 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 | ||||||||
\(733\) | −7.14580 | − | 4.12563i | −0.00974871 | − | 0.00562842i | 0.495118 | − | 0.868826i | \(-0.335125\pi\) |
−0.504866 | + | 0.863197i | \(0.668458\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −818.747 | −1.11092 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −294.686 | −0.398763 | −0.199381 | − | 0.979922i | \(-0.563893\pi\) | ||||
−0.199381 | + | 0.979922i | \(0.563893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1051.37 | + | 548.965i | −1.41885 | + | 0.740843i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −253.191 | + | 438.540i | −0.340769 | + | 0.590229i | −0.984576 | − | 0.174959i | \(-0.944021\pi\) |
0.643807 | + | 0.765188i | \(0.277354\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −79.6034 | + | 114.287i | −0.106564 | + | 0.152995i | ||||
\(748\) | 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 | ||||||||
\(753\) | 1024.69 | + | 651.018i | 1.36081 | + | 0.864566i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 957.457i | − | 1.26480i | −0.774640 | − | 0.632402i | \(-0.782069\pi\) | ||
0.774640 | − | 0.632402i | \(-0.217931\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1522.92 | − | 879.257i | 1.99596 | − | 1.15237i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 729.400 | + | 1263.36i | 0.950978 | + | 1.64714i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −302.360 | + | 523.703i | −0.393186 | + | 0.681018i | −0.992868 | − | 0.119221i | \(-0.961960\pi\) |
0.599682 | + | 0.800238i | \(0.295294\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 123.912 | + | 237.315i | 0.160716 | + | 0.307802i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 596.625 | 0.771831 | 0.385915 | − | 0.922534i | \(-0.373886\pi\) | ||||
0.385915 | + | 0.922534i | \(0.373886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1873.32 | − | 79.4662i | −2.41096 | − | 0.102273i | ||||
\(778\) | 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 | ||||||||
\(783\) | 144.635 | − | 60.5404i | 0.184719 | − | 0.0773186i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −471.499 | − | 272.220i | −0.599109 | − | 0.345896i | 0.169582 | − | 0.985516i | \(-0.445758\pi\) |
−0.768691 | + | 0.639620i | \(0.779092\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1008.11 | + | 42.7642i | 1.27771 | + | 0.0542005i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 874.010i | − | 1.10494i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 929.129i | 1.17166i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −115.508 | + | 200.065i | −0.144928 | + | 0.251023i | −0.929346 | − | 0.369210i | \(-0.879628\pi\) |
0.784418 | + | 0.620232i | \(0.212962\pi\) | |||||||
\(798\) | 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 | ||||||||
\(803\) | 655.306 | + | 1135.02i | 0.816072 | + | 1.41348i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 571.014 | + | 362.783i | 0.707577 | + | 0.449545i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 75.6693i | 0.0935344i | 0.998906 | + | 0.0467672i | \(0.0148919\pi\) | ||||
−0.998906 | + | 0.0467672i | \(0.985108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1184.72 | 1.46081 | 0.730404 | − | 0.683015i | \(-0.239332\pi\) | ||||
0.730404 | + | 0.683015i | \(0.239332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 316.373 | − | 497.967i | 0.389143 | − | 0.612505i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1364.13 | − | 787.579i | 1.66968 | − | 0.963988i | ||||
\(818\) | 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 | ||||||||
\(823\) | −659.371 | − | 380.688i | −0.801180 | − | 0.462562i | 0.0427034 | − | 0.999088i | \(-0.486403\pi\) |
−0.843884 | + | 0.536526i | \(0.819736\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1019.60 | −1.23290 | −0.616448 | − | 0.787396i | \(-0.711429\pi\) | ||||
−0.616448 | + | 0.787396i | \(0.711429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −58.7988 | −0.0709274 | −0.0354637 | − | 0.999371i | \(-0.511291\pi\) | ||||
−0.0354637 | + | 0.999371i | \(0.511291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.6442 | − | 533.809i | 0.0272494 | − | 0.642369i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −601.750 | + | 1042.26i | −0.722388 | + | 1.25121i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −106.444 | + | 139.792i | −0.127173 | + | 0.167016i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1005.77 | − | 580.682i | 1.19877 | − | 0.692112i | 0.238492 | − | 0.971144i | \(-0.423347\pi\) |
0.960282 | + | 0.279032i | \(0.0900136\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −403.638 | + | 699.122i | −0.479950 | + | 0.831298i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.9221 | + | 257.473i | −0.0129562 | + | 0.305425i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1842.46i | − | 2.17528i | ||||||
\(848\) | 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 | ||||||||
\(853\) | 1204.25 | − | 695.272i | 1.41178 | − | 0.815090i | 0.416222 | − | 0.909263i | \(-0.363354\pi\) |
0.995556 | + | 0.0941731i | \(0.0300207\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 528.220 | + | 914.904i | 0.616359 | + | 1.06757i | 0.990144 | + | 0.140050i | \(0.0447264\pi\) |
−0.373785 | + | 0.927515i | \(0.621940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −537.750 | + | 931.410i | −0.626018 | + | 1.08430i | 0.362325 | + | 0.932052i | \(0.381983\pi\) |
−0.988343 | + | 0.152244i | \(0.951350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 575.785 | − | 906.277i | 0.668740 | − | 1.05259i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 66.3453 | 0.0768776 | 0.0384388 | − | 0.999261i | \(-0.487762\pi\) | ||||
0.0384388 | + | 0.999261i | \(0.487762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1052.76 | + | 1657.03i | −1.21426 | + | 1.91122i | ||||
\(868\) | 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 | ||||||||
\(873\) | −562.933 | − | 392.096i | −0.644826 | − | 0.449136i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 366.507 | + | 211.603i | 0.417909 | + | 0.241280i | 0.694182 | − | 0.719799i | \(-0.255766\pi\) |
−0.276273 | + | 0.961079i | \(0.589099\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 44.5609i | − | 0.0504653i | −0.999682 | − | 0.0252327i | \(-0.991967\pi\) | ||
0.999682 | − | 0.0252327i | \(-0.00803266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 706.516 | − | 1223.72i | 0.796523 | − | 1.37962i | −0.125345 | − | 0.992113i | \(-0.540004\pi\) |
0.921868 | − | 0.387505i | \(-0.126663\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −235.174 | − | 407.333i | −0.263352 | − | 0.456140i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.6933 | + | 511.392i | −0.0241843 | + | 0.570113i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.7908i | 0.0420365i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2145.94 | 2.38173 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −719.183 | − | 1377.37i | −0.796438 | − | 1.52533i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −261.298 | + | 150.861i | −0.288090 | + | 0.166329i | −0.637080 | − | 0.770797i | \(-0.719858\pi\) |
0.348990 | + | 0.937126i | \(0.386525\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −238.692 | − | 137.809i | −0.261437 | − | 0.150941i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −586.071 | −0.639117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −309.762 | −0.337064 | −0.168532 | − | 0.985696i | \(-0.553903\pi\) | ||||
−0.168532 | + | 0.985696i | \(0.553903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1526.40 | − | 969.768i | −1.65733 | − | 1.05295i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −215.920 | + | 373.985i | −0.233933 | + | 0.405184i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.9699 | + | 270.256i | −0.0247787 | + | 0.291538i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 416.036 | − | 240.198i | 0.447832 | − | 0.258556i | −0.259082 | − | 0.965855i | \(-0.583420\pi\) |
0.706914 | + | 0.707300i | \(0.250087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −559.507 | + | 969.095i | −0.600975 | + | 1.04092i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −437.982 | + | 228.689i | −0.469435 | + | 0.245112i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 918.055i | 0.979781i | 0.871784 | + | 0.489891i | \(0.162963\pi\) | ||||
−0.871784 | + | 0.489891i | \(0.837037\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 406.798 | − | 234.865i | 0.431387 | − | 0.249061i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 134.189 | + | 232.422i | 0.141699 | + | 0.245430i | 0.928136 | − | 0.372240i | \(-0.121410\pi\) |
−0.786438 | + | 0.617670i | \(0.788077\pi\) | |||||||
\(948\) | 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 | ||||||||
\(953\) | −476.437 | −0.499934 | −0.249967 | − | 0.968254i | \(-0.580420\pi\) | ||||
−0.249967 | + | 0.968254i | \(0.580420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 143.613 | + | 275.046i | 0.150066 | + | 0.287404i | ||||
\(958\) | 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 | ||||||||
\(963\) | −40.0043 | − | 85.2376i | −0.0415413 | − | 0.0885125i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −876.486 | − | 506.040i | −0.906398 | − | 0.523309i | −0.0271272 | − | 0.999632i | \(-0.508636\pi\) |
−0.879270 | + | 0.476323i | \(0.841969\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | − | 139.050i | − | 0.142909i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −812.523 | + | 1407.33i | −0.831651 | + | 1.44046i | 0.0650777 | + | 0.997880i | \(0.479270\pi\) |
−0.896728 | + | 0.442581i | \(0.854063\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 403.300 | + | 698.536i | 0.410275 | + | 0.710616i | 0.994920 | − | 0.100673i | \(-0.0320995\pi\) |
−0.584645 | + | 0.811289i | \(0.698766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −411.287 | + | 214.750i | −0.416704 | + | 0.217579i | ||||
\(988\) | 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 | ||||||||
\(993\) | 1449.86 | + | 61.5030i | 1.46008 | + | 0.0619366i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1530.07 | + | 883.384i | −1.53467 | + | 0.886042i | −0.535533 | + | 0.844514i | \(0.679889\pi\) |
−0.999137 | + | 0.0415279i | \(0.986777\pi\) | |||||||
\(998\) | 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.u.d.149.5 | 32 | ||
3.2 | odd | 2 | 2700.3.u.d.449.14 | 32 | |||
5.2 | odd | 4 | 900.3.p.e.401.7 | yes | 16 | ||
5.3 | odd | 4 | 900.3.p.d.401.2 | yes | 16 | ||
5.4 | even | 2 | inner | 900.3.u.d.149.12 | 32 | ||
9.2 | odd | 6 | inner | 900.3.u.d.749.12 | 32 | ||
9.7 | even | 3 | 2700.3.u.d.2249.3 | 32 | |||
15.2 | even | 4 | 2700.3.p.d.2501.7 | 16 | |||
15.8 | even | 4 | 2700.3.p.e.2501.2 | 16 | |||
15.14 | odd | 2 | 2700.3.u.d.449.3 | 32 | |||
45.2 | even | 12 | 900.3.p.e.101.7 | yes | 16 | ||
45.7 | odd | 12 | 2700.3.p.d.1601.7 | 16 | |||
45.29 | odd | 6 | inner | 900.3.u.d.749.5 | 32 | ||
45.34 | even | 6 | 2700.3.u.d.2249.14 | 32 | |||
45.38 | even | 12 | 900.3.p.d.101.2 | ✓ | 16 | ||
45.43 | odd | 12 | 2700.3.p.e.1601.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.p.d.101.2 | ✓ | 16 | 45.38 | even | 12 | ||
900.3.p.d.401.2 | yes | 16 | 5.3 | odd | 4 | ||
900.3.p.e.101.7 | yes | 16 | 45.2 | even | 12 | ||
900.3.p.e.401.7 | yes | 16 | 5.2 | odd | 4 | ||
900.3.u.d.149.5 | 32 | 1.1 | even | 1 | trivial | ||
900.3.u.d.149.12 | 32 | 5.4 | even | 2 | inner | ||
900.3.u.d.749.5 | 32 | 45.29 | odd | 6 | inner | ||
900.3.u.d.749.12 | 32 | 9.2 | odd | 6 | inner | ||
2700.3.p.d.1601.7 | 16 | 45.7 | odd | 12 | |||
2700.3.p.d.2501.7 | 16 | 15.2 | even | 4 | |||
2700.3.p.e.1601.2 | 16 | 45.43 | odd | 12 | |||
2700.3.p.e.2501.2 | 16 | 15.8 | even | 4 | |||
2700.3.u.d.449.3 | 32 | 15.14 | odd | 2 | |||
2700.3.u.d.449.14 | 32 | 3.2 | odd | 2 | |||
2700.3.u.d.2249.3 | 32 | 9.7 | even | 3 | |||
2700.3.u.d.2249.14 | 32 | 45.34 | even | 6 |