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 | 101.2 | ||
Root | \(0.127146 + 2.99730i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.101 |
Dual form | 900.3.p.d.401.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | 0.306933 | + | 0.951731i | \(0.400697\pi\) |
−0.977690 | + | 0.210053i | \(0.932636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.82376 | − | 8.14732i | 0.424862 | − | 0.905258i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.4241 | + | 8.90510i | 1.40219 | + | 0.809554i | 0.994617 | − | 0.103619i | \(-0.0330422\pi\) |
0.407572 | + | 0.913173i | \(0.366376\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.92181 | + | 11.9889i | 0.532447 | + | 0.922226i | 0.999282 | + | 0.0378812i | \(0.0120608\pi\) |
−0.466835 | + | 0.884344i | \(0.654606\pi\) | |||||||
\(14\) | 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 | \(-0.753005\pi\) |
0.249689 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(24\) | 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 | 0.410777 | − | 0.911736i | \(-0.365257\pi\) |
−0.584198 | + | 0.811612i | \(0.698591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.25379 | − | 5.63573i | −0.104961 | − | 0.181798i | 0.808761 | − | 0.588137i | \(-0.200138\pi\) |
−0.913722 | + | 0.406339i | \(0.866805\pi\) | |||||||
\(32\) | 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 | \(-0.144000\pi\) | ||||
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −36.8146 | − | 19.2224i | −0.943963 | − | 0.492883i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −33.0070 | + | 19.0566i | −0.805049 | + | 0.464795i | −0.845233 | − | 0.534397i | \(-0.820539\pi\) |
0.0401848 | + | 0.999192i | \(0.487205\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.5777 | + | 47.7660i | −0.641342 | + | 1.11084i | 0.343792 | + | 0.939046i | \(0.388289\pi\) |
−0.985133 | + | 0.171791i | \(0.945045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.2631 | + | 8.23479i | 0.303470 | + | 0.175208i | 0.644001 | − | 0.765025i | \(-0.277273\pi\) |
−0.340531 | + | 0.940233i | \(0.610607\pi\) | |||||||
\(48\) | 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 | 0.548380 | − | 0.836229i | \(-0.315245\pi\) |
0.998386 | − | 0.0567963i | \(-0.0180885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33.5580 | + | 58.1242i | −0.550131 | + | 0.952855i | 0.448133 | + | 0.893967i | \(0.352089\pi\) |
−0.998265 | + | 0.0588885i | \(0.981244\pi\) | |||||||
\(62\) | 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 | \(-0.278132\pi\) |
−0.985000 | + | 0.172553i | \(0.944798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.1132 | − | 32.7750i | 0.248018 | − | 0.475000i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 31.1942i | 0.439354i | 0.975573 | + | 0.219677i | \(0.0705004\pi\) | ||||
−0.975573 | + | 0.219677i | \(0.929500\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −73.5877 | −1.00805 | −0.504026 | − | 0.863689i | \(-0.668148\pi\) | ||||
−0.504026 | + | 0.863689i | \(0.668148\pi\) | |||||||
\(74\) | 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 | 0.393892 | + | 0.919157i | \(0.371128\pi\) |
−0.992959 | + | 0.118458i | \(0.962205\pi\) | |||||||
\(80\) | 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 | \(-0.303616\pi\) |
−0.417088 | + | 0.908866i | \(0.636949\pi\) | |||||||
\(84\) | 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 | \(-0.904282\pi\) | ||
0.955127 | − | 0.296196i | \(-0.0957181\pi\) | |||||||
\(90\) | 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 | \(-0.961866\pi\) |
0.599919 | + | 0.800061i | \(0.295199\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 131.531 | − | 91.6140i | 1.32859 | − | 0.925394i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 69.5637 | + | 40.1626i | 0.688750 | + | 0.397650i | 0.803144 | − | 0.595786i | \(-0.203159\pi\) |
−0.114394 | + | 0.993435i | \(0.536493\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0683 | + | 26.0991i | 0.146295 | + | 0.253390i | 0.929855 | − | 0.367926i | \(-0.119932\pi\) |
−0.783561 | + | 0.621315i | \(0.786599\pi\) | |||||||
\(104\) | 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 | \(-0.531557\pi\) |
0.812284 | + | 0.583263i | \(0.198224\pi\) | |||||||
\(114\) | 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 | \(-0.561142\pi\) | ||||
−0.190905 | + | 0.981608i | \(0.561142\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.01278 | − | 165.318i | −0.0543627 | − | 1.28153i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −54.0490 | + | 31.2052i | −0.412588 | + | 0.238208i | −0.691901 | − | 0.721992i | \(-0.743227\pi\) |
0.279313 | + | 0.960200i | \(0.409893\pi\) | |||||||
\(132\) | 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 | \(-0.335822\pi\) |
−0.506755 | + | 0.862090i | \(0.669155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.40371 | − | 12.8236i | −0.0532641 | − | 0.0922562i | 0.838164 | − | 0.545418i | \(-0.183629\pi\) |
−0.891428 | + | 0.453162i | \(0.850296\pi\) | |||||||
\(140\) | 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 | −0.958334 | − | 0.285651i | \(-0.907790\pi\) |
−0.231785 | + | 0.972767i | \(0.574457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.45266 | − | 12.9084i | 0.0493553 | − | 0.0854860i | −0.840292 | − | 0.542134i | \(-0.817617\pi\) |
0.889648 | + | 0.456648i | \(0.150950\pi\) | |||||||
\(152\) | 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 | \(-0.185236\pi\) |
−0.893704 | + | 0.448657i | \(0.851902\pi\) | |||||||
\(158\) | 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 | \(-0.542316\pi\) | ||||
−0.132548 | + | 0.991177i | \(0.542316\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −61.7635 | + | 35.6591i | −0.369841 | + | 0.213528i | −0.673389 | − | 0.739288i | \(-0.735162\pi\) |
0.303548 | + | 0.952816i | \(0.401829\pi\) | |||||||
\(168\) | 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 | \(-0.172069\pi\) |
−0.0169713 | + | 0.999856i | \(0.505402\pi\) | |||||||
\(174\) | 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 | \(0.106554\pi\) | ||||
−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 | ||||||||
\(183\) | −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 | 0.629694 | − | 0.776843i | \(-0.283180\pi\) |
−0.357919 | + | 0.933753i | \(0.616514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −30.6963 | − | 53.1675i | −0.159048 | − | 0.275479i | 0.775478 | − | 0.631375i | \(-0.217509\pi\) |
−0.934526 | + | 0.355896i | \(0.884176\pi\) | |||||||
\(194\) | 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 | −0.999991 | − | 0.00428419i | \(-0.998636\pi\) |
0.496285 | − | 0.868160i | \(-0.334697\pi\) | |||||||
\(212\) | 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 | \(-0.666899\pi\) |
1.00000 | 0.000728529i | \(0.000231898\pi\) | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −117.812 | − | 68.0187i | −0.518995 | − | 0.299642i | 0.217528 | − | 0.976054i | \(-0.430201\pi\) |
−0.736523 | + | 0.676412i | \(0.763534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 197.762 | + | 342.533i | 0.863589 | + | 1.49578i | 0.868442 | + | 0.495791i | \(0.165122\pi\) |
−0.00485333 | + | 0.999988i | \(0.501545\pi\) | |||||||
\(230\) | 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 | 0.552106 | − | 0.833774i | \(-0.313824\pi\) |
0.998122 | − | 0.0612505i | \(-0.0195088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.4457 | + | 47.5373i | −0.113882 | + | 0.197250i | −0.917332 | − | 0.398122i | \(-0.869662\pi\) |
0.803450 | + | 0.595372i | \(0.202995\pi\) | |||||||
\(242\) | 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 | \(0.298434\pi\) | ||||
−0.591759 | + | 0.806115i | \(0.701566\pi\) | |||||||
\(252\) | 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 | \(-0.722212\pi\) |
0.342050 | + | 0.939682i | \(0.388879\pi\) | |||||||
\(258\) | 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 | \(-0.112505\pi\) |
0.169335 | + | 0.985558i | \(0.445838\pi\) | |||||||
\(264\) | 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 | \(-0.862327\pi\) | ||
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 | ||||||||
\(273\) | 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 | \(-0.729155\pi\) |
0.980792 | + | 0.195055i | \(0.0624886\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −58.3578 | + | 4.96001i | −0.209168 | + | 0.0177778i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 74.3930 | + | 42.9508i | 0.264744 | + | 0.152850i | 0.626497 | − | 0.779424i | \(-0.284488\pi\) |
−0.361753 | + | 0.932274i | \(0.617822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 60.9884 | + | 105.635i | 0.215507 | + | 0.373269i | 0.953429 | − | 0.301617i | \(-0.0975263\pi\) |
−0.737922 | + | 0.674886i | \(0.764193\pi\) | |||||||
\(284\) | 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 | \(-0.715264\pi\) |
0.362478 | + | 0.931992i | \(0.381931\pi\) | |||||||
\(294\) | 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 | \(-0.0608828\pi\) | ||||
0.981764 | + | 0.190105i | \(0.0608828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −80.1430 | − | 41.8460i | −0.259362 | − | 0.135424i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 142.632 | − | 82.3487i | 0.458624 | − | 0.264787i | −0.252841 | − | 0.967508i | \(-0.581365\pi\) |
0.711466 | + | 0.702721i | \(0.248032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.33340 | + | 12.7018i | −0.0234294 | + | 0.0405809i | −0.877502 | − | 0.479572i | \(-0.840792\pi\) |
0.854073 | + | 0.520153i | \(0.174125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −408.868 | − | 236.060i | −1.28981 | − | 0.744670i | −0.311186 | − | 0.950349i | \(-0.600726\pi\) |
−0.978619 | + | 0.205679i | \(0.934060\pi\) | |||||||
\(318\) | 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 | 0.225892 | + | 0.974152i | \(0.427470\pi\) |
−0.956587 | + | 0.291448i | \(0.905863\pi\) | |||||||
\(332\) | 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 | −0.998983 | − | 0.0450890i | \(-0.985643\pi\) |
0.460443 | − | 0.887689i | \(-0.347690\pi\) | |||||||
\(338\) | 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 | \(-0.844668\pi\) |
−0.0356015 | + | 0.999366i | \(0.511335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −199.861 | + | 346.170i | −0.572668 | + | 0.991890i | 0.423623 | + | 0.905839i | \(0.360758\pi\) |
−0.996291 | + | 0.0860512i | \(0.972575\pi\) | |||||||
\(350\) | 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 | \(-0.0451242\pi\) |
0.372626 | + | 0.927982i | \(0.378458\pi\) | |||||||
\(354\) | 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 | \(0.383749\pi\) | ||||
−0.357147 | + | 0.934048i | \(0.616251\pi\) | |||||||
\(360\) | 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 | \(-0.874307\pi\) |
0.794677 | + | 0.607033i | \(0.207640\pi\) | |||||||
\(368\) | 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 | \(-0.249778\pi\) |
−0.965745 | + | 0.259492i | \(0.916445\pi\) | |||||||
\(374\) | 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 | 0.503510 | − | 0.863990i | \(-0.332042\pi\) |
0.999992 | − | 0.00405754i | \(-0.00129156\pi\) | |||||||
\(384\) | 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 | 0.993027 | − | 0.117885i | \(-0.0376115\pi\) |
0.394422 | + | 0.918929i | \(0.370945\pi\) | |||||||
\(390\) | 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 | \(-0.600848\pi\) | ||||
−0.311550 | + | 0.950230i | \(0.600848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.0982 | − | 803.822i | −0.0854591 | − | 2.01459i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 369.248 | − | 213.185i | 0.920818 | − | 0.531635i | 0.0369222 | − | 0.999318i | \(-0.488245\pi\) |
0.883896 | + | 0.467684i | \(0.154911\pi\) | |||||||
\(402\) | 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 | 0.739758 | − | 0.672873i | \(-0.234940\pi\) |
−0.952604 | + | 0.304212i | \(0.901607\pi\) | |||||||
\(410\) | 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 | −0.781796 | − | 0.623535i | \(-0.785696\pi\) |
0.149099 | + | 0.988822i | \(0.452363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 140.251 | − | 242.922i | 0.333138 | − | 0.577012i | −0.649987 | − | 0.759945i | \(-0.725226\pi\) |
0.983125 | + | 0.182933i | \(0.0585591\pi\) | |||||||
\(422\) | 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 | \(0.286364\pi\) | ||||
−0.621893 | + | 0.783102i | \(0.713636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 273.497 | 0.631633 | 0.315817 | − | 0.948820i | \(-0.397722\pi\) | ||||
0.315817 | + | 0.948820i | \(0.397722\pi\) | |||||||
\(434\) | 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 | −0.395367 | − | 0.918523i | \(-0.629382\pi\) |
0.993148 | − | 0.116864i | \(-0.0372842\pi\) | |||||||
\(440\) | 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 | \(-0.365199\pi\) |
−0.584050 | + | 0.811718i | \(0.698533\pi\) | |||||||
\(444\) | 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 | \(0.0163458\pi\) | ||||
−0.998682 | + | 0.0513294i | \(0.983654\pi\) | |||||||
\(450\) | 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 | \(-0.899725\pi\) |
0.743722 | + | 0.668489i | \(0.233059\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 822.598 | − | 105.189i | 1.79215 | − | 0.229170i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −362.663 | − | 209.384i | −0.786689 | − | 0.454195i | 0.0521069 | − | 0.998642i | \(-0.483406\pi\) |
−0.838795 | + | 0.544447i | \(0.816740\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 156.514 | + | 271.090i | 0.338043 | + | 0.585507i | 0.984064 | − | 0.177812i | \(-0.0569019\pi\) |
−0.646022 | + | 0.763319i | \(0.723569\pi\) | |||||||
\(464\) | 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 | 0.757307 | − | 0.653059i | \(-0.226515\pi\) |
−0.186912 | + | 0.982377i | \(0.559848\pi\) | |||||||
\(480\) | 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 | \(-0.668818\pi\) | ||||
−0.505843 | + | 0.862626i | \(0.668818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 109.417 | − | 69.5158i | 0.223756 | − | 0.142159i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 719.318 | − | 415.298i | 1.46501 | − | 0.845822i | 0.465770 | − | 0.884906i | \(-0.345777\pi\) |
0.999236 | + | 0.0390843i | \(0.0124441\pi\) | |||||||
\(492\) | 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 | 0.851512 | − | 0.524336i | \(-0.175686\pi\) |
−0.879844 | + | 0.475263i | \(0.842353\pi\) | |||||||
\(500\) | 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 | −0.285855 | − | 0.958273i | \(-0.592277\pi\) |
0.686961 | + | 0.726694i | \(0.258944\pi\) | |||||||
\(510\) | 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 | \(0.188732\pi\) | ||||
−0.829312 | + | 0.558785i | \(0.811268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −201.726 | −0.385709 | −0.192855 | − | 0.981227i | \(-0.561775\pi\) | ||||
−0.192855 | + | 0.981227i | \(0.561775\pi\) | |||||||
\(524\) | 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 | 0.407604 | + | 0.913159i | \(0.366364\pi\) |
−0.994621 | + | 0.103584i | \(0.966969\pi\) | |||||||
\(548\) | 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 | \(-0.937212\pi\) |
−0.320581 | + | 0.947221i | \(0.603878\pi\) | |||||||
\(564\) | 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 | −0.299074 | − | 0.954230i | \(-0.596678\pi\) |
−0.975924 | + | 0.218109i | \(0.930011\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −348.675 | − | 603.922i | −0.610639 | − | 1.05766i | −0.991133 | − | 0.132874i | \(-0.957579\pi\) |
0.380494 | − | 0.924783i | \(-0.375754\pi\) | |||||||
\(572\) | 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 | \(-0.287653\pi\) | ||||
0.618717 | + | 0.785614i | \(0.287653\pi\) | |||||||
\(578\) | 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 | \(-0.0885758\pi\) |
0.242876 | + | 0.970057i | \(0.421909\pi\) | |||||||
\(588\) | 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 | −0.660940 | − | 0.750439i | \(-0.729842\pi\) |
0.319430 | + | 0.947610i | \(0.396509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 84.0789 | − | 145.629i | 0.139898 | − | 0.242311i | −0.787560 | − | 0.616238i | \(-0.788656\pi\) |
0.927458 | + | 0.373927i | \(0.121989\pi\) | |||||||
\(602\) | 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 | \(-0.137777\pi\) |
−0.817143 | + | 0.576435i | \(0.804443\pi\) | |||||||
\(608\) | 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 | \(-0.602230\pi\) | ||||
−0.315671 | + | 0.948869i | \(0.602230\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −333.200 | + | 192.373i | −0.540032 | + | 0.311787i | −0.745092 | − | 0.666962i | \(-0.767594\pi\) |
0.205060 | + | 0.978749i | \(0.434261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 403.446 | − | 698.789i | 0.651771 | − | 1.12890i | −0.330922 | − | 0.943658i | \(-0.607360\pi\) |
0.982693 | − | 0.185242i | \(-0.0593068\pi\) | |||||||
\(620\) | 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 | −0.0164041 | − | 0.999865i | \(-0.505222\pi\) |
−0.874111 | + | 0.485726i | \(0.838555\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 452.382 | + | 783.548i | 0.703549 | + | 1.21858i | 0.967213 | + | 0.253968i | \(0.0817357\pi\) |
−0.263664 | + | 0.964615i | \(0.584931\pi\) | |||||||
\(644\) | 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 | \(-0.561922\pi\) |
0.753035 | + | 0.657980i | \(0.228589\pi\) | |||||||
\(654\) | 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 | 0.840133 | − | 0.542381i | \(-0.182477\pi\) |
−0.0496496 | + | 0.998767i | \(0.515810\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 465.379 | + | 806.060i | 0.704053 | + | 1.21946i | 0.967032 | + | 0.254654i | \(0.0819617\pi\) |
−0.262979 | + | 0.964802i | \(0.584705\pi\) | |||||||
\(662\) | 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 | \(-0.847165\pi\) |
0.843489 | + | 0.537147i | \(0.180498\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 549.689 | + | 317.363i | 0.811948 | + | 0.468778i | 0.847632 | − | 0.530585i | \(-0.178028\pi\) |
−0.0356841 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(678\) | 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 | 0.268535 | + | 0.963270i | \(0.413461\pi\) |
−0.968484 | + | 0.249077i | \(0.919873\pi\) | |||||||
\(692\) | 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 | \(-0.779596\pi\) | ||
0.769703 | − | 0.638402i | \(-0.220404\pi\) | |||||||
\(702\) | 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 | 0.0304761 | − | 0.999535i | \(-0.490298\pi\) |
0.850385 | − | 0.526161i | \(-0.176369\pi\) | |||||||
\(710\) | 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 | \(-0.906065\pi\) | ||
0.956772 | − | 0.290840i | \(-0.0939348\pi\) | |||||||
\(720\) | 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 | \(-0.948867\pi\) |
0.632082 | + | 0.774901i | \(0.282200\pi\) | |||||||
\(728\) | 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 | \(-0.164875\pi\) |
−0.863197 | + | 0.504866i | \(0.831542\pi\) | |||||||
\(734\) | 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 | \(-0.777354\pi\) |
0.174959 | + | 0.984576i | \(0.444021\pi\) | |||||||
\(744\) | 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 | −0.999505 | − | 0.0314493i | \(-0.989988\pi\) |
0.472517 | − | 0.881322i | \(-0.343346\pi\) | |||||||
\(752\) | 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 | \(-0.717931\pi\) | ||||
−0.632402 | + | 0.774640i | \(0.717931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 555.820 | − | 353.129i | 0.732306 | − | 0.465256i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −378.389 | + | 218.463i | −0.497225 | + | 0.287073i | −0.727567 | − | 0.686037i | \(-0.759349\pi\) |
0.230342 | + | 0.973110i | \(0.426016\pi\) | |||||||
\(762\) | 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 | 0.992868 | − | 0.119221i | \(-0.0380396\pi\) |
−0.599682 | + | 0.800238i | \(0.704706\pi\) | |||||||
\(770\) | 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 | \(-0.279092\pi\) |
−0.985516 | + | 0.169582i | \(0.945758\pi\) | |||||||
\(788\) | 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 | \(-0.620372\pi\) |
0.620232 | + | 0.784418i | \(0.287038\pi\) | |||||||
\(798\) | 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 | \(0.0148919\pi\) | ||||
−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 | ||||||||
\(813\) | 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 | −0.997059 | − | 0.0766424i | \(-0.975580\pi\) |
−0.564904 | − | 0.825157i | \(-0.691087\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 380.688 | + | 659.371i | 0.462562 | + | 0.801180i | 0.999088 | − | 0.0427034i | \(-0.0135971\pi\) |
−0.536526 | + | 0.843884i | \(0.680264\pi\) | |||||||
\(824\) | 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 | −0.238492 | − | 0.971144i | \(-0.576653\pi\) |
−0.960282 | + | 0.279032i | \(0.909986\pi\) | |||||||
\(840\) | 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 | −0.0941731 | − | 0.995556i | \(-0.530021\pi\) |
0.909263 | − | 0.416222i | \(-0.136646\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 914.904 | + | 528.220i | 1.06757 | + | 0.616359i | 0.927515 | − | 0.373785i | \(-0.121940\pi\) |
0.140050 | + | 0.990144i | \(0.455274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 537.750 | + | 931.410i | 0.626018 | + | 1.08430i | 0.988343 | + | 0.152244i | \(0.0486498\pi\) |
−0.362325 | + | 0.932052i | \(0.618017\pi\) | |||||||
\(860\) | 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 | \(-0.0890994\pi\) |
−0.719799 | + | 0.694182i | \(0.755766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 123.746 | − | 236.997i | 0.140781 | − | 0.269622i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 525.156i | − | 0.596090i | −0.954552 | − | 0.298045i | \(-0.903665\pi\) | ||
0.954552 | − | 0.298045i | \(-0.0963346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5609 | 0.0504653 | 0.0252327 | − | 0.999682i | \(-0.491967\pi\) | ||||
0.0252327 | + | 0.999682i | \(0.491967\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1223.72 | + | 706.516i | −1.37962 | + | 0.796523i | −0.992113 | − | 0.125345i | \(-0.959996\pi\) |
−0.387505 | + | 0.921868i | \(0.626663\pi\) | |||||||
\(888\) | 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 | \(-0.780142\pi\) |
0.937126 | + | 0.348990i | \(0.113475\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 593.213 | − | 413.186i | 0.652599 | − | 0.454550i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 243.600 | + | 140.643i | 0.267399 | + | 0.154383i | 0.627705 | − | 0.778451i | \(-0.283994\pi\) |
−0.360306 | + | 0.932834i | \(0.617328\pi\) | |||||||
\(912\) | 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 | 0.259082 | − | 0.965855i | \(-0.416580\pi\) |
−0.706914 | + | 0.707300i | \(0.749913\pi\) | |||||||
\(930\) | 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 | \(-0.337037\pi\) | ||||
0.489891 | + | 0.871784i | \(0.337037\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.86482 | − | 43.9609i | −0.00198597 | − | 0.0468167i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1228.87 | − | 709.489i | 1.30592 | − | 0.753973i | 0.324507 | − | 0.945883i | \(-0.394802\pi\) |
0.981413 | + | 0.191910i | \(0.0614682\pi\) | |||||||
\(942\) | 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 | \(-0.288077\pi\) |
−0.372240 | + | 0.928136i | \(0.621410\pi\) | |||||||
\(948\) | 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 | −0.999632 | − | 0.0271272i | \(-0.991364\pi\) |
0.476323 | − | 0.879270i | \(-0.341969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1411.15 | + | 2221.13i | 1.45630 | + | 2.29219i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 772.488i | − | 0.795560i | −0.917481 | − | 0.397780i | \(-0.869781\pi\) | ||
0.917481 | − | 0.397780i | \(-0.130219\pi\) | |||||||
\(972\) | 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 | \(-0.354063\pi\) |
0.997880 | + | 0.0650777i | \(0.0207295\pi\) | |||||||
\(978\) | 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 | \(-0.467900\pi\) |
−0.811289 | + | 0.584645i | \(0.801234\pi\) | |||||||
\(984\) | 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 | 0.0415279 | − | 0.999137i | \(-0.486777\pi\) |
0.844514 | − | 0.535533i | \(-0.179889\pi\) | |||||||
\(998\) | 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.d.101.2 | ✓ | 16 | |
3.2 | odd | 2 | 2700.3.p.e.1601.2 | 16 | |||
5.2 | odd | 4 | 900.3.u.d.749.12 | 32 | |||
5.3 | odd | 4 | 900.3.u.d.749.5 | 32 | |||
5.4 | even | 2 | 900.3.p.e.101.7 | yes | 16 | ||
9.4 | even | 3 | 2700.3.p.e.2501.2 | 16 | |||
9.5 | odd | 6 | inner | 900.3.p.d.401.2 | yes | 16 | |
15.2 | even | 4 | 2700.3.u.d.2249.3 | 32 | |||
15.8 | even | 4 | 2700.3.u.d.2249.14 | 32 | |||
15.14 | odd | 2 | 2700.3.p.d.1601.7 | 16 | |||
45.4 | even | 6 | 2700.3.p.d.2501.7 | 16 | |||
45.13 | odd | 12 | 2700.3.u.d.449.3 | 32 | |||
45.14 | odd | 6 | 900.3.p.e.401.7 | yes | 16 | ||
45.22 | odd | 12 | 2700.3.u.d.449.14 | 32 | |||
45.23 | even | 12 | 900.3.u.d.149.12 | 32 | |||
45.32 | even | 12 | 900.3.u.d.149.5 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.p.d.101.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
900.3.p.d.401.2 | yes | 16 | 9.5 | odd | 6 | inner | |
900.3.p.e.101.7 | yes | 16 | 5.4 | even | 2 | ||
900.3.p.e.401.7 | yes | 16 | 45.14 | odd | 6 | ||
900.3.u.d.149.5 | 32 | 45.32 | even | 12 | |||
900.3.u.d.149.12 | 32 | 45.23 | even | 12 | |||
900.3.u.d.749.5 | 32 | 5.3 | odd | 4 | |||
900.3.u.d.749.12 | 32 | 5.2 | odd | 4 | |||
2700.3.p.d.1601.7 | 16 | 15.14 | odd | 2 | |||
2700.3.p.d.2501.7 | 16 | 45.4 | even | 6 | |||
2700.3.p.e.1601.2 | 16 | 3.2 | odd | 2 | |||
2700.3.p.e.2501.2 | 16 | 9.4 | even | 3 | |||
2700.3.u.d.449.3 | 32 | 45.13 | odd | 12 | |||
2700.3.u.d.449.14 | 32 | 45.22 | odd | 12 | |||
2700.3.u.d.2249.3 | 32 | 15.2 | even | 4 | |||
2700.3.u.d.2249.14 | 32 | 15.8 | even | 4 |