Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2881.1 | ||
Root | \(0.500000 + 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2881 |
Dual form | 3024.2.q.g.2305.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.59097 | + | 2.75564i | −0.711504 | + | 1.23236i | 0.252788 | + | 0.967522i | \(0.418652\pi\) |
−0.964292 | + | 0.264840i | \(0.914681\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56238 | − | 0.658939i | 0.968489 | − | 0.249055i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.59097 | − | 2.75564i | −0.479696 | − | 0.830858i | 0.520033 | − | 0.854146i | \(-0.325920\pi\) |
−0.999729 | + | 0.0232884i | \(0.992586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.85185 | + | 4.93955i | 0.790960 | + | 1.36998i | 0.925373 | + | 0.379058i | \(0.123752\pi\) |
−0.134412 | + | 0.990925i | \(0.542915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.760877 | − | 1.31788i | 0.184540 | − | 0.319632i | −0.758882 | − | 0.651229i | \(-0.774254\pi\) |
0.943421 | + | 0.331596i | \(0.107587\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.641315 | + | 1.11079i | 0.147128 | + | 0.254833i | 0.930165 | − | 0.367142i | \(-0.119664\pi\) |
−0.783037 | + | 0.621975i | \(0.786330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.11956 | + | 1.93914i | −0.233445 | + | 0.404338i | −0.958820 | − | 0.284016i | \(-0.908333\pi\) |
0.725375 | + | 0.688354i | \(0.241666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56238 | − | 4.43818i | −0.512476 | − | 0.887635i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.54063 | − | 6.13255i | 0.657478 | − | 1.13879i | −0.323788 | − | 0.946130i | \(-0.604957\pi\) |
0.981266 | − | 0.192656i | \(-0.0617101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.42107 | 1.69207 | 0.846037 | − | 0.533125i | \(-0.178982\pi\) | ||||
0.846037 | + | 0.533125i | \(0.178982\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.26088 | + | 8.10936i | −0.382158 | + | 1.37073i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.80150 | + | 4.85235i | 0.437522 | + | 0.757810i | 0.997498 | − | 0.0706992i | \(-0.0225230\pi\) |
−0.559976 | + | 0.828509i | \(0.689190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.41423 | + | 5.91362i | −0.520665 | + | 0.901819i | 0.479046 | + | 0.877790i | \(0.340983\pi\) |
−0.999711 | + | 0.0240288i | \(0.992351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.82846 | −0.850168 | −0.425084 | − | 0.905154i | \(-0.639755\pi\) | ||||
−0.425084 | + | 0.905154i | \(0.639755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.13160 | − | 3.37690i | 0.875943 | − | 0.482415i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.02859 | + | 1.78157i | −0.141288 | + | 0.244717i | −0.927982 | − | 0.372626i | \(-0.878458\pi\) |
0.786694 | + | 0.617343i | \(0.211791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1248 | 1.36522 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.12476 | −0.146432 | −0.0732159 | − | 0.997316i | \(-0.523326\pi\) | ||||
−0.0732159 | + | 0.997316i | \(0.523326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.12476 | 0.400085 | 0.200042 | − | 0.979787i | \(-0.435892\pi\) | ||||
0.200042 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.1488 | −2.25109 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9669 | −1.33982 | −0.669910 | − | 0.742442i | \(-0.733667\pi\) | ||||
−0.669910 | + | 0.742442i | \(0.733667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.69002 | 1.03132 | 0.515658 | − | 0.856794i | \(-0.327548\pi\) | ||||
0.515658 | + | 0.856794i | \(0.327548\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.48345 | + | 4.30146i | −0.290666 | + | 0.503448i | −0.973967 | − | 0.226689i | \(-0.927210\pi\) |
0.683302 | + | 0.730136i | \(0.260543\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.89248 | − | 6.01266i | −0.671510 | − | 0.685206i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.13844 | 0.465610 | 0.232805 | − | 0.972523i | \(-0.425210\pi\) | ||||
0.232805 | + | 0.972523i | \(0.425210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.03379 | + | 6.98673i | −0.442766 | + | 0.766893i | −0.997894 | − | 0.0648718i | \(-0.979336\pi\) |
0.555127 | + | 0.831765i | \(0.312669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.42107 | + | 4.19341i | 0.262602 | + | 0.454839i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.112725 | − | 0.195246i | −0.0119488 | − | 0.0206960i | 0.859989 | − | 0.510312i | \(-0.170470\pi\) |
−0.871938 | + | 0.489616i | \(0.837137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5624 | + | 10.7778i | 1.10724 | + | 1.12982i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.08126 | −0.418728 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.42107 | − | 12.8537i | 0.753495 | − | 1.30509i | −0.192624 | − | 0.981273i | \(-0.561700\pi\) |
0.946119 | − | 0.323819i | \(-0.104967\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.29467 | + | 16.0988i | 0.924854 | + | 1.60189i | 0.791796 | + | 0.610786i | \(0.209146\pi\) |
0.133058 | + | 0.991108i | \(0.457520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.141315 | + | 0.244765i | −0.0139242 | + | 0.0241174i | −0.872904 | − | 0.487893i | \(-0.837766\pi\) |
0.858979 | + | 0.512010i | \(0.171099\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.68878 | + | 9.85326i | 0.549955 | + | 0.952550i | 0.998277 | + | 0.0586780i | \(0.0186885\pi\) |
−0.448322 | + | 0.893872i | \(0.647978\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21053 | + | 3.82876i | −0.211731 | + | 0.366728i | −0.952256 | − | 0.305300i | \(-0.901243\pi\) |
0.740526 | + | 0.672028i | \(0.234577\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.60752 | + | 2.78431i | 0.151223 | + | 0.261926i | 0.931677 | − | 0.363287i | \(-0.118345\pi\) |
−0.780454 | + | 0.625213i | \(0.785012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.56238 | − | 6.17023i | −0.332194 | − | 0.575377i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.08126 | − | 3.87828i | 0.0991186 | − | 0.355521i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.437618 | − | 0.757977i | 0.0397835 | − | 0.0689070i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.396990 | 0.0355079 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.1053 | −1.78406 | −0.892030 | − | 0.451976i | \(-0.850719\pi\) | ||||
−0.892030 | + | 0.451976i | \(0.850719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.18194 | + | 5.51129i | −0.278008 | + | 0.481523i | −0.970890 | − | 0.239528i | \(-0.923007\pi\) |
0.692882 | + | 0.721051i | \(0.256341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.37524 | + | 2.42368i | 0.205959 | + | 0.210160i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.37072 | + | 2.37416i | 0.117109 | + | 0.202838i | 0.918621 | − | 0.395140i | \(-0.129304\pi\) |
−0.801512 | + | 0.597979i | \(0.795971\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.98345 | + | 6.89953i | 0.337872 | + | 0.585211i | 0.984032 | − | 0.177991i | \(-0.0569597\pi\) |
−0.646161 | + | 0.763202i | \(0.723626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.07442 | − | 15.7174i | 0.758841 | − | 1.31435i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2661 | + | 19.5134i | 0.935597 | + | 1.62050i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.6300 | + | 20.1437i | −0.952764 | + | 1.65024i | −0.213360 | + | 0.976974i | \(0.568441\pi\) |
−0.739404 | + | 0.673262i | \(0.764893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.06238 | − | 7.03625i | −0.330592 | − | 0.572602i | 0.652036 | − | 0.758188i | \(-0.273915\pi\) |
−0.982628 | + | 0.185586i | \(0.940582\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.9887 | + | 25.9611i | −1.20392 | + | 2.08525i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2632 | −0.898901 | −0.449451 | − | 0.893305i | \(-0.648380\pi\) | ||||
−0.449451 | + | 0.893305i | \(0.648380\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.59097 | + | 5.70653i | −0.125386 | + | 0.449738i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.99028 | + | 3.44727i | 0.155891 | + | 0.270011i | 0.933383 | − | 0.358881i | \(-0.116842\pi\) |
−0.777492 | + | 0.628893i | \(0.783508\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.61956 | + | 4.53721i | 0.202708 | + | 0.351100i | 0.949400 | − | 0.314070i | \(-0.101693\pi\) |
−0.746692 | + | 0.665170i | \(0.768359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.76608 | + | 16.9153i | −0.751237 | + | 1.30118i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.55159 | −0.193994 | −0.0969968 | − | 0.995285i | \(-0.530924\pi\) | ||||
−0.0969968 | + | 0.995285i | \(0.530924\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.49028 | − | 9.68385i | −0.717398 | − | 0.732030i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.51887 | − | 6.09487i | 0.263013 | − | 0.455552i | −0.704028 | − | 0.710172i | \(-0.748617\pi\) |
0.967041 | + | 0.254620i | \(0.0819504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9669 | −0.963822 | −0.481911 | − | 0.876220i | \(-0.660057\pi\) | ||||
−0.481911 | + | 0.876220i | \(0.660057\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.18194 | −0.233941 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.84213 | −0.354092 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.98057 | 0.143309 | 0.0716545 | − | 0.997430i | \(-0.477172\pi\) | ||||
0.0716545 | + | 0.997430i | \(0.477172\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.54583 | −0.327216 | −0.163608 | − | 0.986525i | \(-0.552313\pi\) | ||||
−0.163608 | + | 0.986525i | \(0.552313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8148 | 1.55424 | 0.777120 | − | 0.629353i | \(-0.216680\pi\) | ||||
0.777120 | + | 0.629353i | \(0.216680\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.14132 | + | 10.6371i | −0.435346 | + | 0.754042i | −0.997324 | − | 0.0731106i | \(-0.976707\pi\) |
0.561978 | + | 0.827152i | \(0.310041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.03147 | − | 18.0470i | 0.353140 | − | 1.26665i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.8285 | −1.24519 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.04063 | − | 3.53447i | 0.141153 | − | 0.244485i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.32846 | + | 14.4253i | 0.573355 | + | 0.993080i | 0.996218 | + | 0.0868863i | \(0.0276917\pi\) |
−0.422863 | + | 0.906193i | \(0.638975\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8639 | − | 18.8168i | −0.740911 | − | 1.28330i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.1404 | − | 6.20790i | 1.63876 | − | 0.421420i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.67962 | 0.583854 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.32846 | − | 9.22916i | 0.356820 | − | 0.618031i | −0.630608 | − | 0.776102i | \(-0.717194\pi\) |
0.987428 | + | 0.158071i | \(0.0505276\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.25404 | + | 12.5644i | 0.481468 | + | 0.833926i | 0.999774 | − | 0.0212688i | \(-0.00677059\pi\) |
−0.518306 | + | 0.855195i | \(0.673437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.12476 | + | 8.87635i | −0.338654 | + | 0.586566i | −0.984180 | − | 0.177173i | \(-0.943305\pi\) |
0.645526 | + | 0.763738i | \(0.276638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.540628 | − | 0.936396i | −0.0354177 | − | 0.0613453i | 0.847773 | − | 0.530359i | \(-0.177943\pi\) |
−0.883191 | + | 0.469014i | \(0.844610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.27292 | − | 16.0612i | 0.604898 | − | 1.04771i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.16019 | − | 10.6698i | −0.398470 | − | 0.690170i | 0.595068 | − | 0.803676i | \(-0.297125\pi\) |
−0.993537 | + | 0.113506i | \(0.963792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.50000 | + | 11.2583i | 0.418702 | + | 0.725213i | 0.995809 | − | 0.0914555i | \(-0.0291519\pi\) |
−0.577107 | + | 0.816668i | \(0.695819\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.449657 | + | 22.2691i | −0.0287275 | + | 1.42272i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.65787 | + | 6.33561i | −0.232744 | + | 0.403125i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.11109 | 0.322609 | 0.161305 | − | 0.986905i | \(-0.448430\pi\) | ||||
0.161305 | + | 0.986905i | \(0.448430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.12476 | 0.447930 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.83009 | − | 6.63392i | 0.238915 | − | 0.413813i | −0.721488 | − | 0.692427i | \(-0.756542\pi\) |
0.960403 | + | 0.278614i | \(0.0898750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.85185 | + | 1.88962i | 0.115068 | + | 0.117415i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.54746 | + | 2.68029i | 0.0954208 | + | 0.165274i | 0.909784 | − | 0.415082i | \(-0.136247\pi\) |
−0.814363 | + | 0.580355i | \(0.802914\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.27292 | − | 5.66886i | −0.201054 | − | 0.348235i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4451 | − | 23.2877i | 0.819765 | − | 1.41987i | −0.0860906 | − | 0.996287i | \(-0.527437\pi\) |
0.905855 | − | 0.423587i | \(-0.139229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1082 | + | 19.2400i | 0.674776 | + | 1.16875i | 0.976534 | + | 0.215362i | \(0.0690930\pi\) |
−0.301759 | + | 0.953384i | \(0.597574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.15335 | + | 14.1220i | −0.491666 | + | 0.851590i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.31875 | + | 12.6764i | 0.439741 | + | 0.761653i | 0.997669 | − | 0.0682357i | \(-0.0217370\pi\) |
−0.557928 | + | 0.829889i | \(0.688404\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6992 | + | 20.2636i | −0.697915 | + | 1.20882i | 0.271273 | + | 0.962502i | \(0.412555\pi\) |
−0.969188 | + | 0.246322i | \(0.920778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1248 | 1.55296 | 0.776478 | − | 0.630144i | \(-0.217004\pi\) | ||||
0.776478 | + | 0.630144i | \(0.217004\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3759 | + | 10.5876i | 0.612471 | + | 0.624963i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.34213 | + | 12.7169i | 0.431890 | + | 0.748056i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.9315 | − | 22.3980i | −0.755465 | − | 1.30850i | −0.945143 | − | 0.326657i | \(-0.894078\pi\) |
0.189678 | − | 0.981846i | \(-0.439255\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.78947 | − | 3.09945i | 0.104187 | − | 0.180457i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7713 | −0.738582 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.85185 | + | 17.4027i | −0.279656 | + | 1.00308i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.97141 | + | 8.61073i | −0.284662 | + | 0.493049i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.53216 | −0.201591 | −0.100795 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100795 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.70370 | 0.0966078 | 0.0483039 | − | 0.998833i | \(-0.484618\pi\) | ||||
0.0483039 | + | 0.998833i | \(0.484618\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.84213 | −0.160647 | −0.0803234 | − | 0.996769i | \(-0.525595\pi\) | ||||
−0.0803234 | + | 0.996769i | \(0.525595\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.9201 | 1.39965 | 0.699827 | − | 0.714313i | \(-0.253261\pi\) | ||||
0.699827 | + | 0.714313i | \(0.253261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5322 | −1.26156 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.95185 | 0.108604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.6150 | − | 25.3140i | 0.810697 | − | 1.40417i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.9347 | + | 3.84060i | −0.823379 | + | 0.211739i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.17154 | 0.394183 | 0.197092 | − | 0.980385i | \(-0.436850\pi\) | ||||
0.197092 | + | 0.980385i | \(0.436850\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.4480 | − | 30.2209i | 0.953287 | − | 1.65114i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9211 | − | 18.9158i | −0.594908 | − | 1.03041i | −0.993560 | − | 0.113309i | \(-0.963855\pi\) |
0.398651 | − | 0.917103i | \(-0.369478\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.9887 | − | 25.9611i | −0.811681 | − | 1.40587i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4863 | − | 12.6933i | 0.728193 | − | 0.685372i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.11109 | −0.113329 | −0.0566646 | − | 0.998393i | \(-0.518047\pi\) | ||||
−0.0566646 | + | 0.998393i | \(0.518047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1082 | − | 31.3643i | 0.969310 | − | 1.67889i | 0.271751 | − | 0.962368i | \(-0.412397\pi\) |
0.697559 | − | 0.716527i | \(-0.254269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.24433 | − | 9.08344i | −0.279127 | − | 0.483463i | 0.692041 | − | 0.721858i | \(-0.256712\pi\) |
−0.971168 | + | 0.238396i | \(0.923378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.8256 | + | 23.9466i | −0.733786 | + | 1.27095i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.2209 | + | 28.0955i | 0.856108 | + | 1.48282i | 0.875613 | + | 0.483013i | \(0.160458\pi\) |
−0.0195047 | + | 0.999810i | \(0.506209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.67743 | − | 15.0297i | 0.456707 | − | 0.791039i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.90219 | − | 13.6870i | −0.413620 | − | 0.716410i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.05555 | − | 15.6847i | −0.472696 | − | 0.818733i | 0.526816 | − | 0.849979i | \(-0.323386\pi\) |
−0.999512 | + | 0.0312465i | \(0.990052\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.46169 | + | 5.24284i | −0.0758874 | + | 0.272195i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.83530 | − | 10.1070i | 0.302140 | − | 0.523322i | −0.674480 | − | 0.738293i | \(-0.735632\pi\) |
0.976621 | + | 0.214971i | \(0.0689656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.3893 | 2.08016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2690 | −0.732947 | −0.366474 | − | 0.930428i | \(-0.619435\pi\) | ||||
−0.366474 | + | 0.930428i | \(0.619435\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.824893 | − | 1.42876i | 0.0421501 | − | 0.0730061i | −0.844181 | − | 0.536059i | \(-0.819913\pi\) |
0.886331 | + | 0.463053i | \(0.153246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.9435 | − | 6.67160i | 1.32220 | − | 0.340016i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.0338 | − | 27.7713i | −0.812946 | − | 1.40806i | −0.910794 | − | 0.412862i | \(-0.864529\pi\) |
0.0978483 | − | 0.995201i | \(-0.468804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.70370 | + | 2.95089i | 0.0861596 | + | 0.149233i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.58414 | + | 11.4041i | −0.331284 | + | 0.573800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9669 | − | 32.8516i | −0.951921 | − | 1.64878i | −0.741261 | − | 0.671217i | \(-0.765772\pi\) |
−0.210660 | − | 0.977559i | \(-0.567561\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.30959 | − | 9.19647i | 0.265148 | − | 0.459250i | −0.702454 | − | 0.711729i | \(-0.747913\pi\) |
0.967602 | + | 0.252479i | \(0.0812458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.8675 | + | 46.5358i | 1.33836 | + | 2.31811i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.59097 | − | 2.75564i | 0.0788615 | − | 0.136592i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.54583 | 0.274224 | 0.137112 | − | 0.990556i | \(-0.456218\pi\) | ||||
0.137112 | + | 0.990556i | \(0.456218\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.88207 | + | 0.741150i | −0.141818 | + | 0.0364696i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8353 | − | 22.2314i | −0.630060 | − | 1.09130i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.77455 | + | 4.80566i | 0.135546 | + | 0.234772i | 0.925806 | − | 0.378000i | \(-0.123388\pi\) |
−0.790260 | + | 0.612772i | \(0.790055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.42107 | + | 5.92546i | −0.166733 | + | 0.288789i | −0.937269 | − | 0.348606i | \(-0.886655\pi\) |
0.770537 | + | 0.637396i | \(0.219988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.79863 | −0.378289 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.00684 | − | 2.05903i | 0.387478 | − | 0.0996433i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5539 | − | 28.6722i | 0.797374 | − | 1.38109i | −0.123947 | − | 0.992289i | \(-0.539555\pi\) |
0.921321 | − | 0.388803i | \(-0.127111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1111 | −0.582022 | −0.291011 | − | 0.956720i | \(-0.593992\pi\) | ||||
−0.291011 | + | 0.956720i | \(0.593992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.87197 | −0.137385 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.83422 | 0.421634 | 0.210817 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210817 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.5185 | 0.832328 | 0.416164 | − | 0.909290i | \(-0.363374\pi\) | ||||
0.416164 | + | 0.909290i | \(0.363374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.717370 | 0.0340066 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.2301 | −1.47384 | −0.736920 | − | 0.675980i | \(-0.763720\pi\) | ||||
−0.736920 | + | 0.675980i | \(0.763720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.91423 | − | 15.4399i | 0.419755 | − | 0.727036i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −46.5043 | + | 11.9590i | −2.18015 | + | 0.560645i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.1248 | −1.50273 | −0.751367 | − | 0.659885i | \(-0.770605\pi\) | ||||
−0.751367 | + | 0.659885i | \(0.770605\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.23229 | + | 2.13438i | −0.0573933 | + | 0.0994081i | −0.893295 | − | 0.449472i | \(-0.851612\pi\) |
0.835901 | + | 0.548880i | \(0.184946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.1735 | − | 26.2812i | −0.705171 | − | 1.22139i | −0.966630 | − | 0.256177i | \(-0.917537\pi\) |
0.261459 | − | 0.965215i | \(-0.415796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.98181 | − | 13.8249i | −0.369354 | − | 0.639740i | 0.620110 | − | 0.784515i | \(-0.287088\pi\) |
−0.989465 | + | 0.144774i | \(0.953754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.1014 | + | 7.22651i | −1.29760 | + | 0.333689i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.7278 | 0.999044 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.28659 | − | 5.69254i | 0.150799 | − | 0.261192i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5865 | + | 20.0683i | 0.529399 | + | 0.916946i | 0.999412 | + | 0.0342863i | \(0.0109158\pi\) |
−0.470013 | + | 0.882659i | \(0.655751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.85185 | + | 4.93955i | −0.130033 | + | 0.225224i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.6134 | + | 40.8996i | 1.07223 | + | 1.85716i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.70658 | + | 2.95588i | −0.0773323 | + | 0.133943i | −0.902098 | − | 0.431531i | \(-0.857974\pi\) |
0.824766 | + | 0.565474i | \(0.191307\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.58414 | − | 16.6002i | −0.432526 | − | 0.749157i | 0.564564 | − | 0.825389i | \(-0.309044\pi\) |
−0.997090 | + | 0.0762323i | \(0.975711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.38796 | − | 9.33223i | −0.242662 | − | 0.420302i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.2672 | − | 5.72619i | 0.998819 | − | 0.256855i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.5848 | − | 35.6540i | 0.921503 | − | 1.59609i | 0.124413 | − | 0.992231i | \(-0.460295\pi\) |
0.797090 | − | 0.603860i | \(-0.206371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.4542 | −1.17953 | −0.589767 | − | 0.807574i | \(-0.700780\pi\) | ||||
−0.589767 | + | 0.807574i | \(0.700780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −59.1502 | −2.63215 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.38564 | − | 11.0603i | 0.283039 | − | 0.490237i | −0.689093 | − | 0.724673i | \(-0.741991\pi\) |
0.972132 | + | 0.234436i | \(0.0753242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.52915 | + | 12.6584i | −0.156120 | + | 0.559975i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.449657 | − | 0.778828i | −0.0198142 | − | 0.0343193i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.27292 | + | 16.0612i | 0.407822 | + | 0.706369i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.40615 | − | 5.89962i | 0.149226 | − | 0.258467i | −0.781716 | − | 0.623635i | \(-0.785655\pi\) |
0.930942 | + | 0.365168i | \(0.118988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7535 | − | 25.5538i | −0.645125 | − | 1.11739i | −0.984273 | − | 0.176656i | \(-0.943472\pi\) |
0.339148 | − | 0.940733i | \(-0.389861\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.16827 | − | 12.4158i | 0.312255 | − | 0.540841i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.99316 | + | 15.5766i | 0.391007 | + | 0.677244i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.9789 | + | 27.6763i | −0.692125 | + | 1.19879i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.2028 | −1.56518 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.0607 | − | 11.5239i | −0.821004 | − | 0.496371i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7008 | + | 25.4626i | 0.632038 | + | 1.09472i | 0.987135 | + | 0.159892i | \(0.0511145\pi\) |
−0.355097 | + | 0.934829i | \(0.615552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.03379 | − | 12.1829i | −0.301295 | − | 0.521857i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6150 | + | 30.5102i | −0.753165 | + | 1.30452i | 0.193116 | + | 0.981176i | \(0.438141\pi\) |
−0.946281 | + | 0.323344i | \(0.895193\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.08263 | 0.386933 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6043 | − | 2.72698i | 0.450939 | − | 0.115963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.36909 | − | 5.83543i | 0.142753 | − | 0.247255i | −0.785779 | − | 0.618507i | \(-0.787738\pi\) |
0.928532 | + | 0.371252i | \(0.121071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.9475 | −1.64730 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.45993 | −0.0615286 | −0.0307643 | − | 0.999527i | \(-0.509794\pi\) | ||||
−0.0307643 | + | 0.999527i | \(0.509794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.2301 | −0.430383 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5653 | −0.820218 | −0.410109 | − | 0.912036i | \(-0.634509\pi\) | ||||
−0.410109 | + | 0.912036i | \(0.634509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9259 | 0.917569 | 0.458785 | − | 0.888547i | \(-0.348285\pi\) | ||||
0.458785 | + | 0.888547i | \(0.348285\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.4750 | 0.478540 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3655 | − | 21.4177i | 0.514783 | − | 0.891631i | −0.485069 | − | 0.874476i | \(-0.661206\pi\) |
0.999853 | − | 0.0171554i | \(-0.00546099\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.73229 | + | 20.5607i | −0.237815 | + | 0.853001i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.54583 | 0.271101 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0796 | + | 31.3148i | −0.746226 | + | 1.29250i | 0.203394 | + | 0.979097i | \(0.434803\pi\) |
−0.949620 | + | 0.313404i | \(0.898531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.04187 | + | 10.4648i | 0.248951 | + | 0.431196i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.55391 | + | 13.0838i | 0.310202 | + | 0.537285i | 0.978406 | − | 0.206693i | \(-0.0662700\pi\) |
−0.668204 | + | 0.743978i | \(0.732937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.96690 | + | 9.14978i | 0.367607 | + | 0.375105i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.45417 | −0.222851 | −0.111426 | − | 0.993773i | \(-0.535542\pi\) | ||||
−0.111426 | + | 0.993773i | \(0.535542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.36840 | + | 5.83424i | −0.137400 | + | 0.237984i | −0.926512 | − | 0.376266i | \(-0.877208\pi\) |
0.789112 | + | 0.614250i | \(0.210541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.39248 | + | 2.41184i | 0.0566122 | + | 0.0980553i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.33530 | − | 5.77690i | 0.135376 | − | 0.234477i | −0.790365 | − | 0.612636i | \(-0.790109\pi\) |
0.925741 | + | 0.378159i | \(0.123443\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6219 | − | 28.7899i | −0.672449 | − | 1.16472i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.654988 | − | 1.13447i | 0.0264547 | − | 0.0458209i | −0.852495 | − | 0.522735i | \(-0.824912\pi\) |
0.878950 | + | 0.476915i | \(0.158245\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.2483 | − | 29.8749i | −0.694390 | − | 1.20272i | −0.970386 | − | 0.241560i | \(-0.922341\pi\) |
0.275996 | − | 0.961159i | \(-0.410992\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.22421 | − | 14.2447i | −0.330559 | − | 0.572545i | 0.652063 | − | 0.758165i | \(-0.273904\pi\) |
−0.982622 | + | 0.185620i | \(0.940571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.417500 | − | 0.426015i | −0.0167268 | − | 0.0170679i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1803 | − | 21.0969i | 0.487212 | − | 0.843877i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.52175 | 0.0606763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0118 | 1.19475 | 0.597375 | − | 0.801962i | \(-0.296210\pi\) | ||||
0.597375 | + | 0.801962i | \(0.296210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.9870 | − | 55.4031i | 1.26937 | − | 2.19861i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.1668 | + | 20.6569i | 1.35374 | + | 0.818456i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9497 | + | 24.1615i | 0.550978 | + | 0.954322i | 0.998204 | + | 0.0599014i | \(0.0190786\pi\) |
−0.447226 | + | 0.894421i | \(0.647588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.2524 | − | 24.6859i | −0.562060 | − | 0.973516i | −0.997317 | − | 0.0732100i | \(-0.976676\pi\) |
0.435257 | − | 0.900306i | \(-0.356658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.35705 | − | 14.4748i | 0.328550 | − | 0.569065i | −0.653675 | − | 0.756776i | \(-0.726774\pi\) |
0.982224 | + | 0.187711i | \(0.0601069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.78947 | + | 3.09945i | 0.0702427 | + | 0.121664i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0825 | − | 33.0519i | 0.746756 | − | 1.29342i | −0.202614 | − | 0.979259i | \(-0.564944\pi\) |
0.949370 | − | 0.314161i | \(-0.101723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.1248 | − | 17.5366i | −0.395607 | − | 0.685212i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.37072 | − | 7.57031i | 0.170259 | − | 0.294898i | −0.768251 | − | 0.640148i | \(-0.778873\pi\) |
0.938510 | + | 0.345251i | \(0.112206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0837 | −0.781167 | −0.390584 | − | 0.920567i | \(-0.627727\pi\) | ||||
−0.390584 | + | 0.920567i | \(0.627727\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.4577 | + | 2.68930i | −0.405534 | + | 0.104286i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.92790 | + | 13.7315i | 0.306970 | + | 0.531687i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97141 | − | 8.61073i | −0.191919 | − | 0.332414i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.0264 | + | 29.4906i | −0.656319 | + | 1.13678i | 0.325242 | + | 0.945631i | \(0.394554\pi\) |
−0.981561 | + | 0.191148i | \(0.938779\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.717370 | 0.0275708 | 0.0137854 | − | 0.999905i | \(-0.495612\pi\) | ||||
0.0137854 | + | 0.999905i | \(0.495612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5458 | − | 37.8260i | 0.404712 | − | 1.45163i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.5270 | + | 18.2332i | −0.402803 | + | 0.697675i | −0.994063 | − | 0.108806i | \(-0.965297\pi\) |
0.591260 | + | 0.806481i | \(0.298631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.72313 | −0.333294 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.7335 | −0.447012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.84789 | −0.222464 | −0.111232 | − | 0.993794i | \(-0.535480\pi\) | ||||
−0.111232 | + | 0.993794i | \(0.535480\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.3502 | −0.961588 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.52640 | 0.322960 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.2711 | −0.387935 | −0.193967 | − | 0.981008i | \(-0.562136\pi\) | ||||
−0.193967 | + | 0.981008i | \(0.562136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.641315 | + | 1.11079i | −0.0241877 | + | 0.0418942i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.4246 | + | 35.1268i | 1.29467 | + | 1.32108i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.4854 | 1.63313 | 0.816564 | − | 0.577255i | \(-0.195876\pi\) | ||||
0.816564 | + | 0.577255i | \(0.195876\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.5475 | + | 18.2687i | −0.395006 | + | 0.684170i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.8743 | + | 50.0117i | 1.07984 | + | 1.87033i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.4412 | + | 44.0654i | 0.948796 | + | 1.64336i | 0.747966 | + | 0.663737i | \(0.231031\pi\) |
0.200830 | + | 0.979626i | \(0.435636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.200818 | + | 0.720299i | −0.00747886 | + | 0.0268253i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36.2898 | −1.34777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.07210 | + | 10.5172i | −0.225202 | + | 0.390061i | −0.956380 | − | 0.292126i | \(-0.905637\pi\) |
0.731178 | + | 0.682186i | \(0.238971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.19562 | + | 8.99907i | 0.192167 | + | 0.332843i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0848 | − | 39.9841i | 0.852657 | − | 1.47685i | −0.0261440 | − | 0.999658i | \(-0.508323\pi\) |
0.878801 | − | 0.477188i | \(-0.158344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4480 | + | 30.2209i | 0.642706 | + | 1.11320i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.49604 | − | 4.32327i | 0.0918184 | − | 0.159034i | −0.816458 | − | 0.577405i | \(-0.804065\pi\) |
0.908276 | + | 0.418371i | \(0.137399\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7060 | − | 27.2036i | −0.576198 | − | 0.998004i | −0.995910 | − | 0.0903470i | \(-0.971202\pi\) |
0.419712 | − | 0.907657i | \(-0.362131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.0059 | − | 64.0961i | −1.35579 | − | 2.34830i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.0695 | + | 21.4992i | 0.769863 | + | 0.785565i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.64815 | − | 2.85468i | 0.0601419 | − | 0.104169i | −0.834387 | − | 0.551179i | \(-0.814178\pi\) |
0.894529 | + | 0.447010i | \(0.147511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.8525 | 0.940870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1384 | −0.368488 | −0.184244 | − | 0.982881i | \(-0.558984\pi\) | ||||
−0.184244 | + | 0.982881i | \(0.558984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.03379 | − | 12.1829i | 0.254975 | − | 0.441629i | −0.709914 | − | 0.704288i | \(-0.751266\pi\) |
0.964889 | + | 0.262659i | \(0.0845995\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.14132 | + | 11.2673i | −0.113723 | + | 0.407905i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.20765 | − | 5.55582i | −0.115822 | − | 0.200609i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3461 | + | 19.6520i | 0.409151 | + | 0.708669i | 0.994795 | − | 0.101899i | \(-0.0324918\pi\) |
−0.585644 | + | 0.810568i | \(0.699158\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.327772 | + | 0.567717i | −0.0117891 | + | 0.0204194i | −0.871860 | − | 0.489756i | \(-0.837086\pi\) |
0.860071 | + | 0.510175i | \(0.170419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.1404 | − | 41.8123i | −0.867148 | − | 1.50194i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.59329 | + | 6.22377i | −0.128743 | + | 0.222990i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8256 | − | 23.9466i | −0.494718 | − | 0.856877i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.9194 | − | 31.0374i | 0.639572 | − | 1.10777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.540073 | −0.0192515 | −0.00962576 | − | 0.999954i | \(-0.503064\pi\) | ||||
−0.00962576 | + | 0.999954i | \(0.503064\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.95378 | + | 6.07521i | 0.211692 | + | 0.216010i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.91135 | + | 15.4349i | 0.316451 | + | 0.548110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.5550 | + | 21.7459i | 0.444721 | + | 0.770279i | 0.998033 | − | 0.0626954i | \(-0.0199697\pi\) |
−0.553312 | + | 0.832974i | \(0.686636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.43474 | + | 7.68119i | −0.156890 | + | 0.271741i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.8044 | 0.557725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.1940 | − | 13.4631i | −0.465027 | − | 0.474511i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5865 | − | 25.2645i | 0.512833 | − | 0.888252i | −0.487057 | − | 0.873370i | \(-0.661929\pi\) |
0.999889 | − | 0.0148817i | \(-0.00473717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4290 | 0.541785 | 0.270892 | − | 0.962610i | \(-0.412681\pi\) | ||||
0.270892 | + | 0.962610i | \(0.412681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.6659 | −0.443669 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.75839 | −0.306417 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.48727 | −0.296208 | −0.148104 | − | 0.988972i | \(-0.547317\pi\) | ||||
−0.148104 | + | 0.988972i | \(0.547317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.0974 | −1.01427 | −0.507136 | − | 0.861866i | \(-0.669296\pi\) | ||||
−0.507136 | + | 0.861866i | \(0.669296\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.9396 | −0.902007 | −0.451003 | − | 0.892522i | \(-0.648934\pi\) | ||||
−0.451003 | + | 0.892522i | \(0.648934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.10821 | − | 5.38358i | 0.107953 | − | 0.186979i | −0.806988 | − | 0.590568i | \(-0.798904\pi\) |
0.914941 | + | 0.403588i | \(0.132237\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.215047 | − | 10.6501i | 0.00745093 | − | 0.369004i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.6706 | −0.576910 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.2947 | − | 36.8834i | 0.735174 | − | 1.27336i | −0.219474 | − | 0.975618i | \(-0.570434\pi\) |
0.954647 | − | 0.297740i | \(-0.0962327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5721 | − | 18.3114i | −0.364555 | − | 0.631428i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.0751 | − | 53.8237i | −1.06902 | − | 1.85159i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.621885 | − | 2.23059i | 0.0213682 | − | 0.0766440i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.23912 | −0.0767562 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.6969 | + | 18.5275i | −0.366254 | + | 0.634370i | −0.988976 | − | 0.148073i | \(-0.952693\pi\) |
0.622723 | + | 0.782442i | \(0.286026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.4218 | − | 31.9074i | −0.629275 | − | 1.08994i | −0.987697 | − | 0.156377i | \(-0.950019\pi\) |
0.358422 | − | 0.933560i | \(-0.383315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.81875 | + | 15.2745i | −0.300892 | + | 0.521160i | −0.976338 | − | 0.216249i | \(-0.930618\pi\) |
0.675446 | + | 0.737409i | \(0.263951\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.380438 | − | 0.658939i | −0.0129503 | − | 0.0224305i | 0.859478 | − | 0.511173i | \(-0.170789\pi\) |
−0.872428 | + | 0.488743i | \(0.837456\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.05950 | − | 7.03127i | 0.138027 | − | 0.239070i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.58414 | − | 11.4041i | −0.223351 | − | 0.386856i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.2759 | − | 54.1715i | −1.05974 | − | 1.83553i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.01724 | − | 0.261592i | 0.0343890 | − | 0.00884343i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.7495 | − | 35.9392i | 0.700662 | − | 1.21358i | −0.267573 | − | 0.963538i | \(-0.586222\pi\) |
0.968234 | − | 0.250044i | \(-0.0804451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.35486 | −0.281482 | −0.140741 | − | 0.990046i | \(-0.544949\pi\) | ||||
−0.140741 | + | 0.990046i | \(0.544949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6181 | −1.19864 | −0.599322 | − | 0.800508i | \(-0.704563\pi\) | ||||
−0.599322 | + | 0.800508i | \(0.704563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.5550 | − | 32.1382i | 0.623016 | − | 1.07909i | −0.365905 | − | 0.930652i | \(-0.619241\pi\) |
0.988921 | − | 0.148443i | \(-0.0474260\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −51.5175 | + | 13.2482i | −1.72784 | + | 0.444330i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.73788 | − | 6.47420i | −0.125083 | − | 0.216651i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1969 | + | 19.3935i | 0.374270 | + | 0.648254i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.3565 | − | 57.7751i | 1.11250 | − | 1.92691i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.56526 | + | 2.71111i | 0.0521464 | + | 0.0903202i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.6300 | − | 35.7321i | 0.685763 | − | 1.18778i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.0751 | − | 41.6993i | −0.799401 | − | 1.38460i | −0.920007 | − | 0.391902i | \(-0.871817\pi\) |
0.120606 | − | 0.992700i | \(-0.461516\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.4428 | − | 30.2119i | 0.577906 | − | 1.00096i | −0.417813 | − | 0.908533i | \(-0.637203\pi\) |
0.995719 | − | 0.0924301i | \(-0.0294635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.6706 | 0.849573 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.52175 | + | 16.2187i | −0.149321 | + | 0.535590i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.8675 | + | 44.8037i | 0.853289 | + | 1.47794i | 0.878224 | + | 0.478250i | \(0.158729\pi\) |
−0.0249351 | + | 0.999689i | \(0.507938\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.7826 | + | 42.9248i | 0.815730 | + | 1.41289i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.56238 | − | 4.43818i | 0.0842506 | − | 0.145926i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.8285 | 1.66763 | 0.833814 | − | 0.552046i | \(-0.186153\pi\) | ||||
0.833814 | + | 0.552046i | \(0.186153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.68332 | + | 4.64526i | 0.251811 | + | 0.152242i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.70370 | − | 13.3432i | 0.251938 | − | 0.436369i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.54583 | 0.0831686 | 0.0415843 | − | 0.999135i | \(-0.486759\pi\) | ||||
0.0415843 | + | 0.999135i | \(0.486759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.15787 | −0.0377454 | −0.0188727 | − | 0.999822i | \(-0.506008\pi\) | ||||
−0.0188727 | + | 0.999822i | \(0.506008\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.5458 | −0.408548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.81479 | 0.318938 | 0.159469 | − | 0.987203i | \(-0.449022\pi\) | ||||
0.159469 | + | 0.987203i | \(0.449022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.3297 | −0.919620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.53791 | −0.211784 | −0.105892 | − | 0.994378i | \(-0.533770\pi\) | ||||
−0.105892 | + | 0.994378i | \(0.533770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.15103 | + | 5.45774i | −0.101965 | + | 0.176608i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.07674 | + | 5.18029i | 0.163937 | + | 0.167280i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.7565 | 1.86311 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.23229 | − | 12.5267i | 0.232816 | − | 0.403248i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.4445 | − | 25.0185i | −0.464502 | − | 0.804542i | 0.534677 | − | 0.845057i | \(-0.320433\pi\) |
−0.999179 | + | 0.0405151i | \(0.987100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.66827 | + | 4.62158i | 0.0856289 | + | 0.148314i | 0.905659 | − | 0.424007i | \(-0.139377\pi\) |
−0.820030 | + | 0.572320i | \(0.806043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.7535 | + | 15.0544i | 0.472975 | + | 0.482622i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.0722 | 1.53797 | 0.768983 | − | 0.639269i | \(-0.220763\pi\) | ||||
0.768983 | + | 0.639269i | \(0.220763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.358685 | + | 0.621261i | −0.0114636 | + | 0.0198556i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.7313 | − | 25.5154i | −0.469857 | − | 0.813816i | 0.529549 | − | 0.848279i | \(-0.322361\pi\) |
−0.999406 | + | 0.0344634i | \(0.989028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.7067 | + | 60.1138i | −1.10585 | + | 1.91538i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.64488 | − | 13.2413i | −0.243093 | − | 0.421050i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.4142 | + | 26.6982i | −0.489649 | + | 0.848097i | −0.999929 | − | 0.0119112i | \(-0.996208\pi\) |
0.510280 | + | 0.860008i | \(0.329542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.5413 | − | 33.8466i | −0.619501 | − | 1.07301i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.77292 | − | 4.80283i | −0.0878191 | − | 0.152107i | 0.818770 | − | 0.574122i | \(-0.194656\pi\) |
−0.906589 | + | 0.422015i | \(0.861323\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))