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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.11 | ||
Character | \(\chi\) | \(=\) | 900.101 |
Dual form | 900.3.p.f.401.11 |
$q$-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 | ||||||||
\(3\) | 2.69243 | − | 1.32320i | 0.897475 | − | 0.441065i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.36039 | + | 2.35627i | −0.194342 | + | 0.336610i | −0.946684 | − | 0.322162i | \(-0.895590\pi\) |
0.752343 | + | 0.658772i | \(0.228924\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.49831 | − | 7.12521i | 0.610923 | − | 0.791690i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.77248 | − | 1.60069i | −0.252044 | − | 0.145518i | 0.368656 | − | 0.929566i | \(-0.379818\pi\) |
−0.620700 | + | 0.784048i | \(0.713151\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.99574 | − | 6.92082i | −0.307364 | − | 0.532371i | 0.670421 | − | 0.741981i | \(-0.266114\pi\) |
−0.977785 | + | 0.209611i | \(0.932780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.82475i | − | 0.107338i | −0.998559 | − | 0.0536691i | \(-0.982908\pi\) | ||
0.998559 | − | 0.0536691i | \(-0.0170916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.4409 | 0.812679 | 0.406340 | − | 0.913722i | \(-0.366805\pi\) | ||||
0.406340 | + | 0.913722i | \(0.366805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.544949 | + | 8.14414i | −0.0259499 | + | 0.387816i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 28.0288 | − | 16.1825i | 1.21865 | − | 0.703585i | 0.254017 | − | 0.967200i | \(-0.418248\pi\) |
0.964628 | + | 0.263614i | \(0.0849146\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.37572 | − | 26.4594i | 0.199101 | − | 0.979979i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.5744 | − | 14.7654i | −0.881877 | − | 0.509152i | −0.0106004 | − | 0.999944i | \(-0.503374\pi\) |
−0.871277 | + | 0.490792i | \(0.836708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.5013 | − | 45.9016i | −0.854880 | − | 1.48070i | −0.876756 | − | 0.480935i | \(-0.840297\pi\) |
0.0218756 | − | 0.999761i | \(-0.493036\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.58274 | − | 0.641210i | −0.290386 | − | 0.0194306i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0450 | 0.812028 | 0.406014 | − | 0.913867i | \(-0.366918\pi\) | ||||
0.406014 | + | 0.913867i | \(0.366918\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.9158 | − | 13.3466i | −0.510662 | − | 0.342222i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66.5294 | − | 38.4108i | 1.62267 | − | 0.936848i | 0.636465 | − | 0.771306i | \(-0.280396\pi\) |
0.986203 | − | 0.165542i | \(-0.0529373\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.49000 | + | 7.77691i | −0.104419 | + | 0.180858i | −0.913501 | − | 0.406838i | \(-0.866632\pi\) |
0.809082 | + | 0.587696i | \(0.199965\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2573 | − | 5.92207i | −0.218241 | − | 0.126002i | 0.386894 | − | 0.922124i | \(-0.373548\pi\) |
−0.605136 | + | 0.796122i | \(0.706881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.7987 | + | 36.0244i | 0.424463 | + | 0.735191i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41450 | − | 4.91300i | −0.0473431 | − | 0.0963333i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 28.9838i | 0.546864i | 0.961891 | + | 0.273432i | \(0.0881589\pi\) | ||||
−0.961891 | + | 0.273432i | \(0.911841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 41.5735 | − | 20.4313i | 0.729359 | − | 0.358445i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16.6328 | + | 9.60298i | −0.281913 | + | 0.162762i | −0.634289 | − | 0.773096i | \(-0.718707\pi\) |
0.352376 | + | 0.935858i | \(0.385374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 30.9820 | − | 53.6624i | 0.507902 | − | 0.879712i | −0.492056 | − | 0.870563i | \(-0.663755\pi\) |
0.999958 | − | 0.00914834i | \(-0.00291205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.30905 | + | 22.6485i | 0.147763 | + | 0.359501i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59309 | − | 4.49136i | −0.0387028 | − | 0.0670352i | 0.846025 | − | 0.533143i | \(-0.178989\pi\) |
−0.884728 | + | 0.466108i | \(0.845656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 54.0530 | − | 80.6577i | 0.783377 | − | 1.16895i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 96.0332i | − | 1.35258i | −0.736635 | − | 0.676290i | \(-0.763587\pi\) | ||
0.736635 | − | 0.676290i | \(-0.236413\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −127.394 | −1.74512 | −0.872561 | − | 0.488506i | \(-0.837542\pi\) | ||||
−0.872561 | + | 0.488506i | \(0.837542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.54332 | − | 4.35514i | 0.0979652 | − | 0.0565603i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.2255 | − | 41.9598i | 0.306652 | − | 0.531137i | −0.670976 | − | 0.741479i | \(-0.734125\pi\) |
0.977628 | + | 0.210342i | \(0.0674578\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −20.5373 | − | 78.3532i | −0.253547 | − | 0.967323i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 83.1807 | + | 48.0244i | 1.00218 | + | 0.578608i | 0.908892 | − | 0.417032i | \(-0.136930\pi\) |
0.0932858 | + | 0.995639i | \(0.470263\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −88.3948 | − | 5.91477i | −1.01603 | − | 0.0679858i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 21.4877i | − | 0.241435i | −0.992687 | − | 0.120717i | \(-0.961481\pi\) | ||
0.992687 | − | 0.120717i | \(-0.0385195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.7431 | 0.238935 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −132.090 | − | 88.5202i | −1.42032 | − | 0.951830i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −83.3867 | + | 144.430i | −0.859657 | + | 1.48897i | 0.0125994 | + | 0.999921i | \(0.495989\pi\) |
−0.872256 | + | 0.489049i | \(0.837344\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26.6492 | + | 10.9534i | −0.269184 | + | 0.110641i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.04463 | + | 4.64457i | 0.0796498 | + | 0.0459858i | 0.539296 | − | 0.842116i | \(-0.318690\pi\) |
−0.459646 | + | 0.888102i | \(0.652024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74.4089 | + | 128.880i | 0.722416 | + | 1.25126i | 0.960029 | + | 0.279902i | \(0.0903019\pi\) |
−0.237612 | + | 0.971360i | \(0.576365\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 128.718i | 1.20297i | 0.798884 | + | 0.601486i | \(0.205424\pi\) | ||||
−0.798884 | + | 0.601486i | \(0.794576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −51.9030 | −0.476174 | −0.238087 | − | 0.971244i | \(-0.576520\pi\) | ||||
−0.238087 | + | 0.971244i | \(0.576520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 80.8940 | − | 39.7555i | 0.728775 | − | 0.358158i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 74.2232 | − | 42.8528i | 0.656842 | − | 0.379228i | −0.134230 | − | 0.990950i | \(-0.542856\pi\) |
0.791073 | + | 0.611722i | \(0.209523\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −71.2821 | − | 9.58230i | −0.609248 | − | 0.0819000i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.29959 | + | 2.48237i | 0.0361310 | + | 0.0208603i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −55.3756 | − | 95.9133i | −0.457649 | − | 0.792672i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 128.300 | − | 191.449i | 1.04309 | − | 1.55650i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −44.5884 | −0.351090 | −0.175545 | − | 0.984471i | \(-0.556169\pi\) | ||||
−0.175545 | + | 0.984471i | \(0.556169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.79862 | + | 26.8799i | −0.0139428 | + | 0.208371i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −81.7238 | + | 47.1833i | −0.623846 | + | 0.360178i | −0.778365 | − | 0.627812i | \(-0.783951\pi\) |
0.154519 | + | 0.987990i | \(0.450617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.0057 | + | 36.3829i | −0.157937 | + | 0.273556i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 30.5615 | + | 17.6447i | 0.223077 | + | 0.128793i | 0.607374 | − | 0.794416i | \(-0.292223\pi\) |
−0.384297 | + | 0.923209i | \(0.625556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −61.3817 | − | 106.316i | −0.441595 | − | 0.764864i | 0.556213 | − | 0.831040i | \(-0.312254\pi\) |
−0.997808 | + | 0.0661751i | \(0.978920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −35.4532 | − | 2.37228i | −0.251441 | − | 0.0168247i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.5838i | 0.178908i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 103.666 | + | 69.4722i | 0.705212 | + | 0.472600i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 199.229 | − | 115.025i | 1.33711 | − | 0.771978i | 0.350728 | − | 0.936477i | \(-0.385934\pi\) |
0.986377 | + | 0.164499i | \(0.0526007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −56.8466 | + | 98.4612i | −0.376467 | + | 0.652061i | −0.990545 | − | 0.137185i | \(-0.956195\pi\) |
0.614078 | + | 0.789245i | \(0.289528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.0017 | − | 10.0330i | −0.0849785 | − | 0.0655753i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −81.9039 | − | 141.862i | −0.521681 | − | 0.903578i | −0.999682 | − | 0.0252188i | \(-0.991972\pi\) |
0.478001 | − | 0.878359i | \(-0.341362\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 38.3512 | + | 78.0367i | 0.241203 | + | 0.490797i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 88.0579i | 0.546944i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −237.537 | −1.45728 | −0.728641 | − | 0.684896i | \(-0.759848\pi\) | ||||
−0.728641 | + | 0.684896i | \(0.759848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 195.400 | − | 112.814i | 1.17006 | − | 0.675535i | 0.216367 | − | 0.976312i | \(-0.430579\pi\) |
0.953694 | + | 0.300777i | \(0.0972460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 52.5682 | − | 91.0508i | 0.311054 | − | 0.538762i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 84.8988 | − | 110.020i | 0.496484 | − | 0.643390i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 173.349 | + | 100.083i | 1.00202 | + | 0.578516i | 0.908845 | − | 0.417134i | \(-0.136965\pi\) |
0.0931742 | + | 0.995650i | \(0.470299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32.0761 | + | 47.8638i | −0.181221 | + | 0.270417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 180.163i | 1.00650i | 0.864141 | + | 0.503249i | \(0.167862\pi\) | ||||
−0.864141 | + | 0.503249i | \(0.832138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 264.087 | 1.45904 | 0.729522 | − | 0.683957i | \(-0.239742\pi\) | ||||
0.729522 | + | 0.683957i | \(0.239742\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4108 | − | 185.477i | 0.0678188 | − | 1.01354i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.92086 | + | 5.05908i | −0.0156196 | + | 0.0270539i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 55.0324 | + | 48.6618i | 0.291177 | + | 0.257470i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −195.986 | − | 113.153i | −1.02611 | − | 0.592423i | −0.110240 | − | 0.993905i | \(-0.535162\pi\) |
−0.915867 | + | 0.401482i | \(0.868495\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 108.682 | + | 188.243i | 0.563121 | + | 0.975353i | 0.997222 | + | 0.0744893i | \(0.0237327\pi\) |
−0.434101 | + | 0.900864i | \(0.642934\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 260.058i | − | 1.32009i | −0.751225 | − | 0.660046i | \(-0.770537\pi\) | ||
0.751225 | − | 0.660046i | \(-0.229463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −253.121 | −1.27197 | −0.635983 | − | 0.771703i | \(-0.719405\pi\) | ||||
−0.635983 | + | 0.771703i | \(0.719405\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9246 | − | 8.66148i | −0.0643017 | − | 0.0430919i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 69.5825 | − | 40.1735i | 0.342771 | − | 0.197899i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 38.8077 | − | 288.688i | 0.187477 | − | 1.39463i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −42.8097 | − | 24.7162i | −0.204831 | − | 0.118259i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 147.164 | + | 254.895i | 0.697459 | + | 1.20803i | 0.969345 | + | 0.245704i | \(0.0790192\pi\) |
−0.271886 | + | 0.962329i | \(0.587647\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −127.071 | − | 258.562i | −0.596576 | − | 1.21391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 144.208 | 0.664555 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −342.998 | + | 168.567i | −1.56620 | + | 0.769713i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.6288 | + | 7.29121i | −0.0571437 | + | 0.0329919i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −216.144 | + | 374.373i | −0.969256 | + | 1.67880i | −0.271540 | + | 0.962427i | \(0.587533\pi\) |
−0.697717 | + | 0.716374i | \(0.745801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 353.826 | + | 204.281i | 1.55870 | + | 0.899918i | 0.997381 | + | 0.0723201i | \(0.0230403\pi\) |
0.561322 | + | 0.827598i | \(0.310293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 115.657 | + | 200.323i | 0.505051 | + | 0.874774i | 0.999983 | + | 0.00584253i | \(0.00185974\pi\) |
−0.494932 | + | 0.868932i | \(0.664807\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.5471 | − | 21.7072i | 0.0629746 | − | 0.0939705i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 136.907i | 0.587584i | 0.955869 | + | 0.293792i | \(0.0949173\pi\) | ||||
−0.955869 | + | 0.293792i | \(0.905083\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.70432 | − | 145.029i | 0.0409465 | − | 0.611936i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.1897 | − | 16.2753i | 0.117948 | − | 0.0680976i | −0.439865 | − | 0.898064i | \(-0.644974\pi\) |
0.557814 | + | 0.829966i | \(0.311640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −105.816 | + | 183.279i | −0.439071 | + | 0.760493i | −0.997618 | − | 0.0689800i | \(-0.978026\pi\) |
0.558547 | + | 0.829473i | \(0.311359\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −158.972 | − | 183.785i | −0.654205 | − | 0.756318i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −61.6978 | − | 106.864i | −0.249789 | − | 0.432647i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 287.504 | + | 19.2377i | 1.15463 | + | 0.0772600i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 314.643i | 1.25356i | 0.779197 | + | 0.626779i | \(0.215627\pi\) | ||||
−0.779197 | + | 0.626779i | \(0.784373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −103.613 | −0.409536 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.0876 | + | 15.6391i | −0.105399 | + | 0.0608524i | −0.551773 | − | 0.833994i | \(-0.686049\pi\) |
0.446374 | + | 0.894847i | \(0.352715\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40.8730 | + | 70.7941i | −0.157811 | + | 0.273336i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −245.823 | + | 101.039i | −0.941850 | + | 0.387121i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 259.919 | + | 150.065i | 0.988287 | + | 0.570588i | 0.904762 | − | 0.425918i | \(-0.140049\pi\) |
0.0835251 | + | 0.996506i | \(0.473382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.4324 | − | 57.8540i | −0.106489 | − | 0.216682i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.75658i | 0.0176824i | 0.999961 | + | 0.00884122i | \(0.00281429\pi\) | ||||
−0.999961 | + | 0.00884122i | \(0.997186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −331.919 | −1.22479 | −0.612396 | − | 0.790551i | \(-0.709794\pi\) | ||||
−0.612396 | + | 0.790551i | \(0.709794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 58.5416 | − | 28.7703i | 0.214438 | − | 0.105386i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −159.572 | + | 276.386i | −0.576071 | + | 0.997785i | 0.419853 | + | 0.907592i | \(0.362082\pi\) |
−0.995924 | + | 0.0901929i | \(0.971252\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −472.771 | − | 63.5536i | −1.69452 | − | 0.227791i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 193.228 | + | 111.560i | 0.687643 | + | 0.397011i | 0.802729 | − | 0.596345i | \(-0.203381\pi\) |
−0.115085 | + | 0.993356i | \(0.536714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −95.6888 | − | 165.738i | −0.338123 | − | 0.585646i | 0.645957 | − | 0.763374i | \(-0.276459\pi\) |
−0.984080 | + | 0.177728i | \(0.943125\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 209.015i | 0.728274i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 285.670 | 0.988479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −33.4033 | + | 499.204i | −0.114788 | + | 1.71548i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 327.768 | − | 189.237i | 1.11866 | − | 0.645861i | 0.177604 | − | 0.984102i | \(-0.443165\pi\) |
0.941059 | + | 0.338241i | \(0.109832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −57.2576 | + | 64.7534i | −0.192786 | + | 0.218025i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −223.992 | − | 129.322i | −0.749136 | − | 0.432514i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.2163 | − | 21.1593i | −0.0405858 | − | 0.0702966i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.8052 | + | 1.86053i | 0.0917664 | + | 0.00614037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −346.416 | −1.12839 | −0.564196 | − | 0.825641i | \(-0.690814\pi\) | ||||
−0.564196 | + | 0.825641i | \(0.690814\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 370.874 | + | 248.542i | 1.20024 | + | 0.804344i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 67.4633 | − | 38.9499i | 0.216924 | − | 0.125241i | −0.387601 | − | 0.921827i | \(-0.626696\pi\) |
0.604525 | + | 0.796586i | \(0.293363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2088 | + | 31.5386i | −0.0581752 | + | 0.100762i | −0.893646 | − | 0.448772i | \(-0.851862\pi\) |
0.835471 | + | 0.549534i | \(0.185195\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −207.221 | − | 119.639i | −0.653693 | − | 0.377410i | 0.136177 | − | 0.990685i | \(-0.456518\pi\) |
−0.789869 | + | 0.613275i | \(0.789852\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.2698 | + | 81.8737i | 0.148181 | + | 0.256657i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 170.319 | + | 346.563i | 0.530589 | + | 1.07964i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 28.1758i | − | 0.0872315i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −139.745 | + | 68.6778i | −0.427354 | + | 0.210024i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.9080 | − | 16.1127i | 0.0848266 | − | 0.0489747i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.5386 | + | 42.5021i | −0.0741348 | + | 0.128405i | −0.900710 | − | 0.434422i | \(-0.856953\pi\) |
0.826575 | + | 0.562827i | \(0.190286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 165.197 | − | 214.077i | 0.496087 | − | 0.642875i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 276.158 | + | 478.319i | 0.819459 | + | 1.41934i | 0.906081 | + | 0.423103i | \(0.139059\pi\) |
−0.0866225 | + | 0.996241i | \(0.527607\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 143.138 | − | 213.590i | 0.422235 | − | 0.630058i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 169.682i | 0.497601i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −246.496 | −0.718646 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −347.063 | + | 200.377i | −1.00018 | + | 0.577455i | −0.908302 | − | 0.418315i | \(-0.862621\pi\) |
−0.0918794 | + | 0.995770i | \(0.529287\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −51.5180 | + | 89.2318i | −0.147616 | + | 0.255678i | −0.930346 | − | 0.366683i | \(-0.880493\pi\) |
0.782730 | + | 0.622362i | \(0.213827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −204.601 | + | 68.5205i | −0.582909 | + | 0.195215i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 413.578 | + | 238.779i | 1.17161 | + | 0.676428i | 0.954058 | − | 0.299621i | \(-0.0968602\pi\) |
0.217550 | + | 0.976049i | \(0.430194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.8610 | + | 0.994394i | 0.0416274 | + | 0.00278542i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 585.178i | 1.63002i | 0.579445 | + | 0.815012i | \(0.303269\pi\) | ||||
−0.579445 | + | 0.815012i | \(0.696731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −122.578 | −0.339552 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −276.007 | − | 184.967i | −0.760349 | − | 0.509550i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.9727 | + | 32.8618i | −0.0516968 | + | 0.0895416i | −0.890716 | − | 0.454561i | \(-0.849796\pi\) |
0.839019 | + | 0.544102i | \(0.183130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 92.1141 | − | 685.230i | 0.249632 | − | 1.85699i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −68.2936 | − | 39.4293i | −0.184080 | − | 0.106278i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 57.1561 | + | 98.9972i | 0.153233 | + | 0.265408i | 0.932414 | − | 0.361391i | \(-0.117698\pi\) |
−0.779181 | + | 0.626799i | \(0.784365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 235.995i | 0.625981i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 157.951 | 0.416757 | 0.208378 | − | 0.978048i | \(-0.433181\pi\) | ||||
0.208378 | + | 0.978048i | \(0.433181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −120.051 | + | 58.9992i | −0.315094 | + | 0.154854i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 56.8675 | − | 32.8325i | 0.148479 | − | 0.0857245i | −0.423920 | − | 0.905700i | \(-0.639346\pi\) |
0.572399 | + | 0.819975i | \(0.306013\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.7247 | + | 74.7520i | 0.0793921 | + | 0.193158i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −380.293 | − | 219.562i | −0.977616 | − | 0.564427i | −0.0760665 | − | 0.997103i | \(-0.524236\pi\) |
−0.901550 | + | 0.432676i | \(0.857569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.5289 | − | 51.1456i | −0.0755215 | − | 0.130807i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −157.603 | + | 235.174i | −0.401024 | + | 0.598407i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 108.265 | 0.272707 | 0.136353 | − | 0.990660i | \(-0.456462\pi\) | ||||
0.136353 | + | 0.990660i | \(0.456462\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.41451 | + | 125.753i | −0.0210890 | + | 0.315170i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 84.9001 | − | 49.0171i | 0.211721 | − | 0.122237i | −0.390390 | − | 0.920650i | \(-0.627660\pi\) |
0.602111 | + | 0.798412i | \(0.294326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −211.784 | + | 366.821i | −0.525519 | + | 0.910226i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −83.2994 | − | 48.0929i | −0.204667 | − | 0.118164i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.2529 | + | 52.3996i | 0.0739681 | + | 0.128116i | 0.900637 | − | 0.434572i | \(-0.143100\pi\) |
−0.826669 | + | 0.562689i | \(0.809767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 105.632 | + | 7.06816i | 0.257012 | + | 0.0171975i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 52.2552i | − | 0.126526i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −305.943 | − | 205.028i | −0.733675 | − | 0.491675i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.1092 | + | 6.99127i | −0.0289003 | + | 0.0166856i | −0.514381 | − | 0.857562i | \(-0.671978\pi\) |
0.485480 | + | 0.874248i | \(0.338645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 115.320 | − | 199.740i | 0.273919 | − | 0.474442i | −0.695943 | − | 0.718097i | \(-0.745013\pi\) |
0.969862 | + | 0.243656i | \(0.0783466\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −98.5940 | + | 40.5243i | −0.233083 | + | 0.0958021i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 84.2953 | + | 146.004i | 0.197413 | + | 0.341929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.8524 | + | 68.8825i | 0.0789100 | + | 0.160565i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 153.008i | 0.355008i | 0.984120 | + | 0.177504i | \(0.0568023\pi\) | ||||
−0.984120 | + | 0.177504i | \(0.943198\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −301.530 | −0.696374 | −0.348187 | − | 0.937425i | \(-0.613203\pi\) | ||||
−0.348187 | + | 0.937425i | \(0.613203\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 432.791 | − | 249.872i | 0.990368 | − | 0.571789i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −244.893 | + | 424.167i | −0.557842 | + | 0.966211i | 0.439834 | + | 0.898079i | \(0.355037\pi\) |
−0.997676 | + | 0.0681318i | \(0.978296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 371.039 | + | 49.8780i | 0.841357 | + | 0.113102i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −86.6072 | − | 50.0027i | −0.195502 | − | 0.112873i | 0.399054 | − | 0.916927i | \(-0.369339\pi\) |
−0.594556 | + | 0.804055i | \(0.702672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 384.208 | − | 573.314i | 0.859526 | − | 1.28258i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 561.661i | 1.25092i | 0.780258 | + | 0.625458i | \(0.215088\pi\) | ||||
−0.780258 | + | 0.625458i | \(0.784912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −245.935 | −0.545311 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.7717 | + | 340.318i | −0.0502687 | + | 0.751255i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 297.031 | − | 514.473i | 0.649958 | − | 1.12576i | −0.333174 | − | 0.942865i | \(-0.608120\pi\) |
0.983132 | − | 0.182896i | \(-0.0585470\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −48.2818 | − | 9.80934i | −0.105189 | − | 0.0213711i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 115.530 | + | 66.7015i | 0.250608 | + | 0.144689i | 0.620043 | − | 0.784568i | \(-0.287115\pi\) |
−0.369435 | + | 0.929257i | \(0.620449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −242.017 | − | 419.185i | −0.522714 | − | 0.905368i | −0.999651 | − | 0.0264298i | \(-0.991586\pi\) |
0.476936 | − | 0.878938i | \(-0.341747\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 150.725i | − | 0.322751i | −0.986893 | − | 0.161376i | \(-0.948407\pi\) | ||
0.986893 | − | 0.161376i | \(-0.0515931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.1104 | 0.0300862 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −408.231 | − | 273.577i | −0.866733 | − | 0.580843i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.8969 | − | 14.3742i | 0.0526362 | − | 0.0303895i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 206.516 | + | 159.362i | 0.432947 | + | 0.334092i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −589.607 | − | 340.410i | −1.23091 | − | 0.710667i | −0.263692 | − | 0.964607i | \(-0.584940\pi\) |
−0.967220 | + | 0.253940i | \(0.918274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −120.052 | − | 207.936i | −0.249589 | − | 0.432300i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 116.518 | + | 237.089i | 0.241238 | + | 0.490868i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −684.297 | −1.40513 | −0.702564 | − | 0.711621i | \(-0.747962\pi\) | ||||
−0.702564 | + | 0.711621i | \(0.747962\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −639.550 | + | 314.308i | −1.30787 | + | 0.642756i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 557.013 | − | 321.592i | 1.13445 | − | 0.654973i | 0.189397 | − | 0.981901i | \(-0.439347\pi\) |
0.945049 | + | 0.326927i | \(0.106013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.9432 | + | 46.6669i | −0.0546514 | + | 0.0946591i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 226.280 | + | 130.643i | 0.455291 | + | 0.262863i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −167.805 | − | 290.647i | −0.336283 | − | 0.582459i | 0.647448 | − | 0.762110i | \(-0.275836\pi\) |
−0.983730 | + | 0.179651i | \(0.942503\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 376.825 | − | 562.297i | 0.752146 | − | 1.12235i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 402.227i | 0.799655i | 0.916590 | + | 0.399828i | \(0.130930\pi\) | ||||
−0.916590 | + | 0.399828i | \(0.869070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.0579 | − | 314.705i | 0.0415343 | − | 0.620721i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 825.062 | − | 476.350i | 1.62095 | − | 0.935854i | 0.634279 | − | 0.773104i | \(-0.281297\pi\) |
0.986667 | − | 0.162749i | \(-0.0520362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 173.306 | − | 300.174i | 0.339150 | − | 0.587425i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 83.0061 | − | 408.558i | 0.161805 | − | 0.796409i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.9589 | + | 32.8377i | 0.0366709 | + | 0.0635159i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 599.160 | + | 40.0916i | 1.15445 | + | 0.0772478i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 581.220i | − | 1.11558i | −0.829980 | − | 0.557792i | \(-0.811648\pi\) | ||
0.829980 | − | 0.557792i | \(-0.188352\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 873.203 | 1.66960 | 0.834802 | − | 0.550550i | \(-0.185582\pi\) | ||||
0.834802 | + | 0.550550i | \(0.185582\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −83.7588 | + | 48.3582i | −0.158935 | + | 0.0917613i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 259.244 | − | 449.024i | 0.490064 | − | 0.848817i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.0292 | + | 171.313i | −0.0433695 | + | 0.322623i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −531.668 | − | 306.958i | −0.997500 | − | 0.575907i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 238.391 | + | 485.076i | 0.443932 | + | 0.903307i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 133.169i | − | 0.247067i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 285.224 | 0.527216 | 0.263608 | − | 0.964630i | \(-0.415087\pi\) | ||||
0.263608 | + | 0.964630i | \(0.415087\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 711.035 | − | 349.439i | 1.30946 | − | 0.643534i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 124.431 | − | 215.520i | 0.227479 | − | 0.394004i | −0.729582 | − | 0.683894i | \(-0.760285\pi\) |
0.957060 | + | 0.289889i | \(0.0936185\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −212.008 | − | 515.806i | −0.386170 | − | 0.939537i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −394.893 | − | 227.991i | −0.716684 | − | 0.413777i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 65.9124 | + | 114.164i | 0.119191 | + | 0.206444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 865.154i | − | 1.55324i | −0.629971 | − | 0.776619i | \(-0.716933\pi\) | ||
0.629971 | − | 0.776619i | \(-0.283067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 71.7635 | 0.128378 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.17005 | + | 17.4861i | −0.00208564 | + | 0.0311695i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 51.7396 | − | 29.8719i | 0.0918998 | − | 0.0530584i | −0.453346 | − | 0.891335i | \(-0.649770\pi\) |
0.545246 | + | 0.838276i | \(0.316436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 212.560 | + | 58.1997i | 0.374885 | + | 0.102645i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 539.984 | + | 311.760i | 0.949006 | + | 0.547909i | 0.892772 | − | 0.450509i | \(-0.148757\pi\) |
0.0562337 | + | 0.998418i | \(0.482091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 173.203 | + | 299.996i | 0.303332 | + | 0.525387i | 0.976889 | − | 0.213749i | \(-0.0685675\pi\) |
−0.673556 | + | 0.739136i | \(0.735234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −677.402 | − | 45.3270i | −1.18220 | − | 0.0791047i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 772.123 | 1.33817 | 0.669084 | − | 0.743187i | \(-0.266687\pi\) | ||||
0.669084 | + | 0.743187i | \(0.266687\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 541.701 | + | 363.023i | 0.935581 | + | 0.626982i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −226.317 | + | 130.664i | −0.389530 | + | 0.224895i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.3942 | − | 80.3571i | 0.0795784 | − | 0.137834i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 333.912 | + | 192.784i | 0.568845 | + | 0.328423i | 0.756688 | − | 0.653776i | \(-0.226816\pi\) |
−0.187843 | + | 0.982199i | \(0.560150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −409.204 | − | 708.762i | −0.694744 | − | 1.20333i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −344.108 | − | 700.187i | −0.582247 | − | 1.18475i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 685.677i | − | 1.15628i | −0.815936 | − | 0.578142i | \(-0.803778\pi\) | ||
0.815936 | − | 0.578142i | \(-0.196222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −681.509 | + | 334.929i | −1.14156 | + | 0.561020i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 628.802 | − | 363.039i | 1.04975 | − | 0.606075i | 0.127173 | − | 0.991881i | \(-0.459410\pi\) |
0.922580 | + | 0.385806i | \(0.126076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 53.1719 | − | 92.0964i | 0.0884723 | − | 0.153239i | −0.818393 | − | 0.574659i | \(-0.805135\pi\) |
0.906866 | + | 0.421420i | \(0.138468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −46.2594 | − | 6.21856i | −0.0767155 | − | 0.0103127i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −124.449 | − | 215.552i | −0.205023 | − | 0.355111i | 0.745117 | − | 0.666934i | \(-0.232394\pi\) |
−0.950140 | + | 0.311823i | \(0.899060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 134.188 | − | 200.235i | 0.220342 | − | 0.328794i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 94.6522i | 0.154914i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1125.21 | 1.83558 | 0.917791 | − | 0.397064i | \(-0.129971\pi\) | ||||
0.917791 | + | 0.397064i | \(0.129971\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −214.708 | + | 123.962i | −0.347987 | + | 0.200911i | −0.663798 | − | 0.747912i | \(-0.731057\pi\) |
0.315811 | + | 0.948822i | \(0.397723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −173.326 | + | 300.209i | −0.280009 | + | 0.484990i | −0.971387 | − | 0.237504i | \(-0.923671\pi\) |
0.691378 | + | 0.722494i | \(0.257004\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −277.503 | − | 828.620i | −0.446865 | − | 1.33433i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.6307 | + | 29.2317i | 0.0812693 | + | 0.0469208i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −147.966 | − | 9.90086i | −0.235991 | − | 0.0157909i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 54.8246i | − | 0.0871616i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 380.005 | 0.602226 | 0.301113 | − | 0.953588i | \(-0.402642\pi\) | ||||
0.301113 | + | 0.953588i | \(0.402642\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 733.504 | + | 491.559i | 1.15877 | + | 0.776555i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 166.212 | − | 287.888i | 0.260929 | − | 0.451943i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −684.257 | − | 528.020i | −1.07082 | − | 0.826322i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −947.308 | − | 546.929i | −1.47786 | − | 0.853243i | −0.478173 | − | 0.878266i | \(-0.658701\pi\) |
−0.999687 | + | 0.0250231i | \(0.992034\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −416.678 | − | 721.708i | −0.648022 | − | 1.12241i | −0.983595 | − | 0.180393i | \(-0.942263\pi\) |
0.335573 | − | 0.942014i | \(-0.391070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 801.328i | 1.23853i | 0.785183 | + | 0.619264i | \(0.212569\pi\) | ||||
−0.785183 | + | 0.619264i | \(0.787431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.4857 | 0.0947392 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 388.271 | − | 190.816i | 0.596422 | − | 0.293112i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −799.139 | + | 461.383i | −1.22380 | + | 0.706559i | −0.965725 | − | 0.259567i | \(-0.916420\pi\) |
−0.258071 | + | 0.966126i | \(0.583087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −700.450 | + | 907.708i | −1.06613 | + | 1.38160i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −707.274 | − | 408.345i | −1.07325 | − | 0.619643i | −0.144185 | − | 0.989551i | \(-0.546056\pi\) |
−0.929068 | + | 0.369908i | \(0.879389\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 327.247 | + | 566.808i | 0.495078 | + | 0.857501i | 0.999984 | − | 0.00567397i | \(-0.00180609\pi\) |
−0.504906 | + | 0.863174i | \(0.668473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.3543 | + | 36.3414i | −0.0367334 | + | 0.0548135i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −955.763 | −1.43293 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −86.5836 | + | 1293.97i | −0.129422 | + | 1.93419i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −171.794 | + | 99.1854i | −0.256027 | + | 0.147817i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 237.017 | − | 410.526i | 0.352180 | − | 0.609994i | −0.634451 | − | 0.772963i | \(-0.718774\pi\) |
0.986631 | + | 0.162969i | \(0.0521071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −815.479 | − | 470.817i | −1.20455 | − | 0.695446i | −0.242984 | − | 0.970030i | \(-0.578126\pi\) |
−0.961563 | + | 0.274584i | \(0.911460\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −226.877 | − | 392.963i | −0.334134 | − | 0.578737i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1222.95 | + | 81.8315i | 1.79582 | + | 0.120164i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 388.521i | 0.568845i | 0.958699 | + | 0.284422i | \(0.0918018\pi\) | ||||
−0.958699 | + | 0.284422i | \(0.908198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 576.464 | + | 386.319i | 0.839104 | + | 0.562328i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 200.592 | − | 115.812i | 0.291134 | − | 0.168087i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 465.511 | − | 806.289i | 0.673678 | − | 1.16684i | −0.303176 | − | 0.952935i | \(-0.598047\pi\) |
0.976853 | − | 0.213909i | \(-0.0686198\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.4442 | − | 77.6937i | 0.0150710 | − | 0.112112i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −70.0899 | − | 121.399i | −0.100559 | − | 0.174174i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 181.155 | + | 368.612i | 0.259163 | + | 0.527342i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 213.622i | 0.304739i | 0.988324 | + | 0.152370i | \(0.0486904\pi\) | ||||
−0.988324 | + | 0.152370i | \(0.951310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 463.923 | 0.659919 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.8877 | + | 12.6369i | −0.0309585 | + | 0.0178739i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 236.600 | − | 409.804i | 0.333710 | − | 0.578002i | −0.649526 | − | 0.760339i | \(-0.725033\pi\) |
0.983236 | + | 0.182337i | \(0.0583661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −165.773 | − | 403.320i | −0.233155 | − | 0.567257i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1485.60 | − | 857.712i | −2.08359 | − | 1.20296i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 54.3632 | − | 81.1205i | 0.0758203 | − | 0.113139i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 113.785i | 0.158254i | 0.996865 | + | 0.0791272i | \(0.0252133\pi\) | ||||
−0.996865 | + | 0.0791272i | \(0.974787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −404.901 | −0.561582 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.3880 | + | 633.480i | −0.0586280 | + | 0.876182i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.376667 | + | 0.652407i | −0.000518112 | + | 0.000897396i | −0.866284 | − | 0.499551i | \(-0.833498\pi\) |
0.865766 | + | 0.500449i | \(0.166832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −671.203 | − | 284.477i | −0.920718 | − | 0.390229i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.1909 | + | 8.19312i | 0.0194130 | + | 0.0112081i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 301.475 | + | 522.169i | 0.411289 | + | 0.712373i | 0.995031 | − | 0.0995662i | \(-0.0317455\pi\) |
−0.583742 | + | 0.811939i | \(0.698412\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.6029i | 0.0225277i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 362.775 | 0.490900 | 0.245450 | − | 0.969409i | \(-0.421064\pi\) | ||||
0.245450 | + | 0.969409i | \(0.421064\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −307.518 | − | 206.084i | −0.415005 | − | 0.278116i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −951.039 | + | 549.083i | −1.28000 | + | 0.739008i | −0.976848 | − | 0.213935i | \(-0.931372\pi\) |
−0.303151 | + | 0.952942i | \(0.598039\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 799.537 | − | 328.627i | 1.07033 | − | 0.439930i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −303.294 | − | 175.107i | −0.404932 | − | 0.233787i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −510.640 | − | 884.454i | −0.679946 | − | 1.17770i | −0.974997 | − | 0.222220i | \(-0.928670\pi\) |
0.295051 | − | 0.955482i | \(-0.404664\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 416.334 | + | 847.153i | 0.552901 | + | 1.12504i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 314.598 | 0.415585 | 0.207793 | − | 0.978173i | \(-0.433372\pi\) | ||||
0.207793 | + | 0.978173i | \(0.433372\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −278.969 | + | 137.100i | −0.367549 | + | 0.180632i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 740.520 | − | 427.540i | 0.973089 | − | 0.561813i | 0.0729122 | − | 0.997338i | \(-0.476771\pi\) |
0.900176 | + | 0.435525i | \(0.143437\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 70.6084 | − | 122.297i | 0.0925404 | − | 0.160285i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 132.921 | + | 76.7419i | 0.173300 | + | 0.100055i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 214.504 | + | 371.532i | 0.278939 | + | 0.483136i | 0.971121 | − | 0.238586i | \(-0.0766840\pi\) |
−0.692182 | + | 0.721723i | \(0.743351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.2379 | + | 77.9493i | −0.0677535 | + | 0.101102i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 153.265i | − | 0.198273i | −0.995074 | − | 0.0991366i | \(-0.968392\pi\) | ||
0.995074 | − | 0.0991366i | \(-0.0316081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.3730 | + | 244.691i | −0.0210721 | + | 0.314918i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1027.27 | − | 593.097i | 1.31871 | − | 0.761357i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −153.720 | + | 266.250i | −0.196824 | + | 0.340910i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −528.166 | + | 597.311i | −0.674541 | + | 0.762849i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 188.838 | + | 327.078i | 0.239947 | + | 0.415601i | 0.960699 | − | 0.277593i | \(-0.0895366\pi\) |
−0.720752 | + | 0.693193i | \(0.756203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 898.378 | + | 60.1132i | 1.13863 | + | 0.0761891i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 233.186i | 0.294799i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −495.184 | −0.624444 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 517.022 | − | 298.503i | 0.648711 | − | 0.374533i | −0.139251 | − | 0.990257i | \(-0.544470\pi\) |
0.787962 | + | 0.615724i | \(0.211136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8063 | + | 18.7170i | −0.0135248 | + | 0.0234256i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −153.104 | − | 118.146i | −0.191142 | − | 0.147498i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 353.197 | + | 203.919i | 0.439847 | + | 0.253946i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.29389 | + | 12.8067i | 0.00779911 | + | 0.0158696i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1144.94i | 1.41526i | 0.706585 | + | 0.707628i | \(0.250235\pi\) | ||||
−0.706585 | + | 0.707628i | \(0.749765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 227.892 | 0.281001 | 0.140501 | − | 0.990081i | \(-0.455129\pi\) | ||||
0.140501 | + | 0.990081i | \(0.455129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −893.666 | + | 439.194i | −1.09922 | + | 0.540213i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −69.3297 | + | 120.083i | −0.0848589 | + | 0.146980i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 119.550 | − | 154.924i | 0.145971 | − | 0.189162i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.97405 | + | 5.75852i | 0.0121487 | + | 0.00701403i | 0.506062 | − | 0.862497i | \(-0.331101\pi\) |
−0.493913 | + | 0.869511i | \(0.664434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.1399 | − | 76.4526i | −0.0536330 | − | 0.0928950i | 0.837962 | − | 0.545728i | \(-0.183747\pi\) |
−0.891595 | + | 0.452833i | \(0.850413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 149.980i | 0.181355i | 0.995880 | + | 0.0906773i | \(0.0289032\pi\) | ||||
−0.995880 | + | 0.0906773i | \(0.971097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1074.30 | −1.29589 | −0.647947 | − | 0.761685i | \(-0.724372\pi\) | ||||
−0.647947 | + | 0.761685i | \(0.724372\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −63.9217 | + | 955.295i | −0.0769214 | + | 1.14957i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 65.7354 | − | 37.9523i | 0.0789140 | − | 0.0455610i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1356.99 | + | 454.455i | −1.62126 | + | 0.542957i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −714.738 | − | 412.654i | −0.851893 | − | 0.491840i | 0.00939630 | − | 0.999956i | \(-0.497009\pi\) |
−0.861289 | + | 0.508115i | \(0.830342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.5348 | + | 26.9071i | 0.0184718 | + | 0.0319941i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 667.867 | + | 44.6890i | 0.792251 | + | 0.0530119i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 301.330 | 0.355761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −476.939 | − | 319.622i | −0.561765 | − | 0.376468i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 842.128 | − | 486.203i | 0.989575 | − | 0.571331i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 493.807 | − | 855.298i | 0.578906 | − | 1.00269i | −0.416699 | − | 0.909044i | \(-0.636813\pi\) |
0.995605 | − | 0.0936499i | \(-0.0298534\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −760.254 | − | 438.933i | −0.887111 | − | 0.512174i | −0.0141144 | − | 0.999900i | \(-0.504493\pi\) |
−0.872996 | + | 0.487727i | \(0.837826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 506.900 | + | 877.977i | 0.590105 | + | 1.02209i | 0.994218 | + | 0.107383i | \(0.0342470\pi\) |
−0.404113 | + | 0.914709i | \(0.632420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 276.567 | + | 562.756i | 0.321216 | + | 0.653608i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1206.16i | − | 1.39764i | −0.715300 | − | 0.698818i | \(-0.753710\pi\) | ||
0.715300 | − | 0.698818i | \(-0.246290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 769.146 | − | 377.998i | 0.887135 | − | 0.435984i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −134.330 | + | 77.5553i | −0.154580 | + | 0.0892466i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.7226 | + | 35.8926i | −0.0237917 | + | 0.0412084i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 570.609 | + | 1388.27i | 0.653619 | + | 1.59023i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −90.5257 | − | 156.795i | −0.103222 | − | 0.178786i | 0.809788 | − | 0.586722i | \(-0.199582\pi\) |
−0.913010 | + | 0.407936i | \(0.866249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 632.094 | − | 943.209i | 0.719106 | − | 1.07305i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 442.390i | − | 0.502146i | −0.967968 | − | 0.251073i | \(-0.919217\pi\) | ||
0.967968 | − | 0.251073i | \(-0.0807834\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 177.122 | 0.200591 | 0.100296 | − | 0.994958i | \(-0.468021\pi\) | ||||
0.100296 | + | 0.994958i | \(0.468021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −834.177 | + | 481.612i | −0.940447 | + | 0.542968i | −0.890101 | − | 0.455764i | \(-0.849366\pi\) |
−0.0503469 | + | 0.998732i | \(0.516033\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 60.6577 | − | 105.062i | 0.0682314 | − | 0.118180i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −68.4802 | + | 250.107i | −0.0768577 | + | 0.280703i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −158.383 | − | 91.4422i | −0.177360 | − | 0.102399i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −774.199 | − | 51.8040i | −0.863098 | − | 0.0577525i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1565.21i | 1.74106i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.8881 | 0.0586994 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −60.8894 | − | 40.8052i | −0.0674301 | − | 0.0451885i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 415.179 | − | 719.111i | 0.457750 | − | 0.792846i | −0.541092 | − | 0.840963i | \(-0.681989\pi\) |
0.998842 | + | 0.0481178i | \(0.0153223\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 77.3254 | − | 31.7824i | 0.0850664 | − | 0.0349642i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 508.041 | + | 293.318i | 0.557674 | + | 0.321973i | 0.752212 | − | 0.658922i | \(-0.228987\pi\) |
−0.194537 | + | 0.980895i | \(0.562320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −153.745 | − | 266.294i | −0.168395 | − | 0.291669i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 256.751i | − | 0.279990i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.9078 | −0.0379846 | −0.0189923 | − | 0.999820i | \(-0.506046\pi\) | ||||
−0.0189923 | + | 0.999820i | \(0.506046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −932.700 | + | 458.377i | −1.01270 | + | 0.497695i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −664.628 | + | 383.723i | −0.720074 | + | 0.415735i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1327.42 | + | 178.442i | 1.43195 | + | 0.192494i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1415.66 | − | 817.330i | −1.52385 | − | 0.879796i | −0.999601 | − | 0.0282314i | \(-0.991012\pi\) |
−0.524250 | − | 0.851565i | \(-0.675654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 321.150 | + | 556.249i | 0.344952 | + | 0.597475i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 130.101 | − | 194.137i | 0.139444 | − | 0.208078i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1714.52 | 1.82980 | 0.914898 | − | 0.403684i | \(-0.132270\pi\) | ||||
0.914898 | + | 0.403684i | \(0.132270\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.29414 | + | 109.009i | −0.00776799 | + | 0.116091i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −899.820 | + | 519.511i | −0.956238 | + | 0.552084i | −0.895013 | − | 0.446040i | \(-0.852834\pi\) |
−0.0612251 | + | 0.998124i | \(0.519501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1243.16 | − | 2153.22i | 1.31830 | − | 2.28337i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −708.957 | − | 409.316i | −0.748634 | − | 0.432224i | 0.0765658 | − | 0.997065i | \(-0.475604\pi\) |
−0.825200 | + | 0.564840i | \(0.808938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 509.032 | + | 881.670i | 0.536388 | + | 0.929051i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −716.231 | − | 47.9252i | −0.753135 | − | 0.0503946i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.226778i | 0.000237962i | 1.00000 | 0.000118981i | \(3.78728e-5\pi\) | |||||
−1.00000 | 0.000118981i | \(0.999962\pi\) | ||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 235.605 | + | 157.892i | 0.246192 | + | 0.164986i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −83.1513 | + | 48.0074i | −0.0867062 | + | 0.0500599i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −924.137 | + | 1600.65i | −0.961641 | + | 1.66561i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 917.143 | + | 707.731i | 0.952381 | + | 0.734923i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −83.4831 | − | 144.597i | −0.0863321 | − | 0.149532i | 0.819626 | − | 0.572899i | \(-0.194181\pi\) |
−0.905958 | + | 0.423367i | \(0.860848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.2821 | − | 75.8611i | −0.0384748 | − | 0.0782881i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1818.76i | 1.87308i | 0.350557 | + | 0.936542i | \(0.385992\pi\) | ||||
−0.350557 | + | 0.936542i | \(0.614008\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 334.012 | 0.343281 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −747.609 | + | 431.632i | −0.765209 | + | 0.441794i | −0.831163 | − | 0.556029i | \(-0.812324\pi\) |
0.0659538 | + | 0.997823i | \(0.478991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.3952 | + | 59.5743i | −0.0351330 | + | 0.0608522i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −285.378 | + | 369.820i | −0.290906 | + | 0.376982i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1158.47 | − | 668.841i | −1.17850 | − | 0.680408i | −0.222833 | − | 0.974857i | \(-0.571531\pi\) |
−0.955667 | + | 0.294449i | \(0.904864\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 53.8199 | − | 80.3099i | 0.0545288 | − | 0.0813676i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 290.637i | 0.293870i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −738.550 | −0.745257 | −0.372629 | − | 0.927981i | \(-0.621543\pi\) | ||||
−0.372629 | + | 0.927981i | \(0.621543\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.82974 | + | 146.903i | −0.00989903 | + | 0.147939i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −256.908 | + | 444.977i | −0.257681 | + | 0.446316i | −0.965620 | − | 0.259957i | \(-0.916292\pi\) |
0.707939 | + | 0.706273i | \(0.249625\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 161.514 | − | 794.975i | 0.161676 | − | 0.795771i |
(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.f.101.11 | 24 | ||
3.2 | odd | 2 | 2700.3.p.f.1601.4 | 24 | |||
5.2 | odd | 4 | 180.3.t.a.29.5 | ✓ | 24 | ||
5.3 | odd | 4 | 180.3.t.a.29.8 | yes | 24 | ||
5.4 | even | 2 | inner | 900.3.p.f.101.2 | 24 | ||
9.4 | even | 3 | 2700.3.p.f.2501.4 | 24 | |||
9.5 | odd | 6 | inner | 900.3.p.f.401.11 | 24 | ||
15.2 | even | 4 | 540.3.t.a.89.6 | 24 | |||
15.8 | even | 4 | 540.3.t.a.89.2 | 24 | |||
15.14 | odd | 2 | 2700.3.p.f.1601.9 | 24 | |||
45.2 | even | 12 | 1620.3.b.b.809.5 | 24 | |||
45.4 | even | 6 | 2700.3.p.f.2501.9 | 24 | |||
45.7 | odd | 12 | 1620.3.b.b.809.20 | 24 | |||
45.13 | odd | 12 | 540.3.t.a.449.6 | 24 | |||
45.14 | odd | 6 | inner | 900.3.p.f.401.2 | 24 | ||
45.22 | odd | 12 | 540.3.t.a.449.2 | 24 | |||
45.23 | even | 12 | 180.3.t.a.149.5 | yes | 24 | ||
45.32 | even | 12 | 180.3.t.a.149.8 | yes | 24 | ||
45.38 | even | 12 | 1620.3.b.b.809.19 | 24 | |||
45.43 | odd | 12 | 1620.3.b.b.809.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.t.a.29.5 | ✓ | 24 | 5.2 | odd | 4 | ||
180.3.t.a.29.8 | yes | 24 | 5.3 | odd | 4 | ||
180.3.t.a.149.5 | yes | 24 | 45.23 | even | 12 | ||
180.3.t.a.149.8 | yes | 24 | 45.32 | even | 12 | ||
540.3.t.a.89.2 | 24 | 15.8 | even | 4 | |||
540.3.t.a.89.6 | 24 | 15.2 | even | 4 | |||
540.3.t.a.449.2 | 24 | 45.22 | odd | 12 | |||
540.3.t.a.449.6 | 24 | 45.13 | odd | 12 | |||
900.3.p.f.101.2 | 24 | 5.4 | even | 2 | inner | ||
900.3.p.f.101.11 | 24 | 1.1 | even | 1 | trivial | ||
900.3.p.f.401.2 | 24 | 45.14 | odd | 6 | inner | ||
900.3.p.f.401.11 | 24 | 9.5 | odd | 6 | inner | ||
1620.3.b.b.809.5 | 24 | 45.2 | even | 12 | |||
1620.3.b.b.809.6 | 24 | 45.43 | odd | 12 | |||
1620.3.b.b.809.19 | 24 | 45.38 | even | 12 | |||
1620.3.b.b.809.20 | 24 | 45.7 | odd | 12 | |||
2700.3.p.f.1601.4 | 24 | 3.2 | odd | 2 | |||
2700.3.p.f.1601.9 | 24 | 15.14 | odd | 2 | |||
2700.3.p.f.2501.4 | 24 | 9.4 | even | 3 | |||
2700.3.p.f.2501.9 | 24 | 45.4 | even | 6 |