Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(127,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.d (of order \(2\), degree \(1\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1997017344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 53x^{4} + 56x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(-0.277334i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.127 |
Dual form | 224.3.d.b.127.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 0.554669i | − 0.184890i | −0.995718 | − | 0.0924448i | \(-0.970532\pi\) | ||||
0.995718 | − | 0.0924448i | \(-0.0294682\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.57685 | −0.915371 | −0.457685 | − | 0.889114i | \(-0.651321\pi\) | ||||
−0.457685 | + | 0.889114i | \(0.651321\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.69234 | 0.965816 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.7367i | 1.43061i | 0.698812 | + | 0.715305i | \(0.253712\pi\) | ||||
−0.698812 | + | 0.715305i | \(0.746288\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.57685 | 0.659758 | 0.329879 | − | 0.944023i | \(-0.392992\pi\) | ||||
0.329879 | + | 0.944023i | \(0.392992\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.53864i | 0.169242i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28.3197 | 1.66587 | 0.832933 | − | 0.553374i | \(-0.186660\pi\) | ||||
0.832933 | + | 0.553374i | \(0.186660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.33599i | 0.333473i | 0.986001 | + | 0.166737i | \(0.0533230\pi\) | ||||
−0.986001 | + | 0.166737i | \(0.946677\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.46752 | 0.0698817 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 31.0647i | 1.35064i | 0.737525 | + | 0.675320i | \(0.235995\pi\) | ||||
−0.737525 | + | 0.675320i | \(0.764005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.05242 | −0.162097 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 9.81339i | − 0.363459i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.846294 | −0.0291826 | −0.0145913 | − | 0.999894i | \(-0.504645\pi\) | ||||
−0.0145913 | + | 0.999894i | \(0.504645\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 21.6354i | − 0.697917i | −0.937138 | − | 0.348958i | \(-0.886535\pi\) | ||||
0.937138 | − | 0.348958i | \(-0.113465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.72866 | 0.264505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 12.1092i | − 0.345978i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.6637 | −0.909830 | −0.454915 | − | 0.890535i | \(-0.650330\pi\) | ||||
−0.454915 | + | 0.890535i | \(0.650330\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 4.75731i | − 0.121982i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66.9757 | 1.63355 | 0.816777 | − | 0.576953i | \(-0.195758\pi\) | ||||
0.816777 | + | 0.576953i | \(0.195758\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 44.8781i | 1.04368i | 0.853044 | + | 0.521839i | \(0.174754\pi\) | ||||
−0.853044 | + | 0.521839i | \(0.825246\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −39.7836 | −0.884079 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 38.4528i | 0.818145i | 0.912502 | + | 0.409073i | \(0.134148\pi\) | ||||
−0.912502 | + | 0.409073i | \(0.865852\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 15.7081i | − 0.308001i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.8174 | −0.279574 | −0.139787 | − | 0.990182i | \(-0.544642\pi\) | ||||
−0.139787 | + | 0.990182i | \(0.544642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 72.0246i | − 1.30954i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.51438 | 0.0616557 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.80942i | 0.0984647i | 0.998787 | + | 0.0492323i | \(0.0156775\pi\) | ||||
−0.998787 | + | 0.0492323i | \(0.984323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −52.6015 | −0.862319 | −0.431160 | − | 0.902276i | \(-0.641895\pi\) | ||||
−0.431160 | + | 0.902276i | \(0.641895\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22.9978i | 0.365044i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −39.2550 | −0.603923 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 117.397i | − 1.75219i | −0.482138 | − | 0.876095i | \(-0.660140\pi\) | ||||
0.482138 | − | 0.876095i | \(-0.339860\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.2306 | 0.249719 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 81.2543i | − 1.14443i | −0.820105 | − | 0.572213i | \(-0.806085\pi\) | ||||
0.820105 | − | 0.572213i | \(-0.193915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −47.8054 | −0.654869 | −0.327435 | − | 0.944874i | \(-0.606184\pi\) | ||||
−0.327435 | + | 0.944874i | \(0.606184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.24775i | 0.0299700i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −41.6354 | −0.540720 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 57.4900i | 0.727722i | 0.931453 | + | 0.363861i | \(0.118542\pi\) | ||||
−0.931453 | + | 0.363861i | \(0.881458\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 72.7879 | 0.898616 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 102.855i | − 1.23921i | −0.784913 | − | 0.619606i | \(-0.787292\pi\) | ||||
0.784913 | − | 0.619606i | \(-0.212708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −129.615 | −1.52488 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.469413i | 0.00539555i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −89.2955 | −1.00332 | −0.501660 | − | 0.865065i | \(-0.667277\pi\) | ||||
−0.501660 | + | 0.865065i | \(0.667277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.6922i | 0.249365i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.0005 | −0.129038 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 28.9989i | − 0.305252i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.44452 | −0.0355106 | −0.0177553 | − | 0.999842i | \(-0.505652\pi\) | ||||
−0.0177553 | + | 0.999842i | \(0.505652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 136.789i | 1.38171i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 143.034 | 1.41618 | 0.708089 | − | 0.706123i | \(-0.249557\pi\) | ||||
0.708089 | + | 0.706123i | \(0.249557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 173.424i | − 1.68373i | −0.539688 | − | 0.841865i | \(-0.681458\pi\) | ||||
0.539688 | − | 0.841865i | \(-0.318542\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.71660 | −0.0639676 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 95.5581i | 0.893067i | 0.894767 | + | 0.446533i | \(0.147342\pi\) | ||||
−0.894767 | + | 0.446533i | \(0.852658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 185.517 | 1.70199 | 0.850997 | − | 0.525170i | \(-0.175998\pi\) | ||||
0.850997 | + | 0.525170i | \(0.175998\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.6722i | 0.168218i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −103.409 | −0.915124 | −0.457562 | − | 0.889178i | \(-0.651277\pi\) | ||||
−0.457562 | + | 0.889178i | \(0.651277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 142.179i | − 1.23634i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 74.5529 | 0.637205 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 74.9269i | 0.629638i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −126.644 | −1.04665 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 37.1493i | − 0.302027i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 132.969 | 1.06375 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 147.970i | 1.16512i | 0.812787 | + | 0.582560i | \(0.197949\pi\) | ||||
−0.812787 | + | 0.582560i | \(0.802051\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.8925 | 0.192965 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 259.412i | 1.98025i | 0.140200 | + | 0.990123i | \(0.455225\pi\) | ||||
−0.140200 | + | 0.990123i | \(0.544775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.7635 | −0.126041 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 44.9144i | 0.332700i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.07777 | 0.0224654 | 0.0112327 | − | 0.999937i | \(-0.496424\pi\) | ||||
0.0112327 | + | 0.999937i | \(0.496424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 90.3041i | − 0.649670i | −0.945771 | − | 0.324835i | \(-0.894691\pi\) | ||||
0.945771 | − | 0.324835i | \(-0.105309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.3286 | 0.151266 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 134.971i | 0.943856i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.87336 | 0.0267129 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.88268i | 0.0264128i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 41.3766 | 0.277695 | 0.138848 | − | 0.990314i | \(-0.455660\pi\) | ||||
0.138848 | + | 0.990314i | \(0.455660\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 41.5182i | 0.274955i | 0.990505 | + | 0.137477i | \(0.0438994\pi\) | ||||
−0.990505 | + | 0.137477i | \(0.956101\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 246.165 | 1.60892 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 99.0221i | 0.638853i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −26.9848 | −0.171878 | −0.0859389 | − | 0.996300i | \(-0.527389\pi\) | ||||
−0.0859389 | + | 0.996300i | \(0.527389\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.21875i | 0.0516902i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −82.1895 | −0.510494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 126.684i | − 0.777200i | −0.921407 | − | 0.388600i | \(-0.872959\pi\) | ||||
0.921407 | − | 0.388600i | \(-0.127041\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −39.9498 | −0.242120 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 246.243i | − 1.47451i | −0.675615 | − | 0.737254i | \(-0.736122\pi\) | ||||
0.675615 | − | 0.737254i | \(-0.263878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −95.4376 | −0.564720 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 55.0746i | 0.322074i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 74.5776 | 0.431084 | 0.215542 | − | 0.976495i | \(-0.430848\pi\) | ||||
0.215542 | + | 0.976495i | \(0.430848\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 10.7217i | − 0.0612668i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.22230 | 0.0182051 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 201.073i | − 1.12331i | −0.827371 | − | 0.561656i | \(-0.810165\pi\) | ||||
0.827371 | − | 0.561656i | \(-0.189835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 252.696 | 1.39611 | 0.698054 | − | 0.716045i | \(-0.254050\pi\) | ||||
0.698054 | + | 0.716045i | \(0.254050\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.1764i | 0.159434i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 154.074 | 0.832831 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 445.659i | 2.38320i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.9638 | 0.137375 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 332.333i | 1.73996i | 0.493085 | + | 0.869981i | \(0.335869\pi\) | ||||
−0.493085 | + | 0.869981i | \(0.664131\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −53.2218 | −0.275761 | −0.137880 | − | 0.990449i | \(-0.544029\pi\) | ||||
−0.137880 | + | 0.990449i | \(0.544029\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 21.7735i | 0.111659i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 276.248 | 1.40227 | 0.701137 | − | 0.713026i | \(-0.252676\pi\) | ||||
0.701137 | + | 0.713026i | \(0.252676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 58.5094i | − 0.294017i | −0.989135 | − | 0.147008i | \(-0.953036\pi\) | ||||
0.989135 | − | 0.147008i | \(-0.0469644\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −65.1163 | −0.323962 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.23908i | − 0.0110300i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −306.538 | −1.49531 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 270.025i | 1.30447i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −99.7077 | −0.477070 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 146.237i | − 0.693068i | −0.938037 | − | 0.346534i | \(-0.887359\pi\) | ||||
0.938037 | − | 0.346534i | \(-0.112641\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −45.0692 | −0.211592 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 205.401i | − 0.955351i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 57.2420 | 0.263788 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.5162i | 0.121078i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 242.894 | 1.09907 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 422.290i | − 1.89368i | −0.321709 | − | 0.946839i | \(-0.604257\pi\) | ||||
0.321709 | − | 0.946839i | \(-0.395743\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −35.2250 | −0.156556 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 271.103i | − 1.19429i | −0.802134 | − | 0.597144i | \(-0.796302\pi\) | ||||
0.802134 | − | 0.597144i | \(-0.203698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −400.572 | −1.74922 | −0.874611 | − | 0.484826i | \(-0.838883\pi\) | ||||
−0.874611 | + | 0.484826i | \(0.838883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.0939i | 0.0999734i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −257.611 | −1.10563 | −0.552813 | − | 0.833305i | \(-0.686446\pi\) | ||||
−0.552813 | + | 0.833305i | \(0.686446\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 175.993i | − 0.748906i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.8879 | 0.134548 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 152.650i | − 0.638704i | −0.947636 | − | 0.319352i | \(-0.896535\pi\) | ||||
0.947636 | − | 0.319352i | \(-0.103465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −47.1218 | −0.195526 | −0.0977630 | − | 0.995210i | \(-0.531169\pi\) | ||||
−0.0977630 | + | 0.995210i | \(0.531169\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 128.694i | − 0.529604i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 32.0380 | 0.130767 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 54.3429i | 0.220012i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −57.0502 | −0.229117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 236.051i | 0.940443i | 0.882549 | + | 0.470221i | \(0.155826\pi\) | ||||
−0.882549 | + | 0.470221i | \(0.844174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −488.857 | −1.93224 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 71.8935i | 0.281935i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.5524 | −0.107208 | −0.0536039 | − | 0.998562i | \(-0.517071\pi\) | ||||
−0.0536039 | + | 0.998562i | \(0.517071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 89.0658i | − 0.343883i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.35628 | −0.0281850 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 88.2675i | 0.335618i | 0.985820 | + | 0.167809i | \(0.0536691\pi\) | ||||
−0.985820 | + | 0.167809i | \(0.946331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 67.8170 | 0.255913 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 49.5294i | 0.185503i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.9135 | 0.0814629 | 0.0407314 | − | 0.999170i | \(-0.487031\pi\) | ||||
0.0407314 | + | 0.999170i | \(0.487031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 428.897i | − 1.58265i | −0.611399 | − | 0.791323i | \(-0.709393\pi\) | ||||
0.611399 | − | 0.791323i | \(-0.290607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.5867 | 0.0461050 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 63.7717i | − 0.231897i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −457.076 | −1.65009 | −0.825046 | − | 0.565065i | \(-0.808851\pi\) | ||||
−0.825046 | + | 0.565065i | \(0.808851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 188.063i | − 0.674059i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 95.5032 | 0.339869 | 0.169934 | − | 0.985455i | \(-0.445644\pi\) | ||||
0.169934 | + | 0.985455i | \(0.445644\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 131.804i | − 0.465737i | −0.972508 | − | 0.232869i | \(-0.925189\pi\) | ||||
0.972508 | − | 0.232869i | \(-0.0748112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.0848 | −0.0564379 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 177.201i | 0.617426i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 513.006 | 1.77511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.91057i | 0.00656553i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −325.183 | −1.10984 | −0.554920 | − | 0.831904i | \(-0.687251\pi\) | ||||
−0.554920 | + | 0.831904i | \(0.687251\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 26.5888i | − 0.0901317i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 154.430 | 0.519968 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 266.438i | 0.891096i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −118.736 | −0.394473 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 79.3365i | − 0.261837i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 240.749 | 0.789341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 34.3658i | − 0.111941i | −0.998432 | − | 0.0559704i | \(-0.982175\pi\) | ||||
0.998432 | − | 0.0559704i | \(-0.0178252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −96.1930 | −0.311304 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 195.190i | 0.627620i | 0.949486 | + | 0.313810i | \(0.101606\pi\) | ||||
−0.949486 | + | 0.313810i | \(0.898394\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8987 | 0.0635740 | 0.0317870 | − | 0.999495i | \(-0.489880\pi\) | ||||
0.0317870 | + | 0.999495i | \(0.489880\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 105.257i | − 0.334151i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 168.672 | 0.532088 | 0.266044 | − | 0.963961i | \(-0.414283\pi\) | ||||
0.266044 | + | 0.963961i | \(0.414283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 13.3179i | − 0.0417489i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 53.0031 | 0.165119 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 179.434i | 0.555522i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −34.7570 | −0.106945 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 102.901i | − 0.314681i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −101.737 | −0.309230 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 603.602i | − 1.82357i | −0.410666 | − | 0.911786i | \(-0.634704\pi\) | ||||
0.410666 | − | 0.911786i | \(-0.365296\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −292.616 | −0.878728 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 537.308i | 1.60390i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 189.903 | 0.563511 | 0.281756 | − | 0.959486i | \(-0.409083\pi\) | ||||
0.281756 | + | 0.959486i | \(0.409083\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 57.3578i | 0.169197i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 340.470 | 0.998447 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −78.8621 | −0.228586 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 81.4988i | − 0.234867i | −0.993081 | − | 0.117433i | \(-0.962533\pi\) | ||||
0.993081 | − | 0.117433i | \(-0.0374667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −223.673 | −0.640898 | −0.320449 | − | 0.947266i | \(-0.603834\pi\) | ||||
−0.320449 | + | 0.947266i | \(0.603834\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 84.1680i | − 0.239795i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −613.342 | −1.73751 | −0.868756 | − | 0.495241i | \(-0.835080\pi\) | ||||
−0.868756 | + | 0.495241i | \(0.835080\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 371.889i | 1.04757i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 41.5596 | 0.116414 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 79.0559i | − 0.220212i | −0.993920 | − | 0.110106i | \(-0.964881\pi\) | ||||
0.993920 | − | 0.110106i | \(-0.0351190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 320.855 | 0.888796 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 70.2455i | 0.193514i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 218.798 | 0.599448 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 0.705581i | − 0.00192257i | −1.00000 | 0.000961283i | \(-0.999694\pi\) | |||||
1.00000 | 0.000961283i | \(-0.000305986\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 582.176 | 1.57771 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 39.2031i | − 0.105669i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 250.574 | 0.671781 | 0.335890 | − | 0.941901i | \(-0.390963\pi\) | ||||
0.335890 | + | 0.941901i | \(0.390963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 73.7535i | − 0.196676i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.25854 | −0.0192534 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 532.859i | 1.40596i | 0.711209 | + | 0.702981i | \(0.248148\pi\) | ||||
−0.711209 | + | 0.702981i | \(0.751852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 82.0745 | 0.215419 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 441.226i | − 1.15203i | −0.817441 | − | 0.576013i | \(-0.804608\pi\) | ||||
0.817441 | − | 0.576013i | \(-0.195392\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 190.559 | 0.494959 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 390.096i | 1.00800i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 174.837 | 0.449452 | 0.224726 | − | 0.974422i | \(-0.427851\pi\) | ||||
0.224726 | + | 0.974422i | \(0.427851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 879.744i | 2.24999i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 143.888 | 0.366127 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 263.123i | − 0.666135i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 129.750 | 0.326826 | 0.163413 | − | 0.986558i | \(-0.447750\pi\) | ||||
0.163413 | + | 0.986558i | \(0.447750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.29817i | 0.0233037i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −135.495 | −0.337892 | −0.168946 | − | 0.985625i | \(-0.554036\pi\) | ||||
−0.168946 | + | 0.985625i | \(0.554036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 185.564i | − 0.460456i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −333.140 | −0.822567 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 529.756i | − 1.30161i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 243.575 | 0.595538 | 0.297769 | − | 0.954638i | \(-0.403758\pi\) | ||||
0.297769 | + | 0.954638i | \(0.403758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.70714i | − 0.00415363i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.3703 | −0.0372161 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 470.750i | 1.13434i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −50.0888 | −0.120117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 499.348i | 1.19176i | 0.803073 | + | 0.595881i | \(0.203197\pi\) | ||||
−0.803073 | + | 0.595881i | \(0.796803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 537.031 | 1.27561 | 0.637804 | − | 0.770199i | \(-0.279843\pi\) | ||||
0.637804 | + | 0.770199i | \(0.279843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 334.245i | 0.790178i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −114.763 | −0.270031 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 139.170i | − 0.325926i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 74.8644 | 0.174509 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 559.209i | 1.29747i | 0.761015 | + | 0.648735i | \(0.224702\pi\) | ||||
−0.761015 | + | 0.648735i | \(0.775298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −812.706 | −1.87692 | −0.938459 | − | 0.345389i | \(-0.887747\pi\) | ||||
−0.938459 | + | 0.345389i | \(0.887747\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.14843i | − 0.00493893i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −196.826 | −0.450403 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 346.809i | 0.789998i | 0.918681 | + | 0.394999i | \(0.129255\pi\) | ||||
−0.918681 | + | 0.394999i | \(0.870745\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −60.8464 | −0.137974 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 369.535i | − 0.834166i | −0.908868 | − | 0.417083i | \(-0.863052\pi\) | ||||
0.908868 | − | 0.417083i | \(-0.136948\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 408.692 | 0.918409 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 22.9503i | − 0.0513430i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 315.180 | 0.701961 | 0.350980 | − | 0.936383i | \(-0.385848\pi\) | ||||
0.350980 | + | 0.936383i | \(0.385848\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1053.98i | 2.33698i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.0288 | 0.0508363 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 103.859i | − 0.228261i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 781.559 | 1.71019 | 0.855097 | − | 0.518468i | \(-0.173497\pi\) | ||||
0.855097 | + | 0.518468i | \(0.173497\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 277.912i | − 0.605474i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 526.503 | 1.14209 | 0.571044 | − | 0.820919i | \(-0.306539\pi\) | ||||
0.571044 | + | 0.820919i | \(0.306539\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 754.257i | − 1.62906i | −0.580118 | − | 0.814532i | \(-0.696994\pi\) | ||||
0.580118 | − | 0.814532i | \(-0.303006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 54.9245 | 0.118117 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 480.381i | − 1.02865i | −0.857594 | − | 0.514326i | \(-0.828042\pi\) | ||||
0.857594 | − | 0.514326i | \(-0.171958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 310.603 | 0.662266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.9676i | 0.0317784i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −706.234 | −1.49309 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 25.6761i | − 0.0540549i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −128.798 | −0.270017 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 23.0908i | − 0.0482062i | −0.999709 | − | 0.0241031i | \(-0.992327\pi\) | ||||
0.999709 | − | 0.0241031i | \(-0.00767300\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −288.729 | −0.600267 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 45.5880i | 0.0943850i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.7651 | 0.0325053 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 517.867i | 1.06338i | 0.846939 | + | 0.531691i | \(0.178443\pi\) | ||||
−0.846939 | + | 0.531691i | \(0.821557\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −70.2674 | −0.143696 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 385.683i | − 0.785505i | −0.919644 | − | 0.392753i | \(-0.871523\pi\) | ||||
0.919644 | − | 0.392753i | \(-0.128477\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.9668 | −0.0486142 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 626.063i | − 1.26477i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 214.979 | 0.432552 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 726.518i | − 1.45595i | −0.685605 | − | 0.727974i | \(-0.740462\pi\) | ||||
0.685605 | − | 0.727974i | \(-0.259538\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −136.583 | −0.272621 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 253.383i | − 0.503743i | −0.967761 | − | 0.251872i | \(-0.918954\pi\) | ||||
0.967761 | − | 0.251872i | \(-0.0810461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −654.646 | −1.29633 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 52.9362i | 0.104411i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −338.344 | −0.664723 | −0.332361 | − | 0.943152i | \(-0.607845\pi\) | ||||
−0.332361 | + | 0.943152i | \(0.607845\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 126.481i | − 0.247517i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 62.1776 | 0.121204 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 793.737i | 1.54124i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −605.121 | −1.17045 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 41.3658i | − 0.0797030i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −333.599 | −0.640305 | −0.320152 | − | 0.947366i | \(-0.603734\pi\) | ||||
−0.320152 | + | 0.947366i | \(0.603734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.7942i | 0.0741763i | 0.999312 | + | 0.0370882i | \(0.0118082\pi\) | ||||
−0.999312 | + | 0.0370882i | \(0.988192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.94699 | −0.0113276 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 612.709i | − 1.16264i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −436.017 | −0.824229 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 50.4974i | 0.0950987i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 574.441 | 1.07775 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 437.355i | − 0.817487i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −111.529 | −0.207689 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 110.157i | − 0.204373i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 543.111 | 1.00390 | 0.501951 | − | 0.864896i | \(-0.332616\pi\) | ||||
0.501951 | + | 0.864896i | \(0.332616\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 140.162i | − 0.258126i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −849.086 | −1.55796 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 262.532i | 0.479949i | 0.970779 | + | 0.239974i | \(0.0771391\pi\) | ||||
−0.970779 | + | 0.239974i | \(0.922861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −457.230 | −0.832841 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 5.36212i | − 0.00973161i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −152.104 | −0.275053 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 85.4599i | − 0.153982i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −652.276 | −1.17105 | −0.585526 | − | 0.810654i | \(-0.699112\pi\) | ||||
−0.585526 | + | 0.810654i | \(0.699112\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 384.913i | 0.688574i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 247.193 | 0.440630 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 993.435i | − 1.76454i | −0.470746 | − | 0.882269i | \(-0.656015\pi\) | ||||
0.470746 | − | 0.882269i | \(-0.343985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 473.288 | 0.837678 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 192.579i | 0.339645i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −450.590 | −0.791898 | −0.395949 | − | 0.918272i | \(-0.629584\pi\) | ||||
−0.395949 | + | 0.918272i | \(0.629584\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 373.493i | 0.654103i | 0.945007 | + | 0.327051i | \(0.106055\pi\) | ||||
−0.945007 | + | 0.327051i | \(0.893945\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 184.335 | 0.321701 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 125.887i | − 0.218934i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 370.687 | 0.642439 | 0.321219 | − | 0.947005i | \(-0.395907\pi\) | ||||
0.321219 | + | 0.947005i | \(0.395907\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.5205i | 0.0509853i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 272.128 | 0.468378 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 233.177i | − 0.399961i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −341.218 | −0.583278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 182.976i | 0.311714i | 0.987780 | + | 0.155857i | \(0.0498139\pi\) | ||||
−0.987780 | + | 0.155857i | \(0.950186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 137.082 | 0.232737 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 153.226i | − 0.259266i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 333.716 | 0.562759 | 0.281379 | − | 0.959597i | \(-0.409208\pi\) | ||||
0.281379 | + | 0.959597i | \(0.409208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 342.930i | − 0.576352i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.4533 | −0.0543607 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 219.331i | 0.366163i | 0.983098 | + | 0.183081i | \(0.0586072\pi\) | ||||
−0.983098 | + | 0.183081i | \(0.941393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 268.193 | 0.446245 | 0.223122 | − | 0.974790i | \(-0.428375\pi\) | ||||
0.223122 | + | 0.974790i | \(0.428375\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1020.45i | − 1.69229i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 579.631 | 0.958068 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 585.050i | 0.963839i | 0.876216 | + | 0.481919i | \(0.160060\pi\) | ||||
−0.876216 | + | 0.481919i | \(0.839940\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.24195 | −0.00203933 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 329.804i | 0.539778i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3420 | 0.0478662 | 0.0239331 | − | 0.999714i | \(-0.492381\pi\) | ||||
0.0239331 | + | 0.999714i | \(0.492381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 170.027i | 0.276467i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −413.079 | −0.669497 | −0.334748 | − | 0.942308i | \(-0.608651\pi\) | ||||
−0.334748 | + | 0.942308i | \(0.608651\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 225.596i | − 0.364453i | −0.983257 | − | 0.182226i | \(-0.941670\pi\) | ||||
0.983257 | − | 0.182226i | \(-0.0583304\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 304.850 | 0.490902 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 236.254i | − 0.379219i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −507.267 | −0.811628 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.3047i | 0.0882053i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −953.346 | −1.51565 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 914.619i | 1.44948i | 0.689025 | + | 0.724738i | \(0.258039\pi\) | ||||
−0.689025 | + | 0.724738i | \(0.741961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −81.1132 | −0.128141 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 677.239i | − 1.06652i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −60.0380 | −0.0942511 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 706.290i | − 1.10530i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1025.61 | −1.60002 | −0.800009 | − | 0.599987i | \(-0.795172\pi\) | ||||
−0.800009 | + | 0.599987i | \(0.795172\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 864.377i | 1.34429i | 0.740421 | + | 0.672144i | \(0.234626\pi\) | ||||
−0.740421 | + | 0.672144i | \(0.765374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −113.929 | −0.176634 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 689.240i | 1.06529i | 0.846340 | + | 0.532643i | \(0.178801\pi\) | ||||
−0.846340 | + | 0.532643i | \(0.821199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −91.4211 | −0.140865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 31.7503i | − 0.0487716i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −565.975 | −0.866730 | −0.433365 | − | 0.901218i | \(-0.642674\pi\) | ||||
−0.433365 | + | 0.901218i | \(0.642674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1187.29i | − 1.81266i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −415.541 | −0.632483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 289.064i | − 0.438640i | −0.975653 | − | 0.219320i | \(-0.929616\pi\) | ||||
0.975653 | − | 0.219320i | \(-0.0703838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 283.787 | 0.429329 | 0.214665 | − | 0.976688i | \(-0.431134\pi\) | ||||
0.214665 | + | 0.976688i | \(0.431134\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 134.726i | − 0.203206i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 76.7239 | 0.115374 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 26.2899i | − 0.0394151i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −234.231 | −0.350121 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 827.774i | − 1.23364i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 987.489 | 1.46729 | 0.733647 | − | 0.679531i | \(-0.237817\pi\) | ||||
0.733647 | + | 0.679531i | \(0.237817\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 39.7680i | 0.0589155i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 787.301 | 1.16293 | 0.581463 | − | 0.813573i | \(-0.302481\pi\) | ||||
0.581463 | + | 0.813573i | \(0.302481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 9.11336i | − 0.0134217i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −150.373 | −0.220811 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 193.168i | 0.282823i | 0.989951 | + | 0.141411i | \(0.0451640\pi\) | ||||
−0.989951 | + | 0.141411i | \(0.954836\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0865 | −0.0205642 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 222.185i | 0.323413i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −127.087 | −0.184451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 967.147i | 1.39963i | 0.714322 | + | 0.699817i | \(0.246735\pi\) | ||||
−0.714322 | + | 0.699817i | \(0.753265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −361.909 | −0.522236 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 413.308i | 0.594688i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1896.73 | 2.72128 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 142.889i | 0.204419i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −246.322 | −0.351386 | −0.175693 | − | 0.984445i | \(-0.556217\pi\) | ||||
−0.175693 | + | 0.984445i | \(0.556217\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 213.293i | − 0.303404i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −97.6178 | −0.138465 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 378.432i | 0.535265i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1191.27 | 1.68021 | 0.840103 | − | 0.542428i | \(-0.182495\pi\) | ||||
0.840103 | + | 0.542428i | \(0.182495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 499.723i | 0.702845i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 672.098 | 0.942635 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 617.744i | − 0.863978i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −84.6703 | −0.118090 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 434.163i | 0.603843i | 0.953333 | + | 0.301922i | \(0.0976281\pi\) | ||||
−0.953333 | + | 0.301922i | \(0.902372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 458.838 | 0.636390 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.1370i | 0.0361507i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.42954 | 0.00473040 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 931.815i | 1.28173i | 0.767655 | + | 0.640863i | \(0.221423\pi\) | ||||
−0.767655 | + | 0.640863i | \(0.778577\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 583.709 | 0.800698 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1270.94i | 1.73863i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1426.30 | −1.94584 | −0.972918 | − | 0.231150i | \(-0.925751\pi\) | ||||
−0.972918 | + | 0.231150i | \(0.925751\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 17.7705i | − 0.0241775i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1847.44 | 2.50670 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 216.382i | 0.292804i | 0.989225 | + | 0.146402i | \(0.0467693\pi\) | ||||
−0.989225 | + | 0.146402i | \(0.953231\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.1423 | 0.0406779 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 81.5074i | 0.109700i | 0.998495 | + | 0.0548502i | \(0.0174681\pi\) | ||||
−0.998495 | + | 0.0548502i | \(0.982532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −189.375 | −0.254194 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 894.048i | − 1.19685i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −252.823 | −0.337547 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 142.603i | − 0.189884i | −0.995483 | − | 0.0949422i | \(-0.969733\pi\) | ||||
0.995483 | − | 0.0949422i | \(-0.0302666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 130.930 | 0.173878 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 190.023i | − 0.251686i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −372.503 | −0.492078 | −0.246039 | − | 0.969260i | \(-0.579129\pi\) | ||||
−0.246039 | + | 0.969260i | \(0.579129\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 271.153i | 0.357251i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 663.881 | 0.872380 | 0.436190 | − | 0.899855i | \(-0.356328\pi\) | ||||
0.436190 | + | 0.899855i | \(0.356328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 490.833i | 0.643294i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1126.66 | −1.47276 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 49.8265i | 0.0649628i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 732.653 | 0.952734 | 0.476367 | − | 0.879247i | \(-0.341953\pi\) | ||||
0.476367 | + | 0.879247i | \(0.341953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.2824i | 0.0198216i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −928.973 | −1.20178 | −0.600888 | − | 0.799333i | \(-0.705186\pi\) | ||||
−0.600888 | + | 0.799333i | \(0.705186\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 87.6758i | 0.113130i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −49.4020 | −0.0635804 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 424.358i | 0.544747i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1278.67 | 1.63723 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.30502i | 0.0106067i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 123.506 | 0.157332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 470.202i | 0.597461i | 0.954338 | + | 0.298730i | \(0.0965631\pi\) | ||||
−0.954338 | + | 0.298730i | \(0.903437\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48.9592 | 0.0620522 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 273.595i | − 0.345884i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −451.155 | −0.568922 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 37.6160i | − 0.0473157i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 832.694 | 1.04479 | 0.522393 | − | 0.852705i | \(-0.325040\pi\) | ||||
0.522393 | + | 0.852705i | \(0.325040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1088.97i | 1.36292i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −776.187 | −0.969022 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 752.300i | − 0.936862i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 376.169 | 0.467291 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 12.1547i | − 0.0150616i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 976.293 | 1.20679 | 0.603395 | − | 0.797442i | \(-0.293814\pi\) | ||||
0.603395 | + | 0.797442i | \(0.293814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 564.470i | − 0.696018i | −0.937491 | − | 0.348009i | \(-0.886858\pi\) | ||||
0.937491 | − | 0.348009i | \(-0.113142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −237.896 | −0.292615 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 579.812i | 0.711426i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −284.347 | −0.348038 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 197.249i | 0.240841i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 779.033 | 0.948883 | 0.474441 | − | 0.880287i | \(-0.342650\pi\) | ||||
0.474441 | + | 0.880287i | \(0.342650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 363.394i | − 0.441548i | −0.975325 | − | 0.220774i | \(-0.929142\pi\) | ||||
0.975325 | − | 0.220774i | \(-0.0708582\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35.3722 | −0.0428754 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 620.477i | 0.750275i | 0.926969 | + | 0.375137i | \(0.122404\pi\) | ||||
−0.926969 | + | 0.375137i | \(0.877596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 737.842 | 0.890038 | 0.445019 | − | 0.895521i | \(-0.353197\pi\) | ||||
0.445019 | + | 0.895521i | \(0.353197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 253.525i | 0.305085i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −198.238 | −0.237981 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1127.02i | 1.34972i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −212.317 | −0.253664 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 897.093i | − 1.06924i | −0.845092 | − | 0.534620i | \(-0.820455\pi\) | ||||
0.845092 | − | 0.534620i | \(-0.179545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −840.284 | −0.999148 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 52.9726i | − 0.0628382i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 436.804 | 0.516928 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 335.069i | − 0.395595i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −73.1074 | −0.0861100 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1045.75i | − 1.22885i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1470.98 | −1.72448 | −0.862239 | − | 0.506501i | \(-0.830939\pi\) | ||||
−0.862239 | + | 0.506501i | \(0.830939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 252.068i | − 0.294817i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 851.862 | 0.994005 | 0.497002 | − | 0.867749i | \(-0.334434\pi\) | ||||
0.497002 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 140.400i | − 0.163446i | −0.996655 | − | 0.0817229i | \(-0.973958\pi\) | ||||
0.996655 | − | 0.0817229i | \(-0.0260422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 98.2879 | 0.114156 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 32.1489i | − 0.0372525i | −0.999827 | − | 0.0186263i | \(-0.994071\pi\) | ||||
0.999827 | − | 0.0186263i | \(-0.00592927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −341.330 | −0.394602 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 284.549i | − 0.328199i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −904.704 | −1.04109 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1006.89i | − 1.15602i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.9410 | −0.0342967 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 351.802i | 0.402059i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1039.93 | −1.18578 | −0.592888 | − | 0.805285i | \(-0.702012\pi\) | ||||
−0.592888 | + | 0.805285i | \(0.702012\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 180.369i | 0.205198i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −416.344 | −0.472581 | −0.236291 | − | 0.971682i | \(-0.575932\pi\) | ||||
−0.236291 | + | 0.971682i | \(0.575932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 231.281i | − 0.261926i | −0.991387 | − | 0.130963i | \(-0.958193\pi\) | ||||
0.991387 | − | 0.130963i | \(-0.0418069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.7480 | −0.0166644 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 6.35223i | − 0.00716148i | −0.999994 | − | 0.00358074i | \(-0.998860\pi\) | ||||
0.999994 | − | 0.00358074i | \(-0.00113979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −391.493 | −0.440374 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1145.44i | 1.28557i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −243.637 | −0.272830 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 920.280i | 1.02825i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 147.785 | 0.164754 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.3099i | 0.0203670i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −419.624 | −0.465732 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 65.8593i | 0.0729339i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1156.55 | −1.27796 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 201.716i | − 0.222399i | −0.993798 | − | 0.111200i | \(-0.964531\pi\) | ||||
0.993798 | − | 0.111200i | \(-0.0354693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1243.30 | 1.36777 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 484.675i | 0.532025i | 0.963970 | + | 0.266013i | \(0.0857063\pi\) | ||||
−0.963970 | + | 0.266013i | \(0.914294\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1618.59 | 1.77283 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 133.536i | − 0.145941i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −686.340 | −0.748463 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 650.067i | − 0.707363i | −0.935366 | − | 0.353681i | \(-0.884930\pi\) | ||||
0.935366 | − | 0.353681i | \(-0.115070\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.0616 | −0.0206967 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 696.906i | − 0.755044i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 136.419 | 0.147480 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1507.46i | − 1.62617i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 522.394 | 0.562318 | 0.281159 | − | 0.959661i | \(-0.409281\pi\) | ||||
0.281159 | + | 0.959661i | \(0.409281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 44.3520i | − 0.0476391i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 108.266 | 0.116040 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2039.72i | − 2.18151i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1579.17 | 1.68535 | 0.842676 | − | 0.538422i | \(-0.180979\pi\) | ||||
0.842676 | + | 0.538422i | \(0.180979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 11.0372i | − 0.0117542i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1080.68 | −1.14844 | −0.574218 | − | 0.818703i | \(-0.694694\pi\) | ||||
−0.574218 | + | 0.818703i | \(0.694694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2080.58i | 2.20634i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −118.832 | −0.125749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 538.713i | − 0.568863i | −0.958696 | − | 0.284431i | \(-0.908195\pi\) | ||||
0.958696 | − | 0.284431i | \(-0.0918048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −410.020 | −0.432055 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 93.5570i | − 0.0983775i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1099.01 | −1.15322 | −0.576608 | − | 0.817021i | \(-0.695624\pi\) | ||||
−0.576608 | + | 0.817021i | \(0.695624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1521.04i | − 1.59271i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.38702 | −0.00771893 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.14300i | 0.00849114i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 492.908 | 0.512912 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 830.624i | 0.862538i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 243.588 | 0.252423 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 847.122i | 0.876031i | 0.898967 | + | 0.438016i | \(0.144319\pi\) | ||||
−0.898967 | + | 0.438016i | \(0.855681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 99.5262 | 0.102710 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1059.01i | − 1.09064i | −0.838227 | − | 0.545322i | \(-0.816408\pi\) | ||||
0.838227 | − | 0.545322i | \(-0.183592\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 238.922 | 0.245552 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.2786i | 0.0197729i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1223.46 | −1.25226 | −0.626131 | − | 0.779718i | \(-0.715362\pi\) | ||||
−0.626131 | + | 0.779718i | \(0.715362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1405.22i | − 1.43536i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1612.58 | 1.64381 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 256.802i | 0.261244i | 0.991432 | + | 0.130622i | \(0.0416974\pi\) | ||||
−0.991432 | + | 0.130622i | \(0.958303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1264.35 | −1.28360 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 56.4301i | 0.0571734i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1394.13 | −1.40963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 988.781i | − 0.997761i | −0.866671 | − | 0.498881i | \(-0.833745\pi\) | ||||
0.866671 | − | 0.498881i | \(-0.166255\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −334.799 | −0.337159 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 267.789i | 0.269134i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −581.918 | −0.583669 | −0.291835 | − | 0.956469i | \(-0.594266\pi\) | ||||
−0.291835 | + | 0.956469i | \(0.594266\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 330.355i | 0.330686i |
(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 | 224.3.d.b.127.4 | ✓ | 8 | |
3.2 | odd | 2 | 2016.3.m.c.127.6 | 8 | |||
4.3 | odd | 2 | inner | 224.3.d.b.127.5 | yes | 8 | |
7.6 | odd | 2 | 1568.3.d.n.1471.5 | 8 | |||
8.3 | odd | 2 | 448.3.d.e.127.4 | 8 | |||
8.5 | even | 2 | 448.3.d.e.127.5 | 8 | |||
12.11 | even | 2 | 2016.3.m.c.127.5 | 8 | |||
16.3 | odd | 4 | 1792.3.g.f.127.4 | 8 | |||
16.5 | even | 4 | 1792.3.g.f.127.3 | 8 | |||
16.11 | odd | 4 | 1792.3.g.d.127.5 | 8 | |||
16.13 | even | 4 | 1792.3.g.d.127.6 | 8 | |||
28.27 | even | 2 | 1568.3.d.n.1471.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.d.b.127.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
224.3.d.b.127.5 | yes | 8 | 4.3 | odd | 2 | inner | |
448.3.d.e.127.4 | 8 | 8.3 | odd | 2 | |||
448.3.d.e.127.5 | 8 | 8.5 | even | 2 | |||
1568.3.d.n.1471.4 | 8 | 28.27 | even | 2 | |||
1568.3.d.n.1471.5 | 8 | 7.6 | odd | 2 | |||
1792.3.g.d.127.5 | 8 | 16.11 | odd | 4 | |||
1792.3.g.d.127.6 | 8 | 16.13 | even | 4 | |||
1792.3.g.f.127.3 | 8 | 16.5 | even | 4 | |||
1792.3.g.f.127.4 | 8 | 16.3 | odd | 4 | |||
2016.3.m.c.127.5 | 8 | 12.11 | even | 2 | |||
2016.3.m.c.127.6 | 8 | 3.2 | odd | 2 |