Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(751,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("1200.751");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.e (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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 751.4 | ||
Root | \(-0.309017 + 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.751 |
Dual form | 1200.3.e.n.751.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.28187i | 0.611695i | 0.952081 | + | 0.305848i | \(0.0989398\pi\) | ||||
−0.952081 | + | 0.305848i | \(0.901060\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 11.2101i | − 1.01910i | −0.860442 | − | 0.509549i | \(-0.829812\pi\) | ||||
0.860442 | − | 0.509549i | \(-0.170188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.41641 | −0.416647 | −0.208323 | − | 0.978060i | \(-0.566801\pi\) | ||||
−0.208323 | + | 0.978060i | \(0.566801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41641 | 0.0833181 | 0.0416591 | − | 0.999132i | \(-0.486736\pi\) | ||||
0.0416591 | + | 0.999132i | \(0.486736\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 8.56373i | − 0.450723i | −0.974275 | − | 0.225361i | \(-0.927644\pi\) | ||||
0.974275 | − | 0.225361i | \(-0.0723563\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.41641 | −0.353162 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.0557i | 1.04590i | 0.852364 | + | 0.522949i | \(0.175168\pi\) | ||||
−0.852364 | + | 0.522949i | \(0.824832\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.4164 | −0.876428 | −0.438214 | − | 0.898871i | \(-0.644389\pi\) | ||||
−0.438214 | + | 0.898871i | \(0.644389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 50.1329i | − 1.61719i | −0.588364 | − | 0.808596i | \(-0.700228\pi\) | ||||
0.588364 | − | 0.808596i | \(-0.299772\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 19.4164 | 0.588376 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −60.2492 | −1.62836 | −0.814179 | − | 0.580614i | \(-0.802812\pi\) | ||||
−0.814179 | + | 0.580614i | \(0.802812\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 9.38149i | − 0.240551i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −30.0000 | −0.731707 | −0.365854 | − | 0.930672i | \(-0.619223\pi\) | ||||
−0.365854 | + | 0.930672i | \(0.619223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 37.9121i | − 0.881676i | −0.897587 | − | 0.440838i | \(-0.854681\pi\) | ||||
0.897587 | − | 0.440838i | \(-0.145319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 39.9337i | − 0.849653i | −0.905275 | − | 0.424827i | \(-0.860335\pi\) | ||||
0.905275 | − | 0.424827i | \(-0.139665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 30.6656 | 0.625829 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.45329i | 0.0481037i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16.2492 | 0.306589 | 0.153295 | − | 0.988181i | \(-0.451012\pi\) | ||||
0.153295 | + | 0.988181i | \(0.451012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.8328 | 0.260225 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 81.7415i | 1.38545i | 0.721202 | + | 0.692725i | \(0.243590\pi\) | ||||
−0.721202 | + | 0.692725i | \(0.756410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 94.4984 | 1.54915 | 0.774577 | − | 0.632479i | \(-0.217963\pi\) | ||||
0.774577 | + | 0.632479i | \(0.217963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 12.8456i | − 0.203898i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 129.614i | − 1.93454i | −0.253748 | − | 0.967270i | \(-0.581663\pi\) | ||||
0.253748 | − | 0.967270i | \(-0.418337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −41.6656 | −0.603850 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 102.288i | − 1.44067i | −0.693627 | − | 0.720335i | \(-0.743988\pi\) | ||||
0.693627 | − | 0.720335i | \(-0.256012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −24.8328 | −0.340176 | −0.170088 | − | 0.985429i | \(-0.554405\pi\) | ||||
−0.170088 | + | 0.985429i | \(0.554405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 48.0000 | 0.623377 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 91.7022i | 1.16079i | 0.814336 | + | 0.580393i | \(0.197101\pi\) | ||||
−0.814336 | + | 0.580393i | \(0.802899\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 88.0450i | − 1.06078i | −0.847753 | − | 0.530392i | \(-0.822045\pi\) | ||||
0.847753 | − | 0.530392i | \(-0.177955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 44.0225i | − 0.506006i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −20.8328 | −0.234077 | −0.117038 | − | 0.993127i | \(-0.537340\pi\) | ||||
−0.117038 | + | 0.993127i | \(0.537340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 23.1923i | − 0.254861i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 86.8328 | 0.933686 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0000 | 0.144330 | 0.0721649 | − | 0.997393i | \(-0.477009\pi\) | ||||
0.0721649 | + | 0.997393i | \(0.477009\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33.6302i | 0.339699i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −132.748 | −1.31433 | −0.657167 | − | 0.753745i | \(-0.728245\pi\) | ||||
−0.657167 | + | 0.753745i | \(0.728245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 62.9785i | 0.611442i | 0.952121 | + | 0.305721i | \(0.0988975\pi\) | ||||
−0.952121 | + | 0.305721i | \(0.901102\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 174.455i | − 1.63042i | −0.579168 | − | 0.815208i | \(-0.696623\pi\) | ||||
0.579168 | − | 0.815208i | \(-0.303377\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96.8328 | 0.888374 | 0.444187 | − | 0.895934i | \(-0.353493\pi\) | ||||
0.444187 | + | 0.895934i | \(0.353493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 104.355i | − 0.940133i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −211.082 | −1.86798 | −0.933991 | − | 0.357296i | \(-0.883699\pi\) | ||||
−0.933991 | + | 0.357296i | \(0.883699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.2492 | 0.138882 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.06487i | 0.0509653i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.66563 | −0.0385589 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 51.9615i | − 0.422451i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 44.6017i | − 0.351194i | −0.984462 | − | 0.175597i | \(-0.943814\pi\) | ||||
0.984462 | − | 0.175597i | \(-0.0561856\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 65.6656 | 0.509036 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 161.609i | − 1.23366i | −0.787098 | − | 0.616828i | \(-0.788417\pi\) | ||||
0.787098 | − | 0.616828i | \(-0.211583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 36.6687 | 0.275705 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 106.584 | 0.777982 | 0.388991 | − | 0.921241i | \(-0.372824\pi\) | ||||
0.388991 | + | 0.921241i | \(0.372824\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 24.4418i | − 0.175840i | −0.996128 | − | 0.0879200i | \(-0.971978\pi\) | ||||
0.996128 | − | 0.0879200i | \(-0.0280220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 69.1672 | 0.490547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 60.7183i | 0.424604i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 53.1144i | 0.361323i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 91.0820 | 0.611289 | 0.305644 | − | 0.952146i | \(-0.401128\pi\) | ||||
0.305644 | + | 0.952146i | \(0.401128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 251.914i | − 1.66831i | −0.551533 | − | 0.834153i | \(-0.685957\pi\) | ||||
0.551533 | − | 0.834153i | \(-0.314043\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24922 | −0.0277727 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.4164 | −0.136410 | −0.0682051 | − | 0.997671i | \(-0.521727\pi\) | ||||
−0.0682051 | + | 0.997671i | \(0.521727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.1445i | 0.177009i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −103.003 | −0.639771 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.7197i | 0.0903052i | 0.998980 | + | 0.0451526i | \(0.0143774\pi\) | ||||
−0.998980 | + | 0.0451526i | \(0.985623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 78.7091i | 0.471312i | 0.971837 | + | 0.235656i | \(0.0757239\pi\) | ||||
−0.971837 | + | 0.235656i | \(0.924276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −139.663 | −0.826405 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 25.6912i | 0.150241i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −146.085 | −0.844423 | −0.422211 | − | 0.906497i | \(-0.638746\pi\) | ||||
−0.422211 | + | 0.906497i | \(0.638746\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −141.580 | −0.799890 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 238.682i | − 1.33342i | −0.745316 | − | 0.666711i | \(-0.767702\pi\) | ||||
0.745316 | − | 0.666711i | \(-0.232298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 115.167 | 0.636283 | 0.318141 | − | 0.948043i | \(-0.396941\pi\) | ||||
0.318141 | + | 0.948043i | \(0.396941\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 163.676i | 0.894405i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.8780i | − 0.0849092i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.2492 | 0.117721 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 6.06487i | − 0.0317532i | −0.999874 | − | 0.0158766i | \(-0.994946\pi\) | ||||
0.999874 | − | 0.0158766i | \(-0.00505390\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 358.827 | 1.85921 | 0.929603 | − | 0.368563i | \(-0.120150\pi\) | ||||
0.929603 | + | 0.368563i | \(0.120150\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 141.915 | 0.720380 | 0.360190 | − | 0.932879i | \(-0.382712\pi\) | ||||
0.360190 | + | 0.932879i | \(0.382712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 124.708i | 0.626672i | 0.949642 | + | 0.313336i | \(0.101447\pi\) | ||||
−0.949642 | + | 0.313336i | \(0.898553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 224.498 | 1.11691 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 108.830i | − 0.536107i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 72.1670i | − 0.348633i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −96.0000 | −0.459330 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 102.765i | − 0.487037i | −0.969896 | − | 0.243518i | \(-0.921698\pi\) | ||||
0.969896 | − | 0.243518i | \(-0.0783016\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 177.167 | 0.831771 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 214.663 | 0.989228 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 43.0117i | − 0.196400i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.67184 | −0.0347142 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 39.7862i | − 0.178414i | −0.996013 | − | 0.0892068i | \(-0.971567\pi\) | ||||
0.996013 | − | 0.0892068i | \(-0.0284332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.2425i | 0.0627423i | 0.999508 | + | 0.0313711i | \(0.00998739\pi\) | ||||
−0.999508 | + | 0.0313711i | \(0.990013\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −45.0031 | −0.196520 | −0.0982601 | − | 0.995161i | \(-0.531328\pi\) | ||||
−0.0982601 | + | 0.995161i | \(0.531328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 83.1384i | 0.359907i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −393.915 | −1.69062 | −0.845311 | − | 0.534275i | \(-0.820585\pi\) | ||||
−0.845311 | + | 0.534275i | \(0.820585\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −158.833 | −0.670181 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 329.760i | 1.37975i | 0.723929 | + | 0.689874i | \(0.242334\pi\) | ||||
−0.723929 | + | 0.689874i | \(0.757666\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −210.328 | −0.872731 | −0.436365 | − | 0.899770i | \(-0.643735\pi\) | ||||
−0.436365 | + | 0.899770i | \(0.643735\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 46.3847i | 0.187792i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 152.498 | 0.612444 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 254.083i | 1.01228i | 0.862450 | + | 0.506142i | \(0.168929\pi\) | ||||
−0.862450 | + | 0.506142i | \(0.831071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 269.666 | 1.06587 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −407.410 | −1.58525 | −0.792627 | − | 0.609707i | \(-0.791287\pi\) | ||||
−0.792627 | + | 0.609707i | \(0.791287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 257.979i | − 0.996058i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 76.2492 | 0.292143 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 138.950i | 0.528328i | 0.964478 | + | 0.264164i | \(0.0850960\pi\) | ||||
−0.964478 | + | 0.264164i | \(0.914904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 36.0835i | − 0.135144i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −55.0820 | −0.204766 | −0.102383 | − | 0.994745i | \(-0.532647\pi\) | ||||
−0.102383 | + | 0.994745i | \(0.532647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 406.061i | 1.49838i | 0.662354 | + | 0.749191i | \(0.269557\pi\) | ||||
−0.662354 | + | 0.749191i | \(0.730443\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 40.1703 | 0.147144 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −350.584 | −1.26564 | −0.632822 | − | 0.774297i | \(-0.718104\pi\) | ||||
−0.632822 | + | 0.774297i | \(0.718104\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 150.399i | 0.539064i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −457.161 | −1.62691 | −0.813454 | − | 0.581630i | \(-0.802415\pi\) | ||||
−0.813454 | + | 0.581630i | \(0.802415\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 339.959i | − 1.20127i | −0.799524 | − | 0.600635i | \(-0.794915\pi\) | ||||
0.799524 | − | 0.600635i | \(-0.205085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 128.456i | − 0.447582i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −286.994 | −0.993058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.2487i | 0.0833289i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −575.410 | −1.96386 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −58.2492 | −0.196125 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 130.295i | − 0.435770i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 162.334 | 0.539317 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 229.926i | − 0.758831i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 358.336i | 1.16722i | 0.812035 | + | 0.583609i | \(0.198360\pi\) | ||||
−0.812035 | + | 0.583609i | \(0.801640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −109.082 | −0.353016 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 364.787i | 1.17295i | 0.809968 | + | 0.586474i | \(0.199485\pi\) | ||||
−0.809968 | + | 0.586474i | \(0.800515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 265.502 | 0.848248 | 0.424124 | − | 0.905604i | \(-0.360582\pi\) | ||||
0.424124 | + | 0.905604i | \(0.360582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 459.580 | 1.44978 | 0.724890 | − | 0.688864i | \(-0.241890\pi\) | ||||
0.724890 | + | 0.688864i | \(0.241890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 284.920i | 0.893165i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 302.164 | 0.941321 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 12.1297i | − 0.0375534i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 167.719i | 0.512903i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 170.991 | 0.519729 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 583.219i | 1.76199i | 0.473126 | + | 0.880995i | \(0.343125\pi\) | ||||
−0.473126 | + | 0.880995i | \(0.656875\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 180.748 | 0.542786 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 123.495 | 0.366455 | 0.183228 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183228 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 365.605i | − 1.07848i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −561.994 | −1.64808 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 341.117i | 0.994512i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 487.859i | 1.40593i | 0.711222 | + | 0.702967i | \(0.248142\pi\) | ||||
−0.711222 | + | 0.702967i | \(0.751858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.8328 | −0.0367702 | −0.0183851 | − | 0.999831i | \(-0.505852\pi\) | ||||
−0.0183851 | + | 0.999831i | \(0.505852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.1445i | 0.0801837i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.74457 | 0.0162736 | 0.00813678 | − | 0.999967i | \(-0.497410\pi\) | ||||
0.00813678 | + | 0.999967i | \(0.497410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.5047 | −0.0294248 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 44.8403i | 0.124903i | 0.998048 | + | 0.0624516i | \(0.0198919\pi\) | ||||
−0.998048 | + | 0.0624516i | \(0.980108\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 287.663 | 0.796849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8.08111i | − 0.0222620i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 83.8543i | − 0.228486i | −0.993453 | − | 0.114243i | \(-0.963556\pi\) | ||||
0.993453 | − | 0.114243i | \(-0.0364442\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 90.0000 | 0.243902 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 69.5770i | 0.187539i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −110.413 | −0.296014 | −0.148007 | − | 0.988986i | \(-0.547286\pi\) | ||||
−0.148007 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 137.666 | 0.365161 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 662.791i | − 1.74879i | −0.485216 | − | 0.874394i | \(-0.661259\pi\) | ||||
0.485216 | − | 0.874394i | \(-0.338741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 77.2523 | 0.202762 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 84.7740i | 0.221342i | 0.993857 | + | 0.110671i | \(0.0353000\pi\) | ||||
−0.993857 | + | 0.110671i | \(0.964700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 113.736i | 0.293892i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −379.240 | −0.974910 | −0.487455 | − | 0.873148i | \(-0.662075\pi\) | ||||
−0.487455 | + | 0.873148i | \(0.662075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.0726i | 0.0871423i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 279.915 | 0.712252 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −94.2430 | −0.237388 | −0.118694 | − | 0.992931i | \(-0.537871\pi\) | ||||
−0.118694 | + | 0.992931i | \(0.537871\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 63.5121i | 0.159178i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 246.158 | 0.613860 | 0.306930 | − | 0.951732i | \(-0.400698\pi\) | ||||
0.306930 | + | 0.951732i | \(0.400698\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 271.541i | 0.673798i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 675.398i | 1.65945i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 584.663 | 1.42949 | 0.714746 | − | 0.699384i | \(-0.246542\pi\) | ||||
0.714746 | + | 0.699384i | \(0.246542\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 184.608i | 0.449168i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −350.006 | −0.847473 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 42.3344 | 0.101521 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 645.039i | − 1.53947i | −0.638362 | − | 0.769736i | \(-0.720388\pi\) | ||||
0.638362 | − | 0.769736i | \(-0.279612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 468.991 | 1.11399 | 0.556996 | − | 0.830515i | \(-0.311954\pi\) | ||||
0.556996 | + | 0.830515i | \(0.311954\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 119.801i | 0.283218i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 404.630i | 0.947610i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −105.167 | −0.245145 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 150.876i | − 0.350061i | −0.984563 | − | 0.175030i | \(-0.943998\pi\) | ||||
0.984563 | − | 0.175030i | \(-0.0560023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5016 | 0.0588950 | 0.0294475 | − | 0.999566i | \(-0.490625\pi\) | ||||
0.0294475 | + | 0.999566i | \(0.490625\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 206.006 | 0.471410 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 44.0681i | − 0.100383i | −0.998740 | − | 0.0501914i | \(-0.984017\pi\) | ||||
0.998740 | − | 0.0501914i | \(-0.0159831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −91.9969 | −0.208610 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 95.0644i | 0.214592i | 0.994227 | + | 0.107296i | \(0.0342193\pi\) | ||||
−0.994227 | + | 0.107296i | \(0.965781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 157.759i | 0.352928i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −194.498 | −0.433181 | −0.216591 | − | 0.976263i | \(-0.569494\pi\) | ||||
−0.216591 | + | 0.976263i | \(0.569494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 336.302i | 0.745681i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 436.328 | 0.963197 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −289.659 | −0.633828 | −0.316914 | − | 0.948454i | \(-0.602647\pi\) | ||||
−0.316914 | + | 0.948454i | \(0.602647\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 7.35987i | − 0.0160346i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −640.249 | −1.38883 | −0.694413 | − | 0.719576i | \(-0.744336\pi\) | ||||
−0.694413 | + | 0.719576i | \(0.744336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 514.175i | 1.11053i | 0.831674 | + | 0.555265i | \(0.187383\pi\) | ||||
−0.831674 | + | 0.555265i | \(0.812617\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 69.3732i | 0.148551i | 0.997238 | + | 0.0742754i | \(0.0236644\pi\) | ||||
−0.997238 | + | 0.0742754i | \(0.976336\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 554.991 | 1.18335 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 37.0943i | − 0.0787565i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −424.997 | −0.898514 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −48.7477 | −0.102196 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 502.579i | 1.04923i | 0.851341 | + | 0.524613i | \(0.175790\pi\) | ||||
−0.851341 | + | 0.524613i | \(0.824210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 326.334 | 0.678450 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 178.407i | − 0.369372i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 580.368i | 1.19172i | 0.803088 | + | 0.595861i | \(0.203189\pi\) | ||||
−0.803088 | + | 0.595861i | \(0.796811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.4953 | −0.0521377 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 619.348i | 1.26140i | 0.776027 | + | 0.630700i | \(0.217232\pi\) | ||||
−0.776027 | + | 0.630700i | \(0.782768\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.0000 | −0.0730223 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 437.981 | 0.881250 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 86.7044i | − 0.173756i | −0.996219 | − | 0.0868782i | \(-0.972311\pi\) | ||||
0.996219 | − | 0.0868782i | \(-0.0276891\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −136.328 | −0.272112 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 442.542i | 0.879805i | 0.898046 | + | 0.439902i | \(0.144987\pi\) | ||||
−0.898046 | + | 0.439902i | \(0.855013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 241.903i | − 0.477125i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 861.246 | 1.69204 | 0.846018 | − | 0.533155i | \(-0.178994\pi\) | ||||
0.846018 | + | 0.533155i | \(0.178994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 106.331i | − 0.208084i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −44.4984 | −0.0867416 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −447.659 | −0.865879 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 253.027i | − 0.487528i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −331.495 | −0.636267 | −0.318134 | − | 0.948046i | \(-0.603056\pi\) | ||||
−0.318134 | + | 0.948046i | \(0.603056\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 892.671i | − 1.70683i | −0.521234 | − | 0.853414i | \(-0.674528\pi\) | ||||
0.521234 | − | 0.853414i | \(-0.325472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 71.0087i | − 0.134741i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.6749 | −0.0939035 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 245.225i | − 0.461817i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 162.492 | 0.304863 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 413.410 | 0.769851 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 343.764i | − 0.637781i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −243.495 | −0.450084 | −0.225042 | − | 0.974349i | \(-0.572252\pi\) | ||||
−0.225042 | + | 0.974349i | \(0.572252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 199.475i | 0.367358i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 130.864i | − 0.239239i | −0.992820 | − | 0.119619i | \(-0.961833\pi\) | ||||
0.992820 | − | 0.119619i | \(-0.0381674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −283.495 | −0.516385 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 217.659i | 0.395026i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −392.656 | −0.710048 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 717.915 | 1.28890 | 0.644448 | − | 0.764648i | \(-0.277087\pi\) | ||||
0.644448 | + | 0.764648i | \(0.277087\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 205.347i | 0.367347i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.5016 | 0.0490224 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 777.482i | − 1.38096i | −0.723351 | − | 0.690481i | \(-0.757399\pi\) | ||||
0.723351 | − | 0.690481i | \(-0.242601\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 38.5368i | 0.0679661i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −964.152 | −1.69447 | −0.847233 | − | 0.531221i | \(-0.821733\pi\) | ||||
−0.847233 | + | 0.531221i | \(0.821733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.1352i | 0.0790459i | 0.999219 | + | 0.0395230i | \(0.0125838\pi\) | ||||
−0.999219 | + | 0.0395230i | \(0.987416\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5047 | 0.0183327 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 286.000 | 0.495667 | 0.247834 | − | 0.968803i | \(-0.420281\pi\) | ||||
0.247834 | + | 0.968803i | \(0.420281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 621.506i | 1.07341i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 376.997 | 0.648876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 182.155i | − 0.312444i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 719.080i | − 1.22501i | −0.790467 | − | 0.612504i | \(-0.790162\pi\) | ||||
0.790467 | − | 0.612504i | \(-0.209838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −429.325 | −0.728905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 245.804i | 0.415912i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 360.590 | 0.608077 | 0.304039 | − | 0.952660i | \(-0.401665\pi\) | ||||
0.304039 | + | 0.952660i | \(0.401665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −216.000 | −0.361809 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 58.8790i | − 0.0982954i | −0.998792 | − | 0.0491477i | \(-0.984349\pi\) | ||||
0.998792 | − | 0.0491477i | \(-0.0156505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 570.997 | 0.950078 | 0.475039 | − | 0.879965i | \(-0.342434\pi\) | ||||
0.475039 | + | 0.879965i | \(0.342434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 388.843i | 0.644847i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 667.073i | − 1.09897i | −0.835505 | − | 0.549483i | \(-0.814825\pi\) | ||||
0.835505 | − | 0.549483i | \(-0.185175\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 188.498 | 0.309521 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 216.297i | 0.354005i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −293.246 | −0.478379 | −0.239189 | − | 0.970973i | \(-0.576882\pi\) | ||||
−0.239189 | + | 0.970973i | \(0.576882\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −900.906 | −1.46014 | −0.730069 | − | 0.683373i | \(-0.760512\pi\) | ||||
−0.730069 | + | 0.683373i | \(0.760512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 604.277i | 0.976214i | 0.872784 | + | 0.488107i | \(0.162312\pi\) | ||||
−0.872784 | + | 0.488107i | \(0.837688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 124.997 | 0.201283 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 89.2033i | − 0.143183i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 166.277i | − 0.265194i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −85.3375 | −0.135672 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 162.529i | − 0.257573i | −0.991672 | − | 0.128787i | \(-0.958892\pi\) | ||||
0.991672 | − | 0.128787i | \(-0.0411082\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 177.994 | 0.281191 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −166.098 | −0.260750 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 306.863i | 0.480223i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −507.325 | −0.791459 | −0.395729 | − | 0.918367i | \(-0.629508\pi\) | ||||
−0.395729 | + | 0.918367i | \(0.629508\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 357.087i | − 0.555345i | −0.960676 | − | 0.277672i | \(-0.910437\pi\) | ||||
0.960676 | − | 0.277672i | \(-0.0895630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 130.569i | − 0.201806i | −0.994896 | − | 0.100903i | \(-0.967827\pi\) | ||||
0.994896 | − | 0.100903i | \(-0.0321732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 916.328 | 1.41191 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 371.806i | 0.571131i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1052.74 | −1.61215 | −0.806076 | − | 0.591812i | \(-0.798413\pi\) | ||||
−0.806076 | + | 0.591812i | \(0.798413\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 74.4984 | 0.113392 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.442426i | 0 0.000671360i | 1.00000 | 0.000335680i | \(0.000106850\pi\) | |||||
−1.00000 | 0.000335680i | \(0.999893\pi\) | ||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −255.508 | −0.386547 | −0.193274 | − | 0.981145i | \(-0.561911\pi\) | ||||
−0.193274 | + | 0.981145i | \(0.561911\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 13.2880i | − 0.0200423i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 611.409i | − 0.916655i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68.9117 | 0.103007 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1059.33i | − 1.57874i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 532.492 | 0.791222 | 0.395611 | − | 0.918418i | \(-0.370533\pi\) | ||||
0.395611 | + | 0.918418i | \(0.370533\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 201.246 | 0.297262 | 0.148631 | − | 0.988893i | \(-0.452513\pi\) | ||||
0.148631 | + | 0.988893i | \(0.452513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 59.9461i | 0.0882859i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.6687 | −0.0362243 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 619.586i | − 0.907154i | −0.891217 | − | 0.453577i | \(-0.850148\pi\) | ||||
0.891217 | − | 0.453577i | \(-0.149852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 77.9477i | − 0.113461i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −88.0124 | −0.127739 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 835.133i | − 1.20859i | −0.796762 | − | 0.604293i | \(-0.793456\pi\) | ||||
0.796762 | − | 0.604293i | \(-0.206544\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −144.000 | −0.207792 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.4922 | −0.0609645 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 682.281i | − 0.976081i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 383.921 | 0.547676 | 0.273838 | − | 0.961776i | \(-0.411707\pi\) | ||||
0.273838 | + | 0.961776i | \(0.411707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 515.958i | 0.733938i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 568.408i | − 0.803971i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1127.99 | −1.59096 | −0.795482 | − | 0.605977i | \(-0.792782\pi\) | ||||
−0.795482 | + | 0.605977i | \(0.792782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 275.107i | − 0.386929i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1205.98 | 1.69142 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −571.161 | −0.796598 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 480.159i | 0.667815i | 0.942606 | + | 0.333907i | \(0.108367\pi\) | ||||
−0.942606 | + | 0.333907i | \(0.891633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −269.666 | −0.374016 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 364.299i | − 0.503871i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 626.753i | 0.862109i | 0.902326 | + | 0.431054i | \(0.141858\pi\) | ||||
−0.902326 | + | 0.431054i | \(0.858142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 53.6990i | − 0.0734596i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 721.076 | 0.983732 | 0.491866 | − | 0.870671i | \(-0.336315\pi\) | ||||
0.491866 | + | 0.870671i | \(0.336315\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1452.98 | −1.97149 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 358.245i | 0.484770i | 0.970180 | + | 0.242385i | \(0.0779297\pi\) | ||||
−0.970180 | + | 0.242385i | \(0.922070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −80.3406 | −0.108422 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 847.059i | 1.14005i | 0.821627 | + | 0.570026i | \(0.193067\pi\) | ||||
−0.821627 | + | 0.570026i | \(0.806933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 264.135i | 0.353594i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 746.991 | 0.997317 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1184.81i | − 1.57765i | −0.614619 | − | 0.788824i | \(-0.710690\pi\) | ||||
0.614619 | − | 0.788824i | \(-0.289310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −440.085 | −0.584442 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 462.741 | 0.611283 | 0.305642 | − | 0.952147i | \(-0.401129\pi\) | ||||
0.305642 | + | 0.952147i | \(0.401129\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 467.075i | 0.615382i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 390.158 | 0.512691 | 0.256346 | − | 0.966585i | \(-0.417482\pi\) | ||||
0.256346 | + | 0.966585i | \(0.417482\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 414.625i | 0.543414i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 442.745i | − 0.577243i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −579.981 | −0.754202 | −0.377101 | − | 0.926172i | \(-0.623079\pi\) | ||||
−0.377101 | + | 0.926172i | \(0.623079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 705.655i | − 0.915247i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 744.906 | 0.963655 | 0.481828 | − | 0.876266i | \(-0.339973\pi\) | ||||
0.481828 | + | 0.876266i | \(0.339973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 446.833 | 0.575074 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 256.912i | 0.329797i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1146.65 | −1.46818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 132.068i | 0.168669i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1393.82i | − 1.77105i | −0.464589 | − | 0.885526i | \(-0.653798\pi\) | ||||
0.464589 | − | 0.885526i | \(-0.346202\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −240.669 | −0.305030 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 903.825i | − 1.14264i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −511.842 | −0.645450 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −406.073 | −0.509502 | −0.254751 | − | 0.967007i | \(-0.581993\pi\) | ||||
−0.254751 | + | 0.967007i | \(0.581993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 56.5624i | − 0.0707915i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 62.4984 | 0.0780255 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 278.378i | 0.346672i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 95.4049i | − 0.118222i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −123.325 | −0.152441 | −0.0762207 | − | 0.997091i | \(-0.524285\pi\) | ||||
−0.0762207 | + | 0.997091i | \(0.524285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 183.404i | − 0.226146i | −0.993587 | − | 0.113073i | \(-0.963931\pi\) | ||||
0.993587 | − | 0.113073i | \(-0.0360694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −703.319 | −0.865091 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −324.669 | −0.397391 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 69.5770i | 0.0849536i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 746.912 | 0.909759 | 0.454879 | − | 0.890553i | \(-0.349682\pi\) | ||||
0.454879 | + | 0.890553i | \(0.349682\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.0982i | 0.0633028i | 0.999499 | + | 0.0316514i | \(0.0100766\pi\) | ||||
−0.999499 | + | 0.0316514i | \(0.989923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1327.69i | 1.60543i | 0.596360 | + | 0.802717i | \(0.296613\pi\) | ||||
−0.596360 | + | 0.802717i | \(0.703387\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −798.486 | −0.963192 | −0.481596 | − | 0.876393i | \(-0.659943\pi\) | ||||
−0.481596 | + | 0.876393i | \(0.659943\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 607.229i | − 0.730720i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.4350 | 0.0521429 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −260.498 | −0.311229 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 608.138i | − 0.724836i | −0.932016 | − | 0.362418i | \(-0.881951\pi\) | ||||
0.932016 | − | 0.362418i | \(-0.118049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −195.006 | −0.231874 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 791.826i | − 0.939295i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 19.9776i | − 0.0235863i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 588.827 | 0.693553 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1449.34i | − 1.70310i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 661.404 | 0.775386 | 0.387693 | − | 0.921789i | \(-0.373272\pi\) | ||||
0.387693 | + | 0.921789i | \(0.373272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 291.070 | 0.339638 | 0.169819 | − | 0.985475i | \(-0.445682\pi\) | ||||
0.169819 | + | 0.985475i | \(0.445682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1024.97i | − 1.19321i | −0.802535 | − | 0.596604i | \(-0.796516\pi\) | ||||
0.802535 | − | 0.596604i | \(-0.203484\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 222.492 | 0.258411 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 301.956i | − 0.349891i | −0.984578 | − | 0.174946i | \(-0.944025\pi\) | ||||
0.984578 | − | 0.174946i | \(-0.0559749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 497.088i | − 0.573342i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1027.99 | 1.18295 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 702.044i | 0.806020i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.0000 | −0.0481100 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1358.23 | 1.54872 | 0.774362 | − | 0.632743i | \(-0.218071\pi\) | ||||
0.774362 | + | 0.632743i | \(0.218071\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 996.640i | − 1.13383i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1176.49 | 1.33541 | 0.667703 | − | 0.744428i | \(-0.267278\pi\) | ||||
0.667703 | + | 0.744428i | \(0.267278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 506.418i | 0.573520i | 0.958002 | + | 0.286760i | \(0.0925783\pi\) | ||||
−0.958002 | + | 0.286760i | \(0.907422\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1497.24i | − 1.68798i | −0.536355 | − | 0.843992i | \(-0.680199\pi\) | ||||
0.536355 | − | 0.843992i | \(-0.319801\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 190.978 | 0.214824 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 100.891i | − 0.113233i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −341.981 | −0.382958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 225.678 | 0.251592 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1274.20i | 1.41735i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.0155 | 0.0255444 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 281.171i | 0.311375i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 199.374i | − 0.219816i | −0.993942 | − | 0.109908i | \(-0.964944\pi\) | ||||
0.993942 | − | 0.109908i | \(-0.0350557\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 398.243 | 0.438111 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1385.82i | − 1.52121i | −0.649215 | − | 0.760605i | \(-0.724902\pi\) | ||||
0.649215 | − | 0.760605i | \(-0.275098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −986.991 | −1.08104 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 691.988 | 0.754621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 483.135i | 0.525718i | 0.964834 | + | 0.262859i | \(0.0846654\pi\) | ||||
−0.964834 | + | 0.262859i | \(0.915335\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −620.656 | −0.673894 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 554.031i | 0.600250i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 188.936i | − 0.203814i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1149.15 | −1.23697 | −0.618487 | − | 0.785795i | \(-0.712254\pi\) | ||||
−0.618487 | + | 0.785795i | \(0.712254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 262.612i | − 0.282075i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −631.830 | −0.677202 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1349.00 | 1.43970 | 0.719852 | − | 0.694127i | \(-0.244210\pi\) | ||||
0.719852 | + | 0.694127i | \(0.244210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 459.862i | 0.489736i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1160.07 | 1.23280 | 0.616401 | − | 0.787432i | \(-0.288590\pi\) | ||||
0.616401 | + | 0.787432i | \(0.288590\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 721.670i | − 0.765292i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 620.063i | − 0.654766i | −0.944892 | − | 0.327383i | \(-0.893833\pi\) | ||||
0.944892 | − | 0.327383i | \(-0.106167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 134.505 | 0.141733 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 796.017i | 0.837031i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 545.587 | 0.572494 | 0.286247 | − | 0.958156i | \(-0.407592\pi\) | ||||
0.286247 | + | 0.958156i | \(0.407592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −493.495 | −0.515669 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 456.377i | 0.475888i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1552.31 | −1.61531 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 523.364i | 0.543472i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 181.621i | − 0.187819i | −0.995581 | − | 0.0939097i | \(-0.970064\pi\) | ||||
0.995581 | − | 0.0939097i | \(-0.0299365\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.0093 | 0.0216814 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 337.222i | 0.347293i | 0.984808 | + | 0.173647i | \(0.0555550\pi\) | ||||
−0.984808 | + | 0.173647i | \(0.944445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 104.656 | 0.107560 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −940.249 | −0.962384 | −0.481192 | − | 0.876615i | \(-0.659796\pi\) | ||||
−0.481192 | + | 0.876615i | \(0.659796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 233.537i | 0.238547i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −290.498 | −0.296125 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1651.87i | − 1.68043i | −0.542250 | − | 0.840217i | \(-0.682427\pi\) | ||||
0.542250 | − | 0.840217i | \(-0.317573\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 296.165i | 0.300065i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 912.000 | 0.922144 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 970.903i | − 0.979720i | −0.871801 | − | 0.489860i | \(-0.837048\pi\) | ||||
0.871801 | − | 0.489860i | \(-0.162952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1010.16 | −1.01729 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1285.08 | −1.28894 | −0.644471 | − | 0.764628i | \(-0.722922\pi\) | ||||
−0.644471 | + | 0.764628i | \(0.722922\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 313.064i | 0.313378i |
(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 | 1200.3.e.n.751.4 | 4 | ||
3.2 | odd | 2 | 3600.3.e.bh.3151.3 | 4 | |||
4.3 | odd | 2 | inner | 1200.3.e.n.751.1 | 4 | ||
5.2 | odd | 4 | 1200.3.j.f.799.5 | 8 | |||
5.3 | odd | 4 | 1200.3.j.f.799.3 | 8 | |||
5.4 | even | 2 | 240.3.e.a.31.2 | ✓ | 4 | ||
12.11 | even | 2 | 3600.3.e.bh.3151.2 | 4 | |||
15.2 | even | 4 | 3600.3.j.l.1999.4 | 8 | |||
15.8 | even | 4 | 3600.3.j.l.1999.6 | 8 | |||
15.14 | odd | 2 | 720.3.e.a.271.1 | 4 | |||
20.3 | even | 4 | 1200.3.j.f.799.6 | 8 | |||
20.7 | even | 4 | 1200.3.j.f.799.4 | 8 | |||
20.19 | odd | 2 | 240.3.e.a.31.4 | yes | 4 | ||
40.19 | odd | 2 | 960.3.e.b.511.1 | 4 | |||
40.29 | even | 2 | 960.3.e.b.511.3 | 4 | |||
60.23 | odd | 4 | 3600.3.j.l.1999.3 | 8 | |||
60.47 | odd | 4 | 3600.3.j.l.1999.5 | 8 | |||
60.59 | even | 2 | 720.3.e.a.271.2 | 4 | |||
120.29 | odd | 2 | 2880.3.e.f.2431.3 | 4 | |||
120.59 | even | 2 | 2880.3.e.f.2431.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.3.e.a.31.2 | ✓ | 4 | 5.4 | even | 2 | ||
240.3.e.a.31.4 | yes | 4 | 20.19 | odd | 2 | ||
720.3.e.a.271.1 | 4 | 15.14 | odd | 2 | |||
720.3.e.a.271.2 | 4 | 60.59 | even | 2 | |||
960.3.e.b.511.1 | 4 | 40.19 | odd | 2 | |||
960.3.e.b.511.3 | 4 | 40.29 | even | 2 | |||
1200.3.e.n.751.1 | 4 | 4.3 | odd | 2 | inner | ||
1200.3.e.n.751.4 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.j.f.799.3 | 8 | 5.3 | odd | 4 | |||
1200.3.j.f.799.4 | 8 | 20.7 | even | 4 | |||
1200.3.j.f.799.5 | 8 | 5.2 | odd | 4 | |||
1200.3.j.f.799.6 | 8 | 20.3 | even | 4 | |||
2880.3.e.f.2431.3 | 4 | 120.29 | odd | 2 | |||
2880.3.e.f.2431.4 | 4 | 120.59 | even | 2 | |||
3600.3.e.bh.3151.2 | 4 | 12.11 | even | 2 | |||
3600.3.e.bh.3151.3 | 4 | 3.2 | odd | 2 | |||
3600.3.j.l.1999.3 | 8 | 60.23 | odd | 4 | |||
3600.3.j.l.1999.4 | 8 | 15.2 | even | 4 | |||
3600.3.j.l.1999.5 | 8 | 60.47 | odd | 4 | |||
3600.3.j.l.1999.6 | 8 | 15.8 | even | 4 |