Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.16 | ||
Character | \(\chi\) | \(=\) | 900.149 |
Dual form | 900.3.u.d.749.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.83603 | + | 0.978225i | 0.945344 | + | 0.326075i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.69840 | + | 2.71262i | −0.671200 | + | 0.387517i | −0.796531 | − | 0.604598i | \(-0.793334\pi\) |
0.125331 | + | 0.992115i | \(0.460001\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.08615 | + | 5.54856i | 0.787350 | + | 0.616506i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.81872 | + | 5.09149i | −0.801702 | + | 0.462863i | −0.844066 | − | 0.536239i | \(-0.819844\pi\) |
0.0423639 | + | 0.999102i | \(0.486511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.42184 | − | 2.55295i | −0.340142 | − | 0.196381i | 0.320193 | − | 0.947352i | \(-0.396252\pi\) |
−0.660335 | + | 0.750971i | \(0.729586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.4550 | 1.02676 | 0.513381 | − | 0.858161i | \(-0.328393\pi\) | ||||
0.513381 | + | 0.858161i | \(0.328393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.4980 | 0.920947 | 0.460474 | − | 0.887673i | \(-0.347680\pi\) | ||||
0.460474 | + | 0.887673i | \(0.347680\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −15.9784 | + | 3.09699i | −0.760874 | + | 0.147476i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.41558 | + | 16.3083i | −0.409373 | + | 0.709055i | −0.994820 | − | 0.101656i | \(-0.967586\pi\) |
0.585447 | + | 0.810711i | \(0.300919\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.6688 | + | 22.6677i | 0.543289 | + | 0.839546i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0817 | + | 16.7903i | −1.00282 | + | 0.578976i | −0.909080 | − | 0.416621i | \(-0.863214\pi\) |
−0.0937354 | + | 0.995597i | \(0.529881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25.4881 | + | 44.1467i | −0.822197 | + | 1.42409i | 0.0818455 | + | 0.996645i | \(0.473919\pi\) |
−0.904043 | + | 0.427442i | \(0.859415\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −29.9908 | + | 5.81293i | −0.908812 | + | 0.176149i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.605498i | − | 0.0163648i | −0.999967 | − | 0.00818241i | \(-0.997395\pi\) | ||
0.999967 | − | 0.00818241i | \(-0.00260457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.0431 | − | 11.5658i | −0.257516 | − | 0.296559i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4241 | − | 7.17303i | −0.303026 | − | 0.174952i | 0.340776 | − | 0.940145i | \(-0.389310\pi\) |
−0.643801 | + | 0.765193i | \(0.722644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −44.0400 | + | 25.4265i | −1.02419 | + | 0.591314i | −0.915314 | − | 0.402741i | \(-0.868057\pi\) |
−0.108873 | + | 0.994056i | \(0.534724\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.13494 | + | 1.96577i | 0.0241477 | + | 0.0418250i | 0.877847 | − | 0.478942i | \(-0.158979\pi\) |
−0.853699 | + | 0.520767i | \(0.825646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.78337 | + | 16.9453i | −0.199661 | + | 0.345822i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 49.5028 | + | 17.0749i | 0.970643 | + | 0.334802i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −18.4881 | −0.348832 | −0.174416 | − | 0.984672i | \(-0.555804\pi\) | ||||
−0.174416 | + | 0.984672i | \(0.555804\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 49.6249 | + | 17.1170i | 0.870612 | + | 0.300298i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 70.8221 | + | 40.8892i | 1.20038 | + | 0.693037i | 0.960639 | − | 0.277801i | \(-0.0896056\pi\) |
0.239737 | + | 0.970838i | \(0.422939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.70398 | + | 8.14754i | 0.0771145 | + | 0.133566i | 0.902004 | − | 0.431728i | \(-0.142096\pi\) |
−0.824889 | + | 0.565294i | \(0.808763\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −48.3447 | − | 6.84729i | −0.767376 | − | 0.108687i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.8445 | − | 18.3854i | −0.475291 | − | 0.274409i | 0.243161 | − | 0.969986i | \(-0.421816\pi\) |
−0.718452 | + | 0.695577i | \(0.755149\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −42.6560 | + | 37.0402i | −0.618203 | + | 0.536814i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 57.2046i | 0.805699i | 0.915266 | + | 0.402849i | \(0.131980\pi\) | ||||
−0.915266 | + | 0.402849i | \(0.868020\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 78.9324i | − | 1.08127i | −0.841259 | − | 0.540633i | \(-0.818185\pi\) | ||
0.841259 | − | 0.540633i | \(-0.181815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27.6226 | − | 47.8437i | 0.358735 | − | 0.621347i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.1524 | + | 33.1729i | 0.242435 | + | 0.419910i | 0.961407 | − | 0.275129i | \(-0.0887206\pi\) |
−0.718972 | + | 0.695039i | \(0.755387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 19.4270 | + | 78.6358i | 0.239840 | + | 0.970812i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −38.6629 | − | 66.9661i | −0.465818 | − | 0.806821i | 0.533420 | − | 0.845851i | \(-0.320907\pi\) |
−0.999238 | + | 0.0390298i | \(0.987573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −98.9012 | + | 19.1694i | −1.13680 | + | 0.220338i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 138.264i | 1.55353i | 0.629790 | + | 0.776766i | \(0.283141\pi\) | ||||
−0.629790 | + | 0.776766i | \(0.716859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.7008 | 0.304404 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −115.471 | + | 100.268i | −1.24162 | + | 1.07815i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 101.290 | − | 58.4800i | 1.04423 | − | 0.602887i | 0.123202 | − | 0.992382i | \(-0.460684\pi\) |
0.921029 | + | 0.389495i | \(0.127350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −90.7412 | − | 12.8521i | −0.916578 | − | 0.129819i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 76.0357 | − | 43.8993i | 0.752829 | − | 0.434646i | −0.0738861 | − | 0.997267i | \(-0.523540\pi\) |
0.826715 | + | 0.562621i | \(0.190207\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −163.182 | − | 94.2134i | −1.58429 | − | 0.914693i | −0.994222 | − | 0.107343i | \(-0.965766\pi\) |
−0.590073 | − | 0.807350i | \(-0.700901\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 170.277 | 1.59137 | 0.795685 | − | 0.605711i | \(-0.207111\pi\) | ||||
0.795685 | + | 0.605711i | \(0.207111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 79.0188 | 0.724943 | 0.362471 | − | 0.931995i | \(-0.381933\pi\) | ||||
0.362471 | + | 0.931995i | \(0.381933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.592314 | − | 1.71721i | 0.00533616 | − | 0.0154704i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 24.5318 | − | 42.4903i | 0.217095 | − | 0.376020i | −0.736823 | − | 0.676085i | \(-0.763675\pi\) |
0.953919 | + | 0.300065i | \(0.0970084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.1686 | − | 42.6254i | −0.146740 | − | 0.364320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −82.0104 | + | 47.3487i | −0.689163 | + | 0.397888i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.65342 | + | 14.9882i | −0.0715159 | + | 0.123869i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −28.2182 | − | 32.4965i | −0.229416 | − | 0.264199i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 54.4343i | − | 0.428617i | −0.976766 | − | 0.214308i | \(-0.931250\pi\) | ||
0.976766 | − | 0.214308i | \(-0.0687497\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −149.772 | + | 29.0293i | −1.16102 | + | 0.225034i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.09750 | − | 2.94304i | −0.0389122 | − | 0.0224660i | 0.480418 | − | 0.877040i | \(-0.340485\pi\) |
−0.519330 | + | 0.854574i | \(0.673818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −82.2126 | + | 47.4654i | −0.618140 | + | 0.356883i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.0288 | − | 27.7627i | −0.116999 | − | 0.202648i | 0.801578 | − | 0.597890i | \(-0.203994\pi\) |
−0.918577 | + | 0.395242i | \(0.870661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 122.331 | − | 211.884i | 0.880080 | − | 1.52434i | 0.0288281 | − | 0.999584i | \(-0.490822\pi\) |
0.851251 | − | 0.524758i | \(-0.175844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.29576 | + | 6.68522i | 0.00918976 | + | 0.0474129i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 51.9933 | 0.363590 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −44.3223 | + | 38.4870i | −0.301512 | + | 0.261817i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 142.535 | + | 82.2928i | 0.956613 | + | 0.552301i | 0.895129 | − | 0.445807i | \(-0.147083\pi\) |
0.0614839 | + | 0.998108i | \(0.480417\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 49.5167 | + | 85.7655i | 0.327925 | + | 0.567984i | 0.982100 | − | 0.188360i | \(-0.0603172\pi\) |
−0.654175 | + | 0.756344i | \(0.726984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 123.688 | + | 96.8498i | 0.808421 | + | 0.633005i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −113.488 | − | 65.5221i | −0.722851 | − | 0.417338i | 0.0929500 | − | 0.995671i | \(-0.470370\pi\) |
−0.815801 | + | 0.578332i | \(0.803704\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −52.4329 | − | 18.0856i | −0.329767 | − | 0.113746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 102.164i | − | 0.634556i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6333i | 0.102044i | 0.998698 | + | 0.0510222i | \(0.0162479\pi\) | ||||
−0.998698 | + | 0.0510222i | \(0.983752\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −141.991 | + | 245.936i | −0.850248 | + | 1.47267i | 0.0307367 | + | 0.999528i | \(0.490215\pi\) |
−0.880985 | + | 0.473145i | \(0.843119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −71.4649 | − | 123.781i | −0.422869 | − | 0.732431i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 123.993 | + | 97.0886i | 0.725108 | + | 0.567770i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 105.377 | + | 182.518i | 0.609115 | + | 1.05502i | 0.991387 | + | 0.130969i | \(0.0418087\pi\) |
−0.382271 | + | 0.924050i | \(0.624858\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 160.855 | + | 185.243i | 0.908785 | + | 1.04657i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 236.272i | 1.31996i | 0.751285 | + | 0.659978i | \(0.229434\pi\) | ||||
−0.751285 | + | 0.659978i | \(0.770566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −325.181 | −1.79658 | −0.898290 | − | 0.439404i | \(-0.855190\pi\) | ||||
−0.898290 | + | 0.439404i | \(0.855190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.37052 | + | 27.7082i | 0.0293471 | + | 0.151411i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −153.930 | + | 88.8718i | −0.823157 | + | 0.475250i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −130.409 | − | 66.7111i | −0.689994 | − | 0.352969i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −96.0546 | + | 55.4571i | −0.502903 | + | 0.290351i | −0.729912 | − | 0.683541i | \(-0.760439\pi\) |
0.227008 | + | 0.973893i | \(0.427106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −112.158 | − | 64.7547i | −0.581131 | − | 0.335516i | 0.180452 | − | 0.983584i | \(-0.442244\pi\) |
−0.761583 | + | 0.648068i | \(0.775577\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 335.209 | 1.70157 | 0.850784 | − | 0.525515i | \(-0.176127\pi\) | ||||
0.850784 | + | 0.525515i | \(0.176127\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 341.651 | 1.71684 | 0.858419 | − | 0.512950i | \(-0.171447\pi\) | ||||
0.858419 | + | 0.512950i | \(0.171447\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −72.3269 | − | 83.2927i | −0.359835 | − | 0.414392i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 91.0915 | − | 157.775i | 0.448726 | − | 0.777217i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −157.207 | + | 63.3199i | −0.759456 | + | 0.305893i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −154.310 | + | 89.0909i | −0.738325 | + | 0.426272i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −72.9832 | + | 126.411i | −0.345892 | + | 0.599102i | −0.985515 | − | 0.169586i | \(-0.945757\pi\) |
0.639623 | + | 0.768688i | \(0.279090\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −55.9590 | + | 162.234i | −0.262718 | + | 0.761662i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 276.558i | − | 1.27446i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 77.2137 | − | 223.855i | 0.352574 | − | 1.02217i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −77.1831 | − | 44.5617i | −0.349245 | − | 0.201636i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 295.808 | − | 170.785i | 1.32649 | − | 0.765851i | 0.341737 | − | 0.939796i | \(-0.388985\pi\) |
0.984755 | + | 0.173945i | \(0.0556514\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −41.0966 | − | 71.1813i | −0.181042 | − | 0.313574i | 0.761194 | − | 0.648525i | \(-0.224614\pi\) |
−0.942236 | + | 0.334951i | \(0.891280\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 153.723 | − | 266.256i | 0.671280 | − | 1.16269i | −0.306261 | − | 0.951948i | \(-0.599078\pi\) |
0.977541 | − | 0.210744i | \(-0.0675887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 125.140 | − | 108.665i | 0.541734 | − | 0.470412i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 415.262 | 1.78224 | 0.891121 | − | 0.453766i | \(-0.149920\pi\) | ||||
0.891121 | + | 0.453766i | \(0.149920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.8662 | + | 112.815i | 0.0922623 | + | 0.476011i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 219.813 | + | 126.909i | 0.919719 | + | 0.531000i | 0.883545 | − | 0.468345i | \(-0.155150\pi\) |
0.0361738 | + | 0.999346i | \(0.488483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −79.3285 | − | 137.401i | −0.329164 | − | 0.570129i | 0.653182 | − | 0.757201i | \(-0.273434\pi\) |
−0.982346 | + | 0.187072i | \(0.940100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.8278 | + | 242.018i | −0.0898265 | + | 0.995957i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −77.3734 | − | 44.6715i | −0.313252 | − | 0.180856i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −44.1413 | − | 227.739i | −0.177274 | − | 0.914615i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 470.630i | − | 1.87502i | −0.347961 | − | 0.937509i | \(-0.613126\pi\) | ||
0.347961 | − | 0.937509i | \(-0.386874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 191.757i | − | 0.757934i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 249.363 | − | 431.909i | 0.970283 | − | 1.68058i | 0.275587 | − | 0.961276i | \(-0.411128\pi\) |
0.694696 | − | 0.719304i | \(-0.255539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.64249 | + | 2.84487i | 0.00634165 | + | 0.0109841i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −299.239 | − | 42.3826i | −1.14651 | − | 0.162385i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 124.347 | + | 215.375i | 0.472801 | + | 0.818915i | 0.999515 | − | 0.0311270i | \(-0.00990962\pi\) |
−0.526714 | + | 0.850042i | \(0.676576\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −135.254 | + | 392.122i | −0.506568 | + | 1.46862i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 212.591i | − | 0.790300i | −0.918617 | − | 0.395150i | \(-0.870693\pi\) | ||
0.918617 | − | 0.395150i | \(-0.129307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 150.211 | 0.554284 | 0.277142 | − | 0.960829i | \(-0.410613\pi\) | ||||
0.277142 | + | 0.960829i | \(0.410613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 78.5602 | + | 27.0976i | 0.287766 | + | 0.0992586i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −317.231 | + | 183.153i | −1.14524 | + | 0.661204i | −0.947722 | − | 0.319096i | \(-0.896621\pi\) |
−0.197516 | + | 0.980300i | \(0.563287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −425.563 | + | 171.408i | −1.52532 | + | 0.614365i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −113.933 | + | 65.7791i | −0.405455 | + | 0.234089i | −0.688835 | − | 0.724918i | \(-0.741877\pi\) |
0.283380 | + | 0.959008i | \(0.408544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 233.240 | + | 134.661i | 0.824169 | + | 0.475834i | 0.851852 | − | 0.523783i | \(-0.175480\pi\) |
−0.0276831 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 77.8309 | 0.271188 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6756 | 0.0542409 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 344.469 | − | 66.7664i | 1.18374 | − | 0.229438i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 105.489 | − | 182.712i | 0.360030 | − | 0.623591i | −0.627935 | − | 0.778266i | \(-0.716100\pi\) |
0.987965 | + | 0.154675i | \(0.0494330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −244.773 | − | 125.214i | −0.824151 | − | 0.421597i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 83.2684 | − | 48.0750i | 0.278490 | − | 0.160786i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 137.945 | − | 238.928i | 0.458289 | − | 0.793780i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 258.583 | − | 50.1196i | 0.853410 | − | 0.165411i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 44.9444i | − | 0.146399i | −0.997317 | − | 0.0731993i | \(-0.976679\pi\) | ||
0.997317 | − | 0.0731993i | \(-0.0233209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −370.628 | − | 426.821i | −1.19944 | − | 1.38130i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.48434 | + | 5.47579i | 0.0304963 | + | 0.0176070i | 0.515171 | − | 0.857088i | \(-0.327729\pi\) |
−0.484674 | + | 0.874695i | \(0.661062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −145.186 | + | 83.8232i | −0.463853 | + | 0.267806i | −0.713663 | − | 0.700489i | \(-0.752965\pi\) |
0.249810 | + | 0.968295i | \(0.419632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −117.945 | − | 204.287i | −0.372068 | − | 0.644440i | 0.617816 | − | 0.786323i | \(-0.288018\pi\) |
−0.989883 | + | 0.141883i | \(0.954684\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 170.975 | − | 296.138i | 0.535973 | − | 0.928332i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 482.910 | + | 166.569i | 1.50439 | + | 0.518906i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 305.427 | 0.945594 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 224.100 | + | 77.2982i | 0.685320 | + | 0.236386i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.6648 | − | 6.15733i | −0.0324158 | − | 0.0187153i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 88.5058 | + | 153.297i | 0.267389 | + | 0.463132i | 0.968187 | − | 0.250228i | \(-0.0805057\pi\) |
−0.700798 | + | 0.713360i | \(0.747172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.35964 | − | 4.29065i | 0.0100890 | − | 0.0128848i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −279.959 | − | 161.634i | −0.830738 | − | 0.479627i | 0.0233670 | − | 0.999727i | \(-0.492561\pi\) |
−0.854105 | + | 0.520100i | \(0.825895\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 111.138 | − | 96.5061i | 0.327840 | − | 0.284679i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 519.090i | − | 1.52226i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 371.991i | − | 1.08452i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −193.149 | + | 334.543i | −0.556625 | + | 0.964102i | 0.441151 | + | 0.897433i | \(0.354570\pi\) |
−0.997775 | + | 0.0666690i | \(0.978763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3447 | + | 52.5585i | 0.0869474 | + | 0.150597i | 0.906219 | − | 0.422808i | \(-0.138955\pi\) |
−0.819272 | + | 0.573405i | \(0.805622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.99351 | − | 137.682i | −0.0199245 | − | 0.392256i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −58.9936 | − | 102.180i | −0.167121 | − | 0.289462i | 0.770286 | − | 0.637699i | \(-0.220114\pi\) |
−0.937406 | + | 0.348237i | \(0.886780\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −278.902 | + | 54.0578i | −0.781237 | + | 0.151422i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 503.014i | 1.40115i | 0.713577 | + | 0.700577i | \(0.247074\pi\) | ||||
−0.713577 | + | 0.700577i | \(0.752926\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −54.8201 | −0.151856 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −39.2032 | + | 34.0419i | −0.107998 | + | 0.0937794i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 161.866 | − | 93.4535i | 0.441052 | − | 0.254642i | −0.262992 | − | 0.964798i | \(-0.584709\pi\) |
0.704044 | + | 0.710156i | \(0.251376\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.2388 | − | 119.765i | −0.130728 | − | 0.324566i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 86.8646 | − | 50.1513i | 0.234136 | − | 0.135179i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −44.6509 | − | 25.7792i | −0.119708 | − | 0.0691132i | 0.438951 | − | 0.898511i | \(-0.355350\pi\) |
−0.558658 | + | 0.829398i | \(0.688684\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 171.459 | 0.454799 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 52.8882 | 0.139547 | 0.0697733 | − | 0.997563i | \(-0.477772\pi\) | ||||
0.0697733 | + | 0.997563i | \(0.477772\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 53.2490 | − | 154.377i | 0.139761 | − | 0.405190i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 211.261 | − | 365.915i | 0.551595 | − | 0.955391i | −0.446565 | − | 0.894751i | \(-0.647353\pi\) |
0.998160 | − | 0.0606395i | \(-0.0193140\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −453.155 | − | 64.1824i | −1.17094 | − | 0.165846i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −535.036 | + | 308.903i | −1.37541 | + | 0.794095i | −0.991603 | − | 0.129317i | \(-0.958721\pi\) |
−0.383810 | + | 0.923412i | \(0.625388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −164.349 | + | 284.660i | −0.420329 | + | 0.728031i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.5777 | − | 13.3331i | −0.0294598 | − | 0.0339264i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 451.909i | − | 1.13831i | −0.822230 | − | 0.569155i | \(-0.807270\pi\) | ||
0.822230 | − | 0.569155i | \(-0.192730\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −279.589 | + | 54.1911i | −0.700725 | + | 0.135817i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 644.660 | + | 372.195i | 1.60763 | + | 0.928167i | 0.989898 | + | 0.141779i | \(0.0452823\pi\) |
0.617734 | + | 0.786387i | \(0.288051\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 225.409 | − | 130.140i | 0.559327 | − | 0.322928i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.08289 | + | 5.33972i | 0.00757466 | + | 0.0131197i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 245.998 | − | 426.081i | 0.601462 | − | 1.04176i | −0.391138 | − | 0.920332i | \(-0.627919\pi\) |
0.992600 | − | 0.121430i | \(-0.0387481\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.3000 | − | 94.4158i | −0.0445256 | − | 0.229722i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −443.668 | −1.07426 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 554.205 | − | 481.241i | 1.32903 | − | 1.15406i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 459.193 | + | 265.115i | 1.09593 | + | 0.632733i | 0.935148 | − | 0.354257i | \(-0.115266\pi\) |
0.160778 | + | 0.986991i | \(0.448600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −303.646 | − | 525.931i | −0.721250 | − | 1.24924i | −0.960499 | − | 0.278284i | \(-0.910234\pi\) |
0.239249 | − | 0.970958i | \(-0.423099\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.86485 | + | 20.2270i | −0.00677270 | + | 0.0478181i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44.2024 | − | 25.5203i | −0.103518 | − | 0.0597664i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 147.455 | + | 50.8612i | 0.343717 | + | 0.118558i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 162.849i | − | 0.377841i | −0.981992 | − | 0.188921i | \(-0.939501\pi\) | ||
0.981992 | − | 0.188921i | \(-0.0604989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 283.902i | 0.655662i | 0.944736 | + | 0.327831i | \(0.106318\pi\) | ||||
−0.944736 | + | 0.327831i | \(0.893682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −164.754 | + | 285.362i | −0.377011 | + | 0.653002i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −235.420 | − | 407.760i | −0.536265 | − | 0.928838i | −0.999101 | − | 0.0423939i | \(-0.986502\pi\) |
0.462836 | − | 0.886444i | \(-0.346832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −163.348 | + | 65.7933i | −0.370404 | + | 0.149191i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 399.196 | + | 691.428i | 0.901120 | + | 1.56079i | 0.826043 | + | 0.563607i | \(0.190587\pi\) |
0.0750770 | + | 0.997178i | \(0.476080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 323.734 | + | 372.817i | 0.724237 | + | 0.834042i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 605.367i | − | 1.34826i | −0.738615 | − | 0.674128i | \(-0.764520\pi\) | ||
0.738615 | − | 0.674128i | \(-0.235480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 146.086 | 0.323915 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 56.5330 | + | 291.672i | 0.124797 | + | 0.643868i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 348.420 | − | 201.161i | 0.762408 | − | 0.440176i | −0.0677516 | − | 0.997702i | \(-0.521583\pi\) |
0.830160 | + | 0.557526i | \(0.188249\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 256.043 | + | 395.664i | 0.557829 | + | 0.862014i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −416.769 | + | 240.622i | −0.904054 | + | 0.521956i | −0.878513 | − | 0.477718i | \(-0.841464\pi\) |
−0.0255410 | + | 0.999674i | \(0.508131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −460.450 | − | 265.841i | −0.994493 | − | 0.574171i | −0.0878790 | − | 0.996131i | \(-0.528009\pi\) |
−0.906614 | + | 0.421960i | \(0.861342\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 534.278 | 1.14406 | 0.572032 | − | 0.820231i | \(-0.306155\pi\) | ||||
0.572032 | + | 0.820231i | \(0.306155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 199.491 | 0.425353 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −257.759 | − | 296.839i | −0.547259 | − | 0.630232i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 258.918 | − | 448.459i | 0.547395 | − | 0.948116i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −131.010 | − | 102.582i | −0.274653 | − | 0.215057i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 53.6506 | − | 30.9752i | 0.112005 | − | 0.0646664i | −0.442951 | − | 0.896546i | \(-0.646068\pi\) |
0.554956 | + | 0.831880i | \(0.312735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.54581 | + | 2.67742i | −0.00321374 | + | 0.00556635i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 99.9390 | − | 289.739i | 0.206913 | − | 0.599874i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 693.387i | 1.42379i | 0.702284 | + | 0.711896i | \(0.252163\pi\) | ||||
−0.702284 | + | 0.711896i | \(0.747837\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.2711 | + | 47.1724i | −0.0332742 | + | 0.0964671i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −87.8499 | − | 50.7202i | −0.178920 | − | 0.103300i | 0.407865 | − | 0.913042i | \(-0.366273\pi\) |
−0.586785 | + | 0.809743i | \(0.699607\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −507.619 | + | 293.074i | −1.02965 | + | 0.594471i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −155.174 | − | 268.770i | −0.312222 | − | 0.540785i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −342.467 | + | 593.170i | −0.686307 | + | 1.18872i | 0.286718 | + | 0.958015i | \(0.407436\pi\) |
−0.973024 | + | 0.230703i | \(0.925897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −643.273 | + | 558.584i | −1.28398 | + | 1.11494i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −487.981 | −0.970141 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −81.5911 | − | 420.955i | −0.160929 | − | 0.830286i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 305.197 | + | 176.206i | 0.599601 | + | 0.346180i | 0.768885 | − | 0.639387i | \(-0.220812\pi\) |
−0.169283 | + | 0.985567i | \(0.554145\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 214.114 | + | 370.856i | 0.419009 | + | 0.725745i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 256.675 | + | 396.640i | 0.500341 | + | 0.773177i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.0174 | − | 11.5571i | −0.0387185 | − | 0.0223541i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 120.308 | + | 620.710i | 0.231808 | + | 1.19597i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 297.921i | 0.571825i | 0.958256 | + | 0.285912i | \(0.0922966\pi\) | ||||
−0.958256 | + | 0.285912i | \(0.907703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 66.5684i | 0.127282i | 0.997973 | + | 0.0636409i | \(0.0202712\pi\) | ||||
−0.997973 | + | 0.0636409i | \(0.979729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −444.894 | + | 770.579i | −0.844201 | + | 1.46220i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 87.1938 | + | 151.024i | 0.164828 | + | 0.285490i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 274.980 | + | 682.708i | 0.517854 | + | 1.28570i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.6248 | + | 63.4360i | 0.0687145 | + | 0.119017i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −231.127 | + | 670.075i | −0.430405 | + | 1.24781i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 199.248i | − | 0.369662i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −72.7607 | −0.134493 | −0.0672465 | − | 0.997736i | \(-0.521421\pi\) | ||||
−0.0672465 | + | 0.997736i | \(0.521421\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −922.223 | − | 318.100i | −1.69839 | − | 0.585820i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 138.484 | − | 79.9536i | 0.253169 | − | 0.146167i | −0.368045 | − | 0.929808i | \(-0.619973\pi\) |
0.621215 | + | 0.783640i | \(0.286640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.8739 | + | 83.8350i | −0.0216283 | + | 0.152705i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −508.871 | + | 293.797i | −0.923540 | + | 0.533206i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −179.971 | − | 103.906i | −0.325445 | − | 0.187895i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 610.336 | 1.09576 | 0.547878 | − | 0.836558i | \(-0.315436\pi\) | ||||
0.547878 | + | 0.836558i | \(0.315436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 259.651 | 0.464491 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −523.488 | + | 101.465i | −0.933134 | + | 0.180864i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −454.385 | + | 787.017i | −0.807078 | + | 1.39790i | 0.107802 | + | 0.994172i | \(0.465619\pi\) |
−0.914879 | + | 0.403727i | \(0.867715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −304.585 | − | 316.764i | −0.537187 | − | 0.558667i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −329.712 | + | 190.360i | −0.579459 | + | 0.334551i | −0.760919 | − | 0.648847i | \(-0.775251\pi\) |
0.181459 | + | 0.983398i | \(0.441918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −155.321 | + | 269.024i | −0.272016 | + | 0.471145i | −0.969378 | − | 0.245574i | \(-0.921024\pi\) |
0.697362 | + | 0.716719i | \(0.254357\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −326.663 | + | 63.3151i | −0.570093 | + | 0.110498i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 761.001i | 1.31889i | 0.751752 | + | 0.659446i | \(0.229209\pi\) | ||||
−0.751752 | + | 0.659446i | \(0.770791\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −254.740 | − | 293.362i | −0.439965 | − | 0.506671i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 363.308 | + | 209.756i | 0.625314 | + | 0.361025i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 163.042 | − | 94.1321i | 0.279660 | − | 0.161462i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −208.324 | − | 360.828i | −0.354897 | − | 0.614699i | 0.632204 | − | 0.774802i | \(-0.282151\pi\) |
−0.987100 | + | 0.160103i | \(0.948817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −445.991 | + | 772.479i | −0.757200 | + | 1.31151i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 950.663 | + | 327.910i | 1.60857 | + | 0.554839i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −775.358 | −1.30752 | −0.653759 | − | 0.756703i | \(-0.726809\pi\) | ||||
−0.653759 | + | 0.756703i | \(0.726809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 968.932 | + | 334.211i | 1.62300 | + | 0.559818i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −215.994 | − | 124.704i | −0.360591 | − | 0.208187i | 0.308749 | − | 0.951144i | \(-0.400090\pi\) |
−0.669340 | + | 0.742956i | \(0.733423\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 109.343 | + | 189.388i | 0.181936 | + | 0.315122i | 0.942540 | − | 0.334094i | \(-0.108430\pi\) |
−0.760604 | + | 0.649216i | \(0.775097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −123.642 | − | 306.973i | −0.205045 | − | 0.509076i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 781.026 | + | 450.926i | 1.28670 | + | 0.742876i | 0.978064 | − | 0.208305i | \(-0.0667946\pi\) |
0.308635 | + | 0.951181i | \(0.400128\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 412.678 | − | 358.347i | 0.677632 | − | 0.588419i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11.5898i | − | 0.0189686i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 334.064i | 0.544965i | 0.962161 | + | 0.272483i | \(0.0878447\pi\) | ||||
−0.962161 | + | 0.272483i | \(0.912155\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 89.4659 | − | 154.959i | 0.145001 | − | 0.251150i | −0.784372 | − | 0.620291i | \(-0.787015\pi\) |
0.929373 | + | 0.369141i | \(0.120348\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 201.857 | + | 349.626i | 0.326102 | + | 0.564825i | 0.981735 | − | 0.190255i | \(-0.0609315\pi\) |
−0.655633 | + | 0.755080i | \(0.727598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −507.787 | + | 25.7929i | −0.817692 | + | 0.0415344i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −375.059 | − | 649.621i | −0.602020 | − | 1.04273i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −524.779 | + | 101.715i | −0.836968 | + | 0.162224i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 10.5689i | − | 0.0168028i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −625.992 | −0.992063 | −0.496032 | − | 0.868304i | \(-0.665210\pi\) | ||||
−0.496032 | + | 0.868304i | \(0.665210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −330.641 | + | 287.110i | −0.522339 | + | 0.453571i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 86.5210 | − | 49.9529i | 0.135826 | − | 0.0784190i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −317.403 | + | 405.361i | −0.496718 | + | 0.634367i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −84.0852 | + | 48.5466i | −0.131178 | + | 0.0757357i | −0.564153 | − | 0.825670i | \(-0.690797\pi\) |
0.432975 | + | 0.901406i | \(0.357464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 950.767 | + | 548.925i | 1.47864 | + | 0.853694i | 0.999708 | − | 0.0241567i | \(-0.00769006\pi\) |
0.478934 | + | 0.877851i | \(0.341023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −104.927 | −0.162175 | −0.0810875 | − | 0.996707i | \(-0.525839\pi\) | ||||
−0.0810875 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −832.748 | −1.28312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 270.536 | − | 784.328i | 0.415571 | − | 1.20481i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.32766 | + | 7.49573i | −0.00662735 | + | 0.0114789i | −0.869320 | − | 0.494250i | \(-0.835443\pi\) |
0.862693 | + | 0.505728i | \(0.168776\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 437.961 | − | 559.327i | 0.666607 | − | 0.851334i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 421.081 | − | 243.111i | 0.638969 | − | 0.368909i | −0.145248 | − | 0.989395i | \(-0.546398\pi\) |
0.784217 | + | 0.620486i | \(0.213065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 149.965 | − | 259.746i | 0.226875 | − | 0.392960i | −0.730005 | − | 0.683442i | \(-0.760482\pi\) |
0.956880 | + | 0.290482i | \(0.0938157\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −175.302 | − | 201.881i | −0.264408 | − | 0.304496i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 632.361i | − | 0.948068i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1005.99 | − | 194.984i | 1.50372 | − | 0.291456i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −82.9662 | − | 47.9006i | −0.123646 | − | 0.0713869i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −435.185 | + | 251.254i | −0.646635 | + | 0.373335i | −0.787166 | − | 0.616742i | \(-0.788452\pi\) |
0.140531 | + | 0.990076i | \(0.455119\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −559.863 | − | 969.711i | −0.826976 | − | 1.43236i | −0.900399 | − | 0.435064i | \(-0.856726\pi\) |
0.0734232 | − | 0.997301i | \(-0.476608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −317.268 | + | 549.525i | −0.467258 | + | 0.809315i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −46.9198 | − | 242.074i | −0.0688983 | − | 0.355469i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −819.088 | −1.19925 | −0.599625 | − | 0.800281i | \(-0.704684\pi\) | ||||
−0.599625 | + | 0.800281i | \(0.704684\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 696.423 | − | 604.736i | 1.01372 | − | 0.880256i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 81.7515 | + | 47.1993i | 0.118652 | + | 0.0685040i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 381.408 | + | 660.618i | 0.551965 | + | 0.956032i | 0.998133 | + | 0.0610826i | \(0.0194553\pi\) |
−0.446167 | + | 0.894950i | \(0.647211\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 461.201 | − | 185.762i | 0.665514 | − | 0.268055i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −216.861 | − | 125.205i | −0.311135 | − | 0.179634i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1177.70 | + | 406.220i | 1.68483 | + | 0.581145i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 362.687i | 0.517386i | 0.965960 | + | 0.258693i | \(0.0832918\pi\) | ||||
−0.965960 | + | 0.258693i | \(0.916708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 10.5950i | − | 0.0150711i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −238.164 | + | 412.512i | −0.336866 | + | 0.583469i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 306.313 | + | 530.550i | 0.432036 | + | 0.748308i | 0.997048 | − | 0.0767744i | \(-0.0244621\pi\) |
−0.565013 | + | 0.825082i | \(0.691129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −48.3450 | + | 341.336i | −0.0679958 | + | 0.480078i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −479.971 | − | 831.333i | −0.673171 | − | 1.16597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 499.251 | + | 574.945i | 0.696305 | + | 0.801875i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1031.79i | − | 1.43503i | −0.696544 | − | 0.717515i | \(-0.745280\pi\) | ||
0.696544 | − | 0.717515i | \(-0.254720\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1022.26 | 1.41784 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −90.5690 | − | 467.275i | −0.125268 | − | 0.646300i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.5495 | + | 10.7096i | −0.0255152 | + | 0.0147312i | −0.512703 | − | 0.858566i | \(-0.671356\pi\) |
0.487188 | + | 0.873297i | \(0.338023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −298.652 | + | 665.017i | −0.409674 | + | 0.912232i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −768.717 | + | 443.819i | −1.05160 | + | 0.607139i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −580.882 | − | 335.373i | −0.792472 | − | 0.457534i | 0.0483598 | − | 0.998830i | \(-0.484601\pi\) |
−0.840832 | + | 0.541296i | \(0.817934\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 374.437 | 0.508055 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −925.156 | −1.25190 | −0.625951 | − | 0.779862i | \(-0.715289\pi\) | ||||
−0.625951 | + | 0.779862i | \(0.715289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −175.734 | − | 202.378i | −0.237159 | − | 0.273115i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −254.196 | + | 440.281i | −0.342122 | + | 0.592572i | −0.984827 | − | 0.173542i | \(-0.944479\pi\) |
0.642705 | + | 0.766114i | \(0.277812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 97.5942 | − | 689.055i | 0.130648 | − | 0.922430i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −800.027 | + | 461.896i | −1.06813 | + | 0.616683i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 208.849 | − | 361.737i | 0.278094 | − | 0.481674i | −0.692817 | − | 0.721114i | \(-0.743631\pi\) |
0.970911 | + | 0.239440i | \(0.0769639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 460.382 | − | 1334.72i | 0.611397 | − | 1.77254i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 183.878i | 0.242904i | 0.992597 | + | 0.121452i | \(0.0387550\pi\) | ||||
−0.992597 | + | 0.121452i | \(0.961245\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 187.582 | − | 543.830i | 0.247143 | − | 0.716508i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 991.942 | + | 572.698i | 1.30347 | + | 0.752560i | 0.980998 | − | 0.194019i | \(-0.0621522\pi\) |
0.322474 | + | 0.946578i | \(0.395486\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −371.262 | + | 214.348i | −0.486581 | + | 0.280928i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −208.776 | − | 361.611i | −0.272198 | − | 0.471461i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −652.189 | + | 1129.63i | −0.848101 | + | 1.46895i | 0.0348004 | + | 0.999394i | \(0.488920\pi\) |
−0.882901 | + | 0.469559i | \(0.844413\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1129.70 | − | 980.974i | 1.46525 | − | 1.27234i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 312.549 | 0.404332 | 0.202166 | − | 0.979351i | \(-0.435202\pi\) | ||||
0.202166 | + | 0.979351i | \(0.435202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.87522 | + | 9.67487i | 0.00241341 | + | 0.0124516i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −217.396 | − | 125.514i | −0.279071 | − | 0.161122i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −291.257 | − | 504.472i | −0.372928 | − | 0.645930i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −807.191 | − | 412.921i | −1.03090 | − | 0.527358i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 182.390 | + | 105.303i | 0.231754 | + | 0.133803i | 0.611381 | − | 0.791337i | \(-0.290614\pi\) |
−0.379627 | + | 0.925140i | \(0.623948\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 141.966 | + | 732.449i | 0.179932 | + | 0.928325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 266.182i | 0.336513i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 48.0362i | − | 0.0605752i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −555.552 | + | 962.245i | −0.697054 | + | 1.20733i | 0.272429 | + | 0.962176i | \(0.412173\pi\) |
−0.969483 | + | 0.245158i | \(0.921160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.8103 | + | 34.3125i | 0.0247939 | + | 0.0429443i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −767.167 | + | 979.761i | −0.957762 | + | 1.22317i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 401.884 | + | 696.083i | 0.500478 | + | 0.866853i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 207.962 | − | 602.914i | 0.257697 | − | 0.747105i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1552.47i | − | 1.91900i | −0.281702 | − | 0.959502i | \(-0.590899\pi\) | ||
0.281702 | − | 0.959502i | \(-0.409101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 893.971 | 1.10231 | 0.551154 | − | 0.834404i | \(-0.314188\pi\) | ||||
0.551154 | + | 0.834404i | \(0.314188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 426.003 | + | 146.940i | 0.523989 | + | 0.180738i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −770.612 | + | 444.913i | −0.943222 | + | 0.544569i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 196.292 | + | 153.699i | 0.239672 | + | 0.187667i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1232.21 | − | 711.419i | 1.50087 | − | 0.866528i | 0.500870 | − | 0.865522i | \(-0.333013\pi\) |
0.999999 | − | 0.00100512i | \(-0.000319940\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 332.933 | + | 192.219i | 0.404536 | + | 0.233559i | 0.688439 | − | 0.725294i | \(-0.258296\pi\) |
−0.283903 | + | 0.958853i | \(0.591629\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 228.210 | 0.275949 | 0.137974 | − | 0.990436i | \(-0.455941\pi\) | ||||
0.137974 | + | 0.990436i | \(0.455941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −108.877 | −0.131335 | −0.0656674 | − | 0.997842i | \(-0.520918\pi\) | ||||
−0.0656674 | + | 0.997842i | \(0.520918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1078.84 | + | 209.105i | −1.29825 | + | 0.251631i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −170.768 | + | 295.779i | −0.205004 | + | 0.355077i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1374.59 | + | 69.8217i | −1.64228 | + | 0.0834190i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −809.618 | + | 467.433i | −0.964980 | + | 0.557131i | −0.897702 | − | 0.440603i | \(-0.854765\pi\) |
−0.0672778 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 143.328 | − | 248.252i | 0.170426 | − | 0.295187i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −387.464 | + | 75.0997i | −0.459625 | + | 0.0890862i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 93.8939i | − | 0.110855i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 529.747 | + | 610.064i | 0.623965 | + | 0.718568i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.87462 | + | 5.70111i | 0.0116035 | + | 0.00669931i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1023.49 | − | 590.914i | 1.19988 | − | 0.692748i | 0.239348 | − | 0.970934i | \(-0.423066\pi\) |
0.960527 | + | 0.278185i | \(0.0897330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −491.500 | − | 851.303i | −0.573512 | − | 0.993352i | −0.996202 | − | 0.0870776i | \(-0.972247\pi\) |
0.422689 | − | 0.906275i | \(-0.361086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 764.988 | − | 1325.00i | 0.890557 | − | 1.54249i | 0.0513472 | − | 0.998681i | \(-0.483648\pi\) |
0.839209 | − | 0.543808i | \(-0.183018\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 220.731 | + | 76.1362i | 0.256366 | + | 0.0884276i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −932.711 | −1.08078 | −0.540389 | − | 0.841415i | \(-0.681723\pi\) | ||||
−0.540389 | + | 0.841415i | \(0.681723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 44.4566 | + | 15.3343i | 0.0512763 | + | 0.0176866i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −337.799 | − | 195.028i | −0.388721 | − | 0.224428i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 93.8742 | + | 162.595i | 0.107777 | + | 0.186676i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1042.24 | + | 147.617i | 1.19386 | + | 0.169092i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1088.45 | + | 628.419i | 1.24111 | + | 0.716555i | 0.969320 | − | 0.245802i | \(-0.0790512\pi\) |
0.271790 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 477.903 | − | 414.985i | 0.543690 | − | 0.472111i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 652.425i | − | 0.740551i | −0.928922 | − | 0.370275i | \(-0.879263\pi\) | ||
0.928922 | − | 0.370275i | \(-0.120737\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 618.566i | 0.700527i | 0.936651 | + | 0.350264i | \(0.113908\pi\) | ||||
−0.936651 | + | 0.350264i | \(0.886092\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −745.723 | + | 1291.63i | −0.840725 | + | 1.45618i | 0.0485585 | + | 0.998820i | \(0.484537\pi\) |
−0.889283 | + | 0.457357i | \(0.848796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 147.660 | + | 255.754i | 0.166096 | + | 0.287687i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −571.695 | − | 594.555i | −0.641633 | − | 0.667289i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.8592 | + | 34.3971i | 0.0222387 | + | 0.0385186i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 283.180 | − | 54.8870i | 0.315697 | − | 0.0611895i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1711.81i | − | 1.90413i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −322.709 | −0.358168 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 624.942 | − | 542.666i | 0.692073 | − | 0.600959i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 398.947 | − | 230.332i | 0.439853 | − | 0.253949i | −0.263682 | − | 0.964610i | \(-0.584937\pi\) |
0.703535 | + | 0.710660i | \(0.251604\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 782.378 | + | 110.812i | 0.860702 | + | 0.121905i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1190.05 | + | 687.076i | −1.30631 | + | 0.754200i | −0.981479 | − | 0.191571i | \(-0.938642\pi\) |
−0.324834 | + | 0.945771i | \(0.605308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 681.915 | + | 393.704i | 0.746895 | + | 0.431220i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.9334 | 0.0348238 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1651.74 | −1.79733 | −0.898663 | − | 0.438639i | \(-0.855461\pi\) | ||||
−0.898663 | + | 0.438639i | \(0.855461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.9657 | − | 127.464i | 0.0477369 | − | 0.138397i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 146.041 | − | 252.950i | 0.158224 | − | 0.274052i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −633.587 | − | 1573.04i | −0.683481 | − | 1.69691i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 632.169 | − | 364.983i | 0.680483 | − | 0.392877i | −0.119554 | − | 0.992828i | \(-0.538146\pi\) |
0.800037 | + | 0.599951i | \(0.204813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −171.189 | + | 296.509i | −0.183877 | + | 0.318484i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.5413 | + | 24.8073i | 0.0230883 | + | 0.0265888i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1098.36i | 1.17221i | 0.810236 | + | 0.586104i | \(0.199339\pi\) | ||||
−0.810236 | + | 0.586104i | \(0.800661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −493.750 | + | 95.7006i | −0.525826 | + | 0.101918i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 827.540 | + | 477.781i | 0.879426 | + | 0.507737i | 0.870469 | − | 0.492223i | \(-0.163816\pi\) |
0.00895707 | + | 0.999960i | \(0.497149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 233.959 | − | 135.077i | 0.248101 | − | 0.143241i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −397.289 | − | 688.125i | −0.419524 | − | 0.726636i | 0.576368 | − | 0.817190i | \(-0.304470\pi\) |
−0.995892 | + | 0.0905541i | \(0.971136\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −201.511 | + | 349.026i | −0.212340 | + | 0.367783i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −134.658 | − | 694.743i | −0.141596 | − | 0.730539i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 493.659 | 0.518005 | 0.259003 | − | 0.965877i | \(-0.416606\pi\) | ||||
0.259003 | + | 0.965877i | \(0.416606\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 774.581 | − | 672.604i | 0.809385 | − | 0.702826i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 150.620 | + | 86.9602i | 0.157059 | + | 0.0906780i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −818.788 | − | 1418.18i | −0.852016 | − | 1.47574i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1206.61 | + | 944.789i | 1.25296 | + | 0.981089i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1087.90 | + | 628.097i | 1.12502 | + | 0.649532i | 0.942678 | − | 0.333703i | \(-0.108298\pi\) |
0.182344 | + | 0.983235i | \(0.441632\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 866.200 | + | 298.776i | 0.893911 | + | 0.308335i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 832.692i | − | 0.857562i | −0.903409 | − | 0.428781i | \(-0.858943\pi\) | ||
0.903409 | − | 0.428781i | \(-0.141057\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1327.35i | 1.36418i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −503.542 | + | 872.160i | −0.515396 | + | 0.892691i | 0.484445 | + | 0.874822i | \(0.339022\pi\) |
−0.999840 | + | 0.0178695i | \(0.994312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −703.971 | − | 1219.31i | −0.719072 | − | 1.24547i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 559.939 | + | 438.440i | 0.570784 | + | 0.446932i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 273.430 | + | 473.595i | 0.278159 | + | 0.481785i | 0.970927 | − | 0.239375i | \(-0.0769425\pi\) |
−0.692768 | + | 0.721160i | \(0.743609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.2225 | − | 27.8950i | −0.0245415 | − | 0.0282624i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 957.622i | − | 0.968273i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −610.924 | −0.616472 | −0.308236 | − | 0.951310i | \(-0.599739\pi\) | ||||
−0.308236 | + | 0.951310i | \(0.599739\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 101.047 | + | 521.333i | 0.101759 | + | 0.525008i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −463.727 | + | 267.733i | −0.465123 | + | 0.268539i | −0.714196 | − | 0.699946i | \(-0.753207\pi\) |
0.249073 | + | 0.968485i | \(0.419874\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.7253 | − | 8.88193i | 0.0137390 | − | 0.00889083i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.3.u.d.149.16 | 32 | ||
3.2 | odd | 2 | 2700.3.u.d.449.5 | 32 | |||
5.2 | odd | 4 | 900.3.p.d.401.5 | yes | 16 | ||
5.3 | odd | 4 | 900.3.p.e.401.4 | yes | 16 | ||
5.4 | even | 2 | inner | 900.3.u.d.149.1 | 32 | ||
9.2 | odd | 6 | inner | 900.3.u.d.749.1 | 32 | ||
9.7 | even | 3 | 2700.3.u.d.2249.12 | 32 | |||
15.2 | even | 4 | 2700.3.p.e.2501.3 | 16 | |||
15.8 | even | 4 | 2700.3.p.d.2501.6 | 16 | |||
15.14 | odd | 2 | 2700.3.u.d.449.12 | 32 | |||
45.2 | even | 12 | 900.3.p.d.101.5 | ✓ | 16 | ||
45.7 | odd | 12 | 2700.3.p.e.1601.3 | 16 | |||
45.29 | odd | 6 | inner | 900.3.u.d.749.16 | 32 | ||
45.34 | even | 6 | 2700.3.u.d.2249.5 | 32 | |||
45.38 | even | 12 | 900.3.p.e.101.4 | yes | 16 | ||
45.43 | odd | 12 | 2700.3.p.d.1601.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.p.d.101.5 | ✓ | 16 | 45.2 | even | 12 | ||
900.3.p.d.401.5 | yes | 16 | 5.2 | odd | 4 | ||
900.3.p.e.101.4 | yes | 16 | 45.38 | even | 12 | ||
900.3.p.e.401.4 | yes | 16 | 5.3 | odd | 4 | ||
900.3.u.d.149.1 | 32 | 5.4 | even | 2 | inner | ||
900.3.u.d.149.16 | 32 | 1.1 | even | 1 | trivial | ||
900.3.u.d.749.1 | 32 | 9.2 | odd | 6 | inner | ||
900.3.u.d.749.16 | 32 | 45.29 | odd | 6 | inner | ||
2700.3.p.d.1601.6 | 16 | 45.43 | odd | 12 | |||
2700.3.p.d.2501.6 | 16 | 15.8 | even | 4 | |||
2700.3.p.e.1601.3 | 16 | 45.7 | odd | 12 | |||
2700.3.p.e.2501.3 | 16 | 15.2 | even | 4 | |||
2700.3.u.d.449.5 | 32 | 3.2 | odd | 2 | |||
2700.3.u.d.449.12 | 32 | 15.14 | odd | 2 | |||
2700.3.u.d.2249.5 | 32 | 45.34 | even | 6 | |||
2700.3.u.d.2249.12 | 32 | 9.7 | even | 3 |