Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(949,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.949");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.g (of order \(2\), degree \(1\), 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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 949.9 | ||
Character | \(\chi\) | \(=\) | 1900.949 |
Dual form | 1900.3.g.c.949.10 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.03369 | −0.677896 | −0.338948 | − | 0.940805i | \(-0.610071\pi\) | ||||
−0.338948 | + | 0.940805i | \(0.610071\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.27843i | − | 0.611204i | −0.952159 | − | 0.305602i | \(-0.901142\pi\) | ||
0.952159 | − | 0.305602i | \(-0.0988577\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.86411 | −0.540457 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.47217 | 0.497470 | 0.248735 | − | 0.968572i | \(-0.419985\pi\) | ||||
0.248735 | + | 0.968572i | \(0.419985\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.634081 | −0.0487754 | −0.0243877 | − | 0.999703i | \(-0.507764\pi\) | ||||
−0.0243877 | + | 0.999703i | \(0.507764\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.69271i | 0.0995712i | 0.998760 | + | 0.0497856i | \(0.0158538\pi\) | ||||
−0.998760 | + | 0.0497856i | \(0.984146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.46218 | − | 17.8673i | 0.340115 | − | 0.940384i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.70099i | 0.414333i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 25.9867i | 1.12986i | 0.825139 | + | 0.564929i | \(0.191096\pi\) | ||||
−0.825139 | + | 0.564929i | \(0.808904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 28.1953 | 1.04427 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 48.8696i | − | 1.68516i | −0.538571 | − | 0.842580i | \(-0.681036\pi\) | ||
0.538571 | − | 0.842580i | \(-0.318964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47053i | 0.144211i | 0.997397 | + | 0.0721054i | \(0.0229718\pi\) | ||||
−0.997397 | + | 0.0721054i | \(0.977028\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.1287 | −0.337233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.12833 | −0.165630 | −0.0828152 | − | 0.996565i | \(-0.526391\pi\) | ||||
−0.0828152 | + | 0.996565i | \(0.526391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.28952 | 0.0330647 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.9988i | 0.414605i | 0.978277 | + | 0.207303i | \(0.0664685\pi\) | ||||
−0.978277 | + | 0.207303i | \(0.933532\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.690441i | 0.0160568i | 0.999968 | + | 0.00802838i | \(0.00255554\pi\) | ||||
−0.999968 | + | 0.00802838i | \(0.997444\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 23.0801i | − | 0.491066i | −0.969388 | − | 0.245533i | \(-0.921037\pi\) | ||
0.969388 | − | 0.245533i | \(-0.0789630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 30.6950 | 0.626429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.44245i | − | 0.0674989i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −54.3934 | −1.02629 | −0.513145 | − | 0.858302i | \(-0.671520\pi\) | ||||
−0.513145 | + | 0.858302i | \(0.671520\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.1420 | + | 36.3365i | −0.230562 | + | 0.637482i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.251179i | 0.00425727i | 0.999998 | + | 0.00212863i | \(0.000677566\pi\) | ||||
−0.999998 | + | 0.00212863i | \(0.999322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39.5570 | 0.648475 | 0.324237 | − | 0.945976i | \(-0.394892\pi\) | ||||
0.324237 | + | 0.945976i | \(0.394892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.8108i | 0.330330i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −96.3354 | −1.43784 | −0.718921 | − | 0.695092i | \(-0.755363\pi\) | ||||
−0.718921 | + | 0.695092i | \(0.755363\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 52.8489i | − | 0.765926i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.0568i | − | 0.226152i | −0.993586 | − | 0.113076i | \(-0.963930\pi\) | ||
0.993586 | − | 0.113076i | \(-0.0360704\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70.0291i | 0.959302i | 0.877459 | + | 0.479651i | \(0.159237\pi\) | ||||
−0.877459 | + | 0.479651i | \(0.840763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 23.4123i | − | 0.304056i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.6211i | 0.944570i | 0.881446 | + | 0.472285i | \(0.156571\pi\) | ||||
−0.881446 | + | 0.472285i | \(0.843429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −13.5634 | −0.167449 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.29672i | 0.0156232i | 0.999969 | + | 0.00781159i | \(0.00248653\pi\) | ||||
−0.999969 | + | 0.00781159i | \(0.997513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 99.3856i | 1.14236i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 141.348i | − | 1.58818i | −0.607800 | − | 0.794090i | \(-0.707948\pi\) | ||
0.607800 | − | 0.794090i | \(-0.292052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.71287i | 0.0298117i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.09167i | − | 0.0977598i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −125.110 | −1.28980 | −0.644898 | − | 0.764268i | \(-0.723100\pi\) | ||||
−0.644898 | + | 0.764268i | \(0.723100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26.6173 | −0.268861 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 102.871 | 1.01853 | 0.509263 | − | 0.860611i | \(-0.329918\pi\) | ||||
0.509263 | + | 0.860611i | \(0.329918\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6950 | 0.113544 | 0.0567720 | − | 0.998387i | \(-0.481919\pi\) | ||||
0.0567720 | + | 0.998387i | \(0.481919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −189.935 | −1.77509 | −0.887545 | − | 0.460722i | \(-0.847591\pi\) | ||||
−0.887545 | + | 0.460722i | \(0.847591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 43.6838i | − | 0.400769i | −0.979717 | − | 0.200384i | \(-0.935781\pi\) | ||
0.979717 | − | 0.200384i | \(-0.0642191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.4631 | 0.112280 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 100.896 | 0.892884 | 0.446442 | − | 0.894813i | \(-0.352691\pi\) | ||||
0.446442 | + | 0.894813i | \(0.352691\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.08424 | 0.0263610 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.24214 | 0.0608584 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −91.0554 | −0.752524 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 34.5703i | − | 0.281059i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −140.225 | −1.10414 | −0.552068 | − | 0.833799i | \(-0.686161\pi\) | ||||
−0.552068 | + | 0.833799i | \(0.686161\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.40414i | − | 0.0108848i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −158.825 | −1.21241 | −0.606203 | − | 0.795310i | \(-0.707308\pi\) | ||||
−0.606203 | + | 0.795310i | \(0.707308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −76.4440 | − | 27.6480i | −0.574767 | − | 0.207879i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 74.8377i | 0.546261i | 0.961977 | + | 0.273130i | \(0.0880590\pi\) | ||||
−0.961977 | + | 0.273130i | \(0.911941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.4925 | 0.125846 | 0.0629228 | − | 0.998018i | \(-0.479958\pi\) | ||||
0.0629228 | + | 0.998018i | \(0.479958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 46.9377i | 0.332892i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.46980 | −0.0242643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −62.4241 | −0.424654 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −163.077 | −1.09448 | −0.547239 | − | 0.836976i | \(-0.684321\pi\) | ||||
−0.547239 | + | 0.836976i | \(0.684321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 147.367i | − | 0.975940i | −0.872861 | − | 0.487970i | \(-0.837738\pi\) | ||
0.872861 | − | 0.487970i | \(-0.162262\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 8.23354i | − | 0.0538140i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 208.993i | 1.33117i | 0.746324 | + | 0.665583i | \(0.231817\pi\) | ||||
−0.746324 | + | 0.665583i | \(0.768183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 110.619 | 0.695718 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 111.182 | 0.690574 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 87.2475i | − | 0.535261i | −0.963522 | − | 0.267630i | \(-0.913759\pi\) | ||
0.963522 | − | 0.267630i | \(-0.0862406\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −97.0793 | −0.581313 | −0.290657 | − | 0.956827i | \(-0.593874\pi\) | ||||
−0.290657 | + | 0.956827i | \(0.593874\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.598 | −0.997621 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −31.4328 | + | 86.9086i | −0.183817 | + | 0.508237i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −70.7451 | −0.408931 | −0.204466 | − | 0.978874i | \(-0.565546\pi\) | ||||
−0.204466 | + | 0.978874i | \(0.565546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.510819i | − | 0.00288598i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 176.104i | − | 0.983822i | −0.870646 | − | 0.491911i | \(-0.836299\pi\) | ||
0.870646 | − | 0.491911i | \(-0.163701\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 57.5577i | 0.317998i | 0.987279 | + | 0.158999i | \(0.0508267\pi\) | ||||
−0.987279 | + | 0.158999i | \(0.949173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −80.4465 | −0.439598 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.26280i | 0.0495337i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 120.632i | − | 0.638262i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −145.682 | −0.762731 | −0.381365 | − | 0.924424i | \(-0.624546\pi\) | ||||
−0.381365 | + | 0.924424i | \(0.624546\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 64.1316 | 0.332288 | 0.166144 | − | 0.986101i | \(-0.446868\pi\) | ||||
0.166144 | + | 0.986101i | \(0.446868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.9219i | − | 0.0909739i | −0.998965 | − | 0.0454870i | \(-0.985516\pi\) | ||
0.998965 | − | 0.0454870i | \(-0.0144839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −209.349 | −1.05200 | −0.526002 | − | 0.850483i | \(-0.676310\pi\) | ||||
−0.526002 | + | 0.850483i | \(0.676310\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 195.916 | 0.974707 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −209.085 | −1.02998 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 126.402i | − | 0.610640i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 35.3621 | − | 97.7729i | 0.169197 | − | 0.467813i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 232.975i | − | 1.10415i | −0.833795 | − | 0.552074i | \(-0.813837\pi\) | ||
0.833795 | − | 0.552074i | \(-0.186163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 32.6546i | 0.153308i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.1269 | 0.0881422 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 142.417i | − | 0.650307i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.07332i | − | 0.00485663i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −68.2129 | −0.305887 | −0.152944 | − | 0.988235i | \(-0.548875\pi\) | ||||
−0.152944 | + | 0.988235i | \(0.548875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −143.128 | −0.630520 | −0.315260 | − | 0.949005i | \(-0.602092\pi\) | ||||
−0.315260 | + | 0.949005i | \(0.602092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −135.889 | −0.593403 | −0.296701 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296701 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 47.6133i | 0.206118i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 270.764i | − | 1.16208i | −0.813876 | − | 0.581039i | \(-0.802646\pi\) | ||
0.813876 | − | 0.581039i | \(-0.197354\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 151.756i | − | 0.640320i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −300.071 | −1.25553 | −0.627764 | − | 0.778404i | \(-0.716030\pi\) | ||||
−0.627764 | + | 0.778404i | \(0.716030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 177.442i | 0.736275i | 0.929771 | + | 0.368138i | \(0.120004\pi\) | ||||
−0.929771 | + | 0.368138i | \(0.879996\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −226.174 | −0.930757 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.09754 | + | 11.3293i | −0.0165892 | + | 0.0458676i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.63713i | − | 0.0105909i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −80.0537 | −0.318939 | −0.159469 | − | 0.987203i | \(-0.550978\pi\) | ||||
−0.159469 | + | 0.987203i | \(0.550978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 142.204i | 0.562070i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −147.621 | −0.574402 | −0.287201 | − | 0.957870i | \(-0.592725\pi\) | ||||
−0.287201 | + | 0.957870i | \(0.592725\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.2196i | 0.101234i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 237.707i | 0.910757i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 344.458i | 1.30973i | 0.755747 | + | 0.654864i | \(0.227274\pi\) | ||||
−0.755747 | + | 0.654864i | \(0.772726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 287.458i | 1.07662i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 190.965i | − | 0.709908i | −0.934884 | − | 0.354954i | \(-0.884497\pi\) | ||
0.934884 | − | 0.354954i | \(-0.115503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −265.131 | −0.978342 | −0.489171 | − | 0.872188i | \(-0.662701\pi\) | ||||
−0.489171 | + | 0.872188i | \(0.662701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 5.51713i | − | 0.0202093i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 87.0682i | 0.314326i | 0.987573 | + | 0.157163i | \(0.0502348\pi\) | ||||
−0.987573 | + | 0.157163i | \(0.949765\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 21.7452i | − | 0.0779397i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 233.988i | 0.832697i | 0.909205 | + | 0.416348i | \(0.136690\pi\) | ||||
−0.909205 | + | 0.416348i | \(0.863310\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 190.662i | 0.673718i | 0.941555 | + | 0.336859i | \(0.109365\pi\) | ||||
−0.941555 | + | 0.336859i | \(0.890635\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 72.7283 | 0.253409 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 286.135 | 0.990086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 254.435 | 0.874348 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −230.400 | −0.786348 | −0.393174 | − | 0.919464i | \(-0.628623\pi\) | ||||
−0.393174 | + | 0.919464i | \(0.628623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 154.289 | 0.519493 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 16.4777i | − | 0.0551093i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.95400 | 0.00981396 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −209.208 | −0.690454 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −370.642 | −1.20730 | −0.603652 | − | 0.797248i | \(-0.706288\pi\) | ||||
−0.603652 | + | 0.797248i | \(0.706288\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.7840 | −0.0769710 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2047 | −0.0392433 | −0.0196216 | − | 0.999807i | \(-0.506246\pi\) | ||||
−0.0196216 | + | 0.999807i | \(0.506246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 263.418i | − | 0.841591i | −0.907156 | − | 0.420795i | \(-0.861751\pi\) | ||
0.907156 | − | 0.420795i | \(-0.138249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 328.524 | 1.03635 | 0.518177 | − | 0.855274i | \(-0.326611\pi\) | ||||
0.518177 | + | 0.855274i | \(0.326611\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 267.423i | − | 0.838316i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 386.268 | 1.20333 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.2442 | + | 10.9386i | 0.0936352 | + | 0.0338656i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 88.8392i | 0.271679i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −98.7466 | −0.300142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.2287i | 0.0883043i | 0.999025 | + | 0.0441522i | \(0.0140586\pi\) | ||||
−0.999025 | + | 0.0441522i | \(0.985941\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.8089 | 0.0895162 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −283.044 | −0.839894 | −0.419947 | − | 0.907549i | \(-0.637951\pi\) | ||||
−0.419947 | + | 0.907549i | \(0.637951\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −205.191 | −0.605282 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.4635i | 0.0717405i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 340.970i | − | 0.994080i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 214.566i | 0.618347i | 0.951006 | + | 0.309174i | \(0.100052\pi\) | ||||
−0.951006 | + | 0.309174i | \(0.899948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 627.491 | 1.79797 | 0.898984 | − | 0.437981i | \(-0.144306\pi\) | ||||
0.898984 | + | 0.437981i | \(0.144306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8781 | −0.0509347 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 61.3501i | 0.173796i | 0.996217 | + | 0.0868982i | \(0.0276955\pi\) | ||||
−0.996217 | + | 0.0868982i | \(0.972305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.7283 | −0.0412556 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −303.982 | −0.846748 | −0.423374 | − | 0.905955i | \(-0.639154\pi\) | ||||
−0.423374 | + | 0.905955i | \(0.639154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −277.481 | − | 230.923i | −0.768644 | − | 0.639677i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 185.178 | 0.510133 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 542.618i | − | 1.47852i | −0.673418 | − | 0.739262i | \(-0.735175\pi\) | ||
0.673418 | − | 0.739262i | \(-0.264825\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 82.6842i | − | 0.224076i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 232.718i | 0.627273i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 568.106 | 1.52307 | 0.761536 | − | 0.648123i | \(-0.224446\pi\) | ||||
0.761536 | + | 0.648123i | \(0.224446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.9873i | 0.0821944i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 322.531i | 0.851005i | 0.904957 | + | 0.425502i | \(0.139903\pi\) | ||||
−0.904957 | + | 0.425502i | \(0.860097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 285.175 | 0.748490 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −134.256 | −0.350539 | −0.175269 | − | 0.984521i | \(-0.556080\pi\) | ||||
−0.175269 | + | 0.984521i | \(0.556080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 3.35838i | − | 0.00867800i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 47.9667 | 0.123308 | 0.0616539 | − | 0.998098i | \(-0.480362\pi\) | ||||
0.0616539 | + | 0.998098i | \(0.480362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.9880 | −0.112501 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 323.001 | 0.821885 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 161.948i | − | 0.407928i | −0.978978 | − | 0.203964i | \(-0.934617\pi\) | ||
0.978978 | − | 0.203964i | \(-0.0653826\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 155.463 | + | 56.2273i | 0.389632 | + | 0.140921i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 203.228i | − | 0.506802i | −0.967361 | − | 0.253401i | \(-0.918451\pi\) | ||
0.967361 | − | 0.253401i | \(-0.0815492\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.83468i | − | 0.00703394i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.5352 | −0.0823962 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 651.844i | 1.59375i | 0.604144 | + | 0.796875i | \(0.293515\pi\) | ||||
−0.604144 | + | 0.796875i | \(0.706485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 152.197i | − | 0.370308i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.07465 | 0.00260206 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.5744 | −0.0853102 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 787.718 | 1.88000 | 0.939998 | − | 0.341180i | \(-0.110827\pi\) | ||||
0.939998 | + | 0.341180i | \(0.110827\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 93.6475i | 0.222441i | 0.993796 | + | 0.111220i | \(0.0354759\pi\) | ||||
−0.993796 | + | 0.111220i | \(0.964524\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 112.264i | 0.265400i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 169.242i | − | 0.396351i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.05648 | 0.0164487 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 546.360i | − | 1.26766i | −0.773474 | − | 0.633828i | \(-0.781483\pi\) | ||
0.773474 | − | 0.633828i | \(-0.218517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 843.569 | 1.94820 | 0.974098 | − | 0.226128i | \(-0.0726066\pi\) | ||||
0.974098 | + | 0.226128i | \(0.0726066\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 464.313 | + | 167.931i | 1.06250 | + | 0.384281i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 118.320i | − | 0.269521i | −0.990878 | − | 0.134761i | \(-0.956973\pi\) | ||
0.990878 | − | 0.134761i | \(-0.0430266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −149.304 | −0.338558 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 883.490i | 1.99433i | 0.0752227 | + | 0.997167i | \(0.476033\pi\) | ||||
−0.0752227 | + | 0.997167i | \(0.523967\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 331.648 | 0.741943 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 358.093i | 0.797534i | 0.917052 | + | 0.398767i | \(0.130562\pi\) | ||||
−0.917052 | + | 0.398767i | \(0.869438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 93.0204i | 0.206254i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 299.698i | 0.661585i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 329.340i | 0.720657i | 0.932825 | + | 0.360328i | \(0.117335\pi\) | ||||
−0.932825 | + | 0.360328i | \(0.882665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 47.7265i | 0.103979i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −613.352 | −1.33048 | −0.665240 | − | 0.746629i | \(-0.731671\pi\) | ||||
−0.665240 | + | 0.746629i | \(0.731671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 142.260i | − | 0.307258i | −0.988129 | − | 0.153629i | \(-0.950904\pi\) | ||
0.988129 | − | 0.153629i | \(-0.0490960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 435.333i | − | 0.932191i | −0.884734 | − | 0.466096i | \(-0.845660\pi\) | ||
0.884734 | − | 0.466096i | \(-0.154340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 412.164i | 0.878814i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 425.027i | − | 0.902392i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.77821i | 0.00798776i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 264.575 | 0.554666 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 80.5389 | 0.168140 | 0.0840698 | − | 0.996460i | \(-0.473208\pi\) | ||||
0.0840698 | + | 0.996460i | \(0.473208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.88585 | 0.00807870 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −226.110 | −0.468137 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 168.483 | 0.345960 | 0.172980 | − | 0.984925i | \(-0.444660\pi\) | ||||
0.172980 | + | 0.984925i | \(0.444660\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 177.434i | 0.362851i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 467.906 | 0.952965 | 0.476482 | − | 0.879184i | \(-0.341912\pi\) | ||||
0.476482 | + | 0.879184i | \(0.341912\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 82.7222 | 0.167793 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −68.6980 | −0.138225 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 487.521 | 0.976997 | 0.488498 | − | 0.872565i | \(-0.337545\pi\) | ||||
0.488498 | + | 0.872565i | \(0.337545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 197.429 | 0.394070 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 500.167i | − | 0.994369i | −0.867645 | − | 0.497184i | \(-0.834367\pi\) | ||
0.867645 | − | 0.497184i | \(-0.165633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 342.876 | 0.676283 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 254.504i | 0.500007i | 0.968245 | + | 0.250004i | \(0.0804318\pi\) | ||||
−0.968245 | + | 0.250004i | \(0.919568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 299.614 | 0.586329 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 182.203 | − | 503.773i | 0.355171 | − | 0.982014i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 126.298i | − | 0.244291i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 143.873 | 0.277213 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 676.089i | − | 1.29767i | −0.760927 | − | 0.648837i | \(-0.775256\pi\) | ||
0.760927 | − | 0.648837i | \(-0.224744\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.9971 | 0.0669162 | 0.0334581 | − | 0.999440i | \(-0.489348\pi\) | ||||
0.0334581 | + | 0.999440i | \(0.489348\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.56732 | −0.0143592 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −146.311 | −0.276580 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.22176i | − | 0.00230087i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.7786i | − | 0.0202226i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 358.141i | 0.666929i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 167.968 | 0.311630 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 411.260 | 0.760184 | 0.380092 | − | 0.924949i | \(-0.375892\pi\) | ||||
0.380092 | + | 0.924949i | \(0.375892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 117.054i | − | 0.215570i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 355.828 | 0.650508 | 0.325254 | − | 0.945627i | \(-0.394550\pi\) | ||||
0.325254 | + | 0.945627i | \(0.394550\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −192.410 | −0.350473 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −873.168 | − | 315.804i | −1.58470 | − | 0.573147i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 319.261 | 0.577325 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 823.586i | − | 1.47861i | −0.673370 | − | 0.739305i | \(-0.735154\pi\) | ||
0.673370 | − | 0.739305i | \(-0.264846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.437795i | − | 0.000783176i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 18.8376i | − | 0.0335787i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −753.891 | −1.33906 | −0.669531 | − | 0.742785i | \(-0.733505\pi\) | ||||
−0.669531 | + | 0.742785i | \(0.733505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 58.0299i | 0.102345i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 183.744i | − | 0.322924i | −0.986879 | − | 0.161462i | \(-0.948379\pi\) | ||
0.986879 | − | 0.161462i | \(-0.0516209\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −544.748 | −0.954024 | −0.477012 | − | 0.878897i | \(-0.658280\pi\) | ||||
−0.477012 | + | 0.878897i | \(0.658280\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 296.271 | 0.517052 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 68.9024i | 0.119415i | 0.998216 | + | 0.0597074i | \(0.0190168\pi\) | ||||
−0.998216 | + | 0.0597074i | \(0.980983\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −130.424 | −0.225257 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.54794 | 0.00954895 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −297.650 | −0.510548 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 110.222i | − | 0.187771i | −0.995583 | − | 0.0938857i | \(-0.970071\pi\) | ||
0.995583 | − | 0.0938857i | \(-0.0299288\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 79.8763 | + | 28.8894i | 0.135613 | + | 0.0490482i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.4475i | 0.0616708i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.0895i | − | 0.0254460i | −0.999919 | − | 0.0127230i | \(-0.995950\pi\) | ||
0.999919 | − | 0.0127230i | \(-0.00404996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 425.750 | 0.713150 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 557.545i | 0.930793i | 0.885102 | + | 0.465396i | \(0.154088\pi\) | ||||
−0.885102 | + | 0.465396i | \(0.845912\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 409.791i | 0.681849i | 0.940091 | + | 0.340924i | \(0.110740\pi\) | ||||
−0.940091 | + | 0.340924i | \(0.889260\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 468.586 | 0.777092 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 720.249 | 1.18657 | 0.593286 | − | 0.804992i | \(-0.297830\pi\) | ||||
0.593286 | + | 0.804992i | \(0.297830\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 425.214 | 0.698217 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.6346i | 0.0239520i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 662.266i | − | 1.08037i | −0.841547 | − | 0.540184i | \(-0.818354\pi\) | ||
0.841547 | − | 0.540184i | \(-0.181646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 656.881i | − | 1.06464i | −0.846544 | − | 0.532319i | \(-0.821321\pi\) | ||
0.846544 | − | 0.532319i | \(-0.178679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −454.752 | −0.734656 | −0.367328 | − | 0.930092i | \(-0.619727\pi\) | ||||
−0.367328 | + | 0.930092i | \(0.619727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 732.703i | 1.17988i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −604.748 | −0.970703 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −71.9155 | + | 198.839i | −0.114698 | + | 0.317128i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 10.3735i | − | 0.0164920i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 283.098 | 0.448650 | 0.224325 | − | 0.974514i | \(-0.427982\pi\) | ||||
0.224325 | + | 0.974514i | \(0.427982\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 473.799i | 0.748497i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.4631 | −0.0305544 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 78.1022i | 0.122226i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 470.172i | 0.733497i | 0.930320 | + | 0.366749i | \(0.119529\pi\) | ||||
−0.930320 | + | 0.366749i | \(0.880471\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 916.438i | 1.42525i | 0.701544 | + | 0.712627i | \(0.252495\pi\) | ||||
−0.701544 | + | 0.712627i | \(0.747505\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 582.366i | 0.900101i | 0.893003 | + | 0.450051i | \(0.148594\pi\) | ||||
−0.893003 | + | 0.450051i | \(0.851406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.37449i | 0.00211786i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.8980 | −0.0597512 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 228.094i | − | 0.349301i | −0.984630 | − | 0.174651i | \(-0.944120\pi\) | ||
0.984630 | − | 0.174651i | \(-0.0558796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 340.629i | − | 0.518462i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 250.379i | 0.379938i | 0.981790 | + | 0.189969i | \(0.0608387\pi\) | ||||
−0.981790 | + | 0.189969i | \(0.939161\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 830.133i | 1.25587i | 0.778264 | + | 0.627937i | \(0.216100\pi\) | ||||
−0.778264 | + | 0.627937i | \(0.783900\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.18279i | 0.00329229i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1269.96 | 1.90399 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 138.724 | 0.207360 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 216.462 | 0.322597 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1120.67 | 1.66519 | 0.832595 | − | 0.553882i | \(-0.186854\pi\) | ||||
0.832595 | + | 0.553882i | \(0.186854\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 500.474 | 0.739253 | 0.369626 | − | 0.929181i | \(-0.379486\pi\) | ||||
0.369626 | + | 0.929181i | \(0.379486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 535.275i | 0.788329i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 291.078 | 0.427427 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −253.863 | −0.371688 | −0.185844 | − | 0.982579i | \(-0.559502\pi\) | ||||
−0.185844 | + | 0.982579i | \(0.559502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 276.356 | 0.402265 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.4898 | 0.0500577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 210.478 | 0.304599 | 0.152300 | − | 0.988334i | \(-0.451332\pi\) | ||||
0.152300 | + | 0.988334i | \(0.451332\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 113.880i | 0.164329i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.7741 | −0.0412828 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 550.650i | 0.787768i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 146.797 | 0.209410 | 0.104705 | − | 0.994503i | \(-0.466610\pi\) | ||||
0.104705 | + | 0.994503i | \(0.466610\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.6023 | + | 109.497i | −0.0563333 | + | 0.155756i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 440.127i | − | 0.622527i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −803.083 | −1.13270 | −0.566349 | − | 0.824166i | \(-0.691644\pi\) | ||||
−0.566349 | + | 0.824166i | \(0.691644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 362.965i | − | 0.510500i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −116.175 | −0.162938 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 610.251 | 0.851117 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −637.968 | −0.887299 | −0.443650 | − | 0.896200i | \(-0.646317\pi\) | ||||
−0.443650 | + | 0.896200i | \(0.646317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 50.0364i | − | 0.0693986i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 360.862i | − | 0.499118i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 319.305i | 0.439210i | 0.975589 | + | 0.219605i | \(0.0704768\pi\) | ||||
−0.975589 | + | 0.219605i | \(0.929523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 582.037 | 0.798405 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.16872 | −0.00159879 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1185.22i | − | 1.61694i | −0.588537 | − | 0.808470i | \(-0.700296\pi\) | ||
0.588537 | − | 0.808470i | \(-0.299704\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −527.163 | −0.715283 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −182.023 | −0.246311 | −0.123155 | − | 0.992387i | \(-0.539301\pi\) | ||||
−0.123155 | + | 0.992387i | \(0.539301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.33312 | − | 23.0403i | 0.0112458 | − | 0.0310935i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −827.162 | −1.11327 | −0.556637 | − | 0.830756i | \(-0.687908\pi\) | ||||
−0.556637 | + | 0.830756i | \(0.687908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.30741i | − | 0.00844366i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 812.622i | 1.08494i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1154.06i | 1.53669i | 0.640034 | + | 0.768346i | \(0.278920\pi\) | ||||
−0.640034 | + | 0.768346i | \(0.721080\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 162.804 | 0.216207 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1361.46i | − | 1.79850i | −0.437435 | − | 0.899250i | \(-0.644113\pi\) | ||
0.437435 | − | 0.899250i | \(-0.355887\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 289.198i | − | 0.381025i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −646.107 | −0.849023 | −0.424512 | − | 0.905422i | \(-0.639554\pi\) | ||||
−0.424512 | + | 0.905422i | \(0.639554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −186.898 | −0.244952 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.159268i | − | 0.000207650i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1226.28 | −1.59464 | −0.797318 | − | 0.603559i | \(-0.793749\pi\) | ||||
−0.797318 | + | 0.603559i | \(0.793749\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 300.216 | 0.389385 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 544.100 | 0.703881 | 0.351940 | − | 0.936022i | \(-0.385522\pi\) | ||||
0.351940 | + | 0.936022i | \(0.385522\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 53.3225i | − | 0.0686261i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 303.723 | + | 109.849i | 0.389888 | + | 0.141013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 87.8656i | − | 0.112504i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1377.89i | − | 1.75976i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1035.63 | 1.31592 | 0.657958 | − | 0.753054i | \(-0.271420\pi\) | ||||
0.657958 | + | 0.753054i | \(0.271420\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 700.521i | − | 0.887859i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 431.676i | − | 0.545734i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.0823 | −0.0316296 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1237.45 | 1.55264 | 0.776318 | − | 0.630341i | \(-0.217085\pi\) | ||||
0.776318 | + | 0.630341i | \(0.217085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.0680 | 0.0488961 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 687.533i | 0.858344i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 383.211i | 0.477224i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 388.363i | 0.481243i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 456.534 | 0.564319 | 0.282160 | − | 0.959367i | \(-0.408949\pi\) | ||||
0.282160 | + | 0.959367i | \(0.408949\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1238.50i | − | 1.52712i | −0.645735 | − | 0.763562i | \(-0.723449\pi\) | ||
0.645735 | − | 0.763562i | \(-0.276551\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 539.193 | 0.663214 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3363 | + | 4.46175i | 0.0150995 | + | 0.00546114i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 13.1957i | − | 0.0161120i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 503.379 | 0.613130 | 0.306565 | − | 0.951850i | \(-0.400820\pi\) | ||||
0.306565 | + | 0.951850i | \(0.400820\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 864.599i | 1.05055i | 0.850934 | + | 0.525273i | \(0.176037\pi\) | ||||
−0.850934 | + | 0.525273i | \(0.823963\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1528.37 | −1.84809 | −0.924047 | − | 0.382280i | \(-0.875139\pi\) | ||||
−0.924047 | + | 0.382280i | \(0.875139\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 696.807i | − | 0.840539i | −0.907399 | − | 0.420270i | \(-0.861935\pi\) | ||
0.907399 | − | 0.420270i | \(-0.138065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 177.070i | − | 0.213080i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 51.9578i | 0.0623744i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 126.048i | 0.150595i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1372.41i | 1.63577i | 0.575380 | + | 0.817886i | \(0.304854\pi\) | ||||
−0.575380 | + | 0.817886i | \(0.695146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1547.24 | −1.83976 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 475.858i | − | 0.564482i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 389.574i | 0.459946i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 387.748i | − | 0.456711i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 159.255i | − | 0.187139i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 152.915i | − | 0.179268i | −0.995975 | − | 0.0896339i | \(-0.971430\pi\) | ||
0.995975 | − | 0.0896339i | \(-0.0285697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 621.971 | 0.725754 | 0.362877 | − | 0.931837i | \(-0.381795\pi\) | ||||
0.362877 | + | 0.931837i | \(0.381795\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 710.294 | 0.826885 | 0.413442 | − | 0.910530i | \(-0.364326\pi\) | ||||
0.413442 | + | 0.910530i | \(0.364326\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −147.907 | −0.171785 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −450.250 | −0.521726 | −0.260863 | − | 0.965376i | \(-0.584007\pi\) | ||||
−0.260863 | + | 0.965376i | \(0.584007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −581.909 | −0.671175 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 408.339i | 0.469895i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 61.0844 | 0.0701313 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 608.551 | 0.697080 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 687.264 | 0.783654 | 0.391827 | − | 0.920039i | \(-0.371843\pi\) | ||||
0.391827 | + | 0.920039i | \(0.371843\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 468.561 | 0.533062 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −848.052 | −0.962602 | −0.481301 | − | 0.876555i | \(-0.659836\pi\) | ||||
−0.481301 | + | 0.876555i | \(0.659836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 267.540i | 0.302990i | 0.988458 | + | 0.151495i | \(0.0484088\pi\) | ||||
−0.988458 | + | 0.151495i | \(0.951591\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1189.74 | −1.34130 | −0.670651 | − | 0.741773i | \(-0.733985\pi\) | ||||
−0.670651 | + | 0.741773i | \(0.733985\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 599.944i | 0.674853i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −74.2210 | −0.0833008 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −412.379 | − | 149.148i | −0.461791 | − | 0.167019i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.5105i | 0.0373584i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 218.473 | 0.243018 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 92.0722i | − | 0.102189i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00752 | −0.00665285 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1069.54 | −1.17921 | −0.589605 | − | 0.807692i | \(-0.700717\pi\) | ||||
−0.589605 | + | 0.807692i | \(0.700717\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −500.377 | −0.550469 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1455.41i | − | 1.59760i | −0.601597 | − | 0.798800i | \(-0.705469\pi\) | ||
0.601597 | − | 0.798800i | \(-0.294531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.09589i | 0.00777206i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 679.522i | 0.741027i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −104.189 | −0.113372 | −0.0566862 | − | 0.998392i | \(-0.518053\pi\) | ||||
−0.0566862 | + | 0.998392i | \(0.518053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 753.771 | 0.818426 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.1813i | 0.0110307i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −56.8860 | −0.0613657 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −59.7100 | −0.0642734 | −0.0321367 | − | 0.999483i | \(-0.510231\pi\) | ||||
−0.0321367 | + | 0.999483i | \(0.510231\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 198.357 | − | 548.437i | 0.213058 | − | 0.589084i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.8205 | 0.0266028 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 907.749i | 0.968783i | 0.874851 | + | 0.484391i | \(0.160959\pi\) | ||||
−0.874851 | + | 0.484391i | \(0.839041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 535.710i | 0.570511i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.4652i | 0.0642563i | 0.999484 | + | 0.0321282i | \(0.0102285\pi\) | ||||
−0.999484 | + | 0.0321282i | \(0.989772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −441.744 | −0.468445 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 96.4321i | 0.101829i | 0.998703 | + | 0.0509145i | \(0.0162136\pi\) | ||||
−0.998703 | + | 0.0509145i | \(0.983786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 44.4041i | − | 0.0467904i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −668.115 | −0.702539 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −334.185 | −0.350667 | −0.175333 | − | 0.984509i | \(-0.556100\pi\) | ||||
−0.175333 | + | 0.984509i | \(0.556100\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 543.855i | 0.568291i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 320.188 | 0.333877 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 941.014 | 0.979203 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 923.863 | 0.959360 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1230.05i | − | 1.27203i | −0.771676 | − | 0.636016i | \(-0.780581\pi\) | ||
0.771676 | − | 0.636016i | \(-0.219419\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −61.5072 | − | 22.2457i | −0.0634749 | − | 0.0229574i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1215.04i | − | 1.25133i | −0.780091 | − | 0.625667i | \(-0.784827\pi\) | ||
0.780091 | − | 0.625667i | \(-0.215173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 74.8406i | − | 0.0769174i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −337.236 | −0.345175 | −0.172588 | − | 0.984994i | \(-0.555213\pi\) | ||||
−0.172588 | + | 0.984994i | \(0.555213\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 773.481i | − | 0.790072i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 212.483i | 0.216598i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 73.3754 | 0.0746443 | 0.0373222 | − | 0.999303i | \(-0.488117\pi\) | ||||
0.0373222 | + | 0.999303i | \(0.488117\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 200.820 | 0.203465 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.9423 | −0.0181419 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 635.844i | 0.641618i | 0.947144 | + | 0.320809i | \(0.103955\pi\) | ||||
−0.947144 | + | 0.320809i | \(0.896045\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 59.4421i | − | 0.0598611i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1405.38i | − | 1.40960i | −0.709404 | − | 0.704802i | \(-0.751036\pi\) | ||
0.709404 | − | 0.704802i | \(-0.248964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −172.790 | −0.172963 |
(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 | 1900.3.g.c.949.9 | 24 | ||
5.2 | odd | 4 | 380.3.e.a.341.8 | yes | 12 | ||
5.3 | odd | 4 | 1900.3.e.f.1101.5 | 12 | |||
5.4 | even | 2 | inner | 1900.3.g.c.949.16 | 24 | ||
15.2 | even | 4 | 3420.3.o.a.721.12 | 12 | |||
19.18 | odd | 2 | inner | 1900.3.g.c.949.15 | 24 | ||
20.7 | even | 4 | 1520.3.h.b.721.5 | 12 | |||
95.18 | even | 4 | 1900.3.e.f.1101.8 | 12 | |||
95.37 | even | 4 | 380.3.e.a.341.5 | ✓ | 12 | ||
95.94 | odd | 2 | inner | 1900.3.g.c.949.10 | 24 | ||
285.227 | odd | 4 | 3420.3.o.a.721.11 | 12 | |||
380.227 | odd | 4 | 1520.3.h.b.721.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.e.a.341.5 | ✓ | 12 | 95.37 | even | 4 | ||
380.3.e.a.341.8 | yes | 12 | 5.2 | odd | 4 | ||
1520.3.h.b.721.5 | 12 | 20.7 | even | 4 | |||
1520.3.h.b.721.8 | 12 | 380.227 | odd | 4 | |||
1900.3.e.f.1101.5 | 12 | 5.3 | odd | 4 | |||
1900.3.e.f.1101.8 | 12 | 95.18 | even | 4 | |||
1900.3.g.c.949.9 | 24 | 1.1 | even | 1 | trivial | ||
1900.3.g.c.949.10 | 24 | 95.94 | odd | 2 | inner | ||
1900.3.g.c.949.15 | 24 | 19.18 | odd | 2 | inner | ||
1900.3.g.c.949.16 | 24 | 5.4 | even | 2 | inner | ||
3420.3.o.a.721.11 | 12 | 285.227 | odd | 4 | |||
3420.3.o.a.721.12 | 12 | 15.2 | even | 4 |