Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(3005,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.3005");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3005.52 | ||
Character | \(\chi\) | \(=\) | 6012.3005 |
Dual form | 6012.2.h.a.3005.51 |
$q$-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 \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).
\(n\) | \(3007\) | \(3341\) | \(4681\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.47368 | 1.55348 | 0.776739 | − | 0.629822i | \(-0.216872\pi\) | ||||
0.776739 | + | 0.629822i | \(0.216872\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.93299 | 1.48653 | 0.743264 | − | 0.668998i | \(-0.233276\pi\) | ||||
0.743264 | + | 0.668998i | \(0.233276\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.34291i | 1.30944i | 0.755873 | + | 0.654718i | \(0.227213\pi\) | ||||
−0.755873 | + | 0.654718i | \(0.772787\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.788280i | 0.218629i | 0.994007 | + | 0.109315i | \(0.0348656\pi\) | ||||
−0.994007 | + | 0.109315i | \(0.965134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.32815 | 1.29227 | 0.646133 | − | 0.763225i | \(-0.276385\pi\) | ||||
0.646133 | + | 0.763225i | \(0.276385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.26219 | 0.977812 | 0.488906 | − | 0.872336i | \(-0.337396\pi\) | ||||
0.488906 | + | 0.872336i | \(0.337396\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.69278 | 1.39554 | 0.697770 | − | 0.716321i | \(-0.254176\pi\) | ||||
0.697770 | + | 0.716321i | \(0.254176\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.06648 | 1.41330 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.99865i | − | 1.11392i | −0.830539 | − | 0.556961i | \(-0.811967\pi\) | ||
0.830539 | − | 0.556961i | \(-0.188033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.79664 | −1.22071 | −0.610356 | − | 0.792127i | \(-0.708974\pi\) | ||||
−0.610356 | + | 0.792127i | \(0.708974\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.6619 | 2.30929 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.66119i | 0.766296i | 0.923687 | + | 0.383148i | \(0.125160\pi\) | ||||
−0.923687 | + | 0.383148i | \(0.874840\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.62083 | −0.721652 | −0.360826 | − | 0.932633i | \(-0.617505\pi\) | ||||
−0.360826 | + | 0.932633i | \(0.617505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.6022i | − | 1.76931i | −0.466243 | − | 0.884657i | \(-0.654393\pi\) | ||
0.466243 | − | 0.884657i | \(-0.345607\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 12.6481i | − | 1.84491i | −0.386106 | − | 0.922454i | \(-0.626180\pi\) | ||
0.386106 | − | 0.922454i | \(-0.373820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.46837 | 1.20977 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.406978 | −0.0559028 | −0.0279514 | − | 0.999609i | \(-0.508898\pi\) | ||||
−0.0279514 | + | 0.999609i | \(0.508898\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.0859i | 2.03418i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.56137 | −0.854218 | −0.427109 | − | 0.904200i | \(-0.640468\pi\) | ||||
−0.427109 | + | 0.904200i | \(0.640468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.94490 | −0.633129 | −0.316565 | − | 0.948571i | \(-0.602529\pi\) | ||||
−0.316565 | + | 0.948571i | \(0.602529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.73823i | 0.339636i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.40874i | 0.416444i | 0.978082 | + | 0.208222i | \(0.0667677\pi\) | ||||
−0.978082 | + | 0.208222i | \(0.933232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.507955 | 0.0602832 | 0.0301416 | − | 0.999546i | \(-0.490404\pi\) | ||||
0.0301416 | + | 0.999546i | \(0.490404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.74265i | − | 0.321003i | −0.987036 | − | 0.160501i | \(-0.948689\pi\) | ||
0.987036 | − | 0.160501i | \(-0.0513111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.0806i | 1.94652i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.44663i | 0.837812i | 0.908030 | + | 0.418906i | \(0.137586\pi\) | ||||
−0.908030 | + | 0.418906i | \(0.862414\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.51617 | −0.715242 | −0.357621 | − | 0.933867i | \(-0.616412\pi\) | ||||
−0.357621 | + | 0.933867i | \(0.616412\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.5083 | 2.00751 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.1276i | 1.60352i | 0.597648 | + | 0.801759i | \(0.296102\pi\) | ||||
−0.597648 | + | 0.801759i | \(0.703898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.10029i | 0.324999i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.8055 | 1.51901 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.32370 | −0.337471 | −0.168735 | − | 0.985661i | \(-0.553968\pi\) | ||||
−0.168735 | + | 0.985661i | \(0.553968\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.28457 | 0.923849 | 0.461925 | − | 0.886919i | \(-0.347159\pi\) | ||||
0.461925 | + | 0.886919i | \(0.347159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.46976i | − | 0.834551i | −0.908780 | − | 0.417275i | \(-0.862985\pi\) | ||
0.908780 | − | 0.417275i | \(-0.137015\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.4198i | − | 1.49069i | −0.666680 | − | 0.745344i | \(-0.732285\pi\) | ||
0.666680 | − | 0.745344i | \(-0.267715\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.11253i | 0.872822i | 0.899747 | + | 0.436411i | \(0.143751\pi\) | ||||
−0.899747 | + | 0.436411i | \(0.856249\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.7429 | −1.76318 | −0.881591 | − | 0.472013i | \(-0.843527\pi\) | ||||
−0.881591 | + | 0.472013i | \(0.843527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.2486 | 2.16794 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.9555 | 1.92099 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.86087 | −0.714625 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.17830 | 0.642047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.9978 | −1.68579 | −0.842893 | − | 0.538081i | \(-0.819149\pi\) | ||||
−0.842893 | + | 0.538081i | \(0.819149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.1680 | −1.06312 | −0.531562 | − | 0.847019i | \(-0.678395\pi\) | ||||
−0.531562 | + | 0.847019i | \(0.678395\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.7631 | 1.45355 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.83479i | 0.413064i | 0.978440 | + | 0.206532i | \(0.0662178\pi\) | ||||
−0.978440 | + | 0.206532i | \(0.933782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2167i | 1.20585i | 0.797799 | + | 0.602923i | \(0.205997\pi\) | ||||
−0.797799 | + | 0.602923i | \(0.794003\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.42343 | −0.286281 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 20.8374i | − | 1.73045i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.40998 | −0.197433 | −0.0987165 | − | 0.995116i | \(-0.531474\pi\) | ||||
−0.0987165 | + | 0.995116i | \(0.531474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.37124i | 0.355726i | 0.984055 | + | 0.177863i | \(0.0569184\pi\) | ||||
−0.984055 | + | 0.177863i | \(0.943082\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.6094 | −1.89635 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.86364 | 0.148735 | 0.0743673 | − | 0.997231i | \(-0.476306\pi\) | ||||
0.0743673 | + | 0.997231i | \(0.476306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.3226 | 2.07451 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.5643i | 1.76737i | 0.468079 | + | 0.883686i | \(0.344946\pi\) | ||||
−0.468079 | + | 0.883686i | \(0.655054\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.99239 | − | 8.19464i | −0.773234 | − | 0.634121i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3786 | 0.952201 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 10.0210i | − | 0.761885i | −0.924599 | − | 0.380943i | \(-0.875600\pi\) | ||
0.924599 | − | 0.380943i | \(-0.124400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.7924 | 2.10091 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.7422i | − | 1.40086i | −0.713723 | − | 0.700428i | \(-0.752992\pi\) | ||
0.713723 | − | 0.700428i | \(-0.247008\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2459 | −0.761572 | −0.380786 | − | 0.924663i | \(-0.624347\pi\) | ||||
−0.380786 | + | 0.924663i | \(0.624347\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.1915i | 1.19042i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.1397i | 1.69214i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.2270i | 1.39122i | 0.718421 | + | 0.695608i | \(0.244865\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.61976i | 0.404519i | 0.979332 | + | 0.202259i | \(0.0648284\pi\) | ||||
−0.979332 | + | 0.202259i | \(0.935172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1539 | 1.07967 | 0.539836 | − | 0.841770i | \(-0.318486\pi\) | ||||
0.539836 | + | 0.841770i | \(0.318486\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.38899 | −0.665568 | −0.332784 | − | 0.943003i | \(-0.607988\pi\) | ||||
−0.332784 | + | 0.943003i | \(0.607988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 23.5926i | − | 1.65588i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0513 | −1.12107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.5103i | 1.28038i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.78342 | −0.398147 | −0.199074 | − | 0.979985i | \(-0.563793\pi\) | ||||
−0.199074 | + | 0.979985i | \(0.563793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 40.3023i | − | 2.74859i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.7311 | −1.81462 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.20007i | 0.282528i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.3088 | −1.29301 | −0.646506 | − | 0.762909i | \(-0.723770\pi\) | ||||
−0.646506 | + | 0.762909i | \(0.723770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.98586 | −0.530040 | −0.265020 | − | 0.964243i | \(-0.585379\pi\) | ||||
−0.265020 | + | 0.964243i | \(0.585379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.0329 | 1.58814 | 0.794070 | − | 0.607826i | \(-0.207958\pi\) | ||||
0.794070 | + | 0.607826i | \(0.207958\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.9229i | − | 0.977630i | −0.872388 | − | 0.488815i | \(-0.837429\pi\) | ||
0.872388 | − | 0.488815i | \(-0.162571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 43.9353i | − | 2.86603i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.14553i | 0.0740981i | 0.999313 | + | 0.0370491i | \(0.0117958\pi\) | ||||
−0.999313 | + | 0.0370491i | \(0.988204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.14226i | − | 0.588905i | −0.955666 | − | 0.294452i | \(-0.904863\pi\) | ||
0.955666 | − | 0.294452i | \(-0.0951372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29.4164 | 1.87935 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.35979i | 0.213779i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.57929i | − | 0.352162i | −0.984376 | − | 0.176081i | \(-0.943658\pi\) | ||
0.984376 | − | 0.176081i | \(-0.0563420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.0661i | 1.82737i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.5972 | −1.40957 | −0.704787 | − | 0.709419i | \(-0.748957\pi\) | ||||
−0.704787 | + | 0.709419i | \(0.748957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.3324i | 1.13912i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.8743i | − | 0.855524i | −0.903891 | − | 0.427762i | \(-0.859302\pi\) | ||
0.903891 | − | 0.427762i | \(-0.140698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.41371 | −0.0868438 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.5090 | −0.762690 | −0.381345 | − | 0.924433i | \(-0.624539\pi\) | ||||
−0.381345 | + | 0.924433i | \(0.624539\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.7830i | − | 0.776512i | −0.921552 | − | 0.388256i | \(-0.873078\pi\) | ||
0.921552 | − | 0.388256i | \(-0.126922\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.6891i | 1.85062i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.74046i | 0.104574i | 0.998632 | + | 0.0522869i | \(0.0166510\pi\) | ||||
−0.998632 | + | 0.0522869i | \(0.983349\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.8524i | − | 1.42292i | −0.702728 | − | 0.711458i | \(-0.748035\pi\) | ||
0.702728 | − | 0.711458i | \(-0.251965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3744 | −1.27057 | −0.635287 | − | 0.772276i | \(-0.719118\pi\) | ||||
−0.635287 | + | 0.772276i | \(0.719118\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.1736 | −1.07276 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.3892 | 0.669953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.0998i | − | 0.823719i | −0.911247 | − | 0.411859i | \(-0.864880\pi\) | ||
0.911247 | − | 0.411859i | \(-0.135120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.7921 | −1.32701 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.27578i | 0.305106i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 45.6311i | − | 2.63013i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.1770 | −0.983553 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.02299i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2184i | 0.579432i | 0.957113 | + | 0.289716i | \(0.0935608\pi\) | ||||
−0.957113 | + | 0.289716i | \(0.906439\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6078i | 0.938726i | 0.883005 | + | 0.469363i | \(0.155516\pi\) | ||||
−0.883005 | + | 0.469363i | \(0.844484\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 25.5050i | − | 1.43250i | −0.697842 | − | 0.716252i | \(-0.745856\pi\) | ||
0.697842 | − | 0.716252i | \(-0.254144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.0516 | 1.45861 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.7096 | 1.26359 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.57036i | 0.308988i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 49.7446i | − | 2.74251i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.8955i | 1.53328i | 0.642080 | + | 0.766638i | \(0.278072\pi\) | ||||
−0.642080 | + | 0.766638i | \(0.721928\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.8409i | 0.646937i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.8957 | 1.41063 | 0.705314 | − | 0.708895i | \(-0.250806\pi\) | ||||
0.705314 | + | 0.708895i | \(0.250806\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 29.5172i | − | 1.59845i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.77508 | 0.311825 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.8704 | 1.49616 | 0.748081 | − | 0.663608i | \(-0.230976\pi\) | ||||
0.748081 | + | 0.663608i | \(0.230976\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6541i | 1.53382i | 0.641757 | + | 0.766908i | \(0.278206\pi\) | ||||
−0.641757 | + | 0.766908i | \(0.721794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.19480i | 0.223267i | 0.993749 | + | 0.111633i | \(0.0356083\pi\) | ||||
−0.993749 | + | 0.111633i | \(0.964392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.76447 | 0.0936486 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.52346i | 0.449851i | 0.974376 | + | 0.224925i | \(0.0722138\pi\) | ||||
−0.974376 | + | 0.224925i | \(0.927786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.833772 | −0.0438827 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.52710i | − | 0.498671i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.593513 | −0.0309812 | −0.0154906 | − | 0.999880i | \(-0.504931\pi\) | ||||
−0.0154906 | + | 0.999880i | \(0.504931\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.60064 | −0.0831011 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8382i | 1.28607i | 0.765836 | + | 0.643036i | \(0.222325\pi\) | ||||
−0.765836 | + | 0.643036i | \(0.777675\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.72861 | 0.243536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.1994i | 1.55124i | 0.631200 | + | 0.775620i | \(0.282563\pi\) | ||||
−0.631200 | + | 0.775620i | \(0.717437\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 33.7964i | − | 1.72692i | −0.504420 | − | 0.863458i | \(-0.668294\pi\) | ||
0.504420 | − | 0.863458i | \(-0.331706\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 59.3326i | 3.02387i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.1882 | 1.02358 | 0.511791 | − | 0.859110i | \(-0.328982\pi\) | ||||
0.511791 | + | 0.859110i | \(0.328982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.6601 | 1.80341 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.8673i | 1.30152i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.5320 | −0.930093 | −0.465046 | − | 0.885286i | \(-0.653962\pi\) | ||||
−0.465046 | + | 0.885286i | \(0.653962\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0402 | 0.801007 | 0.400504 | − | 0.916295i | \(-0.368835\pi\) | ||||
0.400504 | + | 0.916295i | \(0.368835\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.35765i | − | 0.266884i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.2432 | −1.00342 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.4443 | 1.40648 | 0.703239 | − | 0.710953i | \(-0.251736\pi\) | ||||
0.703239 | + | 0.710953i | \(0.251736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.8058 | −1.26982 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.6351 | −1.11111 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.24873i | 0.451830i | 0.974147 | + | 0.225915i | \(0.0725372\pi\) | ||||
−0.974147 | + | 0.225915i | \(0.927463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.8984 | 1.74958 | 0.874791 | − | 0.484501i | \(-0.160999\pi\) | ||||
0.874791 | + | 0.484501i | \(0.160999\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37.6513 | 1.82636 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.4482 | −0.941165 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 14.0918i | − | 0.678779i | −0.940646 | − | 0.339389i | \(-0.889780\pi\) | ||
0.940646 | − | 0.339389i | \(-0.110220\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.284485 | −0.0136715 | −0.00683574 | − | 0.999977i | \(-0.502176\pi\) | ||||
−0.00683574 | + | 0.999977i | \(0.502176\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.5259 | 1.36458 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.454366i | 0.0216857i | 0.999941 | + | 0.0108428i | \(0.00345145\pi\) | ||||
−0.999941 | + | 0.0108428i | \(0.996549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.4825 | 1.59080 | 0.795400 | − | 0.606085i | \(-0.207261\pi\) | ||||
0.795400 | + | 0.606085i | \(0.207261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 52.5483i | 2.49103i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3532i | 0.866143i | 0.901360 | + | 0.433072i | \(0.142570\pi\) | ||||
−0.901360 | + | 0.433072i | \(0.857430\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.0678i | − | 0.944957i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7694i | 0.504879i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.3285i | − | 0.576704i | −0.957525 | − | 0.288352i | \(-0.906893\pi\) | ||
0.957525 | − | 0.288352i | \(-0.0931073\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.7458i | 0.547058i | 0.961864 | + | 0.273529i | \(0.0881910\pi\) | ||||
−0.961864 | + | 0.273529i | \(0.911809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 19.8903i | − | 0.924380i | −0.886781 | − | 0.462190i | \(-0.847064\pi\) | ||
0.886781 | − | 0.462190i | \(-0.152936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.2627i | 1.30784i | 0.756563 | + | 0.653921i | \(0.226877\pi\) | ||||
−0.756563 | + | 0.653921i | \(0.773123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4065i | 0.619056i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.3872 | 2.31680 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.1187 | 1.38194 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.7430 | −1.54176 | −0.770879 | − | 0.636981i | \(-0.780183\pi\) | ||||
−0.770879 | + | 0.636981i | \(0.780183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.67432 | −0.167535 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.5455 | −0.524254 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.3213i | 1.05679i | 0.848999 | + | 0.528395i | \(0.177206\pi\) | ||||
−0.848999 | + | 0.528395i | \(0.822794\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.22659i | 0.145614i | 0.997346 | + | 0.0728070i | \(0.0231957\pi\) | ||||
−0.997346 | + | 0.0728070i | \(0.976804\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 31.9617i | − | 1.43948i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.99778 | 0.0896126 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 35.1020i | − | 1.57138i | −0.618621 | − | 0.785690i | \(-0.712308\pi\) | ||
0.618621 | − | 0.785690i | \(-0.287692\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 2.35604i | − | 0.105051i | −0.998620 | − | 0.0525253i | \(-0.983273\pi\) | ||
0.998620 | − | 0.0525253i | \(-0.0167270\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.2517 | 1.43518 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.04422i | 0.179257i | 0.995975 | + | 0.0896284i | \(0.0285679\pi\) | ||||
−0.995975 | + | 0.0896284i | \(0.971432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.7868i | − | 0.477180i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 29.4213i | − | 1.29646i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 54.9294 | 2.41579 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.7536 | 1.52258 | 0.761292 | − | 0.648410i | \(-0.224566\pi\) | ||||
0.761292 | + | 0.648410i | \(0.224566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.98394 | 0.305386 | 0.152693 | − | 0.988274i | \(-0.451205\pi\) | ||||
0.152693 | + | 0.988274i | \(0.451205\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.2135 | −1.57749 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7933 | 0.947534 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.64250i | − | 0.157774i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 53.5635i | − | 2.31575i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.7774i | 1.58411i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1092i | 0.563606i | 0.959472 | + | 0.281803i | \(0.0909325\pi\) | ||||
−0.959472 | + | 0.281803i | \(0.909067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.6541i | 1.35591i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 23.7068i | − | 1.01363i | −0.862055 | − | 0.506815i | \(-0.830823\pi\) | ||
0.862055 | − | 0.506815i | \(-0.169177\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 25.5674i | − | 1.08921i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.2875i | 1.24543i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 13.9063i | − | 0.589230i | −0.955616 | − | 0.294615i | \(-0.904809\pi\) | ||
0.955616 | − | 0.294615i | \(-0.0951914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.14575 | 0.386824 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.83747i | 0.203875i | 0.994791 | + | 0.101938i | \(0.0325042\pi\) | ||||
−0.994791 | + | 0.101938i | \(0.967496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −65.1069 | −2.73907 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.14692 | 0.0900037 | 0.0450019 | − | 0.998987i | \(-0.485671\pi\) | ||||
0.0450019 | + | 0.998987i | \(0.485671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.4846i | 1.56868i | 0.620329 | + | 0.784342i | \(0.286999\pi\) | ||||
−0.620329 | + | 0.784342i | \(0.713001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 47.2944 | 1.97231 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.9723 | 0.540042 | 0.270021 | − | 0.962854i | \(-0.412969\pi\) | ||||
0.270021 | + | 0.962854i | \(0.412969\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.6280 | −1.06323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.76747i | − | 0.0732012i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.5888 | −1.17999 | −0.589994 | − | 0.807408i | \(-0.700870\pi\) | ||||
−0.589994 | + | 0.807408i | \(0.700870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.9685 | −1.19363 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.67910 | 0.192148 | 0.0960739 | − | 0.995374i | \(-0.469371\pi\) | ||||
0.0960739 | + | 0.995374i | \(0.469371\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 72.7929 | 2.98422 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.9092i | 1.09948i | 0.835336 | + | 0.549740i | \(0.185273\pi\) | ||||
−0.835336 | + | 0.549740i | \(0.814727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5403 | 0.633902 | 0.316951 | − | 0.948442i | \(-0.397341\pi\) | ||||
0.316951 | + | 0.948442i | \(0.397341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.3062 | −1.11015 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.06302i | − | 0.164913i | −0.996595 | − | 0.0824564i | \(-0.973723\pi\) | ||
0.996595 | − | 0.0824564i | \(-0.0262765\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.97020 | 0.403351 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.8370 | 0.962769 | 0.481384 | − | 0.876510i | \(-0.340134\pi\) | ||||
0.481384 | + | 0.876510i | \(0.340134\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.21006i | 0.0487152i | 0.999703 | + | 0.0243576i | \(0.00775403\pi\) | ||||
−0.999703 | + | 0.0243576i | \(0.992246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5597i | 0.745977i | 0.927836 | + | 0.372988i | \(0.121667\pi\) | ||||
−0.927836 | + | 0.372988i | \(0.878333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 59.4965i | 2.38367i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.3973 | −0.415890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.8356i | 0.990258i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.6100 | −1.65647 | −0.828234 | − | 0.560382i | \(-0.810654\pi\) | ||||
−0.828234 | + | 0.560382i | \(0.810654\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −65.9925 | −2.61883 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.67544i | 0.264491i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.20133 | 0.363431 | 0.181715 | − | 0.983351i | \(-0.441835\pi\) | ||||
0.181715 | + | 0.983351i | \(0.441835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.18930i | − | 0.204646i | −0.994751 | − | 0.102323i | \(-0.967372\pi\) | ||
0.994751 | − | 0.102323i | \(-0.0326275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.7966 | −1.25005 | −0.625027 | − | 0.780603i | \(-0.714912\pi\) | ||||
−0.625027 | + | 0.780603i | \(0.714912\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.4954i | − | 1.11854i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.2069i | 1.61255i | 0.591542 | + | 0.806275i | \(0.298520\pi\) | ||||
−0.591542 | + | 0.806275i | \(0.701480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42.2678 | −1.65154 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.0275 | 1.32552 | 0.662761 | − | 0.748831i | \(-0.269384\pi\) | ||||
0.662761 | + | 0.748831i | \(0.269384\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.80722i | − | 0.342561i | −0.985222 | − | 0.171281i | \(-0.945210\pi\) | ||
0.985222 | − | 0.171281i | \(-0.0547905\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 58.2298 | 2.25805 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 40.1476i | − | 1.55452i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.4752i | − | 0.829043i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.37773i | − | 0.322938i | −0.986878 | − | 0.161469i | \(-0.948377\pi\) | ||
0.986878 | − | 0.161469i | \(-0.0516231\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.16558i | − | 0.198529i | −0.995061 | − | 0.0992647i | \(-0.968351\pi\) | ||
0.995061 | − | 0.0992647i | \(-0.0316490\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0721 | −0.501660 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.6447 | 0.675157 | 0.337579 | − | 0.941297i | \(-0.390392\pi\) | ||||
0.337579 | + | 0.941297i | \(0.390392\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.7945i | 0.641686i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.320813i | − | 0.0122220i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.5617i | 1.69521i | 0.530629 | + | 0.847604i | \(0.321956\pi\) | ||||
−0.530629 | + | 0.847604i | \(0.678044\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 49.3844i | 1.87326i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.6205 | −0.932567 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.36642i | 0.240456i | 0.992746 | + | 0.120228i | \(0.0383626\pi\) | ||||
−0.992746 | + | 0.120228i | \(0.961637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.8669i | 0.749293i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.5161 | 1.37333 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12.1344i | − | 0.455718i | −0.973694 | − | 0.227859i | \(-0.926828\pi\) | ||
0.973694 | − | 0.227859i | \(-0.0731725\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −45.4884 | −1.70355 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.8919 | −0.444732 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.35686 | −0.162483 | −0.0812417 | − | 0.996694i | \(-0.525889\pi\) | ||||
−0.0812417 | + | 0.996694i | \(0.525889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 33.3115i | − | 1.24058i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 42.3893i | − | 1.57430i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 47.6676i | − | 1.76789i | −0.467587 | − | 0.883947i | \(-0.654876\pi\) | ||
0.467587 | − | 0.883947i | \(-0.345124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 61.8181i | − | 2.28642i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.4188 | −0.643377 | −0.321688 | − | 0.946846i | \(-0.604250\pi\) | ||||
−0.321688 | + | 0.946846i | \(0.604250\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.8039 | −0.545307 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.8508i | 0.399153i | 0.979882 | + | 0.199576i | \(0.0639566\pi\) | ||||
−0.979882 | + | 0.199576i | \(0.936043\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.2937i | − | 0.487699i | −0.969813 | − | 0.243850i | \(-0.921590\pi\) | ||
0.969813 | − | 0.243850i | \(-0.0784103\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.37150 | −0.306708 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 60.6458i | − | 2.21595i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 7.66618i | − | 0.279743i | −0.990170 | − | 0.139871i | \(-0.955331\pi\) | ||
0.990170 | − | 0.139871i | \(-0.0446689\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.1843i | 0.552613i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.28794 | 0.0468109 | 0.0234055 | − | 0.999726i | \(-0.492549\pi\) | ||||
0.0234055 | + | 0.999726i | \(0.492549\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1314i | 0.693511i | 0.937956 | + | 0.346756i | \(0.112717\pi\) | ||||
−0.937956 | + | 0.346756i | \(0.887283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.8395i | 1.29748i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.17219i | − | 0.186757i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.6056i | 0.923360i | 0.887047 | + | 0.461680i | \(0.152753\pi\) | ||||
−0.887047 | + | 0.461680i | \(0.847247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.6184 | 1.53288 | 0.766439 | − | 0.642317i | \(-0.222027\pi\) | ||||
0.766439 | + | 0.642317i | \(0.222027\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −48.0283 | −1.72523 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.6948 | −0.705640 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.20600i | 0.0789370i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.47369 | 0.231056 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 54.9021i | − | 1.95705i | −0.206132 | − | 0.978524i | \(-0.566088\pi\) | ||
0.206132 | − | 0.978524i | \(-0.433912\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −73.7155 | −2.62102 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.89796i | − | 0.138421i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.3457 | 0.933211 | 0.466606 | − | 0.884465i | \(-0.345477\pi\) | ||||
0.466606 | + | 0.884465i | \(0.345477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 67.3908i | − | 2.38411i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.9111 | 0.420333 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 91.4364 | 3.22271 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 44.8080i | − | 1.57537i | −0.616081 | − | 0.787683i | \(-0.711281\pi\) | ||
0.616081 | − | 0.787683i | \(-0.288719\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.29490i | 0.291273i | 0.989338 | + | 0.145637i | \(0.0465230\pi\) | ||||
−0.989338 | + | 0.145637i | \(0.953477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 78.3813i | 2.74558i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 49.4506i | − | 1.73006i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.71316 | 0.199391 | 0.0996954 | − | 0.995018i | \(-0.468213\pi\) | ||||
0.0996954 | + | 0.995018i | \(0.468213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 56.0954i | − | 1.95536i | −0.210094 | − | 0.977681i | \(-0.567377\pi\) | ||
0.210094 | − | 0.977681i | \(-0.432623\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.6624 | −1.48352 | −0.741759 | − | 0.670666i | \(-0.766008\pi\) | ||||
−0.741759 | + | 0.670666i | \(0.766008\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.1129i | − | 0.524892i | −0.964947 | − | 0.262446i | \(-0.915471\pi\) | ||
0.964947 | − | 0.262446i | \(-0.0845291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45.1208 | 1.56334 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.7104 | − | 28.4656i | −1.20120 | − | 0.985093i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.04212i | 0.174073i | 0.996205 | + | 0.0870367i | \(0.0277397\pi\) | ||||
−0.996205 | + | 0.0870367i | \(0.972260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.98379 | −0.240820 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.9994 | 1.47922 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.9167 | −1.06231 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.1963i | 1.06940i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.3744 | 1.41663 | 0.708317 | − | 0.705895i | \(-0.249455\pi\) | ||||
0.708317 | + | 0.705895i | \(0.249455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 55.3879i | 1.89202i | 0.324145 | + | 0.946008i | \(0.394924\pi\) | ||||
−0.324145 | + | 0.946008i | \(0.605076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.34936 | 0.148398 | 0.0741991 | − | 0.997243i | \(-0.476360\pi\) | ||||
0.0741991 | + | 0.997243i | \(0.476360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 48.5230i | − | 1.65174i | −0.563859 | − | 0.825871i | \(-0.690684\pi\) | ||
0.563859 | − | 0.825871i | \(-0.309316\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 34.8099i | − | 1.18357i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.3401 | −1.09706 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.68704 | −0.0910469 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.2322 | 0.954421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.3468 | −1.59879 | −0.799393 | − | 0.600808i | \(-0.794846\pi\) | ||||
−0.799393 | + | 0.600808i | \(0.794846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.5404 | 0.624643 | 0.312322 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312322 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.3061 | −0.582396 | −0.291198 | − | 0.956663i | \(-0.594054\pi\) | ||||
−0.291198 | + | 0.956663i | \(0.594054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.15097 | 0.273683 | 0.136841 | − | 0.990593i | \(-0.456305\pi\) | ||||
0.136841 | + | 0.990593i | \(0.456305\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −74.7182 | −2.50597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 53.9084i | − | 1.80397i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 65.1044i | − | 2.17620i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.7706i | 1.35978i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.16844 | −0.0722413 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.5910 | −1.18309 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.3172 | 1.60435 | 0.802173 | − | 0.597092i | \(-0.203677\pi\) | ||||
0.802173 | + | 0.597092i | \(0.203677\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.6278i | 1.37919i | 0.724195 | + | 0.689595i | \(0.242212\pi\) | ||||
−0.724195 | + | 0.689595i | \(0.757788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 28.2991i | − | 0.936565i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.8566 | −1.58036 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.2093 | 0.501707 | 0.250853 | − | 0.968025i | \(-0.419289\pi\) | ||||
0.250853 | + | 0.968025i | \(0.419289\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.400410i | 0.0131797i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.9382i | 1.08300i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 14.7431i | − | 0.483704i | −0.970313 | − | 0.241852i | \(-0.922245\pi\) | ||
0.970313 | − | 0.241852i | \(-0.0777548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0938 | 1.18293 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 80.3800i | 2.62871i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.8416i | 1.88960i | 0.327643 | + | 0.944801i | \(0.393746\pi\) | ||||
−0.327643 | + | 0.944801i | \(0.606254\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.5591 | −0.702805 | −0.351403 | − | 0.936224i | \(-0.614295\pi\) | ||||
−0.351403 | + | 0.936224i | \(0.614295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.9262 | −1.00709 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 54.2270i | − | 1.76214i | −0.472986 | − | 0.881070i | \(-0.656824\pi\) | ||
0.472986 | − | 0.881070i | \(-0.343176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.16198 | 0.0701807 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.7716 | −1.22354 | −0.611771 | − | 0.791035i | \(-0.709543\pi\) | ||||
−0.611771 | + | 0.791035i | \(0.709543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 66.7885i | 2.16122i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.0152i | 0.614032i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1943 | 0.490138 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.5213i | 0.628411i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.5711 | −1.69057 | −0.845287 | − | 0.534313i | \(-0.820570\pi\) | ||||
−0.845287 | + | 0.534313i | \(0.820570\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.253042 | 0.00812051 | 0.00406026 | − | 0.999992i | \(-0.498708\pi\) | ||||
0.00406026 | + | 0.999992i | \(0.498708\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55.9141i | 1.79252i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.9558 | −1.69421 | −0.847103 | − | 0.531429i | \(-0.821655\pi\) | ||||
−0.847103 | + | 0.531429i | \(0.821655\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −65.6976 | −2.09971 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.1838 | 1.85577 | 0.927887 | − | 0.372862i | \(-0.121623\pi\) | ||||
0.927887 | + | 0.372862i | \(0.121623\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.6400 | 1.67725 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 77.6507i | − | 2.46915i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.4082i | 1.50597i | 0.658036 | + | 0.752986i | \(0.271387\pi\) | ||||
−0.658036 | + | 0.752986i | \(0.728613\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.6144 | −1.03395 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.1546 | −0.669973 | −0.334986 | − | 0.942223i | \(-0.608732\pi\) | ||||
−0.334986 | + | 0.942223i | \(0.608732\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6012.2.h.a.3005.52 | yes | 56 | |
3.2 | odd | 2 | inner | 6012.2.h.a.3005.5 | ✓ | 56 | |
167.166 | odd | 2 | inner | 6012.2.h.a.3005.6 | yes | 56 | |
501.500 | even | 2 | inner | 6012.2.h.a.3005.51 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.h.a.3005.5 | ✓ | 56 | 3.2 | odd | 2 | inner | |
6012.2.h.a.3005.6 | yes | 56 | 167.166 | odd | 2 | inner | |
6012.2.h.a.3005.51 | yes | 56 | 501.500 | even | 2 | inner | |
6012.2.h.a.3005.52 | yes | 56 | 1.1 | even | 1 | trivial |