Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(575,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.575");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 144x^{10} + 12024x^{8} - 766296x^{6} + 11751192x^{4} + 565147728x^{2} + 9666232489 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{4}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.11 | ||
Root | \(8.41502 + 0.655192i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.575 |
Dual form | 1008.4.h.a.575.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.1054i | 1.26163i | 0.775934 | + | 0.630814i | \(0.217279\pi\) | ||||
−0.775934 | + | 0.630814i | \(0.782721\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.1065 | −0.359252 | −0.179626 | − | 0.983735i | \(-0.557489\pi\) | ||||
−0.179626 | + | 0.983735i | \(0.557489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 30.2418 | 0.645197 | 0.322598 | − | 0.946536i | \(-0.395444\pi\) | ||||
0.322598 | + | 0.946536i | \(0.395444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 78.2552i | − 1.11645i | −0.829689 | − | 0.558226i | \(-0.811482\pi\) | ||||
0.829689 | − | 0.558226i | \(-0.188518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 72.0861i | 0.870404i | 0.900333 | + | 0.435202i | \(0.143323\pi\) | ||||
−0.900333 | + | 0.435202i | \(0.856677\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −217.553 | −1.97231 | −0.986153 | − | 0.165840i | \(-0.946967\pi\) | ||||
−0.986153 | + | 0.165840i | \(0.946967\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −73.9633 | −0.591706 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.49080i | − 0.0223526i | −0.999938 | − | 0.0111763i | \(-0.996442\pi\) | ||||
0.999938 | − | 0.0111763i | \(-0.00355760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 305.218i | 1.76835i | 0.467160 | + | 0.884173i | \(0.345277\pi\) | ||||
−0.467160 | + | 0.884173i | \(0.654723\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 98.7380 | 0.476851 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 191.923 | 0.852754 | 0.426377 | − | 0.904546i | \(-0.359790\pi\) | ||||
0.426377 | + | 0.904546i | \(0.359790\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 246.011i | 0.937086i | 0.883441 | + | 0.468543i | \(0.155221\pi\) | ||||
−0.883441 | + | 0.468543i | \(0.844779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 200.959i | − 0.712698i | −0.934353 | − | 0.356349i | \(-0.884021\pi\) | ||||
0.934353 | − | 0.356349i | \(-0.115979\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −338.976 | −1.05202 | −0.526008 | − | 0.850480i | \(-0.676312\pi\) | ||||
−0.526008 | + | 0.850480i | \(0.676312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 423.136i | − 1.09665i | −0.836267 | − | 0.548323i | \(-0.815266\pi\) | ||||
0.836267 | − | 0.548323i | \(-0.184734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 184.873i | − 0.453242i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −366.860 | −0.809509 | −0.404755 | − | 0.914425i | \(-0.632643\pi\) | ||||
−0.404755 | + | 0.914425i | \(0.632643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −730.595 | −1.53349 | −0.766747 | − | 0.641950i | \(-0.778126\pi\) | ||||
−0.766747 | + | 0.641950i | \(0.778126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 426.573i | 0.813999i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1024.29i | − 1.86772i | −0.357633 | − | 0.933862i | \(-0.616416\pi\) | ||||
0.357633 | − | 0.933862i | \(-0.383584\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −79.3885 | −0.132700 | −0.0663499 | − | 0.997796i | \(-0.521135\pi\) | ||||
−0.0663499 | + | 0.997796i | \(0.521135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 127.786 | 0.204880 | 0.102440 | − | 0.994739i | \(-0.467335\pi\) | ||||
0.102440 | + | 0.994739i | \(0.467335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 91.7458i | 0.135784i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 413.860i | − 0.589403i | −0.955589 | − | 0.294701i | \(-0.904780\pi\) | ||||
0.955589 | − | 0.294701i | \(-0.0952202\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −228.695 | −0.302440 | −0.151220 | − | 0.988500i | \(-0.548320\pi\) | ||||
−0.151220 | + | 0.988500i | \(0.548320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1103.82 | 1.40855 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 193.891i | − 0.230926i | −0.993312 | − | 0.115463i | \(-0.963165\pi\) | ||||
0.993312 | − | 0.115463i | \(-0.0368352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 211.692i | − 0.243861i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1016.81 | −1.09813 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1004.12 | 1.05107 | 0.525533 | − | 0.850773i | \(-0.323866\pi\) | ||||
0.525533 | + | 0.850773i | \(0.323866\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 218.638i | 0.215399i | 0.994183 | + | 0.107700i | \(0.0343485\pi\) | ||||
−0.994183 | + | 0.107700i | \(0.965652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 965.671i | − 0.923790i | −0.886935 | − | 0.461895i | \(-0.847170\pi\) | ||||
0.886935 | − | 0.461895i | \(-0.152830\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 333.264 | 0.301102 | 0.150551 | − | 0.988602i | \(-0.451895\pi\) | ||||
0.150551 | + | 0.988602i | \(0.451895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1891.50 | −1.66214 | −0.831068 | − | 0.556170i | \(-0.812270\pi\) | ||||
−0.831068 | + | 0.556170i | \(0.812270\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 255.337i | − 0.212567i | −0.994336 | − | 0.106284i | \(-0.966105\pi\) | ||||
0.994336 | − | 0.106284i | \(-0.0338951\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3068.69i | − 2.48832i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −547.787 | −0.421979 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1159.22 | −0.870938 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 719.895i | 0.515115i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 82.2137i | 0.0574432i | 0.999587 | + | 0.0287216i | \(0.00914363\pi\) | ||||
−0.999587 | + | 0.0287216i | \(0.990856\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1925.25 | −1.28404 | −0.642021 | − | 0.766687i | \(-0.721904\pi\) | ||||
−0.642021 | + | 0.766687i | \(0.721904\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 504.602 | 0.328982 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2062.05i | − 1.28593i | −0.765894 | − | 0.642967i | \(-0.777703\pi\) | ||||
0.765894 | − | 0.642967i | \(-0.222297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 363.818i | − 0.222005i | −0.993820 | − | 0.111002i | \(-0.964594\pi\) | ||||
0.993820 | − | 0.111002i | \(-0.0354061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −396.365 | −0.231788 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 49.2392 | 0.0282007 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 961.387i | − 0.528590i | −0.964442 | − | 0.264295i | \(-0.914861\pi\) | ||||
0.964442 | − | 0.264295i | \(-0.0851393\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2080.34i | 1.12116i | 0.828099 | + | 0.560581i | \(0.189422\pi\) | ||||
−0.828099 | + | 0.560581i | \(0.810578\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4305.23 | −2.23099 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3163.02 | 1.60788 | 0.803939 | − | 0.594712i | \(-0.202734\pi\) | ||||
0.803939 | + | 0.594712i | \(0.202734\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1522.87i | 0.745461i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2325.36i | − 1.11740i | −0.829369 | − | 0.558701i | \(-0.811300\pi\) | ||||
0.829369 | − | 0.558701i | \(-0.188700\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4001.48 | −1.85415 | −0.927077 | − | 0.374870i | \(-0.877687\pi\) | ||||
−0.927077 | + | 0.374870i | \(0.877687\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1282.44 | −0.583721 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1284.23i | − 0.564384i | −0.959358 | − | 0.282192i | \(-0.908938\pi\) | ||||
0.959358 | − | 0.282192i | \(-0.0910616\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 517.743i | 0.223644i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −644.970 | −0.269315 | −0.134657 | − | 0.990892i | \(-0.542993\pi\) | ||||
−0.134657 | + | 0.990892i | \(0.542993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2374.61 | 0.975155 | 0.487578 | − | 0.873080i | \(-0.337881\pi\) | ||||
0.487578 | + | 0.873080i | \(0.337881\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2707.15i | 1.07586i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1025.65i | 0.401087i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4428.79 | −1.67778 | −0.838889 | − | 0.544302i | \(-0.816795\pi\) | ||||
−0.838889 | + | 0.544302i | \(0.816795\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3114.28 | −1.16151 | −0.580753 | − | 0.814080i | \(-0.697242\pi\) | ||||
−0.580753 | + | 0.814080i | \(0.697242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3892.82i | 1.40788i | 0.710260 | + | 0.703939i | \(0.248577\pi\) | ||||
−0.710260 | + | 0.703939i | \(0.751423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1837.29i | 0.654482i | 0.944941 | + | 0.327241i | \(0.106119\pi\) | ||||
−0.944941 | + | 0.327241i | \(0.893881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.4356 | −0.00844848 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3470.10 | −1.18225 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 944.799i | − 0.312694i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1753.48i | − 0.572105i | −0.958214 | − | 0.286053i | \(-0.907657\pi\) | ||||
0.958214 | − | 0.286053i | \(-0.0923433\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2834.62 | 0.899160 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2136.52 | 0.668372 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2366.58i | − 0.720331i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2467.93i | − 0.741098i | −0.928813 | − | 0.370549i | \(-0.879170\pi\) | ||||
0.928813 | − | 0.370549i | \(-0.120830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3753.03 | −1.09735 | −0.548673 | − | 0.836037i | \(-0.684867\pi\) | ||||
−0.548673 | + | 0.836037i | \(0.684867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4115.92 | −1.18772 | −0.593860 | − | 0.804568i | \(-0.702397\pi\) | ||||
−0.593860 | + | 0.804568i | \(0.702397\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 2719.40i | − 0.764608i | −0.924037 | − | 0.382304i | \(-0.875131\pi\) | ||||
0.924037 | − | 0.382304i | \(-0.124869\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 4781.41i | − 1.32725i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3670.35 | 0.993370 | 0.496685 | − | 0.867931i | \(-0.334550\pi\) | ||||
0.496685 | + | 0.867931i | \(0.334550\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3043.03 | 0.813357 | 0.406678 | − | 0.913571i | \(-0.366687\pi\) | ||||
0.406678 | + | 0.913571i | \(0.366687\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 691.166i | − 0.180233i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2180.01i | 0.561582i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1036.93 | 0.260758 | 0.130379 | − | 0.991464i | \(-0.458381\pi\) | ||||
0.130379 | + | 0.991464i | \(0.458381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2851.37 | 0.708554 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 929.028i | 0.225491i | 0.993624 | + | 0.112745i | \(0.0359645\pi\) | ||||
−0.993624 | + | 0.112745i | \(0.964036\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1343.46i | − 0.322311i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1676.15 | 0.392987 | 0.196494 | − | 0.980505i | \(-0.437045\pi\) | ||||
0.196494 | + | 0.980505i | \(0.437045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5968.52 | 1.38356 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1717.55i | 0.389297i | 0.980873 | + | 0.194649i | \(0.0623567\pi\) | ||||
−0.980873 | + | 0.194649i | \(0.937643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 3930.25i | − 0.880981i | −0.897757 | − | 0.440490i | \(-0.854805\pi\) | ||||
0.897757 | − | 0.440490i | \(-0.145195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 969.402 | 0.212571 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4632.58 | −1.00486 | −0.502428 | − | 0.864619i | \(-0.667560\pi\) | ||||
−0.502428 | + | 0.864619i | \(0.667560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4487.15i | 0.952600i | 0.879283 | + | 0.476300i | \(0.158022\pi\) | ||||
−0.879283 | + | 0.476300i | \(0.841978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3633.83i | 0.763281i | 0.924311 | + | 0.381641i | \(0.124641\pi\) | ||||
−0.924311 | + | 0.381641i | \(0.875359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1722.08 | 0.354185 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1210.88 | −0.246464 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3355.27i | − 0.669000i | −0.942396 | − | 0.334500i | \(-0.891433\pi\) | ||||
0.942396 | − | 0.334500i | \(-0.108567\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 5174.71i | − 1.02130i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6579.20 | −1.27253 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1406.72 | −0.269375 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 10305.4i | − 1.93470i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1849.50i | − 0.343832i | −0.985112 | − | 0.171916i | \(-0.945004\pi\) | ||||
0.985112 | − | 0.171916i | \(-0.0549957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1872.43 | 0.341401 | 0.170700 | − | 0.985323i | \(-0.445397\pi\) | ||||
0.170700 | + | 0.985323i | \(0.445397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −114.858 | −0.0207417 | −0.0103709 | − | 0.999946i | \(-0.503301\pi\) | ||||
−0.0103709 | + | 0.999946i | \(0.503301\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7436.55i | 1.31760i | 0.752320 | + | 0.658798i | \(0.228935\pi\) | ||||
−0.752320 | + | 0.658798i | \(0.771065\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.7523i | 0.00803021i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5641.11 | 0.971764 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2236.78 | −0.381767 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2372.83i | 0.397625i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5161.23i | 0.857059i | 0.903528 | + | 0.428530i | \(0.140968\pi\) | ||||
−0.903528 | + | 0.428530i | \(0.859032\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14448.1 | 2.35637 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5415.65 | −0.875398 | −0.437699 | − | 0.899122i | \(-0.644206\pi\) | ||||
−0.437699 | + | 0.899122i | \(0.644206\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4000.35i | − 0.635281i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6577.28 | −1.01754 | −0.508770 | − | 0.860902i | \(-0.669900\pi\) | ||||
−0.508770 | + | 0.860902i | \(0.669900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8587.72 | 1.31716 | 0.658582 | − | 0.752509i | \(-0.271157\pi\) | ||||
0.658582 | + | 0.752509i | \(0.271157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2518.85i | − 0.379788i | −0.981805 | − | 0.189894i | \(-0.939186\pi\) | ||||
0.981805 | − | 0.189894i | \(-0.0608144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1119.81i | − 0.167418i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10688.2 | 1.57132 | 0.785659 | − | 0.618660i | \(-0.212324\pi\) | ||||
0.785659 | + | 0.618660i | \(0.212324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1662.60 | 0.242397 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1802.48i | 0.258482i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 451.872i | − 0.0642712i | −0.999484 | − | 0.0321356i | \(-0.989769\pi\) | ||||
0.999484 | − | 0.0321356i | \(-0.0102308\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2961.95 | −0.414493 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8510.92 | 1.18144 | 0.590722 | − | 0.806875i | \(-0.298843\pi\) | ||||
0.590722 | + | 0.806875i | \(0.298843\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 105.568i | − 0.0144218i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11356.2i | 1.53912i | 0.638574 | + | 0.769561i | \(0.279525\pi\) | ||||
−0.638574 | + | 0.769561i | \(0.720475\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10796.9 | 1.44046 | 0.720229 | − | 0.693736i | \(-0.244037\pi\) | ||||
0.720229 | + | 0.693736i | \(0.244037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1294.11 | −0.171309 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4634.81i | 0.604099i | 0.953292 | + | 0.302049i | \(0.0976708\pi\) | ||||
−0.953292 | + | 0.302049i | \(0.902329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17024.7i | 2.20198i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5837.67 | 0.743608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8193.89 | −1.03587 | −0.517934 | − | 0.855421i | \(-0.673299\pi\) | ||||
−0.517934 | + | 0.855421i | \(0.673299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7505.04i | 0.934623i | 0.884093 | + | 0.467311i | \(0.154777\pi\) | ||||
−0.884093 | + | 0.467311i | \(0.845223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9230.32i | 1.14093i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2515.44 | −0.306353 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 708.588 | 0.0856661 | 0.0428330 | − | 0.999082i | \(-0.486362\pi\) | ||||
0.0428330 | + | 0.999082i | \(0.486362\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2568.02i | 0.305966i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 3225.84i | − 0.381566i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11975.7 | −1.39631 | −0.698153 | − | 0.715949i | \(-0.745994\pi\) | ||||
−0.698153 | + | 0.715949i | \(0.745994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1813.85 | 0.209980 | 0.104990 | − | 0.994473i | \(-0.466519\pi\) | ||||
0.104990 | + | 0.994473i | \(0.466519\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5788.01i | 0.660611i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5114.16i | 0.579606i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9988.53 | 1.11631 | 0.558156 | − | 0.829736i | \(-0.311509\pi\) | ||||
0.558156 | + | 0.829736i | \(0.311509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1385.76 | −0.153800 | −0.0768998 | − | 0.997039i | \(-0.524502\pi\) | ||||
−0.0768998 | + | 0.997039i | \(0.524502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 15682.6i | − 1.71670i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15869.5i | 1.72531i | 0.505795 | + | 0.862653i | \(0.331199\pi\) | ||||
−0.505795 | + | 0.862653i | \(0.668801\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10484.7 | −1.12448 | −0.562240 | − | 0.826974i | \(-0.690060\pi\) | ||||
−0.562240 | + | 0.826974i | \(0.690060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2734.92 | 0.291343 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 2234.73i | − 0.234885i | −0.993080 | − | 0.117442i | \(-0.962530\pi\) | ||||
0.993080 | − | 0.117442i | \(-0.0374695\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3224.36i | − 0.336650i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2986.01 | 0.307663 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17478.3 | −1.78906 | −0.894529 | − | 0.447011i | \(-0.852489\pi\) | ||||
−0.894529 | + | 0.447011i | \(0.852489\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 18276.9i | − 1.84651i | −0.384190 | − | 0.923254i | \(-0.625519\pi\) | ||||
0.384190 | − | 0.923254i | \(-0.374481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15906.7i | 1.59665i | 0.602230 | + | 0.798323i | \(0.294279\pi\) | ||||
−0.602230 | + | 0.798323i | \(0.705721\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8595.46 | 0.851714 | 0.425857 | − | 0.904790i | \(-0.359973\pi\) | ||||
0.425857 | + | 0.904790i | \(0.359973\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7170.06 | −0.705933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2633.88i | 0.256038i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5331.72i | − 0.515023i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19485.8 | 1.85872 | 0.929360 | − | 0.369174i | \(-0.120359\pi\) | ||||
0.929360 | + | 0.369174i | \(0.120359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5804.08 | 0.550194 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14163.6i | 1.32606i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10181.7i | 0.947386i | 0.880690 | + | 0.473693i | \(0.157079\pi\) | ||||
−0.880690 | + | 0.473693i | \(0.842921\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3098.15 | −0.284760 | −0.142380 | − | 0.989812i | \(-0.545476\pi\) | ||||
−0.142380 | + | 0.989812i | \(0.545476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −273.173 | −0.0249556 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 555.720i | 0.0501558i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1116.79i | − 0.100189i | −0.998744 | − | 0.0500944i | \(-0.984048\pi\) | ||||
0.998744 | − | 0.0500944i | \(-0.0159522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2573.33 | −0.228109 | −0.114055 | − | 0.993474i | \(-0.536384\pi\) | ||||
−0.114055 | + | 0.993474i | \(0.536384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3083.99 | −0.271754 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16767.6i | 1.46014i | 0.683373 | + | 0.730069i | \(0.260512\pi\) | ||||
−0.683373 | + | 0.730069i | \(0.739488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 894.502i | − 0.0774373i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13621.2 | 1.16548 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4442.80 | 0.377939 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8773.54i | 0.737766i | 0.929476 | + | 0.368883i | \(0.120260\pi\) | ||||
−0.929476 | + | 0.368883i | \(0.879740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8809.57i | − 0.736550i | −0.929717 | − | 0.368275i | \(-0.879949\pi\) | ||||
0.929717 | − | 0.368275i | \(-0.120051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23884.9 | 1.97427 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35162.5 | 2.88999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7439.82i | 0.604605i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4700.84i | 0.379879i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 642.220 | 0.0513217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −976.663 | −0.0776156 | −0.0388078 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388078 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 26680.4i | − 2.09700i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 19767.5i | − 1.54515i | −0.634922 | − | 0.772576i | \(-0.718968\pi\) | ||||
0.634922 | − | 0.772576i | \(-0.281032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 251.638 | 0.0194558 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2897.02 | −0.222773 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 17079.5i | − 1.29925i | −0.760254 | − | 0.649626i | \(-0.774925\pi\) | ||||
0.760254 | − | 0.649626i | \(-0.225075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 6077.37i | − 0.459831i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7784.65 | −0.582742 | −0.291371 | − | 0.956610i | \(-0.594111\pi\) | ||||
−0.291371 | + | 0.956610i | \(0.594111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3601.64 | 0.268181 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 8845.46i | − 0.651706i | −0.945420 | − | 0.325853i | \(-0.894349\pi\) | ||||
0.945420 | − | 0.325853i | \(-0.105651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50330i | 0 0.000110177i | 1.00000 | 5.50886e-5i | \(1.75352e-5\pi\) | |||||
−1.00000 | 5.50886e-5i | \(0.999982\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16091.0 | 1.16703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2938.69 | 0.212026 | 0.106013 | − | 0.994365i | \(-0.466191\pi\) | ||||
0.106013 | + | 0.994365i | \(0.466191\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1600.86i | 0.114311i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5545.85i | 0.393972i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19938.8 | 1.40198 | 0.700989 | − | 0.713173i | \(-0.252742\pi\) | ||||
0.700989 | + | 0.713173i | \(0.252742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22001.9 | −1.53917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19762.6i | 1.36855i | 0.729222 | + | 0.684277i | \(0.239882\pi\) | ||||
−0.729222 | + | 0.684277i | \(0.760118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 7726.77i | − 0.532381i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10471.7 | 0.714293 | 0.357147 | − | 0.934048i | \(-0.383750\pi\) | ||||
0.357147 | + | 0.934048i | \(0.383750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14290.6 | −0.969924 | −0.484962 | − | 0.874535i | \(-0.661167\pi\) | ||||
−0.484962 | + | 0.874535i | \(0.661167\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 16351.3i | − 1.09880i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26516.3i | 1.77308i | 0.462648 | + | 0.886542i | \(0.346899\pi\) | ||||
−0.462648 | + | 0.886542i | \(0.653101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10251.2 | −0.678757 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25135.2 | 1.65612 | 0.828058 | − | 0.560642i | \(-0.189446\pi\) | ||||
0.828058 | + | 0.560642i | \(0.189446\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 4354.81i | − 0.284146i | −0.989856 | − | 0.142073i | \(-0.954623\pi\) | ||||
0.989856 | − | 0.142073i | \(-0.0453768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 91.2299i | − 0.00592381i | −0.999996 | − | 0.00296190i | \(-0.999057\pi\) | ||||
0.999996 | − | 0.00296190i | \(-0.000942805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1357.24 | −0.0872819 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19399.8 | −1.24159 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 15019.0i | − 0.952059i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1993.10i | − 0.125743i | −0.998022 | − | 0.0628716i | \(-0.979974\pi\) | ||||
0.998022 | − | 0.0628716i | \(-0.0200259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1159.66 | −0.0724720 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1481.85 | −0.0921710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27606.0i | 1.70105i | 0.525937 | + | 0.850523i | \(0.323715\pi\) | ||||
−0.525937 | + | 0.850523i | \(0.676285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3174.43i | − 0.194693i | −0.995251 | − | 0.0973464i | \(-0.968965\pi\) | ||||
0.995251 | − | 0.0973464i | \(-0.0310355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23316.4 | −1.41679 | −0.708395 | − | 0.705816i | \(-0.750580\pi\) | ||||
−0.708395 | + | 0.705816i | \(0.750580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4808.26 | 0.290818 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28631.7i | 1.71584i | 0.513782 | + | 0.857921i | \(0.328244\pi\) | ||||
−0.513782 | + | 0.857921i | \(0.671756\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 27156.4i | − 1.61998i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −538.740 | −0.0318457 | −0.0159229 | − | 0.999873i | \(-0.505069\pi\) | ||||
−0.0159229 | + | 0.999873i | \(0.505069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15272.0 | −0.898656 | −0.449328 | − | 0.893367i | \(-0.648336\pi\) | ||||
−0.449328 | + | 0.893367i | \(0.648336\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7117.64i | 0.415053i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 759.435i | 0.0440861i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9575.57 | 0.550910 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23556.7 | −1.34925 | −0.674625 | − | 0.738161i | \(-0.735695\pi\) | ||||
−0.674625 | + | 0.738161i | \(0.735695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7988.75i | 0.453519i | 0.973951 | + | 0.226760i | \(0.0728132\pi\) | ||||
−0.973951 | + | 0.226760i | \(0.927187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 7028.87i | − 0.397266i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18508.0 | −1.03688 | −0.518439 | − | 0.855115i | \(-0.673487\pi\) | ||||
−0.518439 | + | 0.855115i | \(0.673487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29086.1 | 1.62237 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 12796.4i | − 0.707552i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 24965.2i | − 1.37441i | −0.726462 | − | 0.687207i | \(-0.758837\pi\) | ||||
0.726462 | − | 0.687207i | \(-0.241163\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5131.81 | 0.280087 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19251.7 | 1.04621 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19893.7i | 1.07186i | 0.844262 | + | 0.535931i | \(0.180039\pi\) | ||||
−0.844262 | + | 0.535931i | \(0.819961\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13835.0i | 0.742241i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1530.47 | 0.0814132 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10872.8 | 0.575931 | 0.287966 | − | 0.957641i | \(-0.407021\pi\) | ||||
0.287966 | + | 0.957641i | \(0.407021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 66401.1i | − 3.48772i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5590.90i | − 0.292430i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32431.5 | −1.68218 | −0.841092 | − | 0.540892i | \(-0.818087\pi\) | ||||
−0.841092 | + | 0.540892i | \(0.818087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6759.69 | −0.349160 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 258.191i | 0.0132262i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20606.8i | 1.05126i | 0.850714 | + | 0.525629i | \(0.176170\pi\) | ||||
−0.850714 | + | 0.525629i | \(0.823830\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15726.1 | −0.795693 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2770.73 | −0.139617 | −0.0698085 | − | 0.997560i | \(-0.522239\pi\) | ||||
−0.0698085 | + | 0.997560i | \(0.522239\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13425.0i | 0.670983i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 19617.9i | − 0.976532i | −0.872695 | − | 0.488266i | \(-0.837630\pi\) | ||||
0.872695 | − | 0.488266i | \(-0.162370\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2537.18 | −0.125276 | −0.0626381 | − | 0.998036i | \(-0.519951\pi\) | ||||
−0.0626381 | + | 0.998036i | \(0.519951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13560.8 | 0.666884 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2332.85i | − 0.113806i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28280.3i | 1.37412i | 0.726602 | + | 0.687059i | \(0.241099\pi\) | ||||
−0.726602 | + | 0.687059i | \(0.758901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29344.1 | −1.41449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30129.0 | −1.44658 | −0.723288 | − | 0.690546i | \(-0.757370\pi\) | ||||
−0.723288 | + | 0.690546i | \(0.757370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11243.4i | 0.535573i | 0.963478 | + | 0.267787i | \(0.0862922\pi\) | ||||
−0.963478 | + | 0.267787i | \(0.913708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13240.5i | 0.628229i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11094.5 | −0.522293 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11539.8 | 0.541138 | 0.270569 | − | 0.962701i | \(-0.412788\pi\) | ||||
0.270569 | + | 0.962701i | \(0.412788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 23116.8i | − 1.07562i | −0.843066 | − | 0.537810i | \(-0.819252\pi\) | ||||
0.843066 | − | 0.537810i | \(-0.180748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 22574.9i | − 1.04634i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17734.0 | −0.815643 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1040.51 | 0.0476726 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44615.8i | 2.02854i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1401.68i | 0.0634875i | 0.999496 | + | 0.0317438i | \(0.0101060\pi\) | ||||
−0.999496 | + | 0.0317438i | \(0.989894\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1787.36 | −0.0803429 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22094.5 | −0.989405 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6424.11i | − 0.285513i | −0.989758 | − | 0.142756i | \(-0.954403\pi\) | ||||
0.989758 | − | 0.142756i | \(-0.0455965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26526.7i | 1.17453i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1674.83 | −0.0736034 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21480.8 | −0.940495 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 23279.8i | − 1.01171i | −0.862618 | − | 0.505856i | \(-0.831177\pi\) | ||||
0.862618 | − | 0.505856i | \(-0.168823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 24122.3i | − 1.04445i | −0.852808 | − | 0.522225i | \(-0.825102\pi\) | ||||
0.852808 | − | 0.522225i | \(-0.174898\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32800.3 | 1.40975 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14486.4 | 0.620336 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25808.0i | 1.09708i | 0.836123 | + | 0.548542i | \(0.184817\pi\) | ||||
−0.836123 | + | 0.548542i | \(0.815183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45232.8i | 1.91582i | 0.287073 | + | 0.957909i | \(0.407318\pi\) | ||||
−0.287073 | + | 0.957909i | \(0.592682\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42035.1 | −1.76748 | −0.883740 | − | 0.467979i | \(-0.844982\pi\) | ||||
−0.883740 | + | 0.467979i | \(0.844982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24480.4 | −1.02562 | −0.512810 | − | 0.858502i | \(-0.671395\pi\) | ||||
−0.512810 | + | 0.858502i | \(0.671395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3834.51i | 0.159493i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 56442.6i | − 2.33925i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26751.5 | −1.10079 | −0.550396 | − | 0.834904i | \(-0.685523\pi\) | ||||
−0.550396 | + | 0.834904i | \(0.685523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24376.8 | 0.999500 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 18089.3i | − 0.736439i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8114.53i | 0.329184i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41753.4 | −1.68189 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26977.8 | 1.08289 | 0.541444 | − | 0.840737i | \(-0.317878\pi\) | ||||
0.541444 | + | 0.840737i | \(0.317878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25583.7i | 1.01975i | 0.860250 | + | 0.509873i | \(0.170308\pi\) | ||||
−0.860250 | + | 0.509873i | \(0.829692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31259.1i | 1.24161i | 0.783963 | + | 0.620807i | \(0.213195\pi\) | ||||
−0.783963 | + | 0.620807i | \(0.786805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45428.8 | −1.79190 | −0.895952 | − | 0.444150i | \(-0.853506\pi\) | ||||
−0.895952 | + | 0.444150i | \(0.853506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18114.7 | 0.712043 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5424.27i | 0.211744i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 30976.5i | − 1.20505i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5039.27 | 0.194695 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32177.7 | 1.23895 | 0.619477 | − | 0.785015i | \(-0.287345\pi\) | ||||
0.619477 | + | 0.785015i | \(0.287345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 43816.2i | − 1.67560i | −0.545977 | − | 0.837800i | \(-0.683841\pi\) | ||||
0.545977 | − | 0.837800i | \(-0.316159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 30769.3i | − 1.17267i | −0.810068 | − | 0.586336i | \(-0.800570\pi\) | ||||
0.810068 | − | 0.586336i | \(-0.199430\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20431.3 | 0.773411 | 0.386705 | − | 0.922203i | \(-0.373613\pi\) | ||||
0.386705 | + | 0.922203i | \(0.373613\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 575.496 | 0.0217115 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 24435.5i | − 0.915679i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 9097.59i | − 0.339775i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1065.45 | 0.0395271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33112.6 | −1.22435 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33494.8i | 1.23028i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 18439.6i | − 0.675057i | −0.941315 | − | 0.337529i | \(-0.890409\pi\) | ||||
0.941315 | − | 0.337529i | \(-0.109591\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11953.8 | 0.434737 | 0.217369 | − | 0.976090i | \(-0.430253\pi\) | ||||
0.217369 | + | 0.976090i | \(0.430253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2997.39 | 0.108652 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13476.7i | 0.485322i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 44910.6i | − 1.61204i | −0.591889 | − | 0.806019i | \(-0.701618\pi\) | ||||
0.591889 | − | 0.806019i | \(-0.298382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2400.85 | −0.0856174 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14195.2 | −0.504580 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5294.66i | 0.186988i | 0.995620 | + | 0.0934942i | \(0.0298037\pi\) | ||||
−0.995620 | + | 0.0934942i | \(0.970196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3532.22i | − 0.124343i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14467.3 | −0.506023 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52165.8 | 1.81877 | 0.909383 | − | 0.415960i | \(-0.136554\pi\) | ||||
0.909383 | + | 0.415960i | \(0.136554\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 29115.8i | − 1.00866i | −0.863511 | − | 0.504330i | \(-0.831740\pi\) | ||||
0.863511 | − | 0.504330i | \(-0.168260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 53520.6i | − 1.84822i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14121.4 | 0.484567 | 0.242284 | − | 0.970205i | \(-0.422104\pi\) | ||||
0.242284 | + | 0.970205i | \(0.422104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3864.48 | 0.132188 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5587.57i | 0.189926i | 0.995481 | + | 0.0949629i | \(0.0302732\pi\) | ||||
−0.995481 | + | 0.0949629i | \(0.969727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 62470.0i | − 2.11673i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14434.4 | −0.486037 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −63366.8 | −2.12705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 43928.2i | − 1.46539i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 10370.3i | − 0.344867i | −0.985021 | − | 0.172434i | \(-0.944837\pi\) | ||||
0.985021 | − | 0.172434i | \(-0.0551630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12244.2 | −0.404671 | −0.202335 | − | 0.979316i | \(-0.564853\pi\) | ||||
−0.202335 | + | 0.979316i | \(0.564853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2546.73 | −0.0839098 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 34539.2i | − 1.13102i | −0.824742 | − | 0.565510i | \(-0.808680\pi\) | ||||
0.824742 | − | 0.565510i | \(-0.191320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2541.24i | 0.0829606i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17119.3 | −0.555465 | −0.277732 | − | 0.960659i | \(-0.589583\pi\) | ||||
−0.277732 | + | 0.960659i | \(0.589583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54909.9 | −1.77622 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43719.4i | 1.40566i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 4303.90i | − 0.137959i | −0.997618 | − | 0.0689797i | \(-0.978026\pi\) | ||||
0.997618 | − | 0.0689797i | \(-0.0219744\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25915.7 | −0.825713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10385.4 | 0.329899 | 0.164950 | − | 0.986302i | \(-0.447254\pi\) | ||||
0.164950 | + | 0.986302i | \(0.447254\pi\) | |||||||
\(998\) | 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 | 1008.4.h.a.575.11 | yes | 12 | |
3.2 | odd | 2 | inner | 1008.4.h.a.575.1 | ✓ | 12 | |
4.3 | odd | 2 | inner | 1008.4.h.a.575.12 | yes | 12 | |
12.11 | even | 2 | inner | 1008.4.h.a.575.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.4.h.a.575.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
1008.4.h.a.575.2 | yes | 12 | 12.11 | even | 2 | inner | |
1008.4.h.a.575.11 | yes | 12 | 1.1 | even | 1 | trivial | |
1008.4.h.a.575.12 | yes | 12 | 4.3 | odd | 2 | inner |