Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.a (trivial) |
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: | yes |
Analytic conductor: | \(31.9800860095\) |
Analytic rank: | \(1\) |
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: | \( x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 58 x^{8} - 202 x^{7} - 95 x^{6} + 432 x^{5} + 4 x^{4} + \cdots - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.491103\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.491103 | 0.347262 | 0.173631 | − | 0.984811i | \(-0.444450\pi\) | ||||
0.173631 | + | 0.984811i | \(0.444450\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.75882 | −0.879409 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39011 | −0.525414 | −0.262707 | − | 0.964876i | \(-0.584615\pi\) | ||||
−0.262707 | + | 0.964876i | \(0.584615\pi\) | |||||||
\(8\) | −1.84597 | −0.652648 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.491103 | −0.155300 | ||||||||
\(11\) | −0.843828 | −0.254424 | −0.127212 | − | 0.991876i | \(-0.540603\pi\) | ||||
−0.127212 | + | 0.991876i | \(0.540603\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.66669 | −0.739607 | −0.369804 | − | 0.929110i | \(-0.620575\pi\) | ||||
−0.369804 | + | 0.929110i | \(0.620575\pi\) | |||||||
\(14\) | −0.682689 | −0.182456 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.61108 | 0.652769 | ||||||||
\(17\) | 3.46246 | 0.839771 | 0.419885 | − | 0.907577i | \(-0.362070\pi\) | ||||
0.419885 | + | 0.907577i | \(0.362070\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.51842 | 1.26601 | 0.633006 | − | 0.774147i | \(-0.281821\pi\) | ||||
0.633006 | + | 0.774147i | \(0.281821\pi\) | |||||||
\(20\) | 1.75882 | 0.393284 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.414406 | −0.0883517 | ||||||||
\(23\) | 5.20352 | 1.08501 | 0.542504 | − | 0.840053i | \(-0.317476\pi\) | ||||
0.542504 | + | 0.840053i | \(0.317476\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.30962 | −0.256838 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.44496 | 0.462054 | ||||||||
\(29\) | −0.846016 | −0.157101 | −0.0785507 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785507 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.90482 | 1.59935 | 0.799676 | − | 0.600432i | \(-0.205005\pi\) | ||||
0.799676 | + | 0.600432i | \(0.205005\pi\) | |||||||
\(32\) | 4.97424 | 0.879330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.70043 | 0.291621 | ||||||||
\(35\) | 1.39011 | 0.234972 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.81736 | −1.12077 | −0.560384 | − | 0.828233i | \(-0.689346\pi\) | ||||
−0.560384 | + | 0.828233i | \(0.689346\pi\) | |||||||
\(38\) | 2.71011 | 0.439638 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.84597 | 0.291873 | ||||||||
\(41\) | −7.41095 | −1.15740 | −0.578698 | − | 0.815542i | \(-0.696439\pi\) | ||||
−0.578698 | + | 0.815542i | \(0.696439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.31932 | 0.353693 | 0.176846 | − | 0.984238i | \(-0.443410\pi\) | ||||
0.176846 | + | 0.984238i | \(0.443410\pi\) | |||||||
\(44\) | 1.48414 | 0.223742 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.55546 | 0.376783 | ||||||||
\(47\) | 6.32137 | 0.922067 | 0.461033 | − | 0.887383i | \(-0.347479\pi\) | ||||
0.461033 | + | 0.887383i | \(0.347479\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.06758 | −0.723940 | ||||||||
\(50\) | 0.491103 | 0.0694525 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.69022 | 0.650417 | ||||||||
\(53\) | −3.08500 | −0.423757 | −0.211879 | − | 0.977296i | \(-0.567958\pi\) | ||||
−0.211879 | + | 0.977296i | \(0.567958\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.843828 | 0.113782 | ||||||||
\(56\) | 2.56610 | 0.342910 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.415481 | −0.0545554 | ||||||||
\(59\) | −14.0512 | −1.82931 | −0.914654 | − | 0.404237i | \(-0.867537\pi\) | ||||
−0.914654 | + | 0.404237i | \(0.867537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.19572 | −1.17739 | −0.588696 | − | 0.808355i | \(-0.700358\pi\) | ||||
−0.588696 | + | 0.808355i | \(0.700358\pi\) | |||||||
\(62\) | 4.37318 | 0.555395 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.77929 | −0.347411 | ||||||||
\(65\) | 2.66669 | 0.330762 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.3165 | −1.50470 | −0.752351 | − | 0.658763i | \(-0.771080\pi\) | ||||
−0.752351 | + | 0.658763i | \(0.771080\pi\) | |||||||
\(68\) | −6.08984 | −0.738502 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.682689 | 0.0815970 | ||||||||
\(71\) | 7.32187 | 0.868946 | 0.434473 | − | 0.900685i | \(-0.356935\pi\) | ||||
0.434473 | + | 0.900685i | \(0.356935\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.96382 | −0.932095 | −0.466047 | − | 0.884760i | \(-0.654322\pi\) | ||||
−0.466047 | + | 0.884760i | \(0.654322\pi\) | |||||||
\(74\) | −3.34803 | −0.389200 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.70590 | −1.11334 | ||||||||
\(77\) | 1.17302 | 0.133678 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.56446 | 0.513542 | 0.256771 | − | 0.966472i | \(-0.417341\pi\) | ||||
0.256771 | + | 0.966472i | \(0.417341\pi\) | |||||||
\(80\) | −2.61108 | −0.291927 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.63954 | −0.401920 | ||||||||
\(83\) | −7.49427 | −0.822603 | −0.411302 | − | 0.911499i | \(-0.634926\pi\) | ||||
−0.411302 | + | 0.911499i | \(0.634926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46246 | −0.375557 | ||||||||
\(86\) | 1.13902 | 0.122824 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.55768 | 0.166049 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.70701 | 0.388600 | ||||||||
\(92\) | −9.15204 | −0.954166 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.10445 | 0.320199 | ||||||||
\(95\) | −5.51842 | −0.566178 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2871 | 1.24756 | 0.623781 | − | 0.781599i | \(-0.285596\pi\) | ||||
0.623781 | + | 0.781599i | \(0.285596\pi\) | |||||||
\(98\) | −2.48871 | −0.251397 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.75882 | −0.175882 | ||||||||
\(101\) | −16.3445 | −1.62633 | −0.813167 | − | 0.582030i | \(-0.802258\pi\) | ||||
−0.813167 | + | 0.582030i | \(0.802258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.89199 | 0.284956 | 0.142478 | − | 0.989798i | \(-0.454493\pi\) | ||||
0.142478 | + | 0.989798i | \(0.454493\pi\) | |||||||
\(104\) | 4.92262 | 0.482703 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.51505 | −0.147155 | ||||||||
\(107\) | −4.86649 | −0.470461 | −0.235231 | − | 0.971940i | \(-0.575585\pi\) | ||||
−0.235231 | + | 0.971940i | \(0.575585\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.8869 | −1.90482 | −0.952409 | − | 0.304824i | \(-0.901402\pi\) | ||||
−0.952409 | + | 0.304824i | \(0.901402\pi\) | |||||||
\(110\) | 0.414406 | 0.0395121 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.62969 | −0.342974 | ||||||||
\(113\) | 13.4756 | 1.26768 | 0.633838 | − | 0.773466i | \(-0.281479\pi\) | ||||
0.633838 | + | 0.773466i | \(0.281479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.20352 | −0.485231 | ||||||||
\(116\) | 1.48799 | 0.138156 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.90058 | −0.635250 | ||||||||
\(119\) | −4.81322 | −0.441227 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2880 | −0.935269 | ||||||||
\(122\) | −4.51605 | −0.408864 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.6619 | −1.40648 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.3132 | −1.09262 | −0.546309 | − | 0.837584i | \(-0.683968\pi\) | ||||
−0.546309 | + | 0.837584i | \(0.683968\pi\) | |||||||
\(128\) | −11.3134 | −0.999973 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.30962 | 0.114861 | ||||||||
\(131\) | 18.9390 | 1.65471 | 0.827353 | − | 0.561683i | \(-0.189846\pi\) | ||||
0.827353 | + | 0.561683i | \(0.189846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.67124 | −0.665181 | ||||||||
\(134\) | −6.04868 | −0.522526 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.39159 | −0.548075 | ||||||||
\(137\) | 15.3806 | 1.31405 | 0.657025 | − | 0.753869i | \(-0.271815\pi\) | ||||
0.657025 | + | 0.753869i | \(0.271815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.87907 | −0.753113 | −0.376556 | − | 0.926394i | \(-0.622892\pi\) | ||||
−0.376556 | + | 0.926394i | \(0.622892\pi\) | |||||||
\(140\) | −2.44496 | −0.206637 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.59579 | 0.301752 | ||||||||
\(143\) | 2.25023 | 0.188174 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.846016 | 0.0702578 | ||||||||
\(146\) | −3.91106 | −0.323681 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.9905 | 0.985613 | ||||||||
\(149\) | −13.6746 | −1.12027 | −0.560135 | − | 0.828402i | \(-0.689251\pi\) | ||||
−0.560135 | + | 0.828402i | \(0.689251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0156 | 0.815059 | 0.407530 | − | 0.913192i | \(-0.366390\pi\) | ||||
0.407530 | + | 0.913192i | \(0.366390\pi\) | |||||||
\(152\) | −10.1868 | −0.826260 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.576072 | 0.0464212 | ||||||||
\(155\) | −8.90482 | −0.715252 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8191 | 0.943263 | 0.471632 | − | 0.881796i | \(-0.343665\pi\) | ||||
0.471632 | + | 0.881796i | \(0.343665\pi\) | |||||||
\(158\) | 2.24162 | 0.178334 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.97424 | −0.393248 | ||||||||
\(161\) | −7.23349 | −0.570079 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.72799 | 0.448651 | 0.224325 | − | 0.974514i | \(-0.427982\pi\) | ||||
0.224325 | + | 0.974514i | \(0.427982\pi\) | |||||||
\(164\) | 13.0345 | 1.01782 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.68046 | −0.285659 | ||||||||
\(167\) | 5.55230 | 0.429650 | 0.214825 | − | 0.976653i | \(-0.431082\pi\) | ||||
0.214825 | + | 0.976653i | \(0.431082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.88876 | −0.452981 | ||||||||
\(170\) | −1.70043 | −0.130417 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.07926 | −0.311041 | ||||||||
\(173\) | −17.5445 | −1.33388 | −0.666941 | − | 0.745110i | \(-0.732397\pi\) | ||||
−0.666941 | + | 0.745110i | \(0.732397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.39011 | −0.105083 | ||||||||
\(176\) | −2.20330 | −0.166080 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.491103 | −0.0368097 | ||||||||
\(179\) | 13.3615 | 0.998684 | 0.499342 | − | 0.866405i | \(-0.333575\pi\) | ||||
0.499342 | + | 0.866405i | \(0.333575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.4053 | 1.36806 | 0.684029 | − | 0.729455i | \(-0.260226\pi\) | ||||
0.684029 | + | 0.729455i | \(0.260226\pi\) | |||||||
\(182\) | 1.82052 | 0.134946 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.60553 | −0.708129 | ||||||||
\(185\) | 6.81736 | 0.501222 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.92172 | −0.213658 | ||||||||
\(188\) | −11.1181 | −0.810874 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.71011 | −0.196612 | ||||||||
\(191\) | 26.9635 | 1.95101 | 0.975507 | − | 0.219970i | \(-0.0705959\pi\) | ||||
0.975507 | + | 0.219970i | \(0.0705959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.9722 | −1.50961 | −0.754807 | − | 0.655947i | \(-0.772269\pi\) | ||||
−0.754807 | + | 0.655947i | \(0.772269\pi\) | |||||||
\(194\) | 6.03421 | 0.433231 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.91295 | 0.636640 | ||||||||
\(197\) | 15.2450 | 1.08616 | 0.543080 | − | 0.839681i | \(-0.317258\pi\) | ||||
0.543080 | + | 0.839681i | \(0.317258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6672 | −0.968840 | −0.484420 | − | 0.874836i | \(-0.660969\pi\) | ||||
−0.484420 | + | 0.874836i | \(0.660969\pi\) | |||||||
\(200\) | −1.84597 | −0.130530 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.02681 | −0.564764 | ||||||||
\(203\) | 1.17606 | 0.0825432 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.41095 | 0.517603 | ||||||||
\(206\) | 1.42027 | 0.0989546 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.96293 | −0.482793 | ||||||||
\(209\) | −4.65660 | −0.322104 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.5395 | −1.82706 | −0.913528 | − | 0.406775i | \(-0.866653\pi\) | ||||
−0.913528 | + | 0.406775i | \(0.866653\pi\) | |||||||
\(212\) | 5.42595 | 0.372656 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.38995 | −0.163374 | ||||||||
\(215\) | −2.31932 | −0.158176 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.3787 | −0.840322 | ||||||||
\(218\) | −9.76651 | −0.661471 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.48414 | −0.100061 | ||||||||
\(221\) | −9.23332 | −0.621101 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.64863 | 0.579155 | 0.289578 | − | 0.957155i | \(-0.406485\pi\) | ||||
0.289578 | + | 0.957155i | \(0.406485\pi\) | |||||||
\(224\) | −6.91476 | −0.462012 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.61790 | 0.440216 | ||||||||
\(227\) | 9.64422 | 0.640109 | 0.320055 | − | 0.947399i | \(-0.396299\pi\) | ||||
0.320055 | + | 0.947399i | \(0.396299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.35677 | −0.618313 | −0.309156 | − | 0.951011i | \(-0.600047\pi\) | ||||
−0.309156 | + | 0.951011i | \(0.600047\pi\) | |||||||
\(230\) | −2.55546 | −0.168502 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.56172 | 0.102532 | ||||||||
\(233\) | 2.94961 | 0.193236 | 0.0966178 | − | 0.995322i | \(-0.469198\pi\) | ||||
0.0966178 | + | 0.995322i | \(0.469198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.32137 | −0.412361 | ||||||||
\(236\) | 24.7135 | 1.60871 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.36379 | −0.153222 | ||||||||
\(239\) | 5.92878 | 0.383501 | 0.191751 | − | 0.981444i | \(-0.438584\pi\) | ||||
0.191751 | + | 0.981444i | \(0.438584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.498640 | 0.0321202 | 0.0160601 | − | 0.999871i | \(-0.494888\pi\) | ||||
0.0160601 | + | 0.999871i | \(0.494888\pi\) | |||||||
\(242\) | −5.05245 | −0.324784 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.1736 | 1.03541 | ||||||||
\(245\) | 5.06758 | 0.323756 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.7159 | −0.936352 | ||||||||
\(248\) | −16.4380 | −1.04381 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.491103 | −0.0310601 | ||||||||
\(251\) | −9.48289 | −0.598555 | −0.299277 | − | 0.954166i | \(-0.596746\pi\) | ||||
−0.299277 | + | 0.954166i | \(0.596746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.39087 | −0.276052 | ||||||||
\(254\) | −6.04704 | −0.379425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.00252865 | 0.000158041 0 | ||||||||
\(257\) | 16.6866 | 1.04088 | 0.520442 | − | 0.853897i | \(-0.325767\pi\) | ||||
0.520442 | + | 0.853897i | \(0.325767\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.47691 | 0.588867 | ||||||||
\(260\) | −4.69022 | −0.290875 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.30099 | 0.574617 | ||||||||
\(263\) | −20.6328 | −1.27227 | −0.636136 | − | 0.771577i | \(-0.719468\pi\) | ||||
−0.636136 | + | 0.771577i | \(0.719468\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.08500 | 0.189510 | ||||||||
\(266\) | −3.76737 | −0.230992 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.6625 | 1.32325 | ||||||||
\(269\) | 20.3306 | 1.23958 | 0.619788 | − | 0.784769i | \(-0.287218\pi\) | ||||
0.619788 | + | 0.784769i | \(0.287218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.7783 | −1.07996 | −0.539979 | − | 0.841679i | \(-0.681568\pi\) | ||||
−0.539979 | + | 0.841679i | \(0.681568\pi\) | |||||||
\(272\) | 9.04076 | 0.548176 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.55344 | 0.456320 | ||||||||
\(275\) | −0.843828 | −0.0508847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.5352 | −1.11367 | −0.556835 | − | 0.830623i | \(-0.687984\pi\) | ||||
−0.556835 | + | 0.830623i | \(0.687984\pi\) | |||||||
\(278\) | −4.36054 | −0.261528 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.56610 | −0.153354 | ||||||||
\(281\) | 16.2926 | 0.971936 | 0.485968 | − | 0.873977i | \(-0.338467\pi\) | ||||
0.485968 | + | 0.873977i | \(0.338467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.7171 | −1.94483 | −0.972414 | − | 0.233260i | \(-0.925061\pi\) | ||||
−0.972414 | + | 0.233260i | \(0.925061\pi\) | |||||||
\(284\) | −12.8778 | −0.764159 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.10509 | 0.0653456 | ||||||||
\(287\) | 10.3021 | 0.608112 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.01134 | −0.294785 | ||||||||
\(290\) | 0.415481 | 0.0243979 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.0069 | 0.819693 | ||||||||
\(293\) | −33.3554 | −1.94864 | −0.974322 | − | 0.225161i | \(-0.927709\pi\) | ||||
−0.974322 | + | 0.225161i | \(0.927709\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.0512 | 0.818091 | ||||||||
\(296\) | 12.5846 | 0.731466 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.71565 | −0.389027 | ||||||||
\(299\) | −13.8762 | −0.802480 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.22412 | −0.185835 | ||||||||
\(302\) | 4.91870 | 0.283039 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.4090 | 0.826414 | ||||||||
\(305\) | 9.19572 | 0.526546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.9311 | −1.25167 | −0.625837 | − | 0.779954i | \(-0.715242\pi\) | ||||
−0.625837 | + | 0.779954i | \(0.715242\pi\) | |||||||
\(308\) | −2.06312 | −0.117557 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.37318 | −0.248380 | ||||||||
\(311\) | −28.4307 | −1.61216 | −0.806078 | − | 0.591810i | \(-0.798414\pi\) | ||||
−0.806078 | + | 0.591810i | \(0.798414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.8432 | 0.895510 | 0.447755 | − | 0.894156i | \(-0.352224\pi\) | ||||
0.447755 | + | 0.894156i | \(0.352224\pi\) | |||||||
\(314\) | 5.80437 | 0.327560 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.02806 | −0.451614 | ||||||||
\(317\) | 29.3576 | 1.64888 | 0.824442 | − | 0.565946i | \(-0.191489\pi\) | ||||
0.824442 | + | 0.565946i | \(0.191489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.713892 | 0.0399703 | ||||||||
\(320\) | 2.77929 | 0.155367 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.55239 | −0.197967 | ||||||||
\(323\) | 19.1073 | 1.06316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.66669 | −0.147921 | ||||||||
\(326\) | 2.81303 | 0.155800 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.6804 | 0.755372 | ||||||||
\(329\) | −8.78743 | −0.484467 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3846 | −0.955542 | −0.477771 | − | 0.878485i | \(-0.658555\pi\) | ||||
−0.477771 | + | 0.878485i | \(0.658555\pi\) | |||||||
\(332\) | 13.1811 | 0.723405 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.72675 | 0.149201 | ||||||||
\(335\) | 12.3165 | 0.672923 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.6331 | −0.851588 | −0.425794 | − | 0.904820i | \(-0.640005\pi\) | ||||
−0.425794 | + | 0.904820i | \(0.640005\pi\) | |||||||
\(338\) | −2.89199 | −0.157303 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.08984 | 0.330268 | ||||||||
\(341\) | −7.51413 | −0.406913 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7753 | 0.905782 | ||||||||
\(344\) | −4.28138 | −0.230837 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.61615 | −0.463207 | ||||||||
\(347\) | −25.4096 | −1.36406 | −0.682029 | − | 0.731325i | \(-0.738902\pi\) | ||||
−0.682029 | + | 0.731325i | \(0.738902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.60653 | −0.193053 | −0.0965266 | − | 0.995330i | \(-0.530773\pi\) | ||||
−0.0965266 | + | 0.995330i | \(0.530773\pi\) | |||||||
\(350\) | −0.682689 | −0.0364913 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.19740 | −0.223722 | ||||||||
\(353\) | 13.6806 | 0.728145 | 0.364072 | − | 0.931371i | \(-0.381386\pi\) | ||||
0.364072 | + | 0.931371i | \(0.381386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.32187 | −0.388604 | ||||||||
\(356\) | 1.75882 | 0.0932172 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.56187 | 0.346805 | ||||||||
\(359\) | −7.94331 | −0.419232 | −0.209616 | − | 0.977784i | \(-0.567221\pi\) | ||||
−0.209616 | + | 0.977784i | \(0.567221\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.4530 | 0.602788 | ||||||||
\(362\) | 9.03892 | 0.475075 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.51995 | −0.341738 | ||||||||
\(365\) | 7.96382 | 0.416845 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.168250 | −0.00878258 | −0.00439129 | − | 0.999990i | \(-0.501398\pi\) | ||||
−0.00439129 | + | 0.999990i | \(0.501398\pi\) | |||||||
\(368\) | 13.5868 | 0.708260 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.34803 | 0.174056 | ||||||||
\(371\) | 4.28850 | 0.222648 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.38560 | −0.434190 | −0.217095 | − | 0.976150i | \(-0.569658\pi\) | ||||
−0.217095 | + | 0.976150i | \(0.569658\pi\) | |||||||
\(374\) | −1.43487 | −0.0741952 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.6690 | −0.601785 | ||||||||
\(377\) | 2.25607 | 0.116193 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.4271 | −1.76840 | −0.884201 | − | 0.467107i | \(-0.845296\pi\) | ||||
−0.884201 | + | 0.467107i | \(0.845296\pi\) | |||||||
\(380\) | 9.70590 | 0.497902 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.2419 | 0.677513 | ||||||||
\(383\) | −31.7498 | −1.62234 | −0.811169 | − | 0.584812i | \(-0.801168\pi\) | ||||
−0.811169 | + | 0.584812i | \(0.801168\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.17302 | −0.0597825 | ||||||||
\(386\) | −10.2995 | −0.524232 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.6107 | −1.09712 | ||||||||
\(389\) | −32.9427 | −1.67026 | −0.835131 | − | 0.550051i | \(-0.814608\pi\) | ||||
−0.835131 | + | 0.550051i | \(0.814608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0170 | 0.911159 | ||||||||
\(392\) | 9.35459 | 0.472478 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.48686 | 0.377182 | ||||||||
\(395\) | −4.56446 | −0.229663 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0717 | 0.706238 | 0.353119 | − | 0.935578i | \(-0.385121\pi\) | ||||
0.353119 | + | 0.935578i | \(0.385121\pi\) | |||||||
\(398\) | −6.71199 | −0.336442 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.61108 | 0.130554 | ||||||||
\(401\) | −7.27441 | −0.363267 | −0.181633 | − | 0.983366i | \(-0.558138\pi\) | ||||
−0.181633 | + | 0.983366i | \(0.558138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.7464 | −1.18289 | ||||||||
\(404\) | 28.7469 | 1.43021 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.577566 | 0.0286641 | ||||||||
\(407\) | 5.75268 | 0.285150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.2480 | 1.34733 | 0.673663 | − | 0.739039i | \(-0.264720\pi\) | ||||
0.673663 | + | 0.739039i | \(0.264720\pi\) | |||||||
\(410\) | 3.63954 | 0.179744 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.08648 | −0.250593 | ||||||||
\(413\) | 19.5327 | 0.961144 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.49427 | 0.367879 | ||||||||
\(416\) | −13.2648 | −0.650359 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.28687 | −0.111854 | ||||||||
\(419\) | 13.7713 | 0.672772 | 0.336386 | − | 0.941724i | \(-0.390795\pi\) | ||||
0.336386 | + | 0.941724i | \(0.390795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.36210 | −0.163859 | −0.0819293 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819293 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(422\) | −13.0336 | −0.634468 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.69481 | 0.276564 | ||||||||
\(425\) | 3.46246 | 0.167954 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.7831 | 0.618618 | ||||||||
\(428\) | 8.55927 | 0.413728 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.13902 | −0.0549286 | ||||||||
\(431\) | −5.92980 | −0.285628 | −0.142814 | − | 0.989750i | \(-0.545615\pi\) | ||||
−0.142814 | + | 0.989750i | \(0.545615\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.5057 | −0.793215 | −0.396607 | − | 0.917988i | \(-0.629813\pi\) | ||||
−0.396607 | + | 0.917988i | \(0.629813\pi\) | |||||||
\(434\) | −6.07922 | −0.291812 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 34.9774 | 1.67511 | ||||||||
\(437\) | 28.7152 | 1.37364 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2327 | −0.774747 | −0.387373 | − | 0.921923i | \(-0.626618\pi\) | ||||
−0.387373 | + | 0.921923i | \(0.626618\pi\) | |||||||
\(440\) | −1.55768 | −0.0742594 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.53451 | −0.215685 | ||||||||
\(443\) | 2.61548 | 0.124265 | 0.0621327 | − | 0.998068i | \(-0.480210\pi\) | ||||
0.0621327 | + | 0.998068i | \(0.480210\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | 4.24737 | 0.201119 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.86353 | 0.182534 | ||||||||
\(449\) | 24.4580 | 1.15424 | 0.577122 | − | 0.816658i | \(-0.304176\pi\) | ||||
0.577122 | + | 0.816658i | \(0.304176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.25356 | 0.294469 | ||||||||
\(452\) | −23.7011 | −1.11481 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.73631 | 0.222286 | ||||||||
\(455\) | −3.70701 | −0.173787 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.3711 | 1.65459 | 0.827294 | − | 0.561769i | \(-0.189879\pi\) | ||||
0.827294 | + | 0.561769i | \(0.189879\pi\) | |||||||
\(458\) | −4.59514 | −0.214717 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.15204 | 0.426716 | ||||||||
\(461\) | 7.17198 | 0.334033 | 0.167016 | − | 0.985954i | \(-0.446587\pi\) | ||||
0.167016 | + | 0.985954i | \(0.446587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6301 | −1.37703 | −0.688513 | − | 0.725224i | \(-0.741736\pi\) | ||||
−0.688513 | + | 0.725224i | \(0.741736\pi\) | |||||||
\(464\) | −2.20901 | −0.102551 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.44856 | 0.0671035 | ||||||||
\(467\) | 22.3012 | 1.03198 | 0.515988 | − | 0.856596i | \(-0.327425\pi\) | ||||
0.515988 | + | 0.856596i | \(0.327425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.1214 | 0.790591 | ||||||||
\(470\) | −3.10445 | −0.143197 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25.9380 | 1.19389 | ||||||||
\(473\) | −1.95711 | −0.0899878 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.51842 | 0.253203 | ||||||||
\(476\) | 8.46558 | 0.388019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.91164 | 0.133175 | ||||||||
\(479\) | 4.79431 | 0.219058 | 0.109529 | − | 0.993984i | \(-0.465066\pi\) | ||||
0.109529 | + | 0.993984i | \(0.465066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1798 | 0.828928 | ||||||||
\(482\) | 0.244883 | 0.0111541 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.0946 | 0.822484 | ||||||||
\(485\) | −12.2871 | −0.557926 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.8404 | −0.627168 | −0.313584 | − | 0.949560i | \(-0.601530\pi\) | ||||
−0.313584 | + | 0.949560i | \(0.601530\pi\) | |||||||
\(488\) | 16.9750 | 0.768422 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.48871 | 0.112428 | ||||||||
\(491\) | 19.0079 | 0.857815 | 0.428907 | − | 0.903348i | \(-0.358899\pi\) | ||||
0.428907 | + | 0.903348i | \(0.358899\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.92930 | −0.131929 | ||||||||
\(494\) | −7.22704 | −0.325160 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.2511 | 1.04401 | ||||||||
\(497\) | −10.1782 | −0.456556 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.8767 | −1.11364 | −0.556818 | − | 0.830635i | \(-0.687978\pi\) | ||||
−0.556818 | + | 0.830635i | \(0.687978\pi\) | |||||||
\(500\) | 1.75882 | 0.0786567 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.65707 | −0.207855 | ||||||||
\(503\) | 7.21761 | 0.321817 | 0.160909 | − | 0.986969i | \(-0.448558\pi\) | ||||
0.160909 | + | 0.986969i | \(0.448558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.3445 | 0.727319 | ||||||||
\(506\) | −2.15637 | −0.0958624 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.6566 | 0.960858 | ||||||||
\(509\) | −32.5399 | −1.44230 | −0.721152 | − | 0.692777i | \(-0.756387\pi\) | ||||
−0.721152 | + | 0.692777i | \(0.756387\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0706 | 0.489736 | ||||||||
\(512\) | 22.6280 | 1.00003 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.19485 | 0.361459 | ||||||||
\(515\) | −2.89199 | −0.127436 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.33415 | −0.234596 | ||||||||
\(518\) | 4.65414 | 0.204491 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.92262 | −0.215871 | ||||||||
\(521\) | 17.9351 | 0.785751 | 0.392875 | − | 0.919592i | \(-0.371480\pi\) | ||||
0.392875 | + | 0.919592i | \(0.371480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.3547 | 0.977501 | 0.488751 | − | 0.872424i | \(-0.337453\pi\) | ||||
0.488751 | + | 0.872424i | \(0.337453\pi\) | |||||||
\(524\) | −33.3102 | −1.45516 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1328 | −0.441812 | ||||||||
\(527\) | 30.8326 | 1.34309 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.07662 | 0.177244 | ||||||||
\(530\) | 1.51505 | 0.0658097 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.4923 | 0.584966 | ||||||||
\(533\) | 19.7627 | 0.856018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.86649 | 0.210397 | ||||||||
\(536\) | 22.7359 | 0.982040 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.98440 | 0.430458 | ||||||||
\(539\) | 4.27617 | 0.184188 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3747 | 0.961963 | 0.480981 | − | 0.876731i | \(-0.340280\pi\) | ||||
0.480981 | + | 0.876731i | \(0.340280\pi\) | |||||||
\(542\) | −8.73100 | −0.375028 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.2231 | 0.738436 | ||||||||
\(545\) | 19.8869 | 0.851860 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0682 | 1.24287 | 0.621434 | − | 0.783467i | \(-0.286550\pi\) | ||||
0.621434 | + | 0.783467i | \(0.286550\pi\) | |||||||
\(548\) | −27.0516 | −1.15559 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.414406 | −0.0176703 | ||||||||
\(551\) | −4.66868 | −0.198892 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.34513 | −0.269822 | ||||||||
\(554\) | −9.10268 | −0.386736 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.6167 | 0.662294 | ||||||||
\(557\) | −44.6644 | −1.89249 | −0.946246 | − | 0.323448i | \(-0.895158\pi\) | ||||
−0.946246 | + | 0.323448i | \(0.895158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.18491 | −0.261594 | ||||||||
\(560\) | 3.62969 | 0.153383 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00135 | 0.337517 | ||||||||
\(563\) | −40.5811 | −1.71029 | −0.855144 | − | 0.518390i | \(-0.826531\pi\) | ||||
−0.855144 | + | 0.518390i | \(0.826531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.4756 | −0.566922 | ||||||||
\(566\) | −16.0675 | −0.675366 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.5159 | −0.567116 | ||||||||
\(569\) | −14.1652 | −0.593837 | −0.296919 | − | 0.954903i | \(-0.595959\pi\) | ||||
−0.296919 | + | 0.954903i | \(0.595959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.1693 | −1.09515 | −0.547576 | − | 0.836756i | \(-0.684449\pi\) | ||||
−0.547576 | + | 0.836756i | \(0.684449\pi\) | |||||||
\(572\) | −3.95774 | −0.165481 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.05937 | 0.211174 | ||||||||
\(575\) | 5.20352 | 0.217002 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.7700 | −1.53076 | −0.765378 | − | 0.643581i | \(-0.777448\pi\) | ||||
−0.765378 | + | 0.643581i | \(0.777448\pi\) | |||||||
\(578\) | −2.46109 | −0.102368 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.48799 | −0.0617854 | ||||||||
\(581\) | 10.4179 | 0.432207 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.60321 | 0.107814 | ||||||||
\(584\) | 14.7010 | 0.608330 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.3809 | −0.676690 | ||||||||
\(587\) | 29.4943 | 1.21736 | 0.608680 | − | 0.793416i | \(-0.291699\pi\) | ||||
0.608680 | + | 0.793416i | \(0.291699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.1405 | 2.02480 | ||||||||
\(590\) | 6.90058 | 0.284092 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.8006 | −0.731602 | ||||||||
\(593\) | −19.4743 | −0.799714 | −0.399857 | − | 0.916578i | \(-0.630940\pi\) | ||||
−0.399857 | + | 0.916578i | \(0.630940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.81322 | 0.197323 | ||||||||
\(596\) | 24.0512 | 0.985175 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.81464 | −0.278671 | ||||||||
\(599\) | −11.3938 | −0.465540 | −0.232770 | − | 0.972532i | \(-0.574779\pi\) | ||||
−0.232770 | + | 0.972532i | \(0.574779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9462 | −0.650458 | −0.325229 | − | 0.945635i | \(-0.605441\pi\) | ||||
−0.325229 | + | 0.945635i | \(0.605441\pi\) | |||||||
\(602\) | −1.58337 | −0.0645335 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.6156 | −0.716771 | ||||||||
\(605\) | 10.2880 | 0.418265 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.0138 | −1.09646 | −0.548228 | − | 0.836329i | \(-0.684697\pi\) | ||||
−0.548228 | + | 0.836329i | \(0.684697\pi\) | |||||||
\(608\) | 27.4500 | 1.11324 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.51605 | 0.182849 | ||||||||
\(611\) | −16.8572 | −0.681967 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.7061 | 1.88644 | 0.943221 | − | 0.332166i | \(-0.107779\pi\) | ||||
0.943221 | + | 0.332166i | \(0.107779\pi\) | |||||||
\(614\) | −10.7704 | −0.434659 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.16535 | −0.0872445 | ||||||||
\(617\) | −11.2320 | −0.452183 | −0.226092 | − | 0.974106i | \(-0.572595\pi\) | ||||
−0.226092 | + | 0.974106i | \(0.572595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.61409 | 0.306036 | 0.153018 | − | 0.988223i | \(-0.451101\pi\) | ||||
0.153018 | + | 0.988223i | \(0.451101\pi\) | |||||||
\(620\) | 15.6619 | 0.628999 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.9624 | −0.559841 | ||||||||
\(623\) | 1.39011 | 0.0556938 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.78064 | 0.310977 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.7876 | −0.829514 | ||||||||
\(629\) | −23.6049 | −0.941188 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0786 | −0.640078 | −0.320039 | − | 0.947404i | \(-0.603696\pi\) | ||||
−0.320039 | + | 0.947404i | \(0.603696\pi\) | |||||||
\(632\) | −8.42585 | −0.335162 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.4176 | 0.572596 | ||||||||
\(635\) | 12.3132 | 0.488634 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5137 | 0.535431 | ||||||||
\(638\) | 0.350595 | 0.0138802 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.3134 | 0.447201 | ||||||||
\(641\) | −45.1415 | −1.78298 | −0.891492 | − | 0.453037i | \(-0.850340\pi\) | ||||
−0.891492 | + | 0.453037i | \(0.850340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.2129 | 1.38866 | 0.694330 | − | 0.719657i | \(-0.255701\pi\) | ||||
0.694330 | + | 0.719657i | \(0.255701\pi\) | |||||||
\(644\) | 12.7224 | 0.501332 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.38367 | 0.369196 | ||||||||
\(647\) | −27.4490 | −1.07913 | −0.539566 | − | 0.841943i | \(-0.681412\pi\) | ||||
−0.539566 | + | 0.841943i | \(0.681412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8568 | 0.465419 | ||||||||
\(650\) | −1.30962 | −0.0513675 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0745 | −0.394548 | ||||||||
\(653\) | −25.6784 | −1.00488 | −0.502438 | − | 0.864613i | \(-0.667563\pi\) | ||||
−0.502438 | + | 0.864613i | \(0.667563\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9390 | −0.740007 | ||||||||
\(656\) | −19.3505 | −0.755512 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.31553 | −0.168237 | ||||||||
\(659\) | −51.0988 | −1.99053 | −0.995263 | − | 0.0972197i | \(-0.969005\pi\) | ||||
−0.995263 | + | 0.0972197i | \(0.969005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.9594 | 0.465166 | 0.232583 | − | 0.972577i | \(-0.425282\pi\) | ||||
0.232583 | + | 0.972577i | \(0.425282\pi\) | |||||||
\(662\) | −8.53761 | −0.331824 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.8342 | 0.536870 | ||||||||
\(665\) | 7.67124 | 0.297478 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.40226 | −0.170456 | ||||||||
\(668\) | −9.76548 | −0.377838 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.04868 | 0.233681 | ||||||||
\(671\) | 7.75961 | 0.299556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.6913 | −1.10597 | −0.552984 | − | 0.833192i | \(-0.686511\pi\) | ||||
−0.552984 | + | 0.833192i | \(0.686511\pi\) | |||||||
\(674\) | −7.67745 | −0.295724 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3572 | 0.398356 | ||||||||
\(677\) | 16.8646 | 0.648160 | 0.324080 | − | 0.946030i | \(-0.394945\pi\) | ||||
0.324080 | + | 0.946030i | \(0.394945\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.0804 | −0.655486 | ||||||||
\(680\) | 6.39159 | 0.245106 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.69021 | −0.141306 | ||||||||
\(683\) | 34.6719 | 1.32668 | 0.663342 | − | 0.748317i | \(-0.269138\pi\) | ||||
0.663342 | + | 0.748317i | \(0.269138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.3806 | −0.587661 | ||||||||
\(686\) | 8.23841 | 0.314544 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.05592 | 0.230880 | ||||||||
\(689\) | 8.22675 | 0.313414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.8207 | 0.906182 | 0.453091 | − | 0.891464i | \(-0.350321\pi\) | ||||
0.453091 | + | 0.891464i | \(0.350321\pi\) | |||||||
\(692\) | 30.8575 | 1.17303 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.4787 | −0.473686 | ||||||||
\(695\) | 8.87907 | 0.336802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.6601 | −0.971947 | ||||||||
\(698\) | −1.77118 | −0.0670401 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.44496 | 0.0924107 | ||||||||
\(701\) | 44.0179 | 1.66253 | 0.831267 | − | 0.555874i | \(-0.187616\pi\) | ||||
0.831267 | + | 0.555874i | \(0.187616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.6211 | −1.41891 | ||||||||
\(704\) | 2.34524 | 0.0883895 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.71858 | 0.252857 | ||||||||
\(707\) | 22.7207 | 0.854498 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.5537 | 1.33525 | 0.667623 | − | 0.744499i | \(-0.267312\pi\) | ||||
0.667623 | + | 0.744499i | \(0.267312\pi\) | |||||||
\(710\) | −3.59579 | −0.134948 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.84597 | 0.0691805 | ||||||||
\(713\) | 46.3364 | 1.73531 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.25023 | −0.0841538 | ||||||||
\(716\) | −23.5004 | −0.878252 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.90098 | −0.145583 | ||||||||
\(719\) | 5.13605 | 0.191542 | 0.0957711 | − | 0.995403i | \(-0.469468\pi\) | ||||
0.0957711 | + | 0.995403i | \(0.469468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.02020 | −0.149720 | ||||||||
\(722\) | 5.62459 | 0.209326 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −32.3717 | −1.20308 | ||||||||
\(725\) | −0.846016 | −0.0314203 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3730 | 0.458888 | 0.229444 | − | 0.973322i | \(-0.426309\pi\) | ||||
0.229444 | + | 0.973322i | \(0.426309\pi\) | |||||||
\(728\) | −6.84301 | −0.253619 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.91106 | 0.144755 | ||||||||
\(731\) | 8.03056 | 0.297021 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.5198 | 1.09034 | 0.545169 | − | 0.838326i | \(-0.316466\pi\) | ||||
0.545169 | + | 0.838326i | \(0.316466\pi\) | |||||||
\(734\) | −0.0826281 | −0.00304986 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.8836 | 0.954081 | ||||||||
\(737\) | 10.3930 | 0.382832 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.4459 | −1.89247 | −0.946234 | − | 0.323483i | \(-0.895146\pi\) | ||||
−0.946234 | + | 0.323483i | \(0.895146\pi\) | |||||||
\(740\) | −11.9905 | −0.440779 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.10610 | 0.0773173 | ||||||||
\(743\) | 49.0198 | 1.79836 | 0.899181 | − | 0.437577i | \(-0.144163\pi\) | ||||
0.899181 | + | 0.437577i | \(0.144163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.6746 | 0.501000 | ||||||||
\(746\) | −4.11819 | −0.150778 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.13878 | 0.187892 | ||||||||
\(749\) | 6.76498 | 0.247187 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.30801 | 0.230182 | 0.115091 | − | 0.993355i | \(-0.463284\pi\) | ||||
0.115091 | + | 0.993355i | \(0.463284\pi\) | |||||||
\(752\) | 16.5056 | 0.601897 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.10796 | 0.0403495 | ||||||||
\(755\) | −10.0156 | −0.364506 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.6669 | 0.969224 | 0.484612 | − | 0.874729i | \(-0.338961\pi\) | ||||
0.484612 | + | 0.874729i | \(0.338961\pi\) | |||||||
\(758\) | −16.9073 | −0.614099 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1868 | 0.369515 | ||||||||
\(761\) | 4.84411 | 0.175599 | 0.0877994 | − | 0.996138i | \(-0.472017\pi\) | ||||
0.0877994 | + | 0.996138i | \(0.472017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.6450 | 1.00082 | ||||||||
\(764\) | −47.4240 | −1.71574 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.5924 | −0.563377 | ||||||||
\(767\) | 37.4702 | 1.35297 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.2181 | −0.656962 | −0.328481 | − | 0.944511i | \(-0.606537\pi\) | ||||
−0.328481 | + | 0.944511i | \(0.606537\pi\) | |||||||
\(770\) | −0.576072 | −0.0207602 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 36.8863 | 1.32757 | ||||||||
\(773\) | 16.8245 | 0.605137 | 0.302568 | − | 0.953128i | \(-0.402156\pi\) | ||||
0.302568 | + | 0.953128i | \(0.402156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.90482 | 0.319870 | ||||||||
\(776\) | −22.6815 | −0.814218 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.1783 | −0.580019 | ||||||||
\(779\) | −40.8967 | −1.46528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.17840 | −0.221080 | ||||||||
\(782\) | 8.84820 | 0.316411 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.2318 | −0.472566 | ||||||||
\(785\) | −11.8191 | −0.421840 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.97325 | −0.177277 | −0.0886387 | − | 0.996064i | \(-0.528252\pi\) | ||||
−0.0886387 | + | 0.996064i | \(0.528252\pi\) | |||||||
\(788\) | −26.8132 | −0.955179 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.24162 | −0.0797533 | ||||||||
\(791\) | −18.7326 | −0.666054 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5222 | 0.870807 | ||||||||
\(794\) | 6.91065 | 0.245250 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.0381 | 0.852006 | ||||||||
\(797\) | −14.5828 | −0.516549 | −0.258275 | − | 0.966072i | \(-0.583154\pi\) | ||||
−0.258275 | + | 0.966072i | \(0.583154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.8875 | 0.774325 | ||||||||
\(800\) | 4.97424 | 0.175866 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.57249 | −0.126149 | ||||||||
\(803\) | 6.72009 | 0.237147 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.23349 | 0.254947 | ||||||||
\(806\) | −11.6619 | −0.410774 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.1713 | 1.06142 | ||||||||
\(809\) | −17.6121 | −0.619210 | −0.309605 | − | 0.950865i | \(-0.600197\pi\) | ||||
−0.309605 | + | 0.950865i | \(0.600197\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.2449 | 0.781124 | 0.390562 | − | 0.920577i | \(-0.372281\pi\) | ||||
0.390562 | + | 0.920577i | \(0.372281\pi\) | |||||||
\(812\) | −2.06847 | −0.0725892 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.82516 | 0.0990218 | ||||||||
\(815\) | −5.72799 | −0.200643 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.7990 | 0.447779 | ||||||||
\(818\) | 13.3816 | 0.467875 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.0345 | −0.455185 | ||||||||
\(821\) | −32.6129 | −1.13820 | −0.569099 | − | 0.822269i | \(-0.692708\pi\) | ||||
−0.569099 | + | 0.822269i | \(0.692708\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.9102 | 1.35633 | 0.678163 | − | 0.734912i | \(-0.262776\pi\) | ||||
0.678163 | + | 0.734912i | \(0.262776\pi\) | |||||||
\(824\) | −5.33852 | −0.185976 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.59259 | 0.333769 | ||||||||
\(827\) | 30.4207 | 1.05783 | 0.528915 | − | 0.848675i | \(-0.322599\pi\) | ||||
0.528915 | + | 0.848675i | \(0.322599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.8261 | 0.619125 | 0.309563 | − | 0.950879i | \(-0.399817\pi\) | ||||
0.309563 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(830\) | 3.68046 | 0.127751 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.41150 | 0.256948 | ||||||||
\(833\) | −17.5463 | −0.607944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.55230 | −0.192145 | ||||||||
\(836\) | 8.19011 | 0.283261 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.76312 | 0.233628 | ||||||||
\(839\) | −9.11047 | −0.314528 | −0.157264 | − | 0.987557i | \(-0.550267\pi\) | ||||
−0.157264 | + | 0.987557i | \(0.550267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2843 | −0.975319 | ||||||||
\(842\) | −1.65114 | −0.0569019 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 46.6782 | 1.60673 | ||||||||
\(845\) | 5.88876 | 0.202579 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.3014 | 0.491403 | ||||||||
\(848\) | −8.05517 | −0.276616 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.70043 | 0.0583242 | ||||||||
\(851\) | −35.4743 | −1.21604 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.2521 | −1.17277 | −0.586385 | − | 0.810033i | \(-0.699449\pi\) | ||||
−0.586385 | + | 0.810033i | \(0.699449\pi\) | |||||||
\(854\) | 6.27782 | 0.214823 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.98338 | 0.307046 | ||||||||
\(857\) | −16.3278 | −0.557745 | −0.278873 | − | 0.960328i | \(-0.589961\pi\) | ||||
−0.278873 | + | 0.960328i | \(0.589961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.30761 | −0.283452 | −0.141726 | − | 0.989906i | \(-0.545265\pi\) | ||||
−0.141726 | + | 0.989906i | \(0.545265\pi\) | |||||||
\(860\) | 4.07926 | 0.139102 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.91214 | −0.0991879 | ||||||||
\(863\) | −20.7305 | −0.705675 | −0.352838 | − | 0.935685i | \(-0.614783\pi\) | ||||
−0.352838 | + | 0.935685i | \(0.614783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.5445 | 0.596530 | ||||||||
\(866\) | −8.10601 | −0.275454 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21.7719 | 0.738986 | ||||||||
\(869\) | −3.85162 | −0.130657 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.8443 | 1.11289 | ||||||||
\(872\) | 36.7105 | 1.24318 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.1021 | 0.477012 | ||||||||
\(875\) | 1.39011 | 0.0469944 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.40594 | −0.115010 | −0.0575052 | − | 0.998345i | \(-0.518315\pi\) | ||||
−0.0575052 | + | 0.998345i | \(0.518315\pi\) | |||||||
\(878\) | −7.97195 | −0.269040 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.20330 | 0.0742732 | ||||||||
\(881\) | −28.2254 | −0.950939 | −0.475469 | − | 0.879732i | \(-0.657722\pi\) | ||||
−0.475469 | + | 0.879732i | \(0.657722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8931 | −0.400234 | −0.200117 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200117 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(884\) | 16.2397 | 0.546201 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.28447 | 0.0431527 | ||||||||
\(887\) | 46.2366 | 1.55247 | 0.776236 | − | 0.630442i | \(-0.217126\pi\) | ||||
0.776236 | + | 0.630442i | \(0.217126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.1167 | 0.574076 | ||||||||
\(890\) | 0.491103 | 0.0164618 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.2114 | −0.509314 | ||||||||
\(893\) | 34.8840 | 1.16735 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.3615 | −0.446625 | ||||||||
\(896\) | 15.7269 | 0.525399 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.0114 | 0.400825 | ||||||||
\(899\) | −7.53362 | −0.251260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6817 | −0.355859 | ||||||||
\(902\) | 3.07114 | 0.102258 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.8755 | −0.827346 | ||||||||
\(905\) | −18.4053 | −0.611814 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.53938 | −0.316750 | −0.158375 | − | 0.987379i | \(-0.550625\pi\) | ||||
−0.158375 | + | 0.987379i | \(0.550625\pi\) | |||||||
\(908\) | −16.9624 | −0.562918 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.82052 | −0.0603497 | ||||||||
\(911\) | 25.8522 | 0.856522 | 0.428261 | − | 0.903655i | \(-0.359126\pi\) | ||||
0.428261 | + | 0.903655i | \(0.359126\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.32387 | 0.209290 | ||||||||
\(914\) | 17.3708 | 0.574576 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.4569 | 0.543750 | ||||||||
\(917\) | −26.3273 | −0.869405 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.58561 | 0.184252 | 0.0921261 | − | 0.995747i | \(-0.470634\pi\) | ||||
0.0921261 | + | 0.995747i | \(0.470634\pi\) | |||||||
\(920\) | 9.60553 | 0.316685 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.52218 | 0.115997 | ||||||||
\(923\) | −19.5252 | −0.642679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.81736 | −0.224153 | ||||||||
\(926\) | −14.5514 | −0.478190 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.20829 | −0.138144 | ||||||||
\(929\) | −38.3430 | −1.25799 | −0.628996 | − | 0.777409i | \(-0.716534\pi\) | ||||
−0.628996 | + | 0.777409i | \(0.716534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.9651 | −0.916518 | ||||||||
\(932\) | −5.18783 | −0.169933 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.9522 | 0.358366 | ||||||||
\(935\) | 2.92172 | 0.0955506 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.6816 | −0.577632 | −0.288816 | − | 0.957385i | \(-0.593262\pi\) | ||||
−0.288816 | + | 0.957385i | \(0.593262\pi\) | |||||||
\(938\) | 8.40835 | 0.274542 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.1181 | 0.362634 | ||||||||
\(941\) | −0.603957 | −0.0196884 | −0.00984422 | − | 0.999952i | \(-0.503134\pi\) | ||||
−0.00984422 | + | 0.999952i | \(0.503134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.5630 | −1.25578 | ||||||||
\(944\) | −36.6887 | −1.19412 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.961140 | −0.0312494 | ||||||||
\(947\) | −13.2372 | −0.430151 | −0.215075 | − | 0.976597i | \(-0.569000\pi\) | ||||
−0.215075 | + | 0.976597i | \(0.569000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.2371 | 0.689384 | ||||||||
\(950\) | 2.71011 | 0.0879277 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.88505 | 0.287966 | ||||||||
\(953\) | −33.2791 | −1.07801 | −0.539007 | − | 0.842301i | \(-0.681201\pi\) | ||||
−0.539007 | + | 0.842301i | \(0.681201\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.9635 | −0.872520 | ||||||||
\(956\) | −10.4277 | −0.337254 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.35450 | 0.0760705 | ||||||||
\(959\) | −21.3807 | −0.690420 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.2957 | 1.55793 | ||||||||
\(962\) | 8.92816 | 0.287855 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.877016 | −0.0282468 | ||||||||
\(965\) | 20.9722 | 0.675120 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.7452 | 0.602804 | 0.301402 | − | 0.953497i | \(-0.402545\pi\) | ||||
0.301402 | + | 0.953497i | \(0.402545\pi\) | |||||||
\(968\) | 18.9912 | 0.610401 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.03421 | −0.193747 | ||||||||
\(971\) | 38.2456 | 1.22736 | 0.613679 | − | 0.789556i | \(-0.289689\pi\) | ||||
0.613679 | + | 0.789556i | \(0.289689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.3429 | 0.395696 | ||||||||
\(974\) | −6.79706 | −0.217792 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.0107 | −0.768565 | ||||||||
\(977\) | −12.7711 | −0.408583 | −0.204292 | − | 0.978910i | \(-0.565489\pi\) | ||||
−0.204292 | + | 0.978910i | \(0.565489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.843828 | 0.0269689 | ||||||||
\(980\) | −8.91295 | −0.284714 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.33484 | 0.297887 | ||||||||
\(983\) | 24.6723 | 0.786925 | 0.393462 | − | 0.919341i | \(-0.371277\pi\) | ||||
0.393462 | + | 0.919341i | \(0.371277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2450 | −0.485746 | ||||||||
\(986\) | −1.43859 | −0.0458140 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.8826 | 0.823436 | ||||||||
\(989\) | 12.0686 | 0.383760 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.86629 | −0.122817 | −0.0614084 | − | 0.998113i | \(-0.519559\pi\) | ||||
−0.0614084 | + | 0.998113i | \(0.519559\pi\) | |||||||
\(992\) | 44.2947 | 1.40636 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.99856 | −0.158545 | ||||||||
\(995\) | 13.6672 | 0.433278 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.57469 | 0.176552 | 0.0882761 | − | 0.996096i | \(-0.471864\pi\) | ||||
0.0882761 | + | 0.996096i | \(0.471864\pi\) | |||||||
\(998\) | −12.2170 | −0.386724 | ||||||||
\(999\) | 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 | 4005.2.a.v.1.7 | yes | 12 | |
3.2 | odd | 2 | 4005.2.a.u.1.6 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4005.2.a.u.1.6 | ✓ | 12 | 3.2 | odd | 2 | ||
4005.2.a.v.1.7 | yes | 12 | 1.1 | even | 1 | trivial |