Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,4,Mod(1,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.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: | \(17.7005730017\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 300.1 |
$q$-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 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54.0000 | −1.48015 | −0.740073 | − | 0.672526i | \(-0.765209\pi\) | ||||
−0.740073 | + | 0.672526i | \(0.765209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −55.0000 | −1.17340 | −0.586702 | − | 0.809803i | \(-0.699574\pi\) | ||||
−0.586702 | + | 0.809803i | \(0.699574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.0000 | 0.256802 | 0.128401 | − | 0.991722i | \(-0.459015\pi\) | ||||
0.128401 | + | 0.991722i | \(0.459015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.0000 | −0.301863 | −0.150931 | − | 0.988544i | \(-0.548227\pi\) | ||||
−0.150931 | + | 0.988544i | \(0.548227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.0000 | −0.163185 | −0.0815926 | − | 0.996666i | \(-0.526001\pi\) | ||||
−0.0815926 | + | 0.996666i | \(0.526001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −54.0000 | −0.345778 | −0.172889 | − | 0.984941i | \(-0.555310\pi\) | ||||
−0.172889 | + | 0.984941i | \(0.555310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −271.000 | −1.57010 | −0.785049 | − | 0.619434i | \(-0.787362\pi\) | ||||
−0.785049 | + | 0.619434i | \(0.787362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −162.000 | −0.854563 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 314.000 | 1.39517 | 0.697585 | − | 0.716502i | \(-0.254258\pi\) | ||||
0.697585 | + | 0.716502i | \(0.254258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −165.000 | −0.677465 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −360.000 | −1.37128 | −0.685641 | − | 0.727940i | \(-0.740478\pi\) | ||||
−0.685641 | + | 0.727940i | \(0.740478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −163.000 | −0.578076 | −0.289038 | − | 0.957318i | \(-0.593335\pi\) | ||||
−0.289038 | + | 0.957318i | \(0.593335\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 522.000 | 1.62003 | 0.810016 | − | 0.586407i | \(-0.199458\pi\) | ||||
0.810016 | + | 0.586407i | \(0.199458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −294.000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 54.0000 | 0.148265 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −36.0000 | −0.0933015 | −0.0466508 | − | 0.998911i | \(-0.514855\pi\) | ||||
−0.0466508 | + | 0.998911i | \(0.514855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −75.0000 | −0.174281 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 126.000 | 0.278031 | 0.139015 | − | 0.990290i | \(-0.455606\pi\) | ||||
0.139015 | + | 0.990290i | \(0.455606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.0000 | 0.0986514 | 0.0493257 | − | 0.998783i | \(-0.484293\pi\) | ||||
0.0493257 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −343.000 | −0.625435 | −0.312717 | − | 0.949846i | \(-0.601239\pi\) | ||||
−0.312717 | + | 0.949846i | \(0.601239\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −54.0000 | −0.0942150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1080.00 | −1.80525 | −0.902623 | − | 0.430433i | \(-0.858361\pi\) | ||||
−0.902623 | + | 0.430433i | \(0.858361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1054.00 | −1.68988 | −0.844941 | − | 0.534860i | \(-0.820364\pi\) | ||||
−0.844941 | + | 0.534860i | \(0.820364\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 378.000 | 0.559443 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −568.000 | −0.808924 | −0.404462 | − | 0.914555i | \(-0.632541\pi\) | ||||
−0.404462 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1422.00 | 1.88054 | 0.940270 | − | 0.340430i | \(-0.110573\pi\) | ||||
0.940270 | + | 0.340430i | \(0.110573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −162.000 | −0.199635 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1440.00 | 1.71505 | 0.857526 | − | 0.514440i | \(-0.172000\pi\) | ||||
0.857526 | + | 0.514440i | \(0.172000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 385.000 | 0.443505 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −813.000 | −0.906496 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −439.000 | −0.459523 | −0.229761 | − | 0.973247i | \(-0.573795\pi\) | ||||
−0.229761 | + | 0.973247i | \(0.573795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −486.000 | −0.493382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 828.000 | 0.815733 | 0.407867 | − | 0.913041i | \(-0.366273\pi\) | ||||
0.407867 | + | 0.913041i | \(0.366273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 548.000 | 0.524233 | 0.262117 | − | 0.965036i | \(-0.415579\pi\) | ||||
0.262117 | + | 0.965036i | \(0.415579\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1476.00 | −1.33355 | −0.666777 | − | 0.745257i | \(-0.732327\pi\) | ||||
−0.666777 | + | 0.745257i | \(0.732327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1277.00 | 1.12215 | 0.561075 | − | 0.827765i | \(-0.310388\pi\) | ||||
0.561075 | + | 0.827765i | \(0.310388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 942.000 | 0.805502 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1836.00 | 1.52846 | 0.764232 | − | 0.644942i | \(-0.223118\pi\) | ||||
0.764232 | + | 0.644942i | \(0.223118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −495.000 | −0.391135 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −126.000 | −0.0970622 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1585.00 | 1.19083 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1080.00 | −0.791710 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −592.000 | −0.413634 | −0.206817 | − | 0.978380i | \(-0.566310\pi\) | ||||
−0.206817 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −489.000 | −0.333752 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −468.000 | −0.312132 | −0.156066 | − | 0.987747i | \(-0.549881\pi\) | ||||
−0.156066 | + | 0.987747i | \(0.549881\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 175.000 | 0.114093 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2574.00 | 1.60519 | 0.802597 | − | 0.596521i | \(-0.203451\pi\) | ||||
0.802597 | + | 0.596521i | \(0.203451\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1756.00 | −1.07153 | −0.535763 | − | 0.844369i | \(-0.679976\pi\) | ||||
−0.535763 | + | 0.844369i | \(0.679976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1566.00 | 0.935326 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2970.00 | 1.73681 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −882.000 | −0.494872 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2682.00 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3395.00 | 1.82968 | 0.914838 | − | 0.403820i | \(-0.132318\pi\) | ||||
0.914838 | + | 0.403820i | \(0.132318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 162.000 | 0.0856008 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1549.00 | −0.787412 | −0.393706 | − | 0.919236i | \(-0.628807\pi\) | ||||
−0.393706 | + | 0.919236i | \(0.628807\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −108.000 | −0.0538677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 126.000 | 0.0616782 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −505.000 | −0.242667 | −0.121333 | − | 0.992612i | \(-0.538717\pi\) | ||||
−0.121333 | + | 0.992612i | \(0.538717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1476.00 | −0.683930 | −0.341965 | − | 0.939713i | \(-0.611092\pi\) | ||||
−0.341965 | + | 0.939713i | \(0.611092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 828.000 | 0.376878 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −225.000 | −0.100621 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2358.00 | 1.03627 | 0.518137 | − | 0.855298i | \(-0.326626\pi\) | ||||
0.518137 | + | 0.855298i | \(0.326626\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 378.000 | 0.160521 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1566.00 | 0.653901 | 0.326951 | − | 0.945041i | \(-0.393979\pi\) | ||||
0.326951 | + | 0.945041i | \(0.393979\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 305.000 | 0.125251 | 0.0626256 | − | 0.998037i | \(-0.480053\pi\) | ||||
0.0626256 | + | 0.998037i | \(0.480053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 141.000 | 0.0569564 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −972.000 | −0.380105 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1746.00 | −0.661446 | −0.330723 | − | 0.943728i | \(-0.607293\pi\) | ||||
−0.330723 | + | 0.943728i | \(0.607293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3877.00 | −1.44597 | −0.722986 | − | 0.690863i | \(-0.757231\pi\) | ||||
−0.722986 | + | 0.690863i | \(0.757231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2142.00 | 0.774676 | 0.387338 | − | 0.921938i | \(-0.373395\pi\) | ||||
0.387338 | + | 0.921938i | \(0.373395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4033.00 | −1.43664 | −0.718321 | − | 0.695712i | \(-0.755089\pi\) | ||||
−0.718321 | + | 0.695712i | \(0.755089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1029.00 | −0.361095 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 378.000 | 0.130692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −162.000 | −0.0543951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1350.00 | 0.446801 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4105.00 | −1.33934 | −0.669668 | − | 0.742661i | \(-0.733564\pi\) | ||||
−0.669668 | + | 0.742661i | \(0.733564\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3240.00 | −1.04226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1897.00 | 0.593441 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3162.00 | −0.975654 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −990.000 | −0.301333 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1385.00 | 0.415903 | 0.207952 | − | 0.978139i | \(-0.433320\pi\) | ||||
0.207952 | + | 0.978139i | \(0.433320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2520.00 | −0.736821 | −0.368410 | − | 0.929663i | \(-0.620098\pi\) | ||||
−0.368410 | + | 0.929663i | \(0.620098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5129.00 | 1.48006 | 0.740030 | − | 0.672574i | \(-0.234811\pi\) | ||||
0.740030 | + | 0.672574i | \(0.234811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1134.00 | 0.322994 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3240.00 | −0.910985 | −0.455492 | − | 0.890240i | \(-0.650537\pi\) | ||||
−0.455492 | + | 0.890240i | \(0.650537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1704.00 | −0.467032 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2988.00 | −0.808693 | −0.404347 | − | 0.914606i | \(-0.632501\pi\) | ||||
−0.404347 | + | 0.914606i | \(0.632501\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2647.00 | −0.707503 | −0.353752 | − | 0.935339i | \(-0.615094\pi\) | ||||
−0.353752 | + | 0.935339i | \(0.615094\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1375.00 | 0.354207 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4266.00 | 1.08573 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4212.00 | −1.05920 | −0.529600 | − | 0.848248i | \(-0.677658\pi\) | ||||
−0.529600 | + | 0.848248i | \(0.677658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 972.000 | 0.241538 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5724.00 | 1.38931 | 0.694656 | − | 0.719342i | \(-0.255556\pi\) | ||||
0.694656 | + | 0.719342i | \(0.255556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2198.00 | −0.527325 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −486.000 | −0.115259 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4608.00 | −1.08039 | −0.540193 | − | 0.841541i | \(-0.681649\pi\) | ||||
−0.540193 | + | 0.841541i | \(0.681649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4320.00 | 0.990186 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6426.00 | −1.45651 | −0.728253 | − | 0.685308i | \(-0.759667\pi\) | ||||
−0.728253 | + | 0.685308i | \(0.759667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3376.00 | −0.756743 | −0.378372 | − | 0.925654i | \(-0.623516\pi\) | ||||
−0.378372 | + | 0.925654i | \(0.623516\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1155.00 | 0.256058 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5381.00 | 1.16719 | 0.583597 | − | 0.812043i | \(-0.301645\pi\) | ||||
0.583597 | + | 0.812043i | \(0.301645\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2439.00 | −0.523366 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3474.00 | −0.737514 | −0.368757 | − | 0.929526i | \(-0.620217\pi\) | ||||
−0.368757 | + | 0.929526i | \(0.620217\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2269.00 | −0.476601 | −0.238300 | − | 0.971191i | \(-0.576590\pi\) | ||||
−0.238300 | + | 0.971191i | \(0.576590\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2520.00 | 0.518296 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4589.00 | −0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1317.00 | −0.265306 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1674.00 | −0.333775 | −0.166888 | − | 0.985976i | \(-0.553372\pi\) | ||||
−0.166888 | + | 0.985976i | \(0.553372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1458.00 | −0.284854 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 990.000 | 0.191482 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1141.00 | 0.218492 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2484.00 | 0.470964 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 539.000 | 0.100203 | 0.0501016 | − | 0.998744i | \(-0.484046\pi\) | ||||
0.0501016 | + | 0.998744i | \(0.484046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1644.00 | 0.302666 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1494.00 | 0.272402 | 0.136201 | − | 0.990681i | \(-0.456511\pi\) | ||||
0.136201 | + | 0.990681i | \(0.456511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3997.00 | −0.721801 | −0.360901 | − | 0.932604i | \(-0.617531\pi\) | ||||
−0.360901 | + | 0.932604i | \(0.617531\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3672.00 | −0.650600 | −0.325300 | − | 0.945611i | \(-0.605465\pi\) | ||||
−0.325300 | + | 0.945611i | \(0.605465\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2916.00 | 0.511801 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4428.00 | −0.769928 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −450.000 | −0.0775191 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3831.00 | 0.647874 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3654.00 | −0.612315 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1052.00 | 0.174692 | 0.0873461 | − | 0.996178i | \(-0.472161\pi\) | ||||
0.0873461 | + | 0.996178i | \(0.472161\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2826.00 | 0.465057 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3871.00 | −0.625718 | −0.312859 | − | 0.949800i | \(-0.601287\pi\) | ||||
−0.312859 | + | 0.949800i | \(0.601287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5508.00 | 0.882459 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14634.0 | 2.32398 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4459.00 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7686.00 | −1.18907 | −0.594533 | − | 0.804071i | \(-0.702663\pi\) | ||||
−0.594533 | + | 0.804071i | \(0.702663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −46.0000 | −0.00705537 | −0.00352768 | − | 0.999994i | \(-0.501123\pi\) | ||||
−0.00352768 | + | 0.999994i | \(0.501123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1485.00 | −0.225822 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6714.00 | −1.01232 | −0.506162 | − | 0.862439i | \(-0.668936\pi\) | ||||
−0.506162 | + | 0.862439i | \(0.668936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −378.000 | −0.0560389 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1296.00 | 0.190530 | 0.0952650 | − | 0.995452i | \(-0.469630\pi\) | ||||
0.0952650 | + | 0.995452i | \(0.469630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6234.00 | −0.908879 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4755.00 | 0.687528 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5903.00 | 0.839602 | 0.419801 | − | 0.907616i | \(-0.362100\pi\) | ||||
0.419801 | + | 0.907616i | \(0.362100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3240.00 | −0.457094 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 252.000 | 0.0352647 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8867.00 | 1.23087 | 0.615437 | − | 0.788186i | \(-0.288980\pi\) | ||||
0.615437 | + | 0.788186i | \(0.288980\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2970.00 | 0.405737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8837.00 | 1.19769 | 0.598847 | − | 0.800863i | \(-0.295626\pi\) | ||||
0.598847 | + | 0.800863i | \(0.295626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1776.00 | −0.238812 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10044.0 | −1.34001 | −0.670006 | − | 0.742356i | \(-0.733708\pi\) | ||||
−0.670006 | + | 0.742356i | \(0.733708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1467.00 | −0.192692 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2736.00 | −0.356609 | −0.178304 | − | 0.983975i | \(-0.557061\pi\) | ||||
−0.178304 | + | 0.983975i | \(0.557061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −324.000 | −0.0419064 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1404.00 | −0.180210 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12241.0 | −1.54750 | −0.773751 | − | 0.633490i | \(-0.781622\pi\) | ||||
−0.773751 | + | 0.633490i | \(0.781622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 525.000 | 0.0658719 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9036.00 | 1.12528 | 0.562639 | − | 0.826703i | \(-0.309786\pi\) | ||||
0.562639 | + | 0.826703i | \(0.309786\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14905.0 | 1.84236 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16956.0 | −2.06506 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8549.00 | 1.03355 | 0.516774 | − | 0.856122i | \(-0.327133\pi\) | ||||
0.516774 | + | 0.856122i | \(0.327133\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7722.00 | 0.926760 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −882.000 | −0.105086 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5268.00 | −0.618645 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1548.00 | 0.180489 | 0.0902443 | − | 0.995920i | \(-0.471235\pi\) | ||||
0.0902443 | + | 0.995920i | \(0.471235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6110.00 | 0.707323 | 0.353662 | − | 0.935373i | \(-0.384936\pi\) | ||||
0.353662 | + | 0.935373i | \(0.384936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4698.00 | 0.540011 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −329.000 | −0.0372867 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8910.00 | 1.00275 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5958.00 | 0.665863 | 0.332931 | − | 0.942951i | \(-0.391962\pi\) | ||||
0.332931 | + | 0.942951i | \(0.391962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7163.00 | 0.794993 | 0.397496 | − | 0.917604i | \(-0.369879\pi\) | ||||
0.397496 | + | 0.917604i | \(0.369879\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 450.000 | 0.0492595 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0000 | 0.00184821 | 0.000924107 | − | 1.00000i | \(-0.499706\pi\) | ||||
0.000924107 | 1.00000i | \(0.499706\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2646.00 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9432.00 | −1.01158 | −0.505788 | − | 0.862658i | \(-0.668798\pi\) | ||||
−0.505788 | + | 0.862658i | \(0.668798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8046.00 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15228.0 | −1.60057 | −0.800283 | − | 0.599623i | \(-0.795317\pi\) | ||||
−0.800283 | + | 0.599623i | \(0.795317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19440.0 | 2.02970 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10185.0 | 1.05636 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −250.000 | −0.0255897 | −0.0127949 | − | 0.999918i | \(-0.504073\pi\) | ||||
−0.0127949 | + | 0.999918i | \(0.504073\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 486.000 | 0.0494217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16956.0 | 1.71306 | 0.856529 | − | 0.516099i | \(-0.172616\pi\) | ||||
0.856529 | + | 0.516099i | \(0.172616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4384.00 | −0.440047 | −0.220023 | − | 0.975495i | \(-0.570613\pi\) | ||||
−0.220023 | + | 0.975495i | \(0.570613\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5166.00 | −0.511893 | −0.255946 | − | 0.966691i | \(-0.582387\pi\) | ||||
−0.255946 | + | 0.966691i | \(0.582387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2401.00 | 0.236392 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4647.00 | −0.454612 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8802.00 | 0.855637 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −324.000 | −0.0311005 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6966.00 | 0.664477 | 0.332239 | − | 0.943195i | \(-0.392196\pi\) | ||||
0.332239 | + | 0.943195i | \(0.392196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17270.0 | −1.63710 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 378.000 | 0.0356099 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18431.0 | 1.71497 | 0.857483 | − | 0.514512i | \(-0.172027\pi\) | ||||
0.857483 | + | 0.514512i | \(0.172027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1515.00 | −0.140104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1224.00 | 0.112502 | 0.0562509 | − | 0.998417i | \(-0.482085\pi\) | ||||
0.0562509 | + | 0.998417i | \(0.482085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −972.000 | −0.0887965 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7560.00 | 0.682319 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2449.00 | −0.219704 | −0.109852 | − | 0.993948i | \(-0.535038\pi\) | ||||
−0.109852 | + | 0.993948i | \(0.535038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4428.00 | −0.394867 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3312.00 | −0.293588 | −0.146794 | − | 0.989167i | \(-0.546895\pi\) | ||||
−0.146794 | + | 0.989167i | \(0.546895\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2484.00 | 0.217590 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9162.00 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7378.00 | 0.638715 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −675.000 | −0.0580935 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28188.0 | −2.39789 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7074.00 | 0.598293 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5418.00 | −0.455599 | −0.227799 | − | 0.973708i | \(-0.573153\pi\) | ||||
−0.227799 | + | 0.973708i | \(0.573153\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6829.00 | −0.570959 | −0.285479 | − | 0.958385i | \(-0.592153\pi\) | ||||
−0.285479 | + | 0.958385i | \(0.592153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4878.00 | −0.403205 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11843.0 | −0.973371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1134.00 | 0.0926769 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19800.0 | 1.60907 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4698.00 | 0.377530 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15876.0 | 1.26870 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3053.00 | 0.242622 | 0.121311 | − | 0.992615i | \(-0.461290\pi\) | ||||
0.121311 | + | 0.992615i | \(0.461290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 915.000 | 0.0723138 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20456.0 | 1.59897 | 0.799484 | − | 0.600687i | \(-0.205106\pi\) | ||||
0.799484 | + | 0.600687i | \(0.205106\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 423.000 | 0.0328838 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1350.00 | 0.104377 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3976.00 | 0.305745 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10854.0 | −0.825671 | −0.412835 | − | 0.910806i | \(-0.635462\pi\) | ||||
−0.412835 | + | 0.910806i | \(0.635462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8965.00 | 0.678317 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2916.00 | −0.219454 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24930.0 | −1.86621 | −0.933103 | − | 0.359609i | \(-0.882910\pi\) | ||||
−0.933103 | + | 0.359609i | \(0.882910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24786.0 | −1.82616 | −0.913078 | − | 0.407784i | \(-0.866302\pi\) | ||||
−0.913078 | + | 0.407784i | \(0.866302\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14785.0 | −1.08360 | −0.541798 | − | 0.840509i | \(-0.682256\pi\) | ||||
−0.541798 | + | 0.840509i | \(0.682256\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5238.00 | −0.381886 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15851.0 | 1.14365 | 0.571825 | − | 0.820376i | \(-0.306236\pi\) | ||||
0.571825 | + | 0.820376i | \(0.306236\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11631.0 | −0.834832 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9954.00 | −0.710777 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1944.00 | 0.138100 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23148.0 | 1.62763 | 0.813816 | − | 0.581122i | \(-0.197386\pi\) | ||||
0.813816 | + | 0.581122i | \(0.197386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6775.00 | 0.473954 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6426.00 | 0.447259 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21888.0 | −1.51574 | −0.757869 | − | 0.652407i | \(-0.773759\pi\) | ||||
−0.757869 | + | 0.652407i | \(0.773759\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12099.0 | −0.829446 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10764.0 | 0.734232 | 0.367116 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367116 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25597.0 | −1.73731 | −0.868655 | − | 0.495417i | \(-0.835015\pi\) | ||||
−0.868655 | + | 0.495417i | \(0.835015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3087.00 | −0.208478 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24976.0 | −1.67009 | −0.835045 | − | 0.550182i | \(-0.814558\pi\) | ||||
−0.835045 | + | 0.550182i | \(0.814558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1134.00 | 0.0754548 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28710.0 | −1.90095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2134.00 | −0.140606 | −0.0703030 | − | 0.997526i | \(-0.522397\pi\) | ||||
−0.0703030 | + | 0.997526i | \(0.522397\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13932.0 | 0.909046 | 0.454523 | − | 0.890735i | \(-0.349810\pi\) | ||||
0.454523 | + | 0.890735i | \(0.349810\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10429.0 | −0.677184 | −0.338592 | − | 0.940933i | \(-0.609951\pi\) | ||||
−0.338592 | + | 0.940933i | \(0.609951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −486.000 | −0.0314050 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10080.0 | −0.648229 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4050.00 | 0.257961 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5652.00 | 0.358283 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6283.00 | −0.396390 | −0.198195 | − | 0.980163i | \(-0.563508\pi\) | ||||
−0.198195 | + | 0.980163i | \(0.563508\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12315.0 | −0.773266 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16170.0 | 1.00578 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9720.00 | −0.601748 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20916.0 | −1.28882 | −0.644409 | − | 0.764681i | \(-0.722897\pi\) | ||||
−0.644409 | + | 0.764681i | \(0.722897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23452.0 | −1.43835 | −0.719173 | − | 0.694831i | \(-0.755479\pi\) | ||||
−0.719173 | + | 0.694831i | \(0.755479\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11916.0 | −0.724059 | −0.362030 | − | 0.932167i | \(-0.617916\pi\) | ||||
−0.362030 | + | 0.932167i | \(0.617916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6804.00 | −0.411526 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5691.00 | 0.342623 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31842.0 | 1.90823 | 0.954115 | − | 0.299441i | \(-0.0968003\pi\) | ||||
0.954115 | + | 0.299441i | \(0.0968003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9486.00 | −0.563294 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3672.00 | 0.217057 | 0.108529 | − | 0.994093i | \(-0.465386\pi\) | ||||
0.108529 | + | 0.994093i | \(0.465386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5138.00 | 0.302337 | 0.151169 | − | 0.988508i | \(-0.451696\pi\) | ||||
0.151169 | + | 0.988508i | \(0.451696\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2970.00 | −0.173975 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 972.000 | 0.0564258 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4155.00 | 0.240122 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2538.00 | −0.146018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5050.00 | −0.289247 | −0.144623 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144623 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28458.0 | 1.61555 | 0.807777 | − | 0.589488i | \(-0.200671\pi\) | ||||
0.807777 | + | 0.589488i | \(0.200671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3073.00 | 0.173683 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7560.00 | −0.425404 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24408.0 | 1.36742 | 0.683709 | − | 0.729755i | \(-0.260366\pi\) | ||||
0.683709 | + | 0.729755i | \(0.260366\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15387.0 | 0.854513 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1980.00 | 0.109480 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16328.0 | 0.898909 | 0.449455 | − | 0.893303i | \(-0.351618\pi\) | ||||
0.449455 | + | 0.893303i | \(0.351618\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3402.00 | 0.186481 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6480.00 | −0.352148 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9720.00 | −0.525957 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6246.00 | 0.336531 | 0.168265 | − | 0.985742i | \(-0.446183\pi\) | ||||
0.168265 | + | 0.985742i | \(0.446183\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7850.00 | −0.421150 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5796.00 | −0.308318 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30679.0 | −1.62507 | −0.812535 | − | 0.582913i | \(-0.801913\pi\) | ||||
−0.812535 | + | 0.582913i | \(0.801913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5112.00 | −0.269641 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4878.00 | 0.256217 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8964.00 | −0.466899 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15462.0 | 0.801996 | 0.400998 | − | 0.916079i | \(-0.368663\pi\) | ||||
0.400998 | + | 0.916079i | \(0.368663\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3836.00 | −0.198142 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7941.00 | −0.408477 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26801.0 | 1.36725 | 0.683627 | − | 0.729831i | \(-0.260401\pi\) | ||||
0.683627 | + | 0.729831i | \(0.260401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2934.00 | −0.148451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22858.0 | −1.15181 | −0.575907 | − | 0.817515i | \(-0.695351\pi\) | ||||
−0.575907 | + | 0.817515i | \(0.695351\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18522.0 | 0.925735 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16900.0 | −0.841240 | −0.420620 | − | 0.907237i | \(-0.638187\pi\) | ||||
−0.420620 | + | 0.907237i | \(0.638187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4125.00 | 0.204502 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8028.00 | 0.396391 | 0.198196 | − | 0.980162i | \(-0.436492\pi\) | ||||
0.198196 | + | 0.980162i | \(0.436492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12798.0 | 0.626846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10332.0 | 0.504036 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12448.0 | −0.604839 | −0.302419 | − | 0.953175i | \(-0.597794\pi\) | ||||
−0.302419 | + | 0.953175i | \(0.597794\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12636.0 | −0.611529 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30103.0 | −1.44533 | −0.722663 | − | 0.691200i | \(-0.757082\pi\) | ||||
−0.722663 | + | 0.691200i | \(0.757082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2916.00 | 0.139452 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17748.0 | −0.845420 | −0.422710 | − | 0.906265i | \(-0.638921\pi\) | ||||
−0.422710 | + | 0.906265i | \(0.638921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8939.00 | −0.424133 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6930.00 | −0.326242 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13283.0 | 0.622883 | 0.311442 | − | 0.950265i | \(-0.399188\pi\) | ||||
0.311442 | + | 0.950265i | \(0.399188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17172.0 | 0.802120 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26424.0 | 1.22950 | 0.614751 | − | 0.788721i | \(-0.289256\pi\) | ||||
0.614751 | + | 0.788721i | \(0.289256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6594.00 | −0.304451 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9000.00 | 0.413939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 58320.0 | 2.67203 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1458.00 | −0.0665449 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9709.00 | −0.439757 | −0.219878 | − | 0.975527i | \(-0.570566\pi\) | ||||
−0.219878 | + | 0.975527i | \(0.570566\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13824.0 | −0.623761 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12852.0 | −0.577705 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2585.00 | −0.115758 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7884.00 | −0.350396 | −0.175198 | − | 0.984533i | \(-0.556057\pi\) | ||||
−0.175198 | + | 0.984533i | \(0.556057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9396.00 | 0.416028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12960.0 | 0.571684 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56916.0 | 2.50127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19278.0 | −0.840914 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1476.00 | −0.0641451 | −0.0320726 | − | 0.999486i | \(-0.510211\pi\) | ||||
−0.0320726 | + | 0.999486i | \(0.510211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21455.0 | 0.928960 | 0.464480 | − | 0.885583i | \(-0.346241\pi\) | ||||
0.464480 | + | 0.885583i | \(0.346241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10128.0 | −0.436906 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4075.00 | 0.174500 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3465.00 | 0.147835 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31086.0 | 1.32145 | 0.660724 | − | 0.750629i | \(-0.270249\pi\) | ||||
0.660724 | + | 0.750629i | \(0.270249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23381.0 | 0.990292 | 0.495146 | − | 0.868810i | \(-0.335115\pi\) | ||||
0.495146 | + | 0.868810i | \(0.335115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3636.00 | 0.152885 | 0.0764426 | − | 0.997074i | \(-0.475644\pi\) | ||||
0.0764426 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4058.00 | 0.170012 | 0.0850061 | − | 0.996380i | \(-0.472909\pi\) | ||||
0.0850061 | + | 0.996380i | \(0.472909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16143.0 | 0.673880 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5292.00 | −0.220116 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7317.00 | −0.302165 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 306.000 | 0.0125915 | 0.00629576 | − | 0.999980i | \(-0.497996\pi\) | ||||
0.00629576 | + | 0.999980i | \(0.497996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10422.0 | −0.425804 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11095.0 | −0.450093 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6807.00 | −0.275166 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5652.00 | −0.227671 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42299.0 | 1.69788 | 0.848939 | − | 0.528491i | \(-0.177242\pi\) | ||||
0.848939 | + | 0.528491i | \(0.177242\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11484.0 | −0.457743 | −0.228872 | − | 0.973457i | \(-0.573504\pi\) | ||||
−0.228872 | + | 0.973457i | \(0.573504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33560.0 | 1.33301 | 0.666503 | − | 0.745502i | \(-0.267790\pi\) | ||||
0.666503 | + | 0.745502i | \(0.267790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7560.00 | 0.299238 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14976.0 | −0.590717 | −0.295359 | − | 0.955386i | \(-0.595439\pi\) | ||||
−0.295359 | + | 0.955386i | \(0.595439\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13767.0 | −0.539275 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30672.0 | 1.19733 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18865.0 | 0.733888 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3951.00 | −0.153174 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41893.0 | −1.61303 | −0.806514 | − | 0.591215i | \(-0.798649\pi\) | ||||
−0.806514 | + | 0.591215i | \(0.798649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5022.00 | −0.192705 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −720.000 | −0.0275340 | −0.0137670 | − | 0.999905i | \(-0.504382\pi\) | ||||
−0.0137670 | + | 0.999905i | \(0.504382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17309.0 | 0.659676 | 0.329838 | − | 0.944037i | \(-0.393006\pi\) | ||||
0.329838 | + | 0.944037i | \(0.393006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7002.00 | −0.265055 | −0.132528 | − | 0.991179i | \(-0.542309\pi\) | ||||
−0.132528 | + | 0.991179i | \(0.542309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4144.00 | 0.156339 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4374.00 | −0.164461 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13050.0 | −0.489028 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2970.00 | 0.110552 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14634.0 | 0.542905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −648.000 | −0.0239601 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3423.00 | 0.126147 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1484.00 | 0.0543279 | 0.0271640 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271640 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7452.00 | 0.271911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18882.0 | −0.686705 | −0.343353 | − | 0.939207i | \(-0.611563\pi\) | ||||
−0.343353 | + | 0.939207i | \(0.611563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −76788.0 | −2.78347 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3276.00 | 0.117975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50653.0 | −1.81816 | −0.909080 | − | 0.416622i | \(-0.863214\pi\) | ||||
−0.909080 | + | 0.416622i | \(0.863214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1617.00 | 0.0578523 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 59400.0 | 2.11828 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4932.00 | 0.174744 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35262.0 | 1.24533 | 0.622663 | − | 0.782490i | \(-0.286051\pi\) | ||||
0.622663 | + | 0.782490i | \(0.286051\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7350.00 | 0.258740 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4482.00 | 0.157271 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20279.0 | 0.707029 | 0.353514 | − | 0.935429i | \(-0.384987\pi\) | ||||
0.353514 | + | 0.935429i | \(0.384987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11991.0 | −0.416732 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42390.0 | 1.46852 | 0.734259 | − | 0.678870i | \(-0.237530\pi\) | ||||
0.734259 | + | 0.678870i | \(0.237530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6480.00 | 0.223773 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42426.0 | −1.45582 | −0.727909 | − | 0.685674i | \(-0.759508\pi\) | ||||
−0.727909 | + | 0.685674i | \(0.759508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57970.0 | 1.98291 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11016.0 | −0.375624 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48168.0 | 1.63727 | 0.818633 | − | 0.574317i | \(-0.194732\pi\) | ||||
0.818633 | + | 0.574317i | \(0.194732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8748.00 | 0.295489 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18018.0 | −0.606707 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43650.0 | 1.46521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13284.0 | −0.444518 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51400.0 | −1.70932 | −0.854660 | − | 0.519188i | \(-0.826234\pi\) | ||||
−0.854660 | + | 0.519188i | \(0.826234\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1350.00 | −0.0447557 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33858.0 | 1.11901 | 0.559503 | − | 0.828828i | \(-0.310992\pi\) | ||||
0.559503 | + | 0.828828i | \(0.310992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12292.0 | 0.404998 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47106.0 | 1.54253 | 0.771266 | − | 0.636513i | \(-0.219624\pi\) | ||||
0.771266 | + | 0.636513i | \(0.219624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −77760.0 | −2.53853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11493.0 | 0.374050 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20844.0 | −0.676318 | −0.338159 | − | 0.941089i | \(-0.609804\pi\) | ||||
−0.338159 | + | 0.941089i | \(0.609804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10962.0 | −0.353520 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2934.00 | 0.0943334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4133.00 | 0.132481 | 0.0662407 | − | 0.997804i | \(-0.478899\pi\) | ||||
0.0662407 | + | 0.997804i | \(0.478899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3156.00 | 0.100859 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33122.0 | 1.05214 | 0.526070 | − | 0.850441i | \(-0.323665\pi\) | ||||
0.526070 | + | 0.850441i | \(0.323665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8478.00 | 0.268501 |
(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 | 300.4.a.g.1.1 | yes | 1 | |
3.2 | odd | 2 | 900.4.a.h.1.1 | 1 | |||
4.3 | odd | 2 | 1200.4.a.m.1.1 | 1 | |||
5.2 | odd | 4 | 300.4.d.a.49.1 | 2 | |||
5.3 | odd | 4 | 300.4.d.a.49.2 | 2 | |||
5.4 | even | 2 | 300.4.a.c.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 900.4.d.j.649.1 | 2 | |||
15.8 | even | 4 | 900.4.d.j.649.2 | 2 | |||
15.14 | odd | 2 | 900.4.a.k.1.1 | 1 | |||
20.3 | even | 4 | 1200.4.f.s.49.1 | 2 | |||
20.7 | even | 4 | 1200.4.f.s.49.2 | 2 | |||
20.19 | odd | 2 | 1200.4.a.y.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.4.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
300.4.a.g.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
300.4.d.a.49.1 | 2 | 5.2 | odd | 4 | |||
300.4.d.a.49.2 | 2 | 5.3 | odd | 4 | |||
900.4.a.h.1.1 | 1 | 3.2 | odd | 2 | |||
900.4.a.k.1.1 | 1 | 15.14 | odd | 2 | |||
900.4.d.j.649.1 | 2 | 15.2 | even | 4 | |||
900.4.d.j.649.2 | 2 | 15.8 | even | 4 | |||
1200.4.a.m.1.1 | 1 | 4.3 | odd | 2 | |||
1200.4.a.y.1.1 | 1 | 20.19 | odd | 2 | |||
1200.4.f.s.49.1 | 2 | 20.3 | even | 4 | |||
1200.4.f.s.49.2 | 2 | 20.7 | even | 4 |