Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 158x^{6} + 8461x^{4} + 180672x^{2} + 1232100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.2 | ||
Root | \(-5.92762i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.e.895.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 17.7376i | − | 1.58650i | −0.608899 | − | 0.793248i | \(-0.708389\pi\) | ||
0.608899 | − | 0.793248i | \(-0.291611\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.09706 | + | 18.4011i | −0.113231 | + | 0.993569i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 32.9212i | − | 0.902373i | −0.892430 | − | 0.451186i | \(-0.851001\pi\) | ||
0.892430 | − | 0.451186i | \(-0.148999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 53.7866i | 1.14752i | 0.819025 | + | 0.573758i | \(0.194515\pi\) | ||||
−0.819025 | + | 0.573758i | \(0.805485\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 53.2127i | 0.915963i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 48.1047i | 0.686301i | 0.939280 | + | 0.343150i | \(0.111494\pi\) | ||||
−0.939280 | + | 0.343150i | \(0.888506\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110.800 | 1.33785 | 0.668927 | − | 0.743328i | \(-0.266754\pi\) | ||||
0.668927 | + | 0.743328i | \(0.266754\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.29119 | − | 55.2034i | 0.0653739 | − | 0.573637i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 157.820i | − | 1.43077i | −0.698732 | − | 0.715384i | \(-0.746252\pi\) | ||
0.698732 | − | 0.715384i | \(-0.253748\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −189.621 | −1.51697 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 72.0082 | 0.461089 | 0.230545 | − | 0.973062i | \(-0.425949\pi\) | ||||
0.230545 | + | 0.973062i | \(0.425949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −184.189 | −1.06714 | −0.533570 | − | 0.845756i | \(-0.679150\pi\) | ||||
−0.533570 | + | 0.845756i | \(0.679150\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 98.7635i | 0.520985i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 326.391 | + | 37.1968i | 1.57629 | + | 0.179640i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −422.967 | −1.87933 | −0.939667 | − | 0.342091i | \(-0.888865\pi\) | ||||
−0.939667 | + | 0.342091i | \(0.888865\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 161.360i | − | 0.662519i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 346.448i | 1.31966i | 0.751415 | + | 0.659830i | \(0.229372\pi\) | ||||
−0.751415 | + | 0.659830i | \(0.770628\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 198.168i | − | 0.702800i | −0.936225 | − | 0.351400i | \(-0.885706\pi\) | ||
0.936225 | − | 0.351400i | \(-0.114294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 159.638i | − | 0.528832i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 29.0729 | 0.0902281 | 0.0451141 | − | 0.998982i | \(-0.485635\pi\) | ||||
0.0451141 | + | 0.998982i | \(0.485635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.205 | − | 77.1768i | −0.974358 | − | 0.225005i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 144.314i | − | 0.396236i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −682.553 | −1.76898 | −0.884490 | − | 0.466560i | \(-0.845493\pi\) | ||||
−0.884490 | + | 0.466560i | \(0.845493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −583.941 | −1.43161 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −332.400 | −0.772411 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 305.320 | 0.673716 | 0.336858 | − | 0.941555i | \(-0.390636\pi\) | ||||
0.336858 | + | 0.941555i | \(0.390636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 172.135i | − | 0.361306i | −0.983547 | − | 0.180653i | \(-0.942179\pi\) | ||
0.983547 | − | 0.180653i | \(-0.0578211\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −18.8736 | + | 165.610i | −0.0377436 | + | 0.331190i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 954.042 | 1.82053 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 109.033i | − | 0.198814i | −0.995047 | − | 0.0994071i | \(-0.968305\pi\) | ||
0.995047 | − | 0.0994071i | \(-0.0316946\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 473.459i | 0.826054i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 741.453i | 1.23936i | 0.784856 | + | 0.619678i | \(0.212737\pi\) | ||||
−0.784856 | + | 0.619678i | \(0.787263\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 752.602i | 1.20665i | 0.797496 | + | 0.603325i | \(0.206158\pi\) | ||||
−0.797496 | + | 0.603325i | \(0.793842\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 568.863 | 0.875821 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 605.787 | + | 69.0378i | 0.896569 | + | 0.102176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 449.132i | − | 0.639637i | −0.947479 | − | 0.319818i | \(-0.896378\pi\) | ||
0.947479 | − | 0.319818i | \(-0.103622\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 262.988 | 0.347791 | 0.173895 | − | 0.984764i | \(-0.444365\pi\) | ||||
0.173895 | + | 0.984764i | \(0.444365\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 853.261 | 1.08881 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −216.025 | −0.266210 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 674.294i | − | 0.803090i | −0.915839 | − | 0.401545i | \(-0.868473\pi\) | ||
0.915839 | − | 0.401545i | \(-0.131527\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −989.735 | − | 112.794i | −1.14014 | − | 0.129934i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 552.567 | 0.616113 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1965.32i | − | 2.12250i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1459.49i | 1.52771i | 0.645385 | + | 0.763857i | \(0.276697\pi\) | ||||
−0.645385 | + | 0.763857i | \(0.723303\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 296.290i | − | 0.300791i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 226.672i | 0.223314i | 0.993747 | + | 0.111657i | \(0.0356158\pi\) | ||||
−0.993747 | + | 0.111657i | \(0.964384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −712.681 | −0.681772 | −0.340886 | − | 0.940105i | \(-0.610727\pi\) | ||||
−0.340886 | + | 0.940105i | \(0.610727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −979.174 | − | 111.590i | −0.910073 | − | 0.103715i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 759.426i | 0.686135i | 0.939311 | + | 0.343068i | \(0.111466\pi\) | ||||
−0.939311 | + | 0.343068i | \(0.888534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1081.36 | 0.950231 | 0.475115 | − | 0.879923i | \(-0.342406\pi\) | ||||
0.475115 | + | 0.879923i | \(0.342406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1268.90 | 1.08503 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1934.09 | 1.61013 | 0.805063 | − | 0.593189i | \(-0.202131\pi\) | ||||
0.805063 | + | 0.593189i | \(0.202131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2799.33 | −2.26991 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 484.079i | 0.382505i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −885.183 | − | 100.879i | −0.681887 | − | 0.0777104i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 247.198 | 0.185723 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1039.34i | − | 0.761906i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1146.22i | 0.820166i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2518.01i | 1.75935i | 0.475574 | + | 0.879676i | \(0.342240\pi\) | ||||
−0.475574 | + | 0.879676i | \(0.657760\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 594.505i | 0.405762i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1114.33 | −0.743204 | −0.371602 | − | 0.928392i | \(-0.621191\pi\) | ||||
−0.371602 | + | 0.928392i | \(0.621191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −232.355 | + | 2038.85i | −0.151486 | + | 1.32925i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 478.914i | 0.305321i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 260.914 | 0.162711 | 0.0813555 | − | 0.996685i | \(-0.474075\pi\) | ||||
0.0813555 | + | 0.996685i | \(0.474075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 505.973 | 0.308749 | 0.154374 | − | 0.988012i | \(-0.450664\pi\) | ||||
0.154374 | + | 0.988012i | \(0.450664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −87.2188 | −0.0520932 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1770.72 | 1.03549 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1277.25i | − | 0.731516i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1002.61 | + | 231.530i | 0.562546 | + | 0.129907i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1397.28 | −0.768254 | −0.384127 | − | 0.923280i | \(-0.625497\pi\) | ||||
−0.384127 | + | 0.923280i | \(0.625497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 344.187i | 0.185493i | 0.995690 | + | 0.0927467i | \(0.0295647\pi\) | ||||
−0.995690 | + | 0.0927467i | \(0.970435\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 432.943i | 0.228767i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3267.06i | 1.69301i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2450.31i | 1.24558i | 0.782390 | + | 0.622789i | \(0.214000\pi\) | ||||
−0.782390 | + | 0.622789i | \(0.786000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2047.66 | 1.02132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2904.06 | + | 330.958i | 1.42157 | + | 0.162007i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1749.52i | − | 0.840693i | −0.907364 | − | 0.420346i | \(-0.861909\pi\) | ||
0.907364 | − | 0.420346i | \(-0.138091\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1751.82 | 0.826540 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4072.62 | 1.88712 | 0.943560 | − | 0.331202i | \(-0.107454\pi\) | ||||
0.943560 | + | 0.331202i | \(0.107454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −695.995 | −0.316793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 997.199 | 0.445952 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3988.51i | 1.75284i | 0.481550 | + | 0.876419i | \(0.340074\pi\) | ||||
−0.481550 | + | 0.876419i | \(0.659926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 397.647 | − | 3489.24i | 0.171767 | − | 1.50721i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −915.960 | −0.388970 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 32.2713i | − | 0.0134753i | −0.999977 | − | 0.00673763i | \(-0.997855\pi\) | ||
0.999977 | − | 0.00673763i | \(-0.00214467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 233.112i | − | 0.0957299i | −0.998854 | − | 0.0478650i | \(-0.984758\pi\) | ||
0.998854 | − | 0.0478650i | \(-0.0152417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 516.405i | 0.208600i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7502.40i | 2.98155i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1583.66 | 0.619299 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 56.6208 | − | 496.831i | 0.0217913 | − | 0.191212i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 111.172i | 0.0421158i | 0.999778 | + | 0.0210579i | \(0.00670344\pi\) | ||||
−0.999778 | + | 0.0210579i | \(0.993297\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1713.45 | −0.639052 | −0.319526 | − | 0.947577i | \(-0.603524\pi\) | ||||
−0.319526 | + | 0.947577i | \(0.603524\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2862.13 | −1.05108 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4045.10 | −1.46295 | −0.731475 | − | 0.681868i | \(-0.761168\pi\) | ||||
−0.731475 | + | 0.681868i | \(0.761168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4480.63 | 1.59610 | 0.798048 | − | 0.602594i | \(-0.205866\pi\) | ||||
0.798048 | + | 0.602594i | \(0.205866\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 327.100i | 0.114785i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −151.006 | + | 1325.03i | −0.0522096 | + | 0.458124i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6145.14 | 2.09363 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1420.38i | − | 0.476922i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3647.66i | − | 1.20724i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3937.96i | 1.28483i | 0.766355 | + | 0.642417i | \(0.222068\pi\) | ||||
−0.766355 | + | 0.642417i | \(0.777932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2224.36i | − | 0.715543i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3515.02 | −1.11499 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 386.256 | − | 3389.29i | 0.120833 | − | 1.06028i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2257.81i | − | 0.696659i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2587.39 | −0.787541 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6231.07 | −1.87114 | −0.935568 | − | 0.353147i | \(-0.885112\pi\) | ||||
−0.935568 | + | 0.353147i | \(0.885112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1706.59 | −0.505656 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2627.92 | 0.768377 | 0.384188 | − | 0.923255i | \(-0.374481\pi\) | ||||
0.384188 | + | 0.923255i | \(0.374481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1930.43i | 0.557059i | 0.960428 | + | 0.278530i | \(0.0898471\pi\) | ||||
−0.960428 | + | 0.278530i | \(0.910153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1817.36 | − | 207.113i | −0.517635 | − | 0.0589916i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5138.78 | −1.44486 | −0.722431 | − | 0.691443i | \(-0.756975\pi\) | ||||
−0.722431 | + | 0.691443i | \(0.756975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 515.683i | − | 0.143147i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1347.40i | 0.369294i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5724.04i | 1.54919i | 0.632455 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632455 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5731.84i | 1.53204i | 0.642820 | + | 0.766018i | \(0.277764\pi\) | ||||
−0.642820 | + | 0.766018i | \(0.722236\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1368.93 | + | 5927.97i | −0.356970 | + | 1.54581i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5959.55i | 1.53521i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −788.963 | −0.200797 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2433.43 | −0.611940 | −0.305970 | − | 0.952041i | \(-0.598981\pi\) | ||||
−0.305970 | + | 0.952041i | \(0.598981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5195.60 | −1.29109 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2559.78 | −0.628626 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2495.76i | 0.605762i | 0.953028 | + | 0.302881i | \(0.0979485\pi\) | ||||
−0.953028 | + | 0.302881i | \(0.902051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 886.989 | − | 7783.08i | 0.212799 | − | 1.86725i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 648.074 | 0.153696 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1255.35i | 0.294328i | 0.989112 | + | 0.147164i | \(0.0470146\pi\) | ||||
−0.989112 | + | 0.147164i | \(0.952985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12106.8i | 2.80648i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2022.88i | 0.463664i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2843.99i | − | 0.644614i | −0.946635 | − | 0.322307i | \(-0.895542\pi\) | ||
0.946635 | − | 0.322307i | \(-0.104458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −688.100 | −0.154240 | −0.0771201 | − | 0.997022i | \(-0.524572\pi\) | ||||
−0.0771201 | + | 0.997022i | \(0.524572\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2969.20 | + | 338.382i | 0.658258 | + | 0.0750176i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6242.54i | 1.36887i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3641.63 | −0.789906 | −0.394953 | − | 0.918701i | \(-0.629239\pi\) | ||||
−0.394953 | + | 0.918701i | \(0.629239\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1657.70 | −0.355713 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 471.011 | 0.0999935 | 0.0499967 | − | 0.998749i | \(-0.484079\pi\) | ||||
0.0499967 | + | 0.998749i | \(0.484079\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6928.51 | −1.45533 | −0.727663 | − | 0.685935i | \(-0.759393\pi\) | ||||
−0.727663 | + | 0.685935i | \(0.759393\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5895.96i | 1.22543i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6375.04 | − | 726.523i | −1.31117 | − | 0.149426i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2598.93 | 0.528991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4378.46i | − | 0.882026i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6739.54i | − | 1.34378i | −0.740650 | − | 0.671891i | \(-0.765482\pi\) | ||
0.740650 | − | 0.671891i | \(-0.234518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5415.63i | − | 1.06885i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 888.871i | 0.173662i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8488.57 | 1.64183 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3646.53 | + | 415.572i | 0.698280 | + | 0.0795787i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 680.016i | − | 0.128930i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3053.26 | −0.573210 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7974.24 | 1.48246 | 0.741228 | − | 0.671253i | \(-0.234244\pi\) | ||||
0.741228 | + | 0.671253i | \(0.234244\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2138.04 | 0.393621 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 461.001 | 0.0840546 | 0.0420273 | − | 0.999116i | \(-0.486618\pi\) | ||||
0.0420273 | + | 0.999116i | \(0.486618\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1977.23i | − | 0.357059i | −0.983935 | − | 0.178530i | \(-0.942866\pi\) | ||
0.983935 | − | 0.178530i | \(-0.0571340\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2937.52 | + | 334.771i | 0.525431 | + | 0.0598801i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1570.62 | 0.278280 | 0.139140 | − | 0.990273i | \(-0.455566\pi\) | ||||
0.139140 | + | 0.990273i | \(0.455566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2370.59i | − | 0.416075i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2278.28i | − | 0.396140i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5330.00i | 0.918171i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 10199.1i | − | 1.74074i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3244.07 | −0.548616 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −60.9678 | + | 534.975i | −0.0102166 | + | 0.0896479i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5222.32i | 0.867204i | 0.901104 | + | 0.433602i | \(0.142758\pi\) | ||||
−0.901104 | + | 0.433602i | \(0.857242\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3806.70 | −0.626444 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1933.99 | −0.315418 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3136.18 | −0.506940 | −0.253470 | − | 0.967343i | \(-0.581572\pi\) | ||||
−0.253470 | + | 0.967343i | \(0.581572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5802.28 | −0.929607 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6063.72i | 0.962958i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2120.99 | − | 5987.90i | 0.333886 | − | 0.942614i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8398.00 | 1.31053 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2160.06i | − | 0.334173i | −0.985942 | − | 0.167087i | \(-0.946564\pi\) | ||
0.985942 | − | 0.167087i | \(-0.0534359\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4717.67i | 0.723584i | 0.932259 | + | 0.361792i | \(0.117835\pi\) | ||||
−0.932259 | + | 0.361792i | \(0.882165\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1452.24i | − | 0.220840i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2083.75i | 0.314184i | 0.987584 | + | 0.157092i | \(0.0502119\pi\) | ||||
−0.987584 | + | 0.157092i | \(0.949788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13151.6 | 1.96623 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2655.55 | + | 302.636i | 0.393688 | + | 0.0448661i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2144.44i | 0.315263i | 0.987498 | + | 0.157631i | \(0.0503858\pi\) | ||||
−0.987498 | + | 0.157631i | \(0.949614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5417.62 | 0.789855 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −741.594 | −0.107227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13349.3 | 1.91434 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2435.16 | 0.346361 | 0.173181 | − | 0.984890i | \(-0.444596\pi\) | ||||
0.173181 | + | 0.984890i | \(0.444596\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3118.03i | 0.439887i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1431.36 | − | 12559.8i | 0.200303 | − | 1.75760i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9190.90 | −1.27584 | −0.637918 | − | 0.770105i | \(-0.720204\pi\) | ||||
−0.637918 | + | 0.770105i | \(0.720204\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3438.65i | − | 0.473523i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3873.08i | 0.529108i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3771.98i | − | 0.511223i | −0.966780 | − | 0.255612i | \(-0.917723\pi\) | ||
0.966780 | − | 0.255612i | \(-0.0822769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 7554.04i | − | 1.01576i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3974.64 | 0.530273 | 0.265136 | − | 0.964211i | \(-0.414583\pi\) | ||||
0.265136 | + | 0.964211i | \(0.414583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1224.56 | − | 10745.2i | 0.162102 | − | 1.42240i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 1783.52i | − | 0.234267i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8337.10 | 1.08665 | 0.543326 | − | 0.839522i | \(-0.317165\pi\) | ||||
0.543326 | + | 0.839522i | \(0.317165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7591.87 | 0.981937 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3343.00 | 0.429089 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7966.51 | −1.01478 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8116.13i | 1.02604i | 0.858378 | + | 0.513019i | \(0.171473\pi\) | ||||
−0.858378 | + | 0.513019i | \(0.828527\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 697.064 | − | 6116.54i | 0.0874607 | − | 0.767443i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8543.46 | 1.06394 | 0.531970 | − | 0.846763i | \(-0.321452\pi\) | ||||
0.531970 | + | 0.846763i | \(0.321452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 9906.90i | − | 1.22456i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1436.74i | − | 0.176277i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13924.6i | 1.69586i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4970.55i | 0.600923i | 0.953794 | + | 0.300462i | \(0.0971408\pi\) | ||||
−0.953794 | + | 0.300462i | \(0.902859\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −782.743 | −0.0939412 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −640.276 | + | 5618.24i | −0.0762855 | + | 0.669383i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4664.76i | − | 0.551768i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1517.92 | −0.178256 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11967.9 | −1.39540 | −0.697699 | − | 0.716391i | \(-0.745793\pi\) | ||||
−0.697699 | + | 0.716391i | \(0.745793\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15762.7 | 1.82476 | 0.912381 | − | 0.409341i | \(-0.134241\pi\) | ||||
0.912381 | + | 0.409341i | \(0.134241\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 261.656 | 0.0300760 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 9121.66i | − | 1.04110i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3167.48 | + | 360.979i | 0.358982 | + | 0.0409110i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5312.15 | −0.597839 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3980.94i | 0.444908i | 0.974943 | + | 0.222454i | \(0.0714067\pi\) | ||||
−0.974943 | + | 0.222454i | \(0.928593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7828.52i | − | 0.868856i | −0.900707 | − | 0.434428i | \(-0.856951\pi\) | ||
0.900707 | − | 0.434428i | \(-0.143049\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3831.75i | 0.422341i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 17486.4i | − | 1.91416i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8174.69 | 0.888739 | 0.444370 | − | 0.895844i | \(-0.353428\pi\) | ||||
0.444370 | + | 0.895844i | \(0.353428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3007.84 | − | 694.591i | −0.324786 | − | 0.0750018i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13439.8i | 1.44141i | 0.693243 | + | 0.720704i | \(0.256181\pi\) | ||||
−0.693243 | + | 0.720704i | \(0.743819\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11960.3 | −1.27410 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4191.84 | 0.443551 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8966.31 | −0.942419 | −0.471210 | − | 0.882021i | \(-0.656182\pi\) | ||||
−0.471210 | + | 0.882021i | \(0.656182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11405.5 | 1.19082 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1032.56i | − | 0.107095i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2000.69 | + | 17555.5i | −0.206140 | + | 1.80882i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7444.29 | 0.761990 | 0.380995 | − | 0.924577i | \(-0.375582\pi\) | ||||
0.380995 | + | 0.924577i | \(0.375582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1298.83i | − | 0.132079i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5552.31i | − | 0.560947i | −0.959862 | − | 0.280474i | \(-0.909508\pi\) | ||
0.959862 | − | 0.280474i | \(-0.0904915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3923.67i | − | 0.393841i | −0.980419 | − | 0.196921i | \(-0.936906\pi\) | ||
0.980419 | − | 0.196921i | \(-0.0630941\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 9801.19i | − | 0.977461i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8843.37 | −0.876279 | −0.438140 | − | 0.898907i | \(-0.644362\pi\) | ||||
−0.438140 | + | 0.898907i | \(0.644362\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2006.34 | + | 228.650i | 0.197535 | + | 0.0225119i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7350.92i | − | 0.719134i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6523.93 | −0.634188 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21010.0 | −2.02948 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6142.98 | −0.589660 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19687.6 | 1.87798 | 0.938988 | − | 0.343951i | \(-0.111765\pi\) | ||||
0.938988 | + | 0.343951i | \(0.111765\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 22749.9i | − | 2.15657i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8712.18 | − | 992.874i | −0.820741 | − | 0.0935348i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25887.7 | 2.42371 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17969.6i | − | 1.67203i | −0.548706 | − | 0.836015i | \(-0.684879\pi\) | ||
0.548706 | − | 0.836015i | \(-0.315121\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5248.56i | 0.485374i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2351.82i | − | 0.216163i | −0.994142 | − | 0.108082i | \(-0.965529\pi\) | ||
0.994142 | − | 0.108082i | \(-0.0344708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3463.94i | 0.316446i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5255.47 | −0.477203 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13643.6 | − | 1554.88i | −1.23139 | − | 0.140333i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1548.25i | − | 0.138896i | −0.997586 | − | 0.0694479i | \(-0.977876\pi\) | ||
0.997586 | − | 0.0694479i | \(-0.0221238\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12217.9 | −1.08953 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17661.5 | −1.56558 | −0.782791 | − | 0.622284i | \(-0.786205\pi\) | ||||
−0.782791 | + | 0.622284i | \(0.786205\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4020.61 | 0.354287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2087.98 | 0.182901 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7607.03i | 0.662427i | 0.943556 | + | 0.331214i | \(0.107458\pi\) | ||||
−0.943556 | + | 0.331214i | \(0.892542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13848.7 | − | 1578.25i | −1.19889 | − | 0.136630i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2991.60 | −0.257470 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12641.2i | 1.08163i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 957.114i | − | 0.0814194i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 11965.5i | − | 1.01200i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1121.16i | − | 0.0942781i | −0.998888 | − | 0.0471391i | \(-0.984990\pi\) | ||
0.998888 | − | 0.0471391i | \(-0.0150104\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10129.6 | −0.846918 | −0.423459 | − | 0.905915i | \(-0.639184\pi\) | ||||
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1192.94 | + | 10467.7i | −0.0991700 | + | 0.870189i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8860.37i | − | 0.732379i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12740.0 | −1.04710 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2747.88 | 0.224572 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18634.2 | −1.51433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13470.4 | 1.08855 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 96.8139i | 0.00777994i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2540.75 | + | 11002.4i | −0.203039 | + | 0.879234i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14846.0 | −1.17981 | −0.589907 | − | 0.807471i | \(-0.700836\pi\) | ||||
−0.589907 | + | 0.807471i | \(0.700836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 699.337i | 0.0552697i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 19180.6i | − | 1.50754i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5857.85i | 0.457886i | 0.973440 | + | 0.228943i | \(0.0735269\pi\) | ||||
−0.973440 | + | 0.228943i | \(0.926473\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1549.22i | − | 0.120435i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7978.51 | 0.616871 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8264.55 | + | 941.859i | 0.635523 | + | 0.0724266i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 22507.2i | − | 1.72140i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8589.49 | −0.653408 | −0.326704 | − | 0.945127i | \(-0.605938\pi\) | ||||
−0.326704 | + | 0.945127i | \(0.605938\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10658.8 | 0.806474 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4750.99 | −0.357553 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6159.17 | −0.461062 | −0.230531 | − | 0.973065i | \(-0.574046\pi\) | ||||
−0.230531 | + | 0.973065i | \(0.574046\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 34306.1i | − | 2.55446i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −169.862 | + | 1490.49i | −0.0125812 | + | 0.110397i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14756.9 | −1.08724 | −0.543620 | − | 0.839331i | \(-0.682947\pi\) | ||||
−0.543620 | + | 0.839331i | \(0.682947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11216.5i | − | 0.822059i | −0.911622 | − | 0.411030i | \(-0.865169\pi\) | ||
0.911622 | − | 0.411030i | \(-0.134831\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 333.516i | − | 0.0243156i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29925.9i | 2.17043i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25252.3i | 1.82195i | 0.412461 | + | 0.910975i | \(0.364669\pi\) | ||||
−0.412461 | + | 0.910975i | \(0.635331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5140.36 | 0.368957 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −551.502 | + | 4839.27i | −0.0393807 | + | 0.345554i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22470.4i | 1.59628i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8586.38 | 0.606843 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16488.5 | 1.15938 | 0.579688 | − | 0.814839i | \(-0.303174\pi\) | ||||
0.579688 | + | 0.814839i | \(0.303174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20408.1 | −1.42768 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12135.3 | 0.844634 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8899.79i | − | 0.616308i | −0.951336 | − | 0.308154i | \(-0.900289\pi\) | ||
0.951336 | − | 0.308154i | \(-0.0997112\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1789.34 | + | 15701.0i | −0.123287 | + | 1.08181i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13441.9 | −0.921507 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10099.6i | 0.688911i | 0.938803 | + | 0.344456i | \(0.111936\pi\) | ||||
−0.938803 | + | 0.344456i | \(0.888064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8719.01i | − | 0.591773i | −0.955223 | − | 0.295887i | \(-0.904385\pi\) | ||
0.955223 | − | 0.295887i | \(-0.0956150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 981.300i | − | 0.0662714i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 4384.69i | − | 0.294649i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15841.9 | −1.05931 | −0.529655 | − | 0.848213i | \(-0.677679\pi\) | ||||
−0.529655 | + | 0.848213i | \(0.677679\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 453.018 | − | 3975.10i | 0.0301432 | − | 0.264498i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1563.73i | 0.103538i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6841.48 | 0.450775 | 0.225387 | − | 0.974269i | \(-0.427635\pi\) | ||||
0.225387 | + | 0.974269i | \(0.427635\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18435.4 | −1.20876 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7676.90 | 0.500908 | 0.250454 | − | 0.968129i | \(-0.419420\pi\) | ||||
0.250454 | + | 0.968129i | \(0.419420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1213.39 | 0.0787886 | 0.0393943 | − | 0.999224i | \(-0.487457\pi\) | ||||
0.0393943 | + | 0.999224i | \(0.487457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4261.13i | 0.275351i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12407.8 | + | 1414.04i | 0.797925 | + | 0.0909346i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3371.53 | −0.215778 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10943.0i | 0.697002i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 20346.7i | − | 1.28979i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26695.3i | − | 1.68419i | −0.539328 | − | 0.842096i | \(-0.681322\pi\) | ||
0.539328 | − | 0.842096i | \(-0.318678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 11813.9i | − | 0.741800i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 44663.4 | 2.79120 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4151.08 | − | 17975.7i | 0.258197 | − | 1.11809i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6673.08i | 0.413119i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17576.8 | −1.08306 | −0.541530 | − | 0.840681i | \(-0.682155\pi\) | ||||
−0.541530 | + | 0.840681i | \(0.682155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26186.4 | −1.60605 | −0.803025 | − | 0.595945i | \(-0.796777\pi\) | ||||
−0.803025 | + | 0.595945i | \(0.796777\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10545.1 | 0.643739 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9990.55 | −0.607062 | −0.303531 | − | 0.952822i | \(-0.598166\pi\) | ||||
−0.303531 | + | 0.952822i | \(0.598166\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10051.5i | − | 0.607943i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1158.77 | + | 10167.9i | −0.0697630 | + | 0.612151i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28277.7 | 1.69463 | 0.847315 | − | 0.531091i | \(-0.178218\pi\) | ||||
0.847315 | + | 0.531091i | \(0.178218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19765.6i | 1.17909i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6773.42i | 0.402216i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3090.10i | − | 0.182661i | −0.995821 | − | 0.0913303i | \(-0.970888\pi\) | ||
0.995821 | − | 0.0913303i | \(-0.0291119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11860.9i | 0.697937i | 0.937134 | + | 0.348969i | \(0.113468\pi\) | ||||
−0.937134 | + | 0.348969i | \(0.886532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7762.17 | 0.454687 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36164.1 | + | 4121.40i | 2.10885 | + | 0.240332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11364.3i | − | 0.659712i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18693.2 | 1.08030 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5666.89 | −0.326032 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6269.15 | −0.359076 | −0.179538 | − | 0.983751i | \(-0.557460\pi\) | ||||
−0.179538 | + | 0.983751i | \(0.557460\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5119.76 | 0.291940 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 30107.8i | − | 1.70921i | −0.519275 | − | 0.854607i | \(-0.673798\pi\) | ||
0.519275 | − | 0.854607i | \(-0.326202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26856.2 | − | 3060.64i | −1.51789 | − | 0.172984i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7883.77 | −0.443622 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21336.3i | 1.19533i | 0.801746 | + | 0.597665i | \(0.203905\pi\) | ||||
−0.801746 | + | 0.597665i | \(0.796095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4627.98i | − | 0.258140i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5791.30i | − | 0.321618i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 36712.2i | − | 2.02993i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8597.07 | 0.473297 | 0.236648 | − | 0.971595i | \(-0.423951\pi\) | ||||
0.236648 | + | 0.971595i | \(0.423951\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5452.08 | + | 621.340i | 0.298856 | + | 0.0340588i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8974.73i | − | 0.489829i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16665.8 | −0.905683 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15416.4 | 0.834192 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14251.7 | −0.767872 | −0.383936 | − | 0.923360i | \(-0.625432\pi\) | ||||
−0.383936 | + | 0.923360i | \(0.625432\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46864.7 | −2.51427 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1547.05i | 0.0826457i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4171.03 | − | 475.346i | −0.221878 | − | 0.0252860i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21610.0 | 1.14468 | 0.572342 | − | 0.820015i | \(-0.306035\pi\) | ||||
0.572342 | + | 0.820015i | \(0.306035\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4042.19i | − | 0.213212i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29068.6i | 1.52683i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 31408.2i | − | 1.64280i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 17172.1i | − | 0.894427i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32462.5 | 1.68379 | 0.841896 | − | 0.539639i | \(-0.181439\pi\) | ||||
0.841896 | + | 0.539639i | \(0.181439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1494.54 | − | 13114.1i | 0.0771977 | − | 0.677388i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17195.5i | − | 0.884521i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13654.3 | −0.699458 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27608.0 | −1.40842 | −0.704211 | − | 0.709991i | \(-0.748699\pi\) | ||||
−0.704211 | + | 0.709991i | \(0.748699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9532.84 | 0.482332 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6821.15i | 0.343718i | 0.985122 | + | 0.171859i | \(0.0549773\pi\) | ||||
−0.985122 | + | 0.171859i | \(0.945023\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4106.78 | − | 17783.9i | 0.206097 | − | 0.892476i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3589.50 | −0.179404 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17123.2i | 0.852351i | 0.904641 | + | 0.426175i | \(0.140139\pi\) | ||||
−0.904641 | + | 0.426175i | \(0.859861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 17878.6i | − | 0.886354i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2411.20i | 0.119055i | 0.998227 | + | 0.0595277i | \(0.0189595\pi\) | ||||
−0.998227 | + | 0.0595277i | \(0.981041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24784.4i | 1.21883i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2366.89 | 0.115930 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13974.3 | − | 1592.57i | −0.681723 | − | 0.0776917i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 9873.14i | − | 0.479728i | −0.970806 | − | 0.239864i | \(-0.922897\pi\) | ||
0.970806 | − | 0.239864i | \(-0.0771029\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7300.30 | 0.353304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6105.03 | 0.294284 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17357.4 | −0.833376 | −0.416688 | − | 0.909050i | \(-0.636809\pi\) | ||||
−0.416688 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15586.8 | 0.745409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26432.1i | 1.25909i | 0.776966 | + | 0.629543i | \(0.216758\pi\) | ||||
−0.776966 | + | 0.629543i | \(0.783242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2267.67 | + | 19898.2i | −0.107595 | + | 0.944120i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7679.35 | 0.362938 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16422.1i | 0.773100i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28143.2i | − | 1.31973i | −0.751385 | − | 0.659864i | \(-0.770614\pi\) | ||
0.751385 | − | 0.659864i | \(-0.229386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 7487.27i | − | 0.349737i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 15072.7i | − | 0.701328i | −0.936501 | − | 0.350664i | \(-0.885956\pi\) | ||
0.936501 | − | 0.350664i | \(-0.114044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34926.1 | 1.61882 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2660.97 | + | 23349.2i | −0.122859 | + | 1.07806i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38386.4i | 1.76551i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24409.5 | 1.11836 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1944.22 | −0.0887367 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43462.4 | 1.97610 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22371.5 | 1.01329 | 0.506645 | − | 0.862155i | \(-0.330886\pi\) | ||||
0.506645 | + | 0.862155i | \(0.330886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3766.06i | − | 0.169931i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4055.92 | + | 35589.6i | −0.182316 | + | 1.59977i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9258.56 | 0.414604 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 36320.5i | − | 1.62032i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28223.2i | 1.25435i | 0.778878 | + | 0.627175i | \(0.215789\pi\) | ||||
−0.778878 | + | 0.627175i | \(0.784211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1398.55i | 0.0619236i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6068.64i | − | 0.267697i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24776.5 | 1.08885 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5870.38 | − | 51510.9i | 0.257023 | − | 2.25531i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8531.97i | 0.372168i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 750.987 | 0.0326370 | 0.0163185 | − | 0.999867i | \(-0.494805\pi\) | ||||
0.0163185 | + | 0.999867i | \(0.494805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5362.03 | −0.232166 | −0.116083 | − | 0.993240i | \(-0.537034\pi\) | ||||
−0.116083 | + | 0.993240i | \(0.537034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2064.30 | 0.0890506 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31032.2 | −1.33376 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 21957.0i | − | 0.940244i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8907.61 | − | 1015.15i | −0.380045 | − | 0.0433114i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34039.9 | −1.44702 | −0.723508 | − | 0.690316i | \(-0.757471\pi\) | ||||
−0.723508 | + | 0.690316i | \(0.757471\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3953.11i | − | 0.167432i | −0.996490 | − | 0.0837161i | \(-0.973321\pi\) | ||
0.996490 | − | 0.0837161i | \(-0.0266789\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 18727.6i | − | 0.790317i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22122.3i | − | 0.930190i | −0.885261 | − | 0.465095i | \(-0.846020\pi\) | ||
0.885261 | − | 0.465095i | \(-0.153980\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45342.1i | 1.89963i | 0.312805 | + | 0.949817i | \(0.398731\pi\) | ||||
−0.312805 | + | 0.949817i | \(0.601269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10924.9 | 0.456053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3712.57 | − | 16076.8i | 0.154421 | − | 0.668702i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 72238.4i | − | 2.99391i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4973.10 | 0.205371 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29527.4 | 1.21502 | 0.607508 | − | 0.794313i | \(-0.292169\pi\) | ||||
0.607508 | + | 0.794313i | \(0.292169\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19203.8 | −0.787396 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1413.03 | −0.0577313 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12345.2i | 0.502591i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −518.390 | + | 4548.72i | −0.0210296 | + | 0.184529i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20785.5 | 0.840233 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 66752.5i | 2.68889i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18339.4i | 0.736140i | 0.929798 | + | 0.368070i | \(0.119981\pi\) | ||||
−0.929798 | + | 0.368070i | \(0.880019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 17687.9i | − | 0.707500i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 14576.0i | − | 0.580988i | −0.956877 | − | 0.290494i | \(-0.906180\pi\) | ||
0.956877 | − | 0.290494i | \(-0.0938196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3972.38 | −0.157783 | −0.0788917 | − | 0.996883i | \(-0.525138\pi\) | ||||
−0.0788917 | + | 0.996883i | \(0.525138\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19125.1 | + | 2179.57i | 0.757006 | + | 0.0862712i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 40644.4i | − | 1.60319i | −0.597869 | − | 0.801594i | \(-0.703986\pi\) | ||
0.597869 | − | 0.801594i | \(-0.296014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 70746.4 | 2.78087 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7796.80 | −0.305413 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14785.9 | −0.577191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5864.53 | 0.228142 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13135.4i | 0.509238i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21091.7 | − | 2403.69i | −0.814891 | − | 0.0928681i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9602.49 | 0.369730 | 0.184865 | − | 0.982764i | \(-0.440815\pi\) | ||||
0.184865 | + | 0.982764i | \(0.440815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20218.6i | 0.775833i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5204.78i | 0.199039i | 0.995036 | + | 0.0995196i | \(0.0317306\pi\) | ||||
−0.995036 | + | 0.0995196i | \(0.968269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22108.6i | 0.842596i | 0.906922 | + | 0.421298i | \(0.138425\pi\) | ||||
−0.906922 | + | 0.421298i | \(0.861575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16246.9i | 0.617099i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21305.3 | −0.806497 | −0.403248 | − | 0.915091i | \(-0.632119\pi\) | ||||
−0.403248 | + | 0.915091i | \(0.632119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46334.4 | − | 5280.44i | −1.74804 | − | 0.199213i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2666.61i | − | 0.100264i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3221.28 | 0.120712 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −572.414 | −0.0213784 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25465.7 | −0.947910 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13263.1 | −0.492047 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 32834.1i | − | 1.21405i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10939.6 | − | 1246.72i | −0.403152 | − | 0.0459448i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4134.85 | −0.151875 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5073.71i | − | 0.185744i | −0.995678 | − | 0.0928720i | \(-0.970395\pi\) | ||
0.995678 | − | 0.0928720i | \(-0.0296047\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2040.05i | 0.0744380i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22711.5i | − | 0.825977i | −0.910736 | − | 0.412989i | \(-0.864485\pi\) | ||
0.910736 | − | 0.412989i | \(-0.135515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8657.85i | − | 0.313837i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9159.77 | 0.330943 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2336.83 | − | 20505.0i | 0.0841537 | − | 0.738425i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8104.63i | − | 0.290911i | −0.989365 | − | 0.145455i | \(-0.953535\pi\) | ||
0.989365 | − | 0.145455i | \(-0.0464647\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23922.7 | −0.855897 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39880.2 | −1.42218 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 80203.4 | 2.85089 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6414.13 | −0.227257 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28055.3i | 0.990814i | 0.868661 | + | 0.495407i | \(0.164981\pi\) | ||||
−0.868661 | + | 0.495407i | \(0.835019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37029.8 | − | 8551.18i | −1.30355 | − | 0.301024i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1383.00 | −0.0485290 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 28090.3i | − | 0.982515i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26420.7i | 0.921160i | 0.887618 | + | 0.460580i | \(0.152359\pi\) | ||||
−0.887618 | + | 0.460580i | \(0.847641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5931.69i | 0.206148i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48331.7i | 1.67435i | 0.546931 | + | 0.837177i | \(0.315796\pi\) | ||||
−0.546931 | + | 0.837177i | \(0.684204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54676.2 | 1.88813 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8812.57 | − | 1004.31i | −0.303358 | − | 0.0345718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56278.5i | 1.93116i | 0.260115 | + | 0.965578i | \(0.416240\pi\) | ||||
−0.260115 | + | 0.965578i | \(0.583760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40479.9 | −1.38465 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4711.85 | −0.160665 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6765.72 | 0.229972 | 0.114986 | − | 0.993367i | \(-0.463318\pi\) | ||||
0.114986 | + | 0.993367i | \(0.463318\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1971.92 | 0.0668166 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7111.78i | 0.240221i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −547.154 | + | 4801.12i | −0.0184239 | + | 0.161665i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4134.61 | 0.138787 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6834.83i | 0.228712i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30392.5i | 1.01385i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30443.1i | − | 1.01239i | −0.862418 | − | 0.506196i | \(-0.831051\pi\) | ||
0.862418 | − | 0.506196i | \(-0.168949\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 15990.0i | − | 0.530106i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50571.9 | −1.67140 | −0.835701 | − | 0.549185i | \(-0.814938\pi\) | ||||
−0.835701 | + | 0.549185i | \(0.814938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1061.06 | + | 9310.49i | −0.0349599 | + | 0.306763i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30597.2i | 1.00502i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3249.34 | 0.106403 | 0.0532014 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532014 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22198.5 | −0.724686 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9732.21 | 0.316744 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29605.3 | 0.960592 | 0.480296 | − | 0.877106i | \(-0.340529\pi\) | ||||
0.480296 | + | 0.877106i | \(0.340529\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 71750.1i | 2.32096i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 182.903 | − | 1604.93i | 0.00589856 | − | 0.0517582i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31274.9 | −1.00554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40111.2i | 1.28575i | 0.765972 | + | 0.642873i | \(0.222258\pi\) | ||||
−0.765972 | + | 0.642873i | \(0.777742\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 15667.0i | − | 0.500681i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 79475.4i | − | 2.53220i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50086.1i | 1.59102i | 0.605943 | + | 0.795508i | \(0.292796\pi\) | ||||
−0.605943 | + | 0.795508i | \(0.707204\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11420.1 | 0.361678 |
(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 | 1344.4.b.e.895.2 | 8 | ||
4.3 | odd | 2 | 1344.4.b.f.895.2 | 8 | |||
7.6 | odd | 2 | 1344.4.b.f.895.7 | 8 | |||
8.3 | odd | 2 | 336.4.b.e.223.7 | yes | 8 | ||
8.5 | even | 2 | 336.4.b.f.223.7 | yes | 8 | ||
24.5 | odd | 2 | 1008.4.b.k.559.2 | 8 | |||
24.11 | even | 2 | 1008.4.b.i.559.2 | 8 | |||
28.27 | even | 2 | inner | 1344.4.b.e.895.7 | 8 | ||
56.13 | odd | 2 | 336.4.b.e.223.2 | ✓ | 8 | ||
56.27 | even | 2 | 336.4.b.f.223.2 | yes | 8 | ||
168.83 | odd | 2 | 1008.4.b.k.559.7 | 8 | |||
168.125 | even | 2 | 1008.4.b.i.559.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.b.e.223.2 | ✓ | 8 | 56.13 | odd | 2 | ||
336.4.b.e.223.7 | yes | 8 | 8.3 | odd | 2 | ||
336.4.b.f.223.2 | yes | 8 | 56.27 | even | 2 | ||
336.4.b.f.223.7 | yes | 8 | 8.5 | even | 2 | ||
1008.4.b.i.559.2 | 8 | 24.11 | even | 2 | |||
1008.4.b.i.559.7 | 8 | 168.125 | even | 2 | |||
1008.4.b.k.559.2 | 8 | 24.5 | odd | 2 | |||
1008.4.b.k.559.7 | 8 | 168.83 | odd | 2 | |||
1344.4.b.e.895.2 | 8 | 1.1 | even | 1 | trivial | ||
1344.4.b.e.895.7 | 8 | 28.27 | even | 2 | inner | ||
1344.4.b.f.895.2 | 8 | 4.3 | odd | 2 | |||
1344.4.b.f.895.7 | 8 | 7.6 | odd | 2 |