Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), degree \(2\), 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: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-23})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} - 6x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(2.32666 - 0.765945i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.541 |
Dual form | 1620.4.i.q.1081.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.9599 | + | 25.9114i | −0.807761 | + | 1.39908i | 0.106651 | + | 0.994297i | \(0.465987\pi\) |
−0.914411 | + | 0.404786i | \(0.867346\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.95994 | + | 13.7870i | −0.218183 | + | 0.377904i | −0.954252 | − | 0.299002i | \(-0.903346\pi\) |
0.736070 | + | 0.676906i | \(0.236680\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.9599 | − | 36.3037i | −0.447172 | − | 0.774525i | 0.551028 | − | 0.834487i | \(-0.314236\pi\) |
−0.998201 | + | 0.0599613i | \(0.980902\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −36.9199 | −0.526728 | −0.263364 | − | 0.964696i | \(-0.584832\pi\) | ||||
−0.263364 | + | 0.964696i | \(0.584832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.9199 | −0.131852 | −0.0659261 | − | 0.997825i | \(-0.521000\pi\) | ||||
−0.0659261 | + | 0.997825i | \(0.521000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 57.3397 | + | 99.3153i | 0.519833 | + | 0.900377i | 0.999734 | + | 0.0230548i | \(0.00733923\pi\) |
−0.479901 | + | 0.877323i | \(0.659327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −72.7997 | + | 126.093i | −0.466157 | + | 0.807408i | −0.999253 | − | 0.0386469i | \(-0.987695\pi\) |
0.533096 | + | 0.846055i | \(0.321029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23.2196 | + | 40.2174i | 0.134528 | + | 0.233009i | 0.925417 | − | 0.378951i | \(-0.123715\pi\) |
−0.790889 | + | 0.611959i | \(0.790382\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −149.599 | −0.722483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 74.0000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −167.639 | − | 290.360i | −0.638558 | − | 1.10601i | −0.985749 | − | 0.168221i | \(-0.946198\pi\) |
0.347191 | − | 0.937794i | \(-0.387135\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −42.2003 | + | 73.0931i | −0.149663 | + | 0.259223i | −0.931103 | − | 0.364757i | \(-0.881152\pi\) |
0.781440 | + | 0.623980i | \(0.214485\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −127.599 | + | 221.009i | −0.396006 | + | 0.685902i | −0.993229 | − | 0.116173i | \(-0.962937\pi\) |
0.597223 | + | 0.802075i | \(0.296271\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −276.099 | − | 478.218i | −0.804954 | − | 1.39422i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −399.638 | −1.03574 | −0.517872 | − | 0.855458i | \(-0.673276\pi\) | ||||
−0.517872 | + | 0.855458i | \(0.673276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −79.5994 | −0.195149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.28045 | − | 2.21780i | −0.00282543 | − | 0.00489379i | 0.864609 | − | 0.502445i | \(-0.167566\pi\) |
−0.867435 | + | 0.497551i | \(0.834233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −284.260 | + | 492.352i | −0.596651 | + | 1.03343i | 0.396661 | + | 0.917965i | \(0.370169\pi\) |
−0.993312 | + | 0.115465i | \(0.963164\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 104.800 | − | 181.518i | 0.199982 | − | 0.346378i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −384.760 | − | 666.423i | −0.701580 | − | 1.21517i | −0.967912 | − | 0.251291i | \(-0.919145\pi\) |
0.266331 | − | 0.963881i | \(-0.414188\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 441.837 | 0.738540 | 0.369270 | − | 0.929322i | \(-0.379608\pi\) | ||||
0.369270 | + | 0.929322i | \(0.379608\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 966.317 | 1.54930 | 0.774650 | − | 0.632390i | \(-0.217926\pi\) | ||||
0.774650 | + | 0.632390i | \(0.217926\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −238.160 | − | 412.506i | −0.352479 | − | 0.610511i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −251.620 | + | 435.819i | −0.358348 | + | 0.620677i | −0.987685 | − | 0.156456i | \(-0.949993\pi\) |
0.629337 | + | 0.777132i | \(0.283326\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 635.378 | − | 1100.51i | 0.840263 | − | 1.45538i | −0.0494095 | − | 0.998779i | \(-0.515734\pi\) |
0.889672 | − | 0.456599i | \(-0.150933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −92.2997 | − | 159.868i | −0.117780 | − | 0.204001i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.240385 | −0.000286301 | −0.000143150 | − | 1.00000i | \(-0.500046\pi\) | ||||
−0.000143150 | 1.00000i | \(0.500046\pi\) | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1254.24 | 1.44483 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.2997 | − | 47.2844i | −0.0294830 | − | 0.0510661i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.35897 | − | 5.81791i | 0.00351600 | − | 0.00608989i | −0.864262 | − | 0.503042i | \(-0.832214\pi\) |
0.867778 | + | 0.496952i | \(0.165547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 597.679 | − | 1035.21i | 0.588825 | − | 1.01987i | −0.405562 | − | 0.914068i | \(-0.632924\pi\) |
0.994387 | − | 0.105807i | \(-0.0337426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 228.077 | + | 395.041i | 0.218185 | + | 0.377908i | 0.954253 | − | 0.299000i | \(-0.0966529\pi\) |
−0.736068 | + | 0.676908i | \(0.763320\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1516.47 | 1.37012 | 0.685061 | − | 0.728485i | \(-0.259775\pi\) | ||||
0.685061 | + | 0.728485i | \(0.259775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1485.55 | −1.30541 | −0.652706 | − | 0.757611i | \(-0.726366\pi\) | ||||
−0.652706 | + | 0.757611i | \(0.726366\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −881.478 | − | 1526.76i | −0.733827 | − | 1.27103i | −0.955236 | − | 0.295844i | \(-0.904399\pi\) |
0.221409 | − | 0.975181i | \(-0.428934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −286.699 | + | 496.577i | −0.232476 | + | 0.402661i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 552.319 | − | 956.644i | 0.425471 | − | 0.736937i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 538.779 | + | 933.192i | 0.404793 | + | 0.701121i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 698.481 | 0.488033 | 0.244016 | − | 0.969771i | \(-0.421535\pi\) | ||||
0.244016 | + | 0.969771i | \(0.421535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 590.436 | + | 1022.66i | 0.393791 | + | 0.682066i | 0.992946 | − | 0.118567i | \(-0.0378300\pi\) |
−0.599155 | + | 0.800633i | \(0.704497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 163.361 | − | 282.949i | 0.106505 | − | 0.184472i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 982.976 | − | 1702.56i | 0.613002 | − | 1.06175i | −0.377729 | − | 0.925916i | \(-0.623295\pi\) |
0.990731 | − | 0.135835i | \(-0.0433717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1566.15 | − | 2712.66i | −0.955679 | − | 1.65529i | −0.732806 | − | 0.680438i | \(-0.761790\pi\) |
−0.222874 | − | 0.974847i | \(-0.571544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 667.359 | 0.390261 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −727.997 | −0.416944 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1726.44 | − | 2990.28i | −0.949230 | − | 1.64411i | −0.747052 | − | 0.664766i | \(-0.768531\pi\) |
−0.202178 | − | 0.979349i | \(-0.564802\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −322.000 | + | 557.720i | −0.173536 | + | 0.300574i | −0.939654 | − | 0.342127i | \(-0.888853\pi\) |
0.766117 | + | 0.642701i | \(0.222186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −116.098 | + | 201.087i | −0.0601626 | + | 0.104205i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 761.559 | + | 1319.06i | 0.387128 | + | 0.670525i | 0.992062 | − | 0.125751i | \(-0.0401339\pi\) |
−0.604934 | + | 0.796275i | \(0.706801\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3431.20 | −1.67960 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3805.67 | 1.82873 | 0.914364 | − | 0.404892i | \(-0.132691\pi\) | ||||
0.914364 | + | 0.404892i | \(0.132691\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1551.14 | − | 2686.66i | −0.718748 | − | 1.24491i | −0.961496 | − | 0.274819i | \(-0.911382\pi\) |
0.242748 | − | 0.970089i | \(-0.421951\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 219.862 | − | 380.812i | 0.100074 | − | 0.173333i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1614.45 | + | 2796.31i | −0.709505 | + | 1.22890i | 0.255536 | + | 0.966800i | \(0.417748\pi\) |
−0.965041 | + | 0.262099i | \(0.915585\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −373.998 | − | 647.784i | −0.161552 | − | 0.279816i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −313.276 | −0.130812 | −0.0654059 | − | 0.997859i | \(-0.520834\pi\) | ||||
−0.0654059 | + | 0.997859i | \(0.520834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −542.526 | −0.222793 | −0.111397 | − | 0.993776i | \(-0.535532\pi\) | ||||
−0.111397 | + | 0.993776i | \(0.535532\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 185.000 | + | 320.429i | 0.0735215 | + | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 293.880 | − | 509.015i | 0.114923 | − | 0.199053i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2284.84 | − | 3957.46i | 0.865577 | − | 1.49922i | −0.000896169 | − | 1.00000i | \(-0.500285\pi\) |
0.866473 | − | 0.499224i | \(-0.166381\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2366.48 | + | 4098.86i | 0.882604 | + | 1.52872i | 0.848435 | + | 0.529300i | \(0.177545\pi\) |
0.0341696 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3335.06 | −1.20616 | −0.603079 | − | 0.797681i | \(-0.706060\pi\) | ||||
−0.603079 | + | 0.797681i | \(0.706060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4861.26 | −1.73169 | −0.865844 | − | 0.500315i | \(-0.833218\pi\) | ||||
−0.865844 | + | 0.500315i | \(0.833218\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2178.16 | − | 3772.68i | −0.753087 | − | 1.30438i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 838.197 | − | 1451.80i | 0.285572 | − | 0.494625i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 86.9215 | − | 150.552i | 0.0287679 | − | 0.0498274i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1032.93 | + | 1789.09i | 0.337015 | + | 0.583727i | 0.983870 | − | 0.178886i | \(-0.0572494\pi\) |
−0.646855 | + | 0.762613i | \(0.723916\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −422.003 | −0.133862 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1389.45 | −0.434664 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 773.838 | + | 1340.33i | 0.235538 | + | 0.407964i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2031.47 | − | 3518.62i | 0.610034 | − | 1.05661i | −0.381200 | − | 0.924493i | \(-0.624489\pi\) |
0.991234 | − | 0.132117i | \(-0.0421776\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1346.93 | + | 2332.96i | −0.393828 | + | 0.682131i | −0.992951 | − | 0.118527i | \(-0.962183\pi\) |
0.599122 | + | 0.800657i | \(0.295516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1024.02 | + | 1773.66i | 0.295499 | + | 0.511820i | 0.975101 | − | 0.221762i | \(-0.0711807\pi\) |
−0.679602 | + | 0.733581i | \(0.737847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −799.923 | −0.224913 | −0.112456 | − | 0.993657i | \(-0.535872\pi\) | ||||
−0.112456 | + | 0.993657i | \(0.535872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1275.99 | −0.354198 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −536.926 | − | 929.984i | −0.145317 | − | 0.251697i | 0.784174 | − | 0.620541i | \(-0.213087\pi\) |
−0.929491 | + | 0.368844i | \(0.879754\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2393.70 | − | 4146.00i | 0.639799 | − | 1.10816i | −0.345678 | − | 0.938353i | \(-0.612351\pi\) |
0.985477 | − | 0.169811i | \(-0.0543156\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1380.50 | − | 2391.09i | 0.359987 | − | 0.623515i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 228.880 | + | 396.431i | 0.0589606 | + | 0.102123i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5498.07 | −1.38261 | −0.691305 | − | 0.722563i | \(-0.742964\pi\) | ||||
−0.691305 | + | 0.722563i | \(0.742964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1825.68 | −0.453675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3450.62 | − | 5976.64i | −0.837524 | − | 1.45063i | −0.891959 | − | 0.452116i | \(-0.850669\pi\) |
0.0544354 | − | 0.998517i | \(-0.482664\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1107.04 | + | 1917.44i | −0.265590 | + | 0.460015i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3232.15 | − | 5598.25i | 0.757806 | − | 1.31256i | −0.186161 | − | 0.982519i | \(-0.559605\pi\) |
0.943967 | − | 0.330039i | \(-0.107062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −999.095 | − | 1730.48i | −0.231600 | − | 0.401142i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5349.66 | 1.21254 | 0.606272 | − | 0.795257i | \(-0.292664\pi\) | ||||
0.606272 | + | 0.795257i | \(0.292664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2189.80 | −0.490852 | −0.245426 | − | 0.969415i | \(-0.578928\pi\) | ||||
−0.245426 | + | 0.969415i | \(0.578928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −198.998 | − | 344.675i | −0.0436366 | − | 0.0755807i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −651.954 | + | 1129.22i | −0.141415 | + | 0.244939i | −0.928030 | − | 0.372506i | \(-0.878499\pi\) |
0.786614 | + | 0.617445i | \(0.211832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2702.72 | − | 4681.25i | 0.573776 | − | 0.993808i | −0.422398 | − | 0.906410i | \(-0.638812\pi\) |
0.996173 | − | 0.0873979i | \(-0.0278551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −643.800 | − | 1115.09i | −0.135229 | − | 0.234224i | 0.790456 | − | 0.612519i | \(-0.209844\pi\) |
−0.925685 | + | 0.378295i | \(0.876510\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10031.5 | 2.06321 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3549.92 | −0.722557 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 778.726 | + | 1348.79i | 0.155268 | + | 0.268933i | 0.933157 | − | 0.359470i | \(-0.117042\pi\) |
−0.777888 | + | 0.628403i | \(0.783709\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.40225 | − | 11.0890i | 0.00126357 | − | 0.00218857i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2403.67 | − | 4163.29i | 0.464910 | − | 0.805248i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1262.63 | − | 2186.94i | −0.241783 | − | 0.418780i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2842.60 | −0.533661 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2343.27 | −0.435627 | −0.217813 | − | 0.975990i | \(-0.569892\pi\) | ||||
−0.217813 | + | 0.975990i | \(0.569892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3053.82 | − | 5289.37i | −0.556804 | − | 0.964414i | −0.997761 | − | 0.0668850i | \(-0.978694\pi\) |
0.440956 | − | 0.897529i | \(-0.354639\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1040.89 | − | 1802.87i | 0.187970 | − | 0.325573i | −0.756604 | − | 0.653874i | \(-0.773143\pi\) |
0.944573 | + | 0.328301i | \(0.106476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1805.86 | + | 3127.85i | −0.319960 | + | 0.554187i | −0.980479 | − | 0.196622i | \(-0.937003\pi\) |
0.660519 | + | 0.750809i | \(0.270336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1158.96 | − | 2007.38i | −0.203415 | − | 0.352325i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 403.160 | 0.0694503 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1048.00 | 0.178869 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3817.76 | − | 6612.55i | −0.639756 | − | 1.10809i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3186.87 | + | 5519.83i | −0.529204 | + | 0.916608i | 0.470216 | + | 0.882551i | \(0.344176\pi\) |
−0.999420 | + | 0.0340567i | \(0.989157\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1923.80 | − | 3332.12i | 0.313756 | − | 0.543442i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4773.58 | + | 8268.09i | 0.771613 | + | 1.33647i | 0.936678 | + | 0.350191i | \(0.113883\pi\) |
−0.165065 | + | 0.986283i | \(0.552783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −739.305 | −0.117406 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6259.20 | 0.985321 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4637.52 | − | 8032.42i | −0.717450 | − | 1.24266i | −0.962007 | − | 0.273025i | \(-0.911976\pi\) |
0.244557 | − | 0.969635i | \(-0.421357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2229.73 | − | 3862.01i | 0.341991 | − | 0.592345i | −0.642812 | − | 0.766024i | \(-0.722232\pi\) |
0.984802 | + | 0.173679i | \(0.0555655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4833.22 | − | 8371.38i | 0.728743 | − | 1.26222i | −0.228671 | − | 0.973504i | \(-0.573438\pi\) |
0.957415 | − | 0.288717i | \(-0.0932286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1104.59 | + | 1913.21i | 0.165143 | + | 0.286035i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3789.49 | −0.557108 | −0.278554 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278554 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6739.76 | −0.982615 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2415.79 | + | 4184.28i | 0.346434 | + | 0.600041i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1908.41 | + | 3305.46i | −0.271439 | + | 0.470146i | −0.969231 | − | 0.246155i | \(-0.920833\pi\) |
0.697792 | + | 0.716301i | \(0.254166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5978.56 | − | 10355.2i | 0.836634 | − | 1.44909i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1041.36 | − | 1803.69i | −0.144557 | − | 0.250380i | 0.784651 | − | 0.619938i | \(-0.212842\pi\) |
−0.929208 | + | 0.369558i | \(0.879509\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6103.51 | 0.833811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8074.43 | 1.09434 | 0.547171 | − | 0.837021i | \(-0.315705\pi\) | ||||
0.547171 | + | 0.837021i | \(0.315705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 686.369 | + | 1188.83i | 0.0915713 | + | 0.158606i | 0.908172 | − | 0.418596i | \(-0.137478\pi\) |
−0.816601 | + | 0.577202i | \(0.804144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1190.80 | − | 2062.53i | 0.157633 | − | 0.273029i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5188.51 | + | 8986.77i | −0.676267 | + | 1.17133i | 0.299830 | + | 0.953993i | \(0.403070\pi\) |
−0.976097 | + | 0.217336i | \(0.930263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2116.98 | − | 3666.71i | −0.273811 | − | 0.474254i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2516.20 | −0.320516 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1717.90 | −0.217176 | −0.108588 | − | 0.994087i | \(-0.534633\pi\) | ||||
−0.108588 | + | 0.994087i | \(0.534633\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2579.88 | + | 4468.49i | 0.321280 | + | 0.556473i | 0.980752 | − | 0.195255i | \(-0.0625536\pi\) |
−0.659472 | + | 0.751729i | \(0.729220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 973.361 | − | 1685.91i | 0.120314 | − | 0.208390i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −589.035 | + | 1020.24i | −0.0717381 | + | 0.124254i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3801.65 | + | 6584.65i | 0.459607 | + | 0.796063i | 0.998940 | − | 0.0460296i | \(-0.0146568\pi\) |
−0.539333 | + | 0.842093i | \(0.681324\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 76.6218 | 0.00912908 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6353.78 | 0.751554 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3581.22 | − | 6202.86i | −0.417552 | − | 0.723221i | 0.578141 | − | 0.815937i | \(-0.303778\pi\) |
−0.995693 | + | 0.0927162i | \(0.970445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1293.60 | + | 2240.57i | −0.149753 | + | 0.259380i | −0.931136 | − | 0.364672i | \(-0.881181\pi\) |
0.781383 | + | 0.624052i | \(0.214515\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 461.498 | − | 799.339i | 0.0526728 | − | 0.0912320i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8505.01 | − | 14731.1i | −0.963902 | − | 1.66953i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11053.4 | −1.23532 | −0.617661 | − | 0.786444i | \(-0.711920\pi\) | ||||
−0.617661 | + | 0.786444i | \(0.711920\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2510.68 | −0.278650 | −0.139325 | − | 0.990247i | \(-0.544493\pi\) | ||||
−0.139325 | + | 0.990247i | \(0.544493\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −626.143 | − | 1084.51i | −0.0685411 | − | 0.118717i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3419.75 | + | 5923.17i | −0.371789 | + | 0.643958i | −0.989841 | − | 0.142180i | \(-0.954589\pi\) |
0.618052 | + | 0.786138i | \(0.287922\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6153.48 | + | 10658.1i | −0.659956 | + | 1.14308i | 0.320670 | + | 0.947191i | \(0.396092\pi\) |
−0.980627 | + | 0.195887i | \(0.937242\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.600963 | − | 1.04090i | −6.40188e−5 | − | 0.000110884i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1073.61 | 0.112844 | 0.0564219 | − | 0.998407i | \(-0.482031\pi\) | ||||
0.0564219 | + | 0.998407i | \(0.482031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5337.60 | 0.557290 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3135.59 | + | 5431.01i | 0.323074 | + | 0.559581i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3660.14 | + | 6339.56i | −0.374648 | + | 0.648910i | −0.990274 | − | 0.139128i | \(-0.955570\pi\) |
0.615626 | + | 0.788039i | \(0.288903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 86.5289 | − | 149.872i | 0.00874198 | − | 0.0151415i | −0.861621 | − | 0.507552i | \(-0.830551\pi\) |
0.870363 | + | 0.492410i | \(0.163884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7799.30 | − | 13508.8i | −0.782860 | − | 1.35595i | −0.930269 | − | 0.366878i | \(-0.880427\pi\) |
0.147409 | − | 0.989076i | \(-0.452907\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1561.75 | −0.154752 | −0.0773760 | − | 0.997002i | \(-0.524654\pi\) | ||||
−0.0773760 | + | 0.997002i | \(0.524654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23023.9 | 2.26684 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −671.824 | − | 1163.63i | −0.0653076 | − | 0.113116i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 136.498 | − | 236.422i | 0.0131852 | − | 0.0228375i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2229.55 | + | 3861.69i | −0.212674 | + | 0.368362i | −0.952550 | − | 0.304381i | \(-0.901550\pi\) |
0.739877 | + | 0.672742i | \(0.234884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1551.04 | − | 2686.47i | −0.147029 | − | 0.254662i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.5897 | 0.00314481 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9005.17 | 0.837912 | 0.418956 | − | 0.908007i | \(-0.362396\pi\) | ||||
0.418956 | + | 0.908007i | \(0.362396\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10298.1 | + | 17836.8i | 0.946530 | + | 1.63944i | 0.752658 | + | 0.658412i | \(0.228772\pi\) |
0.193873 | + | 0.981027i | \(0.437895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2687.75 | − | 4655.33i | 0.245538 | − | 0.425285i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6609.85 | + | 11448.6i | −0.596564 | + | 1.03328i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4073.27 | + | 7055.12i | 0.365420 | + | 0.632927i | 0.988844 | − | 0.148958i | \(-0.0475919\pi\) |
−0.623423 | + | 0.781885i | \(0.714259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9277.97 | 0.822434 | 0.411217 | − | 0.911537i | \(-0.365104\pi\) | ||||
0.411217 | + | 0.911537i | \(0.365104\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5976.79 | 0.526661 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4999.88 | + | 8660.05i | 0.435395 | + | 0.754126i | 0.997328 | − | 0.0730568i | \(-0.0232754\pi\) |
−0.561933 | + | 0.827183i | \(0.689942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14456.0 | + | 25038.6i | −1.25146 | + | 2.16760i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1140.38 | + | 1975.20i | −0.0975754 | + | 0.169006i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2031.37 | − | 3518.43i | −0.172803 | − | 0.299304i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17101.2 | −1.43804 | −0.719018 | − | 0.694992i | \(-0.755408\pi\) | ||||
−0.719018 | + | 0.694992i | \(0.755408\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 766.452 | 0.0640815 | 0.0320407 | − | 0.999487i | \(-0.489799\pi\) | ||||
0.0320407 | + | 0.999487i | \(0.489799\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −857.263 | − | 1484.82i | −0.0708595 | − | 0.122732i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −492.192 | + | 852.502i | −0.0404531 | + | 0.0700667i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7027.42 | + | 12171.9i | −0.571091 | + | 0.989159i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3791.19 | + | 6566.53i | 0.306369 | + | 0.530646i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8790.93 | 0.702509 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19609.4 | −1.55837 | −0.779183 | − | 0.626797i | \(-0.784365\pi\) | ||||
−0.779183 | + | 0.626797i | \(0.784365\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3713.88 | − | 6432.63i | −0.291899 | − | 0.505584i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4409.93 | − | 7638.22i | 0.344707 | − | 0.597051i | −0.640593 | − | 0.767880i | \(-0.721312\pi\) |
0.985301 | + | 0.170830i | \(0.0546448\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 794.963 | − | 1376.92i | 0.0614638 | − | 0.106458i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7528.44 | − | 13039.6i | −0.578919 | − | 1.00272i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3398.63 | 0.258536 | 0.129268 | − | 0.991610i | \(-0.458737\pi\) | ||||
0.129268 | + | 0.991610i | \(0.458737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3538.06 | 0.267700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8540.76 | − | 14793.0i | −0.639343 | − | 1.10737i | −0.985577 | − | 0.169227i | \(-0.945873\pi\) |
0.346234 | − | 0.938148i | \(-0.387460\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4407.39 | − | 7633.82i | 0.328177 | − | 0.568420i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4536.89 | + | 7858.13i | −0.334264 | + | 0.578963i | −0.983343 | − | 0.181758i | \(-0.941821\pi\) |
0.649079 | + | 0.760721i | \(0.275155\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12443.6 | + | 21552.9i | 0.911992 | + | 1.57962i | 0.811247 | + | 0.584703i | \(0.198789\pi\) |
0.100744 | + | 0.994912i | \(0.467878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2866.99 | −0.207933 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15279.3 | −1.10240 | −0.551199 | − | 0.834374i | \(-0.685830\pi\) | ||||
−0.551199 | + | 0.834374i | \(0.685830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19010.4 | + | 32927.0i | 1.35746 | + | 2.35119i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3181.09 | − | 5509.81i | 0.225982 | − | 0.391412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −184.519 | + | 319.597i | −0.0129743 | + | 0.0224722i | −0.872440 | − | 0.488722i | \(-0.837463\pi\) |
0.859465 | + | 0.511194i | \(0.170797\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −253.555 | − | 439.169i | −0.0177377 | − | 0.0307227i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7306.60 | −0.505980 | −0.252990 | − | 0.967469i | \(-0.581414\pi\) | ||||
−0.252990 | + | 0.967469i | \(0.581414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5523.19 | 0.380552 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1777.47 | + | 3078.66i | 0.121244 | + | 0.210001i | 0.920259 | − | 0.391311i | \(-0.127978\pi\) |
−0.799014 | + | 0.601312i | \(0.794645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3555.62 | + | 6158.51i | −0.241326 | + | 0.417988i | −0.961092 | − | 0.276228i | \(-0.910916\pi\) |
0.719767 | + | 0.694216i | \(0.244249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2693.89 | + | 4665.96i | −0.181029 | + | 0.313551i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 125.486 | + | 217.347i | 0.00839094 | + | 0.0145335i | 0.870190 | − | 0.492716i | \(-0.163996\pi\) |
−0.861799 | + | 0.507249i | \(0.830662\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10697.9 | 0.708332 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8375.38 | 0.551841 | 0.275921 | − | 0.961180i | \(-0.411017\pi\) | ||||
0.275921 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3870.15 | − | 6703.29i | −0.252522 | − | 0.437382i | 0.711697 | − | 0.702486i | \(-0.247927\pi\) |
−0.964220 | + | 0.265105i | \(0.914593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5650.14 | − | 9786.34i | 0.366880 | − | 0.635454i | −0.622196 | − | 0.782861i | \(-0.713759\pi\) |
0.989076 | + | 0.147407i | \(0.0470928\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.59615 | − | 6.22871i | 0.000231263 | − | 0.000400559i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2732.07 | −0.173187 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13549.6 | −0.854835 | −0.427417 | − | 0.904054i | \(-0.640577\pi\) | ||||
−0.427417 | + | 0.904054i | \(0.640577\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1746.20 | + | 3024.51i | 0.109127 | + | 0.189014i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11574.0 | + | 20046.8i | −0.719907 | + | 1.24691i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2031.81 | − | 3519.19i | 0.125197 | − | 0.216848i | −0.796613 | − | 0.604490i | \(-0.793377\pi\) |
0.921810 | + | 0.387642i | \(0.126710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1795.59 | − | 3110.06i | −0.110126 | − | 0.190744i | 0.805695 | − | 0.592331i | \(-0.201792\pi\) |
−0.915821 | + | 0.401587i | \(0.868459\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11040.5 | 0.670860 | 0.335430 | − | 0.942065i | \(-0.391118\pi\) | ||||
0.335430 | + | 0.942065i | \(0.391118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.7692 | 0.00246584 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9428.86 | + | 16331.3i | 0.565054 | + | 0.978701i | 0.997045 | + | 0.0768236i | \(0.0244778\pi\) |
−0.431991 | + | 0.901878i | \(0.642189\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2952.18 | + | 5113.32i | −0.176109 | + | 0.305029i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12095.9 | − | 20950.7i | 0.715005 | − | 1.23843i | −0.247953 | − | 0.968772i | \(-0.579758\pi\) |
0.962958 | − | 0.269653i | \(-0.0869090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16333.4 | − | 28290.3i | −0.961113 | − | 1.66470i | −0.719714 | − | 0.694271i | \(-0.755727\pi\) |
−0.241399 | − | 0.970426i | \(-0.577606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1633.61 | 0.0952609 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16697.3 | −0.969296 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4525.38 | − | 7838.18i | −0.260358 | − | 0.450953i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13870.4 | − | 24024.2i | 0.794450 | − | 1.37603i | −0.128738 | − | 0.991679i | \(-0.541093\pi\) |
0.923188 | − | 0.384349i | \(-0.125574\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9472.98 | + | 16407.7i | −0.537779 | + | 0.931460i | 0.461245 | + | 0.887273i | \(0.347403\pi\) |
−0.999023 | + | 0.0441869i | \(0.985930\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 100.500 | + | 174.071i | 0.00568017 | + | 0.00983835i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19889.1 | 1.11425 | 0.557125 | − | 0.830428i | \(-0.311904\pi\) | ||||
0.557125 | + | 0.830428i | \(0.311904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9829.76 | 0.548286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8376.38 | + | 14508.3i | 0.463156 | + | 0.802210i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2465.15 | + | 4269.76i | −0.135714 | + | 0.235064i | −0.925870 | − | 0.377842i | \(-0.876666\pi\) |
0.790156 | + | 0.612906i | \(0.210000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7830.77 | − | 13563.3i | 0.427393 | − | 0.740266i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6189.23 | + | 10720.1i | 0.336347 | + | 0.582570i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8173.40 | −0.440378 | −0.220189 | − | 0.975457i | \(-0.570667\pi\) | ||||
−0.220189 | + | 0.975457i | \(0.570667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −808.070 | −0.0433527 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17882.5 | + | 30973.4i | 0.951259 | + | 1.64763i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3849.24 | + | 6667.07i | −0.203894 | + | 0.353155i | −0.949780 | − | 0.312919i | \(-0.898693\pi\) |
0.745886 | + | 0.666074i | \(0.232027\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2662.81 | + | 4612.12i | −0.139864 | + | 0.242251i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1668.40 | + | 2889.75i | 0.0872651 | + | 0.151148i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30407.2 | 1.57719 | 0.788593 | − | 0.614915i | \(-0.210810\pi\) | ||||
0.788593 | + | 0.614915i | \(0.210810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13648.1 | −0.704966 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1819.99 | − | 3152.32i | −0.0932315 | − | 0.161482i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7631.57 | − | 13218.3i | 0.389325 | − | 0.674330i | −0.603034 | − | 0.797715i | \(-0.706042\pi\) |
0.992359 | + | 0.123385i | \(0.0393750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1558.03 | − | 2698.59i | 0.0788315 | − | 0.136540i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3532.12 | + | 6117.80i | 0.177983 | + | 0.308276i | 0.941190 | − | 0.337879i | \(-0.109709\pi\) |
−0.763206 | + | 0.646155i | \(0.776376\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12250.6 | 0.612291 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20382.0 | −1.01457 | −0.507284 | − | 0.861779i | \(-0.669350\pi\) | ||||
−0.507284 | + | 0.861779i | \(0.669350\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15467.5 | + | 26790.5i | 0.763724 | + | 1.32281i | 0.940919 | + | 0.338633i | \(0.109964\pi\) |
−0.177195 | + | 0.984176i | \(0.556702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8632.19 | − | 14951.4i | 0.424509 | − | 0.735270i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22686.4 | + | 39293.9i | −1.10673 | + | 1.91691i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14542.4 | + | 25188.2i | 0.706606 | + | 1.22388i | 0.966109 | + | 0.258135i | \(0.0831080\pi\) |
−0.259503 | + | 0.965742i | \(0.583559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3220.00 | −0.155216 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5538.75 | 0.265930 | 0.132965 | − | 0.991121i | \(-0.457550\pi\) | ||||
0.132965 | + | 0.991121i | \(0.457550\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12652.1 | − | 21914.0i | −0.602677 | − | 1.04387i | −0.992414 | − | 0.122941i | \(-0.960767\pi\) |
0.389737 | − | 0.920926i | \(-0.372566\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22223.8 | − | 38492.7i | 1.05446 | − | 1.82638i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −53.6763 | + | 92.9700i | −0.00252691 | + | 0.00437673i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17531.9 | + | 30366.2i | 0.822129 | + | 1.42397i | 0.904094 | + | 0.427335i | \(0.140547\pi\) |
−0.0819641 | + | 0.996635i | \(0.526119\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32958.1 | −1.53353 | −0.766766 | − | 0.641927i | \(-0.778135\pi\) | ||||
−0.766766 | + | 0.641927i | \(0.778135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1160.98 | −0.0538110 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1830.60 | + | 3170.69i | 0.0841952 | + | 0.145830i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3516.99 | + | 6091.61i | −0.161137 | + | 0.279097i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3807.80 | + | 6595.30i | −0.173129 | + | 0.299868i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1115.28 | + | 1931.73i | 0.0505153 | + | 0.0874951i | 0.890177 | − | 0.455614i | \(-0.150580\pi\) |
−0.839662 | + | 0.543109i | \(0.817247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 52747.4 | 2.37103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23832.3 | 1.06722 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10976.9 | + | 19012.6i | 0.487857 | + | 0.844993i | 0.999902 | − | 0.0139654i | \(-0.00444545\pi\) |
−0.512046 | + | 0.858958i | \(0.671112\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4710.95 | − | 8159.61i | 0.208588 | − | 0.361284i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7691.82 | + | 13322.6i | −0.338031 | + | 0.585486i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8577.99 | − | 14857.5i | −0.375571 | − | 0.650507i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27001.6 | −1.17345 | −0.586727 | − | 0.809785i | \(-0.699584\pi\) | ||||
−0.586727 | + | 0.809785i | \(0.699584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37870.0 | −1.63970 | −0.819850 | − | 0.572579i | \(-0.805943\pi\) | ||||
−0.819850 | + | 0.572579i | \(0.805943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9514.17 | + | 16479.0i | 0.408916 | + | 0.708264i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 460.822 | − | 798.167i | 0.0197333 | − | 0.0341791i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18858.7 | + | 32664.3i | −0.801674 | + | 1.38854i | 0.116839 | + | 0.993151i | \(0.462724\pi\) |
−0.918513 | + | 0.395390i | \(0.870609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8679.38 | + | 15033.1i | 0.367611 | + | 0.636721i | 0.989192 | − | 0.146629i | \(-0.0468424\pi\) |
−0.621580 | + | 0.783350i | \(0.713509\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4418.15 | −0.185773 | −0.0928864 | − | 0.995677i | \(-0.529609\pi\) | ||||
−0.0928864 | + | 0.995677i | \(0.529609\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19161.9 | −0.802797 | −0.401399 | − | 0.915903i | \(-0.631476\pi\) | ||||
−0.401399 | + | 0.915903i | \(0.631476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10193.6 | + | 17655.8i | 0.423992 | + | 0.734376i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7755.71 | − | 13433.3i | 0.321434 | − | 0.556740i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2846.68 | − | 4930.60i | 0.117138 | − | 0.202888i | −0.801495 | − | 0.598002i | \(-0.795961\pi\) |
0.918632 | + | 0.395114i | \(0.129295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1594.91 | + | 2762.47i | 0.0653948 | + | 0.113267i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2198.62 | 0.0895087 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32240.4 | −1.30790 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4243.14 | + | 7349.34i | 0.170920 | + | 0.296042i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 948.837 | − | 1643.43i | 0.0380862 | − | 0.0659673i | −0.846354 | − | 0.532621i | \(-0.821207\pi\) |
0.884440 | + | 0.466654i | \(0.154541\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11150.7 | + | 19313.6i | −0.444459 | + | 0.769826i | −0.998014 | − | 0.0629864i | \(-0.979938\pi\) |
0.553555 | + | 0.832813i | \(0.313271\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14876.4 | − | 25766.7i | −0.590892 | − | 1.02346i | −0.994113 | − | 0.108353i | \(-0.965442\pi\) |
0.403220 | − | 0.915103i | \(-0.367891\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18461.6 | −0.728203 | −0.364102 | − | 0.931359i | \(-0.618624\pi\) | ||||
−0.364102 | + | 0.931359i | \(0.618624\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16144.5 | −0.634601 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4005.76 | − | 6938.18i | −0.156371 | − | 0.270842i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16129.1 | + | 27936.4i | −0.627454 | + | 1.08678i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1869.99 | − | 3238.92i | 0.0722483 | − | 0.125138i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13611.8 | + | 23576.3i | 0.524102 | + | 0.907772i | 0.999606 | + | 0.0280584i | \(0.00893243\pi\) |
−0.475504 | + | 0.879714i | \(0.657734\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24637.3 | −0.942169 | −0.471085 | − | 0.882088i | \(-0.656137\pi\) | ||||
−0.471085 | + | 0.882088i | \(0.656137\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37662.2 | 1.43537 | 0.717686 | − | 0.696367i | \(-0.245201\pi\) | ||||
0.717686 | + | 0.696367i | \(0.245201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1190.86 | − | 2062.63i | −0.0450792 | − | 0.0780794i | 0.842605 | − | 0.538531i | \(-0.181021\pi\) |
−0.887685 | + | 0.460452i | \(0.847687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10449.2 | + | 18098.6i | −0.394214 | + | 0.682798i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1393.37 | − | 2413.39i | 0.0522142 | − | 0.0904377i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −783.189 | − | 1356.52i | −0.0292504 | − | 0.0506632i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6761.50 | −0.250844 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14754.6 | 0.545556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1356.31 | − | 2349.20i | −0.0498181 | − | 0.0862875i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17432.9 | + | 30194.7i | −0.638204 | + | 1.10540i | 0.347622 | + | 0.937635i | \(0.386989\pi\) |
−0.985827 | + | 0.167768i | \(0.946344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26570.6 | + | 46021.5i | −0.966325 | + | 1.67372i | −0.260311 | + | 0.965525i | \(0.583825\pi\) |
−0.706013 | + | 0.708198i | \(0.749508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10115.1 | + | 17519.9i | 0.366662 | + | 0.635077i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35331.5 | −1.27236 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9861.81 | −0.353984 | −0.176992 | − | 0.984212i | \(-0.556637\pi\) | ||||
−0.176992 | + | 0.984212i | \(0.556637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9260.87 | − | 16040.3i | −0.330255 | − | 0.572018i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −925.000 | + | 1602.15i | −0.0328798 | + | 0.0569495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10341.6 | + | 17912.2i | −0.365228 | + | 0.632593i | −0.988813 | − | 0.149163i | \(-0.952342\pi\) |
0.623585 | + | 0.781756i | \(0.285676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3014.97 | + | 5222.08i | 0.106135 | + | 0.183831i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2938.80 | 0.102790 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6795.89 | 0.236939 | 0.118470 | − | 0.992958i | \(-0.462201\pi\) | ||||
0.118470 | + | 0.992958i | \(0.462201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3321.58 | − | 5753.15i | −0.115070 | − | 0.199306i | 0.802738 | − | 0.596332i | \(-0.203376\pi\) |
−0.917808 | + | 0.397025i | \(0.870042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19224.8 | − | 33298.3i | 0.663887 | − | 1.14989i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13217.1 | − | 22892.7i | 0.453535 | − | 0.785545i | −0.545068 | − | 0.838392i | \(-0.683496\pi\) |
0.998603 | + | 0.0528466i | \(0.0168294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20253.9 | − | 35080.9i | −0.692804 | − | 1.19997i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8451.56 | −0.287275 | −0.143637 | − | 0.989630i | \(-0.545880\pi\) | ||||
−0.143637 | + | 0.989630i | \(0.545880\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22848.4 | 0.774196 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29410.5 | + | 50940.5i | 0.990318 | + | 1.71528i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13817.2 | − | 23932.1i | 0.463805 | − | 0.803333i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11832.4 | + | 20494.3i | −0.394713 | + | 0.683662i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7662.42 | + | 13271.7i | 0.254816 | + | 0.441354i | 0.964845 | − | 0.262818i | \(-0.0846518\pi\) |
−0.710030 | + | 0.704172i | \(0.751318\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1686.74 | 0.0557468 | 0.0278734 | − | 0.999611i | \(-0.491126\pi\) | ||||
0.0278734 | + | 0.999611i | \(0.491126\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 93718.2 | 3.08784 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4850.53 | + | 8401.36i | 0.158835 | + | 0.275111i | 0.934449 | − | 0.356097i | \(-0.115893\pi\) |
−0.775614 | + | 0.631208i | \(0.782559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.91345 | − | 3.31419i | 6.24659e−5 | − | 0.000108194i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18228.1 | − | 31572.1i | 0.591442 | − | 1.02441i | −0.402597 | − | 0.915377i | \(-0.631892\pi\) |
0.994038 | − | 0.109030i | \(-0.0347744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8337.65 | − | 14441.2i | −0.269705 | − | 0.467143i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9679.02 | −0.311198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13556.5 | −0.434547 | −0.217274 | − | 0.976111i | \(-0.569716\pi\) | ||||
−0.217274 | + | 0.976111i | \(0.569716\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12153.2 | − | 21049.9i | −0.387217 | − | 0.670680i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30926.6 | + | 53566.5i | −0.982404 | + | 1.70157i | −0.329456 | + | 0.944171i | \(0.606865\pi\) |
−0.652948 | + | 0.757403i | \(0.726468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.4.i.q.541.1 | 4 | ||
3.2 | odd | 2 | 1620.4.i.n.541.1 | 4 | |||
9.2 | odd | 6 | 540.4.a.i.1.2 | yes | 2 | ||
9.4 | even | 3 | inner | 1620.4.i.q.1081.1 | 4 | ||
9.5 | odd | 6 | 1620.4.i.n.1081.1 | 4 | |||
9.7 | even | 3 | 540.4.a.f.1.2 | ✓ | 2 | ||
36.7 | odd | 6 | 2160.4.a.v.1.1 | 2 | |||
36.11 | even | 6 | 2160.4.a.ba.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.4.a.f.1.2 | ✓ | 2 | 9.7 | even | 3 | ||
540.4.a.i.1.2 | yes | 2 | 9.2 | odd | 6 | ||
1620.4.i.n.541.1 | 4 | 3.2 | odd | 2 | |||
1620.4.i.n.1081.1 | 4 | 9.5 | odd | 6 | |||
1620.4.i.q.541.1 | 4 | 1.1 | even | 1 | trivial | ||
1620.4.i.q.1081.1 | 4 | 9.4 | even | 3 | inner | ||
2160.4.a.v.1.1 | 2 | 36.7 | odd | 6 | |||
2160.4.a.ba.1.1 | 2 | 36.11 | even | 6 |