Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 12x^{6} + 23x^{4} + 12x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.7 | ||
Root | \(3.12580i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.h.485.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.80588i | 1.40294i | 0.712698 | + | 0.701471i | \(0.247473\pi\) | ||||
−0.712698 | + | 0.701471i | \(0.752527\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.87298 | −0.968246 | ||||||||
\(5\) | − 2.03151i | − 0.406301i | −0.979148 | − | 0.203151i | \(-0.934882\pi\) | ||||
0.979148 | − | 0.203151i | \(-0.0651181\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.504017 | −0.0720025 | −0.0360012 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360012 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(8\) | 0.356394i | 0.0445492i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.70017 | 0.570017 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.0767 | 1.69820 | 0.849102 | − | 0.528228i | \(-0.177143\pi\) | ||||
0.849102 | + | 0.528228i | \(0.177143\pi\) | |||||||
\(14\) | − 1.41421i | − 0.101015i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.4919 | −1.03075 | ||||||||
\(17\) | − 11.9816i | − 0.704799i | −0.935850 | − | 0.352400i | \(-0.885366\pi\) | ||||
0.935850 | − | 0.352400i | \(-0.114634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.92017 | −0.311588 | −0.155794 | − | 0.987790i | \(-0.549794\pi\) | ||||
−0.155794 | + | 0.987790i | \(0.549794\pi\) | |||||||
\(20\) | 7.86799i | 0.393399i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 42.7628i | − 1.85925i | −0.368502 | − | 0.929627i | \(-0.620129\pi\) | ||||
0.368502 | − | 0.929627i | \(-0.379871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.8730 | 0.834919 | ||||||||
\(26\) | 61.9445i | 2.38248i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.95205 | 0.0697161 | ||||||||
\(29\) | − 36.4765i | − 1.25781i | −0.777482 | − | 0.628905i | \(-0.783503\pi\) | ||||
0.777482 | − | 0.628905i | \(-0.216497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.49193 | −0.112643 | −0.0563215 | − | 0.998413i | \(-0.517937\pi\) | ||||
−0.0563215 | + | 0.998413i | \(0.517937\pi\) | |||||||
\(32\) | − 44.8489i | − 1.40153i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 33.6190 | 0.988793 | ||||||||
\(35\) | 1.02391i | 0.0292547i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.8569 | −0.888023 | −0.444011 | − | 0.896021i | \(-0.646445\pi\) | ||||
−0.444011 | + | 0.896021i | \(0.646445\pi\) | |||||||
\(38\) | − 16.6113i | − 0.437140i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.724016 | 0.0181004 | ||||||||
\(41\) | − 27.2102i | − 0.663665i | −0.943338 | − | 0.331832i | \(-0.892333\pi\) | ||||
0.943338 | − | 0.331832i | \(-0.107667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 58.0737 | 1.35055 | 0.675276 | − | 0.737565i | \(-0.264024\pi\) | ||||
0.675276 | + | 0.737565i | \(0.264024\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 119.988 | 2.60843 | ||||||||
\(47\) | − 11.8298i | − 0.251697i | −0.992049 | − | 0.125849i | \(-0.959835\pi\) | ||||
0.992049 | − | 0.125849i | \(-0.0401654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.7460 | −0.994816 | ||||||||
\(50\) | 58.5672i | 1.17134i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −85.5025 | −1.64428 | ||||||||
\(53\) | 61.7877i | 1.16581i | 0.812542 | + | 0.582903i | \(0.198083\pi\) | ||||
−0.812542 | + | 0.582903i | \(0.801917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 0.179629i | − 0.00320765i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 102.349 | 1.76463 | ||||||||
\(59\) | 59.9359i | 1.01586i | 0.861398 | + | 0.507931i | \(0.169590\pi\) | ||||
−0.861398 | + | 0.507931i | \(0.830410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 49.5055 | 0.811565 | 0.405782 | − | 0.913970i | \(-0.366999\pi\) | ||||
0.405782 | + | 0.913970i | \(0.366999\pi\) | |||||||
\(62\) | − 9.79796i | − 0.158032i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 59.8730 | 0.935515 | ||||||||
\(65\) | − 44.8489i | − 0.689983i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 108.333 | 1.61691 | 0.808453 | − | 0.588561i | \(-0.200305\pi\) | ||||
0.808453 | + | 0.588561i | \(0.200305\pi\) | |||||||
\(68\) | 46.4045i | 0.682419i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.87298 | −0.0410426 | ||||||||
\(71\) | 51.4049i | 0.724013i | 0.932176 | + | 0.362007i | \(0.117908\pi\) | ||||
−0.932176 | + | 0.362007i | \(0.882092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 123.204 | 1.68772 | 0.843861 | − | 0.536561i | \(-0.180277\pi\) | ||||
0.843861 | + | 0.536561i | \(0.180277\pi\) | |||||||
\(74\) | − 92.1925i | − 1.24584i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 22.9287 | 0.301694 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.12820 | 0.115547 | 0.0577734 | − | 0.998330i | \(-0.481600\pi\) | ||||
0.0577734 | + | 0.998330i | \(0.481600\pi\) | |||||||
\(80\) | 33.5035i | 0.418793i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 76.3488 | 0.931083 | ||||||||
\(83\) | 88.2722i | 1.06352i | 0.846895 | + | 0.531760i | \(0.178469\pi\) | ||||
−0.846895 | + | 0.531760i | \(0.821531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.3407 | −0.286361 | ||||||||
\(86\) | 162.948i | 1.89475i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 4.52349i | − 0.0508257i | −0.999677 | − | 0.0254129i | \(-0.991910\pi\) | ||||
0.999677 | − | 0.0254129i | \(-0.00809004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.1270 | −0.122275 | ||||||||
\(92\) | 165.620i | 1.80022i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 33.1930 | 0.353117 | ||||||||
\(95\) | 12.0269i | 0.126599i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 71.1109 | 0.733102 | 0.366551 | − | 0.930398i | \(-0.380539\pi\) | ||||
0.366551 | + | 0.930398i | \(0.380539\pi\) | |||||||
\(98\) | − 136.776i | − 1.39567i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −80.8407 | −0.808407 | ||||||||
\(101\) | − 56.7909i | − 0.562287i | −0.959666 | − | 0.281143i | \(-0.909286\pi\) | ||||
0.959666 | − | 0.281143i | \(-0.0907136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 168.619 | 1.63708 | 0.818539 | − | 0.574452i | \(-0.194785\pi\) | ||||
0.818539 | + | 0.574452i | \(0.194785\pi\) | |||||||
\(104\) | 7.86799i | 0.0756537i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −173.369 | −1.63556 | ||||||||
\(107\) | − 138.818i | − 1.29736i | −0.761061 | − | 0.648680i | \(-0.775321\pi\) | ||||
0.761061 | − | 0.648680i | \(-0.224679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −130.288 | −1.19530 | −0.597651 | − | 0.801756i | \(-0.703899\pi\) | ||||
−0.597651 | + | 0.801756i | \(0.703899\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.31222 | 0.0742162 | ||||||||
\(113\) | − 8.56369i | − 0.0757848i | −0.999282 | − | 0.0378924i | \(-0.987936\pi\) | ||||
0.999282 | − | 0.0378924i | \(-0.0120644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −86.8730 | −0.755417 | ||||||||
\(116\) | 141.273i | 1.21787i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −168.173 | −1.42520 | ||||||||
\(119\) | 6.03893i | 0.0507473i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 138.907i | 1.13858i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.5242 | 0.109066 | ||||||||
\(125\) | − 93.1912i | − 0.745530i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 146.756 | 1.15556 | 0.577781 | − | 0.816192i | \(-0.303919\pi\) | ||||
0.577781 | + | 0.816192i | \(0.303919\pi\) | |||||||
\(128\) | − 11.3989i | − 0.0890536i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 125.841 | 0.968006 | ||||||||
\(131\) | 182.026i | 1.38951i | 0.719246 | + | 0.694756i | \(0.244488\pi\) | ||||
−0.719246 | + | 0.694756i | \(0.755512\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.98387 | 0.0224351 | ||||||||
\(134\) | 303.969i | 2.26842i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.27017 | 0.0313983 | ||||||||
\(137\) | − 156.416i | − 1.14172i | −0.821046 | − | 0.570861i | \(-0.806609\pi\) | ||||
0.821046 | − | 0.570861i | \(-0.193391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 34.0090 | 0.244669 | 0.122334 | − | 0.992489i | \(-0.460962\pi\) | ||||
0.122334 | + | 0.992489i | \(0.460962\pi\) | |||||||
\(140\) | − 3.96560i | − 0.0283257i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −144.236 | −1.01575 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −74.1022 | −0.511050 | ||||||||
\(146\) | 345.695i | 2.36778i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 127.254 | 0.859825 | ||||||||
\(149\) | − 134.377i | − 0.901859i | −0.892559 | − | 0.450930i | \(-0.851093\pi\) | ||||
0.892559 | − | 0.450930i | \(-0.148907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 163.581 | 1.08332 | 0.541659 | − | 0.840598i | \(-0.317796\pi\) | ||||
0.541659 | + | 0.840598i | \(0.317796\pi\) | |||||||
\(152\) | − 2.10991i | − 0.0138810i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.09388i | 0.0457670i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −175.173 | −1.11575 | −0.557877 | − | 0.829924i | \(-0.688384\pi\) | ||||
−0.557877 | + | 0.829924i | \(0.688384\pi\) | |||||||
\(158\) | 25.6127i | 0.162105i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −91.1108 | −0.569442 | ||||||||
\(161\) | 21.5532i | 0.133871i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −144.268 | −0.885080 | −0.442540 | − | 0.896749i | \(-0.645923\pi\) | ||||
−0.442540 | + | 0.896749i | \(0.645923\pi\) | |||||||
\(164\) | 105.385i | 0.642590i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −247.681 | −1.49206 | ||||||||
\(167\) | 260.059i | 1.55724i | 0.627496 | + | 0.778620i | \(0.284080\pi\) | ||||
−0.627496 | + | 0.778620i | \(0.715920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 318.379 | 1.88390 | ||||||||
\(170\) | − 68.2971i | − 0.401748i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −224.919 | −1.30767 | ||||||||
\(173\) | − 269.404i | − 1.55725i | −0.627489 | − | 0.778625i | \(-0.715917\pi\) | ||||
0.627489 | − | 0.778625i | \(-0.284083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.5203 | −0.0601162 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.6924 | 0.0713056 | ||||||||
\(179\) | − 34.3460i | − 0.191877i | −0.995387 | − | 0.0959386i | \(-0.969415\pi\) | ||||
0.995387 | − | 0.0959386i | \(-0.0305852\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −243.190 | −1.34359 | −0.671794 | − | 0.740738i | \(-0.734476\pi\) | ||||
−0.671794 | + | 0.740738i | \(0.734476\pi\) | |||||||
\(182\) | − 31.2211i | − 0.171545i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.2404 | 0.0828284 | ||||||||
\(185\) | 66.7489i | 0.360805i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 45.8165i | 0.243705i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −33.7460 | −0.177610 | ||||||||
\(191\) | − 137.156i | − 0.718094i | −0.933320 | − | 0.359047i | \(-0.883102\pi\) | ||||
0.933320 | − | 0.359047i | \(-0.116898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −133.624 | −0.692352 | −0.346176 | − | 0.938170i | \(-0.612520\pi\) | ||||
−0.346176 | + | 0.938170i | \(0.612520\pi\) | |||||||
\(194\) | 199.529i | 1.02850i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 188.792 | 0.963226 | ||||||||
\(197\) | 166.299i | 0.844160i | 0.906559 | + | 0.422080i | \(0.138700\pi\) | ||||
−0.906559 | + | 0.422080i | \(0.861300\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −309.728 | −1.55642 | −0.778211 | − | 0.628004i | \(-0.783872\pi\) | ||||
−0.778211 | + | 0.628004i | \(0.783872\pi\) | |||||||
\(200\) | 7.43901i | 0.0371950i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 159.349 | 0.788855 | ||||||||
\(203\) | 18.3848i | 0.0905654i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −55.2778 | −0.269648 | ||||||||
\(206\) | 473.125i | 2.29672i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −364.087 | −1.75042 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −207.470 | −0.983271 | −0.491635 | − | 0.870801i | \(-0.663601\pi\) | ||||
−0.491635 | + | 0.870801i | \(0.663601\pi\) | |||||||
\(212\) | − 239.303i | − 1.12879i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 389.506 | 1.82012 | ||||||||
\(215\) | − 117.977i | − 0.548731i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.75999 | 0.00811057 | ||||||||
\(218\) | − 365.573i | − 1.67694i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 264.514i | − 1.19689i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −288.730 | −1.29475 | −0.647376 | − | 0.762171i | \(-0.724134\pi\) | ||||
−0.647376 | + | 0.762171i | \(0.724134\pi\) | |||||||
\(224\) | 22.6046i | 0.100913i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.0287 | 0.106322 | ||||||||
\(227\) | − 400.444i | − 1.76407i | −0.471184 | − | 0.882035i | \(-0.656173\pi\) | ||||
0.471184 | − | 0.882035i | \(-0.343827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4597 | 0.0544090 | 0.0272045 | − | 0.999630i | \(-0.491339\pi\) | ||||
0.0272045 | + | 0.999630i | \(0.491339\pi\) | |||||||
\(230\) | − 243.755i | − 1.05981i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.0000 | 0.0560345 | ||||||||
\(233\) | − 71.3406i | − 0.306183i | −0.988212 | − | 0.153091i | \(-0.951077\pi\) | ||||
0.988212 | − | 0.153091i | \(-0.0489229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0323 | −0.102265 | ||||||||
\(236\) | − 232.131i | − 0.983604i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.9445 | −0.0711955 | ||||||||
\(239\) | − 132.906i | − 0.556093i | −0.960568 | − | 0.278046i | \(-0.910313\pi\) | ||||
0.960568 | − | 0.278046i | \(-0.0896869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 130.884 | 0.543087 | 0.271543 | − | 0.962426i | \(-0.412466\pi\) | ||||
0.271543 | + | 0.962426i | \(0.412466\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −191.734 | −0.785794 | ||||||||
\(245\) | 99.0277i | 0.404195i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −130.698 | −0.529140 | ||||||||
\(248\) | − 1.24450i | − 0.00501816i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 261.484 | 1.04594 | ||||||||
\(251\) | 166.247i | 0.662339i | 0.943571 | + | 0.331169i | \(0.107443\pi\) | ||||
−0.943571 | + | 0.331169i | \(0.892557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 411.781i | 1.62119i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 271.476 | 1.06045 | ||||||||
\(257\) | − 389.435i | − 1.51531i | −0.652655 | − | 0.757655i | \(-0.726345\pi\) | ||||
0.652655 | − | 0.757655i | \(-0.273655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.5604 | 0.0639398 | ||||||||
\(260\) | 173.699i | 0.668073i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −510.744 | −1.94940 | ||||||||
\(263\) | 272.114i | 1.03465i | 0.855788 | + | 0.517327i | \(0.173073\pi\) | ||||
−0.855788 | + | 0.517327i | \(0.826927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 125.522 | 0.473668 | ||||||||
\(266\) | 8.37238i | 0.0314751i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −419.571 | −1.56556 | ||||||||
\(269\) | 237.350i | 0.882341i | 0.897423 | + | 0.441171i | \(0.145437\pi\) | ||||
−0.897423 | + | 0.441171i | \(0.854563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 301.401 | 1.11218 | 0.556091 | − | 0.831122i | \(-0.312301\pi\) | ||||
0.556091 | + | 0.831122i | \(0.312301\pi\) | |||||||
\(272\) | 197.600i | 0.726469i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 438.885 | 1.60177 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.5326 | 0.0560743 | 0.0280371 | − | 0.999607i | \(-0.491074\pi\) | ||||
0.0280371 | + | 0.999607i | \(0.491074\pi\) | |||||||
\(278\) | 95.4252i | 0.343256i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.364917 | −0.00130327 | ||||||||
\(281\) | 211.250i | 0.751781i | 0.926664 | + | 0.375890i | \(0.122663\pi\) | ||||
−0.926664 | + | 0.375890i | \(0.877337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.6649 | −0.104823 | −0.0524114 | − | 0.998626i | \(-0.516691\pi\) | ||||
−0.0524114 | + | 0.998626i | \(0.516691\pi\) | |||||||
\(284\) | − 199.090i | − 0.701023i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.7144i | 0.0477855i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 145.441 | 0.503258 | ||||||||
\(290\) | − 207.922i | − 0.716973i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −477.166 | −1.63413 | ||||||||
\(293\) | 440.744i | 1.50425i | 0.659022 | + | 0.752123i | \(0.270970\pi\) | ||||
−0.659022 | + | 0.752123i | \(0.729030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 121.760 | 0.412746 | ||||||||
\(296\) | − 11.7100i | − 0.0395608i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 377.046 | 1.26526 | ||||||||
\(299\) | − 944.061i | − 3.15739i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.2702 | −0.0972431 | ||||||||
\(302\) | 458.989i | 1.51983i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 97.6350 | 0.321168 | ||||||||
\(305\) | − 100.571i | − 0.329740i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 114.307 | 0.372336 | 0.186168 | − | 0.982518i | \(-0.440393\pi\) | ||||
0.186168 | + | 0.982518i | \(0.440393\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.9046 | −0.0642084 | ||||||||
\(311\) | − 492.303i | − 1.58297i | −0.611190 | − | 0.791484i | \(-0.709309\pi\) | ||||
0.611190 | − | 0.791484i | \(-0.290691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −202.714 | −0.647648 | −0.323824 | − | 0.946117i | \(-0.604969\pi\) | ||||
−0.323824 | + | 0.946117i | \(0.604969\pi\) | |||||||
\(314\) | − 491.516i | − 1.56534i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −35.3534 | −0.111878 | ||||||||
\(317\) | − 400.582i | − 1.26366i | −0.775105 | − | 0.631832i | \(-0.782303\pi\) | ||||
0.775105 | − | 0.631832i | \(-0.217697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 121.632i | − 0.380101i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −60.4758 | −0.187813 | ||||||||
\(323\) | 70.9330i | 0.219607i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 460.806 | 1.41786 | ||||||||
\(326\) | − 404.800i | − 1.24172i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.69757 | 0.0295658 | ||||||||
\(329\) | 5.96241i | 0.0181228i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 433.077 | 1.30839 | 0.654194 | − | 0.756327i | \(-0.273008\pi\) | ||||
0.654194 | + | 0.756327i | \(0.273008\pi\) | |||||||
\(332\) | − 341.877i | − 1.02975i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −729.696 | −2.18472 | ||||||||
\(335\) | − 220.078i | − 0.656951i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 403.120 | 1.19620 | 0.598100 | − | 0.801421i | \(-0.295922\pi\) | ||||
0.598100 | + | 0.801421i | \(0.295922\pi\) | |||||||
\(338\) | 893.334i | 2.64300i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 94.2710 | 0.277268 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 49.2656 | 0.143632 | ||||||||
\(344\) | 20.6971i | 0.0601661i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 755.917 | 2.18473 | ||||||||
\(347\) | 104.418i | 0.300916i | 0.988616 | + | 0.150458i | \(0.0480747\pi\) | ||||
−0.988616 | + | 0.150458i | \(0.951925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 49.2133 | 0.141012 | 0.0705062 | − | 0.997511i | \(-0.477539\pi\) | ||||
0.0705062 | + | 0.997511i | \(0.477539\pi\) | |||||||
\(350\) | − 29.5189i | − 0.0843396i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 234.322i | − 0.663801i | −0.943314 | − | 0.331901i | \(-0.892310\pi\) | ||||
0.943314 | − | 0.331901i | \(-0.107690\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 104.429 | 0.294167 | ||||||||
\(356\) | 17.5194i | 0.0492118i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 96.3709 | 0.269193 | ||||||||
\(359\) | 227.101i | 0.632594i | 0.948660 | + | 0.316297i | \(0.102440\pi\) | ||||
−0.948660 | + | 0.316297i | \(0.897560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −325.952 | −0.902913 | ||||||||
\(362\) | − 682.361i | − 1.88498i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 43.0948 | 0.118392 | ||||||||
\(365\) | − 250.289i | − 0.685724i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −509.982 | −1.38960 | −0.694798 | − | 0.719205i | \(-0.744506\pi\) | ||||
−0.694798 | + | 0.719205i | \(0.744506\pi\) | |||||||
\(368\) | 705.242i | 1.91642i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −187.290 | −0.506188 | ||||||||
\(371\) | − 31.1421i | − 0.0839409i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 416.132 | 1.11564 | 0.557818 | − | 0.829963i | \(-0.311639\pi\) | ||||
0.557818 | + | 0.829963i | \(0.311639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.21606 | 0.0112129 | ||||||||
\(377\) | − 805.279i | − 2.13602i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −372.587 | −0.983078 | −0.491539 | − | 0.870855i | \(-0.663566\pi\) | ||||
−0.491539 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(380\) | − 46.5798i | − 0.122578i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 384.844 | 1.00744 | ||||||||
\(383\) | 649.614i | 1.69612i | 0.529899 | + | 0.848061i | \(0.322230\pi\) | ||||
−0.529899 | + | 0.848061i | \(0.677770\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 374.933i | − 0.971330i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −275.411 | −0.709823 | ||||||||
\(389\) | 448.470i | 1.15288i | 0.817140 | + | 0.576439i | \(0.195558\pi\) | ||||
−0.817140 | + | 0.576439i | \(0.804442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −512.367 | −1.31040 | ||||||||
\(392\) | − 17.3728i | − 0.0443183i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −466.617 | −1.18431 | ||||||||
\(395\) | − 18.5440i | − 0.0469468i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.63508 | −0.0167131 | −0.00835653 | − | 0.999965i | \(-0.502660\pi\) | ||||
−0.00835653 | + | 0.999965i | \(0.502660\pi\) | |||||||
\(398\) | − 869.060i | − 2.18357i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −344.236 | −0.860590 | ||||||||
\(401\) | − 16.2649i | − 0.0405609i | −0.999794 | − | 0.0202804i | \(-0.993544\pi\) | ||||
0.999794 | − | 0.0202804i | \(-0.00645590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −77.0902 | −0.191291 | ||||||||
\(404\) | 219.950i | 0.544432i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −51.5855 | −0.127058 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 80.9908 | 0.198021 | 0.0990107 | − | 0.995086i | \(-0.468432\pi\) | ||||
0.0990107 | + | 0.995086i | \(0.468432\pi\) | |||||||
\(410\) | − 155.103i | − 0.378300i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −653.058 | −1.58509 | ||||||||
\(413\) | − 30.2087i | − 0.0731446i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 179.325 | 0.432109 | ||||||||
\(416\) | − 990.113i | − 2.38008i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 156.122i | − 0.372607i | −0.982492 | − | 0.186303i | \(-0.940349\pi\) | ||||
0.982492 | − | 0.186303i | \(-0.0596508\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −173.540 | −0.412210 | −0.206105 | − | 0.978530i | \(-0.566079\pi\) | ||||
−0.206105 | + | 0.978530i | \(0.566079\pi\) | |||||||
\(422\) | − 582.137i | − 1.37947i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.0208 | −0.0519358 | ||||||||
\(425\) | − 250.092i | − 0.588451i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.9516 | −0.0584347 | ||||||||
\(428\) | 537.638i | 1.25616i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 331.030 | 0.769838 | ||||||||
\(431\) | 204.134i | 0.473629i | 0.971555 | + | 0.236814i | \(0.0761033\pi\) | ||||
−0.971555 | + | 0.236814i | \(0.923897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −345.097 | −0.796990 | −0.398495 | − | 0.917170i | \(-0.630467\pi\) | ||||
−0.398495 | + | 0.917170i | \(0.630467\pi\) | |||||||
\(434\) | 4.93834i | 0.0113787i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 504.603 | 1.15735 | ||||||||
\(437\) | 253.163i | 0.579321i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 688.693 | 1.56878 | 0.784388 | − | 0.620270i | \(-0.212977\pi\) | ||||
0.784388 | + | 0.620270i | \(0.212977\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 742.194 | 1.67917 | ||||||||
\(443\) | 702.545i | 1.58588i | 0.609300 | + | 0.792940i | \(0.291451\pi\) | ||||
−0.609300 | + | 0.792940i | \(0.708549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.18950 | −0.0206506 | ||||||||
\(446\) | − 810.142i | − 1.81646i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −30.1770 | −0.0673594 | ||||||||
\(449\) | − 471.864i | − 1.05092i | −0.850818 | − | 0.525461i | \(-0.823893\pi\) | ||||
0.850818 | − | 0.525461i | \(-0.176107\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 33.1670i | 0.0733784i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1123.60 | 2.47489 | ||||||||
\(455\) | 22.6046i | 0.0496804i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 170.345 | 0.372746 | 0.186373 | − | 0.982479i | \(-0.440327\pi\) | ||||
0.186373 | + | 0.982479i | \(0.440327\pi\) | |||||||
\(458\) | 34.9604i | 0.0763327i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 336.458 | 0.731430 | ||||||||
\(461\) | 279.960i | 0.607289i | 0.952785 | + | 0.303645i | \(0.0982036\pi\) | ||||
−0.952785 | + | 0.303645i | \(0.901796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 147.921 | 0.319485 | 0.159742 | − | 0.987159i | \(-0.448934\pi\) | ||||
0.159742 | + | 0.987159i | \(0.448934\pi\) | |||||||
\(464\) | 601.568i | 1.29648i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 200.173 | 0.429557 | ||||||||
\(467\) | − 826.636i | − 1.77010i | −0.465497 | − | 0.885050i | \(-0.654124\pi\) | ||||
0.465497 | − | 0.885050i | \(-0.345876\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.6015 | −0.116421 | ||||||||
\(470\) | − 67.4317i | − 0.143472i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −21.3608 | −0.0452559 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −123.572 | −0.260151 | ||||||||
\(476\) | − 23.3887i | − 0.0491359i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 372.919 | 0.780166 | ||||||||
\(479\) | − 531.483i | − 1.10957i | −0.831994 | − | 0.554784i | \(-0.812801\pi\) | ||||
0.831994 | − | 0.554784i | \(-0.187199\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −725.370 | −1.50804 | ||||||||
\(482\) | 367.245i | 0.761919i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 144.462i | − 0.297860i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −607.825 | −1.24810 | −0.624050 | − | 0.781385i | \(-0.714514\pi\) | ||||
−0.624050 | + | 0.781385i | \(0.714514\pi\) | |||||||
\(488\) | 17.6434i | 0.0361546i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −277.860 | −0.567062 | ||||||||
\(491\) | 127.294i | 0.259255i | 0.991563 | + | 0.129628i | \(0.0413782\pi\) | ||||
−0.991563 | + | 0.129628i | \(0.958622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −437.046 | −0.886504 | ||||||||
\(494\) | − 366.722i | − 0.742353i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 57.5887 | 0.116106 | ||||||||
\(497\) | − 25.9090i | − 0.0521307i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 380.683 | 0.762893 | 0.381446 | − | 0.924391i | \(-0.375426\pi\) | ||||
0.381446 | + | 0.924391i | \(0.375426\pi\) | |||||||
\(500\) | 360.928i | 0.721856i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −466.470 | −0.929223 | ||||||||
\(503\) | 141.680i | 0.281670i | 0.990033 | + | 0.140835i | \(0.0449788\pi\) | ||||
−0.990033 | + | 0.140835i | \(0.955021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −115.371 | −0.228458 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −568.385 | −1.11887 | ||||||||
\(509\) | − 527.724i | − 1.03679i | −0.855143 | − | 0.518393i | \(-0.826530\pi\) | ||||
0.855143 | − | 0.518393i | \(-0.173470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −62.0968 | −0.121520 | ||||||||
\(512\) | 716.134i | 1.39870i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1092.71 | 2.12589 | ||||||||
\(515\) | − 342.550i | − 0.665146i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 46.4666i | 0.0897039i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.9839 | 0.0307382 | ||||||||
\(521\) | − 20.4491i | − 0.0392496i | −0.999807 | − | 0.0196248i | \(-0.993753\pi\) | ||||
0.999807 | − | 0.0196248i | \(-0.00624717\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −404.213 | −0.772873 | −0.386437 | − | 0.922316i | \(-0.626294\pi\) | ||||
−0.386437 | + | 0.922316i | \(0.626294\pi\) | |||||||
\(524\) | − 704.984i | − 1.34539i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −763.520 | −1.45156 | ||||||||
\(527\) | 41.8389i | 0.0793907i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1299.66 | −2.45683 | ||||||||
\(530\) | 352.201i | 0.664529i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.5565 | −0.0217227 | ||||||||
\(533\) | − 600.711i | − 1.12704i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −282.009 | −0.527119 | ||||||||
\(536\) | 38.6091i | 0.0720319i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −665.976 | −1.23787 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.1928 | 0.0650514 | 0.0325257 | − | 0.999471i | \(-0.489645\pi\) | ||||
0.0325257 | + | 0.999471i | \(0.489645\pi\) | |||||||
\(542\) | 845.697i | 1.56033i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −537.361 | −0.987796 | ||||||||
\(545\) | 264.681i | 0.485653i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −368.347 | −0.673395 | −0.336698 | − | 0.941613i | \(-0.609310\pi\) | ||||
−0.336698 | + | 0.941613i | \(0.609310\pi\) | |||||||
\(548\) | 605.797i | 1.10547i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 215.947i | 0.391918i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.60077 | −0.00831965 | ||||||||
\(554\) | 43.5826i | 0.0786689i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −131.716 | −0.236900 | ||||||||
\(557\) | 178.620i | 0.320683i | 0.987062 | + | 0.160341i | \(0.0512595\pi\) | ||||
−0.987062 | + | 0.160341i | \(0.948741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1282.07 | 2.29351 | ||||||||
\(560\) | − 16.8863i | − 0.0301541i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −592.744 | −1.05470 | ||||||||
\(563\) | 171.436i | 0.304505i | 0.988342 | + | 0.152252i | \(0.0486527\pi\) | ||||
−0.988342 | + | 0.152252i | \(0.951347\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.3972 | −0.0307915 | ||||||||
\(566\) | − 83.2362i | − 0.147060i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.3204 | −0.0322542 | ||||||||
\(569\) | − 653.652i | − 1.14877i | −0.818584 | − | 0.574386i | \(-0.805241\pi\) | ||||
0.818584 | − | 0.574386i | \(-0.194759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −172.238 | −0.301642 | −0.150821 | − | 0.988561i | \(-0.548192\pi\) | ||||
−0.150821 | + | 0.988561i | \(0.548192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −38.4811 | −0.0670402 | ||||||||
\(575\) | − 892.588i | − 1.55233i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 628.202 | 1.08874 | 0.544369 | − | 0.838846i | \(-0.316769\pi\) | ||||
0.544369 | + | 0.838846i | \(0.316769\pi\) | |||||||
\(578\) | 408.092i | 0.706041i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 286.997 | 0.494822 | ||||||||
\(581\) | − 44.4907i | − 0.0765761i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 43.9091i | 0.0751868i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1236.68 | −2.11037 | ||||||||
\(587\) | − 122.740i | − 0.209097i | −0.994520 | − | 0.104549i | \(-0.966660\pi\) | ||||
0.994520 | − | 0.104549i | \(-0.0333398\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.6728 | 0.0350982 | ||||||||
\(590\) | 341.645i | 0.579059i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 541.873 | 0.915326 | ||||||||
\(593\) | 365.467i | 0.616302i | 0.951338 | + | 0.308151i | \(0.0997101\pi\) | ||||
−0.951338 | + | 0.308151i | \(0.900290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.2681 | 0.0206187 | ||||||||
\(596\) | 520.440i | 0.873222i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2648.93 | 4.42964 | ||||||||
\(599\) | 317.385i | 0.529859i | 0.964268 | + | 0.264929i | \(0.0853486\pi\) | ||||
−0.964268 | + | 0.264929i | \(0.914651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −296.732 | −0.493731 | −0.246866 | − | 0.969050i | \(-0.579401\pi\) | ||||
−0.246866 | + | 0.969050i | \(0.579401\pi\) | |||||||
\(602\) | − 82.1287i | − 0.136426i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −633.546 | −1.04892 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −829.161 | −1.36600 | −0.682999 | − | 0.730419i | \(-0.739325\pi\) | ||||
−0.682999 | + | 0.730419i | \(0.739325\pi\) | |||||||
\(608\) | 265.513i | 0.436699i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 282.190 | 0.462606 | ||||||||
\(611\) | − 261.162i | − 0.427434i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −824.364 | −1.34480 | −0.672401 | − | 0.740187i | \(-0.734737\pi\) | ||||
−0.672401 | + | 0.740187i | \(0.734737\pi\) | |||||||
\(614\) | 320.733i | 0.522366i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 147.294i | − 0.238725i | −0.992851 | − | 0.119363i | \(-0.961915\pi\) | ||||
0.992851 | − | 0.119363i | \(-0.0380851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 454.329 | 0.733972 | 0.366986 | − | 0.930227i | \(-0.380390\pi\) | ||||
0.366986 | + | 0.930227i | \(0.380390\pi\) | |||||||
\(620\) | − 27.4745i | − 0.0443137i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1381.35 | 2.22081 | ||||||||
\(623\) | 2.27992i | 0.00365958i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 332.506 | 0.532010 | ||||||||
\(626\) | − 568.791i | − 0.908612i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 678.444 | 1.08032 | ||||||||
\(629\) | 393.677i | 0.625878i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.0464 | 0.0571258 | 0.0285629 | − | 0.999592i | \(-0.490907\pi\) | ||||
0.0285629 | + | 0.999592i | \(0.490907\pi\) | |||||||
\(632\) | 3.25323i | 0.00514752i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1123.99 | 1.77285 | ||||||||
\(635\) | − 298.136i | − 0.469506i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1076.15 | −1.68940 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.1568 | −0.0361826 | ||||||||
\(641\) | 1209.52i | 1.88692i | 0.331486 | + | 0.943460i | \(0.392450\pi\) | ||||
−0.331486 | + | 0.943460i | \(0.607550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1057.01 | 1.64388 | 0.821938 | − | 0.569577i | \(-0.192893\pi\) | ||||
0.821938 | + | 0.569577i | \(0.192893\pi\) | |||||||
\(644\) | − 83.4752i | − 0.129620i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −199.030 | −0.308096 | ||||||||
\(647\) | 730.812i | 1.12954i | 0.825249 | + | 0.564770i | \(0.191035\pi\) | ||||
−0.825249 | + | 0.564770i | \(0.808965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1292.97i | 1.98918i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 558.748 | 0.856975 | ||||||||
\(653\) | − 493.064i | − 0.755076i | −0.925994 | − | 0.377538i | \(-0.876771\pi\) | ||||
0.925994 | − | 0.377538i | \(-0.123229\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 369.787 | 0.564560 | ||||||||
\(656\) | 448.750i | 0.684069i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.7298 | −0.0254253 | ||||||||
\(659\) | 887.112i | 1.34615i | 0.739575 | + | 0.673074i | \(0.235027\pi\) | ||||
−0.739575 | + | 0.673074i | \(0.764973\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −574.603 | −0.869293 | −0.434647 | − | 0.900601i | \(-0.643127\pi\) | ||||
−0.434647 | + | 0.900601i | \(0.643127\pi\) | |||||||
\(662\) | 1215.16i | 1.83559i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.4597 | −0.0473790 | ||||||||
\(665\) | − 6.06174i | − 0.00911540i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1559.84 | −2.33859 | ||||||||
\(668\) | − 1007.20i | − 1.50779i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 617.514 | 0.921663 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −311.362 | −0.462647 | −0.231324 | − | 0.972877i | \(-0.574306\pi\) | ||||
−0.231324 | + | 0.972877i | \(0.574306\pi\) | |||||||
\(674\) | 1131.11i | 1.67820i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1233.08 | −1.82408 | ||||||||
\(677\) | 1283.45i | 1.89580i | 0.318573 | + | 0.947898i | \(0.396796\pi\) | ||||
−0.318573 | + | 0.947898i | \(0.603204\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.8411 | −0.0527851 | ||||||||
\(680\) | − 8.67487i | − 0.0127572i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1285.45i | 1.88206i | 0.338319 | + | 0.941031i | \(0.390142\pi\) | ||||
−0.338319 | + | 0.941031i | \(0.609858\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −317.760 | −0.463883 | ||||||||
\(686\) | 138.234i | 0.201507i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −957.748 | −1.39208 | ||||||||
\(689\) | 1364.07i | 1.97978i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −171.853 | −0.248702 | −0.124351 | − | 0.992238i | \(-0.539685\pi\) | ||||
−0.124351 | + | 0.992238i | \(0.539685\pi\) | |||||||
\(692\) | 1043.40i | 1.50780i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −292.984 | −0.422167 | ||||||||
\(695\) | − 69.0894i | − 0.0994092i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −326.022 | −0.467750 | ||||||||
\(698\) | 138.087i | 0.197832i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 40.7451 | 0.0582073 | ||||||||
\(701\) | − 690.179i | − 0.984564i | −0.870436 | − | 0.492282i | \(-0.836163\pi\) | ||||
0.870436 | − | 0.492282i | \(-0.163837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 194.518 | 0.276697 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 657.480 | 0.931274 | ||||||||
\(707\) | 28.6236i | 0.0404860i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 479.613 | 0.676464 | 0.338232 | − | 0.941063i | \(-0.390171\pi\) | ||||
0.338232 | + | 0.941063i | \(0.390171\pi\) | |||||||
\(710\) | 293.017i | 0.412700i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.61215 | 0.00226425 | ||||||||
\(713\) | 149.325i | 0.209432i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 133.022i | 0.185784i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −637.220 | −0.887493 | ||||||||
\(719\) | 1025.44i | 1.42620i | 0.701064 | + | 0.713099i | \(0.252709\pi\) | ||||
−0.701064 | + | 0.713099i | \(0.747291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −84.9868 | −0.117874 | ||||||||
\(722\) | − 914.582i | − 1.26673i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 941.869 | 1.30092 | ||||||||
\(725\) | − 761.373i | − 1.05017i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −250.204 | −0.344159 | −0.172079 | − | 0.985083i | \(-0.555049\pi\) | ||||
−0.172079 | + | 0.985083i | \(0.555049\pi\) | |||||||
\(728\) | − 3.96560i | − 0.00544725i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 702.282 | 0.962030 | ||||||||
\(731\) | − 695.816i | − 0.951869i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 945.472 | 1.28987 | 0.644933 | − | 0.764239i | \(-0.276885\pi\) | ||||
0.644933 | + | 0.764239i | \(0.276885\pi\) | |||||||
\(734\) | − 1430.95i | − 1.94952i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1917.87 | −2.60580 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −654.012 | −0.884996 | −0.442498 | − | 0.896769i | \(-0.645908\pi\) | ||||
−0.442498 | + | 0.896769i | \(0.645908\pi\) | |||||||
\(740\) | − 258.517i | − 0.349348i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 87.3810 | 0.117764 | ||||||||
\(743\) | 1183.38i | 1.59270i | 0.604837 | + | 0.796349i | \(0.293238\pi\) | ||||
−0.604837 | + | 0.796349i | \(0.706762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −272.988 | −0.366427 | ||||||||
\(746\) | 1167.62i | 1.56517i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 69.9664i | 0.0934132i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 75.3851 | 0.100380 | 0.0501898 | − | 0.998740i | \(-0.484017\pi\) | ||||
0.0501898 | + | 0.998740i | \(0.484017\pi\) | |||||||
\(752\) | 195.096i | 0.259436i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2259.52 | 2.99671 | ||||||||
\(755\) | − 332.316i | − 0.440153i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 488.488 | 0.645294 | 0.322647 | − | 0.946519i | \(-0.395427\pi\) | ||||
0.322647 | + | 0.946519i | \(0.395427\pi\) | |||||||
\(758\) | − 1045.43i | − 1.37920i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.28630 | −0.00563987 | ||||||||
\(761\) | 187.728i | 0.246685i | 0.992364 | + | 0.123343i | \(0.0393614\pi\) | ||||
−0.992364 | + | 0.123343i | \(0.960639\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 65.6673 | 0.0860647 | ||||||||
\(764\) | 531.203i | 0.695291i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1822.74 | −2.37956 | ||||||||
\(767\) | 1323.18i | 1.72514i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 257.324 | 0.334621 | 0.167311 | − | 0.985904i | \(-0.446492\pi\) | ||||
0.167311 | + | 0.985904i | \(0.446492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 517.523 | 0.670367 | ||||||||
\(773\) | 475.467i | 0.615093i | 0.951533 | + | 0.307546i | \(0.0995079\pi\) | ||||
−0.951533 | + | 0.307546i | \(0.900492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −72.8871 | −0.0940478 | ||||||||
\(776\) | 25.3435i | 0.0326591i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1258.35 | −1.61742 | ||||||||
\(779\) | 161.089i | 0.206790i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 1437.64i | − 1.83842i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 803.915 | 1.02540 | ||||||||
\(785\) | 355.866i | 0.453332i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 290.097 | 0.368612 | 0.184306 | − | 0.982869i | \(-0.440996\pi\) | ||||
0.184306 | + | 0.982869i | \(0.440996\pi\) | |||||||
\(788\) | − 644.075i | − 0.817354i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 52.0323 | 0.0658636 | ||||||||
\(791\) | 4.31625i | 0.00545669i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1092.92 | 1.37820 | ||||||||
\(794\) | − 18.6173i | − 0.0234474i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1199.57 | 1.50700 | ||||||||
\(797\) | − 792.022i | − 0.993754i | −0.867821 | − | 0.496877i | \(-0.834480\pi\) | ||||
0.867821 | − | 0.496877i | \(-0.165520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −141.740 | −0.177396 | ||||||||
\(800\) | − 936.130i | − 1.17016i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 45.6374 | 0.0569045 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.7855 | 0.0543919 | ||||||||
\(806\) | − 216.306i | − 0.268370i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.2399 | 0.0250494 | ||||||||
\(809\) | − 1021.86i | − 1.26311i | −0.775331 | − | 0.631556i | \(-0.782417\pi\) | ||||
0.775331 | − | 0.631556i | \(-0.217583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −113.251 | −0.139644 | −0.0698221 | − | 0.997559i | \(-0.522243\pi\) | ||||
−0.0698221 | + | 0.997559i | \(0.522243\pi\) | |||||||
\(812\) | − 71.2039i | − 0.0876896i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 293.082i | 0.359609i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −343.806 | −0.420816 | ||||||||
\(818\) | 227.251i | 0.277813i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 214.090 | 0.261085 | ||||||||
\(821\) | 344.122i | 0.419150i | 0.977793 | + | 0.209575i | \(0.0672080\pi\) | ||||
−0.977793 | + | 0.209575i | \(0.932792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 121.006 | 0.147031 | 0.0735153 | − | 0.997294i | \(-0.476578\pi\) | ||||
0.0735153 | + | 0.997294i | \(0.476578\pi\) | |||||||
\(824\) | 60.0948i | 0.0729306i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 84.7621 | 0.102618 | ||||||||
\(827\) | 251.924i | 0.304624i | 0.988332 | + | 0.152312i | \(0.0486718\pi\) | ||||
−0.988332 | + | 0.152312i | \(0.951328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −226.464 | −0.273177 | −0.136589 | − | 0.990628i | \(-0.543614\pi\) | ||||
−0.136589 | + | 0.990628i | \(0.543614\pi\) | |||||||
\(830\) | 503.166i | 0.606224i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1321.80 | 1.58870 | ||||||||
\(833\) | 584.054i | 0.701146i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 528.312 | 0.632708 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 438.061 | 0.522746 | ||||||||
\(839\) | − 580.612i | − 0.692028i | −0.938229 | − | 0.346014i | \(-0.887535\pi\) | ||||
0.938229 | − | 0.346014i | \(-0.112465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −489.534 | −0.582086 | ||||||||
\(842\) | − 486.934i | − 0.578306i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 803.528 | 0.952048 | ||||||||
\(845\) | − 646.789i | − 0.765431i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 1019.00i | − 1.20165i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 701.728 | 0.825562 | ||||||||
\(851\) | 1405.05i | 1.65106i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1056.85 | −1.23898 | −0.619491 | − | 0.785003i | \(-0.712661\pi\) | ||||
−0.619491 | + | 0.785003i | \(0.712661\pi\) | |||||||
\(854\) | − 70.0113i | − 0.0819804i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.4738 | 0.0577964 | ||||||||
\(857\) | − 1471.20i | − 1.71669i | −0.513071 | − | 0.858346i | \(-0.671492\pi\) | ||||
0.513071 | − | 0.858346i | \(-0.328508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1109.66 | −1.29180 | −0.645902 | − | 0.763421i | \(-0.723518\pi\) | ||||
−0.645902 | + | 0.763421i | \(0.723518\pi\) | |||||||
\(860\) | 456.924i | 0.531307i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −572.776 | −0.664474 | ||||||||
\(863\) | 369.201i | 0.427811i | 0.976854 | + | 0.213906i | \(0.0686185\pi\) | ||||
−0.976854 | + | 0.213906i | \(0.931382\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −547.297 | −0.632713 | ||||||||
\(866\) | − 968.301i | − 1.11813i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.81643 | −0.00785303 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2391.62 | 2.74584 | ||||||||
\(872\) | − 46.4338i | − 0.0532498i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −710.347 | −0.812754 | ||||||||
\(875\) | 46.9700i | 0.0536800i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −84.1500 | −0.0959521 | −0.0479761 | − | 0.998848i | \(-0.515277\pi\) | ||||
−0.0479761 | + | 0.998848i | \(0.515277\pi\) | |||||||
\(878\) | 1932.39i | 2.20090i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 763.999i | − 0.867195i | −0.901107 | − | 0.433598i | \(-0.857244\pi\) | ||||
0.901107 | − | 0.433598i | \(-0.142756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.97183 | −0.00449811 | −0.00224906 | − | 0.999997i | \(-0.500716\pi\) | ||||
−0.00224906 | + | 0.999997i | \(0.500716\pi\) | |||||||
\(884\) | 1024.46i | 1.15889i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1971.26 | −2.22490 | ||||||||
\(887\) | − 1020.39i | − 1.15038i | −0.818021 | − | 0.575189i | \(-0.804929\pi\) | ||||
0.818021 | − | 0.575189i | \(-0.195071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −73.9677 | −0.0832033 | ||||||||
\(890\) | − 25.7847i | − 0.0289715i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1118.25 | 1.25364 | ||||||||
\(893\) | 70.0343i | 0.0784259i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.7741 | −0.0779599 | ||||||||
\(896\) | 5.74522i | 0.00641208i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1324.00 | 1.47438 | ||||||||
\(899\) | 127.373i | 0.141684i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 740.315 | 0.821660 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.05205 | 0.00337616 | ||||||||
\(905\) | 494.041i | 0.545902i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −672.333 | −0.741271 | −0.370635 | − | 0.928778i | \(-0.620860\pi\) | ||||
−0.370635 | + | 0.928778i | \(0.620860\pi\) | |||||||
\(908\) | 1550.91i | 1.70805i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −63.4259 | −0.0696988 | ||||||||
\(911\) | 320.354i | 0.351650i | 0.984421 | + | 0.175825i | \(0.0562594\pi\) | ||||
−0.984421 | + | 0.175825i | \(0.943741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 477.969i | 0.522941i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −48.2561 | −0.0526813 | ||||||||
\(917\) | − 91.7443i | − 0.100048i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 755.334 | 0.821908 | 0.410954 | − | 0.911656i | \(-0.365196\pi\) | ||||
0.410954 | + | 0.911656i | \(0.365196\pi\) | |||||||
\(920\) | − 30.9610i | − 0.0336533i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −785.536 | −0.851992 | ||||||||
\(923\) | 1134.85i | 1.22952i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −685.820 | −0.741428 | ||||||||
\(926\) | 415.050i | 0.448218i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1635.93 | −1.76285 | ||||||||
\(929\) | − 653.730i | − 0.703692i | −0.936058 | − | 0.351846i | \(-0.885554\pi\) | ||||
0.936058 | − | 0.351846i | \(-0.114446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 288.584 | 0.309972 | ||||||||
\(932\) | 276.301i | 0.296460i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2319.45 | 2.48335 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1051.46 | 1.12216 | 0.561078 | − | 0.827763i | \(-0.310387\pi\) | ||||
0.561078 | + | 0.827763i | \(0.310387\pi\) | |||||||
\(938\) | − 153.206i | − 0.163332i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 93.0766 | 0.0990176 | ||||||||
\(941\) | − 503.345i | − 0.534904i | −0.963571 | − | 0.267452i | \(-0.913818\pi\) | ||||
0.963571 | − | 0.267452i | \(-0.0861817\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1163.59 | −1.23392 | ||||||||
\(944\) | − 988.458i | − 1.04710i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 369.018i | − 0.389671i | −0.980836 | − | 0.194836i | \(-0.937583\pi\) | ||||
0.980836 | − | 0.194836i | \(-0.0624173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2719.93 | 2.86610 | ||||||||
\(950\) | − 346.728i | − 0.364976i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.15224 | −0.00226075 | ||||||||
\(953\) | 852.586i | 0.894634i | 0.894375 | + | 0.447317i | \(0.147620\pi\) | ||||
−0.894375 | + | 0.447317i | \(0.852380\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −278.633 | −0.291762 | ||||||||
\(956\) | 514.743i | 0.538435i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1491.28 | 1.55666 | ||||||||
\(959\) | 78.8364i | 0.0822068i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −948.806 | −0.987312 | ||||||||
\(962\) | − 2035.30i | − 2.11570i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −506.911 | −0.525841 | ||||||||
\(965\) | 271.458i | 0.281304i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 683.004 | 0.706312 | 0.353156 | − | 0.935564i | \(-0.385108\pi\) | ||||
0.353156 | + | 0.935564i | \(0.385108\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 405.344 | 0.417881 | ||||||||
\(971\) | − 869.351i | − 0.895315i | −0.894205 | − | 0.447657i | \(-0.852258\pi\) | ||||
0.894205 | − | 0.447657i | \(-0.147742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1411 | −0.0176168 | ||||||||
\(974\) | − 1705.49i | − 1.75101i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −816.441 | −0.836517 | ||||||||
\(977\) | − 743.912i | − 0.761425i | −0.924694 | − | 0.380712i | \(-0.875679\pi\) | ||||
0.924694 | − | 0.380712i | \(-0.124321\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 383.533i | − 0.391360i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −357.173 | −0.363720 | ||||||||
\(983\) | − 352.071i | − 0.358159i | −0.983835 | − | 0.179080i | \(-0.942688\pi\) | ||||
0.983835 | − | 0.179080i | \(-0.0573120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 337.838 | 0.342983 | ||||||||
\(986\) | − 1226.30i | − 1.24371i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 506.190 | 0.512338 | ||||||||
\(989\) | − 2483.40i | − 2.51102i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1939.01 | 1.95662 | 0.978309 | − | 0.207152i | \(-0.0664195\pi\) | ||||
0.978309 | + | 0.207152i | \(0.0664195\pi\) | |||||||
\(992\) | 156.609i | 0.157872i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 72.6976 | 0.0731364 | ||||||||
\(995\) | 629.214i | 0.632376i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −115.855 | −0.116204 | −0.0581020 | − | 0.998311i | \(-0.518505\pi\) | ||||
−0.0581020 | + | 0.998311i | \(0.518505\pi\) | |||||||
\(998\) | 1068.15i | 1.07029i | ||||||||
\(999\) | 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 | 1089.3.b.h.485.7 | yes | 8 | |
3.2 | odd | 2 | inner | 1089.3.b.h.485.2 | yes | 8 | |
11.10 | odd | 2 | inner | 1089.3.b.h.485.1 | ✓ | 8 | |
33.32 | even | 2 | inner | 1089.3.b.h.485.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1089.3.b.h.485.1 | ✓ | 8 | 11.10 | odd | 2 | inner | |
1089.3.b.h.485.2 | yes | 8 | 3.2 | odd | 2 | inner | |
1089.3.b.h.485.7 | yes | 8 | 1.1 | even | 1 | trivial | |
1089.3.b.h.485.8 | yes | 8 | 33.32 | even | 2 | inner |