Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), 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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.4.bt.d.593.5 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.29543 | − | 12.6361i | −0.652523 | − | 1.13020i | −0.982509 | − | 0.186218i | \(-0.940377\pi\) |
0.329985 | − | 0.943986i | \(-0.392956\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.4933 | − | 0.998739i | −0.998545 | − | 0.0539268i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −38.7318 | − | 22.3618i | −1.06164 | − | 0.612940i | −0.135757 | − | 0.990742i | \(-0.543347\pi\) |
−0.925886 | + | 0.377802i | \(0.876680\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 76.8588i | − | 1.63975i | −0.572540 | − | 0.819877i | \(-0.694042\pi\) | ||
0.572540 | − | 0.819877i | \(-0.305958\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −58.3464 | + | 101.059i | −0.832416 | + | 1.44179i | 0.0637008 | + | 0.997969i | \(0.479710\pi\) |
−0.896117 | + | 0.443818i | \(0.853624\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −83.5432 | + | 48.2337i | −1.00874 | + | 0.582398i | −0.910823 | − | 0.412796i | \(-0.864552\pi\) |
−0.0979195 | + | 0.995194i | \(0.531219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.88438 | − | 3.97470i | 0.0624127 | − | 0.0360340i | −0.468469 | − | 0.883480i | \(-0.655194\pi\) |
0.530882 | + | 0.847446i | \(0.321861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −43.9467 | + | 76.1180i | −0.351574 | + | 0.608944i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 86.8540i | − | 0.556151i | −0.960559 | − | 0.278076i | \(-0.910303\pi\) | ||
0.960559 | − | 0.278076i | \(-0.0896966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −216.262 | − | 124.859i | −1.25296 | − | 0.723397i | −0.281265 | − | 0.959630i | \(-0.590754\pi\) |
−0.971696 | + | 0.236233i | \(0.924087\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 122.297 | + | 240.969i | 0.590626 | + | 1.16375i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −160.031 | − | 277.182i | −0.711053 | − | 1.23158i | −0.964462 | − | 0.264221i | \(-0.914885\pi\) |
0.253409 | − | 0.967359i | \(-0.418448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 231.290 | 0.881010 | 0.440505 | − | 0.897750i | \(-0.354799\pi\) | ||||
0.440505 | + | 0.897750i | \(0.354799\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 413.282 | 1.46569 | 0.732847 | − | 0.680393i | \(-0.238191\pi\) | ||||
0.732847 | + | 0.680393i | \(0.238191\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 235.508 | + | 407.911i | 0.730901 | + | 1.26596i | 0.956499 | + | 0.291737i | \(0.0942331\pi\) |
−0.225598 | + | 0.974220i | \(0.572434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 341.005 | + | 36.9400i | 0.994184 | + | 0.107697i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −600.339 | − | 346.606i | −1.55590 | − | 0.898301i | −0.997642 | − | 0.0686360i | \(-0.978135\pi\) |
−0.558261 | − | 0.829665i | \(-0.688531\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 652.557i | 1.59983i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 143.802 | − | 249.072i | 0.317312 | − | 0.549600i | −0.662615 | − | 0.748961i | \(-0.730553\pi\) |
0.979926 | + | 0.199361i | \(0.0638866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 740.898 | − | 427.758i | 1.55512 | − | 0.897849i | 0.557408 | − | 0.830238i | \(-0.311796\pi\) |
0.997712 | − | 0.0676105i | \(-0.0215375\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −971.193 | + | 560.718i | −1.85326 | + | 1.06998i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −240.341 | + | 416.283i | −0.438244 | + | 0.759061i | −0.997554 | − | 0.0698977i | \(-0.977733\pi\) |
0.559310 | + | 0.828958i | \(0.311066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 930.276i | 1.55498i | 0.628897 | + | 0.777489i | \(0.283507\pi\) | ||||
−0.628897 | + | 0.777489i | \(0.716493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −98.4174 | − | 56.8213i | −0.157793 | − | 0.0911018i | 0.419024 | − | 0.907975i | \(-0.362372\pi\) |
−0.576817 | + | 0.816873i | \(0.695706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 693.946 | + | 452.227i | 1.02704 | + | 0.669299i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −111.374 | − | 192.905i | −0.158614 | − | 0.274727i | 0.775755 | − | 0.631034i | \(-0.217369\pi\) |
−0.934369 | + | 0.356307i | \(0.884036\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −692.424 | −0.915703 | −0.457852 | − | 0.889029i | \(-0.651381\pi\) | ||||
−0.457852 | + | 0.889029i | \(0.651381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1702.65 | 2.17268 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 258.667 | + | 448.025i | 0.308075 | + | 0.533602i | 0.977941 | − | 0.208880i | \(-0.0669818\pi\) |
−0.669866 | + | 0.742482i | \(0.733648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −76.7619 | + | 1421.37i | −0.0884267 | + | 1.63737i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1218.97 | + | 703.771i | 1.31646 | + | 0.760057i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 807.511i | − | 0.845261i | −0.906302 | − | 0.422630i | \(-0.861107\pi\) | ||
0.906302 | − | 0.422630i | \(-0.138893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 115.748 | − | 200.482i | 0.114033 | − | 0.197511i | −0.803360 | − | 0.595494i | \(-0.796956\pi\) |
0.917393 | + | 0.397983i | \(0.130290\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1028.60 | − | 593.864i | 0.983992 | − | 0.568108i | 0.0805191 | − | 0.996753i | \(-0.474342\pi\) |
0.903473 | + | 0.428645i | \(0.141009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.77425 | − | 2.17906i | 0.00341000 | − | 0.00196877i | −0.498294 | − | 0.867008i | \(-0.666040\pi\) |
0.501704 | + | 0.865039i | \(0.332707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −113.726 | + | 196.980i | −0.0999360 | + | 0.173094i | −0.911658 | − | 0.410950i | \(-0.865197\pi\) |
0.811722 | + | 0.584044i | \(0.198530\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 517.680i | − | 0.430967i | −0.976507 | − | 0.215483i | \(-0.930867\pi\) | ||
0.976507 | − | 0.215483i | \(-0.0691327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −100.449 | − | 57.9943i | −0.0814515 | − | 0.0470261i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1179.95 | − | 1810.64i | 0.908956 | − | 1.39480i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 334.602 | + | 579.548i | 0.251392 | + | 0.435423i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −541.417 | −0.387406 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1665.46 | 1.16367 | 0.581833 | − | 0.813308i | \(-0.302336\pi\) | ||||
0.581833 | + | 0.813308i | \(0.302336\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 342.534 | + | 593.286i | 0.228453 | + | 0.395692i | 0.957350 | − | 0.288931i | \(-0.0932999\pi\) |
−0.728897 | + | 0.684624i | \(0.759967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1593.16 | − | 808.562i | 1.03868 | − | 0.527152i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 910.457 | + | 525.653i | 0.567778 | + | 0.327807i | 0.756261 | − | 0.654270i | \(-0.227024\pi\) |
−0.188483 | + | 0.982076i | \(0.560357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 26.6372i | − | 0.0162542i | −0.999967 | − | 0.00812712i | \(-0.997413\pi\) | ||
0.999967 | − | 0.00812712i | \(-0.00258697\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1718.70 | + | 2976.88i | −1.00507 | + | 1.74083i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1097.49 | + | 633.638i | −0.628564 | + | 0.362902i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1914.14 | + | 1105.13i | −1.05243 | + | 0.607622i | −0.923329 | − | 0.384010i | \(-0.874543\pi\) |
−0.129102 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −958.101 | + | 1659.48i | −0.516352 | + | 0.894348i | 0.483468 | + | 0.875362i | \(0.339377\pi\) |
−0.999820 | + | 0.0189855i | \(0.993956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3643.60i | 1.88814i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1859.51 | + | 1073.59i | 0.945255 | + | 0.545743i | 0.891604 | − | 0.452816i | \(-0.149581\pi\) |
0.0536515 | + | 0.998560i | \(0.482914\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −131.285 | + | 66.6296i | −0.0642651 | + | 0.0326159i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −713.783 | − | 1236.31i | −0.342993 | − | 0.594081i | 0.641994 | − | 0.766710i | \(-0.278107\pi\) |
−0.984987 | + | 0.172628i | \(0.944774\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −558.327 | −0.258710 | −0.129355 | − | 0.991598i | \(-0.541291\pi\) | ||||
−0.129355 | + | 0.991598i | \(0.541291\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3710.28 | −1.68879 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 317.963 | + | 550.728i | 0.139736 | + | 0.242029i | 0.927397 | − | 0.374080i | \(-0.122041\pi\) |
−0.787661 | + | 0.616109i | \(0.788708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 888.742 | − | 1363.78i | 0.383901 | − | 0.589098i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1071.64 | − | 618.711i | −0.447475 | − | 0.258350i | 0.259288 | − | 0.965800i | \(-0.416512\pi\) |
−0.706763 | + | 0.707450i | \(0.749845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 252.299i | − | 0.103609i | −0.998657 | − | 0.0518046i | \(-0.983503\pi\) | ||
0.998657 | − | 0.0518046i | \(-0.0164973\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2334.99 | + | 4044.33i | −0.927958 | + | 1.60727i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4519.72 | − | 2609.46i | 1.76746 | − | 1.02044i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2004.84 | + | 1157.50i | −0.759505 | + | 0.438500i | −0.829118 | − | 0.559074i | \(-0.811157\pi\) |
0.0696131 | + | 0.997574i | \(0.477824\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1128.33 | + | 1954.32i | −0.420824 | + | 0.728888i | −0.996020 | − | 0.0891273i | \(-0.971592\pi\) |
0.575197 | + | 0.818015i | \(0.304926\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4940.41i | 1.78675i | 0.449312 | + | 0.893375i | \(0.351669\pi\) | ||||
−0.449312 | + | 0.893375i | \(0.648331\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 505.394 | + | 291.789i | 0.180032 | + | 0.103942i | 0.587308 | − | 0.809364i | \(-0.300188\pi\) |
−0.407276 | + | 0.913305i | \(0.633521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −86.7445 | + | 1606.22i | −0.0299915 | + | 0.555342i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1687.36 | − | 2922.59i | −0.574879 | − | 0.995720i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4314.37 | 1.42790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3849.63 | −1.25602 | −0.628009 | − | 0.778206i | \(-0.716130\pi\) | ||||
−0.628009 | + | 0.778206i | \(0.716130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3015.07 | − | 5222.25i | −0.956400 | − | 1.65653i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3874.70 | + | 2525.04i | 1.21213 | + | 0.789913i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7767.27 | + | 4484.43i | 2.36418 | + | 1.36496i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6244.17i | − | 1.87507i | −0.347889 | − | 0.937536i | \(-0.613102\pi\) | ||
0.347889 | − | 0.937536i | \(-0.386898\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −703.572 | + | 1218.62i | −0.205717 | + | 0.356312i | −0.950361 | − | 0.311150i | \(-0.899286\pi\) |
0.744644 | + | 0.667462i | \(0.232619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2122.90 | − | 1225.66i | 0.612600 | − | 0.353685i | −0.161382 | − | 0.986892i | \(-0.551595\pi\) |
0.773982 | + | 0.633207i | \(0.218262\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2021.13 | + | 1166.90i | −0.568278 | + | 0.328095i | −0.756461 | − | 0.654039i | \(-0.773073\pi\) |
0.188184 | + | 0.982134i | \(0.439740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3436.26 | − | 5951.78i | 0.953860 | − | 1.65213i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1158.54i | − | 0.313555i | −0.987634 | − | 0.156778i | \(-0.949889\pi\) | ||
0.987634 | − | 0.156778i | \(-0.0501106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2667.43 | + | 1540.04i | 0.712964 | + | 0.411630i | 0.812158 | − | 0.583438i | \(-0.198293\pi\) |
−0.0991935 | + | 0.995068i | \(0.531626\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2021.00 | − | 4578.45i | −0.527009 | − | 1.19390i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3707.18 | + | 6421.03i | 0.954989 | + | 1.65409i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1292.55 | 0.325039 | 0.162520 | − | 0.986705i | \(-0.448038\pi\) | ||||
0.162520 | + | 0.986705i | \(0.448038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −355.526 | −0.0883468 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −393.202 | − | 681.045i | −0.0954368 | − | 0.165301i | 0.814354 | − | 0.580368i | \(-0.197091\pi\) |
−0.909791 | + | 0.415067i | \(0.863758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2682.67 | + | 5285.85i | 0.643603 | + | 1.26813i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3353.52 | + | 1936.16i | 0.786262 | + | 0.453948i | 0.838645 | − | 0.544679i | \(-0.183348\pi\) |
−0.0523831 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10114.6i | 2.34465i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1629.53 | − | 2822.43i | 0.369347 | − | 0.639727i | −0.620117 | − | 0.784510i | \(-0.712915\pi\) |
0.989464 | + | 0.144782i | \(0.0462481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2607.80 | − | 1505.61i | 0.584548 | − | 0.337489i | −0.178391 | − | 0.983960i | \(-0.557089\pi\) |
0.762939 | + | 0.646471i | \(0.223756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3404.27 | − | 1965.46i | 0.746492 | − | 0.430987i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2955.86 | + | 5119.70i | −0.641157 | + | 1.11052i | 0.344018 | + | 0.938963i | \(0.388212\pi\) |
−0.985175 | + | 0.171553i | \(0.945122\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 594.162i | − | 0.126138i | −0.998009 | − | 0.0630690i | \(-0.979911\pi\) | ||
0.998009 | − | 0.0630690i | \(-0.0200888\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1858.80 | + | 1073.18i | 0.390440 | + | 0.225420i | 0.682351 | − | 0.731025i | \(-0.260958\pi\) |
−0.291911 | + | 0.956446i | \(0.594291\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4277.31 | − | 230.998i | −0.879728 | − | 0.0475101i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4352.10 | − | 7538.06i | −0.885833 | − | 1.53431i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3508.37 | 0.699527 | 0.349763 | − | 0.936838i | \(-0.386262\pi\) | ||||
0.349763 | + | 0.936838i | \(0.386262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4196.38 | −0.828213 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −305.491 | − | 529.125i | −0.0590869 | − | 0.102341i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7642.95 | − | 412.760i | −1.46356 | − | 0.0790403i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10810.4 | − | 6241.36i | −2.02950 | − | 1.17174i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3932.23i | 0.731024i | 0.930807 | + | 0.365512i | \(0.119106\pi\) | ||||
−0.930807 | + | 0.365512i | \(0.880894\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2383.96 | + | 4129.14i | −0.434669 | + | 0.752868i | −0.997269 | − | 0.0738611i | \(-0.976468\pi\) |
0.562600 | + | 0.826729i | \(0.309801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1322.49 | + | 763.537i | −0.238822 | + | 0.137884i | −0.614635 | − | 0.788811i | \(-0.710697\pi\) |
0.375813 | + | 0.926695i | \(0.377363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5430.41 | − | 3135.25i | 0.962152 | − | 0.555499i | 0.0653175 | − | 0.997865i | \(-0.479194\pi\) |
0.896835 | + | 0.442366i | \(0.145861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1942.21 | + | 3364.01i | −0.340888 | + | 0.590435i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11257.0i | − | 1.93919i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5850.34 | + | 3377.69i | 0.998518 | + | 0.576494i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3947.92 | − | 7778.84i | −0.661568 | − | 1.30353i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4010.93 | − | 6947.14i | −0.666045 | − | 1.15362i | −0.979001 | − | 0.203856i | \(-0.934653\pi\) |
0.312956 | − | 0.949768i | \(-0.398681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7013.57 | 1.14386 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7526.55 | 1.21661 | 0.608305 | − | 0.793704i | \(-0.291850\pi\) | ||||
0.608305 | + | 0.793704i | \(0.291850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5584.14 | + | 9672.02i | 0.886799 | + | 1.53598i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6269.42 | − | 1023.72i | −0.986929 | − | 0.161153i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9728.57 | − | 5616.79i | −1.50506 | − | 0.868948i | −0.999983 | − | 0.00587585i | \(-0.998130\pi\) |
−0.505080 | − | 0.863073i | \(-0.668537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 88.0987i | 0.0135124i | 0.999977 | + | 0.00675618i | \(0.00215058\pi\) | ||||
−0.999977 | + | 0.00675618i | \(0.997849\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2911.54 | − | 5042.93i | 0.438996 | − | 0.760363i | −0.558616 | − | 0.829426i | \(-0.688668\pi\) |
0.997612 | + | 0.0690628i | \(0.0220009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11755.0 | − | 6786.77i | 1.75744 | − | 1.01466i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3226.19 | − | 1862.64i | 0.474295 | − | 0.273834i | −0.243741 | − | 0.969840i | \(-0.578375\pi\) |
0.718036 | + | 0.696006i | \(0.245041\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1223.47 | − | 2119.12i | 0.178375 | − | 0.308954i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1658.14i | 0.237784i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8554.28 | − | 4938.81i | −1.21670 | − | 0.702463i | −0.252491 | − | 0.967599i | \(-0.581250\pi\) |
−0.964211 | + | 0.265136i | \(0.914583\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10756.1 | + | 7009.47i | 1.50520 | + | 0.980899i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6764.39 | − | 11716.3i | −0.938999 | − | 1.62639i | −0.767342 | − | 0.641238i | \(-0.778421\pi\) |
−0.171657 | − | 0.985157i | \(-0.554912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6675.50 | −0.911951 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5023.35 | −0.680824 | −0.340412 | − | 0.940276i | \(-0.610567\pi\) | ||||
−0.340412 | + | 0.940276i | \(0.610567\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6925.52 | − | 11995.4i | −0.923962 | − | 1.60035i | −0.793222 | − | 0.608933i | \(-0.791598\pi\) |
−0.130741 | − | 0.991417i | \(-0.541736\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 651.734 | − | 12067.9i | 0.0862739 | − | 1.59750i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3180.84 | + | 1836.46i | 0.414589 | + | 0.239363i | 0.692760 | − | 0.721169i | \(-0.256395\pi\) |
−0.278171 | + | 0.960532i | \(0.589728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 927.637i | 0.119981i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1625.04 | + | 2814.65i | −0.206999 | + | 0.358532i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1790.92 | + | 1033.99i | −0.226407 | + | 0.130716i | −0.608913 | − | 0.793237i | \(-0.708394\pi\) |
0.382506 | + | 0.923953i | \(0.375061\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2813.54 | + | 1624.40i | −0.350377 | + | 0.202290i | −0.664851 | − | 0.746976i | \(-0.731505\pi\) |
0.314474 | + | 0.949266i | \(0.398172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9596.51 | + | 16621.6i | −1.18619 | + | 2.05455i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14314.4i | 1.74333i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4769.99 | − | 2753.96i | −0.576677 | − | 0.332945i | 0.183135 | − | 0.983088i | \(-0.441376\pi\) |
−0.759812 | + | 0.650143i | \(0.774709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2908.13 | + | 4462.54i | −0.346488 | + | 0.531688i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5051.53 | + | 8749.51i | 0.597518 | + | 1.03493i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7281.32 | 0.848964 | 0.424482 | − | 0.905436i | \(-0.360456\pi\) | ||||
0.424482 | + | 0.905436i | \(0.360456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1524.24 | 0.176453 | 0.0882265 | − | 0.996100i | \(-0.471880\pi\) | ||||
0.0882265 | + | 0.996100i | \(0.471880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5128.26 | − | 8882.41i | −0.585311 | − | 1.01379i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14128.9 | + | 7170.70i | −1.60128 | + | 0.812680i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4465.09 | − | 2577.92i | −0.499016 | − | 0.288107i | 0.229291 | − | 0.973358i | \(-0.426359\pi\) |
−0.728307 | + | 0.685251i | \(0.759692\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1041.23i | 0.115562i | 0.998329 | + | 0.0577811i | \(0.0184026\pi\) | ||||
−0.998329 | + | 0.0577811i | \(0.981597\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −383.429 | + | 664.118i | −0.0419723 | + | 0.0726981i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4138.98 | + | 2389.64i | −0.449983 | + | 0.259798i | −0.707823 | − | 0.706390i | \(-0.750323\pi\) |
0.257840 | + | 0.966188i | \(0.416989\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2397.66 | + | 1384.29i | −0.257148 | + | 0.148464i | −0.623033 | − | 0.782196i | \(-0.714100\pi\) |
0.365885 | + | 0.930660i | \(0.380766\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3774.18 | − | 6537.08i | 0.402053 | − | 0.696376i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14237.8i | − | 1.49649i | −0.663422 | − | 0.748245i | \(-0.730897\pi\) | ||
0.663422 | − | 0.748245i | \(-0.269103\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8958.27 | − | 5172.06i | −0.935318 | − | 0.540006i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18520.6 | − | 9399.57i | 1.90826 | − | 0.968481i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1764.03 | + | 3055.39i | 0.180564 | + | 0.312747i | 0.942073 | − | 0.335408i | \(-0.108874\pi\) |
−0.761508 | + | 0.648155i | \(0.775541\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5905.31 | 0.596611 | 0.298306 | − | 0.954470i | \(-0.403579\pi\) | ||||
0.298306 | + | 0.954470i | \(0.403579\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5242.57 | −0.526227 | −0.263113 | − | 0.964765i | \(-0.584749\pi\) | ||||
−0.263113 | + | 0.964765i | \(0.584749\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5974.83 | + | 10348.7i | 0.592039 | + | 1.02544i | 0.993957 | + | 0.109766i | \(0.0350101\pi\) |
−0.401919 | + | 0.915675i | \(0.631657\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4860.46 | − | 7458.41i | 0.478540 | − | 0.734323i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16007.1 | − | 9241.73i | −1.55605 | − | 0.898383i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8478.85i | − | 0.819023i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −886.818 | + | 1536.01i | −0.0845923 | + | 0.146518i | −0.905217 | − | 0.424949i | \(-0.860292\pi\) |
0.820625 | + | 0.571467i | \(0.193625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21303.9 | + | 12299.8i | −2.01949 | + | 1.16595i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10203.8 | + | 5891.14i | −0.955317 | + | 0.551553i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1340.79 | − | 2322.32i | 0.124758 | − | 0.216087i | −0.796880 | − | 0.604137i | \(-0.793518\pi\) |
0.921638 | + | 0.388050i | \(0.126851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5871.49i | − | 0.539667i | −0.962907 | − | 0.269834i | \(-0.913031\pi\) | ||
0.962907 | − | 0.269834i | \(-0.0869687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8777.37 | + | 5067.62i | 0.801852 | + | 0.462949i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 929.103 | − | 17203.9i | 0.0838550 | − | 1.55272i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6882.08 | + | 11920.1i | 0.617403 | + | 1.06937i | 0.989958 | + | 0.141363i | \(0.0451486\pi\) |
−0.372555 | + | 0.928010i | \(0.621518\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9430.25 | −0.835933 | −0.417966 | − | 0.908462i | \(-0.637257\pi\) | ||||
−0.417966 | + | 0.908462i | \(0.637257\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3377.73 | −0.297638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3495.09 | + | 6053.68i | 0.304356 | + | 0.527160i | 0.977118 | − | 0.212699i | \(-0.0682254\pi\) |
−0.672762 | + | 0.739859i | \(0.734892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1763.31 | + | 1149.11i | 0.152650 | + | 0.0994785i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15008.2 | − | 8664.99i | −1.28416 | − | 0.741408i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 21065.5i | − | 1.79199i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8093.72 | − | 14018.7i | 0.680600 | − | 1.17883i | −0.294199 | − | 0.955744i | \(-0.595053\pi\) |
0.974798 | − | 0.223089i | \(-0.0716140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12519.5 | + | 7228.11i | −1.04673 | + | 0.604327i | −0.921731 | − | 0.387830i | \(-0.873225\pi\) |
−0.124995 | + | 0.992157i | \(0.539891\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25236.2 | − | 14570.1i | 2.08597 | − | 1.20434i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6051.90 | + | 10482.2i | −0.497403 | + | 0.861527i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 17776.7i | − | 1.44464i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.0696 | − | 31.7944i | −0.00445021 | − | 0.00256933i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12381.7 | − | 9056.25i | −0.989457 | − | 0.723711i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8083.69 | − | 14001.4i | −0.642412 | − | 1.11269i | −0.984893 | − | 0.173165i | \(-0.944601\pi\) |
0.342481 | − | 0.939525i | \(-0.388733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3318.74 | 0.260842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15779.2 | 1.23340 | 0.616700 | − | 0.787199i | \(-0.288469\pi\) | ||||
0.616700 | + | 0.787199i | \(0.288469\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4189.29 | + | 7256.06i | 0.323901 | + | 0.561014i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1867.00 | + | 3678.68i | 0.143568 | + | 0.282881i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3537.74 | − | 2042.51i | −0.269118 | − | 0.155375i | 0.359369 | − | 0.933196i | \(-0.382992\pi\) |
−0.628487 | + | 0.777820i | \(0.716325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31764.3i | − | 2.40338i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1330.97 | + | 2305.30i | −0.0996332 | + | 0.172570i | −0.911533 | − | 0.411227i | \(-0.865100\pi\) |
0.811900 | + | 0.583797i | \(0.198434\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6541.44 | + | 3776.70i | −0.487080 | + | 0.281216i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11350.6 | + | 6553.27i | −0.836278 | + | 0.482825i | −0.855997 | − | 0.516980i | \(-0.827056\pi\) |
0.0197197 | + | 0.999806i | \(0.493723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3592.46 | − | 6222.32i | 0.263292 | − | 0.456035i | −0.703823 | − | 0.710376i | \(-0.748525\pi\) |
0.967115 | + | 0.254340i | \(0.0818584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 698.700i | 0.0506744i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3870.62 | + | 2234.70i | 0.279265 | + | 0.161234i | 0.633091 | − | 0.774078i | \(-0.281786\pi\) |
−0.353826 | + | 0.935311i | \(0.615119\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12805.2 | + | 691.550i | 0.914371 | + | 0.0493810i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15501.5 | + | 26849.3i | 1.10121 | + | 1.90735i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4137.01 | −0.290891 | −0.145445 | − | 0.989366i | \(-0.546461\pi\) | ||||
−0.145445 | + | 0.989366i | \(0.546461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24089.6 | 1.68522 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12000.7 | + | 20785.8i | 0.831044 | + | 1.43941i | 0.897211 | + | 0.441602i | \(0.145590\pi\) |
−0.0661665 | + | 0.997809i | \(0.521077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −31487.6 | − | 1700.50i | −2.16952 | − | 0.117166i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1301.96 | − | 751.686i | −0.0888089 | − | 0.0512739i | 0.454938 | − | 0.890523i | \(-0.349661\pi\) |
−0.543747 | + | 0.839249i | \(0.682995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3475.50i | − | 0.235888i | −0.993020 | − | 0.117944i | \(-0.962370\pi\) | ||
0.993020 | − | 0.117944i | \(-0.0376303\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4882.14 | − | 8456.11i | 0.328078 | − | 0.568247i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1722.46 | − | 994.463i | 0.115177 | − | 0.0664975i | −0.441305 | − | 0.897357i | \(-0.645484\pi\) |
0.556482 | + | 0.830860i | \(0.312151\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31351.6 | − | 18100.8i | 2.07586 | − | 1.19850i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11830.3 | + | 20490.7i | −0.779479 | + | 1.35010i | 0.152763 | + | 0.988263i | \(0.451183\pi\) |
−0.932242 | + | 0.361835i | \(0.882150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15390.3i | 1.00420i | 0.864811 | + | 0.502098i | \(0.167438\pi\) | ||||
−0.864811 | + | 0.502098i | \(0.832562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6817.56 | − | 3936.12i | −0.442683 | − | 0.255583i | 0.262052 | − | 0.965054i | \(-0.415601\pi\) |
−0.704735 | + | 0.709470i | \(0.748934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4336.16 | − | 8543.81i | −0.278852 | − | 0.549439i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9443.21 | + | 16356.1i | 0.604366 | + | 1.04679i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37349.0 | 2.36757 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6083.98 | −0.383834 | −0.191917 | − | 0.981411i | \(-0.561471\pi\) | ||||
−0.191917 | + | 0.981411i | \(0.561471\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12150.3 | − | 21044.9i | −0.759320 | − | 1.31518i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2839.16 | − | 26209.2i | 0.176596 | − | 1.63022i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20571.8 | − | 11877.2i | −1.26761 | − | 0.731855i | −0.293075 | − | 0.956089i | \(-0.594679\pi\) |
−0.974535 | + | 0.224234i | \(0.928012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12895.8i | 0.790918i | 0.918484 | + | 0.395459i | \(0.129415\pi\) | ||||
−0.918484 | + | 0.395459i | \(0.870585\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −552.298 | + | 956.608i | −0.0335596 | + | 0.0581270i | −0.882317 | − | 0.470655i | \(-0.844018\pi\) |
0.848758 | + | 0.528782i | \(0.177351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11139.4 | + | 6431.33i | −0.673744 | + | 0.388986i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15648.4 | − | 9034.58i | 0.937775 | − | 0.541425i | 0.0485131 | − | 0.998823i | \(-0.484552\pi\) |
0.889262 | + | 0.457398i | \(0.151218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4997.87 | − | 8656.56i | 0.298142 | − | 0.516397i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15980.9i | 0.944656i | 0.881423 | + | 0.472328i | \(0.156586\pi\) | ||||
−0.881423 | + | 0.472328i | \(0.843414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26260.0 | + | 15161.2i | 1.54523 | + | 0.892138i | 0.998496 | + | 0.0548308i | \(0.0174619\pi\) |
0.546733 | + | 0.837307i | \(0.315871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21839.9 | − | 14232.5i | −1.27355 | − | 0.829943i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −345.219 | − | 597.936i | −0.0200404 | − | 0.0347109i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38261.8 | −2.20131 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17767.4 | −1.01766 | −0.508829 | − | 0.860868i | \(-0.669921\pi\) | ||||
−0.508829 | + | 0.860868i | \(0.669921\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8243.00 | + | 14277.3i | 0.467953 | + | 0.810519i | 0.999329 | − | 0.0366172i | \(-0.0116582\pi\) |
−0.531376 | + | 0.847136i | \(0.678325\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −806.493 | + | 14933.6i | −0.0455822 | + | 0.844031i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1757.98 | + | 1014.97i | 0.0984877 | + | 0.0568619i | 0.548435 | − | 0.836193i | \(-0.315224\pi\) |
−0.449947 | + | 0.893055i | \(0.648557\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15339.5i | − | 0.855607i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26639.7 | + | 46141.3i | −1.47299 | + | 2.55130i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27185.8 | − | 15695.7i | 1.49667 | − | 0.864101i | 0.496674 | − | 0.867937i | \(-0.334554\pi\) |
0.999993 | + | 0.00383605i | \(0.00122105\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −336.590 | + | 194.330i | −0.0183706 | + | 0.0106063i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13494.9 | + | 23373.9i | −0.733367 | + | 1.27023i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7749.11i | 0.417517i | 0.977967 | + | 0.208759i | \(0.0669423\pi\) | ||||
−0.977967 | + | 0.208759i | \(0.933058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26739.0 | + | 15437.8i | 1.43454 | + | 0.828232i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2340.79 | + | 3591.96i | −0.124519 | + | 0.191075i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8907.48 | + | 15428.2i | 0.471830 | + | 0.817233i | 0.999481 | − | 0.0322280i | \(-0.0102603\pi\) |
−0.527651 | + | 0.849462i | \(0.676927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1985.11 | −0.104268 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 50154.7 | 2.62333 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10695.4 | + | 18525.0i | 0.554759 | + | 0.960871i | 0.997922 | + | 0.0644299i | \(0.0205229\pi\) |
−0.443163 | + | 0.896441i | \(0.646144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19615.4 | + | 9955.20i | −1.01320 | + | 0.514218i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6611.15 | + | 3816.95i | 0.338665 | + | 0.195528i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27791.9i | − | 1.41780i | −0.705307 | − | 0.708902i | \(-0.749191\pi\) | ||
0.705307 | − | 0.708902i | \(-0.250809\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24113.5 | + | 41765.8i | −1.22007 | + | 2.11322i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17159.5 | + | 9907.02i | −0.864665 | + | 0.499214i | −0.865572 | − | 0.500785i | \(-0.833045\pi\) |
0.000906890 | 1.00000i | \(0.499711\pi\) | ||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18617.7 | − | 10748.9i | 0.930518 | − | 0.537235i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15164.2 | − | 26265.2i | 0.754838 | − | 1.30742i | −0.190617 | − | 0.981664i | \(-0.561049\pi\) |
0.945455 | − | 0.325753i | \(-0.105618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9992.06i | 0.493369i | 0.969096 | + | 0.246685i | \(0.0793411\pi\) | ||||
−0.969096 | + | 0.246685i | \(0.920659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27928.9 | + | 16124.8i | 1.37347 | + | 0.792975i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −71.9746 | + | 36.5286i | −0.00351121 | + | 0.00178201i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19991.9 | − | 34627.1i | −0.971393 | − | 1.68250i | −0.691358 | − | 0.722513i | \(-0.742987\pi\) |
−0.280035 | − | 0.959990i | \(-0.590346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27959.0 | 1.34773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11981.7 | −0.575273 | −0.287637 | − | 0.957740i | \(-0.592870\pi\) | ||||
−0.287637 | + | 0.957740i | \(0.592870\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10395.4 | + | 18005.4i | 0.495182 | + | 0.857680i | 0.999985 | − | 0.00555440i | \(-0.00176803\pi\) |
−0.504803 | + | 0.863235i | \(0.668435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2299.91 | − | 3529.23i | 0.109125 | − | 0.167453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19143.4 | − | 11052.4i | −0.901208 | − | 0.520313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24512.2i | 1.14946i | 0.818344 | + | 0.574728i | \(0.194892\pi\) | ||||
−0.818344 | + | 0.574728i | \(0.805108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18063.2 | + | 31286.4i | −0.840477 | + | 1.45575i | 0.0490158 | + | 0.998798i | \(0.484392\pi\) |
−0.889492 | + | 0.456950i | \(0.848942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19008.0 | − | 10974.3i | 0.881017 | − | 0.508655i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19322.7 | + | 11156.0i | −0.888712 | + | 0.513098i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20802.7 | − | 36031.3i | 0.953109 | − | 1.65083i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 31329.2i | − | 1.42444i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22356.7 | − | 12907.6i | −1.01262 | − | 0.584634i | −0.100660 | − | 0.994921i | \(-0.532095\pi\) |
−0.911957 | + | 0.410287i | \(0.865429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −517.027 | + | 9573.62i | −0.0232407 | + | 0.430340i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32877.0 | − | 56944.6i | −1.47225 | − | 2.55001i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11502.7 | 0.511223 | 0.255612 | − | 0.966780i | \(-0.417723\pi\) | ||||
0.255612 | + | 0.966780i | \(0.417723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54964.1 | −2.43365 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2541.26 | + | 4401.58i | 0.111680 | + | 0.193435i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1799.72 | + | 1172.83i | 0.0787971 | + | 0.0513501i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20637.7 | + | 11915.2i | 0.896887 | + | 0.517818i | 0.876189 | − | 0.481968i | \(-0.160078\pi\) |
0.0206978 | + | 0.999786i | \(0.493411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 319.208i | 0.0138211i | 0.999976 | + | 0.00691055i | \(0.00219971\pi\) | ||||
−0.999976 | + | 0.00691055i | \(0.997800\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10414.7 | + | 18038.8i | −0.447622 | + | 0.775304i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34526.8 | + | 19934.1i | −1.47851 | + | 0.853617i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16147.2 | + | 9322.60i | −0.686409 | + | 0.396298i | −0.802265 | − | 0.596968i | \(-0.796372\pi\) |
0.115857 | + | 0.993266i | \(0.463039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15224.2 | + | 26369.2i | −0.644816 | + | 1.11685i | 0.339528 | + | 0.940596i | \(0.389733\pi\) |
−0.984344 | + | 0.176259i | \(0.943601\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29203.6i | − | 1.22794i | −0.789328 | − | 0.613972i | \(-0.789571\pi\) | ||
0.789328 | − | 0.613972i | \(-0.210429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9997.78 | + | 5772.22i | 0.418863 | + | 0.241830i | 0.694591 | − | 0.719405i | \(-0.255586\pi\) |
−0.275728 | + | 0.961236i | \(0.588919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23629.5 | + | 32306.3i | −0.982850 | + | 1.34375i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4073.24 | + | 7055.05i | 0.168815 | + | 0.292395i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4335.20 | 0.178388 | 0.0891941 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891941 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16845.4 | 0.690696 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27068.1 | + | 46883.3i | 1.10198 | + | 1.90868i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5609.08 | − | 11051.9i | −0.227545 | − | 0.448346i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2203.43 | − | 1272.15i | −0.0887575 | − | 0.0512442i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14779.7i | − | 0.593257i | −0.954993 | − | 0.296629i | \(-0.904138\pi\) | ||
0.954993 | − | 0.296629i | \(-0.0958624\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10530.9 | − | 18240.1i | 0.419754 | − | 0.727036i | −0.576160 | − | 0.817337i | \(-0.695450\pi\) |
0.995915 | + | 0.0903008i | \(0.0287829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22556.0 | − | 13022.7i | 0.895928 | − | 0.517264i | 0.0200509 | − | 0.999799i | \(-0.493617\pi\) |
0.875877 | + | 0.482535i | \(0.160284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26253.5 | − | 15157.5i | 1.03555 | − | 0.597874i | 0.116980 | − | 0.993134i | \(-0.462679\pi\) |
0.918569 | + | 0.395260i | \(0.129345\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4639.36 | − | 8035.60i | 0.182362 | − | 0.315860i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9962.06i | 0.388883i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31995.0 | + | 18472.3i | 1.24467 | + | 0.718612i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10012.6 | + | 540.734i | 0.386843 | + | 0.0208916i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11591.2 | + | 20076.5i | 0.446301 | + | 0.773017i | 0.998142 | − | 0.0609329i | \(-0.0194076\pi\) |
−0.551840 | + | 0.833950i | \(0.686074\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10346.4 | 0.395663 | 0.197832 | − | 0.980236i | \(-0.436610\pi\) | ||||
0.197832 | + | 0.980236i | \(0.436610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11461.4 | 0.436814 | 0.218407 | − | 0.975858i | \(-0.429914\pi\) | ||||
0.218407 | + | 0.975858i | \(0.429914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2162.53 | − | 3745.61i | −0.0818608 | − | 0.141787i | 0.822188 | − | 0.569215i | \(-0.192753\pi\) |
−0.904049 | + | 0.427428i | \(0.859420\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30799.9 | − | 1663.36i | −1.16197 | − | 0.0627529i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39350.1 | − | 22718.8i | −1.47458 | − | 0.851350i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18055.1i | 0.674317i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10844.5 | + | 18783.2i | −0.402319 | + | 0.696836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 70055.2 | − | 40446.4i | 2.59032 | − | 1.49552i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3188.07 | + | 1840.63i | −0.117099 | + | 0.0676074i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7966.77 | + | 13798.9i | −0.291656 | + | 0.505164i | −0.974202 | − | 0.225680i | \(-0.927540\pi\) |
0.682545 | + | 0.730843i | \(0.260873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27990.0i | 1.01795i | 0.860782 | + | 0.508974i | \(0.169975\pi\) | ||||
−0.860782 | + | 0.508974i | \(0.830025\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26818.8 | + | 15483.9i | 0.972151 | + | 0.561271i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5742.05 | − | 11313.9i | −0.206782 | − | 0.407436i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21383.1 | + | 37036.7i | 0.767535 | + | 1.32941i | 0.938896 | + | 0.344201i | \(0.111850\pi\) |
−0.171361 | + | 0.985208i | \(0.554817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 71499.9 | 2.54978 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28131.4 | 0.999951 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18019.2 | − | 31210.2i | −0.636375 | − | 1.10223i | −0.986222 | − | 0.165427i | \(-0.947100\pi\) |
0.349847 | − | 0.936807i | \(-0.386234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30270.4 | + | 13361.8i | −1.06560 | + | 0.470372i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −65946.7 | − | 38074.3i | −2.30662 | − | 1.33173i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36919.6i | 1.28720i | 0.765361 | + | 0.643602i | \(0.222561\pi\) | ||||
−0.765361 | + | 0.643602i | \(0.777439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7399.78 | + | 12816.8i | −0.256351 | + | 0.444013i | −0.965262 | − | 0.261286i | \(-0.915854\pi\) |
0.708911 | + | 0.705298i | \(0.249187\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1592.29 | − | 919.307i | 0.0549862 | − | 0.0317463i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46041.6 | + | 26582.1i | −1.57988 | + | 0.912147i | −0.585010 | + | 0.811026i | \(0.698909\pi\) |
−0.994874 | + | 0.101120i | \(0.967757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4367.22 | + | 7564.24i | −0.149384 | + | 0.258741i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27940.1i | 0.949704i | 0.880066 | + | 0.474852i | \(0.157498\pi\) | ||||
−0.880066 | + | 0.474852i | \(0.842502\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29252.4 | + | 16888.9i | 0.991189 | + | 0.572263i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16312.4 | − | 10630.4i | −0.549274 | − | 0.357948i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16284.0 | + | 28204.7i | 0.546608 | + | 0.946752i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32926.6 | 1.09839 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7724.02 | 0.256864 | 0.128432 | − | 0.991718i | \(-0.459006\pi\) | ||||
0.128432 | + | 0.991718i | \(0.459006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12460.4 | + | 21582.0i | 0.411814 | + | 0.713283i | 0.995088 | − | 0.0989921i | \(-0.0315619\pi\) |
−0.583274 | + | 0.812276i | \(0.698229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.6036 | + | 492.611i | −0.000876540 | + | 0.0162306i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19376.2 | − | 11186.9i | −0.634494 | − | 0.366325i | 0.147997 | − | 0.988988i | \(-0.452717\pi\) |
−0.782490 | + | 0.622663i | \(0.786051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 23137.1i | − | 0.755327i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18175.0 | + | 31480.0i | −0.589717 | + | 1.02142i | 0.404552 | + | 0.914515i | \(0.367427\pi\) |
−0.994269 | + | 0.106905i | \(0.965906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 62427.4 | − | 36042.4i | 2.01939 | − | 1.16590i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2845.19 | − | 1642.67i | 0.0914780 | − | 0.0528148i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3752.26 | + | 6499.11i | −0.120277 | + | 0.208326i | −0.919877 | − | 0.392207i | \(-0.871712\pi\) |
0.799600 | + | 0.600533i | \(0.205045\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8514.92i | − | 0.271298i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40355.2 | − | 23299.1i | −1.28191 | − | 0.740110i | −0.304711 | − | 0.952445i | \(-0.598560\pi\) |
−0.977197 | + | 0.212335i | \(0.931893\pi\) | |||||||
\(998\) | 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 | 1008.4.bt.d.17.5 | 48 | ||
3.2 | odd | 2 | inner | 1008.4.bt.d.17.20 | 48 | ||
4.3 | odd | 2 | 504.4.bl.a.17.5 | ✓ | 48 | ||
7.5 | odd | 6 | inner | 1008.4.bt.d.593.20 | 48 | ||
12.11 | even | 2 | 504.4.bl.a.17.20 | yes | 48 | ||
21.5 | even | 6 | inner | 1008.4.bt.d.593.5 | 48 | ||
28.19 | even | 6 | 504.4.bl.a.89.20 | yes | 48 | ||
84.47 | odd | 6 | 504.4.bl.a.89.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.bl.a.17.5 | ✓ | 48 | 4.3 | odd | 2 | ||
504.4.bl.a.17.20 | yes | 48 | 12.11 | even | 2 | ||
504.4.bl.a.89.5 | yes | 48 | 84.47 | odd | 6 | ||
504.4.bl.a.89.20 | yes | 48 | 28.19 | even | 6 | ||
1008.4.bt.d.17.5 | 48 | 1.1 | even | 1 | trivial | ||
1008.4.bt.d.17.20 | 48 | 3.2 | odd | 2 | inner | ||
1008.4.bt.d.593.5 | 48 | 21.5 | even | 6 | inner | ||
1008.4.bt.d.593.20 | 48 | 7.5 | odd | 6 | inner |