Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2052,3,Mod(125,2052)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2052, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2052.125");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2052.be (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: | \(55.9129502467\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 125.11 | ||
Character | \(\chi\) | \(=\) | 2052.125 |
Dual form | 2052.3.be.a.197.11 |
$q$-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 \(\left(\mathbb{Z}/2052\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1027\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.92443 | + | 2.84312i | −0.984887 | + | 0.568625i | −0.903742 | − | 0.428078i | \(-0.859191\pi\) |
−0.0811448 | + | 0.996702i | \(0.525858\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.27053 | − | 2.20061i | −0.181504 | − | 0.314373i | 0.760889 | − | 0.648882i | \(-0.224763\pi\) |
−0.942393 | + | 0.334508i | \(0.891430\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.6159 | − | 9.59321i | 1.51054 | − | 0.872110i | 0.510614 | − | 0.859810i | \(-0.329418\pi\) |
0.999924 | − | 0.0123002i | \(-0.00391537\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.3309 | 1.17930 | 0.589652 | − | 0.807658i | \(-0.299265\pi\) | ||||
0.589652 | + | 0.807658i | \(0.299265\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.5119 | − | 13.5746i | −1.38305 | − | 0.798506i | −0.390533 | − | 0.920589i | \(-0.627709\pi\) |
−0.992520 | + | 0.122083i | \(0.961043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.43177 | + | 18.6875i | −0.180619 | + | 0.983553i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.0875i | 0.612500i | 0.951951 | + | 0.306250i | \(0.0990744\pi\) | ||||
−0.951951 | + | 0.306250i | \(0.900926\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.66670 | − | 6.35091i | 0.146668 | − | 0.254036i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.83381 | − | 2.21345i | −0.132200 | − | 0.0763260i | 0.432441 | − | 0.901662i | \(-0.357652\pi\) |
−0.564642 | + | 0.825336i | \(0.690986\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.818629 | − | 1.41791i | 0.0264074 | − | 0.0457389i | −0.852520 | − | 0.522695i | \(-0.824927\pi\) |
0.878927 | + | 0.476956i | \(0.158260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.5132 | + | 7.22452i | 0.357521 | + | 0.206415i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2519 | −0.277079 | −0.138540 | − | 0.990357i | \(-0.544241\pi\) | ||||
−0.138540 | + | 0.990357i | \(0.544241\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.3655 | − | 23.8824i | 1.00892 | − | 0.582498i | 0.0980416 | − | 0.995182i | \(-0.468742\pi\) |
0.910874 | + | 0.412685i | \(0.135409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.6865 | 0.643873 | 0.321936 | − | 0.946761i | \(-0.395666\pi\) | ||||
0.321936 | + | 0.946761i | \(0.395666\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −63.5252 | − | 36.6763i | −1.35160 | − | 0.780347i | −0.363127 | − | 0.931740i | \(-0.618291\pi\) |
−0.988474 | + | 0.151393i | \(0.951624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 21.2715 | − | 36.8434i | 0.434113 | − | 0.751906i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −25.9371 | + | 14.9748i | −0.489379 | + | 0.282543i | −0.724317 | − | 0.689467i | \(-0.757845\pi\) |
0.234938 | + | 0.972010i | \(0.424511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −54.5494 | + | 94.4823i | −0.991806 | + | 1.71786i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −94.3617 | + | 54.4798i | −1.59935 | + | 0.923386i | −0.607739 | + | 0.794137i | \(0.707923\pi\) |
−0.991612 | + | 0.129249i | \(0.958743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.4453 | + | 47.5366i | −0.449923 | + | 0.779289i | −0.998381 | − | 0.0568892i | \(-0.981882\pi\) |
0.548458 | + | 0.836178i | \(0.315215\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −75.4962 | + | 43.5878i | −1.16148 | + | 0.670581i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38.5522 | 0.575406 | 0.287703 | − | 0.957720i | \(-0.407108\pi\) | ||||
0.287703 | + | 0.957720i | \(0.407108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −101.956 | − | 58.8645i | −1.43600 | − | 0.829077i | −0.438435 | − | 0.898763i | \(-0.644467\pi\) |
−0.997569 | + | 0.0696859i | \(0.977800\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43.2124 | − | 74.8461i | 0.591951 | − | 1.02529i | −0.402019 | − | 0.915631i | \(-0.631691\pi\) |
0.993969 | − | 0.109657i | \(-0.0349753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −42.2219 | − | 24.3768i | −0.548337 | − | 0.316582i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 126.252 | 1.59813 | 0.799064 | − | 0.601246i | \(-0.205329\pi\) | ||||
0.799064 | + | 0.601246i | \(0.205329\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 35.1083 | − | 20.2698i | 0.422992 | − | 0.244214i | −0.273365 | − | 0.961910i | \(-0.588137\pi\) |
0.696357 | + | 0.717696i | \(0.254803\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 154.377 | 1.81620 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 99.4601 | − | 57.4233i | 1.11753 | − | 0.645206i | 0.176760 | − | 0.984254i | \(-0.443438\pi\) |
0.940769 | + | 0.339048i | \(0.110105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.4783 | − | 33.7375i | −0.214048 | − | 0.370742i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.2314 | − | 101.782i | −0.381383 | − | 1.07139i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 48.6430 | 0.501474 | 0.250737 | − | 0.968055i | \(-0.419327\pi\) | ||||
0.250737 | + | 0.968055i | \(0.419327\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.6614 | + | 11.3515i | 0.194667 | + | 0.112391i | 0.594165 | − | 0.804343i | \(-0.297482\pi\) |
−0.399499 | + | 0.916734i | \(0.630816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 25.6106 | − | 44.3589i | 0.248647 | − | 0.430668i | −0.714504 | − | 0.699631i | \(-0.753348\pi\) |
0.963151 | + | 0.268963i | \(0.0866809\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 67.3620i | − | 0.629552i | −0.949166 | − | 0.314776i | \(-0.898071\pi\) | ||
0.949166 | − | 0.314776i | \(-0.101929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24.1043 | − | 41.7498i | 0.221140 | − | 0.383026i | −0.734014 | − | 0.679134i | \(-0.762356\pi\) |
0.955154 | + | 0.296108i | \(0.0956889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.2621 | + | 8.81158i | 0.135063 | + | 0.0779785i | 0.566009 | − | 0.824399i | \(-0.308487\pi\) |
−0.430946 | + | 0.902378i | \(0.641820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −40.0525 | − | 69.3730i | −0.348283 | − | 0.603243i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 68.9875i | 0.579727i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 123.559 | − | 214.011i | 1.02115 | − | 1.76869i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 100.457i | − | 0.803653i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −75.5505 | − | 130.857i | −0.594885 | − | 1.03037i | −0.993563 | − | 0.113281i | \(-0.963864\pi\) |
0.398678 | − | 0.917091i | \(-0.369469\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 171.741 | − | 99.1549i | 1.31100 | − | 0.756907i | 0.328740 | − | 0.944421i | \(-0.393376\pi\) |
0.982262 | + | 0.187513i | \(0.0600427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 45.4841 | − | 16.1910i | 0.341986 | − | 0.121737i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8433 | + | 6.26037i | 0.0791480 | + | 0.0456961i | 0.539052 | − | 0.842273i | \(-0.318783\pi\) |
−0.459904 | + | 0.887969i | \(0.652116\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 91.1354 | 0.655650 | 0.327825 | − | 0.944738i | \(-0.393684\pi\) | ||||
0.327825 | + | 0.944738i | \(0.393684\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 254.738 | − | 147.073i | 1.78138 | − | 1.02848i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.1725 | 0.173603 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 157.715 | − | 91.0570i | 1.05849 | − | 0.611121i | 0.133478 | − | 0.991052i | \(-0.457386\pi\) |
0.925015 | + | 0.379931i | \(0.124052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −123.511 | − | 213.927i | −0.817951 | − | 1.41673i | −0.907189 | − | 0.420722i | \(-0.861777\pi\) |
0.0892386 | − | 0.996010i | \(-0.471557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.30985i | 0.0600635i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 104.590 | + | 181.155i | 0.666178 | + | 1.15385i | 0.978965 | + | 0.204030i | \(0.0654040\pi\) |
−0.312787 | + | 0.949823i | \(0.601263\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 31.0012 | − | 17.8985i | 0.192554 | − | 0.111171i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.8681 | −0.115755 | −0.0578776 | − | 0.998324i | \(-0.518433\pi\) | ||||
−0.0578776 | + | 0.998324i | \(0.518433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 224.543i | − | 1.34457i | −0.740293 | − | 0.672284i | \(-0.765313\pi\) | ||
0.740293 | − | 0.672284i | \(-0.234687\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 66.0377 | 0.390756 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 73.9870i | 0.427670i | 0.976870 | + | 0.213835i | \(0.0685955\pi\) | ||||
−0.976870 | + | 0.213835i | \(0.931404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.6345 | −0.106483 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 196.345i | 1.09690i | 0.836184 | + | 0.548449i | \(0.184782\pi\) | ||||
−0.836184 | + | 0.548449i | \(0.815218\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4913 | − | 35.4920i | −0.113212 | − | 0.196088i | 0.803852 | − | 0.594830i | \(-0.202780\pi\) |
−0.917063 | + | 0.398741i | \(0.869447\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 50.4850 | − | 29.1475i | 0.272892 | − | 0.157554i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −520.896 | −2.78554 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −71.5656 | + | 41.3184i | −0.374689 | + | 0.216327i | −0.675505 | − | 0.737355i | \(-0.736074\pi\) |
0.300816 | + | 0.953682i | \(0.402741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −163.937 | − | 283.947i | −0.849412 | − | 1.47123i | −0.881733 | − | 0.471748i | \(-0.843623\pi\) |
0.0323211 | − | 0.999478i | \(-0.489710\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 247.337i | − | 1.25552i | −0.778407 | − | 0.627760i | \(-0.783972\pi\) | ||
0.778407 | − | 0.627760i | \(-0.216028\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 70.5278 | + | 122.158i | 0.354411 | + | 0.613858i | 0.987017 | − | 0.160616i | \(-0.0513481\pi\) |
−0.632606 | + | 0.774474i | \(0.718015\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.2490i | 0.0554138i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −135.801 | + | 235.215i | −0.662445 | + | 1.14739i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 122.251 | + | 343.432i | 0.584934 | + | 1.64321i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 96.9990 | + | 168.007i | 0.459711 | + | 0.796243i | 0.998945 | − | 0.0459131i | \(-0.0146197\pi\) |
−0.539235 | + | 0.842156i | \(0.681286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −136.340 | + | 78.7162i | −0.634142 | + | 0.366122i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.16035 | −0.0191721 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −360.459 | − | 208.111i | −1.63104 | − | 0.941680i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 330.514 | 1.48212 | 0.741062 | − | 0.671436i | \(-0.234322\pi\) | ||||
0.741062 | + | 0.671436i | \(0.234322\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −80.2262 | + | 46.3186i | −0.353419 | + | 0.204047i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.312771 | + | 0.949829i | \(0.398743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.5909 | + | 47.7889i | −0.120484 | + | 0.208685i | −0.919959 | − | 0.392015i | \(-0.871778\pi\) |
0.799474 | + | 0.600700i | \(0.205111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.3726 | − | 14.0715i | −0.104603 | − | 0.0603927i | 0.446786 | − | 0.894641i | \(-0.352569\pi\) |
−0.551389 | + | 0.834248i | \(0.685902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 417.101 | 1.77490 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.2620 | − | 14.5850i | −0.105699 | − | 0.0610251i | 0.446219 | − | 0.894924i | \(-0.352770\pi\) |
−0.551917 | + | 0.833899i | \(0.686104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.98576 | + | 6.90354i | −0.0165384 | + | 0.0286454i | −0.874176 | − | 0.485609i | \(-0.838598\pi\) |
0.857638 | + | 0.514254i | \(0.171931\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 241.910i | 0.987389i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −52.6122 | + | 286.497i | −0.213005 | + | 1.15991i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 254.626 | − | 147.009i | 1.01445 | − | 0.585692i | 0.101957 | − | 0.994789i | \(-0.467490\pi\) |
0.912491 | + | 0.409097i | \(0.134156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 135.144 | + | 234.077i | 0.534167 | + | 0.925205i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 53.6039i | 0.208575i | 0.994547 | + | 0.104288i | \(0.0332563\pi\) | ||||
−0.994547 | + | 0.104288i | \(0.966744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0253 | + | 22.5606i | 0.0502909 | + | 0.0871064i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 499.348i | − | 1.89866i | −0.314278 | − | 0.949331i | \(-0.601762\pi\) | ||
0.314278 | − | 0.949331i | \(-0.398238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 85.1504 | − | 147.485i | 0.321322 | − | 0.556546i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −215.111 | − | 124.195i | −0.799670 | − | 0.461690i | 0.0436856 | − | 0.999045i | \(-0.486090\pi\) |
−0.843356 | + | 0.537355i | \(0.819423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 103.664 | − | 179.551i | 0.382524 | − | 0.662552i | −0.608898 | − | 0.793248i | \(-0.708388\pi\) |
0.991422 | + | 0.130697i | \(0.0417215\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 140.702i | − | 0.511642i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −214.427 | − | 371.398i | −0.774104 | − | 1.34079i | −0.935297 | − | 0.353864i | \(-0.884868\pi\) |
0.161193 | − | 0.986923i | \(-0.448466\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −423.424 | − | 244.464i | −1.50685 | − | 0.869978i | −0.999968 | − | 0.00795961i | \(-0.997466\pi\) |
−0.506877 | − | 0.862018i | \(-0.669200\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −174.925 | − | 302.980i | −0.618111 | − | 1.07060i | −0.989830 | − | 0.142254i | \(-0.954565\pi\) |
0.371719 | − | 0.928345i | \(-0.378768\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −105.112 | − | 60.6864i | −0.366244 | − | 0.211451i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 224.039 | + | 388.048i | 0.775223 | + | 1.34273i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.7663 | + | 14.2988i | 0.0845266 | + | 0.0488015i | 0.541668 | − | 0.840593i | \(-0.317793\pi\) |
−0.457141 | + | 0.889394i | \(0.651127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 309.785 | − | 536.564i | 1.05012 | − | 1.81886i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 215.975i | 0.722323i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.1764 | − | 60.9274i | −0.116865 | − | 0.202417i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 312.121i | − | 1.02335i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −98.3532 | + | 170.353i | −0.320369 | + | 0.554895i | −0.980564 | − | 0.196199i | \(-0.937140\pi\) |
0.660195 | + | 0.751094i | \(0.270473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 184.438 | + | 106.485i | 0.593047 | + | 0.342396i | 0.766301 | − | 0.642481i | \(-0.222095\pi\) |
−0.173254 | + | 0.984877i | \(0.555428\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −202.221 | + | 350.256i | −0.646072 | + | 1.11903i | 0.337980 | + | 0.941153i | \(0.390256\pi\) |
−0.984053 | + | 0.177877i | \(0.943077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 184.527 | + | 106.537i | 0.582104 | + | 0.336078i | 0.761969 | − | 0.647613i | \(-0.224233\pi\) |
−0.179865 | + | 0.983691i | \(0.557566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −84.9365 | −0.266259 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 334.363 | − | 392.794i | 1.03518 | − | 1.21608i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 56.2139 | − | 97.3654i | 0.172966 | − | 0.299586i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 186.393i | 0.566543i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.2252 | + | 40.2273i | 0.0701669 | + | 0.121533i | 0.898974 | − | 0.438001i | \(-0.144313\pi\) |
−0.828807 | + | 0.559534i | \(0.810980\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −189.848 | + | 109.609i | −0.566710 | + | 0.327190i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −283.898 | − | 491.725i | −0.842427 | − | 1.45913i | −0.887837 | − | 0.460158i | \(-0.847793\pi\) |
0.0454104 | − | 0.998968i | \(-0.485540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 31.4131i | − | 0.0921205i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −232.616 | −0.678179 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 197.965 | − | 114.295i | 0.570504 | − | 0.329381i | −0.186847 | − | 0.982389i | \(-0.559827\pi\) |
0.757351 | + | 0.653009i | \(0.226493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −125.287 | − | 217.003i | −0.358988 | − | 0.621786i | 0.628804 | − | 0.777564i | \(-0.283545\pi\) |
−0.987792 | + | 0.155778i | \(0.950212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 135.138 | − | 78.0218i | 0.382826 | − | 0.221025i | −0.296221 | − | 0.955119i | \(-0.595726\pi\) |
0.679047 | + | 0.734095i | \(0.262393\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 669.436 | 1.88573 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 262.509 | + | 151.560i | 0.731222 | + | 0.422171i | 0.818869 | − | 0.573980i | \(-0.194601\pi\) |
−0.0876469 | + | 0.996152i | \(0.527935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −337.446 | − | 128.262i | −0.934753 | − | 0.355297i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 491.433i | 1.34639i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1332 | + | 19.2833i | −0.0303358 | + | 0.0525432i | −0.880795 | − | 0.473498i | \(-0.842991\pi\) |
0.850459 | + | 0.526041i | \(0.176324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 65.9075 | + | 38.0517i | 0.177648 | + | 0.102565i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −242.162 | + | 419.437i | −0.649229 | + | 1.12450i | 0.334079 | + | 0.942545i | \(0.391575\pi\) |
−0.983307 | + | 0.181952i | \(0.941759\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −58.7760 | − | 33.9343i | −0.155904 | − | 0.0900114i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −515.865 | −1.36112 | −0.680561 | − | 0.732692i | \(-0.738264\pi\) | ||||
−0.680561 | + | 0.732692i | \(0.738264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 172.390 | − | 99.5296i | 0.450105 | − | 0.259868i | −0.257769 | − | 0.966206i | \(-0.582987\pi\) |
0.707875 | + | 0.706338i | \(0.249654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 277.225 | 0.720066 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −156.994 | − | 90.6403i | −0.403583 | − | 0.233008i | 0.284446 | − | 0.958692i | \(-0.408190\pi\) |
−0.688029 | + | 0.725684i | \(0.741524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 191.232 | − | 331.224i | 0.489085 | − | 0.847120i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −621.720 | + | 358.950i | −1.57398 | + | 0.908735i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −224.772 | + | 389.316i | −0.566176 | + | 0.980645i | 0.430763 | + | 0.902465i | \(0.358244\pi\) |
−0.996939 | + | 0.0781804i | \(0.975089\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −96.1997 | + | 55.5409i | −0.239900 | + | 0.138506i | −0.615131 | − | 0.788425i | \(-0.710897\pi\) |
0.375231 | + | 0.926931i | \(0.377563\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5503 | − | 21.7378i | 0.0311423 | − | 0.0539400i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −170.345 | + | 98.3490i | −0.418539 | + | 0.241644i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 502.935 | 1.22967 | 0.614835 | − | 0.788655i | \(-0.289222\pi\) | ||||
0.614835 | + | 0.788655i | \(0.289222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 239.778 | + | 138.436i | 0.580576 | + | 0.335196i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −115.259 | + | 199.635i | −0.277733 | + | 0.481047i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 411.162 | + | 237.385i | 0.981295 | + | 0.566551i | 0.902661 | − | 0.430353i | \(-0.141611\pi\) |
0.0786339 | + | 0.996904i | \(0.474944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 703.876 | 1.67191 | 0.835957 | − | 0.548795i | \(-0.184913\pi\) | ||||
0.835957 | + | 0.548795i | \(0.184913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −172.422 | + | 99.5479i | −0.405699 | + | 0.234230i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 139.480 | 0.326650 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −704.096 | + | 406.510i | −1.63363 | + | 0.943178i | −0.650672 | + | 0.759359i | \(0.725513\pi\) |
−0.982960 | + | 0.183820i | \(0.941154\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 124.092 | + | 214.934i | 0.286588 | + | 0.496384i | 0.972993 | − | 0.230835i | \(-0.0741457\pi\) |
−0.686405 | + | 0.727219i | \(0.740812\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −263.260 | − | 48.3450i | −0.602426 | − | 0.110629i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −68.9527 | −0.157068 | −0.0785339 | − | 0.996911i | \(-0.525024\pi\) | ||||
−0.0785339 | + | 0.996911i | \(0.525024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −182.038 | − | 105.100i | −0.410922 | − | 0.237246i | 0.280264 | − | 0.959923i | \(-0.409578\pi\) |
−0.691186 | + | 0.722677i | \(0.742911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −326.523 | + | 565.554i | −0.733760 | + | 1.27091i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 478.696i | − | 1.06614i | −0.846072 | − | 0.533069i | \(-0.821039\pi\) | ||
0.846072 | − | 0.533069i | \(-0.178961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 458.218 | − | 793.657i | 1.01600 | − | 1.75977i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 191.840 | + | 110.759i | 0.421626 | + | 0.243426i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 221.421 | + | 383.512i | 0.484510 | + | 0.839195i | 0.999842 | − | 0.0177952i | \(-0.00566470\pi\) |
−0.515332 | + | 0.856991i | \(0.672331\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 717.965i | 1.55741i | 0.627392 | + | 0.778704i | \(0.284122\pi\) | ||||
−0.627392 | + | 0.778704i | \(0.715878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −409.863 | + | 709.903i | −0.885232 | + | 1.53327i | −0.0397854 | + | 0.999208i | \(0.512667\pi\) |
−0.845447 | + | 0.534059i | \(0.820666\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 928.612i | − | 1.98846i | −0.107255 | − | 0.994232i | \(-0.534206\pi\) | ||
0.107255 | − | 0.994232i | \(-0.465794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −48.9815 | − | 84.8385i | −0.104438 | − | 0.180892i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 460.037 | − | 265.603i | 0.972595 | − | 0.561528i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 106.099 | + | 90.3163i | 0.223367 | + | 0.190140i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −395.774 | − | 228.500i | −0.826251 | − | 0.477036i | 0.0263164 | − | 0.999654i | \(-0.491622\pi\) |
−0.852567 | + | 0.522617i | \(0.824956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −157.172 | −0.326761 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −239.539 | + | 138.298i | −0.493895 | + | 0.285151i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 540.475 | 1.10980 | 0.554902 | − | 0.831916i | \(-0.312756\pi\) | ||||
0.554902 | + | 0.831916i | \(0.312756\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 768.591 | − | 443.746i | 1.56536 | − | 0.903760i | 0.568660 | − | 0.822573i | \(-0.307462\pi\) |
0.996699 | − | 0.0811879i | \(-0.0258714\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 60.0935 | + | 104.085i | 0.121893 | + | 0.211126i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 299.155i | 0.601922i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 65.2082 | + | 112.944i | 0.130678 | + | 0.226340i | 0.923938 | − | 0.382542i | \(-0.124951\pi\) |
−0.793260 | + | 0.608883i | \(0.791618\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −246.777 | + | 142.477i | −0.490609 | + | 0.283254i | −0.724827 | − | 0.688931i | \(-0.758080\pi\) |
0.234218 | + | 0.972184i | \(0.424747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −129.095 | −0.255633 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 352.715i | 0.692957i | 0.938058 | + | 0.346479i | \(0.112623\pi\) | ||||
−0.938058 | + | 0.346479i | \(0.887377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −219.610 | −0.429765 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 291.256i | 0.565546i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1407.37 | −2.72219 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 479.212i | 0.919793i | 0.887973 | + | 0.459897i | \(0.152114\pi\) | ||||
−0.887973 | + | 0.459897i | \(0.847886\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −372.327 | − | 644.890i | −0.711907 | − | 1.23306i | −0.964140 | − | 0.265392i | \(-0.914498\pi\) |
0.252234 | − | 0.967666i | \(-0.418835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −38.4950 | + | 22.2251i | −0.0730456 | + | 0.0421729i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 330.542 | 0.624844 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 634.173 | − | 366.140i | 1.18982 | − | 0.686941i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 191.519 | + | 331.720i | 0.357979 | + | 0.620037i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 816.249i | − | 1.51438i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −49.4363 | − | 85.6262i | −0.0913795 | − | 0.158274i | 0.816712 | − | 0.577045i | \(-0.195794\pi\) |
−0.908092 | + | 0.418771i | \(0.862461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 274.125i | 0.502983i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 189.203 | − | 327.710i | 0.345893 | − | 0.599104i | −0.639623 | − | 0.768689i | \(-0.720909\pi\) |
0.985516 | + | 0.169585i | \(0.0542427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.5207 | − | 64.0484i | 0.0989486 | − | 0.116240i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −160.407 | − | 277.832i | −0.290066 | − | 0.502409i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −314.531 | + | 181.594i | −0.564687 | + | 0.326022i | −0.755025 | − | 0.655696i | \(-0.772375\pi\) |
0.190337 | + | 0.981719i | \(0.439042\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 424.460 | 0.759321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 451.834 | + | 260.866i | 0.802546 | + | 0.463350i | 0.844361 | − | 0.535775i | \(-0.179980\pi\) |
−0.0418144 | + | 0.999125i | \(0.513314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −100.210 | −0.177362 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −274.251 | + | 158.339i | −0.481988 | + | 0.278276i | −0.721244 | − | 0.692681i | \(-0.756430\pi\) |
0.239257 | + | 0.970956i | \(0.423096\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 425.013 | − | 736.145i | 0.744331 | − | 1.28922i | −0.206175 | − | 0.978515i | \(-0.566102\pi\) |
0.950506 | − | 0.310705i | \(-0.100565\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 89.4684 | + | 51.6546i | 0.155597 | + | 0.0898341i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 939.590 | 1.62841 | 0.814203 | − | 0.580581i | \(-0.197174\pi\) | ||||
0.814203 | + | 0.580581i | \(0.197174\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −89.2120 | − | 51.5066i | −0.153549 | − | 0.0886516i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −287.313 | + | 497.640i | −0.492818 | + | 0.853585i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 205.221i | − | 0.349610i | −0.984603 | − | 0.174805i | \(-0.944070\pi\) | ||
0.984603 | − | 0.174805i | \(-0.0559295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.6878 | + | 20.1641i | 0.0402170 | + | 0.0342344i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −710.973 | + | 410.481i | −1.19894 | + | 0.692210i | −0.960320 | − | 0.278902i | \(-0.910030\pi\) |
−0.238623 | + | 0.971112i | \(0.576696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −196.140 | − | 339.724i | −0.329647 | − | 0.570965i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 380.778i | − | 0.635689i | −0.948143 | − | 0.317845i | \(-0.897041\pi\) | ||
0.948143 | − | 0.317845i | \(-0.102959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −205.436 | − | 355.826i | −0.341824 | − | 0.592057i | 0.642947 | − | 0.765910i | \(-0.277711\pi\) |
−0.984771 | + | 0.173854i | \(0.944378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1405.18i | 2.32261i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −176.593 | + | 305.869i | −0.290928 | + | 0.503902i | −0.974029 | − | 0.226421i | \(-0.927297\pi\) |
0.683101 | + | 0.730324i | \(0.260631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −973.902 | − | 562.282i | −1.59395 | − | 0.920266i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 84.7338 | − | 146.763i | 0.138228 | − | 0.239418i | −0.788598 | − | 0.614909i | \(-0.789193\pi\) |
0.926826 | + | 0.375491i | \(0.122526\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 128.808i | 0.208766i | 0.994537 | + | 0.104383i | \(0.0332867\pi\) | ||||
−0.994537 | + | 0.104383i | \(0.966713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 185.687 | + | 321.619i | 0.299978 | + | 0.519578i | 0.976131 | − | 0.217184i | \(-0.0696872\pi\) |
−0.676152 | + | 0.736762i | \(0.736354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −252.733 | − | 145.916i | −0.405671 | − | 0.234214i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 377.278 | + | 653.465i | 0.603645 | + | 1.04554i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 241.042 | + | 139.166i | 0.383215 | + | 0.221250i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −120.458 | − | 208.640i | −0.190900 | − | 0.330649i | 0.754649 | − | 0.656129i | \(-0.227807\pi\) |
−0.945549 | + | 0.325480i | \(0.894474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 744.086 | + | 429.599i | 1.17179 | + | 0.676533i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 326.113 | − | 564.844i | 0.511951 | − | 0.886725i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 510.534i | 0.796465i | 0.917285 | + | 0.398232i | \(0.130376\pi\) | ||||
−0.917285 | + | 0.398232i | \(0.869624\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.9822 | + | 43.2704i | 0.0388525 | + | 0.0672946i | 0.884798 | − | 0.465975i | \(-0.154296\pi\) |
−0.845945 | + | 0.533270i | \(0.820963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1066.24i | 1.64798i | 0.566602 | + | 0.823991i | \(0.308258\pi\) | ||||
−0.566602 | + | 0.823991i | \(0.691742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1045.27 | + | 1810.46i | −1.61059 | + | 2.78962i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 689.970 | + | 398.354i | 1.05661 | + | 0.610037i | 0.924494 | − | 0.381197i | \(-0.124488\pi\) |
0.132121 | + | 0.991234i | \(0.457821\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −563.819 | + | 976.563i | −0.860792 | + | 1.49094i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 944.767 | + | 545.461i | 1.43364 | + | 0.827711i | 0.997396 | − | 0.0721190i | \(-0.0229761\pi\) |
0.436241 | + | 0.899830i | \(0.356309\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.9813 | −0.0604861 | −0.0302431 | − | 0.999543i | \(-0.509628\pi\) | ||||
−0.0302431 | + | 0.999543i | \(0.509628\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −177.951 | + | 209.048i | −0.267595 | + | 0.314358i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1820 | − | 54.0088i | 0.0467497 | − | 0.0809728i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1053.15i | 1.56953i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −529.340 | − | 916.844i | −0.786538 | − | 1.36232i | −0.928076 | − | 0.372391i | \(-0.878538\pi\) |
0.141538 | − | 0.989933i | \(-0.454795\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 844.755 | − | 487.719i | 1.24779 | − | 0.720413i | 0.277123 | − | 0.960834i | \(-0.410619\pi\) |
0.970669 | + | 0.240422i | \(0.0772858\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −61.8022 | − | 107.044i | −0.0910194 | − | 0.157650i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 991.533i | − | 1.45173i | −0.687836 | − | 0.725866i | \(-0.741439\pi\) | ||
0.687836 | − | 0.725866i | \(-0.258561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −71.1960 | −0.103936 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −397.640 | + | 229.578i | −0.577127 | + | 0.333204i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −482.918 | − | 836.438i | −0.698868 | − | 1.21047i | −0.968859 | − | 0.247612i | \(-0.920354\pi\) |
0.269991 | − | 0.962863i | \(-0.412979\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −448.790 | + | 259.109i | −0.645741 | + | 0.372819i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1296.78 | −1.86051 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 271.500 | + | 156.751i | 0.387304 | + | 0.223610i | 0.680991 | − | 0.732292i | \(-0.261549\pi\) |
−0.293688 | + | 0.955901i | \(0.594883\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.1823 | − | 191.583i | 0.0500459 | − | 0.272522i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 57.6894i | − | 0.0815975i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −498.245 | + | 862.985i | −0.702743 | + | 1.21719i | 0.264757 | + | 0.964315i | \(0.414708\pi\) |
−0.967500 | + | 0.252871i | \(0.918625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.9748 | + | 11.5324i | 0.0280151 | + | 0.0161745i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −836.293 | + | 1448.50i | −1.16964 | + | 2.02588i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −864.450 | − | 499.090i | −1.20229 | − | 0.694145i | −0.241230 | − | 0.970468i | \(-0.577551\pi\) |
−0.961065 | + | 0.276323i | \(0.910884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −130.156 | −0.180521 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.1149 | + | 16.2321i | −0.0387791 | + | 0.0223891i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 738.667 | 1.01605 | 0.508024 | − | 0.861343i | \(-0.330376\pi\) | ||||
0.508024 | + | 0.861343i | \(0.330376\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −650.963 | − | 375.833i | −0.890510 | − | 0.514136i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −428.638 | + | 742.423i | −0.584773 | + | 1.01286i | 0.410131 | + | 0.912027i | \(0.365483\pi\) |
−0.994904 | + | 0.100829i | \(0.967850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 640.581 | − | 369.839i | 0.869173 | − | 0.501817i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 320.378 | − | 554.910i | 0.433529 | − | 0.750894i | −0.563646 | − | 0.826017i | \(-0.690602\pi\) |
0.997174 | + | 0.0751231i | \(0.0239350\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1085.64 | − | 626.793i | 1.46115 | − | 0.843598i | 0.462090 | − | 0.886833i | \(-0.347100\pi\) |
0.999065 | + | 0.0432348i | \(0.0137663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −517.773 | + | 896.809i | −0.694997 | + | 1.20377i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −148.238 | + | 85.5852i | −0.197914 | + | 0.114266i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −250.171 | −0.333117 | −0.166558 | − | 0.986032i | \(-0.553265\pi\) | ||||
−0.166558 | + | 0.986032i | \(0.553265\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1216.44 | + | 702.312i | 1.61118 | + | 0.930214i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 64.0809 | − | 110.991i | 0.0846512 | − | 0.146620i | −0.820591 | − | 0.571515i | \(-0.806356\pi\) |
0.905243 | + | 0.424895i | \(0.139689\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 157.748 | + | 91.0757i | 0.207290 | + | 0.119679i | 0.600051 | − | 0.799962i | \(-0.295147\pi\) |
−0.392761 | + | 0.919640i | \(0.628480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −122.500 | −0.160551 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1446.65 | + | 835.226i | −1.88612 | + | 1.08895i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1084.06 | 1.40970 | 0.704849 | − | 0.709357i | \(-0.251015\pi\) | ||||
0.704849 | + | 0.709357i | \(0.251015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −524.842 | + | 303.018i | −0.678968 | + | 0.392002i | −0.799466 | − | 0.600711i | \(-0.794884\pi\) |
0.120498 | + | 0.992714i | \(0.461551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00333 | − | 10.3981i | −0.00774623 | − | 0.0134169i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 304.346 | + | 854.978i | 0.390688 | + | 1.09753i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2258.80 | −2.89219 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1030.09 | − | 594.724i | −1.31222 | − | 0.757610i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 431.411 | − | 747.227i | 0.548172 | − | 0.949462i | −0.450228 | − | 0.892914i | \(-0.648657\pi\) |
0.998400 | − | 0.0565482i | \(-0.0180095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 44.7813i | − | 0.0566136i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −420.762 | + | 728.781i | −0.530595 | + | 0.919018i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.8187 | − | 16.6385i | −0.0361590 | − | 0.0208764i | 0.481812 | − | 0.876275i | \(-0.339979\pi\) |
−0.517971 | + | 0.855398i | \(0.673312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 995.732 | + | 1724.66i | 1.24622 | + | 2.15852i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1658.18i | − | 2.06498i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −101.775 | + | 176.280i | −0.126429 | + | 0.218982i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 797.081i | − | 0.985267i | −0.870237 | − | 0.492633i | \(-0.836034\pi\) | ||
0.870237 | − | 0.492633i | \(-0.163966\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −233.636 | − | 404.670i | −0.288084 | − | 0.498977i | 0.685268 | − | 0.728291i | \(-0.259685\pi\) |
−0.973352 | + | 0.229314i | \(0.926352\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 92.9147 | − | 53.6443i | 0.114006 | − | 0.0658213i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −95.0137 | + | 517.392i | −0.116296 | + | 0.633283i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 611.361 | + | 352.970i | 0.744655 | + | 0.429927i | 0.823759 | − | 0.566940i | \(-0.191873\pi\) |
−0.0791046 | + | 0.996866i | \(0.525206\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.3500 | −0.0526732 | −0.0263366 | − | 0.999653i | \(-0.508384\pi\) | ||||
−0.0263366 | + | 0.999653i | \(0.508384\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −272.721 | + | 157.455i | −0.329771 | + | 0.190393i | −0.655739 | − | 0.754987i | \(-0.727643\pi\) |
0.325968 | + | 0.945381i | \(0.394310\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −175.140 | −0.211266 | −0.105633 | − | 0.994405i | \(-0.533687\pi\) | ||||
−0.105633 | + | 0.994405i | \(0.533687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1000.27 | + | 577.505i | −1.20080 | + | 0.693283i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 638.403 | + | 1105.75i | 0.764554 | + | 1.32425i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 223.819i | 0.266769i | 0.991064 | + | 0.133385i | \(0.0425846\pi\) | ||||
−0.991064 | + | 0.133385i | \(0.957415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −410.701 | − | 711.355i | −0.488349 | − | 0.845845i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −325.198 | + | 187.753i | −0.384850 | + | 0.222193i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −627.941 | −0.741371 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 144.424i | − | 0.169711i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1180.41 | −1.38383 | −0.691916 | − | 0.721978i | \(-0.743233\pi\) | ||||
−0.691916 | + | 0.721978i | \(0.743233\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 565.357i | 0.659693i | 0.944035 | + | 0.329847i | \(0.106997\pi\) | ||||
−0.944035 | + | 0.329847i | \(0.893003\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −704.601 | −0.820258 | −0.410129 | − | 0.912028i | \(-0.634516\pi\) | ||||
−0.410129 | + | 0.912028i | \(0.634516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 585.783i | 0.678775i | 0.940647 | + | 0.339388i | \(0.110220\pi\) | ||||
−0.940647 | + | 0.339388i | \(0.889780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −210.354 | − | 364.344i | −0.243184 | − | 0.421207i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2097.80 | − | 1211.16i | 2.41404 | − | 1.39374i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 591.042 | 0.678578 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −221.066 | + | 127.633i | −0.252647 | + | 0.145866i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −675.042 | − | 1169.21i | −0.769717 | − | 1.33319i | −0.937716 | − | 0.347401i | \(-0.887064\pi\) |
0.168000 | − | 0.985787i | \(-0.446269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1018.07i | 1.15558i | 0.816185 | + | 0.577790i | \(0.196085\pi\) | ||||
−0.816185 | + | 0.577790i | \(0.803915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −792.523 | − | 1372.69i | −0.897535 | − | 1.55458i | −0.830636 | − | 0.556816i | \(-0.812023\pi\) |
−0.0668992 | − | 0.997760i | \(-0.521311\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1174.84i | 1.32451i | 0.749277 | + | 0.662256i | \(0.230401\pi\) | ||||
−0.749277 | + | 0.662256i | \(0.769599\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −191.978 | + | 332.515i | −0.215948 | + | 0.374032i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 903.393 | − | 1061.26i | 1.01164 | − | 1.18843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −558.232 | − | 966.887i | −0.623723 | − | 1.08032i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.27694 | + | 3.62399i | −0.00698213 | + | 0.00403114i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 813.107 | 0.902450 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 201.816 | + | 116.519i | 0.223001 | + | 0.128750i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 953.908 | 1.05172 | 0.525859 | − | 0.850572i | \(-0.323744\pi\) | ||||
0.525859 | + | 0.850572i | \(0.323744\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.1810 | + | 16.2703i | −0.0309342 | + | 0.0178599i | −0.515387 | − | 0.856957i | \(-0.672352\pi\) |
0.484453 | + | 0.874817i | \(0.339019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 388.905 | − | 673.603i | 0.425964 | − | 0.737791i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −436.403 | − | 251.958i | −0.475903 | − | 0.274763i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1215.43 | −1.32256 | −0.661280 | − | 0.750139i | \(-0.729986\pi\) | ||||
−0.661280 | + | 0.750139i | \(0.729986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1563.09 | − | 902.448i | −1.69348 | − | 0.977733i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.5908 | + | 65.1091i | −0.0406387 | + | 0.0703883i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1180.08i | 1.27027i | 0.772402 | + | 0.635134i | \(0.219055\pi\) | ||||
−0.772402 | + | 0.635134i | \(0.780945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 615.512 | + | 523.950i | 0.661130 | + | 0.562782i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2565.12 | − | 1480.97i | 2.74344 | − | 1.58393i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 339.618 | + | 588.236i | 0.362453 | + | 0.627786i | 0.988364 | − | 0.152108i | \(-0.0486062\pi\) |
−0.625911 | + | 0.779894i | \(0.715273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 529.877i | 0.563100i | 0.959547 | + | 0.281550i | \(0.0908485\pi\) | ||||
−0.959547 | + | 0.281550i | \(0.909152\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 336.443 | + | 582.737i | 0.356780 | + | 0.617961i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 114.564i | − | 0.120976i | −0.998169 | − | 0.0604880i | \(-0.980734\pi\) | ||
0.998169 | − | 0.0604880i | \(-0.0192657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 662.487 | − | 1147.46i | 0.698089 | − | 1.20913i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −178.049 | − | 102.797i | −0.186830 | − | 0.107867i | 0.403668 | − | 0.914906i | \(-0.367735\pi\) |
−0.590498 | + | 0.807039i | \(0.701069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 234.947 | − | 406.939i | 0.246017 | − | 0.426115i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 31.8158i | − | 0.0331760i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 479.160 | + | 829.929i | 0.498605 | + | 0.863610i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1614.59 | + | 932.184i | 1.67315 | + | 0.965994i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −603.557 | − | 1045.39i | −0.624154 | − | 1.08107i | −0.988704 | − | 0.149882i | \(-0.952110\pi\) |
0.364550 | − | 0.931184i | \(-0.381223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 247.794 | + | 143.064i | 0.255194 | + | 0.147337i | 0.622140 | − | 0.782906i | \(-0.286263\pi\) |
−0.366946 | + | 0.930242i | \(0.619597\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −115.790 | − | 200.554i | −0.119003 | − | 0.206119i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 239.324 | + | 138.174i | 0.244958 | + | 0.141427i | 0.617453 | − | 0.786607i | \(-0.288164\pi\) |
−0.372495 | + | 0.928034i | \(0.621498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1101.75 | − | 1908.28i | 1.12538 | − | 1.94922i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1014.26i | 1.03180i | 0.856650 | + | 0.515899i | \(0.172542\pi\) | ||||
−0.856650 | + | 0.515899i | \(0.827458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 703.211 | + | 1218.00i | 0.713920 | + | 1.23655i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 390.034i | 0.394372i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −668.318 | + | 1157.56i | −0.674388 | + | 1.16807i | 0.302260 | + | 0.953226i | \(0.402259\pi\) |
−0.976647 | + | 0.214848i | \(0.931074\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −694.619 | − | 401.038i | −0.698109 | − | 0.403054i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.0956 | − | 52.1270i | 0.0301861 | − | 0.0522839i | −0.850538 | − | 0.525914i | \(-0.823723\pi\) |
0.880724 | + | 0.473630i | \(0.157057\pi\) | |||||||
\(998\) | 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 | 2052.3.be.a.125.11 | 80 | ||
3.2 | odd | 2 | 684.3.be.a.581.3 | yes | 80 | ||
9.2 | odd | 6 | 2052.3.m.a.1493.30 | 80 | |||
9.7 | even | 3 | 684.3.m.a.353.31 | ✓ | 80 | ||
19.7 | even | 3 | 2052.3.m.a.881.11 | 80 | |||
57.26 | odd | 6 | 684.3.m.a.653.31 | yes | 80 | ||
171.7 | even | 3 | 684.3.be.a.425.3 | yes | 80 | ||
171.83 | odd | 6 | inner | 2052.3.be.a.197.11 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.31 | ✓ | 80 | 9.7 | even | 3 | ||
684.3.m.a.653.31 | yes | 80 | 57.26 | odd | 6 | ||
684.3.be.a.425.3 | yes | 80 | 171.7 | even | 3 | ||
684.3.be.a.581.3 | yes | 80 | 3.2 | odd | 2 | ||
2052.3.m.a.881.11 | 80 | 19.7 | even | 3 | |||
2052.3.m.a.1493.30 | 80 | 9.2 | odd | 6 | |||
2052.3.be.a.125.11 | 80 | 1.1 | even | 1 | trivial | ||
2052.3.be.a.197.11 | 80 | 171.83 | odd | 6 | inner |