Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,4,Mod(55,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.55830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.109 |
Dual form | 162.4.c.j.55.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.401924 | − | 0.696152i | 0.0359492 | − | 0.0622658i | −0.847491 | − | 0.530810i | \(-0.821888\pi\) |
0.883440 | + | 0.468544i | \(0.155221\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.19615 | + | 2.07180i | 0.0645862 | + | 0.111867i | 0.896510 | − | 0.443023i | \(-0.146094\pi\) |
−0.831924 | + | 0.554889i | \(0.812761\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.60770 | 0.0508398 | ||||||||
\(11\) | 29.7846 | + | 51.5885i | 0.816400 | + | 1.41405i | 0.908318 | + | 0.418279i | \(0.137367\pi\) |
−0.0919186 | + | 0.995767i | \(0.529300\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38.8731 | + | 67.3301i | −0.829342 | + | 1.43646i | 0.0692128 | + | 0.997602i | \(0.477951\pi\) |
−0.898555 | + | 0.438861i | \(0.855382\pi\) | |||||||
\(14\) | −2.39230 | + | 4.14359i | −0.0456693 | + | 0.0791016i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.84232 | −0.0405509 | −0.0202754 | − | 0.999794i | \(-0.506454\pi\) | ||||
−0.0202754 | + | 0.999794i | \(0.506454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −118.315 | −1.42860 | −0.714300 | − | 0.699840i | \(-0.753255\pi\) | ||||
−0.714300 | + | 0.699840i | \(0.753255\pi\) | |||||||
\(20\) | 1.60770 | + | 2.78461i | 0.0179746 | + | 0.0311329i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −59.5692 | + | 103.177i | −0.577282 | + | 0.999881i | ||||
\(23\) | 55.3923 | − | 95.9423i | 0.502178 | − | 0.869798i | −0.497819 | − | 0.867281i | \(-0.665866\pi\) |
0.999997 | − | 0.00251677i | \(-0.000801112\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.1769 | + | 107.694i | 0.497415 | + | 0.861549i | ||||
\(26\) | −155.492 | −1.17287 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.56922 | −0.0645862 | ||||||||
\(29\) | 62.8135 | + | 108.796i | 0.402213 | + | 0.696653i | 0.993993 | − | 0.109447i | \(-0.0349079\pi\) |
−0.591780 | + | 0.806100i | \(0.701575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.5307 | + | 54.6128i | −0.182680 | + | 0.316412i | −0.942792 | − | 0.333380i | \(-0.891811\pi\) |
0.760112 | + | 0.649792i | \(0.225144\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.84232 | − | 4.92305i | −0.0143369 | − | 0.0248322i | ||||
\(35\) | 1.92305 | 0.00928727 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −227.392 | −1.01035 | −0.505177 | − | 0.863016i | \(-0.668573\pi\) | ||||
−0.505177 | + | 0.863016i | \(0.668573\pi\) | |||||||
\(38\) | −118.315 | − | 204.928i | −0.505086 | − | 0.874835i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.21539 | + | 5.56922i | −0.0127099 | + | 0.0220143i | ||||
\(41\) | 162.315 | − | 281.138i | 0.618278 | − | 1.07089i | −0.371522 | − | 0.928424i | \(-0.621164\pi\) |
0.989800 | − | 0.142465i | \(-0.0455028\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 136.412 | + | 236.272i | 0.483781 | + | 0.837933i | 0.999826 | − | 0.0186284i | \(-0.00592994\pi\) |
−0.516046 | + | 0.856561i | \(0.672597\pi\) | |||||||
\(44\) | −238.277 | −0.816400 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 221.569 | 0.710187 | ||||||||
\(47\) | −2.46926 | − | 4.27688i | −0.00766336 | − | 0.0132733i | 0.862168 | − | 0.506622i | \(-0.169106\pi\) |
−0.869832 | + | 0.493349i | \(0.835773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 168.638 | − | 292.090i | 0.491657 | − | 0.851575i | ||||
\(50\) | −124.354 | + | 215.387i | −0.351726 | + | 0.609207i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −155.492 | − | 269.321i | −0.414671 | − | 0.718231i | ||||
\(53\) | 598.908 | 1.55219 | 0.776097 | − | 0.630614i | \(-0.217197\pi\) | ||||
0.776097 | + | 0.630614i | \(0.217197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 47.8846 | 0.117396 | ||||||||
\(56\) | −9.56922 | − | 16.5744i | −0.0228347 | − | 0.0395508i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −125.627 | + | 217.592i | −0.284407 | + | 0.492608i | ||||
\(59\) | −335.138 | + | 580.477i | −0.739514 | + | 1.28088i | 0.213201 | + | 0.977008i | \(0.431611\pi\) |
−0.952714 | + | 0.303867i | \(0.901722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −232.265 | − | 402.295i | −0.487517 | − | 0.844404i | 0.512380 | − | 0.858759i | \(-0.328764\pi\) |
−0.999897 | + | 0.0143547i | \(0.995431\pi\) | |||||||
\(62\) | −126.123 | −0.258349 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 31.2480 | + | 54.1232i | 0.0596283 | + | 0.103279i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 384.535 | − | 666.033i | 0.701170 | − | 1.21446i | −0.266886 | − | 0.963728i | \(-0.585995\pi\) |
0.968056 | − | 0.250734i | \(-0.0806718\pi\) | |||||||
\(68\) | 5.68465 | − | 9.84610i | 0.0101377 | − | 0.0175590i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.92305 | + | 3.33082i | 0.00328355 | + | 0.00568727i | ||||
\(71\) | 611.569 | 1.02225 | 0.511126 | − | 0.859506i | \(-0.329228\pi\) | ||||
0.511126 | + | 0.859506i | \(0.329228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 923.831 | 1.48118 | 0.740590 | − | 0.671957i | \(-0.234546\pi\) | ||||
0.740590 | + | 0.671957i | \(0.234546\pi\) | |||||||
\(74\) | −227.392 | − | 393.855i | −0.357214 | − | 0.618712i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 236.631 | − | 409.856i | 0.357150 | − | 0.618602i | ||||
\(77\) | −71.2539 | + | 123.415i | −0.105456 | + | 0.182656i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19.9038 | − | 34.4744i | −0.0283462 | − | 0.0490971i | 0.851504 | − | 0.524348i | \(-0.175691\pi\) |
−0.879851 | + | 0.475251i | \(0.842357\pi\) | |||||||
\(80\) | −12.8616 | −0.0179746 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 649.261 | 0.874377 | ||||||||
\(83\) | 221.885 | + | 384.315i | 0.293434 | + | 0.508242i | 0.974619 | − | 0.223869i | \(-0.0718687\pi\) |
−0.681186 | + | 0.732111i | \(0.738535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.14240 | + | 1.97869i | −0.00145777 | + | 0.00252493i | ||||
\(86\) | −272.823 | + | 472.543i | −0.342085 | + | 0.592508i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −238.277 | − | 412.708i | −0.288641 | − | 0.499941i | ||||
\(89\) | 78.4576 | 0.0934437 | 0.0467218 | − | 0.998908i | \(-0.485123\pi\) | ||||
0.0467218 | + | 0.998908i | \(0.485123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −185.992 | −0.214256 | ||||||||
\(92\) | 221.569 | + | 383.769i | 0.251089 | + | 0.434899i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.93851 | − | 8.55376i | 0.00541882 | − | 0.00938566i | ||||
\(95\) | −47.5538 | + | 82.3655i | −0.0513570 | + | 0.0889529i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 45.5077 | + | 78.8217i | 0.0476352 | + | 0.0825065i | 0.888860 | − | 0.458179i | \(-0.151498\pi\) |
−0.841225 | + | 0.540686i | \(0.818165\pi\) | |||||||
\(98\) | 674.554 | 0.695308 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −497.415 | −0.497415 | ||||||||
\(101\) | −811.261 | − | 1405.15i | −0.799243 | − | 1.38433i | −0.920110 | − | 0.391661i | \(-0.871901\pi\) |
0.120867 | − | 0.992669i | \(-0.461433\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 374.115 | − | 647.987i | 0.357890 | − | 0.619884i | −0.629718 | − | 0.776824i | \(-0.716830\pi\) |
0.987608 | + | 0.156940i | \(0.0501629\pi\) | |||||||
\(104\) | 310.985 | − | 538.641i | 0.293217 | − | 0.507866i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 598.908 | + | 1037.34i | 0.548783 | + | 0.950521i | ||||
\(107\) | −1435.00 | −1.29651 | −0.648255 | − | 0.761423i | \(-0.724501\pi\) | ||||
−0.648255 | + | 0.761423i | \(0.724501\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −83.1305 | −0.0730501 | −0.0365250 | − | 0.999333i | \(-0.511629\pi\) | ||||
−0.0365250 | + | 0.999333i | \(0.511629\pi\) | |||||||
\(110\) | 47.8846 | + | 82.9385i | 0.0415056 | + | 0.0718898i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 19.1384 | − | 33.1487i | 0.0161465 | − | 0.0279666i | ||||
\(113\) | 486.098 | − | 841.946i | 0.404675 | − | 0.700917i | −0.589609 | − | 0.807689i | \(-0.700718\pi\) |
0.994284 | + | 0.106772i | \(0.0340514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −44.5270 | − | 77.1230i | −0.0361058 | − | 0.0625370i | ||||
\(116\) | −502.508 | −0.402213 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1340.55 | −1.04583 | ||||||||
\(119\) | −3.39985 | − | 5.88872i | −0.00261902 | − | 0.00453628i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1108.75 | + | 1920.40i | −0.833017 | + | 1.44283i | ||||
\(122\) | 464.531 | − | 804.591i | 0.344727 | − | 0.597084i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −126.123 | − | 218.451i | −0.0913401 | − | 0.158206i | ||||
\(125\) | 200.442 | 0.143425 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1316.13 | −0.919588 | −0.459794 | − | 0.888026i | \(-0.652077\pi\) | ||||
−0.459794 | + | 0.888026i | \(0.652077\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −62.4960 | + | 108.246i | −0.0421636 | + | 0.0730295i | ||||
\(131\) | −557.638 | + | 965.858i | −0.371917 | + | 0.644179i | −0.989860 | − | 0.142044i | \(-0.954633\pi\) |
0.617944 | + | 0.786222i | \(0.287966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −141.523 | − | 245.125i | −0.0922678 | − | 0.159813i | ||||
\(134\) | 1538.14 | 0.991604 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 22.7386 | 0.0143369 | ||||||||
\(137\) | 308.571 | + | 534.461i | 0.192431 | + | 0.333300i | 0.946055 | − | 0.324005i | \(-0.105030\pi\) |
−0.753624 | + | 0.657305i | \(0.771696\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1078.28 | + | 1867.64i | −0.657978 | + | 1.13965i | 0.323161 | + | 0.946344i | \(0.395255\pi\) |
−0.981138 | + | 0.193307i | \(0.938079\pi\) | |||||||
\(140\) | −3.84610 | + | 6.66164i | −0.00232182 | + | 0.00402151i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 611.569 | + | 1059.27i | 0.361421 | + | 0.625999i | ||||
\(143\) | −4631.28 | −2.70830 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 100.985 | 0.0578368 | ||||||||
\(146\) | 923.831 | + | 1600.12i | 0.523676 | + | 0.907034i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 454.785 | − | 787.710i | 0.252588 | − | 0.437496i | ||||
\(149\) | 1785.84 | − | 3093.17i | 0.981893 | − | 1.70069i | 0.326889 | − | 0.945063i | \(-0.394000\pi\) |
0.655004 | − | 0.755626i | \(-0.272667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1130.72 | + | 1958.46i | 0.609379 | + | 1.05548i | 0.991343 | + | 0.131299i | \(0.0419147\pi\) |
−0.381963 | + | 0.924177i | \(0.624752\pi\) | |||||||
\(152\) | 946.523 | 0.505086 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −285.015 | −0.149138 | ||||||||
\(155\) | 25.3459 | + | 43.9004i | 0.0131344 | + | 0.0227495i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −914.627 | + | 1584.18i | −0.464937 | + | 0.805295i | −0.999199 | − | 0.0400243i | \(-0.987256\pi\) |
0.534261 | + | 0.845319i | \(0.320590\pi\) | |||||||
\(158\) | 39.8076 | − | 68.9488i | 0.0200438 | − | 0.0347169i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.8616 | − | 22.2769i | −0.00635497 | − | 0.0110071i | ||||
\(161\) | 265.031 | 0.129735 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 268.554 | 0.129048 | 0.0645238 | − | 0.997916i | \(-0.479447\pi\) | ||||
0.0645238 | + | 0.997916i | \(0.479447\pi\) | |||||||
\(164\) | 649.261 | + | 1124.55i | 0.309139 | + | 0.535444i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −443.769 | + | 768.631i | −0.207489 | + | 0.359381i | ||||
\(167\) | −2027.26 | + | 3511.32i | −0.939366 | + | 1.62703i | −0.172710 | + | 0.984973i | \(0.555252\pi\) |
−0.766657 | + | 0.642057i | \(0.778081\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1923.73 | − | 3332.00i | −0.875617 | − | 1.51661i | ||||
\(170\) | −4.56959 | −0.00206160 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1091.29 | −0.483781 | ||||||||
\(173\) | 873.675 | + | 1513.25i | 0.383955 | + | 0.665030i | 0.991624 | − | 0.129161i | \(-0.0412283\pi\) |
−0.607668 | + | 0.794191i | \(0.707895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −148.746 | + | 257.636i | −0.0642523 | + | 0.111288i | ||||
\(176\) | 476.554 | − | 825.415i | 0.204100 | − | 0.353511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 78.4576 | + | 135.892i | 0.0330373 | + | 0.0572223i | ||||
\(179\) | 2037.71 | 0.850868 | 0.425434 | − | 0.904989i | \(-0.360121\pi\) | ||||
0.425434 | + | 0.904989i | \(0.360121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2820.68 | 1.15834 | 0.579169 | − | 0.815207i | \(-0.303377\pi\) | ||||
0.579169 | + | 0.815207i | \(0.303377\pi\) | |||||||
\(182\) | −185.992 | − | 322.148i | −0.0757510 | − | 0.131205i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −443.138 | + | 767.538i | −0.177547 | + | 0.307520i | ||||
\(185\) | −91.3944 | + | 158.300i | −0.0363213 | + | 0.0629104i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −84.6575 | − | 146.631i | −0.0331057 | − | 0.0573408i | ||||
\(188\) | 19.7541 | 0.00766336 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −190.215 | −0.0726297 | ||||||||
\(191\) | 219.862 | + | 380.811i | 0.0832912 | + | 0.144265i | 0.904662 | − | 0.426130i | \(-0.140123\pi\) |
−0.821371 | + | 0.570395i | \(0.806790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 231.338 | − | 400.689i | 0.0862802 | − | 0.149442i | −0.819656 | − | 0.572856i | \(-0.805835\pi\) |
0.905936 | + | 0.423415i | \(0.139169\pi\) | |||||||
\(194\) | −91.0155 | + | 157.643i | −0.0336831 | + | 0.0583409i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 674.554 | + | 1168.36i | 0.245829 | + | 0.425788i | ||||
\(197\) | −1036.60 | −0.374896 | −0.187448 | − | 0.982275i | \(-0.560022\pi\) | ||||
−0.187448 | + | 0.982275i | \(0.560022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1190.22 | −0.423980 | −0.211990 | − | 0.977272i | \(-0.567994\pi\) | ||||
−0.211990 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(200\) | −497.415 | − | 861.549i | −0.175863 | − | 0.304603i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1622.52 | − | 2810.29i | 0.565150 | − | 0.978869i | ||||
\(203\) | −150.269 | + | 260.273i | −0.0519547 | + | 0.0899883i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −130.477 | − | 225.992i | −0.0444531 | − | 0.0769951i | ||||
\(206\) | 1496.46 | 0.506133 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1243.94 | 0.414671 | ||||||||
\(209\) | −3523.98 | − | 6103.71i | −1.16631 | − | 2.02011i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2464.00 | − | 4267.78i | 0.803929 | − | 1.39245i | −0.113083 | − | 0.993586i | \(-0.536073\pi\) |
0.917012 | − | 0.398860i | \(-0.130594\pi\) | |||||||
\(212\) | −1197.82 | + | 2074.68i | −0.388049 | + | 0.672120i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1435.00 | − | 2485.49i | −0.458386 | − | 0.793947i | ||||
\(215\) | 219.308 | 0.0695660 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −150.862 | −0.0471945 | ||||||||
\(218\) | −83.1305 | − | 143.986i | −0.0258271 | − | 0.0447339i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −95.7691 | + | 165.877i | −0.0293489 | + | 0.0508338i | ||||
\(221\) | 110.490 | − | 191.374i | 0.0336305 | − | 0.0582498i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 735.235 | + | 1273.46i | 0.220785 | + | 0.382410i | 0.955046 | − | 0.296456i | \(-0.0958049\pi\) |
−0.734262 | + | 0.678866i | \(0.762472\pi\) | |||||||
\(224\) | 76.5538 | 0.0228347 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1944.39 | 0.572296 | ||||||||
\(227\) | 1051.13 | + | 1820.61i | 0.307339 | + | 0.532327i | 0.977779 | − | 0.209637i | \(-0.0672281\pi\) |
−0.670440 | + | 0.741964i | \(0.733895\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 500.519 | − | 866.924i | 0.144433 | − | 0.250166i | −0.784728 | − | 0.619840i | \(-0.787197\pi\) |
0.929161 | + | 0.369674i | \(0.120531\pi\) | |||||||
\(230\) | 89.0539 | − | 154.246i | 0.0255306 | − | 0.0442203i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −502.508 | − | 870.369i | −0.142204 | − | 0.246304i | ||||
\(233\) | 6280.78 | 1.76596 | 0.882978 | − | 0.469415i | \(-0.155535\pi\) | ||||
0.882978 | + | 0.469415i | \(0.155535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.96981 | −0.00110197 | ||||||||
\(236\) | −1340.55 | − | 2321.91i | −0.369757 | − | 0.640438i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.79970 | − | 11.7774i | 0.00185193 | − | 0.00320764i | ||||
\(239\) | −508.685 | + | 881.068i | −0.137674 | + | 0.238458i | −0.926616 | − | 0.376010i | \(-0.877296\pi\) |
0.788942 | + | 0.614468i | \(0.210629\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 460.646 | + | 797.862i | 0.123124 | + | 0.213257i | 0.920998 | − | 0.389567i | \(-0.127375\pi\) |
−0.797874 | + | 0.602824i | \(0.794042\pi\) | |||||||
\(242\) | −4434.98 | −1.17806 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1858.12 | 0.487517 | ||||||||
\(245\) | −135.560 | − | 234.796i | −0.0353493 | − | 0.0612268i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4599.28 | − | 7966.19i | 1.18480 | − | 2.05213i | ||||
\(248\) | 252.246 | − | 436.903i | 0.0645872 | − | 0.111868i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 200.442 | + | 347.177i | 0.0507084 | + | 0.0878295i | ||||
\(251\) | −2262.40 | −0.568930 | −0.284465 | − | 0.958686i | \(-0.591816\pi\) | ||||
−0.284465 | + | 0.958686i | \(0.591816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6599.35 | 1.63991 | ||||||||
\(254\) | −1316.13 | − | 2279.60i | −0.325124 | − | 0.563130i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2393.32 | − | 4145.36i | 0.580901 | − | 1.00615i | −0.414472 | − | 0.910062i | \(-0.636034\pi\) |
0.995373 | − | 0.0960877i | \(-0.0306329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −271.996 | − | 471.111i | −0.0652548 | − | 0.113025i | ||||
\(260\) | −249.984 | −0.0596283 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2230.55 | −0.525970 | ||||||||
\(263\) | −1503.96 | − | 2604.94i | −0.352617 | − | 0.610750i | 0.634090 | − | 0.773259i | \(-0.281375\pi\) |
−0.986707 | + | 0.162509i | \(0.948041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 240.715 | − | 416.931i | 0.0558001 | − | 0.0966485i | ||||
\(266\) | 283.046 | − | 490.251i | 0.0652432 | − | 0.113005i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1538.14 | + | 2664.13i | 0.350585 | + | 0.607231i | ||||
\(269\) | 6559.73 | 1.48682 | 0.743409 | − | 0.668837i | \(-0.233208\pi\) | ||||
0.743409 | + | 0.668837i | \(0.233208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5147.64 | −1.15386 | −0.576931 | − | 0.816793i | \(-0.695750\pi\) | ||||
−0.576931 | + | 0.816793i | \(0.695750\pi\) | |||||||
\(272\) | 22.7386 | + | 39.3844i | 0.00506886 | + | 0.00877952i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −617.143 | + | 1068.92i | −0.136069 | + | 0.235679i | ||||
\(275\) | −3703.83 | + | 6415.22i | −0.812180 | + | 1.40674i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 533.831 | + | 924.622i | 0.115793 | + | 0.200560i | 0.918097 | − | 0.396357i | \(-0.129726\pi\) |
−0.802303 | + | 0.596917i | \(0.796392\pi\) | |||||||
\(278\) | −4313.14 | −0.930521 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.3844 | −0.00328355 | ||||||||
\(281\) | 2093.24 | + | 3625.59i | 0.444384 | + | 0.769696i | 0.998009 | − | 0.0630699i | \(-0.0200891\pi\) |
−0.553625 | + | 0.832766i | \(0.686756\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2678.48 | + | 4639.26i | −0.562611 | + | 0.974471i | 0.434657 | + | 0.900596i | \(0.356870\pi\) |
−0.997268 | + | 0.0738746i | \(0.976464\pi\) | |||||||
\(284\) | −1223.14 | + | 2118.54i | −0.255563 | + | 0.442648i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4631.28 | − | 8021.61i | −0.957528 | − | 1.65849i | ||||
\(287\) | 776.616 | 0.159729 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4904.92 | −0.998356 | ||||||||
\(290\) | 100.985 | + | 174.911i | 0.0204484 | + | 0.0354177i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1847.66 | + | 3200.24i | −0.370295 | + | 0.641370i | ||||
\(293\) | 1447.89 | − | 2507.83i | 0.288692 | − | 0.500030i | −0.684805 | − | 0.728726i | \(-0.740113\pi\) |
0.973498 | + | 0.228696i | \(0.0734462\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 269.400 | + | 466.615i | 0.0531698 | + | 0.0920928i | ||||
\(296\) | 1819.14 | 0.357214 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7143.38 | 1.38861 | ||||||||
\(299\) | 4306.54 | + | 7459.14i | 0.832955 | + | 1.44272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −326.338 | + | 565.234i | −0.0624911 | + | 0.108238i | ||||
\(302\) | −2261.43 | + | 3916.91i | −0.430896 | + | 0.746334i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 946.523 | + | 1639.43i | 0.178575 | + | 0.309301i | ||||
\(305\) | −373.412 | −0.0701033 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1855.49 | 0.344947 | 0.172473 | − | 0.985014i | \(-0.444824\pi\) | ||||
0.172473 | + | 0.985014i | \(0.444824\pi\) | |||||||
\(308\) | −285.015 | − | 493.661i | −0.0527281 | − | 0.0913278i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −50.6918 | + | 87.8008i | −0.00928743 | + | 0.0160863i | ||||
\(311\) | 3585.85 | − | 6210.87i | 0.653809 | − | 1.13243i | −0.328382 | − | 0.944545i | \(-0.606503\pi\) |
0.982191 | − | 0.187886i | \(-0.0601635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 655.415 | + | 1135.21i | 0.118359 | + | 0.205003i | 0.919117 | − | 0.393984i | \(-0.128903\pi\) |
−0.800759 | + | 0.598987i | \(0.795570\pi\) | |||||||
\(314\) | −3658.51 | −0.657521 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 159.230 | 0.0283462 | ||||||||
\(317\) | 1844.63 | + | 3195.00i | 0.326829 | + | 0.566085i | 0.981881 | − | 0.189499i | \(-0.0606865\pi\) |
−0.655052 | + | 0.755584i | \(0.727353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3741.75 | + | 6480.90i | −0.656733 | + | 1.13749i | ||||
\(320\) | 25.7231 | − | 44.5538i | 0.00449364 | − | 0.00778322i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 265.031 | + | 459.046i | 0.0458682 | + | 0.0794461i | ||||
\(323\) | 336.290 | 0.0579310 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9668.03 | −1.65011 | ||||||||
\(326\) | 268.554 | + | 465.149i | 0.0456252 | + | 0.0790252i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1298.52 | + | 2249.11i | −0.218594 | + | 0.378616i | ||||
\(329\) | 5.90721 | − | 10.2316i | 0.000989894 | − | 0.00171455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1622.48 | + | 2810.22i | 0.269425 | + | 0.466657i | 0.968713 | − | 0.248182i | \(-0.0798331\pi\) |
−0.699289 | + | 0.714839i | \(0.746500\pi\) | |||||||
\(332\) | −1775.08 | −0.293434 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8109.04 | −1.32846 | ||||||||
\(335\) | −309.107 | − | 535.389i | −0.0504129 | − | 0.0873177i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2150.83 | + | 3725.35i | −0.347665 | + | 0.602174i | −0.985834 | − | 0.167722i | \(-0.946359\pi\) |
0.638169 | + | 0.769896i | \(0.279692\pi\) | |||||||
\(338\) | 3847.46 | − | 6664.00i | 0.619155 | − | 1.07241i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.56959 | − | 7.91476i | −0.000728885 | − | 0.00126247i | ||||
\(341\) | −3756.52 | −0.596561 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1627.43 | 0.256189 | ||||||||
\(344\) | −1091.29 | − | 1890.17i | −0.171042 | − | 0.296254i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1747.35 | + | 3026.50i | −0.271497 | + | 0.470247i | ||||
\(347\) | −1652.10 | + | 2861.52i | −0.255589 | + | 0.442693i | −0.965055 | − | 0.262046i | \(-0.915603\pi\) |
0.709466 | + | 0.704739i | \(0.248936\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2254.35 | − | 3904.65i | −0.345767 | − | 0.598886i | 0.639726 | − | 0.768603i | \(-0.279048\pi\) |
−0.985493 | + | 0.169717i | \(0.945715\pi\) | |||||||
\(350\) | −594.985 | −0.0908665 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1906.22 | 0.288641 | ||||||||
\(353\) | 3443.37 | + | 5964.09i | 0.519184 | + | 0.899254i | 0.999751 | + | 0.0222956i | \(0.00709751\pi\) |
−0.480567 | + | 0.876958i | \(0.659569\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 245.804 | − | 425.745i | 0.0367491 | − | 0.0636513i | ||||
\(356\) | −156.915 | + | 271.785i | −0.0233609 | + | 0.0404623i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2037.71 | + | 3529.41i | 0.300827 | + | 0.521048i | ||||
\(359\) | 1529.31 | 0.224829 | 0.112415 | − | 0.993661i | \(-0.464141\pi\) | ||||
0.112415 | + | 0.993661i | \(0.464141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7139.52 | 1.04090 | ||||||||
\(362\) | 2820.68 | + | 4885.56i | 0.409534 | + | 0.709335i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 371.985 | − | 644.297i | 0.0535640 | − | 0.0927756i | ||||
\(365\) | 371.310 | − | 643.127i | 0.0532472 | − | 0.0922269i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5115.68 | + | 8860.62i | 0.727620 | + | 1.26027i | 0.957886 | + | 0.287147i | \(0.0927069\pi\) |
−0.230267 | + | 0.973128i | \(0.573960\pi\) | |||||||
\(368\) | −1772.55 | −0.251089 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −365.578 | −0.0513661 | ||||||||
\(371\) | 716.385 | + | 1240.81i | 0.100250 | + | 0.173639i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −473.215 | + | 819.632i | −0.0656894 | + | 0.113777i | −0.897000 | − | 0.442031i | \(-0.854258\pi\) |
0.831310 | + | 0.555809i | \(0.187591\pi\) | |||||||
\(374\) | 169.315 | − | 293.262i | 0.0234093 | − | 0.0405461i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.7541 | + | 34.2150i | 0.00270941 | + | 0.00469283i | ||||
\(377\) | −9767.01 | −1.33429 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8717.46 | −1.18149 | −0.590746 | − | 0.806857i | \(-0.701167\pi\) | ||||
−0.590746 | + | 0.806857i | \(0.701167\pi\) | |||||||
\(380\) | −190.215 | − | 329.462i | −0.0256785 | − | 0.0444764i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −439.723 | + | 761.623i | −0.0588958 | + | 0.102011i | ||||
\(383\) | 6130.77 | − | 10618.8i | 0.817931 | − | 1.41670i | −0.0892728 | − | 0.996007i | \(-0.528454\pi\) |
0.907204 | − | 0.420691i | \(-0.138212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 57.2772 | + | 99.2071i | 0.00758213 | + | 0.0131326i | ||||
\(386\) | 925.353 | 0.122019 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −364.062 | −0.0476352 | ||||||||
\(389\) | −6605.53 | − | 11441.1i | −0.860961 | − | 1.49123i | −0.871003 | − | 0.491278i | \(-0.836530\pi\) |
0.0100423 | − | 0.999950i | \(-0.496803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −157.443 | + | 272.699i | −0.0203638 | + | 0.0352711i | ||||
\(392\) | −1349.11 | + | 2336.72i | −0.173827 | + | 0.301077i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1036.60 | − | 1795.44i | −0.132546 | − | 0.229576i | ||||
\(395\) | −31.9993 | −0.00407609 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5211.93 | −0.658890 | −0.329445 | − | 0.944175i | \(-0.606862\pi\) | ||||
−0.329445 | + | 0.944175i | \(0.606862\pi\) | |||||||
\(398\) | −1190.22 | − | 2061.51i | −0.149900 | − | 0.259634i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 994.831 | − | 1723.10i | 0.124354 | − | 0.215387i | ||||
\(401\) | 492.817 | − | 853.584i | 0.0613719 | − | 0.106299i | −0.833707 | − | 0.552207i | \(-0.813786\pi\) |
0.895079 | + | 0.445908i | \(0.147119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2451.39 | − | 4245.94i | −0.303009 | − | 0.524827i | ||||
\(404\) | 6490.09 | 0.799243 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −601.076 | −0.0734751 | ||||||||
\(407\) | −6772.79 | − | 11730.8i | −0.824852 | − | 1.42869i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 337.323 | − | 584.261i | 0.0407813 | − | 0.0706354i | −0.844914 | − | 0.534902i | \(-0.820349\pi\) |
0.885696 | + | 0.464266i | \(0.153682\pi\) | |||||||
\(410\) | 260.954 | − | 451.985i | 0.0314331 | − | 0.0544438i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1496.46 | + | 2591.95i | 0.178945 | + | 0.309942i | ||||
\(413\) | −1603.51 | −0.191049 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 356.723 | 0.0421948 | ||||||||
\(416\) | 1243.94 | + | 2154.56i | 0.146608 | + | 0.253933i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7047.95 | − | 12207.4i | 0.824705 | − | 1.42843i | ||||
\(419\) | −3752.82 | + | 6500.07i | −0.437559 | + | 0.757874i | −0.997501 | − | 0.0706581i | \(-0.977490\pi\) |
0.559942 | + | 0.828532i | \(0.310823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 676.312 | + | 1171.41i | 0.0782932 | + | 0.135608i | 0.902514 | − | 0.430661i | \(-0.141720\pi\) |
−0.824220 | + | 0.566269i | \(0.808386\pi\) | |||||||
\(422\) | 9856.01 | 1.13693 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4791.26 | −0.548783 | ||||||||
\(425\) | −176.727 | − | 306.100i | −0.0201706 | − | 0.0349365i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 555.650 | − | 962.413i | 0.0629737 | − | 0.109074i | ||||
\(428\) | 2870.00 | − | 4970.98i | 0.324128 | − | 0.561406i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 219.308 | + | 379.853i | 0.0245953 | + | 0.0426003i | ||||
\(431\) | −4003.21 | −0.447397 | −0.223698 | − | 0.974658i | \(-0.571813\pi\) | ||||
−0.223698 | + | 0.974658i | \(0.571813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9975.38 | 1.10713 | 0.553564 | − | 0.832807i | \(-0.313267\pi\) | ||||
0.553564 | + | 0.832807i | \(0.313267\pi\) | |||||||
\(434\) | −150.862 | − | 261.301i | −0.0166858 | − | 0.0289006i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 166.261 | − | 287.973i | 0.0182625 | − | 0.0316316i | ||||
\(437\) | −6553.76 | + | 11351.4i | −0.717412 | + | 1.24259i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8680.46 | − | 15035.0i | −0.943726 | − | 1.63458i | −0.758282 | − | 0.651927i | \(-0.773961\pi\) |
−0.185444 | − | 0.982655i | \(-0.559372\pi\) | |||||||
\(440\) | −383.077 | −0.0415056 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 441.959 | 0.0475608 | ||||||||
\(443\) | 4287.71 | + | 7426.54i | 0.459854 | + | 0.796491i | 0.998953 | − | 0.0457517i | \(-0.0145683\pi\) |
−0.539099 | + | 0.842243i | \(0.681235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.5340 | − | 54.6184i | 0.00335922 | − | 0.00581834i | ||||
\(446\) | −1470.47 | + | 2546.93i | −0.156118 | + | 0.270405i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 76.5538 | + | 132.595i | 0.00807327 | + | 0.0139833i | ||||
\(449\) | 4703.77 | 0.494398 | 0.247199 | − | 0.968965i | \(-0.420490\pi\) | ||||
0.247199 | + | 0.968965i | \(0.420490\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19338.0 | 2.01905 | ||||||||
\(452\) | 1944.39 | + | 3367.78i | 0.202337 | + | 0.350459i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2102.26 | + | 3641.22i | −0.217322 | + | 0.376412i | ||||
\(455\) | −74.7548 | + | 129.479i | −0.00770233 | + | 0.0133408i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3523.40 | + | 6102.71i | 0.360651 | + | 0.624667i | 0.988068 | − | 0.154017i | \(-0.0492211\pi\) |
−0.627417 | + | 0.778684i | \(0.715888\pi\) | |||||||
\(458\) | 2002.08 | 0.204259 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 356.216 | 0.0361058 | ||||||||
\(461\) | −2885.13 | − | 4997.19i | −0.291484 | − | 0.504864i | 0.682677 | − | 0.730720i | \(-0.260816\pi\) |
−0.974161 | + | 0.225856i | \(0.927482\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6799.57 | − | 11777.2i | 0.682511 | − | 1.18214i | −0.291701 | − | 0.956510i | \(-0.594221\pi\) |
0.974212 | − | 0.225634i | \(-0.0724455\pi\) | |||||||
\(464\) | 1005.02 | − | 1740.74i | 0.100553 | − | 0.174163i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6280.78 | + | 10878.6i | 0.624359 | + | 1.08142i | ||||
\(467\) | 5730.52 | 0.567831 | 0.283915 | − | 0.958849i | \(-0.408367\pi\) | ||||
0.283915 | + | 0.958849i | \(0.408367\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1839.85 | 0.181143 | ||||||||
\(470\) | −3.96981 | − | 6.87592i | −0.000389604 | − | 0.000674813i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2681.11 | − | 4643.81i | 0.261458 | − | 0.452858i | ||||
\(473\) | −8125.93 | + | 14074.5i | −0.789917 | + | 1.36818i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7356.48 | − | 12741.8i | −0.710608 | − | 1.23081i | ||||
\(476\) | 27.1988 | 0.00261902 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2034.74 | −0.194701 | ||||||||
\(479\) | −7284.14 | − | 12616.5i | −0.694824 | − | 1.20347i | −0.970240 | − | 0.242145i | \(-0.922149\pi\) |
0.275416 | − | 0.961325i | \(-0.411184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8839.44 | − | 15310.4i | 0.837928 | − | 1.45133i | ||||
\(482\) | −921.292 | + | 1595.72i | −0.0870616 | + | 0.150795i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4434.98 | − | 7681.62i | −0.416509 | − | 0.721414i | ||||
\(485\) | 73.1626 | 0.00684977 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7164.51 | 0.666642 | 0.333321 | − | 0.942813i | \(-0.391831\pi\) | ||||
0.333321 | + | 0.942813i | \(0.391831\pi\) | |||||||
\(488\) | 1858.12 | + | 3218.36i | 0.172363 | + | 0.298542i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 271.119 | − | 469.592i | 0.0249957 | − | 0.0432939i | ||||
\(491\) | 4755.03 | − | 8235.96i | 0.437050 | − | 0.756993i | −0.560410 | − | 0.828215i | \(-0.689357\pi\) |
0.997460 | + | 0.0712222i | \(0.0226899\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −178.536 | − | 309.234i | −0.0163101 | − | 0.0282499i | ||||
\(494\) | 18397.1 | 1.67556 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1008.98 | 0.0913401 | ||||||||
\(497\) | 731.530 | + | 1267.05i | 0.0660234 | + | 0.114356i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10742.8 | + | 18607.1i | −0.963756 | + | 1.66927i | −0.250835 | + | 0.968030i | \(0.580705\pi\) |
−0.712921 | + | 0.701245i | \(0.752628\pi\) | |||||||
\(500\) | −400.885 | + | 694.353i | −0.0358562 | + | 0.0621048i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2262.40 | − | 3918.59i | −0.201147 | − | 0.348397i | ||||
\(503\) | −11603.2 | −1.02855 | −0.514274 | − | 0.857626i | \(-0.671939\pi\) | ||||
−0.514274 | + | 0.857626i | \(0.671939\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1304.26 | −0.114928 | ||||||||
\(506\) | 6599.35 | + | 11430.4i | 0.579796 | + | 1.00424i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2632.26 | − | 4559.21i | 0.229897 | − | 0.398193i | ||||
\(509\) | −4469.87 | + | 7742.04i | −0.389241 | + | 0.674184i | −0.992348 | − | 0.123476i | \(-0.960596\pi\) |
0.603107 | + | 0.797660i | \(0.293929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1105.04 | + | 1913.99i | 0.0956638 | + | 0.165695i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9573.30 | 0.821518 | ||||||||
\(515\) | −300.732 | − | 520.883i | −0.0257317 | − | 0.0445686i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 147.092 | − | 254.770i | 0.0125127 | − | 0.0216727i | ||||
\(518\) | 543.992 | − | 942.221i | 0.0461421 | − | 0.0799205i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −249.984 | − | 432.985i | −0.0210818 | − | 0.0365147i | ||||
\(521\) | −7410.10 | −0.623114 | −0.311557 | − | 0.950227i | \(-0.600851\pi\) | ||||
−0.311557 | + | 0.950227i | \(0.600851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18970.8 | 1.58611 | 0.793054 | − | 0.609151i | \(-0.208490\pi\) | ||||
0.793054 | + | 0.609151i | \(0.208490\pi\) | |||||||
\(524\) | −2230.55 | − | 3863.43i | −0.185958 | − | 0.322089i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3007.92 | − | 5209.88i | 0.249338 | − | 0.431866i | ||||
\(527\) | 89.6206 | − | 155.227i | 0.00740784 | − | 0.0128308i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −53.1149 | − | 91.9977i | −0.00436549 | − | 0.00756124i | ||||
\(530\) | 962.861 | 0.0789132 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1132.19 | 0.0922678 | ||||||||
\(533\) | 12619.4 | + | 21857.4i | 1.02553 | + | 1.77627i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −576.760 | + | 998.978i | −0.0466085 | + | 0.0807282i | ||||
\(536\) | −3076.28 | + | 5328.27i | −0.247901 | + | 0.429377i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6559.73 | + | 11361.8i | 0.525669 | + | 0.910486i | ||||
\(539\) | 20091.3 | 1.60556 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11440.4 | −0.909169 | −0.454584 | − | 0.890704i | \(-0.650212\pi\) | ||||
−0.454584 | + | 0.890704i | \(0.650212\pi\) | |||||||
\(542\) | −5147.64 | − | 8915.97i | −0.407952 | − | 0.706594i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −45.4772 | + | 78.7688i | −0.00358422 | + | 0.00620806i | ||||
\(545\) | −33.4121 | + | 57.8715i | −0.00262609 | + | 0.00454852i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5126.48 | − | 8879.32i | −0.400717 | − | 0.694063i | 0.593095 | − | 0.805132i | \(-0.297906\pi\) |
−0.993813 | + | 0.111070i | \(0.964572\pi\) | |||||||
\(548\) | −2468.57 | −0.192431 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14815.3 | −1.14860 | ||||||||
\(551\) | −7431.80 | − | 12872.3i | −0.574601 | − | 0.995238i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.6160 | − | 82.4733i | 0.00366155 | − | 0.00634199i | ||||
\(554\) | −1067.66 | + | 1849.24i | −0.0818783 | + | 0.141817i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4313.14 | − | 7470.57i | −0.328989 | − | 0.569825i | ||||
\(557\) | −15336.5 | −1.16666 | −0.583328 | − | 0.812236i | \(-0.698250\pi\) | ||||
−0.583328 | + | 0.812236i | \(0.698250\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21210.9 | −1.60488 | ||||||||
\(560\) | −15.3844 | − | 26.6465i | −0.00116091 | − | 0.00201075i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4186.47 | + | 7251.18i | −0.314227 | + | 0.544257i | ||||
\(563\) | 3850.69 | − | 6669.58i | 0.288254 | − | 0.499271i | −0.685139 | − | 0.728412i | \(-0.740259\pi\) |
0.973393 | + | 0.229142i | \(0.0735919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −390.749 | − | 676.796i | −0.0290954 | − | 0.0503948i | ||||
\(566\) | −10713.9 | −0.795652 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4892.55 | −0.361421 | ||||||||
\(569\) | −8869.63 | − | 15362.6i | −0.653487 | − | 1.13187i | −0.982271 | − | 0.187467i | \(-0.939972\pi\) |
0.328784 | − | 0.944405i | \(-0.393361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6911.55 | + | 11971.2i | −0.506549 | + | 0.877369i | 0.493422 | + | 0.869790i | \(0.335746\pi\) |
−0.999971 | + | 0.00757865i | \(0.997588\pi\) | |||||||
\(572\) | 9262.55 | − | 16043.2i | 0.677075 | − | 1.17273i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 776.616 | + | 1345.14i | 0.0564727 | + | 0.0978135i | ||||
\(575\) | 13776.5 | 0.999164 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15339.1 | −1.10672 | −0.553359 | − | 0.832943i | \(-0.686654\pi\) | ||||
−0.553359 | + | 0.832943i | \(0.686654\pi\) | |||||||
\(578\) | −4904.92 | − | 8495.57i | −0.352972 | − | 0.611365i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −201.970 | + | 349.822i | −0.0144592 | + | 0.0250441i | ||||
\(581\) | −530.816 | + | 919.399i | −0.0379035 | + | 0.0656508i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17838.2 | + | 30896.7i | 1.26721 | + | 2.19487i | ||||
\(584\) | −7390.65 | −0.523676 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5791.58 | 0.408273 | ||||||||
\(587\) | 7383.26 | + | 12788.2i | 0.519148 | + | 0.899191i | 0.999752 | + | 0.0222531i | \(0.00708396\pi\) |
−0.480604 | + | 0.876937i | \(0.659583\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3730.57 | − | 6461.54i | 0.260977 | − | 0.452026i | ||||
\(590\) | −538.800 | + | 933.230i | −0.0375967 | + | 0.0651194i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1819.14 | + | 3150.84i | 0.126294 | + | 0.218748i | ||||
\(593\) | −17603.6 | −1.21904 | −0.609522 | − | 0.792769i | \(-0.708639\pi\) | ||||
−0.609522 | + | 0.792769i | \(0.708639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.46593 | −0.000376607 | ||||||||
\(596\) | 7143.38 | + | 12372.7i | 0.490946 | + | 0.850344i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8613.08 | + | 14918.3i | −0.588988 | + | 1.02016i | ||||
\(599\) | 11400.6 | − | 19746.3i | 0.777653 | − | 1.34693i | −0.155638 | − | 0.987814i | \(-0.549743\pi\) |
0.933291 | − | 0.359120i | \(-0.116923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −952.624 | − | 1649.99i | −0.0646562 | − | 0.111988i | 0.831885 | − | 0.554948i | \(-0.187262\pi\) |
−0.896541 | + | 0.442960i | \(0.853928\pi\) | |||||||
\(602\) | −1305.35 | −0.0883757 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9045.72 | −0.609379 | ||||||||
\(605\) | 891.263 | + | 1543.71i | 0.0598925 | + | 0.103737i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1294.61 | − | 2242.33i | 0.0865678 | − | 0.149940i | −0.819490 | − | 0.573093i | \(-0.805743\pi\) |
0.906058 | + | 0.423153i | \(0.139077\pi\) | |||||||
\(608\) | −1893.05 | + | 3278.85i | −0.126272 | + | 0.218709i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −373.412 | − | 646.768i | −0.0247853 | − | 0.0429293i | ||||
\(611\) | 383.950 | 0.0254222 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16930.4 | 1.11552 | 0.557759 | − | 0.830003i | \(-0.311661\pi\) | ||||
0.557759 | + | 0.830003i | \(0.311661\pi\) | |||||||
\(614\) | 1855.49 | + | 3213.81i | 0.121957 | + | 0.211236i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 570.031 | − | 987.323i | 0.0372844 | − | 0.0645785i | ||||
\(617\) | 6406.72 | − | 11096.8i | 0.418030 | − | 0.724050i | −0.577711 | − | 0.816241i | \(-0.696054\pi\) |
0.995741 | + | 0.0921917i | \(0.0293872\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5133.79 | − | 8891.99i | −0.333351 | − | 0.577382i | 0.649815 | − | 0.760092i | \(-0.274846\pi\) |
−0.983167 | + | 0.182711i | \(0.941513\pi\) | |||||||
\(620\) | −202.767 | −0.0131344 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14343.4 | 0.924626 | ||||||||
\(623\) | 93.8472 | + | 162.548i | 0.00603517 | + | 0.0104532i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7691.55 | + | 13322.2i | −0.492259 | + | 0.852618i | ||||
\(626\) | −1310.83 | + | 2270.42i | −0.0836922 | + | 0.144959i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3658.51 | − | 6336.72i | −0.232469 | − | 0.402648i | ||||
\(629\) | 646.322 | 0.0409707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21887.5 | −1.38087 | −0.690433 | − | 0.723397i | \(-0.742580\pi\) | ||||
−0.690433 | + | 0.723397i | \(0.742580\pi\) | |||||||
\(632\) | 159.230 | + | 275.795i | 0.0100219 | + | 0.0173585i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3689.26 | + | 6389.99i | −0.231103 | + | 0.400282i | ||||
\(635\) | −528.984 | + | 916.227i | −0.0330584 | + | 0.0572589i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13111.0 | + | 22708.9i | 0.815504 | + | 1.41249i | ||||
\(638\) | −14967.0 | −0.928760 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 102.892 | 0.00635497 | ||||||||
\(641\) | 8601.84 | + | 14898.8i | 0.530035 | + | 0.918047i | 0.999386 | + | 0.0350356i | \(0.0111545\pi\) |
−0.469351 | + | 0.883012i | \(0.655512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6282.79 | + | 10882.1i | −0.385333 | + | 0.667416i | −0.991815 | − | 0.127681i | \(-0.959247\pi\) |
0.606482 | + | 0.795097i | \(0.292580\pi\) | |||||||
\(644\) | −530.061 | + | 918.093i | −0.0324337 | + | 0.0561769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 336.290 | + | 582.472i | 0.0204817 | + | 0.0354753i | ||||
\(647\) | −3552.55 | −0.215866 | −0.107933 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107933 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39927.9 | −2.41496 | ||||||||
\(650\) | −9668.03 | − | 16745.5i | −0.583402 | − | 1.01048i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −537.108 | + | 930.297i | −0.0322619 | + | 0.0558792i | ||||
\(653\) | 2885.50 | − | 4997.83i | 0.172922 | − | 0.299511i | −0.766518 | − | 0.642223i | \(-0.778012\pi\) |
0.939440 | + | 0.342712i | \(0.111346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 448.256 | + | 776.402i | 0.0267402 | + | 0.0463153i | ||||
\(656\) | −5194.09 | −0.309139 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23.6289 | 0.00139992 | ||||||||
\(659\) | 8239.20 | + | 14270.7i | 0.487032 | + | 0.843564i | 0.999889 | − | 0.0149104i | \(-0.00474631\pi\) |
−0.512857 | + | 0.858474i | \(0.671413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2281.62 | − | 3951.88i | 0.134258 | − | 0.232542i | −0.791056 | − | 0.611744i | \(-0.790468\pi\) |
0.925314 | + | 0.379202i | \(0.123801\pi\) | |||||||
\(662\) | −3244.96 | + | 5620.44i | −0.190512 | + | 0.329977i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1775.08 | − | 3074.52i | −0.103744 | − | 0.179691i | ||||
\(665\) | −227.526 | −0.0132678 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13917.5 | 0.807929 | ||||||||
\(668\) | −8109.04 | − | 14045.3i | −0.469683 | − | 0.813515i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 618.214 | − | 1070.78i | 0.0356473 | − | 0.0617430i | ||||
\(671\) | 13835.9 | − | 23964.4i | 0.796017 | − | 1.37874i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6576.14 | + | 11390.2i | 0.376659 | + | 0.652393i | 0.990574 | − | 0.136980i | \(-0.0437395\pi\) |
−0.613915 | + | 0.789372i | \(0.710406\pi\) | |||||||
\(674\) | −8603.32 | −0.491673 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15389.8 | 0.875617 | ||||||||
\(677\) | 7438.07 | + | 12883.1i | 0.422257 | + | 0.731371i | 0.996160 | − | 0.0875524i | \(-0.0279045\pi\) |
−0.573903 | + | 0.818924i | \(0.694571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −108.868 | + | 188.566i | −0.00615314 | + | 0.0106576i | ||||
\(680\) | 9.13918 | − | 15.8295i | 0.000515399 | − | 0.000892698i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3756.52 | − | 6506.49i | −0.210916 | − | 0.365317i | ||||
\(683\) | 24082.4 | 1.34918 | 0.674588 | − | 0.738195i | \(-0.264321\pi\) | ||||
0.674588 | + | 0.738195i | \(0.264321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 496.089 | 0.0276709 | ||||||||
\(686\) | 1627.43 | + | 2818.79i | 0.0905766 | + | 0.156883i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2182.58 | − | 3780.35i | 0.120945 | − | 0.209483i | ||||
\(689\) | −23281.4 | + | 40324.5i | −1.28730 | + | 2.22967i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6445.10 | − | 11163.2i | −0.354824 | − | 0.614573i | 0.632264 | − | 0.774753i | \(-0.282126\pi\) |
−0.987088 | + | 0.160180i | \(0.948792\pi\) | |||||||
\(692\) | −6989.40 | −0.383955 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6608.40 | −0.361457 | ||||||||
\(695\) | 866.776 | + | 1501.30i | 0.0473075 | + | 0.0819390i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −461.353 | + | 799.086i | −0.0250717 | + | 0.0434255i | ||||
\(698\) | 4508.71 | − | 7809.31i | 0.244494 | − | 0.423477i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −594.985 | − | 1030.54i | −0.0321261 | − | 0.0556441i | ||||
\(701\) | 11887.0 | 0.640467 | 0.320233 | − | 0.947339i | \(-0.396239\pi\) | ||||
0.320233 | + | 0.947339i | \(0.396239\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26904.0 | 1.44339 | ||||||||
\(704\) | 1906.22 | + | 3301.66i | 0.102050 | + | 0.176756i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6886.74 | + | 11928.2i | −0.367119 | + | 0.635868i | ||||
\(707\) | 1940.78 | − | 3361.54i | 0.103240 | − | 0.178817i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2907.22 | − | 5035.45i | −0.153996 | − | 0.266728i | 0.778697 | − | 0.627400i | \(-0.215881\pi\) |
−0.932693 | + | 0.360672i | \(0.882547\pi\) | |||||||
\(710\) | 983.217 | 0.0519711 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −627.661 | −0.0330373 | ||||||||
\(713\) | 3493.12 | + | 6050.26i | 0.183476 | + | 0.317790i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1861.42 | + | 3224.07i | −0.0973611 | + | 0.168634i | ||||
\(716\) | −4075.42 | + | 7058.83i | −0.212717 | + | 0.368437i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1529.31 | + | 2648.84i | 0.0794892 | + | 0.137679i | ||||
\(719\) | −4488.23 | −0.232800 | −0.116400 | − | 0.993202i | \(-0.537135\pi\) | ||||
−0.116400 | + | 0.993202i | \(0.537135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1790.00 | 0.0924590 | ||||||||
\(722\) | 7139.52 | + | 12366.0i | 0.368013 | + | 0.637418i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5641.35 | + | 9771.11i | −0.289585 | + | 0.501575i | ||||
\(725\) | −7811.10 | + | 13529.2i | −0.400134 | + | 0.693052i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11592.0 | − | 20077.9i | −0.591366 | − | 1.02428i | −0.994049 | − | 0.108937i | \(-0.965255\pi\) |
0.402682 | − | 0.915340i | \(-0.368078\pi\) | |||||||
\(728\) | 1487.94 | 0.0757510 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1485.24 | 0.0753029 | ||||||||
\(731\) | −387.726 | − | 671.561i | −0.0196177 | − | 0.0339789i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10338.7 | − | 17907.2i | 0.520967 | − | 0.902341i | −0.478736 | − | 0.877959i | \(-0.658905\pi\) |
0.999703 | − | 0.0243822i | \(-0.00776185\pi\) | |||||||
\(734\) | −10231.4 | + | 17721.2i | −0.514505 | + | 0.891149i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1772.55 | − | 3070.15i | −0.0887734 | − | 0.153760i | ||||
\(737\) | 45812.8 | 2.28974 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13001.7 | −0.647191 | −0.323595 | − | 0.946196i | \(-0.604892\pi\) | ||||
−0.323595 | + | 0.946196i | \(0.604892\pi\) | |||||||
\(740\) | −365.578 | − | 633.199i | −0.0181607 | − | 0.0314552i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1432.77 | + | 2481.63i | −0.0708876 | + | 0.122781i | ||||
\(743\) | 4633.55 | − | 8025.54i | 0.228786 | − | 0.396270i | −0.728662 | − | 0.684873i | \(-0.759858\pi\) |
0.957449 | + | 0.288603i | \(0.0931909\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1435.55 | − | 2486.44i | −0.0705964 | − | 0.122277i | ||||
\(746\) | −1892.86 | −0.0928988 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 677.260 | 0.0331057 | ||||||||
\(749\) | −1716.48 | − | 2973.03i | −0.0837367 | − | 0.145036i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15361.1 | − | 26606.3i | 0.746385 | − | 1.29278i | −0.203159 | − | 0.979146i | \(-0.565121\pi\) |
0.949545 | − | 0.313632i | \(-0.101546\pi\) | |||||||
\(752\) | −39.5081 | + | 68.4300i | −0.00191584 | + | 0.00331833i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9767.01 | − | 16917.0i | −0.471742 | − | 0.817081i | ||||
\(755\) | 1817.85 | 0.0876267 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5356.86 | 0.257197 | 0.128599 | − | 0.991697i | \(-0.458952\pi\) | ||||
0.128599 | + | 0.991697i | \(0.458952\pi\) | |||||||
\(758\) | −8717.46 | − | 15099.1i | −0.417721 | − | 0.723514i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 380.430 | − | 658.924i | 0.0181574 | − | 0.0314496i | ||||
\(761\) | 5009.51 | − | 8676.72i | 0.238626 | − | 0.413313i | −0.721694 | − | 0.692212i | \(-0.756636\pi\) |
0.960320 | + | 0.278899i | \(0.0899696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −99.4368 | − | 172.230i | −0.00471802 | − | 0.00817186i | ||||
\(764\) | −1758.89 | −0.0832912 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24523.1 | 1.15673 | ||||||||
\(767\) | −26055.7 | − | 45129.8i | −1.22662 | − | 2.12457i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8775.55 | − | 15199.7i | 0.411514 | − | 0.712764i | −0.583541 | − | 0.812084i | \(-0.698333\pi\) |
0.995056 | + | 0.0993198i | \(0.0316667\pi\) | |||||||
\(770\) | −114.554 | + | 198.414i | −0.00536137 | + | 0.00928617i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 925.353 | + | 1602.76i | 0.0431401 | + | 0.0747209i | ||||
\(773\) | −17144.5 | −0.797731 | −0.398866 | − | 0.917009i | \(-0.630596\pi\) | ||||
−0.398866 | + | 0.917009i | \(0.630596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7841.94 | −0.363472 | ||||||||
\(776\) | −364.062 | − | 630.574i | −0.0168416 | − | 0.0291705i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13211.1 | − | 22882.2i | 0.608791 | − | 1.05446i | ||||
\(779\) | −19204.4 | + | 33263.0i | −0.883272 | + | 1.52987i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18215.4 | + | 31549.9i | 0.834567 | + | 1.44551i | ||||
\(782\) | −629.771 | −0.0287987 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5396.43 | −0.245829 | ||||||||
\(785\) | 735.220 | + | 1273.44i | 0.0334282 | + | 0.0578994i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4297.73 | − | 7443.89i | 0.194660 | − | 0.337161i | −0.752129 | − | 0.659016i | \(-0.770973\pi\) |
0.946789 | + | 0.321855i | \(0.104306\pi\) | |||||||
\(788\) | 2073.19 | − | 3590.88i | 0.0937239 | − | 0.162335i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −31.9993 | − | 55.4243i | −0.00144112 | − | 0.00249609i | ||||
\(791\) | 2325.79 | 0.104546 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36115.5 | 1.61727 | ||||||||
\(794\) | −5211.93 | − | 9027.33i | −0.232953 | − | 0.403486i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2380.43 | − | 4123.03i | 0.105995 | − | 0.183589i | ||||
\(797\) | 10418.9 | − | 18046.1i | 0.463057 | − | 0.802039i | −0.536054 | − | 0.844184i | \(-0.680086\pi\) |
0.999112 | + | 0.0421447i | \(0.0134190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.01843 | + | 12.1563i | 0.000310756 | + | 0.000538245i | ||||
\(800\) | 3979.32 | 0.175863 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1971.27 | 0.0867929 | ||||||||
\(803\) | 27515.9 | + | 47659.0i | 1.20924 | + | 2.09446i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 106.522 | − | 184.502i | 0.00466386 | − | 0.00807805i | ||||
\(806\) | 4902.79 | − | 8491.88i | 0.214260 | − | 0.371109i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6490.09 | + | 11241.2i | 0.282575 | + | 0.489434i | ||||
\(809\) | −6529.43 | −0.283761 | −0.141880 | − | 0.989884i | \(-0.545315\pi\) | ||||
−0.141880 | + | 0.989884i | \(0.545315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29764.0 | 1.28873 | 0.644363 | − | 0.764720i | \(-0.277123\pi\) | ||||
0.644363 | + | 0.764720i | \(0.277123\pi\) | |||||||
\(812\) | −601.076 | − | 1041.09i | −0.0259774 | − | 0.0449941i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13545.6 | − | 23461.6i | 0.583258 | − | 1.01023i | ||||
\(815\) | 107.938 | − | 186.954i | 0.00463915 | − | 0.00803525i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16139.6 | − | 27954.6i | −0.691129 | − | 1.19707i | ||||
\(818\) | 1349.29 | 0.0576735 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1043.81 | 0.0444531 | ||||||||
\(821\) | −14785.6 | − | 25609.4i | −0.628527 | − | 1.08864i | −0.987847 | − | 0.155426i | \(-0.950325\pi\) |
0.359321 | − | 0.933214i | \(-0.383008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3056.22 | + | 5293.52i | −0.129445 | + | 0.224205i | −0.923462 | − | 0.383691i | \(-0.874653\pi\) |
0.794017 | + | 0.607896i | \(0.207986\pi\) | |||||||
\(824\) | −2992.92 | + | 5183.90i | −0.126533 | + | 0.219162i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1603.51 | − | 2777.35i | −0.0675462 | − | 0.116993i | ||||
\(827\) | 3265.87 | 0.137322 | 0.0686612 | − | 0.997640i | \(-0.478127\pi\) | ||||
0.0686612 | + | 0.997640i | \(0.478127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19327.8 | −0.809747 | −0.404874 | − | 0.914373i | \(-0.632685\pi\) | ||||
−0.404874 | + | 0.914373i | \(0.632685\pi\) | |||||||
\(830\) | 356.723 | + | 617.862i | 0.0149181 | + | 0.0258389i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2487.88 | + | 4309.13i | −0.103668 | + | 0.179558i | ||||
\(833\) | −479.325 | + | 830.215i | −0.0199371 | + | 0.0345321i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1629.61 | + | 2822.57i | 0.0675389 | + | 0.116981i | ||||
\(836\) | 28191.8 | 1.16631 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15011.3 | −0.618801 | ||||||||
\(839\) | −18819.1 | − | 32595.6i | −0.774382 | − | 1.34127i | −0.935141 | − | 0.354275i | \(-0.884728\pi\) |
0.160760 | − | 0.986994i | \(-0.448606\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4303.44 | − | 7453.77i | 0.176450 | − | 0.305620i | ||||
\(842\) | −1352.62 | + | 2342.81i | −0.0553617 | + | 0.0958892i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9856.01 | + | 17071.1i | 0.401964 | + | 0.696223i | ||||
\(845\) | −3092.77 | −0.125911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5304.92 | −0.215206 | ||||||||
\(848\) | −4791.26 | − | 8298.71i | −0.194024 | − | 0.336060i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 353.454 | − | 612.200i | 0.0142628 | − | 0.0247039i | ||||
\(851\) | −12595.8 | + | 21816.5i | −0.507377 | + | 0.878803i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20934.8 | − | 36260.2i | −0.840322 | − | 1.45548i | −0.889623 | − | 0.456696i | \(-0.849033\pi\) |
0.0493012 | − | 0.998784i | \(-0.484301\pi\) | |||||||
\(854\) | 2222.60 | 0.0890583 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11480.0 | 0.458386 | ||||||||
\(857\) | −16536.5 | − | 28642.0i | −0.659131 | − | 1.14165i | −0.980841 | − | 0.194810i | \(-0.937591\pi\) |
0.321711 | − | 0.946838i | \(-0.395742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7304.84 | − | 12652.4i | 0.290149 | − | 0.502553i | −0.683696 | − | 0.729767i | \(-0.739628\pi\) |
0.973845 | + | 0.227214i | \(0.0729618\pi\) | |||||||
\(860\) | −438.616 | + | 759.706i | −0.0173915 | + | 0.0301230i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4003.21 | − | 6933.77i | −0.158179 | − | 0.273973i | ||||
\(863\) | 118.786 | 0.00468543 | 0.00234271 | − | 0.999997i | \(-0.499254\pi\) | ||||
0.00234271 | + | 0.999997i | \(0.499254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1404.60 | 0.0552115 | ||||||||
\(866\) | 9975.38 | + | 17277.9i | 0.391429 | + | 0.677974i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 301.725 | − | 522.602i | 0.0117986 | − | 0.0204358i | ||||
\(869\) | 1185.65 | − | 2053.61i | 0.0462837 | − | 0.0801658i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29896.1 | + | 51781.5i | 1.16302 | + | 2.01441i | ||||
\(872\) | 665.044 | 0.0258271 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −26215.0 | −1.01457 | ||||||||
\(875\) | 239.760 | + | 415.276i | 0.00926327 | + | 0.0160444i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3180.09 | − | 5508.08i | 0.122445 | − | 0.212080i | −0.798287 | − | 0.602278i | \(-0.794260\pi\) |
0.920731 | + | 0.390197i | \(0.127593\pi\) | |||||||
\(878\) | 17360.9 | − | 30070.0i | 0.667315 | − | 1.15582i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −383.077 | − | 663.508i | −0.0146744 | − | 0.0254169i | ||||
\(881\) | −32601.5 | −1.24673 | −0.623367 | − | 0.781930i | \(-0.714236\pi\) | ||||
−0.623367 | + | 0.781930i | \(0.714236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1478.26 | 0.0563392 | 0.0281696 | − | 0.999603i | \(-0.491032\pi\) | ||||
0.0281696 | + | 0.999603i | \(0.491032\pi\) | |||||||
\(884\) | 441.959 | + | 765.496i | 0.0168153 | + | 0.0291249i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8575.43 | + | 14853.1i | −0.325166 | + | 0.563204i | ||||
\(887\) | 22633.6 | − | 39202.5i | 0.856776 | − | 1.48398i | −0.0182111 | − | 0.999834i | \(-0.505797\pi\) |
0.874987 | − | 0.484146i | \(-0.160870\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1574.29 | − | 2726.75i | −0.0593927 | − | 0.102871i | ||||
\(890\) | 126.136 | 0.00475066 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5881.88 | −0.220785 | ||||||||
\(893\) | 292.151 | + | 506.020i | 0.0109479 | + | 0.0189623i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 819.003 | − | 1418.56i | 0.0305880 | − | 0.0529800i | ||||
\(896\) | −153.108 | + | 265.190i | −0.00570866 | + | 0.00988770i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4703.77 | + | 8147.17i | 0.174796 | + | 0.302756i | ||||
\(899\) | −7922.22 | −0.293905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1702.29 | −0.0629428 | ||||||||
\(902\) | 19338.0 | + | 33494.4i | 0.713841 | + | 1.23641i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3888.78 | + | 6735.57i | −0.143074 | + | 0.247812i | ||||
\(905\) | 1133.70 | − | 1963.62i | 0.0416413 | − | 0.0721248i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3630.76 | − | 6288.66i | −0.132919 | − | 0.230222i | 0.791882 | − | 0.610675i | \(-0.209102\pi\) |
−0.924801 | + | 0.380452i | \(0.875768\pi\) | |||||||
\(908\) | −8409.04 | −0.307339 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −299.019 | −0.0108927 | ||||||||
\(911\) | −9717.20 | − | 16830.7i | −0.353398 | − | 0.612103i | 0.633445 | − | 0.773788i | \(-0.281640\pi\) |
−0.986842 | + | 0.161685i | \(0.948307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13217.5 | + | 22893.4i | −0.479118 | + | 0.829857i | ||||
\(914\) | −7046.80 | + | 12205.4i | −0.255019 | + | 0.441706i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2002.08 | + | 3467.70i | 0.0722166 | + | 0.125083i | ||||
\(917\) | −2668.08 | −0.0960827 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24010.2 | −0.861830 | −0.430915 | − | 0.902392i | \(-0.641809\pi\) | ||||
−0.430915 | + | 0.902392i | \(0.641809\pi\) | |||||||
\(920\) | 356.216 | + | 616.984i | 0.0127653 | + | 0.0221102i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5770.26 | − | 9994.38i | 0.206110 | − | 0.356993i | ||||
\(923\) | −23773.6 | + | 41177.0i | −0.847797 | + | 1.46843i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14138.6 | − | 24488.7i | −0.502565 | − | 0.870468i | ||||
\(926\) | 27198.3 | 0.965217 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4020.06 | 0.142204 | ||||||||
\(929\) | 20777.3 | + | 35987.4i | 0.733780 | + | 1.27094i | 0.955257 | + | 0.295778i | \(0.0955790\pi\) |
−0.221477 | + | 0.975166i | \(0.571088\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19952.5 | + | 34558.8i | −0.702382 | + | 1.21656i | ||||
\(932\) | −12561.6 | + | 21757.3i | −0.441489 | + | 0.764681i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5730.52 | + | 9925.55i | 0.200758 | + | 0.347724i | ||||
\(935\) | −136.103 | −0.00476049 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16811.0 | 0.586116 | 0.293058 | − | 0.956095i | \(-0.405327\pi\) | ||||
0.293058 | + | 0.956095i | \(0.405327\pi\) | |||||||
\(938\) | 1839.85 | + | 3186.71i | 0.0640439 | + | 0.110927i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.93962 | − | 13.7518i | 0.000275491 | − | 0.000477165i | ||||
\(941\) | −5366.43 | + | 9294.93i | −0.185909 | + | 0.322004i | −0.943883 | − | 0.330281i | \(-0.892856\pi\) |
0.757973 | + | 0.652286i | \(0.226190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17982.0 | − | 31145.8i | −0.620971 | − | 1.07555i | ||||
\(944\) | 10724.4 | 0.369757 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32503.7 | −1.11711 | ||||||||
\(947\) | 15774.7 | + | 27322.5i | 0.541297 | + | 0.937553i | 0.998830 | + | 0.0483606i | \(0.0153997\pi\) |
−0.457533 | + | 0.889192i | \(0.651267\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35912.1 | + | 62201.6i | −1.22841 | + | 2.12766i | ||||
\(950\) | 14713.0 | − | 25483.6i | 0.502475 | − | 0.870313i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 27.1988 | + | 47.1097i | 0.000925965 | + | 0.00160382i | ||||
\(953\) | −31955.2 | −1.08618 | −0.543090 | − | 0.839675i | \(-0.682746\pi\) | ||||
−0.543090 | + | 0.839675i | \(0.682746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 353.470 | 0.0119770 | ||||||||
\(956\) | −2034.74 | − | 3524.27i | −0.0688370 | − | 0.119229i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14568.3 | − | 25233.0i | 0.491315 | − | 0.850982i | ||||
\(959\) | −738.197 | + | 1278.59i | −0.0248567 | + | 0.0430531i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12907.1 | + | 22355.8i | 0.433256 | + | 0.750421i | ||||
\(962\) | 35357.7 | 1.18501 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3685.17 | −0.123124 | ||||||||
\(965\) | −185.961 | − | 322.093i | −0.00620340 | − | 0.0107446i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19186.1 | + | 33231.3i | −0.638038 | + | 1.10511i | 0.347825 | + | 0.937560i | \(0.386920\pi\) |
−0.985863 | + | 0.167555i | \(0.946413\pi\) | |||||||
\(968\) | 8869.97 | − | 15363.2i | 0.294516 | − | 0.510117i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 73.1626 | + | 126.721i | 0.00242176 | + | 0.00419461i | ||||
\(971\) | −46445.9 | −1.53503 | −0.767517 | − | 0.641028i | \(-0.778508\pi\) | ||||
−0.767517 | + | 0.641028i | \(0.778508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5159.17 | −0.169985 | ||||||||
\(974\) | 7164.51 | + | 12409.3i | 0.235694 | + | 0.408233i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3716.25 | + | 6436.73i | −0.121879 | + | 0.211101i | ||||
\(977\) | 23954.1 | − | 41489.8i | 0.784402 | − | 1.35862i | −0.144954 | − | 0.989438i | \(-0.546303\pi\) |
0.929356 | − | 0.369185i | \(-0.120363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2336.83 | + | 4047.50i | 0.0762874 | + | 0.132134i | ||||
\(980\) | 1084.48 | 0.0353493 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19020.1 | 0.618082 | ||||||||
\(983\) | 20273.8 | + | 35115.3i | 0.657818 | + | 1.13937i | 0.981179 | + | 0.193099i | \(0.0618538\pi\) |
−0.323361 | + | 0.946276i | \(0.604813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −416.633 | + | 721.629i | −0.0134772 | + | 0.0233432i | ||||
\(986\) | 357.072 | − | 618.467i | 0.0115330 | − | 0.0199757i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18397.1 | + | 31864.8i | 0.592399 | + | 1.02607i | ||||
\(989\) | 30224.6 | 0.971776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10651.5 | −0.341428 | −0.170714 | − | 0.985321i | \(-0.554607\pi\) | ||||
−0.170714 | + | 0.985321i | \(0.554607\pi\) | |||||||
\(992\) | 1008.98 | + | 1747.61i | 0.0322936 | + | 0.0559342i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1463.06 | + | 2534.09i | −0.0466856 | + | 0.0808618i | ||||
\(995\) | −478.376 | + | 828.571i | −0.0152417 | + | 0.0263995i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9379.18 | + | 16245.2i | 0.297935 | + | 0.516039i | 0.975663 | − | 0.219273i | \(-0.0703687\pi\) |
−0.677728 | + | 0.735313i | \(0.737035\pi\) | |||||||
\(998\) | −42971.2 | −1.36296 | ||||||||
\(999\) | 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 | 162.4.c.j.109.1 | 4 | ||
3.2 | odd | 2 | 162.4.c.i.109.2 | 4 | |||
9.2 | odd | 6 | 162.4.c.i.55.2 | 4 | |||
9.4 | even | 3 | 162.4.a.e.1.2 | ✓ | 2 | ||
9.5 | odd | 6 | 162.4.a.h.1.1 | yes | 2 | ||
9.7 | even | 3 | inner | 162.4.c.j.55.1 | 4 | ||
36.23 | even | 6 | 1296.4.a.s.1.1 | 2 | |||
36.31 | odd | 6 | 1296.4.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.4.a.e.1.2 | ✓ | 2 | 9.4 | even | 3 | ||
162.4.a.h.1.1 | yes | 2 | 9.5 | odd | 6 | ||
162.4.c.i.55.2 | 4 | 9.2 | odd | 6 | |||
162.4.c.i.109.2 | 4 | 3.2 | odd | 2 | |||
162.4.c.j.55.1 | 4 | 9.7 | even | 3 | inner | ||
162.4.c.j.109.1 | 4 | 1.1 | even | 1 | trivial | ||
1296.4.a.j.1.2 | 2 | 36.31 | odd | 6 | |||
1296.4.a.s.1.1 | 2 | 36.23 | even | 6 |