Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(26,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.26");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Root | \(1.58114 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.26 |
Dual form | 45.3.c.a.26.4 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.65028i | − 1.82514i | −0.408920 | − | 0.912570i | \(-0.634094\pi\) | ||||
0.408920 | − | 0.912570i | \(-0.365906\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −9.32456 | −2.33114 | ||||||||
\(5\) | − 2.23607i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.16228 | 1.02318 | 0.511591 | − | 0.859229i | \(-0.329056\pi\) | ||||
0.511591 | + | 0.859229i | \(0.329056\pi\) | |||||||
\(8\) | 19.4361i | 2.42952i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.16228 | −0.816228 | ||||||||
\(11\) | − 5.42736i | − 0.493396i | −0.969092 | − | 0.246698i | \(-0.920654\pi\) | ||||
0.969092 | − | 0.246698i | \(-0.0793456\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.81139 | 0.754722 | 0.377361 | − | 0.926066i | \(-0.376832\pi\) | ||||
0.377361 | + | 0.926066i | \(0.376832\pi\) | |||||||
\(14\) | − 26.1443i | − 1.86745i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 33.6491 | 2.10307 | ||||||||
\(17\) | 12.2317i | 0.719511i | 0.933047 | + | 0.359756i | \(0.117140\pi\) | ||||
−0.933047 | + | 0.359756i | \(0.882860\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.32456 | 0.332871 | 0.166436 | − | 0.986052i | \(-0.446774\pi\) | ||||
0.166436 | + | 0.986052i | \(0.446774\pi\) | |||||||
\(20\) | 20.8503i | 1.04252i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −19.8114 | −0.900518 | ||||||||
\(23\) | 12.0394i | 0.523454i | 0.965142 | + | 0.261727i | \(0.0842920\pi\) | ||||
−0.965142 | + | 0.261727i | \(0.915708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − 35.8143i | − 1.37747i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −66.7851 | −2.38518 | ||||||||
\(29\) | 44.9881i | 1.55131i | 0.631155 | + | 0.775657i | \(0.282581\pi\) | ||||
−0.631155 | + | 0.775657i | \(0.717419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −58.2719 | −1.87974 | −0.939869 | − | 0.341535i | \(-0.889053\pi\) | ||||
−0.939869 | + | 0.341535i | \(0.889053\pi\) | |||||||
\(32\) | − 45.0842i | − 1.40888i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 44.6491 | 1.31321 | ||||||||
\(35\) | − 16.0153i | − 0.457581i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.4605 | 1.79623 | 0.898115 | − | 0.439761i | \(-0.144937\pi\) | ||||
0.898115 | + | 0.439761i | \(0.144937\pi\) | |||||||
\(38\) | − 23.0864i | − 0.607537i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 43.4605 | 1.08651 | ||||||||
\(41\) | − 16.4743i | − 0.401813i | −0.979610 | − | 0.200906i | \(-0.935611\pi\) | ||||
0.979610 | − | 0.200906i | \(-0.0643887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −43.6228 | −1.01448 | −0.507242 | − | 0.861804i | \(-0.669335\pi\) | ||||
−0.507242 | + | 0.861804i | \(0.669335\pi\) | |||||||
\(44\) | 50.6077i | 1.15018i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 43.9473 | 0.955377 | ||||||||
\(47\) | − 40.0570i | − 0.852276i | −0.904658 | − | 0.426138i | \(-0.859874\pi\) | ||||
0.904658 | − | 0.426138i | \(-0.140126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.29822 | 0.0469025 | ||||||||
\(50\) | 18.2514i | 0.365028i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −91.4868 | −1.75936 | ||||||||
\(53\) | − 13.2242i | − 0.249512i | −0.992187 | − | 0.124756i | \(-0.960185\pi\) | ||||
0.992187 | − | 0.124756i | \(-0.0398149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.1359 | −0.220654 | ||||||||
\(56\) | 139.207i | 2.48584i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 164.219 | 2.83137 | ||||||||
\(59\) | − 25.1519i | − 0.426303i | −0.977019 | − | 0.213151i | \(-0.931627\pi\) | ||||
0.977019 | − | 0.213151i | \(-0.0683728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35.6754 | −0.584843 | −0.292422 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292422 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(62\) | 212.709i | 3.43079i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −29.9737 | −0.468339 | ||||||||
\(65\) | − 21.9389i | − 0.337522i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26.7018 | 0.398534 | 0.199267 | − | 0.979945i | \(-0.436144\pi\) | ||||
0.199267 | + | 0.979945i | \(0.436144\pi\) | |||||||
\(68\) | − 114.055i | − 1.67728i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −58.4605 | −0.835150 | ||||||||
\(71\) | − 92.7301i | − 1.30606i | −0.757333 | − | 0.653029i | \(-0.773498\pi\) | ||||
0.757333 | − | 0.653029i | \(-0.226502\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 60.3246 | 0.826364 | 0.413182 | − | 0.910649i | \(-0.364417\pi\) | ||||
0.413182 | + | 0.910649i | \(0.364417\pi\) | |||||||
\(74\) | − 242.600i | − 3.27837i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −58.9737 | −0.775969 | ||||||||
\(77\) | − 38.8723i | − 0.504834i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −96.2192 | −1.21796 | −0.608982 | − | 0.793184i | \(-0.708422\pi\) | ||||
−0.608982 | + | 0.793184i | \(0.708422\pi\) | |||||||
\(80\) | − 75.2417i | − 0.940521i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −60.1359 | −0.733365 | ||||||||
\(83\) | 79.1215i | 0.953271i | 0.879101 | + | 0.476635i | \(0.158144\pi\) | ||||
−0.879101 | + | 0.476635i | \(0.841856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.3509 | 0.321775 | ||||||||
\(86\) | 159.235i | 1.85157i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 105.487 | 1.19871 | ||||||||
\(89\) | 107.443i | 1.20722i | 0.797278 | + | 0.603612i | \(0.206272\pi\) | ||||
−0.797278 | + | 0.603612i | \(0.793728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 70.2719 | 0.772219 | ||||||||
\(92\) | − 112.262i | − 1.22024i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −146.219 | −1.55552 | ||||||||
\(95\) | − 14.1421i | − 0.148865i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.07900 | −0.0111237 | −0.00556187 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00556187 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(98\) | − 8.38915i | − 0.0856036i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 46.6228 | 0.466228 | ||||||||
\(101\) | 170.282i | 1.68596i | 0.537942 | + | 0.842982i | \(0.319202\pi\) | ||||
−0.537942 | + | 0.842982i | \(0.680798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −128.460 | −1.24719 | −0.623595 | − | 0.781748i | \(-0.714328\pi\) | ||||
−0.623595 | + | 0.781748i | \(0.714328\pi\) | |||||||
\(104\) | 190.695i | 1.83361i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −48.2719 | −0.455395 | ||||||||
\(107\) | − 76.3675i | − 0.713715i | −0.934159 | − | 0.356858i | \(-0.883848\pi\) | ||||
0.934159 | − | 0.356858i | \(-0.116152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0790 | −0.119991 | −0.0599954 | − | 0.998199i | \(-0.519109\pi\) | ||||
−0.0599954 | + | 0.998199i | \(0.519109\pi\) | |||||||
\(110\) | 44.2996i | 0.402724i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 241.004 | 2.15182 | ||||||||
\(113\) | 20.7170i | 0.183336i | 0.995790 | + | 0.0916680i | \(0.0292199\pi\) | ||||
−0.995790 | + | 0.0916680i | \(0.970780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.9210 | 0.234096 | ||||||||
\(116\) | − 419.494i | − 3.61633i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −91.8114 | −0.778063 | ||||||||
\(119\) | 87.6068i | 0.736191i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 91.5438 | 0.756560 | ||||||||
\(122\) | 130.225i | 1.06742i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 543.359 | 4.38193 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −38.0306 | −0.299454 | −0.149727 | − | 0.988727i | \(-0.547839\pi\) | ||||
−0.149727 | + | 0.988727i | \(0.547839\pi\) | |||||||
\(128\) | − 70.9246i | − 0.554098i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −80.0833 | −0.616025 | ||||||||
\(131\) | 83.9409i | 0.640770i | 0.947287 | + | 0.320385i | \(0.103812\pi\) | ||||
−0.947287 | + | 0.320385i | \(0.896188\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 45.2982 | 0.340588 | ||||||||
\(134\) | − 97.4690i | − 0.727381i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −237.737 | −1.74806 | ||||||||
\(137\) | − 15.5936i | − 0.113822i | −0.998379 | − | 0.0569109i | \(-0.981875\pi\) | ||||
0.998379 | − | 0.0569109i | \(-0.0181251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 67.8420 | 0.488072 | 0.244036 | − | 0.969766i | \(-0.421529\pi\) | ||||
0.244036 | + | 0.969766i | \(0.421529\pi\) | |||||||
\(140\) | 149.336i | 1.06669i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −338.491 | −2.38374 | ||||||||
\(143\) | − 53.2499i | − 0.372377i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 100.596 | 0.693769 | ||||||||
\(146\) | − 220.202i | − 1.50823i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −619.715 | −4.18726 | ||||||||
\(149\) | − 233.426i | − 1.56662i | −0.621634 | − | 0.783308i | \(-0.713531\pi\) | ||||
0.621634 | − | 0.783308i | \(-0.286469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 185.351 | 1.22749 | 0.613745 | − | 0.789505i | \(-0.289662\pi\) | ||||
0.613745 | + | 0.789505i | \(0.289662\pi\) | |||||||
\(152\) | 122.925i | 0.808716i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −141.895 | −0.921394 | ||||||||
\(155\) | 130.300i | 0.840645i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −111.276 | −0.708765 | −0.354383 | − | 0.935100i | \(-0.615309\pi\) | ||||
−0.354383 | + | 0.935100i | \(0.615309\pi\) | |||||||
\(158\) | 351.227i | 2.22296i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −100.811 | −0.630071 | ||||||||
\(161\) | 86.2298i | 0.535589i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 118.763 | 0.728607 | 0.364304 | − | 0.931280i | \(-0.381307\pi\) | ||||
0.364304 | + | 0.931280i | \(0.381307\pi\) | |||||||
\(164\) | 153.616i | 0.936682i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 288.816 | 1.73985 | ||||||||
\(167\) | − 221.194i | − 1.32452i | −0.749276 | − | 0.662258i | \(-0.769598\pi\) | ||||
0.749276 | − | 0.662258i | \(-0.230402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −72.7367 | −0.430394 | ||||||||
\(170\) | − 99.8384i | − 0.587285i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 406.763 | 2.36490 | ||||||||
\(173\) | − 190.807i | − 1.10293i | −0.834198 | − | 0.551466i | \(-0.814069\pi\) | ||||
0.834198 | − | 0.551466i | \(-0.185931\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −35.8114 | −0.204637 | ||||||||
\(176\) | − 182.626i | − 1.03765i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 392.197 | 2.20335 | ||||||||
\(179\) | 58.1005i | 0.324584i | 0.986743 | + | 0.162292i | \(0.0518886\pi\) | ||||
−0.986743 | + | 0.162292i | \(0.948111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −162.921 | −0.900116 | −0.450058 | − | 0.892999i | \(-0.648597\pi\) | ||||
−0.450058 | + | 0.892999i | \(0.648597\pi\) | |||||||
\(182\) | − 256.512i | − 1.40941i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −234.000 | −1.27174 | ||||||||
\(185\) | − 148.610i | − 0.803298i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 66.3858 | 0.355004 | ||||||||
\(188\) | 373.513i | 1.98677i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −51.6228 | −0.271699 | ||||||||
\(191\) | − 100.062i | − 0.523884i | −0.965084 | − | 0.261942i | \(-0.915637\pi\) | ||||
0.965084 | − | 0.261942i | \(-0.0843630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −61.8947 | −0.320698 | −0.160349 | − | 0.987060i | \(-0.551262\pi\) | ||||
−0.160349 | + | 0.987060i | \(0.551262\pi\) | |||||||
\(194\) | 3.93866i | 0.0203024i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.4299 | −0.109336 | ||||||||
\(197\) | 24.8791i | 0.126290i | 0.998004 | + | 0.0631449i | \(0.0201130\pi\) | ||||
−0.998004 | + | 0.0631449i | \(0.979887\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −156.491 | −0.786387 | −0.393194 | − | 0.919456i | \(-0.628630\pi\) | ||||
−0.393194 | + | 0.919456i | \(0.628630\pi\) | |||||||
\(200\) | − 97.1806i | − 0.485903i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 621.579 | 3.07712 | ||||||||
\(203\) | 322.217i | 1.58728i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −36.8377 | −0.179696 | ||||||||
\(206\) | 468.917i | 2.27630i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 330.144 | 1.58723 | ||||||||
\(209\) | − 34.3256i | − 0.164237i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 237.789 | 1.12696 | 0.563482 | − | 0.826128i | \(-0.309461\pi\) | ||||
0.563482 | + | 0.826128i | \(0.309461\pi\) | |||||||
\(212\) | 123.309i | 0.581648i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −278.763 | −1.30263 | ||||||||
\(215\) | 97.5435i | 0.453691i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −417.359 | −1.92332 | ||||||||
\(218\) | 47.7420i | 0.219000i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 113.162 | 0.514374 | ||||||||
\(221\) | 120.010i | 0.543031i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −182.302 | −0.817500 | −0.408750 | − | 0.912646i | \(-0.634035\pi\) | ||||
−0.408750 | + | 0.912646i | \(0.634035\pi\) | |||||||
\(224\) | − 322.906i | − 1.44154i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 75.6228 | 0.334614 | ||||||||
\(227\) | 406.078i | 1.78889i | 0.447180 | + | 0.894444i | \(0.352428\pi\) | ||||
−0.447180 | + | 0.894444i | \(0.647572\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.2982 | −0.119206 | −0.0596031 | − | 0.998222i | \(-0.518984\pi\) | ||||
−0.0596031 | + | 0.998222i | \(0.518984\pi\) | |||||||
\(230\) | − 98.2692i | − 0.427257i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −874.394 | −3.76894 | ||||||||
\(233\) | − 356.382i | − 1.52954i | −0.644306 | − | 0.764768i | \(-0.722854\pi\) | ||||
0.644306 | − | 0.764768i | \(-0.277146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −89.5701 | −0.381149 | ||||||||
\(236\) | 234.530i | 0.993771i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 319.789 | 1.34365 | ||||||||
\(239\) | − 271.690i | − 1.13678i | −0.822760 | − | 0.568389i | \(-0.807567\pi\) | ||||
0.822760 | − | 0.568389i | \(-0.192433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −224.438 | −0.931280 | −0.465640 | − | 0.884974i | \(-0.654176\pi\) | ||||
−0.465640 | + | 0.884974i | \(0.654176\pi\) | |||||||
\(242\) | − 334.161i | − 1.38083i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 332.658 | 1.36335 | ||||||||
\(245\) | − 5.13898i | − 0.0209754i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62.0527 | 0.251225 | ||||||||
\(248\) | − 1132.58i | − 4.56685i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 40.8114 | 0.163246 | ||||||||
\(251\) | − 318.775i | − 1.27002i | −0.772504 | − | 0.635010i | \(-0.780996\pi\) | ||||
0.772504 | − | 0.635010i | \(-0.219004\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 65.3423 | 0.258270 | ||||||||
\(254\) | 138.822i | 0.546545i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −378.789 | −1.47965 | ||||||||
\(257\) | 371.975i | 1.44738i | 0.690128 | + | 0.723688i | \(0.257554\pi\) | ||||
−0.690128 | + | 0.723688i | \(0.742446\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 476.009 | 1.83787 | ||||||||
\(260\) | 204.571i | 0.786811i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 306.408 | 1.16950 | ||||||||
\(263\) | 238.549i | 0.907031i | 0.891248 | + | 0.453515i | \(0.149830\pi\) | ||||
−0.891248 | + | 0.453515i | \(0.850170\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.5701 | −0.111585 | ||||||||
\(266\) | − 165.351i | − 0.621621i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −248.982 | −0.929038 | ||||||||
\(269\) | 125.871i | 0.467922i | 0.972246 | + | 0.233961i | \(0.0751688\pi\) | ||||
−0.972246 | + | 0.233961i | \(0.924831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −258.649 | −0.954425 | −0.477212 | − | 0.878788i | \(-0.658353\pi\) | ||||
−0.477212 | + | 0.878788i | \(0.658353\pi\) | |||||||
\(272\) | 411.585i | 1.51318i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −56.9210 | −0.207741 | ||||||||
\(275\) | 27.1368i | 0.0986793i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 227.715 | 0.822074 | 0.411037 | − | 0.911619i | \(-0.365167\pi\) | ||||
0.411037 | + | 0.911619i | \(0.365167\pi\) | |||||||
\(278\) | − 247.642i | − 0.890800i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 311.276 | 1.11170 | ||||||||
\(281\) | − 241.384i | − 0.859016i | −0.903063 | − | 0.429508i | \(-0.858687\pi\) | ||||
0.903063 | − | 0.429508i | \(-0.141313\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 208.333 | 0.736159 | 0.368080 | − | 0.929794i | \(-0.380015\pi\) | ||||
0.368080 | + | 0.929794i | \(0.380015\pi\) | |||||||
\(284\) | 864.667i | 3.04460i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −194.377 | −0.679641 | ||||||||
\(287\) | − 117.994i | − 0.411128i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 139.386 | 0.482304 | ||||||||
\(290\) | − 367.205i | − 1.26623i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −562.500 | −1.92637 | ||||||||
\(293\) | − 201.693i | − 0.688372i | −0.938901 | − | 0.344186i | \(-0.888155\pi\) | ||||
0.938901 | − | 0.344186i | \(-0.111845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −56.2413 | −0.190648 | ||||||||
\(296\) | 1291.73i | 4.36397i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −852.070 | −2.85929 | ||||||||
\(299\) | 118.124i | 0.395062i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −312.438 | −1.03800 | ||||||||
\(302\) | − 676.583i | − 2.24034i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 212.816 | 0.700052 | ||||||||
\(305\) | 79.7727i | 0.261550i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 342.824 | 1.11669 | 0.558346 | − | 0.829608i | \(-0.311436\pi\) | ||||
0.558346 | + | 0.829608i | \(0.311436\pi\) | |||||||
\(308\) | 362.466i | 1.17684i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 475.631 | 1.53429 | ||||||||
\(311\) | − 217.640i | − 0.699807i | −0.936786 | − | 0.349903i | \(-0.886214\pi\) | ||||
0.936786 | − | 0.349903i | \(-0.113786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 281.895 | 0.900622 | 0.450311 | − | 0.892872i | \(-0.351313\pi\) | ||||
0.450311 | + | 0.892872i | \(0.351313\pi\) | |||||||
\(314\) | 406.189i | 1.29360i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 897.201 | 2.83925 | ||||||||
\(317\) | 15.4013i | 0.0485847i | 0.999705 | + | 0.0242923i | \(0.00773325\pi\) | ||||
−0.999705 | + | 0.0242923i | \(0.992267\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 244.167 | 0.765412 | ||||||||
\(320\) | 67.0232i | 0.209447i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 314.763 | 0.977525 | ||||||||
\(323\) | 77.3600i | 0.239505i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −49.0569 | −0.150944 | ||||||||
\(326\) | − 433.518i | − 1.32981i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 320.197 | 0.976211 | ||||||||
\(329\) | − 286.899i | − 0.872034i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 375.517 | 1.13449 | 0.567247 | − | 0.823548i | \(-0.308009\pi\) | ||||
0.567247 | + | 0.823548i | \(0.308009\pi\) | |||||||
\(332\) | − 737.773i | − 2.22221i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −807.421 | −2.41743 | ||||||||
\(335\) | − 59.7070i | − 0.178230i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 188.114 | 0.558201 | 0.279101 | − | 0.960262i | \(-0.409964\pi\) | ||||
0.279101 | + | 0.960262i | \(0.409964\pi\) | |||||||
\(338\) | 265.509i | 0.785530i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −255.035 | −0.750103 | ||||||||
\(341\) | 316.262i | 0.927456i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −334.491 | −0.975193 | ||||||||
\(344\) | − 847.858i | − 2.46470i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −696.500 | −2.01300 | ||||||||
\(347\) | 513.793i | 1.48067i | 0.672237 | + | 0.740336i | \(0.265334\pi\) | ||||
−0.672237 | + | 0.740336i | \(0.734666\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 112.535 | 0.322451 | 0.161225 | − | 0.986918i | \(-0.448455\pi\) | ||||
0.161225 | + | 0.986918i | \(0.448455\pi\) | |||||||
\(350\) | 130.722i | 0.373490i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −244.688 | −0.695137 | ||||||||
\(353\) | − 428.172i | − 1.21295i | −0.795102 | − | 0.606475i | \(-0.792583\pi\) | ||||
0.795102 | − | 0.606475i | \(-0.207417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −207.351 | −0.584087 | ||||||||
\(356\) | − 1001.86i | − 2.81421i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 212.083 | 0.592411 | ||||||||
\(359\) | − 56.1961i | − 0.156535i | −0.996932 | − | 0.0782676i | \(-0.975061\pi\) | ||||
0.996932 | − | 0.0782676i | \(-0.0249389\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −321.000 | −0.889197 | ||||||||
\(362\) | 594.708i | 1.64284i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −655.254 | −1.80015 | ||||||||
\(365\) | − 134.890i | − 0.369561i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −154.364 | −0.420610 | −0.210305 | − | 0.977636i | \(-0.567446\pi\) | ||||
−0.210305 | + | 0.977636i | \(0.567446\pi\) | |||||||
\(368\) | 405.116i | 1.10086i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −542.469 | −1.46613 | ||||||||
\(371\) | − 94.7151i | − 0.255297i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 557.285 | 1.49406 | 0.747030 | − | 0.664790i | \(-0.231479\pi\) | ||||
0.747030 | + | 0.664790i | \(0.231479\pi\) | |||||||
\(374\) | − 242.327i | − 0.647932i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 778.552 | 2.07062 | ||||||||
\(377\) | 441.396i | 1.17081i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 147.404 | 0.388928 | 0.194464 | − | 0.980910i | \(-0.437703\pi\) | ||||
0.194464 | + | 0.980910i | \(0.437703\pi\) | |||||||
\(380\) | 131.869i | 0.347024i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −365.254 | −0.956163 | ||||||||
\(383\) | 736.619i | 1.92329i | 0.274302 | + | 0.961644i | \(0.411553\pi\) | ||||
−0.274302 | + | 0.961644i | \(0.588447\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −86.9210 | −0.225769 | ||||||||
\(386\) | 225.933i | 0.585319i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.0612 | 0.0259310 | ||||||||
\(389\) | 296.408i | 0.761975i | 0.924580 | + | 0.380987i | \(0.124416\pi\) | ||||
−0.924580 | + | 0.380987i | \(0.875584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −147.263 | −0.376631 | ||||||||
\(392\) | 44.6685i | 0.113950i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 90.8157 | 0.230497 | ||||||||
\(395\) | 215.153i | 0.544690i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −457.057 | −1.15128 | −0.575638 | − | 0.817704i | \(-0.695246\pi\) | ||||
−0.575638 | + | 0.817704i | \(0.695246\pi\) | |||||||
\(398\) | 571.237i | 1.43527i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −168.246 | −0.420614 | ||||||||
\(401\) | 391.141i | 0.975415i | 0.873007 | + | 0.487707i | \(0.162167\pi\) | ||||
−0.873007 | + | 0.487707i | \(0.837833\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −571.728 | −1.41868 | ||||||||
\(404\) | − 1587.81i | − 3.93022i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1176.18 | 2.89700 | ||||||||
\(407\) | − 360.705i | − 0.886253i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −411.842 | −1.00695 | −0.503474 | − | 0.864010i | \(-0.667945\pi\) | ||||
−0.503474 | + | 0.864010i | \(0.667945\pi\) | |||||||
\(410\) | 134.468i | 0.327971i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1197.84 | 2.90737 | ||||||||
\(413\) | − 180.145i | − 0.436186i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 176.921 | 0.426316 | ||||||||
\(416\) | − 442.339i | − 1.06331i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −125.298 | −0.299757 | ||||||||
\(419\) | − 653.447i | − 1.55954i | −0.626066 | − | 0.779770i | \(-0.715336\pi\) | ||||
0.626066 | − | 0.779770i | \(-0.284664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 125.035 | 0.296995 | 0.148497 | − | 0.988913i | \(-0.452556\pi\) | ||||
0.148497 | + | 0.988913i | \(0.452556\pi\) | |||||||
\(422\) | − 867.998i | − 2.05687i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 257.026 | 0.606194 | ||||||||
\(425\) | − 61.1584i | − 0.143902i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −255.517 | −0.598401 | ||||||||
\(428\) | 712.093i | 1.66377i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 356.061 | 0.828049 | ||||||||
\(431\) | − 397.208i | − 0.921596i | −0.887505 | − | 0.460798i | \(-0.847563\pi\) | ||||
0.887505 | − | 0.460798i | \(-0.152437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 560.114 | 1.29357 | 0.646783 | − | 0.762674i | \(-0.276114\pi\) | ||||
0.646783 | + | 0.762674i | \(0.276114\pi\) | |||||||
\(434\) | 1523.48i | 3.51032i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 121.956 | 0.279715 | ||||||||
\(437\) | 76.1441i | 0.174243i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −664.386 | −1.51341 | −0.756704 | − | 0.653758i | \(-0.773191\pi\) | ||||
−0.756704 | + | 0.653758i | \(0.773191\pi\) | |||||||
\(440\) | − 235.876i | − 0.536081i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 438.070 | 0.991108 | ||||||||
\(443\) | − 371.305i | − 0.838160i | −0.907949 | − | 0.419080i | \(-0.862353\pi\) | ||||
0.907949 | − | 0.419080i | \(-0.137647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 240.250 | 0.539887 | ||||||||
\(446\) | 665.455i | 1.49205i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −214.680 | −0.479196 | ||||||||
\(449\) | 585.471i | 1.30395i | 0.758243 | + | 0.651973i | \(0.226058\pi\) | ||||
−0.758243 | + | 0.651973i | \(0.773942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −89.4121 | −0.198253 | ||||||||
\(452\) | − 193.177i | − 0.427382i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1482.30 | 3.26497 | ||||||||
\(455\) | − 157.133i | − 0.345347i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 168.641 | 0.369017 | 0.184508 | − | 0.982831i | \(-0.440931\pi\) | ||||
0.184508 | + | 0.982831i | \(0.440931\pi\) | |||||||
\(458\) | 99.6462i | 0.217568i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −251.026 | −0.545709 | ||||||||
\(461\) | − 298.492i | − 0.647487i | −0.946145 | − | 0.323744i | \(-0.895058\pi\) | ||||
0.946145 | − | 0.323744i | \(-0.104942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −595.285 | −1.28571 | −0.642856 | − | 0.765987i | \(-0.722251\pi\) | ||||
−0.642856 | + | 0.765987i | \(0.722251\pi\) | |||||||
\(464\) | 1513.81i | 3.26252i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1300.89 | −2.79162 | ||||||||
\(467\) | − 623.655i | − 1.33545i | −0.744408 | − | 0.667725i | \(-0.767268\pi\) | ||||
0.744408 | − | 0.667725i | \(-0.232732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 191.246 | 0.407773 | ||||||||
\(470\) | 326.956i | 0.695651i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 488.855 | 1.03571 | ||||||||
\(473\) | 236.756i | 0.500542i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −31.6228 | −0.0665743 | ||||||||
\(476\) | − 816.894i | − 1.71616i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −991.745 | −2.07478 | ||||||||
\(479\) | 131.857i | 0.275276i | 0.990483 | + | 0.137638i | \(0.0439510\pi\) | ||||
−0.990483 | + | 0.137638i | \(0.956049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 652.070 | 1.35565 | ||||||||
\(482\) | 819.263i | 1.69972i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −853.605 | −1.76365 | ||||||||
\(485\) | 2.41272i | 0.00497468i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.8028 | 0.0858375 | 0.0429187 | − | 0.999079i | \(-0.486334\pi\) | ||||
0.0429187 | + | 0.999079i | \(0.486334\pi\) | |||||||
\(488\) | − 693.392i | − 1.42089i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.7587 | −0.0382831 | ||||||||
\(491\) | 178.817i | 0.364189i | 0.983281 | + | 0.182095i | \(0.0582877\pi\) | ||||
−0.983281 | + | 0.182095i | \(0.941712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −550.280 | −1.11619 | ||||||||
\(494\) | − 226.510i | − 0.458522i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1960.80 | −3.95322 | ||||||||
\(497\) | − 664.159i | − 1.33634i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.0961 | −0.0783489 | −0.0391744 | − | 0.999232i | \(-0.512473\pi\) | ||||
−0.0391744 | + | 0.999232i | \(0.512473\pi\) | |||||||
\(500\) | − 104.252i | − 0.208503i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1163.62 | −2.31796 | ||||||||
\(503\) | − 578.698i | − 1.15049i | −0.817980 | − | 0.575247i | \(-0.804906\pi\) | ||||
0.817980 | − | 0.575247i | \(-0.195094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 380.763 | 0.753986 | ||||||||
\(506\) | − 238.518i | − 0.471379i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 354.619 | 0.698068 | ||||||||
\(509\) | − 355.743i | − 0.698905i | −0.936954 | − | 0.349453i | \(-0.886368\pi\) | ||||
0.936954 | − | 0.349453i | \(-0.113632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 432.061 | 0.845521 | ||||||||
\(512\) | 1098.99i | 2.14646i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1357.81 | 2.64166 | ||||||||
\(515\) | 287.246i | 0.557760i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −217.404 | −0.420510 | ||||||||
\(518\) | − 1737.57i | − 3.35437i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 426.408 | 0.820015 | ||||||||
\(521\) | 810.952i | 1.55653i | 0.627936 | + | 0.778265i | \(0.283900\pi\) | ||||
−0.627936 | + | 0.778265i | \(0.716100\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 720.483 | 1.37760 | 0.688798 | − | 0.724953i | \(-0.258139\pi\) | ||||
0.688798 | + | 0.724953i | \(0.258139\pi\) | |||||||
\(524\) | − 782.711i | − 1.49372i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 870.772 | 1.65546 | ||||||||
\(527\) | − 712.764i | − 1.35249i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 384.052 | 0.725996 | ||||||||
\(530\) | 107.939i | 0.203659i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −422.386 | −0.793958 | ||||||||
\(533\) | − 161.636i | − 0.303257i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −170.763 | −0.319183 | ||||||||
\(536\) | 518.979i | 0.968245i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 459.465 | 0.854024 | ||||||||
\(539\) | − 12.4733i | − 0.0231415i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 347.149 | 0.641680 | 0.320840 | − | 0.947133i | \(-0.396035\pi\) | ||||
0.320840 | + | 0.947133i | \(0.396035\pi\) | |||||||
\(542\) | 944.142i | 1.74196i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 551.456 | 1.01371 | ||||||||
\(545\) | 29.2455i | 0.0536615i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −720.833 | −1.31779 | −0.658896 | − | 0.752234i | \(-0.728976\pi\) | ||||
−0.658896 | + | 0.752234i | \(0.728976\pi\) | |||||||
\(548\) | 145.403i | 0.265334i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 99.0569 | 0.180104 | ||||||||
\(551\) | 284.530i | 0.516388i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −689.149 | −1.24620 | ||||||||
\(554\) | − 831.222i | − 1.50040i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −632.596 | −1.13776 | ||||||||
\(557\) | 429.102i | 0.770380i | 0.922837 | + | 0.385190i | \(0.125864\pi\) | ||||
−0.922837 | + | 0.385190i | \(0.874136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −428.000 | −0.765653 | ||||||||
\(560\) | − 538.902i | − 0.962325i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −881.118 | −1.56783 | ||||||||
\(563\) | 670.820i | 1.19151i | 0.803166 | + | 0.595755i | \(0.203147\pi\) | ||||
−0.803166 | + | 0.595755i | \(0.796853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46.3246 | 0.0819904 | ||||||||
\(566\) | − 760.474i | − 1.34359i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1802.31 | 3.17309 | ||||||||
\(569\) | − 368.663i | − 0.647914i | −0.946072 | − | 0.323957i | \(-0.894987\pi\) | ||||
0.946072 | − | 0.323957i | \(-0.105013\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 124.289 | 0.217669 | 0.108834 | − | 0.994060i | \(-0.465288\pi\) | ||||
0.108834 | + | 0.994060i | \(0.465288\pi\) | |||||||
\(572\) | 496.532i | 0.868063i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −430.710 | −0.750366 | ||||||||
\(575\) | − 60.1972i | − 0.104691i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 504.236 | 0.873893 | 0.436947 | − | 0.899487i | \(-0.356060\pi\) | ||||
0.436947 | + | 0.899487i | \(0.356060\pi\) | |||||||
\(578\) | − 508.797i | − 0.880272i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −938.017 | −1.61727 | ||||||||
\(581\) | 566.690i | 0.975370i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −71.7722 | −0.123108 | ||||||||
\(584\) | 1172.48i | 2.00766i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −736.236 | −1.25638 | ||||||||
\(587\) | − 39.2256i | − 0.0668238i | −0.999442 | − | 0.0334119i | \(-0.989363\pi\) | ||||
0.999442 | − | 0.0334119i | \(-0.0106373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −368.544 | −0.625711 | ||||||||
\(590\) | 205.297i | 0.347960i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2236.34 | 3.77760 | ||||||||
\(593\) | 621.670i | 1.04835i | 0.851611 | + | 0.524174i | \(0.175626\pi\) | ||||
−0.851611 | + | 0.524174i | \(0.824374\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 195.895 | 0.329235 | ||||||||
\(596\) | 2176.59i | 3.65200i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 431.184 | 0.721044 | ||||||||
\(599\) | 1119.77i | 1.86940i | 0.355436 | + | 0.934701i | \(0.384332\pi\) | ||||
−0.355436 | + | 0.934701i | \(0.615668\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −323.789 | −0.538751 | −0.269375 | − | 0.963035i | \(-0.586817\pi\) | ||||
−0.269375 | + | 0.963035i | \(0.586817\pi\) | |||||||
\(602\) | 1140.49i | 1.89450i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1728.31 | −2.86145 | ||||||||
\(605\) | − 204.698i | − 0.338344i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1025.63 | 1.68966 | 0.844832 | − | 0.535031i | \(-0.179700\pi\) | ||||
0.844832 | + | 0.535031i | \(0.179700\pi\) | |||||||
\(608\) | − 285.138i | − 0.468976i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 291.193 | 0.477365 | ||||||||
\(611\) | − 393.014i | − 0.643232i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 904.153 | 1.47496 | 0.737482 | − | 0.675367i | \(-0.236015\pi\) | ||||
0.737482 | + | 0.675367i | \(0.236015\pi\) | |||||||
\(614\) | − 1251.40i | − 2.03812i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 755.526 | 1.22650 | ||||||||
\(617\) | − 710.716i | − 1.15189i | −0.817488 | − | 0.575945i | \(-0.804634\pi\) | ||||
0.817488 | − | 0.575945i | \(-0.195366\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −583.737 | −0.943032 | −0.471516 | − | 0.881858i | \(-0.656293\pi\) | ||||
−0.471516 | + | 0.881858i | \(0.656293\pi\) | |||||||
\(620\) | − 1214.99i | − 1.95966i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −794.447 | −1.27725 | ||||||||
\(623\) | 769.537i | 1.23521i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − 1028.99i | − 1.64376i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1037.60 | 1.65223 | ||||||||
\(629\) | 812.924i | 1.29241i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0968 | −0.0318491 | −0.0159246 | − | 0.999873i | \(-0.505069\pi\) | ||||
−0.0159246 | + | 0.999873i | \(0.505069\pi\) | |||||||
\(632\) | − 1870.13i | − 2.95906i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 56.2192 | 0.0886738 | ||||||||
\(635\) | 85.0390i | 0.133920i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.5487 | 0.0353983 | ||||||||
\(638\) | − 891.277i | − 1.39699i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −158.592 | −0.247800 | ||||||||
\(641\) | 341.607i | 0.532928i | 0.963845 | + | 0.266464i | \(0.0858553\pi\) | ||||
−0.963845 | + | 0.266464i | \(0.914145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −469.693 | −0.730471 | −0.365235 | − | 0.930915i | \(-0.619011\pi\) | ||||
−0.365235 | + | 0.930915i | \(0.619011\pi\) | |||||||
\(644\) | − 804.054i | − 1.24853i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 282.386 | 0.437130 | ||||||||
\(647\) | − 572.099i | − 0.884234i | −0.896957 | − | 0.442117i | \(-0.854228\pi\) | ||||
0.896957 | − | 0.442117i | \(-0.145772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −136.508 | −0.210336 | ||||||||
\(650\) | 179.072i | 0.275495i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1107.41 | −1.69848 | ||||||||
\(653\) | 213.540i | 0.327014i | 0.986542 | + | 0.163507i | \(0.0522806\pi\) | ||||
−0.986542 | + | 0.163507i | \(0.947719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 187.698 | 0.286561 | ||||||||
\(656\) | − 554.347i | − 0.845040i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1047.26 | −1.59158 | ||||||||
\(659\) | − 420.983i | − 0.638820i | −0.947617 | − | 0.319410i | \(-0.896515\pi\) | ||||
0.947617 | − | 0.319410i | \(-0.103485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 434.272 | 0.656992 | 0.328496 | − | 0.944505i | \(-0.393458\pi\) | ||||
0.328496 | + | 0.944505i | \(0.393458\pi\) | |||||||
\(662\) | − 1370.74i | − 2.07061i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1537.81 | −2.31599 | ||||||||
\(665\) | − 101.290i | − 0.152316i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −541.631 | −0.812041 | ||||||||
\(668\) | 2062.54i | 3.08763i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −217.947 | −0.325295 | ||||||||
\(671\) | 193.623i | 0.288560i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 72.7801 | 0.108143 | 0.0540714 | − | 0.998537i | \(-0.482780\pi\) | ||||
0.0540714 | + | 0.998537i | \(0.482780\pi\) | |||||||
\(674\) | − 686.669i | − 1.01880i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 678.237 | 1.00331 | ||||||||
\(677\) | 172.106i | 0.254219i | 0.991889 | + | 0.127109i | \(0.0405700\pi\) | ||||
−0.991889 | + | 0.127109i | \(0.959430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.72811 | −0.0113816 | ||||||||
\(680\) | 531.595i | 0.781758i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1154.45 | 1.69274 | ||||||||
\(683\) | − 792.592i | − 1.16046i | −0.814454 | − | 0.580228i | \(-0.802963\pi\) | ||||
0.814454 | − | 0.580228i | \(-0.197037\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.8683 | −0.0509027 | ||||||||
\(686\) | 1220.99i | 1.77986i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1467.87 | −2.13353 | ||||||||
\(689\) | − 129.747i | − 0.188313i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 154.851 | 0.224097 | 0.112049 | − | 0.993703i | \(-0.464259\pi\) | ||||
0.112049 | + | 0.993703i | \(0.464259\pi\) | |||||||
\(692\) | 1779.19i | 2.57109i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1875.49 | 2.70244 | ||||||||
\(695\) | − 151.699i | − 0.218272i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 201.509 | 0.289109 | ||||||||
\(698\) | − 410.785i | − 0.588518i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 333.925 | 0.477036 | ||||||||
\(701\) | − 950.544i | − 1.35598i | −0.735070 | − | 0.677991i | \(-0.762851\pi\) | ||||
0.735070 | − | 0.677991i | \(-0.237149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 420.333 | 0.597913 | ||||||||
\(704\) | 162.678i | 0.231076i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1562.95 | −2.21381 | ||||||||
\(707\) | 1219.61i | 1.72505i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 390.350 | 0.550564 | 0.275282 | − | 0.961363i | \(-0.411229\pi\) | ||||
0.275282 | + | 0.961363i | \(0.411229\pi\) | |||||||
\(710\) | 756.889i | 1.06604i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2088.28 | −2.93297 | ||||||||
\(713\) | − 701.561i | − 0.983956i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −119.070 | −0.166532 | ||||||||
\(716\) | − 541.762i | − 0.756650i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −205.132 | −0.285699 | ||||||||
\(719\) | 655.227i | 0.911303i | 0.890158 | + | 0.455651i | \(0.150594\pi\) | ||||
−0.890158 | + | 0.455651i | \(0.849406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −920.070 | −1.27610 | ||||||||
\(722\) | 1171.74i | 1.62291i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1519.17 | 2.09830 | ||||||||
\(725\) | − 224.940i | − 0.310263i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1424.25 | 1.95908 | 0.979539 | − | 0.201254i | \(-0.0645017\pi\) | ||||
0.979539 | + | 0.201254i | \(0.0645017\pi\) | |||||||
\(728\) | 1365.81i | 1.87612i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −492.386 | −0.674501 | ||||||||
\(731\) | − 533.580i | − 0.729932i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −946.749 | −1.29161 | −0.645805 | − | 0.763503i | \(-0.723478\pi\) | ||||
−0.645805 | + | 0.763503i | \(0.723478\pi\) | |||||||
\(734\) | 563.471i | 0.767672i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 542.789 | 0.737485 | ||||||||
\(737\) | − 144.920i | − 0.196635i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 591.429 | 0.800310 | 0.400155 | − | 0.916447i | \(-0.368956\pi\) | ||||
0.400155 | + | 0.916447i | \(0.368956\pi\) | |||||||
\(740\) | 1385.72i | 1.87260i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −345.737 | −0.465952 | ||||||||
\(743\) | − 732.202i | − 0.985467i | −0.870180 | − | 0.492734i | \(-0.835998\pi\) | ||||
0.870180 | − | 0.492734i | \(-0.164002\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −521.956 | −0.700612 | ||||||||
\(746\) | − 2034.25i | − 2.72687i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −619.018 | −0.827564 | ||||||||
\(749\) | − 546.965i | − 0.730261i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −215.359 | −0.286764 | −0.143382 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143382 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(752\) | − 1347.88i | − 1.79240i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1611.22 | 2.13689 | ||||||||
\(755\) | − 414.457i | − 0.548950i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 276.258 | 0.364938 | 0.182469 | − | 0.983212i | \(-0.441591\pi\) | ||||
0.182469 | + | 0.983212i | \(0.441591\pi\) | |||||||
\(758\) | − 538.064i | − 0.709848i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 274.868 | 0.361669 | ||||||||
\(761\) | − 893.373i | − 1.17395i | −0.809606 | − | 0.586973i | \(-0.800319\pi\) | ||||
0.809606 | − | 0.586973i | \(-0.199681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −93.6754 | −0.122773 | ||||||||
\(764\) | 933.033i | 1.22125i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2688.87 | 3.51027 | ||||||||
\(767\) | − 246.775i | − 0.321740i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 284.316 | 0.369722 | 0.184861 | − | 0.982765i | \(-0.440817\pi\) | ||||
0.184861 | + | 0.982765i | \(0.440817\pi\) | |||||||
\(770\) | 317.286i | 0.412060i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 577.140 | 0.747591 | ||||||||
\(773\) | 1059.64i | 1.37081i | 0.728162 | + | 0.685405i | \(0.240375\pi\) | ||||
−0.728162 | + | 0.685405i | \(0.759625\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 291.359 | 0.375948 | ||||||||
\(776\) | − 20.9716i | − 0.0270253i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1081.97 | 1.39071 | ||||||||
\(779\) | − 104.193i | − 0.133752i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −503.280 | −0.644404 | ||||||||
\(782\) | 537.550i | 0.687404i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 77.3331 | 0.0986392 | ||||||||
\(785\) | 248.821i | 0.316970i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −875.517 | −1.11247 | −0.556237 | − | 0.831024i | \(-0.687755\pi\) | ||||
−0.556237 | + | 0.831024i | \(0.687755\pi\) | |||||||
\(788\) | − 231.986i | − 0.294399i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 785.368 | 0.994137 | ||||||||
\(791\) | 148.381i | 0.187586i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −350.026 | −0.441394 | ||||||||
\(794\) | 1668.39i | 2.10124i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1459.21 | 1.83318 | ||||||||
\(797\) | − 742.449i | − 0.931555i | −0.884902 | − | 0.465777i | \(-0.845775\pi\) | ||||
0.884902 | − | 0.465777i | \(-0.154225\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 489.964 | 0.613222 | ||||||||
\(800\) | 225.421i | 0.281776i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1427.78 | 1.78027 | ||||||||
\(803\) | − 327.403i | − 0.407725i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 192.816 | 0.239523 | ||||||||
\(806\) | 2086.97i | 2.58929i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3309.63 | −4.09608 | ||||||||
\(809\) | − 113.720i | − 0.140568i | −0.997527 | − | 0.0702842i | \(-0.977609\pi\) | ||||
0.997527 | − | 0.0702842i | \(-0.0223906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1466.03 | −1.80769 | −0.903844 | − | 0.427863i | \(-0.859267\pi\) | ||||
−0.903844 | + | 0.427863i | \(0.859267\pi\) | |||||||
\(812\) | − 3004.53i | − 3.70016i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1316.67 | −1.61754 | ||||||||
\(815\) | − 265.562i | − 0.325843i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −275.895 | −0.337692 | ||||||||
\(818\) | 1503.34i | 1.83782i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 343.495 | 0.418897 | ||||||||
\(821\) | − 550.073i | − 0.670003i | −0.942218 | − | 0.335002i | \(-0.891263\pi\) | ||||
0.942218 | − | 0.335002i | \(-0.108737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1392.51 | 1.69199 | 0.845997 | − | 0.533187i | \(-0.179006\pi\) | ||||
0.845997 | + | 0.533187i | \(0.179006\pi\) | |||||||
\(824\) | − 2496.77i | − 3.03007i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −657.579 | −0.796100 | ||||||||
\(827\) | 955.922i | 1.15589i | 0.816075 | + | 0.577945i | \(0.196145\pi\) | ||||
−0.816075 | + | 0.577945i | \(0.803855\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1652.69 | −1.99360 | −0.996798 | − | 0.0799552i | \(-0.974522\pi\) | ||||
−0.996798 | + | 0.0799552i | \(0.974522\pi\) | |||||||
\(830\) | − 645.811i | − 0.778086i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −294.083 | −0.353465 | ||||||||
\(833\) | 28.1111i | 0.0337469i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −494.605 | −0.592341 | ||||||||
\(836\) | 320.071i | 0.382860i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2385.27 | −2.84638 | ||||||||
\(839\) | 1568.11i | 1.86903i | 0.355927 | + | 0.934514i | \(0.384165\pi\) | ||||
−0.355927 | + | 0.934514i | \(0.615835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1182.93 | −1.40657 | ||||||||
\(842\) | − 456.413i | − 0.542058i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2217.28 | −2.62711 | ||||||||
\(845\) | 162.644i | 0.192478i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 655.662 | 0.774099 | ||||||||
\(848\) | − 444.981i | − 0.524742i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −223.246 | −0.262642 | ||||||||
\(851\) | 800.147i | 0.940243i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −651.232 | −0.763461 | −0.381730 | − | 0.924274i | \(-0.624672\pi\) | ||||
−0.381730 | + | 0.924274i | \(0.624672\pi\) | |||||||
\(854\) | 932.711i | 1.09217i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1484.29 | 1.73398 | ||||||||
\(857\) | 299.131i | 0.349044i | 0.984653 | + | 0.174522i | \(0.0558380\pi\) | ||||
−0.984653 | + | 0.174522i | \(0.944162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1095.72 | 1.27558 | 0.637788 | − | 0.770212i | \(-0.279850\pi\) | ||||
0.637788 | + | 0.770212i | \(0.279850\pi\) | |||||||
\(860\) | − 909.550i | − 1.05762i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1449.92 | −1.68204 | ||||||||
\(863\) | 1221.95i | 1.41593i | 0.706247 | + | 0.707965i | \(0.250387\pi\) | ||||
−0.706247 | + | 0.707965i | \(0.749613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −426.658 | −0.493246 | ||||||||
\(866\) | − 2044.57i | − 2.36094i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3891.69 | 4.48352 | ||||||||
\(869\) | 522.216i | 0.600939i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 261.982 | 0.300782 | ||||||||
\(872\) | − 254.205i | − 0.291520i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 277.947 | 0.318018 | ||||||||
\(875\) | 80.0767i | 0.0915162i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 766.399 | 0.873887 | 0.436944 | − | 0.899489i | \(-0.356061\pi\) | ||||
0.436944 | + | 0.899489i | \(0.356061\pi\) | |||||||
\(878\) | 2425.20i | 2.76218i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −408.364 | −0.464050 | ||||||||
\(881\) | − 310.097i | − 0.351983i | −0.984392 | − | 0.175992i | \(-0.943687\pi\) | ||||
0.984392 | − | 0.175992i | \(-0.0563132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −122.236 | −0.138433 | −0.0692165 | − | 0.997602i | \(-0.522050\pi\) | ||||
−0.0692165 | + | 0.997602i | \(0.522050\pi\) | |||||||
\(884\) | − 1119.04i | − 1.26588i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1355.37 | −1.52976 | ||||||||
\(887\) | 265.444i | 0.299261i | 0.988742 | + | 0.149630i | \(0.0478084\pi\) | ||||
−0.988742 | + | 0.149630i | \(0.952192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −272.386 | −0.306396 | ||||||||
\(890\) | − 876.980i | − 0.985370i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1699.89 | 1.90571 | ||||||||
\(893\) | − 253.343i | − 0.283698i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 129.917 | 0.145158 | ||||||||
\(896\) | − 507.981i | − 0.566944i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2137.14 | 2.37988 | ||||||||
\(899\) | − 2621.54i | − 2.91606i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 161.754 | 0.179527 | ||||||||
\(902\) | 326.379i | 0.361840i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −402.658 | −0.445418 | ||||||||
\(905\) | 364.302i | 0.402544i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 672.622 | 0.741590 | 0.370795 | − | 0.928715i | \(-0.379085\pi\) | ||||
0.370795 | + | 0.928715i | \(0.379085\pi\) | |||||||
\(908\) | − 3786.49i | − 4.17015i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −573.579 | −0.630306 | ||||||||
\(911\) | 1402.48i | 1.53949i | 0.638350 | + | 0.769746i | \(0.279617\pi\) | ||||
−0.638350 | + | 0.769746i | \(0.720383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 429.421 | 0.470340 | ||||||||
\(914\) | − 615.586i | − 0.673507i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 254.544 | 0.277886 | ||||||||
\(917\) | 601.208i | 0.655625i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −338.255 | −0.368068 | −0.184034 | − | 0.982920i | \(-0.558916\pi\) | ||||
−0.184034 | + | 0.982920i | \(0.558916\pi\) | |||||||
\(920\) | 523.240i | 0.568739i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1089.58 | −1.18176 | ||||||||
\(923\) | − 909.811i | − 0.985711i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −332.302 | −0.359246 | ||||||||
\(926\) | 2172.96i | 2.34661i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2028.25 | 2.18562 | ||||||||
\(929\) | 148.207i | 0.159533i | 0.996814 | + | 0.0797667i | \(0.0254175\pi\) | ||||
−0.996814 | + | 0.0797667i | \(0.974582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.5352 | 0.0156125 | ||||||||
\(932\) | 3323.10i | 3.56556i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2276.52 | −2.43738 | ||||||||
\(935\) | − 148.443i | − 0.158763i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1416.72 | −1.51197 | −0.755987 | − | 0.654587i | \(-0.772843\pi\) | ||||
−0.755987 | + | 0.654587i | \(0.772843\pi\) | |||||||
\(938\) | − 698.100i | − 0.744243i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 835.201 | 0.888512 | ||||||||
\(941\) | − 1398.92i | − 1.48663i | −0.668939 | − | 0.743317i | \(-0.733251\pi\) | ||||
0.668939 | − | 0.743317i | \(-0.266749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 198.342 | 0.210330 | ||||||||
\(944\) | − 846.338i | − 0.896544i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 864.228 | 0.913560 | ||||||||
\(947\) | 1050.57i | 1.10937i | 0.832060 | + | 0.554686i | \(0.187161\pi\) | ||||
−0.832060 | + | 0.554686i | \(0.812839\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 591.868 | 0.623675 | ||||||||
\(950\) | 115.432i | 0.121507i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1702.74 | −1.78859 | ||||||||
\(953\) | − 551.928i | − 0.579148i | −0.957156 | − | 0.289574i | \(-0.906486\pi\) | ||||
0.957156 | − | 0.289574i | \(-0.0935136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −223.745 | −0.234288 | ||||||||
\(956\) | 2533.39i | 2.64999i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 481.315 | 0.502417 | ||||||||
\(959\) | − 111.686i | − 0.116461i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2434.61 | 2.53342 | ||||||||
\(962\) | − 2380.24i | − 2.47426i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2092.79 | 2.17094 | ||||||||
\(965\) | 138.401i | 0.143420i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −357.093 | −0.369279 | −0.184639 | − | 0.982806i | \(-0.559112\pi\) | ||||
−0.184639 | + | 0.982806i | \(0.559112\pi\) | |||||||
\(968\) | 1779.26i | 1.83807i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.80711 | 0.00907950 | ||||||||
\(971\) | 308.206i | 0.317411i | 0.987326 | + | 0.158705i | \(0.0507320\pi\) | ||||
−0.987326 | + | 0.158705i | \(0.949268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 485.903 | 0.499387 | ||||||||
\(974\) | − 152.592i | − 0.156665i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1200.45 | −1.22997 | ||||||||
\(977\) | 253.280i | 0.259243i | 0.991564 | + | 0.129621i | \(0.0413762\pi\) | ||||
−0.991564 | + | 0.129621i | \(0.958624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 583.132 | 0.595640 | ||||||||
\(980\) | 47.9187i | 0.0488966i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 652.732 | 0.664697 | ||||||||
\(983\) | 1068.73i | 1.08722i | 0.839339 | + | 0.543609i | \(0.182942\pi\) | ||||
−0.839339 | + | 0.543609i | \(0.817058\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.6313 | 0.0564785 | ||||||||
\(986\) | 2008.68i | 2.03720i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −578.614 | −0.585641 | ||||||||
\(989\) | − 525.194i | − 0.531035i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 280.631 | 0.283179 | 0.141590 | − | 0.989925i | \(-0.454779\pi\) | ||||
0.141590 | + | 0.989925i | \(0.454779\pi\) | |||||||
\(992\) | 2627.14i | 2.64833i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2424.37 | −2.43900 | ||||||||
\(995\) | 349.925i | 0.351683i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −356.574 | −0.357647 | −0.178824 | − | 0.983881i | \(-0.557229\pi\) | ||||
−0.178824 | + | 0.983881i | \(0.557229\pi\) | |||||||
\(998\) | 142.712i | 0.142998i | ||||||||
\(999\) | 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 | 45.3.c.a.26.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 45.3.c.a.26.4 | yes | 4 | |
4.3 | odd | 2 | 720.3.l.a.161.1 | 4 | |||
5.2 | odd | 4 | 225.3.d.b.224.8 | 8 | |||
5.3 | odd | 4 | 225.3.d.b.224.1 | 8 | |||
5.4 | even | 2 | 225.3.c.c.26.4 | 4 | |||
8.3 | odd | 2 | 2880.3.l.c.1601.3 | 4 | |||
8.5 | even | 2 | 2880.3.l.g.1601.4 | 4 | |||
9.2 | odd | 6 | 405.3.i.d.296.4 | 8 | |||
9.4 | even | 3 | 405.3.i.d.26.4 | 8 | |||
9.5 | odd | 6 | 405.3.i.d.26.1 | 8 | |||
9.7 | even | 3 | 405.3.i.d.296.1 | 8 | |||
12.11 | even | 2 | 720.3.l.a.161.3 | 4 | |||
15.2 | even | 4 | 225.3.d.b.224.2 | 8 | |||
15.8 | even | 4 | 225.3.d.b.224.7 | 8 | |||
15.14 | odd | 2 | 225.3.c.c.26.1 | 4 | |||
20.3 | even | 4 | 3600.3.c.i.449.8 | 8 | |||
20.7 | even | 4 | 3600.3.c.i.449.2 | 8 | |||
20.19 | odd | 2 | 3600.3.l.v.1601.4 | 4 | |||
24.5 | odd | 2 | 2880.3.l.g.1601.2 | 4 | |||
24.11 | even | 2 | 2880.3.l.c.1601.1 | 4 | |||
60.23 | odd | 4 | 3600.3.c.i.449.7 | 8 | |||
60.47 | odd | 4 | 3600.3.c.i.449.1 | 8 | |||
60.59 | even | 2 | 3600.3.l.v.1601.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.c.a.26.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
45.3.c.a.26.4 | yes | 4 | 3.2 | odd | 2 | inner | |
225.3.c.c.26.1 | 4 | 15.14 | odd | 2 | |||
225.3.c.c.26.4 | 4 | 5.4 | even | 2 | |||
225.3.d.b.224.1 | 8 | 5.3 | odd | 4 | |||
225.3.d.b.224.2 | 8 | 15.2 | even | 4 | |||
225.3.d.b.224.7 | 8 | 15.8 | even | 4 | |||
225.3.d.b.224.8 | 8 | 5.2 | odd | 4 | |||
405.3.i.d.26.1 | 8 | 9.5 | odd | 6 | |||
405.3.i.d.26.4 | 8 | 9.4 | even | 3 | |||
405.3.i.d.296.1 | 8 | 9.7 | even | 3 | |||
405.3.i.d.296.4 | 8 | 9.2 | odd | 6 | |||
720.3.l.a.161.1 | 4 | 4.3 | odd | 2 | |||
720.3.l.a.161.3 | 4 | 12.11 | even | 2 | |||
2880.3.l.c.1601.1 | 4 | 24.11 | even | 2 | |||
2880.3.l.c.1601.3 | 4 | 8.3 | odd | 2 | |||
2880.3.l.g.1601.2 | 4 | 24.5 | odd | 2 | |||
2880.3.l.g.1601.4 | 4 | 8.5 | even | 2 | |||
3600.3.c.i.449.1 | 8 | 60.47 | odd | 4 | |||
3600.3.c.i.449.2 | 8 | 20.7 | even | 4 | |||
3600.3.c.i.449.7 | 8 | 60.23 | odd | 4 | |||
3600.3.c.i.449.8 | 8 | 20.3 | even | 4 | |||
3600.3.l.v.1601.3 | 4 | 60.59 | even | 2 | |||
3600.3.l.v.1601.4 | 4 | 20.19 | odd | 2 |