Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,3,Mod(728,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.728");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8638112719\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 728.5 | ||
Character | \(\chi\) | \(=\) | 729.728 |
Dual form | 729.3.b.a.728.26 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.62787i | − 1.31394i | −0.753918 | − | 0.656968i | \(-0.771839\pi\) | ||||
0.753918 | − | 0.656968i | \(-0.228161\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.90572 | −0.726429 | ||||||||
\(5\) | − 6.25111i | − 1.25022i | −0.780536 | − | 0.625111i | \(-0.785054\pi\) | ||||
0.780536 | − | 0.625111i | \(-0.214946\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.11762 | −1.15966 | −0.579830 | − | 0.814737i | \(-0.696881\pi\) | ||||
−0.579830 | + | 0.814737i | \(0.696881\pi\) | |||||||
\(8\) | − 2.87564i | − 0.359455i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −16.4271 | −1.64271 | ||||||||
\(11\) | − 8.11386i | − 0.737623i | −0.929504 | − | 0.368812i | \(-0.879765\pi\) | ||||
0.929504 | − | 0.368812i | \(-0.120235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.70958 | 0.746891 | 0.373445 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373445 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(14\) | 21.3321i | 1.52372i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.1797 | −1.19873 | ||||||||
\(17\) | − 15.0276i | − 0.883977i | −0.897021 | − | 0.441988i | \(-0.854273\pi\) | ||||
0.897021 | − | 0.441988i | \(-0.145727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.8645 | −0.940238 | −0.470119 | − | 0.882603i | \(-0.655789\pi\) | ||||
−0.470119 | + | 0.882603i | \(0.655789\pi\) | |||||||
\(20\) | 18.1640i | 0.908198i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −21.3222 | −0.969190 | ||||||||
\(23\) | 26.3335i | 1.14493i | 0.819928 | + | 0.572467i | \(0.194013\pi\) | ||||
−0.819928 | + | 0.572467i | \(0.805987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.0764 | −0.563055 | ||||||||
\(26\) | − 25.5156i | − 0.981367i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 23.5875 | 0.842411 | ||||||||
\(29\) | − 15.1718i | − 0.523166i | −0.965181 | − | 0.261583i | \(-0.915756\pi\) | ||||
0.965181 | − | 0.261583i | \(-0.0842445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.7337 | 1.05593 | 0.527963 | − | 0.849267i | \(-0.322956\pi\) | ||||
0.527963 | + | 0.849267i | \(0.322956\pi\) | |||||||
\(32\) | 38.8992i | 1.21560i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −39.4906 | −1.16149 | ||||||||
\(35\) | 50.7442i | 1.44983i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 31.6193 | 0.854575 | 0.427287 | − | 0.904116i | \(-0.359469\pi\) | ||||
0.427287 | + | 0.904116i | \(0.359469\pi\) | |||||||
\(38\) | 46.9457i | 1.23541i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17.9759 | −0.449398 | ||||||||
\(41\) | 16.5200i | 0.402928i | 0.979496 | + | 0.201464i | \(0.0645698\pi\) | ||||
−0.979496 | + | 0.201464i | \(0.935430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −83.8240 | −1.94940 | −0.974698 | − | 0.223526i | \(-0.928243\pi\) | ||||
−0.974698 | + | 0.223526i | \(0.928243\pi\) | |||||||
\(44\) | 23.5766i | 0.535831i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 69.2010 | 1.50437 | ||||||||
\(47\) | − 13.1702i | − 0.280216i | −0.990136 | − | 0.140108i | \(-0.955255\pi\) | ||||
0.990136 | − | 0.140108i | \(-0.0447450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.8958 | 0.344813 | ||||||||
\(50\) | 36.9909i | 0.739819i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −28.2133 | −0.542564 | ||||||||
\(53\) | 25.7140i | 0.485169i | 0.970130 | + | 0.242585i | \(0.0779952\pi\) | ||||
−0.970130 | + | 0.242585i | \(0.922005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.7206 | −0.922193 | ||||||||
\(56\) | 23.3433i | 0.416845i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −39.8696 | −0.687407 | ||||||||
\(59\) | 22.7110i | 0.384933i | 0.981304 | + | 0.192466i | \(0.0616486\pi\) | ||||
−0.981304 | + | 0.192466i | \(0.938351\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34.0883 | 0.558824 | 0.279412 | − | 0.960171i | \(-0.409860\pi\) | ||||
0.279412 | + | 0.960171i | \(0.409860\pi\) | |||||||
\(62\) | − 86.0200i | − 1.38742i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 25.5035 | 0.398492 | ||||||||
\(65\) | − 60.6957i | − 0.933780i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.10443 | 0.120962 | 0.0604808 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604808 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(68\) | 43.6660i | 0.642147i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 133.349 | 1.90499 | ||||||||
\(71\) | 41.2871i | 0.581508i | 0.956798 | + | 0.290754i | \(0.0939062\pi\) | ||||
−0.956798 | + | 0.290754i | \(0.906094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −80.8091 | −1.10697 | −0.553487 | − | 0.832858i | \(-0.686703\pi\) | ||||
−0.553487 | + | 0.832858i | \(0.686703\pi\) | |||||||
\(74\) | − 83.0914i | − 1.12286i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 51.9093 | 0.683017 | ||||||||
\(77\) | 65.8652i | 0.855393i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −27.6316 | −0.349767 | −0.174884 | − | 0.984589i | \(-0.555955\pi\) | ||||
−0.174884 | + | 0.984589i | \(0.555955\pi\) | |||||||
\(80\) | 119.894i | 1.49868i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 43.4126 | 0.529421 | ||||||||
\(83\) | 17.5898i | 0.211925i | 0.994370 | + | 0.105963i | \(0.0337924\pi\) | ||||
−0.994370 | + | 0.105963i | \(0.966208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −93.9392 | −1.10517 | ||||||||
\(86\) | 220.279i | 2.56138i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −23.3325 | −0.265142 | ||||||||
\(89\) | − 28.2885i | − 0.317849i | −0.987291 | − | 0.158924i | \(-0.949197\pi\) | ||||
0.987291 | − | 0.158924i | \(-0.0508026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −78.8187 | −0.866140 | ||||||||
\(92\) | − 76.5176i | − 0.831713i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −34.6095 | −0.368187 | ||||||||
\(95\) | 111.673i | 1.17551i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 168.631 | 1.73846 | 0.869232 | − | 0.494405i | \(-0.164614\pi\) | ||||
0.869232 | + | 0.494405i | \(0.164614\pi\) | |||||||
\(98\) | − 44.4001i | − 0.453062i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 40.9020 | 0.409020 | ||||||||
\(101\) | 69.8283i | 0.691369i | 0.938351 | + | 0.345684i | \(0.112353\pi\) | ||||
−0.938351 | + | 0.345684i | \(0.887647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 69.8627 | 0.678279 | 0.339139 | − | 0.940736i | \(-0.389864\pi\) | ||||
0.339139 | + | 0.940736i | \(0.389864\pi\) | |||||||
\(104\) | − 27.9212i | − 0.268473i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 67.5730 | 0.637481 | ||||||||
\(107\) | − 121.432i | − 1.13488i | −0.823416 | − | 0.567438i | \(-0.807935\pi\) | ||||
0.823416 | − | 0.567438i | \(-0.192065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −119.633 | −1.09755 | −0.548777 | − | 0.835969i | \(-0.684907\pi\) | ||||
−0.548777 | + | 0.835969i | \(0.684907\pi\) | |||||||
\(110\) | 133.287i | 1.21170i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 155.693 | 1.39012 | ||||||||
\(113\) | − 124.364i | − 1.10056i | −0.834979 | − | 0.550282i | \(-0.814520\pi\) | ||||
0.834979 | − | 0.550282i | \(-0.185480\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 164.613 | 1.43142 | ||||||||
\(116\) | 44.0850i | 0.380043i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 59.6817 | 0.505777 | ||||||||
\(119\) | 121.988i | 1.02511i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 55.1653 | 0.455912 | ||||||||
\(122\) | − 89.5797i | − 0.734260i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −95.1149 | −0.767055 | ||||||||
\(125\) | − 68.2848i | − 0.546278i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −117.460 | −0.924882 | −0.462441 | − | 0.886650i | \(-0.653026\pi\) | ||||
−0.462441 | + | 0.886650i | \(0.653026\pi\) | |||||||
\(128\) | 88.5769i | 0.692007i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −159.501 | −1.22693 | ||||||||
\(131\) | 4.71281i | 0.0359756i | 0.999838 | + | 0.0179878i | \(0.00572601\pi\) | ||||
−0.999838 | + | 0.0179878i | \(0.994274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 145.018 | 1.09036 | ||||||||
\(134\) | − 21.2974i | − 0.158936i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −43.2139 | −0.317749 | ||||||||
\(137\) | − 220.790i | − 1.61161i | −0.592183 | − | 0.805804i | \(-0.701734\pi\) | ||||
0.592183 | − | 0.805804i | \(-0.298266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −35.7655 | −0.257306 | −0.128653 | − | 0.991690i | \(-0.541065\pi\) | ||||
−0.128653 | + | 0.991690i | \(0.541065\pi\) | |||||||
\(140\) | − 147.448i | − 1.05320i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 108.497 | 0.764065 | ||||||||
\(143\) | − 78.7822i | − 0.550924i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −94.8406 | −0.654073 | ||||||||
\(146\) | 212.356i | 1.45449i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −91.8766 | −0.620788 | ||||||||
\(149\) | − 167.736i | − 1.12575i | −0.826543 | − | 0.562873i | \(-0.809696\pi\) | ||||
0.826543 | − | 0.562873i | \(-0.190304\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −83.7181 | −0.554425 | −0.277212 | − | 0.960809i | \(-0.589411\pi\) | ||||
−0.277212 | + | 0.960809i | \(0.589411\pi\) | |||||||
\(152\) | 51.3719i | 0.337973i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 173.086 | 1.12393 | ||||||||
\(155\) | − 204.622i | − 1.32014i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −74.4442 | −0.474167 | −0.237084 | − | 0.971489i | \(-0.576192\pi\) | ||||
−0.237084 | + | 0.971489i | \(0.576192\pi\) | |||||||
\(158\) | 72.6124i | 0.459572i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 243.163 | 1.51977 | ||||||||
\(161\) | − 213.765i | − 1.32773i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 254.830 | 1.56337 | 0.781687 | − | 0.623670i | \(-0.214359\pi\) | ||||
0.781687 | + | 0.623670i | \(0.214359\pi\) | |||||||
\(164\) | − 48.0025i | − 0.292698i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 46.2238 | 0.278456 | ||||||||
\(167\) | 158.599i | 0.949697i | 0.880067 | + | 0.474849i | \(0.157497\pi\) | ||||
−0.880067 | + | 0.474849i | \(0.842503\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −74.7240 | −0.442154 | ||||||||
\(170\) | 246.860i | 1.45212i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 243.569 | 1.41610 | ||||||||
\(173\) | − 298.081i | − 1.72301i | −0.507747 | − | 0.861506i | \(-0.669521\pi\) | ||||
0.507747 | − | 0.861506i | \(-0.330479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 114.267 | 0.652953 | ||||||||
\(176\) | 155.621i | 0.884211i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −74.3386 | −0.417633 | ||||||||
\(179\) | 29.3291i | 0.163850i | 0.996639 | + | 0.0819248i | \(0.0261067\pi\) | ||||
−0.996639 | + | 0.0819248i | \(0.973893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 83.4039 | 0.460795 | 0.230397 | − | 0.973097i | \(-0.425997\pi\) | ||||
0.230397 | + | 0.973097i | \(0.425997\pi\) | |||||||
\(182\) | 207.126i | 1.13805i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 75.7255 | 0.411552 | ||||||||
\(185\) | − 197.655i | − 1.06841i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −121.932 | −0.652042 | ||||||||
\(188\) | 38.2688i | 0.203557i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 293.463 | 1.54454 | ||||||||
\(191\) | − 156.949i | − 0.821722i | −0.911698 | − | 0.410861i | \(-0.865228\pi\) | ||||
0.911698 | − | 0.410861i | \(-0.134772\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −41.4693 | −0.214867 | −0.107433 | − | 0.994212i | \(-0.534263\pi\) | ||||
−0.107433 | + | 0.994212i | \(0.534263\pi\) | |||||||
\(194\) | − 443.141i | − 2.28423i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −49.0945 | −0.250482 | ||||||||
\(197\) | 210.660i | 1.06934i | 0.845062 | + | 0.534669i | \(0.179564\pi\) | ||||
−0.845062 | + | 0.534669i | \(0.820436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −175.531 | −0.882065 | −0.441032 | − | 0.897491i | \(-0.645388\pi\) | ||||
−0.441032 | + | 0.897491i | \(0.645388\pi\) | |||||||
\(200\) | 40.4785i | 0.202393i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 183.500 | 0.908415 | ||||||||
\(203\) | 123.159i | 0.606695i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 103.269 | 0.503749 | ||||||||
\(206\) | − 183.590i | − 0.891215i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −186.227 | −0.895320 | ||||||||
\(209\) | 144.950i | 0.693542i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −260.854 | −1.23628 | −0.618138 | − | 0.786070i | \(-0.712113\pi\) | ||||
−0.618138 | + | 0.786070i | \(0.712113\pi\) | |||||||
\(212\) | − 74.7175i | − 0.352441i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −319.107 | −1.49115 | ||||||||
\(215\) | 523.993i | 2.43718i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −265.720 | −1.22452 | ||||||||
\(218\) | 314.382i | 1.44212i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 147.380 | 0.669908 | ||||||||
\(221\) | − 145.912i | − 0.660234i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −389.217 | −1.74537 | −0.872684 | − | 0.488286i | \(-0.837622\pi\) | ||||
−0.872684 | + | 0.488286i | \(0.837622\pi\) | |||||||
\(224\) | − 315.769i | − 1.40968i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −326.812 | −1.44607 | ||||||||
\(227\) | − 348.432i | − 1.53494i | −0.641083 | − | 0.767471i | \(-0.721515\pi\) | ||||
0.641083 | − | 0.767471i | \(-0.278485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −364.524 | −1.59181 | −0.795904 | − | 0.605423i | \(-0.793004\pi\) | ||||
−0.795904 | + | 0.605423i | \(0.793004\pi\) | |||||||
\(230\) | − 432.583i | − 1.88080i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −43.6286 | −0.188054 | ||||||||
\(233\) | 189.671i | 0.814037i | 0.913420 | + | 0.407018i | \(0.133431\pi\) | ||||
−0.913420 | + | 0.407018i | \(0.866569\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −82.3282 | −0.350333 | ||||||||
\(236\) | − 65.9918i | − 0.279626i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 320.570 | 1.34693 | ||||||||
\(239\) | − 306.099i | − 1.28075i | −0.768063 | − | 0.640374i | \(-0.778779\pi\) | ||||
0.768063 | − | 0.640374i | \(-0.221221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −294.905 | −1.22367 | −0.611837 | − | 0.790984i | \(-0.709569\pi\) | ||||
−0.611837 | + | 0.790984i | \(0.709569\pi\) | |||||||
\(242\) | − 144.967i | − 0.599039i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −99.0509 | −0.405946 | ||||||||
\(245\) | − 105.618i | − 0.431092i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −173.457 | −0.702255 | ||||||||
\(248\) | − 94.1302i | − 0.379557i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −179.444 | −0.717775 | ||||||||
\(251\) | − 182.909i | − 0.728723i | −0.931258 | − | 0.364361i | \(-0.881287\pi\) | ||||
0.931258 | − | 0.364361i | \(-0.118713\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 213.666 | 0.844530 | ||||||||
\(254\) | 308.670i | 1.21524i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 334.783 | 1.30775 | ||||||||
\(257\) | − 268.364i | − 1.04422i | −0.852879 | − | 0.522109i | \(-0.825145\pi\) | ||||
0.852879 | − | 0.522109i | \(-0.174855\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −256.673 | −0.991016 | ||||||||
\(260\) | 176.364i | 0.678325i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.3847 | 0.0472697 | ||||||||
\(263\) | − 351.976i | − 1.33831i | −0.743122 | − | 0.669156i | \(-0.766656\pi\) | ||||
0.743122 | − | 0.669156i | \(-0.233344\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 160.741 | 0.606569 | ||||||||
\(266\) | − 381.088i | − 1.43266i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.5492 | −0.0878701 | ||||||||
\(269\) | − 164.243i | − 0.610570i | −0.952261 | − | 0.305285i | \(-0.901248\pi\) | ||||
0.952261 | − | 0.305285i | \(-0.0987518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −128.850 | −0.475462 | −0.237731 | − | 0.971331i | \(-0.576404\pi\) | ||||
−0.237731 | + | 0.971331i | \(0.576404\pi\) | |||||||
\(272\) | 288.225i | 1.05965i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −580.209 | −2.11755 | ||||||||
\(275\) | 114.214i | 0.415323i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 150.218 | 0.542303 | 0.271152 | − | 0.962537i | \(-0.412596\pi\) | ||||
0.271152 | + | 0.962537i | \(0.412596\pi\) | |||||||
\(278\) | 93.9872i | 0.338083i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 145.922 | 0.521149 | ||||||||
\(281\) | 460.999i | 1.64057i | 0.571958 | + | 0.820283i | \(0.306184\pi\) | ||||
−0.571958 | + | 0.820283i | \(0.693816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −68.8575 | −0.243313 | −0.121656 | − | 0.992572i | \(-0.538821\pi\) | ||||
−0.121656 | + | 0.992572i | \(0.538821\pi\) | |||||||
\(284\) | − 119.969i | − 0.422425i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −207.030 | −0.723880 | ||||||||
\(287\) | − 134.103i | − 0.467259i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 63.1711 | 0.218585 | ||||||||
\(290\) | 249.229i | 0.859411i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 234.808 | 0.804139 | ||||||||
\(293\) | 510.766i | 1.74323i | 0.490191 | + | 0.871615i | \(0.336927\pi\) | ||||
−0.490191 | + | 0.871615i | \(0.663073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 141.969 | 0.481251 | ||||||||
\(296\) | − 90.9255i | − 0.307181i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −440.789 | −1.47916 | ||||||||
\(299\) | 255.687i | 0.855141i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 680.452 | 2.26064 | ||||||||
\(302\) | 220.001i | 0.728479i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 342.636 | 1.12709 | ||||||||
\(305\) | − 213.090i | − 0.698655i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 52.6035 | 0.171347 | 0.0856734 | − | 0.996323i | \(-0.472696\pi\) | ||||
0.0856734 | + | 0.996323i | \(0.472696\pi\) | |||||||
\(308\) | − 191.386i | − 0.621382i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −537.721 | −1.73458 | ||||||||
\(311\) | − 354.825i | − 1.14092i | −0.821326 | − | 0.570459i | \(-0.806765\pi\) | ||||
0.821326 | − | 0.570459i | \(-0.193235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 168.249 | 0.537536 | 0.268768 | − | 0.963205i | \(-0.413384\pi\) | ||||
0.268768 | + | 0.963205i | \(0.413384\pi\) | |||||||
\(314\) | 195.630i | 0.623026i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 80.2897 | 0.254081 | ||||||||
\(317\) | − 509.988i | − 1.60880i | −0.594091 | − | 0.804398i | \(-0.702488\pi\) | ||||
0.594091 | − | 0.804398i | \(-0.297512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −123.102 | −0.385899 | ||||||||
\(320\) | − 159.425i | − 0.498204i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −561.748 | −1.74456 | ||||||||
\(323\) | 268.461i | 0.831149i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −136.676 | −0.420541 | ||||||||
\(326\) | − 669.661i | − 2.05418i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 47.5056 | 0.144834 | ||||||||
\(329\) | 106.911i | 0.324956i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −339.342 | −1.02520 | −0.512601 | − | 0.858627i | \(-0.671318\pi\) | ||||
−0.512601 | + | 0.858627i | \(0.671318\pi\) | |||||||
\(332\) | − 51.1110i | − 0.153949i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 416.779 | 1.24784 | ||||||||
\(335\) | − 50.6617i | − 0.151229i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −68.2380 | −0.202487 | −0.101243 | − | 0.994862i | \(-0.532282\pi\) | ||||
−0.101243 | + | 0.994862i | \(0.532282\pi\) | |||||||
\(338\) | 196.365i | 0.580962i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 272.961 | 0.802826 | ||||||||
\(341\) | − 265.597i | − 0.778876i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 260.610 | 0.759795 | ||||||||
\(344\) | 241.047i | 0.700719i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −783.320 | −2.26393 | ||||||||
\(347\) | − 173.098i | − 0.498840i | −0.968395 | − | 0.249420i | \(-0.919760\pi\) | ||||
0.968395 | − | 0.249420i | \(-0.0802400\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 459.582 | 1.31685 | 0.658427 | − | 0.752645i | \(-0.271222\pi\) | ||||
0.658427 | + | 0.752645i | \(0.271222\pi\) | |||||||
\(350\) | − 300.278i | − 0.857939i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 315.623 | 0.896655 | ||||||||
\(353\) | 402.250i | 1.13952i | 0.821812 | + | 0.569759i | \(0.192964\pi\) | ||||
−0.821812 | + | 0.569759i | \(0.807036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 258.090 | 0.727015 | ||||||||
\(356\) | 82.1984i | 0.230895i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 77.0731 | 0.215288 | ||||||||
\(359\) | 227.763i | 0.634437i | 0.948352 | + | 0.317219i | \(0.102749\pi\) | ||||
−0.948352 | + | 0.317219i | \(0.897251\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −41.8587 | −0.115952 | ||||||||
\(362\) | − 219.175i | − 0.605455i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 229.025 | 0.629190 | ||||||||
\(365\) | 505.147i | 1.38396i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −235.467 | −0.641599 | −0.320800 | − | 0.947147i | \(-0.603952\pi\) | ||||
−0.320800 | + | 0.947147i | \(0.603952\pi\) | |||||||
\(368\) | − 505.067i | − 1.37247i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −519.413 | −1.40382 | ||||||||
\(371\) | − 208.736i | − 0.562631i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 652.752 | 1.75000 | 0.875002 | − | 0.484119i | \(-0.160860\pi\) | ||||
0.875002 | + | 0.484119i | \(0.160860\pi\) | |||||||
\(374\) | 320.421i | 0.856742i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −37.8726 | −0.100725 | ||||||||
\(377\) | − 147.312i | − 0.390748i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 625.053 | 1.64922 | 0.824608 | − | 0.565705i | \(-0.191396\pi\) | ||||
0.824608 | + | 0.565705i | \(0.191396\pi\) | |||||||
\(380\) | − 324.490i | − 0.853922i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −412.442 | −1.07969 | ||||||||
\(383\) | − 106.540i | − 0.278171i | −0.990280 | − | 0.139086i | \(-0.955584\pi\) | ||||
0.990280 | − | 0.139086i | \(-0.0444163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 411.731 | 1.06943 | ||||||||
\(386\) | 108.976i | 0.282321i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −489.994 | −1.26287 | ||||||||
\(389\) | − 593.632i | − 1.52605i | −0.646371 | − | 0.763023i | \(-0.723714\pi\) | ||||
0.646371 | − | 0.763023i | \(-0.276286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 395.729 | 1.01209 | ||||||||
\(392\) | − 48.5862i | − 0.123944i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 553.587 | 1.40504 | ||||||||
\(395\) | 172.728i | 0.437287i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 374.819 | 0.944129 | 0.472064 | − | 0.881564i | \(-0.343509\pi\) | ||||
0.472064 | + | 0.881564i | \(0.343509\pi\) | |||||||
\(398\) | 461.273i | 1.15898i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 269.980 | 0.674951 | ||||||||
\(401\) | − 274.406i | − 0.684303i | −0.939645 | − | 0.342152i | \(-0.888844\pi\) | ||||
0.939645 | − | 0.342152i | \(-0.111156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 317.831 | 0.788661 | ||||||||
\(404\) | − 202.901i | − 0.502231i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 323.646 | 0.797158 | ||||||||
\(407\) | − 256.554i | − 0.630354i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −551.474 | −1.34835 | −0.674174 | − | 0.738573i | \(-0.735500\pi\) | ||||
−0.674174 | + | 0.738573i | \(0.735500\pi\) | |||||||
\(410\) | − 271.377i | − 0.661894i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −203.001 | −0.492722 | ||||||||
\(413\) | − 184.360i | − 0.446391i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 109.956 | 0.264954 | ||||||||
\(416\) | 377.695i | 0.907921i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 380.911 | 0.911270 | ||||||||
\(419\) | − 87.5877i | − 0.209040i | −0.994523 | − | 0.104520i | \(-0.966669\pi\) | ||||
0.994523 | − | 0.104520i | \(-0.0333306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 296.259 | 0.703704 | 0.351852 | − | 0.936056i | \(-0.385552\pi\) | ||||
0.351852 | + | 0.936056i | \(0.385552\pi\) | |||||||
\(422\) | 685.491i | 1.62439i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 73.9440 | 0.174396 | ||||||||
\(425\) | 211.534i | 0.497728i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −276.716 | −0.648047 | ||||||||
\(428\) | 352.846i | 0.824407i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1376.99 | 3.20230 | ||||||||
\(431\) | 586.175i | 1.36003i | 0.733196 | + | 0.680017i | \(0.238028\pi\) | ||||
−0.733196 | + | 0.680017i | \(0.761972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 415.367 | 0.959277 | 0.479639 | − | 0.877466i | \(-0.340768\pi\) | ||||
0.479639 | + | 0.877466i | \(0.340768\pi\) | |||||||
\(434\) | 698.278i | 1.60894i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 347.621 | 0.797296 | ||||||||
\(437\) | − 470.435i | − 1.07651i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 334.358 | 0.761636 | 0.380818 | − | 0.924650i | \(-0.375642\pi\) | ||||
0.380818 | + | 0.924650i | \(0.375642\pi\) | |||||||
\(440\) | 145.854i | 0.331486i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −383.438 | −0.867506 | ||||||||
\(443\) | 451.642i | 1.01951i | 0.860320 | + | 0.509754i | \(0.170263\pi\) | ||||
−0.860320 | + | 0.509754i | \(0.829737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −176.835 | −0.397381 | ||||||||
\(446\) | 1022.81i | 2.29330i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −207.028 | −0.462116 | ||||||||
\(449\) | − 191.013i | − 0.425420i | −0.977115 | − | 0.212710i | \(-0.931771\pi\) | ||||
0.977115 | − | 0.212710i | \(-0.0682289\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 134.041 | 0.297209 | ||||||||
\(452\) | 361.366i | 0.799482i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −915.635 | −2.01682 | ||||||||
\(455\) | 492.705i | 1.08287i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −385.752 | −0.844097 | −0.422049 | − | 0.906573i | \(-0.638689\pi\) | ||||
−0.422049 | + | 0.906573i | \(0.638689\pi\) | |||||||
\(458\) | 957.923i | 2.09153i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −478.320 | −1.03983 | ||||||||
\(461\) | − 433.054i | − 0.939379i | −0.882832 | − | 0.469689i | \(-0.844366\pi\) | ||||
0.882832 | − | 0.469689i | \(-0.155634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 552.856 | 1.19407 | 0.597037 | − | 0.802214i | \(-0.296345\pi\) | ||||
0.597037 | + | 0.802214i | \(0.296345\pi\) | |||||||
\(464\) | 290.990i | 0.627134i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 498.430 | 1.06959 | ||||||||
\(467\) | 215.313i | 0.461056i | 0.973066 | + | 0.230528i | \(0.0740454\pi\) | ||||
−0.973066 | + | 0.230528i | \(0.925955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −65.7887 | −0.140274 | ||||||||
\(470\) | 216.348i | 0.460315i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 65.3086 | 0.138366 | ||||||||
\(473\) | 680.136i | 1.43792i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 251.468 | 0.529406 | ||||||||
\(476\) | − 354.464i | − 0.744672i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −804.389 | −1.68282 | ||||||||
\(479\) | 226.490i | 0.472839i | 0.971651 | + | 0.236420i | \(0.0759740\pi\) | ||||
−0.971651 | + | 0.236420i | \(0.924026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 307.010 | 0.638274 | ||||||||
\(482\) | 774.974i | 1.60783i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −160.295 | −0.331188 | ||||||||
\(485\) | − 1054.13i | − 2.17347i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −443.130 | −0.909919 | −0.454959 | − | 0.890512i | \(-0.650346\pi\) | ||||
−0.454959 | + | 0.890512i | \(0.650346\pi\) | |||||||
\(488\) | − 98.0255i | − 0.200872i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −277.550 | −0.566428 | ||||||||
\(491\) | 667.456i | 1.35938i | 0.733499 | + | 0.679690i | \(0.237886\pi\) | ||||
−0.733499 | + | 0.679690i | \(0.762114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −227.996 | −0.462466 | ||||||||
\(494\) | 455.823i | 0.922719i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −627.822 | −1.26577 | ||||||||
\(497\) | − 335.153i | − 0.674352i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −57.4845 | −0.115199 | −0.0575997 | − | 0.998340i | \(-0.518345\pi\) | ||||
−0.0575997 | + | 0.998340i | \(0.518345\pi\) | |||||||
\(500\) | 198.416i | 0.396833i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −480.663 | −0.957495 | ||||||||
\(503\) | 488.672i | 0.971515i | 0.874094 | + | 0.485757i | \(0.161456\pi\) | ||||
−0.874094 | + | 0.485757i | \(0.838544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 436.504 | 0.864365 | ||||||||
\(506\) | − 561.487i | − 1.10966i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 341.305 | 0.671861 | ||||||||
\(509\) | 284.252i | 0.558452i | 0.960225 | + | 0.279226i | \(0.0900778\pi\) | ||||
−0.960225 | + | 0.279226i | \(0.909922\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 655.978 | 1.28371 | ||||||||
\(512\) | − 525.459i | − 1.02629i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −705.227 | −1.37204 | ||||||||
\(515\) | − 436.720i | − 0.847999i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −106.861 | −0.206694 | ||||||||
\(518\) | 674.505i | 1.30213i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −174.539 | −0.335651 | ||||||||
\(521\) | − 40.6415i | − 0.0780067i | −0.999239 | − | 0.0390033i | \(-0.987582\pi\) | ||||
0.999239 | − | 0.0390033i | \(-0.0124183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 349.901 | 0.669028 | 0.334514 | − | 0.942391i | \(-0.391428\pi\) | ||||
0.334514 | + | 0.942391i | \(0.391428\pi\) | |||||||
\(524\) | − 13.6941i | − 0.0261338i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −924.949 | −1.75846 | ||||||||
\(527\) | − 491.909i | − 0.933414i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −164.452 | −0.310873 | ||||||||
\(530\) | − 422.406i | − 0.796993i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −421.380 | −0.792067 | ||||||||
\(533\) | 160.403i | 0.300943i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −759.083 | −1.41885 | ||||||||
\(536\) | − 23.3054i | − 0.0434802i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −431.611 | −0.802251 | ||||||||
\(539\) | − 137.090i | − 0.254342i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 145.531 | 0.269003 | 0.134501 | − | 0.990913i | \(-0.457057\pi\) | ||||
0.134501 | + | 0.990913i | \(0.457057\pi\) | |||||||
\(542\) | 338.602i | 0.624727i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 584.562 | 1.07456 | ||||||||
\(545\) | 747.842i | 1.37219i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 486.029 | 0.888535 | 0.444268 | − | 0.895894i | \(-0.353464\pi\) | ||||
0.444268 | + | 0.895894i | \(0.353464\pi\) | |||||||
\(548\) | 641.554i | 1.17072i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 300.139 | 0.545708 | ||||||||
\(551\) | 271.037i | 0.491900i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 224.303 | 0.405611 | ||||||||
\(554\) | − 394.754i | − 0.712552i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 103.924 | 0.186914 | ||||||||
\(557\) | 3.26556i | 0.00586276i | 0.999996 | + | 0.00293138i | \(0.000933088\pi\) | ||||
−0.999996 | + | 0.00293138i | \(0.999067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −813.896 | −1.45599 | ||||||||
\(560\) | − 973.257i | − 1.73796i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1211.45 | 2.15560 | ||||||||
\(563\) | − 664.749i | − 1.18073i | −0.807138 | − | 0.590363i | \(-0.798985\pi\) | ||||
0.807138 | − | 0.590363i | \(-0.201015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −777.411 | −1.37595 | ||||||||
\(566\) | 180.949i | 0.319697i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 118.727 | 0.209026 | ||||||||
\(569\) | − 75.9350i | − 0.133453i | −0.997771 | − | 0.0667267i | \(-0.978744\pi\) | ||||
0.997771 | − | 0.0667267i | \(-0.0212556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −294.091 | −0.515046 | −0.257523 | − | 0.966272i | \(-0.582906\pi\) | ||||
−0.257523 | + | 0.966272i | \(0.582906\pi\) | |||||||
\(572\) | 228.919i | 0.400208i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −352.407 | −0.613949 | ||||||||
\(575\) | − 370.680i | − 0.644661i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1058.59 | 1.83465 | 0.917325 | − | 0.398139i | \(-0.130344\pi\) | ||||
0.917325 | + | 0.398139i | \(0.130344\pi\) | |||||||
\(578\) | − 166.006i | − 0.287207i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 275.580 | 0.475138 | ||||||||
\(581\) | − 142.787i | − 0.245761i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 208.639 | 0.357872 | ||||||||
\(584\) | 232.378i | 0.397907i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1342.23 | 2.29049 | ||||||||
\(587\) | − 138.902i | − 0.236630i | −0.992976 | − | 0.118315i | \(-0.962251\pi\) | ||||
0.992976 | − | 0.118315i | \(-0.0377493\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −584.772 | −0.992822 | ||||||||
\(590\) | − 373.077i | − 0.632334i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −606.447 | −1.02440 | ||||||||
\(593\) | 145.309i | 0.245040i | 0.992466 | + | 0.122520i | \(0.0390975\pi\) | ||||
−0.992466 | + | 0.122520i | \(0.960902\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 762.563 | 1.28162 | ||||||||
\(596\) | 487.394i | 0.817775i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 671.913 | 1.12360 | ||||||||
\(599\) | 22.9725i | 0.0383515i | 0.999816 | + | 0.0191757i | \(0.00610420\pi\) | ||||
−0.999816 | + | 0.0191757i | \(0.993896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −927.369 | −1.54304 | −0.771522 | − | 0.636203i | \(-0.780504\pi\) | ||||
−0.771522 | + | 0.636203i | \(0.780504\pi\) | |||||||
\(602\) | − 1788.14i | − 2.97033i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 243.261 | 0.402750 | ||||||||
\(605\) | − 344.844i | − 0.569991i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 523.972 | 0.863216 | 0.431608 | − | 0.902061i | \(-0.357946\pi\) | ||||
0.431608 | + | 0.902061i | \(0.357946\pi\) | |||||||
\(608\) | − 694.916i | − 1.14295i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −559.973 | −0.917988 | ||||||||
\(611\) | − 127.877i | − 0.209291i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 70.1697 | 0.114469 | 0.0572346 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572346 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(614\) | − 138.235i | − 0.225139i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 189.404 | 0.307475 | ||||||||
\(617\) | 664.561i | 1.07708i | 0.842598 | + | 0.538542i | \(0.181025\pi\) | ||||
−0.842598 | + | 0.538542i | \(0.818975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −970.754 | −1.56826 | −0.784131 | − | 0.620596i | \(-0.786891\pi\) | ||||
−0.784131 | + | 0.620596i | \(0.786891\pi\) | |||||||
\(620\) | 594.574i | 0.958990i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −932.436 | −1.49909 | ||||||||
\(623\) | 229.636i | 0.368596i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −778.765 | −1.24602 | ||||||||
\(626\) | − 442.136i | − 0.706288i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 216.314 | 0.344449 | ||||||||
\(629\) | − 475.162i | − 0.755424i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −189.318 | −0.300028 | −0.150014 | − | 0.988684i | \(-0.547932\pi\) | ||||
−0.150014 | + | 0.988684i | \(0.547932\pi\) | |||||||
\(632\) | 79.4585i | 0.125725i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1340.18 | −2.11386 | ||||||||
\(635\) | 734.255i | 1.15631i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 164.051 | 0.257538 | ||||||||
\(638\) | 323.496i | 0.507047i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 553.704 | 0.865163 | ||||||||
\(641\) | 692.705i | 1.08066i | 0.841452 | + | 0.540332i | \(0.181701\pi\) | ||||
−0.841452 | + | 0.540332i | \(0.818299\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1064.60 | 1.65568 | 0.827841 | − | 0.560962i | \(-0.189569\pi\) | ||||
0.827841 | + | 0.560962i | \(0.189569\pi\) | |||||||
\(644\) | 621.141i | 0.964505i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 705.481 | 1.09208 | ||||||||
\(647\) | 352.755i | 0.545217i | 0.962125 | + | 0.272608i | \(0.0878863\pi\) | ||||
−0.962125 | + | 0.272608i | \(0.912114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 184.274 | 0.283935 | ||||||||
\(650\) | 359.167i | 0.552564i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −740.464 | −1.13568 | ||||||||
\(653\) | − 468.433i | − 0.717355i | −0.933462 | − | 0.358678i | \(-0.883228\pi\) | ||||
0.933462 | − | 0.358678i | \(-0.116772\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.4603 | 0.0449775 | ||||||||
\(656\) | − 316.849i | − 0.483001i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 280.947 | 0.426972 | ||||||||
\(659\) | − 85.9405i | − 0.130410i | −0.997872 | − | 0.0652052i | \(-0.979230\pi\) | ||||
0.997872 | − | 0.0652052i | \(-0.0207702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 123.112 | 0.186251 | 0.0931256 | − | 0.995654i | \(-0.470314\pi\) | ||||
0.0931256 | + | 0.995654i | \(0.470314\pi\) | |||||||
\(662\) | 891.747i | 1.34705i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 50.5819 | 0.0761775 | ||||||||
\(665\) | − 906.520i | − 1.36319i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 399.526 | 0.598990 | ||||||||
\(668\) | − 460.845i | − 0.689888i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −133.132 | −0.198705 | ||||||||
\(671\) | − 276.588i | − 0.412202i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −636.613 | −0.945934 | −0.472967 | − | 0.881080i | \(-0.656817\pi\) | ||||
−0.472967 | + | 0.881080i | \(0.656817\pi\) | |||||||
\(674\) | 179.321i | 0.266054i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 217.127 | 0.321194 | ||||||||
\(677\) | − 165.309i | − 0.244179i | −0.992519 | − | 0.122089i | \(-0.961041\pi\) | ||||
0.992519 | − | 0.122089i | \(-0.0389595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1368.88 | −2.01603 | ||||||||
\(680\) | 270.135i | 0.397257i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −697.954 | −1.02339 | ||||||||
\(683\) | 1304.33i | 1.90970i | 0.297085 | + | 0.954851i | \(0.403986\pi\) | ||||
−0.297085 | + | 0.954851i | \(0.596014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1380.18 | −2.01487 | ||||||||
\(686\) | − 684.849i | − 0.998322i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1607.72 | 2.33680 | ||||||||
\(689\) | 249.672i | 0.362368i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −361.817 | −0.523613 | −0.261807 | − | 0.965120i | \(-0.584318\pi\) | ||||
−0.261807 | + | 0.965120i | \(0.584318\pi\) | |||||||
\(692\) | 866.140i | 1.25165i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −454.879 | −0.655445 | ||||||||
\(695\) | 223.574i | 0.321689i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 248.257 | 0.356179 | ||||||||
\(698\) | − 1207.72i | − 1.73026i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −332.027 | −0.474324 | ||||||||
\(701\) | − 893.344i | − 1.27438i | −0.770705 | − | 0.637192i | \(-0.780096\pi\) | ||||
0.770705 | − | 0.637192i | \(-0.219904\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −564.863 | −0.803504 | ||||||||
\(704\) | − 206.932i | − 0.293937i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1057.06 | 1.49725 | ||||||||
\(707\) | − 566.840i | − 0.801753i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −690.613 | −0.974066 | −0.487033 | − | 0.873384i | \(-0.661921\pi\) | ||||
−0.487033 | + | 0.873384i | \(0.661921\pi\) | |||||||
\(710\) | − 678.228i | − 0.955251i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −81.3475 | −0.114252 | ||||||||
\(713\) | 861.992i | 1.20896i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −492.476 | −0.688778 | ||||||||
\(716\) | − 85.2220i | − 0.119025i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 598.532 | 0.833610 | ||||||||
\(719\) | 482.097i | 0.670511i | 0.942127 | + | 0.335255i | \(0.108823\pi\) | ||||
−0.942127 | + | 0.335255i | \(0.891177\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −567.119 | −0.786573 | ||||||||
\(722\) | 109.999i | 0.152354i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −242.348 | −0.334735 | ||||||||
\(725\) | 213.564i | 0.294571i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 345.033 | 0.474598 | 0.237299 | − | 0.971437i | \(-0.423738\pi\) | ||||
0.237299 | + | 0.971437i | \(0.423738\pi\) | |||||||
\(728\) | 226.654i | 0.311338i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1327.46 | 1.81844 | ||||||||
\(731\) | 1259.67i | 1.72322i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 539.274 | 0.735708 | 0.367854 | − | 0.929884i | \(-0.380093\pi\) | ||||
0.367854 | + | 0.929884i | \(0.380093\pi\) | |||||||
\(734\) | 618.777i | 0.843021i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1024.35 | −1.39178 | ||||||||
\(737\) | − 65.7582i | − 0.0892241i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 737.474 | 0.997935 | 0.498968 | − | 0.866621i | \(-0.333713\pi\) | ||||
0.498968 | + | 0.866621i | \(0.333713\pi\) | |||||||
\(740\) | 574.331i | 0.776123i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −548.532 | −0.739262 | ||||||||
\(743\) | − 1041.25i | − 1.40141i | −0.713450 | − | 0.700706i | \(-0.752868\pi\) | ||||
0.713450 | − | 0.700706i | \(-0.247132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1048.54 | −1.40743 | ||||||||
\(746\) | − 1715.35i | − 2.29939i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 354.299 | 0.473662 | ||||||||
\(749\) | 985.736i | 1.31607i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 241.036 | 0.320953 | 0.160476 | − | 0.987040i | \(-0.448697\pi\) | ||||
0.160476 | + | 0.987040i | \(0.448697\pi\) | |||||||
\(752\) | 252.600i | 0.335904i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −387.117 | −0.513418 | ||||||||
\(755\) | 523.331i | 0.693154i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7615 | 0.0432781 | 0.0216391 | − | 0.999766i | \(-0.493112\pi\) | ||||
0.0216391 | + | 0.999766i | \(0.493112\pi\) | |||||||
\(758\) | − 1642.56i | − 2.16696i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 321.131 | 0.422541 | ||||||||
\(761\) | − 319.353i | − 0.419650i | −0.977739 | − | 0.209825i | \(-0.932711\pi\) | ||||
0.977739 | − | 0.209825i | \(-0.0672894\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 971.140 | 1.27279 | ||||||||
\(764\) | 456.049i | 0.596923i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −279.972 | −0.365499 | ||||||||
\(767\) | 220.515i | 0.287503i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −476.207 | −0.619255 | −0.309628 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309628 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(770\) | − 1081.98i | − 1.40516i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 120.498 | 0.156086 | ||||||||
\(773\) | 1296.29i | 1.67696i | 0.544929 | + | 0.838482i | \(0.316556\pi\) | ||||
−0.544929 | + | 0.838482i | \(0.683444\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −460.772 | −0.594544 | ||||||||
\(776\) | − 484.921i | − 0.624899i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1559.99 | −2.00513 | ||||||||
\(779\) | − 295.123i | − 0.378848i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 334.998 | 0.428934 | ||||||||
\(782\) | − 1039.93i | − 1.32983i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −324.056 | −0.413337 | ||||||||
\(785\) | 465.359i | 0.592814i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 860.953 | 1.09397 | 0.546984 | − | 0.837143i | \(-0.315776\pi\) | ||||
0.546984 | + | 0.837143i | \(0.315776\pi\) | |||||||
\(788\) | − 612.117i | − 0.776799i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 453.908 | 0.574567 | ||||||||
\(791\) | 1009.54i | 1.27628i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 330.983 | 0.417381 | ||||||||
\(794\) | − 984.977i | − 1.24053i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 510.043 | 0.640758 | ||||||||
\(797\) | − 580.125i | − 0.727886i | −0.931421 | − | 0.363943i | \(-0.881430\pi\) | ||||
0.931421 | − | 0.363943i | \(-0.118570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −197.916 | −0.247705 | ||||||||
\(800\) | − 547.560i | − 0.684450i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −721.103 | −0.899131 | ||||||||
\(803\) | 655.674i | 0.816530i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1336.27 | −1.65996 | ||||||||
\(806\) | − 835.218i | − 1.03625i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 200.801 | 0.248516 | ||||||||
\(809\) | 661.323i | 0.817457i | 0.912656 | + | 0.408729i | \(0.134028\pi\) | ||||
−0.912656 | + | 0.408729i | \(0.865972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −168.725 | −0.208045 | −0.104023 | − | 0.994575i | \(-0.533171\pi\) | ||||
−0.104023 | + | 0.994575i | \(0.533171\pi\) | |||||||
\(812\) | − 357.865i | − 0.440721i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −674.192 | −0.828245 | ||||||||
\(815\) | − 1592.97i | − 1.95457i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1497.48 | 1.83290 | ||||||||
\(818\) | 1449.20i | 1.77164i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −300.069 | −0.365938 | ||||||||
\(821\) | 151.578i | 0.184626i | 0.995730 | + | 0.0923132i | \(0.0294261\pi\) | ||||
−0.995730 | + | 0.0923132i | \(0.970574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 224.822 | 0.273173 | 0.136587 | − | 0.990628i | \(-0.456387\pi\) | ||||
0.136587 | + | 0.990628i | \(0.456387\pi\) | |||||||
\(824\) | − 200.900i | − 0.243810i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −484.474 | −0.586530 | ||||||||
\(827\) | 338.159i | 0.408899i | 0.978877 | + | 0.204449i | \(0.0655404\pi\) | ||||
−0.978877 | + | 0.204449i | \(0.934460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −803.612 | −0.969376 | −0.484688 | − | 0.874687i | \(-0.661067\pi\) | ||||
−0.484688 | + | 0.874687i | \(0.661067\pi\) | |||||||
\(830\) | − 288.950i | − 0.348132i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 247.628 | 0.297630 | ||||||||
\(833\) | − 253.904i | − 0.304806i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 991.423 | 1.18733 | ||||||||
\(836\) | − 421.184i | − 0.503809i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −230.169 | −0.274665 | ||||||||
\(839\) | − 853.942i | − 1.01781i | −0.860823 | − | 0.508905i | \(-0.830050\pi\) | ||||
0.860823 | − | 0.508905i | \(-0.169950\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 610.816 | 0.726298 | ||||||||
\(842\) | − 778.532i | − 0.924623i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 757.968 | 0.898067 | ||||||||
\(845\) | 467.108i | 0.552791i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −447.811 | −0.528703 | ||||||||
\(848\) | − 493.185i | − 0.581587i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 555.885 | 0.653982 | ||||||||
\(851\) | 832.645i | 0.978431i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −799.115 | −0.936829 | −0.468414 | − | 0.883509i | \(-0.655175\pi\) | ||||
−0.468414 | + | 0.883509i | \(0.655175\pi\) | |||||||
\(854\) | 727.174i | 0.851492i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −349.193 | −0.407936 | ||||||||
\(857\) | − 1553.26i | − 1.81244i | −0.422809 | − | 0.906219i | \(-0.638956\pi\) | ||||
0.422809 | − | 0.906219i | \(-0.361044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2520 | −0.0328895 | −0.0164447 | − | 0.999865i | \(-0.505235\pi\) | ||||
−0.0164447 | + | 0.999865i | \(0.505235\pi\) | |||||||
\(860\) | − 1522.58i | − 1.77044i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1540.39 | 1.78700 | ||||||||
\(863\) | − 951.550i | − 1.10261i | −0.834305 | − | 0.551304i | \(-0.814131\pi\) | ||||
0.834305 | − | 0.551304i | \(-0.185869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1863.34 | −2.15415 | ||||||||
\(866\) | − 1091.53i | − 1.26043i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 772.107 | 0.889524 | ||||||||
\(869\) | 224.199i | 0.257997i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 78.6906 | 0.0903451 | ||||||||
\(872\) | 344.022i | 0.394521i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1236.24 | −1.41447 | ||||||||
\(875\) | 554.310i | 0.633497i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −228.193 | −0.260197 | −0.130098 | − | 0.991501i | \(-0.541529\pi\) | ||||
−0.130098 | + | 0.991501i | \(0.541529\pi\) | |||||||
\(878\) | − 878.651i | − 1.00074i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 972.805 | 1.10546 | ||||||||
\(881\) | − 1551.18i | − 1.76071i | −0.474318 | − | 0.880354i | \(-0.657305\pi\) | ||||
0.474318 | − | 0.880354i | \(-0.342695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1563.59 | 1.77077 | 0.885384 | − | 0.464859i | \(-0.153895\pi\) | ||||
0.885384 | + | 0.464859i | \(0.153895\pi\) | |||||||
\(884\) | 423.978i | 0.479614i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1186.86 | 1.33957 | ||||||||
\(887\) | 702.161i | 0.791613i | 0.918334 | + | 0.395807i | \(0.129535\pi\) | ||||
−0.918334 | + | 0.395807i | \(0.870465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 953.496 | 1.07255 | ||||||||
\(890\) | 464.699i | 0.522134i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1130.95 | 1.26789 | ||||||||
\(893\) | 235.279i | 0.263470i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 183.339 | 0.204848 | ||||||||
\(896\) | − 719.034i | − 0.802493i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −501.959 | −0.558974 | ||||||||
\(899\) | − 496.629i | − 0.552424i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 386.419 | 0.428878 | ||||||||
\(902\) | − 352.243i | − 0.390514i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −357.625 | −0.395603 | ||||||||
\(905\) | − 521.367i | − 0.576096i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1614.51 | 1.78006 | 0.890030 | − | 0.455903i | \(-0.150683\pi\) | ||||
0.890030 | + | 0.455903i | \(0.150683\pi\) | |||||||
\(908\) | 1012.44i | 1.11503i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1294.77 | 1.42282 | ||||||||
\(911\) | 612.962i | 0.672846i | 0.941711 | + | 0.336423i | \(0.109217\pi\) | ||||
−0.941711 | + | 0.336423i | \(0.890783\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 142.721 | 0.156321 | ||||||||
\(914\) | 1013.71i | 1.10909i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1059.20 | 1.15634 | ||||||||
\(917\) | − 38.2568i | − 0.0417195i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 628.091 | 0.683451 | 0.341725 | − | 0.939800i | \(-0.388989\pi\) | ||||
0.341725 | + | 0.939800i | \(0.388989\pi\) | |||||||
\(920\) | − 473.368i | − 0.514531i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1138.01 | −1.23428 | ||||||||
\(923\) | 400.881i | 0.434323i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −445.085 | −0.481173 | ||||||||
\(926\) | − 1452.84i | − 1.56894i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 590.171 | 0.635961 | ||||||||
\(929\) | 1253.56i | 1.34936i | 0.738109 | + | 0.674681i | \(0.235719\pi\) | ||||
−0.738109 | + | 0.674681i | \(0.764281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −301.836 | −0.324206 | ||||||||
\(932\) | − 551.129i | − 0.591340i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 565.816 | 0.605799 | ||||||||
\(935\) | 762.209i | 0.815197i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −920.264 | −0.982139 | −0.491070 | − | 0.871120i | \(-0.663394\pi\) | ||||
−0.491070 | + | 0.871120i | \(0.663394\pi\) | |||||||
\(938\) | 172.884i | 0.184312i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 239.222 | 0.254492 | ||||||||
\(941\) | − 683.451i | − 0.726303i | −0.931730 | − | 0.363152i | \(-0.881701\pi\) | ||||
0.931730 | − | 0.363152i | \(-0.118299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −435.030 | −0.461325 | ||||||||
\(944\) | − 435.590i | − 0.461430i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1787.31 | 1.88934 | ||||||||
\(947\) | 841.784i | 0.888895i | 0.895805 | + | 0.444448i | \(0.146600\pi\) | ||||
−0.895805 | + | 0.444448i | \(0.853400\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −784.623 | −0.826789 | ||||||||
\(950\) | − 660.825i | − 0.695606i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 350.794 | 0.368481 | ||||||||
\(953\) | − 1475.15i | − 1.54790i | −0.633244 | − | 0.773952i | \(-0.718277\pi\) | ||||
0.633244 | − | 0.773952i | \(-0.281723\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −981.105 | −1.02734 | ||||||||
\(956\) | 889.436i | 0.930373i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 595.187 | 0.621281 | ||||||||
\(959\) | 1792.29i | 1.86892i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 110.495 | 0.114979 | ||||||||
\(962\) | − 806.783i | − 0.838652i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 856.911 | 0.888912 | ||||||||
\(965\) | 259.229i | 0.268631i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 324.748 | 0.335830 | 0.167915 | − | 0.985801i | \(-0.446297\pi\) | ||||
0.167915 | + | 0.985801i | \(0.446297\pi\) | |||||||
\(968\) | − 158.635i | − 0.163879i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2770.12 | −2.85580 | ||||||||
\(971\) | 1203.37i | 1.23931i | 0.784873 | + | 0.619657i | \(0.212728\pi\) | ||||
−0.784873 | + | 0.619657i | \(0.787272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 290.331 | 0.298387 | ||||||||
\(974\) | 1164.49i | 1.19558i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −653.802 | −0.669879 | ||||||||
\(977\) | − 189.328i | − 0.193785i | −0.995295 | − | 0.0968927i | \(-0.969110\pi\) | ||||
0.995295 | − | 0.0968927i | \(-0.0308904\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −229.529 | −0.234453 | ||||||||
\(980\) | 306.895i | 0.313158i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1753.99 | 1.78614 | ||||||||
\(983\) | − 1264.70i | − 1.28657i | −0.765627 | − | 0.643285i | \(-0.777571\pi\) | ||||
0.765627 | − | 0.643285i | \(-0.222429\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1316.86 | 1.33691 | ||||||||
\(986\) | 599.144i | 0.607651i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 504.017 | 0.510139 | ||||||||
\(989\) | − 2207.38i | − 2.23193i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1394.54 | −1.40721 | −0.703604 | − | 0.710593i | \(-0.748427\pi\) | ||||
−0.703604 | + | 0.710593i | \(0.748427\pi\) | |||||||
\(992\) | 1273.32i | 1.28358i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −880.740 | −0.886056 | ||||||||
\(995\) | 1097.26i | 1.10278i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1008.71 | 1.01175 | 0.505875 | − | 0.862607i | \(-0.331170\pi\) | ||||
0.505875 | + | 0.862607i | \(0.331170\pi\) | |||||||
\(998\) | 151.062i | 0.151365i | ||||||||
\(999\) | 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 | 729.3.b.a.728.5 | 30 | ||
3.2 | odd | 2 | inner | 729.3.b.a.728.26 | 30 | ||
27.2 | odd | 18 | 27.3.f.a.23.5 | yes | 30 | ||
27.4 | even | 9 | 243.3.f.c.107.5 | 30 | |||
27.5 | odd | 18 | 243.3.f.a.26.5 | 30 | |||
27.7 | even | 9 | 243.3.f.b.134.1 | 30 | |||
27.11 | odd | 18 | 243.3.f.d.215.1 | 30 | |||
27.13 | even | 9 | 27.3.f.a.20.5 | ✓ | 30 | ||
27.14 | odd | 18 | 81.3.f.a.62.1 | 30 | |||
27.16 | even | 9 | 243.3.f.a.215.5 | 30 | |||
27.20 | odd | 18 | 243.3.f.c.134.5 | 30 | |||
27.22 | even | 9 | 243.3.f.d.26.1 | 30 | |||
27.23 | odd | 18 | 243.3.f.b.107.1 | 30 | |||
27.25 | even | 9 | 81.3.f.a.17.1 | 30 | |||
108.67 | odd | 18 | 432.3.bc.a.209.5 | 30 | |||
108.83 | even | 18 | 432.3.bc.a.401.5 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.20.5 | ✓ | 30 | 27.13 | even | 9 | ||
27.3.f.a.23.5 | yes | 30 | 27.2 | odd | 18 | ||
81.3.f.a.17.1 | 30 | 27.25 | even | 9 | |||
81.3.f.a.62.1 | 30 | 27.14 | odd | 18 | |||
243.3.f.a.26.5 | 30 | 27.5 | odd | 18 | |||
243.3.f.a.215.5 | 30 | 27.16 | even | 9 | |||
243.3.f.b.107.1 | 30 | 27.23 | odd | 18 | |||
243.3.f.b.134.1 | 30 | 27.7 | even | 9 | |||
243.3.f.c.107.5 | 30 | 27.4 | even | 9 | |||
243.3.f.c.134.5 | 30 | 27.20 | odd | 18 | |||
243.3.f.d.26.1 | 30 | 27.22 | even | 9 | |||
243.3.f.d.215.1 | 30 | 27.11 | odd | 18 | |||
432.3.bc.a.209.5 | 30 | 108.67 | odd | 18 | |||
432.3.bc.a.401.5 | 30 | 108.83 | even | 18 | |||
729.3.b.a.728.5 | 30 | 1.1 | even | 1 | trivial | ||
729.3.b.a.728.26 | 30 | 3.2 | odd | 2 | inner |