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 | 728.26 | ||
Character | \(\chi\) | \(=\) | 729.728 |
Dual form | 729.3.b.a.728.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 | \(0.228161\pi\) | ||||
−0.753918 | + | 0.656968i | \(0.771839\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.90572 | −0.726429 | ||||||||
\(5\) | 6.25111i | 1.25022i | 0.780536 | + | 0.625111i | \(0.214946\pi\) | ||||
−0.780536 | + | 0.625111i | \(0.785054\pi\) | |||||||
\(6\) | 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 | \(0.120235\pi\) | ||||
−0.929504 | + | 0.368812i | \(0.879765\pi\) | |||||||
\(12\) | 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 | \(0.145727\pi\) | ||||
−0.897021 | + | 0.441988i | \(0.854273\pi\) | |||||||
\(18\) | 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 | \(-0.805987\pi\) | ||||
0.819928 | − | 0.572467i | \(-0.194013\pi\) | |||||||
\(24\) | 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 | \(0.0842445\pi\) | ||||
−0.965181 | + | 0.261583i | \(0.915756\pi\) | |||||||
\(30\) | 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 | \(-0.935430\pi\) | ||||
0.979496 | − | 0.201464i | \(-0.0645698\pi\) | |||||||
\(42\) | 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 | \(0.0447450\pi\) | ||||
−0.990136 | + | 0.140108i | \(0.955255\pi\) | |||||||
\(48\) | 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 | \(-0.922005\pi\) | ||||
0.970130 | − | 0.242585i | \(-0.0779952\pi\) | |||||||
\(54\) | 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 | \(-0.938351\pi\) | ||||
0.981304 | − | 0.192466i | \(-0.0616486\pi\) | |||||||
\(60\) | 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 | \(-0.906094\pi\) | ||||
0.956798 | − | 0.290754i | \(-0.0939062\pi\) | |||||||
\(72\) | 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 | \(-0.966208\pi\) | ||||
0.994370 | − | 0.105963i | \(-0.0337924\pi\) | |||||||
\(84\) | 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 | \(0.0508026\pi\) | ||||
−0.987291 | + | 0.158924i | \(0.949197\pi\) | |||||||
\(90\) | 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 | \(-0.887647\pi\) | ||||
0.938351 | − | 0.345684i | \(-0.112353\pi\) | |||||||
\(102\) | 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 | \(0.192065\pi\) | ||||
−0.823416 | + | 0.567438i | \(0.807935\pi\) | |||||||
\(108\) | 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 | \(0.185480\pi\) | ||||
−0.834979 | + | 0.550282i | \(0.814520\pi\) | |||||||
\(114\) | 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 | \(-0.994274\pi\) | ||||
0.999838 | − | 0.0179878i | \(-0.00572601\pi\) | |||||||
\(132\) | 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 | \(0.298266\pi\) | ||||
−0.592183 | + | 0.805804i | \(0.701734\pi\) | |||||||
\(138\) | 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 | \(0.190304\pi\) | ||||
−0.826543 | + | 0.562873i | \(0.809696\pi\) | |||||||
\(150\) | 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 | \(-0.842503\pi\) | ||||
0.880067 | − | 0.474849i | \(-0.157497\pi\) | |||||||
\(168\) | 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 | \(0.330479\pi\) | ||||
−0.507747 | + | 0.861506i | \(0.669521\pi\) | |||||||
\(174\) | 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 | \(-0.973893\pi\) | ||||
0.996639 | − | 0.0819248i | \(-0.0261067\pi\) | |||||||
\(180\) | 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 | \(0.134772\pi\) | ||||
−0.911698 | + | 0.410861i | \(0.865228\pi\) | |||||||
\(192\) | 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 | \(-0.820436\pi\) | ||||
0.845062 | − | 0.534669i | \(-0.179564\pi\) | |||||||
\(198\) | 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 | \(0.278485\pi\) | ||||
−0.641083 | + | 0.767471i | \(0.721515\pi\) | |||||||
\(228\) | 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 | \(-0.866569\pi\) | ||||
0.913420 | − | 0.407018i | \(-0.133431\pi\) | |||||||
\(234\) | 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 | \(0.221221\pi\) | ||||
−0.768063 | + | 0.640374i | \(0.778779\pi\) | |||||||
\(240\) | 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 | \(0.118713\pi\) | ||||
−0.931258 | + | 0.364361i | \(0.881287\pi\) | |||||||
\(252\) | 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 | \(0.174855\pi\) | ||||
−0.852879 | + | 0.522109i | \(0.825145\pi\) | |||||||
\(258\) | 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 | \(0.233344\pi\) | ||||
−0.743122 | + | 0.669156i | \(0.766656\pi\) | |||||||
\(264\) | 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 | \(0.0987518\pi\) | ||||
−0.952261 | + | 0.305285i | \(0.901248\pi\) | |||||||
\(270\) | 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 | \(-0.693816\pi\) | ||||
0.571958 | − | 0.820283i | \(-0.306184\pi\) | |||||||
\(282\) | 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 | \(-0.663073\pi\) | ||||
0.490191 | − | 0.871615i | \(-0.336927\pi\) | |||||||
\(294\) | 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 | \(0.193235\pi\) | ||||
−0.821326 | + | 0.570459i | \(0.806765\pi\) | |||||||
\(312\) | 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 | \(0.297512\pi\) | ||||
−0.594091 | + | 0.804398i | \(0.702488\pi\) | |||||||
\(318\) | 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 | \(0.0802400\pi\) | ||||
−0.968395 | + | 0.249420i | \(0.919760\pi\) | |||||||
\(348\) | 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 | \(-0.807036\pi\) | ||||
0.821812 | − | 0.569759i | \(-0.192964\pi\) | |||||||
\(354\) | 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 | \(-0.897251\pi\) | ||||
0.948352 | − | 0.317219i | \(-0.102749\pi\) | |||||||
\(360\) | 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 | \(0.0444163\pi\) | ||||
−0.990280 | + | 0.139086i | \(0.955584\pi\) | |||||||
\(384\) | 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 | \(0.276286\pi\) | ||||
−0.646371 | + | 0.763023i | \(0.723714\pi\) | |||||||
\(390\) | 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 | \(0.111156\pi\) | ||||
−0.939645 | + | 0.342152i | \(0.888844\pi\) | |||||||
\(402\) | 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 | \(0.0333306\pi\) | ||||
−0.994523 | + | 0.104520i | \(0.966669\pi\) | |||||||
\(420\) | 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 | \(-0.761972\pi\) | ||||
0.733196 | − | 0.680017i | \(-0.238028\pi\) | |||||||
\(432\) | 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 | \(-0.829737\pi\) | ||||
0.860320 | − | 0.509754i | \(-0.170263\pi\) | |||||||
\(444\) | 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 | \(0.0682289\pi\) | ||||
−0.977115 | + | 0.212710i | \(0.931771\pi\) | |||||||
\(450\) | 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 | \(0.155634\pi\) | ||||
−0.882832 | + | 0.469689i | \(0.844366\pi\) | |||||||
\(462\) | 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 | \(-0.925955\pi\) | ||||
0.973066 | − | 0.230528i | \(-0.0740454\pi\) | |||||||
\(468\) | 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 | \(-0.924026\pi\) | ||||
0.971651 | − | 0.236420i | \(-0.0759740\pi\) | |||||||
\(480\) | 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 | \(-0.762114\pi\) | ||||
0.733499 | − | 0.679690i | \(-0.237886\pi\) | |||||||
\(492\) | 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 | \(-0.838544\pi\) | ||||
0.874094 | − | 0.485757i | \(-0.161456\pi\) | |||||||
\(504\) | 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 | \(-0.909922\pi\) | ||||
0.960225 | − | 0.279226i | \(-0.0900778\pi\) | |||||||
\(510\) | 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 | \(0.0124183\pi\) | ||||
−0.999239 | + | 0.0390033i | \(0.987582\pi\) | |||||||
\(522\) | 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 | \(-0.999067\pi\) | ||||
0.999996 | − | 0.00293138i | \(-0.000933088\pi\) | |||||||
\(558\) | 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 | \(0.201015\pi\) | ||||
−0.807138 | + | 0.590363i | \(0.798985\pi\) | |||||||
\(564\) | 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 | \(0.0212556\pi\) | ||||
−0.997771 | + | 0.0667267i | \(0.978744\pi\) | |||||||
\(570\) | 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 | \(0.0377493\pi\) | ||||
−0.992976 | + | 0.118315i | \(0.962251\pi\) | |||||||
\(588\) | 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 | \(-0.960902\pi\) | ||||
0.992466 | − | 0.122520i | \(-0.0390975\pi\) | |||||||
\(594\) | 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 | \(-0.993896\pi\) | ||||
0.999816 | − | 0.0191757i | \(-0.00610420\pi\) | |||||||
\(600\) | 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 | \(-0.818975\pi\) | ||||
0.842598 | − | 0.538542i | \(-0.181025\pi\) | |||||||
\(618\) | 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 | \(-0.818299\pi\) | ||||
0.841452 | − | 0.540332i | \(-0.181701\pi\) | |||||||
\(642\) | 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 | \(-0.912114\pi\) | ||||
0.962125 | − | 0.272608i | \(-0.0878863\pi\) | |||||||
\(648\) | 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 | \(0.116772\pi\) | ||||
−0.933462 | + | 0.358678i | \(0.883228\pi\) | |||||||
\(654\) | 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 | \(0.0207702\pi\) | ||||
−0.997872 | + | 0.0652052i | \(0.979230\pi\) | |||||||
\(660\) | 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 | \(0.0389595\pi\) | ||||
−0.992519 | + | 0.122089i | \(0.961041\pi\) | |||||||
\(678\) | 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 | \(-0.596014\pi\) | ||||
0.297085 | − | 0.954851i | \(-0.403986\pi\) | |||||||
\(684\) | 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 | \(0.219904\pi\) | ||||
−0.770705 | + | 0.637192i | \(0.780096\pi\) | |||||||
\(702\) | 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 | \(-0.891177\pi\) | ||||
0.942127 | − | 0.335255i | \(-0.108823\pi\) | |||||||
\(720\) | 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 | \(0.247132\pi\) | ||||
−0.713450 | + | 0.700706i | \(0.752868\pi\) | |||||||
\(744\) | 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 | \(0.0672894\pi\) | ||||
−0.977739 | + | 0.209825i | \(0.932711\pi\) | |||||||
\(762\) | 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 | \(-0.683444\pi\) | ||||
0.544929 | − | 0.838482i | \(-0.316556\pi\) | |||||||
\(774\) | 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 | \(0.118570\pi\) | ||||
−0.931421 | + | 0.363943i | \(0.881430\pi\) | |||||||
\(798\) | 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 | \(-0.865972\pi\) | ||||
0.912656 | − | 0.408729i | \(-0.134028\pi\) | |||||||
\(810\) | 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 | \(-0.970574\pi\) | ||||
0.995730 | − | 0.0923132i | \(-0.0294261\pi\) | |||||||
\(822\) | 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 | \(-0.934460\pi\) | ||||
0.978877 | − | 0.204449i | \(-0.0655404\pi\) | |||||||
\(828\) | 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 | \(0.169950\pi\) | ||||
−0.860823 | + | 0.508905i | \(0.830050\pi\) | |||||||
\(840\) | 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 | \(0.361044\pi\) | ||||
−0.422809 | + | 0.906219i | \(0.638956\pi\) | |||||||
\(858\) | 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 | \(0.185869\pi\) | ||||
−0.834305 | + | 0.551304i | \(0.814131\pi\) | |||||||
\(864\) | 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 | \(0.342695\pi\) | ||||
−0.474318 | + | 0.880354i | \(0.657305\pi\) | |||||||
\(882\) | 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 | \(-0.870465\pi\) | ||||
0.918334 | − | 0.395807i | \(-0.129535\pi\) | |||||||
\(888\) | 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 | \(-0.890783\pi\) | ||||
0.941711 | − | 0.336423i | \(-0.109217\pi\) | |||||||
\(912\) | 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 | \(-0.764281\pi\) | ||||
0.738109 | − | 0.674681i | \(-0.235719\pi\) | |||||||
\(930\) | 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 | \(0.118299\pi\) | ||||
−0.931730 | + | 0.363152i | \(0.881701\pi\) | |||||||
\(942\) | 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 | \(-0.853400\pi\) | ||||
0.895805 | − | 0.444448i | \(-0.146600\pi\) | |||||||
\(948\) | 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 | \(0.281723\pi\) | ||||
−0.633244 | + | 0.773952i | \(0.718277\pi\) | |||||||
\(954\) | 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 | \(-0.787272\pi\) | ||||
0.784873 | − | 0.619657i | \(-0.212728\pi\) | |||||||
\(972\) | 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 | \(0.0308904\pi\) | ||||
−0.995295 | + | 0.0968927i | \(0.969110\pi\) | |||||||
\(978\) | 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 | \(0.222429\pi\) | ||||
−0.765627 | + | 0.643285i | \(0.777571\pi\) | |||||||
\(984\) | 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.728.26 | 30 | ||
3.2 | odd | 2 | inner | 729.3.b.a.728.5 | 30 | ||
27.2 | odd | 18 | 81.3.f.a.17.1 | 30 | |||
27.4 | even | 9 | 243.3.f.b.107.1 | 30 | |||
27.5 | odd | 18 | 243.3.f.d.26.1 | 30 | |||
27.7 | even | 9 | 243.3.f.c.134.5 | 30 | |||
27.11 | odd | 18 | 243.3.f.a.215.5 | 30 | |||
27.13 | even | 9 | 81.3.f.a.62.1 | 30 | |||
27.14 | odd | 18 | 27.3.f.a.20.5 | ✓ | 30 | ||
27.16 | even | 9 | 243.3.f.d.215.1 | 30 | |||
27.20 | odd | 18 | 243.3.f.b.134.1 | 30 | |||
27.22 | even | 9 | 243.3.f.a.26.5 | 30 | |||
27.23 | odd | 18 | 243.3.f.c.107.5 | 30 | |||
27.25 | even | 9 | 27.3.f.a.23.5 | yes | 30 | ||
108.79 | odd | 18 | 432.3.bc.a.401.5 | 30 | |||
108.95 | even | 18 | 432.3.bc.a.209.5 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.20.5 | ✓ | 30 | 27.14 | odd | 18 | ||
27.3.f.a.23.5 | yes | 30 | 27.25 | even | 9 | ||
81.3.f.a.17.1 | 30 | 27.2 | odd | 18 | |||
81.3.f.a.62.1 | 30 | 27.13 | even | 9 | |||
243.3.f.a.26.5 | 30 | 27.22 | even | 9 | |||
243.3.f.a.215.5 | 30 | 27.11 | odd | 18 | |||
243.3.f.b.107.1 | 30 | 27.4 | even | 9 | |||
243.3.f.b.134.1 | 30 | 27.20 | odd | 18 | |||
243.3.f.c.107.5 | 30 | 27.23 | odd | 18 | |||
243.3.f.c.134.5 | 30 | 27.7 | even | 9 | |||
243.3.f.d.26.1 | 30 | 27.5 | odd | 18 | |||
243.3.f.d.215.1 | 30 | 27.16 | even | 9 | |||
432.3.bc.a.209.5 | 30 | 108.95 | even | 18 | |||
432.3.bc.a.401.5 | 30 | 108.79 | odd | 18 | |||
729.3.b.a.728.5 | 30 | 3.2 | odd | 2 | inner | ||
729.3.b.a.728.26 | 30 | 1.1 | even | 1 | trivial |