Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,4,Mod(431,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.431");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(50.9776502450\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 431.13 | ||
Character | \(\chi\) | \(=\) | 864.431 |
Dual form | 864.4.f.b.431.14 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.898373 | 0.0803530 | 0.0401765 | − | 0.999193i | \(-0.487208\pi\) | ||||
0.0401765 | + | 0.999193i | \(0.487208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 20.7150i | − 1.11851i | −0.828997 | − | 0.559253i | \(-0.811088\pi\) | ||||
0.828997 | − | 0.559253i | \(-0.188912\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.351756i | 0.00964166i | 0.999988 | + | 0.00482083i | \(0.00153452\pi\) | ||||
−0.999988 | + | 0.00482083i | \(0.998465\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.6629i | 0.952867i | 0.879211 | + | 0.476433i | \(0.158071\pi\) | ||||
−0.879211 | + | 0.476433i | \(0.841929\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 58.0727i | − 0.828512i | −0.910160 | − | 0.414256i | \(-0.864042\pi\) | ||||
0.910160 | − | 0.414256i | \(-0.135958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 42.4793 | 0.512917 | 0.256459 | − | 0.966555i | \(-0.417444\pi\) | ||||
0.256459 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 196.511 | 1.78154 | 0.890770 | − | 0.454455i | \(-0.150166\pi\) | ||||
0.890770 | + | 0.454455i | \(0.150166\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.193 | −0.993543 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −71.7647 | −0.459530 | −0.229765 | − | 0.973246i | \(-0.573796\pi\) | ||||
−0.229765 | + | 0.973246i | \(0.573796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 96.1796i | − 0.557238i | −0.960402 | − | 0.278619i | \(-0.910123\pi\) | ||||
0.960402 | − | 0.278619i | \(-0.0898766\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 18.6098i | − 0.0898753i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 18.9148i | − 0.0840423i | −0.999117 | − | 0.0420212i | \(-0.986620\pi\) | ||||
0.999117 | − | 0.0420212i | \(-0.0133797\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 322.069i | − 1.22680i | −0.789772 | − | 0.613400i | \(-0.789801\pi\) | ||||
0.789772 | − | 0.613400i | \(-0.210199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 264.193 | 0.936954 | 0.468477 | − | 0.883476i | \(-0.344803\pi\) | ||||
0.468477 | + | 0.883476i | \(0.344803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −370.645 | −1.15030 | −0.575151 | − | 0.818048i | \(-0.695057\pi\) | ||||
−0.575151 | + | 0.818048i | \(0.695057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −86.1123 | −0.251056 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −512.874 | −1.32922 | −0.664610 | − | 0.747190i | \(-0.731402\pi\) | ||||
−0.664610 | + | 0.747190i | \(0.731402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.316008i | 0 0.000774736i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 240.841i | − 0.531438i | −0.964050 | − | 0.265719i | \(-0.914391\pi\) | ||||
0.964050 | − | 0.265719i | \(-0.0856094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 526.724i | 1.10558i | 0.833322 | + | 0.552788i | \(0.186436\pi\) | ||||
−0.833322 | + | 0.552788i | \(0.813564\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 40.1240i | 0.0765657i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 156.199 | 0.284818 | 0.142409 | − | 0.989808i | \(-0.454515\pi\) | ||||
0.142409 | + | 0.989808i | \(0.454515\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −395.199 | −0.660585 | −0.330293 | − | 0.943879i | \(-0.607147\pi\) | ||||
−0.330293 | + | 0.943879i | \(0.607147\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −723.326 | −1.15971 | −0.579856 | − | 0.814719i | \(-0.696891\pi\) | ||||
−0.579856 | + | 0.814719i | \(0.696891\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.28663 | 0.0107843 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 972.700i | − 1.38528i | −0.721282 | − | 0.692641i | \(-0.756447\pi\) | ||||
0.721282 | − | 0.692641i | \(-0.243553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1222.96i | − 1.61732i | −0.588279 | − | 0.808658i | \(-0.700194\pi\) | ||||
0.588279 | − | 0.808658i | \(-0.299806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 52.1710i | − 0.0665734i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1231.35i | − 1.46655i | −0.679931 | − | 0.733276i | \(-0.737990\pi\) | ||||
0.679931 | − | 0.733276i | \(-0.262010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 925.194 | 1.06579 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 38.1623 | 0.0412144 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −499.594 | −0.522949 | −0.261474 | − | 0.965210i | \(-0.584209\pi\) | ||||
−0.261474 | + | 0.965210i | \(0.584209\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1546.93 | 1.52401 | 0.762007 | − | 0.647568i | \(-0.224214\pi\) | ||||
0.762007 | + | 0.647568i | \(0.224214\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 799.583i | 0.764906i | 0.923975 | + | 0.382453i | \(0.124921\pi\) | ||||
−0.923975 | + | 0.382453i | \(0.875079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2113.60i | − 1.90962i | −0.297209 | − | 0.954812i | \(-0.596056\pi\) | ||||
0.297209 | − | 0.954812i | \(-0.403944\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1197.70i | 1.05247i | 0.850339 | + | 0.526235i | \(0.176397\pi\) | ||||
−0.850339 | + | 0.526235i | \(0.823603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1094.53i | − 0.911192i | −0.890187 | − | 0.455596i | \(-0.849426\pi\) | ||||
0.890187 | − | 0.455596i | \(-0.150574\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 176.540 | 0.143152 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1202.98 | −0.926696 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1330.88 | 0.999907 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −223.868 | −0.160187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1729.91i | − 1.20870i | −0.796718 | − | 0.604351i | \(-0.793433\pi\) | ||||
0.796718 | − | 0.604351i | \(-0.206567\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 614.718i | − 0.409986i | −0.978763 | − | 0.204993i | \(-0.934283\pi\) | ||||
0.978763 | − | 0.204993i | \(-0.0657171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 879.961i | − 0.573701i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 99.5146i | − 0.0620592i | −0.999518 | − | 0.0310296i | \(-0.990121\pi\) | ||||
0.999518 | − | 0.0310296i | \(-0.00987861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2788.14 | −1.70134 | −0.850671 | − | 0.525698i | \(-0.823804\pi\) | ||||
−0.850671 | + | 0.525698i | \(0.823804\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.7104 | −0.00918722 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −64.4715 | −0.0369246 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3125.06 | −1.71822 | −0.859111 | − | 0.511789i | \(-0.828983\pi\) | ||||
−0.859111 | + | 0.511789i | \(0.828983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2896.76i | 1.56116i | 0.625056 | + | 0.780580i | \(0.285076\pi\) | ||||
−0.625056 | + | 0.780580i | \(0.714924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 86.4052i | − 0.0447757i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3385.64i | − 1.72104i | −0.509416 | − | 0.860521i | \(-0.670138\pi\) | ||||
0.509416 | − | 0.860521i | \(-0.329862\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 4070.73i | − 1.99266i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 336.736 | 0.161811 | 0.0809054 | − | 0.996722i | \(-0.474219\pi\) | ||||
0.0809054 | + | 0.996722i | \(0.474219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −769.709 | −0.356658 | −0.178329 | − | 0.983971i | \(-0.557069\pi\) | ||||
−0.178329 | + | 0.983971i | \(0.557069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 202.224 | 0.0920454 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1997.45 | −0.877823 | −0.438911 | − | 0.898530i | \(-0.644636\pi\) | ||||
−0.438911 | + | 0.898530i | \(0.644636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2572.66i | 1.11128i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2606.09i | − 1.08820i | −0.839019 | − | 0.544102i | \(-0.816870\pi\) | ||||
0.839019 | − | 0.544102i | \(-0.183130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 458.311i | 0.188210i | 0.995562 | + | 0.0941050i | \(0.0299989\pi\) | ||||
−0.995562 | + | 0.0941050i | \(0.970001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 16.9925i | − 0.00675305i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.4274 | 0.00798823 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1432.72 | 0.542762 | 0.271381 | − | 0.962472i | \(-0.412520\pi\) | ||||
0.271381 | + | 0.962472i | \(0.412520\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4839.58 | 1.80498 | 0.902489 | − | 0.430713i | \(-0.141738\pi\) | ||||
0.902489 | + | 0.430713i | \(0.141738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1209.90 | −0.437572 | −0.218786 | − | 0.975773i | \(-0.570210\pi\) | ||||
−0.218786 | + | 0.975773i | \(0.570210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 53.0166i | − 0.0188857i | −0.999955 | − | 0.00944283i | \(-0.996994\pi\) | ||||
0.999955 | − | 0.00944283i | \(-0.00300579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1486.61i | 0.513987i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 289.339i | − 0.0985770i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.9423i | 0.00494538i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3491.01 | −1.13901 | −0.569505 | − | 0.821988i | \(-0.692865\pi\) | ||||
−0.569505 | + | 0.821988i | \(0.692865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 237.344 | 0.0752870 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1992.36 | −0.623274 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2593.70 | 0.789461 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4119.13i | − 1.23694i | −0.785808 | − | 0.618470i | \(-0.787753\pi\) | ||||
0.785808 | − | 0.618470i | \(-0.212247\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3739.71i | 1.09345i | 0.837312 | + | 0.546725i | \(0.184126\pi\) | ||||
−0.837312 | + | 0.546725i | \(0.815874\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 175.001i | 0.0504995i | 0.999681 | + | 0.0252498i | \(0.00803810\pi\) | ||||
−0.999681 | + | 0.0252498i | \(0.991962\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3450.11i | − 0.970062i | −0.874497 | − | 0.485031i | \(-0.838808\pi\) | ||||
0.874497 | − | 0.485031i | \(-0.161192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −332.978 | −0.0924301 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1133.29 | −0.306722 | −0.153361 | − | 0.988170i | \(-0.549010\pi\) | ||||
−0.153361 | + | 0.988170i | \(0.549010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1350.31 | 0.360918 | 0.180459 | − | 0.983583i | \(-0.442242\pi\) | ||||
0.180459 | + | 0.983583i | \(0.442242\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −77.3610 | −0.0201731 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1897.25i | 0.488742i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 5787.89i | − 1.45549i | −0.685846 | − | 0.727746i | \(-0.740568\pi\) | ||||
0.685846 | − | 0.727746i | \(-0.259432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 69.1239i | 0.0171770i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4252.21i | 1.03208i | 0.856563 | + | 0.516042i | \(0.172595\pi\) | ||||
−0.856563 | + | 0.516042i | \(0.827405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −391.820 | −0.0940019 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6519.24 | 1.52849 | 0.764246 | − | 0.644924i | \(-0.223111\pi\) | ||||
0.764246 | + | 0.644924i | \(0.223111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −460.752 | −0.106807 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −938.205 | −0.212652 | −0.106326 | − | 0.994331i | \(-0.533909\pi\) | ||||
−0.106326 | + | 0.994331i | \(0.533909\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3123.60i | 0.700167i | 0.936719 | + | 0.350083i | \(0.113847\pi\) | ||||
−0.936719 | + | 0.350083i | \(0.886153\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 43.6856i | − 0.00957941i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4328.77i | 0.938954i | 0.882945 | + | 0.469477i | \(0.155558\pi\) | ||||
−0.882945 | + | 0.469477i | \(0.844442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4644.87i | 0.986084i | 0.870006 | + | 0.493042i | \(0.164115\pi\) | ||||
−0.870006 | + | 0.493042i | \(0.835885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 864.160 | 0.181516 | 0.0907580 | − | 0.995873i | \(-0.471071\pi\) | ||||
0.0907580 | + | 0.995873i | \(0.471071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6671.68 | −1.37218 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1540.56 | 0.313568 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8487.85 | 1.69237 | 0.846187 | − | 0.532886i | \(-0.178892\pi\) | ||||
0.846187 | + | 0.532886i | \(0.178892\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 216.365i | − 0.0427027i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8776.76i | 1.69757i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5472.76i | − 1.04799i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 473.195i | 0.0888362i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4082.00 | 0.758867 | 0.379433 | − | 0.925219i | \(-0.376119\pi\) | ||||
0.379433 | + | 0.925219i | \(0.376119\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1366.89 | 0.249226 | 0.124613 | − | 0.992205i | \(-0.460231\pi\) | ||||
0.124613 | + | 0.992205i | \(0.460231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5039.16 | −0.910001 | −0.455001 | − | 0.890491i | \(-0.650361\pi\) | ||||
−0.455001 | + | 0.890491i | \(0.650361\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4699.69 | 0.832685 | 0.416342 | − | 0.909208i | \(-0.363312\pi\) | ||||
0.416342 | + | 0.909208i | \(0.363312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 25.2436i | − 0.00443064i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2466.89i | − 0.424958i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 5546.82i | − 0.946714i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7677.92i | 1.28662i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3220.43 | 0.534776 | 0.267388 | − | 0.963589i | \(-0.413839\pi\) | ||||
0.267388 | + | 0.963589i | \(0.413839\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 140.325 | 0.0228860 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1198.67 | −0.193756 | −0.0968778 | − | 0.995296i | \(-0.530886\pi\) | ||||
−0.0968778 | + | 0.995296i | \(0.530886\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.8317 | 0.00537270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 5321.44i | − 0.837698i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4230.19i | 0.654434i | 0.944949 | + | 0.327217i | \(0.106111\pi\) | ||||
−0.944949 | + | 0.327217i | \(0.893889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3597.47i | 0.551771i | 0.961190 | + | 0.275886i | \(0.0889711\pi\) | ||||
−0.961190 | + | 0.275886i | \(0.911029\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10954.3i | 1.65167i | 0.563911 | + | 0.825836i | \(0.309296\pi\) | ||||
−0.563911 | + | 0.825836i | \(0.690704\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −355.037 | −0.0530800 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8651.30 | −1.27186 | −0.635931 | − | 0.771746i | \(-0.719384\pi\) | ||||
−0.635931 | + | 0.771746i | \(0.719384\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5054.51 | −0.736916 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −649.817 | −0.0931862 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1016.25i | 0.144544i | 0.997385 | + | 0.0722720i | \(0.0230250\pi\) | ||||
−0.997385 | + | 0.0722720i | \(0.976975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10624.2i | 1.48674i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13256.0i | 1.84013i | 0.391767 | + | 0.920065i | \(0.371864\pi\) | ||||
−0.391767 | + | 0.920065i | \(0.628136\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3205.22i | − 0.437871i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −121.292 | −0.0164389 | −0.00821945 | − | 0.999966i | \(-0.502616\pi\) | ||||
−0.00821945 | + | 0.999966i | \(0.502616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8469.57 | 1.12996 | 0.564980 | − | 0.825105i | \(-0.308884\pi\) | ||||
0.564980 | + | 0.825105i | \(0.308884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.54611 | 0.000866547 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10022.4 | −1.30631 | −0.653156 | − | 0.757223i | \(-0.726555\pi\) | ||||
−0.653156 | + | 0.757223i | \(0.726555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 11411.9i | − 1.47603i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 873.848i | − 0.111312i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14528.4i | 1.83668i | 0.395793 | + | 0.918340i | \(0.370470\pi\) | ||||
−0.395793 | + | 0.918340i | \(0.629530\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7080.47i | 0.881750i | 0.897569 | + | 0.440875i | \(0.145332\pi\) | ||||
−0.897569 | + | 0.440875i | \(0.854668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4295.66 | 0.530973 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.65337 | 0.000810308 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6672.53 | −0.806688 | −0.403344 | − | 0.915048i | \(-0.632152\pi\) | ||||
−0.403344 | + | 0.915048i | \(0.632152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4989.03 | −0.594417 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1098.67i | − 0.129956i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13972.2i | 1.62909i | 0.580101 | + | 0.814545i | \(0.303013\pi\) | ||||
−0.580101 | + | 0.814545i | \(0.696987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 13047.1i | − 1.51039i | −0.655499 | − | 0.755196i | \(-0.727541\pi\) | ||||
0.655499 | − | 0.755196i | \(-0.272459\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7212.22i | 0.823162i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10911.1 | 1.23659 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13232.4 | 1.47884 | 0.739422 | − | 0.673242i | \(-0.235099\pi\) | ||||
0.739422 | + | 0.673242i | \(0.235099\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1480.79 | 0.164347 | 0.0821736 | − | 0.996618i | \(-0.473814\pi\) | ||||
0.0821736 | + | 0.996618i | \(0.473814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8347.66 | 0.913782 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 5195.44i | − 0.564840i | −0.959291 | − | 0.282420i | \(-0.908863\pi\) | ||||
0.959291 | − | 0.282420i | \(-0.0911371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11273.5i | 1.20908i | 0.796576 | + | 0.604539i | \(0.206643\pi\) | ||||
−0.796576 | + | 0.604539i | \(0.793357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1106.21i | − 0.117842i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 8863.37i | − 0.931600i | −0.884890 | − | 0.465800i | \(-0.845767\pi\) | ||||
0.884890 | − | 0.465800i | \(-0.154233\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 113.290 | 0.0118284 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 831.169 | 0.0856392 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5663.24 | −0.579683 | −0.289842 | − | 0.957075i | \(-0.593603\pi\) | ||||
−0.289842 | + | 0.957075i | \(0.593603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14366.0 | 1.45139 | 0.725695 | − | 0.688017i | \(-0.241518\pi\) | ||||
0.725695 | + | 0.688017i | \(0.241518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7300.37i | 0.732779i | 0.930462 | + | 0.366390i | \(0.119406\pi\) | ||||
−0.930462 | + | 0.366390i | \(0.880594\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 9456.68i | − 0.937051i | −0.883450 | − | 0.468526i | \(-0.844785\pi\) | ||||
0.883450 | − | 0.468526i | \(-0.155215\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 3235.68i | − 0.318571i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 92.9312i | 0.00903379i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5275.63 | −0.509606 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10398.2 | 0.991869 | 0.495935 | − | 0.868360i | \(-0.334826\pi\) | ||||
0.495935 | + | 0.868360i | \(0.334826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 844.788 | 0.0800811 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −448.822 | −0.0420205 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1299.05i | − 0.120874i | −0.998172 | − | 0.0604369i | \(-0.980751\pi\) | ||||
0.998172 | − | 0.0604369i | \(-0.0192494\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3740.15i | 0.343769i | 0.985117 | + | 0.171885i | \(0.0549856\pi\) | ||||
−0.985117 | + | 0.171885i | \(0.945014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4167.57i | 0.380726i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8186.57i | 0.738869i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4346.25 | 0.389910 | 0.194955 | − | 0.980812i | \(-0.437544\pi\) | ||||
0.194955 | + | 0.980812i | \(0.437544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11191.4 | 0.992052 | 0.496026 | − | 0.868308i | \(-0.334792\pi\) | ||||
0.496026 | + | 0.868308i | \(0.334792\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1389.72 | 0.122459 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14092.9 | −1.22722 | −0.613610 | − | 0.789609i | \(-0.710283\pi\) | ||||
−0.613610 | + | 0.789609i | \(0.710283\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14983.7i | 1.29714i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 718.325i | 0.0614624i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 130.376i | − 0.0110908i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 9859.21i | − 0.829060i | −0.910036 | − | 0.414530i | \(-0.863946\pi\) | ||||
0.910036 | − | 0.414530i | \(-0.136054\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13061.8 | −1.09207 | −0.546037 | − | 0.837761i | \(-0.683864\pi\) | ||||
−0.546037 | + | 0.837761i | \(0.683864\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5585.41 | −0.461678 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26449.6 | 2.17388 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14384.6 | 1.16898 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1898.81i | − 0.153444i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 30.2905i | − 0.00242060i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 10232.9i | − 0.813212i | −0.913604 | − | 0.406606i | \(-0.866712\pi\) | ||||
0.913604 | − | 0.406606i | \(-0.133288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1075.99i | 0.0845691i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14051.5 | −1.09835 | −0.549176 | − | 0.835706i | \(-0.685059\pi\) | ||||
−0.549176 | + | 0.835706i | \(0.685059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3048.52 | −0.235701 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20149.5 | −1.54945 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −390.845 | −0.0297318 | −0.0148659 | − | 0.999889i | \(-0.504732\pi\) | ||||
−0.0148659 | + | 0.999889i | \(0.504732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11799.6i | 0.892792i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7548.18i | 0.565041i | 0.959261 | + | 0.282520i | \(0.0911705\pi\) | ||||
−0.959261 | + | 0.282520i | \(0.908830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 983.296i | − 0.0732170i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13968.1i | 1.02912i | 0.857453 | + | 0.514562i | \(0.172045\pi\) | ||||
−0.857453 | + | 0.514562i | \(0.827955\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1253.22 | −0.0918488 | −0.0459244 | − | 0.998945i | \(-0.514623\pi\) | ||||
−0.0459244 | + | 0.998945i | \(0.514623\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24405.3 | −1.77004 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23968.2 | 1.72930 | 0.864651 | − | 0.502373i | \(-0.167539\pi\) | ||||
0.864651 | + | 0.502373i | \(0.167539\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25333.6 | −1.80898 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 180.406i | − 0.0128159i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 18003.7i | − 1.26592i | −0.774186 | − | 0.632958i | \(-0.781841\pi\) | ||||
0.774186 | − | 0.632958i | \(-0.218159\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 4085.65i | − 0.285817i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 12257.6i | − 0.848835i | −0.905467 | − | 0.424417i | \(-0.860479\pi\) | ||||
0.905467 | − | 0.424417i | \(-0.139521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1080.72 | −0.0744627 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1985.47 | −0.135433 | −0.0677164 | − | 0.997705i | \(-0.521571\pi\) | ||||
−0.0677164 | + | 0.997705i | \(0.521571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8652.96 | −0.587291 | −0.293645 | − | 0.955914i | \(-0.594868\pi\) | ||||
−0.293645 | + | 0.955914i | \(0.594868\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1195.62 | 0.0803455 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16866.0i | − 1.12779i | −0.825846 | − | 0.563896i | \(-0.809302\pi\) | ||||
0.825846 | − | 0.563896i | \(-0.190698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 16554.1i | − 1.09608i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20971.3i | − 1.38176i | −0.722968 | − | 0.690882i | \(-0.757222\pi\) | ||||
0.722968 | − | 0.690882i | \(-0.242778\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7835.37i | 0.511248i | 0.966776 | + | 0.255624i | \(0.0822809\pi\) | ||||
−0.966776 | + | 0.255624i | \(0.917719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2340.76 | −0.151992 | −0.0759960 | − | 0.997108i | \(-0.524214\pi\) | ||||
−0.0759960 | + | 0.997108i | \(0.524214\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25507.5 | −1.64035 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15323.0 | 0.980672 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1098.43 | −0.0696301 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18345.7i | 1.15742i | 0.815534 | + | 0.578709i | \(0.196443\pi\) | ||||
−0.815534 | + | 0.578709i | \(0.803557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1554.11i | − 0.0971228i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3846.03i | − 0.239223i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 10560.3i | − 0.650713i | −0.945591 | − | 0.325357i | \(-0.894516\pi\) | ||||
0.945591 | − | 0.325357i | \(-0.105484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10020.1 | 0.614548 | 0.307274 | − | 0.951621i | \(-0.400583\pi\) | ||||
0.307274 | + | 0.951621i | \(0.400583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3986.01 | −0.242204 | −0.121102 | − | 0.992640i | \(-0.538643\pi\) | ||||
−0.121102 | + | 0.992640i | \(0.538643\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 84.7173 | 0.00512395 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16847.0 | 1.00961 | 0.504804 | − | 0.863234i | \(-0.331565\pi\) | ||||
0.504804 | + | 0.863234i | \(0.331565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 552.246i | − 0.0329436i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2518.82i | − 0.148891i | −0.997225 | − | 0.0744456i | \(-0.976281\pi\) | ||||
0.997225 | − | 0.0744456i | \(-0.0237187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30098.8i | 1.77111i | 0.464530 | + | 0.885557i | \(0.346223\pi\) | ||||
−0.464530 | + | 0.885557i | \(0.653777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 790.533i | − 0.0460986i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14102.6 | −0.818671 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −185.278 | −0.0106596 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4759.03 | 0.272581 | 0.136291 | − | 0.990669i | \(-0.456482\pi\) | ||||
0.136291 | + | 0.990669i | \(0.456482\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19148.9 | 1.08708 | 0.543540 | − | 0.839383i | \(-0.317084\pi\) | ||||
0.543540 | + | 0.839383i | \(0.317084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10349.1i | 0.584922i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9631.82i | − 0.539607i | −0.962915 | − | 0.269803i | \(-0.913041\pi\) | ||||
0.962915 | − | 0.269803i | \(-0.0869587\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 89.4013i | − 0.00498664i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 22906.5i | − 1.26657i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8176.16 | −0.450124 | −0.225062 | − | 0.974344i | \(-0.572258\pi\) | ||||
−0.225062 | + | 0.974344i | \(0.572258\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2504.79 | −0.136708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18703.4 | −1.01642 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6120.23 | −0.329754 | −0.164877 | − | 0.986314i | \(-0.552723\pi\) | ||||
−0.164877 | + | 0.986314i | \(0.552723\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 803.486i | − 0.0431068i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 32044.7i | − 1.70462i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 10678.5i | − 0.565639i | −0.959173 | − | 0.282819i | \(-0.908730\pi\) | ||||
0.959173 | − | 0.282819i | \(-0.0912697\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 18900.4i | − 0.992741i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.1138 | −0.000738220 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17698.3 | 0.917992 | 0.458996 | − | 0.888438i | \(-0.348209\pi\) | ||||
0.458996 | + | 0.888438i | \(0.348209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16563.4 | 0.855552 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8912.67 | 0.456563 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 9538.33i | − 0.486599i | −0.969951 | − | 0.243299i | \(-0.921770\pi\) | ||||
0.969951 | − | 0.243299i | \(-0.0782297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 15342.4i | − 0.776277i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 10543.9i | − 0.531307i | −0.964069 | − | 0.265653i | \(-0.914412\pi\) | ||||
0.964069 | − | 0.265653i | \(-0.0855877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.9440i | 0.00274612i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20329.2 | −1.01194 | −0.505969 | − | 0.862552i | \(-0.668865\pi\) | ||||
−0.505969 | + | 0.862552i | \(0.668865\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19114.3 | 0.943791 | 0.471895 | − | 0.881655i | \(-0.343570\pi\) | ||||
0.471895 | + | 0.881655i | \(0.343570\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2807.47 | −0.138064 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43783.4 | −2.13593 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 24797.9i | − 1.20491i | −0.798152 | − | 0.602456i | \(-0.794189\pi\) | ||||
0.798152 | − | 0.602456i | \(-0.205811\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2602.38i | 0.125444i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7338.12i | 0.352323i | 0.984361 | + | 0.176161i | \(0.0563681\pi\) | ||||
−0.984361 | + | 0.176161i | \(0.943632\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 34547.3i | − 1.64565i | −0.568296 | − | 0.822824i | \(-0.692397\pi\) | ||||
0.568296 | − | 0.822824i | \(-0.307603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24810.5 | 1.17719 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10756.7 | 0.506390 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13988.7 | 0.655977 | 0.327988 | − | 0.944682i | \(-0.393629\pi\) | ||||
0.327988 | + | 0.944682i | \(0.393629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11871.5 | −0.552380 | −0.276190 | − | 0.961103i | \(-0.589072\pi\) | ||||
−0.276190 | + | 0.961103i | \(0.589072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11944.8i | 0.553640i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 13681.3i | − 0.629247i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 139.014i | − 0.00636914i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 3041.57i | − 0.138291i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1362.56 | 0.0617155 | 0.0308577 | − | 0.999524i | \(-0.490176\pi\) | ||||
0.0308577 | + | 0.999524i | \(0.490176\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22673.2 | −1.01917 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23525.0 | −1.05347 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16568.7 | 0.736380 | 0.368190 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368190 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21524.4i | 0.953038i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 254.434i | − 0.0111815i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3657.04i | − 0.160116i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 17086.8i | − 0.742571i | −0.928519 | − | 0.371286i | \(-0.878917\pi\) | ||||
0.928519 | − | 0.371286i | \(-0.121083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15277.5 | 0.661486 | 0.330743 | − | 0.943721i | \(-0.392701\pi\) | ||||
0.330743 | + | 0.943721i | \(0.392701\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 302.514 | 0.0130020 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11222.7 | 0.480580 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27304.1 | −1.16068 | −0.580342 | − | 0.814373i | \(-0.697081\pi\) | ||||
−0.580342 | + | 0.814373i | \(0.697081\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13760.9i | 0.582835i | 0.956596 | + | 0.291418i | \(0.0941270\pi\) | ||||
−0.956596 | + | 0.291418i | \(0.905873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7095.81i | 0.298362i | 0.988810 | + | 0.149181i | \(0.0476637\pi\) | ||||
−0.988810 | + | 0.149181i | \(0.952336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 16873.6i | − 0.706930i | −0.935448 | − | 0.353465i | \(-0.885003\pi\) | ||||
0.935448 | − | 0.353465i | \(-0.114997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5000.77i | 0.208003i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −691.487 | −0.0286585 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3582.07 | −0.147398 | −0.0736989 | − | 0.997281i | \(-0.523480\pi\) | ||||
−0.0736989 | + | 0.997281i | \(0.523480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19238.8 | −0.788832 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 181.672 | 0.00739612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 27569.1i | − 1.11840i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3716.96i | − 0.149725i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32087.2i | 1.28798i | 0.765035 | + | 0.643988i | \(0.222721\pi\) | ||||
−0.765035 | + | 0.643988i | \(0.777279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 34615.5i | − 1.37975i | −0.723931 | − | 0.689873i | \(-0.757666\pi\) | ||||
0.723931 | − | 0.689873i | \(-0.242334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9163.98 | 0.363994 | 0.181997 | − | 0.983299i | \(-0.441744\pi\) | ||||
0.181997 | + | 0.983299i | \(0.441744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9624.28 | 0.379622 | 0.189811 | − | 0.981821i | \(-0.439212\pi\) | ||||
0.189811 | + | 0.981821i | \(0.439212\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1794.46 | −0.0705357 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 342.153 | 0.0133564 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6976.32i | 0.271393i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4637.44i | 0.179170i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6459.97i | 0.248732i | 0.992236 | + | 0.124366i | \(0.0396896\pi\) | ||||
−0.992236 | + | 0.124366i | \(0.960310\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16282.5i | 0.622670i | 0.950300 | + | 0.311335i | \(0.100776\pi\) | ||||
−0.950300 | + | 0.311335i | \(0.899224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44992.8 | 1.71476 | 0.857378 | − | 0.514687i | \(-0.172092\pi\) | ||||
0.857378 | + | 0.514687i | \(0.172092\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28759.6 | −1.08867 | −0.544336 | − | 0.838867i | \(-0.683218\pi\) | ||||
−0.544336 | + | 0.838867i | \(0.683218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35835.2 | −1.35194 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15744.8 | −0.590009 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2341.24i | − 0.0874404i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6902.31i | 0.256068i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29784.0i | 1.10127i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 411.735i | 0.0151232i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10771.9 | −0.394351 | −0.197175 | − | 0.980368i | \(-0.563177\pi\) | ||||
−0.197175 | + | 0.980368i | \(0.563177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6368.46 | 0.231610 | 0.115805 | − | 0.993272i | \(-0.463055\pi\) | ||||
0.115805 | + | 0.993272i | \(0.463055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 430.183 | 0.0155936 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12733.9 | −0.458572 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 21188.6i | − 0.760553i | −0.924873 | − | 0.380277i | \(-0.875829\pi\) | ||||
0.924873 | − | 0.380277i | \(-0.124171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 17650.8i | − 0.629449i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2349.08i | 0.0834997i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 39628.4i | − 1.39953i | −0.714371 | − | 0.699767i | \(-0.753287\pi\) | ||||
0.714371 | − | 0.699767i | \(-0.246713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3657.99 | −0.128771 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.3514 | 0.000641878 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44882.9 | −1.56485 | −0.782423 | − | 0.622747i | \(-0.786017\pi\) | ||||
−0.782423 | + | 0.622747i | \(0.786017\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19290.8 | −0.668290 | −0.334145 | − | 0.942522i | \(-0.608447\pi\) | ||||
−0.334145 | + | 0.942522i | \(0.608447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 63290.2i | − 2.18559i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 25216.9i | − 0.865301i | −0.901562 | − | 0.432651i | \(-0.857578\pi\) | ||||
0.901562 | − | 0.432651i | \(-0.142422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 32305.8i | − 1.10505i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43956.3i | 1.49411i | 0.664764 | + | 0.747054i | \(0.268532\pi\) | ||||
−0.664764 | + | 0.747054i | \(0.731468\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1287.11 | 0.0436126 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2061.45 | −0.0694136 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20540.5 | 0.689486 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4347.75 | 0.145035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12899.3i | 0.428969i | 0.976727 | + | 0.214485i | \(0.0688072\pi\) | ||||
−0.976727 | + | 0.214485i | \(0.931193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15206.8i | 0.502584i | 0.967911 | + | 0.251292i | \(0.0808554\pi\) | ||||
−0.967911 | + | 0.251292i | \(0.919145\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57756.3i | 1.90296i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7912.42i | 0.259100i | 0.991573 | + | 0.129550i | \(0.0413533\pi\) | ||||
−0.991573 | + | 0.129550i | \(0.958647\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 433.135 | 0.0141400 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28573.8 | 0.927123 | 0.463562 | − | 0.886065i | \(-0.346571\pi\) | ||||
0.463562 | + | 0.886065i | \(0.346571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1086.94 | −0.0351602 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51916.8 | 1.66922 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 27399.6i | − 0.878282i | −0.898418 | − | 0.439141i | \(-0.855283\pi\) | ||||
0.898418 | − | 0.439141i | \(-0.144717\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 47.6287i | − 0.00151752i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 484.325i | − 0.0153849i | −0.999970 | − | 0.00769244i | \(-0.997551\pi\) | ||||
0.999970 | − | 0.00769244i | \(-0.00244860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.4.f.b.431.13 | 24 | ||
3.2 | odd | 2 | inner | 864.4.f.b.431.11 | 24 | ||
4.3 | odd | 2 | 216.4.f.b.107.10 | yes | 24 | ||
8.3 | odd | 2 | inner | 864.4.f.b.431.12 | 24 | ||
8.5 | even | 2 | 216.4.f.b.107.16 | yes | 24 | ||
12.11 | even | 2 | 216.4.f.b.107.15 | yes | 24 | ||
24.5 | odd | 2 | 216.4.f.b.107.9 | ✓ | 24 | ||
24.11 | even | 2 | inner | 864.4.f.b.431.14 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.f.b.107.9 | ✓ | 24 | 24.5 | odd | 2 | ||
216.4.f.b.107.10 | yes | 24 | 4.3 | odd | 2 | ||
216.4.f.b.107.15 | yes | 24 | 12.11 | even | 2 | ||
216.4.f.b.107.16 | yes | 24 | 8.5 | even | 2 | ||
864.4.f.b.431.11 | 24 | 3.2 | odd | 2 | inner | ||
864.4.f.b.431.12 | 24 | 8.3 | odd | 2 | inner | ||
864.4.f.b.431.13 | 24 | 1.1 | even | 1 | trivial | ||
864.4.f.b.431.14 | 24 | 24.11 | even | 2 | inner |