Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 921x^{12} + 8986x^{10} + 46812x^{8} + 125072x^{6} + 152129x^{4} + 65614x^{2} + 5041 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.13 | ||
Root | \(2.98036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.i.485.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.98036i | 1.49018i | 0.666963 | + | 0.745091i | \(0.267594\pi\) | ||||
−0.666963 | + | 0.745091i | \(0.732406\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.88257 | −1.22064 | ||||||||
\(5\) | 7.85680i | 1.57136i | 0.618633 | + | 0.785680i | \(0.287687\pi\) | ||||
−0.618633 | + | 0.785680i | \(0.712313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.80793 | 0.401133 | 0.200567 | − | 0.979680i | \(-0.435722\pi\) | ||||
0.200567 | + | 0.979680i | \(0.435722\pi\) | |||||||
\(8\) | − 2.63038i | − 0.328798i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −23.4161 | −2.34161 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.51796 | −0.116766 | −0.0583831 | − | 0.998294i | \(-0.518594\pi\) | ||||
−0.0583831 | + | 0.998294i | \(0.518594\pi\) | |||||||
\(14\) | 8.36866i | 0.597762i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −11.6908 | −0.730674 | ||||||||
\(17\) | − 26.3991i | − 1.55289i | −0.630185 | − | 0.776445i | \(-0.717021\pi\) | ||||
0.630185 | − | 0.776445i | \(-0.282979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.5410 | −0.765316 | −0.382658 | − | 0.923890i | \(-0.624991\pi\) | ||||
−0.382658 | + | 0.923890i | \(0.624991\pi\) | |||||||
\(20\) | − 38.3614i | − 1.91807i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 25.0726i | − 1.09011i | −0.838399 | − | 0.545057i | \(-0.816508\pi\) | ||||
0.838399 | − | 0.545057i | \(-0.183492\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −36.7293 | −1.46917 | ||||||||
\(26\) | − 4.52407i | − 0.174003i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.7099 | −0.489640 | ||||||||
\(29\) | 50.7104i | 1.74863i | 0.485356 | + | 0.874317i | \(0.338690\pi\) | ||||
−0.485356 | + | 0.874317i | \(0.661310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −51.6484 | −1.66608 | −0.833038 | − | 0.553216i | \(-0.813401\pi\) | ||||
−0.833038 | + | 0.553216i | \(0.813401\pi\) | |||||||
\(32\) | − 45.3643i | − 1.41764i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 78.6790 | 2.31409 | ||||||||
\(35\) | 22.0614i | 0.630325i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.5563 | −0.528548 | −0.264274 | − | 0.964448i | \(-0.585132\pi\) | ||||
−0.264274 | + | 0.964448i | \(0.585132\pi\) | |||||||
\(38\) | − 43.3375i | − 1.14046i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 20.6664 | 0.516660 | ||||||||
\(41\) | 30.9353i | 0.754520i | 0.926107 | + | 0.377260i | \(0.123134\pi\) | ||||
−0.926107 | + | 0.377260i | \(0.876866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.11848 | 0.0492670 | 0.0246335 | − | 0.999697i | \(-0.492158\pi\) | ||||
0.0246335 | + | 0.999697i | \(0.492158\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 74.7256 | 1.62447 | ||||||||
\(47\) | − 40.2708i | − 0.856826i | −0.903583 | − | 0.428413i | \(-0.859073\pi\) | ||||
0.903583 | − | 0.428413i | \(-0.140927\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.1155 | −0.839092 | ||||||||
\(50\) | − 109.467i | − 2.18934i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.41155 | 0.142530 | ||||||||
\(53\) | − 41.1436i | − 0.776295i | −0.921597 | − | 0.388147i | \(-0.873115\pi\) | ||||
0.921597 | − | 0.388147i | \(-0.126885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 7.38594i | − 0.131892i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −151.135 | −2.60578 | ||||||||
\(59\) | 96.0644i | 1.62821i | 0.580718 | + | 0.814105i | \(0.302772\pi\) | ||||
−0.580718 | + | 0.814105i | \(0.697228\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.89529 | −0.0474637 | −0.0237319 | − | 0.999718i | \(-0.507555\pi\) | ||||
−0.0237319 | + | 0.999718i | \(0.507555\pi\) | |||||||
\(62\) | − 153.931i | − 2.48276i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 88.4391 | 1.38186 | ||||||||
\(65\) | − 11.9263i | − 0.183482i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −88.2869 | −1.31772 | −0.658858 | − | 0.752268i | \(-0.728960\pi\) | ||||
−0.658858 | + | 0.752268i | \(0.728960\pi\) | |||||||
\(68\) | 128.896i | 1.89552i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −65.7509 | −0.939299 | ||||||||
\(71\) | 11.3261i | 0.159523i | 0.996814 | + | 0.0797614i | \(0.0254158\pi\) | ||||
−0.996814 | + | 0.0797614i | \(0.974584\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 104.776 | 1.43529 | 0.717645 | − | 0.696409i | \(-0.245220\pi\) | ||||
0.717645 | + | 0.696409i | \(0.245220\pi\) | |||||||
\(74\) | − 58.2848i | − 0.787633i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 70.9975 | 0.934178 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.7886 | 0.212514 | 0.106257 | − | 0.994339i | \(-0.466113\pi\) | ||||
0.106257 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(80\) | − 91.8522i | − 1.14815i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −92.1985 | −1.12437 | ||||||||
\(83\) | − 22.7716i | − 0.274356i | −0.990546 | − | 0.137178i | \(-0.956197\pi\) | ||||
0.990546 | − | 0.137178i | \(-0.0438033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 207.413 | 2.44015 | ||||||||
\(86\) | 6.31384i | 0.0734168i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 30.7523i | − 0.345531i | −0.984963 | − | 0.172766i | \(-0.944730\pi\) | ||||
0.984963 | − | 0.172766i | \(-0.0552703\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.26233 | −0.0468388 | ||||||||
\(92\) | 122.419i | 1.33064i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 120.022 | 1.27683 | ||||||||
\(95\) | − 114.246i | − 1.20259i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −28.5285 | −0.294108 | −0.147054 | − | 0.989128i | \(-0.546979\pi\) | ||||
−0.147054 | + | 0.989128i | \(0.546979\pi\) | |||||||
\(98\) | − 122.539i | − 1.25040i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 179.334 | 1.79334 | ||||||||
\(101\) | 3.39859i | 0.0336494i | 0.999858 | + | 0.0168247i | \(0.00535573\pi\) | ||||
−0.999858 | + | 0.0168247i | \(0.994644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 22.3116 | 0.216617 | 0.108309 | − | 0.994117i | \(-0.465457\pi\) | ||||
0.108309 | + | 0.994117i | \(0.465457\pi\) | |||||||
\(104\) | 3.99282i | 0.0383925i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 122.623 | 1.15682 | ||||||||
\(107\) | 12.8713i | 0.120292i | 0.998190 | + | 0.0601461i | \(0.0191567\pi\) | ||||
−0.998190 | + | 0.0601461i | \(0.980843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 109.301 | 1.00277 | 0.501383 | − | 0.865226i | \(-0.332825\pi\) | ||||
0.501383 | + | 0.865226i | \(0.332825\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −32.8269 | −0.293098 | ||||||||
\(113\) | 92.0329i | 0.814451i | 0.913328 | + | 0.407225i | \(0.133504\pi\) | ||||
−0.913328 | + | 0.407225i | \(0.866496\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 196.991 | 1.71296 | ||||||||
\(116\) | − 247.597i | − 2.13446i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −286.307 | −2.42633 | ||||||||
\(119\) | − 74.1270i | − 0.622916i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − 8.62901i | − 0.0707296i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 252.177 | 2.03368 | ||||||||
\(125\) | − 92.1551i | − 0.737241i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.28300 | −0.0652205 | −0.0326102 | − | 0.999468i | \(-0.510382\pi\) | ||||
−0.0326102 | + | 0.999468i | \(0.510382\pi\) | |||||||
\(128\) | 82.1234i | 0.641589i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 35.5448 | 0.273421 | ||||||||
\(131\) | 1.63767i | 0.0125013i | 0.999980 | + | 0.00625065i | \(0.00198966\pi\) | ||||
−0.999980 | + | 0.00625065i | \(0.998010\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −40.8302 | −0.306994 | ||||||||
\(134\) | − 263.127i | − 1.96364i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −69.4398 | −0.510587 | ||||||||
\(137\) | − 198.118i | − 1.44612i | −0.690785 | − | 0.723060i | \(-0.742735\pi\) | ||||
0.690785 | − | 0.723060i | \(-0.257265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −187.446 | −1.34854 | −0.674268 | − | 0.738487i | \(-0.735541\pi\) | ||||
−0.674268 | + | 0.738487i | \(0.735541\pi\) | |||||||
\(140\) | − 107.716i | − 0.769402i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −33.7560 | −0.237718 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −398.421 | −2.74773 | ||||||||
\(146\) | 312.271i | 2.13884i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 95.4849 | 0.645168 | ||||||||
\(149\) | 239.185i | 1.60527i | 0.596470 | + | 0.802636i | \(0.296570\pi\) | ||||
−0.596470 | + | 0.802636i | \(0.703430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 58.6757 | 0.388581 | 0.194290 | − | 0.980944i | \(-0.437760\pi\) | ||||
0.194290 | + | 0.980944i | \(0.437760\pi\) | |||||||
\(152\) | 38.2484i | 0.251634i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 405.791i | − 2.61801i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4204 | 0.130066 | 0.0650330 | − | 0.997883i | \(-0.479285\pi\) | ||||
0.0650330 | + | 0.997883i | \(0.479285\pi\) | |||||||
\(158\) | 50.0361i | 0.316684i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 356.419 | 2.22762 | ||||||||
\(161\) | − 70.4023i | − 0.437281i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104.554 | 0.641434 | 0.320717 | − | 0.947175i | \(-0.396076\pi\) | ||||
0.320717 | + | 0.947175i | \(0.396076\pi\) | |||||||
\(164\) | − 151.044i | − 0.920999i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 67.8676 | 0.408841 | ||||||||
\(167\) | 39.2102i | 0.234792i | 0.993085 | + | 0.117396i | \(0.0374546\pi\) | ||||
−0.993085 | + | 0.117396i | \(0.962545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −166.696 | −0.986366 | ||||||||
\(170\) | 618.165i | 3.63627i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.3436 | −0.0601374 | ||||||||
\(173\) | 91.4277i | 0.528484i | 0.964456 | + | 0.264242i | \(0.0851217\pi\) | ||||
−0.964456 | + | 0.264242i | \(0.914878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −103.134 | −0.589334 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 91.6530 | 0.514904 | ||||||||
\(179\) | 218.182i | 1.21890i | 0.792826 | + | 0.609448i | \(0.208609\pi\) | ||||
−0.792826 | + | 0.609448i | \(0.791391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −44.8209 | −0.247629 | −0.123815 | − | 0.992305i | \(-0.539513\pi\) | ||||
−0.123815 | + | 0.992305i | \(0.539513\pi\) | |||||||
\(182\) | − 12.7033i | − 0.0697983i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −65.9506 | −0.358427 | ||||||||
\(185\) | − 153.650i | − 0.830540i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 196.625i | 1.04588i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 340.494 | 1.79207 | ||||||||
\(191\) | 148.973i | 0.779964i | 0.920822 | + | 0.389982i | \(0.127519\pi\) | ||||
−0.920822 | + | 0.389982i | \(0.872481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 193.706 | 1.00366 | 0.501830 | − | 0.864966i | \(-0.332660\pi\) | ||||
0.501830 | + | 0.864966i | \(0.332660\pi\) | |||||||
\(194\) | − 85.0253i | − 0.438275i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 200.749 | 1.02423 | ||||||||
\(197\) | 331.307i | 1.68176i | 0.541220 | + | 0.840881i | \(0.317963\pi\) | ||||
−0.541220 | + | 0.840881i | \(0.682037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −294.829 | −1.48155 | −0.740775 | − | 0.671753i | \(-0.765542\pi\) | ||||
−0.740775 | + | 0.671753i | \(0.765542\pi\) | |||||||
\(200\) | 96.6123i | 0.483061i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.1290 | −0.0501438 | ||||||||
\(203\) | 142.391i | 0.701435i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −243.053 | −1.18562 | ||||||||
\(206\) | 66.4966i | 0.322799i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.7461 | 0.0853180 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −115.727 | −0.548470 | −0.274235 | − | 0.961663i | \(-0.588425\pi\) | ||||
−0.274235 | + | 0.961663i | \(0.588425\pi\) | |||||||
\(212\) | 200.887i | 0.947579i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −38.3611 | −0.179257 | ||||||||
\(215\) | 16.6445i | 0.0774162i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −145.025 | −0.668319 | ||||||||
\(218\) | 325.758i | 1.49430i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.0728i | 0.181325i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −244.092 | −1.09458 | −0.547291 | − | 0.836942i | \(-0.684341\pi\) | ||||
−0.547291 | + | 0.836942i | \(0.684341\pi\) | |||||||
\(224\) | − 127.380i | − 0.568661i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −274.292 | −1.21368 | ||||||||
\(227\) | 268.225i | 1.18161i | 0.806815 | + | 0.590804i | \(0.201189\pi\) | ||||
−0.806815 | + | 0.590804i | \(0.798811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 186.092 | 0.812628 | 0.406314 | − | 0.913734i | \(-0.366814\pi\) | ||||
0.406314 | + | 0.913734i | \(0.366814\pi\) | |||||||
\(230\) | 587.104i | 2.55263i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 133.388 | 0.574947 | ||||||||
\(233\) | − 162.181i | − 0.696056i | −0.937484 | − | 0.348028i | \(-0.886851\pi\) | ||||
0.937484 | − | 0.348028i | \(-0.113149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 316.400 | 1.34638 | ||||||||
\(236\) | − 469.041i | − 1.98746i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 220.925 | 0.928258 | ||||||||
\(239\) | − 71.0937i | − 0.297463i | −0.988878 | − | 0.148732i | \(-0.952481\pi\) | ||||
0.988878 | − | 0.148732i | \(-0.0475190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 212.799 | 0.882984 | 0.441492 | − | 0.897265i | \(-0.354449\pi\) | ||||
0.441492 | + | 0.897265i | \(0.354449\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.1364 | 0.0579363 | ||||||||
\(245\) | − 323.036i | − 1.31852i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.0727 | 0.0893631 | ||||||||
\(248\) | 135.855i | 0.547802i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 274.656 | 1.09862 | ||||||||
\(251\) | 187.607i | 0.747437i | 0.927542 | + | 0.373718i | \(0.121917\pi\) | ||||
−0.927542 | + | 0.373718i | \(0.878083\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 24.6864i | − 0.0971904i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 108.999 | 0.425776 | ||||||||
\(257\) | 290.794i | 1.13149i | 0.824579 | + | 0.565747i | \(0.191412\pi\) | ||||
−0.824579 | + | 0.565747i | \(0.808588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −54.9127 | −0.212018 | ||||||||
\(260\) | 58.2311i | 0.223966i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.88086 | −0.0186292 | ||||||||
\(263\) | − 458.564i | − 1.74359i | −0.489870 | − | 0.871795i | \(-0.662956\pi\) | ||||
0.489870 | − | 0.871795i | \(-0.337044\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 323.257 | 1.21984 | ||||||||
\(266\) | − 121.689i | − 0.457477i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 431.067 | 1.60846 | ||||||||
\(269\) | − 208.752i | − 0.776030i | −0.921653 | − | 0.388015i | \(-0.873161\pi\) | ||||
0.921653 | − | 0.388015i | \(-0.126839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −460.949 | −1.70092 | −0.850459 | − | 0.526042i | \(-0.823676\pi\) | ||||
−0.850459 | + | 0.526042i | \(0.823676\pi\) | |||||||
\(272\) | 308.626i | 1.13466i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 590.465 | 2.15498 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −105.652 | −0.381417 | −0.190708 | − | 0.981647i | \(-0.561078\pi\) | ||||
−0.190708 | + | 0.981647i | \(0.561078\pi\) | |||||||
\(278\) | − 558.659i | − 2.00956i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 58.0299 | 0.207250 | ||||||||
\(281\) | 430.979i | 1.53373i | 0.641806 | + | 0.766867i | \(0.278185\pi\) | ||||
−0.641806 | + | 0.766867i | \(0.721815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 301.717 | 1.06614 | 0.533068 | − | 0.846072i | \(-0.321039\pi\) | ||||
0.533068 | + | 0.846072i | \(0.321039\pi\) | |||||||
\(284\) | − 55.3006i | − 0.194720i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 86.8643i | 0.302663i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −407.914 | −1.41147 | ||||||||
\(290\) | − 1187.44i | − 4.09462i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −511.577 | −1.75198 | ||||||||
\(293\) | − 46.3147i | − 0.158071i | −0.996872 | − | 0.0790354i | \(-0.974816\pi\) | ||||
0.996872 | − | 0.0790354i | \(-0.0251840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −754.759 | −2.55851 | ||||||||
\(296\) | 51.4405i | 0.173786i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −712.860 | −2.39215 | ||||||||
\(299\) | 38.0593i | 0.127289i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.94855 | 0.0197626 | ||||||||
\(302\) | 174.875i | 0.579056i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 169.996 | 0.559197 | ||||||||
\(305\) | − 22.7477i | − 0.0745826i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −448.259 | −1.46013 | −0.730063 | − | 0.683379i | \(-0.760509\pi\) | ||||
−0.730063 | + | 0.683379i | \(0.760509\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1209.40 | 3.90131 | ||||||||
\(311\) | − 334.674i | − 1.07612i | −0.842906 | − | 0.538062i | \(-0.819157\pi\) | ||||
0.842906 | − | 0.538062i | \(-0.180843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 102.316 | 0.326888 | 0.163444 | − | 0.986553i | \(-0.447740\pi\) | ||||
0.163444 | + | 0.986553i | \(0.447740\pi\) | |||||||
\(314\) | 60.8601i | 0.193822i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −81.9714 | −0.259403 | ||||||||
\(317\) | 377.875i | 1.19204i | 0.802971 | + | 0.596018i | \(0.203251\pi\) | ||||
−0.802971 | + | 0.596018i | \(0.796749\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 694.848i | 2.17140i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 209.824 | 0.651629 | ||||||||
\(323\) | 383.870i | 1.18845i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 55.7537 | 0.171550 | ||||||||
\(326\) | 311.608i | 0.955853i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 81.3717 | 0.248084 | ||||||||
\(329\) | − 113.078i | − 0.343701i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −170.972 | −0.516533 | −0.258266 | − | 0.966074i | \(-0.583151\pi\) | ||||
−0.258266 | + | 0.966074i | \(0.583151\pi\) | |||||||
\(332\) | 111.184i | 0.334891i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −116.861 | −0.349882 | ||||||||
\(335\) | − 693.653i | − 2.07061i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 191.936 | 0.569543 | 0.284772 | − | 0.958595i | \(-0.408082\pi\) | ||||
0.284772 | + | 0.958595i | \(0.408082\pi\) | |||||||
\(338\) | − 496.814i | − 1.46986i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1012.71 | −2.97855 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −253.038 | −0.737721 | ||||||||
\(344\) | − 5.57241i | − 0.0161989i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −272.488 | −0.787537 | ||||||||
\(347\) | − 185.859i | − 0.535616i | −0.963472 | − | 0.267808i | \(-0.913701\pi\) | ||||
0.963472 | − | 0.267808i | \(-0.0862992\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −176.390 | −0.505416 | −0.252708 | − | 0.967543i | \(-0.581321\pi\) | ||||
−0.252708 | + | 0.967543i | \(0.581321\pi\) | |||||||
\(350\) | − 307.375i | − 0.878216i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 232.825i | 0.659561i | 0.944058 | + | 0.329780i | \(0.106975\pi\) | ||||
−0.944058 | + | 0.329780i | \(0.893025\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −88.9871 | −0.250668 | ||||||||
\(356\) | 150.150i | 0.421770i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −650.263 | −1.81638 | ||||||||
\(359\) | − 403.124i | − 1.12291i | −0.827508 | − | 0.561454i | \(-0.810242\pi\) | ||||
0.827508 | − | 0.561454i | \(-0.189758\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −149.559 | −0.414291 | ||||||||
\(362\) | − 133.583i | − 0.369012i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.8111 | 0.0571734 | ||||||||
\(365\) | 823.205i | 2.25536i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −541.513 | −1.47551 | −0.737757 | − | 0.675067i | \(-0.764115\pi\) | ||||
−0.737757 | + | 0.675067i | \(0.764115\pi\) | |||||||
\(368\) | 293.119i | 0.796518i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 457.932 | 1.23766 | ||||||||
\(371\) | − 115.529i | − 0.311398i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −160.025 | −0.429021 | −0.214510 | − | 0.976722i | \(-0.568816\pi\) | ||||
−0.214510 | + | 0.976722i | \(0.568816\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −105.928 | −0.281723 | ||||||||
\(377\) | − 76.9763i | − 0.204181i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −378.620 | −0.998998 | −0.499499 | − | 0.866314i | \(-0.666483\pi\) | ||||
−0.499499 | + | 0.866314i | \(0.666483\pi\) | |||||||
\(380\) | 557.813i | 1.46793i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −443.994 | −1.16229 | ||||||||
\(383\) | − 239.567i | − 0.625502i | −0.949835 | − | 0.312751i | \(-0.898750\pi\) | ||||
0.949835 | − | 0.312751i | \(-0.101250\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 577.315i | 1.49564i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 139.292 | 0.359001 | ||||||||
\(389\) | − 502.620i | − 1.29208i | −0.763302 | − | 0.646042i | \(-0.776423\pi\) | ||||
0.763302 | − | 0.646042i | \(-0.223577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −661.896 | −1.69283 | ||||||||
\(392\) | 108.150i | 0.275892i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −987.416 | −2.50613 | ||||||||
\(395\) | 131.905i | 0.333935i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 97.1039 | 0.244594 | 0.122297 | − | 0.992494i | \(-0.460974\pi\) | ||||
0.122297 | + | 0.992494i | \(0.460974\pi\) | |||||||
\(398\) | − 878.696i | − 2.20778i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 429.395 | 1.07349 | ||||||||
\(401\) | 657.148i | 1.63877i | 0.573241 | + | 0.819387i | \(0.305686\pi\) | ||||
−0.573241 | + | 0.819387i | \(0.694314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 78.4002 | 0.194541 | ||||||||
\(404\) | − 16.5939i | − 0.0410739i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −424.378 | −1.04527 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 101.555 | 0.248302 | 0.124151 | − | 0.992263i | \(-0.460379\pi\) | ||||
0.124151 | + | 0.992263i | \(0.460379\pi\) | |||||||
\(410\) | − 724.385i | − 1.76679i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −108.938 | −0.264412 | ||||||||
\(413\) | 269.742i | 0.653129i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 178.912 | 0.431113 | ||||||||
\(416\) | 68.8613i | 0.165532i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 0.439819i | − 0.00104969i | −1.00000 | 0.000524844i | \(-0.999833\pi\) | |||||
1.00000 | 0.000524844i | \(-0.000167063\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −418.561 | −0.994208 | −0.497104 | − | 0.867691i | \(-0.665603\pi\) | ||||
−0.497104 | + | 0.867691i | \(0.665603\pi\) | |||||||
\(422\) | − 344.909i | − 0.817320i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −108.224 | −0.255244 | ||||||||
\(425\) | 969.622i | 2.28146i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.12977 | −0.0190393 | ||||||||
\(428\) | − 62.8449i | − 0.146834i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −49.6066 | −0.115364 | ||||||||
\(431\) | 252.069i | 0.584846i | 0.956289 | + | 0.292423i | \(0.0944615\pi\) | ||||
−0.956289 | + | 0.292423i | \(0.905538\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −124.450 | −0.287412 | −0.143706 | − | 0.989620i | \(-0.545902\pi\) | ||||
−0.143706 | + | 0.989620i | \(0.545902\pi\) | |||||||
\(434\) | − 432.228i | − 0.995916i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −533.672 | −1.22402 | ||||||||
\(437\) | 364.581i | 0.834283i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −73.6933 | −0.167866 | −0.0839332 | − | 0.996471i | \(-0.526748\pi\) | ||||
−0.0839332 | + | 0.996471i | \(0.526748\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −119.432 | −0.270207 | ||||||||
\(443\) | 369.937i | 0.835071i | 0.908661 | + | 0.417536i | \(0.137106\pi\) | ||||
−0.908661 | + | 0.417536i | \(0.862894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 241.614 | 0.542954 | ||||||||
\(446\) | − 727.483i | − 1.63113i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 248.331 | 0.554310 | ||||||||
\(449\) | − 726.549i | − 1.61815i | −0.587705 | − | 0.809075i | \(-0.699969\pi\) | ||||
0.587705 | − | 0.809075i | \(-0.300031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 449.357i | − 0.994153i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −799.409 | −1.76081 | ||||||||
\(455\) | − 33.4883i | − 0.0736006i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −365.520 | −0.799825 | −0.399912 | − | 0.916553i | \(-0.630959\pi\) | ||||
−0.399912 | + | 0.916553i | \(0.630959\pi\) | |||||||
\(458\) | 554.621i | 1.21096i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −961.821 | −2.09092 | ||||||||
\(461\) | − 153.670i | − 0.333340i | −0.986013 | − | 0.166670i | \(-0.946699\pi\) | ||||
0.986013 | − | 0.166670i | \(-0.0533014\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 325.357 | 0.702714 | 0.351357 | − | 0.936242i | \(-0.385720\pi\) | ||||
0.351357 | + | 0.936242i | \(0.385720\pi\) | |||||||
\(464\) | − 592.844i | − 1.27768i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 483.359 | 1.03725 | ||||||||
\(467\) | − 835.965i | − 1.79007i | −0.445991 | − | 0.895037i | \(-0.647149\pi\) | ||||
0.445991 | − | 0.895037i | \(-0.352851\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −247.904 | −0.528580 | ||||||||
\(470\) | 942.987i | 2.00635i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 252.686 | 0.535352 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 534.082 | 1.12438 | ||||||||
\(476\) | 361.930i | 0.760357i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 211.885 | 0.443274 | ||||||||
\(479\) | − 335.742i | − 0.700922i | −0.936577 | − | 0.350461i | \(-0.886025\pi\) | ||||
0.936577 | − | 0.350461i | \(-0.113975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.6857 | 0.0617165 | ||||||||
\(482\) | 634.219i | 1.31581i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 224.143i | − 0.462150i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 585.442 | 1.20214 | 0.601070 | − | 0.799196i | \(-0.294741\pi\) | ||||
0.601070 | + | 0.799196i | \(0.294741\pi\) | |||||||
\(488\) | 7.61572i | 0.0156060i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 962.766 | 1.96483 | ||||||||
\(491\) | 325.583i | 0.663102i | 0.943437 | + | 0.331551i | \(0.107572\pi\) | ||||
−0.943437 | + | 0.331551i | \(0.892428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1338.71 | 2.71543 | ||||||||
\(494\) | 65.7846i | 0.133167i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 603.810 | 1.21736 | ||||||||
\(497\) | 31.8030i | 0.0639899i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 403.323 | 0.808262 | 0.404131 | − | 0.914701i | \(-0.367574\pi\) | ||||
0.404131 | + | 0.914701i | \(0.367574\pi\) | |||||||
\(500\) | 449.954i | 0.899908i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −559.136 | −1.11382 | ||||||||
\(503\) | − 676.545i | − 1.34502i | −0.740088 | − | 0.672510i | \(-0.765216\pi\) | ||||
0.740088 | − | 0.672510i | \(-0.234784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.7021 | −0.0528754 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 40.4423 | 0.0796109 | ||||||||
\(509\) | 672.614i | 1.32144i | 0.750632 | + | 0.660721i | \(0.229749\pi\) | ||||
−0.750632 | + | 0.660721i | \(0.770251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 294.204 | 0.575742 | ||||||||
\(512\) | 653.350i | 1.27607i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −866.672 | −1.68613 | ||||||||
\(515\) | 175.297i | 0.340383i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 163.660i | − 0.315946i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −31.3708 | −0.0603284 | ||||||||
\(521\) | 73.6126i | 0.141291i | 0.997501 | + | 0.0706455i | \(0.0225059\pi\) | ||||
−0.997501 | + | 0.0706455i | \(0.977494\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −534.934 | −1.02282 | −0.511409 | − | 0.859337i | \(-0.670876\pi\) | ||||
−0.511409 | + | 0.859337i | \(0.670876\pi\) | |||||||
\(524\) | − 7.99604i | − 0.0152596i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1366.69 | 2.59827 | ||||||||
\(527\) | 1363.47i | 2.58723i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −99.6371 | −0.188350 | ||||||||
\(530\) | 963.425i | 1.81778i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 199.356 | 0.374730 | ||||||||
\(533\) | − 46.9586i | − 0.0881024i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −101.127 | −0.189023 | ||||||||
\(536\) | 232.228i | 0.433262i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 622.158 | 1.15643 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3834 | 0.0284351 | 0.0142176 | − | 0.999899i | \(-0.495474\pi\) | ||||
0.0142176 | + | 0.999899i | \(0.495474\pi\) | |||||||
\(542\) | − 1373.79i | − 2.53468i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1197.58 | −2.20143 | ||||||||
\(545\) | 858.760i | 1.57571i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −182.142 | −0.332984 | −0.166492 | − | 0.986043i | \(-0.553244\pi\) | ||||
−0.166492 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(548\) | 967.328i | 1.76520i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 737.380i | − 1.33826i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.1412 | 0.0852463 | ||||||||
\(554\) | − 314.883i | − 0.568380i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 915.221 | 1.64608 | ||||||||
\(557\) | − 268.975i | − 0.482899i | −0.970413 | − | 0.241450i | \(-0.922377\pi\) | ||||
0.970413 | − | 0.241450i | \(-0.0776229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.21577 | −0.00575272 | ||||||||
\(560\) | − 257.915i | − 0.460562i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1284.47 | −2.28554 | ||||||||
\(563\) | 400.943i | 0.712155i | 0.934456 | + | 0.356078i | \(0.115886\pi\) | ||||
−0.934456 | + | 0.356078i | \(0.884114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −723.085 | −1.27980 | ||||||||
\(566\) | 899.225i | 1.58874i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.7920 | 0.0524508 | ||||||||
\(569\) | − 183.406i | − 0.322330i | −0.986927 | − | 0.161165i | \(-0.948475\pi\) | ||||
0.986927 | − | 0.161165i | \(-0.0515252\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 693.995 | 1.21540 | 0.607701 | − | 0.794166i | \(-0.292092\pi\) | ||||
0.607701 | + | 0.794166i | \(0.292092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −258.887 | −0.451023 | ||||||||
\(575\) | 920.902i | 1.60157i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 531.359 | 0.920900 | 0.460450 | − | 0.887686i | \(-0.347688\pi\) | ||||
0.460450 | + | 0.887686i | \(0.347688\pi\) | |||||||
\(578\) | − 1215.73i | − 2.10334i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1945.32 | 3.35400 | ||||||||
\(581\) | − 63.9411i | − 0.110053i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 275.601i | − 0.471920i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 138.035 | 0.235554 | ||||||||
\(587\) | 536.946i | 0.914728i | 0.889279 | + | 0.457364i | \(0.151206\pi\) | ||||
−0.889279 | + | 0.457364i | \(0.848794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 751.019 | 1.27508 | ||||||||
\(590\) | − 2249.46i | − 3.81264i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 228.628 | 0.386196 | ||||||||
\(593\) | 228.398i | 0.385156i | 0.981282 | + | 0.192578i | \(0.0616849\pi\) | ||||
−0.981282 | + | 0.192578i | \(0.938315\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 582.401 | 0.978825 | ||||||||
\(596\) | − 1167.84i | − 1.95946i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −113.430 | −0.189683 | ||||||||
\(599\) | 595.595i | 0.994315i | 0.867660 | + | 0.497158i | \(0.165623\pi\) | ||||
−0.867660 | + | 0.497158i | \(0.834377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 792.909 | 1.31932 | 0.659658 | − | 0.751566i | \(-0.270701\pi\) | ||||
0.659658 | + | 0.751566i | \(0.270701\pi\) | |||||||
\(602\) | 17.7288i | 0.0294499i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −286.488 | −0.474318 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −873.253 | −1.43864 | −0.719318 | − | 0.694680i | \(-0.755546\pi\) | ||||
−0.719318 | + | 0.694680i | \(0.755546\pi\) | |||||||
\(608\) | 659.643i | 1.08494i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 67.7964 | 0.111142 | ||||||||
\(611\) | 61.1295i | 0.100048i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 315.018 | 0.513895 | 0.256948 | − | 0.966425i | \(-0.417283\pi\) | ||||
0.256948 | + | 0.966425i | \(0.417283\pi\) | |||||||
\(614\) | − 1335.97i | − 2.17585i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 738.239i | 1.19650i | 0.801311 | + | 0.598249i | \(0.204136\pi\) | ||||
−0.801311 | + | 0.598249i | \(0.795864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 925.109 | 1.49452 | 0.747261 | − | 0.664531i | \(-0.231369\pi\) | ||||
0.747261 | + | 0.664531i | \(0.231369\pi\) | |||||||
\(620\) | 1981.30i | 3.19565i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 997.451 | 1.60362 | ||||||||
\(623\) | − 86.3503i | − 0.138604i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −194.189 | −0.310702 | ||||||||
\(626\) | 304.938i | 0.487122i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −99.7039 | −0.158764 | ||||||||
\(629\) | 516.269i | 0.820777i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −352.401 | −0.558481 | −0.279240 | − | 0.960221i | \(-0.590083\pi\) | ||||
−0.279240 | + | 0.960221i | \(0.590083\pi\) | |||||||
\(632\) | − 44.1604i | − 0.0698740i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1126.21 | −1.77635 | ||||||||
\(635\) | − 65.0779i | − 0.102485i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 62.4117 | 0.0979776 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −645.227 | −1.00817 | ||||||||
\(641\) | 247.035i | 0.385390i | 0.981259 | + | 0.192695i | \(0.0617227\pi\) | ||||
−0.981259 | + | 0.192695i | \(0.938277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 657.375 | 1.02236 | 0.511178 | − | 0.859475i | \(-0.329209\pi\) | ||||
0.511178 | + | 0.859475i | \(0.329209\pi\) | |||||||
\(644\) | 343.744i | 0.533764i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1144.07 | −1.77101 | ||||||||
\(647\) | 645.586i | 0.997814i | 0.866655 | + | 0.498907i | \(0.166265\pi\) | ||||
−0.866655 | + | 0.498907i | \(0.833735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 166.166i | 0.255640i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −510.491 | −0.782961 | ||||||||
\(653\) | − 35.5445i | − 0.0544326i | −0.999630 | − | 0.0272163i | \(-0.991336\pi\) | ||||
0.999630 | − | 0.0272163i | \(-0.00866429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.8669 | −0.0196441 | ||||||||
\(656\) | − 361.658i | − 0.551308i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 337.013 | 0.512178 | ||||||||
\(659\) | − 721.237i | − 1.09444i | −0.836988 | − | 0.547221i | \(-0.815686\pi\) | ||||
0.836988 | − | 0.547221i | \(-0.184314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −617.542 | −0.934253 | −0.467127 | − | 0.884190i | \(-0.654711\pi\) | ||||
−0.467127 | + | 0.884190i | \(0.654711\pi\) | |||||||
\(662\) | − 509.560i | − 0.769728i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −59.8980 | −0.0902078 | ||||||||
\(665\) | − 320.795i | − 0.482398i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1271.44 | 1.90621 | ||||||||
\(668\) | − 191.447i | − 0.286597i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2067.34 | 3.08558 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −840.469 | −1.24884 | −0.624420 | − | 0.781089i | \(-0.714665\pi\) | ||||
−0.624420 | + | 0.781089i | \(0.714665\pi\) | |||||||
\(674\) | 572.039i | 0.848723i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 813.904 | 1.20400 | ||||||||
\(677\) | − 386.555i | − 0.570983i | −0.958381 | − | 0.285491i | \(-0.907843\pi\) | ||||
0.958381 | − | 0.285491i | \(-0.0921568\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −80.1061 | −0.117977 | ||||||||
\(680\) | − 545.575i | − 0.802316i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 122.406i | 0.179219i | 0.995977 | + | 0.0896094i | \(0.0285619\pi\) | ||||
−0.995977 | + | 0.0896094i | \(0.971438\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1556.58 | 2.27238 | ||||||||
\(686\) | − 754.146i | − 1.09934i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.7667 | −0.0359981 | ||||||||
\(689\) | 62.4544i | 0.0906450i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 244.981 | 0.354532 | 0.177266 | − | 0.984163i | \(-0.443275\pi\) | ||||
0.177266 | + | 0.984163i | \(0.443275\pi\) | |||||||
\(692\) | − 446.402i | − 0.645090i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 553.926 | 0.798165 | ||||||||
\(695\) | − 1472.73i | − 2.11904i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 816.665 | 1.17169 | ||||||||
\(698\) | − 525.707i | − 0.753162i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 503.557 | 0.719367 | ||||||||
\(701\) | − 197.380i | − 0.281569i | −0.990040 | − | 0.140785i | \(-0.955037\pi\) | ||||
0.990040 | − | 0.140785i | \(-0.0449625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 284.368 | 0.404506 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −693.903 | −0.982865 | ||||||||
\(707\) | 9.54302i | 0.0134979i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −525.864 | −0.741698 | −0.370849 | − | 0.928693i | \(-0.620933\pi\) | ||||
−0.370849 | + | 0.928693i | \(0.620933\pi\) | |||||||
\(710\) | − 265.214i | − 0.373541i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −80.8903 | −0.113610 | ||||||||
\(713\) | 1294.96i | 1.81621i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 1065.29i | − 1.48784i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1201.46 | 1.67334 | ||||||||
\(719\) | − 54.4556i | − 0.0757379i | −0.999283 | − | 0.0378690i | \(-0.987943\pi\) | ||||
0.999283 | − | 0.0378690i | \(-0.0120569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.6493 | 0.0868923 | ||||||||
\(722\) | − 445.740i | − 0.617369i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 218.841 | 0.302267 | ||||||||
\(725\) | − 1862.56i | − 2.56905i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1312.96 | 1.80600 | 0.902999 | − | 0.429642i | \(-0.141360\pi\) | ||||
0.902999 | + | 0.429642i | \(0.141360\pi\) | |||||||
\(728\) | 11.2116i | 0.0154005i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2453.45 | −3.36089 | ||||||||
\(731\) | − 55.9260i | − 0.0765062i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 395.593 | 0.539690 | 0.269845 | − | 0.962904i | \(-0.413027\pi\) | ||||
0.269845 | + | 0.962904i | \(0.413027\pi\) | |||||||
\(734\) | − 1613.91i | − 2.19878i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1137.40 | −1.54538 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1425.40 | 1.92883 | 0.964413 | − | 0.264401i | \(-0.0851742\pi\) | ||||
0.964413 | + | 0.264401i | \(0.0851742\pi\) | |||||||
\(740\) | 750.206i | 1.01379i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 344.317 | 0.464039 | ||||||||
\(743\) | − 648.328i | − 0.872581i | −0.899806 | − | 0.436291i | \(-0.856292\pi\) | ||||
0.899806 | − | 0.436291i | \(-0.143708\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1879.23 | −2.52246 | ||||||||
\(746\) | − 476.932i | − 0.639319i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.1417i | 0.0482532i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −520.551 | −0.693144 | −0.346572 | − | 0.938023i | \(-0.612654\pi\) | ||||
−0.346572 | + | 0.938023i | \(0.612654\pi\) | |||||||
\(752\) | 470.797i | 0.626060i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 229.418 | 0.304267 | ||||||||
\(755\) | 461.003i | 0.610600i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −546.651 | −0.722128 | −0.361064 | − | 0.932541i | \(-0.617586\pi\) | ||||
−0.361064 | + | 0.932541i | \(0.617586\pi\) | |||||||
\(758\) | − 1128.43i | − 1.48869i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −300.510 | −0.395408 | ||||||||
\(761\) | 825.999i | 1.08541i | 0.839922 | + | 0.542707i | \(0.182600\pi\) | ||||
−0.839922 | + | 0.542707i | \(0.817400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 306.911 | 0.402243 | ||||||||
\(764\) | − 727.372i | − 0.952058i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 713.997 | 0.932111 | ||||||||
\(767\) | − 145.822i | − 0.190120i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 712.096 | 0.926003 | 0.463001 | − | 0.886358i | \(-0.346772\pi\) | ||||
0.463001 | + | 0.886358i | \(0.346772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −945.785 | −1.22511 | ||||||||
\(773\) | − 276.314i | − 0.357456i | −0.983899 | − | 0.178728i | \(-0.942802\pi\) | ||||
0.983899 | − | 0.178728i | \(-0.0571982\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1897.01 | 2.44776 | ||||||||
\(776\) | 75.0409i | 0.0967022i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1497.99 | 1.92544 | ||||||||
\(779\) | − 449.831i | − 0.577446i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 1972.69i | − 2.52262i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 480.673 | 0.613103 | ||||||||
\(785\) | 160.439i | 0.204381i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 955.911 | 1.21463 | 0.607313 | − | 0.794463i | \(-0.292247\pi\) | ||||
0.607313 | + | 0.794463i | \(0.292247\pi\) | |||||||
\(788\) | − 1617.63i | − 2.05283i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −393.124 | −0.497625 | ||||||||
\(791\) | 258.422i | 0.326703i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.39493 | 0.00554216 | ||||||||
\(794\) | 289.405i | 0.364490i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1439.52 | 1.80844 | ||||||||
\(797\) | 1060.39i | 1.33048i | 0.746631 | + | 0.665238i | \(0.231670\pi\) | ||||
−0.746631 | + | 0.665238i | \(0.768330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1063.11 | −1.33056 | ||||||||
\(800\) | 1666.20i | 2.08275i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1958.54 | −2.44207 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 553.137 | 0.687126 | ||||||||
\(806\) | 233.661i | 0.289902i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.93960 | 0.0110639 | ||||||||
\(809\) | − 366.478i | − 0.453001i | −0.974011 | − | 0.226501i | \(-0.927271\pi\) | ||||
0.974011 | − | 0.226501i | \(-0.0727286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 600.466 | 0.740402 | 0.370201 | − | 0.928952i | \(-0.379289\pi\) | ||||
0.370201 | + | 0.928952i | \(0.379289\pi\) | |||||||
\(812\) | − 695.236i | − 0.856202i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 821.458i | 1.00792i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.8048 | −0.0377048 | ||||||||
\(818\) | 302.672i | 0.370015i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1186.72 | 1.44722 | ||||||||
\(821\) | 796.899i | 0.970645i | 0.874335 | + | 0.485322i | \(0.161298\pi\) | ||||
−0.874335 | + | 0.485322i | \(0.838702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 822.371 | 0.999235 | 0.499618 | − | 0.866246i | \(-0.333474\pi\) | ||||
0.499618 | + | 0.866246i | \(0.333474\pi\) | |||||||
\(824\) | − 58.6879i | − 0.0712232i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −803.931 | −0.973282 | ||||||||
\(827\) | 913.876i | 1.10505i | 0.833497 | + | 0.552524i | \(0.186335\pi\) | ||||
−0.833497 | + | 0.552524i | \(0.813665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1298.36 | −1.56618 | −0.783091 | − | 0.621908i | \(-0.786358\pi\) | ||||
−0.783091 | + | 0.621908i | \(0.786358\pi\) | |||||||
\(830\) | 533.222i | 0.642437i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −134.247 | −0.161355 | ||||||||
\(833\) | 1085.41i | 1.30302i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −308.067 | −0.368942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.31082 | 0.00156423 | ||||||||
\(839\) | − 58.6568i | − 0.0699128i | −0.999389 | − | 0.0349564i | \(-0.988871\pi\) | ||||
0.999389 | − | 0.0349564i | \(-0.0111292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1730.54 | −2.05772 | ||||||||
\(842\) | − 1247.47i | − 1.48155i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 565.046 | 0.669485 | ||||||||
\(845\) | − 1309.70i | − 1.54994i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 481.001i | 0.567218i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2889.83 | −3.39980 | ||||||||
\(851\) | 490.327i | 0.576178i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1144.33 | −1.34154 | −0.670771 | − | 0.741665i | \(-0.734036\pi\) | ||||
−0.670771 | + | 0.741665i | \(0.734036\pi\) | |||||||
\(854\) | − 24.2297i | − 0.0283720i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.8564 | 0.0395519 | ||||||||
\(857\) | 1380.38i | 1.61071i | 0.592790 | + | 0.805357i | \(0.298027\pi\) | ||||
−0.592790 | + | 0.805357i | \(0.701973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 210.196 | 0.244698 | 0.122349 | − | 0.992487i | \(-0.460957\pi\) | ||||
0.122349 | + | 0.992487i | \(0.460957\pi\) | |||||||
\(860\) | − 81.2679i | − 0.0944975i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −751.256 | −0.871527 | ||||||||
\(863\) | 201.367i | 0.233333i | 0.993171 | + | 0.116667i | \(0.0372209\pi\) | ||||
−0.993171 | + | 0.116667i | \(0.962779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −718.329 | −0.830439 | ||||||||
\(866\) | − 370.905i | − 0.428297i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 708.096 | 0.815778 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 134.016 | 0.153865 | ||||||||
\(872\) | − 287.505i | − 0.329707i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1086.59 | −1.24323 | ||||||||
\(875\) | − 258.765i | − 0.295732i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1058.24 | −1.20666 | −0.603332 | − | 0.797490i | \(-0.706160\pi\) | ||||
−0.603332 | + | 0.797490i | \(0.706160\pi\) | |||||||
\(878\) | − 219.633i | − 0.250151i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 402.743i | − 0.457144i | −0.973527 | − | 0.228572i | \(-0.926594\pi\) | ||||
0.973527 | − | 0.228572i | \(-0.0734056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1161.84 | −1.31579 | −0.657893 | − | 0.753111i | \(-0.728552\pi\) | ||||
−0.657893 | + | 0.753111i | \(0.728552\pi\) | |||||||
\(884\) | − 195.658i | − 0.221333i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1102.55 | −1.24441 | ||||||||
\(887\) | 488.442i | 0.550668i | 0.961349 | + | 0.275334i | \(0.0887884\pi\) | ||||
−0.961349 | + | 0.275334i | \(0.911212\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.2581 | −0.0261621 | ||||||||
\(890\) | 720.099i | 0.809100i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1191.80 | 1.33609 | ||||||||
\(893\) | 585.578i | 0.655743i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1714.22 | −1.91532 | ||||||||
\(896\) | 230.597i | 0.257363i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2165.38 | 2.41134 | ||||||||
\(899\) | − 2619.11i | − 2.91336i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1086.16 | −1.20550 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 242.082 | 0.267790 | ||||||||
\(905\) | − 352.149i | − 0.389115i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1687.27 | −1.86028 | −0.930138 | − | 0.367210i | \(-0.880313\pi\) | ||||
−0.930138 | + | 0.367210i | \(0.880313\pi\) | |||||||
\(908\) | − 1309.63i | − 1.44232i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 99.8073 | 0.109678 | ||||||||
\(911\) | 1092.72i | 1.19947i | 0.800199 | + | 0.599735i | \(0.204727\pi\) | ||||
−0.800199 | + | 0.599735i | \(0.795273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 1089.38i | − 1.19188i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −908.606 | −0.991928 | ||||||||
\(917\) | 4.59847i | 0.00501469i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1204.42 | 1.31058 | 0.655288 | − | 0.755379i | \(-0.272547\pi\) | ||||
0.655288 | + | 0.755379i | \(0.272547\pi\) | |||||||
\(920\) | − 518.161i | − 0.563219i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 457.992 | 0.496737 | ||||||||
\(923\) | − 17.1926i | − 0.0186269i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 718.289 | 0.776529 | ||||||||
\(926\) | 969.682i | 1.04717i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2300.44 | 2.47892 | ||||||||
\(929\) | 227.170i | 0.244531i | 0.992497 | + | 0.122266i | \(0.0390160\pi\) | ||||
−0.992497 | + | 0.122266i | \(0.960984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 597.861 | 0.642171 | ||||||||
\(932\) | 791.861i | 0.849636i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2491.48 | 2.66754 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 355.723 | 0.379640 | 0.189820 | − | 0.981819i | \(-0.439209\pi\) | ||||
0.189820 | + | 0.981819i | \(0.439209\pi\) | |||||||
\(938\) | − 738.844i | − 0.787680i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1544.84 | −1.64345 | ||||||||
\(941\) | − 1363.18i | − 1.44866i | −0.689456 | − | 0.724328i | \(-0.742150\pi\) | ||||
0.689456 | − | 0.724328i | \(-0.257850\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 775.630 | 0.822513 | ||||||||
\(944\) | − 1123.07i | − 1.18969i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 90.3298i | − 0.0953852i | −0.998862 | − | 0.0476926i | \(-0.984813\pi\) | ||||
0.998862 | − | 0.0476926i | \(-0.0151868\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −159.046 | −0.167593 | ||||||||
\(950\) | 1591.76i | 1.67553i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −194.982 | −0.204813 | ||||||||
\(953\) | − 612.654i | − 0.642869i | −0.946932 | − | 0.321434i | \(-0.895835\pi\) | ||||
0.946932 | − | 0.321434i | \(-0.104165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1170.45 | −1.22561 | ||||||||
\(956\) | 347.120i | 0.363096i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1000.63 | 1.04450 | ||||||||
\(959\) | − 556.303i | − 0.580087i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1706.55 | 1.77581 | ||||||||
\(962\) | 88.4741i | 0.0919689i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1039.01 | −1.07781 | ||||||||
\(965\) | 1521.91i | 1.57711i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −446.224 | −0.461452 | −0.230726 | − | 0.973019i | \(-0.574110\pi\) | ||||
−0.230726 | + | 0.973019i | \(0.574110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 668.027 | 0.688688 | ||||||||
\(971\) | − 152.782i | − 0.157345i | −0.996901 | − | 0.0786723i | \(-0.974932\pi\) | ||||
0.996901 | − | 0.0786723i | \(-0.0250681\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −526.337 | −0.540943 | ||||||||
\(974\) | 1744.83i | 1.79141i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33.8482 | 0.0346805 | ||||||||
\(977\) | − 564.811i | − 0.578107i | −0.957313 | − | 0.289054i | \(-0.906659\pi\) | ||||
0.957313 | − | 0.289054i | \(-0.0933406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1577.25i | 1.60944i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −970.356 | −0.988142 | ||||||||
\(983\) | − 945.431i | − 0.961781i | −0.876781 | − | 0.480890i | \(-0.840313\pi\) | ||||
0.876781 | − | 0.480890i | \(-0.159687\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2603.01 | −2.64265 | ||||||||
\(986\) | 3989.84i | 4.04649i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −107.771 | −0.109080 | ||||||||
\(989\) | − 53.1159i | − 0.0537067i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1225.61 | 1.23674 | 0.618371 | − | 0.785886i | \(-0.287793\pi\) | ||||
0.618371 | + | 0.785886i | \(0.287793\pi\) | |||||||
\(992\) | 2342.99i | 2.36189i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −94.7845 | −0.0953566 | ||||||||
\(995\) | − 2316.41i | − 2.32805i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1276.52 | −1.28036 | −0.640180 | − | 0.768225i | \(-0.721140\pi\) | ||||
−0.640180 | + | 0.768225i | \(0.721140\pi\) | |||||||
\(998\) | 1202.05i | 1.20446i | ||||||||
\(999\) | 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 | 1089.3.b.i.485.13 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.i.485.4 | 16 | ||
11.5 | even | 5 | 99.3.l.a.80.2 | yes | 32 | ||
11.9 | even | 5 | 99.3.l.a.26.7 | yes | 32 | ||
11.10 | odd | 2 | 1089.3.b.j.485.4 | 16 | |||
33.5 | odd | 10 | 99.3.l.a.80.7 | yes | 32 | ||
33.20 | odd | 10 | 99.3.l.a.26.2 | ✓ | 32 | ||
33.32 | even | 2 | 1089.3.b.j.485.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.26.2 | ✓ | 32 | 33.20 | odd | 10 | ||
99.3.l.a.26.7 | yes | 32 | 11.9 | even | 5 | ||
99.3.l.a.80.2 | yes | 32 | 11.5 | even | 5 | ||
99.3.l.a.80.7 | yes | 32 | 33.5 | odd | 10 | ||
1089.3.b.i.485.4 | 16 | 3.2 | odd | 2 | inner | ||
1089.3.b.i.485.13 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.b.j.485.4 | 16 | 11.10 | odd | 2 | |||
1089.3.b.j.485.13 | 16 | 33.32 | even | 2 |