Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.15 | ||
Character | \(\chi\) | \(=\) | 2100.1349 |
Dual form | 2100.2.bo.i.1949.15 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 1.68089 | + | 0.417865i | 0.970462 | + | 0.241255i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.33003 | + | 1.25338i | −0.880669 | + | 0.473732i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.65078 | + | 1.40477i | 0.883592 | + | 0.468257i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.63831 | − | 2.67793i | 1.39850 | − | 0.807426i | 0.404268 | − | 0.914641i | \(-0.367526\pi\) |
0.994236 | + | 0.107214i | \(0.0341931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.13670 | −1.14732 | −0.573658 | − | 0.819095i | \(-0.694476\pi\) | ||||
−0.573658 | + | 0.819095i | \(0.694476\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.134025 | + | 0.0773793i | −0.0325058 | + | 0.0187672i | −0.516165 | − | 0.856489i | \(-0.672641\pi\) |
0.483659 | + | 0.875257i | \(0.339307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.40485 | + | 1.96579i | 0.781126 | + | 0.450983i | 0.836829 | − | 0.547464i | \(-0.184407\pi\) |
−0.0557031 | + | 0.998447i | \(0.517740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.44027 | + | 1.13315i | −0.968946 | + | 0.247273i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.99803 | − | 5.19273i | 0.625132 | − | 1.08276i | −0.363384 | − | 0.931640i | \(-0.618379\pi\) |
0.988515 | − | 0.151120i | \(-0.0482880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.86866 | + | 3.46893i | 0.744524 | + | 0.667596i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.3150i | 1.91544i | 0.287703 | + | 0.957720i | \(0.407108\pi\) | ||||
−0.287703 | + | 0.957720i | \(0.592892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.70071 | − | 3.86866i | 1.20348 | − | 0.694832i | 0.242156 | − | 0.970237i | \(-0.422146\pi\) |
0.961328 | + | 0.275406i | \(0.0888122\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.91550 | − | 2.56312i | 1.55199 | − | 0.446181i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.07719 | + | 5.24072i | 1.49228 | + | 0.861569i | 0.999961 | − | 0.00884571i | \(-0.00281571\pi\) |
0.492320 | + | 0.870414i | \(0.336149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.95334 | − | 1.72858i | −1.11343 | − | 0.276795i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.33876 | −0.365253 | −0.182627 | − | 0.983182i | \(-0.558460\pi\) | ||||
−0.182627 | + | 0.983182i | \(0.558460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.78236i | 0.271807i | 0.990722 | + | 0.135903i | \(0.0433937\pi\) | ||||
−0.990722 | + | 0.135903i | \(0.956606\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.11974 | − | 1.80118i | −0.455061 | − | 0.262729i | 0.254905 | − | 0.966966i | \(-0.417956\pi\) |
−0.709965 | + | 0.704237i | \(0.751289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.85809 | − | 5.84082i | 0.551156 | − | 0.834402i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.257615 | + | 0.0740617i | −0.0360733 | + | 0.0103707i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.47955 | + | 4.29470i | 0.340592 | + | 0.589923i | 0.984543 | − | 0.175144i | \(-0.0560392\pi\) |
−0.643951 | + | 0.765067i | \(0.722706\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.90174 | + | 4.72705i | 0.649251 | + | 0.626112i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.27011 | + | 9.12810i | 0.686110 | + | 1.18838i | 0.973087 | + | 0.230440i | \(0.0740165\pi\) |
−0.286976 | + | 0.957938i | \(0.592650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.25602 | − | 1.87987i | −0.416891 | − | 0.240692i | 0.276855 | − | 0.960912i | \(-0.410708\pi\) |
−0.693746 | + | 0.720219i | \(0.744041\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.93710 | + | 0.0492651i | −0.999981 | + | 0.00620682i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.770225 | − | 0.444690i | 0.0940980 | − | 0.0543275i | −0.452213 | − | 0.891910i | \(-0.649365\pi\) |
0.546311 | + | 0.837583i | \(0.316032\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.20921 | − | 7.47564i | 0.867887 | − | 0.899961i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.6200i | 1.37904i | 0.724269 | + | 0.689518i | \(0.242178\pi\) | ||||
−0.724269 | + | 0.689518i | \(0.757822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.12550 | − | 10.6097i | −0.716935 | − | 1.24177i | −0.962208 | − | 0.272314i | \(-0.912211\pi\) |
0.245273 | − | 0.969454i | \(-0.421122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.45095 | + | 12.0532i | −0.849115 | + | 1.37359i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.61147 | + | 6.25525i | −0.406322 | + | 0.703770i | −0.994474 | − | 0.104980i | \(-0.966522\pi\) |
0.588152 | + | 0.808750i | \(0.299856\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.05324 | + | 7.44747i | 0.561471 | + | 0.827496i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.14180i | − | 0.564386i | −0.959358 | − | 0.282193i | \(-0.908938\pi\) | ||
0.959358 | − | 0.282193i | \(-0.0910618\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.31026 | + | 17.3383i | −0.462108 | + | 1.85886i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.58428 | − | 14.8684i | 0.909932 | − | 1.57605i | 0.0957761 | − | 0.995403i | \(-0.469467\pi\) |
0.814156 | − | 0.580646i | \(-0.197200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.63865 | − | 5.18485i | 1.01041 | − | 0.543520i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.8797 | − | 3.70279i | 1.33557 | − | 0.383962i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.28309 | −0.434882 | −0.217441 | − | 0.976073i | \(-0.569771\pi\) | ||||
−0.217441 | + | 0.976073i | \(0.569771\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.0570 | − | 0.582836i | 1.61379 | − | 0.0585772i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.04794 | + | 5.27919i | 0.303282 | + | 0.525299i | 0.976877 | − | 0.213801i | \(-0.0685844\pi\) |
−0.673596 | + | 0.739100i | \(0.735251\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.15428 | + | 3.73132i | −0.212267 | + | 0.367658i | −0.952424 | − | 0.304777i | \(-0.901418\pi\) |
0.740157 | + | 0.672435i | \(0.234751\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.28953 | + | 14.3579i | −0.801379 | + | 1.38803i | 0.117330 | + | 0.993093i | \(0.462567\pi\) |
−0.918709 | + | 0.394936i | \(0.870767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.92426 | + | 3.33292i | 0.184311 | + | 0.319236i | 0.943344 | − | 0.331816i | \(-0.107661\pi\) |
−0.759033 | + | 0.651052i | \(0.774328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.0678 | + | 12.6021i | 1.24034 | + | 1.19614i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.94281 | 0.935341 | 0.467671 | − | 0.883903i | \(-0.345093\pi\) | ||||
0.467671 | + | 0.883903i | \(0.345093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.9655 | − | 5.81112i | −1.01376 | − | 0.537238i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.215297 | − | 0.348280i | 0.0197362 | − | 0.0319268i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.84262 | − | 15.3159i | 0.803875 | − | 1.39235i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.93120 | − | 0.977287i | −0.354464 | − | 0.0881190i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.64472i | 0.412152i | 0.978536 | + | 0.206076i | \(0.0660694\pi\) | ||||
−0.978536 | + | 0.206076i | \(0.933931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.744784 | + | 2.99594i | −0.0655746 | + | 0.263778i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.31417 | − | 5.74031i | 0.289561 | − | 0.501534i | −0.684144 | − | 0.729347i | \(-0.739824\pi\) |
0.973705 | + | 0.227813i | \(0.0731575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3973 | − | 0.312794i | −0.901559 | − | 0.0271227i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.35783 | + | 4.08389i | 0.201443 | + | 0.348910i | 0.948994 | − | 0.315295i | \(-0.102103\pi\) |
−0.747550 | + | 0.664205i | \(0.768770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.56273i | − | 0.811100i | −0.914073 | − | 0.405550i | \(-0.867080\pi\) | ||
0.914073 | − | 0.405550i | \(-0.132920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.49128 | − | 4.33122i | −0.378234 | − | 0.364754i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.1873 | + | 11.0778i | −1.60452 | + | 0.926373i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.92570 | − | 8.20560i | 0.736179 | − | 0.676787i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6339 | − | 10.1809i | −1.44462 | − | 0.834054i | −0.446471 | − | 0.894798i | \(-0.647319\pi\) |
−0.998153 | + | 0.0607437i | \(0.980653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.69396 | − | 9.86223i | −0.463368 | − | 0.802577i | 0.535758 | − | 0.844371i | \(-0.320026\pi\) |
−0.999126 | + | 0.0417947i | \(0.986692\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.463970 | + | 0.0168412i | −0.0375098 | + | 0.00136153i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.40612 | − | 5.89957i | −0.271838 | − | 0.470837i | 0.697495 | − | 0.716590i | \(-0.254298\pi\) |
−0.969332 | + | 0.245753i | \(0.920965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.37324 | + | 8.25504i | 0.188210 | + | 0.654667i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.477042 | + | 15.8569i | −0.0375962 | + | 1.24970i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.85180 | − | 3.95589i | −0.536674 | − | 0.309849i | 0.207056 | − | 0.978329i | \(-0.433612\pi\) |
−0.743730 | + | 0.668480i | \(0.766945\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.2507i | − | 1.48966i | −0.667252 | − | 0.744832i | \(-0.732530\pi\) | ||
0.667252 | − | 0.744832i | \(-0.267470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.11232 | 0.316332 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.26402 | + | 9.99391i | 0.479021 | + | 0.764253i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.2478 | + | 7.07129i | 0.931186 | + | 0.537621i | 0.887186 | − | 0.461411i | \(-0.152657\pi\) |
0.0439995 | + | 0.999032i | \(0.485990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.04416 | + | 17.5455i | 0.379142 | + | 1.31880i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.79606 | − | 1.03696i | 0.134244 | − | 0.0775058i | −0.431374 | − | 0.902173i | \(-0.641971\pi\) |
0.565618 | + | 0.824667i | \(0.308638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.7401i | − | 1.61593i | −0.589231 | − | 0.807965i | \(-0.700569\pi\) | ||
0.589231 | − | 0.807965i | \(-0.299431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.68749 | − | 4.52043i | −0.346509 | − | 0.334160i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.414433 | + | 0.717819i | −0.0303063 | + | 0.0524921i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.3620 | − | 3.23383i | −0.971941 | − | 0.235226i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00687 | − | 1.15867i | −0.145212 | − | 0.0838383i | 0.425634 | − | 0.904896i | \(-0.360051\pi\) |
−0.570846 | + | 0.821057i | \(0.693385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4707 | − | 8.93203i | 1.11361 | − | 0.642942i | 0.173846 | − | 0.984773i | \(-0.444380\pi\) |
0.939761 | + | 0.341831i | \(0.111047\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.3849 | −1.30987 | −0.654936 | − | 0.755685i | \(-0.727304\pi\) | ||||
−0.654936 | + | 0.755685i | \(0.727304\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.70763 | − | 0.985902i | 0.121051 | − | 0.0698887i | −0.438252 | − | 0.898852i | \(-0.644402\pi\) |
0.559303 | + | 0.828963i | \(0.311069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.48048 | − | 0.425624i | 0.104425 | − | 0.0300212i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.9285 | − | 24.0342i | −0.907405 | − | 1.68687i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.2417 | − | 9.55324i | 1.05937 | − | 0.663996i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.0570 | 1.45654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.07968 | 0.0743282 | 0.0371641 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371641 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.85558 | + | 19.5319i | −0.332699 | + | 1.33830i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7640 | + | 17.4126i | −0.730707 | + | 1.18205i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.86287 | − | 20.3933i | −0.396176 | − | 1.37805i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.554421 | − | 0.320095i | 0.0372944 | − | 0.0215319i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.3841 | −1.03020 | −0.515099 | − | 0.857131i | \(-0.672245\pi\) | ||||
−0.515099 | + | 0.857131i | \(0.672245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.68946 | − | 0.975410i | 0.112133 | − | 0.0647402i | −0.442884 | − | 0.896579i | \(-0.646045\pi\) |
0.555018 | + | 0.831838i | \(0.312711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.44750 | − | 1.41307i | −0.161735 | − | 0.0933780i | 0.416948 | − | 0.908930i | \(-0.363100\pi\) |
−0.578683 | + | 0.815553i | \(0.696433\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.5608 | + | 17.1466i | −1.15542 | + | 1.12817i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.19563 | − | 3.80293i | 0.143840 | − | 0.249139i | −0.785099 | − | 0.619370i | \(-0.787388\pi\) |
0.928940 | + | 0.370231i | \(0.120722\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.68433 | + | 9.00527i | −0.564108 | + | 0.584955i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6724i | 1.14313i | 0.820556 | + | 0.571566i | \(0.193664\pi\) | ||||
−0.820556 | + | 0.571566i | \(0.806336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.69148 | + | 2.13128i | −0.237789 | + | 0.137288i | −0.614160 | − | 0.789181i | \(-0.710505\pi\) |
0.376371 | + | 0.926469i | \(0.377172\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.38190 | + | 14.6299i | 0.345249 | + | 0.938511i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0849 | − | 8.13190i | −0.896198 | − | 0.517420i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.14858 | − | 8.64280i | 0.136161 | − | 0.547715i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.87820 | −0.244790 | −0.122395 | − | 0.992481i | \(-0.539057\pi\) | ||||
−0.122395 | + | 0.992481i | \(0.539057\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 32.1140i | − | 2.01899i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.3384 | + | 8.85563i | 0.956784 | + | 0.552399i | 0.895182 | − | 0.445702i | \(-0.147046\pi\) |
0.0616020 | + | 0.998101i | \(0.480379\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.7187 | − | 0.833896i | −1.72236 | − | 0.0518158i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.4901 | + | 27.3427i | −0.896917 | + | 1.69247i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.79964 | − | 4.84912i | −0.172633 | − | 0.299010i | 0.766706 | − | 0.641998i | \(-0.221894\pi\) |
−0.939340 | + | 0.342988i | \(0.888561\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.6422 | − | 21.4051i | 1.26328 | − | 1.30997i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.53335 | − | 14.7802i | −0.520288 | − | 0.901165i | −0.999722 | − | 0.0235867i | \(-0.992491\pi\) |
0.479434 | − | 0.877578i | \(-0.340842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7661 | + | 8.52521i | 0.896977 | + | 0.517870i | 0.876218 | − | 0.481915i | \(-0.160059\pi\) |
0.0207586 | + | 0.999785i | \(0.493392\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.3681 | − | 4.68750i | 1.11169 | − | 0.283701i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.12563 | + | 5.26868i | −0.548306 | + | 0.316565i | −0.748438 | − | 0.663204i | \(-0.769196\pi\) |
0.200133 | + | 0.979769i | \(0.435863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.1967 | − | 0.841992i | 1.38875 | − | 0.0504087i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.2208i | − | 1.14662i | −0.819339 | − | 0.573309i | \(-0.805660\pi\) | ||
0.819339 | − | 0.573309i | \(-0.194340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.99126 | + | 15.5733i | 0.534475 | + | 0.925738i | 0.999189 | + | 0.0402770i | \(0.0128240\pi\) |
−0.464713 | + | 0.885461i | \(0.653843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.44939 | − | 2.93135i | 0.321667 | − | 0.173032i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.48802 | + | 14.7017i | −0.499296 | + | 0.864805i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.19940 | − | 1.78975i | −0.422036 | − | 0.104917i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.2153i | 1.47309i | 0.676388 | + | 0.736546i | \(0.263544\pi\) | ||||
−0.676388 | + | 0.736546i | \(0.736456\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.2336 | + | 5.72998i | 1.58025 | + | 0.332487i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.4019 | + | 21.4808i | −0.717223 | + | 1.24227i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.23396 | − | 4.15294i | −0.128764 | − | 0.239372i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.91726 | + | 10.1474i | 0.167592 | + | 0.582951i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.28693 | −0.472960 | −0.236480 | − | 0.971636i | \(-0.575994\pi\) | ||||
−0.236480 | + | 0.971636i | \(0.575994\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.18029 | + | 5.37173i | −0.294696 | + | 0.305587i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.28958 | + | 7.42977i | 0.243240 | + | 0.421304i | 0.961635 | − | 0.274331i | \(-0.0884564\pi\) |
−0.718395 | + | 0.695635i | \(0.755123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.466406 | + | 0.807839i | −0.0263628 | + | 0.0456617i | −0.878906 | − | 0.476995i | \(-0.841726\pi\) |
0.852543 | + | 0.522657i | \(0.175059\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.49108 | − | 2.58262i | 0.0837472 | − | 0.145054i | −0.821109 | − | 0.570771i | \(-0.806645\pi\) |
0.904857 | + | 0.425716i | \(0.139978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.6227 | + | 47.8440i | 1.54658 | + | 2.67875i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.9334 | + | 20.6701i | −1.11258 | + | 1.15369i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.608446 | −0.0338549 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.84176 | + | 6.40636i | 0.101850 | + | 0.354272i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.52665 | + | 0.286602i | 0.525221 | + | 0.0158009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9541 | − | 18.9730i | 0.602091 | − | 1.04285i | −0.390413 | − | 0.920640i | \(-0.627668\pi\) |
0.992504 | − | 0.122213i | \(-0.0389990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.6996 | + | 26.6433i | 0.915133 | + | 1.46005i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 36.4696i | − | 1.98663i | −0.115448 | − | 0.993314i | \(-0.536830\pi\) | ||
0.115448 | − | 0.993314i | \(-0.463170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.7128 | + | 4.15476i | 0.907713 | + | 0.225655i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7200 | − | 35.8881i | 1.12205 | − | 1.94345i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.66873 | + | 18.4449i | −0.0901031 | + | 0.995932i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.09509 | + | 3.62881i | 0.112471 | + | 0.194805i | 0.916766 | − | 0.399425i | \(-0.130790\pi\) |
−0.804295 | + | 0.594230i | \(0.797457\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.2897i | − | 1.19314i | −0.802560 | − | 0.596571i | \(-0.796530\pi\) | ||
0.802560 | − | 0.596571i | \(-0.203470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.0035 | − | 14.3499i | −0.854203 | − | 0.765943i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.1073 | − | 8.72220i | 0.804080 | − | 0.464236i | −0.0408157 | − | 0.999167i | \(-0.512996\pi\) |
0.844896 | + | 0.534931i | \(0.179662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.507424 | − | 0.495455i | 0.0268557 | − | 0.0262223i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.2564 | − | 14.5818i | −1.33298 | − | 0.769599i | −0.347228 | − | 0.937781i | \(-0.612877\pi\) |
−0.985756 | + | 0.168182i | \(0.946210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.77133 | − | 3.06803i | −0.0932279 | − | 0.161476i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.2634 | − | 22.0493i | 1.11604 | − | 1.15729i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3734 | − | 23.1633i | −0.698084 | − | 1.20912i | −0.969130 | − | 0.246550i | \(-0.920703\pi\) |
0.271046 | − | 0.962566i | \(-0.412630\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.19954 | − | 3.28542i | −0.322735 | − | 0.171032i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.1603 | − | 6.89898i | −0.579414 | − | 0.358177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.44649 | + | 2.56718i | 0.230231 | + | 0.132924i | 0.610678 | − | 0.791879i | \(-0.290897\pi\) |
−0.380448 | + | 0.924802i | \(0.624230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 42.6699i | − | 2.19761i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3320 | 0.890284 | 0.445142 | − | 0.895460i | \(-0.353153\pi\) | ||||
0.445142 | + | 0.895460i | \(0.353153\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.94087 | + | 7.80726i | −0.0994336 | + | 0.399978i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.7852 | + | 10.8457i | 0.959881 | + | 0.554188i | 0.896136 | − | 0.443779i | \(-0.146362\pi\) |
0.0637447 | + | 0.997966i | \(0.479696\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.50380 | + | 4.72463i | −0.127275 | + | 0.240166i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.6759 | + | 6.74110i | −0.591993 | + | 0.341787i | −0.765885 | − | 0.642977i | \(-0.777699\pi\) |
0.173892 | + | 0.984765i | \(0.444366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.927941i | 0.0469280i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.96943 | − | 8.26396i | 0.402005 | − | 0.416861i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.85891 | − | 11.8800i | 0.344239 | − | 0.596240i | −0.640976 | − | 0.767561i | \(-0.721470\pi\) |
0.985215 | + | 0.171321i | \(0.0548036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.3460 | − | 4.87044i | −0.868385 | − | 0.243827i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.4976 | − | 9.52487i | −0.823849 | − | 0.475649i | 0.0278932 | − | 0.999611i | \(-0.491120\pi\) |
−0.851742 | + | 0.523962i | \(0.824453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.7189 | + | 16.0035i | −1.38078 | + | 0.797191i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 56.1371 | 2.78261 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.1428 | + | 17.4030i | −1.49047 | + | 0.860521i | −0.999941 | − | 0.0109054i | \(-0.996529\pi\) |
−0.490526 | + | 0.871427i | \(0.663195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.25674 | + | 7.84982i | 0.111317 | + | 0.387203i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.7205 | − | 14.6633i | −1.16721 | − | 0.721535i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.99593 | − | 16.0739i | 0.195682 | − | 0.787142i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7934 | 0.966971 | 0.483486 | − | 0.875352i | \(-0.339371\pi\) | ||||
0.483486 | + | 0.875352i | \(0.339371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2279 | −0.595951 | −0.297975 | − | 0.954574i | \(-0.596311\pi\) | ||||
−0.297975 | + | 0.954574i | \(0.596311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.73949 | − | 9.15705i | −0.279063 | − | 0.445231i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.94282 | + | 0.299122i | 0.481167 | + | 0.0144755i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −36.8808 | + | 10.6029i | −1.78062 | + | 0.511910i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.22781 | + | 5.32768i | −0.444488 | + | 0.256625i | −0.705499 | − | 0.708711i | \(-0.749277\pi\) |
0.261012 | + | 0.965336i | \(0.415944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5027 | −1.22558 | −0.612791 | − | 0.790245i | \(-0.709953\pi\) | ||||
−0.612791 | + | 0.790245i | \(0.709953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.4157 | − | 11.7870i | 0.976613 | − | 0.563848i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.8206 | − | 13.7528i | −1.13689 | − | 0.656386i | −0.191234 | − | 0.981544i | \(-0.561249\pi\) |
−0.945660 | + | 0.325158i | \(0.894582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4319 | − | 10.0630i | 0.877712 | − | 0.479189i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.68708 | + | 16.7785i | −0.460247 | + | 0.797171i | −0.998973 | − | 0.0453099i | \(-0.985572\pi\) |
0.538726 | + | 0.842481i | \(0.318906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.3864 | − | 24.4816i | −1.20073 | − | 1.15794i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.9504i | 1.27187i | 0.771744 | + | 0.635934i | \(0.219385\pi\) | ||||
−0.771744 | + | 0.635934i | \(0.780615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8479 | + | 6.26304i | −0.510808 | + | 0.294915i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.44983 | − | 18.9566i | −0.256056 | − | 0.890660i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.9124 | − | 9.18704i | −0.744352 | − | 0.429752i | 0.0792977 | − | 0.996851i | \(-0.474732\pi\) |
−0.823649 | + | 0.567099i | \(0.808066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.786920 | − | 0.165569i | −0.0367303 | − | 0.00772810i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2344 | −0.569814 | −0.284907 | − | 0.958555i | \(-0.591963\pi\) | ||||
−0.284907 | + | 0.958555i | \(0.591963\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4136i | 0.530433i | 0.964189 | + | 0.265217i | \(0.0854435\pi\) | ||||
−0.964189 | + | 0.265217i | \(0.914556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.15336 | − | 0.665893i | −0.0533711 | − | 0.0308138i | 0.473077 | − | 0.881021i | \(-0.343143\pi\) |
−0.526448 | + | 0.850207i | \(0.676477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.23728 | + | 2.00152i | −0.0571325 | + | 0.0924218i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.26008 | − | 11.3398i | −0.150217 | − | 0.522511i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.77302 | + | 8.26712i | 0.219464 | + | 0.380123i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.539659 | + | 14.8675i | 0.0247093 | + | 0.680736i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.7342 | − | 18.5922i | −0.490458 | − | 0.849498i | 0.509482 | − | 0.860481i | \(-0.329837\pi\) |
−0.999940 | + | 0.0109835i | \(0.996504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.5496 | − | 21.6793i | −1.71212 | − | 0.988491i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.42790 | + | 26.4543i | −0.337981 | + | 1.20371i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0115 | + | 13.8630i | −1.08807 | + | 0.628195i | −0.933061 | − | 0.359719i | \(-0.882873\pi\) |
−0.155004 | + | 0.987914i | \(0.549539\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.86409 | − | 9.51254i | −0.446070 | − | 0.430172i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.536100i | − | 0.0241938i | −0.999927 | − | 0.0120969i | \(-0.996149\pi\) | ||
0.999927 | − | 0.0120969i | \(-0.00385066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.798164 | − | 1.38246i | −0.0359475 | − | 0.0622629i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.5642 | − | 27.0749i | −0.653293 | − | 1.21447i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.1191 | + | 26.1870i | −0.676823 | + | 1.17229i | 0.299110 | + | 0.954219i | \(0.403310\pi\) |
−0.975933 | + | 0.218072i | \(0.930023\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.04420 | − | 32.3583i | 0.359388 | − | 1.44566i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.5176i | − | 1.44989i | −0.688807 | − | 0.724945i | \(-0.741865\pi\) | ||
0.688807 | − | 0.724945i | \(-0.258135\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.91235 | + | 1.71839i | 0.306988 | + | 0.0763166i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.1885 | − | 22.8432i | 0.584570 | − | 1.01251i | −0.410359 | − | 0.911924i | \(-0.634597\pi\) |
0.994929 | − | 0.100581i | \(-0.0320702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.5705 | + | 17.0433i | 1.21965 | + | 0.753952i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.35301 | + | 19.4162i | 0.280492 | + | 0.857245i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.2938 | −0.848538 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.6324 | + | 17.0040i | 0.773977 | + | 0.746393i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.39842 | − | 9.35035i | −0.236509 | − | 0.409646i | 0.723201 | − | 0.690638i | \(-0.242670\pi\) |
−0.959710 | + | 0.280992i | \(0.909337\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.119197 | + | 0.206455i | −0.00521211 | + | 0.00902764i | −0.868620 | − | 0.495479i | \(-0.834992\pi\) |
0.863408 | + | 0.504507i | \(0.168326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.598708 | + | 1.03699i | −0.0260801 | + | 0.0451721i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.47632 | − | 11.2173i | −0.281579 | − | 0.487709i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.14701 | + | 31.5999i | 0.0497760 | + | 1.37132i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.67476 | 0.419061 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.45229 | − | 0.992498i | 0.148977 | − | 0.0428294i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.25374 | − | 37.4232i | 0.0970753 | − | 1.61193i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.28056 | + | 2.21799i | −0.0550555 | + | 0.0953588i | −0.892240 | − | 0.451562i | \(-0.850867\pi\) |
0.837184 | + | 0.546921i | \(0.184200\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.08444 | − | 36.5427i | 0.389850 | − | 1.56820i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 27.1549i | − | 1.16106i | −0.814239 | − | 0.580529i | \(-0.802846\pi\) | ||
0.814239 | − | 0.580529i | \(-0.197154\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.99022 | − | 9.55707i | −0.255656 | − | 0.407886i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.2770 | + | 35.1209i | −0.863831 | + | 1.49620i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.574652 | − | 19.1015i | 0.0244367 | − | 0.812277i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.0080 | + | 20.7984i | 0.508794 | + | 0.881257i | 0.999948 | + | 0.0101846i | \(0.00324193\pi\) |
−0.491154 | + | 0.871073i | \(0.663425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.37308i | − | 0.311848i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.996567 | + | 1.03340i | −0.0420751 | + | 0.0436300i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.8986 | + | 20.1487i | −1.47080 | + | 0.849168i | −0.999462 | − | 0.0327839i | \(-0.989563\pi\) |
−0.471340 | + | 0.881952i | \(0.656229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.1087 | − | 11.0192i | −0.886482 | − | 0.462763i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.46883 | + | 2.58008i | 0.187343 | + | 0.108163i | 0.590738 | − | 0.806863i | \(-0.298837\pi\) |
−0.403395 | + | 0.915026i | \(0.632170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.841937 | + | 1.45828i | 0.0352340 | + | 0.0610270i | 0.883105 | − | 0.469176i | \(-0.155449\pi\) |
−0.847871 | + | 0.530203i | \(0.822116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.88916 | − | 2.78620i | −0.120697 | − | 0.116395i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.7284 | − | 25.5104i | −0.613153 | − | 1.06201i | −0.990706 | − | 0.136024i | \(-0.956568\pi\) |
0.377552 | − | 0.925988i | \(-0.376766\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.7370 | − | 8.54907i | 1.23583 | − | 0.355287i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.44461 | + | 11.9806i | 0.267368 | + | 0.497037i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.0018 | + | 13.2801i | 0.952638 | + | 0.550006i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.9862i | 1.89805i | 0.315195 | + | 0.949027i | \(0.397930\pi\) | ||||
−0.315195 | + | 0.949027i | \(0.602070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.4199 | 1.25343 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.9030 | − | 7.68242i | −1.27118 | − | 0.316012i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.65252 | − | 0.954084i | −0.0678610 | − | 0.0391795i | 0.465686 | − | 0.884950i | \(-0.345808\pi\) |
−0.533547 | + | 0.845771i | \(0.679141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.28231 | − | 0.943632i | 0.134336 | − | 0.0386203i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2188 | + | 10.5186i | −0.744401 | + | 0.429780i | −0.823667 | − | 0.567073i | \(-0.808076\pi\) |
0.0792661 | + | 0.996853i | \(0.474742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.3573i | 1.23830i | 0.785273 | + | 0.619150i | \(0.212523\pi\) | ||||
−0.785273 | + | 0.619150i | \(0.787477\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.66638 | − | 0.0967842i | 0.108583 | − | 0.00394136i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.89399 | − | 15.4049i | 0.360996 | − | 0.625264i | −0.627129 | − | 0.778915i | \(-0.715770\pi\) |
0.988125 | + | 0.153652i | \(0.0491034\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.6884 | − | 45.8012i | −0.473637 | − | 1.85596i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.9054 | + | 7.45095i | 0.522098 | + | 0.301433i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.1276 | − | 14.5074i | 1.01490 | − | 0.585950i | 0.102274 | − | 0.994756i | \(-0.467388\pi\) |
0.912621 | + | 0.408806i | \(0.134055\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.32967 | −0.134047 | −0.0670237 | − | 0.997751i | \(-0.521350\pi\) | ||||
−0.0670237 | + | 0.997751i | \(0.521350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.6135 | + | 24.0256i | −1.67259 | + | 0.965669i | −0.706406 | + | 0.707806i | \(0.749685\pi\) |
−0.966182 | + | 0.257863i | \(0.916982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.6116 | − | 9.68897i | 1.18827 | − | 0.388805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.36592 | + | 45.4032i | −0.0547244 | + | 1.81904i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35.3945 | + | 8.79899i | 1.41352 | + | 0.351398i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.62209 | −0.0646771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.8726 | 0.631878 | 0.315939 | − | 0.948779i | \(-0.397680\pi\) | ||||
0.315939 | + | 0.948779i | \(0.397680\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.81482 | + | 0.451160i | 0.0721327 | + | 0.0179320i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.9598 | + | 24.1617i | −0.632350 | + | 0.957322i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.3234 | + | 30.8019i | −0.645743 | + | 1.21851i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.34785 | − | 1.93288i | 0.132232 | − | 0.0763443i | −0.432425 | − | 0.901670i | \(-0.642342\pi\) |
0.564657 | + | 0.825326i | \(0.309009\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.7423 | −1.48841 | −0.744206 | − | 0.667950i | \(-0.767172\pi\) | ||||
−0.744206 | + | 0.667950i | \(0.767172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.9193 | + | 10.9230i | −0.743793 | + | 0.429429i | −0.823447 | − | 0.567393i | \(-0.807952\pi\) |
0.0796536 | + | 0.996823i | \(0.474619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.8888 | + | 28.2260i | 1.91905 | + | 1.10797i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.3692 | + | 24.7708i | −0.994297 | + | 0.970844i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.81473 | + | 3.14321i | −0.0710159 | + | 0.123003i | −0.899347 | − | 0.437236i | \(-0.855957\pi\) |
0.828331 | + | 0.560239i | \(0.189291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.33318 | − | 36.7288i | −0.0520123 | − | 1.43293i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.4040i | − | 0.872737i | −0.899768 | − | 0.436369i | \(-0.856264\pi\) | ||
0.899768 | − | 0.436369i | \(-0.143736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6525 | − | 7.88230i | 0.531023 | − | 0.306586i | −0.210410 | − | 0.977613i | \(-0.567480\pi\) |
0.741433 | + | 0.671027i | \(0.234147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.06568 | − | 0.306371i | 0.0413875 | − | 0.0118985i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.5628 | + | 30.9245i | 2.07396 | + | 1.19740i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.8590 | − | 6.42849i | −0.999767 | − | 0.248540i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.1366 | −0.777365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.84031i | 0.340769i | 0.985378 | + | 0.170385i | \(0.0545010\pi\) | ||||
−0.985378 | + | 0.170385i | \(0.945499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5519 | − | 7.82417i | −0.520840 | − | 0.300707i | 0.216438 | − | 0.976296i | \(-0.430556\pi\) |
−0.737278 | + | 0.675589i | \(0.763889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.97974 | − | 5.36833i | 0.382987 | − | 0.206018i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.24738 | − | 0.933590i | 0.124440 | − | 0.0357752i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.9193 | + | 32.7691i | 0.723926 | + | 1.25388i | 0.959415 | + | 0.281999i | \(0.0909975\pi\) |
−0.235489 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.52351 | − | 3.39793i | −0.134430 | − | 0.129639i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.2572 | − | 17.7659i | −0.390766 | − | 0.676827i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5792 | − | 8.41732i | −0.554620 | − | 0.320210i | 0.196363 | − | 0.980531i | \(-0.437087\pi\) |
−0.750983 | + | 0.660321i | \(0.770420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −36.6828 | + | 21.4835i | −1.39347 | + | 0.816091i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.313452 | − | 0.180972i | 0.0118729 | − | 0.00685480i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.27972 | − | 5.47484i | 0.199697 | − | 0.207077i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 28.2554i | − | 1.06719i | −0.845740 | − | 0.533596i | \(-0.820840\pi\) | ||
0.845740 | − | 0.533596i | \(-0.179160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.6043 | + | 35.6877i | 0.777106 | + | 1.34599i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.7186 | − | 8.48046i | −0.515942 | − | 0.318940i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.40632 | − | 12.8281i | 0.278150 | − | 0.481770i | −0.692775 | − | 0.721154i | \(-0.743612\pi\) |
0.970925 | + | 0.239384i | \(0.0769454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.3604 | + | 11.5080i | −0.688568 | + | 0.431583i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 46.3934i | − | 1.73744i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.38467 | + | 29.7053i | −0.275786 | + | 1.10937i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.1406 | + | 17.5640i | −0.378179 | + | 0.655025i | −0.990797 | − | 0.135353i | \(-0.956783\pi\) |
0.612618 | + | 0.790379i | \(0.290116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.342786 | − | 11.3942i | 0.0127660 | − | 0.424342i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.09555 | + | 2.03990i | −0.263886 | + | 0.0758646i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.81854 | −0.104534 | −0.0522670 | − | 0.998633i | \(-0.516645\pi\) | ||||
−0.0522670 | + | 0.998633i | \(0.516645\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.93304 | + | 26.8402i | 0.108631 | + | 0.994082i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.137917 | − | 0.238880i | −0.00510106 | − | 0.00883530i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.4457 | − | 30.2169i | 0.644372 | − | 1.11609i | −0.340074 | − | 0.940399i | \(-0.610452\pi\) |
0.984446 | − | 0.175687i | \(-0.0562146\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.38170 | − | 4.12522i | 0.0877309 | − | 0.151954i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.4220 | − | 23.2476i | −0.493737 | − | 0.855177i | 0.506237 | − | 0.862394i | \(-0.331036\pi\) |
−0.999974 | + | 0.00721695i | \(0.997703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.2770 | − | 19.5544i | −0.744896 | − | 0.718348i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.24499 | 0.0823607 | 0.0411804 | − | 0.999152i | \(-0.486888\pi\) | ||||
0.0411804 | + | 0.999152i | \(0.486888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.22305 | − | 13.6298i | 0.264277 | − | 0.498687i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.31902 | − | 43.8442i | 0.0481959 | − | 1.60203i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.56634 | + | 2.71297i | −0.0571564 | + | 0.0989978i | −0.893188 | − | 0.449684i | \(-0.851537\pi\) |
0.836031 | + | 0.548682i | \(0.184870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.51882 | − | 1.62056i | −0.237559 | − | 0.0590566i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.5473i | − | 0.928532i | −0.885696 | − | 0.464266i | \(-0.846318\pi\) | ||
0.885696 | − | 0.464266i | \(-0.153682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.4193 | − | 53.9801i | 0.487091 | − | 1.95935i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.16163 | + | 3.74406i | −0.0783591 | + | 0.135722i | −0.902542 | − | 0.430602i | \(-0.858301\pi\) |
0.824183 | + | 0.566324i | \(0.191635\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.66100 | − | 5.35399i | −0.313549 | − | 0.193827i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.8009 | − | 37.7603i | −0.787185 | − | 1.36344i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.4529i | − | 1.24240i | −0.783650 | − | 0.621202i | \(-0.786645\pi\) | ||
0.783650 | − | 0.621202i | \(-0.213355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0817 | + | 21.2947i | 0.795253 | + | 0.766911i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.99408 | − | 5.19273i | 0.323494 | − | 0.186770i | −0.329455 | − | 0.944171i | \(-0.606865\pi\) |
0.652949 | + | 0.757402i | \(0.273532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −46.2437 | − | 12.9844i | −1.65898 | − | 0.465812i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.96313 | − | 4.59752i | −0.285309 | − | 0.164723i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.1174 | + | 53.8970i | 1.11347 | + | 1.92859i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.7819 | + | 39.9050i | −1.27874 | + | 1.42609i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4590 | + | 37.1681i | 0.764931 | + | 1.32490i | 0.940283 | + | 0.340394i | \(0.110560\pi\) |
−0.175352 | + | 0.984506i | \(0.556106\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.67961 | − | 9.32071i | −0.0953966 | − | 0.331826i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.1671 | + | 12.4621i | −0.823726 | + | 0.443101i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4692 | + | 7.77645i | 0.478306 | + | 0.276150i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 19.3628i | − | 0.685866i | −0.939360 | − | 0.342933i | \(-0.888580\pi\) | ||
0.939360 | − | 0.342933i | \(-0.111420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.557497 | 0.0197228 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 43.6417 | − | 27.3539i | 1.54200 | − | 0.966503i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −56.8239 | − | 32.8073i | −2.00527 | − | 1.15774i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.16749 | − | 28.4097i | −0.287509 | − | 1.00007i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.120667 | − | 0.0696669i | 0.00424241 | − | 0.00244936i | −0.497877 | − | 0.867247i | \(-0.665887\pi\) |
0.502120 | + | 0.864798i | \(0.332554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.5559i | − | 1.52945i | −0.644354 | − | 0.764727i | \(-0.722874\pi\) | ||
0.644354 | − | 0.764727i | \(-0.277126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.2578 | + | 20.5002i | 0.745543 | + | 0.718973i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.50374 | + | 6.06865i | −0.122580 | + | 0.212315i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 32.8334 | − | 0.203795i | 1.14729 | − | 0.00712118i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.9212 | + | 23.0485i | 1.39326 | + | 0.804400i | 0.993675 | − | 0.112296i | \(-0.0358204\pi\) |
0.399586 | + | 0.916696i | \(0.369154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.4726 | − | 11.2425i | 0.678772 | − | 0.391889i | −0.120620 | − | 0.992699i | \(-0.538488\pi\) |
0.799392 | + | 0.600809i | \(0.205155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.2536 | 1.81704 | 0.908518 | − | 0.417846i | \(-0.137215\pi\) | ||||
0.908518 | + | 0.417846i | \(0.137215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.26705 | + | 1.88623i | −0.113469 | + | 0.0655115i | −0.555661 | − | 0.831409i | \(-0.687535\pi\) |
0.442191 | + | 0.896921i | \(0.354201\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5408 | + | 5.04279i | −0.608483 | + | 0.174933i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.0651222 | + | 1.08135i | −0.00225635 | + | 0.0374666i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.3429 | + | 8.27779i | 1.35989 | + | 0.286122i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.7191 | 1.40578 | 0.702890 | − | 0.711299i | \(-0.251893\pi\) | ||||
0.702890 | + | 0.711299i | \(0.251893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −77.3983 | −2.66891 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.03171 | − | 32.3081i | 0.276627 | − | 1.11275i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.40703 | + | 46.7696i | −0.0483460 | + | 1.60702i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.60577 | + | 29.9342i | 0.295349 | + | 1.02734i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.4273 | − | 31.4236i | 1.86574 | − | 1.07719i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.21298 | 0.110010 | 0.0550051 | − | 0.998486i | \(-0.482482\pi\) | ||||
0.0550051 | + | 0.998486i | \(0.482482\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.6653 | + | 24.0555i | −1.42326 | + | 0.821720i | −0.996576 | − | 0.0826803i | \(-0.973652\pi\) |
−0.426685 | + | 0.904400i | \(0.640319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.4266 | − | 6.01978i | −0.355750 | − | 0.205392i | 0.311465 | − | 0.950258i | \(-0.399180\pi\) |
−0.667215 | + | 0.744865i | \(0.732514\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.3847 | − | 2.65017i | 0.353911 | − | 0.0903174i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.75993 | + | 6.51239i | −0.127989 | + | 0.221684i | −0.922898 | − | 0.385046i | \(-0.874186\pi\) |
0.794908 | + | 0.606730i | \(0.207519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.4108 | + | 21.1651i | −0.693186 | + | 0.718803i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.6851i | 1.31230i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.18619 | + | 1.83955i | −0.107960 | + | 0.0623308i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.3535 | − | 6.01676i | −0.384259 | − | 0.203636i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.8156 | + | 16.6367i | 0.973033 | + | 0.561781i | 0.900160 | − | 0.435560i | \(-0.143450\pi\) |
0.0728736 | + | 0.997341i | \(0.476783\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5366 | + | 42.3841i | −0.355390 | + | 1.42958i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.9614 | 0.672515 | 0.336258 | − | 0.941770i | \(-0.390839\pi\) | ||||
0.336258 | + | 0.941770i | \(0.390839\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 51.3120i | − | 1.72679i | −0.504533 | − | 0.863393i | \(-0.668335\pi\) | ||
0.504533 | − | 0.863393i | \(-0.331665\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.2280 | − | 9.94659i | −0.578460 | − | 0.333974i | 0.182061 | − | 0.983287i | \(-0.441723\pi\) |
−0.760521 | + | 0.649313i | \(0.775056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.82158 | − | 10.8223i | −0.195250 | − | 0.362970i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.3823 | + | 21.0114i | 1.45336 | + | 0.703910i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.08149 | − | 12.2655i | −0.236973 | − | 0.410450i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.8224 | + | 30.9245i | −0.995740 | + | 1.03254i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.9050 | + | 69.1176i | 1.33091 | + | 2.30520i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.664642 | − | 0.383731i | −0.0221424 | − | 0.0127839i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.01967 | − | 7.91414i | −0.0672106 | − | 0.263366i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.1005 | + | 21.4200i | −1.23190 | + | 0.711239i | −0.967426 | − | 0.253153i | \(-0.918532\pi\) |
−0.264476 | + | 0.964392i | \(0.585199\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.663367 | + | 18.2756i | 0.0220025 | + | 0.606164i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.5359i | − | 0.945437i | −0.881213 | − | 0.472719i | \(-0.843273\pi\) | ||
0.881213 | − | 0.472719i | \(-0.156727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7694 | − | 23.8493i | −0.455700 | − | 0.789296i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.527347 | + | 17.5290i | −0.0174145 | + | 0.578859i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.41160 | + | 7.64112i | −0.145525 | + | 0.252057i | −0.929569 | − | 0.368649i | \(-0.879821\pi\) |
0.784043 | + | 0.620706i | \(0.213154\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.9294 | − | 3.46282i | −0.458990 | − | 0.114104i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 48.0683i | − | 1.58219i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.9521 | + | 6.86463i | −0.359716 | + | 0.225464i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.1691 | + | 47.0583i | −0.891389 | + | 1.54393i | −0.0531782 | + | 0.998585i | \(0.516935\pi\) |
−0.838211 | + | 0.545346i | \(0.816398\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6180 | − | 12.3029i | 0.806824 | − | 0.403211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.10567 | + | 14.2811i | 0.134414 | + | 0.467542i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.3198 | 0.533144 | 0.266572 | − | 0.963815i | \(-0.414109\pi\) | ||||
0.266572 | + | 0.963815i | \(0.414109\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.12154 | + | 1.16299i | −0.0366002 | + | 0.0379528i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.80594 | + | 6.59208i | 0.124070 | + | 0.214896i | 0.921369 | − | 0.388689i | \(-0.127072\pi\) |
−0.797299 | + | 0.603585i | \(0.793739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.01167 | + | 12.1446i | −0.228331 | + | 0.395481i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.4912 | + | 19.9034i | −0.373415 | + | 0.646774i | −0.990088 | − | 0.140445i | \(-0.955147\pi\) |
0.616673 | + | 0.787219i | \(0.288480\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.3394 | + | 43.8891i | 0.822551 | + | 1.42470i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.58552 | − | 3.71803i | 0.116269 | − | 0.120565i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.5633 | 1.31397 | 0.656986 | − | 0.753902i | \(-0.271831\pi\) | ||||
0.656986 | + | 0.753902i | \(0.271831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.4384 | + | 91.9630i | 0.854633 | + | 2.97274i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.6125 | − | 6.56034i | −0.342695 | − | 0.211844i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4330 | − | 24.9988i | 0.465582 | − | 0.806412i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.1432 | + | 26.4147i | −1.35805 | + | 0.851201i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.10140i | 0.0997343i | 0.998756 | + | 0.0498672i | \(0.0158798\pi\) | ||||
−0.998756 | + | 0.0498672i | \(0.984120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.02273 | − | 0.254249i | −0.0328549 | − | 0.00816764i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.5212 | + | 39.0078i | −0.722739 | + | 1.25182i | 0.237159 | + | 0.971471i | \(0.423784\pi\) |
−0.959898 | + | 0.280350i | \(0.909550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.9857 | + | 22.2815i | 0.384244 | + | 0.714311i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.6207 | + | 21.8598i | 0.403773 | + | 0.699356i | 0.994178 | − | 0.107751i | \(-0.0343651\pi\) |
−0.590404 | + | 0.807108i | \(0.701032\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 91.9525i | − | 2.93881i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.418805 | + | 11.5380i | 0.0133714 | + | 0.368379i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.2661 | − | 30.1759i | 1.66703 | − | 0.962461i | 0.697805 | − | 0.716288i | \(-0.254160\pi\) |
0.969226 | − | 0.246173i | \(-0.0791730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.8935 | + | 4.46260i | 0.505895 | + | 0.142046i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.25530 | + | 5.34355i | 0.294301 | + | 0.169915i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.93445 | + | 8.54672i | 0.156748 | + | 0.271495i | 0.933694 | − | 0.358072i | \(-0.116566\pi\) |
−0.776946 | + | 0.629567i | \(0.783232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.3408 | − | 27.3142i | 0.835900 | − | 0.866792i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.4745 | − | 23.3385i | −0.426742 | − | 0.739138i | 0.569840 | − | 0.821756i | \(-0.307005\pi\) |
−0.996581 | + | 0.0826177i | \(0.973672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.9369 | + | 51.7627i | 0.535859 | + | 1.63770i |
(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 | 2100.2.bo.i.1349.15 | 32 | ||
3.2 | odd | 2 | inner | 2100.2.bo.i.1349.7 | 32 | ||
5.2 | odd | 4 | 2100.2.bi.l.1601.6 | yes | 16 | ||
5.3 | odd | 4 | 2100.2.bi.m.1601.3 | yes | 16 | ||
5.4 | even | 2 | inner | 2100.2.bo.i.1349.2 | 32 | ||
7.3 | odd | 6 | inner | 2100.2.bo.i.1949.10 | 32 | ||
15.2 | even | 4 | 2100.2.bi.l.1601.8 | yes | 16 | ||
15.8 | even | 4 | 2100.2.bi.m.1601.1 | yes | 16 | ||
15.14 | odd | 2 | inner | 2100.2.bo.i.1349.10 | 32 | ||
21.17 | even | 6 | inner | 2100.2.bo.i.1949.2 | 32 | ||
35.3 | even | 12 | 2100.2.bi.m.101.1 | yes | 16 | ||
35.17 | even | 12 | 2100.2.bi.l.101.8 | yes | 16 | ||
35.24 | odd | 6 | inner | 2100.2.bo.i.1949.7 | 32 | ||
105.17 | odd | 12 | 2100.2.bi.l.101.6 | ✓ | 16 | ||
105.38 | odd | 12 | 2100.2.bi.m.101.3 | yes | 16 | ||
105.59 | even | 6 | inner | 2100.2.bo.i.1949.15 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.6 | ✓ | 16 | 105.17 | odd | 12 | ||
2100.2.bi.l.101.8 | yes | 16 | 35.17 | even | 12 | ||
2100.2.bi.l.1601.6 | yes | 16 | 5.2 | odd | 4 | ||
2100.2.bi.l.1601.8 | yes | 16 | 15.2 | even | 4 | ||
2100.2.bi.m.101.1 | yes | 16 | 35.3 | even | 12 | ||
2100.2.bi.m.101.3 | yes | 16 | 105.38 | odd | 12 | ||
2100.2.bi.m.1601.1 | yes | 16 | 15.8 | even | 4 | ||
2100.2.bi.m.1601.3 | yes | 16 | 5.3 | odd | 4 | ||
2100.2.bo.i.1349.2 | 32 | 5.4 | even | 2 | inner | ||
2100.2.bo.i.1349.7 | 32 | 3.2 | odd | 2 | inner | ||
2100.2.bo.i.1349.10 | 32 | 15.14 | odd | 2 | inner | ||
2100.2.bo.i.1349.15 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.bo.i.1949.2 | 32 | 21.17 | even | 6 | inner | ||
2100.2.bo.i.1949.7 | 32 | 35.24 | odd | 6 | inner | ||
2100.2.bo.i.1949.10 | 32 | 7.3 | odd | 6 | inner | ||
2100.2.bo.i.1949.15 | 32 | 105.59 | even | 6 | inner |