Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2175,2,Mod(349,2175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2175.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2175 = 3 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2175.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.3674624396\) |
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: | \( x^{16} + 28x^{14} + 308x^{12} + 1671x^{10} + 4568x^{8} + 5616x^{6} + 2105x^{4} + 256x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.16 | ||
Root | \(2.72810i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2175.349 |
Dual form | 2175.2.c.p.349.1 |
$q$-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 \(\left(\mathbb{Z}/2175\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1451\) | \(2002\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.72810i | 1.92906i | 0.263981 | + | 0.964528i | \(0.414964\pi\) | ||||
−0.263981 | + | 0.964528i | \(0.585036\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −5.44251 | −2.72126 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.72810 | −1.11374 | ||||||||
\(7\) | 4.61695i | 1.74504i | 0.488577 | + | 0.872521i | \(0.337516\pi\) | ||||
−0.488577 | + | 0.872521i | \(0.662484\pi\) | |||||||
\(8\) | − 9.39150i | − 3.32040i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.87758 | −0.566110 | −0.283055 | − | 0.959104i | \(-0.591348\pi\) | ||||
−0.283055 | + | 0.959104i | \(0.591348\pi\) | |||||||
\(12\) | − 5.44251i | − 1.57112i | ||||||||
\(13\) | − 5.48400i | − 1.52099i | −0.649345 | − | 0.760494i | \(-0.724957\pi\) | ||||
0.649345 | − | 0.760494i | \(-0.275043\pi\) | |||||||
\(14\) | −12.5955 | −3.36628 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.7359 | 3.68398 | ||||||||
\(17\) | − 5.74056i | − 1.39229i | −0.717901 | − | 0.696145i | \(-0.754897\pi\) | ||||
0.717901 | − | 0.696145i | \(-0.245103\pi\) | |||||||
\(18\) | − 2.72810i | − 0.643019i | ||||||||
\(19\) | 5.40455 | 1.23989 | 0.619944 | − | 0.784646i | \(-0.287155\pi\) | ||||
0.619944 | + | 0.784646i | \(0.287155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.61695 | −1.00750 | ||||||||
\(22\) | − 5.12221i | − 1.09206i | ||||||||
\(23\) | 0.137016i | 0.0285698i | 0.999898 | + | 0.0142849i | \(0.00454719\pi\) | ||||
−0.999898 | + | 0.0142849i | \(0.995453\pi\) | |||||||
\(24\) | 9.39150 | 1.91703 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.9609 | 2.93407 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 25.1278i | − 4.74870i | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.18167 | −1.46947 | −0.734736 | − | 0.678353i | \(-0.762694\pi\) | ||||
−0.734736 | + | 0.678353i | \(0.762694\pi\) | |||||||
\(32\) | 21.4180i | 3.78620i | ||||||||
\(33\) | − 1.87758i | − 0.326844i | ||||||||
\(34\) | 15.6608 | 2.68581 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.44251 | 0.907085 | ||||||||
\(37\) | − 4.45785i | − 0.732866i | −0.930444 | − | 0.366433i | \(-0.880579\pi\) | ||||
0.930444 | − | 0.366433i | \(-0.119421\pi\) | |||||||
\(38\) | 14.7441i | 2.39181i | ||||||||
\(39\) | 5.48400 | 0.878142 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.215243 | −0.0336153 | −0.0168076 | − | 0.999859i | \(-0.505350\pi\) | ||||
−0.0168076 | + | 0.999859i | \(0.505350\pi\) | |||||||
\(42\) | − 12.5955i | − 1.94352i | ||||||||
\(43\) | − 7.17115i | − 1.09359i | −0.837266 | − | 0.546795i | \(-0.815848\pi\) | ||||
0.837266 | − | 0.546795i | \(-0.184152\pi\) | |||||||
\(44\) | 10.2187 | 1.54053 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.373793 | −0.0551128 | ||||||||
\(47\) | − 9.91293i | − 1.44595i | −0.690874 | − | 0.722975i | \(-0.742774\pi\) | ||||
0.690874 | − | 0.722975i | \(-0.257226\pi\) | |||||||
\(48\) | 14.7359i | 2.12695i | ||||||||
\(49\) | −14.3162 | −2.04517 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.74056 | 0.803839 | ||||||||
\(52\) | 29.8467i | 4.13899i | ||||||||
\(53\) | 1.14754i | 0.157627i | 0.996889 | + | 0.0788134i | \(0.0251131\pi\) | ||||
−0.996889 | + | 0.0788134i | \(0.974887\pi\) | |||||||
\(54\) | 2.72810 | 0.371247 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 43.3601 | 5.79423 | ||||||||
\(57\) | 5.40455i | 0.715850i | ||||||||
\(58\) | − 2.72810i | − 0.358217i | ||||||||
\(59\) | 0.244913 | 0.0318849 | 0.0159425 | − | 0.999873i | \(-0.494925\pi\) | ||||
0.0159425 | + | 0.999873i | \(0.494925\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.75284 | 1.12069 | 0.560343 | − | 0.828260i | \(-0.310669\pi\) | ||||
0.560343 | + | 0.828260i | \(0.310669\pi\) | |||||||
\(62\) | − 22.3204i | − 2.83469i | ||||||||
\(63\) | − 4.61695i | − 0.581680i | ||||||||
\(64\) | −28.9585 | −3.61981 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.12221 | 0.630500 | ||||||||
\(67\) | − 6.53295i | − 0.798127i | −0.916923 | − | 0.399064i | \(-0.869335\pi\) | ||||
0.916923 | − | 0.399064i | \(-0.130665\pi\) | |||||||
\(68\) | 31.2431i | 3.78878i | ||||||||
\(69\) | −0.137016 | −0.0164948 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.277412 | −0.0329227 | −0.0164614 | − | 0.999865i | \(-0.505240\pi\) | ||||
−0.0164614 | + | 0.999865i | \(0.505240\pi\) | |||||||
\(72\) | 9.39150i | 1.10680i | ||||||||
\(73\) | 11.4933i | 1.34519i | 0.740011 | + | 0.672594i | \(0.234820\pi\) | ||||
−0.740011 | + | 0.672594i | \(0.765180\pi\) | |||||||
\(74\) | 12.1614 | 1.41374 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29.4143 | −3.37405 | ||||||||
\(77\) | − 8.66866i | − 0.987886i | ||||||||
\(78\) | 14.9609i | 1.69399i | ||||||||
\(79\) | −1.66223 | −0.187015 | −0.0935076 | − | 0.995619i | \(-0.529808\pi\) | ||||
−0.0935076 | + | 0.995619i | \(0.529808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.587203i | − 0.0648457i | ||||||||
\(83\) | − 9.58514i | − 1.05211i | −0.850452 | − | 0.526053i | \(-0.823671\pi\) | ||||
0.850452 | − | 0.526053i | \(-0.176329\pi\) | |||||||
\(84\) | 25.1278 | 2.74167 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 19.5636 | 2.10960 | ||||||||
\(87\) | − 1.00000i | − 0.107211i | ||||||||
\(88\) | 17.6333i | 1.87971i | ||||||||
\(89\) | −16.3332 | −1.73132 | −0.865659 | − | 0.500634i | \(-0.833100\pi\) | ||||
−0.865659 | + | 0.500634i | \(0.833100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.3193 | 2.65419 | ||||||||
\(92\) | − 0.745712i | − 0.0777458i | ||||||||
\(93\) | − 8.18167i | − 0.848400i | ||||||||
\(94\) | 27.0434 | 2.78932 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −21.4180 | −2.18596 | ||||||||
\(97\) | 8.04128i | 0.816468i | 0.912877 | + | 0.408234i | \(0.133855\pi\) | ||||
−0.912877 | + | 0.408234i | \(0.866145\pi\) | |||||||
\(98\) | − 39.0559i | − 3.94525i | ||||||||
\(99\) | 1.87758 | 0.188703 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.3239 | −1.22627 | −0.613135 | − | 0.789978i | \(-0.710092\pi\) | ||||
−0.613135 | + | 0.789978i | \(0.710092\pi\) | |||||||
\(102\) | 15.6608i | 1.55065i | ||||||||
\(103\) | 0.660912i | 0.0651216i | 0.999470 | + | 0.0325608i | \(0.0103663\pi\) | ||||
−0.999470 | + | 0.0325608i | \(0.989634\pi\) | |||||||
\(104\) | −51.5030 | −5.05028 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.13060 | −0.304071 | ||||||||
\(107\) | − 14.5868i | − 1.41016i | −0.709128 | − | 0.705079i | \(-0.750911\pi\) | ||||
0.709128 | − | 0.705079i | \(-0.249089\pi\) | |||||||
\(108\) | 5.44251i | 0.523706i | ||||||||
\(109\) | −15.5050 | −1.48511 | −0.742557 | − | 0.669783i | \(-0.766387\pi\) | ||||
−0.742557 | + | 0.669783i | \(0.766387\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.45785 | 0.423120 | ||||||||
\(112\) | 68.0349i | 6.42869i | ||||||||
\(113\) | 7.80660i | 0.734383i | 0.930145 | + | 0.367191i | \(0.119681\pi\) | ||||
−0.930145 | + | 0.367191i | \(0.880319\pi\) | |||||||
\(114\) | −14.7441 | −1.38091 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.44251 | 0.505325 | ||||||||
\(117\) | 5.48400i | 0.506996i | ||||||||
\(118\) | 0.668145i | 0.0615078i | ||||||||
\(119\) | 26.5038 | 2.42960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.47471 | −0.679519 | ||||||||
\(122\) | 23.8786i | 2.16187i | ||||||||
\(123\) | − 0.215243i | − 0.0194078i | ||||||||
\(124\) | 44.5289 | 3.99881 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 12.5955 | 1.12209 | ||||||||
\(127\) | 19.7106i | 1.74903i | 0.484999 | + | 0.874515i | \(0.338820\pi\) | ||||
−0.484999 | + | 0.874515i | \(0.661180\pi\) | |||||||
\(128\) | − 36.1656i | − 3.19662i | ||||||||
\(129\) | 7.17115 | 0.631385 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.05738 | −0.0923834 | −0.0461917 | − | 0.998933i | \(-0.514709\pi\) | ||||
−0.0461917 | + | 0.998933i | \(0.514709\pi\) | |||||||
\(132\) | 10.2187i | 0.889426i | ||||||||
\(133\) | 24.9525i | 2.16366i | ||||||||
\(134\) | 17.8225 | 1.53963 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −53.9125 | −4.62296 | ||||||||
\(137\) | 3.21467i | 0.274648i | 0.990526 | + | 0.137324i | \(0.0438501\pi\) | ||||
−0.990526 | + | 0.137324i | \(0.956150\pi\) | |||||||
\(138\) | − 0.373793i | − 0.0318194i | ||||||||
\(139\) | −8.48410 | −0.719612 | −0.359806 | − | 0.933027i | \(-0.617157\pi\) | ||||
−0.359806 | + | 0.933027i | \(0.617157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.91293 | 0.834820 | ||||||||
\(142\) | − 0.756807i | − 0.0635098i | ||||||||
\(143\) | 10.2966i | 0.861046i | ||||||||
\(144\) | −14.7359 | −1.22799 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −31.3548 | −2.59494 | ||||||||
\(147\) | − 14.3162i | − 1.18078i | ||||||||
\(148\) | 24.2619i | 1.99432i | ||||||||
\(149\) | 5.93205 | 0.485972 | 0.242986 | − | 0.970030i | \(-0.421873\pi\) | ||||
0.242986 | + | 0.970030i | \(0.421873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.06281 | 0.656142 | 0.328071 | − | 0.944653i | \(-0.393601\pi\) | ||||
0.328071 | + | 0.944653i | \(0.393601\pi\) | |||||||
\(152\) | − 50.7568i | − 4.11692i | ||||||||
\(153\) | 5.74056i | 0.464097i | ||||||||
\(154\) | 23.6490 | 1.90569 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −29.8467 | −2.38965 | ||||||||
\(157\) | − 9.87127i | − 0.787813i | −0.919151 | − | 0.393906i | \(-0.871123\pi\) | ||||
0.919151 | − | 0.393906i | \(-0.128877\pi\) | |||||||
\(158\) | − 4.53472i | − 0.360763i | ||||||||
\(159\) | −1.14754 | −0.0910058 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.632596 | −0.0498555 | ||||||||
\(162\) | 2.72810i | 0.214340i | ||||||||
\(163\) | − 1.25711i | − 0.0984643i | −0.998787 | − | 0.0492321i | \(-0.984323\pi\) | ||||
0.998787 | − | 0.0492321i | \(-0.0156774\pi\) | |||||||
\(164\) | 1.17146 | 0.0914757 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.1492 | 2.02957 | ||||||||
\(167\) | − 15.1462i | − 1.17205i | −0.810294 | − | 0.586024i | \(-0.800692\pi\) | ||||
0.810294 | − | 0.586024i | \(-0.199308\pi\) | |||||||
\(168\) | 43.3601i | 3.34530i | ||||||||
\(169\) | −17.0742 | −1.31340 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.40455 | −0.413296 | ||||||||
\(172\) | 39.0291i | 2.97594i | ||||||||
\(173\) | − 2.34929i | − 0.178613i | −0.996004 | − | 0.0893065i | \(-0.971535\pi\) | ||||
0.996004 | − | 0.0893065i | \(-0.0284651\pi\) | |||||||
\(174\) | 2.72810 | 0.206816 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −27.6678 | −2.08554 | ||||||||
\(177\) | 0.244913i | 0.0184088i | ||||||||
\(178\) | − 44.5586i | − 3.33981i | ||||||||
\(179\) | 17.7814 | 1.32904 | 0.664520 | − | 0.747270i | \(-0.268636\pi\) | ||||
0.664520 | + | 0.747270i | \(0.268636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.69871 | −0.200594 | −0.100297 | − | 0.994958i | \(-0.531979\pi\) | ||||
−0.100297 | + | 0.994958i | \(0.531979\pi\) | |||||||
\(182\) | 69.0735i | 5.12007i | ||||||||
\(183\) | 8.75284i | 0.647029i | ||||||||
\(184\) | 1.28679 | 0.0948632 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 22.3204 | 1.63661 | ||||||||
\(187\) | 10.7783i | 0.788190i | ||||||||
\(188\) | 53.9512i | 3.93480i | ||||||||
\(189\) | 4.61695 | 0.335833 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.7997 | 0.781442 | 0.390721 | − | 0.920509i | \(-0.372226\pi\) | ||||
0.390721 | + | 0.920509i | \(0.372226\pi\) | |||||||
\(192\) | − 28.9585i | − 2.08990i | ||||||||
\(193\) | 4.18447i | 0.301205i | 0.988594 | + | 0.150602i | \(0.0481213\pi\) | ||||
−0.988594 | + | 0.150602i | \(0.951879\pi\) | |||||||
\(194\) | −21.9374 | −1.57501 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 77.9160 | 5.56543 | ||||||||
\(197\) | 5.76856i | 0.410993i | 0.978658 | + | 0.205496i | \(0.0658809\pi\) | ||||
−0.978658 | + | 0.205496i | \(0.934119\pi\) | |||||||
\(198\) | 5.12221i | 0.364019i | ||||||||
\(199\) | 5.45094 | 0.386407 | 0.193203 | − | 0.981159i | \(-0.438112\pi\) | ||||
0.193203 | + | 0.981159i | \(0.438112\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.53295 | 0.460799 | ||||||||
\(202\) | − 33.6207i | − 2.36554i | ||||||||
\(203\) | − 4.61695i | − 0.324046i | ||||||||
\(204\) | −31.2431 | −2.18745 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.80303 | −0.125623 | ||||||||
\(207\) | − 0.137016i | − 0.00952328i | ||||||||
\(208\) | − 80.8117i | − 5.60328i | ||||||||
\(209\) | −10.1474 | −0.701914 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.863332 | 0.0594342 | 0.0297171 | − | 0.999558i | \(-0.490539\pi\) | ||||
0.0297171 | + | 0.999558i | \(0.490539\pi\) | |||||||
\(212\) | − 6.24550i | − 0.428943i | ||||||||
\(213\) | − 0.277412i | − 0.0190080i | ||||||||
\(214\) | 39.7942 | 2.72027 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.39150 | −0.639011 | ||||||||
\(217\) | − 37.7743i | − 2.56429i | ||||||||
\(218\) | − 42.2993i | − 2.86487i | ||||||||
\(219\) | −11.4933 | −0.776645 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.4812 | −2.11766 | ||||||||
\(222\) | 12.1614i | 0.816223i | ||||||||
\(223\) | 0.615197i | 0.0411967i | 0.999788 | + | 0.0205983i | \(0.00655712\pi\) | ||||
−0.999788 | + | 0.0205983i | \(0.993443\pi\) | |||||||
\(224\) | −98.8856 | −6.60707 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.2972 | −1.41667 | ||||||||
\(227\) | − 23.7230i | − 1.57455i | −0.616602 | − | 0.787275i | \(-0.711491\pi\) | ||||
0.616602 | − | 0.787275i | \(-0.288509\pi\) | |||||||
\(228\) | − 29.4143i | − 1.94801i | ||||||||
\(229\) | 20.9808 | 1.38645 | 0.693226 | − | 0.720721i | \(-0.256189\pi\) | ||||
0.693226 | + | 0.720721i | \(0.256189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.66866 | 0.570356 | ||||||||
\(232\) | 9.39150i | 0.616582i | ||||||||
\(233\) | 7.95482i | 0.521138i | 0.965455 | + | 0.260569i | \(0.0839101\pi\) | ||||
−0.965455 | + | 0.260569i | \(0.916090\pi\) | |||||||
\(234\) | −14.9609 | −0.978023 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.33294 | −0.0867670 | ||||||||
\(237\) | − 1.66223i | − 0.107973i | ||||||||
\(238\) | 72.3051i | 4.68684i | ||||||||
\(239\) | −17.4888 | −1.13125 | −0.565627 | − | 0.824661i | \(-0.691366\pi\) | ||||
−0.565627 | + | 0.824661i | \(0.691366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7743 | −0.951699 | −0.475849 | − | 0.879527i | \(-0.657859\pi\) | ||||
−0.475849 | + | 0.879527i | \(0.657859\pi\) | |||||||
\(242\) | − 20.3917i | − 1.31083i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −47.6375 | −3.04968 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.587203 | 0.0374387 | ||||||||
\(247\) | − 29.6385i | − 1.88585i | ||||||||
\(248\) | 76.8382i | 4.87923i | ||||||||
\(249\) | 9.58514 | 0.607433 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.30996 | −0.208923 | −0.104461 | − | 0.994529i | \(-0.533312\pi\) | ||||
−0.104461 | + | 0.994529i | \(0.533312\pi\) | |||||||
\(252\) | 25.1278i | 1.58290i | ||||||||
\(253\) | − 0.257258i | − 0.0161737i | ||||||||
\(254\) | −53.7723 | −3.37398 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 40.7463 | 2.54664 | ||||||||
\(257\) | − 30.8668i | − 1.92542i | −0.270539 | − | 0.962709i | \(-0.587202\pi\) | ||||
0.270539 | − | 0.962709i | \(-0.412798\pi\) | |||||||
\(258\) | 19.5636i | 1.21798i | ||||||||
\(259\) | 20.5816 | 1.27888 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | − 2.88463i | − 0.178213i | ||||||||
\(263\) | − 19.4833i | − 1.20139i | −0.799477 | − | 0.600697i | \(-0.794890\pi\) | ||||
0.799477 | − | 0.600697i | \(-0.205110\pi\) | |||||||
\(264\) | −17.6333 | −1.08525 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −68.0728 | −4.17381 | ||||||||
\(267\) | − 16.3332i | − 0.999577i | ||||||||
\(268\) | 35.5557i | 2.17191i | ||||||||
\(269\) | −20.8385 | −1.27055 | −0.635273 | − | 0.772287i | \(-0.719113\pi\) | ||||
−0.635273 | + | 0.772287i | \(0.719113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.5849 | 1.49343 | 0.746713 | − | 0.665146i | \(-0.231631\pi\) | ||||
0.746713 | + | 0.665146i | \(0.231631\pi\) | |||||||
\(272\) | − 84.5924i | − 5.12916i | ||||||||
\(273\) | 25.3193i | 1.53239i | ||||||||
\(274\) | −8.76994 | −0.529811 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.745712 | 0.0448866 | ||||||||
\(277\) | 1.89904i | 0.114102i | 0.998371 | + | 0.0570510i | \(0.0181698\pi\) | ||||
−0.998371 | + | 0.0570510i | \(0.981830\pi\) | |||||||
\(278\) | − 23.1455i | − 1.38817i | ||||||||
\(279\) | 8.18167 | 0.489824 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.4916 | 1.93828 | 0.969142 | − | 0.246503i | \(-0.0792814\pi\) | ||||
0.969142 | + | 0.246503i | \(0.0792814\pi\) | |||||||
\(282\) | 27.0434i | 1.61041i | ||||||||
\(283\) | 11.9151i | 0.708279i | 0.935193 | + | 0.354140i | \(0.115226\pi\) | ||||
−0.935193 | + | 0.354140i | \(0.884774\pi\) | |||||||
\(284\) | 1.50982 | 0.0895912 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.0902 | −1.66101 | ||||||||
\(287\) | − 0.993764i | − 0.0586600i | ||||||||
\(288\) | − 21.4180i | − 1.26207i | ||||||||
\(289\) | −15.9540 | −0.938472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.04128 | −0.471388 | ||||||||
\(292\) | − 62.5524i | − 3.66060i | ||||||||
\(293\) | − 20.7359i | − 1.21140i | −0.795692 | − | 0.605702i | \(-0.792892\pi\) | ||||
0.795692 | − | 0.605702i | \(-0.207108\pi\) | |||||||
\(294\) | 39.0559 | 2.27779 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −41.8659 | −2.43341 | ||||||||
\(297\) | 1.87758i | 0.108948i | ||||||||
\(298\) | 16.1832i | 0.937467i | ||||||||
\(299\) | 0.751396 | 0.0434544 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.1088 | 1.90836 | ||||||||
\(302\) | 21.9961i | 1.26574i | ||||||||
\(303\) | − 12.3239i | − 0.707987i | ||||||||
\(304\) | 79.6409 | 4.56772 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −15.6608 | −0.895268 | ||||||||
\(307\) | − 16.9755i | − 0.968842i | −0.874835 | − | 0.484421i | \(-0.839030\pi\) | ||||
0.874835 | − | 0.484421i | \(-0.160970\pi\) | |||||||
\(308\) | 47.1793i | 2.68829i | ||||||||
\(309\) | −0.660912 | −0.0375980 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9019 | −1.18524 | −0.592619 | − | 0.805483i | \(-0.701906\pi\) | ||||
−0.592619 | + | 0.805483i | \(0.701906\pi\) | |||||||
\(312\) | − 51.5030i | − 2.91578i | ||||||||
\(313\) | − 12.7754i | − 0.722110i | −0.932545 | − | 0.361055i | \(-0.882417\pi\) | ||||
0.932545 | − | 0.361055i | \(-0.117583\pi\) | |||||||
\(314\) | 26.9298 | 1.51973 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04669 | 0.508916 | ||||||||
\(317\) | 15.0552i | 0.845582i | 0.906227 | + | 0.422791i | \(0.138950\pi\) | ||||
−0.906227 | + | 0.422791i | \(0.861050\pi\) | |||||||
\(318\) | − 3.13060i | − 0.175555i | ||||||||
\(319\) | 1.87758 | 0.105124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5868 | 0.814155 | ||||||||
\(322\) | − 1.72578i | − 0.0961741i | ||||||||
\(323\) | − 31.0251i | − 1.72628i | ||||||||
\(324\) | −5.44251 | −0.302362 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.42951 | 0.189943 | ||||||||
\(327\) | − 15.5050i | − 0.857431i | ||||||||
\(328\) | 2.02145i | 0.111616i | ||||||||
\(329\) | 45.7675 | 2.52324 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.7325 | −0.974668 | −0.487334 | − | 0.873216i | \(-0.662031\pi\) | ||||
−0.487334 | + | 0.873216i | \(0.662031\pi\) | |||||||
\(332\) | 52.1672i | 2.86305i | ||||||||
\(333\) | 4.45785i | 0.244289i | ||||||||
\(334\) | 41.3203 | 2.26095 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −68.0349 | −3.71161 | ||||||||
\(337\) | − 17.5905i | − 0.958217i | −0.877756 | − | 0.479108i | \(-0.840960\pi\) | ||||
0.877756 | − | 0.479108i | \(-0.159040\pi\) | |||||||
\(338\) | − 46.5801i | − 2.53363i | ||||||||
\(339\) | −7.80660 | −0.423996 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.3617 | 0.831883 | ||||||||
\(342\) | − 14.7441i | − 0.797271i | ||||||||
\(343\) | − 33.7784i | − 1.82386i | ||||||||
\(344\) | −67.3479 | −3.63115 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.40909 | 0.344555 | ||||||||
\(347\) | − 21.0789i | − 1.13157i | −0.824552 | − | 0.565787i | \(-0.808573\pi\) | ||||
0.824552 | − | 0.565787i | \(-0.191427\pi\) | |||||||
\(348\) | 5.44251i | 0.291749i | ||||||||
\(349\) | 0.723154 | 0.0387096 | 0.0193548 | − | 0.999813i | \(-0.493839\pi\) | ||||
0.0193548 | + | 0.999813i | \(0.493839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.48400 | −0.292714 | ||||||||
\(352\) | − 40.2139i | − 2.14341i | ||||||||
\(353\) | − 5.93891i | − 0.316096i | −0.987431 | − | 0.158048i | \(-0.949480\pi\) | ||||
0.987431 | − | 0.158048i | \(-0.0505201\pi\) | |||||||
\(354\) | −0.668145 | −0.0355115 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 88.8938 | 4.71136 | ||||||||
\(357\) | 26.5038i | 1.40273i | ||||||||
\(358\) | 48.5092i | 2.56379i | ||||||||
\(359\) | 2.30973 | 0.121903 | 0.0609514 | − | 0.998141i | \(-0.480587\pi\) | ||||
0.0609514 | + | 0.998141i | \(0.480587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2091 | 0.537323 | ||||||||
\(362\) | − 7.36234i | − 0.386956i | ||||||||
\(363\) | − 7.47471i | − 0.392321i | ||||||||
\(364\) | −137.801 | −7.22272 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −23.8786 | −1.24815 | ||||||||
\(367\) | 22.9235i | 1.19660i | 0.801274 | + | 0.598298i | \(0.204156\pi\) | ||||
−0.801274 | + | 0.598298i | \(0.795844\pi\) | |||||||
\(368\) | 2.01906i | 0.105251i | ||||||||
\(369\) | 0.215243 | 0.0112051 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.29813 | −0.275065 | ||||||||
\(372\) | 44.5289i | 2.30871i | ||||||||
\(373\) | 2.83182i | 0.146626i | 0.997309 | + | 0.0733129i | \(0.0233572\pi\) | ||||
−0.997309 | + | 0.0733129i | \(0.976643\pi\) | |||||||
\(374\) | −29.4043 | −1.52046 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −93.0973 | −4.80113 | ||||||||
\(377\) | 5.48400i | 0.282440i | ||||||||
\(378\) | 12.5955i | 0.647841i | ||||||||
\(379\) | 29.2539 | 1.50267 | 0.751335 | − | 0.659921i | \(-0.229410\pi\) | ||||
0.751335 | + | 0.659921i | \(0.229410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.7106 | −1.00980 | ||||||||
\(382\) | 29.4627i | 1.50744i | ||||||||
\(383\) | 2.99063i | 0.152814i | 0.997077 | + | 0.0764070i | \(0.0243448\pi\) | ||||
−0.997077 | + | 0.0764070i | \(0.975655\pi\) | |||||||
\(384\) | 36.1656 | 1.84557 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.4156 | −0.581040 | ||||||||
\(387\) | 7.17115i | 0.364530i | ||||||||
\(388\) | − 43.7648i | − 2.22182i | ||||||||
\(389\) | 8.57339 | 0.434688 | 0.217344 | − | 0.976095i | \(-0.430261\pi\) | ||||
0.217344 | + | 0.976095i | \(0.430261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.786549 | 0.0397775 | ||||||||
\(392\) | 134.451i | 6.79078i | ||||||||
\(393\) | − 1.05738i | − 0.0533376i | ||||||||
\(394\) | −15.7372 | −0.792828 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.2187 | −0.513510 | ||||||||
\(397\) | 9.29605i | 0.466556i | 0.972410 | + | 0.233278i | \(0.0749451\pi\) | ||||
−0.972410 | + | 0.233278i | \(0.925055\pi\) | |||||||
\(398\) | 14.8707i | 0.745400i | ||||||||
\(399\) | −24.9525 | −1.24919 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5392 | 0.975739 | 0.487870 | − | 0.872916i | \(-0.337774\pi\) | ||||
0.487870 | + | 0.872916i | \(0.337774\pi\) | |||||||
\(402\) | 17.8225i | 0.888907i | ||||||||
\(403\) | 44.8683i | 2.23505i | ||||||||
\(404\) | 67.0728 | 3.33700 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.5955 | 0.625103 | ||||||||
\(407\) | 8.36995i | 0.414883i | ||||||||
\(408\) | − 53.9125i | − 2.66907i | ||||||||
\(409\) | −37.9582 | −1.87691 | −0.938456 | − | 0.345398i | \(-0.887744\pi\) | ||||
−0.938456 | + | 0.345398i | \(0.887744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.21467 | −0.158568 | ||||||||
\(412\) | − 3.59702i | − 0.177213i | ||||||||
\(413\) | 1.13075i | 0.0556405i | ||||||||
\(414\) | 0.373793 | 0.0183709 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 117.456 | 5.75876 | ||||||||
\(417\) | − 8.48410i | − 0.415468i | ||||||||
\(418\) | − 27.6832i | − 1.35403i | ||||||||
\(419\) | 10.0952 | 0.493184 | 0.246592 | − | 0.969119i | \(-0.420689\pi\) | ||||
0.246592 | + | 0.969119i | \(0.420689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8521 | 0.675111 | 0.337556 | − | 0.941306i | \(-0.390400\pi\) | ||||
0.337556 | + | 0.941306i | \(0.390400\pi\) | |||||||
\(422\) | 2.35525i | 0.114652i | ||||||||
\(423\) | 9.91293i | 0.481983i | ||||||||
\(424\) | 10.7771 | 0.523384 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.756807 | 0.0366674 | ||||||||
\(427\) | 40.4114i | 1.95565i | ||||||||
\(428\) | 79.3888i | 3.83740i | ||||||||
\(429\) | −10.2966 | −0.497125 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.2149 | 0.877380 | 0.438690 | − | 0.898638i | \(-0.355443\pi\) | ||||
0.438690 | + | 0.898638i | \(0.355443\pi\) | |||||||
\(432\) | − 14.7359i | − 0.708982i | ||||||||
\(433\) | − 6.73476i | − 0.323652i | −0.986819 | − | 0.161826i | \(-0.948262\pi\) | ||||
0.986819 | − | 0.161826i | \(-0.0517383\pi\) | |||||||
\(434\) | 103.052 | 4.94666 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 84.3864 | 4.04137 | ||||||||
\(437\) | 0.740510i | 0.0354234i | ||||||||
\(438\) | − 31.3548i | − 1.49819i | ||||||||
\(439\) | −30.9590 | −1.47759 | −0.738795 | − | 0.673930i | \(-0.764605\pi\) | ||||
−0.738795 | + | 0.673930i | \(0.764605\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.3162 | 0.681723 | ||||||||
\(442\) | − 85.8838i | − 4.08508i | ||||||||
\(443\) | − 21.4432i | − 1.01880i | −0.860531 | − | 0.509398i | \(-0.829868\pi\) | ||||
0.860531 | − | 0.509398i | \(-0.170132\pi\) | |||||||
\(444\) | −24.2619 | −1.15142 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.67832 | −0.0794707 | ||||||||
\(447\) | 5.93205i | 0.280576i | ||||||||
\(448\) | − 133.700i | − 6.31672i | ||||||||
\(449\) | −25.6895 | −1.21236 | −0.606180 | − | 0.795327i | \(-0.707299\pi\) | ||||
−0.606180 | + | 0.795327i | \(0.707299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.404134 | 0.0190299 | ||||||||
\(452\) | − 42.4875i | − 1.99844i | ||||||||
\(453\) | 8.06281i | 0.378824i | ||||||||
\(454\) | 64.7186 | 3.03739 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 50.7568 | 2.37691 | ||||||||
\(457\) | 30.3278i | 1.41868i | 0.704868 | + | 0.709338i | \(0.251006\pi\) | ||||
−0.704868 | + | 0.709338i | \(0.748994\pi\) | |||||||
\(458\) | 57.2377i | 2.67454i | ||||||||
\(459\) | −5.74056 | −0.267946 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.0026 | −1.44393 | −0.721967 | − | 0.691928i | \(-0.756762\pi\) | ||||
−0.721967 | + | 0.691928i | \(0.756762\pi\) | |||||||
\(462\) | 23.6490i | 1.10025i | ||||||||
\(463\) | 27.6990i | 1.28728i | 0.765328 | + | 0.643640i | \(0.222577\pi\) | ||||
−0.765328 | + | 0.643640i | \(0.777423\pi\) | |||||||
\(464\) | −14.7359 | −0.684097 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.7015 | −1.00530 | ||||||||
\(467\) | − 4.03243i | − 0.186598i | −0.995638 | − | 0.0932992i | \(-0.970259\pi\) | ||||
0.995638 | − | 0.0932992i | \(-0.0297413\pi\) | |||||||
\(468\) | − 29.8467i | − 1.37966i | ||||||||
\(469\) | 30.1623 | 1.39277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.87127 | 0.454844 | ||||||||
\(472\) | − 2.30010i | − 0.105871i | ||||||||
\(473\) | 13.4644i | 0.619093i | ||||||||
\(474\) | 4.53472 | 0.208286 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −144.248 | −6.61157 | ||||||||
\(477\) | − 1.14754i | − 0.0525422i | ||||||||
\(478\) | − 47.7110i | − 2.18225i | ||||||||
\(479\) | −1.32186 | −0.0603973 | −0.0301986 | − | 0.999544i | \(-0.509614\pi\) | ||||
−0.0301986 | + | 0.999544i | \(0.509614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.4468 | −1.11468 | ||||||||
\(482\) | − 40.3058i | − 1.83588i | ||||||||
\(483\) | − 0.632596i | − 0.0287841i | ||||||||
\(484\) | 40.6812 | 1.84915 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.72810 | −0.123749 | ||||||||
\(487\) | − 9.89390i | − 0.448335i | −0.974551 | − | 0.224168i | \(-0.928034\pi\) | ||||
0.974551 | − | 0.224168i | \(-0.0719663\pi\) | |||||||
\(488\) | − 82.2024i | − 3.72113i | ||||||||
\(489\) | 1.25711 | 0.0568484 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1305 | 0.773089 | 0.386545 | − | 0.922271i | \(-0.373669\pi\) | ||||
0.386545 | + | 0.922271i | \(0.373669\pi\) | |||||||
\(492\) | 1.17146i | 0.0528135i | ||||||||
\(493\) | 5.74056i | 0.258542i | ||||||||
\(494\) | 80.8568 | 3.63792 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −120.564 | −5.41350 | ||||||||
\(497\) | − 1.28080i | − 0.0574516i | ||||||||
\(498\) | 26.1492i | 1.17177i | ||||||||
\(499\) | 7.95477 | 0.356104 | 0.178052 | − | 0.984021i | \(-0.443020\pi\) | ||||
0.178052 | + | 0.984021i | \(0.443020\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.1462 | 0.676683 | ||||||||
\(502\) | − 9.02989i | − 0.403024i | ||||||||
\(503\) | − 13.3471i | − 0.595119i | −0.954703 | − | 0.297559i | \(-0.903827\pi\) | ||||
0.954703 | − | 0.297559i | \(-0.0961727\pi\) | |||||||
\(504\) | −43.3601 | −1.93141 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.701825 | 0.0311999 | ||||||||
\(507\) | − 17.0742i | − 0.758293i | ||||||||
\(508\) | − 107.275i | − 4.75956i | ||||||||
\(509\) | 5.55324 | 0.246143 | 0.123071 | − | 0.992398i | \(-0.460726\pi\) | ||||
0.123071 | + | 0.992398i | \(0.460726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.0639 | −2.34741 | ||||||||
\(512\) | 38.8286i | 1.71600i | ||||||||
\(513\) | − 5.40455i | − 0.238617i | ||||||||
\(514\) | 84.2076 | 3.71424 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −39.0291 | −1.71816 | ||||||||
\(517\) | 18.6123i | 0.818567i | ||||||||
\(518\) | 56.1487i | 2.46703i | ||||||||
\(519\) | 2.34929 | 0.103122 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.5095 | 1.81857 | 0.909283 | − | 0.416179i | \(-0.136631\pi\) | ||||
0.909283 | + | 0.416179i | \(0.136631\pi\) | |||||||
\(522\) | 2.72810i | 0.119406i | ||||||||
\(523\) | 11.6261i | 0.508375i | 0.967155 | + | 0.254188i | \(0.0818081\pi\) | ||||
−0.967155 | + | 0.254188i | \(0.918192\pi\) | |||||||
\(524\) | 5.75479 | 0.251399 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 53.1525 | 2.31756 | ||||||||
\(527\) | 46.9674i | 2.04593i | ||||||||
\(528\) | − 27.6678i | − 1.20409i | ||||||||
\(529\) | 22.9812 | 0.999184 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.244913 | −0.0106283 | ||||||||
\(532\) | − 135.804i | − 5.88786i | ||||||||
\(533\) | 1.18039i | 0.0511284i | ||||||||
\(534\) | 44.5586 | 1.92824 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −61.3543 | −2.65010 | ||||||||
\(537\) | 17.7814i | 0.767322i | ||||||||
\(538\) | − 56.8495i | − 2.45096i | ||||||||
\(539\) | 26.8797 | 1.15779 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.29830 | −0.227792 | −0.113896 | − | 0.993493i | \(-0.536333\pi\) | ||||
−0.113896 | + | 0.993493i | \(0.536333\pi\) | |||||||
\(542\) | 67.0700i | 2.88090i | ||||||||
\(543\) | − 2.69871i | − 0.115813i | ||||||||
\(544\) | 122.951 | 5.27149 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −69.0735 | −2.95607 | ||||||||
\(547\) | − 6.78093i | − 0.289932i | −0.989437 | − | 0.144966i | \(-0.953693\pi\) | ||||
0.989437 | − | 0.144966i | \(-0.0463072\pi\) | |||||||
\(548\) | − 17.4959i | − 0.747387i | ||||||||
\(549\) | −8.75284 | −0.373562 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.40455 | −0.230241 | ||||||||
\(552\) | 1.28679i | 0.0547693i | ||||||||
\(553\) | − 7.67441i | − 0.326349i | ||||||||
\(554\) | −5.18076 | −0.220109 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 46.1748 | 1.95825 | ||||||||
\(557\) | 0.186307i | 0.00789410i | 0.999992 | + | 0.00394705i | \(0.00125639\pi\) | ||||
−0.999992 | + | 0.00394705i | \(0.998744\pi\) | |||||||
\(558\) | 22.3204i | 0.944898i | ||||||||
\(559\) | −39.3266 | −1.66334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.7783 | −0.455062 | ||||||||
\(562\) | 88.6401i | 3.73906i | ||||||||
\(563\) | 27.1382i | 1.14374i | 0.820345 | + | 0.571869i | \(0.193781\pi\) | ||||
−0.820345 | + | 0.571869i | \(0.806219\pi\) | |||||||
\(564\) | −53.9512 | −2.27176 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −32.5056 | −1.36631 | ||||||||
\(567\) | 4.61695i | 0.193893i | ||||||||
\(568\) | 2.60532i | 0.109317i | ||||||||
\(569\) | −22.8795 | −0.959157 | −0.479578 | − | 0.877499i | \(-0.659210\pi\) | ||||
−0.479578 | + | 0.877499i | \(0.659210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.3621 | 1.60541 | 0.802703 | − | 0.596379i | \(-0.203394\pi\) | ||||
0.802703 | + | 0.596379i | \(0.203394\pi\) | |||||||
\(572\) | − 56.0395i | − 2.34313i | ||||||||
\(573\) | 10.7997i | 0.451165i | ||||||||
\(574\) | 2.71108 | 0.113158 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 28.9585 | 1.20660 | ||||||||
\(577\) | − 12.0497i | − 0.501637i | −0.968034 | − | 0.250818i | \(-0.919300\pi\) | ||||
0.968034 | − | 0.250818i | \(-0.0806997\pi\) | |||||||
\(578\) | − 43.5241i | − 1.81036i | ||||||||
\(579\) | −4.18447 | −0.173901 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.2541 | 1.83597 | ||||||||
\(582\) | − 21.9374i | − 0.909334i | ||||||||
\(583\) | − 2.15459i | − 0.0892341i | ||||||||
\(584\) | 107.939 | 4.46656 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 56.5695 | 2.33687 | ||||||||
\(587\) | − 23.6704i | − 0.976982i | −0.872569 | − | 0.488491i | \(-0.837547\pi\) | ||||
0.872569 | − | 0.488491i | \(-0.162453\pi\) | |||||||
\(588\) | 77.9160i | 3.21320i | ||||||||
\(589\) | −44.2183 | −1.82198 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.76856 | −0.237287 | ||||||||
\(592\) | − 65.6905i | − 2.69986i | ||||||||
\(593\) | − 25.9414i | − 1.06529i | −0.846340 | − | 0.532643i | \(-0.821199\pi\) | ||||
0.846340 | − | 0.532643i | \(-0.178801\pi\) | |||||||
\(594\) | −5.12221 | −0.210167 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32.2852 | −1.32245 | ||||||||
\(597\) | 5.45094i | 0.223092i | ||||||||
\(598\) | 2.04988i | 0.0838259i | ||||||||
\(599\) | 17.2886 | 0.706393 | 0.353196 | − | 0.935549i | \(-0.385095\pi\) | ||||
0.353196 | + | 0.935549i | \(0.385095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.8997 | −1.26042 | −0.630212 | − | 0.776423i | \(-0.717032\pi\) | ||||
−0.630212 | + | 0.776423i | \(0.717032\pi\) | |||||||
\(602\) | 90.3240i | 3.68133i | ||||||||
\(603\) | 6.53295i | 0.266042i | ||||||||
\(604\) | −43.8820 | −1.78553 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 33.6207 | 1.36575 | ||||||||
\(607\) | 4.07152i | 0.165258i | 0.996580 | + | 0.0826290i | \(0.0263317\pi\) | ||||
−0.996580 | + | 0.0826290i | \(0.973668\pi\) | |||||||
\(608\) | 115.754i | 4.69446i | ||||||||
\(609\) | 4.61695 | 0.187088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54.3625 | −2.19927 | ||||||||
\(612\) | − 31.2431i | − 1.26293i | ||||||||
\(613\) | − 32.3595i | − 1.30699i | −0.756931 | − | 0.653494i | \(-0.773302\pi\) | ||||
0.756931 | − | 0.653494i | \(-0.226698\pi\) | |||||||
\(614\) | 46.3108 | 1.86895 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −81.4118 | −3.28017 | ||||||||
\(617\) | − 33.4957i | − 1.34849i | −0.738509 | − | 0.674243i | \(-0.764470\pi\) | ||||
0.738509 | − | 0.674243i | \(-0.235530\pi\) | |||||||
\(618\) | − 1.80303i | − 0.0725286i | ||||||||
\(619\) | 16.6857 | 0.670656 | 0.335328 | − | 0.942101i | \(-0.391153\pi\) | ||||
0.335328 | + | 0.942101i | \(0.391153\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.137016 | 0.00549827 | ||||||||
\(622\) | − 57.0224i | − 2.28639i | ||||||||
\(623\) | − 75.4096i | − 3.02122i | ||||||||
\(624\) | 80.8117 | 3.23506 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 34.8526 | 1.39299 | ||||||||
\(627\) | − 10.1474i | − 0.405250i | ||||||||
\(628\) | 53.7245i | 2.14384i | ||||||||
\(629\) | −25.5905 | −1.02036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.91590 | 0.394746 | 0.197373 | − | 0.980328i | \(-0.436759\pi\) | ||||
0.197373 | + | 0.980328i | \(0.436759\pi\) | |||||||
\(632\) | 15.6108i | 0.620965i | ||||||||
\(633\) | 0.863332i | 0.0343143i | ||||||||
\(634\) | −41.0719 | −1.63118 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.24550 | 0.247650 | ||||||||
\(637\) | 78.5099i | 3.11068i | ||||||||
\(638\) | 5.12221i | 0.202790i | ||||||||
\(639\) | 0.277412 | 0.0109742 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9862 | −0.907902 | −0.453951 | − | 0.891027i | \(-0.649986\pi\) | ||||
−0.453951 | + | 0.891027i | \(0.649986\pi\) | |||||||
\(642\) | 39.7942i | 1.57055i | ||||||||
\(643\) | 12.9117i | 0.509190i | 0.967048 | + | 0.254595i | \(0.0819421\pi\) | ||||
−0.967048 | + | 0.254595i | \(0.918058\pi\) | |||||||
\(644\) | 3.44291 | 0.135670 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 84.6395 | 3.33010 | ||||||||
\(647\) | 16.6096i | 0.652989i | 0.945199 | + | 0.326494i | \(0.105867\pi\) | ||||
−0.945199 | + | 0.326494i | \(0.894133\pi\) | |||||||
\(648\) | − 9.39150i | − 0.368933i | ||||||||
\(649\) | −0.459842 | −0.0180504 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.7743 | 1.48049 | ||||||||
\(652\) | 6.84182i | 0.267947i | ||||||||
\(653\) | 21.5638i | 0.843858i | 0.906629 | + | 0.421929i | \(0.138647\pi\) | ||||
−0.906629 | + | 0.421929i | \(0.861353\pi\) | |||||||
\(654\) | 42.2993 | 1.65403 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.17180 | −0.123838 | ||||||||
\(657\) | − 11.4933i | − 0.448396i | ||||||||
\(658\) | 124.858i | 4.86747i | ||||||||
\(659\) | −31.7863 | −1.23822 | −0.619110 | − | 0.785305i | \(-0.712506\pi\) | ||||
−0.619110 | + | 0.785305i | \(0.712506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.0046 | 1.16704 | 0.583521 | − | 0.812098i | \(-0.301674\pi\) | ||||
0.583521 | + | 0.812098i | \(0.301674\pi\) | |||||||
\(662\) | − 48.3760i | − 1.88019i | ||||||||
\(663\) | − 31.4812i | − 1.22263i | ||||||||
\(664\) | −90.0189 | −3.49341 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.1614 | −0.471246 | ||||||||
\(667\) | − 0.137016i | − 0.00530529i | ||||||||
\(668\) | 82.4334i | 3.18944i | ||||||||
\(669\) | −0.615197 | −0.0237849 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.4341 | −0.634432 | ||||||||
\(672\) | − 98.8856i | − 3.81460i | ||||||||
\(673\) | 35.0842i | 1.35240i | 0.736719 | + | 0.676199i | \(0.236374\pi\) | ||||
−0.736719 | + | 0.676199i | \(0.763626\pi\) | |||||||
\(674\) | 47.9886 | 1.84845 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 92.9267 | 3.57410 | ||||||||
\(677\) | 42.1433i | 1.61970i | 0.586638 | + | 0.809849i | \(0.300451\pi\) | ||||
−0.586638 | + | 0.809849i | \(0.699549\pi\) | |||||||
\(678\) | − 21.2972i | − 0.817912i | ||||||||
\(679\) | −37.1261 | −1.42477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.7230 | 0.909067 | ||||||||
\(682\) | 41.9082i | 1.60475i | ||||||||
\(683\) | 31.8895i | 1.22022i | 0.792318 | + | 0.610109i | \(0.208874\pi\) | ||||
−0.792318 | + | 0.610109i | \(0.791126\pi\) | |||||||
\(684\) | 29.4143 | 1.12468 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 92.1508 | 3.51833 | ||||||||
\(687\) | 20.9808i | 0.800468i | ||||||||
\(688\) | − 105.673i | − 4.02876i | ||||||||
\(689\) | 6.29311 | 0.239748 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2963 | 0.429732 | 0.214866 | − | 0.976644i | \(-0.431069\pi\) | ||||
0.214866 | + | 0.976644i | \(0.431069\pi\) | |||||||
\(692\) | 12.7860i | 0.486052i | ||||||||
\(693\) | 8.66866i | 0.329295i | ||||||||
\(694\) | 57.5052 | 2.18287 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.39150 | −0.355984 | ||||||||
\(697\) | 1.23561i | 0.0468022i | ||||||||
\(698\) | 1.97283i | 0.0746729i | ||||||||
\(699\) | −7.95482 | −0.300879 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.39354 | −0.0526332 | −0.0263166 | − | 0.999654i | \(-0.508378\pi\) | ||||
−0.0263166 | + | 0.999654i | \(0.508378\pi\) | |||||||
\(702\) | − 14.9609i | − 0.564662i | ||||||||
\(703\) | − 24.0927i | − 0.908672i | ||||||||
\(704\) | 54.3717 | 2.04921 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.2019 | 0.609767 | ||||||||
\(707\) | − 56.8986i | − 2.13989i | ||||||||
\(708\) | − 1.33294i | − 0.0500949i | ||||||||
\(709\) | −5.24967 | −0.197156 | −0.0985778 | − | 0.995129i | \(-0.531429\pi\) | ||||
−0.0985778 | + | 0.995129i | \(0.531429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.66223 | 0.0623384 | ||||||||
\(712\) | 153.394i | 5.74867i | ||||||||
\(713\) | − 1.12102i | − 0.0419826i | ||||||||
\(714\) | −72.3051 | −2.70595 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −96.7752 | −3.61666 | ||||||||
\(717\) | − 17.4888i | − 0.653130i | ||||||||
\(718\) | 6.30116i | 0.235157i | ||||||||
\(719\) | −46.4801 | −1.73341 | −0.866707 | − | 0.498817i | \(-0.833768\pi\) | ||||
−0.866707 | + | 0.498817i | \(0.833768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.05140 | −0.113640 | ||||||||
\(722\) | 27.8515i | 1.03653i | ||||||||
\(723\) | − 14.7743i | − 0.549464i | ||||||||
\(724\) | 14.6878 | 0.545866 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.3917 | 0.756808 | ||||||||
\(727\) | 43.3101i | 1.60628i | 0.595790 | + | 0.803141i | \(0.296839\pi\) | ||||
−0.595790 | + | 0.803141i | \(0.703161\pi\) | |||||||
\(728\) | − 237.786i | − 8.81295i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.1664 | −1.52259 | ||||||||
\(732\) | − 47.6375i | − 1.76073i | ||||||||
\(733\) | − 18.6793i | − 0.689936i | −0.938614 | − | 0.344968i | \(-0.887890\pi\) | ||||
0.938614 | − | 0.344968i | \(-0.112110\pi\) | |||||||
\(734\) | −62.5375 | −2.30830 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.93461 | −0.108171 | ||||||||
\(737\) | 12.2661i | 0.451828i | ||||||||
\(738\) | 0.587203i | 0.0216152i | ||||||||
\(739\) | −41.3256 | −1.52019 | −0.760093 | − | 0.649815i | \(-0.774847\pi\) | ||||
−0.760093 | + | 0.649815i | \(0.774847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.6385 | 1.08880 | ||||||||
\(742\) | − 14.4538i | − 0.530616i | ||||||||
\(743\) | − 32.3390i | − 1.18640i | −0.805054 | − | 0.593202i | \(-0.797864\pi\) | ||||
0.805054 | − | 0.593202i | \(-0.202136\pi\) | |||||||
\(744\) | −76.8382 | −2.81703 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.72547 | −0.282849 | ||||||||
\(747\) | 9.58514i | 0.350702i | ||||||||
\(748\) | − 58.6612i | − 2.14487i | ||||||||
\(749\) | 67.3464 | 2.46078 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.34454 | −0.340987 | −0.170494 | − | 0.985359i | \(-0.554536\pi\) | ||||
−0.170494 | + | 0.985359i | \(0.554536\pi\) | |||||||
\(752\) | − 146.076i | − 5.32685i | ||||||||
\(753\) | − 3.30996i | − 0.120622i | ||||||||
\(754\) | −14.9609 | −0.544843 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −25.1278 | −0.913888 | ||||||||
\(757\) | 5.01932i | 0.182430i | 0.995831 | + | 0.0912151i | \(0.0290751\pi\) | ||||
−0.995831 | + | 0.0912151i | \(0.970925\pi\) | |||||||
\(758\) | 79.8074i | 2.89873i | ||||||||
\(759\) | 0.257258 | 0.00933788 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.9103 | −1.26550 | −0.632748 | − | 0.774358i | \(-0.718073\pi\) | ||||
−0.632748 | + | 0.774358i | \(0.718073\pi\) | |||||||
\(762\) | − 53.7723i | − 1.94797i | ||||||||
\(763\) | − 71.5859i | − 2.59159i | ||||||||
\(764\) | −58.7777 | −2.12650 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.15872 | −0.294787 | ||||||||
\(767\) | − 1.34310i | − 0.0484965i | ||||||||
\(768\) | 40.7463i | 1.47031i | ||||||||
\(769\) | −37.4889 | −1.35189 | −0.675943 | − | 0.736954i | \(-0.736263\pi\) | ||||
−0.675943 | + | 0.736954i | \(0.736263\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.8668 | 1.11164 | ||||||||
\(772\) | − 22.7740i | − 0.819655i | ||||||||
\(773\) | − 33.7332i | − 1.21330i | −0.794970 | − | 0.606649i | \(-0.792513\pi\) | ||||
0.794970 | − | 0.606649i | \(-0.207487\pi\) | |||||||
\(774\) | −19.5636 | −0.703199 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 75.5197 | 2.71100 | ||||||||
\(777\) | 20.5816i | 0.738362i | ||||||||
\(778\) | 23.3890i | 0.838538i | ||||||||
\(779\) | −1.16329 | −0.0416792 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.520862 | 0.0186379 | ||||||||
\(782\) | 2.14578i | 0.0767330i | ||||||||
\(783\) | 1.00000i | 0.0357371i | ||||||||
\(784\) | −210.962 | −7.53436 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.88463 | 0.102891 | ||||||||
\(787\) | − 11.5508i | − 0.411740i | −0.978579 | − | 0.205870i | \(-0.933998\pi\) | ||||
0.978579 | − | 0.205870i | \(-0.0660025\pi\) | |||||||
\(788\) | − 31.3955i | − 1.11842i | ||||||||
\(789\) | 19.4833 | 0.693626 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0426 | −1.28153 | ||||||||
\(792\) | − 17.6333i | − 0.626571i | ||||||||
\(793\) | − 48.0006i | − 1.70455i | ||||||||
\(794\) | −25.3605 | −0.900012 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.6668 | −1.05151 | ||||||||
\(797\) | − 9.11795i | − 0.322974i | −0.986875 | − | 0.161487i | \(-0.948371\pi\) | ||||
0.986875 | − | 0.161487i | \(-0.0516291\pi\) | |||||||
\(798\) | − 68.0728i | − 2.40975i | ||||||||
\(799\) | −56.9058 | −2.01318 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.3332 | 0.577106 | ||||||||
\(802\) | 53.3047i | 1.88226i | ||||||||
\(803\) | − 21.5795i | − 0.761525i | ||||||||
\(804\) | −35.5557 | −1.25395 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −122.405 | −4.31153 | ||||||||
\(807\) | − 20.8385i | − 0.733551i | ||||||||
\(808\) | 115.740i | 4.07171i | ||||||||
\(809\) | 11.9809 | 0.421227 | 0.210613 | − | 0.977569i | \(-0.432454\pi\) | ||||
0.210613 | + | 0.977569i | \(0.432454\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.2172 | −0.674807 | −0.337403 | − | 0.941360i | \(-0.609549\pi\) | ||||
−0.337403 | + | 0.941360i | \(0.609549\pi\) | |||||||
\(812\) | 25.1278i | 0.881812i | ||||||||
\(813\) | 24.5849i | 0.862230i | ||||||||
\(814\) | −22.8340 | −0.800332 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 84.5924 | 2.96132 | ||||||||
\(817\) | − 38.7568i | − 1.35593i | ||||||||
\(818\) | − 103.554i | − 3.62067i | ||||||||
\(819\) | −25.3193 | −0.884728 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.5611 | −0.368585 | −0.184292 | − | 0.982871i | \(-0.558999\pi\) | ||||
−0.184292 | + | 0.982871i | \(0.558999\pi\) | |||||||
\(822\) | − 8.76994i | − 0.305887i | ||||||||
\(823\) | − 29.1655i | − 1.01665i | −0.861166 | − | 0.508323i | \(-0.830266\pi\) | ||||
0.861166 | − | 0.508323i | \(-0.169734\pi\) | |||||||
\(824\) | 6.20696 | 0.216230 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.08479 | −0.107334 | ||||||||
\(827\) | − 40.5140i | − 1.40881i | −0.709798 | − | 0.704405i | \(-0.751214\pi\) | ||||
0.709798 | − | 0.704405i | \(-0.248786\pi\) | |||||||
\(828\) | 0.745712i | 0.0259153i | ||||||||
\(829\) | −51.3925 | −1.78494 | −0.892468 | − | 0.451111i | \(-0.851028\pi\) | ||||
−0.892468 | + | 0.451111i | \(0.851028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.89904 | −0.0658769 | ||||||||
\(832\) | 158.808i | 5.50569i | ||||||||
\(833\) | 82.1829i | 2.84747i | ||||||||
\(834\) | 23.1455 | 0.801461 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 55.2276 | 1.91009 | ||||||||
\(837\) | 8.18167i | 0.282800i | ||||||||
\(838\) | 27.5407i | 0.951379i | ||||||||
\(839\) | 30.2352 | 1.04383 | 0.521917 | − | 0.852996i | \(-0.325217\pi\) | ||||
0.521917 | + | 0.852996i | \(0.325217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 37.7899i | 1.30233i | ||||||||
\(843\) | 32.4916i | 1.11907i | ||||||||
\(844\) | −4.69869 | −0.161736 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27.0434 | −0.929773 | ||||||||
\(847\) | − 34.5103i | − 1.18579i | ||||||||
\(848\) | 16.9100i | 0.580693i | ||||||||
\(849\) | −11.9151 | −0.408925 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.610797 | 0.0209379 | ||||||||
\(852\) | 1.50982i | 0.0517255i | ||||||||
\(853\) | 0.163336i | 0.00559252i | 0.999996 | + | 0.00279626i | \(0.000890079\pi\) | ||||
−0.999996 | + | 0.00279626i | \(0.999110\pi\) | |||||||
\(854\) | −110.246 | −3.77255 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −136.992 | −4.68229 | ||||||||
\(857\) | 0.869730i | 0.0297094i | 0.999890 | + | 0.0148547i | \(0.00472857\pi\) | ||||
−0.999890 | + | 0.0148547i | \(0.995271\pi\) | |||||||
\(858\) | − 28.0902i | − 0.958983i | ||||||||
\(859\) | 50.5362 | 1.72427 | 0.862136 | − | 0.506677i | \(-0.169126\pi\) | ||||
0.862136 | + | 0.506677i | \(0.169126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.993764 | 0.0338674 | ||||||||
\(862\) | 49.6920i | 1.69251i | ||||||||
\(863\) | 43.1139i | 1.46761i | 0.679358 | + | 0.733807i | \(0.262258\pi\) | ||||
−0.679358 | + | 0.733807i | \(0.737742\pi\) | |||||||
\(864\) | 21.4180 | 0.728654 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.3731 | 0.624342 | ||||||||
\(867\) | − 15.9540i | − 0.541827i | ||||||||
\(868\) | 205.587i | 6.97809i | ||||||||
\(869\) | 3.12096 | 0.105871 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.8267 | −1.21394 | ||||||||
\(872\) | 145.616i | 4.93117i | ||||||||
\(873\) | − 8.04128i | − 0.272156i | ||||||||
\(874\) | −2.02018 | −0.0683337 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 62.5524 | 2.11345 | ||||||||
\(877\) | − 3.23901i | − 0.109374i | −0.998504 | − | 0.0546868i | \(-0.982584\pi\) | ||||
0.998504 | − | 0.0546868i | \(-0.0174160\pi\) | |||||||
\(878\) | − 84.4590i | − 2.85035i | ||||||||
\(879\) | 20.7359 | 0.699404 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.49218 | 0.319800 | 0.159900 | − | 0.987133i | \(-0.448883\pi\) | ||||
0.159900 | + | 0.987133i | \(0.448883\pi\) | |||||||
\(882\) | 39.0559i | 1.31508i | ||||||||
\(883\) | 40.4268i | 1.36047i | 0.732994 | + | 0.680235i | \(0.238122\pi\) | ||||
−0.732994 | + | 0.680235i | \(0.761878\pi\) | |||||||
\(884\) | 171.337 | 5.76268 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 58.4991 | 1.96532 | ||||||||
\(887\) | 17.5249i | 0.588430i | 0.955739 | + | 0.294215i | \(0.0950582\pi\) | ||||
−0.955739 | + | 0.294215i | \(0.904942\pi\) | |||||||
\(888\) | − 41.8659i | − 1.40493i | ||||||||
\(889\) | −91.0026 | −3.05213 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.87758 | −0.0629011 | ||||||||
\(892\) | − 3.34822i | − 0.112107i | ||||||||
\(893\) | − 53.5749i | − 1.79282i | ||||||||
\(894\) | −16.1832 | −0.541247 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 166.975 | 5.57823 | ||||||||
\(897\) | 0.751396i | 0.0250884i | ||||||||
\(898\) | − 70.0833i | − 2.33871i | ||||||||
\(899\) | 8.18167 | 0.272874 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.58752 | 0.219462 | ||||||||
\(902\) | 1.10252i | 0.0367098i | ||||||||
\(903\) | 33.1088i | 1.10179i | ||||||||
\(904\) | 73.3157 | 2.43844 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.9961 | −0.730773 | ||||||||
\(907\) | 34.8878i | 1.15843i | 0.815174 | + | 0.579216i | \(0.196641\pi\) | ||||
−0.815174 | + | 0.579216i | \(0.803359\pi\) | |||||||
\(908\) | 129.113i | 4.28475i | ||||||||
\(909\) | 12.3239 | 0.408757 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.5212 | 1.44192 | 0.720960 | − | 0.692976i | \(-0.243701\pi\) | ||||
0.720960 | + | 0.692976i | \(0.243701\pi\) | |||||||
\(912\) | 79.6409i | 2.63717i | ||||||||
\(913\) | 17.9968i | 0.595608i | ||||||||
\(914\) | −82.7373 | −2.73671 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −114.188 | −3.77289 | ||||||||
\(917\) | − 4.88185i | − 0.161213i | ||||||||
\(918\) | − 15.6608i | − 0.516883i | ||||||||
\(919\) | 38.2543 | 1.26189 | 0.630946 | − | 0.775827i | \(-0.282667\pi\) | ||||
0.630946 | + | 0.775827i | \(0.282667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.9755 | 0.559361 | ||||||||
\(922\) | − 84.5780i | − 2.78543i | ||||||||
\(923\) | 1.52133i | 0.0500751i | ||||||||
\(924\) | −47.1793 | −1.55209 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −75.5655 | −2.48324 | ||||||||
\(927\) | − 0.660912i | − 0.0217072i | ||||||||
\(928\) | − 21.4180i | − 0.703079i | ||||||||
\(929\) | −40.3492 | −1.32381 | −0.661906 | − | 0.749586i | \(-0.730252\pi\) | ||||
−0.661906 | + | 0.749586i | \(0.730252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −77.3725 | −2.53578 | ||||||||
\(932\) | − 43.2942i | − 1.41815i | ||||||||
\(933\) | − 20.9019i | − 0.684298i | ||||||||
\(934\) | 11.0009 | 0.359959 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 51.5030 | 1.68343 | ||||||||
\(937\) | − 4.95384i | − 0.161835i | −0.996721 | − | 0.0809174i | \(-0.974215\pi\) | ||||
0.996721 | − | 0.0809174i | \(-0.0257850\pi\) | |||||||
\(938\) | 82.2857i | 2.68672i | ||||||||
\(939\) | 12.7754 | 0.416910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.5220 | −1.54917 | −0.774587 | − | 0.632467i | \(-0.782042\pi\) | ||||
−0.774587 | + | 0.632467i | \(0.782042\pi\) | |||||||
\(942\) | 26.9298i | 0.877419i | ||||||||
\(943\) | − 0.0294917i | 0 0.000960383i | ||||||||
\(944\) | 3.60901 | 0.117463 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.7321 | −1.19426 | ||||||||
\(947\) | − 37.1547i | − 1.20736i | −0.797225 | − | 0.603682i | \(-0.793700\pi\) | ||||
0.797225 | − | 0.603682i | \(-0.206300\pi\) | |||||||
\(948\) | 9.04669i | 0.293823i | ||||||||
\(949\) | 63.0292 | 2.04601 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.0552 | −0.488197 | ||||||||
\(952\) | − 248.911i | − 8.06725i | ||||||||
\(953\) | − 44.5351i | − 1.44263i | −0.692606 | − | 0.721316i | \(-0.743537\pi\) | ||||
0.692606 | − | 0.721316i | \(-0.256463\pi\) | |||||||
\(954\) | 3.13060 | 0.101357 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 95.1828 | 3.07843 | ||||||||
\(957\) | 1.87758i | 0.0606934i | ||||||||
\(958\) | − 3.60616i | − 0.116510i | ||||||||
\(959\) | −14.8420 | −0.479272 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.9398 | 1.15935 | ||||||||
\(962\) | − 66.6933i | − 2.15028i | ||||||||
\(963\) | 14.5868i | 0.470053i | ||||||||
\(964\) | 80.4095 | 2.58982 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.72578 | 0.0555262 | ||||||||
\(967\) | 48.7291i | 1.56702i | 0.621379 | + | 0.783511i | \(0.286573\pi\) | ||||
−0.621379 | + | 0.783511i | \(0.713427\pi\) | |||||||
\(968\) | 70.1988i | 2.25627i | ||||||||
\(969\) | 31.0251 | 0.996671 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.7448 | −1.66057 | −0.830285 | − | 0.557339i | \(-0.811822\pi\) | ||||
−0.830285 | + | 0.557339i | \(0.811822\pi\) | |||||||
\(972\) | − 5.44251i | − 0.174569i | ||||||||
\(973\) | − 39.1706i | − 1.25575i | ||||||||
\(974\) | 26.9915 | 0.864864 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 128.981 | 4.12858 | ||||||||
\(977\) | 37.7726i | 1.20845i | 0.796813 | + | 0.604227i | \(0.206518\pi\) | ||||
−0.796813 | + | 0.604227i | \(0.793482\pi\) | |||||||
\(978\) | 3.42951i | 0.109664i | ||||||||
\(979\) | 30.6669 | 0.980117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5050 | 0.495038 | ||||||||
\(982\) | 46.7337i | 1.49133i | ||||||||
\(983\) | 21.1318i | 0.673999i | 0.941505 | + | 0.336999i | \(0.109412\pi\) | ||||
−0.941505 | + | 0.336999i | \(0.890588\pi\) | |||||||
\(984\) | −2.02145 | −0.0644416 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.6608 | −0.498742 | ||||||||
\(987\) | 45.7675i | 1.45679i | ||||||||
\(988\) | 161.308i | 5.13189i | ||||||||
\(989\) | 0.982563 | 0.0312437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0241 | 0.350191 | 0.175096 | − | 0.984551i | \(-0.443977\pi\) | ||||
0.175096 | + | 0.984551i | \(0.443977\pi\) | |||||||
\(992\) | − 175.235i | − 5.56371i | ||||||||
\(993\) | − 17.7325i | − 0.562725i | ||||||||
\(994\) | 3.49414 | 0.110827 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −52.1672 | −1.65298 | ||||||||
\(997\) | 28.2785i | 0.895589i | 0.894136 | + | 0.447795i | \(0.147790\pi\) | ||||
−0.894136 | + | 0.447795i | \(0.852210\pi\) | |||||||
\(998\) | 21.7014i | 0.686945i | ||||||||
\(999\) | −4.45785 | −0.141040 |
(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 | 2175.2.c.p.349.16 | 16 | ||
5.2 | odd | 4 | 2175.2.a.bd.1.1 | yes | 8 | ||
5.3 | odd | 4 | 2175.2.a.bc.1.8 | ✓ | 8 | ||
5.4 | even | 2 | inner | 2175.2.c.p.349.1 | 16 | ||
15.2 | even | 4 | 6525.2.a.by.1.8 | 8 | |||
15.8 | even | 4 | 6525.2.a.bz.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2175.2.a.bc.1.8 | ✓ | 8 | 5.3 | odd | 4 | ||
2175.2.a.bd.1.1 | yes | 8 | 5.2 | odd | 4 | ||
2175.2.c.p.349.1 | 16 | 5.4 | even | 2 | inner | ||
2175.2.c.p.349.16 | 16 | 1.1 | even | 1 | trivial | ||
6525.2.a.by.1.8 | 8 | 15.2 | even | 4 | |||
6525.2.a.bz.1.1 | 8 | 15.8 | even | 4 |