Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3750,2,Mod(1249,3750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3750, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3750.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3750 = 2 \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3750.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: | \(29.9439007580\) |
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: | \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.11 | ||
Root | \(-1.16141 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3750.1249 |
Dual form | 3750.2.c.k.1249.6 |
$q$-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 \(\left(\mathbb{Z}/3750\mathbb{Z}\right)^\times\).
\(n\) | \(2501\) | \(3127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 0.533559i | − 0.201666i | −0.994903 | − | 0.100833i | \(-0.967849\pi\) | ||||
0.994903 | − | 0.100833i | \(-0.0321508\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.43425 | −0.432444 | −0.216222 | − | 0.976344i | \(-0.569373\pi\) | ||||
−0.216222 | + | 0.976344i | \(0.569373\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − 6.57392i | − 1.82328i | −0.410991 | − | 0.911639i | \(-0.634817\pi\) | ||||
0.410991 | − | 0.911639i | \(-0.365183\pi\) | |||||||
\(14\) | 0.533559 | 0.142600 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 0.958413i | − 0.232449i | −0.993223 | − | 0.116225i | \(-0.962921\pi\) | ||||
0.993223 | − | 0.116225i | \(-0.0370793\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | −0.212889 | −0.0488401 | −0.0244201 | − | 0.999702i | \(-0.507774\pi\) | ||||
−0.0244201 | + | 0.999702i | \(0.507774\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.533559 | −0.116432 | ||||||||
\(22\) | − 1.43425i | − 0.305784i | ||||||||
\(23\) | − 3.76401i | − 0.784850i | −0.919784 | − | 0.392425i | \(-0.871636\pi\) | ||||
0.919784 | − | 0.392425i | \(-0.128364\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.57392 | 1.28925 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.533559i | 0.100833i | ||||||||
\(29\) | −6.19448 | −1.15029 | −0.575143 | − | 0.818053i | \(-0.695054\pi\) | ||||
−0.575143 | + | 0.818053i | \(0.695054\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.33773 | −0.419869 | −0.209934 | − | 0.977716i | \(-0.567325\pi\) | ||||
−0.209934 | + | 0.977716i | \(0.567325\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.43425i | 0.249671i | ||||||||
\(34\) | 0.958413 | 0.164367 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.06291i | 0.667938i | 0.942584 | + | 0.333969i | \(0.108388\pi\) | ||||
−0.942584 | + | 0.333969i | \(0.891612\pi\) | |||||||
\(38\) | − 0.212889i | − 0.0345352i | ||||||||
\(39\) | −6.57392 | −1.05267 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.94156 | −1.24026 | −0.620132 | − | 0.784497i | \(-0.712921\pi\) | ||||
−0.620132 | + | 0.784497i | \(0.712921\pi\) | |||||||
\(42\) | − 0.533559i | − 0.0823300i | ||||||||
\(43\) | 11.3607i | 1.73250i | 0.499614 | + | 0.866248i | \(0.333475\pi\) | ||||
−0.499614 | + | 0.866248i | \(0.666525\pi\) | |||||||
\(44\) | 1.43425 | 0.216222 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.76401 | 0.554973 | ||||||||
\(47\) | 10.1489i | 1.48037i | 0.672402 | + | 0.740186i | \(0.265263\pi\) | ||||
−0.672402 | + | 0.740186i | \(0.734737\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 6.71531 | 0.959331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.958413 | −0.134205 | ||||||||
\(52\) | 6.57392i | 0.911639i | ||||||||
\(53\) | 3.23354i | 0.444162i | 0.975028 | + | 0.222081i | \(0.0712849\pi\) | ||||
−0.975028 | + | 0.222081i | \(0.928715\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.533559 | −0.0712998 | ||||||||
\(57\) | 0.212889i | 0.0281978i | ||||||||
\(58\) | − 6.19448i | − 0.813375i | ||||||||
\(59\) | −7.52455 | −0.979613 | −0.489806 | − | 0.871831i | \(-0.662933\pi\) | ||||
−0.489806 | + | 0.871831i | \(0.662933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5721 | 1.60969 | 0.804844 | − | 0.593486i | \(-0.202249\pi\) | ||||
0.804844 | + | 0.593486i | \(0.202249\pi\) | |||||||
\(62\) | − 2.33773i | − 0.296892i | ||||||||
\(63\) | 0.533559i | 0.0672221i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.43425 | −0.176544 | ||||||||
\(67\) | − 6.91285i | − 0.844539i | −0.906470 | − | 0.422269i | \(-0.861234\pi\) | ||||
0.906470 | − | 0.422269i | \(-0.138766\pi\) | |||||||
\(68\) | 0.958413i | 0.116225i | ||||||||
\(69\) | −3.76401 | −0.453134 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1247 | 1.20158 | 0.600789 | − | 0.799408i | \(-0.294853\pi\) | ||||
0.600789 | + | 0.799408i | \(0.294853\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 13.9771i | 1.63589i | 0.575294 | + | 0.817947i | \(0.304888\pi\) | ||||
−0.575294 | + | 0.817947i | \(0.695112\pi\) | |||||||
\(74\) | −4.06291 | −0.472304 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.212889 | 0.0244201 | ||||||||
\(77\) | 0.765259i | 0.0872093i | ||||||||
\(78\) | − 6.57392i | − 0.744350i | ||||||||
\(79\) | −15.5279 | −1.74703 | −0.873515 | − | 0.486798i | \(-0.838165\pi\) | ||||
−0.873515 | + | 0.486798i | \(0.838165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 7.94156i | − 0.876999i | ||||||||
\(83\) | − 16.3308i | − 1.79254i | −0.443508 | − | 0.896270i | \(-0.646266\pi\) | ||||
0.443508 | − | 0.896270i | \(-0.353734\pi\) | |||||||
\(84\) | 0.533559 | 0.0582161 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.3607 | −1.22506 | ||||||||
\(87\) | 6.19448i | 0.664118i | ||||||||
\(88\) | 1.43425i | 0.152892i | ||||||||
\(89\) | −5.62220 | −0.595951 | −0.297976 | − | 0.954573i | \(-0.596311\pi\) | ||||
−0.297976 | + | 0.954573i | \(0.596311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50758 | −0.367694 | ||||||||
\(92\) | 3.76401i | 0.392425i | ||||||||
\(93\) | 2.33773i | 0.242411i | ||||||||
\(94\) | −10.1489 | −1.04678 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 5.56558i | − 0.565099i | −0.959253 | − | 0.282549i | \(-0.908820\pi\) | ||||
0.959253 | − | 0.282549i | \(-0.0911801\pi\) | |||||||
\(98\) | 6.71531i | 0.678349i | ||||||||
\(99\) | 1.43425 | 0.144148 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.42708 | −0.938029 | −0.469015 | − | 0.883190i | \(-0.655391\pi\) | ||||
−0.469015 | + | 0.883190i | \(0.655391\pi\) | |||||||
\(102\) | − 0.958413i | − 0.0948971i | ||||||||
\(103\) | − 7.99871i | − 0.788137i | −0.919081 | − | 0.394068i | \(-0.871067\pi\) | ||||
0.919081 | − | 0.394068i | \(-0.128933\pi\) | |||||||
\(104\) | −6.57392 | −0.644626 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.23354 | −0.314070 | ||||||||
\(107\) | 18.9260i | 1.82964i | 0.403857 | + | 0.914822i | \(0.367669\pi\) | ||||
−0.403857 | + | 0.914822i | \(0.632331\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | 2.65524 | 0.254326 | 0.127163 | − | 0.991882i | \(-0.459413\pi\) | ||||
0.127163 | + | 0.991882i | \(0.459413\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.06291 | 0.385634 | ||||||||
\(112\) | − 0.533559i | − 0.0504166i | ||||||||
\(113\) | − 3.06283i | − 0.288127i | −0.989568 | − | 0.144063i | \(-0.953983\pi\) | ||||
0.989568 | − | 0.144063i | \(-0.0460169\pi\) | |||||||
\(114\) | −0.212889 | −0.0199389 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.19448 | 0.575143 | ||||||||
\(117\) | 6.57392i | 0.607759i | ||||||||
\(118\) | − 7.52455i | − 0.692691i | ||||||||
\(119\) | −0.511370 | −0.0468772 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.94292 | −0.812993 | ||||||||
\(122\) | 12.5721i | 1.13822i | ||||||||
\(123\) | 7.94156i | 0.716067i | ||||||||
\(124\) | 2.33773 | 0.209934 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.533559 | −0.0475332 | ||||||||
\(127\) | − 6.48257i | − 0.575235i | −0.957745 | − | 0.287618i | \(-0.907137\pi\) | ||||
0.957745 | − | 0.287618i | \(-0.0928632\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 11.3607 | 1.00026 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.45794 | −0.826344 | −0.413172 | − | 0.910653i | \(-0.635579\pi\) | ||||
−0.413172 | + | 0.910653i | \(0.635579\pi\) | |||||||
\(132\) | − 1.43425i | − 0.124836i | ||||||||
\(133\) | 0.113589i | 0.00984941i | ||||||||
\(134\) | 6.91285 | 0.597179 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.958413 | −0.0821833 | ||||||||
\(137\) | − 12.3361i | − 1.05394i | −0.849883 | − | 0.526971i | \(-0.823328\pi\) | ||||
0.849883 | − | 0.526971i | \(-0.176672\pi\) | |||||||
\(138\) | − 3.76401i | − 0.320414i | ||||||||
\(139\) | −4.53918 | −0.385008 | −0.192504 | − | 0.981296i | \(-0.561661\pi\) | ||||
−0.192504 | + | 0.981296i | \(0.561661\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.1489 | 0.854693 | ||||||||
\(142\) | 10.1247i | 0.849643i | ||||||||
\(143\) | 9.42867i | 0.788465i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.9771 | −1.15675 | ||||||||
\(147\) | − 6.71531i | − 0.553870i | ||||||||
\(148\) | − 4.06291i | − 0.333969i | ||||||||
\(149\) | −11.0750 | −0.907303 | −0.453651 | − | 0.891179i | \(-0.649879\pi\) | ||||
−0.453651 | + | 0.891179i | \(0.649879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.63387 | −0.132962 | −0.0664812 | − | 0.997788i | \(-0.521177\pi\) | ||||
−0.0664812 | + | 0.997788i | \(0.521177\pi\) | |||||||
\(152\) | 0.212889i | 0.0172676i | ||||||||
\(153\) | 0.958413i | 0.0774831i | ||||||||
\(154\) | −0.765259 | −0.0616663 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.57392 | 0.526335 | ||||||||
\(157\) | 6.64544i | 0.530364i | 0.964198 | + | 0.265182i | \(0.0854320\pi\) | ||||
−0.964198 | + | 0.265182i | \(0.914568\pi\) | |||||||
\(158\) | − 15.5279i | − 1.23534i | ||||||||
\(159\) | 3.23354 | 0.256437 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00832 | −0.158278 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 10.1134i | 0.792142i | 0.918220 | + | 0.396071i | \(0.129627\pi\) | ||||
−0.918220 | + | 0.396071i | \(0.870373\pi\) | |||||||
\(164\) | 7.94156 | 0.620132 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.3308 | 1.26752 | ||||||||
\(167\) | 12.7885i | 0.989600i | 0.869007 | + | 0.494800i | \(0.164759\pi\) | ||||
−0.869007 | + | 0.494800i | \(0.835241\pi\) | |||||||
\(168\) | 0.533559i | 0.0411650i | ||||||||
\(169\) | −30.2165 | −2.32434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.212889 | 0.0162800 | ||||||||
\(172\) | − 11.3607i | − 0.866248i | ||||||||
\(173\) | 13.6575i | 1.03836i | 0.854664 | + | 0.519182i | \(0.173763\pi\) | ||||
−0.854664 | + | 0.519182i | \(0.826237\pi\) | |||||||
\(174\) | −6.19448 | −0.469602 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.43425 | −0.108111 | ||||||||
\(177\) | 7.52455i | 0.565580i | ||||||||
\(178\) | − 5.62220i | − 0.421401i | ||||||||
\(179\) | −2.99142 | −0.223589 | −0.111795 | − | 0.993731i | \(-0.535660\pi\) | ||||
−0.111795 | + | 0.993731i | \(0.535660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.62285 | 0.566602 | 0.283301 | − | 0.959031i | \(-0.408570\pi\) | ||||
0.283301 | + | 0.959031i | \(0.408570\pi\) | |||||||
\(182\) | − 3.50758i | − 0.259999i | ||||||||
\(183\) | − 12.5721i | − 0.929354i | ||||||||
\(184\) | −3.76401 | −0.277487 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.33773 | −0.171411 | ||||||||
\(187\) | 1.37461i | 0.100521i | ||||||||
\(188\) | − 10.1489i | − 0.740186i | ||||||||
\(189\) | 0.533559 | 0.0388107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.40045 | −0.607835 | −0.303917 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303917 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 10.5266i | 0.757723i | 0.925453 | + | 0.378861i | \(0.123684\pi\) | ||||
−0.925453 | + | 0.378861i | \(0.876316\pi\) | |||||||
\(194\) | 5.56558 | 0.399585 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.71531 | −0.479665 | ||||||||
\(197\) | − 10.2080i | − 0.727293i | −0.931537 | − | 0.363647i | \(-0.881532\pi\) | ||||
0.931537 | − | 0.363647i | \(-0.118468\pi\) | |||||||
\(198\) | 1.43425i | 0.101928i | ||||||||
\(199\) | −3.84318 | −0.272436 | −0.136218 | − | 0.990679i | \(-0.543495\pi\) | ||||
−0.136218 | + | 0.990679i | \(0.543495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.91285 | −0.487595 | ||||||||
\(202\) | − 9.42708i | − 0.663287i | ||||||||
\(203\) | 3.30512i | 0.231974i | ||||||||
\(204\) | 0.958413 | 0.0671023 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.99871 | 0.557297 | ||||||||
\(207\) | 3.76401i | 0.261617i | ||||||||
\(208\) | − 6.57392i | − 0.455820i | ||||||||
\(209\) | 0.305337 | 0.0211206 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.24920 | 0.361370 | 0.180685 | − | 0.983541i | \(-0.442169\pi\) | ||||
0.180685 | + | 0.983541i | \(0.442169\pi\) | |||||||
\(212\) | − 3.23354i | − 0.222081i | ||||||||
\(213\) | − 10.1247i | − 0.693731i | ||||||||
\(214\) | −18.9260 | −1.29375 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.24732i | 0.0846734i | ||||||||
\(218\) | 2.65524i | 0.179836i | ||||||||
\(219\) | 13.9771 | 0.944484 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.30054 | −0.423820 | ||||||||
\(222\) | 4.06291i | 0.272685i | ||||||||
\(223\) | 19.2782i | 1.29097i | 0.763774 | + | 0.645483i | \(0.223344\pi\) | ||||
−0.763774 | + | 0.645483i | \(0.776656\pi\) | |||||||
\(224\) | 0.533559 | 0.0356499 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.06283 | 0.203736 | ||||||||
\(227\) | 8.43957i | 0.560154i | 0.959978 | + | 0.280077i | \(0.0903600\pi\) | ||||
−0.959978 | + | 0.280077i | \(0.909640\pi\) | |||||||
\(228\) | − 0.212889i | − 0.0140989i | ||||||||
\(229\) | −5.95568 | −0.393563 | −0.196781 | − | 0.980447i | \(-0.563049\pi\) | ||||
−0.196781 | + | 0.980447i | \(0.563049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.765259 | 0.0503503 | ||||||||
\(232\) | 6.19448i | 0.406688i | ||||||||
\(233\) | 2.09293i | 0.137112i | 0.997647 | + | 0.0685561i | \(0.0218392\pi\) | ||||
−0.997647 | + | 0.0685561i | \(0.978161\pi\) | |||||||
\(234\) | −6.57392 | −0.429751 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.52455 | 0.489806 | ||||||||
\(237\) | 15.5279i | 1.00865i | ||||||||
\(238\) | − 0.511370i | − 0.0331472i | ||||||||
\(239\) | −9.89840 | −0.640274 | −0.320137 | − | 0.947371i | \(-0.603729\pi\) | ||||
−0.320137 | + | 0.947371i | \(0.603729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4567 | −1.38215 | −0.691074 | − | 0.722784i | \(-0.742862\pi\) | ||||
−0.691074 | + | 0.722784i | \(0.742862\pi\) | |||||||
\(242\) | − 8.94292i | − 0.574873i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −12.5721 | −0.804844 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.94156 | −0.506336 | ||||||||
\(247\) | 1.39952i | 0.0890491i | ||||||||
\(248\) | 2.33773i | 0.148446i | ||||||||
\(249\) | −16.3308 | −1.03492 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.10753 | −0.259265 | −0.129632 | − | 0.991562i | \(-0.541380\pi\) | ||||
−0.129632 | + | 0.991562i | \(0.541380\pi\) | |||||||
\(252\) | − 0.533559i | − 0.0336111i | ||||||||
\(253\) | 5.39854i | 0.339404i | ||||||||
\(254\) | 6.48257 | 0.406753 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 30.7748i | − 1.91968i | −0.280552 | − | 0.959839i | \(-0.590518\pi\) | ||||
0.280552 | − | 0.959839i | \(-0.409482\pi\) | |||||||
\(258\) | 11.3607i | 0.707289i | ||||||||
\(259\) | 2.16780 | 0.134701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.19448 | 0.383429 | ||||||||
\(262\) | − 9.45794i | − 0.584313i | ||||||||
\(263\) | 28.3729i | 1.74955i | 0.484533 | + | 0.874773i | \(0.338989\pi\) | ||||
−0.484533 | + | 0.874773i | \(0.661011\pi\) | |||||||
\(264\) | 1.43425 | 0.0882722 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.113589 | −0.00696458 | ||||||||
\(267\) | 5.62220i | 0.344073i | ||||||||
\(268\) | 6.91285i | 0.422269i | ||||||||
\(269\) | −10.6668 | −0.650364 | −0.325182 | − | 0.945651i | \(-0.605426\pi\) | ||||
−0.325182 | + | 0.945651i | \(0.605426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.8439 | 1.38767 | 0.693835 | − | 0.720134i | \(-0.255920\pi\) | ||||
0.693835 | + | 0.720134i | \(0.255920\pi\) | |||||||
\(272\) | − 0.958413i | − 0.0581123i | ||||||||
\(273\) | 3.50758i | 0.212288i | ||||||||
\(274\) | 12.3361 | 0.745250 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.76401 | 0.226567 | ||||||||
\(277\) | − 31.4592i | − 1.89020i | −0.326784 | − | 0.945099i | \(-0.605965\pi\) | ||||
0.326784 | − | 0.945099i | \(-0.394035\pi\) | |||||||
\(278\) | − 4.53918i | − 0.272242i | ||||||||
\(279\) | 2.33773 | 0.139956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.7785 | −0.642992 | −0.321496 | − | 0.946911i | \(-0.604186\pi\) | ||||
−0.321496 | + | 0.946911i | \(0.604186\pi\) | |||||||
\(282\) | 10.1489i | 0.604359i | ||||||||
\(283\) | 4.16428i | 0.247541i | 0.992311 | + | 0.123770i | \(0.0394986\pi\) | ||||
−0.992311 | + | 0.123770i | \(0.960501\pi\) | |||||||
\(284\) | −10.1247 | −0.600789 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.42867 | −0.557529 | ||||||||
\(287\) | 4.23729i | 0.250120i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | 16.0814 | 0.945967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.56558 | −0.326260 | ||||||||
\(292\) | − 13.9771i | − 0.817947i | ||||||||
\(293\) | 17.9603i | 1.04925i | 0.851333 | + | 0.524626i | \(0.175795\pi\) | ||||
−0.851333 | + | 0.524626i | \(0.824205\pi\) | |||||||
\(294\) | 6.71531 | 0.391645 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.06291 | 0.236152 | ||||||||
\(297\) | − 1.43425i | − 0.0832238i | ||||||||
\(298\) | − 11.0750i | − 0.641560i | ||||||||
\(299\) | −24.7443 | −1.43100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.06163 | 0.349386 | ||||||||
\(302\) | − 1.63387i | − 0.0940187i | ||||||||
\(303\) | 9.42708i | 0.541571i | ||||||||
\(304\) | −0.212889 | −0.0122100 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.958413 | −0.0547888 | ||||||||
\(307\) | − 20.8174i | − 1.18811i | −0.804423 | − | 0.594056i | \(-0.797526\pi\) | ||||
0.804423 | − | 0.594056i | \(-0.202474\pi\) | |||||||
\(308\) | − 0.765259i | − 0.0436047i | ||||||||
\(309\) | −7.99871 | −0.455031 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4526 | −1.10305 | −0.551527 | − | 0.834157i | \(-0.685955\pi\) | ||||
−0.551527 | + | 0.834157i | \(0.685955\pi\) | |||||||
\(312\) | 6.57392i | 0.372175i | ||||||||
\(313\) | − 5.88310i | − 0.332532i | −0.986081 | − | 0.166266i | \(-0.946829\pi\) | ||||
0.986081 | − | 0.166266i | \(-0.0531711\pi\) | |||||||
\(314\) | −6.64544 | −0.375024 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.5279 | 0.873515 | ||||||||
\(317\) | − 10.7610i | − 0.604400i | −0.953245 | − | 0.302200i | \(-0.902279\pi\) | ||||
0.953245 | − | 0.302200i | \(-0.0977210\pi\) | |||||||
\(318\) | 3.23354i | 0.181328i | ||||||||
\(319\) | 8.88445 | 0.497434 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.9260 | 1.05635 | ||||||||
\(322\) | − 2.00832i | − 0.111919i | ||||||||
\(323\) | 0.204036i | 0.0113528i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.1134 | −0.560129 | ||||||||
\(327\) | − 2.65524i | − 0.146835i | ||||||||
\(328\) | 7.94156i | 0.438500i | ||||||||
\(329\) | 5.41505 | 0.298541 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.617092 | −0.0339184 | −0.0169592 | − | 0.999856i | \(-0.505399\pi\) | ||||
−0.0169592 | + | 0.999856i | \(0.505399\pi\) | |||||||
\(332\) | 16.3308i | 0.896270i | ||||||||
\(333\) | − 4.06291i | − 0.222646i | ||||||||
\(334\) | −12.7885 | −0.699753 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.533559 | −0.0291080 | ||||||||
\(337\) | − 15.4106i | − 0.839471i | −0.907647 | − | 0.419735i | \(-0.862123\pi\) | ||||
0.907647 | − | 0.419735i | \(-0.137877\pi\) | |||||||
\(338\) | − 30.2165i | − 1.64356i | ||||||||
\(339\) | −3.06283 | −0.166350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.35289 | 0.181569 | ||||||||
\(342\) | 0.212889i | 0.0115117i | ||||||||
\(343\) | − 7.31793i | − 0.395131i | ||||||||
\(344\) | 11.3607 | 0.612530 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.6575 | −0.734234 | ||||||||
\(347\) | 22.6565i | 1.21627i | 0.793835 | + | 0.608133i | \(0.208081\pi\) | ||||
−0.793835 | + | 0.608133i | \(0.791919\pi\) | |||||||
\(348\) | − 6.19448i | − 0.332059i | ||||||||
\(349\) | 16.9543 | 0.907544 | 0.453772 | − | 0.891118i | \(-0.350078\pi\) | ||||
0.453772 | + | 0.891118i | \(0.350078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.57392 | 0.350890 | ||||||||
\(352\) | − 1.43425i | − 0.0764459i | ||||||||
\(353\) | − 6.06255i | − 0.322677i | −0.986899 | − | 0.161339i | \(-0.948419\pi\) | ||||
0.986899 | − | 0.161339i | \(-0.0515811\pi\) | |||||||
\(354\) | −7.52455 | −0.399925 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.62220 | 0.297976 | ||||||||
\(357\) | 0.511370i | 0.0270646i | ||||||||
\(358\) | − 2.99142i | − 0.158101i | ||||||||
\(359\) | −18.8987 | −0.997437 | −0.498718 | − | 0.866764i | \(-0.666196\pi\) | ||||
−0.498718 | + | 0.866764i | \(0.666196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9547 | −0.997615 | ||||||||
\(362\) | 7.62285i | 0.400648i | ||||||||
\(363\) | 8.94292i | 0.469381i | ||||||||
\(364\) | 3.50758 | 0.183847 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.5721 | 0.657152 | ||||||||
\(367\) | − 25.0483i | − 1.30751i | −0.756705 | − | 0.653756i | \(-0.773192\pi\) | ||||
0.756705 | − | 0.653756i | \(-0.226808\pi\) | |||||||
\(368\) | − 3.76401i | − 0.196213i | ||||||||
\(369\) | 7.94156 | 0.413421 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.72529 | 0.0895725 | ||||||||
\(372\) | − 2.33773i | − 0.121206i | ||||||||
\(373\) | 11.8954i | 0.615922i | 0.951399 | + | 0.307961i | \(0.0996466\pi\) | ||||
−0.951399 | + | 0.307961i | \(0.900353\pi\) | |||||||
\(374\) | −1.37461 | −0.0710792 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.1489 | 0.523390 | ||||||||
\(377\) | 40.7220i | 2.09729i | ||||||||
\(378\) | 0.533559i | 0.0274433i | ||||||||
\(379\) | −27.5184 | −1.41353 | −0.706763 | − | 0.707450i | \(-0.749845\pi\) | ||||
−0.706763 | + | 0.707450i | \(0.749845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.48257 | −0.332112 | ||||||||
\(382\) | − 8.40045i | − 0.429804i | ||||||||
\(383\) | 22.0314i | 1.12575i | 0.826541 | + | 0.562877i | \(0.190305\pi\) | ||||
−0.826541 | + | 0.562877i | \(0.809695\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.5266 | −0.535791 | ||||||||
\(387\) | − 11.3607i | − 0.577499i | ||||||||
\(388\) | 5.56558i | 0.282549i | ||||||||
\(389\) | −17.4892 | −0.886738 | −0.443369 | − | 0.896339i | \(-0.646217\pi\) | ||||
−0.443369 | + | 0.896339i | \(0.646217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.60748 | −0.182438 | ||||||||
\(392\) | − 6.71531i | − 0.339175i | ||||||||
\(393\) | 9.45794i | 0.477090i | ||||||||
\(394\) | 10.2080 | 0.514274 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.43425 | −0.0720739 | ||||||||
\(397\) | − 24.4990i | − 1.22957i | −0.788694 | − | 0.614786i | \(-0.789242\pi\) | ||||
0.788694 | − | 0.614786i | \(-0.210758\pi\) | |||||||
\(398\) | − 3.84318i | − 0.192641i | ||||||||
\(399\) | 0.113589 | 0.00568656 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.04105 | 0.0519875 | 0.0259937 | − | 0.999662i | \(-0.491725\pi\) | ||||
0.0259937 | + | 0.999662i | \(0.491725\pi\) | |||||||
\(402\) | − 6.91285i | − 0.344782i | ||||||||
\(403\) | 15.3681i | 0.765537i | ||||||||
\(404\) | 9.42708 | 0.469015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.30512 | −0.164030 | ||||||||
\(407\) | − 5.82724i | − 0.288845i | ||||||||
\(408\) | 0.958413i | 0.0474485i | ||||||||
\(409\) | −22.2568 | −1.10053 | −0.550263 | − | 0.834991i | \(-0.685473\pi\) | ||||
−0.550263 | + | 0.834991i | \(0.685473\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3361 | −0.608494 | ||||||||
\(412\) | 7.99871i | 0.394068i | ||||||||
\(413\) | 4.01479i | 0.197555i | ||||||||
\(414\) | −3.76401 | −0.184991 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.57392 | 0.322313 | ||||||||
\(417\) | 4.53918i | 0.222284i | ||||||||
\(418\) | 0.305337i | 0.0149345i | ||||||||
\(419\) | 23.1294 | 1.12994 | 0.564972 | − | 0.825110i | \(-0.308887\pi\) | ||||
0.564972 | + | 0.825110i | \(0.308887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.76139 | 0.475741 | 0.237870 | − | 0.971297i | \(-0.423551\pi\) | ||||
0.237870 | + | 0.971297i | \(0.423551\pi\) | |||||||
\(422\) | 5.24920i | 0.255527i | ||||||||
\(423\) | − 10.1489i | − 0.493457i | ||||||||
\(424\) | 3.23354 | 0.157035 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.1247 | 0.490542 | ||||||||
\(427\) | − 6.70794i | − 0.324620i | ||||||||
\(428\) | − 18.9260i | − 0.914822i | ||||||||
\(429\) | 9.42867 | 0.455220 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.49298 | 0.409093 | 0.204546 | − | 0.978857i | \(-0.434428\pi\) | ||||
0.204546 | + | 0.978857i | \(0.434428\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − 22.0042i | − 1.05745i | −0.848792 | − | 0.528727i | \(-0.822670\pi\) | ||||
0.848792 | − | 0.528727i | \(-0.177330\pi\) | |||||||
\(434\) | −1.24732 | −0.0598731 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.65524 | −0.127163 | ||||||||
\(437\) | 0.801317i | 0.0383322i | ||||||||
\(438\) | 13.9771i | 0.667851i | ||||||||
\(439\) | 38.3582 | 1.83074 | 0.915369 | − | 0.402615i | \(-0.131899\pi\) | ||||
0.915369 | + | 0.402615i | \(0.131899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.71531 | −0.319777 | ||||||||
\(442\) | − 6.30054i | − 0.299686i | ||||||||
\(443\) | − 12.7478i | − 0.605666i | −0.953044 | − | 0.302833i | \(-0.902068\pi\) | ||||
0.953044 | − | 0.302833i | \(-0.0979324\pi\) | |||||||
\(444\) | −4.06291 | −0.192817 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.2782 | −0.912851 | ||||||||
\(447\) | 11.0750i | 0.523831i | ||||||||
\(448\) | 0.533559i | 0.0252083i | ||||||||
\(449\) | −18.0358 | −0.851161 | −0.425580 | − | 0.904921i | \(-0.639930\pi\) | ||||
−0.425580 | + | 0.904921i | \(0.639930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3902 | 0.536344 | ||||||||
\(452\) | 3.06283i | 0.144063i | ||||||||
\(453\) | 1.63387i | 0.0767659i | ||||||||
\(454\) | −8.43957 | −0.396089 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.212889 | 0.00996944 | ||||||||
\(457\) | − 21.1495i | − 0.989334i | −0.869083 | − | 0.494667i | \(-0.835290\pi\) | ||||
0.869083 | − | 0.494667i | \(-0.164710\pi\) | |||||||
\(458\) | − 5.95568i | − 0.278291i | ||||||||
\(459\) | 0.958413 | 0.0447349 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.0085 | 1.49078 | 0.745391 | − | 0.666627i | \(-0.232263\pi\) | ||||
0.745391 | + | 0.666627i | \(0.232263\pi\) | |||||||
\(462\) | 0.765259i | 0.0356031i | ||||||||
\(463\) | − 28.7776i | − 1.33741i | −0.743529 | − | 0.668703i | \(-0.766850\pi\) | ||||
0.743529 | − | 0.668703i | \(-0.233150\pi\) | |||||||
\(464\) | −6.19448 | −0.287572 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.09293 | −0.0969529 | ||||||||
\(467\) | 5.20326i | 0.240778i | 0.992727 | + | 0.120389i | \(0.0384142\pi\) | ||||
−0.992727 | + | 0.120389i | \(0.961586\pi\) | |||||||
\(468\) | − 6.57392i | − 0.303880i | ||||||||
\(469\) | −3.68841 | −0.170315 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.64544 | 0.306206 | ||||||||
\(472\) | 7.52455i | 0.346345i | ||||||||
\(473\) | − 16.2942i | − 0.749207i | ||||||||
\(474\) | −15.5279 | −0.713222 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.511370 | 0.0234386 | ||||||||
\(477\) | − 3.23354i | − 0.148054i | ||||||||
\(478\) | − 9.89840i | − 0.452742i | ||||||||
\(479\) | 39.6385 | 1.81113 | 0.905565 | − | 0.424206i | \(-0.139447\pi\) | ||||
0.905565 | + | 0.424206i | \(0.139447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.7093 | 1.21784 | ||||||||
\(482\) | − 21.4567i | − 0.977326i | ||||||||
\(483\) | 2.00832i | 0.0913818i | ||||||||
\(484\) | 8.94292 | 0.406496 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − 5.44308i | − 0.246649i | −0.992366 | − | 0.123325i | \(-0.960644\pi\) | ||||
0.992366 | − | 0.123325i | \(-0.0393557\pi\) | |||||||
\(488\) | − 12.5721i | − 0.569111i | ||||||||
\(489\) | 10.1134 | 0.457344 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.873965 | 0.0394415 | 0.0197207 | − | 0.999806i | \(-0.493722\pi\) | ||||
0.0197207 | + | 0.999806i | \(0.493722\pi\) | |||||||
\(492\) | − 7.94156i | − 0.358033i | ||||||||
\(493\) | 5.93687i | 0.267383i | ||||||||
\(494\) | −1.39952 | −0.0629672 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.33773 | −0.104967 | ||||||||
\(497\) | − 5.40211i | − 0.242318i | ||||||||
\(498\) | − 16.3308i | − 0.731802i | ||||||||
\(499\) | 34.9604 | 1.56504 | 0.782522 | − | 0.622623i | \(-0.213933\pi\) | ||||
0.782522 | + | 0.622623i | \(0.213933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.7885 | 0.571346 | ||||||||
\(502\) | − 4.10753i | − 0.183328i | ||||||||
\(503\) | 0.319724i | 0.0142558i | 0.999975 | + | 0.00712790i | \(0.00226890\pi\) | ||||
−0.999975 | + | 0.00712790i | \(0.997731\pi\) | |||||||
\(504\) | 0.533559 | 0.0237666 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.39854 | −0.239995 | ||||||||
\(507\) | 30.2165i | 1.34196i | ||||||||
\(508\) | 6.48257i | 0.287618i | ||||||||
\(509\) | −20.6259 | −0.914225 | −0.457113 | − | 0.889409i | \(-0.651116\pi\) | ||||
−0.457113 | + | 0.889409i | \(0.651116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.45760 | 0.329905 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 0.212889i | − 0.00939928i | ||||||||
\(514\) | 30.7748 | 1.35742 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.3607 | −0.500129 | ||||||||
\(517\) | − 14.5561i | − 0.640177i | ||||||||
\(518\) | 2.16780i | 0.0952477i | ||||||||
\(519\) | 13.6575 | 0.599500 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.22039 | −0.184899 | −0.0924493 | − | 0.995717i | \(-0.529470\pi\) | ||||
−0.0924493 | + | 0.995717i | \(0.529470\pi\) | |||||||
\(522\) | 6.19448i | 0.271125i | ||||||||
\(523\) | − 21.5579i | − 0.942659i | −0.881957 | − | 0.471330i | \(-0.843774\pi\) | ||||
0.881957 | − | 0.471330i | \(-0.156226\pi\) | |||||||
\(524\) | 9.45794 | 0.413172 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.3729 | −1.23712 | ||||||||
\(527\) | 2.24051i | 0.0975982i | ||||||||
\(528\) | 1.43425i | 0.0624178i | ||||||||
\(529\) | 8.83222 | 0.384010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.52455 | 0.326538 | ||||||||
\(532\) | − 0.113589i | − 0.00492470i | ||||||||
\(533\) | 52.2072i | 2.26135i | ||||||||
\(534\) | −5.62220 | −0.243296 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.91285 | −0.298590 | ||||||||
\(537\) | 2.99142i | 0.129089i | ||||||||
\(538\) | − 10.6668i | − 0.459877i | ||||||||
\(539\) | −9.63146 | −0.414856 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.93662 | −0.384215 | −0.192108 | − | 0.981374i | \(-0.561532\pi\) | ||||
−0.192108 | + | 0.981374i | \(0.561532\pi\) | |||||||
\(542\) | 22.8439i | 0.981231i | ||||||||
\(543\) | − 7.62285i | − 0.327128i | ||||||||
\(544\) | 0.958413 | 0.0410916 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.50758 | −0.150110 | ||||||||
\(547\) | − 12.0786i | − 0.516443i | −0.966086 | − | 0.258222i | \(-0.916864\pi\) | ||||
0.966086 | − | 0.258222i | \(-0.0831365\pi\) | |||||||
\(548\) | 12.3361i | 0.526971i | ||||||||
\(549\) | −12.5721 | −0.536563 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.31874 | 0.0561801 | ||||||||
\(552\) | 3.76401i | 0.160207i | ||||||||
\(553\) | 8.28507i | 0.352317i | ||||||||
\(554\) | 31.4592 | 1.33657 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.53918 | 0.192504 | ||||||||
\(557\) | 8.23596i | 0.348969i | 0.984660 | + | 0.174484i | \(0.0558259\pi\) | ||||
−0.984660 | + | 0.174484i | \(0.944174\pi\) | |||||||
\(558\) | 2.33773i | 0.0989640i | ||||||||
\(559\) | 74.6846 | 3.15882 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.37461 | 0.0580360 | ||||||||
\(562\) | − 10.7785i | − 0.454664i | ||||||||
\(563\) | 14.6358i | 0.616825i | 0.951253 | + | 0.308413i | \(0.0997978\pi\) | ||||
−0.951253 | + | 0.308413i | \(0.900202\pi\) | |||||||
\(564\) | −10.1489 | −0.427347 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.16428 | −0.175038 | ||||||||
\(567\) | − 0.533559i | − 0.0224074i | ||||||||
\(568\) | − 10.1247i | − 0.424822i | ||||||||
\(569\) | −31.2471 | −1.30995 | −0.654974 | − | 0.755651i | \(-0.727321\pi\) | ||||
−0.654974 | + | 0.755651i | \(0.727321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.2261 | 1.09753 | 0.548763 | − | 0.835978i | \(-0.315099\pi\) | ||||
0.548763 | + | 0.835978i | \(0.315099\pi\) | |||||||
\(572\) | − 9.42867i | − 0.394233i | ||||||||
\(573\) | 8.40045i | 0.350934i | ||||||||
\(574\) | −4.23729 | −0.176861 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 8.93340i | 0.371902i | 0.982559 | + | 0.185951i | \(0.0595366\pi\) | ||||
−0.982559 | + | 0.185951i | \(0.940463\pi\) | |||||||
\(578\) | 16.0814i | 0.668900i | ||||||||
\(579\) | 10.5266 | 0.437471 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.71346 | −0.361495 | ||||||||
\(582\) | − 5.56558i | − 0.230701i | ||||||||
\(583\) | − 4.63772i | − 0.192075i | ||||||||
\(584\) | 13.9771 | 0.578376 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.9603 | −0.741933 | ||||||||
\(587\) | 3.99360i | 0.164833i | 0.996598 | + | 0.0824167i | \(0.0262638\pi\) | ||||
−0.996598 | + | 0.0824167i | \(0.973736\pi\) | |||||||
\(588\) | 6.71531i | 0.276935i | ||||||||
\(589\) | 0.497677 | 0.0205064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2080 | −0.419903 | ||||||||
\(592\) | 4.06291i | 0.166985i | ||||||||
\(593\) | − 11.2114i | − 0.460396i | −0.973144 | − | 0.230198i | \(-0.926063\pi\) | ||||
0.973144 | − | 0.230198i | \(-0.0739374\pi\) | |||||||
\(594\) | 1.43425 | 0.0588481 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.0750 | 0.453651 | ||||||||
\(597\) | 3.84318i | 0.157291i | ||||||||
\(598\) | − 24.7443i | − 1.01187i | ||||||||
\(599\) | 6.64762 | 0.271614 | 0.135807 | − | 0.990735i | \(-0.456637\pi\) | ||||
0.135807 | + | 0.990735i | \(0.456637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.7465 | −0.438359 | −0.219179 | − | 0.975685i | \(-0.570338\pi\) | ||||
−0.219179 | + | 0.975685i | \(0.570338\pi\) | |||||||
\(602\) | 6.06163i | 0.247053i | ||||||||
\(603\) | 6.91285i | 0.281513i | ||||||||
\(604\) | 1.63387 | 0.0664812 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.42708 | −0.382949 | ||||||||
\(607\) | 15.4591i | 0.627466i | 0.949511 | + | 0.313733i | \(0.101580\pi\) | ||||
−0.949511 | + | 0.313733i | \(0.898420\pi\) | |||||||
\(608\) | − 0.212889i | − 0.00863379i | ||||||||
\(609\) | 3.30512 | 0.133930 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 66.7182 | 2.69913 | ||||||||
\(612\) | − 0.958413i | − 0.0387416i | ||||||||
\(613\) | 24.4867i | 0.989007i | 0.869176 | + | 0.494503i | \(0.164650\pi\) | ||||
−0.869176 | + | 0.494503i | \(0.835350\pi\) | |||||||
\(614\) | 20.8174 | 0.840122 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.765259 | 0.0308332 | ||||||||
\(617\) | − 18.9157i | − 0.761515i | −0.924675 | − | 0.380758i | \(-0.875663\pi\) | ||||
0.924675 | − | 0.380758i | \(-0.124337\pi\) | |||||||
\(618\) | − 7.99871i | − 0.321755i | ||||||||
\(619\) | −2.55005 | −0.102495 | −0.0512476 | − | 0.998686i | \(-0.516320\pi\) | ||||
−0.0512476 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.76401 | 0.151045 | ||||||||
\(622\) | − 19.4526i | − 0.779978i | ||||||||
\(623\) | 2.99977i | 0.120183i | ||||||||
\(624\) | −6.57392 | −0.263168 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.88310 | 0.235136 | ||||||||
\(627\) | − 0.305337i | − 0.0121940i | ||||||||
\(628\) | − 6.64544i | − 0.265182i | ||||||||
\(629\) | 3.89395 | 0.155262 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4530 | −1.45117 | −0.725585 | − | 0.688133i | \(-0.758431\pi\) | ||||
−0.725585 | + | 0.688133i | \(0.758431\pi\) | |||||||
\(632\) | 15.5279i | 0.617668i | ||||||||
\(633\) | − 5.24920i | − 0.208637i | ||||||||
\(634\) | 10.7610 | 0.427375 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.23354 | −0.128218 | ||||||||
\(637\) | − 44.1460i | − 1.74913i | ||||||||
\(638\) | 8.88445i | 0.351739i | ||||||||
\(639\) | −10.1247 | −0.400526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3669 | −0.804444 | −0.402222 | − | 0.915542i | \(-0.631762\pi\) | ||||
−0.402222 | + | 0.915542i | \(0.631762\pi\) | |||||||
\(642\) | 18.9260i | 0.746949i | ||||||||
\(643\) | 11.4218i | 0.450433i | 0.974309 | + | 0.225217i | \(0.0723090\pi\) | ||||
−0.974309 | + | 0.225217i | \(0.927691\pi\) | |||||||
\(644\) | 2.00832 | 0.0791390 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.204036 | −0.00802768 | ||||||||
\(647\) | 5.89217i | 0.231645i | 0.993270 | + | 0.115823i | \(0.0369504\pi\) | ||||
−0.993270 | + | 0.115823i | \(0.963050\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 10.7921 | 0.423627 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.24732 | 0.0488862 | ||||||||
\(652\) | − 10.1134i | − 0.396071i | ||||||||
\(653\) | − 17.1063i | − 0.669422i | −0.942321 | − | 0.334711i | \(-0.891361\pi\) | ||||
0.942321 | − | 0.334711i | \(-0.108639\pi\) | |||||||
\(654\) | 2.65524 | 0.103828 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.94156 | −0.310066 | ||||||||
\(657\) | − 13.9771i | − 0.545298i | ||||||||
\(658\) | 5.41505i | 0.211101i | ||||||||
\(659\) | 29.7191 | 1.15769 | 0.578846 | − | 0.815437i | \(-0.303503\pi\) | ||||
0.578846 | + | 0.815437i | \(0.303503\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.3036 | 1.80100 | 0.900501 | − | 0.434854i | \(-0.143200\pi\) | ||||
0.900501 | + | 0.434854i | \(0.143200\pi\) | |||||||
\(662\) | − 0.617092i | − 0.0239840i | ||||||||
\(663\) | 6.30054i | 0.244693i | ||||||||
\(664\) | −16.3308 | −0.633759 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.06291 | 0.157435 | ||||||||
\(667\) | 23.3161i | 0.902803i | ||||||||
\(668\) | − 12.7885i | − 0.494800i | ||||||||
\(669\) | 19.2782 | 0.745340 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.0315 | −0.696099 | ||||||||
\(672\) | − 0.533559i | − 0.0205825i | ||||||||
\(673\) | − 19.7080i | − 0.759689i | −0.925050 | − | 0.379845i | \(-0.875977\pi\) | ||||
0.925050 | − | 0.379845i | \(-0.124023\pi\) | |||||||
\(674\) | 15.4106 | 0.593595 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 30.2165 | 1.16217 | ||||||||
\(677\) | − 24.7774i | − 0.952273i | −0.879371 | − | 0.476137i | \(-0.842037\pi\) | ||||
0.879371 | − | 0.476137i | \(-0.157963\pi\) | |||||||
\(678\) | − 3.06283i | − 0.117627i | ||||||||
\(679\) | −2.96957 | −0.113961 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.43957 | 0.323405 | ||||||||
\(682\) | 3.35289i | 0.128389i | ||||||||
\(683\) | 16.5874i | 0.634699i | 0.948309 | + | 0.317349i | \(0.102793\pi\) | ||||
−0.948309 | + | 0.317349i | \(0.897207\pi\) | |||||||
\(684\) | −0.212889 | −0.00814002 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.31793 | 0.279400 | ||||||||
\(687\) | 5.95568i | 0.227224i | ||||||||
\(688\) | 11.3607i | 0.433124i | ||||||||
\(689\) | 21.2571 | 0.809830 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.2893 | 1.60876 | 0.804381 | − | 0.594114i | \(-0.202497\pi\) | ||||
0.804381 | + | 0.594114i | \(0.202497\pi\) | |||||||
\(692\) | − 13.6575i | − 0.519182i | ||||||||
\(693\) | − 0.765259i | − 0.0290698i | ||||||||
\(694\) | −22.6565 | −0.860031 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.19448 | 0.234801 | ||||||||
\(697\) | 7.61130i | 0.288299i | ||||||||
\(698\) | 16.9543i | 0.641731i | ||||||||
\(699\) | 2.09293 | 0.0791617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.7240 | −0.858273 | −0.429137 | − | 0.903240i | \(-0.641182\pi\) | ||||
−0.429137 | + | 0.903240i | \(0.641182\pi\) | |||||||
\(702\) | 6.57392i | 0.248117i | ||||||||
\(703\) | − 0.864949i | − 0.0326222i | ||||||||
\(704\) | 1.43425 | 0.0540554 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.06255 | 0.228167 | ||||||||
\(707\) | 5.02990i | 0.189169i | ||||||||
\(708\) | − 7.52455i | − 0.282790i | ||||||||
\(709\) | −46.4122 | −1.74305 | −0.871524 | − | 0.490353i | \(-0.836868\pi\) | ||||
−0.871524 | + | 0.490353i | \(0.836868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.5279 | 0.582343 | ||||||||
\(712\) | 5.62220i | 0.210701i | ||||||||
\(713\) | 8.79924i | 0.329534i | ||||||||
\(714\) | −0.511370 | −0.0191375 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.99142 | 0.111795 | ||||||||
\(717\) | 9.89840i | 0.369662i | ||||||||
\(718\) | − 18.8987i | − 0.705294i | ||||||||
\(719\) | 28.2066 | 1.05193 | 0.525964 | − | 0.850507i | \(-0.323705\pi\) | ||||
0.525964 | + | 0.850507i | \(0.323705\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.26779 | −0.158941 | ||||||||
\(722\) | − 18.9547i | − 0.705420i | ||||||||
\(723\) | 21.4567i | 0.797983i | ||||||||
\(724\) | −7.62285 | −0.283301 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.94292 | −0.331903 | ||||||||
\(727\) | − 0.851592i | − 0.0315838i | −0.999875 | − | 0.0157919i | \(-0.994973\pi\) | ||||
0.999875 | − | 0.0157919i | \(-0.00502693\pi\) | |||||||
\(728\) | 3.50758i | 0.129999i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8883 | 0.402718 | ||||||||
\(732\) | 12.5721i | 0.464677i | ||||||||
\(733\) | 30.7299i | 1.13504i | 0.823361 | + | 0.567518i | \(0.192096\pi\) | ||||
−0.823361 | + | 0.567518i | \(0.807904\pi\) | |||||||
\(734\) | 25.0483 | 0.924551 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.76401 | 0.138743 | ||||||||
\(737\) | 9.91477i | 0.365215i | ||||||||
\(738\) | 7.94156i | 0.292333i | ||||||||
\(739\) | −2.06485 | −0.0759566 | −0.0379783 | − | 0.999279i | \(-0.512092\pi\) | ||||
−0.0379783 | + | 0.999279i | \(0.512092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.39952 | 0.0514125 | ||||||||
\(742\) | 1.72529i | 0.0633373i | ||||||||
\(743\) | − 37.8972i | − 1.39031i | −0.718858 | − | 0.695157i | \(-0.755335\pi\) | ||||
0.718858 | − | 0.695157i | \(-0.244665\pi\) | |||||||
\(744\) | 2.33773 | 0.0857053 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.8954 | −0.435522 | ||||||||
\(747\) | 16.3308i | 0.597514i | ||||||||
\(748\) | − 1.37461i | − 0.0502606i | ||||||||
\(749\) | 10.0981 | 0.368978 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.6331 | −1.48272 | −0.741361 | − | 0.671106i | \(-0.765819\pi\) | ||||
−0.741361 | + | 0.671106i | \(0.765819\pi\) | |||||||
\(752\) | 10.1489i | 0.370093i | ||||||||
\(753\) | 4.10753i | 0.149687i | ||||||||
\(754\) | −40.7220 | −1.48301 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.533559 | −0.0194054 | ||||||||
\(757\) | − 10.0032i | − 0.363572i | −0.983338 | − | 0.181786i | \(-0.941812\pi\) | ||||
0.983338 | − | 0.181786i | \(-0.0581877\pi\) | |||||||
\(758\) | − 27.5184i | − 0.999514i | ||||||||
\(759\) | 5.39854 | 0.195955 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.1813 | −1.09407 | −0.547035 | − | 0.837110i | \(-0.684244\pi\) | ||||
−0.547035 | + | 0.837110i | \(0.684244\pi\) | |||||||
\(762\) | − 6.48257i | − 0.234839i | ||||||||
\(763\) | − 1.41673i | − 0.0512890i | ||||||||
\(764\) | 8.40045 | 0.303917 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.0314 | −0.796028 | ||||||||
\(767\) | 49.4658i | 1.78611i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | −21.1468 | −0.762571 | −0.381286 | − | 0.924457i | \(-0.624519\pi\) | ||||
−0.381286 | + | 0.924457i | \(0.624519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.7748 | −1.10833 | ||||||||
\(772\) | − 10.5266i | − 0.378861i | ||||||||
\(773\) | − 29.4470i | − 1.05913i | −0.848268 | − | 0.529567i | \(-0.822354\pi\) | ||||
0.848268 | − | 0.529567i | \(-0.177646\pi\) | |||||||
\(774\) | 11.3607 | 0.408353 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.56558 | −0.199793 | ||||||||
\(777\) | − 2.16780i | − 0.0777695i | ||||||||
\(778\) | − 17.4892i | − 0.627019i | ||||||||
\(779\) | 1.69067 | 0.0605746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.5213 | −0.519614 | ||||||||
\(782\) | − 3.60748i | − 0.129003i | ||||||||
\(783\) | − 6.19448i | − 0.221373i | ||||||||
\(784\) | 6.71531 | 0.239833 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.45794 | −0.337353 | ||||||||
\(787\) | 5.16875i | 0.184246i | 0.995748 | + | 0.0921230i | \(0.0293653\pi\) | ||||
−0.995748 | + | 0.0921230i | \(0.970635\pi\) | |||||||
\(788\) | 10.2080i | 0.363647i | ||||||||
\(789\) | 28.3729 | 1.01010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.63420 | −0.0581055 | ||||||||
\(792\) | − 1.43425i | − 0.0509640i | ||||||||
\(793\) | − 82.6478i | − 2.93491i | ||||||||
\(794\) | 24.4990 | 0.869439 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.84318 | 0.136218 | ||||||||
\(797\) | 3.75807i | 0.133118i | 0.997783 | + | 0.0665588i | \(0.0212020\pi\) | ||||
−0.997783 | + | 0.0665588i | \(0.978798\pi\) | |||||||
\(798\) | 0.113589i | 0.00402100i | ||||||||
\(799\) | 9.72686 | 0.344111 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.62220 | 0.198650 | ||||||||
\(802\) | 1.04105i | 0.0367607i | ||||||||
\(803\) | − 20.0467i | − 0.707432i | ||||||||
\(804\) | 6.91285 | 0.243797 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.3681 | −0.541317 | ||||||||
\(807\) | 10.6668i | 0.375488i | ||||||||
\(808\) | 9.42708i | 0.331643i | ||||||||
\(809\) | 20.8847 | 0.734266 | 0.367133 | − | 0.930168i | \(-0.380339\pi\) | ||||
0.367133 | + | 0.930168i | \(0.380339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5032 | −1.28180 | −0.640900 | − | 0.767625i | \(-0.721439\pi\) | ||||
−0.640900 | + | 0.767625i | \(0.721439\pi\) | |||||||
\(812\) | − 3.30512i | − 0.115987i | ||||||||
\(813\) | − 22.8439i | − 0.801172i | ||||||||
\(814\) | 5.82724 | 0.204245 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.958413 | −0.0335512 | ||||||||
\(817\) | − 2.41858i | − 0.0846153i | ||||||||
\(818\) | − 22.2568i | − 0.778190i | ||||||||
\(819\) | 3.50758 | 0.122565 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.2221 | 1.15946 | 0.579730 | − | 0.814809i | \(-0.303158\pi\) | ||||
0.579730 | + | 0.814809i | \(0.303158\pi\) | |||||||
\(822\) | − 12.3361i | − 0.430270i | ||||||||
\(823\) | − 32.7898i | − 1.14298i | −0.820609 | − | 0.571490i | \(-0.806366\pi\) | ||||
0.820609 | − | 0.571490i | \(-0.193634\pi\) | |||||||
\(824\) | −7.99871 | −0.278648 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.01479 | −0.139692 | ||||||||
\(827\) | − 5.18915i | − 0.180444i | −0.995922 | − | 0.0902222i | \(-0.971242\pi\) | ||||
0.995922 | − | 0.0902222i | \(-0.0287577\pi\) | |||||||
\(828\) | − 3.76401i | − 0.130808i | ||||||||
\(829\) | 5.55820 | 0.193044 | 0.0965221 | − | 0.995331i | \(-0.469228\pi\) | ||||
0.0965221 | + | 0.995331i | \(0.469228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.4592 | −1.09131 | ||||||||
\(832\) | 6.57392i | 0.227910i | ||||||||
\(833\) | − 6.43605i | − 0.222996i | ||||||||
\(834\) | −4.53918 | −0.157179 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.305337 | −0.0105603 | ||||||||
\(837\) | − 2.33773i | − 0.0808037i | ||||||||
\(838\) | 23.1294i | 0.798991i | ||||||||
\(839\) | −43.4383 | −1.49966 | −0.749828 | − | 0.661633i | \(-0.769864\pi\) | ||||
−0.749828 | + | 0.661633i | \(0.769864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.37160 | 0.323159 | ||||||||
\(842\) | 9.76139i | 0.336400i | ||||||||
\(843\) | 10.7785i | 0.371232i | ||||||||
\(844\) | −5.24920 | −0.180685 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.1489 | 0.348927 | ||||||||
\(847\) | 4.77158i | 0.163953i | ||||||||
\(848\) | 3.23354i | 0.111040i | ||||||||
\(849\) | 4.16428 | 0.142918 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.2928 | 0.524231 | ||||||||
\(852\) | 10.1247i | 0.346865i | ||||||||
\(853\) | 3.34342i | 0.114477i | 0.998361 | + | 0.0572383i | \(0.0182295\pi\) | ||||
−0.998361 | + | 0.0572383i | \(0.981771\pi\) | |||||||
\(854\) | 6.70794 | 0.229541 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9260 | 0.646877 | ||||||||
\(857\) | 34.5415i | 1.17991i | 0.807434 | + | 0.589957i | \(0.200855\pi\) | ||||
−0.807434 | + | 0.589957i | \(0.799145\pi\) | |||||||
\(858\) | 9.42867i | 0.321889i | ||||||||
\(859\) | 23.8513 | 0.813796 | 0.406898 | − | 0.913474i | \(-0.366610\pi\) | ||||
0.406898 | + | 0.913474i | \(0.366610\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.23729 | 0.144407 | ||||||||
\(862\) | 8.49298i | 0.289272i | ||||||||
\(863\) | 5.73061i | 0.195072i | 0.995232 | + | 0.0975361i | \(0.0310962\pi\) | ||||
−0.995232 | + | 0.0975361i | \(0.968904\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.0042 | 0.747733 | ||||||||
\(867\) | − 16.0814i | − 0.546154i | ||||||||
\(868\) | − 1.24732i | − 0.0423367i | ||||||||
\(869\) | 22.2710 | 0.755492 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.4445 | −1.53983 | ||||||||
\(872\) | − 2.65524i | − 0.0899178i | ||||||||
\(873\) | 5.56558i | 0.188366i | ||||||||
\(874\) | −0.801317 | −0.0271049 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.9771 | −0.472242 | ||||||||
\(877\) | − 49.8482i | − 1.68325i | −0.540059 | − | 0.841627i | \(-0.681598\pi\) | ||||
0.540059 | − | 0.841627i | \(-0.318402\pi\) | |||||||
\(878\) | 38.3582i | 1.29453i | ||||||||
\(879\) | 17.9603 | 0.605786 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.65609 | −0.257940 | −0.128970 | − | 0.991648i | \(-0.541167\pi\) | ||||
−0.128970 | + | 0.991648i | \(0.541167\pi\) | |||||||
\(882\) | − 6.71531i | − 0.226116i | ||||||||
\(883\) | 38.9959i | 1.31232i | 0.754623 | + | 0.656158i | \(0.227820\pi\) | ||||
−0.754623 | + | 0.656158i | \(0.772180\pi\) | |||||||
\(884\) | 6.30054 | 0.211910 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.7478 | 0.428270 | ||||||||
\(887\) | 32.5338i | 1.09238i | 0.837662 | + | 0.546189i | \(0.183922\pi\) | ||||
−0.837662 | + | 0.546189i | \(0.816078\pi\) | |||||||
\(888\) | − 4.06291i | − 0.136342i | ||||||||
\(889\) | −3.45884 | −0.116006 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.43425 | −0.0480493 | ||||||||
\(892\) | − 19.2782i | − 0.645483i | ||||||||
\(893\) | − 2.16059i | − 0.0723015i | ||||||||
\(894\) | −11.0750 | −0.370405 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.533559 | −0.0178250 | ||||||||
\(897\) | 24.7443i | 0.826189i | ||||||||
\(898\) | − 18.0358i | − 0.601862i | ||||||||
\(899\) | 14.4810 | 0.482969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.09907 | 0.103245 | ||||||||
\(902\) | 11.3902i | 0.379253i | ||||||||
\(903\) | − 6.06163i | − 0.201718i | ||||||||
\(904\) | −3.06283 | −0.101868 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.63387 | −0.0542817 | ||||||||
\(907\) | − 16.5820i | − 0.550595i | −0.961359 | − | 0.275297i | \(-0.911224\pi\) | ||||
0.961359 | − | 0.275297i | \(-0.0887763\pi\) | |||||||
\(908\) | − 8.43957i | − 0.280077i | ||||||||
\(909\) | 9.42708 | 0.312676 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5720 | −0.946633 | −0.473316 | − | 0.880893i | \(-0.656943\pi\) | ||||
−0.473316 | + | 0.880893i | \(0.656943\pi\) | |||||||
\(912\) | 0.212889i | 0.00704946i | ||||||||
\(913\) | 23.4225i | 0.775173i | ||||||||
\(914\) | 21.1495 | 0.699565 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.95568 | 0.196781 | ||||||||
\(917\) | 5.04637i | 0.166646i | ||||||||
\(918\) | 0.958413i | 0.0316324i | ||||||||
\(919\) | 0.382861 | 0.0126294 | 0.00631471 | − | 0.999980i | \(-0.497990\pi\) | ||||
0.00631471 | + | 0.999980i | \(0.497990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.8174 | −0.685957 | ||||||||
\(922\) | 32.0085i | 1.05414i | ||||||||
\(923\) | − 66.5588i | − 2.19081i | ||||||||
\(924\) | −0.765259 | −0.0251752 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.7776 | 0.945689 | ||||||||
\(927\) | 7.99871i | 0.262712i | ||||||||
\(928\) | − 6.19448i | − 0.203344i | ||||||||
\(929\) | 6.25711 | 0.205289 | 0.102645 | − | 0.994718i | \(-0.467270\pi\) | ||||
0.102645 | + | 0.994718i | \(0.467270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.42962 | −0.0468538 | ||||||||
\(932\) | − 2.09293i | − 0.0685561i | ||||||||
\(933\) | 19.4526i | 0.636849i | ||||||||
\(934\) | −5.20326 | −0.170256 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.57392 | 0.214875 | ||||||||
\(937\) | 4.93214i | 0.161126i | 0.996750 | + | 0.0805630i | \(0.0256718\pi\) | ||||
−0.996750 | + | 0.0805630i | \(0.974328\pi\) | |||||||
\(938\) | − 3.68841i | − 0.120431i | ||||||||
\(939\) | −5.88310 | −0.191988 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.8107 | 0.971801 | 0.485901 | − | 0.874014i | \(-0.338492\pi\) | ||||
0.485901 | + | 0.874014i | \(0.338492\pi\) | |||||||
\(942\) | 6.64544i | 0.216520i | ||||||||
\(943\) | 29.8921i | 0.973422i | ||||||||
\(944\) | −7.52455 | −0.244903 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.2942 | 0.529769 | ||||||||
\(947\) | 26.9125i | 0.874539i | 0.899330 | + | 0.437270i | \(0.144054\pi\) | ||||
−0.899330 | + | 0.437270i | \(0.855946\pi\) | |||||||
\(948\) | − 15.5279i | − 0.504324i | ||||||||
\(949\) | 91.8843 | 2.98269 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.7610 | −0.348950 | ||||||||
\(952\) | 0.511370i | 0.0165736i | ||||||||
\(953\) | 37.2337i | 1.20612i | 0.797697 | + | 0.603059i | \(0.206051\pi\) | ||||
−0.797697 | + | 0.603059i | \(0.793949\pi\) | |||||||
\(954\) | 3.23354 | 0.104690 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.89840 | 0.320137 | ||||||||
\(957\) | − 8.88445i | − 0.287194i | ||||||||
\(958\) | 39.6385i | 1.28066i | ||||||||
\(959\) | −6.58203 | −0.212545 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5350 | −0.823710 | ||||||||
\(962\) | 26.7093i | 0.861141i | ||||||||
\(963\) | − 18.9260i | − 0.609882i | ||||||||
\(964\) | 21.4567 | 0.691074 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.00832 | −0.0646167 | ||||||||
\(967\) | − 16.0845i | − 0.517244i | −0.965979 | − | 0.258622i | \(-0.916732\pi\) | ||||
0.965979 | − | 0.258622i | \(-0.0832683\pi\) | |||||||
\(968\) | 8.94292i | 0.287436i | ||||||||
\(969\) | 0.204036 | 0.00655457 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2569 | 0.393342 | 0.196671 | − | 0.980470i | \(-0.436987\pi\) | ||||
0.196671 | + | 0.980470i | \(0.436987\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 2.42192i | 0.0776431i | ||||||||
\(974\) | 5.44308 | 0.174407 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.5721 | 0.402422 | ||||||||
\(977\) | − 18.0218i | − 0.576569i | −0.957545 | − | 0.288285i | \(-0.906915\pi\) | ||||
0.957545 | − | 0.288285i | \(-0.0930849\pi\) | |||||||
\(978\) | 10.1134i | 0.323391i | ||||||||
\(979\) | 8.06365 | 0.257715 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.65524 | −0.0847753 | ||||||||
\(982\) | 0.873965i | 0.0278893i | ||||||||
\(983\) | 49.4029i | 1.57571i | 0.615862 | + | 0.787854i | \(0.288808\pi\) | ||||
−0.615862 | + | 0.787854i | \(0.711192\pi\) | |||||||
\(984\) | 7.94156 | 0.253168 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.93687 | −0.189069 | ||||||||
\(987\) | − 5.41505i | − 0.172363i | ||||||||
\(988\) | − 1.39952i | − 0.0445246i | ||||||||
\(989\) | 42.7619 | 1.35975 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.5664 | −0.970972 | −0.485486 | − | 0.874244i | \(-0.661357\pi\) | ||||
−0.485486 | + | 0.874244i | \(0.661357\pi\) | |||||||
\(992\) | − 2.33773i | − 0.0742230i | ||||||||
\(993\) | 0.617092i | 0.0195828i | ||||||||
\(994\) | 5.40211 | 0.171345 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.3308 | 0.517462 | ||||||||
\(997\) | − 6.81050i | − 0.215691i | −0.994168 | − | 0.107845i | \(-0.965605\pi\) | ||||
0.994168 | − | 0.107845i | \(-0.0343952\pi\) | |||||||
\(998\) | 34.9604i | 1.10665i | ||||||||
\(999\) | −4.06291 | −0.128545 |
(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 | 3750.2.c.k.1249.11 | 16 | ||
5.2 | odd | 4 | 3750.2.a.u.1.6 | 8 | |||
5.3 | odd | 4 | 3750.2.a.v.1.3 | 8 | |||
5.4 | even | 2 | inner | 3750.2.c.k.1249.6 | 16 | ||
25.3 | odd | 20 | 750.2.g.f.451.2 | 16 | |||
25.4 | even | 10 | 750.2.h.d.49.2 | 16 | |||
25.6 | even | 5 | 750.2.h.d.199.1 | 16 | |||
25.8 | odd | 20 | 750.2.g.f.301.2 | 16 | |||
25.17 | odd | 20 | 750.2.g.g.301.3 | 16 | |||
25.19 | even | 10 | 150.2.h.b.139.3 | yes | 16 | ||
25.21 | even | 5 | 150.2.h.b.109.3 | ✓ | 16 | ||
25.22 | odd | 20 | 750.2.g.g.451.3 | 16 | |||
75.44 | odd | 10 | 450.2.l.c.289.2 | 16 | |||
75.71 | odd | 10 | 450.2.l.c.109.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.b.109.3 | ✓ | 16 | 25.21 | even | 5 | ||
150.2.h.b.139.3 | yes | 16 | 25.19 | even | 10 | ||
450.2.l.c.109.2 | 16 | 75.71 | odd | 10 | |||
450.2.l.c.289.2 | 16 | 75.44 | odd | 10 | |||
750.2.g.f.301.2 | 16 | 25.8 | odd | 20 | |||
750.2.g.f.451.2 | 16 | 25.3 | odd | 20 | |||
750.2.g.g.301.3 | 16 | 25.17 | odd | 20 | |||
750.2.g.g.451.3 | 16 | 25.22 | odd | 20 | |||
750.2.h.d.49.2 | 16 | 25.4 | even | 10 | |||
750.2.h.d.199.1 | 16 | 25.6 | even | 5 | |||
3750.2.a.u.1.6 | 8 | 5.2 | odd | 4 | |||
3750.2.a.v.1.3 | 8 | 5.3 | odd | 4 | |||
3750.2.c.k.1249.6 | 16 | 5.4 | even | 2 | inner | ||
3750.2.c.k.1249.11 | 16 | 1.1 | even | 1 | trivial |