Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.08546 | −1.20404 | −0.602019 | − | 0.798482i | \(-0.705637\pi\) | ||||
−0.602019 | + | 0.798482i | \(0.705637\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.642029 | −0.287124 | −0.143562 | − | 0.989641i | \(-0.545856\pi\) | ||||
−0.143562 | + | 0.989641i | \(0.545856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.54125 | 0.582540 | 0.291270 | − | 0.956641i | \(-0.405922\pi\) | ||||
0.291270 | + | 0.956641i | \(0.405922\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.34913 | 0.449709 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0501981 | −0.0151353 | −0.00756765 | − | 0.999971i | \(-0.502409\pi\) | ||||
−0.00756765 | + | 0.999971i | \(0.502409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.91068 | 1.63933 | 0.819664 | − | 0.572845i | \(-0.194160\pi\) | ||||
0.819664 | + | 0.572845i | \(0.194160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.33892 | 0.345709 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.47527 | 0.357805 | 0.178903 | − | 0.983867i | \(-0.442745\pi\) | ||||
0.178903 | + | 0.983867i | \(0.442745\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.81866 | −0.417230 | −0.208615 | − | 0.977998i | \(-0.566896\pi\) | ||||
−0.208615 | + | 0.977998i | \(0.566896\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.21422 | −0.701400 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0921709 | 0.0192190 | 0.00960948 | − | 0.999954i | \(-0.496941\pi\) | ||||
0.00960948 | + | 0.999954i | \(0.496941\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58780 | −0.917560 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.44283 | 0.662572 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4043 | −1.93203 | −0.966016 | − | 0.258481i | \(-0.916778\pi\) | ||||
−0.966016 | + | 0.258481i | \(0.916778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.864148 | −0.155206 | −0.0776028 | − | 0.996984i | \(-0.524727\pi\) | ||||
−0.0776028 | + | 0.996984i | \(0.524727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.104686 | 0.0182235 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.989531 | −0.167261 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.04976 | −1.15897 | −0.579487 | − | 0.814982i | \(-0.696747\pi\) | ||||
−0.579487 | + | 0.814982i | \(0.696747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.3265 | −1.97381 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.73678 | −1.36446 | −0.682228 | − | 0.731140i | \(-0.738989\pi\) | ||||
−0.682228 | + | 0.731140i | \(0.738989\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.81571 | −0.429392 | −0.214696 | − | 0.976681i | \(-0.568876\pi\) | ||||
−0.214696 | + | 0.976681i | \(0.568876\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.866178 | −0.129122 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2378 | 1.63920 | 0.819599 | − | 0.572938i | \(-0.194197\pi\) | ||||
0.819599 | + | 0.572938i | \(0.194197\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.62453 | −0.660648 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.07661 | −0.430811 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.08975 | 0.699131 | 0.349565 | − | 0.936912i | \(-0.386329\pi\) | ||||
0.349565 | + | 0.936912i | \(0.386329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0322287 | 0.00434571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.79274 | 0.502361 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.28163 | 0.557421 | 0.278710 | − | 0.960375i | \(-0.410093\pi\) | ||||
0.278710 | + | 0.960375i | \(0.410093\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7408 | 1.75933 | 0.879665 | − | 0.475593i | \(-0.157767\pi\) | ||||
0.879665 | + | 0.475593i | \(0.157767\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.07935 | 0.261973 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.79483 | −0.470691 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.92186 | −0.845640 | −0.422820 | − | 0.906214i | \(-0.638960\pi\) | ||||
−0.422820 | + | 0.906214i | \(0.638960\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.192218 | −0.0231404 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.95662 | 0.825599 | 0.412799 | − | 0.910822i | \(-0.364551\pi\) | ||||
0.412799 | + | 0.910822i | \(0.364551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.20107 | 1.07690 | 0.538452 | − | 0.842656i | \(-0.319009\pi\) | ||||
0.538452 | + | 0.842656i | \(0.319009\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.56765 | 1.10478 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0773681 | −0.00881692 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.91915 | −1.11599 | −0.557996 | − | 0.829844i | \(-0.688429\pi\) | ||||
−0.557996 | + | 0.829844i | \(0.688429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2272 | −1.24747 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.3935 | 1.79942 | 0.899711 | − | 0.436486i | \(-0.143777\pi\) | ||||
0.899711 | + | 0.436486i | \(0.143777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.947165 | −0.102735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.6977 | 2.32624 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60753 | 0.170398 | 0.0851991 | − | 0.996364i | \(-0.472847\pi\) | ||||
0.0851991 | + | 0.996364i | \(0.472847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.10986 | 0.954973 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.80214 | 0.186874 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.16764 | 0.119797 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.53207 | −0.358628 | −0.179314 | − | 0.983792i | \(-0.557388\pi\) | ||||
−0.179314 | + | 0.983792i | \(0.557388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0677236 | −0.00680648 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.43385 | −0.938704 | −0.469352 | − | 0.883011i | \(-0.655512\pi\) | ||||
−0.469352 | + | 0.883011i | \(0.655512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5896 | 1.04342 | 0.521712 | − | 0.853121i | \(-0.325293\pi\) | ||||
0.521712 | + | 0.853121i | \(0.325293\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.06362 | 0.201389 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.37416 | −0.616213 | −0.308107 | − | 0.951352i | \(-0.599695\pi\) | ||||
−0.308107 | + | 0.951352i | \(0.599695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.85130 | −0.368887 | −0.184444 | − | 0.982843i | \(-0.559048\pi\) | ||||
−0.184444 | + | 0.982843i | \(0.559048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.7020 | 1.39545 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.72562 | 0.444549 | 0.222275 | − | 0.974984i | \(-0.428652\pi\) | ||||
0.222275 | + | 0.974984i | \(0.428652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0591764 | −0.00551823 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.97425 | 0.737220 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.27376 | 0.208436 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9975 | −0.999771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.2202 | 1.64286 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.15565 | 0.550578 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.96695 | 0.263275 | 0.131637 | − | 0.991298i | \(-0.457977\pi\) | ||||
0.131637 | + | 0.991298i | \(0.457977\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.87204 | 0.517004 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4114 | −0.997017 | −0.498508 | − | 0.866885i | \(-0.666119\pi\) | ||||
−0.498508 | + | 0.866885i | \(0.666119\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.80302 | −0.243053 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.21040 | −0.190241 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.41797 | 0.462889 | 0.231444 | − | 0.972848i | \(-0.425655\pi\) | ||||
0.231444 | + | 0.972848i | \(0.425655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.4051 | −1.64592 | −0.822959 | − | 0.568101i | \(-0.807678\pi\) | ||||
−0.822959 | + | 0.568101i | \(0.807678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.4359 | −1.97366 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.296705 | −0.0248117 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.67988 | 0.554733 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.64426 | 0.795445 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0999 | −1.31895 | −0.659476 | − | 0.751725i | \(-0.729222\pi\) | ||||
−0.659476 | + | 0.751725i | \(0.729222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.26939 | −0.266059 | −0.133029 | − | 0.991112i | \(-0.542471\pi\) | ||||
−0.133029 | + | 0.991112i | \(0.542471\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.99032 | 0.160908 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.554809 | 0.0445633 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9713 | −1.03522 | −0.517609 | − | 0.855617i | \(-0.673178\pi\) | ||||
−0.517609 | + | 0.855617i | \(0.673178\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.6144 | −0.841780 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.142059 | 0.0111958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0026 | −1.09677 | −0.548385 | − | 0.836226i | \(-0.684757\pi\) | ||||
−0.548385 | + | 0.836226i | \(0.684757\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0672115 | −0.00523241 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.00593 | 0.387370 | 0.193685 | − | 0.981064i | \(-0.437956\pi\) | ||||
0.193685 | + | 0.981064i | \(0.437956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.9361 | 1.68740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.45361 | −0.187632 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.40960 | −0.639370 | −0.319685 | − | 0.947524i | \(-0.603577\pi\) | ||||
−0.319685 | + | 0.947524i | \(0.603577\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.07097 | −0.534515 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.92915 | −0.671156 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.34033 | 0.249668 | 0.124834 | − | 0.992178i | \(-0.460160\pi\) | ||||
0.124834 | + | 0.992178i | \(0.460160\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.1120 | −1.27192 | −0.635961 | − | 0.771721i | \(-0.719396\pi\) | ||||
−0.635961 | + | 0.771721i | \(0.719396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −28.6559 | −2.11830 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.52615 | 0.332769 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0740557 | −0.00541549 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.30627 | 0.385974 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3928 | 1.83736 | 0.918678 | − | 0.395006i | \(-0.129258\pi\) | ||||
0.918678 | + | 0.395006i | \(0.129258\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0475098 | 0.00341983 | 0.00170992 | − | 0.999999i | \(-0.499456\pi\) | ||||
0.00170992 | + | 0.999999i | \(0.499456\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.91395 | 0.566730 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.8514 | 0.986872 | 0.493436 | − | 0.869782i | \(-0.335741\pi\) | ||||
0.493436 | + | 0.869782i | \(0.335741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.23782 | −0.229523 | −0.114761 | − | 0.993393i | \(-0.536610\pi\) | ||||
−0.114761 | + | 0.993393i | \(0.536610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.4352 | 1.01818 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0357 | −1.12549 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.60927 | 0.391768 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.124350 | 0.00864293 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0912936 | 0.00631491 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.4682 | −1.34025 | −0.670124 | − | 0.742249i | \(-0.733759\pi\) | ||||
−0.670124 | + | 0.742249i | \(0.733759\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.5077 | −0.994052 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.80777 | 0.123289 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.33187 | −0.0904134 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.1884 | −1.29663 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.71984 | 0.586560 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.90612 | 0.194608 | 0.0973041 | − | 0.995255i | \(-0.468978\pi\) | ||||
0.0973041 | + | 0.995255i | \(0.468978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.18952 | −0.412634 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.03346 | −0.201338 | −0.100669 | − | 0.994920i | \(-0.532098\pi\) | ||||
−0.100669 | + | 0.994920i | \(0.532098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.8418 | −1.24510 | −0.622550 | − | 0.782580i | \(-0.713903\pi\) | ||||
−0.622550 | + | 0.782580i | \(0.713903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.161348 | 0.0106159 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.18903 | −0.0778959 | −0.0389480 | − | 0.999241i | \(-0.512401\pi\) | ||||
−0.0389480 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.21498 | −0.470653 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.6859 | 1.34370 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.22584 | −0.402716 | −0.201358 | − | 0.979518i | \(-0.564535\pi\) | ||||
−0.201358 | + | 0.979518i | \(0.564535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1906 | 0.720851 | 0.360425 | − | 0.932788i | \(-0.382632\pi\) | ||||
0.360425 | + | 0.932788i | \(0.382632\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.0854 | 0.839431 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.96909 | 0.189688 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.7495 | −0.683977 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −34.1880 | −2.16657 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.07544 | −0.257239 | −0.128620 | − | 0.991694i | \(-0.541055\pi\) | ||||
−0.128620 | + | 0.991694i | \(0.541055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.00462681 | −0.000290885 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.97527 | 0.123696 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.9796 | −1.30867 | −0.654334 | − | 0.756205i | \(-0.727051\pi\) | ||||
−0.654334 | + | 0.756205i | \(0.727051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.8655 | −0.675148 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.0367 | −0.868852 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.9152 | 1.41301 | 0.706507 | − | 0.707706i | \(-0.250270\pi\) | ||||
0.706507 | + | 0.707706i | \(0.250270\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.26777 | −0.200737 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.35244 | −0.205166 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.45474 | 0.576465 | 0.288233 | − | 0.957560i | \(-0.406932\pi\) | ||||
0.288233 | + | 0.957560i | \(0.406932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.6847 | 1.68173 | 0.840863 | − | 0.541249i | \(-0.182048\pi\) | ||||
0.840863 | + | 0.541249i | \(0.182048\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.9982 | −1.14982 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.230299 | 0.0138875 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.57740 | −0.335114 | −0.167557 | − | 0.985862i | \(-0.553588\pi\) | ||||
−0.167557 | + | 0.985862i | \(0.553588\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.16584 | −0.0697973 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.1712 | −1.32262 | −0.661312 | − | 0.750111i | \(-0.730000\pi\) | ||||
−0.661312 | + | 0.750111i | \(0.730000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9925 | 0.772325 | 0.386163 | − | 0.922431i | \(-0.373800\pi\) | ||||
0.386163 | + | 0.922431i | \(0.373800\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.43505 | −0.144240 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4656 | −0.794849 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8236 | −0.871976 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.36598 | 0.431802 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.0045 | 0.934992 | 0.467496 | − | 0.883995i | \(-0.345156\pi\) | ||||
0.467496 | + | 0.883995i | \(0.345156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.74893 | −0.160049 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.172823 | −0.0100282 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.544793 | 0.0315062 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.33973 | −0.250138 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.6739 | 1.13024 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.82200 | −0.505147 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.6056 | −1.74675 | −0.873377 | − | 0.487045i | \(-0.838075\pi\) | ||||
−0.873377 | + | 0.487045i | \(0.838075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.0842 | −1.25632 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.17447 | −0.0665979 | −0.0332990 | − | 0.999445i | \(-0.510601\pi\) | ||||
−0.0332990 | + | 0.999445i | \(0.510601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.3467 | −1.54573 | −0.772863 | − | 0.634572i | \(-0.781176\pi\) | ||||
−0.772863 | + | 0.634572i | \(0.781176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.33500 | −0.0752188 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.6836 | −0.656219 | −0.328110 | − | 0.944640i | \(-0.606412\pi\) | ||||
−0.328110 | + | 0.944640i | \(0.606412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.522277 | 0.0292419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.2930 | 0.741945 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.68302 | −0.149287 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.1170 | −1.50418 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.03171 | 0.444154 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.3203 | 0.954897 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.9504 | −1.42636 | −0.713181 | − | 0.700980i | \(-0.752746\pi\) | ||||
−0.713181 | + | 0.700980i | \(0.752746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.51101 | −0.521200 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.44404 | 0.242804 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4647 | −1.11478 | −0.557392 | − | 0.830249i | \(-0.688198\pi\) | ||||
−0.557392 | + | 0.830249i | \(0.688198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.85508 | −0.535254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0433786 | 0.00234908 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.9164 | −0.967393 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.123410 | 0.00664416 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.34715 | −0.287050 | −0.143525 | − | 0.989647i | \(-0.545844\pi\) | ||||
−0.143525 | + | 0.989647i | \(0.545844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.8729 | 1.54553 | 0.772766 | − | 0.634692i | \(-0.218873\pi\) | ||||
0.772766 | + | 0.634692i | \(0.218873\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.3494 | 1.08617 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9605 | 0.689820 | 0.344910 | − | 0.938636i | \(-0.387909\pi\) | ||||
0.344910 | + | 0.938636i | \(0.387909\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.46635 | −0.237049 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.74183 | −0.250964 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.1233 | −1.37874 | −0.689368 | − | 0.724411i | \(-0.742112\pi\) | ||||
−0.689368 | + | 0.724411i | \(0.742112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6925 | −0.825919 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.9348 | 1.20376 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.90736 | −0.309205 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.97620 | 0.468554 | 0.234277 | − | 0.972170i | \(-0.424728\pi\) | ||||
0.234277 | + | 0.972170i | \(0.424728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.7870 | −0.613607 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.84460 | 0.407271 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7106 | −0.761688 | −0.380844 | − | 0.924639i | \(-0.624367\pi\) | ||||
−0.380844 | + | 0.924639i | \(0.624367\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.8373 | −0.662917 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −61.4966 | −3.16723 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.1235 | 1.18777 | 0.593886 | − | 0.804549i | \(-0.297593\pi\) | ||||
0.593886 | + | 0.804549i | \(0.297593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.18745 | −0.316993 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.17455 | 0.417700 | 0.208850 | − | 0.977948i | \(-0.433028\pi\) | ||||
0.208850 | + | 0.977948i | \(0.433028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0496726 | 0.00253155 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.79875 | −0.193101 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7191 | −0.543480 | −0.271740 | − | 0.962371i | \(-0.587599\pi\) | ||||
−0.271740 | + | 0.962371i | \(0.587599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.135977 | 0.00687664 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.7979 | 1.20045 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.36838 | 0.320428 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.2188 | −1.16532 | −0.582658 | − | 0.812717i | \(-0.697987\pi\) | ||||
−0.582658 | + | 0.812717i | \(0.697987\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.84558 | 0.292645 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.80075 | 0.289676 | 0.144838 | − | 0.989455i | \(-0.453734\pi\) | ||||
0.144838 | + | 0.989455i | \(0.453734\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.10770 | −0.254433 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.20822 | 0.358179 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.353885 | 0.0175414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.4473 | 1.65386 | 0.826931 | − | 0.562304i | \(-0.190085\pi\) | ||||
0.826931 | + | 0.562304i | \(0.190085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.2989 | −0.557336 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.59908 | 0.324720 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.5251 | −0.516658 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.4684 | 1.98175 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7263 | 0.963691 | 0.481846 | − | 0.876256i | \(-0.339967\pi\) | ||||
0.481846 | + | 0.876256i | \(0.339967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8019 | −0.965086 | −0.482543 | − | 0.875872i | \(-0.660287\pi\) | ||||
−0.482543 | + | 0.875872i | \(0.660287\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.1612 | 0.737161 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.76823 | −0.328307 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.1781 | 1.02488 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.618765 | 0.0298743 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.65053 | −0.127672 | −0.0638358 | − | 0.997960i | \(-0.520333\pi\) | ||||
−0.0638358 | + | 0.997960i | \(0.520333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.1746 | −0.777303 | −0.388651 | − | 0.921385i | \(-0.627059\pi\) | ||||
−0.388651 | + | 0.921385i | \(0.627059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.9306 | −0.667920 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.167628 | −0.00801873 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.28436 | 0.395391 | 0.197695 | − | 0.980263i | \(-0.436654\pi\) | ||||
0.197695 | + | 0.980263i | \(0.436654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.23908 | −0.297099 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.99960 | −0.427584 | −0.213792 | − | 0.976879i | \(-0.568581\pi\) | ||||
−0.213792 | + | 0.976879i | \(0.568581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.03208 | −0.0489255 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 33.5756 | 1.58807 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.80196 | 0.273811 | 0.136906 | − | 0.990584i | \(-0.456284\pi\) | ||||
0.136906 | + | 0.990584i | \(0.456284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.438570 | 0.0206514 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.81816 | 0.320345 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.84880 | −0.274196 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.2264 | −0.571928 | −0.285964 | − | 0.958240i | \(-0.592314\pi\) | ||||
−0.285964 | + | 0.958240i | \(0.592314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.07909 | 0.237072 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.32633 | −0.387796 | −0.193898 | − | 0.981022i | \(-0.562113\pi\) | ||||
−0.193898 | + | 0.981022i | \(0.562113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.7604 | 1.10424 | 0.552120 | − | 0.833765i | \(-0.313819\pi\) | ||||
0.552120 | + | 0.833765i | \(0.313819\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.15703 | −0.0536559 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.21135 | −0.379976 | −0.189988 | − | 0.981786i | \(-0.560845\pi\) | ||||
−0.189988 | + | 0.981786i | \(0.560845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6684 | −0.492619 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.0510 | 1.24644 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.141343 | 0.00649898 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.34366 | 0.382834 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.86671 | 0.314405 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.98344 | −0.273390 | −0.136695 | − | 0.990613i | \(-0.543648\pi\) | ||||
−0.136695 | + | 0.990613i | \(0.543648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.6689 | −1.89994 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.296257 | −0.0134802 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.26769 | 0.102971 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.7539 | −1.12170 | −0.560852 | − | 0.827916i | \(-0.689526\pi\) | ||||
−0.560852 | + | 0.827916i | \(0.689526\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.2019 | 1.32055 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.2139 | −1.27328 | −0.636638 | − | 0.771163i | \(-0.719676\pi\) | ||||
−0.636638 | + | 0.771163i | \(0.719676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.3492 | −0.691291 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0434805 | 0.00195430 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.7219 | 0.480944 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.9382 | 1.47452 | 0.737258 | − | 0.675611i | \(-0.236120\pi\) | ||||
0.737258 | + | 0.675611i | \(0.236120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.4396 | −0.466409 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.83380 | 0.215529 | 0.107764 | − | 0.994176i | \(-0.465631\pi\) | ||||
0.107764 | + | 0.994176i | \(0.465631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.05681 | 0.269525 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −45.7469 | −2.03169 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.3878 | −0.770701 | −0.385350 | − | 0.922770i | \(-0.625919\pi\) | ||||
−0.385350 | + | 0.922770i | \(0.625919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.1812 | 0.627339 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.26134 | −0.276445 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.79884 | −0.299593 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.564115 | −0.0248098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.5378 | 0.769826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.4075 | −1.72647 | −0.863236 | − | 0.504800i | \(-0.831566\pi\) | ||||
−0.863236 | + | 0.504800i | \(0.831566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0790 | 0.746811 | 0.373406 | − | 0.927668i | \(-0.378190\pi\) | ||||
0.373406 | + | 0.927668i | \(0.378190\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.7462 | 0.643576 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.27485 | −0.0555334 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9915 | −0.999631 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.77645 | 0.250677 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −51.6403 | −2.23679 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.09240 | 0.176930 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.96611 | −0.300610 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.232143 | 0.00999911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.5944 | −1.74529 | −0.872645 | − | 0.488356i | \(-0.837597\pi\) | ||||
−0.872645 | + | 0.488356i | \(0.837597\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.6863 | 1.53144 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.47264 | 0.105916 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.9615 | −0.939008 | −0.469504 | − | 0.882930i | \(-0.655567\pi\) | ||||
−0.469504 | + | 0.882930i | \(0.655567\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.5381 | 0.791186 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.9220 | 0.806102 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.2879 | −0.650109 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.43909 | −0.400667 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.0017 | 1.69493 | 0.847464 | − | 0.530853i | \(-0.178128\pi\) | ||||
0.847464 | + | 0.530853i | \(0.178128\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.6428 | −0.703914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.154440 | 0.00652046 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.22300 | 0.304413 | 0.152206 | − | 0.988349i | \(-0.451362\pi\) | ||||
0.152206 | + | 0.988349i | \(0.451362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.03399 | −0.127641 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.3040 | −0.726701 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.0952 | −1.68088 | −0.840438 | − | 0.541907i | \(-0.817702\pi\) | ||||
−0.840438 | + | 0.541907i | \(0.817702\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3778 | −1.60606 | −0.803030 | − | 0.595939i | \(-0.796780\pi\) | ||||
−0.803030 | + | 0.595939i | \(0.796780\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −52.9555 | −2.21225 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.422861 | −0.0176345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.0470 | 1.54229 | 0.771143 | − | 0.636662i | \(-0.219685\pi\) | ||||
0.771143 | + | 0.636662i | \(0.219685\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.0990796 | −0.00411761 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.2666 | 1.04823 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.255496 | −0.0105816 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.11970 | −0.211674 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.3856 | 0.469935 | 0.234967 | − | 0.972003i | \(-0.424502\pi\) | ||||
0.234967 | + | 0.972003i | \(0.424502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.57160 | 0.0647565 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.8865 | −1.18823 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.1895 | −0.705890 | −0.352945 | − | 0.935644i | \(-0.614820\pi\) | ||||
−0.352945 | + | 0.935644i | \(0.614820\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.45982 | −0.0598469 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.75233 | 0.276354 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.96812 | 0.366428 | 0.183214 | − | 0.983073i | \(-0.441350\pi\) | ||||
0.183214 | + | 0.983073i | \(0.441350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.4485 | 0.956485 | 0.478242 | − | 0.878228i | \(-0.341274\pi\) | ||||
0.478242 | + | 0.878228i | \(0.341274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.33846 | −0.380292 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.06071 | 0.287058 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.5102 | −0.426595 | −0.213298 | − | 0.976987i | \(-0.568420\pi\) | ||||
−0.213298 | + | 0.976987i | \(0.568420\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.4417 | 1.35513 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 66.4229 | 2.68718 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.85872 | 0.398190 | 0.199095 | − | 0.979980i | \(-0.436200\pi\) | ||||
0.199095 | + | 0.979980i | \(0.436200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.6979 | −0.471704 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0795 | 0.566819 | 0.283409 | − | 0.958999i | \(-0.408534\pi\) | ||||
0.283409 | + | 0.958999i | \(0.408534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.0924 | 1.16932 | 0.584660 | − | 0.811278i | \(-0.301228\pi\) | ||||
0.584660 | + | 0.811278i | \(0.301228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.317328 | 0.0127339 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.47762 | 0.0992637 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.9869 | 0.759475 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.190389 | −0.00760339 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.4003 | −0.414687 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.88008 | −0.353511 | −0.176755 | − | 0.984255i | \(-0.556560\pi\) | ||||
−0.176755 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 40.6001 | 1.61371 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.90487 | −0.0755925 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.3341 | −1.08302 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.38535 | 0.371279 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.6249 | −1.05162 | −0.525810 | − | 0.850602i | \(-0.676238\pi\) | ||||
−0.525810 | + | 0.850602i | \(0.676238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.1245 | −0.951379 | −0.475689 | − | 0.879613i | \(-0.657801\pi\) | ||||
−0.475689 | + | 0.879613i | \(0.657801\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.77002 | −0.148444 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.26986 | 0.246493 | 0.123247 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123247 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.214930 | −0.00843673 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.77756 | 0.108861 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.8395 | 0.502448 | 0.251224 | − | 0.967929i | \(-0.419167\pi\) | ||||
0.251224 | + | 0.967929i | \(0.419167\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.32644 | 0.286268 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.4134 | 0.484293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.1704 | −1.91541 | −0.957703 | − | 0.287758i | \(-0.907090\pi\) | ||||
−0.957703 | + | 0.287758i | \(0.907090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.6539 | −1.27009 | −0.635045 | − | 0.772475i | \(-0.719019\pi\) | ||||
−0.635045 | + | 0.772475i | \(0.719019\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.1848 | −0.706241 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.79962 | 0.0697864 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.958975 | −0.0371317 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.06058 | −0.234316 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.689763 | −0.0266280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7798 | −1.22502 | −0.612511 | − | 0.790462i | \(-0.709840\pi\) | ||||
−0.612511 | + | 0.790462i | \(0.709840\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.7950 | −0.607949 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.5105 | −1.05732 | −0.528658 | − | 0.848835i | \(-0.677305\pi\) | ||||
−0.528658 | + | 0.848835i | \(0.677305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.44382 | −0.208915 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.32614 | 0.242418 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.8314 | −1.21799 | −0.608997 | − | 0.793173i | \(-0.708428\pi\) | ||||
−0.608997 | + | 0.793173i | \(0.708428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.47850 | −0.132907 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.2937 | 1.49915 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.0839 | 1.14610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6656 | −0.710074 | −0.355037 | − | 0.934852i | \(-0.615532\pi\) | ||||
−0.355037 | + | 0.934852i | \(0.615532\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.104379 | −0.00396504 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.4586 | 0.472583 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.8891 | −0.488209 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.47967 | 0.0937897 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.8342 | 1.58006 | 0.790029 | − | 0.613070i | \(-0.210066\pi\) | ||||
0.790029 | + | 0.613070i | \(0.210066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.8211 | 0.483559 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.0465 | 0.566685 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.5400 | −0.546832 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.1050 | 1.35595 | 0.677976 | − | 0.735084i | \(-0.262857\pi\) | ||||
0.677976 | + | 0.735084i | \(0.262857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.3822 | −0.501871 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.0796493 | −0.00298289 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.190493 | 0.00712405 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9837 | 0.484886 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.8607 | −1.89678 | −0.948392 | − | 0.317101i | \(-0.897291\pi\) | ||||
−0.948392 | + | 0.317101i | \(0.897291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.3213 | 0.607836 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.3375 | −0.867932 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 47.7329 | 1.77276 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.40123 | −0.274497 | −0.137248 | − | 0.990537i | \(-0.543826\pi\) | ||||
−0.137248 | + | 0.990537i | \(0.543826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.39263 | 0.236764 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.15393 | −0.153639 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.86308 | −0.290430 | −0.145215 | − | 0.989400i | \(-0.546387\pi\) | ||||
−0.145215 | + | 0.989400i | \(0.546387\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.19190 | −0.228392 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.347465 | 0.0127990 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.7204 | −0.394357 | −0.197179 | − | 0.980368i | \(-0.563178\pi\) | ||||
−0.197179 | + | 0.980368i | \(0.563178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.4177 | 0.823535 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.6548 | 1.78497 | 0.892485 | − | 0.451077i | \(-0.148960\pi\) | ||||
0.892485 | + | 0.451077i | \(0.148960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3366 | 0.378703 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.1169 | 0.809216 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.82421 | −0.358969 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.49914 | 0.309726 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.09904 | 0.0763920 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0966 | −0.548695 | −0.274347 | − | 0.961631i | \(-0.588462\pi\) | ||||
−0.274347 | + | 0.961631i | \(0.588462\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.00964900 | 0.000350237 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.7099 | 0.931982 | 0.465991 | − | 0.884789i | \(-0.345698\pi\) | ||||
0.465991 | + | 0.884789i | \(0.345698\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.93583 | −0.214891 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.27785 | −0.0462006 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.3073 | 0.913795 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.1074 | 0.905397 | 0.452699 | − | 0.891664i | \(-0.350461\pi\) | ||||
0.452699 | + | 0.891664i | \(0.350461\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.7519 | 1.57569 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.2918 | −0.765814 | −0.382907 | − | 0.923787i | \(-0.625077\pi\) | ||||
−0.382907 | + | 0.923787i | \(0.625077\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.96454 | 0.142410 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.6595 | 0.812904 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.8893 | 0.569292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.349209 | −0.0124957 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.8202 | −1.28011 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.32792 | 0.297236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.5407 | 1.87287 | 0.936436 | − | 0.350838i | \(-0.114103\pi\) | ||||
0.936436 | + | 0.350838i | \(0.114103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −47.7887 | −1.70132 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.28339 | 0.258968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 81.2175 | 2.88412 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.81479 | 0.241696 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.2143 | 0.538917 | 0.269459 | − | 0.963012i | \(-0.413155\pi\) | ||||
0.269459 | + | 0.963012i | \(0.413155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.5787 | 0.586513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.16877 | 0.0766296 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.461876 | −0.0162993 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0912059 | −0.00321459 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.7174 | −0.694087 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.6243 | 1.28764 | 0.643822 | − | 0.765176i | \(-0.277348\pi\) | ||||
0.643822 | + | 0.765176i | \(0.277348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.4004 | −0.962160 | −0.481080 | − | 0.876677i | \(-0.659755\pi\) | ||||
−0.481080 | + | 0.876677i | \(0.659755\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −57.7352 | −2.02486 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.99010 | 0.314910 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.12083 | 0.179155 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.2904 | 0.429460 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.4789 | −1.02882 | −0.514411 | − | 0.857544i | \(-0.671989\pi\) | ||||
−0.514411 | + | 0.857544i | \(0.671989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.7350 | −1.21079 | −0.605393 | − | 0.795926i | \(-0.706984\pi\) | ||||
−0.605393 | + | 0.795926i | \(0.706984\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.480278 | −0.0167211 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.67951 | 0.267043 | 0.133521 | − | 0.991046i | \(-0.457372\pi\) | ||||
0.133521 | + | 0.991046i | \(0.457372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.3990 | 1.15999 | 0.579997 | − | 0.814618i | \(-0.303054\pi\) | ||||
0.579997 | + | 0.814618i | \(0.303054\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.6314 | 0.403490 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.82243 | −0.236383 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.21395 | −0.111223 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.97511 | −0.102835 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.4432 | −0.912922 | −0.456461 | − | 0.889743i | \(-0.650883\pi\) | ||||
−0.456461 | + | 0.889743i | \(0.650883\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.2498 | 2.73275 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46.2371 | 1.59249 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.0836 | −0.484492 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.9499 | −0.582406 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.0953 | −0.929909 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.649783 | −0.0222743 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.50180 | −0.119899 | −0.0599497 | − | 0.998201i | \(-0.519094\pi\) | ||||
−0.0599497 | + | 0.998201i | \(0.519094\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.57529 | 0.0538737 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.3142 | 0.933037 | 0.466518 | − | 0.884512i | \(-0.345508\pi\) | ||||
0.466518 | + | 0.884512i | \(0.345508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.8721 | −1.22394 | −0.611970 | − | 0.790881i | \(-0.709623\pi\) | ||||
−0.611970 | + | 0.790881i | \(0.709623\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.0819 | 0.957029 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.2786 | 1.40514 | 0.702570 | − | 0.711615i | \(-0.252036\pi\) | ||||
0.702570 | + | 0.711615i | \(0.252036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.39921 | 0.183579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.9139 | 1.04989 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.497923 | 0.0168909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.9129 | −1.38628 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.76521 | −0.161278 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.48742 | 0.320733 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.1733 | 0.681203 | 0.340602 | − | 0.940208i | \(-0.389369\pi\) | ||||
0.340602 | + | 0.940208i | \(0.389369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.3766 | −1.12577 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.4979 | −0.656901 | −0.328451 | − | 0.944521i | \(-0.606526\pi\) | ||||
−0.328451 | + | 0.944521i | \(0.606526\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.4599 | 0.520267 | 0.260133 | − | 0.965573i | \(-0.416233\pi\) | ||||
0.260133 | + | 0.965573i | \(0.416233\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.73277 | 0.192705 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.30232 | 0.0773042 | 0.0386521 | − | 0.999253i | \(-0.487694\pi\) | ||||
0.0386521 | + | 0.999253i | \(0.487694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.57283 | 0.153368 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.563586 | 0.0188809 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.4377 | −0.683923 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.14459 | −0.0716857 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.13614 | −0.0379346 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.99087 | 0.299862 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.50874 | 0.250153 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.05031 | 0.301175 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9864 | 0.365200 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.0716 | −1.23094 | −0.615471 | − | 0.788159i | \(-0.711034\pi\) | ||||
−0.615471 | + | 0.788159i | \(0.711034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.7275 | −0.422143 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.9981 | 0.530040 | 0.265020 | − | 0.964243i | \(-0.414621\pi\) | ||||
0.265020 | + | 0.964243i | \(0.414621\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.822924 | −0.0272348 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.3979 | 0.608216 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.5878 | −0.580802 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.52056 | −0.0501586 | −0.0250793 | − | 0.999685i | \(-0.507984\pi\) | ||||
−0.0250793 | + | 0.999685i | \(0.507984\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 63.8266 | 2.10316 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.1183 | 1.35343 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.3429 | 1.06343 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2867 | 0.469237 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.7168 | −0.909359 | −0.454680 | − | 0.890655i | \(-0.650246\pi\) | ||||
−0.454680 | + | 0.890655i | \(0.650246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.41047 | 0.275642 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.44930 | 0.0801864 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0475459 | 0.00155492 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.8797 | −1.59683 | −0.798415 | − | 0.602108i | \(-0.794328\pi\) | ||||
−0.798415 | + | 0.602108i | \(0.794328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 57.0303 | 1.86111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.7097 | −1.71829 | −0.859144 | − | 0.511734i | \(-0.829003\pi\) | ||||
−0.859144 | + | 0.511734i | \(0.829003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.805276 | −0.0262234 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.40678 | −0.110823 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.9828 | 1.29927 | 0.649634 | − | 0.760247i | \(-0.274922\pi\) | ||||
0.649634 | + | 0.760247i | \(0.274922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.3846 | 1.76540 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.3657 | 0.790113 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.7459 | 0.833993 | 0.416996 | − | 0.908908i | \(-0.363083\pi\) | ||||
0.416996 | + | 0.908908i | \(0.363083\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.3029 | −0.527550 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.08919 | −0.0352084 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.35048 | 0.269651 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2532 | −0.975911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.59954 | −0.277116 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0305027 | −0.000981916 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.22972 | 0.136019 | 0.0680093 | − | 0.997685i | \(-0.478335\pi\) | ||||
0.0680093 | + | 0.997685i | \(0.478335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.59531 | 0.179747 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.5328 | −0.979843 | −0.489922 | − | 0.871767i | \(-0.662975\pi\) | ||||
−0.489922 | + | 0.871767i | \(0.662975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.9082 | −0.958812 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 56.5513 | 1.81109 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.0283 | −0.992682 | −0.496341 | − | 0.868128i | \(-0.665324\pi\) | ||||
−0.496341 | + | 0.868128i | \(0.665324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0806952 | −0.00257903 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.19588 | −0.165892 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0224 | −0.702407 | −0.351203 | − | 0.936299i | \(-0.614227\pi\) | ||||
−0.351203 | + | 0.936299i | \(0.614227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.89302 | −0.283355 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36.1206 | −1.14973 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.259526 | −0.00825246 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.40511 | 0.139933 | 0.0699665 | − | 0.997549i | \(-0.477711\pi\) | ||||
0.0699665 | + | 0.997549i | \(0.477711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54.1184 | 1.71739 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.07877 | 0.0659016 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.6821 | −0.338305 | −0.169153 | − | 0.985590i | \(-0.554103\pi\) | ||||
−0.169153 | + | 0.985590i | \(0.554103\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.2711 | −0.767904 |
(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 | 6008.2.a.c.1.10 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.c.1.10 | ✓ | 44 | 1.1 | even | 1 | trivial |