Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.308270 | 0.217980 | 0.108990 | − | 0.994043i | \(-0.465238\pi\) | ||||
0.108990 | + | 0.994043i | \(0.465238\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.90497 | −0.952485 | ||||||||
\(5\) | 2.48291 | 1.11039 | 0.555196 | − | 0.831719i | \(-0.312643\pi\) | ||||
0.555196 | + | 0.831719i | \(0.312643\pi\) | |||||||
\(6\) | 0.308270 | 0.125851 | ||||||||
\(7\) | 3.17570 | 1.20030 | 0.600152 | − | 0.799886i | \(-0.295107\pi\) | ||||
0.600152 | + | 0.799886i | \(0.295107\pi\) | |||||||
\(8\) | −1.20379 | −0.425603 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.765408 | 0.242043 | ||||||||
\(11\) | −2.66964 | −0.804926 | −0.402463 | − | 0.915436i | \(-0.631846\pi\) | ||||
−0.402463 | + | 0.915436i | \(0.631846\pi\) | |||||||
\(12\) | −1.90497 | −0.549917 | ||||||||
\(13\) | 6.37503 | 1.76812 | 0.884058 | − | 0.467378i | \(-0.154801\pi\) | ||||
0.884058 | + | 0.467378i | \(0.154801\pi\) | |||||||
\(14\) | 0.978975 | 0.261642 | ||||||||
\(15\) | 2.48291 | 0.641086 | ||||||||
\(16\) | 3.43885 | 0.859712 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.308270 | 0.0726600 | ||||||||
\(19\) | 8.52916 | 1.95672 | 0.978362 | − | 0.206903i | \(-0.0663384\pi\) | ||||
0.978362 | + | 0.206903i | \(0.0663384\pi\) | |||||||
\(20\) | −4.72988 | −1.05763 | ||||||||
\(21\) | 3.17570 | 0.692995 | ||||||||
\(22\) | −0.822969 | −0.175458 | ||||||||
\(23\) | 6.90544 | 1.43988 | 0.719942 | − | 0.694034i | \(-0.244168\pi\) | ||||
0.719942 | + | 0.694034i | \(0.244168\pi\) | |||||||
\(24\) | −1.20379 | −0.245722 | ||||||||
\(25\) | 1.16486 | 0.232973 | ||||||||
\(26\) | 1.96523 | 0.385414 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.04962 | −1.14327 | ||||||||
\(29\) | −2.52889 | −0.469604 | −0.234802 | − | 0.972043i | \(-0.575444\pi\) | ||||
−0.234802 | + | 0.972043i | \(0.575444\pi\) | |||||||
\(30\) | 0.765408 | 0.139744 | ||||||||
\(31\) | −10.7183 | −1.92506 | −0.962529 | − | 0.271178i | \(-0.912587\pi\) | ||||
−0.962529 | + | 0.271178i | \(0.912587\pi\) | |||||||
\(32\) | 3.46767 | 0.613002 | ||||||||
\(33\) | −2.66964 | −0.464724 | ||||||||
\(34\) | 0.308270 | 0.0528679 | ||||||||
\(35\) | 7.88500 | 1.33281 | ||||||||
\(36\) | −1.90497 | −0.317495 | ||||||||
\(37\) | −10.4005 | −1.70983 | −0.854916 | − | 0.518767i | \(-0.826391\pi\) | ||||
−0.854916 | + | 0.518767i | \(0.826391\pi\) | |||||||
\(38\) | 2.62929 | 0.426526 | ||||||||
\(39\) | 6.37503 | 1.02082 | ||||||||
\(40\) | −2.98890 | −0.472586 | ||||||||
\(41\) | −1.66405 | −0.259881 | −0.129940 | − | 0.991522i | \(-0.541479\pi\) | ||||
−0.129940 | + | 0.991522i | \(0.541479\pi\) | |||||||
\(42\) | 0.978975 | 0.151059 | ||||||||
\(43\) | −1.09029 | −0.166268 | −0.0831340 | − | 0.996538i | \(-0.526493\pi\) | ||||
−0.0831340 | + | 0.996538i | \(0.526493\pi\) | |||||||
\(44\) | 5.08558 | 0.766680 | ||||||||
\(45\) | 2.48291 | 0.370131 | ||||||||
\(46\) | 2.12874 | 0.313866 | ||||||||
\(47\) | 3.69443 | 0.538887 | 0.269444 | − | 0.963016i | \(-0.413160\pi\) | ||||
0.269444 | + | 0.963016i | \(0.413160\pi\) | |||||||
\(48\) | 3.43885 | 0.496355 | ||||||||
\(49\) | 3.08509 | 0.440727 | ||||||||
\(50\) | 0.359092 | 0.0507833 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −12.1442 | −1.68410 | ||||||||
\(53\) | −0.219567 | −0.0301598 | −0.0150799 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150799 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(54\) | 0.308270 | 0.0419503 | ||||||||
\(55\) | −6.62848 | −0.893784 | ||||||||
\(56\) | −3.82287 | −0.510852 | ||||||||
\(57\) | 8.52916 | 1.12971 | ||||||||
\(58\) | −0.779582 | −0.102364 | ||||||||
\(59\) | 10.6739 | 1.38963 | 0.694815 | − | 0.719189i | \(-0.255486\pi\) | ||||
0.694815 | + | 0.719189i | \(0.255486\pi\) | |||||||
\(60\) | −4.72988 | −0.610624 | ||||||||
\(61\) | −4.77746 | −0.611691 | −0.305845 | − | 0.952081i | \(-0.598939\pi\) | ||||
−0.305845 | + | 0.952081i | \(0.598939\pi\) | |||||||
\(62\) | −3.30412 | −0.419624 | ||||||||
\(63\) | 3.17570 | 0.400101 | ||||||||
\(64\) | −5.80872 | −0.726090 | ||||||||
\(65\) | 15.8287 | 1.96330 | ||||||||
\(66\) | −0.822969 | −0.101301 | ||||||||
\(67\) | −11.3088 | −1.38159 | −0.690797 | − | 0.723049i | \(-0.742740\pi\) | ||||
−0.690797 | + | 0.723049i | \(0.742740\pi\) | |||||||
\(68\) | −1.90497 | −0.231011 | ||||||||
\(69\) | 6.90544 | 0.831318 | ||||||||
\(70\) | 2.43071 | 0.290525 | ||||||||
\(71\) | −10.3718 | −1.23091 | −0.615453 | − | 0.788173i | \(-0.711027\pi\) | ||||
−0.615453 | + | 0.788173i | \(0.711027\pi\) | |||||||
\(72\) | −1.20379 | −0.141868 | ||||||||
\(73\) | 11.2993 | 1.32248 | 0.661241 | − | 0.750173i | \(-0.270030\pi\) | ||||
0.661241 | + | 0.750173i | \(0.270030\pi\) | |||||||
\(74\) | −3.20616 | −0.372709 | ||||||||
\(75\) | 1.16486 | 0.134507 | ||||||||
\(76\) | −16.2478 | −1.86375 | ||||||||
\(77\) | −8.47797 | −0.966155 | ||||||||
\(78\) | 1.96523 | 0.222519 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 8.53836 | 0.954618 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.512977 | −0.0566488 | ||||||||
\(83\) | −10.9627 | −1.20331 | −0.601655 | − | 0.798756i | \(-0.705492\pi\) | ||||
−0.601655 | + | 0.798756i | \(0.705492\pi\) | |||||||
\(84\) | −6.04962 | −0.660067 | ||||||||
\(85\) | 2.48291 | 0.269310 | ||||||||
\(86\) | −0.336105 | −0.0362431 | ||||||||
\(87\) | −2.52889 | −0.271126 | ||||||||
\(88\) | 3.21367 | 0.342578 | ||||||||
\(89\) | 14.0122 | 1.48529 | 0.742643 | − | 0.669687i | \(-0.233572\pi\) | ||||
0.742643 | + | 0.669687i | \(0.233572\pi\) | |||||||
\(90\) | 0.765408 | 0.0806811 | ||||||||
\(91\) | 20.2452 | 2.12227 | ||||||||
\(92\) | −13.1547 | −1.37147 | ||||||||
\(93\) | −10.7183 | −1.11143 | ||||||||
\(94\) | 1.13888 | 0.117467 | ||||||||
\(95\) | 21.1772 | 2.17273 | ||||||||
\(96\) | 3.46767 | 0.353917 | ||||||||
\(97\) | 6.68616 | 0.678877 | 0.339438 | − | 0.940628i | \(-0.389763\pi\) | ||||
0.339438 | + | 0.940628i | \(0.389763\pi\) | |||||||
\(98\) | 0.951042 | 0.0960698 | ||||||||
\(99\) | −2.66964 | −0.268309 | ||||||||
\(100\) | −2.21903 | −0.221903 | ||||||||
\(101\) | 3.44515 | 0.342805 | 0.171403 | − | 0.985201i | \(-0.445170\pi\) | ||||
0.171403 | + | 0.985201i | \(0.445170\pi\) | |||||||
\(102\) | 0.308270 | 0.0305233 | ||||||||
\(103\) | −3.22307 | −0.317578 | −0.158789 | − | 0.987313i | \(-0.550759\pi\) | ||||
−0.158789 | + | 0.987313i | \(0.550759\pi\) | |||||||
\(104\) | −7.67417 | −0.752514 | ||||||||
\(105\) | 7.88500 | 0.769497 | ||||||||
\(106\) | −0.0676858 | −0.00657423 | ||||||||
\(107\) | 17.3765 | 1.67985 | 0.839925 | − | 0.542702i | \(-0.182599\pi\) | ||||
0.839925 | + | 0.542702i | \(0.182599\pi\) | |||||||
\(108\) | −1.90497 | −0.183306 | ||||||||
\(109\) | −7.64031 | −0.731809 | −0.365905 | − | 0.930652i | \(-0.619240\pi\) | ||||
−0.365905 | + | 0.930652i | \(0.619240\pi\) | |||||||
\(110\) | −2.04336 | −0.194827 | ||||||||
\(111\) | −10.4005 | −0.987172 | ||||||||
\(112\) | 10.9208 | 1.03191 | ||||||||
\(113\) | 4.47356 | 0.420837 | 0.210419 | − | 0.977611i | \(-0.432517\pi\) | ||||
0.210419 | + | 0.977611i | \(0.432517\pi\) | |||||||
\(114\) | 2.62929 | 0.246255 | ||||||||
\(115\) | 17.1456 | 1.59884 | ||||||||
\(116\) | 4.81746 | 0.447290 | ||||||||
\(117\) | 6.37503 | 0.589372 | ||||||||
\(118\) | 3.29046 | 0.302911 | ||||||||
\(119\) | 3.17570 | 0.291116 | ||||||||
\(120\) | −2.98890 | −0.272848 | ||||||||
\(121\) | −3.87304 | −0.352094 | ||||||||
\(122\) | −1.47275 | −0.133336 | ||||||||
\(123\) | −1.66405 | −0.150042 | ||||||||
\(124\) | 20.4180 | 1.83359 | ||||||||
\(125\) | −9.52232 | −0.851702 | ||||||||
\(126\) | 0.978975 | 0.0872140 | ||||||||
\(127\) | −3.47704 | −0.308538 | −0.154269 | − | 0.988029i | \(-0.549302\pi\) | ||||
−0.154269 | + | 0.988029i | \(0.549302\pi\) | |||||||
\(128\) | −8.72599 | −0.771275 | ||||||||
\(129\) | −1.09029 | −0.0959949 | ||||||||
\(130\) | 4.87950 | 0.427961 | ||||||||
\(131\) | 8.52888 | 0.745172 | 0.372586 | − | 0.927998i | \(-0.378471\pi\) | ||||
0.372586 | + | 0.927998i | \(0.378471\pi\) | |||||||
\(132\) | 5.08558 | 0.442643 | ||||||||
\(133\) | 27.0861 | 2.34866 | ||||||||
\(134\) | −3.48618 | −0.301160 | ||||||||
\(135\) | 2.48291 | 0.213695 | ||||||||
\(136\) | −1.20379 | −0.103224 | ||||||||
\(137\) | 14.7316 | 1.25860 | 0.629301 | − | 0.777162i | \(-0.283341\pi\) | ||||
0.629301 | + | 0.777162i | \(0.283341\pi\) | |||||||
\(138\) | 2.12874 | 0.181211 | ||||||||
\(139\) | 8.75975 | 0.742992 | 0.371496 | − | 0.928435i | \(-0.378845\pi\) | ||||
0.371496 | + | 0.928435i | \(0.378845\pi\) | |||||||
\(140\) | −15.0207 | −1.26948 | ||||||||
\(141\) | 3.69443 | 0.311127 | ||||||||
\(142\) | −3.19732 | −0.268313 | ||||||||
\(143\) | −17.0190 | −1.42320 | ||||||||
\(144\) | 3.43885 | 0.286571 | ||||||||
\(145\) | −6.27903 | −0.521445 | ||||||||
\(146\) | 3.48324 | 0.288275 | ||||||||
\(147\) | 3.08509 | 0.254454 | ||||||||
\(148\) | 19.8126 | 1.62859 | ||||||||
\(149\) | −0.927884 | −0.0760152 | −0.0380076 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380076 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(150\) | 0.359092 | 0.0293198 | ||||||||
\(151\) | −7.69312 | −0.626057 | −0.313028 | − | 0.949744i | \(-0.601344\pi\) | ||||
−0.313028 | + | 0.949744i | \(0.601344\pi\) | |||||||
\(152\) | −10.2673 | −0.832786 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −2.61351 | −0.210602 | ||||||||
\(155\) | −26.6125 | −2.13757 | ||||||||
\(156\) | −12.1442 | −0.972317 | ||||||||
\(157\) | −22.5272 | −1.79786 | −0.898932 | − | 0.438087i | \(-0.855656\pi\) | ||||
−0.898932 | + | 0.438087i | \(0.855656\pi\) | |||||||
\(158\) | 0.308270 | 0.0245247 | ||||||||
\(159\) | −0.219567 | −0.0174128 | ||||||||
\(160\) | 8.60992 | 0.680674 | ||||||||
\(161\) | 21.9296 | 1.72830 | ||||||||
\(162\) | 0.308270 | 0.0242200 | ||||||||
\(163\) | 5.28450 | 0.413914 | 0.206957 | − | 0.978350i | \(-0.433644\pi\) | ||||
0.206957 | + | 0.978350i | \(0.433644\pi\) | |||||||
\(164\) | 3.16996 | 0.247532 | ||||||||
\(165\) | −6.62848 | −0.516026 | ||||||||
\(166\) | −3.37947 | −0.262298 | ||||||||
\(167\) | −14.9243 | −1.15488 | −0.577438 | − | 0.816435i | \(-0.695947\pi\) | ||||
−0.577438 | + | 0.816435i | \(0.695947\pi\) | |||||||
\(168\) | −3.82287 | −0.294941 | ||||||||
\(169\) | 27.6410 | 2.12623 | ||||||||
\(170\) | 0.765408 | 0.0587041 | ||||||||
\(171\) | 8.52916 | 0.652241 | ||||||||
\(172\) | 2.07697 | 0.158368 | ||||||||
\(173\) | 20.1069 | 1.52870 | 0.764350 | − | 0.644802i | \(-0.223060\pi\) | ||||
0.764350 | + | 0.644802i | \(0.223060\pi\) | |||||||
\(174\) | −0.779582 | −0.0591000 | ||||||||
\(175\) | 3.69926 | 0.279638 | ||||||||
\(176\) | −9.18047 | −0.692004 | ||||||||
\(177\) | 10.6739 | 0.802303 | ||||||||
\(178\) | 4.31953 | 0.323763 | ||||||||
\(179\) | −17.3799 | −1.29903 | −0.649517 | − | 0.760347i | \(-0.725029\pi\) | ||||
−0.649517 | + | 0.760347i | \(0.725029\pi\) | |||||||
\(180\) | −4.72988 | −0.352544 | ||||||||
\(181\) | 16.7714 | 1.24661 | 0.623304 | − | 0.781980i | \(-0.285790\pi\) | ||||
0.623304 | + | 0.781980i | \(0.285790\pi\) | |||||||
\(182\) | 6.24099 | 0.462613 | ||||||||
\(183\) | −4.77746 | −0.353160 | ||||||||
\(184\) | −8.31267 | −0.612818 | ||||||||
\(185\) | −25.8235 | −1.89858 | ||||||||
\(186\) | −3.30412 | −0.242270 | ||||||||
\(187\) | −2.66964 | −0.195223 | ||||||||
\(188\) | −7.03777 | −0.513282 | ||||||||
\(189\) | 3.17570 | 0.230998 | ||||||||
\(190\) | 6.52829 | 0.473612 | ||||||||
\(191\) | −15.8317 | −1.14554 | −0.572772 | − | 0.819715i | \(-0.694132\pi\) | ||||
−0.572772 | + | 0.819715i | \(0.694132\pi\) | |||||||
\(192\) | −5.80872 | −0.419208 | ||||||||
\(193\) | −16.7147 | −1.20315 | −0.601575 | − | 0.798817i | \(-0.705460\pi\) | ||||
−0.601575 | + | 0.798817i | \(0.705460\pi\) | |||||||
\(194\) | 2.06114 | 0.147982 | ||||||||
\(195\) | 15.8287 | 1.13351 | ||||||||
\(196\) | −5.87701 | −0.419786 | ||||||||
\(197\) | 2.20508 | 0.157105 | 0.0785527 | − | 0.996910i | \(-0.474970\pi\) | ||||
0.0785527 | + | 0.996910i | \(0.474970\pi\) | |||||||
\(198\) | −0.822969 | −0.0584859 | ||||||||
\(199\) | −6.40547 | −0.454072 | −0.227036 | − | 0.973886i | \(-0.572903\pi\) | ||||
−0.227036 | + | 0.973886i | \(0.572903\pi\) | |||||||
\(200\) | −1.40225 | −0.0991537 | ||||||||
\(201\) | −11.3088 | −0.797664 | ||||||||
\(202\) | 1.06204 | 0.0747246 | ||||||||
\(203\) | −8.03102 | −0.563667 | ||||||||
\(204\) | −1.90497 | −0.133375 | ||||||||
\(205\) | −4.13169 | −0.288570 | ||||||||
\(206\) | −0.993575 | −0.0692256 | ||||||||
\(207\) | 6.90544 | 0.479961 | ||||||||
\(208\) | 21.9228 | 1.52007 | ||||||||
\(209\) | −22.7698 | −1.57502 | ||||||||
\(210\) | 2.43071 | 0.167735 | ||||||||
\(211\) | 1.83566 | 0.126372 | 0.0631859 | − | 0.998002i | \(-0.479874\pi\) | ||||
0.0631859 | + | 0.998002i | \(0.479874\pi\) | |||||||
\(212\) | 0.418268 | 0.0287267 | ||||||||
\(213\) | −10.3718 | −0.710664 | ||||||||
\(214\) | 5.35666 | 0.366174 | ||||||||
\(215\) | −2.70710 | −0.184623 | ||||||||
\(216\) | −1.20379 | −0.0819072 | ||||||||
\(217\) | −34.0380 | −2.31065 | ||||||||
\(218\) | −2.35528 | −0.159520 | ||||||||
\(219\) | 11.2993 | 0.763535 | ||||||||
\(220\) | 12.6271 | 0.851316 | ||||||||
\(221\) | 6.37503 | 0.428831 | ||||||||
\(222\) | −3.20616 | −0.215184 | ||||||||
\(223\) | 6.27182 | 0.419992 | 0.209996 | − | 0.977702i | \(-0.432655\pi\) | ||||
0.209996 | + | 0.977702i | \(0.432655\pi\) | |||||||
\(224\) | 11.0123 | 0.735789 | ||||||||
\(225\) | 1.16486 | 0.0776575 | ||||||||
\(226\) | 1.37907 | 0.0917341 | ||||||||
\(227\) | 25.3970 | 1.68566 | 0.842829 | − | 0.538182i | \(-0.180889\pi\) | ||||
0.842829 | + | 0.538182i | \(0.180889\pi\) | |||||||
\(228\) | −16.2478 | −1.07604 | ||||||||
\(229\) | −4.87536 | −0.322173 | −0.161087 | − | 0.986940i | \(-0.551500\pi\) | ||||
−0.161087 | + | 0.986940i | \(0.551500\pi\) | |||||||
\(230\) | 5.28548 | 0.348514 | ||||||||
\(231\) | −8.47797 | −0.557810 | ||||||||
\(232\) | 3.04425 | 0.199865 | ||||||||
\(233\) | 7.18402 | 0.470641 | 0.235320 | − | 0.971918i | \(-0.424386\pi\) | ||||
0.235320 | + | 0.971918i | \(0.424386\pi\) | |||||||
\(234\) | 1.96523 | 0.128471 | ||||||||
\(235\) | 9.17294 | 0.598377 | ||||||||
\(236\) | −20.3335 | −1.32360 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 0.978975 | 0.0634575 | ||||||||
\(239\) | −1.15315 | −0.0745913 | −0.0372956 | − | 0.999304i | \(-0.511874\pi\) | ||||
−0.0372956 | + | 0.999304i | \(0.511874\pi\) | |||||||
\(240\) | 8.53836 | 0.551149 | ||||||||
\(241\) | −10.8434 | −0.698486 | −0.349243 | − | 0.937032i | \(-0.613561\pi\) | ||||
−0.349243 | + | 0.937032i | \(0.613561\pi\) | |||||||
\(242\) | −1.19394 | −0.0767495 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.10091 | 0.582626 | ||||||||
\(245\) | 7.66002 | 0.489381 | ||||||||
\(246\) | −0.512977 | −0.0327062 | ||||||||
\(247\) | 54.3736 | 3.45971 | ||||||||
\(248\) | 12.9025 | 0.819310 | ||||||||
\(249\) | −10.9627 | −0.694732 | ||||||||
\(250\) | −2.93545 | −0.185654 | ||||||||
\(251\) | 15.8366 | 0.999600 | 0.499800 | − | 0.866141i | \(-0.333407\pi\) | ||||
0.499800 | + | 0.866141i | \(0.333407\pi\) | |||||||
\(252\) | −6.04962 | −0.381090 | ||||||||
\(253\) | −18.4350 | −1.15900 | ||||||||
\(254\) | −1.07187 | −0.0672550 | ||||||||
\(255\) | 2.48291 | 0.155486 | ||||||||
\(256\) | 8.92747 | 0.557967 | ||||||||
\(257\) | 8.89323 | 0.554745 | 0.277372 | − | 0.960763i | \(-0.410536\pi\) | ||||
0.277372 | + | 0.960763i | \(0.410536\pi\) | |||||||
\(258\) | −0.336105 | −0.0209250 | ||||||||
\(259\) | −33.0289 | −2.05232 | ||||||||
\(260\) | −30.1531 | −1.87002 | ||||||||
\(261\) | −2.52889 | −0.156535 | ||||||||
\(262\) | 2.62920 | 0.162432 | ||||||||
\(263\) | −1.67803 | −0.103472 | −0.0517358 | − | 0.998661i | \(-0.516475\pi\) | ||||
−0.0517358 | + | 0.998661i | \(0.516475\pi\) | |||||||
\(264\) | 3.21367 | 0.197788 | ||||||||
\(265\) | −0.545165 | −0.0334892 | ||||||||
\(266\) | 8.34983 | 0.511961 | ||||||||
\(267\) | 14.0122 | 0.857531 | ||||||||
\(268\) | 21.5430 | 1.31595 | ||||||||
\(269\) | −13.9950 | −0.853291 | −0.426645 | − | 0.904419i | \(-0.640305\pi\) | ||||
−0.426645 | + | 0.904419i | \(0.640305\pi\) | |||||||
\(270\) | 0.765408 | 0.0465813 | ||||||||
\(271\) | −28.1446 | −1.70966 | −0.854831 | − | 0.518906i | \(-0.826339\pi\) | ||||
−0.854831 | + | 0.518906i | \(0.826339\pi\) | |||||||
\(272\) | 3.43885 | 0.208511 | ||||||||
\(273\) | 20.2452 | 1.22530 | ||||||||
\(274\) | 4.54130 | 0.274350 | ||||||||
\(275\) | −3.10976 | −0.187526 | ||||||||
\(276\) | −13.1547 | −0.791817 | ||||||||
\(277\) | 9.08819 | 0.546057 | 0.273028 | − | 0.962006i | \(-0.411975\pi\) | ||||
0.273028 | + | 0.962006i | \(0.411975\pi\) | |||||||
\(278\) | 2.70037 | 0.161957 | ||||||||
\(279\) | −10.7183 | −0.641686 | ||||||||
\(280\) | −9.49185 | −0.567246 | ||||||||
\(281\) | −18.0375 | −1.07603 | −0.538014 | − | 0.842936i | \(-0.680825\pi\) | ||||
−0.538014 | + | 0.842936i | \(0.680825\pi\) | |||||||
\(282\) | 1.13888 | 0.0678194 | ||||||||
\(283\) | −7.22656 | −0.429575 | −0.214787 | − | 0.976661i | \(-0.568906\pi\) | ||||
−0.214787 | + | 0.976661i | \(0.568906\pi\) | |||||||
\(284\) | 19.7580 | 1.17242 | ||||||||
\(285\) | 21.1772 | 1.25443 | ||||||||
\(286\) | −5.24646 | −0.310229 | ||||||||
\(287\) | −5.28453 | −0.311936 | ||||||||
\(288\) | 3.46767 | 0.204334 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.93564 | −0.113664 | ||||||||
\(291\) | 6.68616 | 0.391950 | ||||||||
\(292\) | −21.5248 | −1.25964 | ||||||||
\(293\) | 2.41975 | 0.141363 | 0.0706817 | − | 0.997499i | \(-0.477483\pi\) | ||||
0.0706817 | + | 0.997499i | \(0.477483\pi\) | |||||||
\(294\) | 0.951042 | 0.0554659 | ||||||||
\(295\) | 26.5025 | 1.54304 | ||||||||
\(296\) | 12.5200 | 0.727709 | ||||||||
\(297\) | −2.66964 | −0.154908 | ||||||||
\(298\) | −0.286039 | −0.0165698 | ||||||||
\(299\) | 44.0224 | 2.54588 | ||||||||
\(300\) | −2.21903 | −0.128116 | ||||||||
\(301\) | −3.46245 | −0.199572 | ||||||||
\(302\) | −2.37156 | −0.136468 | ||||||||
\(303\) | 3.44515 | 0.197919 | ||||||||
\(304\) | 29.3305 | 1.68222 | ||||||||
\(305\) | −11.8620 | −0.679217 | ||||||||
\(306\) | 0.308270 | 0.0176226 | ||||||||
\(307\) | 16.2282 | 0.926194 | 0.463097 | − | 0.886308i | \(-0.346738\pi\) | ||||
0.463097 | + | 0.886308i | \(0.346738\pi\) | |||||||
\(308\) | 16.1503 | 0.920248 | ||||||||
\(309\) | −3.22307 | −0.183354 | ||||||||
\(310\) | −8.20386 | −0.465948 | ||||||||
\(311\) | 17.8581 | 1.01264 | 0.506321 | − | 0.862345i | \(-0.331005\pi\) | ||||
0.506321 | + | 0.862345i | \(0.331005\pi\) | |||||||
\(312\) | −7.67417 | −0.434464 | ||||||||
\(313\) | −1.70694 | −0.0964821 | −0.0482411 | − | 0.998836i | \(-0.515362\pi\) | ||||
−0.0482411 | + | 0.998836i | \(0.515362\pi\) | |||||||
\(314\) | −6.94446 | −0.391898 | ||||||||
\(315\) | 7.88500 | 0.444269 | ||||||||
\(316\) | −1.90497 | −0.107163 | ||||||||
\(317\) | 15.3198 | 0.860447 | 0.430223 | − | 0.902723i | \(-0.358435\pi\) | ||||
0.430223 | + | 0.902723i | \(0.358435\pi\) | |||||||
\(318\) | −0.0676858 | −0.00379563 | ||||||||
\(319\) | 6.75123 | 0.377996 | ||||||||
\(320\) | −14.4225 | −0.806245 | ||||||||
\(321\) | 17.3765 | 0.969862 | ||||||||
\(322\) | 6.76025 | 0.376734 | ||||||||
\(323\) | 8.52916 | 0.474575 | ||||||||
\(324\) | −1.90497 | −0.105832 | ||||||||
\(325\) | 7.42603 | 0.411922 | ||||||||
\(326\) | 1.62906 | 0.0902250 | ||||||||
\(327\) | −7.64031 | −0.422510 | ||||||||
\(328\) | 2.00316 | 0.110606 | ||||||||
\(329\) | 11.7324 | 0.646828 | ||||||||
\(330\) | −2.04336 | −0.112483 | ||||||||
\(331\) | 8.91869 | 0.490216 | 0.245108 | − | 0.969496i | \(-0.421177\pi\) | ||||
0.245108 | + | 0.969496i | \(0.421177\pi\) | |||||||
\(332\) | 20.8836 | 1.14613 | ||||||||
\(333\) | −10.4005 | −0.569944 | ||||||||
\(334\) | −4.60071 | −0.251740 | ||||||||
\(335\) | −28.0789 | −1.53411 | ||||||||
\(336\) | 10.9208 | 0.595776 | ||||||||
\(337\) | −33.3454 | −1.81644 | −0.908220 | − | 0.418494i | \(-0.862558\pi\) | ||||
−0.908220 | + | 0.418494i | \(0.862558\pi\) | |||||||
\(338\) | 8.52090 | 0.463476 | ||||||||
\(339\) | 4.47356 | 0.242971 | ||||||||
\(340\) | −4.72988 | −0.256514 | ||||||||
\(341\) | 28.6139 | 1.54953 | ||||||||
\(342\) | 2.62929 | 0.142175 | ||||||||
\(343\) | −12.4326 | −0.671297 | ||||||||
\(344\) | 1.31248 | 0.0707641 | ||||||||
\(345\) | 17.1456 | 0.923089 | ||||||||
\(346\) | 6.19836 | 0.333226 | ||||||||
\(347\) | −12.4751 | −0.669697 | −0.334848 | − | 0.942272i | \(-0.608685\pi\) | ||||
−0.334848 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(348\) | 4.81746 | 0.258243 | ||||||||
\(349\) | −22.4032 | −1.19922 | −0.599608 | − | 0.800294i | \(-0.704677\pi\) | ||||
−0.599608 | + | 0.800294i | \(0.704677\pi\) | |||||||
\(350\) | 1.14037 | 0.0609554 | ||||||||
\(351\) | 6.37503 | 0.340274 | ||||||||
\(352\) | −9.25741 | −0.493422 | ||||||||
\(353\) | 0.970716 | 0.0516660 | 0.0258330 | − | 0.999666i | \(-0.491776\pi\) | ||||
0.0258330 | + | 0.999666i | \(0.491776\pi\) | |||||||
\(354\) | 3.29046 | 0.174886 | ||||||||
\(355\) | −25.7523 | −1.36679 | ||||||||
\(356\) | −26.6927 | −1.41471 | ||||||||
\(357\) | 3.17570 | 0.168076 | ||||||||
\(358\) | −5.35770 | −0.283163 | ||||||||
\(359\) | −24.2927 | −1.28212 | −0.641061 | − | 0.767490i | \(-0.721505\pi\) | ||||
−0.641061 | + | 0.767490i | \(0.721505\pi\) | |||||||
\(360\) | −2.98890 | −0.157529 | ||||||||
\(361\) | 53.7465 | 2.82876 | ||||||||
\(362\) | 5.17012 | 0.271736 | ||||||||
\(363\) | −3.87304 | −0.203282 | ||||||||
\(364\) | −38.5665 | −2.02143 | ||||||||
\(365\) | 28.0552 | 1.46847 | ||||||||
\(366\) | −1.47275 | −0.0769818 | ||||||||
\(367\) | 30.6216 | 1.59843 | 0.799216 | − | 0.601043i | \(-0.205248\pi\) | ||||
0.799216 | + | 0.601043i | \(0.205248\pi\) | |||||||
\(368\) | 23.7468 | 1.23789 | ||||||||
\(369\) | −1.66405 | −0.0866269 | ||||||||
\(370\) | −7.96063 | −0.413853 | ||||||||
\(371\) | −0.697278 | −0.0362009 | ||||||||
\(372\) | 20.4180 | 1.05862 | ||||||||
\(373\) | −22.7812 | −1.17956 | −0.589782 | − | 0.807563i | \(-0.700786\pi\) | ||||
−0.589782 | + | 0.807563i | \(0.700786\pi\) | |||||||
\(374\) | −0.822969 | −0.0425547 | ||||||||
\(375\) | −9.52232 | −0.491730 | ||||||||
\(376\) | −4.44730 | −0.229352 | ||||||||
\(377\) | −16.1218 | −0.830313 | ||||||||
\(378\) | 0.978975 | 0.0503530 | ||||||||
\(379\) | −10.4079 | −0.534619 | −0.267309 | − | 0.963611i | \(-0.586135\pi\) | ||||
−0.267309 | + | 0.963611i | \(0.586135\pi\) | |||||||
\(380\) | −40.3419 | −2.06949 | ||||||||
\(381\) | −3.47704 | −0.178134 | ||||||||
\(382\) | −4.88045 | −0.249705 | ||||||||
\(383\) | 21.1881 | 1.08266 | 0.541332 | − | 0.840809i | \(-0.317920\pi\) | ||||
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(384\) | −8.72599 | −0.445296 | ||||||||
\(385\) | −21.0501 | −1.07281 | ||||||||
\(386\) | −5.15264 | −0.262262 | ||||||||
\(387\) | −1.09029 | −0.0554227 | ||||||||
\(388\) | −12.7369 | −0.646620 | ||||||||
\(389\) | −18.7504 | −0.950685 | −0.475343 | − | 0.879801i | \(-0.657676\pi\) | ||||
−0.475343 | + | 0.879801i | \(0.657676\pi\) | |||||||
\(390\) | 4.87950 | 0.247083 | ||||||||
\(391\) | 6.90544 | 0.349223 | ||||||||
\(392\) | −3.71379 | −0.187575 | ||||||||
\(393\) | 8.52888 | 0.430225 | ||||||||
\(394\) | 0.679760 | 0.0342458 | ||||||||
\(395\) | 2.48291 | 0.124929 | ||||||||
\(396\) | 5.08558 | 0.255560 | ||||||||
\(397\) | 0.491395 | 0.0246624 | 0.0123312 | − | 0.999924i | \(-0.496075\pi\) | ||||
0.0123312 | + | 0.999924i | \(0.496075\pi\) | |||||||
\(398\) | −1.97461 | −0.0989785 | ||||||||
\(399\) | 27.0861 | 1.35600 | ||||||||
\(400\) | 4.00579 | 0.200289 | ||||||||
\(401\) | 17.5979 | 0.878796 | 0.439398 | − | 0.898293i | \(-0.355192\pi\) | ||||
0.439398 | + | 0.898293i | \(0.355192\pi\) | |||||||
\(402\) | −3.48618 | −0.173875 | ||||||||
\(403\) | −68.3293 | −3.40372 | ||||||||
\(404\) | −6.56290 | −0.326517 | ||||||||
\(405\) | 2.48291 | 0.123377 | ||||||||
\(406\) | −2.47572 | −0.122868 | ||||||||
\(407\) | 27.7656 | 1.37629 | ||||||||
\(408\) | −1.20379 | −0.0595963 | ||||||||
\(409\) | 21.3567 | 1.05602 | 0.528009 | − | 0.849239i | \(-0.322939\pi\) | ||||
0.528009 | + | 0.849239i | \(0.322939\pi\) | |||||||
\(410\) | −1.27368 | −0.0629024 | ||||||||
\(411\) | 14.7316 | 0.726654 | ||||||||
\(412\) | 6.13984 | 0.302488 | ||||||||
\(413\) | 33.8973 | 1.66798 | ||||||||
\(414\) | 2.12874 | 0.104622 | ||||||||
\(415\) | −27.2194 | −1.33615 | ||||||||
\(416\) | 22.1065 | 1.08386 | ||||||||
\(417\) | 8.75975 | 0.428967 | ||||||||
\(418\) | −7.01924 | −0.343322 | ||||||||
\(419\) | 15.3366 | 0.749242 | 0.374621 | − | 0.927178i | \(-0.377773\pi\) | ||||
0.374621 | + | 0.927178i | \(0.377773\pi\) | |||||||
\(420\) | −15.0207 | −0.732934 | ||||||||
\(421\) | 3.12005 | 0.152062 | 0.0760309 | − | 0.997105i | \(-0.475775\pi\) | ||||
0.0760309 | + | 0.997105i | \(0.475775\pi\) | |||||||
\(422\) | 0.565878 | 0.0275465 | ||||||||
\(423\) | 3.69443 | 0.179629 | ||||||||
\(424\) | 0.264311 | 0.0128361 | ||||||||
\(425\) | 1.16486 | 0.0565041 | ||||||||
\(426\) | −3.19732 | −0.154911 | ||||||||
\(427\) | −15.1718 | −0.734214 | ||||||||
\(428\) | −33.1017 | −1.60003 | ||||||||
\(429\) | −17.0190 | −0.821686 | ||||||||
\(430\) | −0.834519 | −0.0402441 | ||||||||
\(431\) | 17.0120 | 0.819439 | 0.409720 | − | 0.912212i | \(-0.365627\pi\) | ||||
0.409720 | + | 0.912212i | \(0.365627\pi\) | |||||||
\(432\) | 3.43885 | 0.165452 | ||||||||
\(433\) | −14.5796 | −0.700649 | −0.350325 | − | 0.936628i | \(-0.613929\pi\) | ||||
−0.350325 | + | 0.936628i | \(0.613929\pi\) | |||||||
\(434\) | −10.4929 | −0.503676 | ||||||||
\(435\) | −6.27903 | −0.301056 | ||||||||
\(436\) | 14.5546 | 0.697037 | ||||||||
\(437\) | 58.8976 | 2.81745 | ||||||||
\(438\) | 3.48324 | 0.166435 | ||||||||
\(439\) | 10.9217 | 0.521264 | 0.260632 | − | 0.965438i | \(-0.416069\pi\) | ||||
0.260632 | + | 0.965438i | \(0.416069\pi\) | |||||||
\(440\) | 7.97927 | 0.380397 | ||||||||
\(441\) | 3.08509 | 0.146909 | ||||||||
\(442\) | 1.96523 | 0.0934765 | ||||||||
\(443\) | 8.27778 | 0.393289 | 0.196645 | − | 0.980475i | \(-0.436996\pi\) | ||||
0.196645 | + | 0.980475i | \(0.436996\pi\) | |||||||
\(444\) | 19.8126 | 0.940266 | ||||||||
\(445\) | 34.7910 | 1.64925 | ||||||||
\(446\) | 1.93341 | 0.0915498 | ||||||||
\(447\) | −0.927884 | −0.0438874 | ||||||||
\(448\) | −18.4468 | −0.871528 | ||||||||
\(449\) | −30.0245 | −1.41694 | −0.708472 | − | 0.705739i | \(-0.750615\pi\) | ||||
−0.708472 | + | 0.705739i | \(0.750615\pi\) | |||||||
\(450\) | 0.359092 | 0.0169278 | ||||||||
\(451\) | 4.44241 | 0.209185 | ||||||||
\(452\) | −8.52200 | −0.400841 | ||||||||
\(453\) | −7.69312 | −0.361454 | ||||||||
\(454\) | 7.82914 | 0.367440 | ||||||||
\(455\) | 50.2671 | 2.35656 | ||||||||
\(456\) | −10.2673 | −0.480809 | ||||||||
\(457\) | 10.6431 | 0.497861 | 0.248930 | − | 0.968521i | \(-0.419921\pi\) | ||||
0.248930 | + | 0.968521i | \(0.419921\pi\) | |||||||
\(458\) | −1.50293 | −0.0702273 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −32.6619 | −1.52287 | ||||||||
\(461\) | −25.3204 | −1.17929 | −0.589645 | − | 0.807663i | \(-0.700732\pi\) | ||||
−0.589645 | + | 0.807663i | \(0.700732\pi\) | |||||||
\(462\) | −2.61351 | −0.121591 | ||||||||
\(463\) | −11.3424 | −0.527128 | −0.263564 | − | 0.964642i | \(-0.584898\pi\) | ||||
−0.263564 | + | 0.964642i | \(0.584898\pi\) | |||||||
\(464\) | −8.69648 | −0.403724 | ||||||||
\(465\) | −26.6125 | −1.23413 | ||||||||
\(466\) | 2.21462 | 0.102590 | ||||||||
\(467\) | 36.8602 | 1.70569 | 0.852844 | − | 0.522166i | \(-0.174876\pi\) | ||||
0.852844 | + | 0.522166i | \(0.174876\pi\) | |||||||
\(468\) | −12.1442 | −0.561368 | ||||||||
\(469\) | −35.9135 | −1.65833 | ||||||||
\(470\) | 2.82774 | 0.130434 | ||||||||
\(471\) | −22.5272 | −1.03800 | ||||||||
\(472\) | −12.8491 | −0.591430 | ||||||||
\(473\) | 2.91068 | 0.133833 | ||||||||
\(474\) | 0.308270 | 0.0141593 | ||||||||
\(475\) | 9.93530 | 0.455863 | ||||||||
\(476\) | −6.04962 | −0.277284 | ||||||||
\(477\) | −0.219567 | −0.0100533 | ||||||||
\(478\) | −0.355483 | −0.0162594 | ||||||||
\(479\) | 16.4430 | 0.751300 | 0.375650 | − | 0.926762i | \(-0.377419\pi\) | ||||
0.375650 | + | 0.926762i | \(0.377419\pi\) | |||||||
\(480\) | 8.60992 | 0.392987 | ||||||||
\(481\) | −66.3035 | −3.02318 | ||||||||
\(482\) | −3.34270 | −0.152256 | ||||||||
\(483\) | 21.9296 | 0.997833 | ||||||||
\(484\) | 7.37802 | 0.335365 | ||||||||
\(485\) | 16.6012 | 0.753820 | ||||||||
\(486\) | 0.308270 | 0.0139834 | ||||||||
\(487\) | 33.0200 | 1.49628 | 0.748139 | − | 0.663542i | \(-0.230947\pi\) | ||||
0.748139 | + | 0.663542i | \(0.230947\pi\) | |||||||
\(488\) | 5.75104 | 0.260337 | ||||||||
\(489\) | 5.28450 | 0.238974 | ||||||||
\(490\) | 2.36136 | 0.106675 | ||||||||
\(491\) | −5.58343 | −0.251977 | −0.125988 | − | 0.992032i | \(-0.540210\pi\) | ||||
−0.125988 | + | 0.992032i | \(0.540210\pi\) | |||||||
\(492\) | 3.16996 | 0.142913 | ||||||||
\(493\) | −2.52889 | −0.113896 | ||||||||
\(494\) | 16.7618 | 0.754148 | ||||||||
\(495\) | −6.62848 | −0.297928 | ||||||||
\(496\) | −36.8585 | −1.65500 | ||||||||
\(497\) | −32.9378 | −1.47746 | ||||||||
\(498\) | −3.37947 | −0.151438 | ||||||||
\(499\) | −20.1760 | −0.903203 | −0.451601 | − | 0.892220i | \(-0.649147\pi\) | ||||
−0.451601 | + | 0.892220i | \(0.649147\pi\) | |||||||
\(500\) | 18.1397 | 0.811233 | ||||||||
\(501\) | −14.9243 | −0.666768 | ||||||||
\(502\) | 4.88197 | 0.217893 | ||||||||
\(503\) | 16.5401 | 0.737485 | 0.368742 | − | 0.929532i | \(-0.379788\pi\) | ||||
0.368742 | + | 0.929532i | \(0.379788\pi\) | |||||||
\(504\) | −3.82287 | −0.170284 | ||||||||
\(505\) | 8.55401 | 0.380648 | ||||||||
\(506\) | −5.68297 | −0.252639 | ||||||||
\(507\) | 27.6410 | 1.22758 | ||||||||
\(508\) | 6.62366 | 0.293877 | ||||||||
\(509\) | −34.0855 | −1.51081 | −0.755407 | − | 0.655256i | \(-0.772561\pi\) | ||||
−0.755407 | + | 0.655256i | \(0.772561\pi\) | |||||||
\(510\) | 0.765408 | 0.0338929 | ||||||||
\(511\) | 35.8832 | 1.58738 | ||||||||
\(512\) | 20.2040 | 0.892901 | ||||||||
\(513\) | 8.52916 | 0.376572 | ||||||||
\(514\) | 2.74152 | 0.120923 | ||||||||
\(515\) | −8.00259 | −0.352636 | ||||||||
\(516\) | 2.07697 | 0.0914337 | ||||||||
\(517\) | −9.86277 | −0.433764 | ||||||||
\(518\) | −10.1818 | −0.447364 | ||||||||
\(519\) | 20.1069 | 0.882595 | ||||||||
\(520\) | −19.0543 | −0.835587 | ||||||||
\(521\) | −6.96670 | −0.305217 | −0.152608 | − | 0.988287i | \(-0.548767\pi\) | ||||
−0.152608 | + | 0.988287i | \(0.548767\pi\) | |||||||
\(522\) | −0.779582 | −0.0341214 | ||||||||
\(523\) | −40.5036 | −1.77110 | −0.885549 | − | 0.464547i | \(-0.846217\pi\) | ||||
−0.885549 | + | 0.464547i | \(0.846217\pi\) | |||||||
\(524\) | −16.2473 | −0.709765 | ||||||||
\(525\) | 3.69926 | 0.161449 | ||||||||
\(526\) | −0.517286 | −0.0225547 | ||||||||
\(527\) | −10.7183 | −0.466895 | ||||||||
\(528\) | −9.18047 | −0.399529 | ||||||||
\(529\) | 24.6851 | 1.07327 | ||||||||
\(530\) | −0.168058 | −0.00729998 | ||||||||
\(531\) | 10.6739 | 0.463210 | ||||||||
\(532\) | −51.5981 | −2.23706 | ||||||||
\(533\) | −10.6084 | −0.459499 | ||||||||
\(534\) | 4.31953 | 0.186924 | ||||||||
\(535\) | 43.1444 | 1.86529 | ||||||||
\(536\) | 13.6134 | 0.588010 | ||||||||
\(537\) | −17.3799 | −0.749998 | ||||||||
\(538\) | −4.31425 | −0.186000 | ||||||||
\(539\) | −8.23608 | −0.354753 | ||||||||
\(540\) | −4.72988 | −0.203541 | ||||||||
\(541\) | 21.6771 | 0.931973 | 0.465987 | − | 0.884792i | \(-0.345699\pi\) | ||||
0.465987 | + | 0.884792i | \(0.345699\pi\) | |||||||
\(542\) | −8.67614 | −0.372672 | ||||||||
\(543\) | 16.7714 | 0.719729 | ||||||||
\(544\) | 3.46767 | 0.148675 | ||||||||
\(545\) | −18.9702 | −0.812596 | ||||||||
\(546\) | 6.24099 | 0.267090 | ||||||||
\(547\) | 11.6608 | 0.498581 | 0.249291 | − | 0.968429i | \(-0.419803\pi\) | ||||
0.249291 | + | 0.968429i | \(0.419803\pi\) | |||||||
\(548\) | −28.0632 | −1.19880 | ||||||||
\(549\) | −4.77746 | −0.203897 | ||||||||
\(550\) | −0.958646 | −0.0408768 | ||||||||
\(551\) | −21.5693 | −0.918884 | ||||||||
\(552\) | −8.31267 | −0.353811 | ||||||||
\(553\) | 3.17570 | 0.135045 | ||||||||
\(554\) | 2.80162 | 0.119029 | ||||||||
\(555\) | −25.8235 | −1.09615 | ||||||||
\(556\) | −16.6870 | −0.707689 | ||||||||
\(557\) | −31.8534 | −1.34967 | −0.674837 | − | 0.737967i | \(-0.735786\pi\) | ||||
−0.674837 | + | 0.737967i | \(0.735786\pi\) | |||||||
\(558\) | −3.30412 | −0.139875 | ||||||||
\(559\) | −6.95065 | −0.293981 | ||||||||
\(560\) | 27.1153 | 1.14583 | ||||||||
\(561\) | −2.66964 | −0.112712 | ||||||||
\(562\) | −5.56043 | −0.234553 | ||||||||
\(563\) | 2.28644 | 0.0963619 | 0.0481810 | − | 0.998839i | \(-0.484658\pi\) | ||||
0.0481810 | + | 0.998839i | \(0.484658\pi\) | |||||||
\(564\) | −7.03777 | −0.296343 | ||||||||
\(565\) | 11.1075 | 0.467295 | ||||||||
\(566\) | −2.22773 | −0.0936387 | ||||||||
\(567\) | 3.17570 | 0.133367 | ||||||||
\(568\) | 12.4854 | 0.523877 | ||||||||
\(569\) | −34.0593 | −1.42784 | −0.713919 | − | 0.700228i | \(-0.753082\pi\) | ||||
−0.713919 | + | 0.700228i | \(0.753082\pi\) | |||||||
\(570\) | 6.52829 | 0.273440 | ||||||||
\(571\) | −1.12238 | −0.0469701 | −0.0234850 | − | 0.999724i | \(-0.507476\pi\) | ||||
−0.0234850 | + | 0.999724i | \(0.507476\pi\) | |||||||
\(572\) | 32.4207 | 1.35558 | ||||||||
\(573\) | −15.8317 | −0.661380 | ||||||||
\(574\) | −1.62906 | −0.0679957 | ||||||||
\(575\) | 8.04389 | 0.335453 | ||||||||
\(576\) | −5.80872 | −0.242030 | ||||||||
\(577\) | 8.44834 | 0.351709 | 0.175854 | − | 0.984416i | \(-0.443731\pi\) | ||||
0.175854 | + | 0.984416i | \(0.443731\pi\) | |||||||
\(578\) | 0.308270 | 0.0128224 | ||||||||
\(579\) | −16.7147 | −0.694639 | ||||||||
\(580\) | 11.9614 | 0.496668 | ||||||||
\(581\) | −34.8142 | −1.44434 | ||||||||
\(582\) | 2.06114 | 0.0854372 | ||||||||
\(583\) | 0.586163 | 0.0242764 | ||||||||
\(584\) | −13.6019 | −0.562852 | ||||||||
\(585\) | 15.8287 | 0.654434 | ||||||||
\(586\) | 0.745937 | 0.0308144 | ||||||||
\(587\) | −33.0442 | −1.36388 | −0.681940 | − | 0.731408i | \(-0.738863\pi\) | ||||
−0.681940 | + | 0.731408i | \(0.738863\pi\) | |||||||
\(588\) | −5.87701 | −0.242364 | ||||||||
\(589\) | −91.4178 | −3.76681 | ||||||||
\(590\) | 8.16993 | 0.336351 | ||||||||
\(591\) | 2.20508 | 0.0907049 | ||||||||
\(592\) | −35.7657 | −1.46996 | ||||||||
\(593\) | −25.9449 | −1.06543 | −0.532715 | − | 0.846295i | \(-0.678828\pi\) | ||||
−0.532715 | + | 0.846295i | \(0.678828\pi\) | |||||||
\(594\) | −0.822969 | −0.0337668 | ||||||||
\(595\) | 7.88500 | 0.323253 | ||||||||
\(596\) | 1.76759 | 0.0724033 | ||||||||
\(597\) | −6.40547 | −0.262158 | ||||||||
\(598\) | 13.5708 | 0.554951 | ||||||||
\(599\) | −33.1246 | −1.35343 | −0.676716 | − | 0.736244i | \(-0.736598\pi\) | ||||
−0.676716 | + | 0.736244i | \(0.736598\pi\) | |||||||
\(600\) | −1.40225 | −0.0572464 | ||||||||
\(601\) | −23.4938 | −0.958330 | −0.479165 | − | 0.877725i | \(-0.659061\pi\) | ||||
−0.479165 | + | 0.877725i | \(0.659061\pi\) | |||||||
\(602\) | −1.06737 | −0.0435027 | ||||||||
\(603\) | −11.3088 | −0.460531 | ||||||||
\(604\) | 14.6552 | 0.596310 | ||||||||
\(605\) | −9.61642 | −0.390963 | ||||||||
\(606\) | 1.06204 | 0.0431423 | ||||||||
\(607\) | 32.2185 | 1.30771 | 0.653854 | − | 0.756621i | \(-0.273151\pi\) | ||||
0.653854 | + | 0.756621i | \(0.273151\pi\) | |||||||
\(608\) | 29.5763 | 1.19948 | ||||||||
\(609\) | −8.03102 | −0.325433 | ||||||||
\(610\) | −3.65671 | −0.148056 | ||||||||
\(611\) | 23.5521 | 0.952815 | ||||||||
\(612\) | −1.90497 | −0.0770038 | ||||||||
\(613\) | 24.4103 | 0.985921 | 0.492961 | − | 0.870052i | \(-0.335915\pi\) | ||||
0.492961 | + | 0.870052i | \(0.335915\pi\) | |||||||
\(614\) | 5.00268 | 0.201892 | ||||||||
\(615\) | −4.13169 | −0.166606 | ||||||||
\(616\) | 10.2057 | 0.411198 | ||||||||
\(617\) | 13.2441 | 0.533186 | 0.266593 | − | 0.963809i | \(-0.414102\pi\) | ||||
0.266593 | + | 0.963809i | \(0.414102\pi\) | |||||||
\(618\) | −0.993575 | −0.0399674 | ||||||||
\(619\) | −20.0734 | −0.806816 | −0.403408 | − | 0.915020i | \(-0.632175\pi\) | ||||
−0.403408 | + | 0.915020i | \(0.632175\pi\) | |||||||
\(620\) | 50.6961 | 2.03600 | ||||||||
\(621\) | 6.90544 | 0.277106 | ||||||||
\(622\) | 5.50513 | 0.220736 | ||||||||
\(623\) | 44.4985 | 1.78279 | ||||||||
\(624\) | 21.9228 | 0.877613 | ||||||||
\(625\) | −29.4674 | −1.17870 | ||||||||
\(626\) | −0.526200 | −0.0210312 | ||||||||
\(627\) | −22.7698 | −0.909336 | ||||||||
\(628\) | 42.9136 | 1.71244 | ||||||||
\(629\) | −10.4005 | −0.414695 | ||||||||
\(630\) | 2.43071 | 0.0968418 | ||||||||
\(631\) | 7.18197 | 0.285910 | 0.142955 | − | 0.989729i | \(-0.454340\pi\) | ||||
0.142955 | + | 0.989729i | \(0.454340\pi\) | |||||||
\(632\) | −1.20379 | −0.0478840 | ||||||||
\(633\) | 1.83566 | 0.0729608 | ||||||||
\(634\) | 4.72264 | 0.187560 | ||||||||
\(635\) | −8.63320 | −0.342598 | ||||||||
\(636\) | 0.418268 | 0.0165854 | ||||||||
\(637\) | 19.6676 | 0.779257 | ||||||||
\(638\) | 2.08120 | 0.0823956 | ||||||||
\(639\) | −10.3718 | −0.410302 | ||||||||
\(640\) | −21.6659 | −0.856419 | ||||||||
\(641\) | 7.88544 | 0.311456 | 0.155728 | − | 0.987800i | \(-0.450228\pi\) | ||||
0.155728 | + | 0.987800i | \(0.450228\pi\) | |||||||
\(642\) | 5.35666 | 0.211410 | ||||||||
\(643\) | −6.17922 | −0.243685 | −0.121842 | − | 0.992549i | \(-0.538880\pi\) | ||||
−0.121842 | + | 0.992549i | \(0.538880\pi\) | |||||||
\(644\) | −41.7753 | −1.64618 | ||||||||
\(645\) | −2.70710 | −0.106592 | ||||||||
\(646\) | 2.62929 | 0.103448 | ||||||||
\(647\) | −40.8799 | −1.60715 | −0.803577 | − | 0.595201i | \(-0.797072\pi\) | ||||
−0.803577 | + | 0.595201i | \(0.797072\pi\) | |||||||
\(648\) | −1.20379 | −0.0472892 | ||||||||
\(649\) | −28.4956 | −1.11855 | ||||||||
\(650\) | 2.28923 | 0.0897908 | ||||||||
\(651\) | −34.0380 | −1.33406 | ||||||||
\(652\) | −10.0668 | −0.394247 | ||||||||
\(653\) | −43.0718 | −1.68553 | −0.842764 | − | 0.538282i | \(-0.819073\pi\) | ||||
−0.842764 | + | 0.538282i | \(0.819073\pi\) | |||||||
\(654\) | −2.35528 | −0.0920988 | ||||||||
\(655\) | 21.1765 | 0.827433 | ||||||||
\(656\) | −5.72241 | −0.223423 | ||||||||
\(657\) | 11.2993 | 0.440827 | ||||||||
\(658\) | 3.61675 | 0.140996 | ||||||||
\(659\) | 30.7760 | 1.19886 | 0.599432 | − | 0.800426i | \(-0.295393\pi\) | ||||
0.599432 | + | 0.800426i | \(0.295393\pi\) | |||||||
\(660\) | 12.6271 | 0.491507 | ||||||||
\(661\) | −44.9574 | −1.74864 | −0.874321 | − | 0.485348i | \(-0.838693\pi\) | ||||
−0.874321 | + | 0.485348i | \(0.838693\pi\) | |||||||
\(662\) | 2.74937 | 0.106857 | ||||||||
\(663\) | 6.37503 | 0.247586 | ||||||||
\(664\) | 13.1967 | 0.512132 | ||||||||
\(665\) | 67.2524 | 2.60794 | ||||||||
\(666\) | −3.20616 | −0.124236 | ||||||||
\(667\) | −17.4631 | −0.676175 | ||||||||
\(668\) | 28.4303 | 1.10000 | ||||||||
\(669\) | 6.27182 | 0.242482 | ||||||||
\(670\) | −8.65588 | −0.334406 | ||||||||
\(671\) | 12.7541 | 0.492366 | ||||||||
\(672\) | 11.0123 | 0.424808 | ||||||||
\(673\) | 8.36670 | 0.322513 | 0.161256 | − | 0.986913i | \(-0.448445\pi\) | ||||
0.161256 | + | 0.986913i | \(0.448445\pi\) | |||||||
\(674\) | −10.2794 | −0.395947 | ||||||||
\(675\) | 1.16486 | 0.0448356 | ||||||||
\(676\) | −52.6553 | −2.02520 | ||||||||
\(677\) | −19.6219 | −0.754131 | −0.377065 | − | 0.926187i | \(-0.623067\pi\) | ||||
−0.377065 | + | 0.926187i | \(0.623067\pi\) | |||||||
\(678\) | 1.37907 | 0.0529627 | ||||||||
\(679\) | 21.2333 | 0.814858 | ||||||||
\(680\) | −2.98890 | −0.114619 | ||||||||
\(681\) | 25.3970 | 0.973215 | ||||||||
\(682\) | 8.82081 | 0.337766 | ||||||||
\(683\) | 46.7556 | 1.78905 | 0.894526 | − | 0.447016i | \(-0.147513\pi\) | ||||
0.894526 | + | 0.447016i | \(0.147513\pi\) | |||||||
\(684\) | −16.2478 | −0.621250 | ||||||||
\(685\) | 36.5772 | 1.39754 | ||||||||
\(686\) | −3.83260 | −0.146329 | ||||||||
\(687\) | −4.87536 | −0.186007 | ||||||||
\(688\) | −3.74935 | −0.142943 | ||||||||
\(689\) | −1.39974 | −0.0533260 | ||||||||
\(690\) | 5.28548 | 0.201215 | ||||||||
\(691\) | −22.1127 | −0.841206 | −0.420603 | − | 0.907245i | \(-0.638181\pi\) | ||||
−0.420603 | + | 0.907245i | \(0.638181\pi\) | |||||||
\(692\) | −38.3030 | −1.45606 | ||||||||
\(693\) | −8.47797 | −0.322052 | ||||||||
\(694\) | −3.84569 | −0.145980 | ||||||||
\(695\) | 21.7497 | 0.825013 | ||||||||
\(696\) | 3.04425 | 0.115392 | ||||||||
\(697\) | −1.66405 | −0.0630303 | ||||||||
\(698\) | −6.90624 | −0.261405 | ||||||||
\(699\) | 7.18402 | 0.271725 | ||||||||
\(700\) | −7.04697 | −0.266351 | ||||||||
\(701\) | −10.3861 | −0.392278 | −0.196139 | − | 0.980576i | \(-0.562840\pi\) | ||||
−0.196139 | + | 0.980576i | \(0.562840\pi\) | |||||||
\(702\) | 1.96523 | 0.0741729 | ||||||||
\(703\) | −88.7075 | −3.34567 | ||||||||
\(704\) | 15.5072 | 0.584448 | ||||||||
\(705\) | 9.17294 | 0.345473 | ||||||||
\(706\) | 0.299243 | 0.0112622 | ||||||||
\(707\) | 10.9408 | 0.411470 | ||||||||
\(708\) | −20.3335 | −0.764181 | ||||||||
\(709\) | −38.4299 | −1.44327 | −0.721633 | − | 0.692276i | \(-0.756608\pi\) | ||||
−0.721633 | + | 0.692276i | \(0.756608\pi\) | |||||||
\(710\) | −7.93867 | −0.297933 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −16.8676 | −0.632142 | ||||||||
\(713\) | −74.0144 | −2.77186 | ||||||||
\(714\) | 0.978975 | 0.0366372 | ||||||||
\(715\) | −42.2568 | −1.58031 | ||||||||
\(716\) | 33.1082 | 1.23731 | ||||||||
\(717\) | −1.15315 | −0.0430653 | ||||||||
\(718\) | −7.48873 | −0.279477 | ||||||||
\(719\) | −41.9706 | −1.56524 | −0.782621 | − | 0.622499i | \(-0.786117\pi\) | ||||
−0.782621 | + | 0.622499i | \(0.786117\pi\) | |||||||
\(720\) | 8.53836 | 0.318206 | ||||||||
\(721\) | −10.2355 | −0.381190 | ||||||||
\(722\) | 16.5685 | 0.616614 | ||||||||
\(723\) | −10.8434 | −0.403271 | ||||||||
\(724\) | −31.9490 | −1.18737 | ||||||||
\(725\) | −2.94581 | −0.109405 | ||||||||
\(726\) | −1.19394 | −0.0443114 | ||||||||
\(727\) | −15.2135 | −0.564239 | −0.282119 | − | 0.959379i | \(-0.591037\pi\) | ||||
−0.282119 | + | 0.959379i | \(0.591037\pi\) | |||||||
\(728\) | −24.3709 | −0.903245 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.64857 | 0.320098 | ||||||||
\(731\) | −1.09029 | −0.0403259 | ||||||||
\(732\) | 9.10091 | 0.336379 | ||||||||
\(733\) | 13.0377 | 0.481559 | 0.240780 | − | 0.970580i | \(-0.422597\pi\) | ||||
0.240780 | + | 0.970580i | \(0.422597\pi\) | |||||||
\(734\) | 9.43972 | 0.348426 | ||||||||
\(735\) | 7.66002 | 0.282544 | ||||||||
\(736\) | 23.9458 | 0.882653 | ||||||||
\(737\) | 30.1905 | 1.11208 | ||||||||
\(738\) | −0.512977 | −0.0188829 | ||||||||
\(739\) | −24.7703 | −0.911191 | −0.455596 | − | 0.890187i | \(-0.650574\pi\) | ||||
−0.455596 | + | 0.890187i | \(0.650574\pi\) | |||||||
\(740\) | 49.1931 | 1.80837 | ||||||||
\(741\) | 54.3736 | 1.99747 | ||||||||
\(742\) | −0.214950 | −0.00789107 | ||||||||
\(743\) | −0.886641 | −0.0325277 | −0.0162638 | − | 0.999868i | \(-0.505177\pi\) | ||||
−0.0162638 | + | 0.999868i | \(0.505177\pi\) | |||||||
\(744\) | 12.9025 | 0.473029 | ||||||||
\(745\) | −2.30386 | −0.0844068 | ||||||||
\(746\) | −7.02275 | −0.257121 | ||||||||
\(747\) | −10.9627 | −0.401104 | ||||||||
\(748\) | 5.08558 | 0.185947 | ||||||||
\(749\) | 55.1826 | 2.01633 | ||||||||
\(750\) | −2.93545 | −0.107187 | ||||||||
\(751\) | 34.0442 | 1.24229 | 0.621146 | − | 0.783695i | \(-0.286668\pi\) | ||||
0.621146 | + | 0.783695i | \(0.286668\pi\) | |||||||
\(752\) | 12.7046 | 0.463288 | ||||||||
\(753\) | 15.8366 | 0.577120 | ||||||||
\(754\) | −4.96986 | −0.180992 | ||||||||
\(755\) | −19.1013 | −0.695169 | ||||||||
\(756\) | −6.04962 | −0.220022 | ||||||||
\(757\) | 9.99230 | 0.363176 | 0.181588 | − | 0.983375i | \(-0.441876\pi\) | ||||
0.181588 | + | 0.983375i | \(0.441876\pi\) | |||||||
\(758\) | −3.20845 | −0.116536 | ||||||||
\(759\) | −18.4350 | −0.669149 | ||||||||
\(760\) | −25.4928 | −0.924720 | ||||||||
\(761\) | −46.9128 | −1.70059 | −0.850294 | − | 0.526308i | \(-0.823576\pi\) | ||||
−0.850294 | + | 0.526308i | \(0.823576\pi\) | |||||||
\(762\) | −1.07187 | −0.0388297 | ||||||||
\(763\) | −24.2634 | −0.878393 | ||||||||
\(764\) | 30.1589 | 1.09111 | ||||||||
\(765\) | 2.48291 | 0.0897700 | ||||||||
\(766\) | 6.53167 | 0.235999 | ||||||||
\(767\) | 68.0467 | 2.45703 | ||||||||
\(768\) | 8.92747 | 0.322142 | ||||||||
\(769\) | −7.06792 | −0.254876 | −0.127438 | − | 0.991847i | \(-0.540675\pi\) | ||||
−0.127438 | + | 0.991847i | \(0.540675\pi\) | |||||||
\(770\) | −6.48911 | −0.233851 | ||||||||
\(771\) | 8.89323 | 0.320282 | ||||||||
\(772\) | 31.8410 | 1.14598 | ||||||||
\(773\) | 44.8961 | 1.61480 | 0.807400 | − | 0.590005i | \(-0.200874\pi\) | ||||
0.807400 | + | 0.590005i | \(0.200874\pi\) | |||||||
\(774\) | −0.336105 | −0.0120810 | ||||||||
\(775\) | −12.4853 | −0.448486 | ||||||||
\(776\) | −8.04870 | −0.288932 | ||||||||
\(777\) | −33.0289 | −1.18491 | ||||||||
\(778\) | −5.78020 | −0.207230 | ||||||||
\(779\) | −14.1929 | −0.508515 | ||||||||
\(780\) | −30.1531 | −1.07965 | ||||||||
\(781\) | 27.6889 | 0.990788 | ||||||||
\(782\) | 2.12874 | 0.0761237 | ||||||||
\(783\) | −2.52889 | −0.0903753 | ||||||||
\(784\) | 10.6092 | 0.378899 | ||||||||
\(785\) | −55.9331 | −1.99634 | ||||||||
\(786\) | 2.62920 | 0.0937804 | ||||||||
\(787\) | 1.18545 | 0.0422566 | 0.0211283 | − | 0.999777i | \(-0.493274\pi\) | ||||
0.0211283 | + | 0.999777i | \(0.493274\pi\) | |||||||
\(788\) | −4.20061 | −0.149641 | ||||||||
\(789\) | −1.67803 | −0.0597393 | ||||||||
\(790\) | 0.765408 | 0.0272320 | ||||||||
\(791\) | 14.2067 | 0.505132 | ||||||||
\(792\) | 3.21367 | 0.114193 | ||||||||
\(793\) | −30.4564 | −1.08154 | ||||||||
\(794\) | 0.151482 | 0.00537591 | ||||||||
\(795\) | −0.545165 | −0.0193350 | ||||||||
\(796\) | 12.2022 | 0.432496 | ||||||||
\(797\) | 27.3862 | 0.970071 | 0.485035 | − | 0.874495i | \(-0.338807\pi\) | ||||
0.485035 | + | 0.874495i | \(0.338807\pi\) | |||||||
\(798\) | 8.34983 | 0.295581 | ||||||||
\(799\) | 3.69443 | 0.130699 | ||||||||
\(800\) | 4.03935 | 0.142813 | ||||||||
\(801\) | 14.0122 | 0.495096 | ||||||||
\(802\) | 5.42490 | 0.191560 | ||||||||
\(803\) | −30.1650 | −1.06450 | ||||||||
\(804\) | 21.5430 | 0.759763 | ||||||||
\(805\) | 54.4494 | 1.91909 | ||||||||
\(806\) | −21.0639 | −0.741944 | ||||||||
\(807\) | −13.9950 | −0.492648 | ||||||||
\(808\) | −4.14722 | −0.145899 | ||||||||
\(809\) | 44.8128 | 1.57554 | 0.787768 | − | 0.615972i | \(-0.211237\pi\) | ||||
0.787768 | + | 0.615972i | \(0.211237\pi\) | |||||||
\(810\) | 0.765408 | 0.0268937 | ||||||||
\(811\) | 12.8672 | 0.451830 | 0.225915 | − | 0.974147i | \(-0.427463\pi\) | ||||
0.225915 | + | 0.974147i | \(0.427463\pi\) | |||||||
\(812\) | 15.2988 | 0.536884 | ||||||||
\(813\) | −28.1446 | −0.987074 | ||||||||
\(814\) | 8.55929 | 0.300003 | ||||||||
\(815\) | 13.1210 | 0.459608 | ||||||||
\(816\) | 3.43885 | 0.120384 | ||||||||
\(817\) | −9.29928 | −0.325340 | ||||||||
\(818\) | 6.58362 | 0.230191 | ||||||||
\(819\) | 20.2452 | 0.707425 | ||||||||
\(820\) | 7.87074 | 0.274858 | ||||||||
\(821\) | −43.1356 | −1.50544 | −0.752722 | − | 0.658338i | \(-0.771260\pi\) | ||||
−0.752722 | + | 0.658338i | \(0.771260\pi\) | |||||||
\(822\) | 4.54130 | 0.158396 | ||||||||
\(823\) | 39.6752 | 1.38299 | 0.691495 | − | 0.722382i | \(-0.256953\pi\) | ||||
0.691495 | + | 0.722382i | \(0.256953\pi\) | |||||||
\(824\) | 3.87988 | 0.135162 | ||||||||
\(825\) | −3.10976 | −0.108268 | ||||||||
\(826\) | 10.4495 | 0.363585 | ||||||||
\(827\) | 27.5850 | 0.959226 | 0.479613 | − | 0.877480i | \(-0.340777\pi\) | ||||
0.479613 | + | 0.877480i | \(0.340777\pi\) | |||||||
\(828\) | −13.1547 | −0.457156 | ||||||||
\(829\) | 2.66595 | 0.0925924 | 0.0462962 | − | 0.998928i | \(-0.485258\pi\) | ||||
0.0462962 | + | 0.998928i | \(0.485258\pi\) | |||||||
\(830\) | −8.39093 | −0.291253 | ||||||||
\(831\) | 9.08819 | 0.315266 | ||||||||
\(832\) | −37.0307 | −1.28381 | ||||||||
\(833\) | 3.08509 | 0.106892 | ||||||||
\(834\) | 2.70037 | 0.0935061 | ||||||||
\(835\) | −37.0557 | −1.28237 | ||||||||
\(836\) | 43.3757 | 1.50018 | ||||||||
\(837\) | −10.7183 | −0.370478 | ||||||||
\(838\) | 4.72782 | 0.163320 | ||||||||
\(839\) | −12.2946 | −0.424457 | −0.212229 | − | 0.977220i | \(-0.568072\pi\) | ||||
−0.212229 | + | 0.977220i | \(0.568072\pi\) | |||||||
\(840\) | −9.49185 | −0.327500 | ||||||||
\(841\) | −22.6047 | −0.779472 | ||||||||
\(842\) | 0.961818 | 0.0331464 | ||||||||
\(843\) | −18.0375 | −0.621245 | ||||||||
\(844\) | −3.49687 | −0.120367 | ||||||||
\(845\) | 68.6302 | 2.36095 | ||||||||
\(846\) | 1.13888 | 0.0391555 | ||||||||
\(847\) | −12.2996 | −0.422620 | ||||||||
\(848\) | −0.755056 | −0.0259287 | ||||||||
\(849\) | −7.22656 | −0.248015 | ||||||||
\(850\) | 0.359092 | 0.0123168 | ||||||||
\(851\) | −71.8200 | −2.46196 | ||||||||
\(852\) | 19.7580 | 0.676897 | ||||||||
\(853\) | −25.6995 | −0.879936 | −0.439968 | − | 0.898014i | \(-0.645010\pi\) | ||||
−0.439968 | + | 0.898014i | \(0.645010\pi\) | |||||||
\(854\) | −4.67701 | −0.160044 | ||||||||
\(855\) | 21.1772 | 0.724244 | ||||||||
\(856\) | −20.9176 | −0.714948 | ||||||||
\(857\) | 20.3237 | 0.694246 | 0.347123 | − | 0.937820i | \(-0.387159\pi\) | ||||
0.347123 | + | 0.937820i | \(0.387159\pi\) | |||||||
\(858\) | −5.24646 | −0.179111 | ||||||||
\(859\) | 4.72667 | 0.161272 | 0.0806360 | − | 0.996744i | \(-0.474305\pi\) | ||||
0.0806360 | + | 0.996744i | \(0.474305\pi\) | |||||||
\(860\) | 5.15695 | 0.175850 | ||||||||
\(861\) | −5.28453 | −0.180096 | ||||||||
\(862\) | 5.24429 | 0.178621 | ||||||||
\(863\) | 14.2759 | 0.485958 | 0.242979 | − | 0.970031i | \(-0.421875\pi\) | ||||
0.242979 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(864\) | 3.46767 | 0.117972 | ||||||||
\(865\) | 49.9237 | 1.69746 | ||||||||
\(866\) | −4.49445 | −0.152727 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 64.8414 | 2.20086 | ||||||||
\(869\) | −2.66964 | −0.0905612 | ||||||||
\(870\) | −1.93564 | −0.0656242 | ||||||||
\(871\) | −72.0942 | −2.44282 | ||||||||
\(872\) | 9.19730 | 0.311460 | ||||||||
\(873\) | 6.68616 | 0.226292 | ||||||||
\(874\) | 18.1564 | 0.614149 | ||||||||
\(875\) | −30.2401 | −1.02230 | ||||||||
\(876\) | −21.5248 | −0.727256 | ||||||||
\(877\) | 14.5218 | 0.490368 | 0.245184 | − | 0.969477i | \(-0.421152\pi\) | ||||
0.245184 | + | 0.969477i | \(0.421152\pi\) | |||||||
\(878\) | 3.36683 | 0.113625 | ||||||||
\(879\) | 2.41975 | 0.0816162 | ||||||||
\(880\) | −22.7943 | −0.768397 | ||||||||
\(881\) | 27.4767 | 0.925712 | 0.462856 | − | 0.886433i | \(-0.346825\pi\) | ||||
0.462856 | + | 0.886433i | \(0.346825\pi\) | |||||||
\(882\) | 0.951042 | 0.0320233 | ||||||||
\(883\) | −18.6394 | −0.627265 | −0.313632 | − | 0.949544i | \(-0.601546\pi\) | ||||
−0.313632 | + | 0.949544i | \(0.601546\pi\) | |||||||
\(884\) | −12.1442 | −0.408455 | ||||||||
\(885\) | 26.5025 | 0.890872 | ||||||||
\(886\) | 2.55179 | 0.0857291 | ||||||||
\(887\) | −8.22724 | −0.276244 | −0.138122 | − | 0.990415i | \(-0.544107\pi\) | ||||
−0.138122 | + | 0.990415i | \(0.544107\pi\) | |||||||
\(888\) | 12.5200 | 0.420143 | ||||||||
\(889\) | −11.0421 | −0.370339 | ||||||||
\(890\) | 10.7250 | 0.359504 | ||||||||
\(891\) | −2.66964 | −0.0894362 | ||||||||
\(892\) | −11.9476 | −0.400036 | ||||||||
\(893\) | 31.5103 | 1.05445 | ||||||||
\(894\) | −0.286039 | −0.00956658 | ||||||||
\(895\) | −43.1528 | −1.44244 | ||||||||
\(896\) | −27.7111 | −0.925764 | ||||||||
\(897\) | 44.0224 | 1.46987 | ||||||||
\(898\) | −9.25567 | −0.308866 | ||||||||
\(899\) | 27.1054 | 0.904015 | ||||||||
\(900\) | −2.21903 | −0.0739676 | ||||||||
\(901\) | −0.219567 | −0.00731482 | ||||||||
\(902\) | 1.36946 | 0.0455981 | ||||||||
\(903\) | −3.46245 | −0.115223 | ||||||||
\(904\) | −5.38521 | −0.179109 | ||||||||
\(905\) | 41.6419 | 1.38422 | ||||||||
\(906\) | −2.37156 | −0.0787898 | ||||||||
\(907\) | −16.5562 | −0.549740 | −0.274870 | − | 0.961481i | \(-0.588635\pi\) | ||||
−0.274870 | + | 0.961481i | \(0.588635\pi\) | |||||||
\(908\) | −48.3805 | −1.60556 | ||||||||
\(909\) | 3.44515 | 0.114268 | ||||||||
\(910\) | 15.4959 | 0.513682 | ||||||||
\(911\) | 34.4530 | 1.14148 | 0.570740 | − | 0.821131i | \(-0.306656\pi\) | ||||
0.570740 | + | 0.821131i | \(0.306656\pi\) | |||||||
\(912\) | 29.3305 | 0.971229 | ||||||||
\(913\) | 29.2664 | 0.968576 | ||||||||
\(914\) | 3.28094 | 0.108524 | ||||||||
\(915\) | −11.8620 | −0.392146 | ||||||||
\(916\) | 9.28742 | 0.306865 | ||||||||
\(917\) | 27.0852 | 0.894432 | ||||||||
\(918\) | 0.308270 | 0.0101744 | ||||||||
\(919\) | 39.8674 | 1.31510 | 0.657552 | − | 0.753409i | \(-0.271592\pi\) | ||||
0.657552 | + | 0.753409i | \(0.271592\pi\) | |||||||
\(920\) | −20.6397 | −0.680469 | ||||||||
\(921\) | 16.2282 | 0.534738 | ||||||||
\(922\) | −7.80553 | −0.257062 | ||||||||
\(923\) | −66.1206 | −2.17638 | ||||||||
\(924\) | 16.1503 | 0.531305 | ||||||||
\(925\) | −12.1152 | −0.398344 | ||||||||
\(926\) | −3.49654 | −0.114903 | ||||||||
\(927\) | −3.22307 | −0.105859 | ||||||||
\(928\) | −8.76936 | −0.287868 | ||||||||
\(929\) | 7.12093 | 0.233630 | 0.116815 | − | 0.993154i | \(-0.462732\pi\) | ||||
0.116815 | + | 0.993154i | \(0.462732\pi\) | |||||||
\(930\) | −8.20386 | −0.269015 | ||||||||
\(931\) | 26.3132 | 0.862382 | ||||||||
\(932\) | −13.6853 | −0.448278 | ||||||||
\(933\) | 17.8581 | 0.584649 | ||||||||
\(934\) | 11.3629 | 0.371806 | ||||||||
\(935\) | −6.62848 | −0.216774 | ||||||||
\(936\) | −7.67417 | −0.250838 | ||||||||
\(937\) | −42.9110 | −1.40184 | −0.700921 | − | 0.713239i | \(-0.747227\pi\) | ||||
−0.700921 | + | 0.713239i | \(0.747227\pi\) | |||||||
\(938\) | −11.0711 | −0.361483 | ||||||||
\(939\) | −1.70694 | −0.0557040 | ||||||||
\(940\) | −17.4742 | −0.569945 | ||||||||
\(941\) | −18.9403 | −0.617438 | −0.308719 | − | 0.951153i | \(-0.599900\pi\) | ||||
−0.308719 | + | 0.951153i | \(0.599900\pi\) | |||||||
\(942\) | −6.94446 | −0.226263 | ||||||||
\(943\) | −11.4910 | −0.374198 | ||||||||
\(944\) | 36.7061 | 1.19468 | ||||||||
\(945\) | 7.88500 | 0.256499 | ||||||||
\(946\) | 0.897277 | 0.0291730 | ||||||||
\(947\) | 51.2717 | 1.66610 | 0.833052 | − | 0.553194i | \(-0.186591\pi\) | ||||
0.833052 | + | 0.553194i | \(0.186591\pi\) | |||||||
\(948\) | −1.90497 | −0.0618705 | ||||||||
\(949\) | 72.0333 | 2.33830 | ||||||||
\(950\) | 3.06276 | 0.0993689 | ||||||||
\(951\) | 15.3198 | 0.496779 | ||||||||
\(952\) | −3.82287 | −0.123900 | ||||||||
\(953\) | 0.0503342 | 0.00163048 | 0.000815242 | − | 1.00000i | \(-0.499741\pi\) | ||||
0.000815242 | 1.00000i | \(0.499741\pi\) | ||||||||
\(954\) | −0.0676858 | −0.00219141 | ||||||||
\(955\) | −39.3088 | −1.27200 | ||||||||
\(956\) | 2.19672 | 0.0710470 | ||||||||
\(957\) | 6.75123 | 0.218236 | ||||||||
\(958\) | 5.06889 | 0.163768 | ||||||||
\(959\) | 46.7831 | 1.51070 | ||||||||
\(960\) | −14.4225 | −0.465486 | ||||||||
\(961\) | 83.8813 | 2.70585 | ||||||||
\(962\) | −20.4394 | −0.658992 | ||||||||
\(963\) | 17.3765 | 0.559950 | ||||||||
\(964\) | 20.6564 | 0.665298 | ||||||||
\(965\) | −41.5011 | −1.33597 | ||||||||
\(966\) | 6.76025 | 0.217508 | ||||||||
\(967\) | 8.92585 | 0.287036 | 0.143518 | − | 0.989648i | \(-0.454159\pi\) | ||||
0.143518 | + | 0.989648i | \(0.454159\pi\) | |||||||
\(968\) | 4.66231 | 0.149852 | ||||||||
\(969\) | 8.52916 | 0.273996 | ||||||||
\(970\) | 5.11764 | 0.164318 | ||||||||
\(971\) | 9.84156 | 0.315831 | 0.157915 | − | 0.987453i | \(-0.449523\pi\) | ||||
0.157915 | + | 0.987453i | \(0.449523\pi\) | |||||||
\(972\) | −1.90497 | −0.0611019 | ||||||||
\(973\) | 27.8184 | 0.891816 | ||||||||
\(974\) | 10.1791 | 0.326159 | ||||||||
\(975\) | 7.42603 | 0.237823 | ||||||||
\(976\) | −16.4290 | −0.525878 | ||||||||
\(977\) | −49.4226 | −1.58117 | −0.790584 | − | 0.612354i | \(-0.790223\pi\) | ||||
−0.790584 | + | 0.612354i | \(0.790223\pi\) | |||||||
\(978\) | 1.62906 | 0.0520914 | ||||||||
\(979\) | −37.4074 | −1.19555 | ||||||||
\(980\) | −14.5921 | −0.466128 | ||||||||
\(981\) | −7.64031 | −0.243936 | ||||||||
\(982\) | −1.72121 | −0.0549259 | ||||||||
\(983\) | −7.22029 | −0.230291 | −0.115146 | − | 0.993349i | \(-0.536733\pi\) | ||||
−0.115146 | + | 0.993349i | \(0.536733\pi\) | |||||||
\(984\) | 2.00316 | 0.0638584 | ||||||||
\(985\) | 5.47502 | 0.174449 | ||||||||
\(986\) | −0.779582 | −0.0248270 | ||||||||
\(987\) | 11.7324 | 0.373446 | ||||||||
\(988\) | −103.580 | −3.29532 | ||||||||
\(989\) | −7.52895 | −0.239407 | ||||||||
\(990\) | −2.04336 | −0.0649423 | ||||||||
\(991\) | −53.4752 | −1.69870 | −0.849349 | − | 0.527832i | \(-0.823005\pi\) | ||||
−0.849349 | + | 0.527832i | \(0.823005\pi\) | |||||||
\(992\) | −37.1674 | −1.18007 | ||||||||
\(993\) | 8.91869 | 0.283026 | ||||||||
\(994\) | −10.1537 | −0.322057 | ||||||||
\(995\) | −15.9042 | −0.504198 | ||||||||
\(996\) | 20.8836 | 0.661721 | ||||||||
\(997\) | 39.2086 | 1.24175 | 0.620875 | − | 0.783910i | \(-0.286778\pi\) | ||||
0.620875 | + | 0.783910i | \(0.286778\pi\) | |||||||
\(998\) | −6.21967 | −0.196880 | ||||||||
\(999\) | −10.4005 | −0.329057 |
(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 | 4029.2.a.k.1.17 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.17 | ✓ | 31 | 1.1 | even | 1 | trivial |