Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6035,2,Mod(1,6035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6035, 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("6035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.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: | \(48.1897176198\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00836 | −1.42013 | −0.710063 | − | 0.704138i | \(-0.751334\pi\) | ||||
−0.710063 | + | 0.704138i | \(0.751334\pi\) | |||||||
\(3\) | 0.177134 | 0.102268 | 0.0511342 | − | 0.998692i | \(-0.483716\pi\) | ||||
0.0511342 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(4\) | 2.03352 | 1.01676 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.355749 | −0.145234 | ||||||||
\(7\) | −1.65376 | −0.625063 | −0.312532 | − | 0.949907i | \(-0.601177\pi\) | ||||
−0.312532 | + | 0.949907i | \(0.601177\pi\) | |||||||
\(8\) | −0.0673116 | −0.0237982 | ||||||||
\(9\) | −2.96862 | −0.989541 | ||||||||
\(10\) | −2.00836 | −0.635100 | ||||||||
\(11\) | 3.65244 | 1.10125 | 0.550626 | − | 0.834752i | \(-0.314389\pi\) | ||||
0.550626 | + | 0.834752i | \(0.314389\pi\) | |||||||
\(12\) | 0.360205 | 0.103982 | ||||||||
\(13\) | −3.93545 | −1.09150 | −0.545749 | − | 0.837949i | \(-0.683755\pi\) | ||||
−0.545749 | + | 0.837949i | \(0.683755\pi\) | |||||||
\(14\) | 3.32135 | 0.887669 | ||||||||
\(15\) | 0.177134 | 0.0457358 | ||||||||
\(16\) | −3.93185 | −0.982961 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.96207 | 1.40527 | ||||||||
\(19\) | 2.30295 | 0.528333 | 0.264167 | − | 0.964477i | \(-0.414903\pi\) | ||||
0.264167 | + | 0.964477i | \(0.414903\pi\) | |||||||
\(20\) | 2.03352 | 0.454708 | ||||||||
\(21\) | −0.292937 | −0.0639242 | ||||||||
\(22\) | −7.33542 | −1.56392 | ||||||||
\(23\) | 6.71610 | 1.40040 | 0.700202 | − | 0.713945i | \(-0.253093\pi\) | ||||
0.700202 | + | 0.713945i | \(0.253093\pi\) | |||||||
\(24\) | −0.0119232 | −0.00243381 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.90381 | 1.55006 | ||||||||
\(27\) | −1.05725 | −0.203467 | ||||||||
\(28\) | −3.36295 | −0.635538 | ||||||||
\(29\) | 0.825756 | 0.153339 | 0.0766696 | − | 0.997057i | \(-0.475571\pi\) | ||||
0.0766696 | + | 0.997057i | \(0.475571\pi\) | |||||||
\(30\) | −0.355749 | −0.0649506 | ||||||||
\(31\) | −1.46380 | −0.262906 | −0.131453 | − | 0.991322i | \(-0.541964\pi\) | ||||
−0.131453 | + | 0.991322i | \(0.541964\pi\) | |||||||
\(32\) | 8.03119 | 1.41973 | ||||||||
\(33\) | 0.646971 | 0.112623 | ||||||||
\(34\) | −2.00836 | −0.344431 | ||||||||
\(35\) | −1.65376 | −0.279537 | ||||||||
\(36\) | −6.03674 | −1.00612 | ||||||||
\(37\) | −4.65274 | −0.764906 | −0.382453 | − | 0.923975i | \(-0.624921\pi\) | ||||
−0.382453 | + | 0.923975i | \(0.624921\pi\) | |||||||
\(38\) | −4.62516 | −0.750299 | ||||||||
\(39\) | −0.697102 | −0.111626 | ||||||||
\(40\) | −0.0673116 | −0.0106429 | ||||||||
\(41\) | 10.9166 | 1.70488 | 0.852442 | − | 0.522822i | \(-0.175121\pi\) | ||||
0.852442 | + | 0.522822i | \(0.175121\pi\) | |||||||
\(42\) | 0.588324 | 0.0907804 | ||||||||
\(43\) | 2.83622 | 0.432520 | 0.216260 | − | 0.976336i | \(-0.430614\pi\) | ||||
0.216260 | + | 0.976336i | \(0.430614\pi\) | |||||||
\(44\) | 7.42729 | 1.11971 | ||||||||
\(45\) | −2.96862 | −0.442536 | ||||||||
\(46\) | −13.4884 | −1.98875 | ||||||||
\(47\) | −5.31053 | −0.774621 | −0.387311 | − | 0.921949i | \(-0.626596\pi\) | ||||
−0.387311 | + | 0.921949i | \(0.626596\pi\) | |||||||
\(48\) | −0.696463 | −0.100526 | ||||||||
\(49\) | −4.26507 | −0.609296 | ||||||||
\(50\) | −2.00836 | −0.284025 | ||||||||
\(51\) | 0.177134 | 0.0248037 | ||||||||
\(52\) | −8.00280 | −1.10979 | ||||||||
\(53\) | −2.16736 | −0.297710 | −0.148855 | − | 0.988859i | \(-0.547559\pi\) | ||||
−0.148855 | + | 0.988859i | \(0.547559\pi\) | |||||||
\(54\) | 2.12333 | 0.288949 | ||||||||
\(55\) | 3.65244 | 0.492495 | ||||||||
\(56\) | 0.111317 | 0.0148754 | ||||||||
\(57\) | 0.407931 | 0.0540317 | ||||||||
\(58\) | −1.65842 | −0.217761 | ||||||||
\(59\) | 5.58656 | 0.727308 | 0.363654 | − | 0.931534i | \(-0.381529\pi\) | ||||
0.363654 | + | 0.931534i | \(0.381529\pi\) | |||||||
\(60\) | 0.360205 | 0.0465022 | ||||||||
\(61\) | −10.4573 | −1.33892 | −0.669461 | − | 0.742847i | \(-0.733475\pi\) | ||||
−0.669461 | + | 0.742847i | \(0.733475\pi\) | |||||||
\(62\) | 2.93984 | 0.373359 | ||||||||
\(63\) | 4.90940 | 0.618526 | ||||||||
\(64\) | −8.26584 | −1.03323 | ||||||||
\(65\) | −3.93545 | −0.488132 | ||||||||
\(66\) | −1.29935 | −0.159939 | ||||||||
\(67\) | −9.86643 | −1.20538 | −0.602688 | − | 0.797977i | \(-0.705904\pi\) | ||||
−0.602688 | + | 0.797977i | \(0.705904\pi\) | |||||||
\(68\) | 2.03352 | 0.246600 | ||||||||
\(69\) | 1.18965 | 0.143217 | ||||||||
\(70\) | 3.32135 | 0.396977 | ||||||||
\(71\) | 1.00000 | 0.118678 | ||||||||
\(72\) | 0.199823 | 0.0235493 | ||||||||
\(73\) | 0.726747 | 0.0850594 | 0.0425297 | − | 0.999095i | \(-0.486458\pi\) | ||||
0.0425297 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(74\) | 9.34439 | 1.08626 | ||||||||
\(75\) | 0.177134 | 0.0204537 | ||||||||
\(76\) | 4.68309 | 0.537187 | ||||||||
\(77\) | −6.04026 | −0.688352 | ||||||||
\(78\) | 1.40003 | 0.158522 | ||||||||
\(79\) | 12.4095 | 1.39618 | 0.698088 | − | 0.716012i | \(-0.254035\pi\) | ||||
0.698088 | + | 0.716012i | \(0.254035\pi\) | |||||||
\(80\) | −3.93185 | −0.439594 | ||||||||
\(81\) | 8.71860 | 0.968733 | ||||||||
\(82\) | −21.9244 | −2.42115 | ||||||||
\(83\) | 4.93092 | 0.541239 | 0.270619 | − | 0.962686i | \(-0.412771\pi\) | ||||
0.270619 | + | 0.962686i | \(0.412771\pi\) | |||||||
\(84\) | −0.595693 | −0.0649954 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | −5.69616 | −0.614233 | ||||||||
\(87\) | 0.146269 | 0.0156817 | ||||||||
\(88\) | −0.245851 | −0.0262078 | ||||||||
\(89\) | −16.6630 | −1.76627 | −0.883135 | − | 0.469118i | \(-0.844572\pi\) | ||||
−0.883135 | + | 0.469118i | \(0.844572\pi\) | |||||||
\(90\) | 5.96207 | 0.628457 | ||||||||
\(91\) | 6.50830 | 0.682255 | ||||||||
\(92\) | 13.6573 | 1.42387 | ||||||||
\(93\) | −0.259288 | −0.0268869 | ||||||||
\(94\) | 10.6655 | 1.10006 | ||||||||
\(95\) | 2.30295 | 0.236278 | ||||||||
\(96\) | 1.42260 | 0.145193 | ||||||||
\(97\) | −9.51989 | −0.966599 | −0.483299 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483299 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(98\) | 8.56580 | 0.865277 | ||||||||
\(99\) | −10.8427 | −1.08973 | ||||||||
\(100\) | 2.03352 | 0.203352 | ||||||||
\(101\) | 13.6698 | 1.36019 | 0.680096 | − | 0.733123i | \(-0.261938\pi\) | ||||
0.680096 | + | 0.733123i | \(0.261938\pi\) | |||||||
\(102\) | −0.355749 | −0.0352244 | ||||||||
\(103\) | −2.43188 | −0.239620 | −0.119810 | − | 0.992797i | \(-0.538229\pi\) | ||||
−0.119810 | + | 0.992797i | \(0.538229\pi\) | |||||||
\(104\) | 0.264901 | 0.0259757 | ||||||||
\(105\) | −0.292937 | −0.0285878 | ||||||||
\(106\) | 4.35285 | 0.422786 | ||||||||
\(107\) | 5.64044 | 0.545281 | 0.272641 | − | 0.962116i | \(-0.412103\pi\) | ||||
0.272641 | + | 0.962116i | \(0.412103\pi\) | |||||||
\(108\) | −2.14993 | −0.206877 | ||||||||
\(109\) | −12.6398 | −1.21067 | −0.605336 | − | 0.795970i | \(-0.706961\pi\) | ||||
−0.605336 | + | 0.795970i | \(0.706961\pi\) | |||||||
\(110\) | −7.33542 | −0.699404 | ||||||||
\(111\) | −0.824158 | −0.0782256 | ||||||||
\(112\) | 6.50234 | 0.614413 | ||||||||
\(113\) | −5.07155 | −0.477091 | −0.238546 | − | 0.971131i | \(-0.576671\pi\) | ||||
−0.238546 | + | 0.971131i | \(0.576671\pi\) | |||||||
\(114\) | −0.819272 | −0.0767319 | ||||||||
\(115\) | 6.71610 | 0.626280 | ||||||||
\(116\) | 1.67919 | 0.155909 | ||||||||
\(117\) | 11.6829 | 1.08008 | ||||||||
\(118\) | −11.2198 | −1.03287 | ||||||||
\(119\) | −1.65376 | −0.151600 | ||||||||
\(120\) | −0.0119232 | −0.00108843 | ||||||||
\(121\) | 2.34030 | 0.212755 | ||||||||
\(122\) | 21.0021 | 1.90144 | ||||||||
\(123\) | 1.93370 | 0.174356 | ||||||||
\(124\) | −2.97666 | −0.267312 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −9.85984 | −0.878385 | ||||||||
\(127\) | 0.0180324 | 0.00160011 | 0.000800057 | − | 1.00000i | \(-0.499745\pi\) | ||||
0.000800057 | 1.00000i | \(0.499745\pi\) | ||||||||
\(128\) | 0.538417 | 0.0475898 | ||||||||
\(129\) | 0.502391 | 0.0442331 | ||||||||
\(130\) | 7.90381 | 0.693210 | ||||||||
\(131\) | 19.3083 | 1.68698 | 0.843488 | − | 0.537148i | \(-0.180498\pi\) | ||||
0.843488 | + | 0.537148i | \(0.180498\pi\) | |||||||
\(132\) | 1.31563 | 0.114510 | ||||||||
\(133\) | −3.80853 | −0.330242 | ||||||||
\(134\) | 19.8154 | 1.71179 | ||||||||
\(135\) | −1.05725 | −0.0909932 | ||||||||
\(136\) | −0.0673116 | −0.00577192 | ||||||||
\(137\) | 18.3264 | 1.56573 | 0.782865 | − | 0.622192i | \(-0.213758\pi\) | ||||
0.782865 | + | 0.622192i | \(0.213758\pi\) | |||||||
\(138\) | −2.38925 | −0.203386 | ||||||||
\(139\) | 5.88400 | 0.499074 | 0.249537 | − | 0.968365i | \(-0.419722\pi\) | ||||
0.249537 | + | 0.968365i | \(0.419722\pi\) | |||||||
\(140\) | −3.36295 | −0.284221 | ||||||||
\(141\) | −0.940676 | −0.0792192 | ||||||||
\(142\) | −2.00836 | −0.168538 | ||||||||
\(143\) | −14.3740 | −1.20201 | ||||||||
\(144\) | 11.6722 | 0.972681 | ||||||||
\(145\) | 0.825756 | 0.0685753 | ||||||||
\(146\) | −1.45957 | −0.120795 | ||||||||
\(147\) | −0.755489 | −0.0623117 | ||||||||
\(148\) | −9.46142 | −0.777724 | ||||||||
\(149\) | 14.3188 | 1.17304 | 0.586522 | − | 0.809934i | \(-0.300497\pi\) | ||||
0.586522 | + | 0.809934i | \(0.300497\pi\) | |||||||
\(150\) | −0.355749 | −0.0290468 | ||||||||
\(151\) | 1.10586 | 0.0899938 | 0.0449969 | − | 0.998987i | \(-0.485672\pi\) | ||||
0.0449969 | + | 0.998987i | \(0.485672\pi\) | |||||||
\(152\) | −0.155015 | −0.0125734 | ||||||||
\(153\) | −2.96862 | −0.239999 | ||||||||
\(154\) | 12.1310 | 0.977546 | ||||||||
\(155\) | −1.46380 | −0.117575 | ||||||||
\(156\) | −1.41757 | −0.113496 | ||||||||
\(157\) | −11.6735 | −0.931643 | −0.465821 | − | 0.884879i | \(-0.654241\pi\) | ||||
−0.465821 | + | 0.884879i | \(0.654241\pi\) | |||||||
\(158\) | −24.9227 | −1.98274 | ||||||||
\(159\) | −0.383913 | −0.0304463 | ||||||||
\(160\) | 8.03119 | 0.634921 | ||||||||
\(161\) | −11.1068 | −0.875342 | ||||||||
\(162\) | −17.5101 | −1.37572 | ||||||||
\(163\) | 5.40040 | 0.422992 | 0.211496 | − | 0.977379i | \(-0.432166\pi\) | ||||
0.211496 | + | 0.977379i | \(0.432166\pi\) | |||||||
\(164\) | 22.1990 | 1.73345 | ||||||||
\(165\) | 0.646971 | 0.0503666 | ||||||||
\(166\) | −9.90307 | −0.768627 | ||||||||
\(167\) | 10.3466 | 0.800644 | 0.400322 | − | 0.916375i | \(-0.368898\pi\) | ||||
0.400322 | + | 0.916375i | \(0.368898\pi\) | |||||||
\(168\) | 0.0197181 | 0.00152128 | ||||||||
\(169\) | 2.48777 | 0.191367 | ||||||||
\(170\) | −2.00836 | −0.154034 | ||||||||
\(171\) | −6.83659 | −0.522807 | ||||||||
\(172\) | 5.76751 | 0.439768 | ||||||||
\(173\) | 6.20238 | 0.471558 | 0.235779 | − | 0.971807i | \(-0.424236\pi\) | ||||
0.235779 | + | 0.971807i | \(0.424236\pi\) | |||||||
\(174\) | −0.293762 | −0.0222700 | ||||||||
\(175\) | −1.65376 | −0.125013 | ||||||||
\(176\) | −14.3608 | −1.08249 | ||||||||
\(177\) | 0.989569 | 0.0743805 | ||||||||
\(178\) | 33.4653 | 2.50833 | ||||||||
\(179\) | −2.29474 | −0.171517 | −0.0857585 | − | 0.996316i | \(-0.527331\pi\) | ||||
−0.0857585 | + | 0.996316i | \(0.527331\pi\) | |||||||
\(180\) | −6.03674 | −0.449952 | ||||||||
\(181\) | 2.80181 | 0.208257 | 0.104128 | − | 0.994564i | \(-0.466795\pi\) | ||||
0.104128 | + | 0.994564i | \(0.466795\pi\) | |||||||
\(182\) | −13.0710 | −0.968888 | ||||||||
\(183\) | −1.85235 | −0.136929 | ||||||||
\(184\) | −0.452072 | −0.0333272 | ||||||||
\(185\) | −4.65274 | −0.342076 | ||||||||
\(186\) | 0.520745 | 0.0381828 | ||||||||
\(187\) | 3.65244 | 0.267093 | ||||||||
\(188\) | −10.7991 | −0.787602 | ||||||||
\(189\) | 1.74843 | 0.127180 | ||||||||
\(190\) | −4.62516 | −0.335544 | ||||||||
\(191\) | 7.82504 | 0.566200 | 0.283100 | − | 0.959090i | \(-0.408637\pi\) | ||||
0.283100 | + | 0.959090i | \(0.408637\pi\) | |||||||
\(192\) | −1.46416 | −0.105667 | ||||||||
\(193\) | −4.79443 | −0.345111 | −0.172555 | − | 0.985000i | \(-0.555202\pi\) | ||||
−0.172555 | + | 0.985000i | \(0.555202\pi\) | |||||||
\(194\) | 19.1194 | 1.37269 | ||||||||
\(195\) | −0.697102 | −0.0499205 | ||||||||
\(196\) | −8.67309 | −0.619506 | ||||||||
\(197\) | −12.8939 | −0.918653 | −0.459326 | − | 0.888268i | \(-0.651909\pi\) | ||||
−0.459326 | + | 0.888268i | \(0.651909\pi\) | |||||||
\(198\) | 21.7761 | 1.54756 | ||||||||
\(199\) | 4.18811 | 0.296887 | 0.148444 | − | 0.988921i | \(-0.452574\pi\) | ||||
0.148444 | + | 0.988921i | \(0.452574\pi\) | |||||||
\(200\) | −0.0673116 | −0.00475965 | ||||||||
\(201\) | −1.74768 | −0.123272 | ||||||||
\(202\) | −27.4538 | −1.93164 | ||||||||
\(203\) | −1.36560 | −0.0958467 | ||||||||
\(204\) | 0.360205 | 0.0252194 | ||||||||
\(205\) | 10.9166 | 0.762447 | ||||||||
\(206\) | 4.88408 | 0.340290 | ||||||||
\(207\) | −19.9376 | −1.38576 | ||||||||
\(208\) | 15.4736 | 1.07290 | ||||||||
\(209\) | 8.41138 | 0.581828 | ||||||||
\(210\) | 0.588324 | 0.0405982 | ||||||||
\(211\) | −10.2783 | −0.707588 | −0.353794 | − | 0.935323i | \(-0.615109\pi\) | ||||
−0.353794 | + | 0.935323i | \(0.615109\pi\) | |||||||
\(212\) | −4.40736 | −0.302699 | ||||||||
\(213\) | 0.177134 | 0.0121370 | ||||||||
\(214\) | −11.3280 | −0.774368 | ||||||||
\(215\) | 2.83622 | 0.193429 | ||||||||
\(216\) | 0.0711649 | 0.00484216 | ||||||||
\(217\) | 2.42077 | 0.164333 | ||||||||
\(218\) | 25.3852 | 1.71931 | ||||||||
\(219\) | 0.128732 | 0.00869888 | ||||||||
\(220\) | 7.42729 | 0.500748 | ||||||||
\(221\) | −3.93545 | −0.264727 | ||||||||
\(222\) | 1.65521 | 0.111090 | ||||||||
\(223\) | 6.19438 | 0.414806 | 0.207403 | − | 0.978256i | \(-0.433499\pi\) | ||||
0.207403 | + | 0.978256i | \(0.433499\pi\) | |||||||
\(224\) | −13.2817 | −0.887419 | ||||||||
\(225\) | −2.96862 | −0.197908 | ||||||||
\(226\) | 10.1855 | 0.677530 | ||||||||
\(227\) | −15.6112 | −1.03615 | −0.518077 | − | 0.855334i | \(-0.673352\pi\) | ||||
−0.518077 | + | 0.855334i | \(0.673352\pi\) | |||||||
\(228\) | 0.829533 | 0.0549372 | ||||||||
\(229\) | 13.2502 | 0.875597 | 0.437799 | − | 0.899073i | \(-0.355758\pi\) | ||||
0.437799 | + | 0.899073i | \(0.355758\pi\) | |||||||
\(230\) | −13.4884 | −0.889396 | ||||||||
\(231\) | −1.06994 | −0.0703966 | ||||||||
\(232\) | −0.0555830 | −0.00364920 | ||||||||
\(233\) | 3.25183 | 0.213034 | 0.106517 | − | 0.994311i | \(-0.466030\pi\) | ||||
0.106517 | + | 0.994311i | \(0.466030\pi\) | |||||||
\(234\) | −23.4634 | −1.53385 | ||||||||
\(235\) | −5.31053 | −0.346421 | ||||||||
\(236\) | 11.3604 | 0.739496 | ||||||||
\(237\) | 2.19814 | 0.142784 | ||||||||
\(238\) | 3.32135 | 0.215291 | ||||||||
\(239\) | 27.2189 | 1.76065 | 0.880323 | − | 0.474374i | \(-0.157326\pi\) | ||||
0.880323 | + | 0.474374i | \(0.157326\pi\) | |||||||
\(240\) | −0.696463 | −0.0449565 | ||||||||
\(241\) | 4.37592 | 0.281878 | 0.140939 | − | 0.990018i | \(-0.454988\pi\) | ||||
0.140939 | + | 0.990018i | \(0.454988\pi\) | |||||||
\(242\) | −4.70018 | −0.302139 | ||||||||
\(243\) | 4.71610 | 0.302538 | ||||||||
\(244\) | −21.2651 | −1.36136 | ||||||||
\(245\) | −4.26507 | −0.272485 | ||||||||
\(246\) | −3.88356 | −0.247607 | ||||||||
\(247\) | −9.06315 | −0.576674 | ||||||||
\(248\) | 0.0985306 | 0.00625670 | ||||||||
\(249\) | 0.873433 | 0.0553516 | ||||||||
\(250\) | −2.00836 | −0.127020 | ||||||||
\(251\) | −5.87688 | −0.370945 | −0.185473 | − | 0.982649i | \(-0.559382\pi\) | ||||
−0.185473 | + | 0.982649i | \(0.559382\pi\) | |||||||
\(252\) | 9.98334 | 0.628891 | ||||||||
\(253\) | 24.5302 | 1.54220 | ||||||||
\(254\) | −0.0362155 | −0.00227236 | ||||||||
\(255\) | 0.177134 | 0.0110926 | ||||||||
\(256\) | 15.4503 | 0.965647 | ||||||||
\(257\) | −9.05219 | −0.564660 | −0.282330 | − | 0.959317i | \(-0.591107\pi\) | ||||
−0.282330 | + | 0.959317i | \(0.591107\pi\) | |||||||
\(258\) | −1.00898 | −0.0628166 | ||||||||
\(259\) | 7.69453 | 0.478115 | ||||||||
\(260\) | −8.00280 | −0.496313 | ||||||||
\(261\) | −2.45136 | −0.151735 | ||||||||
\(262\) | −38.7781 | −2.39572 | ||||||||
\(263\) | −0.980568 | −0.0604644 | −0.0302322 | − | 0.999543i | \(-0.509625\pi\) | ||||
−0.0302322 | + | 0.999543i | \(0.509625\pi\) | |||||||
\(264\) | −0.0435486 | −0.00268023 | ||||||||
\(265\) | −2.16736 | −0.133140 | ||||||||
\(266\) | 7.64891 | 0.468985 | ||||||||
\(267\) | −2.95158 | −0.180634 | ||||||||
\(268\) | −20.0635 | −1.22558 | ||||||||
\(269\) | 20.4279 | 1.24551 | 0.622754 | − | 0.782417i | \(-0.286014\pi\) | ||||
0.622754 | + | 0.782417i | \(0.286014\pi\) | |||||||
\(270\) | 2.12333 | 0.129222 | ||||||||
\(271\) | 30.3650 | 1.84455 | 0.922273 | − | 0.386540i | \(-0.126330\pi\) | ||||
0.922273 | + | 0.386540i | \(0.126330\pi\) | |||||||
\(272\) | −3.93185 | −0.238403 | ||||||||
\(273\) | 1.15284 | 0.0697731 | ||||||||
\(274\) | −36.8060 | −2.22353 | ||||||||
\(275\) | 3.65244 | 0.220250 | ||||||||
\(276\) | 2.41917 | 0.145617 | ||||||||
\(277\) | 16.4346 | 0.987458 | 0.493729 | − | 0.869616i | \(-0.335633\pi\) | ||||
0.493729 | + | 0.869616i | \(0.335633\pi\) | |||||||
\(278\) | −11.8172 | −0.708748 | ||||||||
\(279\) | 4.34547 | 0.260156 | ||||||||
\(280\) | 0.111317 | 0.00665248 | ||||||||
\(281\) | −12.5015 | −0.745777 | −0.372888 | − | 0.927876i | \(-0.621633\pi\) | ||||
−0.372888 | + | 0.927876i | \(0.621633\pi\) | |||||||
\(282\) | 1.88922 | 0.112501 | ||||||||
\(283\) | 6.98244 | 0.415063 | 0.207531 | − | 0.978228i | \(-0.433457\pi\) | ||||
0.207531 | + | 0.978228i | \(0.433457\pi\) | |||||||
\(284\) | 2.03352 | 0.120667 | ||||||||
\(285\) | 0.407931 | 0.0241637 | ||||||||
\(286\) | 28.8682 | 1.70701 | ||||||||
\(287\) | −18.0534 | −1.06566 | ||||||||
\(288\) | −23.8416 | −1.40488 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.65842 | −0.0973856 | ||||||||
\(291\) | −1.68630 | −0.0988524 | ||||||||
\(292\) | 1.47785 | 0.0864848 | ||||||||
\(293\) | −25.2987 | −1.47797 | −0.738983 | − | 0.673724i | \(-0.764694\pi\) | ||||
−0.738983 | + | 0.673724i | \(0.764694\pi\) | |||||||
\(294\) | 1.51729 | 0.0884904 | ||||||||
\(295\) | 5.58656 | 0.325262 | ||||||||
\(296\) | 0.313183 | 0.0182034 | ||||||||
\(297\) | −3.86152 | −0.224068 | ||||||||
\(298\) | −28.7574 | −1.66587 | ||||||||
\(299\) | −26.4309 | −1.52854 | ||||||||
\(300\) | 0.360205 | 0.0207964 | ||||||||
\(301\) | −4.69044 | −0.270352 | ||||||||
\(302\) | −2.22097 | −0.127802 | ||||||||
\(303\) | 2.42138 | 0.139105 | ||||||||
\(304\) | −9.05484 | −0.519331 | ||||||||
\(305\) | −10.4573 | −0.598784 | ||||||||
\(306\) | 5.96207 | 0.340829 | ||||||||
\(307\) | −10.4225 | −0.594842 | −0.297421 | − | 0.954746i | \(-0.596126\pi\) | ||||
−0.297421 | + | 0.954746i | \(0.596126\pi\) | |||||||
\(308\) | −12.2830 | −0.699887 | ||||||||
\(309\) | −0.430768 | −0.0245055 | ||||||||
\(310\) | 2.93984 | 0.166971 | ||||||||
\(311\) | 21.4581 | 1.21678 | 0.608389 | − | 0.793639i | \(-0.291816\pi\) | ||||
0.608389 | + | 0.793639i | \(0.291816\pi\) | |||||||
\(312\) | 0.0469230 | 0.00265649 | ||||||||
\(313\) | −29.2304 | −1.65220 | −0.826101 | − | 0.563523i | \(-0.809446\pi\) | ||||
−0.826101 | + | 0.563523i | \(0.809446\pi\) | |||||||
\(314\) | 23.4445 | 1.32305 | ||||||||
\(315\) | 4.90940 | 0.276613 | ||||||||
\(316\) | 25.2349 | 1.41957 | ||||||||
\(317\) | 29.7942 | 1.67341 | 0.836704 | − | 0.547656i | \(-0.184480\pi\) | ||||
0.836704 | + | 0.547656i | \(0.184480\pi\) | |||||||
\(318\) | 0.771037 | 0.0432376 | ||||||||
\(319\) | 3.01602 | 0.168865 | ||||||||
\(320\) | −8.26584 | −0.462075 | ||||||||
\(321\) | 0.999112 | 0.0557650 | ||||||||
\(322\) | 22.3065 | 1.24310 | ||||||||
\(323\) | 2.30295 | 0.128140 | ||||||||
\(324\) | 17.7294 | 0.984967 | ||||||||
\(325\) | −3.93545 | −0.218299 | ||||||||
\(326\) | −10.8460 | −0.600702 | ||||||||
\(327\) | −2.23893 | −0.123813 | ||||||||
\(328\) | −0.734812 | −0.0405732 | ||||||||
\(329\) | 8.78236 | 0.484187 | ||||||||
\(330\) | −1.29935 | −0.0715269 | ||||||||
\(331\) | 20.0926 | 1.10439 | 0.552195 | − | 0.833715i | \(-0.313790\pi\) | ||||
0.552195 | + | 0.833715i | \(0.313790\pi\) | |||||||
\(332\) | 10.0271 | 0.550309 | ||||||||
\(333\) | 13.8122 | 0.756906 | ||||||||
\(334\) | −20.7797 | −1.13702 | ||||||||
\(335\) | −9.86643 | −0.539060 | ||||||||
\(336\) | 1.15178 | 0.0628350 | ||||||||
\(337\) | −7.84023 | −0.427084 | −0.213542 | − | 0.976934i | \(-0.568500\pi\) | ||||
−0.213542 | + | 0.976934i | \(0.568500\pi\) | |||||||
\(338\) | −4.99633 | −0.271765 | ||||||||
\(339\) | −0.898343 | −0.0487913 | ||||||||
\(340\) | 2.03352 | 0.110283 | ||||||||
\(341\) | −5.34643 | −0.289525 | ||||||||
\(342\) | 13.7303 | 0.742452 | ||||||||
\(343\) | 18.6297 | 1.00591 | ||||||||
\(344\) | −0.190911 | −0.0102932 | ||||||||
\(345\) | 1.18965 | 0.0640486 | ||||||||
\(346\) | −12.4566 | −0.669672 | ||||||||
\(347\) | −26.6311 | −1.42963 | −0.714816 | − | 0.699313i | \(-0.753490\pi\) | ||||
−0.714816 | + | 0.699313i | \(0.753490\pi\) | |||||||
\(348\) | 0.297441 | 0.0159445 | ||||||||
\(349\) | 17.5815 | 0.941118 | 0.470559 | − | 0.882368i | \(-0.344052\pi\) | ||||
0.470559 | + | 0.882368i | \(0.344052\pi\) | |||||||
\(350\) | 3.32135 | 0.177534 | ||||||||
\(351\) | 4.16074 | 0.222084 | ||||||||
\(352\) | 29.3334 | 1.56348 | ||||||||
\(353\) | 6.41713 | 0.341549 | 0.170775 | − | 0.985310i | \(-0.445373\pi\) | ||||
0.170775 | + | 0.985310i | \(0.445373\pi\) | |||||||
\(354\) | −1.98741 | −0.105630 | ||||||||
\(355\) | 1.00000 | 0.0530745 | ||||||||
\(356\) | −33.8844 | −1.79587 | ||||||||
\(357\) | −0.292937 | −0.0155039 | ||||||||
\(358\) | 4.60867 | 0.243576 | ||||||||
\(359\) | −25.6463 | −1.35356 | −0.676779 | − | 0.736186i | \(-0.736625\pi\) | ||||
−0.676779 | + | 0.736186i | \(0.736625\pi\) | |||||||
\(360\) | 0.199823 | 0.0105316 | ||||||||
\(361\) | −13.6964 | −0.720864 | ||||||||
\(362\) | −5.62704 | −0.295751 | ||||||||
\(363\) | 0.414547 | 0.0217581 | ||||||||
\(364\) | 13.2347 | 0.693688 | ||||||||
\(365\) | 0.726747 | 0.0380397 | ||||||||
\(366\) | 3.72018 | 0.194457 | ||||||||
\(367\) | 15.7468 | 0.821976 | 0.410988 | − | 0.911641i | \(-0.365184\pi\) | ||||
0.410988 | + | 0.911641i | \(0.365184\pi\) | |||||||
\(368\) | −26.4067 | −1.37654 | ||||||||
\(369\) | −32.4072 | −1.68705 | ||||||||
\(370\) | 9.34439 | 0.485792 | ||||||||
\(371\) | 3.58430 | 0.186088 | ||||||||
\(372\) | −0.527267 | −0.0273375 | ||||||||
\(373\) | 1.66257 | 0.0860846 | 0.0430423 | − | 0.999073i | \(-0.486295\pi\) | ||||
0.0430423 | + | 0.999073i | \(0.486295\pi\) | |||||||
\(374\) | −7.33542 | −0.379305 | ||||||||
\(375\) | 0.177134 | 0.00914716 | ||||||||
\(376\) | 0.357460 | 0.0184346 | ||||||||
\(377\) | −3.24972 | −0.167369 | ||||||||
\(378\) | −3.51149 | −0.180611 | ||||||||
\(379\) | 5.14326 | 0.264192 | 0.132096 | − | 0.991237i | \(-0.457829\pi\) | ||||
0.132096 | + | 0.991237i | \(0.457829\pi\) | |||||||
\(380\) | 4.68309 | 0.240237 | ||||||||
\(381\) | 0.00319415 | 0.000163641 0 | ||||||||
\(382\) | −15.7155 | −0.804076 | ||||||||
\(383\) | −0.311861 | −0.0159354 | −0.00796769 | − | 0.999968i | \(-0.502536\pi\) | ||||
−0.00796769 | + | 0.999968i | \(0.502536\pi\) | |||||||
\(384\) | 0.0953719 | 0.00486693 | ||||||||
\(385\) | −6.04026 | −0.307840 | ||||||||
\(386\) | 9.62895 | 0.490101 | ||||||||
\(387\) | −8.41968 | −0.427996 | ||||||||
\(388\) | −19.3589 | −0.982797 | ||||||||
\(389\) | 22.9490 | 1.16356 | 0.581780 | − | 0.813346i | \(-0.302357\pi\) | ||||
0.581780 | + | 0.813346i | \(0.302357\pi\) | |||||||
\(390\) | 1.40003 | 0.0708934 | ||||||||
\(391\) | 6.71610 | 0.339648 | ||||||||
\(392\) | 0.287089 | 0.0145002 | ||||||||
\(393\) | 3.42016 | 0.172524 | ||||||||
\(394\) | 25.8956 | 1.30460 | ||||||||
\(395\) | 12.4095 | 0.624389 | ||||||||
\(396\) | −22.0488 | −1.10800 | ||||||||
\(397\) | 6.68613 | 0.335567 | 0.167784 | − | 0.985824i | \(-0.446339\pi\) | ||||
0.167784 | + | 0.985824i | \(0.446339\pi\) | |||||||
\(398\) | −8.41124 | −0.421617 | ||||||||
\(399\) | −0.674620 | −0.0337733 | ||||||||
\(400\) | −3.93185 | −0.196592 | ||||||||
\(401\) | 0.519070 | 0.0259211 | 0.0129606 | − | 0.999916i | \(-0.495874\pi\) | ||||
0.0129606 | + | 0.999916i | \(0.495874\pi\) | |||||||
\(402\) | 3.50997 | 0.175061 | ||||||||
\(403\) | 5.76070 | 0.286961 | ||||||||
\(404\) | 27.7977 | 1.38299 | ||||||||
\(405\) | 8.71860 | 0.433231 | ||||||||
\(406\) | 2.74263 | 0.136114 | ||||||||
\(407\) | −16.9938 | −0.842354 | ||||||||
\(408\) | −0.0119232 | −0.000590285 0 | ||||||||
\(409\) | 35.8801 | 1.77416 | 0.887078 | − | 0.461620i | \(-0.152732\pi\) | ||||
0.887078 | + | 0.461620i | \(0.152732\pi\) | |||||||
\(410\) | −21.9244 | −1.08277 | ||||||||
\(411\) | 3.24623 | 0.160124 | ||||||||
\(412\) | −4.94526 | −0.243635 | ||||||||
\(413\) | −9.23884 | −0.454613 | ||||||||
\(414\) | 40.0419 | 1.96795 | ||||||||
\(415\) | 4.93092 | 0.242049 | ||||||||
\(416\) | −31.6063 | −1.54963 | ||||||||
\(417\) | 1.04226 | 0.0510395 | ||||||||
\(418\) | −16.8931 | −0.826268 | ||||||||
\(419\) | −36.1761 | −1.76732 | −0.883659 | − | 0.468131i | \(-0.844927\pi\) | ||||
−0.883659 | + | 0.468131i | \(0.844927\pi\) | |||||||
\(420\) | −0.595693 | −0.0290668 | ||||||||
\(421\) | −12.6971 | −0.618821 | −0.309410 | − | 0.950929i | \(-0.600132\pi\) | ||||
−0.309410 | + | 0.950929i | \(0.600132\pi\) | |||||||
\(422\) | 20.6426 | 1.00486 | ||||||||
\(423\) | 15.7650 | 0.766519 | ||||||||
\(424\) | 0.145889 | 0.00708498 | ||||||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | −0.355749 | −0.0172361 | ||||||||
\(427\) | 17.2939 | 0.836911 | ||||||||
\(428\) | 11.4699 | 0.554419 | ||||||||
\(429\) | −2.54612 | −0.122928 | ||||||||
\(430\) | −5.69616 | −0.274693 | ||||||||
\(431\) | −17.0952 | −0.823447 | −0.411723 | − | 0.911309i | \(-0.635073\pi\) | ||||
−0.411723 | + | 0.911309i | \(0.635073\pi\) | |||||||
\(432\) | 4.15693 | 0.200000 | ||||||||
\(433\) | 29.0572 | 1.39640 | 0.698199 | − | 0.715903i | \(-0.253985\pi\) | ||||
0.698199 | + | 0.715903i | \(0.253985\pi\) | |||||||
\(434\) | −4.86179 | −0.233373 | ||||||||
\(435\) | 0.146269 | 0.00701308 | ||||||||
\(436\) | −25.7032 | −1.23096 | ||||||||
\(437\) | 15.4669 | 0.739880 | ||||||||
\(438\) | −0.258540 | −0.0123535 | ||||||||
\(439\) | −30.9008 | −1.47481 | −0.737406 | − | 0.675449i | \(-0.763950\pi\) | ||||
−0.737406 | + | 0.675449i | \(0.763950\pi\) | |||||||
\(440\) | −0.245851 | −0.0117205 | ||||||||
\(441\) | 12.6614 | 0.602923 | ||||||||
\(442\) | 7.90381 | 0.375946 | ||||||||
\(443\) | 14.0348 | 0.666812 | 0.333406 | − | 0.942783i | \(-0.391802\pi\) | ||||
0.333406 | + | 0.942783i | \(0.391802\pi\) | |||||||
\(444\) | −1.67594 | −0.0795365 | ||||||||
\(445\) | −16.6630 | −0.789900 | ||||||||
\(446\) | −12.4405 | −0.589077 | ||||||||
\(447\) | 2.53635 | 0.119965 | ||||||||
\(448\) | 13.6697 | 0.645834 | ||||||||
\(449\) | −9.79645 | −0.462323 | −0.231162 | − | 0.972915i | \(-0.574253\pi\) | ||||
−0.231162 | + | 0.972915i | \(0.574253\pi\) | |||||||
\(450\) | 5.96207 | 0.281055 | ||||||||
\(451\) | 39.8721 | 1.87751 | ||||||||
\(452\) | −10.3131 | −0.485086 | ||||||||
\(453\) | 0.195886 | 0.00920351 | ||||||||
\(454\) | 31.3530 | 1.47147 | ||||||||
\(455\) | 6.50830 | 0.305114 | ||||||||
\(456\) | −0.0274585 | −0.00128586 | ||||||||
\(457\) | −39.8414 | −1.86370 | −0.931851 | − | 0.362841i | \(-0.881807\pi\) | ||||
−0.931851 | + | 0.362841i | \(0.881807\pi\) | |||||||
\(458\) | −26.6112 | −1.24346 | ||||||||
\(459\) | −1.05725 | −0.0493480 | ||||||||
\(460\) | 13.6573 | 0.636775 | ||||||||
\(461\) | −0.123718 | −0.00576211 | −0.00288105 | − | 0.999996i | \(-0.500917\pi\) | ||||
−0.00288105 | + | 0.999996i | \(0.500917\pi\) | |||||||
\(462\) | 2.14882 | 0.0999720 | ||||||||
\(463\) | 33.0773 | 1.53723 | 0.768615 | − | 0.639712i | \(-0.220946\pi\) | ||||
0.768615 | + | 0.639712i | \(0.220946\pi\) | |||||||
\(464\) | −3.24675 | −0.150726 | ||||||||
\(465\) | −0.259288 | −0.0120242 | ||||||||
\(466\) | −6.53084 | −0.302536 | ||||||||
\(467\) | −4.33109 | −0.200419 | −0.100210 | − | 0.994966i | \(-0.531951\pi\) | ||||
−0.100210 | + | 0.994966i | \(0.531951\pi\) | |||||||
\(468\) | 23.7573 | 1.09818 | ||||||||
\(469\) | 16.3167 | 0.753436 | ||||||||
\(470\) | 10.6655 | 0.491962 | ||||||||
\(471\) | −2.06776 | −0.0952776 | ||||||||
\(472\) | −0.376040 | −0.0173086 | ||||||||
\(473\) | 10.3591 | 0.476313 | ||||||||
\(474\) | −4.41466 | −0.202772 | ||||||||
\(475\) | 2.30295 | 0.105667 | ||||||||
\(476\) | −3.36295 | −0.154141 | ||||||||
\(477\) | 6.43408 | 0.294596 | ||||||||
\(478\) | −54.6655 | −2.50034 | ||||||||
\(479\) | 30.1415 | 1.37720 | 0.688600 | − | 0.725141i | \(-0.258226\pi\) | ||||
0.688600 | + | 0.725141i | \(0.258226\pi\) | |||||||
\(480\) | 1.42260 | 0.0649323 | ||||||||
\(481\) | 18.3106 | 0.834893 | ||||||||
\(482\) | −8.78843 | −0.400302 | ||||||||
\(483\) | −1.96740 | −0.0895197 | ||||||||
\(484\) | 4.75904 | 0.216320 | ||||||||
\(485\) | −9.51989 | −0.432276 | ||||||||
\(486\) | −9.47163 | −0.429642 | ||||||||
\(487\) | 22.1133 | 1.00205 | 0.501025 | − | 0.865433i | \(-0.332956\pi\) | ||||
0.501025 | + | 0.865433i | \(0.332956\pi\) | |||||||
\(488\) | 0.703898 | 0.0318640 | ||||||||
\(489\) | 0.956594 | 0.0432587 | ||||||||
\(490\) | 8.56580 | 0.386964 | ||||||||
\(491\) | 14.2567 | 0.643397 | 0.321698 | − | 0.946842i | \(-0.395746\pi\) | ||||
0.321698 | + | 0.946842i | \(0.395746\pi\) | |||||||
\(492\) | 3.93220 | 0.177277 | ||||||||
\(493\) | 0.825756 | 0.0371902 | ||||||||
\(494\) | 18.2021 | 0.818950 | ||||||||
\(495\) | −10.8427 | −0.487344 | ||||||||
\(496\) | 5.75543 | 0.258426 | ||||||||
\(497\) | −1.65376 | −0.0741814 | ||||||||
\(498\) | −1.75417 | −0.0786062 | ||||||||
\(499\) | 24.1031 | 1.07900 | 0.539502 | − | 0.841984i | \(-0.318613\pi\) | ||||
0.539502 | + | 0.841984i | \(0.318613\pi\) | |||||||
\(500\) | 2.03352 | 0.0909416 | ||||||||
\(501\) | 1.83273 | 0.0818805 | ||||||||
\(502\) | 11.8029 | 0.526789 | ||||||||
\(503\) | 22.1111 | 0.985886 | 0.492943 | − | 0.870061i | \(-0.335921\pi\) | ||||
0.492943 | + | 0.870061i | \(0.335921\pi\) | |||||||
\(504\) | −0.330459 | −0.0147198 | ||||||||
\(505\) | 13.6698 | 0.608296 | ||||||||
\(506\) | −49.2654 | −2.19011 | ||||||||
\(507\) | 0.440668 | 0.0195707 | ||||||||
\(508\) | 0.0366691 | 0.00162693 | ||||||||
\(509\) | −4.83268 | −0.214205 | −0.107102 | − | 0.994248i | \(-0.534157\pi\) | ||||
−0.107102 | + | 0.994248i | \(0.534157\pi\) | |||||||
\(510\) | −0.355749 | −0.0157528 | ||||||||
\(511\) | −1.20187 | −0.0531675 | ||||||||
\(512\) | −32.1067 | −1.41893 | ||||||||
\(513\) | −2.43478 | −0.107498 | ||||||||
\(514\) | 18.1801 | 0.801889 | ||||||||
\(515\) | −2.43188 | −0.107161 | ||||||||
\(516\) | 1.02162 | 0.0449743 | ||||||||
\(517\) | −19.3964 | −0.853053 | ||||||||
\(518\) | −15.4534 | −0.678983 | ||||||||
\(519\) | 1.09865 | 0.0482255 | ||||||||
\(520\) | 0.264901 | 0.0116167 | ||||||||
\(521\) | 30.1778 | 1.32211 | 0.661056 | − | 0.750336i | \(-0.270108\pi\) | ||||
0.661056 | + | 0.750336i | \(0.270108\pi\) | |||||||
\(522\) | 4.92322 | 0.215483 | ||||||||
\(523\) | 44.8735 | 1.96218 | 0.981092 | − | 0.193544i | \(-0.0619983\pi\) | ||||
0.981092 | + | 0.193544i | \(0.0619983\pi\) | |||||||
\(524\) | 39.2638 | 1.71525 | ||||||||
\(525\) | −0.292937 | −0.0127848 | ||||||||
\(526\) | 1.96933 | 0.0858671 | ||||||||
\(527\) | −1.46380 | −0.0637640 | ||||||||
\(528\) | −2.54379 | −0.110704 | ||||||||
\(529\) | 22.1061 | 0.961133 | ||||||||
\(530\) | 4.35285 | 0.189076 | ||||||||
\(531\) | −16.5844 | −0.719701 | ||||||||
\(532\) | −7.74471 | −0.335776 | ||||||||
\(533\) | −42.9617 | −1.86088 | ||||||||
\(534\) | 5.92783 | 0.256522 | ||||||||
\(535\) | 5.64044 | 0.243857 | ||||||||
\(536\) | 0.664125 | 0.0286858 | ||||||||
\(537\) | −0.406477 | −0.0175408 | ||||||||
\(538\) | −41.0265 | −1.76878 | ||||||||
\(539\) | −15.5779 | −0.670988 | ||||||||
\(540\) | −2.14993 | −0.0925181 | ||||||||
\(541\) | 42.4678 | 1.82583 | 0.912916 | − | 0.408148i | \(-0.133825\pi\) | ||||
0.912916 | + | 0.408148i | \(0.133825\pi\) | |||||||
\(542\) | −60.9840 | −2.61949 | ||||||||
\(543\) | 0.496295 | 0.0212981 | ||||||||
\(544\) | 8.03119 | 0.344334 | ||||||||
\(545\) | −12.6398 | −0.541429 | ||||||||
\(546\) | −2.31532 | −0.0990866 | ||||||||
\(547\) | −6.80140 | −0.290807 | −0.145404 | − | 0.989372i | \(-0.546448\pi\) | ||||
−0.145404 | + | 0.989372i | \(0.546448\pi\) | |||||||
\(548\) | 37.2670 | 1.59197 | ||||||||
\(549\) | 31.0438 | 1.32492 | ||||||||
\(550\) | −7.33542 | −0.312783 | ||||||||
\(551\) | 1.90168 | 0.0810141 | ||||||||
\(552\) | −0.0800772 | −0.00340831 | ||||||||
\(553\) | −20.5223 | −0.872698 | ||||||||
\(554\) | −33.0066 | −1.40232 | ||||||||
\(555\) | −0.824158 | −0.0349836 | ||||||||
\(556\) | 11.9652 | 0.507437 | ||||||||
\(557\) | −17.6436 | −0.747582 | −0.373791 | − | 0.927513i | \(-0.621942\pi\) | ||||
−0.373791 | + | 0.927513i | \(0.621942\pi\) | |||||||
\(558\) | −8.72726 | −0.369455 | ||||||||
\(559\) | −11.1618 | −0.472095 | ||||||||
\(560\) | 6.50234 | 0.274774 | ||||||||
\(561\) | 0.646971 | 0.0273151 | ||||||||
\(562\) | 25.1075 | 1.05910 | ||||||||
\(563\) | 28.7571 | 1.21197 | 0.605983 | − | 0.795478i | \(-0.292780\pi\) | ||||
0.605983 | + | 0.795478i | \(0.292780\pi\) | |||||||
\(564\) | −1.91288 | −0.0805467 | ||||||||
\(565\) | −5.07155 | −0.213362 | ||||||||
\(566\) | −14.0233 | −0.589442 | ||||||||
\(567\) | −14.4185 | −0.605519 | ||||||||
\(568\) | −0.0673116 | −0.00282433 | ||||||||
\(569\) | −25.7672 | −1.08022 | −0.540109 | − | 0.841595i | \(-0.681617\pi\) | ||||
−0.540109 | + | 0.841595i | \(0.681617\pi\) | |||||||
\(570\) | −0.819272 | −0.0343155 | ||||||||
\(571\) | −31.0067 | −1.29759 | −0.648794 | − | 0.760964i | \(-0.724726\pi\) | ||||
−0.648794 | + | 0.760964i | \(0.724726\pi\) | |||||||
\(572\) | −29.2297 | −1.22216 | ||||||||
\(573\) | 1.38608 | 0.0579043 | ||||||||
\(574\) | 36.2578 | 1.51337 | ||||||||
\(575\) | 6.71610 | 0.280081 | ||||||||
\(576\) | 24.5382 | 1.02242 | ||||||||
\(577\) | −34.6463 | −1.44235 | −0.721173 | − | 0.692755i | \(-0.756397\pi\) | ||||
−0.721173 | + | 0.692755i | \(0.756397\pi\) | |||||||
\(578\) | −2.00836 | −0.0835368 | ||||||||
\(579\) | −0.849256 | −0.0352939 | ||||||||
\(580\) | 1.67919 | 0.0697245 | ||||||||
\(581\) | −8.15457 | −0.338309 | ||||||||
\(582\) | 3.38669 | 0.140383 | ||||||||
\(583\) | −7.91616 | −0.327854 | ||||||||
\(584\) | −0.0489185 | −0.00202426 | ||||||||
\(585\) | 11.6829 | 0.483027 | ||||||||
\(586\) | 50.8089 | 2.09890 | ||||||||
\(587\) | 27.4750 | 1.13401 | 0.567007 | − | 0.823713i | \(-0.308101\pi\) | ||||
0.567007 | + | 0.823713i | \(0.308101\pi\) | |||||||
\(588\) | −1.53630 | −0.0633559 | ||||||||
\(589\) | −3.37105 | −0.138902 | ||||||||
\(590\) | −11.2198 | −0.461913 | ||||||||
\(591\) | −2.28395 | −0.0939491 | ||||||||
\(592\) | 18.2939 | 0.751873 | ||||||||
\(593\) | 0.336283 | 0.0138095 | 0.00690474 | − | 0.999976i | \(-0.497802\pi\) | ||||
0.00690474 | + | 0.999976i | \(0.497802\pi\) | |||||||
\(594\) | 7.75534 | 0.318205 | ||||||||
\(595\) | −1.65376 | −0.0677976 | ||||||||
\(596\) | 29.1175 | 1.19270 | ||||||||
\(597\) | 0.741856 | 0.0303622 | ||||||||
\(598\) | 53.0828 | 2.17072 | ||||||||
\(599\) | 41.1644 | 1.68193 | 0.840967 | − | 0.541087i | \(-0.181987\pi\) | ||||
0.840967 | + | 0.541087i | \(0.181987\pi\) | |||||||
\(600\) | −0.0119232 | −0.000486761 0 | ||||||||
\(601\) | −22.5177 | −0.918516 | −0.459258 | − | 0.888303i | \(-0.651885\pi\) | ||||
−0.459258 | + | 0.888303i | \(0.651885\pi\) | |||||||
\(602\) | 9.42010 | 0.383934 | ||||||||
\(603\) | 29.2897 | 1.19277 | ||||||||
\(604\) | 2.24879 | 0.0915019 | ||||||||
\(605\) | 2.34030 | 0.0951469 | ||||||||
\(606\) | −4.86300 | −0.197546 | ||||||||
\(607\) | −44.1978 | −1.79394 | −0.896968 | − | 0.442096i | \(-0.854235\pi\) | ||||
−0.896968 | + | 0.442096i | \(0.854235\pi\) | |||||||
\(608\) | 18.4954 | 0.750089 | ||||||||
\(609\) | −0.241895 | −0.00980208 | ||||||||
\(610\) | 21.0021 | 0.850349 | ||||||||
\(611\) | 20.8993 | 0.845497 | ||||||||
\(612\) | −6.03674 | −0.244021 | ||||||||
\(613\) | 41.6637 | 1.68278 | 0.841390 | − | 0.540428i | \(-0.181738\pi\) | ||||
0.841390 | + | 0.540428i | \(0.181738\pi\) | |||||||
\(614\) | 20.9321 | 0.844750 | ||||||||
\(615\) | 1.93370 | 0.0779742 | ||||||||
\(616\) | 0.406580 | 0.0163816 | ||||||||
\(617\) | 9.38216 | 0.377711 | 0.188856 | − | 0.982005i | \(-0.439522\pi\) | ||||
0.188856 | + | 0.982005i | \(0.439522\pi\) | |||||||
\(618\) | 0.865137 | 0.0348009 | ||||||||
\(619\) | 24.4679 | 0.983449 | 0.491725 | − | 0.870751i | \(-0.336367\pi\) | ||||
0.491725 | + | 0.870751i | \(0.336367\pi\) | |||||||
\(620\) | −2.97666 | −0.119545 | ||||||||
\(621\) | −7.10057 | −0.284936 | ||||||||
\(622\) | −43.0957 | −1.72798 | ||||||||
\(623\) | 27.5566 | 1.10403 | ||||||||
\(624\) | 2.74090 | 0.109724 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 58.7053 | 2.34633 | ||||||||
\(627\) | 1.48994 | 0.0595025 | ||||||||
\(628\) | −23.7381 | −0.947255 | ||||||||
\(629\) | −4.65274 | −0.185517 | ||||||||
\(630\) | −9.85984 | −0.392826 | ||||||||
\(631\) | 19.6827 | 0.783557 | 0.391779 | − | 0.920060i | \(-0.371860\pi\) | ||||
0.391779 | + | 0.920060i | \(0.371860\pi\) | |||||||
\(632\) | −0.835302 | −0.0332265 | ||||||||
\(633\) | −1.82064 | −0.0723639 | ||||||||
\(634\) | −59.8375 | −2.37645 | ||||||||
\(635\) | 0.0180324 | 0.000715593 0 | ||||||||
\(636\) | −0.780694 | −0.0309565 | ||||||||
\(637\) | 16.7850 | 0.665045 | ||||||||
\(638\) | −6.05727 | −0.239810 | ||||||||
\(639\) | −2.96862 | −0.117437 | ||||||||
\(640\) | 0.538417 | 0.0212828 | ||||||||
\(641\) | 36.8693 | 1.45625 | 0.728124 | − | 0.685446i | \(-0.240393\pi\) | ||||
0.728124 | + | 0.685446i | \(0.240393\pi\) | |||||||
\(642\) | −2.00658 | −0.0791934 | ||||||||
\(643\) | −48.1641 | −1.89941 | −0.949703 | − | 0.313151i | \(-0.898615\pi\) | ||||
−0.949703 | + | 0.313151i | \(0.898615\pi\) | |||||||
\(644\) | −22.5859 | −0.890010 | ||||||||
\(645\) | 0.502391 | 0.0197816 | ||||||||
\(646\) | −4.62516 | −0.181974 | ||||||||
\(647\) | 0.840589 | 0.0330470 | 0.0165235 | − | 0.999863i | \(-0.494740\pi\) | ||||
0.0165235 | + | 0.999863i | \(0.494740\pi\) | |||||||
\(648\) | −0.586863 | −0.0230541 | ||||||||
\(649\) | 20.4046 | 0.800949 | ||||||||
\(650\) | 7.90381 | 0.310013 | ||||||||
\(651\) | 0.428801 | 0.0168060 | ||||||||
\(652\) | 10.9818 | 0.430081 | ||||||||
\(653\) | −3.81467 | −0.149279 | −0.0746397 | − | 0.997211i | \(-0.523781\pi\) | ||||
−0.0746397 | + | 0.997211i | \(0.523781\pi\) | |||||||
\(654\) | 4.49659 | 0.175830 | ||||||||
\(655\) | 19.3083 | 0.754439 | ||||||||
\(656\) | −42.9223 | −1.67583 | ||||||||
\(657\) | −2.15744 | −0.0841697 | ||||||||
\(658\) | −17.6382 | −0.687607 | ||||||||
\(659\) | 42.0446 | 1.63782 | 0.818912 | − | 0.573919i | \(-0.194578\pi\) | ||||
0.818912 | + | 0.573919i | \(0.194578\pi\) | |||||||
\(660\) | 1.31563 | 0.0512106 | ||||||||
\(661\) | 49.1719 | 1.91257 | 0.956284 | − | 0.292441i | \(-0.0944676\pi\) | ||||
0.956284 | + | 0.292441i | \(0.0944676\pi\) | |||||||
\(662\) | −40.3533 | −1.56837 | ||||||||
\(663\) | −0.697102 | −0.0270732 | ||||||||
\(664\) | −0.331908 | −0.0128805 | ||||||||
\(665\) | −3.80853 | −0.147689 | ||||||||
\(666\) | −27.7400 | −1.07490 | ||||||||
\(667\) | 5.54587 | 0.214737 | ||||||||
\(668\) | 21.0400 | 0.814061 | ||||||||
\(669\) | 1.09723 | 0.0424215 | ||||||||
\(670\) | 19.8154 | 0.765534 | ||||||||
\(671\) | −38.1947 | −1.47449 | ||||||||
\(672\) | −2.35264 | −0.0907549 | ||||||||
\(673\) | 39.8547 | 1.53629 | 0.768144 | − | 0.640278i | \(-0.221181\pi\) | ||||
0.768144 | + | 0.640278i | \(0.221181\pi\) | |||||||
\(674\) | 15.7460 | 0.606514 | ||||||||
\(675\) | −1.05725 | −0.0406934 | ||||||||
\(676\) | 5.05891 | 0.194574 | ||||||||
\(677\) | 40.5156 | 1.55714 | 0.778571 | − | 0.627557i | \(-0.215945\pi\) | ||||
0.778571 | + | 0.627557i | \(0.215945\pi\) | |||||||
\(678\) | 1.80420 | 0.0692898 | ||||||||
\(679\) | 15.7436 | 0.604185 | ||||||||
\(680\) | −0.0673116 | −0.00258128 | ||||||||
\(681\) | −2.76528 | −0.105966 | ||||||||
\(682\) | 10.7376 | 0.411163 | ||||||||
\(683\) | 38.5400 | 1.47469 | 0.737346 | − | 0.675516i | \(-0.236079\pi\) | ||||
0.737346 | + | 0.675516i | \(0.236079\pi\) | |||||||
\(684\) | −13.9023 | −0.531568 | ||||||||
\(685\) | 18.3264 | 0.700215 | ||||||||
\(686\) | −37.4153 | −1.42852 | ||||||||
\(687\) | 2.34706 | 0.0895459 | ||||||||
\(688\) | −11.1516 | −0.425150 | ||||||||
\(689\) | 8.52954 | 0.324950 | ||||||||
\(690\) | −2.38925 | −0.0909571 | ||||||||
\(691\) | 1.55240 | 0.0590560 | 0.0295280 | − | 0.999564i | \(-0.490600\pi\) | ||||
0.0295280 | + | 0.999564i | \(0.490600\pi\) | |||||||
\(692\) | 12.6126 | 0.479461 | ||||||||
\(693\) | 17.9313 | 0.681153 | ||||||||
\(694\) | 53.4849 | 2.03026 | ||||||||
\(695\) | 5.88400 | 0.223193 | ||||||||
\(696\) | −0.00984563 | −0.000373198 0 | ||||||||
\(697\) | 10.9166 | 0.413495 | ||||||||
\(698\) | −35.3101 | −1.33651 | ||||||||
\(699\) | 0.576009 | 0.0217867 | ||||||||
\(700\) | −3.36295 | −0.127108 | ||||||||
\(701\) | 4.21754 | 0.159294 | 0.0796471 | − | 0.996823i | \(-0.474621\pi\) | ||||
0.0796471 | + | 0.996823i | \(0.474621\pi\) | |||||||
\(702\) | −8.35626 | −0.315387 | ||||||||
\(703\) | −10.7150 | −0.404125 | ||||||||
\(704\) | −30.1905 | −1.13785 | ||||||||
\(705\) | −0.940676 | −0.0354279 | ||||||||
\(706\) | −12.8879 | −0.485043 | ||||||||
\(707\) | −22.6065 | −0.850206 | ||||||||
\(708\) | 2.01230 | 0.0756270 | ||||||||
\(709\) | −15.4181 | −0.579037 | −0.289519 | − | 0.957172i | \(-0.593495\pi\) | ||||
−0.289519 | + | 0.957172i | \(0.593495\pi\) | |||||||
\(710\) | −2.00836 | −0.0753725 | ||||||||
\(711\) | −36.8391 | −1.38157 | ||||||||
\(712\) | 1.12161 | 0.0420341 | ||||||||
\(713\) | −9.83102 | −0.368175 | ||||||||
\(714\) | 0.588324 | 0.0220175 | ||||||||
\(715\) | −14.3740 | −0.537557 | ||||||||
\(716\) | −4.66639 | −0.174391 | ||||||||
\(717\) | 4.82140 | 0.180058 | ||||||||
\(718\) | 51.5070 | 1.92222 | ||||||||
\(719\) | 28.7877 | 1.07360 | 0.536801 | − | 0.843709i | \(-0.319633\pi\) | ||||
0.536801 | + | 0.843709i | \(0.319633\pi\) | |||||||
\(720\) | 11.6722 | 0.434996 | ||||||||
\(721\) | 4.02174 | 0.149778 | ||||||||
\(722\) | 27.5074 | 1.02372 | ||||||||
\(723\) | 0.775124 | 0.0288272 | ||||||||
\(724\) | 5.69752 | 0.211747 | ||||||||
\(725\) | 0.825756 | 0.0306678 | ||||||||
\(726\) | −0.832561 | −0.0308992 | ||||||||
\(727\) | −10.0382 | −0.372296 | −0.186148 | − | 0.982522i | \(-0.559600\pi\) | ||||
−0.186148 | + | 0.982522i | \(0.559600\pi\) | |||||||
\(728\) | −0.438084 | −0.0162365 | ||||||||
\(729\) | −25.3204 | −0.937793 | ||||||||
\(730\) | −1.45957 | −0.0540212 | ||||||||
\(731\) | 2.83622 | 0.104902 | ||||||||
\(732\) | −3.76677 | −0.139224 | ||||||||
\(733\) | −34.2867 | −1.26641 | −0.633204 | − | 0.773985i | \(-0.718261\pi\) | ||||
−0.633204 | + | 0.773985i | \(0.718261\pi\) | |||||||
\(734\) | −31.6253 | −1.16731 | ||||||||
\(735\) | −0.755489 | −0.0278666 | ||||||||
\(736\) | 53.9383 | 1.98819 | ||||||||
\(737\) | −36.0365 | −1.32742 | ||||||||
\(738\) | 65.0854 | 2.39583 | ||||||||
\(739\) | 21.6428 | 0.796142 | 0.398071 | − | 0.917355i | \(-0.369680\pi\) | ||||
0.398071 | + | 0.917355i | \(0.369680\pi\) | |||||||
\(740\) | −9.46142 | −0.347809 | ||||||||
\(741\) | −1.60539 | −0.0589755 | ||||||||
\(742\) | −7.19857 | −0.264268 | ||||||||
\(743\) | −5.84064 | −0.214272 | −0.107136 | − | 0.994244i | \(-0.534168\pi\) | ||||
−0.107136 | + | 0.994244i | \(0.534168\pi\) | |||||||
\(744\) | 0.0174531 | 0.000639862 0 | ||||||||
\(745\) | 14.3188 | 0.524601 | ||||||||
\(746\) | −3.33904 | −0.122251 | ||||||||
\(747\) | −14.6380 | −0.535578 | ||||||||
\(748\) | 7.42729 | 0.271569 | ||||||||
\(749\) | −9.32794 | −0.340835 | ||||||||
\(750\) | −0.355749 | −0.0129901 | ||||||||
\(751\) | 4.83817 | 0.176547 | 0.0882737 | − | 0.996096i | \(-0.471865\pi\) | ||||
0.0882737 | + | 0.996096i | \(0.471865\pi\) | |||||||
\(752\) | 20.8802 | 0.761423 | ||||||||
\(753\) | −1.04099 | −0.0379359 | ||||||||
\(754\) | 6.52662 | 0.237685 | ||||||||
\(755\) | 1.10586 | 0.0402464 | ||||||||
\(756\) | 3.55547 | 0.129311 | ||||||||
\(757\) | 34.5801 | 1.25684 | 0.628418 | − | 0.777875i | \(-0.283703\pi\) | ||||
0.628418 | + | 0.777875i | \(0.283703\pi\) | |||||||
\(758\) | −10.3295 | −0.375186 | ||||||||
\(759\) | 4.34512 | 0.157718 | ||||||||
\(760\) | −0.155015 | −0.00562299 | ||||||||
\(761\) | 0.122668 | 0.00444671 | 0.00222335 | − | 0.999998i | \(-0.499292\pi\) | ||||
0.00222335 | + | 0.999998i | \(0.499292\pi\) | |||||||
\(762\) | −0.00641500 | −0.000232391 0 | ||||||||
\(763\) | 20.9032 | 0.756746 | ||||||||
\(764\) | 15.9123 | 0.575689 | ||||||||
\(765\) | −2.96862 | −0.107331 | ||||||||
\(766\) | 0.626331 | 0.0226302 | ||||||||
\(767\) | −21.9856 | −0.793855 | ||||||||
\(768\) | 2.73678 | 0.0987551 | ||||||||
\(769\) | −5.25406 | −0.189466 | −0.0947331 | − | 0.995503i | \(-0.530200\pi\) | ||||
−0.0947331 | + | 0.995503i | \(0.530200\pi\) | |||||||
\(770\) | 12.1310 | 0.437172 | ||||||||
\(771\) | −1.60345 | −0.0577469 | ||||||||
\(772\) | −9.74955 | −0.350894 | ||||||||
\(773\) | 44.8626 | 1.61360 | 0.806798 | − | 0.590828i | \(-0.201199\pi\) | ||||
0.806798 | + | 0.590828i | \(0.201199\pi\) | |||||||
\(774\) | 16.9098 | 0.607809 | ||||||||
\(775\) | −1.46380 | −0.0525812 | ||||||||
\(776\) | 0.640799 | 0.0230033 | ||||||||
\(777\) | 1.36296 | 0.0488960 | ||||||||
\(778\) | −46.0898 | −1.65240 | ||||||||
\(779\) | 25.1403 | 0.900746 | ||||||||
\(780\) | −1.41757 | −0.0507570 | ||||||||
\(781\) | 3.65244 | 0.130695 | ||||||||
\(782\) | −13.4884 | −0.482343 | ||||||||
\(783\) | −0.873027 | −0.0311995 | ||||||||
\(784\) | 16.7696 | 0.598914 | ||||||||
\(785\) | −11.6735 | −0.416643 | ||||||||
\(786\) | −6.86892 | −0.245006 | ||||||||
\(787\) | −13.1881 | −0.470106 | −0.235053 | − | 0.971983i | \(-0.575526\pi\) | ||||
−0.235053 | + | 0.971983i | \(0.575526\pi\) | |||||||
\(788\) | −26.2200 | −0.934047 | ||||||||
\(789\) | −0.173692 | −0.00618359 | ||||||||
\(790\) | −24.9227 | −0.886710 | ||||||||
\(791\) | 8.38714 | 0.298212 | ||||||||
\(792\) | 0.729840 | 0.0259337 | ||||||||
\(793\) | 41.1542 | 1.46143 | ||||||||
\(794\) | −13.4282 | −0.476547 | ||||||||
\(795\) | −0.383913 | −0.0136160 | ||||||||
\(796\) | 8.51659 | 0.301862 | ||||||||
\(797\) | 1.34147 | 0.0475173 | 0.0237586 | − | 0.999718i | \(-0.492437\pi\) | ||||
0.0237586 | + | 0.999718i | \(0.492437\pi\) | |||||||
\(798\) | 1.35488 | 0.0479623 | ||||||||
\(799\) | −5.31053 | −0.187873 | ||||||||
\(800\) | 8.03119 | 0.283945 | ||||||||
\(801\) | 49.4661 | 1.74780 | ||||||||
\(802\) | −1.04248 | −0.0368112 | ||||||||
\(803\) | 2.65440 | 0.0936717 | ||||||||
\(804\) | −3.55393 | −0.125338 | ||||||||
\(805\) | −11.1068 | −0.391465 | ||||||||
\(806\) | −11.5696 | −0.407521 | ||||||||
\(807\) | 3.61847 | 0.127376 | ||||||||
\(808\) | −0.920133 | −0.0323702 | ||||||||
\(809\) | −25.6195 | −0.900732 | −0.450366 | − | 0.892844i | \(-0.648707\pi\) | ||||
−0.450366 | + | 0.892844i | \(0.648707\pi\) | |||||||
\(810\) | −17.5101 | −0.615242 | ||||||||
\(811\) | 22.0020 | 0.772596 | 0.386298 | − | 0.922374i | \(-0.373754\pi\) | ||||
0.386298 | + | 0.922374i | \(0.373754\pi\) | |||||||
\(812\) | −2.77698 | −0.0974528 | ||||||||
\(813\) | 5.37868 | 0.188639 | ||||||||
\(814\) | 34.1298 | 1.19625 | ||||||||
\(815\) | 5.40040 | 0.189168 | ||||||||
\(816\) | −0.696463 | −0.0243811 | ||||||||
\(817\) | 6.53168 | 0.228515 | ||||||||
\(818\) | −72.0602 | −2.51952 | ||||||||
\(819\) | −19.3207 | −0.675119 | ||||||||
\(820\) | 22.1990 | 0.775224 | ||||||||
\(821\) | −2.30062 | −0.0802920 | −0.0401460 | − | 0.999194i | \(-0.512782\pi\) | ||||
−0.0401460 | + | 0.999194i | \(0.512782\pi\) | |||||||
\(822\) | −6.51959 | −0.227397 | ||||||||
\(823\) | 27.4210 | 0.955837 | 0.477919 | − | 0.878404i | \(-0.341391\pi\) | ||||
0.477919 | + | 0.878404i | \(0.341391\pi\) | |||||||
\(824\) | 0.163693 | 0.00570253 | ||||||||
\(825\) | 0.646971 | 0.0225246 | ||||||||
\(826\) | 18.5549 | 0.645608 | ||||||||
\(827\) | 15.7534 | 0.547799 | 0.273900 | − | 0.961758i | \(-0.411686\pi\) | ||||
0.273900 | + | 0.961758i | \(0.411686\pi\) | |||||||
\(828\) | −40.5434 | −1.40898 | ||||||||
\(829\) | 25.8772 | 0.898751 | 0.449376 | − | 0.893343i | \(-0.351646\pi\) | ||||
0.449376 | + | 0.893343i | \(0.351646\pi\) | |||||||
\(830\) | −9.90307 | −0.343741 | ||||||||
\(831\) | 2.91112 | 0.100986 | ||||||||
\(832\) | 32.5298 | 1.12777 | ||||||||
\(833\) | −4.26507 | −0.147776 | ||||||||
\(834\) | −2.09323 | −0.0724825 | ||||||||
\(835\) | 10.3466 | 0.358059 | ||||||||
\(836\) | 17.1047 | 0.591578 | ||||||||
\(837\) | 1.54759 | 0.0534927 | ||||||||
\(838\) | 72.6547 | 2.50981 | ||||||||
\(839\) | 35.5601 | 1.22767 | 0.613835 | − | 0.789434i | \(-0.289626\pi\) | ||||
0.613835 | + | 0.789434i | \(0.289626\pi\) | |||||||
\(840\) | 0.0197181 | 0.000680338 0 | ||||||||
\(841\) | −28.3181 | −0.976487 | ||||||||
\(842\) | 25.5005 | 0.878804 | ||||||||
\(843\) | −2.21444 | −0.0762693 | ||||||||
\(844\) | −20.9011 | −0.719446 | ||||||||
\(845\) | 2.48777 | 0.0855818 | ||||||||
\(846\) | −31.6618 | −1.08855 | ||||||||
\(847\) | −3.87031 | −0.132985 | ||||||||
\(848\) | 8.52173 | 0.292637 | ||||||||
\(849\) | 1.23683 | 0.0424478 | ||||||||
\(850\) | −2.00836 | −0.0688862 | ||||||||
\(851\) | −31.2483 | −1.07118 | ||||||||
\(852\) | 0.360205 | 0.0123404 | ||||||||
\(853\) | −25.2721 | −0.865299 | −0.432649 | − | 0.901562i | \(-0.642421\pi\) | ||||
−0.432649 | + | 0.901562i | \(0.642421\pi\) | |||||||
\(854\) | −34.7324 | −1.18852 | ||||||||
\(855\) | −6.83659 | −0.233807 | ||||||||
\(856\) | −0.379667 | −0.0129767 | ||||||||
\(857\) | 16.0224 | 0.547316 | 0.273658 | − | 0.961827i | \(-0.411766\pi\) | ||||
0.273658 | + | 0.961827i | \(0.411766\pi\) | |||||||
\(858\) | 5.11353 | 0.174573 | ||||||||
\(859\) | 25.0244 | 0.853822 | 0.426911 | − | 0.904294i | \(-0.359602\pi\) | ||||
0.426911 | + | 0.904294i | \(0.359602\pi\) | |||||||
\(860\) | 5.76751 | 0.196670 | ||||||||
\(861\) | −3.19788 | −0.108983 | ||||||||
\(862\) | 34.3333 | 1.16940 | ||||||||
\(863\) | −1.75853 | −0.0598610 | −0.0299305 | − | 0.999552i | \(-0.509529\pi\) | ||||
−0.0299305 | + | 0.999552i | \(0.509529\pi\) | |||||||
\(864\) | −8.49094 | −0.288868 | ||||||||
\(865\) | 6.20238 | 0.210887 | ||||||||
\(866\) | −58.3573 | −1.98306 | ||||||||
\(867\) | 0.177134 | 0.00601578 | ||||||||
\(868\) | 4.92268 | 0.167087 | ||||||||
\(869\) | 45.3248 | 1.53754 | ||||||||
\(870\) | −0.293762 | −0.00995946 | ||||||||
\(871\) | 38.8288 | 1.31566 | ||||||||
\(872\) | 0.850803 | 0.0288118 | ||||||||
\(873\) | 28.2610 | 0.956489 | ||||||||
\(874\) | −31.0630 | −1.05072 | ||||||||
\(875\) | −1.65376 | −0.0559074 | ||||||||
\(876\) | 0.261778 | 0.00884465 | ||||||||
\(877\) | −49.8773 | −1.68424 | −0.842118 | − | 0.539294i | \(-0.818691\pi\) | ||||
−0.842118 | + | 0.539294i | \(0.818691\pi\) | |||||||
\(878\) | 62.0599 | 2.09442 | ||||||||
\(879\) | −4.48126 | −0.151149 | ||||||||
\(880\) | −14.3608 | −0.484103 | ||||||||
\(881\) | −1.57314 | −0.0530003 | −0.0265001 | − | 0.999649i | \(-0.508436\pi\) | ||||
−0.0265001 | + | 0.999649i | \(0.508436\pi\) | |||||||
\(882\) | −25.4286 | −0.856227 | ||||||||
\(883\) | −14.2007 | −0.477893 | −0.238947 | − | 0.971033i | \(-0.576802\pi\) | ||||
−0.238947 | + | 0.971033i | \(0.576802\pi\) | |||||||
\(884\) | −8.00280 | −0.269163 | ||||||||
\(885\) | 0.989569 | 0.0332640 | ||||||||
\(886\) | −28.1869 | −0.946957 | ||||||||
\(887\) | −41.0553 | −1.37850 | −0.689250 | − | 0.724523i | \(-0.742060\pi\) | ||||
−0.689250 | + | 0.724523i | \(0.742060\pi\) | |||||||
\(888\) | 0.0554754 | 0.00186163 | ||||||||
\(889\) | −0.0298213 | −0.00100017 | ||||||||
\(890\) | 33.4653 | 1.12176 | ||||||||
\(891\) | 31.8441 | 1.06682 | ||||||||
\(892\) | 12.5964 | 0.421757 | ||||||||
\(893\) | −12.2299 | −0.409258 | ||||||||
\(894\) | −5.09390 | −0.170366 | ||||||||
\(895\) | −2.29474 | −0.0767047 | ||||||||
\(896\) | −0.890414 | −0.0297466 | ||||||||
\(897\) | −4.68181 | −0.156321 | ||||||||
\(898\) | 19.6748 | 0.656557 | ||||||||
\(899\) | −1.20874 | −0.0403138 | ||||||||
\(900\) | −6.03674 | −0.201225 | ||||||||
\(901\) | −2.16736 | −0.0722053 | ||||||||
\(902\) | −80.0777 | −2.66630 | ||||||||
\(903\) | −0.830836 | −0.0276485 | ||||||||
\(904\) | 0.341374 | 0.0113539 | ||||||||
\(905\) | 2.80181 | 0.0931352 | ||||||||
\(906\) | −0.393409 | −0.0130701 | ||||||||
\(907\) | −25.7429 | −0.854780 | −0.427390 | − | 0.904067i | \(-0.640567\pi\) | ||||
−0.427390 | + | 0.904067i | \(0.640567\pi\) | |||||||
\(908\) | −31.7457 | −1.05352 | ||||||||
\(909\) | −40.5804 | −1.34597 | ||||||||
\(910\) | −13.0710 | −0.433300 | ||||||||
\(911\) | −54.4958 | −1.80553 | −0.902764 | − | 0.430136i | \(-0.858466\pi\) | ||||
−0.902764 | + | 0.430136i | \(0.858466\pi\) | |||||||
\(912\) | −1.60392 | −0.0531111 | ||||||||
\(913\) | 18.0099 | 0.596040 | ||||||||
\(914\) | 80.0159 | 2.64669 | ||||||||
\(915\) | −1.85235 | −0.0612366 | ||||||||
\(916\) | 26.9445 | 0.890270 | ||||||||
\(917\) | −31.9314 | −1.05447 | ||||||||
\(918\) | 2.12333 | 0.0700804 | ||||||||
\(919\) | 39.5948 | 1.30611 | 0.653056 | − | 0.757309i | \(-0.273487\pi\) | ||||
0.653056 | + | 0.757309i | \(0.273487\pi\) | |||||||
\(920\) | −0.452072 | −0.0149044 | ||||||||
\(921\) | −1.84617 | −0.0608335 | ||||||||
\(922\) | 0.248470 | 0.00818292 | ||||||||
\(923\) | −3.93545 | −0.129537 | ||||||||
\(924\) | −2.17573 | −0.0715763 | ||||||||
\(925\) | −4.65274 | −0.152981 | ||||||||
\(926\) | −66.4311 | −2.18306 | ||||||||
\(927\) | 7.21932 | 0.237114 | ||||||||
\(928\) | 6.63181 | 0.217700 | ||||||||
\(929\) | −0.205805 | −0.00675225 | −0.00337612 | − | 0.999994i | \(-0.501075\pi\) | ||||
−0.00337612 | + | 0.999994i | \(0.501075\pi\) | |||||||
\(930\) | 0.520745 | 0.0170759 | ||||||||
\(931\) | −9.82225 | −0.321911 | ||||||||
\(932\) | 6.61264 | 0.216604 | ||||||||
\(933\) | 3.80096 | 0.124438 | ||||||||
\(934\) | 8.69840 | 0.284620 | ||||||||
\(935\) | 3.65244 | 0.119447 | ||||||||
\(936\) | −0.786392 | −0.0257040 | ||||||||
\(937\) | 45.9808 | 1.50213 | 0.751063 | − | 0.660231i | \(-0.229542\pi\) | ||||
0.751063 | + | 0.660231i | \(0.229542\pi\) | |||||||
\(938\) | −32.7699 | −1.06997 | ||||||||
\(939\) | −5.17770 | −0.168968 | ||||||||
\(940\) | −10.7991 | −0.352226 | ||||||||
\(941\) | −28.6038 | −0.932459 | −0.466229 | − | 0.884664i | \(-0.654388\pi\) | ||||
−0.466229 | + | 0.884664i | \(0.654388\pi\) | |||||||
\(942\) | 4.15282 | 0.135306 | ||||||||
\(943\) | 73.3169 | 2.38753 | ||||||||
\(944\) | −21.9655 | −0.714915 | ||||||||
\(945\) | 1.74843 | 0.0568765 | ||||||||
\(946\) | −20.8049 | −0.676425 | ||||||||
\(947\) | −7.73287 | −0.251284 | −0.125642 | − | 0.992076i | \(-0.540099\pi\) | ||||
−0.125642 | + | 0.992076i | \(0.540099\pi\) | |||||||
\(948\) | 4.46995 | 0.145177 | ||||||||
\(949\) | −2.86008 | −0.0928421 | ||||||||
\(950\) | −4.62516 | −0.150060 | ||||||||
\(951\) | 5.27756 | 0.171137 | ||||||||
\(952\) | 0.111317 | 0.00360782 | ||||||||
\(953\) | 41.9645 | 1.35936 | 0.679681 | − | 0.733507i | \(-0.262118\pi\) | ||||
0.679681 | + | 0.733507i | \(0.262118\pi\) | |||||||
\(954\) | −12.9220 | −0.418364 | ||||||||
\(955\) | 7.82504 | 0.253212 | ||||||||
\(956\) | 55.3501 | 1.79015 | ||||||||
\(957\) | 0.534240 | 0.0172695 | ||||||||
\(958\) | −60.5350 | −1.95580 | ||||||||
\(959\) | −30.3075 | −0.978680 | ||||||||
\(960\) | −1.46416 | −0.0472556 | ||||||||
\(961\) | −28.8573 | −0.930881 | ||||||||
\(962\) | −36.7744 | −1.18565 | ||||||||
\(963\) | −16.7443 | −0.539578 | ||||||||
\(964\) | 8.89851 | 0.286602 | ||||||||
\(965\) | −4.79443 | −0.154338 | ||||||||
\(966\) | 3.95125 | 0.127129 | ||||||||
\(967\) | 0.842616 | 0.0270967 | 0.0135483 | − | 0.999908i | \(-0.495687\pi\) | ||||
0.0135483 | + | 0.999908i | \(0.495687\pi\) | |||||||
\(968\) | −0.157530 | −0.00506319 | ||||||||
\(969\) | 0.407931 | 0.0131046 | ||||||||
\(970\) | 19.1194 | 0.613887 | ||||||||
\(971\) | 25.2873 | 0.811509 | 0.405755 | − | 0.913982i | \(-0.367009\pi\) | ||||
0.405755 | + | 0.913982i | \(0.367009\pi\) | |||||||
\(972\) | 9.59026 | 0.307608 | ||||||||
\(973\) | −9.73073 | −0.311953 | ||||||||
\(974\) | −44.4116 | −1.42304 | ||||||||
\(975\) | −0.697102 | −0.0223251 | ||||||||
\(976\) | 41.1165 | 1.31611 | ||||||||
\(977\) | 17.8565 | 0.571281 | 0.285640 | − | 0.958337i | \(-0.407794\pi\) | ||||
0.285640 | + | 0.958337i | \(0.407794\pi\) | |||||||
\(978\) | −1.92119 | −0.0614328 | ||||||||
\(979\) | −60.8605 | −1.94511 | ||||||||
\(980\) | −8.67309 | −0.277052 | ||||||||
\(981\) | 37.5227 | 1.19801 | ||||||||
\(982\) | −28.6326 | −0.913704 | ||||||||
\(983\) | 6.31868 | 0.201535 | 0.100767 | − | 0.994910i | \(-0.467870\pi\) | ||||
0.100767 | + | 0.994910i | \(0.467870\pi\) | |||||||
\(984\) | −0.130160 | −0.00414936 | ||||||||
\(985\) | −12.8939 | −0.410834 | ||||||||
\(986\) | −1.65842 | −0.0528148 | ||||||||
\(987\) | 1.55565 | 0.0495170 | ||||||||
\(988\) | −18.4300 | −0.586338 | ||||||||
\(989\) | 19.0484 | 0.605703 | ||||||||
\(990\) | 21.7761 | 0.692090 | ||||||||
\(991\) | −12.1787 | −0.386868 | −0.193434 | − | 0.981113i | \(-0.561963\pi\) | ||||
−0.193434 | + | 0.981113i | \(0.561963\pi\) | |||||||
\(992\) | −11.7560 | −0.373255 | ||||||||
\(993\) | 3.55909 | 0.112944 | ||||||||
\(994\) | 3.32135 | 0.105347 | ||||||||
\(995\) | 4.18811 | 0.132772 | ||||||||
\(996\) | 1.77614 | 0.0562792 | ||||||||
\(997\) | 1.37060 | 0.0434075 | 0.0217037 | − | 0.999764i | \(-0.493091\pi\) | ||||
0.0217037 | + | 0.999764i | \(0.493091\pi\) | |||||||
\(998\) | −48.4078 | −1.53232 | ||||||||
\(999\) | 4.91909 | 0.155633 |
(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 | 6035.2.a.g.1.12 | ✓ | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6035.2.a.g.1.12 | ✓ | 58 | 1.1 | even | 1 | trivial |