Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8005,2,Mod(1,8005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8005 = 5 \cdot 1601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8005.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: | \(63.9202468180\) |
Analytic rank: | \(1\) |
Dimension: | \(127\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51650 | −1.77943 | −0.889717 | − | 0.456512i | \(-0.849098\pi\) | ||||
−0.889717 | + | 0.456512i | \(0.849098\pi\) | |||||||
\(3\) | 0.753102 | 0.434804 | 0.217402 | − | 0.976082i | \(-0.430242\pi\) | ||||
0.217402 | + | 0.976082i | \(0.430242\pi\) | |||||||
\(4\) | 4.33277 | 2.16639 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.89518 | −0.773705 | ||||||||
\(7\) | 3.99606 | 1.51037 | 0.755183 | − | 0.655513i | \(-0.227548\pi\) | ||||
0.755183 | + | 0.655513i | \(0.227548\pi\) | |||||||
\(8\) | −5.87042 | −2.07551 | ||||||||
\(9\) | −2.43284 | −0.810946 | ||||||||
\(10\) | 2.51650 | 0.795787 | ||||||||
\(11\) | −2.93325 | −0.884407 | −0.442204 | − | 0.896915i | \(-0.645803\pi\) | ||||
−0.442204 | + | 0.896915i | \(0.645803\pi\) | |||||||
\(12\) | 3.26302 | 0.941953 | ||||||||
\(13\) | 2.05745 | 0.570633 | 0.285317 | − | 0.958433i | \(-0.407901\pi\) | ||||
0.285317 | + | 0.958433i | \(0.407901\pi\) | |||||||
\(14\) | −10.0561 | −2.68760 | ||||||||
\(15\) | −0.753102 | −0.194450 | ||||||||
\(16\) | 6.10737 | 1.52684 | ||||||||
\(17\) | −5.01088 | −1.21532 | −0.607658 | − | 0.794199i | \(-0.707891\pi\) | ||||
−0.607658 | + | 0.794199i | \(0.707891\pi\) | |||||||
\(18\) | 6.12223 | 1.44302 | ||||||||
\(19\) | −0.166190 | −0.0381265 | −0.0190632 | − | 0.999818i | \(-0.506068\pi\) | ||||
−0.0190632 | + | 0.999818i | \(0.506068\pi\) | |||||||
\(20\) | −4.33277 | −0.968837 | ||||||||
\(21\) | 3.00944 | 0.656713 | ||||||||
\(22\) | 7.38152 | 1.57374 | ||||||||
\(23\) | −5.55870 | −1.15907 | −0.579535 | − | 0.814947i | \(-0.696766\pi\) | ||||
−0.579535 | + | 0.814947i | \(0.696766\pi\) | |||||||
\(24\) | −4.42103 | −0.902439 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.17757 | −1.01540 | ||||||||
\(27\) | −4.09148 | −0.787406 | ||||||||
\(28\) | 17.3140 | 3.27204 | ||||||||
\(29\) | 5.25849 | 0.976476 | 0.488238 | − | 0.872710i | \(-0.337640\pi\) | ||||
0.488238 | + | 0.872710i | \(0.337640\pi\) | |||||||
\(30\) | 1.89518 | 0.346011 | ||||||||
\(31\) | 0.0944094 | 0.0169564 | 0.00847822 | − | 0.999964i | \(-0.497301\pi\) | ||||
0.00847822 | + | 0.999964i | \(0.497301\pi\) | |||||||
\(32\) | −3.62836 | −0.641409 | ||||||||
\(33\) | −2.20904 | −0.384544 | ||||||||
\(34\) | 12.6099 | 2.16258 | ||||||||
\(35\) | −3.99606 | −0.675457 | ||||||||
\(36\) | −10.5409 | −1.75682 | ||||||||
\(37\) | −7.37787 | −1.21292 | −0.606458 | − | 0.795116i | \(-0.707410\pi\) | ||||
−0.606458 | + | 0.795116i | \(0.707410\pi\) | |||||||
\(38\) | 0.418216 | 0.0678436 | ||||||||
\(39\) | 1.54947 | 0.248114 | ||||||||
\(40\) | 5.87042 | 0.928195 | ||||||||
\(41\) | 4.05592 | 0.633428 | 0.316714 | − | 0.948521i | \(-0.397420\pi\) | ||||
0.316714 | + | 0.948521i | \(0.397420\pi\) | |||||||
\(42\) | −7.57325 | −1.16858 | ||||||||
\(43\) | 7.97811 | 1.21665 | 0.608325 | − | 0.793688i | \(-0.291842\pi\) | ||||
0.608325 | + | 0.793688i | \(0.291842\pi\) | |||||||
\(44\) | −12.7091 | −1.91597 | ||||||||
\(45\) | 2.43284 | 0.362666 | ||||||||
\(46\) | 13.9885 | 2.06249 | ||||||||
\(47\) | 2.45961 | 0.358771 | 0.179385 | − | 0.983779i | \(-0.442589\pi\) | ||||
0.179385 | + | 0.983779i | \(0.442589\pi\) | |||||||
\(48\) | 4.59948 | 0.663877 | ||||||||
\(49\) | 8.96846 | 1.28121 | ||||||||
\(50\) | −2.51650 | −0.355887 | ||||||||
\(51\) | −3.77370 | −0.528424 | ||||||||
\(52\) | 8.91445 | 1.23621 | ||||||||
\(53\) | 8.25694 | 1.13418 | 0.567089 | − | 0.823657i | \(-0.308070\pi\) | ||||
0.567089 | + | 0.823657i | \(0.308070\pi\) | |||||||
\(54\) | 10.2962 | 1.40114 | ||||||||
\(55\) | 2.93325 | 0.395519 | ||||||||
\(56\) | −23.4585 | −3.13478 | ||||||||
\(57\) | −0.125158 | −0.0165775 | ||||||||
\(58\) | −13.2330 | −1.73758 | ||||||||
\(59\) | 4.93979 | 0.643106 | 0.321553 | − | 0.946892i | \(-0.395795\pi\) | ||||
0.321553 | + | 0.946892i | \(0.395795\pi\) | |||||||
\(60\) | −3.26302 | −0.421254 | ||||||||
\(61\) | 7.37984 | 0.944892 | 0.472446 | − | 0.881360i | \(-0.343371\pi\) | ||||
0.472446 | + | 0.881360i | \(0.343371\pi\) | |||||||
\(62\) | −0.237581 | −0.0301729 | ||||||||
\(63\) | −9.72175 | −1.22483 | ||||||||
\(64\) | −3.08398 | −0.385498 | ||||||||
\(65\) | −2.05745 | −0.255195 | ||||||||
\(66\) | 5.55904 | 0.684270 | ||||||||
\(67\) | 3.23307 | 0.394982 | 0.197491 | − | 0.980305i | \(-0.436721\pi\) | ||||
0.197491 | + | 0.980305i | \(0.436721\pi\) | |||||||
\(68\) | −21.7110 | −2.63284 | ||||||||
\(69\) | −4.18627 | −0.503968 | ||||||||
\(70\) | 10.0561 | 1.20193 | ||||||||
\(71\) | −1.69878 | −0.201608 | −0.100804 | − | 0.994906i | \(-0.532142\pi\) | ||||
−0.100804 | + | 0.994906i | \(0.532142\pi\) | |||||||
\(72\) | 14.2818 | 1.68312 | ||||||||
\(73\) | −12.2421 | −1.43283 | −0.716414 | − | 0.697676i | \(-0.754218\pi\) | ||||
−0.716414 | + | 0.697676i | \(0.754218\pi\) | |||||||
\(74\) | 18.5664 | 2.15830 | ||||||||
\(75\) | 0.753102 | 0.0869608 | ||||||||
\(76\) | −0.720061 | −0.0825967 | ||||||||
\(77\) | −11.7214 | −1.33578 | ||||||||
\(78\) | −3.89924 | −0.441502 | ||||||||
\(79\) | 4.89167 | 0.550356 | 0.275178 | − | 0.961393i | \(-0.411263\pi\) | ||||
0.275178 | + | 0.961393i | \(0.411263\pi\) | |||||||
\(80\) | −6.10737 | −0.682825 | ||||||||
\(81\) | 4.21720 | 0.468578 | ||||||||
\(82\) | −10.2067 | −1.12714 | ||||||||
\(83\) | 8.21795 | 0.902038 | 0.451019 | − | 0.892514i | \(-0.351061\pi\) | ||||
0.451019 | + | 0.892514i | \(0.351061\pi\) | |||||||
\(84\) | 13.0392 | 1.42270 | ||||||||
\(85\) | 5.01088 | 0.543506 | ||||||||
\(86\) | −20.0769 | −2.16495 | ||||||||
\(87\) | 3.96018 | 0.424576 | ||||||||
\(88\) | 17.2194 | 1.83559 | ||||||||
\(89\) | −9.46497 | −1.00329 | −0.501643 | − | 0.865075i | \(-0.667271\pi\) | ||||
−0.501643 | + | 0.865075i | \(0.667271\pi\) | |||||||
\(90\) | −6.12223 | −0.645340 | ||||||||
\(91\) | 8.22168 | 0.861866 | ||||||||
\(92\) | −24.0846 | −2.51099 | ||||||||
\(93\) | 0.0711000 | 0.00737272 | ||||||||
\(94\) | −6.18961 | −0.638409 | ||||||||
\(95\) | 0.166190 | 0.0170507 | ||||||||
\(96\) | −2.73252 | −0.278887 | ||||||||
\(97\) | 18.4022 | 1.86846 | 0.934228 | − | 0.356675i | \(-0.116090\pi\) | ||||
0.934228 | + | 0.356675i | \(0.116090\pi\) | |||||||
\(98\) | −22.5691 | −2.27983 | ||||||||
\(99\) | 7.13611 | 0.717206 | ||||||||
\(100\) | 4.33277 | 0.433277 | ||||||||
\(101\) | 7.52463 | 0.748729 | 0.374364 | − | 0.927282i | \(-0.377861\pi\) | ||||
0.374364 | + | 0.927282i | \(0.377861\pi\) | |||||||
\(102\) | 9.49653 | 0.940296 | ||||||||
\(103\) | −1.50301 | −0.148096 | −0.0740478 | − | 0.997255i | \(-0.523592\pi\) | ||||
−0.0740478 | + | 0.997255i | \(0.523592\pi\) | |||||||
\(104\) | −12.0781 | −1.18435 | ||||||||
\(105\) | −3.00944 | −0.293691 | ||||||||
\(106\) | −20.7786 | −2.01819 | ||||||||
\(107\) | −5.06875 | −0.490015 | −0.245008 | − | 0.969521i | \(-0.578790\pi\) | ||||
−0.245008 | + | 0.969521i | \(0.578790\pi\) | |||||||
\(108\) | −17.7275 | −1.70583 | ||||||||
\(109\) | 10.8875 | 1.04284 | 0.521418 | − | 0.853302i | \(-0.325403\pi\) | ||||
0.521418 | + | 0.853302i | \(0.325403\pi\) | |||||||
\(110\) | −7.38152 | −0.703800 | ||||||||
\(111\) | −5.55630 | −0.527380 | ||||||||
\(112\) | 24.4054 | 2.30609 | ||||||||
\(113\) | −2.91635 | −0.274347 | −0.137174 | − | 0.990547i | \(-0.543802\pi\) | ||||
−0.137174 | + | 0.990547i | \(0.543802\pi\) | |||||||
\(114\) | 0.314959 | 0.0294987 | ||||||||
\(115\) | 5.55870 | 0.518352 | ||||||||
\(116\) | 22.7838 | 2.11542 | ||||||||
\(117\) | −5.00543 | −0.462753 | ||||||||
\(118\) | −12.4310 | −1.14437 | ||||||||
\(119\) | −20.0237 | −1.83557 | ||||||||
\(120\) | 4.42103 | 0.403583 | ||||||||
\(121\) | −2.39606 | −0.217824 | ||||||||
\(122\) | −18.5714 | −1.68137 | ||||||||
\(123\) | 3.05452 | 0.275417 | ||||||||
\(124\) | 0.409055 | 0.0367342 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 24.4648 | 2.17950 | ||||||||
\(127\) | −8.19089 | −0.726824 | −0.363412 | − | 0.931629i | \(-0.618388\pi\) | ||||
−0.363412 | + | 0.931629i | \(0.618388\pi\) | |||||||
\(128\) | 15.0176 | 1.32738 | ||||||||
\(129\) | 6.00833 | 0.529004 | ||||||||
\(130\) | 5.17757 | 0.454103 | ||||||||
\(131\) | −15.5734 | −1.36066 | −0.680329 | − | 0.732907i | \(-0.738163\pi\) | ||||
−0.680329 | + | 0.732907i | \(0.738163\pi\) | |||||||
\(132\) | −9.57125 | −0.833070 | ||||||||
\(133\) | −0.664102 | −0.0575850 | ||||||||
\(134\) | −8.13602 | −0.702845 | ||||||||
\(135\) | 4.09148 | 0.352139 | ||||||||
\(136\) | 29.4160 | 2.52240 | ||||||||
\(137\) | −1.56824 | −0.133984 | −0.0669918 | − | 0.997754i | \(-0.521340\pi\) | ||||
−0.0669918 | + | 0.997754i | \(0.521340\pi\) | |||||||
\(138\) | 10.5348 | 0.896778 | ||||||||
\(139\) | −19.0766 | −1.61806 | −0.809029 | − | 0.587768i | \(-0.800007\pi\) | ||||
−0.809029 | + | 0.587768i | \(0.800007\pi\) | |||||||
\(140\) | −17.3140 | −1.46330 | ||||||||
\(141\) | 1.85234 | 0.155995 | ||||||||
\(142\) | 4.27498 | 0.358749 | ||||||||
\(143\) | −6.03500 | −0.504672 | ||||||||
\(144\) | −14.8582 | −1.23819 | ||||||||
\(145\) | −5.25849 | −0.436693 | ||||||||
\(146\) | 30.8072 | 2.54962 | ||||||||
\(147\) | 6.75417 | 0.557074 | ||||||||
\(148\) | −31.9667 | −2.62764 | ||||||||
\(149\) | −11.0172 | −0.902563 | −0.451282 | − | 0.892382i | \(-0.649033\pi\) | ||||
−0.451282 | + | 0.892382i | \(0.649033\pi\) | |||||||
\(150\) | −1.89518 | −0.154741 | ||||||||
\(151\) | −10.0933 | −0.821378 | −0.410689 | − | 0.911776i | \(-0.634712\pi\) | ||||
−0.410689 | + | 0.911776i | \(0.634712\pi\) | |||||||
\(152\) | 0.975602 | 0.0791318 | ||||||||
\(153\) | 12.1906 | 0.985555 | ||||||||
\(154\) | 29.4969 | 2.37693 | ||||||||
\(155\) | −0.0944094 | −0.00758315 | ||||||||
\(156\) | 6.71350 | 0.537510 | ||||||||
\(157\) | 11.2029 | 0.894089 | 0.447045 | − | 0.894512i | \(-0.352476\pi\) | ||||
0.447045 | + | 0.894512i | \(0.352476\pi\) | |||||||
\(158\) | −12.3099 | −0.979322 | ||||||||
\(159\) | 6.21832 | 0.493145 | ||||||||
\(160\) | 3.62836 | 0.286847 | ||||||||
\(161\) | −22.2129 | −1.75062 | ||||||||
\(162\) | −10.6126 | −0.833804 | ||||||||
\(163\) | −1.41195 | −0.110592 | −0.0552961 | − | 0.998470i | \(-0.517610\pi\) | ||||
−0.0552961 | + | 0.998470i | \(0.517610\pi\) | |||||||
\(164\) | 17.5734 | 1.37225 | ||||||||
\(165\) | 2.20904 | 0.171973 | ||||||||
\(166\) | −20.6805 | −1.60512 | ||||||||
\(167\) | 2.91798 | 0.225800 | 0.112900 | − | 0.993606i | \(-0.463986\pi\) | ||||
0.112900 | + | 0.993606i | \(0.463986\pi\) | |||||||
\(168\) | −17.6667 | −1.36301 | ||||||||
\(169\) | −8.76691 | −0.674378 | ||||||||
\(170\) | −12.6099 | −0.967133 | ||||||||
\(171\) | 0.404312 | 0.0309185 | ||||||||
\(172\) | 34.5673 | 2.63573 | ||||||||
\(173\) | −7.50937 | −0.570927 | −0.285464 | − | 0.958390i | \(-0.592148\pi\) | ||||
−0.285464 | + | 0.958390i | \(0.592148\pi\) | |||||||
\(174\) | −9.96579 | −0.755505 | ||||||||
\(175\) | 3.99606 | 0.302073 | ||||||||
\(176\) | −17.9144 | −1.35035 | ||||||||
\(177\) | 3.72017 | 0.279625 | ||||||||
\(178\) | 23.8186 | 1.78528 | ||||||||
\(179\) | −20.7665 | −1.55216 | −0.776080 | − | 0.630634i | \(-0.782795\pi\) | ||||
−0.776080 | + | 0.630634i | \(0.782795\pi\) | |||||||
\(180\) | 10.5409 | 0.785674 | ||||||||
\(181\) | 8.69763 | 0.646490 | 0.323245 | − | 0.946315i | \(-0.395226\pi\) | ||||
0.323245 | + | 0.946315i | \(0.395226\pi\) | |||||||
\(182\) | −20.6898 | −1.53363 | ||||||||
\(183\) | 5.55778 | 0.410843 | ||||||||
\(184\) | 32.6319 | 2.40566 | ||||||||
\(185\) | 7.37787 | 0.542432 | ||||||||
\(186\) | −0.178923 | −0.0131193 | ||||||||
\(187\) | 14.6981 | 1.07483 | ||||||||
\(188\) | 10.6569 | 0.777236 | ||||||||
\(189\) | −16.3498 | −1.18927 | ||||||||
\(190\) | −0.418216 | −0.0303406 | ||||||||
\(191\) | −0.397811 | −0.0287846 | −0.0143923 | − | 0.999896i | \(-0.504581\pi\) | ||||
−0.0143923 | + | 0.999896i | \(0.504581\pi\) | |||||||
\(192\) | −2.32255 | −0.167616 | ||||||||
\(193\) | −23.6175 | −1.70002 | −0.850012 | − | 0.526763i | \(-0.823405\pi\) | ||||
−0.850012 | + | 0.526763i | \(0.823405\pi\) | |||||||
\(194\) | −46.3090 | −3.32480 | ||||||||
\(195\) | −1.54947 | −0.110960 | ||||||||
\(196\) | 38.8583 | 2.77559 | ||||||||
\(197\) | −16.3979 | −1.16831 | −0.584153 | − | 0.811644i | \(-0.698573\pi\) | ||||
−0.584153 | + | 0.811644i | \(0.698573\pi\) | |||||||
\(198\) | −17.9580 | −1.27622 | ||||||||
\(199\) | −2.20919 | −0.156605 | −0.0783027 | − | 0.996930i | \(-0.524950\pi\) | ||||
−0.0783027 | + | 0.996930i | \(0.524950\pi\) | |||||||
\(200\) | −5.87042 | −0.415101 | ||||||||
\(201\) | 2.43483 | 0.171740 | ||||||||
\(202\) | −18.9357 | −1.33231 | ||||||||
\(203\) | 21.0132 | 1.47484 | ||||||||
\(204\) | −16.3506 | −1.14477 | ||||||||
\(205\) | −4.05592 | −0.283278 | ||||||||
\(206\) | 3.78232 | 0.263527 | ||||||||
\(207\) | 13.5234 | 0.939942 | ||||||||
\(208\) | 12.5656 | 0.871268 | ||||||||
\(209\) | 0.487475 | 0.0337193 | ||||||||
\(210\) | 7.57325 | 0.522604 | ||||||||
\(211\) | −21.4320 | −1.47544 | −0.737720 | − | 0.675107i | \(-0.764097\pi\) | ||||
−0.737720 | + | 0.675107i | \(0.764097\pi\) | |||||||
\(212\) | 35.7754 | 2.45707 | ||||||||
\(213\) | −1.27936 | −0.0876601 | ||||||||
\(214\) | 12.7555 | 0.871949 | ||||||||
\(215\) | −7.97811 | −0.544102 | ||||||||
\(216\) | 24.0187 | 1.63427 | ||||||||
\(217\) | 0.377265 | 0.0256104 | ||||||||
\(218\) | −27.3984 | −1.85566 | ||||||||
\(219\) | −9.21954 | −0.622999 | ||||||||
\(220\) | 12.7091 | 0.856847 | ||||||||
\(221\) | −10.3096 | −0.693500 | ||||||||
\(222\) | 13.9824 | 0.938438 | ||||||||
\(223\) | 22.0336 | 1.47548 | 0.737739 | − | 0.675086i | \(-0.235894\pi\) | ||||
0.737739 | + | 0.675086i | \(0.235894\pi\) | |||||||
\(224\) | −14.4991 | −0.968763 | ||||||||
\(225\) | −2.43284 | −0.162189 | ||||||||
\(226\) | 7.33900 | 0.488183 | ||||||||
\(227\) | −13.2707 | −0.880810 | −0.440405 | − | 0.897799i | \(-0.645165\pi\) | ||||
−0.440405 | + | 0.897799i | \(0.645165\pi\) | |||||||
\(228\) | −0.542280 | −0.0359134 | ||||||||
\(229\) | −18.6307 | −1.23115 | −0.615576 | − | 0.788078i | \(-0.711077\pi\) | ||||
−0.615576 | + | 0.788078i | \(0.711077\pi\) | |||||||
\(230\) | −13.9885 | −0.922373 | ||||||||
\(231\) | −8.82743 | −0.580802 | ||||||||
\(232\) | −30.8695 | −2.02668 | ||||||||
\(233\) | 12.4126 | 0.813174 | 0.406587 | − | 0.913612i | \(-0.366719\pi\) | ||||
0.406587 | + | 0.913612i | \(0.366719\pi\) | |||||||
\(234\) | 12.5962 | 0.823438 | ||||||||
\(235\) | −2.45961 | −0.160447 | ||||||||
\(236\) | 21.4030 | 1.39322 | ||||||||
\(237\) | 3.68393 | 0.239297 | ||||||||
\(238\) | 50.3898 | 3.26628 | ||||||||
\(239\) | −15.6207 | −1.01042 | −0.505210 | − | 0.862997i | \(-0.668585\pi\) | ||||
−0.505210 | + | 0.862997i | \(0.668585\pi\) | |||||||
\(240\) | −4.59948 | −0.296895 | ||||||||
\(241\) | 12.3797 | 0.797449 | 0.398724 | − | 0.917071i | \(-0.369453\pi\) | ||||
0.398724 | + | 0.917071i | \(0.369453\pi\) | |||||||
\(242\) | 6.02969 | 0.387603 | ||||||||
\(243\) | 15.4504 | 0.991146 | ||||||||
\(244\) | 31.9752 | 2.04700 | ||||||||
\(245\) | −8.96846 | −0.572974 | ||||||||
\(246\) | −7.68671 | −0.490087 | ||||||||
\(247\) | −0.341926 | −0.0217562 | ||||||||
\(248\) | −0.554223 | −0.0351932 | ||||||||
\(249\) | 6.18896 | 0.392209 | ||||||||
\(250\) | 2.51650 | 0.159157 | ||||||||
\(251\) | −4.49831 | −0.283930 | −0.141965 | − | 0.989872i | \(-0.545342\pi\) | ||||
−0.141965 | + | 0.989872i | \(0.545342\pi\) | |||||||
\(252\) | −42.1221 | −2.65344 | ||||||||
\(253\) | 16.3051 | 1.02509 | ||||||||
\(254\) | 20.6124 | 1.29334 | ||||||||
\(255\) | 3.77370 | 0.236319 | ||||||||
\(256\) | −31.6237 | −1.97648 | ||||||||
\(257\) | −23.6484 | −1.47515 | −0.737573 | − | 0.675267i | \(-0.764028\pi\) | ||||
−0.737573 | + | 0.675267i | \(0.764028\pi\) | |||||||
\(258\) | −15.1200 | −0.941328 | ||||||||
\(259\) | −29.4824 | −1.83195 | ||||||||
\(260\) | −8.91445 | −0.552851 | ||||||||
\(261\) | −12.7930 | −0.791869 | ||||||||
\(262\) | 39.1906 | 2.42120 | ||||||||
\(263\) | −29.8265 | −1.83918 | −0.919591 | − | 0.392877i | \(-0.871480\pi\) | ||||
−0.919591 | + | 0.392877i | \(0.871480\pi\) | |||||||
\(264\) | 12.9680 | 0.798123 | ||||||||
\(265\) | −8.25694 | −0.507220 | ||||||||
\(266\) | 1.67121 | 0.102469 | ||||||||
\(267\) | −7.12809 | −0.436232 | ||||||||
\(268\) | 14.0082 | 0.855685 | ||||||||
\(269\) | 10.8485 | 0.661447 | 0.330724 | − | 0.943728i | \(-0.392707\pi\) | ||||
0.330724 | + | 0.943728i | \(0.392707\pi\) | |||||||
\(270\) | −10.2962 | −0.626608 | ||||||||
\(271\) | −19.2702 | −1.17058 | −0.585291 | − | 0.810823i | \(-0.699020\pi\) | ||||
−0.585291 | + | 0.810823i | \(0.699020\pi\) | |||||||
\(272\) | −30.6033 | −1.85560 | ||||||||
\(273\) | 6.19176 | 0.374743 | ||||||||
\(274\) | 3.94647 | 0.238415 | ||||||||
\(275\) | −2.93325 | −0.176881 | ||||||||
\(276\) | −18.1382 | −1.09179 | ||||||||
\(277\) | −10.9023 | −0.655058 | −0.327529 | − | 0.944841i | \(-0.606216\pi\) | ||||
−0.327529 | + | 0.944841i | \(0.606216\pi\) | |||||||
\(278\) | 48.0063 | 2.87923 | ||||||||
\(279\) | −0.229683 | −0.0137507 | ||||||||
\(280\) | 23.4585 | 1.40192 | ||||||||
\(281\) | −17.7515 | −1.05896 | −0.529482 | − | 0.848321i | \(-0.677614\pi\) | ||||
−0.529482 | + | 0.848321i | \(0.677614\pi\) | |||||||
\(282\) | −4.66141 | −0.277583 | ||||||||
\(283\) | 8.34685 | 0.496169 | 0.248085 | − | 0.968738i | \(-0.420199\pi\) | ||||
0.248085 | + | 0.968738i | \(0.420199\pi\) | |||||||
\(284\) | −7.36044 | −0.436761 | ||||||||
\(285\) | 0.125158 | 0.00741370 | ||||||||
\(286\) | 15.1871 | 0.898031 | ||||||||
\(287\) | 16.2077 | 0.956709 | ||||||||
\(288\) | 8.82720 | 0.520148 | ||||||||
\(289\) | 8.10889 | 0.476994 | ||||||||
\(290\) | 13.2330 | 0.777067 | ||||||||
\(291\) | 13.8587 | 0.812412 | ||||||||
\(292\) | −53.0422 | −3.10406 | ||||||||
\(293\) | 3.98033 | 0.232533 | 0.116267 | − | 0.993218i | \(-0.462907\pi\) | ||||
0.116267 | + | 0.993218i | \(0.462907\pi\) | |||||||
\(294\) | −16.9969 | −0.991277 | ||||||||
\(295\) | −4.93979 | −0.287606 | ||||||||
\(296\) | 43.3112 | 2.51741 | ||||||||
\(297\) | 12.0013 | 0.696388 | ||||||||
\(298\) | 27.7248 | 1.60605 | ||||||||
\(299\) | −11.4367 | −0.661404 | ||||||||
\(300\) | 3.26302 | 0.188391 | ||||||||
\(301\) | 31.8810 | 1.83759 | ||||||||
\(302\) | 25.3997 | 1.46159 | ||||||||
\(303\) | 5.66682 | 0.325550 | ||||||||
\(304\) | −1.01498 | −0.0582132 | ||||||||
\(305\) | −7.37984 | −0.422568 | ||||||||
\(306\) | −30.6778 | −1.75373 | ||||||||
\(307\) | −12.1070 | −0.690982 | −0.345491 | − | 0.938422i | \(-0.612288\pi\) | ||||
−0.345491 | + | 0.938422i | \(0.612288\pi\) | |||||||
\(308\) | −50.7862 | −2.89381 | ||||||||
\(309\) | −1.13192 | −0.0643926 | ||||||||
\(310\) | 0.237581 | 0.0134937 | ||||||||
\(311\) | −3.74541 | −0.212383 | −0.106191 | − | 0.994346i | \(-0.533866\pi\) | ||||
−0.106191 | + | 0.994346i | \(0.533866\pi\) | |||||||
\(312\) | −9.09604 | −0.514962 | ||||||||
\(313\) | −1.79610 | −0.101521 | −0.0507607 | − | 0.998711i | \(-0.516165\pi\) | ||||
−0.0507607 | + | 0.998711i | \(0.516165\pi\) | |||||||
\(314\) | −28.1921 | −1.59097 | ||||||||
\(315\) | 9.72175 | 0.547759 | ||||||||
\(316\) | 21.1945 | 1.19228 | ||||||||
\(317\) | −1.74388 | −0.0979463 | −0.0489732 | − | 0.998800i | \(-0.515595\pi\) | ||||
−0.0489732 | + | 0.998800i | \(0.515595\pi\) | |||||||
\(318\) | −15.6484 | −0.877519 | ||||||||
\(319\) | −15.4244 | −0.863603 | ||||||||
\(320\) | 3.08398 | 0.172400 | ||||||||
\(321\) | −3.81729 | −0.213060 | ||||||||
\(322\) | 55.8987 | 3.11511 | ||||||||
\(323\) | 0.832755 | 0.0463357 | ||||||||
\(324\) | 18.2722 | 1.01512 | ||||||||
\(325\) | 2.05745 | 0.114127 | ||||||||
\(326\) | 3.55316 | 0.196792 | ||||||||
\(327\) | 8.19942 | 0.453429 | ||||||||
\(328\) | −23.8100 | −1.31468 | ||||||||
\(329\) | 9.82874 | 0.541876 | ||||||||
\(330\) | −5.55904 | −0.306015 | ||||||||
\(331\) | 5.32362 | 0.292613 | 0.146306 | − | 0.989239i | \(-0.453261\pi\) | ||||
0.146306 | + | 0.989239i | \(0.453261\pi\) | |||||||
\(332\) | 35.6065 | 1.95416 | ||||||||
\(333\) | 17.9492 | 0.983608 | ||||||||
\(334\) | −7.34309 | −0.401796 | ||||||||
\(335\) | −3.23307 | −0.176642 | ||||||||
\(336\) | 18.3798 | 1.00270 | ||||||||
\(337\) | 1.73739 | 0.0946417 | 0.0473208 | − | 0.998880i | \(-0.484932\pi\) | ||||
0.0473208 | + | 0.998880i | \(0.484932\pi\) | |||||||
\(338\) | 22.0619 | 1.20001 | ||||||||
\(339\) | −2.19631 | −0.119287 | ||||||||
\(340\) | 21.7110 | 1.17744 | ||||||||
\(341\) | −0.276926 | −0.0149964 | ||||||||
\(342\) | −1.01745 | −0.0550174 | ||||||||
\(343\) | 7.86607 | 0.424728 | ||||||||
\(344\) | −46.8349 | −2.52517 | ||||||||
\(345\) | 4.18627 | 0.225381 | ||||||||
\(346\) | 18.8973 | 1.01593 | ||||||||
\(347\) | 17.4519 | 0.936869 | 0.468435 | − | 0.883498i | \(-0.344818\pi\) | ||||
0.468435 | + | 0.883498i | \(0.344818\pi\) | |||||||
\(348\) | 17.1586 | 0.919795 | ||||||||
\(349\) | −22.4777 | −1.20320 | −0.601601 | − | 0.798797i | \(-0.705470\pi\) | ||||
−0.601601 | + | 0.798797i | \(0.705470\pi\) | |||||||
\(350\) | −10.0561 | −0.537520 | ||||||||
\(351\) | −8.41801 | −0.449320 | ||||||||
\(352\) | 10.6429 | 0.567267 | ||||||||
\(353\) | 18.8829 | 1.00504 | 0.502518 | − | 0.864567i | \(-0.332407\pi\) | ||||
0.502518 | + | 0.864567i | \(0.332407\pi\) | |||||||
\(354\) | −9.36181 | −0.497575 | ||||||||
\(355\) | 1.69878 | 0.0901620 | ||||||||
\(356\) | −41.0096 | −2.17350 | ||||||||
\(357\) | −15.0799 | −0.798115 | ||||||||
\(358\) | 52.2589 | 2.76197 | ||||||||
\(359\) | −4.32684 | −0.228362 | −0.114181 | − | 0.993460i | \(-0.536424\pi\) | ||||
−0.114181 | + | 0.993460i | \(0.536424\pi\) | |||||||
\(360\) | −14.2818 | −0.752716 | ||||||||
\(361\) | −18.9724 | −0.998546 | ||||||||
\(362\) | −21.8876 | −1.15039 | ||||||||
\(363\) | −1.80448 | −0.0947106 | ||||||||
\(364\) | 35.6227 | 1.86713 | ||||||||
\(365\) | 12.2421 | 0.640780 | ||||||||
\(366\) | −13.9861 | −0.731067 | ||||||||
\(367\) | −14.6523 | −0.764844 | −0.382422 | − | 0.923988i | \(-0.624910\pi\) | ||||
−0.382422 | + | 0.923988i | \(0.624910\pi\) | |||||||
\(368\) | −33.9491 | −1.76972 | ||||||||
\(369\) | −9.86739 | −0.513676 | ||||||||
\(370\) | −18.5664 | −0.965222 | ||||||||
\(371\) | 32.9952 | 1.71302 | ||||||||
\(372\) | 0.308060 | 0.0159722 | ||||||||
\(373\) | −1.20013 | −0.0621403 | −0.0310701 | − | 0.999517i | \(-0.509892\pi\) | ||||
−0.0310701 | + | 0.999517i | \(0.509892\pi\) | |||||||
\(374\) | −36.9879 | −1.91260 | ||||||||
\(375\) | −0.753102 | −0.0388900 | ||||||||
\(376\) | −14.4389 | −0.744632 | ||||||||
\(377\) | 10.8191 | 0.557210 | ||||||||
\(378\) | 41.1443 | 2.11623 | ||||||||
\(379\) | 20.8052 | 1.06869 | 0.534346 | − | 0.845266i | \(-0.320558\pi\) | ||||
0.534346 | + | 0.845266i | \(0.320558\pi\) | |||||||
\(380\) | 0.720061 | 0.0369384 | ||||||||
\(381\) | −6.16858 | −0.316026 | ||||||||
\(382\) | 1.00109 | 0.0512202 | ||||||||
\(383\) | −6.69396 | −0.342045 | −0.171023 | − | 0.985267i | \(-0.554707\pi\) | ||||
−0.171023 | + | 0.985267i | \(0.554707\pi\) | |||||||
\(384\) | 11.3098 | 0.577149 | ||||||||
\(385\) | 11.7214 | 0.597379 | ||||||||
\(386\) | 59.4334 | 3.02508 | ||||||||
\(387\) | −19.4094 | −0.986637 | ||||||||
\(388\) | 79.7324 | 4.04780 | ||||||||
\(389\) | 33.4831 | 1.69766 | 0.848830 | − | 0.528666i | \(-0.177308\pi\) | ||||
0.848830 | + | 0.528666i | \(0.177308\pi\) | |||||||
\(390\) | 3.89924 | 0.197446 | ||||||||
\(391\) | 27.8540 | 1.40864 | ||||||||
\(392\) | −52.6486 | −2.65916 | ||||||||
\(393\) | −11.7284 | −0.591619 | ||||||||
\(394\) | 41.2654 | 2.07892 | ||||||||
\(395\) | −4.89167 | −0.246127 | ||||||||
\(396\) | 30.9191 | 1.55375 | ||||||||
\(397\) | −21.2884 | −1.06843 | −0.534216 | − | 0.845348i | \(-0.679393\pi\) | ||||
−0.534216 | + | 0.845348i | \(0.679393\pi\) | |||||||
\(398\) | 5.55943 | 0.278669 | ||||||||
\(399\) | −0.500137 | −0.0250382 | ||||||||
\(400\) | 6.10737 | 0.305369 | ||||||||
\(401\) | −24.0840 | −1.20270 | −0.601350 | − | 0.798986i | \(-0.705370\pi\) | ||||
−0.601350 | + | 0.798986i | \(0.705370\pi\) | |||||||
\(402\) | −6.12726 | −0.305600 | ||||||||
\(403\) | 0.194242 | 0.00967591 | ||||||||
\(404\) | 32.6025 | 1.62204 | ||||||||
\(405\) | −4.21720 | −0.209555 | ||||||||
\(406\) | −52.8797 | −2.62438 | ||||||||
\(407\) | 21.6411 | 1.07271 | ||||||||
\(408\) | 22.1532 | 1.09675 | ||||||||
\(409\) | −22.8579 | −1.13025 | −0.565126 | − | 0.825005i | \(-0.691172\pi\) | ||||
−0.565126 | + | 0.825005i | \(0.691172\pi\) | |||||||
\(410\) | 10.2067 | 0.504074 | ||||||||
\(411\) | −1.18104 | −0.0582566 | ||||||||
\(412\) | −6.51219 | −0.320832 | ||||||||
\(413\) | 19.7397 | 0.971327 | ||||||||
\(414\) | −34.0317 | −1.67257 | ||||||||
\(415\) | −8.21795 | −0.403403 | ||||||||
\(416\) | −7.46516 | −0.366009 | ||||||||
\(417\) | −14.3667 | −0.703538 | ||||||||
\(418\) | −1.22673 | −0.0600014 | ||||||||
\(419\) | 7.91441 | 0.386644 | 0.193322 | − | 0.981135i | \(-0.438074\pi\) | ||||
0.193322 | + | 0.981135i | \(0.438074\pi\) | |||||||
\(420\) | −13.0392 | −0.636249 | ||||||||
\(421\) | −28.7996 | −1.40361 | −0.701804 | − | 0.712370i | \(-0.747622\pi\) | ||||
−0.701804 | + | 0.712370i | \(0.747622\pi\) | |||||||
\(422\) | 53.9336 | 2.62545 | ||||||||
\(423\) | −5.98383 | −0.290944 | ||||||||
\(424\) | −48.4717 | −2.35399 | ||||||||
\(425\) | −5.01088 | −0.243063 | ||||||||
\(426\) | 3.21950 | 0.155985 | ||||||||
\(427\) | 29.4903 | 1.42713 | ||||||||
\(428\) | −21.9618 | −1.06156 | ||||||||
\(429\) | −4.54498 | −0.219434 | ||||||||
\(430\) | 20.0769 | 0.968194 | ||||||||
\(431\) | −7.13540 | −0.343700 | −0.171850 | − | 0.985123i | \(-0.554974\pi\) | ||||
−0.171850 | + | 0.985123i | \(0.554974\pi\) | |||||||
\(432\) | −24.9882 | −1.20225 | ||||||||
\(433\) | 25.3279 | 1.21718 | 0.608589 | − | 0.793485i | \(-0.291736\pi\) | ||||
0.608589 | + | 0.793485i | \(0.291736\pi\) | |||||||
\(434\) | −0.949388 | −0.0455721 | ||||||||
\(435\) | −3.96018 | −0.189876 | ||||||||
\(436\) | 47.1731 | 2.25918 | ||||||||
\(437\) | 0.923798 | 0.0441913 | ||||||||
\(438\) | 23.2010 | 1.10859 | ||||||||
\(439\) | −12.0492 | −0.575075 | −0.287538 | − | 0.957769i | \(-0.592837\pi\) | ||||
−0.287538 | + | 0.957769i | \(0.592837\pi\) | |||||||
\(440\) | −17.2194 | −0.820903 | ||||||||
\(441\) | −21.8188 | −1.03899 | ||||||||
\(442\) | 25.9442 | 1.23404 | ||||||||
\(443\) | 4.96577 | 0.235931 | 0.117965 | − | 0.993018i | \(-0.462363\pi\) | ||||
0.117965 | + | 0.993018i | \(0.462363\pi\) | |||||||
\(444\) | −24.0742 | −1.14251 | ||||||||
\(445\) | 9.46497 | 0.448683 | ||||||||
\(446\) | −55.4475 | −2.62552 | ||||||||
\(447\) | −8.29707 | −0.392438 | ||||||||
\(448\) | −12.3238 | −0.582243 | ||||||||
\(449\) | 16.4040 | 0.774155 | 0.387077 | − | 0.922047i | \(-0.373485\pi\) | ||||
0.387077 | + | 0.922047i | \(0.373485\pi\) | |||||||
\(450\) | 6.12223 | 0.288605 | ||||||||
\(451\) | −11.8970 | −0.560209 | ||||||||
\(452\) | −12.6359 | −0.594342 | ||||||||
\(453\) | −7.60126 | −0.357138 | ||||||||
\(454\) | 33.3958 | 1.56734 | ||||||||
\(455\) | −8.22168 | −0.385438 | ||||||||
\(456\) | 0.734729 | 0.0344068 | ||||||||
\(457\) | 31.5273 | 1.47479 | 0.737393 | − | 0.675464i | \(-0.236056\pi\) | ||||
0.737393 | + | 0.675464i | \(0.236056\pi\) | |||||||
\(458\) | 46.8842 | 2.19075 | ||||||||
\(459\) | 20.5019 | 0.956948 | ||||||||
\(460\) | 24.0846 | 1.12295 | ||||||||
\(461\) | 2.39850 | 0.111709 | 0.0558547 | − | 0.998439i | \(-0.482212\pi\) | ||||
0.0558547 | + | 0.998439i | \(0.482212\pi\) | |||||||
\(462\) | 22.2142 | 1.03350 | ||||||||
\(463\) | −21.0691 | −0.979165 | −0.489582 | − | 0.871957i | \(-0.662851\pi\) | ||||
−0.489582 | + | 0.871957i | \(0.662851\pi\) | |||||||
\(464\) | 32.1155 | 1.49093 | ||||||||
\(465\) | −0.0711000 | −0.00329718 | ||||||||
\(466\) | −31.2362 | −1.44699 | ||||||||
\(467\) | 19.1836 | 0.887709 | 0.443855 | − | 0.896099i | \(-0.353611\pi\) | ||||
0.443855 | + | 0.896099i | \(0.353611\pi\) | |||||||
\(468\) | −21.6874 | −1.00250 | ||||||||
\(469\) | 12.9195 | 0.596568 | ||||||||
\(470\) | 6.18961 | 0.285505 | ||||||||
\(471\) | 8.43694 | 0.388754 | ||||||||
\(472\) | −28.9987 | −1.33477 | ||||||||
\(473\) | −23.4018 | −1.07601 | ||||||||
\(474\) | −9.27060 | −0.425813 | ||||||||
\(475\) | −0.166190 | −0.00762530 | ||||||||
\(476\) | −86.7583 | −3.97656 | ||||||||
\(477\) | −20.0878 | −0.919756 | ||||||||
\(478\) | 39.3095 | 1.79798 | ||||||||
\(479\) | 3.48238 | 0.159114 | 0.0795569 | − | 0.996830i | \(-0.474649\pi\) | ||||
0.0795569 | + | 0.996830i | \(0.474649\pi\) | |||||||
\(480\) | 2.73252 | 0.124722 | ||||||||
\(481\) | −15.1796 | −0.692130 | ||||||||
\(482\) | −31.1536 | −1.41901 | ||||||||
\(483\) | −16.7286 | −0.761177 | ||||||||
\(484\) | −10.3816 | −0.471890 | ||||||||
\(485\) | −18.4022 | −0.835599 | ||||||||
\(486\) | −38.8810 | −1.76368 | ||||||||
\(487\) | 9.07055 | 0.411026 | 0.205513 | − | 0.978654i | \(-0.434114\pi\) | ||||
0.205513 | + | 0.978654i | \(0.434114\pi\) | |||||||
\(488\) | −43.3228 | −1.96113 | ||||||||
\(489\) | −1.06334 | −0.0480859 | ||||||||
\(490\) | 22.5691 | 1.01957 | ||||||||
\(491\) | −26.6063 | −1.20073 | −0.600364 | − | 0.799727i | \(-0.704977\pi\) | ||||
−0.600364 | + | 0.799727i | \(0.704977\pi\) | |||||||
\(492\) | 13.2346 | 0.596660 | ||||||||
\(493\) | −26.3496 | −1.18673 | ||||||||
\(494\) | 0.860457 | 0.0387138 | ||||||||
\(495\) | −7.13611 | −0.320744 | ||||||||
\(496\) | 0.576593 | 0.0258898 | ||||||||
\(497\) | −6.78843 | −0.304503 | ||||||||
\(498\) | −15.5745 | −0.697911 | ||||||||
\(499\) | −25.3493 | −1.13479 | −0.567396 | − | 0.823445i | \(-0.692049\pi\) | ||||
−0.567396 | + | 0.823445i | \(0.692049\pi\) | |||||||
\(500\) | −4.33277 | −0.193767 | ||||||||
\(501\) | 2.19753 | 0.0981786 | ||||||||
\(502\) | 11.3200 | 0.505236 | ||||||||
\(503\) | −14.6855 | −0.654794 | −0.327397 | − | 0.944887i | \(-0.606172\pi\) | ||||
−0.327397 | + | 0.944887i | \(0.606172\pi\) | |||||||
\(504\) | 57.0708 | 2.54213 | ||||||||
\(505\) | −7.52463 | −0.334842 | ||||||||
\(506\) | −41.0317 | −1.82408 | ||||||||
\(507\) | −6.60238 | −0.293222 | ||||||||
\(508\) | −35.4893 | −1.57458 | ||||||||
\(509\) | 5.78678 | 0.256495 | 0.128247 | − | 0.991742i | \(-0.459065\pi\) | ||||
0.128247 | + | 0.991742i | \(0.459065\pi\) | |||||||
\(510\) | −9.49653 | −0.420513 | ||||||||
\(511\) | −48.9200 | −2.16410 | ||||||||
\(512\) | 49.5460 | 2.18964 | ||||||||
\(513\) | 0.679961 | 0.0300210 | ||||||||
\(514\) | 59.5112 | 2.62493 | ||||||||
\(515\) | 1.50301 | 0.0662304 | ||||||||
\(516\) | 26.0327 | 1.14603 | ||||||||
\(517\) | −7.21464 | −0.317300 | ||||||||
\(518\) | 74.1925 | 3.25983 | ||||||||
\(519\) | −5.65533 | −0.248241 | ||||||||
\(520\) | 12.0781 | 0.529659 | ||||||||
\(521\) | −39.6468 | −1.73696 | −0.868478 | − | 0.495727i | \(-0.834902\pi\) | ||||
−0.868478 | + | 0.495727i | \(0.834902\pi\) | |||||||
\(522\) | 32.1937 | 1.40908 | ||||||||
\(523\) | 16.3443 | 0.714686 | 0.357343 | − | 0.933973i | \(-0.383683\pi\) | ||||
0.357343 | + | 0.933973i | \(0.383683\pi\) | |||||||
\(524\) | −67.4762 | −2.94771 | ||||||||
\(525\) | 3.00944 | 0.131343 | ||||||||
\(526\) | 75.0584 | 3.27270 | ||||||||
\(527\) | −0.473074 | −0.0206074 | ||||||||
\(528\) | −13.4914 | −0.587138 | ||||||||
\(529\) | 7.89918 | 0.343443 | ||||||||
\(530\) | 20.7786 | 0.902564 | ||||||||
\(531\) | −12.0177 | −0.521524 | ||||||||
\(532\) | −2.87740 | −0.124751 | ||||||||
\(533\) | 8.34484 | 0.361455 | ||||||||
\(534\) | 17.9378 | 0.776247 | ||||||||
\(535\) | 5.06875 | 0.219141 | ||||||||
\(536\) | −18.9795 | −0.819789 | ||||||||
\(537\) | −15.6393 | −0.674886 | ||||||||
\(538\) | −27.3003 | −1.17700 | ||||||||
\(539\) | −26.3067 | −1.13311 | ||||||||
\(540\) | 17.7275 | 0.762869 | ||||||||
\(541\) | 28.8949 | 1.24229 | 0.621144 | − | 0.783696i | \(-0.286668\pi\) | ||||
0.621144 | + | 0.783696i | \(0.286668\pi\) | |||||||
\(542\) | 48.4935 | 2.08298 | ||||||||
\(543\) | 6.55021 | 0.281096 | ||||||||
\(544\) | 18.1813 | 0.779515 | ||||||||
\(545\) | −10.8875 | −0.466370 | ||||||||
\(546\) | −15.5816 | −0.666830 | ||||||||
\(547\) | 34.4502 | 1.47299 | 0.736493 | − | 0.676445i | \(-0.236480\pi\) | ||||
0.736493 | + | 0.676445i | \(0.236480\pi\) | |||||||
\(548\) | −6.79482 | −0.290260 | ||||||||
\(549\) | −17.9539 | −0.766256 | ||||||||
\(550\) | 7.38152 | 0.314749 | ||||||||
\(551\) | −0.873905 | −0.0372296 | ||||||||
\(552\) | 24.5752 | 1.04599 | ||||||||
\(553\) | 19.5474 | 0.831239 | ||||||||
\(554\) | 27.4357 | 1.16563 | ||||||||
\(555\) | 5.55630 | 0.235852 | ||||||||
\(556\) | −82.6547 | −3.50534 | ||||||||
\(557\) | −37.2548 | −1.57854 | −0.789268 | − | 0.614048i | \(-0.789540\pi\) | ||||
−0.789268 | + | 0.614048i | \(0.789540\pi\) | |||||||
\(558\) | 0.577997 | 0.0244685 | ||||||||
\(559\) | 16.4145 | 0.694261 | ||||||||
\(560\) | −24.4054 | −1.03132 | ||||||||
\(561\) | 11.0692 | 0.467342 | ||||||||
\(562\) | 44.6716 | 1.88436 | ||||||||
\(563\) | 10.2636 | 0.432558 | 0.216279 | − | 0.976332i | \(-0.430608\pi\) | ||||
0.216279 | + | 0.976332i | \(0.430608\pi\) | |||||||
\(564\) | 8.02576 | 0.337945 | ||||||||
\(565\) | 2.91635 | 0.122692 | ||||||||
\(566\) | −21.0049 | −0.882900 | ||||||||
\(567\) | 16.8522 | 0.707725 | ||||||||
\(568\) | 9.97257 | 0.418440 | ||||||||
\(569\) | 24.6216 | 1.03219 | 0.516095 | − | 0.856532i | \(-0.327385\pi\) | ||||
0.516095 | + | 0.856532i | \(0.327385\pi\) | |||||||
\(570\) | −0.314959 | −0.0131922 | ||||||||
\(571\) | −1.75610 | −0.0734905 | −0.0367452 | − | 0.999325i | \(-0.511699\pi\) | ||||
−0.0367452 | + | 0.999325i | \(0.511699\pi\) | |||||||
\(572\) | −26.1483 | −1.09332 | ||||||||
\(573\) | −0.299592 | −0.0125156 | ||||||||
\(574\) | −40.7866 | −1.70240 | ||||||||
\(575\) | −5.55870 | −0.231814 | ||||||||
\(576\) | 7.50283 | 0.312618 | ||||||||
\(577\) | −43.3354 | −1.80407 | −0.902037 | − | 0.431658i | \(-0.857929\pi\) | ||||
−0.902037 | + | 0.431658i | \(0.857929\pi\) | |||||||
\(578\) | −20.4060 | −0.848779 | ||||||||
\(579\) | −17.7864 | −0.739177 | ||||||||
\(580\) | −22.7838 | −0.946047 | ||||||||
\(581\) | 32.8394 | 1.36241 | ||||||||
\(582\) | −34.8755 | −1.44563 | ||||||||
\(583\) | −24.2196 | −1.00307 | ||||||||
\(584\) | 71.8662 | 2.97384 | ||||||||
\(585\) | 5.00543 | 0.206949 | ||||||||
\(586\) | −10.0165 | −0.413778 | ||||||||
\(587\) | 21.2092 | 0.875397 | 0.437698 | − | 0.899122i | \(-0.355794\pi\) | ||||
0.437698 | + | 0.899122i | \(0.355794\pi\) | |||||||
\(588\) | 29.2643 | 1.20684 | ||||||||
\(589\) | −0.0156899 | −0.000646489 0 | ||||||||
\(590\) | 12.4310 | 0.511776 | ||||||||
\(591\) | −12.3493 | −0.507984 | ||||||||
\(592\) | −45.0594 | −1.85193 | ||||||||
\(593\) | 35.8639 | 1.47276 | 0.736378 | − | 0.676571i | \(-0.236535\pi\) | ||||
0.736378 | + | 0.676571i | \(0.236535\pi\) | |||||||
\(594\) | −30.2013 | −1.23918 | ||||||||
\(595\) | 20.0237 | 0.820893 | ||||||||
\(596\) | −47.7350 | −1.95530 | ||||||||
\(597\) | −1.66375 | −0.0680926 | ||||||||
\(598\) | 28.7806 | 1.17692 | ||||||||
\(599\) | 41.4774 | 1.69472 | 0.847361 | − | 0.531018i | \(-0.178190\pi\) | ||||
0.847361 | + | 0.531018i | \(0.178190\pi\) | |||||||
\(600\) | −4.42103 | −0.180488 | ||||||||
\(601\) | 19.6940 | 0.803334 | 0.401667 | − | 0.915786i | \(-0.368431\pi\) | ||||
0.401667 | + | 0.915786i | \(0.368431\pi\) | |||||||
\(602\) | −80.2284 | −3.26987 | ||||||||
\(603\) | −7.86553 | −0.320309 | ||||||||
\(604\) | −43.7318 | −1.77942 | ||||||||
\(605\) | 2.39606 | 0.0974137 | ||||||||
\(606\) | −14.2605 | −0.579295 | ||||||||
\(607\) | 1.75836 | 0.0713695 | 0.0356848 | − | 0.999363i | \(-0.488639\pi\) | ||||
0.0356848 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(608\) | 0.602995 | 0.0244547 | ||||||||
\(609\) | 15.8251 | 0.641265 | ||||||||
\(610\) | 18.5714 | 0.751933 | ||||||||
\(611\) | 5.06052 | 0.204727 | ||||||||
\(612\) | 52.8193 | 2.13509 | ||||||||
\(613\) | 16.5802 | 0.669670 | 0.334835 | − | 0.942277i | \(-0.391319\pi\) | ||||
0.334835 | + | 0.942277i | \(0.391319\pi\) | |||||||
\(614\) | 30.4672 | 1.22956 | ||||||||
\(615\) | −3.05452 | −0.123170 | ||||||||
\(616\) | 68.8097 | 2.77242 | ||||||||
\(617\) | 12.2308 | 0.492392 | 0.246196 | − | 0.969220i | \(-0.420819\pi\) | ||||
0.246196 | + | 0.969220i | \(0.420819\pi\) | |||||||
\(618\) | 2.84847 | 0.114582 | ||||||||
\(619\) | 21.0497 | 0.846061 | 0.423030 | − | 0.906115i | \(-0.360966\pi\) | ||||
0.423030 | + | 0.906115i | \(0.360966\pi\) | |||||||
\(620\) | −0.409055 | −0.0164280 | ||||||||
\(621\) | 22.7433 | 0.912659 | ||||||||
\(622\) | 9.42532 | 0.377921 | ||||||||
\(623\) | −37.8226 | −1.51533 | ||||||||
\(624\) | 9.46318 | 0.378831 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.51988 | 0.180651 | ||||||||
\(627\) | 0.367119 | 0.0146613 | ||||||||
\(628\) | 48.5396 | 1.93694 | ||||||||
\(629\) | 36.9696 | 1.47408 | ||||||||
\(630\) | −24.4648 | −0.974700 | ||||||||
\(631\) | −12.1107 | −0.482120 | −0.241060 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241060 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(632\) | −28.7162 | −1.14227 | ||||||||
\(633\) | −16.1405 | −0.641527 | ||||||||
\(634\) | 4.38849 | 0.174289 | ||||||||
\(635\) | 8.19089 | 0.325046 | ||||||||
\(636\) | 26.9426 | 1.06834 | ||||||||
\(637\) | 18.4521 | 0.731100 | ||||||||
\(638\) | 38.8156 | 1.53672 | ||||||||
\(639\) | 4.13286 | 0.163493 | ||||||||
\(640\) | −15.0176 | −0.593621 | ||||||||
\(641\) | 12.0727 | 0.476844 | 0.238422 | − | 0.971162i | \(-0.423370\pi\) | ||||
0.238422 | + | 0.971162i | \(0.423370\pi\) | |||||||
\(642\) | 9.60621 | 0.379127 | ||||||||
\(643\) | 4.59818 | 0.181335 | 0.0906674 | − | 0.995881i | \(-0.471100\pi\) | ||||
0.0906674 | + | 0.995881i | \(0.471100\pi\) | |||||||
\(644\) | −96.2434 | −3.79252 | ||||||||
\(645\) | −6.00833 | −0.236578 | ||||||||
\(646\) | −2.09563 | −0.0824514 | ||||||||
\(647\) | 22.5734 | 0.887454 | 0.443727 | − | 0.896162i | \(-0.353656\pi\) | ||||
0.443727 | + | 0.896162i | \(0.353656\pi\) | |||||||
\(648\) | −24.7568 | −0.972538 | ||||||||
\(649\) | −14.4896 | −0.568768 | ||||||||
\(650\) | −5.17757 | −0.203081 | ||||||||
\(651\) | 0.284119 | 0.0111355 | ||||||||
\(652\) | −6.11764 | −0.239585 | ||||||||
\(653\) | −26.5754 | −1.03998 | −0.519988 | − | 0.854173i | \(-0.674064\pi\) | ||||
−0.519988 | + | 0.854173i | \(0.674064\pi\) | |||||||
\(654\) | −20.6338 | −0.806847 | ||||||||
\(655\) | 15.5734 | 0.608505 | ||||||||
\(656\) | 24.7710 | 0.967145 | ||||||||
\(657\) | 29.7830 | 1.16194 | ||||||||
\(658\) | −24.7340 | −0.964232 | ||||||||
\(659\) | 45.8432 | 1.78580 | 0.892899 | − | 0.450256i | \(-0.148667\pi\) | ||||
0.892899 | + | 0.450256i | \(0.148667\pi\) | |||||||
\(660\) | 9.57125 | 0.372560 | ||||||||
\(661\) | −8.43433 | −0.328058 | −0.164029 | − | 0.986456i | \(-0.552449\pi\) | ||||
−0.164029 | + | 0.986456i | \(0.552449\pi\) | |||||||
\(662\) | −13.3969 | −0.520685 | ||||||||
\(663\) | −7.76420 | −0.301537 | ||||||||
\(664\) | −48.2428 | −1.87219 | ||||||||
\(665\) | 0.664102 | 0.0257528 | ||||||||
\(666\) | −45.1691 | −1.75027 | ||||||||
\(667\) | −29.2304 | −1.13180 | ||||||||
\(668\) | 12.6429 | 0.489169 | ||||||||
\(669\) | 16.5935 | 0.641543 | ||||||||
\(670\) | 8.13602 | 0.314322 | ||||||||
\(671\) | −21.6469 | −0.835669 | ||||||||
\(672\) | −10.9193 | −0.421222 | ||||||||
\(673\) | −3.27540 | −0.126258 | −0.0631288 | − | 0.998005i | \(-0.520108\pi\) | ||||
−0.0631288 | + | 0.998005i | \(0.520108\pi\) | |||||||
\(674\) | −4.37214 | −0.168409 | ||||||||
\(675\) | −4.09148 | −0.157481 | ||||||||
\(676\) | −37.9850 | −1.46096 | ||||||||
\(677\) | 46.5928 | 1.79071 | 0.895353 | − | 0.445356i | \(-0.146923\pi\) | ||||
0.895353 | + | 0.445356i | \(0.146923\pi\) | |||||||
\(678\) | 5.52702 | 0.212264 | ||||||||
\(679\) | 73.5361 | 2.82206 | ||||||||
\(680\) | −29.4160 | −1.12805 | ||||||||
\(681\) | −9.99423 | −0.382980 | ||||||||
\(682\) | 0.696885 | 0.0266851 | ||||||||
\(683\) | −18.1601 | −0.694879 | −0.347439 | − | 0.937702i | \(-0.612949\pi\) | ||||
−0.347439 | + | 0.937702i | \(0.612949\pi\) | |||||||
\(684\) | 1.75179 | 0.0669814 | ||||||||
\(685\) | 1.56824 | 0.0599193 | ||||||||
\(686\) | −19.7950 | −0.755776 | ||||||||
\(687\) | −14.0308 | −0.535310 | ||||||||
\(688\) | 48.7253 | 1.85763 | ||||||||
\(689\) | 16.9882 | 0.647199 | ||||||||
\(690\) | −10.5348 | −0.401051 | ||||||||
\(691\) | −39.9667 | −1.52041 | −0.760203 | − | 0.649685i | \(-0.774901\pi\) | ||||
−0.760203 | + | 0.649685i | \(0.774901\pi\) | |||||||
\(692\) | −32.5364 | −1.23685 | ||||||||
\(693\) | 28.5163 | 1.08324 | ||||||||
\(694\) | −43.9178 | −1.66710 | ||||||||
\(695\) | 19.0766 | 0.723618 | ||||||||
\(696\) | −23.2479 | −0.881210 | ||||||||
\(697\) | −20.3237 | −0.769816 | ||||||||
\(698\) | 56.5651 | 2.14102 | ||||||||
\(699\) | 9.34793 | 0.353571 | ||||||||
\(700\) | 17.3140 | 0.654408 | ||||||||
\(701\) | −40.5683 | −1.53225 | −0.766123 | − | 0.642694i | \(-0.777817\pi\) | ||||
−0.766123 | + | 0.642694i | \(0.777817\pi\) | |||||||
\(702\) | 21.1839 | 0.799536 | ||||||||
\(703\) | 1.22613 | 0.0462442 | ||||||||
\(704\) | 9.04608 | 0.340937 | ||||||||
\(705\) | −1.85234 | −0.0697631 | ||||||||
\(706\) | −47.5188 | −1.78839 | ||||||||
\(707\) | 30.0688 | 1.13086 | ||||||||
\(708\) | 16.1187 | 0.605776 | ||||||||
\(709\) | −32.3272 | −1.21407 | −0.607037 | − | 0.794674i | \(-0.707642\pi\) | ||||
−0.607037 | + | 0.794674i | \(0.707642\pi\) | |||||||
\(710\) | −4.27498 | −0.160437 | ||||||||
\(711\) | −11.9006 | −0.446309 | ||||||||
\(712\) | 55.5634 | 2.08233 | ||||||||
\(713\) | −0.524794 | −0.0196537 | ||||||||
\(714\) | 37.9486 | 1.42019 | ||||||||
\(715\) | 6.03500 | 0.225696 | ||||||||
\(716\) | −89.9765 | −3.36258 | ||||||||
\(717\) | −11.7640 | −0.439334 | ||||||||
\(718\) | 10.8885 | 0.406355 | ||||||||
\(719\) | −22.5771 | −0.841983 | −0.420992 | − | 0.907065i | \(-0.638318\pi\) | ||||
−0.420992 | + | 0.907065i | \(0.638318\pi\) | |||||||
\(720\) | 14.8582 | 0.553734 | ||||||||
\(721\) | −6.00610 | −0.223679 | ||||||||
\(722\) | 47.7440 | 1.77685 | ||||||||
\(723\) | 9.32321 | 0.346734 | ||||||||
\(724\) | 37.6849 | 1.40055 | ||||||||
\(725\) | 5.25849 | 0.195295 | ||||||||
\(726\) | 4.54097 | 0.168531 | ||||||||
\(727\) | 38.4524 | 1.42612 | 0.713059 | − | 0.701104i | \(-0.247309\pi\) | ||||
0.713059 | + | 0.701104i | \(0.247309\pi\) | |||||||
\(728\) | −48.2647 | −1.78881 | ||||||||
\(729\) | −1.01585 | −0.0376241 | ||||||||
\(730\) | −30.8072 | −1.14023 | ||||||||
\(731\) | −39.9773 | −1.47861 | ||||||||
\(732\) | 24.0806 | 0.890044 | ||||||||
\(733\) | 46.6025 | 1.72130 | 0.860652 | − | 0.509194i | \(-0.170057\pi\) | ||||
0.860652 | + | 0.509194i | \(0.170057\pi\) | |||||||
\(734\) | 36.8725 | 1.36099 | ||||||||
\(735\) | −6.75417 | −0.249131 | ||||||||
\(736\) | 20.1690 | 0.743438 | ||||||||
\(737\) | −9.48340 | −0.349325 | ||||||||
\(738\) | 24.8313 | 0.914052 | ||||||||
\(739\) | 23.0438 | 0.847681 | 0.423841 | − | 0.905737i | \(-0.360682\pi\) | ||||
0.423841 | + | 0.905737i | \(0.360682\pi\) | |||||||
\(740\) | 31.9667 | 1.17512 | ||||||||
\(741\) | −0.257506 | −0.00945970 | ||||||||
\(742\) | −83.0324 | −3.04821 | ||||||||
\(743\) | 19.3194 | 0.708760 | 0.354380 | − | 0.935102i | \(-0.384692\pi\) | ||||
0.354380 | + | 0.935102i | \(0.384692\pi\) | |||||||
\(744\) | −0.417387 | −0.0153021 | ||||||||
\(745\) | 11.0172 | 0.403638 | ||||||||
\(746\) | 3.02012 | 0.110575 | ||||||||
\(747\) | −19.9929 | −0.731503 | ||||||||
\(748\) | 63.6837 | 2.32851 | ||||||||
\(749\) | −20.2550 | −0.740102 | ||||||||
\(750\) | 1.89518 | 0.0692023 | ||||||||
\(751\) | −46.3090 | −1.68984 | −0.844920 | − | 0.534893i | \(-0.820352\pi\) | ||||
−0.844920 | + | 0.534893i | \(0.820352\pi\) | |||||||
\(752\) | 15.0217 | 0.547787 | ||||||||
\(753\) | −3.38768 | −0.123454 | ||||||||
\(754\) | −27.2262 | −0.991519 | ||||||||
\(755\) | 10.0933 | 0.367331 | ||||||||
\(756\) | −70.8399 | −2.57642 | ||||||||
\(757\) | −36.9789 | −1.34402 | −0.672011 | − | 0.740541i | \(-0.734569\pi\) | ||||
−0.672011 | + | 0.740541i | \(0.734569\pi\) | |||||||
\(758\) | −52.3564 | −1.90167 | ||||||||
\(759\) | 12.2794 | 0.445713 | ||||||||
\(760\) | −0.975602 | −0.0353888 | ||||||||
\(761\) | −30.0375 | −1.08886 | −0.544429 | − | 0.838807i | \(-0.683254\pi\) | ||||
−0.544429 | + | 0.838807i | \(0.683254\pi\) | |||||||
\(762\) | 15.5232 | 0.562347 | ||||||||
\(763\) | 43.5071 | 1.57506 | ||||||||
\(764\) | −1.72362 | −0.0623585 | ||||||||
\(765\) | −12.1906 | −0.440754 | ||||||||
\(766\) | 16.8454 | 0.608647 | ||||||||
\(767\) | 10.1634 | 0.366978 | ||||||||
\(768\) | −23.8159 | −0.859382 | ||||||||
\(769\) | −49.3885 | −1.78100 | −0.890498 | − | 0.454987i | \(-0.849644\pi\) | ||||
−0.890498 | + | 0.454987i | \(0.849644\pi\) | |||||||
\(770\) | −29.4969 | −1.06300 | ||||||||
\(771\) | −17.8097 | −0.641399 | ||||||||
\(772\) | −102.329 | −3.68291 | ||||||||
\(773\) | −2.37992 | −0.0855996 | −0.0427998 | − | 0.999084i | \(-0.513628\pi\) | ||||
−0.0427998 | + | 0.999084i | \(0.513628\pi\) | |||||||
\(774\) | 48.8438 | 1.75566 | ||||||||
\(775\) | 0.0944094 | 0.00339129 | ||||||||
\(776\) | −108.028 | −3.87800 | ||||||||
\(777\) | −22.2033 | −0.796538 | ||||||||
\(778\) | −84.2602 | −3.02087 | ||||||||
\(779\) | −0.674051 | −0.0241504 | ||||||||
\(780\) | −6.71350 | −0.240382 | ||||||||
\(781\) | 4.98295 | 0.178304 | ||||||||
\(782\) | −70.0945 | −2.50658 | ||||||||
\(783\) | −21.5150 | −0.768884 | ||||||||
\(784\) | 54.7737 | 1.95620 | ||||||||
\(785\) | −11.2029 | −0.399849 | ||||||||
\(786\) | 29.5145 | 1.05275 | ||||||||
\(787\) | −26.1423 | −0.931871 | −0.465935 | − | 0.884819i | \(-0.654282\pi\) | ||||
−0.465935 | + | 0.884819i | \(0.654282\pi\) | |||||||
\(788\) | −71.0486 | −2.53100 | ||||||||
\(789\) | −22.4624 | −0.799683 | ||||||||
\(790\) | 12.3099 | 0.437966 | ||||||||
\(791\) | −11.6539 | −0.414365 | ||||||||
\(792\) | −41.8920 | −1.48857 | ||||||||
\(793\) | 15.1836 | 0.539187 | ||||||||
\(794\) | 53.5722 | 1.90120 | ||||||||
\(795\) | −6.21832 | −0.220541 | ||||||||
\(796\) | −9.57192 | −0.339268 | ||||||||
\(797\) | −29.4977 | −1.04486 | −0.522431 | − | 0.852681i | \(-0.674975\pi\) | ||||
−0.522431 | + | 0.852681i | \(0.674975\pi\) | |||||||
\(798\) | 1.25860 | 0.0445538 | ||||||||
\(799\) | −12.3248 | −0.436020 | ||||||||
\(800\) | −3.62836 | −0.128282 | ||||||||
\(801\) | 23.0267 | 0.813610 | ||||||||
\(802\) | 60.6075 | 2.14012 | ||||||||
\(803\) | 35.9091 | 1.26720 | ||||||||
\(804\) | 10.5496 | 0.372055 | ||||||||
\(805\) | 22.2129 | 0.782901 | ||||||||
\(806\) | −0.488811 | −0.0172176 | ||||||||
\(807\) | 8.17006 | 0.287600 | ||||||||
\(808\) | −44.1728 | −1.55399 | ||||||||
\(809\) | −2.41340 | −0.0848507 | −0.0424254 | − | 0.999100i | \(-0.513508\pi\) | ||||
−0.0424254 | + | 0.999100i | \(0.513508\pi\) | |||||||
\(810\) | 10.6126 | 0.372889 | ||||||||
\(811\) | −17.9036 | −0.628682 | −0.314341 | − | 0.949310i | \(-0.601784\pi\) | ||||
−0.314341 | + | 0.949310i | \(0.601784\pi\) | |||||||
\(812\) | 91.0454 | 3.19507 | ||||||||
\(813\) | −14.5125 | −0.508974 | ||||||||
\(814\) | −54.4599 | −1.90882 | ||||||||
\(815\) | 1.41195 | 0.0494583 | ||||||||
\(816\) | −23.0474 | −0.806821 | ||||||||
\(817\) | −1.32588 | −0.0463866 | ||||||||
\(818\) | 57.5220 | 2.01121 | ||||||||
\(819\) | −20.0020 | −0.698926 | ||||||||
\(820\) | −17.5734 | −0.613689 | ||||||||
\(821\) | −44.1546 | −1.54100 | −0.770502 | − | 0.637437i | \(-0.779995\pi\) | ||||
−0.770502 | + | 0.637437i | \(0.779995\pi\) | |||||||
\(822\) | 2.97210 | 0.103664 | ||||||||
\(823\) | −43.2535 | −1.50772 | −0.753862 | − | 0.657033i | \(-0.771811\pi\) | ||||
−0.753862 | + | 0.657033i | \(0.771811\pi\) | |||||||
\(824\) | 8.82328 | 0.307374 | ||||||||
\(825\) | −2.20904 | −0.0769088 | ||||||||
\(826\) | −49.6749 | −1.72841 | ||||||||
\(827\) | 11.0394 | 0.383876 | 0.191938 | − | 0.981407i | \(-0.438523\pi\) | ||||
0.191938 | + | 0.981407i | \(0.438523\pi\) | |||||||
\(828\) | 58.5939 | 2.03628 | ||||||||
\(829\) | −41.4653 | −1.44015 | −0.720075 | − | 0.693896i | \(-0.755893\pi\) | ||||
−0.720075 | + | 0.693896i | \(0.755893\pi\) | |||||||
\(830\) | 20.6805 | 0.717830 | ||||||||
\(831\) | −8.21057 | −0.284822 | ||||||||
\(832\) | −6.34513 | −0.219978 | ||||||||
\(833\) | −44.9398 | −1.55707 | ||||||||
\(834\) | 36.1537 | 1.25190 | ||||||||
\(835\) | −2.91798 | −0.100981 | ||||||||
\(836\) | 2.11212 | 0.0730491 | ||||||||
\(837\) | −0.386275 | −0.0133516 | ||||||||
\(838\) | −19.9166 | −0.688008 | ||||||||
\(839\) | 35.7175 | 1.23310 | 0.616552 | − | 0.787314i | \(-0.288529\pi\) | ||||
0.616552 | + | 0.787314i | \(0.288529\pi\) | |||||||
\(840\) | 17.6667 | 0.609558 | ||||||||
\(841\) | −1.34833 | −0.0464941 | ||||||||
\(842\) | 72.4743 | 2.49763 | ||||||||
\(843\) | −13.3687 | −0.460442 | ||||||||
\(844\) | −92.8600 | −3.19637 | ||||||||
\(845\) | 8.76691 | 0.301591 | ||||||||
\(846\) | 15.0583 | 0.517715 | ||||||||
\(847\) | −9.57479 | −0.328994 | ||||||||
\(848\) | 50.4282 | 1.73171 | ||||||||
\(849\) | 6.28604 | 0.215736 | ||||||||
\(850\) | 12.6099 | 0.432515 | ||||||||
\(851\) | 41.0114 | 1.40585 | ||||||||
\(852\) | −5.54316 | −0.189906 | ||||||||
\(853\) | −34.4609 | −1.17992 | −0.589959 | − | 0.807433i | \(-0.700856\pi\) | ||||
−0.589959 | + | 0.807433i | \(0.700856\pi\) | |||||||
\(854\) | −74.2122 | −2.53949 | ||||||||
\(855\) | −0.404312 | −0.0138272 | ||||||||
\(856\) | 29.7557 | 1.01703 | ||||||||
\(857\) | 7.94566 | 0.271419 | 0.135709 | − | 0.990749i | \(-0.456669\pi\) | ||||
0.135709 | + | 0.990749i | \(0.456669\pi\) | |||||||
\(858\) | 11.4374 | 0.390468 | ||||||||
\(859\) | −13.7030 | −0.467541 | −0.233771 | − | 0.972292i | \(-0.575106\pi\) | ||||
−0.233771 | + | 0.972292i | \(0.575106\pi\) | |||||||
\(860\) | −34.5673 | −1.17874 | ||||||||
\(861\) | 12.2060 | 0.415981 | ||||||||
\(862\) | 17.9562 | 0.611592 | ||||||||
\(863\) | 11.8714 | 0.404109 | 0.202054 | − | 0.979374i | \(-0.435238\pi\) | ||||
0.202054 | + | 0.979374i | \(0.435238\pi\) | |||||||
\(864\) | 14.8454 | 0.505049 | ||||||||
\(865\) | 7.50937 | 0.255326 | ||||||||
\(866\) | −63.7375 | −2.16589 | ||||||||
\(867\) | 6.10683 | 0.207399 | ||||||||
\(868\) | 1.63460 | 0.0554821 | ||||||||
\(869\) | −14.3485 | −0.486739 | ||||||||
\(870\) | 9.96579 | 0.337872 | ||||||||
\(871\) | 6.65188 | 0.225390 | ||||||||
\(872\) | −63.9143 | −2.16441 | ||||||||
\(873\) | −44.7695 | −1.51522 | ||||||||
\(874\) | −2.32474 | −0.0786354 | ||||||||
\(875\) | −3.99606 | −0.135091 | ||||||||
\(876\) | −39.9462 | −1.34966 | ||||||||
\(877\) | 55.0907 | 1.86028 | 0.930140 | − | 0.367205i | \(-0.119685\pi\) | ||||
0.930140 | + | 0.367205i | \(0.119685\pi\) | |||||||
\(878\) | 30.3217 | 1.02331 | ||||||||
\(879\) | 2.99759 | 0.101106 | ||||||||
\(880\) | 17.9144 | 0.603895 | ||||||||
\(881\) | 37.5632 | 1.26554 | 0.632768 | − | 0.774342i | \(-0.281919\pi\) | ||||
0.632768 | + | 0.774342i | \(0.281919\pi\) | |||||||
\(882\) | 54.9070 | 1.84881 | ||||||||
\(883\) | 31.4013 | 1.05674 | 0.528368 | − | 0.849015i | \(-0.322804\pi\) | ||||
0.528368 | + | 0.849015i | \(0.322804\pi\) | |||||||
\(884\) | −44.6692 | −1.50239 | ||||||||
\(885\) | −3.72017 | −0.125052 | ||||||||
\(886\) | −12.4964 | −0.419823 | ||||||||
\(887\) | −41.8321 | −1.40459 | −0.702293 | − | 0.711888i | \(-0.747840\pi\) | ||||
−0.702293 | + | 0.711888i | \(0.747840\pi\) | |||||||
\(888\) | 32.6178 | 1.09458 | ||||||||
\(889\) | −32.7312 | −1.09777 | ||||||||
\(890\) | −23.8186 | −0.798401 | ||||||||
\(891\) | −12.3701 | −0.414414 | ||||||||
\(892\) | 95.4665 | 3.19645 | ||||||||
\(893\) | −0.408761 | −0.0136787 | ||||||||
\(894\) | 20.8796 | 0.698318 | ||||||||
\(895\) | 20.7665 | 0.694147 | ||||||||
\(896\) | 60.0110 | 2.00483 | ||||||||
\(897\) | −8.61304 | −0.287581 | ||||||||
\(898\) | −41.2808 | −1.37756 | ||||||||
\(899\) | 0.496451 | 0.0165576 | ||||||||
\(900\) | −10.5409 | −0.351364 | ||||||||
\(901\) | −41.3745 | −1.37838 | ||||||||
\(902\) | 29.9388 | 0.996854 | ||||||||
\(903\) | 24.0096 | 0.798990 | ||||||||
\(904\) | 17.1202 | 0.569410 | ||||||||
\(905\) | −8.69763 | −0.289119 | ||||||||
\(906\) | 19.1286 | 0.635504 | ||||||||
\(907\) | −14.4937 | −0.481254 | −0.240627 | − | 0.970618i | \(-0.577353\pi\) | ||||
−0.240627 | + | 0.970618i | \(0.577353\pi\) | |||||||
\(908\) | −57.4991 | −1.90818 | ||||||||
\(909\) | −18.3062 | −0.607178 | ||||||||
\(910\) | 20.6898 | 0.685862 | ||||||||
\(911\) | 1.14461 | 0.0379226 | 0.0189613 | − | 0.999820i | \(-0.493964\pi\) | ||||
0.0189613 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(912\) | −0.764385 | −0.0253113 | ||||||||
\(913\) | −24.1053 | −0.797769 | ||||||||
\(914\) | −79.3385 | −2.62429 | ||||||||
\(915\) | −5.55778 | −0.183734 | ||||||||
\(916\) | −80.7226 | −2.66715 | ||||||||
\(917\) | −62.2323 | −2.05509 | ||||||||
\(918\) | −51.5931 | −1.70283 | ||||||||
\(919\) | −24.1791 | −0.797596 | −0.398798 | − | 0.917039i | \(-0.630573\pi\) | ||||
−0.398798 | + | 0.917039i | \(0.630573\pi\) | |||||||
\(920\) | −32.6319 | −1.07584 | ||||||||
\(921\) | −9.11779 | −0.300442 | ||||||||
\(922\) | −6.03583 | −0.198780 | ||||||||
\(923\) | −3.49516 | −0.115044 | ||||||||
\(924\) | −38.2472 | −1.25824 | ||||||||
\(925\) | −7.37787 | −0.242583 | ||||||||
\(926\) | 53.0204 | 1.74236 | ||||||||
\(927\) | 3.65657 | 0.120098 | ||||||||
\(928\) | −19.0797 | −0.626321 | ||||||||
\(929\) | −12.9899 | −0.426184 | −0.213092 | − | 0.977032i | \(-0.568353\pi\) | ||||
−0.213092 | + | 0.977032i | \(0.568353\pi\) | |||||||
\(930\) | 0.178923 | 0.00586712 | ||||||||
\(931\) | −1.49046 | −0.0488480 | ||||||||
\(932\) | 53.7808 | 1.76165 | ||||||||
\(933\) | −2.82068 | −0.0923448 | ||||||||
\(934\) | −48.2754 | −1.57962 | ||||||||
\(935\) | −14.6981 | −0.480681 | ||||||||
\(936\) | 29.3840 | 0.960447 | ||||||||
\(937\) | −35.6713 | −1.16533 | −0.582664 | − | 0.812713i | \(-0.697990\pi\) | ||||
−0.582664 | + | 0.812713i | \(0.697990\pi\) | |||||||
\(938\) | −32.5120 | −1.06155 | ||||||||
\(939\) | −1.35265 | −0.0441419 | ||||||||
\(940\) | −10.6569 | −0.347591 | ||||||||
\(941\) | −50.3647 | −1.64184 | −0.820922 | − | 0.571041i | \(-0.806540\pi\) | ||||
−0.820922 | + | 0.571041i | \(0.806540\pi\) | |||||||
\(942\) | −21.2316 | −0.691761 | ||||||||
\(943\) | −22.5457 | −0.734188 | ||||||||
\(944\) | 30.1692 | 0.981922 | ||||||||
\(945\) | 16.3498 | 0.531859 | ||||||||
\(946\) | 58.8905 | 1.91470 | ||||||||
\(947\) | −0.334759 | −0.0108782 | −0.00543911 | − | 0.999985i | \(-0.501731\pi\) | ||||
−0.00543911 | + | 0.999985i | \(0.501731\pi\) | |||||||
\(948\) | 15.9616 | 0.518409 | ||||||||
\(949\) | −25.1874 | −0.817619 | ||||||||
\(950\) | 0.418216 | 0.0135687 | ||||||||
\(951\) | −1.31332 | −0.0425874 | ||||||||
\(952\) | 117.548 | 3.80975 | ||||||||
\(953\) | 3.28444 | 0.106393 | 0.0531967 | − | 0.998584i | \(-0.483059\pi\) | ||||
0.0531967 | + | 0.998584i | \(0.483059\pi\) | |||||||
\(954\) | 50.5509 | 1.63665 | ||||||||
\(955\) | 0.397811 | 0.0128728 | ||||||||
\(956\) | −67.6810 | −2.18896 | ||||||||
\(957\) | −11.6162 | −0.375498 | ||||||||
\(958\) | −8.76340 | −0.283133 | ||||||||
\(959\) | −6.26677 | −0.202364 | ||||||||
\(960\) | 2.32255 | 0.0749601 | ||||||||
\(961\) | −30.9911 | −0.999712 | ||||||||
\(962\) | 38.1994 | 1.23160 | ||||||||
\(963\) | 12.3315 | 0.397375 | ||||||||
\(964\) | 53.6386 | 1.72758 | ||||||||
\(965\) | 23.6175 | 0.760274 | ||||||||
\(966\) | 42.0975 | 1.35446 | ||||||||
\(967\) | −44.6783 | −1.43676 | −0.718379 | − | 0.695652i | \(-0.755116\pi\) | ||||
−0.718379 | + | 0.695652i | \(0.755116\pi\) | |||||||
\(968\) | 14.0659 | 0.452095 | ||||||||
\(969\) | 0.627150 | 0.0201470 | ||||||||
\(970\) | 46.3090 | 1.48689 | ||||||||
\(971\) | 13.5657 | 0.435343 | 0.217671 | − | 0.976022i | \(-0.430154\pi\) | ||||
0.217671 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(972\) | 66.9432 | 2.14720 | ||||||||
\(973\) | −76.2313 | −2.44386 | ||||||||
\(974\) | −22.8260 | −0.731393 | ||||||||
\(975\) | 1.54947 | 0.0496227 | ||||||||
\(976\) | 45.0714 | 1.44270 | ||||||||
\(977\) | −2.71231 | −0.0867745 | −0.0433872 | − | 0.999058i | \(-0.513815\pi\) | ||||
−0.0433872 | + | 0.999058i | \(0.513815\pi\) | |||||||
\(978\) | 2.67590 | 0.0855658 | ||||||||
\(979\) | 27.7631 | 0.887313 | ||||||||
\(980\) | −38.8583 | −1.24128 | ||||||||
\(981\) | −26.4876 | −0.845682 | ||||||||
\(982\) | 66.9548 | 2.13661 | ||||||||
\(983\) | 55.4615 | 1.76895 | 0.884473 | − | 0.466591i | \(-0.154518\pi\) | ||||
0.884473 | + | 0.466591i | \(0.154518\pi\) | |||||||
\(984\) | −17.9313 | −0.571630 | ||||||||
\(985\) | 16.3979 | 0.522482 | ||||||||
\(986\) | 66.3088 | 2.11170 | ||||||||
\(987\) | 7.40204 | 0.235610 | ||||||||
\(988\) | −1.48149 | −0.0471324 | ||||||||
\(989\) | −44.3479 | −1.41018 | ||||||||
\(990\) | 17.9580 | 0.570743 | ||||||||
\(991\) | 22.7289 | 0.722007 | 0.361004 | − | 0.932564i | \(-0.382434\pi\) | ||||
0.361004 | + | 0.932564i | \(0.382434\pi\) | |||||||
\(992\) | −0.342551 | −0.0108760 | ||||||||
\(993\) | 4.00923 | 0.127229 | ||||||||
\(994\) | 17.0831 | 0.541842 | ||||||||
\(995\) | 2.20919 | 0.0700360 | ||||||||
\(996\) | 26.8154 | 0.849677 | ||||||||
\(997\) | −16.7659 | −0.530982 | −0.265491 | − | 0.964113i | \(-0.585534\pi\) | ||||
−0.265491 | + | 0.964113i | \(0.585534\pi\) | |||||||
\(998\) | 63.7916 | 2.01929 | ||||||||
\(999\) | 30.1864 | 0.955057 |
(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 | 8005.2.a.f.1.9 | ✓ | 127 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8005.2.a.f.1.9 | ✓ | 127 | 1.1 | even | 1 | trivial |