Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, 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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0191532 | −0.0135434 | −0.00677168 | − | 0.999977i | \(-0.502156\pi\) | ||||
−0.00677168 | + | 0.999977i | \(0.502156\pi\) | |||||||
\(3\) | 1.86649 | 1.07762 | 0.538810 | − | 0.842427i | \(-0.318874\pi\) | ||||
0.538810 | + | 0.842427i | \(0.318874\pi\) | |||||||
\(4\) | −1.99963 | −0.999817 | ||||||||
\(5\) | −3.05402 | −1.36580 | −0.682900 | − | 0.730512i | \(-0.739281\pi\) | ||||
−0.682900 | + | 0.730512i | \(0.739281\pi\) | |||||||
\(6\) | −0.0357493 | −0.0145946 | ||||||||
\(7\) | −1.55451 | −0.587549 | −0.293774 | − | 0.955875i | \(-0.594911\pi\) | ||||
−0.293774 | + | 0.955875i | \(0.594911\pi\) | |||||||
\(8\) | 0.0766058 | 0.0270842 | ||||||||
\(9\) | 0.483795 | 0.161265 | ||||||||
\(10\) | 0.0584943 | 0.0184975 | ||||||||
\(11\) | 1.27925 | 0.385708 | 0.192854 | − | 0.981227i | \(-0.438226\pi\) | ||||
0.192854 | + | 0.981227i | \(0.438226\pi\) | |||||||
\(12\) | −3.73230 | −1.07742 | ||||||||
\(13\) | 3.24016 | 0.898659 | 0.449330 | − | 0.893366i | \(-0.351663\pi\) | ||||
0.449330 | + | 0.893366i | \(0.351663\pi\) | |||||||
\(14\) | 0.0297738 | 0.00795739 | ||||||||
\(15\) | −5.70031 | −1.47181 | ||||||||
\(16\) | 3.99780 | 0.999450 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.00926623 | −0.00218407 | ||||||||
\(19\) | 6.72577 | 1.54300 | 0.771499 | − | 0.636230i | \(-0.219507\pi\) | ||||
0.771499 | + | 0.636230i | \(0.219507\pi\) | |||||||
\(20\) | 6.10692 | 1.36555 | ||||||||
\(21\) | −2.90148 | −0.633154 | ||||||||
\(22\) | −0.0245017 | −0.00522379 | ||||||||
\(23\) | 8.38656 | 1.74872 | 0.874360 | − | 0.485278i | \(-0.161282\pi\) | ||||
0.874360 | + | 0.485278i | \(0.161282\pi\) | |||||||
\(24\) | 0.142984 | 0.0291865 | ||||||||
\(25\) | 4.32704 | 0.865408 | ||||||||
\(26\) | −0.0620595 | −0.0121709 | ||||||||
\(27\) | −4.69648 | −0.903838 | ||||||||
\(28\) | 3.10845 | 0.587441 | ||||||||
\(29\) | 5.42429 | 1.00727 | 0.503633 | − | 0.863918i | \(-0.331997\pi\) | ||||
0.503633 | + | 0.863918i | \(0.331997\pi\) | |||||||
\(30\) | 0.109179 | 0.0199333 | ||||||||
\(31\) | 0.0319668 | 0.00574141 | 0.00287070 | − | 0.999996i | \(-0.499086\pi\) | ||||
0.00287070 | + | 0.999996i | \(0.499086\pi\) | |||||||
\(32\) | −0.229782 | −0.0406202 | ||||||||
\(33\) | 2.38771 | 0.415647 | ||||||||
\(34\) | 0.0191532 | 0.00328475 | ||||||||
\(35\) | 4.74750 | 0.802474 | ||||||||
\(36\) | −0.967412 | −0.161235 | ||||||||
\(37\) | −5.26718 | −0.865919 | −0.432960 | − | 0.901413i | \(-0.642531\pi\) | ||||
−0.432960 | + | 0.901413i | \(0.642531\pi\) | |||||||
\(38\) | −0.128820 | −0.0208974 | ||||||||
\(39\) | 6.04774 | 0.968413 | ||||||||
\(40\) | −0.233956 | −0.0369917 | ||||||||
\(41\) | 3.84825 | 0.600996 | 0.300498 | − | 0.953782i | \(-0.402847\pi\) | ||||
0.300498 | + | 0.953782i | \(0.402847\pi\) | |||||||
\(42\) | 0.0555726 | 0.00857504 | ||||||||
\(43\) | −1.23767 | −0.188743 | −0.0943714 | − | 0.995537i | \(-0.530084\pi\) | ||||
−0.0943714 | + | 0.995537i | \(0.530084\pi\) | |||||||
\(44\) | −2.55803 | −0.385637 | ||||||||
\(45\) | −1.47752 | −0.220256 | ||||||||
\(46\) | −0.160630 | −0.0236835 | ||||||||
\(47\) | 7.94885 | 1.15946 | 0.579729 | − | 0.814809i | \(-0.303158\pi\) | ||||
0.579729 | + | 0.814809i | \(0.303158\pi\) | |||||||
\(48\) | 7.46186 | 1.07703 | ||||||||
\(49\) | −4.58350 | −0.654786 | ||||||||
\(50\) | −0.0828767 | −0.0117205 | ||||||||
\(51\) | −1.86649 | −0.261361 | ||||||||
\(52\) | −6.47914 | −0.898495 | ||||||||
\(53\) | 7.06796 | 0.970859 | 0.485429 | − | 0.874276i | \(-0.338663\pi\) | ||||
0.485429 | + | 0.874276i | \(0.338663\pi\) | |||||||
\(54\) | 0.0899526 | 0.0122410 | ||||||||
\(55\) | −3.90685 | −0.526800 | ||||||||
\(56\) | −0.119084 | −0.0159133 | ||||||||
\(57\) | 12.5536 | 1.66277 | ||||||||
\(58\) | −0.103893 | −0.0136418 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 11.3985 | 1.47154 | ||||||||
\(61\) | −6.33365 | −0.810941 | −0.405470 | − | 0.914108i | \(-0.632892\pi\) | ||||
−0.405470 | + | 0.914108i | \(0.632892\pi\) | |||||||
\(62\) | −0.000612267 0 | −7.77580e−5 0 | ||||||||
\(63\) | −0.752063 | −0.0947511 | ||||||||
\(64\) | −7.99120 | −0.998900 | ||||||||
\(65\) | −9.89552 | −1.22739 | ||||||||
\(66\) | −0.0457323 | −0.00562926 | ||||||||
\(67\) | 6.61210 | 0.807796 | 0.403898 | − | 0.914804i | \(-0.367655\pi\) | ||||
0.403898 | + | 0.914804i | \(0.367655\pi\) | |||||||
\(68\) | 1.99963 | 0.242491 | ||||||||
\(69\) | 15.6535 | 1.88446 | ||||||||
\(70\) | −0.0909299 | −0.0108682 | ||||||||
\(71\) | −1.04893 | −0.124485 | −0.0622427 | − | 0.998061i | \(-0.519825\pi\) | ||||
−0.0622427 | + | 0.998061i | \(0.519825\pi\) | |||||||
\(72\) | 0.0370615 | 0.00436774 | ||||||||
\(73\) | 4.13553 | 0.484027 | 0.242014 | − | 0.970273i | \(-0.422192\pi\) | ||||
0.242014 | + | 0.970273i | \(0.422192\pi\) | |||||||
\(74\) | 0.100883 | 0.0117275 | ||||||||
\(75\) | 8.07639 | 0.932581 | ||||||||
\(76\) | −13.4491 | −1.54272 | ||||||||
\(77\) | −1.98860 | −0.226622 | ||||||||
\(78\) | −0.115834 | −0.0131156 | ||||||||
\(79\) | 5.60337 | 0.630429 | 0.315214 | − | 0.949021i | \(-0.397924\pi\) | ||||
0.315214 | + | 0.949021i | \(0.397924\pi\) | |||||||
\(80\) | −12.2094 | −1.36505 | ||||||||
\(81\) | −10.2173 | −1.13526 | ||||||||
\(82\) | −0.0737064 | −0.00813951 | ||||||||
\(83\) | −2.78891 | −0.306122 | −0.153061 | − | 0.988217i | \(-0.548913\pi\) | ||||
−0.153061 | + | 0.988217i | \(0.548913\pi\) | |||||||
\(84\) | 5.80189 | 0.633038 | ||||||||
\(85\) | 3.05402 | 0.331255 | ||||||||
\(86\) | 0.0237053 | 0.00255621 | ||||||||
\(87\) | 10.1244 | 1.08545 | ||||||||
\(88\) | 0.0979979 | 0.0104466 | ||||||||
\(89\) | −4.28437 | −0.454142 | −0.227071 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227071 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(90\) | 0.0282992 | 0.00298300 | ||||||||
\(91\) | −5.03686 | −0.528006 | ||||||||
\(92\) | −16.7701 | −1.74840 | ||||||||
\(93\) | 0.0596658 | 0.00618706 | ||||||||
\(94\) | −0.152246 | −0.0157030 | ||||||||
\(95\) | −20.5407 | −2.10743 | ||||||||
\(96\) | −0.428887 | −0.0437731 | ||||||||
\(97\) | −5.05989 | −0.513754 | −0.256877 | − | 0.966444i | \(-0.582694\pi\) | ||||
−0.256877 | + | 0.966444i | \(0.582694\pi\) | |||||||
\(98\) | 0.0877888 | 0.00886801 | ||||||||
\(99\) | 0.618894 | 0.0622012 | ||||||||
\(100\) | −8.65250 | −0.865250 | ||||||||
\(101\) | 3.67012 | 0.365190 | 0.182595 | − | 0.983188i | \(-0.441550\pi\) | ||||
0.182595 | + | 0.983188i | \(0.441550\pi\) | |||||||
\(102\) | 0.0357493 | 0.00353971 | ||||||||
\(103\) | 16.0220 | 1.57869 | 0.789345 | − | 0.613950i | \(-0.210420\pi\) | ||||
0.789345 | + | 0.613950i | \(0.210420\pi\) | |||||||
\(104\) | 0.248215 | 0.0243395 | ||||||||
\(105\) | 8.86117 | 0.864762 | ||||||||
\(106\) | −0.135374 | −0.0131487 | ||||||||
\(107\) | −17.8627 | −1.72685 | −0.863424 | − | 0.504478i | \(-0.831685\pi\) | ||||
−0.863424 | + | 0.504478i | \(0.831685\pi\) | |||||||
\(108\) | 9.39123 | 0.903672 | ||||||||
\(109\) | 7.36384 | 0.705328 | 0.352664 | − | 0.935750i | \(-0.385276\pi\) | ||||
0.352664 | + | 0.935750i | \(0.385276\pi\) | |||||||
\(110\) | 0.0748288 | 0.00713465 | ||||||||
\(111\) | −9.83115 | −0.933132 | ||||||||
\(112\) | −6.21461 | −0.587226 | ||||||||
\(113\) | −5.86956 | −0.552162 | −0.276081 | − | 0.961134i | \(-0.589036\pi\) | ||||
−0.276081 | + | 0.961134i | \(0.589036\pi\) | |||||||
\(114\) | −0.240442 | −0.0225195 | ||||||||
\(115\) | −25.6127 | −2.38840 | ||||||||
\(116\) | −10.8466 | −1.00708 | ||||||||
\(117\) | 1.56757 | 0.144922 | ||||||||
\(118\) | −0.0191532 | −0.00176320 | ||||||||
\(119\) | 1.55451 | 0.142502 | ||||||||
\(120\) | −0.436677 | −0.0398629 | ||||||||
\(121\) | −9.36352 | −0.851229 | ||||||||
\(122\) | 0.121310 | 0.0109829 | ||||||||
\(123\) | 7.18273 | 0.647645 | ||||||||
\(124\) | −0.0639219 | −0.00574036 | ||||||||
\(125\) | 2.05523 | 0.183825 | ||||||||
\(126\) | 0.0144044 | 0.00128325 | ||||||||
\(127\) | 13.3973 | 1.18882 | 0.594411 | − | 0.804161i | \(-0.297385\pi\) | ||||
0.594411 | + | 0.804161i | \(0.297385\pi\) | |||||||
\(128\) | 0.612622 | 0.0541486 | ||||||||
\(129\) | −2.31010 | −0.203393 | ||||||||
\(130\) | 0.189531 | 0.0166230 | ||||||||
\(131\) | 20.9107 | 1.82697 | 0.913487 | − | 0.406868i | \(-0.133379\pi\) | ||||
0.913487 | + | 0.406868i | \(0.133379\pi\) | |||||||
\(132\) | −4.77454 | −0.415571 | ||||||||
\(133\) | −10.4553 | −0.906587 | ||||||||
\(134\) | −0.126643 | −0.0109403 | ||||||||
\(135\) | 14.3431 | 1.23446 | ||||||||
\(136\) | −0.0766058 | −0.00656889 | ||||||||
\(137\) | 0.638567 | 0.0545565 | 0.0272782 | − | 0.999628i | \(-0.491316\pi\) | ||||
0.0272782 | + | 0.999628i | \(0.491316\pi\) | |||||||
\(138\) | −0.299814 | −0.0255219 | ||||||||
\(139\) | −9.45404 | −0.801881 | −0.400940 | − | 0.916104i | \(-0.631317\pi\) | ||||
−0.400940 | + | 0.916104i | \(0.631317\pi\) | |||||||
\(140\) | −9.49326 | −0.802327 | ||||||||
\(141\) | 14.8365 | 1.24946 | ||||||||
\(142\) | 0.0200904 | 0.00168595 | ||||||||
\(143\) | 4.14498 | 0.346620 | ||||||||
\(144\) | 1.93412 | 0.161176 | ||||||||
\(145\) | −16.5659 | −1.37572 | ||||||||
\(146\) | −0.0792087 | −0.00655535 | ||||||||
\(147\) | −8.55508 | −0.705611 | ||||||||
\(148\) | 10.5324 | 0.865760 | ||||||||
\(149\) | 13.3088 | 1.09030 | 0.545148 | − | 0.838340i | \(-0.316473\pi\) | ||||
0.545148 | + | 0.838340i | \(0.316473\pi\) | |||||||
\(150\) | −0.154689 | −0.0126303 | ||||||||
\(151\) | 12.2023 | 0.993010 | 0.496505 | − | 0.868034i | \(-0.334616\pi\) | ||||
0.496505 | + | 0.868034i | \(0.334616\pi\) | |||||||
\(152\) | 0.515233 | 0.0417910 | ||||||||
\(153\) | −0.483795 | −0.0391125 | ||||||||
\(154\) | 0.0380881 | 0.00306923 | ||||||||
\(155\) | −0.0976273 | −0.00784161 | ||||||||
\(156\) | −12.0933 | −0.968236 | ||||||||
\(157\) | 10.2953 | 0.821652 | 0.410826 | − | 0.911714i | \(-0.365240\pi\) | ||||
0.410826 | + | 0.911714i | \(0.365240\pi\) | |||||||
\(158\) | −0.107323 | −0.00853812 | ||||||||
\(159\) | 13.1923 | 1.04622 | ||||||||
\(160\) | 0.701760 | 0.0554790 | ||||||||
\(161\) | −13.0370 | −1.02746 | ||||||||
\(162\) | 0.195695 | 0.0153752 | ||||||||
\(163\) | −4.22266 | −0.330744 | −0.165372 | − | 0.986231i | \(-0.552883\pi\) | ||||
−0.165372 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(164\) | −7.69509 | −0.600886 | ||||||||
\(165\) | −7.29211 | −0.567690 | ||||||||
\(166\) | 0.0534166 | 0.00414593 | ||||||||
\(167\) | 20.6542 | 1.59827 | 0.799135 | − | 0.601152i | \(-0.205291\pi\) | ||||
0.799135 | + | 0.601152i | \(0.205291\pi\) | |||||||
\(168\) | −0.222270 | −0.0171485 | ||||||||
\(169\) | −2.50135 | −0.192411 | ||||||||
\(170\) | −0.0584943 | −0.00448631 | ||||||||
\(171\) | 3.25390 | 0.248832 | ||||||||
\(172\) | 2.47488 | 0.188708 | ||||||||
\(173\) | 4.03662 | 0.306899 | 0.153449 | − | 0.988157i | \(-0.450962\pi\) | ||||
0.153449 | + | 0.988157i | \(0.450962\pi\) | |||||||
\(174\) | −0.193915 | −0.0147006 | ||||||||
\(175\) | −6.72642 | −0.508470 | ||||||||
\(176\) | 5.11418 | 0.385496 | ||||||||
\(177\) | 1.86649 | 0.140294 | ||||||||
\(178\) | 0.0820594 | 0.00615062 | ||||||||
\(179\) | 25.9761 | 1.94155 | 0.970773 | − | 0.239998i | \(-0.0771467\pi\) | ||||
0.970773 | + | 0.239998i | \(0.0771467\pi\) | |||||||
\(180\) | 2.95450 | 0.220215 | ||||||||
\(181\) | −7.58334 | −0.563665 | −0.281832 | − | 0.959464i | \(-0.590942\pi\) | ||||
−0.281832 | + | 0.959464i | \(0.590942\pi\) | |||||||
\(182\) | 0.0964720 | 0.00715098 | ||||||||
\(183\) | −11.8217 | −0.873886 | ||||||||
\(184\) | 0.642460 | 0.0473627 | ||||||||
\(185\) | 16.0861 | 1.18267 | ||||||||
\(186\) | −0.00114279 | −8.37936e−5 0 | ||||||||
\(187\) | −1.27925 | −0.0935480 | ||||||||
\(188\) | −15.8948 | −1.15925 | ||||||||
\(189\) | 7.30071 | 0.531049 | ||||||||
\(190\) | 0.393419 | 0.0285416 | ||||||||
\(191\) | −13.5965 | −0.983811 | −0.491906 | − | 0.870649i | \(-0.663699\pi\) | ||||
−0.491906 | + | 0.870649i | \(0.663699\pi\) | |||||||
\(192\) | −14.9155 | −1.07643 | ||||||||
\(193\) | −10.9354 | −0.787150 | −0.393575 | − | 0.919293i | \(-0.628762\pi\) | ||||
−0.393575 | + | 0.919293i | \(0.628762\pi\) | |||||||
\(194\) | 0.0969132 | 0.00695796 | ||||||||
\(195\) | −18.4699 | −1.32266 | ||||||||
\(196\) | 9.16533 | 0.654666 | ||||||||
\(197\) | 4.27287 | 0.304429 | 0.152215 | − | 0.988347i | \(-0.451359\pi\) | ||||
0.152215 | + | 0.988347i | \(0.451359\pi\) | |||||||
\(198\) | −0.0118538 | −0.000842414 0 | ||||||||
\(199\) | −2.43533 | −0.172636 | −0.0863179 | − | 0.996268i | \(-0.527510\pi\) | ||||
−0.0863179 | + | 0.996268i | \(0.527510\pi\) | |||||||
\(200\) | 0.331477 | 0.0234389 | ||||||||
\(201\) | 12.3414 | 0.870497 | ||||||||
\(202\) | −0.0702946 | −0.00494591 | ||||||||
\(203\) | −8.43210 | −0.591818 | ||||||||
\(204\) | 3.73230 | 0.261313 | ||||||||
\(205\) | −11.7526 | −0.820840 | ||||||||
\(206\) | −0.306872 | −0.0213808 | ||||||||
\(207\) | 4.05738 | 0.282007 | ||||||||
\(208\) | 12.9535 | 0.898165 | ||||||||
\(209\) | 8.60394 | 0.595147 | ||||||||
\(210\) | −0.169720 | −0.0117118 | ||||||||
\(211\) | 19.8832 | 1.36881 | 0.684407 | − | 0.729100i | \(-0.260061\pi\) | ||||
0.684407 | + | 0.729100i | \(0.260061\pi\) | |||||||
\(212\) | −14.1333 | −0.970681 | ||||||||
\(213\) | −1.95783 | −0.134148 | ||||||||
\(214\) | 0.342127 | 0.0233873 | ||||||||
\(215\) | 3.77987 | 0.257785 | ||||||||
\(216\) | −0.359778 | −0.0244798 | ||||||||
\(217\) | −0.0496927 | −0.00337336 | ||||||||
\(218\) | −0.141041 | −0.00955252 | ||||||||
\(219\) | 7.71893 | 0.521597 | ||||||||
\(220\) | 7.81227 | 0.526703 | ||||||||
\(221\) | −3.24016 | −0.217957 | ||||||||
\(222\) | 0.188298 | 0.0126377 | ||||||||
\(223\) | −9.57676 | −0.641307 | −0.320654 | − | 0.947197i | \(-0.603903\pi\) | ||||
−0.320654 | + | 0.947197i | \(0.603903\pi\) | |||||||
\(224\) | 0.357199 | 0.0238663 | ||||||||
\(225\) | 2.09340 | 0.139560 | ||||||||
\(226\) | 0.112421 | 0.00747813 | ||||||||
\(227\) | 12.9958 | 0.862558 | 0.431279 | − | 0.902219i | \(-0.358062\pi\) | ||||
0.431279 | + | 0.902219i | \(0.358062\pi\) | |||||||
\(228\) | −25.1026 | −1.66246 | ||||||||
\(229\) | −15.4677 | −1.02213 | −0.511067 | − | 0.859541i | \(-0.670750\pi\) | ||||
−0.511067 | + | 0.859541i | \(0.670750\pi\) | |||||||
\(230\) | 0.490566 | 0.0323470 | ||||||||
\(231\) | −3.71171 | −0.244213 | ||||||||
\(232\) | 0.415532 | 0.0272810 | ||||||||
\(233\) | −3.30958 | −0.216818 | −0.108409 | − | 0.994106i | \(-0.534576\pi\) | ||||
−0.108409 | + | 0.994106i | \(0.534576\pi\) | |||||||
\(234\) | −0.0300241 | −0.00196274 | ||||||||
\(235\) | −24.2759 | −1.58359 | ||||||||
\(236\) | −1.99963 | −0.130165 | ||||||||
\(237\) | 10.4587 | 0.679362 | ||||||||
\(238\) | −0.0297738 | −0.00192995 | ||||||||
\(239\) | 0.398777 | 0.0257947 | 0.0128974 | − | 0.999917i | \(-0.495895\pi\) | ||||
0.0128974 | + | 0.999917i | \(0.495895\pi\) | |||||||
\(240\) | −22.7887 | −1.47100 | ||||||||
\(241\) | −3.25734 | −0.209824 | −0.104912 | − | 0.994482i | \(-0.533456\pi\) | ||||
−0.104912 | + | 0.994482i | \(0.533456\pi\) | |||||||
\(242\) | 0.179342 | 0.0115285 | ||||||||
\(243\) | −4.98113 | −0.319540 | ||||||||
\(244\) | 12.6650 | 0.810792 | ||||||||
\(245\) | 13.9981 | 0.894307 | ||||||||
\(246\) | −0.137572 | −0.00877130 | ||||||||
\(247\) | 21.7926 | 1.38663 | ||||||||
\(248\) | 0.00244884 | 0.000155502 0 | ||||||||
\(249\) | −5.20548 | −0.329884 | ||||||||
\(250\) | −0.0393643 | −0.00248961 | ||||||||
\(251\) | −24.9075 | −1.57215 | −0.786074 | − | 0.618132i | \(-0.787890\pi\) | ||||
−0.786074 | + | 0.618132i | \(0.787890\pi\) | |||||||
\(252\) | 1.50385 | 0.0947337 | ||||||||
\(253\) | 10.7285 | 0.674495 | ||||||||
\(254\) | −0.256602 | −0.0161007 | ||||||||
\(255\) | 5.70031 | 0.356967 | ||||||||
\(256\) | 15.9707 | 0.998166 | ||||||||
\(257\) | 22.6703 | 1.41414 | 0.707068 | − | 0.707145i | \(-0.250017\pi\) | ||||
0.707068 | + | 0.707145i | \(0.250017\pi\) | |||||||
\(258\) | 0.0442458 | 0.00275463 | ||||||||
\(259\) | 8.18787 | 0.508770 | ||||||||
\(260\) | 19.7874 | 1.22716 | ||||||||
\(261\) | 2.62424 | 0.162437 | ||||||||
\(262\) | −0.400507 | −0.0247434 | ||||||||
\(263\) | 6.08012 | 0.374916 | 0.187458 | − | 0.982273i | \(-0.439975\pi\) | ||||
0.187458 | + | 0.982273i | \(0.439975\pi\) | |||||||
\(264\) | 0.182912 | 0.0112575 | ||||||||
\(265\) | −21.5857 | −1.32600 | ||||||||
\(266\) | 0.200252 | 0.0122782 | ||||||||
\(267\) | −7.99675 | −0.489393 | ||||||||
\(268\) | −13.2218 | −0.807648 | ||||||||
\(269\) | −3.85797 | −0.235225 | −0.117612 | − | 0.993060i | \(-0.537524\pi\) | ||||
−0.117612 | + | 0.993060i | \(0.537524\pi\) | |||||||
\(270\) | −0.274717 | −0.0167188 | ||||||||
\(271\) | 0.470992 | 0.0286107 | 0.0143054 | − | 0.999898i | \(-0.495446\pi\) | ||||
0.0143054 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(272\) | −3.99780 | −0.242402 | ||||||||
\(273\) | −9.40126 | −0.568990 | ||||||||
\(274\) | −0.0122306 | −0.000738879 0 | ||||||||
\(275\) | 5.53536 | 0.333795 | ||||||||
\(276\) | −31.3012 | −1.88411 | ||||||||
\(277\) | −31.5468 | −1.89546 | −0.947731 | − | 0.319070i | \(-0.896630\pi\) | ||||
−0.947731 | + | 0.319070i | \(0.896630\pi\) | |||||||
\(278\) | 0.181075 | 0.0108602 | ||||||||
\(279\) | 0.0154654 | 0.000925888 0 | ||||||||
\(280\) | 0.363686 | 0.0217344 | ||||||||
\(281\) | 7.89501 | 0.470977 | 0.235489 | − | 0.971877i | \(-0.424331\pi\) | ||||
0.235489 | + | 0.971877i | \(0.424331\pi\) | |||||||
\(282\) | −0.284166 | −0.0169218 | ||||||||
\(283\) | −10.5762 | −0.628687 | −0.314344 | − | 0.949309i | \(-0.601784\pi\) | ||||
−0.314344 | + | 0.949309i | \(0.601784\pi\) | |||||||
\(284\) | 2.09748 | 0.124463 | ||||||||
\(285\) | −38.3390 | −2.27101 | ||||||||
\(286\) | −0.0793896 | −0.00469441 | ||||||||
\(287\) | −5.98214 | −0.353114 | ||||||||
\(288\) | −0.111168 | −0.00655061 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.317290 | 0.0186319 | ||||||||
\(291\) | −9.44425 | −0.553632 | ||||||||
\(292\) | −8.26954 | −0.483938 | ||||||||
\(293\) | −18.8541 | −1.10147 | −0.550734 | − | 0.834680i | \(-0.685652\pi\) | ||||
−0.550734 | + | 0.834680i | \(0.685652\pi\) | |||||||
\(294\) | 0.163857 | 0.00955635 | ||||||||
\(295\) | −3.05402 | −0.177812 | ||||||||
\(296\) | −0.403497 | −0.0234528 | ||||||||
\(297\) | −6.00797 | −0.348618 | ||||||||
\(298\) | −0.254906 | −0.0147663 | ||||||||
\(299\) | 27.1738 | 1.57150 | ||||||||
\(300\) | −16.1498 | −0.932410 | ||||||||
\(301\) | 1.92397 | 0.110896 | ||||||||
\(302\) | −0.233713 | −0.0134487 | ||||||||
\(303\) | 6.85025 | 0.393537 | ||||||||
\(304\) | 26.8883 | 1.54215 | ||||||||
\(305\) | 19.3431 | 1.10758 | ||||||||
\(306\) | 0.00926623 | 0.000529715 0 | ||||||||
\(307\) | −18.9909 | −1.08387 | −0.541933 | − | 0.840421i | \(-0.682308\pi\) | ||||
−0.541933 | + | 0.840421i | \(0.682308\pi\) | |||||||
\(308\) | 3.97648 | 0.226581 | ||||||||
\(309\) | 29.9049 | 1.70123 | ||||||||
\(310\) | 0.00186988 | 0.000106202 0 | ||||||||
\(311\) | −5.90441 | −0.334809 | −0.167404 | − | 0.985888i | \(-0.553539\pi\) | ||||
−0.167404 | + | 0.985888i | \(0.553539\pi\) | |||||||
\(312\) | 0.463292 | 0.0262287 | ||||||||
\(313\) | −19.8488 | −1.12192 | −0.560959 | − | 0.827843i | \(-0.689568\pi\) | ||||
−0.560959 | + | 0.827843i | \(0.689568\pi\) | |||||||
\(314\) | −0.197187 | −0.0111279 | ||||||||
\(315\) | 2.29682 | 0.129411 | ||||||||
\(316\) | −11.2047 | −0.630313 | ||||||||
\(317\) | −2.89777 | −0.162755 | −0.0813774 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813774 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(318\) | −0.252675 | −0.0141693 | ||||||||
\(319\) | 6.93902 | 0.388510 | ||||||||
\(320\) | 24.4053 | 1.36430 | ||||||||
\(321\) | −33.3405 | −1.86089 | ||||||||
\(322\) | 0.249700 | 0.0139152 | ||||||||
\(323\) | −6.72577 | −0.374232 | ||||||||
\(324\) | 20.4309 | 1.13505 | ||||||||
\(325\) | 14.0203 | 0.777707 | ||||||||
\(326\) | 0.0808775 | 0.00447939 | ||||||||
\(327\) | 13.7446 | 0.760076 | ||||||||
\(328\) | 0.294798 | 0.0162775 | ||||||||
\(329\) | −12.3566 | −0.681239 | ||||||||
\(330\) | 0.139667 | 0.00768844 | ||||||||
\(331\) | −18.0331 | −0.991189 | −0.495594 | − | 0.868554i | \(-0.665050\pi\) | ||||
−0.495594 | + | 0.868554i | \(0.665050\pi\) | |||||||
\(332\) | 5.57679 | 0.306066 | ||||||||
\(333\) | −2.54823 | −0.139642 | ||||||||
\(334\) | −0.395594 | −0.0216459 | ||||||||
\(335\) | −20.1935 | −1.10329 | ||||||||
\(336\) | −11.5995 | −0.632806 | ||||||||
\(337\) | −18.3604 | −1.00016 | −0.500078 | − | 0.865980i | \(-0.666695\pi\) | ||||
−0.500078 | + | 0.865980i | \(0.666695\pi\) | |||||||
\(338\) | 0.0479088 | 0.00260589 | ||||||||
\(339\) | −10.9555 | −0.595021 | ||||||||
\(340\) | −6.10692 | −0.331194 | ||||||||
\(341\) | 0.0408935 | 0.00221451 | ||||||||
\(342\) | −0.0623226 | −0.00337002 | ||||||||
\(343\) | 18.0067 | 0.972268 | ||||||||
\(344\) | −0.0948126 | −0.00511196 | ||||||||
\(345\) | −47.8060 | −2.57379 | ||||||||
\(346\) | −0.0773143 | −0.00415644 | ||||||||
\(347\) | 17.3667 | 0.932292 | 0.466146 | − | 0.884708i | \(-0.345642\pi\) | ||||
0.466146 | + | 0.884708i | \(0.345642\pi\) | |||||||
\(348\) | −20.2451 | −1.08525 | ||||||||
\(349\) | −10.6426 | −0.569688 | −0.284844 | − | 0.958574i | \(-0.591942\pi\) | ||||
−0.284844 | + | 0.958574i | \(0.591942\pi\) | |||||||
\(350\) | 0.128833 | 0.00688639 | ||||||||
\(351\) | −15.2174 | −0.812242 | ||||||||
\(352\) | −0.293949 | −0.0156675 | ||||||||
\(353\) | 1.48876 | 0.0792388 | 0.0396194 | − | 0.999215i | \(-0.487385\pi\) | ||||
0.0396194 | + | 0.999215i | \(0.487385\pi\) | |||||||
\(354\) | −0.0357493 | −0.00190006 | ||||||||
\(355\) | 3.20346 | 0.170022 | ||||||||
\(356\) | 8.56717 | 0.454059 | ||||||||
\(357\) | 2.90148 | 0.153563 | ||||||||
\(358\) | −0.497526 | −0.0262951 | ||||||||
\(359\) | −21.1583 | −1.11669 | −0.558346 | − | 0.829608i | \(-0.688564\pi\) | ||||
−0.558346 | + | 0.829608i | \(0.688564\pi\) | |||||||
\(360\) | −0.113187 | −0.00596546 | ||||||||
\(361\) | 26.2360 | 1.38084 | ||||||||
\(362\) | 0.145245 | 0.00763392 | ||||||||
\(363\) | −17.4769 | −0.917302 | ||||||||
\(364\) | 10.0719 | 0.527910 | ||||||||
\(365\) | −12.6300 | −0.661084 | ||||||||
\(366\) | 0.226424 | 0.0118354 | ||||||||
\(367\) | 14.9663 | 0.781232 | 0.390616 | − | 0.920554i | \(-0.372262\pi\) | ||||
0.390616 | + | 0.920554i | \(0.372262\pi\) | |||||||
\(368\) | 33.5278 | 1.74776 | ||||||||
\(369\) | 1.86176 | 0.0969196 | ||||||||
\(370\) | −0.308100 | −0.0160174 | ||||||||
\(371\) | −10.9872 | −0.570427 | ||||||||
\(372\) | −0.119310 | −0.00618592 | ||||||||
\(373\) | −22.2215 | −1.15059 | −0.575294 | − | 0.817947i | \(-0.695112\pi\) | ||||
−0.575294 | + | 0.817947i | \(0.695112\pi\) | |||||||
\(374\) | 0.0245017 | 0.00126695 | ||||||||
\(375\) | 3.83607 | 0.198094 | ||||||||
\(376\) | 0.608928 | 0.0314031 | ||||||||
\(377\) | 17.5756 | 0.905188 | ||||||||
\(378\) | −0.139832 | −0.00719219 | ||||||||
\(379\) | 2.57221 | 0.132126 | 0.0660629 | − | 0.997815i | \(-0.478956\pi\) | ||||
0.0660629 | + | 0.997815i | \(0.478956\pi\) | |||||||
\(380\) | 41.0738 | 2.10704 | ||||||||
\(381\) | 25.0060 | 1.28110 | ||||||||
\(382\) | 0.260417 | 0.0133241 | ||||||||
\(383\) | 33.8756 | 1.73096 | 0.865480 | − | 0.500943i | \(-0.167013\pi\) | ||||
0.865480 | + | 0.500943i | \(0.167013\pi\) | |||||||
\(384\) | 1.14345 | 0.0583516 | ||||||||
\(385\) | 6.07324 | 0.309521 | ||||||||
\(386\) | 0.209449 | 0.0106607 | ||||||||
\(387\) | −0.598778 | −0.0304376 | ||||||||
\(388\) | 10.1179 | 0.513660 | ||||||||
\(389\) | −22.8193 | −1.15698 | −0.578492 | − | 0.815688i | \(-0.696358\pi\) | ||||
−0.578492 | + | 0.815688i | \(0.696358\pi\) | |||||||
\(390\) | 0.353758 | 0.0179132 | ||||||||
\(391\) | −8.38656 | −0.424127 | ||||||||
\(392\) | −0.351123 | −0.0177344 | ||||||||
\(393\) | 39.0296 | 1.96878 | ||||||||
\(394\) | −0.0818392 | −0.00412300 | ||||||||
\(395\) | −17.1128 | −0.861039 | ||||||||
\(396\) | −1.23756 | −0.0621898 | ||||||||
\(397\) | −38.0344 | −1.90889 | −0.954447 | − | 0.298381i | \(-0.903553\pi\) | ||||
−0.954447 | + | 0.298381i | \(0.903553\pi\) | |||||||
\(398\) | 0.0466443 | 0.00233807 | ||||||||
\(399\) | −19.5147 | −0.976956 | ||||||||
\(400\) | 17.2986 | 0.864932 | ||||||||
\(401\) | −2.13057 | −0.106396 | −0.0531978 | − | 0.998584i | \(-0.516941\pi\) | ||||
−0.0531978 | + | 0.998584i | \(0.516941\pi\) | |||||||
\(402\) | −0.236378 | −0.0117895 | ||||||||
\(403\) | 0.103578 | 0.00515957 | ||||||||
\(404\) | −7.33889 | −0.365123 | ||||||||
\(405\) | 31.2039 | 1.55054 | ||||||||
\(406\) | 0.161502 | 0.00801520 | ||||||||
\(407\) | −6.73804 | −0.333992 | ||||||||
\(408\) | −0.142984 | −0.00707877 | ||||||||
\(409\) | 34.2649 | 1.69429 | 0.847144 | − | 0.531363i | \(-0.178320\pi\) | ||||
0.847144 | + | 0.531363i | \(0.178320\pi\) | |||||||
\(410\) | 0.225101 | 0.0111169 | ||||||||
\(411\) | 1.19188 | 0.0587912 | ||||||||
\(412\) | −32.0380 | −1.57840 | ||||||||
\(413\) | −1.55451 | −0.0764924 | ||||||||
\(414\) | −0.0777118 | −0.00381933 | ||||||||
\(415\) | 8.51738 | 0.418102 | ||||||||
\(416\) | −0.744532 | −0.0365037 | ||||||||
\(417\) | −17.6459 | −0.864123 | ||||||||
\(418\) | −0.164793 | −0.00806030 | ||||||||
\(419\) | −12.4579 | −0.608607 | −0.304303 | − | 0.952575i | \(-0.598424\pi\) | ||||
−0.304303 | + | 0.952575i | \(0.598424\pi\) | |||||||
\(420\) | −17.7191 | −0.864603 | ||||||||
\(421\) | −6.29159 | −0.306633 | −0.153317 | − | 0.988177i | \(-0.548995\pi\) | ||||
−0.153317 | + | 0.988177i | \(0.548995\pi\) | |||||||
\(422\) | −0.380827 | −0.0185384 | ||||||||
\(423\) | 3.84561 | 0.186980 | ||||||||
\(424\) | 0.541447 | 0.0262950 | ||||||||
\(425\) | −4.32704 | −0.209892 | ||||||||
\(426\) | 0.0374987 | 0.00181682 | ||||||||
\(427\) | 9.84571 | 0.476467 | ||||||||
\(428\) | 35.7188 | 1.72653 | ||||||||
\(429\) | 7.73657 | 0.373525 | ||||||||
\(430\) | −0.0723966 | −0.00349127 | ||||||||
\(431\) | 34.4498 | 1.65939 | 0.829694 | − | 0.558219i | \(-0.188515\pi\) | ||||
0.829694 | + | 0.558219i | \(0.188515\pi\) | |||||||
\(432\) | −18.7756 | −0.903340 | ||||||||
\(433\) | 12.1163 | 0.582274 | 0.291137 | − | 0.956681i | \(-0.405967\pi\) | ||||
0.291137 | + | 0.956681i | \(0.405967\pi\) | |||||||
\(434\) | 0.000951774 0 | 4.56866e−5 0 | ||||||||
\(435\) | −30.9201 | −1.48251 | ||||||||
\(436\) | −14.7250 | −0.705199 | ||||||||
\(437\) | 56.4061 | 2.69827 | ||||||||
\(438\) | −0.147842 | −0.00706418 | ||||||||
\(439\) | −25.1601 | −1.20082 | −0.600412 | − | 0.799691i | \(-0.704997\pi\) | ||||
−0.600412 | + | 0.799691i | \(0.704997\pi\) | |||||||
\(440\) | −0.299288 | −0.0142680 | ||||||||
\(441\) | −2.21748 | −0.105594 | ||||||||
\(442\) | 0.0620595 | 0.00295187 | ||||||||
\(443\) | −18.8947 | −0.897713 | −0.448856 | − | 0.893604i | \(-0.648169\pi\) | ||||
−0.448856 | + | 0.893604i | \(0.648169\pi\) | |||||||
\(444\) | 19.6587 | 0.932961 | ||||||||
\(445\) | 13.0846 | 0.620267 | ||||||||
\(446\) | 0.183426 | 0.00868546 | ||||||||
\(447\) | 24.8407 | 1.17493 | ||||||||
\(448\) | 12.4224 | 0.586902 | ||||||||
\(449\) | −22.2605 | −1.05054 | −0.525270 | − | 0.850936i | \(-0.676036\pi\) | ||||
−0.525270 | + | 0.850936i | \(0.676036\pi\) | |||||||
\(450\) | −0.0400953 | −0.00189011 | ||||||||
\(451\) | 4.92287 | 0.231809 | ||||||||
\(452\) | 11.7370 | 0.552061 | ||||||||
\(453\) | 22.7755 | 1.07009 | ||||||||
\(454\) | −0.248910 | −0.0116819 | ||||||||
\(455\) | 15.3827 | 0.721151 | ||||||||
\(456\) | 0.961680 | 0.0450348 | ||||||||
\(457\) | 2.89748 | 0.135538 | 0.0677692 | − | 0.997701i | \(-0.478412\pi\) | ||||
0.0677692 | + | 0.997701i | \(0.478412\pi\) | |||||||
\(458\) | 0.296256 | 0.0138431 | ||||||||
\(459\) | 4.69648 | 0.219213 | ||||||||
\(460\) | 51.2161 | 2.38796 | ||||||||
\(461\) | 26.3573 | 1.22758 | 0.613790 | − | 0.789469i | \(-0.289644\pi\) | ||||
0.613790 | + | 0.789469i | \(0.289644\pi\) | |||||||
\(462\) | 0.0710912 | 0.00330746 | ||||||||
\(463\) | −22.3854 | −1.04034 | −0.520170 | − | 0.854063i | \(-0.674131\pi\) | ||||
−0.520170 | + | 0.854063i | \(0.674131\pi\) | |||||||
\(464\) | 21.6852 | 1.00671 | ||||||||
\(465\) | −0.182221 | −0.00845028 | ||||||||
\(466\) | 0.0633891 | 0.00293644 | ||||||||
\(467\) | −40.8398 | −1.88984 | −0.944920 | − | 0.327303i | \(-0.893860\pi\) | ||||
−0.944920 | + | 0.327303i | \(0.893860\pi\) | |||||||
\(468\) | −3.13457 | −0.144896 | ||||||||
\(469\) | −10.2786 | −0.474620 | ||||||||
\(470\) | 0.464962 | 0.0214471 | ||||||||
\(471\) | 19.2160 | 0.885428 | ||||||||
\(472\) | 0.0766058 | 0.00352607 | ||||||||
\(473\) | −1.58329 | −0.0727996 | ||||||||
\(474\) | −0.200317 | −0.00920085 | ||||||||
\(475\) | 29.1027 | 1.33532 | ||||||||
\(476\) | −3.10845 | −0.142475 | ||||||||
\(477\) | 3.41944 | 0.156566 | ||||||||
\(478\) | −0.00763786 | −0.000349348 0 | ||||||||
\(479\) | 24.9826 | 1.14149 | 0.570743 | − | 0.821129i | \(-0.306655\pi\) | ||||
0.570743 | + | 0.821129i | \(0.306655\pi\) | |||||||
\(480\) | 1.30983 | 0.0597853 | ||||||||
\(481\) | −17.0665 | −0.778166 | ||||||||
\(482\) | 0.0623886 | 0.00284172 | ||||||||
\(483\) | −24.3334 | −1.10721 | ||||||||
\(484\) | 18.7236 | 0.851073 | ||||||||
\(485\) | 15.4530 | 0.701685 | ||||||||
\(486\) | 0.0954047 | 0.00432764 | ||||||||
\(487\) | 14.8054 | 0.670898 | 0.335449 | − | 0.942058i | \(-0.391112\pi\) | ||||
0.335449 | + | 0.942058i | \(0.391112\pi\) | |||||||
\(488\) | −0.485194 | −0.0219637 | ||||||||
\(489\) | −7.88157 | −0.356417 | ||||||||
\(490\) | −0.268109 | −0.0121119 | ||||||||
\(491\) | −9.65823 | −0.435870 | −0.217935 | − | 0.975963i | \(-0.569932\pi\) | ||||
−0.217935 | + | 0.975963i | \(0.569932\pi\) | |||||||
\(492\) | −14.3628 | −0.647526 | ||||||||
\(493\) | −5.42429 | −0.244298 | ||||||||
\(494\) | −0.417398 | −0.0187796 | ||||||||
\(495\) | −1.89012 | −0.0849544 | ||||||||
\(496\) | 0.127797 | 0.00573825 | ||||||||
\(497\) | 1.63058 | 0.0731413 | ||||||||
\(498\) | 0.0997016 | 0.00446774 | ||||||||
\(499\) | 29.2660 | 1.31013 | 0.655063 | − | 0.755574i | \(-0.272642\pi\) | ||||
0.655063 | + | 0.755574i | \(0.272642\pi\) | |||||||
\(500\) | −4.10971 | −0.183792 | ||||||||
\(501\) | 38.5509 | 1.72233 | ||||||||
\(502\) | 0.477059 | 0.0212922 | ||||||||
\(503\) | 18.5421 | 0.826749 | 0.413375 | − | 0.910561i | \(-0.364350\pi\) | ||||
0.413375 | + | 0.910561i | \(0.364350\pi\) | |||||||
\(504\) | −0.0576124 | −0.00256626 | ||||||||
\(505\) | −11.2086 | −0.498777 | ||||||||
\(506\) | −0.205485 | −0.00913494 | ||||||||
\(507\) | −4.66874 | −0.207346 | ||||||||
\(508\) | −26.7898 | −1.18860 | ||||||||
\(509\) | 32.8543 | 1.45624 | 0.728120 | − | 0.685450i | \(-0.240395\pi\) | ||||
0.728120 | + | 0.685450i | \(0.240395\pi\) | |||||||
\(510\) | −0.109179 | −0.00483454 | ||||||||
\(511\) | −6.42871 | −0.284390 | ||||||||
\(512\) | −1.53113 | −0.0676672 | ||||||||
\(513\) | −31.5875 | −1.39462 | ||||||||
\(514\) | −0.434210 | −0.0191522 | ||||||||
\(515\) | −48.9314 | −2.15617 | ||||||||
\(516\) | 4.61935 | 0.203356 | ||||||||
\(517\) | 10.1686 | 0.447213 | ||||||||
\(518\) | −0.156824 | −0.00689045 | ||||||||
\(519\) | 7.53433 | 0.330720 | ||||||||
\(520\) | −0.758055 | −0.0332429 | ||||||||
\(521\) | 12.9195 | 0.566012 | 0.283006 | − | 0.959118i | \(-0.408668\pi\) | ||||
0.283006 | + | 0.959118i | \(0.408668\pi\) | |||||||
\(522\) | −0.0502627 | −0.00219994 | ||||||||
\(523\) | 30.3367 | 1.32653 | 0.663267 | − | 0.748383i | \(-0.269170\pi\) | ||||
0.663267 | + | 0.748383i | \(0.269170\pi\) | |||||||
\(524\) | −41.8137 | −1.82664 | ||||||||
\(525\) | −12.5548 | −0.547937 | ||||||||
\(526\) | −0.116454 | −0.00507763 | ||||||||
\(527\) | −0.0319668 | −0.00139250 | ||||||||
\(528\) | 9.54558 | 0.415418 | ||||||||
\(529\) | 47.3344 | 2.05802 | ||||||||
\(530\) | 0.413435 | 0.0179585 | ||||||||
\(531\) | 0.483795 | 0.0209949 | ||||||||
\(532\) | 20.9067 | 0.906421 | ||||||||
\(533\) | 12.4690 | 0.540091 | ||||||||
\(534\) | 0.153163 | 0.00662803 | ||||||||
\(535\) | 54.5529 | 2.35853 | ||||||||
\(536\) | 0.506525 | 0.0218786 | ||||||||
\(537\) | 48.4843 | 2.09225 | ||||||||
\(538\) | 0.0738926 | 0.00318574 | ||||||||
\(539\) | −5.86344 | −0.252556 | ||||||||
\(540\) | −28.6810 | −1.23423 | ||||||||
\(541\) | −12.0883 | −0.519717 | −0.259858 | − | 0.965647i | \(-0.583676\pi\) | ||||
−0.259858 | + | 0.965647i | \(0.583676\pi\) | |||||||
\(542\) | −0.00902100 | −0.000387485 0 | ||||||||
\(543\) | −14.1542 | −0.607417 | ||||||||
\(544\) | 0.229782 | 0.00985184 | ||||||||
\(545\) | −22.4893 | −0.963337 | ||||||||
\(546\) | 0.180064 | 0.00770604 | ||||||||
\(547\) | −27.1223 | −1.15967 | −0.579833 | − | 0.814736i | \(-0.696882\pi\) | ||||
−0.579833 | + | 0.814736i | \(0.696882\pi\) | |||||||
\(548\) | −1.27690 | −0.0545465 | ||||||||
\(549\) | −3.06419 | −0.130776 | ||||||||
\(550\) | −0.106020 | −0.00452071 | ||||||||
\(551\) | 36.4825 | 1.55421 | ||||||||
\(552\) | 1.19915 | 0.0510390 | ||||||||
\(553\) | −8.71049 | −0.370408 | ||||||||
\(554\) | 0.604222 | 0.0256709 | ||||||||
\(555\) | 30.0245 | 1.27447 | ||||||||
\(556\) | 18.9046 | 0.801734 | ||||||||
\(557\) | 27.1148 | 1.14889 | 0.574445 | − | 0.818543i | \(-0.305218\pi\) | ||||
0.574445 | + | 0.818543i | \(0.305218\pi\) | |||||||
\(558\) | −0.000296212 0 | −1.25396e−5 0 | ||||||||
\(559\) | −4.01025 | −0.169615 | ||||||||
\(560\) | 18.9796 | 0.802032 | ||||||||
\(561\) | −2.38771 | −0.100809 | ||||||||
\(562\) | −0.151215 | −0.00637861 | ||||||||
\(563\) | 13.3183 | 0.561299 | 0.280650 | − | 0.959810i | \(-0.409450\pi\) | ||||
0.280650 | + | 0.959810i | \(0.409450\pi\) | |||||||
\(564\) | −29.6675 | −1.24923 | ||||||||
\(565\) | 17.9258 | 0.754143 | ||||||||
\(566\) | 0.202567 | 0.00851454 | ||||||||
\(567\) | 15.8829 | 0.667020 | ||||||||
\(568\) | −0.0803544 | −0.00337160 | ||||||||
\(569\) | 26.0910 | 1.09379 | 0.546896 | − | 0.837200i | \(-0.315809\pi\) | ||||
0.546896 | + | 0.837200i | \(0.315809\pi\) | |||||||
\(570\) | 0.734315 | 0.0307571 | ||||||||
\(571\) | 27.7143 | 1.15981 | 0.579903 | − | 0.814685i | \(-0.303090\pi\) | ||||
0.579903 | + | 0.814685i | \(0.303090\pi\) | |||||||
\(572\) | −8.28843 | −0.346557 | ||||||||
\(573\) | −25.3778 | −1.06017 | ||||||||
\(574\) | 0.114577 | 0.00478236 | ||||||||
\(575\) | 36.2890 | 1.51336 | ||||||||
\(576\) | −3.86610 | −0.161088 | ||||||||
\(577\) | 32.2828 | 1.34395 | 0.671976 | − | 0.740573i | \(-0.265446\pi\) | ||||
0.671976 | + | 0.740573i | \(0.265446\pi\) | |||||||
\(578\) | −0.0191532 | −0.000796669 0 | ||||||||
\(579\) | −20.4109 | −0.848248 | ||||||||
\(580\) | 33.1257 | 1.37547 | ||||||||
\(581\) | 4.33538 | 0.179862 | ||||||||
\(582\) | 0.180888 | 0.00749804 | ||||||||
\(583\) | 9.04168 | 0.374468 | ||||||||
\(584\) | 0.316806 | 0.0131095 | ||||||||
\(585\) | −4.78740 | −0.197935 | ||||||||
\(586\) | 0.361117 | 0.0149176 | ||||||||
\(587\) | −30.3876 | −1.25423 | −0.627114 | − | 0.778927i | \(-0.715764\pi\) | ||||
−0.627114 | + | 0.778927i | \(0.715764\pi\) | |||||||
\(588\) | 17.1070 | 0.705481 | ||||||||
\(589\) | 0.215002 | 0.00885898 | ||||||||
\(590\) | 0.0584943 | 0.00240817 | ||||||||
\(591\) | 7.97528 | 0.328059 | ||||||||
\(592\) | −21.0571 | −0.865443 | ||||||||
\(593\) | −2.55216 | −0.104805 | −0.0524024 | − | 0.998626i | \(-0.516688\pi\) | ||||
−0.0524024 | + | 0.998626i | \(0.516688\pi\) | |||||||
\(594\) | 0.115072 | 0.00472146 | ||||||||
\(595\) | −4.74750 | −0.194629 | ||||||||
\(596\) | −26.6126 | −1.09010 | ||||||||
\(597\) | −4.54552 | −0.186036 | ||||||||
\(598\) | −0.520466 | −0.0212834 | ||||||||
\(599\) | −6.54443 | −0.267398 | −0.133699 | − | 0.991022i | \(-0.542686\pi\) | ||||
−0.133699 | + | 0.991022i | \(0.542686\pi\) | |||||||
\(600\) | 0.618699 | 0.0252583 | ||||||||
\(601\) | −31.2786 | −1.27588 | −0.637940 | − | 0.770086i | \(-0.720213\pi\) | ||||
−0.637940 | + | 0.770086i | \(0.720213\pi\) | |||||||
\(602\) | −0.0368501 | −0.00150190 | ||||||||
\(603\) | 3.19890 | 0.130269 | ||||||||
\(604\) | −24.4001 | −0.992828 | ||||||||
\(605\) | 28.5964 | 1.16261 | ||||||||
\(606\) | −0.131204 | −0.00532981 | ||||||||
\(607\) | −30.7224 | −1.24698 | −0.623492 | − | 0.781830i | \(-0.714286\pi\) | ||||
−0.623492 | + | 0.781830i | \(0.714286\pi\) | |||||||
\(608\) | −1.54546 | −0.0626768 | ||||||||
\(609\) | −15.7385 | −0.637754 | ||||||||
\(610\) | −0.370482 | −0.0150004 | ||||||||
\(611\) | 25.7556 | 1.04196 | ||||||||
\(612\) | 0.967412 | 0.0391053 | ||||||||
\(613\) | −5.41588 | −0.218745 | −0.109373 | − | 0.994001i | \(-0.534884\pi\) | ||||
−0.109373 | + | 0.994001i | \(0.534884\pi\) | |||||||
\(614\) | 0.363736 | 0.0146792 | ||||||||
\(615\) | −21.9362 | −0.884554 | ||||||||
\(616\) | −0.152339 | −0.00613790 | ||||||||
\(617\) | 2.64249 | 0.106382 | 0.0531912 | − | 0.998584i | \(-0.483061\pi\) | ||||
0.0531912 | + | 0.998584i | \(0.483061\pi\) | |||||||
\(618\) | −0.572774 | −0.0230404 | ||||||||
\(619\) | 47.3007 | 1.90117 | 0.950587 | − | 0.310459i | \(-0.100483\pi\) | ||||
0.950587 | + | 0.310459i | \(0.100483\pi\) | |||||||
\(620\) | 0.195219 | 0.00784017 | ||||||||
\(621\) | −39.3873 | −1.58056 | ||||||||
\(622\) | 0.113088 | 0.00453443 | ||||||||
\(623\) | 6.66009 | 0.266831 | ||||||||
\(624\) | 24.1776 | 0.967881 | ||||||||
\(625\) | −27.9119 | −1.11648 | ||||||||
\(626\) | 0.380168 | 0.0151946 | ||||||||
\(627\) | 16.0592 | 0.641342 | ||||||||
\(628\) | −20.5868 | −0.821501 | ||||||||
\(629\) | 5.26718 | 0.210016 | ||||||||
\(630\) | −0.0439914 | −0.00175266 | ||||||||
\(631\) | −35.1144 | −1.39788 | −0.698942 | − | 0.715178i | \(-0.746345\pi\) | ||||
−0.698942 | + | 0.715178i | \(0.746345\pi\) | |||||||
\(632\) | 0.429251 | 0.0170747 | ||||||||
\(633\) | 37.1118 | 1.47506 | ||||||||
\(634\) | 0.0555016 | 0.00220425 | ||||||||
\(635\) | −40.9158 | −1.62369 | ||||||||
\(636\) | −26.3797 | −1.04602 | ||||||||
\(637\) | −14.8513 | −0.588430 | ||||||||
\(638\) | −0.132904 | −0.00526174 | ||||||||
\(639\) | −0.507469 | −0.0200752 | ||||||||
\(640\) | −1.87096 | −0.0739562 | ||||||||
\(641\) | −32.5758 | −1.28667 | −0.643333 | − | 0.765587i | \(-0.722449\pi\) | ||||
−0.643333 | + | 0.765587i | \(0.722449\pi\) | |||||||
\(642\) | 0.638578 | 0.0252027 | ||||||||
\(643\) | −33.1924 | −1.30898 | −0.654489 | − | 0.756071i | \(-0.727116\pi\) | ||||
−0.654489 | + | 0.756071i | \(0.727116\pi\) | |||||||
\(644\) | 26.0692 | 1.02727 | ||||||||
\(645\) | 7.05509 | 0.277794 | ||||||||
\(646\) | 0.128820 | 0.00506836 | ||||||||
\(647\) | −37.6793 | −1.48133 | −0.740664 | − | 0.671876i | \(-0.765489\pi\) | ||||
−0.740664 | + | 0.671876i | \(0.765489\pi\) | |||||||
\(648\) | −0.782707 | −0.0307476 | ||||||||
\(649\) | 1.27925 | 0.0502149 | ||||||||
\(650\) | −0.268534 | −0.0105328 | ||||||||
\(651\) | −0.0927510 | −0.00363520 | ||||||||
\(652\) | 8.44377 | 0.330684 | ||||||||
\(653\) | 32.2777 | 1.26312 | 0.631562 | − | 0.775326i | \(-0.282414\pi\) | ||||
0.631562 | + | 0.775326i | \(0.282414\pi\) | |||||||
\(654\) | −0.263252 | −0.0102940 | ||||||||
\(655\) | −63.8616 | −2.49528 | ||||||||
\(656\) | 15.3845 | 0.600665 | ||||||||
\(657\) | 2.00075 | 0.0780566 | ||||||||
\(658\) | 0.236668 | 0.00922627 | ||||||||
\(659\) | −36.2590 | −1.41245 | −0.706225 | − | 0.707987i | \(-0.749603\pi\) | ||||
−0.706225 | + | 0.707987i | \(0.749603\pi\) | |||||||
\(660\) | 14.5816 | 0.567586 | ||||||||
\(661\) | −5.70626 | −0.221948 | −0.110974 | − | 0.993823i | \(-0.535397\pi\) | ||||
−0.110974 | + | 0.993823i | \(0.535397\pi\) | |||||||
\(662\) | 0.345392 | 0.0134240 | ||||||||
\(663\) | −6.04774 | −0.234875 | ||||||||
\(664\) | −0.213647 | −0.00829110 | ||||||||
\(665\) | 31.9306 | 1.23822 | ||||||||
\(666\) | 0.0488069 | 0.00189123 | ||||||||
\(667\) | 45.4911 | 1.76142 | ||||||||
\(668\) | −41.3008 | −1.59798 | ||||||||
\(669\) | −17.8749 | −0.691085 | ||||||||
\(670\) | 0.386770 | 0.0149422 | ||||||||
\(671\) | −8.10231 | −0.312786 | ||||||||
\(672\) | 0.666708 | 0.0257188 | ||||||||
\(673\) | 39.5766 | 1.52557 | 0.762783 | − | 0.646655i | \(-0.223833\pi\) | ||||
0.762783 | + | 0.646655i | \(0.223833\pi\) | |||||||
\(674\) | 0.351661 | 0.0135455 | ||||||||
\(675\) | −20.3219 | −0.782189 | ||||||||
\(676\) | 5.00177 | 0.192376 | ||||||||
\(677\) | −43.4891 | −1.67142 | −0.835711 | − | 0.549170i | \(-0.814944\pi\) | ||||
−0.835711 | + | 0.549170i | \(0.814944\pi\) | |||||||
\(678\) | 0.209833 | 0.00805859 | ||||||||
\(679\) | 7.86564 | 0.301856 | ||||||||
\(680\) | 0.233956 | 0.00897179 | ||||||||
\(681\) | 24.2565 | 0.929510 | ||||||||
\(682\) | −0.000783242 0 | −2.99919e−5 0 | ||||||||
\(683\) | 12.3529 | 0.472670 | 0.236335 | − | 0.971672i | \(-0.424054\pi\) | ||||
0.236335 | + | 0.971672i | \(0.424054\pi\) | |||||||
\(684\) | −6.50660 | −0.248786 | ||||||||
\(685\) | −1.95020 | −0.0745132 | ||||||||
\(686\) | −0.344885 | −0.0131678 | ||||||||
\(687\) | −28.8703 | −1.10147 | ||||||||
\(688\) | −4.94795 | −0.188639 | ||||||||
\(689\) | 22.9013 | 0.872471 | ||||||||
\(690\) | 0.915638 | 0.0348577 | ||||||||
\(691\) | −11.3531 | −0.431892 | −0.215946 | − | 0.976405i | \(-0.569284\pi\) | ||||
−0.215946 | + | 0.976405i | \(0.569284\pi\) | |||||||
\(692\) | −8.07177 | −0.306843 | ||||||||
\(693\) | −0.962076 | −0.0365463 | ||||||||
\(694\) | −0.332628 | −0.0126264 | ||||||||
\(695\) | 28.8728 | 1.09521 | ||||||||
\(696\) | 0.775588 | 0.0293986 | ||||||||
\(697\) | −3.84825 | −0.145763 | ||||||||
\(698\) | 0.203841 | 0.00771549 | ||||||||
\(699\) | −6.17731 | −0.233647 | ||||||||
\(700\) | 13.4504 | 0.508376 | ||||||||
\(701\) | 48.2615 | 1.82281 | 0.911406 | − | 0.411508i | \(-0.134998\pi\) | ||||
0.911406 | + | 0.411508i | \(0.134998\pi\) | |||||||
\(702\) | 0.291461 | 0.0110005 | ||||||||
\(703\) | −35.4259 | −1.33611 | ||||||||
\(704\) | −10.2227 | −0.385284 | ||||||||
\(705\) | −45.3109 | −1.70651 | ||||||||
\(706\) | −0.0285146 | −0.00107316 | ||||||||
\(707\) | −5.70523 | −0.214567 | ||||||||
\(708\) | −3.73230 | −0.140268 | ||||||||
\(709\) | 14.0407 | 0.527309 | 0.263654 | − | 0.964617i | \(-0.415072\pi\) | ||||
0.263654 | + | 0.964617i | \(0.415072\pi\) | |||||||
\(710\) | −0.0613566 | −0.00230267 | ||||||||
\(711\) | 2.71088 | 0.101666 | ||||||||
\(712\) | −0.328208 | −0.0123001 | ||||||||
\(713\) | 0.268092 | 0.0100401 | ||||||||
\(714\) | −0.0555726 | −0.00207975 | ||||||||
\(715\) | −12.6588 | −0.473414 | ||||||||
\(716\) | −51.9427 | −1.94119 | ||||||||
\(717\) | 0.744314 | 0.0277969 | ||||||||
\(718\) | 0.405249 | 0.0151238 | ||||||||
\(719\) | −47.0040 | −1.75295 | −0.876476 | − | 0.481445i | \(-0.840112\pi\) | ||||
−0.876476 | + | 0.481445i | \(0.840112\pi\) | |||||||
\(720\) | −5.90683 | −0.220134 | ||||||||
\(721\) | −24.9063 | −0.927558 | ||||||||
\(722\) | −0.502505 | −0.0187013 | ||||||||
\(723\) | −6.07981 | −0.226111 | ||||||||
\(724\) | 15.1639 | 0.563561 | ||||||||
\(725\) | 23.4711 | 0.871696 | ||||||||
\(726\) | 0.334740 | 0.0124234 | ||||||||
\(727\) | −14.5747 | −0.540545 | −0.270273 | − | 0.962784i | \(-0.587114\pi\) | ||||
−0.270273 | + | 0.962784i | \(0.587114\pi\) | |||||||
\(728\) | −0.385853 | −0.0143007 | ||||||||
\(729\) | 21.3547 | 0.790916 | ||||||||
\(730\) | 0.241905 | 0.00895330 | ||||||||
\(731\) | 1.23767 | 0.0457768 | ||||||||
\(732\) | 23.6391 | 0.873725 | ||||||||
\(733\) | 32.0936 | 1.18540 | 0.592701 | − | 0.805422i | \(-0.298061\pi\) | ||||
0.592701 | + | 0.805422i | \(0.298061\pi\) | |||||||
\(734\) | −0.286652 | −0.0105805 | ||||||||
\(735\) | 26.1274 | 0.963723 | ||||||||
\(736\) | −1.92708 | −0.0710333 | ||||||||
\(737\) | 8.45852 | 0.311574 | ||||||||
\(738\) | −0.0356588 | −0.00131262 | ||||||||
\(739\) | −20.7196 | −0.762182 | −0.381091 | − | 0.924537i | \(-0.624452\pi\) | ||||
−0.381091 | + | 0.924537i | \(0.624452\pi\) | |||||||
\(740\) | −32.1662 | −1.18245 | ||||||||
\(741\) | 40.6757 | 1.49426 | ||||||||
\(742\) | 0.210440 | 0.00772550 | ||||||||
\(743\) | −47.3465 | −1.73698 | −0.868488 | − | 0.495710i | \(-0.834908\pi\) | ||||
−0.868488 | + | 0.495710i | \(0.834908\pi\) | |||||||
\(744\) | 0.00457075 | 0.000167572 0 | ||||||||
\(745\) | −40.6452 | −1.48913 | ||||||||
\(746\) | 0.425614 | 0.0155828 | ||||||||
\(747\) | −1.34926 | −0.0493668 | ||||||||
\(748\) | 2.55803 | 0.0935308 | ||||||||
\(749\) | 27.7677 | 1.01461 | ||||||||
\(750\) | −0.0734731 | −0.00268286 | ||||||||
\(751\) | −32.0162 | −1.16829 | −0.584144 | − | 0.811650i | \(-0.698570\pi\) | ||||
−0.584144 | + | 0.811650i | \(0.698570\pi\) | |||||||
\(752\) | 31.7779 | 1.15882 | ||||||||
\(753\) | −46.4897 | −1.69418 | ||||||||
\(754\) | −0.336629 | −0.0122593 | ||||||||
\(755\) | −37.2661 | −1.35625 | ||||||||
\(756\) | −14.5988 | −0.530951 | ||||||||
\(757\) | −0.251509 | −0.00914126 | −0.00457063 | − | 0.999990i | \(-0.501455\pi\) | ||||
−0.00457063 | + | 0.999990i | \(0.501455\pi\) | |||||||
\(758\) | −0.0492662 | −0.00178943 | ||||||||
\(759\) | 20.0247 | 0.726850 | ||||||||
\(760\) | −1.57353 | −0.0570781 | ||||||||
\(761\) | 4.65013 | 0.168567 | 0.0842835 | − | 0.996442i | \(-0.473140\pi\) | ||||
0.0842835 | + | 0.996442i | \(0.473140\pi\) | |||||||
\(762\) | −0.478946 | −0.0173504 | ||||||||
\(763\) | −11.4472 | −0.414415 | ||||||||
\(764\) | 27.1881 | 0.983631 | ||||||||
\(765\) | 1.47752 | 0.0534198 | ||||||||
\(766\) | −0.648826 | −0.0234430 | ||||||||
\(767\) | 3.24016 | 0.116995 | ||||||||
\(768\) | 29.8091 | 1.07564 | ||||||||
\(769\) | 38.1782 | 1.37674 | 0.688371 | − | 0.725359i | \(-0.258326\pi\) | ||||
0.688371 | + | 0.725359i | \(0.258326\pi\) | |||||||
\(770\) | −0.116322 | −0.00419195 | ||||||||
\(771\) | 42.3140 | 1.52390 | ||||||||
\(772\) | 21.8669 | 0.787005 | ||||||||
\(773\) | 26.5983 | 0.956673 | 0.478337 | − | 0.878177i | \(-0.341240\pi\) | ||||
0.478337 | + | 0.878177i | \(0.341240\pi\) | |||||||
\(774\) | 0.0114685 | 0.000412227 0 | ||||||||
\(775\) | 0.138322 | 0.00496866 | ||||||||
\(776\) | −0.387617 | −0.0139146 | ||||||||
\(777\) | 15.2826 | 0.548261 | ||||||||
\(778\) | 0.437062 | 0.0156694 | ||||||||
\(779\) | 25.8825 | 0.927336 | ||||||||
\(780\) | 36.9331 | 1.32242 | ||||||||
\(781\) | −1.34185 | −0.0480151 | ||||||||
\(782\) | 0.160630 | 0.00574410 | ||||||||
\(783\) | −25.4751 | −0.910404 | ||||||||
\(784\) | −18.3239 | −0.654426 | ||||||||
\(785\) | −31.4420 | −1.12221 | ||||||||
\(786\) | −0.747543 | −0.0266640 | ||||||||
\(787\) | −44.3438 | −1.58069 | −0.790343 | − | 0.612665i | \(-0.790098\pi\) | ||||
−0.790343 | + | 0.612665i | \(0.790098\pi\) | |||||||
\(788\) | −8.54417 | −0.304374 | ||||||||
\(789\) | 11.3485 | 0.404017 | ||||||||
\(790\) | 0.327765 | 0.0116614 | ||||||||
\(791\) | 9.12429 | 0.324422 | ||||||||
\(792\) | 0.0474109 | 0.00168467 | ||||||||
\(793\) | −20.5221 | −0.728759 | ||||||||
\(794\) | 0.728482 | 0.0258528 | ||||||||
\(795\) | −40.2895 | −1.42892 | ||||||||
\(796\) | 4.86976 | 0.172604 | ||||||||
\(797\) | 19.6861 | 0.697318 | 0.348659 | − | 0.937250i | \(-0.386637\pi\) | ||||
0.348659 | + | 0.937250i | \(0.386637\pi\) | |||||||
\(798\) | 0.373769 | 0.0132313 | ||||||||
\(799\) | −7.94885 | −0.281210 | ||||||||
\(800\) | −0.994278 | −0.0351530 | ||||||||
\(801\) | −2.07276 | −0.0732373 | ||||||||
\(802\) | 0.0408072 | 0.00144095 | ||||||||
\(803\) | 5.29037 | 0.186693 | ||||||||
\(804\) | −24.6783 | −0.870338 | ||||||||
\(805\) | 39.8152 | 1.40330 | ||||||||
\(806\) | −0.00198384 | −6.98780e−5 0 | ||||||||
\(807\) | −7.20088 | −0.253483 | ||||||||
\(808\) | 0.281152 | 0.00989091 | ||||||||
\(809\) | 18.9912 | 0.667695 | 0.333848 | − | 0.942627i | \(-0.391653\pi\) | ||||
0.333848 | + | 0.942627i | \(0.391653\pi\) | |||||||
\(810\) | −0.597655 | −0.0209995 | ||||||||
\(811\) | −26.4131 | −0.927488 | −0.463744 | − | 0.885969i | \(-0.653494\pi\) | ||||
−0.463744 | + | 0.885969i | \(0.653494\pi\) | |||||||
\(812\) | 16.8611 | 0.591709 | ||||||||
\(813\) | 0.879103 | 0.0308315 | ||||||||
\(814\) | 0.129055 | 0.00452338 | ||||||||
\(815\) | 12.8961 | 0.451731 | ||||||||
\(816\) | −7.46186 | −0.261217 | ||||||||
\(817\) | −8.32428 | −0.291230 | ||||||||
\(818\) | −0.656282 | −0.0229464 | ||||||||
\(819\) | −2.43681 | −0.0851489 | ||||||||
\(820\) | 23.5010 | 0.820689 | ||||||||
\(821\) | 7.22225 | 0.252058 | 0.126029 | − | 0.992027i | \(-0.459777\pi\) | ||||
0.126029 | + | 0.992027i | \(0.459777\pi\) | |||||||
\(822\) | −0.0228284 | −0.000796230 0 | ||||||||
\(823\) | −23.0573 | −0.803728 | −0.401864 | − | 0.915699i | \(-0.631638\pi\) | ||||
−0.401864 | + | 0.915699i | \(0.631638\pi\) | |||||||
\(824\) | 1.22737 | 0.0427576 | ||||||||
\(825\) | 10.3317 | 0.359704 | ||||||||
\(826\) | 0.0297738 | 0.00103596 | ||||||||
\(827\) | 43.0813 | 1.49808 | 0.749042 | − | 0.662523i | \(-0.230514\pi\) | ||||
0.749042 | + | 0.662523i | \(0.230514\pi\) | |||||||
\(828\) | −8.11327 | −0.281955 | ||||||||
\(829\) | 33.1999 | 1.15308 | 0.576539 | − | 0.817069i | \(-0.304403\pi\) | ||||
0.576539 | + | 0.817069i | \(0.304403\pi\) | |||||||
\(830\) | −0.163135 | −0.00566251 | ||||||||
\(831\) | −58.8818 | −2.04259 | ||||||||
\(832\) | −25.8928 | −0.897671 | ||||||||
\(833\) | 4.58350 | 0.158809 | ||||||||
\(834\) | 0.337975 | 0.0117031 | ||||||||
\(835\) | −63.0783 | −2.18292 | ||||||||
\(836\) | −17.2047 | −0.595038 | ||||||||
\(837\) | −0.150131 | −0.00518930 | ||||||||
\(838\) | 0.238608 | 0.00824258 | ||||||||
\(839\) | −48.6889 | −1.68093 | −0.840463 | − | 0.541869i | \(-0.817717\pi\) | ||||
−0.840463 | + | 0.541869i | \(0.817717\pi\) | |||||||
\(840\) | 0.678818 | 0.0234214 | ||||||||
\(841\) | 0.422909 | 0.0145831 | ||||||||
\(842\) | 0.120504 | 0.00415285 | ||||||||
\(843\) | 14.7360 | 0.507534 | ||||||||
\(844\) | −39.7591 | −1.36856 | ||||||||
\(845\) | 7.63916 | 0.262795 | ||||||||
\(846\) | −0.0736558 | −0.00253234 | ||||||||
\(847\) | 14.5557 | 0.500139 | ||||||||
\(848\) | 28.2563 | 0.970325 | ||||||||
\(849\) | −19.7403 | −0.677486 | ||||||||
\(850\) | 0.0828767 | 0.00284265 | ||||||||
\(851\) | −44.1735 | −1.51425 | ||||||||
\(852\) | 3.91493 | 0.134123 | ||||||||
\(853\) | 33.3026 | 1.14026 | 0.570129 | − | 0.821555i | \(-0.306893\pi\) | ||||
0.570129 | + | 0.821555i | \(0.306893\pi\) | |||||||
\(854\) | −0.188577 | −0.00645297 | ||||||||
\(855\) | −9.93746 | −0.339854 | ||||||||
\(856\) | −1.36838 | −0.0467704 | ||||||||
\(857\) | −10.6484 | −0.363742 | −0.181871 | − | 0.983322i | \(-0.558215\pi\) | ||||
−0.181871 | + | 0.983322i | \(0.558215\pi\) | |||||||
\(858\) | −0.148180 | −0.00505879 | ||||||||
\(859\) | 37.4215 | 1.27681 | 0.638403 | − | 0.769702i | \(-0.279595\pi\) | ||||
0.638403 | + | 0.769702i | \(0.279595\pi\) | |||||||
\(860\) | −7.55835 | −0.257737 | ||||||||
\(861\) | −11.1656 | −0.380523 | ||||||||
\(862\) | −0.659824 | −0.0224737 | ||||||||
\(863\) | 13.6271 | 0.463872 | 0.231936 | − | 0.972731i | \(-0.425494\pi\) | ||||
0.231936 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(864\) | 1.07917 | 0.0367140 | ||||||||
\(865\) | −12.3279 | −0.419162 | ||||||||
\(866\) | −0.232067 | −0.00788594 | ||||||||
\(867\) | 1.86649 | 0.0633894 | ||||||||
\(868\) | 0.0993671 | 0.00337274 | ||||||||
\(869\) | 7.16811 | 0.243161 | ||||||||
\(870\) | 0.592219 | 0.0200781 | ||||||||
\(871\) | 21.4243 | 0.725934 | ||||||||
\(872\) | 0.564113 | 0.0191033 | ||||||||
\(873\) | −2.44795 | −0.0828505 | ||||||||
\(874\) | −1.08036 | −0.0365437 | ||||||||
\(875\) | −3.19487 | −0.108006 | ||||||||
\(876\) | −15.4350 | −0.521502 | ||||||||
\(877\) | 3.20321 | 0.108165 | 0.0540823 | − | 0.998536i | \(-0.482777\pi\) | ||||
0.0540823 | + | 0.998536i | \(0.482777\pi\) | |||||||
\(878\) | 0.481896 | 0.0162632 | ||||||||
\(879\) | −35.1911 | −1.18697 | ||||||||
\(880\) | −15.6188 | −0.526510 | ||||||||
\(881\) | −33.8961 | −1.14199 | −0.570994 | − | 0.820954i | \(-0.693442\pi\) | ||||
−0.570994 | + | 0.820954i | \(0.693442\pi\) | |||||||
\(882\) | 0.0424718 | 0.00143010 | ||||||||
\(883\) | 44.2816 | 1.49019 | 0.745097 | − | 0.666956i | \(-0.232403\pi\) | ||||
0.745097 | + | 0.666956i | \(0.232403\pi\) | |||||||
\(884\) | 6.47914 | 0.217917 | ||||||||
\(885\) | −5.70031 | −0.191614 | ||||||||
\(886\) | 0.361894 | 0.0121581 | ||||||||
\(887\) | 3.37449 | 0.113304 | 0.0566521 | − | 0.998394i | \(-0.481957\pi\) | ||||
0.0566521 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(888\) | −0.753123 | −0.0252732 | ||||||||
\(889\) | −20.8263 | −0.698491 | ||||||||
\(890\) | −0.250611 | −0.00840051 | ||||||||
\(891\) | −13.0705 | −0.437879 | ||||||||
\(892\) | 19.1500 | 0.641189 | ||||||||
\(893\) | 53.4622 | 1.78904 | ||||||||
\(894\) | −0.475779 | −0.0159124 | ||||||||
\(895\) | −79.3316 | −2.65176 | ||||||||
\(896\) | −0.952326 | −0.0318150 | ||||||||
\(897\) | 50.7198 | 1.69348 | ||||||||
\(898\) | 0.426361 | 0.0142278 | ||||||||
\(899\) | 0.173397 | 0.00578312 | ||||||||
\(900\) | −4.18603 | −0.139534 | ||||||||
\(901\) | −7.06796 | −0.235468 | ||||||||
\(902\) | −0.0942888 | −0.00313947 | ||||||||
\(903\) | 3.59107 | 0.119503 | ||||||||
\(904\) | −0.449643 | −0.0149549 | ||||||||
\(905\) | 23.1597 | 0.769853 | ||||||||
\(906\) | −0.436224 | −0.0144926 | ||||||||
\(907\) | 4.18661 | 0.139014 | 0.0695070 | − | 0.997581i | \(-0.477857\pi\) | ||||
0.0695070 | + | 0.997581i | \(0.477857\pi\) | |||||||
\(908\) | −25.9867 | −0.862400 | ||||||||
\(909\) | 1.77559 | 0.0588924 | ||||||||
\(910\) | −0.294628 | −0.00976681 | ||||||||
\(911\) | −27.0651 | −0.896706 | −0.448353 | − | 0.893857i | \(-0.647989\pi\) | ||||
−0.448353 | + | 0.893857i | \(0.647989\pi\) | |||||||
\(912\) | 50.1868 | 1.66185 | ||||||||
\(913\) | −3.56771 | −0.118074 | ||||||||
\(914\) | −0.0554960 | −0.00183565 | ||||||||
\(915\) | 36.1037 | 1.19355 | ||||||||
\(916\) | 30.9297 | 1.02195 | ||||||||
\(917\) | −32.5058 | −1.07344 | ||||||||
\(918\) | −0.0899526 | −0.00296888 | ||||||||
\(919\) | −34.6546 | −1.14315 | −0.571575 | − | 0.820550i | \(-0.693668\pi\) | ||||
−0.571575 | + | 0.820550i | \(0.693668\pi\) | |||||||
\(920\) | −1.96208 | −0.0646880 | ||||||||
\(921\) | −35.4463 | −1.16800 | ||||||||
\(922\) | −0.504826 | −0.0166256 | ||||||||
\(923\) | −3.39871 | −0.111870 | ||||||||
\(924\) | 7.42207 | 0.244168 | ||||||||
\(925\) | −22.7913 | −0.749373 | ||||||||
\(926\) | 0.428753 | 0.0140897 | ||||||||
\(927\) | 7.75134 | 0.254587 | ||||||||
\(928\) | −1.24641 | −0.0409153 | ||||||||
\(929\) | 19.6352 | 0.644211 | 0.322105 | − | 0.946704i | \(-0.395609\pi\) | ||||
0.322105 | + | 0.946704i | \(0.395609\pi\) | |||||||
\(930\) | 0.00349011 | 0.000114445 0 | ||||||||
\(931\) | −30.8276 | −1.01033 | ||||||||
\(932\) | 6.61795 | 0.216778 | ||||||||
\(933\) | −11.0205 | −0.360796 | ||||||||
\(934\) | 0.782213 | 0.0255948 | ||||||||
\(935\) | 3.90685 | 0.127768 | ||||||||
\(936\) | 0.120085 | 0.00392511 | ||||||||
\(937\) | 28.0019 | 0.914783 | 0.457392 | − | 0.889265i | \(-0.348784\pi\) | ||||
0.457392 | + | 0.889265i | \(0.348784\pi\) | |||||||
\(938\) | 0.196867 | 0.00642795 | ||||||||
\(939\) | −37.0476 | −1.20900 | ||||||||
\(940\) | 48.5430 | 1.58330 | ||||||||
\(941\) | 3.62509 | 0.118175 | 0.0590873 | − | 0.998253i | \(-0.481181\pi\) | ||||
0.0590873 | + | 0.998253i | \(0.481181\pi\) | |||||||
\(942\) | −0.368049 | −0.0119917 | ||||||||
\(943\) | 32.2736 | 1.05097 | ||||||||
\(944\) | 3.99780 | 0.130117 | ||||||||
\(945\) | −22.2965 | −0.725306 | ||||||||
\(946\) | 0.0303250 | 0.000985952 0 | ||||||||
\(947\) | −9.48566 | −0.308243 | −0.154121 | − | 0.988052i | \(-0.549255\pi\) | ||||
−0.154121 | + | 0.988052i | \(0.549255\pi\) | |||||||
\(948\) | −20.9135 | −0.679238 | ||||||||
\(949\) | 13.3998 | 0.434975 | ||||||||
\(950\) | −0.557410 | −0.0180848 | ||||||||
\(951\) | −5.40866 | −0.175388 | ||||||||
\(952\) | 0.119084 | 0.00385955 | ||||||||
\(953\) | −12.6228 | −0.408894 | −0.204447 | − | 0.978878i | \(-0.565540\pi\) | ||||
−0.204447 | + | 0.978878i | \(0.565540\pi\) | |||||||
\(954\) | −0.0654933 | −0.00212042 | ||||||||
\(955\) | 41.5241 | 1.34369 | ||||||||
\(956\) | −0.797408 | −0.0257900 | ||||||||
\(957\) | 12.9516 | 0.418667 | ||||||||
\(958\) | −0.478498 | −0.0154596 | ||||||||
\(959\) | −0.992658 | −0.0320546 | ||||||||
\(960\) | 45.5523 | 1.47019 | ||||||||
\(961\) | −30.9990 | −0.999967 | ||||||||
\(962\) | 0.326879 | 0.0105390 | ||||||||
\(963\) | −8.64186 | −0.278480 | ||||||||
\(964\) | 6.51349 | 0.209785 | ||||||||
\(965\) | 33.3970 | 1.07509 | ||||||||
\(966\) | 0.466063 | 0.0149953 | ||||||||
\(967\) | 23.8248 | 0.766153 | 0.383077 | − | 0.923717i | \(-0.374865\pi\) | ||||
0.383077 | + | 0.923717i | \(0.374865\pi\) | |||||||
\(968\) | −0.717300 | −0.0230549 | ||||||||
\(969\) | −12.5536 | −0.403280 | ||||||||
\(970\) | −0.295975 | −0.00950318 | ||||||||
\(971\) | 29.7437 | 0.954519 | 0.477260 | − | 0.878762i | \(-0.341630\pi\) | ||||
0.477260 | + | 0.878762i | \(0.341630\pi\) | |||||||
\(972\) | 9.96044 | 0.319481 | ||||||||
\(973\) | 14.6964 | 0.471144 | ||||||||
\(974\) | −0.283572 | −0.00908622 | ||||||||
\(975\) | 26.1688 | 0.838073 | ||||||||
\(976\) | −25.3207 | −0.810494 | ||||||||
\(977\) | 58.8180 | 1.88175 | 0.940877 | − | 0.338747i | \(-0.110003\pi\) | ||||
0.940877 | + | 0.338747i | \(0.110003\pi\) | |||||||
\(978\) | 0.150957 | 0.00482708 | ||||||||
\(979\) | −5.48078 | −0.175166 | ||||||||
\(980\) | −27.9911 | −0.894143 | ||||||||
\(981\) | 3.56259 | 0.113745 | ||||||||
\(982\) | 0.184986 | 0.00590314 | ||||||||
\(983\) | 53.6016 | 1.70963 | 0.854813 | − | 0.518936i | \(-0.173672\pi\) | ||||
0.854813 | + | 0.518936i | \(0.173672\pi\) | |||||||
\(984\) | 0.550239 | 0.0175410 | ||||||||
\(985\) | −13.0494 | −0.415790 | ||||||||
\(986\) | 0.103893 | 0.00330861 | ||||||||
\(987\) | −23.0634 | −0.734117 | ||||||||
\(988\) | −43.5772 | −1.38638 | ||||||||
\(989\) | −10.3798 | −0.330058 | ||||||||
\(990\) | 0.0362018 | 0.00115057 | ||||||||
\(991\) | −29.3965 | −0.933811 | −0.466905 | − | 0.884307i | \(-0.654631\pi\) | ||||
−0.466905 | + | 0.884307i | \(0.654631\pi\) | |||||||
\(992\) | −0.00734541 | −0.000233217 0 | ||||||||
\(993\) | −33.6586 | −1.06812 | ||||||||
\(994\) | −0.0312308 | −0.000990580 0 | ||||||||
\(995\) | 7.43754 | 0.235786 | ||||||||
\(996\) | 10.4090 | 0.329823 | ||||||||
\(997\) | −22.9518 | −0.726890 | −0.363445 | − | 0.931616i | \(-0.618400\pi\) | ||||
−0.363445 | + | 0.931616i | \(0.618400\pi\) | |||||||
\(998\) | −0.560538 | −0.0177435 | ||||||||
\(999\) | 24.7372 | 0.782650 |
(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 | 1003.2.a.j.1.10 | ✓ | 22 | |
3.2 | odd | 2 | 9027.2.a.s.1.13 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.j.1.10 | ✓ | 22 | 1.1 | even | 1 | trivial | |
9027.2.a.s.1.13 | 22 | 3.2 | odd | 2 |