Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8045,2,Mod(1,8045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8045, 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("8045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8045 = 5 \cdot 1609 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8045.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: | \(64.2396484261\) |
Analytic rank: | \(1\) |
Dimension: | \(127\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49863 | −1.76680 | −0.883400 | − | 0.468620i | \(-0.844751\pi\) | ||||
−0.883400 | + | 0.468620i | \(0.844751\pi\) | |||||||
\(3\) | 2.41476 | 1.39416 | 0.697082 | − | 0.716991i | \(-0.254481\pi\) | ||||
0.697082 | + | 0.716991i | \(0.254481\pi\) | |||||||
\(4\) | 4.24316 | 2.12158 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −6.03361 | −2.46321 | ||||||||
\(7\) | 1.44699 | 0.546911 | 0.273456 | − | 0.961885i | \(-0.411833\pi\) | ||||
0.273456 | + | 0.961885i | \(0.411833\pi\) | |||||||
\(8\) | −5.60483 | −1.98161 | ||||||||
\(9\) | 2.83108 | 0.943695 | ||||||||
\(10\) | −2.49863 | −0.790137 | ||||||||
\(11\) | −2.48494 | −0.749238 | −0.374619 | − | 0.927179i | \(-0.622226\pi\) | ||||
−0.374619 | + | 0.927179i | \(0.622226\pi\) | |||||||
\(12\) | 10.2462 | 2.95783 | ||||||||
\(13\) | −5.50824 | −1.52771 | −0.763855 | − | 0.645388i | \(-0.776696\pi\) | ||||
−0.763855 | + | 0.645388i | \(0.776696\pi\) | |||||||
\(14\) | −3.61550 | −0.966282 | ||||||||
\(15\) | 2.41476 | 0.623489 | ||||||||
\(16\) | 5.51809 | 1.37952 | ||||||||
\(17\) | 1.30802 | 0.317241 | 0.158620 | − | 0.987340i | \(-0.449295\pi\) | ||||
0.158620 | + | 0.987340i | \(0.449295\pi\) | |||||||
\(18\) | −7.07384 | −1.66732 | ||||||||
\(19\) | 7.78323 | 1.78560 | 0.892798 | − | 0.450457i | \(-0.148739\pi\) | ||||
0.892798 | + | 0.450457i | \(0.148739\pi\) | |||||||
\(20\) | 4.24316 | 0.948799 | ||||||||
\(21\) | 3.49414 | 0.762484 | ||||||||
\(22\) | 6.20895 | 1.32375 | ||||||||
\(23\) | −4.73454 | −0.987220 | −0.493610 | − | 0.869683i | \(-0.664323\pi\) | ||||
−0.493610 | + | 0.869683i | \(0.664323\pi\) | |||||||
\(24\) | −13.5343 | −2.76269 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 13.7631 | 2.69916 | ||||||||
\(27\) | −0.407891 | −0.0784987 | ||||||||
\(28\) | 6.13981 | 1.16032 | ||||||||
\(29\) | 3.55204 | 0.659597 | 0.329798 | − | 0.944051i | \(-0.393019\pi\) | ||||
0.329798 | + | 0.944051i | \(0.393019\pi\) | |||||||
\(30\) | −6.03361 | −1.10158 | ||||||||
\(31\) | 0.736339 | 0.132250 | 0.0661252 | − | 0.997811i | \(-0.478936\pi\) | ||||
0.0661252 | + | 0.997811i | \(0.478936\pi\) | |||||||
\(32\) | −2.57800 | −0.455731 | ||||||||
\(33\) | −6.00055 | −1.04456 | ||||||||
\(34\) | −3.26825 | −0.560501 | ||||||||
\(35\) | 1.44699 | 0.244586 | ||||||||
\(36\) | 12.0127 | 2.00212 | ||||||||
\(37\) | −8.95720 | −1.47255 | −0.736277 | − | 0.676680i | \(-0.763418\pi\) | ||||
−0.736277 | + | 0.676680i | \(0.763418\pi\) | |||||||
\(38\) | −19.4474 | −3.15479 | ||||||||
\(39\) | −13.3011 | −2.12988 | ||||||||
\(40\) | −5.60483 | −0.886201 | ||||||||
\(41\) | 1.00361 | 0.156738 | 0.0783689 | − | 0.996924i | \(-0.475029\pi\) | ||||
0.0783689 | + | 0.996924i | \(0.475029\pi\) | |||||||
\(42\) | −8.73057 | −1.34716 | ||||||||
\(43\) | −10.8969 | −1.66176 | −0.830880 | − | 0.556452i | \(-0.812162\pi\) | ||||
−0.830880 | + | 0.556452i | \(0.812162\pi\) | |||||||
\(44\) | −10.5440 | −1.58957 | ||||||||
\(45\) | 2.83108 | 0.422033 | ||||||||
\(46\) | 11.8299 | 1.74422 | ||||||||
\(47\) | 3.12224 | 0.455425 | 0.227713 | − | 0.973728i | \(-0.426875\pi\) | ||||
0.227713 | + | 0.973728i | \(0.426875\pi\) | |||||||
\(48\) | 13.3249 | 1.92328 | ||||||||
\(49\) | −4.90622 | −0.700888 | ||||||||
\(50\) | −2.49863 | −0.353360 | ||||||||
\(51\) | 3.15855 | 0.442286 | ||||||||
\(52\) | −23.3723 | −3.24116 | ||||||||
\(53\) | −11.6301 | −1.59752 | −0.798761 | − | 0.601649i | \(-0.794511\pi\) | ||||
−0.798761 | + | 0.601649i | \(0.794511\pi\) | |||||||
\(54\) | 1.01917 | 0.138691 | ||||||||
\(55\) | −2.48494 | −0.335069 | ||||||||
\(56\) | −8.11014 | −1.08376 | ||||||||
\(57\) | 18.7947 | 2.48942 | ||||||||
\(58\) | −8.87523 | −1.16537 | ||||||||
\(59\) | 0.923057 | 0.120172 | 0.0600859 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600859 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(60\) | 10.2462 | 1.32278 | ||||||||
\(61\) | −9.46226 | −1.21152 | −0.605759 | − | 0.795648i | \(-0.707131\pi\) | ||||
−0.605759 | + | 0.795648i | \(0.707131\pi\) | |||||||
\(62\) | −1.83984 | −0.233660 | ||||||||
\(63\) | 4.09655 | 0.516117 | ||||||||
\(64\) | −4.59469 | −0.574336 | ||||||||
\(65\) | −5.50824 | −0.683213 | ||||||||
\(66\) | 14.9932 | 1.84553 | ||||||||
\(67\) | −3.31802 | −0.405361 | −0.202680 | − | 0.979245i | \(-0.564965\pi\) | ||||
−0.202680 | + | 0.979245i | \(0.564965\pi\) | |||||||
\(68\) | 5.55012 | 0.673051 | ||||||||
\(69\) | −11.4328 | −1.37635 | ||||||||
\(70\) | −3.61550 | −0.432134 | ||||||||
\(71\) | 10.2493 | 1.21637 | 0.608183 | − | 0.793797i | \(-0.291899\pi\) | ||||
0.608183 | + | 0.793797i | \(0.291899\pi\) | |||||||
\(72\) | −15.8677 | −1.87003 | ||||||||
\(73\) | −7.50674 | −0.878597 | −0.439298 | − | 0.898341i | \(-0.644773\pi\) | ||||
−0.439298 | + | 0.898341i | \(0.644773\pi\) | |||||||
\(74\) | 22.3807 | 2.60171 | ||||||||
\(75\) | 2.41476 | 0.278833 | ||||||||
\(76\) | 33.0255 | 3.78829 | ||||||||
\(77\) | −3.59569 | −0.409767 | ||||||||
\(78\) | 33.2345 | 3.76307 | ||||||||
\(79\) | 4.07064 | 0.457983 | 0.228991 | − | 0.973428i | \(-0.426457\pi\) | ||||
0.228991 | + | 0.973428i | \(0.426457\pi\) | |||||||
\(80\) | 5.51809 | 0.616941 | ||||||||
\(81\) | −9.47821 | −1.05313 | ||||||||
\(82\) | −2.50765 | −0.276924 | ||||||||
\(83\) | 8.23799 | 0.904236 | 0.452118 | − | 0.891958i | \(-0.350669\pi\) | ||||
0.452118 | + | 0.891958i | \(0.350669\pi\) | |||||||
\(84\) | 14.8262 | 1.61767 | ||||||||
\(85\) | 1.30802 | 0.141874 | ||||||||
\(86\) | 27.2273 | 2.93600 | ||||||||
\(87\) | 8.57733 | 0.919586 | ||||||||
\(88\) | 13.9277 | 1.48470 | ||||||||
\(89\) | −4.44209 | −0.470861 | −0.235431 | − | 0.971891i | \(-0.575650\pi\) | ||||
−0.235431 | + | 0.971891i | \(0.575650\pi\) | |||||||
\(90\) | −7.07384 | −0.745648 | ||||||||
\(91\) | −7.97037 | −0.835522 | ||||||||
\(92\) | −20.0894 | −2.09447 | ||||||||
\(93\) | 1.77808 | 0.184379 | ||||||||
\(94\) | −7.80132 | −0.804645 | ||||||||
\(95\) | 7.78323 | 0.798543 | ||||||||
\(96\) | −6.22527 | −0.635364 | ||||||||
\(97\) | 4.92639 | 0.500199 | 0.250100 | − | 0.968220i | \(-0.419537\pi\) | ||||
0.250100 | + | 0.968220i | \(0.419537\pi\) | |||||||
\(98\) | 12.2588 | 1.23833 | ||||||||
\(99\) | −7.03508 | −0.707052 | ||||||||
\(100\) | 4.24316 | 0.424316 | ||||||||
\(101\) | −9.94164 | −0.989230 | −0.494615 | − | 0.869112i | \(-0.664691\pi\) | ||||
−0.494615 | + | 0.869112i | \(0.664691\pi\) | |||||||
\(102\) | −7.89206 | −0.781430 | ||||||||
\(103\) | 5.84798 | 0.576219 | 0.288110 | − | 0.957597i | \(-0.406973\pi\) | ||||
0.288110 | + | 0.957597i | \(0.406973\pi\) | |||||||
\(104\) | 30.8727 | 3.02732 | ||||||||
\(105\) | 3.49414 | 0.340993 | ||||||||
\(106\) | 29.0594 | 2.82250 | ||||||||
\(107\) | 8.68309 | 0.839426 | 0.419713 | − | 0.907657i | \(-0.362131\pi\) | ||||
0.419713 | + | 0.907657i | \(0.362131\pi\) | |||||||
\(108\) | −1.73075 | −0.166541 | ||||||||
\(109\) | −19.6761 | −1.88463 | −0.942313 | − | 0.334733i | \(-0.891354\pi\) | ||||
−0.942313 | + | 0.334733i | \(0.891354\pi\) | |||||||
\(110\) | 6.20895 | 0.592000 | ||||||||
\(111\) | −21.6295 | −2.05298 | ||||||||
\(112\) | 7.98462 | 0.754476 | ||||||||
\(113\) | −11.2022 | −1.05381 | −0.526905 | − | 0.849924i | \(-0.676648\pi\) | ||||
−0.526905 | + | 0.849924i | \(0.676648\pi\) | |||||||
\(114\) | −46.9610 | −4.39830 | ||||||||
\(115\) | −4.73454 | −0.441498 | ||||||||
\(116\) | 15.0719 | 1.39939 | ||||||||
\(117\) | −15.5943 | −1.44169 | ||||||||
\(118\) | −2.30638 | −0.212320 | ||||||||
\(119\) | 1.89269 | 0.173502 | ||||||||
\(120\) | −13.5343 | −1.23551 | ||||||||
\(121\) | −4.82507 | −0.438642 | ||||||||
\(122\) | 23.6427 | 2.14051 | ||||||||
\(123\) | 2.42348 | 0.218518 | ||||||||
\(124\) | 3.12440 | 0.280580 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −10.2358 | −0.911875 | ||||||||
\(127\) | 13.8649 | 1.23031 | 0.615155 | − | 0.788406i | \(-0.289094\pi\) | ||||
0.615155 | + | 0.788406i | \(0.289094\pi\) | |||||||
\(128\) | 16.6364 | 1.47047 | ||||||||
\(129\) | −26.3134 | −2.31677 | ||||||||
\(130\) | 13.7631 | 1.20710 | ||||||||
\(131\) | 12.5570 | 1.09711 | 0.548555 | − | 0.836114i | \(-0.315178\pi\) | ||||
0.548555 | + | 0.836114i | \(0.315178\pi\) | |||||||
\(132\) | −25.4613 | −2.21612 | ||||||||
\(133\) | 11.2623 | 0.976562 | ||||||||
\(134\) | 8.29052 | 0.716191 | ||||||||
\(135\) | −0.407891 | −0.0351057 | ||||||||
\(136\) | −7.33121 | −0.628646 | ||||||||
\(137\) | −1.25640 | −0.107342 | −0.0536709 | − | 0.998559i | \(-0.517092\pi\) | ||||
−0.0536709 | + | 0.998559i | \(0.517092\pi\) | |||||||
\(138\) | 28.5664 | 2.43173 | ||||||||
\(139\) | −14.3477 | −1.21696 | −0.608480 | − | 0.793569i | \(-0.708220\pi\) | ||||
−0.608480 | + | 0.793569i | \(0.708220\pi\) | |||||||
\(140\) | 6.13981 | 0.518909 | ||||||||
\(141\) | 7.53947 | 0.634938 | ||||||||
\(142\) | −25.6092 | −2.14908 | ||||||||
\(143\) | 13.6877 | 1.14462 | ||||||||
\(144\) | 15.6222 | 1.30185 | ||||||||
\(145\) | 3.55204 | 0.294981 | ||||||||
\(146\) | 18.7566 | 1.55230 | ||||||||
\(147\) | −11.8474 | −0.977154 | ||||||||
\(148\) | −38.0068 | −3.12414 | ||||||||
\(149\) | 1.37793 | 0.112884 | 0.0564422 | − | 0.998406i | \(-0.482024\pi\) | ||||
0.0564422 | + | 0.998406i | \(0.482024\pi\) | |||||||
\(150\) | −6.03361 | −0.492642 | ||||||||
\(151\) | −6.34924 | −0.516693 | −0.258347 | − | 0.966052i | \(-0.583178\pi\) | ||||
−0.258347 | + | 0.966052i | \(0.583178\pi\) | |||||||
\(152\) | −43.6237 | −3.53835 | ||||||||
\(153\) | 3.70311 | 0.299378 | ||||||||
\(154\) | 8.98430 | 0.723975 | ||||||||
\(155\) | 0.736339 | 0.0591441 | ||||||||
\(156\) | −56.4387 | −4.51871 | ||||||||
\(157\) | 1.26479 | 0.100942 | 0.0504708 | − | 0.998726i | \(-0.483928\pi\) | ||||
0.0504708 | + | 0.998726i | \(0.483928\pi\) | |||||||
\(158\) | −10.1710 | −0.809163 | ||||||||
\(159\) | −28.0840 | −2.22721 | ||||||||
\(160\) | −2.57800 | −0.203809 | ||||||||
\(161\) | −6.85084 | −0.539922 | ||||||||
\(162\) | 23.6826 | 1.86068 | ||||||||
\(163\) | 8.32875 | 0.652358 | 0.326179 | − | 0.945308i | \(-0.394239\pi\) | ||||
0.326179 | + | 0.945308i | \(0.394239\pi\) | |||||||
\(164\) | 4.25848 | 0.332532 | ||||||||
\(165\) | −6.00055 | −0.467142 | ||||||||
\(166\) | −20.5837 | −1.59760 | ||||||||
\(167\) | −14.1115 | −1.09198 | −0.545991 | − | 0.837791i | \(-0.683847\pi\) | ||||
−0.545991 | + | 0.837791i | \(0.683847\pi\) | |||||||
\(168\) | −19.5841 | −1.51094 | ||||||||
\(169\) | 17.3407 | 1.33390 | ||||||||
\(170\) | −3.26825 | −0.250663 | ||||||||
\(171\) | 22.0350 | 1.68506 | ||||||||
\(172\) | −46.2372 | −3.52556 | ||||||||
\(173\) | −5.18347 | −0.394092 | −0.197046 | − | 0.980394i | \(-0.563135\pi\) | ||||
−0.197046 | + | 0.980394i | \(0.563135\pi\) | |||||||
\(174\) | −21.4316 | −1.62472 | ||||||||
\(175\) | 1.44699 | 0.109382 | ||||||||
\(176\) | −13.7121 | −1.03359 | ||||||||
\(177\) | 2.22897 | 0.167539 | ||||||||
\(178\) | 11.0992 | 0.831917 | ||||||||
\(179\) | −12.9026 | −0.964383 | −0.482191 | − | 0.876066i | \(-0.660159\pi\) | ||||
−0.482191 | + | 0.876066i | \(0.660159\pi\) | |||||||
\(180\) | 12.0127 | 0.895377 | ||||||||
\(181\) | 10.1403 | 0.753721 | 0.376860 | − | 0.926270i | \(-0.377004\pi\) | ||||
0.376860 | + | 0.926270i | \(0.377004\pi\) | |||||||
\(182\) | 19.9150 | 1.47620 | ||||||||
\(183\) | −22.8491 | −1.68906 | ||||||||
\(184\) | 26.5363 | 1.95628 | ||||||||
\(185\) | −8.95720 | −0.658547 | ||||||||
\(186\) | −4.44278 | −0.325760 | ||||||||
\(187\) | −3.25034 | −0.237689 | ||||||||
\(188\) | 13.2482 | 0.966221 | ||||||||
\(189\) | −0.590214 | −0.0429318 | ||||||||
\(190\) | −19.4474 | −1.41087 | ||||||||
\(191\) | 24.9694 | 1.80672 | 0.903361 | − | 0.428882i | \(-0.141092\pi\) | ||||
0.903361 | + | 0.428882i | \(0.141092\pi\) | |||||||
\(192\) | −11.0951 | −0.800719 | ||||||||
\(193\) | −16.3647 | −1.17795 | −0.588977 | − | 0.808150i | \(-0.700469\pi\) | ||||
−0.588977 | + | 0.808150i | \(0.700469\pi\) | |||||||
\(194\) | −12.3092 | −0.883752 | ||||||||
\(195\) | −13.3011 | −0.952511 | ||||||||
\(196\) | −20.8179 | −1.48699 | ||||||||
\(197\) | −2.82979 | −0.201614 | −0.100807 | − | 0.994906i | \(-0.532142\pi\) | ||||
−0.100807 | + | 0.994906i | \(0.532142\pi\) | |||||||
\(198\) | 17.5781 | 1.24922 | ||||||||
\(199\) | 13.0368 | 0.924156 | 0.462078 | − | 0.886839i | \(-0.347104\pi\) | ||||
0.462078 | + | 0.886839i | \(0.347104\pi\) | |||||||
\(200\) | −5.60483 | −0.396321 | ||||||||
\(201\) | −8.01224 | −0.565140 | ||||||||
\(202\) | 24.8405 | 1.74777 | ||||||||
\(203\) | 5.13976 | 0.360741 | ||||||||
\(204\) | 13.4022 | 0.938344 | ||||||||
\(205\) | 1.00361 | 0.0700952 | ||||||||
\(206\) | −14.6120 | −1.01806 | ||||||||
\(207\) | −13.4039 | −0.931635 | ||||||||
\(208\) | −30.3949 | −2.10751 | ||||||||
\(209\) | −19.3409 | −1.33784 | ||||||||
\(210\) | −8.73057 | −0.602467 | ||||||||
\(211\) | −10.0705 | −0.693284 | −0.346642 | − | 0.937997i | \(-0.612678\pi\) | ||||
−0.346642 | + | 0.937997i | \(0.612678\pi\) | |||||||
\(212\) | −49.3485 | −3.38927 | ||||||||
\(213\) | 24.7496 | 1.69582 | ||||||||
\(214\) | −21.6958 | −1.48310 | ||||||||
\(215\) | −10.8969 | −0.743162 | ||||||||
\(216\) | 2.28616 | 0.155553 | ||||||||
\(217\) | 1.06547 | 0.0723292 | ||||||||
\(218\) | 49.1633 | 3.32976 | ||||||||
\(219\) | −18.1270 | −1.22491 | ||||||||
\(220\) | −10.5440 | −0.710877 | ||||||||
\(221\) | −7.20487 | −0.484652 | ||||||||
\(222\) | 54.0442 | 3.62721 | ||||||||
\(223\) | −4.07100 | −0.272614 | −0.136307 | − | 0.990667i | \(-0.543523\pi\) | ||||
−0.136307 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(224\) | −3.73035 | −0.249244 | ||||||||
\(225\) | 2.83108 | 0.188739 | ||||||||
\(226\) | 27.9900 | 1.86187 | ||||||||
\(227\) | −12.6440 | −0.839214 | −0.419607 | − | 0.907706i | \(-0.637832\pi\) | ||||
−0.419607 | + | 0.907706i | \(0.637832\pi\) | |||||||
\(228\) | 79.7488 | 5.28149 | ||||||||
\(229\) | 27.5577 | 1.82106 | 0.910531 | − | 0.413440i | \(-0.135673\pi\) | ||||
0.910531 | + | 0.413440i | \(0.135673\pi\) | |||||||
\(230\) | 11.8299 | 0.780039 | ||||||||
\(231\) | −8.68273 | −0.571282 | ||||||||
\(232\) | −19.9086 | −1.30706 | ||||||||
\(233\) | 14.5411 | 0.952620 | 0.476310 | − | 0.879277i | \(-0.341974\pi\) | ||||
0.476310 | + | 0.879277i | \(0.341974\pi\) | |||||||
\(234\) | 38.9644 | 2.54718 | ||||||||
\(235\) | 3.12224 | 0.203672 | ||||||||
\(236\) | 3.91668 | 0.254954 | ||||||||
\(237\) | 9.82963 | 0.638503 | ||||||||
\(238\) | −4.72913 | −0.306544 | ||||||||
\(239\) | 24.7594 | 1.60155 | 0.800776 | − | 0.598964i | \(-0.204421\pi\) | ||||
0.800776 | + | 0.598964i | \(0.204421\pi\) | |||||||
\(240\) | 13.3249 | 0.860117 | ||||||||
\(241\) | −26.4374 | −1.70298 | −0.851490 | − | 0.524370i | \(-0.824301\pi\) | ||||
−0.851490 | + | 0.524370i | \(0.824301\pi\) | |||||||
\(242\) | 12.0561 | 0.774993 | ||||||||
\(243\) | −21.6640 | −1.38974 | ||||||||
\(244\) | −40.1499 | −2.57033 | ||||||||
\(245\) | −4.90622 | −0.313447 | ||||||||
\(246\) | −6.05539 | −0.386078 | ||||||||
\(247\) | −42.8719 | −2.72787 | ||||||||
\(248\) | −4.12705 | −0.262068 | ||||||||
\(249\) | 19.8928 | 1.26065 | ||||||||
\(250\) | −2.49863 | −0.158027 | ||||||||
\(251\) | −7.73280 | −0.488090 | −0.244045 | − | 0.969764i | \(-0.578474\pi\) | ||||
−0.244045 | + | 0.969764i | \(0.578474\pi\) | |||||||
\(252\) | 17.3823 | 1.09498 | ||||||||
\(253\) | 11.7651 | 0.739663 | ||||||||
\(254\) | −34.6432 | −2.17371 | ||||||||
\(255\) | 3.15855 | 0.197796 | ||||||||
\(256\) | −32.3790 | −2.02369 | ||||||||
\(257\) | 11.1312 | 0.694343 | 0.347172 | − | 0.937802i | \(-0.387142\pi\) | ||||
0.347172 | + | 0.937802i | \(0.387142\pi\) | |||||||
\(258\) | 65.7475 | 4.09326 | ||||||||
\(259\) | −12.9610 | −0.805357 | ||||||||
\(260\) | −23.3723 | −1.44949 | ||||||||
\(261\) | 10.0561 | 0.622458 | ||||||||
\(262\) | −31.3753 | −1.93837 | ||||||||
\(263\) | 20.4844 | 1.26312 | 0.631562 | − | 0.775325i | \(-0.282414\pi\) | ||||
0.631562 | + | 0.775325i | \(0.282414\pi\) | |||||||
\(264\) | 33.6320 | 2.06991 | ||||||||
\(265\) | −11.6301 | −0.714433 | ||||||||
\(266\) | −28.1403 | −1.72539 | ||||||||
\(267\) | −10.7266 | −0.656458 | ||||||||
\(268\) | −14.0789 | −0.860006 | ||||||||
\(269\) | 28.3194 | 1.72667 | 0.863333 | − | 0.504634i | \(-0.168373\pi\) | ||||
0.863333 | + | 0.504634i | \(0.168373\pi\) | |||||||
\(270\) | 1.01917 | 0.0620247 | ||||||||
\(271\) | −19.6254 | −1.19216 | −0.596078 | − | 0.802926i | \(-0.703275\pi\) | ||||
−0.596078 | + | 0.802926i | \(0.703275\pi\) | |||||||
\(272\) | 7.21775 | 0.437640 | ||||||||
\(273\) | −19.2466 | −1.16485 | ||||||||
\(274\) | 3.13929 | 0.189652 | ||||||||
\(275\) | −2.48494 | −0.149848 | ||||||||
\(276\) | −48.5112 | −2.92003 | ||||||||
\(277\) | −10.5941 | −0.636536 | −0.318268 | − | 0.948001i | \(-0.603101\pi\) | ||||
−0.318268 | + | 0.948001i | \(0.603101\pi\) | |||||||
\(278\) | 35.8497 | 2.15012 | ||||||||
\(279\) | 2.08464 | 0.124804 | ||||||||
\(280\) | −8.11014 | −0.484673 | ||||||||
\(281\) | −13.8012 | −0.823312 | −0.411656 | − | 0.911339i | \(-0.635049\pi\) | ||||
−0.411656 | + | 0.911339i | \(0.635049\pi\) | |||||||
\(282\) | −18.8384 | −1.12181 | ||||||||
\(283\) | −31.6037 | −1.87865 | −0.939324 | − | 0.343032i | \(-0.888546\pi\) | ||||
−0.939324 | + | 0.343032i | \(0.888546\pi\) | |||||||
\(284\) | 43.4894 | 2.58062 | ||||||||
\(285\) | 18.7947 | 1.11330 | ||||||||
\(286\) | −34.2004 | −2.02231 | ||||||||
\(287\) | 1.45222 | 0.0857216 | ||||||||
\(288\) | −7.29855 | −0.430071 | ||||||||
\(289\) | −15.2891 | −0.899358 | ||||||||
\(290\) | −8.87523 | −0.521171 | ||||||||
\(291\) | 11.8961 | 0.697360 | ||||||||
\(292\) | −31.8523 | −1.86401 | ||||||||
\(293\) | −21.3344 | −1.24637 | −0.623184 | − | 0.782075i | \(-0.714161\pi\) | ||||
−0.623184 | + | 0.782075i | \(0.714161\pi\) | |||||||
\(294\) | 29.6022 | 1.72643 | ||||||||
\(295\) | 0.923057 | 0.0537425 | ||||||||
\(296\) | 50.2036 | 2.91802 | ||||||||
\(297\) | 1.01359 | 0.0588142 | ||||||||
\(298\) | −3.44294 | −0.199444 | ||||||||
\(299\) | 26.0790 | 1.50819 | ||||||||
\(300\) | 10.2462 | 0.591566 | ||||||||
\(301\) | −15.7677 | −0.908835 | ||||||||
\(302\) | 15.8644 | 0.912894 | ||||||||
\(303\) | −24.0067 | −1.37915 | ||||||||
\(304\) | 42.9486 | 2.46327 | ||||||||
\(305\) | −9.46226 | −0.541807 | ||||||||
\(306\) | −9.25270 | −0.528941 | ||||||||
\(307\) | −0.936988 | −0.0534767 | −0.0267384 | − | 0.999642i | \(-0.508512\pi\) | ||||
−0.0267384 | + | 0.999642i | \(0.508512\pi\) | |||||||
\(308\) | −15.2571 | −0.869352 | ||||||||
\(309\) | 14.1215 | 0.803344 | ||||||||
\(310\) | −1.83984 | −0.104496 | ||||||||
\(311\) | −9.18545 | −0.520859 | −0.260430 | − | 0.965493i | \(-0.583864\pi\) | ||||
−0.260430 | + | 0.965493i | \(0.583864\pi\) | |||||||
\(312\) | 74.5504 | 4.22058 | ||||||||
\(313\) | −22.4962 | −1.27156 | −0.635782 | − | 0.771869i | \(-0.719322\pi\) | ||||
−0.635782 | + | 0.771869i | \(0.719322\pi\) | |||||||
\(314\) | −3.16026 | −0.178344 | ||||||||
\(315\) | 4.09655 | 0.230815 | ||||||||
\(316\) | 17.2724 | 0.971647 | ||||||||
\(317\) | −29.0285 | −1.63041 | −0.815203 | − | 0.579176i | \(-0.803375\pi\) | ||||
−0.815203 | + | 0.579176i | \(0.803375\pi\) | |||||||
\(318\) | 70.1716 | 3.93503 | ||||||||
\(319\) | −8.82660 | −0.494195 | ||||||||
\(320\) | −4.59469 | −0.256851 | ||||||||
\(321\) | 20.9676 | 1.17030 | ||||||||
\(322\) | 17.1177 | 0.953933 | ||||||||
\(323\) | 10.1806 | 0.566464 | ||||||||
\(324\) | −40.2176 | −2.23431 | ||||||||
\(325\) | −5.50824 | −0.305542 | ||||||||
\(326\) | −20.8105 | −1.15259 | ||||||||
\(327\) | −47.5131 | −2.62748 | ||||||||
\(328\) | −5.62507 | −0.310592 | ||||||||
\(329\) | 4.51785 | 0.249077 | ||||||||
\(330\) | 14.9932 | 0.825346 | ||||||||
\(331\) | −1.60625 | −0.0882876 | −0.0441438 | − | 0.999025i | \(-0.514056\pi\) | ||||
−0.0441438 | + | 0.999025i | \(0.514056\pi\) | |||||||
\(332\) | 34.9551 | 1.91841 | ||||||||
\(333\) | −25.3586 | −1.38964 | ||||||||
\(334\) | 35.2595 | 1.92931 | ||||||||
\(335\) | −3.31802 | −0.181283 | ||||||||
\(336\) | 19.2810 | 1.05186 | ||||||||
\(337\) | 31.4333 | 1.71228 | 0.856141 | − | 0.516743i | \(-0.172856\pi\) | ||||
0.856141 | + | 0.516743i | \(0.172856\pi\) | |||||||
\(338\) | −43.3280 | −2.35673 | ||||||||
\(339\) | −27.0505 | −1.46918 | ||||||||
\(340\) | 5.55012 | 0.300998 | ||||||||
\(341\) | −1.82976 | −0.0990870 | ||||||||
\(342\) | −55.0573 | −2.97716 | ||||||||
\(343\) | −17.2282 | −0.930235 | ||||||||
\(344\) | 61.0752 | 3.29295 | ||||||||
\(345\) | −11.4328 | −0.615521 | ||||||||
\(346\) | 12.9516 | 0.696281 | ||||||||
\(347\) | −26.1957 | −1.40626 | −0.703129 | − | 0.711062i | \(-0.748214\pi\) | ||||
−0.703129 | + | 0.711062i | \(0.748214\pi\) | |||||||
\(348\) | 36.3950 | 1.95098 | ||||||||
\(349\) | −5.04512 | −0.270059 | −0.135030 | − | 0.990842i | \(-0.543113\pi\) | ||||
−0.135030 | + | 0.990842i | \(0.543113\pi\) | |||||||
\(350\) | −3.61550 | −0.193256 | ||||||||
\(351\) | 2.24676 | 0.119923 | ||||||||
\(352\) | 6.40619 | 0.341451 | ||||||||
\(353\) | 26.2670 | 1.39805 | 0.699026 | − | 0.715096i | \(-0.253617\pi\) | ||||
0.699026 | + | 0.715096i | \(0.253617\pi\) | |||||||
\(354\) | −5.56936 | −0.296008 | ||||||||
\(355\) | 10.2493 | 0.543976 | ||||||||
\(356\) | −18.8485 | −0.998969 | ||||||||
\(357\) | 4.57039 | 0.241891 | ||||||||
\(358\) | 32.2388 | 1.70387 | ||||||||
\(359\) | −13.7718 | −0.726847 | −0.363423 | − | 0.931624i | \(-0.618392\pi\) | ||||
−0.363423 | + | 0.931624i | \(0.618392\pi\) | |||||||
\(360\) | −15.8677 | −0.836304 | ||||||||
\(361\) | 41.5787 | 2.18835 | ||||||||
\(362\) | −25.3368 | −1.33167 | ||||||||
\(363\) | −11.6514 | −0.611540 | ||||||||
\(364\) | −33.8196 | −1.77263 | ||||||||
\(365\) | −7.50674 | −0.392920 | ||||||||
\(366\) | 57.0915 | 2.98422 | ||||||||
\(367\) | 17.6511 | 0.921379 | 0.460689 | − | 0.887561i | \(-0.347602\pi\) | ||||
0.460689 | + | 0.887561i | \(0.347602\pi\) | |||||||
\(368\) | −26.1256 | −1.36189 | ||||||||
\(369\) | 2.84131 | 0.147913 | ||||||||
\(370\) | 22.3807 | 1.16352 | ||||||||
\(371\) | −16.8287 | −0.873702 | ||||||||
\(372\) | 7.54469 | 0.391174 | ||||||||
\(373\) | −17.4992 | −0.906073 | −0.453036 | − | 0.891492i | \(-0.649659\pi\) | ||||
−0.453036 | + | 0.891492i | \(0.649659\pi\) | |||||||
\(374\) | 8.12141 | 0.419948 | ||||||||
\(375\) | 2.41476 | 0.124698 | ||||||||
\(376\) | −17.4996 | −0.902474 | ||||||||
\(377\) | −19.5655 | −1.00767 | ||||||||
\(378\) | 1.47473 | 0.0758518 | ||||||||
\(379\) | 34.2792 | 1.76081 | 0.880403 | − | 0.474226i | \(-0.157272\pi\) | ||||
0.880403 | + | 0.474226i | \(0.157272\pi\) | |||||||
\(380\) | 33.0255 | 1.69417 | ||||||||
\(381\) | 33.4804 | 1.71525 | ||||||||
\(382\) | −62.3893 | −3.19211 | ||||||||
\(383\) | 35.7192 | 1.82517 | 0.912584 | − | 0.408890i | \(-0.134084\pi\) | ||||
0.912584 | + | 0.408890i | \(0.134084\pi\) | |||||||
\(384\) | 40.1731 | 2.05007 | ||||||||
\(385\) | −3.59569 | −0.183253 | ||||||||
\(386\) | 40.8892 | 2.08121 | ||||||||
\(387\) | −30.8500 | −1.56819 | ||||||||
\(388\) | 20.9035 | 1.06121 | ||||||||
\(389\) | −6.08946 | −0.308748 | −0.154374 | − | 0.988013i | \(-0.549336\pi\) | ||||
−0.154374 | + | 0.988013i | \(0.549336\pi\) | |||||||
\(390\) | 33.2345 | 1.68290 | ||||||||
\(391\) | −6.19286 | −0.313186 | ||||||||
\(392\) | 27.4985 | 1.38889 | ||||||||
\(393\) | 30.3222 | 1.52955 | ||||||||
\(394\) | 7.07060 | 0.356212 | ||||||||
\(395\) | 4.07064 | 0.204816 | ||||||||
\(396\) | −29.8510 | −1.50007 | ||||||||
\(397\) | −23.2515 | −1.16696 | −0.583481 | − | 0.812127i | \(-0.698310\pi\) | ||||
−0.583481 | + | 0.812127i | \(0.698310\pi\) | |||||||
\(398\) | −32.5742 | −1.63280 | ||||||||
\(399\) | 27.1957 | 1.36149 | ||||||||
\(400\) | 5.51809 | 0.275904 | ||||||||
\(401\) | −14.2343 | −0.710828 | −0.355414 | − | 0.934709i | \(-0.615660\pi\) | ||||
−0.355414 | + | 0.934709i | \(0.615660\pi\) | |||||||
\(402\) | 20.0196 | 0.998489 | ||||||||
\(403\) | −4.05593 | −0.202040 | ||||||||
\(404\) | −42.1840 | −2.09873 | ||||||||
\(405\) | −9.47821 | −0.470976 | ||||||||
\(406\) | −12.8424 | −0.637356 | ||||||||
\(407\) | 22.2581 | 1.10329 | ||||||||
\(408\) | −17.7031 | −0.876436 | ||||||||
\(409\) | 30.9854 | 1.53213 | 0.766064 | − | 0.642765i | \(-0.222213\pi\) | ||||
0.766064 | + | 0.642765i | \(0.222213\pi\) | |||||||
\(410\) | −2.50765 | −0.123844 | ||||||||
\(411\) | −3.03392 | −0.149652 | ||||||||
\(412\) | 24.8139 | 1.22249 | ||||||||
\(413\) | 1.33566 | 0.0657233 | ||||||||
\(414\) | 33.4914 | 1.64601 | ||||||||
\(415\) | 8.23799 | 0.404387 | ||||||||
\(416\) | 14.2003 | 0.696225 | ||||||||
\(417\) | −34.6464 | −1.69664 | ||||||||
\(418\) | 48.3257 | 2.36369 | ||||||||
\(419\) | −18.7604 | −0.916505 | −0.458253 | − | 0.888822i | \(-0.651525\pi\) | ||||
−0.458253 | + | 0.888822i | \(0.651525\pi\) | |||||||
\(420\) | 14.8262 | 0.723444 | ||||||||
\(421\) | 7.06630 | 0.344391 | 0.172195 | − | 0.985063i | \(-0.444914\pi\) | ||||
0.172195 | + | 0.985063i | \(0.444914\pi\) | |||||||
\(422\) | 25.1626 | 1.22489 | ||||||||
\(423\) | 8.83932 | 0.429782 | ||||||||
\(424\) | 65.1849 | 3.16566 | ||||||||
\(425\) | 1.30802 | 0.0634481 | ||||||||
\(426\) | −61.8402 | −2.99617 | ||||||||
\(427\) | −13.6918 | −0.662593 | ||||||||
\(428\) | 36.8437 | 1.78091 | ||||||||
\(429\) | 33.0524 | 1.59579 | ||||||||
\(430\) | 27.2273 | 1.31302 | ||||||||
\(431\) | 14.6287 | 0.704641 | 0.352321 | − | 0.935879i | \(-0.385393\pi\) | ||||
0.352321 | + | 0.935879i | \(0.385393\pi\) | |||||||
\(432\) | −2.25078 | −0.108291 | ||||||||
\(433\) | −10.1692 | −0.488702 | −0.244351 | − | 0.969687i | \(-0.578575\pi\) | ||||
−0.244351 | + | 0.969687i | \(0.578575\pi\) | |||||||
\(434\) | −2.66223 | −0.127791 | ||||||||
\(435\) | 8.57733 | 0.411251 | ||||||||
\(436\) | −83.4887 | −3.99838 | ||||||||
\(437\) | −36.8501 | −1.76278 | ||||||||
\(438\) | 45.2927 | 2.16417 | ||||||||
\(439\) | 13.4253 | 0.640755 | 0.320378 | − | 0.947290i | \(-0.396190\pi\) | ||||
0.320378 | + | 0.947290i | \(0.396190\pi\) | |||||||
\(440\) | 13.9277 | 0.663976 | ||||||||
\(441\) | −13.8899 | −0.661425 | ||||||||
\(442\) | 18.0023 | 0.856283 | ||||||||
\(443\) | −3.13989 | −0.149181 | −0.0745903 | − | 0.997214i | \(-0.523765\pi\) | ||||
−0.0745903 | + | 0.997214i | \(0.523765\pi\) | |||||||
\(444\) | −91.7775 | −4.35557 | ||||||||
\(445\) | −4.44209 | −0.210575 | ||||||||
\(446\) | 10.1719 | 0.481654 | ||||||||
\(447\) | 3.32737 | 0.157379 | ||||||||
\(448\) | −6.64847 | −0.314111 | ||||||||
\(449\) | −9.03784 | −0.426522 | −0.213261 | − | 0.976995i | \(-0.568408\pi\) | ||||
−0.213261 | + | 0.976995i | \(0.568408\pi\) | |||||||
\(450\) | −7.07384 | −0.333464 | ||||||||
\(451\) | −2.49391 | −0.117434 | ||||||||
\(452\) | −47.5325 | −2.23574 | ||||||||
\(453\) | −15.3319 | −0.720356 | ||||||||
\(454\) | 31.5928 | 1.48272 | ||||||||
\(455\) | −7.97037 | −0.373657 | ||||||||
\(456\) | −105.341 | −4.93304 | ||||||||
\(457\) | −7.66439 | −0.358525 | −0.179263 | − | 0.983801i | \(-0.557371\pi\) | ||||
−0.179263 | + | 0.983801i | \(0.557371\pi\) | |||||||
\(458\) | −68.8565 | −3.21745 | ||||||||
\(459\) | −0.533528 | −0.0249030 | ||||||||
\(460\) | −20.0894 | −0.936674 | ||||||||
\(461\) | 9.53198 | 0.443948 | 0.221974 | − | 0.975053i | \(-0.428750\pi\) | ||||
0.221974 | + | 0.975053i | \(0.428750\pi\) | |||||||
\(462\) | 21.6950 | 1.00934 | ||||||||
\(463\) | 16.3712 | 0.760835 | 0.380417 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380417 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(464\) | 19.6004 | 0.909928 | ||||||||
\(465\) | 1.77808 | 0.0824567 | ||||||||
\(466\) | −36.3329 | −1.68309 | ||||||||
\(467\) | −22.4664 | −1.03962 | −0.519811 | − | 0.854281i | \(-0.673998\pi\) | ||||
−0.519811 | + | 0.854281i | \(0.673998\pi\) | |||||||
\(468\) | −66.1691 | −3.05867 | ||||||||
\(469\) | −4.80115 | −0.221696 | ||||||||
\(470\) | −7.80132 | −0.359848 | ||||||||
\(471\) | 3.05418 | 0.140729 | ||||||||
\(472\) | −5.17358 | −0.238133 | ||||||||
\(473\) | 27.0781 | 1.24505 | ||||||||
\(474\) | −24.5606 | −1.12811 | ||||||||
\(475\) | 7.78323 | 0.357119 | ||||||||
\(476\) | 8.03098 | 0.368099 | ||||||||
\(477\) | −32.9259 | −1.50757 | ||||||||
\(478\) | −61.8646 | −2.82962 | ||||||||
\(479\) | −23.7555 | −1.08542 | −0.542709 | − | 0.839921i | \(-0.682601\pi\) | ||||
−0.542709 | + | 0.839921i | \(0.682601\pi\) | |||||||
\(480\) | −6.22527 | −0.284143 | ||||||||
\(481\) | 49.3384 | 2.24964 | ||||||||
\(482\) | 66.0573 | 3.00883 | ||||||||
\(483\) | −16.5432 | −0.752740 | ||||||||
\(484\) | −20.4735 | −0.930615 | ||||||||
\(485\) | 4.92639 | 0.223696 | ||||||||
\(486\) | 54.1303 | 2.45540 | ||||||||
\(487\) | 28.8998 | 1.30957 | 0.654786 | − | 0.755814i | \(-0.272759\pi\) | ||||
0.654786 | + | 0.755814i | \(0.272759\pi\) | |||||||
\(488\) | 53.0344 | 2.40075 | ||||||||
\(489\) | 20.1120 | 0.909494 | ||||||||
\(490\) | 12.2588 | 0.553798 | ||||||||
\(491\) | 13.7481 | 0.620445 | 0.310222 | − | 0.950664i | \(-0.399597\pi\) | ||||
0.310222 | + | 0.950664i | \(0.399597\pi\) | |||||||
\(492\) | 10.2832 | 0.463604 | ||||||||
\(493\) | 4.64612 | 0.209251 | ||||||||
\(494\) | 107.121 | 4.81961 | ||||||||
\(495\) | −7.03508 | −0.316203 | ||||||||
\(496\) | 4.06318 | 0.182442 | ||||||||
\(497\) | 14.8306 | 0.665244 | ||||||||
\(498\) | −49.7048 | −2.22732 | ||||||||
\(499\) | 11.2546 | 0.503825 | 0.251913 | − | 0.967750i | \(-0.418940\pi\) | ||||
0.251913 | + | 0.967750i | \(0.418940\pi\) | |||||||
\(500\) | 4.24316 | 0.189760 | ||||||||
\(501\) | −34.0760 | −1.52240 | ||||||||
\(502\) | 19.3214 | 0.862357 | ||||||||
\(503\) | −16.7179 | −0.745415 | −0.372707 | − | 0.927949i | \(-0.621570\pi\) | ||||
−0.372707 | + | 0.927949i | \(0.621570\pi\) | |||||||
\(504\) | −22.9605 | −1.02274 | ||||||||
\(505\) | −9.94164 | −0.442397 | ||||||||
\(506\) | −29.3966 | −1.30684 | ||||||||
\(507\) | 41.8737 | 1.85968 | ||||||||
\(508\) | 58.8309 | 2.61020 | ||||||||
\(509\) | −35.5775 | −1.57694 | −0.788472 | − | 0.615071i | \(-0.789127\pi\) | ||||
−0.788472 | + | 0.615071i | \(0.789127\pi\) | |||||||
\(510\) | −7.89206 | −0.349466 | ||||||||
\(511\) | −10.8622 | −0.480514 | ||||||||
\(512\) | 47.6302 | 2.10498 | ||||||||
\(513\) | −3.17471 | −0.140167 | ||||||||
\(514\) | −27.8127 | −1.22677 | ||||||||
\(515\) | 5.84798 | 0.257693 | ||||||||
\(516\) | −111.652 | −4.91521 | ||||||||
\(517\) | −7.75858 | −0.341222 | ||||||||
\(518\) | 32.3847 | 1.42290 | ||||||||
\(519\) | −12.5169 | −0.549429 | ||||||||
\(520\) | 30.8727 | 1.35386 | ||||||||
\(521\) | 38.7174 | 1.69624 | 0.848120 | − | 0.529804i | \(-0.177735\pi\) | ||||
0.848120 | + | 0.529804i | \(0.177735\pi\) | |||||||
\(522\) | −25.1265 | −1.09976 | ||||||||
\(523\) | −3.10085 | −0.135591 | −0.0677954 | − | 0.997699i | \(-0.521597\pi\) | ||||
−0.0677954 | + | 0.997699i | \(0.521597\pi\) | |||||||
\(524\) | 53.2814 | 2.32761 | ||||||||
\(525\) | 3.49414 | 0.152497 | ||||||||
\(526\) | −51.1830 | −2.23169 | ||||||||
\(527\) | 0.963143 | 0.0419552 | ||||||||
\(528\) | −33.1115 | −1.44099 | ||||||||
\(529\) | −0.584110 | −0.0253961 | ||||||||
\(530\) | 29.0594 | 1.26226 | ||||||||
\(531\) | 2.61325 | 0.113406 | ||||||||
\(532\) | 47.7876 | 2.07186 | ||||||||
\(533\) | −5.52813 | −0.239450 | ||||||||
\(534\) | 26.8018 | 1.15983 | ||||||||
\(535\) | 8.68309 | 0.375403 | ||||||||
\(536\) | 18.5970 | 0.803266 | ||||||||
\(537\) | −31.1566 | −1.34451 | ||||||||
\(538\) | −70.7598 | −3.05067 | ||||||||
\(539\) | 12.1917 | 0.525132 | ||||||||
\(540\) | −1.73075 | −0.0744795 | ||||||||
\(541\) | 12.7434 | 0.547880 | 0.273940 | − | 0.961747i | \(-0.411673\pi\) | ||||
0.273940 | + | 0.961747i | \(0.411673\pi\) | |||||||
\(542\) | 49.0366 | 2.10630 | ||||||||
\(543\) | 24.4864 | 1.05081 | ||||||||
\(544\) | −3.37207 | −0.144576 | ||||||||
\(545\) | −19.6761 | −0.842830 | ||||||||
\(546\) | 48.0901 | 2.05806 | ||||||||
\(547\) | −36.0931 | −1.54323 | −0.771614 | − | 0.636091i | \(-0.780550\pi\) | ||||
−0.771614 | + | 0.636091i | \(0.780550\pi\) | |||||||
\(548\) | −5.33112 | −0.227734 | ||||||||
\(549\) | −26.7885 | −1.14330 | ||||||||
\(550\) | 6.20895 | 0.264751 | ||||||||
\(551\) | 27.6463 | 1.17777 | ||||||||
\(552\) | 64.0789 | 2.72738 | ||||||||
\(553\) | 5.89017 | 0.250476 | ||||||||
\(554\) | 26.4707 | 1.12463 | ||||||||
\(555\) | −21.6295 | −0.918122 | ||||||||
\(556\) | −60.8798 | −2.58188 | ||||||||
\(557\) | 30.3294 | 1.28510 | 0.642549 | − | 0.766245i | \(-0.277877\pi\) | ||||
0.642549 | + | 0.766245i | \(0.277877\pi\) | |||||||
\(558\) | −5.20874 | −0.220504 | ||||||||
\(559\) | 60.0227 | 2.53869 | ||||||||
\(560\) | 7.98462 | 0.337412 | ||||||||
\(561\) | −7.84882 | −0.331377 | ||||||||
\(562\) | 34.4842 | 1.45463 | ||||||||
\(563\) | 11.5831 | 0.488170 | 0.244085 | − | 0.969754i | \(-0.421512\pi\) | ||||
0.244085 | + | 0.969754i | \(0.421512\pi\) | |||||||
\(564\) | 31.9912 | 1.34707 | ||||||||
\(565\) | −11.2022 | −0.471278 | ||||||||
\(566\) | 78.9661 | 3.31919 | ||||||||
\(567\) | −13.7149 | −0.575971 | ||||||||
\(568\) | −57.4455 | −2.41036 | ||||||||
\(569\) | 7.89884 | 0.331137 | 0.165568 | − | 0.986198i | \(-0.447054\pi\) | ||||
0.165568 | + | 0.986198i | \(0.447054\pi\) | |||||||
\(570\) | −46.9610 | −1.96698 | ||||||||
\(571\) | 12.0596 | 0.504677 | 0.252339 | − | 0.967639i | \(-0.418800\pi\) | ||||
0.252339 | + | 0.967639i | \(0.418800\pi\) | |||||||
\(572\) | 58.0789 | 2.42840 | ||||||||
\(573\) | 60.2952 | 2.51887 | ||||||||
\(574\) | −3.62855 | −0.151453 | ||||||||
\(575\) | −4.73454 | −0.197444 | ||||||||
\(576\) | −13.0080 | −0.541998 | ||||||||
\(577\) | −2.82176 | −0.117471 | −0.0587356 | − | 0.998274i | \(-0.518707\pi\) | ||||
−0.0587356 | + | 0.998274i | \(0.518707\pi\) | |||||||
\(578\) | 38.2018 | 1.58899 | ||||||||
\(579\) | −39.5168 | −1.64226 | ||||||||
\(580\) | 15.0719 | 0.625825 | ||||||||
\(581\) | 11.9203 | 0.494537 | ||||||||
\(582\) | −29.7239 | −1.23210 | ||||||||
\(583\) | 28.9002 | 1.19692 | ||||||||
\(584\) | 42.0740 | 1.74103 | ||||||||
\(585\) | −15.5943 | −0.644745 | ||||||||
\(586\) | 53.3068 | 2.20208 | ||||||||
\(587\) | −22.9085 | −0.945533 | −0.472767 | − | 0.881188i | \(-0.656745\pi\) | ||||
−0.472767 | + | 0.881188i | \(0.656745\pi\) | |||||||
\(588\) | −50.2702 | −2.07311 | ||||||||
\(589\) | 5.73110 | 0.236146 | ||||||||
\(590\) | −2.30638 | −0.0949522 | ||||||||
\(591\) | −6.83327 | −0.281083 | ||||||||
\(592\) | −49.4266 | −2.03142 | ||||||||
\(593\) | −36.3653 | −1.49334 | −0.746672 | − | 0.665192i | \(-0.768350\pi\) | ||||
−0.746672 | + | 0.665192i | \(0.768350\pi\) | |||||||
\(594\) | −2.53258 | −0.103913 | ||||||||
\(595\) | 1.89269 | 0.0775926 | ||||||||
\(596\) | 5.84677 | 0.239493 | ||||||||
\(597\) | 31.4809 | 1.28843 | ||||||||
\(598\) | −65.1618 | −2.66466 | ||||||||
\(599\) | 13.6674 | 0.558436 | 0.279218 | − | 0.960228i | \(-0.409925\pi\) | ||||
0.279218 | + | 0.960228i | \(0.409925\pi\) | |||||||
\(600\) | −13.5343 | −0.552537 | ||||||||
\(601\) | −47.3929 | −1.93320 | −0.966599 | − | 0.256293i | \(-0.917499\pi\) | ||||
−0.966599 | + | 0.256293i | \(0.917499\pi\) | |||||||
\(602\) | 39.3977 | 1.60573 | ||||||||
\(603\) | −9.39360 | −0.382537 | ||||||||
\(604\) | −26.9408 | −1.09621 | ||||||||
\(605\) | −4.82507 | −0.196167 | ||||||||
\(606\) | 59.9839 | 2.43668 | ||||||||
\(607\) | 26.1737 | 1.06236 | 0.531180 | − | 0.847259i | \(-0.321749\pi\) | ||||
0.531180 | + | 0.847259i | \(0.321749\pi\) | |||||||
\(608\) | −20.0652 | −0.813752 | ||||||||
\(609\) | 12.4113 | 0.502932 | ||||||||
\(610\) | 23.6427 | 0.957265 | ||||||||
\(611\) | −17.1980 | −0.695758 | ||||||||
\(612\) | 15.7129 | 0.635155 | ||||||||
\(613\) | −13.1757 | −0.532163 | −0.266082 | − | 0.963951i | \(-0.585729\pi\) | ||||
−0.266082 | + | 0.963951i | \(0.585729\pi\) | |||||||
\(614\) | 2.34119 | 0.0944827 | ||||||||
\(615\) | 2.42348 | 0.0977243 | ||||||||
\(616\) | 20.1532 | 0.811996 | ||||||||
\(617\) | −31.8421 | −1.28192 | −0.640958 | − | 0.767576i | \(-0.721463\pi\) | ||||
−0.640958 | + | 0.767576i | \(0.721463\pi\) | |||||||
\(618\) | −35.2844 | −1.41935 | ||||||||
\(619\) | −24.1610 | −0.971113 | −0.485556 | − | 0.874205i | \(-0.661383\pi\) | ||||
−0.485556 | + | 0.874205i | \(0.661383\pi\) | |||||||
\(620\) | 3.12440 | 0.125479 | ||||||||
\(621\) | 1.93118 | 0.0774955 | ||||||||
\(622\) | 22.9511 | 0.920254 | ||||||||
\(623\) | −6.42767 | −0.257519 | ||||||||
\(624\) | −73.3966 | −2.93822 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 56.2098 | 2.24660 | ||||||||
\(627\) | −46.7037 | −1.86516 | ||||||||
\(628\) | 5.36673 | 0.214156 | ||||||||
\(629\) | −11.7162 | −0.467154 | ||||||||
\(630\) | −10.2358 | −0.407803 | ||||||||
\(631\) | 22.8875 | 0.911139 | 0.455569 | − | 0.890200i | \(-0.349436\pi\) | ||||
0.455569 | + | 0.890200i | \(0.349436\pi\) | |||||||
\(632\) | −22.8152 | −0.907541 | ||||||||
\(633\) | −24.3180 | −0.966553 | ||||||||
\(634\) | 72.5316 | 2.88060 | ||||||||
\(635\) | 13.8649 | 0.550211 | ||||||||
\(636\) | −119.165 | −4.72520 | ||||||||
\(637\) | 27.0246 | 1.07075 | ||||||||
\(638\) | 22.0544 | 0.873143 | ||||||||
\(639\) | 29.0166 | 1.14788 | ||||||||
\(640\) | 16.6364 | 0.657613 | ||||||||
\(641\) | −26.3132 | −1.03931 | −0.519654 | − | 0.854377i | \(-0.673939\pi\) | ||||
−0.519654 | + | 0.854377i | \(0.673939\pi\) | |||||||
\(642\) | −52.3903 | −2.06768 | ||||||||
\(643\) | 31.5128 | 1.24274 | 0.621372 | − | 0.783516i | \(-0.286576\pi\) | ||||
0.621372 | + | 0.783516i | \(0.286576\pi\) | |||||||
\(644\) | −29.0692 | −1.14549 | ||||||||
\(645\) | −26.3134 | −1.03609 | ||||||||
\(646\) | −25.4376 | −1.00083 | ||||||||
\(647\) | 19.8520 | 0.780464 | 0.390232 | − | 0.920717i | \(-0.372395\pi\) | ||||
0.390232 | + | 0.920717i | \(0.372395\pi\) | |||||||
\(648\) | 53.1238 | 2.08690 | ||||||||
\(649\) | −2.29374 | −0.0900373 | ||||||||
\(650\) | 13.7631 | 0.539832 | ||||||||
\(651\) | 2.57287 | 0.100839 | ||||||||
\(652\) | 35.3402 | 1.38403 | ||||||||
\(653\) | 24.7533 | 0.968673 | 0.484337 | − | 0.874882i | \(-0.339061\pi\) | ||||
0.484337 | + | 0.874882i | \(0.339061\pi\) | |||||||
\(654\) | 118.718 | 4.64223 | ||||||||
\(655\) | 12.5570 | 0.490643 | ||||||||
\(656\) | 5.53801 | 0.216223 | ||||||||
\(657\) | −21.2522 | −0.829127 | ||||||||
\(658\) | −11.2884 | −0.440069 | ||||||||
\(659\) | 40.6886 | 1.58500 | 0.792502 | − | 0.609869i | \(-0.208778\pi\) | ||||
0.792502 | + | 0.609869i | \(0.208778\pi\) | |||||||
\(660\) | −25.4613 | −0.991079 | ||||||||
\(661\) | −24.9617 | −0.970896 | −0.485448 | − | 0.874265i | \(-0.661344\pi\) | ||||
−0.485448 | + | 0.874265i | \(0.661344\pi\) | |||||||
\(662\) | 4.01343 | 0.155986 | ||||||||
\(663\) | −17.3981 | −0.675684 | ||||||||
\(664\) | −46.1725 | −1.79184 | ||||||||
\(665\) | 11.2623 | 0.436732 | ||||||||
\(666\) | 63.3618 | 2.45522 | ||||||||
\(667\) | −16.8173 | −0.651167 | ||||||||
\(668\) | −59.8774 | −2.31673 | ||||||||
\(669\) | −9.83050 | −0.380069 | ||||||||
\(670\) | 8.29052 | 0.320291 | ||||||||
\(671\) | 23.5132 | 0.907716 | ||||||||
\(672\) | −9.00791 | −0.347488 | ||||||||
\(673\) | 14.8449 | 0.572230 | 0.286115 | − | 0.958195i | \(-0.407636\pi\) | ||||
0.286115 | + | 0.958195i | \(0.407636\pi\) | |||||||
\(674\) | −78.5403 | −3.02526 | ||||||||
\(675\) | −0.407891 | −0.0156997 | ||||||||
\(676\) | 73.5793 | 2.82997 | ||||||||
\(677\) | 12.6868 | 0.487593 | 0.243797 | − | 0.969826i | \(-0.421607\pi\) | ||||
0.243797 | + | 0.969826i | \(0.421607\pi\) | |||||||
\(678\) | 67.5894 | 2.59575 | ||||||||
\(679\) | 7.12845 | 0.273565 | ||||||||
\(680\) | −7.33121 | −0.281139 | ||||||||
\(681\) | −30.5324 | −1.17000 | ||||||||
\(682\) | 4.57189 | 0.175067 | ||||||||
\(683\) | −0.00966065 | −0.000369654 0 | −0.000184827 | − | 1.00000i | \(-0.500059\pi\) | ||||
−0.000184827 | 1.00000i | \(0.500059\pi\) | ||||||||
\(684\) | 93.4980 | 3.57499 | ||||||||
\(685\) | −1.25640 | −0.0480047 | ||||||||
\(686\) | 43.0469 | 1.64354 | ||||||||
\(687\) | 66.5453 | 2.53886 | ||||||||
\(688\) | −60.1300 | −2.29243 | ||||||||
\(689\) | 64.0615 | 2.44055 | ||||||||
\(690\) | 28.5664 | 1.08750 | ||||||||
\(691\) | 22.1972 | 0.844422 | 0.422211 | − | 0.906498i | \(-0.361254\pi\) | ||||
0.422211 | + | 0.906498i | \(0.361254\pi\) | |||||||
\(692\) | −21.9943 | −0.836097 | ||||||||
\(693\) | −10.1797 | −0.386695 | ||||||||
\(694\) | 65.4533 | 2.48458 | ||||||||
\(695\) | −14.3477 | −0.544241 | ||||||||
\(696\) | −48.0745 | −1.82226 | ||||||||
\(697\) | 1.31274 | 0.0497236 | ||||||||
\(698\) | 12.6059 | 0.477140 | ||||||||
\(699\) | 35.1134 | 1.32811 | ||||||||
\(700\) | 6.13981 | 0.232063 | ||||||||
\(701\) | 12.6821 | 0.478995 | 0.239497 | − | 0.970897i | \(-0.423017\pi\) | ||||
0.239497 | + | 0.970897i | \(0.423017\pi\) | |||||||
\(702\) | −5.61383 | −0.211880 | ||||||||
\(703\) | −69.7160 | −2.62939 | ||||||||
\(704\) | 11.4175 | 0.430315 | ||||||||
\(705\) | 7.53947 | 0.283953 | ||||||||
\(706\) | −65.6316 | −2.47008 | ||||||||
\(707\) | −14.3855 | −0.541021 | ||||||||
\(708\) | 9.45786 | 0.355448 | ||||||||
\(709\) | 39.8334 | 1.49597 | 0.747987 | − | 0.663713i | \(-0.231020\pi\) | ||||
0.747987 | + | 0.663713i | \(0.231020\pi\) | |||||||
\(710\) | −25.6092 | −0.961096 | ||||||||
\(711\) | 11.5243 | 0.432196 | ||||||||
\(712\) | 24.8972 | 0.933061 | ||||||||
\(713\) | −3.48623 | −0.130560 | ||||||||
\(714\) | −11.4197 | −0.427373 | ||||||||
\(715\) | 13.6877 | 0.511889 | ||||||||
\(716\) | −54.7476 | −2.04602 | ||||||||
\(717\) | 59.7881 | 2.23283 | ||||||||
\(718\) | 34.4106 | 1.28419 | ||||||||
\(719\) | 48.8639 | 1.82232 | 0.911158 | − | 0.412057i | \(-0.135190\pi\) | ||||
0.911158 | + | 0.412057i | \(0.135190\pi\) | |||||||
\(720\) | 15.6222 | 0.582204 | ||||||||
\(721\) | 8.46198 | 0.315141 | ||||||||
\(722\) | −103.890 | −3.86638 | ||||||||
\(723\) | −63.8400 | −2.37424 | ||||||||
\(724\) | 43.0268 | 1.59908 | ||||||||
\(725\) | 3.55204 | 0.131919 | ||||||||
\(726\) | 29.1125 | 1.08047 | ||||||||
\(727\) | 5.38627 | 0.199766 | 0.0998828 | − | 0.994999i | \(-0.468153\pi\) | ||||
0.0998828 | + | 0.994999i | \(0.468153\pi\) | |||||||
\(728\) | 44.6726 | 1.65568 | ||||||||
\(729\) | −23.8787 | −0.884398 | ||||||||
\(730\) | 18.7566 | 0.694212 | ||||||||
\(731\) | −14.2533 | −0.527178 | ||||||||
\(732\) | −96.9525 | −3.58347 | ||||||||
\(733\) | 24.8205 | 0.916768 | 0.458384 | − | 0.888754i | \(-0.348428\pi\) | ||||
0.458384 | + | 0.888754i | \(0.348428\pi\) | |||||||
\(734\) | −44.1035 | −1.62789 | ||||||||
\(735\) | −11.8474 | −0.436996 | ||||||||
\(736\) | 12.2057 | 0.449907 | ||||||||
\(737\) | 8.24509 | 0.303712 | ||||||||
\(738\) | −7.09938 | −0.261332 | ||||||||
\(739\) | −33.4440 | −1.23026 | −0.615130 | − | 0.788426i | \(-0.710896\pi\) | ||||
−0.615130 | + | 0.788426i | \(0.710896\pi\) | |||||||
\(740\) | −38.0068 | −1.39716 | ||||||||
\(741\) | −103.526 | −3.80311 | ||||||||
\(742\) | 42.0487 | 1.54366 | ||||||||
\(743\) | −16.4660 | −0.604080 | −0.302040 | − | 0.953295i | \(-0.597668\pi\) | ||||
−0.302040 | + | 0.953295i | \(0.597668\pi\) | |||||||
\(744\) | −9.96586 | −0.365366 | ||||||||
\(745\) | 1.37793 | 0.0504834 | ||||||||
\(746\) | 43.7240 | 1.60085 | ||||||||
\(747\) | 23.3224 | 0.853323 | ||||||||
\(748\) | −13.7917 | −0.504276 | ||||||||
\(749\) | 12.5643 | 0.459091 | ||||||||
\(750\) | −6.03361 | −0.220316 | ||||||||
\(751\) | −37.2968 | −1.36098 | −0.680490 | − | 0.732757i | \(-0.738233\pi\) | ||||
−0.680490 | + | 0.732757i | \(0.738233\pi\) | |||||||
\(752\) | 17.2288 | 0.628269 | ||||||||
\(753\) | −18.6729 | −0.680477 | ||||||||
\(754\) | 48.8869 | 1.78036 | ||||||||
\(755\) | −6.34924 | −0.231072 | ||||||||
\(756\) | −2.50437 | −0.0910832 | ||||||||
\(757\) | 3.47328 | 0.126239 | 0.0631193 | − | 0.998006i | \(-0.479895\pi\) | ||||
0.0631193 | + | 0.998006i | \(0.479895\pi\) | |||||||
\(758\) | −85.6512 | −3.11099 | ||||||||
\(759\) | 28.4098 | 1.03121 | ||||||||
\(760\) | −43.6237 | −1.58240 | ||||||||
\(761\) | −24.2763 | −0.880014 | −0.440007 | − | 0.897994i | \(-0.645024\pi\) | ||||
−0.440007 | + | 0.897994i | \(0.645024\pi\) | |||||||
\(762\) | −83.6552 | −3.03051 | ||||||||
\(763\) | −28.4711 | −1.03072 | ||||||||
\(764\) | 105.949 | 3.83310 | ||||||||
\(765\) | 3.70311 | 0.133886 | ||||||||
\(766\) | −89.2492 | −3.22470 | ||||||||
\(767\) | −5.08442 | −0.183588 | ||||||||
\(768\) | −78.1876 | −2.82135 | ||||||||
\(769\) | −48.4764 | −1.74810 | −0.874051 | − | 0.485834i | \(-0.838516\pi\) | ||||
−0.874051 | + | 0.485834i | \(0.838516\pi\) | |||||||
\(770\) | 8.98430 | 0.323772 | ||||||||
\(771\) | 26.8792 | 0.968029 | ||||||||
\(772\) | −69.4378 | −2.49912 | ||||||||
\(773\) | −18.1920 | −0.654322 | −0.327161 | − | 0.944969i | \(-0.606092\pi\) | ||||
−0.327161 | + | 0.944969i | \(0.606092\pi\) | |||||||
\(774\) | 77.0828 | 2.77068 | ||||||||
\(775\) | 0.736339 | 0.0264501 | ||||||||
\(776\) | −27.6116 | −0.991199 | ||||||||
\(777\) | −31.2977 | −1.12280 | ||||||||
\(778\) | 15.2153 | 0.545495 | ||||||||
\(779\) | 7.81134 | 0.279870 | ||||||||
\(780\) | −56.4387 | −2.02083 | ||||||||
\(781\) | −25.4689 | −0.911348 | ||||||||
\(782\) | 15.4737 | 0.553338 | ||||||||
\(783\) | −1.44884 | −0.0517774 | ||||||||
\(784\) | −27.0729 | −0.966891 | ||||||||
\(785\) | 1.26479 | 0.0451425 | ||||||||
\(786\) | −75.7640 | −2.70241 | ||||||||
\(787\) | −33.0744 | −1.17897 | −0.589487 | − | 0.807778i | \(-0.700670\pi\) | ||||
−0.589487 | + | 0.807778i | \(0.700670\pi\) | |||||||
\(788\) | −12.0072 | −0.427740 | ||||||||
\(789\) | 49.4651 | 1.76100 | ||||||||
\(790\) | −10.1710 | −0.361869 | ||||||||
\(791\) | −16.2094 | −0.576340 | ||||||||
\(792\) | 39.4304 | 1.40110 | ||||||||
\(793\) | 52.1204 | 1.85085 | ||||||||
\(794\) | 58.0970 | 2.06179 | ||||||||
\(795\) | −28.0840 | −0.996037 | ||||||||
\(796\) | 55.3173 | 1.96067 | ||||||||
\(797\) | 37.4388 | 1.32615 | 0.663075 | − | 0.748553i | \(-0.269251\pi\) | ||||
0.663075 | + | 0.748553i | \(0.269251\pi\) | |||||||
\(798\) | −67.9521 | −2.40548 | ||||||||
\(799\) | 4.08394 | 0.144479 | ||||||||
\(800\) | −2.57800 | −0.0911462 | ||||||||
\(801\) | −12.5759 | −0.444349 | ||||||||
\(802\) | 35.5663 | 1.25589 | ||||||||
\(803\) | 18.6538 | 0.658278 | ||||||||
\(804\) | −33.9972 | −1.19899 | ||||||||
\(805\) | −6.85084 | −0.241460 | ||||||||
\(806\) | 10.1343 | 0.356964 | ||||||||
\(807\) | 68.3848 | 2.40726 | ||||||||
\(808\) | 55.7212 | 1.96027 | ||||||||
\(809\) | −14.7661 | −0.519147 | −0.259573 | − | 0.965723i | \(-0.583582\pi\) | ||||
−0.259573 | + | 0.965723i | \(0.583582\pi\) | |||||||
\(810\) | 23.6826 | 0.832121 | ||||||||
\(811\) | 44.8113 | 1.57354 | 0.786769 | − | 0.617247i | \(-0.211752\pi\) | ||||
0.786769 | + | 0.617247i | \(0.211752\pi\) | |||||||
\(812\) | 21.8088 | 0.765340 | ||||||||
\(813\) | −47.3906 | −1.66206 | ||||||||
\(814\) | −55.6148 | −1.94930 | ||||||||
\(815\) | 8.32875 | 0.291743 | ||||||||
\(816\) | 17.4292 | 0.610143 | ||||||||
\(817\) | −84.8130 | −2.96723 | ||||||||
\(818\) | −77.4210 | −2.70696 | ||||||||
\(819\) | −22.5648 | −0.788478 | ||||||||
\(820\) | 4.25848 | 0.148713 | ||||||||
\(821\) | −36.6367 | −1.27863 | −0.639315 | − | 0.768945i | \(-0.720782\pi\) | ||||
−0.639315 | + | 0.768945i | \(0.720782\pi\) | |||||||
\(822\) | 7.58065 | 0.264405 | ||||||||
\(823\) | −18.8314 | −0.656420 | −0.328210 | − | 0.944605i | \(-0.606445\pi\) | ||||
−0.328210 | + | 0.944605i | \(0.606445\pi\) | |||||||
\(824\) | −32.7770 | −1.14184 | ||||||||
\(825\) | −6.00055 | −0.208912 | ||||||||
\(826\) | −3.33731 | −0.116120 | ||||||||
\(827\) | −25.7635 | −0.895884 | −0.447942 | − | 0.894063i | \(-0.647843\pi\) | ||||
−0.447942 | + | 0.894063i | \(0.647843\pi\) | |||||||
\(828\) | −56.8748 | −1.97654 | ||||||||
\(829\) | −33.6683 | −1.16935 | −0.584675 | − | 0.811268i | \(-0.698778\pi\) | ||||
−0.584675 | + | 0.811268i | \(0.698778\pi\) | |||||||
\(830\) | −20.5837 | −0.714470 | ||||||||
\(831\) | −25.5822 | −0.887436 | ||||||||
\(832\) | 25.3087 | 0.877420 | ||||||||
\(833\) | −6.41742 | −0.222350 | ||||||||
\(834\) | 86.5686 | 2.99763 | ||||||||
\(835\) | −14.1115 | −0.488349 | ||||||||
\(836\) | −82.0665 | −2.83833 | ||||||||
\(837\) | −0.300346 | −0.0103815 | ||||||||
\(838\) | 46.8753 | 1.61928 | ||||||||
\(839\) | 31.8624 | 1.10001 | 0.550005 | − | 0.835161i | \(-0.314626\pi\) | ||||
0.550005 | + | 0.835161i | \(0.314626\pi\) | |||||||
\(840\) | −19.5841 | −0.675714 | ||||||||
\(841\) | −16.3830 | −0.564932 | ||||||||
\(842\) | −17.6561 | −0.608469 | ||||||||
\(843\) | −33.3267 | −1.14783 | ||||||||
\(844\) | −42.7309 | −1.47086 | ||||||||
\(845\) | 17.3407 | 0.596538 | ||||||||
\(846\) | −22.0862 | −0.759339 | ||||||||
\(847\) | −6.98183 | −0.239898 | ||||||||
\(848\) | −64.1761 | −2.20381 | ||||||||
\(849\) | −76.3156 | −2.61914 | ||||||||
\(850\) | −3.26825 | −0.112100 | ||||||||
\(851\) | 42.4083 | 1.45374 | ||||||||
\(852\) | 105.017 | 3.59781 | ||||||||
\(853\) | −1.60687 | −0.0550182 | −0.0275091 | − | 0.999622i | \(-0.508758\pi\) | ||||
−0.0275091 | + | 0.999622i | \(0.508758\pi\) | |||||||
\(854\) | 34.2108 | 1.17067 | ||||||||
\(855\) | 22.0350 | 0.753581 | ||||||||
\(856\) | −48.6672 | −1.66341 | ||||||||
\(857\) | 19.6947 | 0.672758 | 0.336379 | − | 0.941727i | \(-0.390798\pi\) | ||||
0.336379 | + | 0.941727i | \(0.390798\pi\) | |||||||
\(858\) | −82.5859 | −2.81944 | ||||||||
\(859\) | −11.7540 | −0.401040 | −0.200520 | − | 0.979690i | \(-0.564263\pi\) | ||||
−0.200520 | + | 0.979690i | \(0.564263\pi\) | |||||||
\(860\) | −46.2372 | −1.57668 | ||||||||
\(861\) | 3.50676 | 0.119510 | ||||||||
\(862\) | −36.5518 | −1.24496 | ||||||||
\(863\) | −32.2841 | −1.09896 | −0.549482 | − | 0.835505i | \(-0.685175\pi\) | ||||
−0.549482 | + | 0.835505i | \(0.685175\pi\) | |||||||
\(864\) | 1.05154 | 0.0357743 | ||||||||
\(865\) | −5.18347 | −0.176243 | ||||||||
\(866\) | 25.4091 | 0.863438 | ||||||||
\(867\) | −36.9195 | −1.25385 | ||||||||
\(868\) | 4.52098 | 0.153452 | ||||||||
\(869\) | −10.1153 | −0.343138 | ||||||||
\(870\) | −21.4316 | −0.726599 | ||||||||
\(871\) | 18.2765 | 0.619274 | ||||||||
\(872\) | 110.281 | 3.73459 | ||||||||
\(873\) | 13.9470 | 0.472036 | ||||||||
\(874\) | 92.0747 | 3.11447 | ||||||||
\(875\) | 1.44699 | 0.0489172 | ||||||||
\(876\) | −76.9157 | −2.59874 | ||||||||
\(877\) | −40.5928 | −1.37072 | −0.685361 | − | 0.728203i | \(-0.740356\pi\) | ||||
−0.685361 | + | 0.728203i | \(0.740356\pi\) | |||||||
\(878\) | −33.5449 | −1.13209 | ||||||||
\(879\) | −51.5175 | −1.73764 | ||||||||
\(880\) | −13.7121 | −0.462235 | ||||||||
\(881\) | 15.6056 | 0.525765 | 0.262882 | − | 0.964828i | \(-0.415327\pi\) | ||||
0.262882 | + | 0.964828i | \(0.415327\pi\) | |||||||
\(882\) | 34.7058 | 1.16860 | ||||||||
\(883\) | −14.2212 | −0.478581 | −0.239291 | − | 0.970948i | \(-0.576915\pi\) | ||||
−0.239291 | + | 0.970948i | \(0.576915\pi\) | |||||||
\(884\) | −30.5714 | −1.02823 | ||||||||
\(885\) | 2.22897 | 0.0749259 | ||||||||
\(886\) | 7.84542 | 0.263572 | ||||||||
\(887\) | 55.0102 | 1.84706 | 0.923530 | − | 0.383526i | \(-0.125290\pi\) | ||||
0.923530 | + | 0.383526i | \(0.125290\pi\) | |||||||
\(888\) | 121.230 | 4.06821 | ||||||||
\(889\) | 20.0624 | 0.672870 | ||||||||
\(890\) | 11.0992 | 0.372045 | ||||||||
\(891\) | 23.5528 | 0.789049 | ||||||||
\(892\) | −17.2739 | −0.578373 | ||||||||
\(893\) | 24.3011 | 0.813206 | ||||||||
\(894\) | −8.31388 | −0.278058 | ||||||||
\(895\) | −12.9026 | −0.431285 | ||||||||
\(896\) | 24.0728 | 0.804215 | ||||||||
\(897\) | 62.9746 | 2.10266 | ||||||||
\(898\) | 22.5822 | 0.753579 | ||||||||
\(899\) | 2.61550 | 0.0872319 | ||||||||
\(900\) | 12.0127 | 0.400425 | ||||||||
\(901\) | −15.2124 | −0.506799 | ||||||||
\(902\) | 6.23137 | 0.207482 | ||||||||
\(903\) | −38.0753 | −1.26707 | ||||||||
\(904\) | 62.7862 | 2.08824 | ||||||||
\(905\) | 10.1403 | 0.337074 | ||||||||
\(906\) | 38.3088 | 1.27272 | ||||||||
\(907\) | 11.4747 | 0.381012 | 0.190506 | − | 0.981686i | \(-0.438987\pi\) | ||||
0.190506 | + | 0.981686i | \(0.438987\pi\) | |||||||
\(908\) | −53.6507 | −1.78046 | ||||||||
\(909\) | −28.1456 | −0.933531 | ||||||||
\(910\) | 19.9150 | 0.660176 | ||||||||
\(911\) | −34.1664 | −1.13198 | −0.565991 | − | 0.824411i | \(-0.691506\pi\) | ||||
−0.565991 | + | 0.824411i | \(0.691506\pi\) | |||||||
\(912\) | 103.711 | 3.43420 | ||||||||
\(913\) | −20.4709 | −0.677488 | ||||||||
\(914\) | 19.1505 | 0.633442 | ||||||||
\(915\) | −22.8491 | −0.755369 | ||||||||
\(916\) | 116.932 | 3.86353 | ||||||||
\(917\) | 18.1699 | 0.600022 | ||||||||
\(918\) | 1.33309 | 0.0439985 | ||||||||
\(919\) | 17.8279 | 0.588088 | 0.294044 | − | 0.955792i | \(-0.404999\pi\) | ||||
0.294044 | + | 0.955792i | \(0.404999\pi\) | |||||||
\(920\) | 26.5363 | 0.874876 | ||||||||
\(921\) | −2.26261 | −0.0745554 | ||||||||
\(922\) | −23.8169 | −0.784368 | ||||||||
\(923\) | −56.4555 | −1.85826 | ||||||||
\(924\) | −36.8422 | −1.21202 | ||||||||
\(925\) | −8.95720 | −0.294511 | ||||||||
\(926\) | −40.9056 | −1.34424 | ||||||||
\(927\) | 16.5561 | 0.543775 | ||||||||
\(928\) | −9.15716 | −0.300599 | ||||||||
\(929\) | −0.900419 | −0.0295418 | −0.0147709 | − | 0.999891i | \(-0.504702\pi\) | ||||
−0.0147709 | + | 0.999891i | \(0.504702\pi\) | |||||||
\(930\) | −4.44278 | −0.145684 | ||||||||
\(931\) | −38.1862 | −1.25150 | ||||||||
\(932\) | 61.7003 | 2.02106 | ||||||||
\(933\) | −22.1807 | −0.726163 | ||||||||
\(934\) | 56.1353 | 1.83680 | ||||||||
\(935\) | −3.25034 | −0.106298 | ||||||||
\(936\) | 87.4033 | 2.85687 | ||||||||
\(937\) | −20.2468 | −0.661434 | −0.330717 | − | 0.943730i | \(-0.607291\pi\) | ||||
−0.330717 | + | 0.943730i | \(0.607291\pi\) | |||||||
\(938\) | 11.9963 | 0.391693 | ||||||||
\(939\) | −54.3231 | −1.77277 | ||||||||
\(940\) | 13.2482 | 0.432107 | ||||||||
\(941\) | 2.58717 | 0.0843394 | 0.0421697 | − | 0.999110i | \(-0.486573\pi\) | ||||
0.0421697 | + | 0.999110i | \(0.486573\pi\) | |||||||
\(942\) | −7.63127 | −0.248640 | ||||||||
\(943\) | −4.75164 | −0.154735 | ||||||||
\(944\) | 5.09351 | 0.165780 | ||||||||
\(945\) | −0.590214 | −0.0191997 | ||||||||
\(946\) | −67.6583 | −2.19976 | ||||||||
\(947\) | −13.8701 | −0.450719 | −0.225359 | − | 0.974276i | \(-0.572356\pi\) | ||||
−0.225359 | + | 0.974276i | \(0.572356\pi\) | |||||||
\(948\) | 41.7087 | 1.35464 | ||||||||
\(949\) | 41.3489 | 1.34224 | ||||||||
\(950\) | −19.4474 | −0.630958 | ||||||||
\(951\) | −70.0971 | −2.27305 | ||||||||
\(952\) | −10.6082 | −0.343814 | ||||||||
\(953\) | −33.2057 | −1.07564 | −0.537820 | − | 0.843060i | \(-0.680752\pi\) | ||||
−0.537820 | + | 0.843060i | \(0.680752\pi\) | |||||||
\(954\) | 82.2696 | 2.66358 | ||||||||
\(955\) | 24.9694 | 0.807990 | ||||||||
\(956\) | 105.058 | 3.39782 | ||||||||
\(957\) | −21.3142 | −0.688989 | ||||||||
\(958\) | 59.3563 | 1.91772 | ||||||||
\(959\) | −1.81801 | −0.0587064 | ||||||||
\(960\) | −11.0951 | −0.358093 | ||||||||
\(961\) | −30.4578 | −0.982510 | ||||||||
\(962\) | −123.279 | −3.97466 | ||||||||
\(963\) | 24.5826 | 0.792162 | ||||||||
\(964\) | −112.178 | −3.61301 | ||||||||
\(965\) | −16.3647 | −0.526797 | ||||||||
\(966\) | 41.3353 | 1.32994 | ||||||||
\(967\) | −1.84359 | −0.0592858 | −0.0296429 | − | 0.999561i | \(-0.509437\pi\) | ||||
−0.0296429 | + | 0.999561i | \(0.509437\pi\) | |||||||
\(968\) | 27.0437 | 0.869217 | ||||||||
\(969\) | 24.5837 | 0.789744 | ||||||||
\(970\) | −12.3092 | −0.395226 | ||||||||
\(971\) | 34.3365 | 1.10191 | 0.550956 | − | 0.834534i | \(-0.314263\pi\) | ||||
0.550956 | + | 0.834534i | \(0.314263\pi\) | |||||||
\(972\) | −91.9237 | −2.94845 | ||||||||
\(973\) | −20.7610 | −0.665569 | ||||||||
\(974\) | −72.2098 | −2.31375 | ||||||||
\(975\) | −13.3011 | −0.425976 | ||||||||
\(976\) | −52.2136 | −1.67132 | ||||||||
\(977\) | −1.78151 | −0.0569954 | −0.0284977 | − | 0.999594i | \(-0.509072\pi\) | ||||
−0.0284977 | + | 0.999594i | \(0.509072\pi\) | |||||||
\(978\) | −50.2524 | −1.60689 | ||||||||
\(979\) | 11.0383 | 0.352787 | ||||||||
\(980\) | −20.8179 | −0.665002 | ||||||||
\(981\) | −55.7046 | −1.77851 | ||||||||
\(982\) | −34.3515 | −1.09620 | ||||||||
\(983\) | 62.4345 | 1.99135 | 0.995675 | − | 0.0929015i | \(-0.0296142\pi\) | ||||
0.995675 | + | 0.0929015i | \(0.0296142\pi\) | |||||||
\(984\) | −13.5832 | −0.433017 | ||||||||
\(985\) | −2.82979 | −0.0901645 | ||||||||
\(986\) | −11.6090 | −0.369704 | ||||||||
\(987\) | 10.9095 | 0.347254 | ||||||||
\(988\) | −181.912 | −5.78740 | ||||||||
\(989\) | 51.5918 | 1.64052 | ||||||||
\(990\) | 17.5781 | 0.558668 | ||||||||
\(991\) | −36.3717 | −1.15538 | −0.577692 | − | 0.816255i | \(-0.696047\pi\) | ||||
−0.577692 | + | 0.816255i | \(0.696047\pi\) | |||||||
\(992\) | −1.89828 | −0.0602706 | ||||||||
\(993\) | −3.87872 | −0.123087 | ||||||||
\(994\) | −37.0563 | −1.17535 | ||||||||
\(995\) | 13.0368 | 0.413295 | ||||||||
\(996\) | 84.4083 | 2.67458 | ||||||||
\(997\) | 39.5482 | 1.25250 | 0.626251 | − | 0.779621i | \(-0.284588\pi\) | ||||
0.626251 | + | 0.779621i | \(0.284588\pi\) | |||||||
\(998\) | −28.1211 | −0.890158 | ||||||||
\(999\) | 3.65356 | 0.115594 |
(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 | 8045.2.a.c.1.12 | ✓ | 127 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8045.2.a.c.1.12 | ✓ | 127 | 1.1 | even | 1 | trivial |