Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51184 | −1.77614 | −0.888068 | − | 0.459711i | \(-0.847953\pi\) | ||||
−0.888068 | + | 0.459711i | \(0.847953\pi\) | |||||||
\(3\) | −2.51408 | −1.45151 | −0.725753 | − | 0.687956i | \(-0.758508\pi\) | ||||
−0.725753 | + | 0.687956i | \(0.758508\pi\) | |||||||
\(4\) | 4.30932 | 2.15466 | ||||||||
\(5\) | 3.86977 | 1.73061 | 0.865307 | − | 0.501243i | \(-0.167124\pi\) | ||||
0.865307 | + | 0.501243i | \(0.167124\pi\) | |||||||
\(6\) | 6.31496 | 2.57807 | ||||||||
\(7\) | 2.24136 | 0.847155 | 0.423578 | − | 0.905860i | \(-0.360774\pi\) | ||||
0.423578 | + | 0.905860i | \(0.360774\pi\) | |||||||
\(8\) | −5.80064 | −2.05084 | ||||||||
\(9\) | 3.32060 | 1.10687 | ||||||||
\(10\) | −9.72023 | −3.07381 | ||||||||
\(11\) | −3.66849 | −1.10609 | −0.553045 | − | 0.833151i | \(-0.686534\pi\) | ||||
−0.553045 | + | 0.833151i | \(0.686534\pi\) | |||||||
\(12\) | −10.8340 | −3.12750 | ||||||||
\(13\) | −4.71240 | −1.30699 | −0.653493 | − | 0.756933i | \(-0.726697\pi\) | ||||
−0.653493 | + | 0.756933i | \(0.726697\pi\) | |||||||
\(14\) | −5.62993 | −1.50466 | ||||||||
\(15\) | −9.72891 | −2.51199 | ||||||||
\(16\) | 5.95162 | 1.48791 | ||||||||
\(17\) | 5.95455 | 1.44419 | 0.722095 | − | 0.691794i | \(-0.243179\pi\) | ||||
0.722095 | + | 0.691794i | \(0.243179\pi\) | |||||||
\(18\) | −8.34081 | −1.96595 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 16.6761 | 3.72889 | ||||||||
\(21\) | −5.63496 | −1.22965 | ||||||||
\(22\) | 9.21464 | 1.96457 | ||||||||
\(23\) | −5.33707 | −1.11286 | −0.556428 | − | 0.830896i | \(-0.687828\pi\) | ||||
−0.556428 | + | 0.830896i | \(0.687828\pi\) | |||||||
\(24\) | 14.5833 | 2.97680 | ||||||||
\(25\) | 9.97511 | 1.99502 | ||||||||
\(26\) | 11.8368 | 2.32138 | ||||||||
\(27\) | −0.806021 | −0.155119 | ||||||||
\(28\) | 9.65875 | 1.82533 | ||||||||
\(29\) | −4.89281 | −0.908572 | −0.454286 | − | 0.890856i | \(-0.650106\pi\) | ||||
−0.454286 | + | 0.890856i | \(0.650106\pi\) | |||||||
\(30\) | 24.4374 | 4.46165 | ||||||||
\(31\) | 1.00382 | 0.180292 | 0.0901460 | − | 0.995929i | \(-0.471267\pi\) | ||||
0.0901460 | + | 0.995929i | \(0.471267\pi\) | |||||||
\(32\) | −3.34822 | −0.591887 | ||||||||
\(33\) | 9.22288 | 1.60550 | ||||||||
\(34\) | −14.9569 | −2.56508 | ||||||||
\(35\) | 8.67355 | 1.46610 | ||||||||
\(36\) | 14.3096 | 2.38493 | ||||||||
\(37\) | 5.73851 | 0.943405 | 0.471703 | − | 0.881758i | \(-0.343640\pi\) | ||||
0.471703 | + | 0.881758i | \(0.343640\pi\) | |||||||
\(38\) | −2.51184 | −0.407474 | ||||||||
\(39\) | 11.8474 | 1.89710 | ||||||||
\(40\) | −22.4472 | −3.54921 | ||||||||
\(41\) | −8.57893 | −1.33980 | −0.669902 | − | 0.742449i | \(-0.733664\pi\) | ||||
−0.669902 | + | 0.742449i | \(0.733664\pi\) | |||||||
\(42\) | 14.1541 | 2.18403 | ||||||||
\(43\) | −1.69839 | −0.259002 | −0.129501 | − | 0.991579i | \(-0.541337\pi\) | ||||
−0.129501 | + | 0.991579i | \(0.541337\pi\) | |||||||
\(44\) | −15.8087 | −2.38325 | ||||||||
\(45\) | 12.8500 | 1.91556 | ||||||||
\(46\) | 13.4058 | 1.97658 | ||||||||
\(47\) | 0.701681 | 0.102351 | 0.0511753 | − | 0.998690i | \(-0.483703\pi\) | ||||
0.0511753 | + | 0.998690i | \(0.483703\pi\) | |||||||
\(48\) | −14.9629 | −2.15970 | ||||||||
\(49\) | −1.97630 | −0.282328 | ||||||||
\(50\) | −25.0559 | −3.54343 | ||||||||
\(51\) | −14.9702 | −2.09625 | ||||||||
\(52\) | −20.3073 | −2.81611 | ||||||||
\(53\) | 0.437181 | 0.0600514 | 0.0300257 | − | 0.999549i | \(-0.490441\pi\) | ||||
0.0300257 | + | 0.999549i | \(0.490441\pi\) | |||||||
\(54\) | 2.02459 | 0.275512 | ||||||||
\(55\) | −14.1962 | −1.91422 | ||||||||
\(56\) | −13.0013 | −1.73738 | ||||||||
\(57\) | −2.51408 | −0.332998 | ||||||||
\(58\) | 12.2899 | 1.61375 | ||||||||
\(59\) | 13.5962 | 1.77008 | 0.885040 | − | 0.465515i | \(-0.154131\pi\) | ||||
0.885040 | + | 0.465515i | \(0.154131\pi\) | |||||||
\(60\) | −41.9250 | −5.41250 | ||||||||
\(61\) | −0.0150536 | −0.00192742 | −0.000963711 | − | 1.00000i | \(-0.500307\pi\) | ||||
−0.000963711 | 1.00000i | \(0.500307\pi\) | ||||||||
\(62\) | −2.52144 | −0.320223 | ||||||||
\(63\) | 7.44267 | 0.937688 | ||||||||
\(64\) | −3.49307 | −0.436634 | ||||||||
\(65\) | −18.2359 | −2.26189 | ||||||||
\(66\) | −23.1664 | −2.85158 | ||||||||
\(67\) | 1.84947 | 0.225948 | 0.112974 | − | 0.993598i | \(-0.463962\pi\) | ||||
0.112974 | + | 0.993598i | \(0.463962\pi\) | |||||||
\(68\) | 25.6601 | 3.11174 | ||||||||
\(69\) | 13.4178 | 1.61532 | ||||||||
\(70\) | −21.7865 | −2.60399 | ||||||||
\(71\) | −13.3069 | −1.57924 | −0.789621 | − | 0.613595i | \(-0.789723\pi\) | ||||
−0.789621 | + | 0.613595i | \(0.789723\pi\) | |||||||
\(72\) | −19.2616 | −2.27001 | ||||||||
\(73\) | −8.08633 | −0.946434 | −0.473217 | − | 0.880946i | \(-0.656907\pi\) | ||||
−0.473217 | + | 0.880946i | \(0.656907\pi\) | |||||||
\(74\) | −14.4142 | −1.67562 | ||||||||
\(75\) | −25.0782 | −2.89579 | ||||||||
\(76\) | 4.30932 | 0.494313 | ||||||||
\(77\) | −8.22241 | −0.937030 | ||||||||
\(78\) | −29.7586 | −3.36950 | ||||||||
\(79\) | −4.80577 | −0.540691 | −0.270346 | − | 0.962763i | \(-0.587138\pi\) | ||||
−0.270346 | + | 0.962763i | \(0.587138\pi\) | |||||||
\(80\) | 23.0314 | 2.57499 | ||||||||
\(81\) | −7.93541 | −0.881712 | ||||||||
\(82\) | 21.5489 | 2.37968 | ||||||||
\(83\) | −15.3828 | −1.68848 | −0.844241 | − | 0.535964i | \(-0.819948\pi\) | ||||
−0.844241 | + | 0.535964i | \(0.819948\pi\) | |||||||
\(84\) | −24.2829 | −2.64948 | ||||||||
\(85\) | 23.0427 | 2.49933 | ||||||||
\(86\) | 4.26607 | 0.460022 | ||||||||
\(87\) | 12.3009 | 1.31880 | ||||||||
\(88\) | 21.2796 | 2.26841 | ||||||||
\(89\) | 8.34046 | 0.884087 | 0.442044 | − | 0.896994i | \(-0.354254\pi\) | ||||
0.442044 | + | 0.896994i | \(0.354254\pi\) | |||||||
\(90\) | −32.2770 | −3.40230 | ||||||||
\(91\) | −10.5622 | −1.10722 | ||||||||
\(92\) | −22.9992 | −2.39783 | ||||||||
\(93\) | −2.52369 | −0.261695 | ||||||||
\(94\) | −1.76251 | −0.181789 | ||||||||
\(95\) | 3.86977 | 0.397030 | ||||||||
\(96\) | 8.41769 | 0.859127 | ||||||||
\(97\) | 0.165235 | 0.0167770 | 0.00838852 | − | 0.999965i | \(-0.497330\pi\) | ||||
0.00838852 | + | 0.999965i | \(0.497330\pi\) | |||||||
\(98\) | 4.96414 | 0.501454 | ||||||||
\(99\) | −12.1816 | −1.22430 | ||||||||
\(100\) | 42.9860 | 4.29860 | ||||||||
\(101\) | 9.50154 | 0.945438 | 0.472719 | − | 0.881213i | \(-0.343273\pi\) | ||||
0.472719 | + | 0.881213i | \(0.343273\pi\) | |||||||
\(102\) | 37.6027 | 3.72323 | ||||||||
\(103\) | 3.86988 | 0.381311 | 0.190656 | − | 0.981657i | \(-0.438939\pi\) | ||||
0.190656 | + | 0.981657i | \(0.438939\pi\) | |||||||
\(104\) | 27.3350 | 2.68041 | ||||||||
\(105\) | −21.8060 | −2.12805 | ||||||||
\(106\) | −1.09813 | −0.106659 | ||||||||
\(107\) | −5.54097 | −0.535665 | −0.267833 | − | 0.963465i | \(-0.586307\pi\) | ||||
−0.267833 | + | 0.963465i | \(0.586307\pi\) | |||||||
\(108\) | −3.47341 | −0.334229 | ||||||||
\(109\) | 1.31470 | 0.125926 | 0.0629628 | − | 0.998016i | \(-0.479945\pi\) | ||||
0.0629628 | + | 0.998016i | \(0.479945\pi\) | |||||||
\(110\) | 35.6585 | 3.39991 | ||||||||
\(111\) | −14.4271 | −1.36936 | ||||||||
\(112\) | 13.3397 | 1.26049 | ||||||||
\(113\) | 5.08727 | 0.478570 | 0.239285 | − | 0.970949i | \(-0.423087\pi\) | ||||
0.239285 | + | 0.970949i | \(0.423087\pi\) | |||||||
\(114\) | 6.31496 | 0.591450 | ||||||||
\(115\) | −20.6532 | −1.92592 | ||||||||
\(116\) | −21.0847 | −1.95766 | ||||||||
\(117\) | −15.6480 | −1.44666 | ||||||||
\(118\) | −34.1515 | −3.14390 | ||||||||
\(119\) | 13.3463 | 1.22345 | ||||||||
\(120\) | 56.4340 | 5.15169 | ||||||||
\(121\) | 2.45780 | 0.223437 | ||||||||
\(122\) | 0.0378123 | 0.00342336 | ||||||||
\(123\) | 21.5681 | 1.94473 | ||||||||
\(124\) | 4.32580 | 0.388468 | ||||||||
\(125\) | 19.2525 | 1.72200 | ||||||||
\(126\) | −18.6948 | −1.66546 | ||||||||
\(127\) | −8.44650 | −0.749506 | −0.374753 | − | 0.927125i | \(-0.622272\pi\) | ||||
−0.374753 | + | 0.927125i | \(0.622272\pi\) | |||||||
\(128\) | 15.4705 | 1.36741 | ||||||||
\(129\) | 4.26988 | 0.375942 | ||||||||
\(130\) | 45.8056 | 4.01742 | ||||||||
\(131\) | −19.3216 | −1.68814 | −0.844068 | − | 0.536235i | \(-0.819846\pi\) | ||||
−0.844068 | + | 0.536235i | \(0.819846\pi\) | |||||||
\(132\) | 39.7444 | 3.45930 | ||||||||
\(133\) | 2.24136 | 0.194351 | ||||||||
\(134\) | −4.64556 | −0.401315 | ||||||||
\(135\) | −3.11912 | −0.268451 | ||||||||
\(136\) | −34.5402 | −2.96180 | ||||||||
\(137\) | −11.2507 | −0.961210 | −0.480605 | − | 0.876937i | \(-0.659583\pi\) | ||||
−0.480605 | + | 0.876937i | \(0.659583\pi\) | |||||||
\(138\) | −33.7034 | −2.86902 | ||||||||
\(139\) | −17.6209 | −1.49459 | −0.747294 | − | 0.664494i | \(-0.768647\pi\) | ||||
−0.747294 | + | 0.664494i | \(0.768647\pi\) | |||||||
\(140\) | 37.3771 | 3.15895 | ||||||||
\(141\) | −1.76408 | −0.148563 | ||||||||
\(142\) | 33.4248 | 2.80495 | ||||||||
\(143\) | 17.2874 | 1.44564 | ||||||||
\(144\) | 19.7630 | 1.64691 | ||||||||
\(145\) | −18.9340 | −1.57239 | ||||||||
\(146\) | 20.3115 | 1.68100 | ||||||||
\(147\) | 4.96857 | 0.409801 | ||||||||
\(148\) | 24.7291 | 2.03272 | ||||||||
\(149\) | −2.69684 | −0.220934 | −0.110467 | − | 0.993880i | \(-0.535235\pi\) | ||||
−0.110467 | + | 0.993880i | \(0.535235\pi\) | |||||||
\(150\) | 62.9924 | 5.14331 | ||||||||
\(151\) | 6.78790 | 0.552391 | 0.276196 | − | 0.961101i | \(-0.410926\pi\) | ||||
0.276196 | + | 0.961101i | \(0.410926\pi\) | |||||||
\(152\) | −5.80064 | −0.470494 | ||||||||
\(153\) | 19.7727 | 1.59853 | ||||||||
\(154\) | 20.6533 | 1.66429 | ||||||||
\(155\) | 3.88456 | 0.312016 | ||||||||
\(156\) | 51.0541 | 4.08760 | ||||||||
\(157\) | 21.5192 | 1.71742 | 0.858710 | − | 0.512461i | \(-0.171266\pi\) | ||||
0.858710 | + | 0.512461i | \(0.171266\pi\) | |||||||
\(158\) | 12.0713 | 0.960342 | ||||||||
\(159\) | −1.09911 | −0.0871649 | ||||||||
\(160\) | −12.9568 | −1.02433 | ||||||||
\(161\) | −11.9623 | −0.942761 | ||||||||
\(162\) | 19.9324 | 1.56604 | ||||||||
\(163\) | 10.4381 | 0.817571 | 0.408786 | − | 0.912630i | \(-0.365952\pi\) | ||||
0.408786 | + | 0.912630i | \(0.365952\pi\) | |||||||
\(164\) | −36.9694 | −2.88683 | ||||||||
\(165\) | 35.6904 | 2.77849 | ||||||||
\(166\) | 38.6391 | 2.99897 | ||||||||
\(167\) | −7.03352 | −0.544270 | −0.272135 | − | 0.962259i | \(-0.587730\pi\) | ||||
−0.272135 | + | 0.962259i | \(0.587730\pi\) | |||||||
\(168\) | 32.6864 | 2.52181 | ||||||||
\(169\) | 9.20673 | 0.708210 | ||||||||
\(170\) | −57.8796 | −4.43916 | ||||||||
\(171\) | 3.32060 | 0.253933 | ||||||||
\(172\) | −7.31890 | −0.558061 | ||||||||
\(173\) | 16.2628 | 1.23644 | 0.618218 | − | 0.786007i | \(-0.287855\pi\) | ||||
0.618218 | + | 0.786007i | \(0.287855\pi\) | |||||||
\(174\) | −30.8979 | −2.34236 | ||||||||
\(175\) | 22.3578 | 1.69009 | ||||||||
\(176\) | −21.8335 | −1.64576 | ||||||||
\(177\) | −34.1821 | −2.56928 | ||||||||
\(178\) | −20.9499 | −1.57026 | ||||||||
\(179\) | −16.3585 | −1.22269 | −0.611344 | − | 0.791365i | \(-0.709371\pi\) | ||||
−0.611344 | + | 0.791365i | \(0.709371\pi\) | |||||||
\(180\) | 55.3747 | 4.12738 | ||||||||
\(181\) | −20.9874 | −1.55998 | −0.779990 | − | 0.625792i | \(-0.784776\pi\) | ||||
−0.779990 | + | 0.625792i | \(0.784776\pi\) | |||||||
\(182\) | 26.5305 | 1.96657 | ||||||||
\(183\) | 0.0378461 | 0.00279766 | ||||||||
\(184\) | 30.9584 | 2.28229 | ||||||||
\(185\) | 22.2067 | 1.63267 | ||||||||
\(186\) | 6.33910 | 0.464806 | ||||||||
\(187\) | −21.8442 | −1.59741 | ||||||||
\(188\) | 3.02377 | 0.220531 | ||||||||
\(189\) | −1.80659 | −0.131410 | ||||||||
\(190\) | −9.72023 | −0.705179 | ||||||||
\(191\) | −9.80803 | −0.709684 | −0.354842 | − | 0.934926i | \(-0.615465\pi\) | ||||
−0.354842 | + | 0.934926i | \(0.615465\pi\) | |||||||
\(192\) | 8.78186 | 0.633776 | ||||||||
\(193\) | 15.2445 | 1.09732 | 0.548660 | − | 0.836046i | \(-0.315138\pi\) | ||||
0.548660 | + | 0.836046i | \(0.315138\pi\) | |||||||
\(194\) | −0.415043 | −0.0297983 | ||||||||
\(195\) | 45.8465 | 3.28314 | ||||||||
\(196\) | −8.51651 | −0.608322 | ||||||||
\(197\) | 20.1164 | 1.43323 | 0.716616 | − | 0.697468i | \(-0.245690\pi\) | ||||
0.716616 | + | 0.697468i | \(0.245690\pi\) | |||||||
\(198\) | 30.5982 | 2.17452 | ||||||||
\(199\) | 17.9659 | 1.27357 | 0.636785 | − | 0.771042i | \(-0.280264\pi\) | ||||
0.636785 | + | 0.771042i | \(0.280264\pi\) | |||||||
\(200\) | −57.8621 | −4.09147 | ||||||||
\(201\) | −4.64971 | −0.327965 | ||||||||
\(202\) | −23.8663 | −1.67923 | ||||||||
\(203\) | −10.9666 | −0.769701 | ||||||||
\(204\) | −64.5115 | −4.51671 | ||||||||
\(205\) | −33.1985 | −2.31868 | ||||||||
\(206\) | −9.72052 | −0.677261 | ||||||||
\(207\) | −17.7223 | −1.23178 | ||||||||
\(208\) | −28.0464 | −1.94467 | ||||||||
\(209\) | −3.66849 | −0.253755 | ||||||||
\(210\) | 54.7731 | 3.77971 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 1.88395 | 0.129390 | ||||||||
\(213\) | 33.4547 | 2.29228 | ||||||||
\(214\) | 13.9180 | 0.951415 | ||||||||
\(215\) | −6.57236 | −0.448231 | ||||||||
\(216\) | 4.67544 | 0.318124 | ||||||||
\(217\) | 2.24993 | 0.152735 | ||||||||
\(218\) | −3.30232 | −0.223661 | ||||||||
\(219\) | 20.3297 | 1.37375 | ||||||||
\(220\) | −61.1760 | −4.12449 | ||||||||
\(221\) | −28.0602 | −1.88753 | ||||||||
\(222\) | 36.2385 | 2.43217 | ||||||||
\(223\) | 7.87139 | 0.527107 | 0.263554 | − | 0.964645i | \(-0.415105\pi\) | ||||
0.263554 | + | 0.964645i | \(0.415105\pi\) | |||||||
\(224\) | −7.50457 | −0.501420 | ||||||||
\(225\) | 33.1234 | 2.20823 | ||||||||
\(226\) | −12.7784 | −0.850006 | ||||||||
\(227\) | −23.4109 | −1.55384 | −0.776918 | − | 0.629602i | \(-0.783218\pi\) | ||||
−0.776918 | + | 0.629602i | \(0.783218\pi\) | |||||||
\(228\) | −10.8340 | −0.717498 | ||||||||
\(229\) | 3.65273 | 0.241379 | 0.120690 | − | 0.992690i | \(-0.461489\pi\) | ||||
0.120690 | + | 0.992690i | \(0.461489\pi\) | |||||||
\(230\) | 51.8775 | 3.42070 | ||||||||
\(231\) | 20.6718 | 1.36010 | ||||||||
\(232\) | 28.3814 | 1.86333 | ||||||||
\(233\) | 24.4712 | 1.60316 | 0.801581 | − | 0.597887i | \(-0.203993\pi\) | ||||
0.801581 | + | 0.597887i | \(0.203993\pi\) | |||||||
\(234\) | 39.3053 | 2.56947 | ||||||||
\(235\) | 2.71534 | 0.177129 | ||||||||
\(236\) | 58.5906 | 3.81392 | ||||||||
\(237\) | 12.0821 | 0.784816 | ||||||||
\(238\) | −33.5237 | −2.17302 | ||||||||
\(239\) | −19.1928 | −1.24148 | −0.620740 | − | 0.784016i | \(-0.713168\pi\) | ||||
−0.620740 | + | 0.784016i | \(0.713168\pi\) | |||||||
\(240\) | −57.9028 | −3.73761 | ||||||||
\(241\) | −15.0736 | −0.970977 | −0.485489 | − | 0.874243i | \(-0.661358\pi\) | ||||
−0.485489 | + | 0.874243i | \(0.661358\pi\) | |||||||
\(242\) | −6.17360 | −0.396854 | ||||||||
\(243\) | 22.3683 | 1.43493 | ||||||||
\(244\) | −0.0648710 | −0.00415294 | ||||||||
\(245\) | −7.64782 | −0.488601 | ||||||||
\(246\) | −54.1756 | −3.45411 | ||||||||
\(247\) | −4.71240 | −0.299843 | ||||||||
\(248\) | −5.82282 | −0.369749 | ||||||||
\(249\) | 38.6736 | 2.45084 | ||||||||
\(250\) | −48.3592 | −3.05851 | ||||||||
\(251\) | −26.0152 | −1.64207 | −0.821034 | − | 0.570879i | \(-0.806602\pi\) | ||||
−0.821034 | + | 0.570879i | \(0.806602\pi\) | |||||||
\(252\) | 32.0729 | 2.02040 | ||||||||
\(253\) | 19.5790 | 1.23092 | ||||||||
\(254\) | 21.2162 | 1.33122 | ||||||||
\(255\) | −57.9313 | −3.62780 | ||||||||
\(256\) | −31.8731 | −1.99207 | ||||||||
\(257\) | −29.6834 | −1.85160 | −0.925799 | − | 0.378017i | \(-0.876606\pi\) | ||||
−0.925799 | + | 0.378017i | \(0.876606\pi\) | |||||||
\(258\) | −10.7252 | −0.667725 | ||||||||
\(259\) | 12.8621 | 0.799211 | ||||||||
\(260\) | −78.5844 | −4.87360 | ||||||||
\(261\) | −16.2471 | −1.00567 | ||||||||
\(262\) | 48.5327 | 2.99836 | ||||||||
\(263\) | −23.3222 | −1.43811 | −0.719053 | − | 0.694955i | \(-0.755424\pi\) | ||||
−0.719053 | + | 0.694955i | \(0.755424\pi\) | |||||||
\(264\) | −53.4986 | −3.29261 | ||||||||
\(265\) | 1.69179 | 0.103926 | ||||||||
\(266\) | −5.62993 | −0.345193 | ||||||||
\(267\) | −20.9686 | −1.28326 | ||||||||
\(268\) | 7.96996 | 0.486842 | ||||||||
\(269\) | −19.1515 | −1.16769 | −0.583843 | − | 0.811866i | \(-0.698452\pi\) | ||||
−0.583843 | + | 0.811866i | \(0.698452\pi\) | |||||||
\(270\) | 7.83471 | 0.476805 | ||||||||
\(271\) | −5.71778 | −0.347331 | −0.173665 | − | 0.984805i | \(-0.555561\pi\) | ||||
−0.173665 | + | 0.984805i | \(0.555561\pi\) | |||||||
\(272\) | 35.4392 | 2.14882 | ||||||||
\(273\) | 26.5542 | 1.60713 | ||||||||
\(274\) | 28.2599 | 1.70724 | ||||||||
\(275\) | −36.5936 | −2.20668 | ||||||||
\(276\) | 57.8217 | 3.48046 | ||||||||
\(277\) | 16.8896 | 1.01480 | 0.507399 | − | 0.861711i | \(-0.330607\pi\) | ||||
0.507399 | + | 0.861711i | \(0.330607\pi\) | |||||||
\(278\) | 44.2609 | 2.65459 | ||||||||
\(279\) | 3.33330 | 0.199559 | ||||||||
\(280\) | −50.3122 | −3.00673 | ||||||||
\(281\) | −15.4220 | −0.920002 | −0.460001 | − | 0.887918i | \(-0.652151\pi\) | ||||
−0.460001 | + | 0.887918i | \(0.652151\pi\) | |||||||
\(282\) | 4.43109 | 0.263867 | ||||||||
\(283\) | −10.9939 | −0.653517 | −0.326758 | − | 0.945108i | \(-0.605956\pi\) | ||||
−0.326758 | + | 0.945108i | \(0.605956\pi\) | |||||||
\(284\) | −57.3438 | −3.40273 | ||||||||
\(285\) | −9.72891 | −0.576291 | ||||||||
\(286\) | −43.4231 | −2.56766 | ||||||||
\(287\) | −19.2285 | −1.13502 | ||||||||
\(288\) | −11.1181 | −0.655141 | ||||||||
\(289\) | 18.4566 | 1.08568 | ||||||||
\(290\) | 47.5592 | 2.79277 | ||||||||
\(291\) | −0.415413 | −0.0243520 | ||||||||
\(292\) | −34.8466 | −2.03924 | ||||||||
\(293\) | −1.44814 | −0.0846012 | −0.0423006 | − | 0.999105i | \(-0.513469\pi\) | ||||
−0.0423006 | + | 0.999105i | \(0.513469\pi\) | |||||||
\(294\) | −12.4802 | −0.727863 | ||||||||
\(295\) | 52.6143 | 3.06332 | ||||||||
\(296\) | −33.2871 | −1.93477 | ||||||||
\(297\) | 2.95688 | 0.171576 | ||||||||
\(298\) | 6.77403 | 0.392409 | ||||||||
\(299\) | 25.1504 | 1.45449 | ||||||||
\(300\) | −108.070 | −6.23944 | ||||||||
\(301\) | −3.80670 | −0.219414 | ||||||||
\(302\) | −17.0501 | −0.981123 | ||||||||
\(303\) | −23.8876 | −1.37231 | ||||||||
\(304\) | 5.95162 | 0.341349 | ||||||||
\(305\) | −0.0582541 | −0.00333562 | ||||||||
\(306\) | −49.6658 | −2.83920 | ||||||||
\(307\) | 3.45110 | 0.196965 | 0.0984823 | − | 0.995139i | \(-0.468601\pi\) | ||||
0.0984823 | + | 0.995139i | \(0.468601\pi\) | |||||||
\(308\) | −35.4330 | −2.01898 | ||||||||
\(309\) | −9.72920 | −0.553475 | ||||||||
\(310\) | −9.75739 | −0.554182 | ||||||||
\(311\) | −3.20625 | −0.181810 | −0.0909049 | − | 0.995860i | \(-0.528976\pi\) | ||||
−0.0909049 | + | 0.995860i | \(0.528976\pi\) | |||||||
\(312\) | −68.7223 | −3.89064 | ||||||||
\(313\) | −4.24418 | −0.239895 | −0.119948 | − | 0.992780i | \(-0.538273\pi\) | ||||
−0.119948 | + | 0.992780i | \(0.538273\pi\) | |||||||
\(314\) | −54.0528 | −3.05037 | ||||||||
\(315\) | 28.8014 | 1.62278 | ||||||||
\(316\) | −20.7096 | −1.16501 | ||||||||
\(317\) | 26.1975 | 1.47140 | 0.735699 | − | 0.677309i | \(-0.236854\pi\) | ||||
0.735699 | + | 0.677309i | \(0.236854\pi\) | |||||||
\(318\) | 2.76078 | 0.154817 | ||||||||
\(319\) | 17.9492 | 1.00496 | ||||||||
\(320\) | −13.5174 | −0.755644 | ||||||||
\(321\) | 13.9304 | 0.777521 | ||||||||
\(322\) | 30.0473 | 1.67447 | ||||||||
\(323\) | 5.95455 | 0.331320 | ||||||||
\(324\) | −34.1962 | −1.89979 | ||||||||
\(325\) | −47.0067 | −2.60746 | ||||||||
\(326\) | −26.2187 | −1.45212 | ||||||||
\(327\) | −3.30527 | −0.182782 | ||||||||
\(328\) | 49.7633 | 2.74772 | ||||||||
\(329\) | 1.57272 | 0.0867069 | ||||||||
\(330\) | −89.6485 | −4.93499 | ||||||||
\(331\) | 17.7740 | 0.976945 | 0.488472 | − | 0.872579i | \(-0.337554\pi\) | ||||
0.488472 | + | 0.872579i | \(0.337554\pi\) | |||||||
\(332\) | −66.2894 | −3.63811 | ||||||||
\(333\) | 19.0553 | 1.04422 | ||||||||
\(334\) | 17.6670 | 0.966698 | ||||||||
\(335\) | 7.15701 | 0.391029 | ||||||||
\(336\) | −33.5372 | −1.82960 | ||||||||
\(337\) | 18.5094 | 1.00827 | 0.504135 | − | 0.863625i | \(-0.331811\pi\) | ||||
0.504135 | + | 0.863625i | \(0.331811\pi\) | |||||||
\(338\) | −23.1258 | −1.25788 | ||||||||
\(339\) | −12.7898 | −0.694647 | ||||||||
\(340\) | 99.2986 | 5.38522 | ||||||||
\(341\) | −3.68251 | −0.199419 | ||||||||
\(342\) | −8.34081 | −0.451019 | ||||||||
\(343\) | −20.1191 | −1.08633 | ||||||||
\(344\) | 9.85174 | 0.531170 | ||||||||
\(345\) | 51.9239 | 2.79549 | ||||||||
\(346\) | −40.8495 | −2.19608 | ||||||||
\(347\) | 4.93695 | 0.265030 | 0.132515 | − | 0.991181i | \(-0.457695\pi\) | ||||
0.132515 | + | 0.991181i | \(0.457695\pi\) | |||||||
\(348\) | 53.0086 | 2.84156 | ||||||||
\(349\) | 21.4593 | 1.14869 | 0.574346 | − | 0.818613i | \(-0.305257\pi\) | ||||
0.574346 | + | 0.818613i | \(0.305257\pi\) | |||||||
\(350\) | −56.1592 | −3.00184 | ||||||||
\(351\) | 3.79830 | 0.202738 | ||||||||
\(352\) | 12.2829 | 0.654681 | ||||||||
\(353\) | −19.8723 | −1.05770 | −0.528848 | − | 0.848717i | \(-0.677376\pi\) | ||||
−0.528848 | + | 0.848717i | \(0.677376\pi\) | |||||||
\(354\) | 85.8597 | 4.56339 | ||||||||
\(355\) | −51.4947 | −2.73306 | ||||||||
\(356\) | 35.9418 | 1.90491 | ||||||||
\(357\) | −33.5537 | −1.77585 | ||||||||
\(358\) | 41.0898 | 2.17166 | ||||||||
\(359\) | −23.3055 | −1.23002 | −0.615009 | − | 0.788520i | \(-0.710848\pi\) | ||||
−0.615009 | + | 0.788520i | \(0.710848\pi\) | |||||||
\(360\) | −74.5381 | −3.92850 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 52.7169 | 2.77074 | ||||||||
\(363\) | −6.17912 | −0.324320 | ||||||||
\(364\) | −45.5159 | −2.38568 | ||||||||
\(365\) | −31.2922 | −1.63791 | ||||||||
\(366\) | −0.0950631 | −0.00496903 | ||||||||
\(367\) | −5.44203 | −0.284071 | −0.142036 | − | 0.989862i | \(-0.545365\pi\) | ||||
−0.142036 | + | 0.989862i | \(0.545365\pi\) | |||||||
\(368\) | −31.7642 | −1.65582 | ||||||||
\(369\) | −28.4872 | −1.48299 | ||||||||
\(370\) | −55.7796 | −2.89985 | ||||||||
\(371\) | 0.979880 | 0.0508728 | ||||||||
\(372\) | −10.8754 | −0.563864 | ||||||||
\(373\) | 10.1229 | 0.524144 | 0.262072 | − | 0.965048i | \(-0.415594\pi\) | ||||
0.262072 | + | 0.965048i | \(0.415594\pi\) | |||||||
\(374\) | 54.8690 | 2.83721 | ||||||||
\(375\) | −48.4024 | −2.49949 | ||||||||
\(376\) | −4.07020 | −0.209905 | ||||||||
\(377\) | 23.0569 | 1.18749 | ||||||||
\(378\) | 4.53785 | 0.233402 | ||||||||
\(379\) | 25.3608 | 1.30270 | 0.651348 | − | 0.758779i | \(-0.274204\pi\) | ||||
0.651348 | + | 0.758779i | \(0.274204\pi\) | |||||||
\(380\) | 16.6761 | 0.855465 | ||||||||
\(381\) | 21.2352 | 1.08791 | ||||||||
\(382\) | 24.6362 | 1.26050 | ||||||||
\(383\) | −6.28404 | −0.321100 | −0.160550 | − | 0.987028i | \(-0.551327\pi\) | ||||
−0.160550 | + | 0.987028i | \(0.551327\pi\) | |||||||
\(384\) | −38.8940 | −1.98480 | ||||||||
\(385\) | −31.8188 | −1.62164 | ||||||||
\(386\) | −38.2916 | −1.94899 | ||||||||
\(387\) | −5.63967 | −0.286680 | ||||||||
\(388\) | 0.712050 | 0.0361489 | ||||||||
\(389\) | 4.92909 | 0.249915 | 0.124958 | − | 0.992162i | \(-0.460121\pi\) | ||||
0.124958 | + | 0.992162i | \(0.460121\pi\) | |||||||
\(390\) | −115.159 | −5.83130 | ||||||||
\(391\) | −31.7798 | −1.60717 | ||||||||
\(392\) | 11.4638 | 0.579009 | ||||||||
\(393\) | 48.5761 | 2.45034 | ||||||||
\(394\) | −50.5290 | −2.54562 | ||||||||
\(395\) | −18.5972 | −0.935728 | ||||||||
\(396\) | −52.4944 | −2.63794 | ||||||||
\(397\) | 30.2060 | 1.51599 | 0.757997 | − | 0.652258i | \(-0.226178\pi\) | ||||
0.757997 | + | 0.652258i | \(0.226178\pi\) | |||||||
\(398\) | −45.1274 | −2.26203 | ||||||||
\(399\) | −5.63496 | −0.282101 | ||||||||
\(400\) | 59.3681 | 2.96841 | ||||||||
\(401\) | −9.21321 | −0.460086 | −0.230043 | − | 0.973181i | \(-0.573887\pi\) | ||||
−0.230043 | + | 0.973181i | \(0.573887\pi\) | |||||||
\(402\) | 11.6793 | 0.582511 | ||||||||
\(403\) | −4.73042 | −0.235639 | ||||||||
\(404\) | 40.9452 | 2.03710 | ||||||||
\(405\) | −30.7082 | −1.52590 | ||||||||
\(406\) | 27.5462 | 1.36709 | ||||||||
\(407\) | −21.0517 | −1.04349 | ||||||||
\(408\) | 86.8369 | 4.29907 | ||||||||
\(409\) | 3.70221 | 0.183062 | 0.0915312 | − | 0.995802i | \(-0.470824\pi\) | ||||
0.0915312 | + | 0.995802i | \(0.470824\pi\) | |||||||
\(410\) | 83.3892 | 4.11830 | ||||||||
\(411\) | 28.2851 | 1.39520 | ||||||||
\(412\) | 16.6766 | 0.821596 | ||||||||
\(413\) | 30.4741 | 1.49953 | ||||||||
\(414\) | 44.5155 | 2.18782 | ||||||||
\(415\) | −59.5279 | −2.92211 | ||||||||
\(416\) | 15.7782 | 0.773587 | ||||||||
\(417\) | 44.3004 | 2.16940 | ||||||||
\(418\) | 9.21464 | 0.450703 | ||||||||
\(419\) | −31.9262 | −1.55970 | −0.779849 | − | 0.625967i | \(-0.784704\pi\) | ||||
−0.779849 | + | 0.625967i | \(0.784704\pi\) | |||||||
\(420\) | −93.9692 | −4.58523 | ||||||||
\(421\) | 19.1099 | 0.931360 | 0.465680 | − | 0.884953i | \(-0.345810\pi\) | ||||
0.465680 | + | 0.884953i | \(0.345810\pi\) | |||||||
\(422\) | −2.51184 | −0.122274 | ||||||||
\(423\) | 2.33000 | 0.113289 | ||||||||
\(424\) | −2.53593 | −0.123156 | ||||||||
\(425\) | 59.3973 | 2.88119 | ||||||||
\(426\) | −84.0327 | −4.07140 | ||||||||
\(427\) | −0.0337407 | −0.00163282 | ||||||||
\(428\) | −23.8778 | −1.15418 | ||||||||
\(429\) | −43.4619 | −2.09836 | ||||||||
\(430\) | 16.5087 | 0.796120 | ||||||||
\(431\) | 33.5101 | 1.61412 | 0.807062 | − | 0.590467i | \(-0.201056\pi\) | ||||
0.807062 | + | 0.590467i | \(0.201056\pi\) | |||||||
\(432\) | −4.79714 | −0.230802 | ||||||||
\(433\) | −18.0900 | −0.869351 | −0.434675 | − | 0.900587i | \(-0.643137\pi\) | ||||
−0.434675 | + | 0.900587i | \(0.643137\pi\) | |||||||
\(434\) | −5.65146 | −0.271279 | ||||||||
\(435\) | 47.6017 | 2.28233 | ||||||||
\(436\) | 5.66548 | 0.271327 | ||||||||
\(437\) | −5.33707 | −0.255307 | ||||||||
\(438\) | −51.0649 | −2.43997 | ||||||||
\(439\) | 7.49629 | 0.357778 | 0.178889 | − | 0.983869i | \(-0.442750\pi\) | ||||
0.178889 | + | 0.983869i | \(0.442750\pi\) | |||||||
\(440\) | 82.3471 | 3.92574 | ||||||||
\(441\) | −6.56250 | −0.312500 | ||||||||
\(442\) | 70.4827 | 3.35252 | ||||||||
\(443\) | −10.0173 | −0.475935 | −0.237967 | − | 0.971273i | \(-0.576481\pi\) | ||||
−0.237967 | + | 0.971273i | \(0.576481\pi\) | |||||||
\(444\) | −62.1710 | −2.95050 | ||||||||
\(445\) | 32.2757 | 1.53001 | ||||||||
\(446\) | −19.7716 | −0.936215 | ||||||||
\(447\) | 6.78008 | 0.320687 | ||||||||
\(448\) | −7.82923 | −0.369896 | ||||||||
\(449\) | −2.44501 | −0.115387 | −0.0576937 | − | 0.998334i | \(-0.518375\pi\) | ||||
−0.0576937 | + | 0.998334i | \(0.518375\pi\) | |||||||
\(450\) | −83.2005 | −3.92211 | ||||||||
\(451\) | 31.4717 | 1.48195 | ||||||||
\(452\) | 21.9227 | 1.03116 | ||||||||
\(453\) | −17.0653 | −0.801799 | ||||||||
\(454\) | 58.8044 | 2.75983 | ||||||||
\(455\) | −40.8733 | −1.91617 | ||||||||
\(456\) | 14.5833 | 0.682925 | ||||||||
\(457\) | −26.7420 | −1.25094 | −0.625470 | − | 0.780248i | \(-0.715093\pi\) | ||||
−0.625470 | + | 0.780248i | \(0.715093\pi\) | |||||||
\(458\) | −9.17506 | −0.428723 | ||||||||
\(459\) | −4.79949 | −0.224021 | ||||||||
\(460\) | −89.0014 | −4.14971 | ||||||||
\(461\) | 3.88863 | 0.181112 | 0.0905558 | − | 0.995891i | \(-0.471136\pi\) | ||||
0.0905558 | + | 0.995891i | \(0.471136\pi\) | |||||||
\(462\) | −51.9242 | −2.41573 | ||||||||
\(463\) | 2.74342 | 0.127497 | 0.0637487 | − | 0.997966i | \(-0.479694\pi\) | ||||
0.0637487 | + | 0.997966i | \(0.479694\pi\) | |||||||
\(464\) | −29.1202 | −1.35187 | ||||||||
\(465\) | −9.76611 | −0.452892 | ||||||||
\(466\) | −61.4676 | −2.84743 | ||||||||
\(467\) | 41.1650 | 1.90489 | 0.952444 | − | 0.304715i | \(-0.0985612\pi\) | ||||
0.952444 | + | 0.304715i | \(0.0985612\pi\) | |||||||
\(468\) | −67.4324 | −3.11706 | ||||||||
\(469\) | 4.14533 | 0.191413 | ||||||||
\(470\) | −6.82050 | −0.314606 | ||||||||
\(471\) | −54.1011 | −2.49284 | ||||||||
\(472\) | −78.8670 | −3.63015 | ||||||||
\(473\) | 6.23051 | 0.286479 | ||||||||
\(474\) | −30.3482 | −1.39394 | ||||||||
\(475\) | 9.97511 | 0.457690 | ||||||||
\(476\) | 57.5135 | 2.63613 | ||||||||
\(477\) | 1.45170 | 0.0664689 | ||||||||
\(478\) | 48.2092 | 2.20504 | ||||||||
\(479\) | −19.9855 | −0.913159 | −0.456580 | − | 0.889683i | \(-0.650926\pi\) | ||||
−0.456580 | + | 0.889683i | \(0.650926\pi\) | |||||||
\(480\) | 32.5745 | 1.48682 | ||||||||
\(481\) | −27.0422 | −1.23302 | ||||||||
\(482\) | 37.8625 | 1.72459 | ||||||||
\(483\) | 30.0742 | 1.36842 | ||||||||
\(484\) | 10.5915 | 0.481431 | ||||||||
\(485\) | 0.639420 | 0.0290346 | ||||||||
\(486\) | −56.1856 | −2.54863 | ||||||||
\(487\) | −22.1530 | −1.00385 | −0.501923 | − | 0.864912i | \(-0.667374\pi\) | ||||
−0.501923 | + | 0.864912i | \(0.667374\pi\) | |||||||
\(488\) | 0.0873208 | 0.00395283 | ||||||||
\(489\) | −26.2421 | −1.18671 | ||||||||
\(490\) | 19.2101 | 0.867822 | ||||||||
\(491\) | 28.4675 | 1.28472 | 0.642360 | − | 0.766403i | \(-0.277956\pi\) | ||||
0.642360 | + | 0.766403i | \(0.277956\pi\) | |||||||
\(492\) | 92.9441 | 4.19024 | ||||||||
\(493\) | −29.1345 | −1.31215 | ||||||||
\(494\) | 11.8368 | 0.532562 | ||||||||
\(495\) | −47.1399 | −2.11878 | ||||||||
\(496\) | 5.97438 | 0.268257 | ||||||||
\(497\) | −29.8256 | −1.33786 | ||||||||
\(498\) | −97.1417 | −4.35303 | ||||||||
\(499\) | −5.14118 | −0.230151 | −0.115075 | − | 0.993357i | \(-0.536711\pi\) | ||||
−0.115075 | + | 0.993357i | \(0.536711\pi\) | |||||||
\(500\) | 82.9654 | 3.71033 | ||||||||
\(501\) | 17.6828 | 0.790011 | ||||||||
\(502\) | 65.3461 | 2.91654 | ||||||||
\(503\) | 4.36152 | 0.194471 | 0.0972353 | − | 0.995261i | \(-0.469000\pi\) | ||||
0.0972353 | + | 0.995261i | \(0.469000\pi\) | |||||||
\(504\) | −43.1723 | −1.92305 | ||||||||
\(505\) | 36.7688 | 1.63619 | ||||||||
\(506\) | −49.1792 | −2.18628 | ||||||||
\(507\) | −23.1465 | −1.02797 | ||||||||
\(508\) | −36.3987 | −1.61493 | ||||||||
\(509\) | 1.86957 | 0.0828670 | 0.0414335 | − | 0.999141i | \(-0.486808\pi\) | ||||
0.0414335 | + | 0.999141i | \(0.486808\pi\) | |||||||
\(510\) | 145.514 | 6.44346 | ||||||||
\(511\) | −18.1244 | −0.801776 | ||||||||
\(512\) | 49.1192 | 2.17078 | ||||||||
\(513\) | −0.806021 | −0.0355867 | ||||||||
\(514\) | 74.5598 | 3.28869 | ||||||||
\(515\) | 14.9756 | 0.659902 | ||||||||
\(516\) | 18.4003 | 0.810028 | ||||||||
\(517\) | −2.57411 | −0.113209 | ||||||||
\(518\) | −32.3074 | −1.41951 | ||||||||
\(519\) | −40.8859 | −1.79469 | ||||||||
\(520\) | 105.780 | 4.63876 | ||||||||
\(521\) | −27.0090 | −1.18329 | −0.591644 | − | 0.806200i | \(-0.701521\pi\) | ||||
−0.591644 | + | 0.806200i | \(0.701521\pi\) | |||||||
\(522\) | 40.8100 | 1.78620 | ||||||||
\(523\) | 23.3456 | 1.02083 | 0.510416 | − | 0.859928i | \(-0.329492\pi\) | ||||
0.510416 | + | 0.859928i | \(0.329492\pi\) | |||||||
\(524\) | −83.2631 | −3.63736 | ||||||||
\(525\) | −56.2094 | −2.45318 | ||||||||
\(526\) | 58.5815 | 2.55427 | ||||||||
\(527\) | 5.97731 | 0.260376 | ||||||||
\(528\) | 54.8911 | 2.38883 | ||||||||
\(529\) | 5.48429 | 0.238447 | ||||||||
\(530\) | −4.24950 | −0.184586 | ||||||||
\(531\) | 45.1477 | 1.95924 | ||||||||
\(532\) | 9.65875 | 0.418760 | ||||||||
\(533\) | 40.4274 | 1.75110 | ||||||||
\(534\) | 52.6697 | 2.27924 | ||||||||
\(535\) | −21.4423 | −0.927030 | ||||||||
\(536\) | −10.7281 | −0.463384 | ||||||||
\(537\) | 41.1265 | 1.77474 | ||||||||
\(538\) | 48.1054 | 2.07397 | ||||||||
\(539\) | 7.25003 | 0.312281 | ||||||||
\(540\) | −13.4413 | −0.578421 | ||||||||
\(541\) | −36.8758 | −1.58541 | −0.792706 | − | 0.609604i | \(-0.791329\pi\) | ||||
−0.792706 | + | 0.609604i | \(0.791329\pi\) | |||||||
\(542\) | 14.3621 | 0.616907 | ||||||||
\(543\) | 52.7640 | 2.26432 | ||||||||
\(544\) | −19.9371 | −0.854797 | ||||||||
\(545\) | 5.08759 | 0.217929 | ||||||||
\(546\) | −66.6999 | −2.85449 | ||||||||
\(547\) | −46.6362 | −1.99402 | −0.997009 | − | 0.0772843i | \(-0.975375\pi\) | ||||
−0.997009 | + | 0.0772843i | \(0.975375\pi\) | |||||||
\(548\) | −48.4828 | −2.07108 | ||||||||
\(549\) | −0.0499872 | −0.00213340 | ||||||||
\(550\) | 91.9171 | 3.91936 | ||||||||
\(551\) | −4.89281 | −0.208441 | ||||||||
\(552\) | −77.8320 | −3.31275 | ||||||||
\(553\) | −10.7715 | −0.458049 | ||||||||
\(554\) | −42.4239 | −1.80242 | ||||||||
\(555\) | −55.8295 | −2.36983 | ||||||||
\(556\) | −75.9343 | −3.22033 | ||||||||
\(557\) | 20.8434 | 0.883165 | 0.441582 | − | 0.897221i | \(-0.354417\pi\) | ||||
0.441582 | + | 0.897221i | \(0.354417\pi\) | |||||||
\(558\) | −8.37270 | −0.354445 | ||||||||
\(559\) | 8.00348 | 0.338511 | ||||||||
\(560\) | 51.6217 | 2.18142 | ||||||||
\(561\) | 54.9181 | 2.31864 | ||||||||
\(562\) | 38.7377 | 1.63405 | ||||||||
\(563\) | −25.4415 | −1.07223 | −0.536115 | − | 0.844145i | \(-0.680109\pi\) | ||||
−0.536115 | + | 0.844145i | \(0.680109\pi\) | |||||||
\(564\) | −7.60200 | −0.320102 | ||||||||
\(565\) | 19.6866 | 0.828219 | ||||||||
\(566\) | 27.6148 | 1.16074 | ||||||||
\(567\) | −17.7861 | −0.746947 | ||||||||
\(568\) | 77.1887 | 3.23877 | ||||||||
\(569\) | −28.6096 | −1.19938 | −0.599689 | − | 0.800233i | \(-0.704709\pi\) | ||||
−0.599689 | + | 0.800233i | \(0.704709\pi\) | |||||||
\(570\) | 24.4374 | 1.02357 | ||||||||
\(571\) | 37.2341 | 1.55820 | 0.779099 | − | 0.626901i | \(-0.215677\pi\) | ||||
0.779099 | + | 0.626901i | \(0.215677\pi\) | |||||||
\(572\) | 74.4970 | 3.11487 | ||||||||
\(573\) | 24.6582 | 1.03011 | ||||||||
\(574\) | 48.2988 | 2.01595 | ||||||||
\(575\) | −53.2379 | −2.22017 | ||||||||
\(576\) | −11.5991 | −0.483296 | ||||||||
\(577\) | 13.9850 | 0.582204 | 0.291102 | − | 0.956692i | \(-0.405978\pi\) | ||||
0.291102 | + | 0.956692i | \(0.405978\pi\) | |||||||
\(578\) | −46.3601 | −1.92832 | ||||||||
\(579\) | −38.3258 | −1.59277 | ||||||||
\(580\) | −81.5929 | −3.38796 | ||||||||
\(581\) | −34.4784 | −1.43041 | ||||||||
\(582\) | 1.04345 | 0.0432524 | ||||||||
\(583\) | −1.60379 | −0.0664223 | ||||||||
\(584\) | 46.9059 | 1.94098 | ||||||||
\(585\) | −60.5542 | −2.50361 | ||||||||
\(586\) | 3.63749 | 0.150263 | ||||||||
\(587\) | 23.5859 | 0.973494 | 0.486747 | − | 0.873543i | \(-0.338183\pi\) | ||||
0.486747 | + | 0.873543i | \(0.338183\pi\) | |||||||
\(588\) | 21.4112 | 0.882983 | ||||||||
\(589\) | 1.00382 | 0.0413618 | ||||||||
\(590\) | −132.159 | −5.44088 | ||||||||
\(591\) | −50.5742 | −2.08034 | ||||||||
\(592\) | 34.1535 | 1.40370 | ||||||||
\(593\) | 1.45578 | 0.0597816 | 0.0298908 | − | 0.999553i | \(-0.490484\pi\) | ||||
0.0298908 | + | 0.999553i | \(0.490484\pi\) | |||||||
\(594\) | −7.42720 | −0.304742 | ||||||||
\(595\) | 51.6471 | 2.11732 | ||||||||
\(596\) | −11.6216 | −0.476038 | ||||||||
\(597\) | −45.1677 | −1.84859 | ||||||||
\(598\) | −63.1737 | −2.58337 | ||||||||
\(599\) | 28.6379 | 1.17011 | 0.585057 | − | 0.810992i | \(-0.301072\pi\) | ||||
0.585057 | + | 0.810992i | \(0.301072\pi\) | |||||||
\(600\) | 145.470 | 5.93879 | ||||||||
\(601\) | 5.63985 | 0.230054 | 0.115027 | − | 0.993362i | \(-0.463304\pi\) | ||||
0.115027 | + | 0.993362i | \(0.463304\pi\) | |||||||
\(602\) | 9.56180 | 0.389710 | ||||||||
\(603\) | 6.14135 | 0.250095 | ||||||||
\(604\) | 29.2513 | 1.19022 | ||||||||
\(605\) | 9.51114 | 0.386683 | ||||||||
\(606\) | 60.0018 | 2.43741 | ||||||||
\(607\) | −2.85271 | −0.115788 | −0.0578940 | − | 0.998323i | \(-0.518439\pi\) | ||||
−0.0578940 | + | 0.998323i | \(0.518439\pi\) | |||||||
\(608\) | −3.34822 | −0.135788 | ||||||||
\(609\) | 27.5708 | 1.11723 | ||||||||
\(610\) | 0.146325 | 0.00592452 | ||||||||
\(611\) | −3.30660 | −0.133771 | ||||||||
\(612\) | 85.2069 | 3.44429 | ||||||||
\(613\) | −38.7463 | −1.56495 | −0.782474 | − | 0.622684i | \(-0.786042\pi\) | ||||
−0.782474 | + | 0.622684i | \(0.786042\pi\) | |||||||
\(614\) | −8.66860 | −0.349836 | ||||||||
\(615\) | 83.4637 | 3.36558 | ||||||||
\(616\) | 47.6953 | 1.92170 | ||||||||
\(617\) | −3.84843 | −0.154932 | −0.0774660 | − | 0.996995i | \(-0.524683\pi\) | ||||
−0.0774660 | + | 0.996995i | \(0.524683\pi\) | |||||||
\(618\) | 24.4382 | 0.983047 | ||||||||
\(619\) | 15.3763 | 0.618024 | 0.309012 | − | 0.951058i | \(-0.400002\pi\) | ||||
0.309012 | + | 0.951058i | \(0.400002\pi\) | |||||||
\(620\) | 16.7398 | 0.672288 | ||||||||
\(621\) | 4.30179 | 0.172625 | ||||||||
\(622\) | 8.05358 | 0.322919 | ||||||||
\(623\) | 18.6940 | 0.748959 | ||||||||
\(624\) | 70.5110 | 2.82270 | ||||||||
\(625\) | 24.6273 | 0.985093 | ||||||||
\(626\) | 10.6607 | 0.426087 | ||||||||
\(627\) | 9.22288 | 0.368326 | ||||||||
\(628\) | 92.7333 | 3.70046 | ||||||||
\(629\) | 34.1702 | 1.36246 | ||||||||
\(630\) | −72.3445 | −2.88227 | ||||||||
\(631\) | −21.5442 | −0.857662 | −0.428831 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428831 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(632\) | 27.8766 | 1.10887 | ||||||||
\(633\) | −2.51408 | −0.0999257 | ||||||||
\(634\) | −65.8038 | −2.61340 | ||||||||
\(635\) | −32.6860 | −1.29710 | ||||||||
\(636\) | −4.73641 | −0.187811 | ||||||||
\(637\) | 9.31311 | 0.368999 | ||||||||
\(638\) | −45.0855 | −1.78495 | ||||||||
\(639\) | −44.1870 | −1.74801 | ||||||||
\(640\) | 59.8671 | 2.36645 | ||||||||
\(641\) | −5.09331 | −0.201174 | −0.100587 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100587 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(642\) | −34.9910 | −1.38098 | ||||||||
\(643\) | 43.2382 | 1.70515 | 0.852573 | − | 0.522607i | \(-0.175041\pi\) | ||||
0.852573 | + | 0.522607i | \(0.175041\pi\) | |||||||
\(644\) | −51.5494 | −2.03133 | ||||||||
\(645\) | 16.5235 | 0.650610 | ||||||||
\(646\) | −14.9569 | −0.588469 | ||||||||
\(647\) | −25.1713 | −0.989587 | −0.494793 | − | 0.869011i | \(-0.664756\pi\) | ||||
−0.494793 | + | 0.869011i | \(0.664756\pi\) | |||||||
\(648\) | 46.0305 | 1.80825 | ||||||||
\(649\) | −49.8777 | −1.95787 | ||||||||
\(650\) | 118.073 | 4.63121 | ||||||||
\(651\) | −5.65651 | −0.221696 | ||||||||
\(652\) | 44.9810 | 1.76159 | ||||||||
\(653\) | −45.8672 | −1.79492 | −0.897461 | − | 0.441094i | \(-0.854591\pi\) | ||||
−0.897461 | + | 0.441094i | \(0.854591\pi\) | |||||||
\(654\) | 8.30229 | 0.324645 | ||||||||
\(655\) | −74.7702 | −2.92151 | ||||||||
\(656\) | −51.0586 | −1.99350 | ||||||||
\(657\) | −26.8515 | −1.04758 | ||||||||
\(658\) | −3.95042 | −0.154003 | ||||||||
\(659\) | −5.20393 | −0.202716 | −0.101358 | − | 0.994850i | \(-0.532319\pi\) | ||||
−0.101358 | + | 0.994850i | \(0.532319\pi\) | |||||||
\(660\) | 153.801 | 5.98671 | ||||||||
\(661\) | −32.1290 | −1.24967 | −0.624837 | − | 0.780755i | \(-0.714835\pi\) | ||||
−0.624837 | + | 0.780755i | \(0.714835\pi\) | |||||||
\(662\) | −44.6453 | −1.73519 | ||||||||
\(663\) | 70.5457 | 2.73977 | ||||||||
\(664\) | 89.2301 | 3.46280 | ||||||||
\(665\) | 8.67355 | 0.336346 | ||||||||
\(666\) | −47.8638 | −1.85469 | ||||||||
\(667\) | 26.1132 | 1.01111 | ||||||||
\(668\) | −30.3097 | −1.17272 | ||||||||
\(669\) | −19.7893 | −0.765099 | ||||||||
\(670\) | −17.9772 | −0.694522 | ||||||||
\(671\) | 0.0552241 | 0.00213190 | ||||||||
\(672\) | 18.8671 | 0.727814 | ||||||||
\(673\) | −19.9867 | −0.770432 | −0.385216 | − | 0.922826i | \(-0.625873\pi\) | ||||
−0.385216 | + | 0.922826i | \(0.625873\pi\) | |||||||
\(674\) | −46.4925 | −1.79083 | ||||||||
\(675\) | −8.04016 | −0.309466 | ||||||||
\(676\) | 39.6748 | 1.52595 | ||||||||
\(677\) | −27.9200 | −1.07305 | −0.536526 | − | 0.843884i | \(-0.680264\pi\) | ||||
−0.536526 | + | 0.843884i | \(0.680264\pi\) | |||||||
\(678\) | 32.1259 | 1.23379 | ||||||||
\(679\) | 0.370351 | 0.0142128 | ||||||||
\(680\) | −133.663 | −5.12573 | ||||||||
\(681\) | 58.8569 | 2.25540 | ||||||||
\(682\) | 9.24987 | 0.354196 | ||||||||
\(683\) | −36.0837 | −1.38071 | −0.690353 | − | 0.723473i | \(-0.742545\pi\) | ||||
−0.690353 | + | 0.723473i | \(0.742545\pi\) | |||||||
\(684\) | 14.3096 | 0.547139 | ||||||||
\(685\) | −43.5375 | −1.66348 | ||||||||
\(686\) | 50.5360 | 1.92947 | ||||||||
\(687\) | −9.18326 | −0.350363 | ||||||||
\(688\) | −10.1082 | −0.385370 | ||||||||
\(689\) | −2.06017 | −0.0784863 | ||||||||
\(690\) | −130.424 | −4.96517 | ||||||||
\(691\) | −47.9756 | −1.82508 | −0.912539 | − | 0.408990i | \(-0.865881\pi\) | ||||
−0.912539 | + | 0.408990i | \(0.865881\pi\) | |||||||
\(692\) | 70.0816 | 2.66410 | ||||||||
\(693\) | −27.3034 | −1.03717 | ||||||||
\(694\) | −12.4008 | −0.470729 | ||||||||
\(695\) | −68.1889 | −2.58655 | ||||||||
\(696\) | −71.3532 | −2.70464 | ||||||||
\(697\) | −51.0837 | −1.93493 | ||||||||
\(698\) | −53.9023 | −2.04023 | ||||||||
\(699\) | −61.5226 | −2.32700 | ||||||||
\(700\) | 96.3472 | 3.64158 | ||||||||
\(701\) | 19.7008 | 0.744090 | 0.372045 | − | 0.928215i | \(-0.378657\pi\) | ||||
0.372045 | + | 0.928215i | \(0.378657\pi\) | |||||||
\(702\) | −9.54070 | −0.360091 | ||||||||
\(703\) | 5.73851 | 0.216432 | ||||||||
\(704\) | 12.8143 | 0.482956 | ||||||||
\(705\) | −6.82659 | −0.257104 | ||||||||
\(706\) | 49.9160 | 1.87861 | ||||||||
\(707\) | 21.2964 | 0.800933 | ||||||||
\(708\) | −147.302 | −5.53593 | ||||||||
\(709\) | −43.7682 | −1.64375 | −0.821874 | − | 0.569669i | \(-0.807071\pi\) | ||||
−0.821874 | + | 0.569669i | \(0.807071\pi\) | |||||||
\(710\) | 129.346 | 4.85428 | ||||||||
\(711\) | −15.9581 | −0.598474 | ||||||||
\(712\) | −48.3801 | −1.81312 | ||||||||
\(713\) | −5.35747 | −0.200639 | ||||||||
\(714\) | 84.2813 | 3.15415 | ||||||||
\(715\) | 66.8982 | 2.50185 | ||||||||
\(716\) | −70.4939 | −2.63448 | ||||||||
\(717\) | 48.2523 | 1.80202 | ||||||||
\(718\) | 58.5397 | 2.18468 | ||||||||
\(719\) | −9.88300 | −0.368574 | −0.184287 | − | 0.982872i | \(-0.558998\pi\) | ||||
−0.184287 | + | 0.982872i | \(0.558998\pi\) | |||||||
\(720\) | 76.4782 | 2.85017 | ||||||||
\(721\) | 8.67381 | 0.323030 | ||||||||
\(722\) | −2.51184 | −0.0934809 | ||||||||
\(723\) | 37.8963 | 1.40938 | ||||||||
\(724\) | −90.4414 | −3.36123 | ||||||||
\(725\) | −48.8063 | −1.81262 | ||||||||
\(726\) | 15.5209 | 0.576036 | ||||||||
\(727\) | 45.9201 | 1.70308 | 0.851540 | − | 0.524289i | \(-0.175669\pi\) | ||||
0.851540 | + | 0.524289i | \(0.175669\pi\) | |||||||
\(728\) | 61.2675 | 2.27073 | ||||||||
\(729\) | −32.4295 | −1.20109 | ||||||||
\(730\) | 78.6010 | 2.90915 | ||||||||
\(731\) | −10.1131 | −0.374047 | ||||||||
\(732\) | 0.163091 | 0.00602802 | ||||||||
\(733\) | 16.6835 | 0.616218 | 0.308109 | − | 0.951351i | \(-0.400304\pi\) | ||||
0.308109 | + | 0.951351i | \(0.400304\pi\) | |||||||
\(734\) | 13.6695 | 0.504550 | ||||||||
\(735\) | 19.2272 | 0.709207 | ||||||||
\(736\) | 17.8697 | 0.658685 | ||||||||
\(737\) | −6.78475 | −0.249919 | ||||||||
\(738\) | 71.5553 | 2.63399 | ||||||||
\(739\) | 18.8710 | 0.694182 | 0.347091 | − | 0.937831i | \(-0.387169\pi\) | ||||
0.347091 | + | 0.937831i | \(0.387169\pi\) | |||||||
\(740\) | 95.6959 | 3.51785 | ||||||||
\(741\) | 11.8474 | 0.435224 | ||||||||
\(742\) | −2.46130 | −0.0903571 | ||||||||
\(743\) | 14.3438 | 0.526221 | 0.263111 | − | 0.964766i | \(-0.415252\pi\) | ||||
0.263111 | + | 0.964766i | \(0.415252\pi\) | |||||||
\(744\) | 14.6390 | 0.536693 | ||||||||
\(745\) | −10.4362 | −0.382351 | ||||||||
\(746\) | −25.4271 | −0.930952 | ||||||||
\(747\) | −51.0802 | −1.86892 | ||||||||
\(748\) | −94.1337 | −3.44187 | ||||||||
\(749\) | −12.4193 | −0.453792 | ||||||||
\(750\) | 121.579 | 4.43944 | ||||||||
\(751\) | −29.9408 | −1.09255 | −0.546277 | − | 0.837605i | \(-0.683955\pi\) | ||||
−0.546277 | + | 0.837605i | \(0.683955\pi\) | |||||||
\(752\) | 4.17614 | 0.152288 | ||||||||
\(753\) | 65.4044 | 2.38347 | ||||||||
\(754\) | −57.9151 | −2.10914 | ||||||||
\(755\) | 26.2676 | 0.955976 | ||||||||
\(756\) | −7.78516 | −0.283144 | ||||||||
\(757\) | −1.44824 | −0.0526371 | −0.0263185 | − | 0.999654i | \(-0.508378\pi\) | ||||
−0.0263185 | + | 0.999654i | \(0.508378\pi\) | |||||||
\(758\) | −63.7022 | −2.31377 | ||||||||
\(759\) | −49.2231 | −1.78669 | ||||||||
\(760\) | −22.4472 | −0.814244 | ||||||||
\(761\) | −48.5606 | −1.76032 | −0.880159 | − | 0.474678i | \(-0.842564\pi\) | ||||
−0.880159 | + | 0.474678i | \(0.842564\pi\) | |||||||
\(762\) | −53.3393 | −1.93228 | ||||||||
\(763\) | 2.94672 | 0.106679 | ||||||||
\(764\) | −42.2660 | −1.52913 | ||||||||
\(765\) | 76.5157 | 2.76643 | ||||||||
\(766\) | 15.7845 | 0.570317 | ||||||||
\(767\) | −64.0710 | −2.31347 | ||||||||
\(768\) | 80.1316 | 2.89150 | ||||||||
\(769\) | 7.63086 | 0.275176 | 0.137588 | − | 0.990490i | \(-0.456065\pi\) | ||||
0.137588 | + | 0.990490i | \(0.456065\pi\) | |||||||
\(770\) | 79.9237 | 2.88025 | ||||||||
\(771\) | 74.6264 | 2.68760 | ||||||||
\(772\) | 65.6933 | 2.36435 | ||||||||
\(773\) | 15.6049 | 0.561270 | 0.280635 | − | 0.959815i | \(-0.409455\pi\) | ||||
0.280635 | + | 0.959815i | \(0.409455\pi\) | |||||||
\(774\) | 14.1659 | 0.509184 | ||||||||
\(775\) | 10.0132 | 0.359687 | ||||||||
\(776\) | −0.958468 | −0.0344070 | ||||||||
\(777\) | −32.3363 | −1.16006 | ||||||||
\(778\) | −12.3811 | −0.443883 | ||||||||
\(779\) | −8.57893 | −0.307372 | ||||||||
\(780\) | 197.568 | 7.07406 | ||||||||
\(781\) | 48.8163 | 1.74678 | ||||||||
\(782\) | 79.8257 | 2.85456 | ||||||||
\(783\) | 3.94371 | 0.140937 | ||||||||
\(784\) | −11.7622 | −0.420078 | ||||||||
\(785\) | 83.2744 | 2.97219 | ||||||||
\(786\) | −122.015 | −4.35214 | ||||||||
\(787\) | −38.7918 | −1.38278 | −0.691389 | − | 0.722483i | \(-0.743001\pi\) | ||||
−0.691389 | + | 0.722483i | \(0.743001\pi\) | |||||||
\(788\) | 86.6879 | 3.08813 | ||||||||
\(789\) | 58.6338 | 2.08742 | ||||||||
\(790\) | 46.7132 | 1.66198 | ||||||||
\(791\) | 11.4024 | 0.405423 | ||||||||
\(792\) | 70.6611 | 2.51083 | ||||||||
\(793\) | 0.0709388 | 0.00251911 | ||||||||
\(794\) | −75.8725 | −2.69261 | ||||||||
\(795\) | −4.25329 | −0.150849 | ||||||||
\(796\) | 77.4209 | 2.74411 | ||||||||
\(797\) | 28.7351 | 1.01785 | 0.508925 | − | 0.860811i | \(-0.330043\pi\) | ||||
0.508925 | + | 0.860811i | \(0.330043\pi\) | |||||||
\(798\) | 14.1541 | 0.501050 | ||||||||
\(799\) | 4.17819 | 0.147814 | ||||||||
\(800\) | −33.3989 | −1.18083 | ||||||||
\(801\) | 27.6954 | 0.978568 | ||||||||
\(802\) | 23.1421 | 0.817175 | ||||||||
\(803\) | 29.6646 | 1.04684 | ||||||||
\(804\) | −20.0371 | −0.706654 | ||||||||
\(805\) | −46.2913 | −1.63156 | ||||||||
\(806\) | 11.8820 | 0.418527 | ||||||||
\(807\) | 48.1484 | 1.69490 | ||||||||
\(808\) | −55.1150 | −1.93894 | ||||||||
\(809\) | 13.4142 | 0.471619 | 0.235809 | − | 0.971799i | \(-0.424226\pi\) | ||||
0.235809 | + | 0.971799i | \(0.424226\pi\) | |||||||
\(810\) | 77.1340 | 2.71021 | ||||||||
\(811\) | 51.1579 | 1.79640 | 0.898199 | − | 0.439589i | \(-0.144876\pi\) | ||||
0.898199 | + | 0.439589i | \(0.144876\pi\) | |||||||
\(812\) | −47.2584 | −1.65845 | ||||||||
\(813\) | 14.3750 | 0.504152 | ||||||||
\(814\) | 52.8783 | 1.85338 | ||||||||
\(815\) | 40.3929 | 1.41490 | ||||||||
\(816\) | −89.0971 | −3.11902 | ||||||||
\(817\) | −1.69839 | −0.0594190 | ||||||||
\(818\) | −9.29934 | −0.325144 | ||||||||
\(819\) | −35.0729 | −1.22554 | ||||||||
\(820\) | −143.063 | −4.99598 | ||||||||
\(821\) | 17.7760 | 0.620386 | 0.310193 | − | 0.950674i | \(-0.399606\pi\) | ||||
0.310193 | + | 0.950674i | \(0.399606\pi\) | |||||||
\(822\) | −71.0476 | −2.47807 | ||||||||
\(823\) | −24.5914 | −0.857201 | −0.428600 | − | 0.903494i | \(-0.640993\pi\) | ||||
−0.428600 | + | 0.903494i | \(0.640993\pi\) | |||||||
\(824\) | −22.4478 | −0.782007 | ||||||||
\(825\) | 91.9992 | 3.20300 | ||||||||
\(826\) | −76.5460 | −2.66337 | ||||||||
\(827\) | −39.2562 | −1.36507 | −0.682536 | − | 0.730852i | \(-0.739123\pi\) | ||||
−0.682536 | + | 0.730852i | \(0.739123\pi\) | |||||||
\(828\) | −76.3711 | −2.65408 | ||||||||
\(829\) | −32.1395 | −1.11625 | −0.558126 | − | 0.829756i | \(-0.688479\pi\) | ||||
−0.558126 | + | 0.829756i | \(0.688479\pi\) | |||||||
\(830\) | 149.524 | 5.19006 | ||||||||
\(831\) | −42.4619 | −1.47299 | ||||||||
\(832\) | 16.4607 | 0.570674 | ||||||||
\(833\) | −11.7680 | −0.407736 | ||||||||
\(834\) | −111.275 | −3.85316 | ||||||||
\(835\) | −27.2181 | −0.941921 | ||||||||
\(836\) | −15.8087 | −0.546755 | ||||||||
\(837\) | −0.809103 | −0.0279667 | ||||||||
\(838\) | 80.1935 | 2.77024 | ||||||||
\(839\) | −34.0142 | −1.17430 | −0.587150 | − | 0.809478i | \(-0.699750\pi\) | ||||
−0.587150 | + | 0.809478i | \(0.699750\pi\) | |||||||
\(840\) | 126.489 | 4.36428 | ||||||||
\(841\) | −5.06043 | −0.174497 | ||||||||
\(842\) | −48.0010 | −1.65422 | ||||||||
\(843\) | 38.7723 | 1.33539 | ||||||||
\(844\) | 4.30932 | 0.148333 | ||||||||
\(845\) | 35.6279 | 1.22564 | ||||||||
\(846\) | −5.85259 | −0.201216 | ||||||||
\(847\) | 5.50883 | 0.189286 | ||||||||
\(848\) | 2.60193 | 0.0893508 | ||||||||
\(849\) | 27.6394 | 0.948583 | ||||||||
\(850\) | −149.196 | −5.11739 | ||||||||
\(851\) | −30.6268 | −1.04987 | ||||||||
\(852\) | 144.167 | 4.93908 | ||||||||
\(853\) | −51.8556 | −1.77550 | −0.887750 | − | 0.460325i | \(-0.847733\pi\) | ||||
−0.887750 | + | 0.460325i | \(0.847733\pi\) | |||||||
\(854\) | 0.0847510 | 0.00290012 | ||||||||
\(855\) | 12.8500 | 0.439460 | ||||||||
\(856\) | 32.1412 | 1.09856 | ||||||||
\(857\) | 19.0989 | 0.652405 | 0.326202 | − | 0.945300i | \(-0.394231\pi\) | ||||
0.326202 | + | 0.945300i | \(0.394231\pi\) | |||||||
\(858\) | 109.169 | 3.72697 | ||||||||
\(859\) | −16.9110 | −0.576996 | −0.288498 | − | 0.957480i | \(-0.593156\pi\) | ||||
−0.288498 | + | 0.957480i | \(0.593156\pi\) | |||||||
\(860\) | −28.3224 | −0.965787 | ||||||||
\(861\) | 48.3420 | 1.64749 | ||||||||
\(862\) | −84.1719 | −2.86690 | ||||||||
\(863\) | −29.6949 | −1.01082 | −0.505412 | − | 0.862878i | \(-0.668660\pi\) | ||||
−0.505412 | + | 0.862878i | \(0.668660\pi\) | |||||||
\(864\) | 2.69874 | 0.0918129 | ||||||||
\(865\) | 62.9332 | 2.13979 | ||||||||
\(866\) | 45.4392 | 1.54409 | ||||||||
\(867\) | −46.4015 | −1.57588 | ||||||||
\(868\) | 9.69568 | 0.329093 | ||||||||
\(869\) | 17.6299 | 0.598054 | ||||||||
\(870\) | −119.568 | −4.05373 | ||||||||
\(871\) | −8.71544 | −0.295311 | ||||||||
\(872\) | −7.62612 | −0.258253 | ||||||||
\(873\) | 0.548679 | 0.0185700 | ||||||||
\(874\) | 13.4058 | 0.453459 | ||||||||
\(875\) | 43.1519 | 1.45880 | ||||||||
\(876\) | 87.6072 | 2.95997 | ||||||||
\(877\) | −39.8740 | −1.34645 | −0.673224 | − | 0.739439i | \(-0.735091\pi\) | ||||
−0.673224 | + | 0.739439i | \(0.735091\pi\) | |||||||
\(878\) | −18.8295 | −0.635463 | ||||||||
\(879\) | 3.64074 | 0.122799 | ||||||||
\(880\) | −84.4905 | −2.84817 | ||||||||
\(881\) | −10.3416 | −0.348416 | −0.174208 | − | 0.984709i | \(-0.555736\pi\) | ||||
−0.174208 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(882\) | 16.4839 | 0.555043 | ||||||||
\(883\) | −23.4206 | −0.788167 | −0.394083 | − | 0.919075i | \(-0.628938\pi\) | ||||
−0.394083 | + | 0.919075i | \(0.628938\pi\) | |||||||
\(884\) | −120.921 | −4.06700 | ||||||||
\(885\) | −132.277 | −4.44643 | ||||||||
\(886\) | 25.1617 | 0.845326 | ||||||||
\(887\) | −35.6887 | −1.19831 | −0.599155 | − | 0.800633i | \(-0.704497\pi\) | ||||
−0.599155 | + | 0.800633i | \(0.704497\pi\) | |||||||
\(888\) | 83.6864 | 2.80833 | ||||||||
\(889\) | −18.9317 | −0.634947 | ||||||||
\(890\) | −81.0712 | −2.71751 | ||||||||
\(891\) | 29.1109 | 0.975253 | ||||||||
\(892\) | 33.9204 | 1.13574 | ||||||||
\(893\) | 0.701681 | 0.0234809 | ||||||||
\(894\) | −17.0305 | −0.569584 | ||||||||
\(895\) | −63.3035 | −2.11600 | ||||||||
\(896\) | 34.6749 | 1.15841 | ||||||||
\(897\) | −63.2302 | −2.11119 | ||||||||
\(898\) | 6.14148 | 0.204944 | ||||||||
\(899\) | −4.91151 | −0.163808 | ||||||||
\(900\) | 142.739 | 4.75798 | ||||||||
\(901\) | 2.60321 | 0.0867256 | ||||||||
\(902\) | −79.0518 | −2.63214 | ||||||||
\(903\) | 9.57035 | 0.318481 | ||||||||
\(904\) | −29.5094 | −0.981469 | ||||||||
\(905\) | −81.2163 | −2.69972 | ||||||||
\(906\) | 42.8653 | 1.42410 | ||||||||
\(907\) | 45.9570 | 1.52598 | 0.762988 | − | 0.646413i | \(-0.223731\pi\) | ||||
0.762988 | + | 0.646413i | \(0.223731\pi\) | |||||||
\(908\) | −100.885 | −3.34799 | ||||||||
\(909\) | 31.5508 | 1.04648 | ||||||||
\(910\) | 102.667 | 3.40338 | ||||||||
\(911\) | 37.8284 | 1.25331 | 0.626655 | − | 0.779297i | \(-0.284424\pi\) | ||||
0.626655 | + | 0.779297i | \(0.284424\pi\) | |||||||
\(912\) | −14.9629 | −0.495470 | ||||||||
\(913\) | 56.4316 | 1.86761 | ||||||||
\(914\) | 67.1717 | 2.22184 | ||||||||
\(915\) | 0.146456 | 0.00484167 | ||||||||
\(916\) | 15.7408 | 0.520091 | ||||||||
\(917\) | −43.3067 | −1.43011 | ||||||||
\(918\) | 12.0555 | 0.397892 | ||||||||
\(919\) | 51.1854 | 1.68845 | 0.844225 | − | 0.535988i | \(-0.180061\pi\) | ||||
0.844225 | + | 0.535988i | \(0.180061\pi\) | |||||||
\(920\) | 119.802 | 3.94975 | ||||||||
\(921\) | −8.67634 | −0.285895 | ||||||||
\(922\) | −9.76761 | −0.321679 | ||||||||
\(923\) | 62.7076 | 2.06404 | ||||||||
\(924\) | 89.0815 | 2.93057 | ||||||||
\(925\) | 57.2423 | 1.88212 | ||||||||
\(926\) | −6.89101 | −0.226453 | ||||||||
\(927\) | 12.8503 | 0.422061 | ||||||||
\(928\) | 16.3822 | 0.537772 | ||||||||
\(929\) | 0.523188 | 0.0171652 | 0.00858262 | − | 0.999963i | \(-0.497268\pi\) | ||||
0.00858262 | + | 0.999963i | \(0.497268\pi\) | |||||||
\(930\) | 24.5309 | 0.804399 | ||||||||
\(931\) | −1.97630 | −0.0647706 | ||||||||
\(932\) | 105.454 | 3.45427 | ||||||||
\(933\) | 8.06077 | 0.263898 | ||||||||
\(934\) | −103.400 | −3.38334 | ||||||||
\(935\) | −84.5320 | −2.76449 | ||||||||
\(936\) | 90.7686 | 2.96686 | ||||||||
\(937\) | −12.6585 | −0.413536 | −0.206768 | − | 0.978390i | \(-0.566294\pi\) | ||||
−0.206768 | + | 0.978390i | \(0.566294\pi\) | |||||||
\(938\) | −10.4124 | −0.339976 | ||||||||
\(939\) | 10.6702 | 0.348209 | ||||||||
\(940\) | 11.7013 | 0.381654 | ||||||||
\(941\) | −29.5087 | −0.961957 | −0.480978 | − | 0.876732i | \(-0.659718\pi\) | ||||
−0.480978 | + | 0.876732i | \(0.659718\pi\) | |||||||
\(942\) | 135.893 | 4.42763 | ||||||||
\(943\) | 45.7863 | 1.49101 | ||||||||
\(944\) | 80.9197 | 2.63371 | ||||||||
\(945\) | −6.99107 | −0.227419 | ||||||||
\(946\) | −15.6500 | −0.508826 | ||||||||
\(947\) | −5.55968 | −0.180665 | −0.0903327 | − | 0.995912i | \(-0.528793\pi\) | ||||
−0.0903327 | + | 0.995912i | \(0.528793\pi\) | |||||||
\(948\) | 52.0656 | 1.69101 | ||||||||
\(949\) | 38.1060 | 1.23697 | ||||||||
\(950\) | −25.0559 | −0.812919 | ||||||||
\(951\) | −65.8626 | −2.13574 | ||||||||
\(952\) | −77.4171 | −2.50910 | ||||||||
\(953\) | −38.6940 | −1.25342 | −0.626711 | − | 0.779252i | \(-0.715599\pi\) | ||||
−0.626711 | + | 0.779252i | \(0.715599\pi\) | |||||||
\(954\) | −3.64644 | −0.118058 | ||||||||
\(955\) | −37.9548 | −1.22819 | ||||||||
\(956\) | −82.7081 | −2.67497 | ||||||||
\(957\) | −45.1258 | −1.45871 | ||||||||
\(958\) | 50.2002 | 1.62190 | ||||||||
\(959\) | −25.2168 | −0.814294 | ||||||||
\(960\) | 33.9838 | 1.09682 | ||||||||
\(961\) | −29.9923 | −0.967495 | ||||||||
\(962\) | 67.9255 | 2.19001 | ||||||||
\(963\) | −18.3993 | −0.592911 | ||||||||
\(964\) | −64.9571 | −2.09213 | ||||||||
\(965\) | 58.9925 | 1.89904 | ||||||||
\(966\) | −75.5414 | −2.43051 | ||||||||
\(967\) | 45.5036 | 1.46330 | 0.731649 | − | 0.681682i | \(-0.238751\pi\) | ||||
0.731649 | + | 0.681682i | \(0.238751\pi\) | |||||||
\(968\) | −14.2569 | −0.458233 | ||||||||
\(969\) | −14.9702 | −0.480913 | ||||||||
\(970\) | −1.60612 | −0.0515694 | ||||||||
\(971\) | 39.9132 | 1.28087 | 0.640437 | − | 0.768010i | \(-0.278753\pi\) | ||||
0.640437 | + | 0.768010i | \(0.278753\pi\) | |||||||
\(972\) | 96.3923 | 3.09178 | ||||||||
\(973\) | −39.4949 | −1.26615 | ||||||||
\(974\) | 55.6446 | 1.78297 | ||||||||
\(975\) | 118.179 | 3.78475 | ||||||||
\(976\) | −0.0895936 | −0.00286782 | ||||||||
\(977\) | −21.2315 | −0.679255 | −0.339628 | − | 0.940560i | \(-0.610301\pi\) | ||||
−0.339628 | + | 0.940560i | \(0.610301\pi\) | |||||||
\(978\) | 65.9159 | 2.10776 | ||||||||
\(979\) | −30.5969 | −0.977881 | ||||||||
\(980\) | −32.9569 | −1.05277 | ||||||||
\(981\) | 4.36560 | 0.139383 | ||||||||
\(982\) | −71.5056 | −2.28184 | ||||||||
\(983\) | 7.98369 | 0.254640 | 0.127320 | − | 0.991862i | \(-0.459362\pi\) | ||||
0.127320 | + | 0.991862i | \(0.459362\pi\) | |||||||
\(984\) | −125.109 | −3.98833 | ||||||||
\(985\) | 77.8457 | 2.48037 | ||||||||
\(986\) | 73.1810 | 2.33056 | ||||||||
\(987\) | −3.95395 | −0.125855 | ||||||||
\(988\) | −20.3073 | −0.646060 | ||||||||
\(989\) | 9.06440 | 0.288231 | ||||||||
\(990\) | 118.408 | 3.76325 | ||||||||
\(991\) | 17.0428 | 0.541381 | 0.270691 | − | 0.962666i | \(-0.412748\pi\) | ||||
0.270691 | + | 0.962666i | \(0.412748\pi\) | |||||||
\(992\) | −3.36102 | −0.106712 | ||||||||
\(993\) | −44.6851 | −1.41804 | ||||||||
\(994\) | 74.9171 | 2.37623 | ||||||||
\(995\) | 69.5239 | 2.20406 | ||||||||
\(996\) | 166.657 | 5.28073 | ||||||||
\(997\) | 17.1096 | 0.541866 | 0.270933 | − | 0.962598i | \(-0.412668\pi\) | ||||
0.270933 | + | 0.962598i | \(0.412668\pi\) | |||||||
\(998\) | 12.9138 | 0.408779 | ||||||||
\(999\) | −4.62536 | −0.146340 |
(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 | 4009.2.a.c.1.7 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.7 | ✓ | 71 | 1.1 | even | 1 | trivial |