Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23793 | −1.58246 | −0.791228 | − | 0.611521i | \(-0.790558\pi\) | ||||
−0.791228 | + | 0.611521i | \(0.790558\pi\) | |||||||
\(3\) | 1.90424 | 1.09942 | 0.549708 | − | 0.835357i | \(-0.314739\pi\) | ||||
0.549708 | + | 0.835357i | \(0.314739\pi\) | |||||||
\(4\) | 3.00834 | 1.50417 | ||||||||
\(5\) | 4.23440 | 1.89368 | 0.946842 | − | 0.321700i | \(-0.104254\pi\) | ||||
0.946842 | + | 0.321700i | \(0.104254\pi\) | |||||||
\(6\) | −4.26157 | −1.73978 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.25659 | −0.797825 | ||||||||
\(9\) | 0.626144 | 0.208715 | ||||||||
\(10\) | −9.47631 | −2.99667 | ||||||||
\(11\) | −0.780283 | −0.235264 | −0.117632 | − | 0.993057i | \(-0.537530\pi\) | ||||
−0.117632 | + | 0.993057i | \(0.537530\pi\) | |||||||
\(12\) | 5.72861 | 1.65371 | ||||||||
\(13\) | −5.45043 | −1.51168 | −0.755839 | − | 0.654757i | \(-0.772771\pi\) | ||||
−0.755839 | + | 0.654757i | \(0.772771\pi\) | |||||||
\(14\) | −2.23793 | −0.598112 | ||||||||
\(15\) | 8.06334 | 2.08195 | ||||||||
\(16\) | −0.966582 | −0.241645 | ||||||||
\(17\) | 1.79938 | 0.436414 | 0.218207 | − | 0.975902i | \(-0.429979\pi\) | ||||
0.218207 | + | 0.975902i | \(0.429979\pi\) | |||||||
\(18\) | −1.40127 | −0.330282 | ||||||||
\(19\) | −4.44901 | −1.02067 | −0.510336 | − | 0.859975i | \(-0.670479\pi\) | ||||
−0.510336 | + | 0.859975i | \(0.670479\pi\) | |||||||
\(20\) | 12.7385 | 2.84842 | ||||||||
\(21\) | 1.90424 | 0.415540 | ||||||||
\(22\) | 1.74622 | 0.372296 | ||||||||
\(23\) | 7.54904 | 1.57408 | 0.787042 | − | 0.616900i | \(-0.211612\pi\) | ||||
0.787042 | + | 0.616900i | \(0.211612\pi\) | |||||||
\(24\) | −4.29710 | −0.877141 | ||||||||
\(25\) | 12.9302 | 2.58604 | ||||||||
\(26\) | 12.1977 | 2.39216 | ||||||||
\(27\) | −4.52040 | −0.869951 | ||||||||
\(28\) | 3.00834 | 0.568522 | ||||||||
\(29\) | 4.65814 | 0.864994 | 0.432497 | − | 0.901635i | \(-0.357633\pi\) | ||||
0.432497 | + | 0.901635i | \(0.357633\pi\) | |||||||
\(30\) | −18.0452 | −3.29459 | ||||||||
\(31\) | 9.66318 | 1.73556 | 0.867780 | − | 0.496949i | \(-0.165546\pi\) | ||||
0.867780 | + | 0.496949i | \(0.165546\pi\) | |||||||
\(32\) | 6.67632 | 1.18022 | ||||||||
\(33\) | −1.48585 | −0.258653 | ||||||||
\(34\) | −4.02690 | −0.690607 | ||||||||
\(35\) | 4.23440 | 0.715745 | ||||||||
\(36\) | 1.88365 | 0.313942 | ||||||||
\(37\) | −2.02034 | −0.332143 | −0.166071 | − | 0.986114i | \(-0.553108\pi\) | ||||
−0.166071 | + | 0.986114i | \(0.553108\pi\) | |||||||
\(38\) | 9.95657 | 1.61517 | ||||||||
\(39\) | −10.3790 | −1.66196 | ||||||||
\(40\) | −9.55531 | −1.51083 | ||||||||
\(41\) | 9.44210 | 1.47461 | 0.737304 | − | 0.675561i | \(-0.236099\pi\) | ||||
0.737304 | + | 0.675561i | \(0.236099\pi\) | |||||||
\(42\) | −4.26157 | −0.657574 | ||||||||
\(43\) | −8.07255 | −1.23105 | −0.615526 | − | 0.788117i | \(-0.711056\pi\) | ||||
−0.615526 | + | 0.788117i | \(0.711056\pi\) | |||||||
\(44\) | −2.34736 | −0.353877 | ||||||||
\(45\) | 2.65135 | 0.395240 | ||||||||
\(46\) | −16.8942 | −2.49092 | ||||||||
\(47\) | 8.51500 | 1.24204 | 0.621020 | − | 0.783794i | \(-0.286718\pi\) | ||||
0.621020 | + | 0.783794i | \(0.286718\pi\) | |||||||
\(48\) | −1.84061 | −0.265669 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −28.9369 | −4.09229 | ||||||||
\(51\) | 3.42646 | 0.479801 | ||||||||
\(52\) | −16.3967 | −2.27382 | ||||||||
\(53\) | −11.9054 | −1.63534 | −0.817668 | − | 0.575691i | \(-0.804733\pi\) | ||||
−0.817668 | + | 0.575691i | \(0.804733\pi\) | |||||||
\(54\) | 10.1163 | 1.37666 | ||||||||
\(55\) | −3.30404 | −0.445516 | ||||||||
\(56\) | −2.25659 | −0.301549 | ||||||||
\(57\) | −8.47199 | −1.12214 | ||||||||
\(58\) | −10.4246 | −1.36882 | ||||||||
\(59\) | 8.64103 | 1.12497 | 0.562483 | − | 0.826809i | \(-0.309846\pi\) | ||||
0.562483 | + | 0.826809i | \(0.309846\pi\) | |||||||
\(60\) | 24.2572 | 3.13160 | ||||||||
\(61\) | −4.55315 | −0.582971 | −0.291485 | − | 0.956575i | \(-0.594149\pi\) | ||||
−0.291485 | + | 0.956575i | \(0.594149\pi\) | |||||||
\(62\) | −21.6255 | −2.74645 | ||||||||
\(63\) | 0.626144 | 0.0788867 | ||||||||
\(64\) | −13.0080 | −1.62600 | ||||||||
\(65\) | −23.0793 | −2.86264 | ||||||||
\(66\) | 3.32523 | 0.409308 | ||||||||
\(67\) | −4.69394 | −0.573455 | −0.286728 | − | 0.958012i | \(-0.592568\pi\) | ||||
−0.286728 | + | 0.958012i | \(0.592568\pi\) | |||||||
\(68\) | 5.41315 | 0.656441 | ||||||||
\(69\) | 14.3752 | 1.73057 | ||||||||
\(70\) | −9.47631 | −1.13264 | ||||||||
\(71\) | 14.4213 | 1.71150 | 0.855748 | − | 0.517393i | \(-0.173097\pi\) | ||||
0.855748 | + | 0.517393i | \(0.173097\pi\) | |||||||
\(72\) | −1.41295 | −0.166518 | ||||||||
\(73\) | 8.77726 | 1.02730 | 0.513650 | − | 0.858000i | \(-0.328293\pi\) | ||||
0.513650 | + | 0.858000i | \(0.328293\pi\) | |||||||
\(74\) | 4.52139 | 0.525601 | ||||||||
\(75\) | 24.6222 | 2.84313 | ||||||||
\(76\) | −13.3841 | −1.53526 | ||||||||
\(77\) | −0.780283 | −0.0889215 | ||||||||
\(78\) | 23.2274 | 2.62998 | ||||||||
\(79\) | −6.49617 | −0.730876 | −0.365438 | − | 0.930836i | \(-0.619081\pi\) | ||||
−0.365438 | + | 0.930836i | \(0.619081\pi\) | |||||||
\(80\) | −4.09290 | −0.457600 | ||||||||
\(81\) | −10.4864 | −1.16515 | ||||||||
\(82\) | −21.1308 | −2.33350 | ||||||||
\(83\) | −0.00279464 | −0.000306752 0 | −0.000153376 | − | 1.00000i | \(-0.500049\pi\) | ||||
−0.000153376 | 1.00000i | \(0.500049\pi\) | ||||||||
\(84\) | 5.72861 | 0.625042 | ||||||||
\(85\) | 7.61932 | 0.826431 | ||||||||
\(86\) | 18.0658 | 1.94809 | ||||||||
\(87\) | 8.87023 | 0.950988 | ||||||||
\(88\) | 1.76078 | 0.187700 | ||||||||
\(89\) | 8.85786 | 0.938931 | 0.469466 | − | 0.882951i | \(-0.344447\pi\) | ||||
0.469466 | + | 0.882951i | \(0.344447\pi\) | |||||||
\(90\) | −5.93353 | −0.625449 | ||||||||
\(91\) | −5.45043 | −0.571361 | ||||||||
\(92\) | 22.7101 | 2.36769 | ||||||||
\(93\) | 18.4011 | 1.90810 | ||||||||
\(94\) | −19.0560 | −1.96548 | ||||||||
\(95\) | −18.8389 | −1.93283 | ||||||||
\(96\) | 12.7133 | 1.29755 | ||||||||
\(97\) | 5.10013 | 0.517840 | 0.258920 | − | 0.965899i | \(-0.416633\pi\) | ||||
0.258920 | + | 0.965899i | \(0.416633\pi\) | |||||||
\(98\) | −2.23793 | −0.226065 | ||||||||
\(99\) | −0.488570 | −0.0491031 | ||||||||
\(100\) | 38.8984 | 3.88984 | ||||||||
\(101\) | 7.80750 | 0.776875 | 0.388438 | − | 0.921475i | \(-0.373015\pi\) | ||||
0.388438 | + | 0.921475i | \(0.373015\pi\) | |||||||
\(102\) | −7.66819 | −0.759264 | ||||||||
\(103\) | −6.10831 | −0.601870 | −0.300935 | − | 0.953645i | \(-0.597299\pi\) | ||||
−0.300935 | + | 0.953645i | \(0.597299\pi\) | |||||||
\(104\) | 12.2994 | 1.20605 | ||||||||
\(105\) | 8.06334 | 0.786901 | ||||||||
\(106\) | 26.6435 | 2.58785 | ||||||||
\(107\) | −15.0486 | −1.45481 | −0.727404 | − | 0.686210i | \(-0.759273\pi\) | ||||
−0.727404 | + | 0.686210i | \(0.759273\pi\) | |||||||
\(108\) | −13.5989 | −1.30855 | ||||||||
\(109\) | 8.87387 | 0.849963 | 0.424981 | − | 0.905202i | \(-0.360281\pi\) | ||||
0.424981 | + | 0.905202i | \(0.360281\pi\) | |||||||
\(110\) | 7.39421 | 0.705010 | ||||||||
\(111\) | −3.84723 | −0.365163 | ||||||||
\(112\) | −0.966582 | −0.0913334 | ||||||||
\(113\) | −8.23910 | −0.775069 | −0.387534 | − | 0.921855i | \(-0.626673\pi\) | ||||
−0.387534 | + | 0.921855i | \(0.626673\pi\) | |||||||
\(114\) | 18.9597 | 1.77574 | ||||||||
\(115\) | 31.9657 | 2.98082 | ||||||||
\(116\) | 14.0132 | 1.30110 | ||||||||
\(117\) | −3.41276 | −0.315509 | ||||||||
\(118\) | −19.3380 | −1.78021 | ||||||||
\(119\) | 1.79938 | 0.164949 | ||||||||
\(120\) | −18.1956 | −1.66103 | ||||||||
\(121\) | −10.3912 | −0.944651 | ||||||||
\(122\) | 10.1896 | 0.922526 | ||||||||
\(123\) | 17.9801 | 1.62121 | ||||||||
\(124\) | 29.0701 | 2.61057 | ||||||||
\(125\) | 33.5796 | 3.00345 | ||||||||
\(126\) | −1.40127 | −0.124835 | ||||||||
\(127\) | −0.0938159 | −0.00832482 | −0.00416241 | − | 0.999991i | \(-0.501325\pi\) | ||||
−0.00416241 | + | 0.999991i | \(0.501325\pi\) | |||||||
\(128\) | 15.7583 | 1.39285 | ||||||||
\(129\) | −15.3721 | −1.35344 | ||||||||
\(130\) | 51.6500 | 4.53000 | ||||||||
\(131\) | 9.13967 | 0.798537 | 0.399268 | − | 0.916834i | \(-0.369264\pi\) | ||||
0.399268 | + | 0.916834i | \(0.369264\pi\) | |||||||
\(132\) | −4.46994 | −0.389058 | ||||||||
\(133\) | −4.44901 | −0.385778 | ||||||||
\(134\) | 10.5047 | 0.907468 | ||||||||
\(135\) | −19.1412 | −1.64741 | ||||||||
\(136\) | −4.06047 | −0.348182 | ||||||||
\(137\) | 6.41396 | 0.547981 | 0.273991 | − | 0.961732i | \(-0.411656\pi\) | ||||
0.273991 | + | 0.961732i | \(0.411656\pi\) | |||||||
\(138\) | −32.1707 | −2.73855 | ||||||||
\(139\) | −17.9791 | −1.52497 | −0.762483 | − | 0.647008i | \(-0.776020\pi\) | ||||
−0.762483 | + | 0.647008i | \(0.776020\pi\) | |||||||
\(140\) | 12.7385 | 1.07660 | ||||||||
\(141\) | 16.2146 | 1.36552 | ||||||||
\(142\) | −32.2739 | −2.70837 | ||||||||
\(143\) | 4.25288 | 0.355644 | ||||||||
\(144\) | −0.605219 | −0.0504350 | ||||||||
\(145\) | 19.7244 | 1.63803 | ||||||||
\(146\) | −19.6429 | −1.62566 | ||||||||
\(147\) | 1.90424 | 0.157059 | ||||||||
\(148\) | −6.07788 | −0.499599 | ||||||||
\(149\) | −17.0364 | −1.39568 | −0.697838 | − | 0.716256i | \(-0.745854\pi\) | ||||
−0.697838 | + | 0.716256i | \(0.745854\pi\) | |||||||
\(150\) | −55.1028 | −4.49913 | ||||||||
\(151\) | 19.4012 | 1.57884 | 0.789422 | − | 0.613850i | \(-0.210380\pi\) | ||||
0.789422 | + | 0.613850i | \(0.210380\pi\) | |||||||
\(152\) | 10.0396 | 0.814318 | ||||||||
\(153\) | 1.12667 | 0.0910861 | ||||||||
\(154\) | 1.74622 | 0.140714 | ||||||||
\(155\) | 40.9178 | 3.28660 | ||||||||
\(156\) | −31.2234 | −2.49987 | ||||||||
\(157\) | 16.4556 | 1.31330 | 0.656649 | − | 0.754196i | \(-0.271973\pi\) | ||||
0.656649 | + | 0.754196i | \(0.271973\pi\) | |||||||
\(158\) | 14.5380 | 1.15658 | ||||||||
\(159\) | −22.6708 | −1.79791 | ||||||||
\(160\) | 28.2703 | 2.23496 | ||||||||
\(161\) | 7.54904 | 0.594948 | ||||||||
\(162\) | 23.4678 | 1.84380 | ||||||||
\(163\) | 16.3744 | 1.28254 | 0.641269 | − | 0.767316i | \(-0.278408\pi\) | ||||
0.641269 | + | 0.767316i | \(0.278408\pi\) | |||||||
\(164\) | 28.4050 | 2.21806 | ||||||||
\(165\) | −6.29169 | −0.489807 | ||||||||
\(166\) | 0.00625422 | 0.000485421 0 | ||||||||
\(167\) | −8.56460 | −0.662748 | −0.331374 | − | 0.943499i | \(-0.607512\pi\) | ||||
−0.331374 | + | 0.943499i | \(0.607512\pi\) | |||||||
\(168\) | −4.29710 | −0.331528 | ||||||||
\(169\) | 16.7072 | 1.28517 | ||||||||
\(170\) | −17.0515 | −1.30779 | ||||||||
\(171\) | −2.78572 | −0.213029 | ||||||||
\(172\) | −24.2849 | −1.85171 | ||||||||
\(173\) | 7.37599 | 0.560786 | 0.280393 | − | 0.959885i | \(-0.409535\pi\) | ||||
0.280393 | + | 0.959885i | \(0.409535\pi\) | |||||||
\(174\) | −19.8510 | −1.50490 | ||||||||
\(175\) | 12.9302 | 0.977430 | ||||||||
\(176\) | 0.754208 | 0.0568505 | ||||||||
\(177\) | 16.4546 | 1.23681 | ||||||||
\(178\) | −19.8233 | −1.48582 | ||||||||
\(179\) | 16.4120 | 1.22669 | 0.613346 | − | 0.789815i | \(-0.289823\pi\) | ||||
0.613346 | + | 0.789815i | \(0.289823\pi\) | |||||||
\(180\) | 7.97615 | 0.594507 | ||||||||
\(181\) | −17.4423 | −1.29648 | −0.648240 | − | 0.761436i | \(-0.724495\pi\) | ||||
−0.648240 | + | 0.761436i | \(0.724495\pi\) | |||||||
\(182\) | 12.1977 | 0.904153 | ||||||||
\(183\) | −8.67030 | −0.640927 | ||||||||
\(184\) | −17.0351 | −1.25584 | ||||||||
\(185\) | −8.55496 | −0.628973 | ||||||||
\(186\) | −41.1803 | −3.01949 | ||||||||
\(187\) | −1.40403 | −0.102673 | ||||||||
\(188\) | 25.6160 | 1.86824 | ||||||||
\(189\) | −4.52040 | −0.328811 | ||||||||
\(190\) | 42.1602 | 3.05862 | ||||||||
\(191\) | −15.0200 | −1.08681 | −0.543406 | − | 0.839470i | \(-0.682866\pi\) | ||||
−0.543406 | + | 0.839470i | \(0.682866\pi\) | |||||||
\(192\) | −24.7704 | −1.78765 | ||||||||
\(193\) | 10.6285 | 0.765055 | 0.382527 | − | 0.923944i | \(-0.375054\pi\) | ||||
0.382527 | + | 0.923944i | \(0.375054\pi\) | |||||||
\(194\) | −11.4137 | −0.819459 | ||||||||
\(195\) | −43.9487 | −3.14723 | ||||||||
\(196\) | 3.00834 | 0.214881 | ||||||||
\(197\) | −6.49218 | −0.462549 | −0.231274 | − | 0.972889i | \(-0.574289\pi\) | ||||
−0.231274 | + | 0.972889i | \(0.574289\pi\) | |||||||
\(198\) | 1.09339 | 0.0777035 | ||||||||
\(199\) | −23.2383 | −1.64732 | −0.823661 | − | 0.567083i | \(-0.808072\pi\) | ||||
−0.823661 | + | 0.567083i | \(0.808072\pi\) | |||||||
\(200\) | −29.1781 | −2.06320 | ||||||||
\(201\) | −8.93840 | −0.630466 | ||||||||
\(202\) | −17.4726 | −1.22937 | ||||||||
\(203\) | 4.65814 | 0.326937 | ||||||||
\(204\) | 10.3080 | 0.721701 | ||||||||
\(205\) | 39.9817 | 2.79244 | ||||||||
\(206\) | 13.6700 | 0.952433 | ||||||||
\(207\) | 4.72679 | 0.328534 | ||||||||
\(208\) | 5.26829 | 0.365290 | ||||||||
\(209\) | 3.47149 | 0.240128 | ||||||||
\(210\) | −18.0452 | −1.24524 | ||||||||
\(211\) | −11.2526 | −0.774660 | −0.387330 | − | 0.921941i | \(-0.626603\pi\) | ||||
−0.387330 | + | 0.921941i | \(0.626603\pi\) | |||||||
\(212\) | −35.8155 | −2.45982 | ||||||||
\(213\) | 27.4617 | 1.88165 | ||||||||
\(214\) | 33.6778 | 2.30217 | ||||||||
\(215\) | −34.1824 | −2.33122 | ||||||||
\(216\) | 10.2007 | 0.694069 | ||||||||
\(217\) | 9.66318 | 0.655980 | ||||||||
\(218\) | −19.8591 | −1.34503 | ||||||||
\(219\) | 16.7140 | 1.12943 | ||||||||
\(220\) | −9.93965 | −0.670131 | ||||||||
\(221\) | −9.80742 | −0.659718 | ||||||||
\(222\) | 8.60984 | 0.577854 | ||||||||
\(223\) | 3.09800 | 0.207458 | 0.103729 | − | 0.994606i | \(-0.466923\pi\) | ||||
0.103729 | + | 0.994606i | \(0.466923\pi\) | |||||||
\(224\) | 6.67632 | 0.446081 | ||||||||
\(225\) | 8.09616 | 0.539744 | ||||||||
\(226\) | 18.4385 | 1.22651 | ||||||||
\(227\) | 7.62786 | 0.506279 | 0.253139 | − | 0.967430i | \(-0.418537\pi\) | ||||
0.253139 | + | 0.967430i | \(0.418537\pi\) | |||||||
\(228\) | −25.4866 | −1.68789 | ||||||||
\(229\) | 9.39304 | 0.620709 | 0.310355 | − | 0.950621i | \(-0.399552\pi\) | ||||
0.310355 | + | 0.950621i | \(0.399552\pi\) | |||||||
\(230\) | −71.5370 | −4.71701 | ||||||||
\(231\) | −1.48585 | −0.0977617 | ||||||||
\(232\) | −10.5115 | −0.690114 | ||||||||
\(233\) | 13.7944 | 0.903699 | 0.451849 | − | 0.892094i | \(-0.350764\pi\) | ||||
0.451849 | + | 0.892094i | \(0.350764\pi\) | |||||||
\(234\) | 7.63752 | 0.499280 | ||||||||
\(235\) | 36.0560 | 2.35203 | ||||||||
\(236\) | 25.9951 | 1.69214 | ||||||||
\(237\) | −12.3703 | −0.803536 | ||||||||
\(238\) | −4.02690 | −0.261025 | ||||||||
\(239\) | 16.4955 | 1.06700 | 0.533501 | − | 0.845799i | \(-0.320876\pi\) | ||||
0.533501 | + | 0.845799i | \(0.320876\pi\) | |||||||
\(240\) | −7.79388 | −0.503093 | ||||||||
\(241\) | −2.85396 | −0.183840 | −0.0919198 | − | 0.995766i | \(-0.529300\pi\) | ||||
−0.0919198 | + | 0.995766i | \(0.529300\pi\) | |||||||
\(242\) | 23.2547 | 1.49487 | ||||||||
\(243\) | −6.40741 | −0.411036 | ||||||||
\(244\) | −13.6974 | −0.876886 | ||||||||
\(245\) | 4.23440 | 0.270526 | ||||||||
\(246\) | −40.2381 | −2.56549 | ||||||||
\(247\) | 24.2490 | 1.54293 | ||||||||
\(248\) | −21.8058 | −1.38467 | ||||||||
\(249\) | −0.00532168 | −0.000337248 0 | ||||||||
\(250\) | −75.1489 | −4.75283 | ||||||||
\(251\) | 11.3670 | 0.717479 | 0.358739 | − | 0.933438i | \(-0.383207\pi\) | ||||
0.358739 | + | 0.933438i | \(0.383207\pi\) | |||||||
\(252\) | 1.88365 | 0.118659 | ||||||||
\(253\) | −5.89039 | −0.370326 | ||||||||
\(254\) | 0.209954 | 0.0131737 | ||||||||
\(255\) | 14.5090 | 0.908591 | ||||||||
\(256\) | −9.25011 | −0.578132 | ||||||||
\(257\) | 25.7357 | 1.60535 | 0.802676 | − | 0.596415i | \(-0.203409\pi\) | ||||
0.802676 | + | 0.596415i | \(0.203409\pi\) | |||||||
\(258\) | 34.4017 | 2.14176 | ||||||||
\(259\) | −2.02034 | −0.125538 | ||||||||
\(260\) | −69.4304 | −4.30589 | ||||||||
\(261\) | 2.91667 | 0.180537 | ||||||||
\(262\) | −20.4540 | −1.26365 | ||||||||
\(263\) | 12.2326 | 0.754297 | 0.377148 | − | 0.926153i | \(-0.376905\pi\) | ||||
0.377148 | + | 0.926153i | \(0.376905\pi\) | |||||||
\(264\) | 3.35295 | 0.206360 | ||||||||
\(265\) | −50.4124 | −3.09681 | ||||||||
\(266\) | 9.95657 | 0.610477 | ||||||||
\(267\) | 16.8675 | 1.03228 | ||||||||
\(268\) | −14.1209 | −0.862574 | ||||||||
\(269\) | 2.04516 | 0.124696 | 0.0623478 | − | 0.998054i | \(-0.480141\pi\) | ||||
0.0623478 | + | 0.998054i | \(0.480141\pi\) | |||||||
\(270\) | 42.8367 | 2.60696 | ||||||||
\(271\) | 12.5732 | 0.763770 | 0.381885 | − | 0.924210i | \(-0.375275\pi\) | ||||
0.381885 | + | 0.924210i | \(0.375275\pi\) | |||||||
\(272\) | −1.73925 | −0.105458 | ||||||||
\(273\) | −10.3790 | −0.628163 | ||||||||
\(274\) | −14.3540 | −0.867157 | ||||||||
\(275\) | −10.0892 | −0.608402 | ||||||||
\(276\) | 43.2455 | 2.60307 | ||||||||
\(277\) | −17.7884 | −1.06880 | −0.534401 | − | 0.845231i | \(-0.679463\pi\) | ||||
−0.534401 | + | 0.845231i | \(0.679463\pi\) | |||||||
\(278\) | 40.2360 | 2.41319 | ||||||||
\(279\) | 6.05055 | 0.362237 | ||||||||
\(280\) | −9.55531 | −0.571039 | ||||||||
\(281\) | −14.7088 | −0.877455 | −0.438727 | − | 0.898620i | \(-0.644571\pi\) | ||||
−0.438727 | + | 0.898620i | \(0.644571\pi\) | |||||||
\(282\) | −36.2873 | −2.16087 | ||||||||
\(283\) | 14.1547 | 0.841409 | 0.420704 | − | 0.907198i | \(-0.361783\pi\) | ||||
0.420704 | + | 0.907198i | \(0.361783\pi\) | |||||||
\(284\) | 43.3842 | 2.57438 | ||||||||
\(285\) | −35.8738 | −2.12498 | ||||||||
\(286\) | −9.51766 | −0.562791 | ||||||||
\(287\) | 9.44210 | 0.557349 | ||||||||
\(288\) | 4.18034 | 0.246329 | ||||||||
\(289\) | −13.7622 | −0.809542 | ||||||||
\(290\) | −44.1419 | −2.59210 | ||||||||
\(291\) | 9.71189 | 0.569321 | ||||||||
\(292\) | 26.4050 | 1.54523 | ||||||||
\(293\) | 4.05424 | 0.236851 | 0.118426 | − | 0.992963i | \(-0.462215\pi\) | ||||
0.118426 | + | 0.992963i | \(0.462215\pi\) | |||||||
\(294\) | −4.26157 | −0.248540 | ||||||||
\(295\) | 36.5896 | 2.13033 | ||||||||
\(296\) | 4.55909 | 0.264992 | ||||||||
\(297\) | 3.52719 | 0.204669 | ||||||||
\(298\) | 38.1263 | 2.20860 | ||||||||
\(299\) | −41.1455 | −2.37951 | ||||||||
\(300\) | 74.0719 | 4.27655 | ||||||||
\(301\) | −8.07255 | −0.465294 | ||||||||
\(302\) | −43.4185 | −2.49845 | ||||||||
\(303\) | 14.8674 | 0.854109 | ||||||||
\(304\) | 4.30033 | 0.246641 | ||||||||
\(305\) | −19.2799 | −1.10396 | ||||||||
\(306\) | −2.52142 | −0.144140 | ||||||||
\(307\) | 5.72061 | 0.326492 | 0.163246 | − | 0.986585i | \(-0.447804\pi\) | ||||
0.163246 | + | 0.986585i | \(0.447804\pi\) | |||||||
\(308\) | −2.34736 | −0.133753 | ||||||||
\(309\) | −11.6317 | −0.661705 | ||||||||
\(310\) | −91.5713 | −5.20090 | ||||||||
\(311\) | 2.26376 | 0.128366 | 0.0641830 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641830 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(312\) | 23.4210 | 1.32596 | ||||||||
\(313\) | −8.47529 | −0.479052 | −0.239526 | − | 0.970890i | \(-0.576992\pi\) | ||||
−0.239526 | + | 0.970890i | \(0.576992\pi\) | |||||||
\(314\) | −36.8265 | −2.07824 | ||||||||
\(315\) | 2.65135 | 0.149387 | ||||||||
\(316\) | −19.5427 | −1.09936 | ||||||||
\(317\) | 21.5313 | 1.20932 | 0.604658 | − | 0.796485i | \(-0.293310\pi\) | ||||
0.604658 | + | 0.796485i | \(0.293310\pi\) | |||||||
\(318\) | 50.7357 | 2.84512 | ||||||||
\(319\) | −3.63467 | −0.203502 | ||||||||
\(320\) | −55.0811 | −3.07913 | ||||||||
\(321\) | −28.6563 | −1.59944 | ||||||||
\(322\) | −16.8942 | −0.941479 | ||||||||
\(323\) | −8.00547 | −0.445436 | ||||||||
\(324\) | −31.5466 | −1.75259 | ||||||||
\(325\) | −70.4751 | −3.90926 | ||||||||
\(326\) | −36.6447 | −2.02956 | ||||||||
\(327\) | 16.8980 | 0.934462 | ||||||||
\(328\) | −21.3069 | −1.17648 | ||||||||
\(329\) | 8.51500 | 0.469447 | ||||||||
\(330\) | 14.0804 | 0.775099 | ||||||||
\(331\) | −17.8763 | −0.982568 | −0.491284 | − | 0.870999i | \(-0.663472\pi\) | ||||
−0.491284 | + | 0.870999i | \(0.663472\pi\) | |||||||
\(332\) | −0.00840723 | −0.000461407 0 | ||||||||
\(333\) | −1.26503 | −0.0693231 | ||||||||
\(334\) | 19.1670 | 1.04877 | ||||||||
\(335\) | −19.8760 | −1.08594 | ||||||||
\(336\) | −1.84061 | −0.100413 | ||||||||
\(337\) | −9.61868 | −0.523963 | −0.261982 | − | 0.965073i | \(-0.584376\pi\) | ||||
−0.261982 | + | 0.965073i | \(0.584376\pi\) | |||||||
\(338\) | −37.3896 | −2.03373 | ||||||||
\(339\) | −15.6892 | −0.852123 | ||||||||
\(340\) | 22.9215 | 1.24309 | ||||||||
\(341\) | −7.54002 | −0.408315 | ||||||||
\(342\) | 6.23425 | 0.337110 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 18.2164 | 0.982164 | ||||||||
\(345\) | 60.8705 | 3.27716 | ||||||||
\(346\) | −16.5070 | −0.887420 | ||||||||
\(347\) | −13.9224 | −0.747394 | −0.373697 | − | 0.927551i | \(-0.621910\pi\) | ||||
−0.373697 | + | 0.927551i | \(0.621910\pi\) | |||||||
\(348\) | 26.6846 | 1.43045 | ||||||||
\(349\) | 2.49357 | 0.133478 | 0.0667388 | − | 0.997770i | \(-0.478741\pi\) | ||||
0.0667388 | + | 0.997770i | \(0.478741\pi\) | |||||||
\(350\) | −28.9369 | −1.54674 | ||||||||
\(351\) | 24.6381 | 1.31509 | ||||||||
\(352\) | −5.20942 | −0.277663 | ||||||||
\(353\) | −16.2742 | −0.866188 | −0.433094 | − | 0.901349i | \(-0.642578\pi\) | ||||
−0.433094 | + | 0.901349i | \(0.642578\pi\) | |||||||
\(354\) | −36.8243 | −1.95719 | ||||||||
\(355\) | 61.0657 | 3.24103 | ||||||||
\(356\) | 26.6474 | 1.41231 | ||||||||
\(357\) | 3.42646 | 0.181348 | ||||||||
\(358\) | −36.7290 | −1.94119 | ||||||||
\(359\) | −8.64553 | −0.456294 | −0.228147 | − | 0.973627i | \(-0.573267\pi\) | ||||
−0.228147 | + | 0.973627i | \(0.573267\pi\) | |||||||
\(360\) | −5.98300 | −0.315332 | ||||||||
\(361\) | 0.793661 | 0.0417717 | ||||||||
\(362\) | 39.0348 | 2.05162 | ||||||||
\(363\) | −19.7873 | −1.03856 | ||||||||
\(364\) | −16.3967 | −0.859423 | ||||||||
\(365\) | 37.1665 | 1.94538 | ||||||||
\(366\) | 19.4035 | 1.01424 | ||||||||
\(367\) | 17.5346 | 0.915300 | 0.457650 | − | 0.889132i | \(-0.348691\pi\) | ||||
0.457650 | + | 0.889132i | \(0.348691\pi\) | |||||||
\(368\) | −7.29676 | −0.380370 | ||||||||
\(369\) | 5.91211 | 0.307772 | ||||||||
\(370\) | 19.1454 | 0.995323 | ||||||||
\(371\) | −11.9054 | −0.618099 | ||||||||
\(372\) | 55.3566 | 2.87011 | ||||||||
\(373\) | 5.93136 | 0.307114 | 0.153557 | − | 0.988140i | \(-0.450927\pi\) | ||||
0.153557 | + | 0.988140i | \(0.450927\pi\) | |||||||
\(374\) | 3.14212 | 0.162475 | ||||||||
\(375\) | 63.9438 | 3.30204 | ||||||||
\(376\) | −19.2149 | −0.990931 | ||||||||
\(377\) | −25.3889 | −1.30759 | ||||||||
\(378\) | 10.1163 | 0.520329 | ||||||||
\(379\) | 6.61805 | 0.339946 | 0.169973 | − | 0.985449i | \(-0.445632\pi\) | ||||
0.169973 | + | 0.985449i | \(0.445632\pi\) | |||||||
\(380\) | −56.6737 | −2.90730 | ||||||||
\(381\) | −0.178648 | −0.00915244 | ||||||||
\(382\) | 33.6138 | 1.71983 | ||||||||
\(383\) | −7.88970 | −0.403145 | −0.201573 | − | 0.979474i | \(-0.564605\pi\) | ||||
−0.201573 | + | 0.979474i | \(0.564605\pi\) | |||||||
\(384\) | 30.0077 | 1.53133 | ||||||||
\(385\) | −3.30404 | −0.168389 | ||||||||
\(386\) | −23.7858 | −1.21067 | ||||||||
\(387\) | −5.05458 | −0.256939 | ||||||||
\(388\) | 15.3429 | 0.778918 | ||||||||
\(389\) | −3.94552 | −0.200046 | −0.100023 | − | 0.994985i | \(-0.531892\pi\) | ||||
−0.100023 | + | 0.994985i | \(0.531892\pi\) | |||||||
\(390\) | 98.3542 | 4.98036 | ||||||||
\(391\) | 13.5836 | 0.686953 | ||||||||
\(392\) | −2.25659 | −0.113975 | ||||||||
\(393\) | 17.4042 | 0.877924 | ||||||||
\(394\) | 14.5291 | 0.731963 | ||||||||
\(395\) | −27.5074 | −1.38405 | ||||||||
\(396\) | −1.46978 | −0.0738594 | ||||||||
\(397\) | −30.8311 | −1.54737 | −0.773685 | − | 0.633570i | \(-0.781589\pi\) | ||||
−0.773685 | + | 0.633570i | \(0.781589\pi\) | |||||||
\(398\) | 52.0058 | 2.60681 | ||||||||
\(399\) | −8.47199 | −0.424130 | ||||||||
\(400\) | −12.4981 | −0.624904 | ||||||||
\(401\) | −19.0739 | −0.952508 | −0.476254 | − | 0.879308i | \(-0.658006\pi\) | ||||
−0.476254 | + | 0.879308i | \(0.658006\pi\) | |||||||
\(402\) | 20.0035 | 0.997685 | ||||||||
\(403\) | −52.6685 | −2.62361 | ||||||||
\(404\) | 23.4876 | 1.16855 | ||||||||
\(405\) | −44.4036 | −2.20643 | ||||||||
\(406\) | −10.4246 | −0.517364 | ||||||||
\(407\) | 1.57644 | 0.0781413 | ||||||||
\(408\) | −7.73212 | −0.382797 | ||||||||
\(409\) | 9.11863 | 0.450887 | 0.225444 | − | 0.974256i | \(-0.427617\pi\) | ||||
0.225444 | + | 0.974256i | \(0.427617\pi\) | |||||||
\(410\) | −89.4762 | −4.41892 | ||||||||
\(411\) | 12.2137 | 0.602459 | ||||||||
\(412\) | −18.3759 | −0.905314 | ||||||||
\(413\) | 8.64103 | 0.425197 | ||||||||
\(414\) | −10.5782 | −0.519891 | ||||||||
\(415\) | −0.0118336 | −0.000580891 0 | ||||||||
\(416\) | −36.3889 | −1.78411 | ||||||||
\(417\) | −34.2366 | −1.67657 | ||||||||
\(418\) | −7.76895 | −0.379992 | ||||||||
\(419\) | −13.7693 | −0.672674 | −0.336337 | − | 0.941742i | \(-0.609188\pi\) | ||||
−0.336337 | + | 0.941742i | \(0.609188\pi\) | |||||||
\(420\) | 24.2572 | 1.18363 | ||||||||
\(421\) | −15.8348 | −0.771743 | −0.385872 | − | 0.922553i | \(-0.626099\pi\) | ||||
−0.385872 | + | 0.922553i | \(0.626099\pi\) | |||||||
\(422\) | 25.1825 | 1.22587 | ||||||||
\(423\) | 5.33162 | 0.259232 | ||||||||
\(424\) | 26.8656 | 1.30471 | ||||||||
\(425\) | 23.2664 | 1.12858 | ||||||||
\(426\) | −61.4574 | −2.97762 | ||||||||
\(427\) | −4.55315 | −0.220342 | ||||||||
\(428\) | −45.2714 | −2.18828 | ||||||||
\(429\) | 8.09852 | 0.391000 | ||||||||
\(430\) | 76.4980 | 3.68906 | ||||||||
\(431\) | −25.7789 | −1.24173 | −0.620864 | − | 0.783918i | \(-0.713218\pi\) | ||||
−0.620864 | + | 0.783918i | \(0.713218\pi\) | |||||||
\(432\) | 4.36934 | 0.210220 | ||||||||
\(433\) | 39.9652 | 1.92060 | 0.960302 | − | 0.278964i | \(-0.0899909\pi\) | ||||
0.960302 | + | 0.278964i | \(0.0899909\pi\) | |||||||
\(434\) | −21.6255 | −1.03806 | ||||||||
\(435\) | 37.5601 | 1.80087 | ||||||||
\(436\) | 26.6956 | 1.27849 | ||||||||
\(437\) | −33.5857 | −1.60662 | ||||||||
\(438\) | −37.4049 | −1.78727 | ||||||||
\(439\) | 33.6744 | 1.60719 | 0.803597 | − | 0.595174i | \(-0.202917\pi\) | ||||
0.803597 | + | 0.595174i | \(0.202917\pi\) | |||||||
\(440\) | 7.45585 | 0.355444 | ||||||||
\(441\) | 0.626144 | 0.0298164 | ||||||||
\(442\) | 21.9483 | 1.04398 | ||||||||
\(443\) | −16.4230 | −0.780282 | −0.390141 | − | 0.920755i | \(-0.627574\pi\) | ||||
−0.390141 | + | 0.920755i | \(0.627574\pi\) | |||||||
\(444\) | −11.5738 | −0.549266 | ||||||||
\(445\) | 37.5078 | 1.77804 | ||||||||
\(446\) | −6.93312 | −0.328293 | ||||||||
\(447\) | −32.4414 | −1.53443 | ||||||||
\(448\) | −13.0080 | −0.614570 | ||||||||
\(449\) | 15.5613 | 0.734385 | 0.367193 | − | 0.930145i | \(-0.380319\pi\) | ||||
0.367193 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(450\) | −18.1186 | −0.854121 | ||||||||
\(451\) | −7.36751 | −0.346923 | ||||||||
\(452\) | −24.7860 | −1.16583 | ||||||||
\(453\) | 36.9446 | 1.73581 | ||||||||
\(454\) | −17.0706 | −0.801164 | ||||||||
\(455\) | −23.0793 | −1.08198 | ||||||||
\(456\) | 19.1178 | 0.895274 | ||||||||
\(457\) | 16.7543 | 0.783735 | 0.391868 | − | 0.920022i | \(-0.371829\pi\) | ||||
0.391868 | + | 0.920022i | \(0.371829\pi\) | |||||||
\(458\) | −21.0210 | −0.982246 | ||||||||
\(459\) | −8.13393 | −0.379659 | ||||||||
\(460\) | 96.1636 | 4.48365 | ||||||||
\(461\) | 27.6748 | 1.28894 | 0.644472 | − | 0.764628i | \(-0.277077\pi\) | ||||
0.644472 | + | 0.764628i | \(0.277077\pi\) | |||||||
\(462\) | 3.32523 | 0.154704 | ||||||||
\(463\) | −34.3806 | −1.59780 | −0.798902 | − | 0.601461i | \(-0.794585\pi\) | ||||
−0.798902 | + | 0.601461i | \(0.794585\pi\) | |||||||
\(464\) | −4.50247 | −0.209022 | ||||||||
\(465\) | 77.9175 | 3.61334 | ||||||||
\(466\) | −30.8708 | −1.43006 | ||||||||
\(467\) | 35.6963 | 1.65183 | 0.825915 | − | 0.563795i | \(-0.190659\pi\) | ||||
0.825915 | + | 0.563795i | \(0.190659\pi\) | |||||||
\(468\) | −10.2667 | −0.474579 | ||||||||
\(469\) | −4.69394 | −0.216746 | ||||||||
\(470\) | −80.6908 | −3.72199 | ||||||||
\(471\) | 31.3355 | 1.44386 | ||||||||
\(472\) | −19.4993 | −0.897526 | ||||||||
\(473\) | 6.29888 | 0.289623 | ||||||||
\(474\) | 27.6838 | 1.27156 | ||||||||
\(475\) | −57.5265 | −2.63950 | ||||||||
\(476\) | 5.41315 | 0.248111 | ||||||||
\(477\) | −7.45451 | −0.341318 | ||||||||
\(478\) | −36.9157 | −1.68849 | ||||||||
\(479\) | 19.0655 | 0.871124 | 0.435562 | − | 0.900159i | \(-0.356550\pi\) | ||||
0.435562 | + | 0.900159i | \(0.356550\pi\) | |||||||
\(480\) | 53.8335 | 2.45715 | ||||||||
\(481\) | 11.0118 | 0.502093 | ||||||||
\(482\) | 6.38696 | 0.290918 | ||||||||
\(483\) | 14.3752 | 0.654095 | ||||||||
\(484\) | −31.2601 | −1.42091 | ||||||||
\(485\) | 21.5960 | 0.980625 | ||||||||
\(486\) | 14.3394 | 0.650446 | ||||||||
\(487\) | −28.0193 | −1.26968 | −0.634838 | − | 0.772645i | \(-0.718933\pi\) | ||||
−0.634838 | + | 0.772645i | \(0.718933\pi\) | |||||||
\(488\) | 10.2746 | 0.465108 | ||||||||
\(489\) | 31.1808 | 1.41004 | ||||||||
\(490\) | −9.47631 | −0.428096 | ||||||||
\(491\) | 26.7259 | 1.20612 | 0.603062 | − | 0.797695i | \(-0.293947\pi\) | ||||
0.603062 | + | 0.797695i | \(0.293947\pi\) | |||||||
\(492\) | 54.0901 | 2.43857 | ||||||||
\(493\) | 8.38177 | 0.377496 | ||||||||
\(494\) | −54.2676 | −2.44162 | ||||||||
\(495\) | −2.06880 | −0.0929858 | ||||||||
\(496\) | −9.34026 | −0.419390 | ||||||||
\(497\) | 14.4213 | 0.646885 | ||||||||
\(498\) | 0.0119096 | 0.000533680 0 | ||||||||
\(499\) | 15.9997 | 0.716246 | 0.358123 | − | 0.933674i | \(-0.383417\pi\) | ||||
0.358123 | + | 0.933674i | \(0.383417\pi\) | |||||||
\(500\) | 101.019 | 4.51770 | ||||||||
\(501\) | −16.3091 | −0.728636 | ||||||||
\(502\) | −25.4386 | −1.13538 | ||||||||
\(503\) | −6.61831 | −0.295096 | −0.147548 | − | 0.989055i | \(-0.547138\pi\) | ||||
−0.147548 | + | 0.989055i | \(0.547138\pi\) | |||||||
\(504\) | −1.41295 | −0.0629378 | ||||||||
\(505\) | 33.0601 | 1.47116 | ||||||||
\(506\) | 13.1823 | 0.586024 | ||||||||
\(507\) | 31.8146 | 1.41294 | ||||||||
\(508\) | −0.282230 | −0.0125219 | ||||||||
\(509\) | −24.7080 | −1.09516 | −0.547582 | − | 0.836752i | \(-0.684452\pi\) | ||||
−0.547582 | + | 0.836752i | \(0.684452\pi\) | |||||||
\(510\) | −32.4702 | −1.43781 | ||||||||
\(511\) | 8.77726 | 0.388283 | ||||||||
\(512\) | −10.8156 | −0.477985 | ||||||||
\(513\) | 20.1113 | 0.887935 | ||||||||
\(514\) | −57.5948 | −2.54040 | ||||||||
\(515\) | −25.8651 | −1.13975 | ||||||||
\(516\) | −46.2445 | −2.03580 | ||||||||
\(517\) | −6.64412 | −0.292208 | ||||||||
\(518\) | 4.52139 | 0.198659 | ||||||||
\(519\) | 14.0457 | 0.616537 | ||||||||
\(520\) | 52.0806 | 2.28389 | ||||||||
\(521\) | 40.3144 | 1.76621 | 0.883103 | − | 0.469180i | \(-0.155450\pi\) | ||||
0.883103 | + | 0.469180i | \(0.155450\pi\) | |||||||
\(522\) | −6.52730 | −0.285692 | ||||||||
\(523\) | −10.3379 | −0.452046 | −0.226023 | − | 0.974122i | \(-0.572572\pi\) | ||||
−0.226023 | + | 0.974122i | \(0.572572\pi\) | |||||||
\(524\) | 27.4952 | 1.20113 | ||||||||
\(525\) | 24.6222 | 1.07460 | ||||||||
\(526\) | −27.3758 | −1.19364 | ||||||||
\(527\) | 17.3878 | 0.757423 | ||||||||
\(528\) | 1.43620 | 0.0625024 | ||||||||
\(529\) | 33.9880 | 1.47774 | ||||||||
\(530\) | 112.819 | 4.90056 | ||||||||
\(531\) | 5.41053 | 0.234797 | ||||||||
\(532\) | −13.3841 | −0.580275 | ||||||||
\(533\) | −51.4635 | −2.22913 | ||||||||
\(534\) | −37.7484 | −1.63353 | ||||||||
\(535\) | −63.7221 | −2.75494 | ||||||||
\(536\) | 10.5923 | 0.457517 | ||||||||
\(537\) | 31.2525 | 1.34864 | ||||||||
\(538\) | −4.57693 | −0.197325 | ||||||||
\(539\) | −0.780283 | −0.0336092 | ||||||||
\(540\) | −57.5832 | −2.47799 | ||||||||
\(541\) | 9.41479 | 0.404773 | 0.202387 | − | 0.979306i | \(-0.435130\pi\) | ||||
0.202387 | + | 0.979306i | \(0.435130\pi\) | |||||||
\(542\) | −28.1380 | −1.20863 | ||||||||
\(543\) | −33.2145 | −1.42537 | ||||||||
\(544\) | 12.0133 | 0.515064 | ||||||||
\(545\) | 37.5756 | 1.60956 | ||||||||
\(546\) | 23.2274 | 0.994040 | ||||||||
\(547\) | −1.02258 | −0.0437222 | −0.0218611 | − | 0.999761i | \(-0.506959\pi\) | ||||
−0.0218611 | + | 0.999761i | \(0.506959\pi\) | |||||||
\(548\) | 19.2953 | 0.824256 | ||||||||
\(549\) | −2.85093 | −0.121675 | ||||||||
\(550\) | 22.5790 | 0.962770 | ||||||||
\(551\) | −20.7241 | −0.882876 | ||||||||
\(552\) | −32.4389 | −1.38069 | ||||||||
\(553\) | −6.49617 | −0.276245 | ||||||||
\(554\) | 39.8093 | 1.69133 | ||||||||
\(555\) | −16.2907 | −0.691503 | ||||||||
\(556\) | −54.0872 | −2.29381 | ||||||||
\(557\) | 5.97881 | 0.253330 | 0.126665 | − | 0.991946i | \(-0.459573\pi\) | ||||
0.126665 | + | 0.991946i | \(0.459573\pi\) | |||||||
\(558\) | −13.5407 | −0.573224 | ||||||||
\(559\) | 43.9989 | 1.86095 | ||||||||
\(560\) | −4.09290 | −0.172957 | ||||||||
\(561\) | −2.67361 | −0.112880 | ||||||||
\(562\) | 32.9173 | 1.38853 | ||||||||
\(563\) | −44.6473 | −1.88166 | −0.940830 | − | 0.338879i | \(-0.889952\pi\) | ||||
−0.940830 | + | 0.338879i | \(0.889952\pi\) | |||||||
\(564\) | 48.7791 | 2.05397 | ||||||||
\(565\) | −34.8877 | −1.46774 | ||||||||
\(566\) | −31.6772 | −1.33149 | ||||||||
\(567\) | −10.4864 | −0.440386 | ||||||||
\(568\) | −32.5430 | −1.36547 | ||||||||
\(569\) | −16.7375 | −0.701671 | −0.350835 | − | 0.936437i | \(-0.614102\pi\) | ||||
−0.350835 | + | 0.936437i | \(0.614102\pi\) | |||||||
\(570\) | 80.2832 | 3.36269 | ||||||||
\(571\) | 1.66825 | 0.0698140 | 0.0349070 | − | 0.999391i | \(-0.488886\pi\) | ||||
0.0349070 | + | 0.999391i | \(0.488886\pi\) | |||||||
\(572\) | 12.7941 | 0.534948 | ||||||||
\(573\) | −28.6018 | −1.19486 | ||||||||
\(574\) | −21.1308 | −0.881981 | ||||||||
\(575\) | 97.6105 | 4.07064 | ||||||||
\(576\) | −8.14488 | −0.339370 | ||||||||
\(577\) | 10.2857 | 0.428198 | 0.214099 | − | 0.976812i | \(-0.431318\pi\) | ||||
0.214099 | + | 0.976812i | \(0.431318\pi\) | |||||||
\(578\) | 30.7989 | 1.28107 | ||||||||
\(579\) | 20.2392 | 0.841113 | ||||||||
\(580\) | 59.3378 | 2.46387 | ||||||||
\(581\) | −0.00279464 | −0.000115941 0 | ||||||||
\(582\) | −21.7345 | −0.900926 | ||||||||
\(583\) | 9.28960 | 0.384736 | ||||||||
\(584\) | −19.8067 | −0.819606 | ||||||||
\(585\) | −14.4510 | −0.597475 | ||||||||
\(586\) | −9.07311 | −0.374807 | ||||||||
\(587\) | 39.6359 | 1.63595 | 0.817975 | − | 0.575254i | \(-0.195097\pi\) | ||||
0.817975 | + | 0.575254i | \(0.195097\pi\) | |||||||
\(588\) | 5.72861 | 0.236244 | ||||||||
\(589\) | −42.9916 | −1.77144 | ||||||||
\(590\) | −81.8850 | −3.37115 | ||||||||
\(591\) | −12.3627 | −0.508533 | ||||||||
\(592\) | 1.95283 | 0.0802608 | ||||||||
\(593\) | −32.1884 | −1.32182 | −0.660910 | − | 0.750465i | \(-0.729830\pi\) | ||||
−0.660910 | + | 0.750465i | \(0.729830\pi\) | |||||||
\(594\) | −7.89362 | −0.323879 | ||||||||
\(595\) | 7.61932 | 0.312361 | ||||||||
\(596\) | −51.2512 | −2.09933 | ||||||||
\(597\) | −44.2514 | −1.81109 | ||||||||
\(598\) | 92.0809 | 3.76547 | ||||||||
\(599\) | −34.0952 | −1.39309 | −0.696547 | − | 0.717512i | \(-0.745281\pi\) | ||||
−0.696547 | + | 0.717512i | \(0.745281\pi\) | |||||||
\(600\) | −55.5622 | −2.26832 | ||||||||
\(601\) | −9.01124 | −0.367576 | −0.183788 | − | 0.982966i | \(-0.558836\pi\) | ||||
−0.183788 | + | 0.982966i | \(0.558836\pi\) | |||||||
\(602\) | 18.0658 | 0.736307 | ||||||||
\(603\) | −2.93908 | −0.119689 | ||||||||
\(604\) | 58.3653 | 2.37485 | ||||||||
\(605\) | −44.0004 | −1.78887 | ||||||||
\(606\) | −33.2722 | −1.35159 | ||||||||
\(607\) | 5.59646 | 0.227153 | 0.113577 | − | 0.993529i | \(-0.463769\pi\) | ||||
0.113577 | + | 0.993529i | \(0.463769\pi\) | |||||||
\(608\) | −29.7030 | −1.20462 | ||||||||
\(609\) | 8.87023 | 0.359440 | ||||||||
\(610\) | 43.1470 | 1.74697 | ||||||||
\(611\) | −46.4105 | −1.87757 | ||||||||
\(612\) | 3.38941 | 0.137009 | ||||||||
\(613\) | −4.20474 | −0.169828 | −0.0849139 | − | 0.996388i | \(-0.527062\pi\) | ||||
−0.0849139 | + | 0.996388i | \(0.527062\pi\) | |||||||
\(614\) | −12.8023 | −0.516660 | ||||||||
\(615\) | 76.1348 | 3.07005 | ||||||||
\(616\) | 1.76078 | 0.0709438 | ||||||||
\(617\) | −27.9644 | −1.12580 | −0.562902 | − | 0.826524i | \(-0.690315\pi\) | ||||
−0.562902 | + | 0.826524i | \(0.690315\pi\) | |||||||
\(618\) | 26.0310 | 1.04712 | ||||||||
\(619\) | 20.5778 | 0.827090 | 0.413545 | − | 0.910484i | \(-0.364290\pi\) | ||||
0.413545 | + | 0.910484i | \(0.364290\pi\) | |||||||
\(620\) | 123.095 | 4.94360 | ||||||||
\(621\) | −34.1247 | −1.36938 | ||||||||
\(622\) | −5.06614 | −0.203134 | ||||||||
\(623\) | 8.85786 | 0.354883 | ||||||||
\(624\) | 10.0321 | 0.401606 | ||||||||
\(625\) | 77.5387 | 3.10155 | ||||||||
\(626\) | 18.9671 | 0.758079 | ||||||||
\(627\) | 6.61056 | 0.264000 | ||||||||
\(628\) | 49.5040 | 1.97542 | ||||||||
\(629\) | −3.63537 | −0.144952 | ||||||||
\(630\) | −5.93353 | −0.236398 | ||||||||
\(631\) | 29.9688 | 1.19304 | 0.596520 | − | 0.802598i | \(-0.296550\pi\) | ||||
0.596520 | + | 0.802598i | \(0.296550\pi\) | |||||||
\(632\) | 14.6592 | 0.583111 | ||||||||
\(633\) | −21.4277 | −0.851673 | ||||||||
\(634\) | −48.1855 | −1.91369 | ||||||||
\(635\) | −0.397255 | −0.0157646 | ||||||||
\(636\) | −68.2015 | −2.70436 | ||||||||
\(637\) | −5.45043 | −0.215954 | ||||||||
\(638\) | 8.13414 | 0.322034 | ||||||||
\(639\) | 9.02982 | 0.357214 | ||||||||
\(640\) | 66.7272 | 2.63762 | ||||||||
\(641\) | −20.3207 | −0.802618 | −0.401309 | − | 0.915943i | \(-0.631445\pi\) | ||||
−0.401309 | + | 0.915943i | \(0.631445\pi\) | |||||||
\(642\) | 64.1308 | 2.53104 | ||||||||
\(643\) | −1.16807 | −0.0460644 | −0.0230322 | − | 0.999735i | \(-0.507332\pi\) | ||||
−0.0230322 | + | 0.999735i | \(0.507332\pi\) | |||||||
\(644\) | 22.7101 | 0.894901 | ||||||||
\(645\) | −65.0917 | −2.56298 | ||||||||
\(646\) | 17.9157 | 0.704883 | ||||||||
\(647\) | −42.6597 | −1.67712 | −0.838562 | − | 0.544806i | \(-0.816603\pi\) | ||||
−0.838562 | + | 0.544806i | \(0.816603\pi\) | |||||||
\(648\) | 23.6634 | 0.929588 | ||||||||
\(649\) | −6.74245 | −0.264664 | ||||||||
\(650\) | 157.718 | 6.18623 | ||||||||
\(651\) | 18.4011 | 0.721194 | ||||||||
\(652\) | 49.2596 | 1.92915 | ||||||||
\(653\) | 10.4011 | 0.407025 | 0.203513 | − | 0.979072i | \(-0.434764\pi\) | ||||
0.203513 | + | 0.979072i | \(0.434764\pi\) | |||||||
\(654\) | −37.8166 | −1.47875 | ||||||||
\(655\) | 38.7011 | 1.51218 | ||||||||
\(656\) | −9.12656 | −0.356332 | ||||||||
\(657\) | 5.49583 | 0.214413 | ||||||||
\(658\) | −19.0560 | −0.742880 | ||||||||
\(659\) | −3.73389 | −0.145452 | −0.0727258 | − | 0.997352i | \(-0.523170\pi\) | ||||
−0.0727258 | + | 0.997352i | \(0.523170\pi\) | |||||||
\(660\) | −18.9275 | −0.736753 | ||||||||
\(661\) | −28.1953 | −1.09667 | −0.548335 | − | 0.836259i | \(-0.684738\pi\) | ||||
−0.548335 | + | 0.836259i | \(0.684738\pi\) | |||||||
\(662\) | 40.0058 | 1.55487 | ||||||||
\(663\) | −18.6757 | −0.725304 | ||||||||
\(664\) | 0.00630636 | 0.000244734 0 | ||||||||
\(665\) | −18.8389 | −0.730541 | ||||||||
\(666\) | 2.83104 | 0.109701 | ||||||||
\(667\) | 35.1645 | 1.36157 | ||||||||
\(668\) | −25.7652 | −0.996885 | ||||||||
\(669\) | 5.89935 | 0.228082 | ||||||||
\(670\) | 44.4812 | 1.71846 | ||||||||
\(671\) | 3.55274 | 0.137152 | ||||||||
\(672\) | 12.7133 | 0.490428 | ||||||||
\(673\) | −16.0766 | −0.619707 | −0.309853 | − | 0.950784i | \(-0.600280\pi\) | ||||
−0.309853 | + | 0.950784i | \(0.600280\pi\) | |||||||
\(674\) | 21.5260 | 0.829149 | ||||||||
\(675\) | −58.4496 | −2.24973 | ||||||||
\(676\) | 50.2610 | 1.93311 | ||||||||
\(677\) | −45.9928 | −1.76765 | −0.883824 | − | 0.467819i | \(-0.845040\pi\) | ||||
−0.883824 | + | 0.467819i | \(0.845040\pi\) | |||||||
\(678\) | 35.1115 | 1.34845 | ||||||||
\(679\) | 5.10013 | 0.195725 | ||||||||
\(680\) | −17.1937 | −0.659347 | ||||||||
\(681\) | 14.5253 | 0.556611 | ||||||||
\(682\) | 16.8741 | 0.646141 | ||||||||
\(683\) | 11.2252 | 0.429519 | 0.214759 | − | 0.976667i | \(-0.431103\pi\) | ||||
0.214759 | + | 0.976667i | \(0.431103\pi\) | |||||||
\(684\) | −8.38038 | −0.320432 | ||||||||
\(685\) | 27.1593 | 1.03770 | ||||||||
\(686\) | −2.23793 | −0.0854446 | ||||||||
\(687\) | 17.8866 | 0.682418 | ||||||||
\(688\) | 7.80278 | 0.297478 | ||||||||
\(689\) | 64.8897 | 2.47210 | ||||||||
\(690\) | −136.224 | −5.18596 | ||||||||
\(691\) | 19.0803 | 0.725850 | 0.362925 | − | 0.931818i | \(-0.381778\pi\) | ||||
0.362925 | + | 0.931818i | \(0.381778\pi\) | |||||||
\(692\) | 22.1895 | 0.843517 | ||||||||
\(693\) | −0.488570 | −0.0185592 | ||||||||
\(694\) | 31.1574 | 1.18272 | ||||||||
\(695\) | −76.1308 | −2.88780 | ||||||||
\(696\) | −20.0165 | −0.758722 | ||||||||
\(697\) | 16.9900 | 0.643540 | ||||||||
\(698\) | −5.58043 | −0.211222 | ||||||||
\(699\) | 26.2678 | 0.993540 | ||||||||
\(700\) | 38.8984 | 1.47022 | ||||||||
\(701\) | 12.2294 | 0.461897 | 0.230948 | − | 0.972966i | \(-0.425817\pi\) | ||||
0.230948 | + | 0.972966i | \(0.425817\pi\) | |||||||
\(702\) | −55.1385 | −2.08107 | ||||||||
\(703\) | 8.98853 | 0.339009 | ||||||||
\(704\) | 10.1499 | 0.382539 | ||||||||
\(705\) | 68.6593 | 2.58586 | ||||||||
\(706\) | 36.4205 | 1.37070 | ||||||||
\(707\) | 7.80750 | 0.293631 | ||||||||
\(708\) | 49.5011 | 1.86036 | ||||||||
\(709\) | 18.4448 | 0.692710 | 0.346355 | − | 0.938103i | \(-0.387419\pi\) | ||||
0.346355 | + | 0.938103i | \(0.387419\pi\) | |||||||
\(710\) | −136.661 | −5.12879 | ||||||||
\(711\) | −4.06754 | −0.152544 | ||||||||
\(712\) | −19.9885 | −0.749103 | ||||||||
\(713\) | 72.9478 | 2.73191 | ||||||||
\(714\) | −7.66819 | −0.286975 | ||||||||
\(715\) | 18.0084 | 0.673477 | ||||||||
\(716\) | 49.3729 | 1.84515 | ||||||||
\(717\) | 31.4114 | 1.17308 | ||||||||
\(718\) | 19.3481 | 0.722065 | ||||||||
\(719\) | −7.97734 | −0.297505 | −0.148752 | − | 0.988874i | \(-0.547526\pi\) | ||||
−0.148752 | + | 0.988874i | \(0.547526\pi\) | |||||||
\(720\) | −2.56274 | −0.0955078 | ||||||||
\(721\) | −6.10831 | −0.227486 | ||||||||
\(722\) | −1.77616 | −0.0661018 | ||||||||
\(723\) | −5.43463 | −0.202116 | ||||||||
\(724\) | −52.4725 | −1.95012 | ||||||||
\(725\) | 60.2306 | 2.23691 | ||||||||
\(726\) | 44.2826 | 1.64348 | ||||||||
\(727\) | −0.553970 | −0.0205456 | −0.0102728 | − | 0.999947i | \(-0.503270\pi\) | ||||
−0.0102728 | + | 0.999947i | \(0.503270\pi\) | |||||||
\(728\) | 12.2994 | 0.455846 | ||||||||
\(729\) | 19.2578 | 0.713254 | ||||||||
\(730\) | −83.1760 | −3.07848 | ||||||||
\(731\) | −14.5256 | −0.537249 | ||||||||
\(732\) | −26.0832 | −0.964062 | ||||||||
\(733\) | −42.8652 | −1.58326 | −0.791632 | − | 0.610998i | \(-0.790768\pi\) | ||||
−0.791632 | + | 0.610998i | \(0.790768\pi\) | |||||||
\(734\) | −39.2413 | −1.44842 | ||||||||
\(735\) | 8.06334 | 0.297421 | ||||||||
\(736\) | 50.3998 | 1.85776 | ||||||||
\(737\) | 3.66260 | 0.134914 | ||||||||
\(738\) | −13.2309 | −0.487036 | ||||||||
\(739\) | −8.92735 | −0.328398 | −0.164199 | − | 0.986427i | \(-0.552504\pi\) | ||||
−0.164199 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(740\) | −25.7362 | −0.946082 | ||||||||
\(741\) | 46.1760 | 1.69632 | ||||||||
\(742\) | 26.6435 | 0.978114 | ||||||||
\(743\) | 6.35803 | 0.233253 | 0.116627 | − | 0.993176i | \(-0.462792\pi\) | ||||
0.116627 | + | 0.993176i | \(0.462792\pi\) | |||||||
\(744\) | −41.5236 | −1.52233 | ||||||||
\(745\) | −72.1390 | −2.64297 | ||||||||
\(746\) | −13.2740 | −0.485995 | ||||||||
\(747\) | −0.00174985 | −6.40236e−5 0 | ||||||||
\(748\) | −4.22379 | −0.154437 | ||||||||
\(749\) | −15.0486 | −0.549866 | ||||||||
\(750\) | −143.102 | −5.22534 | ||||||||
\(751\) | 12.2653 | 0.447566 | 0.223783 | − | 0.974639i | \(-0.428159\pi\) | ||||
0.223783 | + | 0.974639i | \(0.428159\pi\) | |||||||
\(752\) | −8.23045 | −0.300133 | ||||||||
\(753\) | 21.6455 | 0.788808 | ||||||||
\(754\) | 56.8185 | 2.06921 | ||||||||
\(755\) | 82.1524 | 2.98983 | ||||||||
\(756\) | −13.5989 | −0.494587 | ||||||||
\(757\) | −0.000105885 0 | −3.84844e−6 0 | −1.92422e−6 | − | 1.00000i | \(-0.500001\pi\) | ||||
−1.92422e−6 | 1.00000i | \(0.500001\pi\) | ||||||||
\(758\) | −14.8107 | −0.537950 | ||||||||
\(759\) | −11.2167 | −0.407142 | ||||||||
\(760\) | 42.5117 | 1.54206 | ||||||||
\(761\) | 41.4132 | 1.50123 | 0.750613 | − | 0.660742i | \(-0.229758\pi\) | ||||
0.750613 | + | 0.660742i | \(0.229758\pi\) | |||||||
\(762\) | 0.399803 | 0.0144833 | ||||||||
\(763\) | 8.87387 | 0.321256 | ||||||||
\(764\) | −45.1853 | −1.63475 | ||||||||
\(765\) | 4.77079 | 0.172488 | ||||||||
\(766\) | 17.6566 | 0.637959 | ||||||||
\(767\) | −47.0973 | −1.70059 | ||||||||
\(768\) | −17.6145 | −0.635607 | ||||||||
\(769\) | −39.5973 | −1.42792 | −0.713958 | − | 0.700188i | \(-0.753099\pi\) | ||||
−0.713958 | + | 0.700188i | \(0.753099\pi\) | |||||||
\(770\) | 7.39421 | 0.266469 | ||||||||
\(771\) | 49.0071 | 1.76495 | ||||||||
\(772\) | 31.9741 | 1.15077 | ||||||||
\(773\) | −22.6307 | −0.813969 | −0.406984 | − | 0.913435i | \(-0.633420\pi\) | ||||
−0.406984 | + | 0.913435i | \(0.633420\pi\) | |||||||
\(774\) | 11.3118 | 0.406594 | ||||||||
\(775\) | 124.947 | 4.48822 | ||||||||
\(776\) | −11.5089 | −0.413145 | ||||||||
\(777\) | −3.84723 | −0.138019 | ||||||||
\(778\) | 8.82980 | 0.316563 | ||||||||
\(779\) | −42.0080 | −1.50509 | ||||||||
\(780\) | −132.212 | −4.73397 | ||||||||
\(781\) | −11.2527 | −0.402654 | ||||||||
\(782\) | −30.3992 | −1.08707 | ||||||||
\(783\) | −21.0566 | −0.752503 | ||||||||
\(784\) | −0.966582 | −0.0345208 | ||||||||
\(785\) | 69.6796 | 2.48697 | ||||||||
\(786\) | −38.9493 | −1.38928 | ||||||||
\(787\) | 23.0942 | 0.823220 | 0.411610 | − | 0.911360i | \(-0.364967\pi\) | ||||
0.411610 | + | 0.911360i | \(0.364967\pi\) | |||||||
\(788\) | −19.5307 | −0.695751 | ||||||||
\(789\) | 23.2939 | 0.829286 | ||||||||
\(790\) | 61.5597 | 2.19019 | ||||||||
\(791\) | −8.23910 | −0.292949 | ||||||||
\(792\) | 1.10250 | 0.0391757 | ||||||||
\(793\) | 24.8166 | 0.881264 | ||||||||
\(794\) | 68.9980 | 2.44865 | ||||||||
\(795\) | −95.9974 | −3.40468 | ||||||||
\(796\) | −69.9087 | −2.47785 | ||||||||
\(797\) | −14.3777 | −0.509284 | −0.254642 | − | 0.967035i | \(-0.581958\pi\) | ||||
−0.254642 | + | 0.967035i | \(0.581958\pi\) | |||||||
\(798\) | 18.9597 | 0.671168 | ||||||||
\(799\) | 15.3217 | 0.542045 | ||||||||
\(800\) | 86.3261 | 3.05209 | ||||||||
\(801\) | 5.54630 | 0.195969 | ||||||||
\(802\) | 42.6862 | 1.50730 | ||||||||
\(803\) | −6.84875 | −0.241687 | ||||||||
\(804\) | −26.8897 | −0.948327 | ||||||||
\(805\) | 31.9657 | 1.12664 | ||||||||
\(806\) | 117.869 | 4.15174 | ||||||||
\(807\) | 3.89448 | 0.137092 | ||||||||
\(808\) | −17.6183 | −0.619810 | ||||||||
\(809\) | 10.5974 | 0.372583 | 0.186292 | − | 0.982494i | \(-0.440353\pi\) | ||||
0.186292 | + | 0.982494i | \(0.440353\pi\) | |||||||
\(810\) | 99.3721 | 3.49158 | ||||||||
\(811\) | −35.0589 | −1.23108 | −0.615542 | − | 0.788104i | \(-0.711063\pi\) | ||||
−0.615542 | + | 0.788104i | \(0.711063\pi\) | |||||||
\(812\) | 14.0132 | 0.491769 | ||||||||
\(813\) | 23.9425 | 0.839700 | ||||||||
\(814\) | −3.52797 | −0.123655 | ||||||||
\(815\) | 69.3356 | 2.42872 | ||||||||
\(816\) | −3.31196 | −0.115942 | ||||||||
\(817\) | 35.9148 | 1.25650 | ||||||||
\(818\) | −20.4069 | −0.713510 | ||||||||
\(819\) | −3.41276 | −0.119251 | ||||||||
\(820\) | 120.278 | 4.20030 | ||||||||
\(821\) | 16.0098 | 0.558747 | 0.279374 | − | 0.960182i | \(-0.409873\pi\) | ||||
0.279374 | + | 0.960182i | \(0.409873\pi\) | |||||||
\(822\) | −27.3335 | −0.953365 | ||||||||
\(823\) | −30.7692 | −1.07255 | −0.536273 | − | 0.844044i | \(-0.680168\pi\) | ||||
−0.536273 | + | 0.844044i | \(0.680168\pi\) | |||||||
\(824\) | 13.7840 | 0.480187 | ||||||||
\(825\) | −19.2123 | −0.668887 | ||||||||
\(826\) | −19.3380 | −0.672856 | ||||||||
\(827\) | −28.7589 | −1.00004 | −0.500022 | − | 0.866013i | \(-0.666675\pi\) | ||||
−0.500022 | + | 0.866013i | \(0.666675\pi\) | |||||||
\(828\) | 14.2198 | 0.494171 | ||||||||
\(829\) | −25.3858 | −0.881686 | −0.440843 | − | 0.897584i | \(-0.645320\pi\) | ||||
−0.440843 | + | 0.897584i | \(0.645320\pi\) | |||||||
\(830\) | 0.0264829 | 0.000919235 0 | ||||||||
\(831\) | −33.8735 | −1.17506 | ||||||||
\(832\) | 70.8992 | 2.45799 | ||||||||
\(833\) | 1.79938 | 0.0623449 | ||||||||
\(834\) | 76.6191 | 2.65310 | ||||||||
\(835\) | −36.2660 | −1.25504 | ||||||||
\(836\) | 10.4434 | 0.361193 | ||||||||
\(837\) | −43.6815 | −1.50985 | ||||||||
\(838\) | 30.8148 | 1.06448 | ||||||||
\(839\) | −2.51518 | −0.0868336 | −0.0434168 | − | 0.999057i | \(-0.513824\pi\) | ||||
−0.0434168 | + | 0.999057i | \(0.513824\pi\) | |||||||
\(840\) | −18.1956 | −0.627809 | ||||||||
\(841\) | −7.30175 | −0.251785 | ||||||||
\(842\) | 35.4373 | 1.22125 | ||||||||
\(843\) | −28.0092 | −0.964688 | ||||||||
\(844\) | −33.8516 | −1.16522 | ||||||||
\(845\) | 70.7451 | 2.43371 | ||||||||
\(846\) | −11.9318 | −0.410224 | ||||||||
\(847\) | −10.3912 | −0.357044 | ||||||||
\(848\) | 11.5076 | 0.395171 | ||||||||
\(849\) | 26.9540 | 0.925058 | ||||||||
\(850\) | −52.0685 | −1.78593 | ||||||||
\(851\) | −15.2517 | −0.522820 | ||||||||
\(852\) | 82.6141 | 2.83031 | ||||||||
\(853\) | −39.1245 | −1.33960 | −0.669799 | − | 0.742542i | \(-0.733620\pi\) | ||||
−0.669799 | + | 0.742542i | \(0.733620\pi\) | |||||||
\(854\) | 10.1896 | 0.348682 | ||||||||
\(855\) | −11.7959 | −0.403410 | ||||||||
\(856\) | 33.9586 | 1.16068 | ||||||||
\(857\) | −17.9728 | −0.613938 | −0.306969 | − | 0.951719i | \(-0.599315\pi\) | ||||
−0.306969 | + | 0.951719i | \(0.599315\pi\) | |||||||
\(858\) | −18.1239 | −0.618741 | ||||||||
\(859\) | −10.6897 | −0.364727 | −0.182363 | − | 0.983231i | \(-0.558375\pi\) | ||||
−0.182363 | + | 0.983231i | \(0.558375\pi\) | |||||||
\(860\) | −102.832 | −3.50655 | ||||||||
\(861\) | 17.9801 | 0.612759 | ||||||||
\(862\) | 57.6915 | 1.96498 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −30.1797 | −1.02673 | ||||||||
\(865\) | 31.2329 | 1.06195 | ||||||||
\(866\) | −89.4393 | −3.03927 | ||||||||
\(867\) | −26.2066 | −0.890024 | ||||||||
\(868\) | 29.0701 | 0.986704 | ||||||||
\(869\) | 5.06885 | 0.171949 | ||||||||
\(870\) | −84.0570 | −2.84980 | ||||||||
\(871\) | 25.5840 | 0.866880 | ||||||||
\(872\) | −20.0247 | −0.678121 | ||||||||
\(873\) | 3.19342 | 0.108081 | ||||||||
\(874\) | 75.1625 | 2.54241 | ||||||||
\(875\) | 33.5796 | 1.13520 | ||||||||
\(876\) | 50.2815 | 1.69885 | ||||||||
\(877\) | 21.2618 | 0.717959 | 0.358979 | − | 0.933345i | \(-0.383125\pi\) | ||||
0.358979 | + | 0.933345i | \(0.383125\pi\) | |||||||
\(878\) | −75.3611 | −2.54331 | ||||||||
\(879\) | 7.72026 | 0.260398 | ||||||||
\(880\) | 3.19362 | 0.107657 | ||||||||
\(881\) | 43.4081 | 1.46246 | 0.731229 | − | 0.682133i | \(-0.238947\pi\) | ||||
0.731229 | + | 0.682133i | \(0.238947\pi\) | |||||||
\(882\) | −1.40127 | −0.0471831 | ||||||||
\(883\) | −39.5040 | −1.32942 | −0.664708 | − | 0.747103i | \(-0.731444\pi\) | ||||
−0.664708 | + | 0.747103i | \(0.731444\pi\) | |||||||
\(884\) | −29.5040 | −0.992327 | ||||||||
\(885\) | 69.6755 | 2.34212 | ||||||||
\(886\) | 36.7537 | 1.23476 | ||||||||
\(887\) | 4.54739 | 0.152686 | 0.0763432 | − | 0.997082i | \(-0.475676\pi\) | ||||
0.0763432 | + | 0.997082i | \(0.475676\pi\) | |||||||
\(888\) | 8.68162 | 0.291336 | ||||||||
\(889\) | −0.0938159 | −0.00314649 | ||||||||
\(890\) | −83.9398 | −2.81367 | ||||||||
\(891\) | 8.18235 | 0.274119 | ||||||||
\(892\) | 9.31984 | 0.312051 | ||||||||
\(893\) | −37.8833 | −1.26772 | ||||||||
\(894\) | 72.6017 | 2.42816 | ||||||||
\(895\) | 69.4951 | 2.32297 | ||||||||
\(896\) | 15.7583 | 0.526449 | ||||||||
\(897\) | −78.3511 | −2.61607 | ||||||||
\(898\) | −34.8252 | −1.16213 | ||||||||
\(899\) | 45.0124 | 1.50125 | ||||||||
\(900\) | 24.3560 | 0.811866 | ||||||||
\(901\) | −21.4224 | −0.713684 | ||||||||
\(902\) | 16.4880 | 0.548990 | ||||||||
\(903\) | −15.3721 | −0.511551 | ||||||||
\(904\) | 18.5923 | 0.618369 | ||||||||
\(905\) | −73.8580 | −2.45512 | ||||||||
\(906\) | −82.6794 | −2.74684 | ||||||||
\(907\) | 36.2902 | 1.20500 | 0.602499 | − | 0.798120i | \(-0.294172\pi\) | ||||
0.602499 | + | 0.798120i | \(0.294172\pi\) | |||||||
\(908\) | 22.9472 | 0.761528 | ||||||||
\(909\) | 4.88862 | 0.162145 | ||||||||
\(910\) | 51.6500 | 1.71218 | ||||||||
\(911\) | −15.0322 | −0.498038 | −0.249019 | − | 0.968499i | \(-0.580108\pi\) | ||||
−0.249019 | + | 0.968499i | \(0.580108\pi\) | |||||||
\(912\) | 8.18887 | 0.271161 | ||||||||
\(913\) | 0.00218061 | 7.21678e−5 0 | ||||||||
\(914\) | −37.4951 | −1.24023 | ||||||||
\(915\) | −36.7136 | −1.21371 | ||||||||
\(916\) | 28.2574 | 0.933652 | ||||||||
\(917\) | 9.13967 | 0.301818 | ||||||||
\(918\) | 18.2032 | 0.600794 | ||||||||
\(919\) | 4.76330 | 0.157127 | 0.0785634 | − | 0.996909i | \(-0.474967\pi\) | ||||
0.0785634 | + | 0.996909i | \(0.474967\pi\) | |||||||
\(920\) | −72.1334 | −2.37817 | ||||||||
\(921\) | 10.8934 | 0.358951 | ||||||||
\(922\) | −61.9343 | −2.03970 | ||||||||
\(923\) | −78.6024 | −2.58723 | ||||||||
\(924\) | −4.46994 | −0.147050 | ||||||||
\(925\) | −26.1234 | −0.858933 | ||||||||
\(926\) | 76.9415 | 2.52845 | ||||||||
\(927\) | −3.82469 | −0.125619 | ||||||||
\(928\) | 31.0992 | 1.02088 | ||||||||
\(929\) | 29.4215 | 0.965287 | 0.482643 | − | 0.875817i | \(-0.339677\pi\) | ||||
0.482643 | + | 0.875817i | \(0.339677\pi\) | |||||||
\(930\) | −174.374 | −5.71795 | ||||||||
\(931\) | −4.44901 | −0.145810 | ||||||||
\(932\) | 41.4981 | 1.35931 | ||||||||
\(933\) | 4.31075 | 0.141128 | ||||||||
\(934\) | −79.8860 | −2.61395 | ||||||||
\(935\) | −5.94523 | −0.194430 | ||||||||
\(936\) | 7.70119 | 0.251721 | ||||||||
\(937\) | −46.3376 | −1.51378 | −0.756892 | − | 0.653540i | \(-0.773283\pi\) | ||||
−0.756892 | + | 0.653540i | \(0.773283\pi\) | |||||||
\(938\) | 10.5047 | 0.342991 | ||||||||
\(939\) | −16.1390 | −0.526677 | ||||||||
\(940\) | 108.469 | 3.53785 | ||||||||
\(941\) | −25.4229 | −0.828762 | −0.414381 | − | 0.910104i | \(-0.636002\pi\) | ||||
−0.414381 | + | 0.910104i | \(0.636002\pi\) | |||||||
\(942\) | −70.1266 | −2.28485 | ||||||||
\(943\) | 71.2788 | 2.32116 | ||||||||
\(944\) | −8.35226 | −0.271843 | ||||||||
\(945\) | −19.1412 | −0.622663 | ||||||||
\(946\) | −14.0965 | −0.458315 | ||||||||
\(947\) | 19.6320 | 0.637955 | 0.318978 | − | 0.947762i | \(-0.396660\pi\) | ||||
0.318978 | + | 0.947762i | \(0.396660\pi\) | |||||||
\(948\) | −37.2140 | −1.20865 | ||||||||
\(949\) | −47.8399 | −1.55295 | ||||||||
\(950\) | 128.740 | 4.17689 | ||||||||
\(951\) | 41.0008 | 1.32954 | ||||||||
\(952\) | −4.06047 | −0.131601 | ||||||||
\(953\) | −23.8559 | −0.772767 | −0.386384 | − | 0.922338i | \(-0.626276\pi\) | ||||
−0.386384 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(954\) | 16.6827 | 0.540122 | ||||||||
\(955\) | −63.6009 | −2.05808 | ||||||||
\(956\) | 49.6239 | 1.60495 | ||||||||
\(957\) | −6.92129 | −0.223734 | ||||||||
\(958\) | −42.6672 | −1.37852 | ||||||||
\(959\) | 6.41396 | 0.207117 | ||||||||
\(960\) | −104.888 | −3.38524 | ||||||||
\(961\) | 62.3771 | 2.01217 | ||||||||
\(962\) | −24.6436 | −0.794540 | ||||||||
\(963\) | −9.42262 | −0.303640 | ||||||||
\(964\) | −8.58567 | −0.276526 | ||||||||
\(965\) | 45.0053 | 1.44877 | ||||||||
\(966\) | −32.1707 | −1.03508 | ||||||||
\(967\) | 7.92873 | 0.254971 | 0.127485 | − | 0.991840i | \(-0.459309\pi\) | ||||
0.127485 | + | 0.991840i | \(0.459309\pi\) | |||||||
\(968\) | 23.4486 | 0.753666 | ||||||||
\(969\) | −15.2444 | −0.489719 | ||||||||
\(970\) | −48.3304 | −1.55180 | ||||||||
\(971\) | 40.4870 | 1.29929 | 0.649644 | − | 0.760239i | \(-0.274918\pi\) | ||||
0.649644 | + | 0.760239i | \(0.274918\pi\) | |||||||
\(972\) | −19.2757 | −0.618267 | ||||||||
\(973\) | −17.9791 | −0.576383 | ||||||||
\(974\) | 62.7053 | 2.00921 | ||||||||
\(975\) | −134.202 | −4.29790 | ||||||||
\(976\) | 4.40099 | 0.140872 | ||||||||
\(977\) | −59.1027 | −1.89086 | −0.945432 | − | 0.325820i | \(-0.894360\pi\) | ||||
−0.945432 | + | 0.325820i | \(0.894360\pi\) | |||||||
\(978\) | −69.7804 | −2.23133 | ||||||||
\(979\) | −6.91164 | −0.220897 | ||||||||
\(980\) | 12.7385 | 0.406917 | ||||||||
\(981\) | 5.55632 | 0.177400 | ||||||||
\(982\) | −59.8108 | −1.90864 | ||||||||
\(983\) | −6.75717 | −0.215520 | −0.107760 | − | 0.994177i | \(-0.534368\pi\) | ||||
−0.107760 | + | 0.994177i | \(0.534368\pi\) | |||||||
\(984\) | −40.5736 | −1.29344 | ||||||||
\(985\) | −27.4905 | −0.875921 | ||||||||
\(986\) | −18.7578 | −0.597371 | ||||||||
\(987\) | 16.2146 | 0.516118 | ||||||||
\(988\) | 72.9492 | 2.32082 | ||||||||
\(989\) | −60.9400 | −1.93778 | ||||||||
\(990\) | 4.62984 | 0.147146 | ||||||||
\(991\) | −17.6290 | −0.560002 | −0.280001 | − | 0.960000i | \(-0.590335\pi\) | ||||
−0.280001 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(992\) | 64.5145 | 2.04834 | ||||||||
\(993\) | −34.0408 | −1.08025 | ||||||||
\(994\) | −32.2739 | −1.02367 | ||||||||
\(995\) | −98.4005 | −3.11950 | ||||||||
\(996\) | −0.0160094 | −0.000507278 0 | ||||||||
\(997\) | 31.1846 | 0.987625 | 0.493813 | − | 0.869568i | \(-0.335603\pi\) | ||||
0.493813 | + | 0.869568i | \(0.335603\pi\) | |||||||
\(998\) | −35.8063 | −1.13343 | ||||||||
\(999\) | 9.13277 | 0.288948 |
(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 | 6041.2.a.f.1.19 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.19 | ✓ | 132 | 1.1 | even | 1 | trivial |