Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 36 x^{10} + 105 x^{9} + 465 x^{8} - 1287 x^{7} - 2668 x^{6} + 6443 x^{5} + 7140 x^{4} - 10858 x^{3} - 10086 x^{2} + 2072 x + 1496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.45965\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.45965 | −1.09999 | −0.549994 | − | 0.835169i | \(-0.685370\pi\) | ||||
−0.549994 | + | 0.835169i | \(0.685370\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.70163 | −1.77705 | −0.888524 | − | 0.458830i | \(-0.848269\pi\) | ||||
−0.888524 | + | 0.458830i | \(0.848269\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.45965 | 0.777809 | ||||||||
\(11\) | 1.91016 | 0.575934 | 0.287967 | − | 0.957640i | \(-0.407021\pi\) | ||||
0.287967 | + | 0.957640i | \(0.407021\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.90772 | −1.63851 | −0.819254 | − | 0.573431i | \(-0.805612\pi\) | ||||
−0.819254 | + | 0.573431i | \(0.805612\pi\) | |||||||
\(14\) | 4.70163 | 1.25656 | ||||||||
\(15\) | 2.45965 | 0.635079 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.14256 | −0.277112 | −0.138556 | − | 0.990355i | \(-0.544246\pi\) | ||||
−0.138556 | + | 0.990355i | \(0.544246\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.45965 | −0.549994 | ||||||||
\(21\) | 4.70163 | 1.02598 | ||||||||
\(22\) | −1.91016 | −0.407247 | ||||||||
\(23\) | 3.30477 | 0.689092 | 0.344546 | − | 0.938769i | \(-0.388033\pi\) | ||||
0.344546 | + | 0.938769i | \(0.388033\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.04987 | 0.209974 | ||||||||
\(26\) | 5.90772 | 1.15860 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.70163 | −0.888524 | ||||||||
\(29\) | 2.41724 | 0.448869 | 0.224435 | − | 0.974489i | \(-0.427946\pi\) | ||||
0.224435 | + | 0.974489i | \(0.427946\pi\) | |||||||
\(30\) | −2.45965 | −0.449068 | ||||||||
\(31\) | 7.67209 | 1.37795 | 0.688974 | − | 0.724786i | \(-0.258061\pi\) | ||||
0.688974 | + | 0.724786i | \(0.258061\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.91016 | −0.332516 | ||||||||
\(34\) | 1.14256 | 0.195948 | ||||||||
\(35\) | 11.5643 | 1.95473 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.55685 | −0.749142 | −0.374571 | − | 0.927198i | \(-0.622210\pi\) | ||||
−0.374571 | + | 0.927198i | \(0.622210\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 5.90772 | 0.945993 | ||||||||
\(40\) | 2.45965 | 0.388905 | ||||||||
\(41\) | 6.19475 | 0.967457 | 0.483728 | − | 0.875218i | \(-0.339282\pi\) | ||||
0.483728 | + | 0.875218i | \(0.339282\pi\) | |||||||
\(42\) | −4.70163 | −0.725477 | ||||||||
\(43\) | −5.22642 | −0.797022 | −0.398511 | − | 0.917164i | \(-0.630473\pi\) | ||||
−0.398511 | + | 0.917164i | \(0.630473\pi\) | |||||||
\(44\) | 1.91016 | 0.287967 | ||||||||
\(45\) | −2.45965 | −0.366663 | ||||||||
\(46\) | −3.30477 | −0.487262 | ||||||||
\(47\) | 5.78403 | 0.843687 | 0.421844 | − | 0.906669i | \(-0.361383\pi\) | ||||
0.421844 | + | 0.906669i | \(0.361383\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 15.1053 | 2.15790 | ||||||||
\(50\) | −1.04987 | −0.148474 | ||||||||
\(51\) | 1.14256 | 0.159991 | ||||||||
\(52\) | −5.90772 | −0.819254 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −4.69832 | −0.633521 | ||||||||
\(56\) | 4.70163 | 0.628281 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −2.41724 | −0.317399 | ||||||||
\(59\) | −5.66428 | −0.737426 | −0.368713 | − | 0.929543i | \(-0.620202\pi\) | ||||
−0.368713 | + | 0.929543i | \(0.620202\pi\) | |||||||
\(60\) | 2.45965 | 0.317539 | ||||||||
\(61\) | 13.6683 | 1.75005 | 0.875026 | − | 0.484076i | \(-0.160844\pi\) | ||||
0.875026 | + | 0.484076i | \(0.160844\pi\) | |||||||
\(62\) | −7.67209 | −0.974356 | ||||||||
\(63\) | −4.70163 | −0.592349 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.5309 | 1.80234 | ||||||||
\(66\) | 1.91016 | 0.235124 | ||||||||
\(67\) | −3.23769 | −0.395546 | −0.197773 | − | 0.980248i | \(-0.563371\pi\) | ||||
−0.197773 | + | 0.980248i | \(0.563371\pi\) | |||||||
\(68\) | −1.14256 | −0.138556 | ||||||||
\(69\) | −3.30477 | −0.397848 | ||||||||
\(70\) | −11.5643 | −1.38220 | ||||||||
\(71\) | 1.22023 | 0.144815 | 0.0724076 | − | 0.997375i | \(-0.476932\pi\) | ||||
0.0724076 | + | 0.997375i | \(0.476932\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 7.85807 | 0.919718 | 0.459859 | − | 0.887992i | \(-0.347900\pi\) | ||||
0.459859 | + | 0.887992i | \(0.347900\pi\) | |||||||
\(74\) | 4.55685 | 0.529723 | ||||||||
\(75\) | −1.04987 | −0.121229 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −8.98085 | −1.02346 | ||||||||
\(78\) | −5.90772 | −0.668918 | ||||||||
\(79\) | 15.2607 | 1.71697 | 0.858483 | − | 0.512842i | \(-0.171407\pi\) | ||||
0.858483 | + | 0.512842i | \(0.171407\pi\) | |||||||
\(80\) | −2.45965 | −0.274997 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.19475 | −0.684095 | ||||||||
\(83\) | −14.6060 | −1.60322 | −0.801611 | − | 0.597846i | \(-0.796023\pi\) | ||||
−0.801611 | + | 0.597846i | \(0.796023\pi\) | |||||||
\(84\) | 4.70163 | 0.512990 | ||||||||
\(85\) | 2.81030 | 0.304820 | ||||||||
\(86\) | 5.22642 | 0.563580 | ||||||||
\(87\) | −2.41724 | −0.259155 | ||||||||
\(88\) | −1.91016 | −0.203624 | ||||||||
\(89\) | −5.90313 | −0.625731 | −0.312865 | − | 0.949797i | \(-0.601289\pi\) | ||||
−0.312865 | + | 0.949797i | \(0.601289\pi\) | |||||||
\(90\) | 2.45965 | 0.259270 | ||||||||
\(91\) | 27.7759 | 2.91171 | ||||||||
\(92\) | 3.30477 | 0.344546 | ||||||||
\(93\) | −7.67209 | −0.795559 | ||||||||
\(94\) | −5.78403 | −0.596577 | ||||||||
\(95\) | 2.45965 | 0.252355 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −0.0999559 | −0.0101490 | −0.00507449 | − | 0.999987i | \(-0.501615\pi\) | ||||
−0.00507449 | + | 0.999987i | \(0.501615\pi\) | |||||||
\(98\) | −15.1053 | −1.52587 | ||||||||
\(99\) | 1.91016 | 0.191978 | ||||||||
\(100\) | 1.04987 | 0.104987 | ||||||||
\(101\) | −17.7871 | −1.76988 | −0.884942 | − | 0.465701i | \(-0.845802\pi\) | ||||
−0.884942 | + | 0.465701i | \(0.845802\pi\) | |||||||
\(102\) | −1.14256 | −0.113131 | ||||||||
\(103\) | 14.3083 | 1.40984 | 0.704918 | − | 0.709289i | \(-0.250984\pi\) | ||||
0.704918 | + | 0.709289i | \(0.250984\pi\) | |||||||
\(104\) | 5.90772 | 0.579300 | ||||||||
\(105\) | −11.5643 | −1.12856 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 1.86376 | 0.180177 | 0.0900883 | − | 0.995934i | \(-0.471285\pi\) | ||||
0.0900883 | + | 0.995934i | \(0.471285\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 5.31128 | 0.508728 | 0.254364 | − | 0.967108i | \(-0.418134\pi\) | ||||
0.254364 | + | 0.967108i | \(0.418134\pi\) | |||||||
\(110\) | 4.69832 | 0.447967 | ||||||||
\(111\) | 4.55685 | 0.432517 | ||||||||
\(112\) | −4.70163 | −0.444262 | ||||||||
\(113\) | −0.179709 | −0.0169056 | −0.00845278 | − | 0.999964i | \(-0.502691\pi\) | ||||
−0.00845278 | + | 0.999964i | \(0.502691\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −8.12857 | −0.757993 | ||||||||
\(116\) | 2.41724 | 0.224435 | ||||||||
\(117\) | −5.90772 | −0.546169 | ||||||||
\(118\) | 5.66428 | 0.521439 | ||||||||
\(119\) | 5.37190 | 0.492442 | ||||||||
\(120\) | −2.45965 | −0.224534 | ||||||||
\(121\) | −7.35130 | −0.668300 | ||||||||
\(122\) | −13.6683 | −1.23747 | ||||||||
\(123\) | −6.19475 | −0.558561 | ||||||||
\(124\) | 7.67209 | 0.688974 | ||||||||
\(125\) | 9.71593 | 0.869019 | ||||||||
\(126\) | 4.70163 | 0.418854 | ||||||||
\(127\) | 1.73478 | 0.153937 | 0.0769683 | − | 0.997034i | \(-0.475476\pi\) | ||||
0.0769683 | + | 0.997034i | \(0.475476\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.22642 | 0.460161 | ||||||||
\(130\) | −14.5309 | −1.27445 | ||||||||
\(131\) | −13.5180 | −1.18108 | −0.590539 | − | 0.807009i | \(-0.701085\pi\) | ||||
−0.590539 | + | 0.807009i | \(0.701085\pi\) | |||||||
\(132\) | −1.91016 | −0.166258 | ||||||||
\(133\) | 4.70163 | 0.407683 | ||||||||
\(134\) | 3.23769 | 0.279694 | ||||||||
\(135\) | 2.45965 | 0.211693 | ||||||||
\(136\) | 1.14256 | 0.0979740 | ||||||||
\(137\) | 6.46378 | 0.552238 | 0.276119 | − | 0.961123i | \(-0.410952\pi\) | ||||
0.276119 | + | 0.961123i | \(0.410952\pi\) | |||||||
\(138\) | 3.30477 | 0.281321 | ||||||||
\(139\) | 6.32384 | 0.536381 | 0.268191 | − | 0.963366i | \(-0.413574\pi\) | ||||
0.268191 | + | 0.963366i | \(0.413574\pi\) | |||||||
\(140\) | 11.5643 | 0.977366 | ||||||||
\(141\) | −5.78403 | −0.487103 | ||||||||
\(142\) | −1.22023 | −0.102400 | ||||||||
\(143\) | −11.2847 | −0.943673 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.94555 | −0.493751 | ||||||||
\(146\) | −7.85807 | −0.650339 | ||||||||
\(147\) | −15.1053 | −1.24586 | ||||||||
\(148\) | −4.55685 | −0.374571 | ||||||||
\(149\) | 20.9266 | 1.71437 | 0.857185 | − | 0.515008i | \(-0.172211\pi\) | ||||
0.857185 | + | 0.515008i | \(0.172211\pi\) | |||||||
\(150\) | 1.04987 | 0.0857216 | ||||||||
\(151\) | 17.4133 | 1.41707 | 0.708536 | − | 0.705674i | \(-0.249356\pi\) | ||||
0.708536 | + | 0.705674i | \(0.249356\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −1.14256 | −0.0923707 | ||||||||
\(154\) | 8.98085 | 0.723698 | ||||||||
\(155\) | −18.8706 | −1.51573 | ||||||||
\(156\) | 5.90772 | 0.472996 | ||||||||
\(157\) | −13.2749 | −1.05945 | −0.529724 | − | 0.848170i | \(-0.677705\pi\) | ||||
−0.529724 | + | 0.848170i | \(0.677705\pi\) | |||||||
\(158\) | −15.2607 | −1.21408 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | 2.45965 | 0.194452 | ||||||||
\(161\) | −15.5378 | −1.22455 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.5174 | 0.823786 | 0.411893 | − | 0.911232i | \(-0.364868\pi\) | ||||
0.411893 | + | 0.911232i | \(0.364868\pi\) | |||||||
\(164\) | 6.19475 | 0.483728 | ||||||||
\(165\) | 4.69832 | 0.365764 | ||||||||
\(166\) | 14.6060 | 1.13365 | ||||||||
\(167\) | −1.01870 | −0.0788297 | −0.0394148 | − | 0.999223i | \(-0.512549\pi\) | ||||
−0.0394148 | + | 0.999223i | \(0.512549\pi\) | |||||||
\(168\) | −4.70163 | −0.362738 | ||||||||
\(169\) | 21.9012 | 1.68471 | ||||||||
\(170\) | −2.81030 | −0.215540 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −5.22642 | −0.398511 | ||||||||
\(173\) | −13.8755 | −1.05494 | −0.527468 | − | 0.849575i | \(-0.676859\pi\) | ||||
−0.527468 | + | 0.849575i | \(0.676859\pi\) | |||||||
\(174\) | 2.41724 | 0.183250 | ||||||||
\(175\) | −4.93610 | −0.373134 | ||||||||
\(176\) | 1.91016 | 0.143984 | ||||||||
\(177\) | 5.66428 | 0.425753 | ||||||||
\(178\) | 5.90313 | 0.442458 | ||||||||
\(179\) | −1.61613 | −0.120795 | −0.0603977 | − | 0.998174i | \(-0.519237\pi\) | ||||
−0.0603977 | + | 0.998174i | \(0.519237\pi\) | |||||||
\(180\) | −2.45965 | −0.183331 | ||||||||
\(181\) | −13.5282 | −1.00554 | −0.502770 | − | 0.864420i | \(-0.667686\pi\) | ||||
−0.502770 | + | 0.864420i | \(0.667686\pi\) | |||||||
\(182\) | −27.7759 | −2.05889 | ||||||||
\(183\) | −13.6683 | −1.01039 | ||||||||
\(184\) | −3.30477 | −0.243631 | ||||||||
\(185\) | 11.2083 | 0.824048 | ||||||||
\(186\) | 7.67209 | 0.562545 | ||||||||
\(187\) | −2.18248 | −0.159598 | ||||||||
\(188\) | 5.78403 | 0.421844 | ||||||||
\(189\) | 4.70163 | 0.341993 | ||||||||
\(190\) | −2.45965 | −0.178442 | ||||||||
\(191\) | −11.2029 | −0.810614 | −0.405307 | − | 0.914181i | \(-0.632835\pi\) | ||||
−0.405307 | + | 0.914181i | \(0.632835\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −20.0363 | −1.44224 | −0.721121 | − | 0.692809i | \(-0.756373\pi\) | ||||
−0.721121 | + | 0.692809i | \(0.756373\pi\) | |||||||
\(194\) | 0.0999559 | 0.00717641 | ||||||||
\(195\) | −14.5309 | −1.04058 | ||||||||
\(196\) | 15.1053 | 1.07895 | ||||||||
\(197\) | 21.7120 | 1.54691 | 0.773456 | − | 0.633849i | \(-0.218526\pi\) | ||||
0.773456 | + | 0.633849i | \(0.218526\pi\) | |||||||
\(198\) | −1.91016 | −0.135749 | ||||||||
\(199\) | 10.6531 | 0.755176 | 0.377588 | − | 0.925974i | \(-0.376754\pi\) | ||||
0.377588 | + | 0.925974i | \(0.376754\pi\) | |||||||
\(200\) | −1.04987 | −0.0742371 | ||||||||
\(201\) | 3.23769 | 0.228369 | ||||||||
\(202\) | 17.7871 | 1.25150 | ||||||||
\(203\) | −11.3649 | −0.797662 | ||||||||
\(204\) | 1.14256 | 0.0799954 | ||||||||
\(205\) | −15.2369 | −1.06419 | ||||||||
\(206\) | −14.3083 | −0.996905 | ||||||||
\(207\) | 3.30477 | 0.229697 | ||||||||
\(208\) | −5.90772 | −0.409627 | ||||||||
\(209\) | −1.91016 | −0.132128 | ||||||||
\(210\) | 11.5643 | 0.798016 | ||||||||
\(211\) | −4.80428 | −0.330740 | −0.165370 | − | 0.986232i | \(-0.552882\pi\) | ||||
−0.165370 | + | 0.986232i | \(0.552882\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | −1.22023 | −0.0836091 | ||||||||
\(214\) | −1.86376 | −0.127404 | ||||||||
\(215\) | 12.8552 | 0.876715 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −36.0713 | −2.44868 | ||||||||
\(218\) | −5.31128 | −0.359725 | ||||||||
\(219\) | −7.85807 | −0.530999 | ||||||||
\(220\) | −4.69832 | −0.316760 | ||||||||
\(221\) | 6.74995 | 0.454051 | ||||||||
\(222\) | −4.55685 | −0.305836 | ||||||||
\(223\) | 10.6493 | 0.713128 | 0.356564 | − | 0.934271i | \(-0.383948\pi\) | ||||
0.356564 | + | 0.934271i | \(0.383948\pi\) | |||||||
\(224\) | 4.70163 | 0.314141 | ||||||||
\(225\) | 1.04987 | 0.0699914 | ||||||||
\(226\) | 0.179709 | 0.0119540 | ||||||||
\(227\) | 6.99635 | 0.464364 | 0.232182 | − | 0.972672i | \(-0.425414\pi\) | ||||
0.232182 | + | 0.972672i | \(0.425414\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −14.2907 | −0.944354 | −0.472177 | − | 0.881504i | \(-0.656532\pi\) | ||||
−0.472177 | + | 0.881504i | \(0.656532\pi\) | |||||||
\(230\) | 8.12857 | 0.535982 | ||||||||
\(231\) | 8.98085 | 0.590897 | ||||||||
\(232\) | −2.41724 | −0.158699 | ||||||||
\(233\) | −0.544364 | −0.0356624 | −0.0178312 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178312 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(234\) | 5.90772 | 0.386200 | ||||||||
\(235\) | −14.2267 | −0.928046 | ||||||||
\(236\) | −5.66428 | −0.368713 | ||||||||
\(237\) | −15.2607 | −0.991291 | ||||||||
\(238\) | −5.37190 | −0.348209 | ||||||||
\(239\) | −7.02584 | −0.454464 | −0.227232 | − | 0.973841i | \(-0.572968\pi\) | ||||
−0.227232 | + | 0.973841i | \(0.572968\pi\) | |||||||
\(240\) | 2.45965 | 0.158770 | ||||||||
\(241\) | −3.00462 | −0.193545 | −0.0967723 | − | 0.995307i | \(-0.530852\pi\) | ||||
−0.0967723 | + | 0.995307i | \(0.530852\pi\) | |||||||
\(242\) | 7.35130 | 0.472559 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.6683 | 0.875026 | ||||||||
\(245\) | −37.1537 | −2.37366 | ||||||||
\(246\) | 6.19475 | 0.394963 | ||||||||
\(247\) | 5.90772 | 0.375899 | ||||||||
\(248\) | −7.67209 | −0.487178 | ||||||||
\(249\) | 14.6060 | 0.925620 | ||||||||
\(250\) | −9.71593 | −0.614489 | ||||||||
\(251\) | −17.3184 | −1.09313 | −0.546563 | − | 0.837418i | \(-0.684064\pi\) | ||||
−0.546563 | + | 0.837418i | \(0.684064\pi\) | |||||||
\(252\) | −4.70163 | −0.296175 | ||||||||
\(253\) | 6.31263 | 0.396872 | ||||||||
\(254\) | −1.73478 | −0.108850 | ||||||||
\(255\) | −2.81030 | −0.175988 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.24806 | 0.576878 | 0.288439 | − | 0.957498i | \(-0.406864\pi\) | ||||
0.288439 | + | 0.957498i | \(0.406864\pi\) | |||||||
\(258\) | −5.22642 | −0.325383 | ||||||||
\(259\) | 21.4246 | 1.33126 | ||||||||
\(260\) | 14.5309 | 0.901170 | ||||||||
\(261\) | 2.41724 | 0.149623 | ||||||||
\(262\) | 13.5180 | 0.835148 | ||||||||
\(263\) | 5.43686 | 0.335251 | 0.167626 | − | 0.985851i | \(-0.446390\pi\) | ||||
0.167626 | + | 0.985851i | \(0.446390\pi\) | |||||||
\(264\) | 1.91016 | 0.117562 | ||||||||
\(265\) | 2.45965 | 0.151095 | ||||||||
\(266\) | −4.70163 | −0.288275 | ||||||||
\(267\) | 5.90313 | 0.361266 | ||||||||
\(268\) | −3.23769 | −0.197773 | ||||||||
\(269\) | −22.6746 | −1.38250 | −0.691248 | − | 0.722618i | \(-0.742939\pi\) | ||||
−0.691248 | + | 0.722618i | \(0.742939\pi\) | |||||||
\(270\) | −2.45965 | −0.149689 | ||||||||
\(271\) | −12.4883 | −0.758608 | −0.379304 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379304 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(272\) | −1.14256 | −0.0692781 | ||||||||
\(273\) | −27.7759 | −1.68107 | ||||||||
\(274\) | −6.46378 | −0.390492 | ||||||||
\(275\) | 2.00542 | 0.120931 | ||||||||
\(276\) | −3.30477 | −0.198924 | ||||||||
\(277\) | 6.80678 | 0.408980 | 0.204490 | − | 0.978869i | \(-0.434446\pi\) | ||||
0.204490 | + | 0.978869i | \(0.434446\pi\) | |||||||
\(278\) | −6.32384 | −0.379279 | ||||||||
\(279\) | 7.67209 | 0.459316 | ||||||||
\(280\) | −11.5643 | −0.691102 | ||||||||
\(281\) | −22.1604 | −1.32198 | −0.660989 | − | 0.750396i | \(-0.729863\pi\) | ||||
−0.660989 | + | 0.750396i | \(0.729863\pi\) | |||||||
\(282\) | 5.78403 | 0.344434 | ||||||||
\(283\) | −2.66711 | −0.158543 | −0.0792717 | − | 0.996853i | \(-0.525259\pi\) | ||||
−0.0792717 | + | 0.996853i | \(0.525259\pi\) | |||||||
\(284\) | 1.22023 | 0.0724076 | ||||||||
\(285\) | −2.45965 | −0.145697 | ||||||||
\(286\) | 11.2847 | 0.667277 | ||||||||
\(287\) | −29.1254 | −1.71922 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.6945 | −0.923209 | ||||||||
\(290\) | 5.94555 | 0.349135 | ||||||||
\(291\) | 0.0999559 | 0.00585952 | ||||||||
\(292\) | 7.85807 | 0.459859 | ||||||||
\(293\) | 13.2532 | 0.774261 | 0.387130 | − | 0.922025i | \(-0.373466\pi\) | ||||
0.387130 | + | 0.922025i | \(0.373466\pi\) | |||||||
\(294\) | 15.1053 | 0.880959 | ||||||||
\(295\) | 13.9321 | 0.811160 | ||||||||
\(296\) | 4.55685 | 0.264862 | ||||||||
\(297\) | −1.91016 | −0.110839 | ||||||||
\(298\) | −20.9266 | −1.21224 | ||||||||
\(299\) | −19.5237 | −1.12908 | ||||||||
\(300\) | −1.04987 | −0.0606143 | ||||||||
\(301\) | 24.5727 | 1.41635 | ||||||||
\(302\) | −17.4133 | −1.00202 | ||||||||
\(303\) | 17.7871 | 1.02184 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −33.6193 | −1.92504 | ||||||||
\(306\) | 1.14256 | 0.0653160 | ||||||||
\(307\) | −3.64574 | −0.208073 | −0.104037 | − | 0.994573i | \(-0.533176\pi\) | ||||
−0.104037 | + | 0.994573i | \(0.533176\pi\) | |||||||
\(308\) | −8.98085 | −0.511731 | ||||||||
\(309\) | −14.3083 | −0.813969 | ||||||||
\(310\) | 18.8706 | 1.07178 | ||||||||
\(311\) | −31.7037 | −1.79775 | −0.898877 | − | 0.438202i | \(-0.855615\pi\) | ||||
−0.898877 | + | 0.438202i | \(0.855615\pi\) | |||||||
\(312\) | −5.90772 | −0.334459 | ||||||||
\(313\) | 22.2063 | 1.25518 | 0.627588 | − | 0.778546i | \(-0.284042\pi\) | ||||
0.627588 | + | 0.778546i | \(0.284042\pi\) | |||||||
\(314\) | 13.2749 | 0.749143 | ||||||||
\(315\) | 11.5643 | 0.651577 | ||||||||
\(316\) | 15.2607 | 0.858483 | ||||||||
\(317\) | 28.9210 | 1.62437 | 0.812184 | − | 0.583402i | \(-0.198279\pi\) | ||||
0.812184 | + | 0.583402i | \(0.198279\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | 4.61730 | 0.258519 | ||||||||
\(320\) | −2.45965 | −0.137499 | ||||||||
\(321\) | −1.86376 | −0.104025 | ||||||||
\(322\) | 15.5378 | 0.865887 | ||||||||
\(323\) | 1.14256 | 0.0635739 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −6.20235 | −0.344044 | ||||||||
\(326\) | −10.5174 | −0.582505 | ||||||||
\(327\) | −5.31128 | −0.293715 | ||||||||
\(328\) | −6.19475 | −0.342048 | ||||||||
\(329\) | −27.1943 | −1.49927 | ||||||||
\(330\) | −4.69832 | −0.258634 | ||||||||
\(331\) | −18.6818 | −1.02685 | −0.513423 | − | 0.858136i | \(-0.671623\pi\) | ||||
−0.513423 | + | 0.858136i | \(0.671623\pi\) | |||||||
\(332\) | −14.6060 | −0.801611 | ||||||||
\(333\) | −4.55685 | −0.249714 | ||||||||
\(334\) | 1.01870 | 0.0557410 | ||||||||
\(335\) | 7.96357 | 0.435097 | ||||||||
\(336\) | 4.70163 | 0.256495 | ||||||||
\(337\) | 1.11190 | 0.0605689 | 0.0302845 | − | 0.999541i | \(-0.490359\pi\) | ||||
0.0302845 | + | 0.999541i | \(0.490359\pi\) | |||||||
\(338\) | −21.9012 | −1.19127 | ||||||||
\(339\) | 0.179709 | 0.00976043 | ||||||||
\(340\) | 2.81030 | 0.152410 | ||||||||
\(341\) | 14.6549 | 0.793608 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −38.1081 | −2.05764 | ||||||||
\(344\) | 5.22642 | 0.281790 | ||||||||
\(345\) | 8.12857 | 0.437628 | ||||||||
\(346\) | 13.8755 | 0.745953 | ||||||||
\(347\) | −13.0010 | −0.697928 | −0.348964 | − | 0.937136i | \(-0.613466\pi\) | ||||
−0.348964 | + | 0.937136i | \(0.613466\pi\) | |||||||
\(348\) | −2.41724 | −0.129577 | ||||||||
\(349\) | 10.6628 | 0.570769 | 0.285385 | − | 0.958413i | \(-0.407879\pi\) | ||||
0.285385 | + | 0.958413i | \(0.407879\pi\) | |||||||
\(350\) | 4.93610 | 0.263846 | ||||||||
\(351\) | 5.90772 | 0.315331 | ||||||||
\(352\) | −1.91016 | −0.101812 | ||||||||
\(353\) | 17.9807 | 0.957015 | 0.478507 | − | 0.878084i | \(-0.341178\pi\) | ||||
0.478507 | + | 0.878084i | \(0.341178\pi\) | |||||||
\(354\) | −5.66428 | −0.301053 | ||||||||
\(355\) | −3.00135 | −0.159295 | ||||||||
\(356\) | −5.90313 | −0.312865 | ||||||||
\(357\) | −5.37190 | −0.284311 | ||||||||
\(358\) | 1.61613 | 0.0854152 | ||||||||
\(359\) | −25.5705 | −1.34956 | −0.674781 | − | 0.738018i | \(-0.735762\pi\) | ||||
−0.674781 | + | 0.738018i | \(0.735762\pi\) | |||||||
\(360\) | 2.45965 | 0.129635 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 13.5282 | 0.711024 | ||||||||
\(363\) | 7.35130 | 0.385843 | ||||||||
\(364\) | 27.7759 | 1.45585 | ||||||||
\(365\) | −19.3281 | −1.01168 | ||||||||
\(366\) | 13.6683 | 0.714456 | ||||||||
\(367\) | −4.42367 | −0.230914 | −0.115457 | − | 0.993312i | \(-0.536833\pi\) | ||||
−0.115457 | + | 0.993312i | \(0.536833\pi\) | |||||||
\(368\) | 3.30477 | 0.172273 | ||||||||
\(369\) | 6.19475 | 0.322486 | ||||||||
\(370\) | −11.2083 | −0.582690 | ||||||||
\(371\) | 4.70163 | 0.244096 | ||||||||
\(372\) | −7.67209 | −0.397779 | ||||||||
\(373\) | 17.4917 | 0.905686 | 0.452843 | − | 0.891590i | \(-0.350410\pi\) | ||||
0.452843 | + | 0.891590i | \(0.350410\pi\) | |||||||
\(374\) | 2.18248 | 0.112853 | ||||||||
\(375\) | −9.71593 | −0.501728 | ||||||||
\(376\) | −5.78403 | −0.298288 | ||||||||
\(377\) | −14.2804 | −0.735476 | ||||||||
\(378\) | −4.70163 | −0.241826 | ||||||||
\(379\) | 15.5294 | 0.797689 | 0.398845 | − | 0.917019i | \(-0.369411\pi\) | ||||
0.398845 | + | 0.917019i | \(0.369411\pi\) | |||||||
\(380\) | 2.45965 | 0.126177 | ||||||||
\(381\) | −1.73478 | −0.0888753 | ||||||||
\(382\) | 11.2029 | 0.573190 | ||||||||
\(383\) | −23.9671 | −1.22466 | −0.612331 | − | 0.790601i | \(-0.709768\pi\) | ||||
−0.612331 | + | 0.790601i | \(0.709768\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 22.0897 | 1.12580 | ||||||||
\(386\) | 20.0363 | 1.01982 | ||||||||
\(387\) | −5.22642 | −0.265674 | ||||||||
\(388\) | −0.0999559 | −0.00507449 | ||||||||
\(389\) | 30.1549 | 1.52892 | 0.764458 | − | 0.644673i | \(-0.223007\pi\) | ||||
0.764458 | + | 0.644673i | \(0.223007\pi\) | |||||||
\(390\) | 14.5309 | 0.735802 | ||||||||
\(391\) | −3.77591 | −0.190956 | ||||||||
\(392\) | −15.1053 | −0.762933 | ||||||||
\(393\) | 13.5180 | 0.681895 | ||||||||
\(394\) | −21.7120 | −1.09383 | ||||||||
\(395\) | −37.5360 | −1.88864 | ||||||||
\(396\) | 1.91016 | 0.0959891 | ||||||||
\(397\) | 26.0606 | 1.30795 | 0.653973 | − | 0.756518i | \(-0.273101\pi\) | ||||
0.653973 | + | 0.756518i | \(0.273101\pi\) | |||||||
\(398\) | −10.6531 | −0.533990 | ||||||||
\(399\) | −4.70163 | −0.235376 | ||||||||
\(400\) | 1.04987 | 0.0524936 | ||||||||
\(401\) | 24.5456 | 1.22575 | 0.612876 | − | 0.790179i | \(-0.290013\pi\) | ||||
0.612876 | + | 0.790179i | \(0.290013\pi\) | |||||||
\(402\) | −3.23769 | −0.161481 | ||||||||
\(403\) | −45.3246 | −2.25778 | ||||||||
\(404\) | −17.7871 | −0.884942 | ||||||||
\(405\) | −2.45965 | −0.122221 | ||||||||
\(406\) | 11.3649 | 0.564033 | ||||||||
\(407\) | −8.70431 | −0.431457 | ||||||||
\(408\) | −1.14256 | −0.0565653 | ||||||||
\(409\) | −24.8079 | −1.22667 | −0.613335 | − | 0.789823i | \(-0.710172\pi\) | ||||
−0.613335 | + | 0.789823i | \(0.710172\pi\) | |||||||
\(410\) | 15.2369 | 0.752497 | ||||||||
\(411\) | −6.46378 | −0.318835 | ||||||||
\(412\) | 14.3083 | 0.704918 | ||||||||
\(413\) | 26.6313 | 1.31044 | ||||||||
\(414\) | −3.30477 | −0.162421 | ||||||||
\(415\) | 35.9257 | 1.76352 | ||||||||
\(416\) | 5.90772 | 0.289650 | ||||||||
\(417\) | −6.32384 | −0.309680 | ||||||||
\(418\) | 1.91016 | 0.0934289 | ||||||||
\(419\) | 3.30387 | 0.161405 | 0.0807023 | − | 0.996738i | \(-0.474284\pi\) | ||||
0.0807023 | + | 0.996738i | \(0.474284\pi\) | |||||||
\(420\) | −11.5643 | −0.564282 | ||||||||
\(421\) | −17.0365 | −0.830306 | −0.415153 | − | 0.909752i | \(-0.636272\pi\) | ||||
−0.415153 | + | 0.909752i | \(0.636272\pi\) | |||||||
\(422\) | 4.80428 | 0.233869 | ||||||||
\(423\) | 5.78403 | 0.281229 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | −1.19954 | −0.0581864 | ||||||||
\(426\) | 1.22023 | 0.0591206 | ||||||||
\(427\) | −64.2635 | −3.10993 | ||||||||
\(428\) | 1.86376 | 0.0900883 | ||||||||
\(429\) | 11.2847 | 0.544830 | ||||||||
\(430\) | −12.8552 | −0.619931 | ||||||||
\(431\) | 14.8752 | 0.716512 | 0.358256 | − | 0.933623i | \(-0.383371\pi\) | ||||
0.358256 | + | 0.933623i | \(0.383371\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 9.55069 | 0.458977 | 0.229488 | − | 0.973311i | \(-0.426295\pi\) | ||||
0.229488 | + | 0.973311i | \(0.426295\pi\) | |||||||
\(434\) | 36.0713 | 1.73148 | ||||||||
\(435\) | 5.94555 | 0.285067 | ||||||||
\(436\) | 5.31128 | 0.254364 | ||||||||
\(437\) | −3.30477 | −0.158089 | ||||||||
\(438\) | 7.85807 | 0.375473 | ||||||||
\(439\) | −15.0945 | −0.720422 | −0.360211 | − | 0.932871i | \(-0.617295\pi\) | ||||
−0.360211 | + | 0.932871i | \(0.617295\pi\) | |||||||
\(440\) | 4.69832 | 0.223983 | ||||||||
\(441\) | 15.1053 | 0.719300 | ||||||||
\(442\) | −6.74995 | −0.321062 | ||||||||
\(443\) | 10.8991 | 0.517830 | 0.258915 | − | 0.965900i | \(-0.416635\pi\) | ||||
0.258915 | + | 0.965900i | \(0.416635\pi\) | |||||||
\(444\) | 4.55685 | 0.216259 | ||||||||
\(445\) | 14.5196 | 0.688296 | ||||||||
\(446\) | −10.6493 | −0.504258 | ||||||||
\(447\) | −20.9266 | −0.989792 | ||||||||
\(448\) | −4.70163 | −0.222131 | ||||||||
\(449\) | 13.4361 | 0.634086 | 0.317043 | − | 0.948411i | \(-0.397310\pi\) | ||||
0.317043 | + | 0.948411i | \(0.397310\pi\) | |||||||
\(450\) | −1.04987 | −0.0494914 | ||||||||
\(451\) | 11.8329 | 0.557192 | ||||||||
\(452\) | −0.179709 | −0.00845278 | ||||||||
\(453\) | −17.4133 | −0.818147 | ||||||||
\(454\) | −6.99635 | −0.328355 | ||||||||
\(455\) | −68.3190 | −3.20284 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 10.4744 | 0.489973 | 0.244987 | − | 0.969526i | \(-0.421216\pi\) | ||||
0.244987 | + | 0.969526i | \(0.421216\pi\) | |||||||
\(458\) | 14.2907 | 0.667759 | ||||||||
\(459\) | 1.14256 | 0.0533303 | ||||||||
\(460\) | −8.12857 | −0.378997 | ||||||||
\(461\) | −11.0887 | −0.516452 | −0.258226 | − | 0.966085i | \(-0.583138\pi\) | ||||
−0.258226 | + | 0.966085i | \(0.583138\pi\) | |||||||
\(462\) | −8.98085 | −0.417827 | ||||||||
\(463\) | 0.621532 | 0.0288851 | 0.0144425 | − | 0.999896i | \(-0.495403\pi\) | ||||
0.0144425 | + | 0.999896i | \(0.495403\pi\) | |||||||
\(464\) | 2.41724 | 0.112217 | ||||||||
\(465\) | 18.8706 | 0.875105 | ||||||||
\(466\) | 0.544364 | 0.0252172 | ||||||||
\(467\) | −30.9060 | −1.43016 | −0.715080 | − | 0.699043i | \(-0.753610\pi\) | ||||
−0.715080 | + | 0.699043i | \(0.753610\pi\) | |||||||
\(468\) | −5.90772 | −0.273085 | ||||||||
\(469\) | 15.2224 | 0.702905 | ||||||||
\(470\) | 14.2267 | 0.656228 | ||||||||
\(471\) | 13.2749 | 0.611673 | ||||||||
\(472\) | 5.66428 | 0.260720 | ||||||||
\(473\) | −9.98330 | −0.459032 | ||||||||
\(474\) | 15.2607 | 0.700949 | ||||||||
\(475\) | −1.04987 | −0.0481714 | ||||||||
\(476\) | 5.37190 | 0.246221 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 7.02584 | 0.321355 | ||||||||
\(479\) | 23.7155 | 1.08359 | 0.541795 | − | 0.840510i | \(-0.317745\pi\) | ||||
0.541795 | + | 0.840510i | \(0.317745\pi\) | |||||||
\(480\) | −2.45965 | −0.112267 | ||||||||
\(481\) | 26.9206 | 1.22748 | ||||||||
\(482\) | 3.00462 | 0.136857 | ||||||||
\(483\) | 15.5378 | 0.706994 | ||||||||
\(484\) | −7.35130 | −0.334150 | ||||||||
\(485\) | 0.245856 | 0.0111638 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −9.42158 | −0.426932 | −0.213466 | − | 0.976950i | \(-0.568475\pi\) | ||||
−0.213466 | + | 0.976950i | \(0.568475\pi\) | |||||||
\(488\) | −13.6683 | −0.618737 | ||||||||
\(489\) | −10.5174 | −0.475613 | ||||||||
\(490\) | 37.1537 | 1.67843 | ||||||||
\(491\) | −13.0936 | −0.590906 | −0.295453 | − | 0.955357i | \(-0.595471\pi\) | ||||
−0.295453 | + | 0.955357i | \(0.595471\pi\) | |||||||
\(492\) | −6.19475 | −0.279281 | ||||||||
\(493\) | −2.76184 | −0.124387 | ||||||||
\(494\) | −5.90772 | −0.265801 | ||||||||
\(495\) | −4.69832 | −0.211174 | ||||||||
\(496\) | 7.67209 | 0.344487 | ||||||||
\(497\) | −5.73709 | −0.257344 | ||||||||
\(498\) | −14.6060 | −0.654512 | ||||||||
\(499\) | −9.16202 | −0.410149 | −0.205074 | − | 0.978746i | \(-0.565744\pi\) | ||||
−0.205074 | + | 0.978746i | \(0.565744\pi\) | |||||||
\(500\) | 9.71593 | 0.434510 | ||||||||
\(501\) | 1.01870 | 0.0455123 | ||||||||
\(502\) | 17.3184 | 0.772957 | ||||||||
\(503\) | 15.3316 | 0.683602 | 0.341801 | − | 0.939772i | \(-0.388963\pi\) | ||||
0.341801 | + | 0.939772i | \(0.388963\pi\) | |||||||
\(504\) | 4.70163 | 0.209427 | ||||||||
\(505\) | 43.7501 | 1.94685 | ||||||||
\(506\) | −6.31263 | −0.280631 | ||||||||
\(507\) | −21.9012 | −0.972666 | ||||||||
\(508\) | 1.73478 | 0.0769683 | ||||||||
\(509\) | −29.0500 | −1.28762 | −0.643809 | − | 0.765187i | \(-0.722647\pi\) | ||||
−0.643809 | + | 0.765187i | \(0.722647\pi\) | |||||||
\(510\) | 2.81030 | 0.124442 | ||||||||
\(511\) | −36.9457 | −1.63438 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −9.24806 | −0.407915 | ||||||||
\(515\) | −35.1933 | −1.55080 | ||||||||
\(516\) | 5.22642 | 0.230080 | ||||||||
\(517\) | 11.0484 | 0.485908 | ||||||||
\(518\) | −21.4246 | −0.941344 | ||||||||
\(519\) | 13.8755 | 0.609068 | ||||||||
\(520\) | −14.5309 | −0.637223 | ||||||||
\(521\) | −0.299447 | −0.0131190 | −0.00655951 | − | 0.999978i | \(-0.502088\pi\) | ||||
−0.00655951 | + | 0.999978i | \(0.502088\pi\) | |||||||
\(522\) | −2.41724 | −0.105800 | ||||||||
\(523\) | 34.4182 | 1.50500 | 0.752502 | − | 0.658590i | \(-0.228847\pi\) | ||||
0.752502 | + | 0.658590i | \(0.228847\pi\) | |||||||
\(524\) | −13.5180 | −0.590539 | ||||||||
\(525\) | 4.93610 | 0.215429 | ||||||||
\(526\) | −5.43686 | −0.237058 | ||||||||
\(527\) | −8.76585 | −0.381846 | ||||||||
\(528\) | −1.91016 | −0.0831290 | ||||||||
\(529\) | −12.0785 | −0.525152 | ||||||||
\(530\) | −2.45965 | −0.106840 | ||||||||
\(531\) | −5.66428 | −0.245809 | ||||||||
\(532\) | 4.70163 | 0.203841 | ||||||||
\(533\) | −36.5968 | −1.58519 | ||||||||
\(534\) | −5.90313 | −0.255453 | ||||||||
\(535\) | −4.58420 | −0.198192 | ||||||||
\(536\) | 3.23769 | 0.139847 | ||||||||
\(537\) | 1.61613 | 0.0697412 | ||||||||
\(538\) | 22.6746 | 0.977572 | ||||||||
\(539\) | 28.8535 | 1.24281 | ||||||||
\(540\) | 2.45965 | 0.105846 | ||||||||
\(541\) | 10.7819 | 0.463549 | 0.231775 | − | 0.972770i | \(-0.425547\pi\) | ||||
0.231775 | + | 0.972770i | \(0.425547\pi\) | |||||||
\(542\) | 12.4883 | 0.536417 | ||||||||
\(543\) | 13.5282 | 0.580549 | ||||||||
\(544\) | 1.14256 | 0.0489870 | ||||||||
\(545\) | −13.0639 | −0.559595 | ||||||||
\(546\) | 27.7759 | 1.18870 | ||||||||
\(547\) | 13.5372 | 0.578807 | 0.289403 | − | 0.957207i | \(-0.406543\pi\) | ||||
0.289403 | + | 0.957207i | \(0.406543\pi\) | |||||||
\(548\) | 6.46378 | 0.276119 | ||||||||
\(549\) | 13.6683 | 0.583351 | ||||||||
\(550\) | −2.00542 | −0.0855114 | ||||||||
\(551\) | −2.41724 | −0.102978 | ||||||||
\(552\) | 3.30477 | 0.140660 | ||||||||
\(553\) | −71.7503 | −3.05113 | ||||||||
\(554\) | −6.80678 | −0.289193 | ||||||||
\(555\) | −11.2083 | −0.475764 | ||||||||
\(556\) | 6.32384 | 0.268191 | ||||||||
\(557\) | −6.94401 | −0.294227 | −0.147114 | − | 0.989120i | \(-0.546998\pi\) | ||||
−0.147114 | + | 0.989120i | \(0.546998\pi\) | |||||||
\(558\) | −7.67209 | −0.324785 | ||||||||
\(559\) | 30.8763 | 1.30593 | ||||||||
\(560\) | 11.5643 | 0.488683 | ||||||||
\(561\) | 2.18248 | 0.0921442 | ||||||||
\(562\) | 22.1604 | 0.934779 | ||||||||
\(563\) | −15.1283 | −0.637580 | −0.318790 | − | 0.947825i | \(-0.603276\pi\) | ||||
−0.318790 | + | 0.947825i | \(0.603276\pi\) | |||||||
\(564\) | −5.78403 | −0.243552 | ||||||||
\(565\) | 0.442020 | 0.0185959 | ||||||||
\(566\) | 2.66711 | 0.112107 | ||||||||
\(567\) | −4.70163 | −0.197450 | ||||||||
\(568\) | −1.22023 | −0.0511999 | ||||||||
\(569\) | −29.6326 | −1.24226 | −0.621132 | − | 0.783706i | \(-0.713327\pi\) | ||||
−0.621132 | + | 0.783706i | \(0.713327\pi\) | |||||||
\(570\) | 2.45965 | 0.103023 | ||||||||
\(571\) | −32.1379 | −1.34493 | −0.672465 | − | 0.740129i | \(-0.734764\pi\) | ||||
−0.672465 | + | 0.740129i | \(0.734764\pi\) | |||||||
\(572\) | −11.2847 | −0.471836 | ||||||||
\(573\) | 11.2029 | 0.468008 | ||||||||
\(574\) | 29.1254 | 1.21567 | ||||||||
\(575\) | 3.46958 | 0.144692 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.0365 | 0.542718 | 0.271359 | − | 0.962478i | \(-0.412527\pi\) | ||||
0.271359 | + | 0.962478i | \(0.412527\pi\) | |||||||
\(578\) | 15.6945 | 0.652807 | ||||||||
\(579\) | 20.0363 | 0.832679 | ||||||||
\(580\) | −5.94555 | −0.246876 | ||||||||
\(581\) | 68.6722 | 2.84900 | ||||||||
\(582\) | −0.0999559 | −0.00414330 | ||||||||
\(583\) | −1.91016 | −0.0791107 | ||||||||
\(584\) | −7.85807 | −0.325169 | ||||||||
\(585\) | 14.5309 | 0.600780 | ||||||||
\(586\) | −13.2532 | −0.547485 | ||||||||
\(587\) | −2.89693 | −0.119569 | −0.0597846 | − | 0.998211i | \(-0.519041\pi\) | ||||
−0.0597846 | + | 0.998211i | \(0.519041\pi\) | |||||||
\(588\) | −15.1053 | −0.622932 | ||||||||
\(589\) | −7.67209 | −0.316123 | ||||||||
\(590\) | −13.9321 | −0.573577 | ||||||||
\(591\) | −21.7120 | −0.893111 | ||||||||
\(592\) | −4.55685 | −0.187286 | ||||||||
\(593\) | 14.7541 | 0.605879 | 0.302939 | − | 0.953010i | \(-0.402032\pi\) | ||||
0.302939 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(594\) | 1.91016 | 0.0783747 | ||||||||
\(595\) | −13.2130 | −0.541680 | ||||||||
\(596\) | 20.9266 | 0.857185 | ||||||||
\(597\) | −10.6531 | −0.436001 | ||||||||
\(598\) | 19.5237 | 0.798382 | ||||||||
\(599\) | 13.3995 | 0.547488 | 0.273744 | − | 0.961803i | \(-0.411738\pi\) | ||||
0.273744 | + | 0.961803i | \(0.411738\pi\) | |||||||
\(600\) | 1.04987 | 0.0428608 | ||||||||
\(601\) | 38.9454 | 1.58862 | 0.794309 | − | 0.607514i | \(-0.207833\pi\) | ||||
0.794309 | + | 0.607514i | \(0.207833\pi\) | |||||||
\(602\) | −24.5727 | −1.00151 | ||||||||
\(603\) | −3.23769 | −0.131849 | ||||||||
\(604\) | 17.4133 | 0.708536 | ||||||||
\(605\) | 18.0816 | 0.735122 | ||||||||
\(606\) | −17.7871 | −0.722552 | ||||||||
\(607\) | −38.8800 | −1.57809 | −0.789045 | − | 0.614336i | \(-0.789424\pi\) | ||||
−0.789045 | + | 0.614336i | \(0.789424\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 11.3649 | 0.460531 | ||||||||
\(610\) | 33.6193 | 1.36121 | ||||||||
\(611\) | −34.1704 | −1.38239 | ||||||||
\(612\) | −1.14256 | −0.0461854 | ||||||||
\(613\) | 1.59254 | 0.0643220 | 0.0321610 | − | 0.999483i | \(-0.489761\pi\) | ||||
0.0321610 | + | 0.999483i | \(0.489761\pi\) | |||||||
\(614\) | 3.64574 | 0.147130 | ||||||||
\(615\) | 15.2369 | 0.614411 | ||||||||
\(616\) | 8.98085 | 0.361849 | ||||||||
\(617\) | 26.2045 | 1.05495 | 0.527476 | − | 0.849570i | \(-0.323138\pi\) | ||||
0.527476 | + | 0.849570i | \(0.323138\pi\) | |||||||
\(618\) | 14.3083 | 0.575563 | ||||||||
\(619\) | 25.5487 | 1.02689 | 0.513445 | − | 0.858122i | \(-0.328369\pi\) | ||||
0.513445 | + | 0.858122i | \(0.328369\pi\) | |||||||
\(620\) | −18.8706 | −0.757863 | ||||||||
\(621\) | −3.30477 | −0.132616 | ||||||||
\(622\) | 31.7037 | 1.27120 | ||||||||
\(623\) | 27.7543 | 1.11195 | ||||||||
\(624\) | 5.90772 | 0.236498 | ||||||||
\(625\) | −29.1471 | −1.16589 | ||||||||
\(626\) | −22.2063 | −0.887543 | ||||||||
\(627\) | 1.91016 | 0.0762844 | ||||||||
\(628\) | −13.2749 | −0.529724 | ||||||||
\(629\) | 5.20649 | 0.207596 | ||||||||
\(630\) | −11.5643 | −0.460735 | ||||||||
\(631\) | −12.1464 | −0.483540 | −0.241770 | − | 0.970334i | \(-0.577728\pi\) | ||||
−0.241770 | + | 0.970334i | \(0.577728\pi\) | |||||||
\(632\) | −15.2607 | −0.607039 | ||||||||
\(633\) | 4.80428 | 0.190953 | ||||||||
\(634\) | −28.9210 | −1.14860 | ||||||||
\(635\) | −4.26694 | −0.169328 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | −89.2379 | −3.53573 | ||||||||
\(638\) | −4.61730 | −0.182801 | ||||||||
\(639\) | 1.22023 | 0.0482717 | ||||||||
\(640\) | 2.45965 | 0.0972261 | ||||||||
\(641\) | −14.4032 | −0.568892 | −0.284446 | − | 0.958692i | \(-0.591810\pi\) | ||||
−0.284446 | + | 0.958692i | \(0.591810\pi\) | |||||||
\(642\) | 1.86376 | 0.0735568 | ||||||||
\(643\) | −20.6470 | −0.814239 | −0.407120 | − | 0.913375i | \(-0.633467\pi\) | ||||
−0.407120 | + | 0.913375i | \(0.633467\pi\) | |||||||
\(644\) | −15.5378 | −0.612275 | ||||||||
\(645\) | −12.8552 | −0.506172 | ||||||||
\(646\) | −1.14256 | −0.0449535 | ||||||||
\(647\) | −13.2938 | −0.522635 | −0.261318 | − | 0.965253i | \(-0.584157\pi\) | ||||
−0.261318 | + | 0.965253i | \(0.584157\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −10.8197 | −0.424709 | ||||||||
\(650\) | 6.20235 | 0.243276 | ||||||||
\(651\) | 36.0713 | 1.41375 | ||||||||
\(652\) | 10.5174 | 0.411893 | ||||||||
\(653\) | −15.9776 | −0.625253 | −0.312626 | − | 0.949876i | \(-0.601209\pi\) | ||||
−0.312626 | + | 0.949876i | \(0.601209\pi\) | |||||||
\(654\) | 5.31128 | 0.207688 | ||||||||
\(655\) | 33.2497 | 1.29917 | ||||||||
\(656\) | 6.19475 | 0.241864 | ||||||||
\(657\) | 7.85807 | 0.306573 | ||||||||
\(658\) | 27.1943 | 1.06015 | ||||||||
\(659\) | −41.8008 | −1.62833 | −0.814164 | − | 0.580634i | \(-0.802805\pi\) | ||||
−0.814164 | + | 0.580634i | \(0.802805\pi\) | |||||||
\(660\) | 4.69832 | 0.182882 | ||||||||
\(661\) | 10.6457 | 0.414068 | 0.207034 | − | 0.978334i | \(-0.433619\pi\) | ||||
0.207034 | + | 0.978334i | \(0.433619\pi\) | |||||||
\(662\) | 18.6818 | 0.726089 | ||||||||
\(663\) | −6.74995 | −0.262146 | ||||||||
\(664\) | 14.6060 | 0.566824 | ||||||||
\(665\) | −11.5643 | −0.448446 | ||||||||
\(666\) | 4.55685 | 0.176574 | ||||||||
\(667\) | 7.98841 | 0.309312 | ||||||||
\(668\) | −1.01870 | −0.0394148 | ||||||||
\(669\) | −10.6493 | −0.411725 | ||||||||
\(670\) | −7.96357 | −0.307660 | ||||||||
\(671\) | 26.1087 | 1.00792 | ||||||||
\(672\) | −4.70163 | −0.181369 | ||||||||
\(673\) | −33.7745 | −1.30191 | −0.650955 | − | 0.759116i | \(-0.725631\pi\) | ||||
−0.650955 | + | 0.759116i | \(0.725631\pi\) | |||||||
\(674\) | −1.11190 | −0.0428287 | ||||||||
\(675\) | −1.04987 | −0.0404096 | ||||||||
\(676\) | 21.9012 | 0.842354 | ||||||||
\(677\) | −38.4563 | −1.47800 | −0.738999 | − | 0.673707i | \(-0.764701\pi\) | ||||
−0.738999 | + | 0.673707i | \(0.764701\pi\) | |||||||
\(678\) | −0.179709 | −0.00690166 | ||||||||
\(679\) | 0.469955 | 0.0180352 | ||||||||
\(680\) | −2.81030 | −0.107770 | ||||||||
\(681\) | −6.99635 | −0.268101 | ||||||||
\(682\) | −14.6549 | −0.561165 | ||||||||
\(683\) | 45.5455 | 1.74275 | 0.871375 | − | 0.490617i | \(-0.163228\pi\) | ||||
0.871375 | + | 0.490617i | \(0.163228\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | −15.8986 | −0.607456 | ||||||||
\(686\) | 38.1081 | 1.45497 | ||||||||
\(687\) | 14.2907 | 0.545223 | ||||||||
\(688\) | −5.22642 | −0.199256 | ||||||||
\(689\) | 5.90772 | 0.225066 | ||||||||
\(690\) | −8.12857 | −0.309449 | ||||||||
\(691\) | −40.3712 | −1.53579 | −0.767897 | − | 0.640574i | \(-0.778697\pi\) | ||||
−0.767897 | + | 0.640574i | \(0.778697\pi\) | |||||||
\(692\) | −13.8755 | −0.527468 | ||||||||
\(693\) | −8.98085 | −0.341154 | ||||||||
\(694\) | 13.0010 | 0.493509 | ||||||||
\(695\) | −15.5544 | −0.590013 | ||||||||
\(696\) | 2.41724 | 0.0916251 | ||||||||
\(697\) | −7.07789 | −0.268094 | ||||||||
\(698\) | −10.6628 | −0.403595 | ||||||||
\(699\) | 0.544364 | 0.0205897 | ||||||||
\(700\) | −4.93610 | −0.186567 | ||||||||
\(701\) | 7.09800 | 0.268088 | 0.134044 | − | 0.990975i | \(-0.457204\pi\) | ||||
0.134044 | + | 0.990975i | \(0.457204\pi\) | |||||||
\(702\) | −5.90772 | −0.222973 | ||||||||
\(703\) | 4.55685 | 0.171865 | ||||||||
\(704\) | 1.91016 | 0.0719918 | ||||||||
\(705\) | 14.2267 | 0.535808 | ||||||||
\(706\) | −17.9807 | −0.676712 | ||||||||
\(707\) | 83.6284 | 3.14517 | ||||||||
\(708\) | 5.66428 | 0.212877 | ||||||||
\(709\) | −0.475003 | −0.0178391 | −0.00891956 | − | 0.999960i | \(-0.502839\pi\) | ||||
−0.00891956 | + | 0.999960i | \(0.502839\pi\) | |||||||
\(710\) | 3.00135 | 0.112639 | ||||||||
\(711\) | 15.2607 | 0.572322 | ||||||||
\(712\) | 5.90313 | 0.221229 | ||||||||
\(713\) | 25.3545 | 0.949533 | ||||||||
\(714\) | 5.37190 | 0.201038 | ||||||||
\(715\) | 27.7564 | 1.03803 | ||||||||
\(716\) | −1.61613 | −0.0603977 | ||||||||
\(717\) | 7.02584 | 0.262385 | ||||||||
\(718\) | 25.5705 | 0.954284 | ||||||||
\(719\) | −31.9718 | −1.19235 | −0.596173 | − | 0.802856i | \(-0.703313\pi\) | ||||
−0.596173 | + | 0.802856i | \(0.703313\pi\) | |||||||
\(720\) | −2.45965 | −0.0916657 | ||||||||
\(721\) | −67.2722 | −2.50535 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 3.00462 | 0.111743 | ||||||||
\(724\) | −13.5282 | −0.502770 | ||||||||
\(725\) | 2.53779 | 0.0942510 | ||||||||
\(726\) | −7.35130 | −0.272832 | ||||||||
\(727\) | −32.2269 | −1.19523 | −0.597615 | − | 0.801783i | \(-0.703885\pi\) | ||||
−0.597615 | + | 0.801783i | \(0.703885\pi\) | |||||||
\(728\) | −27.7759 | −1.02944 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.3281 | 0.715365 | ||||||||
\(731\) | 5.97152 | 0.220865 | ||||||||
\(732\) | −13.6683 | −0.505197 | ||||||||
\(733\) | −5.96157 | −0.220196 | −0.110098 | − | 0.993921i | \(-0.535116\pi\) | ||||
−0.110098 | + | 0.993921i | \(0.535116\pi\) | |||||||
\(734\) | 4.42367 | 0.163281 | ||||||||
\(735\) | 37.1537 | 1.37044 | ||||||||
\(736\) | −3.30477 | −0.121815 | ||||||||
\(737\) | −6.18449 | −0.227809 | ||||||||
\(738\) | −6.19475 | −0.228032 | ||||||||
\(739\) | 10.8385 | 0.398701 | 0.199350 | − | 0.979928i | \(-0.436117\pi\) | ||||
0.199350 | + | 0.979928i | \(0.436117\pi\) | |||||||
\(740\) | 11.2083 | 0.412024 | ||||||||
\(741\) | −5.90772 | −0.217026 | ||||||||
\(742\) | −4.70163 | −0.172602 | ||||||||
\(743\) | 7.57622 | 0.277945 | 0.138972 | − | 0.990296i | \(-0.455620\pi\) | ||||
0.138972 | + | 0.990296i | \(0.455620\pi\) | |||||||
\(744\) | 7.67209 | 0.281272 | ||||||||
\(745\) | −51.4720 | −1.88579 | ||||||||
\(746\) | −17.4917 | −0.640416 | ||||||||
\(747\) | −14.6060 | −0.534407 | ||||||||
\(748\) | −2.18248 | −0.0797992 | ||||||||
\(749\) | −8.76271 | −0.320182 | ||||||||
\(750\) | 9.71593 | 0.354776 | ||||||||
\(751\) | −46.7407 | −1.70559 | −0.852795 | − | 0.522245i | \(-0.825095\pi\) | ||||
−0.852795 | + | 0.522245i | \(0.825095\pi\) | |||||||
\(752\) | 5.78403 | 0.210922 | ||||||||
\(753\) | 17.3184 | 0.631116 | ||||||||
\(754\) | 14.2804 | 0.520060 | ||||||||
\(755\) | −42.8306 | −1.55876 | ||||||||
\(756\) | 4.70163 | 0.170997 | ||||||||
\(757\) | 22.7514 | 0.826913 | 0.413457 | − | 0.910524i | \(-0.364321\pi\) | ||||
0.413457 | + | 0.910524i | \(0.364321\pi\) | |||||||
\(758\) | −15.5294 | −0.564052 | ||||||||
\(759\) | −6.31263 | −0.229134 | ||||||||
\(760\) | −2.45965 | −0.0892208 | ||||||||
\(761\) | −24.6727 | −0.894384 | −0.447192 | − | 0.894438i | \(-0.647576\pi\) | ||||
−0.447192 | + | 0.894438i | \(0.647576\pi\) | |||||||
\(762\) | 1.73478 | 0.0628444 | ||||||||
\(763\) | −24.9717 | −0.904035 | ||||||||
\(764\) | −11.2029 | −0.405307 | ||||||||
\(765\) | 2.81030 | 0.101607 | ||||||||
\(766\) | 23.9671 | 0.865967 | ||||||||
\(767\) | 33.4630 | 1.20828 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 15.8286 | 0.570793 | 0.285396 | − | 0.958410i | \(-0.407875\pi\) | ||||
0.285396 | + | 0.958410i | \(0.407875\pi\) | |||||||
\(770\) | −22.0897 | −0.796059 | ||||||||
\(771\) | −9.24806 | −0.333061 | ||||||||
\(772\) | −20.0363 | −0.721121 | ||||||||
\(773\) | 20.6158 | 0.741498 | 0.370749 | − | 0.928733i | \(-0.379101\pi\) | ||||
0.370749 | + | 0.928733i | \(0.379101\pi\) | |||||||
\(774\) | 5.22642 | 0.187860 | ||||||||
\(775\) | 8.05471 | 0.289334 | ||||||||
\(776\) | 0.0999559 | 0.00358821 | ||||||||
\(777\) | −21.4246 | −0.768604 | ||||||||
\(778\) | −30.1549 | −1.08111 | ||||||||
\(779\) | −6.19475 | −0.221950 | ||||||||
\(780\) | −14.5309 | −0.520291 | ||||||||
\(781\) | 2.33084 | 0.0834041 | ||||||||
\(782\) | 3.77591 | 0.135026 | ||||||||
\(783\) | −2.41724 | −0.0863850 | ||||||||
\(784\) | 15.1053 | 0.539475 | ||||||||
\(785\) | 32.6515 | 1.16538 | ||||||||
\(786\) | −13.5180 | −0.482173 | ||||||||
\(787\) | 13.7562 | 0.490355 | 0.245178 | − | 0.969478i | \(-0.421154\pi\) | ||||
0.245178 | + | 0.969478i | \(0.421154\pi\) | |||||||
\(788\) | 21.7120 | 0.773456 | ||||||||
\(789\) | −5.43686 | −0.193557 | ||||||||
\(790\) | 37.5360 | 1.33547 | ||||||||
\(791\) | 0.844922 | 0.0300420 | ||||||||
\(792\) | −1.91016 | −0.0678745 | ||||||||
\(793\) | −80.7488 | −2.86747 | ||||||||
\(794\) | −26.0606 | −0.924857 | ||||||||
\(795\) | −2.45965 | −0.0872347 | ||||||||
\(796\) | 10.6531 | 0.377588 | ||||||||
\(797\) | 7.10558 | 0.251693 | 0.125846 | − | 0.992050i | \(-0.459835\pi\) | ||||
0.125846 | + | 0.992050i | \(0.459835\pi\) | |||||||
\(798\) | 4.70163 | 0.166436 | ||||||||
\(799\) | −6.60862 | −0.233796 | ||||||||
\(800\) | −1.04987 | −0.0371186 | ||||||||
\(801\) | −5.90313 | −0.208577 | ||||||||
\(802\) | −24.5456 | −0.866737 | ||||||||
\(803\) | 15.0102 | 0.529697 | ||||||||
\(804\) | 3.23769 | 0.114184 | ||||||||
\(805\) | 38.2175 | 1.34699 | ||||||||
\(806\) | 45.3246 | 1.59649 | ||||||||
\(807\) | 22.6746 | 0.798184 | ||||||||
\(808\) | 17.7871 | 0.625749 | ||||||||
\(809\) | −16.1001 | −0.566049 | −0.283025 | − | 0.959113i | \(-0.591338\pi\) | ||||
−0.283025 | + | 0.959113i | \(0.591338\pi\) | |||||||
\(810\) | 2.45965 | 0.0864232 | ||||||||
\(811\) | 38.9957 | 1.36932 | 0.684662 | − | 0.728860i | \(-0.259950\pi\) | ||||
0.684662 | + | 0.728860i | \(0.259950\pi\) | |||||||
\(812\) | −11.3649 | −0.398831 | ||||||||
\(813\) | 12.4883 | 0.437983 | ||||||||
\(814\) | 8.70431 | 0.305086 | ||||||||
\(815\) | −25.8691 | −0.906155 | ||||||||
\(816\) | 1.14256 | 0.0399977 | ||||||||
\(817\) | 5.22642 | 0.182849 | ||||||||
\(818\) | 24.8079 | 0.867387 | ||||||||
\(819\) | 27.7759 | 0.970569 | ||||||||
\(820\) | −15.2369 | −0.532096 | ||||||||
\(821\) | 3.24548 | 0.113268 | 0.0566340 | − | 0.998395i | \(-0.481963\pi\) | ||||
0.0566340 | + | 0.998395i | \(0.481963\pi\) | |||||||
\(822\) | 6.46378 | 0.225450 | ||||||||
\(823\) | −29.2411 | −1.01928 | −0.509640 | − | 0.860387i | \(-0.670222\pi\) | ||||
−0.509640 | + | 0.860387i | \(0.670222\pi\) | |||||||
\(824\) | −14.3083 | −0.498452 | ||||||||
\(825\) | −2.00542 | −0.0698198 | ||||||||
\(826\) | −26.6313 | −0.926622 | ||||||||
\(827\) | −47.6510 | −1.65699 | −0.828494 | − | 0.559997i | \(-0.810802\pi\) | ||||
−0.828494 | + | 0.559997i | \(0.810802\pi\) | |||||||
\(828\) | 3.30477 | 0.114849 | ||||||||
\(829\) | 21.6971 | 0.753572 | 0.376786 | − | 0.926300i | \(-0.377029\pi\) | ||||
0.376786 | + | 0.926300i | \(0.377029\pi\) | |||||||
\(830\) | −35.9257 | −1.24700 | ||||||||
\(831\) | −6.80678 | −0.236125 | ||||||||
\(832\) | −5.90772 | −0.204813 | ||||||||
\(833\) | −17.2588 | −0.597980 | ||||||||
\(834\) | 6.32384 | 0.218977 | ||||||||
\(835\) | 2.50565 | 0.0867117 | ||||||||
\(836\) | −1.91016 | −0.0660642 | ||||||||
\(837\) | −7.67209 | −0.265186 | ||||||||
\(838\) | −3.30387 | −0.114130 | ||||||||
\(839\) | −28.8691 | −0.996671 | −0.498335 | − | 0.866984i | \(-0.666055\pi\) | ||||
−0.498335 | + | 0.866984i | \(0.666055\pi\) | |||||||
\(840\) | 11.5643 | 0.399008 | ||||||||
\(841\) | −23.1570 | −0.798516 | ||||||||
\(842\) | 17.0365 | 0.587115 | ||||||||
\(843\) | 22.1604 | 0.763244 | ||||||||
\(844\) | −4.80428 | −0.165370 | ||||||||
\(845\) | −53.8693 | −1.85316 | ||||||||
\(846\) | −5.78403 | −0.198859 | ||||||||
\(847\) | 34.5631 | 1.18760 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 2.66711 | 0.0915351 | ||||||||
\(850\) | 1.19954 | 0.0411440 | ||||||||
\(851\) | −15.0594 | −0.516228 | ||||||||
\(852\) | −1.22023 | −0.0418046 | ||||||||
\(853\) | −47.6587 | −1.63180 | −0.815902 | − | 0.578191i | \(-0.803759\pi\) | ||||
−0.815902 | + | 0.578191i | \(0.803759\pi\) | |||||||
\(854\) | 64.2635 | 2.19905 | ||||||||
\(855\) | 2.45965 | 0.0841182 | ||||||||
\(856\) | −1.86376 | −0.0637020 | ||||||||
\(857\) | 18.8446 | 0.643718 | 0.321859 | − | 0.946788i | \(-0.395692\pi\) | ||||
0.321859 | + | 0.946788i | \(0.395692\pi\) | |||||||
\(858\) | −11.2847 | −0.385253 | ||||||||
\(859\) | −6.79165 | −0.231728 | −0.115864 | − | 0.993265i | \(-0.536964\pi\) | ||||
−0.115864 | + | 0.993265i | \(0.536964\pi\) | |||||||
\(860\) | 12.8552 | 0.438358 | ||||||||
\(861\) | 29.1254 | 0.992590 | ||||||||
\(862\) | −14.8752 | −0.506651 | ||||||||
\(863\) | 36.1406 | 1.23024 | 0.615119 | − | 0.788434i | \(-0.289108\pi\) | ||||
0.615119 | + | 0.788434i | \(0.289108\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 34.1289 | 1.16042 | ||||||||
\(866\) | −9.55069 | −0.324546 | ||||||||
\(867\) | 15.6945 | 0.533015 | ||||||||
\(868\) | −36.0713 | −1.22434 | ||||||||
\(869\) | 29.1504 | 0.988860 | ||||||||
\(870\) | −5.94555 | −0.201573 | ||||||||
\(871\) | 19.1274 | 0.648106 | ||||||||
\(872\) | −5.31128 | −0.179863 | ||||||||
\(873\) | −0.0999559 | −0.00338299 | ||||||||
\(874\) | 3.30477 | 0.111786 | ||||||||
\(875\) | −45.6807 | −1.54429 | ||||||||
\(876\) | −7.85807 | −0.265500 | ||||||||
\(877\) | 33.1313 | 1.11877 | 0.559383 | − | 0.828909i | \(-0.311038\pi\) | ||||
0.559383 | + | 0.828909i | \(0.311038\pi\) | |||||||
\(878\) | 15.0945 | 0.509415 | ||||||||
\(879\) | −13.2532 | −0.447020 | ||||||||
\(880\) | −4.69832 | −0.158380 | ||||||||
\(881\) | −18.6265 | −0.627544 | −0.313772 | − | 0.949498i | \(-0.601593\pi\) | ||||
−0.313772 | + | 0.949498i | \(0.601593\pi\) | |||||||
\(882\) | −15.1053 | −0.508622 | ||||||||
\(883\) | 13.9277 | 0.468703 | 0.234351 | − | 0.972152i | \(-0.424703\pi\) | ||||
0.234351 | + | 0.972152i | \(0.424703\pi\) | |||||||
\(884\) | 6.74995 | 0.227025 | ||||||||
\(885\) | −13.9321 | −0.468324 | ||||||||
\(886\) | −10.8991 | −0.366161 | ||||||||
\(887\) | −57.8038 | −1.94086 | −0.970430 | − | 0.241382i | \(-0.922399\pi\) | ||||
−0.970430 | + | 0.241382i | \(0.922399\pi\) | |||||||
\(888\) | −4.55685 | −0.152918 | ||||||||
\(889\) | −8.15628 | −0.273553 | ||||||||
\(890\) | −14.5196 | −0.486699 | ||||||||
\(891\) | 1.91016 | 0.0639927 | ||||||||
\(892\) | 10.6493 | 0.356564 | ||||||||
\(893\) | −5.78403 | −0.193555 | ||||||||
\(894\) | 20.9266 | 0.699889 | ||||||||
\(895\) | 3.97512 | 0.132873 | ||||||||
\(896\) | 4.70163 | 0.157070 | ||||||||
\(897\) | 19.5237 | 0.651876 | ||||||||
\(898\) | −13.4361 | −0.448367 | ||||||||
\(899\) | 18.5453 | 0.618519 | ||||||||
\(900\) | 1.04987 | 0.0349957 | ||||||||
\(901\) | 1.14256 | 0.0380643 | ||||||||
\(902\) | −11.8329 | −0.393994 | ||||||||
\(903\) | −24.5727 | −0.817728 | ||||||||
\(904\) | 0.179709 | 0.00597702 | ||||||||
\(905\) | 33.2745 | 1.10608 | ||||||||
\(906\) | 17.4133 | 0.578518 | ||||||||
\(907\) | −11.4415 | −0.379908 | −0.189954 | − | 0.981793i | \(-0.560834\pi\) | ||||
−0.189954 | + | 0.981793i | \(0.560834\pi\) | |||||||
\(908\) | 6.99635 | 0.232182 | ||||||||
\(909\) | −17.7871 | −0.589961 | ||||||||
\(910\) | 68.3190 | 2.26475 | ||||||||
\(911\) | 10.1995 | 0.337925 | 0.168962 | − | 0.985623i | \(-0.445958\pi\) | ||||
0.168962 | + | 0.985623i | \(0.445958\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −27.8998 | −0.923350 | ||||||||
\(914\) | −10.4744 | −0.346463 | ||||||||
\(915\) | 33.6193 | 1.11142 | ||||||||
\(916\) | −14.2907 | −0.472177 | ||||||||
\(917\) | 63.5568 | 2.09883 | ||||||||
\(918\) | −1.14256 | −0.0377102 | ||||||||
\(919\) | −47.6073 | −1.57042 | −0.785210 | − | 0.619229i | \(-0.787445\pi\) | ||||
−0.785210 | + | 0.619229i | \(0.787445\pi\) | |||||||
\(920\) | 8.12857 | 0.267991 | ||||||||
\(921\) | 3.64574 | 0.120131 | ||||||||
\(922\) | 11.0887 | 0.365187 | ||||||||
\(923\) | −7.20881 | −0.237281 | ||||||||
\(924\) | 8.98085 | 0.295448 | ||||||||
\(925\) | −4.78411 | −0.157301 | ||||||||
\(926\) | −0.621532 | −0.0204248 | ||||||||
\(927\) | 14.3083 | 0.469945 | ||||||||
\(928\) | −2.41724 | −0.0793496 | ||||||||
\(929\) | 8.12727 | 0.266647 | 0.133324 | − | 0.991073i | \(-0.457435\pi\) | ||||
0.133324 | + | 0.991073i | \(0.457435\pi\) | |||||||
\(930\) | −18.8706 | −0.618793 | ||||||||
\(931\) | −15.1053 | −0.495056 | ||||||||
\(932\) | −0.544364 | −0.0178312 | ||||||||
\(933\) | 31.7037 | 1.03793 | ||||||||
\(934\) | 30.9060 | 1.01128 | ||||||||
\(935\) | 5.36812 | 0.175556 | ||||||||
\(936\) | 5.90772 | 0.193100 | ||||||||
\(937\) | 21.3791 | 0.698426 | 0.349213 | − | 0.937043i | \(-0.386449\pi\) | ||||
0.349213 | + | 0.937043i | \(0.386449\pi\) | |||||||
\(938\) | −15.2224 | −0.497029 | ||||||||
\(939\) | −22.2063 | −0.724676 | ||||||||
\(940\) | −14.2267 | −0.464023 | ||||||||
\(941\) | −39.8229 | −1.29819 | −0.649094 | − | 0.760708i | \(-0.724852\pi\) | ||||
−0.649094 | + | 0.760708i | \(0.724852\pi\) | |||||||
\(942\) | −13.2749 | −0.432518 | ||||||||
\(943\) | 20.4722 | 0.666667 | ||||||||
\(944\) | −5.66428 | −0.184357 | ||||||||
\(945\) | −11.5643 | −0.376188 | ||||||||
\(946\) | 9.98330 | 0.324585 | ||||||||
\(947\) | 4.11934 | 0.133860 | 0.0669302 | − | 0.997758i | \(-0.478680\pi\) | ||||
0.0669302 | + | 0.997758i | \(0.478680\pi\) | |||||||
\(948\) | −15.2607 | −0.495646 | ||||||||
\(949\) | −46.4233 | −1.50697 | ||||||||
\(950\) | 1.04987 | 0.0340623 | ||||||||
\(951\) | −28.9210 | −0.937829 | ||||||||
\(952\) | −5.37190 | −0.174104 | ||||||||
\(953\) | 1.91115 | 0.0619081 | 0.0309541 | − | 0.999521i | \(-0.490145\pi\) | ||||
0.0309541 | + | 0.999521i | \(0.490145\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | 27.5552 | 0.891665 | ||||||||
\(956\) | −7.02584 | −0.227232 | ||||||||
\(957\) | −4.61730 | −0.149256 | ||||||||
\(958\) | −23.7155 | −0.766214 | ||||||||
\(959\) | −30.3903 | −0.981354 | ||||||||
\(960\) | 2.45965 | 0.0793848 | ||||||||
\(961\) | 27.8610 | 0.898741 | ||||||||
\(962\) | −26.9206 | −0.867956 | ||||||||
\(963\) | 1.86376 | 0.0600588 | ||||||||
\(964\) | −3.00462 | −0.0967723 | ||||||||
\(965\) | 49.2822 | 1.58645 | ||||||||
\(966\) | −15.5378 | −0.499920 | ||||||||
\(967\) | −22.9112 | −0.736775 | −0.368387 | − | 0.929672i | \(-0.620090\pi\) | ||||
−0.368387 | + | 0.929672i | \(0.620090\pi\) | |||||||
\(968\) | 7.35130 | 0.236280 | ||||||||
\(969\) | −1.14256 | −0.0367044 | ||||||||
\(970\) | −0.245856 | −0.00789397 | ||||||||
\(971\) | 27.9653 | 0.897448 | 0.448724 | − | 0.893670i | \(-0.351879\pi\) | ||||
0.448724 | + | 0.893670i | \(0.351879\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −29.7323 | −0.953175 | ||||||||
\(974\) | 9.42158 | 0.301887 | ||||||||
\(975\) | 6.20235 | 0.198634 | ||||||||
\(976\) | 13.6683 | 0.437513 | ||||||||
\(977\) | −36.4664 | −1.16666 | −0.583331 | − | 0.812234i | \(-0.698251\pi\) | ||||
−0.583331 | + | 0.812234i | \(0.698251\pi\) | |||||||
\(978\) | 10.5174 | 0.336309 | ||||||||
\(979\) | −11.2759 | −0.360380 | ||||||||
\(980\) | −37.1537 | −1.18683 | ||||||||
\(981\) | 5.31128 | 0.169576 | ||||||||
\(982\) | 13.0936 | 0.417834 | ||||||||
\(983\) | 43.7564 | 1.39561 | 0.697806 | − | 0.716287i | \(-0.254160\pi\) | ||||
0.697806 | + | 0.716287i | \(0.254160\pi\) | |||||||
\(984\) | 6.19475 | 0.197481 | ||||||||
\(985\) | −53.4038 | −1.70159 | ||||||||
\(986\) | 2.76184 | 0.0879550 | ||||||||
\(987\) | 27.1943 | 0.865605 | ||||||||
\(988\) | 5.90772 | 0.187950 | ||||||||
\(989\) | −17.2721 | −0.549222 | ||||||||
\(990\) | 4.69832 | 0.149322 | ||||||||
\(991\) | 45.8946 | 1.45789 | 0.728945 | − | 0.684573i | \(-0.240011\pi\) | ||||
0.728945 | + | 0.684573i | \(0.240011\pi\) | |||||||
\(992\) | −7.67209 | −0.243589 | ||||||||
\(993\) | 18.6818 | 0.592849 | ||||||||
\(994\) | 5.73709 | 0.181969 | ||||||||
\(995\) | −26.2028 | −0.830685 | ||||||||
\(996\) | 14.6060 | 0.462810 | ||||||||
\(997\) | 5.88414 | 0.186353 | 0.0931764 | − | 0.995650i | \(-0.470298\pi\) | ||||
0.0931764 | + | 0.995650i | \(0.470298\pi\) | |||||||
\(998\) | 9.16202 | 0.290019 | ||||||||
\(999\) | 4.55685 | 0.144172 |
(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 | 6042.2.a.be.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.be.1.5 | ✓ | 12 | 1.1 | even | 1 | trivial |