Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39631 | −1.69445 | −0.847224 | − | 0.531236i | \(-0.821728\pi\) | ||||
−0.847224 | + | 0.531236i | \(0.821728\pi\) | |||||||
\(3\) | −0.467815 | −0.270093 | −0.135046 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135046 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(4\) | 3.74231 | 1.87115 | ||||||||
\(5\) | 2.01057 | 0.899153 | 0.449577 | − | 0.893242i | \(-0.351575\pi\) | ||||
0.449577 | + | 0.893242i | \(0.351575\pi\) | |||||||
\(6\) | 1.12103 | 0.457658 | ||||||||
\(7\) | −2.84779 | −1.07636 | −0.538182 | − | 0.842829i | \(-0.680889\pi\) | ||||
−0.538182 | + | 0.842829i | \(0.680889\pi\) | |||||||
\(8\) | −4.17511 | −1.47612 | ||||||||
\(9\) | −2.78115 | −0.927050 | ||||||||
\(10\) | −4.81795 | −1.52357 | ||||||||
\(11\) | 3.93458 | 1.18632 | 0.593160 | − | 0.805085i | \(-0.297880\pi\) | ||||
0.593160 | + | 0.805085i | \(0.297880\pi\) | |||||||
\(12\) | −1.75071 | −0.505385 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 6.82420 | 1.82384 | ||||||||
\(15\) | −0.940573 | −0.242855 | ||||||||
\(16\) | 2.52025 | 0.630062 | ||||||||
\(17\) | 6.24553 | 1.51476 | 0.757381 | − | 0.652973i | \(-0.226478\pi\) | ||||
0.757381 | + | 0.652973i | \(0.226478\pi\) | |||||||
\(18\) | 6.66450 | 1.57084 | ||||||||
\(19\) | 4.17763 | 0.958415 | 0.479208 | − | 0.877702i | \(-0.340924\pi\) | ||||
0.479208 | + | 0.877702i | \(0.340924\pi\) | |||||||
\(20\) | 7.52416 | 1.68245 | ||||||||
\(21\) | 1.33224 | 0.290718 | ||||||||
\(22\) | −9.42848 | −2.01016 | ||||||||
\(23\) | 2.17631 | 0.453793 | 0.226896 | − | 0.973919i | \(-0.427142\pi\) | ||||
0.226896 | + | 0.973919i | \(0.427142\pi\) | |||||||
\(24\) | 1.95318 | 0.398691 | ||||||||
\(25\) | −0.957616 | −0.191523 | ||||||||
\(26\) | 2.39631 | 0.469955 | ||||||||
\(27\) | 2.70451 | 0.520483 | ||||||||
\(28\) | −10.6573 | −2.01404 | ||||||||
\(29\) | −10.0386 | −1.86411 | −0.932057 | − | 0.362312i | \(-0.881987\pi\) | ||||
−0.932057 | + | 0.362312i | \(0.881987\pi\) | |||||||
\(30\) | 2.25391 | 0.411505 | ||||||||
\(31\) | −5.13693 | −0.922620 | −0.461310 | − | 0.887239i | \(-0.652620\pi\) | ||||
−0.461310 | + | 0.887239i | \(0.652620\pi\) | |||||||
\(32\) | 2.31092 | 0.408517 | ||||||||
\(33\) | −1.84065 | −0.320417 | ||||||||
\(34\) | −14.9662 | −2.56669 | ||||||||
\(35\) | −5.72568 | −0.967816 | ||||||||
\(36\) | −10.4079 | −1.73465 | ||||||||
\(37\) | −5.97286 | −0.981932 | −0.490966 | − | 0.871179i | \(-0.663356\pi\) | ||||
−0.490966 | + | 0.871179i | \(0.663356\pi\) | |||||||
\(38\) | −10.0109 | −1.62398 | ||||||||
\(39\) | 0.467815 | 0.0749103 | ||||||||
\(40\) | −8.39434 | −1.32726 | ||||||||
\(41\) | 9.83118 | 1.53537 | 0.767686 | − | 0.640826i | \(-0.221408\pi\) | ||||
0.767686 | + | 0.640826i | \(0.221408\pi\) | |||||||
\(42\) | −3.19246 | −0.492607 | ||||||||
\(43\) | −9.39726 | −1.43307 | −0.716535 | − | 0.697552i | \(-0.754273\pi\) | ||||
−0.716535 | + | 0.697552i | \(0.754273\pi\) | |||||||
\(44\) | 14.7244 | 2.21979 | ||||||||
\(45\) | −5.59169 | −0.833560 | ||||||||
\(46\) | −5.21512 | −0.768928 | ||||||||
\(47\) | 4.75131 | 0.693049 | 0.346525 | − | 0.938041i | \(-0.387362\pi\) | ||||
0.346525 | + | 0.938041i | \(0.387362\pi\) | |||||||
\(48\) | −1.17901 | −0.170175 | ||||||||
\(49\) | 1.10992 | 0.158560 | ||||||||
\(50\) | 2.29475 | 0.324526 | ||||||||
\(51\) | −2.92175 | −0.409127 | ||||||||
\(52\) | −3.74231 | −0.518965 | ||||||||
\(53\) | 4.79505 | 0.658651 | 0.329325 | − | 0.944217i | \(-0.393179\pi\) | ||||
0.329325 | + | 0.944217i | \(0.393179\pi\) | |||||||
\(54\) | −6.48084 | −0.881930 | ||||||||
\(55\) | 7.91074 | 1.06668 | ||||||||
\(56\) | 11.8898 | 1.58885 | ||||||||
\(57\) | −1.95436 | −0.258861 | ||||||||
\(58\) | 24.0555 | 3.15864 | ||||||||
\(59\) | −10.1207 | −1.31761 | −0.658804 | − | 0.752315i | \(-0.728937\pi\) | ||||
−0.658804 | + | 0.752315i | \(0.728937\pi\) | |||||||
\(60\) | −3.51991 | −0.454419 | ||||||||
\(61\) | −2.61639 | −0.334994 | −0.167497 | − | 0.985873i | \(-0.553569\pi\) | ||||
−0.167497 | + | 0.985873i | \(0.553569\pi\) | |||||||
\(62\) | 12.3097 | 1.56333 | ||||||||
\(63\) | 7.92014 | 0.997843 | ||||||||
\(64\) | −10.5782 | −1.32227 | ||||||||
\(65\) | −2.01057 | −0.249380 | ||||||||
\(66\) | 4.41078 | 0.542929 | ||||||||
\(67\) | 7.15184 | 0.873736 | 0.436868 | − | 0.899526i | \(-0.356088\pi\) | ||||
0.436868 | + | 0.899526i | \(0.356088\pi\) | |||||||
\(68\) | 23.3727 | 2.83435 | ||||||||
\(69\) | −1.01811 | −0.122566 | ||||||||
\(70\) | 13.7205 | 1.63991 | ||||||||
\(71\) | −11.5021 | −1.36504 | −0.682522 | − | 0.730865i | \(-0.739117\pi\) | ||||
−0.682522 | + | 0.730865i | \(0.739117\pi\) | |||||||
\(72\) | 11.6116 | 1.36844 | ||||||||
\(73\) | −13.4207 | −1.57078 | −0.785389 | − | 0.619002i | \(-0.787537\pi\) | ||||
−0.785389 | + | 0.619002i | \(0.787537\pi\) | |||||||
\(74\) | 14.3128 | 1.66383 | ||||||||
\(75\) | 0.447987 | 0.0517291 | ||||||||
\(76\) | 15.6340 | 1.79334 | ||||||||
\(77\) | −11.2049 | −1.27691 | ||||||||
\(78\) | −1.12103 | −0.126932 | ||||||||
\(79\) | 2.13610 | 0.240329 | 0.120165 | − | 0.992754i | \(-0.461658\pi\) | ||||
0.120165 | + | 0.992754i | \(0.461658\pi\) | |||||||
\(80\) | 5.06713 | 0.566522 | ||||||||
\(81\) | 7.07824 | 0.786471 | ||||||||
\(82\) | −23.5586 | −2.60161 | ||||||||
\(83\) | 4.34501 | 0.476927 | 0.238463 | − | 0.971152i | \(-0.423356\pi\) | ||||
0.238463 | + | 0.971152i | \(0.423356\pi\) | |||||||
\(84\) | 4.98565 | 0.543979 | ||||||||
\(85\) | 12.5571 | 1.36200 | ||||||||
\(86\) | 22.5188 | 2.42826 | ||||||||
\(87\) | 4.69619 | 0.503484 | ||||||||
\(88\) | −16.4273 | −1.75116 | ||||||||
\(89\) | 16.8366 | 1.78468 | 0.892340 | − | 0.451364i | \(-0.149062\pi\) | ||||
0.892340 | + | 0.451364i | \(0.149062\pi\) | |||||||
\(90\) | 13.3994 | 1.41242 | ||||||||
\(91\) | 2.84779 | 0.298530 | ||||||||
\(92\) | 8.14443 | 0.849116 | ||||||||
\(93\) | 2.40313 | 0.249193 | ||||||||
\(94\) | −11.3856 | −1.17434 | ||||||||
\(95\) | 8.39942 | 0.861762 | ||||||||
\(96\) | −1.08108 | −0.110338 | ||||||||
\(97\) | −0.381896 | −0.0387756 | −0.0193878 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193878 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(98\) | −2.65971 | −0.268671 | ||||||||
\(99\) | −10.9427 | −1.09978 | ||||||||
\(100\) | −3.58369 | −0.358369 | ||||||||
\(101\) | 6.25916 | 0.622809 | 0.311405 | − | 0.950277i | \(-0.399201\pi\) | ||||
0.311405 | + | 0.950277i | \(0.399201\pi\) | |||||||
\(102\) | 7.00142 | 0.693244 | ||||||||
\(103\) | 5.22663 | 0.514996 | 0.257498 | − | 0.966279i | \(-0.417102\pi\) | ||||
0.257498 | + | 0.966279i | \(0.417102\pi\) | |||||||
\(104\) | 4.17511 | 0.409403 | ||||||||
\(105\) | 2.67856 | 0.261400 | ||||||||
\(106\) | −11.4904 | −1.11605 | ||||||||
\(107\) | −6.75189 | −0.652730 | −0.326365 | − | 0.945244i | \(-0.605824\pi\) | ||||
−0.326365 | + | 0.945244i | \(0.605824\pi\) | |||||||
\(108\) | 10.1211 | 0.973903 | ||||||||
\(109\) | −1.76444 | −0.169002 | −0.0845012 | − | 0.996423i | \(-0.526930\pi\) | ||||
−0.0845012 | + | 0.996423i | \(0.526930\pi\) | |||||||
\(110\) | −18.9566 | −1.80744 | ||||||||
\(111\) | 2.79419 | 0.265213 | ||||||||
\(112\) | −7.17714 | −0.678176 | ||||||||
\(113\) | 15.1277 | 1.42309 | 0.711545 | − | 0.702640i | \(-0.247996\pi\) | ||||
0.711545 | + | 0.702640i | \(0.247996\pi\) | |||||||
\(114\) | 4.68325 | 0.438627 | ||||||||
\(115\) | 4.37563 | 0.408029 | ||||||||
\(116\) | −37.5674 | −3.48804 | ||||||||
\(117\) | 2.78115 | 0.257117 | ||||||||
\(118\) | 24.2524 | 2.23262 | ||||||||
\(119\) | −17.7860 | −1.63044 | ||||||||
\(120\) | 3.92700 | 0.358484 | ||||||||
\(121\) | 4.48091 | 0.407356 | ||||||||
\(122\) | 6.26969 | 0.567631 | ||||||||
\(123\) | −4.59917 | −0.414693 | ||||||||
\(124\) | −19.2240 | −1.72636 | ||||||||
\(125\) | −11.9782 | −1.07136 | ||||||||
\(126\) | −18.9791 | −1.69079 | ||||||||
\(127\) | −6.17853 | −0.548256 | −0.274128 | − | 0.961693i | \(-0.588389\pi\) | ||||
−0.274128 | + | 0.961693i | \(0.588389\pi\) | |||||||
\(128\) | 20.7268 | 1.83201 | ||||||||
\(129\) | 4.39618 | 0.387062 | ||||||||
\(130\) | 4.81795 | 0.422562 | ||||||||
\(131\) | −17.3072 | −1.51214 | −0.756070 | − | 0.654491i | \(-0.772883\pi\) | ||||
−0.756070 | + | 0.654491i | \(0.772883\pi\) | |||||||
\(132\) | −6.88829 | −0.599549 | ||||||||
\(133\) | −11.8970 | −1.03160 | ||||||||
\(134\) | −17.1380 | −1.48050 | ||||||||
\(135\) | 5.43759 | 0.467994 | ||||||||
\(136\) | −26.0758 | −2.23598 | ||||||||
\(137\) | −14.0679 | −1.20190 | −0.600950 | − | 0.799287i | \(-0.705211\pi\) | ||||
−0.600950 | + | 0.799287i | \(0.705211\pi\) | |||||||
\(138\) | 2.43971 | 0.207682 | ||||||||
\(139\) | −5.44710 | −0.462017 | −0.231009 | − | 0.972952i | \(-0.574203\pi\) | ||||
−0.231009 | + | 0.972952i | \(0.574203\pi\) | |||||||
\(140\) | −21.4272 | −1.81093 | ||||||||
\(141\) | −2.22273 | −0.187188 | ||||||||
\(142\) | 27.5625 | 2.31300 | ||||||||
\(143\) | −3.93458 | −0.329026 | ||||||||
\(144\) | −7.00918 | −0.584099 | ||||||||
\(145\) | −20.1832 | −1.67612 | ||||||||
\(146\) | 32.1603 | 2.66160 | ||||||||
\(147\) | −0.519236 | −0.0428259 | ||||||||
\(148\) | −22.3523 | −1.83735 | ||||||||
\(149\) | −0.757208 | −0.0620329 | −0.0310165 | − | 0.999519i | \(-0.509874\pi\) | ||||
−0.0310165 | + | 0.999519i | \(0.509874\pi\) | |||||||
\(150\) | −1.07352 | −0.0876522 | ||||||||
\(151\) | 12.1697 | 0.990355 | 0.495177 | − | 0.868792i | \(-0.335103\pi\) | ||||
0.495177 | + | 0.868792i | \(0.335103\pi\) | |||||||
\(152\) | −17.4421 | −1.41474 | ||||||||
\(153\) | −17.3697 | −1.40426 | ||||||||
\(154\) | 26.8503 | 2.16366 | ||||||||
\(155\) | −10.3281 | −0.829577 | ||||||||
\(156\) | 1.75071 | 0.140169 | ||||||||
\(157\) | 21.0201 | 1.67759 | 0.838794 | − | 0.544449i | \(-0.183261\pi\) | ||||
0.838794 | + | 0.544449i | \(0.183261\pi\) | |||||||
\(158\) | −5.11875 | −0.407226 | ||||||||
\(159\) | −2.24319 | −0.177897 | ||||||||
\(160\) | 4.64627 | 0.367320 | ||||||||
\(161\) | −6.19769 | −0.488446 | ||||||||
\(162\) | −16.9617 | −1.33263 | ||||||||
\(163\) | −8.82872 | −0.691518 | −0.345759 | − | 0.938323i | \(-0.612379\pi\) | ||||
−0.345759 | + | 0.938323i | \(0.612379\pi\) | |||||||
\(164\) | 36.7913 | 2.87292 | ||||||||
\(165\) | −3.70076 | −0.288104 | ||||||||
\(166\) | −10.4120 | −0.808127 | ||||||||
\(167\) | 12.5955 | 0.974667 | 0.487333 | − | 0.873216i | \(-0.337970\pi\) | ||||
0.487333 | + | 0.873216i | \(0.337970\pi\) | |||||||
\(168\) | −5.56224 | −0.429136 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −30.0906 | −2.30784 | ||||||||
\(171\) | −11.6186 | −0.888499 | ||||||||
\(172\) | −35.1674 | −2.68149 | ||||||||
\(173\) | −1.84505 | −0.140276 | −0.0701382 | − | 0.997537i | \(-0.522344\pi\) | ||||
−0.0701382 | + | 0.997537i | \(0.522344\pi\) | |||||||
\(174\) | −11.2535 | −0.853127 | ||||||||
\(175\) | 2.72709 | 0.206149 | ||||||||
\(176\) | 9.91611 | 0.747455 | ||||||||
\(177\) | 4.73463 | 0.355877 | ||||||||
\(178\) | −40.3458 | −3.02405 | ||||||||
\(179\) | −18.2217 | −1.36195 | −0.680976 | − | 0.732305i | \(-0.738444\pi\) | ||||
−0.680976 | + | 0.732305i | \(0.738444\pi\) | |||||||
\(180\) | −20.9258 | −1.55972 | ||||||||
\(181\) | −26.3820 | −1.96096 | −0.980479 | − | 0.196625i | \(-0.937002\pi\) | ||||
−0.980479 | + | 0.196625i | \(0.937002\pi\) | |||||||
\(182\) | −6.82420 | −0.505843 | ||||||||
\(183\) | 1.22399 | 0.0904796 | ||||||||
\(184\) | −9.08635 | −0.669854 | ||||||||
\(185\) | −12.0088 | −0.882908 | ||||||||
\(186\) | −5.75865 | −0.422245 | ||||||||
\(187\) | 24.5735 | 1.79699 | ||||||||
\(188\) | 17.7808 | 1.29680 | ||||||||
\(189\) | −7.70187 | −0.560229 | ||||||||
\(190\) | −20.1276 | −1.46021 | ||||||||
\(191\) | 4.49622 | 0.325335 | 0.162668 | − | 0.986681i | \(-0.447990\pi\) | ||||
0.162668 | + | 0.986681i | \(0.447990\pi\) | |||||||
\(192\) | 4.94863 | 0.357137 | ||||||||
\(193\) | −2.19085 | −0.157701 | −0.0788505 | − | 0.996886i | \(-0.525125\pi\) | ||||
−0.0788505 | + | 0.996886i | \(0.525125\pi\) | |||||||
\(194\) | 0.915140 | 0.0657033 | ||||||||
\(195\) | 0.940573 | 0.0673558 | ||||||||
\(196\) | 4.15366 | 0.296690 | ||||||||
\(197\) | −18.2275 | −1.29865 | −0.649327 | − | 0.760510i | \(-0.724949\pi\) | ||||
−0.649327 | + | 0.760510i | \(0.724949\pi\) | |||||||
\(198\) | 26.2220 | 1.86352 | ||||||||
\(199\) | 12.3473 | 0.875278 | 0.437639 | − | 0.899151i | \(-0.355815\pi\) | ||||
0.437639 | + | 0.899151i | \(0.355815\pi\) | |||||||
\(200\) | 3.99815 | 0.282712 | ||||||||
\(201\) | −3.34574 | −0.235990 | ||||||||
\(202\) | −14.9989 | −1.05532 | ||||||||
\(203\) | 28.5877 | 2.00647 | ||||||||
\(204\) | −10.9341 | −0.765539 | ||||||||
\(205\) | 19.7663 | 1.38053 | ||||||||
\(206\) | −12.5246 | −0.872633 | ||||||||
\(207\) | −6.05265 | −0.420688 | ||||||||
\(208\) | −2.52025 | −0.174748 | ||||||||
\(209\) | 16.4372 | 1.13699 | ||||||||
\(210\) | −6.41866 | −0.442929 | ||||||||
\(211\) | 2.01021 | 0.138389 | 0.0691943 | − | 0.997603i | \(-0.477957\pi\) | ||||
0.0691943 | + | 0.997603i | \(0.477957\pi\) | |||||||
\(212\) | 17.9445 | 1.23244 | ||||||||
\(213\) | 5.38083 | 0.368689 | ||||||||
\(214\) | 16.1796 | 1.10602 | ||||||||
\(215\) | −18.8938 | −1.28855 | ||||||||
\(216\) | −11.2916 | −0.768297 | ||||||||
\(217\) | 14.6289 | 0.993075 | ||||||||
\(218\) | 4.22814 | 0.286366 | ||||||||
\(219\) | 6.27842 | 0.424256 | ||||||||
\(220\) | 29.6044 | 1.99593 | ||||||||
\(221\) | −6.24553 | −0.420120 | ||||||||
\(222\) | −6.69575 | −0.449389 | ||||||||
\(223\) | 19.9498 | 1.33593 | 0.667967 | − | 0.744191i | \(-0.267165\pi\) | ||||
0.667967 | + | 0.744191i | \(0.267165\pi\) | |||||||
\(224\) | −6.58103 | −0.439713 | ||||||||
\(225\) | 2.66327 | 0.177552 | ||||||||
\(226\) | −36.2506 | −2.41135 | ||||||||
\(227\) | −25.1071 | −1.66641 | −0.833207 | − | 0.552961i | \(-0.813498\pi\) | ||||
−0.833207 | + | 0.552961i | \(0.813498\pi\) | |||||||
\(228\) | −7.31381 | −0.484369 | ||||||||
\(229\) | −11.8858 | −0.785434 | −0.392717 | − | 0.919659i | \(-0.628465\pi\) | ||||
−0.392717 | + | 0.919659i | \(0.628465\pi\) | |||||||
\(230\) | −10.4854 | −0.691384 | ||||||||
\(231\) | 5.24180 | 0.344885 | ||||||||
\(232\) | 41.9121 | 2.75166 | ||||||||
\(233\) | 27.7935 | 1.82081 | 0.910407 | − | 0.413713i | \(-0.135768\pi\) | ||||
0.910407 | + | 0.413713i | \(0.135768\pi\) | |||||||
\(234\) | −6.66450 | −0.435672 | ||||||||
\(235\) | 9.55282 | 0.623157 | ||||||||
\(236\) | −37.8749 | −2.46545 | ||||||||
\(237\) | −0.999297 | −0.0649113 | ||||||||
\(238\) | 42.6207 | 2.76269 | ||||||||
\(239\) | 15.6532 | 1.01252 | 0.506260 | − | 0.862381i | \(-0.331028\pi\) | ||||
0.506260 | + | 0.862381i | \(0.331028\pi\) | |||||||
\(240\) | −2.37048 | −0.153014 | ||||||||
\(241\) | −12.6601 | −0.815509 | −0.407754 | − | 0.913092i | \(-0.633688\pi\) | ||||
−0.407754 | + | 0.913092i | \(0.633688\pi\) | |||||||
\(242\) | −10.7377 | −0.690243 | ||||||||
\(243\) | −11.4248 | −0.732903 | ||||||||
\(244\) | −9.79134 | −0.626826 | ||||||||
\(245\) | 2.23157 | 0.142570 | ||||||||
\(246\) | 11.0210 | 0.702676 | ||||||||
\(247\) | −4.17763 | −0.265817 | ||||||||
\(248\) | 21.4472 | 1.36190 | ||||||||
\(249\) | −2.03266 | −0.128814 | ||||||||
\(250\) | 28.7035 | 1.81537 | ||||||||
\(251\) | −9.54280 | −0.602336 | −0.301168 | − | 0.953571i | \(-0.597377\pi\) | ||||
−0.301168 | + | 0.953571i | \(0.597377\pi\) | |||||||
\(252\) | 29.6396 | 1.86712 | ||||||||
\(253\) | 8.56288 | 0.538343 | ||||||||
\(254\) | 14.8057 | 0.928991 | ||||||||
\(255\) | −5.87437 | −0.367868 | ||||||||
\(256\) | −28.5114 | −1.78196 | ||||||||
\(257\) | 18.9925 | 1.18472 | 0.592361 | − | 0.805673i | \(-0.298196\pi\) | ||||
0.592361 | + | 0.805673i | \(0.298196\pi\) | |||||||
\(258\) | −10.5346 | −0.655856 | ||||||||
\(259\) | 17.0095 | 1.05692 | ||||||||
\(260\) | −7.52416 | −0.466629 | ||||||||
\(261\) | 27.9187 | 1.72813 | ||||||||
\(262\) | 41.4735 | 2.56224 | ||||||||
\(263\) | 23.2697 | 1.43487 | 0.717436 | − | 0.696624i | \(-0.245315\pi\) | ||||
0.717436 | + | 0.696624i | \(0.245315\pi\) | |||||||
\(264\) | 7.68493 | 0.472975 | ||||||||
\(265\) | 9.64077 | 0.592228 | ||||||||
\(266\) | 28.5090 | 1.74800 | ||||||||
\(267\) | −7.87643 | −0.482029 | ||||||||
\(268\) | 26.7644 | 1.63489 | ||||||||
\(269\) | 22.7962 | 1.38991 | 0.694954 | − | 0.719054i | \(-0.255425\pi\) | ||||
0.694954 | + | 0.719054i | \(0.255425\pi\) | |||||||
\(270\) | −13.0302 | −0.792991 | ||||||||
\(271\) | 11.7381 | 0.713042 | 0.356521 | − | 0.934287i | \(-0.383963\pi\) | ||||
0.356521 | + | 0.934287i | \(0.383963\pi\) | |||||||
\(272\) | 15.7403 | 0.954394 | ||||||||
\(273\) | −1.33224 | −0.0806308 | ||||||||
\(274\) | 33.7110 | 2.03656 | ||||||||
\(275\) | −3.76782 | −0.227208 | ||||||||
\(276\) | −3.81008 | −0.229340 | ||||||||
\(277\) | −19.2798 | −1.15841 | −0.579206 | − | 0.815181i | \(-0.696637\pi\) | ||||
−0.579206 | + | 0.815181i | \(0.696637\pi\) | |||||||
\(278\) | 13.0529 | 0.782864 | ||||||||
\(279\) | 14.2866 | 0.855314 | ||||||||
\(280\) | 23.9053 | 1.42862 | ||||||||
\(281\) | −12.3166 | −0.734746 | −0.367373 | − | 0.930074i | \(-0.619743\pi\) | ||||
−0.367373 | + | 0.930074i | \(0.619743\pi\) | |||||||
\(282\) | 5.32635 | 0.317180 | ||||||||
\(283\) | −32.0267 | −1.90379 | −0.951896 | − | 0.306422i | \(-0.900868\pi\) | ||||
−0.951896 | + | 0.306422i | \(0.900868\pi\) | |||||||
\(284\) | −43.0442 | −2.55421 | ||||||||
\(285\) | −3.92937 | −0.232756 | ||||||||
\(286\) | 9.42848 | 0.557517 | ||||||||
\(287\) | −27.9971 | −1.65262 | ||||||||
\(288\) | −6.42702 | −0.378716 | ||||||||
\(289\) | 22.0066 | 1.29451 | ||||||||
\(290\) | 48.3652 | 2.84010 | ||||||||
\(291\) | 0.178656 | 0.0104730 | ||||||||
\(292\) | −50.2245 | −2.93917 | ||||||||
\(293\) | −5.26310 | −0.307474 | −0.153737 | − | 0.988112i | \(-0.549131\pi\) | ||||
−0.153737 | + | 0.988112i | \(0.549131\pi\) | |||||||
\(294\) | 1.24425 | 0.0725662 | ||||||||
\(295\) | −20.3484 | −1.18473 | ||||||||
\(296\) | 24.9373 | 1.44945 | ||||||||
\(297\) | 10.6411 | 0.617459 | ||||||||
\(298\) | 1.81451 | 0.105112 | ||||||||
\(299\) | −2.17631 | −0.125859 | ||||||||
\(300\) | 1.67650 | 0.0967930 | ||||||||
\(301\) | 26.7615 | 1.54250 | ||||||||
\(302\) | −29.1623 | −1.67810 | ||||||||
\(303\) | −2.92812 | −0.168216 | ||||||||
\(304\) | 10.5287 | 0.603861 | ||||||||
\(305\) | −5.26043 | −0.301211 | ||||||||
\(306\) | 41.6233 | 2.37945 | ||||||||
\(307\) | 3.53681 | 0.201856 | 0.100928 | − | 0.994894i | \(-0.467819\pi\) | ||||
0.100928 | + | 0.994894i | \(0.467819\pi\) | |||||||
\(308\) | −41.9320 | −2.38930 | ||||||||
\(309\) | −2.44510 | −0.139097 | ||||||||
\(310\) | 24.7494 | 1.40567 | ||||||||
\(311\) | −4.37339 | −0.247992 | −0.123996 | − | 0.992283i | \(-0.539571\pi\) | ||||
−0.123996 | + | 0.992283i | \(0.539571\pi\) | |||||||
\(312\) | −1.95318 | −0.110577 | ||||||||
\(313\) | 15.5436 | 0.878574 | 0.439287 | − | 0.898347i | \(-0.355231\pi\) | ||||
0.439287 | + | 0.898347i | \(0.355231\pi\) | |||||||
\(314\) | −50.3708 | −2.84259 | ||||||||
\(315\) | 15.9240 | 0.897214 | ||||||||
\(316\) | 7.99392 | 0.449693 | ||||||||
\(317\) | −9.49770 | −0.533444 | −0.266722 | − | 0.963773i | \(-0.585941\pi\) | ||||
−0.266722 | + | 0.963773i | \(0.585941\pi\) | |||||||
\(318\) | 5.37539 | 0.301437 | ||||||||
\(319\) | −39.4975 | −2.21144 | ||||||||
\(320\) | −21.2682 | −1.18893 | ||||||||
\(321\) | 3.15863 | 0.176298 | ||||||||
\(322\) | 14.8516 | 0.827647 | ||||||||
\(323\) | 26.0915 | 1.45177 | ||||||||
\(324\) | 26.4889 | 1.47161 | ||||||||
\(325\) | 0.957616 | 0.0531190 | ||||||||
\(326\) | 21.1564 | 1.17174 | ||||||||
\(327\) | 0.825430 | 0.0456464 | ||||||||
\(328\) | −41.0462 | −2.26640 | ||||||||
\(329\) | −13.5307 | −0.745973 | ||||||||
\(330\) | 8.86817 | 0.488177 | ||||||||
\(331\) | 14.3158 | 0.786865 | 0.393432 | − | 0.919354i | \(-0.371288\pi\) | ||||
0.393432 | + | 0.919354i | \(0.371288\pi\) | |||||||
\(332\) | 16.2604 | 0.892403 | ||||||||
\(333\) | 16.6114 | 0.910300 | ||||||||
\(334\) | −30.1827 | −1.65152 | ||||||||
\(335\) | 14.3793 | 0.785623 | ||||||||
\(336\) | 3.35757 | 0.183171 | ||||||||
\(337\) | 32.7525 | 1.78415 | 0.892073 | − | 0.451892i | \(-0.149251\pi\) | ||||
0.892073 | + | 0.451892i | \(0.149251\pi\) | |||||||
\(338\) | −2.39631 | −0.130342 | ||||||||
\(339\) | −7.07694 | −0.384367 | ||||||||
\(340\) | 46.9924 | 2.54852 | ||||||||
\(341\) | −20.2117 | −1.09452 | ||||||||
\(342\) | 27.8418 | 1.50551 | ||||||||
\(343\) | 16.7737 | 0.905696 | ||||||||
\(344\) | 39.2346 | 2.11539 | ||||||||
\(345\) | −2.04698 | −0.110206 | ||||||||
\(346\) | 4.42131 | 0.237691 | ||||||||
\(347\) | 1.81334 | 0.0973454 | 0.0486727 | − | 0.998815i | \(-0.484501\pi\) | ||||
0.0486727 | + | 0.998815i | \(0.484501\pi\) | |||||||
\(348\) | 17.5746 | 0.942096 | ||||||||
\(349\) | −18.0235 | −0.964774 | −0.482387 | − | 0.875958i | \(-0.660230\pi\) | ||||
−0.482387 | + | 0.875958i | \(0.660230\pi\) | |||||||
\(350\) | −6.53496 | −0.349308 | ||||||||
\(351\) | −2.70451 | −0.144356 | ||||||||
\(352\) | 9.09251 | 0.484632 | ||||||||
\(353\) | −12.4036 | −0.660177 | −0.330089 | − | 0.943950i | \(-0.607079\pi\) | ||||
−0.330089 | + | 0.943950i | \(0.607079\pi\) | |||||||
\(354\) | −11.3456 | −0.603014 | ||||||||
\(355\) | −23.1257 | −1.22738 | ||||||||
\(356\) | 63.0079 | 3.33941 | ||||||||
\(357\) | 8.32053 | 0.440369 | ||||||||
\(358\) | 43.6648 | 2.30776 | ||||||||
\(359\) | −35.6576 | −1.88194 | −0.940968 | − | 0.338496i | \(-0.890082\pi\) | ||||
−0.940968 | + | 0.338496i | \(0.890082\pi\) | |||||||
\(360\) | 23.3459 | 1.23044 | ||||||||
\(361\) | −1.54737 | −0.0814406 | ||||||||
\(362\) | 63.2195 | 3.32274 | ||||||||
\(363\) | −2.09624 | −0.110024 | ||||||||
\(364\) | 10.6573 | 0.558595 | ||||||||
\(365\) | −26.9833 | −1.41237 | ||||||||
\(366\) | −2.93305 | −0.153313 | ||||||||
\(367\) | −0.292180 | −0.0152517 | −0.00762583 | − | 0.999971i | \(-0.502427\pi\) | ||||
−0.00762583 | + | 0.999971i | \(0.502427\pi\) | |||||||
\(368\) | 5.48485 | 0.285917 | ||||||||
\(369\) | −27.3420 | −1.42337 | ||||||||
\(370\) | 28.7769 | 1.49604 | ||||||||
\(371\) | −13.6553 | −0.708948 | ||||||||
\(372\) | 8.99325 | 0.466278 | ||||||||
\(373\) | −23.1064 | −1.19640 | −0.598202 | − | 0.801346i | \(-0.704118\pi\) | ||||
−0.598202 | + | 0.801346i | \(0.704118\pi\) | |||||||
\(374\) | −58.8858 | −3.04491 | ||||||||
\(375\) | 5.60357 | 0.289367 | ||||||||
\(376\) | −19.8372 | −1.02303 | ||||||||
\(377\) | 10.0386 | 0.517012 | ||||||||
\(378\) | 18.4561 | 0.949278 | ||||||||
\(379\) | −21.7120 | −1.11527 | −0.557635 | − | 0.830086i | \(-0.688291\pi\) | ||||
−0.557635 | + | 0.830086i | \(0.688291\pi\) | |||||||
\(380\) | 31.4332 | 1.61249 | ||||||||
\(381\) | 2.89041 | 0.148080 | ||||||||
\(382\) | −10.7744 | −0.551264 | ||||||||
\(383\) | −3.86968 | −0.197732 | −0.0988658 | − | 0.995101i | \(-0.531521\pi\) | ||||
−0.0988658 | + | 0.995101i | \(0.531521\pi\) | |||||||
\(384\) | −9.69629 | −0.494812 | ||||||||
\(385\) | −22.5281 | −1.14814 | ||||||||
\(386\) | 5.24996 | 0.267216 | ||||||||
\(387\) | 26.1352 | 1.32853 | ||||||||
\(388\) | −1.42917 | −0.0725551 | ||||||||
\(389\) | −37.7862 | −1.91584 | −0.957919 | − | 0.287037i | \(-0.907330\pi\) | ||||
−0.957919 | + | 0.287037i | \(0.907330\pi\) | |||||||
\(390\) | −2.25391 | −0.114131 | ||||||||
\(391\) | 13.5922 | 0.687388 | ||||||||
\(392\) | −4.63403 | −0.234054 | ||||||||
\(393\) | 8.09658 | 0.408418 | ||||||||
\(394\) | 43.6787 | 2.20050 | ||||||||
\(395\) | 4.29476 | 0.216093 | ||||||||
\(396\) | −40.9508 | −2.05785 | ||||||||
\(397\) | −24.9587 | −1.25264 | −0.626320 | − | 0.779566i | \(-0.715440\pi\) | ||||
−0.626320 | + | 0.779566i | \(0.715440\pi\) | |||||||
\(398\) | −29.5880 | −1.48311 | ||||||||
\(399\) | 5.56561 | 0.278629 | ||||||||
\(400\) | −2.41343 | −0.120671 | ||||||||
\(401\) | −4.09085 | −0.204287 | −0.102144 | − | 0.994770i | \(-0.532570\pi\) | ||||
−0.102144 | + | 0.994770i | \(0.532570\pi\) | |||||||
\(402\) | 8.01742 | 0.399873 | ||||||||
\(403\) | 5.13693 | 0.255889 | ||||||||
\(404\) | 23.4237 | 1.16537 | ||||||||
\(405\) | 14.2313 | 0.707158 | ||||||||
\(406\) | −68.5051 | −3.39985 | ||||||||
\(407\) | −23.5007 | −1.16489 | ||||||||
\(408\) | 12.1986 | 0.603922 | ||||||||
\(409\) | −14.7898 | −0.731309 | −0.365654 | − | 0.930751i | \(-0.619155\pi\) | ||||
−0.365654 | + | 0.930751i | \(0.619155\pi\) | |||||||
\(410\) | −47.3661 | −2.33924 | ||||||||
\(411\) | 6.58116 | 0.324625 | ||||||||
\(412\) | 19.5597 | 0.963636 | ||||||||
\(413\) | 28.8218 | 1.41823 | ||||||||
\(414\) | 14.5040 | 0.712835 | ||||||||
\(415\) | 8.73593 | 0.428830 | ||||||||
\(416\) | −2.31092 | −0.113302 | ||||||||
\(417\) | 2.54823 | 0.124788 | ||||||||
\(418\) | −39.3887 | −1.92657 | ||||||||
\(419\) | −32.0938 | −1.56788 | −0.783942 | − | 0.620834i | \(-0.786794\pi\) | ||||
−0.783942 | + | 0.620834i | \(0.786794\pi\) | |||||||
\(420\) | 10.0240 | 0.489120 | ||||||||
\(421\) | −34.6060 | −1.68659 | −0.843295 | − | 0.537450i | \(-0.819388\pi\) | ||||
−0.843295 | + | 0.537450i | \(0.819388\pi\) | |||||||
\(422\) | −4.81709 | −0.234492 | ||||||||
\(423\) | −13.2141 | −0.642491 | ||||||||
\(424\) | −20.0199 | −0.972250 | ||||||||
\(425\) | −5.98082 | −0.290112 | ||||||||
\(426\) | −12.8942 | −0.624724 | ||||||||
\(427\) | 7.45094 | 0.360576 | ||||||||
\(428\) | −25.2676 | −1.22136 | ||||||||
\(429\) | 1.84065 | 0.0888676 | ||||||||
\(430\) | 45.2755 | 2.18338 | ||||||||
\(431\) | 19.9857 | 0.962676 | 0.481338 | − | 0.876535i | \(-0.340151\pi\) | ||||
0.481338 | + | 0.876535i | \(0.340151\pi\) | |||||||
\(432\) | 6.81602 | 0.327936 | ||||||||
\(433\) | −17.5098 | −0.841469 | −0.420734 | − | 0.907184i | \(-0.638228\pi\) | ||||
−0.420734 | + | 0.907184i | \(0.638228\pi\) | |||||||
\(434\) | −35.0554 | −1.68271 | ||||||||
\(435\) | 9.44200 | 0.452709 | ||||||||
\(436\) | −6.60307 | −0.316229 | ||||||||
\(437\) | 9.09184 | 0.434922 | ||||||||
\(438\) | −15.0450 | −0.718880 | ||||||||
\(439\) | −7.38986 | −0.352699 | −0.176349 | − | 0.984328i | \(-0.556429\pi\) | ||||
−0.176349 | + | 0.984328i | \(0.556429\pi\) | |||||||
\(440\) | −33.0282 | −1.57456 | ||||||||
\(441\) | −3.08685 | −0.146993 | ||||||||
\(442\) | 14.9662 | 0.711871 | ||||||||
\(443\) | 28.9317 | 1.37459 | 0.687293 | − | 0.726380i | \(-0.258799\pi\) | ||||
0.687293 | + | 0.726380i | \(0.258799\pi\) | |||||||
\(444\) | 10.4567 | 0.496254 | ||||||||
\(445\) | 33.8512 | 1.60470 | ||||||||
\(446\) | −47.8058 | −2.26367 | ||||||||
\(447\) | 0.354233 | 0.0167547 | ||||||||
\(448\) | 30.1245 | 1.42325 | ||||||||
\(449\) | 10.7850 | 0.508976 | 0.254488 | − | 0.967076i | \(-0.418093\pi\) | ||||
0.254488 | + | 0.967076i | \(0.418093\pi\) | |||||||
\(450\) | −6.38203 | −0.300852 | ||||||||
\(451\) | 38.6815 | 1.82144 | ||||||||
\(452\) | 56.6123 | 2.66282 | ||||||||
\(453\) | −5.69316 | −0.267488 | ||||||||
\(454\) | 60.1643 | 2.82365 | ||||||||
\(455\) | 5.72568 | 0.268424 | ||||||||
\(456\) | 8.15966 | 0.382111 | ||||||||
\(457\) | 7.80116 | 0.364923 | 0.182461 | − | 0.983213i | \(-0.441594\pi\) | ||||
0.182461 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(458\) | 28.4820 | 1.33088 | ||||||||
\(459\) | 16.8911 | 0.788408 | ||||||||
\(460\) | 16.3749 | 0.763485 | ||||||||
\(461\) | −3.48670 | −0.162392 | −0.0811960 | − | 0.996698i | \(-0.525874\pi\) | ||||
−0.0811960 | + | 0.996698i | \(0.525874\pi\) | |||||||
\(462\) | −12.5610 | −0.584390 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | −25.2996 | −1.17451 | ||||||||
\(465\) | 4.83166 | 0.224063 | ||||||||
\(466\) | −66.6019 | −3.08527 | ||||||||
\(467\) | 18.0970 | 0.837428 | 0.418714 | − | 0.908118i | \(-0.362481\pi\) | ||||
0.418714 | + | 0.908118i | \(0.362481\pi\) | |||||||
\(468\) | 10.4079 | 0.481106 | ||||||||
\(469\) | −20.3670 | −0.940458 | ||||||||
\(470\) | −22.8915 | −1.05591 | ||||||||
\(471\) | −9.83352 | −0.453105 | ||||||||
\(472\) | 42.2552 | 1.94495 | ||||||||
\(473\) | −36.9743 | −1.70008 | ||||||||
\(474\) | 2.39463 | 0.109989 | ||||||||
\(475\) | −4.00057 | −0.183559 | ||||||||
\(476\) | −66.5605 | −3.05080 | ||||||||
\(477\) | −13.3357 | −0.610602 | ||||||||
\(478\) | −37.5099 | −1.71566 | ||||||||
\(479\) | −10.2940 | −0.470346 | −0.235173 | − | 0.971953i | \(-0.575566\pi\) | ||||
−0.235173 | + | 0.971953i | \(0.575566\pi\) | |||||||
\(480\) | −2.17359 | −0.0992104 | ||||||||
\(481\) | 5.97286 | 0.272339 | ||||||||
\(482\) | 30.3375 | 1.38184 | ||||||||
\(483\) | 2.89937 | 0.131926 | ||||||||
\(484\) | 16.7690 | 0.762225 | ||||||||
\(485\) | −0.767827 | −0.0348652 | ||||||||
\(486\) | 27.3774 | 1.24187 | ||||||||
\(487\) | −9.82419 | −0.445176 | −0.222588 | − | 0.974913i | \(-0.571451\pi\) | ||||
−0.222588 | + | 0.974913i | \(0.571451\pi\) | |||||||
\(488\) | 10.9237 | 0.494493 | ||||||||
\(489\) | 4.13020 | 0.186774 | ||||||||
\(490\) | −5.34753 | −0.241577 | ||||||||
\(491\) | 4.04593 | 0.182590 | 0.0912951 | − | 0.995824i | \(-0.470899\pi\) | ||||
0.0912951 | + | 0.995824i | \(0.470899\pi\) | |||||||
\(492\) | −17.2115 | −0.775954 | ||||||||
\(493\) | −62.6961 | −2.82369 | ||||||||
\(494\) | 10.0109 | 0.450412 | ||||||||
\(495\) | −22.0009 | −0.988869 | ||||||||
\(496\) | −12.9463 | −0.581307 | ||||||||
\(497\) | 32.7555 | 1.46928 | ||||||||
\(498\) | 4.87088 | 0.218269 | ||||||||
\(499\) | 8.22113 | 0.368028 | 0.184014 | − | 0.982924i | \(-0.441091\pi\) | ||||
0.184014 | + | 0.982924i | \(0.441091\pi\) | |||||||
\(500\) | −44.8261 | −2.00468 | ||||||||
\(501\) | −5.89235 | −0.263251 | ||||||||
\(502\) | 22.8675 | 1.02063 | ||||||||
\(503\) | 18.2359 | 0.813098 | 0.406549 | − | 0.913629i | \(-0.366732\pi\) | ||||
0.406549 | + | 0.913629i | \(0.366732\pi\) | |||||||
\(504\) | −33.0674 | −1.47294 | ||||||||
\(505\) | 12.5845 | 0.560001 | ||||||||
\(506\) | −20.5193 | −0.912195 | ||||||||
\(507\) | −0.467815 | −0.0207764 | ||||||||
\(508\) | −23.1219 | −1.02587 | ||||||||
\(509\) | 7.95577 | 0.352634 | 0.176317 | − | 0.984333i | \(-0.443582\pi\) | ||||
0.176317 | + | 0.984333i | \(0.443582\pi\) | |||||||
\(510\) | 14.0768 | 0.623333 | ||||||||
\(511\) | 38.2195 | 1.69073 | ||||||||
\(512\) | 26.8687 | 1.18744 | ||||||||
\(513\) | 11.2984 | 0.498838 | ||||||||
\(514\) | −45.5120 | −2.00745 | ||||||||
\(515\) | 10.5085 | 0.463060 | ||||||||
\(516\) | 16.4518 | 0.724252 | ||||||||
\(517\) | 18.6944 | 0.822178 | ||||||||
\(518\) | −40.7600 | −1.79089 | ||||||||
\(519\) | 0.863140 | 0.0378877 | ||||||||
\(520\) | 8.39434 | 0.368116 | ||||||||
\(521\) | −12.2503 | −0.536696 | −0.268348 | − | 0.963322i | \(-0.586478\pi\) | ||||
−0.268348 | + | 0.963322i | \(0.586478\pi\) | |||||||
\(522\) | −66.9020 | −2.92822 | ||||||||
\(523\) | 29.8998 | 1.30743 | 0.653713 | − | 0.756742i | \(-0.273210\pi\) | ||||
0.653713 | + | 0.756742i | \(0.273210\pi\) | |||||||
\(524\) | −64.7690 | −2.82945 | ||||||||
\(525\) | −1.27577 | −0.0556793 | ||||||||
\(526\) | −55.7615 | −2.43132 | ||||||||
\(527\) | −32.0828 | −1.39755 | ||||||||
\(528\) | −4.63890 | −0.201882 | ||||||||
\(529\) | −18.2637 | −0.794072 | ||||||||
\(530\) | −23.1023 | −1.00350 | ||||||||
\(531\) | 28.1473 | 1.22149 | ||||||||
\(532\) | −44.5224 | −1.93029 | ||||||||
\(533\) | −9.83118 | −0.425836 | ||||||||
\(534\) | 18.8744 | 0.816774 | ||||||||
\(535\) | −13.5751 | −0.586904 | ||||||||
\(536\) | −29.8597 | −1.28974 | ||||||||
\(537\) | 8.52437 | 0.367854 | ||||||||
\(538\) | −54.6268 | −2.35513 | ||||||||
\(539\) | 4.36706 | 0.188103 | ||||||||
\(540\) | 20.3491 | 0.875688 | ||||||||
\(541\) | −37.3343 | −1.60513 | −0.802564 | − | 0.596566i | \(-0.796532\pi\) | ||||
−0.802564 | + | 0.596566i | \(0.796532\pi\) | |||||||
\(542\) | −28.1282 | −1.20821 | ||||||||
\(543\) | 12.3419 | 0.529641 | ||||||||
\(544\) | 14.4329 | 0.618807 | ||||||||
\(545\) | −3.54752 | −0.151959 | ||||||||
\(546\) | 3.19246 | 0.136625 | ||||||||
\(547\) | 22.5833 | 0.965592 | 0.482796 | − | 0.875733i | \(-0.339621\pi\) | ||||
0.482796 | + | 0.875733i | \(0.339621\pi\) | |||||||
\(548\) | −52.6463 | −2.24894 | ||||||||
\(549\) | 7.27657 | 0.310557 | ||||||||
\(550\) | 9.02886 | 0.384992 | ||||||||
\(551\) | −41.9374 | −1.78659 | ||||||||
\(552\) | 4.25073 | 0.180923 | ||||||||
\(553\) | −6.08315 | −0.258682 | ||||||||
\(554\) | 46.2004 | 1.96287 | ||||||||
\(555\) | 5.61791 | 0.238467 | ||||||||
\(556\) | −20.3847 | −0.864505 | ||||||||
\(557\) | −7.57210 | −0.320840 | −0.160420 | − | 0.987049i | \(-0.551285\pi\) | ||||
−0.160420 | + | 0.987049i | \(0.551285\pi\) | |||||||
\(558\) | −34.2351 | −1.44929 | ||||||||
\(559\) | 9.39726 | 0.397462 | ||||||||
\(560\) | −14.4301 | −0.609784 | ||||||||
\(561\) | −11.4959 | −0.485355 | ||||||||
\(562\) | 29.5144 | 1.24499 | ||||||||
\(563\) | −31.4051 | −1.32357 | −0.661784 | − | 0.749695i | \(-0.730200\pi\) | ||||
−0.661784 | + | 0.749695i | \(0.730200\pi\) | |||||||
\(564\) | −8.31814 | −0.350257 | ||||||||
\(565\) | 30.4152 | 1.27958 | ||||||||
\(566\) | 76.7460 | 3.22588 | ||||||||
\(567\) | −20.1574 | −0.846529 | ||||||||
\(568\) | 48.0224 | 2.01497 | ||||||||
\(569\) | −33.4899 | −1.40397 | −0.701985 | − | 0.712192i | \(-0.747703\pi\) | ||||
−0.701985 | + | 0.712192i | \(0.747703\pi\) | |||||||
\(570\) | 9.41599 | 0.394393 | ||||||||
\(571\) | 26.8201 | 1.12239 | 0.561194 | − | 0.827684i | \(-0.310342\pi\) | ||||
0.561194 | + | 0.827684i | \(0.310342\pi\) | |||||||
\(572\) | −14.7244 | −0.615658 | ||||||||
\(573\) | −2.10340 | −0.0878708 | ||||||||
\(574\) | 67.0899 | 2.80028 | ||||||||
\(575\) | −2.08407 | −0.0869119 | ||||||||
\(576\) | 29.4195 | 1.22581 | ||||||||
\(577\) | −7.95789 | −0.331291 | −0.165646 | − | 0.986185i | \(-0.552971\pi\) | ||||
−0.165646 | + | 0.986185i | \(0.552971\pi\) | |||||||
\(578\) | −52.7347 | −2.19347 | ||||||||
\(579\) | 1.02491 | 0.0425939 | ||||||||
\(580\) | −75.5318 | −3.13629 | ||||||||
\(581\) | −12.3737 | −0.513347 | ||||||||
\(582\) | −0.428116 | −0.0177460 | ||||||||
\(583\) | 18.8665 | 0.781371 | ||||||||
\(584\) | 56.0331 | 2.31866 | ||||||||
\(585\) | 5.59169 | 0.231188 | ||||||||
\(586\) | 12.6120 | 0.520998 | ||||||||
\(587\) | 13.5868 | 0.560786 | 0.280393 | − | 0.959885i | \(-0.409535\pi\) | ||||
0.280393 | + | 0.959885i | \(0.409535\pi\) | |||||||
\(588\) | −1.94314 | −0.0801338 | ||||||||
\(589\) | −21.4602 | −0.884253 | ||||||||
\(590\) | 48.7612 | 2.00747 | ||||||||
\(591\) | 8.52708 | 0.350757 | ||||||||
\(592\) | −15.0531 | −0.618678 | ||||||||
\(593\) | −23.3075 | −0.957124 | −0.478562 | − | 0.878054i | \(-0.658842\pi\) | ||||
−0.478562 | + | 0.878054i | \(0.658842\pi\) | |||||||
\(594\) | −25.4994 | −1.04625 | ||||||||
\(595\) | −35.7599 | −1.46601 | ||||||||
\(596\) | −2.83371 | −0.116073 | ||||||||
\(597\) | −5.77626 | −0.236407 | ||||||||
\(598\) | 5.21512 | 0.213262 | ||||||||
\(599\) | −12.4832 | −0.510048 | −0.255024 | − | 0.966935i | \(-0.582083\pi\) | ||||
−0.255024 | + | 0.966935i | \(0.582083\pi\) | |||||||
\(600\) | −1.87039 | −0.0763585 | ||||||||
\(601\) | 5.84598 | 0.238462 | 0.119231 | − | 0.992867i | \(-0.461957\pi\) | ||||
0.119231 | + | 0.992867i | \(0.461957\pi\) | |||||||
\(602\) | −64.1288 | −2.61369 | ||||||||
\(603\) | −19.8903 | −0.809997 | ||||||||
\(604\) | 45.5427 | 1.85311 | ||||||||
\(605\) | 9.00918 | 0.366275 | ||||||||
\(606\) | 7.01670 | 0.285034 | ||||||||
\(607\) | 3.92658 | 0.159375 | 0.0796874 | − | 0.996820i | \(-0.474608\pi\) | ||||
0.0796874 | + | 0.996820i | \(0.474608\pi\) | |||||||
\(608\) | 9.65419 | 0.391529 | ||||||||
\(609\) | −13.3738 | −0.541932 | ||||||||
\(610\) | 12.6056 | 0.510387 | ||||||||
\(611\) | −4.75131 | −0.192217 | ||||||||
\(612\) | −65.0029 | −2.62759 | ||||||||
\(613\) | 27.6069 | 1.11503 | 0.557516 | − | 0.830167i | \(-0.311755\pi\) | ||||
0.557516 | + | 0.830167i | \(0.311755\pi\) | |||||||
\(614\) | −8.47530 | −0.342035 | ||||||||
\(615\) | −9.24694 | −0.372873 | ||||||||
\(616\) | 46.7815 | 1.88488 | ||||||||
\(617\) | −39.8336 | −1.60364 | −0.801821 | − | 0.597565i | \(-0.796135\pi\) | ||||
−0.801821 | + | 0.597565i | \(0.796135\pi\) | |||||||
\(618\) | 5.85921 | 0.235692 | ||||||||
\(619\) | −12.4259 | −0.499438 | −0.249719 | − | 0.968318i | \(-0.580338\pi\) | ||||
−0.249719 | + | 0.968318i | \(0.580338\pi\) | |||||||
\(620\) | −38.6511 | −1.55227 | ||||||||
\(621\) | 5.88585 | 0.236191 | ||||||||
\(622\) | 10.4800 | 0.420210 | ||||||||
\(623\) | −47.9472 | −1.92097 | ||||||||
\(624\) | 1.17901 | 0.0471981 | ||||||||
\(625\) | −19.2949 | −0.771796 | ||||||||
\(626\) | −37.2472 | −1.48870 | ||||||||
\(627\) | −7.68958 | −0.307092 | ||||||||
\(628\) | 78.6637 | 3.13903 | ||||||||
\(629\) | −37.3037 | −1.48739 | ||||||||
\(630\) | −38.1588 | −1.52028 | ||||||||
\(631\) | 20.2478 | 0.806054 | 0.403027 | − | 0.915188i | \(-0.367958\pi\) | ||||
0.403027 | + | 0.915188i | \(0.367958\pi\) | |||||||
\(632\) | −8.91843 | −0.354756 | ||||||||
\(633\) | −0.940406 | −0.0373778 | ||||||||
\(634\) | 22.7595 | 0.903893 | ||||||||
\(635\) | −12.4224 | −0.492966 | ||||||||
\(636\) | −8.39472 | −0.332872 | ||||||||
\(637\) | −1.10992 | −0.0439766 | ||||||||
\(638\) | 94.6483 | 3.74716 | ||||||||
\(639\) | 31.9890 | 1.26546 | ||||||||
\(640\) | 41.6726 | 1.64725 | ||||||||
\(641\) | −29.4215 | −1.16208 | −0.581040 | − | 0.813875i | \(-0.697354\pi\) | ||||
−0.581040 | + | 0.813875i | \(0.697354\pi\) | |||||||
\(642\) | −7.56907 | −0.298727 | ||||||||
\(643\) | −13.2214 | −0.521402 | −0.260701 | − | 0.965420i | \(-0.583954\pi\) | ||||
−0.260701 | + | 0.965420i | \(0.583954\pi\) | |||||||
\(644\) | −23.1936 | −0.913958 | ||||||||
\(645\) | 8.83881 | 0.348028 | ||||||||
\(646\) | −62.5234 | −2.45995 | ||||||||
\(647\) | −6.70718 | −0.263687 | −0.131843 | − | 0.991271i | \(-0.542090\pi\) | ||||
−0.131843 | + | 0.991271i | \(0.542090\pi\) | |||||||
\(648\) | −29.5524 | −1.16093 | ||||||||
\(649\) | −39.8209 | −1.56311 | ||||||||
\(650\) | −2.29475 | −0.0900074 | ||||||||
\(651\) | −6.84362 | −0.268222 | ||||||||
\(652\) | −33.0398 | −1.29394 | ||||||||
\(653\) | 12.6801 | 0.496210 | 0.248105 | − | 0.968733i | \(-0.420192\pi\) | ||||
0.248105 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(654\) | −1.97799 | −0.0773454 | ||||||||
\(655\) | −34.7974 | −1.35965 | ||||||||
\(656\) | 24.7770 | 0.967379 | ||||||||
\(657\) | 37.3251 | 1.45619 | ||||||||
\(658\) | 32.4238 | 1.26401 | ||||||||
\(659\) | −8.87171 | −0.345593 | −0.172796 | − | 0.984958i | \(-0.555280\pi\) | ||||
−0.172796 | + | 0.984958i | \(0.555280\pi\) | |||||||
\(660\) | −13.8494 | −0.539086 | ||||||||
\(661\) | −12.1598 | −0.472960 | −0.236480 | − | 0.971636i | \(-0.575994\pi\) | ||||
−0.236480 | + | 0.971636i | \(0.575994\pi\) | |||||||
\(662\) | −34.3050 | −1.33330 | ||||||||
\(663\) | 2.92175 | 0.113471 | ||||||||
\(664\) | −18.1409 | −0.704003 | ||||||||
\(665\) | −23.9198 | −0.927570 | ||||||||
\(666\) | −39.8061 | −1.54246 | ||||||||
\(667\) | −21.8471 | −0.845921 | ||||||||
\(668\) | 47.1361 | 1.82375 | ||||||||
\(669\) | −9.33279 | −0.360826 | ||||||||
\(670\) | −34.4572 | −1.33120 | ||||||||
\(671\) | −10.2944 | −0.397411 | ||||||||
\(672\) | 3.07870 | 0.118763 | ||||||||
\(673\) | 32.9877 | 1.27158 | 0.635792 | − | 0.771861i | \(-0.280674\pi\) | ||||
0.635792 | + | 0.771861i | \(0.280674\pi\) | |||||||
\(674\) | −78.4853 | −3.02314 | ||||||||
\(675\) | −2.58988 | −0.0996845 | ||||||||
\(676\) | 3.74231 | 0.143935 | ||||||||
\(677\) | −2.49942 | −0.0960606 | −0.0480303 | − | 0.998846i | \(-0.515294\pi\) | ||||
−0.0480303 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(678\) | 16.9585 | 0.651289 | ||||||||
\(679\) | 1.08756 | 0.0417367 | ||||||||
\(680\) | −52.4271 | −2.01049 | ||||||||
\(681\) | 11.7455 | 0.450087 | ||||||||
\(682\) | 48.4334 | 1.85461 | ||||||||
\(683\) | −20.1647 | −0.771581 | −0.385790 | − | 0.922586i | \(-0.626071\pi\) | ||||
−0.385790 | + | 0.922586i | \(0.626071\pi\) | |||||||
\(684\) | −43.4805 | −1.66252 | ||||||||
\(685\) | −28.2844 | −1.08069 | ||||||||
\(686\) | −40.1951 | −1.53465 | ||||||||
\(687\) | 5.56034 | 0.212140 | ||||||||
\(688\) | −23.6834 | −0.902922 | ||||||||
\(689\) | −4.79505 | −0.182677 | ||||||||
\(690\) | 4.90521 | 0.186738 | ||||||||
\(691\) | 3.89707 | 0.148251 | 0.0741257 | − | 0.997249i | \(-0.476383\pi\) | ||||
0.0741257 | + | 0.997249i | \(0.476383\pi\) | |||||||
\(692\) | −6.90473 | −0.262479 | ||||||||
\(693\) | 31.1624 | 1.18376 | ||||||||
\(694\) | −4.34533 | −0.164947 | ||||||||
\(695\) | −10.9518 | −0.415424 | ||||||||
\(696\) | −19.6071 | −0.743205 | ||||||||
\(697\) | 61.4009 | 2.32572 | ||||||||
\(698\) | 43.1898 | 1.63476 | ||||||||
\(699\) | −13.0022 | −0.491789 | ||||||||
\(700\) | 10.2056 | 0.385736 | ||||||||
\(701\) | −11.3525 | −0.428778 | −0.214389 | − | 0.976748i | \(-0.568776\pi\) | ||||
−0.214389 | + | 0.976748i | \(0.568776\pi\) | |||||||
\(702\) | 6.48084 | 0.244603 | ||||||||
\(703\) | −24.9524 | −0.941098 | ||||||||
\(704\) | −41.6207 | −1.56864 | ||||||||
\(705\) | −4.46895 | −0.168310 | ||||||||
\(706\) | 29.7229 | 1.11864 | ||||||||
\(707\) | −17.8248 | −0.670370 | ||||||||
\(708\) | 17.7184 | 0.665900 | ||||||||
\(709\) | −38.2924 | −1.43810 | −0.719051 | − | 0.694958i | \(-0.755423\pi\) | ||||
−0.719051 | + | 0.694958i | \(0.755423\pi\) | |||||||
\(710\) | 55.4163 | 2.07974 | ||||||||
\(711\) | −5.94080 | −0.222797 | ||||||||
\(712\) | −70.2948 | −2.63441 | ||||||||
\(713\) | −11.1796 | −0.418678 | ||||||||
\(714\) | −19.9386 | −0.746183 | ||||||||
\(715\) | −7.91074 | −0.295845 | ||||||||
\(716\) | −68.1911 | −2.54842 | ||||||||
\(717\) | −7.32278 | −0.273474 | ||||||||
\(718\) | 85.4467 | 3.18884 | ||||||||
\(719\) | −4.37499 | −0.163160 | −0.0815798 | − | 0.996667i | \(-0.525997\pi\) | ||||
−0.0815798 | + | 0.996667i | \(0.525997\pi\) | |||||||
\(720\) | −14.0924 | −0.525194 | ||||||||
\(721\) | −14.8844 | −0.554323 | ||||||||
\(722\) | 3.70798 | 0.137997 | ||||||||
\(723\) | 5.92258 | 0.220263 | ||||||||
\(724\) | −98.7295 | −3.66925 | ||||||||
\(725\) | 9.61309 | 0.357021 | ||||||||
\(726\) | 5.02324 | 0.186430 | ||||||||
\(727\) | −16.7606 | −0.621616 | −0.310808 | − | 0.950473i | \(-0.600600\pi\) | ||||
−0.310808 | + | 0.950473i | \(0.600600\pi\) | |||||||
\(728\) | −11.8898 | −0.440667 | ||||||||
\(729\) | −15.8900 | −0.588519 | ||||||||
\(730\) | 64.6604 | 2.39319 | ||||||||
\(731\) | −58.6909 | −2.17076 | ||||||||
\(732\) | 4.58053 | 0.169301 | ||||||||
\(733\) | −45.3073 | −1.67346 | −0.836732 | − | 0.547613i | \(-0.815537\pi\) | ||||
−0.836732 | + | 0.547613i | \(0.815537\pi\) | |||||||
\(734\) | 0.700154 | 0.0258431 | ||||||||
\(735\) | −1.04396 | −0.0385070 | ||||||||
\(736\) | 5.02929 | 0.185382 | ||||||||
\(737\) | 28.1395 | 1.03653 | ||||||||
\(738\) | 65.5199 | 2.41182 | ||||||||
\(739\) | 16.1646 | 0.594626 | 0.297313 | − | 0.954780i | \(-0.403909\pi\) | ||||
0.297313 | + | 0.954780i | \(0.403909\pi\) | |||||||
\(740\) | −44.9408 | −1.65206 | ||||||||
\(741\) | 1.95436 | 0.0717952 | ||||||||
\(742\) | 32.7224 | 1.20128 | ||||||||
\(743\) | −13.9951 | −0.513429 | −0.256715 | − | 0.966487i | \(-0.582640\pi\) | ||||
−0.256715 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(744\) | −10.0333 | −0.367840 | ||||||||
\(745\) | −1.52242 | −0.0557771 | ||||||||
\(746\) | 55.3701 | 2.02724 | ||||||||
\(747\) | −12.0841 | −0.442135 | ||||||||
\(748\) | 91.9617 | 3.36245 | ||||||||
\(749\) | 19.2280 | 0.702575 | ||||||||
\(750\) | −13.4279 | −0.490318 | ||||||||
\(751\) | 35.9601 | 1.31220 | 0.656101 | − | 0.754673i | \(-0.272205\pi\) | ||||
0.656101 | + | 0.754673i | \(0.272205\pi\) | |||||||
\(752\) | 11.9745 | 0.436664 | ||||||||
\(753\) | 4.46426 | 0.162687 | ||||||||
\(754\) | −24.0555 | −0.876050 | ||||||||
\(755\) | 24.4680 | 0.890481 | ||||||||
\(756\) | −28.8228 | −1.04827 | ||||||||
\(757\) | −33.8182 | −1.22915 | −0.614573 | − | 0.788860i | \(-0.710671\pi\) | ||||
−0.614573 | + | 0.788860i | \(0.710671\pi\) | |||||||
\(758\) | 52.0287 | 1.88977 | ||||||||
\(759\) | −4.00584 | −0.145403 | ||||||||
\(760\) | −35.0685 | −1.27207 | ||||||||
\(761\) | 52.7614 | 1.91260 | 0.956300 | − | 0.292386i | \(-0.0944492\pi\) | ||||
0.956300 | + | 0.292386i | \(0.0944492\pi\) | |||||||
\(762\) | −6.92631 | −0.250914 | ||||||||
\(763\) | 5.02475 | 0.181908 | ||||||||
\(764\) | 16.8262 | 0.608752 | ||||||||
\(765\) | −34.9231 | −1.26265 | ||||||||
\(766\) | 9.27296 | 0.335046 | ||||||||
\(767\) | 10.1207 | 0.365439 | ||||||||
\(768\) | 13.3381 | 0.481296 | ||||||||
\(769\) | 15.4646 | 0.557666 | 0.278833 | − | 0.960340i | \(-0.410052\pi\) | ||||
0.278833 | + | 0.960340i | \(0.410052\pi\) | |||||||
\(770\) | 53.9844 | 1.94546 | ||||||||
\(771\) | −8.88499 | −0.319985 | ||||||||
\(772\) | −8.19884 | −0.295083 | ||||||||
\(773\) | −27.7960 | −0.999753 | −0.499877 | − | 0.866097i | \(-0.666621\pi\) | ||||
−0.499877 | + | 0.866097i | \(0.666621\pi\) | |||||||
\(774\) | −62.6281 | −2.25112 | ||||||||
\(775\) | 4.91921 | 0.176703 | ||||||||
\(776\) | 1.59446 | 0.0572376 | ||||||||
\(777\) | −7.95728 | −0.285466 | ||||||||
\(778\) | 90.5476 | 3.24629 | ||||||||
\(779\) | 41.0711 | 1.47152 | ||||||||
\(780\) | 3.51991 | 0.126033 | ||||||||
\(781\) | −45.2558 | −1.61938 | ||||||||
\(782\) | −32.5712 | −1.16474 | ||||||||
\(783\) | −27.1493 | −0.970239 | ||||||||
\(784\) | 2.79727 | 0.0999025 | ||||||||
\(785\) | 42.2624 | 1.50841 | ||||||||
\(786\) | −19.4019 | −0.692044 | ||||||||
\(787\) | 13.5449 | 0.482825 | 0.241412 | − | 0.970423i | \(-0.422389\pi\) | ||||
0.241412 | + | 0.970423i | \(0.422389\pi\) | |||||||
\(788\) | −68.2128 | −2.42998 | ||||||||
\(789\) | −10.8859 | −0.387549 | ||||||||
\(790\) | −10.2916 | −0.366158 | ||||||||
\(791\) | −43.0804 | −1.53176 | ||||||||
\(792\) | 45.6868 | 1.62341 | ||||||||
\(793\) | 2.61639 | 0.0929107 | ||||||||
\(794\) | 59.8087 | 2.12253 | ||||||||
\(795\) | −4.51009 | −0.159957 | ||||||||
\(796\) | 46.2075 | 1.63778 | ||||||||
\(797\) | 1.77673 | 0.0629352 | 0.0314676 | − | 0.999505i | \(-0.489982\pi\) | ||||
0.0314676 | + | 0.999505i | \(0.489982\pi\) | |||||||
\(798\) | −13.3369 | −0.472122 | ||||||||
\(799\) | 29.6744 | 1.04980 | ||||||||
\(800\) | −2.21298 | −0.0782406 | ||||||||
\(801\) | −46.8252 | −1.65449 | ||||||||
\(802\) | 9.80295 | 0.346154 | ||||||||
\(803\) | −52.8050 | −1.86345 | ||||||||
\(804\) | −12.5208 | −0.441573 | ||||||||
\(805\) | −12.4609 | −0.439188 | ||||||||
\(806\) | −12.3097 | −0.433590 | ||||||||
\(807\) | −10.6644 | −0.375404 | ||||||||
\(808\) | −26.1327 | −0.919344 | ||||||||
\(809\) | 28.0992 | 0.987916 | 0.493958 | − | 0.869486i | \(-0.335550\pi\) | ||||
0.493958 | + | 0.869486i | \(0.335550\pi\) | |||||||
\(810\) | −34.1026 | −1.19824 | ||||||||
\(811\) | −17.8135 | −0.625518 | −0.312759 | − | 0.949833i | \(-0.601253\pi\) | ||||
−0.312759 | + | 0.949833i | \(0.601253\pi\) | |||||||
\(812\) | 106.984 | 3.75440 | ||||||||
\(813\) | −5.49128 | −0.192587 | ||||||||
\(814\) | 56.3150 | 1.97384 | ||||||||
\(815\) | −17.7507 | −0.621781 | ||||||||
\(816\) | −7.36353 | −0.257775 | ||||||||
\(817\) | −39.2583 | −1.37348 | ||||||||
\(818\) | 35.4410 | 1.23916 | ||||||||
\(819\) | −7.92014 | −0.276752 | ||||||||
\(820\) | 73.9714 | 2.58319 | ||||||||
\(821\) | −2.41218 | −0.0841857 | −0.0420929 | − | 0.999114i | \(-0.513403\pi\) | ||||
−0.0420929 | + | 0.999114i | \(0.513403\pi\) | |||||||
\(822\) | −15.7705 | −0.550059 | ||||||||
\(823\) | −29.8032 | −1.03887 | −0.519437 | − | 0.854509i | \(-0.673858\pi\) | ||||
−0.519437 | + | 0.854509i | \(0.673858\pi\) | |||||||
\(824\) | −21.8218 | −0.760197 | ||||||||
\(825\) | 1.76264 | 0.0613672 | ||||||||
\(826\) | −69.0659 | −2.40311 | ||||||||
\(827\) | 22.4131 | 0.779381 | 0.389691 | − | 0.920946i | \(-0.372582\pi\) | ||||
0.389691 | + | 0.920946i | \(0.372582\pi\) | |||||||
\(828\) | −22.6509 | −0.787173 | ||||||||
\(829\) | −41.7553 | −1.45022 | −0.725111 | − | 0.688632i | \(-0.758211\pi\) | ||||
−0.725111 | + | 0.688632i | \(0.758211\pi\) | |||||||
\(830\) | −20.9340 | −0.726630 | ||||||||
\(831\) | 9.01938 | 0.312879 | ||||||||
\(832\) | 10.5782 | 0.366733 | ||||||||
\(833\) | 6.93203 | 0.240181 | ||||||||
\(834\) | −6.10636 | −0.211446 | ||||||||
\(835\) | 25.3241 | 0.876375 | ||||||||
\(836\) | 61.5132 | 2.12748 | ||||||||
\(837\) | −13.8929 | −0.480207 | ||||||||
\(838\) | 76.9067 | 2.65670 | ||||||||
\(839\) | −24.4753 | −0.844980 | −0.422490 | − | 0.906368i | \(-0.638844\pi\) | ||||
−0.422490 | + | 0.906368i | \(0.638844\pi\) | |||||||
\(840\) | −11.1833 | −0.385859 | ||||||||
\(841\) | 71.7727 | 2.47492 | ||||||||
\(842\) | 82.9266 | 2.85784 | ||||||||
\(843\) | 5.76188 | 0.198450 | ||||||||
\(844\) | 7.52282 | 0.258946 | ||||||||
\(845\) | 2.01057 | 0.0691656 | ||||||||
\(846\) | 31.6651 | 1.08867 | ||||||||
\(847\) | −12.7607 | −0.438463 | ||||||||
\(848\) | 12.0847 | 0.414991 | ||||||||
\(849\) | 14.9826 | 0.514201 | ||||||||
\(850\) | 14.3319 | 0.491580 | ||||||||
\(851\) | −12.9988 | −0.445594 | ||||||||
\(852\) | 20.1367 | 0.689873 | ||||||||
\(853\) | 5.20965 | 0.178375 | 0.0891875 | − | 0.996015i | \(-0.471573\pi\) | ||||
0.0891875 | + | 0.996015i | \(0.471573\pi\) | |||||||
\(854\) | −17.8548 | −0.610977 | ||||||||
\(855\) | −23.3600 | −0.798896 | ||||||||
\(856\) | 28.1899 | 0.963510 | ||||||||
\(857\) | 33.4396 | 1.14228 | 0.571138 | − | 0.820854i | \(-0.306502\pi\) | ||||
0.571138 | + | 0.820854i | \(0.306502\pi\) | |||||||
\(858\) | −4.41078 | −0.150582 | ||||||||
\(859\) | −49.7923 | −1.69889 | −0.849446 | − | 0.527676i | \(-0.823064\pi\) | ||||
−0.849446 | + | 0.527676i | \(0.823064\pi\) | |||||||
\(860\) | −70.7065 | −2.41107 | ||||||||
\(861\) | 13.0975 | 0.446361 | ||||||||
\(862\) | −47.8919 | −1.63120 | ||||||||
\(863\) | −7.94831 | −0.270564 | −0.135282 | − | 0.990807i | \(-0.543194\pi\) | ||||
−0.135282 | + | 0.990807i | \(0.543194\pi\) | |||||||
\(864\) | 6.24991 | 0.212626 | ||||||||
\(865\) | −3.70959 | −0.126130 | ||||||||
\(866\) | 41.9590 | 1.42582 | ||||||||
\(867\) | −10.2950 | −0.349637 | ||||||||
\(868\) | 54.7459 | 1.85820 | ||||||||
\(869\) | 8.40464 | 0.285108 | ||||||||
\(870\) | −22.6260 | −0.767092 | ||||||||
\(871\) | −7.15184 | −0.242331 | ||||||||
\(872\) | 7.36672 | 0.249469 | ||||||||
\(873\) | 1.06211 | 0.0359469 | ||||||||
\(874\) | −21.7869 | −0.736952 | ||||||||
\(875\) | 34.1114 | 1.15318 | ||||||||
\(876\) | 23.4958 | 0.793849 | ||||||||
\(877\) | −24.7177 | −0.834658 | −0.417329 | − | 0.908756i | \(-0.637034\pi\) | ||||
−0.417329 | + | 0.908756i | \(0.637034\pi\) | |||||||
\(878\) | 17.7084 | 0.597630 | ||||||||
\(879\) | 2.46215 | 0.0830464 | ||||||||
\(880\) | 19.9370 | 0.672077 | ||||||||
\(881\) | −49.4786 | −1.66698 | −0.833488 | − | 0.552537i | \(-0.813660\pi\) | ||||
−0.833488 | + | 0.552537i | \(0.813660\pi\) | |||||||
\(882\) | 7.39705 | 0.249072 | ||||||||
\(883\) | 22.8327 | 0.768380 | 0.384190 | − | 0.923254i | \(-0.374481\pi\) | ||||
0.384190 | + | 0.923254i | \(0.374481\pi\) | |||||||
\(884\) | −23.3727 | −0.786108 | ||||||||
\(885\) | 9.51930 | 0.319988 | ||||||||
\(886\) | −69.3294 | −2.32917 | ||||||||
\(887\) | 32.7464 | 1.09952 | 0.549758 | − | 0.835324i | \(-0.314720\pi\) | ||||
0.549758 | + | 0.835324i | \(0.314720\pi\) | |||||||
\(888\) | −11.6661 | −0.391487 | ||||||||
\(889\) | 17.5952 | 0.590123 | ||||||||
\(890\) | −81.1180 | −2.71908 | ||||||||
\(891\) | 27.8499 | 0.933007 | ||||||||
\(892\) | 74.6581 | 2.49974 | ||||||||
\(893\) | 19.8492 | 0.664229 | ||||||||
\(894\) | −0.848853 | −0.0283899 | ||||||||
\(895\) | −36.6359 | −1.22460 | ||||||||
\(896\) | −59.0255 | −1.97190 | ||||||||
\(897\) | 1.01811 | 0.0339937 | ||||||||
\(898\) | −25.8442 | −0.862433 | ||||||||
\(899\) | 51.5674 | 1.71987 | ||||||||
\(900\) | 9.96679 | 0.332226 | ||||||||
\(901\) | 29.9476 | 0.997700 | ||||||||
\(902\) | −92.6930 | −3.08634 | ||||||||
\(903\) | −12.5194 | −0.416619 | ||||||||
\(904\) | −63.1596 | −2.10066 | ||||||||
\(905\) | −53.0428 | −1.76320 | ||||||||
\(906\) | 13.6426 | 0.453244 | ||||||||
\(907\) | 16.6782 | 0.553790 | 0.276895 | − | 0.960900i | \(-0.410695\pi\) | ||||
0.276895 | + | 0.960900i | \(0.410695\pi\) | |||||||
\(908\) | −93.9583 | −3.11812 | ||||||||
\(909\) | −17.4076 | −0.577375 | ||||||||
\(910\) | −13.7205 | −0.454830 | ||||||||
\(911\) | 50.3435 | 1.66796 | 0.833978 | − | 0.551798i | \(-0.186058\pi\) | ||||
0.833978 | + | 0.551798i | \(0.186058\pi\) | |||||||
\(912\) | −4.92547 | −0.163098 | ||||||||
\(913\) | 17.0958 | 0.565788 | ||||||||
\(914\) | −18.6940 | −0.618343 | ||||||||
\(915\) | 2.46091 | 0.0813551 | ||||||||
\(916\) | −44.4802 | −1.46967 | ||||||||
\(917\) | 49.2874 | 1.62761 | ||||||||
\(918\) | −40.4763 | −1.33592 | ||||||||
\(919\) | −24.6359 | −0.812665 | −0.406332 | − | 0.913725i | \(-0.633193\pi\) | ||||
−0.406332 | + | 0.913725i | \(0.633193\pi\) | |||||||
\(920\) | −18.2687 | −0.602302 | ||||||||
\(921\) | −1.65457 | −0.0545200 | ||||||||
\(922\) | 8.35523 | 0.275165 | ||||||||
\(923\) | 11.5021 | 0.378595 | ||||||||
\(924\) | 19.6164 | 0.645333 | ||||||||
\(925\) | 5.71971 | 0.188063 | ||||||||
\(926\) | 2.39631 | 0.0787477 | ||||||||
\(927\) | −14.5361 | −0.477427 | ||||||||
\(928\) | −23.1983 | −0.761523 | ||||||||
\(929\) | −7.41679 | −0.243337 | −0.121668 | − | 0.992571i | \(-0.538824\pi\) | ||||
−0.121668 | + | 0.992571i | \(0.538824\pi\) | |||||||
\(930\) | −11.5782 | −0.379663 | ||||||||
\(931\) | 4.63684 | 0.151966 | ||||||||
\(932\) | 104.012 | 3.40702 | ||||||||
\(933\) | 2.04594 | 0.0669809 | ||||||||
\(934\) | −43.3660 | −1.41898 | ||||||||
\(935\) | 49.4067 | 1.61577 | ||||||||
\(936\) | −11.6116 | −0.379537 | ||||||||
\(937\) | 41.4803 | 1.35510 | 0.677551 | − | 0.735476i | \(-0.263041\pi\) | ||||
0.677551 | + | 0.735476i | \(0.263041\pi\) | |||||||
\(938\) | 48.8056 | 1.59356 | ||||||||
\(939\) | −7.27151 | −0.237297 | ||||||||
\(940\) | 35.7496 | 1.16602 | ||||||||
\(941\) | 27.0010 | 0.880206 | 0.440103 | − | 0.897947i | \(-0.354942\pi\) | ||||
0.440103 | + | 0.897947i | \(0.354942\pi\) | |||||||
\(942\) | 23.5642 | 0.767762 | ||||||||
\(943\) | 21.3957 | 0.696741 | ||||||||
\(944\) | −25.5068 | −0.830175 | ||||||||
\(945\) | −15.4851 | −0.503732 | ||||||||
\(946\) | 88.6019 | 2.88070 | ||||||||
\(947\) | −3.25673 | −0.105829 | −0.0529147 | − | 0.998599i | \(-0.516851\pi\) | ||||
−0.0529147 | + | 0.998599i | \(0.516851\pi\) | |||||||
\(948\) | −3.73967 | −0.121459 | ||||||||
\(949\) | 13.4207 | 0.435656 | ||||||||
\(950\) | 9.58661 | 0.311031 | ||||||||
\(951\) | 4.44316 | 0.144079 | ||||||||
\(952\) | 74.2583 | 2.40673 | ||||||||
\(953\) | −33.9932 | −1.10115 | −0.550574 | − | 0.834786i | \(-0.685591\pi\) | ||||
−0.550574 | + | 0.834786i | \(0.685591\pi\) | |||||||
\(954\) | 31.9566 | 1.03463 | ||||||||
\(955\) | 9.03996 | 0.292526 | ||||||||
\(956\) | 58.5790 | 1.89458 | ||||||||
\(957\) | 18.4775 | 0.597293 | ||||||||
\(958\) | 24.6677 | 0.796978 | ||||||||
\(959\) | 40.0624 | 1.29368 | ||||||||
\(960\) | 9.94956 | 0.321121 | ||||||||
\(961\) | −4.61196 | −0.148773 | ||||||||
\(962\) | −14.3128 | −0.461464 | ||||||||
\(963\) | 18.7780 | 0.605113 | ||||||||
\(964\) | −47.3780 | −1.52594 | ||||||||
\(965\) | −4.40486 | −0.141797 | ||||||||
\(966\) | −6.94779 | −0.223541 | ||||||||
\(967\) | −47.6609 | −1.53267 | −0.766335 | − | 0.642441i | \(-0.777922\pi\) | ||||
−0.766335 | + | 0.642441i | \(0.777922\pi\) | |||||||
\(968\) | −18.7083 | −0.601308 | ||||||||
\(969\) | −12.2060 | −0.392113 | ||||||||
\(970\) | 1.83995 | 0.0590773 | ||||||||
\(971\) | −53.3486 | −1.71204 | −0.856018 | − | 0.516946i | \(-0.827069\pi\) | ||||
−0.856018 | + | 0.516946i | \(0.827069\pi\) | |||||||
\(972\) | −42.7552 | −1.37137 | ||||||||
\(973\) | 15.5122 | 0.497299 | ||||||||
\(974\) | 23.5418 | 0.754328 | ||||||||
\(975\) | −0.447987 | −0.0143471 | ||||||||
\(976\) | −6.59395 | −0.211067 | ||||||||
\(977\) | −21.0622 | −0.673840 | −0.336920 | − | 0.941533i | \(-0.609385\pi\) | ||||
−0.336920 | + | 0.941533i | \(0.609385\pi\) | |||||||
\(978\) | −9.89725 | −0.316479 | ||||||||
\(979\) | 66.2451 | 2.11720 | ||||||||
\(980\) | 8.35121 | 0.266770 | ||||||||
\(981\) | 4.90716 | 0.156674 | ||||||||
\(982\) | −9.69531 | −0.309390 | ||||||||
\(983\) | −33.6243 | −1.07245 | −0.536224 | − | 0.844076i | \(-0.680150\pi\) | ||||
−0.536224 | + | 0.844076i | \(0.680150\pi\) | |||||||
\(984\) | 19.2020 | 0.612138 | ||||||||
\(985\) | −36.6476 | −1.16769 | ||||||||
\(986\) | 150.239 | 4.78460 | ||||||||
\(987\) | 6.32987 | 0.201482 | ||||||||
\(988\) | −15.6340 | −0.497383 | ||||||||
\(989\) | −20.4514 | −0.650316 | ||||||||
\(990\) | 52.7211 | 1.67559 | ||||||||
\(991\) | 43.5186 | 1.38241 | 0.691207 | − | 0.722657i | \(-0.257079\pi\) | ||||
0.691207 | + | 0.722657i | \(0.257079\pi\) | |||||||
\(992\) | −11.8710 | −0.376906 | ||||||||
\(993\) | −6.69712 | −0.212527 | ||||||||
\(994\) | −78.4923 | −2.48963 | ||||||||
\(995\) | 24.8251 | 0.787010 | ||||||||
\(996\) | −7.60683 | −0.241032 | ||||||||
\(997\) | −47.2702 | −1.49706 | −0.748531 | − | 0.663100i | \(-0.769240\pi\) | ||||
−0.748531 | + | 0.663100i | \(0.769240\pi\) | |||||||
\(998\) | −19.7004 | −0.623605 | ||||||||
\(999\) | −16.1536 | −0.511078 |
(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 | 6019.2.a.c.1.11 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.11 | ✓ | 108 | 1.1 | even | 1 | trivial |