Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27621 | −1.60952 | −0.804760 | − | 0.593600i | \(-0.797706\pi\) | ||||
−0.804760 | + | 0.593600i | \(0.797706\pi\) | |||||||
\(3\) | −2.60153 | −1.50199 | −0.750996 | − | 0.660306i | \(-0.770426\pi\) | ||||
−0.750996 | + | 0.660306i | \(0.770426\pi\) | |||||||
\(4\) | 3.18111 | 1.59055 | ||||||||
\(5\) | 2.30412 | 1.03043 | 0.515216 | − | 0.857060i | \(-0.327712\pi\) | ||||
0.515216 | + | 0.857060i | \(0.327712\pi\) | |||||||
\(6\) | 5.92161 | 2.41749 | ||||||||
\(7\) | 1.78008 | 0.672808 | 0.336404 | − | 0.941718i | \(-0.390789\pi\) | ||||
0.336404 | + | 0.941718i | \(0.390789\pi\) | |||||||
\(8\) | −2.68845 | −0.950510 | ||||||||
\(9\) | 3.76795 | 1.25598 | ||||||||
\(10\) | −5.24464 | −1.65850 | ||||||||
\(11\) | 3.06113 | 0.922966 | 0.461483 | − | 0.887149i | \(-0.347317\pi\) | ||||
0.461483 | + | 0.887149i | \(0.347317\pi\) | |||||||
\(12\) | −8.27574 | −2.38900 | ||||||||
\(13\) | 2.16510 | 0.600492 | 0.300246 | − | 0.953862i | \(-0.402931\pi\) | ||||
0.300246 | + | 0.953862i | \(0.402931\pi\) | |||||||
\(14\) | −4.05183 | −1.08290 | ||||||||
\(15\) | −5.99422 | −1.54770 | ||||||||
\(16\) | −0.242762 | −0.0606906 | ||||||||
\(17\) | −2.52261 | −0.611823 | −0.305912 | − | 0.952060i | \(-0.598961\pi\) | ||||
−0.305912 | + | 0.952060i | \(0.598961\pi\) | |||||||
\(18\) | −8.57662 | −2.02153 | ||||||||
\(19\) | −3.18685 | −0.731114 | −0.365557 | − | 0.930789i | \(-0.619121\pi\) | ||||
−0.365557 | + | 0.930789i | \(0.619121\pi\) | |||||||
\(20\) | 7.32965 | 1.63896 | ||||||||
\(21\) | −4.63093 | −1.01055 | ||||||||
\(22\) | −6.96777 | −1.48553 | ||||||||
\(23\) | −4.94642 | −1.03140 | −0.515700 | − | 0.856769i | \(-0.672468\pi\) | ||||
−0.515700 | + | 0.856769i | \(0.672468\pi\) | |||||||
\(24\) | 6.99407 | 1.42766 | ||||||||
\(25\) | 0.308954 | 0.0617908 | ||||||||
\(26\) | −4.92822 | −0.966503 | ||||||||
\(27\) | −1.99784 | −0.384484 | ||||||||
\(28\) | 5.66263 | 1.07014 | ||||||||
\(29\) | 4.73582 | 0.879419 | 0.439710 | − | 0.898140i | \(-0.355081\pi\) | ||||
0.439710 | + | 0.898140i | \(0.355081\pi\) | |||||||
\(30\) | 13.6441 | 2.49106 | ||||||||
\(31\) | −4.47090 | −0.802998 | −0.401499 | − | 0.915860i | \(-0.631511\pi\) | ||||
−0.401499 | + | 0.915860i | \(0.631511\pi\) | |||||||
\(32\) | 5.92947 | 1.04819 | ||||||||
\(33\) | −7.96362 | −1.38629 | ||||||||
\(34\) | 5.74198 | 0.984742 | ||||||||
\(35\) | 4.10152 | 0.693283 | ||||||||
\(36\) | 11.9863 | 1.99771 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 7.25393 | 1.17674 | ||||||||
\(39\) | −5.63258 | −0.901934 | ||||||||
\(40\) | −6.19450 | −0.979436 | ||||||||
\(41\) | −7.23262 | −1.12955 | −0.564773 | − | 0.825246i | \(-0.691036\pi\) | ||||
−0.564773 | + | 0.825246i | \(0.691036\pi\) | |||||||
\(42\) | 10.5409 | 1.62650 | ||||||||
\(43\) | 11.0794 | 1.68959 | 0.844793 | − | 0.535093i | \(-0.179723\pi\) | ||||
0.844793 | + | 0.535093i | \(0.179723\pi\) | |||||||
\(44\) | 9.73780 | 1.46803 | ||||||||
\(45\) | 8.68179 | 1.29421 | ||||||||
\(46\) | 11.2591 | 1.66006 | ||||||||
\(47\) | 7.47598 | 1.09048 | 0.545242 | − | 0.838279i | \(-0.316438\pi\) | ||||
0.545242 | + | 0.838279i | \(0.316438\pi\) | |||||||
\(48\) | 0.631553 | 0.0911568 | ||||||||
\(49\) | −3.83131 | −0.547330 | ||||||||
\(50\) | −0.703243 | −0.0994535 | ||||||||
\(51\) | 6.56264 | 0.918954 | ||||||||
\(52\) | 6.88743 | 0.955115 | ||||||||
\(53\) | −4.10255 | −0.563528 | −0.281764 | − | 0.959484i | \(-0.590920\pi\) | ||||
−0.281764 | + | 0.959484i | \(0.590920\pi\) | |||||||
\(54\) | 4.54749 | 0.618835 | ||||||||
\(55\) | 7.05321 | 0.951054 | ||||||||
\(56\) | −4.78565 | −0.639510 | ||||||||
\(57\) | 8.29068 | 1.09813 | ||||||||
\(58\) | −10.7797 | −1.41544 | ||||||||
\(59\) | −2.91589 | −0.379616 | −0.189808 | − | 0.981821i | \(-0.560787\pi\) | ||||
−0.189808 | + | 0.981821i | \(0.560787\pi\) | |||||||
\(60\) | −19.0683 | −2.46170 | ||||||||
\(61\) | 5.95510 | 0.762473 | 0.381236 | − | 0.924478i | \(-0.375498\pi\) | ||||
0.381236 | + | 0.924478i | \(0.375498\pi\) | |||||||
\(62\) | 10.1767 | 1.29244 | ||||||||
\(63\) | 6.70725 | 0.845035 | ||||||||
\(64\) | −13.0112 | −1.62640 | ||||||||
\(65\) | 4.98865 | 0.618766 | ||||||||
\(66\) | 18.1268 | 2.23126 | ||||||||
\(67\) | 14.6837 | 1.79390 | 0.896952 | − | 0.442127i | \(-0.145776\pi\) | ||||
0.896952 | + | 0.442127i | \(0.145776\pi\) | |||||||
\(68\) | −8.02470 | −0.973138 | ||||||||
\(69\) | 12.8683 | 1.54916 | ||||||||
\(70\) | −9.33589 | −1.11585 | ||||||||
\(71\) | −2.66884 | −0.316733 | −0.158366 | − | 0.987380i | \(-0.550623\pi\) | ||||
−0.158366 | + | 0.987380i | \(0.550623\pi\) | |||||||
\(72\) | −10.1299 | −1.19382 | ||||||||
\(73\) | −6.69619 | −0.783729 | −0.391865 | − | 0.920023i | \(-0.628170\pi\) | ||||
−0.391865 | + | 0.920023i | \(0.628170\pi\) | |||||||
\(74\) | −2.27621 | −0.264603 | ||||||||
\(75\) | −0.803752 | −0.0928093 | ||||||||
\(76\) | −10.1377 | −1.16288 | ||||||||
\(77\) | 5.44907 | 0.620979 | ||||||||
\(78\) | 12.8209 | 1.45168 | ||||||||
\(79\) | 5.77436 | 0.649666 | 0.324833 | − | 0.945771i | \(-0.394692\pi\) | ||||
0.324833 | + | 0.945771i | \(0.394692\pi\) | |||||||
\(80\) | −0.559353 | −0.0625375 | ||||||||
\(81\) | −6.10641 | −0.678490 | ||||||||
\(82\) | 16.4629 | 1.81803 | ||||||||
\(83\) | 10.0472 | 1.10282 | 0.551411 | − | 0.834234i | \(-0.314090\pi\) | ||||
0.551411 | + | 0.834234i | \(0.314090\pi\) | |||||||
\(84\) | −14.7315 | −1.60734 | ||||||||
\(85\) | −5.81239 | −0.630442 | ||||||||
\(86\) | −25.2189 | −2.71942 | ||||||||
\(87\) | −12.3204 | −1.32088 | ||||||||
\(88\) | −8.22969 | −0.877288 | ||||||||
\(89\) | 11.7392 | 1.24436 | 0.622178 | − | 0.782876i | \(-0.286248\pi\) | ||||
0.622178 | + | 0.782876i | \(0.286248\pi\) | |||||||
\(90\) | −19.7615 | −2.08305 | ||||||||
\(91\) | 3.85406 | 0.404015 | ||||||||
\(92\) | −15.7351 | −1.64050 | ||||||||
\(93\) | 11.6312 | 1.20610 | ||||||||
\(94\) | −17.0169 | −1.75516 | ||||||||
\(95\) | −7.34288 | −0.753363 | ||||||||
\(96\) | −15.4257 | −1.57438 | ||||||||
\(97\) | 0.218286 | 0.0221635 | 0.0110818 | − | 0.999939i | \(-0.496472\pi\) | ||||
0.0110818 | + | 0.999939i | \(0.496472\pi\) | |||||||
\(98\) | 8.72085 | 0.880939 | ||||||||
\(99\) | 11.5342 | 1.15923 | ||||||||
\(100\) | 0.982816 | 0.0982816 | ||||||||
\(101\) | 1.67934 | 0.167100 | 0.0835502 | − | 0.996504i | \(-0.473374\pi\) | ||||
0.0835502 | + | 0.996504i | \(0.473374\pi\) | |||||||
\(102\) | −14.9379 | −1.47907 | ||||||||
\(103\) | 0.793145 | 0.0781509 | 0.0390754 | − | 0.999236i | \(-0.487559\pi\) | ||||
0.0390754 | + | 0.999236i | \(0.487559\pi\) | |||||||
\(104\) | −5.82077 | −0.570773 | ||||||||
\(105\) | −10.6702 | −1.04131 | ||||||||
\(106\) | 9.33824 | 0.907010 | ||||||||
\(107\) | 12.3414 | 1.19309 | 0.596545 | − | 0.802579i | \(-0.296540\pi\) | ||||
0.596545 | + | 0.802579i | \(0.296540\pi\) | |||||||
\(108\) | −6.35534 | −0.611543 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −16.0545 | −1.53074 | ||||||||
\(111\) | −2.60153 | −0.246926 | ||||||||
\(112\) | −0.432137 | −0.0408331 | ||||||||
\(113\) | −7.35071 | −0.691497 | −0.345749 | − | 0.938327i | \(-0.612375\pi\) | ||||
−0.345749 | + | 0.938327i | \(0.612375\pi\) | |||||||
\(114\) | −18.8713 | −1.76746 | ||||||||
\(115\) | −11.3971 | −1.06279 | ||||||||
\(116\) | 15.0652 | 1.39876 | ||||||||
\(117\) | 8.15800 | 0.754207 | ||||||||
\(118\) | 6.63715 | 0.611000 | ||||||||
\(119\) | −4.49045 | −0.411639 | ||||||||
\(120\) | 16.1152 | 1.47111 | ||||||||
\(121\) | −1.62947 | −0.148133 | ||||||||
\(122\) | −13.5550 | −1.22722 | ||||||||
\(123\) | 18.8159 | 1.69657 | ||||||||
\(124\) | −14.2224 | −1.27721 | ||||||||
\(125\) | −10.8087 | −0.966761 | ||||||||
\(126\) | −15.2671 | −1.36010 | ||||||||
\(127\) | 9.40888 | 0.834904 | 0.417452 | − | 0.908699i | \(-0.362923\pi\) | ||||
0.417452 | + | 0.908699i | \(0.362923\pi\) | |||||||
\(128\) | 17.7571 | 1.56952 | ||||||||
\(129\) | −28.8233 | −2.53775 | ||||||||
\(130\) | −11.3552 | −0.995916 | ||||||||
\(131\) | 13.4113 | 1.17175 | 0.585874 | − | 0.810402i | \(-0.300751\pi\) | ||||
0.585874 | + | 0.810402i | \(0.300751\pi\) | |||||||
\(132\) | −25.3332 | −2.20497 | ||||||||
\(133\) | −5.67285 | −0.491899 | ||||||||
\(134\) | −33.4232 | −2.88733 | ||||||||
\(135\) | −4.60325 | −0.396185 | ||||||||
\(136\) | 6.78191 | 0.581544 | ||||||||
\(137\) | 0.961966 | 0.0821863 | 0.0410931 | − | 0.999155i | \(-0.486916\pi\) | ||||
0.0410931 | + | 0.999155i | \(0.486916\pi\) | |||||||
\(138\) | −29.2908 | −2.49340 | ||||||||
\(139\) | −17.1814 | −1.45731 | −0.728653 | − | 0.684883i | \(-0.759853\pi\) | ||||
−0.728653 | + | 0.684883i | \(0.759853\pi\) | |||||||
\(140\) | 13.0474 | 1.10270 | ||||||||
\(141\) | −19.4490 | −1.63790 | ||||||||
\(142\) | 6.07482 | 0.509787 | ||||||||
\(143\) | 6.62767 | 0.554233 | ||||||||
\(144\) | −0.914716 | −0.0762263 | ||||||||
\(145\) | 10.9119 | 0.906182 | ||||||||
\(146\) | 15.2419 | 1.26143 | ||||||||
\(147\) | 9.96726 | 0.822086 | ||||||||
\(148\) | 3.18111 | 0.261486 | ||||||||
\(149\) | 6.61781 | 0.542152 | 0.271076 | − | 0.962558i | \(-0.412621\pi\) | ||||
0.271076 | + | 0.962558i | \(0.412621\pi\) | |||||||
\(150\) | 1.82951 | 0.149378 | ||||||||
\(151\) | −0.0342275 | −0.00278540 | −0.00139270 | − | 0.999999i | \(-0.500443\pi\) | ||||
−0.00139270 | + | 0.999999i | \(0.500443\pi\) | |||||||
\(152\) | 8.56768 | 0.694931 | ||||||||
\(153\) | −9.50507 | −0.768439 | ||||||||
\(154\) | −12.4032 | −0.999477 | ||||||||
\(155\) | −10.3015 | −0.827435 | ||||||||
\(156\) | −17.9178 | −1.43458 | ||||||||
\(157\) | 0.603937 | 0.0481994 | 0.0240997 | − | 0.999710i | \(-0.492328\pi\) | ||||
0.0240997 | + | 0.999710i | \(0.492328\pi\) | |||||||
\(158\) | −13.1436 | −1.04565 | ||||||||
\(159\) | 10.6729 | 0.846416 | ||||||||
\(160\) | 13.6622 | 1.08009 | ||||||||
\(161\) | −8.80504 | −0.693934 | ||||||||
\(162\) | 13.8994 | 1.09204 | ||||||||
\(163\) | −19.7366 | −1.54589 | −0.772943 | − | 0.634475i | \(-0.781216\pi\) | ||||
−0.772943 | + | 0.634475i | \(0.781216\pi\) | |||||||
\(164\) | −23.0078 | −1.79660 | ||||||||
\(165\) | −18.3491 | −1.42848 | ||||||||
\(166\) | −22.8695 | −1.77501 | ||||||||
\(167\) | 9.92336 | 0.767893 | 0.383946 | − | 0.923355i | \(-0.374565\pi\) | ||||
0.383946 | + | 0.923355i | \(0.374565\pi\) | |||||||
\(168\) | 12.4500 | 0.960539 | ||||||||
\(169\) | −8.31233 | −0.639410 | ||||||||
\(170\) | 13.2302 | 1.01471 | ||||||||
\(171\) | −12.0079 | −0.918266 | ||||||||
\(172\) | 35.2447 | 2.68738 | ||||||||
\(173\) | 22.0909 | 1.67954 | 0.839769 | − | 0.542943i | \(-0.182690\pi\) | ||||
0.839769 | + | 0.542943i | \(0.182690\pi\) | |||||||
\(174\) | 28.0437 | 2.12599 | ||||||||
\(175\) | 0.549963 | 0.0415733 | ||||||||
\(176\) | −0.743128 | −0.0560154 | ||||||||
\(177\) | 7.58576 | 0.570181 | ||||||||
\(178\) | −26.7209 | −2.00282 | ||||||||
\(179\) | 24.1558 | 1.80549 | 0.902746 | − | 0.430175i | \(-0.141548\pi\) | ||||
0.902746 | + | 0.430175i | \(0.141548\pi\) | |||||||
\(180\) | 27.6177 | 2.05850 | ||||||||
\(181\) | 12.9350 | 0.961452 | 0.480726 | − | 0.876871i | \(-0.340373\pi\) | ||||
0.480726 | + | 0.876871i | \(0.340373\pi\) | |||||||
\(182\) | −8.77263 | −0.650271 | ||||||||
\(183\) | −15.4924 | −1.14523 | ||||||||
\(184\) | 13.2982 | 0.980356 | ||||||||
\(185\) | 2.30412 | 0.169402 | ||||||||
\(186\) | −26.4749 | −1.94124 | ||||||||
\(187\) | −7.72205 | −0.564692 | ||||||||
\(188\) | 23.7819 | 1.73447 | ||||||||
\(189\) | −3.55631 | −0.258684 | ||||||||
\(190\) | 16.7139 | 1.21255 | ||||||||
\(191\) | −12.0463 | −0.871642 | −0.435821 | − | 0.900033i | \(-0.643542\pi\) | ||||
−0.435821 | + | 0.900033i | \(0.643542\pi\) | |||||||
\(192\) | 33.8489 | 2.44283 | ||||||||
\(193\) | −6.94115 | −0.499635 | −0.249817 | − | 0.968293i | \(-0.580371\pi\) | ||||
−0.249817 | + | 0.968293i | \(0.580371\pi\) | |||||||
\(194\) | −0.496863 | −0.0356727 | ||||||||
\(195\) | −12.9781 | −0.929382 | ||||||||
\(196\) | −12.1878 | −0.870558 | ||||||||
\(197\) | −9.13803 | −0.651058 | −0.325529 | − | 0.945532i | \(-0.605542\pi\) | ||||
−0.325529 | + | 0.945532i | \(0.605542\pi\) | |||||||
\(198\) | −26.2542 | −1.86580 | ||||||||
\(199\) | 1.17005 | 0.0829430 | 0.0414715 | − | 0.999140i | \(-0.486795\pi\) | ||||
0.0414715 | + | 0.999140i | \(0.486795\pi\) | |||||||
\(200\) | −0.830606 | −0.0587327 | ||||||||
\(201\) | −38.2002 | −2.69443 | ||||||||
\(202\) | −3.82252 | −0.268952 | ||||||||
\(203\) | 8.43014 | 0.591680 | ||||||||
\(204\) | 20.8765 | 1.46165 | ||||||||
\(205\) | −16.6648 | −1.16392 | ||||||||
\(206\) | −1.80536 | −0.125785 | ||||||||
\(207\) | −18.6379 | −1.29542 | ||||||||
\(208\) | −0.525606 | −0.0364442 | ||||||||
\(209\) | −9.75538 | −0.674793 | ||||||||
\(210\) | 24.2876 | 1.67600 | ||||||||
\(211\) | −9.49782 | −0.653857 | −0.326928 | − | 0.945049i | \(-0.606014\pi\) | ||||
−0.326928 | + | 0.945049i | \(0.606014\pi\) | |||||||
\(212\) | −13.0507 | −0.896323 | ||||||||
\(213\) | 6.94305 | 0.475730 | ||||||||
\(214\) | −28.0916 | −1.92030 | ||||||||
\(215\) | 25.5281 | 1.74100 | ||||||||
\(216\) | 5.37108 | 0.365456 | ||||||||
\(217\) | −7.95857 | −0.540263 | ||||||||
\(218\) | 2.27621 | 0.154164 | ||||||||
\(219\) | 17.4203 | 1.17716 | ||||||||
\(220\) | 22.4370 | 1.51270 | ||||||||
\(221\) | −5.46171 | −0.367395 | ||||||||
\(222\) | 5.92161 | 0.397433 | ||||||||
\(223\) | 6.74230 | 0.451498 | 0.225749 | − | 0.974186i | \(-0.427517\pi\) | ||||
0.225749 | + | 0.974186i | \(0.427517\pi\) | |||||||
\(224\) | 10.5549 | 0.705232 | ||||||||
\(225\) | 1.16412 | 0.0776082 | ||||||||
\(226\) | 16.7317 | 1.11298 | ||||||||
\(227\) | 6.33521 | 0.420483 | 0.210241 | − | 0.977650i | \(-0.432575\pi\) | ||||
0.210241 | + | 0.977650i | \(0.432575\pi\) | |||||||
\(228\) | 26.3736 | 1.74663 | ||||||||
\(229\) | −11.9262 | −0.788103 | −0.394051 | − | 0.919088i | \(-0.628927\pi\) | ||||
−0.394051 | + | 0.919088i | \(0.628927\pi\) | |||||||
\(230\) | 25.9422 | 1.71058 | ||||||||
\(231\) | −14.1759 | −0.932705 | ||||||||
\(232\) | −12.7320 | −0.835896 | ||||||||
\(233\) | 22.3073 | 1.46140 | 0.730700 | − | 0.682698i | \(-0.239194\pi\) | ||||
0.730700 | + | 0.682698i | \(0.239194\pi\) | |||||||
\(234\) | −18.5693 | −1.21391 | ||||||||
\(235\) | 17.2255 | 1.12367 | ||||||||
\(236\) | −9.27575 | −0.603800 | ||||||||
\(237\) | −15.0222 | −0.975794 | ||||||||
\(238\) | 10.2212 | 0.662541 | ||||||||
\(239\) | −26.4152 | −1.70866 | −0.854329 | − | 0.519732i | \(-0.826032\pi\) | ||||
−0.854329 | + | 0.519732i | \(0.826032\pi\) | |||||||
\(240\) | 1.45517 | 0.0939309 | ||||||||
\(241\) | 5.64714 | 0.363764 | 0.181882 | − | 0.983320i | \(-0.441781\pi\) | ||||
0.181882 | + | 0.983320i | \(0.441781\pi\) | |||||||
\(242\) | 3.70900 | 0.238424 | ||||||||
\(243\) | 21.8795 | 1.40357 | ||||||||
\(244\) | 18.9438 | 1.21275 | ||||||||
\(245\) | −8.82779 | −0.563987 | ||||||||
\(246\) | −42.8288 | −2.73066 | ||||||||
\(247\) | −6.89986 | −0.439028 | ||||||||
\(248\) | 12.0198 | 0.763257 | ||||||||
\(249\) | −26.1380 | −1.65643 | ||||||||
\(250\) | 24.6029 | 1.55602 | ||||||||
\(251\) | 13.8354 | 0.873285 | 0.436642 | − | 0.899635i | \(-0.356168\pi\) | ||||
0.436642 | + | 0.899635i | \(0.356168\pi\) | |||||||
\(252\) | 21.3365 | 1.34407 | ||||||||
\(253\) | −15.1417 | −0.951948 | ||||||||
\(254\) | −21.4166 | −1.34379 | ||||||||
\(255\) | 15.1211 | 0.946920 | ||||||||
\(256\) | −14.3966 | −0.899785 | ||||||||
\(257\) | 23.9869 | 1.49626 | 0.748132 | − | 0.663550i | \(-0.230951\pi\) | ||||
0.748132 | + | 0.663550i | \(0.230951\pi\) | |||||||
\(258\) | 65.6077 | 4.08455 | ||||||||
\(259\) | 1.78008 | 0.110609 | ||||||||
\(260\) | 15.8694 | 0.984181 | ||||||||
\(261\) | 17.8443 | 1.10454 | ||||||||
\(262\) | −30.5268 | −1.88595 | ||||||||
\(263\) | 7.12389 | 0.439278 | 0.219639 | − | 0.975581i | \(-0.429512\pi\) | ||||
0.219639 | + | 0.975581i | \(0.429512\pi\) | |||||||
\(264\) | 21.4098 | 1.31768 | ||||||||
\(265\) | −9.45275 | −0.580678 | ||||||||
\(266\) | 12.9126 | 0.791721 | ||||||||
\(267\) | −30.5399 | −1.86901 | ||||||||
\(268\) | 46.7106 | 2.85330 | ||||||||
\(269\) | −3.57039 | −0.217691 | −0.108845 | − | 0.994059i | \(-0.534715\pi\) | ||||
−0.108845 | + | 0.994059i | \(0.534715\pi\) | |||||||
\(270\) | 10.4779 | 0.637668 | ||||||||
\(271\) | 14.5470 | 0.883669 | 0.441835 | − | 0.897097i | \(-0.354328\pi\) | ||||
0.441835 | + | 0.897097i | \(0.354328\pi\) | |||||||
\(272\) | 0.612395 | 0.0371319 | ||||||||
\(273\) | −10.0264 | −0.606828 | ||||||||
\(274\) | −2.18963 | −0.132280 | ||||||||
\(275\) | 0.945749 | 0.0570308 | ||||||||
\(276\) | 40.9353 | 2.46402 | ||||||||
\(277\) | −6.75810 | −0.406055 | −0.203027 | − | 0.979173i | \(-0.565078\pi\) | ||||
−0.203027 | + | 0.979173i | \(0.565078\pi\) | |||||||
\(278\) | 39.1083 | 2.34556 | ||||||||
\(279\) | −16.8461 | −1.00855 | ||||||||
\(280\) | −11.0267 | −0.658972 | ||||||||
\(281\) | 15.7938 | 0.942180 | 0.471090 | − | 0.882085i | \(-0.343861\pi\) | ||||
0.471090 | + | 0.882085i | \(0.343861\pi\) | |||||||
\(282\) | 44.2699 | 2.63623 | ||||||||
\(283\) | 3.42122 | 0.203371 | 0.101685 | − | 0.994817i | \(-0.467577\pi\) | ||||
0.101685 | + | 0.994817i | \(0.467577\pi\) | |||||||
\(284\) | −8.48986 | −0.503780 | ||||||||
\(285\) | 19.1027 | 1.13155 | ||||||||
\(286\) | −15.0859 | −0.892050 | ||||||||
\(287\) | −12.8747 | −0.759967 | ||||||||
\(288\) | 22.3419 | 1.31651 | ||||||||
\(289\) | −10.6364 | −0.625672 | ||||||||
\(290\) | −24.8377 | −1.45852 | ||||||||
\(291\) | −0.567876 | −0.0332895 | ||||||||
\(292\) | −21.3013 | −1.24656 | ||||||||
\(293\) | 21.3139 | 1.24517 | 0.622587 | − | 0.782551i | \(-0.286082\pi\) | ||||
0.622587 | + | 0.782551i | \(0.286082\pi\) | |||||||
\(294\) | −22.6875 | −1.32316 | ||||||||
\(295\) | −6.71854 | −0.391169 | ||||||||
\(296\) | −2.68845 | −0.156263 | ||||||||
\(297\) | −6.11565 | −0.354866 | ||||||||
\(298\) | −15.0635 | −0.872604 | ||||||||
\(299\) | −10.7095 | −0.619347 | ||||||||
\(300\) | −2.55682 | −0.147618 | ||||||||
\(301\) | 19.7222 | 1.13677 | ||||||||
\(302\) | 0.0779089 | 0.00448315 | ||||||||
\(303\) | −4.36885 | −0.250984 | ||||||||
\(304\) | 0.773647 | 0.0443717 | ||||||||
\(305\) | 13.7213 | 0.785677 | ||||||||
\(306\) | 21.6355 | 1.23682 | ||||||||
\(307\) | 13.2408 | 0.755691 | 0.377845 | − | 0.925869i | \(-0.376665\pi\) | ||||
0.377845 | + | 0.925869i | \(0.376665\pi\) | |||||||
\(308\) | 17.3341 | 0.987700 | ||||||||
\(309\) | −2.06339 | −0.117382 | ||||||||
\(310\) | 23.4483 | 1.33177 | ||||||||
\(311\) | −14.1311 | −0.801299 | −0.400649 | − | 0.916232i | \(-0.631215\pi\) | ||||
−0.400649 | + | 0.916232i | \(0.631215\pi\) | |||||||
\(312\) | 15.1429 | 0.857297 | ||||||||
\(313\) | −15.4827 | −0.875132 | −0.437566 | − | 0.899186i | \(-0.644159\pi\) | ||||
−0.437566 | + | 0.899186i | \(0.644159\pi\) | |||||||
\(314\) | −1.37468 | −0.0775779 | ||||||||
\(315\) | 15.4543 | 0.870751 | ||||||||
\(316\) | 18.3689 | 1.03333 | ||||||||
\(317\) | −21.1989 | −1.19065 | −0.595325 | − | 0.803485i | \(-0.702977\pi\) | ||||
−0.595325 | + | 0.803485i | \(0.702977\pi\) | |||||||
\(318\) | −24.2937 | −1.36232 | ||||||||
\(319\) | 14.4970 | 0.811674 | ||||||||
\(320\) | −29.9792 | −1.67589 | ||||||||
\(321\) | −32.1066 | −1.79201 | ||||||||
\(322\) | 20.0421 | 1.11690 | ||||||||
\(323\) | 8.03919 | 0.447312 | ||||||||
\(324\) | −19.4252 | −1.07918 | ||||||||
\(325\) | 0.668917 | 0.0371049 | ||||||||
\(326\) | 44.9245 | 2.48814 | ||||||||
\(327\) | 2.60153 | 0.143865 | ||||||||
\(328\) | 19.4445 | 1.07364 | ||||||||
\(329\) | 13.3079 | 0.733686 | ||||||||
\(330\) | 41.7663 | 2.29916 | ||||||||
\(331\) | 8.52828 | 0.468757 | 0.234378 | − | 0.972145i | \(-0.424695\pi\) | ||||
0.234378 | + | 0.972145i | \(0.424695\pi\) | |||||||
\(332\) | 31.9612 | 1.75410 | ||||||||
\(333\) | 3.76795 | 0.206482 | ||||||||
\(334\) | −22.5876 | −1.23594 | ||||||||
\(335\) | 33.8331 | 1.84850 | ||||||||
\(336\) | 1.12422 | 0.0613310 | ||||||||
\(337\) | −26.3753 | −1.43675 | −0.718377 | − | 0.695654i | \(-0.755115\pi\) | ||||
−0.718377 | + | 0.695654i | \(0.755115\pi\) | |||||||
\(338\) | 18.9206 | 1.02914 | ||||||||
\(339\) | 19.1231 | 1.03862 | ||||||||
\(340\) | −18.4899 | −1.00275 | ||||||||
\(341\) | −13.6860 | −0.741140 | ||||||||
\(342\) | 27.3324 | 1.47797 | ||||||||
\(343\) | −19.2806 | −1.04106 | ||||||||
\(344\) | −29.7863 | −1.60597 | ||||||||
\(345\) | 29.6500 | 1.59630 | ||||||||
\(346\) | −50.2834 | −2.70325 | ||||||||
\(347\) | −1.09619 | −0.0588468 | −0.0294234 | − | 0.999567i | \(-0.509367\pi\) | ||||
−0.0294234 | + | 0.999567i | \(0.509367\pi\) | |||||||
\(348\) | −39.1924 | −2.10093 | ||||||||
\(349\) | 33.8074 | 1.80967 | 0.904835 | − | 0.425761i | \(-0.139994\pi\) | ||||
0.904835 | + | 0.425761i | \(0.139994\pi\) | |||||||
\(350\) | −1.25183 | −0.0669131 | ||||||||
\(351\) | −4.32553 | −0.230880 | ||||||||
\(352\) | 18.1509 | 0.967446 | ||||||||
\(353\) | −8.07857 | −0.429979 | −0.214990 | − | 0.976616i | \(-0.568972\pi\) | ||||
−0.214990 | + | 0.976616i | \(0.568972\pi\) | |||||||
\(354\) | −17.2667 | −0.917717 | ||||||||
\(355\) | −6.14931 | −0.326371 | ||||||||
\(356\) | 37.3438 | 1.97922 | ||||||||
\(357\) | 11.6820 | 0.618279 | ||||||||
\(358\) | −54.9836 | −2.90597 | ||||||||
\(359\) | 21.8228 | 1.15177 | 0.575883 | − | 0.817532i | \(-0.304659\pi\) | ||||
0.575883 | + | 0.817532i | \(0.304659\pi\) | |||||||
\(360\) | −23.3405 | −1.23015 | ||||||||
\(361\) | −8.84398 | −0.465473 | ||||||||
\(362\) | −29.4427 | −1.54748 | ||||||||
\(363\) | 4.23910 | 0.222495 | ||||||||
\(364\) | 12.2602 | 0.642608 | ||||||||
\(365\) | −15.4288 | −0.807580 | ||||||||
\(366\) | 35.2638 | 1.84327 | ||||||||
\(367\) | 27.7672 | 1.44944 | 0.724719 | − | 0.689044i | \(-0.241969\pi\) | ||||
0.724719 | + | 0.689044i | \(0.241969\pi\) | |||||||
\(368\) | 1.20081 | 0.0625963 | ||||||||
\(369\) | −27.2521 | −1.41869 | ||||||||
\(370\) | −5.24464 | −0.272656 | ||||||||
\(371\) | −7.30287 | −0.379146 | ||||||||
\(372\) | 37.0000 | 1.91836 | ||||||||
\(373\) | 16.1304 | 0.835200 | 0.417600 | − | 0.908631i | \(-0.362871\pi\) | ||||
0.417600 | + | 0.908631i | \(0.362871\pi\) | |||||||
\(374\) | 17.5770 | 0.908883 | ||||||||
\(375\) | 28.1192 | 1.45207 | ||||||||
\(376\) | −20.0988 | −1.03652 | ||||||||
\(377\) | 10.2535 | 0.528084 | ||||||||
\(378\) | 8.09490 | 0.416357 | ||||||||
\(379\) | 27.0434 | 1.38913 | 0.694563 | − | 0.719432i | \(-0.255598\pi\) | ||||
0.694563 | + | 0.719432i | \(0.255598\pi\) | |||||||
\(380\) | −23.3585 | −1.19827 | ||||||||
\(381\) | −24.4775 | −1.25402 | ||||||||
\(382\) | 27.4199 | 1.40293 | ||||||||
\(383\) | 28.9379 | 1.47866 | 0.739328 | − | 0.673345i | \(-0.235143\pi\) | ||||
0.739328 | + | 0.673345i | \(0.235143\pi\) | |||||||
\(384\) | −46.1957 | −2.35741 | ||||||||
\(385\) | 12.5553 | 0.639876 | ||||||||
\(386\) | 15.7995 | 0.804172 | ||||||||
\(387\) | 41.7464 | 2.12209 | ||||||||
\(388\) | 0.694390 | 0.0352523 | ||||||||
\(389\) | 26.0718 | 1.32189 | 0.660946 | − | 0.750433i | \(-0.270155\pi\) | ||||
0.660946 | + | 0.750433i | \(0.270155\pi\) | |||||||
\(390\) | 29.5409 | 1.49586 | ||||||||
\(391\) | 12.4779 | 0.631035 | ||||||||
\(392\) | 10.3003 | 0.520242 | ||||||||
\(393\) | −34.8898 | −1.75996 | ||||||||
\(394\) | 20.8000 | 1.04789 | ||||||||
\(395\) | 13.3048 | 0.669437 | ||||||||
\(396\) | 36.6915 | 1.84382 | ||||||||
\(397\) | −5.57264 | −0.279683 | −0.139841 | − | 0.990174i | \(-0.544659\pi\) | ||||
−0.139841 | + | 0.990174i | \(0.544659\pi\) | |||||||
\(398\) | −2.66328 | −0.133498 | ||||||||
\(399\) | 14.7581 | 0.738829 | ||||||||
\(400\) | −0.0750024 | −0.00375012 | ||||||||
\(401\) | −7.45875 | −0.372472 | −0.186236 | − | 0.982505i | \(-0.559629\pi\) | ||||
−0.186236 | + | 0.982505i | \(0.559629\pi\) | |||||||
\(402\) | 86.9514 | 4.33674 | ||||||||
\(403\) | −9.67997 | −0.482193 | ||||||||
\(404\) | 5.34216 | 0.265782 | ||||||||
\(405\) | −14.0699 | −0.699138 | ||||||||
\(406\) | −19.1887 | −0.952321 | ||||||||
\(407\) | 3.06113 | 0.151735 | ||||||||
\(408\) | −17.6433 | −0.873474 | ||||||||
\(409\) | −26.7456 | −1.32248 | −0.661242 | − | 0.750173i | \(-0.729970\pi\) | ||||
−0.661242 | + | 0.750173i | \(0.729970\pi\) | |||||||
\(410\) | 37.9325 | 1.87335 | ||||||||
\(411\) | −2.50258 | −0.123443 | ||||||||
\(412\) | 2.52308 | 0.124303 | ||||||||
\(413\) | −5.19051 | −0.255408 | ||||||||
\(414\) | 42.4236 | 2.08501 | ||||||||
\(415\) | 23.1499 | 1.13638 | ||||||||
\(416\) | 12.8379 | 0.629431 | ||||||||
\(417\) | 44.6978 | 2.18886 | ||||||||
\(418\) | 22.2052 | 1.08609 | ||||||||
\(419\) | −20.2407 | −0.988824 | −0.494412 | − | 0.869228i | \(-0.664617\pi\) | ||||
−0.494412 | + | 0.869228i | \(0.664617\pi\) | |||||||
\(420\) | −33.9431 | −1.65625 | ||||||||
\(421\) | 12.8898 | 0.628210 | 0.314105 | − | 0.949388i | \(-0.398296\pi\) | ||||
0.314105 | + | 0.949388i | \(0.398296\pi\) | |||||||
\(422\) | 21.6190 | 1.05240 | ||||||||
\(423\) | 28.1691 | 1.36963 | ||||||||
\(424\) | 11.0295 | 0.535639 | ||||||||
\(425\) | −0.779371 | −0.0378050 | ||||||||
\(426\) | −15.8038 | −0.765697 | ||||||||
\(427\) | 10.6006 | 0.512997 | ||||||||
\(428\) | 39.2594 | 1.89768 | ||||||||
\(429\) | −17.2421 | −0.832455 | ||||||||
\(430\) | −58.1073 | −2.80218 | ||||||||
\(431\) | −19.9228 | −0.959647 | −0.479824 | − | 0.877365i | \(-0.659299\pi\) | ||||
−0.479824 | + | 0.877365i | \(0.659299\pi\) | |||||||
\(432\) | 0.485000 | 0.0233346 | ||||||||
\(433\) | 32.8998 | 1.58106 | 0.790532 | − | 0.612420i | \(-0.209804\pi\) | ||||
0.790532 | + | 0.612420i | \(0.209804\pi\) | |||||||
\(434\) | 18.1153 | 0.869564 | ||||||||
\(435\) | −28.3876 | −1.36108 | ||||||||
\(436\) | −3.18111 | −0.152348 | ||||||||
\(437\) | 15.7635 | 0.754071 | ||||||||
\(438\) | −39.6522 | −1.89466 | ||||||||
\(439\) | −0.709157 | −0.0338462 | −0.0169231 | − | 0.999857i | \(-0.505387\pi\) | ||||
−0.0169231 | + | 0.999857i | \(0.505387\pi\) | |||||||
\(440\) | −18.9622 | −0.903986 | ||||||||
\(441\) | −14.4362 | −0.687437 | ||||||||
\(442\) | 12.4320 | 0.591329 | ||||||||
\(443\) | 13.9415 | 0.662379 | 0.331189 | − | 0.943564i | \(-0.392550\pi\) | ||||
0.331189 | + | 0.943564i | \(0.392550\pi\) | |||||||
\(444\) | −8.27574 | −0.392749 | ||||||||
\(445\) | 27.0485 | 1.28222 | ||||||||
\(446\) | −15.3469 | −0.726695 | ||||||||
\(447\) | −17.2164 | −0.814308 | ||||||||
\(448\) | −23.1609 | −1.09425 | ||||||||
\(449\) | 7.39625 | 0.349051 | 0.174525 | − | 0.984653i | \(-0.444161\pi\) | ||||
0.174525 | + | 0.984653i | \(0.444161\pi\) | |||||||
\(450\) | −2.64978 | −0.124912 | ||||||||
\(451\) | −22.1400 | −1.04253 | ||||||||
\(452\) | −23.3834 | −1.09986 | ||||||||
\(453\) | 0.0890439 | 0.00418365 | ||||||||
\(454\) | −14.4202 | −0.676776 | ||||||||
\(455\) | 8.88020 | 0.416310 | ||||||||
\(456\) | −22.2891 | −1.04378 | ||||||||
\(457\) | −21.2702 | −0.994976 | −0.497488 | − | 0.867471i | \(-0.665744\pi\) | ||||
−0.497488 | + | 0.867471i | \(0.665744\pi\) | |||||||
\(458\) | 27.1464 | 1.26847 | ||||||||
\(459\) | 5.03977 | 0.235236 | ||||||||
\(460\) | −36.2555 | −1.69042 | ||||||||
\(461\) | −4.36175 | −0.203147 | −0.101573 | − | 0.994828i | \(-0.532388\pi\) | ||||
−0.101573 | + | 0.994828i | \(0.532388\pi\) | |||||||
\(462\) | 32.2672 | 1.50121 | ||||||||
\(463\) | −23.2399 | −1.08005 | −0.540026 | − | 0.841649i | \(-0.681585\pi\) | ||||
−0.540026 | + | 0.841649i | \(0.681585\pi\) | |||||||
\(464\) | −1.14968 | −0.0533725 | ||||||||
\(465\) | 26.7996 | 1.24280 | ||||||||
\(466\) | −50.7760 | −2.35215 | ||||||||
\(467\) | 37.6605 | 1.74272 | 0.871360 | − | 0.490645i | \(-0.163239\pi\) | ||||
0.871360 | + | 0.490645i | \(0.163239\pi\) | |||||||
\(468\) | 25.9515 | 1.19961 | ||||||||
\(469\) | 26.1383 | 1.20695 | ||||||||
\(470\) | −39.2089 | −1.80857 | ||||||||
\(471\) | −1.57116 | −0.0723951 | ||||||||
\(472\) | 7.83920 | 0.360829 | ||||||||
\(473\) | 33.9154 | 1.55943 | ||||||||
\(474\) | 34.1935 | 1.57056 | ||||||||
\(475\) | −0.984590 | −0.0451761 | ||||||||
\(476\) | −14.2846 | −0.654735 | ||||||||
\(477\) | −15.4582 | −0.707782 | ||||||||
\(478\) | 60.1265 | 2.75012 | ||||||||
\(479\) | 18.8384 | 0.860749 | 0.430374 | − | 0.902651i | \(-0.358382\pi\) | ||||
0.430374 | + | 0.902651i | \(0.358382\pi\) | |||||||
\(480\) | −35.5426 | −1.62229 | ||||||||
\(481\) | 2.16510 | 0.0987202 | ||||||||
\(482\) | −12.8540 | −0.585485 | ||||||||
\(483\) | 22.9065 | 1.04228 | ||||||||
\(484\) | −5.18351 | −0.235614 | ||||||||
\(485\) | 0.502956 | 0.0228380 | ||||||||
\(486\) | −49.8023 | −2.25908 | ||||||||
\(487\) | −10.3555 | −0.469251 | −0.234625 | − | 0.972086i | \(-0.575386\pi\) | ||||
−0.234625 | + | 0.972086i | \(0.575386\pi\) | |||||||
\(488\) | −16.0100 | −0.724738 | ||||||||
\(489\) | 51.3452 | 2.32191 | ||||||||
\(490\) | 20.0939 | 0.907748 | ||||||||
\(491\) | 41.7718 | 1.88514 | 0.942568 | − | 0.334013i | \(-0.108403\pi\) | ||||
0.942568 | + | 0.334013i | \(0.108403\pi\) | |||||||
\(492\) | 59.8553 | 2.69849 | ||||||||
\(493\) | −11.9466 | −0.538049 | ||||||||
\(494\) | 15.7055 | 0.706624 | ||||||||
\(495\) | 26.5761 | 1.19451 | ||||||||
\(496\) | 1.08537 | 0.0487344 | ||||||||
\(497\) | −4.75074 | −0.213100 | ||||||||
\(498\) | 59.4955 | 2.66606 | ||||||||
\(499\) | 11.4619 | 0.513106 | 0.256553 | − | 0.966530i | \(-0.417413\pi\) | ||||
0.256553 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(500\) | −34.3837 | −1.53769 | ||||||||
\(501\) | −25.8159 | −1.15337 | ||||||||
\(502\) | −31.4923 | −1.40557 | ||||||||
\(503\) | 0.661678 | 0.0295028 | 0.0147514 | − | 0.999891i | \(-0.495304\pi\) | ||||
0.0147514 | + | 0.999891i | \(0.495304\pi\) | |||||||
\(504\) | −18.0321 | −0.803213 | ||||||||
\(505\) | 3.86939 | 0.172186 | ||||||||
\(506\) | 34.4655 | 1.53218 | ||||||||
\(507\) | 21.6248 | 0.960389 | ||||||||
\(508\) | 29.9307 | 1.32796 | ||||||||
\(509\) | 4.60859 | 0.204272 | 0.102136 | − | 0.994770i | \(-0.467432\pi\) | ||||
0.102136 | + | 0.994770i | \(0.467432\pi\) | |||||||
\(510\) | −34.4187 | −1.52409 | ||||||||
\(511\) | −11.9198 | −0.527299 | ||||||||
\(512\) | −2.74476 | −0.121302 | ||||||||
\(513\) | 6.36681 | 0.281102 | ||||||||
\(514\) | −54.5992 | −2.40827 | ||||||||
\(515\) | 1.82750 | 0.0805292 | ||||||||
\(516\) | −91.6899 | −4.03642 | ||||||||
\(517\) | 22.8850 | 1.00648 | ||||||||
\(518\) | −4.05183 | −0.178027 | ||||||||
\(519\) | −57.4701 | −2.52266 | ||||||||
\(520\) | −13.4117 | −0.588143 | ||||||||
\(521\) | −27.7391 | −1.21527 | −0.607636 | − | 0.794216i | \(-0.707882\pi\) | ||||
−0.607636 | + | 0.794216i | \(0.707882\pi\) | |||||||
\(522\) | −40.6173 | −1.77777 | ||||||||
\(523\) | 19.4634 | 0.851074 | 0.425537 | − | 0.904941i | \(-0.360085\pi\) | ||||
0.425537 | + | 0.904941i | \(0.360085\pi\) | |||||||
\(524\) | 42.6627 | 1.86373 | ||||||||
\(525\) | −1.43074 | −0.0624428 | ||||||||
\(526\) | −16.2154 | −0.707027 | ||||||||
\(527\) | 11.2783 | 0.491293 | ||||||||
\(528\) | 1.93327 | 0.0841347 | ||||||||
\(529\) | 1.46710 | 0.0637870 | ||||||||
\(530\) | 21.5164 | 0.934613 | ||||||||
\(531\) | −10.9869 | −0.476791 | ||||||||
\(532\) | −18.0460 | −0.782392 | ||||||||
\(533\) | −15.6594 | −0.678283 | ||||||||
\(534\) | 69.5151 | 3.00821 | ||||||||
\(535\) | 28.4361 | 1.22940 | ||||||||
\(536\) | −39.4765 | −1.70512 | ||||||||
\(537\) | −62.8421 | −2.71184 | ||||||||
\(538\) | 8.12695 | 0.350378 | ||||||||
\(539\) | −11.7281 | −0.505167 | ||||||||
\(540\) | −14.6434 | −0.630154 | ||||||||
\(541\) | −42.4407 | −1.82467 | −0.912333 | − | 0.409448i | \(-0.865721\pi\) | ||||
−0.912333 | + | 0.409448i | \(0.865721\pi\) | |||||||
\(542\) | −33.1120 | −1.42228 | ||||||||
\(543\) | −33.6508 | −1.44409 | ||||||||
\(544\) | −14.9577 | −0.641308 | ||||||||
\(545\) | −2.30412 | −0.0986975 | ||||||||
\(546\) | 22.8222 | 0.976702 | ||||||||
\(547\) | −2.03806 | −0.0871410 | −0.0435705 | − | 0.999050i | \(-0.513873\pi\) | ||||
−0.0435705 | + | 0.999050i | \(0.513873\pi\) | |||||||
\(548\) | 3.06012 | 0.130722 | ||||||||
\(549\) | 22.4385 | 0.957653 | ||||||||
\(550\) | −2.15272 | −0.0917922 | ||||||||
\(551\) | −15.0923 | −0.642956 | ||||||||
\(552\) | −34.5956 | −1.47249 | ||||||||
\(553\) | 10.2788 | 0.437100 | ||||||||
\(554\) | 15.3828 | 0.653553 | ||||||||
\(555\) | −5.99422 | −0.254441 | ||||||||
\(556\) | −54.6559 | −2.31792 | ||||||||
\(557\) | −28.6139 | −1.21241 | −0.606204 | − | 0.795309i | \(-0.707309\pi\) | ||||
−0.606204 | + | 0.795309i | \(0.707309\pi\) | |||||||
\(558\) | 38.3452 | 1.62328 | ||||||||
\(559\) | 23.9880 | 1.01458 | ||||||||
\(560\) | −0.995693 | −0.0420757 | ||||||||
\(561\) | 20.0891 | 0.848163 | ||||||||
\(562\) | −35.9500 | −1.51646 | ||||||||
\(563\) | −9.54571 | −0.402304 | −0.201152 | − | 0.979560i | \(-0.564468\pi\) | ||||
−0.201152 | + | 0.979560i | \(0.564468\pi\) | |||||||
\(564\) | −61.8693 | −2.60517 | ||||||||
\(565\) | −16.9369 | −0.712541 | ||||||||
\(566\) | −7.78741 | −0.327329 | ||||||||
\(567\) | −10.8699 | −0.456493 | ||||||||
\(568\) | 7.17502 | 0.301057 | ||||||||
\(569\) | 39.3428 | 1.64933 | 0.824667 | − | 0.565618i | \(-0.191362\pi\) | ||||
0.824667 | + | 0.565618i | \(0.191362\pi\) | |||||||
\(570\) | −43.4817 | −1.82125 | ||||||||
\(571\) | −4.95288 | −0.207272 | −0.103636 | − | 0.994615i | \(-0.533048\pi\) | ||||
−0.103636 | + | 0.994615i | \(0.533048\pi\) | |||||||
\(572\) | 21.0833 | 0.881539 | ||||||||
\(573\) | 31.3389 | 1.30920 | ||||||||
\(574\) | 29.3054 | 1.22318 | ||||||||
\(575\) | −1.52822 | −0.0637311 | ||||||||
\(576\) | −49.0254 | −2.04272 | ||||||||
\(577\) | −7.41897 | −0.308856 | −0.154428 | − | 0.988004i | \(-0.549353\pi\) | ||||
−0.154428 | + | 0.988004i | \(0.549353\pi\) | |||||||
\(578\) | 24.2107 | 1.00703 | ||||||||
\(579\) | 18.0576 | 0.750448 | ||||||||
\(580\) | 34.7119 | 1.44133 | ||||||||
\(581\) | 17.8848 | 0.741987 | ||||||||
\(582\) | 1.29260 | 0.0535801 | ||||||||
\(583\) | −12.5584 | −0.520118 | ||||||||
\(584\) | 18.0023 | 0.744942 | ||||||||
\(585\) | 18.7970 | 0.777159 | ||||||||
\(586\) | −48.5149 | −2.00413 | ||||||||
\(587\) | −25.6191 | −1.05741 | −0.528707 | − | 0.848805i | \(-0.677323\pi\) | ||||
−0.528707 | + | 0.848805i | \(0.677323\pi\) | |||||||
\(588\) | 31.7069 | 1.30757 | ||||||||
\(589\) | 14.2481 | 0.587083 | ||||||||
\(590\) | 15.2928 | 0.629594 | ||||||||
\(591\) | 23.7728 | 0.977884 | ||||||||
\(592\) | −0.242762 | −0.00997747 | ||||||||
\(593\) | 7.74015 | 0.317850 | 0.158925 | − | 0.987291i | \(-0.449197\pi\) | ||||
0.158925 | + | 0.987291i | \(0.449197\pi\) | |||||||
\(594\) | 13.9205 | 0.571164 | ||||||||
\(595\) | −10.3465 | −0.424166 | ||||||||
\(596\) | 21.0520 | 0.862322 | ||||||||
\(597\) | −3.04393 | −0.124580 | ||||||||
\(598\) | 24.3771 | 0.996852 | ||||||||
\(599\) | −19.4907 | −0.796367 | −0.398184 | − | 0.917306i | \(-0.630359\pi\) | ||||
−0.398184 | + | 0.917306i | \(0.630359\pi\) | |||||||
\(600\) | 2.16085 | 0.0882162 | ||||||||
\(601\) | 21.3851 | 0.872318 | 0.436159 | − | 0.899870i | \(-0.356339\pi\) | ||||
0.436159 | + | 0.899870i | \(0.356339\pi\) | |||||||
\(602\) | −44.8917 | −1.82965 | ||||||||
\(603\) | 55.3276 | 2.25311 | ||||||||
\(604\) | −0.108882 | −0.00443033 | ||||||||
\(605\) | −3.75448 | −0.152641 | ||||||||
\(606\) | 9.94439 | 0.403963 | ||||||||
\(607\) | −31.6412 | −1.28428 | −0.642138 | − | 0.766589i | \(-0.721953\pi\) | ||||
−0.642138 | + | 0.766589i | \(0.721953\pi\) | |||||||
\(608\) | −18.8963 | −0.766348 | ||||||||
\(609\) | −21.9312 | −0.888699 | ||||||||
\(610\) | −31.2324 | −1.26456 | ||||||||
\(611\) | 16.1863 | 0.654827 | ||||||||
\(612\) | −30.2367 | −1.22224 | ||||||||
\(613\) | 12.4421 | 0.502531 | 0.251265 | − | 0.967918i | \(-0.419153\pi\) | ||||
0.251265 | + | 0.967918i | \(0.419153\pi\) | |||||||
\(614\) | −30.1387 | −1.21630 | ||||||||
\(615\) | 43.3540 | 1.74820 | ||||||||
\(616\) | −14.6495 | −0.590246 | ||||||||
\(617\) | −1.84147 | −0.0741346 | −0.0370673 | − | 0.999313i | \(-0.511802\pi\) | ||||
−0.0370673 | + | 0.999313i | \(0.511802\pi\) | |||||||
\(618\) | 4.69669 | 0.188929 | ||||||||
\(619\) | −33.5204 | −1.34730 | −0.673650 | − | 0.739051i | \(-0.735274\pi\) | ||||
−0.673650 | + | 0.739051i | \(0.735274\pi\) | |||||||
\(620\) | −32.7701 | −1.31608 | ||||||||
\(621\) | 9.88215 | 0.396557 | ||||||||
\(622\) | 32.1652 | 1.28971 | ||||||||
\(623\) | 20.8968 | 0.837212 | ||||||||
\(624\) | 1.36738 | 0.0547389 | ||||||||
\(625\) | −26.4493 | −1.05797 | ||||||||
\(626\) | 35.2417 | 1.40854 | ||||||||
\(627\) | 25.3789 | 1.01353 | ||||||||
\(628\) | 1.92119 | 0.0766637 | ||||||||
\(629\) | −2.52261 | −0.100583 | ||||||||
\(630\) | −35.1771 | −1.40149 | ||||||||
\(631\) | 31.6029 | 1.25809 | 0.629045 | − | 0.777369i | \(-0.283446\pi\) | ||||
0.629045 | + | 0.777369i | \(0.283446\pi\) | |||||||
\(632\) | −15.5241 | −0.617514 | ||||||||
\(633\) | 24.7088 | 0.982088 | ||||||||
\(634\) | 48.2531 | 1.91638 | ||||||||
\(635\) | 21.6792 | 0.860312 | ||||||||
\(636\) | 33.9516 | 1.34627 | ||||||||
\(637\) | −8.29518 | −0.328667 | ||||||||
\(638\) | −32.9981 | −1.30641 | ||||||||
\(639\) | −10.0560 | −0.397811 | ||||||||
\(640\) | 40.9145 | 1.61729 | ||||||||
\(641\) | −43.4450 | −1.71597 | −0.857987 | − | 0.513672i | \(-0.828285\pi\) | ||||
−0.857987 | + | 0.513672i | \(0.828285\pi\) | |||||||
\(642\) | 73.0811 | 2.88428 | ||||||||
\(643\) | −29.3200 | −1.15627 | −0.578134 | − | 0.815942i | \(-0.696219\pi\) | ||||
−0.578134 | + | 0.815942i | \(0.696219\pi\) | |||||||
\(644\) | −28.0098 | −1.10374 | ||||||||
\(645\) | −66.4122 | −2.61498 | ||||||||
\(646\) | −18.2988 | −0.719958 | ||||||||
\(647\) | 32.3450 | 1.27161 | 0.635807 | − | 0.771848i | \(-0.280668\pi\) | ||||
0.635807 | + | 0.771848i | \(0.280668\pi\) | |||||||
\(648\) | 16.4168 | 0.644911 | ||||||||
\(649\) | −8.92591 | −0.350373 | ||||||||
\(650\) | −1.52259 | −0.0597210 | ||||||||
\(651\) | 20.7044 | 0.811471 | ||||||||
\(652\) | −62.7842 | −2.45882 | ||||||||
\(653\) | 13.4291 | 0.525523 | 0.262761 | − | 0.964861i | \(-0.415367\pi\) | ||||
0.262761 | + | 0.964861i | \(0.415367\pi\) | |||||||
\(654\) | −5.92161 | −0.231553 | ||||||||
\(655\) | 30.9012 | 1.20741 | ||||||||
\(656\) | 1.75581 | 0.0685528 | ||||||||
\(657\) | −25.2309 | −0.984350 | ||||||||
\(658\) | −30.2914 | −1.18088 | ||||||||
\(659\) | −25.3452 | −0.987310 | −0.493655 | − | 0.869658i | \(-0.664339\pi\) | ||||
−0.493655 | + | 0.869658i | \(0.664339\pi\) | |||||||
\(660\) | −58.3705 | −2.27207 | ||||||||
\(661\) | −11.0144 | −0.428411 | −0.214205 | − | 0.976789i | \(-0.568716\pi\) | ||||
−0.214205 | + | 0.976789i | \(0.568716\pi\) | |||||||
\(662\) | −19.4121 | −0.754473 | ||||||||
\(663\) | 14.2088 | 0.551824 | ||||||||
\(664\) | −27.0113 | −1.04824 | ||||||||
\(665\) | −13.0709 | −0.506869 | ||||||||
\(666\) | −8.57662 | −0.332337 | ||||||||
\(667\) | −23.4254 | −0.907033 | ||||||||
\(668\) | 31.5673 | 1.22138 | ||||||||
\(669\) | −17.5403 | −0.678147 | ||||||||
\(670\) | −77.0110 | −2.97519 | ||||||||
\(671\) | 18.2294 | 0.703737 | ||||||||
\(672\) | −27.4590 | −1.05925 | ||||||||
\(673\) | 29.2102 | 1.12597 | 0.562985 | − | 0.826467i | \(-0.309653\pi\) | ||||
0.562985 | + | 0.826467i | \(0.309653\pi\) | |||||||
\(674\) | 60.0356 | 2.31248 | ||||||||
\(675\) | −0.617240 | −0.0237576 | ||||||||
\(676\) | −26.4424 | −1.01702 | ||||||||
\(677\) | 19.6309 | 0.754478 | 0.377239 | − | 0.926116i | \(-0.376874\pi\) | ||||
0.377239 | + | 0.926116i | \(0.376874\pi\) | |||||||
\(678\) | −43.5281 | −1.67169 | ||||||||
\(679\) | 0.388566 | 0.0149118 | ||||||||
\(680\) | 15.6263 | 0.599241 | ||||||||
\(681\) | −16.4812 | −0.631562 | ||||||||
\(682\) | 31.1522 | 1.19288 | ||||||||
\(683\) | −41.0700 | −1.57150 | −0.785749 | − | 0.618545i | \(-0.787722\pi\) | ||||
−0.785749 | + | 0.618545i | \(0.787722\pi\) | |||||||
\(684\) | −38.1984 | −1.46055 | ||||||||
\(685\) | 2.21648 | 0.0846874 | ||||||||
\(686\) | 43.8866 | 1.67560 | ||||||||
\(687\) | 31.0262 | 1.18372 | ||||||||
\(688\) | −2.68965 | −0.102542 | ||||||||
\(689\) | −8.88244 | −0.338394 | ||||||||
\(690\) | −67.4894 | −2.56928 | ||||||||
\(691\) | −3.77631 | −0.143658 | −0.0718288 | − | 0.997417i | \(-0.522884\pi\) | ||||
−0.0718288 | + | 0.997417i | \(0.522884\pi\) | |||||||
\(692\) | 70.2735 | 2.67140 | ||||||||
\(693\) | 20.5318 | 0.779938 | ||||||||
\(694\) | 2.49516 | 0.0947151 | ||||||||
\(695\) | −39.5879 | −1.50165 | ||||||||
\(696\) | 33.1226 | 1.25551 | ||||||||
\(697\) | 18.2451 | 0.691082 | ||||||||
\(698\) | −76.9527 | −2.91270 | ||||||||
\(699\) | −58.0331 | −2.19501 | ||||||||
\(700\) | 1.74949 | 0.0661246 | ||||||||
\(701\) | −36.7183 | −1.38683 | −0.693416 | − | 0.720538i | \(-0.743895\pi\) | ||||
−0.693416 | + | 0.720538i | \(0.743895\pi\) | |||||||
\(702\) | 9.84578 | 0.371605 | ||||||||
\(703\) | −3.18685 | −0.120194 | ||||||||
\(704\) | −39.8289 | −1.50111 | ||||||||
\(705\) | −44.8127 | −1.68774 | ||||||||
\(706\) | 18.3885 | 0.692060 | ||||||||
\(707\) | 2.98936 | 0.112426 | ||||||||
\(708\) | 24.1311 | 0.906903 | ||||||||
\(709\) | 24.8667 | 0.933889 | 0.466945 | − | 0.884287i | \(-0.345355\pi\) | ||||
0.466945 | + | 0.884287i | \(0.345355\pi\) | |||||||
\(710\) | 13.9971 | 0.525301 | ||||||||
\(711\) | 21.7575 | 0.815969 | ||||||||
\(712\) | −31.5603 | −1.18277 | ||||||||
\(713\) | 22.1150 | 0.828212 | ||||||||
\(714\) | −26.5907 | −0.995133 | ||||||||
\(715\) | 15.2709 | 0.571100 | ||||||||
\(716\) | 76.8423 | 2.87173 | ||||||||
\(717\) | 68.7199 | 2.56639 | ||||||||
\(718\) | −49.6732 | −1.85379 | ||||||||
\(719\) | 23.2438 | 0.866846 | 0.433423 | − | 0.901191i | \(-0.357306\pi\) | ||||
0.433423 | + | 0.901191i | \(0.357306\pi\) | |||||||
\(720\) | −2.10761 | −0.0785461 | ||||||||
\(721\) | 1.41186 | 0.0525805 | ||||||||
\(722\) | 20.1307 | 0.749187 | ||||||||
\(723\) | −14.6912 | −0.546371 | ||||||||
\(724\) | 41.1477 | 1.52924 | ||||||||
\(725\) | 1.46315 | 0.0543400 | ||||||||
\(726\) | −9.64907 | −0.358111 | ||||||||
\(727\) | −2.05092 | −0.0760643 | −0.0380321 | − | 0.999277i | \(-0.512109\pi\) | ||||
−0.0380321 | + | 0.999277i | \(0.512109\pi\) | |||||||
\(728\) | −10.3614 | −0.384020 | ||||||||
\(729\) | −38.6009 | −1.42966 | ||||||||
\(730\) | 35.1191 | 1.29982 | ||||||||
\(731\) | −27.9489 | −1.03373 | ||||||||
\(732\) | −49.2829 | −1.82155 | ||||||||
\(733\) | −13.0524 | −0.482102 | −0.241051 | − | 0.970512i | \(-0.577492\pi\) | ||||
−0.241051 | + | 0.970512i | \(0.577492\pi\) | |||||||
\(734\) | −63.2039 | −2.33290 | ||||||||
\(735\) | 22.9657 | 0.847104 | ||||||||
\(736\) | −29.3297 | −1.08111 | ||||||||
\(737\) | 44.9489 | 1.65571 | ||||||||
\(738\) | 62.0315 | 2.28341 | ||||||||
\(739\) | −7.45642 | −0.274289 | −0.137144 | − | 0.990551i | \(-0.543792\pi\) | ||||
−0.137144 | + | 0.990551i | \(0.543792\pi\) | |||||||
\(740\) | 7.32965 | 0.269443 | ||||||||
\(741\) | 17.9502 | 0.659417 | ||||||||
\(742\) | 16.6228 | 0.610243 | ||||||||
\(743\) | −23.4636 | −0.860796 | −0.430398 | − | 0.902639i | \(-0.641627\pi\) | ||||
−0.430398 | + | 0.902639i | \(0.641627\pi\) | |||||||
\(744\) | −31.2698 | −1.14641 | ||||||||
\(745\) | 15.2482 | 0.558651 | ||||||||
\(746\) | −36.7161 | −1.34427 | ||||||||
\(747\) | 37.8573 | 1.38513 | ||||||||
\(748\) | −24.5647 | −0.898174 | ||||||||
\(749\) | 21.9687 | 0.802720 | ||||||||
\(750\) | −64.0050 | −2.33713 | ||||||||
\(751\) | −32.2120 | −1.17543 | −0.587716 | − | 0.809067i | \(-0.699973\pi\) | ||||
−0.587716 | + | 0.809067i | \(0.699973\pi\) | |||||||
\(752\) | −1.81489 | −0.0661821 | ||||||||
\(753\) | −35.9933 | −1.31167 | ||||||||
\(754\) | −23.3391 | −0.849962 | ||||||||
\(755\) | −0.0788643 | −0.00287016 | ||||||||
\(756\) | −11.3130 | −0.411451 | ||||||||
\(757\) | 48.7545 | 1.77201 | 0.886006 | − | 0.463673i | \(-0.153469\pi\) | ||||
0.886006 | + | 0.463673i | \(0.153469\pi\) | |||||||
\(758\) | −61.5563 | −2.23583 | ||||||||
\(759\) | 39.3914 | 1.42982 | ||||||||
\(760\) | 19.7409 | 0.716079 | ||||||||
\(761\) | 22.9274 | 0.831119 | 0.415560 | − | 0.909566i | \(-0.363586\pi\) | ||||
0.415560 | + | 0.909566i | \(0.363586\pi\) | |||||||
\(762\) | 55.7158 | 2.01837 | ||||||||
\(763\) | −1.78008 | −0.0644433 | ||||||||
\(764\) | −38.3207 | −1.38639 | ||||||||
\(765\) | −21.9008 | −0.791825 | ||||||||
\(766\) | −65.8686 | −2.37993 | ||||||||
\(767\) | −6.31319 | −0.227956 | ||||||||
\(768\) | 37.4531 | 1.35147 | ||||||||
\(769\) | 13.6321 | 0.491588 | 0.245794 | − | 0.969322i | \(-0.420951\pi\) | ||||
0.245794 | + | 0.969322i | \(0.420951\pi\) | |||||||
\(770\) | −28.5784 | −1.02989 | ||||||||
\(771\) | −62.4027 | −2.24738 | ||||||||
\(772\) | −22.0806 | −0.794697 | ||||||||
\(773\) | −1.06631 | −0.0383525 | −0.0191763 | − | 0.999816i | \(-0.506104\pi\) | ||||
−0.0191763 | + | 0.999816i | \(0.506104\pi\) | |||||||
\(774\) | −95.0235 | −3.41555 | ||||||||
\(775\) | −1.38130 | −0.0496179 | ||||||||
\(776\) | −0.586849 | −0.0210667 | ||||||||
\(777\) | −4.63093 | −0.166134 | ||||||||
\(778\) | −59.3447 | −2.12761 | ||||||||
\(779\) | 23.0493 | 0.825827 | ||||||||
\(780\) | −41.2848 | −1.47823 | ||||||||
\(781\) | −8.16966 | −0.292333 | ||||||||
\(782\) | −28.4023 | −1.01566 | ||||||||
\(783\) | −9.46140 | −0.338123 | ||||||||
\(784\) | 0.930098 | 0.0332178 | ||||||||
\(785\) | 1.39154 | 0.0496662 | ||||||||
\(786\) | 79.4164 | 2.83269 | ||||||||
\(787\) | 40.9392 | 1.45932 | 0.729662 | − | 0.683808i | \(-0.239678\pi\) | ||||
0.729662 | + | 0.683808i | \(0.239678\pi\) | |||||||
\(788\) | −29.0691 | −1.03554 | ||||||||
\(789\) | −18.5330 | −0.659793 | ||||||||
\(790\) | −30.2844 | −1.07747 | ||||||||
\(791\) | −13.0849 | −0.465244 | ||||||||
\(792\) | −31.0091 | −1.10186 | ||||||||
\(793\) | 12.8934 | 0.457859 | ||||||||
\(794\) | 12.6845 | 0.450155 | ||||||||
\(795\) | 24.5916 | 0.872174 | ||||||||
\(796\) | 3.72207 | 0.131925 | ||||||||
\(797\) | −20.2227 | −0.716323 | −0.358162 | − | 0.933660i | \(-0.616596\pi\) | ||||
−0.358162 | + | 0.933660i | \(0.616596\pi\) | |||||||
\(798\) | −33.5924 | −1.18916 | ||||||||
\(799\) | −18.8590 | −0.667184 | ||||||||
\(800\) | 1.83193 | 0.0647686 | ||||||||
\(801\) | 44.2328 | 1.56289 | ||||||||
\(802\) | 16.9776 | 0.599502 | ||||||||
\(803\) | −20.4979 | −0.723356 | ||||||||
\(804\) | −121.519 | −4.28564 | ||||||||
\(805\) | −20.2878 | −0.715052 | ||||||||
\(806\) | 22.0336 | 0.776100 | ||||||||
\(807\) | 9.28848 | 0.326970 | ||||||||
\(808\) | −4.51481 | −0.158831 | ||||||||
\(809\) | 39.8473 | 1.40096 | 0.700479 | − | 0.713673i | \(-0.252970\pi\) | ||||
0.700479 | + | 0.713673i | \(0.252970\pi\) | |||||||
\(810\) | 32.0259 | 1.12528 | ||||||||
\(811\) | −40.2351 | −1.41284 | −0.706422 | − | 0.707791i | \(-0.749692\pi\) | ||||
−0.706422 | + | 0.707791i | \(0.749692\pi\) | |||||||
\(812\) | 26.8172 | 0.941099 | ||||||||
\(813\) | −37.8445 | −1.32726 | ||||||||
\(814\) | −6.96777 | −0.244220 | ||||||||
\(815\) | −45.4753 | −1.59293 | ||||||||
\(816\) | −1.59316 | −0.0557719 | ||||||||
\(817\) | −35.3083 | −1.23528 | ||||||||
\(818\) | 60.8784 | 2.12856 | ||||||||
\(819\) | 14.5219 | 0.507436 | ||||||||
\(820\) | −53.0126 | −1.85128 | ||||||||
\(821\) | 10.2981 | 0.359406 | 0.179703 | − | 0.983721i | \(-0.442486\pi\) | ||||
0.179703 | + | 0.983721i | \(0.442486\pi\) | |||||||
\(822\) | 5.69639 | 0.198684 | ||||||||
\(823\) | −0.385341 | −0.0134322 | −0.00671608 | − | 0.999977i | \(-0.502138\pi\) | ||||
−0.00671608 | + | 0.999977i | \(0.502138\pi\) | |||||||
\(824\) | −2.13233 | −0.0742831 | ||||||||
\(825\) | −2.46039 | −0.0856599 | ||||||||
\(826\) | 11.8147 | 0.411085 | ||||||||
\(827\) | 25.4124 | 0.883674 | 0.441837 | − | 0.897095i | \(-0.354327\pi\) | ||||
0.441837 | + | 0.897095i | \(0.354327\pi\) | |||||||
\(828\) | −59.2891 | −2.06044 | ||||||||
\(829\) | −24.1983 | −0.840441 | −0.420220 | − | 0.907422i | \(-0.638047\pi\) | ||||
−0.420220 | + | 0.907422i | \(0.638047\pi\) | |||||||
\(830\) | −52.6939 | −1.82903 | ||||||||
\(831\) | 17.5814 | 0.609891 | ||||||||
\(832\) | −28.1705 | −0.976637 | ||||||||
\(833\) | 9.66491 | 0.334869 | ||||||||
\(834\) | −101.741 | −3.52302 | ||||||||
\(835\) | 22.8646 | 0.791261 | ||||||||
\(836\) | −31.0329 | −1.07330 | ||||||||
\(837\) | 8.93214 | 0.308740 | ||||||||
\(838\) | 46.0720 | 1.59153 | ||||||||
\(839\) | 21.5310 | 0.743334 | 0.371667 | − | 0.928366i | \(-0.378786\pi\) | ||||
0.371667 | + | 0.928366i | \(0.378786\pi\) | |||||||
\(840\) | 28.6863 | 0.989771 | ||||||||
\(841\) | −6.57203 | −0.226622 | ||||||||
\(842\) | −29.3398 | −1.01112 | ||||||||
\(843\) | −41.0881 | −1.41515 | ||||||||
\(844\) | −30.2136 | −1.03999 | ||||||||
\(845\) | −19.1526 | −0.658869 | ||||||||
\(846\) | −64.1187 | −2.20445 | ||||||||
\(847\) | −2.90058 | −0.0996652 | ||||||||
\(848\) | 0.995944 | 0.0342009 | ||||||||
\(849\) | −8.90041 | −0.305461 | ||||||||
\(850\) | 1.77401 | 0.0608480 | ||||||||
\(851\) | −4.94642 | −0.169561 | ||||||||
\(852\) | 22.0866 | 0.756675 | ||||||||
\(853\) | 23.7664 | 0.813745 | 0.406872 | − | 0.913485i | \(-0.366619\pi\) | ||||
0.406872 | + | 0.913485i | \(0.366619\pi\) | |||||||
\(854\) | −24.1291 | −0.825680 | ||||||||
\(855\) | −27.6676 | −0.946211 | ||||||||
\(856\) | −33.1793 | −1.13404 | ||||||||
\(857\) | 13.5643 | 0.463347 | 0.231673 | − | 0.972794i | \(-0.425580\pi\) | ||||
0.231673 | + | 0.972794i | \(0.425580\pi\) | |||||||
\(858\) | 39.2465 | 1.33985 | ||||||||
\(859\) | 2.32578 | 0.0793546 | 0.0396773 | − | 0.999213i | \(-0.487367\pi\) | ||||
0.0396773 | + | 0.999213i | \(0.487367\pi\) | |||||||
\(860\) | 81.2078 | 2.76916 | ||||||||
\(861\) | 33.4938 | 1.14146 | ||||||||
\(862\) | 45.3484 | 1.54457 | ||||||||
\(863\) | 45.2954 | 1.54187 | 0.770936 | − | 0.636912i | \(-0.219789\pi\) | ||||
0.770936 | + | 0.636912i | \(0.219789\pi\) | |||||||
\(864\) | −11.8461 | −0.403013 | ||||||||
\(865\) | 50.9000 | 1.73065 | ||||||||
\(866\) | −74.8867 | −2.54475 | ||||||||
\(867\) | 27.6710 | 0.939756 | ||||||||
\(868\) | −25.3171 | −0.859318 | ||||||||
\(869\) | 17.6761 | 0.599620 | ||||||||
\(870\) | 64.6159 | 2.19068 | ||||||||
\(871\) | 31.7918 | 1.07722 | ||||||||
\(872\) | 2.68845 | 0.0910423 | ||||||||
\(873\) | 0.822489 | 0.0278370 | ||||||||
\(874\) | −35.8810 | −1.21369 | ||||||||
\(875\) | −19.2404 | −0.650444 | ||||||||
\(876\) | 55.4159 | 1.87233 | ||||||||
\(877\) | −10.3254 | −0.348664 | −0.174332 | − | 0.984687i | \(-0.555777\pi\) | ||||
−0.174332 | + | 0.984687i | \(0.555777\pi\) | |||||||
\(878\) | 1.61419 | 0.0544762 | ||||||||
\(879\) | −55.4488 | −1.87024 | ||||||||
\(880\) | −1.71225 | −0.0577200 | ||||||||
\(881\) | 39.2242 | 1.32150 | 0.660748 | − | 0.750608i | \(-0.270239\pi\) | ||||
0.660748 | + | 0.750608i | \(0.270239\pi\) | |||||||
\(882\) | 32.8597 | 1.10644 | ||||||||
\(883\) | 6.47276 | 0.217826 | 0.108913 | − | 0.994051i | \(-0.465263\pi\) | ||||
0.108913 | + | 0.994051i | \(0.465263\pi\) | |||||||
\(884\) | −17.3743 | −0.584361 | ||||||||
\(885\) | 17.4785 | 0.587532 | ||||||||
\(886\) | −31.7336 | −1.06611 | ||||||||
\(887\) | −15.6828 | −0.526576 | −0.263288 | − | 0.964717i | \(-0.584807\pi\) | ||||
−0.263288 | + | 0.964717i | \(0.584807\pi\) | |||||||
\(888\) | 6.99407 | 0.234706 | ||||||||
\(889\) | 16.7486 | 0.561729 | ||||||||
\(890\) | −61.5680 | −2.06377 | ||||||||
\(891\) | −18.6925 | −0.626224 | ||||||||
\(892\) | 21.4480 | 0.718132 | ||||||||
\(893\) | −23.8249 | −0.797268 | ||||||||
\(894\) | 39.1881 | 1.31065 | ||||||||
\(895\) | 55.6579 | 1.86044 | ||||||||
\(896\) | 31.6092 | 1.05599 | ||||||||
\(897\) | 27.8611 | 0.930255 | ||||||||
\(898\) | −16.8354 | −0.561804 | ||||||||
\(899\) | −21.1734 | −0.706172 | ||||||||
\(900\) | 3.70320 | 0.123440 | ||||||||
\(901\) | 10.3491 | 0.344780 | ||||||||
\(902\) | 50.3952 | 1.67798 | ||||||||
\(903\) | −51.3078 | −1.70742 | ||||||||
\(904\) | 19.7620 | 0.657275 | ||||||||
\(905\) | 29.8038 | 0.990711 | ||||||||
\(906\) | −0.202682 | −0.00673367 | ||||||||
\(907\) | 39.0872 | 1.29787 | 0.648935 | − | 0.760844i | \(-0.275215\pi\) | ||||
0.648935 | + | 0.760844i | \(0.275215\pi\) | |||||||
\(908\) | 20.1530 | 0.668801 | ||||||||
\(909\) | 6.32766 | 0.209875 | ||||||||
\(910\) | −20.2132 | −0.670060 | ||||||||
\(911\) | 28.8625 | 0.956256 | 0.478128 | − | 0.878290i | \(-0.341315\pi\) | ||||
0.478128 | + | 0.878290i | \(0.341315\pi\) | |||||||
\(912\) | −2.01267 | −0.0666460 | ||||||||
\(913\) | 30.7558 | 1.01787 | ||||||||
\(914\) | 48.4152 | 1.60143 | ||||||||
\(915\) | −35.6962 | −1.18008 | ||||||||
\(916\) | −37.9384 | −1.25352 | ||||||||
\(917\) | 23.8732 | 0.788361 | ||||||||
\(918\) | −11.4715 | −0.378617 | ||||||||
\(919\) | −9.09122 | −0.299892 | −0.149946 | − | 0.988694i | \(-0.547910\pi\) | ||||
−0.149946 | + | 0.988694i | \(0.547910\pi\) | |||||||
\(920\) | 30.6406 | 1.01019 | ||||||||
\(921\) | −34.4462 | −1.13504 | ||||||||
\(922\) | 9.92824 | 0.326969 | ||||||||
\(923\) | −5.77830 | −0.190195 | ||||||||
\(924\) | −45.0951 | −1.48352 | ||||||||
\(925\) | 0.308954 | 0.0101583 | ||||||||
\(926\) | 52.8989 | 1.73836 | ||||||||
\(927\) | 2.98853 | 0.0981561 | ||||||||
\(928\) | 28.0809 | 0.921800 | ||||||||
\(929\) | 14.8996 | 0.488839 | 0.244420 | − | 0.969670i | \(-0.421403\pi\) | ||||
0.244420 | + | 0.969670i | \(0.421403\pi\) | |||||||
\(930\) | −61.0014 | −2.00031 | ||||||||
\(931\) | 12.2098 | 0.400161 | ||||||||
\(932\) | 70.9620 | 2.32444 | ||||||||
\(933\) | 36.7623 | 1.20354 | ||||||||
\(934\) | −85.7230 | −2.80494 | ||||||||
\(935\) | −17.7925 | −0.581877 | ||||||||
\(936\) | −21.9323 | −0.716881 | ||||||||
\(937\) | −21.3836 | −0.698570 | −0.349285 | − | 0.937016i | \(-0.613576\pi\) | ||||
−0.349285 | + | 0.937016i | \(0.613576\pi\) | |||||||
\(938\) | −59.4960 | −1.94261 | ||||||||
\(939\) | 40.2786 | 1.31444 | ||||||||
\(940\) | 54.7963 | 1.78726 | ||||||||
\(941\) | 57.8756 | 1.88669 | 0.943346 | − | 0.331811i | \(-0.107660\pi\) | ||||
0.943346 | + | 0.331811i | \(0.107660\pi\) | |||||||
\(942\) | 3.57628 | 0.116521 | ||||||||
\(943\) | 35.7756 | 1.16501 | ||||||||
\(944\) | 0.707867 | 0.0230391 | ||||||||
\(945\) | −8.19416 | −0.266556 | ||||||||
\(946\) | −77.1984 | −2.50994 | ||||||||
\(947\) | −19.8508 | −0.645064 | −0.322532 | − | 0.946559i | \(-0.604534\pi\) | ||||
−0.322532 | + | 0.946559i | \(0.604534\pi\) | |||||||
\(948\) | −47.7871 | −1.55205 | ||||||||
\(949\) | −14.4979 | −0.470623 | ||||||||
\(950\) | 2.24113 | 0.0727118 | ||||||||
\(951\) | 55.1496 | 1.78835 | ||||||||
\(952\) | 12.0723 | 0.391267 | ||||||||
\(953\) | −48.2282 | −1.56226 | −0.781132 | − | 0.624366i | \(-0.785357\pi\) | ||||
−0.781132 | + | 0.624366i | \(0.785357\pi\) | |||||||
\(954\) | 35.1860 | 1.13919 | ||||||||
\(955\) | −27.7562 | −0.898168 | ||||||||
\(956\) | −84.0297 | −2.71771 | ||||||||
\(957\) | −37.7143 | −1.21913 | ||||||||
\(958\) | −42.8801 | −1.38539 | ||||||||
\(959\) | 1.71238 | 0.0552955 | ||||||||
\(960\) | 77.9918 | 2.51718 | ||||||||
\(961\) | −11.0110 | −0.355195 | ||||||||
\(962\) | −4.92822 | −0.158892 | ||||||||
\(963\) | 46.5018 | 1.49850 | ||||||||
\(964\) | 17.9642 | 0.578586 | ||||||||
\(965\) | −15.9932 | −0.514840 | ||||||||
\(966\) | −52.1400 | −1.67758 | ||||||||
\(967\) | 32.9861 | 1.06076 | 0.530380 | − | 0.847760i | \(-0.322049\pi\) | ||||
0.530380 | + | 0.847760i | \(0.322049\pi\) | |||||||
\(968\) | 4.38074 | 0.140802 | ||||||||
\(969\) | −20.9142 | −0.671860 | ||||||||
\(970\) | −1.14483 | −0.0367583 | ||||||||
\(971\) | −16.3461 | −0.524571 | −0.262285 | − | 0.964990i | \(-0.584476\pi\) | ||||
−0.262285 | + | 0.964990i | \(0.584476\pi\) | |||||||
\(972\) | 69.6011 | 2.23246 | ||||||||
\(973\) | −30.5843 | −0.980486 | ||||||||
\(974\) | 23.5711 | 0.755268 | ||||||||
\(975\) | −1.74021 | −0.0557312 | ||||||||
\(976\) | −1.44567 | −0.0462749 | ||||||||
\(977\) | 35.7362 | 1.14330 | 0.571651 | − | 0.820497i | \(-0.306303\pi\) | ||||
0.571651 | + | 0.820497i | \(0.306303\pi\) | |||||||
\(978\) | −116.872 | −3.73716 | ||||||||
\(979\) | 35.9353 | 1.14850 | ||||||||
\(980\) | −28.0822 | −0.897051 | ||||||||
\(981\) | −3.76795 | −0.120301 | ||||||||
\(982\) | −95.0813 | −3.03417 | ||||||||
\(983\) | 27.5874 | 0.879902 | 0.439951 | − | 0.898022i | \(-0.354996\pi\) | ||||
0.439951 | + | 0.898022i | \(0.354996\pi\) | |||||||
\(984\) | −50.5855 | −1.61261 | ||||||||
\(985\) | −21.0551 | −0.670871 | ||||||||
\(986\) | 27.1930 | 0.866001 | ||||||||
\(987\) | −34.6208 | −1.10199 | ||||||||
\(988\) | −21.9492 | −0.698298 | ||||||||
\(989\) | −54.8032 | −1.74264 | ||||||||
\(990\) | −60.4927 | −1.92258 | ||||||||
\(991\) | −47.8239 | −1.51918 | −0.759589 | − | 0.650404i | \(-0.774600\pi\) | ||||
−0.759589 | + | 0.650404i | \(0.774600\pi\) | |||||||
\(992\) | −26.5101 | −0.841696 | ||||||||
\(993\) | −22.1866 | −0.704069 | ||||||||
\(994\) | 10.8137 | 0.342989 | ||||||||
\(995\) | 2.69594 | 0.0854671 | ||||||||
\(996\) | −83.1479 | −2.63464 | ||||||||
\(997\) | 9.60225 | 0.304106 | 0.152053 | − | 0.988372i | \(-0.451411\pi\) | ||||
0.152053 | + | 0.988372i | \(0.451411\pi\) | |||||||
\(998\) | −26.0897 | −0.825854 | ||||||||
\(999\) | −1.99784 | −0.0632088 |
(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 | 4033.2.a.f.1.9 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.9 | ✓ | 85 | 1.1 | even | 1 | trivial |