Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 20x^{7} + 69x^{6} + 27x^{5} - 185x^{4} + 8x^{3} + 109x^{2} - 8x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-4.36993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.36993 | 1.95429 | 0.977146 | − | 0.212569i | \(-0.0681830\pi\) | ||||
0.977146 | + | 0.212569i | \(0.0681830\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.18318 | −1.58110 | −0.790548 | − | 0.612401i | \(-0.790204\pi\) | ||||
−0.790548 | + | 0.612401i | \(0.790204\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.36993 | 1.38189 | ||||||||
\(11\) | −0.462917 | −0.139575 | −0.0697874 | − | 0.997562i | \(-0.522232\pi\) | ||||
−0.0697874 | + | 0.997562i | \(0.522232\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.66621 | −1.57152 | −0.785762 | − | 0.618529i | \(-0.787729\pi\) | ||||
−0.785762 | + | 0.618529i | \(0.787729\pi\) | |||||||
\(14\) | −4.18318 | −1.11800 | ||||||||
\(15\) | −4.36993 | −1.12831 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.64277 | −1.85364 | −0.926822 | − | 0.375500i | \(-0.877471\pi\) | ||||
−0.926822 | + | 0.375500i | \(0.877471\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 4.36993 | 0.977146 | ||||||||
\(21\) | 4.18318 | 0.912846 | ||||||||
\(22\) | −0.462917 | −0.0986943 | ||||||||
\(23\) | 5.05356 | 1.05374 | 0.526870 | − | 0.849946i | \(-0.323366\pi\) | ||||
0.526870 | + | 0.849946i | \(0.323366\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 14.0963 | 2.81926 | ||||||||
\(26\) | −5.66621 | −1.11124 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.18318 | −0.790548 | ||||||||
\(29\) | 0.972185 | 0.180530 | 0.0902651 | − | 0.995918i | \(-0.471229\pi\) | ||||
0.0902651 | + | 0.995918i | \(0.471229\pi\) | |||||||
\(30\) | −4.36993 | −0.797836 | ||||||||
\(31\) | 6.32253 | 1.13556 | 0.567780 | − | 0.823180i | \(-0.307802\pi\) | ||||
0.567780 | + | 0.823180i | \(0.307802\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.462917 | 0.0805835 | ||||||||
\(34\) | −7.64277 | −1.31072 | ||||||||
\(35\) | −18.2802 | −3.08992 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.67622 | −1.42636 | −0.713181 | − | 0.700980i | \(-0.752746\pi\) | ||||
−0.713181 | + | 0.700980i | \(0.752746\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 5.66621 | 0.907320 | ||||||||
\(40\) | 4.36993 | 0.690947 | ||||||||
\(41\) | −3.87511 | −0.605190 | −0.302595 | − | 0.953119i | \(-0.597853\pi\) | ||||
−0.302595 | + | 0.953119i | \(0.597853\pi\) | |||||||
\(42\) | 4.18318 | 0.645479 | ||||||||
\(43\) | −7.90866 | −1.20606 | −0.603029 | − | 0.797719i | \(-0.706040\pi\) | ||||
−0.603029 | + | 0.797719i | \(0.706040\pi\) | |||||||
\(44\) | −0.462917 | −0.0697874 | ||||||||
\(45\) | 4.36993 | 0.651431 | ||||||||
\(46\) | 5.05356 | 0.745106 | ||||||||
\(47\) | 5.36140 | 0.782040 | 0.391020 | − | 0.920382i | \(-0.372122\pi\) | ||||
0.391020 | + | 0.920382i | \(0.372122\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 10.4990 | 1.49986 | ||||||||
\(50\) | 14.0963 | 1.99352 | ||||||||
\(51\) | 7.64277 | 1.07020 | ||||||||
\(52\) | −5.66621 | −0.785762 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.02292 | −0.272770 | ||||||||
\(56\) | −4.18318 | −0.559002 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0.972185 | 0.127654 | ||||||||
\(59\) | 11.8679 | 1.54506 | 0.772532 | − | 0.634976i | \(-0.218990\pi\) | ||||
0.772532 | + | 0.634976i | \(0.218990\pi\) | |||||||
\(60\) | −4.36993 | −0.564156 | ||||||||
\(61\) | −2.69186 | −0.344657 | −0.172329 | − | 0.985040i | \(-0.555129\pi\) | ||||
−0.172329 | + | 0.985040i | \(0.555129\pi\) | |||||||
\(62\) | 6.32253 | 0.802962 | ||||||||
\(63\) | −4.18318 | −0.527032 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −24.7609 | −3.07122 | ||||||||
\(66\) | 0.462917 | 0.0569812 | ||||||||
\(67\) | −8.85931 | −1.08234 | −0.541168 | − | 0.840914i | \(-0.682018\pi\) | ||||
−0.541168 | + | 0.840914i | \(0.682018\pi\) | |||||||
\(68\) | −7.64277 | −0.926822 | ||||||||
\(69\) | −5.05356 | −0.608377 | ||||||||
\(70\) | −18.2802 | −2.18490 | ||||||||
\(71\) | −9.10783 | −1.08090 | −0.540450 | − | 0.841376i | \(-0.681746\pi\) | ||||
−0.540450 | + | 0.841376i | \(0.681746\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.12473 | −0.950928 | −0.475464 | − | 0.879735i | \(-0.657720\pi\) | ||||
−0.475464 | + | 0.879735i | \(0.657720\pi\) | |||||||
\(74\) | −8.67622 | −1.00859 | ||||||||
\(75\) | −14.0963 | −1.62770 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 1.93647 | 0.220681 | ||||||||
\(78\) | 5.66621 | 0.641572 | ||||||||
\(79\) | −3.22329 | −0.362648 | −0.181324 | − | 0.983423i | \(-0.558038\pi\) | ||||
−0.181324 | + | 0.983423i | \(0.558038\pi\) | |||||||
\(80\) | 4.36993 | 0.488573 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.87511 | −0.427934 | ||||||||
\(83\) | 10.8534 | 1.19132 | 0.595658 | − | 0.803238i | \(-0.296891\pi\) | ||||
0.595658 | + | 0.803238i | \(0.296891\pi\) | |||||||
\(84\) | 4.18318 | 0.456423 | ||||||||
\(85\) | −33.3984 | −3.62256 | ||||||||
\(86\) | −7.90866 | −0.852812 | ||||||||
\(87\) | −0.972185 | −0.104229 | ||||||||
\(88\) | −0.462917 | −0.0493471 | ||||||||
\(89\) | −17.1661 | −1.81960 | −0.909800 | − | 0.415047i | \(-0.863765\pi\) | ||||
−0.909800 | + | 0.415047i | \(0.863765\pi\) | |||||||
\(90\) | 4.36993 | 0.460631 | ||||||||
\(91\) | 23.7028 | 2.48473 | ||||||||
\(92\) | 5.05356 | 0.526870 | ||||||||
\(93\) | −6.32253 | −0.655616 | ||||||||
\(94\) | 5.36140 | 0.552986 | ||||||||
\(95\) | 4.36993 | 0.448345 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.7574 | −1.29532 | −0.647658 | − | 0.761932i | \(-0.724251\pi\) | ||||
−0.647658 | + | 0.761932i | \(0.724251\pi\) | |||||||
\(98\) | 10.4990 | 1.06056 | ||||||||
\(99\) | −0.462917 | −0.0465249 | ||||||||
\(100\) | 14.0963 | 1.40963 | ||||||||
\(101\) | −14.9630 | −1.48887 | −0.744437 | − | 0.667693i | \(-0.767282\pi\) | ||||
−0.744437 | + | 0.667693i | \(0.767282\pi\) | |||||||
\(102\) | 7.64277 | 0.756747 | ||||||||
\(103\) | −11.2134 | −1.10489 | −0.552444 | − | 0.833550i | \(-0.686305\pi\) | ||||
−0.552444 | + | 0.833550i | \(0.686305\pi\) | |||||||
\(104\) | −5.66621 | −0.555618 | ||||||||
\(105\) | 18.2802 | 1.78397 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −15.8051 | −1.52794 | −0.763968 | − | 0.645254i | \(-0.776751\pi\) | ||||
−0.763968 | + | 0.645254i | \(0.776751\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −13.5273 | −1.29568 | −0.647840 | − | 0.761776i | \(-0.724328\pi\) | ||||
−0.647840 | + | 0.761776i | \(0.724328\pi\) | |||||||
\(110\) | −2.02292 | −0.192877 | ||||||||
\(111\) | 8.67622 | 0.823511 | ||||||||
\(112\) | −4.18318 | −0.395274 | ||||||||
\(113\) | −0.380231 | −0.0357691 | −0.0178846 | − | 0.999840i | \(-0.505693\pi\) | ||||
−0.0178846 | + | 0.999840i | \(0.505693\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 22.0837 | 2.05931 | ||||||||
\(116\) | 0.972185 | 0.0902651 | ||||||||
\(117\) | −5.66621 | −0.523841 | ||||||||
\(118\) | 11.8679 | 1.09252 | ||||||||
\(119\) | 31.9711 | 2.93079 | ||||||||
\(120\) | −4.36993 | −0.398918 | ||||||||
\(121\) | −10.7857 | −0.980519 | ||||||||
\(122\) | −2.69186 | −0.243709 | ||||||||
\(123\) | 3.87511 | 0.349407 | ||||||||
\(124\) | 6.32253 | 0.567780 | ||||||||
\(125\) | 39.7501 | 3.55536 | ||||||||
\(126\) | −4.18318 | −0.372668 | ||||||||
\(127\) | −8.23191 | −0.730464 | −0.365232 | − | 0.930916i | \(-0.619010\pi\) | ||||
−0.365232 | + | 0.930916i | \(0.619010\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.90866 | 0.696318 | ||||||||
\(130\) | −24.7609 | −2.17168 | ||||||||
\(131\) | 9.88981 | 0.864076 | 0.432038 | − | 0.901855i | \(-0.357795\pi\) | ||||
0.432038 | + | 0.901855i | \(0.357795\pi\) | |||||||
\(132\) | 0.462917 | 0.0402918 | ||||||||
\(133\) | −4.18318 | −0.362728 | ||||||||
\(134\) | −8.85931 | −0.765328 | ||||||||
\(135\) | −4.36993 | −0.376104 | ||||||||
\(136\) | −7.64277 | −0.655362 | ||||||||
\(137\) | −9.88872 | −0.844850 | −0.422425 | − | 0.906398i | \(-0.638821\pi\) | ||||
−0.422425 | + | 0.906398i | \(0.638821\pi\) | |||||||
\(138\) | −5.05356 | −0.430187 | ||||||||
\(139\) | −5.37706 | −0.456076 | −0.228038 | − | 0.973652i | \(-0.573231\pi\) | ||||
−0.228038 | + | 0.973652i | \(0.573231\pi\) | |||||||
\(140\) | −18.2802 | −1.54496 | ||||||||
\(141\) | −5.36140 | −0.451511 | ||||||||
\(142\) | −9.10783 | −0.764312 | ||||||||
\(143\) | 2.62299 | 0.219345 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.24838 | 0.352809 | ||||||||
\(146\) | −8.12473 | −0.672408 | ||||||||
\(147\) | −10.4990 | −0.865946 | ||||||||
\(148\) | −8.67622 | −0.713181 | ||||||||
\(149\) | 6.00567 | 0.492004 | 0.246002 | − | 0.969269i | \(-0.420883\pi\) | ||||
0.246002 | + | 0.969269i | \(0.420883\pi\) | |||||||
\(150\) | −14.0963 | −1.15096 | ||||||||
\(151\) | −5.75130 | −0.468034 | −0.234017 | − | 0.972233i | \(-0.575187\pi\) | ||||
−0.234017 | + | 0.972233i | \(0.575187\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −7.64277 | −0.617882 | ||||||||
\(154\) | 1.93647 | 0.156045 | ||||||||
\(155\) | 27.6290 | 2.21922 | ||||||||
\(156\) | 5.66621 | 0.453660 | ||||||||
\(157\) | 0.329748 | 0.0263168 | 0.0131584 | − | 0.999913i | \(-0.495811\pi\) | ||||
0.0131584 | + | 0.999913i | \(0.495811\pi\) | |||||||
\(158\) | −3.22329 | −0.256431 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | 4.36993 | 0.345473 | ||||||||
\(161\) | −21.1400 | −1.66606 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −18.6873 | −1.46370 | −0.731850 | − | 0.681466i | \(-0.761343\pi\) | ||||
−0.731850 | + | 0.681466i | \(0.761343\pi\) | |||||||
\(164\) | −3.87511 | −0.302595 | ||||||||
\(165\) | 2.02292 | 0.157484 | ||||||||
\(166\) | 10.8534 | 0.842388 | ||||||||
\(167\) | 16.5992 | 1.28448 | 0.642242 | − | 0.766502i | \(-0.278004\pi\) | ||||
0.642242 | + | 0.766502i | \(0.278004\pi\) | |||||||
\(168\) | 4.18318 | 0.322740 | ||||||||
\(169\) | 19.1059 | 1.46969 | ||||||||
\(170\) | −33.3984 | −2.56154 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −7.90866 | −0.603029 | ||||||||
\(173\) | −4.31430 | −0.328010 | −0.164005 | − | 0.986459i | \(-0.552441\pi\) | ||||
−0.164005 | + | 0.986459i | \(0.552441\pi\) | |||||||
\(174\) | −0.972185 | −0.0737012 | ||||||||
\(175\) | −58.9674 | −4.45751 | ||||||||
\(176\) | −0.462917 | −0.0348937 | ||||||||
\(177\) | −11.8679 | −0.892043 | ||||||||
\(178\) | −17.1661 | −1.28665 | ||||||||
\(179\) | 5.74119 | 0.429117 | 0.214558 | − | 0.976711i | \(-0.431169\pi\) | ||||
0.214558 | + | 0.976711i | \(0.431169\pi\) | |||||||
\(180\) | 4.36993 | 0.325715 | ||||||||
\(181\) | −17.6145 | −1.30927 | −0.654637 | − | 0.755944i | \(-0.727178\pi\) | ||||
−0.654637 | + | 0.755944i | \(0.727178\pi\) | |||||||
\(182\) | 23.7028 | 1.75697 | ||||||||
\(183\) | 2.69186 | 0.198988 | ||||||||
\(184\) | 5.05356 | 0.372553 | ||||||||
\(185\) | −37.9145 | −2.78753 | ||||||||
\(186\) | −6.32253 | −0.463590 | ||||||||
\(187\) | 3.53797 | 0.258722 | ||||||||
\(188\) | 5.36140 | 0.391020 | ||||||||
\(189\) | 4.18318 | 0.304282 | ||||||||
\(190\) | 4.36993 | 0.317028 | ||||||||
\(191\) | 17.8500 | 1.29158 | 0.645790 | − | 0.763515i | \(-0.276528\pi\) | ||||
0.645790 | + | 0.763515i | \(0.276528\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.80102 | 0.633512 | 0.316756 | − | 0.948507i | \(-0.397406\pi\) | ||||
0.316756 | + | 0.948507i | \(0.397406\pi\) | |||||||
\(194\) | −12.7574 | −0.915926 | ||||||||
\(195\) | 24.7609 | 1.77317 | ||||||||
\(196\) | 10.4990 | 0.749931 | ||||||||
\(197\) | 11.0422 | 0.786721 | 0.393361 | − | 0.919384i | \(-0.371312\pi\) | ||||
0.393361 | + | 0.919384i | \(0.371312\pi\) | |||||||
\(198\) | −0.462917 | −0.0328981 | ||||||||
\(199\) | 5.15706 | 0.365574 | 0.182787 | − | 0.983153i | \(-0.441488\pi\) | ||||
0.182787 | + | 0.983153i | \(0.441488\pi\) | |||||||
\(200\) | 14.0963 | 0.996758 | ||||||||
\(201\) | 8.85931 | 0.624887 | ||||||||
\(202\) | −14.9630 | −1.05279 | ||||||||
\(203\) | −4.06683 | −0.285436 | ||||||||
\(204\) | 7.64277 | 0.535101 | ||||||||
\(205\) | −16.9339 | −1.18272 | ||||||||
\(206\) | −11.2134 | −0.781274 | ||||||||
\(207\) | 5.05356 | 0.351247 | ||||||||
\(208\) | −5.66621 | −0.392881 | ||||||||
\(209\) | −0.462917 | −0.0320207 | ||||||||
\(210\) | 18.2802 | 1.26146 | ||||||||
\(211\) | 8.38109 | 0.576978 | 0.288489 | − | 0.957483i | \(-0.406847\pi\) | ||||
0.288489 | + | 0.957483i | \(0.406847\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | 9.10783 | 0.624058 | ||||||||
\(214\) | −15.8051 | −1.08041 | ||||||||
\(215\) | −34.5603 | −2.35699 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −26.4483 | −1.79543 | ||||||||
\(218\) | −13.5273 | −0.916184 | ||||||||
\(219\) | 8.12473 | 0.549019 | ||||||||
\(220\) | −2.02292 | −0.136385 | ||||||||
\(221\) | 43.3056 | 2.91305 | ||||||||
\(222\) | 8.67622 | 0.582310 | ||||||||
\(223\) | 13.4343 | 0.899628 | 0.449814 | − | 0.893122i | \(-0.351490\pi\) | ||||
0.449814 | + | 0.893122i | \(0.351490\pi\) | |||||||
\(224\) | −4.18318 | −0.279501 | ||||||||
\(225\) | 14.0963 | 0.939753 | ||||||||
\(226\) | −0.380231 | −0.0252926 | ||||||||
\(227\) | 21.2391 | 1.40969 | 0.704844 | − | 0.709362i | \(-0.251017\pi\) | ||||
0.704844 | + | 0.709362i | \(0.251017\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | 14.2131 | 0.939226 | 0.469613 | − | 0.882872i | \(-0.344394\pi\) | ||||
0.469613 | + | 0.882872i | \(0.344394\pi\) | |||||||
\(230\) | 22.0837 | 1.45616 | ||||||||
\(231\) | −1.93647 | −0.127410 | ||||||||
\(232\) | 0.972185 | 0.0638271 | ||||||||
\(233\) | −7.85524 | −0.514614 | −0.257307 | − | 0.966330i | \(-0.582835\pi\) | ||||
−0.257307 | + | 0.966330i | \(0.582835\pi\) | |||||||
\(234\) | −5.66621 | −0.370412 | ||||||||
\(235\) | 23.4289 | 1.52834 | ||||||||
\(236\) | 11.8679 | 0.772532 | ||||||||
\(237\) | 3.22329 | 0.209375 | ||||||||
\(238\) | 31.9711 | 2.07238 | ||||||||
\(239\) | 14.4480 | 0.934564 | 0.467282 | − | 0.884108i | \(-0.345233\pi\) | ||||
0.467282 | + | 0.884108i | \(0.345233\pi\) | |||||||
\(240\) | −4.36993 | −0.282078 | ||||||||
\(241\) | −13.1851 | −0.849330 | −0.424665 | − | 0.905351i | \(-0.639608\pi\) | ||||
−0.424665 | + | 0.905351i | \(0.639608\pi\) | |||||||
\(242\) | −10.7857 | −0.693332 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.69186 | −0.172329 | ||||||||
\(245\) | 45.8800 | 2.93117 | ||||||||
\(246\) | 3.87511 | 0.247068 | ||||||||
\(247\) | −5.66621 | −0.360532 | ||||||||
\(248\) | 6.32253 | 0.401481 | ||||||||
\(249\) | −10.8534 | −0.687807 | ||||||||
\(250\) | 39.7501 | 2.51402 | ||||||||
\(251\) | −8.60144 | −0.542918 | −0.271459 | − | 0.962450i | \(-0.587506\pi\) | ||||
−0.271459 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(252\) | −4.18318 | −0.263516 | ||||||||
\(253\) | −2.33938 | −0.147075 | ||||||||
\(254\) | −8.23191 | −0.516516 | ||||||||
\(255\) | 33.3984 | 2.09149 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.5374 | 1.46822 | 0.734111 | − | 0.679030i | \(-0.237599\pi\) | ||||
0.734111 | + | 0.679030i | \(0.237599\pi\) | |||||||
\(258\) | 7.90866 | 0.492371 | ||||||||
\(259\) | 36.2943 | 2.25522 | ||||||||
\(260\) | −24.7609 | −1.53561 | ||||||||
\(261\) | 0.972185 | 0.0601767 | ||||||||
\(262\) | 9.88981 | 0.610994 | ||||||||
\(263\) | −3.24994 | −0.200400 | −0.100200 | − | 0.994967i | \(-0.531948\pi\) | ||||
−0.100200 | + | 0.994967i | \(0.531948\pi\) | |||||||
\(264\) | 0.462917 | 0.0284906 | ||||||||
\(265\) | −4.36993 | −0.268443 | ||||||||
\(266\) | −4.18318 | −0.256488 | ||||||||
\(267\) | 17.1661 | 1.05055 | ||||||||
\(268\) | −8.85931 | −0.541168 | ||||||||
\(269\) | 15.4797 | 0.943816 | 0.471908 | − | 0.881648i | \(-0.343566\pi\) | ||||
0.471908 | + | 0.881648i | \(0.343566\pi\) | |||||||
\(270\) | −4.36993 | −0.265945 | ||||||||
\(271\) | −30.8138 | −1.87180 | −0.935902 | − | 0.352261i | \(-0.885413\pi\) | ||||
−0.935902 | + | 0.352261i | \(0.885413\pi\) | |||||||
\(272\) | −7.64277 | −0.463411 | ||||||||
\(273\) | −23.7028 | −1.43456 | ||||||||
\(274\) | −9.88872 | −0.597399 | ||||||||
\(275\) | −6.52541 | −0.393497 | ||||||||
\(276\) | −5.05356 | −0.304188 | ||||||||
\(277\) | 0.982640 | 0.0590411 | 0.0295206 | − | 0.999564i | \(-0.490602\pi\) | ||||
0.0295206 | + | 0.999564i | \(0.490602\pi\) | |||||||
\(278\) | −5.37706 | −0.322495 | ||||||||
\(279\) | 6.32253 | 0.378520 | ||||||||
\(280\) | −18.2802 | −1.09245 | ||||||||
\(281\) | 13.3044 | 0.793675 | 0.396837 | − | 0.917889i | \(-0.370108\pi\) | ||||
0.396837 | + | 0.917889i | \(0.370108\pi\) | |||||||
\(282\) | −5.36140 | −0.319267 | ||||||||
\(283\) | −5.49847 | −0.326850 | −0.163425 | − | 0.986556i | \(-0.552254\pi\) | ||||
−0.163425 | + | 0.986556i | \(0.552254\pi\) | |||||||
\(284\) | −9.10783 | −0.540450 | ||||||||
\(285\) | −4.36993 | −0.258852 | ||||||||
\(286\) | 2.62299 | 0.155100 | ||||||||
\(287\) | 16.2103 | 0.956863 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 41.4120 | 2.43600 | ||||||||
\(290\) | 4.24838 | 0.249474 | ||||||||
\(291\) | 12.7574 | 0.747850 | ||||||||
\(292\) | −8.12473 | −0.475464 | ||||||||
\(293\) | 15.9482 | 0.931705 | 0.465853 | − | 0.884862i | \(-0.345748\pi\) | ||||
0.465853 | + | 0.884862i | \(0.345748\pi\) | |||||||
\(294\) | −10.4990 | −0.612316 | ||||||||
\(295\) | 51.8617 | 3.01951 | ||||||||
\(296\) | −8.67622 | −0.504295 | ||||||||
\(297\) | 0.462917 | 0.0268612 | ||||||||
\(298\) | 6.00567 | 0.347899 | ||||||||
\(299\) | −28.6345 | −1.65598 | ||||||||
\(300\) | −14.0963 | −0.813850 | ||||||||
\(301\) | 33.0834 | 1.90689 | ||||||||
\(302\) | −5.75130 | −0.330950 | ||||||||
\(303\) | 14.9630 | 0.859602 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −11.7632 | −0.673561 | ||||||||
\(306\) | −7.64277 | −0.436908 | ||||||||
\(307\) | −13.1936 | −0.753001 | −0.376501 | − | 0.926416i | \(-0.622873\pi\) | ||||
−0.376501 | + | 0.926416i | \(0.622873\pi\) | |||||||
\(308\) | 1.93647 | 0.110341 | ||||||||
\(309\) | 11.2134 | 0.637907 | ||||||||
\(310\) | 27.6290 | 1.56922 | ||||||||
\(311\) | −11.4478 | −0.649147 | −0.324573 | − | 0.945861i | \(-0.605221\pi\) | ||||
−0.324573 | + | 0.945861i | \(0.605221\pi\) | |||||||
\(312\) | 5.66621 | 0.320786 | ||||||||
\(313\) | 7.86254 | 0.444417 | 0.222209 | − | 0.974999i | \(-0.428673\pi\) | ||||
0.222209 | + | 0.974999i | \(0.428673\pi\) | |||||||
\(314\) | 0.329748 | 0.0186088 | ||||||||
\(315\) | −18.2802 | −1.02997 | ||||||||
\(316\) | −3.22329 | −0.181324 | ||||||||
\(317\) | 13.7246 | 0.770850 | 0.385425 | − | 0.922739i | \(-0.374055\pi\) | ||||
0.385425 | + | 0.922739i | \(0.374055\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | −0.450041 | −0.0251975 | ||||||||
\(320\) | 4.36993 | 0.244287 | ||||||||
\(321\) | 15.8051 | 0.882154 | ||||||||
\(322\) | −21.1400 | −1.17808 | ||||||||
\(323\) | −7.64277 | −0.425255 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −79.8725 | −4.43053 | ||||||||
\(326\) | −18.6873 | −1.03499 | ||||||||
\(327\) | 13.5273 | 0.748061 | ||||||||
\(328\) | −3.87511 | −0.213967 | ||||||||
\(329\) | −22.4277 | −1.23648 | ||||||||
\(330\) | 2.02292 | 0.111358 | ||||||||
\(331\) | −8.55029 | −0.469966 | −0.234983 | − | 0.971999i | \(-0.575503\pi\) | ||||
−0.234983 | + | 0.971999i | \(0.575503\pi\) | |||||||
\(332\) | 10.8534 | 0.595658 | ||||||||
\(333\) | −8.67622 | −0.475454 | ||||||||
\(334\) | 16.5992 | 0.908267 | ||||||||
\(335\) | −38.7146 | −2.11520 | ||||||||
\(336\) | 4.18318 | 0.228211 | ||||||||
\(337\) | 1.35714 | 0.0739279 | 0.0369640 | − | 0.999317i | \(-0.488231\pi\) | ||||
0.0369640 | + | 0.999317i | \(0.488231\pi\) | |||||||
\(338\) | 19.1059 | 1.03923 | ||||||||
\(339\) | 0.380231 | 0.0206513 | ||||||||
\(340\) | −33.3984 | −1.81128 | ||||||||
\(341\) | −2.92681 | −0.158496 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −14.6371 | −0.790330 | ||||||||
\(344\) | −7.90866 | −0.426406 | ||||||||
\(345\) | −22.0837 | −1.18895 | ||||||||
\(346\) | −4.31430 | −0.231938 | ||||||||
\(347\) | 14.8543 | 0.797422 | 0.398711 | − | 0.917077i | \(-0.369458\pi\) | ||||
0.398711 | + | 0.917077i | \(0.369458\pi\) | |||||||
\(348\) | −0.972185 | −0.0521146 | ||||||||
\(349\) | 8.57010 | 0.458747 | 0.229373 | − | 0.973338i | \(-0.426332\pi\) | ||||
0.229373 | + | 0.973338i | \(0.426332\pi\) | |||||||
\(350\) | −58.9674 | −3.15194 | ||||||||
\(351\) | 5.66621 | 0.302440 | ||||||||
\(352\) | −0.462917 | −0.0246736 | ||||||||
\(353\) | −27.4357 | −1.46025 | −0.730126 | − | 0.683312i | \(-0.760539\pi\) | ||||
−0.730126 | + | 0.683312i | \(0.760539\pi\) | |||||||
\(354\) | −11.8679 | −0.630770 | ||||||||
\(355\) | −39.8006 | −2.11240 | ||||||||
\(356\) | −17.1661 | −0.909800 | ||||||||
\(357\) | −31.9711 | −1.69209 | ||||||||
\(358\) | 5.74119 | 0.303431 | ||||||||
\(359\) | −22.3571 | −1.17996 | −0.589980 | − | 0.807418i | \(-0.700864\pi\) | ||||
−0.589980 | + | 0.807418i | \(0.700864\pi\) | |||||||
\(360\) | 4.36993 | 0.230316 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −17.6145 | −0.925796 | ||||||||
\(363\) | 10.7857 | 0.566103 | ||||||||
\(364\) | 23.7028 | 1.24236 | ||||||||
\(365\) | −35.5045 | −1.85839 | ||||||||
\(366\) | 2.69186 | 0.140706 | ||||||||
\(367\) | −34.2891 | −1.78987 | −0.894937 | − | 0.446192i | \(-0.852780\pi\) | ||||
−0.894937 | + | 0.446192i | \(0.852780\pi\) | |||||||
\(368\) | 5.05356 | 0.263435 | ||||||||
\(369\) | −3.87511 | −0.201730 | ||||||||
\(370\) | −37.9145 | −1.97108 | ||||||||
\(371\) | 4.18318 | 0.217180 | ||||||||
\(372\) | −6.32253 | −0.327808 | ||||||||
\(373\) | 15.6803 | 0.811894 | 0.405947 | − | 0.913897i | \(-0.366942\pi\) | ||||
0.405947 | + | 0.913897i | \(0.366942\pi\) | |||||||
\(374\) | 3.53797 | 0.182944 | ||||||||
\(375\) | −39.7501 | −2.05269 | ||||||||
\(376\) | 5.36140 | 0.276493 | ||||||||
\(377\) | −5.50860 | −0.283708 | ||||||||
\(378\) | 4.18318 | 0.215160 | ||||||||
\(379\) | 0.666461 | 0.0342338 | 0.0171169 | − | 0.999853i | \(-0.494551\pi\) | ||||
0.0171169 | + | 0.999853i | \(0.494551\pi\) | |||||||
\(380\) | 4.36993 | 0.224173 | ||||||||
\(381\) | 8.23191 | 0.421734 | ||||||||
\(382\) | 17.8500 | 0.913285 | ||||||||
\(383\) | 11.4556 | 0.585354 | 0.292677 | − | 0.956211i | \(-0.405454\pi\) | ||||
0.292677 | + | 0.956211i | \(0.405454\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 8.46223 | 0.431275 | ||||||||
\(386\) | 8.80102 | 0.447960 | ||||||||
\(387\) | −7.90866 | −0.402020 | ||||||||
\(388\) | −12.7574 | −0.647658 | ||||||||
\(389\) | 21.0287 | 1.06620 | 0.533099 | − | 0.846053i | \(-0.321027\pi\) | ||||
0.533099 | + | 0.846053i | \(0.321027\pi\) | |||||||
\(390\) | 24.7609 | 1.25382 | ||||||||
\(391\) | −38.6232 | −1.95326 | ||||||||
\(392\) | 10.4990 | 0.530281 | ||||||||
\(393\) | −9.88981 | −0.498875 | ||||||||
\(394\) | 11.0422 | 0.556296 | ||||||||
\(395\) | −14.0855 | −0.708720 | ||||||||
\(396\) | −0.462917 | −0.0232625 | ||||||||
\(397\) | −32.8051 | −1.64644 | −0.823222 | − | 0.567720i | \(-0.807826\pi\) | ||||
−0.823222 | + | 0.567720i | \(0.807826\pi\) | |||||||
\(398\) | 5.15706 | 0.258500 | ||||||||
\(399\) | 4.18318 | 0.209421 | ||||||||
\(400\) | 14.0963 | 0.704814 | ||||||||
\(401\) | 36.2376 | 1.80962 | 0.904810 | − | 0.425815i | \(-0.140013\pi\) | ||||
0.904810 | + | 0.425815i | \(0.140013\pi\) | |||||||
\(402\) | 8.85931 | 0.441862 | ||||||||
\(403\) | −35.8248 | −1.78456 | ||||||||
\(404\) | −14.9630 | −0.744437 | ||||||||
\(405\) | 4.36993 | 0.217144 | ||||||||
\(406\) | −4.06683 | −0.201833 | ||||||||
\(407\) | 4.01637 | 0.199084 | ||||||||
\(408\) | 7.64277 | 0.378374 | ||||||||
\(409\) | −3.38851 | −0.167551 | −0.0837755 | − | 0.996485i | \(-0.526698\pi\) | ||||
−0.0837755 | + | 0.996485i | \(0.526698\pi\) | |||||||
\(410\) | −16.9339 | −0.836308 | ||||||||
\(411\) | 9.88872 | 0.487775 | ||||||||
\(412\) | −11.2134 | −0.552444 | ||||||||
\(413\) | −49.6454 | −2.44289 | ||||||||
\(414\) | 5.05356 | 0.248369 | ||||||||
\(415\) | 47.4287 | 2.32818 | ||||||||
\(416\) | −5.66621 | −0.277809 | ||||||||
\(417\) | 5.37706 | 0.263316 | ||||||||
\(418\) | −0.462917 | −0.0226420 | ||||||||
\(419\) | 23.9914 | 1.17206 | 0.586029 | − | 0.810290i | \(-0.300690\pi\) | ||||
0.586029 | + | 0.810290i | \(0.300690\pi\) | |||||||
\(420\) | 18.2802 | 0.891984 | ||||||||
\(421\) | −4.33701 | −0.211373 | −0.105686 | − | 0.994400i | \(-0.533704\pi\) | ||||
−0.105686 | + | 0.994400i | \(0.533704\pi\) | |||||||
\(422\) | 8.38109 | 0.407985 | ||||||||
\(423\) | 5.36140 | 0.260680 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | −107.735 | −5.22590 | ||||||||
\(426\) | 9.10783 | 0.441276 | ||||||||
\(427\) | 11.2605 | 0.544936 | ||||||||
\(428\) | −15.8051 | −0.763968 | ||||||||
\(429\) | −2.62299 | −0.126639 | ||||||||
\(430\) | −34.5603 | −1.66664 | ||||||||
\(431\) | 20.6639 | 0.995347 | 0.497673 | − | 0.867365i | \(-0.334188\pi\) | ||||
0.497673 | + | 0.867365i | \(0.334188\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.41555 | 0.212198 | 0.106099 | − | 0.994356i | \(-0.466164\pi\) | ||||
0.106099 | + | 0.994356i | \(0.466164\pi\) | |||||||
\(434\) | −26.4483 | −1.26956 | ||||||||
\(435\) | −4.24838 | −0.203694 | ||||||||
\(436\) | −13.5273 | −0.647840 | ||||||||
\(437\) | 5.05356 | 0.241744 | ||||||||
\(438\) | 8.12473 | 0.388215 | ||||||||
\(439\) | 30.7827 | 1.46918 | 0.734589 | − | 0.678512i | \(-0.237375\pi\) | ||||
0.734589 | + | 0.678512i | \(0.237375\pi\) | |||||||
\(440\) | −2.02292 | −0.0964387 | ||||||||
\(441\) | 10.4990 | 0.499954 | ||||||||
\(442\) | 43.3056 | 2.05984 | ||||||||
\(443\) | 12.9311 | 0.614377 | 0.307188 | − | 0.951649i | \(-0.400612\pi\) | ||||
0.307188 | + | 0.951649i | \(0.400612\pi\) | |||||||
\(444\) | 8.67622 | 0.411755 | ||||||||
\(445\) | −75.0145 | −3.55603 | ||||||||
\(446\) | 13.4343 | 0.636133 | ||||||||
\(447\) | −6.00567 | −0.284059 | ||||||||
\(448\) | −4.18318 | −0.197637 | ||||||||
\(449\) | −23.5987 | −1.11369 | −0.556846 | − | 0.830616i | \(-0.687988\pi\) | ||||
−0.556846 | + | 0.830616i | \(0.687988\pi\) | |||||||
\(450\) | 14.0963 | 0.664505 | ||||||||
\(451\) | 1.79385 | 0.0844693 | ||||||||
\(452\) | −0.380231 | −0.0178846 | ||||||||
\(453\) | 5.75130 | 0.270220 | ||||||||
\(454\) | 21.2391 | 0.996800 | ||||||||
\(455\) | 103.580 | 4.85589 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −7.65871 | −0.358260 | −0.179130 | − | 0.983825i | \(-0.557328\pi\) | ||||
−0.179130 | + | 0.983825i | \(0.557328\pi\) | |||||||
\(458\) | 14.2131 | 0.664133 | ||||||||
\(459\) | 7.64277 | 0.356734 | ||||||||
\(460\) | 22.0837 | 1.02966 | ||||||||
\(461\) | −10.5593 | −0.491795 | −0.245898 | − | 0.969296i | \(-0.579083\pi\) | ||||
−0.245898 | + | 0.969296i | \(0.579083\pi\) | |||||||
\(462\) | −1.93647 | −0.0900927 | ||||||||
\(463\) | 14.7577 | 0.685846 | 0.342923 | − | 0.939363i | \(-0.388583\pi\) | ||||
0.342923 | + | 0.939363i | \(0.388583\pi\) | |||||||
\(464\) | 0.972185 | 0.0451326 | ||||||||
\(465\) | −27.6290 | −1.28126 | ||||||||
\(466\) | −7.85524 | −0.363887 | ||||||||
\(467\) | −18.3402 | −0.848682 | −0.424341 | − | 0.905502i | \(-0.639494\pi\) | ||||
−0.424341 | + | 0.905502i | \(0.639494\pi\) | |||||||
\(468\) | −5.66621 | −0.261921 | ||||||||
\(469\) | 37.0601 | 1.71128 | ||||||||
\(470\) | 23.4289 | 1.08070 | ||||||||
\(471\) | −0.329748 | −0.0151940 | ||||||||
\(472\) | 11.8679 | 0.546262 | ||||||||
\(473\) | 3.66105 | 0.168335 | ||||||||
\(474\) | 3.22329 | 0.148050 | ||||||||
\(475\) | 14.0963 | 0.646782 | ||||||||
\(476\) | 31.9711 | 1.46539 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 14.4480 | 0.660836 | ||||||||
\(479\) | −20.7969 | −0.950237 | −0.475118 | − | 0.879922i | \(-0.657595\pi\) | ||||
−0.475118 | + | 0.879922i | \(0.657595\pi\) | |||||||
\(480\) | −4.36993 | −0.199459 | ||||||||
\(481\) | 49.1613 | 2.24156 | ||||||||
\(482\) | −13.1851 | −0.600567 | ||||||||
\(483\) | 21.1400 | 0.961902 | ||||||||
\(484\) | −10.7857 | −0.490259 | ||||||||
\(485\) | −55.7488 | −2.53142 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 4.73868 | 0.214730 | 0.107365 | − | 0.994220i | \(-0.465759\pi\) | ||||
0.107365 | + | 0.994220i | \(0.465759\pi\) | |||||||
\(488\) | −2.69186 | −0.121855 | ||||||||
\(489\) | 18.6873 | 0.845068 | ||||||||
\(490\) | 45.8800 | 2.07265 | ||||||||
\(491\) | 7.66928 | 0.346110 | 0.173055 | − | 0.984912i | \(-0.444636\pi\) | ||||
0.173055 | + | 0.984912i | \(0.444636\pi\) | |||||||
\(492\) | 3.87511 | 0.174703 | ||||||||
\(493\) | −7.43019 | −0.334639 | ||||||||
\(494\) | −5.66621 | −0.254935 | ||||||||
\(495\) | −2.02292 | −0.0909233 | ||||||||
\(496\) | 6.32253 | 0.283890 | ||||||||
\(497\) | 38.0997 | 1.70901 | ||||||||
\(498\) | −10.8534 | −0.486353 | ||||||||
\(499\) | −16.1706 | −0.723895 | −0.361948 | − | 0.932198i | \(-0.617888\pi\) | ||||
−0.361948 | + | 0.932198i | \(0.617888\pi\) | |||||||
\(500\) | 39.7501 | 1.77768 | ||||||||
\(501\) | −16.5992 | −0.741597 | ||||||||
\(502\) | −8.60144 | −0.383901 | ||||||||
\(503\) | −4.14454 | −0.184796 | −0.0923980 | − | 0.995722i | \(-0.529453\pi\) | ||||
−0.0923980 | + | 0.995722i | \(0.529453\pi\) | |||||||
\(504\) | −4.18318 | −0.186334 | ||||||||
\(505\) | −65.3873 | −2.90970 | ||||||||
\(506\) | −2.33938 | −0.103998 | ||||||||
\(507\) | −19.1059 | −0.848524 | ||||||||
\(508\) | −8.23191 | −0.365232 | ||||||||
\(509\) | −8.16352 | −0.361842 | −0.180921 | − | 0.983498i | \(-0.557908\pi\) | ||||
−0.180921 | + | 0.983498i | \(0.557908\pi\) | |||||||
\(510\) | 33.3984 | 1.47891 | ||||||||
\(511\) | 33.9873 | 1.50351 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 23.5374 | 1.03819 | ||||||||
\(515\) | −49.0017 | −2.15927 | ||||||||
\(516\) | 7.90866 | 0.348159 | ||||||||
\(517\) | −2.48188 | −0.109153 | ||||||||
\(518\) | 36.2943 | 1.59468 | ||||||||
\(519\) | 4.31430 | 0.189377 | ||||||||
\(520\) | −24.7609 | −1.08584 | ||||||||
\(521\) | −33.1616 | −1.45283 | −0.726417 | − | 0.687254i | \(-0.758816\pi\) | ||||
−0.726417 | + | 0.687254i | \(0.758816\pi\) | |||||||
\(522\) | 0.972185 | 0.0425514 | ||||||||
\(523\) | 3.91437 | 0.171163 | 0.0855816 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855816 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(524\) | 9.88981 | 0.432038 | ||||||||
\(525\) | 58.9674 | 2.57355 | ||||||||
\(526\) | −3.24994 | −0.141704 | ||||||||
\(527\) | −48.3217 | −2.10492 | ||||||||
\(528\) | 0.462917 | 0.0201459 | ||||||||
\(529\) | 2.53844 | 0.110367 | ||||||||
\(530\) | −4.36993 | −0.189818 | ||||||||
\(531\) | 11.8679 | 0.515021 | ||||||||
\(532\) | −4.18318 | −0.181364 | ||||||||
\(533\) | 21.9572 | 0.951070 | ||||||||
\(534\) | 17.1661 | 0.742849 | ||||||||
\(535\) | −69.0671 | −2.98603 | ||||||||
\(536\) | −8.85931 | −0.382664 | ||||||||
\(537\) | −5.74119 | −0.247751 | ||||||||
\(538\) | 15.4797 | 0.667378 | ||||||||
\(539\) | −4.86018 | −0.209343 | ||||||||
\(540\) | −4.36993 | −0.188052 | ||||||||
\(541\) | 39.4448 | 1.69586 | 0.847932 | − | 0.530105i | \(-0.177847\pi\) | ||||
0.847932 | + | 0.530105i | \(0.177847\pi\) | |||||||
\(542\) | −30.8138 | −1.32356 | ||||||||
\(543\) | 17.6145 | 0.755909 | ||||||||
\(544\) | −7.64277 | −0.327681 | ||||||||
\(545\) | −59.1134 | −2.53214 | ||||||||
\(546\) | −23.7028 | −1.01439 | ||||||||
\(547\) | 7.37946 | 0.315523 | 0.157761 | − | 0.987477i | \(-0.449572\pi\) | ||||
0.157761 | + | 0.987477i | \(0.449572\pi\) | |||||||
\(548\) | −9.88872 | −0.422425 | ||||||||
\(549\) | −2.69186 | −0.114886 | ||||||||
\(550\) | −6.52541 | −0.278245 | ||||||||
\(551\) | 0.972185 | 0.0414165 | ||||||||
\(552\) | −5.05356 | −0.215094 | ||||||||
\(553\) | 13.4836 | 0.573381 | ||||||||
\(554\) | 0.982640 | 0.0417484 | ||||||||
\(555\) | 37.9145 | 1.60938 | ||||||||
\(556\) | −5.37706 | −0.228038 | ||||||||
\(557\) | 8.53921 | 0.361818 | 0.180909 | − | 0.983500i | \(-0.442096\pi\) | ||||
0.180909 | + | 0.983500i | \(0.442096\pi\) | |||||||
\(558\) | 6.32253 | 0.267654 | ||||||||
\(559\) | 44.8121 | 1.89535 | ||||||||
\(560\) | −18.2802 | −0.772480 | ||||||||
\(561\) | −3.53797 | −0.149373 | ||||||||
\(562\) | 13.3044 | 0.561213 | ||||||||
\(563\) | −41.6161 | −1.75391 | −0.876956 | − | 0.480572i | \(-0.840429\pi\) | ||||
−0.876956 | + | 0.480572i | \(0.840429\pi\) | |||||||
\(564\) | −5.36140 | −0.225756 | ||||||||
\(565\) | −1.66158 | −0.0699033 | ||||||||
\(566\) | −5.49847 | −0.231118 | ||||||||
\(567\) | −4.18318 | −0.175677 | ||||||||
\(568\) | −9.10783 | −0.382156 | ||||||||
\(569\) | 23.3829 | 0.980264 | 0.490132 | − | 0.871648i | \(-0.336949\pi\) | ||||
0.490132 | + | 0.871648i | \(0.336949\pi\) | |||||||
\(570\) | −4.36993 | −0.183036 | ||||||||
\(571\) | 6.61125 | 0.276672 | 0.138336 | − | 0.990385i | \(-0.455825\pi\) | ||||
0.138336 | + | 0.990385i | \(0.455825\pi\) | |||||||
\(572\) | 2.62299 | 0.109673 | ||||||||
\(573\) | −17.8500 | −0.745694 | ||||||||
\(574\) | 16.2103 | 0.676604 | ||||||||
\(575\) | 71.2364 | 2.97076 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −4.40595 | −0.183422 | −0.0917110 | − | 0.995786i | \(-0.529234\pi\) | ||||
−0.0917110 | + | 0.995786i | \(0.529234\pi\) | |||||||
\(578\) | 41.4120 | 1.72251 | ||||||||
\(579\) | −8.80102 | −0.365758 | ||||||||
\(580\) | 4.24838 | 0.176404 | ||||||||
\(581\) | −45.4018 | −1.88359 | ||||||||
\(582\) | 12.7574 | 0.528810 | ||||||||
\(583\) | 0.462917 | 0.0191721 | ||||||||
\(584\) | −8.12473 | −0.336204 | ||||||||
\(585\) | −24.7609 | −1.02374 | ||||||||
\(586\) | 15.9482 | 0.658815 | ||||||||
\(587\) | 17.3677 | 0.716840 | 0.358420 | − | 0.933560i | \(-0.383316\pi\) | ||||
0.358420 | + | 0.933560i | \(0.383316\pi\) | |||||||
\(588\) | −10.4990 | −0.432973 | ||||||||
\(589\) | 6.32253 | 0.260515 | ||||||||
\(590\) | 51.8617 | 2.13511 | ||||||||
\(591\) | −11.0422 | −0.454214 | ||||||||
\(592\) | −8.67622 | −0.356591 | ||||||||
\(593\) | −4.65942 | −0.191339 | −0.0956696 | − | 0.995413i | \(-0.530499\pi\) | ||||
−0.0956696 | + | 0.995413i | \(0.530499\pi\) | |||||||
\(594\) | 0.462917 | 0.0189937 | ||||||||
\(595\) | 139.712 | 5.72762 | ||||||||
\(596\) | 6.00567 | 0.246002 | ||||||||
\(597\) | −5.15706 | −0.211064 | ||||||||
\(598\) | −28.6345 | −1.17095 | ||||||||
\(599\) | 22.4463 | 0.917132 | 0.458566 | − | 0.888660i | \(-0.348363\pi\) | ||||
0.458566 | + | 0.888660i | \(0.348363\pi\) | |||||||
\(600\) | −14.0963 | −0.575479 | ||||||||
\(601\) | 23.2169 | 0.947037 | 0.473518 | − | 0.880784i | \(-0.342984\pi\) | ||||
0.473518 | + | 0.880784i | \(0.342984\pi\) | |||||||
\(602\) | 33.0834 | 1.34838 | ||||||||
\(603\) | −8.85931 | −0.360779 | ||||||||
\(604\) | −5.75130 | −0.234017 | ||||||||
\(605\) | −47.1328 | −1.91622 | ||||||||
\(606\) | 14.9630 | 0.607830 | ||||||||
\(607\) | −4.61777 | −0.187430 | −0.0937148 | − | 0.995599i | \(-0.529874\pi\) | ||||
−0.0937148 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 4.06683 | 0.164796 | ||||||||
\(610\) | −11.7632 | −0.476280 | ||||||||
\(611\) | −30.3788 | −1.22900 | ||||||||
\(612\) | −7.64277 | −0.308941 | ||||||||
\(613\) | 40.5344 | 1.63717 | 0.818584 | − | 0.574386i | \(-0.194759\pi\) | ||||
0.818584 | + | 0.574386i | \(0.194759\pi\) | |||||||
\(614\) | −13.1936 | −0.532452 | ||||||||
\(615\) | 16.9339 | 0.682843 | ||||||||
\(616\) | 1.93647 | 0.0780225 | ||||||||
\(617\) | 12.4860 | 0.502669 | 0.251334 | − | 0.967900i | \(-0.419131\pi\) | ||||
0.251334 | + | 0.967900i | \(0.419131\pi\) | |||||||
\(618\) | 11.2134 | 0.451069 | ||||||||
\(619\) | −40.5165 | −1.62850 | −0.814248 | − | 0.580517i | \(-0.802850\pi\) | ||||
−0.814248 | + | 0.580517i | \(0.802850\pi\) | |||||||
\(620\) | 27.6290 | 1.10961 | ||||||||
\(621\) | −5.05356 | −0.202792 | ||||||||
\(622\) | −11.4478 | −0.459016 | ||||||||
\(623\) | 71.8089 | 2.87696 | ||||||||
\(624\) | 5.66621 | 0.226830 | ||||||||
\(625\) | 103.224 | 4.12896 | ||||||||
\(626\) | 7.86254 | 0.314250 | ||||||||
\(627\) | 0.462917 | 0.0184871 | ||||||||
\(628\) | 0.329748 | 0.0131584 | ||||||||
\(629\) | 66.3104 | 2.64397 | ||||||||
\(630\) | −18.2802 | −0.728302 | ||||||||
\(631\) | 6.88667 | 0.274154 | 0.137077 | − | 0.990560i | \(-0.456229\pi\) | ||||
0.137077 | + | 0.990560i | \(0.456229\pi\) | |||||||
\(632\) | −3.22329 | −0.128215 | ||||||||
\(633\) | −8.38109 | −0.333119 | ||||||||
\(634\) | 13.7246 | 0.545073 | ||||||||
\(635\) | −35.9729 | −1.42754 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | −59.4897 | −2.35707 | ||||||||
\(638\) | −0.450041 | −0.0178173 | ||||||||
\(639\) | −9.10783 | −0.360300 | ||||||||
\(640\) | 4.36993 | 0.172737 | ||||||||
\(641\) | 6.80835 | 0.268914 | 0.134457 | − | 0.990919i | \(-0.457071\pi\) | ||||
0.134457 | + | 0.990919i | \(0.457071\pi\) | |||||||
\(642\) | 15.8051 | 0.623777 | ||||||||
\(643\) | 32.7345 | 1.29092 | 0.645461 | − | 0.763793i | \(-0.276665\pi\) | ||||
0.645461 | + | 0.763793i | \(0.276665\pi\) | |||||||
\(644\) | −21.1400 | −0.833031 | ||||||||
\(645\) | 34.5603 | 1.36081 | ||||||||
\(646\) | −7.64277 | −0.300701 | ||||||||
\(647\) | 35.5943 | 1.39936 | 0.699678 | − | 0.714458i | \(-0.253327\pi\) | ||||
0.699678 | + | 0.714458i | \(0.253327\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.49384 | −0.215652 | ||||||||
\(650\) | −79.8725 | −3.13286 | ||||||||
\(651\) | 26.4483 | 1.03659 | ||||||||
\(652\) | −18.6873 | −0.731850 | ||||||||
\(653\) | −9.12422 | −0.357058 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(654\) | 13.5273 | 0.528959 | ||||||||
\(655\) | 43.2178 | 1.68866 | ||||||||
\(656\) | −3.87511 | −0.151297 | ||||||||
\(657\) | −8.12473 | −0.316976 | ||||||||
\(658\) | −22.4277 | −0.874324 | ||||||||
\(659\) | −1.10571 | −0.0430722 | −0.0215361 | − | 0.999768i | \(-0.506856\pi\) | ||||
−0.0215361 | + | 0.999768i | \(0.506856\pi\) | |||||||
\(660\) | 2.02292 | 0.0787419 | ||||||||
\(661\) | −33.3931 | −1.29884 | −0.649420 | − | 0.760430i | \(-0.724988\pi\) | ||||
−0.649420 | + | 0.760430i | \(0.724988\pi\) | |||||||
\(662\) | −8.55029 | −0.332316 | ||||||||
\(663\) | −43.3056 | −1.68185 | ||||||||
\(664\) | 10.8534 | 0.421194 | ||||||||
\(665\) | −18.2802 | −0.708877 | ||||||||
\(666\) | −8.67622 | −0.336197 | ||||||||
\(667\) | 4.91299 | 0.190232 | ||||||||
\(668\) | 16.5992 | 0.642242 | ||||||||
\(669\) | −13.4343 | −0.519401 | ||||||||
\(670\) | −38.7146 | −1.49567 | ||||||||
\(671\) | 1.24611 | 0.0481055 | ||||||||
\(672\) | 4.18318 | 0.161370 | ||||||||
\(673\) | −48.1559 | −1.85627 | −0.928136 | − | 0.372240i | \(-0.878590\pi\) | ||||
−0.928136 | + | 0.372240i | \(0.878590\pi\) | |||||||
\(674\) | 1.35714 | 0.0522749 | ||||||||
\(675\) | −14.0963 | −0.542566 | ||||||||
\(676\) | 19.1059 | 0.734843 | ||||||||
\(677\) | −39.1433 | −1.50440 | −0.752200 | − | 0.658934i | \(-0.771007\pi\) | ||||
−0.752200 | + | 0.658934i | \(0.771007\pi\) | |||||||
\(678\) | 0.380231 | 0.0146027 | ||||||||
\(679\) | 53.3665 | 2.04802 | ||||||||
\(680\) | −33.3984 | −1.28077 | ||||||||
\(681\) | −21.2391 | −0.813884 | ||||||||
\(682\) | −2.92681 | −0.112073 | ||||||||
\(683\) | 14.7869 | 0.565805 | 0.282902 | − | 0.959149i | \(-0.408703\pi\) | ||||
0.282902 | + | 0.959149i | \(0.408703\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −43.2130 | −1.65108 | ||||||||
\(686\) | −14.6371 | −0.558848 | ||||||||
\(687\) | −14.2131 | −0.542262 | ||||||||
\(688\) | −7.90866 | −0.301515 | ||||||||
\(689\) | 5.66621 | 0.215865 | ||||||||
\(690\) | −22.0837 | −0.840712 | ||||||||
\(691\) | −2.93764 | −0.111753 | −0.0558765 | − | 0.998438i | \(-0.517795\pi\) | ||||
−0.0558765 | + | 0.998438i | \(0.517795\pi\) | |||||||
\(692\) | −4.31430 | −0.164005 | ||||||||
\(693\) | 1.93647 | 0.0735603 | ||||||||
\(694\) | 14.8543 | 0.563862 | ||||||||
\(695\) | −23.4974 | −0.891306 | ||||||||
\(696\) | −0.972185 | −0.0368506 | ||||||||
\(697\) | 29.6166 | 1.12181 | ||||||||
\(698\) | 8.57010 | 0.324383 | ||||||||
\(699\) | 7.85524 | 0.297113 | ||||||||
\(700\) | −58.9674 | −2.22876 | ||||||||
\(701\) | −19.3762 | −0.731828 | −0.365914 | − | 0.930649i | \(-0.619244\pi\) | ||||
−0.365914 | + | 0.930649i | \(0.619244\pi\) | |||||||
\(702\) | 5.66621 | 0.213857 | ||||||||
\(703\) | −8.67622 | −0.327230 | ||||||||
\(704\) | −0.462917 | −0.0174468 | ||||||||
\(705\) | −23.4289 | −0.882385 | ||||||||
\(706\) | −27.4357 | −1.03255 | ||||||||
\(707\) | 62.5930 | 2.35405 | ||||||||
\(708\) | −11.8679 | −0.446021 | ||||||||
\(709\) | 1.81717 | 0.0682452 | 0.0341226 | − | 0.999418i | \(-0.489136\pi\) | ||||
0.0341226 | + | 0.999418i | \(0.489136\pi\) | |||||||
\(710\) | −39.8006 | −1.49369 | ||||||||
\(711\) | −3.22329 | −0.120883 | ||||||||
\(712\) | −17.1661 | −0.643326 | ||||||||
\(713\) | 31.9513 | 1.19658 | ||||||||
\(714\) | −31.9711 | −1.19649 | ||||||||
\(715\) | 11.4623 | 0.428664 | ||||||||
\(716\) | 5.74119 | 0.214558 | ||||||||
\(717\) | −14.4480 | −0.539571 | ||||||||
\(718\) | −22.3571 | −0.834358 | ||||||||
\(719\) | −42.8677 | −1.59870 | −0.799348 | − | 0.600869i | \(-0.794821\pi\) | ||||
−0.799348 | + | 0.600869i | \(0.794821\pi\) | |||||||
\(720\) | 4.36993 | 0.162858 | ||||||||
\(721\) | 46.9077 | 1.74693 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 13.1851 | 0.490361 | ||||||||
\(724\) | −17.6145 | −0.654637 | ||||||||
\(725\) | 13.7042 | 0.508961 | ||||||||
\(726\) | 10.7857 | 0.400295 | ||||||||
\(727\) | 46.7541 | 1.73401 | 0.867006 | − | 0.498297i | \(-0.166041\pi\) | ||||
0.867006 | + | 0.498297i | \(0.166041\pi\) | |||||||
\(728\) | 23.7028 | 0.878484 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −35.5045 | −1.31408 | ||||||||
\(731\) | 60.4441 | 2.23560 | ||||||||
\(732\) | 2.69186 | 0.0994940 | ||||||||
\(733\) | 42.7273 | 1.57817 | 0.789084 | − | 0.614286i | \(-0.210556\pi\) | ||||
0.789084 | + | 0.614286i | \(0.210556\pi\) | |||||||
\(734\) | −34.2891 | −1.26563 | ||||||||
\(735\) | −45.8800 | −1.69231 | ||||||||
\(736\) | 5.05356 | 0.186277 | ||||||||
\(737\) | 4.10113 | 0.151067 | ||||||||
\(738\) | −3.87511 | −0.142645 | ||||||||
\(739\) | −16.6710 | −0.613252 | −0.306626 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306626 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(740\) | −37.9145 | −1.39376 | ||||||||
\(741\) | 5.66621 | 0.208153 | ||||||||
\(742\) | 4.18318 | 0.153570 | ||||||||
\(743\) | 1.56657 | 0.0574719 | 0.0287359 | − | 0.999587i | \(-0.490852\pi\) | ||||
0.0287359 | + | 0.999587i | \(0.490852\pi\) | |||||||
\(744\) | −6.32253 | −0.231795 | ||||||||
\(745\) | 26.2444 | 0.961520 | ||||||||
\(746\) | 15.6803 | 0.574096 | ||||||||
\(747\) | 10.8534 | 0.397106 | ||||||||
\(748\) | 3.53797 | 0.129361 | ||||||||
\(749\) | 66.1156 | 2.41581 | ||||||||
\(750\) | −39.7501 | −1.45147 | ||||||||
\(751\) | 13.8383 | 0.504966 | 0.252483 | − | 0.967601i | \(-0.418753\pi\) | ||||
0.252483 | + | 0.967601i | \(0.418753\pi\) | |||||||
\(752\) | 5.36140 | 0.195510 | ||||||||
\(753\) | 8.60144 | 0.313454 | ||||||||
\(754\) | −5.50860 | −0.200612 | ||||||||
\(755\) | −25.1328 | −0.914675 | ||||||||
\(756\) | 4.18318 | 0.152141 | ||||||||
\(757\) | 13.8095 | 0.501914 | 0.250957 | − | 0.967998i | \(-0.419255\pi\) | ||||
0.250957 | + | 0.967998i | \(0.419255\pi\) | |||||||
\(758\) | 0.666461 | 0.0242070 | ||||||||
\(759\) | 2.33938 | 0.0849141 | ||||||||
\(760\) | 4.36993 | 0.158514 | ||||||||
\(761\) | 46.7409 | 1.69436 | 0.847179 | − | 0.531308i | \(-0.178299\pi\) | ||||
0.847179 | + | 0.531308i | \(0.178299\pi\) | |||||||
\(762\) | 8.23191 | 0.298211 | ||||||||
\(763\) | 56.5872 | 2.04859 | ||||||||
\(764\) | 17.8500 | 0.645790 | ||||||||
\(765\) | −33.3984 | −1.20752 | ||||||||
\(766\) | 11.4556 | 0.413908 | ||||||||
\(767\) | −67.2458 | −2.42810 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 17.6905 | 0.637935 | 0.318968 | − | 0.947766i | \(-0.396664\pi\) | ||||
0.318968 | + | 0.947766i | \(0.396664\pi\) | |||||||
\(770\) | 8.46223 | 0.304958 | ||||||||
\(771\) | −23.5374 | −0.847678 | ||||||||
\(772\) | 8.80102 | 0.316756 | ||||||||
\(773\) | 20.2522 | 0.728421 | 0.364211 | − | 0.931317i | \(-0.381339\pi\) | ||||
0.364211 | + | 0.931317i | \(0.381339\pi\) | |||||||
\(774\) | −7.90866 | −0.284271 | ||||||||
\(775\) | 89.1242 | 3.20144 | ||||||||
\(776\) | −12.7574 | −0.457963 | ||||||||
\(777\) | −36.2943 | −1.30205 | ||||||||
\(778\) | 21.0287 | 0.753916 | ||||||||
\(779\) | −3.87511 | −0.138840 | ||||||||
\(780\) | 24.7609 | 0.886584 | ||||||||
\(781\) | 4.21617 | 0.150866 | ||||||||
\(782\) | −38.6232 | −1.38116 | ||||||||
\(783\) | −0.972185 | −0.0347431 | ||||||||
\(784\) | 10.4990 | 0.374966 | ||||||||
\(785\) | 1.44098 | 0.0514307 | ||||||||
\(786\) | −9.88981 | −0.352758 | ||||||||
\(787\) | −20.7858 | −0.740934 | −0.370467 | − | 0.928846i | \(-0.620802\pi\) | ||||
−0.370467 | + | 0.928846i | \(0.620802\pi\) | |||||||
\(788\) | 11.0422 | 0.393361 | ||||||||
\(789\) | 3.24994 | 0.115701 | ||||||||
\(790\) | −14.0855 | −0.501141 | ||||||||
\(791\) | 1.59058 | 0.0565544 | ||||||||
\(792\) | −0.462917 | −0.0164490 | ||||||||
\(793\) | 15.2526 | 0.541637 | ||||||||
\(794\) | −32.8051 | −1.16421 | ||||||||
\(795\) | 4.36993 | 0.154985 | ||||||||
\(796\) | 5.15706 | 0.182787 | ||||||||
\(797\) | −26.5141 | −0.939177 | −0.469589 | − | 0.882885i | \(-0.655598\pi\) | ||||
−0.469589 | + | 0.882885i | \(0.655598\pi\) | |||||||
\(798\) | 4.18318 | 0.148083 | ||||||||
\(799\) | −40.9760 | −1.44963 | ||||||||
\(800\) | 14.0963 | 0.498379 | ||||||||
\(801\) | −17.1661 | −0.606533 | ||||||||
\(802\) | 36.2376 | 1.27959 | ||||||||
\(803\) | 3.76108 | 0.132726 | ||||||||
\(804\) | 8.85931 | 0.312444 | ||||||||
\(805\) | −92.3802 | −3.25597 | ||||||||
\(806\) | −35.8248 | −1.26187 | ||||||||
\(807\) | −15.4797 | −0.544912 | ||||||||
\(808\) | −14.9630 | −0.526397 | ||||||||
\(809\) | 45.9823 | 1.61665 | 0.808326 | − | 0.588736i | \(-0.200374\pi\) | ||||
0.808326 | + | 0.588736i | \(0.200374\pi\) | |||||||
\(810\) | 4.36993 | 0.153544 | ||||||||
\(811\) | 12.3784 | 0.434666 | 0.217333 | − | 0.976098i | \(-0.430264\pi\) | ||||
0.217333 | + | 0.976098i | \(0.430264\pi\) | |||||||
\(812\) | −4.06683 | −0.142718 | ||||||||
\(813\) | 30.8138 | 1.08069 | ||||||||
\(814\) | 4.01637 | 0.140774 | ||||||||
\(815\) | −81.6621 | −2.86050 | ||||||||
\(816\) | 7.64277 | 0.267551 | ||||||||
\(817\) | −7.90866 | −0.276689 | ||||||||
\(818\) | −3.38851 | −0.118476 | ||||||||
\(819\) | 23.7028 | 0.828243 | ||||||||
\(820\) | −16.9339 | −0.591359 | ||||||||
\(821\) | −29.1984 | −1.01903 | −0.509516 | − | 0.860461i | \(-0.670175\pi\) | ||||
−0.509516 | + | 0.860461i | \(0.670175\pi\) | |||||||
\(822\) | 9.88872 | 0.344909 | ||||||||
\(823\) | 8.25456 | 0.287736 | 0.143868 | − | 0.989597i | \(-0.454046\pi\) | ||||
0.143868 | + | 0.989597i | \(0.454046\pi\) | |||||||
\(824\) | −11.2134 | −0.390637 | ||||||||
\(825\) | 6.52541 | 0.227186 | ||||||||
\(826\) | −49.6454 | −1.72739 | ||||||||
\(827\) | 19.0354 | 0.661925 | 0.330962 | − | 0.943644i | \(-0.392627\pi\) | ||||
0.330962 | + | 0.943644i | \(0.392627\pi\) | |||||||
\(828\) | 5.05356 | 0.175623 | ||||||||
\(829\) | −18.5500 | −0.644269 | −0.322134 | − | 0.946694i | \(-0.604400\pi\) | ||||
−0.322134 | + | 0.946694i | \(0.604400\pi\) | |||||||
\(830\) | 47.4287 | 1.64627 | ||||||||
\(831\) | −0.982640 | −0.0340874 | ||||||||
\(832\) | −5.66621 | −0.196440 | ||||||||
\(833\) | −80.2418 | −2.78021 | ||||||||
\(834\) | 5.37706 | 0.186192 | ||||||||
\(835\) | 72.5373 | 2.51026 | ||||||||
\(836\) | −0.462917 | −0.0160103 | ||||||||
\(837\) | −6.32253 | −0.218539 | ||||||||
\(838\) | 23.9914 | 0.828770 | ||||||||
\(839\) | −41.8878 | −1.44613 | −0.723064 | − | 0.690781i | \(-0.757267\pi\) | ||||
−0.723064 | + | 0.690781i | \(0.757267\pi\) | |||||||
\(840\) | 18.2802 | 0.630728 | ||||||||
\(841\) | −28.0549 | −0.967409 | ||||||||
\(842\) | −4.33701 | −0.149463 | ||||||||
\(843\) | −13.3044 | −0.458228 | ||||||||
\(844\) | 8.38109 | 0.288489 | ||||||||
\(845\) | 83.4916 | 2.87220 | ||||||||
\(846\) | 5.36140 | 0.184329 | ||||||||
\(847\) | 45.1186 | 1.55029 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 5.49847 | 0.188707 | ||||||||
\(850\) | −107.735 | −3.69527 | ||||||||
\(851\) | −43.8458 | −1.50301 | ||||||||
\(852\) | 9.10783 | 0.312029 | ||||||||
\(853\) | 17.3721 | 0.594808 | 0.297404 | − | 0.954752i | \(-0.403879\pi\) | ||||
0.297404 | + | 0.954752i | \(0.403879\pi\) | |||||||
\(854\) | 11.2605 | 0.385328 | ||||||||
\(855\) | 4.36993 | 0.149448 | ||||||||
\(856\) | −15.8051 | −0.540207 | ||||||||
\(857\) | 8.41806 | 0.287556 | 0.143778 | − | 0.989610i | \(-0.454075\pi\) | ||||
0.143778 | + | 0.989610i | \(0.454075\pi\) | |||||||
\(858\) | −2.62299 | −0.0895473 | ||||||||
\(859\) | −10.5012 | −0.358295 | −0.179148 | − | 0.983822i | \(-0.557334\pi\) | ||||
−0.179148 | + | 0.983822i | \(0.557334\pi\) | |||||||
\(860\) | −34.5603 | −1.17850 | ||||||||
\(861\) | −16.2103 | −0.552445 | ||||||||
\(862\) | 20.6639 | 0.703816 | ||||||||
\(863\) | −48.4929 | −1.65072 | −0.825358 | − | 0.564609i | \(-0.809027\pi\) | ||||
−0.825358 | + | 0.564609i | \(0.809027\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −18.8532 | −0.641028 | ||||||||
\(866\) | 4.41555 | 0.150047 | ||||||||
\(867\) | −41.4120 | −1.40643 | ||||||||
\(868\) | −26.4483 | −0.897714 | ||||||||
\(869\) | 1.49211 | 0.0506165 | ||||||||
\(870\) | −4.24838 | −0.144034 | ||||||||
\(871\) | 50.1987 | 1.70092 | ||||||||
\(872\) | −13.5273 | −0.458092 | ||||||||
\(873\) | −12.7574 | −0.431772 | ||||||||
\(874\) | 5.05356 | 0.170939 | ||||||||
\(875\) | −166.282 | −5.62136 | ||||||||
\(876\) | 8.12473 | 0.274509 | ||||||||
\(877\) | 14.4814 | 0.489001 | 0.244501 | − | 0.969649i | \(-0.421376\pi\) | ||||
0.244501 | + | 0.969649i | \(0.421376\pi\) | |||||||
\(878\) | 30.7827 | 1.03887 | ||||||||
\(879\) | −15.9482 | −0.537920 | ||||||||
\(880\) | −2.02292 | −0.0681925 | ||||||||
\(881\) | 28.9785 | 0.976310 | 0.488155 | − | 0.872757i | \(-0.337670\pi\) | ||||
0.488155 | + | 0.872757i | \(0.337670\pi\) | |||||||
\(882\) | 10.4990 | 0.353521 | ||||||||
\(883\) | 33.1809 | 1.11663 | 0.558313 | − | 0.829631i | \(-0.311449\pi\) | ||||
0.558313 | + | 0.829631i | \(0.311449\pi\) | |||||||
\(884\) | 43.3056 | 1.45652 | ||||||||
\(885\) | −51.8617 | −1.74331 | ||||||||
\(886\) | 12.9311 | 0.434430 | ||||||||
\(887\) | 23.8738 | 0.801602 | 0.400801 | − | 0.916165i | \(-0.368732\pi\) | ||||
0.400801 | + | 0.916165i | \(0.368732\pi\) | |||||||
\(888\) | 8.67622 | 0.291155 | ||||||||
\(889\) | 34.4356 | 1.15493 | ||||||||
\(890\) | −75.0145 | −2.51449 | ||||||||
\(891\) | −0.462917 | −0.0155083 | ||||||||
\(892\) | 13.4343 | 0.449814 | ||||||||
\(893\) | 5.36140 | 0.179412 | ||||||||
\(894\) | −6.00567 | −0.200860 | ||||||||
\(895\) | 25.0886 | 0.838620 | ||||||||
\(896\) | −4.18318 | −0.139750 | ||||||||
\(897\) | 28.6345 | 0.956079 | ||||||||
\(898\) | −23.5987 | −0.787499 | ||||||||
\(899\) | 6.14667 | 0.205003 | ||||||||
\(900\) | 14.0963 | 0.469876 | ||||||||
\(901\) | 7.64277 | 0.254618 | ||||||||
\(902\) | 1.79385 | 0.0597288 | ||||||||
\(903\) | −33.0834 | −1.10095 | ||||||||
\(904\) | −0.380231 | −0.0126463 | ||||||||
\(905\) | −76.9740 | −2.55870 | ||||||||
\(906\) | 5.75130 | 0.191074 | ||||||||
\(907\) | −8.02094 | −0.266331 | −0.133165 | − | 0.991094i | \(-0.542514\pi\) | ||||
−0.133165 | + | 0.991094i | \(0.542514\pi\) | |||||||
\(908\) | 21.2391 | 0.704844 | ||||||||
\(909\) | −14.9630 | −0.496291 | ||||||||
\(910\) | 103.580 | 3.43363 | ||||||||
\(911\) | −37.5553 | −1.24426 | −0.622131 | − | 0.782913i | \(-0.713733\pi\) | ||||
−0.622131 | + | 0.782913i | \(0.713733\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | −5.02423 | −0.166278 | ||||||||
\(914\) | −7.65871 | −0.253328 | ||||||||
\(915\) | 11.7632 | 0.388881 | ||||||||
\(916\) | 14.2131 | 0.469613 | ||||||||
\(917\) | −41.3709 | −1.36619 | ||||||||
\(918\) | 7.64277 | 0.252249 | ||||||||
\(919\) | 51.3959 | 1.69539 | 0.847697 | − | 0.530480i | \(-0.177988\pi\) | ||||
0.847697 | + | 0.530480i | \(0.177988\pi\) | |||||||
\(920\) | 22.0837 | 0.728078 | ||||||||
\(921\) | 13.1936 | 0.434745 | ||||||||
\(922\) | −10.5593 | −0.347752 | ||||||||
\(923\) | 51.6069 | 1.69866 | ||||||||
\(924\) | −1.93647 | −0.0637051 | ||||||||
\(925\) | −122.303 | −4.02128 | ||||||||
\(926\) | 14.7577 | 0.484967 | ||||||||
\(927\) | −11.2134 | −0.368296 | ||||||||
\(928\) | 0.972185 | 0.0319135 | ||||||||
\(929\) | −37.0142 | −1.21440 | −0.607198 | − | 0.794551i | \(-0.707706\pi\) | ||||
−0.607198 | + | 0.794551i | \(0.707706\pi\) | |||||||
\(930\) | −27.6290 | −0.905991 | ||||||||
\(931\) | 10.4990 | 0.344092 | ||||||||
\(932\) | −7.85524 | −0.257307 | ||||||||
\(933\) | 11.4478 | 0.374785 | ||||||||
\(934\) | −18.3402 | −0.600109 | ||||||||
\(935\) | 15.4607 | 0.505619 | ||||||||
\(936\) | −5.66621 | −0.185206 | ||||||||
\(937\) | −32.6951 | −1.06810 | −0.534051 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534051 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(938\) | 37.0601 | 1.21006 | ||||||||
\(939\) | −7.86254 | −0.256584 | ||||||||
\(940\) | 23.4289 | 0.764168 | ||||||||
\(941\) | −46.4722 | −1.51495 | −0.757475 | − | 0.652865i | \(-0.773567\pi\) | ||||
−0.757475 | + | 0.652865i | \(0.773567\pi\) | |||||||
\(942\) | −0.329748 | −0.0107438 | ||||||||
\(943\) | −19.5831 | −0.637713 | ||||||||
\(944\) | 11.8679 | 0.386266 | ||||||||
\(945\) | 18.2802 | 0.594656 | ||||||||
\(946\) | 3.66105 | 0.119031 | ||||||||
\(947\) | 56.0273 | 1.82064 | 0.910321 | − | 0.413903i | \(-0.135835\pi\) | ||||
0.910321 | + | 0.413903i | \(0.135835\pi\) | |||||||
\(948\) | 3.22329 | 0.104687 | ||||||||
\(949\) | 46.0364 | 1.49441 | ||||||||
\(950\) | 14.0963 | 0.457344 | ||||||||
\(951\) | −13.7246 | −0.445050 | ||||||||
\(952\) | 31.9711 | 1.03619 | ||||||||
\(953\) | −2.71220 | −0.0878567 | −0.0439283 | − | 0.999035i | \(-0.513987\pi\) | ||||
−0.0439283 | + | 0.999035i | \(0.513987\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | 78.0032 | 2.52413 | ||||||||
\(956\) | 14.4480 | 0.467282 | ||||||||
\(957\) | 0.450041 | 0.0145478 | ||||||||
\(958\) | −20.7969 | −0.671919 | ||||||||
\(959\) | 41.3663 | 1.33579 | ||||||||
\(960\) | −4.36993 | −0.141039 | ||||||||
\(961\) | 8.97439 | 0.289496 | ||||||||
\(962\) | 49.1613 | 1.58502 | ||||||||
\(963\) | −15.8051 | −0.509312 | ||||||||
\(964\) | −13.1851 | −0.424665 | ||||||||
\(965\) | 38.4599 | 1.23807 | ||||||||
\(966\) | 21.1400 | 0.680167 | ||||||||
\(967\) | 9.67385 | 0.311090 | 0.155545 | − | 0.987829i | \(-0.450287\pi\) | ||||
0.155545 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(968\) | −10.7857 | −0.346666 | ||||||||
\(969\) | 7.64277 | 0.245521 | ||||||||
\(970\) | −55.7488 | −1.78999 | ||||||||
\(971\) | 3.05353 | 0.0979924 | 0.0489962 | − | 0.998799i | \(-0.484398\pi\) | ||||
0.0489962 | + | 0.998799i | \(0.484398\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 22.4932 | 0.721100 | ||||||||
\(974\) | 4.73868 | 0.151837 | ||||||||
\(975\) | 79.8725 | 2.55797 | ||||||||
\(976\) | −2.69186 | −0.0861643 | ||||||||
\(977\) | −29.2886 | −0.937027 | −0.468513 | − | 0.883456i | \(-0.655210\pi\) | ||||
−0.468513 | + | 0.883456i | \(0.655210\pi\) | |||||||
\(978\) | 18.6873 | 0.597553 | ||||||||
\(979\) | 7.94647 | 0.253970 | ||||||||
\(980\) | 45.8800 | 1.46558 | ||||||||
\(981\) | −13.5273 | −0.431893 | ||||||||
\(982\) | 7.66928 | 0.244737 | ||||||||
\(983\) | −14.3083 | −0.456365 | −0.228183 | − | 0.973618i | \(-0.573278\pi\) | ||||
−0.228183 | + | 0.973618i | \(0.573278\pi\) | |||||||
\(984\) | 3.87511 | 0.123534 | ||||||||
\(985\) | 48.2535 | 1.53748 | ||||||||
\(986\) | −7.43019 | −0.236625 | ||||||||
\(987\) | 22.4277 | 0.713882 | ||||||||
\(988\) | −5.66621 | −0.180266 | ||||||||
\(989\) | −39.9668 | −1.27087 | ||||||||
\(990\) | −2.02292 | −0.0642925 | ||||||||
\(991\) | −45.3779 | −1.44148 | −0.720739 | − | 0.693207i | \(-0.756197\pi\) | ||||
−0.720739 | + | 0.693207i | \(0.756197\pi\) | |||||||
\(992\) | 6.32253 | 0.200741 | ||||||||
\(993\) | 8.55029 | 0.271335 | ||||||||
\(994\) | 38.0997 | 1.20845 | ||||||||
\(995\) | 22.5360 | 0.714438 | ||||||||
\(996\) | −10.8534 | −0.343904 | ||||||||
\(997\) | −48.0528 | −1.52185 | −0.760923 | − | 0.648842i | \(-0.775254\pi\) | ||||
−0.760923 | + | 0.648842i | \(0.775254\pi\) | |||||||
\(998\) | −16.1706 | −0.511871 | ||||||||
\(999\) | 8.67622 | 0.274504 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6042.2.a.bc.1.9 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bc.1.9 | ✓ | 9 | 1.1 | even | 1 | trivial |