Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −2.39522 | −1.38288 | −0.691440 | − | 0.722434i | \(-0.743023\pi\) | ||||
−0.691440 | + | 0.722434i | \(0.743023\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.491091 | 0.219622 | 0.109811 | − | 0.993952i | \(-0.464975\pi\) | ||||
0.109811 | + | 0.993952i | \(0.464975\pi\) | |||||||
\(6\) | 2.39522 | 0.977843 | ||||||||
\(7\) | 3.07111 | 1.16077 | 0.580385 | − | 0.814342i | \(-0.302902\pi\) | ||||
0.580385 | + | 0.814342i | \(0.302902\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.73707 | 0.912355 | ||||||||
\(10\) | −0.491091 | −0.155296 | ||||||||
\(11\) | 4.17695 | 1.25940 | 0.629699 | − | 0.776839i | \(-0.283178\pi\) | ||||
0.629699 | + | 0.776839i | \(0.283178\pi\) | |||||||
\(12\) | −2.39522 | −0.691440 | ||||||||
\(13\) | 5.66744 | 1.57187 | 0.785933 | − | 0.618312i | \(-0.212183\pi\) | ||||
0.785933 | + | 0.618312i | \(0.212183\pi\) | |||||||
\(14\) | −3.07111 | −0.820789 | ||||||||
\(15\) | −1.17627 | −0.303711 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.34713 | −1.29687 | −0.648434 | − | 0.761271i | \(-0.724576\pi\) | ||||
−0.648434 | + | 0.761271i | \(0.724576\pi\) | |||||||
\(18\) | −2.73707 | −0.645133 | ||||||||
\(19\) | 3.22494 | 0.739852 | 0.369926 | − | 0.929061i | \(-0.379383\pi\) | ||||
0.369926 | + | 0.929061i | \(0.379383\pi\) | |||||||
\(20\) | 0.491091 | 0.109811 | ||||||||
\(21\) | −7.35598 | −1.60521 | ||||||||
\(22\) | −4.17695 | −0.890529 | ||||||||
\(23\) | −8.14473 | −1.69829 | −0.849147 | − | 0.528157i | \(-0.822883\pi\) | ||||
−0.849147 | + | 0.528157i | \(0.822883\pi\) | |||||||
\(24\) | 2.39522 | 0.488922 | ||||||||
\(25\) | −4.75883 | −0.951766 | ||||||||
\(26\) | −5.66744 | −1.11148 | ||||||||
\(27\) | 0.629784 | 0.121202 | ||||||||
\(28\) | 3.07111 | 0.580385 | ||||||||
\(29\) | 3.25118 | 0.603729 | 0.301864 | − | 0.953351i | \(-0.402391\pi\) | ||||
0.301864 | + | 0.953351i | \(0.402391\pi\) | |||||||
\(30\) | 1.17627 | 0.214756 | ||||||||
\(31\) | −9.37775 | −1.68429 | −0.842147 | − | 0.539248i | \(-0.818708\pi\) | ||||
−0.842147 | + | 0.539248i | \(0.818708\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −10.0047 | −1.74160 | ||||||||
\(34\) | 5.34713 | 0.917024 | ||||||||
\(35\) | 1.50819 | 0.254931 | ||||||||
\(36\) | 2.73707 | 0.456178 | ||||||||
\(37\) | −2.98089 | −0.490056 | −0.245028 | − | 0.969516i | \(-0.578797\pi\) | ||||
−0.245028 | + | 0.969516i | \(0.578797\pi\) | |||||||
\(38\) | −3.22494 | −0.523155 | ||||||||
\(39\) | −13.5748 | −2.17370 | ||||||||
\(40\) | −0.491091 | −0.0776482 | ||||||||
\(41\) | −7.26806 | −1.13508 | −0.567540 | − | 0.823346i | \(-0.692105\pi\) | ||||
−0.567540 | + | 0.823346i | \(0.692105\pi\) | |||||||
\(42\) | 7.35598 | 1.13505 | ||||||||
\(43\) | −2.20220 | −0.335832 | −0.167916 | − | 0.985801i | \(-0.553704\pi\) | ||||
−0.167916 | + | 0.985801i | \(0.553704\pi\) | |||||||
\(44\) | 4.17695 | 0.629699 | ||||||||
\(45\) | 1.34415 | 0.200374 | ||||||||
\(46\) | 8.14473 | 1.20088 | ||||||||
\(47\) | −5.87041 | −0.856287 | −0.428143 | − | 0.903711i | \(-0.640832\pi\) | ||||
−0.428143 | + | 0.903711i | \(0.640832\pi\) | |||||||
\(48\) | −2.39522 | −0.345720 | ||||||||
\(49\) | 2.43171 | 0.347388 | ||||||||
\(50\) | 4.75883 | 0.673000 | ||||||||
\(51\) | 12.8075 | 1.79341 | ||||||||
\(52\) | 5.66744 | 0.785933 | ||||||||
\(53\) | −0.642744 | −0.0882876 | −0.0441438 | − | 0.999025i | \(-0.514056\pi\) | ||||
−0.0441438 | + | 0.999025i | \(0.514056\pi\) | |||||||
\(54\) | −0.629784 | −0.0857027 | ||||||||
\(55\) | 2.05126 | 0.276592 | ||||||||
\(56\) | −3.07111 | −0.410394 | ||||||||
\(57\) | −7.72443 | −1.02313 | ||||||||
\(58\) | −3.25118 | −0.426901 | ||||||||
\(59\) | −9.99028 | −1.30062 | −0.650312 | − | 0.759668i | \(-0.725362\pi\) | ||||
−0.650312 | + | 0.759668i | \(0.725362\pi\) | |||||||
\(60\) | −1.17627 | −0.151856 | ||||||||
\(61\) | −7.53520 | −0.964783 | −0.482392 | − | 0.875956i | \(-0.660232\pi\) | ||||
−0.482392 | + | 0.875956i | \(0.660232\pi\) | |||||||
\(62\) | 9.37775 | 1.19098 | ||||||||
\(63\) | 8.40583 | 1.05904 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.78323 | 0.345217 | ||||||||
\(66\) | 10.0047 | 1.23149 | ||||||||
\(67\) | 9.38047 | 1.14601 | 0.573003 | − | 0.819553i | \(-0.305778\pi\) | ||||
0.573003 | + | 0.819553i | \(0.305778\pi\) | |||||||
\(68\) | −5.34713 | −0.648434 | ||||||||
\(69\) | 19.5084 | 2.34854 | ||||||||
\(70\) | −1.50819 | −0.180264 | ||||||||
\(71\) | −12.1271 | −1.43922 | −0.719610 | − | 0.694379i | \(-0.755679\pi\) | ||||
−0.719610 | + | 0.694379i | \(0.755679\pi\) | |||||||
\(72\) | −2.73707 | −0.322566 | ||||||||
\(73\) | 9.49214 | 1.11097 | 0.555486 | − | 0.831526i | \(-0.312532\pi\) | ||||
0.555486 | + | 0.831526i | \(0.312532\pi\) | |||||||
\(74\) | 2.98089 | 0.346522 | ||||||||
\(75\) | 11.3984 | 1.31618 | ||||||||
\(76\) | 3.22494 | 0.369926 | ||||||||
\(77\) | 12.8279 | 1.46187 | ||||||||
\(78\) | 13.5748 | 1.53704 | ||||||||
\(79\) | −12.4184 | −1.39717 | −0.698587 | − | 0.715525i | \(-0.746188\pi\) | ||||
−0.698587 | + | 0.715525i | \(0.746188\pi\) | |||||||
\(80\) | 0.491091 | 0.0549056 | ||||||||
\(81\) | −9.71967 | −1.07996 | ||||||||
\(82\) | 7.26806 | 0.802623 | ||||||||
\(83\) | 4.34233 | 0.476633 | 0.238316 | − | 0.971188i | \(-0.423405\pi\) | ||||
0.238316 | + | 0.971188i | \(0.423405\pi\) | |||||||
\(84\) | −7.35598 | −0.802603 | ||||||||
\(85\) | −2.62592 | −0.284821 | ||||||||
\(86\) | 2.20220 | 0.237469 | ||||||||
\(87\) | −7.78728 | −0.834884 | ||||||||
\(88\) | −4.17695 | −0.445264 | ||||||||
\(89\) | −10.1770 | −1.07876 | −0.539378 | − | 0.842064i | \(-0.681340\pi\) | ||||
−0.539378 | + | 0.842064i | \(0.681340\pi\) | |||||||
\(90\) | −1.34415 | −0.141686 | ||||||||
\(91\) | 17.4053 | 1.82457 | ||||||||
\(92\) | −8.14473 | −0.849147 | ||||||||
\(93\) | 22.4617 | 2.32917 | ||||||||
\(94\) | 5.87041 | 0.605486 | ||||||||
\(95\) | 1.58374 | 0.162488 | ||||||||
\(96\) | 2.39522 | 0.244461 | ||||||||
\(97\) | 7.98956 | 0.811217 | 0.405608 | − | 0.914047i | \(-0.367060\pi\) | ||||
0.405608 | + | 0.914047i | \(0.367060\pi\) | |||||||
\(98\) | −2.43171 | −0.245640 | ||||||||
\(99\) | 11.4326 | 1.14902 | ||||||||
\(100\) | −4.75883 | −0.475883 | ||||||||
\(101\) | −1.68806 | −0.167968 | −0.0839842 | − | 0.996467i | \(-0.526765\pi\) | ||||
−0.0839842 | + | 0.996467i | \(0.526765\pi\) | |||||||
\(102\) | −12.8075 | −1.26813 | ||||||||
\(103\) | −1.91205 | −0.188400 | −0.0941998 | − | 0.995553i | \(-0.530029\pi\) | ||||
−0.0941998 | + | 0.995553i | \(0.530029\pi\) | |||||||
\(104\) | −5.66744 | −0.555738 | ||||||||
\(105\) | −3.61245 | −0.352539 | ||||||||
\(106\) | 0.642744 | 0.0624288 | ||||||||
\(107\) | 8.77566 | 0.848376 | 0.424188 | − | 0.905574i | \(-0.360560\pi\) | ||||
0.424188 | + | 0.905574i | \(0.360560\pi\) | |||||||
\(108\) | 0.629784 | 0.0606009 | ||||||||
\(109\) | −14.1944 | −1.35957 | −0.679786 | − | 0.733410i | \(-0.737927\pi\) | ||||
−0.679786 | + | 0.733410i | \(0.737927\pi\) | |||||||
\(110\) | −2.05126 | −0.195580 | ||||||||
\(111\) | 7.13988 | 0.677688 | ||||||||
\(112\) | 3.07111 | 0.290193 | ||||||||
\(113\) | 9.20454 | 0.865891 | 0.432945 | − | 0.901420i | \(-0.357474\pi\) | ||||
0.432945 | + | 0.901420i | \(0.357474\pi\) | |||||||
\(114\) | 7.72443 | 0.723460 | ||||||||
\(115\) | −3.99980 | −0.372983 | ||||||||
\(116\) | 3.25118 | 0.301864 | ||||||||
\(117\) | 15.5122 | 1.43410 | ||||||||
\(118\) | 9.99028 | 0.919679 | ||||||||
\(119\) | −16.4216 | −1.50537 | ||||||||
\(120\) | 1.17627 | 0.107378 | ||||||||
\(121\) | 6.44691 | 0.586082 | ||||||||
\(122\) | 7.53520 | 0.682205 | ||||||||
\(123\) | 17.4086 | 1.56968 | ||||||||
\(124\) | −9.37775 | −0.842147 | ||||||||
\(125\) | −4.79247 | −0.428652 | ||||||||
\(126\) | −8.40583 | −0.748851 | ||||||||
\(127\) | −4.22504 | −0.374911 | −0.187456 | − | 0.982273i | \(-0.560024\pi\) | ||||
−0.187456 | + | 0.982273i | \(0.560024\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.27474 | 0.464415 | ||||||||
\(130\) | −2.78323 | −0.244105 | ||||||||
\(131\) | 4.88496 | 0.426801 | 0.213401 | − | 0.976965i | \(-0.431546\pi\) | ||||
0.213401 | + | 0.976965i | \(0.431546\pi\) | |||||||
\(132\) | −10.0047 | −0.870798 | ||||||||
\(133\) | 9.90415 | 0.858798 | ||||||||
\(134\) | −9.38047 | −0.810349 | ||||||||
\(135\) | 0.309281 | 0.0266187 | ||||||||
\(136\) | 5.34713 | 0.458512 | ||||||||
\(137\) | −0.798475 | −0.0682183 | −0.0341092 | − | 0.999418i | \(-0.510859\pi\) | ||||
−0.0341092 | + | 0.999418i | \(0.510859\pi\) | |||||||
\(138\) | −19.5084 | −1.66067 | ||||||||
\(139\) | 9.77048 | 0.828722 | 0.414361 | − | 0.910113i | \(-0.364005\pi\) | ||||
0.414361 | + | 0.910113i | \(0.364005\pi\) | |||||||
\(140\) | 1.50819 | 0.127466 | ||||||||
\(141\) | 14.0609 | 1.18414 | ||||||||
\(142\) | 12.1271 | 1.01768 | ||||||||
\(143\) | 23.6726 | 1.97960 | ||||||||
\(144\) | 2.73707 | 0.228089 | ||||||||
\(145\) | 1.59662 | 0.132592 | ||||||||
\(146\) | −9.49214 | −0.785575 | ||||||||
\(147\) | −5.82448 | −0.480395 | ||||||||
\(148\) | −2.98089 | −0.245028 | ||||||||
\(149\) | −21.1919 | −1.73610 | −0.868052 | − | 0.496473i | \(-0.834628\pi\) | ||||
−0.868052 | + | 0.496473i | \(0.834628\pi\) | |||||||
\(150\) | −11.3984 | −0.930678 | ||||||||
\(151\) | 17.9796 | 1.46316 | 0.731578 | − | 0.681758i | \(-0.238784\pi\) | ||||
0.731578 | + | 0.681758i | \(0.238784\pi\) | |||||||
\(152\) | −3.22494 | −0.261577 | ||||||||
\(153\) | −14.6354 | −1.18320 | ||||||||
\(154\) | −12.8279 | −1.03370 | ||||||||
\(155\) | −4.60532 | −0.369909 | ||||||||
\(156\) | −13.5748 | −1.08685 | ||||||||
\(157\) | −11.9540 | −0.954031 | −0.477015 | − | 0.878895i | \(-0.658281\pi\) | ||||
−0.477015 | + | 0.878895i | \(0.658281\pi\) | |||||||
\(158\) | 12.4184 | 0.987952 | ||||||||
\(159\) | 1.53951 | 0.122091 | ||||||||
\(160\) | −0.491091 | −0.0388241 | ||||||||
\(161\) | −25.0134 | −1.97133 | ||||||||
\(162\) | 9.71967 | 0.763649 | ||||||||
\(163\) | −11.0917 | −0.868770 | −0.434385 | − | 0.900727i | \(-0.643034\pi\) | ||||
−0.434385 | + | 0.900727i | \(0.643034\pi\) | |||||||
\(164\) | −7.26806 | −0.567540 | ||||||||
\(165\) | −4.91321 | −0.382493 | ||||||||
\(166\) | −4.34233 | −0.337030 | ||||||||
\(167\) | −16.7829 | −1.29870 | −0.649351 | − | 0.760489i | \(-0.724959\pi\) | ||||
−0.649351 | + | 0.760489i | \(0.724959\pi\) | |||||||
\(168\) | 7.35598 | 0.567526 | ||||||||
\(169\) | 19.1199 | 1.47076 | ||||||||
\(170\) | 2.62592 | 0.201399 | ||||||||
\(171\) | 8.82688 | 0.675008 | ||||||||
\(172\) | −2.20220 | −0.167916 | ||||||||
\(173\) | −9.99615 | −0.759993 | −0.379996 | − | 0.924988i | \(-0.624075\pi\) | ||||
−0.379996 | + | 0.924988i | \(0.624075\pi\) | |||||||
\(174\) | 7.78728 | 0.590352 | ||||||||
\(175\) | −14.6149 | −1.10478 | ||||||||
\(176\) | 4.17695 | 0.314849 | ||||||||
\(177\) | 23.9289 | 1.79861 | ||||||||
\(178\) | 10.1770 | 0.762795 | ||||||||
\(179\) | −10.9214 | −0.816304 | −0.408152 | − | 0.912914i | \(-0.633827\pi\) | ||||
−0.408152 | + | 0.912914i | \(0.633827\pi\) | |||||||
\(180\) | 1.34415 | 0.100187 | ||||||||
\(181\) | 3.90061 | 0.289930 | 0.144965 | − | 0.989437i | \(-0.453693\pi\) | ||||
0.144965 | + | 0.989437i | \(0.453693\pi\) | |||||||
\(182\) | −17.4053 | −1.29017 | ||||||||
\(183\) | 18.0484 | 1.33418 | ||||||||
\(184\) | 8.14473 | 0.600438 | ||||||||
\(185\) | −1.46389 | −0.107627 | ||||||||
\(186\) | −22.4617 | −1.64698 | ||||||||
\(187\) | −22.3347 | −1.63327 | ||||||||
\(188\) | −5.87041 | −0.428143 | ||||||||
\(189\) | 1.93413 | 0.140688 | ||||||||
\(190\) | −1.58374 | −0.114896 | ||||||||
\(191\) | 2.97007 | 0.214907 | 0.107453 | − | 0.994210i | \(-0.465730\pi\) | ||||
0.107453 | + | 0.994210i | \(0.465730\pi\) | |||||||
\(192\) | −2.39522 | −0.172860 | ||||||||
\(193\) | 7.73876 | 0.557048 | 0.278524 | − | 0.960429i | \(-0.410155\pi\) | ||||
0.278524 | + | 0.960429i | \(0.410155\pi\) | |||||||
\(194\) | −7.98956 | −0.573617 | ||||||||
\(195\) | −6.66643 | −0.477393 | ||||||||
\(196\) | 2.43171 | 0.173694 | ||||||||
\(197\) | 0.354426 | 0.0252518 | 0.0126259 | − | 0.999920i | \(-0.495981\pi\) | ||||
0.0126259 | + | 0.999920i | \(0.495981\pi\) | |||||||
\(198\) | −11.4326 | −0.812479 | ||||||||
\(199\) | 14.1460 | 1.00278 | 0.501390 | − | 0.865221i | \(-0.332822\pi\) | ||||
0.501390 | + | 0.865221i | \(0.332822\pi\) | |||||||
\(200\) | 4.75883 | 0.336500 | ||||||||
\(201\) | −22.4683 | −1.58479 | ||||||||
\(202\) | 1.68806 | 0.118772 | ||||||||
\(203\) | 9.98472 | 0.700790 | ||||||||
\(204\) | 12.8075 | 0.896706 | ||||||||
\(205\) | −3.56928 | −0.249289 | ||||||||
\(206\) | 1.91205 | 0.133219 | ||||||||
\(207\) | −22.2927 | −1.54945 | ||||||||
\(208\) | 5.66744 | 0.392966 | ||||||||
\(209\) | 13.4704 | 0.931768 | ||||||||
\(210\) | 3.61245 | 0.249283 | ||||||||
\(211\) | 24.6919 | 1.69986 | 0.849931 | − | 0.526894i | \(-0.176644\pi\) | ||||
0.849931 | + | 0.526894i | \(0.176644\pi\) | |||||||
\(212\) | −0.642744 | −0.0441438 | ||||||||
\(213\) | 29.0470 | 1.99027 | ||||||||
\(214\) | −8.77566 | −0.599892 | ||||||||
\(215\) | −1.08148 | −0.0737563 | ||||||||
\(216\) | −0.629784 | −0.0428513 | ||||||||
\(217\) | −28.8001 | −1.95508 | ||||||||
\(218\) | 14.1944 | 0.961363 | ||||||||
\(219\) | −22.7357 | −1.53634 | ||||||||
\(220\) | 2.05126 | 0.138296 | ||||||||
\(221\) | −30.3045 | −2.03850 | ||||||||
\(222\) | −7.13988 | −0.479198 | ||||||||
\(223\) | −27.1716 | −1.81955 | −0.909774 | − | 0.415105i | \(-0.863745\pi\) | ||||
−0.909774 | + | 0.415105i | \(0.863745\pi\) | |||||||
\(224\) | −3.07111 | −0.205197 | ||||||||
\(225\) | −13.0252 | −0.868349 | ||||||||
\(226\) | −9.20454 | −0.612277 | ||||||||
\(227\) | 11.4716 | 0.761400 | 0.380700 | − | 0.924699i | \(-0.375683\pi\) | ||||
0.380700 | + | 0.924699i | \(0.375683\pi\) | |||||||
\(228\) | −7.72443 | −0.511563 | ||||||||
\(229\) | −6.94051 | −0.458642 | −0.229321 | − | 0.973351i | \(-0.573651\pi\) | ||||
−0.229321 | + | 0.973351i | \(0.573651\pi\) | |||||||
\(230\) | 3.99980 | 0.263739 | ||||||||
\(231\) | −30.7255 | −2.02159 | ||||||||
\(232\) | −3.25118 | −0.213450 | ||||||||
\(233\) | −16.4108 | −1.07511 | −0.537553 | − | 0.843230i | \(-0.680651\pi\) | ||||
−0.537553 | + | 0.843230i | \(0.680651\pi\) | |||||||
\(234\) | −15.5122 | −1.01406 | ||||||||
\(235\) | −2.88290 | −0.188060 | ||||||||
\(236\) | −9.99028 | −0.650312 | ||||||||
\(237\) | 29.7447 | 1.93212 | ||||||||
\(238\) | 16.4216 | 1.06445 | ||||||||
\(239\) | 22.3045 | 1.44276 | 0.721379 | − | 0.692540i | \(-0.243508\pi\) | ||||
0.721379 | + | 0.692540i | \(0.243508\pi\) | |||||||
\(240\) | −1.17627 | −0.0759278 | ||||||||
\(241\) | −22.4473 | −1.44596 | −0.722979 | − | 0.690870i | \(-0.757228\pi\) | ||||
−0.722979 | + | 0.690870i | \(0.757228\pi\) | |||||||
\(242\) | −6.44691 | −0.414423 | ||||||||
\(243\) | 21.3914 | 1.37226 | ||||||||
\(244\) | −7.53520 | −0.482392 | ||||||||
\(245\) | 1.19419 | 0.0762941 | ||||||||
\(246\) | −17.4086 | −1.10993 | ||||||||
\(247\) | 18.2772 | 1.16295 | ||||||||
\(248\) | 9.37775 | 0.595488 | ||||||||
\(249\) | −10.4008 | −0.659125 | ||||||||
\(250\) | 4.79247 | 0.303102 | ||||||||
\(251\) | 20.4423 | 1.29031 | 0.645153 | − | 0.764053i | \(-0.276793\pi\) | ||||
0.645153 | + | 0.764053i | \(0.276793\pi\) | |||||||
\(252\) | 8.40583 | 0.529518 | ||||||||
\(253\) | −34.0201 | −2.13883 | ||||||||
\(254\) | 4.22504 | 0.265102 | ||||||||
\(255\) | 6.28966 | 0.393874 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.3192 | −0.768450 | −0.384225 | − | 0.923239i | \(-0.625531\pi\) | ||||
−0.384225 | + | 0.923239i | \(0.625531\pi\) | |||||||
\(258\) | −5.27474 | −0.328391 | ||||||||
\(259\) | −9.15465 | −0.568842 | ||||||||
\(260\) | 2.78323 | 0.172608 | ||||||||
\(261\) | 8.89869 | 0.550815 | ||||||||
\(262\) | −4.88496 | −0.301794 | ||||||||
\(263\) | 17.1786 | 1.05928 | 0.529640 | − | 0.848223i | \(-0.322327\pi\) | ||||
0.529640 | + | 0.848223i | \(0.322327\pi\) | |||||||
\(264\) | 10.0047 | 0.615747 | ||||||||
\(265\) | −0.315645 | −0.0193899 | ||||||||
\(266\) | −9.90415 | −0.607262 | ||||||||
\(267\) | 24.3760 | 1.49179 | ||||||||
\(268\) | 9.38047 | 0.573003 | ||||||||
\(269\) | −0.264663 | −0.0161368 | −0.00806840 | − | 0.999967i | \(-0.502568\pi\) | ||||
−0.00806840 | + | 0.999967i | \(0.502568\pi\) | |||||||
\(270\) | −0.309281 | −0.0188222 | ||||||||
\(271\) | −9.31291 | −0.565719 | −0.282859 | − | 0.959161i | \(-0.591283\pi\) | ||||
−0.282859 | + | 0.959161i | \(0.591283\pi\) | |||||||
\(272\) | −5.34713 | −0.324217 | ||||||||
\(273\) | −41.6896 | −2.52317 | ||||||||
\(274\) | 0.798475 | 0.0482376 | ||||||||
\(275\) | −19.8774 | −1.19865 | ||||||||
\(276\) | 19.5084 | 1.17427 | ||||||||
\(277\) | −12.0706 | −0.725254 | −0.362627 | − | 0.931934i | \(-0.618120\pi\) | ||||
−0.362627 | + | 0.931934i | \(0.618120\pi\) | |||||||
\(278\) | −9.77048 | −0.585995 | ||||||||
\(279\) | −25.6675 | −1.53667 | ||||||||
\(280\) | −1.50819 | −0.0901318 | ||||||||
\(281\) | −20.0764 | −1.19766 | −0.598828 | − | 0.800878i | \(-0.704367\pi\) | ||||
−0.598828 | + | 0.800878i | \(0.704367\pi\) | |||||||
\(282\) | −14.0609 | −0.837314 | ||||||||
\(283\) | 33.1312 | 1.96944 | 0.984722 | − | 0.174133i | \(-0.0557124\pi\) | ||||
0.984722 | + | 0.174133i | \(0.0557124\pi\) | |||||||
\(284\) | −12.1271 | −0.719610 | ||||||||
\(285\) | −3.79340 | −0.224701 | ||||||||
\(286\) | −23.6726 | −1.39979 | ||||||||
\(287\) | −22.3210 | −1.31757 | ||||||||
\(288\) | −2.73707 | −0.161283 | ||||||||
\(289\) | 11.5917 | 0.681868 | ||||||||
\(290\) | −1.59662 | −0.0937569 | ||||||||
\(291\) | −19.1367 | −1.12182 | ||||||||
\(292\) | 9.49214 | 0.555486 | ||||||||
\(293\) | 23.7516 | 1.38758 | 0.693792 | − | 0.720176i | \(-0.255939\pi\) | ||||
0.693792 | + | 0.720176i | \(0.255939\pi\) | |||||||
\(294\) | 5.82448 | 0.339691 | ||||||||
\(295\) | −4.90613 | −0.285646 | ||||||||
\(296\) | 2.98089 | 0.173261 | ||||||||
\(297\) | 2.63057 | 0.152641 | ||||||||
\(298\) | 21.1919 | 1.22761 | ||||||||
\(299\) | −46.1598 | −2.66949 | ||||||||
\(300\) | 11.3984 | 0.658089 | ||||||||
\(301\) | −6.76319 | −0.389824 | ||||||||
\(302\) | −17.9796 | −1.03461 | ||||||||
\(303\) | 4.04328 | 0.232280 | ||||||||
\(304\) | 3.22494 | 0.184963 | ||||||||
\(305\) | −3.70046 | −0.211888 | ||||||||
\(306\) | 14.6354 | 0.836652 | ||||||||
\(307\) | 9.38157 | 0.535435 | 0.267717 | − | 0.963498i | \(-0.413731\pi\) | ||||
0.267717 | + | 0.963498i | \(0.413731\pi\) | |||||||
\(308\) | 12.8279 | 0.730936 | ||||||||
\(309\) | 4.57977 | 0.260534 | ||||||||
\(310\) | 4.60532 | 0.261565 | ||||||||
\(311\) | −5.26368 | −0.298476 | −0.149238 | − | 0.988801i | \(-0.547682\pi\) | ||||
−0.149238 | + | 0.988801i | \(0.547682\pi\) | |||||||
\(312\) | 13.5748 | 0.768519 | ||||||||
\(313\) | 24.8871 | 1.40670 | 0.703350 | − | 0.710844i | \(-0.251687\pi\) | ||||
0.703350 | + | 0.710844i | \(0.251687\pi\) | |||||||
\(314\) | 11.9540 | 0.674602 | ||||||||
\(315\) | 4.12802 | 0.232588 | ||||||||
\(316\) | −12.4184 | −0.698587 | ||||||||
\(317\) | 16.8876 | 0.948502 | 0.474251 | − | 0.880390i | \(-0.342719\pi\) | ||||
0.474251 | + | 0.880390i | \(0.342719\pi\) | |||||||
\(318\) | −1.53951 | −0.0863315 | ||||||||
\(319\) | 13.5800 | 0.760334 | ||||||||
\(320\) | 0.491091 | 0.0274528 | ||||||||
\(321\) | −21.0196 | −1.17320 | ||||||||
\(322\) | 25.0134 | 1.39394 | ||||||||
\(323\) | −17.2442 | −0.959491 | ||||||||
\(324\) | −9.71967 | −0.539982 | ||||||||
\(325\) | −26.9704 | −1.49605 | ||||||||
\(326\) | 11.0917 | 0.614313 | ||||||||
\(327\) | 33.9986 | 1.88012 | ||||||||
\(328\) | 7.26806 | 0.401311 | ||||||||
\(329\) | −18.0287 | −0.993952 | ||||||||
\(330\) | 4.91321 | 0.270464 | ||||||||
\(331\) | 22.3758 | 1.22988 | 0.614941 | − | 0.788573i | \(-0.289180\pi\) | ||||
0.614941 | + | 0.788573i | \(0.289180\pi\) | |||||||
\(332\) | 4.34233 | 0.238316 | ||||||||
\(333\) | −8.15890 | −0.447105 | ||||||||
\(334\) | 16.7829 | 0.918321 | ||||||||
\(335\) | 4.60666 | 0.251689 | ||||||||
\(336\) | −7.35598 | −0.401301 | ||||||||
\(337\) | 21.8971 | 1.19281 | 0.596406 | − | 0.802683i | \(-0.296595\pi\) | ||||
0.596406 | + | 0.802683i | \(0.296595\pi\) | |||||||
\(338\) | −19.1199 | −1.03999 | ||||||||
\(339\) | −22.0469 | −1.19742 | ||||||||
\(340\) | −2.62592 | −0.142411 | ||||||||
\(341\) | −39.1704 | −2.12120 | ||||||||
\(342\) | −8.82688 | −0.477303 | ||||||||
\(343\) | −14.0297 | −0.757533 | ||||||||
\(344\) | 2.20220 | 0.118735 | ||||||||
\(345\) | 9.58039 | 0.515791 | ||||||||
\(346\) | 9.99615 | 0.537396 | ||||||||
\(347\) | −12.6063 | −0.676744 | −0.338372 | − | 0.941012i | \(-0.609876\pi\) | ||||
−0.338372 | + | 0.941012i | \(0.609876\pi\) | |||||||
\(348\) | −7.78728 | −0.417442 | ||||||||
\(349\) | −28.4651 | −1.52370 | −0.761852 | − | 0.647752i | \(-0.775709\pi\) | ||||
−0.761852 | + | 0.647752i | \(0.775709\pi\) | |||||||
\(350\) | 14.6149 | 0.781199 | ||||||||
\(351\) | 3.56926 | 0.190513 | ||||||||
\(352\) | −4.17695 | −0.222632 | ||||||||
\(353\) | 8.69186 | 0.462621 | 0.231311 | − | 0.972880i | \(-0.425699\pi\) | ||||
0.231311 | + | 0.972880i | \(0.425699\pi\) | |||||||
\(354\) | −23.9289 | −1.27181 | ||||||||
\(355\) | −5.95549 | −0.316085 | ||||||||
\(356\) | −10.1770 | −0.539378 | ||||||||
\(357\) | 39.3333 | 2.08174 | ||||||||
\(358\) | 10.9214 | 0.577214 | ||||||||
\(359\) | 12.1148 | 0.639394 | 0.319697 | − | 0.947520i | \(-0.396419\pi\) | ||||
0.319697 | + | 0.947520i | \(0.396419\pi\) | |||||||
\(360\) | −1.34415 | −0.0708428 | ||||||||
\(361\) | −8.59976 | −0.452619 | ||||||||
\(362\) | −3.90061 | −0.205012 | ||||||||
\(363\) | −15.4417 | −0.810481 | ||||||||
\(364\) | 17.4053 | 0.912287 | ||||||||
\(365\) | 4.66150 | 0.243994 | ||||||||
\(366\) | −18.0484 | −0.943407 | ||||||||
\(367\) | −32.7058 | −1.70723 | −0.853615 | − | 0.520904i | \(-0.825595\pi\) | ||||
−0.853615 | + | 0.520904i | \(0.825595\pi\) | |||||||
\(368\) | −8.14473 | −0.424573 | ||||||||
\(369\) | −19.8932 | −1.03560 | ||||||||
\(370\) | 1.46389 | 0.0761039 | ||||||||
\(371\) | −1.97394 | −0.102482 | ||||||||
\(372\) | 22.4617 | 1.16459 | ||||||||
\(373\) | −14.0290 | −0.726394 | −0.363197 | − | 0.931712i | \(-0.618315\pi\) | ||||
−0.363197 | + | 0.931712i | \(0.618315\pi\) | |||||||
\(374\) | 22.3347 | 1.15490 | ||||||||
\(375\) | 11.4790 | 0.592773 | ||||||||
\(376\) | 5.87041 | 0.302743 | ||||||||
\(377\) | 18.4259 | 0.948980 | ||||||||
\(378\) | −1.93413 | −0.0994811 | ||||||||
\(379\) | −7.19822 | −0.369748 | −0.184874 | − | 0.982762i | \(-0.559188\pi\) | ||||
−0.184874 | + | 0.982762i | \(0.559188\pi\) | |||||||
\(380\) | 1.58374 | 0.0812441 | ||||||||
\(381\) | 10.1199 | 0.518457 | ||||||||
\(382\) | −2.97007 | −0.151962 | ||||||||
\(383\) | 6.09068 | 0.311219 | 0.155610 | − | 0.987819i | \(-0.450266\pi\) | ||||
0.155610 | + | 0.987819i | \(0.450266\pi\) | |||||||
\(384\) | 2.39522 | 0.122230 | ||||||||
\(385\) | 6.29965 | 0.321060 | ||||||||
\(386\) | −7.73876 | −0.393893 | ||||||||
\(387\) | −6.02756 | −0.306398 | ||||||||
\(388\) | 7.98956 | 0.405608 | ||||||||
\(389\) | −16.9965 | −0.861758 | −0.430879 | − | 0.902410i | \(-0.641796\pi\) | ||||
−0.430879 | + | 0.902410i | \(0.641796\pi\) | |||||||
\(390\) | 6.66643 | 0.337568 | ||||||||
\(391\) | 43.5509 | 2.20246 | ||||||||
\(392\) | −2.43171 | −0.122820 | ||||||||
\(393\) | −11.7005 | −0.590214 | ||||||||
\(394\) | −0.354426 | −0.0178557 | ||||||||
\(395\) | −6.09854 | −0.306851 | ||||||||
\(396\) | 11.4326 | 0.574509 | ||||||||
\(397\) | −32.9086 | −1.65164 | −0.825818 | − | 0.563937i | \(-0.809286\pi\) | ||||
−0.825818 | + | 0.563937i | \(0.809286\pi\) | |||||||
\(398\) | −14.1460 | −0.709072 | ||||||||
\(399\) | −23.7226 | −1.18761 | ||||||||
\(400\) | −4.75883 | −0.237942 | ||||||||
\(401\) | −24.4612 | −1.22153 | −0.610767 | − | 0.791811i | \(-0.709139\pi\) | ||||
−0.610767 | + | 0.791811i | \(0.709139\pi\) | |||||||
\(402\) | 22.4683 | 1.12061 | ||||||||
\(403\) | −53.1478 | −2.64748 | ||||||||
\(404\) | −1.68806 | −0.0839842 | ||||||||
\(405\) | −4.77324 | −0.237184 | ||||||||
\(406\) | −9.98472 | −0.495533 | ||||||||
\(407\) | −12.4510 | −0.617175 | ||||||||
\(408\) | −12.8075 | −0.634067 | ||||||||
\(409\) | 2.74577 | 0.135769 | 0.0678847 | − | 0.997693i | \(-0.478375\pi\) | ||||
0.0678847 | + | 0.997693i | \(0.478375\pi\) | |||||||
\(410\) | 3.56928 | 0.176274 | ||||||||
\(411\) | 1.91252 | 0.0943377 | ||||||||
\(412\) | −1.91205 | −0.0941998 | ||||||||
\(413\) | −30.6812 | −1.50972 | ||||||||
\(414\) | 22.2927 | 1.09562 | ||||||||
\(415\) | 2.13248 | 0.104679 | ||||||||
\(416\) | −5.66744 | −0.277869 | ||||||||
\(417\) | −23.4024 | −1.14602 | ||||||||
\(418\) | −13.4704 | −0.658860 | ||||||||
\(419\) | −12.3308 | −0.602398 | −0.301199 | − | 0.953561i | \(-0.597387\pi\) | ||||
−0.301199 | + | 0.953561i | \(0.597387\pi\) | |||||||
\(420\) | −3.61245 | −0.176270 | ||||||||
\(421\) | −2.41067 | −0.117489 | −0.0587446 | − | 0.998273i | \(-0.518710\pi\) | ||||
−0.0587446 | + | 0.998273i | \(0.518710\pi\) | |||||||
\(422\) | −24.6919 | −1.20198 | ||||||||
\(423\) | −16.0677 | −0.781238 | ||||||||
\(424\) | 0.642744 | 0.0312144 | ||||||||
\(425\) | 25.4461 | 1.23432 | ||||||||
\(426\) | −29.0470 | −1.40733 | ||||||||
\(427\) | −23.1414 | −1.11989 | ||||||||
\(428\) | 8.77566 | 0.424188 | ||||||||
\(429\) | −56.7011 | −2.73755 | ||||||||
\(430\) | 1.08148 | 0.0521535 | ||||||||
\(431\) | −12.0286 | −0.579396 | −0.289698 | − | 0.957118i | \(-0.593555\pi\) | ||||
−0.289698 | + | 0.957118i | \(0.593555\pi\) | |||||||
\(432\) | 0.629784 | 0.0303005 | ||||||||
\(433\) | 27.1227 | 1.30343 | 0.651716 | − | 0.758463i | \(-0.274049\pi\) | ||||
0.651716 | + | 0.758463i | \(0.274049\pi\) | |||||||
\(434\) | 28.8001 | 1.38245 | ||||||||
\(435\) | −3.82426 | −0.183359 | ||||||||
\(436\) | −14.1944 | −0.679786 | ||||||||
\(437\) | −26.2663 | −1.25649 | ||||||||
\(438\) | 22.7357 | 1.08636 | ||||||||
\(439\) | −28.9910 | −1.38366 | −0.691832 | − | 0.722059i | \(-0.743196\pi\) | ||||
−0.691832 | + | 0.722059i | \(0.743196\pi\) | |||||||
\(440\) | −2.05126 | −0.0977900 | ||||||||
\(441\) | 6.65576 | 0.316941 | ||||||||
\(442\) | 30.3045 | 1.44144 | ||||||||
\(443\) | 11.4191 | 0.542539 | 0.271269 | − | 0.962503i | \(-0.412557\pi\) | ||||
0.271269 | + | 0.962503i | \(0.412557\pi\) | |||||||
\(444\) | 7.13988 | 0.338844 | ||||||||
\(445\) | −4.99781 | −0.236919 | ||||||||
\(446\) | 27.1716 | 1.28661 | ||||||||
\(447\) | 50.7591 | 2.40082 | ||||||||
\(448\) | 3.07111 | 0.145096 | ||||||||
\(449\) | −16.5317 | −0.780181 | −0.390091 | − | 0.920776i | \(-0.627556\pi\) | ||||
−0.390091 | + | 0.920776i | \(0.627556\pi\) | |||||||
\(450\) | 13.0252 | 0.614015 | ||||||||
\(451\) | −30.3583 | −1.42952 | ||||||||
\(452\) | 9.20454 | 0.432945 | ||||||||
\(453\) | −43.0650 | −2.02337 | ||||||||
\(454\) | −11.4716 | −0.538391 | ||||||||
\(455\) | 8.54760 | 0.400718 | ||||||||
\(456\) | 7.72443 | 0.361730 | ||||||||
\(457\) | −26.9824 | −1.26218 | −0.631092 | − | 0.775708i | \(-0.717393\pi\) | ||||
−0.631092 | + | 0.775708i | \(0.717393\pi\) | |||||||
\(458\) | 6.94051 | 0.324309 | ||||||||
\(459\) | −3.36753 | −0.157183 | ||||||||
\(460\) | −3.99980 | −0.186492 | ||||||||
\(461\) | 16.6346 | 0.774751 | 0.387375 | − | 0.921922i | \(-0.373382\pi\) | ||||
0.387375 | + | 0.921922i | \(0.373382\pi\) | |||||||
\(462\) | 30.7255 | 1.42948 | ||||||||
\(463\) | −26.3819 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(464\) | 3.25118 | 0.150932 | ||||||||
\(465\) | 11.0308 | 0.511539 | ||||||||
\(466\) | 16.4108 | 0.760215 | ||||||||
\(467\) | 20.9194 | 0.968034 | 0.484017 | − | 0.875058i | \(-0.339177\pi\) | ||||
0.484017 | + | 0.875058i | \(0.339177\pi\) | |||||||
\(468\) | 15.5122 | 0.717050 | ||||||||
\(469\) | 28.8084 | 1.33025 | ||||||||
\(470\) | 2.88290 | 0.132978 | ||||||||
\(471\) | 28.6324 | 1.31931 | ||||||||
\(472\) | 9.99028 | 0.459840 | ||||||||
\(473\) | −9.19847 | −0.422946 | ||||||||
\(474\) | −29.7447 | −1.36622 | ||||||||
\(475\) | −15.3469 | −0.704166 | ||||||||
\(476\) | −16.4216 | −0.752683 | ||||||||
\(477\) | −1.75923 | −0.0805497 | ||||||||
\(478\) | −22.3045 | −1.02018 | ||||||||
\(479\) | 17.9881 | 0.821898 | 0.410949 | − | 0.911658i | \(-0.365197\pi\) | ||||
0.410949 | + | 0.911658i | \(0.365197\pi\) | |||||||
\(480\) | 1.17627 | 0.0536891 | ||||||||
\(481\) | −16.8940 | −0.770301 | ||||||||
\(482\) | 22.4473 | 1.02245 | ||||||||
\(483\) | 59.9124 | 2.72611 | ||||||||
\(484\) | 6.44691 | 0.293041 | ||||||||
\(485\) | 3.92360 | 0.178161 | ||||||||
\(486\) | −21.3914 | −0.970332 | ||||||||
\(487\) | 38.3070 | 1.73585 | 0.867927 | − | 0.496692i | \(-0.165452\pi\) | ||||
0.867927 | + | 0.496692i | \(0.165452\pi\) | |||||||
\(488\) | 7.53520 | 0.341102 | ||||||||
\(489\) | 26.5671 | 1.20140 | ||||||||
\(490\) | −1.19419 | −0.0539481 | ||||||||
\(491\) | 36.3842 | 1.64200 | 0.820998 | − | 0.570931i | \(-0.193418\pi\) | ||||
0.820998 | + | 0.570931i | \(0.193418\pi\) | |||||||
\(492\) | 17.4086 | 0.784840 | ||||||||
\(493\) | −17.3845 | −0.782956 | ||||||||
\(494\) | −18.2772 | −0.822329 | ||||||||
\(495\) | 5.61444 | 0.252350 | ||||||||
\(496\) | −9.37775 | −0.421073 | ||||||||
\(497\) | −37.2436 | −1.67060 | ||||||||
\(498\) | 10.4008 | 0.466072 | ||||||||
\(499\) | 24.6930 | 1.10541 | 0.552705 | − | 0.833377i | \(-0.313596\pi\) | ||||
0.552705 | + | 0.833377i | \(0.313596\pi\) | |||||||
\(500\) | −4.79247 | −0.214326 | ||||||||
\(501\) | 40.1988 | 1.79595 | ||||||||
\(502\) | −20.4423 | −0.912385 | ||||||||
\(503\) | −21.1450 | −0.942809 | −0.471404 | − | 0.881917i | \(-0.656253\pi\) | ||||
−0.471404 | + | 0.881917i | \(0.656253\pi\) | |||||||
\(504\) | −8.40583 | −0.374425 | ||||||||
\(505\) | −0.828992 | −0.0368896 | ||||||||
\(506\) | 34.0201 | 1.51238 | ||||||||
\(507\) | −45.7963 | −2.03389 | ||||||||
\(508\) | −4.22504 | −0.187456 | ||||||||
\(509\) | −12.3985 | −0.549553 | −0.274776 | − | 0.961508i | \(-0.588604\pi\) | ||||
−0.274776 | + | 0.961508i | \(0.588604\pi\) | |||||||
\(510\) | −6.28966 | −0.278511 | ||||||||
\(511\) | 29.1514 | 1.28958 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.03101 | 0.0896715 | ||||||||
\(514\) | 12.3192 | 0.543376 | ||||||||
\(515\) | −0.938989 | −0.0413768 | ||||||||
\(516\) | 5.27474 | 0.232208 | ||||||||
\(517\) | −24.5204 | −1.07841 | ||||||||
\(518\) | 9.15465 | 0.402232 | ||||||||
\(519\) | 23.9429 | 1.05098 | ||||||||
\(520\) | −2.78323 | −0.122053 | ||||||||
\(521\) | −7.01193 | −0.307198 | −0.153599 | − | 0.988133i | \(-0.549086\pi\) | ||||
−0.153599 | + | 0.988133i | \(0.549086\pi\) | |||||||
\(522\) | −8.89869 | −0.389485 | ||||||||
\(523\) | 29.6863 | 1.29809 | 0.649045 | − | 0.760750i | \(-0.275169\pi\) | ||||
0.649045 | + | 0.760750i | \(0.275169\pi\) | |||||||
\(524\) | 4.88496 | 0.213401 | ||||||||
\(525\) | 35.0058 | 1.52778 | ||||||||
\(526\) | −17.1786 | −0.749024 | ||||||||
\(527\) | 50.1440 | 2.18431 | ||||||||
\(528\) | −10.0047 | −0.435399 | ||||||||
\(529\) | 43.3367 | 1.88420 | ||||||||
\(530\) | 0.315645 | 0.0137108 | ||||||||
\(531\) | −27.3440 | −1.18663 | ||||||||
\(532\) | 9.90415 | 0.429399 | ||||||||
\(533\) | −41.1913 | −1.78419 | ||||||||
\(534\) | −24.3760 | −1.05485 | ||||||||
\(535\) | 4.30965 | 0.186322 | ||||||||
\(536\) | −9.38047 | −0.405175 | ||||||||
\(537\) | 26.1591 | 1.12885 | ||||||||
\(538\) | 0.264663 | 0.0114104 | ||||||||
\(539\) | 10.1571 | 0.437499 | ||||||||
\(540\) | 0.309281 | 0.0133093 | ||||||||
\(541\) | −0.402620 | −0.0173100 | −0.00865499 | − | 0.999963i | \(-0.502755\pi\) | ||||
−0.00865499 | + | 0.999963i | \(0.502755\pi\) | |||||||
\(542\) | 9.31291 | 0.400024 | ||||||||
\(543\) | −9.34281 | −0.400938 | ||||||||
\(544\) | 5.34713 | 0.229256 | ||||||||
\(545\) | −6.97071 | −0.298593 | ||||||||
\(546\) | 41.6896 | 1.78415 | ||||||||
\(547\) | 25.9079 | 1.10774 | 0.553871 | − | 0.832602i | \(-0.313150\pi\) | ||||
0.553871 | + | 0.832602i | \(0.313150\pi\) | |||||||
\(548\) | −0.798475 | −0.0341092 | ||||||||
\(549\) | −20.6243 | −0.880225 | ||||||||
\(550\) | 19.8774 | 0.847575 | ||||||||
\(551\) | 10.4849 | 0.446670 | ||||||||
\(552\) | −19.5084 | −0.830333 | ||||||||
\(553\) | −38.1381 | −1.62180 | ||||||||
\(554\) | 12.0706 | 0.512832 | ||||||||
\(555\) | 3.50633 | 0.148835 | ||||||||
\(556\) | 9.77048 | 0.414361 | ||||||||
\(557\) | −21.2299 | −0.899538 | −0.449769 | − | 0.893145i | \(-0.648494\pi\) | ||||
−0.449769 | + | 0.893145i | \(0.648494\pi\) | |||||||
\(558\) | 25.6675 | 1.08659 | ||||||||
\(559\) | −12.4808 | −0.527883 | ||||||||
\(560\) | 1.50819 | 0.0637328 | ||||||||
\(561\) | 53.4964 | 2.25862 | ||||||||
\(562\) | 20.0764 | 0.846870 | ||||||||
\(563\) | −20.0942 | −0.846872 | −0.423436 | − | 0.905926i | \(-0.639176\pi\) | ||||
−0.423436 | + | 0.905926i | \(0.639176\pi\) | |||||||
\(564\) | 14.0609 | 0.592071 | ||||||||
\(565\) | 4.52027 | 0.190169 | ||||||||
\(566\) | −33.1312 | −1.39261 | ||||||||
\(567\) | −29.8502 | −1.25359 | ||||||||
\(568\) | 12.1271 | 0.508841 | ||||||||
\(569\) | 18.0634 | 0.757258 | 0.378629 | − | 0.925549i | \(-0.376396\pi\) | ||||
0.378629 | + | 0.925549i | \(0.376396\pi\) | |||||||
\(570\) | 3.79340 | 0.158888 | ||||||||
\(571\) | −16.1702 | −0.676702 | −0.338351 | − | 0.941020i | \(-0.609869\pi\) | ||||
−0.338351 | + | 0.941020i | \(0.609869\pi\) | |||||||
\(572\) | 23.6726 | 0.989802 | ||||||||
\(573\) | −7.11396 | −0.297190 | ||||||||
\(574\) | 22.3210 | 0.931661 | ||||||||
\(575\) | 38.7594 | 1.61638 | ||||||||
\(576\) | 2.73707 | 0.114044 | ||||||||
\(577\) | 44.0917 | 1.83556 | 0.917781 | − | 0.397088i | \(-0.129979\pi\) | ||||
0.917781 | + | 0.397088i | \(0.129979\pi\) | |||||||
\(578\) | −11.5917 | −0.482153 | ||||||||
\(579\) | −18.5360 | −0.770330 | ||||||||
\(580\) | 1.59662 | 0.0662962 | ||||||||
\(581\) | 13.3358 | 0.553261 | ||||||||
\(582\) | 19.1367 | 0.793243 | ||||||||
\(583\) | −2.68471 | −0.111189 | ||||||||
\(584\) | −9.49214 | −0.392788 | ||||||||
\(585\) | 7.61788 | 0.314960 | ||||||||
\(586\) | −23.7516 | −0.981170 | ||||||||
\(587\) | 2.45312 | 0.101251 | 0.0506256 | − | 0.998718i | \(-0.483878\pi\) | ||||
0.0506256 | + | 0.998718i | \(0.483878\pi\) | |||||||
\(588\) | −5.82448 | −0.240198 | ||||||||
\(589\) | −30.2427 | −1.24613 | ||||||||
\(590\) | 4.90613 | 0.201982 | ||||||||
\(591\) | −0.848927 | −0.0349202 | ||||||||
\(592\) | −2.98089 | −0.122514 | ||||||||
\(593\) | −38.4514 | −1.57901 | −0.789505 | − | 0.613744i | \(-0.789663\pi\) | ||||
−0.789505 | + | 0.613744i | \(0.789663\pi\) | |||||||
\(594\) | −2.63057 | −0.107934 | ||||||||
\(595\) | −8.06450 | −0.330612 | ||||||||
\(596\) | −21.1919 | −0.868052 | ||||||||
\(597\) | −33.8826 | −1.38672 | ||||||||
\(598\) | 46.1598 | 1.88761 | ||||||||
\(599\) | 28.2670 | 1.15496 | 0.577479 | − | 0.816406i | \(-0.304037\pi\) | ||||
0.577479 | + | 0.816406i | \(0.304037\pi\) | |||||||
\(600\) | −11.3984 | −0.465339 | ||||||||
\(601\) | −35.8944 | −1.46416 | −0.732082 | − | 0.681217i | \(-0.761451\pi\) | ||||
−0.732082 | + | 0.681217i | \(0.761451\pi\) | |||||||
\(602\) | 6.76319 | 0.275647 | ||||||||
\(603\) | 25.6750 | 1.04557 | ||||||||
\(604\) | 17.9796 | 0.731578 | ||||||||
\(605\) | 3.16601 | 0.128717 | ||||||||
\(606\) | −4.04328 | −0.164247 | ||||||||
\(607\) | −10.0515 | −0.407976 | −0.203988 | − | 0.978973i | \(-0.565390\pi\) | ||||
−0.203988 | + | 0.978973i | \(0.565390\pi\) | |||||||
\(608\) | −3.22494 | −0.130789 | ||||||||
\(609\) | −23.9156 | −0.969108 | ||||||||
\(610\) | 3.70046 | 0.149827 | ||||||||
\(611\) | −33.2702 | −1.34597 | ||||||||
\(612\) | −14.6354 | −0.591602 | ||||||||
\(613\) | 13.7202 | 0.554154 | 0.277077 | − | 0.960848i | \(-0.410634\pi\) | ||||
0.277077 | + | 0.960848i | \(0.410634\pi\) | |||||||
\(614\) | −9.38157 | −0.378609 | ||||||||
\(615\) | 8.54919 | 0.344737 | ||||||||
\(616\) | −12.8279 | −0.516850 | ||||||||
\(617\) | 4.83317 | 0.194576 | 0.0972881 | − | 0.995256i | \(-0.468983\pi\) | ||||
0.0972881 | + | 0.995256i | \(0.468983\pi\) | |||||||
\(618\) | −4.57977 | −0.184225 | ||||||||
\(619\) | 9.03192 | 0.363024 | 0.181512 | − | 0.983389i | \(-0.441901\pi\) | ||||
0.181512 | + | 0.983389i | \(0.441901\pi\) | |||||||
\(620\) | −4.60532 | −0.184954 | ||||||||
\(621\) | −5.12942 | −0.205836 | ||||||||
\(622\) | 5.26368 | 0.211054 | ||||||||
\(623\) | −31.2546 | −1.25219 | ||||||||
\(624\) | −13.5748 | −0.543425 | ||||||||
\(625\) | 21.4406 | 0.857625 | ||||||||
\(626\) | −24.8871 | −0.994687 | ||||||||
\(627\) | −32.2646 | −1.28852 | ||||||||
\(628\) | −11.9540 | −0.477015 | ||||||||
\(629\) | 15.9392 | 0.635538 | ||||||||
\(630\) | −4.12802 | −0.164464 | ||||||||
\(631\) | 3.48726 | 0.138826 | 0.0694129 | − | 0.997588i | \(-0.477887\pi\) | ||||
0.0694129 | + | 0.997588i | \(0.477887\pi\) | |||||||
\(632\) | 12.4184 | 0.493976 | ||||||||
\(633\) | −59.1425 | −2.35070 | ||||||||
\(634\) | −16.8876 | −0.670692 | ||||||||
\(635\) | −2.07488 | −0.0823390 | ||||||||
\(636\) | 1.53951 | 0.0610456 | ||||||||
\(637\) | 13.7816 | 0.546047 | ||||||||
\(638\) | −13.5800 | −0.537638 | ||||||||
\(639\) | −33.1926 | −1.31308 | ||||||||
\(640\) | −0.491091 | −0.0194121 | ||||||||
\(641\) | 10.2789 | 0.405992 | 0.202996 | − | 0.979180i | \(-0.434932\pi\) | ||||
0.202996 | + | 0.979180i | \(0.434932\pi\) | |||||||
\(642\) | 21.0196 | 0.829578 | ||||||||
\(643\) | −6.19060 | −0.244133 | −0.122067 | − | 0.992522i | \(-0.538952\pi\) | ||||
−0.122067 | + | 0.992522i | \(0.538952\pi\) | |||||||
\(644\) | −25.0134 | −0.985665 | ||||||||
\(645\) | 2.59038 | 0.101996 | ||||||||
\(646\) | 17.2442 | 0.678463 | ||||||||
\(647\) | 20.5889 | 0.809433 | 0.404717 | − | 0.914442i | \(-0.367370\pi\) | ||||
0.404717 | + | 0.914442i | \(0.367370\pi\) | |||||||
\(648\) | 9.71967 | 0.381825 | ||||||||
\(649\) | −41.7289 | −1.63800 | ||||||||
\(650\) | 26.9704 | 1.05787 | ||||||||
\(651\) | 68.9825 | 2.70364 | ||||||||
\(652\) | −11.0917 | −0.434385 | ||||||||
\(653\) | 27.1456 | 1.06229 | 0.531145 | − | 0.847281i | \(-0.321762\pi\) | ||||
0.531145 | + | 0.847281i | \(0.321762\pi\) | |||||||
\(654\) | −33.9986 | −1.32945 | ||||||||
\(655\) | 2.39896 | 0.0937351 | ||||||||
\(656\) | −7.26806 | −0.283770 | ||||||||
\(657\) | 25.9806 | 1.01360 | ||||||||
\(658\) | 18.0287 | 0.702831 | ||||||||
\(659\) | 30.8015 | 1.19986 | 0.599929 | − | 0.800053i | \(-0.295196\pi\) | ||||
0.599929 | + | 0.800053i | \(0.295196\pi\) | |||||||
\(660\) | −4.91321 | −0.191247 | ||||||||
\(661\) | 23.5729 | 0.916881 | 0.458441 | − | 0.888725i | \(-0.348408\pi\) | ||||
0.458441 | + | 0.888725i | \(0.348408\pi\) | |||||||
\(662\) | −22.3758 | −0.869659 | ||||||||
\(663\) | 72.5859 | 2.81900 | ||||||||
\(664\) | −4.34233 | −0.168515 | ||||||||
\(665\) | 4.86383 | 0.188611 | ||||||||
\(666\) | 8.15890 | 0.316151 | ||||||||
\(667\) | −26.4800 | −1.02531 | ||||||||
\(668\) | −16.7829 | −0.649351 | ||||||||
\(669\) | 65.0820 | 2.51621 | ||||||||
\(670\) | −4.60666 | −0.177971 | ||||||||
\(671\) | −31.4741 | −1.21505 | ||||||||
\(672\) | 7.35598 | 0.283763 | ||||||||
\(673\) | 8.13234 | 0.313479 | 0.156739 | − | 0.987640i | \(-0.449902\pi\) | ||||
0.156739 | + | 0.987640i | \(0.449902\pi\) | |||||||
\(674\) | −21.8971 | −0.843445 | ||||||||
\(675\) | −2.99703 | −0.115356 | ||||||||
\(676\) | 19.1199 | 0.735381 | ||||||||
\(677\) | 51.4609 | 1.97780 | 0.988901 | − | 0.148578i | \(-0.0474696\pi\) | ||||
0.988901 | + | 0.148578i | \(0.0474696\pi\) | |||||||
\(678\) | 22.0469 | 0.846705 | ||||||||
\(679\) | 24.5368 | 0.941637 | ||||||||
\(680\) | 2.62592 | 0.100700 | ||||||||
\(681\) | −27.4771 | −1.05292 | ||||||||
\(682\) | 39.1704 | 1.49991 | ||||||||
\(683\) | −2.92145 | −0.111786 | −0.0558930 | − | 0.998437i | \(-0.517801\pi\) | ||||
−0.0558930 | + | 0.998437i | \(0.517801\pi\) | |||||||
\(684\) | 8.82688 | 0.337504 | ||||||||
\(685\) | −0.392124 | −0.0149823 | ||||||||
\(686\) | 14.0297 | 0.535657 | ||||||||
\(687\) | 16.6240 | 0.634246 | ||||||||
\(688\) | −2.20220 | −0.0839580 | ||||||||
\(689\) | −3.64271 | −0.138776 | ||||||||
\(690\) | −9.58039 | −0.364719 | ||||||||
\(691\) | 35.1316 | 1.33647 | 0.668234 | − | 0.743951i | \(-0.267050\pi\) | ||||
0.668234 | + | 0.743951i | \(0.267050\pi\) | |||||||
\(692\) | −9.99615 | −0.379996 | ||||||||
\(693\) | 35.1107 | 1.33375 | ||||||||
\(694\) | 12.6063 | 0.478530 | ||||||||
\(695\) | 4.79819 | 0.182006 | ||||||||
\(696\) | 7.78728 | 0.295176 | ||||||||
\(697\) | 38.8632 | 1.47205 | ||||||||
\(698\) | 28.4651 | 1.07742 | ||||||||
\(699\) | 39.3074 | 1.48674 | ||||||||
\(700\) | −14.6149 | −0.552391 | ||||||||
\(701\) | 9.01787 | 0.340600 | 0.170300 | − | 0.985392i | \(-0.445526\pi\) | ||||
0.170300 | + | 0.985392i | \(0.445526\pi\) | |||||||
\(702\) | −3.56926 | −0.134713 | ||||||||
\(703\) | −9.61320 | −0.362569 | ||||||||
\(704\) | 4.17695 | 0.157425 | ||||||||
\(705\) | 6.90518 | 0.260064 | ||||||||
\(706\) | −8.69186 | −0.327123 | ||||||||
\(707\) | −5.18422 | −0.194973 | ||||||||
\(708\) | 23.9289 | 0.899303 | ||||||||
\(709\) | 51.0066 | 1.91559 | 0.957796 | − | 0.287450i | \(-0.0928074\pi\) | ||||
0.957796 | + | 0.287450i | \(0.0928074\pi\) | |||||||
\(710\) | 5.95549 | 0.223506 | ||||||||
\(711\) | −33.9899 | −1.27472 | ||||||||
\(712\) | 10.1770 | 0.381398 | ||||||||
\(713\) | 76.3793 | 2.86043 | ||||||||
\(714\) | −39.3333 | −1.47201 | ||||||||
\(715\) | 11.6254 | 0.434765 | ||||||||
\(716\) | −10.9214 | −0.408152 | ||||||||
\(717\) | −53.4242 | −1.99516 | ||||||||
\(718\) | −12.1148 | −0.452120 | ||||||||
\(719\) | −40.9282 | −1.52637 | −0.763183 | − | 0.646183i | \(-0.776364\pi\) | ||||
−0.763183 | + | 0.646183i | \(0.776364\pi\) | |||||||
\(720\) | 1.34415 | 0.0500934 | ||||||||
\(721\) | −5.87211 | −0.218689 | ||||||||
\(722\) | 8.59976 | 0.320050 | ||||||||
\(723\) | 53.7661 | 1.99958 | ||||||||
\(724\) | 3.90061 | 0.144965 | ||||||||
\(725\) | −15.4718 | −0.574608 | ||||||||
\(726\) | 15.4417 | 0.573097 | ||||||||
\(727\) | 23.3071 | 0.864413 | 0.432206 | − | 0.901775i | \(-0.357735\pi\) | ||||
0.432206 | + | 0.901775i | \(0.357735\pi\) | |||||||
\(728\) | −17.4053 | −0.645085 | ||||||||
\(729\) | −22.0780 | −0.817702 | ||||||||
\(730\) | −4.66150 | −0.172530 | ||||||||
\(731\) | 11.7754 | 0.435530 | ||||||||
\(732\) | 18.0484 | 0.667089 | ||||||||
\(733\) | −32.1927 | −1.18906 | −0.594532 | − | 0.804072i | \(-0.702663\pi\) | ||||
−0.594532 | + | 0.804072i | \(0.702663\pi\) | |||||||
\(734\) | 32.7058 | 1.20719 | ||||||||
\(735\) | −2.86035 | −0.105506 | ||||||||
\(736\) | 8.14473 | 0.300219 | ||||||||
\(737\) | 39.1817 | 1.44328 | ||||||||
\(738\) | 19.8932 | 0.732277 | ||||||||
\(739\) | −37.3545 | −1.37411 | −0.687053 | − | 0.726607i | \(-0.741096\pi\) | ||||
−0.687053 | + | 0.726607i | \(0.741096\pi\) | |||||||
\(740\) | −1.46389 | −0.0538136 | ||||||||
\(741\) | −43.7778 | −1.60822 | ||||||||
\(742\) | 1.97394 | 0.0724655 | ||||||||
\(743\) | −10.6076 | −0.389156 | −0.194578 | − | 0.980887i | \(-0.562334\pi\) | ||||
−0.194578 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(744\) | −22.4617 | −0.823488 | ||||||||
\(745\) | −10.4071 | −0.381287 | ||||||||
\(746\) | 14.0290 | 0.513638 | ||||||||
\(747\) | 11.8852 | 0.434858 | ||||||||
\(748\) | −22.3347 | −0.816636 | ||||||||
\(749\) | 26.9510 | 0.984769 | ||||||||
\(750\) | −11.4790 | −0.419154 | ||||||||
\(751\) | −5.39998 | −0.197048 | −0.0985240 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985240 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(752\) | −5.87041 | −0.214072 | ||||||||
\(753\) | −48.9638 | −1.78434 | ||||||||
\(754\) | −18.4259 | −0.671030 | ||||||||
\(755\) | 8.82959 | 0.321342 | ||||||||
\(756\) | 1.93413 | 0.0703438 | ||||||||
\(757\) | 40.6092 | 1.47597 | 0.737983 | − | 0.674819i | \(-0.235778\pi\) | ||||
0.737983 | + | 0.674819i | \(0.235778\pi\) | |||||||
\(758\) | 7.19822 | 0.261451 | ||||||||
\(759\) | 81.4856 | 2.95774 | ||||||||
\(760\) | −1.58374 | −0.0574482 | ||||||||
\(761\) | 2.77011 | 0.100417 | 0.0502083 | − | 0.998739i | \(-0.484011\pi\) | ||||
0.0502083 | + | 0.998739i | \(0.484011\pi\) | |||||||
\(762\) | −10.1199 | −0.366605 | ||||||||
\(763\) | −43.5924 | −1.57815 | ||||||||
\(764\) | 2.97007 | 0.107453 | ||||||||
\(765\) | −7.18733 | −0.259858 | ||||||||
\(766\) | −6.09068 | −0.220065 | ||||||||
\(767\) | −56.6193 | −2.04440 | ||||||||
\(768\) | −2.39522 | −0.0864300 | ||||||||
\(769\) | −17.8199 | −0.642603 | −0.321301 | − | 0.946977i | \(-0.604120\pi\) | ||||
−0.321301 | + | 0.946977i | \(0.604120\pi\) | |||||||
\(770\) | −6.29965 | −0.227023 | ||||||||
\(771\) | 29.5071 | 1.06267 | ||||||||
\(772\) | 7.73876 | 0.278524 | ||||||||
\(773\) | −23.3260 | −0.838977 | −0.419489 | − | 0.907761i | \(-0.637791\pi\) | ||||
−0.419489 | + | 0.907761i | \(0.637791\pi\) | |||||||
\(774\) | 6.02756 | 0.216656 | ||||||||
\(775\) | 44.6271 | 1.60305 | ||||||||
\(776\) | −7.98956 | −0.286808 | ||||||||
\(777\) | 21.9274 | 0.786640 | ||||||||
\(778\) | 16.9965 | 0.609355 | ||||||||
\(779\) | −23.4391 | −0.839792 | ||||||||
\(780\) | −6.66643 | −0.238697 | ||||||||
\(781\) | −50.6542 | −1.81255 | ||||||||
\(782\) | −43.5509 | −1.55738 | ||||||||
\(783\) | 2.04754 | 0.0731730 | ||||||||
\(784\) | 2.43171 | 0.0868469 | ||||||||
\(785\) | −5.87048 | −0.209526 | ||||||||
\(786\) | 11.7005 | 0.417345 | ||||||||
\(787\) | 20.2693 | 0.722523 | 0.361262 | − | 0.932464i | \(-0.382346\pi\) | ||||
0.361262 | + | 0.932464i | \(0.382346\pi\) | |||||||
\(788\) | 0.354426 | 0.0126259 | ||||||||
\(789\) | −41.1466 | −1.46486 | ||||||||
\(790\) | 6.09854 | 0.216976 | ||||||||
\(791\) | 28.2682 | 1.00510 | ||||||||
\(792\) | −11.4326 | −0.406239 | ||||||||
\(793\) | −42.7053 | −1.51651 | ||||||||
\(794\) | 32.9086 | 1.16788 | ||||||||
\(795\) | 0.756039 | 0.0268139 | ||||||||
\(796\) | 14.1460 | 0.501390 | ||||||||
\(797\) | 12.3513 | 0.437504 | 0.218752 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218752 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(798\) | 23.7226 | 0.839770 | ||||||||
\(799\) | 31.3898 | 1.11049 | ||||||||
\(800\) | 4.75883 | 0.168250 | ||||||||
\(801\) | −27.8550 | −0.984208 | ||||||||
\(802\) | 24.4612 | 0.863754 | ||||||||
\(803\) | 39.6482 | 1.39915 | ||||||||
\(804\) | −22.4683 | −0.792394 | ||||||||
\(805\) | −12.2838 | −0.432948 | ||||||||
\(806\) | 53.1478 | 1.87205 | ||||||||
\(807\) | 0.633926 | 0.0223152 | ||||||||
\(808\) | 1.68806 | 0.0593858 | ||||||||
\(809\) | 19.0325 | 0.669148 | 0.334574 | − | 0.942369i | \(-0.391408\pi\) | ||||
0.334574 | + | 0.942369i | \(0.391408\pi\) | |||||||
\(810\) | 4.77324 | 0.167714 | ||||||||
\(811\) | −27.9661 | −0.982022 | −0.491011 | − | 0.871153i | \(-0.663373\pi\) | ||||
−0.491011 | + | 0.871153i | \(0.663373\pi\) | |||||||
\(812\) | 9.98472 | 0.350395 | ||||||||
\(813\) | 22.3064 | 0.782321 | ||||||||
\(814\) | 12.4510 | 0.436409 | ||||||||
\(815\) | −5.44704 | −0.190801 | ||||||||
\(816\) | 12.8075 | 0.448353 | ||||||||
\(817\) | −7.10196 | −0.248466 | ||||||||
\(818\) | −2.74577 | −0.0960035 | ||||||||
\(819\) | 47.6396 | 1.66466 | ||||||||
\(820\) | −3.56928 | −0.124645 | ||||||||
\(821\) | 25.4108 | 0.886844 | 0.443422 | − | 0.896313i | \(-0.353764\pi\) | ||||
0.443422 | + | 0.896313i | \(0.353764\pi\) | |||||||
\(822\) | −1.91252 | −0.0667068 | ||||||||
\(823\) | 35.1045 | 1.22367 | 0.611833 | − | 0.790987i | \(-0.290432\pi\) | ||||
0.611833 | + | 0.790987i | \(0.290432\pi\) | |||||||
\(824\) | 1.91205 | 0.0666093 | ||||||||
\(825\) | 47.6107 | 1.65759 | ||||||||
\(826\) | 30.6812 | 1.06754 | ||||||||
\(827\) | −33.0004 | −1.14754 | −0.573768 | − | 0.819018i | \(-0.694519\pi\) | ||||
−0.573768 | + | 0.819018i | \(0.694519\pi\) | |||||||
\(828\) | −22.2927 | −0.774724 | ||||||||
\(829\) | 9.61320 | 0.333880 | 0.166940 | − | 0.985967i | \(-0.446611\pi\) | ||||
0.166940 | + | 0.985967i | \(0.446611\pi\) | |||||||
\(830\) | −2.13248 | −0.0740194 | ||||||||
\(831\) | 28.9118 | 1.00294 | ||||||||
\(832\) | 5.66744 | 0.196483 | ||||||||
\(833\) | −13.0027 | −0.450516 | ||||||||
\(834\) | 23.4024 | 0.810360 | ||||||||
\(835\) | −8.24194 | −0.285224 | ||||||||
\(836\) | 13.4704 | 0.465884 | ||||||||
\(837\) | −5.90595 | −0.204140 | ||||||||
\(838\) | 12.3308 | 0.425959 | ||||||||
\(839\) | −46.8043 | −1.61587 | −0.807933 | − | 0.589275i | \(-0.799414\pi\) | ||||
−0.807933 | + | 0.589275i | \(0.799414\pi\) | |||||||
\(840\) | 3.61245 | 0.124641 | ||||||||
\(841\) | −18.4298 | −0.635512 | ||||||||
\(842\) | 2.41067 | 0.0830773 | ||||||||
\(843\) | 48.0873 | 1.65621 | ||||||||
\(844\) | 24.6919 | 0.849931 | ||||||||
\(845\) | 9.38960 | 0.323012 | ||||||||
\(846\) | 16.0677 | 0.552419 | ||||||||
\(847\) | 19.7992 | 0.680307 | ||||||||
\(848\) | −0.642744 | −0.0220719 | ||||||||
\(849\) | −79.3564 | −2.72350 | ||||||||
\(850\) | −25.4461 | −0.872793 | ||||||||
\(851\) | 24.2786 | 0.832258 | ||||||||
\(852\) | 29.0470 | 0.995133 | ||||||||
\(853\) | −23.6958 | −0.811328 | −0.405664 | − | 0.914022i | \(-0.632960\pi\) | ||||
−0.405664 | + | 0.914022i | \(0.632960\pi\) | |||||||
\(854\) | 23.1414 | 0.791883 | ||||||||
\(855\) | 4.33480 | 0.148247 | ||||||||
\(856\) | −8.77566 | −0.299946 | ||||||||
\(857\) | 33.1710 | 1.13310 | 0.566550 | − | 0.824027i | \(-0.308278\pi\) | ||||
0.566550 | + | 0.824027i | \(0.308278\pi\) | |||||||
\(858\) | 56.7011 | 1.93574 | ||||||||
\(859\) | −2.65757 | −0.0906751 | −0.0453375 | − | 0.998972i | \(-0.514436\pi\) | ||||
−0.0453375 | + | 0.998972i | \(0.514436\pi\) | |||||||
\(860\) | −1.08148 | −0.0368781 | ||||||||
\(861\) | 53.4637 | 1.82204 | ||||||||
\(862\) | 12.0286 | 0.409695 | ||||||||
\(863\) | −36.7289 | −1.25027 | −0.625133 | − | 0.780518i | \(-0.714955\pi\) | ||||
−0.625133 | + | 0.780518i | \(0.714955\pi\) | |||||||
\(864\) | −0.629784 | −0.0214257 | ||||||||
\(865\) | −4.90901 | −0.166911 | ||||||||
\(866\) | −27.1227 | −0.921666 | ||||||||
\(867\) | −27.7648 | −0.942941 | ||||||||
\(868\) | −28.8001 | −0.977539 | ||||||||
\(869\) | −51.8709 | −1.75960 | ||||||||
\(870\) | 3.82426 | 0.129655 | ||||||||
\(871\) | 53.1633 | 1.80137 | ||||||||
\(872\) | 14.1944 | 0.480681 | ||||||||
\(873\) | 21.8680 | 0.740118 | ||||||||
\(874\) | 26.2663 | 0.888470 | ||||||||
\(875\) | −14.7182 | −0.497566 | ||||||||
\(876\) | −22.7357 | −0.768170 | ||||||||
\(877\) | 0.989371 | 0.0334087 | 0.0167043 | − | 0.999860i | \(-0.494683\pi\) | ||||
0.0167043 | + | 0.999860i | \(0.494683\pi\) | |||||||
\(878\) | 28.9910 | 0.978398 | ||||||||
\(879\) | −56.8903 | −1.91886 | ||||||||
\(880\) | 2.05126 | 0.0691480 | ||||||||
\(881\) | −27.2205 | −0.917082 | −0.458541 | − | 0.888673i | \(-0.651628\pi\) | ||||
−0.458541 | + | 0.888673i | \(0.651628\pi\) | |||||||
\(882\) | −6.65576 | −0.224111 | ||||||||
\(883\) | 24.4715 | 0.823530 | 0.411765 | − | 0.911290i | \(-0.364912\pi\) | ||||
0.411765 | + | 0.911290i | \(0.364912\pi\) | |||||||
\(884\) | −30.3045 | −1.01925 | ||||||||
\(885\) | 11.7512 | 0.395014 | ||||||||
\(886\) | −11.4191 | −0.383633 | ||||||||
\(887\) | −24.1615 | −0.811263 | −0.405631 | − | 0.914037i | \(-0.632948\pi\) | ||||
−0.405631 | + | 0.914037i | \(0.632948\pi\) | |||||||
\(888\) | −7.13988 | −0.239599 | ||||||||
\(889\) | −12.9756 | −0.435186 | ||||||||
\(890\) | 4.99781 | 0.167527 | ||||||||
\(891\) | −40.5986 | −1.36010 | ||||||||
\(892\) | −27.1716 | −0.909774 | ||||||||
\(893\) | −18.9317 | −0.633526 | ||||||||
\(894\) | −50.7591 | −1.69764 | ||||||||
\(895\) | −5.36340 | −0.179279 | ||||||||
\(896\) | −3.07111 | −0.102599 | ||||||||
\(897\) | 110.563 | 3.69158 | ||||||||
\(898\) | 16.5317 | 0.551672 | ||||||||
\(899\) | −30.4887 | −1.01686 | ||||||||
\(900\) | −13.0252 | −0.434174 | ||||||||
\(901\) | 3.43683 | 0.114497 | ||||||||
\(902\) | 30.3583 | 1.01082 | ||||||||
\(903\) | 16.1993 | 0.539080 | ||||||||
\(904\) | −9.20454 | −0.306139 | ||||||||
\(905\) | 1.91555 | 0.0636752 | ||||||||
\(906\) | 43.0650 | 1.43074 | ||||||||
\(907\) | 47.7732 | 1.58628 | 0.793142 | − | 0.609037i | \(-0.208444\pi\) | ||||
0.793142 | + | 0.609037i | \(0.208444\pi\) | |||||||
\(908\) | 11.4716 | 0.380700 | ||||||||
\(909\) | −4.62034 | −0.153247 | ||||||||
\(910\) | −8.54760 | −0.283350 | ||||||||
\(911\) | −40.6459 | −1.34666 | −0.673330 | − | 0.739342i | \(-0.735137\pi\) | ||||
−0.673330 | + | 0.739342i | \(0.735137\pi\) | |||||||
\(912\) | −7.72443 | −0.255782 | ||||||||
\(913\) | 18.1377 | 0.600270 | ||||||||
\(914\) | 26.9824 | 0.892499 | ||||||||
\(915\) | 8.86342 | 0.293016 | ||||||||
\(916\) | −6.94051 | −0.229321 | ||||||||
\(917\) | 15.0023 | 0.495418 | ||||||||
\(918\) | 3.36753 | 0.111145 | ||||||||
\(919\) | 16.1240 | 0.531881 | 0.265940 | − | 0.963989i | \(-0.414318\pi\) | ||||
0.265940 | + | 0.963989i | \(0.414318\pi\) | |||||||
\(920\) | 3.99980 | 0.131870 | ||||||||
\(921\) | −22.4709 | −0.740441 | ||||||||
\(922\) | −16.6346 | −0.547831 | ||||||||
\(923\) | −68.7295 | −2.26226 | ||||||||
\(924\) | −30.7255 | −1.01080 | ||||||||
\(925\) | 14.1856 | 0.466418 | ||||||||
\(926\) | 26.3819 | 0.866964 | ||||||||
\(927\) | −5.23340 | −0.171887 | ||||||||
\(928\) | −3.25118 | −0.106725 | ||||||||
\(929\) | −3.68430 | −0.120878 | −0.0604390 | − | 0.998172i | \(-0.519250\pi\) | ||||
−0.0604390 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(930\) | −11.0308 | −0.361713 | ||||||||
\(931\) | 7.84214 | 0.257016 | ||||||||
\(932\) | −16.4108 | −0.537553 | ||||||||
\(933\) | 12.6076 | 0.412756 | ||||||||
\(934\) | −20.9194 | −0.684504 | ||||||||
\(935\) | −10.9683 | −0.358703 | ||||||||
\(936\) | −15.5122 | −0.507031 | ||||||||
\(937\) | 30.4101 | 0.993456 | 0.496728 | − | 0.867906i | \(-0.334535\pi\) | ||||
0.496728 | + | 0.867906i | \(0.334535\pi\) | |||||||
\(938\) | −28.8084 | −0.940629 | ||||||||
\(939\) | −59.6099 | −1.94530 | ||||||||
\(940\) | −2.88290 | −0.0940299 | ||||||||
\(941\) | 52.1075 | 1.69866 | 0.849329 | − | 0.527865i | \(-0.177007\pi\) | ||||
0.849329 | + | 0.527865i | \(0.177007\pi\) | |||||||
\(942\) | −28.6324 | −0.932893 | ||||||||
\(943\) | 59.1964 | 1.92770 | ||||||||
\(944\) | −9.99028 | −0.325156 | ||||||||
\(945\) | 0.949835 | 0.0308981 | ||||||||
\(946\) | 9.19847 | 0.299068 | ||||||||
\(947\) | 2.95686 | 0.0960852 | 0.0480426 | − | 0.998845i | \(-0.484702\pi\) | ||||
0.0480426 | + | 0.998845i | \(0.484702\pi\) | |||||||
\(948\) | 29.7447 | 0.966062 | ||||||||
\(949\) | 53.7962 | 1.74630 | ||||||||
\(950\) | 15.3469 | 0.497921 | ||||||||
\(951\) | −40.4495 | −1.31166 | ||||||||
\(952\) | 16.4216 | 0.532227 | ||||||||
\(953\) | −25.0877 | −0.812669 | −0.406334 | − | 0.913724i | \(-0.633193\pi\) | ||||
−0.406334 | + | 0.913724i | \(0.633193\pi\) | |||||||
\(954\) | 1.75923 | 0.0569572 | ||||||||
\(955\) | 1.45857 | 0.0471983 | ||||||||
\(956\) | 22.3045 | 0.721379 | ||||||||
\(957\) | −32.5271 | −1.05145 | ||||||||
\(958\) | −17.9881 | −0.581170 | ||||||||
\(959\) | −2.45220 | −0.0791858 | ||||||||
\(960\) | −1.17627 | −0.0379639 | ||||||||
\(961\) | 56.9422 | 1.83684 | ||||||||
\(962\) | 16.8940 | 0.544685 | ||||||||
\(963\) | 24.0196 | 0.774020 | ||||||||
\(964\) | −22.4473 | −0.722979 | ||||||||
\(965\) | 3.80043 | 0.122340 | ||||||||
\(966\) | −59.9124 | −1.92765 | ||||||||
\(967\) | 3.29962 | 0.106109 | 0.0530543 | − | 0.998592i | \(-0.483104\pi\) | ||||
0.0530543 | + | 0.998592i | \(0.483104\pi\) | |||||||
\(968\) | −6.44691 | −0.207211 | ||||||||
\(969\) | 41.3035 | 1.32686 | ||||||||
\(970\) | −3.92360 | −0.125979 | ||||||||
\(971\) | −3.20895 | −0.102980 | −0.0514900 | − | 0.998674i | \(-0.516397\pi\) | ||||
−0.0514900 | + | 0.998674i | \(0.516397\pi\) | |||||||
\(972\) | 21.3914 | 0.686128 | ||||||||
\(973\) | 30.0062 | 0.961955 | ||||||||
\(974\) | −38.3070 | −1.22743 | ||||||||
\(975\) | 64.6000 | 2.06885 | ||||||||
\(976\) | −7.53520 | −0.241196 | ||||||||
\(977\) | −52.1630 | −1.66884 | −0.834421 | − | 0.551127i | \(-0.814198\pi\) | ||||
−0.834421 | + | 0.551127i | \(0.814198\pi\) | |||||||
\(978\) | −26.5671 | −0.849521 | ||||||||
\(979\) | −42.5086 | −1.35858 | ||||||||
\(980\) | 1.19419 | 0.0381471 | ||||||||
\(981\) | −38.8509 | −1.24041 | ||||||||
\(982\) | −36.3842 | −1.16107 | ||||||||
\(983\) | 23.5438 | 0.750930 | 0.375465 | − | 0.926837i | \(-0.377483\pi\) | ||||
0.375465 | + | 0.926837i | \(0.377483\pi\) | |||||||
\(984\) | −17.4086 | −0.554965 | ||||||||
\(985\) | 0.174055 | 0.00554586 | ||||||||
\(986\) | 17.3845 | 0.553634 | ||||||||
\(987\) | 43.1826 | 1.37452 | ||||||||
\(988\) | 18.2772 | 0.581474 | ||||||||
\(989\) | 17.9363 | 0.570342 | ||||||||
\(990\) | −5.61444 | −0.178438 | ||||||||
\(991\) | 20.4687 | 0.650211 | 0.325105 | − | 0.945678i | \(-0.394600\pi\) | ||||
0.325105 | + | 0.945678i | \(0.394600\pi\) | |||||||
\(992\) | 9.37775 | 0.297744 | ||||||||
\(993\) | −53.5948 | −1.70078 | ||||||||
\(994\) | 37.2436 | 1.18129 | ||||||||
\(995\) | 6.94694 | 0.220233 | ||||||||
\(996\) | −10.4008 | −0.329563 | ||||||||
\(997\) | 28.5292 | 0.903530 | 0.451765 | − | 0.892137i | \(-0.350795\pi\) | ||||
0.451765 | + | 0.892137i | \(0.350795\pi\) | |||||||
\(998\) | −24.6930 | −0.781642 | ||||||||
\(999\) | −1.87732 | −0.0593957 |
(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 | 4006.2.a.g.1.5 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.5 | ✓ | 40 | 1.1 | even | 1 | trivial |