Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37596 | −1.68006 | −0.840028 | − | 0.542542i | \(-0.817462\pi\) | ||||
−0.840028 | + | 0.542542i | \(0.817462\pi\) | |||||||
\(3\) | 1.38475 | 0.799486 | 0.399743 | − | 0.916627i | \(-0.369099\pi\) | ||||
0.399743 | + | 0.916627i | \(0.369099\pi\) | |||||||
\(4\) | 3.64518 | 1.82259 | ||||||||
\(5\) | 0.740241 | 0.331046 | 0.165523 | − | 0.986206i | \(-0.447069\pi\) | ||||
0.165523 | + | 0.986206i | \(0.447069\pi\) | |||||||
\(6\) | −3.29011 | −1.34318 | ||||||||
\(7\) | −0.0236528 | −0.00893990 | −0.00446995 | − | 0.999990i | \(-0.501423\pi\) | ||||
−0.00446995 | + | 0.999990i | \(0.501423\pi\) | |||||||
\(8\) | −3.90889 | −1.38200 | ||||||||
\(9\) | −1.08246 | −0.360821 | ||||||||
\(10\) | −1.75878 | −0.556176 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 5.04767 | 1.45714 | ||||||||
\(13\) | −2.69585 | −0.747693 | −0.373847 | − | 0.927491i | \(-0.621961\pi\) | ||||
−0.373847 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(14\) | 0.0561980 | 0.0150195 | ||||||||
\(15\) | 1.02505 | 0.264667 | ||||||||
\(16\) | 1.99699 | 0.499247 | ||||||||
\(17\) | 0.455891 | 0.110570 | 0.0552849 | − | 0.998471i | \(-0.482393\pi\) | ||||
0.0552849 | + | 0.998471i | \(0.482393\pi\) | |||||||
\(18\) | 2.57189 | 0.606200 | ||||||||
\(19\) | −1.92790 | −0.442292 | −0.221146 | − | 0.975241i | \(-0.570980\pi\) | ||||
−0.221146 | + | 0.975241i | \(0.570980\pi\) | |||||||
\(20\) | 2.69831 | 0.603361 | ||||||||
\(21\) | −0.0327532 | −0.00714733 | ||||||||
\(22\) | −2.37596 | −0.506556 | ||||||||
\(23\) | 4.19781 | 0.875304 | 0.437652 | − | 0.899144i | \(-0.355810\pi\) | ||||
0.437652 | + | 0.899144i | \(0.355810\pi\) | |||||||
\(24\) | −5.41283 | −1.10489 | ||||||||
\(25\) | −4.45204 | −0.890409 | ||||||||
\(26\) | 6.40522 | 1.25617 | ||||||||
\(27\) | −5.65320 | −1.08796 | ||||||||
\(28\) | −0.0862186 | −0.0162938 | ||||||||
\(29\) | −6.59167 | −1.22404 | −0.612021 | − | 0.790841i | \(-0.709643\pi\) | ||||
−0.612021 | + | 0.790841i | \(0.709643\pi\) | |||||||
\(30\) | −2.43547 | −0.444655 | ||||||||
\(31\) | 8.95500 | 1.60837 | 0.804183 | − | 0.594382i | \(-0.202603\pi\) | ||||
0.804183 | + | 0.594382i | \(0.202603\pi\) | |||||||
\(32\) | 3.07301 | 0.543236 | ||||||||
\(33\) | 1.38475 | 0.241054 | ||||||||
\(34\) | −1.08318 | −0.185764 | ||||||||
\(35\) | −0.0175087 | −0.00295952 | ||||||||
\(36\) | −3.94578 | −0.657630 | ||||||||
\(37\) | 10.5100 | 1.72783 | 0.863916 | − | 0.503637i | \(-0.168005\pi\) | ||||
0.863916 | + | 0.503637i | \(0.168005\pi\) | |||||||
\(38\) | 4.58062 | 0.743075 | ||||||||
\(39\) | −3.73308 | −0.597771 | ||||||||
\(40\) | −2.89352 | −0.457505 | ||||||||
\(41\) | −12.2011 | −1.90548 | −0.952742 | − | 0.303781i | \(-0.901751\pi\) | ||||
−0.952742 | + | 0.303781i | \(0.901751\pi\) | |||||||
\(42\) | 0.0778202 | 0.0120079 | ||||||||
\(43\) | 8.91127 | 1.35896 | 0.679478 | − | 0.733696i | \(-0.262206\pi\) | ||||
0.679478 | + | 0.733696i | \(0.262206\pi\) | |||||||
\(44\) | 3.64518 | 0.549532 | ||||||||
\(45\) | −0.801284 | −0.119448 | ||||||||
\(46\) | −9.97383 | −1.47056 | ||||||||
\(47\) | −6.38200 | −0.930910 | −0.465455 | − | 0.885072i | \(-0.654109\pi\) | ||||
−0.465455 | + | 0.885072i | \(0.654109\pi\) | |||||||
\(48\) | 2.76533 | 0.399141 | ||||||||
\(49\) | −6.99944 | −0.999920 | ||||||||
\(50\) | 10.5779 | 1.49594 | ||||||||
\(51\) | 0.631296 | 0.0883991 | ||||||||
\(52\) | −9.82685 | −1.36274 | ||||||||
\(53\) | 12.7888 | 1.75667 | 0.878336 | − | 0.478044i | \(-0.158654\pi\) | ||||
0.878336 | + | 0.478044i | \(0.158654\pi\) | |||||||
\(54\) | 13.4318 | 1.82783 | ||||||||
\(55\) | 0.740241 | 0.0998140 | ||||||||
\(56\) | 0.0924559 | 0.0123549 | ||||||||
\(57\) | −2.66967 | −0.353606 | ||||||||
\(58\) | 15.6615 | 2.05646 | ||||||||
\(59\) | −1.06255 | −0.138333 | −0.0691663 | − | 0.997605i | \(-0.522034\pi\) | ||||
−0.0691663 | + | 0.997605i | \(0.522034\pi\) | |||||||
\(60\) | 3.73649 | 0.482379 | ||||||||
\(61\) | 9.20916 | 1.17911 | 0.589556 | − | 0.807728i | \(-0.299303\pi\) | ||||
0.589556 | + | 0.807728i | \(0.299303\pi\) | |||||||
\(62\) | −21.2767 | −2.70215 | ||||||||
\(63\) | 0.0256033 | 0.00322571 | ||||||||
\(64\) | −11.2953 | −1.41191 | ||||||||
\(65\) | −1.99558 | −0.247521 | ||||||||
\(66\) | −3.29011 | −0.404985 | ||||||||
\(67\) | −12.8056 | −1.56446 | −0.782228 | − | 0.622992i | \(-0.785917\pi\) | ||||
−0.782228 | + | 0.622992i | \(0.785917\pi\) | |||||||
\(68\) | 1.66181 | 0.201524 | ||||||||
\(69\) | 5.81292 | 0.699794 | ||||||||
\(70\) | 0.0416000 | 0.00497215 | ||||||||
\(71\) | 12.9039 | 1.53141 | 0.765705 | − | 0.643192i | \(-0.222390\pi\) | ||||
0.765705 | + | 0.643192i | \(0.222390\pi\) | |||||||
\(72\) | 4.23123 | 0.498655 | ||||||||
\(73\) | −11.4506 | −1.34020 | −0.670098 | − | 0.742273i | \(-0.733748\pi\) | ||||
−0.670098 | + | 0.742273i | \(0.733748\pi\) | |||||||
\(74\) | −24.9713 | −2.90285 | ||||||||
\(75\) | −6.16497 | −0.711870 | ||||||||
\(76\) | −7.02756 | −0.806117 | ||||||||
\(77\) | −0.0236528 | −0.00269548 | ||||||||
\(78\) | 8.86964 | 1.00429 | ||||||||
\(79\) | −7.58395 | −0.853261 | −0.426631 | − | 0.904426i | \(-0.640300\pi\) | ||||
−0.426631 | + | 0.904426i | \(0.640300\pi\) | |||||||
\(80\) | 1.47825 | 0.165274 | ||||||||
\(81\) | −4.58088 | −0.508986 | ||||||||
\(82\) | 28.9892 | 3.20132 | ||||||||
\(83\) | 14.3889 | 1.57938 | 0.789691 | − | 0.613505i | \(-0.210241\pi\) | ||||
0.789691 | + | 0.613505i | \(0.210241\pi\) | |||||||
\(84\) | −0.119391 | −0.0130267 | ||||||||
\(85\) | 0.337469 | 0.0366037 | ||||||||
\(86\) | −21.1728 | −2.28312 | ||||||||
\(87\) | −9.12783 | −0.978606 | ||||||||
\(88\) | −3.90889 | −0.416689 | ||||||||
\(89\) | −9.90297 | −1.04971 | −0.524856 | − | 0.851191i | \(-0.675881\pi\) | ||||
−0.524856 | + | 0.851191i | \(0.675881\pi\) | |||||||
\(90\) | 1.90382 | 0.200680 | ||||||||
\(91\) | 0.0637642 | 0.00668430 | ||||||||
\(92\) | 15.3018 | 1.59532 | ||||||||
\(93\) | 12.4004 | 1.28587 | ||||||||
\(94\) | 15.1634 | 1.56398 | ||||||||
\(95\) | −1.42711 | −0.146419 | ||||||||
\(96\) | 4.25535 | 0.434310 | ||||||||
\(97\) | 10.9611 | 1.11293 | 0.556467 | − | 0.830870i | \(-0.312157\pi\) | ||||
0.556467 | + | 0.830870i | \(0.312157\pi\) | |||||||
\(98\) | 16.6304 | 1.67992 | ||||||||
\(99\) | −1.08246 | −0.108792 | ||||||||
\(100\) | −16.2285 | −1.62285 | ||||||||
\(101\) | −0.00336168 | −0.000334500 0 | −0.000167250 | − | 1.00000i | \(-0.500053\pi\) | ||||
−0.000167250 | 1.00000i | \(0.500053\pi\) | ||||||||
\(102\) | −1.49993 | −0.148516 | ||||||||
\(103\) | 4.33393 | 0.427035 | 0.213517 | − | 0.976939i | \(-0.431508\pi\) | ||||
0.213517 | + | 0.976939i | \(0.431508\pi\) | |||||||
\(104\) | 10.5378 | 1.03331 | ||||||||
\(105\) | −0.0242452 | −0.00236609 | ||||||||
\(106\) | −30.3856 | −2.95131 | ||||||||
\(107\) | 3.76297 | 0.363780 | 0.181890 | − | 0.983319i | \(-0.441779\pi\) | ||||
0.181890 | + | 0.983319i | \(0.441779\pi\) | |||||||
\(108\) | −20.6069 | −1.98290 | ||||||||
\(109\) | −11.8950 | −1.13933 | −0.569666 | − | 0.821876i | \(-0.692928\pi\) | ||||
−0.569666 | + | 0.821876i | \(0.692928\pi\) | |||||||
\(110\) | −1.75878 | −0.167693 | ||||||||
\(111\) | 14.5537 | 1.38138 | ||||||||
\(112\) | −0.0472343 | −0.00446322 | ||||||||
\(113\) | −7.17418 | −0.674890 | −0.337445 | − | 0.941345i | \(-0.609563\pi\) | ||||
−0.337445 | + | 0.941345i | \(0.609563\pi\) | |||||||
\(114\) | 6.34302 | 0.594078 | ||||||||
\(115\) | 3.10739 | 0.289766 | ||||||||
\(116\) | −24.0278 | −2.23093 | ||||||||
\(117\) | 2.91816 | 0.269784 | ||||||||
\(118\) | 2.52458 | 0.232407 | ||||||||
\(119\) | −0.0107831 | −0.000988484 0 | ||||||||
\(120\) | −4.00680 | −0.365769 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −21.8806 | −1.98097 | ||||||||
\(123\) | −16.8954 | −1.52341 | ||||||||
\(124\) | 32.6426 | 2.93139 | ||||||||
\(125\) | −6.99679 | −0.625812 | ||||||||
\(126\) | −0.0608323 | −0.00541937 | ||||||||
\(127\) | −8.47494 | −0.752029 | −0.376015 | − | 0.926614i | \(-0.622706\pi\) | ||||
−0.376015 | + | 0.926614i | \(0.622706\pi\) | |||||||
\(128\) | 20.6912 | 1.82886 | ||||||||
\(129\) | 12.3399 | 1.08647 | ||||||||
\(130\) | 4.74140 | 0.415849 | ||||||||
\(131\) | −10.4785 | −0.915511 | −0.457756 | − | 0.889078i | \(-0.651347\pi\) | ||||
−0.457756 | + | 0.889078i | \(0.651347\pi\) | |||||||
\(132\) | 5.04767 | 0.439343 | ||||||||
\(133\) | 0.0456002 | 0.00395404 | ||||||||
\(134\) | 30.4256 | 2.62838 | ||||||||
\(135\) | −4.18473 | −0.360164 | ||||||||
\(136\) | −1.78203 | −0.152807 | ||||||||
\(137\) | −11.8644 | −1.01365 | −0.506824 | − | 0.862050i | \(-0.669181\pi\) | ||||
−0.506824 | + | 0.862050i | \(0.669181\pi\) | |||||||
\(138\) | −13.8113 | −1.17569 | ||||||||
\(139\) | −4.94092 | −0.419083 | −0.209542 | − | 0.977800i | \(-0.567197\pi\) | ||||
−0.209542 | + | 0.977800i | \(0.567197\pi\) | |||||||
\(140\) | −0.0638225 | −0.00539399 | ||||||||
\(141\) | −8.83748 | −0.744250 | ||||||||
\(142\) | −30.6591 | −2.57285 | ||||||||
\(143\) | −2.69585 | −0.225438 | ||||||||
\(144\) | −2.16167 | −0.180139 | ||||||||
\(145\) | −4.87942 | −0.405214 | ||||||||
\(146\) | 27.2063 | 2.25161 | ||||||||
\(147\) | −9.69248 | −0.799423 | ||||||||
\(148\) | 38.3108 | 3.14913 | ||||||||
\(149\) | 3.35133 | 0.274552 | 0.137276 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137276 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(150\) | 14.6477 | 1.19598 | ||||||||
\(151\) | −8.26299 | −0.672433 | −0.336216 | − | 0.941785i | \(-0.609147\pi\) | ||||
−0.336216 | + | 0.941785i | \(0.609147\pi\) | |||||||
\(152\) | 7.53596 | 0.611247 | ||||||||
\(153\) | −0.493486 | −0.0398960 | ||||||||
\(154\) | 0.0561980 | 0.00452856 | ||||||||
\(155\) | 6.62885 | 0.532442 | ||||||||
\(156\) | −13.6077 | −1.08949 | ||||||||
\(157\) | −9.98978 | −0.797271 | −0.398636 | − | 0.917109i | \(-0.630516\pi\) | ||||
−0.398636 | + | 0.917109i | \(0.630516\pi\) | |||||||
\(158\) | 18.0192 | 1.43353 | ||||||||
\(159\) | 17.7093 | 1.40444 | ||||||||
\(160\) | 2.27477 | 0.179836 | ||||||||
\(161\) | −0.0992898 | −0.00782513 | ||||||||
\(162\) | 10.8840 | 0.855126 | ||||||||
\(163\) | −24.1202 | −1.88924 | −0.944621 | − | 0.328162i | \(-0.893571\pi\) | ||||
−0.944621 | + | 0.328162i | \(0.893571\pi\) | |||||||
\(164\) | −44.4750 | −3.47292 | ||||||||
\(165\) | 1.02505 | 0.0798000 | ||||||||
\(166\) | −34.1873 | −2.65345 | ||||||||
\(167\) | 11.8559 | 0.917441 | 0.458720 | − | 0.888581i | \(-0.348308\pi\) | ||||
0.458720 | + | 0.888581i | \(0.348308\pi\) | |||||||
\(168\) | 0.128028 | 0.00987761 | ||||||||
\(169\) | −5.73241 | −0.440955 | ||||||||
\(170\) | −0.801813 | −0.0614963 | ||||||||
\(171\) | 2.08689 | 0.159588 | ||||||||
\(172\) | 32.4832 | 2.47682 | ||||||||
\(173\) | −23.8978 | −1.81692 | −0.908459 | − | 0.417973i | \(-0.862741\pi\) | ||||
−0.908459 | + | 0.417973i | \(0.862741\pi\) | |||||||
\(174\) | 21.6873 | 1.64411 | ||||||||
\(175\) | 0.105303 | 0.00796017 | ||||||||
\(176\) | 1.99699 | 0.150529 | ||||||||
\(177\) | −1.47137 | −0.110595 | ||||||||
\(178\) | 23.5291 | 1.76358 | ||||||||
\(179\) | −18.5890 | −1.38941 | −0.694704 | − | 0.719296i | \(-0.744465\pi\) | ||||
−0.694704 | + | 0.719296i | \(0.744465\pi\) | |||||||
\(180\) | −2.92083 | −0.217706 | ||||||||
\(181\) | −6.13112 | −0.455722 | −0.227861 | − | 0.973694i | \(-0.573173\pi\) | ||||
−0.227861 | + | 0.973694i | \(0.573173\pi\) | |||||||
\(182\) | −0.151501 | −0.0112300 | ||||||||
\(183\) | 12.7524 | 0.942684 | ||||||||
\(184\) | −16.4088 | −1.20967 | ||||||||
\(185\) | 7.77992 | 0.571991 | ||||||||
\(186\) | −29.4630 | −2.16033 | ||||||||
\(187\) | 0.455891 | 0.0333381 | ||||||||
\(188\) | −23.2635 | −1.69667 | ||||||||
\(189\) | 0.133714 | 0.00972624 | ||||||||
\(190\) | 3.39076 | 0.245992 | ||||||||
\(191\) | 12.4253 | 0.899061 | 0.449531 | − | 0.893265i | \(-0.351591\pi\) | ||||
0.449531 | + | 0.893265i | \(0.351591\pi\) | |||||||
\(192\) | −15.6412 | −1.12881 | ||||||||
\(193\) | −26.0289 | −1.87360 | −0.936802 | − | 0.349859i | \(-0.886229\pi\) | ||||
−0.936802 | + | 0.349859i | \(0.886229\pi\) | |||||||
\(194\) | −26.0432 | −1.86979 | ||||||||
\(195\) | −2.76337 | −0.197889 | ||||||||
\(196\) | −25.5142 | −1.82245 | ||||||||
\(197\) | −18.5248 | −1.31983 | −0.659917 | − | 0.751338i | \(-0.729409\pi\) | ||||
−0.659917 | + | 0.751338i | \(0.729409\pi\) | |||||||
\(198\) | 2.57189 | 0.182776 | ||||||||
\(199\) | 11.7367 | 0.831995 | 0.415997 | − | 0.909366i | \(-0.363433\pi\) | ||||
0.415997 | + | 0.909366i | \(0.363433\pi\) | |||||||
\(200\) | 17.4025 | 1.23054 | ||||||||
\(201\) | −17.7326 | −1.25076 | ||||||||
\(202\) | 0.00798722 | 0.000561979 0 | ||||||||
\(203\) | 0.155911 | 0.0109428 | ||||||||
\(204\) | 2.30119 | 0.161115 | ||||||||
\(205\) | −9.03171 | −0.630802 | ||||||||
\(206\) | −10.2972 | −0.717443 | ||||||||
\(207\) | −4.54398 | −0.315828 | ||||||||
\(208\) | −5.38357 | −0.373284 | ||||||||
\(209\) | −1.92790 | −0.133356 | ||||||||
\(210\) | 0.0576057 | 0.00397517 | ||||||||
\(211\) | −17.1680 | −1.18190 | −0.590949 | − | 0.806709i | \(-0.701246\pi\) | ||||
−0.590949 | + | 0.806709i | \(0.701246\pi\) | |||||||
\(212\) | 46.6174 | 3.20169 | ||||||||
\(213\) | 17.8687 | 1.22434 | ||||||||
\(214\) | −8.94065 | −0.611171 | ||||||||
\(215\) | 6.59648 | 0.449876 | ||||||||
\(216\) | 22.0977 | 1.50356 | ||||||||
\(217\) | −0.211810 | −0.0143786 | ||||||||
\(218\) | 28.2620 | 1.91414 | ||||||||
\(219\) | −15.8563 | −1.07147 | ||||||||
\(220\) | 2.69831 | 0.181920 | ||||||||
\(221\) | −1.22901 | −0.0826723 | ||||||||
\(222\) | −34.5790 | −2.32079 | ||||||||
\(223\) | 6.32896 | 0.423819 | 0.211909 | − | 0.977289i | \(-0.432032\pi\) | ||||
0.211909 | + | 0.977289i | \(0.432032\pi\) | |||||||
\(224\) | −0.0726851 | −0.00485648 | ||||||||
\(225\) | 4.81918 | 0.321279 | ||||||||
\(226\) | 17.0456 | 1.13385 | ||||||||
\(227\) | 3.14572 | 0.208789 | 0.104394 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104394 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(228\) | −9.73142 | −0.644479 | ||||||||
\(229\) | 8.98263 | 0.593589 | 0.296794 | − | 0.954941i | \(-0.404082\pi\) | ||||
0.296794 | + | 0.954941i | \(0.404082\pi\) | |||||||
\(230\) | −7.38303 | −0.486823 | ||||||||
\(231\) | −0.0327532 | −0.00215500 | ||||||||
\(232\) | 25.7661 | 1.69163 | ||||||||
\(233\) | −25.6478 | −1.68025 | −0.840123 | − | 0.542396i | \(-0.817517\pi\) | ||||
−0.840123 | + | 0.542396i | \(0.817517\pi\) | |||||||
\(234\) | −6.93342 | −0.453252 | ||||||||
\(235\) | −4.72421 | −0.308174 | ||||||||
\(236\) | −3.87320 | −0.252124 | ||||||||
\(237\) | −10.5019 | −0.682171 | ||||||||
\(238\) | 0.0256202 | 0.00166071 | ||||||||
\(239\) | 23.4249 | 1.51523 | 0.757616 | − | 0.652700i | \(-0.226364\pi\) | ||||
0.757616 | + | 0.652700i | \(0.226364\pi\) | |||||||
\(240\) | 2.04701 | 0.132134 | ||||||||
\(241\) | 6.89908 | 0.444409 | 0.222205 | − | 0.975000i | \(-0.428675\pi\) | ||||
0.222205 | + | 0.975000i | \(0.428675\pi\) | |||||||
\(242\) | −2.37596 | −0.152732 | ||||||||
\(243\) | 10.6162 | 0.681030 | ||||||||
\(244\) | 33.5691 | 2.14904 | ||||||||
\(245\) | −5.18127 | −0.331019 | ||||||||
\(246\) | 40.1428 | 2.55941 | ||||||||
\(247\) | 5.19733 | 0.330698 | ||||||||
\(248\) | −35.0041 | −2.22276 | ||||||||
\(249\) | 19.9250 | 1.26269 | ||||||||
\(250\) | 16.6241 | 1.05140 | ||||||||
\(251\) | 14.0297 | 0.885544 | 0.442772 | − | 0.896634i | \(-0.353995\pi\) | ||||
0.442772 | + | 0.896634i | \(0.353995\pi\) | |||||||
\(252\) | 0.0933286 | 0.00587915 | ||||||||
\(253\) | 4.19781 | 0.263914 | ||||||||
\(254\) | 20.1361 | 1.26345 | ||||||||
\(255\) | 0.467311 | 0.0292641 | ||||||||
\(256\) | −26.5708 | −1.66068 | ||||||||
\(257\) | −3.27357 | −0.204200 | −0.102100 | − | 0.994774i | \(-0.532556\pi\) | ||||
−0.102100 | + | 0.994774i | \(0.532556\pi\) | |||||||
\(258\) | −29.3191 | −1.82533 | ||||||||
\(259\) | −0.248590 | −0.0154466 | ||||||||
\(260\) | −7.27423 | −0.451129 | ||||||||
\(261\) | 7.13525 | 0.441661 | ||||||||
\(262\) | 24.8965 | 1.53811 | ||||||||
\(263\) | 6.93509 | 0.427636 | 0.213818 | − | 0.976874i | \(-0.431410\pi\) | ||||
0.213818 | + | 0.976874i | \(0.431410\pi\) | |||||||
\(264\) | −5.41283 | −0.333137 | ||||||||
\(265\) | 9.46676 | 0.581539 | ||||||||
\(266\) | −0.108344 | −0.00664302 | ||||||||
\(267\) | −13.7131 | −0.839231 | ||||||||
\(268\) | −46.6788 | −2.85136 | ||||||||
\(269\) | −0.549062 | −0.0334769 | −0.0167384 | − | 0.999860i | \(-0.505328\pi\) | ||||
−0.0167384 | + | 0.999860i | \(0.505328\pi\) | |||||||
\(270\) | 9.94274 | 0.605096 | ||||||||
\(271\) | −15.7272 | −0.955362 | −0.477681 | − | 0.878533i | \(-0.658523\pi\) | ||||
−0.477681 | + | 0.878533i | \(0.658523\pi\) | |||||||
\(272\) | 0.910409 | 0.0552017 | ||||||||
\(273\) | 0.0882975 | 0.00534401 | ||||||||
\(274\) | 28.1894 | 1.70299 | ||||||||
\(275\) | −4.45204 | −0.268468 | ||||||||
\(276\) | 21.1892 | 1.27544 | ||||||||
\(277\) | −8.10336 | −0.486884 | −0.243442 | − | 0.969915i | \(-0.578277\pi\) | ||||
−0.243442 | + | 0.969915i | \(0.578277\pi\) | |||||||
\(278\) | 11.7394 | 0.704084 | ||||||||
\(279\) | −9.69347 | −0.580333 | ||||||||
\(280\) | 0.0684396 | 0.00409005 | ||||||||
\(281\) | −25.9155 | −1.54599 | −0.772994 | − | 0.634413i | \(-0.781242\pi\) | ||||
−0.772994 | + | 0.634413i | \(0.781242\pi\) | |||||||
\(282\) | 20.9975 | 1.25038 | ||||||||
\(283\) | −16.0686 | −0.955182 | −0.477591 | − | 0.878582i | \(-0.658490\pi\) | ||||
−0.477591 | + | 0.878582i | \(0.658490\pi\) | |||||||
\(284\) | 47.0370 | 2.79113 | ||||||||
\(285\) | −1.97620 | −0.117060 | ||||||||
\(286\) | 6.40522 | 0.378749 | ||||||||
\(287\) | 0.288588 | 0.0170348 | ||||||||
\(288\) | −3.32642 | −0.196011 | ||||||||
\(289\) | −16.7922 | −0.987774 | ||||||||
\(290\) | 11.5933 | 0.680783 | ||||||||
\(291\) | 15.1784 | 0.889775 | ||||||||
\(292\) | −41.7397 | −2.44263 | ||||||||
\(293\) | 28.0396 | 1.63809 | 0.819047 | − | 0.573727i | \(-0.194503\pi\) | ||||
0.819047 | + | 0.573727i | \(0.194503\pi\) | |||||||
\(294\) | 23.0289 | 1.34308 | ||||||||
\(295\) | −0.786545 | −0.0457944 | ||||||||
\(296\) | −41.0823 | −2.38786 | ||||||||
\(297\) | −5.65320 | −0.328032 | ||||||||
\(298\) | −7.96262 | −0.461262 | ||||||||
\(299\) | −11.3167 | −0.654459 | ||||||||
\(300\) | −22.4724 | −1.29745 | ||||||||
\(301\) | −0.210776 | −0.0121489 | ||||||||
\(302\) | 19.6325 | 1.12973 | ||||||||
\(303\) | −0.00465509 | −0.000267428 0 | ||||||||
\(304\) | −3.85000 | −0.220813 | ||||||||
\(305\) | 6.81699 | 0.390340 | ||||||||
\(306\) | 1.17250 | 0.0670275 | ||||||||
\(307\) | 15.6188 | 0.891413 | 0.445706 | − | 0.895179i | \(-0.352953\pi\) | ||||
0.445706 | + | 0.895179i | \(0.352953\pi\) | |||||||
\(308\) | −0.0862186 | −0.00491276 | ||||||||
\(309\) | 6.00141 | 0.341409 | ||||||||
\(310\) | −15.7499 | −0.894533 | ||||||||
\(311\) | 26.6381 | 1.51051 | 0.755254 | − | 0.655433i | \(-0.227514\pi\) | ||||
0.755254 | + | 0.655433i | \(0.227514\pi\) | |||||||
\(312\) | 14.5922 | 0.826119 | ||||||||
\(313\) | −1.27151 | −0.0718698 | −0.0359349 | − | 0.999354i | \(-0.511441\pi\) | ||||
−0.0359349 | + | 0.999354i | \(0.511441\pi\) | |||||||
\(314\) | 23.7353 | 1.33946 | ||||||||
\(315\) | 0.0189526 | 0.00106786 | ||||||||
\(316\) | −27.6449 | −1.55515 | ||||||||
\(317\) | −31.7844 | −1.78519 | −0.892594 | − | 0.450861i | \(-0.851117\pi\) | ||||
−0.892594 | + | 0.450861i | \(0.851117\pi\) | |||||||
\(318\) | −42.0765 | −2.35953 | ||||||||
\(319\) | −6.59167 | −0.369063 | ||||||||
\(320\) | −8.36125 | −0.467408 | ||||||||
\(321\) | 5.21077 | 0.290837 | ||||||||
\(322\) | 0.235909 | 0.0131467 | ||||||||
\(323\) | −0.878915 | −0.0489041 | ||||||||
\(324\) | −16.6981 | −0.927674 | ||||||||
\(325\) | 12.0020 | 0.665753 | ||||||||
\(326\) | 57.3087 | 3.17404 | ||||||||
\(327\) | −16.4716 | −0.910881 | ||||||||
\(328\) | 47.6925 | 2.63338 | ||||||||
\(329\) | 0.150952 | 0.00832224 | ||||||||
\(330\) | −2.43547 | −0.134068 | ||||||||
\(331\) | 3.46925 | 0.190687 | 0.0953437 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953437 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(332\) | 52.4500 | 2.87857 | ||||||||
\(333\) | −11.3767 | −0.623439 | ||||||||
\(334\) | −28.1692 | −1.54135 | ||||||||
\(335\) | −9.47925 | −0.517906 | ||||||||
\(336\) | −0.0654077 | −0.00356828 | ||||||||
\(337\) | −21.8333 | −1.18933 | −0.594667 | − | 0.803972i | \(-0.702716\pi\) | ||||
−0.594667 | + | 0.803972i | \(0.702716\pi\) | |||||||
\(338\) | 13.6200 | 0.740829 | ||||||||
\(339\) | −9.93445 | −0.539566 | ||||||||
\(340\) | 1.23014 | 0.0667135 | ||||||||
\(341\) | 8.95500 | 0.484940 | ||||||||
\(342\) | −4.95836 | −0.268117 | ||||||||
\(343\) | 0.331125 | 0.0178791 | ||||||||
\(344\) | −34.8331 | −1.87808 | ||||||||
\(345\) | 4.30296 | 0.231664 | ||||||||
\(346\) | 56.7803 | 3.05253 | ||||||||
\(347\) | 0.110564 | 0.00593538 | 0.00296769 | − | 0.999996i | \(-0.499055\pi\) | ||||
0.00296769 | + | 0.999996i | \(0.499055\pi\) | |||||||
\(348\) | −33.2726 | −1.78360 | ||||||||
\(349\) | −20.4887 | −1.09673 | −0.548367 | − | 0.836238i | \(-0.684750\pi\) | ||||
−0.548367 | + | 0.836238i | \(0.684750\pi\) | |||||||
\(350\) | −0.250196 | −0.0133735 | ||||||||
\(351\) | 15.2402 | 0.813459 | ||||||||
\(352\) | 3.07301 | 0.163792 | ||||||||
\(353\) | −0.114179 | −0.00607714 | −0.00303857 | − | 0.999995i | \(-0.500967\pi\) | ||||
−0.00303857 | + | 0.999995i | \(0.500967\pi\) | |||||||
\(354\) | 3.49592 | 0.185806 | ||||||||
\(355\) | 9.55198 | 0.506966 | ||||||||
\(356\) | −36.0981 | −1.91320 | ||||||||
\(357\) | −0.0149319 | −0.000790279 0 | ||||||||
\(358\) | 44.1667 | 2.33428 | ||||||||
\(359\) | 6.29292 | 0.332128 | 0.166064 | − | 0.986115i | \(-0.446894\pi\) | ||||
0.166064 | + | 0.986115i | \(0.446894\pi\) | |||||||
\(360\) | 3.13213 | 0.165078 | ||||||||
\(361\) | −15.2832 | −0.804378 | ||||||||
\(362\) | 14.5673 | 0.765639 | ||||||||
\(363\) | 1.38475 | 0.0726806 | ||||||||
\(364\) | 0.232432 | 0.0121828 | ||||||||
\(365\) | −8.47623 | −0.443666 | ||||||||
\(366\) | −30.2992 | −1.58376 | ||||||||
\(367\) | −18.3331 | −0.956981 | −0.478490 | − | 0.878093i | \(-0.658816\pi\) | ||||
−0.478490 | + | 0.878093i | \(0.658816\pi\) | |||||||
\(368\) | 8.38298 | 0.436993 | ||||||||
\(369\) | 13.2072 | 0.687539 | ||||||||
\(370\) | −18.4848 | −0.960978 | ||||||||
\(371\) | −0.302490 | −0.0157045 | ||||||||
\(372\) | 45.2019 | 2.34361 | ||||||||
\(373\) | −13.8887 | −0.719128 | −0.359564 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359564 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(374\) | −1.08318 | −0.0560098 | ||||||||
\(375\) | −9.68881 | −0.500328 | ||||||||
\(376\) | 24.9465 | 1.28652 | ||||||||
\(377\) | 17.7701 | 0.915209 | ||||||||
\(378\) | −0.317698 | −0.0163406 | ||||||||
\(379\) | −2.16780 | −0.111353 | −0.0556763 | − | 0.998449i | \(-0.517731\pi\) | ||||
−0.0556763 | + | 0.998449i | \(0.517731\pi\) | |||||||
\(380\) | −5.20209 | −0.266861 | ||||||||
\(381\) | −11.7357 | −0.601237 | ||||||||
\(382\) | −29.5219 | −1.51047 | ||||||||
\(383\) | 23.7594 | 1.21405 | 0.607025 | − | 0.794683i | \(-0.292363\pi\) | ||||
0.607025 | + | 0.794683i | \(0.292363\pi\) | |||||||
\(384\) | 28.6522 | 1.46215 | ||||||||
\(385\) | −0.0175087 | −0.000892328 0 | ||||||||
\(386\) | 61.8437 | 3.14776 | ||||||||
\(387\) | −9.64613 | −0.490340 | ||||||||
\(388\) | 39.9553 | 2.02842 | ||||||||
\(389\) | 23.9556 | 1.21460 | 0.607299 | − | 0.794473i | \(-0.292253\pi\) | ||||
0.607299 | + | 0.794473i | \(0.292253\pi\) | |||||||
\(390\) | 6.56567 | 0.332465 | ||||||||
\(391\) | 1.91374 | 0.0967822 | ||||||||
\(392\) | 27.3600 | 1.38189 | ||||||||
\(393\) | −14.5101 | −0.731939 | ||||||||
\(394\) | 44.0141 | 2.21740 | ||||||||
\(395\) | −5.61395 | −0.282468 | ||||||||
\(396\) | −3.94578 | −0.198283 | ||||||||
\(397\) | −3.14305 | −0.157745 | −0.0788727 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788727 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(398\) | −27.8860 | −1.39780 | ||||||||
\(399\) | 0.0631450 | 0.00316120 | ||||||||
\(400\) | −8.89068 | −0.444534 | ||||||||
\(401\) | 33.8638 | 1.69108 | 0.845540 | − | 0.533913i | \(-0.179279\pi\) | ||||
0.845540 | + | 0.533913i | \(0.179279\pi\) | |||||||
\(402\) | 42.1319 | 2.10135 | ||||||||
\(403\) | −24.1413 | −1.20256 | ||||||||
\(404\) | −0.0122539 | −0.000609657 0 | ||||||||
\(405\) | −3.39095 | −0.168498 | ||||||||
\(406\) | −0.370439 | −0.0183846 | ||||||||
\(407\) | 10.5100 | 0.520961 | ||||||||
\(408\) | −2.46766 | −0.122168 | ||||||||
\(409\) | 21.5966 | 1.06788 | 0.533942 | − | 0.845521i | \(-0.320710\pi\) | ||||
0.533942 | + | 0.845521i | \(0.320710\pi\) | |||||||
\(410\) | 21.4590 | 1.05978 | ||||||||
\(411\) | −16.4293 | −0.810398 | ||||||||
\(412\) | 15.7980 | 0.778310 | ||||||||
\(413\) | 0.0251323 | 0.00123668 | ||||||||
\(414\) | 10.7963 | 0.530610 | ||||||||
\(415\) | 10.6512 | 0.522848 | ||||||||
\(416\) | −8.28436 | −0.406174 | ||||||||
\(417\) | −6.84194 | −0.335051 | ||||||||
\(418\) | 4.58062 | 0.224046 | ||||||||
\(419\) | 16.1028 | 0.786673 | 0.393336 | − | 0.919395i | \(-0.371321\pi\) | ||||
0.393336 | + | 0.919395i | \(0.371321\pi\) | |||||||
\(420\) | −0.0883783 | −0.00431242 | ||||||||
\(421\) | −1.32384 | −0.0645201 | −0.0322600 | − | 0.999480i | \(-0.510270\pi\) | ||||
−0.0322600 | + | 0.999480i | \(0.510270\pi\) | |||||||
\(422\) | 40.7906 | 1.98565 | ||||||||
\(423\) | 6.90828 | 0.335892 | ||||||||
\(424\) | −49.9898 | −2.42772 | ||||||||
\(425\) | −2.02965 | −0.0984524 | ||||||||
\(426\) | −42.4552 | −2.05696 | ||||||||
\(427\) | −0.217822 | −0.0105411 | ||||||||
\(428\) | 13.7167 | 0.663022 | ||||||||
\(429\) | −3.73308 | −0.180235 | ||||||||
\(430\) | −15.6730 | −0.755818 | ||||||||
\(431\) | 40.3712 | 1.94461 | 0.972307 | − | 0.233708i | \(-0.0750861\pi\) | ||||
0.972307 | + | 0.233708i | \(0.0750861\pi\) | |||||||
\(432\) | −11.2894 | −0.543160 | ||||||||
\(433\) | 15.1868 | 0.729831 | 0.364916 | − | 0.931041i | \(-0.381098\pi\) | ||||
0.364916 | + | 0.931041i | \(0.381098\pi\) | |||||||
\(434\) | 0.503253 | 0.0241569 | ||||||||
\(435\) | −6.75679 | −0.323963 | ||||||||
\(436\) | −43.3594 | −2.07654 | ||||||||
\(437\) | −8.09298 | −0.387140 | ||||||||
\(438\) | 37.6739 | 1.80013 | ||||||||
\(439\) | −15.6349 | −0.746215 | −0.373108 | − | 0.927788i | \(-0.621708\pi\) | ||||
−0.373108 | + | 0.927788i | \(0.621708\pi\) | |||||||
\(440\) | −2.89352 | −0.137943 | ||||||||
\(441\) | 7.57664 | 0.360793 | ||||||||
\(442\) | 2.92008 | 0.138894 | ||||||||
\(443\) | 0.200075 | 0.00950587 | 0.00475293 | − | 0.999989i | \(-0.498487\pi\) | ||||
0.00475293 | + | 0.999989i | \(0.498487\pi\) | |||||||
\(444\) | 53.0509 | 2.51769 | ||||||||
\(445\) | −7.33058 | −0.347503 | ||||||||
\(446\) | −15.0374 | −0.712040 | ||||||||
\(447\) | 4.64076 | 0.219500 | ||||||||
\(448\) | 0.267165 | 0.0126224 | ||||||||
\(449\) | 27.4542 | 1.29564 | 0.647822 | − | 0.761792i | \(-0.275680\pi\) | ||||
0.647822 | + | 0.761792i | \(0.275680\pi\) | |||||||
\(450\) | −11.4502 | −0.539766 | ||||||||
\(451\) | −12.2011 | −0.574525 | ||||||||
\(452\) | −26.1512 | −1.23005 | ||||||||
\(453\) | −11.4422 | −0.537601 | ||||||||
\(454\) | −7.47411 | −0.350777 | ||||||||
\(455\) | 0.0472009 | 0.00221281 | ||||||||
\(456\) | 10.4354 | 0.488684 | ||||||||
\(457\) | 33.9830 | 1.58966 | 0.794829 | − | 0.606833i | \(-0.207560\pi\) | ||||
0.794829 | + | 0.606833i | \(0.207560\pi\) | |||||||
\(458\) | −21.3424 | −0.997263 | ||||||||
\(459\) | −2.57724 | −0.120295 | ||||||||
\(460\) | 11.3270 | 0.528124 | ||||||||
\(461\) | −8.86716 | −0.412985 | −0.206492 | − | 0.978448i | \(-0.566205\pi\) | ||||
−0.206492 | + | 0.978448i | \(0.566205\pi\) | |||||||
\(462\) | 0.0778202 | 0.00362052 | ||||||||
\(463\) | 11.9162 | 0.553795 | 0.276897 | − | 0.960899i | \(-0.410694\pi\) | ||||
0.276897 | + | 0.960899i | \(0.410694\pi\) | |||||||
\(464\) | −13.1635 | −0.611100 | ||||||||
\(465\) | 9.17931 | 0.425680 | ||||||||
\(466\) | 60.9382 | 2.82291 | ||||||||
\(467\) | −9.43492 | −0.436596 | −0.218298 | − | 0.975882i | \(-0.570050\pi\) | ||||
−0.218298 | + | 0.975882i | \(0.570050\pi\) | |||||||
\(468\) | 10.6372 | 0.491705 | ||||||||
\(469\) | 0.302888 | 0.0139861 | ||||||||
\(470\) | 11.2245 | 0.517749 | ||||||||
\(471\) | −13.8334 | −0.637407 | ||||||||
\(472\) | 4.15340 | 0.191176 | ||||||||
\(473\) | 8.91127 | 0.409741 | ||||||||
\(474\) | 24.9520 | 1.14609 | ||||||||
\(475\) | 8.58311 | 0.393820 | ||||||||
\(476\) | −0.0393063 | −0.00180160 | ||||||||
\(477\) | −13.8434 | −0.633845 | ||||||||
\(478\) | −55.6567 | −2.54568 | ||||||||
\(479\) | −16.5305 | −0.755300 | −0.377650 | − | 0.925948i | \(-0.623268\pi\) | ||||
−0.377650 | + | 0.925948i | \(0.623268\pi\) | |||||||
\(480\) | 3.14999 | 0.143776 | ||||||||
\(481\) | −28.3333 | −1.29189 | ||||||||
\(482\) | −16.3919 | −0.746632 | ||||||||
\(483\) | −0.137492 | −0.00625609 | ||||||||
\(484\) | 3.64518 | 0.165690 | ||||||||
\(485\) | 8.11387 | 0.368432 | ||||||||
\(486\) | −25.2237 | −1.14417 | ||||||||
\(487\) | 4.75603 | 0.215516 | 0.107758 | − | 0.994177i | \(-0.465633\pi\) | ||||
0.107758 | + | 0.994177i | \(0.465633\pi\) | |||||||
\(488\) | −35.9975 | −1.62953 | ||||||||
\(489\) | −33.4005 | −1.51042 | ||||||||
\(490\) | 12.3105 | 0.556131 | ||||||||
\(491\) | 19.9136 | 0.898687 | 0.449343 | − | 0.893359i | \(-0.351658\pi\) | ||||
0.449343 | + | 0.893359i | \(0.351658\pi\) | |||||||
\(492\) | −61.5869 | −2.77655 | ||||||||
\(493\) | −3.00509 | −0.135342 | ||||||||
\(494\) | −12.3487 | −0.555592 | ||||||||
\(495\) | −0.801284 | −0.0360150 | ||||||||
\(496\) | 17.8830 | 0.802971 | ||||||||
\(497\) | −0.305212 | −0.0136906 | ||||||||
\(498\) | −47.3410 | −2.12140 | ||||||||
\(499\) | −27.8491 | −1.24670 | −0.623349 | − | 0.781944i | \(-0.714228\pi\) | ||||
−0.623349 | + | 0.781944i | \(0.714228\pi\) | |||||||
\(500\) | −25.5046 | −1.14060 | ||||||||
\(501\) | 16.4175 | 0.733481 | ||||||||
\(502\) | −33.3339 | −1.48776 | ||||||||
\(503\) | −16.3229 | −0.727803 | −0.363902 | − | 0.931437i | \(-0.618556\pi\) | ||||
−0.363902 | + | 0.931437i | \(0.618556\pi\) | |||||||
\(504\) | −0.100080 | −0.00445793 | ||||||||
\(505\) | −0.00248845 | −0.000110735 0 | ||||||||
\(506\) | −9.97383 | −0.443391 | ||||||||
\(507\) | −7.93796 | −0.352537 | ||||||||
\(508\) | −30.8927 | −1.37064 | ||||||||
\(509\) | −25.8239 | −1.14462 | −0.572312 | − | 0.820036i | \(-0.693953\pi\) | ||||
−0.572312 | + | 0.820036i | \(0.693953\pi\) | |||||||
\(510\) | −1.11031 | −0.0491654 | ||||||||
\(511\) | 0.270839 | 0.0119812 | ||||||||
\(512\) | 21.7488 | 0.961168 | ||||||||
\(513\) | 10.8988 | 0.481195 | ||||||||
\(514\) | 7.77787 | 0.343067 | ||||||||
\(515\) | 3.20815 | 0.141368 | ||||||||
\(516\) | 44.9811 | 1.98018 | ||||||||
\(517\) | −6.38200 | −0.280680 | ||||||||
\(518\) | 0.590640 | 0.0259512 | ||||||||
\(519\) | −33.0925 | −1.45260 | ||||||||
\(520\) | 7.80047 | 0.342073 | ||||||||
\(521\) | 35.9772 | 1.57619 | 0.788095 | − | 0.615554i | \(-0.211068\pi\) | ||||
0.788095 | + | 0.615554i | \(0.211068\pi\) | |||||||
\(522\) | −16.9531 | −0.742015 | ||||||||
\(523\) | −26.0216 | −1.13785 | −0.568923 | − | 0.822391i | \(-0.692640\pi\) | ||||
−0.568923 | + | 0.822391i | \(0.692640\pi\) | |||||||
\(524\) | −38.1961 | −1.66860 | ||||||||
\(525\) | 0.145819 | 0.00636405 | ||||||||
\(526\) | −16.4775 | −0.718452 | ||||||||
\(527\) | 4.08250 | 0.177837 | ||||||||
\(528\) | 2.76533 | 0.120346 | ||||||||
\(529\) | −5.37838 | −0.233843 | ||||||||
\(530\) | −22.4926 | −0.977018 | ||||||||
\(531\) | 1.15018 | 0.0499134 | ||||||||
\(532\) | 0.166221 | 0.00720660 | ||||||||
\(533\) | 32.8922 | 1.42472 | ||||||||
\(534\) | 32.5819 | 1.40996 | ||||||||
\(535\) | 2.78550 | 0.120428 | ||||||||
\(536\) | 50.0557 | 2.16208 | ||||||||
\(537\) | −25.7411 | −1.11081 | ||||||||
\(538\) | 1.30455 | 0.0562431 | ||||||||
\(539\) | −6.99944 | −0.301487 | ||||||||
\(540\) | −15.2541 | −0.656431 | ||||||||
\(541\) | −10.1232 | −0.435229 | −0.217615 | − | 0.976035i | \(-0.569828\pi\) | ||||
−0.217615 | + | 0.976035i | \(0.569828\pi\) | |||||||
\(542\) | 37.3673 | 1.60506 | ||||||||
\(543\) | −8.49007 | −0.364344 | ||||||||
\(544\) | 1.40096 | 0.0600656 | ||||||||
\(545\) | −8.80515 | −0.377171 | ||||||||
\(546\) | −0.209791 | −0.00897824 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | −43.2481 | −1.84747 | ||||||||
\(549\) | −9.96858 | −0.425449 | ||||||||
\(550\) | 10.5779 | 0.451042 | ||||||||
\(551\) | 12.7081 | 0.541384 | ||||||||
\(552\) | −22.7221 | −0.967115 | ||||||||
\(553\) | 0.179381 | 0.00762807 | ||||||||
\(554\) | 19.2533 | 0.817993 | ||||||||
\(555\) | 10.7733 | 0.457299 | ||||||||
\(556\) | −18.0105 | −0.763817 | ||||||||
\(557\) | 6.08001 | 0.257618 | 0.128809 | − | 0.991669i | \(-0.458885\pi\) | ||||
0.128809 | + | 0.991669i | \(0.458885\pi\) | |||||||
\(558\) | 23.0313 | 0.974992 | ||||||||
\(559\) | −24.0234 | −1.01608 | ||||||||
\(560\) | −0.0349647 | −0.00147753 | ||||||||
\(561\) | 0.631296 | 0.0266533 | ||||||||
\(562\) | 61.5741 | 2.59735 | ||||||||
\(563\) | 11.1344 | 0.469258 | 0.234629 | − | 0.972085i | \(-0.424612\pi\) | ||||
0.234629 | + | 0.972085i | \(0.424612\pi\) | |||||||
\(564\) | −32.2142 | −1.35646 | ||||||||
\(565\) | −5.31062 | −0.223419 | ||||||||
\(566\) | 38.1784 | 1.60476 | ||||||||
\(567\) | 0.108350 | 0.00455029 | ||||||||
\(568\) | −50.4398 | −2.11641 | ||||||||
\(569\) | −36.8049 | −1.54294 | −0.771470 | − | 0.636265i | \(-0.780478\pi\) | ||||
−0.771470 | + | 0.636265i | \(0.780478\pi\) | |||||||
\(570\) | 4.69536 | 0.196667 | ||||||||
\(571\) | 7.13030 | 0.298394 | 0.149197 | − | 0.988808i | \(-0.452331\pi\) | ||||
0.149197 | + | 0.988808i | \(0.452331\pi\) | |||||||
\(572\) | −9.82685 | −0.410881 | ||||||||
\(573\) | 17.2059 | 0.718787 | ||||||||
\(574\) | −0.685674 | −0.0286195 | ||||||||
\(575\) | −18.6888 | −0.779378 | ||||||||
\(576\) | 12.2268 | 0.509449 | ||||||||
\(577\) | −38.6237 | −1.60793 | −0.803964 | − | 0.594678i | \(-0.797279\pi\) | ||||
−0.803964 | + | 0.594678i | \(0.797279\pi\) | |||||||
\(578\) | 39.8975 | 1.65952 | ||||||||
\(579\) | −36.0436 | −1.49792 | ||||||||
\(580\) | −17.7864 | −0.738540 | ||||||||
\(581\) | −0.340336 | −0.0141195 | ||||||||
\(582\) | −36.0633 | −1.49487 | ||||||||
\(583\) | 12.7888 | 0.529657 | ||||||||
\(584\) | 44.7592 | 1.85215 | ||||||||
\(585\) | 2.16014 | 0.0893107 | ||||||||
\(586\) | −66.6210 | −2.75209 | ||||||||
\(587\) | 17.0231 | 0.702617 | 0.351308 | − | 0.936260i | \(-0.385737\pi\) | ||||
0.351308 | + | 0.936260i | \(0.385737\pi\) | |||||||
\(588\) | −35.3309 | −1.45702 | ||||||||
\(589\) | −17.2644 | −0.711366 | ||||||||
\(590\) | 1.86880 | 0.0769372 | ||||||||
\(591\) | −25.6522 | −1.05519 | ||||||||
\(592\) | 20.9883 | 0.862615 | ||||||||
\(593\) | −22.9062 | −0.940644 | −0.470322 | − | 0.882495i | \(-0.655862\pi\) | ||||
−0.470322 | + | 0.882495i | \(0.655862\pi\) | |||||||
\(594\) | 13.4318 | 0.551112 | ||||||||
\(595\) | −0.00798208 | −0.000327233 0 | ||||||||
\(596\) | 12.2162 | 0.500395 | ||||||||
\(597\) | 16.2524 | 0.665168 | ||||||||
\(598\) | 26.8879 | 1.09953 | ||||||||
\(599\) | −19.9739 | −0.816112 | −0.408056 | − | 0.912957i | \(-0.633793\pi\) | ||||
−0.408056 | + | 0.912957i | \(0.633793\pi\) | |||||||
\(600\) | 24.0982 | 0.983804 | ||||||||
\(601\) | 7.26975 | 0.296539 | 0.148270 | − | 0.988947i | \(-0.452630\pi\) | ||||
0.148270 | + | 0.988947i | \(0.452630\pi\) | |||||||
\(602\) | 0.500795 | 0.0204109 | ||||||||
\(603\) | 13.8616 | 0.564489 | ||||||||
\(604\) | −30.1201 | −1.22557 | ||||||||
\(605\) | 0.740241 | 0.0300951 | ||||||||
\(606\) | 0.0110603 | 0.000449295 0 | ||||||||
\(607\) | 40.3674 | 1.63846 | 0.819231 | − | 0.573464i | \(-0.194401\pi\) | ||||
0.819231 | + | 0.573464i | \(0.194401\pi\) | |||||||
\(608\) | −5.92447 | −0.240269 | ||||||||
\(609\) | 0.215898 | 0.00874864 | ||||||||
\(610\) | −16.1969 | −0.655793 | ||||||||
\(611\) | 17.2049 | 0.696035 | ||||||||
\(612\) | −1.79885 | −0.0727140 | ||||||||
\(613\) | −12.6973 | −0.512841 | −0.256420 | − | 0.966565i | \(-0.582543\pi\) | ||||
−0.256420 | + | 0.966565i | \(0.582543\pi\) | |||||||
\(614\) | −37.1097 | −1.49762 | ||||||||
\(615\) | −12.5067 | −0.504318 | ||||||||
\(616\) | 0.0924559 | 0.00372515 | ||||||||
\(617\) | −14.1349 | −0.569051 | −0.284525 | − | 0.958669i | \(-0.591836\pi\) | ||||
−0.284525 | + | 0.958669i | \(0.591836\pi\) | |||||||
\(618\) | −14.2591 | −0.573586 | ||||||||
\(619\) | −10.6455 | −0.427880 | −0.213940 | − | 0.976847i | \(-0.568630\pi\) | ||||
−0.213940 | + | 0.976847i | \(0.568630\pi\) | |||||||
\(620\) | 24.1634 | 0.970425 | ||||||||
\(621\) | −23.7311 | −0.952294 | ||||||||
\(622\) | −63.2910 | −2.53774 | ||||||||
\(623\) | 0.234233 | 0.00938433 | ||||||||
\(624\) | −7.45491 | −0.298435 | ||||||||
\(625\) | 17.0809 | 0.683237 | ||||||||
\(626\) | 3.02105 | 0.120745 | ||||||||
\(627\) | −2.66967 | −0.106616 | ||||||||
\(628\) | −36.4146 | −1.45310 | ||||||||
\(629\) | 4.79141 | 0.191046 | ||||||||
\(630\) | −0.0450305 | −0.00179406 | ||||||||
\(631\) | −4.53215 | −0.180422 | −0.0902111 | − | 0.995923i | \(-0.528754\pi\) | ||||
−0.0902111 | + | 0.995923i | \(0.528754\pi\) | |||||||
\(632\) | 29.6448 | 1.17921 | ||||||||
\(633\) | −23.7735 | −0.944911 | ||||||||
\(634\) | 75.5184 | 2.99922 | ||||||||
\(635\) | −6.27349 | −0.248956 | ||||||||
\(636\) | 64.5535 | 2.55971 | ||||||||
\(637\) | 18.8694 | 0.747634 | ||||||||
\(638\) | 15.6615 | 0.620046 | ||||||||
\(639\) | −13.9680 | −0.552565 | ||||||||
\(640\) | 15.3165 | 0.605437 | ||||||||
\(641\) | 23.3323 | 0.921569 | 0.460785 | − | 0.887512i | \(-0.347568\pi\) | ||||
0.460785 | + | 0.887512i | \(0.347568\pi\) | |||||||
\(642\) | −12.3806 | −0.488623 | ||||||||
\(643\) | −26.1118 | −1.02975 | −0.514875 | − | 0.857265i | \(-0.672162\pi\) | ||||
−0.514875 | + | 0.857265i | \(0.672162\pi\) | |||||||
\(644\) | −0.361929 | −0.0142620 | ||||||||
\(645\) | 9.13449 | 0.359670 | ||||||||
\(646\) | 2.08827 | 0.0821617 | ||||||||
\(647\) | 8.91290 | 0.350402 | 0.175201 | − | 0.984533i | \(-0.443942\pi\) | ||||
0.175201 | + | 0.984533i | \(0.443942\pi\) | |||||||
\(648\) | 17.9061 | 0.703419 | ||||||||
\(649\) | −1.06255 | −0.0417088 | ||||||||
\(650\) | −28.5163 | −1.11850 | ||||||||
\(651\) | −0.293305 | −0.0114955 | ||||||||
\(652\) | −87.9226 | −3.44332 | ||||||||
\(653\) | 9.94054 | 0.389003 | 0.194502 | − | 0.980902i | \(-0.437691\pi\) | ||||
0.194502 | + | 0.980902i | \(0.437691\pi\) | |||||||
\(654\) | 39.1358 | 1.53033 | ||||||||
\(655\) | −7.75662 | −0.303076 | ||||||||
\(656\) | −24.3653 | −0.951307 | ||||||||
\(657\) | 12.3949 | 0.483571 | ||||||||
\(658\) | −0.358655 | −0.0139818 | ||||||||
\(659\) | −42.6225 | −1.66034 | −0.830168 | − | 0.557513i | \(-0.811756\pi\) | ||||
−0.830168 | + | 0.557513i | \(0.811756\pi\) | |||||||
\(660\) | 3.73649 | 0.145443 | ||||||||
\(661\) | −18.6726 | −0.726280 | −0.363140 | − | 0.931734i | \(-0.618295\pi\) | ||||
−0.363140 | + | 0.931734i | \(0.618295\pi\) | |||||||
\(662\) | −8.24280 | −0.320366 | ||||||||
\(663\) | −1.70188 | −0.0660954 | ||||||||
\(664\) | −56.2444 | −2.18271 | ||||||||
\(665\) | 0.0337552 | 0.00130897 | ||||||||
\(666\) | 27.0305 | 1.04741 | ||||||||
\(667\) | −27.6706 | −1.07141 | ||||||||
\(668\) | 43.2171 | 1.67212 | ||||||||
\(669\) | 8.76404 | 0.338837 | ||||||||
\(670\) | 22.5223 | 0.870112 | ||||||||
\(671\) | 9.20916 | 0.355516 | ||||||||
\(672\) | −0.100651 | −0.00388269 | ||||||||
\(673\) | −9.88167 | −0.380910 | −0.190455 | − | 0.981696i | \(-0.560996\pi\) | ||||
−0.190455 | + | 0.981696i | \(0.560996\pi\) | |||||||
\(674\) | 51.8749 | 1.99815 | ||||||||
\(675\) | 25.1683 | 0.968728 | ||||||||
\(676\) | −20.8957 | −0.803680 | ||||||||
\(677\) | −18.6069 | −0.715121 | −0.357561 | − | 0.933890i | \(-0.616391\pi\) | ||||
−0.357561 | + | 0.933890i | \(0.616391\pi\) | |||||||
\(678\) | 23.6039 | 0.906501 | ||||||||
\(679\) | −0.259261 | −0.00994952 | ||||||||
\(680\) | −1.31913 | −0.0505863 | ||||||||
\(681\) | 4.35604 | 0.166924 | ||||||||
\(682\) | −21.2767 | −0.814727 | ||||||||
\(683\) | −29.0955 | −1.11331 | −0.556654 | − | 0.830744i | \(-0.687915\pi\) | ||||
−0.556654 | + | 0.830744i | \(0.687915\pi\) | |||||||
\(684\) | 7.60708 | 0.290864 | ||||||||
\(685\) | −8.78255 | −0.335564 | ||||||||
\(686\) | −0.786740 | −0.0300379 | ||||||||
\(687\) | 12.4387 | 0.474566 | ||||||||
\(688\) | 17.7957 | 0.678455 | ||||||||
\(689\) | −34.4765 | −1.31345 | ||||||||
\(690\) | −10.2237 | −0.389208 | ||||||||
\(691\) | 5.72111 | 0.217641 | 0.108821 | − | 0.994061i | \(-0.465293\pi\) | ||||
0.108821 | + | 0.994061i | \(0.465293\pi\) | |||||||
\(692\) | −87.1119 | −3.31150 | ||||||||
\(693\) | 0.0256033 | 0.000972588 0 | ||||||||
\(694\) | −0.262695 | −0.00997177 | ||||||||
\(695\) | −3.65747 | −0.138736 | ||||||||
\(696\) | 35.6796 | 1.35243 | ||||||||
\(697\) | −5.56235 | −0.210689 | ||||||||
\(698\) | 48.6803 | 1.84258 | ||||||||
\(699\) | −35.5159 | −1.34333 | ||||||||
\(700\) | 0.383849 | 0.0145081 | ||||||||
\(701\) | −32.6620 | −1.23363 | −0.616814 | − | 0.787109i | \(-0.711577\pi\) | ||||
−0.616814 | + | 0.787109i | \(0.711577\pi\) | |||||||
\(702\) | −36.2100 | −1.36666 | ||||||||
\(703\) | −20.2623 | −0.764205 | ||||||||
\(704\) | −11.2953 | −0.425708 | ||||||||
\(705\) | −6.54186 | −0.246381 | ||||||||
\(706\) | 0.271285 | 0.0102099 | ||||||||
\(707\) | 7.95131e−5 0 | 2.99040e−6 0 | ||||||||
\(708\) | −5.36342 | −0.201569 | ||||||||
\(709\) | 12.0320 | 0.451873 | 0.225936 | − | 0.974142i | \(-0.427456\pi\) | ||||
0.225936 | + | 0.974142i | \(0.427456\pi\) | |||||||
\(710\) | −22.6951 | −0.851733 | ||||||||
\(711\) | 8.20935 | 0.307875 | ||||||||
\(712\) | 38.7096 | 1.45070 | ||||||||
\(713\) | 37.5914 | 1.40781 | ||||||||
\(714\) | 0.0354776 | 0.00132771 | ||||||||
\(715\) | −1.99558 | −0.0746303 | ||||||||
\(716\) | −67.7603 | −2.53232 | ||||||||
\(717\) | 32.4377 | 1.21141 | ||||||||
\(718\) | −14.9517 | −0.557993 | ||||||||
\(719\) | 21.3720 | 0.797040 | 0.398520 | − | 0.917160i | \(-0.369524\pi\) | ||||
0.398520 | + | 0.917160i | \(0.369524\pi\) | |||||||
\(720\) | −1.60015 | −0.0596342 | ||||||||
\(721\) | −0.102509 | −0.00381765 | ||||||||
\(722\) | 36.3122 | 1.35140 | ||||||||
\(723\) | 9.55351 | 0.355299 | ||||||||
\(724\) | −22.3490 | −0.830595 | ||||||||
\(725\) | 29.3464 | 1.08990 | ||||||||
\(726\) | −3.29011 | −0.122108 | ||||||||
\(727\) | −9.21347 | −0.341709 | −0.170854 | − | 0.985296i | \(-0.554653\pi\) | ||||
−0.170854 | + | 0.985296i | \(0.554653\pi\) | |||||||
\(728\) | −0.249247 | −0.00923771 | ||||||||
\(729\) | 28.4435 | 1.05346 | ||||||||
\(730\) | 20.1392 | 0.745384 | ||||||||
\(731\) | 4.06257 | 0.150260 | ||||||||
\(732\) | 46.4848 | 1.71813 | ||||||||
\(733\) | −46.2437 | −1.70805 | −0.854026 | − | 0.520231i | \(-0.825846\pi\) | ||||
−0.854026 | + | 0.520231i | \(0.825846\pi\) | |||||||
\(734\) | 43.5587 | 1.60778 | ||||||||
\(735\) | −7.17477 | −0.264645 | ||||||||
\(736\) | 12.8999 | 0.475497 | ||||||||
\(737\) | −12.8056 | −0.471701 | ||||||||
\(738\) | −31.3798 | −1.15511 | ||||||||
\(739\) | 10.5290 | 0.387315 | 0.193657 | − | 0.981069i | \(-0.437965\pi\) | ||||
0.193657 | + | 0.981069i | \(0.437965\pi\) | |||||||
\(740\) | 28.3592 | 1.04251 | ||||||||
\(741\) | 7.19701 | 0.264389 | ||||||||
\(742\) | 0.718703 | 0.0263844 | ||||||||
\(743\) | −32.6415 | −1.19750 | −0.598750 | − | 0.800936i | \(-0.704336\pi\) | ||||
−0.598750 | + | 0.800936i | \(0.704336\pi\) | |||||||
\(744\) | −48.4719 | −1.77707 | ||||||||
\(745\) | 2.48079 | 0.0908891 | ||||||||
\(746\) | 32.9989 | 1.20818 | ||||||||
\(747\) | −15.5754 | −0.569875 | ||||||||
\(748\) | 1.66181 | 0.0607617 | ||||||||
\(749\) | −0.0890045 | −0.00325215 | ||||||||
\(750\) | 23.0202 | 0.840579 | ||||||||
\(751\) | 7.21461 | 0.263265 | 0.131632 | − | 0.991299i | \(-0.457978\pi\) | ||||
0.131632 | + | 0.991299i | \(0.457978\pi\) | |||||||
\(752\) | −12.7448 | −0.464754 | ||||||||
\(753\) | 19.4276 | 0.707981 | ||||||||
\(754\) | −42.2211 | −1.53760 | ||||||||
\(755\) | −6.11660 | −0.222606 | ||||||||
\(756\) | 0.487411 | 0.0177270 | ||||||||
\(757\) | 4.72327 | 0.171670 | 0.0858351 | − | 0.996309i | \(-0.472644\pi\) | ||||
0.0858351 | + | 0.996309i | \(0.472644\pi\) | |||||||
\(758\) | 5.15061 | 0.187079 | ||||||||
\(759\) | 5.81292 | 0.210996 | ||||||||
\(760\) | 5.57842 | 0.202351 | ||||||||
\(761\) | −18.0472 | −0.654211 | −0.327106 | − | 0.944988i | \(-0.606073\pi\) | ||||
−0.327106 | + | 0.944988i | \(0.606073\pi\) | |||||||
\(762\) | 27.8835 | 1.01011 | ||||||||
\(763\) | 0.281349 | 0.0101855 | ||||||||
\(764\) | 45.2924 | 1.63862 | ||||||||
\(765\) | −0.365298 | −0.0132074 | ||||||||
\(766\) | −56.4514 | −2.03967 | ||||||||
\(767\) | 2.86448 | 0.103430 | ||||||||
\(768\) | −36.7940 | −1.32769 | ||||||||
\(769\) | −22.5757 | −0.814099 | −0.407050 | − | 0.913406i | \(-0.633442\pi\) | ||||
−0.407050 | + | 0.913406i | \(0.633442\pi\) | |||||||
\(770\) | 0.0416000 | 0.00149916 | ||||||||
\(771\) | −4.53308 | −0.163255 | ||||||||
\(772\) | −94.8802 | −3.41481 | ||||||||
\(773\) | −42.3119 | −1.52185 | −0.760927 | − | 0.648837i | \(-0.775256\pi\) | ||||
−0.760927 | + | 0.648837i | \(0.775256\pi\) | |||||||
\(774\) | 22.9188 | 0.823800 | ||||||||
\(775\) | −39.8680 | −1.43210 | ||||||||
\(776\) | −42.8458 | −1.53807 | ||||||||
\(777\) | −0.344236 | −0.0123494 | ||||||||
\(778\) | −56.9176 | −2.04060 | ||||||||
\(779\) | 23.5225 | 0.842779 | ||||||||
\(780\) | −10.0730 | −0.360671 | ||||||||
\(781\) | 12.9039 | 0.461737 | ||||||||
\(782\) | −4.54698 | −0.162600 | ||||||||
\(783\) | 37.2640 | 1.33171 | ||||||||
\(784\) | −13.9778 | −0.499207 | ||||||||
\(785\) | −7.39484 | −0.263933 | ||||||||
\(786\) | 34.4755 | 1.22970 | ||||||||
\(787\) | −28.3379 | −1.01014 | −0.505068 | − | 0.863080i | \(-0.668533\pi\) | ||||
−0.505068 | + | 0.863080i | \(0.668533\pi\) | |||||||
\(788\) | −67.5261 | −2.40552 | ||||||||
\(789\) | 9.60337 | 0.341889 | ||||||||
\(790\) | 13.3385 | 0.474563 | ||||||||
\(791\) | 0.169689 | 0.00603345 | ||||||||
\(792\) | 4.23123 | 0.150350 | ||||||||
\(793\) | −24.8265 | −0.881614 | ||||||||
\(794\) | 7.46777 | 0.265021 | ||||||||
\(795\) | 13.1091 | 0.464932 | ||||||||
\(796\) | 42.7825 | 1.51639 | ||||||||
\(797\) | 4.58337 | 0.162351 | 0.0811757 | − | 0.996700i | \(-0.474133\pi\) | ||||
0.0811757 | + | 0.996700i | \(0.474133\pi\) | |||||||
\(798\) | −0.150030 | −0.00531100 | ||||||||
\(799\) | −2.90950 | −0.102931 | ||||||||
\(800\) | −13.6812 | −0.483702 | ||||||||
\(801\) | 10.7196 | 0.378759 | ||||||||
\(802\) | −80.4591 | −2.84111 | ||||||||
\(803\) | −11.4506 | −0.404084 | ||||||||
\(804\) | −64.6386 | −2.27963 | ||||||||
\(805\) | −0.0734983 | −0.00259048 | ||||||||
\(806\) | 57.3587 | 2.02038 | ||||||||
\(807\) | −0.760314 | −0.0267643 | ||||||||
\(808\) | 0.0131404 | 0.000462279 0 | ||||||||
\(809\) | 32.7136 | 1.15015 | 0.575075 | − | 0.818101i | \(-0.304973\pi\) | ||||
0.575075 | + | 0.818101i | \(0.304973\pi\) | |||||||
\(810\) | 8.05676 | 0.283086 | ||||||||
\(811\) | 20.4644 | 0.718602 | 0.359301 | − | 0.933222i | \(-0.383015\pi\) | ||||
0.359301 | + | 0.933222i | \(0.383015\pi\) | |||||||
\(812\) | 0.568325 | 0.0199443 | ||||||||
\(813\) | −21.7783 | −0.763799 | ||||||||
\(814\) | −24.9713 | −0.875244 | ||||||||
\(815\) | −17.8548 | −0.625426 | ||||||||
\(816\) | 1.26069 | 0.0441330 | ||||||||
\(817\) | −17.1801 | −0.601055 | ||||||||
\(818\) | −51.3127 | −1.79411 | ||||||||
\(819\) | −0.0690225 | −0.00241184 | ||||||||
\(820\) | −32.9222 | −1.14969 | ||||||||
\(821\) | 54.4837 | 1.90149 | 0.950747 | − | 0.309968i | \(-0.100318\pi\) | ||||
0.950747 | + | 0.309968i | \(0.100318\pi\) | |||||||
\(822\) | 39.0354 | 1.36151 | ||||||||
\(823\) | 0.912794 | 0.0318180 | 0.0159090 | − | 0.999873i | \(-0.494936\pi\) | ||||
0.0159090 | + | 0.999873i | \(0.494936\pi\) | |||||||
\(824\) | −16.9408 | −0.590162 | ||||||||
\(825\) | −6.16497 | −0.214637 | ||||||||
\(826\) | −0.0597133 | −0.00207769 | ||||||||
\(827\) | 48.1650 | 1.67486 | 0.837430 | − | 0.546545i | \(-0.184057\pi\) | ||||
0.837430 | + | 0.546545i | \(0.184057\pi\) | |||||||
\(828\) | −16.5636 | −0.575626 | ||||||||
\(829\) | 10.1069 | 0.351027 | 0.175514 | − | 0.984477i | \(-0.443841\pi\) | ||||
0.175514 | + | 0.984477i | \(0.443841\pi\) | |||||||
\(830\) | −25.3069 | −0.878414 | ||||||||
\(831\) | −11.2211 | −0.389257 | ||||||||
\(832\) | 30.4504 | 1.05568 | ||||||||
\(833\) | −3.19098 | −0.110561 | ||||||||
\(834\) | 16.2562 | 0.562905 | ||||||||
\(835\) | 8.77625 | 0.303715 | ||||||||
\(836\) | −7.02756 | −0.243053 | ||||||||
\(837\) | −50.6244 | −1.74983 | ||||||||
\(838\) | −38.2596 | −1.32166 | ||||||||
\(839\) | −2.71956 | −0.0938897 | −0.0469448 | − | 0.998897i | \(-0.514949\pi\) | ||||
−0.0469448 | + | 0.998897i | \(0.514949\pi\) | |||||||
\(840\) | 0.0947718 | 0.00326994 | ||||||||
\(841\) | 14.4501 | 0.498281 | ||||||||
\(842\) | 3.14539 | 0.108397 | ||||||||
\(843\) | −35.8865 | −1.23600 | ||||||||
\(844\) | −62.5807 | −2.15411 | ||||||||
\(845\) | −4.24336 | −0.145976 | ||||||||
\(846\) | −16.4138 | −0.564318 | ||||||||
\(847\) | −0.0236528 | −0.000812718 0 | ||||||||
\(848\) | 25.5390 | 0.877013 | ||||||||
\(849\) | −22.2511 | −0.763655 | ||||||||
\(850\) | 4.82236 | 0.165406 | ||||||||
\(851\) | 44.1189 | 1.51238 | ||||||||
\(852\) | 65.1346 | 2.23147 | ||||||||
\(853\) | 13.0713 | 0.447552 | 0.223776 | − | 0.974641i | \(-0.428162\pi\) | ||||
0.223776 | + | 0.974641i | \(0.428162\pi\) | |||||||
\(854\) | 0.517536 | 0.0177097 | ||||||||
\(855\) | 1.54480 | 0.0528310 | ||||||||
\(856\) | −14.7090 | −0.502743 | ||||||||
\(857\) | −24.8268 | −0.848068 | −0.424034 | − | 0.905646i | \(-0.639386\pi\) | ||||
−0.424034 | + | 0.905646i | \(0.639386\pi\) | |||||||
\(858\) | 8.86964 | 0.302804 | ||||||||
\(859\) | −40.9652 | −1.39771 | −0.698857 | − | 0.715262i | \(-0.746307\pi\) | ||||
−0.698857 | + | 0.715262i | \(0.746307\pi\) | |||||||
\(860\) | 24.0454 | 0.819941 | ||||||||
\(861\) | 0.399623 | 0.0136191 | ||||||||
\(862\) | −95.9204 | −3.26706 | ||||||||
\(863\) | −23.9378 | −0.814852 | −0.407426 | − | 0.913238i | \(-0.633574\pi\) | ||||
−0.407426 | + | 0.913238i | \(0.633574\pi\) | |||||||
\(864\) | −17.3723 | −0.591019 | ||||||||
\(865\) | −17.6901 | −0.601483 | ||||||||
\(866\) | −36.0832 | −1.22616 | ||||||||
\(867\) | −23.2530 | −0.789712 | ||||||||
\(868\) | −0.772087 | −0.0262064 | ||||||||
\(869\) | −7.58395 | −0.257268 | ||||||||
\(870\) | 16.0539 | 0.544277 | ||||||||
\(871\) | 34.5220 | 1.16973 | ||||||||
\(872\) | 46.4961 | 1.57456 | ||||||||
\(873\) | −11.8650 | −0.401570 | ||||||||
\(874\) | 19.2286 | 0.650417 | ||||||||
\(875\) | 0.165493 | 0.00559469 | ||||||||
\(876\) | −57.7990 | −1.95285 | ||||||||
\(877\) | 8.26172 | 0.278979 | 0.139489 | − | 0.990224i | \(-0.455454\pi\) | ||||
0.139489 | + | 0.990224i | \(0.455454\pi\) | |||||||
\(878\) | 37.1480 | 1.25368 | ||||||||
\(879\) | 38.8279 | 1.30963 | ||||||||
\(880\) | 1.47825 | 0.0498319 | ||||||||
\(881\) | −47.6116 | −1.60408 | −0.802038 | − | 0.597273i | \(-0.796251\pi\) | ||||
−0.802038 | + | 0.597273i | \(0.796251\pi\) | |||||||
\(882\) | −18.0018 | −0.606152 | ||||||||
\(883\) | 25.6560 | 0.863394 | 0.431697 | − | 0.902019i | \(-0.357915\pi\) | ||||
0.431697 | + | 0.902019i | \(0.357915\pi\) | |||||||
\(884\) | −4.47997 | −0.150678 | ||||||||
\(885\) | −1.08917 | −0.0366120 | ||||||||
\(886\) | −0.475371 | −0.0159704 | ||||||||
\(887\) | 36.2618 | 1.21755 | 0.608776 | − | 0.793342i | \(-0.291661\pi\) | ||||
0.608776 | + | 0.793342i | \(0.291661\pi\) | |||||||
\(888\) | −56.8888 | −1.90906 | ||||||||
\(889\) | 0.200456 | 0.00672307 | ||||||||
\(890\) | 17.4172 | 0.583825 | ||||||||
\(891\) | −4.58088 | −0.153465 | ||||||||
\(892\) | 23.0702 | 0.772448 | ||||||||
\(893\) | 12.3039 | 0.411734 | ||||||||
\(894\) | −11.0263 | −0.368773 | ||||||||
\(895\) | −13.7603 | −0.459957 | ||||||||
\(896\) | −0.489404 | −0.0163498 | ||||||||
\(897\) | −15.6707 | −0.523231 | ||||||||
\(898\) | −65.2301 | −2.17676 | ||||||||
\(899\) | −59.0284 | −1.96871 | ||||||||
\(900\) | 17.5668 | 0.585559 | ||||||||
\(901\) | 5.83029 | 0.194235 | ||||||||
\(902\) | 28.9892 | 0.965235 | ||||||||
\(903\) | −0.291872 | −0.00971291 | ||||||||
\(904\) | 28.0430 | 0.932698 | ||||||||
\(905\) | −4.53850 | −0.150865 | ||||||||
\(906\) | 27.1862 | 0.903200 | ||||||||
\(907\) | 11.7981 | 0.391748 | 0.195874 | − | 0.980629i | \(-0.437246\pi\) | ||||
0.195874 | + | 0.980629i | \(0.437246\pi\) | |||||||
\(908\) | 11.4667 | 0.380537 | ||||||||
\(909\) | 0.00363890 | 0.000120695 0 | ||||||||
\(910\) | −0.112147 | −0.00371765 | ||||||||
\(911\) | −2.86242 | −0.0948363 | −0.0474182 | − | 0.998875i | \(-0.515099\pi\) | ||||
−0.0474182 | + | 0.998875i | \(0.515099\pi\) | |||||||
\(912\) | −5.33129 | −0.176537 | ||||||||
\(913\) | 14.3889 | 0.476202 | ||||||||
\(914\) | −80.7423 | −2.67072 | ||||||||
\(915\) | 9.43984 | 0.312071 | ||||||||
\(916\) | 32.7433 | 1.08187 | ||||||||
\(917\) | 0.247846 | 0.00818458 | ||||||||
\(918\) | 6.12342 | 0.202103 | ||||||||
\(919\) | 49.9337 | 1.64716 | 0.823581 | − | 0.567199i | \(-0.191973\pi\) | ||||
0.823581 | + | 0.567199i | \(0.191973\pi\) | |||||||
\(920\) | −12.1464 | −0.400456 | ||||||||
\(921\) | 21.6282 | 0.712672 | ||||||||
\(922\) | 21.0680 | 0.693838 | ||||||||
\(923\) | −34.7869 | −1.14502 | ||||||||
\(924\) | −0.119391 | −0.00392769 | ||||||||
\(925\) | −46.7909 | −1.53848 | ||||||||
\(926\) | −28.3125 | −0.930407 | ||||||||
\(927\) | −4.69132 | −0.154083 | ||||||||
\(928\) | −20.2563 | −0.664945 | ||||||||
\(929\) | −13.9415 | −0.457406 | −0.228703 | − | 0.973496i | \(-0.573448\pi\) | ||||
−0.228703 | + | 0.973496i | \(0.573448\pi\) | |||||||
\(930\) | −21.8097 | −0.715167 | ||||||||
\(931\) | 13.4943 | 0.442256 | ||||||||
\(932\) | −93.4911 | −3.06240 | ||||||||
\(933\) | 36.8871 | 1.20763 | ||||||||
\(934\) | 22.4170 | 0.733506 | ||||||||
\(935\) | 0.337469 | 0.0110364 | ||||||||
\(936\) | −11.4067 | −0.372841 | ||||||||
\(937\) | 5.58943 | 0.182599 | 0.0912993 | − | 0.995823i | \(-0.470898\pi\) | ||||
0.0912993 | + | 0.995823i | \(0.470898\pi\) | |||||||
\(938\) | −0.719650 | −0.0234974 | ||||||||
\(939\) | −1.76072 | −0.0574589 | ||||||||
\(940\) | −17.2206 | −0.561675 | ||||||||
\(941\) | 49.2201 | 1.60453 | 0.802265 | − | 0.596968i | \(-0.203628\pi\) | ||||
0.802265 | + | 0.596968i | \(0.203628\pi\) | |||||||
\(942\) | 32.8675 | 1.07088 | ||||||||
\(943\) | −51.2177 | −1.66788 | ||||||||
\(944\) | −2.12190 | −0.0690621 | ||||||||
\(945\) | 0.0989803 | 0.00321983 | ||||||||
\(946\) | −21.1728 | −0.688387 | ||||||||
\(947\) | 55.5109 | 1.80386 | 0.901931 | − | 0.431881i | \(-0.142150\pi\) | ||||
0.901931 | + | 0.431881i | \(0.142150\pi\) | |||||||
\(948\) | −38.2813 | −1.24332 | ||||||||
\(949\) | 30.8692 | 1.00206 | ||||||||
\(950\) | −20.3931 | −0.661640 | ||||||||
\(951\) | −44.0134 | −1.42723 | ||||||||
\(952\) | 0.0421498 | 0.00136608 | ||||||||
\(953\) | −21.3410 | −0.691304 | −0.345652 | − | 0.938363i | \(-0.612342\pi\) | ||||
−0.345652 | + | 0.938363i | \(0.612342\pi\) | |||||||
\(954\) | 32.8913 | 1.06490 | ||||||||
\(955\) | 9.19769 | 0.297630 | ||||||||
\(956\) | 85.3881 | 2.76165 | ||||||||
\(957\) | −9.12783 | −0.295061 | ||||||||
\(958\) | 39.2759 | 1.26895 | ||||||||
\(959\) | 0.280627 | 0.00906191 | ||||||||
\(960\) | −11.5783 | −0.373687 | ||||||||
\(961\) | 49.1920 | 1.58684 | ||||||||
\(962\) | 67.3188 | 2.17044 | ||||||||
\(963\) | −4.07328 | −0.131260 | ||||||||
\(964\) | 25.1484 | 0.809976 | ||||||||
\(965\) | −19.2677 | −0.620249 | ||||||||
\(966\) | 0.326675 | 0.0105106 | ||||||||
\(967\) | 0.792195 | 0.0254753 | 0.0127376 | − | 0.999919i | \(-0.495945\pi\) | ||||
0.0127376 | + | 0.999919i | \(0.495945\pi\) | |||||||
\(968\) | −3.90889 | −0.125636 | ||||||||
\(969\) | −1.21708 | −0.0390982 | ||||||||
\(970\) | −19.2782 | −0.618987 | ||||||||
\(971\) | −50.4127 | −1.61782 | −0.808910 | − | 0.587932i | \(-0.799942\pi\) | ||||
−0.808910 | + | 0.587932i | \(0.799942\pi\) | |||||||
\(972\) | 38.6980 | 1.24124 | ||||||||
\(973\) | 0.116866 | 0.00374656 | ||||||||
\(974\) | −11.3001 | −0.362079 | ||||||||
\(975\) | 16.6198 | 0.532260 | ||||||||
\(976\) | 18.3906 | 0.588668 | ||||||||
\(977\) | 6.57833 | 0.210460 | 0.105230 | − | 0.994448i | \(-0.466442\pi\) | ||||
0.105230 | + | 0.994448i | \(0.466442\pi\) | |||||||
\(978\) | 79.3583 | 2.53760 | ||||||||
\(979\) | −9.90297 | −0.316500 | ||||||||
\(980\) | −18.8867 | −0.603313 | ||||||||
\(981\) | 12.8759 | 0.411096 | ||||||||
\(982\) | −47.3138 | −1.50984 | ||||||||
\(983\) | −22.7119 | −0.724396 | −0.362198 | − | 0.932101i | \(-0.617974\pi\) | ||||
−0.362198 | + | 0.932101i | \(0.617974\pi\) | |||||||
\(984\) | 66.0423 | 2.10535 | ||||||||
\(985\) | −13.7128 | −0.436926 | ||||||||
\(986\) | 7.13996 | 0.227383 | ||||||||
\(987\) | 0.209031 | 0.00665352 | ||||||||
\(988\) | 18.9452 | 0.602728 | ||||||||
\(989\) | 37.4078 | 1.18950 | ||||||||
\(990\) | 1.90382 | 0.0605073 | ||||||||
\(991\) | −26.2906 | −0.835149 | −0.417575 | − | 0.908643i | \(-0.637120\pi\) | ||||
−0.417575 | + | 0.908643i | \(0.637120\pi\) | |||||||
\(992\) | 27.5188 | 0.873723 | ||||||||
\(993\) | 4.80405 | 0.152452 | ||||||||
\(994\) | 0.725172 | 0.0230011 | ||||||||
\(995\) | 8.68800 | 0.275428 | ||||||||
\(996\) | 72.6302 | 2.30138 | ||||||||
\(997\) | −7.58425 | −0.240196 | −0.120098 | − | 0.992762i | \(-0.538321\pi\) | ||||
−0.120098 | + | 0.992762i | \(0.538321\pi\) | |||||||
\(998\) | 66.1684 | 2.09452 | ||||||||
\(999\) | −59.4150 | −1.87981 |
(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 | 6017.2.a.c.1.13 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.13 | ✓ | 106 | 1.1 | even | 1 | trivial |