Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17408 | −0.830198 | −0.415099 | − | 0.909776i | \(-0.636253\pi\) | ||||
−0.415099 | + | 0.909776i | \(0.636253\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.621542 | −0.310771 | ||||||||
\(5\) | 3.86856 | 1.73007 | 0.865037 | − | 0.501709i | \(-0.167295\pi\) | ||||
0.865037 | + | 0.501709i | \(0.167295\pi\) | |||||||
\(6\) | 1.17408 | 0.479315 | ||||||||
\(7\) | 3.06255 | 1.15753 | 0.578767 | − | 0.815493i | \(-0.303534\pi\) | ||||
0.578767 | + | 0.815493i | \(0.303534\pi\) | |||||||
\(8\) | 3.07789 | 1.08820 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.54199 | −1.43630 | ||||||||
\(11\) | 1.94563 | 0.586628 | 0.293314 | − | 0.956016i | \(-0.405242\pi\) | ||||
0.293314 | + | 0.956016i | \(0.405242\pi\) | |||||||
\(12\) | 0.621542 | 0.179424 | ||||||||
\(13\) | −4.31087 | −1.19562 | −0.597809 | − | 0.801638i | \(-0.703962\pi\) | ||||
−0.597809 | + | 0.801638i | \(0.703962\pi\) | |||||||
\(14\) | −3.59567 | −0.960983 | ||||||||
\(15\) | −3.86856 | −0.998858 | ||||||||
\(16\) | −2.37060 | −0.592651 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.17408 | −0.276733 | ||||||||
\(19\) | −5.08811 | −1.16729 | −0.583647 | − | 0.812008i | \(-0.698375\pi\) | ||||
−0.583647 | + | 0.812008i | \(0.698375\pi\) | |||||||
\(20\) | −2.40447 | −0.537656 | ||||||||
\(21\) | −3.06255 | −0.668303 | ||||||||
\(22\) | −2.28432 | −0.487018 | ||||||||
\(23\) | −2.65257 | −0.553100 | −0.276550 | − | 0.961000i | \(-0.589191\pi\) | ||||
−0.276550 | + | 0.961000i | \(0.589191\pi\) | |||||||
\(24\) | −3.07789 | −0.628272 | ||||||||
\(25\) | 9.96577 | 1.99315 | ||||||||
\(26\) | 5.06129 | 0.992601 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.90350 | −0.359728 | ||||||||
\(29\) | 5.36141 | 0.995590 | 0.497795 | − | 0.867295i | \(-0.334143\pi\) | ||||
0.497795 | + | 0.867295i | \(0.334143\pi\) | |||||||
\(30\) | 4.54199 | 0.829251 | ||||||||
\(31\) | 0.729477 | 0.131018 | 0.0655090 | − | 0.997852i | \(-0.479133\pi\) | ||||
0.0655090 | + | 0.997852i | \(0.479133\pi\) | |||||||
\(32\) | −3.37252 | −0.596182 | ||||||||
\(33\) | −1.94563 | −0.338690 | ||||||||
\(34\) | 1.17408 | 0.201353 | ||||||||
\(35\) | 11.8477 | 2.00262 | ||||||||
\(36\) | −0.621542 | −0.103590 | ||||||||
\(37\) | −6.55851 | −1.07821 | −0.539106 | − | 0.842238i | \(-0.681238\pi\) | ||||
−0.539106 | + | 0.842238i | \(0.681238\pi\) | |||||||
\(38\) | 5.97384 | 0.969085 | ||||||||
\(39\) | 4.31087 | 0.690291 | ||||||||
\(40\) | 11.9070 | 1.88267 | ||||||||
\(41\) | 8.81303 | 1.37636 | 0.688182 | − | 0.725538i | \(-0.258409\pi\) | ||||
0.688182 | + | 0.725538i | \(0.258409\pi\) | |||||||
\(42\) | 3.59567 | 0.554824 | ||||||||
\(43\) | 5.21086 | 0.794649 | 0.397324 | − | 0.917678i | \(-0.369939\pi\) | ||||
0.397324 | + | 0.917678i | \(0.369939\pi\) | |||||||
\(44\) | −1.20929 | −0.182307 | ||||||||
\(45\) | 3.86856 | 0.576691 | ||||||||
\(46\) | 3.11433 | 0.459183 | ||||||||
\(47\) | 5.95297 | 0.868330 | 0.434165 | − | 0.900833i | \(-0.357043\pi\) | ||||
0.434165 | + | 0.900833i | \(0.357043\pi\) | |||||||
\(48\) | 2.37060 | 0.342167 | ||||||||
\(49\) | 2.37920 | 0.339886 | ||||||||
\(50\) | −11.7006 | −1.65471 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 2.67938 | 0.371563 | ||||||||
\(53\) | −1.03559 | −0.142249 | −0.0711243 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711243 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(54\) | 1.17408 | 0.159772 | ||||||||
\(55\) | 7.52677 | 1.01491 | ||||||||
\(56\) | 9.42620 | 1.25963 | ||||||||
\(57\) | 5.08811 | 0.673937 | ||||||||
\(58\) | −6.29472 | −0.826537 | ||||||||
\(59\) | 12.5431 | 1.63297 | 0.816484 | − | 0.577368i | \(-0.195920\pi\) | ||||
0.816484 | + | 0.577368i | \(0.195920\pi\) | |||||||
\(60\) | 2.40447 | 0.310416 | ||||||||
\(61\) | 5.20694 | 0.666681 | 0.333340 | − | 0.942807i | \(-0.391824\pi\) | ||||
0.333340 | + | 0.942807i | \(0.391824\pi\) | |||||||
\(62\) | −0.856463 | −0.108771 | ||||||||
\(63\) | 3.06255 | 0.385845 | ||||||||
\(64\) | 8.70080 | 1.08760 | ||||||||
\(65\) | −16.6768 | −2.06851 | ||||||||
\(66\) | 2.28432 | 0.281180 | ||||||||
\(67\) | −7.84025 | −0.957839 | −0.478920 | − | 0.877859i | \(-0.658972\pi\) | ||||
−0.478920 | + | 0.877859i | \(0.658972\pi\) | |||||||
\(68\) | 0.621542 | 0.0753730 | ||||||||
\(69\) | 2.65257 | 0.319332 | ||||||||
\(70\) | −13.9101 | −1.66257 | ||||||||
\(71\) | 12.0605 | 1.43132 | 0.715658 | − | 0.698451i | \(-0.246127\pi\) | ||||
0.715658 | + | 0.698451i | \(0.246127\pi\) | |||||||
\(72\) | 3.07789 | 0.362733 | ||||||||
\(73\) | −14.0089 | −1.63962 | −0.819810 | − | 0.572636i | \(-0.805921\pi\) | ||||
−0.819810 | + | 0.572636i | \(0.805921\pi\) | |||||||
\(74\) | 7.70020 | 0.895130 | ||||||||
\(75\) | −9.96577 | −1.15075 | ||||||||
\(76\) | 3.16247 | 0.362761 | ||||||||
\(77\) | 5.95857 | 0.679042 | ||||||||
\(78\) | −5.06129 | −0.573078 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −9.17082 | −1.02533 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.3472 | −1.14265 | ||||||||
\(83\) | 1.61708 | 0.177497 | 0.0887487 | − | 0.996054i | \(-0.471713\pi\) | ||||
0.0887487 | + | 0.996054i | \(0.471713\pi\) | |||||||
\(84\) | 1.90350 | 0.207689 | ||||||||
\(85\) | −3.86856 | −0.419604 | ||||||||
\(86\) | −6.11795 | −0.659716 | ||||||||
\(87\) | −5.36141 | −0.574804 | ||||||||
\(88\) | 5.98843 | 0.638369 | ||||||||
\(89\) | −2.37602 | −0.251858 | −0.125929 | − | 0.992039i | \(-0.540191\pi\) | ||||
−0.125929 | + | 0.992039i | \(0.540191\pi\) | |||||||
\(90\) | −4.54199 | −0.478768 | ||||||||
\(91\) | −13.2022 | −1.38397 | ||||||||
\(92\) | 1.64869 | 0.171887 | ||||||||
\(93\) | −0.729477 | −0.0756433 | ||||||||
\(94\) | −6.98925 | −0.720886 | ||||||||
\(95\) | −19.6837 | −2.01950 | ||||||||
\(96\) | 3.37252 | 0.344206 | ||||||||
\(97\) | 15.2428 | 1.54767 | 0.773834 | − | 0.633389i | \(-0.218337\pi\) | ||||
0.773834 | + | 0.633389i | \(0.218337\pi\) | |||||||
\(98\) | −2.79337 | −0.282173 | ||||||||
\(99\) | 1.94563 | 0.195543 | ||||||||
\(100\) | −6.19414 | −0.619414 | ||||||||
\(101\) | 3.95894 | 0.393930 | 0.196965 | − | 0.980411i | \(-0.436892\pi\) | ||||
0.196965 | + | 0.980411i | \(0.436892\pi\) | |||||||
\(102\) | −1.17408 | −0.116251 | ||||||||
\(103\) | 6.36157 | 0.626824 | 0.313412 | − | 0.949617i | \(-0.398528\pi\) | ||||
0.313412 | + | 0.949617i | \(0.398528\pi\) | |||||||
\(104\) | −13.2684 | −1.30107 | ||||||||
\(105\) | −11.8477 | −1.15621 | ||||||||
\(106\) | 1.21586 | 0.118095 | ||||||||
\(107\) | 8.16730 | 0.789563 | 0.394781 | − | 0.918775i | \(-0.370820\pi\) | ||||
0.394781 | + | 0.918775i | \(0.370820\pi\) | |||||||
\(108\) | 0.621542 | 0.0598079 | ||||||||
\(109\) | 17.9770 | 1.72189 | 0.860944 | − | 0.508700i | \(-0.169874\pi\) | ||||
0.860944 | + | 0.508700i | \(0.169874\pi\) | |||||||
\(110\) | −8.83702 | −0.842577 | ||||||||
\(111\) | 6.55851 | 0.622506 | ||||||||
\(112\) | −7.26008 | −0.686014 | ||||||||
\(113\) | −1.08216 | −0.101801 | −0.0509005 | − | 0.998704i | \(-0.516209\pi\) | ||||
−0.0509005 | + | 0.998704i | \(0.516209\pi\) | |||||||
\(114\) | −5.97384 | −0.559501 | ||||||||
\(115\) | −10.2616 | −0.956904 | ||||||||
\(116\) | −3.33234 | −0.309400 | ||||||||
\(117\) | −4.31087 | −0.398540 | ||||||||
\(118\) | −14.7265 | −1.35569 | ||||||||
\(119\) | −3.06255 | −0.280743 | ||||||||
\(120\) | −11.9070 | −1.08696 | ||||||||
\(121\) | −7.21454 | −0.655867 | ||||||||
\(122\) | −6.11336 | −0.553477 | ||||||||
\(123\) | −8.81303 | −0.794644 | ||||||||
\(124\) | −0.453401 | −0.0407166 | ||||||||
\(125\) | 19.2104 | 1.71823 | ||||||||
\(126\) | −3.59567 | −0.320328 | ||||||||
\(127\) | 2.99327 | 0.265610 | 0.132805 | − | 0.991142i | \(-0.457602\pi\) | ||||
0.132805 | + | 0.991142i | \(0.457602\pi\) | |||||||
\(128\) | −3.47038 | −0.306742 | ||||||||
\(129\) | −5.21086 | −0.458791 | ||||||||
\(130\) | 19.5799 | 1.71727 | ||||||||
\(131\) | −11.3887 | −0.995031 | −0.497516 | − | 0.867455i | \(-0.665754\pi\) | ||||
−0.497516 | + | 0.867455i | \(0.665754\pi\) | |||||||
\(132\) | 1.20929 | 0.105255 | ||||||||
\(133\) | −15.5826 | −1.35118 | ||||||||
\(134\) | 9.20507 | 0.795197 | ||||||||
\(135\) | −3.86856 | −0.332953 | ||||||||
\(136\) | −3.07789 | −0.263927 | ||||||||
\(137\) | −6.43962 | −0.550174 | −0.275087 | − | 0.961419i | \(-0.588707\pi\) | ||||
−0.275087 | + | 0.961419i | \(0.588707\pi\) | |||||||
\(138\) | −3.11433 | −0.265109 | ||||||||
\(139\) | −7.72668 | −0.655369 | −0.327684 | − | 0.944787i | \(-0.606268\pi\) | ||||
−0.327684 | + | 0.944787i | \(0.606268\pi\) | |||||||
\(140\) | −7.36381 | −0.622356 | ||||||||
\(141\) | −5.95297 | −0.501331 | ||||||||
\(142\) | −14.1599 | −1.18828 | ||||||||
\(143\) | −8.38733 | −0.701384 | ||||||||
\(144\) | −2.37060 | −0.197550 | ||||||||
\(145\) | 20.7410 | 1.72244 | ||||||||
\(146\) | 16.4476 | 1.36121 | ||||||||
\(147\) | −2.37920 | −0.196233 | ||||||||
\(148\) | 4.07639 | 0.335077 | ||||||||
\(149\) | −5.37588 | −0.440410 | −0.220205 | − | 0.975454i | \(-0.570673\pi\) | ||||
−0.220205 | + | 0.975454i | \(0.570673\pi\) | |||||||
\(150\) | 11.7006 | 0.955349 | ||||||||
\(151\) | 14.5639 | 1.18519 | 0.592597 | − | 0.805499i | \(-0.298103\pi\) | ||||
0.592597 | + | 0.805499i | \(0.298103\pi\) | |||||||
\(152\) | −15.6607 | −1.27025 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −6.99583 | −0.563740 | ||||||||
\(155\) | 2.82203 | 0.226671 | ||||||||
\(156\) | −2.67938 | −0.214522 | ||||||||
\(157\) | 17.2692 | 1.37823 | 0.689115 | − | 0.724652i | \(-0.258000\pi\) | ||||
0.689115 | + | 0.724652i | \(0.258000\pi\) | |||||||
\(158\) | −1.17408 | −0.0934046 | ||||||||
\(159\) | 1.03559 | 0.0821273 | ||||||||
\(160\) | −13.0468 | −1.03144 | ||||||||
\(161\) | −8.12364 | −0.640232 | ||||||||
\(162\) | −1.17408 | −0.0922443 | ||||||||
\(163\) | 1.10148 | 0.0862742 | 0.0431371 | − | 0.999069i | \(-0.486265\pi\) | ||||
0.0431371 | + | 0.999069i | \(0.486265\pi\) | |||||||
\(164\) | −5.47766 | −0.427734 | ||||||||
\(165\) | −7.52677 | −0.585959 | ||||||||
\(166\) | −1.89858 | −0.147358 | ||||||||
\(167\) | −13.5588 | −1.04922 | −0.524608 | − | 0.851344i | \(-0.675788\pi\) | ||||
−0.524608 | + | 0.851344i | \(0.675788\pi\) | |||||||
\(168\) | −9.42620 | −0.727247 | ||||||||
\(169\) | 5.58356 | 0.429505 | ||||||||
\(170\) | 4.54199 | 0.348355 | ||||||||
\(171\) | −5.08811 | −0.389098 | ||||||||
\(172\) | −3.23877 | −0.246954 | ||||||||
\(173\) | 23.7333 | 1.80441 | 0.902204 | − | 0.431310i | \(-0.141948\pi\) | ||||
0.902204 | + | 0.431310i | \(0.141948\pi\) | |||||||
\(174\) | 6.29472 | 0.477201 | ||||||||
\(175\) | 30.5207 | 2.30714 | ||||||||
\(176\) | −4.61231 | −0.347666 | ||||||||
\(177\) | −12.5431 | −0.942795 | ||||||||
\(178\) | 2.78963 | 0.209092 | ||||||||
\(179\) | −1.96158 | −0.146616 | −0.0733078 | − | 0.997309i | \(-0.523356\pi\) | ||||
−0.0733078 | + | 0.997309i | \(0.523356\pi\) | |||||||
\(180\) | −2.40447 | −0.179219 | ||||||||
\(181\) | −25.4621 | −1.89258 | −0.946291 | − | 0.323318i | \(-0.895202\pi\) | ||||
−0.946291 | + | 0.323318i | \(0.895202\pi\) | |||||||
\(182\) | 15.5004 | 1.14897 | ||||||||
\(183\) | −5.20694 | −0.384908 | ||||||||
\(184\) | −8.16434 | −0.601883 | ||||||||
\(185\) | −25.3720 | −1.86539 | ||||||||
\(186\) | 0.856463 | 0.0627989 | ||||||||
\(187\) | −1.94563 | −0.142278 | ||||||||
\(188\) | −3.70002 | −0.269852 | ||||||||
\(189\) | −3.06255 | −0.222768 | ||||||||
\(190\) | 23.1102 | 1.67659 | ||||||||
\(191\) | 16.0338 | 1.16016 | 0.580082 | − | 0.814558i | \(-0.303021\pi\) | ||||
0.580082 | + | 0.814558i | \(0.303021\pi\) | |||||||
\(192\) | −8.70080 | −0.627926 | ||||||||
\(193\) | 19.9539 | 1.43632 | 0.718158 | − | 0.695881i | \(-0.244986\pi\) | ||||
0.718158 | + | 0.695881i | \(0.244986\pi\) | |||||||
\(194\) | −17.8962 | −1.28487 | ||||||||
\(195\) | 16.6768 | 1.19425 | ||||||||
\(196\) | −1.47877 | −0.105627 | ||||||||
\(197\) | 10.1361 | 0.722169 | 0.361085 | − | 0.932533i | \(-0.382407\pi\) | ||||
0.361085 | + | 0.932533i | \(0.382407\pi\) | |||||||
\(198\) | −2.28432 | −0.162339 | ||||||||
\(199\) | 16.8867 | 1.19707 | 0.598535 | − | 0.801097i | \(-0.295750\pi\) | ||||
0.598535 | + | 0.801097i | \(0.295750\pi\) | |||||||
\(200\) | 30.6736 | 2.16895 | ||||||||
\(201\) | 7.84025 | 0.553009 | ||||||||
\(202\) | −4.64811 | −0.327040 | ||||||||
\(203\) | 16.4196 | 1.15243 | ||||||||
\(204\) | −0.621542 | −0.0435166 | ||||||||
\(205\) | 34.0937 | 2.38121 | ||||||||
\(206\) | −7.46898 | −0.520389 | ||||||||
\(207\) | −2.65257 | −0.184367 | ||||||||
\(208\) | 10.2193 | 0.708584 | ||||||||
\(209\) | −9.89956 | −0.684767 | ||||||||
\(210\) | 13.9101 | 0.959886 | ||||||||
\(211\) | 26.1952 | 1.80335 | 0.901677 | − | 0.432410i | \(-0.142337\pi\) | ||||
0.901677 | + | 0.432410i | \(0.142337\pi\) | |||||||
\(212\) | 0.643660 | 0.0442067 | ||||||||
\(213\) | −12.0605 | −0.826371 | ||||||||
\(214\) | −9.58905 | −0.655494 | ||||||||
\(215\) | 20.1585 | 1.37480 | ||||||||
\(216\) | −3.07789 | −0.209424 | ||||||||
\(217\) | 2.23406 | 0.151658 | ||||||||
\(218\) | −21.1064 | −1.42951 | ||||||||
\(219\) | 14.0089 | 0.946635 | ||||||||
\(220\) | −4.67820 | −0.315404 | ||||||||
\(221\) | 4.31087 | 0.289980 | ||||||||
\(222\) | −7.70020 | −0.516804 | ||||||||
\(223\) | −14.8016 | −0.991185 | −0.495593 | − | 0.868555i | \(-0.665049\pi\) | ||||
−0.495593 | + | 0.868555i | \(0.665049\pi\) | |||||||
\(224\) | −10.3285 | −0.690101 | ||||||||
\(225\) | 9.96577 | 0.664385 | ||||||||
\(226\) | 1.27054 | 0.0845150 | ||||||||
\(227\) | 12.5129 | 0.830509 | 0.415255 | − | 0.909705i | \(-0.363692\pi\) | ||||
0.415255 | + | 0.909705i | \(0.363692\pi\) | |||||||
\(228\) | −3.16247 | −0.209440 | ||||||||
\(229\) | −26.3090 | −1.73855 | −0.869275 | − | 0.494328i | \(-0.835414\pi\) | ||||
−0.869275 | + | 0.494328i | \(0.835414\pi\) | |||||||
\(230\) | 12.0480 | 0.794420 | ||||||||
\(231\) | −5.95857 | −0.392045 | ||||||||
\(232\) | 16.5019 | 1.08340 | ||||||||
\(233\) | −24.8250 | −1.62634 | −0.813170 | − | 0.582026i | \(-0.802260\pi\) | ||||
−0.813170 | + | 0.582026i | \(0.802260\pi\) | |||||||
\(234\) | 5.06129 | 0.330867 | ||||||||
\(235\) | 23.0294 | 1.50227 | ||||||||
\(236\) | −7.79604 | −0.507479 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 3.59567 | 0.233073 | ||||||||
\(239\) | −18.5884 | −1.20239 | −0.601193 | − | 0.799104i | \(-0.705308\pi\) | ||||
−0.601193 | + | 0.799104i | \(0.705308\pi\) | |||||||
\(240\) | 9.17082 | 0.591974 | ||||||||
\(241\) | 5.15833 | 0.332277 | 0.166139 | − | 0.986102i | \(-0.446870\pi\) | ||||
0.166139 | + | 0.986102i | \(0.446870\pi\) | |||||||
\(242\) | 8.47043 | 0.544500 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.23633 | −0.207185 | ||||||||
\(245\) | 9.20409 | 0.588028 | ||||||||
\(246\) | 10.3472 | 0.659712 | ||||||||
\(247\) | 21.9342 | 1.39564 | ||||||||
\(248\) | 2.24525 | 0.142574 | ||||||||
\(249\) | −1.61708 | −0.102478 | ||||||||
\(250\) | −22.5545 | −1.42647 | ||||||||
\(251\) | 27.7239 | 1.74992 | 0.874958 | − | 0.484199i | \(-0.160889\pi\) | ||||
0.874958 | + | 0.484199i | \(0.160889\pi\) | |||||||
\(252\) | −1.90350 | −0.119909 | ||||||||
\(253\) | −5.16092 | −0.324464 | ||||||||
\(254\) | −3.51433 | −0.220509 | ||||||||
\(255\) | 3.86856 | 0.242259 | ||||||||
\(256\) | −13.3271 | −0.832944 | ||||||||
\(257\) | 22.5261 | 1.40514 | 0.702569 | − | 0.711616i | \(-0.252036\pi\) | ||||
0.702569 | + | 0.711616i | \(0.252036\pi\) | |||||||
\(258\) | 6.11795 | 0.380887 | ||||||||
\(259\) | −20.0858 | −1.24807 | ||||||||
\(260\) | 10.3654 | 0.642832 | ||||||||
\(261\) | 5.36141 | 0.331863 | ||||||||
\(262\) | 13.3712 | 0.826073 | ||||||||
\(263\) | −8.77673 | −0.541196 | −0.270598 | − | 0.962692i | \(-0.587221\pi\) | ||||
−0.270598 | + | 0.962692i | \(0.587221\pi\) | |||||||
\(264\) | −5.98843 | −0.368562 | ||||||||
\(265\) | −4.00623 | −0.246101 | ||||||||
\(266\) | 18.2952 | 1.12175 | ||||||||
\(267\) | 2.37602 | 0.145410 | ||||||||
\(268\) | 4.87304 | 0.297669 | ||||||||
\(269\) | −5.93332 | −0.361761 | −0.180880 | − | 0.983505i | \(-0.557895\pi\) | ||||
−0.180880 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(270\) | 4.54199 | 0.276417 | ||||||||
\(271\) | −5.77322 | −0.350698 | −0.175349 | − | 0.984506i | \(-0.556105\pi\) | ||||
−0.175349 | + | 0.984506i | \(0.556105\pi\) | |||||||
\(272\) | 2.37060 | 0.143739 | ||||||||
\(273\) | 13.2022 | 0.799035 | ||||||||
\(274\) | 7.56061 | 0.456753 | ||||||||
\(275\) | 19.3897 | 1.16924 | ||||||||
\(276\) | −1.64869 | −0.0992392 | ||||||||
\(277\) | 21.3232 | 1.28119 | 0.640593 | − | 0.767881i | \(-0.278689\pi\) | ||||
0.640593 | + | 0.767881i | \(0.278689\pi\) | |||||||
\(278\) | 9.07173 | 0.544086 | ||||||||
\(279\) | 0.729477 | 0.0436727 | ||||||||
\(280\) | 36.4658 | 2.17925 | ||||||||
\(281\) | −26.4249 | −1.57638 | −0.788190 | − | 0.615432i | \(-0.788982\pi\) | ||||
−0.788190 | + | 0.615432i | \(0.788982\pi\) | |||||||
\(282\) | 6.98925 | 0.416204 | ||||||||
\(283\) | 12.9095 | 0.767389 | 0.383695 | − | 0.923460i | \(-0.374652\pi\) | ||||
0.383695 | + | 0.923460i | \(0.374652\pi\) | |||||||
\(284\) | −7.49609 | −0.444811 | ||||||||
\(285\) | 19.6837 | 1.16596 | ||||||||
\(286\) | 9.84738 | 0.582288 | ||||||||
\(287\) | 26.9903 | 1.59319 | ||||||||
\(288\) | −3.37252 | −0.198727 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −24.3515 | −1.42997 | ||||||||
\(291\) | −15.2428 | −0.893546 | ||||||||
\(292\) | 8.70713 | 0.509546 | ||||||||
\(293\) | −28.7843 | −1.68159 | −0.840797 | − | 0.541350i | \(-0.817913\pi\) | ||||
−0.840797 | + | 0.541350i | \(0.817913\pi\) | |||||||
\(294\) | 2.79337 | 0.162912 | ||||||||
\(295\) | 48.5236 | 2.82516 | ||||||||
\(296\) | −20.1864 | −1.17331 | ||||||||
\(297\) | −1.94563 | −0.112897 | ||||||||
\(298\) | 6.31171 | 0.365627 | ||||||||
\(299\) | 11.4349 | 0.661297 | ||||||||
\(300\) | 6.19414 | 0.357619 | ||||||||
\(301\) | 15.9585 | 0.919833 | ||||||||
\(302\) | −17.0992 | −0.983946 | ||||||||
\(303\) | −3.95894 | −0.227435 | ||||||||
\(304\) | 12.0619 | 0.691797 | ||||||||
\(305\) | 20.1434 | 1.15341 | ||||||||
\(306\) | 1.17408 | 0.0671176 | ||||||||
\(307\) | −5.62415 | −0.320987 | −0.160494 | − | 0.987037i | \(-0.551309\pi\) | ||||
−0.160494 | + | 0.987037i | \(0.551309\pi\) | |||||||
\(308\) | −3.70350 | −0.211027 | ||||||||
\(309\) | −6.36157 | −0.361897 | ||||||||
\(310\) | −3.31328 | −0.188182 | ||||||||
\(311\) | −12.4134 | −0.703902 | −0.351951 | − | 0.936018i | \(-0.614482\pi\) | ||||
−0.351951 | + | 0.936018i | \(0.614482\pi\) | |||||||
\(312\) | 13.2684 | 0.751174 | ||||||||
\(313\) | 0.954605 | 0.0539575 | 0.0269787 | − | 0.999636i | \(-0.491411\pi\) | ||||
0.0269787 | + | 0.999636i | \(0.491411\pi\) | |||||||
\(314\) | −20.2753 | −1.14420 | ||||||||
\(315\) | 11.8477 | 0.667540 | ||||||||
\(316\) | −0.621542 | −0.0349645 | ||||||||
\(317\) | −4.18916 | −0.235286 | −0.117643 | − | 0.993056i | \(-0.537534\pi\) | ||||
−0.117643 | + | 0.993056i | \(0.537534\pi\) | |||||||
\(318\) | −1.21586 | −0.0681819 | ||||||||
\(319\) | 10.4313 | 0.584041 | ||||||||
\(320\) | 33.6596 | 1.88163 | ||||||||
\(321\) | −8.16730 | −0.455854 | ||||||||
\(322\) | 9.53778 | 0.531520 | ||||||||
\(323\) | 5.08811 | 0.283110 | ||||||||
\(324\) | −0.621542 | −0.0345301 | ||||||||
\(325\) | −42.9611 | −2.38305 | ||||||||
\(326\) | −1.29322 | −0.0716247 | ||||||||
\(327\) | −17.9770 | −0.994132 | ||||||||
\(328\) | 27.1256 | 1.49776 | ||||||||
\(329\) | 18.2313 | 1.00512 | ||||||||
\(330\) | 8.83702 | 0.486462 | ||||||||
\(331\) | 6.26454 | 0.344330 | 0.172165 | − | 0.985068i | \(-0.444924\pi\) | ||||
0.172165 | + | 0.985068i | \(0.444924\pi\) | |||||||
\(332\) | −1.00508 | −0.0551610 | ||||||||
\(333\) | −6.55851 | −0.359404 | ||||||||
\(334\) | 15.9191 | 0.871057 | ||||||||
\(335\) | −30.3305 | −1.65713 | ||||||||
\(336\) | 7.26008 | 0.396070 | ||||||||
\(337\) | −9.69837 | −0.528304 | −0.264152 | − | 0.964481i | \(-0.585092\pi\) | ||||
−0.264152 | + | 0.964481i | \(0.585092\pi\) | |||||||
\(338\) | −6.55553 | −0.356574 | ||||||||
\(339\) | 1.08216 | 0.0587748 | ||||||||
\(340\) | 2.40447 | 0.130401 | ||||||||
\(341\) | 1.41929 | 0.0768589 | ||||||||
\(342\) | 5.97384 | 0.323028 | ||||||||
\(343\) | −14.1514 | −0.764105 | ||||||||
\(344\) | 16.0385 | 0.864736 | ||||||||
\(345\) | 10.2616 | 0.552469 | ||||||||
\(346\) | −27.8647 | −1.49802 | ||||||||
\(347\) | 17.1481 | 0.920558 | 0.460279 | − | 0.887774i | \(-0.347749\pi\) | ||||
0.460279 | + | 0.887774i | \(0.347749\pi\) | |||||||
\(348\) | 3.33234 | 0.178632 | ||||||||
\(349\) | 18.1728 | 0.972765 | 0.486383 | − | 0.873746i | \(-0.338316\pi\) | ||||
0.486383 | + | 0.873746i | \(0.338316\pi\) | |||||||
\(350\) | −35.8336 | −1.91539 | ||||||||
\(351\) | 4.31087 | 0.230097 | ||||||||
\(352\) | −6.56165 | −0.349737 | ||||||||
\(353\) | −25.1078 | −1.33636 | −0.668178 | − | 0.744001i | \(-0.732926\pi\) | ||||
−0.668178 | + | 0.744001i | \(0.732926\pi\) | |||||||
\(354\) | 14.7265 | 0.782707 | ||||||||
\(355\) | 46.6567 | 2.47628 | ||||||||
\(356\) | 1.47680 | 0.0782700 | ||||||||
\(357\) | 3.06255 | 0.162087 | ||||||||
\(358\) | 2.30305 | 0.121720 | ||||||||
\(359\) | −22.9349 | −1.21046 | −0.605230 | − | 0.796051i | \(-0.706919\pi\) | ||||
−0.605230 | + | 0.796051i | \(0.706919\pi\) | |||||||
\(360\) | 11.9070 | 0.627555 | ||||||||
\(361\) | 6.88890 | 0.362574 | ||||||||
\(362\) | 29.8945 | 1.57122 | ||||||||
\(363\) | 7.21454 | 0.378665 | ||||||||
\(364\) | 8.20574 | 0.430097 | ||||||||
\(365\) | −54.1944 | −2.83666 | ||||||||
\(366\) | 6.11336 | 0.319550 | ||||||||
\(367\) | 29.2301 | 1.52580 | 0.762900 | − | 0.646517i | \(-0.223775\pi\) | ||||
0.762900 | + | 0.646517i | \(0.223775\pi\) | |||||||
\(368\) | 6.28820 | 0.327795 | ||||||||
\(369\) | 8.81303 | 0.458788 | ||||||||
\(370\) | 29.7887 | 1.54864 | ||||||||
\(371\) | −3.17153 | −0.164658 | ||||||||
\(372\) | 0.453401 | 0.0235077 | ||||||||
\(373\) | −10.7822 | −0.558284 | −0.279142 | − | 0.960250i | \(-0.590050\pi\) | ||||
−0.279142 | + | 0.960250i | \(0.590050\pi\) | |||||||
\(374\) | 2.28432 | 0.118119 | ||||||||
\(375\) | −19.2104 | −0.992020 | ||||||||
\(376\) | 18.3226 | 0.944916 | ||||||||
\(377\) | −23.1123 | −1.19035 | ||||||||
\(378\) | 3.59567 | 0.184941 | ||||||||
\(379\) | 6.51981 | 0.334900 | 0.167450 | − | 0.985881i | \(-0.446447\pi\) | ||||
0.167450 | + | 0.985881i | \(0.446447\pi\) | |||||||
\(380\) | 12.2342 | 0.627603 | ||||||||
\(381\) | −2.99327 | −0.153350 | ||||||||
\(382\) | −18.8249 | −0.963166 | ||||||||
\(383\) | −6.34519 | −0.324224 | −0.162112 | − | 0.986772i | \(-0.551831\pi\) | ||||
−0.162112 | + | 0.986772i | \(0.551831\pi\) | |||||||
\(384\) | 3.47038 | 0.177097 | ||||||||
\(385\) | 23.0511 | 1.17479 | ||||||||
\(386\) | −23.4275 | −1.19243 | ||||||||
\(387\) | 5.21086 | 0.264883 | ||||||||
\(388\) | −9.47401 | −0.480970 | ||||||||
\(389\) | 23.3425 | 1.18351 | 0.591755 | − | 0.806118i | \(-0.298435\pi\) | ||||
0.591755 | + | 0.806118i | \(0.298435\pi\) | |||||||
\(390\) | −19.5799 | −0.991468 | ||||||||
\(391\) | 2.65257 | 0.134146 | ||||||||
\(392\) | 7.32293 | 0.369864 | ||||||||
\(393\) | 11.3887 | 0.574482 | ||||||||
\(394\) | −11.9006 | −0.599544 | ||||||||
\(395\) | 3.86856 | 0.194648 | ||||||||
\(396\) | −1.20929 | −0.0607690 | ||||||||
\(397\) | −12.8069 | −0.642760 | −0.321380 | − | 0.946950i | \(-0.604147\pi\) | ||||
−0.321380 | + | 0.946950i | \(0.604147\pi\) | |||||||
\(398\) | −19.8263 | −0.993805 | ||||||||
\(399\) | 15.5826 | 0.780105 | ||||||||
\(400\) | −23.6249 | −1.18124 | ||||||||
\(401\) | −9.01114 | −0.449995 | −0.224997 | − | 0.974359i | \(-0.572237\pi\) | ||||
−0.224997 | + | 0.974359i | \(0.572237\pi\) | |||||||
\(402\) | −9.20507 | −0.459107 | ||||||||
\(403\) | −3.14468 | −0.156648 | ||||||||
\(404\) | −2.46065 | −0.122422 | ||||||||
\(405\) | 3.86856 | 0.192230 | ||||||||
\(406\) | −19.2779 | −0.956745 | ||||||||
\(407\) | −12.7604 | −0.632510 | ||||||||
\(408\) | 3.07789 | 0.152378 | ||||||||
\(409\) | 17.9837 | 0.889238 | 0.444619 | − | 0.895720i | \(-0.353339\pi\) | ||||
0.444619 | + | 0.895720i | \(0.353339\pi\) | |||||||
\(410\) | −40.0287 | −1.97688 | ||||||||
\(411\) | 6.43962 | 0.317643 | ||||||||
\(412\) | −3.95398 | −0.194799 | ||||||||
\(413\) | 38.4138 | 1.89022 | ||||||||
\(414\) | 3.11433 | 0.153061 | ||||||||
\(415\) | 6.25577 | 0.307083 | ||||||||
\(416\) | 14.5385 | 0.712807 | ||||||||
\(417\) | 7.72668 | 0.378377 | ||||||||
\(418\) | 11.6229 | 0.568493 | ||||||||
\(419\) | −7.33658 | −0.358415 | −0.179208 | − | 0.983811i | \(-0.557353\pi\) | ||||
−0.179208 | + | 0.983811i | \(0.557353\pi\) | |||||||
\(420\) | 7.36381 | 0.359317 | ||||||||
\(421\) | −1.71174 | −0.0834251 | −0.0417125 | − | 0.999130i | \(-0.513281\pi\) | ||||
−0.0417125 | + | 0.999130i | \(0.513281\pi\) | |||||||
\(422\) | −30.7552 | −1.49714 | ||||||||
\(423\) | 5.95297 | 0.289443 | ||||||||
\(424\) | −3.18742 | −0.154795 | ||||||||
\(425\) | −9.96577 | −0.483411 | ||||||||
\(426\) | 14.1599 | 0.686052 | ||||||||
\(427\) | 15.9465 | 0.771706 | ||||||||
\(428\) | −5.07632 | −0.245373 | ||||||||
\(429\) | 8.38733 | 0.404944 | ||||||||
\(430\) | −23.6677 | −1.14136 | ||||||||
\(431\) | 32.8465 | 1.58216 | 0.791081 | − | 0.611711i | \(-0.209519\pi\) | ||||
0.791081 | + | 0.611711i | \(0.209519\pi\) | |||||||
\(432\) | 2.37060 | 0.114056 | ||||||||
\(433\) | 31.9411 | 1.53499 | 0.767495 | − | 0.641055i | \(-0.221503\pi\) | ||||
0.767495 | + | 0.641055i | \(0.221503\pi\) | |||||||
\(434\) | −2.62296 | −0.125906 | ||||||||
\(435\) | −20.7410 | −0.994453 | ||||||||
\(436\) | −11.1735 | −0.535112 | ||||||||
\(437\) | 13.4966 | 0.645630 | ||||||||
\(438\) | −16.4476 | −0.785895 | ||||||||
\(439\) | 31.0882 | 1.48376 | 0.741879 | − | 0.670534i | \(-0.233935\pi\) | ||||
0.741879 | + | 0.670534i | \(0.233935\pi\) | |||||||
\(440\) | 23.1666 | 1.10442 | ||||||||
\(441\) | 2.37920 | 0.113295 | ||||||||
\(442\) | −5.06129 | −0.240741 | ||||||||
\(443\) | 30.2297 | 1.43626 | 0.718129 | − | 0.695910i | \(-0.244999\pi\) | ||||
0.718129 | + | 0.695910i | \(0.244999\pi\) | |||||||
\(444\) | −4.07639 | −0.193457 | ||||||||
\(445\) | −9.19178 | −0.435732 | ||||||||
\(446\) | 17.3782 | 0.822880 | ||||||||
\(447\) | 5.37588 | 0.254271 | ||||||||
\(448\) | 26.6466 | 1.25893 | ||||||||
\(449\) | −24.1267 | −1.13861 | −0.569305 | − | 0.822126i | \(-0.692788\pi\) | ||||
−0.569305 | + | 0.822126i | \(0.692788\pi\) | |||||||
\(450\) | −11.7006 | −0.551571 | ||||||||
\(451\) | 17.1469 | 0.807414 | ||||||||
\(452\) | 0.672607 | 0.0316368 | ||||||||
\(453\) | −14.5639 | −0.684272 | ||||||||
\(454\) | −14.6911 | −0.689487 | ||||||||
\(455\) | −51.0737 | −2.39437 | ||||||||
\(456\) | 15.6607 | 0.733378 | ||||||||
\(457\) | −35.1710 | −1.64523 | −0.822616 | − | 0.568598i | \(-0.807486\pi\) | ||||
−0.822616 | + | 0.568598i | \(0.807486\pi\) | |||||||
\(458\) | 30.8889 | 1.44334 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 6.37804 | 0.297378 | ||||||||
\(461\) | 6.98243 | 0.325204 | 0.162602 | − | 0.986692i | \(-0.448011\pi\) | ||||
0.162602 | + | 0.986692i | \(0.448011\pi\) | |||||||
\(462\) | 6.99583 | 0.325475 | ||||||||
\(463\) | −29.5160 | −1.37172 | −0.685862 | − | 0.727732i | \(-0.740574\pi\) | ||||
−0.685862 | + | 0.727732i | \(0.740574\pi\) | |||||||
\(464\) | −12.7098 | −0.590037 | ||||||||
\(465\) | −2.82203 | −0.130868 | ||||||||
\(466\) | 29.1465 | 1.35018 | ||||||||
\(467\) | −25.4834 | −1.17923 | −0.589615 | − | 0.807684i | \(-0.700721\pi\) | ||||
−0.589615 | + | 0.807684i | \(0.700721\pi\) | |||||||
\(468\) | 2.67938 | 0.123854 | ||||||||
\(469\) | −24.0112 | −1.10873 | ||||||||
\(470\) | −27.0383 | −1.24719 | ||||||||
\(471\) | −17.2692 | −0.795721 | ||||||||
\(472\) | 38.6062 | 1.77700 | ||||||||
\(473\) | 10.1384 | 0.466163 | ||||||||
\(474\) | 1.17408 | 0.0539272 | ||||||||
\(475\) | −50.7070 | −2.32660 | ||||||||
\(476\) | 1.90350 | 0.0872468 | ||||||||
\(477\) | −1.03559 | −0.0474162 | ||||||||
\(478\) | 21.8243 | 0.998219 | ||||||||
\(479\) | 34.7839 | 1.58932 | 0.794658 | − | 0.607057i | \(-0.207650\pi\) | ||||
0.794658 | + | 0.607057i | \(0.207650\pi\) | |||||||
\(480\) | 13.0468 | 0.595502 | ||||||||
\(481\) | 28.2729 | 1.28913 | ||||||||
\(482\) | −6.05628 | −0.275856 | ||||||||
\(483\) | 8.12364 | 0.369638 | ||||||||
\(484\) | 4.48414 | 0.203824 | ||||||||
\(485\) | 58.9675 | 2.67758 | ||||||||
\(486\) | 1.17408 | 0.0532572 | ||||||||
\(487\) | −34.6682 | −1.57097 | −0.785483 | − | 0.618883i | \(-0.787585\pi\) | ||||
−0.785483 | + | 0.618883i | \(0.787585\pi\) | |||||||
\(488\) | 16.0264 | 0.725482 | ||||||||
\(489\) | −1.10148 | −0.0498104 | ||||||||
\(490\) | −10.8063 | −0.488179 | ||||||||
\(491\) | −0.471690 | −0.0212871 | −0.0106435 | − | 0.999943i | \(-0.503388\pi\) | ||||
−0.0106435 | + | 0.999943i | \(0.503388\pi\) | |||||||
\(492\) | 5.47766 | 0.246952 | ||||||||
\(493\) | −5.36141 | −0.241466 | ||||||||
\(494\) | −25.7524 | −1.15866 | ||||||||
\(495\) | 7.52677 | 0.338303 | ||||||||
\(496\) | −1.72930 | −0.0776479 | ||||||||
\(497\) | 36.9358 | 1.65680 | ||||||||
\(498\) | 1.89858 | 0.0850772 | ||||||||
\(499\) | −12.6542 | −0.566480 | −0.283240 | − | 0.959049i | \(-0.591409\pi\) | ||||
−0.283240 | + | 0.959049i | \(0.591409\pi\) | |||||||
\(500\) | −11.9401 | −0.533976 | ||||||||
\(501\) | 13.5588 | 0.605765 | ||||||||
\(502\) | −32.5500 | −1.45278 | ||||||||
\(503\) | 4.17905 | 0.186335 | 0.0931673 | − | 0.995650i | \(-0.470301\pi\) | ||||
0.0931673 | + | 0.995650i | \(0.470301\pi\) | |||||||
\(504\) | 9.42620 | 0.419876 | ||||||||
\(505\) | 15.3154 | 0.681527 | ||||||||
\(506\) | 6.05932 | 0.269370 | ||||||||
\(507\) | −5.58356 | −0.247975 | ||||||||
\(508\) | −1.86044 | −0.0825438 | ||||||||
\(509\) | −9.49524 | −0.420869 | −0.210435 | − | 0.977608i | \(-0.567488\pi\) | ||||
−0.210435 | + | 0.977608i | \(0.567488\pi\) | |||||||
\(510\) | −4.54199 | −0.201123 | ||||||||
\(511\) | −42.9030 | −1.89792 | ||||||||
\(512\) | 22.5878 | 0.998250 | ||||||||
\(513\) | 5.08811 | 0.224646 | ||||||||
\(514\) | −26.4474 | −1.16654 | ||||||||
\(515\) | 24.6101 | 1.08445 | ||||||||
\(516\) | 3.23877 | 0.142579 | ||||||||
\(517\) | 11.5823 | 0.509387 | ||||||||
\(518\) | 23.5822 | 1.03614 | ||||||||
\(519\) | −23.7333 | −1.04178 | ||||||||
\(520\) | −51.3296 | −2.25095 | ||||||||
\(521\) | 15.3199 | 0.671178 | 0.335589 | − | 0.942008i | \(-0.391065\pi\) | ||||
0.335589 | + | 0.942008i | \(0.391065\pi\) | |||||||
\(522\) | −6.29472 | −0.275512 | ||||||||
\(523\) | −11.8995 | −0.520327 | −0.260164 | − | 0.965565i | \(-0.583777\pi\) | ||||
−0.260164 | + | 0.965565i | \(0.583777\pi\) | |||||||
\(524\) | 7.07852 | 0.309227 | ||||||||
\(525\) | −30.5207 | −1.33203 | ||||||||
\(526\) | 10.3046 | 0.449300 | ||||||||
\(527\) | −0.729477 | −0.0317765 | ||||||||
\(528\) | 4.61231 | 0.200725 | ||||||||
\(529\) | −15.9638 | −0.694080 | ||||||||
\(530\) | 4.70362 | 0.204312 | ||||||||
\(531\) | 12.5431 | 0.544323 | ||||||||
\(532\) | 9.68523 | 0.419908 | ||||||||
\(533\) | −37.9918 | −1.64561 | ||||||||
\(534\) | −2.78963 | −0.120719 | ||||||||
\(535\) | 31.5957 | 1.36600 | ||||||||
\(536\) | −24.1315 | −1.04232 | ||||||||
\(537\) | 1.96158 | 0.0846485 | ||||||||
\(538\) | 6.96618 | 0.300333 | ||||||||
\(539\) | 4.62904 | 0.199387 | ||||||||
\(540\) | 2.40447 | 0.103472 | ||||||||
\(541\) | 12.7572 | 0.548474 | 0.274237 | − | 0.961662i | \(-0.411575\pi\) | ||||
0.274237 | + | 0.961662i | \(0.411575\pi\) | |||||||
\(542\) | 6.77821 | 0.291149 | ||||||||
\(543\) | 25.4621 | 1.09268 | ||||||||
\(544\) | 3.37252 | 0.144595 | ||||||||
\(545\) | 69.5453 | 2.97899 | ||||||||
\(546\) | −15.5004 | −0.663358 | ||||||||
\(547\) | 19.9692 | 0.853822 | 0.426911 | − | 0.904294i | \(-0.359602\pi\) | ||||
0.426911 | + | 0.904294i | \(0.359602\pi\) | |||||||
\(548\) | 4.00249 | 0.170978 | ||||||||
\(549\) | 5.20694 | 0.222227 | ||||||||
\(550\) | −22.7650 | −0.970702 | ||||||||
\(551\) | −27.2795 | −1.16215 | ||||||||
\(552\) | 8.16434 | 0.347497 | ||||||||
\(553\) | 3.06255 | 0.130233 | ||||||||
\(554\) | −25.0351 | −1.06364 | ||||||||
\(555\) | 25.3720 | 1.07698 | ||||||||
\(556\) | 4.80246 | 0.203669 | ||||||||
\(557\) | −23.7516 | −1.00639 | −0.503194 | − | 0.864173i | \(-0.667842\pi\) | ||||
−0.503194 | + | 0.864173i | \(0.667842\pi\) | |||||||
\(558\) | −0.856463 | −0.0362570 | ||||||||
\(559\) | −22.4633 | −0.950097 | ||||||||
\(560\) | −28.0861 | −1.18685 | ||||||||
\(561\) | 1.94563 | 0.0821444 | ||||||||
\(562\) | 31.0249 | 1.30871 | ||||||||
\(563\) | −25.9984 | −1.09570 | −0.547850 | − | 0.836577i | \(-0.684554\pi\) | ||||
−0.547850 | + | 0.836577i | \(0.684554\pi\) | |||||||
\(564\) | 3.70002 | 0.155799 | ||||||||
\(565\) | −4.18640 | −0.176123 | ||||||||
\(566\) | −15.1567 | −0.637085 | ||||||||
\(567\) | 3.06255 | 0.128615 | ||||||||
\(568\) | 37.1209 | 1.55756 | ||||||||
\(569\) | −15.8543 | −0.664649 | −0.332324 | − | 0.943165i | \(-0.607833\pi\) | ||||
−0.332324 | + | 0.943165i | \(0.607833\pi\) | |||||||
\(570\) | −23.1102 | −0.967979 | ||||||||
\(571\) | 9.65382 | 0.404000 | 0.202000 | − | 0.979386i | \(-0.435256\pi\) | ||||
0.202000 | + | 0.979386i | \(0.435256\pi\) | |||||||
\(572\) | 5.21308 | 0.217970 | ||||||||
\(573\) | −16.0338 | −0.669821 | ||||||||
\(574\) | −31.6887 | −1.32266 | ||||||||
\(575\) | −26.4350 | −1.10241 | ||||||||
\(576\) | 8.70080 | 0.362533 | ||||||||
\(577\) | 9.77777 | 0.407054 | 0.203527 | − | 0.979069i | \(-0.434760\pi\) | ||||
0.203527 | + | 0.979069i | \(0.434760\pi\) | |||||||
\(578\) | −1.17408 | −0.0488352 | ||||||||
\(579\) | −19.9539 | −0.829257 | ||||||||
\(580\) | −12.8914 | −0.535285 | ||||||||
\(581\) | 4.95238 | 0.205459 | ||||||||
\(582\) | 17.8962 | 0.741820 | ||||||||
\(583\) | −2.01486 | −0.0834471 | ||||||||
\(584\) | −43.1180 | −1.78423 | ||||||||
\(585\) | −16.6768 | −0.689503 | ||||||||
\(586\) | 33.7950 | 1.39606 | ||||||||
\(587\) | −18.0640 | −0.745582 | −0.372791 | − | 0.927915i | \(-0.621599\pi\) | ||||
−0.372791 | + | 0.927915i | \(0.621599\pi\) | |||||||
\(588\) | 1.47877 | 0.0609836 | ||||||||
\(589\) | −3.71166 | −0.152936 | ||||||||
\(590\) | −56.9705 | −2.34544 | ||||||||
\(591\) | −10.1361 | −0.416945 | ||||||||
\(592\) | 15.5476 | 0.639003 | ||||||||
\(593\) | −20.5894 | −0.845505 | −0.422753 | − | 0.906245i | \(-0.638936\pi\) | ||||
−0.422753 | + | 0.906245i | \(0.638936\pi\) | |||||||
\(594\) | 2.28432 | 0.0937266 | ||||||||
\(595\) | −11.8477 | −0.485707 | ||||||||
\(596\) | 3.34134 | 0.136866 | ||||||||
\(597\) | −16.8867 | −0.691128 | ||||||||
\(598\) | −13.4255 | −0.549007 | ||||||||
\(599\) | −45.5410 | −1.86076 | −0.930378 | − | 0.366603i | \(-0.880521\pi\) | ||||
−0.930378 | + | 0.366603i | \(0.880521\pi\) | |||||||
\(600\) | −30.6736 | −1.25224 | ||||||||
\(601\) | −32.4613 | −1.32412 | −0.662062 | − | 0.749449i | \(-0.730319\pi\) | ||||
−0.662062 | + | 0.749449i | \(0.730319\pi\) | |||||||
\(602\) | −18.7365 | −0.763644 | ||||||||
\(603\) | −7.84025 | −0.319280 | ||||||||
\(604\) | −9.05208 | −0.368324 | ||||||||
\(605\) | −27.9099 | −1.13470 | ||||||||
\(606\) | 4.64811 | 0.188816 | ||||||||
\(607\) | 15.4134 | 0.625609 | 0.312804 | − | 0.949818i | \(-0.398732\pi\) | ||||
0.312804 | + | 0.949818i | \(0.398732\pi\) | |||||||
\(608\) | 17.1597 | 0.695919 | ||||||||
\(609\) | −16.4196 | −0.665355 | ||||||||
\(610\) | −23.6499 | −0.957556 | ||||||||
\(611\) | −25.6625 | −1.03819 | ||||||||
\(612\) | 0.621542 | 0.0251243 | ||||||||
\(613\) | −38.6256 | −1.56007 | −0.780037 | − | 0.625734i | \(-0.784800\pi\) | ||||
−0.780037 | + | 0.625734i | \(0.784800\pi\) | |||||||
\(614\) | 6.60319 | 0.266483 | ||||||||
\(615\) | −34.0937 | −1.37479 | ||||||||
\(616\) | 18.3399 | 0.738934 | ||||||||
\(617\) | 16.0846 | 0.647540 | 0.323770 | − | 0.946136i | \(-0.395050\pi\) | ||||
0.323770 | + | 0.946136i | \(0.395050\pi\) | |||||||
\(618\) | 7.46898 | 0.300446 | ||||||||
\(619\) | −7.16318 | −0.287913 | −0.143956 | − | 0.989584i | \(-0.545982\pi\) | ||||
−0.143956 | + | 0.989584i | \(0.545982\pi\) | |||||||
\(620\) | −1.75401 | −0.0704427 | ||||||||
\(621\) | 2.65257 | 0.106444 | ||||||||
\(622\) | 14.5744 | 0.584378 | ||||||||
\(623\) | −7.27668 | −0.291534 | ||||||||
\(624\) | −10.2193 | −0.409101 | ||||||||
\(625\) | 24.4877 | 0.979509 | ||||||||
\(626\) | −1.12078 | −0.0447954 | ||||||||
\(627\) | 9.89956 | 0.395351 | ||||||||
\(628\) | −10.7335 | −0.428313 | ||||||||
\(629\) | 6.55851 | 0.261505 | ||||||||
\(630\) | −13.9101 | −0.554190 | ||||||||
\(631\) | 6.77064 | 0.269535 | 0.134767 | − | 0.990877i | \(-0.456971\pi\) | ||||
0.134767 | + | 0.990877i | \(0.456971\pi\) | |||||||
\(632\) | 3.07789 | 0.122432 | ||||||||
\(633\) | −26.1952 | −1.04117 | ||||||||
\(634\) | 4.91839 | 0.195334 | ||||||||
\(635\) | 11.5797 | 0.459525 | ||||||||
\(636\) | −0.643660 | −0.0255228 | ||||||||
\(637\) | −10.2564 | −0.406374 | ||||||||
\(638\) | −12.2472 | −0.484870 | ||||||||
\(639\) | 12.0605 | 0.477105 | ||||||||
\(640\) | −13.4254 | −0.530685 | ||||||||
\(641\) | 23.3188 | 0.921038 | 0.460519 | − | 0.887650i | \(-0.347663\pi\) | ||||
0.460519 | + | 0.887650i | \(0.347663\pi\) | |||||||
\(642\) | 9.58905 | 0.378449 | ||||||||
\(643\) | 0.529220 | 0.0208704 | 0.0104352 | − | 0.999946i | \(-0.496678\pi\) | ||||
0.0104352 | + | 0.999946i | \(0.496678\pi\) | |||||||
\(644\) | 5.04918 | 0.198966 | ||||||||
\(645\) | −20.1585 | −0.793741 | ||||||||
\(646\) | −5.97384 | −0.235038 | ||||||||
\(647\) | 11.0009 | 0.432488 | 0.216244 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216244 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(648\) | 3.07789 | 0.120911 | ||||||||
\(649\) | 24.4041 | 0.957946 | ||||||||
\(650\) | 50.4397 | 1.97841 | ||||||||
\(651\) | −2.23406 | −0.0875597 | ||||||||
\(652\) | −0.684613 | −0.0268115 | ||||||||
\(653\) | −5.25251 | −0.205547 | −0.102773 | − | 0.994705i | \(-0.532772\pi\) | ||||
−0.102773 | + | 0.994705i | \(0.532772\pi\) | |||||||
\(654\) | 21.1064 | 0.825327 | ||||||||
\(655\) | −44.0577 | −1.72148 | ||||||||
\(656\) | −20.8922 | −0.815703 | ||||||||
\(657\) | −14.0089 | −0.546540 | ||||||||
\(658\) | −21.4049 | −0.834450 | ||||||||
\(659\) | −19.4695 | −0.758423 | −0.379212 | − | 0.925310i | \(-0.623805\pi\) | ||||
−0.379212 | + | 0.925310i | \(0.623805\pi\) | |||||||
\(660\) | 4.67820 | 0.182099 | ||||||||
\(661\) | −3.62286 | −0.140913 | −0.0704565 | − | 0.997515i | \(-0.522446\pi\) | ||||
−0.0704565 | + | 0.997515i | \(0.522446\pi\) | |||||||
\(662\) | −7.35506 | −0.285862 | ||||||||
\(663\) | −4.31087 | −0.167420 | ||||||||
\(664\) | 4.97719 | 0.193153 | ||||||||
\(665\) | −60.2822 | −2.33764 | ||||||||
\(666\) | 7.70020 | 0.298377 | ||||||||
\(667\) | −14.2216 | −0.550661 | ||||||||
\(668\) | 8.42739 | 0.326066 | ||||||||
\(669\) | 14.8016 | 0.572261 | ||||||||
\(670\) | 35.6104 | 1.37575 | ||||||||
\(671\) | 10.1308 | 0.391094 | ||||||||
\(672\) | 10.3285 | 0.398430 | ||||||||
\(673\) | −25.9398 | −0.999907 | −0.499953 | − | 0.866052i | \(-0.666650\pi\) | ||||
−0.499953 | + | 0.866052i | \(0.666650\pi\) | |||||||
\(674\) | 11.3866 | 0.438597 | ||||||||
\(675\) | −9.96577 | −0.383583 | ||||||||
\(676\) | −3.47041 | −0.133477 | ||||||||
\(677\) | 29.0251 | 1.11553 | 0.557763 | − | 0.830000i | \(-0.311660\pi\) | ||||
0.557763 | + | 0.830000i | \(0.311660\pi\) | |||||||
\(678\) | −1.27054 | −0.0487948 | ||||||||
\(679\) | 46.6817 | 1.79148 | ||||||||
\(680\) | −11.9070 | −0.456613 | ||||||||
\(681\) | −12.5129 | −0.479495 | ||||||||
\(682\) | −1.66636 | −0.0638081 | ||||||||
\(683\) | 40.5109 | 1.55011 | 0.775053 | − | 0.631896i | \(-0.217723\pi\) | ||||
0.775053 | + | 0.631896i | \(0.217723\pi\) | |||||||
\(684\) | 3.16247 | 0.120920 | ||||||||
\(685\) | −24.9121 | −0.951841 | ||||||||
\(686\) | 16.6149 | 0.634358 | ||||||||
\(687\) | 26.3090 | 1.00375 | ||||||||
\(688\) | −12.3529 | −0.470949 | ||||||||
\(689\) | 4.46427 | 0.170075 | ||||||||
\(690\) | −12.0480 | −0.458658 | ||||||||
\(691\) | 32.0842 | 1.22054 | 0.610271 | − | 0.792193i | \(-0.291061\pi\) | ||||
0.610271 | + | 0.792193i | \(0.291061\pi\) | |||||||
\(692\) | −14.7512 | −0.560757 | ||||||||
\(693\) | 5.95857 | 0.226347 | ||||||||
\(694\) | −20.1332 | −0.764246 | ||||||||
\(695\) | −29.8912 | −1.13384 | ||||||||
\(696\) | −16.5019 | −0.625502 | ||||||||
\(697\) | −8.81303 | −0.333817 | ||||||||
\(698\) | −21.3362 | −0.807588 | ||||||||
\(699\) | 24.8250 | 0.938968 | ||||||||
\(700\) | −18.9699 | −0.716993 | ||||||||
\(701\) | 11.6041 | 0.438281 | 0.219141 | − | 0.975693i | \(-0.429675\pi\) | ||||
0.219141 | + | 0.975693i | \(0.429675\pi\) | |||||||
\(702\) | −5.06129 | −0.191026 | ||||||||
\(703\) | 33.3704 | 1.25859 | ||||||||
\(704\) | 16.9285 | 0.638017 | ||||||||
\(705\) | −23.0294 | −0.867339 | ||||||||
\(706\) | 29.4786 | 1.10944 | ||||||||
\(707\) | 12.1245 | 0.455987 | ||||||||
\(708\) | 7.79604 | 0.292993 | ||||||||
\(709\) | 37.5902 | 1.41173 | 0.705865 | − | 0.708346i | \(-0.250559\pi\) | ||||
0.705865 | + | 0.708346i | \(0.250559\pi\) | |||||||
\(710\) | −54.7786 | −2.05581 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −7.31314 | −0.274071 | ||||||||
\(713\) | −1.93499 | −0.0724661 | ||||||||
\(714\) | −3.59567 | −0.134565 | ||||||||
\(715\) | −32.4469 | −1.21345 | ||||||||
\(716\) | 1.21920 | 0.0455638 | ||||||||
\(717\) | 18.5884 | 0.694198 | ||||||||
\(718\) | 26.9274 | 1.00492 | ||||||||
\(719\) | 11.3046 | 0.421590 | 0.210795 | − | 0.977530i | \(-0.432395\pi\) | ||||
0.210795 | + | 0.977530i | \(0.432395\pi\) | |||||||
\(720\) | −9.17082 | −0.341776 | ||||||||
\(721\) | 19.4826 | 0.725571 | ||||||||
\(722\) | −8.08810 | −0.301008 | ||||||||
\(723\) | −5.15833 | −0.191840 | ||||||||
\(724\) | 15.8257 | 0.588159 | ||||||||
\(725\) | 53.4306 | 1.98436 | ||||||||
\(726\) | −8.47043 | −0.314367 | ||||||||
\(727\) | −39.3354 | −1.45887 | −0.729434 | − | 0.684051i | \(-0.760217\pi\) | ||||
−0.729434 | + | 0.684051i | \(0.760217\pi\) | |||||||
\(728\) | −40.6351 | −1.50604 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 63.6284 | 2.35499 | ||||||||
\(731\) | −5.21086 | −0.192731 | ||||||||
\(732\) | 3.23633 | 0.119618 | ||||||||
\(733\) | 19.6713 | 0.726576 | 0.363288 | − | 0.931677i | \(-0.381654\pi\) | ||||
0.363288 | + | 0.931677i | \(0.381654\pi\) | |||||||
\(734\) | −34.3184 | −1.26672 | ||||||||
\(735\) | −9.20409 | −0.339498 | ||||||||
\(736\) | 8.94585 | 0.329748 | ||||||||
\(737\) | −15.2542 | −0.561896 | ||||||||
\(738\) | −10.3472 | −0.380885 | ||||||||
\(739\) | 48.7842 | 1.79456 | 0.897278 | − | 0.441466i | \(-0.145541\pi\) | ||||
0.897278 | + | 0.441466i | \(0.145541\pi\) | |||||||
\(740\) | 15.7698 | 0.579708 | ||||||||
\(741\) | −21.9342 | −0.805772 | ||||||||
\(742\) | 3.72362 | 0.136699 | ||||||||
\(743\) | 1.75663 | 0.0644447 | 0.0322223 | − | 0.999481i | \(-0.489742\pi\) | ||||
0.0322223 | + | 0.999481i | \(0.489742\pi\) | |||||||
\(744\) | −2.24525 | −0.0823150 | ||||||||
\(745\) | −20.7969 | −0.761941 | ||||||||
\(746\) | 12.6592 | 0.463486 | ||||||||
\(747\) | 1.61708 | 0.0591658 | ||||||||
\(748\) | 1.20929 | 0.0442159 | ||||||||
\(749\) | 25.0128 | 0.913946 | ||||||||
\(750\) | 22.5545 | 0.823574 | ||||||||
\(751\) | 36.6840 | 1.33862 | 0.669309 | − | 0.742984i | \(-0.266590\pi\) | ||||
0.669309 | + | 0.742984i | \(0.266590\pi\) | |||||||
\(752\) | −14.1121 | −0.514616 | ||||||||
\(753\) | −27.7239 | −1.01031 | ||||||||
\(754\) | 27.1357 | 0.988223 | ||||||||
\(755\) | 56.3414 | 2.05047 | ||||||||
\(756\) | 1.90350 | 0.0692297 | ||||||||
\(757\) | 7.30491 | 0.265501 | 0.132751 | − | 0.991149i | \(-0.457619\pi\) | ||||
0.132751 | + | 0.991149i | \(0.457619\pi\) | |||||||
\(758\) | −7.65477 | −0.278034 | ||||||||
\(759\) | 5.16092 | 0.187329 | ||||||||
\(760\) | −60.5843 | −2.19762 | ||||||||
\(761\) | 40.6772 | 1.47455 | 0.737274 | − | 0.675594i | \(-0.236113\pi\) | ||||
0.737274 | + | 0.675594i | \(0.236113\pi\) | |||||||
\(762\) | 3.51433 | 0.127311 | ||||||||
\(763\) | 55.0555 | 1.99314 | ||||||||
\(764\) | −9.96566 | −0.360545 | ||||||||
\(765\) | −3.86856 | −0.139868 | ||||||||
\(766\) | 7.44975 | 0.269170 | ||||||||
\(767\) | −54.0715 | −1.95241 | ||||||||
\(768\) | 13.3271 | 0.480900 | ||||||||
\(769\) | −45.8801 | −1.65448 | −0.827239 | − | 0.561851i | \(-0.810089\pi\) | ||||
−0.827239 | + | 0.561851i | \(0.810089\pi\) | |||||||
\(770\) | −27.0638 | −0.975311 | ||||||||
\(771\) | −22.5261 | −0.811257 | ||||||||
\(772\) | −12.4022 | −0.446365 | ||||||||
\(773\) | −31.0341 | −1.11622 | −0.558109 | − | 0.829768i | \(-0.688473\pi\) | ||||
−0.558109 | + | 0.829768i | \(0.688473\pi\) | |||||||
\(774\) | −6.11795 | −0.219905 | ||||||||
\(775\) | 7.26981 | 0.261139 | ||||||||
\(776\) | 46.9156 | 1.68417 | ||||||||
\(777\) | 20.0858 | 0.720572 | ||||||||
\(778\) | −27.4059 | −0.982548 | ||||||||
\(779\) | −44.8417 | −1.60662 | ||||||||
\(780\) | −10.3654 | −0.371139 | ||||||||
\(781\) | 23.4652 | 0.839651 | ||||||||
\(782\) | −3.11433 | −0.111368 | ||||||||
\(783\) | −5.36141 | −0.191601 | ||||||||
\(784\) | −5.64014 | −0.201434 | ||||||||
\(785\) | 66.8068 | 2.38444 | ||||||||
\(786\) | −13.3712 | −0.476934 | ||||||||
\(787\) | −17.3722 | −0.619253 | −0.309627 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309627 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(788\) | −6.30003 | −0.224429 | ||||||||
\(789\) | 8.77673 | 0.312460 | ||||||||
\(790\) | −4.54199 | −0.161597 | ||||||||
\(791\) | −3.31417 | −0.117838 | ||||||||
\(792\) | 5.98843 | 0.212790 | ||||||||
\(793\) | −22.4464 | −0.797096 | ||||||||
\(794\) | 15.0363 | 0.533618 | ||||||||
\(795\) | 4.00623 | 0.142086 | ||||||||
\(796\) | −10.4958 | −0.372014 | ||||||||
\(797\) | 17.3491 | 0.614538 | 0.307269 | − | 0.951623i | \(-0.400585\pi\) | ||||
0.307269 | + | 0.951623i | \(0.400585\pi\) | |||||||
\(798\) | −18.2952 | −0.647642 | ||||||||
\(799\) | −5.95297 | −0.210601 | ||||||||
\(800\) | −33.6097 | −1.18828 | ||||||||
\(801\) | −2.37602 | −0.0839526 | ||||||||
\(802\) | 10.5798 | 0.373585 | ||||||||
\(803\) | −27.2561 | −0.961847 | ||||||||
\(804\) | −4.87304 | −0.171859 | ||||||||
\(805\) | −31.4268 | −1.10765 | ||||||||
\(806\) | 3.69210 | 0.130049 | ||||||||
\(807\) | 5.93332 | 0.208863 | ||||||||
\(808\) | 12.1852 | 0.428674 | ||||||||
\(809\) | −12.7366 | −0.447794 | −0.223897 | − | 0.974613i | \(-0.571878\pi\) | ||||
−0.223897 | + | 0.974613i | \(0.571878\pi\) | |||||||
\(810\) | −4.54199 | −0.159589 | ||||||||
\(811\) | −6.71379 | −0.235753 | −0.117876 | − | 0.993028i | \(-0.537609\pi\) | ||||
−0.117876 | + | 0.993028i | \(0.537609\pi\) | |||||||
\(812\) | −10.2055 | −0.358141 | ||||||||
\(813\) | 5.77322 | 0.202476 | ||||||||
\(814\) | 14.9817 | 0.525109 | ||||||||
\(815\) | 4.26112 | 0.149261 | ||||||||
\(816\) | −2.37060 | −0.0829877 | ||||||||
\(817\) | −26.5134 | −0.927588 | ||||||||
\(818\) | −21.1143 | −0.738244 | ||||||||
\(819\) | −13.2022 | −0.461323 | ||||||||
\(820\) | −21.1907 | −0.740011 | ||||||||
\(821\) | −56.4520 | −1.97019 | −0.985094 | − | 0.172018i | \(-0.944971\pi\) | ||||
−0.985094 | + | 0.172018i | \(0.944971\pi\) | |||||||
\(822\) | −7.56061 | −0.263707 | ||||||||
\(823\) | 36.6848 | 1.27875 | 0.639375 | − | 0.768895i | \(-0.279193\pi\) | ||||
0.639375 | + | 0.768895i | \(0.279193\pi\) | |||||||
\(824\) | 19.5802 | 0.682110 | ||||||||
\(825\) | −19.3897 | −0.675061 | ||||||||
\(826\) | −45.1007 | −1.56926 | ||||||||
\(827\) | 3.03726 | 0.105616 | 0.0528080 | − | 0.998605i | \(-0.483183\pi\) | ||||
0.0528080 | + | 0.998605i | \(0.483183\pi\) | |||||||
\(828\) | 1.64869 | 0.0572958 | ||||||||
\(829\) | 22.7431 | 0.789900 | 0.394950 | − | 0.918703i | \(-0.370762\pi\) | ||||
0.394950 | + | 0.918703i | \(0.370762\pi\) | |||||||
\(830\) | −7.34475 | −0.254940 | ||||||||
\(831\) | −21.3232 | −0.739693 | ||||||||
\(832\) | −37.5080 | −1.30036 | ||||||||
\(833\) | −2.37920 | −0.0824344 | ||||||||
\(834\) | −9.07173 | −0.314128 | ||||||||
\(835\) | −52.4532 | −1.81522 | ||||||||
\(836\) | 6.15299 | 0.212806 | ||||||||
\(837\) | −0.729477 | −0.0252144 | ||||||||
\(838\) | 8.61372 | 0.297556 | ||||||||
\(839\) | −15.5849 | −0.538049 | −0.269025 | − | 0.963133i | \(-0.586701\pi\) | ||||
−0.269025 | + | 0.963133i | \(0.586701\pi\) | |||||||
\(840\) | −36.4658 | −1.25819 | ||||||||
\(841\) | −0.255231 | −0.00880106 | ||||||||
\(842\) | 2.00972 | 0.0692594 | ||||||||
\(843\) | 26.4249 | 0.910124 | ||||||||
\(844\) | −16.2814 | −0.560430 | ||||||||
\(845\) | 21.6003 | 0.743074 | ||||||||
\(846\) | −6.98925 | −0.240295 | ||||||||
\(847\) | −22.0949 | −0.759189 | ||||||||
\(848\) | 2.45496 | 0.0843038 | ||||||||
\(849\) | −12.9095 | −0.443052 | ||||||||
\(850\) | 11.7006 | 0.401327 | ||||||||
\(851\) | 17.3969 | 0.596359 | ||||||||
\(852\) | 7.49609 | 0.256812 | ||||||||
\(853\) | 6.94574 | 0.237818 | 0.118909 | − | 0.992905i | \(-0.462060\pi\) | ||||
0.118909 | + | 0.992905i | \(0.462060\pi\) | |||||||
\(854\) | −18.7224 | −0.640669 | ||||||||
\(855\) | −19.6837 | −0.673168 | ||||||||
\(856\) | 25.1381 | 0.859202 | ||||||||
\(857\) | 30.2494 | 1.03330 | 0.516650 | − | 0.856196i | \(-0.327179\pi\) | ||||
0.516650 | + | 0.856196i | \(0.327179\pi\) | |||||||
\(858\) | −9.84738 | −0.336184 | ||||||||
\(859\) | 25.6789 | 0.876152 | 0.438076 | − | 0.898938i | \(-0.355660\pi\) | ||||
0.438076 | + | 0.898938i | \(0.355660\pi\) | |||||||
\(860\) | −12.5294 | −0.427248 | ||||||||
\(861\) | −26.9903 | −0.919827 | ||||||||
\(862\) | −38.5644 | −1.31351 | ||||||||
\(863\) | −2.72120 | −0.0926308 | −0.0463154 | − | 0.998927i | \(-0.514748\pi\) | ||||
−0.0463154 | + | 0.998927i | \(0.514748\pi\) | |||||||
\(864\) | 3.37252 | 0.114735 | ||||||||
\(865\) | 91.8137 | 3.12176 | ||||||||
\(866\) | −37.5013 | −1.27435 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −1.38856 | −0.0471308 | ||||||||
\(869\) | 1.94563 | 0.0660008 | ||||||||
\(870\) | 24.3515 | 0.825593 | ||||||||
\(871\) | 33.7983 | 1.14521 | ||||||||
\(872\) | 55.3314 | 1.87376 | ||||||||
\(873\) | 15.2428 | 0.515889 | ||||||||
\(874\) | −15.8461 | −0.536001 | ||||||||
\(875\) | 58.8328 | 1.98891 | ||||||||
\(876\) | −8.70713 | −0.294187 | ||||||||
\(877\) | −46.0784 | −1.55596 | −0.777979 | − | 0.628291i | \(-0.783755\pi\) | ||||
−0.777979 | + | 0.628291i | \(0.783755\pi\) | |||||||
\(878\) | −36.4999 | −1.23181 | ||||||||
\(879\) | 28.7843 | 0.970869 | ||||||||
\(880\) | −17.8430 | −0.601487 | ||||||||
\(881\) | −15.5276 | −0.523139 | −0.261570 | − | 0.965185i | \(-0.584240\pi\) | ||||
−0.261570 | + | 0.965185i | \(0.584240\pi\) | |||||||
\(882\) | −2.79337 | −0.0940576 | ||||||||
\(883\) | 37.3026 | 1.25533 | 0.627666 | − | 0.778483i | \(-0.284010\pi\) | ||||
0.627666 | + | 0.778483i | \(0.284010\pi\) | |||||||
\(884\) | −2.67938 | −0.0901174 | ||||||||
\(885\) | −48.5236 | −1.63110 | ||||||||
\(886\) | −35.4921 | −1.19238 | ||||||||
\(887\) | 51.0006 | 1.71243 | 0.856216 | − | 0.516618i | \(-0.172809\pi\) | ||||
0.856216 | + | 0.516618i | \(0.172809\pi\) | |||||||
\(888\) | 20.1864 | 0.677411 | ||||||||
\(889\) | 9.16704 | 0.307453 | ||||||||
\(890\) | 10.7919 | 0.361744 | ||||||||
\(891\) | 1.94563 | 0.0651809 | ||||||||
\(892\) | 9.19978 | 0.308031 | ||||||||
\(893\) | −30.2894 | −1.01360 | ||||||||
\(894\) | −6.31171 | −0.211095 | ||||||||
\(895\) | −7.58850 | −0.253656 | ||||||||
\(896\) | −10.6282 | −0.355064 | ||||||||
\(897\) | −11.4349 | −0.381800 | ||||||||
\(898\) | 28.3266 | 0.945272 | ||||||||
\(899\) | 3.91103 | 0.130440 | ||||||||
\(900\) | −6.19414 | −0.206471 | ||||||||
\(901\) | 1.03559 | 0.0345004 | ||||||||
\(902\) | −20.1317 | −0.670313 | ||||||||
\(903\) | −15.9585 | −0.531066 | ||||||||
\(904\) | −3.33077 | −0.110780 | ||||||||
\(905\) | −98.5016 | −3.27430 | ||||||||
\(906\) | 17.0992 | 0.568082 | ||||||||
\(907\) | 16.9256 | 0.562006 | 0.281003 | − | 0.959707i | \(-0.409333\pi\) | ||||
0.281003 | + | 0.959707i | \(0.409333\pi\) | |||||||
\(908\) | −7.77728 | −0.258098 | ||||||||
\(909\) | 3.95894 | 0.131310 | ||||||||
\(910\) | 59.9644 | 1.98780 | ||||||||
\(911\) | −29.6254 | −0.981532 | −0.490766 | − | 0.871291i | \(-0.663283\pi\) | ||||
−0.490766 | + | 0.871291i | \(0.663283\pi\) | |||||||
\(912\) | −12.0619 | −0.399409 | ||||||||
\(913\) | 3.14623 | 0.104125 | ||||||||
\(914\) | 41.2935 | 1.36587 | ||||||||
\(915\) | −20.1434 | −0.665920 | ||||||||
\(916\) | 16.3522 | 0.540291 | ||||||||
\(917\) | −34.8783 | −1.15178 | ||||||||
\(918\) | −1.17408 | −0.0387503 | ||||||||
\(919\) | −10.8176 | −0.356841 | −0.178421 | − | 0.983954i | \(-0.557099\pi\) | ||||
−0.178421 | + | 0.983954i | \(0.557099\pi\) | |||||||
\(920\) | −31.5843 | −1.04130 | ||||||||
\(921\) | 5.62415 | 0.185322 | ||||||||
\(922\) | −8.19791 | −0.269984 | ||||||||
\(923\) | −51.9911 | −1.71131 | ||||||||
\(924\) | 3.70350 | 0.121836 | ||||||||
\(925\) | −65.3606 | −2.14904 | ||||||||
\(926\) | 34.6540 | 1.13880 | ||||||||
\(927\) | 6.36157 | 0.208941 | ||||||||
\(928\) | −18.0815 | −0.593553 | ||||||||
\(929\) | −6.84401 | −0.224545 | −0.112272 | − | 0.993677i | \(-0.535813\pi\) | ||||
−0.112272 | + | 0.993677i | \(0.535813\pi\) | |||||||
\(930\) | 3.31328 | 0.108647 | ||||||||
\(931\) | −12.1056 | −0.396746 | ||||||||
\(932\) | 15.4298 | 0.505419 | ||||||||
\(933\) | 12.4134 | 0.406398 | ||||||||
\(934\) | 29.9195 | 0.978995 | ||||||||
\(935\) | −7.52677 | −0.246152 | ||||||||
\(936\) | −13.2684 | −0.433691 | ||||||||
\(937\) | −16.8134 | −0.549270 | −0.274635 | − | 0.961549i | \(-0.588557\pi\) | ||||
−0.274635 | + | 0.961549i | \(0.588557\pi\) | |||||||
\(938\) | 28.1910 | 0.920467 | ||||||||
\(939\) | −0.954605 | −0.0311524 | ||||||||
\(940\) | −14.3138 | −0.466863 | ||||||||
\(941\) | 17.7542 | 0.578769 | 0.289385 | − | 0.957213i | \(-0.406549\pi\) | ||||
0.289385 | + | 0.957213i | \(0.406549\pi\) | |||||||
\(942\) | 20.2753 | 0.660606 | ||||||||
\(943\) | −23.3772 | −0.761267 | ||||||||
\(944\) | −29.7346 | −0.967780 | ||||||||
\(945\) | −11.8477 | −0.385404 | ||||||||
\(946\) | −11.9032 | −0.387008 | ||||||||
\(947\) | −35.6574 | −1.15871 | −0.579355 | − | 0.815075i | \(-0.696696\pi\) | ||||
−0.579355 | + | 0.815075i | \(0.696696\pi\) | |||||||
\(948\) | 0.621542 | 0.0201867 | ||||||||
\(949\) | 60.3906 | 1.96036 | ||||||||
\(950\) | 59.5339 | 1.93154 | ||||||||
\(951\) | 4.18916 | 0.135843 | ||||||||
\(952\) | −9.42620 | −0.305505 | ||||||||
\(953\) | 15.8288 | 0.512746 | 0.256373 | − | 0.966578i | \(-0.417472\pi\) | ||||
0.256373 | + | 0.966578i | \(0.417472\pi\) | |||||||
\(954\) | 1.21586 | 0.0393649 | ||||||||
\(955\) | 62.0277 | 2.00717 | ||||||||
\(956\) | 11.5535 | 0.373667 | ||||||||
\(957\) | −10.4313 | −0.337196 | ||||||||
\(958\) | −40.8390 | −1.31945 | ||||||||
\(959\) | −19.7216 | −0.636845 | ||||||||
\(960\) | −33.6596 | −1.08636 | ||||||||
\(961\) | −30.4679 | −0.982834 | ||||||||
\(962\) | −33.1945 | −1.07023 | ||||||||
\(963\) | 8.16730 | 0.263188 | ||||||||
\(964\) | −3.20612 | −0.103262 | ||||||||
\(965\) | 77.1930 | 2.48493 | ||||||||
\(966\) | −9.53778 | −0.306873 | ||||||||
\(967\) | 15.8624 | 0.510102 | 0.255051 | − | 0.966928i | \(-0.417908\pi\) | ||||
0.255051 | + | 0.966928i | \(0.417908\pi\) | |||||||
\(968\) | −22.2056 | −0.713715 | ||||||||
\(969\) | −5.08811 | −0.163454 | ||||||||
\(970\) | −69.2325 | −2.22292 | ||||||||
\(971\) | −1.91689 | −0.0615161 | −0.0307580 | − | 0.999527i | \(-0.509792\pi\) | ||||
−0.0307580 | + | 0.999527i | \(0.509792\pi\) | |||||||
\(972\) | 0.621542 | 0.0199360 | ||||||||
\(973\) | −23.6633 | −0.758612 | ||||||||
\(974\) | 40.7032 | 1.30421 | ||||||||
\(975\) | 42.9611 | 1.37586 | ||||||||
\(976\) | −12.3436 | −0.395109 | ||||||||
\(977\) | −20.1733 | −0.645400 | −0.322700 | − | 0.946501i | \(-0.604590\pi\) | ||||
−0.322700 | + | 0.946501i | \(0.604590\pi\) | |||||||
\(978\) | 1.29322 | 0.0413525 | ||||||||
\(979\) | −4.62285 | −0.147747 | ||||||||
\(980\) | −5.72072 | −0.182742 | ||||||||
\(981\) | 17.9770 | 0.573963 | ||||||||
\(982\) | 0.553801 | 0.0176725 | ||||||||
\(983\) | −42.6481 | −1.36026 | −0.680132 | − | 0.733090i | \(-0.738078\pi\) | ||||
−0.680132 | + | 0.733090i | \(0.738078\pi\) | |||||||
\(984\) | −27.1256 | −0.864731 | ||||||||
\(985\) | 39.2122 | 1.24941 | ||||||||
\(986\) | 6.29472 | 0.200465 | ||||||||
\(987\) | −18.2313 | −0.580307 | ||||||||
\(988\) | −13.6330 | −0.433724 | ||||||||
\(989\) | −13.8222 | −0.439520 | ||||||||
\(990\) | −8.83702 | −0.280859 | ||||||||
\(991\) | −13.6091 | −0.432309 | −0.216154 | − | 0.976359i | \(-0.569351\pi\) | ||||
−0.216154 | + | 0.976359i | \(0.569351\pi\) | |||||||
\(992\) | −2.46017 | −0.0781106 | ||||||||
\(993\) | −6.26454 | −0.198799 | ||||||||
\(994\) | −43.3655 | −1.37547 | ||||||||
\(995\) | 65.3274 | 2.07102 | ||||||||
\(996\) | 1.00508 | 0.0318472 | ||||||||
\(997\) | 11.7369 | 0.371712 | 0.185856 | − | 0.982577i | \(-0.440494\pi\) | ||||
0.185856 | + | 0.982577i | \(0.440494\pi\) | |||||||
\(998\) | 14.8570 | 0.470291 | ||||||||
\(999\) | 6.55851 | 0.207502 |
(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 | 4029.2.a.l.1.12 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.12 | ✓ | 32 | 1.1 | even | 1 | trivial |