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: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73737 | −1.22850 | −0.614251 | − | 0.789110i | \(-0.710542\pi\) | ||||
−0.614251 | + | 0.789110i | \(0.710542\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.01844 | 0.509219 | ||||||||
\(5\) | 3.91288 | 1.74989 | 0.874947 | − | 0.484219i | \(-0.160896\pi\) | ||||
0.874947 | + | 0.484219i | \(0.160896\pi\) | |||||||
\(6\) | −1.73737 | −0.709276 | ||||||||
\(7\) | 2.21072 | 0.835574 | 0.417787 | − | 0.908545i | \(-0.362806\pi\) | ||||
0.417787 | + | 0.908545i | \(0.362806\pi\) | |||||||
\(8\) | 1.70533 | 0.602926 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.79810 | −2.14975 | ||||||||
\(11\) | −0.251112 | −0.0757132 | −0.0378566 | − | 0.999283i | \(-0.512053\pi\) | ||||
−0.0378566 | + | 0.999283i | \(0.512053\pi\) | |||||||
\(12\) | 1.01844 | 0.293998 | ||||||||
\(13\) | 1.93652 | 0.537095 | 0.268547 | − | 0.963267i | \(-0.413456\pi\) | ||||
0.268547 | + | 0.963267i | \(0.413456\pi\) | |||||||
\(14\) | −3.84083 | −1.02650 | ||||||||
\(15\) | 3.91288 | 1.01030 | ||||||||
\(16\) | −4.99966 | −1.24992 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.73737 | −0.409501 | ||||||||
\(19\) | 1.08362 | 0.248600 | 0.124300 | − | 0.992245i | \(-0.460331\pi\) | ||||
0.124300 | + | 0.992245i | \(0.460331\pi\) | |||||||
\(20\) | 3.98503 | 0.891079 | ||||||||
\(21\) | 2.21072 | 0.482419 | ||||||||
\(22\) | 0.436274 | 0.0930139 | ||||||||
\(23\) | −0.204447 | −0.0426302 | −0.0213151 | − | 0.999773i | \(-0.506785\pi\) | ||||
−0.0213151 | + | 0.999773i | \(0.506785\pi\) | |||||||
\(24\) | 1.70533 | 0.348099 | ||||||||
\(25\) | 10.3106 | 2.06213 | ||||||||
\(26\) | −3.36445 | −0.659822 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.25148 | 0.425490 | ||||||||
\(29\) | 0.225940 | 0.0419560 | 0.0209780 | − | 0.999780i | \(-0.493322\pi\) | ||||
0.0209780 | + | 0.999780i | \(0.493322\pi\) | |||||||
\(30\) | −6.79810 | −1.24116 | ||||||||
\(31\) | −2.46050 | −0.441919 | −0.220959 | − | 0.975283i | \(-0.570919\pi\) | ||||
−0.220959 | + | 0.975283i | \(0.570919\pi\) | |||||||
\(32\) | 5.27557 | 0.932598 | ||||||||
\(33\) | −0.251112 | −0.0437131 | ||||||||
\(34\) | 1.73737 | 0.297956 | ||||||||
\(35\) | 8.65029 | 1.46217 | ||||||||
\(36\) | 1.01844 | 0.169740 | ||||||||
\(37\) | −1.51392 | −0.248887 | −0.124443 | − | 0.992227i | \(-0.539714\pi\) | ||||
−0.124443 | + | 0.992227i | \(0.539714\pi\) | |||||||
\(38\) | −1.88265 | −0.305406 | ||||||||
\(39\) | 1.93652 | 0.310092 | ||||||||
\(40\) | 6.67276 | 1.05506 | ||||||||
\(41\) | −1.25010 | −0.195233 | −0.0976163 | − | 0.995224i | \(-0.531122\pi\) | ||||
−0.0976163 | + | 0.995224i | \(0.531122\pi\) | |||||||
\(42\) | −3.84083 | −0.592653 | ||||||||
\(43\) | −6.94797 | −1.05956 | −0.529778 | − | 0.848136i | \(-0.677725\pi\) | ||||
−0.529778 | + | 0.848136i | \(0.677725\pi\) | |||||||
\(44\) | −0.255742 | −0.0385546 | ||||||||
\(45\) | 3.91288 | 0.583298 | ||||||||
\(46\) | 0.355200 | 0.0523713 | ||||||||
\(47\) | −0.145293 | −0.0211931 | −0.0105966 | − | 0.999944i | \(-0.503373\pi\) | ||||
−0.0105966 | + | 0.999944i | \(0.503373\pi\) | |||||||
\(48\) | −4.99966 | −0.721639 | ||||||||
\(49\) | −2.11271 | −0.301816 | ||||||||
\(50\) | −17.9134 | −2.53333 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 1.97223 | 0.273499 | ||||||||
\(53\) | −5.50273 | −0.755858 | −0.377929 | − | 0.925835i | \(-0.623364\pi\) | ||||
−0.377929 | + | 0.925835i | \(0.623364\pi\) | |||||||
\(54\) | −1.73737 | −0.236425 | ||||||||
\(55\) | −0.982573 | −0.132490 | ||||||||
\(56\) | 3.77001 | 0.503789 | ||||||||
\(57\) | 1.08362 | 0.143529 | ||||||||
\(58\) | −0.392540 | −0.0515430 | ||||||||
\(59\) | 12.8788 | 1.67668 | 0.838339 | − | 0.545150i | \(-0.183527\pi\) | ||||
0.838339 | + | 0.545150i | \(0.183527\pi\) | |||||||
\(60\) | 3.98503 | 0.514465 | ||||||||
\(61\) | 15.2747 | 1.95573 | 0.977863 | − | 0.209245i | \(-0.0671005\pi\) | ||||
0.977863 | + | 0.209245i | \(0.0671005\pi\) | |||||||
\(62\) | 4.27479 | 0.542898 | ||||||||
\(63\) | 2.21072 | 0.278525 | ||||||||
\(64\) | 0.833725 | 0.104216 | ||||||||
\(65\) | 7.57738 | 0.939858 | ||||||||
\(66\) | 0.436274 | 0.0537016 | ||||||||
\(67\) | 12.3682 | 1.51102 | 0.755508 | − | 0.655139i | \(-0.227390\pi\) | ||||
0.755508 | + | 0.655139i | \(0.227390\pi\) | |||||||
\(68\) | −1.01844 | −0.123504 | ||||||||
\(69\) | −0.204447 | −0.0246126 | ||||||||
\(70\) | −15.0287 | −1.79627 | ||||||||
\(71\) | 6.57427 | 0.780222 | 0.390111 | − | 0.920768i | \(-0.372437\pi\) | ||||
0.390111 | + | 0.920768i | \(0.372437\pi\) | |||||||
\(72\) | 1.70533 | 0.200975 | ||||||||
\(73\) | 12.3282 | 1.44290 | 0.721452 | − | 0.692464i | \(-0.243475\pi\) | ||||
0.721452 | + | 0.692464i | \(0.243475\pi\) | |||||||
\(74\) | 2.63023 | 0.305758 | ||||||||
\(75\) | 10.3106 | 1.19057 | ||||||||
\(76\) | 1.10360 | 0.126592 | ||||||||
\(77\) | −0.555139 | −0.0632640 | ||||||||
\(78\) | −3.36445 | −0.380948 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | −19.5631 | −2.18722 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.17188 | 0.239844 | ||||||||
\(83\) | 0.945634 | 0.103797 | 0.0518984 | − | 0.998652i | \(-0.483473\pi\) | ||||
0.0518984 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(84\) | 2.25148 | 0.245657 | ||||||||
\(85\) | −3.91288 | −0.424412 | ||||||||
\(86\) | 12.0712 | 1.30167 | ||||||||
\(87\) | 0.225940 | 0.0242233 | ||||||||
\(88\) | −0.428230 | −0.0456495 | ||||||||
\(89\) | −1.35133 | −0.143241 | −0.0716206 | − | 0.997432i | \(-0.522817\pi\) | ||||
−0.0716206 | + | 0.997432i | \(0.522817\pi\) | |||||||
\(90\) | −6.79810 | −0.716583 | ||||||||
\(91\) | 4.28111 | 0.448782 | ||||||||
\(92\) | −0.208217 | −0.0217081 | ||||||||
\(93\) | −2.46050 | −0.255142 | ||||||||
\(94\) | 0.252426 | 0.0260358 | ||||||||
\(95\) | 4.24008 | 0.435024 | ||||||||
\(96\) | 5.27557 | 0.538436 | ||||||||
\(97\) | −13.8447 | −1.40571 | −0.702856 | − | 0.711332i | \(-0.748092\pi\) | ||||
−0.702856 | + | 0.711332i | \(0.748092\pi\) | |||||||
\(98\) | 3.67056 | 0.370782 | ||||||||
\(99\) | −0.251112 | −0.0252377 | ||||||||
\(100\) | 10.5007 | 1.05007 | ||||||||
\(101\) | 4.43251 | 0.441052 | 0.220526 | − | 0.975381i | \(-0.429223\pi\) | ||||
0.220526 | + | 0.975381i | \(0.429223\pi\) | |||||||
\(102\) | 1.73737 | 0.172025 | ||||||||
\(103\) | 11.6964 | 1.15248 | 0.576239 | − | 0.817281i | \(-0.304520\pi\) | ||||
0.576239 | + | 0.817281i | \(0.304520\pi\) | |||||||
\(104\) | 3.30241 | 0.323828 | ||||||||
\(105\) | 8.65029 | 0.844182 | ||||||||
\(106\) | 9.56025 | 0.928574 | ||||||||
\(107\) | −6.87350 | −0.664487 | −0.332243 | − | 0.943194i | \(-0.607806\pi\) | ||||
−0.332243 | + | 0.943194i | \(0.607806\pi\) | |||||||
\(108\) | 1.01844 | 0.0979992 | ||||||||
\(109\) | −13.4885 | −1.29196 | −0.645981 | − | 0.763354i | \(-0.723551\pi\) | ||||
−0.645981 | + | 0.763354i | \(0.723551\pi\) | |||||||
\(110\) | 1.70709 | 0.162764 | ||||||||
\(111\) | −1.51392 | −0.143695 | ||||||||
\(112\) | −11.0529 | −1.04440 | ||||||||
\(113\) | 9.32760 | 0.877466 | 0.438733 | − | 0.898617i | \(-0.355427\pi\) | ||||
0.438733 | + | 0.898617i | \(0.355427\pi\) | |||||||
\(114\) | −1.88265 | −0.176326 | ||||||||
\(115\) | −0.799978 | −0.0745983 | ||||||||
\(116\) | 0.230106 | 0.0213648 | ||||||||
\(117\) | 1.93652 | 0.179032 | ||||||||
\(118\) | −22.3752 | −2.05980 | ||||||||
\(119\) | −2.21072 | −0.202656 | ||||||||
\(120\) | 6.67276 | 0.609137 | ||||||||
\(121\) | −10.9369 | −0.994268 | ||||||||
\(122\) | −26.5378 | −2.40262 | ||||||||
\(123\) | −1.25010 | −0.112718 | ||||||||
\(124\) | −2.50587 | −0.225033 | ||||||||
\(125\) | 20.7799 | 1.85861 | ||||||||
\(126\) | −3.84083 | −0.342168 | ||||||||
\(127\) | 7.73496 | 0.686366 | 0.343183 | − | 0.939269i | \(-0.388495\pi\) | ||||
0.343183 | + | 0.939269i | \(0.388495\pi\) | |||||||
\(128\) | −11.9996 | −1.06063 | ||||||||
\(129\) | −6.94797 | −0.611735 | ||||||||
\(130\) | −13.1647 | −1.15462 | ||||||||
\(131\) | 6.07699 | 0.530949 | 0.265475 | − | 0.964118i | \(-0.414471\pi\) | ||||
0.265475 | + | 0.964118i | \(0.414471\pi\) | |||||||
\(132\) | −0.255742 | −0.0222595 | ||||||||
\(133\) | 2.39559 | 0.207724 | ||||||||
\(134\) | −21.4881 | −1.85629 | ||||||||
\(135\) | 3.91288 | 0.336767 | ||||||||
\(136\) | −1.70533 | −0.146231 | ||||||||
\(137\) | 6.48607 | 0.554143 | 0.277071 | − | 0.960849i | \(-0.410636\pi\) | ||||
0.277071 | + | 0.960849i | \(0.410636\pi\) | |||||||
\(138\) | 0.355200 | 0.0302366 | ||||||||
\(139\) | −4.23617 | −0.359307 | −0.179654 | − | 0.983730i | \(-0.557498\pi\) | ||||
−0.179654 | + | 0.983730i | \(0.557498\pi\) | |||||||
\(140\) | 8.80978 | 0.744562 | ||||||||
\(141\) | −0.145293 | −0.0122358 | ||||||||
\(142\) | −11.4219 | −0.958505 | ||||||||
\(143\) | −0.486285 | −0.0406652 | ||||||||
\(144\) | −4.99966 | −0.416638 | ||||||||
\(145\) | 0.884076 | 0.0734185 | ||||||||
\(146\) | −21.4186 | −1.77261 | ||||||||
\(147\) | −2.11271 | −0.174254 | ||||||||
\(148\) | −1.54183 | −0.126738 | ||||||||
\(149\) | −4.13335 | −0.338617 | −0.169309 | − | 0.985563i | \(-0.554154\pi\) | ||||
−0.169309 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(150\) | −17.9134 | −1.46262 | ||||||||
\(151\) | −16.5867 | −1.34981 | −0.674905 | − | 0.737905i | \(-0.735815\pi\) | ||||
−0.674905 | + | 0.737905i | \(0.735815\pi\) | |||||||
\(152\) | 1.84794 | 0.149887 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.964480 | 0.0777200 | ||||||||
\(155\) | −9.62764 | −0.773311 | ||||||||
\(156\) | 1.97223 | 0.157905 | ||||||||
\(157\) | −13.0467 | −1.04124 | −0.520620 | − | 0.853788i | \(-0.674299\pi\) | ||||
−0.520620 | + | 0.853788i | \(0.674299\pi\) | |||||||
\(158\) | 1.73737 | 0.138217 | ||||||||
\(159\) | −5.50273 | −0.436395 | ||||||||
\(160\) | 20.6427 | 1.63195 | ||||||||
\(161\) | −0.451976 | −0.0356207 | ||||||||
\(162\) | −1.73737 | −0.136500 | ||||||||
\(163\) | 21.7381 | 1.70266 | 0.851330 | − | 0.524630i | \(-0.175796\pi\) | ||||
0.851330 | + | 0.524630i | \(0.175796\pi\) | |||||||
\(164\) | −1.27315 | −0.0994162 | ||||||||
\(165\) | −0.982573 | −0.0764932 | ||||||||
\(166\) | −1.64291 | −0.127515 | ||||||||
\(167\) | −4.07053 | −0.314987 | −0.157493 | − | 0.987520i | \(-0.550341\pi\) | ||||
−0.157493 | + | 0.987520i | \(0.550341\pi\) | |||||||
\(168\) | 3.77001 | 0.290863 | ||||||||
\(169\) | −9.24988 | −0.711529 | ||||||||
\(170\) | 6.79810 | 0.521391 | ||||||||
\(171\) | 1.08362 | 0.0828666 | ||||||||
\(172\) | −7.07608 | −0.539546 | ||||||||
\(173\) | 14.9989 | 1.14035 | 0.570174 | − | 0.821524i | \(-0.306876\pi\) | ||||
0.570174 | + | 0.821524i | \(0.306876\pi\) | |||||||
\(174\) | −0.392540 | −0.0297584 | ||||||||
\(175\) | 22.7940 | 1.72306 | ||||||||
\(176\) | 1.25548 | 0.0946351 | ||||||||
\(177\) | 12.8788 | 0.968030 | ||||||||
\(178\) | 2.34776 | 0.175972 | ||||||||
\(179\) | 5.32282 | 0.397847 | 0.198923 | − | 0.980015i | \(-0.436256\pi\) | ||||
0.198923 | + | 0.980015i | \(0.436256\pi\) | |||||||
\(180\) | 3.98503 | 0.297026 | ||||||||
\(181\) | −22.9663 | −1.70707 | −0.853534 | − | 0.521036i | \(-0.825546\pi\) | ||||
−0.853534 | + | 0.521036i | \(0.825546\pi\) | |||||||
\(182\) | −7.43785 | −0.551330 | ||||||||
\(183\) | 15.2747 | 1.12914 | ||||||||
\(184\) | −0.348651 | −0.0257029 | ||||||||
\(185\) | −5.92378 | −0.435525 | ||||||||
\(186\) | 4.27479 | 0.313443 | ||||||||
\(187\) | 0.251112 | 0.0183632 | ||||||||
\(188\) | −0.147971 | −0.0107919 | ||||||||
\(189\) | 2.21072 | 0.160806 | ||||||||
\(190\) | −7.36658 | −0.534428 | ||||||||
\(191\) | 8.04363 | 0.582016 | 0.291008 | − | 0.956721i | \(-0.406009\pi\) | ||||
0.291008 | + | 0.956721i | \(0.406009\pi\) | |||||||
\(192\) | 0.833725 | 0.0601689 | ||||||||
\(193\) | 7.87585 | 0.566916 | 0.283458 | − | 0.958985i | \(-0.408518\pi\) | ||||
0.283458 | + | 0.958985i | \(0.408518\pi\) | |||||||
\(194\) | 24.0532 | 1.72692 | ||||||||
\(195\) | 7.57738 | 0.542628 | ||||||||
\(196\) | −2.15167 | −0.153691 | ||||||||
\(197\) | −7.23692 | −0.515609 | −0.257805 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257805 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(198\) | 0.436274 | 0.0310046 | ||||||||
\(199\) | −8.61742 | −0.610873 | −0.305437 | − | 0.952212i | \(-0.598802\pi\) | ||||
−0.305437 | + | 0.952212i | \(0.598802\pi\) | |||||||
\(200\) | 17.5831 | 1.24331 | ||||||||
\(201\) | 12.3682 | 0.872385 | ||||||||
\(202\) | −7.70089 | −0.541833 | ||||||||
\(203\) | 0.499490 | 0.0350573 | ||||||||
\(204\) | −1.01844 | −0.0713049 | ||||||||
\(205\) | −4.89149 | −0.341636 | ||||||||
\(206\) | −20.3209 | −1.41582 | ||||||||
\(207\) | −0.204447 | −0.0142101 | ||||||||
\(208\) | −9.68195 | −0.671323 | ||||||||
\(209\) | −0.272111 | −0.0188223 | ||||||||
\(210\) | −15.0287 | −1.03708 | ||||||||
\(211\) | −21.3932 | −1.47277 | −0.736385 | − | 0.676563i | \(-0.763469\pi\) | ||||
−0.736385 | + | 0.676563i | \(0.763469\pi\) | |||||||
\(212\) | −5.60419 | −0.384897 | ||||||||
\(213\) | 6.57427 | 0.450462 | ||||||||
\(214\) | 11.9418 | 0.816324 | ||||||||
\(215\) | −27.1866 | −1.85411 | ||||||||
\(216\) | 1.70533 | 0.116033 | ||||||||
\(217\) | −5.43948 | −0.369256 | ||||||||
\(218\) | 23.4344 | 1.58718 | ||||||||
\(219\) | 12.3282 | 0.833062 | ||||||||
\(220\) | −1.00069 | −0.0674665 | ||||||||
\(221\) | −1.93652 | −0.130265 | ||||||||
\(222\) | 2.63023 | 0.176529 | ||||||||
\(223\) | −10.5593 | −0.707101 | −0.353550 | − | 0.935416i | \(-0.615026\pi\) | ||||
−0.353550 | + | 0.935416i | \(0.615026\pi\) | |||||||
\(224\) | 11.6628 | 0.779255 | ||||||||
\(225\) | 10.3106 | 0.687376 | ||||||||
\(226\) | −16.2054 | −1.07797 | ||||||||
\(227\) | 7.61930 | 0.505711 | 0.252855 | − | 0.967504i | \(-0.418630\pi\) | ||||
0.252855 | + | 0.967504i | \(0.418630\pi\) | |||||||
\(228\) | 1.10360 | 0.0730878 | ||||||||
\(229\) | −24.1252 | −1.59424 | −0.797120 | − | 0.603821i | \(-0.793644\pi\) | ||||
−0.797120 | + | 0.603821i | \(0.793644\pi\) | |||||||
\(230\) | 1.38985 | 0.0916443 | ||||||||
\(231\) | −0.555139 | −0.0365255 | ||||||||
\(232\) | 0.385303 | 0.0252964 | ||||||||
\(233\) | −12.6213 | −0.826848 | −0.413424 | − | 0.910539i | \(-0.635667\pi\) | ||||
−0.413424 | + | 0.910539i | \(0.635667\pi\) | |||||||
\(234\) | −3.36445 | −0.219941 | ||||||||
\(235\) | −0.568513 | −0.0370857 | ||||||||
\(236\) | 13.1163 | 0.853796 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 3.84083 | 0.248964 | ||||||||
\(239\) | 27.0754 | 1.75136 | 0.875680 | − | 0.482892i | \(-0.160414\pi\) | ||||
0.875680 | + | 0.482892i | \(0.160414\pi\) | |||||||
\(240\) | −19.5631 | −1.26279 | ||||||||
\(241\) | −6.79346 | −0.437605 | −0.218802 | − | 0.975769i | \(-0.570215\pi\) | ||||
−0.218802 | + | 0.975769i | \(0.570215\pi\) | |||||||
\(242\) | 19.0015 | 1.22146 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 15.5563 | 0.995893 | ||||||||
\(245\) | −8.26680 | −0.528147 | ||||||||
\(246\) | 2.17188 | 0.138474 | ||||||||
\(247\) | 2.09846 | 0.133522 | ||||||||
\(248\) | −4.19597 | −0.266444 | ||||||||
\(249\) | 0.945634 | 0.0599271 | ||||||||
\(250\) | −36.1023 | −2.28331 | ||||||||
\(251\) | −11.5630 | −0.729848 | −0.364924 | − | 0.931037i | \(-0.618905\pi\) | ||||
−0.364924 | + | 0.931037i | \(0.618905\pi\) | |||||||
\(252\) | 2.25148 | 0.141830 | ||||||||
\(253\) | 0.0513392 | 0.00322767 | ||||||||
\(254\) | −13.4384 | −0.843203 | ||||||||
\(255\) | −3.91288 | −0.245034 | ||||||||
\(256\) | 19.1803 | 1.19877 | ||||||||
\(257\) | 4.91211 | 0.306409 | 0.153204 | − | 0.988195i | \(-0.451041\pi\) | ||||
0.153204 | + | 0.988195i | \(0.451041\pi\) | |||||||
\(258\) | 12.0712 | 0.751518 | ||||||||
\(259\) | −3.34685 | −0.207963 | ||||||||
\(260\) | 7.71709 | 0.478594 | ||||||||
\(261\) | 0.225940 | 0.0139853 | ||||||||
\(262\) | −10.5580 | −0.652273 | ||||||||
\(263\) | −2.63845 | −0.162694 | −0.0813470 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813470 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(264\) | −0.428230 | −0.0263557 | ||||||||
\(265\) | −21.5315 | −1.32267 | ||||||||
\(266\) | −4.16201 | −0.255189 | ||||||||
\(267\) | −1.35133 | −0.0827004 | ||||||||
\(268\) | 12.5962 | 0.769438 | ||||||||
\(269\) | −13.2737 | −0.809314 | −0.404657 | − | 0.914468i | \(-0.632609\pi\) | ||||
−0.404657 | + | 0.914468i | \(0.632609\pi\) | |||||||
\(270\) | −6.79810 | −0.413719 | ||||||||
\(271\) | −10.0676 | −0.611562 | −0.305781 | − | 0.952102i | \(-0.598918\pi\) | ||||
−0.305781 | + | 0.952102i | \(0.598918\pi\) | |||||||
\(272\) | 4.99966 | 0.303149 | ||||||||
\(273\) | 4.28111 | 0.259105 | ||||||||
\(274\) | −11.2687 | −0.680766 | ||||||||
\(275\) | −2.58913 | −0.156130 | ||||||||
\(276\) | −0.208217 | −0.0125332 | ||||||||
\(277\) | −8.38310 | −0.503692 | −0.251846 | − | 0.967767i | \(-0.581038\pi\) | ||||
−0.251846 | + | 0.967767i | \(0.581038\pi\) | |||||||
\(278\) | 7.35977 | 0.441410 | ||||||||
\(279\) | −2.46050 | −0.147306 | ||||||||
\(280\) | 14.7516 | 0.881577 | ||||||||
\(281\) | 30.8757 | 1.84189 | 0.920945 | − | 0.389692i | \(-0.127419\pi\) | ||||
0.920945 | + | 0.389692i | \(0.127419\pi\) | |||||||
\(282\) | 0.252426 | 0.0150318 | ||||||||
\(283\) | −4.62332 | −0.274828 | −0.137414 | − | 0.990514i | \(-0.543879\pi\) | ||||
−0.137414 | + | 0.990514i | \(0.543879\pi\) | |||||||
\(284\) | 6.69549 | 0.397304 | ||||||||
\(285\) | 4.24008 | 0.251161 | ||||||||
\(286\) | 0.844854 | 0.0499573 | ||||||||
\(287\) | −2.76362 | −0.163131 | ||||||||
\(288\) | 5.27557 | 0.310866 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.53596 | −0.0901949 | ||||||||
\(291\) | −13.8447 | −0.811588 | ||||||||
\(292\) | 12.5555 | 0.734755 | ||||||||
\(293\) | 20.4561 | 1.19506 | 0.597530 | − | 0.801846i | \(-0.296149\pi\) | ||||
0.597530 | + | 0.801846i | \(0.296149\pi\) | |||||||
\(294\) | 3.67056 | 0.214071 | ||||||||
\(295\) | 50.3932 | 2.93401 | ||||||||
\(296\) | −2.58173 | −0.150060 | ||||||||
\(297\) | −0.251112 | −0.0145710 | ||||||||
\(298\) | 7.18114 | 0.415993 | ||||||||
\(299\) | −0.395917 | −0.0228965 | ||||||||
\(300\) | 10.5007 | 0.606261 | ||||||||
\(301\) | −15.3600 | −0.885337 | ||||||||
\(302\) | 28.8172 | 1.65824 | ||||||||
\(303\) | 4.43251 | 0.254641 | ||||||||
\(304\) | −5.41774 | −0.310729 | ||||||||
\(305\) | 59.7681 | 3.42231 | ||||||||
\(306\) | 1.73737 | 0.0993186 | ||||||||
\(307\) | 26.1751 | 1.49389 | 0.746946 | − | 0.664885i | \(-0.231519\pi\) | ||||
0.746946 | + | 0.664885i | \(0.231519\pi\) | |||||||
\(308\) | −0.565375 | −0.0322152 | ||||||||
\(309\) | 11.6964 | 0.665384 | ||||||||
\(310\) | 16.7267 | 0.950015 | ||||||||
\(311\) | 32.0019 | 1.81466 | 0.907331 | − | 0.420417i | \(-0.138116\pi\) | ||||
0.907331 | + | 0.420417i | \(0.138116\pi\) | |||||||
\(312\) | 3.30241 | 0.186962 | ||||||||
\(313\) | −18.7322 | −1.05881 | −0.529404 | − | 0.848370i | \(-0.677584\pi\) | ||||
−0.529404 | + | 0.848370i | \(0.677584\pi\) | |||||||
\(314\) | 22.6669 | 1.27917 | ||||||||
\(315\) | 8.65029 | 0.487389 | ||||||||
\(316\) | −1.01844 | −0.0572916 | ||||||||
\(317\) | −20.1536 | −1.13194 | −0.565968 | − | 0.824427i | \(-0.691498\pi\) | ||||
−0.565968 | + | 0.824427i | \(0.691498\pi\) | |||||||
\(318\) | 9.56025 | 0.536112 | ||||||||
\(319\) | −0.0567363 | −0.00317662 | ||||||||
\(320\) | 3.26227 | 0.182366 | ||||||||
\(321\) | −6.87350 | −0.383642 | ||||||||
\(322\) | 0.785247 | 0.0437601 | ||||||||
\(323\) | −1.08362 | −0.0602943 | ||||||||
\(324\) | 1.01844 | 0.0565799 | ||||||||
\(325\) | 19.9668 | 1.10756 | ||||||||
\(326\) | −37.7670 | −2.09172 | ||||||||
\(327\) | −13.4885 | −0.745915 | ||||||||
\(328\) | −2.13183 | −0.117711 | ||||||||
\(329\) | −0.321201 | −0.0177084 | ||||||||
\(330\) | 1.70709 | 0.0939721 | ||||||||
\(331\) | −21.2552 | −1.16829 | −0.584145 | − | 0.811649i | \(-0.698570\pi\) | ||||
−0.584145 | + | 0.811649i | \(0.698570\pi\) | |||||||
\(332\) | 0.963070 | 0.0528553 | ||||||||
\(333\) | −1.51392 | −0.0829622 | ||||||||
\(334\) | 7.07199 | 0.386962 | ||||||||
\(335\) | 48.3953 | 2.64412 | ||||||||
\(336\) | −11.0529 | −0.602982 | ||||||||
\(337\) | −1.26935 | −0.0691460 | −0.0345730 | − | 0.999402i | \(-0.511007\pi\) | ||||
−0.0345730 | + | 0.999402i | \(0.511007\pi\) | |||||||
\(338\) | 16.0704 | 0.874116 | ||||||||
\(339\) | 9.32760 | 0.506605 | ||||||||
\(340\) | −3.98503 | −0.216118 | ||||||||
\(341\) | 0.617862 | 0.0334591 | ||||||||
\(342\) | −1.88265 | −0.101802 | ||||||||
\(343\) | −20.1457 | −1.08776 | ||||||||
\(344\) | −11.8486 | −0.638834 | ||||||||
\(345\) | −0.799978 | −0.0430694 | ||||||||
\(346\) | −26.0586 | −1.40092 | ||||||||
\(347\) | 15.6083 | 0.837900 | 0.418950 | − | 0.908009i | \(-0.362398\pi\) | ||||
0.418950 | + | 0.908009i | \(0.362398\pi\) | |||||||
\(348\) | 0.230106 | 0.0123350 | ||||||||
\(349\) | 17.1071 | 0.915720 | 0.457860 | − | 0.889024i | \(-0.348616\pi\) | ||||
0.457860 | + | 0.889024i | \(0.348616\pi\) | |||||||
\(350\) | −39.6014 | −2.11678 | ||||||||
\(351\) | 1.93652 | 0.103364 | ||||||||
\(352\) | −1.32476 | −0.0706100 | ||||||||
\(353\) | 14.2995 | 0.761084 | 0.380542 | − | 0.924764i | \(-0.375738\pi\) | ||||
0.380542 | + | 0.924764i | \(0.375738\pi\) | |||||||
\(354\) | −22.3752 | −1.18923 | ||||||||
\(355\) | 25.7243 | 1.36531 | ||||||||
\(356\) | −1.37625 | −0.0729411 | ||||||||
\(357\) | −2.21072 | −0.117004 | ||||||||
\(358\) | −9.24769 | −0.488756 | ||||||||
\(359\) | −7.56972 | −0.399514 | −0.199757 | − | 0.979845i | \(-0.564015\pi\) | ||||
−0.199757 | + | 0.979845i | \(0.564015\pi\) | |||||||
\(360\) | 6.67276 | 0.351685 | ||||||||
\(361\) | −17.8258 | −0.938198 | ||||||||
\(362\) | 39.9008 | 2.09714 | ||||||||
\(363\) | −10.9369 | −0.574041 | ||||||||
\(364\) | 4.36004 | 0.228528 | ||||||||
\(365\) | 48.2387 | 2.52493 | ||||||||
\(366\) | −26.5378 | −1.38715 | ||||||||
\(367\) | −7.29852 | −0.380980 | −0.190490 | − | 0.981689i | \(-0.561008\pi\) | ||||
−0.190490 | + | 0.981689i | \(0.561008\pi\) | |||||||
\(368\) | 1.02217 | 0.0532841 | ||||||||
\(369\) | −1.25010 | −0.0650776 | ||||||||
\(370\) | 10.2918 | 0.535044 | ||||||||
\(371\) | −12.1650 | −0.631575 | ||||||||
\(372\) | −2.50587 | −0.129923 | ||||||||
\(373\) | 12.9327 | 0.669631 | 0.334816 | − | 0.942284i | \(-0.391326\pi\) | ||||
0.334816 | + | 0.942284i | \(0.391326\pi\) | |||||||
\(374\) | −0.436274 | −0.0225592 | ||||||||
\(375\) | 20.7799 | 1.07307 | ||||||||
\(376\) | −0.247772 | −0.0127779 | ||||||||
\(377\) | 0.437538 | 0.0225343 | ||||||||
\(378\) | −3.84083 | −0.197551 | ||||||||
\(379\) | 0.752794 | 0.0386684 | 0.0193342 | − | 0.999813i | \(-0.493845\pi\) | ||||
0.0193342 | + | 0.999813i | \(0.493845\pi\) | |||||||
\(380\) | 4.31826 | 0.221522 | ||||||||
\(381\) | 7.73496 | 0.396274 | ||||||||
\(382\) | −13.9747 | −0.715009 | ||||||||
\(383\) | 6.43116 | 0.328617 | 0.164309 | − | 0.986409i | \(-0.447461\pi\) | ||||
0.164309 | + | 0.986409i | \(0.447461\pi\) | |||||||
\(384\) | −11.9996 | −0.612353 | ||||||||
\(385\) | −2.17219 | −0.110705 | ||||||||
\(386\) | −13.6832 | −0.696458 | ||||||||
\(387\) | −6.94797 | −0.353185 | ||||||||
\(388\) | −14.0999 | −0.715815 | ||||||||
\(389\) | 7.87471 | 0.399264 | 0.199632 | − | 0.979871i | \(-0.436025\pi\) | ||||
0.199632 | + | 0.979871i | \(0.436025\pi\) | |||||||
\(390\) | −13.1647 | −0.666619 | ||||||||
\(391\) | 0.204447 | 0.0103393 | ||||||||
\(392\) | −3.60288 | −0.181973 | ||||||||
\(393\) | 6.07699 | 0.306544 | ||||||||
\(394\) | 12.5732 | 0.633428 | ||||||||
\(395\) | −3.91288 | −0.196878 | ||||||||
\(396\) | −0.255742 | −0.0128515 | ||||||||
\(397\) | −22.3825 | −1.12335 | −0.561674 | − | 0.827359i | \(-0.689842\pi\) | ||||
−0.561674 | + | 0.827359i | \(0.689842\pi\) | |||||||
\(398\) | 14.9716 | 0.750459 | ||||||||
\(399\) | 2.39559 | 0.119929 | ||||||||
\(400\) | −51.5497 | −2.57749 | ||||||||
\(401\) | −24.4098 | −1.21897 | −0.609483 | − | 0.792799i | \(-0.708623\pi\) | ||||
−0.609483 | + | 0.792799i | \(0.708623\pi\) | |||||||
\(402\) | −21.4881 | −1.07173 | ||||||||
\(403\) | −4.76481 | −0.237352 | ||||||||
\(404\) | 4.51424 | 0.224592 | ||||||||
\(405\) | 3.91288 | 0.194433 | ||||||||
\(406\) | −0.867797 | −0.0430680 | ||||||||
\(407\) | 0.380164 | 0.0188440 | ||||||||
\(408\) | −1.70533 | −0.0844265 | ||||||||
\(409\) | −6.57814 | −0.325268 | −0.162634 | − | 0.986686i | \(-0.551999\pi\) | ||||
−0.162634 | + | 0.986686i | \(0.551999\pi\) | |||||||
\(410\) | 8.49830 | 0.419701 | ||||||||
\(411\) | 6.48607 | 0.319934 | ||||||||
\(412\) | 11.9120 | 0.586864 | ||||||||
\(413\) | 28.4714 | 1.40099 | ||||||||
\(414\) | 0.355200 | 0.0174571 | ||||||||
\(415\) | 3.70016 | 0.181633 | ||||||||
\(416\) | 10.2163 | 0.500893 | ||||||||
\(417\) | −4.23617 | −0.207446 | ||||||||
\(418\) | 0.472756 | 0.0231233 | ||||||||
\(419\) | 1.03889 | 0.0507532 | 0.0253766 | − | 0.999678i | \(-0.491922\pi\) | ||||
0.0253766 | + | 0.999678i | \(0.491922\pi\) | |||||||
\(420\) | 8.80978 | 0.429873 | ||||||||
\(421\) | 34.1288 | 1.66334 | 0.831668 | − | 0.555273i | \(-0.187386\pi\) | ||||
0.831668 | + | 0.555273i | \(0.187386\pi\) | |||||||
\(422\) | 37.1678 | 1.80930 | ||||||||
\(423\) | −0.145293 | −0.00706437 | ||||||||
\(424\) | −9.38398 | −0.455726 | ||||||||
\(425\) | −10.3106 | −0.500140 | ||||||||
\(426\) | −11.4219 | −0.553393 | ||||||||
\(427\) | 33.7681 | 1.63415 | ||||||||
\(428\) | −7.00024 | −0.338369 | ||||||||
\(429\) | −0.486285 | −0.0234780 | ||||||||
\(430\) | 47.2330 | 2.27778 | ||||||||
\(431\) | −12.3414 | −0.594464 | −0.297232 | − | 0.954805i | \(-0.596063\pi\) | ||||
−0.297232 | + | 0.954805i | \(0.596063\pi\) | |||||||
\(432\) | −4.99966 | −0.240546 | ||||||||
\(433\) | 9.62887 | 0.462734 | 0.231367 | − | 0.972867i | \(-0.425680\pi\) | ||||
0.231367 | + | 0.972867i | \(0.425680\pi\) | |||||||
\(434\) | 9.45036 | 0.453632 | ||||||||
\(435\) | 0.884076 | 0.0423882 | ||||||||
\(436\) | −13.7372 | −0.657891 | ||||||||
\(437\) | −0.221544 | −0.0105979 | ||||||||
\(438\) | −21.4186 | −1.02342 | ||||||||
\(439\) | 7.22772 | 0.344960 | 0.172480 | − | 0.985013i | \(-0.444822\pi\) | ||||
0.172480 | + | 0.985013i | \(0.444822\pi\) | |||||||
\(440\) | −1.67561 | −0.0798817 | ||||||||
\(441\) | −2.11271 | −0.100605 | ||||||||
\(442\) | 3.36445 | 0.160030 | ||||||||
\(443\) | −28.2387 | −1.34166 | −0.670830 | − | 0.741612i | \(-0.734062\pi\) | ||||
−0.670830 | + | 0.741612i | \(0.734062\pi\) | |||||||
\(444\) | −1.54183 | −0.0731721 | ||||||||
\(445\) | −5.28761 | −0.250657 | ||||||||
\(446\) | 18.3453 | 0.868675 | ||||||||
\(447\) | −4.13335 | −0.195501 | ||||||||
\(448\) | 1.84313 | 0.0870799 | ||||||||
\(449\) | 18.8981 | 0.891857 | 0.445929 | − | 0.895069i | \(-0.352874\pi\) | ||||
0.445929 | + | 0.895069i | \(0.352874\pi\) | |||||||
\(450\) | −17.9134 | −0.844444 | ||||||||
\(451\) | 0.313915 | 0.0147817 | ||||||||
\(452\) | 9.49958 | 0.446823 | ||||||||
\(453\) | −16.5867 | −0.779313 | ||||||||
\(454\) | −13.2375 | −0.621267 | ||||||||
\(455\) | 16.7515 | 0.785321 | ||||||||
\(456\) | 1.84794 | 0.0865375 | ||||||||
\(457\) | −4.80011 | −0.224540 | −0.112270 | − | 0.993678i | \(-0.535812\pi\) | ||||
−0.112270 | + | 0.993678i | \(0.535812\pi\) | |||||||
\(458\) | 41.9143 | 1.95853 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −0.814728 | −0.0379869 | ||||||||
\(461\) | −11.0763 | −0.515873 | −0.257937 | − | 0.966162i | \(-0.583043\pi\) | ||||
−0.257937 | + | 0.966162i | \(0.583043\pi\) | |||||||
\(462\) | 0.964480 | 0.0448717 | ||||||||
\(463\) | −20.9078 | −0.971667 | −0.485834 | − | 0.874051i | \(-0.661484\pi\) | ||||
−0.485834 | + | 0.874051i | \(0.661484\pi\) | |||||||
\(464\) | −1.12962 | −0.0524414 | ||||||||
\(465\) | −9.62764 | −0.446471 | ||||||||
\(466\) | 21.9278 | 1.01579 | ||||||||
\(467\) | 12.2481 | 0.566776 | 0.283388 | − | 0.959005i | \(-0.408542\pi\) | ||||
0.283388 | + | 0.959005i | \(0.408542\pi\) | |||||||
\(468\) | 1.97223 | 0.0911662 | ||||||||
\(469\) | 27.3426 | 1.26257 | ||||||||
\(470\) | 0.987714 | 0.0455599 | ||||||||
\(471\) | −13.0467 | −0.601160 | ||||||||
\(472\) | 21.9626 | 1.01091 | ||||||||
\(473\) | 1.74472 | 0.0802224 | ||||||||
\(474\) | 1.73737 | 0.0797998 | ||||||||
\(475\) | 11.1728 | 0.512645 | ||||||||
\(476\) | −2.25148 | −0.103196 | ||||||||
\(477\) | −5.50273 | −0.251953 | ||||||||
\(478\) | −47.0398 | −2.15155 | ||||||||
\(479\) | −5.73414 | −0.262000 | −0.131000 | − | 0.991382i | \(-0.541819\pi\) | ||||
−0.131000 | + | 0.991382i | \(0.541819\pi\) | |||||||
\(480\) | 20.6427 | 0.942205 | ||||||||
\(481\) | −2.93174 | −0.133676 | ||||||||
\(482\) | 11.8027 | 0.537599 | ||||||||
\(483\) | −0.451976 | −0.0205656 | ||||||||
\(484\) | −11.1386 | −0.506300 | ||||||||
\(485\) | −54.1725 | −2.45985 | ||||||||
\(486\) | −1.73737 | −0.0788085 | ||||||||
\(487\) | 34.1870 | 1.54916 | 0.774581 | − | 0.632475i | \(-0.217961\pi\) | ||||
0.774581 | + | 0.632475i | \(0.217961\pi\) | |||||||
\(488\) | 26.0485 | 1.17916 | ||||||||
\(489\) | 21.7381 | 0.983031 | ||||||||
\(490\) | 14.3625 | 0.648829 | ||||||||
\(491\) | 2.08344 | 0.0940244 | 0.0470122 | − | 0.998894i | \(-0.485030\pi\) | ||||
0.0470122 | + | 0.998894i | \(0.485030\pi\) | |||||||
\(492\) | −1.27315 | −0.0573980 | ||||||||
\(493\) | −0.225940 | −0.0101758 | ||||||||
\(494\) | −3.64579 | −0.164032 | ||||||||
\(495\) | −0.982573 | −0.0441634 | ||||||||
\(496\) | 12.3017 | 0.552361 | ||||||||
\(497\) | 14.5339 | 0.651933 | ||||||||
\(498\) | −1.64291 | −0.0736207 | ||||||||
\(499\) | −26.5308 | −1.18768 | −0.593841 | − | 0.804583i | \(-0.702389\pi\) | ||||
−0.593841 | + | 0.804583i | \(0.702389\pi\) | |||||||
\(500\) | 21.1631 | 0.946441 | ||||||||
\(501\) | −4.07053 | −0.181858 | ||||||||
\(502\) | 20.0891 | 0.896620 | ||||||||
\(503\) | −32.8461 | −1.46453 | −0.732267 | − | 0.681017i | \(-0.761538\pi\) | ||||
−0.732267 | + | 0.681017i | \(0.761538\pi\) | |||||||
\(504\) | 3.77001 | 0.167930 | ||||||||
\(505\) | 17.3439 | 0.771793 | ||||||||
\(506\) | −0.0891950 | −0.00396520 | ||||||||
\(507\) | −9.24988 | −0.410802 | ||||||||
\(508\) | 7.87757 | 0.349511 | ||||||||
\(509\) | 2.18583 | 0.0968850 | 0.0484425 | − | 0.998826i | \(-0.484574\pi\) | ||||
0.0484425 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(510\) | 6.79810 | 0.301025 | ||||||||
\(511\) | 27.2542 | 1.20565 | ||||||||
\(512\) | −9.32391 | −0.412062 | ||||||||
\(513\) | 1.08362 | 0.0478431 | ||||||||
\(514\) | −8.53413 | −0.376424 | ||||||||
\(515\) | 45.7666 | 2.01672 | ||||||||
\(516\) | −7.07608 | −0.311507 | ||||||||
\(517\) | 0.0364848 | 0.00160460 | ||||||||
\(518\) | 5.81470 | 0.255483 | ||||||||
\(519\) | 14.9989 | 0.658381 | ||||||||
\(520\) | 12.9219 | 0.566665 | ||||||||
\(521\) | −29.1503 | −1.27710 | −0.638549 | − | 0.769581i | \(-0.720465\pi\) | ||||
−0.638549 | + | 0.769581i | \(0.720465\pi\) | |||||||
\(522\) | −0.392540 | −0.0171810 | ||||||||
\(523\) | 3.72874 | 0.163046 | 0.0815232 | − | 0.996671i | \(-0.474022\pi\) | ||||
0.0815232 | + | 0.996671i | \(0.474022\pi\) | |||||||
\(524\) | 6.18904 | 0.270370 | ||||||||
\(525\) | 22.7940 | 0.994810 | ||||||||
\(526\) | 4.58396 | 0.199870 | ||||||||
\(527\) | 2.46050 | 0.107181 | ||||||||
\(528\) | 1.25548 | 0.0546376 | ||||||||
\(529\) | −22.9582 | −0.998183 | ||||||||
\(530\) | 37.4081 | 1.62491 | ||||||||
\(531\) | 12.8788 | 0.558892 | ||||||||
\(532\) | 2.43976 | 0.105777 | ||||||||
\(533\) | −2.42084 | −0.104858 | ||||||||
\(534\) | 2.34776 | 0.101598 | ||||||||
\(535\) | −26.8952 | −1.16278 | ||||||||
\(536\) | 21.0919 | 0.911031 | ||||||||
\(537\) | 5.32282 | 0.229697 | ||||||||
\(538\) | 23.0613 | 0.994245 | ||||||||
\(539\) | 0.530529 | 0.0228515 | ||||||||
\(540\) | 3.98503 | 0.171488 | ||||||||
\(541\) | 30.4126 | 1.30754 | 0.653769 | − | 0.756694i | \(-0.273187\pi\) | ||||
0.653769 | + | 0.756694i | \(0.273187\pi\) | |||||||
\(542\) | 17.4911 | 0.751306 | ||||||||
\(543\) | −22.9663 | −0.985577 | ||||||||
\(544\) | −5.27557 | −0.226188 | ||||||||
\(545\) | −52.7788 | −2.26080 | ||||||||
\(546\) | −7.43785 | −0.318311 | ||||||||
\(547\) | 6.09974 | 0.260806 | 0.130403 | − | 0.991461i | \(-0.458373\pi\) | ||||
0.130403 | + | 0.991461i | \(0.458373\pi\) | |||||||
\(548\) | 6.60566 | 0.282180 | ||||||||
\(549\) | 15.2747 | 0.651909 | ||||||||
\(550\) | 4.49826 | 0.191807 | ||||||||
\(551\) | 0.244833 | 0.0104303 | ||||||||
\(552\) | −0.348651 | −0.0148396 | ||||||||
\(553\) | −2.21072 | −0.0940094 | ||||||||
\(554\) | 14.5645 | 0.618787 | ||||||||
\(555\) | −5.92378 | −0.251451 | ||||||||
\(556\) | −4.31428 | −0.182966 | ||||||||
\(557\) | −8.11702 | −0.343929 | −0.171965 | − | 0.985103i | \(-0.555011\pi\) | ||||
−0.171965 | + | 0.985103i | \(0.555011\pi\) | |||||||
\(558\) | 4.27479 | 0.180966 | ||||||||
\(559\) | −13.4549 | −0.569082 | ||||||||
\(560\) | −43.2485 | −1.82758 | ||||||||
\(561\) | 0.251112 | 0.0106020 | ||||||||
\(562\) | −53.6424 | −2.26277 | ||||||||
\(563\) | −47.2869 | −1.99291 | −0.996453 | − | 0.0841553i | \(-0.973181\pi\) | ||||
−0.996453 | + | 0.0841553i | \(0.973181\pi\) | |||||||
\(564\) | −0.147971 | −0.00623072 | ||||||||
\(565\) | 36.4978 | 1.53547 | ||||||||
\(566\) | 8.03239 | 0.337626 | ||||||||
\(567\) | 2.21072 | 0.0928415 | ||||||||
\(568\) | 11.2113 | 0.470416 | ||||||||
\(569\) | 39.3622 | 1.65015 | 0.825075 | − | 0.565023i | \(-0.191133\pi\) | ||||
0.825075 | + | 0.565023i | \(0.191133\pi\) | |||||||
\(570\) | −7.36658 | −0.308552 | ||||||||
\(571\) | 4.72298 | 0.197650 | 0.0988252 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988252 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(572\) | −0.495251 | −0.0207075 | ||||||||
\(573\) | 8.04363 | 0.336027 | ||||||||
\(574\) | 4.80142 | 0.200407 | ||||||||
\(575\) | −2.10798 | −0.0879090 | ||||||||
\(576\) | 0.833725 | 0.0347386 | ||||||||
\(577\) | 6.85425 | 0.285346 | 0.142673 | − | 0.989770i | \(-0.454430\pi\) | ||||
0.142673 | + | 0.989770i | \(0.454430\pi\) | |||||||
\(578\) | −1.73737 | −0.0722649 | ||||||||
\(579\) | 7.87585 | 0.327309 | ||||||||
\(580\) | 0.900377 | 0.0373861 | ||||||||
\(581\) | 2.09053 | 0.0867299 | ||||||||
\(582\) | 24.0532 | 0.997038 | ||||||||
\(583\) | 1.38180 | 0.0572284 | ||||||||
\(584\) | 21.0236 | 0.869965 | ||||||||
\(585\) | 7.57738 | 0.313286 | ||||||||
\(586\) | −35.5398 | −1.46813 | ||||||||
\(587\) | 15.9574 | 0.658631 | 0.329316 | − | 0.944220i | \(-0.393182\pi\) | ||||
0.329316 | + | 0.944220i | \(0.393182\pi\) | |||||||
\(588\) | −2.15167 | −0.0887333 | ||||||||
\(589\) | −2.66625 | −0.109861 | ||||||||
\(590\) | −87.5514 | −3.60444 | ||||||||
\(591\) | −7.23692 | −0.297687 | ||||||||
\(592\) | 7.56907 | 0.311087 | ||||||||
\(593\) | 12.8763 | 0.528767 | 0.264383 | − | 0.964418i | \(-0.414832\pi\) | ||||
0.264383 | + | 0.964418i | \(0.414832\pi\) | |||||||
\(594\) | 0.436274 | 0.0179005 | ||||||||
\(595\) | −8.65029 | −0.354627 | ||||||||
\(596\) | −4.20956 | −0.172430 | ||||||||
\(597\) | −8.61742 | −0.352688 | ||||||||
\(598\) | 0.687852 | 0.0281284 | ||||||||
\(599\) | 14.2486 | 0.582180 | 0.291090 | − | 0.956696i | \(-0.405982\pi\) | ||||
0.291090 | + | 0.956696i | \(0.405982\pi\) | |||||||
\(600\) | 17.5831 | 0.717826 | ||||||||
\(601\) | −17.2942 | −0.705445 | −0.352722 | − | 0.935728i | \(-0.614744\pi\) | ||||
−0.352722 | + | 0.935728i | \(0.614744\pi\) | |||||||
\(602\) | 26.6860 | 1.08764 | ||||||||
\(603\) | 12.3682 | 0.503672 | ||||||||
\(604\) | −16.8926 | −0.687349 | ||||||||
\(605\) | −42.7950 | −1.73986 | ||||||||
\(606\) | −7.70089 | −0.312827 | ||||||||
\(607\) | 2.81368 | 0.114204 | 0.0571019 | − | 0.998368i | \(-0.481814\pi\) | ||||
0.0571019 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(608\) | 5.71673 | 0.231844 | ||||||||
\(609\) | 0.499490 | 0.0202404 | ||||||||
\(610\) | −103.839 | −4.20432 | ||||||||
\(611\) | −0.281362 | −0.0113827 | ||||||||
\(612\) | −1.01844 | −0.0411679 | ||||||||
\(613\) | −14.2980 | −0.577489 | −0.288744 | − | 0.957406i | \(-0.593238\pi\) | ||||
−0.288744 | + | 0.957406i | \(0.593238\pi\) | |||||||
\(614\) | −45.4757 | −1.83525 | ||||||||
\(615\) | −4.89149 | −0.197244 | ||||||||
\(616\) | −0.946697 | −0.0381435 | ||||||||
\(617\) | −47.3397 | −1.90582 | −0.952912 | − | 0.303247i | \(-0.901929\pi\) | ||||
−0.952912 | + | 0.303247i | \(0.901929\pi\) | |||||||
\(618\) | −20.3209 | −0.817426 | ||||||||
\(619\) | 13.1078 | 0.526849 | 0.263424 | − | 0.964680i | \(-0.415148\pi\) | ||||
0.263424 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(620\) | −9.80516 | −0.393785 | ||||||||
\(621\) | −0.204447 | −0.00820419 | ||||||||
\(622\) | −55.5990 | −2.22932 | ||||||||
\(623\) | −2.98742 | −0.119689 | ||||||||
\(624\) | −9.68195 | −0.387588 | ||||||||
\(625\) | 29.7561 | 1.19025 | ||||||||
\(626\) | 32.5447 | 1.30075 | ||||||||
\(627\) | −0.272111 | −0.0108671 | ||||||||
\(628\) | −13.2873 | −0.530219 | ||||||||
\(629\) | 1.51392 | 0.0603639 | ||||||||
\(630\) | −15.0287 | −0.598758 | ||||||||
\(631\) | 1.39625 | 0.0555840 | 0.0277920 | − | 0.999614i | \(-0.491152\pi\) | ||||
0.0277920 | + | 0.999614i | \(0.491152\pi\) | |||||||
\(632\) | −1.70533 | −0.0678345 | ||||||||
\(633\) | −21.3932 | −0.850304 | ||||||||
\(634\) | 35.0141 | 1.39059 | ||||||||
\(635\) | 30.2660 | 1.20107 | ||||||||
\(636\) | −5.60419 | −0.222221 | ||||||||
\(637\) | −4.09132 | −0.162104 | ||||||||
\(638\) | 0.0985717 | 0.00390249 | ||||||||
\(639\) | 6.57427 | 0.260074 | ||||||||
\(640\) | −46.9531 | −1.85599 | ||||||||
\(641\) | 41.6634 | 1.64560 | 0.822802 | − | 0.568328i | \(-0.192410\pi\) | ||||
0.822802 | + | 0.568328i | \(0.192410\pi\) | |||||||
\(642\) | 11.9418 | 0.471305 | ||||||||
\(643\) | 40.3886 | 1.59277 | 0.796386 | − | 0.604789i | \(-0.206743\pi\) | ||||
0.796386 | + | 0.604789i | \(0.206743\pi\) | |||||||
\(644\) | −0.460309 | −0.0181387 | ||||||||
\(645\) | −27.1866 | −1.07047 | ||||||||
\(646\) | 1.88265 | 0.0740718 | ||||||||
\(647\) | −21.2985 | −0.837331 | −0.418666 | − | 0.908140i | \(-0.637502\pi\) | ||||
−0.418666 | + | 0.908140i | \(0.637502\pi\) | |||||||
\(648\) | 1.70533 | 0.0669918 | ||||||||
\(649\) | −3.23403 | −0.126947 | ||||||||
\(650\) | −34.6896 | −1.36064 | ||||||||
\(651\) | −5.43948 | −0.213190 | ||||||||
\(652\) | 22.1389 | 0.867027 | ||||||||
\(653\) | −13.5145 | −0.528865 | −0.264433 | − | 0.964404i | \(-0.585185\pi\) | ||||
−0.264433 | + | 0.964404i | \(0.585185\pi\) | |||||||
\(654\) | 23.4344 | 0.916358 | ||||||||
\(655\) | 23.7786 | 0.929105 | ||||||||
\(656\) | 6.25007 | 0.244024 | ||||||||
\(657\) | 12.3282 | 0.480968 | ||||||||
\(658\) | 0.558044 | 0.0217548 | ||||||||
\(659\) | 39.6021 | 1.54268 | 0.771340 | − | 0.636423i | \(-0.219587\pi\) | ||||
0.771340 | + | 0.636423i | \(0.219587\pi\) | |||||||
\(660\) | −1.00069 | −0.0389518 | ||||||||
\(661\) | −0.739657 | −0.0287693 | −0.0143847 | − | 0.999897i | \(-0.504579\pi\) | ||||
−0.0143847 | + | 0.999897i | \(0.504579\pi\) | |||||||
\(662\) | 36.9280 | 1.43525 | ||||||||
\(663\) | −1.93652 | −0.0752083 | ||||||||
\(664\) | 1.61262 | 0.0625818 | ||||||||
\(665\) | 9.37364 | 0.363494 | ||||||||
\(666\) | 2.63023 | 0.101919 | ||||||||
\(667\) | −0.0461928 | −0.00178859 | ||||||||
\(668\) | −4.14558 | −0.160397 | ||||||||
\(669\) | −10.5593 | −0.408245 | ||||||||
\(670\) | −84.0803 | −3.24831 | ||||||||
\(671\) | −3.83567 | −0.148074 | ||||||||
\(672\) | 11.6628 | 0.449903 | ||||||||
\(673\) | −10.7466 | −0.414253 | −0.207126 | − | 0.978314i | \(-0.566411\pi\) | ||||
−0.207126 | + | 0.978314i | \(0.566411\pi\) | |||||||
\(674\) | 2.20533 | 0.0849461 | ||||||||
\(675\) | 10.3106 | 0.396857 | ||||||||
\(676\) | −9.42043 | −0.362324 | ||||||||
\(677\) | −10.4011 | −0.399749 | −0.199874 | − | 0.979822i | \(-0.564053\pi\) | ||||
−0.199874 | + | 0.979822i | \(0.564053\pi\) | |||||||
\(678\) | −16.2054 | −0.622366 | ||||||||
\(679\) | −30.6067 | −1.17458 | ||||||||
\(680\) | −6.67276 | −0.255889 | ||||||||
\(681\) | 7.61930 | 0.291972 | ||||||||
\(682\) | −1.07345 | −0.0411046 | ||||||||
\(683\) | −13.8578 | −0.530253 | −0.265127 | − | 0.964214i | \(-0.585414\pi\) | ||||
−0.265127 | + | 0.964214i | \(0.585414\pi\) | |||||||
\(684\) | 1.10360 | 0.0421973 | ||||||||
\(685\) | 25.3792 | 0.969691 | ||||||||
\(686\) | 35.0004 | 1.33632 | ||||||||
\(687\) | −24.1252 | −0.920435 | ||||||||
\(688\) | 34.7375 | 1.32435 | ||||||||
\(689\) | −10.6562 | −0.405967 | ||||||||
\(690\) | 1.38985 | 0.0529108 | ||||||||
\(691\) | 32.1785 | 1.22413 | 0.612063 | − | 0.790809i | \(-0.290340\pi\) | ||||
0.612063 | + | 0.790809i | \(0.290340\pi\) | |||||||
\(692\) | 15.2755 | 0.580687 | ||||||||
\(693\) | −0.555139 | −0.0210880 | ||||||||
\(694\) | −27.1174 | −1.02936 | ||||||||
\(695\) | −16.5756 | −0.628750 | ||||||||
\(696\) | 0.385303 | 0.0146049 | ||||||||
\(697\) | 1.25010 | 0.0473509 | ||||||||
\(698\) | −29.7212 | −1.12496 | ||||||||
\(699\) | −12.6213 | −0.477381 | ||||||||
\(700\) | 23.2142 | 0.877415 | ||||||||
\(701\) | −11.5234 | −0.435232 | −0.217616 | − | 0.976034i | \(-0.569828\pi\) | ||||
−0.217616 | + | 0.976034i | \(0.569828\pi\) | |||||||
\(702\) | −3.36445 | −0.126983 | ||||||||
\(703\) | −1.64051 | −0.0618732 | ||||||||
\(704\) | −0.209359 | −0.00789051 | ||||||||
\(705\) | −0.568513 | −0.0214114 | ||||||||
\(706\) | −24.8434 | −0.934993 | ||||||||
\(707\) | 9.79905 | 0.368531 | ||||||||
\(708\) | 13.1163 | 0.492939 | ||||||||
\(709\) | 19.4682 | 0.731142 | 0.365571 | − | 0.930783i | \(-0.380874\pi\) | ||||
0.365571 | + | 0.930783i | \(0.380874\pi\) | |||||||
\(710\) | −44.6926 | −1.67728 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | −2.30447 | −0.0863638 | ||||||||
\(713\) | 0.503043 | 0.0188391 | ||||||||
\(714\) | 3.84083 | 0.143739 | ||||||||
\(715\) | −1.90277 | −0.0711597 | ||||||||
\(716\) | 5.42097 | 0.202591 | ||||||||
\(717\) | 27.0754 | 1.01115 | ||||||||
\(718\) | 13.1514 | 0.490804 | ||||||||
\(719\) | 11.5836 | 0.431997 | 0.215998 | − | 0.976394i | \(-0.430699\pi\) | ||||
0.215998 | + | 0.976394i | \(0.430699\pi\) | |||||||
\(720\) | −19.5631 | −0.729073 | ||||||||
\(721\) | 25.8574 | 0.962981 | ||||||||
\(722\) | 30.9699 | 1.15258 | ||||||||
\(723\) | −6.79346 | −0.252651 | ||||||||
\(724\) | −23.3897 | −0.869272 | ||||||||
\(725\) | 2.32959 | 0.0865186 | ||||||||
\(726\) | 19.0015 | 0.705210 | ||||||||
\(727\) | −6.87787 | −0.255086 | −0.127543 | − | 0.991833i | \(-0.540709\pi\) | ||||
−0.127543 | + | 0.991833i | \(0.540709\pi\) | |||||||
\(728\) | 7.30071 | 0.270582 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −83.8083 | −3.10188 | ||||||||
\(731\) | 6.94797 | 0.256980 | ||||||||
\(732\) | 15.5563 | 0.574979 | ||||||||
\(733\) | −44.7822 | −1.65407 | −0.827034 | − | 0.562153i | \(-0.809973\pi\) | ||||
−0.827034 | + | 0.562153i | \(0.809973\pi\) | |||||||
\(734\) | 12.6802 | 0.468035 | ||||||||
\(735\) | −8.26680 | −0.304926 | ||||||||
\(736\) | −1.07858 | −0.0397569 | ||||||||
\(737\) | −3.10581 | −0.114404 | ||||||||
\(738\) | 2.17188 | 0.0799479 | ||||||||
\(739\) | −7.46477 | −0.274596 | −0.137298 | − | 0.990530i | \(-0.543842\pi\) | ||||
−0.137298 | + | 0.990530i | \(0.543842\pi\) | |||||||
\(740\) | −6.03300 | −0.221778 | ||||||||
\(741\) | 2.09846 | 0.0770888 | ||||||||
\(742\) | 21.1350 | 0.775892 | ||||||||
\(743\) | 40.0866 | 1.47063 | 0.735317 | − | 0.677724i | \(-0.237033\pi\) | ||||
0.735317 | + | 0.677724i | \(0.237033\pi\) | |||||||
\(744\) | −4.19597 | −0.153832 | ||||||||
\(745\) | −16.1733 | −0.592545 | ||||||||
\(746\) | −22.4689 | −0.822644 | ||||||||
\(747\) | 0.945634 | 0.0345990 | ||||||||
\(748\) | 0.255742 | 0.00935087 | ||||||||
\(749\) | −15.1954 | −0.555228 | ||||||||
\(750\) | −36.1023 | −1.31827 | ||||||||
\(751\) | 25.7287 | 0.938852 | 0.469426 | − | 0.882972i | \(-0.344461\pi\) | ||||
0.469426 | + | 0.882972i | \(0.344461\pi\) | |||||||
\(752\) | 0.726414 | 0.0264896 | ||||||||
\(753\) | −11.5630 | −0.421378 | ||||||||
\(754\) | −0.760163 | −0.0276835 | ||||||||
\(755\) | −64.9020 | −2.36202 | ||||||||
\(756\) | 2.25148 | 0.0818856 | ||||||||
\(757\) | −51.0981 | −1.85719 | −0.928596 | − | 0.371092i | \(-0.878984\pi\) | ||||
−0.928596 | + | 0.371092i | \(0.878984\pi\) | |||||||
\(758\) | −1.30788 | −0.0475043 | ||||||||
\(759\) | 0.0513392 | 0.00186350 | ||||||||
\(760\) | 7.23075 | 0.262287 | ||||||||
\(761\) | −40.4674 | −1.46694 | −0.733471 | − | 0.679720i | \(-0.762101\pi\) | ||||
−0.733471 | + | 0.679720i | \(0.762101\pi\) | |||||||
\(762\) | −13.4384 | −0.486823 | ||||||||
\(763\) | −29.8193 | −1.07953 | ||||||||
\(764\) | 8.19194 | 0.296374 | ||||||||
\(765\) | −3.91288 | −0.141471 | ||||||||
\(766\) | −11.1733 | −0.403707 | ||||||||
\(767\) | 24.9401 | 0.900534 | ||||||||
\(768\) | 19.1803 | 0.692109 | ||||||||
\(769\) | 43.8169 | 1.58008 | 0.790038 | − | 0.613058i | \(-0.210061\pi\) | ||||
0.790038 | + | 0.613058i | \(0.210061\pi\) | |||||||
\(770\) | 3.77389 | 0.136002 | ||||||||
\(771\) | 4.91211 | 0.176905 | ||||||||
\(772\) | 8.02106 | 0.288684 | ||||||||
\(773\) | 4.94099 | 0.177715 | 0.0888576 | − | 0.996044i | \(-0.471678\pi\) | ||||
0.0888576 | + | 0.996044i | \(0.471678\pi\) | |||||||
\(774\) | 12.0712 | 0.433889 | ||||||||
\(775\) | −25.3693 | −0.911293 | ||||||||
\(776\) | −23.6097 | −0.847540 | ||||||||
\(777\) | −3.34685 | −0.120068 | ||||||||
\(778\) | −13.6812 | −0.490496 | ||||||||
\(779\) | −1.35463 | −0.0485348 | ||||||||
\(780\) | 7.71709 | 0.276316 | ||||||||
\(781\) | −1.65088 | −0.0590732 | ||||||||
\(782\) | −0.355200 | −0.0127019 | ||||||||
\(783\) | 0.225940 | 0.00807443 | ||||||||
\(784\) | 10.5629 | 0.377245 | ||||||||
\(785\) | −51.0502 | −1.82206 | ||||||||
\(786\) | −10.5580 | −0.376590 | ||||||||
\(787\) | −28.8053 | −1.02680 | −0.513399 | − | 0.858150i | \(-0.671614\pi\) | ||||
−0.513399 | + | 0.858150i | \(0.671614\pi\) | |||||||
\(788\) | −7.37036 | −0.262558 | ||||||||
\(789\) | −2.63845 | −0.0939314 | ||||||||
\(790\) | 6.79810 | 0.241866 | ||||||||
\(791\) | 20.6207 | 0.733188 | ||||||||
\(792\) | −0.428230 | −0.0152165 | ||||||||
\(793\) | 29.5798 | 1.05041 | ||||||||
\(794\) | 38.8867 | 1.38004 | ||||||||
\(795\) | −21.5315 | −0.763645 | ||||||||
\(796\) | −8.77631 | −0.311068 | ||||||||
\(797\) | 13.8433 | 0.490354 | 0.245177 | − | 0.969478i | \(-0.421154\pi\) | ||||
0.245177 | + | 0.969478i | \(0.421154\pi\) | |||||||
\(798\) | −4.16201 | −0.147333 | ||||||||
\(799\) | 0.145293 | 0.00514008 | ||||||||
\(800\) | 54.3945 | 1.92314 | ||||||||
\(801\) | −1.35133 | −0.0477471 | ||||||||
\(802\) | 42.4087 | 1.49750 | ||||||||
\(803\) | −3.09576 | −0.109247 | ||||||||
\(804\) | 12.5962 | 0.444235 | ||||||||
\(805\) | −1.76853 | −0.0623324 | ||||||||
\(806\) | 8.27822 | 0.291588 | ||||||||
\(807\) | −13.2737 | −0.467258 | ||||||||
\(808\) | 7.55891 | 0.265921 | ||||||||
\(809\) | −16.7477 | −0.588818 | −0.294409 | − | 0.955679i | \(-0.595123\pi\) | ||||
−0.294409 | + | 0.955679i | \(0.595123\pi\) | |||||||
\(810\) | −6.79810 | −0.238861 | ||||||||
\(811\) | −17.0947 | −0.600275 | −0.300138 | − | 0.953896i | \(-0.597033\pi\) | ||||
−0.300138 | + | 0.953896i | \(0.597033\pi\) | |||||||
\(812\) | 0.508700 | 0.0178519 | ||||||||
\(813\) | −10.0676 | −0.353086 | ||||||||
\(814\) | −0.660483 | −0.0231499 | ||||||||
\(815\) | 85.0587 | 2.97947 | ||||||||
\(816\) | 4.99966 | 0.175023 | ||||||||
\(817\) | −7.52898 | −0.263406 | ||||||||
\(818\) | 11.4286 | 0.399593 | ||||||||
\(819\) | 4.28111 | 0.149594 | ||||||||
\(820\) | −4.98168 | −0.173968 | ||||||||
\(821\) | −18.4262 | −0.643079 | −0.321539 | − | 0.946896i | \(-0.604200\pi\) | ||||
−0.321539 | + | 0.946896i | \(0.604200\pi\) | |||||||
\(822\) | −11.2687 | −0.393040 | ||||||||
\(823\) | 9.22044 | 0.321404 | 0.160702 | − | 0.987003i | \(-0.448624\pi\) | ||||
0.160702 | + | 0.987003i | \(0.448624\pi\) | |||||||
\(824\) | 19.9462 | 0.694859 | ||||||||
\(825\) | −2.58913 | −0.0901419 | ||||||||
\(826\) | −49.4653 | −1.72112 | ||||||||
\(827\) | −36.5561 | −1.27118 | −0.635590 | − | 0.772027i | \(-0.719243\pi\) | ||||
−0.635590 | + | 0.772027i | \(0.719243\pi\) | |||||||
\(828\) | −0.208217 | −0.00723604 | ||||||||
\(829\) | 31.4955 | 1.09388 | 0.546942 | − | 0.837170i | \(-0.315792\pi\) | ||||
0.546942 | + | 0.837170i | \(0.315792\pi\) | |||||||
\(830\) | −6.42852 | −0.223137 | ||||||||
\(831\) | −8.38310 | −0.290807 | ||||||||
\(832\) | 1.61453 | 0.0559737 | ||||||||
\(833\) | 2.11271 | 0.0732012 | ||||||||
\(834\) | 7.35977 | 0.254848 | ||||||||
\(835\) | −15.9275 | −0.551194 | ||||||||
\(836\) | −0.277128 | −0.00958467 | ||||||||
\(837\) | −2.46050 | −0.0850473 | ||||||||
\(838\) | −1.80494 | −0.0623505 | ||||||||
\(839\) | 40.5201 | 1.39891 | 0.699455 | − | 0.714676i | \(-0.253426\pi\) | ||||
0.699455 | + | 0.714676i | \(0.253426\pi\) | |||||||
\(840\) | 14.7516 | 0.508979 | ||||||||
\(841\) | −28.9490 | −0.998240 | ||||||||
\(842\) | −59.2942 | −2.04341 | ||||||||
\(843\) | 30.8757 | 1.06342 | ||||||||
\(844\) | −21.7877 | −0.749963 | ||||||||
\(845\) | −36.1937 | −1.24510 | ||||||||
\(846\) | 0.252426 | 0.00867860 | ||||||||
\(847\) | −24.1785 | −0.830784 | ||||||||
\(848\) | 27.5118 | 0.944758 | ||||||||
\(849\) | −4.62332 | −0.158672 | ||||||||
\(850\) | 17.9134 | 0.614423 | ||||||||
\(851\) | 0.309516 | 0.0106101 | ||||||||
\(852\) | 6.69549 | 0.229384 | ||||||||
\(853\) | 43.9649 | 1.50533 | 0.752665 | − | 0.658403i | \(-0.228768\pi\) | ||||
0.752665 | + | 0.658403i | \(0.228768\pi\) | |||||||
\(854\) | −58.6676 | −2.00756 | ||||||||
\(855\) | 4.24008 | 0.145008 | ||||||||
\(856\) | −11.7216 | −0.400636 | ||||||||
\(857\) | −37.2423 | −1.27217 | −0.636087 | − | 0.771618i | \(-0.719448\pi\) | ||||
−0.636087 | + | 0.771618i | \(0.719448\pi\) | |||||||
\(858\) | 0.844854 | 0.0288428 | ||||||||
\(859\) | −30.4889 | −1.04027 | −0.520134 | − | 0.854085i | \(-0.674118\pi\) | ||||
−0.520134 | + | 0.854085i | \(0.674118\pi\) | |||||||
\(860\) | −27.6879 | −0.944148 | ||||||||
\(861\) | −2.76362 | −0.0941839 | ||||||||
\(862\) | 21.4415 | 0.730300 | ||||||||
\(863\) | 8.19926 | 0.279106 | 0.139553 | − | 0.990215i | \(-0.455433\pi\) | ||||
0.139553 | + | 0.990215i | \(0.455433\pi\) | |||||||
\(864\) | 5.27557 | 0.179479 | ||||||||
\(865\) | 58.6891 | 1.99549 | ||||||||
\(866\) | −16.7289 | −0.568470 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −5.53977 | −0.188032 | ||||||||
\(869\) | 0.251112 | 0.00851840 | ||||||||
\(870\) | −1.53596 | −0.0520740 | ||||||||
\(871\) | 23.9513 | 0.811558 | ||||||||
\(872\) | −23.0023 | −0.778957 | ||||||||
\(873\) | −13.8447 | −0.468571 | ||||||||
\(874\) | 0.384902 | 0.0130195 | ||||||||
\(875\) | 45.9386 | 1.55301 | ||||||||
\(876\) | 12.5555 | 0.424211 | ||||||||
\(877\) | −34.2171 | −1.15543 | −0.577715 | − | 0.816238i | \(-0.696056\pi\) | ||||
−0.577715 | + | 0.816238i | \(0.696056\pi\) | |||||||
\(878\) | −12.5572 | −0.423785 | ||||||||
\(879\) | 20.4561 | 0.689968 | ||||||||
\(880\) | 4.91253 | 0.165601 | ||||||||
\(881\) | −57.3270 | −1.93139 | −0.965697 | − | 0.259671i | \(-0.916386\pi\) | ||||
−0.965697 | + | 0.259671i | \(0.916386\pi\) | |||||||
\(882\) | 3.67056 | 0.123594 | ||||||||
\(883\) | −31.5028 | −1.06015 | −0.530077 | − | 0.847950i | \(-0.677837\pi\) | ||||
−0.530077 | + | 0.847950i | \(0.677837\pi\) | |||||||
\(884\) | −1.97223 | −0.0663332 | ||||||||
\(885\) | 50.3932 | 1.69395 | ||||||||
\(886\) | 49.0609 | 1.64823 | ||||||||
\(887\) | −6.35239 | −0.213292 | −0.106646 | − | 0.994297i | \(-0.534011\pi\) | ||||
−0.106646 | + | 0.994297i | \(0.534011\pi\) | |||||||
\(888\) | −2.58173 | −0.0866373 | ||||||||
\(889\) | 17.0998 | 0.573510 | ||||||||
\(890\) | 9.18652 | 0.307933 | ||||||||
\(891\) | −0.251112 | −0.00841258 | ||||||||
\(892\) | −10.7540 | −0.360069 | ||||||||
\(893\) | −0.157442 | −0.00526860 | ||||||||
\(894\) | 7.18114 | 0.240173 | ||||||||
\(895\) | 20.8276 | 0.696189 | ||||||||
\(896\) | −26.5278 | −0.886232 | ||||||||
\(897\) | −0.395917 | −0.0132193 | ||||||||
\(898\) | −32.8329 | −1.09565 | ||||||||
\(899\) | −0.555925 | −0.0185411 | ||||||||
\(900\) | 10.5007 | 0.350025 | ||||||||
\(901\) | 5.50273 | 0.183322 | ||||||||
\(902\) | −0.545386 | −0.0181594 | ||||||||
\(903\) | −15.3600 | −0.511150 | ||||||||
\(904\) | 15.9066 | 0.529047 | ||||||||
\(905\) | −89.8643 | −2.98719 | ||||||||
\(906\) | 28.8172 | 0.957388 | ||||||||
\(907\) | 1.03147 | 0.0342495 | 0.0171248 | − | 0.999853i | \(-0.494549\pi\) | ||||
0.0171248 | + | 0.999853i | \(0.494549\pi\) | |||||||
\(908\) | 7.75979 | 0.257518 | ||||||||
\(909\) | 4.43251 | 0.147017 | ||||||||
\(910\) | −29.1034 | −0.964769 | ||||||||
\(911\) | 10.6471 | 0.352753 | 0.176377 | − | 0.984323i | \(-0.443562\pi\) | ||||
0.176377 | + | 0.984323i | \(0.443562\pi\) | |||||||
\(912\) | −5.41774 | −0.179399 | ||||||||
\(913\) | −0.237460 | −0.00785879 | ||||||||
\(914\) | 8.33955 | 0.275848 | ||||||||
\(915\) | 59.7681 | 1.97587 | ||||||||
\(916\) | −24.5700 | −0.811817 | ||||||||
\(917\) | 13.4345 | 0.443647 | ||||||||
\(918\) | 1.73737 | 0.0573416 | ||||||||
\(919\) | −21.1582 | −0.697944 | −0.348972 | − | 0.937133i | \(-0.613469\pi\) | ||||
−0.348972 | + | 0.937133i | \(0.613469\pi\) | |||||||
\(920\) | −1.36423 | −0.0449773 | ||||||||
\(921\) | 26.1751 | 0.862499 | ||||||||
\(922\) | 19.2435 | 0.633752 | ||||||||
\(923\) | 12.7312 | 0.419053 | ||||||||
\(924\) | −0.565375 | −0.0185995 | ||||||||
\(925\) | −15.6095 | −0.513236 | ||||||||
\(926\) | 36.3245 | 1.19370 | ||||||||
\(927\) | 11.6964 | 0.384160 | ||||||||
\(928\) | 1.19196 | 0.0391281 | ||||||||
\(929\) | 47.3661 | 1.55403 | 0.777015 | − | 0.629482i | \(-0.216733\pi\) | ||||
0.777015 | + | 0.629482i | \(0.216733\pi\) | |||||||
\(930\) | 16.7267 | 0.548491 | ||||||||
\(931\) | −2.28938 | −0.0750315 | ||||||||
\(932\) | −12.8540 | −0.421047 | ||||||||
\(933\) | 32.0019 | 1.04770 | ||||||||
\(934\) | −21.2795 | −0.696286 | ||||||||
\(935\) | 0.982573 | 0.0321336 | ||||||||
\(936\) | 3.30241 | 0.107943 | ||||||||
\(937\) | 23.8234 | 0.778276 | 0.389138 | − | 0.921179i | \(-0.372773\pi\) | ||||
0.389138 | + | 0.921179i | \(0.372773\pi\) | |||||||
\(938\) | −47.5041 | −1.55106 | ||||||||
\(939\) | −18.7322 | −0.611303 | ||||||||
\(940\) | −0.578995 | −0.0188847 | ||||||||
\(941\) | −37.3366 | −1.21714 | −0.608570 | − | 0.793501i | \(-0.708256\pi\) | ||||
−0.608570 | + | 0.793501i | \(0.708256\pi\) | |||||||
\(942\) | 22.6669 | 0.738527 | ||||||||
\(943\) | 0.255579 | 0.00832281 | ||||||||
\(944\) | −64.3896 | −2.09570 | ||||||||
\(945\) | 8.65029 | 0.281394 | ||||||||
\(946\) | −3.03122 | −0.0985534 | ||||||||
\(947\) | 2.93765 | 0.0954606 | 0.0477303 | − | 0.998860i | \(-0.484801\pi\) | ||||
0.0477303 | + | 0.998860i | \(0.484801\pi\) | |||||||
\(948\) | −1.01844 | −0.0330773 | ||||||||
\(949\) | 23.8738 | 0.774976 | ||||||||
\(950\) | −19.4113 | −0.629786 | ||||||||
\(951\) | −20.1536 | −0.653524 | ||||||||
\(952\) | −3.77001 | −0.122187 | ||||||||
\(953\) | −48.7093 | −1.57785 | −0.788924 | − | 0.614490i | \(-0.789362\pi\) | ||||
−0.788924 | + | 0.614490i | \(0.789362\pi\) | |||||||
\(954\) | 9.56025 | 0.309525 | ||||||||
\(955\) | 31.4738 | 1.01847 | ||||||||
\(956\) | 27.5746 | 0.891825 | ||||||||
\(957\) | −0.0567363 | −0.00183402 | ||||||||
\(958\) | 9.96230 | 0.321867 | ||||||||
\(959\) | 14.3389 | 0.463027 | ||||||||
\(960\) | 3.26227 | 0.105289 | ||||||||
\(961\) | −24.9459 | −0.804708 | ||||||||
\(962\) | 5.09349 | 0.164221 | ||||||||
\(963\) | −6.87350 | −0.221496 | ||||||||
\(964\) | −6.91871 | −0.222837 | ||||||||
\(965\) | 30.8173 | 0.992043 | ||||||||
\(966\) | 0.785247 | 0.0252649 | ||||||||
\(967\) | −6.44367 | −0.207215 | −0.103607 | − | 0.994618i | \(-0.533039\pi\) | ||||
−0.103607 | + | 0.994618i | \(0.533039\pi\) | |||||||
\(968\) | −18.6511 | −0.599470 | ||||||||
\(969\) | −1.08362 | −0.0348110 | ||||||||
\(970\) | 94.1174 | 3.02193 | ||||||||
\(971\) | −40.4855 | −1.29924 | −0.649621 | − | 0.760258i | \(-0.725072\pi\) | ||||
−0.649621 | + | 0.760258i | \(0.725072\pi\) | |||||||
\(972\) | 1.01844 | 0.0326664 | ||||||||
\(973\) | −9.36499 | −0.300228 | ||||||||
\(974\) | −59.3954 | −1.90315 | ||||||||
\(975\) | 19.9668 | 0.639449 | ||||||||
\(976\) | −76.3684 | −2.44449 | ||||||||
\(977\) | 18.4251 | 0.589470 | 0.294735 | − | 0.955579i | \(-0.404769\pi\) | ||||
0.294735 | + | 0.955579i | \(0.404769\pi\) | |||||||
\(978\) | −37.7670 | −1.20766 | ||||||||
\(979\) | 0.339337 | 0.0108453 | ||||||||
\(980\) | −8.41922 | −0.268942 | ||||||||
\(981\) | −13.4885 | −0.430654 | ||||||||
\(982\) | −3.61970 | −0.115509 | ||||||||
\(983\) | −13.6544 | −0.435507 | −0.217754 | − | 0.976004i | \(-0.569873\pi\) | ||||
−0.217754 | + | 0.976004i | \(0.569873\pi\) | |||||||
\(984\) | −2.13183 | −0.0679604 | ||||||||
\(985\) | −28.3172 | −0.902262 | ||||||||
\(986\) | 0.392540 | 0.0125010 | ||||||||
\(987\) | −0.321201 | −0.0102240 | ||||||||
\(988\) | 2.13715 | 0.0679918 | ||||||||
\(989\) | 1.42049 | 0.0451691 | ||||||||
\(990\) | 1.70709 | 0.0542548 | ||||||||
\(991\) | −21.1235 | −0.671010 | −0.335505 | − | 0.942038i | \(-0.608907\pi\) | ||||
−0.335505 | + | 0.942038i | \(0.608907\pi\) | |||||||
\(992\) | −12.9805 | −0.412133 | ||||||||
\(993\) | −21.2552 | −0.674512 | ||||||||
\(994\) | −25.2507 | −0.800902 | ||||||||
\(995\) | −33.7190 | −1.06896 | ||||||||
\(996\) | 0.963070 | 0.0305160 | ||||||||
\(997\) | 46.1042 | 1.46013 | 0.730067 | − | 0.683375i | \(-0.239489\pi\) | ||||
0.730067 | + | 0.683375i | \(0.239489\pi\) | |||||||
\(998\) | 46.0937 | 1.45907 | ||||||||
\(999\) | −1.51392 | −0.0478982 |
(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.j.1.5 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.j.1.5 | ✓ | 25 | 1.1 | even | 1 | trivial |