Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61699 | −1.85049 | −0.925245 | − | 0.379370i | \(-0.876141\pi\) | ||||
−0.925245 | + | 0.379370i | \(0.876141\pi\) | |||||||
\(3\) | 0.399813 | 0.230832 | 0.115416 | − | 0.993317i | \(-0.463180\pi\) | ||||
0.115416 | + | 0.993317i | \(0.463180\pi\) | |||||||
\(4\) | 4.84863 | 2.42431 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.04630 | −0.427152 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −7.45482 | −2.63568 | ||||||||
\(9\) | −2.84015 | −0.946717 | ||||||||
\(10\) | 2.61699 | 0.827564 | ||||||||
\(11\) | 1.74534 | 0.526241 | 0.263120 | − | 0.964763i | \(-0.415248\pi\) | ||||
0.263120 | + | 0.964763i | \(0.415248\pi\) | |||||||
\(12\) | 1.93854 | 0.559609 | ||||||||
\(13\) | 4.62721 | 1.28336 | 0.641679 | − | 0.766974i | \(-0.278238\pi\) | ||||
0.641679 | + | 0.766974i | \(0.278238\pi\) | |||||||
\(14\) | 2.61699 | 0.699419 | ||||||||
\(15\) | −0.399813 | −0.103231 | ||||||||
\(16\) | 9.81192 | 2.45298 | ||||||||
\(17\) | 5.87048 | 1.42380 | 0.711901 | − | 0.702280i | \(-0.247835\pi\) | ||||
0.711901 | + | 0.702280i | \(0.247835\pi\) | |||||||
\(18\) | 7.43264 | 1.75189 | ||||||||
\(19\) | 7.96108 | 1.82640 | 0.913199 | − | 0.407514i | \(-0.133604\pi\) | ||||
0.913199 | + | 0.407514i | \(0.133604\pi\) | |||||||
\(20\) | −4.84863 | −1.08419 | ||||||||
\(21\) | −0.399813 | −0.0872462 | ||||||||
\(22\) | −4.56754 | −0.973803 | ||||||||
\(23\) | −1.11824 | −0.233169 | −0.116584 | − | 0.993181i | \(-0.537195\pi\) | ||||
−0.116584 | + | 0.993181i | \(0.537195\pi\) | |||||||
\(24\) | −2.98053 | −0.608398 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −12.1094 | −2.37484 | ||||||||
\(27\) | −2.33497 | −0.449364 | ||||||||
\(28\) | −4.84863 | −0.916304 | ||||||||
\(29\) | −5.02093 | −0.932364 | −0.466182 | − | 0.884689i | \(-0.654371\pi\) | ||||
−0.466182 | + | 0.884689i | \(0.654371\pi\) | |||||||
\(30\) | 1.04630 | 0.191028 | ||||||||
\(31\) | 4.42471 | 0.794701 | 0.397350 | − | 0.917667i | \(-0.369930\pi\) | ||||
0.397350 | + | 0.917667i | \(0.369930\pi\) | |||||||
\(32\) | −10.7680 | −1.90354 | ||||||||
\(33\) | 0.697810 | 0.121473 | ||||||||
\(34\) | −15.3630 | −2.63473 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −13.7708 | −2.29514 | ||||||||
\(37\) | 3.11946 | 0.512836 | 0.256418 | − | 0.966566i | \(-0.417458\pi\) | ||||
0.256418 | + | 0.966566i | \(0.417458\pi\) | |||||||
\(38\) | −20.8341 | −3.37973 | ||||||||
\(39\) | 1.85002 | 0.296240 | ||||||||
\(40\) | 7.45482 | 1.17871 | ||||||||
\(41\) | −4.19477 | −0.655112 | −0.327556 | − | 0.944832i | \(-0.606225\pi\) | ||||
−0.327556 | + | 0.944832i | \(0.606225\pi\) | |||||||
\(42\) | 1.04630 | 0.161448 | ||||||||
\(43\) | 11.0065 | 1.67847 | 0.839235 | − | 0.543768i | \(-0.183003\pi\) | ||||
0.839235 | + | 0.543768i | \(0.183003\pi\) | |||||||
\(44\) | 8.46252 | 1.27577 | ||||||||
\(45\) | 2.84015 | 0.423385 | ||||||||
\(46\) | 2.92641 | 0.431476 | ||||||||
\(47\) | 11.0169 | 1.60698 | 0.803491 | − | 0.595317i | \(-0.202974\pi\) | ||||
0.803491 | + | 0.595317i | \(0.202974\pi\) | |||||||
\(48\) | 3.92293 | 0.566226 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.61699 | −0.370098 | ||||||||
\(51\) | 2.34709 | 0.328659 | ||||||||
\(52\) | 22.4356 | 3.11126 | ||||||||
\(53\) | −4.04621 | −0.555790 | −0.277895 | − | 0.960611i | \(-0.589637\pi\) | ||||
−0.277895 | + | 0.960611i | \(0.589637\pi\) | |||||||
\(54\) | 6.11058 | 0.831544 | ||||||||
\(55\) | −1.74534 | −0.235342 | ||||||||
\(56\) | 7.45482 | 0.996192 | ||||||||
\(57\) | 3.18294 | 0.421591 | ||||||||
\(58\) | 13.1397 | 1.72533 | ||||||||
\(59\) | 4.62878 | 0.602615 | 0.301308 | − | 0.953527i | \(-0.402577\pi\) | ||||
0.301308 | + | 0.953527i | \(0.402577\pi\) | |||||||
\(60\) | −1.93854 | −0.250265 | ||||||||
\(61\) | 3.73455 | 0.478160 | 0.239080 | − | 0.971000i | \(-0.423154\pi\) | ||||
0.239080 | + | 0.971000i | \(0.423154\pi\) | |||||||
\(62\) | −11.5794 | −1.47059 | ||||||||
\(63\) | 2.84015 | 0.357825 | ||||||||
\(64\) | 8.55599 | 1.06950 | ||||||||
\(65\) | −4.62721 | −0.573935 | ||||||||
\(66\) | −1.82616 | −0.224785 | ||||||||
\(67\) | −3.77666 | −0.461392 | −0.230696 | − | 0.973026i | \(-0.574100\pi\) | ||||
−0.230696 | + | 0.973026i | \(0.574100\pi\) | |||||||
\(68\) | 28.4638 | 3.45174 | ||||||||
\(69\) | −0.447085 | −0.0538228 | ||||||||
\(70\) | −2.61699 | −0.312790 | ||||||||
\(71\) | 8.09433 | 0.960620 | 0.480310 | − | 0.877099i | \(-0.340524\pi\) | ||||
0.480310 | + | 0.877099i | \(0.340524\pi\) | |||||||
\(72\) | 21.1728 | 2.49524 | ||||||||
\(73\) | −0.980406 | −0.114748 | −0.0573739 | − | 0.998353i | \(-0.518273\pi\) | ||||
−0.0573739 | + | 0.998353i | \(0.518273\pi\) | |||||||
\(74\) | −8.16358 | −0.948997 | ||||||||
\(75\) | 0.399813 | 0.0461664 | ||||||||
\(76\) | 38.6003 | 4.42776 | ||||||||
\(77\) | −1.74534 | −0.198900 | ||||||||
\(78\) | −4.84147 | −0.548189 | ||||||||
\(79\) | 16.1440 | 1.81634 | 0.908171 | − | 0.418599i | \(-0.137479\pi\) | ||||
0.908171 | + | 0.418599i | \(0.137479\pi\) | |||||||
\(80\) | −9.81192 | −1.09701 | ||||||||
\(81\) | 7.58690 | 0.842989 | ||||||||
\(82\) | 10.9777 | 1.21228 | ||||||||
\(83\) | 3.27280 | 0.359237 | 0.179618 | − | 0.983736i | \(-0.442514\pi\) | ||||
0.179618 | + | 0.983736i | \(0.442514\pi\) | |||||||
\(84\) | −1.93854 | −0.211512 | ||||||||
\(85\) | −5.87048 | −0.636743 | ||||||||
\(86\) | −28.8038 | −3.10599 | ||||||||
\(87\) | −2.00743 | −0.215219 | ||||||||
\(88\) | −13.0112 | −1.38700 | ||||||||
\(89\) | −18.0829 | −1.91678 | −0.958391 | − | 0.285457i | \(-0.907854\pi\) | ||||
−0.958391 | + | 0.285457i | \(0.907854\pi\) | |||||||
\(90\) | −7.43264 | −0.783469 | ||||||||
\(91\) | −4.62721 | −0.485063 | ||||||||
\(92\) | −5.42192 | −0.565274 | ||||||||
\(93\) | 1.76905 | 0.183442 | ||||||||
\(94\) | −28.8311 | −2.97370 | ||||||||
\(95\) | −7.96108 | −0.816790 | ||||||||
\(96\) | −4.30520 | −0.439397 | ||||||||
\(97\) | −12.0081 | −1.21924 | −0.609619 | − | 0.792694i | \(-0.708678\pi\) | ||||
−0.609619 | + | 0.792694i | \(0.708678\pi\) | |||||||
\(98\) | −2.61699 | −0.264356 | ||||||||
\(99\) | −4.95704 | −0.498201 | ||||||||
\(100\) | 4.84863 | 0.484863 | ||||||||
\(101\) | −17.1467 | −1.70616 | −0.853081 | − | 0.521778i | \(-0.825269\pi\) | ||||
−0.853081 | + | 0.521778i | \(0.825269\pi\) | |||||||
\(102\) | −6.14231 | −0.608180 | ||||||||
\(103\) | 4.67886 | 0.461022 | 0.230511 | − | 0.973070i | \(-0.425960\pi\) | ||||
0.230511 | + | 0.973070i | \(0.425960\pi\) | |||||||
\(104\) | −34.4950 | −3.38251 | ||||||||
\(105\) | 0.399813 | 0.0390177 | ||||||||
\(106\) | 10.5889 | 1.02848 | ||||||||
\(107\) | 15.6843 | 1.51626 | 0.758128 | − | 0.652106i | \(-0.226114\pi\) | ||||
0.758128 | + | 0.652106i | \(0.226114\pi\) | |||||||
\(108\) | −11.3214 | −1.08940 | ||||||||
\(109\) | −10.0647 | −0.964022 | −0.482011 | − | 0.876165i | \(-0.660094\pi\) | ||||
−0.482011 | + | 0.876165i | \(0.660094\pi\) | |||||||
\(110\) | 4.56754 | 0.435498 | ||||||||
\(111\) | 1.24720 | 0.118379 | ||||||||
\(112\) | −9.81192 | −0.927139 | ||||||||
\(113\) | 10.3814 | 0.976602 | 0.488301 | − | 0.872675i | \(-0.337617\pi\) | ||||
0.488301 | + | 0.872675i | \(0.337617\pi\) | |||||||
\(114\) | −8.32972 | −0.780149 | ||||||||
\(115\) | 1.11824 | 0.104276 | ||||||||
\(116\) | −24.3446 | −2.26034 | ||||||||
\(117\) | −13.1420 | −1.21498 | ||||||||
\(118\) | −12.1134 | −1.11513 | ||||||||
\(119\) | −5.87048 | −0.538146 | ||||||||
\(120\) | 2.98053 | 0.272084 | ||||||||
\(121\) | −7.95378 | −0.723071 | ||||||||
\(122\) | −9.77326 | −0.884830 | ||||||||
\(123\) | −1.67712 | −0.151221 | ||||||||
\(124\) | 21.4537 | 1.92660 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.43264 | −0.662152 | ||||||||
\(127\) | −2.59810 | −0.230544 | −0.115272 | − | 0.993334i | \(-0.536774\pi\) | ||||
−0.115272 | + | 0.993334i | \(0.536774\pi\) | |||||||
\(128\) | −0.854844 | −0.0755582 | ||||||||
\(129\) | 4.40052 | 0.387445 | ||||||||
\(130\) | 12.1094 | 1.06206 | ||||||||
\(131\) | 5.88602 | 0.514264 | 0.257132 | − | 0.966376i | \(-0.417223\pi\) | ||||
0.257132 | + | 0.966376i | \(0.417223\pi\) | |||||||
\(132\) | 3.38342 | 0.294489 | ||||||||
\(133\) | −7.96108 | −0.690313 | ||||||||
\(134\) | 9.88346 | 0.853801 | ||||||||
\(135\) | 2.33497 | 0.200962 | ||||||||
\(136\) | −43.7634 | −3.75268 | ||||||||
\(137\) | −12.3957 | −1.05904 | −0.529519 | − | 0.848298i | \(-0.677627\pi\) | ||||
−0.529519 | + | 0.848298i | \(0.677627\pi\) | |||||||
\(138\) | 1.17002 | 0.0995985 | ||||||||
\(139\) | −0.288058 | −0.0244328 | −0.0122164 | − | 0.999925i | \(-0.503889\pi\) | ||||
−0.0122164 | + | 0.999925i | \(0.503889\pi\) | |||||||
\(140\) | 4.84863 | 0.409784 | ||||||||
\(141\) | 4.40470 | 0.370943 | ||||||||
\(142\) | −21.1828 | −1.77762 | ||||||||
\(143\) | 8.07607 | 0.675355 | ||||||||
\(144\) | −27.8673 | −2.32228 | ||||||||
\(145\) | 5.02093 | 0.416966 | ||||||||
\(146\) | 2.56571 | 0.212340 | ||||||||
\(147\) | 0.399813 | 0.0329760 | ||||||||
\(148\) | 15.1251 | 1.24327 | ||||||||
\(149\) | −7.05276 | −0.577785 | −0.288892 | − | 0.957362i | \(-0.593287\pi\) | ||||
−0.288892 | + | 0.957362i | \(0.593287\pi\) | |||||||
\(150\) | −1.04630 | −0.0854304 | ||||||||
\(151\) | 4.99633 | 0.406595 | 0.203298 | − | 0.979117i | \(-0.434834\pi\) | ||||
0.203298 | + | 0.979117i | \(0.434834\pi\) | |||||||
\(152\) | −59.3484 | −4.81379 | ||||||||
\(153\) | −16.6730 | −1.34794 | ||||||||
\(154\) | 4.56754 | 0.368063 | ||||||||
\(155\) | −4.42471 | −0.355401 | ||||||||
\(156\) | 8.97004 | 0.718178 | ||||||||
\(157\) | 20.9123 | 1.66898 | 0.834491 | − | 0.551021i | \(-0.185762\pi\) | ||||
0.834491 | + | 0.551021i | \(0.185762\pi\) | |||||||
\(158\) | −42.2487 | −3.36112 | ||||||||
\(159\) | −1.61773 | −0.128294 | ||||||||
\(160\) | 10.7680 | 0.851288 | ||||||||
\(161\) | 1.11824 | 0.0881295 | ||||||||
\(162\) | −19.8548 | −1.55994 | ||||||||
\(163\) | −15.8104 | −1.23836 | −0.619182 | − | 0.785247i | \(-0.712536\pi\) | ||||
−0.619182 | + | 0.785247i | \(0.712536\pi\) | |||||||
\(164\) | −20.3389 | −1.58820 | ||||||||
\(165\) | −0.697810 | −0.0543245 | ||||||||
\(166\) | −8.56488 | −0.664764 | ||||||||
\(167\) | −1.06983 | −0.0827856 | −0.0413928 | − | 0.999143i | \(-0.513179\pi\) | ||||
−0.0413928 | + | 0.999143i | \(0.513179\pi\) | |||||||
\(168\) | 2.98053 | 0.229953 | ||||||||
\(169\) | 8.41107 | 0.647006 | ||||||||
\(170\) | 15.3630 | 1.17829 | ||||||||
\(171\) | −22.6107 | −1.72908 | ||||||||
\(172\) | 53.3663 | 4.06914 | ||||||||
\(173\) | 17.0568 | 1.29680 | 0.648402 | − | 0.761298i | \(-0.275438\pi\) | ||||
0.648402 | + | 0.761298i | \(0.275438\pi\) | |||||||
\(174\) | 5.25342 | 0.398261 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 17.1252 | 1.29086 | ||||||||
\(177\) | 1.85064 | 0.139103 | ||||||||
\(178\) | 47.3227 | 3.54699 | ||||||||
\(179\) | −10.9703 | −0.819957 | −0.409978 | − | 0.912095i | \(-0.634464\pi\) | ||||
−0.409978 | + | 0.912095i | \(0.634464\pi\) | |||||||
\(180\) | 13.7708 | 1.02642 | ||||||||
\(181\) | −26.1359 | −1.94267 | −0.971334 | − | 0.237719i | \(-0.923600\pi\) | ||||
−0.971334 | + | 0.237719i | \(0.923600\pi\) | |||||||
\(182\) | 12.1094 | 0.897605 | ||||||||
\(183\) | 1.49312 | 0.110374 | ||||||||
\(184\) | 8.33626 | 0.614557 | ||||||||
\(185\) | −3.11946 | −0.229347 | ||||||||
\(186\) | −4.62959 | −0.339458 | ||||||||
\(187\) | 10.2460 | 0.749262 | ||||||||
\(188\) | 53.4169 | 3.89583 | ||||||||
\(189\) | 2.33497 | 0.169844 | ||||||||
\(190\) | 20.8341 | 1.51146 | ||||||||
\(191\) | 14.8135 | 1.07187 | 0.535933 | − | 0.844260i | \(-0.319960\pi\) | ||||
0.535933 | + | 0.844260i | \(0.319960\pi\) | |||||||
\(192\) | 3.42079 | 0.246874 | ||||||||
\(193\) | 6.19822 | 0.446158 | 0.223079 | − | 0.974800i | \(-0.428389\pi\) | ||||
0.223079 | + | 0.974800i | \(0.428389\pi\) | |||||||
\(194\) | 31.4251 | 2.25619 | ||||||||
\(195\) | −1.85002 | −0.132482 | ||||||||
\(196\) | 4.84863 | 0.346330 | ||||||||
\(197\) | 27.3227 | 1.94667 | 0.973333 | − | 0.229398i | \(-0.0736759\pi\) | ||||
0.973333 | + | 0.229398i | \(0.0736759\pi\) | |||||||
\(198\) | 12.9725 | 0.921916 | ||||||||
\(199\) | −6.64068 | −0.470745 | −0.235373 | − | 0.971905i | \(-0.575631\pi\) | ||||
−0.235373 | + | 0.971905i | \(0.575631\pi\) | |||||||
\(200\) | −7.45482 | −0.527135 | ||||||||
\(201\) | −1.50995 | −0.106504 | ||||||||
\(202\) | 44.8728 | 3.15724 | ||||||||
\(203\) | 5.02093 | 0.352400 | ||||||||
\(204\) | 11.3802 | 0.796771 | ||||||||
\(205\) | 4.19477 | 0.292975 | ||||||||
\(206\) | −12.2445 | −0.853117 | ||||||||
\(207\) | 3.17596 | 0.220745 | ||||||||
\(208\) | 45.4018 | 3.14805 | ||||||||
\(209\) | 13.8948 | 0.961125 | ||||||||
\(210\) | −1.04630 | −0.0722019 | ||||||||
\(211\) | −1.42768 | −0.0982859 | −0.0491429 | − | 0.998792i | \(-0.515649\pi\) | ||||
−0.0491429 | + | 0.998792i | \(0.515649\pi\) | |||||||
\(212\) | −19.6186 | −1.34741 | ||||||||
\(213\) | 3.23622 | 0.221742 | ||||||||
\(214\) | −41.0456 | −2.80582 | ||||||||
\(215\) | −11.0065 | −0.750635 | ||||||||
\(216\) | 17.4067 | 1.18438 | ||||||||
\(217\) | −4.42471 | −0.300369 | ||||||||
\(218\) | 26.3392 | 1.78391 | ||||||||
\(219\) | −0.391979 | −0.0264875 | ||||||||
\(220\) | −8.46252 | −0.570543 | ||||||||
\(221\) | 27.1640 | 1.82725 | ||||||||
\(222\) | −3.26390 | −0.219059 | ||||||||
\(223\) | −24.4896 | −1.63994 | −0.819972 | − | 0.572404i | \(-0.806011\pi\) | ||||
−0.819972 | + | 0.572404i | \(0.806011\pi\) | |||||||
\(224\) | 10.7680 | 0.719470 | ||||||||
\(225\) | −2.84015 | −0.189343 | ||||||||
\(226\) | −27.1680 | −1.80719 | ||||||||
\(227\) | 19.5428 | 1.29710 | 0.648549 | − | 0.761173i | \(-0.275376\pi\) | ||||
0.648549 | + | 0.761173i | \(0.275376\pi\) | |||||||
\(228\) | 15.4329 | 1.02207 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −2.92641 | −0.192962 | ||||||||
\(231\) | −0.697810 | −0.0459125 | ||||||||
\(232\) | 37.4301 | 2.45741 | ||||||||
\(233\) | −19.9048 | −1.30401 | −0.652005 | − | 0.758215i | \(-0.726072\pi\) | ||||
−0.652005 | + | 0.758215i | \(0.726072\pi\) | |||||||
\(234\) | 34.3924 | 2.24830 | ||||||||
\(235\) | −11.0169 | −0.718664 | ||||||||
\(236\) | 22.4432 | 1.46093 | ||||||||
\(237\) | 6.45457 | 0.419270 | ||||||||
\(238\) | 15.3630 | 0.995834 | ||||||||
\(239\) | −19.7477 | −1.27737 | −0.638687 | − | 0.769467i | \(-0.720522\pi\) | ||||
−0.638687 | + | 0.769467i | \(0.720522\pi\) | |||||||
\(240\) | −3.92293 | −0.253224 | ||||||||
\(241\) | −7.36370 | −0.474337 | −0.237169 | − | 0.971468i | \(-0.576219\pi\) | ||||
−0.237169 | + | 0.971468i | \(0.576219\pi\) | |||||||
\(242\) | 20.8149 | 1.33803 | ||||||||
\(243\) | 10.0382 | 0.643953 | ||||||||
\(244\) | 18.1074 | 1.15921 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 4.38900 | 0.279833 | ||||||||
\(247\) | 36.8376 | 2.34392 | ||||||||
\(248\) | −32.9854 | −2.09457 | ||||||||
\(249\) | 1.30851 | 0.0829233 | ||||||||
\(250\) | 2.61699 | 0.165513 | ||||||||
\(251\) | −16.6724 | −1.05235 | −0.526176 | − | 0.850375i | \(-0.676375\pi\) | ||||
−0.526176 | + | 0.850375i | \(0.676375\pi\) | |||||||
\(252\) | 13.7708 | 0.867480 | ||||||||
\(253\) | −1.95171 | −0.122703 | ||||||||
\(254\) | 6.79918 | 0.426619 | ||||||||
\(255\) | −2.34709 | −0.146981 | ||||||||
\(256\) | −14.8749 | −0.929679 | ||||||||
\(257\) | −27.6047 | −1.72194 | −0.860968 | − | 0.508659i | \(-0.830142\pi\) | ||||
−0.860968 | + | 0.508659i | \(0.830142\pi\) | |||||||
\(258\) | −11.5161 | −0.716962 | ||||||||
\(259\) | −3.11946 | −0.193834 | ||||||||
\(260\) | −22.4356 | −1.39140 | ||||||||
\(261\) | 14.2602 | 0.882684 | ||||||||
\(262\) | −15.4036 | −0.951640 | ||||||||
\(263\) | 1.22268 | 0.0753939 | 0.0376970 | − | 0.999289i | \(-0.487998\pi\) | ||||
0.0376970 | + | 0.999289i | \(0.487998\pi\) | |||||||
\(264\) | −5.20205 | −0.320164 | ||||||||
\(265\) | 4.04621 | 0.248557 | ||||||||
\(266\) | 20.8341 | 1.27742 | ||||||||
\(267\) | −7.22977 | −0.442455 | ||||||||
\(268\) | −18.3116 | −1.11856 | ||||||||
\(269\) | −8.34156 | −0.508594 | −0.254297 | − | 0.967126i | \(-0.581844\pi\) | ||||
−0.254297 | + | 0.967126i | \(0.581844\pi\) | |||||||
\(270\) | −6.11058 | −0.371878 | ||||||||
\(271\) | 28.8883 | 1.75484 | 0.877418 | − | 0.479726i | \(-0.159264\pi\) | ||||
0.877418 | + | 0.479726i | \(0.159264\pi\) | |||||||
\(272\) | 57.6007 | 3.49256 | ||||||||
\(273\) | −1.85002 | −0.111968 | ||||||||
\(274\) | 32.4394 | 1.95974 | ||||||||
\(275\) | 1.74534 | 0.105248 | ||||||||
\(276\) | −2.16775 | −0.130483 | ||||||||
\(277\) | 3.67855 | 0.221022 | 0.110511 | − | 0.993875i | \(-0.464751\pi\) | ||||
0.110511 | + | 0.993875i | \(0.464751\pi\) | |||||||
\(278\) | 0.753845 | 0.0452126 | ||||||||
\(279\) | −12.5668 | −0.752357 | ||||||||
\(280\) | −7.45482 | −0.445511 | ||||||||
\(281\) | 5.35347 | 0.319361 | 0.159681 | − | 0.987169i | \(-0.448954\pi\) | ||||
0.159681 | + | 0.987169i | \(0.448954\pi\) | |||||||
\(282\) | −11.5270 | −0.686426 | ||||||||
\(283\) | 7.28641 | 0.433132 | 0.216566 | − | 0.976268i | \(-0.430514\pi\) | ||||
0.216566 | + | 0.976268i | \(0.430514\pi\) | |||||||
\(284\) | 39.2464 | 2.32884 | ||||||||
\(285\) | −3.18294 | −0.188541 | ||||||||
\(286\) | −21.1350 | −1.24974 | ||||||||
\(287\) | 4.19477 | 0.247609 | ||||||||
\(288\) | 30.5829 | 1.80211 | ||||||||
\(289\) | 17.4626 | 1.02721 | ||||||||
\(290\) | −13.1397 | −0.771591 | ||||||||
\(291\) | −4.80099 | −0.281439 | ||||||||
\(292\) | −4.75362 | −0.278185 | ||||||||
\(293\) | 17.2228 | 1.00617 | 0.503085 | − | 0.864237i | \(-0.332198\pi\) | ||||
0.503085 | + | 0.864237i | \(0.332198\pi\) | |||||||
\(294\) | −1.04630 | −0.0610217 | ||||||||
\(295\) | −4.62878 | −0.269498 | ||||||||
\(296\) | −23.2550 | −1.35167 | ||||||||
\(297\) | −4.07532 | −0.236474 | ||||||||
\(298\) | 18.4570 | 1.06918 | ||||||||
\(299\) | −5.17432 | −0.299239 | ||||||||
\(300\) | 1.93854 | 0.111922 | ||||||||
\(301\) | −11.0065 | −0.634402 | ||||||||
\(302\) | −13.0753 | −0.752401 | ||||||||
\(303\) | −6.85547 | −0.393837 | ||||||||
\(304\) | 78.1135 | 4.48012 | ||||||||
\(305\) | −3.73455 | −0.213840 | ||||||||
\(306\) | 43.6332 | 2.49434 | ||||||||
\(307\) | −16.6755 | −0.951724 | −0.475862 | − | 0.879520i | \(-0.657864\pi\) | ||||
−0.475862 | + | 0.879520i | \(0.657864\pi\) | |||||||
\(308\) | −8.46252 | −0.482197 | ||||||||
\(309\) | 1.87067 | 0.106419 | ||||||||
\(310\) | 11.5794 | 0.657666 | ||||||||
\(311\) | −18.4942 | −1.04871 | −0.524356 | − | 0.851499i | \(-0.675694\pi\) | ||||
−0.524356 | + | 0.851499i | \(0.675694\pi\) | |||||||
\(312\) | −13.7915 | −0.780792 | ||||||||
\(313\) | 14.3145 | 0.809104 | 0.404552 | − | 0.914515i | \(-0.367427\pi\) | ||||
0.404552 | + | 0.914515i | \(0.367427\pi\) | |||||||
\(314\) | −54.7272 | −3.08844 | ||||||||
\(315\) | −2.84015 | −0.160024 | ||||||||
\(316\) | 78.2762 | 4.40338 | ||||||||
\(317\) | −9.01546 | −0.506358 | −0.253179 | − | 0.967419i | \(-0.581476\pi\) | ||||
−0.253179 | + | 0.967419i | \(0.581476\pi\) | |||||||
\(318\) | 4.23357 | 0.237407 | ||||||||
\(319\) | −8.76325 | −0.490648 | ||||||||
\(320\) | −8.55599 | −0.478294 | ||||||||
\(321\) | 6.27077 | 0.350000 | ||||||||
\(322\) | −2.92641 | −0.163083 | ||||||||
\(323\) | 46.7354 | 2.60043 | ||||||||
\(324\) | 36.7860 | 2.04367 | ||||||||
\(325\) | 4.62721 | 0.256671 | ||||||||
\(326\) | 41.3756 | 2.29158 | ||||||||
\(327\) | −4.02399 | −0.222527 | ||||||||
\(328\) | 31.2712 | 1.72666 | ||||||||
\(329\) | −11.0169 | −0.607382 | ||||||||
\(330\) | 1.82616 | 0.100527 | ||||||||
\(331\) | 26.8503 | 1.47583 | 0.737913 | − | 0.674896i | \(-0.235812\pi\) | ||||
0.737913 | + | 0.674896i | \(0.235812\pi\) | |||||||
\(332\) | 15.8686 | 0.870902 | ||||||||
\(333\) | −8.85972 | −0.485510 | ||||||||
\(334\) | 2.79972 | 0.153194 | ||||||||
\(335\) | 3.77666 | 0.206341 | ||||||||
\(336\) | −3.92293 | −0.214013 | ||||||||
\(337\) | −0.0243478 | −0.00132631 | −0.000663153 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000663153 | 1.00000i | \(0.500211\pi\) | ||||||||
\(338\) | −22.0117 | −1.19728 | ||||||||
\(339\) | 4.15062 | 0.225431 | ||||||||
\(340\) | −28.4638 | −1.54366 | ||||||||
\(341\) | 7.72263 | 0.418204 | ||||||||
\(342\) | 59.1718 | 3.19965 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −82.0513 | −4.42391 | ||||||||
\(345\) | 0.447085 | 0.0240703 | ||||||||
\(346\) | −44.6374 | −2.39972 | ||||||||
\(347\) | −15.2660 | −0.819520 | −0.409760 | − | 0.912193i | \(-0.634387\pi\) | ||||
−0.409760 | + | 0.912193i | \(0.634387\pi\) | |||||||
\(348\) | −9.73328 | −0.521759 | ||||||||
\(349\) | 13.3273 | 0.713396 | 0.356698 | − | 0.934220i | \(-0.383903\pi\) | ||||
0.356698 | + | 0.934220i | \(0.383903\pi\) | |||||||
\(350\) | 2.61699 | 0.139884 | ||||||||
\(351\) | −10.8044 | −0.576695 | ||||||||
\(352\) | −18.7939 | −1.00172 | ||||||||
\(353\) | −6.19490 | −0.329721 | −0.164860 | − | 0.986317i | \(-0.552717\pi\) | ||||
−0.164860 | + | 0.986317i | \(0.552717\pi\) | |||||||
\(354\) | −4.84311 | −0.257408 | ||||||||
\(355\) | −8.09433 | −0.429603 | ||||||||
\(356\) | −87.6772 | −4.64688 | ||||||||
\(357\) | −2.34709 | −0.124221 | ||||||||
\(358\) | 28.7091 | 1.51732 | ||||||||
\(359\) | −18.2903 | −0.965327 | −0.482663 | − | 0.875806i | \(-0.660331\pi\) | ||||
−0.482663 | + | 0.875806i | \(0.660331\pi\) | |||||||
\(360\) | −21.1728 | −1.11590 | ||||||||
\(361\) | 44.3788 | 2.33573 | ||||||||
\(362\) | 68.3974 | 3.59489 | ||||||||
\(363\) | −3.18002 | −0.166908 | ||||||||
\(364\) | −22.4356 | −1.17595 | ||||||||
\(365\) | 0.980406 | 0.0513168 | ||||||||
\(366\) | −3.90747 | −0.204247 | ||||||||
\(367\) | 1.92784 | 0.100632 | 0.0503162 | − | 0.998733i | \(-0.483977\pi\) | ||||
0.0503162 | + | 0.998733i | \(0.483977\pi\) | |||||||
\(368\) | −10.9721 | −0.571958 | ||||||||
\(369\) | 11.9138 | 0.620206 | ||||||||
\(370\) | 8.16358 | 0.424404 | ||||||||
\(371\) | 4.04621 | 0.210069 | ||||||||
\(372\) | 8.57748 | 0.444721 | ||||||||
\(373\) | 21.3939 | 1.10773 | 0.553867 | − | 0.832605i | \(-0.313152\pi\) | ||||
0.553867 | + | 0.832605i | \(0.313152\pi\) | |||||||
\(374\) | −26.8137 | −1.38650 | ||||||||
\(375\) | −0.399813 | −0.0206462 | ||||||||
\(376\) | −82.1291 | −4.23548 | ||||||||
\(377\) | −23.2329 | −1.19656 | ||||||||
\(378\) | −6.11058 | −0.314294 | ||||||||
\(379\) | 3.18364 | 0.163533 | 0.0817663 | − | 0.996652i | \(-0.473944\pi\) | ||||
0.0817663 | + | 0.996652i | \(0.473944\pi\) | |||||||
\(380\) | −38.6003 | −1.98015 | ||||||||
\(381\) | −1.03875 | −0.0532168 | ||||||||
\(382\) | −38.7667 | −1.98348 | ||||||||
\(383\) | 26.9179 | 1.37544 | 0.687719 | − | 0.725977i | \(-0.258612\pi\) | ||||
0.687719 | + | 0.725977i | \(0.258612\pi\) | |||||||
\(384\) | −0.341777 | −0.0174412 | ||||||||
\(385\) | 1.74534 | 0.0889509 | ||||||||
\(386\) | −16.2207 | −0.825610 | ||||||||
\(387\) | −31.2600 | −1.58904 | ||||||||
\(388\) | −58.2228 | −2.95581 | ||||||||
\(389\) | −27.8349 | −1.41128 | −0.705642 | − | 0.708569i | \(-0.749341\pi\) | ||||
−0.705642 | + | 0.708569i | \(0.749341\pi\) | |||||||
\(390\) | 4.84147 | 0.245157 | ||||||||
\(391\) | −6.56459 | −0.331986 | ||||||||
\(392\) | −7.45482 | −0.376525 | ||||||||
\(393\) | 2.35330 | 0.118708 | ||||||||
\(394\) | −71.5033 | −3.60228 | ||||||||
\(395\) | −16.1440 | −0.812293 | ||||||||
\(396\) | −24.0348 | −1.20780 | ||||||||
\(397\) | −11.3496 | −0.569618 | −0.284809 | − | 0.958584i | \(-0.591930\pi\) | ||||
−0.284809 | + | 0.958584i | \(0.591930\pi\) | |||||||
\(398\) | 17.3786 | 0.871110 | ||||||||
\(399\) | −3.18294 | −0.159346 | ||||||||
\(400\) | 9.81192 | 0.490596 | ||||||||
\(401\) | 12.1063 | 0.604557 | 0.302279 | − | 0.953220i | \(-0.402253\pi\) | ||||
0.302279 | + | 0.953220i | \(0.402253\pi\) | |||||||
\(402\) | 3.95153 | 0.197084 | ||||||||
\(403\) | 20.4740 | 1.01989 | ||||||||
\(404\) | −83.1380 | −4.13627 | ||||||||
\(405\) | −7.58690 | −0.376996 | ||||||||
\(406\) | −13.1397 | −0.652113 | ||||||||
\(407\) | 5.44452 | 0.269875 | ||||||||
\(408\) | −17.4971 | −0.866238 | ||||||||
\(409\) | 34.3705 | 1.69951 | 0.849755 | − | 0.527177i | \(-0.176750\pi\) | ||||
0.849755 | + | 0.527177i | \(0.176750\pi\) | |||||||
\(410\) | −10.9777 | −0.542148 | ||||||||
\(411\) | −4.95596 | −0.244460 | ||||||||
\(412\) | 22.6861 | 1.11766 | ||||||||
\(413\) | −4.62878 | −0.227767 | ||||||||
\(414\) | −8.31146 | −0.408486 | ||||||||
\(415\) | −3.27280 | −0.160656 | ||||||||
\(416\) | −49.8260 | −2.44292 | ||||||||
\(417\) | −0.115169 | −0.00563986 | ||||||||
\(418\) | −36.3626 | −1.77855 | ||||||||
\(419\) | −34.4905 | −1.68497 | −0.842485 | − | 0.538719i | \(-0.818908\pi\) | ||||
−0.842485 | + | 0.538719i | \(0.818908\pi\) | |||||||
\(420\) | 1.93854 | 0.0945911 | ||||||||
\(421\) | −4.21410 | −0.205383 | −0.102691 | − | 0.994713i | \(-0.532745\pi\) | ||||
−0.102691 | + | 0.994713i | \(0.532745\pi\) | |||||||
\(422\) | 3.73623 | 0.181877 | ||||||||
\(423\) | −31.2897 | −1.52136 | ||||||||
\(424\) | 30.1638 | 1.46488 | ||||||||
\(425\) | 5.87048 | 0.284760 | ||||||||
\(426\) | −8.46914 | −0.410331 | ||||||||
\(427\) | −3.73455 | −0.180727 | ||||||||
\(428\) | 76.0472 | 3.67588 | ||||||||
\(429\) | 3.22891 | 0.155893 | ||||||||
\(430\) | 28.8038 | 1.38904 | ||||||||
\(431\) | 2.04410 | 0.0984606 | 0.0492303 | − | 0.998787i | \(-0.484323\pi\) | ||||
0.0492303 | + | 0.998787i | \(0.484323\pi\) | |||||||
\(432\) | −22.9105 | −1.10228 | ||||||||
\(433\) | 12.4201 | 0.596873 | 0.298437 | − | 0.954429i | \(-0.403535\pi\) | ||||
0.298437 | + | 0.954429i | \(0.403535\pi\) | |||||||
\(434\) | 11.5794 | 0.555829 | ||||||||
\(435\) | 2.00743 | 0.0962490 | ||||||||
\(436\) | −48.7999 | −2.33709 | ||||||||
\(437\) | −8.90238 | −0.425859 | ||||||||
\(438\) | 1.02580 | 0.0490148 | ||||||||
\(439\) | −19.1695 | −0.914912 | −0.457456 | − | 0.889232i | \(-0.651239\pi\) | ||||
−0.457456 | + | 0.889232i | \(0.651239\pi\) | |||||||
\(440\) | 13.0112 | 0.620286 | ||||||||
\(441\) | −2.84015 | −0.135245 | ||||||||
\(442\) | −71.0877 | −3.38130 | ||||||||
\(443\) | 13.1937 | 0.626853 | 0.313426 | − | 0.949613i | \(-0.398523\pi\) | ||||
0.313426 | + | 0.949613i | \(0.398523\pi\) | |||||||
\(444\) | 6.04720 | 0.286987 | ||||||||
\(445\) | 18.0829 | 0.857211 | ||||||||
\(446\) | 64.0889 | 3.03470 | ||||||||
\(447\) | −2.81978 | −0.133371 | ||||||||
\(448\) | −8.55599 | −0.404233 | ||||||||
\(449\) | 37.3597 | 1.76311 | 0.881556 | − | 0.472080i | \(-0.156497\pi\) | ||||
0.881556 | + | 0.472080i | \(0.156497\pi\) | |||||||
\(450\) | 7.43264 | 0.350378 | ||||||||
\(451\) | −7.32131 | −0.344747 | ||||||||
\(452\) | 50.3356 | 2.36759 | ||||||||
\(453\) | 1.99759 | 0.0938552 | ||||||||
\(454\) | −51.1432 | −2.40027 | ||||||||
\(455\) | 4.62721 | 0.216927 | ||||||||
\(456\) | −23.7282 | −1.11118 | ||||||||
\(457\) | 9.80953 | 0.458870 | 0.229435 | − | 0.973324i | \(-0.426312\pi\) | ||||
0.229435 | + | 0.973324i | \(0.426312\pi\) | |||||||
\(458\) | −2.61699 | −0.122284 | ||||||||
\(459\) | −13.7074 | −0.639805 | ||||||||
\(460\) | 5.42192 | 0.252798 | ||||||||
\(461\) | −19.4924 | −0.907852 | −0.453926 | − | 0.891039i | \(-0.649977\pi\) | ||||
−0.453926 | + | 0.891039i | \(0.649977\pi\) | |||||||
\(462\) | 1.82616 | 0.0849607 | ||||||||
\(463\) | 26.3337 | 1.22383 | 0.611915 | − | 0.790923i | \(-0.290399\pi\) | ||||
0.611915 | + | 0.790923i | \(0.290399\pi\) | |||||||
\(464\) | −49.2650 | −2.28707 | ||||||||
\(465\) | −1.76905 | −0.0820379 | ||||||||
\(466\) | 52.0907 | 2.41306 | ||||||||
\(467\) | −20.7782 | −0.961501 | −0.480750 | − | 0.876858i | \(-0.659636\pi\) | ||||
−0.480750 | + | 0.876858i | \(0.659636\pi\) | |||||||
\(468\) | −63.7205 | −2.94548 | ||||||||
\(469\) | 3.77666 | 0.174390 | ||||||||
\(470\) | 28.8311 | 1.32988 | ||||||||
\(471\) | 8.36100 | 0.385254 | ||||||||
\(472\) | −34.5067 | −1.58830 | ||||||||
\(473\) | 19.2101 | 0.883280 | ||||||||
\(474\) | −16.8915 | −0.775854 | ||||||||
\(475\) | 7.96108 | 0.365280 | ||||||||
\(476\) | −28.4638 | −1.30463 | ||||||||
\(477\) | 11.4919 | 0.526176 | ||||||||
\(478\) | 51.6796 | 2.36377 | ||||||||
\(479\) | −41.0377 | −1.87506 | −0.937530 | − | 0.347905i | \(-0.886893\pi\) | ||||
−0.937530 | + | 0.347905i | \(0.886893\pi\) | |||||||
\(480\) | 4.30520 | 0.196504 | ||||||||
\(481\) | 14.4344 | 0.658151 | ||||||||
\(482\) | 19.2707 | 0.877756 | ||||||||
\(483\) | 0.447085 | 0.0203431 | ||||||||
\(484\) | −38.5649 | −1.75295 | ||||||||
\(485\) | 12.0081 | 0.545260 | ||||||||
\(486\) | −26.2699 | −1.19163 | ||||||||
\(487\) | −5.20716 | −0.235959 | −0.117980 | − | 0.993016i | \(-0.537642\pi\) | ||||
−0.117980 | + | 0.993016i | \(0.537642\pi\) | |||||||
\(488\) | −27.8404 | −1.26027 | ||||||||
\(489\) | −6.32119 | −0.285854 | ||||||||
\(490\) | 2.61699 | 0.118223 | ||||||||
\(491\) | 22.6705 | 1.02311 | 0.511553 | − | 0.859252i | \(-0.329071\pi\) | ||||
0.511553 | + | 0.859252i | \(0.329071\pi\) | |||||||
\(492\) | −8.13173 | −0.366607 | ||||||||
\(493\) | −29.4753 | −1.32750 | ||||||||
\(494\) | −96.4036 | −4.33740 | ||||||||
\(495\) | 4.95704 | 0.222802 | ||||||||
\(496\) | 43.4149 | 1.94939 | ||||||||
\(497\) | −8.09433 | −0.363080 | ||||||||
\(498\) | −3.42435 | −0.153449 | ||||||||
\(499\) | 31.3705 | 1.40434 | 0.702168 | − | 0.712011i | \(-0.252215\pi\) | ||||
0.702168 | + | 0.712011i | \(0.252215\pi\) | |||||||
\(500\) | −4.84863 | −0.216837 | ||||||||
\(501\) | −0.427730 | −0.0191095 | ||||||||
\(502\) | 43.6315 | 1.94737 | ||||||||
\(503\) | 32.8822 | 1.46615 | 0.733073 | − | 0.680150i | \(-0.238085\pi\) | ||||
0.733073 | + | 0.680150i | \(0.238085\pi\) | |||||||
\(504\) | −21.1728 | −0.943112 | ||||||||
\(505\) | 17.1467 | 0.763019 | ||||||||
\(506\) | 5.10760 | 0.227060 | ||||||||
\(507\) | 3.36285 | 0.149350 | ||||||||
\(508\) | −12.5972 | −0.558910 | ||||||||
\(509\) | −31.4170 | −1.39253 | −0.696266 | − | 0.717784i | \(-0.745157\pi\) | ||||
−0.696266 | + | 0.717784i | \(0.745157\pi\) | |||||||
\(510\) | 6.14231 | 0.271986 | ||||||||
\(511\) | 0.980406 | 0.0433706 | ||||||||
\(512\) | 40.6370 | 1.79592 | ||||||||
\(513\) | −18.5888 | −0.820718 | ||||||||
\(514\) | 72.2413 | 3.18643 | ||||||||
\(515\) | −4.67886 | −0.206175 | ||||||||
\(516\) | 21.3365 | 0.939287 | ||||||||
\(517\) | 19.2283 | 0.845660 | ||||||||
\(518\) | 8.16358 | 0.358687 | ||||||||
\(519\) | 6.81952 | 0.299344 | ||||||||
\(520\) | 34.4950 | 1.51271 | ||||||||
\(521\) | 34.2747 | 1.50160 | 0.750800 | − | 0.660529i | \(-0.229668\pi\) | ||||
0.750800 | + | 0.660529i | \(0.229668\pi\) | |||||||
\(522\) | −37.3188 | −1.63340 | ||||||||
\(523\) | 13.2657 | 0.580070 | 0.290035 | − | 0.957016i | \(-0.406333\pi\) | ||||
0.290035 | + | 0.957016i | \(0.406333\pi\) | |||||||
\(524\) | 28.5391 | 1.24674 | ||||||||
\(525\) | −0.399813 | −0.0174492 | ||||||||
\(526\) | −3.19975 | −0.139516 | ||||||||
\(527\) | 25.9752 | 1.13150 | ||||||||
\(528\) | 6.84686 | 0.297971 | ||||||||
\(529\) | −21.7495 | −0.945632 | ||||||||
\(530\) | −10.5889 | −0.459952 | ||||||||
\(531\) | −13.1464 | −0.570506 | ||||||||
\(532\) | −38.6003 | −1.67354 | ||||||||
\(533\) | −19.4101 | −0.840743 | ||||||||
\(534\) | 18.9202 | 0.818758 | ||||||||
\(535\) | −15.6843 | −0.678090 | ||||||||
\(536\) | 28.1543 | 1.21608 | ||||||||
\(537\) | −4.38605 | −0.189272 | ||||||||
\(538\) | 21.8298 | 0.941148 | ||||||||
\(539\) | 1.74534 | 0.0751773 | ||||||||
\(540\) | 11.3214 | 0.487194 | ||||||||
\(541\) | 4.00772 | 0.172306 | 0.0861528 | − | 0.996282i | \(-0.472543\pi\) | ||||
0.0861528 | + | 0.996282i | \(0.472543\pi\) | |||||||
\(542\) | −75.6002 | −3.24731 | ||||||||
\(543\) | −10.4495 | −0.448430 | ||||||||
\(544\) | −63.2136 | −2.71026 | ||||||||
\(545\) | 10.0647 | 0.431124 | ||||||||
\(546\) | 4.84147 | 0.207196 | ||||||||
\(547\) | −45.1572 | −1.93078 | −0.965390 | − | 0.260810i | \(-0.916011\pi\) | ||||
−0.965390 | + | 0.260810i | \(0.916011\pi\) | |||||||
\(548\) | −60.1022 | −2.56744 | ||||||||
\(549\) | −10.6067 | −0.452682 | ||||||||
\(550\) | −4.56754 | −0.194761 | ||||||||
\(551\) | −39.9721 | −1.70287 | ||||||||
\(552\) | 3.33294 | 0.141859 | ||||||||
\(553\) | −16.1440 | −0.686513 | ||||||||
\(554\) | −9.62671 | −0.409000 | ||||||||
\(555\) | −1.24720 | −0.0529406 | ||||||||
\(556\) | −1.39669 | −0.0592327 | ||||||||
\(557\) | −3.57824 | −0.151615 | −0.0758073 | − | 0.997122i | \(-0.524153\pi\) | ||||
−0.0758073 | + | 0.997122i | \(0.524153\pi\) | |||||||
\(558\) | 32.8872 | 1.39223 | ||||||||
\(559\) | 50.9293 | 2.15408 | ||||||||
\(560\) | 9.81192 | 0.414629 | ||||||||
\(561\) | 4.09648 | 0.172954 | ||||||||
\(562\) | −14.0100 | −0.590975 | ||||||||
\(563\) | 36.3504 | 1.53199 | 0.765994 | − | 0.642848i | \(-0.222247\pi\) | ||||
0.765994 | + | 0.642848i | \(0.222247\pi\) | |||||||
\(564\) | 21.3567 | 0.899281 | ||||||||
\(565\) | −10.3814 | −0.436750 | ||||||||
\(566\) | −19.0684 | −0.801507 | ||||||||
\(567\) | −7.58690 | −0.318620 | ||||||||
\(568\) | −60.3418 | −2.53188 | ||||||||
\(569\) | 32.3304 | 1.35536 | 0.677681 | − | 0.735356i | \(-0.262985\pi\) | ||||
0.677681 | + | 0.735356i | \(0.262985\pi\) | |||||||
\(570\) | 8.32972 | 0.348893 | ||||||||
\(571\) | 38.8893 | 1.62747 | 0.813734 | − | 0.581237i | \(-0.197431\pi\) | ||||
0.813734 | + | 0.581237i | \(0.197431\pi\) | |||||||
\(572\) | 39.1579 | 1.63727 | ||||||||
\(573\) | 5.92262 | 0.247421 | ||||||||
\(574\) | −10.9777 | −0.458198 | ||||||||
\(575\) | −1.11824 | −0.0466337 | ||||||||
\(576\) | −24.3003 | −1.01251 | ||||||||
\(577\) | −3.75212 | −0.156203 | −0.0781015 | − | 0.996945i | \(-0.524886\pi\) | ||||
−0.0781015 | + | 0.996945i | \(0.524886\pi\) | |||||||
\(578\) | −45.6993 | −1.90084 | ||||||||
\(579\) | 2.47813 | 0.102987 | ||||||||
\(580\) | 24.3446 | 1.01086 | ||||||||
\(581\) | −3.27280 | −0.135779 | ||||||||
\(582\) | 12.5641 | 0.520800 | ||||||||
\(583\) | −7.06203 | −0.292480 | ||||||||
\(584\) | 7.30875 | 0.302438 | ||||||||
\(585\) | 13.1420 | 0.543354 | ||||||||
\(586\) | −45.0720 | −1.86191 | ||||||||
\(587\) | 15.5047 | 0.639946 | 0.319973 | − | 0.947427i | \(-0.396326\pi\) | ||||
0.319973 | + | 0.947427i | \(0.396326\pi\) | |||||||
\(588\) | 1.93854 | 0.0799441 | ||||||||
\(589\) | 35.2255 | 1.45144 | ||||||||
\(590\) | 12.1134 | 0.498703 | ||||||||
\(591\) | 10.9240 | 0.449352 | ||||||||
\(592\) | 30.6079 | 1.25798 | ||||||||
\(593\) | −19.3929 | −0.796370 | −0.398185 | − | 0.917305i | \(-0.630360\pi\) | ||||
−0.398185 | + | 0.917305i | \(0.630360\pi\) | |||||||
\(594\) | 10.6651 | 0.437592 | ||||||||
\(595\) | 5.87048 | 0.240666 | ||||||||
\(596\) | −34.1962 | −1.40073 | ||||||||
\(597\) | −2.65503 | −0.108663 | ||||||||
\(598\) | 13.5411 | 0.553738 | ||||||||
\(599\) | 1.58856 | 0.0649067 | 0.0324534 | − | 0.999473i | \(-0.489668\pi\) | ||||
0.0324534 | + | 0.999473i | \(0.489668\pi\) | |||||||
\(600\) | −2.98053 | −0.121680 | ||||||||
\(601\) | 0.541877 | 0.0221036 | 0.0110518 | − | 0.999939i | \(-0.496482\pi\) | ||||
0.0110518 | + | 0.999939i | \(0.496482\pi\) | |||||||
\(602\) | 28.8038 | 1.17396 | ||||||||
\(603\) | 10.7263 | 0.436807 | ||||||||
\(604\) | 24.2253 | 0.985714 | ||||||||
\(605\) | 7.95378 | 0.323367 | ||||||||
\(606\) | 17.9407 | 0.728791 | ||||||||
\(607\) | 29.7086 | 1.20583 | 0.602917 | − | 0.797804i | \(-0.294005\pi\) | ||||
0.602917 | + | 0.797804i | \(0.294005\pi\) | |||||||
\(608\) | −85.7253 | −3.47662 | ||||||||
\(609\) | 2.00743 | 0.0813452 | ||||||||
\(610\) | 9.77326 | 0.395708 | ||||||||
\(611\) | 50.9776 | 2.06233 | ||||||||
\(612\) | −80.8414 | −3.26782 | ||||||||
\(613\) | 13.8927 | 0.561121 | 0.280560 | − | 0.959836i | \(-0.409480\pi\) | ||||
0.280560 | + | 0.959836i | \(0.409480\pi\) | |||||||
\(614\) | 43.6397 | 1.76115 | ||||||||
\(615\) | 1.67712 | 0.0676280 | ||||||||
\(616\) | 13.0112 | 0.524237 | ||||||||
\(617\) | 9.63940 | 0.388068 | 0.194034 | − | 0.980995i | \(-0.437843\pi\) | ||||
0.194034 | + | 0.980995i | \(0.437843\pi\) | |||||||
\(618\) | −4.89552 | −0.196927 | ||||||||
\(619\) | −16.2902 | −0.654759 | −0.327380 | − | 0.944893i | \(-0.606166\pi\) | ||||
−0.327380 | + | 0.944893i | \(0.606166\pi\) | |||||||
\(620\) | −21.4537 | −0.861603 | ||||||||
\(621\) | 2.61105 | 0.104778 | ||||||||
\(622\) | 48.3992 | 1.94063 | ||||||||
\(623\) | 18.0829 | 0.724476 | ||||||||
\(624\) | 18.1522 | 0.726670 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −37.4609 | −1.49724 | ||||||||
\(627\) | 5.55532 | 0.221858 | ||||||||
\(628\) | 101.396 | 4.04614 | ||||||||
\(629\) | 18.3127 | 0.730176 | ||||||||
\(630\) | 7.43264 | 0.296123 | ||||||||
\(631\) | −15.4851 | −0.616452 | −0.308226 | − | 0.951313i | \(-0.599735\pi\) | ||||
−0.308226 | + | 0.951313i | \(0.599735\pi\) | |||||||
\(632\) | −120.351 | −4.78729 | ||||||||
\(633\) | −0.570806 | −0.0226875 | ||||||||
\(634\) | 23.5933 | 0.937011 | ||||||||
\(635\) | 2.59810 | 0.103102 | ||||||||
\(636\) | −7.84375 | −0.311025 | ||||||||
\(637\) | 4.62721 | 0.183337 | ||||||||
\(638\) | 22.9333 | 0.907939 | ||||||||
\(639\) | −22.9891 | −0.909435 | ||||||||
\(640\) | 0.854844 | 0.0337907 | ||||||||
\(641\) | 4.01235 | 0.158478 | 0.0792391 | − | 0.996856i | \(-0.474751\pi\) | ||||
0.0792391 | + | 0.996856i | \(0.474751\pi\) | |||||||
\(642\) | −16.4105 | −0.647672 | ||||||||
\(643\) | 31.5934 | 1.24592 | 0.622961 | − | 0.782253i | \(-0.285929\pi\) | ||||
0.622961 | + | 0.782253i | \(0.285929\pi\) | |||||||
\(644\) | 5.42192 | 0.213653 | ||||||||
\(645\) | −4.40052 | −0.173270 | ||||||||
\(646\) | −122.306 | −4.81206 | ||||||||
\(647\) | −36.8732 | −1.44963 | −0.724817 | − | 0.688942i | \(-0.758076\pi\) | ||||
−0.724817 | + | 0.688942i | \(0.758076\pi\) | |||||||
\(648\) | −56.5590 | −2.22185 | ||||||||
\(649\) | 8.07880 | 0.317121 | ||||||||
\(650\) | −12.1094 | −0.474968 | ||||||||
\(651\) | −1.76905 | −0.0693347 | ||||||||
\(652\) | −76.6586 | −3.00218 | ||||||||
\(653\) | −48.5667 | −1.90056 | −0.950281 | − | 0.311394i | \(-0.899204\pi\) | ||||
−0.950281 | + | 0.311394i | \(0.899204\pi\) | |||||||
\(654\) | 10.5307 | 0.411784 | ||||||||
\(655\) | −5.88602 | −0.229986 | ||||||||
\(656\) | −41.1587 | −1.60698 | ||||||||
\(657\) | 2.78450 | 0.108634 | ||||||||
\(658\) | 28.8311 | 1.12395 | ||||||||
\(659\) | −43.7606 | −1.70467 | −0.852335 | − | 0.522996i | \(-0.824814\pi\) | ||||
−0.852335 | + | 0.522996i | \(0.824814\pi\) | |||||||
\(660\) | −3.38342 | −0.131699 | ||||||||
\(661\) | −40.1405 | −1.56129 | −0.780643 | − | 0.624977i | \(-0.785108\pi\) | ||||
−0.780643 | + | 0.624977i | \(0.785108\pi\) | |||||||
\(662\) | −70.2669 | −2.73100 | ||||||||
\(663\) | 10.8605 | 0.421786 | ||||||||
\(664\) | −24.3982 | −0.946832 | ||||||||
\(665\) | 7.96108 | 0.308718 | ||||||||
\(666\) | 23.1858 | 0.898431 | ||||||||
\(667\) | 5.61460 | 0.217398 | ||||||||
\(668\) | −5.18718 | −0.200698 | ||||||||
\(669\) | −9.79124 | −0.378551 | ||||||||
\(670\) | −9.88346 | −0.381831 | ||||||||
\(671\) | 6.51807 | 0.251627 | ||||||||
\(672\) | 4.30520 | 0.166077 | ||||||||
\(673\) | −3.67180 | −0.141537 | −0.0707687 | − | 0.997493i | \(-0.522545\pi\) | ||||
−0.0707687 | + | 0.997493i | \(0.522545\pi\) | |||||||
\(674\) | 0.0637178 | 0.00245432 | ||||||||
\(675\) | −2.33497 | −0.0898728 | ||||||||
\(676\) | 40.7822 | 1.56854 | ||||||||
\(677\) | 26.9689 | 1.03650 | 0.518250 | − | 0.855229i | \(-0.326584\pi\) | ||||
0.518250 | + | 0.855229i | \(0.326584\pi\) | |||||||
\(678\) | −10.8621 | −0.417157 | ||||||||
\(679\) | 12.0081 | 0.460829 | ||||||||
\(680\) | 43.7634 | 1.67825 | ||||||||
\(681\) | 7.81344 | 0.299412 | ||||||||
\(682\) | −20.2100 | −0.773882 | ||||||||
\(683\) | 42.0721 | 1.60984 | 0.804921 | − | 0.593381i | \(-0.202207\pi\) | ||||
0.804921 | + | 0.593381i | \(0.202207\pi\) | |||||||
\(684\) | −109.631 | −4.19183 | ||||||||
\(685\) | 12.3957 | 0.473616 | ||||||||
\(686\) | 2.61699 | 0.0999171 | ||||||||
\(687\) | 0.399813 | 0.0152538 | ||||||||
\(688\) | 107.995 | 4.11726 | ||||||||
\(689\) | −18.7227 | −0.713277 | ||||||||
\(690\) | −1.17002 | −0.0445418 | ||||||||
\(691\) | 39.4007 | 1.49887 | 0.749436 | − | 0.662077i | \(-0.230325\pi\) | ||||
0.749436 | + | 0.662077i | \(0.230325\pi\) | |||||||
\(692\) | 82.7020 | 3.14386 | ||||||||
\(693\) | 4.95704 | 0.188302 | ||||||||
\(694\) | 39.9508 | 1.51651 | ||||||||
\(695\) | 0.288058 | 0.0109267 | ||||||||
\(696\) | 14.9650 | 0.567248 | ||||||||
\(697\) | −24.6253 | −0.932750 | ||||||||
\(698\) | −34.8775 | −1.32013 | ||||||||
\(699\) | −7.95821 | −0.301007 | ||||||||
\(700\) | −4.84863 | −0.183261 | ||||||||
\(701\) | 12.3263 | 0.465558 | 0.232779 | − | 0.972530i | \(-0.425218\pi\) | ||||
0.232779 | + | 0.972530i | \(0.425218\pi\) | |||||||
\(702\) | 28.2749 | 1.06717 | ||||||||
\(703\) | 24.8343 | 0.936642 | ||||||||
\(704\) | 14.9331 | 0.562814 | ||||||||
\(705\) | −4.40470 | −0.165891 | ||||||||
\(706\) | 16.2120 | 0.610145 | ||||||||
\(707\) | 17.1467 | 0.644869 | ||||||||
\(708\) | 8.97307 | 0.337229 | ||||||||
\(709\) | 14.7548 | 0.554128 | 0.277064 | − | 0.960851i | \(-0.410639\pi\) | ||||
0.277064 | + | 0.960851i | \(0.410639\pi\) | |||||||
\(710\) | 21.1828 | 0.794975 | ||||||||
\(711\) | −45.8514 | −1.71956 | ||||||||
\(712\) | 134.805 | 5.05202 | ||||||||
\(713\) | −4.94787 | −0.185299 | ||||||||
\(714\) | 6.14231 | 0.229870 | ||||||||
\(715\) | −8.07607 | −0.302028 | ||||||||
\(716\) | −53.1908 | −1.98783 | ||||||||
\(717\) | −7.89539 | −0.294859 | ||||||||
\(718\) | 47.8656 | 1.78633 | ||||||||
\(719\) | 21.2135 | 0.791130 | 0.395565 | − | 0.918438i | \(-0.370549\pi\) | ||||
0.395565 | + | 0.918438i | \(0.370549\pi\) | |||||||
\(720\) | 27.8673 | 1.03855 | ||||||||
\(721\) | −4.67886 | −0.174250 | ||||||||
\(722\) | −116.139 | −4.32224 | ||||||||
\(723\) | −2.94410 | −0.109492 | ||||||||
\(724\) | −126.723 | −4.70963 | ||||||||
\(725\) | −5.02093 | −0.186473 | ||||||||
\(726\) | 8.32207 | 0.308861 | ||||||||
\(727\) | 6.23478 | 0.231235 | 0.115618 | − | 0.993294i | \(-0.463115\pi\) | ||||
0.115618 | + | 0.993294i | \(0.463115\pi\) | |||||||
\(728\) | 34.4950 | 1.27847 | ||||||||
\(729\) | −18.7473 | −0.694344 | ||||||||
\(730\) | −2.56571 | −0.0949612 | ||||||||
\(731\) | 64.6133 | 2.38981 | ||||||||
\(732\) | 7.23957 | 0.267582 | ||||||||
\(733\) | −45.2162 | −1.67010 | −0.835049 | − | 0.550175i | \(-0.814561\pi\) | ||||
−0.835049 | + | 0.550175i | \(0.814561\pi\) | |||||||
\(734\) | −5.04513 | −0.186219 | ||||||||
\(735\) | −0.399813 | −0.0147473 | ||||||||
\(736\) | 12.0412 | 0.443846 | ||||||||
\(737\) | −6.59156 | −0.242803 | ||||||||
\(738\) | −31.1782 | −1.14768 | ||||||||
\(739\) | 47.6842 | 1.75409 | 0.877046 | − | 0.480406i | \(-0.159511\pi\) | ||||
0.877046 | + | 0.480406i | \(0.159511\pi\) | |||||||
\(740\) | −15.1251 | −0.556009 | ||||||||
\(741\) | 14.7281 | 0.541052 | ||||||||
\(742\) | −10.5889 | −0.388730 | ||||||||
\(743\) | −24.3019 | −0.891550 | −0.445775 | − | 0.895145i | \(-0.647072\pi\) | ||||
−0.445775 | + | 0.895145i | \(0.647072\pi\) | |||||||
\(744\) | −13.1880 | −0.483495 | ||||||||
\(745\) | 7.05276 | 0.258393 | ||||||||
\(746\) | −55.9875 | −2.04985 | ||||||||
\(747\) | −9.29525 | −0.340095 | ||||||||
\(748\) | 49.6791 | 1.81645 | ||||||||
\(749\) | −15.6843 | −0.573091 | ||||||||
\(750\) | 1.04630 | 0.0382056 | ||||||||
\(751\) | −7.15359 | −0.261038 | −0.130519 | − | 0.991446i | \(-0.541664\pi\) | ||||
−0.130519 | + | 0.991446i | \(0.541664\pi\) | |||||||
\(752\) | 108.097 | 3.94189 | ||||||||
\(753\) | −6.66584 | −0.242917 | ||||||||
\(754\) | 60.8002 | 2.21421 | ||||||||
\(755\) | −4.99633 | −0.181835 | ||||||||
\(756\) | 11.3214 | 0.411754 | ||||||||
\(757\) | 20.6426 | 0.750266 | 0.375133 | − | 0.926971i | \(-0.377597\pi\) | ||||
0.375133 | + | 0.926971i | \(0.377597\pi\) | |||||||
\(758\) | −8.33154 | −0.302615 | ||||||||
\(759\) | −0.780318 | −0.0283237 | ||||||||
\(760\) | 59.3484 | 2.15279 | ||||||||
\(761\) | 15.4737 | 0.560921 | 0.280461 | − | 0.959866i | \(-0.409513\pi\) | ||||
0.280461 | + | 0.959866i | \(0.409513\pi\) | |||||||
\(762\) | 2.71840 | 0.0984772 | ||||||||
\(763\) | 10.0647 | 0.364366 | ||||||||
\(764\) | 71.8251 | 2.59854 | ||||||||
\(765\) | 16.6730 | 0.602815 | ||||||||
\(766\) | −70.4437 | −2.54524 | ||||||||
\(767\) | 21.4183 | 0.773371 | ||||||||
\(768\) | −5.94716 | −0.214600 | ||||||||
\(769\) | 6.69276 | 0.241347 | 0.120673 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120673 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(770\) | −4.56754 | −0.164603 | ||||||||
\(771\) | −11.0367 | −0.397478 | ||||||||
\(772\) | 30.0528 | 1.08163 | ||||||||
\(773\) | 16.9051 | 0.608033 | 0.304017 | − | 0.952667i | \(-0.401672\pi\) | ||||
0.304017 | + | 0.952667i | \(0.401672\pi\) | |||||||
\(774\) | 81.8071 | 2.94050 | ||||||||
\(775\) | 4.42471 | 0.158940 | ||||||||
\(776\) | 89.5182 | 3.21352 | ||||||||
\(777\) | −1.24720 | −0.0447430 | ||||||||
\(778\) | 72.8435 | 2.61157 | ||||||||
\(779\) | −33.3949 | −1.19650 | ||||||||
\(780\) | −8.97004 | −0.321179 | ||||||||
\(781\) | 14.1274 | 0.505518 | ||||||||
\(782\) | 17.1795 | 0.614336 | ||||||||
\(783\) | 11.7237 | 0.418971 | ||||||||
\(784\) | 9.81192 | 0.350426 | ||||||||
\(785\) | −20.9123 | −0.746392 | ||||||||
\(786\) | −6.15857 | −0.219669 | ||||||||
\(787\) | −24.1160 | −0.859642 | −0.429821 | − | 0.902914i | \(-0.641423\pi\) | ||||
−0.429821 | + | 0.902914i | \(0.641423\pi\) | |||||||
\(788\) | 132.478 | 4.71933 | ||||||||
\(789\) | 0.488845 | 0.0174033 | ||||||||
\(790\) | 42.2487 | 1.50314 | ||||||||
\(791\) | −10.3814 | −0.369121 | ||||||||
\(792\) | 36.9538 | 1.31310 | ||||||||
\(793\) | 17.2805 | 0.613650 | ||||||||
\(794\) | 29.7016 | 1.05407 | ||||||||
\(795\) | 1.61773 | 0.0573749 | ||||||||
\(796\) | −32.1982 | −1.14123 | ||||||||
\(797\) | −15.4285 | −0.546504 | −0.273252 | − | 0.961942i | \(-0.588099\pi\) | ||||
−0.273252 | + | 0.961942i | \(0.588099\pi\) | |||||||
\(798\) | 8.32972 | 0.294869 | ||||||||
\(799\) | 64.6746 | 2.28802 | ||||||||
\(800\) | −10.7680 | −0.380708 | ||||||||
\(801\) | 51.3581 | 1.81465 | ||||||||
\(802\) | −31.6819 | −1.11873 | ||||||||
\(803\) | −1.71115 | −0.0603850 | ||||||||
\(804\) | −7.32120 | −0.258199 | ||||||||
\(805\) | −1.11824 | −0.0394127 | ||||||||
\(806\) | −53.5803 | −1.88729 | ||||||||
\(807\) | −3.33506 | −0.117400 | ||||||||
\(808\) | 127.826 | 4.49689 | ||||||||
\(809\) | −9.75800 | −0.343073 | −0.171536 | − | 0.985178i | \(-0.554873\pi\) | ||||
−0.171536 | + | 0.985178i | \(0.554873\pi\) | |||||||
\(810\) | 19.8548 | 0.697628 | ||||||||
\(811\) | −51.4393 | −1.80628 | −0.903139 | − | 0.429348i | \(-0.858743\pi\) | ||||
−0.903139 | + | 0.429348i | \(0.858743\pi\) | |||||||
\(812\) | 24.3446 | 0.854329 | ||||||||
\(813\) | 11.5499 | 0.405072 | ||||||||
\(814\) | −14.2483 | −0.499401 | ||||||||
\(815\) | 15.8104 | 0.553813 | ||||||||
\(816\) | 23.0295 | 0.806193 | ||||||||
\(817\) | 87.6234 | 3.06556 | ||||||||
\(818\) | −89.9471 | −3.14493 | ||||||||
\(819\) | 13.1420 | 0.459218 | ||||||||
\(820\) | 20.3389 | 0.710264 | ||||||||
\(821\) | 46.1717 | 1.61140 | 0.805701 | − | 0.592322i | \(-0.201789\pi\) | ||||
0.805701 | + | 0.592322i | \(0.201789\pi\) | |||||||
\(822\) | 12.9697 | 0.452370 | ||||||||
\(823\) | −36.3201 | −1.26604 | −0.633019 | − | 0.774136i | \(-0.718184\pi\) | ||||
−0.633019 | + | 0.774136i | \(0.718184\pi\) | |||||||
\(824\) | −34.8801 | −1.21511 | ||||||||
\(825\) | 0.697810 | 0.0242946 | ||||||||
\(826\) | 12.1134 | 0.421481 | ||||||||
\(827\) | −8.67073 | −0.301511 | −0.150755 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150755 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(828\) | 15.3991 | 0.535154 | ||||||||
\(829\) | −18.2959 | −0.635444 | −0.317722 | − | 0.948184i | \(-0.602918\pi\) | ||||
−0.317722 | + | 0.948184i | \(0.602918\pi\) | |||||||
\(830\) | 8.56488 | 0.297291 | ||||||||
\(831\) | 1.47073 | 0.0510190 | ||||||||
\(832\) | 39.5904 | 1.37255 | ||||||||
\(833\) | 5.87048 | 0.203400 | ||||||||
\(834\) | 0.301397 | 0.0104365 | ||||||||
\(835\) | 1.06983 | 0.0370228 | ||||||||
\(836\) | 67.3708 | 2.33007 | ||||||||
\(837\) | −10.3315 | −0.357110 | ||||||||
\(838\) | 90.2612 | 3.11802 | ||||||||
\(839\) | 10.3271 | 0.356531 | 0.178265 | − | 0.983982i | \(-0.442951\pi\) | ||||
0.178265 | + | 0.983982i | \(0.442951\pi\) | |||||||
\(840\) | −2.98053 | −0.102838 | ||||||||
\(841\) | −3.79024 | −0.130698 | ||||||||
\(842\) | 11.0282 | 0.380058 | ||||||||
\(843\) | 2.14039 | 0.0737188 | ||||||||
\(844\) | −6.92231 | −0.238276 | ||||||||
\(845\) | −8.41107 | −0.289350 | ||||||||
\(846\) | 81.8847 | 2.81525 | ||||||||
\(847\) | 7.95378 | 0.273295 | ||||||||
\(848\) | −39.7011 | −1.36334 | ||||||||
\(849\) | 2.91320 | 0.0999807 | ||||||||
\(850\) | −15.3630 | −0.526946 | ||||||||
\(851\) | −3.48829 | −0.119577 | ||||||||
\(852\) | 15.6912 | 0.537572 | ||||||||
\(853\) | −16.3801 | −0.560843 | −0.280421 | − | 0.959877i | \(-0.590474\pi\) | ||||
−0.280421 | + | 0.959877i | \(0.590474\pi\) | |||||||
\(854\) | 9.77326 | 0.334434 | ||||||||
\(855\) | 22.6107 | 0.773269 | ||||||||
\(856\) | −116.923 | −3.99636 | ||||||||
\(857\) | −25.9394 | −0.886073 | −0.443036 | − | 0.896504i | \(-0.646099\pi\) | ||||
−0.443036 | + | 0.896504i | \(0.646099\pi\) | |||||||
\(858\) | −8.45003 | −0.288479 | ||||||||
\(859\) | −37.2587 | −1.27125 | −0.635625 | − | 0.771998i | \(-0.719258\pi\) | ||||
−0.635625 | + | 0.771998i | \(0.719258\pi\) | |||||||
\(860\) | −53.3663 | −1.81977 | ||||||||
\(861\) | 1.67712 | 0.0571561 | ||||||||
\(862\) | −5.34937 | −0.182200 | ||||||||
\(863\) | 44.4899 | 1.51445 | 0.757227 | − | 0.653152i | \(-0.226554\pi\) | ||||
0.757227 | + | 0.653152i | \(0.226554\pi\) | |||||||
\(864\) | 25.1430 | 0.855382 | ||||||||
\(865\) | −17.0568 | −0.579948 | ||||||||
\(866\) | −32.5033 | −1.10451 | ||||||||
\(867\) | 6.98175 | 0.237113 | ||||||||
\(868\) | −21.4537 | −0.728188 | ||||||||
\(869\) | 28.1768 | 0.955833 | ||||||||
\(870\) | −5.25342 | −0.178108 | ||||||||
\(871\) | −17.4754 | −0.592131 | ||||||||
\(872\) | 75.0304 | 2.54085 | ||||||||
\(873\) | 34.1048 | 1.15427 | ||||||||
\(874\) | 23.2974 | 0.788047 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −1.90056 | −0.0642139 | ||||||||
\(877\) | −23.6685 | −0.799229 | −0.399614 | − | 0.916683i | \(-0.630856\pi\) | ||||
−0.399614 | + | 0.916683i | \(0.630856\pi\) | |||||||
\(878\) | 50.1664 | 1.69303 | ||||||||
\(879\) | 6.88591 | 0.232256 | ||||||||
\(880\) | −17.1252 | −0.577290 | ||||||||
\(881\) | −34.2932 | −1.15537 | −0.577683 | − | 0.816261i | \(-0.696043\pi\) | ||||
−0.577683 | + | 0.816261i | \(0.696043\pi\) | |||||||
\(882\) | 7.43264 | 0.250270 | ||||||||
\(883\) | 33.5949 | 1.13056 | 0.565279 | − | 0.824900i | \(-0.308769\pi\) | ||||
0.565279 | + | 0.824900i | \(0.308769\pi\) | |||||||
\(884\) | 131.708 | 4.42981 | ||||||||
\(885\) | −1.85064 | −0.0622087 | ||||||||
\(886\) | −34.5278 | −1.15998 | ||||||||
\(887\) | −57.5722 | −1.93308 | −0.966542 | − | 0.256508i | \(-0.917428\pi\) | ||||
−0.966542 | + | 0.256508i | \(0.917428\pi\) | |||||||
\(888\) | −9.29764 | −0.312008 | ||||||||
\(889\) | 2.59810 | 0.0871373 | ||||||||
\(890\) | −47.3227 | −1.58626 | ||||||||
\(891\) | 13.2418 | 0.443615 | ||||||||
\(892\) | −118.741 | −3.97574 | ||||||||
\(893\) | 87.7065 | 2.93499 | ||||||||
\(894\) | 7.37933 | 0.246802 | ||||||||
\(895\) | 10.9703 | 0.366696 | ||||||||
\(896\) | 0.854844 | 0.0285583 | ||||||||
\(897\) | −2.06876 | −0.0690738 | ||||||||
\(898\) | −97.7698 | −3.26262 | ||||||||
\(899\) | −22.2162 | −0.740950 | ||||||||
\(900\) | −13.7708 | −0.459027 | ||||||||
\(901\) | −23.7532 | −0.791335 | ||||||||
\(902\) | 19.1598 | 0.637951 | ||||||||
\(903\) | −4.40052 | −0.146440 | ||||||||
\(904\) | −77.3916 | −2.57401 | ||||||||
\(905\) | 26.1359 | 0.868787 | ||||||||
\(906\) | −5.22768 | −0.173678 | ||||||||
\(907\) | 6.19626 | 0.205743 | 0.102872 | − | 0.994695i | \(-0.467197\pi\) | ||||
0.102872 | + | 0.994695i | \(0.467197\pi\) | |||||||
\(908\) | 94.7555 | 3.14457 | ||||||||
\(909\) | 48.6993 | 1.61525 | ||||||||
\(910\) | −12.1094 | −0.401421 | ||||||||
\(911\) | 16.2533 | 0.538497 | 0.269248 | − | 0.963071i | \(-0.413225\pi\) | ||||
0.269248 | + | 0.963071i | \(0.413225\pi\) | |||||||
\(912\) | 31.2308 | 1.03415 | ||||||||
\(913\) | 5.71216 | 0.189045 | ||||||||
\(914\) | −25.6714 | −0.849135 | ||||||||
\(915\) | −1.49312 | −0.0493610 | ||||||||
\(916\) | 4.84863 | 0.160203 | ||||||||
\(917\) | −5.88602 | −0.194373 | ||||||||
\(918\) | 35.8720 | 1.18395 | ||||||||
\(919\) | −46.2406 | −1.52534 | −0.762668 | − | 0.646791i | \(-0.776111\pi\) | ||||
−0.762668 | + | 0.646791i | \(0.776111\pi\) | |||||||
\(920\) | −8.33626 | −0.274838 | ||||||||
\(921\) | −6.66709 | −0.219688 | ||||||||
\(922\) | 51.0114 | 1.67997 | ||||||||
\(923\) | 37.4542 | 1.23282 | ||||||||
\(924\) | −3.38342 | −0.111306 | ||||||||
\(925\) | 3.11946 | 0.102567 | ||||||||
\(926\) | −68.9150 | −2.26469 | ||||||||
\(927\) | −13.2887 | −0.436457 | ||||||||
\(928\) | 54.0656 | 1.77479 | ||||||||
\(929\) | 22.9290 | 0.752278 | 0.376139 | − | 0.926563i | \(-0.377252\pi\) | ||||
0.376139 | + | 0.926563i | \(0.377252\pi\) | |||||||
\(930\) | 4.62959 | 0.151810 | ||||||||
\(931\) | 7.96108 | 0.260914 | ||||||||
\(932\) | −96.5111 | −3.16133 | ||||||||
\(933\) | −7.39423 | −0.242076 | ||||||||
\(934\) | 54.3763 | 1.77925 | ||||||||
\(935\) | −10.2460 | −0.335080 | ||||||||
\(936\) | 97.9710 | 3.20228 | ||||||||
\(937\) | 7.64838 | 0.249862 | 0.124931 | − | 0.992165i | \(-0.460129\pi\) | ||||
0.124931 | + | 0.992165i | \(0.460129\pi\) | |||||||
\(938\) | −9.88346 | −0.322706 | ||||||||
\(939\) | 5.72312 | 0.186767 | ||||||||
\(940\) | −53.4169 | −1.74227 | ||||||||
\(941\) | −12.2603 | −0.399674 | −0.199837 | − | 0.979829i | \(-0.564041\pi\) | ||||
−0.199837 | + | 0.979829i | \(0.564041\pi\) | |||||||
\(942\) | −21.8806 | −0.712909 | ||||||||
\(943\) | 4.69075 | 0.152752 | ||||||||
\(944\) | 45.4172 | 1.47820 | ||||||||
\(945\) | −2.33497 | −0.0759564 | ||||||||
\(946\) | −50.2725 | −1.63450 | ||||||||
\(947\) | 25.8125 | 0.838792 | 0.419396 | − | 0.907803i | \(-0.362242\pi\) | ||||
0.419396 | + | 0.907803i | \(0.362242\pi\) | |||||||
\(948\) | 31.2958 | 1.01644 | ||||||||
\(949\) | −4.53654 | −0.147262 | ||||||||
\(950\) | −20.8341 | −0.675946 | ||||||||
\(951\) | −3.60449 | −0.116884 | ||||||||
\(952\) | 43.7634 | 1.41838 | ||||||||
\(953\) | −5.59674 | −0.181296 | −0.0906481 | − | 0.995883i | \(-0.528894\pi\) | ||||
−0.0906481 | + | 0.995883i | \(0.528894\pi\) | |||||||
\(954\) | −30.0740 | −0.973683 | ||||||||
\(955\) | −14.8135 | −0.479353 | ||||||||
\(956\) | −95.7493 | −3.09676 | ||||||||
\(957\) | −3.50366 | −0.113257 | ||||||||
\(958\) | 107.395 | 3.46978 | ||||||||
\(959\) | 12.3957 | 0.400278 | ||||||||
\(960\) | −3.42079 | −0.110406 | ||||||||
\(961\) | −11.4220 | −0.368451 | ||||||||
\(962\) | −37.7746 | −1.21790 | ||||||||
\(963\) | −44.5457 | −1.43547 | ||||||||
\(964\) | −35.7038 | −1.14994 | ||||||||
\(965\) | −6.19822 | −0.199528 | ||||||||
\(966\) | −1.17002 | −0.0376447 | ||||||||
\(967\) | −18.3100 | −0.588811 | −0.294405 | − | 0.955681i | \(-0.595122\pi\) | ||||
−0.294405 | + | 0.955681i | \(0.595122\pi\) | |||||||
\(968\) | 59.2940 | 1.90578 | ||||||||
\(969\) | 18.6854 | 0.600261 | ||||||||
\(970\) | −31.4251 | −1.00900 | ||||||||
\(971\) | 48.9631 | 1.57130 | 0.785650 | − | 0.618671i | \(-0.212329\pi\) | ||||
0.785650 | + | 0.618671i | \(0.212329\pi\) | |||||||
\(972\) | 48.6716 | 1.56114 | ||||||||
\(973\) | 0.288058 | 0.00923472 | ||||||||
\(974\) | 13.6271 | 0.436640 | ||||||||
\(975\) | 1.85002 | 0.0592479 | ||||||||
\(976\) | 36.6431 | 1.17292 | ||||||||
\(977\) | −58.9481 | −1.88592 | −0.942958 | − | 0.332912i | \(-0.891969\pi\) | ||||
−0.942958 | + | 0.332912i | \(0.891969\pi\) | |||||||
\(978\) | 16.5425 | 0.528970 | ||||||||
\(979\) | −31.5609 | −1.00869 | ||||||||
\(980\) | −4.84863 | −0.154884 | ||||||||
\(981\) | 28.5852 | 0.912656 | ||||||||
\(982\) | −59.3284 | −1.89325 | ||||||||
\(983\) | −32.4578 | −1.03524 | −0.517621 | − | 0.855610i | \(-0.673182\pi\) | ||||
−0.517621 | + | 0.855610i | \(0.673182\pi\) | |||||||
\(984\) | 12.5026 | 0.398569 | ||||||||
\(985\) | −27.3227 | −0.870575 | ||||||||
\(986\) | 77.1365 | 2.45653 | ||||||||
\(987\) | −4.40470 | −0.140203 | ||||||||
\(988\) | 178.612 | 5.68240 | ||||||||
\(989\) | −12.3079 | −0.391367 | ||||||||
\(990\) | −12.9725 | −0.412293 | ||||||||
\(991\) | 57.7768 | 1.83534 | 0.917670 | − | 0.397343i | \(-0.130068\pi\) | ||||
0.917670 | + | 0.397343i | \(0.130068\pi\) | |||||||
\(992\) | −47.6454 | −1.51274 | ||||||||
\(993\) | 10.7351 | 0.340668 | ||||||||
\(994\) | 21.1828 | 0.671877 | ||||||||
\(995\) | 6.64068 | 0.210524 | ||||||||
\(996\) | 6.34446 | 0.201032 | ||||||||
\(997\) | 30.7798 | 0.974806 | 0.487403 | − | 0.873177i | \(-0.337944\pi\) | ||||
0.487403 | + | 0.873177i | \(0.337944\pi\) | |||||||
\(998\) | −82.0963 | −2.59871 | ||||||||
\(999\) | −7.28382 | −0.230450 |
(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 | 8015.2.a.l.1.3 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.3 | ✓ | 62 | 1.1 | even | 1 | trivial |