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 | 1.52 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.01854 | 1.42732 | 0.713662 | − | 0.700490i | \(-0.247035\pi\) | ||||
0.713662 | + | 0.700490i | \(0.247035\pi\) | |||||||
\(3\) | −0.120356 | −0.0694877 | −0.0347439 | − | 0.999396i | \(-0.511062\pi\) | ||||
−0.0347439 | + | 0.999396i | \(0.511062\pi\) | |||||||
\(4\) | 2.07451 | 1.03725 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.242944 | −0.0991815 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.150396 | 0.0531729 | ||||||||
\(9\) | −2.98551 | −0.995171 | ||||||||
\(10\) | −2.01854 | −0.638319 | ||||||||
\(11\) | 2.98599 | 0.900310 | 0.450155 | − | 0.892950i | \(-0.351369\pi\) | ||||
0.450155 | + | 0.892950i | \(0.351369\pi\) | |||||||
\(12\) | −0.249680 | −0.0720764 | ||||||||
\(13\) | −0.821835 | −0.227936 | −0.113968 | − | 0.993484i | \(-0.536356\pi\) | ||||
−0.113968 | + | 0.993484i | \(0.536356\pi\) | |||||||
\(14\) | −2.01854 | −0.539478 | ||||||||
\(15\) | 0.120356 | 0.0310758 | ||||||||
\(16\) | −3.84543 | −0.961359 | ||||||||
\(17\) | −1.51410 | −0.367223 | −0.183612 | − | 0.982999i | \(-0.558779\pi\) | ||||
−0.183612 | + | 0.982999i | \(0.558779\pi\) | |||||||
\(18\) | −6.02638 | −1.42043 | ||||||||
\(19\) | −2.64727 | −0.607326 | −0.303663 | − | 0.952779i | \(-0.598210\pi\) | ||||
−0.303663 | + | 0.952779i | \(0.598210\pi\) | |||||||
\(20\) | −2.07451 | −0.463874 | ||||||||
\(21\) | 0.120356 | 0.0262639 | ||||||||
\(22\) | 6.02734 | 1.28503 | ||||||||
\(23\) | −3.02307 | −0.630353 | −0.315176 | − | 0.949033i | \(-0.602064\pi\) | ||||
−0.315176 | + | 0.949033i | \(0.602064\pi\) | |||||||
\(24\) | −0.0181011 | −0.00369486 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.65891 | −0.325339 | ||||||||
\(27\) | 0.720394 | 0.138640 | ||||||||
\(28\) | −2.07451 | −0.392045 | ||||||||
\(29\) | 0.285570 | 0.0530290 | 0.0265145 | − | 0.999648i | \(-0.491559\pi\) | ||||
0.0265145 | + | 0.999648i | \(0.491559\pi\) | |||||||
\(30\) | 0.242944 | 0.0443553 | ||||||||
\(31\) | 10.8458 | 1.94796 | 0.973978 | − | 0.226643i | \(-0.0727750\pi\) | ||||
0.973978 | + | 0.226643i | \(0.0727750\pi\) | |||||||
\(32\) | −8.06296 | −1.42534 | ||||||||
\(33\) | −0.359383 | −0.0625605 | ||||||||
\(34\) | −3.05627 | −0.524147 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −6.19347 | −1.03225 | ||||||||
\(37\) | 8.77302 | 1.44228 | 0.721138 | − | 0.692792i | \(-0.243620\pi\) | ||||
0.721138 | + | 0.692792i | \(0.243620\pi\) | |||||||
\(38\) | −5.34363 | −0.866851 | ||||||||
\(39\) | 0.0989130 | 0.0158388 | ||||||||
\(40\) | −0.150396 | −0.0237797 | ||||||||
\(41\) | 4.58429 | 0.715946 | 0.357973 | − | 0.933732i | \(-0.383468\pi\) | ||||
0.357973 | + | 0.933732i | \(0.383468\pi\) | |||||||
\(42\) | 0.242944 | 0.0374871 | ||||||||
\(43\) | 11.3637 | 1.73295 | 0.866476 | − | 0.499219i | \(-0.166380\pi\) | ||||
0.866476 | + | 0.499219i | \(0.166380\pi\) | |||||||
\(44\) | 6.19446 | 0.933850 | ||||||||
\(45\) | 2.98551 | 0.445054 | ||||||||
\(46\) | −6.10218 | −0.899718 | ||||||||
\(47\) | −4.30252 | −0.627587 | −0.313794 | − | 0.949491i | \(-0.601600\pi\) | ||||
−0.313794 | + | 0.949491i | \(0.601600\pi\) | |||||||
\(48\) | 0.462822 | 0.0668026 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.01854 | 0.285465 | ||||||||
\(51\) | 0.182231 | 0.0255175 | ||||||||
\(52\) | −1.70490 | −0.236427 | ||||||||
\(53\) | −14.5128 | −1.99349 | −0.996743 | − | 0.0806401i | \(-0.974304\pi\) | ||||
−0.996743 | + | 0.0806401i | \(0.974304\pi\) | |||||||
\(54\) | 1.45414 | 0.197884 | ||||||||
\(55\) | −2.98599 | −0.402631 | ||||||||
\(56\) | −0.150396 | −0.0200975 | ||||||||
\(57\) | 0.318616 | 0.0422017 | ||||||||
\(58\) | 0.576434 | 0.0756895 | ||||||||
\(59\) | 7.32785 | 0.954005 | 0.477002 | − | 0.878902i | \(-0.341723\pi\) | ||||
0.477002 | + | 0.878902i | \(0.341723\pi\) | |||||||
\(60\) | 0.249680 | 0.0322335 | ||||||||
\(61\) | −7.06064 | −0.904022 | −0.452011 | − | 0.892012i | \(-0.649293\pi\) | ||||
−0.452011 | + | 0.892012i | \(0.649293\pi\) | |||||||
\(62\) | 21.8926 | 2.78036 | ||||||||
\(63\) | 2.98551 | 0.376139 | ||||||||
\(64\) | −8.58454 | −1.07307 | ||||||||
\(65\) | 0.821835 | 0.101936 | ||||||||
\(66\) | −0.725428 | −0.0892941 | ||||||||
\(67\) | 13.8295 | 1.68954 | 0.844772 | − | 0.535127i | \(-0.179736\pi\) | ||||
0.844772 | + | 0.535127i | \(0.179736\pi\) | |||||||
\(68\) | −3.14101 | −0.380904 | ||||||||
\(69\) | 0.363845 | 0.0438018 | ||||||||
\(70\) | 2.01854 | 0.241262 | ||||||||
\(71\) | 2.79792 | 0.332052 | 0.166026 | − | 0.986121i | \(-0.446906\pi\) | ||||
0.166026 | + | 0.986121i | \(0.446906\pi\) | |||||||
\(72\) | −0.449009 | −0.0529162 | ||||||||
\(73\) | 14.0562 | 1.64515 | 0.822577 | − | 0.568654i | \(-0.192536\pi\) | ||||
0.822577 | + | 0.568654i | \(0.192536\pi\) | |||||||
\(74\) | 17.7087 | 2.05859 | ||||||||
\(75\) | −0.120356 | −0.0138975 | ||||||||
\(76\) | −5.49179 | −0.629951 | ||||||||
\(77\) | −2.98599 | −0.340285 | ||||||||
\(78\) | 0.199660 | 0.0226070 | ||||||||
\(79\) | −9.81451 | −1.10422 | −0.552109 | − | 0.833772i | \(-0.686177\pi\) | ||||
−0.552109 | + | 0.833772i | \(0.686177\pi\) | |||||||
\(80\) | 3.84543 | 0.429933 | ||||||||
\(81\) | 8.86984 | 0.985538 | ||||||||
\(82\) | 9.25358 | 1.02189 | ||||||||
\(83\) | 8.73512 | 0.958804 | 0.479402 | − | 0.877596i | \(-0.340854\pi\) | ||||
0.479402 | + | 0.877596i | \(0.340854\pi\) | |||||||
\(84\) | 0.249680 | 0.0272423 | ||||||||
\(85\) | 1.51410 | 0.164227 | ||||||||
\(86\) | 22.9381 | 2.47348 | ||||||||
\(87\) | −0.0343701 | −0.00368486 | ||||||||
\(88\) | 0.449080 | 0.0478721 | ||||||||
\(89\) | 5.44007 | 0.576646 | 0.288323 | − | 0.957533i | \(-0.406902\pi\) | ||||
0.288323 | + | 0.957533i | \(0.406902\pi\) | |||||||
\(90\) | 6.02638 | 0.635237 | ||||||||
\(91\) | 0.821835 | 0.0861517 | ||||||||
\(92\) | −6.27137 | −0.653836 | ||||||||
\(93\) | −1.30535 | −0.135359 | ||||||||
\(94\) | −8.68482 | −0.895771 | ||||||||
\(95\) | 2.64727 | 0.271605 | ||||||||
\(96\) | 0.970427 | 0.0990438 | ||||||||
\(97\) | −0.253552 | −0.0257443 | −0.0128722 | − | 0.999917i | \(-0.504097\pi\) | ||||
−0.0128722 | + | 0.999917i | \(0.504097\pi\) | |||||||
\(98\) | 2.01854 | 0.203903 | ||||||||
\(99\) | −8.91472 | −0.895963 | ||||||||
\(100\) | 2.07451 | 0.207451 | ||||||||
\(101\) | 11.9362 | 1.18769 | 0.593847 | − | 0.804578i | \(-0.297608\pi\) | ||||
0.593847 | + | 0.804578i | \(0.297608\pi\) | |||||||
\(102\) | 0.367842 | 0.0364217 | ||||||||
\(103\) | −10.7124 | −1.05552 | −0.527761 | − | 0.849393i | \(-0.676969\pi\) | ||||
−0.527761 | + | 0.849393i | \(0.676969\pi\) | |||||||
\(104\) | −0.123600 | −0.0121200 | ||||||||
\(105\) | −0.120356 | −0.0117456 | ||||||||
\(106\) | −29.2947 | −2.84535 | ||||||||
\(107\) | 2.14088 | 0.206967 | 0.103484 | − | 0.994631i | \(-0.467001\pi\) | ||||
0.103484 | + | 0.994631i | \(0.467001\pi\) | |||||||
\(108\) | 1.49446 | 0.143805 | ||||||||
\(109\) | 3.50768 | 0.335975 | 0.167988 | − | 0.985789i | \(-0.446273\pi\) | ||||
0.167988 | + | 0.985789i | \(0.446273\pi\) | |||||||
\(110\) | −6.02734 | −0.574685 | ||||||||
\(111\) | −1.05589 | −0.100220 | ||||||||
\(112\) | 3.84543 | 0.363359 | ||||||||
\(113\) | −7.79191 | −0.733001 | −0.366501 | − | 0.930418i | \(-0.619444\pi\) | ||||
−0.366501 | + | 0.930418i | \(0.619444\pi\) | |||||||
\(114\) | 0.643139 | 0.0602355 | ||||||||
\(115\) | 3.02307 | 0.281902 | ||||||||
\(116\) | 0.592417 | 0.0550045 | ||||||||
\(117\) | 2.45360 | 0.226835 | ||||||||
\(118\) | 14.7916 | 1.36167 | ||||||||
\(119\) | 1.51410 | 0.138797 | ||||||||
\(120\) | 0.0181011 | 0.00165239 | ||||||||
\(121\) | −2.08386 | −0.189442 | ||||||||
\(122\) | −14.2522 | −1.29033 | ||||||||
\(123\) | −0.551748 | −0.0497494 | ||||||||
\(124\) | 22.4996 | 2.02052 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.02638 | 0.536873 | ||||||||
\(127\) | 19.1524 | 1.69950 | 0.849749 | − | 0.527187i | \(-0.176753\pi\) | ||||
0.849749 | + | 0.527187i | \(0.176753\pi\) | |||||||
\(128\) | −1.20233 | −0.106272 | ||||||||
\(129\) | −1.36769 | −0.120419 | ||||||||
\(130\) | 1.65891 | 0.145496 | ||||||||
\(131\) | −4.72072 | −0.412452 | −0.206226 | − | 0.978504i | \(-0.566118\pi\) | ||||
−0.206226 | + | 0.978504i | \(0.566118\pi\) | |||||||
\(132\) | −0.745542 | −0.0648911 | ||||||||
\(133\) | 2.64727 | 0.229548 | ||||||||
\(134\) | 27.9154 | 2.41153 | ||||||||
\(135\) | −0.720394 | −0.0620016 | ||||||||
\(136\) | −0.227714 | −0.0195263 | ||||||||
\(137\) | 4.06542 | 0.347332 | 0.173666 | − | 0.984805i | \(-0.444439\pi\) | ||||
0.173666 | + | 0.984805i | \(0.444439\pi\) | |||||||
\(138\) | 0.734436 | 0.0625193 | ||||||||
\(139\) | 11.0486 | 0.937129 | 0.468565 | − | 0.883429i | \(-0.344771\pi\) | ||||
0.468565 | + | 0.883429i | \(0.344771\pi\) | |||||||
\(140\) | 2.07451 | 0.175328 | ||||||||
\(141\) | 0.517835 | 0.0436096 | ||||||||
\(142\) | 5.64772 | 0.473946 | ||||||||
\(143\) | −2.45399 | −0.205213 | ||||||||
\(144\) | 11.4806 | 0.956717 | ||||||||
\(145\) | −0.285570 | −0.0237153 | ||||||||
\(146\) | 28.3730 | 2.34817 | ||||||||
\(147\) | −0.120356 | −0.00992681 | ||||||||
\(148\) | 18.1997 | 1.49601 | ||||||||
\(149\) | −22.9093 | −1.87680 | −0.938402 | − | 0.345545i | \(-0.887694\pi\) | ||||
−0.938402 | + | 0.345545i | \(0.887694\pi\) | |||||||
\(150\) | −0.242944 | −0.0198363 | ||||||||
\(151\) | −0.773441 | −0.0629418 | −0.0314709 | − | 0.999505i | \(-0.510019\pi\) | ||||
−0.0314709 | + | 0.999505i | \(0.510019\pi\) | |||||||
\(152\) | −0.398139 | −0.0322933 | ||||||||
\(153\) | 4.52037 | 0.365450 | ||||||||
\(154\) | −6.02734 | −0.485697 | ||||||||
\(155\) | −10.8458 | −0.871152 | ||||||||
\(156\) | 0.205196 | 0.0164288 | ||||||||
\(157\) | 12.7942 | 1.02109 | 0.510546 | − | 0.859851i | \(-0.329443\pi\) | ||||
0.510546 | + | 0.859851i | \(0.329443\pi\) | |||||||
\(158\) | −19.8110 | −1.57608 | ||||||||
\(159\) | 1.74671 | 0.138523 | ||||||||
\(160\) | 8.06296 | 0.637433 | ||||||||
\(161\) | 3.02307 | 0.238251 | ||||||||
\(162\) | 17.9041 | 1.40668 | ||||||||
\(163\) | 10.1285 | 0.793322 | 0.396661 | − | 0.917965i | \(-0.370169\pi\) | ||||
0.396661 | + | 0.917965i | \(0.370169\pi\) | |||||||
\(164\) | 9.51014 | 0.742617 | ||||||||
\(165\) | 0.359383 | 0.0279779 | ||||||||
\(166\) | 17.6322 | 1.36852 | ||||||||
\(167\) | 14.3083 | 1.10721 | 0.553604 | − | 0.832780i | \(-0.313252\pi\) | ||||
0.553604 | + | 0.832780i | \(0.313252\pi\) | |||||||
\(168\) | 0.0181011 | 0.00139653 | ||||||||
\(169\) | −12.3246 | −0.948045 | ||||||||
\(170\) | 3.05627 | 0.234405 | ||||||||
\(171\) | 7.90347 | 0.604394 | ||||||||
\(172\) | 23.5741 | 1.79751 | ||||||||
\(173\) | −0.230042 | −0.0174897 | −0.00874487 | − | 0.999962i | \(-0.502784\pi\) | ||||
−0.00874487 | + | 0.999962i | \(0.502784\pi\) | |||||||
\(174\) | −0.0693775 | −0.00525949 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −11.4824 | −0.865521 | ||||||||
\(177\) | −0.881952 | −0.0662916 | ||||||||
\(178\) | 10.9810 | 0.823061 | ||||||||
\(179\) | 2.12800 | 0.159054 | 0.0795270 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795270 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(180\) | 6.19347 | 0.461634 | ||||||||
\(181\) | −4.12887 | −0.306897 | −0.153448 | − | 0.988157i | \(-0.549038\pi\) | ||||
−0.153448 | + | 0.988157i | \(0.549038\pi\) | |||||||
\(182\) | 1.65891 | 0.122966 | ||||||||
\(183\) | 0.849792 | 0.0628184 | ||||||||
\(184\) | −0.454656 | −0.0335177 | ||||||||
\(185\) | −8.77302 | −0.645005 | ||||||||
\(186\) | −2.63491 | −0.193201 | ||||||||
\(187\) | −4.52109 | −0.330615 | ||||||||
\(188\) | −8.92561 | −0.650967 | ||||||||
\(189\) | −0.720394 | −0.0524009 | ||||||||
\(190\) | 5.34363 | 0.387668 | ||||||||
\(191\) | −17.8444 | −1.29118 | −0.645589 | − | 0.763685i | \(-0.723388\pi\) | ||||
−0.645589 | + | 0.763685i | \(0.723388\pi\) | |||||||
\(192\) | 1.03320 | 0.0745650 | ||||||||
\(193\) | 14.3542 | 1.03324 | 0.516620 | − | 0.856215i | \(-0.327190\pi\) | ||||
0.516620 | + | 0.856215i | \(0.327190\pi\) | |||||||
\(194\) | −0.511805 | −0.0367455 | ||||||||
\(195\) | −0.0989130 | −0.00708330 | ||||||||
\(196\) | 2.07451 | 0.148179 | ||||||||
\(197\) | −5.18092 | −0.369125 | −0.184563 | − | 0.982821i | \(-0.559087\pi\) | ||||
−0.184563 | + | 0.982821i | \(0.559087\pi\) | |||||||
\(198\) | −17.9947 | −1.27883 | ||||||||
\(199\) | 13.9001 | 0.985349 | 0.492675 | − | 0.870214i | \(-0.336019\pi\) | ||||
0.492675 | + | 0.870214i | \(0.336019\pi\) | |||||||
\(200\) | 0.150396 | 0.0106346 | ||||||||
\(201\) | −1.66447 | −0.117402 | ||||||||
\(202\) | 24.0937 | 1.69523 | ||||||||
\(203\) | −0.285570 | −0.0200431 | ||||||||
\(204\) | 0.378040 | 0.0264681 | ||||||||
\(205\) | −4.58429 | −0.320181 | ||||||||
\(206\) | −21.6234 | −1.50657 | ||||||||
\(207\) | 9.02541 | 0.627309 | ||||||||
\(208\) | 3.16031 | 0.219128 | ||||||||
\(209\) | −7.90473 | −0.546782 | ||||||||
\(210\) | −0.242944 | −0.0167647 | ||||||||
\(211\) | 13.9829 | 0.962623 | 0.481311 | − | 0.876550i | \(-0.340161\pi\) | ||||
0.481311 | + | 0.876550i | \(0.340161\pi\) | |||||||
\(212\) | −30.1069 | −2.06775 | ||||||||
\(213\) | −0.336747 | −0.0230735 | ||||||||
\(214\) | 4.32146 | 0.295409 | ||||||||
\(215\) | −11.3637 | −0.774999 | ||||||||
\(216\) | 0.108344 | 0.00737189 | ||||||||
\(217\) | −10.8458 | −0.736258 | ||||||||
\(218\) | 7.08040 | 0.479545 | ||||||||
\(219\) | −1.69175 | −0.114318 | ||||||||
\(220\) | −6.19446 | −0.417630 | ||||||||
\(221\) | 1.24434 | 0.0837034 | ||||||||
\(222\) | −2.13135 | −0.143047 | ||||||||
\(223\) | −1.92404 | −0.128843 | −0.0644217 | − | 0.997923i | \(-0.520520\pi\) | ||||
−0.0644217 | + | 0.997923i | \(0.520520\pi\) | |||||||
\(224\) | 8.06296 | 0.538729 | ||||||||
\(225\) | −2.98551 | −0.199034 | ||||||||
\(226\) | −15.7283 | −1.04623 | ||||||||
\(227\) | −25.9778 | −1.72421 | −0.862105 | − | 0.506730i | \(-0.830854\pi\) | ||||
−0.862105 | + | 0.506730i | \(0.830854\pi\) | |||||||
\(228\) | 0.660971 | 0.0437739 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 6.10218 | 0.402366 | ||||||||
\(231\) | 0.359383 | 0.0236456 | ||||||||
\(232\) | 0.0429485 | 0.00281971 | ||||||||
\(233\) | 3.83628 | 0.251323 | 0.125662 | − | 0.992073i | \(-0.459895\pi\) | ||||
0.125662 | + | 0.992073i | \(0.459895\pi\) | |||||||
\(234\) | 4.95269 | 0.323768 | ||||||||
\(235\) | 4.30252 | 0.280666 | ||||||||
\(236\) | 15.2017 | 0.989545 | ||||||||
\(237\) | 1.18124 | 0.0767296 | ||||||||
\(238\) | 3.05627 | 0.198109 | ||||||||
\(239\) | 2.97210 | 0.192249 | 0.0961247 | − | 0.995369i | \(-0.469355\pi\) | ||||
0.0961247 | + | 0.995369i | \(0.469355\pi\) | |||||||
\(240\) | −0.462822 | −0.0298750 | ||||||||
\(241\) | −8.38102 | −0.539869 | −0.269934 | − | 0.962879i | \(-0.587002\pi\) | ||||
−0.269934 | + | 0.962879i | \(0.587002\pi\) | |||||||
\(242\) | −4.20636 | −0.270395 | ||||||||
\(243\) | −3.22872 | −0.207123 | ||||||||
\(244\) | −14.6473 | −0.937700 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −1.11373 | −0.0710086 | ||||||||
\(247\) | 2.17562 | 0.138432 | ||||||||
\(248\) | 1.63116 | 0.103579 | ||||||||
\(249\) | −1.05133 | −0.0666251 | ||||||||
\(250\) | −2.01854 | −0.127664 | ||||||||
\(251\) | −10.8118 | −0.682433 | −0.341217 | − | 0.939985i | \(-0.610839\pi\) | ||||
−0.341217 | + | 0.939985i | \(0.610839\pi\) | |||||||
\(252\) | 6.19347 | 0.390152 | ||||||||
\(253\) | −9.02685 | −0.567513 | ||||||||
\(254\) | 38.6599 | 2.42574 | ||||||||
\(255\) | −0.182231 | −0.0114118 | ||||||||
\(256\) | 14.7421 | 0.921383 | ||||||||
\(257\) | −2.99285 | −0.186689 | −0.0933443 | − | 0.995634i | \(-0.529756\pi\) | ||||
−0.0933443 | + | 0.995634i | \(0.529756\pi\) | |||||||
\(258\) | −2.76075 | −0.171877 | ||||||||
\(259\) | −8.77302 | −0.545129 | ||||||||
\(260\) | 1.70490 | 0.105734 | ||||||||
\(261\) | −0.852573 | −0.0527729 | ||||||||
\(262\) | −9.52898 | −0.588702 | ||||||||
\(263\) | −9.74849 | −0.601117 | −0.300559 | − | 0.953763i | \(-0.597173\pi\) | ||||
−0.300559 | + | 0.953763i | \(0.597173\pi\) | |||||||
\(264\) | −0.0540496 | −0.00332652 | ||||||||
\(265\) | 14.5128 | 0.891514 | ||||||||
\(266\) | 5.34363 | 0.327639 | ||||||||
\(267\) | −0.654746 | −0.0400698 | ||||||||
\(268\) | 28.6894 | 1.75248 | ||||||||
\(269\) | 14.7391 | 0.898659 | 0.449330 | − | 0.893366i | \(-0.351663\pi\) | ||||
0.449330 | + | 0.893366i | \(0.351663\pi\) | |||||||
\(270\) | −1.45414 | −0.0884964 | ||||||||
\(271\) | 28.1816 | 1.71191 | 0.855954 | − | 0.517052i | \(-0.172971\pi\) | ||||
0.855954 | + | 0.517052i | \(0.172971\pi\) | |||||||
\(272\) | 5.82237 | 0.353033 | ||||||||
\(273\) | −0.0989130 | −0.00598649 | ||||||||
\(274\) | 8.20621 | 0.495755 | ||||||||
\(275\) | 2.98599 | 0.180062 | ||||||||
\(276\) | 0.754799 | 0.0454335 | ||||||||
\(277\) | −25.0942 | −1.50776 | −0.753882 | − | 0.657009i | \(-0.771821\pi\) | ||||
−0.753882 | + | 0.657009i | \(0.771821\pi\) | |||||||
\(278\) | 22.3020 | 1.33759 | ||||||||
\(279\) | −32.3802 | −1.93855 | ||||||||
\(280\) | 0.150396 | 0.00898786 | ||||||||
\(281\) | 1.34593 | 0.0802917 | 0.0401458 | − | 0.999194i | \(-0.487218\pi\) | ||||
0.0401458 | + | 0.999194i | \(0.487218\pi\) | |||||||
\(282\) | 1.04527 | 0.0622450 | ||||||||
\(283\) | 4.90900 | 0.291809 | 0.145905 | − | 0.989299i | \(-0.453391\pi\) | ||||
0.145905 | + | 0.989299i | \(0.453391\pi\) | |||||||
\(284\) | 5.80430 | 0.344422 | ||||||||
\(285\) | −0.318616 | −0.0188732 | ||||||||
\(286\) | −4.95348 | −0.292906 | ||||||||
\(287\) | −4.58429 | −0.270602 | ||||||||
\(288\) | 24.0721 | 1.41846 | ||||||||
\(289\) | −14.7075 | −0.865147 | ||||||||
\(290\) | −0.576434 | −0.0338494 | ||||||||
\(291\) | 0.0305166 | 0.00178891 | ||||||||
\(292\) | 29.1597 | 1.70644 | ||||||||
\(293\) | −4.75988 | −0.278075 | −0.139038 | − | 0.990287i | \(-0.544401\pi\) | ||||
−0.139038 | + | 0.990287i | \(0.544401\pi\) | |||||||
\(294\) | −0.242944 | −0.0141688 | ||||||||
\(295\) | −7.32785 | −0.426644 | ||||||||
\(296\) | 1.31942 | 0.0766900 | ||||||||
\(297\) | 2.15109 | 0.124819 | ||||||||
\(298\) | −46.2434 | −2.67881 | ||||||||
\(299\) | 2.48446 | 0.143680 | ||||||||
\(300\) | −0.249680 | −0.0144153 | ||||||||
\(301\) | −11.3637 | −0.654994 | ||||||||
\(302\) | −1.56122 | −0.0898383 | ||||||||
\(303\) | −1.43659 | −0.0825302 | ||||||||
\(304\) | 10.1799 | 0.583858 | ||||||||
\(305\) | 7.06064 | 0.404291 | ||||||||
\(306\) | 9.12455 | 0.521616 | ||||||||
\(307\) | 6.36296 | 0.363153 | 0.181577 | − | 0.983377i | \(-0.441880\pi\) | ||||
0.181577 | + | 0.983377i | \(0.441880\pi\) | |||||||
\(308\) | −6.19446 | −0.352962 | ||||||||
\(309\) | 1.28930 | 0.0733459 | ||||||||
\(310\) | −21.8926 | −1.24342 | ||||||||
\(311\) | 7.14344 | 0.405067 | 0.202534 | − | 0.979275i | \(-0.435082\pi\) | ||||
0.202534 | + | 0.979275i | \(0.435082\pi\) | |||||||
\(312\) | 0.0148761 | 0.000842193 0 | ||||||||
\(313\) | 32.8188 | 1.85503 | 0.927515 | − | 0.373785i | \(-0.121940\pi\) | ||||
0.927515 | + | 0.373785i | \(0.121940\pi\) | |||||||
\(314\) | 25.8257 | 1.45743 | ||||||||
\(315\) | −2.98551 | −0.168215 | ||||||||
\(316\) | −20.3603 | −1.14535 | ||||||||
\(317\) | 20.8644 | 1.17186 | 0.585931 | − | 0.810361i | \(-0.300729\pi\) | ||||
0.585931 | + | 0.810361i | \(0.300729\pi\) | |||||||
\(318\) | 3.52580 | 0.197717 | ||||||||
\(319\) | 0.852709 | 0.0477425 | ||||||||
\(320\) | 8.58454 | 0.479890 | ||||||||
\(321\) | −0.257669 | −0.0143817 | ||||||||
\(322\) | 6.10218 | 0.340061 | ||||||||
\(323\) | 4.00824 | 0.223024 | ||||||||
\(324\) | 18.4005 | 1.02225 | ||||||||
\(325\) | −0.821835 | −0.0455872 | ||||||||
\(326\) | 20.4447 | 1.13233 | ||||||||
\(327\) | −0.422172 | −0.0233461 | ||||||||
\(328\) | 0.689458 | 0.0380689 | ||||||||
\(329\) | 4.30252 | 0.237206 | ||||||||
\(330\) | 0.725428 | 0.0399335 | ||||||||
\(331\) | 22.7009 | 1.24775 | 0.623877 | − | 0.781523i | \(-0.285557\pi\) | ||||
0.623877 | + | 0.781523i | \(0.285557\pi\) | |||||||
\(332\) | 18.1211 | 0.994523 | ||||||||
\(333\) | −26.1920 | −1.43531 | ||||||||
\(334\) | 28.8819 | 1.58034 | ||||||||
\(335\) | −13.8295 | −0.755587 | ||||||||
\(336\) | −0.462822 | −0.0252490 | ||||||||
\(337\) | 26.0804 | 1.42069 | 0.710346 | − | 0.703852i | \(-0.248538\pi\) | ||||
0.710346 | + | 0.703852i | \(0.248538\pi\) | |||||||
\(338\) | −24.8777 | −1.35317 | ||||||||
\(339\) | 0.937805 | 0.0509346 | ||||||||
\(340\) | 3.14101 | 0.170345 | ||||||||
\(341\) | 32.3853 | 1.75376 | ||||||||
\(342\) | 15.9535 | 0.862666 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.70905 | 0.0921461 | ||||||||
\(345\) | −0.363845 | −0.0195887 | ||||||||
\(346\) | −0.464348 | −0.0249635 | ||||||||
\(347\) | 26.9574 | 1.44715 | 0.723574 | − | 0.690247i | \(-0.242498\pi\) | ||||
0.723574 | + | 0.690247i | \(0.242498\pi\) | |||||||
\(348\) | −0.0713010 | −0.00382214 | ||||||||
\(349\) | −12.6296 | −0.676049 | −0.338024 | − | 0.941137i | \(-0.609759\pi\) | ||||
−0.338024 | + | 0.941137i | \(0.609759\pi\) | |||||||
\(350\) | −2.01854 | −0.107896 | ||||||||
\(351\) | −0.592045 | −0.0316010 | ||||||||
\(352\) | −24.0759 | −1.28325 | ||||||||
\(353\) | −24.6136 | −1.31005 | −0.655025 | − | 0.755607i | \(-0.727342\pi\) | ||||
−0.655025 | + | 0.755607i | \(0.727342\pi\) | |||||||
\(354\) | −1.78026 | −0.0946196 | ||||||||
\(355\) | −2.79792 | −0.148498 | ||||||||
\(356\) | 11.2855 | 0.598128 | ||||||||
\(357\) | −0.182231 | −0.00964471 | ||||||||
\(358\) | 4.29545 | 0.227022 | ||||||||
\(359\) | −27.3321 | −1.44253 | −0.721266 | − | 0.692658i | \(-0.756439\pi\) | ||||
−0.721266 | + | 0.692658i | \(0.756439\pi\) | |||||||
\(360\) | 0.449009 | 0.0236648 | ||||||||
\(361\) | −11.9919 | −0.631155 | ||||||||
\(362\) | −8.33430 | −0.438041 | ||||||||
\(363\) | 0.250806 | 0.0131639 | ||||||||
\(364\) | 1.70490 | 0.0893612 | ||||||||
\(365\) | −14.0562 | −0.735735 | ||||||||
\(366\) | 1.71534 | 0.0896623 | ||||||||
\(367\) | 4.72242 | 0.246508 | 0.123254 | − | 0.992375i | \(-0.460667\pi\) | ||||
0.123254 | + | 0.992375i | \(0.460667\pi\) | |||||||
\(368\) | 11.6250 | 0.605995 | ||||||||
\(369\) | −13.6865 | −0.712489 | ||||||||
\(370\) | −17.7087 | −0.920631 | ||||||||
\(371\) | 14.5128 | 0.753467 | ||||||||
\(372\) | −2.70797 | −0.140402 | ||||||||
\(373\) | −27.7541 | −1.43705 | −0.718526 | − | 0.695500i | \(-0.755183\pi\) | ||||
−0.718526 | + | 0.695500i | \(0.755183\pi\) | |||||||
\(374\) | −9.12600 | −0.471894 | ||||||||
\(375\) | 0.120356 | 0.00621517 | ||||||||
\(376\) | −0.647081 | −0.0333707 | ||||||||
\(377\) | −0.234691 | −0.0120872 | ||||||||
\(378\) | −1.45414 | −0.0747931 | ||||||||
\(379\) | −11.8613 | −0.609273 | −0.304636 | − | 0.952469i | \(-0.598535\pi\) | ||||
−0.304636 | + | 0.952469i | \(0.598535\pi\) | |||||||
\(380\) | 5.49179 | 0.281723 | ||||||||
\(381\) | −2.30511 | −0.118094 | ||||||||
\(382\) | −36.0197 | −1.84293 | ||||||||
\(383\) | −3.24910 | −0.166021 | −0.0830106 | − | 0.996549i | \(-0.526454\pi\) | ||||
−0.0830106 | + | 0.996549i | \(0.526454\pi\) | |||||||
\(384\) | 0.144708 | 0.00738460 | ||||||||
\(385\) | 2.98599 | 0.152180 | ||||||||
\(386\) | 28.9746 | 1.47477 | ||||||||
\(387\) | −33.9266 | −1.72458 | ||||||||
\(388\) | −0.525996 | −0.0267034 | ||||||||
\(389\) | −27.5946 | −1.39910 | −0.699550 | − | 0.714583i | \(-0.746616\pi\) | ||||
−0.699550 | + | 0.714583i | \(0.746616\pi\) | |||||||
\(390\) | −0.199660 | −0.0101102 | ||||||||
\(391\) | 4.57723 | 0.231480 | ||||||||
\(392\) | 0.150396 | 0.00759613 | ||||||||
\(393\) | 0.568169 | 0.0286603 | ||||||||
\(394\) | −10.4579 | −0.526861 | ||||||||
\(395\) | 9.81451 | 0.493821 | ||||||||
\(396\) | −18.4936 | −0.929341 | ||||||||
\(397\) | 23.7727 | 1.19312 | 0.596559 | − | 0.802570i | \(-0.296534\pi\) | ||||
0.596559 | + | 0.802570i | \(0.296534\pi\) | |||||||
\(398\) | 28.0578 | 1.40641 | ||||||||
\(399\) | −0.318616 | −0.0159507 | ||||||||
\(400\) | −3.84543 | −0.192272 | ||||||||
\(401\) | −1.62548 | −0.0811728 | −0.0405864 | − | 0.999176i | \(-0.512923\pi\) | ||||
−0.0405864 | + | 0.999176i | \(0.512923\pi\) | |||||||
\(402\) | −3.35980 | −0.167571 | ||||||||
\(403\) | −8.91343 | −0.444009 | ||||||||
\(404\) | 24.7617 | 1.23194 | ||||||||
\(405\) | −8.86984 | −0.440746 | ||||||||
\(406\) | −0.576434 | −0.0286080 | ||||||||
\(407\) | 26.1961 | 1.29849 | ||||||||
\(408\) | 0.0274068 | 0.00135684 | ||||||||
\(409\) | −11.1149 | −0.549596 | −0.274798 | − | 0.961502i | \(-0.588611\pi\) | ||||
−0.274798 | + | 0.961502i | \(0.588611\pi\) | |||||||
\(410\) | −9.25358 | −0.457002 | ||||||||
\(411\) | −0.489298 | −0.0241353 | ||||||||
\(412\) | −22.2229 | −1.09484 | ||||||||
\(413\) | −7.32785 | −0.360580 | ||||||||
\(414\) | 18.2182 | 0.895373 | ||||||||
\(415\) | −8.73512 | −0.428790 | ||||||||
\(416\) | 6.62642 | 0.324887 | ||||||||
\(417\) | −1.32977 | −0.0651190 | ||||||||
\(418\) | −15.9560 | −0.780435 | ||||||||
\(419\) | 36.4669 | 1.78152 | 0.890762 | − | 0.454470i | \(-0.150171\pi\) | ||||
0.890762 | + | 0.454470i | \(0.150171\pi\) | |||||||
\(420\) | −0.249680 | −0.0121831 | ||||||||
\(421\) | −6.47846 | −0.315741 | −0.157870 | − | 0.987460i | \(-0.550463\pi\) | ||||
−0.157870 | + | 0.987460i | \(0.550463\pi\) | |||||||
\(422\) | 28.2251 | 1.37397 | ||||||||
\(423\) | 12.8452 | 0.624557 | ||||||||
\(424\) | −2.18266 | −0.105999 | ||||||||
\(425\) | −1.51410 | −0.0734447 | ||||||||
\(426\) | −0.679738 | −0.0329334 | ||||||||
\(427\) | 7.06064 | 0.341688 | ||||||||
\(428\) | 4.44128 | 0.214677 | ||||||||
\(429\) | 0.295353 | 0.0142598 | ||||||||
\(430\) | −22.9381 | −1.10618 | ||||||||
\(431\) | 0.605717 | 0.0291764 | 0.0145882 | − | 0.999894i | \(-0.495356\pi\) | ||||
0.0145882 | + | 0.999894i | \(0.495356\pi\) | |||||||
\(432\) | −2.77023 | −0.133283 | ||||||||
\(433\) | 40.0413 | 1.92426 | 0.962132 | − | 0.272585i | \(-0.0878786\pi\) | ||||
0.962132 | + | 0.272585i | \(0.0878786\pi\) | |||||||
\(434\) | −21.8926 | −1.05088 | ||||||||
\(435\) | 0.0343701 | 0.00164792 | ||||||||
\(436\) | 7.27672 | 0.348491 | ||||||||
\(437\) | 8.00288 | 0.382830 | ||||||||
\(438\) | −3.41487 | −0.163169 | ||||||||
\(439\) | 14.0004 | 0.668201 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(440\) | −0.449080 | −0.0214091 | ||||||||
\(441\) | −2.98551 | −0.142167 | ||||||||
\(442\) | 2.51175 | 0.119472 | ||||||||
\(443\) | 30.6569 | 1.45655 | 0.728277 | − | 0.685283i | \(-0.240321\pi\) | ||||
0.728277 | + | 0.685283i | \(0.240321\pi\) | |||||||
\(444\) | −2.19045 | −0.103954 | ||||||||
\(445\) | −5.44007 | −0.257884 | ||||||||
\(446\) | −3.88376 | −0.183901 | ||||||||
\(447\) | 2.75728 | 0.130415 | ||||||||
\(448\) | 8.58454 | 0.405581 | ||||||||
\(449\) | 20.4269 | 0.964006 | 0.482003 | − | 0.876170i | \(-0.339909\pi\) | ||||
0.482003 | + | 0.876170i | \(0.339909\pi\) | |||||||
\(450\) | −6.02638 | −0.284086 | ||||||||
\(451\) | 13.6886 | 0.644573 | ||||||||
\(452\) | −16.1644 | −0.760308 | ||||||||
\(453\) | 0.0930885 | 0.00437368 | ||||||||
\(454\) | −52.4373 | −2.46101 | ||||||||
\(455\) | −0.821835 | −0.0385282 | ||||||||
\(456\) | 0.0479185 | 0.00224399 | ||||||||
\(457\) | −26.9185 | −1.25920 | −0.629598 | − | 0.776921i | \(-0.716780\pi\) | ||||
−0.629598 | + | 0.776921i | \(0.716780\pi\) | |||||||
\(458\) | 2.01854 | 0.0943202 | ||||||||
\(459\) | −1.09075 | −0.0509118 | ||||||||
\(460\) | 6.27137 | 0.292404 | ||||||||
\(461\) | 40.7205 | 1.89654 | 0.948271 | − | 0.317462i | \(-0.102830\pi\) | ||||
0.948271 | + | 0.317462i | \(0.102830\pi\) | |||||||
\(462\) | 0.725428 | 0.0337500 | ||||||||
\(463\) | −19.8876 | −0.924256 | −0.462128 | − | 0.886813i | \(-0.652914\pi\) | ||||
−0.462128 | + | 0.886813i | \(0.652914\pi\) | |||||||
\(464\) | −1.09814 | −0.0509799 | ||||||||
\(465\) | 1.30535 | 0.0605344 | ||||||||
\(466\) | 7.74369 | 0.358720 | ||||||||
\(467\) | −19.1949 | −0.888232 | −0.444116 | − | 0.895969i | \(-0.646482\pi\) | ||||
−0.444116 | + | 0.895969i | \(0.646482\pi\) | |||||||
\(468\) | 5.09001 | 0.235286 | ||||||||
\(469\) | −13.8295 | −0.638587 | ||||||||
\(470\) | 8.68482 | 0.400601 | ||||||||
\(471\) | −1.53987 | −0.0709533 | ||||||||
\(472\) | 1.10208 | 0.0507272 | ||||||||
\(473\) | 33.9320 | 1.56019 | ||||||||
\(474\) | 2.38438 | 0.109518 | ||||||||
\(475\) | −2.64727 | −0.121465 | ||||||||
\(476\) | 3.14101 | 0.143968 | ||||||||
\(477\) | 43.3282 | 1.98386 | ||||||||
\(478\) | 5.99931 | 0.274402 | ||||||||
\(479\) | −13.0349 | −0.595579 | −0.297789 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297789 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(480\) | −0.970427 | −0.0442937 | ||||||||
\(481\) | −7.20997 | −0.328747 | ||||||||
\(482\) | −16.9174 | −0.770567 | ||||||||
\(483\) | −0.363845 | −0.0165555 | ||||||||
\(484\) | −4.32299 | −0.196499 | ||||||||
\(485\) | 0.253552 | 0.0115132 | ||||||||
\(486\) | −6.51731 | −0.295631 | ||||||||
\(487\) | −1.39679 | −0.0632944 | −0.0316472 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316472 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(488\) | −1.06189 | −0.0480695 | ||||||||
\(489\) | −1.21902 | −0.0551261 | ||||||||
\(490\) | −2.01854 | −0.0911884 | ||||||||
\(491\) | 19.4386 | 0.877251 | 0.438625 | − | 0.898670i | \(-0.355465\pi\) | ||||
0.438625 | + | 0.898670i | \(0.355465\pi\) | |||||||
\(492\) | −1.14461 | −0.0516028 | ||||||||
\(493\) | −0.432381 | −0.0194735 | ||||||||
\(494\) | 4.39158 | 0.197587 | ||||||||
\(495\) | 8.91472 | 0.400687 | ||||||||
\(496\) | −41.7067 | −1.87268 | ||||||||
\(497\) | −2.79792 | −0.125504 | ||||||||
\(498\) | −2.12214 | −0.0950956 | ||||||||
\(499\) | 16.8089 | 0.752470 | 0.376235 | − | 0.926524i | \(-0.377219\pi\) | ||||
0.376235 | + | 0.926524i | \(0.377219\pi\) | |||||||
\(500\) | −2.07451 | −0.0927748 | ||||||||
\(501\) | −1.72209 | −0.0769374 | ||||||||
\(502\) | −21.8240 | −0.974054 | ||||||||
\(503\) | 40.5525 | 1.80815 | 0.904073 | − | 0.427378i | \(-0.140562\pi\) | ||||
0.904073 | + | 0.427378i | \(0.140562\pi\) | |||||||
\(504\) | 0.449009 | 0.0200004 | ||||||||
\(505\) | −11.9362 | −0.531153 | ||||||||
\(506\) | −18.2211 | −0.810025 | ||||||||
\(507\) | 1.48334 | 0.0658775 | ||||||||
\(508\) | 39.7317 | 1.76281 | ||||||||
\(509\) | −0.740309 | −0.0328136 | −0.0164068 | − | 0.999865i | \(-0.505223\pi\) | ||||
−0.0164068 | + | 0.999865i | \(0.505223\pi\) | |||||||
\(510\) | −0.367842 | −0.0162883 | ||||||||
\(511\) | −14.0562 | −0.621810 | ||||||||
\(512\) | 32.1622 | 1.42138 | ||||||||
\(513\) | −1.90708 | −0.0841996 | ||||||||
\(514\) | −6.04118 | −0.266465 | ||||||||
\(515\) | 10.7124 | 0.472044 | ||||||||
\(516\) | −2.83729 | −0.124905 | ||||||||
\(517\) | −12.8473 | −0.565023 | ||||||||
\(518\) | −17.7087 | −0.778075 | ||||||||
\(519\) | 0.0276869 | 0.00121532 | ||||||||
\(520\) | 0.123600 | 0.00542024 | ||||||||
\(521\) | −35.4362 | −1.55249 | −0.776245 | − | 0.630432i | \(-0.782878\pi\) | ||||
−0.776245 | + | 0.630432i | \(0.782878\pi\) | |||||||
\(522\) | −1.72095 | −0.0753241 | ||||||||
\(523\) | 11.4006 | 0.498513 | 0.249257 | − | 0.968437i | \(-0.419814\pi\) | ||||
0.249257 | + | 0.968437i | \(0.419814\pi\) | |||||||
\(524\) | −9.79318 | −0.427817 | ||||||||
\(525\) | 0.120356 | 0.00525278 | ||||||||
\(526\) | −19.6777 | −0.857989 | ||||||||
\(527\) | −16.4216 | −0.715335 | ||||||||
\(528\) | 1.38198 | 0.0601430 | ||||||||
\(529\) | −13.8611 | −0.602655 | ||||||||
\(530\) | 29.2947 | 1.27248 | ||||||||
\(531\) | −21.8774 | −0.949398 | ||||||||
\(532\) | 5.49179 | 0.238099 | ||||||||
\(533\) | −3.76753 | −0.163190 | ||||||||
\(534\) | −1.32163 | −0.0571926 | ||||||||
\(535\) | −2.14088 | −0.0925585 | ||||||||
\(536\) | 2.07990 | 0.0898380 | ||||||||
\(537\) | −0.256118 | −0.0110523 | ||||||||
\(538\) | 29.7515 | 1.28268 | ||||||||
\(539\) | 2.98599 | 0.128616 | ||||||||
\(540\) | −1.49446 | −0.0643114 | ||||||||
\(541\) | 23.4058 | 1.00629 | 0.503146 | − | 0.864201i | \(-0.332176\pi\) | ||||
0.503146 | + | 0.864201i | \(0.332176\pi\) | |||||||
\(542\) | 56.8856 | 2.44345 | ||||||||
\(543\) | 0.496935 | 0.0213255 | ||||||||
\(544\) | 12.2081 | 0.523419 | ||||||||
\(545\) | −3.50768 | −0.150253 | ||||||||
\(546\) | −0.199660 | −0.00854465 | ||||||||
\(547\) | −13.1125 | −0.560649 | −0.280325 | − | 0.959905i | \(-0.590442\pi\) | ||||
−0.280325 | + | 0.959905i | \(0.590442\pi\) | |||||||
\(548\) | 8.43374 | 0.360271 | ||||||||
\(549\) | 21.0796 | 0.899657 | ||||||||
\(550\) | 6.02734 | 0.257007 | ||||||||
\(551\) | −0.755981 | −0.0322059 | ||||||||
\(552\) | 0.0547207 | 0.00232907 | ||||||||
\(553\) | 9.81451 | 0.417355 | ||||||||
\(554\) | −50.6537 | −2.15207 | ||||||||
\(555\) | 1.05589 | 0.0448199 | ||||||||
\(556\) | 22.9204 | 0.972041 | ||||||||
\(557\) | 4.01859 | 0.170273 | 0.0851365 | − | 0.996369i | \(-0.472867\pi\) | ||||
0.0851365 | + | 0.996369i | \(0.472867\pi\) | |||||||
\(558\) | −65.3607 | −2.76694 | ||||||||
\(559\) | −9.33910 | −0.395002 | ||||||||
\(560\) | −3.84543 | −0.162499 | ||||||||
\(561\) | 0.544141 | 0.0229737 | ||||||||
\(562\) | 2.71682 | 0.114602 | ||||||||
\(563\) | 23.6255 | 0.995695 | 0.497847 | − | 0.867265i | \(-0.334124\pi\) | ||||
0.497847 | + | 0.867265i | \(0.334124\pi\) | |||||||
\(564\) | 1.07425 | 0.0452342 | ||||||||
\(565\) | 7.79191 | 0.327808 | ||||||||
\(566\) | 9.90901 | 0.416507 | ||||||||
\(567\) | −8.86984 | −0.372498 | ||||||||
\(568\) | 0.420795 | 0.0176562 | ||||||||
\(569\) | 0.466002 | 0.0195358 | 0.00976792 | − | 0.999952i | \(-0.496891\pi\) | ||||
0.00976792 | + | 0.999952i | \(0.496891\pi\) | |||||||
\(570\) | −0.643139 | −0.0269381 | ||||||||
\(571\) | 9.13380 | 0.382238 | 0.191119 | − | 0.981567i | \(-0.438788\pi\) | ||||
0.191119 | + | 0.981567i | \(0.438788\pi\) | |||||||
\(572\) | −5.09082 | −0.212858 | ||||||||
\(573\) | 2.14769 | 0.0897211 | ||||||||
\(574\) | −9.25358 | −0.386237 | ||||||||
\(575\) | −3.02307 | −0.126071 | ||||||||
\(576\) | 25.6293 | 1.06789 | ||||||||
\(577\) | 17.2137 | 0.716616 | 0.358308 | − | 0.933604i | \(-0.383354\pi\) | ||||
0.358308 | + | 0.933604i | \(0.383354\pi\) | |||||||
\(578\) | −29.6877 | −1.23485 | ||||||||
\(579\) | −1.72762 | −0.0717975 | ||||||||
\(580\) | −0.592417 | −0.0245988 | ||||||||
\(581\) | −8.73512 | −0.362394 | ||||||||
\(582\) | 0.0615990 | 0.00255336 | ||||||||
\(583\) | −43.3351 | −1.79476 | ||||||||
\(584\) | 2.11399 | 0.0874776 | ||||||||
\(585\) | −2.45360 | −0.101444 | ||||||||
\(586\) | −9.60801 | −0.396903 | ||||||||
\(587\) | 13.5138 | 0.557775 | 0.278887 | − | 0.960324i | \(-0.410034\pi\) | ||||
0.278887 | + | 0.960324i | \(0.410034\pi\) | |||||||
\(588\) | −0.249680 | −0.0102966 | ||||||||
\(589\) | −28.7117 | −1.18304 | ||||||||
\(590\) | −14.7916 | −0.608959 | ||||||||
\(591\) | 0.623556 | 0.0256497 | ||||||||
\(592\) | −33.7361 | −1.38654 | ||||||||
\(593\) | −21.3194 | −0.875484 | −0.437742 | − | 0.899101i | \(-0.644222\pi\) | ||||
−0.437742 | + | 0.899101i | \(0.644222\pi\) | |||||||
\(594\) | 4.34206 | 0.178157 | ||||||||
\(595\) | −1.51410 | −0.0620721 | ||||||||
\(596\) | −47.5255 | −1.94672 | ||||||||
\(597\) | −1.67296 | −0.0684696 | ||||||||
\(598\) | 5.01499 | 0.205078 | ||||||||
\(599\) | −23.9550 | −0.978775 | −0.489388 | − | 0.872066i | \(-0.662780\pi\) | ||||
−0.489388 | + | 0.872066i | \(0.662780\pi\) | |||||||
\(600\) | −0.0181011 | −0.000738973 0 | ||||||||
\(601\) | 20.0702 | 0.818681 | 0.409340 | − | 0.912382i | \(-0.365759\pi\) | ||||
0.409340 | + | 0.912382i | \(0.365759\pi\) | |||||||
\(602\) | −22.9381 | −0.934889 | ||||||||
\(603\) | −41.2882 | −1.68139 | ||||||||
\(604\) | −1.60451 | −0.0652866 | ||||||||
\(605\) | 2.08386 | 0.0847210 | ||||||||
\(606\) | −2.89982 | −0.117797 | ||||||||
\(607\) | 5.41787 | 0.219905 | 0.109952 | − | 0.993937i | \(-0.464930\pi\) | ||||
0.109952 | + | 0.993937i | \(0.464930\pi\) | |||||||
\(608\) | 21.3449 | 0.865648 | ||||||||
\(609\) | 0.0343701 | 0.00139275 | ||||||||
\(610\) | 14.2522 | 0.577054 | ||||||||
\(611\) | 3.53596 | 0.143050 | ||||||||
\(612\) | 9.37754 | 0.379064 | ||||||||
\(613\) | −10.8001 | −0.436213 | −0.218106 | − | 0.975925i | \(-0.569988\pi\) | ||||
−0.218106 | + | 0.975925i | \(0.569988\pi\) | |||||||
\(614\) | 12.8439 | 0.518337 | ||||||||
\(615\) | 0.551748 | 0.0222486 | ||||||||
\(616\) | −0.449080 | −0.0180940 | ||||||||
\(617\) | −6.15143 | −0.247647 | −0.123824 | − | 0.992304i | \(-0.539516\pi\) | ||||
−0.123824 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(618\) | 2.60251 | 0.104688 | ||||||||
\(619\) | 11.3119 | 0.454665 | 0.227333 | − | 0.973817i | \(-0.427000\pi\) | ||||
0.227333 | + | 0.973817i | \(0.427000\pi\) | |||||||
\(620\) | −22.4996 | −0.903606 | ||||||||
\(621\) | −2.17780 | −0.0873920 | ||||||||
\(622\) | 14.4193 | 0.578162 | ||||||||
\(623\) | −5.44007 | −0.217952 | ||||||||
\(624\) | −0.380363 | −0.0152267 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 66.2462 | 2.64773 | ||||||||
\(627\) | 0.951384 | 0.0379946 | ||||||||
\(628\) | 26.5417 | 1.05913 | ||||||||
\(629\) | −13.2832 | −0.529637 | ||||||||
\(630\) | −6.02638 | −0.240097 | ||||||||
\(631\) | −31.9598 | −1.27230 | −0.636150 | − | 0.771566i | \(-0.719474\pi\) | ||||
−0.636150 | + | 0.771566i | \(0.719474\pi\) | |||||||
\(632\) | −1.47606 | −0.0587145 | ||||||||
\(633\) | −1.68293 | −0.0668904 | ||||||||
\(634\) | 42.1157 | 1.67263 | ||||||||
\(635\) | −19.1524 | −0.760039 | ||||||||
\(636\) | 3.62355 | 0.143683 | ||||||||
\(637\) | −0.821835 | −0.0325623 | ||||||||
\(638\) | 1.72123 | 0.0681440 | ||||||||
\(639\) | −8.35323 | −0.330449 | ||||||||
\(640\) | 1.20233 | 0.0475263 | ||||||||
\(641\) | −1.77275 | −0.0700196 | −0.0350098 | − | 0.999387i | \(-0.511146\pi\) | ||||
−0.0350098 | + | 0.999387i | \(0.511146\pi\) | |||||||
\(642\) | −0.520115 | −0.0205273 | ||||||||
\(643\) | −8.92532 | −0.351980 | −0.175990 | − | 0.984392i | \(-0.556313\pi\) | ||||
−0.175990 | + | 0.984392i | \(0.556313\pi\) | |||||||
\(644\) | 6.27137 | 0.247127 | ||||||||
\(645\) | 1.36769 | 0.0538529 | ||||||||
\(646\) | 8.09079 | 0.318328 | ||||||||
\(647\) | −33.4910 | −1.31667 | −0.658334 | − | 0.752726i | \(-0.728739\pi\) | ||||
−0.658334 | + | 0.752726i | \(0.728739\pi\) | |||||||
\(648\) | 1.33399 | 0.0524039 | ||||||||
\(649\) | 21.8809 | 0.858900 | ||||||||
\(650\) | −1.65891 | −0.0650677 | ||||||||
\(651\) | 1.30535 | 0.0511609 | ||||||||
\(652\) | 21.0115 | 0.822876 | ||||||||
\(653\) | 24.1848 | 0.946426 | 0.473213 | − | 0.880948i | \(-0.343094\pi\) | ||||
0.473213 | + | 0.880948i | \(0.343094\pi\) | |||||||
\(654\) | −0.852171 | −0.0333225 | ||||||||
\(655\) | 4.72072 | 0.184454 | ||||||||
\(656\) | −17.6286 | −0.688281 | ||||||||
\(657\) | −41.9650 | −1.63721 | ||||||||
\(658\) | 8.68482 | 0.338569 | ||||||||
\(659\) | −24.4776 | −0.953512 | −0.476756 | − | 0.879036i | \(-0.658187\pi\) | ||||
−0.476756 | + | 0.879036i | \(0.658187\pi\) | |||||||
\(660\) | 0.745542 | 0.0290202 | ||||||||
\(661\) | 36.2043 | 1.40818 | 0.704091 | − | 0.710109i | \(-0.251355\pi\) | ||||
0.704091 | + | 0.710109i | \(0.251355\pi\) | |||||||
\(662\) | 45.8227 | 1.78095 | ||||||||
\(663\) | −0.149764 | −0.00581636 | ||||||||
\(664\) | 1.31372 | 0.0509824 | ||||||||
\(665\) | −2.64727 | −0.102657 | ||||||||
\(666\) | −52.8696 | −2.04865 | ||||||||
\(667\) | −0.863296 | −0.0334270 | ||||||||
\(668\) | 29.6826 | 1.14846 | ||||||||
\(669\) | 0.231571 | 0.00895303 | ||||||||
\(670\) | −27.9154 | −1.07847 | ||||||||
\(671\) | −21.0830 | −0.813900 | ||||||||
\(672\) | −0.970427 | −0.0374350 | ||||||||
\(673\) | −10.8707 | −0.419034 | −0.209517 | − | 0.977805i | \(-0.567189\pi\) | ||||
−0.209517 | + | 0.977805i | \(0.567189\pi\) | |||||||
\(674\) | 52.6444 | 2.02779 | ||||||||
\(675\) | 0.720394 | 0.0277280 | ||||||||
\(676\) | −25.5674 | −0.983363 | ||||||||
\(677\) | −13.4130 | −0.515503 | −0.257752 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257752 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(678\) | 1.89300 | 0.0727002 | ||||||||
\(679\) | 0.253552 | 0.00973044 | ||||||||
\(680\) | 0.227714 | 0.00873244 | ||||||||
\(681\) | 3.12659 | 0.119811 | ||||||||
\(682\) | 65.3711 | 2.50319 | ||||||||
\(683\) | 28.0061 | 1.07162 | 0.535811 | − | 0.844338i | \(-0.320006\pi\) | ||||
0.535811 | + | 0.844338i | \(0.320006\pi\) | |||||||
\(684\) | 16.3958 | 0.626910 | ||||||||
\(685\) | −4.06542 | −0.155332 | ||||||||
\(686\) | −2.01854 | −0.0770682 | ||||||||
\(687\) | −0.120356 | −0.00459188 | ||||||||
\(688\) | −43.6984 | −1.66599 | ||||||||
\(689\) | 11.9271 | 0.454387 | ||||||||
\(690\) | −0.734436 | −0.0279595 | ||||||||
\(691\) | −41.6412 | −1.58411 | −0.792053 | − | 0.610452i | \(-0.790988\pi\) | ||||
−0.792053 | + | 0.610452i | \(0.790988\pi\) | |||||||
\(692\) | −0.477223 | −0.0181413 | ||||||||
\(693\) | 8.91472 | 0.338642 | ||||||||
\(694\) | 54.4146 | 2.06555 | ||||||||
\(695\) | −11.0486 | −0.419097 | ||||||||
\(696\) | −0.00516912 | −0.000195935 0 | ||||||||
\(697\) | −6.94108 | −0.262912 | ||||||||
\(698\) | −25.4934 | −0.964941 | ||||||||
\(699\) | −0.461721 | −0.0174639 | ||||||||
\(700\) | −2.07451 | −0.0784090 | ||||||||
\(701\) | −13.0563 | −0.493129 | −0.246564 | − | 0.969126i | \(-0.579302\pi\) | ||||
−0.246564 | + | 0.969126i | \(0.579302\pi\) | |||||||
\(702\) | −1.19507 | −0.0451049 | ||||||||
\(703\) | −23.2246 | −0.875932 | ||||||||
\(704\) | −25.6334 | −0.966093 | ||||||||
\(705\) | −0.517835 | −0.0195028 | ||||||||
\(706\) | −49.6836 | −1.86987 | ||||||||
\(707\) | −11.9362 | −0.448906 | ||||||||
\(708\) | −1.82962 | −0.0687612 | ||||||||
\(709\) | −35.4715 | −1.33216 | −0.666081 | − | 0.745879i | \(-0.732030\pi\) | ||||
−0.666081 | + | 0.745879i | \(0.732030\pi\) | |||||||
\(710\) | −5.64772 | −0.211955 | ||||||||
\(711\) | 29.3014 | 1.09889 | ||||||||
\(712\) | 0.818163 | 0.0306620 | ||||||||
\(713\) | −32.7874 | −1.22790 | ||||||||
\(714\) | −0.367842 | −0.0137661 | ||||||||
\(715\) | 2.45399 | 0.0917741 | ||||||||
\(716\) | 4.41455 | 0.164979 | ||||||||
\(717\) | −0.357711 | −0.0133590 | ||||||||
\(718\) | −55.1709 | −2.05896 | ||||||||
\(719\) | 3.15811 | 0.117778 | 0.0588889 | − | 0.998265i | \(-0.481244\pi\) | ||||
0.0588889 | + | 0.998265i | \(0.481244\pi\) | |||||||
\(720\) | −11.4806 | −0.427857 | ||||||||
\(721\) | 10.7124 | 0.398950 | ||||||||
\(722\) | −24.2062 | −0.900862 | ||||||||
\(723\) | 1.00871 | 0.0375142 | ||||||||
\(724\) | −8.56537 | −0.318330 | ||||||||
\(725\) | 0.285570 | 0.0106058 | ||||||||
\(726\) | 0.506262 | 0.0187891 | ||||||||
\(727\) | −2.07992 | −0.0771401 | −0.0385701 | − | 0.999256i | \(-0.512280\pi\) | ||||
−0.0385701 | + | 0.999256i | \(0.512280\pi\) | |||||||
\(728\) | 0.123600 | 0.00458094 | ||||||||
\(729\) | −26.2209 | −0.971145 | ||||||||
\(730\) | −28.3730 | −1.05013 | ||||||||
\(731\) | −17.2058 | −0.636380 | ||||||||
\(732\) | 1.76290 | 0.0651586 | ||||||||
\(733\) | −16.5428 | −0.611022 | −0.305511 | − | 0.952189i | \(-0.598827\pi\) | ||||
−0.305511 | + | 0.952189i | \(0.598827\pi\) | |||||||
\(734\) | 9.53239 | 0.351847 | ||||||||
\(735\) | 0.120356 | 0.00443941 | ||||||||
\(736\) | 24.3749 | 0.898469 | ||||||||
\(737\) | 41.2948 | 1.52111 | ||||||||
\(738\) | −27.6267 | −1.01695 | ||||||||
\(739\) | 17.3838 | 0.639472 | 0.319736 | − | 0.947507i | \(-0.396406\pi\) | ||||
0.319736 | + | 0.947507i | \(0.396406\pi\) | |||||||
\(740\) | −18.1997 | −0.669034 | ||||||||
\(741\) | −0.261850 | −0.00961929 | ||||||||
\(742\) | 29.2947 | 1.07544 | ||||||||
\(743\) | −7.12855 | −0.261521 | −0.130761 | − | 0.991414i | \(-0.541742\pi\) | ||||
−0.130761 | + | 0.991414i | \(0.541742\pi\) | |||||||
\(744\) | −0.196320 | −0.00719743 | ||||||||
\(745\) | 22.9093 | 0.839332 | ||||||||
\(746\) | −56.0228 | −2.05114 | ||||||||
\(747\) | −26.0788 | −0.954174 | ||||||||
\(748\) | −9.37903 | −0.342931 | ||||||||
\(749\) | −2.14088 | −0.0782262 | ||||||||
\(750\) | 0.242944 | 0.00887106 | ||||||||
\(751\) | −45.6608 | −1.66618 | −0.833092 | − | 0.553134i | \(-0.813432\pi\) | ||||
−0.833092 | + | 0.553134i | \(0.813432\pi\) | |||||||
\(752\) | 16.5451 | 0.603337 | ||||||||
\(753\) | 1.30126 | 0.0474207 | ||||||||
\(754\) | −0.473734 | −0.0172524 | ||||||||
\(755\) | 0.773441 | 0.0281484 | ||||||||
\(756\) | −1.49446 | −0.0543531 | ||||||||
\(757\) | 23.3090 | 0.847180 | 0.423590 | − | 0.905854i | \(-0.360770\pi\) | ||||
0.423590 | + | 0.905854i | \(0.360770\pi\) | |||||||
\(758\) | −23.9425 | −0.869630 | ||||||||
\(759\) | 1.08644 | 0.0394352 | ||||||||
\(760\) | 0.398139 | 0.0144420 | ||||||||
\(761\) | 36.5513 | 1.32498 | 0.662492 | − | 0.749069i | \(-0.269499\pi\) | ||||
0.662492 | + | 0.749069i | \(0.269499\pi\) | |||||||
\(762\) | −4.65296 | −0.168559 | ||||||||
\(763\) | −3.50768 | −0.126987 | ||||||||
\(764\) | −37.0184 | −1.33928 | ||||||||
\(765\) | −4.52037 | −0.163434 | ||||||||
\(766\) | −6.55844 | −0.236966 | ||||||||
\(767\) | −6.02228 | −0.217452 | ||||||||
\(768\) | −1.77431 | −0.0640248 | ||||||||
\(769\) | 32.8931 | 1.18616 | 0.593078 | − | 0.805145i | \(-0.297913\pi\) | ||||
0.593078 | + | 0.805145i | \(0.297913\pi\) | |||||||
\(770\) | 6.02734 | 0.217210 | ||||||||
\(771\) | 0.360208 | 0.0129726 | ||||||||
\(772\) | 29.7780 | 1.07173 | ||||||||
\(773\) | −22.2418 | −0.799981 | −0.399991 | − | 0.916519i | \(-0.630987\pi\) | ||||
−0.399991 | + | 0.916519i | \(0.630987\pi\) | |||||||
\(774\) | −68.4821 | −2.46154 | ||||||||
\(775\) | 10.8458 | 0.389591 | ||||||||
\(776\) | −0.0381332 | −0.00136890 | ||||||||
\(777\) | 1.05589 | 0.0378798 | ||||||||
\(778\) | −55.7008 | −1.99697 | ||||||||
\(779\) | −12.1359 | −0.434813 | ||||||||
\(780\) | −0.205196 | −0.00734718 | ||||||||
\(781\) | 8.35456 | 0.298950 | ||||||||
\(782\) | 9.23932 | 0.330397 | ||||||||
\(783\) | 0.205723 | 0.00735193 | ||||||||
\(784\) | −3.84543 | −0.137337 | ||||||||
\(785\) | −12.7942 | −0.456646 | ||||||||
\(786\) | 1.14687 | 0.0409076 | ||||||||
\(787\) | 1.42465 | 0.0507831 | 0.0253916 | − | 0.999678i | \(-0.491917\pi\) | ||||
0.0253916 | + | 0.999678i | \(0.491917\pi\) | |||||||
\(788\) | −10.7479 | −0.382877 | ||||||||
\(789\) | 1.17329 | 0.0417703 | ||||||||
\(790\) | 19.8110 | 0.704843 | ||||||||
\(791\) | 7.79191 | 0.277049 | ||||||||
\(792\) | −1.34074 | −0.0476410 | ||||||||
\(793\) | 5.80268 | 0.206059 | ||||||||
\(794\) | 47.9861 | 1.70296 | ||||||||
\(795\) | −1.74671 | −0.0619493 | ||||||||
\(796\) | 28.8358 | 1.02206 | ||||||||
\(797\) | −37.2617 | −1.31988 | −0.659939 | − | 0.751319i | \(-0.729418\pi\) | ||||
−0.659939 | + | 0.751319i | \(0.729418\pi\) | |||||||
\(798\) | −0.643139 | −0.0227669 | ||||||||
\(799\) | 6.51445 | 0.230465 | ||||||||
\(800\) | −8.06296 | −0.285069 | ||||||||
\(801\) | −16.2414 | −0.573862 | ||||||||
\(802\) | −3.28110 | −0.115860 | ||||||||
\(803\) | 41.9717 | 1.48115 | ||||||||
\(804\) | −3.45295 | −0.121776 | ||||||||
\(805\) | −3.02307 | −0.106549 | ||||||||
\(806\) | −17.9921 | −0.633745 | ||||||||
\(807\) | −1.77394 | −0.0624458 | ||||||||
\(808\) | 1.79515 | 0.0631532 | ||||||||
\(809\) | −19.9105 | −0.700016 | −0.350008 | − | 0.936747i | \(-0.613821\pi\) | ||||
−0.350008 | + | 0.936747i | \(0.613821\pi\) | |||||||
\(810\) | −17.9041 | −0.629087 | ||||||||
\(811\) | 17.9295 | 0.629589 | 0.314795 | − | 0.949160i | \(-0.398064\pi\) | ||||
0.314795 | + | 0.949160i | \(0.398064\pi\) | |||||||
\(812\) | −0.592417 | −0.0207897 | ||||||||
\(813\) | −3.39183 | −0.118957 | ||||||||
\(814\) | 52.8780 | 1.85337 | ||||||||
\(815\) | −10.1285 | −0.354784 | ||||||||
\(816\) | −0.700759 | −0.0245315 | ||||||||
\(817\) | −30.0829 | −1.05247 | ||||||||
\(818\) | −22.4358 | −0.784451 | ||||||||
\(819\) | −2.45360 | −0.0857357 | ||||||||
\(820\) | −9.51014 | −0.332109 | ||||||||
\(821\) | −5.29890 | −0.184933 | −0.0924664 | − | 0.995716i | \(-0.529475\pi\) | ||||
−0.0924664 | + | 0.995716i | \(0.529475\pi\) | |||||||
\(822\) | −0.987669 | −0.0344489 | ||||||||
\(823\) | −12.2789 | −0.428017 | −0.214008 | − | 0.976832i | \(-0.568652\pi\) | ||||
−0.214008 | + | 0.976832i | \(0.568652\pi\) | |||||||
\(824\) | −1.61110 | −0.0561252 | ||||||||
\(825\) | −0.359383 | −0.0125121 | ||||||||
\(826\) | −14.7916 | −0.514664 | ||||||||
\(827\) | 29.5684 | 1.02819 | 0.514097 | − | 0.857732i | \(-0.328127\pi\) | ||||
0.514097 | + | 0.857732i | \(0.328127\pi\) | |||||||
\(828\) | 18.7233 | 0.650679 | ||||||||
\(829\) | −31.3691 | −1.08950 | −0.544748 | − | 0.838600i | \(-0.683375\pi\) | ||||
−0.544748 | + | 0.838600i | \(0.683375\pi\) | |||||||
\(830\) | −17.6322 | −0.612022 | ||||||||
\(831\) | 3.02024 | 0.104771 | ||||||||
\(832\) | 7.05508 | 0.244591 | ||||||||
\(833\) | −1.51410 | −0.0524605 | ||||||||
\(834\) | −2.68419 | −0.0929459 | ||||||||
\(835\) | −14.3083 | −0.495159 | ||||||||
\(836\) | −16.3984 | −0.567151 | ||||||||
\(837\) | 7.81322 | 0.270064 | ||||||||
\(838\) | 73.6099 | 2.54281 | ||||||||
\(839\) | 34.7611 | 1.20009 | 0.600044 | − | 0.799967i | \(-0.295150\pi\) | ||||
0.600044 | + | 0.799967i | \(0.295150\pi\) | |||||||
\(840\) | −0.0181011 | −0.000624546 0 | ||||||||
\(841\) | −28.9184 | −0.997188 | ||||||||
\(842\) | −13.0770 | −0.450665 | ||||||||
\(843\) | −0.161992 | −0.00557928 | ||||||||
\(844\) | 29.0076 | 0.998484 | ||||||||
\(845\) | 12.3246 | 0.423979 | ||||||||
\(846\) | 25.9286 | 0.891445 | ||||||||
\(847\) | 2.08386 | 0.0716023 | ||||||||
\(848\) | 55.8080 | 1.91646 | ||||||||
\(849\) | −0.590828 | −0.0202772 | ||||||||
\(850\) | −3.05627 | −0.104829 | ||||||||
\(851\) | −26.5214 | −0.909142 | ||||||||
\(852\) | −0.698584 | −0.0239331 | ||||||||
\(853\) | −32.0906 | −1.09876 | −0.549381 | − | 0.835572i | \(-0.685137\pi\) | ||||
−0.549381 | + | 0.835572i | \(0.685137\pi\) | |||||||
\(854\) | 14.2522 | 0.487700 | ||||||||
\(855\) | −7.90347 | −0.270293 | ||||||||
\(856\) | 0.321980 | 0.0110050 | ||||||||
\(857\) | 37.3455 | 1.27570 | 0.637849 | − | 0.770161i | \(-0.279824\pi\) | ||||
0.637849 | + | 0.770161i | \(0.279824\pi\) | |||||||
\(858\) | 0.596182 | 0.0203533 | ||||||||
\(859\) | −48.6768 | −1.66083 | −0.830416 | − | 0.557144i | \(-0.811897\pi\) | ||||
−0.830416 | + | 0.557144i | \(0.811897\pi\) | |||||||
\(860\) | −23.5741 | −0.803871 | ||||||||
\(861\) | 0.551748 | 0.0188035 | ||||||||
\(862\) | 1.22266 | 0.0416441 | ||||||||
\(863\) | 3.21053 | 0.109288 | 0.0546438 | − | 0.998506i | \(-0.482598\pi\) | ||||
0.0546438 | + | 0.998506i | \(0.482598\pi\) | |||||||
\(864\) | −5.80851 | −0.197609 | ||||||||
\(865\) | 0.230042 | 0.00782165 | ||||||||
\(866\) | 80.8251 | 2.74655 | ||||||||
\(867\) | 1.77014 | 0.0601171 | ||||||||
\(868\) | −22.4996 | −0.763686 | ||||||||
\(869\) | −29.3060 | −0.994139 | ||||||||
\(870\) | 0.0693775 | 0.00235212 | ||||||||
\(871\) | −11.3656 | −0.385108 | ||||||||
\(872\) | 0.527541 | 0.0178648 | ||||||||
\(873\) | 0.756984 | 0.0256200 | ||||||||
\(874\) | 16.1541 | 0.546422 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −3.50955 | −0.118577 | ||||||||
\(877\) | 18.4976 | 0.624621 | 0.312310 | − | 0.949980i | \(-0.398897\pi\) | ||||
0.312310 | + | 0.949980i | \(0.398897\pi\) | |||||||
\(878\) | 28.2603 | 0.953740 | ||||||||
\(879\) | 0.572881 | 0.0193228 | ||||||||
\(880\) | 11.4824 | 0.387073 | ||||||||
\(881\) | 18.7894 | 0.633032 | 0.316516 | − | 0.948587i | \(-0.397487\pi\) | ||||
0.316516 | + | 0.948587i | \(0.397487\pi\) | |||||||
\(882\) | −6.02638 | −0.202919 | ||||||||
\(883\) | −10.1513 | −0.341618 | −0.170809 | − | 0.985304i | \(-0.554638\pi\) | ||||
−0.170809 | + | 0.985304i | \(0.554638\pi\) | |||||||
\(884\) | 2.58139 | 0.0868217 | ||||||||
\(885\) | 0.881952 | 0.0296465 | ||||||||
\(886\) | 61.8823 | 2.07897 | ||||||||
\(887\) | 15.7594 | 0.529149 | 0.264575 | − | 0.964365i | \(-0.414768\pi\) | ||||
0.264575 | + | 0.964365i | \(0.414768\pi\) | |||||||
\(888\) | −0.158801 | −0.00532901 | ||||||||
\(889\) | −19.1524 | −0.642350 | ||||||||
\(890\) | −10.9810 | −0.368084 | ||||||||
\(891\) | 26.4853 | 0.887289 | ||||||||
\(892\) | −3.99144 | −0.133643 | ||||||||
\(893\) | 11.3900 | 0.381150 | ||||||||
\(894\) | 5.56568 | 0.186144 | ||||||||
\(895\) | −2.12800 | −0.0711311 | ||||||||
\(896\) | 1.20233 | 0.0401671 | ||||||||
\(897\) | −0.299020 | −0.00998400 | ||||||||
\(898\) | 41.2326 | 1.37595 | ||||||||
\(899\) | 3.09722 | 0.103298 | ||||||||
\(900\) | −6.19347 | −0.206449 | ||||||||
\(901\) | 21.9738 | 0.732055 | ||||||||
\(902\) | 27.6311 | 0.920015 | ||||||||
\(903\) | 1.36769 | 0.0455140 | ||||||||
\(904\) | −1.17187 | −0.0389758 | ||||||||
\(905\) | 4.12887 | 0.137248 | ||||||||
\(906\) | 0.187903 | 0.00624266 | ||||||||
\(907\) | −45.6118 | −1.51451 | −0.757257 | − | 0.653117i | \(-0.773461\pi\) | ||||
−0.757257 | + | 0.653117i | \(0.773461\pi\) | |||||||
\(908\) | −53.8912 | −1.78844 | ||||||||
\(909\) | −35.6356 | −1.18196 | ||||||||
\(910\) | −1.65891 | −0.0549923 | ||||||||
\(911\) | 13.9943 | 0.463651 | 0.231826 | − | 0.972757i | \(-0.425530\pi\) | ||||
0.231826 | + | 0.972757i | \(0.425530\pi\) | |||||||
\(912\) | −1.22522 | −0.0405710 | ||||||||
\(913\) | 26.0830 | 0.863221 | ||||||||
\(914\) | −54.3362 | −1.79728 | ||||||||
\(915\) | −0.849792 | −0.0280933 | ||||||||
\(916\) | 2.07451 | 0.0685436 | ||||||||
\(917\) | 4.72072 | 0.155892 | ||||||||
\(918\) | −2.20172 | −0.0726676 | ||||||||
\(919\) | 20.6800 | 0.682170 | 0.341085 | − | 0.940033i | \(-0.389206\pi\) | ||||
0.341085 | + | 0.940033i | \(0.389206\pi\) | |||||||
\(920\) | 0.454656 | 0.0149896 | ||||||||
\(921\) | −0.765821 | −0.0252347 | ||||||||
\(922\) | 82.1960 | 2.70698 | ||||||||
\(923\) | −2.29943 | −0.0756866 | ||||||||
\(924\) | 0.745542 | 0.0245265 | ||||||||
\(925\) | 8.77302 | 0.288455 | ||||||||
\(926\) | −40.1440 | −1.31921 | ||||||||
\(927\) | 31.9820 | 1.05043 | ||||||||
\(928\) | −2.30254 | −0.0755845 | ||||||||
\(929\) | −7.05111 | −0.231339 | −0.115670 | − | 0.993288i | \(-0.536901\pi\) | ||||
−0.115670 | + | 0.993288i | \(0.536901\pi\) | |||||||
\(930\) | 2.63491 | 0.0864022 | ||||||||
\(931\) | −2.64727 | −0.0867609 | ||||||||
\(932\) | 7.95840 | 0.260686 | ||||||||
\(933\) | −0.859757 | −0.0281472 | ||||||||
\(934\) | −38.7456 | −1.26780 | ||||||||
\(935\) | 4.52109 | 0.147855 | ||||||||
\(936\) | 0.369011 | 0.0120615 | ||||||||
\(937\) | 18.9884 | 0.620325 | 0.310163 | − | 0.950684i | \(-0.399617\pi\) | ||||
0.310163 | + | 0.950684i | \(0.399617\pi\) | |||||||
\(938\) | −27.9154 | −0.911471 | ||||||||
\(939\) | −3.94995 | −0.128902 | ||||||||
\(940\) | 8.92561 | 0.291121 | ||||||||
\(941\) | 5.49813 | 0.179234 | 0.0896170 | − | 0.995976i | \(-0.471436\pi\) | ||||
0.0896170 | + | 0.995976i | \(0.471436\pi\) | |||||||
\(942\) | −3.10828 | −0.101273 | ||||||||
\(943\) | −13.8586 | −0.451299 | ||||||||
\(944\) | −28.1788 | −0.917140 | ||||||||
\(945\) | 0.720394 | 0.0234344 | ||||||||
\(946\) | 68.4930 | 2.22690 | ||||||||
\(947\) | 60.6523 | 1.97093 | 0.985467 | − | 0.169868i | \(-0.0543342\pi\) | ||||
0.985467 | + | 0.169868i | \(0.0543342\pi\) | |||||||
\(948\) | 2.45048 | 0.0795881 | ||||||||
\(949\) | −11.5519 | −0.374990 | ||||||||
\(950\) | −5.34363 | −0.173370 | ||||||||
\(951\) | −2.51116 | −0.0814300 | ||||||||
\(952\) | 0.227714 | 0.00738026 | ||||||||
\(953\) | −32.2600 | −1.04500 | −0.522502 | − | 0.852638i | \(-0.675001\pi\) | ||||
−0.522502 | + | 0.852638i | \(0.675001\pi\) | |||||||
\(954\) | 87.4597 | 2.83161 | ||||||||
\(955\) | 17.8444 | 0.577433 | ||||||||
\(956\) | 6.16565 | 0.199411 | ||||||||
\(957\) | −0.102629 | −0.00331752 | ||||||||
\(958\) | −26.3114 | −0.850084 | ||||||||
\(959\) | −4.06542 | −0.131279 | ||||||||
\(960\) | −1.03320 | −0.0333465 | ||||||||
\(961\) | 86.6305 | 2.79453 | ||||||||
\(962\) | −14.5536 | −0.469228 | ||||||||
\(963\) | −6.39164 | −0.205968 | ||||||||
\(964\) | −17.3865 | −0.559981 | ||||||||
\(965\) | −14.3542 | −0.462079 | ||||||||
\(966\) | −0.734436 | −0.0236301 | ||||||||
\(967\) | 2.64984 | 0.0852132 | 0.0426066 | − | 0.999092i | \(-0.486434\pi\) | ||||
0.0426066 | + | 0.999092i | \(0.486434\pi\) | |||||||
\(968\) | −0.313404 | −0.0100732 | ||||||||
\(969\) | −0.482416 | −0.0154974 | ||||||||
\(970\) | 0.511805 | 0.0164331 | ||||||||
\(971\) | −10.1530 | −0.325825 | −0.162913 | − | 0.986640i | \(-0.552089\pi\) | ||||
−0.162913 | + | 0.986640i | \(0.552089\pi\) | |||||||
\(972\) | −6.69801 | −0.214839 | ||||||||
\(973\) | −11.0486 | −0.354202 | ||||||||
\(974\) | −2.81947 | −0.0903416 | ||||||||
\(975\) | 0.0989130 | 0.00316775 | ||||||||
\(976\) | 27.1512 | 0.869090 | ||||||||
\(977\) | 44.2425 | 1.41544 | 0.707722 | − | 0.706491i | \(-0.249723\pi\) | ||||
0.707722 | + | 0.706491i | \(0.249723\pi\) | |||||||
\(978\) | −2.46065 | −0.0786828 | ||||||||
\(979\) | 16.2440 | 0.519160 | ||||||||
\(980\) | −2.07451 | −0.0662677 | ||||||||
\(981\) | −10.4722 | −0.334353 | ||||||||
\(982\) | 39.2376 | 1.25212 | ||||||||
\(983\) | 32.2834 | 1.02968 | 0.514840 | − | 0.857286i | \(-0.327851\pi\) | ||||
0.514840 | + | 0.857286i | \(0.327851\pi\) | |||||||
\(984\) | −0.0829805 | −0.00264532 | ||||||||
\(985\) | 5.18092 | 0.165078 | ||||||||
\(986\) | −0.872779 | −0.0277950 | ||||||||
\(987\) | −0.517835 | −0.0164829 | ||||||||
\(988\) | 4.51334 | 0.143589 | ||||||||
\(989\) | −34.3533 | −1.09237 | ||||||||
\(990\) | 17.9947 | 0.571910 | ||||||||
\(991\) | −5.92942 | −0.188354 | −0.0941770 | − | 0.995555i | \(-0.530022\pi\) | ||||
−0.0941770 | + | 0.995555i | \(0.530022\pi\) | |||||||
\(992\) | −87.4489 | −2.77651 | ||||||||
\(993\) | −2.73219 | −0.0867035 | ||||||||
\(994\) | −5.64772 | −0.179135 | ||||||||
\(995\) | −13.9001 | −0.440662 | ||||||||
\(996\) | −2.18098 | −0.0691071 | ||||||||
\(997\) | 11.2013 | 0.354748 | 0.177374 | − | 0.984143i | \(-0.443240\pi\) | ||||
0.177374 | + | 0.984143i | \(0.443240\pi\) | |||||||
\(998\) | 33.9295 | 1.07402 | ||||||||
\(999\) | 6.32003 | 0.199957 |
(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.1.52 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.52 | ✓ | 62 | 1.1 | even | 1 | trivial |