Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.02842 | −1.17111 | −0.585553 | − | 0.810634i | \(-0.699123\pi\) | ||||
−0.585553 | + | 0.810634i | \(0.699123\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.47134 | 1.10522 | 0.552608 | − | 0.833441i | \(-0.313633\pi\) | ||||
0.552608 | + | 0.833441i | \(0.313633\pi\) | |||||||
\(6\) | −2.02842 | −0.828097 | ||||||||
\(7\) | 1.41486 | 0.534767 | 0.267384 | − | 0.963590i | \(-0.413841\pi\) | ||||
0.267384 | + | 0.963590i | \(0.413841\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.11447 | 0.371490 | ||||||||
\(10\) | 2.47134 | 0.781505 | ||||||||
\(11\) | −1.90125 | −0.573248 | −0.286624 | − | 0.958043i | \(-0.592533\pi\) | ||||
−0.286624 | + | 0.958043i | \(0.592533\pi\) | |||||||
\(12\) | −2.02842 | −0.585553 | ||||||||
\(13\) | 3.04945 | 0.845766 | 0.422883 | − | 0.906184i | \(-0.361018\pi\) | ||||
0.422883 | + | 0.906184i | \(0.361018\pi\) | |||||||
\(14\) | 1.41486 | 0.378138 | ||||||||
\(15\) | −5.01290 | −1.29432 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.777246 | −0.188510 | −0.0942549 | − | 0.995548i | \(-0.530047\pi\) | ||||
−0.0942549 | + | 0.995548i | \(0.530047\pi\) | |||||||
\(18\) | 1.11447 | 0.262683 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.47134 | 0.552608 | ||||||||
\(21\) | −2.86993 | −0.626269 | ||||||||
\(22\) | −1.90125 | −0.405348 | ||||||||
\(23\) | −7.98162 | −1.66428 | −0.832141 | − | 0.554564i | \(-0.812885\pi\) | ||||
−0.832141 | + | 0.554564i | \(0.812885\pi\) | |||||||
\(24\) | −2.02842 | −0.414049 | ||||||||
\(25\) | 1.10751 | 0.221502 | ||||||||
\(26\) | 3.04945 | 0.598047 | ||||||||
\(27\) | 3.82464 | 0.736052 | ||||||||
\(28\) | 1.41486 | 0.267384 | ||||||||
\(29\) | −5.89103 | −1.09394 | −0.546969 | − | 0.837153i | \(-0.684218\pi\) | ||||
−0.546969 | + | 0.837153i | \(0.684218\pi\) | |||||||
\(30\) | −5.01290 | −0.915226 | ||||||||
\(31\) | −5.52189 | −0.991761 | −0.495880 | − | 0.868391i | \(-0.665155\pi\) | ||||
−0.495880 | + | 0.868391i | \(0.665155\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.85652 | 0.671335 | ||||||||
\(34\) | −0.777246 | −0.133297 | ||||||||
\(35\) | 3.49660 | 0.591033 | ||||||||
\(36\) | 1.11447 | 0.185745 | ||||||||
\(37\) | −3.09139 | −0.508221 | −0.254111 | − | 0.967175i | \(-0.581783\pi\) | ||||
−0.254111 | + | 0.967175i | \(0.581783\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −6.18556 | −0.990482 | ||||||||
\(40\) | 2.47134 | 0.390753 | ||||||||
\(41\) | −6.61679 | −1.03337 | −0.516684 | − | 0.856176i | \(-0.672834\pi\) | ||||
−0.516684 | + | 0.856176i | \(0.672834\pi\) | |||||||
\(42\) | −2.86993 | −0.442839 | ||||||||
\(43\) | 11.4467 | 1.74560 | 0.872799 | − | 0.488080i | \(-0.162303\pi\) | ||||
0.872799 | + | 0.488080i | \(0.162303\pi\) | |||||||
\(44\) | −1.90125 | −0.286624 | ||||||||
\(45\) | 2.75423 | 0.410577 | ||||||||
\(46\) | −7.98162 | −1.17683 | ||||||||
\(47\) | −6.04983 | −0.882459 | −0.441230 | − | 0.897394i | \(-0.645458\pi\) | ||||
−0.441230 | + | 0.897394i | \(0.645458\pi\) | |||||||
\(48\) | −2.02842 | −0.292777 | ||||||||
\(49\) | −4.99817 | −0.714024 | ||||||||
\(50\) | 1.10751 | 0.156625 | ||||||||
\(51\) | 1.57658 | 0.220765 | ||||||||
\(52\) | 3.04945 | 0.422883 | ||||||||
\(53\) | −3.46843 | −0.476426 | −0.238213 | − | 0.971213i | \(-0.576562\pi\) | ||||
−0.238213 | + | 0.971213i | \(0.576562\pi\) | |||||||
\(54\) | 3.82464 | 0.520467 | ||||||||
\(55\) | −4.69863 | −0.633563 | ||||||||
\(56\) | 1.41486 | 0.189069 | ||||||||
\(57\) | −2.02842 | −0.268670 | ||||||||
\(58\) | −5.89103 | −0.773530 | ||||||||
\(59\) | −1.73246 | −0.225547 | −0.112774 | − | 0.993621i | \(-0.535974\pi\) | ||||
−0.112774 | + | 0.993621i | \(0.535974\pi\) | |||||||
\(60\) | −5.01290 | −0.647162 | ||||||||
\(61\) | −11.6171 | −1.48742 | −0.743709 | − | 0.668504i | \(-0.766935\pi\) | ||||
−0.743709 | + | 0.668504i | \(0.766935\pi\) | |||||||
\(62\) | −5.52189 | −0.701281 | ||||||||
\(63\) | 1.57682 | 0.198661 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.53623 | 0.934754 | ||||||||
\(66\) | 3.85652 | 0.474705 | ||||||||
\(67\) | 5.11260 | 0.624604 | 0.312302 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312302 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(68\) | −0.777246 | −0.0942549 | ||||||||
\(69\) | 16.1900 | 1.94905 | ||||||||
\(70\) | 3.49660 | 0.417924 | ||||||||
\(71\) | −0.661692 | −0.0785284 | −0.0392642 | − | 0.999229i | \(-0.512501\pi\) | ||||
−0.0392642 | + | 0.999229i | \(0.512501\pi\) | |||||||
\(72\) | 1.11447 | 0.131342 | ||||||||
\(73\) | −11.5032 | −1.34635 | −0.673173 | − | 0.739485i | \(-0.735069\pi\) | ||||
−0.673173 | + | 0.739485i | \(0.735069\pi\) | |||||||
\(74\) | −3.09139 | −0.359367 | ||||||||
\(75\) | −2.24649 | −0.259402 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −2.69001 | −0.306555 | ||||||||
\(78\) | −6.18556 | −0.700377 | ||||||||
\(79\) | −15.7474 | −1.77172 | −0.885858 | − | 0.463956i | \(-0.846429\pi\) | ||||
−0.885858 | + | 0.463956i | \(0.846429\pi\) | |||||||
\(80\) | 2.47134 | 0.276304 | ||||||||
\(81\) | −11.1014 | −1.23349 | ||||||||
\(82\) | −6.61679 | −0.730702 | ||||||||
\(83\) | 13.7324 | 1.50732 | 0.753661 | − | 0.657263i | \(-0.228286\pi\) | ||||
0.753661 | + | 0.657263i | \(0.228286\pi\) | |||||||
\(84\) | −2.86993 | −0.313135 | ||||||||
\(85\) | −1.92084 | −0.208344 | ||||||||
\(86\) | 11.4467 | 1.23432 | ||||||||
\(87\) | 11.9495 | 1.28112 | ||||||||
\(88\) | −1.90125 | −0.202674 | ||||||||
\(89\) | −5.29706 | −0.561488 | −0.280744 | − | 0.959783i | \(-0.590581\pi\) | ||||
−0.280744 | + | 0.959783i | \(0.590581\pi\) | |||||||
\(90\) | 2.75423 | 0.290321 | ||||||||
\(91\) | 4.31455 | 0.452288 | ||||||||
\(92\) | −7.98162 | −0.832141 | ||||||||
\(93\) | 11.2007 | 1.16146 | ||||||||
\(94\) | −6.04983 | −0.623993 | ||||||||
\(95\) | 2.47134 | 0.253554 | ||||||||
\(96\) | −2.02842 | −0.207024 | ||||||||
\(97\) | 11.1561 | 1.13273 | 0.566364 | − | 0.824155i | \(-0.308350\pi\) | ||||
0.566364 | + | 0.824155i | \(0.308350\pi\) | |||||||
\(98\) | −4.99817 | −0.504891 | ||||||||
\(99\) | −2.11889 | −0.212956 | ||||||||
\(100\) | 1.10751 | 0.110751 | ||||||||
\(101\) | −2.64209 | −0.262898 | −0.131449 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131449 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(102\) | 1.57658 | 0.156104 | ||||||||
\(103\) | 0.481843 | 0.0474774 | 0.0237387 | − | 0.999718i | \(-0.492443\pi\) | ||||
0.0237387 | + | 0.999718i | \(0.492443\pi\) | |||||||
\(104\) | 3.04945 | 0.299024 | ||||||||
\(105\) | −7.09256 | −0.692163 | ||||||||
\(106\) | −3.46843 | −0.336884 | ||||||||
\(107\) | 10.6017 | 1.02490 | 0.512451 | − | 0.858716i | \(-0.328738\pi\) | ||||
0.512451 | + | 0.858716i | \(0.328738\pi\) | |||||||
\(108\) | 3.82464 | 0.368026 | ||||||||
\(109\) | −11.9045 | −1.14025 | −0.570124 | − | 0.821559i | \(-0.693105\pi\) | ||||
−0.570124 | + | 0.821559i | \(0.693105\pi\) | |||||||
\(110\) | −4.69863 | −0.447997 | ||||||||
\(111\) | 6.27062 | 0.595181 | ||||||||
\(112\) | 1.41486 | 0.133692 | ||||||||
\(113\) | 3.01625 | 0.283745 | 0.141872 | − | 0.989885i | \(-0.454688\pi\) | ||||
0.141872 | + | 0.989885i | \(0.454688\pi\) | |||||||
\(114\) | −2.02842 | −0.189979 | ||||||||
\(115\) | −19.7253 | −1.83939 | ||||||||
\(116\) | −5.89103 | −0.546969 | ||||||||
\(117\) | 3.39852 | 0.314194 | ||||||||
\(118\) | −1.73246 | −0.159486 | ||||||||
\(119\) | −1.09970 | −0.100809 | ||||||||
\(120\) | −5.01290 | −0.457613 | ||||||||
\(121\) | −7.38525 | −0.671386 | ||||||||
\(122\) | −11.6171 | −1.05176 | ||||||||
\(123\) | 13.4216 | 1.21018 | ||||||||
\(124\) | −5.52189 | −0.495880 | ||||||||
\(125\) | −9.61966 | −0.860409 | ||||||||
\(126\) | 1.57682 | 0.140474 | ||||||||
\(127\) | 18.1456 | 1.61016 | 0.805079 | − | 0.593168i | \(-0.202123\pi\) | ||||
0.805079 | + | 0.593168i | \(0.202123\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −23.2186 | −2.04428 | ||||||||
\(130\) | 7.53623 | 0.660971 | ||||||||
\(131\) | 5.03267 | 0.439706 | 0.219853 | − | 0.975533i | \(-0.429442\pi\) | ||||
0.219853 | + | 0.975533i | \(0.429442\pi\) | |||||||
\(132\) | 3.85652 | 0.335667 | ||||||||
\(133\) | 1.41486 | 0.122684 | ||||||||
\(134\) | 5.11260 | 0.441662 | ||||||||
\(135\) | 9.45197 | 0.813496 | ||||||||
\(136\) | −0.777246 | −0.0666483 | ||||||||
\(137\) | −9.66429 | −0.825676 | −0.412838 | − | 0.910805i | \(-0.635462\pi\) | ||||
−0.412838 | + | 0.910805i | \(0.635462\pi\) | |||||||
\(138\) | 16.1900 | 1.37819 | ||||||||
\(139\) | 6.20866 | 0.526612 | 0.263306 | − | 0.964712i | \(-0.415187\pi\) | ||||
0.263306 | + | 0.964712i | \(0.415187\pi\) | |||||||
\(140\) | 3.49660 | 0.295517 | ||||||||
\(141\) | 12.2716 | 1.03345 | ||||||||
\(142\) | −0.661692 | −0.0555280 | ||||||||
\(143\) | −5.79777 | −0.484834 | ||||||||
\(144\) | 1.11447 | 0.0928725 | ||||||||
\(145\) | −14.5587 | −1.20904 | ||||||||
\(146\) | −11.5032 | −0.952010 | ||||||||
\(147\) | 10.1384 | 0.836198 | ||||||||
\(148\) | −3.09139 | −0.254111 | ||||||||
\(149\) | 14.0579 | 1.15167 | 0.575833 | − | 0.817567i | \(-0.304678\pi\) | ||||
0.575833 | + | 0.817567i | \(0.304678\pi\) | |||||||
\(150\) | −2.24649 | −0.183425 | ||||||||
\(151\) | −8.58786 | −0.698870 | −0.349435 | − | 0.936961i | \(-0.613626\pi\) | ||||
−0.349435 | + | 0.936961i | \(0.613626\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −0.866217 | −0.0700295 | ||||||||
\(154\) | −2.69001 | −0.216767 | ||||||||
\(155\) | −13.6465 | −1.09611 | ||||||||
\(156\) | −6.18556 | −0.495241 | ||||||||
\(157\) | 10.2251 | 0.816055 | 0.408027 | − | 0.912970i | \(-0.366217\pi\) | ||||
0.408027 | + | 0.912970i | \(0.366217\pi\) | |||||||
\(158\) | −15.7474 | −1.25279 | ||||||||
\(159\) | 7.03542 | 0.557945 | ||||||||
\(160\) | 2.47134 | 0.195376 | ||||||||
\(161\) | −11.2929 | −0.890004 | ||||||||
\(162\) | −11.1014 | −0.872206 | ||||||||
\(163\) | −13.0794 | −1.02446 | −0.512229 | − | 0.858849i | \(-0.671180\pi\) | ||||
−0.512229 | + | 0.858849i | \(0.671180\pi\) | |||||||
\(164\) | −6.61679 | −0.516684 | ||||||||
\(165\) | 9.53077 | 0.741970 | ||||||||
\(166\) | 13.7324 | 1.06584 | ||||||||
\(167\) | −22.6408 | −1.75200 | −0.875999 | − | 0.482313i | \(-0.839797\pi\) | ||||
−0.875999 | + | 0.482313i | \(0.839797\pi\) | |||||||
\(168\) | −2.86993 | −0.221420 | ||||||||
\(169\) | −3.70083 | −0.284679 | ||||||||
\(170\) | −1.92084 | −0.147321 | ||||||||
\(171\) | 1.11447 | 0.0852257 | ||||||||
\(172\) | 11.4467 | 0.872799 | ||||||||
\(173\) | 12.6704 | 0.963316 | 0.481658 | − | 0.876359i | \(-0.340035\pi\) | ||||
0.481658 | + | 0.876359i | \(0.340035\pi\) | |||||||
\(174\) | 11.9495 | 0.905886 | ||||||||
\(175\) | 1.56697 | 0.118452 | ||||||||
\(176\) | −1.90125 | −0.143312 | ||||||||
\(177\) | 3.51415 | 0.264140 | ||||||||
\(178\) | −5.29706 | −0.397032 | ||||||||
\(179\) | 24.8335 | 1.85614 | 0.928070 | − | 0.372405i | \(-0.121467\pi\) | ||||
0.928070 | + | 0.372405i | \(0.121467\pi\) | |||||||
\(180\) | 2.75423 | 0.205288 | ||||||||
\(181\) | −9.34261 | −0.694431 | −0.347215 | − | 0.937785i | \(-0.612873\pi\) | ||||
−0.347215 | + | 0.937785i | \(0.612873\pi\) | |||||||
\(182\) | 4.31455 | 0.319816 | ||||||||
\(183\) | 23.5643 | 1.74192 | ||||||||
\(184\) | −7.98162 | −0.588413 | ||||||||
\(185\) | −7.63986 | −0.561694 | ||||||||
\(186\) | 11.2007 | 0.821274 | ||||||||
\(187\) | 1.47774 | 0.108063 | ||||||||
\(188\) | −6.04983 | −0.441230 | ||||||||
\(189\) | 5.41133 | 0.393617 | ||||||||
\(190\) | 2.47134 | 0.179290 | ||||||||
\(191\) | 20.9150 | 1.51335 | 0.756677 | − | 0.653789i | \(-0.226822\pi\) | ||||
0.756677 | + | 0.653789i | \(0.226822\pi\) | |||||||
\(192\) | −2.02842 | −0.146388 | ||||||||
\(193\) | −19.1158 | −1.37599 | −0.687993 | − | 0.725717i | \(-0.741508\pi\) | ||||
−0.687993 | + | 0.725717i | \(0.741508\pi\) | |||||||
\(194\) | 11.1561 | 0.800959 | ||||||||
\(195\) | −15.2866 | −1.09470 | ||||||||
\(196\) | −4.99817 | −0.357012 | ||||||||
\(197\) | 17.4473 | 1.24307 | 0.621534 | − | 0.783387i | \(-0.286510\pi\) | ||||
0.621534 | + | 0.783387i | \(0.286510\pi\) | |||||||
\(198\) | −2.11889 | −0.150583 | ||||||||
\(199\) | −2.95613 | −0.209554 | −0.104777 | − | 0.994496i | \(-0.533413\pi\) | ||||
−0.104777 | + | 0.994496i | \(0.533413\pi\) | |||||||
\(200\) | 1.10751 | 0.0783126 | ||||||||
\(201\) | −10.3705 | −0.731478 | ||||||||
\(202\) | −2.64209 | −0.185897 | ||||||||
\(203\) | −8.33499 | −0.585002 | ||||||||
\(204\) | 1.57658 | 0.110383 | ||||||||
\(205\) | −16.3523 | −1.14209 | ||||||||
\(206\) | 0.481843 | 0.0335716 | ||||||||
\(207\) | −8.89527 | −0.618264 | ||||||||
\(208\) | 3.04945 | 0.211442 | ||||||||
\(209\) | −1.90125 | −0.131512 | ||||||||
\(210\) | −7.09256 | −0.489433 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −3.46843 | −0.238213 | ||||||||
\(213\) | 1.34219 | 0.0919651 | ||||||||
\(214\) | 10.6017 | 0.724716 | ||||||||
\(215\) | 28.2885 | 1.92926 | ||||||||
\(216\) | 3.82464 | 0.260234 | ||||||||
\(217\) | −7.81271 | −0.530361 | ||||||||
\(218\) | −11.9045 | −0.806277 | ||||||||
\(219\) | 23.3332 | 1.57671 | ||||||||
\(220\) | −4.69863 | −0.316782 | ||||||||
\(221\) | −2.37018 | −0.159435 | ||||||||
\(222\) | 6.27062 | 0.420857 | ||||||||
\(223\) | −1.94987 | −0.130573 | −0.0652866 | − | 0.997867i | \(-0.520796\pi\) | ||||
−0.0652866 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(224\) | 1.41486 | 0.0945344 | ||||||||
\(225\) | 1.23428 | 0.0822856 | ||||||||
\(226\) | 3.01625 | 0.200638 | ||||||||
\(227\) | 10.1743 | 0.675295 | 0.337647 | − | 0.941273i | \(-0.390369\pi\) | ||||
0.337647 | + | 0.941273i | \(0.390369\pi\) | |||||||
\(228\) | −2.02842 | −0.134335 | ||||||||
\(229\) | −15.9728 | −1.05551 | −0.527756 | − | 0.849396i | \(-0.676966\pi\) | ||||
−0.527756 | + | 0.849396i | \(0.676966\pi\) | |||||||
\(230\) | −19.7253 | −1.30065 | ||||||||
\(231\) | 5.45645 | 0.359008 | ||||||||
\(232\) | −5.89103 | −0.386765 | ||||||||
\(233\) | 1.97470 | 0.129367 | 0.0646835 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646835 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(234\) | 3.39852 | 0.222168 | ||||||||
\(235\) | −14.9512 | −0.975308 | ||||||||
\(236\) | −1.73246 | −0.112774 | ||||||||
\(237\) | 31.9422 | 2.07487 | ||||||||
\(238\) | −1.09970 | −0.0712827 | ||||||||
\(239\) | 4.17581 | 0.270110 | 0.135055 | − | 0.990838i | \(-0.456879\pi\) | ||||
0.135055 | + | 0.990838i | \(0.456879\pi\) | |||||||
\(240\) | −5.01290 | −0.323581 | ||||||||
\(241\) | −9.50085 | −0.612003 | −0.306002 | − | 0.952031i | \(-0.598991\pi\) | ||||
−0.306002 | + | 0.952031i | \(0.598991\pi\) | |||||||
\(242\) | −7.38525 | −0.474742 | ||||||||
\(243\) | 11.0443 | 0.708490 | ||||||||
\(244\) | −11.6171 | −0.743709 | ||||||||
\(245\) | −12.3522 | −0.789150 | ||||||||
\(246\) | 13.4216 | 0.855729 | ||||||||
\(247\) | 3.04945 | 0.194032 | ||||||||
\(248\) | −5.52189 | −0.350640 | ||||||||
\(249\) | −27.8549 | −1.76524 | ||||||||
\(250\) | −9.61966 | −0.608401 | ||||||||
\(251\) | −2.77413 | −0.175101 | −0.0875507 | − | 0.996160i | \(-0.527904\pi\) | ||||
−0.0875507 | + | 0.996160i | \(0.527904\pi\) | |||||||
\(252\) | 1.57682 | 0.0993304 | ||||||||
\(253\) | 15.1750 | 0.954047 | ||||||||
\(254\) | 18.1456 | 1.13855 | ||||||||
\(255\) | 3.89626 | 0.243993 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.3757 | 0.834350 | 0.417175 | − | 0.908826i | \(-0.363020\pi\) | ||||
0.417175 | + | 0.908826i | \(0.363020\pi\) | |||||||
\(258\) | −23.2186 | −1.44552 | ||||||||
\(259\) | −4.37389 | −0.271780 | ||||||||
\(260\) | 7.53623 | 0.467377 | ||||||||
\(261\) | −6.56538 | −0.406387 | ||||||||
\(262\) | 5.03267 | 0.310919 | ||||||||
\(263\) | 5.46318 | 0.336874 | 0.168437 | − | 0.985712i | \(-0.446128\pi\) | ||||
0.168437 | + | 0.985712i | \(0.446128\pi\) | |||||||
\(264\) | 3.85652 | 0.237353 | ||||||||
\(265\) | −8.57167 | −0.526553 | ||||||||
\(266\) | 1.41486 | 0.0867507 | ||||||||
\(267\) | 10.7446 | 0.657562 | ||||||||
\(268\) | 5.11260 | 0.312302 | ||||||||
\(269\) | −5.59912 | −0.341385 | −0.170692 | − | 0.985324i | \(-0.554600\pi\) | ||||
−0.170692 | + | 0.985324i | \(0.554600\pi\) | |||||||
\(270\) | 9.45197 | 0.575229 | ||||||||
\(271\) | −6.95593 | −0.422543 | −0.211271 | − | 0.977427i | \(-0.567760\pi\) | ||||
−0.211271 | + | 0.977427i | \(0.567760\pi\) | |||||||
\(272\) | −0.777246 | −0.0471275 | ||||||||
\(273\) | −8.75171 | −0.529678 | ||||||||
\(274\) | −9.66429 | −0.583841 | ||||||||
\(275\) | −2.10565 | −0.126975 | ||||||||
\(276\) | 16.1900 | 0.974526 | ||||||||
\(277\) | 16.3010 | 0.979430 | 0.489715 | − | 0.871882i | \(-0.337101\pi\) | ||||
0.489715 | + | 0.871882i | \(0.337101\pi\) | |||||||
\(278\) | 6.20866 | 0.372371 | ||||||||
\(279\) | −6.15398 | −0.368429 | ||||||||
\(280\) | 3.49660 | 0.208962 | ||||||||
\(281\) | 25.7357 | 1.53526 | 0.767632 | − | 0.640891i | \(-0.221435\pi\) | ||||
0.767632 | + | 0.640891i | \(0.221435\pi\) | |||||||
\(282\) | 12.2716 | 0.730762 | ||||||||
\(283\) | 0.131593 | 0.00782241 | 0.00391121 | − | 0.999992i | \(-0.498755\pi\) | ||||
0.00391121 | + | 0.999992i | \(0.498755\pi\) | |||||||
\(284\) | −0.661692 | −0.0392642 | ||||||||
\(285\) | −5.01290 | −0.296939 | ||||||||
\(286\) | −5.79777 | −0.342829 | ||||||||
\(287\) | −9.36183 | −0.552612 | ||||||||
\(288\) | 1.11447 | 0.0656708 | ||||||||
\(289\) | −16.3959 | −0.964464 | ||||||||
\(290\) | −14.5587 | −0.854918 | ||||||||
\(291\) | −22.6291 | −1.32654 | ||||||||
\(292\) | −11.5032 | −0.673173 | ||||||||
\(293\) | 3.62743 | 0.211917 | 0.105958 | − | 0.994371i | \(-0.466209\pi\) | ||||
0.105958 | + | 0.994371i | \(0.466209\pi\) | |||||||
\(294\) | 10.1384 | 0.591281 | ||||||||
\(295\) | −4.28150 | −0.249278 | ||||||||
\(296\) | −3.09139 | −0.179683 | ||||||||
\(297\) | −7.27159 | −0.421941 | ||||||||
\(298\) | 14.0579 | 0.814351 | ||||||||
\(299\) | −24.3396 | −1.40759 | ||||||||
\(300\) | −2.24649 | −0.129701 | ||||||||
\(301\) | 16.1954 | 0.933489 | ||||||||
\(302\) | −8.58786 | −0.494176 | ||||||||
\(303\) | 5.35925 | 0.307881 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −28.7098 | −1.64392 | ||||||||
\(306\) | −0.866217 | −0.0495183 | ||||||||
\(307\) | 0.382256 | 0.0218165 | 0.0109082 | − | 0.999941i | \(-0.496528\pi\) | ||||
0.0109082 | + | 0.999941i | \(0.496528\pi\) | |||||||
\(308\) | −2.69001 | −0.153277 | ||||||||
\(309\) | −0.977378 | −0.0556011 | ||||||||
\(310\) | −13.6465 | −0.775067 | ||||||||
\(311\) | 14.8067 | 0.839613 | 0.419807 | − | 0.907614i | \(-0.362098\pi\) | ||||
0.419807 | + | 0.907614i | \(0.362098\pi\) | |||||||
\(312\) | −6.18556 | −0.350188 | ||||||||
\(313\) | −18.6361 | −1.05337 | −0.526686 | − | 0.850060i | \(-0.676566\pi\) | ||||
−0.526686 | + | 0.850060i | \(0.676566\pi\) | |||||||
\(314\) | 10.2251 | 0.577038 | ||||||||
\(315\) | 3.89686 | 0.219563 | ||||||||
\(316\) | −15.7474 | −0.885858 | ||||||||
\(317\) | 0.143542 | 0.00806212 | 0.00403106 | − | 0.999992i | \(-0.498717\pi\) | ||||
0.00403106 | + | 0.999992i | \(0.498717\pi\) | |||||||
\(318\) | 7.03542 | 0.394527 | ||||||||
\(319\) | 11.2003 | 0.627098 | ||||||||
\(320\) | 2.47134 | 0.138152 | ||||||||
\(321\) | −21.5046 | −1.20027 | ||||||||
\(322\) | −11.2929 | −0.629328 | ||||||||
\(323\) | −0.777246 | −0.0432471 | ||||||||
\(324\) | −11.1014 | −0.616743 | ||||||||
\(325\) | 3.37729 | 0.187339 | ||||||||
\(326\) | −13.0794 | −0.724401 | ||||||||
\(327\) | 24.1474 | 1.33535 | ||||||||
\(328\) | −6.61679 | −0.365351 | ||||||||
\(329\) | −8.55968 | −0.471910 | ||||||||
\(330\) | 9.53077 | 0.524652 | ||||||||
\(331\) | −26.5807 | −1.46101 | −0.730505 | − | 0.682908i | \(-0.760715\pi\) | ||||
−0.730505 | + | 0.682908i | \(0.760715\pi\) | |||||||
\(332\) | 13.7324 | 0.753661 | ||||||||
\(333\) | −3.44526 | −0.188799 | ||||||||
\(334\) | −22.6408 | −1.23885 | ||||||||
\(335\) | 12.6350 | 0.690322 | ||||||||
\(336\) | −2.86993 | −0.156567 | ||||||||
\(337\) | −8.74594 | −0.476422 | −0.238211 | − | 0.971213i | \(-0.576561\pi\) | ||||
−0.238211 | + | 0.971213i | \(0.576561\pi\) | |||||||
\(338\) | −3.70083 | −0.201299 | ||||||||
\(339\) | −6.11820 | −0.332295 | ||||||||
\(340\) | −1.92084 | −0.104172 | ||||||||
\(341\) | 10.4985 | 0.568525 | ||||||||
\(342\) | 1.11447 | 0.0602636 | ||||||||
\(343\) | −16.9757 | −0.916604 | ||||||||
\(344\) | 11.4467 | 0.617162 | ||||||||
\(345\) | 40.0110 | 2.15412 | ||||||||
\(346\) | 12.6704 | 0.681167 | ||||||||
\(347\) | −13.8668 | −0.744408 | −0.372204 | − | 0.928151i | \(-0.621398\pi\) | ||||
−0.372204 | + | 0.928151i | \(0.621398\pi\) | |||||||
\(348\) | 11.9495 | 0.640558 | ||||||||
\(349\) | 7.60207 | 0.406930 | 0.203465 | − | 0.979082i | \(-0.434780\pi\) | ||||
0.203465 | + | 0.979082i | \(0.434780\pi\) | |||||||
\(350\) | 1.56697 | 0.0837581 | ||||||||
\(351\) | 11.6631 | 0.622528 | ||||||||
\(352\) | −1.90125 | −0.101337 | ||||||||
\(353\) | 5.74221 | 0.305627 | 0.152813 | − | 0.988255i | \(-0.451167\pi\) | ||||
0.152813 | + | 0.988255i | \(0.451167\pi\) | |||||||
\(354\) | 3.51415 | 0.186775 | ||||||||
\(355\) | −1.63526 | −0.0867908 | ||||||||
\(356\) | −5.29706 | −0.280744 | ||||||||
\(357\) | 2.23064 | 0.118058 | ||||||||
\(358\) | 24.8335 | 1.31249 | ||||||||
\(359\) | −12.4080 | −0.654869 | −0.327434 | − | 0.944874i | \(-0.606184\pi\) | ||||
−0.327434 | + | 0.944874i | \(0.606184\pi\) | |||||||
\(360\) | 2.75423 | 0.145161 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −9.34261 | −0.491037 | ||||||||
\(363\) | 14.9804 | 0.786265 | ||||||||
\(364\) | 4.31455 | 0.226144 | ||||||||
\(365\) | −28.4282 | −1.48800 | ||||||||
\(366\) | 23.5643 | 1.23173 | ||||||||
\(367\) | −3.66093 | −0.191099 | −0.0955495 | − | 0.995425i | \(-0.530461\pi\) | ||||
−0.0955495 | + | 0.995425i | \(0.530461\pi\) | |||||||
\(368\) | −7.98162 | −0.416071 | ||||||||
\(369\) | −7.37421 | −0.383886 | ||||||||
\(370\) | −7.63986 | −0.397178 | ||||||||
\(371\) | −4.90735 | −0.254777 | ||||||||
\(372\) | 11.2007 | 0.580729 | ||||||||
\(373\) | −35.5897 | −1.84276 | −0.921382 | − | 0.388658i | \(-0.872939\pi\) | ||||
−0.921382 | + | 0.388658i | \(0.872939\pi\) | |||||||
\(374\) | 1.47774 | 0.0764120 | ||||||||
\(375\) | 19.5127 | 1.00763 | ||||||||
\(376\) | −6.04983 | −0.311996 | ||||||||
\(377\) | −17.9644 | −0.925215 | ||||||||
\(378\) | 5.41133 | 0.278329 | ||||||||
\(379\) | 33.7772 | 1.73502 | 0.867508 | − | 0.497423i | \(-0.165720\pi\) | ||||
0.867508 | + | 0.497423i | \(0.165720\pi\) | |||||||
\(380\) | 2.47134 | 0.126777 | ||||||||
\(381\) | −36.8067 | −1.88567 | ||||||||
\(382\) | 20.9150 | 1.07010 | ||||||||
\(383\) | 25.0970 | 1.28240 | 0.641199 | − | 0.767375i | \(-0.278437\pi\) | ||||
0.641199 | + | 0.767375i | \(0.278437\pi\) | |||||||
\(384\) | −2.02842 | −0.103512 | ||||||||
\(385\) | −6.64791 | −0.338809 | ||||||||
\(386\) | −19.1158 | −0.972969 | ||||||||
\(387\) | 12.7569 | 0.648472 | ||||||||
\(388\) | 11.1561 | 0.566364 | ||||||||
\(389\) | 14.8264 | 0.751730 | 0.375865 | − | 0.926674i | \(-0.377346\pi\) | ||||
0.375865 | + | 0.926674i | \(0.377346\pi\) | |||||||
\(390\) | −15.2866 | −0.774067 | ||||||||
\(391\) | 6.20368 | 0.313734 | ||||||||
\(392\) | −4.99817 | −0.252446 | ||||||||
\(393\) | −10.2083 | −0.514943 | ||||||||
\(394\) | 17.4473 | 0.878981 | ||||||||
\(395\) | −38.9170 | −1.95813 | ||||||||
\(396\) | −2.11889 | −0.106478 | ||||||||
\(397\) | −17.7690 | −0.891801 | −0.445900 | − | 0.895083i | \(-0.647116\pi\) | ||||
−0.445900 | + | 0.895083i | \(0.647116\pi\) | |||||||
\(398\) | −2.95613 | −0.148177 | ||||||||
\(399\) | −2.86993 | −0.143676 | ||||||||
\(400\) | 1.10751 | 0.0553754 | ||||||||
\(401\) | −8.78872 | −0.438888 | −0.219444 | − | 0.975625i | \(-0.570424\pi\) | ||||
−0.219444 | + | 0.975625i | \(0.570424\pi\) | |||||||
\(402\) | −10.3705 | −0.517233 | ||||||||
\(403\) | −16.8388 | −0.838798 | ||||||||
\(404\) | −2.64209 | −0.131449 | ||||||||
\(405\) | −27.4352 | −1.36327 | ||||||||
\(406\) | −8.33499 | −0.413659 | ||||||||
\(407\) | 5.87750 | 0.291337 | ||||||||
\(408\) | 1.57658 | 0.0780522 | ||||||||
\(409\) | 3.01022 | 0.148846 | 0.0744229 | − | 0.997227i | \(-0.476289\pi\) | ||||
0.0744229 | + | 0.997227i | \(0.476289\pi\) | |||||||
\(410\) | −16.3523 | −0.807583 | ||||||||
\(411\) | 19.6032 | 0.966954 | ||||||||
\(412\) | 0.481843 | 0.0237387 | ||||||||
\(413\) | −2.45119 | −0.120615 | ||||||||
\(414\) | −8.89527 | −0.437179 | ||||||||
\(415\) | 33.9373 | 1.66592 | ||||||||
\(416\) | 3.04945 | 0.149512 | ||||||||
\(417\) | −12.5937 | −0.616719 | ||||||||
\(418\) | −1.90125 | −0.0929932 | ||||||||
\(419\) | −16.5426 | −0.808157 | −0.404079 | − | 0.914724i | \(-0.632408\pi\) | ||||
−0.404079 | + | 0.914724i | \(0.632408\pi\) | |||||||
\(420\) | −7.09256 | −0.346081 | ||||||||
\(421\) | 0.785599 | 0.0382877 | 0.0191439 | − | 0.999817i | \(-0.493906\pi\) | ||||
0.0191439 | + | 0.999817i | \(0.493906\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −6.74236 | −0.327825 | ||||||||
\(424\) | −3.46843 | −0.168442 | ||||||||
\(425\) | −0.860806 | −0.0417552 | ||||||||
\(426\) | 1.34219 | 0.0650292 | ||||||||
\(427\) | −16.4366 | −0.795422 | ||||||||
\(428\) | 10.6017 | 0.512451 | ||||||||
\(429\) | 11.7603 | 0.567792 | ||||||||
\(430\) | 28.2885 | 1.36419 | ||||||||
\(431\) | 12.1340 | 0.584473 | 0.292237 | − | 0.956346i | \(-0.405601\pi\) | ||||
0.292237 | + | 0.956346i | \(0.405601\pi\) | |||||||
\(432\) | 3.82464 | 0.184013 | ||||||||
\(433\) | −18.7692 | −0.901990 | −0.450995 | − | 0.892527i | \(-0.648931\pi\) | ||||
−0.450995 | + | 0.892527i | \(0.648931\pi\) | |||||||
\(434\) | −7.81271 | −0.375022 | ||||||||
\(435\) | 29.5311 | 1.41591 | ||||||||
\(436\) | −11.9045 | −0.570124 | ||||||||
\(437\) | −7.98162 | −0.381812 | ||||||||
\(438\) | 23.3332 | 1.11490 | ||||||||
\(439\) | −36.7958 | −1.75617 | −0.878084 | − | 0.478506i | \(-0.841179\pi\) | ||||
−0.878084 | + | 0.478506i | \(0.841179\pi\) | |||||||
\(440\) | −4.69863 | −0.223998 | ||||||||
\(441\) | −5.57031 | −0.265253 | ||||||||
\(442\) | −2.37018 | −0.112738 | ||||||||
\(443\) | −25.3134 | −1.20267 | −0.601337 | − | 0.798995i | \(-0.705365\pi\) | ||||
−0.601337 | + | 0.798995i | \(0.705365\pi\) | |||||||
\(444\) | 6.27062 | 0.297590 | ||||||||
\(445\) | −13.0908 | −0.620565 | ||||||||
\(446\) | −1.94987 | −0.0923292 | ||||||||
\(447\) | −28.5152 | −1.34872 | ||||||||
\(448\) | 1.41486 | 0.0668459 | ||||||||
\(449\) | −7.49329 | −0.353630 | −0.176815 | − | 0.984244i | \(-0.556579\pi\) | ||||
−0.176815 | + | 0.984244i | \(0.556579\pi\) | |||||||
\(450\) | 1.23428 | 0.0581847 | ||||||||
\(451\) | 12.5802 | 0.592377 | ||||||||
\(452\) | 3.01625 | 0.141872 | ||||||||
\(453\) | 17.4198 | 0.818451 | ||||||||
\(454\) | 10.1743 | 0.477505 | ||||||||
\(455\) | 10.6627 | 0.499876 | ||||||||
\(456\) | −2.02842 | −0.0949893 | ||||||||
\(457\) | 10.7570 | 0.503193 | 0.251596 | − | 0.967832i | \(-0.419044\pi\) | ||||
0.251596 | + | 0.967832i | \(0.419044\pi\) | |||||||
\(458\) | −15.9728 | −0.746359 | ||||||||
\(459\) | −2.97268 | −0.138753 | ||||||||
\(460\) | −19.7253 | −0.919695 | ||||||||
\(461\) | −17.7218 | −0.825386 | −0.412693 | − | 0.910870i | \(-0.635412\pi\) | ||||
−0.412693 | + | 0.910870i | \(0.635412\pi\) | |||||||
\(462\) | 5.45645 | 0.253857 | ||||||||
\(463\) | 18.3631 | 0.853404 | 0.426702 | − | 0.904392i | \(-0.359675\pi\) | ||||
0.426702 | + | 0.904392i | \(0.359675\pi\) | |||||||
\(464\) | −5.89103 | −0.273484 | ||||||||
\(465\) | 27.6807 | 1.28366 | ||||||||
\(466\) | 1.97470 | 0.0914763 | ||||||||
\(467\) | −3.64293 | −0.168575 | −0.0842874 | − | 0.996441i | \(-0.526861\pi\) | ||||
−0.0842874 | + | 0.996441i | \(0.526861\pi\) | |||||||
\(468\) | 3.39852 | 0.157097 | ||||||||
\(469\) | 7.23363 | 0.334018 | ||||||||
\(470\) | −14.9512 | −0.689647 | ||||||||
\(471\) | −20.7408 | −0.955687 | ||||||||
\(472\) | −1.73246 | −0.0797430 | ||||||||
\(473\) | −21.7629 | −1.00066 | ||||||||
\(474\) | 31.9422 | 1.46715 | ||||||||
\(475\) | 1.10751 | 0.0508159 | ||||||||
\(476\) | −1.09970 | −0.0504045 | ||||||||
\(477\) | −3.86546 | −0.176987 | ||||||||
\(478\) | 4.17581 | 0.190997 | ||||||||
\(479\) | 10.6715 | 0.487592 | 0.243796 | − | 0.969827i | \(-0.421607\pi\) | ||||
0.243796 | + | 0.969827i | \(0.421607\pi\) | |||||||
\(480\) | −5.01290 | −0.228806 | ||||||||
\(481\) | −9.42705 | −0.429836 | ||||||||
\(482\) | −9.50085 | −0.432752 | ||||||||
\(483\) | 22.9067 | 1.04229 | ||||||||
\(484\) | −7.38525 | −0.335693 | ||||||||
\(485\) | 27.5704 | 1.25191 | ||||||||
\(486\) | 11.0443 | 0.500978 | ||||||||
\(487\) | 13.0919 | 0.593249 | 0.296624 | − | 0.954994i | \(-0.404139\pi\) | ||||
0.296624 | + | 0.954994i | \(0.404139\pi\) | |||||||
\(488\) | −11.6171 | −0.525882 | ||||||||
\(489\) | 26.5305 | 1.19975 | ||||||||
\(490\) | −12.3522 | −0.558014 | ||||||||
\(491\) | −13.4801 | −0.608350 | −0.304175 | − | 0.952616i | \(-0.598381\pi\) | ||||
−0.304175 | + | 0.952616i | \(0.598381\pi\) | |||||||
\(492\) | 13.4216 | 0.605092 | ||||||||
\(493\) | 4.57878 | 0.206218 | ||||||||
\(494\) | 3.04945 | 0.137201 | ||||||||
\(495\) | −5.23648 | −0.235362 | ||||||||
\(496\) | −5.52189 | −0.247940 | ||||||||
\(497\) | −0.936203 | −0.0419944 | ||||||||
\(498\) | −27.8549 | −1.24821 | ||||||||
\(499\) | −29.7634 | −1.33239 | −0.666197 | − | 0.745776i | \(-0.732079\pi\) | ||||
−0.666197 | + | 0.745776i | \(0.732079\pi\) | |||||||
\(500\) | −9.61966 | −0.430204 | ||||||||
\(501\) | 45.9250 | 2.05178 | ||||||||
\(502\) | −2.77413 | −0.123815 | ||||||||
\(503\) | −23.4365 | −1.04498 | −0.522492 | − | 0.852644i | \(-0.674997\pi\) | ||||
−0.522492 | + | 0.852644i | \(0.674997\pi\) | |||||||
\(504\) | 1.57682 | 0.0702372 | ||||||||
\(505\) | −6.52949 | −0.290559 | ||||||||
\(506\) | 15.1750 | 0.674613 | ||||||||
\(507\) | 7.50683 | 0.333390 | ||||||||
\(508\) | 18.1456 | 0.805079 | ||||||||
\(509\) | 20.1337 | 0.892412 | 0.446206 | − | 0.894930i | \(-0.352775\pi\) | ||||
0.446206 | + | 0.894930i | \(0.352775\pi\) | |||||||
\(510\) | 3.89626 | 0.172529 | ||||||||
\(511\) | −16.2754 | −0.719982 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.82464 | 0.168862 | ||||||||
\(514\) | 13.3757 | 0.589975 | ||||||||
\(515\) | 1.19080 | 0.0524728 | ||||||||
\(516\) | −23.2186 | −1.02214 | ||||||||
\(517\) | 11.5022 | 0.505868 | ||||||||
\(518\) | −4.37389 | −0.192178 | ||||||||
\(519\) | −25.7009 | −1.12814 | ||||||||
\(520\) | 7.53623 | 0.330485 | ||||||||
\(521\) | 9.00411 | 0.394477 | 0.197239 | − | 0.980356i | \(-0.436803\pi\) | ||||
0.197239 | + | 0.980356i | \(0.436803\pi\) | |||||||
\(522\) | −6.56538 | −0.287359 | ||||||||
\(523\) | 10.0738 | 0.440495 | 0.220247 | − | 0.975444i | \(-0.429314\pi\) | ||||
0.220247 | + | 0.975444i | \(0.429314\pi\) | |||||||
\(524\) | 5.03267 | 0.219853 | ||||||||
\(525\) | −3.17847 | −0.138720 | ||||||||
\(526\) | 5.46318 | 0.238206 | ||||||||
\(527\) | 4.29187 | 0.186957 | ||||||||
\(528\) | 3.85652 | 0.167834 | ||||||||
\(529\) | 40.7062 | 1.76983 | ||||||||
\(530\) | −8.57167 | −0.372329 | ||||||||
\(531\) | −1.93078 | −0.0837886 | ||||||||
\(532\) | 1.41486 | 0.0613420 | ||||||||
\(533\) | −20.1776 | −0.873988 | ||||||||
\(534\) | 10.7446 | 0.464966 | ||||||||
\(535\) | 26.2003 | 1.13274 | ||||||||
\(536\) | 5.11260 | 0.220831 | ||||||||
\(537\) | −50.3726 | −2.17374 | ||||||||
\(538\) | −5.59912 | −0.241395 | ||||||||
\(539\) | 9.50276 | 0.409313 | ||||||||
\(540\) | 9.45197 | 0.406748 | ||||||||
\(541\) | 3.52908 | 0.151727 | 0.0758635 | − | 0.997118i | \(-0.475829\pi\) | ||||
0.0758635 | + | 0.997118i | \(0.475829\pi\) | |||||||
\(542\) | −6.95593 | −0.298783 | ||||||||
\(543\) | 18.9507 | 0.813252 | ||||||||
\(544\) | −0.777246 | −0.0333241 | ||||||||
\(545\) | −29.4201 | −1.26022 | ||||||||
\(546\) | −8.75171 | −0.374539 | ||||||||
\(547\) | −3.83335 | −0.163902 | −0.0819512 | − | 0.996636i | \(-0.526115\pi\) | ||||
−0.0819512 | + | 0.996636i | \(0.526115\pi\) | |||||||
\(548\) | −9.66429 | −0.412838 | ||||||||
\(549\) | −12.9469 | −0.552561 | ||||||||
\(550\) | −2.10565 | −0.0897852 | ||||||||
\(551\) | −5.89103 | −0.250966 | ||||||||
\(552\) | 16.1900 | 0.689094 | ||||||||
\(553\) | −22.2803 | −0.947456 | ||||||||
\(554\) | 16.3010 | 0.692562 | ||||||||
\(555\) | 15.4968 | 0.657803 | ||||||||
\(556\) | 6.20866 | 0.263306 | ||||||||
\(557\) | −0.553697 | −0.0234609 | −0.0117304 | − | 0.999931i | \(-0.503734\pi\) | ||||
−0.0117304 | + | 0.999931i | \(0.503734\pi\) | |||||||
\(558\) | −6.15398 | −0.260519 | ||||||||
\(559\) | 34.9060 | 1.47637 | ||||||||
\(560\) | 3.49660 | 0.147758 | ||||||||
\(561\) | −2.99747 | −0.126553 | ||||||||
\(562\) | 25.7357 | 1.08559 | ||||||||
\(563\) | 8.85702 | 0.373279 | 0.186640 | − | 0.982428i | \(-0.440240\pi\) | ||||
0.186640 | + | 0.982428i | \(0.440240\pi\) | |||||||
\(564\) | 12.2716 | 0.516727 | ||||||||
\(565\) | 7.45416 | 0.313599 | ||||||||
\(566\) | 0.131593 | 0.00553128 | ||||||||
\(567\) | −15.7069 | −0.659628 | ||||||||
\(568\) | −0.661692 | −0.0277640 | ||||||||
\(569\) | 8.30103 | 0.347997 | 0.173999 | − | 0.984746i | \(-0.444331\pi\) | ||||
0.173999 | + | 0.984746i | \(0.444331\pi\) | |||||||
\(570\) | −5.01290 | −0.209967 | ||||||||
\(571\) | −17.5829 | −0.735823 | −0.367912 | − | 0.929861i | \(-0.619927\pi\) | ||||
−0.367912 | + | 0.929861i | \(0.619927\pi\) | |||||||
\(572\) | −5.79777 | −0.242417 | ||||||||
\(573\) | −42.4242 | −1.77230 | ||||||||
\(574\) | −9.36183 | −0.390755 | ||||||||
\(575\) | −8.83970 | −0.368641 | ||||||||
\(576\) | 1.11447 | 0.0464362 | ||||||||
\(577\) | −18.3546 | −0.764111 | −0.382056 | − | 0.924139i | \(-0.624784\pi\) | ||||
−0.382056 | + | 0.924139i | \(0.624784\pi\) | |||||||
\(578\) | −16.3959 | −0.681979 | ||||||||
\(579\) | 38.7748 | 1.61143 | ||||||||
\(580\) | −14.5587 | −0.604518 | ||||||||
\(581\) | 19.4294 | 0.806067 | ||||||||
\(582\) | −22.6291 | −0.938008 | ||||||||
\(583\) | 6.59436 | 0.273110 | ||||||||
\(584\) | −11.5032 | −0.476005 | ||||||||
\(585\) | 8.39890 | 0.347252 | ||||||||
\(586\) | 3.62743 | 0.149848 | ||||||||
\(587\) | 15.9962 | 0.660233 | 0.330116 | − | 0.943940i | \(-0.392912\pi\) | ||||
0.330116 | + | 0.943940i | \(0.392912\pi\) | |||||||
\(588\) | 10.1384 | 0.418099 | ||||||||
\(589\) | −5.52189 | −0.227526 | ||||||||
\(590\) | −4.28150 | −0.176266 | ||||||||
\(591\) | −35.3903 | −1.45576 | ||||||||
\(592\) | −3.09139 | −0.127055 | ||||||||
\(593\) | −28.0311 | −1.15110 | −0.575550 | − | 0.817767i | \(-0.695212\pi\) | ||||
−0.575550 | + | 0.817767i | \(0.695212\pi\) | |||||||
\(594\) | −7.27159 | −0.298357 | ||||||||
\(595\) | −2.71772 | −0.111416 | ||||||||
\(596\) | 14.0579 | 0.575833 | ||||||||
\(597\) | 5.99625 | 0.245410 | ||||||||
\(598\) | −24.3396 | −0.995319 | ||||||||
\(599\) | 8.11967 | 0.331761 | 0.165880 | − | 0.986146i | \(-0.446953\pi\) | ||||
0.165880 | + | 0.986146i | \(0.446953\pi\) | |||||||
\(600\) | −2.24649 | −0.0917124 | ||||||||
\(601\) | −3.79839 | −0.154940 | −0.0774698 | − | 0.996995i | \(-0.524684\pi\) | ||||
−0.0774698 | + | 0.996995i | \(0.524684\pi\) | |||||||
\(602\) | 16.1954 | 0.660076 | ||||||||
\(603\) | 5.69784 | 0.232034 | ||||||||
\(604\) | −8.58786 | −0.349435 | ||||||||
\(605\) | −18.2514 | −0.742027 | ||||||||
\(606\) | 5.35925 | 0.217705 | ||||||||
\(607\) | −3.64245 | −0.147842 | −0.0739212 | − | 0.997264i | \(-0.523551\pi\) | ||||
−0.0739212 | + | 0.997264i | \(0.523551\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 16.9068 | 0.685099 | ||||||||
\(610\) | −28.7098 | −1.16242 | ||||||||
\(611\) | −18.4487 | −0.746354 | ||||||||
\(612\) | −0.866217 | −0.0350148 | ||||||||
\(613\) | −44.5363 | −1.79881 | −0.899403 | − | 0.437120i | \(-0.855998\pi\) | ||||
−0.899403 | + | 0.437120i | \(0.855998\pi\) | |||||||
\(614\) | 0.382256 | 0.0154266 | ||||||||
\(615\) | 33.1693 | 1.33751 | ||||||||
\(616\) | −2.69001 | −0.108383 | ||||||||
\(617\) | −36.8606 | −1.48395 | −0.741976 | − | 0.670426i | \(-0.766111\pi\) | ||||
−0.741976 | + | 0.670426i | \(0.766111\pi\) | |||||||
\(618\) | −0.977378 | −0.0393159 | ||||||||
\(619\) | −44.3504 | −1.78259 | −0.891296 | − | 0.453421i | \(-0.850203\pi\) | ||||
−0.891296 | + | 0.453421i | \(0.850203\pi\) | |||||||
\(620\) | −13.6465 | −0.548055 | ||||||||
\(621\) | −30.5268 | −1.22500 | ||||||||
\(622\) | 14.8067 | 0.593696 | ||||||||
\(623\) | −7.49461 | −0.300265 | ||||||||
\(624\) | −6.18556 | −0.247621 | ||||||||
\(625\) | −29.3110 | −1.17244 | ||||||||
\(626\) | −18.6361 | −0.744847 | ||||||||
\(627\) | 3.85652 | 0.154015 | ||||||||
\(628\) | 10.2251 | 0.408027 | ||||||||
\(629\) | 2.40277 | 0.0958047 | ||||||||
\(630\) | 3.89686 | 0.155254 | ||||||||
\(631\) | −25.8963 | −1.03092 | −0.515458 | − | 0.856915i | \(-0.672378\pi\) | ||||
−0.515458 | + | 0.856915i | \(0.672378\pi\) | |||||||
\(632\) | −15.7474 | −0.626396 | ||||||||
\(633\) | 2.02842 | 0.0806223 | ||||||||
\(634\) | 0.143542 | 0.00570078 | ||||||||
\(635\) | 44.8438 | 1.77957 | ||||||||
\(636\) | 7.03542 | 0.278973 | ||||||||
\(637\) | −15.2417 | −0.603897 | ||||||||
\(638\) | 11.2003 | 0.443425 | ||||||||
\(639\) | −0.737436 | −0.0291725 | ||||||||
\(640\) | 2.47134 | 0.0976882 | ||||||||
\(641\) | 14.8972 | 0.588404 | 0.294202 | − | 0.955743i | \(-0.404946\pi\) | ||||
0.294202 | + | 0.955743i | \(0.404946\pi\) | |||||||
\(642\) | −21.5046 | −0.848719 | ||||||||
\(643\) | 10.8458 | 0.427717 | 0.213858 | − | 0.976865i | \(-0.431397\pi\) | ||||
0.213858 | + | 0.976865i | \(0.431397\pi\) | |||||||
\(644\) | −11.2929 | −0.445002 | ||||||||
\(645\) | −57.3809 | −2.25937 | ||||||||
\(646\) | −0.777246 | −0.0305803 | ||||||||
\(647\) | −33.6114 | −1.32140 | −0.660700 | − | 0.750650i | \(-0.729741\pi\) | ||||
−0.660700 | + | 0.750650i | \(0.729741\pi\) | |||||||
\(648\) | −11.1014 | −0.436103 | ||||||||
\(649\) | 3.29384 | 0.129295 | ||||||||
\(650\) | 3.37729 | 0.132468 | ||||||||
\(651\) | 15.8474 | 0.621110 | ||||||||
\(652\) | −13.0794 | −0.512229 | ||||||||
\(653\) | −9.13589 | −0.357515 | −0.178757 | − | 0.983893i | \(-0.557208\pi\) | ||||
−0.178757 | + | 0.983893i | \(0.557208\pi\) | |||||||
\(654\) | 24.1474 | 0.944236 | ||||||||
\(655\) | 12.4374 | 0.485970 | ||||||||
\(656\) | −6.61679 | −0.258342 | ||||||||
\(657\) | −12.8199 | −0.500154 | ||||||||
\(658\) | −8.55968 | −0.333691 | ||||||||
\(659\) | −6.11303 | −0.238130 | −0.119065 | − | 0.992886i | \(-0.537990\pi\) | ||||
−0.119065 | + | 0.992886i | \(0.537990\pi\) | |||||||
\(660\) | 9.53077 | 0.370985 | ||||||||
\(661\) | 33.6797 | 1.30999 | 0.654994 | − | 0.755634i | \(-0.272671\pi\) | ||||
0.654994 | + | 0.755634i | \(0.272671\pi\) | |||||||
\(662\) | −26.5807 | −1.03309 | ||||||||
\(663\) | 4.80770 | 0.186716 | ||||||||
\(664\) | 13.7324 | 0.532919 | ||||||||
\(665\) | 3.49660 | 0.135592 | ||||||||
\(666\) | −3.44526 | −0.133501 | ||||||||
\(667\) | 47.0200 | 1.82062 | ||||||||
\(668\) | −22.6408 | −0.875999 | ||||||||
\(669\) | 3.95516 | 0.152915 | ||||||||
\(670\) | 12.6350 | 0.488131 | ||||||||
\(671\) | 22.0870 | 0.852660 | ||||||||
\(672\) | −2.86993 | −0.110710 | ||||||||
\(673\) | 20.3592 | 0.784790 | 0.392395 | − | 0.919797i | \(-0.371647\pi\) | ||||
0.392395 | + | 0.919797i | \(0.371647\pi\) | |||||||
\(674\) | −8.74594 | −0.336881 | ||||||||
\(675\) | 4.23582 | 0.163037 | ||||||||
\(676\) | −3.70083 | −0.142340 | ||||||||
\(677\) | 7.62176 | 0.292928 | 0.146464 | − | 0.989216i | \(-0.453211\pi\) | ||||
0.146464 | + | 0.989216i | \(0.453211\pi\) | |||||||
\(678\) | −6.11820 | −0.234968 | ||||||||
\(679\) | 15.7843 | 0.605746 | ||||||||
\(680\) | −1.92084 | −0.0736607 | ||||||||
\(681\) | −20.6378 | −0.790842 | ||||||||
\(682\) | 10.4985 | 0.402008 | ||||||||
\(683\) | 26.5582 | 1.01622 | 0.508111 | − | 0.861292i | \(-0.330344\pi\) | ||||
0.508111 | + | 0.861292i | \(0.330344\pi\) | |||||||
\(684\) | 1.11447 | 0.0426128 | ||||||||
\(685\) | −23.8837 | −0.912550 | ||||||||
\(686\) | −16.9757 | −0.648137 | ||||||||
\(687\) | 32.3995 | 1.23612 | ||||||||
\(688\) | 11.4467 | 0.436399 | ||||||||
\(689\) | −10.5768 | −0.402945 | ||||||||
\(690\) | 40.0110 | 1.52319 | ||||||||
\(691\) | −40.5853 | −1.54394 | −0.771969 | − | 0.635660i | \(-0.780728\pi\) | ||||
−0.771969 | + | 0.635660i | \(0.780728\pi\) | |||||||
\(692\) | 12.6704 | 0.481658 | ||||||||
\(693\) | −2.99793 | −0.113882 | ||||||||
\(694\) | −13.8668 | −0.526376 | ||||||||
\(695\) | 15.3437 | 0.582020 | ||||||||
\(696\) | 11.9495 | 0.452943 | ||||||||
\(697\) | 5.14287 | 0.194800 | ||||||||
\(698\) | 7.60207 | 0.287743 | ||||||||
\(699\) | −4.00552 | −0.151503 | ||||||||
\(700\) | 1.56697 | 0.0592259 | ||||||||
\(701\) | 27.6768 | 1.04534 | 0.522670 | − | 0.852535i | \(-0.324936\pi\) | ||||
0.522670 | + | 0.852535i | \(0.324936\pi\) | |||||||
\(702\) | 11.6631 | 0.440194 | ||||||||
\(703\) | −3.09139 | −0.116594 | ||||||||
\(704\) | −1.90125 | −0.0716560 | ||||||||
\(705\) | 30.3272 | 1.14219 | ||||||||
\(706\) | 5.74221 | 0.216111 | ||||||||
\(707\) | −3.73819 | −0.140589 | ||||||||
\(708\) | 3.51415 | 0.132070 | ||||||||
\(709\) | 13.7299 | 0.515639 | 0.257820 | − | 0.966193i | \(-0.416996\pi\) | ||||
0.257820 | + | 0.966193i | \(0.416996\pi\) | |||||||
\(710\) | −1.63526 | −0.0613704 | ||||||||
\(711\) | −17.5500 | −0.658175 | ||||||||
\(712\) | −5.29706 | −0.198516 | ||||||||
\(713\) | 44.0736 | 1.65057 | ||||||||
\(714\) | 2.23064 | 0.0834796 | ||||||||
\(715\) | −14.3283 | −0.535846 | ||||||||
\(716\) | 24.8335 | 0.928070 | ||||||||
\(717\) | −8.47027 | −0.316328 | ||||||||
\(718\) | −12.4080 | −0.463062 | ||||||||
\(719\) | 11.3179 | 0.422088 | 0.211044 | − | 0.977477i | \(-0.432314\pi\) | ||||
0.211044 | + | 0.977477i | \(0.432314\pi\) | |||||||
\(720\) | 2.75423 | 0.102644 | ||||||||
\(721\) | 0.681741 | 0.0253894 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 19.2717 | 0.716721 | ||||||||
\(724\) | −9.34261 | −0.347215 | ||||||||
\(725\) | −6.52436 | −0.242309 | ||||||||
\(726\) | 14.9804 | 0.555973 | ||||||||
\(727\) | 11.8370 | 0.439010 | 0.219505 | − | 0.975611i | \(-0.429556\pi\) | ||||
0.219505 | + | 0.975611i | \(0.429556\pi\) | |||||||
\(728\) | 4.31455 | 0.159908 | ||||||||
\(729\) | 10.9017 | 0.403768 | ||||||||
\(730\) | −28.4282 | −1.05218 | ||||||||
\(731\) | −8.89686 | −0.329062 | ||||||||
\(732\) | 23.5643 | 0.870962 | ||||||||
\(733\) | 27.3043 | 1.00851 | 0.504254 | − | 0.863555i | \(-0.331768\pi\) | ||||
0.504254 | + | 0.863555i | \(0.331768\pi\) | |||||||
\(734\) | −3.66093 | −0.135127 | ||||||||
\(735\) | 25.0553 | 0.924179 | ||||||||
\(736\) | −7.98162 | −0.294206 | ||||||||
\(737\) | −9.72034 | −0.358053 | ||||||||
\(738\) | −7.37421 | −0.271448 | ||||||||
\(739\) | 35.4056 | 1.30242 | 0.651208 | − | 0.758899i | \(-0.274262\pi\) | ||||
0.651208 | + | 0.758899i | \(0.274262\pi\) | |||||||
\(740\) | −7.63986 | −0.280847 | ||||||||
\(741\) | −6.18556 | −0.227232 | ||||||||
\(742\) | −4.90735 | −0.180155 | ||||||||
\(743\) | −7.81352 | −0.286650 | −0.143325 | − | 0.989676i | \(-0.545779\pi\) | ||||
−0.143325 | + | 0.989676i | \(0.545779\pi\) | |||||||
\(744\) | 11.2007 | 0.410637 | ||||||||
\(745\) | 34.7418 | 1.27284 | ||||||||
\(746\) | −35.5897 | −1.30303 | ||||||||
\(747\) | 15.3043 | 0.559955 | ||||||||
\(748\) | 1.47774 | 0.0540315 | ||||||||
\(749\) | 14.9999 | 0.548084 | ||||||||
\(750\) | 19.5127 | 0.712502 | ||||||||
\(751\) | −28.6632 | −1.04593 | −0.522967 | − | 0.852353i | \(-0.675175\pi\) | ||||
−0.522967 | + | 0.852353i | \(0.675175\pi\) | |||||||
\(752\) | −6.04983 | −0.220615 | ||||||||
\(753\) | 5.62709 | 0.205062 | ||||||||
\(754\) | −17.9644 | −0.654226 | ||||||||
\(755\) | −21.2235 | −0.772402 | ||||||||
\(756\) | 5.41133 | 0.196808 | ||||||||
\(757\) | 38.3471 | 1.39375 | 0.696875 | − | 0.717192i | \(-0.254573\pi\) | ||||
0.696875 | + | 0.717192i | \(0.254573\pi\) | |||||||
\(758\) | 33.7772 | 1.22684 | ||||||||
\(759\) | −30.7813 | −1.11729 | ||||||||
\(760\) | 2.47134 | 0.0896448 | ||||||||
\(761\) | 12.5038 | 0.453264 | 0.226632 | − | 0.973980i | \(-0.427228\pi\) | ||||
0.226632 | + | 0.973980i | \(0.427228\pi\) | |||||||
\(762\) | −36.8067 | −1.33337 | ||||||||
\(763\) | −16.8433 | −0.609768 | ||||||||
\(764\) | 20.9150 | 0.756677 | ||||||||
\(765\) | −2.14072 | −0.0773977 | ||||||||
\(766\) | 25.0970 | 0.906792 | ||||||||
\(767\) | −5.28306 | −0.190760 | ||||||||
\(768\) | −2.02842 | −0.0731941 | ||||||||
\(769\) | −42.3418 | −1.52688 | −0.763442 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763442 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(770\) | −6.64791 | −0.239574 | ||||||||
\(771\) | −27.1314 | −0.977113 | ||||||||
\(772\) | −19.1158 | −0.687993 | ||||||||
\(773\) | 21.5922 | 0.776619 | 0.388310 | − | 0.921529i | \(-0.373059\pi\) | ||||
0.388310 | + | 0.921529i | \(0.373059\pi\) | |||||||
\(774\) | 12.7569 | 0.458539 | ||||||||
\(775\) | −6.11554 | −0.219677 | ||||||||
\(776\) | 11.1561 | 0.400480 | ||||||||
\(777\) | 8.87206 | 0.318283 | ||||||||
\(778\) | 14.8264 | 0.531553 | ||||||||
\(779\) | −6.61679 | −0.237071 | ||||||||
\(780\) | −15.2866 | −0.547348 | ||||||||
\(781\) | 1.25804 | 0.0450163 | ||||||||
\(782\) | 6.20368 | 0.221843 | ||||||||
\(783\) | −22.5311 | −0.805195 | ||||||||
\(784\) | −4.99817 | −0.178506 | ||||||||
\(785\) | 25.2698 | 0.901916 | ||||||||
\(786\) | −10.2083 | −0.364119 | ||||||||
\(787\) | −15.4220 | −0.549734 | −0.274867 | − | 0.961482i | \(-0.588634\pi\) | ||||
−0.274867 | + | 0.961482i | \(0.588634\pi\) | |||||||
\(788\) | 17.4473 | 0.621534 | ||||||||
\(789\) | −11.0816 | −0.394516 | ||||||||
\(790\) | −38.9170 | −1.38461 | ||||||||
\(791\) | 4.26757 | 0.151737 | ||||||||
\(792\) | −2.11889 | −0.0752913 | ||||||||
\(793\) | −35.4258 | −1.25801 | ||||||||
\(794\) | −17.7690 | −0.630598 | ||||||||
\(795\) | 17.3869 | 0.616650 | ||||||||
\(796\) | −2.95613 | −0.104777 | ||||||||
\(797\) | 30.0978 | 1.06612 | 0.533060 | − | 0.846078i | \(-0.321042\pi\) | ||||
0.533060 | + | 0.846078i | \(0.321042\pi\) | |||||||
\(798\) | −2.86993 | −0.101594 | ||||||||
\(799\) | 4.70221 | 0.166352 | ||||||||
\(800\) | 1.10751 | 0.0391563 | ||||||||
\(801\) | −5.90342 | −0.208587 | ||||||||
\(802\) | −8.78872 | −0.310341 | ||||||||
\(803\) | 21.8704 | 0.771790 | ||||||||
\(804\) | −10.3705 | −0.365739 | ||||||||
\(805\) | −27.9085 | −0.983646 | ||||||||
\(806\) | −16.8388 | −0.593120 | ||||||||
\(807\) | 11.3573 | 0.399798 | ||||||||
\(808\) | −2.64209 | −0.0929483 | ||||||||
\(809\) | −13.4974 | −0.474542 | −0.237271 | − | 0.971443i | \(-0.576253\pi\) | ||||
−0.237271 | + | 0.971443i | \(0.576253\pi\) | |||||||
\(810\) | −27.4352 | −0.963975 | ||||||||
\(811\) | 30.4280 | 1.06847 | 0.534236 | − | 0.845335i | \(-0.320599\pi\) | ||||
0.534236 | + | 0.845335i | \(0.320599\pi\) | |||||||
\(812\) | −8.33499 | −0.292501 | ||||||||
\(813\) | 14.1095 | 0.494843 | ||||||||
\(814\) | 5.87750 | 0.206006 | ||||||||
\(815\) | −32.3236 | −1.13225 | ||||||||
\(816\) | 1.57658 | 0.0551913 | ||||||||
\(817\) | 11.4467 | 0.400468 | ||||||||
\(818\) | 3.01022 | 0.105250 | ||||||||
\(819\) | 4.80844 | 0.168021 | ||||||||
\(820\) | −16.3523 | −0.571047 | ||||||||
\(821\) | 41.4936 | 1.44814 | 0.724069 | − | 0.689728i | \(-0.242270\pi\) | ||||
0.724069 | + | 0.689728i | \(0.242270\pi\) | |||||||
\(822\) | 19.6032 | 0.683740 | ||||||||
\(823\) | 25.7677 | 0.898205 | 0.449103 | − | 0.893480i | \(-0.351744\pi\) | ||||
0.449103 | + | 0.893480i | \(0.351744\pi\) | |||||||
\(824\) | 0.481843 | 0.0167858 | ||||||||
\(825\) | 4.27113 | 0.148702 | ||||||||
\(826\) | −2.45119 | −0.0852879 | ||||||||
\(827\) | −42.4322 | −1.47551 | −0.737756 | − | 0.675068i | \(-0.764114\pi\) | ||||
−0.737756 | + | 0.675068i | \(0.764114\pi\) | |||||||
\(828\) | −8.89527 | −0.309132 | ||||||||
\(829\) | −14.3266 | −0.497583 | −0.248792 | − | 0.968557i | \(-0.580033\pi\) | ||||
−0.248792 | + | 0.968557i | \(0.580033\pi\) | |||||||
\(830\) | 33.9373 | 1.17798 | ||||||||
\(831\) | −33.0651 | −1.14702 | ||||||||
\(832\) | 3.04945 | 0.105721 | ||||||||
\(833\) | 3.88480 | 0.134601 | ||||||||
\(834\) | −12.5937 | −0.436086 | ||||||||
\(835\) | −55.9531 | −1.93634 | ||||||||
\(836\) | −1.90125 | −0.0657561 | ||||||||
\(837\) | −21.1192 | −0.729988 | ||||||||
\(838\) | −16.5426 | −0.571454 | ||||||||
\(839\) | 5.05886 | 0.174651 | 0.0873257 | − | 0.996180i | \(-0.472168\pi\) | ||||
0.0873257 | + | 0.996180i | \(0.472168\pi\) | |||||||
\(840\) | −7.09256 | −0.244717 | ||||||||
\(841\) | 5.70425 | 0.196698 | ||||||||
\(842\) | 0.785599 | 0.0270735 | ||||||||
\(843\) | −52.2027 | −1.79796 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −9.14601 | −0.314632 | ||||||||
\(846\) | −6.74236 | −0.231807 | ||||||||
\(847\) | −10.4491 | −0.359036 | ||||||||
\(848\) | −3.46843 | −0.119106 | ||||||||
\(849\) | −0.266926 | −0.00916087 | ||||||||
\(850\) | −0.860806 | −0.0295254 | ||||||||
\(851\) | 24.6743 | 0.845823 | ||||||||
\(852\) | 1.34219 | 0.0459826 | ||||||||
\(853\) | 15.5422 | 0.532156 | 0.266078 | − | 0.963951i | \(-0.414272\pi\) | ||||
0.266078 | + | 0.963951i | \(0.414272\pi\) | |||||||
\(854\) | −16.4366 | −0.562449 | ||||||||
\(855\) | 2.75423 | 0.0941927 | ||||||||
\(856\) | 10.6017 | 0.362358 | ||||||||
\(857\) | −0.110482 | −0.00377400 | −0.00188700 | − | 0.999998i | \(-0.500601\pi\) | ||||
−0.00188700 | + | 0.999998i | \(0.500601\pi\) | |||||||
\(858\) | 11.7603 | 0.401490 | ||||||||
\(859\) | −43.3466 | −1.47897 | −0.739484 | − | 0.673174i | \(-0.764930\pi\) | ||||
−0.739484 | + | 0.673174i | \(0.764930\pi\) | |||||||
\(860\) | 28.2885 | 0.964631 | ||||||||
\(861\) | 18.9897 | 0.647167 | ||||||||
\(862\) | 12.1340 | 0.413285 | ||||||||
\(863\) | 0.477080 | 0.0162400 | 0.00811999 | − | 0.999967i | \(-0.497415\pi\) | ||||
0.00811999 | + | 0.999967i | \(0.497415\pi\) | |||||||
\(864\) | 3.82464 | 0.130117 | ||||||||
\(865\) | 31.3129 | 1.06467 | ||||||||
\(866\) | −18.7692 | −0.637803 | ||||||||
\(867\) | 33.2577 | 1.12949 | ||||||||
\(868\) | −7.81271 | −0.265181 | ||||||||
\(869\) | 29.9397 | 1.01563 | ||||||||
\(870\) | 29.5311 | 1.00120 | ||||||||
\(871\) | 15.5906 | 0.528269 | ||||||||
\(872\) | −11.9045 | −0.403139 | ||||||||
\(873\) | 12.4331 | 0.420797 | ||||||||
\(874\) | −7.98162 | −0.269982 | ||||||||
\(875\) | −13.6105 | −0.460118 | ||||||||
\(876\) | 23.3332 | 0.788357 | ||||||||
\(877\) | 16.5224 | 0.557922 | 0.278961 | − | 0.960302i | \(-0.410010\pi\) | ||||
0.278961 | + | 0.960302i | \(0.410010\pi\) | |||||||
\(878\) | −36.7958 | −1.24180 | ||||||||
\(879\) | −7.35794 | −0.248177 | ||||||||
\(880\) | −4.69863 | −0.158391 | ||||||||
\(881\) | −20.8866 | −0.703688 | −0.351844 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351844 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(882\) | −5.57031 | −0.187562 | ||||||||
\(883\) | −19.5105 | −0.656580 | −0.328290 | − | 0.944577i | \(-0.606472\pi\) | ||||
−0.328290 | + | 0.944577i | \(0.606472\pi\) | |||||||
\(884\) | −2.37018 | −0.0797176 | ||||||||
\(885\) | 8.68466 | 0.291932 | ||||||||
\(886\) | −25.3134 | −0.850420 | ||||||||
\(887\) | 18.4635 | 0.619944 | 0.309972 | − | 0.950746i | \(-0.399680\pi\) | ||||
0.309972 | + | 0.950746i | \(0.399680\pi\) | |||||||
\(888\) | 6.27062 | 0.210428 | ||||||||
\(889\) | 25.6735 | 0.861060 | ||||||||
\(890\) | −13.0908 | −0.438806 | ||||||||
\(891\) | 21.1065 | 0.707093 | ||||||||
\(892\) | −1.94987 | −0.0652866 | ||||||||
\(893\) | −6.04983 | −0.202450 | ||||||||
\(894\) | −28.5152 | −0.953692 | ||||||||
\(895\) | 61.3719 | 2.05144 | ||||||||
\(896\) | 1.41486 | 0.0472672 | ||||||||
\(897\) | 49.3708 | 1.64844 | ||||||||
\(898\) | −7.49329 | −0.250054 | ||||||||
\(899\) | 32.5296 | 1.08492 | ||||||||
\(900\) | 1.23428 | 0.0411428 | ||||||||
\(901\) | 2.69582 | 0.0898109 | ||||||||
\(902\) | 12.5802 | 0.418874 | ||||||||
\(903\) | −32.8511 | −1.09321 | ||||||||
\(904\) | 3.01625 | 0.100319 | ||||||||
\(905\) | −23.0887 | −0.767496 | ||||||||
\(906\) | 17.4198 | 0.578732 | ||||||||
\(907\) | 59.4568 | 1.97423 | 0.987115 | − | 0.160014i | \(-0.0511540\pi\) | ||||
0.987115 | + | 0.160014i | \(0.0511540\pi\) | |||||||
\(908\) | 10.1743 | 0.337647 | ||||||||
\(909\) | −2.94453 | −0.0976638 | ||||||||
\(910\) | 10.6627 | 0.353466 | ||||||||
\(911\) | −37.6820 | −1.24846 | −0.624230 | − | 0.781241i | \(-0.714587\pi\) | ||||
−0.624230 | + | 0.781241i | \(0.714587\pi\) | |||||||
\(912\) | −2.02842 | −0.0671676 | ||||||||
\(913\) | −26.1087 | −0.864070 | ||||||||
\(914\) | 10.7570 | 0.355811 | ||||||||
\(915\) | 58.2354 | 1.92520 | ||||||||
\(916\) | −15.9728 | −0.527756 | ||||||||
\(917\) | 7.12053 | 0.235140 | ||||||||
\(918\) | −2.97268 | −0.0981132 | ||||||||
\(919\) | −41.5015 | −1.36901 | −0.684505 | − | 0.729008i | \(-0.739981\pi\) | ||||
−0.684505 | + | 0.729008i | \(0.739981\pi\) | |||||||
\(920\) | −19.7253 | −0.650323 | ||||||||
\(921\) | −0.775374 | −0.0255494 | ||||||||
\(922\) | −17.7218 | −0.583636 | ||||||||
\(923\) | −2.01780 | −0.0664167 | ||||||||
\(924\) | 5.45645 | 0.179504 | ||||||||
\(925\) | −3.42374 | −0.112572 | ||||||||
\(926\) | 18.3631 | 0.603448 | ||||||||
\(927\) | 0.537000 | 0.0176374 | ||||||||
\(928\) | −5.89103 | −0.193383 | ||||||||
\(929\) | 26.0963 | 0.856190 | 0.428095 | − | 0.903734i | \(-0.359185\pi\) | ||||
0.428095 | + | 0.903734i | \(0.359185\pi\) | |||||||
\(930\) | 27.6807 | 0.907685 | ||||||||
\(931\) | −4.99817 | −0.163808 | ||||||||
\(932\) | 1.97470 | 0.0646835 | ||||||||
\(933\) | −30.0342 | −0.983277 | ||||||||
\(934\) | −3.64293 | −0.119200 | ||||||||
\(935\) | 3.65199 | 0.119433 | ||||||||
\(936\) | 3.39852 | 0.111084 | ||||||||
\(937\) | −12.4921 | −0.408099 | −0.204049 | − | 0.978961i | \(-0.565410\pi\) | ||||
−0.204049 | + | 0.978961i | \(0.565410\pi\) | |||||||
\(938\) | 7.23363 | 0.236186 | ||||||||
\(939\) | 37.8017 | 1.23361 | ||||||||
\(940\) | −14.9512 | −0.487654 | ||||||||
\(941\) | −8.05821 | −0.262690 | −0.131345 | − | 0.991337i | \(-0.541930\pi\) | ||||
−0.131345 | + | 0.991337i | \(0.541930\pi\) | |||||||
\(942\) | −20.7408 | −0.675773 | ||||||||
\(943\) | 52.8126 | 1.71982 | ||||||||
\(944\) | −1.73246 | −0.0563868 | ||||||||
\(945\) | 13.3732 | 0.435031 | ||||||||
\(946\) | −21.7629 | −0.707574 | ||||||||
\(947\) | −24.0892 | −0.782793 | −0.391397 | − | 0.920222i | \(-0.628008\pi\) | ||||
−0.391397 | + | 0.920222i | \(0.628008\pi\) | |||||||
\(948\) | 31.9422 | 1.03743 | ||||||||
\(949\) | −35.0784 | −1.13869 | ||||||||
\(950\) | 1.10751 | 0.0359323 | ||||||||
\(951\) | −0.291163 | −0.00944160 | ||||||||
\(952\) | −1.09970 | −0.0356413 | ||||||||
\(953\) | 43.3397 | 1.40391 | 0.701956 | − | 0.712221i | \(-0.252310\pi\) | ||||
0.701956 | + | 0.712221i | \(0.252310\pi\) | |||||||
\(954\) | −3.86546 | −0.125149 | ||||||||
\(955\) | 51.6879 | 1.67258 | ||||||||
\(956\) | 4.17581 | 0.135055 | ||||||||
\(957\) | −22.7189 | −0.734398 | ||||||||
\(958\) | 10.6715 | 0.344779 | ||||||||
\(959\) | −13.6736 | −0.441544 | ||||||||
\(960\) | −5.01290 | −0.161791 | ||||||||
\(961\) | −0.508718 | −0.0164103 | ||||||||
\(962\) | −9.42705 | −0.303940 | ||||||||
\(963\) | 11.8152 | 0.380741 | ||||||||
\(964\) | −9.50085 | −0.306002 | ||||||||
\(965\) | −47.2416 | −1.52076 | ||||||||
\(966\) | 22.9067 | 0.737010 | ||||||||
\(967\) | 21.8390 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(968\) | −7.38525 | −0.237371 | ||||||||
\(969\) | 1.57658 | 0.0506470 | ||||||||
\(970\) | 27.5704 | 0.885233 | ||||||||
\(971\) | −29.3389 | −0.941530 | −0.470765 | − | 0.882259i | \(-0.656022\pi\) | ||||
−0.470765 | + | 0.882259i | \(0.656022\pi\) | |||||||
\(972\) | 11.0443 | 0.354245 | ||||||||
\(973\) | 8.78440 | 0.281615 | ||||||||
\(974\) | 13.0919 | 0.419490 | ||||||||
\(975\) | −6.85055 | −0.219393 | ||||||||
\(976\) | −11.6171 | −0.371854 | ||||||||
\(977\) | 5.51365 | 0.176397 | 0.0881987 | − | 0.996103i | \(-0.471889\pi\) | ||||
0.0881987 | + | 0.996103i | \(0.471889\pi\) | |||||||
\(978\) | 26.5305 | 0.848351 | ||||||||
\(979\) | 10.0710 | 0.321872 | ||||||||
\(980\) | −12.3522 | −0.394575 | ||||||||
\(981\) | −13.2673 | −0.423591 | ||||||||
\(982\) | −13.4801 | −0.430168 | ||||||||
\(983\) | −36.3953 | −1.16083 | −0.580416 | − | 0.814320i | \(-0.697110\pi\) | ||||
−0.580416 | + | 0.814320i | \(0.697110\pi\) | |||||||
\(984\) | 13.4216 | 0.427865 | ||||||||
\(985\) | 43.1181 | 1.37386 | ||||||||
\(986\) | 4.57878 | 0.145818 | ||||||||
\(987\) | 17.3626 | 0.552657 | ||||||||
\(988\) | 3.04945 | 0.0970160 | ||||||||
\(989\) | −91.3628 | −2.90517 | ||||||||
\(990\) | −5.23648 | −0.166426 | ||||||||
\(991\) | 5.69743 | 0.180985 | 0.0904924 | − | 0.995897i | \(-0.471156\pi\) | ||||
0.0904924 | + | 0.995897i | \(0.471156\pi\) | |||||||
\(992\) | −5.52189 | −0.175320 | ||||||||
\(993\) | 53.9168 | 1.71100 | ||||||||
\(994\) | −0.936203 | −0.0296945 | ||||||||
\(995\) | −7.30558 | −0.231603 | ||||||||
\(996\) | −27.8549 | −0.882618 | ||||||||
\(997\) | −1.79005 | −0.0566916 | −0.0283458 | − | 0.999598i | \(-0.509024\pi\) | ||||
−0.0283458 | + | 0.999598i | \(0.509024\pi\) | |||||||
\(998\) | −29.7634 | −0.942145 | ||||||||
\(999\) | −11.8234 | −0.374077 |
(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 | 8018.2.a.d.1.8 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.8 | ✓ | 30 | 1.1 | even | 1 | trivial |