Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82377 | −1.99671 | −0.998353 | − | 0.0573723i | \(-0.981728\pi\) | ||||
−0.998353 | + | 0.0573723i | \(0.981728\pi\) | |||||||
\(3\) | 0.0811365 | 0.0468442 | 0.0234221 | − | 0.999726i | \(-0.492544\pi\) | ||||
0.0234221 | + | 0.999726i | \(0.492544\pi\) | |||||||
\(4\) | 5.97367 | 2.98683 | ||||||||
\(5\) | 1.22528 | 0.547961 | 0.273980 | − | 0.961735i | \(-0.411660\pi\) | ||||
0.273980 | + | 0.961735i | \(0.411660\pi\) | |||||||
\(6\) | −0.229111 | −0.0935340 | ||||||||
\(7\) | 1.93678 | 0.732035 | 0.366017 | − | 0.930608i | \(-0.380721\pi\) | ||||
0.366017 | + | 0.930608i | \(0.380721\pi\) | |||||||
\(8\) | −11.2207 | −3.96712 | ||||||||
\(9\) | −2.99342 | −0.997806 | ||||||||
\(10\) | −3.45990 | −1.09412 | ||||||||
\(11\) | 1.10465 | 0.333066 | 0.166533 | − | 0.986036i | \(-0.446743\pi\) | ||||
0.166533 | + | 0.986036i | \(0.446743\pi\) | |||||||
\(12\) | 0.484682 | 0.139916 | ||||||||
\(13\) | −6.90923 | −1.91628 | −0.958138 | − | 0.286307i | \(-0.907572\pi\) | ||||
−0.958138 | + | 0.286307i | \(0.907572\pi\) | |||||||
\(14\) | −5.46902 | −1.46166 | ||||||||
\(15\) | 0.0994147 | 0.0256688 | ||||||||
\(16\) | 19.7374 | 4.93434 | ||||||||
\(17\) | 1.76873 | 0.428981 | 0.214491 | − | 0.976726i | \(-0.431191\pi\) | ||||
0.214491 | + | 0.976726i | \(0.431191\pi\) | |||||||
\(18\) | 8.45272 | 1.99232 | ||||||||
\(19\) | 7.08725 | 1.62593 | 0.812964 | − | 0.582314i | \(-0.197853\pi\) | ||||
0.812964 | + | 0.582314i | \(0.197853\pi\) | |||||||
\(20\) | 7.31940 | 1.63667 | ||||||||
\(21\) | 0.157144 | 0.0342916 | ||||||||
\(22\) | −3.11928 | −0.665034 | ||||||||
\(23\) | 7.96464 | 1.66074 | 0.830371 | − | 0.557211i | \(-0.188129\pi\) | ||||
0.830371 | + | 0.557211i | \(0.188129\pi\) | |||||||
\(24\) | −0.910409 | −0.185837 | ||||||||
\(25\) | −3.49869 | −0.699739 | ||||||||
\(26\) | 19.5101 | 3.82624 | ||||||||
\(27\) | −0.486285 | −0.0935855 | ||||||||
\(28\) | 11.5697 | 2.18647 | ||||||||
\(29\) | −5.37427 | −0.997977 | −0.498989 | − | 0.866608i | \(-0.666295\pi\) | ||||
−0.498989 | + | 0.866608i | \(0.666295\pi\) | |||||||
\(30\) | −0.280724 | −0.0512530 | ||||||||
\(31\) | −2.15671 | −0.387356 | −0.193678 | − | 0.981065i | \(-0.562042\pi\) | ||||
−0.193678 | + | 0.981065i | \(0.562042\pi\) | |||||||
\(32\) | −33.2923 | −5.88531 | ||||||||
\(33\) | 0.0896277 | 0.0156022 | ||||||||
\(34\) | −4.99450 | −0.856549 | ||||||||
\(35\) | 2.37310 | 0.401126 | ||||||||
\(36\) | −17.8817 | −2.98028 | ||||||||
\(37\) | −3.79792 | −0.624374 | −0.312187 | − | 0.950021i | \(-0.601061\pi\) | ||||
−0.312187 | + | 0.950021i | \(0.601061\pi\) | |||||||
\(38\) | −20.0128 | −3.24650 | ||||||||
\(39\) | −0.560591 | −0.0897664 | ||||||||
\(40\) | −13.7485 | −2.17383 | ||||||||
\(41\) | 9.77275 | 1.52625 | 0.763124 | − | 0.646252i | \(-0.223665\pi\) | ||||
0.763124 | + | 0.646252i | \(0.223665\pi\) | |||||||
\(42\) | −0.443737 | −0.0684702 | ||||||||
\(43\) | −6.40853 | −0.977291 | −0.488646 | − | 0.872482i | \(-0.662509\pi\) | ||||
−0.488646 | + | 0.872482i | \(0.662509\pi\) | |||||||
\(44\) | 6.59883 | 0.994811 | ||||||||
\(45\) | −3.66777 | −0.546758 | ||||||||
\(46\) | −22.4903 | −3.31601 | ||||||||
\(47\) | −1.80885 | −0.263847 | −0.131924 | − | 0.991260i | \(-0.542115\pi\) | ||||
−0.131924 | + | 0.991260i | \(0.542115\pi\) | |||||||
\(48\) | 1.60142 | 0.231145 | ||||||||
\(49\) | −3.24887 | −0.464125 | ||||||||
\(50\) | 9.87950 | 1.39717 | ||||||||
\(51\) | 0.143509 | 0.0200953 | ||||||||
\(52\) | −41.2735 | −5.72360 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.37316 | 0.186863 | ||||||||
\(55\) | 1.35351 | 0.182507 | ||||||||
\(56\) | −21.7321 | −2.90407 | ||||||||
\(57\) | 0.575035 | 0.0761652 | ||||||||
\(58\) | 15.1757 | 1.99267 | ||||||||
\(59\) | −2.90833 | −0.378633 | −0.189316 | − | 0.981916i | \(-0.560627\pi\) | ||||
−0.189316 | + | 0.981916i | \(0.560627\pi\) | |||||||
\(60\) | 0.593871 | 0.0766684 | ||||||||
\(61\) | −4.10954 | −0.526173 | −0.263086 | − | 0.964772i | \(-0.584740\pi\) | ||||
−0.263086 | + | 0.964772i | \(0.584740\pi\) | |||||||
\(62\) | 6.09004 | 0.773436 | ||||||||
\(63\) | −5.79760 | −0.730428 | ||||||||
\(64\) | 54.5351 | 6.81688 | ||||||||
\(65\) | −8.46573 | −1.05004 | ||||||||
\(66\) | −0.253088 | −0.0311530 | ||||||||
\(67\) | 11.3085 | 1.38155 | 0.690774 | − | 0.723071i | \(-0.257270\pi\) | ||||
0.690774 | + | 0.723071i | \(0.257270\pi\) | |||||||
\(68\) | 10.5658 | 1.28130 | ||||||||
\(69\) | 0.646223 | 0.0777961 | ||||||||
\(70\) | −6.70107 | −0.800932 | ||||||||
\(71\) | −12.9010 | −1.53106 | −0.765531 | − | 0.643399i | \(-0.777523\pi\) | ||||
−0.765531 | + | 0.643399i | \(0.777523\pi\) | |||||||
\(72\) | 33.5883 | 3.95842 | ||||||||
\(73\) | 5.22639 | 0.611703 | 0.305851 | − | 0.952079i | \(-0.401059\pi\) | ||||
0.305851 | + | 0.952079i | \(0.401059\pi\) | |||||||
\(74\) | 10.7244 | 1.24669 | ||||||||
\(75\) | −0.283872 | −0.0327787 | ||||||||
\(76\) | 42.3369 | 4.85637 | ||||||||
\(77\) | 2.13947 | 0.243816 | ||||||||
\(78\) | 1.58298 | 0.179237 | ||||||||
\(79\) | −6.41878 | −0.722169 | −0.361085 | − | 0.932533i | \(-0.617593\pi\) | ||||
−0.361085 | + | 0.932533i | \(0.617593\pi\) | |||||||
\(80\) | 24.1838 | 2.70383 | ||||||||
\(81\) | 8.94080 | 0.993422 | ||||||||
\(82\) | −27.5960 | −3.04747 | ||||||||
\(83\) | 5.11469 | 0.561410 | 0.280705 | − | 0.959794i | \(-0.409432\pi\) | ||||
0.280705 | + | 0.959794i | \(0.409432\pi\) | |||||||
\(84\) | 0.938724 | 0.102423 | ||||||||
\(85\) | 2.16719 | 0.235065 | ||||||||
\(86\) | 18.0962 | 1.95136 | ||||||||
\(87\) | −0.436050 | −0.0467494 | ||||||||
\(88\) | −12.3950 | −1.32131 | ||||||||
\(89\) | 10.1425 | 1.07511 | 0.537554 | − | 0.843230i | \(-0.319349\pi\) | ||||
0.537554 | + | 0.843230i | \(0.319349\pi\) | |||||||
\(90\) | 10.3569 | 1.09172 | ||||||||
\(91\) | −13.3817 | −1.40278 | ||||||||
\(92\) | 47.5781 | 4.96036 | ||||||||
\(93\) | −0.174988 | −0.0181454 | ||||||||
\(94\) | 5.10776 | 0.526826 | ||||||||
\(95\) | 8.68385 | 0.890945 | ||||||||
\(96\) | −2.70122 | −0.275692 | ||||||||
\(97\) | −9.09837 | −0.923799 | −0.461900 | − | 0.886932i | \(-0.652832\pi\) | ||||
−0.461900 | + | 0.886932i | \(0.652832\pi\) | |||||||
\(98\) | 9.17407 | 0.926721 | ||||||||
\(99\) | −3.30669 | −0.332335 | ||||||||
\(100\) | −20.9000 | −2.09000 | ||||||||
\(101\) | 13.1521 | 1.30869 | 0.654343 | − | 0.756198i | \(-0.272945\pi\) | ||||
0.654343 | + | 0.756198i | \(0.272945\pi\) | |||||||
\(102\) | −0.405236 | −0.0401243 | ||||||||
\(103\) | −9.75259 | −0.960951 | −0.480475 | − | 0.877008i | \(-0.659536\pi\) | ||||
−0.480475 | + | 0.877008i | \(0.659536\pi\) | |||||||
\(104\) | 77.5265 | 7.60210 | ||||||||
\(105\) | 0.192545 | 0.0187904 | ||||||||
\(106\) | 2.82377 | 0.274269 | ||||||||
\(107\) | −11.5027 | −1.11200 | −0.556002 | − | 0.831181i | \(-0.687665\pi\) | ||||
−0.556002 | + | 0.831181i | \(0.687665\pi\) | |||||||
\(108\) | −2.90490 | −0.279524 | ||||||||
\(109\) | 4.31270 | 0.413082 | 0.206541 | − | 0.978438i | \(-0.433779\pi\) | ||||
0.206541 | + | 0.978438i | \(0.433779\pi\) | |||||||
\(110\) | −3.82199 | −0.364413 | ||||||||
\(111\) | −0.308150 | −0.0292483 | ||||||||
\(112\) | 38.2270 | 3.61211 | ||||||||
\(113\) | −1.67681 | −0.157741 | −0.0788703 | − | 0.996885i | \(-0.525131\pi\) | ||||
−0.0788703 | + | 0.996885i | \(0.525131\pi\) | |||||||
\(114\) | −1.62376 | −0.152080 | ||||||||
\(115\) | 9.75889 | 0.910021 | ||||||||
\(116\) | −32.1041 | −2.98079 | ||||||||
\(117\) | 20.6822 | 1.91207 | ||||||||
\(118\) | 8.21246 | 0.756018 | ||||||||
\(119\) | 3.42565 | 0.314029 | ||||||||
\(120\) | −1.11550 | −0.101831 | ||||||||
\(121\) | −9.77974 | −0.889067 | ||||||||
\(122\) | 11.6044 | 1.05061 | ||||||||
\(123\) | 0.792927 | 0.0714958 | ||||||||
\(124\) | −12.8834 | −1.15697 | ||||||||
\(125\) | −10.4133 | −0.931390 | ||||||||
\(126\) | 16.3711 | 1.45845 | ||||||||
\(127\) | −7.80232 | −0.692344 | −0.346172 | − | 0.938171i | \(-0.612519\pi\) | ||||
−0.346172 | + | 0.938171i | \(0.612519\pi\) | |||||||
\(128\) | −87.4097 | −7.72600 | ||||||||
\(129\) | −0.519965 | −0.0457804 | ||||||||
\(130\) | 23.9053 | 2.09663 | ||||||||
\(131\) | 1.94212 | 0.169683 | 0.0848417 | − | 0.996394i | \(-0.472962\pi\) | ||||
0.0848417 | + | 0.996394i | \(0.472962\pi\) | |||||||
\(132\) | 0.535406 | 0.0466011 | ||||||||
\(133\) | 13.7265 | 1.19024 | ||||||||
\(134\) | −31.9325 | −2.75854 | ||||||||
\(135\) | −0.595834 | −0.0512812 | ||||||||
\(136\) | −19.8465 | −1.70182 | ||||||||
\(137\) | −1.23048 | −0.105127 | −0.0525636 | − | 0.998618i | \(-0.516739\pi\) | ||||
−0.0525636 | + | 0.998618i | \(0.516739\pi\) | |||||||
\(138\) | −1.82478 | −0.155336 | ||||||||
\(139\) | 1.84023 | 0.156086 | 0.0780430 | − | 0.996950i | \(-0.475133\pi\) | ||||
0.0780430 | + | 0.996950i | \(0.475133\pi\) | |||||||
\(140\) | 14.1761 | 1.19810 | ||||||||
\(141\) | −0.146763 | −0.0123597 | ||||||||
\(142\) | 36.4293 | 3.05708 | ||||||||
\(143\) | −7.63231 | −0.638245 | ||||||||
\(144\) | −59.0822 | −4.92351 | ||||||||
\(145\) | −6.58498 | −0.546853 | ||||||||
\(146\) | −14.7581 | −1.22139 | ||||||||
\(147\) | −0.263602 | −0.0217415 | ||||||||
\(148\) | −22.6875 | −1.86490 | ||||||||
\(149\) | 10.0824 | 0.825979 | 0.412989 | − | 0.910736i | \(-0.364485\pi\) | ||||
0.412989 | + | 0.910736i | \(0.364485\pi\) | |||||||
\(150\) | 0.801588 | 0.0654494 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | −79.5240 | −6.45025 | ||||||||
\(153\) | −5.29456 | −0.428040 | ||||||||
\(154\) | −6.04138 | −0.486828 | ||||||||
\(155\) | −2.64256 | −0.212256 | ||||||||
\(156\) | −3.34878 | −0.268117 | ||||||||
\(157\) | −4.48934 | −0.358288 | −0.179144 | − | 0.983823i | \(-0.557333\pi\) | ||||
−0.179144 | + | 0.983823i | \(0.557333\pi\) | |||||||
\(158\) | 18.1251 | 1.44196 | ||||||||
\(159\) | −0.0811365 | −0.00643454 | ||||||||
\(160\) | −40.7923 | −3.22492 | ||||||||
\(161\) | 15.4258 | 1.21572 | ||||||||
\(162\) | −25.2467 | −1.98357 | ||||||||
\(163\) | −8.44188 | −0.661219 | −0.330610 | − | 0.943768i | \(-0.607254\pi\) | ||||
−0.330610 | + | 0.943768i | \(0.607254\pi\) | |||||||
\(164\) | 58.3792 | 4.55865 | ||||||||
\(165\) | 0.109819 | 0.00854938 | ||||||||
\(166\) | −14.4427 | −1.12097 | ||||||||
\(167\) | 4.04845 | 0.313278 | 0.156639 | − | 0.987656i | \(-0.449934\pi\) | ||||
0.156639 | + | 0.987656i | \(0.449934\pi\) | |||||||
\(168\) | −1.76326 | −0.136039 | ||||||||
\(169\) | 34.7375 | 2.67211 | ||||||||
\(170\) | −6.11965 | −0.469356 | ||||||||
\(171\) | −21.2151 | −1.62236 | ||||||||
\(172\) | −38.2824 | −2.91901 | ||||||||
\(173\) | −4.53681 | −0.344927 | −0.172464 | − | 0.985016i | \(-0.555173\pi\) | ||||
−0.172464 | + | 0.985016i | \(0.555173\pi\) | |||||||
\(174\) | 1.23130 | 0.0933448 | ||||||||
\(175\) | −6.77621 | −0.512233 | ||||||||
\(176\) | 21.8029 | 1.64346 | ||||||||
\(177\) | −0.235972 | −0.0177367 | ||||||||
\(178\) | −28.6402 | −2.14667 | ||||||||
\(179\) | −15.8720 | −1.18633 | −0.593164 | − | 0.805082i | \(-0.702121\pi\) | ||||
−0.593164 | + | 0.805082i | \(0.702121\pi\) | |||||||
\(180\) | −21.9100 | −1.63308 | ||||||||
\(181\) | −1.85688 | −0.138021 | −0.0690106 | − | 0.997616i | \(-0.521984\pi\) | ||||
−0.0690106 | + | 0.997616i | \(0.521984\pi\) | |||||||
\(182\) | 37.7868 | 2.80094 | ||||||||
\(183\) | −0.333434 | −0.0246481 | ||||||||
\(184\) | −89.3689 | −6.58836 | ||||||||
\(185\) | −4.65350 | −0.342132 | ||||||||
\(186\) | 0.494124 | 0.0362310 | ||||||||
\(187\) | 1.95384 | 0.142879 | ||||||||
\(188\) | −10.8054 | −0.788068 | ||||||||
\(189\) | −0.941828 | −0.0685079 | ||||||||
\(190\) | −24.5212 | −1.77895 | ||||||||
\(191\) | 1.25950 | 0.0911343 | 0.0455671 | − | 0.998961i | \(-0.485491\pi\) | ||||
0.0455671 | + | 0.998961i | \(0.485491\pi\) | |||||||
\(192\) | 4.42478 | 0.319331 | ||||||||
\(193\) | −10.1036 | −0.727274 | −0.363637 | − | 0.931541i | \(-0.618465\pi\) | ||||
−0.363637 | + | 0.931541i | \(0.618465\pi\) | |||||||
\(194\) | 25.6917 | 1.84456 | ||||||||
\(195\) | −0.686879 | −0.0491885 | ||||||||
\(196\) | −19.4077 | −1.38626 | ||||||||
\(197\) | −11.8175 | −0.841963 | −0.420981 | − | 0.907069i | \(-0.638314\pi\) | ||||
−0.420981 | + | 0.907069i | \(0.638314\pi\) | |||||||
\(198\) | 9.33732 | 0.663574 | ||||||||
\(199\) | 8.75342 | 0.620514 | 0.310257 | − | 0.950653i | \(-0.399585\pi\) | ||||
0.310257 | + | 0.950653i | \(0.399585\pi\) | |||||||
\(200\) | 39.2579 | 2.77595 | ||||||||
\(201\) | 0.917529 | 0.0647175 | ||||||||
\(202\) | −37.1386 | −2.61306 | ||||||||
\(203\) | −10.4088 | −0.730554 | ||||||||
\(204\) | 0.857275 | 0.0600212 | ||||||||
\(205\) | 11.9743 | 0.836324 | ||||||||
\(206\) | 27.5390 | 1.91874 | ||||||||
\(207\) | −23.8415 | −1.65710 | ||||||||
\(208\) | −136.370 | −9.45556 | ||||||||
\(209\) | 7.82896 | 0.541540 | ||||||||
\(210\) | −0.543702 | −0.0375190 | ||||||||
\(211\) | −11.1938 | −0.770610 | −0.385305 | − | 0.922789i | \(-0.625904\pi\) | ||||
−0.385305 | + | 0.922789i | \(0.625904\pi\) | |||||||
\(212\) | −5.97367 | −0.410273 | ||||||||
\(213\) | −1.04674 | −0.0717213 | ||||||||
\(214\) | 32.4808 | 2.22034 | ||||||||
\(215\) | −7.85223 | −0.535517 | ||||||||
\(216\) | 5.45646 | 0.371265 | ||||||||
\(217\) | −4.17707 | −0.283558 | ||||||||
\(218\) | −12.1781 | −0.824803 | ||||||||
\(219\) | 0.424051 | 0.0286547 | ||||||||
\(220\) | 8.08540 | 0.545118 | ||||||||
\(221\) | −12.2206 | −0.822047 | ||||||||
\(222\) | 0.870143 | 0.0584002 | ||||||||
\(223\) | −25.4096 | −1.70155 | −0.850777 | − | 0.525526i | \(-0.823869\pi\) | ||||
−0.850777 | + | 0.525526i | \(0.823869\pi\) | |||||||
\(224\) | −64.4800 | −4.30825 | ||||||||
\(225\) | 10.4731 | 0.698203 | ||||||||
\(226\) | 4.73491 | 0.314962 | ||||||||
\(227\) | 29.3348 | 1.94702 | 0.973511 | − | 0.228640i | \(-0.0734279\pi\) | ||||
0.973511 | + | 0.228640i | \(0.0734279\pi\) | |||||||
\(228\) | 3.43507 | 0.227493 | ||||||||
\(229\) | −8.40064 | −0.555130 | −0.277565 | − | 0.960707i | \(-0.589527\pi\) | ||||
−0.277565 | + | 0.960707i | \(0.589527\pi\) | |||||||
\(230\) | −27.5569 | −1.81704 | ||||||||
\(231\) | 0.173589 | 0.0114213 | ||||||||
\(232\) | 60.3032 | 3.95910 | ||||||||
\(233\) | 15.2658 | 1.00009 | 0.500047 | − | 0.865998i | \(-0.333316\pi\) | ||||
0.500047 | + | 0.865998i | \(0.333316\pi\) | |||||||
\(234\) | −58.4018 | −3.81784 | ||||||||
\(235\) | −2.21634 | −0.144578 | ||||||||
\(236\) | −17.3734 | −1.13091 | ||||||||
\(237\) | −0.520797 | −0.0338294 | ||||||||
\(238\) | −9.67325 | −0.627024 | ||||||||
\(239\) | 20.0737 | 1.29846 | 0.649231 | − | 0.760592i | \(-0.275091\pi\) | ||||
0.649231 | + | 0.760592i | \(0.275091\pi\) | |||||||
\(240\) | 1.96218 | 0.126658 | ||||||||
\(241\) | 16.2200 | 1.04482 | 0.522411 | − | 0.852694i | \(-0.325033\pi\) | ||||
0.522411 | + | 0.852694i | \(0.325033\pi\) | |||||||
\(242\) | 27.6157 | 1.77521 | ||||||||
\(243\) | 2.18428 | 0.140122 | ||||||||
\(244\) | −24.5490 | −1.57159 | ||||||||
\(245\) | −3.98077 | −0.254322 | ||||||||
\(246\) | −2.23904 | −0.142756 | ||||||||
\(247\) | −48.9675 | −3.11573 | ||||||||
\(248\) | 24.1998 | 1.53669 | ||||||||
\(249\) | 0.414988 | 0.0262988 | ||||||||
\(250\) | 29.4046 | 1.85971 | ||||||||
\(251\) | 5.96305 | 0.376385 | 0.188192 | − | 0.982132i | \(-0.439737\pi\) | ||||
0.188192 | + | 0.982132i | \(0.439737\pi\) | |||||||
\(252\) | −34.6329 | −2.18167 | ||||||||
\(253\) | 8.79816 | 0.553136 | ||||||||
\(254\) | 22.0319 | 1.38241 | ||||||||
\(255\) | 0.175838 | 0.0110114 | ||||||||
\(256\) | 137.755 | 8.60967 | ||||||||
\(257\) | 5.03217 | 0.313898 | 0.156949 | − | 0.987607i | \(-0.449834\pi\) | ||||
0.156949 | + | 0.987607i | \(0.449834\pi\) | |||||||
\(258\) | 1.46826 | 0.0914100 | ||||||||
\(259\) | −7.35574 | −0.457063 | ||||||||
\(260\) | −50.5714 | −3.13631 | ||||||||
\(261\) | 16.0874 | 0.995788 | ||||||||
\(262\) | −5.48409 | −0.338808 | ||||||||
\(263\) | −20.7176 | −1.27750 | −0.638751 | − | 0.769413i | \(-0.720549\pi\) | ||||
−0.638751 | + | 0.769413i | \(0.720549\pi\) | |||||||
\(264\) | −1.00569 | −0.0618957 | ||||||||
\(265\) | −1.22528 | −0.0752682 | ||||||||
\(266\) | −38.7604 | −2.37655 | ||||||||
\(267\) | 0.822930 | 0.0503625 | ||||||||
\(268\) | 67.5530 | 4.12645 | ||||||||
\(269\) | 9.32887 | 0.568792 | 0.284396 | − | 0.958707i | \(-0.408207\pi\) | ||||
0.284396 | + | 0.958707i | \(0.408207\pi\) | |||||||
\(270\) | 1.68250 | 0.102393 | ||||||||
\(271\) | −20.4843 | −1.24434 | −0.622168 | − | 0.782884i | \(-0.713748\pi\) | ||||
−0.622168 | + | 0.782884i | \(0.713748\pi\) | |||||||
\(272\) | 34.9102 | 2.11674 | ||||||||
\(273\) | −1.08574 | −0.0657121 | ||||||||
\(274\) | 3.47460 | 0.209908 | ||||||||
\(275\) | −3.86484 | −0.233059 | ||||||||
\(276\) | 3.86032 | 0.232364 | ||||||||
\(277\) | −18.3536 | −1.10276 | −0.551380 | − | 0.834254i | \(-0.685898\pi\) | ||||
−0.551380 | + | 0.834254i | \(0.685898\pi\) | |||||||
\(278\) | −5.19638 | −0.311658 | ||||||||
\(279\) | 6.45592 | 0.386506 | ||||||||
\(280\) | −26.6278 | −1.59132 | ||||||||
\(281\) | 20.4488 | 1.21987 | 0.609935 | − | 0.792451i | \(-0.291196\pi\) | ||||
0.609935 | + | 0.792451i | \(0.291196\pi\) | |||||||
\(282\) | 0.414426 | 0.0246787 | ||||||||
\(283\) | 14.9635 | 0.889486 | 0.444743 | − | 0.895658i | \(-0.353295\pi\) | ||||
0.444743 | + | 0.895658i | \(0.353295\pi\) | |||||||
\(284\) | −77.0660 | −4.57303 | ||||||||
\(285\) | 0.704577 | 0.0417356 | ||||||||
\(286\) | 21.5519 | 1.27439 | ||||||||
\(287\) | 18.9277 | 1.11727 | ||||||||
\(288\) | 99.6578 | 5.87239 | ||||||||
\(289\) | −13.8716 | −0.815975 | ||||||||
\(290\) | 18.5945 | 1.09190 | ||||||||
\(291\) | −0.738210 | −0.0432746 | ||||||||
\(292\) | 31.2207 | 1.82705 | ||||||||
\(293\) | 21.6604 | 1.26541 | 0.632706 | − | 0.774392i | \(-0.281944\pi\) | ||||
0.632706 | + | 0.774392i | \(0.281944\pi\) | |||||||
\(294\) | 0.744352 | 0.0434115 | ||||||||
\(295\) | −3.56352 | −0.207476 | ||||||||
\(296\) | 42.6153 | 2.47697 | ||||||||
\(297\) | −0.537176 | −0.0311701 | ||||||||
\(298\) | −28.4702 | −1.64924 | ||||||||
\(299\) | −55.0295 | −3.18244 | ||||||||
\(300\) | −1.69576 | −0.0979045 | ||||||||
\(301\) | −12.4119 | −0.715411 | ||||||||
\(302\) | 2.82377 | 0.162490 | ||||||||
\(303\) | 1.06712 | 0.0613043 | ||||||||
\(304\) | 139.884 | 8.02288 | ||||||||
\(305\) | −5.03533 | −0.288322 | ||||||||
\(306\) | 14.9506 | 0.854670 | ||||||||
\(307\) | 28.8136 | 1.64448 | 0.822240 | − | 0.569141i | \(-0.192724\pi\) | ||||
0.822240 | + | 0.569141i | \(0.192724\pi\) | |||||||
\(308\) | 12.7805 | 0.728237 | ||||||||
\(309\) | −0.791290 | −0.0450149 | ||||||||
\(310\) | 7.46199 | 0.423813 | ||||||||
\(311\) | 2.74194 | 0.155481 | 0.0777407 | − | 0.996974i | \(-0.475229\pi\) | ||||
0.0777407 | + | 0.996974i | \(0.475229\pi\) | |||||||
\(312\) | 6.29023 | 0.356114 | ||||||||
\(313\) | −25.8282 | −1.45989 | −0.729947 | − | 0.683504i | \(-0.760455\pi\) | ||||
−0.729947 | + | 0.683504i | \(0.760455\pi\) | |||||||
\(314\) | 12.6769 | 0.715396 | ||||||||
\(315\) | −7.10367 | −0.400246 | ||||||||
\(316\) | −38.3437 | −2.15700 | ||||||||
\(317\) | −34.9778 | −1.96455 | −0.982274 | − | 0.187450i | \(-0.939978\pi\) | ||||
−0.982274 | + | 0.187450i | \(0.939978\pi\) | |||||||
\(318\) | 0.229111 | 0.0128479 | ||||||||
\(319\) | −5.93671 | −0.332392 | ||||||||
\(320\) | 66.8206 | 3.73539 | ||||||||
\(321\) | −0.933285 | −0.0520909 | ||||||||
\(322\) | −43.5588 | −2.42744 | ||||||||
\(323\) | 12.5355 | 0.697492 | ||||||||
\(324\) | 53.4093 | 2.96719 | ||||||||
\(325\) | 24.1733 | 1.34089 | ||||||||
\(326\) | 23.8379 | 1.32026 | ||||||||
\(327\) | 0.349917 | 0.0193505 | ||||||||
\(328\) | −109.657 | −6.05481 | ||||||||
\(329\) | −3.50334 | −0.193145 | ||||||||
\(330\) | −0.310103 | −0.0170706 | ||||||||
\(331\) | −11.8999 | −0.654076 | −0.327038 | − | 0.945011i | \(-0.606050\pi\) | ||||
−0.327038 | + | 0.945011i | \(0.606050\pi\) | |||||||
\(332\) | 30.5535 | 1.67684 | ||||||||
\(333\) | 11.3687 | 0.623003 | ||||||||
\(334\) | −11.4319 | −0.625524 | ||||||||
\(335\) | 13.8560 | 0.757034 | ||||||||
\(336\) | 3.10160 | 0.169206 | ||||||||
\(337\) | −6.54525 | −0.356542 | −0.178271 | − | 0.983981i | \(-0.557050\pi\) | ||||
−0.178271 | + | 0.983981i | \(0.557050\pi\) | |||||||
\(338\) | −98.0906 | −5.33543 | ||||||||
\(339\) | −0.136050 | −0.00738923 | ||||||||
\(340\) | 12.9461 | 0.702100 | ||||||||
\(341\) | −2.38241 | −0.129015 | ||||||||
\(342\) | 59.9065 | 3.23937 | ||||||||
\(343\) | −19.8498 | −1.07179 | ||||||||
\(344\) | 71.9083 | 3.87703 | ||||||||
\(345\) | 0.791802 | 0.0426292 | ||||||||
\(346\) | 12.8109 | 0.688718 | ||||||||
\(347\) | −14.5490 | −0.781033 | −0.390517 | − | 0.920596i | \(-0.627704\pi\) | ||||
−0.390517 | + | 0.920596i | \(0.627704\pi\) | |||||||
\(348\) | −2.60482 | −0.139633 | ||||||||
\(349\) | −19.0582 | −1.02016 | −0.510082 | − | 0.860126i | \(-0.670385\pi\) | ||||
−0.510082 | + | 0.860126i | \(0.670385\pi\) | |||||||
\(350\) | 19.1344 | 1.02278 | ||||||||
\(351\) | 3.35985 | 0.179336 | ||||||||
\(352\) | −36.7765 | −1.96019 | ||||||||
\(353\) | 8.64074 | 0.459900 | 0.229950 | − | 0.973202i | \(-0.426144\pi\) | ||||
0.229950 | + | 0.973202i | \(0.426144\pi\) | |||||||
\(354\) | 0.666330 | 0.0354150 | ||||||||
\(355\) | −15.8072 | −0.838962 | ||||||||
\(356\) | 60.5882 | 3.21117 | ||||||||
\(357\) | 0.277946 | 0.0147104 | ||||||||
\(358\) | 44.8188 | 2.36875 | ||||||||
\(359\) | −27.2990 | −1.44079 | −0.720394 | − | 0.693565i | \(-0.756039\pi\) | ||||
−0.720394 | + | 0.693565i | \(0.756039\pi\) | |||||||
\(360\) | 41.1550 | 2.16906 | ||||||||
\(361\) | 31.2291 | 1.64364 | ||||||||
\(362\) | 5.24341 | 0.275588 | ||||||||
\(363\) | −0.793494 | −0.0416476 | ||||||||
\(364\) | −79.9377 | −4.18987 | ||||||||
\(365\) | 6.40378 | 0.335189 | ||||||||
\(366\) | 0.941539 | 0.0492151 | ||||||||
\(367\) | −9.09308 | −0.474655 | −0.237327 | − | 0.971430i | \(-0.576271\pi\) | ||||
−0.237327 | + | 0.971430i | \(0.576271\pi\) | |||||||
\(368\) | 157.201 | 8.19467 | ||||||||
\(369\) | −29.2539 | −1.52290 | ||||||||
\(370\) | 13.1404 | 0.683138 | ||||||||
\(371\) | −1.93678 | −0.100553 | ||||||||
\(372\) | −1.04532 | −0.0541972 | ||||||||
\(373\) | −24.3983 | −1.26330 | −0.631649 | − | 0.775254i | \(-0.717622\pi\) | ||||
−0.631649 | + | 0.775254i | \(0.717622\pi\) | |||||||
\(374\) | −5.51719 | −0.285287 | ||||||||
\(375\) | −0.844895 | −0.0436302 | ||||||||
\(376\) | 20.2966 | 1.04671 | ||||||||
\(377\) | 37.1321 | 1.91240 | ||||||||
\(378\) | 2.65950 | 0.136790 | ||||||||
\(379\) | −37.6829 | −1.93564 | −0.967820 | − | 0.251643i | \(-0.919029\pi\) | ||||
−0.967820 | + | 0.251643i | \(0.919029\pi\) | |||||||
\(380\) | 51.8745 | 2.66110 | ||||||||
\(381\) | −0.633053 | −0.0324323 | ||||||||
\(382\) | −3.55654 | −0.181968 | ||||||||
\(383\) | −7.77167 | −0.397114 | −0.198557 | − | 0.980089i | \(-0.563625\pi\) | ||||
−0.198557 | + | 0.980089i | \(0.563625\pi\) | |||||||
\(384\) | −7.09212 | −0.361918 | ||||||||
\(385\) | 2.62145 | 0.133601 | ||||||||
\(386\) | 28.5303 | 1.45215 | ||||||||
\(387\) | 19.1834 | 0.975147 | ||||||||
\(388\) | −54.3506 | −2.75924 | ||||||||
\(389\) | −0.723666 | −0.0366913 | −0.0183457 | − | 0.999832i | \(-0.505840\pi\) | ||||
−0.0183457 | + | 0.999832i | \(0.505840\pi\) | |||||||
\(390\) | 1.93959 | 0.0982149 | ||||||||
\(391\) | 14.0873 | 0.712427 | ||||||||
\(392\) | 36.4547 | 1.84124 | ||||||||
\(393\) | 0.157576 | 0.00794868 | ||||||||
\(394\) | 33.3699 | 1.68115 | ||||||||
\(395\) | −7.86479 | −0.395720 | ||||||||
\(396\) | −19.7531 | −0.992628 | ||||||||
\(397\) | −10.2245 | −0.513152 | −0.256576 | − | 0.966524i | \(-0.582594\pi\) | ||||
−0.256576 | + | 0.966524i | \(0.582594\pi\) | |||||||
\(398\) | −24.7176 | −1.23898 | ||||||||
\(399\) | 1.11372 | 0.0557556 | ||||||||
\(400\) | −69.0550 | −3.45275 | ||||||||
\(401\) | −31.0775 | −1.55194 | −0.775969 | − | 0.630771i | \(-0.782739\pi\) | ||||
−0.775969 | + | 0.630771i | \(0.782739\pi\) | |||||||
\(402\) | −2.59089 | −0.129222 | ||||||||
\(403\) | 14.9012 | 0.742281 | ||||||||
\(404\) | 78.5665 | 3.90883 | ||||||||
\(405\) | 10.9550 | 0.544356 | ||||||||
\(406\) | 29.3920 | 1.45870 | ||||||||
\(407\) | −4.19538 | −0.207957 | ||||||||
\(408\) | −1.61027 | −0.0797204 | ||||||||
\(409\) | 17.9693 | 0.888525 | 0.444263 | − | 0.895897i | \(-0.353466\pi\) | ||||
0.444263 | + | 0.895897i | \(0.353466\pi\) | |||||||
\(410\) | −33.8128 | −1.66989 | ||||||||
\(411\) | −0.0998370 | −0.00492459 | ||||||||
\(412\) | −58.2587 | −2.87020 | ||||||||
\(413\) | −5.63281 | −0.277172 | ||||||||
\(414\) | 67.3228 | 3.30874 | ||||||||
\(415\) | 6.26692 | 0.307631 | ||||||||
\(416\) | 230.024 | 11.2779 | ||||||||
\(417\) | 0.149310 | 0.00731172 | ||||||||
\(418\) | −22.1072 | −1.08130 | ||||||||
\(419\) | −3.31775 | −0.162083 | −0.0810414 | − | 0.996711i | \(-0.525825\pi\) | ||||
−0.0810414 | + | 0.996711i | \(0.525825\pi\) | |||||||
\(420\) | 1.15020 | 0.0561239 | ||||||||
\(421\) | 14.4108 | 0.702338 | 0.351169 | − | 0.936312i | \(-0.385784\pi\) | ||||
0.351169 | + | 0.936312i | \(0.385784\pi\) | |||||||
\(422\) | 31.6086 | 1.53868 | ||||||||
\(423\) | 5.41463 | 0.263268 | ||||||||
\(424\) | 11.2207 | 0.544926 | ||||||||
\(425\) | −6.18826 | −0.300175 | ||||||||
\(426\) | 2.95574 | 0.143206 | ||||||||
\(427\) | −7.95929 | −0.385177 | ||||||||
\(428\) | −68.7130 | −3.32137 | ||||||||
\(429\) | −0.619258 | −0.0298981 | ||||||||
\(430\) | 22.1729 | 1.06927 | ||||||||
\(431\) | 17.0058 | 0.819140 | 0.409570 | − | 0.912279i | \(-0.365679\pi\) | ||||
0.409570 | + | 0.912279i | \(0.365679\pi\) | |||||||
\(432\) | −9.59798 | −0.461783 | ||||||||
\(433\) | −3.49382 | −0.167902 | −0.0839511 | − | 0.996470i | \(-0.526754\pi\) | ||||
−0.0839511 | + | 0.996470i | \(0.526754\pi\) | |||||||
\(434\) | 11.7951 | 0.566182 | ||||||||
\(435\) | −0.534282 | −0.0256169 | ||||||||
\(436\) | 25.7626 | 1.23381 | ||||||||
\(437\) | 56.4474 | 2.70024 | ||||||||
\(438\) | −1.19742 | −0.0572150 | ||||||||
\(439\) | −30.4567 | −1.45362 | −0.726809 | − | 0.686840i | \(-0.758997\pi\) | ||||
−0.726809 | + | 0.686840i | \(0.758997\pi\) | |||||||
\(440\) | −15.1873 | −0.724027 | ||||||||
\(441\) | 9.72524 | 0.463107 | ||||||||
\(442\) | 34.5081 | 1.64138 | ||||||||
\(443\) | 10.8599 | 0.515969 | 0.257985 | − | 0.966149i | \(-0.416942\pi\) | ||||
0.257985 | + | 0.966149i | \(0.416942\pi\) | |||||||
\(444\) | −1.84078 | −0.0873597 | ||||||||
\(445\) | 12.4274 | 0.589117 | ||||||||
\(446\) | 71.7509 | 3.39750 | ||||||||
\(447\) | 0.818047 | 0.0386923 | ||||||||
\(448\) | 105.623 | 4.99020 | ||||||||
\(449\) | −36.3079 | −1.71348 | −0.856738 | − | 0.515752i | \(-0.827512\pi\) | ||||
−0.856738 | + | 0.515752i | \(0.827512\pi\) | |||||||
\(450\) | −29.5735 | −1.39411 | ||||||||
\(451\) | 10.7955 | 0.508340 | ||||||||
\(452\) | −10.0167 | −0.471145 | ||||||||
\(453\) | −0.0811365 | −0.00381212 | ||||||||
\(454\) | −82.8348 | −3.88763 | ||||||||
\(455\) | −16.3963 | −0.768669 | ||||||||
\(456\) | −6.45230 | −0.302157 | ||||||||
\(457\) | −11.0568 | −0.517217 | −0.258608 | − | 0.965982i | \(-0.583264\pi\) | ||||
−0.258608 | + | 0.965982i | \(0.583264\pi\) | |||||||
\(458\) | 23.7215 | 1.10843 | ||||||||
\(459\) | −0.860109 | −0.0401464 | ||||||||
\(460\) | 58.2964 | 2.71808 | ||||||||
\(461\) | 38.1048 | 1.77472 | 0.887359 | − | 0.461079i | \(-0.152537\pi\) | ||||
0.887359 | + | 0.461079i | \(0.152537\pi\) | |||||||
\(462\) | −0.490176 | −0.0228050 | ||||||||
\(463\) | −6.44200 | −0.299385 | −0.149693 | − | 0.988733i | \(-0.547828\pi\) | ||||
−0.149693 | + | 0.988733i | \(0.547828\pi\) | |||||||
\(464\) | −106.074 | −4.92436 | ||||||||
\(465\) | −0.214408 | −0.00994295 | ||||||||
\(466\) | −43.1070 | −1.99689 | ||||||||
\(467\) | −40.3737 | −1.86827 | −0.934135 | − | 0.356919i | \(-0.883827\pi\) | ||||
−0.934135 | + | 0.356919i | \(0.883827\pi\) | |||||||
\(468\) | 123.549 | 5.71104 | ||||||||
\(469\) | 21.9020 | 1.01134 | ||||||||
\(470\) | 6.25843 | 0.288680 | ||||||||
\(471\) | −0.364249 | −0.0167837 | ||||||||
\(472\) | 32.6336 | 1.50208 | ||||||||
\(473\) | −7.07920 | −0.325502 | ||||||||
\(474\) | 1.47061 | 0.0675474 | ||||||||
\(475\) | −24.7961 | −1.13772 | ||||||||
\(476\) | 20.4637 | 0.937953 | ||||||||
\(477\) | 2.99342 | 0.137059 | ||||||||
\(478\) | −56.6835 | −2.59264 | ||||||||
\(479\) | −31.5792 | −1.44289 | −0.721445 | − | 0.692471i | \(-0.756522\pi\) | ||||
−0.721445 | + | 0.692471i | \(0.756522\pi\) | |||||||
\(480\) | −3.30975 | −0.151069 | ||||||||
\(481\) | 26.2407 | 1.19647 | ||||||||
\(482\) | −45.8015 | −2.08620 | ||||||||
\(483\) | 1.25159 | 0.0569494 | ||||||||
\(484\) | −58.4209 | −2.65550 | ||||||||
\(485\) | −11.1480 | −0.506206 | ||||||||
\(486\) | −6.16790 | −0.279782 | ||||||||
\(487\) | 32.7210 | 1.48273 | 0.741366 | − | 0.671101i | \(-0.234178\pi\) | ||||
0.741366 | + | 0.671101i | \(0.234178\pi\) | |||||||
\(488\) | 46.1120 | 2.08739 | ||||||||
\(489\) | −0.684944 | −0.0309743 | ||||||||
\(490\) | 11.2408 | 0.507807 | ||||||||
\(491\) | 16.3507 | 0.737896 | 0.368948 | − | 0.929450i | \(-0.379718\pi\) | ||||
0.368948 | + | 0.929450i | \(0.379718\pi\) | |||||||
\(492\) | 4.73668 | 0.213546 | ||||||||
\(493\) | −9.50566 | −0.428114 | ||||||||
\(494\) | 138.273 | 6.22119 | ||||||||
\(495\) | −4.05161 | −0.182106 | ||||||||
\(496\) | −42.5677 | −1.91135 | ||||||||
\(497\) | −24.9863 | −1.12079 | ||||||||
\(498\) | −1.17183 | −0.0525110 | ||||||||
\(499\) | 26.6948 | 1.19502 | 0.597511 | − | 0.801861i | \(-0.296156\pi\) | ||||
0.597511 | + | 0.801861i | \(0.296156\pi\) | |||||||
\(500\) | −62.2054 | −2.78191 | ||||||||
\(501\) | 0.328477 | 0.0146753 | ||||||||
\(502\) | −16.8383 | −0.751529 | ||||||||
\(503\) | 33.3942 | 1.48898 | 0.744488 | − | 0.667636i | \(-0.232694\pi\) | ||||
0.744488 | + | 0.667636i | \(0.232694\pi\) | |||||||
\(504\) | 65.0532 | 2.89770 | ||||||||
\(505\) | 16.1150 | 0.717109 | ||||||||
\(506\) | −24.8440 | −1.10445 | ||||||||
\(507\) | 2.81848 | 0.125173 | ||||||||
\(508\) | −46.6085 | −2.06792 | ||||||||
\(509\) | −43.2833 | −1.91850 | −0.959248 | − | 0.282565i | \(-0.908815\pi\) | ||||
−0.959248 | + | 0.282565i | \(0.908815\pi\) | |||||||
\(510\) | −0.496527 | −0.0219866 | ||||||||
\(511\) | 10.1224 | 0.447788 | ||||||||
\(512\) | −214.168 | −9.46498 | ||||||||
\(513\) | −3.44642 | −0.152163 | ||||||||
\(514\) | −14.2097 | −0.626762 | ||||||||
\(515\) | −11.9496 | −0.526563 | ||||||||
\(516\) | −3.10610 | −0.136738 | ||||||||
\(517\) | −1.99815 | −0.0878785 | ||||||||
\(518\) | 20.7709 | 0.912621 | ||||||||
\(519\) | −0.368101 | −0.0161578 | ||||||||
\(520\) | 94.9915 | 4.16565 | ||||||||
\(521\) | 0.0361531 | 0.00158390 | 0.000791949 | − | 1.00000i | \(-0.499748\pi\) | ||||
0.000791949 | 1.00000i | \(0.499748\pi\) | ||||||||
\(522\) | −45.4272 | −1.98829 | ||||||||
\(523\) | 11.7968 | 0.515840 | 0.257920 | − | 0.966166i | \(-0.416963\pi\) | ||||
0.257920 | + | 0.966166i | \(0.416963\pi\) | |||||||
\(524\) | 11.6016 | 0.506816 | ||||||||
\(525\) | −0.549798 | −0.0239951 | ||||||||
\(526\) | 58.5017 | 2.55080 | ||||||||
\(527\) | −3.81464 | −0.166168 | ||||||||
\(528\) | 1.76901 | 0.0769865 | ||||||||
\(529\) | 40.4354 | 1.75806 | ||||||||
\(530\) | 3.45990 | 0.150288 | ||||||||
\(531\) | 8.70586 | 0.377802 | ||||||||
\(532\) | 81.9973 | 3.55504 | ||||||||
\(533\) | −67.5222 | −2.92471 | ||||||||
\(534\) | −2.32376 | −0.100559 | ||||||||
\(535\) | −14.0940 | −0.609335 | ||||||||
\(536\) | −126.889 | −5.48077 | ||||||||
\(537\) | −1.28780 | −0.0555725 | ||||||||
\(538\) | −26.3426 | −1.13571 | ||||||||
\(539\) | −3.58888 | −0.154584 | ||||||||
\(540\) | −3.55931 | −0.153168 | ||||||||
\(541\) | −3.42784 | −0.147374 | −0.0736871 | − | 0.997281i | \(-0.523477\pi\) | ||||
−0.0736871 | + | 0.997281i | \(0.523477\pi\) | |||||||
\(542\) | 57.8431 | 2.48457 | ||||||||
\(543\) | −0.150661 | −0.00646548 | ||||||||
\(544\) | −58.8853 | −2.52469 | ||||||||
\(545\) | 5.28426 | 0.226353 | ||||||||
\(546\) | 3.06588 | 0.131208 | ||||||||
\(547\) | −15.1618 | −0.648272 | −0.324136 | − | 0.946011i | \(-0.605074\pi\) | ||||
−0.324136 | + | 0.946011i | \(0.605074\pi\) | |||||||
\(548\) | −7.35049 | −0.313997 | ||||||||
\(549\) | 12.3016 | 0.525018 | ||||||||
\(550\) | 10.9134 | 0.465350 | ||||||||
\(551\) | −38.0888 | −1.62264 | ||||||||
\(552\) | −7.25108 | −0.308626 | ||||||||
\(553\) | −12.4318 | −0.528653 | ||||||||
\(554\) | 51.8262 | 2.20189 | ||||||||
\(555\) | −0.377569 | −0.0160269 | ||||||||
\(556\) | 10.9929 | 0.466203 | ||||||||
\(557\) | −43.6401 | −1.84909 | −0.924545 | − | 0.381073i | \(-0.875554\pi\) | ||||
−0.924545 | + | 0.381073i | \(0.875554\pi\) | |||||||
\(558\) | −18.2300 | −0.771739 | ||||||||
\(559\) | 44.2780 | 1.87276 | ||||||||
\(560\) | 46.8387 | 1.97930 | ||||||||
\(561\) | 0.158528 | 0.00669304 | ||||||||
\(562\) | −57.7425 | −2.43572 | ||||||||
\(563\) | −46.5469 | −1.96172 | −0.980858 | − | 0.194723i | \(-0.937619\pi\) | ||||
−0.980858 | + | 0.194723i | \(0.937619\pi\) | |||||||
\(564\) | −0.876716 | −0.0369164 | ||||||||
\(565\) | −2.05455 | −0.0864357 | ||||||||
\(566\) | −42.2534 | −1.77604 | ||||||||
\(567\) | 17.3164 | 0.727219 | ||||||||
\(568\) | 144.758 | 6.07391 | ||||||||
\(569\) | 36.4341 | 1.52740 | 0.763698 | − | 0.645574i | \(-0.223382\pi\) | ||||
0.763698 | + | 0.645574i | \(0.223382\pi\) | |||||||
\(570\) | −1.98956 | −0.0833336 | ||||||||
\(571\) | −10.8218 | −0.452877 | −0.226438 | − | 0.974026i | \(-0.572708\pi\) | ||||
−0.226438 | + | 0.974026i | \(0.572708\pi\) | |||||||
\(572\) | −45.5929 | −1.90633 | ||||||||
\(573\) | 0.102191 | 0.00426911 | ||||||||
\(574\) | −53.4474 | −2.23085 | ||||||||
\(575\) | −27.8658 | −1.16209 | ||||||||
\(576\) | −163.246 | −6.80192 | ||||||||
\(577\) | 6.12082 | 0.254813 | 0.127407 | − | 0.991851i | \(-0.459335\pi\) | ||||
0.127407 | + | 0.991851i | \(0.459335\pi\) | |||||||
\(578\) | 39.1701 | 1.62926 | ||||||||
\(579\) | −0.819772 | −0.0340686 | ||||||||
\(580\) | −39.3365 | −1.63336 | ||||||||
\(581\) | 9.90604 | 0.410972 | ||||||||
\(582\) | 2.08453 | 0.0864067 | ||||||||
\(583\) | −1.10465 | −0.0457501 | ||||||||
\(584\) | −58.6439 | −2.42670 | ||||||||
\(585\) | 25.3415 | 1.04774 | ||||||||
\(586\) | −61.1639 | −2.52666 | ||||||||
\(587\) | 32.1446 | 1.32675 | 0.663374 | − | 0.748288i | \(-0.269124\pi\) | ||||
0.663374 | + | 0.748288i | \(0.269124\pi\) | |||||||
\(588\) | −1.57467 | −0.0649384 | ||||||||
\(589\) | −15.2851 | −0.629813 | ||||||||
\(590\) | 10.0625 | 0.414268 | ||||||||
\(591\) | −0.958831 | −0.0394410 | ||||||||
\(592\) | −74.9609 | −3.08087 | ||||||||
\(593\) | 4.61461 | 0.189499 | 0.0947496 | − | 0.995501i | \(-0.469795\pi\) | ||||
0.0947496 | + | 0.995501i | \(0.469795\pi\) | |||||||
\(594\) | 1.51686 | 0.0622375 | ||||||||
\(595\) | 4.19738 | 0.172076 | ||||||||
\(596\) | 60.2286 | 2.46706 | ||||||||
\(597\) | 0.710222 | 0.0290674 | ||||||||
\(598\) | 155.391 | 6.35439 | ||||||||
\(599\) | −25.1452 | −1.02741 | −0.513704 | − | 0.857968i | \(-0.671727\pi\) | ||||
−0.513704 | + | 0.857968i | \(0.671727\pi\) | |||||||
\(600\) | 3.18524 | 0.130037 | ||||||||
\(601\) | 22.1039 | 0.901636 | 0.450818 | − | 0.892616i | \(-0.351132\pi\) | ||||
0.450818 | + | 0.892616i | \(0.351132\pi\) | |||||||
\(602\) | 35.0484 | 1.42847 | ||||||||
\(603\) | −33.8509 | −1.37852 | ||||||||
\(604\) | −5.97367 | −0.243065 | ||||||||
\(605\) | −11.9829 | −0.487174 | ||||||||
\(606\) | −3.01329 | −0.122407 | ||||||||
\(607\) | −0.102767 | −0.00417119 | −0.00208559 | − | 0.999998i | \(-0.500664\pi\) | ||||
−0.00208559 | + | 0.999998i | \(0.500664\pi\) | |||||||
\(608\) | −235.951 | −9.56908 | ||||||||
\(609\) | −0.844533 | −0.0342222 | ||||||||
\(610\) | 14.2186 | 0.575694 | ||||||||
\(611\) | 12.4977 | 0.505604 | ||||||||
\(612\) | −31.6279 | −1.27848 | ||||||||
\(613\) | −26.9614 | −1.08896 | −0.544481 | − | 0.838773i | \(-0.683273\pi\) | ||||
−0.544481 | + | 0.838773i | \(0.683273\pi\) | |||||||
\(614\) | −81.3630 | −3.28354 | ||||||||
\(615\) | 0.971556 | 0.0391769 | ||||||||
\(616\) | −24.0064 | −0.967246 | ||||||||
\(617\) | 24.2051 | 0.974459 | 0.487229 | − | 0.873274i | \(-0.338008\pi\) | ||||
0.487229 | + | 0.873274i | \(0.338008\pi\) | |||||||
\(618\) | 2.23442 | 0.0898816 | ||||||||
\(619\) | −7.80737 | −0.313805 | −0.156902 | − | 0.987614i | \(-0.550151\pi\) | ||||
−0.156902 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(620\) | −15.7858 | −0.633973 | ||||||||
\(621\) | −3.87308 | −0.155421 | ||||||||
\(622\) | −7.74262 | −0.310451 | ||||||||
\(623\) | 19.6439 | 0.787016 | ||||||||
\(624\) | −11.0646 | −0.442938 | ||||||||
\(625\) | 4.73433 | 0.189373 | ||||||||
\(626\) | 72.9328 | 2.91498 | ||||||||
\(627\) | 0.635214 | 0.0253680 | ||||||||
\(628\) | −26.8178 | −1.07015 | ||||||||
\(629\) | −6.71751 | −0.267845 | ||||||||
\(630\) | 20.0591 | 0.799174 | ||||||||
\(631\) | 7.70459 | 0.306715 | 0.153358 | − | 0.988171i | \(-0.450991\pi\) | ||||
0.153358 | + | 0.988171i | \(0.450991\pi\) | |||||||
\(632\) | 72.0233 | 2.86493 | ||||||||
\(633\) | −0.908222 | −0.0360986 | ||||||||
\(634\) | 98.7692 | 3.92263 | ||||||||
\(635\) | −9.56001 | −0.379377 | ||||||||
\(636\) | −0.484682 | −0.0192189 | ||||||||
\(637\) | 22.4472 | 0.889392 | ||||||||
\(638\) | 16.7639 | 0.663689 | ||||||||
\(639\) | 38.6179 | 1.52770 | ||||||||
\(640\) | −107.101 | −4.23355 | ||||||||
\(641\) | 20.3954 | 0.805570 | 0.402785 | − | 0.915295i | \(-0.368042\pi\) | ||||
0.402785 | + | 0.915295i | \(0.368042\pi\) | |||||||
\(642\) | 2.63538 | 0.104010 | ||||||||
\(643\) | −17.4909 | −0.689776 | −0.344888 | − | 0.938644i | \(-0.612083\pi\) | ||||
−0.344888 | + | 0.938644i | \(0.612083\pi\) | |||||||
\(644\) | 92.1484 | 3.63116 | ||||||||
\(645\) | −0.637102 | −0.0250859 | ||||||||
\(646\) | −35.3973 | −1.39269 | ||||||||
\(647\) | 28.3210 | 1.11341 | 0.556707 | − | 0.830709i | \(-0.312065\pi\) | ||||
0.556707 | + | 0.830709i | \(0.312065\pi\) | |||||||
\(648\) | −100.322 | −3.94103 | ||||||||
\(649\) | −3.21270 | −0.126110 | ||||||||
\(650\) | −68.2598 | −2.67737 | ||||||||
\(651\) | −0.338913 | −0.0132830 | ||||||||
\(652\) | −50.4290 | −1.97495 | ||||||||
\(653\) | 17.4540 | 0.683026 | 0.341513 | − | 0.939877i | \(-0.389061\pi\) | ||||
0.341513 | + | 0.939877i | \(0.389061\pi\) | |||||||
\(654\) | −0.988085 | −0.0386372 | ||||||||
\(655\) | 2.37963 | 0.0929799 | ||||||||
\(656\) | 192.888 | 7.53103 | ||||||||
\(657\) | −15.6448 | −0.610361 | ||||||||
\(658\) | 9.89263 | 0.385655 | ||||||||
\(659\) | −12.7872 | −0.498120 | −0.249060 | − | 0.968488i | \(-0.580122\pi\) | ||||
−0.249060 | + | 0.968488i | \(0.580122\pi\) | |||||||
\(660\) | 0.656021 | 0.0255356 | ||||||||
\(661\) | 20.9020 | 0.812992 | 0.406496 | − | 0.913653i | \(-0.366751\pi\) | ||||
0.406496 | + | 0.913653i | \(0.366751\pi\) | |||||||
\(662\) | 33.6025 | 1.30600 | ||||||||
\(663\) | −0.991536 | −0.0385081 | ||||||||
\(664\) | −57.3905 | −2.22718 | ||||||||
\(665\) | 16.8187 | 0.652202 | ||||||||
\(666\) | −32.1027 | −1.24395 | ||||||||
\(667\) | −42.8041 | −1.65738 | ||||||||
\(668\) | 24.1841 | 0.935710 | ||||||||
\(669\) | −2.06165 | −0.0797079 | ||||||||
\(670\) | −39.1261 | −1.51157 | ||||||||
\(671\) | −4.53962 | −0.175250 | ||||||||
\(672\) | −5.23168 | −0.201816 | ||||||||
\(673\) | −24.1019 | −0.929061 | −0.464530 | − | 0.885557i | \(-0.653777\pi\) | ||||
−0.464530 | + | 0.885557i | \(0.653777\pi\) | |||||||
\(674\) | 18.4823 | 0.711910 | ||||||||
\(675\) | 1.70136 | 0.0654854 | ||||||||
\(676\) | 207.510 | 7.98116 | ||||||||
\(677\) | −12.3085 | −0.473054 | −0.236527 | − | 0.971625i | \(-0.576009\pi\) | ||||
−0.236527 | + | 0.971625i | \(0.576009\pi\) | |||||||
\(678\) | 0.384174 | 0.0147541 | ||||||||
\(679\) | −17.6216 | −0.676253 | ||||||||
\(680\) | −24.3174 | −0.932531 | ||||||||
\(681\) | 2.38013 | 0.0912066 | ||||||||
\(682\) | 6.72738 | 0.257605 | ||||||||
\(683\) | −1.46615 | −0.0561005 | −0.0280503 | − | 0.999607i | \(-0.508930\pi\) | ||||
−0.0280503 | + | 0.999607i | \(0.508930\pi\) | |||||||
\(684\) | −126.732 | −4.84572 | ||||||||
\(685\) | −1.50768 | −0.0576056 | ||||||||
\(686\) | 56.0513 | 2.14005 | ||||||||
\(687\) | −0.681598 | −0.0260046 | ||||||||
\(688\) | −126.487 | −4.82229 | ||||||||
\(689\) | 6.90923 | 0.263221 | ||||||||
\(690\) | −2.23587 | −0.0851180 | ||||||||
\(691\) | 45.0709 | 1.71458 | 0.857289 | − | 0.514836i | \(-0.172147\pi\) | ||||
0.857289 | + | 0.514836i | \(0.172147\pi\) | |||||||
\(692\) | −27.1014 | −1.03024 | ||||||||
\(693\) | −6.40433 | −0.243281 | ||||||||
\(694\) | 41.0831 | 1.55949 | ||||||||
\(695\) | 2.25479 | 0.0855291 | ||||||||
\(696\) | 4.89279 | 0.185461 | ||||||||
\(697\) | 17.2854 | 0.654732 | ||||||||
\(698\) | 53.8161 | 2.03697 | ||||||||
\(699\) | 1.23861 | 0.0468486 | ||||||||
\(700\) | −40.4788 | −1.52996 | ||||||||
\(701\) | 36.8357 | 1.39127 | 0.695633 | − | 0.718398i | \(-0.255124\pi\) | ||||
0.695633 | + | 0.718398i | \(0.255124\pi\) | |||||||
\(702\) | −9.48745 | −0.358081 | ||||||||
\(703\) | −26.9168 | −1.01519 | ||||||||
\(704\) | 60.2423 | 2.27047 | ||||||||
\(705\) | −0.179826 | −0.00677264 | ||||||||
\(706\) | −24.3995 | −0.918286 | ||||||||
\(707\) | 25.4728 | 0.958004 | ||||||||
\(708\) | −1.40962 | −0.0529767 | ||||||||
\(709\) | 26.2623 | 0.986301 | 0.493150 | − | 0.869944i | \(-0.335845\pi\) | ||||
0.493150 | + | 0.869944i | \(0.335845\pi\) | |||||||
\(710\) | 44.6360 | 1.67516 | ||||||||
\(711\) | 19.2141 | 0.720584 | ||||||||
\(712\) | −113.807 | −4.26508 | ||||||||
\(713\) | −17.1774 | −0.643298 | ||||||||
\(714\) | −0.784854 | −0.0293724 | ||||||||
\(715\) | −9.35170 | −0.349734 | ||||||||
\(716\) | −94.8139 | −3.54336 | ||||||||
\(717\) | 1.62871 | 0.0608253 | ||||||||
\(718\) | 77.0861 | 2.87683 | ||||||||
\(719\) | −24.2956 | −0.906074 | −0.453037 | − | 0.891492i | \(-0.649659\pi\) | ||||
−0.453037 | + | 0.891492i | \(0.649659\pi\) | |||||||
\(720\) | −72.3921 | −2.69789 | ||||||||
\(721\) | −18.8886 | −0.703450 | ||||||||
\(722\) | −88.1839 | −3.28186 | ||||||||
\(723\) | 1.31603 | 0.0489438 | ||||||||
\(724\) | −11.0924 | −0.412246 | ||||||||
\(725\) | 18.8029 | 0.698324 | ||||||||
\(726\) | 2.24064 | 0.0831580 | ||||||||
\(727\) | −3.31603 | −0.122985 | −0.0614923 | − | 0.998108i | \(-0.519586\pi\) | ||||
−0.0614923 | + | 0.998108i | \(0.519586\pi\) | |||||||
\(728\) | 150.152 | 5.56500 | ||||||||
\(729\) | −26.6452 | −0.986858 | ||||||||
\(730\) | −18.0828 | −0.669274 | ||||||||
\(731\) | −11.3350 | −0.419240 | ||||||||
\(732\) | −1.99182 | −0.0736199 | ||||||||
\(733\) | −28.0806 | −1.03718 | −0.518590 | − | 0.855023i | \(-0.673543\pi\) | ||||
−0.518590 | + | 0.855023i | \(0.673543\pi\) | |||||||
\(734\) | 25.6768 | 0.947746 | ||||||||
\(735\) | −0.322986 | −0.0119135 | ||||||||
\(736\) | −265.161 | −9.77397 | ||||||||
\(737\) | 12.4919 | 0.460146 | ||||||||
\(738\) | 82.6063 | 3.04078 | ||||||||
\(739\) | 3.63715 | 0.133795 | 0.0668974 | − | 0.997760i | \(-0.478690\pi\) | ||||
0.0668974 | + | 0.997760i | \(0.478690\pi\) | |||||||
\(740\) | −27.7985 | −1.02189 | ||||||||
\(741\) | −3.97305 | −0.145954 | ||||||||
\(742\) | 5.46902 | 0.200774 | ||||||||
\(743\) | 49.0671 | 1.80010 | 0.900050 | − | 0.435788i | \(-0.143530\pi\) | ||||
0.900050 | + | 0.435788i | \(0.143530\pi\) | |||||||
\(744\) | 1.96349 | 0.0719849 | ||||||||
\(745\) | 12.3537 | 0.452604 | ||||||||
\(746\) | 68.8953 | 2.52243 | ||||||||
\(747\) | −15.3104 | −0.560178 | ||||||||
\(748\) | 11.6716 | 0.426755 | ||||||||
\(749\) | −22.2781 | −0.814026 | ||||||||
\(750\) | 2.38579 | 0.0871167 | ||||||||
\(751\) | 22.6939 | 0.828114 | 0.414057 | − | 0.910251i | \(-0.364111\pi\) | ||||
0.414057 | + | 0.910251i | \(0.364111\pi\) | |||||||
\(752\) | −35.7019 | −1.30191 | ||||||||
\(753\) | 0.483821 | 0.0176314 | ||||||||
\(754\) | −104.852 | −3.81850 | ||||||||
\(755\) | −1.22528 | −0.0445924 | ||||||||
\(756\) | −5.62616 | −0.204622 | ||||||||
\(757\) | −40.5323 | −1.47317 | −0.736586 | − | 0.676343i | \(-0.763564\pi\) | ||||
−0.736586 | + | 0.676343i | \(0.763564\pi\) | |||||||
\(758\) | 106.408 | 3.86490 | ||||||||
\(759\) | 0.713852 | 0.0259112 | ||||||||
\(760\) | −97.4390 | −3.53449 | ||||||||
\(761\) | −11.8092 | −0.428083 | −0.214042 | − | 0.976825i | \(-0.568663\pi\) | ||||
−0.214042 | + | 0.976825i | \(0.568663\pi\) | |||||||
\(762\) | 1.78759 | 0.0647577 | ||||||||
\(763\) | 8.35276 | 0.302390 | ||||||||
\(764\) | 7.52384 | 0.272203 | ||||||||
\(765\) | −6.48731 | −0.234549 | ||||||||
\(766\) | 21.9454 | 0.792919 | ||||||||
\(767\) | 20.0944 | 0.725565 | ||||||||
\(768\) | 11.1769 | 0.403313 | ||||||||
\(769\) | 12.2726 | 0.442561 | 0.221280 | − | 0.975210i | \(-0.428976\pi\) | ||||
0.221280 | + | 0.975210i | \(0.428976\pi\) | |||||||
\(770\) | −7.40236 | −0.266763 | ||||||||
\(771\) | 0.408292 | 0.0147043 | ||||||||
\(772\) | −60.3556 | −2.17225 | ||||||||
\(773\) | −27.0527 | −0.973018 | −0.486509 | − | 0.873675i | \(-0.661730\pi\) | ||||
−0.486509 | + | 0.873675i | \(0.661730\pi\) | |||||||
\(774\) | −54.1695 | −1.94708 | ||||||||
\(775\) | 7.54566 | 0.271048 | ||||||||
\(776\) | 102.090 | 3.66483 | ||||||||
\(777\) | −0.596819 | −0.0214107 | ||||||||
\(778\) | 2.04347 | 0.0732618 | ||||||||
\(779\) | 69.2620 | 2.48157 | ||||||||
\(780\) | −4.10319 | −0.146918 | ||||||||
\(781\) | −14.2511 | −0.509944 | ||||||||
\(782\) | −39.7794 | −1.42251 | ||||||||
\(783\) | 2.61343 | 0.0933963 | ||||||||
\(784\) | −64.1242 | −2.29015 | ||||||||
\(785\) | −5.50069 | −0.196328 | ||||||||
\(786\) | −0.444959 | −0.0158712 | ||||||||
\(787\) | 26.0946 | 0.930174 | 0.465087 | − | 0.885265i | \(-0.346023\pi\) | ||||
0.465087 | + | 0.885265i | \(0.346023\pi\) | |||||||
\(788\) | −70.5939 | −2.51480 | ||||||||
\(789\) | −1.68095 | −0.0598435 | ||||||||
\(790\) | 22.2083 | 0.790137 | ||||||||
\(791\) | −3.24761 | −0.115472 | ||||||||
\(792\) | 37.1034 | 1.31841 | ||||||||
\(793\) | 28.3938 | 1.00829 | ||||||||
\(794\) | 28.8715 | 1.02461 | ||||||||
\(795\) | −0.0994147 | −0.00352588 | ||||||||
\(796\) | 52.2900 | 1.85337 | ||||||||
\(797\) | 14.7113 | 0.521101 | 0.260551 | − | 0.965460i | \(-0.416096\pi\) | ||||
0.260551 | + | 0.965460i | \(0.416096\pi\) | |||||||
\(798\) | −3.14488 | −0.111327 | ||||||||
\(799\) | −3.19937 | −0.113186 | ||||||||
\(800\) | 116.480 | 4.11818 | ||||||||
\(801\) | −30.3609 | −1.07275 | ||||||||
\(802\) | 87.7558 | 3.09876 | ||||||||
\(803\) | 5.77335 | 0.203737 | ||||||||
\(804\) | 5.48101 | 0.193300 | ||||||||
\(805\) | 18.9008 | 0.666167 | ||||||||
\(806\) | −42.0775 | −1.48212 | ||||||||
\(807\) | 0.756912 | 0.0266446 | ||||||||
\(808\) | −147.576 | −5.19172 | ||||||||
\(809\) | −21.6964 | −0.762804 | −0.381402 | − | 0.924409i | \(-0.624559\pi\) | ||||
−0.381402 | + | 0.924409i | \(0.624559\pi\) | |||||||
\(810\) | −30.9343 | −1.08692 | ||||||||
\(811\) | 3.32491 | 0.116754 | 0.0583768 | − | 0.998295i | \(-0.481408\pi\) | ||||
0.0583768 | + | 0.998295i | \(0.481408\pi\) | |||||||
\(812\) | −62.1787 | −2.18204 | ||||||||
\(813\) | −1.66203 | −0.0582899 | ||||||||
\(814\) | 11.8468 | 0.415230 | ||||||||
\(815\) | −10.3436 | −0.362322 | ||||||||
\(816\) | 2.83249 | 0.0991569 | ||||||||
\(817\) | −45.4189 | −1.58900 | ||||||||
\(818\) | −50.7412 | −1.77412 | ||||||||
\(819\) | 40.0569 | 1.39970 | ||||||||
\(820\) | 71.5307 | 2.49796 | ||||||||
\(821\) | 15.5133 | 0.541417 | 0.270708 | − | 0.962661i | \(-0.412742\pi\) | ||||
0.270708 | + | 0.962661i | \(0.412742\pi\) | |||||||
\(822\) | 0.281916 | 0.00983296 | ||||||||
\(823\) | −49.6057 | −1.72915 | −0.864574 | − | 0.502506i | \(-0.832411\pi\) | ||||
−0.864574 | + | 0.502506i | \(0.832411\pi\) | |||||||
\(824\) | 109.431 | 3.81221 | ||||||||
\(825\) | −0.313580 | −0.0109174 | ||||||||
\(826\) | 15.9057 | 0.553432 | ||||||||
\(827\) | 29.5445 | 1.02736 | 0.513682 | − | 0.857981i | \(-0.328281\pi\) | ||||
0.513682 | + | 0.857981i | \(0.328281\pi\) | |||||||
\(828\) | −142.421 | −4.94947 | ||||||||
\(829\) | 37.9640 | 1.31854 | 0.659272 | − | 0.751904i | \(-0.270864\pi\) | ||||
0.659272 | + | 0.751904i | \(0.270864\pi\) | |||||||
\(830\) | −17.6963 | −0.614248 | ||||||||
\(831\) | −1.48914 | −0.0516579 | ||||||||
\(832\) | −376.795 | −13.0630 | ||||||||
\(833\) | −5.74640 | −0.199101 | ||||||||
\(834\) | −0.421616 | −0.0145994 | ||||||||
\(835\) | 4.96047 | 0.171664 | ||||||||
\(836\) | 46.7676 | 1.61749 | ||||||||
\(837\) | 1.04877 | 0.0362509 | ||||||||
\(838\) | 9.36856 | 0.323632 | ||||||||
\(839\) | −49.8255 | −1.72017 | −0.860084 | − | 0.510152i | \(-0.829589\pi\) | ||||
−0.860084 | + | 0.510152i | \(0.829589\pi\) | |||||||
\(840\) | −2.16049 | −0.0745440 | ||||||||
\(841\) | −0.117188 | −0.00404096 | ||||||||
\(842\) | −40.6927 | −1.40236 | ||||||||
\(843\) | 1.65914 | 0.0571438 | ||||||||
\(844\) | −66.8678 | −2.30168 | ||||||||
\(845\) | 42.5631 | 1.46421 | ||||||||
\(846\) | −15.2897 | −0.525670 | ||||||||
\(847\) | −18.9412 | −0.650828 | ||||||||
\(848\) | −19.7374 | −0.677784 | ||||||||
\(849\) | 1.21408 | 0.0416672 | ||||||||
\(850\) | 17.4742 | 0.599361 | ||||||||
\(851\) | −30.2490 | −1.03692 | ||||||||
\(852\) | −6.25286 | −0.214220 | ||||||||
\(853\) | −36.7361 | −1.25782 | −0.628909 | − | 0.777479i | \(-0.716498\pi\) | ||||
−0.628909 | + | 0.777479i | \(0.716498\pi\) | |||||||
\(854\) | 22.4752 | 0.769085 | ||||||||
\(855\) | −25.9944 | −0.888989 | ||||||||
\(856\) | 129.068 | 4.41146 | ||||||||
\(857\) | −2.56397 | −0.0875835 | −0.0437917 | − | 0.999041i | \(-0.513944\pi\) | ||||
−0.0437917 | + | 0.999041i | \(0.513944\pi\) | |||||||
\(858\) | 1.74864 | 0.0596977 | ||||||||
\(859\) | 40.0871 | 1.36775 | 0.683877 | − | 0.729597i | \(-0.260293\pi\) | ||||
0.683877 | + | 0.729597i | \(0.260293\pi\) | |||||||
\(860\) | −46.9066 | −1.59950 | ||||||||
\(861\) | 1.53573 | 0.0523374 | ||||||||
\(862\) | −48.0204 | −1.63558 | ||||||||
\(863\) | −14.4172 | −0.490767 | −0.245383 | − | 0.969426i | \(-0.578914\pi\) | ||||
−0.245383 | + | 0.969426i | \(0.578914\pi\) | |||||||
\(864\) | 16.1895 | 0.550780 | ||||||||
\(865\) | −5.55885 | −0.189007 | ||||||||
\(866\) | 9.86573 | 0.335251 | ||||||||
\(867\) | −1.12549 | −0.0382237 | ||||||||
\(868\) | −24.9524 | −0.846941 | ||||||||
\(869\) | −7.09053 | −0.240530 | ||||||||
\(870\) | 1.50869 | 0.0511493 | ||||||||
\(871\) | −78.1328 | −2.64743 | ||||||||
\(872\) | −48.3916 | −1.63875 | ||||||||
\(873\) | 27.2352 | 0.921772 | ||||||||
\(874\) | −159.394 | −5.39159 | ||||||||
\(875\) | −20.1682 | −0.681810 | ||||||||
\(876\) | 2.53314 | 0.0855869 | ||||||||
\(877\) | 12.9610 | 0.437663 | 0.218831 | − | 0.975763i | \(-0.429776\pi\) | ||||
0.218831 | + | 0.975763i | \(0.429776\pi\) | |||||||
\(878\) | 86.0026 | 2.90245 | ||||||||
\(879\) | 1.75745 | 0.0592772 | ||||||||
\(880\) | 26.7147 | 0.900551 | ||||||||
\(881\) | 0.0190464 | 0.000641689 0 | 0.000320845 | − | 1.00000i | \(-0.499898\pi\) | ||||
0.000320845 | 1.00000i | \(0.499898\pi\) | ||||||||
\(882\) | −27.4618 | −0.924687 | ||||||||
\(883\) | −38.9098 | −1.30942 | −0.654709 | − | 0.755881i | \(-0.727209\pi\) | ||||
−0.654709 | + | 0.755881i | \(0.727209\pi\) | |||||||
\(884\) | −73.0018 | −2.45532 | ||||||||
\(885\) | −0.289131 | −0.00971904 | ||||||||
\(886\) | −30.6658 | −1.03024 | ||||||||
\(887\) | 11.7221 | 0.393590 | 0.196795 | − | 0.980445i | \(-0.436947\pi\) | ||||
0.196795 | + | 0.980445i | \(0.436947\pi\) | |||||||
\(888\) | 3.45766 | 0.116031 | ||||||||
\(889\) | −15.1114 | −0.506820 | ||||||||
\(890\) | −35.0922 | −1.17629 | ||||||||
\(891\) | 9.87648 | 0.330874 | ||||||||
\(892\) | −151.789 | −5.08226 | ||||||||
\(893\) | −12.8198 | −0.428997 | ||||||||
\(894\) | −2.30997 | −0.0772571 | ||||||||
\(895\) | −19.4476 | −0.650061 | ||||||||
\(896\) | −169.294 | −5.65570 | ||||||||
\(897\) | −4.46490 | −0.149079 | ||||||||
\(898\) | 102.525 | 3.42131 | ||||||||
\(899\) | 11.5907 | 0.386572 | ||||||||
\(900\) | 62.5625 | 2.08542 | ||||||||
\(901\) | −1.76873 | −0.0589251 | ||||||||
\(902\) | −30.4840 | −1.01501 | ||||||||
\(903\) | −1.00706 | −0.0335128 | ||||||||
\(904\) | 18.8150 | 0.625776 | ||||||||
\(905\) | −2.27520 | −0.0756302 | ||||||||
\(906\) | 0.229111 | 0.00761169 | ||||||||
\(907\) | −39.7141 | −1.31868 | −0.659342 | − | 0.751843i | \(-0.729165\pi\) | ||||
−0.659342 | + | 0.751843i | \(0.729165\pi\) | |||||||
\(908\) | 175.237 | 5.81543 | ||||||||
\(909\) | −39.3698 | −1.30581 | ||||||||
\(910\) | 46.2993 | 1.53481 | ||||||||
\(911\) | −12.3113 | −0.407892 | −0.203946 | − | 0.978982i | \(-0.565377\pi\) | ||||
−0.203946 | + | 0.978982i | \(0.565377\pi\) | |||||||
\(912\) | 11.3497 | 0.375825 | ||||||||
\(913\) | 5.64996 | 0.186986 | ||||||||
\(914\) | 31.2219 | 1.03273 | ||||||||
\(915\) | −0.408549 | −0.0135062 | ||||||||
\(916\) | −50.1826 | −1.65808 | ||||||||
\(917\) | 3.76146 | 0.124214 | ||||||||
\(918\) | 2.42875 | 0.0801606 | ||||||||
\(919\) | 22.6517 | 0.747211 | 0.373606 | − | 0.927588i | \(-0.378121\pi\) | ||||
0.373606 | + | 0.927588i | \(0.378121\pi\) | |||||||
\(920\) | −109.502 | −3.61017 | ||||||||
\(921\) | 2.33784 | 0.0770343 | ||||||||
\(922\) | −107.599 | −3.54359 | ||||||||
\(923\) | 89.1357 | 2.93394 | ||||||||
\(924\) | 1.03696 | 0.0341136 | ||||||||
\(925\) | 13.2877 | 0.436898 | ||||||||
\(926\) | 18.1907 | 0.597784 | ||||||||
\(927\) | 29.1936 | 0.958842 | ||||||||
\(928\) | 178.922 | 5.87340 | ||||||||
\(929\) | −27.4350 | −0.900113 | −0.450056 | − | 0.893000i | \(-0.648596\pi\) | ||||
−0.450056 | + | 0.893000i | \(0.648596\pi\) | |||||||
\(930\) | 0.605440 | 0.0198531 | ||||||||
\(931\) | −23.0256 | −0.754633 | ||||||||
\(932\) | 91.1927 | 2.98711 | ||||||||
\(933\) | 0.222472 | 0.00728340 | ||||||||
\(934\) | 114.006 | 3.73039 | ||||||||
\(935\) | 2.39400 | 0.0782920 | ||||||||
\(936\) | −232.069 | −7.58542 | ||||||||
\(937\) | 39.6368 | 1.29488 | 0.647438 | − | 0.762118i | \(-0.275840\pi\) | ||||
0.647438 | + | 0.762118i | \(0.275840\pi\) | |||||||
\(938\) | −61.8462 | −2.01935 | ||||||||
\(939\) | −2.09561 | −0.0683875 | ||||||||
\(940\) | −13.2397 | −0.431831 | ||||||||
\(941\) | −57.2313 | −1.86569 | −0.932844 | − | 0.360280i | \(-0.882681\pi\) | ||||
−0.932844 | + | 0.360280i | \(0.882681\pi\) | |||||||
\(942\) | 1.02856 | 0.0335121 | ||||||||
\(943\) | 77.8364 | 2.53470 | ||||||||
\(944\) | −57.4029 | −1.86830 | ||||||||
\(945\) | −1.15400 | −0.0375396 | ||||||||
\(946\) | 19.9900 | 0.649932 | ||||||||
\(947\) | −49.0227 | −1.59302 | −0.796511 | − | 0.604624i | \(-0.793323\pi\) | ||||
−0.796511 | + | 0.604624i | \(0.793323\pi\) | |||||||
\(948\) | −3.11107 | −0.101043 | ||||||||
\(949\) | −36.1104 | −1.17219 | ||||||||
\(950\) | 70.0185 | 2.27170 | ||||||||
\(951\) | −2.83797 | −0.0920276 | ||||||||
\(952\) | −38.4383 | −1.24579 | ||||||||
\(953\) | −48.3708 | −1.56688 | −0.783442 | − | 0.621465i | \(-0.786538\pi\) | ||||
−0.783442 | + | 0.621465i | \(0.786538\pi\) | |||||||
\(954\) | −8.45272 | −0.273667 | ||||||||
\(955\) | 1.54324 | 0.0499380 | ||||||||
\(956\) | 119.914 | 3.87829 | ||||||||
\(957\) | −0.481684 | −0.0155706 | ||||||||
\(958\) | 89.1724 | 2.88103 | ||||||||
\(959\) | −2.38317 | −0.0769567 | ||||||||
\(960\) | 5.42159 | 0.174981 | ||||||||
\(961\) | −26.3486 | −0.849955 | ||||||||
\(962\) | −74.0976 | −2.38900 | ||||||||
\(963\) | 34.4322 | 1.10956 | ||||||||
\(964\) | 96.8929 | 3.12071 | ||||||||
\(965\) | −12.3797 | −0.398518 | ||||||||
\(966\) | −3.53421 | −0.113711 | ||||||||
\(967\) | −43.7009 | −1.40532 | −0.702662 | − | 0.711523i | \(-0.748006\pi\) | ||||
−0.702662 | + | 0.711523i | \(0.748006\pi\) | |||||||
\(968\) | 109.736 | 3.52704 | ||||||||
\(969\) | 1.01708 | 0.0326734 | ||||||||
\(970\) | 31.4795 | 1.01074 | ||||||||
\(971\) | −58.3573 | −1.87277 | −0.936387 | − | 0.350970i | \(-0.885852\pi\) | ||||
−0.936387 | + | 0.350970i | \(0.885852\pi\) | |||||||
\(972\) | 13.0482 | 0.418520 | ||||||||
\(973\) | 3.56412 | 0.114260 | ||||||||
\(974\) | −92.3966 | −2.96058 | ||||||||
\(975\) | 1.96134 | 0.0628130 | ||||||||
\(976\) | −81.1115 | −2.59632 | ||||||||
\(977\) | 10.0169 | 0.320469 | 0.160234 | − | 0.987079i | \(-0.448775\pi\) | ||||
0.160234 | + | 0.987079i | \(0.448775\pi\) | |||||||
\(978\) | 1.93412 | 0.0618465 | ||||||||
\(979\) | 11.2040 | 0.358081 | ||||||||
\(980\) | −23.7798 | −0.759619 | ||||||||
\(981\) | −12.9097 | −0.412175 | ||||||||
\(982\) | −46.1706 | −1.47336 | ||||||||
\(983\) | 42.8038 | 1.36523 | 0.682615 | − | 0.730778i | \(-0.260843\pi\) | ||||
0.682615 | + | 0.730778i | \(0.260843\pi\) | |||||||
\(984\) | −8.89721 | −0.283633 | ||||||||
\(985\) | −14.4797 | −0.461363 | ||||||||
\(986\) | 26.8418 | 0.854817 | ||||||||
\(987\) | −0.284249 | −0.00904774 | ||||||||
\(988\) | −292.515 | −9.30615 | ||||||||
\(989\) | −51.0416 | −1.62303 | ||||||||
\(990\) | 11.4408 | 0.363613 | ||||||||
\(991\) | −32.6973 | −1.03866 | −0.519332 | − | 0.854573i | \(-0.673819\pi\) | ||||
−0.519332 | + | 0.854573i | \(0.673819\pi\) | |||||||
\(992\) | 71.8018 | 2.27971 | ||||||||
\(993\) | −0.965513 | −0.0306396 | ||||||||
\(994\) | 70.5556 | 2.23789 | ||||||||
\(995\) | 10.7254 | 0.340017 | ||||||||
\(996\) | 2.47900 | 0.0785501 | ||||||||
\(997\) | 9.62079 | 0.304693 | 0.152347 | − | 0.988327i | \(-0.451317\pi\) | ||||
0.152347 | + | 0.988327i | \(0.451317\pi\) | |||||||
\(998\) | −75.3798 | −2.38611 | ||||||||
\(999\) | 1.84687 | 0.0584323 |
(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 | 8003.2.a.b.1.1 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.1 | ✓ | 153 | 1.1 | even | 1 | trivial |