Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4013,2,Mod(1,4013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4013.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0439663311\) |
Analytic rank: | \(1\) |
Dimension: | \(157\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51500 | −1.77837 | −0.889185 | − | 0.457548i | \(-0.848728\pi\) | ||||
−0.889185 | + | 0.457548i | \(0.848728\pi\) | |||||||
\(3\) | −3.29902 | −1.90469 | −0.952346 | − | 0.305019i | \(-0.901337\pi\) | ||||
−0.952346 | + | 0.305019i | \(0.901337\pi\) | |||||||
\(4\) | 4.32520 | 2.16260 | ||||||||
\(5\) | −0.150822 | −0.0674498 | −0.0337249 | − | 0.999431i | \(-0.510737\pi\) | ||||
−0.0337249 | + | 0.999431i | \(0.510737\pi\) | |||||||
\(6\) | 8.29703 | 3.38725 | ||||||||
\(7\) | −3.52495 | −1.33230 | −0.666152 | − | 0.745816i | \(-0.732060\pi\) | ||||
−0.666152 | + | 0.745816i | \(0.732060\pi\) | |||||||
\(8\) | −5.84787 | −2.06753 | ||||||||
\(9\) | 7.88356 | 2.62785 | ||||||||
\(10\) | 0.379318 | 0.119951 | ||||||||
\(11\) | 1.90159 | 0.573350 | 0.286675 | − | 0.958028i | \(-0.407450\pi\) | ||||
0.286675 | + | 0.958028i | \(0.407450\pi\) | |||||||
\(12\) | −14.2689 | −4.11909 | ||||||||
\(13\) | 3.94141 | 1.09315 | 0.546575 | − | 0.837410i | \(-0.315931\pi\) | ||||
0.546575 | + | 0.837410i | \(0.315931\pi\) | |||||||
\(14\) | 8.86522 | 2.36933 | ||||||||
\(15\) | 0.497567 | 0.128471 | ||||||||
\(16\) | 6.05697 | 1.51424 | ||||||||
\(17\) | 7.17750 | 1.74080 | 0.870400 | − | 0.492345i | \(-0.163860\pi\) | ||||
0.870400 | + | 0.492345i | \(0.163860\pi\) | |||||||
\(18\) | −19.8271 | −4.67330 | ||||||||
\(19\) | −0.695126 | −0.159473 | −0.0797365 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797365 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(20\) | −0.652337 | −0.145867 | ||||||||
\(21\) | 11.6289 | 2.53763 | ||||||||
\(22\) | −4.78248 | −1.01963 | ||||||||
\(23\) | −7.98884 | −1.66579 | −0.832894 | − | 0.553432i | \(-0.813318\pi\) | ||||
−0.832894 | + | 0.553432i | \(0.813318\pi\) | |||||||
\(24\) | 19.2923 | 3.93802 | ||||||||
\(25\) | −4.97725 | −0.995451 | ||||||||
\(26\) | −9.91263 | −1.94403 | ||||||||
\(27\) | −16.1110 | −3.10056 | ||||||||
\(28\) | −15.2461 | −2.88124 | ||||||||
\(29\) | −3.37498 | −0.626719 | −0.313359 | − | 0.949635i | \(-0.601454\pi\) | ||||
−0.313359 | + | 0.949635i | \(0.601454\pi\) | |||||||
\(30\) | −1.25138 | −0.228469 | ||||||||
\(31\) | 5.48811 | 0.985693 | 0.492847 | − | 0.870116i | \(-0.335956\pi\) | ||||
0.492847 | + | 0.870116i | \(0.335956\pi\) | |||||||
\(32\) | −3.53750 | −0.625348 | ||||||||
\(33\) | −6.27338 | −1.09206 | ||||||||
\(34\) | −18.0514 | −3.09579 | ||||||||
\(35\) | 0.531641 | 0.0898637 | ||||||||
\(36\) | 34.0980 | 5.68300 | ||||||||
\(37\) | −1.10392 | −0.181483 | −0.0907413 | − | 0.995874i | \(-0.528924\pi\) | ||||
−0.0907413 | + | 0.995874i | \(0.528924\pi\) | |||||||
\(38\) | 1.74824 | 0.283602 | ||||||||
\(39\) | −13.0028 | −2.08212 | ||||||||
\(40\) | 0.881990 | 0.139455 | ||||||||
\(41\) | 4.65892 | 0.727602 | 0.363801 | − | 0.931477i | \(-0.381479\pi\) | ||||
0.363801 | + | 0.931477i | \(0.381479\pi\) | |||||||
\(42\) | −29.2466 | −4.51285 | ||||||||
\(43\) | 2.81935 | 0.429947 | 0.214973 | − | 0.976620i | \(-0.431034\pi\) | ||||
0.214973 | + | 0.976620i | \(0.431034\pi\) | |||||||
\(44\) | 8.22474 | 1.23993 | ||||||||
\(45\) | −1.18902 | −0.177248 | ||||||||
\(46\) | 20.0919 | 2.96239 | ||||||||
\(47\) | 2.50183 | 0.364929 | 0.182464 | − | 0.983212i | \(-0.441593\pi\) | ||||
0.182464 | + | 0.983212i | \(0.441593\pi\) | |||||||
\(48\) | −19.9821 | −2.88417 | ||||||||
\(49\) | 5.42525 | 0.775036 | ||||||||
\(50\) | 12.5178 | 1.77028 | ||||||||
\(51\) | −23.6788 | −3.31569 | ||||||||
\(52\) | 17.0474 | 2.36405 | ||||||||
\(53\) | −7.70124 | −1.05785 | −0.528923 | − | 0.848670i | \(-0.677404\pi\) | ||||
−0.528923 | + | 0.848670i | \(0.677404\pi\) | |||||||
\(54\) | 40.5191 | 5.51395 | ||||||||
\(55\) | −0.286802 | −0.0386723 | ||||||||
\(56\) | 20.6134 | 2.75459 | ||||||||
\(57\) | 2.29324 | 0.303747 | ||||||||
\(58\) | 8.48807 | 1.11454 | ||||||||
\(59\) | −12.7793 | −1.66372 | −0.831861 | − | 0.554983i | \(-0.812725\pi\) | ||||
−0.831861 | + | 0.554983i | \(0.812725\pi\) | |||||||
\(60\) | 2.15208 | 0.277832 | ||||||||
\(61\) | 4.56957 | 0.585074 | 0.292537 | − | 0.956254i | \(-0.405501\pi\) | ||||
0.292537 | + | 0.956254i | \(0.405501\pi\) | |||||||
\(62\) | −13.8026 | −1.75293 | ||||||||
\(63\) | −27.7891 | −3.50110 | ||||||||
\(64\) | −3.21714 | −0.402142 | ||||||||
\(65\) | −0.594453 | −0.0737328 | ||||||||
\(66\) | 15.7775 | 1.94208 | ||||||||
\(67\) | −12.5575 | −1.53415 | −0.767074 | − | 0.641559i | \(-0.778288\pi\) | ||||
−0.767074 | + | 0.641559i | \(0.778288\pi\) | |||||||
\(68\) | 31.0442 | 3.76466 | ||||||||
\(69\) | 26.3554 | 3.17282 | ||||||||
\(70\) | −1.33707 | −0.159811 | ||||||||
\(71\) | −0.590444 | −0.0700728 | −0.0350364 | − | 0.999386i | \(-0.511155\pi\) | ||||
−0.0350364 | + | 0.999386i | \(0.511155\pi\) | |||||||
\(72\) | −46.1021 | −5.43318 | ||||||||
\(73\) | −8.48233 | −0.992782 | −0.496391 | − | 0.868099i | \(-0.665342\pi\) | ||||
−0.496391 | + | 0.868099i | \(0.665342\pi\) | |||||||
\(74\) | 2.77634 | 0.322743 | ||||||||
\(75\) | 16.4201 | 1.89603 | ||||||||
\(76\) | −3.00656 | −0.344876 | ||||||||
\(77\) | −6.70299 | −0.763877 | ||||||||
\(78\) | 32.7020 | 3.70277 | ||||||||
\(79\) | 9.09185 | 1.02291 | 0.511457 | − | 0.859309i | \(-0.329106\pi\) | ||||
0.511457 | + | 0.859309i | \(0.329106\pi\) | |||||||
\(80\) | −0.913526 | −0.102135 | ||||||||
\(81\) | 29.4999 | 3.27776 | ||||||||
\(82\) | −11.7172 | −1.29395 | ||||||||
\(83\) | 1.99877 | 0.219393 | 0.109697 | − | 0.993965i | \(-0.465012\pi\) | ||||
0.109697 | + | 0.993965i | \(0.465012\pi\) | |||||||
\(84\) | 50.2973 | 5.48788 | ||||||||
\(85\) | −1.08253 | −0.117417 | ||||||||
\(86\) | −7.09065 | −0.764605 | ||||||||
\(87\) | 11.1342 | 1.19371 | ||||||||
\(88\) | −11.1202 | −1.18542 | ||||||||
\(89\) | 6.75561 | 0.716093 | 0.358047 | − | 0.933704i | \(-0.383443\pi\) | ||||
0.358047 | + | 0.933704i | \(0.383443\pi\) | |||||||
\(90\) | 2.99037 | 0.315213 | ||||||||
\(91\) | −13.8933 | −1.45641 | ||||||||
\(92\) | −34.5534 | −3.60244 | ||||||||
\(93\) | −18.1054 | −1.87744 | ||||||||
\(94\) | −6.29208 | −0.648978 | ||||||||
\(95\) | 0.104841 | 0.0107564 | ||||||||
\(96\) | 11.6703 | 1.19110 | ||||||||
\(97\) | −9.29359 | −0.943621 | −0.471810 | − | 0.881700i | \(-0.656399\pi\) | ||||
−0.471810 | + | 0.881700i | \(0.656399\pi\) | |||||||
\(98\) | −13.6445 | −1.37830 | ||||||||
\(99\) | 14.9913 | 1.50668 | ||||||||
\(100\) | −21.5276 | −2.15276 | ||||||||
\(101\) | 18.0037 | 1.79143 | 0.895715 | − | 0.444628i | \(-0.146664\pi\) | ||||
0.895715 | + | 0.444628i | \(0.146664\pi\) | |||||||
\(102\) | 59.5520 | 5.89652 | ||||||||
\(103\) | 7.29629 | 0.718925 | 0.359463 | − | 0.933160i | \(-0.382960\pi\) | ||||
0.359463 | + | 0.933160i | \(0.382960\pi\) | |||||||
\(104\) | −23.0489 | −2.26013 | ||||||||
\(105\) | −1.75390 | −0.171163 | ||||||||
\(106\) | 19.3686 | 1.88124 | ||||||||
\(107\) | 12.2465 | 1.18391 | 0.591957 | − | 0.805970i | \(-0.298356\pi\) | ||||
0.591957 | + | 0.805970i | \(0.298356\pi\) | |||||||
\(108\) | −69.6833 | −6.70528 | ||||||||
\(109\) | 2.85671 | 0.273623 | 0.136811 | − | 0.990597i | \(-0.456315\pi\) | ||||
0.136811 | + | 0.990597i | \(0.456315\pi\) | |||||||
\(110\) | 0.721305 | 0.0687737 | ||||||||
\(111\) | 3.64185 | 0.345669 | ||||||||
\(112\) | −21.3505 | −2.01743 | ||||||||
\(113\) | −8.85220 | −0.832745 | −0.416372 | − | 0.909194i | \(-0.636699\pi\) | ||||
−0.416372 | + | 0.909194i | \(0.636699\pi\) | |||||||
\(114\) | −5.76749 | −0.540175 | ||||||||
\(115\) | 1.20490 | 0.112357 | ||||||||
\(116\) | −14.5975 | −1.35534 | ||||||||
\(117\) | 31.0723 | 2.87264 | ||||||||
\(118\) | 32.1399 | 2.95872 | ||||||||
\(119\) | −25.3003 | −2.31928 | ||||||||
\(120\) | −2.90971 | −0.265619 | ||||||||
\(121\) | −7.38397 | −0.671270 | ||||||||
\(122\) | −11.4925 | −1.04048 | ||||||||
\(123\) | −15.3699 | −1.38586 | ||||||||
\(124\) | 23.7372 | 2.13166 | ||||||||
\(125\) | 1.50479 | 0.134593 | ||||||||
\(126\) | 69.8895 | 6.22626 | ||||||||
\(127\) | −18.9318 | −1.67992 | −0.839961 | − | 0.542646i | \(-0.817422\pi\) | ||||
−0.839961 | + | 0.542646i | \(0.817422\pi\) | |||||||
\(128\) | 15.1661 | 1.34051 | ||||||||
\(129\) | −9.30110 | −0.818917 | ||||||||
\(130\) | 1.49505 | 0.131124 | ||||||||
\(131\) | 14.3516 | 1.25391 | 0.626953 | − | 0.779057i | \(-0.284302\pi\) | ||||
0.626953 | + | 0.779057i | \(0.284302\pi\) | |||||||
\(132\) | −27.1336 | −2.36168 | ||||||||
\(133\) | 2.45028 | 0.212467 | ||||||||
\(134\) | 31.5822 | 2.72828 | ||||||||
\(135\) | 2.42990 | 0.209132 | ||||||||
\(136\) | −41.9731 | −3.59917 | ||||||||
\(137\) | 12.0624 | 1.03056 | 0.515282 | − | 0.857021i | \(-0.327687\pi\) | ||||
0.515282 | + | 0.857021i | \(0.327687\pi\) | |||||||
\(138\) | −66.2837 | −5.64244 | ||||||||
\(139\) | −9.77838 | −0.829391 | −0.414696 | − | 0.909960i | \(-0.636112\pi\) | ||||
−0.414696 | + | 0.909960i | \(0.636112\pi\) | |||||||
\(140\) | 2.29945 | 0.194339 | ||||||||
\(141\) | −8.25358 | −0.695077 | ||||||||
\(142\) | 1.48496 | 0.124615 | ||||||||
\(143\) | 7.49493 | 0.626758 | ||||||||
\(144\) | 47.7505 | 3.97921 | ||||||||
\(145\) | 0.509023 | 0.0422720 | ||||||||
\(146\) | 21.3330 | 1.76553 | ||||||||
\(147\) | −17.8980 | −1.47620 | ||||||||
\(148\) | −4.77466 | −0.392475 | ||||||||
\(149\) | −15.8608 | −1.29937 | −0.649683 | − | 0.760205i | \(-0.725098\pi\) | ||||
−0.649683 | + | 0.760205i | \(0.725098\pi\) | |||||||
\(150\) | −41.2964 | −3.37184 | ||||||||
\(151\) | 8.02664 | 0.653199 | 0.326599 | − | 0.945163i | \(-0.394097\pi\) | ||||
0.326599 | + | 0.945163i | \(0.394097\pi\) | |||||||
\(152\) | 4.06501 | 0.329716 | ||||||||
\(153\) | 56.5843 | 4.57457 | ||||||||
\(154\) | 16.8580 | 1.35846 | ||||||||
\(155\) | −0.827729 | −0.0664848 | ||||||||
\(156\) | −56.2398 | −4.50278 | ||||||||
\(157\) | −2.95198 | −0.235594 | −0.117797 | − | 0.993038i | \(-0.537583\pi\) | ||||
−0.117797 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(158\) | −22.8660 | −1.81912 | ||||||||
\(159\) | 25.4066 | 2.01487 | ||||||||
\(160\) | 0.533534 | 0.0421796 | ||||||||
\(161\) | 28.1602 | 2.21934 | ||||||||
\(162\) | −74.1920 | −5.82908 | ||||||||
\(163\) | 12.5471 | 0.982766 | 0.491383 | − | 0.870943i | \(-0.336491\pi\) | ||||
0.491383 | + | 0.870943i | \(0.336491\pi\) | |||||||
\(164\) | 20.1508 | 1.57351 | ||||||||
\(165\) | 0.946166 | 0.0736589 | ||||||||
\(166\) | −5.02689 | −0.390163 | ||||||||
\(167\) | 12.8231 | 0.992280 | 0.496140 | − | 0.868243i | \(-0.334750\pi\) | ||||
0.496140 | + | 0.868243i | \(0.334750\pi\) | |||||||
\(168\) | −68.0042 | −5.24664 | ||||||||
\(169\) | 2.53471 | 0.194978 | ||||||||
\(170\) | 2.72255 | 0.208810 | ||||||||
\(171\) | −5.48007 | −0.419072 | ||||||||
\(172\) | 12.1943 | 0.929803 | ||||||||
\(173\) | 24.5434 | 1.86600 | 0.933000 | − | 0.359877i | \(-0.117181\pi\) | ||||
0.933000 | + | 0.359877i | \(0.117181\pi\) | |||||||
\(174\) | −28.0023 | −2.12285 | ||||||||
\(175\) | 17.5446 | 1.32624 | ||||||||
\(176\) | 11.5178 | 0.868190 | ||||||||
\(177\) | 42.1592 | 3.16888 | ||||||||
\(178\) | −16.9903 | −1.27348 | ||||||||
\(179\) | −19.7541 | −1.47649 | −0.738247 | − | 0.674531i | \(-0.764346\pi\) | ||||
−0.738247 | + | 0.674531i | \(0.764346\pi\) | |||||||
\(180\) | −5.14274 | −0.383317 | ||||||||
\(181\) | 2.31328 | 0.171945 | 0.0859723 | − | 0.996298i | \(-0.472600\pi\) | ||||
0.0859723 | + | 0.996298i | \(0.472600\pi\) | |||||||
\(182\) | 34.9415 | 2.59004 | ||||||||
\(183\) | −15.0751 | −1.11439 | ||||||||
\(184\) | 46.7177 | 3.44408 | ||||||||
\(185\) | 0.166495 | 0.0122410 | ||||||||
\(186\) | 45.5350 | 3.33879 | ||||||||
\(187\) | 13.6486 | 0.998088 | ||||||||
\(188\) | 10.8209 | 0.789195 | ||||||||
\(189\) | 56.7904 | 4.13089 | ||||||||
\(190\) | −0.263674 | −0.0191289 | ||||||||
\(191\) | −0.932938 | −0.0675050 | −0.0337525 | − | 0.999430i | \(-0.510746\pi\) | ||||
−0.0337525 | + | 0.999430i | \(0.510746\pi\) | |||||||
\(192\) | 10.6134 | 0.765957 | ||||||||
\(193\) | 12.2883 | 0.884532 | 0.442266 | − | 0.896884i | \(-0.354175\pi\) | ||||
0.442266 | + | 0.896884i | \(0.354175\pi\) | |||||||
\(194\) | 23.3733 | 1.67811 | ||||||||
\(195\) | 1.96111 | 0.140438 | ||||||||
\(196\) | 23.4653 | 1.67609 | ||||||||
\(197\) | 20.0658 | 1.42963 | 0.714816 | − | 0.699313i | \(-0.246511\pi\) | ||||
0.714816 | + | 0.699313i | \(0.246511\pi\) | |||||||
\(198\) | −37.7030 | −2.67943 | ||||||||
\(199\) | −13.2050 | −0.936078 | −0.468039 | − | 0.883708i | \(-0.655039\pi\) | ||||
−0.468039 | + | 0.883708i | \(0.655039\pi\) | |||||||
\(200\) | 29.1063 | 2.05813 | ||||||||
\(201\) | 41.4276 | 2.92208 | ||||||||
\(202\) | −45.2791 | −3.18583 | ||||||||
\(203\) | 11.8966 | 0.834980 | ||||||||
\(204\) | −102.415 | −7.17051 | ||||||||
\(205\) | −0.702670 | −0.0490766 | ||||||||
\(206\) | −18.3501 | −1.27852 | ||||||||
\(207\) | −62.9805 | −4.37745 | ||||||||
\(208\) | 23.8730 | 1.65529 | ||||||||
\(209\) | −1.32184 | −0.0914338 | ||||||||
\(210\) | 4.41104 | 0.304391 | ||||||||
\(211\) | 0.133147 | 0.00916625 | 0.00458313 | − | 0.999989i | \(-0.498541\pi\) | ||||
0.00458313 | + | 0.999989i | \(0.498541\pi\) | |||||||
\(212\) | −33.3094 | −2.28770 | ||||||||
\(213\) | 1.94789 | 0.133467 | ||||||||
\(214\) | −30.7999 | −2.10544 | ||||||||
\(215\) | −0.425221 | −0.0289998 | ||||||||
\(216\) | 94.2150 | 6.41052 | ||||||||
\(217\) | −19.3453 | −1.31324 | ||||||||
\(218\) | −7.18461 | −0.486603 | ||||||||
\(219\) | 27.9834 | 1.89094 | ||||||||
\(220\) | −1.24048 | −0.0836328 | ||||||||
\(221\) | 28.2895 | 1.90296 | ||||||||
\(222\) | −9.15922 | −0.614727 | ||||||||
\(223\) | 6.17458 | 0.413480 | 0.206740 | − | 0.978396i | \(-0.433715\pi\) | ||||
0.206740 | + | 0.978396i | \(0.433715\pi\) | |||||||
\(224\) | 12.4695 | 0.833154 | ||||||||
\(225\) | −39.2385 | −2.61590 | ||||||||
\(226\) | 22.2632 | 1.48093 | ||||||||
\(227\) | −5.79378 | −0.384546 | −0.192273 | − | 0.981341i | \(-0.561586\pi\) | ||||
−0.192273 | + | 0.981341i | \(0.561586\pi\) | |||||||
\(228\) | 9.91872 | 0.656883 | ||||||||
\(229\) | −16.6592 | −1.10087 | −0.550435 | − | 0.834878i | \(-0.685538\pi\) | ||||
−0.550435 | + | 0.834878i | \(0.685538\pi\) | |||||||
\(230\) | −3.03031 | −0.199813 | ||||||||
\(231\) | 22.1133 | 1.45495 | ||||||||
\(232\) | 19.7365 | 1.29576 | ||||||||
\(233\) | 7.63997 | 0.500511 | 0.250255 | − | 0.968180i | \(-0.419485\pi\) | ||||
0.250255 | + | 0.968180i | \(0.419485\pi\) | |||||||
\(234\) | −78.1468 | −5.10862 | ||||||||
\(235\) | −0.377331 | −0.0246144 | ||||||||
\(236\) | −55.2730 | −3.59797 | ||||||||
\(237\) | −29.9942 | −1.94834 | ||||||||
\(238\) | 63.6302 | 4.12453 | ||||||||
\(239\) | 11.8748 | 0.768120 | 0.384060 | − | 0.923308i | \(-0.374526\pi\) | ||||
0.384060 | + | 0.923308i | \(0.374526\pi\) | |||||||
\(240\) | 3.01374 | 0.194536 | ||||||||
\(241\) | −4.94514 | −0.318544 | −0.159272 | − | 0.987235i | \(-0.550915\pi\) | ||||
−0.159272 | + | 0.987235i | \(0.550915\pi\) | |||||||
\(242\) | 18.5706 | 1.19377 | ||||||||
\(243\) | −48.9878 | −3.14257 | ||||||||
\(244\) | 19.7643 | 1.26528 | ||||||||
\(245\) | −0.818249 | −0.0522760 | ||||||||
\(246\) | 38.6552 | 2.46457 | ||||||||
\(247\) | −2.73978 | −0.174328 | ||||||||
\(248\) | −32.0937 | −2.03795 | ||||||||
\(249\) | −6.59399 | −0.417877 | ||||||||
\(250\) | −3.78455 | −0.239356 | ||||||||
\(251\) | 27.7390 | 1.75087 | 0.875435 | − | 0.483336i | \(-0.160575\pi\) | ||||
0.875435 | + | 0.483336i | \(0.160575\pi\) | |||||||
\(252\) | −120.194 | −7.57149 | ||||||||
\(253\) | −15.1915 | −0.955080 | ||||||||
\(254\) | 47.6133 | 2.98752 | ||||||||
\(255\) | 3.57129 | 0.223643 | ||||||||
\(256\) | −31.7084 | −1.98177 | ||||||||
\(257\) | 18.2638 | 1.13927 | 0.569634 | − | 0.821899i | \(-0.307085\pi\) | ||||
0.569634 | + | 0.821899i | \(0.307085\pi\) | |||||||
\(258\) | 23.3922 | 1.45634 | ||||||||
\(259\) | 3.89124 | 0.241790 | ||||||||
\(260\) | −2.57113 | −0.159455 | ||||||||
\(261\) | −26.6069 | −1.64692 | ||||||||
\(262\) | −36.0942 | −2.22991 | ||||||||
\(263\) | 13.2174 | 0.815018 | 0.407509 | − | 0.913201i | \(-0.366398\pi\) | ||||
0.407509 | + | 0.913201i | \(0.366398\pi\) | |||||||
\(264\) | 36.6859 | 2.25786 | ||||||||
\(265\) | 1.16152 | 0.0713515 | ||||||||
\(266\) | −6.16245 | −0.377844 | ||||||||
\(267\) | −22.2869 | −1.36394 | ||||||||
\(268\) | −54.3139 | −3.31775 | ||||||||
\(269\) | 0.281881 | 0.0171866 | 0.00859329 | − | 0.999963i | \(-0.497265\pi\) | ||||
0.00859329 | + | 0.999963i | \(0.497265\pi\) | |||||||
\(270\) | −6.11118 | −0.371915 | ||||||||
\(271\) | −18.6029 | −1.13004 | −0.565021 | − | 0.825076i | \(-0.691132\pi\) | ||||
−0.565021 | + | 0.825076i | \(0.691132\pi\) | |||||||
\(272\) | 43.4739 | 2.63599 | ||||||||
\(273\) | 45.8342 | 2.77401 | ||||||||
\(274\) | −30.3370 | −1.83272 | ||||||||
\(275\) | −9.46468 | −0.570741 | ||||||||
\(276\) | 113.992 | 6.86153 | ||||||||
\(277\) | −24.9290 | −1.49784 | −0.748919 | − | 0.662662i | \(-0.769427\pi\) | ||||
−0.748919 | + | 0.662662i | \(0.769427\pi\) | |||||||
\(278\) | 24.5926 | 1.47496 | ||||||||
\(279\) | 43.2658 | 2.59026 | ||||||||
\(280\) | −3.10897 | −0.185796 | ||||||||
\(281\) | −12.3799 | −0.738520 | −0.369260 | − | 0.929326i | \(-0.620389\pi\) | ||||
−0.369260 | + | 0.929326i | \(0.620389\pi\) | |||||||
\(282\) | 20.7577 | 1.23610 | ||||||||
\(283\) | −21.4059 | −1.27245 | −0.636224 | − | 0.771505i | \(-0.719504\pi\) | ||||
−0.636224 | + | 0.771505i | \(0.719504\pi\) | |||||||
\(284\) | −2.55379 | −0.151539 | ||||||||
\(285\) | −0.345872 | −0.0204877 | ||||||||
\(286\) | −18.8497 | −1.11461 | ||||||||
\(287\) | −16.4225 | −0.969387 | ||||||||
\(288\) | −27.8881 | −1.64332 | ||||||||
\(289\) | 34.5166 | 2.03039 | ||||||||
\(290\) | −1.28019 | −0.0751754 | ||||||||
\(291\) | 30.6598 | 1.79731 | ||||||||
\(292\) | −36.6878 | −2.14699 | ||||||||
\(293\) | −25.0848 | −1.46547 | −0.732736 | − | 0.680513i | \(-0.761757\pi\) | ||||
−0.732736 | + | 0.680513i | \(0.761757\pi\) | |||||||
\(294\) | 45.0135 | 2.62524 | ||||||||
\(295\) | 1.92740 | 0.112218 | ||||||||
\(296\) | 6.45556 | 0.375222 | ||||||||
\(297\) | −30.6364 | −1.77771 | ||||||||
\(298\) | 39.8898 | 2.31075 | ||||||||
\(299\) | −31.4873 | −1.82096 | ||||||||
\(300\) | 71.0201 | 4.10035 | ||||||||
\(301\) | −9.93806 | −0.572820 | ||||||||
\(302\) | −20.1870 | −1.16163 | ||||||||
\(303\) | −59.3945 | −3.41213 | ||||||||
\(304\) | −4.21036 | −0.241481 | ||||||||
\(305\) | −0.689194 | −0.0394631 | ||||||||
\(306\) | −142.309 | −8.13528 | ||||||||
\(307\) | 11.0033 | 0.627990 | 0.313995 | − | 0.949425i | \(-0.398333\pi\) | ||||
0.313995 | + | 0.949425i | \(0.398333\pi\) | |||||||
\(308\) | −28.9918 | −1.65196 | ||||||||
\(309\) | −24.0706 | −1.36933 | ||||||||
\(310\) | 2.08174 | 0.118235 | ||||||||
\(311\) | −14.2091 | −0.805726 | −0.402863 | − | 0.915260i | \(-0.631985\pi\) | ||||
−0.402863 | + | 0.915260i | \(0.631985\pi\) | |||||||
\(312\) | 76.0387 | 4.30485 | ||||||||
\(313\) | −19.4290 | −1.09819 | −0.549096 | − | 0.835759i | \(-0.685028\pi\) | ||||
−0.549096 | + | 0.835759i | \(0.685028\pi\) | |||||||
\(314\) | 7.42422 | 0.418973 | ||||||||
\(315\) | 4.19122 | 0.236149 | ||||||||
\(316\) | 39.3241 | 2.21215 | ||||||||
\(317\) | −0.199190 | −0.0111876 | −0.00559382 | − | 0.999984i | \(-0.501781\pi\) | ||||
−0.00559382 | + | 0.999984i | \(0.501781\pi\) | |||||||
\(318\) | −63.8974 | −3.58319 | ||||||||
\(319\) | −6.41782 | −0.359329 | ||||||||
\(320\) | 0.485216 | 0.0271244 | ||||||||
\(321\) | −40.4015 | −2.25499 | ||||||||
\(322\) | −70.8229 | −3.94680 | ||||||||
\(323\) | −4.98927 | −0.277611 | ||||||||
\(324\) | 127.593 | 7.08849 | ||||||||
\(325\) | −19.6174 | −1.08818 | ||||||||
\(326\) | −31.5560 | −1.74772 | ||||||||
\(327\) | −9.42435 | −0.521168 | ||||||||
\(328\) | −27.2448 | −1.50434 | ||||||||
\(329\) | −8.81880 | −0.486196 | ||||||||
\(330\) | −2.37960 | −0.130993 | ||||||||
\(331\) | −22.5383 | −1.23882 | −0.619408 | − | 0.785069i | \(-0.712627\pi\) | ||||
−0.619408 | + | 0.785069i | \(0.712627\pi\) | |||||||
\(332\) | 8.64508 | 0.474460 | ||||||||
\(333\) | −8.70279 | −0.476910 | ||||||||
\(334\) | −32.2500 | −1.76464 | ||||||||
\(335\) | 1.89396 | 0.103478 | ||||||||
\(336\) | 70.4358 | 3.84259 | ||||||||
\(337\) | 10.9611 | 0.597090 | 0.298545 | − | 0.954395i | \(-0.403499\pi\) | ||||
0.298545 | + | 0.954395i | \(0.403499\pi\) | |||||||
\(338\) | −6.37479 | −0.346743 | ||||||||
\(339\) | 29.2036 | 1.58612 | ||||||||
\(340\) | −4.68215 | −0.253925 | ||||||||
\(341\) | 10.4361 | 0.565147 | ||||||||
\(342\) | 13.7824 | 0.745264 | ||||||||
\(343\) | 5.55091 | 0.299721 | ||||||||
\(344\) | −16.4872 | −0.888930 | ||||||||
\(345\) | −3.97498 | −0.214006 | ||||||||
\(346\) | −61.7265 | −3.31844 | ||||||||
\(347\) | −3.92998 | −0.210972 | −0.105486 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105486 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(348\) | 48.1574 | 2.58151 | ||||||||
\(349\) | 29.5659 | 1.58263 | 0.791313 | − | 0.611411i | \(-0.209398\pi\) | ||||
0.791313 | + | 0.611411i | \(0.209398\pi\) | |||||||
\(350\) | −44.1245 | −2.35855 | ||||||||
\(351\) | −63.5000 | −3.38938 | ||||||||
\(352\) | −6.72686 | −0.358543 | ||||||||
\(353\) | −6.12162 | −0.325821 | −0.162910 | − | 0.986641i | \(-0.552088\pi\) | ||||
−0.162910 | + | 0.986641i | \(0.552088\pi\) | |||||||
\(354\) | −106.030 | −5.63544 | ||||||||
\(355\) | 0.0890521 | 0.00472640 | ||||||||
\(356\) | 29.2194 | 1.54862 | ||||||||
\(357\) | 83.4664 | 4.41751 | ||||||||
\(358\) | 49.6816 | 2.62575 | ||||||||
\(359\) | −6.36050 | −0.335694 | −0.167847 | − | 0.985813i | \(-0.553682\pi\) | ||||
−0.167847 | + | 0.985813i | \(0.553682\pi\) | |||||||
\(360\) | 6.95322 | 0.366467 | ||||||||
\(361\) | −18.5168 | −0.974568 | ||||||||
\(362\) | −5.81788 | −0.305781 | ||||||||
\(363\) | 24.3599 | 1.27856 | ||||||||
\(364\) | −60.0912 | −3.14963 | ||||||||
\(365\) | 1.27933 | 0.0669630 | ||||||||
\(366\) | 37.9139 | 1.98179 | ||||||||
\(367\) | 23.5872 | 1.23124 | 0.615620 | − | 0.788043i | \(-0.288906\pi\) | ||||
0.615620 | + | 0.788043i | \(0.288906\pi\) | |||||||
\(368\) | −48.3882 | −2.52241 | ||||||||
\(369\) | 36.7289 | 1.91203 | ||||||||
\(370\) | −0.418735 | −0.0217690 | ||||||||
\(371\) | 27.1465 | 1.40937 | ||||||||
\(372\) | −78.3095 | −4.06016 | ||||||||
\(373\) | −37.9909 | −1.96709 | −0.983547 | − | 0.180653i | \(-0.942179\pi\) | ||||
−0.983547 | + | 0.180653i | \(0.942179\pi\) | |||||||
\(374\) | −34.3263 | −1.77497 | ||||||||
\(375\) | −4.96435 | −0.256358 | ||||||||
\(376\) | −14.6304 | −0.754503 | ||||||||
\(377\) | −13.3022 | −0.685098 | ||||||||
\(378\) | −142.828 | −7.34626 | ||||||||
\(379\) | 1.60110 | 0.0822427 | 0.0411214 | − | 0.999154i | \(-0.486907\pi\) | ||||
0.0411214 | + | 0.999154i | \(0.486907\pi\) | |||||||
\(380\) | 0.453457 | 0.0232618 | ||||||||
\(381\) | 62.4564 | 3.19974 | ||||||||
\(382\) | 2.34633 | 0.120049 | ||||||||
\(383\) | −14.6006 | −0.746057 | −0.373028 | − | 0.927820i | \(-0.621681\pi\) | ||||
−0.373028 | + | 0.927820i | \(0.621681\pi\) | |||||||
\(384\) | −50.0333 | −2.55325 | ||||||||
\(385\) | 1.01096 | 0.0515233 | ||||||||
\(386\) | −30.9051 | −1.57303 | ||||||||
\(387\) | 22.2265 | 1.12984 | ||||||||
\(388\) | −40.1966 | −2.04068 | ||||||||
\(389\) | −18.0605 | −0.915705 | −0.457853 | − | 0.889028i | \(-0.651381\pi\) | ||||
−0.457853 | + | 0.889028i | \(0.651381\pi\) | |||||||
\(390\) | −4.93219 | −0.249751 | ||||||||
\(391\) | −57.3399 | −2.89981 | ||||||||
\(392\) | −31.7262 | −1.60241 | ||||||||
\(393\) | −47.3463 | −2.38831 | ||||||||
\(394\) | −50.4655 | −2.54241 | ||||||||
\(395\) | −1.37125 | −0.0689953 | ||||||||
\(396\) | 64.8403 | 3.25835 | ||||||||
\(397\) | 2.61309 | 0.131147 | 0.0655736 | − | 0.997848i | \(-0.479112\pi\) | ||||
0.0655736 | + | 0.997848i | \(0.479112\pi\) | |||||||
\(398\) | 33.2105 | 1.66469 | ||||||||
\(399\) | −8.08355 | −0.404683 | ||||||||
\(400\) | −30.1471 | −1.50735 | ||||||||
\(401\) | −16.4845 | −0.823195 | −0.411597 | − | 0.911366i | \(-0.635029\pi\) | ||||
−0.411597 | + | 0.911366i | \(0.635029\pi\) | |||||||
\(402\) | −104.190 | −5.19654 | ||||||||
\(403\) | 21.6309 | 1.07751 | ||||||||
\(404\) | 77.8695 | 3.87415 | ||||||||
\(405\) | −4.44924 | −0.221084 | ||||||||
\(406\) | −29.9200 | −1.48490 | ||||||||
\(407\) | −2.09919 | −0.104053 | ||||||||
\(408\) | 138.470 | 6.85530 | ||||||||
\(409\) | −16.3719 | −0.809539 | −0.404770 | − | 0.914419i | \(-0.632648\pi\) | ||||
−0.404770 | + | 0.914419i | \(0.632648\pi\) | |||||||
\(410\) | 1.76721 | 0.0872763 | ||||||||
\(411\) | −39.7943 | −1.96291 | ||||||||
\(412\) | 31.5579 | 1.55475 | ||||||||
\(413\) | 45.0463 | 2.21659 | ||||||||
\(414\) | 158.396 | 7.78473 | ||||||||
\(415\) | −0.301459 | −0.0147980 | ||||||||
\(416\) | −13.9427 | −0.683599 | ||||||||
\(417\) | 32.2591 | 1.57974 | ||||||||
\(418\) | 3.32443 | 0.162603 | ||||||||
\(419\) | 31.5030 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220500\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220500\pi\) | |||||||
\(420\) | −7.58595 | −0.370157 | ||||||||
\(421\) | −8.98468 | −0.437887 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(422\) | −0.334865 | −0.0163010 | ||||||||
\(423\) | 19.7233 | 0.958979 | ||||||||
\(424\) | 45.0358 | 2.18713 | ||||||||
\(425\) | −35.7243 | −1.73288 | ||||||||
\(426\) | −4.89893 | −0.237354 | ||||||||
\(427\) | −16.1075 | −0.779497 | ||||||||
\(428\) | 52.9686 | 2.56033 | ||||||||
\(429\) | −24.7260 | −1.19378 | ||||||||
\(430\) | 1.06943 | 0.0515724 | ||||||||
\(431\) | 36.4786 | 1.75711 | 0.878555 | − | 0.477641i | \(-0.158508\pi\) | ||||
0.878555 | + | 0.477641i | \(0.158508\pi\) | |||||||
\(432\) | −97.5837 | −4.69500 | ||||||||
\(433\) | −9.56452 | −0.459642 | −0.229821 | − | 0.973233i | \(-0.573814\pi\) | ||||
−0.229821 | + | 0.973233i | \(0.573814\pi\) | |||||||
\(434\) | 48.6533 | 2.33543 | ||||||||
\(435\) | −1.67928 | −0.0805153 | ||||||||
\(436\) | 12.3558 | 0.591737 | ||||||||
\(437\) | 5.55326 | 0.265648 | ||||||||
\(438\) | −70.3782 | −3.36280 | ||||||||
\(439\) | −7.89468 | −0.376793 | −0.188396 | − | 0.982093i | \(-0.560329\pi\) | ||||
−0.188396 | + | 0.982093i | \(0.560329\pi\) | |||||||
\(440\) | 1.67718 | 0.0799564 | ||||||||
\(441\) | 42.7703 | 2.03668 | ||||||||
\(442\) | −71.1479 | −3.38416 | ||||||||
\(443\) | 37.6642 | 1.78948 | 0.894740 | − | 0.446587i | \(-0.147361\pi\) | ||||
0.894740 | + | 0.446587i | \(0.147361\pi\) | |||||||
\(444\) | 15.7517 | 0.747543 | ||||||||
\(445\) | −1.01890 | −0.0483004 | ||||||||
\(446\) | −15.5290 | −0.735321 | ||||||||
\(447\) | 52.3251 | 2.47489 | ||||||||
\(448\) | 11.3402 | 0.535776 | ||||||||
\(449\) | 4.67544 | 0.220648 | 0.110324 | − | 0.993896i | \(-0.464811\pi\) | ||||
0.110324 | + | 0.993896i | \(0.464811\pi\) | |||||||
\(450\) | 98.6846 | 4.65204 | ||||||||
\(451\) | 8.85935 | 0.417170 | ||||||||
\(452\) | −38.2875 | −1.80089 | ||||||||
\(453\) | −26.4801 | −1.24414 | ||||||||
\(454\) | 14.5713 | 0.683866 | ||||||||
\(455\) | 2.09541 | 0.0982345 | ||||||||
\(456\) | −13.4106 | −0.628007 | ||||||||
\(457\) | 32.9275 | 1.54028 | 0.770142 | − | 0.637873i | \(-0.220186\pi\) | ||||
0.770142 | + | 0.637873i | \(0.220186\pi\) | |||||||
\(458\) | 41.8978 | 1.95775 | ||||||||
\(459\) | −115.637 | −5.39746 | ||||||||
\(460\) | 5.21142 | 0.242984 | ||||||||
\(461\) | −25.4711 | −1.18631 | −0.593154 | − | 0.805089i | \(-0.702117\pi\) | ||||
−0.593154 | + | 0.805089i | \(0.702117\pi\) | |||||||
\(462\) | −55.6149 | −2.58744 | ||||||||
\(463\) | 14.0628 | 0.653553 | 0.326777 | − | 0.945102i | \(-0.394038\pi\) | ||||
0.326777 | + | 0.945102i | \(0.394038\pi\) | |||||||
\(464\) | −20.4422 | −0.949003 | ||||||||
\(465\) | 2.73070 | 0.126633 | ||||||||
\(466\) | −19.2145 | −0.890094 | ||||||||
\(467\) | −38.4864 | −1.78094 | −0.890469 | − | 0.455043i | \(-0.849624\pi\) | ||||
−0.890469 | + | 0.455043i | \(0.849624\pi\) | |||||||
\(468\) | 134.394 | 6.21237 | ||||||||
\(469\) | 44.2647 | 2.04395 | ||||||||
\(470\) | 0.948986 | 0.0437735 | ||||||||
\(471\) | 9.73865 | 0.448733 | ||||||||
\(472\) | 74.7317 | 3.43981 | ||||||||
\(473\) | 5.36124 | 0.246510 | ||||||||
\(474\) | 75.4354 | 3.46486 | ||||||||
\(475\) | 3.45982 | 0.158747 | ||||||||
\(476\) | −109.429 | −5.01567 | ||||||||
\(477\) | −60.7132 | −2.77987 | ||||||||
\(478\) | −29.8652 | −1.36600 | ||||||||
\(479\) | 0.628161 | 0.0287014 | 0.0143507 | − | 0.999897i | \(-0.495432\pi\) | ||||
0.0143507 | + | 0.999897i | \(0.495432\pi\) | |||||||
\(480\) | −1.76014 | −0.0803391 | ||||||||
\(481\) | −4.35098 | −0.198388 | ||||||||
\(482\) | 12.4370 | 0.566490 | ||||||||
\(483\) | −92.9013 | −4.22716 | ||||||||
\(484\) | −31.9372 | −1.45169 | ||||||||
\(485\) | 1.40168 | 0.0636470 | ||||||||
\(486\) | 123.204 | 5.58865 | ||||||||
\(487\) | −43.7780 | −1.98377 | −0.991885 | − | 0.127138i | \(-0.959421\pi\) | ||||
−0.991885 | + | 0.127138i | \(0.959421\pi\) | |||||||
\(488\) | −26.7223 | −1.20966 | ||||||||
\(489\) | −41.3933 | −1.87187 | ||||||||
\(490\) | 2.05789 | 0.0929661 | ||||||||
\(491\) | −35.8852 | −1.61947 | −0.809737 | − | 0.586793i | \(-0.800390\pi\) | ||||
−0.809737 | + | 0.586793i | \(0.800390\pi\) | |||||||
\(492\) | −66.4779 | −2.99706 | ||||||||
\(493\) | −24.2240 | −1.09099 | ||||||||
\(494\) | 6.89053 | 0.310020 | ||||||||
\(495\) | −2.26102 | −0.101625 | ||||||||
\(496\) | 33.2413 | 1.49258 | ||||||||
\(497\) | 2.08128 | 0.0933583 | ||||||||
\(498\) | 16.5838 | 0.743140 | ||||||||
\(499\) | −25.9599 | −1.16213 | −0.581063 | − | 0.813859i | \(-0.697363\pi\) | ||||
−0.581063 | + | 0.813859i | \(0.697363\pi\) | |||||||
\(500\) | 6.50853 | 0.291070 | ||||||||
\(501\) | −42.3037 | −1.88999 | ||||||||
\(502\) | −69.7634 | −3.11369 | ||||||||
\(503\) | −5.06465 | −0.225822 | −0.112911 | − | 0.993605i | \(-0.536017\pi\) | ||||
−0.112911 | + | 0.993605i | \(0.536017\pi\) | |||||||
\(504\) | 162.507 | 7.23865 | ||||||||
\(505\) | −2.71535 | −0.120832 | ||||||||
\(506\) | 38.2065 | 1.69849 | ||||||||
\(507\) | −8.36207 | −0.371373 | ||||||||
\(508\) | −81.8837 | −3.63300 | ||||||||
\(509\) | 34.6317 | 1.53502 | 0.767511 | − | 0.641035i | \(-0.221495\pi\) | ||||
0.767511 | + | 0.641035i | \(0.221495\pi\) | |||||||
\(510\) | −8.98177 | −0.397719 | ||||||||
\(511\) | 29.8998 | 1.32269 | ||||||||
\(512\) | 49.4142 | 2.18382 | ||||||||
\(513\) | 11.1992 | 0.494456 | ||||||||
\(514\) | −45.9335 | −2.02604 | ||||||||
\(515\) | −1.10044 | −0.0484914 | ||||||||
\(516\) | −40.2292 | −1.77099 | ||||||||
\(517\) | 4.75744 | 0.209232 | ||||||||
\(518\) | −9.78646 | −0.429992 | ||||||||
\(519\) | −80.9692 | −3.55415 | ||||||||
\(520\) | 3.47628 | 0.152445 | ||||||||
\(521\) | −34.7811 | −1.52379 | −0.761894 | − | 0.647702i | \(-0.775730\pi\) | ||||
−0.761894 | + | 0.647702i | \(0.775730\pi\) | |||||||
\(522\) | 66.9162 | 2.92884 | ||||||||
\(523\) | −36.7470 | −1.60683 | −0.803416 | − | 0.595418i | \(-0.796987\pi\) | ||||
−0.803416 | + | 0.595418i | \(0.796987\pi\) | |||||||
\(524\) | 62.0736 | 2.71170 | ||||||||
\(525\) | −57.8799 | −2.52609 | ||||||||
\(526\) | −33.2416 | −1.44940 | ||||||||
\(527\) | 39.3909 | 1.71590 | ||||||||
\(528\) | −37.9977 | −1.65364 | ||||||||
\(529\) | 40.8216 | 1.77485 | ||||||||
\(530\) | −2.92121 | −0.126889 | ||||||||
\(531\) | −100.746 | −4.37202 | ||||||||
\(532\) | 10.5980 | 0.459480 | ||||||||
\(533\) | 18.3627 | 0.795378 | ||||||||
\(534\) | 56.0515 | 2.42559 | ||||||||
\(535\) | −1.84705 | −0.0798547 | ||||||||
\(536\) | 73.4349 | 3.17190 | ||||||||
\(537\) | 65.1694 | 2.81227 | ||||||||
\(538\) | −0.708929 | −0.0305641 | ||||||||
\(539\) | 10.3166 | 0.444367 | ||||||||
\(540\) | 10.5098 | 0.452270 | ||||||||
\(541\) | 35.5884 | 1.53007 | 0.765033 | − | 0.643991i | \(-0.222723\pi\) | ||||
0.765033 | + | 0.643991i | \(0.222723\pi\) | |||||||
\(542\) | 46.7861 | 2.00963 | ||||||||
\(543\) | −7.63156 | −0.327502 | ||||||||
\(544\) | −25.3904 | −1.08861 | ||||||||
\(545\) | −0.430855 | −0.0184558 | ||||||||
\(546\) | −115.273 | −4.93322 | ||||||||
\(547\) | 1.74655 | 0.0746773 | 0.0373386 | − | 0.999303i | \(-0.488112\pi\) | ||||
0.0373386 | + | 0.999303i | \(0.488112\pi\) | |||||||
\(548\) | 52.1725 | 2.22870 | ||||||||
\(549\) | 36.0245 | 1.53749 | ||||||||
\(550\) | 23.8036 | 1.01499 | ||||||||
\(551\) | 2.34604 | 0.0999447 | ||||||||
\(552\) | −154.123 | −6.55991 | ||||||||
\(553\) | −32.0483 | −1.36283 | ||||||||
\(554\) | 62.6963 | 2.66371 | ||||||||
\(555\) | −0.549272 | −0.0233153 | ||||||||
\(556\) | −42.2935 | −1.79364 | ||||||||
\(557\) | 2.15745 | 0.0914139 | 0.0457070 | − | 0.998955i | \(-0.485446\pi\) | ||||
0.0457070 | + | 0.998955i | \(0.485446\pi\) | |||||||
\(558\) | −108.813 | −4.60644 | ||||||||
\(559\) | 11.1122 | 0.469997 | ||||||||
\(560\) | 3.22013 | 0.136075 | ||||||||
\(561\) | −45.0272 | −1.90105 | ||||||||
\(562\) | 31.1353 | 1.31336 | ||||||||
\(563\) | −19.5302 | −0.823101 | −0.411550 | − | 0.911387i | \(-0.635013\pi\) | ||||
−0.411550 | + | 0.911387i | \(0.635013\pi\) | |||||||
\(564\) | −35.6984 | −1.50317 | ||||||||
\(565\) | 1.33511 | 0.0561685 | ||||||||
\(566\) | 53.8357 | 2.26288 | ||||||||
\(567\) | −103.985 | −4.36698 | ||||||||
\(568\) | 3.45284 | 0.144878 | ||||||||
\(569\) | 25.4911 | 1.06864 | 0.534320 | − | 0.845282i | \(-0.320568\pi\) | ||||
0.534320 | + | 0.845282i | \(0.320568\pi\) | |||||||
\(570\) | 0.869866 | 0.0364347 | ||||||||
\(571\) | 18.0382 | 0.754877 | 0.377439 | − | 0.926035i | \(-0.376805\pi\) | ||||
0.377439 | + | 0.926035i | \(0.376805\pi\) | |||||||
\(572\) | 32.4171 | 1.35543 | ||||||||
\(573\) | 3.07778 | 0.128576 | ||||||||
\(574\) | 41.3024 | 1.72393 | ||||||||
\(575\) | 39.7625 | 1.65821 | ||||||||
\(576\) | −25.3625 | −1.05677 | ||||||||
\(577\) | −9.93437 | −0.413573 | −0.206787 | − | 0.978386i | \(-0.566301\pi\) | ||||
−0.206787 | + | 0.978386i | \(0.566301\pi\) | |||||||
\(578\) | −86.8090 | −3.61078 | ||||||||
\(579\) | −40.5395 | −1.68476 | ||||||||
\(580\) | 2.20163 | 0.0914176 | ||||||||
\(581\) | −7.04555 | −0.292299 | ||||||||
\(582\) | −77.1092 | −3.19628 | ||||||||
\(583\) | −14.6446 | −0.606516 | ||||||||
\(584\) | 49.6036 | 2.05261 | ||||||||
\(585\) | −4.68640 | −0.193759 | ||||||||
\(586\) | 63.0883 | 2.60615 | ||||||||
\(587\) | −18.6128 | −0.768234 | −0.384117 | − | 0.923284i | \(-0.625494\pi\) | ||||
−0.384117 | + | 0.923284i | \(0.625494\pi\) | |||||||
\(588\) | −77.4126 | −3.19244 | ||||||||
\(589\) | −3.81493 | −0.157191 | ||||||||
\(590\) | −4.84741 | −0.199565 | ||||||||
\(591\) | −66.1977 | −2.72301 | ||||||||
\(592\) | −6.68638 | −0.274809 | ||||||||
\(593\) | 18.8547 | 0.774268 | 0.387134 | − | 0.922023i | \(-0.373465\pi\) | ||||
0.387134 | + | 0.922023i | \(0.373465\pi\) | |||||||
\(594\) | 77.0505 | 3.16142 | ||||||||
\(595\) | 3.81585 | 0.156435 | ||||||||
\(596\) | −68.6011 | −2.81001 | ||||||||
\(597\) | 43.5636 | 1.78294 | ||||||||
\(598\) | 79.1904 | 3.23834 | ||||||||
\(599\) | −10.3390 | −0.422438 | −0.211219 | − | 0.977439i | \(-0.567743\pi\) | ||||
−0.211219 | + | 0.977439i | \(0.567743\pi\) | |||||||
\(600\) | −96.0225 | −3.92010 | ||||||||
\(601\) | 23.9834 | 0.978303 | 0.489152 | − | 0.872199i | \(-0.337306\pi\) | ||||
0.489152 | + | 0.872199i | \(0.337306\pi\) | |||||||
\(602\) | 24.9942 | 1.01869 | ||||||||
\(603\) | −98.9982 | −4.03152 | ||||||||
\(604\) | 34.7168 | 1.41261 | ||||||||
\(605\) | 1.11367 | 0.0452770 | ||||||||
\(606\) | 149.377 | 6.06802 | ||||||||
\(607\) | −18.2857 | −0.742194 | −0.371097 | − | 0.928594i | \(-0.621018\pi\) | ||||
−0.371097 | + | 0.928594i | \(0.621018\pi\) | |||||||
\(608\) | 2.45901 | 0.0997260 | ||||||||
\(609\) | −39.2473 | −1.59038 | ||||||||
\(610\) | 1.73332 | 0.0701800 | ||||||||
\(611\) | 9.86072 | 0.398922 | ||||||||
\(612\) | 244.739 | 9.89297 | ||||||||
\(613\) | −35.8606 | −1.44839 | −0.724197 | − | 0.689593i | \(-0.757789\pi\) | ||||
−0.724197 | + | 0.689593i | \(0.757789\pi\) | |||||||
\(614\) | −27.6732 | −1.11680 | ||||||||
\(615\) | 2.31812 | 0.0934758 | ||||||||
\(616\) | 39.1982 | 1.57934 | ||||||||
\(617\) | 29.4296 | 1.18479 | 0.592395 | − | 0.805648i | \(-0.298182\pi\) | ||||
0.592395 | + | 0.805648i | \(0.298182\pi\) | |||||||
\(618\) | 60.5376 | 2.43518 | ||||||||
\(619\) | 6.62785 | 0.266396 | 0.133198 | − | 0.991089i | \(-0.457475\pi\) | ||||
0.133198 | + | 0.991089i | \(0.457475\pi\) | |||||||
\(620\) | −3.58010 | −0.143780 | ||||||||
\(621\) | 128.708 | 5.16488 | ||||||||
\(622\) | 35.7359 | 1.43288 | ||||||||
\(623\) | −23.8132 | −0.954055 | ||||||||
\(624\) | −78.7576 | −3.15283 | ||||||||
\(625\) | 24.6593 | 0.986372 | ||||||||
\(626\) | 48.8638 | 1.95299 | ||||||||
\(627\) | 4.36079 | 0.174153 | ||||||||
\(628\) | −12.7679 | −0.509495 | ||||||||
\(629\) | −7.92336 | −0.315925 | ||||||||
\(630\) | −10.5409 | −0.419960 | ||||||||
\(631\) | 45.2096 | 1.79976 | 0.899882 | − | 0.436133i | \(-0.143652\pi\) | ||||
0.899882 | + | 0.436133i | \(0.143652\pi\) | |||||||
\(632\) | −53.1680 | −2.11491 | ||||||||
\(633\) | −0.439257 | −0.0174589 | ||||||||
\(634\) | 0.500962 | 0.0198958 | ||||||||
\(635\) | 2.85533 | 0.113310 | ||||||||
\(636\) | 109.889 | 4.35736 | ||||||||
\(637\) | 21.3831 | 0.847230 | ||||||||
\(638\) | 16.1408 | 0.639020 | ||||||||
\(639\) | −4.65480 | −0.184141 | ||||||||
\(640\) | −2.28738 | −0.0904168 | ||||||||
\(641\) | −7.96162 | −0.314465 | −0.157232 | − | 0.987562i | \(-0.550257\pi\) | ||||
−0.157232 | + | 0.987562i | \(0.550257\pi\) | |||||||
\(642\) | 101.610 | 4.01021 | ||||||||
\(643\) | 47.4334 | 1.87059 | 0.935295 | − | 0.353870i | \(-0.115134\pi\) | ||||
0.935295 | + | 0.353870i | \(0.115134\pi\) | |||||||
\(644\) | 121.799 | 4.79954 | ||||||||
\(645\) | 1.40281 | 0.0552358 | ||||||||
\(646\) | 12.5480 | 0.493694 | ||||||||
\(647\) | −1.27384 | −0.0500797 | −0.0250398 | − | 0.999686i | \(-0.507971\pi\) | ||||
−0.0250398 | + | 0.999686i | \(0.507971\pi\) | |||||||
\(648\) | −172.511 | −6.77689 | ||||||||
\(649\) | −24.3009 | −0.953895 | ||||||||
\(650\) | 49.3377 | 1.93518 | ||||||||
\(651\) | 63.8206 | 2.50133 | ||||||||
\(652\) | 54.2688 | 2.12533 | ||||||||
\(653\) | −5.96234 | −0.233324 | −0.116662 | − | 0.993172i | \(-0.537219\pi\) | ||||
−0.116662 | + | 0.993172i | \(0.537219\pi\) | |||||||
\(654\) | 23.7022 | 0.926829 | ||||||||
\(655\) | −2.16454 | −0.0845757 | ||||||||
\(656\) | 28.2189 | 1.10176 | ||||||||
\(657\) | −66.8710 | −2.60889 | ||||||||
\(658\) | 22.1792 | 0.864637 | ||||||||
\(659\) | 8.90616 | 0.346935 | 0.173467 | − | 0.984840i | \(-0.444503\pi\) | ||||
0.173467 | + | 0.984840i | \(0.444503\pi\) | |||||||
\(660\) | 4.09236 | 0.159295 | ||||||||
\(661\) | −17.6859 | −0.687903 | −0.343951 | − | 0.938987i | \(-0.611766\pi\) | ||||
−0.343951 | + | 0.938987i | \(0.611766\pi\) | |||||||
\(662\) | 56.6837 | 2.20307 | ||||||||
\(663\) | −93.3277 | −3.62455 | ||||||||
\(664\) | −11.6885 | −0.453603 | ||||||||
\(665\) | −0.369558 | −0.0143308 | ||||||||
\(666\) | 21.8875 | 0.848122 | ||||||||
\(667\) | 26.9622 | 1.04398 | ||||||||
\(668\) | 55.4624 | 2.14591 | ||||||||
\(669\) | −20.3701 | −0.787553 | ||||||||
\(670\) | −4.76330 | −0.184022 | ||||||||
\(671\) | 8.68944 | 0.335452 | ||||||||
\(672\) | −41.1372 | −1.58690 | ||||||||
\(673\) | 30.3014 | 1.16803 | 0.584017 | − | 0.811741i | \(-0.301480\pi\) | ||||
0.584017 | + | 0.811741i | \(0.301480\pi\) | |||||||
\(674\) | −27.5672 | −1.06185 | ||||||||
\(675\) | 80.1885 | 3.08646 | ||||||||
\(676\) | 10.9631 | 0.421659 | ||||||||
\(677\) | −40.9957 | −1.57559 | −0.787797 | − | 0.615936i | \(-0.788778\pi\) | ||||
−0.787797 | + | 0.615936i | \(0.788778\pi\) | |||||||
\(678\) | −73.4469 | −2.82071 | ||||||||
\(679\) | 32.7594 | 1.25719 | ||||||||
\(680\) | 6.33049 | 0.242763 | ||||||||
\(681\) | 19.1138 | 0.732443 | ||||||||
\(682\) | −26.2468 | −1.00504 | ||||||||
\(683\) | 16.8091 | 0.643182 | 0.321591 | − | 0.946879i | \(-0.395782\pi\) | ||||
0.321591 | + | 0.946879i | \(0.395782\pi\) | |||||||
\(684\) | −23.7024 | −0.906285 | ||||||||
\(685\) | −1.81929 | −0.0695114 | ||||||||
\(686\) | −13.9605 | −0.533015 | ||||||||
\(687\) | 54.9591 | 2.09682 | ||||||||
\(688\) | 17.0767 | 0.651043 | ||||||||
\(689\) | −30.3537 | −1.15639 | ||||||||
\(690\) | 9.99706 | 0.380582 | ||||||||
\(691\) | −6.08506 | −0.231487 | −0.115743 | − | 0.993279i | \(-0.536925\pi\) | ||||
−0.115743 | + | 0.993279i | \(0.536925\pi\) | |||||||
\(692\) | 106.155 | 4.03541 | ||||||||
\(693\) | −52.8434 | −2.00736 | ||||||||
\(694\) | 9.88389 | 0.375187 | ||||||||
\(695\) | 1.47480 | 0.0559423 | ||||||||
\(696\) | −65.1111 | −2.46803 | ||||||||
\(697\) | 33.4394 | 1.26661 | ||||||||
\(698\) | −74.3581 | −2.81450 | ||||||||
\(699\) | −25.2044 | −0.953319 | ||||||||
\(700\) | 75.8837 | 2.86814 | ||||||||
\(701\) | −1.13901 | −0.0430199 | −0.0215100 | − | 0.999769i | \(-0.506847\pi\) | ||||
−0.0215100 | + | 0.999769i | \(0.506847\pi\) | |||||||
\(702\) | 159.702 | 6.02757 | ||||||||
\(703\) | 0.767361 | 0.0289416 | ||||||||
\(704\) | −6.11766 | −0.230568 | ||||||||
\(705\) | 1.24482 | 0.0468828 | ||||||||
\(706\) | 15.3958 | 0.579430 | ||||||||
\(707\) | −63.4619 | −2.38673 | ||||||||
\(708\) | 182.347 | 6.85302 | ||||||||
\(709\) | −23.6107 | −0.886718 | −0.443359 | − | 0.896344i | \(-0.646213\pi\) | ||||
−0.443359 | + | 0.896344i | \(0.646213\pi\) | |||||||
\(710\) | −0.223966 | −0.00840528 | ||||||||
\(711\) | 71.6762 | 2.68807 | ||||||||
\(712\) | −39.5060 | −1.48055 | ||||||||
\(713\) | −43.8436 | −1.64196 | ||||||||
\(714\) | −209.918 | −7.85597 | ||||||||
\(715\) | −1.13040 | −0.0422747 | ||||||||
\(716\) | −85.4406 | −3.19307 | ||||||||
\(717\) | −39.1754 | −1.46303 | ||||||||
\(718\) | 15.9966 | 0.596989 | ||||||||
\(719\) | −30.2433 | −1.12789 | −0.563943 | − | 0.825813i | \(-0.690716\pi\) | ||||
−0.563943 | + | 0.825813i | \(0.690716\pi\) | |||||||
\(720\) | −7.20184 | −0.268397 | ||||||||
\(721\) | −25.7190 | −0.957827 | ||||||||
\(722\) | 46.5697 | 1.73314 | ||||||||
\(723\) | 16.3141 | 0.606729 | ||||||||
\(724\) | 10.0054 | 0.371847 | ||||||||
\(725\) | 16.7981 | 0.623867 | ||||||||
\(726\) | −61.2650 | −2.27376 | ||||||||
\(727\) | −21.8659 | −0.810961 | −0.405480 | − | 0.914104i | \(-0.632896\pi\) | ||||
−0.405480 | + | 0.914104i | \(0.632896\pi\) | |||||||
\(728\) | 81.2460 | 3.01118 | ||||||||
\(729\) | 73.1123 | 2.70786 | ||||||||
\(730\) | −3.21750 | −0.119085 | ||||||||
\(731\) | 20.2359 | 0.748452 | ||||||||
\(732\) | −65.2030 | −2.40997 | ||||||||
\(733\) | −5.06688 | −0.187149 | −0.0935747 | − | 0.995612i | \(-0.529829\pi\) | ||||
−0.0935747 | + | 0.995612i | \(0.529829\pi\) | |||||||
\(734\) | −59.3216 | −2.18960 | ||||||||
\(735\) | 2.69942 | 0.0995697 | ||||||||
\(736\) | 28.2605 | 1.04170 | ||||||||
\(737\) | −23.8793 | −0.879604 | ||||||||
\(738\) | −92.3730 | −3.40030 | ||||||||
\(739\) | 39.1473 | 1.44006 | 0.720028 | − | 0.693945i | \(-0.244129\pi\) | ||||
0.720028 | + | 0.693945i | \(0.244129\pi\) | |||||||
\(740\) | 0.720125 | 0.0264723 | ||||||||
\(741\) | 9.03859 | 0.332041 | ||||||||
\(742\) | −68.2732 | −2.50639 | ||||||||
\(743\) | −1.86043 | −0.0682525 | −0.0341263 | − | 0.999418i | \(-0.510865\pi\) | ||||
−0.0341263 | + | 0.999418i | \(0.510865\pi\) | |||||||
\(744\) | 105.878 | 3.88168 | ||||||||
\(745\) | 2.39216 | 0.0876420 | ||||||||
\(746\) | 95.5469 | 3.49822 | ||||||||
\(747\) | 15.7574 | 0.576534 | ||||||||
\(748\) | 59.0331 | 2.15847 | ||||||||
\(749\) | −43.1682 | −1.57733 | ||||||||
\(750\) | 12.4853 | 0.455899 | ||||||||
\(751\) | −20.2295 | −0.738185 | −0.369092 | − | 0.929393i | \(-0.620331\pi\) | ||||
−0.369092 | + | 0.929393i | \(0.620331\pi\) | |||||||
\(752\) | 15.1535 | 0.552590 | ||||||||
\(753\) | −91.5116 | −3.33487 | ||||||||
\(754\) | 33.4549 | 1.21836 | ||||||||
\(755\) | −1.21060 | −0.0440581 | ||||||||
\(756\) | 245.630 | 8.93347 | ||||||||
\(757\) | 38.7283 | 1.40761 | 0.703803 | − | 0.710396i | \(-0.251484\pi\) | ||||
0.703803 | + | 0.710396i | \(0.251484\pi\) | |||||||
\(758\) | −4.02675 | −0.146258 | ||||||||
\(759\) | 50.1170 | 1.81913 | ||||||||
\(760\) | −0.613094 | −0.0222393 | ||||||||
\(761\) | 5.68803 | 0.206191 | 0.103095 | − | 0.994671i | \(-0.467125\pi\) | ||||
0.103095 | + | 0.994671i | \(0.467125\pi\) | |||||||
\(762\) | −157.077 | −5.69032 | ||||||||
\(763\) | −10.0697 | −0.364549 | ||||||||
\(764\) | −4.03514 | −0.145986 | ||||||||
\(765\) | −8.53418 | −0.308554 | ||||||||
\(766\) | 36.7205 | 1.32677 | ||||||||
\(767\) | −50.3684 | −1.81870 | ||||||||
\(768\) | 104.607 | 3.77467 | ||||||||
\(769\) | 18.5730 | 0.669758 | 0.334879 | − | 0.942261i | \(-0.391305\pi\) | ||||
0.334879 | + | 0.942261i | \(0.391305\pi\) | |||||||
\(770\) | −2.54256 | −0.0916276 | ||||||||
\(771\) | −60.2529 | −2.16995 | ||||||||
\(772\) | 53.1494 | 1.91289 | ||||||||
\(773\) | −28.3628 | −1.02014 | −0.510069 | − | 0.860133i | \(-0.670380\pi\) | ||||
−0.510069 | + | 0.860133i | \(0.670380\pi\) | |||||||
\(774\) | −55.8996 | −2.00927 | ||||||||
\(775\) | −27.3157 | −0.981209 | ||||||||
\(776\) | 54.3477 | 1.95097 | ||||||||
\(777\) | −12.8373 | −0.460536 | ||||||||
\(778\) | 45.4222 | 1.62846 | ||||||||
\(779\) | −3.23854 | −0.116033 | ||||||||
\(780\) | 8.48221 | 0.303712 | ||||||||
\(781\) | −1.12278 | −0.0401762 | ||||||||
\(782\) | 144.210 | 5.15693 | ||||||||
\(783\) | 54.3743 | 1.94318 | ||||||||
\(784\) | 32.8606 | 1.17359 | ||||||||
\(785\) | 0.445225 | 0.0158907 | ||||||||
\(786\) | 119.076 | 4.24729 | ||||||||
\(787\) | 12.7290 | 0.453740 | 0.226870 | − | 0.973925i | \(-0.427151\pi\) | ||||
0.226870 | + | 0.973925i | \(0.427151\pi\) | |||||||
\(788\) | 86.7888 | 3.09172 | ||||||||
\(789\) | −43.6044 | −1.55236 | ||||||||
\(790\) | 3.44870 | 0.122699 | ||||||||
\(791\) | 31.2035 | 1.10947 | ||||||||
\(792\) | −87.6670 | −3.11511 | ||||||||
\(793\) | 18.0106 | 0.639574 | ||||||||
\(794\) | −6.57191 | −0.233228 | ||||||||
\(795\) | −3.83188 | −0.135903 | ||||||||
\(796\) | −57.1143 | −2.02436 | ||||||||
\(797\) | −1.95301 | −0.0691791 | −0.0345895 | − | 0.999402i | \(-0.511012\pi\) | ||||
−0.0345895 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(798\) | 20.3301 | 0.719677 | ||||||||
\(799\) | 17.9569 | 0.635268 | ||||||||
\(800\) | 17.6070 | 0.622503 | ||||||||
\(801\) | 53.2583 | 1.88179 | ||||||||
\(802\) | 41.4584 | 1.46395 | ||||||||
\(803\) | −16.1299 | −0.569211 | ||||||||
\(804\) | 179.183 | 6.31929 | ||||||||
\(805\) | −4.24719 | −0.149694 | ||||||||
\(806\) | −54.4016 | −1.91621 | ||||||||
\(807\) | −0.929932 | −0.0327352 | ||||||||
\(808\) | −105.283 | −3.70385 | ||||||||
\(809\) | −17.4774 | −0.614471 | −0.307236 | − | 0.951633i | \(-0.599404\pi\) | ||||
−0.307236 | + | 0.951633i | \(0.599404\pi\) | |||||||
\(810\) | 11.1898 | 0.393170 | ||||||||
\(811\) | −52.0046 | −1.82613 | −0.913064 | − | 0.407815i | \(-0.866291\pi\) | ||||
−0.913064 | + | 0.407815i | \(0.866291\pi\) | |||||||
\(812\) | 51.4553 | 1.80573 | ||||||||
\(813\) | 61.3713 | 2.15238 | ||||||||
\(814\) | 5.27946 | 0.185045 | ||||||||
\(815\) | −1.89239 | −0.0662874 | ||||||||
\(816\) | −143.421 | −5.02076 | ||||||||
\(817\) | −1.95980 | −0.0685649 | ||||||||
\(818\) | 41.1753 | 1.43966 | ||||||||
\(819\) | −109.528 | −3.82723 | ||||||||
\(820\) | −3.03919 | −0.106133 | ||||||||
\(821\) | −39.9260 | −1.39343 | −0.696713 | − | 0.717350i | \(-0.745355\pi\) | ||||
−0.696713 | + | 0.717350i | \(0.745355\pi\) | |||||||
\(822\) | 100.082 | 3.49078 | ||||||||
\(823\) | −48.5794 | −1.69337 | −0.846686 | − | 0.532093i | \(-0.821406\pi\) | ||||
−0.846686 | + | 0.532093i | \(0.821406\pi\) | |||||||
\(824\) | −42.6678 | −1.48640 | ||||||||
\(825\) | 31.2242 | 1.08709 | ||||||||
\(826\) | −113.291 | −3.94191 | ||||||||
\(827\) | 29.6403 | 1.03069 | 0.515347 | − | 0.856982i | \(-0.327663\pi\) | ||||
0.515347 | + | 0.856982i | \(0.327663\pi\) | |||||||
\(828\) | −272.404 | −9.46668 | ||||||||
\(829\) | −18.4186 | −0.639704 | −0.319852 | − | 0.947468i | \(-0.603633\pi\) | ||||
−0.319852 | + | 0.947468i | \(0.603633\pi\) | |||||||
\(830\) | 0.758168 | 0.0263164 | ||||||||
\(831\) | 82.2413 | 2.85292 | ||||||||
\(832\) | −12.6801 | −0.439602 | ||||||||
\(833\) | 38.9398 | 1.34918 | ||||||||
\(834\) | −81.1315 | −2.80935 | ||||||||
\(835\) | −1.93401 | −0.0669291 | ||||||||
\(836\) | −5.71724 | −0.197735 | ||||||||
\(837\) | −88.4188 | −3.05620 | ||||||||
\(838\) | −79.2298 | −2.73695 | ||||||||
\(839\) | −37.7087 | −1.30185 | −0.650925 | − | 0.759142i | \(-0.725619\pi\) | ||||
−0.650925 | + | 0.759142i | \(0.725619\pi\) | |||||||
\(840\) | 10.2566 | 0.353885 | ||||||||
\(841\) | −17.6095 | −0.607224 | ||||||||
\(842\) | 22.5964 | 0.778724 | ||||||||
\(843\) | 40.8414 | 1.40665 | ||||||||
\(844\) | 0.575890 | 0.0198229 | ||||||||
\(845\) | −0.382291 | −0.0131512 | ||||||||
\(846\) | −49.6040 | −1.70542 | ||||||||
\(847\) | 26.0281 | 0.894336 | ||||||||
\(848\) | −46.6461 | −1.60183 | ||||||||
\(849\) | 70.6185 | 2.42362 | ||||||||
\(850\) | 89.8463 | 3.08170 | ||||||||
\(851\) | 8.81901 | 0.302312 | ||||||||
\(852\) | 8.42501 | 0.288636 | ||||||||
\(853\) | −13.2943 | −0.455188 | −0.227594 | − | 0.973756i | \(-0.573086\pi\) | ||||
−0.227594 | + | 0.973756i | \(0.573086\pi\) | |||||||
\(854\) | 40.5103 | 1.38623 | ||||||||
\(855\) | 0.826517 | 0.0282663 | ||||||||
\(856\) | −71.6159 | −2.44778 | ||||||||
\(857\) | −9.90941 | −0.338499 | −0.169250 | − | 0.985573i | \(-0.554134\pi\) | ||||
−0.169250 | + | 0.985573i | \(0.554134\pi\) | |||||||
\(858\) | 62.1857 | 2.12298 | ||||||||
\(859\) | 23.5268 | 0.802725 | 0.401362 | − | 0.915919i | \(-0.368537\pi\) | ||||
0.401362 | + | 0.915919i | \(0.368537\pi\) | |||||||
\(860\) | −1.83917 | −0.0627151 | ||||||||
\(861\) | 54.1781 | 1.84638 | ||||||||
\(862\) | −91.7434 | −3.12479 | ||||||||
\(863\) | 42.0676 | 1.43200 | 0.715999 | − | 0.698101i | \(-0.245971\pi\) | ||||
0.715999 | + | 0.698101i | \(0.245971\pi\) | |||||||
\(864\) | 56.9926 | 1.93893 | ||||||||
\(865\) | −3.70169 | −0.125861 | ||||||||
\(866\) | 24.0547 | 0.817413 | ||||||||
\(867\) | −113.871 | −3.86726 | ||||||||
\(868\) | −83.6723 | −2.84002 | ||||||||
\(869\) | 17.2889 | 0.586487 | ||||||||
\(870\) | 4.22338 | 0.143186 | ||||||||
\(871\) | −49.4944 | −1.67705 | ||||||||
\(872\) | −16.7057 | −0.565725 | ||||||||
\(873\) | −73.2666 | −2.47970 | ||||||||
\(874\) | −13.9664 | −0.472421 | ||||||||
\(875\) | −5.30431 | −0.179319 | ||||||||
\(876\) | 121.034 | 4.08936 | ||||||||
\(877\) | −24.8528 | −0.839219 | −0.419610 | − | 0.907705i | \(-0.637833\pi\) | ||||
−0.419610 | + | 0.907705i | \(0.637833\pi\) | |||||||
\(878\) | 19.8551 | 0.670077 | ||||||||
\(879\) | 82.7555 | 2.79127 | ||||||||
\(880\) | −1.73715 | −0.0585593 | ||||||||
\(881\) | 35.8262 | 1.20702 | 0.603508 | − | 0.797357i | \(-0.293769\pi\) | ||||
0.603508 | + | 0.797357i | \(0.293769\pi\) | |||||||
\(882\) | −107.567 | −3.62197 | ||||||||
\(883\) | −6.43434 | −0.216533 | −0.108266 | − | 0.994122i | \(-0.534530\pi\) | ||||
−0.108266 | + | 0.994122i | \(0.534530\pi\) | |||||||
\(884\) | 122.358 | 4.11534 | ||||||||
\(885\) | −6.35855 | −0.213740 | ||||||||
\(886\) | −94.7253 | −3.18236 | ||||||||
\(887\) | 29.2088 | 0.980735 | 0.490367 | − | 0.871516i | \(-0.336863\pi\) | ||||
0.490367 | + | 0.871516i | \(0.336863\pi\) | |||||||
\(888\) | −21.2970 | −0.714682 | ||||||||
\(889\) | 66.7335 | 2.23817 | ||||||||
\(890\) | 2.56252 | 0.0858959 | ||||||||
\(891\) | 56.0965 | 1.87930 | ||||||||
\(892\) | 26.7063 | 0.894193 | ||||||||
\(893\) | −1.73908 | −0.0581963 | ||||||||
\(894\) | −131.597 | −4.40128 | ||||||||
\(895\) | 2.97936 | 0.0995892 | ||||||||
\(896\) | −53.4596 | −1.78596 | ||||||||
\(897\) | 103.877 | 3.46836 | ||||||||
\(898\) | −11.7587 | −0.392393 | ||||||||
\(899\) | −18.5223 | −0.617752 | ||||||||
\(900\) | −169.714 | −5.65714 | ||||||||
\(901\) | −55.2757 | −1.84150 | ||||||||
\(902\) | −22.2812 | −0.741883 | ||||||||
\(903\) | 32.7859 | 1.09105 | ||||||||
\(904\) | 51.7665 | 1.72173 | ||||||||
\(905\) | −0.348894 | −0.0115976 | ||||||||
\(906\) | 66.5973 | 2.21255 | ||||||||
\(907\) | 53.5598 | 1.77842 | 0.889212 | − | 0.457496i | \(-0.151254\pi\) | ||||
0.889212 | + | 0.457496i | \(0.151254\pi\) | |||||||
\(908\) | −25.0593 | −0.831621 | ||||||||
\(909\) | 141.933 | 4.70762 | ||||||||
\(910\) | −5.26996 | −0.174697 | ||||||||
\(911\) | −2.01259 | −0.0666799 | −0.0333400 | − | 0.999444i | \(-0.510614\pi\) | ||||
−0.0333400 | + | 0.999444i | \(0.510614\pi\) | |||||||
\(912\) | 13.8901 | 0.459946 | ||||||||
\(913\) | 3.80083 | 0.125789 | ||||||||
\(914\) | −82.8125 | −2.73919 | ||||||||
\(915\) | 2.27367 | 0.0751651 | ||||||||
\(916\) | −72.0543 | −2.38074 | ||||||||
\(917\) | −50.5887 | −1.67059 | ||||||||
\(918\) | 290.826 | 9.59868 | ||||||||
\(919\) | 57.3266 | 1.89103 | 0.945515 | − | 0.325579i | \(-0.105559\pi\) | ||||
0.945515 | + | 0.325579i | \(0.105559\pi\) | |||||||
\(920\) | −7.04608 | −0.232302 | ||||||||
\(921\) | −36.3001 | −1.19613 | ||||||||
\(922\) | 64.0597 | 2.10969 | ||||||||
\(923\) | −2.32718 | −0.0766001 | ||||||||
\(924\) | 95.6446 | 3.14648 | ||||||||
\(925\) | 5.49447 | 0.180657 | ||||||||
\(926\) | −35.3678 | −1.16226 | ||||||||
\(927\) | 57.5208 | 1.88923 | ||||||||
\(928\) | 11.9390 | 0.391917 | ||||||||
\(929\) | 4.28569 | 0.140609 | 0.0703044 | − | 0.997526i | \(-0.477603\pi\) | ||||
0.0703044 | + | 0.997526i | \(0.477603\pi\) | |||||||
\(930\) | −6.86770 | −0.225201 | ||||||||
\(931\) | −3.77123 | −0.123597 | ||||||||
\(932\) | 33.0444 | 1.08241 | ||||||||
\(933\) | 46.8763 | 1.53466 | ||||||||
\(934\) | 96.7931 | 3.16717 | ||||||||
\(935\) | −2.05852 | −0.0673208 | ||||||||
\(936\) | −181.707 | −5.93928 | ||||||||
\(937\) | −6.00355 | −0.196127 | −0.0980637 | − | 0.995180i | \(-0.531265\pi\) | ||||
−0.0980637 | + | 0.995180i | \(0.531265\pi\) | |||||||
\(938\) | −111.325 | −3.63490 | ||||||||
\(939\) | 64.0967 | 2.09172 | ||||||||
\(940\) | −1.63203 | −0.0532311 | ||||||||
\(941\) | −19.1884 | −0.625524 | −0.312762 | − | 0.949831i | \(-0.601254\pi\) | ||||
−0.312762 | + | 0.949831i | \(0.601254\pi\) | |||||||
\(942\) | −24.4927 | −0.798014 | ||||||||
\(943\) | −37.2194 | −1.21203 | ||||||||
\(944\) | −77.4038 | −2.51928 | ||||||||
\(945\) | −8.56526 | −0.278628 | ||||||||
\(946\) | −13.4835 | −0.438386 | ||||||||
\(947\) | −10.2630 | −0.333503 | −0.166751 | − | 0.985999i | \(-0.553328\pi\) | ||||
−0.166751 | + | 0.985999i | \(0.553328\pi\) | |||||||
\(948\) | −129.731 | −4.21347 | ||||||||
\(949\) | −33.4324 | −1.08526 | ||||||||
\(950\) | −8.70143 | −0.282312 | ||||||||
\(951\) | 0.657133 | 0.0213090 | ||||||||
\(952\) | 147.953 | 4.79519 | ||||||||
\(953\) | −37.5809 | −1.21737 | −0.608683 | − | 0.793414i | \(-0.708302\pi\) | ||||
−0.608683 | + | 0.793414i | \(0.708302\pi\) | |||||||
\(954\) | 152.693 | 4.94363 | ||||||||
\(955\) | 0.140708 | 0.00455320 | ||||||||
\(956\) | 51.3611 | 1.66114 | ||||||||
\(957\) | 21.1725 | 0.684411 | ||||||||
\(958\) | −1.57982 | −0.0510418 | ||||||||
\(959\) | −42.5195 | −1.37303 | ||||||||
\(960\) | −1.60074 | −0.0516637 | ||||||||
\(961\) | −0.880679 | −0.0284090 | ||||||||
\(962\) | 10.9427 | 0.352807 | ||||||||
\(963\) | 96.5460 | 3.11115 | ||||||||
\(964\) | −21.3887 | −0.688884 | ||||||||
\(965\) | −1.85335 | −0.0596615 | ||||||||
\(966\) | 233.646 | 7.51745 | ||||||||
\(967\) | −9.60114 | −0.308752 | −0.154376 | − | 0.988012i | \(-0.549337\pi\) | ||||
−0.154376 | + | 0.988012i | \(0.549337\pi\) | |||||||
\(968\) | 43.1805 | 1.38787 | ||||||||
\(969\) | 16.4597 | 0.528763 | ||||||||
\(970\) | −3.52522 | −0.113188 | ||||||||
\(971\) | −17.3263 | −0.556027 | −0.278013 | − | 0.960577i | \(-0.589676\pi\) | ||||
−0.278013 | + | 0.960577i | \(0.589676\pi\) | |||||||
\(972\) | −211.882 | −6.79612 | ||||||||
\(973\) | 34.4683 | 1.10500 | ||||||||
\(974\) | 110.101 | 3.52788 | ||||||||
\(975\) | 64.7183 | 2.07264 | ||||||||
\(976\) | 27.6777 | 0.885943 | ||||||||
\(977\) | −3.98944 | −0.127633 | −0.0638167 | − | 0.997962i | \(-0.520327\pi\) | ||||
−0.0638167 | + | 0.997962i | \(0.520327\pi\) | |||||||
\(978\) | 104.104 | 3.32887 | ||||||||
\(979\) | 12.8464 | 0.410572 | ||||||||
\(980\) | −3.53909 | −0.113052 | ||||||||
\(981\) | 22.5210 | 0.719041 | ||||||||
\(982\) | 90.2510 | 2.88003 | ||||||||
\(983\) | 46.5343 | 1.48421 | 0.742106 | − | 0.670282i | \(-0.233827\pi\) | ||||
0.742106 | + | 0.670282i | \(0.233827\pi\) | |||||||
\(984\) | 89.8812 | 2.86531 | ||||||||
\(985\) | −3.02638 | −0.0964284 | ||||||||
\(986\) | 60.9231 | 1.94019 | ||||||||
\(987\) | 29.0934 | 0.926054 | ||||||||
\(988\) | −11.8501 | −0.377002 | ||||||||
\(989\) | −22.5233 | −0.716201 | ||||||||
\(990\) | 5.68645 | 0.180727 | ||||||||
\(991\) | 13.8831 | 0.441010 | 0.220505 | − | 0.975386i | \(-0.429230\pi\) | ||||
0.220505 | + | 0.975386i | \(0.429230\pi\) | |||||||
\(992\) | −19.4142 | −0.616401 | ||||||||
\(993\) | 74.3544 | 2.35956 | ||||||||
\(994\) | −5.23442 | −0.166026 | ||||||||
\(995\) | 1.99161 | 0.0631383 | ||||||||
\(996\) | −28.5203 | −0.903701 | ||||||||
\(997\) | 16.2041 | 0.513190 | 0.256595 | − | 0.966519i | \(-0.417399\pi\) | ||||
0.256595 | + | 0.966519i | \(0.417399\pi\) | |||||||
\(998\) | 65.2891 | 2.06669 | ||||||||
\(999\) | 17.7852 | 0.562698 |
(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 | 4013.2.a.b.1.13 | ✓ | 157 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4013.2.a.b.1.13 | ✓ | 157 | 1.1 | even | 1 | trivial |