Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32315 | −1.64271 | −0.821356 | − | 0.570416i | \(-0.806782\pi\) | ||||
−0.821356 | + | 0.570416i | \(0.806782\pi\) | |||||||
\(3\) | 1.73935 | 1.00421 | 0.502107 | − | 0.864806i | \(-0.332558\pi\) | ||||
0.502107 | + | 0.864806i | \(0.332558\pi\) | |||||||
\(4\) | 3.39700 | 1.69850 | ||||||||
\(5\) | 3.06159 | 1.36918 | 0.684592 | − | 0.728926i | \(-0.259980\pi\) | ||||
0.684592 | + | 0.728926i | \(0.259980\pi\) | |||||||
\(6\) | −4.04076 | −1.64963 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.24544 | −1.14744 | ||||||||
\(9\) | 0.0253336 | 0.00844452 | ||||||||
\(10\) | −7.11252 | −2.24918 | ||||||||
\(11\) | 2.06097 | 0.621404 | 0.310702 | − | 0.950507i | \(-0.399436\pi\) | ||||
0.310702 | + | 0.950507i | \(0.399436\pi\) | |||||||
\(12\) | 5.90857 | 1.70566 | ||||||||
\(13\) | −0.884192 | −0.245231 | −0.122615 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122615 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(14\) | 2.32315 | 0.620887 | ||||||||
\(15\) | 5.32517 | 1.37495 | ||||||||
\(16\) | 0.745624 | 0.186406 | ||||||||
\(17\) | 4.69427 | 1.13853 | 0.569264 | − | 0.822155i | \(-0.307228\pi\) | ||||
0.569264 | + | 0.822155i | \(0.307228\pi\) | |||||||
\(18\) | −0.0588535 | −0.0138719 | ||||||||
\(19\) | −6.61397 | −1.51735 | −0.758675 | − | 0.651470i | \(-0.774153\pi\) | ||||
−0.758675 | + | 0.651470i | \(0.774153\pi\) | |||||||
\(20\) | 10.4002 | 2.32556 | ||||||||
\(21\) | −1.73935 | −0.379557 | ||||||||
\(22\) | −4.78792 | −1.02079 | ||||||||
\(23\) | 6.07691 | 1.26712 | 0.633561 | − | 0.773692i | \(-0.281592\pi\) | ||||
0.633561 | + | 0.773692i | \(0.281592\pi\) | |||||||
\(24\) | −5.64495 | −1.15227 | ||||||||
\(25\) | 4.37333 | 0.874666 | ||||||||
\(26\) | 2.05411 | 0.402843 | ||||||||
\(27\) | −5.17398 | −0.995733 | ||||||||
\(28\) | −3.39700 | −0.641973 | ||||||||
\(29\) | −5.10968 | −0.948843 | −0.474422 | − | 0.880298i | \(-0.657343\pi\) | ||||
−0.474422 | + | 0.880298i | \(0.657343\pi\) | |||||||
\(30\) | −12.3711 | −2.25865 | ||||||||
\(31\) | −7.85495 | −1.41079 | −0.705395 | − | 0.708814i | \(-0.749230\pi\) | ||||
−0.705395 | + | 0.708814i | \(0.749230\pi\) | |||||||
\(32\) | 4.75869 | 0.841225 | ||||||||
\(33\) | 3.58474 | 0.624023 | ||||||||
\(34\) | −10.9055 | −1.87027 | ||||||||
\(35\) | −3.06159 | −0.517503 | ||||||||
\(36\) | 0.0860582 | 0.0143430 | ||||||||
\(37\) | −9.91398 | −1.62985 | −0.814925 | − | 0.579567i | \(-0.803222\pi\) | ||||
−0.814925 | + | 0.579567i | \(0.803222\pi\) | |||||||
\(38\) | 15.3652 | 2.49257 | ||||||||
\(39\) | −1.53792 | −0.246264 | ||||||||
\(40\) | −9.93621 | −1.57105 | ||||||||
\(41\) | −1.44396 | −0.225509 | −0.112755 | − | 0.993623i | \(-0.535967\pi\) | ||||
−0.112755 | + | 0.993623i | \(0.535967\pi\) | |||||||
\(42\) | 4.04076 | 0.623503 | ||||||||
\(43\) | −10.0263 | −1.52900 | −0.764502 | − | 0.644622i | \(-0.777015\pi\) | ||||
−0.764502 | + | 0.644622i | \(0.777015\pi\) | |||||||
\(44\) | 7.00111 | 1.05546 | ||||||||
\(45\) | 0.0775609 | 0.0115621 | ||||||||
\(46\) | −14.1175 | −2.08152 | ||||||||
\(47\) | −10.0511 | −1.46610 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(48\) | 1.29690 | 0.187191 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −10.1599 | −1.43682 | ||||||||
\(51\) | 8.16497 | 1.14332 | ||||||||
\(52\) | −3.00360 | −0.416525 | ||||||||
\(53\) | −2.62722 | −0.360877 | −0.180438 | − | 0.983586i | \(-0.557752\pi\) | ||||
−0.180438 | + | 0.983586i | \(0.557752\pi\) | |||||||
\(54\) | 12.0199 | 1.63570 | ||||||||
\(55\) | 6.30983 | 0.850817 | ||||||||
\(56\) | 3.24544 | 0.433690 | ||||||||
\(57\) | −11.5040 | −1.52374 | ||||||||
\(58\) | 11.8705 | 1.55868 | ||||||||
\(59\) | −5.96037 | −0.775974 | −0.387987 | − | 0.921665i | \(-0.626829\pi\) | ||||
−0.387987 | + | 0.921665i | \(0.626829\pi\) | |||||||
\(60\) | 18.0896 | 2.33536 | ||||||||
\(61\) | −8.54092 | −1.09355 | −0.546777 | − | 0.837279i | \(-0.684145\pi\) | ||||
−0.546777 | + | 0.837279i | \(0.684145\pi\) | |||||||
\(62\) | 18.2482 | 2.31752 | ||||||||
\(63\) | −0.0253336 | −0.00319173 | ||||||||
\(64\) | −12.5464 | −1.56830 | ||||||||
\(65\) | −2.70703 | −0.335766 | ||||||||
\(66\) | −8.32786 | −1.02509 | ||||||||
\(67\) | 7.99440 | 0.976671 | 0.488335 | − | 0.872656i | \(-0.337604\pi\) | ||||
0.488335 | + | 0.872656i | \(0.337604\pi\) | |||||||
\(68\) | 15.9465 | 1.93379 | ||||||||
\(69\) | 10.5699 | 1.27246 | ||||||||
\(70\) | 7.11252 | 0.850108 | ||||||||
\(71\) | −5.11844 | −0.607446 | −0.303723 | − | 0.952760i | \(-0.598230\pi\) | ||||
−0.303723 | + | 0.952760i | \(0.598230\pi\) | |||||||
\(72\) | −0.0822185 | −0.00968955 | ||||||||
\(73\) | −8.12457 | −0.950909 | −0.475455 | − | 0.879740i | \(-0.657716\pi\) | ||||
−0.475455 | + | 0.879740i | \(0.657716\pi\) | |||||||
\(74\) | 23.0316 | 2.67737 | ||||||||
\(75\) | 7.60675 | 0.878351 | ||||||||
\(76\) | −22.4677 | −2.57722 | ||||||||
\(77\) | −2.06097 | −0.234869 | ||||||||
\(78\) | 3.57280 | 0.404541 | ||||||||
\(79\) | −2.16221 | −0.243267 | −0.121634 | − | 0.992575i | \(-0.538813\pi\) | ||||
−0.121634 | + | 0.992575i | \(0.538813\pi\) | |||||||
\(80\) | 2.28280 | 0.255224 | ||||||||
\(81\) | −9.07536 | −1.00837 | ||||||||
\(82\) | 3.35453 | 0.370446 | ||||||||
\(83\) | 12.3065 | 1.35082 | 0.675408 | − | 0.737444i | \(-0.263967\pi\) | ||||
0.675408 | + | 0.737444i | \(0.263967\pi\) | |||||||
\(84\) | −5.90857 | −0.644678 | ||||||||
\(85\) | 14.3719 | 1.55885 | ||||||||
\(86\) | 23.2927 | 2.51171 | ||||||||
\(87\) | −8.88751 | −0.952841 | ||||||||
\(88\) | −6.68874 | −0.713022 | ||||||||
\(89\) | 6.23287 | 0.660683 | 0.330341 | − | 0.943862i | \(-0.392836\pi\) | ||||
0.330341 | + | 0.943862i | \(0.392836\pi\) | |||||||
\(90\) | −0.180185 | −0.0189932 | ||||||||
\(91\) | 0.884192 | 0.0926885 | ||||||||
\(92\) | 20.6433 | 2.15221 | ||||||||
\(93\) | −13.6625 | −1.41673 | ||||||||
\(94\) | 23.3502 | 2.40839 | ||||||||
\(95\) | −20.2493 | −2.07753 | ||||||||
\(96\) | 8.27702 | 0.844770 | ||||||||
\(97\) | −12.9710 | −1.31700 | −0.658502 | − | 0.752579i | \(-0.728810\pi\) | ||||
−0.658502 | + | 0.752579i | \(0.728810\pi\) | |||||||
\(98\) | −2.32315 | −0.234673 | ||||||||
\(99\) | 0.0522116 | 0.00524746 | ||||||||
\(100\) | 14.8562 | 1.48562 | ||||||||
\(101\) | 7.47567 | 0.743857 | 0.371928 | − | 0.928261i | \(-0.378697\pi\) | ||||
0.371928 | + | 0.928261i | \(0.378697\pi\) | |||||||
\(102\) | −18.9684 | −1.87815 | ||||||||
\(103\) | −19.4840 | −1.91981 | −0.959906 | − | 0.280323i | \(-0.909558\pi\) | ||||
−0.959906 | + | 0.280323i | \(0.909558\pi\) | |||||||
\(104\) | 2.86959 | 0.281387 | ||||||||
\(105\) | −5.32517 | −0.519684 | ||||||||
\(106\) | 6.10342 | 0.592817 | ||||||||
\(107\) | 17.6296 | 1.70432 | 0.852160 | − | 0.523282i | \(-0.175293\pi\) | ||||
0.852160 | + | 0.523282i | \(0.175293\pi\) | |||||||
\(108\) | −17.5760 | −1.69125 | ||||||||
\(109\) | 6.95439 | 0.666110 | 0.333055 | − | 0.942907i | \(-0.391921\pi\) | ||||
0.333055 | + | 0.942907i | \(0.391921\pi\) | |||||||
\(110\) | −14.6586 | −1.39765 | ||||||||
\(111\) | −17.2439 | −1.63672 | ||||||||
\(112\) | −0.745624 | −0.0704549 | ||||||||
\(113\) | −8.85733 | −0.833228 | −0.416614 | − | 0.909083i | \(-0.636783\pi\) | ||||
−0.416614 | + | 0.909083i | \(0.636783\pi\) | |||||||
\(114\) | 26.7255 | 2.50307 | ||||||||
\(115\) | 18.6050 | 1.73492 | ||||||||
\(116\) | −17.3576 | −1.61161 | ||||||||
\(117\) | −0.0223997 | −0.00207085 | ||||||||
\(118\) | 13.8468 | 1.27470 | ||||||||
\(119\) | −4.69427 | −0.430323 | ||||||||
\(120\) | −17.2825 | −1.57767 | ||||||||
\(121\) | −6.75242 | −0.613857 | ||||||||
\(122\) | 19.8418 | 1.79639 | ||||||||
\(123\) | −2.51155 | −0.226459 | ||||||||
\(124\) | −26.6833 | −2.39623 | ||||||||
\(125\) | −1.91861 | −0.171605 | ||||||||
\(126\) | 0.0588535 | 0.00524309 | ||||||||
\(127\) | 10.4228 | 0.924877 | 0.462439 | − | 0.886651i | \(-0.346975\pi\) | ||||
0.462439 | + | 0.886651i | \(0.346975\pi\) | |||||||
\(128\) | 19.6297 | 1.73503 | ||||||||
\(129\) | −17.4393 | −1.53545 | ||||||||
\(130\) | 6.28883 | 0.551567 | ||||||||
\(131\) | −4.60012 | −0.401914 | −0.200957 | − | 0.979600i | \(-0.564405\pi\) | ||||
−0.200957 | + | 0.979600i | \(0.564405\pi\) | |||||||
\(132\) | 12.1774 | 1.05990 | ||||||||
\(133\) | 6.61397 | 0.573504 | ||||||||
\(134\) | −18.5721 | −1.60439 | ||||||||
\(135\) | −15.8406 | −1.36334 | ||||||||
\(136\) | −15.2350 | −1.30639 | ||||||||
\(137\) | 8.02917 | 0.685978 | 0.342989 | − | 0.939339i | \(-0.388561\pi\) | ||||
0.342989 | + | 0.939339i | \(0.388561\pi\) | |||||||
\(138\) | −24.5553 | −2.09029 | ||||||||
\(139\) | 5.45904 | 0.463030 | 0.231515 | − | 0.972831i | \(-0.425632\pi\) | ||||
0.231515 | + | 0.972831i | \(0.425632\pi\) | |||||||
\(140\) | −10.4002 | −0.878980 | ||||||||
\(141\) | −17.4824 | −1.47228 | ||||||||
\(142\) | 11.8909 | 0.997859 | ||||||||
\(143\) | −1.82229 | −0.152387 | ||||||||
\(144\) | 0.0188893 | 0.00157411 | ||||||||
\(145\) | −15.6437 | −1.29914 | ||||||||
\(146\) | 18.8746 | 1.56207 | ||||||||
\(147\) | 1.73935 | 0.143459 | ||||||||
\(148\) | −33.6778 | −2.76830 | ||||||||
\(149\) | 2.85330 | 0.233751 | 0.116876 | − | 0.993147i | \(-0.462712\pi\) | ||||
0.116876 | + | 0.993147i | \(0.462712\pi\) | |||||||
\(150\) | −17.6716 | −1.44288 | ||||||||
\(151\) | 3.17905 | 0.258707 | 0.129354 | − | 0.991599i | \(-0.458710\pi\) | ||||
0.129354 | + | 0.991599i | \(0.458710\pi\) | |||||||
\(152\) | 21.4653 | 1.74106 | ||||||||
\(153\) | 0.118923 | 0.00961432 | ||||||||
\(154\) | 4.78792 | 0.385822 | ||||||||
\(155\) | −24.0486 | −1.93163 | ||||||||
\(156\) | −5.22431 | −0.418280 | ||||||||
\(157\) | 16.4550 | 1.31325 | 0.656625 | − | 0.754217i | \(-0.271984\pi\) | ||||
0.656625 | + | 0.754217i | \(0.271984\pi\) | |||||||
\(158\) | 5.02312 | 0.399618 | ||||||||
\(159\) | −4.56966 | −0.362397 | ||||||||
\(160\) | 14.5692 | 1.15179 | ||||||||
\(161\) | −6.07691 | −0.478927 | ||||||||
\(162\) | 21.0834 | 1.65647 | ||||||||
\(163\) | −17.8968 | −1.40179 | −0.700893 | − | 0.713266i | \(-0.747215\pi\) | ||||
−0.700893 | + | 0.713266i | \(0.747215\pi\) | |||||||
\(164\) | −4.90515 | −0.383028 | ||||||||
\(165\) | 10.9750 | 0.854402 | ||||||||
\(166\) | −28.5899 | −2.21900 | ||||||||
\(167\) | −2.39694 | −0.185481 | −0.0927404 | − | 0.995690i | \(-0.529563\pi\) | ||||
−0.0927404 | + | 0.995690i | \(0.529563\pi\) | |||||||
\(168\) | 5.64495 | 0.435518 | ||||||||
\(169\) | −12.2182 | −0.939862 | ||||||||
\(170\) | −33.3881 | −2.56075 | ||||||||
\(171\) | −0.167555 | −0.0128133 | ||||||||
\(172\) | −34.0595 | −2.59701 | ||||||||
\(173\) | 24.7394 | 1.88090 | 0.940450 | − | 0.339933i | \(-0.110404\pi\) | ||||
0.940450 | + | 0.339933i | \(0.110404\pi\) | |||||||
\(174\) | 20.6470 | 1.56524 | ||||||||
\(175\) | −4.37333 | −0.330593 | ||||||||
\(176\) | 1.53671 | 0.115834 | ||||||||
\(177\) | −10.3672 | −0.779243 | ||||||||
\(178\) | −14.4799 | −1.08531 | ||||||||
\(179\) | −24.8924 | −1.86054 | −0.930272 | − | 0.366871i | \(-0.880429\pi\) | ||||
−0.930272 | + | 0.366871i | \(0.880429\pi\) | |||||||
\(180\) | 0.263475 | 0.0196382 | ||||||||
\(181\) | 6.79276 | 0.504902 | 0.252451 | − | 0.967610i | \(-0.418763\pi\) | ||||
0.252451 | + | 0.967610i | \(0.418763\pi\) | |||||||
\(182\) | −2.05411 | −0.152260 | ||||||||
\(183\) | −14.8556 | −1.09816 | ||||||||
\(184\) | −19.7222 | −1.45394 | ||||||||
\(185\) | −30.3526 | −2.23156 | ||||||||
\(186\) | 31.7399 | 2.32729 | ||||||||
\(187\) | 9.67473 | 0.707486 | ||||||||
\(188\) | −34.1436 | −2.49018 | ||||||||
\(189\) | 5.17398 | 0.376352 | ||||||||
\(190\) | 47.0420 | 3.41279 | ||||||||
\(191\) | 10.2100 | 0.738769 | 0.369384 | − | 0.929277i | \(-0.379569\pi\) | ||||
0.369384 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(192\) | −21.8225 | −1.57490 | ||||||||
\(193\) | 20.5579 | 1.47979 | 0.739895 | − | 0.672722i | \(-0.234875\pi\) | ||||
0.739895 | + | 0.672722i | \(0.234875\pi\) | |||||||
\(194\) | 30.1335 | 2.16346 | ||||||||
\(195\) | −4.70847 | −0.337181 | ||||||||
\(196\) | 3.39700 | 0.242643 | ||||||||
\(197\) | −13.8711 | −0.988277 | −0.494139 | − | 0.869383i | \(-0.664516\pi\) | ||||
−0.494139 | + | 0.869383i | \(0.664516\pi\) | |||||||
\(198\) | −0.121295 | −0.00862006 | ||||||||
\(199\) | 17.7999 | 1.26180 | 0.630900 | − | 0.775864i | \(-0.282686\pi\) | ||||
0.630900 | + | 0.775864i | \(0.282686\pi\) | |||||||
\(200\) | −14.1934 | −1.00362 | ||||||||
\(201\) | 13.9050 | 0.980786 | ||||||||
\(202\) | −17.3671 | −1.22194 | ||||||||
\(203\) | 5.10968 | 0.358629 | ||||||||
\(204\) | 27.7364 | 1.94194 | ||||||||
\(205\) | −4.42082 | −0.308764 | ||||||||
\(206\) | 45.2641 | 3.15370 | ||||||||
\(207\) | 0.153950 | 0.0107002 | ||||||||
\(208\) | −0.659275 | −0.0457125 | ||||||||
\(209\) | −13.6312 | −0.942888 | ||||||||
\(210\) | 12.3711 | 0.853690 | ||||||||
\(211\) | −17.6608 | −1.21582 | −0.607910 | − | 0.794006i | \(-0.707992\pi\) | ||||
−0.607910 | + | 0.794006i | \(0.707992\pi\) | |||||||
\(212\) | −8.92469 | −0.612950 | ||||||||
\(213\) | −8.90274 | −0.610006 | ||||||||
\(214\) | −40.9562 | −2.79970 | ||||||||
\(215\) | −30.6965 | −2.09349 | ||||||||
\(216\) | 16.7919 | 1.14254 | ||||||||
\(217\) | 7.85495 | 0.533228 | ||||||||
\(218\) | −16.1561 | −1.09423 | ||||||||
\(219\) | −14.1315 | −0.954916 | ||||||||
\(220\) | 21.4345 | 1.44511 | ||||||||
\(221\) | −4.15063 | −0.279202 | ||||||||
\(222\) | 40.0600 | 2.68865 | ||||||||
\(223\) | −4.00578 | −0.268247 | −0.134124 | − | 0.990965i | \(-0.542822\pi\) | ||||
−0.134124 | + | 0.990965i | \(0.542822\pi\) | |||||||
\(224\) | −4.75869 | −0.317953 | ||||||||
\(225\) | 0.110792 | 0.00738613 | ||||||||
\(226\) | 20.5769 | 1.36875 | ||||||||
\(227\) | 7.00929 | 0.465223 | 0.232611 | − | 0.972570i | \(-0.425273\pi\) | ||||
0.232611 | + | 0.972570i | \(0.425273\pi\) | |||||||
\(228\) | −39.0791 | −2.58808 | ||||||||
\(229\) | 4.82238 | 0.318672 | 0.159336 | − | 0.987224i | \(-0.449065\pi\) | ||||
0.159336 | + | 0.987224i | \(0.449065\pi\) | |||||||
\(230\) | −43.2221 | −2.84998 | ||||||||
\(231\) | −3.58474 | −0.235858 | ||||||||
\(232\) | 16.5832 | 1.08874 | ||||||||
\(233\) | 6.24966 | 0.409429 | 0.204714 | − | 0.978822i | \(-0.434373\pi\) | ||||
0.204714 | + | 0.978822i | \(0.434373\pi\) | |||||||
\(234\) | 0.0520378 | 0.00340182 | ||||||||
\(235\) | −30.7723 | −2.00737 | ||||||||
\(236\) | −20.2474 | −1.31799 | ||||||||
\(237\) | −3.76083 | −0.244292 | ||||||||
\(238\) | 10.9055 | 0.706897 | ||||||||
\(239\) | −17.0974 | −1.10594 | −0.552968 | − | 0.833202i | \(-0.686505\pi\) | ||||
−0.552968 | + | 0.833202i | \(0.686505\pi\) | |||||||
\(240\) | 3.97058 | 0.256300 | ||||||||
\(241\) | −16.0006 | −1.03069 | −0.515344 | − | 0.856984i | \(-0.672336\pi\) | ||||
−0.515344 | + | 0.856984i | \(0.672336\pi\) | |||||||
\(242\) | 15.6869 | 1.00839 | ||||||||
\(243\) | −0.263267 | −0.0168886 | ||||||||
\(244\) | −29.0135 | −1.85740 | ||||||||
\(245\) | 3.06159 | 0.195598 | ||||||||
\(246\) | 5.83471 | 0.372007 | ||||||||
\(247\) | 5.84802 | 0.372101 | ||||||||
\(248\) | 25.4928 | 1.61879 | ||||||||
\(249\) | 21.4053 | 1.35651 | ||||||||
\(250\) | 4.45720 | 0.281898 | ||||||||
\(251\) | 26.3702 | 1.66447 | 0.832237 | − | 0.554420i | \(-0.187060\pi\) | ||||
0.832237 | + | 0.554420i | \(0.187060\pi\) | |||||||
\(252\) | −0.0860582 | −0.00542115 | ||||||||
\(253\) | 12.5243 | 0.787396 | ||||||||
\(254\) | −24.2138 | −1.51931 | ||||||||
\(255\) | 24.9978 | 1.56542 | ||||||||
\(256\) | −20.5098 | −1.28186 | ||||||||
\(257\) | −28.8048 | −1.79680 | −0.898398 | − | 0.439181i | \(-0.855269\pi\) | ||||
−0.898398 | + | 0.439181i | \(0.855269\pi\) | |||||||
\(258\) | 40.5140 | 2.52229 | ||||||||
\(259\) | 9.91398 | 0.616025 | ||||||||
\(260\) | −9.19579 | −0.570299 | ||||||||
\(261\) | −0.129446 | −0.00801252 | ||||||||
\(262\) | 10.6867 | 0.660229 | ||||||||
\(263\) | 15.3175 | 0.944519 | 0.472260 | − | 0.881460i | \(-0.343438\pi\) | ||||
0.472260 | + | 0.881460i | \(0.343438\pi\) | |||||||
\(264\) | −11.6341 | −0.716026 | ||||||||
\(265\) | −8.04348 | −0.494107 | ||||||||
\(266\) | −15.3652 | −0.942102 | ||||||||
\(267\) | 10.8411 | 0.663466 | ||||||||
\(268\) | 27.1570 | 1.65888 | ||||||||
\(269\) | 28.8371 | 1.75823 | 0.879116 | − | 0.476608i | \(-0.158134\pi\) | ||||
0.879116 | + | 0.476608i | \(0.158134\pi\) | |||||||
\(270\) | 36.8000 | 2.23958 | ||||||||
\(271\) | −0.295646 | −0.0179592 | −0.00897961 | − | 0.999960i | \(-0.502858\pi\) | ||||
−0.00897961 | + | 0.999960i | \(0.502858\pi\) | |||||||
\(272\) | 3.50016 | 0.212228 | ||||||||
\(273\) | 1.53792 | 0.0930790 | ||||||||
\(274\) | −18.6529 | −1.12686 | ||||||||
\(275\) | 9.01328 | 0.543521 | ||||||||
\(276\) | 35.9058 | 2.16128 | ||||||||
\(277\) | 28.0470 | 1.68518 | 0.842590 | − | 0.538555i | \(-0.181030\pi\) | ||||
0.842590 | + | 0.538555i | \(0.181030\pi\) | |||||||
\(278\) | −12.6821 | −0.760624 | ||||||||
\(279\) | −0.198994 | −0.0119134 | ||||||||
\(280\) | 9.93621 | 0.593802 | ||||||||
\(281\) | −13.9797 | −0.833957 | −0.416979 | − | 0.908916i | \(-0.636911\pi\) | ||||
−0.416979 | + | 0.908916i | \(0.636911\pi\) | |||||||
\(282\) | 40.6141 | 2.41853 | ||||||||
\(283\) | 2.65985 | 0.158112 | 0.0790559 | − | 0.996870i | \(-0.474809\pi\) | ||||
0.0790559 | + | 0.996870i | \(0.474809\pi\) | |||||||
\(284\) | −17.3873 | −1.03175 | ||||||||
\(285\) | −35.2205 | −2.08628 | ||||||||
\(286\) | 4.23344 | 0.250329 | ||||||||
\(287\) | 1.44396 | 0.0852344 | ||||||||
\(288\) | 0.120554 | 0.00710374 | ||||||||
\(289\) | 5.03617 | 0.296246 | ||||||||
\(290\) | 36.3427 | 2.13411 | ||||||||
\(291\) | −22.5611 | −1.32255 | ||||||||
\(292\) | −27.5992 | −1.61512 | ||||||||
\(293\) | 25.9655 | 1.51692 | 0.758460 | − | 0.651719i | \(-0.225952\pi\) | ||||
0.758460 | + | 0.651719i | \(0.225952\pi\) | |||||||
\(294\) | −4.04076 | −0.235662 | ||||||||
\(295\) | −18.2482 | −1.06245 | ||||||||
\(296\) | 32.1753 | 1.87015 | ||||||||
\(297\) | −10.6634 | −0.618753 | ||||||||
\(298\) | −6.62862 | −0.383986 | ||||||||
\(299\) | −5.37315 | −0.310737 | ||||||||
\(300\) | 25.8401 | 1.49188 | ||||||||
\(301\) | 10.0263 | 0.577909 | ||||||||
\(302\) | −7.38539 | −0.424981 | ||||||||
\(303\) | 13.0028 | 0.746991 | ||||||||
\(304\) | −4.93154 | −0.282843 | ||||||||
\(305\) | −26.1488 | −1.49728 | ||||||||
\(306\) | −0.276274 | −0.0157936 | ||||||||
\(307\) | −7.88495 | −0.450018 | −0.225009 | − | 0.974357i | \(-0.572241\pi\) | ||||
−0.225009 | + | 0.974357i | \(0.572241\pi\) | |||||||
\(308\) | −7.00111 | −0.398925 | ||||||||
\(309\) | −33.8894 | −1.92790 | ||||||||
\(310\) | 55.8684 | 3.17311 | ||||||||
\(311\) | −31.2910 | −1.77435 | −0.887176 | − | 0.461431i | \(-0.847336\pi\) | ||||
−0.887176 | + | 0.461431i | \(0.847336\pi\) | |||||||
\(312\) | 4.99122 | 0.282572 | ||||||||
\(313\) | 5.35827 | 0.302867 | 0.151434 | − | 0.988467i | \(-0.451611\pi\) | ||||
0.151434 | + | 0.988467i | \(0.451611\pi\) | |||||||
\(314\) | −38.2273 | −2.15729 | ||||||||
\(315\) | −0.0775609 | −0.00437006 | ||||||||
\(316\) | −7.34503 | −0.413190 | ||||||||
\(317\) | 5.38115 | 0.302235 | 0.151118 | − | 0.988516i | \(-0.451713\pi\) | ||||
0.151118 | + | 0.988516i | \(0.451713\pi\) | |||||||
\(318\) | 10.6160 | 0.595314 | ||||||||
\(319\) | −10.5309 | −0.589615 | ||||||||
\(320\) | −38.4118 | −2.14729 | ||||||||
\(321\) | 30.6640 | 1.71150 | ||||||||
\(322\) | 14.1175 | 0.786740 | ||||||||
\(323\) | −31.0478 | −1.72754 | ||||||||
\(324\) | −30.8290 | −1.71272 | ||||||||
\(325\) | −3.86686 | −0.214495 | ||||||||
\(326\) | 41.5769 | 2.30273 | ||||||||
\(327\) | 12.0961 | 0.668916 | ||||||||
\(328\) | 4.68630 | 0.258757 | ||||||||
\(329\) | 10.0511 | 0.554135 | ||||||||
\(330\) | −25.4965 | −1.40354 | ||||||||
\(331\) | −4.50073 | −0.247383 | −0.123691 | − | 0.992321i | \(-0.539473\pi\) | ||||
−0.123691 | + | 0.992321i | \(0.539473\pi\) | |||||||
\(332\) | 41.8053 | 2.29436 | ||||||||
\(333\) | −0.251156 | −0.0137633 | ||||||||
\(334\) | 5.56844 | 0.304692 | ||||||||
\(335\) | 24.4756 | 1.33724 | ||||||||
\(336\) | −1.29690 | −0.0707517 | ||||||||
\(337\) | 35.8161 | 1.95103 | 0.975514 | − | 0.219935i | \(-0.0705847\pi\) | ||||
0.975514 | + | 0.219935i | \(0.0705847\pi\) | |||||||
\(338\) | 28.3847 | 1.54392 | ||||||||
\(339\) | −15.4060 | −0.836739 | ||||||||
\(340\) | 48.8215 | 2.64772 | ||||||||
\(341\) | −16.1888 | −0.876671 | ||||||||
\(342\) | 0.389256 | 0.0210485 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 32.5399 | 1.75443 | ||||||||
\(345\) | 32.3606 | 1.74223 | ||||||||
\(346\) | −57.4731 | −3.08978 | ||||||||
\(347\) | 23.7280 | 1.27378 | 0.636892 | − | 0.770953i | \(-0.280220\pi\) | ||||
0.636892 | + | 0.770953i | \(0.280220\pi\) | |||||||
\(348\) | −30.1909 | −1.61840 | ||||||||
\(349\) | 20.2816 | 1.08565 | 0.542824 | − | 0.839847i | \(-0.317355\pi\) | ||||
0.542824 | + | 0.839847i | \(0.317355\pi\) | |||||||
\(350\) | 10.1599 | 0.543068 | ||||||||
\(351\) | 4.57479 | 0.244184 | ||||||||
\(352\) | 9.80749 | 0.522741 | ||||||||
\(353\) | 20.0201 | 1.06556 | 0.532780 | − | 0.846254i | \(-0.321147\pi\) | ||||
0.532780 | + | 0.846254i | \(0.321147\pi\) | |||||||
\(354\) | 24.0844 | 1.28007 | ||||||||
\(355\) | −15.6705 | −0.831706 | ||||||||
\(356\) | 21.1731 | 1.12217 | ||||||||
\(357\) | −8.16497 | −0.432136 | ||||||||
\(358\) | 57.8286 | 3.05634 | ||||||||
\(359\) | −4.07508 | −0.215075 | −0.107537 | − | 0.994201i | \(-0.534297\pi\) | ||||
−0.107537 | + | 0.994201i | \(0.534297\pi\) | |||||||
\(360\) | −0.251719 | −0.0132668 | ||||||||
\(361\) | 24.7446 | 1.30235 | ||||||||
\(362\) | −15.7806 | −0.829409 | ||||||||
\(363\) | −11.7448 | −0.616443 | ||||||||
\(364\) | 3.00360 | 0.157431 | ||||||||
\(365\) | −24.8741 | −1.30197 | ||||||||
\(366\) | 34.5118 | 1.80396 | ||||||||
\(367\) | 8.55206 | 0.446414 | 0.223207 | − | 0.974771i | \(-0.428347\pi\) | ||||
0.223207 | + | 0.974771i | \(0.428347\pi\) | |||||||
\(368\) | 4.53109 | 0.236199 | ||||||||
\(369\) | −0.0365807 | −0.00190432 | ||||||||
\(370\) | 70.5134 | 3.66582 | ||||||||
\(371\) | 2.62722 | 0.136399 | ||||||||
\(372\) | −46.4115 | −2.40633 | ||||||||
\(373\) | 5.63015 | 0.291518 | 0.145759 | − | 0.989320i | \(-0.453438\pi\) | ||||
0.145759 | + | 0.989320i | \(0.453438\pi\) | |||||||
\(374\) | −22.4758 | −1.16220 | ||||||||
\(375\) | −3.33712 | −0.172328 | ||||||||
\(376\) | 32.6202 | 1.68226 | ||||||||
\(377\) | 4.51793 | 0.232685 | ||||||||
\(378\) | −12.0199 | −0.618237 | ||||||||
\(379\) | 3.26015 | 0.167462 | 0.0837312 | − | 0.996488i | \(-0.473316\pi\) | ||||
0.0837312 | + | 0.996488i | \(0.473316\pi\) | |||||||
\(380\) | −68.7868 | −3.52869 | ||||||||
\(381\) | 18.1289 | 0.928774 | ||||||||
\(382\) | −23.7193 | −1.21358 | ||||||||
\(383\) | 34.2169 | 1.74840 | 0.874201 | − | 0.485564i | \(-0.161386\pi\) | ||||
0.874201 | + | 0.485564i | \(0.161386\pi\) | |||||||
\(384\) | 34.1428 | 1.74234 | ||||||||
\(385\) | −6.30983 | −0.321579 | ||||||||
\(386\) | −47.7590 | −2.43087 | ||||||||
\(387\) | −0.254003 | −0.0129117 | ||||||||
\(388\) | −44.0625 | −2.23693 | ||||||||
\(389\) | 3.88942 | 0.197201 | 0.0986007 | − | 0.995127i | \(-0.468563\pi\) | ||||
0.0986007 | + | 0.995127i | \(0.468563\pi\) | |||||||
\(390\) | 10.9385 | 0.553891 | ||||||||
\(391\) | 28.5266 | 1.44265 | ||||||||
\(392\) | −3.24544 | −0.163920 | ||||||||
\(393\) | −8.00121 | −0.403608 | ||||||||
\(394\) | 32.2247 | 1.62345 | ||||||||
\(395\) | −6.61980 | −0.333078 | ||||||||
\(396\) | 0.177363 | 0.00891282 | ||||||||
\(397\) | 34.6189 | 1.73747 | 0.868736 | − | 0.495275i | \(-0.164933\pi\) | ||||
0.868736 | + | 0.495275i | \(0.164933\pi\) | |||||||
\(398\) | −41.3517 | −2.07277 | ||||||||
\(399\) | 11.5040 | 0.575921 | ||||||||
\(400\) | 3.26086 | 0.163043 | ||||||||
\(401\) | 11.4096 | 0.569767 | 0.284884 | − | 0.958562i | \(-0.408045\pi\) | ||||
0.284884 | + | 0.958562i | \(0.408045\pi\) | |||||||
\(402\) | −32.3034 | −1.61115 | ||||||||
\(403\) | 6.94528 | 0.345969 | ||||||||
\(404\) | 25.3949 | 1.26344 | ||||||||
\(405\) | −27.7850 | −1.38065 | ||||||||
\(406\) | −11.8705 | −0.589124 | ||||||||
\(407\) | −20.4324 | −1.01280 | ||||||||
\(408\) | −26.4989 | −1.31189 | ||||||||
\(409\) | −27.5113 | −1.36034 | −0.680172 | − | 0.733052i | \(-0.738095\pi\) | ||||
−0.680172 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(410\) | 10.2702 | 0.507209 | ||||||||
\(411\) | 13.9655 | 0.688868 | ||||||||
\(412\) | −66.1871 | −3.26080 | ||||||||
\(413\) | 5.96037 | 0.293291 | ||||||||
\(414\) | −0.357647 | −0.0175774 | ||||||||
\(415\) | 37.6775 | 1.84952 | ||||||||
\(416\) | −4.20759 | −0.206294 | ||||||||
\(417\) | 9.49517 | 0.464980 | ||||||||
\(418\) | 31.6672 | 1.54889 | ||||||||
\(419\) | 33.9004 | 1.65614 | 0.828071 | − | 0.560623i | \(-0.189438\pi\) | ||||
0.828071 | + | 0.560623i | \(0.189438\pi\) | |||||||
\(420\) | −18.0896 | −0.882683 | ||||||||
\(421\) | −29.5310 | −1.43925 | −0.719627 | − | 0.694361i | \(-0.755687\pi\) | ||||
−0.719627 | + | 0.694361i | \(0.755687\pi\) | |||||||
\(422\) | 41.0286 | 1.99724 | ||||||||
\(423\) | −0.254630 | −0.0123805 | ||||||||
\(424\) | 8.52650 | 0.414083 | ||||||||
\(425\) | 20.5296 | 0.995832 | ||||||||
\(426\) | 20.6824 | 1.00206 | ||||||||
\(427\) | 8.54092 | 0.413324 | ||||||||
\(428\) | 59.8879 | 2.89479 | ||||||||
\(429\) | −3.16959 | −0.153029 | ||||||||
\(430\) | 71.3125 | 3.43900 | ||||||||
\(431\) | −5.40775 | −0.260482 | −0.130241 | − | 0.991482i | \(-0.541575\pi\) | ||||
−0.130241 | + | 0.991482i | \(0.541575\pi\) | |||||||
\(432\) | −3.85785 | −0.185611 | ||||||||
\(433\) | −21.1114 | −1.01455 | −0.507276 | − | 0.861784i | \(-0.669347\pi\) | ||||
−0.507276 | + | 0.861784i | \(0.669347\pi\) | |||||||
\(434\) | −18.2482 | −0.875941 | ||||||||
\(435\) | −27.2099 | −1.30462 | ||||||||
\(436\) | 23.6241 | 1.13139 | ||||||||
\(437\) | −40.1925 | −1.92267 | ||||||||
\(438\) | 32.8294 | 1.56865 | ||||||||
\(439\) | 7.65621 | 0.365411 | 0.182706 | − | 0.983168i | \(-0.441514\pi\) | ||||
0.182706 | + | 0.983168i | \(0.441514\pi\) | |||||||
\(440\) | −20.4782 | −0.976259 | ||||||||
\(441\) | 0.0253336 | 0.00120636 | ||||||||
\(442\) | 9.64253 | 0.458648 | ||||||||
\(443\) | −25.7033 | −1.22120 | −0.610601 | − | 0.791938i | \(-0.709072\pi\) | ||||
−0.610601 | + | 0.791938i | \(0.709072\pi\) | |||||||
\(444\) | −58.5775 | −2.77997 | ||||||||
\(445\) | 19.0825 | 0.904596 | ||||||||
\(446\) | 9.30602 | 0.440653 | ||||||||
\(447\) | 4.96288 | 0.234736 | ||||||||
\(448\) | 12.5464 | 0.592760 | ||||||||
\(449\) | 13.3918 | 0.631996 | 0.315998 | − | 0.948760i | \(-0.397661\pi\) | ||||
0.315998 | + | 0.948760i | \(0.397661\pi\) | |||||||
\(450\) | −0.257386 | −0.0121333 | ||||||||
\(451\) | −2.97596 | −0.140132 | ||||||||
\(452\) | −30.0884 | −1.41524 | ||||||||
\(453\) | 5.52947 | 0.259797 | ||||||||
\(454\) | −16.2836 | −0.764227 | ||||||||
\(455\) | 2.70703 | 0.126908 | ||||||||
\(456\) | 37.3356 | 1.74840 | ||||||||
\(457\) | −32.0863 | −1.50093 | −0.750466 | − | 0.660909i | \(-0.770171\pi\) | ||||
−0.750466 | + | 0.660909i | \(0.770171\pi\) | |||||||
\(458\) | −11.2031 | −0.523486 | ||||||||
\(459\) | −24.2881 | −1.13367 | ||||||||
\(460\) | 63.2012 | 2.94677 | ||||||||
\(461\) | 6.41971 | 0.298996 | 0.149498 | − | 0.988762i | \(-0.452234\pi\) | ||||
0.149498 | + | 0.988762i | \(0.452234\pi\) | |||||||
\(462\) | 8.32786 | 0.387447 | ||||||||
\(463\) | −38.3267 | −1.78119 | −0.890595 | − | 0.454797i | \(-0.849712\pi\) | ||||
−0.890595 | + | 0.454797i | \(0.849712\pi\) | |||||||
\(464\) | −3.80990 | −0.176870 | ||||||||
\(465\) | −41.8289 | −1.93977 | ||||||||
\(466\) | −14.5189 | −0.672574 | ||||||||
\(467\) | −28.0367 | −1.29739 | −0.648693 | − | 0.761050i | \(-0.724684\pi\) | ||||
−0.648693 | + | 0.761050i | \(0.724684\pi\) | |||||||
\(468\) | −0.0760919 | −0.00351735 | ||||||||
\(469\) | −7.99440 | −0.369147 | ||||||||
\(470\) | 71.4886 | 3.29752 | ||||||||
\(471\) | 28.6209 | 1.31878 | ||||||||
\(472\) | 19.3440 | 0.890381 | ||||||||
\(473\) | −20.6639 | −0.950129 | ||||||||
\(474\) | 8.73696 | 0.401302 | ||||||||
\(475\) | −28.9251 | −1.32717 | ||||||||
\(476\) | −15.9465 | −0.730904 | ||||||||
\(477\) | −0.0665569 | −0.00304743 | ||||||||
\(478\) | 39.7197 | 1.81673 | ||||||||
\(479\) | −20.3528 | −0.929943 | −0.464972 | − | 0.885326i | \(-0.653935\pi\) | ||||
−0.464972 | + | 0.885326i | \(0.653935\pi\) | |||||||
\(480\) | 25.3408 | 1.15665 | ||||||||
\(481\) | 8.76586 | 0.399689 | ||||||||
\(482\) | 37.1717 | 1.69312 | ||||||||
\(483\) | −10.5699 | −0.480945 | ||||||||
\(484\) | −22.9380 | −1.04264 | ||||||||
\(485\) | −39.7118 | −1.80322 | ||||||||
\(486\) | 0.611607 | 0.0277431 | ||||||||
\(487\) | −8.64816 | −0.391886 | −0.195943 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195943 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(488\) | 27.7191 | 1.25478 | ||||||||
\(489\) | −31.1288 | −1.40769 | ||||||||
\(490\) | −7.11252 | −0.321311 | ||||||||
\(491\) | 6.68506 | 0.301692 | 0.150846 | − | 0.988557i | \(-0.451800\pi\) | ||||
0.150846 | + | 0.988557i | \(0.451800\pi\) | |||||||
\(492\) | −8.53176 | −0.384641 | ||||||||
\(493\) | −23.9862 | −1.08028 | ||||||||
\(494\) | −13.5858 | −0.611254 | ||||||||
\(495\) | 0.159850 | 0.00718474 | ||||||||
\(496\) | −5.85684 | −0.262980 | ||||||||
\(497\) | 5.11844 | 0.229593 | ||||||||
\(498\) | −49.7277 | −2.22835 | ||||||||
\(499\) | 42.2531 | 1.89151 | 0.945754 | − | 0.324884i | \(-0.105325\pi\) | ||||
0.945754 | + | 0.324884i | \(0.105325\pi\) | |||||||
\(500\) | −6.51751 | −0.291472 | ||||||||
\(501\) | −4.16912 | −0.186262 | ||||||||
\(502\) | −61.2619 | −2.73425 | ||||||||
\(503\) | −13.5222 | −0.602926 | −0.301463 | − | 0.953478i | \(-0.597475\pi\) | ||||
−0.301463 | + | 0.953478i | \(0.597475\pi\) | |||||||
\(504\) | 0.0822185 | 0.00366231 | ||||||||
\(505\) | 22.8874 | 1.01848 | ||||||||
\(506\) | −29.0958 | −1.29346 | ||||||||
\(507\) | −21.2517 | −0.943822 | ||||||||
\(508\) | 35.4064 | 1.57091 | ||||||||
\(509\) | 35.7174 | 1.58314 | 0.791572 | − | 0.611075i | \(-0.209263\pi\) | ||||
0.791572 | + | 0.611075i | \(0.209263\pi\) | |||||||
\(510\) | −58.0735 | −2.57154 | ||||||||
\(511\) | 8.12457 | 0.359410 | ||||||||
\(512\) | 8.38795 | 0.370699 | ||||||||
\(513\) | 34.2206 | 1.51088 | ||||||||
\(514\) | 66.9178 | 2.95162 | ||||||||
\(515\) | −59.6519 | −2.62858 | ||||||||
\(516\) | −59.2414 | −2.60796 | ||||||||
\(517\) | −20.7150 | −0.911043 | ||||||||
\(518\) | −23.0316 | −1.01195 | ||||||||
\(519\) | 43.0304 | 1.88882 | ||||||||
\(520\) | 8.78551 | 0.385270 | ||||||||
\(521\) | 17.9359 | 0.785786 | 0.392893 | − | 0.919584i | \(-0.371474\pi\) | ||||
0.392893 | + | 0.919584i | \(0.371474\pi\) | |||||||
\(522\) | 0.300722 | 0.0131623 | ||||||||
\(523\) | −9.20478 | −0.402497 | −0.201249 | − | 0.979540i | \(-0.564500\pi\) | ||||
−0.201249 | + | 0.979540i | \(0.564500\pi\) | |||||||
\(524\) | −15.6266 | −0.682652 | ||||||||
\(525\) | −7.60675 | −0.331986 | ||||||||
\(526\) | −35.5848 | −1.55157 | ||||||||
\(527\) | −36.8732 | −1.60622 | ||||||||
\(528\) | 2.67287 | 0.116322 | ||||||||
\(529\) | 13.9288 | 0.605600 | ||||||||
\(530\) | 18.6862 | 0.811675 | ||||||||
\(531\) | −0.150997 | −0.00655273 | ||||||||
\(532\) | 22.4677 | 0.974098 | ||||||||
\(533\) | 1.27674 | 0.0553017 | ||||||||
\(534\) | −25.1855 | −1.08988 | ||||||||
\(535\) | 53.9746 | 2.33353 | ||||||||
\(536\) | −25.9453 | −1.12067 | ||||||||
\(537\) | −43.2965 | −1.86838 | ||||||||
\(538\) | −66.9929 | −2.88827 | ||||||||
\(539\) | 2.06097 | 0.0887721 | ||||||||
\(540\) | −53.8106 | −2.31564 | ||||||||
\(541\) | 2.33347 | 0.100324 | 0.0501619 | − | 0.998741i | \(-0.484026\pi\) | ||||
0.0501619 | + | 0.998741i | \(0.484026\pi\) | |||||||
\(542\) | 0.686829 | 0.0295018 | ||||||||
\(543\) | 11.8150 | 0.507030 | ||||||||
\(544\) | 22.3386 | 0.957758 | ||||||||
\(545\) | 21.2915 | 0.912027 | ||||||||
\(546\) | −3.57280 | −0.152902 | ||||||||
\(547\) | 16.8512 | 0.720504 | 0.360252 | − | 0.932855i | \(-0.382691\pi\) | ||||
0.360252 | + | 0.932855i | \(0.382691\pi\) | |||||||
\(548\) | 27.2751 | 1.16513 | ||||||||
\(549\) | −0.216372 | −0.00923453 | ||||||||
\(550\) | −20.9392 | −0.892849 | ||||||||
\(551\) | 33.7953 | 1.43973 | ||||||||
\(552\) | −34.3039 | −1.46007 | ||||||||
\(553\) | 2.16221 | 0.0919465 | ||||||||
\(554\) | −65.1572 | −2.76827 | ||||||||
\(555\) | −52.7937 | −2.24097 | ||||||||
\(556\) | 18.5444 | 0.786456 | ||||||||
\(557\) | −30.7324 | −1.30217 | −0.651087 | − | 0.759003i | \(-0.725687\pi\) | ||||
−0.651087 | + | 0.759003i | \(0.725687\pi\) | |||||||
\(558\) | 0.462291 | 0.0195703 | ||||||||
\(559\) | 8.86521 | 0.374958 | ||||||||
\(560\) | −2.28280 | −0.0964657 | ||||||||
\(561\) | 16.8277 | 0.710467 | ||||||||
\(562\) | 32.4768 | 1.36995 | ||||||||
\(563\) | −32.1862 | −1.35649 | −0.678243 | − | 0.734838i | \(-0.737258\pi\) | ||||
−0.678243 | + | 0.734838i | \(0.737258\pi\) | |||||||
\(564\) | −59.3876 | −2.50067 | ||||||||
\(565\) | −27.1175 | −1.14084 | ||||||||
\(566\) | −6.17922 | −0.259732 | ||||||||
\(567\) | 9.07536 | 0.381129 | ||||||||
\(568\) | 16.6116 | 0.697006 | ||||||||
\(569\) | 34.0146 | 1.42597 | 0.712984 | − | 0.701181i | \(-0.247343\pi\) | ||||
0.712984 | + | 0.701181i | \(0.247343\pi\) | |||||||
\(570\) | 81.8224 | 3.42716 | ||||||||
\(571\) | −36.4868 | −1.52692 | −0.763462 | − | 0.645852i | \(-0.776502\pi\) | ||||
−0.763462 | + | 0.645852i | \(0.776502\pi\) | |||||||
\(572\) | −6.19032 | −0.258830 | ||||||||
\(573\) | 17.7587 | 0.741881 | ||||||||
\(574\) | −3.35453 | −0.140016 | ||||||||
\(575\) | 26.5763 | 1.10831 | ||||||||
\(576\) | −0.317844 | −0.0132435 | ||||||||
\(577\) | −20.7746 | −0.864857 | −0.432429 | − | 0.901668i | \(-0.642343\pi\) | ||||
−0.432429 | + | 0.901668i | \(0.642343\pi\) | |||||||
\(578\) | −11.6998 | −0.486646 | ||||||||
\(579\) | 35.7574 | 1.48603 | ||||||||
\(580\) | −53.1418 | −2.20659 | ||||||||
\(581\) | −12.3065 | −0.510561 | ||||||||
\(582\) | 52.4126 | 2.17257 | ||||||||
\(583\) | −5.41462 | −0.224250 | ||||||||
\(584\) | 26.3678 | 1.09111 | ||||||||
\(585\) | −0.0685787 | −0.00283538 | ||||||||
\(586\) | −60.3216 | −2.49186 | ||||||||
\(587\) | 3.52820 | 0.145625 | 0.0728123 | − | 0.997346i | \(-0.476803\pi\) | ||||
0.0728123 | + | 0.997346i | \(0.476803\pi\) | |||||||
\(588\) | 5.90857 | 0.243665 | ||||||||
\(589\) | 51.9524 | 2.14066 | ||||||||
\(590\) | 42.3932 | 1.74530 | ||||||||
\(591\) | −24.1267 | −0.992441 | ||||||||
\(592\) | −7.39211 | −0.303814 | ||||||||
\(593\) | 42.7442 | 1.75529 | 0.877646 | − | 0.479309i | \(-0.159113\pi\) | ||||
0.877646 | + | 0.479309i | \(0.159113\pi\) | |||||||
\(594\) | 24.7726 | 1.01643 | ||||||||
\(595\) | −14.3719 | −0.589192 | ||||||||
\(596\) | 9.69265 | 0.397027 | ||||||||
\(597\) | 30.9602 | 1.26712 | ||||||||
\(598\) | 12.4826 | 0.510452 | ||||||||
\(599\) | −15.4713 | −0.632141 | −0.316071 | − | 0.948736i | \(-0.602364\pi\) | ||||
−0.316071 | + | 0.948736i | \(0.602364\pi\) | |||||||
\(600\) | −24.6872 | −1.00785 | ||||||||
\(601\) | 18.1397 | 0.739933 | 0.369967 | − | 0.929045i | \(-0.379369\pi\) | ||||
0.369967 | + | 0.929045i | \(0.379369\pi\) | |||||||
\(602\) | −23.2927 | −0.949338 | ||||||||
\(603\) | 0.202526 | 0.00824751 | ||||||||
\(604\) | 10.7992 | 0.439415 | ||||||||
\(605\) | −20.6731 | −0.840483 | ||||||||
\(606\) | −30.2074 | −1.22709 | ||||||||
\(607\) | −17.9881 | −0.730115 | −0.365057 | − | 0.930985i | \(-0.618951\pi\) | ||||
−0.365057 | + | 0.930985i | \(0.618951\pi\) | |||||||
\(608\) | −31.4738 | −1.27643 | ||||||||
\(609\) | 8.88751 | 0.360140 | ||||||||
\(610\) | 60.7475 | 2.45959 | ||||||||
\(611\) | 8.88710 | 0.359533 | ||||||||
\(612\) | 0.403980 | 0.0163299 | ||||||||
\(613\) | −15.2541 | −0.616108 | −0.308054 | − | 0.951369i | \(-0.599678\pi\) | ||||
−0.308054 | + | 0.951369i | \(0.599678\pi\) | |||||||
\(614\) | 18.3179 | 0.739250 | ||||||||
\(615\) | −7.68935 | −0.310064 | ||||||||
\(616\) | 6.68874 | 0.269497 | ||||||||
\(617\) | −16.6211 | −0.669141 | −0.334571 | − | 0.942371i | \(-0.608591\pi\) | ||||
−0.334571 | + | 0.942371i | \(0.608591\pi\) | |||||||
\(618\) | 78.7300 | 3.16698 | ||||||||
\(619\) | 45.3224 | 1.82166 | 0.910830 | − | 0.412782i | \(-0.135443\pi\) | ||||
0.910830 | + | 0.412782i | \(0.135443\pi\) | |||||||
\(620\) | −81.6932 | −3.28088 | ||||||||
\(621\) | −31.4418 | −1.26172 | ||||||||
\(622\) | 72.6936 | 2.91475 | ||||||||
\(623\) | −6.23287 | −0.249715 | ||||||||
\(624\) | −1.14671 | −0.0459051 | ||||||||
\(625\) | −27.7406 | −1.10963 | ||||||||
\(626\) | −12.4480 | −0.497524 | ||||||||
\(627\) | −23.7094 | −0.946860 | ||||||||
\(628\) | 55.8976 | 2.23056 | ||||||||
\(629\) | −46.5389 | −1.85563 | ||||||||
\(630\) | 0.180185 | 0.00717875 | ||||||||
\(631\) | 21.5872 | 0.859374 | 0.429687 | − | 0.902978i | \(-0.358624\pi\) | ||||
0.429687 | + | 0.902978i | \(0.358624\pi\) | |||||||
\(632\) | 7.01732 | 0.279134 | ||||||||
\(633\) | −30.7183 | −1.22094 | ||||||||
\(634\) | −12.5012 | −0.496486 | ||||||||
\(635\) | 31.9105 | 1.26633 | ||||||||
\(636\) | −15.5231 | −0.615533 | ||||||||
\(637\) | −0.884192 | −0.0350329 | ||||||||
\(638\) | 24.4647 | 0.968568 | ||||||||
\(639\) | −0.129668 | −0.00512959 | ||||||||
\(640\) | 60.0980 | 2.37558 | ||||||||
\(641\) | −38.8820 | −1.53575 | −0.767873 | − | 0.640602i | \(-0.778685\pi\) | ||||
−0.767873 | + | 0.640602i | \(0.778685\pi\) | |||||||
\(642\) | −71.2370 | −2.81150 | ||||||||
\(643\) | −35.7062 | −1.40811 | −0.704057 | − | 0.710144i | \(-0.748630\pi\) | ||||
−0.704057 | + | 0.710144i | \(0.748630\pi\) | |||||||
\(644\) | −20.6433 | −0.813459 | ||||||||
\(645\) | −53.3920 | −2.10231 | ||||||||
\(646\) | 72.1285 | 2.83786 | ||||||||
\(647\) | −23.0677 | −0.906887 | −0.453443 | − | 0.891285i | \(-0.649805\pi\) | ||||
−0.453443 | + | 0.891285i | \(0.649805\pi\) | |||||||
\(648\) | 29.4535 | 1.15704 | ||||||||
\(649\) | −12.2841 | −0.482194 | ||||||||
\(650\) | 8.98328 | 0.352353 | ||||||||
\(651\) | 13.6625 | 0.535475 | ||||||||
\(652\) | −60.7955 | −2.38094 | ||||||||
\(653\) | −3.59950 | −0.140859 | −0.0704297 | − | 0.997517i | \(-0.522437\pi\) | ||||
−0.0704297 | + | 0.997517i | \(0.522437\pi\) | |||||||
\(654\) | −28.1010 | −1.09884 | ||||||||
\(655\) | −14.0837 | −0.550295 | ||||||||
\(656\) | −1.07665 | −0.0420363 | ||||||||
\(657\) | −0.205824 | −0.00802997 | ||||||||
\(658\) | −23.3502 | −0.910284 | ||||||||
\(659\) | 47.0382 | 1.83235 | 0.916174 | − | 0.400780i | \(-0.131261\pi\) | ||||
0.916174 | + | 0.400780i | \(0.131261\pi\) | |||||||
\(660\) | 37.2821 | 1.45120 | ||||||||
\(661\) | −19.5162 | −0.759091 | −0.379546 | − | 0.925173i | \(-0.623920\pi\) | ||||
−0.379546 | + | 0.925173i | \(0.623920\pi\) | |||||||
\(662\) | 10.4558 | 0.406378 | ||||||||
\(663\) | −7.21940 | −0.280378 | ||||||||
\(664\) | −39.9401 | −1.54998 | ||||||||
\(665\) | 20.2493 | 0.785233 | ||||||||
\(666\) | 0.583473 | 0.0226091 | ||||||||
\(667\) | −31.0510 | −1.20230 | ||||||||
\(668\) | −8.14242 | −0.315040 | ||||||||
\(669\) | −6.96746 | −0.269377 | ||||||||
\(670\) | −56.8603 | −2.19670 | ||||||||
\(671\) | −17.6025 | −0.679539 | ||||||||
\(672\) | −8.27702 | −0.319293 | ||||||||
\(673\) | −0.570063 | −0.0219743 | −0.0109871 | − | 0.999940i | \(-0.503497\pi\) | ||||
−0.0109871 | + | 0.999940i | \(0.503497\pi\) | |||||||
\(674\) | −83.2061 | −3.20498 | ||||||||
\(675\) | −22.6275 | −0.870934 | ||||||||
\(676\) | −41.5053 | −1.59636 | ||||||||
\(677\) | −39.2953 | −1.51024 | −0.755121 | − | 0.655586i | \(-0.772422\pi\) | ||||
−0.755121 | + | 0.655586i | \(0.772422\pi\) | |||||||
\(678\) | 35.7904 | 1.37452 | ||||||||
\(679\) | 12.9710 | 0.497781 | ||||||||
\(680\) | −46.6432 | −1.78869 | ||||||||
\(681\) | 12.1916 | 0.467183 | ||||||||
\(682\) | 37.6089 | 1.44012 | ||||||||
\(683\) | −15.2252 | −0.582577 | −0.291288 | − | 0.956635i | \(-0.594084\pi\) | ||||
−0.291288 | + | 0.956635i | \(0.594084\pi\) | |||||||
\(684\) | −0.569186 | −0.0217634 | ||||||||
\(685\) | 24.5820 | 0.939230 | ||||||||
\(686\) | 2.32315 | 0.0886981 | ||||||||
\(687\) | 8.38780 | 0.320015 | ||||||||
\(688\) | −7.47588 | −0.285015 | ||||||||
\(689\) | 2.32297 | 0.0884981 | ||||||||
\(690\) | −75.1783 | −2.86199 | ||||||||
\(691\) | 1.37795 | 0.0524195 | 0.0262098 | − | 0.999656i | \(-0.491656\pi\) | ||||
0.0262098 | + | 0.999656i | \(0.491656\pi\) | |||||||
\(692\) | 84.0397 | 3.19471 | ||||||||
\(693\) | −0.0522116 | −0.00198335 | ||||||||
\(694\) | −55.1236 | −2.09246 | ||||||||
\(695\) | 16.7133 | 0.633973 | ||||||||
\(696\) | 28.8439 | 1.09332 | ||||||||
\(697\) | −6.77835 | −0.256748 | ||||||||
\(698\) | −47.1170 | −1.78341 | ||||||||
\(699\) | 10.8703 | 0.411154 | ||||||||
\(700\) | −14.8562 | −0.561512 | ||||||||
\(701\) | −13.4507 | −0.508026 | −0.254013 | − | 0.967201i | \(-0.581751\pi\) | ||||
−0.254013 | + | 0.967201i | \(0.581751\pi\) | |||||||
\(702\) | −10.6279 | −0.401124 | ||||||||
\(703\) | 65.5708 | 2.47305 | ||||||||
\(704\) | −25.8576 | −0.974546 | ||||||||
\(705\) | −53.5238 | −2.01582 | ||||||||
\(706\) | −46.5095 | −1.75041 | ||||||||
\(707\) | −7.47567 | −0.281151 | ||||||||
\(708\) | −35.2173 | −1.32355 | ||||||||
\(709\) | 26.3310 | 0.988881 | 0.494440 | − | 0.869212i | \(-0.335373\pi\) | ||||
0.494440 | + | 0.869212i | \(0.335373\pi\) | |||||||
\(710\) | 36.4050 | 1.36625 | ||||||||
\(711\) | −0.0547764 | −0.00205428 | ||||||||
\(712\) | −20.2284 | −0.758092 | ||||||||
\(713\) | −47.7338 | −1.78764 | ||||||||
\(714\) | 18.9684 | 0.709875 | ||||||||
\(715\) | −5.57910 | −0.208646 | ||||||||
\(716\) | −84.5595 | −3.16014 | ||||||||
\(717\) | −29.7383 | −1.11060 | ||||||||
\(718\) | 9.46701 | 0.353306 | ||||||||
\(719\) | 40.7114 | 1.51828 | 0.759140 | − | 0.650927i | \(-0.225620\pi\) | ||||
0.759140 | + | 0.650927i | \(0.225620\pi\) | |||||||
\(720\) | 0.0578313 | 0.00215525 | ||||||||
\(721\) | 19.4840 | 0.725621 | ||||||||
\(722\) | −57.4854 | −2.13939 | ||||||||
\(723\) | −27.8306 | −1.03503 | ||||||||
\(724\) | 23.0750 | 0.857577 | ||||||||
\(725\) | −22.3463 | −0.829921 | ||||||||
\(726\) | 27.2849 | 1.01264 | ||||||||
\(727\) | 8.52507 | 0.316177 | 0.158089 | − | 0.987425i | \(-0.449467\pi\) | ||||
0.158089 | + | 0.987425i | \(0.449467\pi\) | |||||||
\(728\) | −2.86959 | −0.106354 | ||||||||
\(729\) | 26.7682 | 0.991413 | ||||||||
\(730\) | 57.7862 | 2.13876 | ||||||||
\(731\) | −47.0664 | −1.74081 | ||||||||
\(732\) | −50.4647 | −1.86523 | ||||||||
\(733\) | −9.96215 | −0.367960 | −0.183980 | − | 0.982930i | \(-0.558898\pi\) | ||||
−0.183980 | + | 0.982930i | \(0.558898\pi\) | |||||||
\(734\) | −19.8677 | −0.733329 | ||||||||
\(735\) | 5.32517 | 0.196422 | ||||||||
\(736\) | 28.9181 | 1.06594 | ||||||||
\(737\) | 16.4762 | 0.606908 | ||||||||
\(738\) | 0.0849823 | 0.00312824 | ||||||||
\(739\) | 0.612502 | 0.0225313 | 0.0112656 | − | 0.999937i | \(-0.496414\pi\) | ||||
0.0112656 | + | 0.999937i | \(0.496414\pi\) | |||||||
\(740\) | −103.108 | −3.79032 | ||||||||
\(741\) | 10.1717 | 0.373668 | ||||||||
\(742\) | −6.10342 | −0.224064 | ||||||||
\(743\) | 11.7103 | 0.429610 | 0.214805 | − | 0.976657i | \(-0.431088\pi\) | ||||
0.214805 | + | 0.976657i | \(0.431088\pi\) | |||||||
\(744\) | 44.3408 | 1.62561 | ||||||||
\(745\) | 8.73562 | 0.320048 | ||||||||
\(746\) | −13.0797 | −0.478880 | ||||||||
\(747\) | 0.311768 | 0.0114070 | ||||||||
\(748\) | 32.8651 | 1.20167 | ||||||||
\(749\) | −17.6296 | −0.644172 | ||||||||
\(750\) | 7.75262 | 0.283086 | ||||||||
\(751\) | −32.5115 | −1.18636 | −0.593180 | − | 0.805070i | \(-0.702128\pi\) | ||||
−0.593180 | + | 0.805070i | \(0.702128\pi\) | |||||||
\(752\) | −7.49434 | −0.273291 | ||||||||
\(753\) | 45.8670 | 1.67149 | ||||||||
\(754\) | −10.4958 | −0.382235 | ||||||||
\(755\) | 9.73294 | 0.354218 | ||||||||
\(756\) | 17.5760 | 0.639234 | ||||||||
\(757\) | 14.7155 | 0.534843 | 0.267422 | − | 0.963580i | \(-0.413828\pi\) | ||||
0.267422 | + | 0.963580i | \(0.413828\pi\) | |||||||
\(758\) | −7.57379 | −0.275092 | ||||||||
\(759\) | 21.7841 | 0.790713 | ||||||||
\(760\) | 65.7178 | 2.38384 | ||||||||
\(761\) | −32.4647 | −1.17684 | −0.588422 | − | 0.808554i | \(-0.700251\pi\) | ||||
−0.588422 | + | 0.808554i | \(0.700251\pi\) | |||||||
\(762\) | −42.1162 | −1.52571 | ||||||||
\(763\) | −6.95439 | −0.251766 | ||||||||
\(764\) | 34.6834 | 1.25480 | ||||||||
\(765\) | 0.364092 | 0.0131638 | ||||||||
\(766\) | −79.4908 | −2.87212 | ||||||||
\(767\) | 5.27011 | 0.190293 | ||||||||
\(768\) | −35.6737 | −1.28726 | ||||||||
\(769\) | −42.2398 | −1.52321 | −0.761604 | − | 0.648043i | \(-0.775588\pi\) | ||||
−0.761604 | + | 0.648043i | \(0.775588\pi\) | |||||||
\(770\) | 14.6586 | 0.528261 | ||||||||
\(771\) | −50.1017 | −1.80437 | ||||||||
\(772\) | 69.8353 | 2.51343 | ||||||||
\(773\) | −36.9608 | −1.32939 | −0.664694 | − | 0.747116i | \(-0.731438\pi\) | ||||
−0.664694 | + | 0.747116i | \(0.731438\pi\) | |||||||
\(774\) | 0.590086 | 0.0212102 | ||||||||
\(775\) | −34.3523 | −1.23397 | ||||||||
\(776\) | 42.0966 | 1.51118 | ||||||||
\(777\) | 17.2439 | 0.618621 | ||||||||
\(778\) | −9.03568 | −0.323945 | ||||||||
\(779\) | 9.55033 | 0.342176 | ||||||||
\(780\) | −15.9947 | −0.572702 | ||||||||
\(781\) | −10.5489 | −0.377470 | ||||||||
\(782\) | −66.2715 | −2.36987 | ||||||||
\(783\) | 26.4374 | 0.944795 | ||||||||
\(784\) | 0.745624 | 0.0266294 | ||||||||
\(785\) | 50.3784 | 1.79808 | ||||||||
\(786\) | 18.5880 | 0.663011 | ||||||||
\(787\) | −18.7479 | −0.668292 | −0.334146 | − | 0.942521i | \(-0.608448\pi\) | ||||
−0.334146 | + | 0.942521i | \(0.608448\pi\) | |||||||
\(788\) | −47.1203 | −1.67859 | ||||||||
\(789\) | 26.6425 | 0.948499 | ||||||||
\(790\) | 15.3787 | 0.547151 | ||||||||
\(791\) | 8.85733 | 0.314931 | ||||||||
\(792\) | −0.169450 | −0.00602113 | ||||||||
\(793\) | 7.55181 | 0.268173 | ||||||||
\(794\) | −80.4247 | −2.85417 | ||||||||
\(795\) | −13.9904 | −0.496189 | ||||||||
\(796\) | 60.4663 | 2.14317 | ||||||||
\(797\) | −25.8851 | −0.916897 | −0.458448 | − | 0.888721i | \(-0.651595\pi\) | ||||
−0.458448 | + | 0.888721i | \(0.651595\pi\) | |||||||
\(798\) | −26.7255 | −0.946072 | ||||||||
\(799\) | −47.1826 | −1.66920 | ||||||||
\(800\) | 20.8113 | 0.735791 | ||||||||
\(801\) | 0.157901 | 0.00557915 | ||||||||
\(802\) | −26.5061 | −0.935964 | ||||||||
\(803\) | −16.7445 | −0.590899 | ||||||||
\(804\) | 47.2355 | 1.66587 | ||||||||
\(805\) | −18.6050 | −0.655740 | ||||||||
\(806\) | −16.1349 | −0.568327 | ||||||||
\(807\) | 50.1578 | 1.76564 | ||||||||
\(808\) | −24.2618 | −0.853528 | ||||||||
\(809\) | 0.0816777 | 0.00287163 | 0.00143582 | − | 0.999999i | \(-0.499543\pi\) | ||||
0.00143582 | + | 0.999999i | \(0.499543\pi\) | |||||||
\(810\) | 64.5486 | 2.26801 | ||||||||
\(811\) | −19.6446 | −0.689816 | −0.344908 | − | 0.938637i | \(-0.612090\pi\) | ||||
−0.344908 | + | 0.938637i | \(0.612090\pi\) | |||||||
\(812\) | 17.3576 | 0.609132 | ||||||||
\(813\) | −0.514232 | −0.0180349 | ||||||||
\(814\) | 47.4674 | 1.66373 | ||||||||
\(815\) | −54.7927 | −1.91930 | ||||||||
\(816\) | 6.08800 | 0.213123 | ||||||||
\(817\) | 66.3140 | 2.32003 | ||||||||
\(818\) | 63.9127 | 2.23465 | ||||||||
\(819\) | 0.0223997 | 0.000782709 0 | ||||||||
\(820\) | −15.0175 | −0.524435 | ||||||||
\(821\) | −29.4710 | −1.02855 | −0.514273 | − | 0.857626i | \(-0.671938\pi\) | ||||
−0.514273 | + | 0.857626i | \(0.671938\pi\) | |||||||
\(822\) | −32.4439 | −1.13161 | ||||||||
\(823\) | −51.9968 | −1.81249 | −0.906247 | − | 0.422748i | \(-0.861066\pi\) | ||||
−0.906247 | + | 0.422748i | \(0.861066\pi\) | |||||||
\(824\) | 63.2340 | 2.20286 | ||||||||
\(825\) | 15.6772 | 0.545811 | ||||||||
\(826\) | −13.8468 | −0.481792 | ||||||||
\(827\) | −7.85703 | −0.273216 | −0.136608 | − | 0.990625i | \(-0.543620\pi\) | ||||
−0.136608 | + | 0.990625i | \(0.543620\pi\) | |||||||
\(828\) | 0.522967 | 0.0181744 | ||||||||
\(829\) | −42.8275 | −1.48746 | −0.743730 | − | 0.668480i | \(-0.766945\pi\) | ||||
−0.743730 | + | 0.668480i | \(0.766945\pi\) | |||||||
\(830\) | −87.5304 | −3.03822 | ||||||||
\(831\) | 48.7835 | 1.69228 | ||||||||
\(832\) | 11.0934 | 0.384594 | ||||||||
\(833\) | 4.69427 | 0.162647 | ||||||||
\(834\) | −22.0587 | −0.763829 | ||||||||
\(835\) | −7.33845 | −0.253958 | ||||||||
\(836\) | −46.3051 | −1.60150 | ||||||||
\(837\) | 40.6413 | 1.40477 | ||||||||
\(838\) | −78.7555 | −2.72057 | ||||||||
\(839\) | 35.6886 | 1.23211 | 0.616053 | − | 0.787704i | \(-0.288731\pi\) | ||||
0.616053 | + | 0.787704i | \(0.288731\pi\) | |||||||
\(840\) | 17.2825 | 0.596304 | ||||||||
\(841\) | −2.89120 | −0.0996966 | ||||||||
\(842\) | 68.6049 | 2.36428 | ||||||||
\(843\) | −24.3155 | −0.837471 | ||||||||
\(844\) | −59.9938 | −2.06507 | ||||||||
\(845\) | −37.4071 | −1.28684 | ||||||||
\(846\) | 0.591543 | 0.0203377 | ||||||||
\(847\) | 6.75242 | 0.232016 | ||||||||
\(848\) | −1.95892 | −0.0672696 | ||||||||
\(849\) | 4.62641 | 0.158778 | ||||||||
\(850\) | −47.6932 | −1.63586 | ||||||||
\(851\) | −60.2464 | −2.06522 | ||||||||
\(852\) | −30.2426 | −1.03610 | ||||||||
\(853\) | 12.7148 | 0.435347 | 0.217673 | − | 0.976022i | \(-0.430153\pi\) | ||||
0.217673 | + | 0.976022i | \(0.430153\pi\) | |||||||
\(854\) | −19.8418 | −0.678972 | ||||||||
\(855\) | −0.512986 | −0.0175438 | ||||||||
\(856\) | −57.2159 | −1.95560 | ||||||||
\(857\) | 43.3587 | 1.48110 | 0.740552 | − | 0.671999i | \(-0.234564\pi\) | ||||
0.740552 | + | 0.671999i | \(0.234564\pi\) | |||||||
\(858\) | 7.36343 | 0.251383 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | −104.276 | −3.55579 | ||||||||
\(861\) | 2.51155 | 0.0855935 | ||||||||
\(862\) | 12.5630 | 0.427897 | ||||||||
\(863\) | −26.0261 | −0.885939 | −0.442969 | − | 0.896537i | \(-0.646075\pi\) | ||||
−0.442969 | + | 0.896537i | \(0.646075\pi\) | |||||||
\(864\) | −24.6214 | −0.837636 | ||||||||
\(865\) | 75.7418 | 2.57530 | ||||||||
\(866\) | 49.0449 | 1.66661 | ||||||||
\(867\) | 8.75966 | 0.297494 | ||||||||
\(868\) | 26.6833 | 0.905689 | ||||||||
\(869\) | −4.45624 | −0.151167 | ||||||||
\(870\) | 63.2126 | 2.14311 | ||||||||
\(871\) | −7.06858 | −0.239510 | ||||||||
\(872\) | −22.5701 | −0.764319 | ||||||||
\(873\) | −0.328601 | −0.0111215 | ||||||||
\(874\) | 93.3730 | 3.15839 | ||||||||
\(875\) | 1.91861 | 0.0648607 | ||||||||
\(876\) | −48.0046 | −1.62193 | ||||||||
\(877\) | 15.7967 | 0.533418 | 0.266709 | − | 0.963777i | \(-0.414064\pi\) | ||||
0.266709 | + | 0.963777i | \(0.414064\pi\) | |||||||
\(878\) | −17.7865 | −0.600265 | ||||||||
\(879\) | 45.1631 | 1.52331 | ||||||||
\(880\) | 4.70476 | 0.158597 | ||||||||
\(881\) | −15.0221 | −0.506106 | −0.253053 | − | 0.967452i | \(-0.581435\pi\) | ||||
−0.253053 | + | 0.967452i | \(0.581435\pi\) | |||||||
\(882\) | −0.0588535 | −0.00198170 | ||||||||
\(883\) | 2.19915 | 0.0740072 | 0.0370036 | − | 0.999315i | \(-0.488219\pi\) | ||||
0.0370036 | + | 0.999315i | \(0.488219\pi\) | |||||||
\(884\) | −14.0997 | −0.474225 | ||||||||
\(885\) | −31.7400 | −1.06693 | ||||||||
\(886\) | 59.7126 | 2.00608 | ||||||||
\(887\) | 23.2978 | 0.782265 | 0.391132 | − | 0.920334i | \(-0.372083\pi\) | ||||
0.391132 | + | 0.920334i | \(0.372083\pi\) | |||||||
\(888\) | 55.9640 | 1.87803 | ||||||||
\(889\) | −10.4228 | −0.349571 | ||||||||
\(890\) | −44.3314 | −1.48599 | ||||||||
\(891\) | −18.7040 | −0.626608 | ||||||||
\(892\) | −13.6077 | −0.455618 | ||||||||
\(893\) | 66.4777 | 2.22459 | ||||||||
\(894\) | −11.5295 | −0.385603 | ||||||||
\(895\) | −76.2102 | −2.54743 | ||||||||
\(896\) | −19.6297 | −0.655781 | ||||||||
\(897\) | −9.34578 | −0.312047 | ||||||||
\(898\) | −31.1110 | −1.03819 | ||||||||
\(899\) | 40.1362 | 1.33862 | ||||||||
\(900\) | 0.376361 | 0.0125454 | ||||||||
\(901\) | −12.3329 | −0.410868 | ||||||||
\(902\) | 6.91358 | 0.230197 | ||||||||
\(903\) | 17.4393 | 0.580344 | ||||||||
\(904\) | 28.7460 | 0.956076 | ||||||||
\(905\) | 20.7967 | 0.691304 | ||||||||
\(906\) | −12.8458 | −0.426772 | ||||||||
\(907\) | 27.2122 | 0.903568 | 0.451784 | − | 0.892127i | \(-0.350788\pi\) | ||||
0.451784 | + | 0.892127i | \(0.350788\pi\) | |||||||
\(908\) | 23.8106 | 0.790182 | ||||||||
\(909\) | 0.189385 | 0.00628151 | ||||||||
\(910\) | −6.28883 | −0.208473 | ||||||||
\(911\) | −22.3310 | −0.739860 | −0.369930 | − | 0.929060i | \(-0.620618\pi\) | ||||
−0.369930 | + | 0.929060i | \(0.620618\pi\) | |||||||
\(912\) | −8.57766 | −0.284035 | ||||||||
\(913\) | 25.3633 | 0.839404 | ||||||||
\(914\) | 74.5411 | 2.46560 | ||||||||
\(915\) | −45.4819 | −1.50358 | ||||||||
\(916\) | 16.3816 | 0.541265 | ||||||||
\(917\) | 4.60012 | 0.151909 | ||||||||
\(918\) | 56.4247 | 1.86229 | ||||||||
\(919\) | −29.0316 | −0.957665 | −0.478832 | − | 0.877906i | \(-0.658940\pi\) | ||||
−0.478832 | + | 0.877906i | \(0.658940\pi\) | |||||||
\(920\) | −60.3814 | −1.99072 | ||||||||
\(921\) | −13.7147 | −0.451914 | ||||||||
\(922\) | −14.9139 | −0.491163 | ||||||||
\(923\) | 4.52568 | 0.148964 | ||||||||
\(924\) | −12.1774 | −0.400606 | ||||||||
\(925\) | −43.3571 | −1.42557 | ||||||||
\(926\) | 89.0384 | 2.92598 | ||||||||
\(927\) | −0.493598 | −0.0162119 | ||||||||
\(928\) | −24.3154 | −0.798191 | ||||||||
\(929\) | 32.0249 | 1.05070 | 0.525352 | − | 0.850885i | \(-0.323934\pi\) | ||||
0.525352 | + | 0.850885i | \(0.323934\pi\) | |||||||
\(930\) | 97.1747 | 3.18648 | ||||||||
\(931\) | −6.61397 | −0.216764 | ||||||||
\(932\) | 21.2301 | 0.695416 | ||||||||
\(933\) | −54.4260 | −1.78183 | ||||||||
\(934\) | 65.1334 | 2.13123 | ||||||||
\(935\) | 29.6200 | 0.968679 | ||||||||
\(936\) | 0.0726969 | 0.00237617 | ||||||||
\(937\) | 11.0748 | 0.361799 | 0.180900 | − | 0.983502i | \(-0.442099\pi\) | ||||
0.180900 | + | 0.983502i | \(0.442099\pi\) | |||||||
\(938\) | 18.5721 | 0.606402 | ||||||||
\(939\) | 9.31990 | 0.304143 | ||||||||
\(940\) | −104.534 | −3.40951 | ||||||||
\(941\) | 42.5748 | 1.38790 | 0.693950 | − | 0.720023i | \(-0.255869\pi\) | ||||
0.693950 | + | 0.720023i | \(0.255869\pi\) | |||||||
\(942\) | −66.4906 | −2.16638 | ||||||||
\(943\) | −8.77483 | −0.285748 | ||||||||
\(944\) | −4.44420 | −0.144646 | ||||||||
\(945\) | 15.8406 | 0.515295 | ||||||||
\(946\) | 48.0053 | 1.56079 | ||||||||
\(947\) | −23.7632 | −0.772200 | −0.386100 | − | 0.922457i | \(-0.626178\pi\) | ||||
−0.386100 | + | 0.922457i | \(0.626178\pi\) | |||||||
\(948\) | −12.7756 | −0.414931 | ||||||||
\(949\) | 7.18368 | 0.233192 | ||||||||
\(950\) | 67.1972 | 2.18016 | ||||||||
\(951\) | 9.35969 | 0.303509 | ||||||||
\(952\) | 15.2350 | 0.493768 | ||||||||
\(953\) | 19.1639 | 0.620780 | 0.310390 | − | 0.950609i | \(-0.399540\pi\) | ||||
0.310390 | + | 0.950609i | \(0.399540\pi\) | |||||||
\(954\) | 0.154621 | 0.00500605 | ||||||||
\(955\) | 31.2588 | 1.01151 | ||||||||
\(956\) | −58.0798 | −1.87843 | ||||||||
\(957\) | −18.3168 | −0.592100 | ||||||||
\(958\) | 47.2825 | 1.52763 | ||||||||
\(959\) | −8.02917 | −0.259275 | ||||||||
\(960\) | −66.8116 | −2.15633 | ||||||||
\(961\) | 30.7002 | 0.990328 | ||||||||
\(962\) | −20.3644 | −0.656574 | ||||||||
\(963\) | 0.446621 | 0.0143922 | ||||||||
\(964\) | −54.3540 | −1.75062 | ||||||||
\(965\) | 62.9399 | 2.02611 | ||||||||
\(966\) | 24.5553 | 0.790054 | ||||||||
\(967\) | 3.20953 | 0.103212 | 0.0516058 | − | 0.998668i | \(-0.483566\pi\) | ||||
0.0516058 | + | 0.998668i | \(0.483566\pi\) | |||||||
\(968\) | 21.9146 | 0.704362 | ||||||||
\(969\) | −54.0029 | −1.73482 | ||||||||
\(970\) | 92.2564 | 2.96217 | ||||||||
\(971\) | 9.62335 | 0.308828 | 0.154414 | − | 0.988006i | \(-0.450651\pi\) | ||||
0.154414 | + | 0.988006i | \(0.450651\pi\) | |||||||
\(972\) | −0.894319 | −0.0286853 | ||||||||
\(973\) | −5.45904 | −0.175009 | ||||||||
\(974\) | 20.0909 | 0.643755 | ||||||||
\(975\) | −6.72582 | −0.215399 | ||||||||
\(976\) | −6.36832 | −0.203845 | ||||||||
\(977\) | −14.4061 | −0.460893 | −0.230446 | − | 0.973085i | \(-0.574019\pi\) | ||||
−0.230446 | + | 0.973085i | \(0.574019\pi\) | |||||||
\(978\) | 72.3167 | 2.31243 | ||||||||
\(979\) | 12.8457 | 0.410551 | ||||||||
\(980\) | 10.4002 | 0.332223 | ||||||||
\(981\) | 0.176179 | 0.00562497 | ||||||||
\(982\) | −15.5304 | −0.495594 | ||||||||
\(983\) | −20.0242 | −0.638674 | −0.319337 | − | 0.947641i | \(-0.603460\pi\) | ||||
−0.319337 | + | 0.947641i | \(0.603460\pi\) | |||||||
\(984\) | 8.15110 | 0.259848 | ||||||||
\(985\) | −42.4677 | −1.35313 | ||||||||
\(986\) | 55.7234 | 1.77460 | ||||||||
\(987\) | 17.4824 | 0.556470 | ||||||||
\(988\) | 19.8657 | 0.632013 | ||||||||
\(989\) | −60.9292 | −1.93743 | ||||||||
\(990\) | −0.371356 | −0.0118025 | ||||||||
\(991\) | −4.19638 | −0.133302 | −0.0666512 | − | 0.997776i | \(-0.521231\pi\) | ||||
−0.0666512 | + | 0.997776i | \(0.521231\pi\) | |||||||
\(992\) | −37.3792 | −1.18679 | ||||||||
\(993\) | −7.82834 | −0.248425 | ||||||||
\(994\) | −11.8909 | −0.377155 | ||||||||
\(995\) | 54.4959 | 1.72764 | ||||||||
\(996\) | 72.7140 | 2.30403 | ||||||||
\(997\) | −28.1424 | −0.891278 | −0.445639 | − | 0.895213i | \(-0.647023\pi\) | ||||
−0.445639 | + | 0.895213i | \(0.647023\pi\) | |||||||
\(998\) | −98.1600 | −3.10720 | ||||||||
\(999\) | 51.2948 | 1.62289 |
(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 | 6013.2.a.c.1.17 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.c.1.17 | ✓ | 104 | 1.1 | even | 1 | trivial |