Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67819 | −1.89376 | −0.946882 | − | 0.321581i | \(-0.895786\pi\) | ||||
−0.946882 | + | 0.321581i | \(0.895786\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.17269 | 2.58634 | ||||||||
\(5\) | −0.816148 | −0.364992 | −0.182496 | − | 0.983207i | \(-0.558418\pi\) | ||||
−0.182496 | + | 0.983207i | \(0.558418\pi\) | |||||||
\(6\) | 2.67819 | 1.09337 | ||||||||
\(7\) | 2.66447 | 1.00707 | 0.503537 | − | 0.863974i | \(-0.332032\pi\) | ||||
0.503537 | + | 0.863974i | \(0.332032\pi\) | |||||||
\(8\) | −8.49705 | −3.00416 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.18580 | 0.691209 | ||||||||
\(11\) | −4.90582 | −1.47916 | −0.739581 | − | 0.673068i | \(-0.764976\pi\) | ||||
−0.739581 | + | 0.673068i | \(0.764976\pi\) | |||||||
\(12\) | −5.17269 | −1.49323 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −7.13595 | −1.90716 | ||||||||
\(15\) | 0.816148 | 0.210728 | ||||||||
\(16\) | 12.4113 | 3.10283 | ||||||||
\(17\) | −0.150239 | −0.0364383 | −0.0182191 | − | 0.999834i | \(-0.505800\pi\) | ||||
−0.0182191 | + | 0.999834i | \(0.505800\pi\) | |||||||
\(18\) | −2.67819 | −0.631255 | ||||||||
\(19\) | −3.45812 | −0.793348 | −0.396674 | − | 0.917960i | \(-0.629836\pi\) | ||||
−0.396674 | + | 0.917960i | \(0.629836\pi\) | |||||||
\(20\) | −4.22168 | −0.943995 | ||||||||
\(21\) | −2.66447 | −0.581435 | ||||||||
\(22\) | 13.1387 | 2.80118 | ||||||||
\(23\) | 5.22262 | 1.08899 | 0.544496 | − | 0.838764i | \(-0.316721\pi\) | ||||
0.544496 | + | 0.838764i | \(0.316721\pi\) | |||||||
\(24\) | 8.49705 | 1.73445 | ||||||||
\(25\) | −4.33390 | −0.866781 | ||||||||
\(26\) | −2.67819 | −0.525236 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 13.7825 | 2.60464 | ||||||||
\(29\) | 1.72389 | 0.320119 | 0.160060 | − | 0.987107i | \(-0.448831\pi\) | ||||
0.160060 | + | 0.987107i | \(0.448831\pi\) | |||||||
\(30\) | −2.18580 | −0.399070 | ||||||||
\(31\) | 3.01241 | 0.541045 | 0.270522 | − | 0.962714i | \(-0.412804\pi\) | ||||
0.270522 | + | 0.962714i | \(0.412804\pi\) | |||||||
\(32\) | −16.2457 | −2.87186 | ||||||||
\(33\) | 4.90582 | 0.853994 | ||||||||
\(34\) | 0.402368 | 0.0690055 | ||||||||
\(35\) | −2.17460 | −0.367574 | ||||||||
\(36\) | 5.17269 | 0.862114 | ||||||||
\(37\) | 2.05174 | 0.337304 | 0.168652 | − | 0.985676i | \(-0.446059\pi\) | ||||
0.168652 | + | 0.985676i | \(0.446059\pi\) | |||||||
\(38\) | 9.26150 | 1.50241 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 6.93485 | 1.09650 | ||||||||
\(41\) | 2.13055 | 0.332736 | 0.166368 | − | 0.986064i | \(-0.446796\pi\) | ||||
0.166368 | + | 0.986064i | \(0.446796\pi\) | |||||||
\(42\) | 7.13595 | 1.10110 | ||||||||
\(43\) | 10.9396 | 1.66827 | 0.834136 | − | 0.551559i | \(-0.185967\pi\) | ||||
0.834136 | + | 0.551559i | \(0.185967\pi\) | |||||||
\(44\) | −25.3763 | −3.82562 | ||||||||
\(45\) | −0.816148 | −0.121664 | ||||||||
\(46\) | −13.9871 | −2.06229 | ||||||||
\(47\) | −11.7752 | −1.71759 | −0.858794 | − | 0.512321i | \(-0.828786\pi\) | ||||
−0.858794 | + | 0.512321i | \(0.828786\pi\) | |||||||
\(48\) | −12.4113 | −1.79142 | ||||||||
\(49\) | 0.0993928 | 0.0141990 | ||||||||
\(50\) | 11.6070 | 1.64148 | ||||||||
\(51\) | 0.150239 | 0.0210377 | ||||||||
\(52\) | 5.17269 | 0.717323 | ||||||||
\(53\) | −1.20350 | −0.165314 | −0.0826569 | − | 0.996578i | \(-0.526341\pi\) | ||||
−0.0826569 | + | 0.996578i | \(0.526341\pi\) | |||||||
\(54\) | 2.67819 | 0.364455 | ||||||||
\(55\) | 4.00388 | 0.539883 | ||||||||
\(56\) | −22.6401 | −3.02541 | ||||||||
\(57\) | 3.45812 | 0.458039 | ||||||||
\(58\) | −4.61691 | −0.606230 | ||||||||
\(59\) | 7.75006 | 1.00897 | 0.504486 | − | 0.863420i | \(-0.331682\pi\) | ||||
0.504486 | + | 0.863420i | \(0.331682\pi\) | |||||||
\(60\) | 4.22168 | 0.545016 | ||||||||
\(61\) | 1.57774 | 0.202008 | 0.101004 | − | 0.994886i | \(-0.467794\pi\) | ||||
0.101004 | + | 0.994886i | \(0.467794\pi\) | |||||||
\(62\) | −8.06780 | −1.02461 | ||||||||
\(63\) | 2.66447 | 0.335691 | ||||||||
\(64\) | 18.6865 | 2.33581 | ||||||||
\(65\) | −0.816148 | −0.101231 | ||||||||
\(66\) | −13.1387 | −1.61726 | ||||||||
\(67\) | 2.58696 | 0.316047 | 0.158023 | − | 0.987435i | \(-0.449488\pi\) | ||||
0.158023 | + | 0.987435i | \(0.449488\pi\) | |||||||
\(68\) | −0.777139 | −0.0942419 | ||||||||
\(69\) | −5.22262 | −0.628729 | ||||||||
\(70\) | 5.82398 | 0.696099 | ||||||||
\(71\) | 6.48544 | 0.769680 | 0.384840 | − | 0.922983i | \(-0.374257\pi\) | ||||
0.384840 | + | 0.922983i | \(0.374257\pi\) | |||||||
\(72\) | −8.49705 | −1.00139 | ||||||||
\(73\) | −4.43124 | −0.518637 | −0.259319 | − | 0.965792i | \(-0.583498\pi\) | ||||
−0.259319 | + | 0.965792i | \(0.583498\pi\) | |||||||
\(74\) | −5.49495 | −0.638775 | ||||||||
\(75\) | 4.33390 | 0.500436 | ||||||||
\(76\) | −17.8878 | −2.05187 | ||||||||
\(77\) | −13.0714 | −1.48963 | ||||||||
\(78\) | 2.67819 | 0.303245 | ||||||||
\(79\) | −16.8786 | −1.89899 | −0.949497 | − | 0.313776i | \(-0.898406\pi\) | ||||
−0.949497 | + | 0.313776i | \(0.898406\pi\) | |||||||
\(80\) | −10.1295 | −1.13251 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.70601 | −0.630123 | ||||||||
\(83\) | −6.17640 | −0.677948 | −0.338974 | − | 0.940796i | \(-0.610080\pi\) | ||||
−0.338974 | + | 0.940796i | \(0.610080\pi\) | |||||||
\(84\) | −13.7825 | −1.50379 | ||||||||
\(85\) | 0.122617 | 0.0132997 | ||||||||
\(86\) | −29.2983 | −3.15931 | ||||||||
\(87\) | −1.72389 | −0.184821 | ||||||||
\(88\) | 41.6850 | 4.44364 | ||||||||
\(89\) | −6.83716 | −0.724738 | −0.362369 | − | 0.932035i | \(-0.618032\pi\) | ||||
−0.362369 | + | 0.932035i | \(0.618032\pi\) | |||||||
\(90\) | 2.18580 | 0.230403 | ||||||||
\(91\) | 2.66447 | 0.279312 | ||||||||
\(92\) | 27.0150 | 2.81651 | ||||||||
\(93\) | −3.01241 | −0.312372 | ||||||||
\(94\) | 31.5362 | 3.25271 | ||||||||
\(95\) | 2.82234 | 0.289566 | ||||||||
\(96\) | 16.2457 | 1.65807 | ||||||||
\(97\) | −10.1862 | −1.03426 | −0.517128 | − | 0.855908i | \(-0.672999\pi\) | ||||
−0.517128 | + | 0.855908i | \(0.672999\pi\) | |||||||
\(98\) | −0.266192 | −0.0268895 | ||||||||
\(99\) | −4.90582 | −0.493054 | ||||||||
\(100\) | −22.4179 | −2.24179 | ||||||||
\(101\) | 13.5461 | 1.34789 | 0.673944 | − | 0.738782i | \(-0.264599\pi\) | ||||
0.673944 | + | 0.738782i | \(0.264599\pi\) | |||||||
\(102\) | −0.402368 | −0.0398404 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −8.49705 | −0.833204 | ||||||||
\(105\) | 2.17460 | 0.212219 | ||||||||
\(106\) | 3.22321 | 0.313065 | ||||||||
\(107\) | −11.5565 | −1.11721 | −0.558604 | − | 0.829434i | \(-0.688663\pi\) | ||||
−0.558604 | + | 0.829434i | \(0.688663\pi\) | |||||||
\(108\) | −5.17269 | −0.497742 | ||||||||
\(109\) | −6.71143 | −0.642838 | −0.321419 | − | 0.946937i | \(-0.604160\pi\) | ||||
−0.321419 | + | 0.946937i | \(0.604160\pi\) | |||||||
\(110\) | −10.7231 | −1.02241 | ||||||||
\(111\) | −2.05174 | −0.194743 | ||||||||
\(112\) | 33.0696 | 3.12478 | ||||||||
\(113\) | 5.83028 | 0.548467 | 0.274233 | − | 0.961663i | \(-0.411576\pi\) | ||||
0.274233 | + | 0.961663i | \(0.411576\pi\) | |||||||
\(114\) | −9.26150 | −0.867419 | ||||||||
\(115\) | −4.26243 | −0.397473 | ||||||||
\(116\) | 8.91716 | 0.827938 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −20.7561 | −1.91075 | ||||||||
\(119\) | −0.400307 | −0.0366961 | ||||||||
\(120\) | −6.93485 | −0.633062 | ||||||||
\(121\) | 13.0671 | 1.18792 | ||||||||
\(122\) | −4.22547 | −0.382556 | ||||||||
\(123\) | −2.13055 | −0.192105 | ||||||||
\(124\) | 15.5823 | 1.39933 | ||||||||
\(125\) | 7.61784 | 0.681361 | ||||||||
\(126\) | −7.13595 | −0.635721 | ||||||||
\(127\) | 5.37964 | 0.477366 | 0.238683 | − | 0.971098i | \(-0.423284\pi\) | ||||
0.238683 | + | 0.971098i | \(0.423284\pi\) | |||||||
\(128\) | −17.5544 | −1.55160 | ||||||||
\(129\) | −10.9396 | −0.963177 | ||||||||
\(130\) | 2.18580 | 0.191707 | ||||||||
\(131\) | 6.39454 | 0.558694 | 0.279347 | − | 0.960190i | \(-0.409882\pi\) | ||||
0.279347 | + | 0.960190i | \(0.409882\pi\) | |||||||
\(132\) | 25.3763 | 2.20872 | ||||||||
\(133\) | −9.21406 | −0.798960 | ||||||||
\(134\) | −6.92835 | −0.598518 | ||||||||
\(135\) | 0.816148 | 0.0702428 | ||||||||
\(136\) | 1.27659 | 0.109466 | ||||||||
\(137\) | −14.7694 | −1.26184 | −0.630919 | − | 0.775849i | \(-0.717322\pi\) | ||||
−0.630919 | + | 0.775849i | \(0.717322\pi\) | |||||||
\(138\) | 13.9871 | 1.19067 | ||||||||
\(139\) | 11.8823 | 1.00784 | 0.503920 | − | 0.863750i | \(-0.331891\pi\) | ||||
0.503920 | + | 0.863750i | \(0.331891\pi\) | |||||||
\(140\) | −11.2485 | −0.950674 | ||||||||
\(141\) | 11.7752 | 0.991650 | ||||||||
\(142\) | −17.3692 | −1.45759 | ||||||||
\(143\) | −4.90582 | −0.410246 | ||||||||
\(144\) | 12.4113 | 1.03428 | ||||||||
\(145\) | −1.40695 | −0.116841 | ||||||||
\(146\) | 11.8677 | 0.982177 | ||||||||
\(147\) | −0.0993928 | −0.00819778 | ||||||||
\(148\) | 10.6130 | 0.872384 | ||||||||
\(149\) | 14.6445 | 1.19972 | 0.599861 | − | 0.800104i | \(-0.295222\pi\) | ||||
0.599861 | + | 0.800104i | \(0.295222\pi\) | |||||||
\(150\) | −11.6070 | −0.947708 | ||||||||
\(151\) | 1.53386 | 0.124823 | 0.0624117 | − | 0.998050i | \(-0.480121\pi\) | ||||
0.0624117 | + | 0.998050i | \(0.480121\pi\) | |||||||
\(152\) | 29.3838 | 2.38334 | ||||||||
\(153\) | −0.150239 | −0.0121461 | ||||||||
\(154\) | 35.0077 | 2.82100 | ||||||||
\(155\) | −2.45857 | −0.197477 | ||||||||
\(156\) | −5.17269 | −0.414146 | ||||||||
\(157\) | 4.15537 | 0.331635 | 0.165817 | − | 0.986156i | \(-0.446974\pi\) | ||||
0.165817 | + | 0.986156i | \(0.446974\pi\) | |||||||
\(158\) | 45.2041 | 3.59625 | ||||||||
\(159\) | 1.20350 | 0.0954440 | ||||||||
\(160\) | 13.2589 | 1.04821 | ||||||||
\(161\) | 13.9155 | 1.09670 | ||||||||
\(162\) | −2.67819 | −0.210418 | ||||||||
\(163\) | −16.2436 | −1.27230 | −0.636149 | − | 0.771566i | \(-0.719474\pi\) | ||||
−0.636149 | + | 0.771566i | \(0.719474\pi\) | |||||||
\(164\) | 11.0207 | 0.860569 | ||||||||
\(165\) | −4.00388 | −0.311701 | ||||||||
\(166\) | 16.5416 | 1.28387 | ||||||||
\(167\) | −17.6564 | −1.36629 | −0.683147 | − | 0.730281i | \(-0.739389\pi\) | ||||
−0.683147 | + | 0.730281i | \(0.739389\pi\) | |||||||
\(168\) | 22.6401 | 1.74672 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.328392 | −0.0251865 | ||||||||
\(171\) | −3.45812 | −0.264449 | ||||||||
\(172\) | 56.5871 | 4.31472 | ||||||||
\(173\) | −0.127174 | −0.00966882 | −0.00483441 | − | 0.999988i | \(-0.501539\pi\) | ||||
−0.00483441 | + | 0.999988i | \(0.501539\pi\) | |||||||
\(174\) | 4.61691 | 0.350007 | ||||||||
\(175\) | −11.5475 | −0.872913 | ||||||||
\(176\) | −60.8877 | −4.58958 | ||||||||
\(177\) | −7.75006 | −0.582530 | ||||||||
\(178\) | 18.3112 | 1.37248 | ||||||||
\(179\) | 20.7246 | 1.54903 | 0.774515 | − | 0.632555i | \(-0.217994\pi\) | ||||
0.774515 | + | 0.632555i | \(0.217994\pi\) | |||||||
\(180\) | −4.22168 | −0.314665 | ||||||||
\(181\) | 9.58936 | 0.712771 | 0.356386 | − | 0.934339i | \(-0.384009\pi\) | ||||
0.356386 | + | 0.934339i | \(0.384009\pi\) | |||||||
\(182\) | −7.13595 | −0.528951 | ||||||||
\(183\) | −1.57774 | −0.116630 | ||||||||
\(184\) | −44.3768 | −3.27150 | ||||||||
\(185\) | −1.67452 | −0.123113 | ||||||||
\(186\) | 8.06780 | 0.591560 | ||||||||
\(187\) | 0.737046 | 0.0538981 | ||||||||
\(188\) | −60.9094 | −4.44227 | ||||||||
\(189\) | −2.66447 | −0.193812 | ||||||||
\(190\) | −7.55875 | −0.548369 | ||||||||
\(191\) | −2.60615 | −0.188574 | −0.0942872 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942872 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(192\) | −18.6865 | −1.34858 | ||||||||
\(193\) | −11.9245 | −0.858344 | −0.429172 | − | 0.903223i | \(-0.641195\pi\) | ||||
−0.429172 | + | 0.903223i | \(0.641195\pi\) | |||||||
\(194\) | 27.2806 | 1.95864 | ||||||||
\(195\) | 0.816148 | 0.0584455 | ||||||||
\(196\) | 0.514128 | 0.0367234 | ||||||||
\(197\) | −3.22487 | −0.229763 | −0.114881 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114881 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(198\) | 13.1387 | 0.933728 | ||||||||
\(199\) | −10.3872 | −0.736332 | −0.368166 | − | 0.929760i | \(-0.620014\pi\) | ||||
−0.368166 | + | 0.929760i | \(0.620014\pi\) | |||||||
\(200\) | 36.8254 | 2.60395 | ||||||||
\(201\) | −2.58696 | −0.182470 | ||||||||
\(202\) | −36.2790 | −2.55258 | ||||||||
\(203\) | 4.59326 | 0.322384 | ||||||||
\(204\) | 0.777139 | 0.0544106 | ||||||||
\(205\) | −1.73884 | −0.121446 | ||||||||
\(206\) | −2.67819 | −0.186598 | ||||||||
\(207\) | 5.22262 | 0.362997 | ||||||||
\(208\) | 12.4113 | 0.860570 | ||||||||
\(209\) | 16.9649 | 1.17349 | ||||||||
\(210\) | −5.82398 | −0.401893 | ||||||||
\(211\) | −24.1156 | −1.66019 | −0.830093 | − | 0.557625i | \(-0.811713\pi\) | ||||
−0.830093 | + | 0.557625i | \(0.811713\pi\) | |||||||
\(212\) | −6.22534 | −0.427558 | ||||||||
\(213\) | −6.48544 | −0.444375 | ||||||||
\(214\) | 30.9505 | 2.11573 | ||||||||
\(215\) | −8.92832 | −0.608906 | ||||||||
\(216\) | 8.49705 | 0.578151 | ||||||||
\(217\) | 8.02647 | 0.544872 | ||||||||
\(218\) | 17.9745 | 1.21738 | ||||||||
\(219\) | 4.43124 | 0.299435 | ||||||||
\(220\) | 20.7108 | 1.39632 | ||||||||
\(221\) | −0.150239 | −0.0101062 | ||||||||
\(222\) | 5.49495 | 0.368797 | ||||||||
\(223\) | 7.68138 | 0.514383 | 0.257192 | − | 0.966360i | \(-0.417203\pi\) | ||||
0.257192 | + | 0.966360i | \(0.417203\pi\) | |||||||
\(224\) | −43.2862 | −2.89218 | ||||||||
\(225\) | −4.33390 | −0.288927 | ||||||||
\(226\) | −15.6146 | −1.03867 | ||||||||
\(227\) | −19.5030 | −1.29446 | −0.647231 | − | 0.762294i | \(-0.724073\pi\) | ||||
−0.647231 | + | 0.762294i | \(0.724073\pi\) | |||||||
\(228\) | 17.8878 | 1.18465 | ||||||||
\(229\) | 22.7830 | 1.50555 | 0.752773 | − | 0.658280i | \(-0.228716\pi\) | ||||
0.752773 | + | 0.658280i | \(0.228716\pi\) | |||||||
\(230\) | 11.4156 | 0.752721 | ||||||||
\(231\) | 13.0714 | 0.860036 | ||||||||
\(232\) | −14.6480 | −0.961689 | ||||||||
\(233\) | 15.3466 | 1.00539 | 0.502694 | − | 0.864464i | \(-0.332342\pi\) | ||||
0.502694 | + | 0.864464i | \(0.332342\pi\) | |||||||
\(234\) | −2.67819 | −0.175079 | ||||||||
\(235\) | 9.61029 | 0.626906 | ||||||||
\(236\) | 40.0886 | 2.60955 | ||||||||
\(237\) | 16.8786 | 1.09638 | ||||||||
\(238\) | 1.07210 | 0.0694937 | ||||||||
\(239\) | 25.2224 | 1.63150 | 0.815750 | − | 0.578405i | \(-0.196325\pi\) | ||||
0.815750 | + | 0.578405i | \(0.196325\pi\) | |||||||
\(240\) | 10.1295 | 0.653854 | ||||||||
\(241\) | 10.1216 | 0.651990 | 0.325995 | − | 0.945371i | \(-0.394301\pi\) | ||||
0.325995 | + | 0.945371i | \(0.394301\pi\) | |||||||
\(242\) | −34.9962 | −2.24964 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.16113 | 0.522463 | ||||||||
\(245\) | −0.0811192 | −0.00518251 | ||||||||
\(246\) | 5.70601 | 0.363802 | ||||||||
\(247\) | −3.45812 | −0.220035 | ||||||||
\(248\) | −25.5966 | −1.62539 | ||||||||
\(249\) | 6.17640 | 0.391413 | ||||||||
\(250\) | −20.4020 | −1.29034 | ||||||||
\(251\) | −13.0005 | −0.820586 | −0.410293 | − | 0.911954i | \(-0.634574\pi\) | ||||
−0.410293 | + | 0.911954i | \(0.634574\pi\) | |||||||
\(252\) | 13.7825 | 0.868213 | ||||||||
\(253\) | −25.6212 | −1.61079 | ||||||||
\(254\) | −14.4077 | −0.904018 | ||||||||
\(255\) | −0.122617 | −0.00767858 | ||||||||
\(256\) | 9.64102 | 0.602564 | ||||||||
\(257\) | −6.57923 | −0.410401 | −0.205201 | − | 0.978720i | \(-0.565785\pi\) | ||||
−0.205201 | + | 0.978720i | \(0.565785\pi\) | |||||||
\(258\) | 29.2983 | 1.82403 | ||||||||
\(259\) | 5.46680 | 0.339690 | ||||||||
\(260\) | −4.22168 | −0.261817 | ||||||||
\(261\) | 1.72389 | 0.106706 | ||||||||
\(262\) | −17.1258 | −1.05803 | ||||||||
\(263\) | −25.5709 | −1.57677 | −0.788386 | − | 0.615181i | \(-0.789083\pi\) | ||||
−0.788386 | + | 0.615181i | \(0.789083\pi\) | |||||||
\(264\) | −41.6850 | −2.56554 | ||||||||
\(265\) | 0.982236 | 0.0603383 | ||||||||
\(266\) | 24.6770 | 1.51304 | ||||||||
\(267\) | 6.83716 | 0.418428 | ||||||||
\(268\) | 13.3815 | 0.817406 | ||||||||
\(269\) | 25.5158 | 1.55572 | 0.777862 | − | 0.628435i | \(-0.216304\pi\) | ||||
0.777862 | + | 0.628435i | \(0.216304\pi\) | |||||||
\(270\) | −2.18580 | −0.133023 | ||||||||
\(271\) | 14.6062 | 0.887262 | 0.443631 | − | 0.896209i | \(-0.353690\pi\) | ||||
0.443631 | + | 0.896209i | \(0.353690\pi\) | |||||||
\(272\) | −1.86466 | −0.113062 | ||||||||
\(273\) | −2.66447 | −0.161261 | ||||||||
\(274\) | 39.5553 | 2.38962 | ||||||||
\(275\) | 21.2614 | 1.28211 | ||||||||
\(276\) | −27.0150 | −1.62611 | ||||||||
\(277\) | −26.7074 | −1.60469 | −0.802346 | − | 0.596860i | \(-0.796415\pi\) | ||||
−0.802346 | + | 0.596860i | \(0.796415\pi\) | |||||||
\(278\) | −31.8229 | −1.90861 | ||||||||
\(279\) | 3.01241 | 0.180348 | ||||||||
\(280\) | 18.4777 | 1.10425 | ||||||||
\(281\) | 10.6028 | 0.632511 | 0.316256 | − | 0.948674i | \(-0.397574\pi\) | ||||
0.316256 | + | 0.948674i | \(0.397574\pi\) | |||||||
\(282\) | −31.5362 | −1.87795 | ||||||||
\(283\) | −23.3746 | −1.38948 | −0.694738 | − | 0.719263i | \(-0.744480\pi\) | ||||
−0.694738 | + | 0.719263i | \(0.744480\pi\) | |||||||
\(284\) | 33.5471 | 1.99066 | ||||||||
\(285\) | −2.82234 | −0.167181 | ||||||||
\(286\) | 13.1387 | 0.776908 | ||||||||
\(287\) | 5.67678 | 0.335090 | ||||||||
\(288\) | −16.2457 | −0.957288 | ||||||||
\(289\) | −16.9774 | −0.998672 | ||||||||
\(290\) | 3.76808 | 0.221269 | ||||||||
\(291\) | 10.1862 | 0.597128 | ||||||||
\(292\) | −22.9214 | −1.34137 | ||||||||
\(293\) | −4.37189 | −0.255409 | −0.127704 | − | 0.991812i | \(-0.540761\pi\) | ||||
−0.127704 | + | 0.991812i | \(0.540761\pi\) | |||||||
\(294\) | 0.266192 | 0.0155247 | ||||||||
\(295\) | −6.32519 | −0.368267 | ||||||||
\(296\) | −17.4337 | −1.01332 | ||||||||
\(297\) | 4.90582 | 0.284665 | ||||||||
\(298\) | −39.2207 | −2.27199 | ||||||||
\(299\) | 5.22262 | 0.302032 | ||||||||
\(300\) | 22.4179 | 1.29430 | ||||||||
\(301\) | 29.1482 | 1.68007 | ||||||||
\(302\) | −4.10795 | −0.236386 | ||||||||
\(303\) | −13.5461 | −0.778204 | ||||||||
\(304\) | −42.9198 | −2.46162 | ||||||||
\(305\) | −1.28767 | −0.0737315 | ||||||||
\(306\) | 0.402368 | 0.0230018 | ||||||||
\(307\) | 12.8794 | 0.735065 | 0.367532 | − | 0.930011i | \(-0.380203\pi\) | ||||
0.367532 | + | 0.930011i | \(0.380203\pi\) | |||||||
\(308\) | −67.6143 | −3.85268 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 6.58451 | 0.373975 | ||||||||
\(311\) | 6.88182 | 0.390232 | 0.195116 | − | 0.980780i | \(-0.437492\pi\) | ||||
0.195116 | + | 0.980780i | \(0.437492\pi\) | |||||||
\(312\) | 8.49705 | 0.481051 | ||||||||
\(313\) | −1.55141 | −0.0876911 | −0.0438456 | − | 0.999038i | \(-0.513961\pi\) | ||||
−0.0438456 | + | 0.999038i | \(0.513961\pi\) | |||||||
\(314\) | −11.1289 | −0.628038 | ||||||||
\(315\) | −2.17460 | −0.122525 | ||||||||
\(316\) | −87.3079 | −4.91145 | ||||||||
\(317\) | 5.47049 | 0.307253 | 0.153627 | − | 0.988129i | \(-0.450905\pi\) | ||||
0.153627 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(318\) | −3.22321 | −0.180748 | ||||||||
\(319\) | −8.45712 | −0.473508 | ||||||||
\(320\) | −15.2509 | −0.852552 | ||||||||
\(321\) | 11.5565 | 0.645021 | ||||||||
\(322\) | −37.2683 | −2.07688 | ||||||||
\(323\) | 0.519544 | 0.0289082 | ||||||||
\(324\) | 5.17269 | 0.287371 | ||||||||
\(325\) | −4.33390 | −0.240402 | ||||||||
\(326\) | 43.5035 | 2.40943 | ||||||||
\(327\) | 6.71143 | 0.371143 | ||||||||
\(328\) | −18.1034 | −0.999592 | ||||||||
\(329\) | −31.3746 | −1.72974 | ||||||||
\(330\) | 10.7231 | 0.590289 | ||||||||
\(331\) | −2.13491 | −0.117345 | −0.0586727 | − | 0.998277i | \(-0.518687\pi\) | ||||
−0.0586727 | + | 0.998277i | \(0.518687\pi\) | |||||||
\(332\) | −31.9486 | −1.75341 | ||||||||
\(333\) | 2.05174 | 0.112435 | ||||||||
\(334\) | 47.2871 | 2.58744 | ||||||||
\(335\) | −2.11134 | −0.115355 | ||||||||
\(336\) | −33.0696 | −1.80409 | ||||||||
\(337\) | −11.6444 | −0.634312 | −0.317156 | − | 0.948373i | \(-0.602728\pi\) | ||||
−0.317156 | + | 0.948373i | \(0.602728\pi\) | |||||||
\(338\) | −2.67819 | −0.145674 | ||||||||
\(339\) | −5.83028 | −0.316658 | ||||||||
\(340\) | 0.634260 | 0.0343976 | ||||||||
\(341\) | −14.7784 | −0.800293 | ||||||||
\(342\) | 9.26150 | 0.500804 | ||||||||
\(343\) | −18.3865 | −0.992775 | ||||||||
\(344\) | −92.9542 | −5.01176 | ||||||||
\(345\) | 4.26243 | 0.229481 | ||||||||
\(346\) | 0.340594 | 0.0183105 | ||||||||
\(347\) | −13.1131 | −0.703946 | −0.351973 | − | 0.936010i | \(-0.614489\pi\) | ||||
−0.351973 | + | 0.936010i | \(0.614489\pi\) | |||||||
\(348\) | −8.91716 | −0.478010 | ||||||||
\(349\) | −27.7442 | −1.48511 | −0.742557 | − | 0.669783i | \(-0.766387\pi\) | ||||
−0.742557 | + | 0.669783i | \(0.766387\pi\) | |||||||
\(350\) | 30.9265 | 1.65309 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 79.6986 | 4.24795 | ||||||||
\(353\) | −2.13348 | −0.113554 | −0.0567768 | − | 0.998387i | \(-0.518082\pi\) | ||||
−0.0567768 | + | 0.998387i | \(0.518082\pi\) | |||||||
\(354\) | 20.7561 | 1.10317 | ||||||||
\(355\) | −5.29307 | −0.280927 | ||||||||
\(356\) | −35.3665 | −1.87442 | ||||||||
\(357\) | 0.400307 | 0.0211865 | ||||||||
\(358\) | −55.5044 | −2.93350 | ||||||||
\(359\) | −37.3887 | −1.97330 | −0.986649 | − | 0.162862i | \(-0.947927\pi\) | ||||
−0.986649 | + | 0.162862i | \(0.947927\pi\) | |||||||
\(360\) | 6.93485 | 0.365498 | ||||||||
\(361\) | −7.04139 | −0.370600 | ||||||||
\(362\) | −25.6821 | −1.34982 | ||||||||
\(363\) | −13.0671 | −0.685845 | ||||||||
\(364\) | 13.7825 | 0.722397 | ||||||||
\(365\) | 3.61655 | 0.189299 | ||||||||
\(366\) | 4.22547 | 0.220869 | ||||||||
\(367\) | 15.3139 | 0.799378 | 0.399689 | − | 0.916651i | \(-0.369118\pi\) | ||||
0.399689 | + | 0.916651i | \(0.369118\pi\) | |||||||
\(368\) | 64.8195 | 3.37895 | ||||||||
\(369\) | 2.13055 | 0.110912 | ||||||||
\(370\) | 4.48469 | 0.233148 | ||||||||
\(371\) | −3.20670 | −0.166483 | ||||||||
\(372\) | −15.5823 | −0.807902 | ||||||||
\(373\) | 33.2937 | 1.72388 | 0.861941 | − | 0.507009i | \(-0.169249\pi\) | ||||
0.861941 | + | 0.507009i | \(0.169249\pi\) | |||||||
\(374\) | −1.97395 | −0.102070 | ||||||||
\(375\) | −7.61784 | −0.393384 | ||||||||
\(376\) | 100.054 | 5.15991 | ||||||||
\(377\) | 1.72389 | 0.0887850 | ||||||||
\(378\) | 7.13595 | 0.367033 | ||||||||
\(379\) | −0.138115 | −0.00709448 | −0.00354724 | − | 0.999994i | \(-0.501129\pi\) | ||||
−0.00354724 | + | 0.999994i | \(0.501129\pi\) | |||||||
\(380\) | 14.5991 | 0.748916 | ||||||||
\(381\) | −5.37964 | −0.275607 | ||||||||
\(382\) | 6.97976 | 0.357115 | ||||||||
\(383\) | −15.2032 | −0.776848 | −0.388424 | − | 0.921481i | \(-0.626980\pi\) | ||||
−0.388424 | + | 0.921481i | \(0.626980\pi\) | |||||||
\(384\) | 17.5544 | 0.895819 | ||||||||
\(385\) | 10.6682 | 0.543702 | ||||||||
\(386\) | 31.9360 | 1.62550 | ||||||||
\(387\) | 10.9396 | 0.556091 | ||||||||
\(388\) | −52.6902 | −2.67494 | ||||||||
\(389\) | −17.2775 | −0.876006 | −0.438003 | − | 0.898973i | \(-0.644314\pi\) | ||||
−0.438003 | + | 0.898973i | \(0.644314\pi\) | |||||||
\(390\) | −2.18580 | −0.110682 | ||||||||
\(391\) | −0.784641 | −0.0396810 | ||||||||
\(392\) | −0.844545 | −0.0426560 | ||||||||
\(393\) | −6.39454 | −0.322562 | ||||||||
\(394\) | 8.63681 | 0.435116 | ||||||||
\(395\) | 13.7755 | 0.693118 | ||||||||
\(396\) | −25.3763 | −1.27521 | ||||||||
\(397\) | 14.4199 | 0.723716 | 0.361858 | − | 0.932233i | \(-0.382143\pi\) | ||||
0.361858 | + | 0.932233i | \(0.382143\pi\) | |||||||
\(398\) | 27.8190 | 1.39444 | ||||||||
\(399\) | 9.21406 | 0.461280 | ||||||||
\(400\) | −53.7894 | −2.68947 | ||||||||
\(401\) | −24.2583 | −1.21140 | −0.605702 | − | 0.795692i | \(-0.707108\pi\) | ||||
−0.605702 | + | 0.795692i | \(0.707108\pi\) | |||||||
\(402\) | 6.92835 | 0.345555 | ||||||||
\(403\) | 3.01241 | 0.150059 | ||||||||
\(404\) | 70.0698 | 3.48610 | ||||||||
\(405\) | −0.816148 | −0.0405547 | ||||||||
\(406\) | −12.3016 | −0.610519 | ||||||||
\(407\) | −10.0655 | −0.498927 | ||||||||
\(408\) | −1.27659 | −0.0632005 | ||||||||
\(409\) | −32.5377 | −1.60889 | −0.804443 | − | 0.594029i | \(-0.797536\pi\) | ||||
−0.804443 | + | 0.594029i | \(0.797536\pi\) | |||||||
\(410\) | 4.65694 | 0.229990 | ||||||||
\(411\) | 14.7694 | 0.728522 | ||||||||
\(412\) | 5.17269 | 0.254840 | ||||||||
\(413\) | 20.6498 | 1.01611 | ||||||||
\(414\) | −13.9871 | −0.687431 | ||||||||
\(415\) | 5.04085 | 0.247446 | ||||||||
\(416\) | −16.2457 | −0.796512 | ||||||||
\(417\) | −11.8823 | −0.581877 | ||||||||
\(418\) | −45.4353 | −2.22231 | ||||||||
\(419\) | −12.0506 | −0.588711 | −0.294355 | − | 0.955696i | \(-0.595105\pi\) | ||||
−0.294355 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(420\) | 11.2485 | 0.548872 | ||||||||
\(421\) | −27.5759 | −1.34397 | −0.671984 | − | 0.740566i | \(-0.734557\pi\) | ||||
−0.671984 | + | 0.740566i | \(0.734557\pi\) | |||||||
\(422\) | 64.5861 | 3.14400 | ||||||||
\(423\) | −11.7752 | −0.572529 | ||||||||
\(424\) | 10.2262 | 0.496629 | ||||||||
\(425\) | 0.651121 | 0.0315840 | ||||||||
\(426\) | 17.3692 | 0.841541 | ||||||||
\(427\) | 4.20383 | 0.203437 | ||||||||
\(428\) | −59.7781 | −2.88948 | ||||||||
\(429\) | 4.90582 | 0.236855 | ||||||||
\(430\) | 23.9117 | 1.15313 | ||||||||
\(431\) | 10.4532 | 0.503513 | 0.251756 | − | 0.967791i | \(-0.418992\pi\) | ||||
0.251756 | + | 0.967791i | \(0.418992\pi\) | |||||||
\(432\) | −12.4113 | −0.597140 | ||||||||
\(433\) | −19.2962 | −0.927317 | −0.463659 | − | 0.886014i | \(-0.653464\pi\) | ||||
−0.463659 | + | 0.886014i | \(0.653464\pi\) | |||||||
\(434\) | −21.4964 | −1.03186 | ||||||||
\(435\) | 1.40695 | 0.0674582 | ||||||||
\(436\) | −34.7161 | −1.66260 | ||||||||
\(437\) | −18.0605 | −0.863949 | ||||||||
\(438\) | −11.8677 | −0.567060 | ||||||||
\(439\) | −18.6809 | −0.891591 | −0.445796 | − | 0.895135i | \(-0.647079\pi\) | ||||
−0.445796 | + | 0.895135i | \(0.647079\pi\) | |||||||
\(440\) | −34.0211 | −1.62189 | ||||||||
\(441\) | 0.0993928 | 0.00473299 | ||||||||
\(442\) | 0.402368 | 0.0191387 | ||||||||
\(443\) | −28.8522 | −1.37081 | −0.685404 | − | 0.728163i | \(-0.740375\pi\) | ||||
−0.685404 | + | 0.728163i | \(0.740375\pi\) | |||||||
\(444\) | −10.6130 | −0.503671 | ||||||||
\(445\) | 5.58013 | 0.264524 | ||||||||
\(446\) | −20.5722 | −0.974121 | ||||||||
\(447\) | −14.6445 | −0.692660 | ||||||||
\(448\) | 49.7895 | 2.35233 | ||||||||
\(449\) | −9.96075 | −0.470077 | −0.235039 | − | 0.971986i | \(-0.575522\pi\) | ||||
−0.235039 | + | 0.971986i | \(0.575522\pi\) | |||||||
\(450\) | 11.6070 | 0.547159 | ||||||||
\(451\) | −10.4521 | −0.492170 | ||||||||
\(452\) | 30.1582 | 1.41852 | ||||||||
\(453\) | −1.53386 | −0.0720668 | ||||||||
\(454\) | 52.2328 | 2.45141 | ||||||||
\(455\) | −2.17460 | −0.101947 | ||||||||
\(456\) | −29.3838 | −1.37602 | ||||||||
\(457\) | 28.6561 | 1.34048 | 0.670239 | − | 0.742145i | \(-0.266192\pi\) | ||||
0.670239 | + | 0.742145i | \(0.266192\pi\) | |||||||
\(458\) | −61.0173 | −2.85115 | ||||||||
\(459\) | 0.150239 | 0.00701255 | ||||||||
\(460\) | −22.0482 | −1.02800 | ||||||||
\(461\) | 1.24025 | 0.0577643 | 0.0288822 | − | 0.999583i | \(-0.490805\pi\) | ||||
0.0288822 | + | 0.999583i | \(0.490805\pi\) | |||||||
\(462\) | −35.0077 | −1.62871 | ||||||||
\(463\) | 12.6747 | 0.589044 | 0.294522 | − | 0.955645i | \(-0.404840\pi\) | ||||
0.294522 | + | 0.955645i | \(0.404840\pi\) | |||||||
\(464\) | 21.3958 | 0.993274 | ||||||||
\(465\) | 2.45857 | 0.114014 | ||||||||
\(466\) | −41.1010 | −1.90397 | ||||||||
\(467\) | −16.7390 | −0.774588 | −0.387294 | − | 0.921956i | \(-0.626590\pi\) | ||||
−0.387294 | + | 0.921956i | \(0.626590\pi\) | |||||||
\(468\) | 5.17269 | 0.239108 | ||||||||
\(469\) | 6.89286 | 0.318283 | ||||||||
\(470\) | −25.7382 | −1.18721 | ||||||||
\(471\) | −4.15537 | −0.191470 | ||||||||
\(472\) | −65.8526 | −3.03111 | ||||||||
\(473\) | −53.6677 | −2.46764 | ||||||||
\(474\) | −45.2041 | −2.07629 | ||||||||
\(475\) | 14.9872 | 0.687658 | ||||||||
\(476\) | −2.07066 | −0.0949086 | ||||||||
\(477\) | −1.20350 | −0.0551046 | ||||||||
\(478\) | −67.5502 | −3.08968 | ||||||||
\(479\) | 9.29020 | 0.424480 | 0.212240 | − | 0.977218i | \(-0.431924\pi\) | ||||
0.212240 | + | 0.977218i | \(0.431924\pi\) | |||||||
\(480\) | −13.2589 | −0.605183 | ||||||||
\(481\) | 2.05174 | 0.0935513 | ||||||||
\(482\) | −27.1076 | −1.23472 | ||||||||
\(483\) | −13.9155 | −0.633177 | ||||||||
\(484\) | 67.5920 | 3.07237 | ||||||||
\(485\) | 8.31347 | 0.377495 | ||||||||
\(486\) | 2.67819 | 0.121485 | ||||||||
\(487\) | −25.2243 | −1.14302 | −0.571511 | − | 0.820595i | \(-0.693642\pi\) | ||||
−0.571511 | + | 0.820595i | \(0.693642\pi\) | |||||||
\(488\) | −13.4061 | −0.606865 | ||||||||
\(489\) | 16.2436 | 0.734562 | ||||||||
\(490\) | 0.217252 | 0.00981446 | ||||||||
\(491\) | 12.6253 | 0.569770 | 0.284885 | − | 0.958562i | \(-0.408045\pi\) | ||||
0.284885 | + | 0.958562i | \(0.408045\pi\) | |||||||
\(492\) | −11.0207 | −0.496850 | ||||||||
\(493\) | −0.258996 | −0.0116646 | ||||||||
\(494\) | 9.26150 | 0.416694 | ||||||||
\(495\) | 4.00388 | 0.179961 | ||||||||
\(496\) | 37.3880 | 1.67877 | ||||||||
\(497\) | 17.2802 | 0.775125 | ||||||||
\(498\) | −16.5416 | −0.741245 | ||||||||
\(499\) | −13.0265 | −0.583144 | −0.291572 | − | 0.956549i | \(-0.594178\pi\) | ||||
−0.291572 | + | 0.956549i | \(0.594178\pi\) | |||||||
\(500\) | 39.4047 | 1.76223 | ||||||||
\(501\) | 17.6564 | 0.788830 | ||||||||
\(502\) | 34.8178 | 1.55400 | ||||||||
\(503\) | −30.8736 | −1.37658 | −0.688292 | − | 0.725433i | \(-0.741639\pi\) | ||||
−0.688292 | + | 0.725433i | \(0.741639\pi\) | |||||||
\(504\) | −22.6401 | −1.00847 | ||||||||
\(505\) | −11.0556 | −0.491969 | ||||||||
\(506\) | 68.6185 | 3.05046 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 27.8272 | 1.23463 | ||||||||
\(509\) | −16.0289 | −0.710468 | −0.355234 | − | 0.934777i | \(-0.615599\pi\) | ||||
−0.355234 | + | 0.934777i | \(0.615599\pi\) | |||||||
\(510\) | 0.328392 | 0.0145414 | ||||||||
\(511\) | −11.8069 | −0.522306 | ||||||||
\(512\) | 9.28832 | 0.410490 | ||||||||
\(513\) | 3.45812 | 0.152680 | ||||||||
\(514\) | 17.6204 | 0.777203 | ||||||||
\(515\) | −0.816148 | −0.0359638 | ||||||||
\(516\) | −56.5871 | −2.49111 | ||||||||
\(517\) | 57.7670 | 2.54059 | ||||||||
\(518\) | −14.6411 | −0.643294 | ||||||||
\(519\) | 0.127174 | 0.00558230 | ||||||||
\(520\) | 6.93485 | 0.304113 | ||||||||
\(521\) | −15.2180 | −0.666713 | −0.333357 | − | 0.942801i | \(-0.608181\pi\) | ||||
−0.333357 | + | 0.942801i | \(0.608181\pi\) | |||||||
\(522\) | −4.61691 | −0.202077 | ||||||||
\(523\) | −3.52280 | −0.154041 | −0.0770207 | − | 0.997029i | \(-0.524541\pi\) | ||||
−0.0770207 | + | 0.997029i | \(0.524541\pi\) | |||||||
\(524\) | 33.0770 | 1.44497 | ||||||||
\(525\) | 11.5475 | 0.503976 | ||||||||
\(526\) | 68.4838 | 2.98603 | ||||||||
\(527\) | −0.452581 | −0.0197147 | ||||||||
\(528\) | 60.8877 | 2.64980 | ||||||||
\(529\) | 4.27574 | 0.185902 | ||||||||
\(530\) | −2.63061 | −0.114266 | ||||||||
\(531\) | 7.75006 | 0.336324 | ||||||||
\(532\) | −47.6614 | −2.06639 | ||||||||
\(533\) | 2.13055 | 0.0922843 | ||||||||
\(534\) | −18.3112 | −0.792403 | ||||||||
\(535\) | 9.43181 | 0.407773 | ||||||||
\(536\) | −21.9815 | −0.949456 | ||||||||
\(537\) | −20.7246 | −0.894333 | ||||||||
\(538\) | −68.3360 | −2.94617 | ||||||||
\(539\) | −0.487603 | −0.0210026 | ||||||||
\(540\) | 4.22168 | 0.181672 | ||||||||
\(541\) | −40.9206 | −1.75931 | −0.879657 | − | 0.475608i | \(-0.842228\pi\) | ||||
−0.879657 | + | 0.475608i | \(0.842228\pi\) | |||||||
\(542\) | −39.1181 | −1.68027 | ||||||||
\(543\) | −9.58936 | −0.411519 | ||||||||
\(544\) | 2.44074 | 0.104646 | ||||||||
\(545\) | 5.47752 | 0.234631 | ||||||||
\(546\) | 7.13595 | 0.305390 | ||||||||
\(547\) | 41.7784 | 1.78632 | 0.893158 | − | 0.449742i | \(-0.148484\pi\) | ||||
0.893158 | + | 0.449742i | \(0.148484\pi\) | |||||||
\(548\) | −76.3977 | −3.26355 | ||||||||
\(549\) | 1.57774 | 0.0673361 | ||||||||
\(550\) | −56.9419 | −2.42801 | ||||||||
\(551\) | −5.96143 | −0.253966 | ||||||||
\(552\) | 44.3768 | 1.88880 | ||||||||
\(553\) | −44.9726 | −1.91243 | ||||||||
\(554\) | 71.5274 | 3.03891 | ||||||||
\(555\) | 1.67452 | 0.0710796 | ||||||||
\(556\) | 61.4632 | 2.60662 | ||||||||
\(557\) | 32.7538 | 1.38782 | 0.693912 | − | 0.720060i | \(-0.255886\pi\) | ||||
0.693912 | + | 0.720060i | \(0.255886\pi\) | |||||||
\(558\) | −8.06780 | −0.341537 | ||||||||
\(559\) | 10.9396 | 0.462695 | ||||||||
\(560\) | −26.9896 | −1.14052 | ||||||||
\(561\) | −0.737046 | −0.0311181 | ||||||||
\(562\) | −28.3963 | −1.19783 | ||||||||
\(563\) | −5.07078 | −0.213708 | −0.106854 | − | 0.994275i | \(-0.534078\pi\) | ||||
−0.106854 | + | 0.994275i | \(0.534078\pi\) | |||||||
\(564\) | 60.9094 | 2.56475 | ||||||||
\(565\) | −4.75837 | −0.200186 | ||||||||
\(566\) | 62.6016 | 2.63134 | ||||||||
\(567\) | 2.66447 | 0.111897 | ||||||||
\(568\) | −55.1071 | −2.31224 | ||||||||
\(569\) | −24.0298 | −1.00738 | −0.503690 | − | 0.863884i | \(-0.668025\pi\) | ||||
−0.503690 | + | 0.863884i | \(0.668025\pi\) | |||||||
\(570\) | 7.55875 | 0.316601 | ||||||||
\(571\) | 8.71072 | 0.364532 | 0.182266 | − | 0.983249i | \(-0.441657\pi\) | ||||
0.182266 | + | 0.983249i | \(0.441657\pi\) | |||||||
\(572\) | −25.3763 | −1.06104 | ||||||||
\(573\) | 2.60615 | 0.108873 | ||||||||
\(574\) | −15.2035 | −0.634581 | ||||||||
\(575\) | −22.6343 | −0.943916 | ||||||||
\(576\) | 18.6865 | 0.778602 | ||||||||
\(577\) | −20.0534 | −0.834832 | −0.417416 | − | 0.908715i | \(-0.637064\pi\) | ||||
−0.417416 | + | 0.908715i | \(0.637064\pi\) | |||||||
\(578\) | 45.4687 | 1.89125 | ||||||||
\(579\) | 11.9245 | 0.495565 | ||||||||
\(580\) | −7.27772 | −0.302191 | ||||||||
\(581\) | −16.4568 | −0.682744 | ||||||||
\(582\) | −27.2806 | −1.13082 | ||||||||
\(583\) | 5.90417 | 0.244526 | ||||||||
\(584\) | 37.6525 | 1.55807 | ||||||||
\(585\) | −0.816148 | −0.0337435 | ||||||||
\(586\) | 11.7087 | 0.483684 | ||||||||
\(587\) | −41.5153 | −1.71352 | −0.856760 | − | 0.515715i | \(-0.827526\pi\) | ||||
−0.856760 | + | 0.515715i | \(0.827526\pi\) | |||||||
\(588\) | −0.514128 | −0.0212023 | ||||||||
\(589\) | −10.4173 | −0.429237 | ||||||||
\(590\) | 16.9400 | 0.697410 | ||||||||
\(591\) | 3.22487 | 0.132653 | ||||||||
\(592\) | 25.4648 | 1.04660 | ||||||||
\(593\) | −11.7441 | −0.482272 | −0.241136 | − | 0.970491i | \(-0.577520\pi\) | ||||
−0.241136 | + | 0.970491i | \(0.577520\pi\) | |||||||
\(594\) | −13.1387 | −0.539088 | ||||||||
\(595\) | 0.326709 | 0.0133938 | ||||||||
\(596\) | 75.7513 | 3.10290 | ||||||||
\(597\) | 10.3872 | 0.425121 | ||||||||
\(598\) | −13.9871 | −0.571977 | ||||||||
\(599\) | −2.26982 | −0.0927425 | −0.0463713 | − | 0.998924i | \(-0.514766\pi\) | ||||
−0.0463713 | + | 0.998924i | \(0.514766\pi\) | |||||||
\(600\) | −36.8254 | −1.50339 | ||||||||
\(601\) | 27.9757 | 1.14115 | 0.570577 | − | 0.821244i | \(-0.306720\pi\) | ||||
0.570577 | + | 0.821244i | \(0.306720\pi\) | |||||||
\(602\) | −78.0643 | −3.18166 | ||||||||
\(603\) | 2.58696 | 0.105349 | ||||||||
\(604\) | 7.93415 | 0.322836 | ||||||||
\(605\) | −10.6647 | −0.433581 | ||||||||
\(606\) | 36.2790 | 1.47373 | ||||||||
\(607\) | 31.8822 | 1.29406 | 0.647029 | − | 0.762466i | \(-0.276011\pi\) | ||||
0.647029 | + | 0.762466i | \(0.276011\pi\) | |||||||
\(608\) | 56.1797 | 2.27839 | ||||||||
\(609\) | −4.59326 | −0.186128 | ||||||||
\(610\) | 3.44861 | 0.139630 | ||||||||
\(611\) | −11.7752 | −0.476373 | ||||||||
\(612\) | −0.777139 | −0.0314140 | ||||||||
\(613\) | 0.702727 | 0.0283829 | 0.0141914 | − | 0.999899i | \(-0.495483\pi\) | ||||
0.0141914 | + | 0.999899i | \(0.495483\pi\) | |||||||
\(614\) | −34.4934 | −1.39204 | ||||||||
\(615\) | 1.73884 | 0.0701169 | ||||||||
\(616\) | 111.068 | 4.47507 | ||||||||
\(617\) | −24.0725 | −0.969122 | −0.484561 | − | 0.874757i | \(-0.661021\pi\) | ||||
−0.484561 | + | 0.874757i | \(0.661021\pi\) | |||||||
\(618\) | 2.67819 | 0.107732 | ||||||||
\(619\) | −3.99167 | −0.160439 | −0.0802195 | − | 0.996777i | \(-0.525562\pi\) | ||||
−0.0802195 | + | 0.996777i | \(0.525562\pi\) | |||||||
\(620\) | −12.7174 | −0.510744 | ||||||||
\(621\) | −5.22262 | −0.209576 | ||||||||
\(622\) | −18.4308 | −0.739008 | ||||||||
\(623\) | −18.2174 | −0.729865 | ||||||||
\(624\) | −12.4113 | −0.496850 | ||||||||
\(625\) | 15.4522 | 0.618089 | ||||||||
\(626\) | 4.15498 | 0.166066 | ||||||||
\(627\) | −16.9649 | −0.677514 | ||||||||
\(628\) | 21.4944 | 0.857722 | ||||||||
\(629\) | −0.308251 | −0.0122908 | ||||||||
\(630\) | 5.82398 | 0.232033 | ||||||||
\(631\) | −27.6683 | −1.10146 | −0.550729 | − | 0.834684i | \(-0.685650\pi\) | ||||
−0.550729 | + | 0.834684i | \(0.685650\pi\) | |||||||
\(632\) | 143.419 | 5.70488 | ||||||||
\(633\) | 24.1156 | 0.958509 | ||||||||
\(634\) | −14.6510 | −0.581866 | ||||||||
\(635\) | −4.39058 | −0.174235 | ||||||||
\(636\) | 6.22534 | 0.246851 | ||||||||
\(637\) | 0.0993928 | 0.00393808 | ||||||||
\(638\) | 22.6497 | 0.896712 | ||||||||
\(639\) | 6.48544 | 0.256560 | ||||||||
\(640\) | 14.3270 | 0.566323 | ||||||||
\(641\) | −46.3459 | −1.83055 | −0.915277 | − | 0.402824i | \(-0.868029\pi\) | ||||
−0.915277 | + | 0.402824i | \(0.868029\pi\) | |||||||
\(642\) | −30.9505 | −1.22152 | ||||||||
\(643\) | 1.02396 | 0.0403809 | 0.0201905 | − | 0.999796i | \(-0.493573\pi\) | ||||
0.0201905 | + | 0.999796i | \(0.493573\pi\) | |||||||
\(644\) | 71.9805 | 2.83643 | ||||||||
\(645\) | 8.92832 | 0.351552 | ||||||||
\(646\) | −1.39144 | −0.0547454 | ||||||||
\(647\) | −6.13766 | −0.241296 | −0.120648 | − | 0.992695i | \(-0.538497\pi\) | ||||
−0.120648 | + | 0.992695i | \(0.538497\pi\) | |||||||
\(648\) | −8.49705 | −0.333796 | ||||||||
\(649\) | −38.0204 | −1.49243 | ||||||||
\(650\) | 11.6070 | 0.455264 | ||||||||
\(651\) | −8.02647 | −0.314582 | ||||||||
\(652\) | −84.0232 | −3.29060 | ||||||||
\(653\) | 4.79883 | 0.187793 | 0.0938963 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938963 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(654\) | −17.9745 | −0.702857 | ||||||||
\(655\) | −5.21889 | −0.203919 | ||||||||
\(656\) | 26.4429 | 1.03242 | ||||||||
\(657\) | −4.43124 | −0.172879 | ||||||||
\(658\) | 84.0271 | 3.27572 | ||||||||
\(659\) | 35.2741 | 1.37408 | 0.687042 | − | 0.726618i | \(-0.258909\pi\) | ||||
0.687042 | + | 0.726618i | \(0.258909\pi\) | |||||||
\(660\) | −20.7108 | −0.806167 | ||||||||
\(661\) | 34.4135 | 1.33853 | 0.669266 | − | 0.743023i | \(-0.266609\pi\) | ||||
0.669266 | + | 0.743023i | \(0.266609\pi\) | |||||||
\(662\) | 5.71769 | 0.222224 | ||||||||
\(663\) | 0.150239 | 0.00583480 | ||||||||
\(664\) | 52.4812 | 2.03666 | ||||||||
\(665\) | 7.52003 | 0.291614 | ||||||||
\(666\) | −5.49495 | −0.212925 | ||||||||
\(667\) | 9.00324 | 0.348607 | ||||||||
\(668\) | −91.3310 | −3.53370 | ||||||||
\(669\) | −7.68138 | −0.296979 | ||||||||
\(670\) | 5.65456 | 0.218455 | ||||||||
\(671\) | −7.74009 | −0.298803 | ||||||||
\(672\) | 43.2862 | 1.66980 | ||||||||
\(673\) | 7.06552 | 0.272356 | 0.136178 | − | 0.990684i | \(-0.456518\pi\) | ||||
0.136178 | + | 0.990684i | \(0.456518\pi\) | |||||||
\(674\) | 31.1859 | 1.20124 | ||||||||
\(675\) | 4.33390 | 0.166812 | ||||||||
\(676\) | 5.17269 | 0.198949 | ||||||||
\(677\) | 27.9632 | 1.07471 | 0.537357 | − | 0.843355i | \(-0.319423\pi\) | ||||
0.537357 | + | 0.843355i | \(0.319423\pi\) | |||||||
\(678\) | 15.6146 | 0.599675 | ||||||||
\(679\) | −27.1409 | −1.04157 | ||||||||
\(680\) | −1.04188 | −0.0399544 | ||||||||
\(681\) | 19.5030 | 0.747358 | ||||||||
\(682\) | 39.5792 | 1.51557 | ||||||||
\(683\) | −8.66084 | −0.331398 | −0.165699 | − | 0.986176i | \(-0.552988\pi\) | ||||
−0.165699 | + | 0.986176i | \(0.552988\pi\) | |||||||
\(684\) | −17.8878 | −0.683956 | ||||||||
\(685\) | 12.0540 | 0.460561 | ||||||||
\(686\) | 49.2424 | 1.88008 | ||||||||
\(687\) | −22.7830 | −0.869227 | ||||||||
\(688\) | 135.775 | 5.17636 | ||||||||
\(689\) | −1.20350 | −0.0458498 | ||||||||
\(690\) | −11.4156 | −0.434584 | ||||||||
\(691\) | −48.4024 | −1.84131 | −0.920657 | − | 0.390373i | \(-0.872346\pi\) | ||||
−0.920657 | + | 0.390373i | \(0.872346\pi\) | |||||||
\(692\) | −0.657829 | −0.0250069 | ||||||||
\(693\) | −13.0714 | −0.496542 | ||||||||
\(694\) | 35.1192 | 1.33311 | ||||||||
\(695\) | −9.69767 | −0.367854 | ||||||||
\(696\) | 14.6480 | 0.555231 | ||||||||
\(697\) | −0.320091 | −0.0121243 | ||||||||
\(698\) | 74.3042 | 2.81245 | ||||||||
\(699\) | −15.3466 | −0.580461 | ||||||||
\(700\) | −59.7318 | −2.25765 | ||||||||
\(701\) | 14.5904 | 0.551071 | 0.275536 | − | 0.961291i | \(-0.411145\pi\) | ||||
0.275536 | + | 0.961291i | \(0.411145\pi\) | |||||||
\(702\) | 2.67819 | 0.101082 | ||||||||
\(703\) | −7.09517 | −0.267599 | ||||||||
\(704\) | −91.6725 | −3.45504 | ||||||||
\(705\) | −9.61029 | −0.361944 | ||||||||
\(706\) | 5.71386 | 0.215044 | ||||||||
\(707\) | 36.0932 | 1.35742 | ||||||||
\(708\) | −40.0886 | −1.50662 | ||||||||
\(709\) | 22.9639 | 0.862426 | 0.431213 | − | 0.902250i | \(-0.358086\pi\) | ||||
0.431213 | + | 0.902250i | \(0.358086\pi\) | |||||||
\(710\) | 14.1758 | 0.532010 | ||||||||
\(711\) | −16.8786 | −0.632998 | ||||||||
\(712\) | 58.0957 | 2.17723 | ||||||||
\(713\) | 15.7327 | 0.589193 | ||||||||
\(714\) | −1.07210 | −0.0401222 | ||||||||
\(715\) | 4.00388 | 0.149736 | ||||||||
\(716\) | 107.202 | 4.00632 | ||||||||
\(717\) | −25.2224 | −0.941947 | ||||||||
\(718\) | 100.134 | 3.73696 | ||||||||
\(719\) | −11.5638 | −0.431255 | −0.215628 | − | 0.976476i | \(-0.569180\pi\) | ||||
−0.215628 | + | 0.976476i | \(0.569180\pi\) | |||||||
\(720\) | −10.1295 | −0.377503 | ||||||||
\(721\) | 2.66447 | 0.0992300 | ||||||||
\(722\) | 18.8582 | 0.701828 | ||||||||
\(723\) | −10.1216 | −0.376427 | ||||||||
\(724\) | 49.6027 | 1.84347 | ||||||||
\(725\) | −7.47119 | −0.277473 | ||||||||
\(726\) | 34.9962 | 1.29883 | ||||||||
\(727\) | −13.1023 | −0.485938 | −0.242969 | − | 0.970034i | \(-0.578121\pi\) | ||||
−0.242969 | + | 0.970034i | \(0.578121\pi\) | |||||||
\(728\) | −22.6401 | −0.839099 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.68579 | −0.358487 | ||||||||
\(731\) | −1.64355 | −0.0607890 | ||||||||
\(732\) | −8.16113 | −0.301644 | ||||||||
\(733\) | −25.6709 | −0.948177 | −0.474088 | − | 0.880477i | \(-0.657222\pi\) | ||||
−0.474088 | + | 0.880477i | \(0.657222\pi\) | |||||||
\(734\) | −41.0134 | −1.51383 | ||||||||
\(735\) | 0.0811192 | 0.00299213 | ||||||||
\(736\) | −84.8452 | −3.12744 | ||||||||
\(737\) | −12.6911 | −0.467484 | ||||||||
\(738\) | −5.70601 | −0.210041 | ||||||||
\(739\) | −7.02608 | −0.258458 | −0.129229 | − | 0.991615i | \(-0.541250\pi\) | ||||
−0.129229 | + | 0.991615i | \(0.541250\pi\) | |||||||
\(740\) | −8.66179 | −0.318414 | ||||||||
\(741\) | 3.45812 | 0.127037 | ||||||||
\(742\) | 8.58813 | 0.315280 | ||||||||
\(743\) | −16.3989 | −0.601619 | −0.300809 | − | 0.953684i | \(-0.597257\pi\) | ||||
−0.300809 | + | 0.953684i | \(0.597257\pi\) | |||||||
\(744\) | 25.5966 | 0.938417 | ||||||||
\(745\) | −11.9521 | −0.437890 | ||||||||
\(746\) | −89.1667 | −3.26463 | ||||||||
\(747\) | −6.17640 | −0.225983 | ||||||||
\(748\) | 3.81251 | 0.139399 | ||||||||
\(749\) | −30.7919 | −1.12511 | ||||||||
\(750\) | 20.4020 | 0.744976 | ||||||||
\(751\) | 21.4762 | 0.783679 | 0.391840 | − | 0.920034i | \(-0.371839\pi\) | ||||
0.391840 | + | 0.920034i | \(0.371839\pi\) | |||||||
\(752\) | −146.146 | −5.32938 | ||||||||
\(753\) | 13.0005 | 0.473766 | ||||||||
\(754\) | −4.61691 | −0.168138 | ||||||||
\(755\) | −1.25185 | −0.0455596 | ||||||||
\(756\) | −13.7825 | −0.501263 | ||||||||
\(757\) | −14.0078 | −0.509123 | −0.254561 | − | 0.967057i | \(-0.581931\pi\) | ||||
−0.254561 | + | 0.967057i | \(0.581931\pi\) | |||||||
\(758\) | 0.369897 | 0.0134353 | ||||||||
\(759\) | 25.6212 | 0.929992 | ||||||||
\(760\) | −23.9815 | −0.869902 | ||||||||
\(761\) | 31.0577 | 1.12584 | 0.562920 | − | 0.826512i | \(-0.309678\pi\) | ||||
0.562920 | + | 0.826512i | \(0.309678\pi\) | |||||||
\(762\) | 14.4077 | 0.521935 | ||||||||
\(763\) | −17.8824 | −0.647386 | ||||||||
\(764\) | −13.4808 | −0.487718 | ||||||||
\(765\) | 0.122617 | 0.00443323 | ||||||||
\(766\) | 40.7171 | 1.47117 | ||||||||
\(767\) | 7.75006 | 0.279838 | ||||||||
\(768\) | −9.64102 | −0.347890 | ||||||||
\(769\) | −32.4314 | −1.16951 | −0.584753 | − | 0.811211i | \(-0.698809\pi\) | ||||
−0.584753 | + | 0.811211i | \(0.698809\pi\) | |||||||
\(770\) | −28.5714 | −1.02964 | ||||||||
\(771\) | 6.57923 | 0.236945 | ||||||||
\(772\) | −61.6817 | −2.21997 | ||||||||
\(773\) | −5.08050 | −0.182733 | −0.0913665 | − | 0.995817i | \(-0.529123\pi\) | ||||
−0.0913665 | + | 0.995817i | \(0.529123\pi\) | |||||||
\(774\) | −29.2983 | −1.05310 | ||||||||
\(775\) | −13.0555 | −0.468967 | ||||||||
\(776\) | 86.5529 | 3.10707 | ||||||||
\(777\) | −5.46680 | −0.196120 | ||||||||
\(778\) | 46.2725 | 1.65895 | ||||||||
\(779\) | −7.36770 | −0.263975 | ||||||||
\(780\) | 4.22168 | 0.151160 | ||||||||
\(781\) | −31.8164 | −1.13848 | ||||||||
\(782\) | 2.10141 | 0.0751464 | ||||||||
\(783\) | −1.72389 | −0.0616069 | ||||||||
\(784\) | 1.23359 | 0.0440569 | ||||||||
\(785\) | −3.39140 | −0.121044 | ||||||||
\(786\) | 17.1258 | 0.610856 | ||||||||
\(787\) | −38.7331 | −1.38068 | −0.690342 | − | 0.723483i | \(-0.742540\pi\) | ||||
−0.690342 | + | 0.723483i | \(0.742540\pi\) | |||||||
\(788\) | −16.6812 | −0.594245 | ||||||||
\(789\) | 25.5709 | 0.910349 | ||||||||
\(790\) | −36.8932 | −1.31260 | ||||||||
\(791\) | 15.5346 | 0.552347 | ||||||||
\(792\) | 41.6850 | 1.48121 | ||||||||
\(793\) | 1.57774 | 0.0560270 | ||||||||
\(794\) | −38.6193 | −1.37055 | ||||||||
\(795\) | −0.982236 | −0.0348363 | ||||||||
\(796\) | −53.7299 | −1.90441 | ||||||||
\(797\) | 37.6080 | 1.33214 | 0.666071 | − | 0.745888i | \(-0.267975\pi\) | ||||
0.666071 | + | 0.745888i | \(0.267975\pi\) | |||||||
\(798\) | −24.6770 | −0.873555 | ||||||||
\(799\) | 1.76909 | 0.0625860 | ||||||||
\(800\) | 70.4074 | 2.48928 | ||||||||
\(801\) | −6.83716 | −0.241579 | ||||||||
\(802\) | 64.9684 | 2.29411 | ||||||||
\(803\) | 21.7389 | 0.767148 | ||||||||
\(804\) | −13.3815 | −0.471929 | ||||||||
\(805\) | −11.3571 | −0.400285 | ||||||||
\(806\) | −8.06780 | −0.284176 | ||||||||
\(807\) | −25.5158 | −0.898198 | ||||||||
\(808\) | −115.102 | −4.04927 | ||||||||
\(809\) | −20.8270 | −0.732237 | −0.366118 | − | 0.930568i | \(-0.619313\pi\) | ||||
−0.366118 | + | 0.930568i | \(0.619313\pi\) | |||||||
\(810\) | 2.18580 | 0.0768010 | ||||||||
\(811\) | −55.5606 | −1.95100 | −0.975499 | − | 0.220006i | \(-0.929392\pi\) | ||||
−0.975499 | + | 0.220006i | \(0.929392\pi\) | |||||||
\(812\) | 23.7595 | 0.833795 | ||||||||
\(813\) | −14.6062 | −0.512261 | ||||||||
\(814\) | 26.9572 | 0.944851 | ||||||||
\(815\) | 13.2572 | 0.464379 | ||||||||
\(816\) | 1.86466 | 0.0652762 | ||||||||
\(817\) | −37.8304 | −1.32352 | ||||||||
\(818\) | 87.1421 | 3.04685 | ||||||||
\(819\) | 2.66447 | 0.0931041 | ||||||||
\(820\) | −8.99448 | −0.314101 | ||||||||
\(821\) | 27.6589 | 0.965301 | 0.482651 | − | 0.875813i | \(-0.339674\pi\) | ||||
0.482651 | + | 0.875813i | \(0.339674\pi\) | |||||||
\(822\) | −39.5553 | −1.37965 | ||||||||
\(823\) | 18.7980 | 0.655257 | 0.327628 | − | 0.944807i | \(-0.393751\pi\) | ||||
0.327628 | + | 0.944807i | \(0.393751\pi\) | |||||||
\(824\) | −8.49705 | −0.296009 | ||||||||
\(825\) | −21.2614 | −0.740226 | ||||||||
\(826\) | −55.3040 | −1.92427 | ||||||||
\(827\) | −5.84876 | −0.203381 | −0.101691 | − | 0.994816i | \(-0.532425\pi\) | ||||
−0.101691 | + | 0.994816i | \(0.532425\pi\) | |||||||
\(828\) | 27.0150 | 0.938835 | ||||||||
\(829\) | 41.8824 | 1.45463 | 0.727317 | − | 0.686301i | \(-0.240767\pi\) | ||||
0.727317 | + | 0.686301i | \(0.240767\pi\) | |||||||
\(830\) | −13.5003 | −0.468604 | ||||||||
\(831\) | 26.7074 | 0.926469 | ||||||||
\(832\) | 18.6865 | 0.647836 | ||||||||
\(833\) | −0.0149327 | −0.000517386 0 | ||||||||
\(834\) | 31.8229 | 1.10194 | ||||||||
\(835\) | 14.4102 | 0.498686 | ||||||||
\(836\) | 87.7543 | 3.03505 | ||||||||
\(837\) | −3.01241 | −0.104124 | ||||||||
\(838\) | 32.2738 | 1.11488 | ||||||||
\(839\) | 50.7004 | 1.75037 | 0.875186 | − | 0.483787i | \(-0.160739\pi\) | ||||
0.875186 | + | 0.483787i | \(0.160739\pi\) | |||||||
\(840\) | −18.4777 | −0.637540 | ||||||||
\(841\) | −26.0282 | −0.897524 | ||||||||
\(842\) | 73.8534 | 2.54516 | ||||||||
\(843\) | −10.6028 | −0.365181 | ||||||||
\(844\) | −124.742 | −4.29381 | ||||||||
\(845\) | −0.816148 | −0.0280763 | ||||||||
\(846\) | 31.5362 | 1.08424 | ||||||||
\(847\) | 34.8169 | 1.19632 | ||||||||
\(848\) | −14.9371 | −0.512940 | ||||||||
\(849\) | 23.3746 | 0.802214 | ||||||||
\(850\) | −1.74382 | −0.0598127 | ||||||||
\(851\) | 10.7155 | 0.367321 | ||||||||
\(852\) | −33.5471 | −1.14931 | ||||||||
\(853\) | 47.2740 | 1.61863 | 0.809315 | − | 0.587374i | \(-0.199838\pi\) | ||||
0.809315 | + | 0.587374i | \(0.199838\pi\) | |||||||
\(854\) | −11.2586 | −0.385263 | ||||||||
\(855\) | 2.82234 | 0.0965219 | ||||||||
\(856\) | 98.1961 | 3.35627 | ||||||||
\(857\) | −15.5304 | −0.530507 | −0.265254 | − | 0.964179i | \(-0.585456\pi\) | ||||
−0.265254 | + | 0.964179i | \(0.585456\pi\) | |||||||
\(858\) | −13.1387 | −0.448548 | ||||||||
\(859\) | −29.3255 | −1.00057 | −0.500287 | − | 0.865860i | \(-0.666772\pi\) | ||||
−0.500287 | + | 0.865860i | \(0.666772\pi\) | |||||||
\(860\) | −46.1834 | −1.57484 | ||||||||
\(861\) | −5.67678 | −0.193464 | ||||||||
\(862\) | −27.9956 | −0.953534 | ||||||||
\(863\) | 2.74592 | 0.0934721 | 0.0467361 | − | 0.998907i | \(-0.485118\pi\) | ||||
0.0467361 | + | 0.998907i | \(0.485118\pi\) | |||||||
\(864\) | 16.2457 | 0.552691 | ||||||||
\(865\) | 0.103792 | 0.00352905 | ||||||||
\(866\) | 51.6789 | 1.75612 | ||||||||
\(867\) | 16.9774 | 0.576584 | ||||||||
\(868\) | 41.5184 | 1.40923 | ||||||||
\(869\) | 82.8036 | 2.80892 | ||||||||
\(870\) | −3.76808 | −0.127750 | ||||||||
\(871\) | 2.58696 | 0.0876556 | ||||||||
\(872\) | 57.0273 | 1.93119 | ||||||||
\(873\) | −10.1862 | −0.344752 | ||||||||
\(874\) | 48.3693 | 1.63611 | ||||||||
\(875\) | 20.2975 | 0.686181 | ||||||||
\(876\) | 22.9214 | 0.774443 | ||||||||
\(877\) | −7.85720 | −0.265319 | −0.132659 | − | 0.991162i | \(-0.542352\pi\) | ||||
−0.132659 | + | 0.991162i | \(0.542352\pi\) | |||||||
\(878\) | 50.0310 | 1.68846 | ||||||||
\(879\) | 4.37189 | 0.147460 | ||||||||
\(880\) | 49.6934 | 1.67516 | ||||||||
\(881\) | 29.0418 | 0.978442 | 0.489221 | − | 0.872160i | \(-0.337281\pi\) | ||||
0.489221 | + | 0.872160i | \(0.337281\pi\) | |||||||
\(882\) | −0.266192 | −0.00896316 | ||||||||
\(883\) | −30.7479 | −1.03475 | −0.517375 | − | 0.855759i | \(-0.673091\pi\) | ||||
−0.517375 | + | 0.855759i | \(0.673091\pi\) | |||||||
\(884\) | −0.777139 | −0.0261380 | ||||||||
\(885\) | 6.32519 | 0.212619 | ||||||||
\(886\) | 77.2715 | 2.59599 | ||||||||
\(887\) | −16.8822 | −0.566849 | −0.283424 | − | 0.958995i | \(-0.591471\pi\) | ||||
−0.283424 | + | 0.958995i | \(0.591471\pi\) | |||||||
\(888\) | 17.4337 | 0.585038 | ||||||||
\(889\) | 14.3339 | 0.480743 | ||||||||
\(890\) | −14.9446 | −0.500946 | ||||||||
\(891\) | −4.90582 | −0.164351 | ||||||||
\(892\) | 39.7334 | 1.33037 | ||||||||
\(893\) | 40.7200 | 1.36264 | ||||||||
\(894\) | 39.2207 | 1.31174 | ||||||||
\(895\) | −16.9143 | −0.565384 | ||||||||
\(896\) | −46.7731 | −1.56258 | ||||||||
\(897\) | −5.22262 | −0.174378 | ||||||||
\(898\) | 26.6768 | 0.890215 | ||||||||
\(899\) | 5.19307 | 0.173199 | ||||||||
\(900\) | −22.4179 | −0.747264 | ||||||||
\(901\) | 0.180813 | 0.00602375 | ||||||||
\(902\) | 27.9927 | 0.932054 | ||||||||
\(903\) | −29.1482 | −0.969991 | ||||||||
\(904\) | −49.5402 | −1.64768 | ||||||||
\(905\) | −7.82633 | −0.260156 | ||||||||
\(906\) | 4.10795 | 0.136478 | ||||||||
\(907\) | −33.3470 | −1.10727 | −0.553635 | − | 0.832759i | \(-0.686760\pi\) | ||||
−0.553635 | + | 0.832759i | \(0.686760\pi\) | |||||||
\(908\) | −100.883 | −3.34792 | ||||||||
\(909\) | 13.5461 | 0.449296 | ||||||||
\(910\) | 5.82398 | 0.193063 | ||||||||
\(911\) | 25.9815 | 0.860804 | 0.430402 | − | 0.902637i | \(-0.358372\pi\) | ||||
0.430402 | + | 0.902637i | \(0.358372\pi\) | |||||||
\(912\) | 42.9198 | 1.42122 | ||||||||
\(913\) | 30.3003 | 1.00279 | ||||||||
\(914\) | −76.7465 | −2.53855 | ||||||||
\(915\) | 1.28767 | 0.0425689 | ||||||||
\(916\) | 117.850 | 3.89386 | ||||||||
\(917\) | 17.0381 | 0.562646 | ||||||||
\(918\) | −0.402368 | −0.0132801 | ||||||||
\(919\) | −7.50664 | −0.247621 | −0.123811 | − | 0.992306i | \(-0.539512\pi\) | ||||
−0.123811 | + | 0.992306i | \(0.539512\pi\) | |||||||
\(920\) | 36.2181 | 1.19407 | ||||||||
\(921\) | −12.8794 | −0.424390 | ||||||||
\(922\) | −3.32163 | −0.109392 | ||||||||
\(923\) | 6.48544 | 0.213471 | ||||||||
\(924\) | 67.6143 | 2.22435 | ||||||||
\(925\) | −8.89205 | −0.292369 | ||||||||
\(926\) | −33.9452 | −1.11551 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −28.0059 | −0.919339 | ||||||||
\(929\) | −25.0236 | −0.820998 | −0.410499 | − | 0.911861i | \(-0.634646\pi\) | ||||
−0.410499 | + | 0.911861i | \(0.634646\pi\) | |||||||
\(930\) | −6.58451 | −0.215915 | ||||||||
\(931\) | −0.343712 | −0.0112647 | ||||||||
\(932\) | 79.3831 | 2.60028 | ||||||||
\(933\) | −6.88182 | −0.225301 | ||||||||
\(934\) | 44.8301 | 1.46689 | ||||||||
\(935\) | −0.601538 | −0.0196724 | ||||||||
\(936\) | −8.49705 | −0.277735 | ||||||||
\(937\) | 0.861259 | 0.0281361 | 0.0140681 | − | 0.999901i | \(-0.495522\pi\) | ||||
0.0140681 | + | 0.999901i | \(0.495522\pi\) | |||||||
\(938\) | −18.4604 | −0.602753 | ||||||||
\(939\) | 1.55141 | 0.0506285 | ||||||||
\(940\) | 49.7110 | 1.62139 | ||||||||
\(941\) | 9.66241 | 0.314985 | 0.157493 | − | 0.987520i | \(-0.449659\pi\) | ||||
0.157493 | + | 0.987520i | \(0.449659\pi\) | |||||||
\(942\) | 11.1289 | 0.362598 | ||||||||
\(943\) | 11.1270 | 0.362346 | ||||||||
\(944\) | 96.1884 | 3.13066 | ||||||||
\(945\) | 2.17460 | 0.0707397 | ||||||||
\(946\) | 143.732 | 4.67314 | ||||||||
\(947\) | −14.9556 | −0.485993 | −0.242997 | − | 0.970027i | \(-0.578130\pi\) | ||||
−0.242997 | + | 0.970027i | \(0.578130\pi\) | |||||||
\(948\) | 87.3079 | 2.83563 | ||||||||
\(949\) | −4.43124 | −0.143844 | ||||||||
\(950\) | −40.1384 | −1.30226 | ||||||||
\(951\) | −5.47049 | −0.177393 | ||||||||
\(952\) | 3.40143 | 0.110241 | ||||||||
\(953\) | 21.8622 | 0.708185 | 0.354092 | − | 0.935210i | \(-0.384790\pi\) | ||||
0.354092 | + | 0.935210i | \(0.384790\pi\) | |||||||
\(954\) | 3.22321 | 0.104355 | ||||||||
\(955\) | 2.12700 | 0.0688282 | ||||||||
\(956\) | 130.467 | 4.21962 | ||||||||
\(957\) | 8.45712 | 0.273380 | ||||||||
\(958\) | −24.8809 | −0.803866 | ||||||||
\(959\) | −39.3527 | −1.27076 | ||||||||
\(960\) | 15.2509 | 0.492221 | ||||||||
\(961\) | −21.9254 | −0.707270 | ||||||||
\(962\) | −5.49495 | −0.177164 | ||||||||
\(963\) | −11.5565 | −0.372403 | ||||||||
\(964\) | 52.3559 | 1.68627 | ||||||||
\(965\) | 9.73215 | 0.313289 | ||||||||
\(966\) | 37.2683 | 1.19909 | ||||||||
\(967\) | −19.1339 | −0.615304 | −0.307652 | − | 0.951499i | \(-0.599543\pi\) | ||||
−0.307652 | + | 0.951499i | \(0.599543\pi\) | |||||||
\(968\) | −111.032 | −3.56870 | ||||||||
\(969\) | −0.519544 | −0.0166902 | ||||||||
\(970\) | −22.2650 | −0.714887 | ||||||||
\(971\) | −37.6026 | −1.20672 | −0.603362 | − | 0.797467i | \(-0.706173\pi\) | ||||
−0.603362 | + | 0.797467i | \(0.706173\pi\) | |||||||
\(972\) | −5.17269 | −0.165914 | ||||||||
\(973\) | 31.6599 | 1.01497 | ||||||||
\(974\) | 67.5553 | 2.16461 | ||||||||
\(975\) | 4.33390 | 0.138796 | ||||||||
\(976\) | 19.5818 | 0.626797 | ||||||||
\(977\) | 19.2526 | 0.615944 | 0.307972 | − | 0.951395i | \(-0.400350\pi\) | ||||
0.307972 | + | 0.951395i | \(0.400350\pi\) | |||||||
\(978\) | −43.5035 | −1.39109 | ||||||||
\(979\) | 33.5419 | 1.07200 | ||||||||
\(980\) | −0.419604 | −0.0134038 | ||||||||
\(981\) | −6.71143 | −0.214279 | ||||||||
\(982\) | −33.8128 | −1.07901 | ||||||||
\(983\) | −38.1682 | −1.21738 | −0.608689 | − | 0.793409i | \(-0.708304\pi\) | ||||
−0.608689 | + | 0.793409i | \(0.708304\pi\) | |||||||
\(984\) | 18.1034 | 0.577114 | ||||||||
\(985\) | 2.63197 | 0.0838616 | ||||||||
\(986\) | 0.693640 | 0.0220900 | ||||||||
\(987\) | 31.3746 | 0.998665 | ||||||||
\(988\) | −17.8878 | −0.569086 | ||||||||
\(989\) | 57.1333 | 1.81673 | ||||||||
\(990\) | −10.7231 | −0.340803 | ||||||||
\(991\) | 52.7417 | 1.67540 | 0.837698 | − | 0.546134i | \(-0.183901\pi\) | ||||
0.837698 | + | 0.546134i | \(0.183901\pi\) | |||||||
\(992\) | −48.9388 | −1.55381 | ||||||||
\(993\) | 2.13491 | 0.0677494 | ||||||||
\(994\) | −46.2797 | −1.46790 | ||||||||
\(995\) | 8.47752 | 0.268755 | ||||||||
\(996\) | 31.9486 | 1.01233 | ||||||||
\(997\) | −1.95733 | −0.0619891 | −0.0309946 | − | 0.999520i | \(-0.509867\pi\) | ||||
−0.0309946 | + | 0.999520i | \(0.509867\pi\) | |||||||
\(998\) | 34.8873 | 1.10434 | ||||||||
\(999\) | −2.05174 | −0.0649142 |
(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 | 4017.2.a.h.1.3 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.h.1.3 | ✓ | 25 | 1.1 | even | 1 | trivial |