Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56636 | −1.81469 | −0.907345 | − | 0.420386i | \(-0.861895\pi\) | ||||
−0.907345 | + | 0.420386i | \(0.861895\pi\) | |||||||
\(3\) | 2.86321 | 1.65307 | 0.826537 | − | 0.562882i | \(-0.190307\pi\) | ||||
0.826537 | + | 0.562882i | \(0.190307\pi\) | |||||||
\(4\) | 4.58620 | 2.29310 | ||||||||
\(5\) | −1.49629 | −0.669160 | −0.334580 | − | 0.942367i | \(-0.608594\pi\) | ||||
−0.334580 | + | 0.942367i | \(0.608594\pi\) | |||||||
\(6\) | −7.34803 | −2.99982 | ||||||||
\(7\) | −1.31440 | −0.496796 | −0.248398 | − | 0.968658i | \(-0.579904\pi\) | ||||
−0.248398 | + | 0.968658i | \(0.579904\pi\) | |||||||
\(8\) | −6.63713 | −2.34658 | ||||||||
\(9\) | 5.19797 | 1.73266 | ||||||||
\(10\) | 3.84001 | 1.21432 | ||||||||
\(11\) | 5.98208 | 1.80367 | 0.901833 | − | 0.432086i | \(-0.142222\pi\) | ||||
0.901833 | + | 0.432086i | \(0.142222\pi\) | |||||||
\(12\) | 13.1313 | 3.79067 | ||||||||
\(13\) | 1.85013 | 0.513135 | 0.256567 | − | 0.966526i | \(-0.417408\pi\) | ||||
0.256567 | + | 0.966526i | \(0.417408\pi\) | |||||||
\(14\) | 3.37322 | 0.901531 | ||||||||
\(15\) | −4.28419 | −1.10617 | ||||||||
\(16\) | 7.86086 | 1.96522 | ||||||||
\(17\) | −3.46147 | −0.839531 | −0.419765 | − | 0.907633i | \(-0.637888\pi\) | ||||
−0.419765 | + | 0.907633i | \(0.637888\pi\) | |||||||
\(18\) | −13.3399 | −3.14423 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −6.86228 | −1.53445 | ||||||||
\(21\) | −3.76340 | −0.821241 | ||||||||
\(22\) | −15.3522 | −3.27309 | ||||||||
\(23\) | 0.442595 | 0.0922874 | 0.0461437 | − | 0.998935i | \(-0.485307\pi\) | ||||
0.0461437 | + | 0.998935i | \(0.485307\pi\) | |||||||
\(24\) | −19.0035 | −3.87907 | ||||||||
\(25\) | −2.76112 | −0.552224 | ||||||||
\(26\) | −4.74811 | −0.931181 | ||||||||
\(27\) | 6.29324 | 1.21113 | ||||||||
\(28\) | −6.02810 | −1.13920 | ||||||||
\(29\) | −2.74531 | −0.509791 | −0.254896 | − | 0.966969i | \(-0.582041\pi\) | ||||
−0.254896 | + | 0.966969i | \(0.582041\pi\) | |||||||
\(30\) | 10.9948 | 2.00736 | ||||||||
\(31\) | 0.0954084 | 0.0171359 | 0.00856793 | − | 0.999963i | \(-0.497273\pi\) | ||||
0.00856793 | + | 0.999963i | \(0.497273\pi\) | |||||||
\(32\) | −6.89954 | −1.21968 | ||||||||
\(33\) | 17.1279 | 2.98159 | ||||||||
\(34\) | 8.88339 | 1.52349 | ||||||||
\(35\) | 1.96672 | 0.332436 | ||||||||
\(36\) | 23.8389 | 3.97316 | ||||||||
\(37\) | −10.1880 | −1.67490 | −0.837450 | − | 0.546514i | \(-0.815955\pi\) | ||||
−0.837450 | + | 0.546514i | \(0.815955\pi\) | |||||||
\(38\) | 2.56636 | 0.416319 | ||||||||
\(39\) | 5.29732 | 0.848250 | ||||||||
\(40\) | 9.93106 | 1.57024 | ||||||||
\(41\) | −2.51996 | −0.393552 | −0.196776 | − | 0.980448i | \(-0.563047\pi\) | ||||
−0.196776 | + | 0.980448i | \(0.563047\pi\) | |||||||
\(42\) | 9.65824 | 1.49030 | ||||||||
\(43\) | −7.29343 | −1.11224 | −0.556119 | − | 0.831103i | \(-0.687710\pi\) | ||||
−0.556119 | + | 0.831103i | \(0.687710\pi\) | |||||||
\(44\) | 27.4350 | 4.13599 | ||||||||
\(45\) | −7.77765 | −1.15942 | ||||||||
\(46\) | −1.13586 | −0.167473 | ||||||||
\(47\) | −3.12300 | −0.455537 | −0.227768 | − | 0.973715i | \(-0.573143\pi\) | ||||
−0.227768 | + | 0.973715i | \(0.573143\pi\) | |||||||
\(48\) | 22.5073 | 3.24865 | ||||||||
\(49\) | −5.27235 | −0.753194 | ||||||||
\(50\) | 7.08603 | 1.00212 | ||||||||
\(51\) | −9.91092 | −1.38781 | ||||||||
\(52\) | 8.48509 | 1.17667 | ||||||||
\(53\) | −10.9108 | −1.49871 | −0.749354 | − | 0.662170i | \(-0.769636\pi\) | ||||
−0.749354 | + | 0.662170i | \(0.769636\pi\) | |||||||
\(54\) | −16.1507 | −2.19783 | ||||||||
\(55\) | −8.95091 | −1.20694 | ||||||||
\(56\) | 8.72384 | 1.16577 | ||||||||
\(57\) | −2.86321 | −0.379241 | ||||||||
\(58\) | 7.04545 | 0.925114 | ||||||||
\(59\) | −4.29096 | −0.558636 | −0.279318 | − | 0.960199i | \(-0.590108\pi\) | ||||
−0.279318 | + | 0.960199i | \(0.590108\pi\) | |||||||
\(60\) | −19.6481 | −2.53657 | ||||||||
\(61\) | −0.761735 | −0.0975302 | −0.0487651 | − | 0.998810i | \(-0.515529\pi\) | ||||
−0.0487651 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(62\) | −0.244852 | −0.0310963 | ||||||||
\(63\) | −6.83220 | −0.860777 | ||||||||
\(64\) | 1.98498 | 0.248122 | ||||||||
\(65\) | −2.76833 | −0.343369 | ||||||||
\(66\) | −43.9565 | −5.41067 | ||||||||
\(67\) | −8.54232 | −1.04361 | −0.521805 | − | 0.853065i | \(-0.674741\pi\) | ||||
−0.521805 | + | 0.853065i | \(0.674741\pi\) | |||||||
\(68\) | −15.8750 | −1.92513 | ||||||||
\(69\) | 1.26724 | 0.152558 | ||||||||
\(70\) | −5.04731 | −0.603269 | ||||||||
\(71\) | 6.58317 | 0.781279 | 0.390639 | − | 0.920544i | \(-0.372254\pi\) | ||||
0.390639 | + | 0.920544i | \(0.372254\pi\) | |||||||
\(72\) | −34.4996 | −4.06581 | ||||||||
\(73\) | −2.57828 | −0.301765 | −0.150883 | − | 0.988552i | \(-0.548212\pi\) | ||||
−0.150883 | + | 0.988552i | \(0.548212\pi\) | |||||||
\(74\) | 26.1461 | 3.03943 | ||||||||
\(75\) | −7.90567 | −0.912868 | ||||||||
\(76\) | −4.58620 | −0.526074 | ||||||||
\(77\) | −7.86284 | −0.896054 | ||||||||
\(78\) | −13.5948 | −1.53931 | ||||||||
\(79\) | 0.758087 | 0.0852915 | 0.0426457 | − | 0.999090i | \(-0.486421\pi\) | ||||
0.0426457 | + | 0.999090i | \(0.486421\pi\) | |||||||
\(80\) | −11.7621 | −1.31504 | ||||||||
\(81\) | 2.42495 | 0.269439 | ||||||||
\(82\) | 6.46713 | 0.714176 | ||||||||
\(83\) | −11.7656 | −1.29145 | −0.645723 | − | 0.763571i | \(-0.723444\pi\) | ||||
−0.645723 | + | 0.763571i | \(0.723444\pi\) | |||||||
\(84\) | −17.2597 | −1.88319 | ||||||||
\(85\) | 5.17936 | 0.561781 | ||||||||
\(86\) | 18.7176 | 2.01837 | ||||||||
\(87\) | −7.86040 | −0.842723 | ||||||||
\(88\) | −39.7039 | −4.23245 | ||||||||
\(89\) | 1.41961 | 0.150479 | 0.0752394 | − | 0.997165i | \(-0.476028\pi\) | ||||
0.0752394 | + | 0.997165i | \(0.476028\pi\) | |||||||
\(90\) | 19.9603 | 2.10400 | ||||||||
\(91\) | −2.43181 | −0.254923 | ||||||||
\(92\) | 2.02983 | 0.211624 | ||||||||
\(93\) | 0.273174 | 0.0283268 | ||||||||
\(94\) | 8.01475 | 0.826658 | ||||||||
\(95\) | 1.49629 | 0.153516 | ||||||||
\(96\) | −19.7548 | −2.01622 | ||||||||
\(97\) | −14.5041 | −1.47267 | −0.736335 | − | 0.676617i | \(-0.763445\pi\) | ||||
−0.736335 | + | 0.676617i | \(0.763445\pi\) | |||||||
\(98\) | 13.5308 | 1.36681 | ||||||||
\(99\) | 31.0946 | 3.12513 | ||||||||
\(100\) | −12.6631 | −1.26631 | ||||||||
\(101\) | −0.875507 | −0.0871162 | −0.0435581 | − | 0.999051i | \(-0.513869\pi\) | ||||
−0.0435581 | + | 0.999051i | \(0.513869\pi\) | |||||||
\(102\) | 25.4350 | 2.51844 | ||||||||
\(103\) | 17.3091 | 1.70551 | 0.852757 | − | 0.522308i | \(-0.174929\pi\) | ||||
0.852757 | + | 0.522308i | \(0.174929\pi\) | |||||||
\(104\) | −12.2796 | −1.20411 | ||||||||
\(105\) | 5.63113 | 0.549542 | ||||||||
\(106\) | 28.0009 | 2.71969 | ||||||||
\(107\) | 3.86462 | 0.373607 | 0.186804 | − | 0.982397i | \(-0.440187\pi\) | ||||
0.186804 | + | 0.982397i | \(0.440187\pi\) | |||||||
\(108\) | 28.8621 | 2.77725 | ||||||||
\(109\) | 13.7614 | 1.31811 | 0.659053 | − | 0.752096i | \(-0.270957\pi\) | ||||
0.659053 | + | 0.752096i | \(0.270957\pi\) | |||||||
\(110\) | 22.9713 | 2.19022 | ||||||||
\(111\) | −29.1704 | −2.76874 | ||||||||
\(112\) | −10.3323 | −0.976312 | ||||||||
\(113\) | −6.56733 | −0.617802 | −0.308901 | − | 0.951094i | \(-0.599961\pi\) | ||||
−0.308901 | + | 0.951094i | \(0.599961\pi\) | |||||||
\(114\) | 7.34803 | 0.688206 | ||||||||
\(115\) | −0.662249 | −0.0617551 | ||||||||
\(116\) | −12.5906 | −1.16900 | ||||||||
\(117\) | 9.61693 | 0.889086 | ||||||||
\(118\) | 11.0122 | 1.01375 | ||||||||
\(119\) | 4.54976 | 0.417076 | ||||||||
\(120\) | 28.4347 | 2.59572 | ||||||||
\(121\) | 24.7853 | 2.25321 | ||||||||
\(122\) | 1.95489 | 0.176987 | ||||||||
\(123\) | −7.21518 | −0.650571 | ||||||||
\(124\) | 0.437562 | 0.0392943 | ||||||||
\(125\) | 11.6129 | 1.03869 | ||||||||
\(126\) | 17.5339 | 1.56204 | ||||||||
\(127\) | −1.98474 | −0.176117 | −0.0880584 | − | 0.996115i | \(-0.528066\pi\) | ||||
−0.0880584 | + | 0.996115i | \(0.528066\pi\) | |||||||
\(128\) | 8.70491 | 0.769413 | ||||||||
\(129\) | −20.8826 | −1.83861 | ||||||||
\(130\) | 7.10454 | 0.623109 | ||||||||
\(131\) | −4.35732 | −0.380701 | −0.190350 | − | 0.981716i | \(-0.560962\pi\) | ||||
−0.190350 | + | 0.981716i | \(0.560962\pi\) | |||||||
\(132\) | 78.5523 | 6.83710 | ||||||||
\(133\) | 1.31440 | 0.113973 | ||||||||
\(134\) | 21.9227 | 1.89383 | ||||||||
\(135\) | −9.41649 | −0.810443 | ||||||||
\(136\) | 22.9743 | 1.97003 | ||||||||
\(137\) | 6.45791 | 0.551737 | 0.275868 | − | 0.961195i | \(-0.411035\pi\) | ||||
0.275868 | + | 0.961195i | \(0.411035\pi\) | |||||||
\(138\) | −3.25220 | −0.276846 | ||||||||
\(139\) | −6.89376 | −0.584721 | −0.292360 | − | 0.956308i | \(-0.594441\pi\) | ||||
−0.292360 | + | 0.956308i | \(0.594441\pi\) | |||||||
\(140\) | 9.01978 | 0.762310 | ||||||||
\(141\) | −8.94181 | −0.753036 | ||||||||
\(142\) | −16.8948 | −1.41778 | ||||||||
\(143\) | 11.0676 | 0.925523 | ||||||||
\(144\) | 40.8605 | 3.40504 | ||||||||
\(145\) | 4.10777 | 0.341132 | ||||||||
\(146\) | 6.61680 | 0.547610 | ||||||||
\(147\) | −15.0959 | −1.24509 | ||||||||
\(148\) | −46.7244 | −3.84072 | ||||||||
\(149\) | 19.8092 | 1.62283 | 0.811416 | − | 0.584468i | \(-0.198697\pi\) | ||||
0.811416 | + | 0.584468i | \(0.198697\pi\) | |||||||
\(150\) | 20.2888 | 1.65657 | ||||||||
\(151\) | 15.8862 | 1.29280 | 0.646399 | − | 0.763000i | \(-0.276274\pi\) | ||||
0.646399 | + | 0.763000i | \(0.276274\pi\) | |||||||
\(152\) | 6.63713 | 0.538342 | ||||||||
\(153\) | −17.9926 | −1.45462 | ||||||||
\(154\) | 20.1789 | 1.62606 | ||||||||
\(155\) | −0.142758 | −0.0114666 | ||||||||
\(156\) | 24.2946 | 1.94512 | ||||||||
\(157\) | 5.68950 | 0.454072 | 0.227036 | − | 0.973886i | \(-0.427097\pi\) | ||||
0.227036 | + | 0.973886i | \(0.427097\pi\) | |||||||
\(158\) | −1.94552 | −0.154778 | ||||||||
\(159\) | −31.2398 | −2.47748 | ||||||||
\(160\) | 10.3237 | 0.816160 | ||||||||
\(161\) | −0.581746 | −0.0458480 | ||||||||
\(162\) | −6.22330 | −0.488948 | ||||||||
\(163\) | −12.1043 | −0.948084 | −0.474042 | − | 0.880502i | \(-0.657206\pi\) | ||||
−0.474042 | + | 0.880502i | \(0.657206\pi\) | |||||||
\(164\) | −11.5571 | −0.902455 | ||||||||
\(165\) | −25.6283 | −1.99516 | ||||||||
\(166\) | 30.1949 | 2.34358 | ||||||||
\(167\) | 3.61094 | 0.279423 | 0.139712 | − | 0.990192i | \(-0.455382\pi\) | ||||
0.139712 | + | 0.990192i | \(0.455382\pi\) | |||||||
\(168\) | 24.9782 | 1.92711 | ||||||||
\(169\) | −9.57701 | −0.736693 | ||||||||
\(170\) | −13.2921 | −1.01946 | ||||||||
\(171\) | −5.19797 | −0.397498 | ||||||||
\(172\) | −33.4491 | −2.55047 | ||||||||
\(173\) | 21.9374 | 1.66787 | 0.833934 | − | 0.551864i | \(-0.186083\pi\) | ||||
0.833934 | + | 0.551864i | \(0.186083\pi\) | |||||||
\(174\) | 20.1726 | 1.52928 | ||||||||
\(175\) | 3.62922 | 0.274343 | ||||||||
\(176\) | 47.0243 | 3.54459 | ||||||||
\(177\) | −12.2859 | −0.923466 | ||||||||
\(178\) | −3.64324 | −0.273073 | ||||||||
\(179\) | −3.58063 | −0.267629 | −0.133814 | − | 0.991006i | \(-0.542723\pi\) | ||||
−0.133814 | + | 0.991006i | \(0.542723\pi\) | |||||||
\(180\) | −35.6699 | −2.65868 | ||||||||
\(181\) | −24.7806 | −1.84193 | −0.920964 | − | 0.389647i | \(-0.872597\pi\) | ||||
−0.920964 | + | 0.389647i | \(0.872597\pi\) | |||||||
\(182\) | 6.24091 | 0.462607 | ||||||||
\(183\) | −2.18101 | −0.161225 | ||||||||
\(184\) | −2.93756 | −0.216560 | ||||||||
\(185\) | 15.2442 | 1.12078 | ||||||||
\(186\) | −0.701063 | −0.0514045 | ||||||||
\(187\) | −20.7068 | −1.51423 | ||||||||
\(188\) | −14.3227 | −1.04459 | ||||||||
\(189\) | −8.27182 | −0.601687 | ||||||||
\(190\) | −3.84001 | −0.278584 | ||||||||
\(191\) | −3.32468 | −0.240565 | −0.120283 | − | 0.992740i | \(-0.538380\pi\) | ||||
−0.120283 | + | 0.992740i | \(0.538380\pi\) | |||||||
\(192\) | 5.68340 | 0.410164 | ||||||||
\(193\) | −16.1728 | −1.16414 | −0.582071 | − | 0.813138i | \(-0.697757\pi\) | ||||
−0.582071 | + | 0.813138i | \(0.697757\pi\) | |||||||
\(194\) | 37.2228 | 2.67244 | ||||||||
\(195\) | −7.92631 | −0.567615 | ||||||||
\(196\) | −24.1801 | −1.72715 | ||||||||
\(197\) | 18.6870 | 1.33140 | 0.665698 | − | 0.746221i | \(-0.268134\pi\) | ||||
0.665698 | + | 0.746221i | \(0.268134\pi\) | |||||||
\(198\) | −79.8001 | −5.67114 | ||||||||
\(199\) | −15.2624 | −1.08192 | −0.540962 | − | 0.841047i | \(-0.681940\pi\) | ||||
−0.540962 | + | 0.841047i | \(0.681940\pi\) | |||||||
\(200\) | 18.3259 | 1.29584 | ||||||||
\(201\) | −24.4585 | −1.72517 | ||||||||
\(202\) | 2.24687 | 0.158089 | ||||||||
\(203\) | 3.60843 | 0.253262 | ||||||||
\(204\) | −45.4535 | −3.18238 | ||||||||
\(205\) | 3.77059 | 0.263350 | ||||||||
\(206\) | −44.4213 | −3.09498 | ||||||||
\(207\) | 2.30059 | 0.159902 | ||||||||
\(208\) | 14.5436 | 1.00842 | ||||||||
\(209\) | −5.98208 | −0.413789 | ||||||||
\(210\) | −14.4515 | −0.997249 | ||||||||
\(211\) | 3.43041 | 0.236159 | 0.118080 | − | 0.993004i | \(-0.462326\pi\) | ||||
0.118080 | + | 0.993004i | \(0.462326\pi\) | |||||||
\(212\) | −50.0390 | −3.43669 | ||||||||
\(213\) | 18.8490 | 1.29151 | ||||||||
\(214\) | −9.91802 | −0.677982 | ||||||||
\(215\) | 10.9131 | 0.744265 | ||||||||
\(216\) | −41.7690 | −2.84202 | ||||||||
\(217\) | −0.125405 | −0.00851303 | ||||||||
\(218\) | −35.3168 | −2.39196 | ||||||||
\(219\) | −7.38216 | −0.498840 | ||||||||
\(220\) | −41.0507 | −2.76764 | ||||||||
\(221\) | −6.40419 | −0.430792 | ||||||||
\(222\) | 74.8618 | 5.02440 | ||||||||
\(223\) | −0.693707 | −0.0464541 | −0.0232270 | − | 0.999730i | \(-0.507394\pi\) | ||||
−0.0232270 | + | 0.999730i | \(0.507394\pi\) | |||||||
\(224\) | 9.06875 | 0.605931 | ||||||||
\(225\) | −14.3522 | −0.956815 | ||||||||
\(226\) | 16.8541 | 1.12112 | ||||||||
\(227\) | 9.65783 | 0.641013 | 0.320506 | − | 0.947246i | \(-0.396147\pi\) | ||||
0.320506 | + | 0.947246i | \(0.396147\pi\) | |||||||
\(228\) | −13.1313 | −0.869639 | ||||||||
\(229\) | 1.06564 | 0.0704193 | 0.0352096 | − | 0.999380i | \(-0.488790\pi\) | ||||
0.0352096 | + | 0.999380i | \(0.488790\pi\) | |||||||
\(230\) | 1.69957 | 0.112066 | ||||||||
\(231\) | −22.5130 | −1.48124 | ||||||||
\(232\) | 18.2210 | 1.19627 | ||||||||
\(233\) | 23.5170 | 1.54065 | 0.770324 | − | 0.637653i | \(-0.220095\pi\) | ||||
0.770324 | + | 0.637653i | \(0.220095\pi\) | |||||||
\(234\) | −24.6805 | −1.61342 | ||||||||
\(235\) | 4.67291 | 0.304827 | ||||||||
\(236\) | −19.6792 | −1.28101 | ||||||||
\(237\) | 2.17056 | 0.140993 | ||||||||
\(238\) | −11.6763 | −0.756863 | ||||||||
\(239\) | −11.0307 | −0.713516 | −0.356758 | − | 0.934197i | \(-0.616118\pi\) | ||||
−0.356758 | + | 0.934197i | \(0.616118\pi\) | |||||||
\(240\) | −33.6774 | −2.17387 | ||||||||
\(241\) | −15.0306 | −0.968208 | −0.484104 | − | 0.875010i | \(-0.660854\pi\) | ||||
−0.484104 | + | 0.875010i | \(0.660854\pi\) | |||||||
\(242\) | −63.6080 | −4.08888 | ||||||||
\(243\) | −11.9366 | −0.765731 | ||||||||
\(244\) | −3.49347 | −0.223647 | ||||||||
\(245\) | 7.88896 | 0.504007 | ||||||||
\(246\) | 18.5168 | 1.18059 | ||||||||
\(247\) | −1.85013 | −0.117721 | ||||||||
\(248\) | −0.633238 | −0.0402107 | ||||||||
\(249\) | −33.6875 | −2.13486 | ||||||||
\(250\) | −29.8028 | −1.88490 | ||||||||
\(251\) | 28.6078 | 1.80571 | 0.902855 | − | 0.429944i | \(-0.141467\pi\) | ||||
0.902855 | + | 0.429944i | \(0.141467\pi\) | |||||||
\(252\) | −31.3339 | −1.97385 | ||||||||
\(253\) | 2.64764 | 0.166456 | ||||||||
\(254\) | 5.09355 | 0.319598 | ||||||||
\(255\) | 14.8296 | 0.928665 | ||||||||
\(256\) | −26.3099 | −1.64437 | ||||||||
\(257\) | −13.6738 | −0.852949 | −0.426474 | − | 0.904500i | \(-0.640245\pi\) | ||||
−0.426474 | + | 0.904500i | \(0.640245\pi\) | |||||||
\(258\) | 53.5923 | 3.33651 | ||||||||
\(259\) | 13.3911 | 0.832084 | ||||||||
\(260\) | −12.6961 | −0.787381 | ||||||||
\(261\) | −14.2700 | −0.883293 | ||||||||
\(262\) | 11.1824 | 0.690854 | ||||||||
\(263\) | −6.92100 | −0.426767 | −0.213384 | − | 0.976969i | \(-0.568448\pi\) | ||||
−0.213384 | + | 0.976969i | \(0.568448\pi\) | |||||||
\(264\) | −113.680 | −6.99655 | ||||||||
\(265\) | 16.3256 | 1.00288 | ||||||||
\(266\) | −3.37322 | −0.206825 | ||||||||
\(267\) | 4.06465 | 0.248753 | ||||||||
\(268\) | −39.1768 | −2.39311 | ||||||||
\(269\) | −6.23030 | −0.379868 | −0.189934 | − | 0.981797i | \(-0.560827\pi\) | ||||
−0.189934 | + | 0.981797i | \(0.560827\pi\) | |||||||
\(270\) | 24.1661 | 1.47070 | ||||||||
\(271\) | −14.1717 | −0.860871 | −0.430436 | − | 0.902621i | \(-0.641640\pi\) | ||||
−0.430436 | + | 0.902621i | \(0.641640\pi\) | |||||||
\(272\) | −27.2102 | −1.64986 | ||||||||
\(273\) | −6.96279 | −0.421407 | ||||||||
\(274\) | −16.5733 | −1.00123 | ||||||||
\(275\) | −16.5173 | −0.996028 | ||||||||
\(276\) | 5.81183 | 0.349831 | ||||||||
\(277\) | −28.0618 | −1.68607 | −0.843035 | − | 0.537859i | \(-0.819233\pi\) | ||||
−0.843035 | + | 0.537859i | \(0.819233\pi\) | |||||||
\(278\) | 17.6919 | 1.06109 | ||||||||
\(279\) | 0.495930 | 0.0296905 | ||||||||
\(280\) | −13.0534 | −0.780088 | ||||||||
\(281\) | 25.3189 | 1.51040 | 0.755199 | − | 0.655495i | \(-0.227540\pi\) | ||||
0.755199 | + | 0.655495i | \(0.227540\pi\) | |||||||
\(282\) | 22.9479 | 1.36653 | ||||||||
\(283\) | 2.35984 | 0.140278 | 0.0701389 | − | 0.997537i | \(-0.477656\pi\) | ||||
0.0701389 | + | 0.997537i | \(0.477656\pi\) | |||||||
\(284\) | 30.1918 | 1.79155 | ||||||||
\(285\) | 4.28419 | 0.253773 | ||||||||
\(286\) | −28.4036 | −1.67954 | ||||||||
\(287\) | 3.31224 | 0.195515 | ||||||||
\(288\) | −35.8636 | −2.11328 | ||||||||
\(289\) | −5.01820 | −0.295188 | ||||||||
\(290\) | −10.5420 | −0.619049 | ||||||||
\(291\) | −41.5283 | −2.43443 | ||||||||
\(292\) | −11.8245 | −0.691978 | ||||||||
\(293\) | 28.0673 | 1.63971 | 0.819854 | − | 0.572572i | \(-0.194054\pi\) | ||||
0.819854 | + | 0.572572i | \(0.194054\pi\) | |||||||
\(294\) | 38.7414 | 2.25944 | ||||||||
\(295\) | 6.42051 | 0.373817 | ||||||||
\(296\) | 67.6192 | 3.93029 | ||||||||
\(297\) | 37.6466 | 2.18448 | ||||||||
\(298\) | −50.8375 | −2.94494 | ||||||||
\(299\) | 0.818860 | 0.0473559 | ||||||||
\(300\) | −36.2570 | −2.09330 | ||||||||
\(301\) | 9.58647 | 0.552555 | ||||||||
\(302\) | −40.7696 | −2.34603 | ||||||||
\(303\) | −2.50676 | −0.144010 | ||||||||
\(304\) | −7.86086 | −0.450851 | ||||||||
\(305\) | 1.13978 | 0.0652633 | ||||||||
\(306\) | 46.1756 | 2.63968 | ||||||||
\(307\) | −9.12746 | −0.520932 | −0.260466 | − | 0.965483i | \(-0.583876\pi\) | ||||
−0.260466 | + | 0.965483i | \(0.583876\pi\) | |||||||
\(308\) | −36.0606 | −2.05474 | ||||||||
\(309\) | 49.5595 | 2.81934 | ||||||||
\(310\) | 0.366370 | 0.0208084 | ||||||||
\(311\) | 15.1187 | 0.857302 | 0.428651 | − | 0.903470i | \(-0.358989\pi\) | ||||
0.428651 | + | 0.903470i | \(0.358989\pi\) | |||||||
\(312\) | −35.1590 | −1.99049 | ||||||||
\(313\) | −7.05095 | −0.398543 | −0.199272 | − | 0.979944i | \(-0.563858\pi\) | ||||
−0.199272 | + | 0.979944i | \(0.563858\pi\) | |||||||
\(314\) | −14.6013 | −0.824000 | ||||||||
\(315\) | 10.2229 | 0.575997 | ||||||||
\(316\) | 3.47674 | 0.195582 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | 80.1725 | 4.49585 | ||||||||
\(319\) | −16.4227 | −0.919493 | ||||||||
\(320\) | −2.97010 | −0.166033 | ||||||||
\(321\) | 11.0652 | 0.617601 | ||||||||
\(322\) | 1.49297 | 0.0832000 | ||||||||
\(323\) | 3.46147 | 0.192602 | ||||||||
\(324\) | 11.1213 | 0.617851 | ||||||||
\(325\) | −5.10845 | −0.283366 | ||||||||
\(326\) | 31.0641 | 1.72048 | ||||||||
\(327\) | 39.4019 | 2.17893 | ||||||||
\(328\) | 16.7253 | 0.923502 | ||||||||
\(329\) | 4.10487 | 0.226309 | ||||||||
\(330\) | 65.7715 | 3.62060 | ||||||||
\(331\) | −21.3182 | −1.17175 | −0.585877 | − | 0.810400i | \(-0.699250\pi\) | ||||
−0.585877 | + | 0.810400i | \(0.699250\pi\) | |||||||
\(332\) | −53.9596 | −2.96142 | ||||||||
\(333\) | −52.9570 | −2.90203 | ||||||||
\(334\) | −9.26698 | −0.507066 | ||||||||
\(335\) | 12.7818 | 0.698343 | ||||||||
\(336\) | −29.5836 | −1.61392 | ||||||||
\(337\) | 10.7426 | 0.585187 | 0.292593 | − | 0.956237i | \(-0.405482\pi\) | ||||
0.292593 | + | 0.956237i | \(0.405482\pi\) | |||||||
\(338\) | 24.5780 | 1.33687 | ||||||||
\(339\) | −18.8036 | −1.02127 | ||||||||
\(340\) | 23.7536 | 1.28822 | ||||||||
\(341\) | 0.570741 | 0.0309073 | ||||||||
\(342\) | 13.3399 | 0.721337 | ||||||||
\(343\) | 16.1308 | 0.870980 | ||||||||
\(344\) | 48.4074 | 2.60995 | ||||||||
\(345\) | −1.89616 | −0.102086 | ||||||||
\(346\) | −56.2992 | −3.02666 | ||||||||
\(347\) | −30.2575 | −1.62431 | −0.812153 | − | 0.583444i | \(-0.801705\pi\) | ||||
−0.812153 | + | 0.583444i | \(0.801705\pi\) | |||||||
\(348\) | −36.0494 | −1.93245 | ||||||||
\(349\) | 4.24882 | 0.227434 | 0.113717 | − | 0.993513i | \(-0.463724\pi\) | ||||
0.113717 | + | 0.993513i | \(0.463724\pi\) | |||||||
\(350\) | −9.31388 | −0.497848 | ||||||||
\(351\) | 11.6433 | 0.621475 | ||||||||
\(352\) | −41.2736 | −2.19989 | ||||||||
\(353\) | −2.32893 | −0.123957 | −0.0619783 | − | 0.998077i | \(-0.519741\pi\) | ||||
−0.0619783 | + | 0.998077i | \(0.519741\pi\) | |||||||
\(354\) | 31.5301 | 1.67581 | ||||||||
\(355\) | −9.85032 | −0.522801 | ||||||||
\(356\) | 6.51064 | 0.345063 | ||||||||
\(357\) | 13.0269 | 0.689457 | ||||||||
\(358\) | 9.18918 | 0.485663 | ||||||||
\(359\) | −13.3658 | −0.705420 | −0.352710 | − | 0.935733i | \(-0.614740\pi\) | ||||
−0.352710 | + | 0.935733i | \(0.614740\pi\) | |||||||
\(360\) | 51.6213 | 2.72068 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 63.5960 | 3.34253 | ||||||||
\(363\) | 70.9655 | 3.72472 | ||||||||
\(364\) | −11.1528 | −0.584565 | ||||||||
\(365\) | 3.85785 | 0.201929 | ||||||||
\(366\) | 5.59725 | 0.292573 | ||||||||
\(367\) | −25.2979 | −1.32054 | −0.660271 | − | 0.751028i | \(-0.729559\pi\) | ||||
−0.660271 | + | 0.751028i | \(0.729559\pi\) | |||||||
\(368\) | 3.47918 | 0.181365 | ||||||||
\(369\) | −13.0987 | −0.681890 | ||||||||
\(370\) | −39.1221 | −2.03386 | ||||||||
\(371\) | 14.3411 | 0.744552 | ||||||||
\(372\) | 1.25283 | 0.0649564 | ||||||||
\(373\) | −11.7457 | −0.608167 | −0.304084 | − | 0.952645i | \(-0.598350\pi\) | ||||
−0.304084 | + | 0.952645i | \(0.598350\pi\) | |||||||
\(374\) | 53.1412 | 2.74786 | ||||||||
\(375\) | 33.2501 | 1.71703 | ||||||||
\(376\) | 20.7278 | 1.06895 | ||||||||
\(377\) | −5.07919 | −0.261592 | ||||||||
\(378\) | 21.2285 | 1.09188 | ||||||||
\(379\) | 36.9167 | 1.89629 | 0.948143 | − | 0.317844i | \(-0.102959\pi\) | ||||
0.948143 | + | 0.317844i | \(0.102959\pi\) | |||||||
\(380\) | 6.86228 | 0.352028 | ||||||||
\(381\) | −5.68271 | −0.291134 | ||||||||
\(382\) | 8.53232 | 0.436551 | ||||||||
\(383\) | −8.62707 | −0.440823 | −0.220411 | − | 0.975407i | \(-0.570740\pi\) | ||||
−0.220411 | + | 0.975407i | \(0.570740\pi\) | |||||||
\(384\) | 24.9240 | 1.27190 | ||||||||
\(385\) | 11.7651 | 0.599604 | ||||||||
\(386\) | 41.5051 | 2.11256 | ||||||||
\(387\) | −37.9110 | −1.92712 | ||||||||
\(388\) | −66.5189 | −3.37698 | ||||||||
\(389\) | −11.8358 | −0.600097 | −0.300049 | − | 0.953924i | \(-0.597003\pi\) | ||||
−0.300049 | + | 0.953924i | \(0.597003\pi\) | |||||||
\(390\) | 20.3418 | 1.03005 | ||||||||
\(391\) | −1.53203 | −0.0774781 | ||||||||
\(392\) | 34.9933 | 1.76743 | ||||||||
\(393\) | −12.4759 | −0.629327 | ||||||||
\(394\) | −47.9577 | −2.41607 | ||||||||
\(395\) | −1.13432 | −0.0570737 | ||||||||
\(396\) | 142.606 | 7.16624 | ||||||||
\(397\) | 12.7775 | 0.641284 | 0.320642 | − | 0.947200i | \(-0.396101\pi\) | ||||
0.320642 | + | 0.947200i | \(0.396101\pi\) | |||||||
\(398\) | 39.1689 | 1.96336 | ||||||||
\(399\) | 3.76340 | 0.188406 | ||||||||
\(400\) | −21.7048 | −1.08524 | ||||||||
\(401\) | −27.8859 | −1.39256 | −0.696278 | − | 0.717772i | \(-0.745162\pi\) | ||||
−0.696278 | + | 0.717772i | \(0.745162\pi\) | |||||||
\(402\) | 62.7692 | 3.13064 | ||||||||
\(403\) | 0.176518 | 0.00879300 | ||||||||
\(404\) | −4.01526 | −0.199766 | ||||||||
\(405\) | −3.62842 | −0.180298 | ||||||||
\(406\) | −9.26054 | −0.459593 | ||||||||
\(407\) | −60.9456 | −3.02096 | ||||||||
\(408\) | 65.7801 | 3.25660 | ||||||||
\(409\) | 27.7163 | 1.37048 | 0.685240 | − | 0.728317i | \(-0.259697\pi\) | ||||
0.685240 | + | 0.728317i | \(0.259697\pi\) | |||||||
\(410\) | −9.67670 | −0.477898 | ||||||||
\(411\) | 18.4904 | 0.912062 | ||||||||
\(412\) | 79.3829 | 3.91092 | ||||||||
\(413\) | 5.64004 | 0.277528 | ||||||||
\(414\) | −5.90415 | −0.290173 | ||||||||
\(415\) | 17.6048 | 0.864185 | ||||||||
\(416\) | −12.7651 | −0.625859 | ||||||||
\(417\) | −19.7383 | −0.966587 | ||||||||
\(418\) | 15.3522 | 0.750899 | ||||||||
\(419\) | 27.3216 | 1.33475 | 0.667374 | − | 0.744723i | \(-0.267418\pi\) | ||||
0.667374 | + | 0.744723i | \(0.267418\pi\) | |||||||
\(420\) | 25.8255 | 1.26016 | ||||||||
\(421\) | 9.11114 | 0.444050 | 0.222025 | − | 0.975041i | \(-0.428733\pi\) | ||||
0.222025 | + | 0.975041i | \(0.428733\pi\) | |||||||
\(422\) | −8.80366 | −0.428556 | ||||||||
\(423\) | −16.2333 | −0.789288 | ||||||||
\(424\) | 72.4162 | 3.51684 | ||||||||
\(425\) | 9.55755 | 0.463609 | ||||||||
\(426\) | −48.3733 | −2.34369 | ||||||||
\(427\) | 1.00122 | 0.0484526 | ||||||||
\(428\) | 17.7240 | 0.856720 | ||||||||
\(429\) | 31.6890 | 1.52996 | ||||||||
\(430\) | −28.0069 | −1.35061 | ||||||||
\(431\) | −24.3199 | −1.17145 | −0.585725 | − | 0.810510i | \(-0.699190\pi\) | ||||
−0.585725 | + | 0.810510i | \(0.699190\pi\) | |||||||
\(432\) | 49.4703 | 2.38014 | ||||||||
\(433\) | −8.86237 | −0.425898 | −0.212949 | − | 0.977063i | \(-0.568307\pi\) | ||||
−0.212949 | + | 0.977063i | \(0.568307\pi\) | |||||||
\(434\) | 0.321834 | 0.0154485 | ||||||||
\(435\) | 11.7614 | 0.563917 | ||||||||
\(436\) | 63.1128 | 3.02255 | ||||||||
\(437\) | −0.442595 | −0.0211722 | ||||||||
\(438\) | 18.9453 | 0.905241 | ||||||||
\(439\) | −0.791614 | −0.0377817 | −0.0188908 | − | 0.999822i | \(-0.506013\pi\) | ||||
−0.0188908 | + | 0.999822i | \(0.506013\pi\) | |||||||
\(440\) | 59.4084 | 2.83218 | ||||||||
\(441\) | −27.4055 | −1.30502 | ||||||||
\(442\) | 16.4355 | 0.781755 | ||||||||
\(443\) | 11.3287 | 0.538241 | 0.269121 | − | 0.963106i | \(-0.413267\pi\) | ||||
0.269121 | + | 0.963106i | \(0.413267\pi\) | |||||||
\(444\) | −133.782 | −6.34899 | ||||||||
\(445\) | −2.12415 | −0.100694 | ||||||||
\(446\) | 1.78030 | 0.0842998 | ||||||||
\(447\) | 56.7179 | 2.68266 | ||||||||
\(448\) | −2.60905 | −0.123266 | ||||||||
\(449\) | 9.19039 | 0.433721 | 0.216861 | − | 0.976203i | \(-0.430418\pi\) | ||||
0.216861 | + | 0.976203i | \(0.430418\pi\) | |||||||
\(450\) | 36.8330 | 1.73632 | ||||||||
\(451\) | −15.0746 | −0.709836 | ||||||||
\(452\) | −30.1191 | −1.41668 | ||||||||
\(453\) | 45.4854 | 2.13709 | ||||||||
\(454\) | −24.7855 | −1.16324 | ||||||||
\(455\) | 3.63869 | 0.170585 | ||||||||
\(456\) | 19.0035 | 0.889920 | ||||||||
\(457\) | −26.7160 | −1.24972 | −0.624860 | − | 0.780737i | \(-0.714844\pi\) | ||||
−0.624860 | + | 0.780737i | \(0.714844\pi\) | |||||||
\(458\) | −2.73481 | −0.127789 | ||||||||
\(459\) | −21.7839 | −1.01678 | ||||||||
\(460\) | −3.03721 | −0.141611 | ||||||||
\(461\) | 6.37718 | 0.297015 | 0.148507 | − | 0.988911i | \(-0.452553\pi\) | ||||
0.148507 | + | 0.988911i | \(0.452553\pi\) | |||||||
\(462\) | 57.7764 | 2.68800 | ||||||||
\(463\) | 20.0954 | 0.933910 | 0.466955 | − | 0.884281i | \(-0.345351\pi\) | ||||
0.466955 | + | 0.884281i | \(0.345351\pi\) | |||||||
\(464\) | −21.5805 | −1.00185 | ||||||||
\(465\) | −0.408747 | −0.0189552 | ||||||||
\(466\) | −60.3530 | −2.79580 | ||||||||
\(467\) | −31.4372 | −1.45474 | −0.727369 | − | 0.686246i | \(-0.759257\pi\) | ||||
−0.727369 | + | 0.686246i | \(0.759257\pi\) | |||||||
\(468\) | 44.1052 | 2.03876 | ||||||||
\(469\) | 11.2280 | 0.518462 | ||||||||
\(470\) | −11.9924 | −0.553167 | ||||||||
\(471\) | 16.2902 | 0.750615 | ||||||||
\(472\) | 28.4797 | 1.31088 | ||||||||
\(473\) | −43.6299 | −2.00610 | ||||||||
\(474\) | −5.57044 | −0.255859 | ||||||||
\(475\) | 2.76112 | 0.126689 | ||||||||
\(476\) | 20.8661 | 0.956397 | ||||||||
\(477\) | −56.7138 | −2.59674 | ||||||||
\(478\) | 28.3087 | 1.29481 | ||||||||
\(479\) | 9.44859 | 0.431717 | 0.215858 | − | 0.976425i | \(-0.430745\pi\) | ||||
0.215858 | + | 0.976425i | \(0.430745\pi\) | |||||||
\(480\) | 29.5589 | 1.34917 | ||||||||
\(481\) | −18.8492 | −0.859450 | ||||||||
\(482\) | 38.5740 | 1.75700 | ||||||||
\(483\) | −1.66566 | −0.0757902 | ||||||||
\(484\) | 113.670 | 5.16684 | ||||||||
\(485\) | 21.7023 | 0.985453 | ||||||||
\(486\) | 30.6335 | 1.38956 | ||||||||
\(487\) | 26.0689 | 1.18129 | 0.590647 | − | 0.806930i | \(-0.298872\pi\) | ||||
0.590647 | + | 0.806930i | \(0.298872\pi\) | |||||||
\(488\) | 5.05574 | 0.228862 | ||||||||
\(489\) | −34.6572 | −1.56725 | ||||||||
\(490\) | −20.2459 | −0.914617 | ||||||||
\(491\) | −28.8172 | −1.30050 | −0.650250 | − | 0.759720i | \(-0.725336\pi\) | ||||
−0.650250 | + | 0.759720i | \(0.725336\pi\) | |||||||
\(492\) | −33.0903 | −1.49183 | ||||||||
\(493\) | 9.50282 | 0.427986 | ||||||||
\(494\) | 4.74811 | 0.213628 | ||||||||
\(495\) | −46.5265 | −2.09121 | ||||||||
\(496\) | 0.749992 | 0.0336756 | ||||||||
\(497\) | −8.65291 | −0.388136 | ||||||||
\(498\) | 86.4542 | 3.87411 | ||||||||
\(499\) | 29.3483 | 1.31381 | 0.656906 | − | 0.753973i | \(-0.271865\pi\) | ||||
0.656906 | + | 0.753973i | \(0.271865\pi\) | |||||||
\(500\) | 53.2590 | 2.38182 | ||||||||
\(501\) | 10.3389 | 0.461907 | ||||||||
\(502\) | −73.4180 | −3.27681 | ||||||||
\(503\) | −9.35889 | −0.417292 | −0.208646 | − | 0.977991i | \(-0.566906\pi\) | ||||
−0.208646 | + | 0.977991i | \(0.566906\pi\) | |||||||
\(504\) | 45.3462 | 2.01988 | ||||||||
\(505\) | 1.31001 | 0.0582947 | ||||||||
\(506\) | −6.79479 | −0.302065 | ||||||||
\(507\) | −27.4210 | −1.21781 | ||||||||
\(508\) | −9.10240 | −0.403854 | ||||||||
\(509\) | 16.5734 | 0.734603 | 0.367301 | − | 0.930102i | \(-0.380282\pi\) | ||||
0.367301 | + | 0.930102i | \(0.380282\pi\) | |||||||
\(510\) | −38.0581 | −1.68524 | ||||||||
\(511\) | 3.38889 | 0.149916 | ||||||||
\(512\) | 50.1108 | 2.21461 | ||||||||
\(513\) | −6.29324 | −0.277853 | ||||||||
\(514\) | 35.0919 | 1.54784 | ||||||||
\(515\) | −25.8994 | −1.14126 | ||||||||
\(516\) | −95.7719 | −4.21612 | ||||||||
\(517\) | −18.6821 | −0.821636 | ||||||||
\(518\) | −34.3665 | −1.50998 | ||||||||
\(519\) | 62.8113 | 2.75711 | ||||||||
\(520\) | 18.3738 | 0.805744 | ||||||||
\(521\) | 15.1454 | 0.663530 | 0.331765 | − | 0.943362i | \(-0.392356\pi\) | ||||
0.331765 | + | 0.943362i | \(0.392356\pi\) | |||||||
\(522\) | 36.6220 | 1.60290 | ||||||||
\(523\) | −7.95709 | −0.347939 | −0.173970 | − | 0.984751i | \(-0.555659\pi\) | ||||
−0.173970 | + | 0.984751i | \(0.555659\pi\) | |||||||
\(524\) | −19.9836 | −0.872985 | ||||||||
\(525\) | 10.3912 | 0.453509 | ||||||||
\(526\) | 17.7618 | 0.774450 | ||||||||
\(527\) | −0.330254 | −0.0143861 | ||||||||
\(528\) | 134.640 | 5.85947 | ||||||||
\(529\) | −22.8041 | −0.991483 | ||||||||
\(530\) | −41.8975 | −1.81991 | ||||||||
\(531\) | −22.3043 | −0.967923 | ||||||||
\(532\) | 6.02810 | 0.261351 | ||||||||
\(533\) | −4.66227 | −0.201945 | ||||||||
\(534\) | −10.4314 | −0.451409 | ||||||||
\(535\) | −5.78259 | −0.250003 | ||||||||
\(536\) | 56.6965 | 2.44892 | ||||||||
\(537\) | −10.2521 | −0.442410 | ||||||||
\(538\) | 15.9892 | 0.689343 | ||||||||
\(539\) | −31.5397 | −1.35851 | ||||||||
\(540\) | −43.1860 | −1.85843 | ||||||||
\(541\) | 26.1488 | 1.12422 | 0.562112 | − | 0.827061i | \(-0.309989\pi\) | ||||
0.562112 | + | 0.827061i | \(0.309989\pi\) | |||||||
\(542\) | 36.3698 | 1.56222 | ||||||||
\(543\) | −70.9521 | −3.04484 | ||||||||
\(544\) | 23.8826 | 1.02396 | ||||||||
\(545\) | −20.5911 | −0.882025 | ||||||||
\(546\) | 17.8690 | 0.764724 | ||||||||
\(547\) | −16.0755 | −0.687338 | −0.343669 | − | 0.939091i | \(-0.611670\pi\) | ||||
−0.343669 | + | 0.939091i | \(0.611670\pi\) | |||||||
\(548\) | 29.6173 | 1.26519 | ||||||||
\(549\) | −3.95947 | −0.168986 | ||||||||
\(550\) | 42.3892 | 1.80748 | ||||||||
\(551\) | 2.74531 | 0.116954 | ||||||||
\(552\) | −8.41085 | −0.357990 | ||||||||
\(553\) | −0.996429 | −0.0423725 | ||||||||
\(554\) | 72.0167 | 3.05970 | ||||||||
\(555\) | 43.6474 | 1.85273 | ||||||||
\(556\) | −31.6162 | −1.34082 | ||||||||
\(557\) | −17.1493 | −0.726641 | −0.363320 | − | 0.931664i | \(-0.618357\pi\) | ||||
−0.363320 | + | 0.931664i | \(0.618357\pi\) | |||||||
\(558\) | −1.27273 | −0.0538791 | ||||||||
\(559\) | −13.4938 | −0.570728 | ||||||||
\(560\) | 15.4601 | 0.653309 | ||||||||
\(561\) | −59.2879 | −2.50314 | ||||||||
\(562\) | −64.9774 | −2.74091 | ||||||||
\(563\) | 18.1791 | 0.766158 | 0.383079 | − | 0.923716i | \(-0.374864\pi\) | ||||
0.383079 | + | 0.923716i | \(0.374864\pi\) | |||||||
\(564\) | −41.0090 | −1.72679 | ||||||||
\(565\) | 9.82661 | 0.413409 | ||||||||
\(566\) | −6.05620 | −0.254561 | ||||||||
\(567\) | −3.18735 | −0.133856 | ||||||||
\(568\) | −43.6934 | −1.83333 | ||||||||
\(569\) | −2.43407 | −0.102041 | −0.0510207 | − | 0.998698i | \(-0.516247\pi\) | ||||
−0.0510207 | + | 0.998698i | \(0.516247\pi\) | |||||||
\(570\) | −10.9948 | −0.460520 | ||||||||
\(571\) | 11.4311 | 0.478375 | 0.239188 | − | 0.970973i | \(-0.423119\pi\) | ||||
0.239188 | + | 0.970973i | \(0.423119\pi\) | |||||||
\(572\) | 50.7585 | 2.12232 | ||||||||
\(573\) | −9.51925 | −0.397672 | ||||||||
\(574\) | −8.50040 | −0.354800 | ||||||||
\(575\) | −1.22206 | −0.0509634 | ||||||||
\(576\) | 10.3178 | 0.429910 | ||||||||
\(577\) | −24.7817 | −1.03167 | −0.515837 | − | 0.856687i | \(-0.672519\pi\) | ||||
−0.515837 | + | 0.856687i | \(0.672519\pi\) | |||||||
\(578\) | 12.8785 | 0.535675 | ||||||||
\(579\) | −46.3060 | −1.92441 | ||||||||
\(580\) | 18.8391 | 0.782251 | ||||||||
\(581\) | 15.4647 | 0.641586 | ||||||||
\(582\) | 106.577 | 4.41774 | ||||||||
\(583\) | −65.2690 | −2.70317 | ||||||||
\(584\) | 17.1124 | 0.708116 | ||||||||
\(585\) | −14.3897 | −0.594941 | ||||||||
\(586\) | −72.0308 | −2.97556 | ||||||||
\(587\) | −40.7999 | −1.68399 | −0.841996 | − | 0.539485i | \(-0.818619\pi\) | ||||
−0.841996 | + | 0.539485i | \(0.818619\pi\) | |||||||
\(588\) | −69.2327 | −2.85511 | ||||||||
\(589\) | −0.0954084 | −0.00393124 | ||||||||
\(590\) | −16.4774 | −0.678362 | ||||||||
\(591\) | 53.5049 | 2.20090 | ||||||||
\(592\) | −80.0866 | −3.29154 | ||||||||
\(593\) | −6.91800 | −0.284088 | −0.142044 | − | 0.989860i | \(-0.545368\pi\) | ||||
−0.142044 | + | 0.989860i | \(0.545368\pi\) | |||||||
\(594\) | −96.6148 | −3.96415 | ||||||||
\(595\) | −6.80775 | −0.279091 | ||||||||
\(596\) | 90.8490 | 3.72132 | ||||||||
\(597\) | −43.6995 | −1.78850 | ||||||||
\(598\) | −2.10149 | −0.0859363 | ||||||||
\(599\) | −24.8997 | −1.01737 | −0.508687 | − | 0.860951i | \(-0.669869\pi\) | ||||
−0.508687 | + | 0.860951i | \(0.669869\pi\) | |||||||
\(600\) | 52.4710 | 2.14212 | ||||||||
\(601\) | −22.3530 | −0.911796 | −0.455898 | − | 0.890032i | \(-0.650682\pi\) | ||||
−0.455898 | + | 0.890032i | \(0.650682\pi\) | |||||||
\(602\) | −24.6023 | −1.00272 | ||||||||
\(603\) | −44.4027 | −1.80822 | ||||||||
\(604\) | 72.8572 | 2.96452 | ||||||||
\(605\) | −37.0859 | −1.50776 | ||||||||
\(606\) | 6.43325 | 0.261333 | ||||||||
\(607\) | 14.7877 | 0.600213 | 0.300106 | − | 0.953906i | \(-0.402978\pi\) | ||||
0.300106 | + | 0.953906i | \(0.402978\pi\) | |||||||
\(608\) | 6.89954 | 0.279813 | ||||||||
\(609\) | 10.3317 | 0.418662 | ||||||||
\(610\) | −2.92507 | −0.118433 | ||||||||
\(611\) | −5.77797 | −0.233752 | ||||||||
\(612\) | −82.5179 | −3.33559 | ||||||||
\(613\) | 26.6884 | 1.07793 | 0.538967 | − | 0.842327i | \(-0.318815\pi\) | ||||
0.538967 | + | 0.842327i | \(0.318815\pi\) | |||||||
\(614\) | 23.4243 | 0.945330 | ||||||||
\(615\) | 10.7960 | 0.435336 | ||||||||
\(616\) | 52.1867 | 2.10266 | ||||||||
\(617\) | −12.3279 | −0.496301 | −0.248151 | − | 0.968721i | \(-0.579823\pi\) | ||||
−0.248151 | + | 0.968721i | \(0.579823\pi\) | |||||||
\(618\) | −127.187 | −5.11623 | ||||||||
\(619\) | 19.4973 | 0.783664 | 0.391832 | − | 0.920037i | \(-0.371841\pi\) | ||||
0.391832 | + | 0.920037i | \(0.371841\pi\) | |||||||
\(620\) | −0.654719 | −0.0262942 | ||||||||
\(621\) | 2.78535 | 0.111772 | ||||||||
\(622\) | −38.8000 | −1.55574 | ||||||||
\(623\) | −1.86594 | −0.0747573 | ||||||||
\(624\) | 41.6415 | 1.66699 | ||||||||
\(625\) | −3.57059 | −0.142824 | ||||||||
\(626\) | 18.0953 | 0.723233 | ||||||||
\(627\) | −17.1279 | −0.684024 | ||||||||
\(628\) | 26.0932 | 1.04123 | ||||||||
\(629\) | 35.2656 | 1.40613 | ||||||||
\(630\) | −26.2357 | −1.04526 | ||||||||
\(631\) | −21.9021 | −0.871907 | −0.435954 | − | 0.899969i | \(-0.643589\pi\) | ||||
−0.435954 | + | 0.899969i | \(0.643589\pi\) | |||||||
\(632\) | −5.03153 | −0.200143 | ||||||||
\(633\) | 9.82198 | 0.390389 | ||||||||
\(634\) | 2.56636 | 0.101923 | ||||||||
\(635\) | 2.96974 | 0.117850 | ||||||||
\(636\) | −143.272 | −5.68111 | ||||||||
\(637\) | −9.75456 | −0.386490 | ||||||||
\(638\) | 42.1465 | 1.66860 | ||||||||
\(639\) | 34.2191 | 1.35369 | ||||||||
\(640\) | −13.0251 | −0.514860 | ||||||||
\(641\) | 28.6660 | 1.13224 | 0.566120 | − | 0.824323i | \(-0.308444\pi\) | ||||
0.566120 | + | 0.824323i | \(0.308444\pi\) | |||||||
\(642\) | −28.3974 | −1.12075 | ||||||||
\(643\) | 13.4375 | 0.529923 | 0.264961 | − | 0.964259i | \(-0.414641\pi\) | ||||
0.264961 | + | 0.964259i | \(0.414641\pi\) | |||||||
\(644\) | −2.66801 | −0.105134 | ||||||||
\(645\) | 31.2464 | 1.23033 | ||||||||
\(646\) | −8.88339 | −0.349512 | ||||||||
\(647\) | −24.3150 | −0.955922 | −0.477961 | − | 0.878381i | \(-0.658624\pi\) | ||||
−0.477961 | + | 0.878381i | \(0.658624\pi\) | |||||||
\(648\) | −16.0947 | −0.632260 | ||||||||
\(649\) | −25.6689 | −1.00759 | ||||||||
\(650\) | 13.1101 | 0.514221 | ||||||||
\(651\) | −0.359060 | −0.0140727 | ||||||||
\(652\) | −55.5129 | −2.17405 | ||||||||
\(653\) | 37.2541 | 1.45787 | 0.728933 | − | 0.684585i | \(-0.240016\pi\) | ||||
0.728933 | + | 0.684585i | \(0.240016\pi\) | |||||||
\(654\) | −101.119 | −3.95408 | ||||||||
\(655\) | 6.51980 | 0.254750 | ||||||||
\(656\) | −19.8091 | −0.773415 | ||||||||
\(657\) | −13.4018 | −0.522855 | ||||||||
\(658\) | −10.5346 | −0.410681 | ||||||||
\(659\) | −15.4699 | −0.602620 | −0.301310 | − | 0.953526i | \(-0.597424\pi\) | ||||
−0.301310 | + | 0.953526i | \(0.597424\pi\) | |||||||
\(660\) | −117.537 | −4.57511 | ||||||||
\(661\) | −13.8542 | −0.538867 | −0.269433 | − | 0.963019i | \(-0.586836\pi\) | ||||
−0.269433 | + | 0.963019i | \(0.586836\pi\) | |||||||
\(662\) | 54.7102 | 2.12637 | ||||||||
\(663\) | −18.3365 | −0.712132 | ||||||||
\(664\) | 78.0901 | 3.03048 | ||||||||
\(665\) | −1.96672 | −0.0762661 | ||||||||
\(666\) | 135.907 | 5.26628 | ||||||||
\(667\) | −1.21506 | −0.0470473 | ||||||||
\(668\) | 16.5605 | 0.640746 | ||||||||
\(669\) | −1.98623 | −0.0767920 | ||||||||
\(670\) | −32.8026 | −1.26728 | ||||||||
\(671\) | −4.55676 | −0.175912 | ||||||||
\(672\) | 25.9657 | 1.00165 | ||||||||
\(673\) | −14.0871 | −0.543016 | −0.271508 | − | 0.962436i | \(-0.587522\pi\) | ||||
−0.271508 | + | 0.962436i | \(0.587522\pi\) | |||||||
\(674\) | −27.5694 | −1.06193 | ||||||||
\(675\) | −17.3764 | −0.668818 | ||||||||
\(676\) | −43.9221 | −1.68931 | ||||||||
\(677\) | 33.5710 | 1.29024 | 0.645119 | − | 0.764082i | \(-0.276808\pi\) | ||||
0.645119 | + | 0.764082i | \(0.276808\pi\) | |||||||
\(678\) | 48.2569 | 1.85329 | ||||||||
\(679\) | 19.0642 | 0.731617 | ||||||||
\(680\) | −34.3761 | −1.31826 | ||||||||
\(681\) | 27.6524 | 1.05964 | ||||||||
\(682\) | −1.46473 | −0.0560873 | ||||||||
\(683\) | −37.4025 | −1.43117 | −0.715584 | − | 0.698526i | \(-0.753839\pi\) | ||||
−0.715584 | + | 0.698526i | \(0.753839\pi\) | |||||||
\(684\) | −23.8389 | −0.911504 | ||||||||
\(685\) | −9.66290 | −0.369200 | ||||||||
\(686\) | −41.3974 | −1.58056 | ||||||||
\(687\) | 3.05114 | 0.116408 | ||||||||
\(688\) | −57.3326 | −2.18579 | ||||||||
\(689\) | −20.1864 | −0.769039 | ||||||||
\(690\) | 4.86623 | 0.185254 | ||||||||
\(691\) | 17.4251 | 0.662884 | 0.331442 | − | 0.943476i | \(-0.392465\pi\) | ||||
0.331442 | + | 0.943476i | \(0.392465\pi\) | |||||||
\(692\) | 100.609 | 3.82459 | ||||||||
\(693\) | −40.8708 | −1.55255 | ||||||||
\(694\) | 77.6516 | 2.94761 | ||||||||
\(695\) | 10.3150 | 0.391272 | ||||||||
\(696\) | 52.1705 | 1.97752 | ||||||||
\(697\) | 8.72279 | 0.330399 | ||||||||
\(698\) | −10.9040 | −0.412722 | ||||||||
\(699\) | 67.3340 | 2.54680 | ||||||||
\(700\) | 16.6443 | 0.629097 | ||||||||
\(701\) | −4.78410 | −0.180693 | −0.0903465 | − | 0.995910i | \(-0.528797\pi\) | ||||
−0.0903465 | + | 0.995910i | \(0.528797\pi\) | |||||||
\(702\) | −29.8810 | −1.12778 | ||||||||
\(703\) | 10.1880 | 0.384249 | ||||||||
\(704\) | 11.8743 | 0.447529 | ||||||||
\(705\) | 13.3795 | 0.503902 | ||||||||
\(706\) | 5.97688 | 0.224943 | ||||||||
\(707\) | 1.15077 | 0.0432790 | ||||||||
\(708\) | −56.3457 | −2.11760 | ||||||||
\(709\) | 42.3685 | 1.59118 | 0.795592 | − | 0.605833i | \(-0.207160\pi\) | ||||
0.795592 | + | 0.605833i | \(0.207160\pi\) | |||||||
\(710\) | 25.2795 | 0.948721 | ||||||||
\(711\) | 3.94051 | 0.147781 | ||||||||
\(712\) | −9.42217 | −0.353111 | ||||||||
\(713\) | 0.0422273 | 0.00158142 | ||||||||
\(714\) | −33.4317 | −1.25115 | ||||||||
\(715\) | −16.5604 | −0.619323 | ||||||||
\(716\) | −16.4215 | −0.613700 | ||||||||
\(717\) | −31.5831 | −1.17949 | ||||||||
\(718\) | 34.3015 | 1.28012 | ||||||||
\(719\) | 41.0988 | 1.53273 | 0.766364 | − | 0.642407i | \(-0.222064\pi\) | ||||
0.766364 | + | 0.642407i | \(0.222064\pi\) | |||||||
\(720\) | −61.1391 | −2.27852 | ||||||||
\(721\) | −22.7510 | −0.847293 | ||||||||
\(722\) | −2.56636 | −0.0955100 | ||||||||
\(723\) | −43.0358 | −1.60052 | ||||||||
\(724\) | −113.649 | −4.22373 | ||||||||
\(725\) | 7.58014 | 0.281519 | ||||||||
\(726\) | −182.123 | −6.75922 | ||||||||
\(727\) | −3.81832 | −0.141614 | −0.0708069 | − | 0.997490i | \(-0.522557\pi\) | ||||
−0.0708069 | + | 0.997490i | \(0.522557\pi\) | |||||||
\(728\) | 16.1403 | 0.598198 | ||||||||
\(729\) | −41.4517 | −1.53525 | ||||||||
\(730\) | −9.90064 | −0.366439 | ||||||||
\(731\) | 25.2460 | 0.933757 | ||||||||
\(732\) | −10.0025 | −0.369705 | ||||||||
\(733\) | 6.99734 | 0.258452 | 0.129226 | − | 0.991615i | \(-0.458751\pi\) | ||||
0.129226 | + | 0.991615i | \(0.458751\pi\) | |||||||
\(734\) | 64.9236 | 2.39637 | ||||||||
\(735\) | 22.5877 | 0.833161 | ||||||||
\(736\) | −3.05370 | −0.112561 | ||||||||
\(737\) | −51.1009 | −1.88232 | ||||||||
\(738\) | 33.6159 | 1.23742 | ||||||||
\(739\) | 29.1231 | 1.07131 | 0.535656 | − | 0.844436i | \(-0.320064\pi\) | ||||
0.535656 | + | 0.844436i | \(0.320064\pi\) | |||||||
\(740\) | 69.9131 | 2.57006 | ||||||||
\(741\) | −5.29732 | −0.194602 | ||||||||
\(742\) | −36.8044 | −1.35113 | ||||||||
\(743\) | −0.0682136 | −0.00250252 | −0.00125126 | − | 0.999999i | \(-0.500398\pi\) | ||||
−0.00125126 | + | 0.999999i | \(0.500398\pi\) | |||||||
\(744\) | −1.81309 | −0.0664712 | ||||||||
\(745\) | −29.6403 | −1.08594 | ||||||||
\(746\) | 30.1436 | 1.10364 | ||||||||
\(747\) | −61.1574 | −2.23763 | ||||||||
\(748\) | −94.9657 | −3.47229 | ||||||||
\(749\) | −5.07966 | −0.185607 | ||||||||
\(750\) | −85.3317 | −3.11587 | ||||||||
\(751\) | −18.4564 | −0.673485 | −0.336743 | − | 0.941597i | \(-0.609325\pi\) | ||||
−0.336743 | + | 0.941597i | \(0.609325\pi\) | |||||||
\(752\) | −24.5495 | −0.895228 | ||||||||
\(753\) | 81.9102 | 2.98497 | ||||||||
\(754\) | 13.0350 | 0.474708 | ||||||||
\(755\) | −23.7703 | −0.865089 | ||||||||
\(756\) | −37.9363 | −1.37973 | ||||||||
\(757\) | 39.0394 | 1.41891 | 0.709456 | − | 0.704750i | \(-0.248941\pi\) | ||||
0.709456 | + | 0.704750i | \(0.248941\pi\) | |||||||
\(758\) | −94.7417 | −3.44117 | ||||||||
\(759\) | 7.58074 | 0.275163 | ||||||||
\(760\) | −9.93106 | −0.360237 | ||||||||
\(761\) | 13.8369 | 0.501586 | 0.250793 | − | 0.968041i | \(-0.419309\pi\) | ||||
0.250793 | + | 0.968041i | \(0.419309\pi\) | |||||||
\(762\) | 14.5839 | 0.528319 | ||||||||
\(763\) | −18.0880 | −0.654830 | ||||||||
\(764\) | −15.2476 | −0.551641 | ||||||||
\(765\) | 26.9221 | 0.973372 | ||||||||
\(766\) | 22.1402 | 0.799957 | ||||||||
\(767\) | −7.93885 | −0.286655 | ||||||||
\(768\) | −75.3307 | −2.71826 | ||||||||
\(769\) | 33.7081 | 1.21555 | 0.607773 | − | 0.794111i | \(-0.292063\pi\) | ||||
0.607773 | + | 0.794111i | \(0.292063\pi\) | |||||||
\(770\) | −30.1934 | −1.08810 | ||||||||
\(771\) | −39.1510 | −1.40999 | ||||||||
\(772\) | −74.1716 | −2.66949 | ||||||||
\(773\) | −9.19751 | −0.330812 | −0.165406 | − | 0.986226i | \(-0.552893\pi\) | ||||
−0.165406 | + | 0.986226i | \(0.552893\pi\) | |||||||
\(774\) | 97.2932 | 3.49713 | ||||||||
\(775\) | −0.263434 | −0.00946284 | ||||||||
\(776\) | 96.2658 | 3.45574 | ||||||||
\(777\) | 38.3416 | 1.37550 | ||||||||
\(778\) | 30.3748 | 1.08899 | ||||||||
\(779\) | 2.51996 | 0.0902871 | ||||||||
\(780\) | −36.3517 | −1.30160 | ||||||||
\(781\) | 39.3811 | 1.40917 | ||||||||
\(782\) | 3.93174 | 0.140599 | ||||||||
\(783\) | −17.2769 | −0.617425 | ||||||||
\(784\) | −41.4453 | −1.48019 | ||||||||
\(785\) | −8.51314 | −0.303847 | ||||||||
\(786\) | 32.0177 | 1.14203 | ||||||||
\(787\) | 36.2607 | 1.29255 | 0.646277 | − | 0.763103i | \(-0.276325\pi\) | ||||
0.646277 | + | 0.763103i | \(0.276325\pi\) | |||||||
\(788\) | 85.7025 | 3.05303 | ||||||||
\(789\) | −19.8163 | −0.705478 | ||||||||
\(790\) | 2.91107 | 0.103571 | ||||||||
\(791\) | 8.63209 | 0.306922 | ||||||||
\(792\) | −206.379 | −7.33337 | ||||||||
\(793\) | −1.40931 | −0.0500461 | ||||||||
\(794\) | −32.7916 | −1.16373 | ||||||||
\(795\) | 46.7437 | 1.65783 | ||||||||
\(796\) | −69.9966 | −2.48096 | ||||||||
\(797\) | 17.5761 | 0.622576 | 0.311288 | − | 0.950316i | \(-0.399240\pi\) | ||||
0.311288 | + | 0.950316i | \(0.399240\pi\) | |||||||
\(798\) | −9.65824 | −0.341898 | ||||||||
\(799\) | 10.8102 | 0.382437 | ||||||||
\(800\) | 19.0505 | 0.673536 | ||||||||
\(801\) | 7.37911 | 0.260728 | ||||||||
\(802\) | 71.5653 | 2.52706 | ||||||||
\(803\) | −15.4235 | −0.544283 | ||||||||
\(804\) | −112.171 | −3.95598 | ||||||||
\(805\) | 0.870460 | 0.0306797 | ||||||||
\(806\) | −0.453010 | −0.0159566 | ||||||||
\(807\) | −17.8387 | −0.627950 | ||||||||
\(808\) | 5.81086 | 0.204425 | ||||||||
\(809\) | −9.09040 | −0.319601 | −0.159801 | − | 0.987149i | \(-0.551085\pi\) | ||||
−0.159801 | + | 0.987149i | \(0.551085\pi\) | |||||||
\(810\) | 9.31184 | 0.327185 | ||||||||
\(811\) | −28.6532 | −1.00615 | −0.503074 | − | 0.864243i | \(-0.667798\pi\) | ||||
−0.503074 | + | 0.864243i | \(0.667798\pi\) | |||||||
\(812\) | 16.5490 | 0.580757 | ||||||||
\(813\) | −40.5766 | −1.42308 | ||||||||
\(814\) | 156.408 | 5.48211 | ||||||||
\(815\) | 18.1116 | 0.634420 | ||||||||
\(816\) | −77.9084 | −2.72734 | ||||||||
\(817\) | 7.29343 | 0.255165 | ||||||||
\(818\) | −71.1299 | −2.48700 | ||||||||
\(819\) | −12.6405 | −0.441694 | ||||||||
\(820\) | 17.2927 | 0.603887 | ||||||||
\(821\) | −16.3321 | −0.569993 | −0.284997 | − | 0.958529i | \(-0.591992\pi\) | ||||
−0.284997 | + | 0.958529i | \(0.591992\pi\) | |||||||
\(822\) | −47.4529 | −1.65511 | ||||||||
\(823\) | 29.1737 | 1.01693 | 0.508465 | − | 0.861082i | \(-0.330213\pi\) | ||||
0.508465 | + | 0.861082i | \(0.330213\pi\) | |||||||
\(824\) | −114.883 | −4.00212 | ||||||||
\(825\) | −47.2924 | −1.64651 | ||||||||
\(826\) | −14.4744 | −0.503628 | ||||||||
\(827\) | 26.8841 | 0.934850 | 0.467425 | − | 0.884033i | \(-0.345182\pi\) | ||||
0.467425 | + | 0.884033i | \(0.345182\pi\) | |||||||
\(828\) | 10.5510 | 0.366672 | ||||||||
\(829\) | −42.5353 | −1.47731 | −0.738656 | − | 0.674083i | \(-0.764539\pi\) | ||||
−0.738656 | + | 0.674083i | \(0.764539\pi\) | |||||||
\(830\) | −45.1802 | −1.56823 | ||||||||
\(831\) | −80.3468 | −2.78720 | ||||||||
\(832\) | 3.67247 | 0.127320 | ||||||||
\(833\) | 18.2501 | 0.632329 | ||||||||
\(834\) | 50.6555 | 1.75406 | ||||||||
\(835\) | −5.40301 | −0.186979 | ||||||||
\(836\) | −27.4350 | −0.948861 | ||||||||
\(837\) | 0.600428 | 0.0207538 | ||||||||
\(838\) | −70.1171 | −2.42215 | ||||||||
\(839\) | 0.618499 | 0.0213530 | 0.0106765 | − | 0.999943i | \(-0.496602\pi\) | ||||
0.0106765 | + | 0.999943i | \(0.496602\pi\) | |||||||
\(840\) | −37.3745 | −1.28954 | ||||||||
\(841\) | −21.4633 | −0.740113 | ||||||||
\(842\) | −23.3825 | −0.805813 | ||||||||
\(843\) | 72.4933 | 2.49680 | ||||||||
\(844\) | 15.7326 | 0.541537 | ||||||||
\(845\) | 14.3300 | 0.492966 | ||||||||
\(846\) | 41.6604 | 1.43231 | ||||||||
\(847\) | −32.5778 | −1.11939 | ||||||||
\(848\) | −85.7680 | −2.94528 | ||||||||
\(849\) | 6.75671 | 0.231890 | ||||||||
\(850\) | −24.5281 | −0.841308 | ||||||||
\(851\) | −4.50917 | −0.154572 | ||||||||
\(852\) | 86.4453 | 2.96157 | ||||||||
\(853\) | −8.51838 | −0.291664 | −0.145832 | − | 0.989309i | \(-0.546586\pi\) | ||||
−0.145832 | + | 0.989309i | \(0.546586\pi\) | |||||||
\(854\) | −2.56950 | −0.0879265 | ||||||||
\(855\) | 7.77765 | 0.265990 | ||||||||
\(856\) | −25.6500 | −0.876699 | ||||||||
\(857\) | 39.6183 | 1.35334 | 0.676668 | − | 0.736288i | \(-0.263423\pi\) | ||||
0.676668 | + | 0.736288i | \(0.263423\pi\) | |||||||
\(858\) | −81.3254 | −2.77640 | ||||||||
\(859\) | −31.0116 | −1.05810 | −0.529052 | − | 0.848590i | \(-0.677452\pi\) | ||||
−0.529052 | + | 0.848590i | \(0.677452\pi\) | |||||||
\(860\) | 50.0496 | 1.70668 | ||||||||
\(861\) | 9.48363 | 0.323201 | ||||||||
\(862\) | 62.4137 | 2.12582 | ||||||||
\(863\) | 39.6641 | 1.35018 | 0.675091 | − | 0.737735i | \(-0.264104\pi\) | ||||
0.675091 | + | 0.737735i | \(0.264104\pi\) | |||||||
\(864\) | −43.4204 | −1.47719 | ||||||||
\(865\) | −32.8246 | −1.11607 | ||||||||
\(866\) | 22.7440 | 0.772873 | ||||||||
\(867\) | −14.3681 | −0.487968 | ||||||||
\(868\) | −0.575132 | −0.0195212 | ||||||||
\(869\) | 4.53494 | 0.153837 | ||||||||
\(870\) | −30.1840 | −1.02333 | ||||||||
\(871\) | −15.8044 | −0.535513 | ||||||||
\(872\) | −91.3365 | −3.09304 | ||||||||
\(873\) | −75.3919 | −2.55163 | ||||||||
\(874\) | 1.13586 | 0.0384210 | ||||||||
\(875\) | −15.2640 | −0.516016 | ||||||||
\(876\) | −33.8561 | −1.14389 | ||||||||
\(877\) | 2.90897 | 0.0982288 | 0.0491144 | − | 0.998793i | \(-0.484360\pi\) | ||||
0.0491144 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(878\) | 2.03157 | 0.0685620 | ||||||||
\(879\) | 80.3625 | 2.71056 | ||||||||
\(880\) | −70.3619 | −2.37190 | ||||||||
\(881\) | −22.7326 | −0.765882 | −0.382941 | − | 0.923773i | \(-0.625089\pi\) | ||||
−0.382941 | + | 0.923773i | \(0.625089\pi\) | |||||||
\(882\) | 70.3324 | 2.36822 | ||||||||
\(883\) | 0.716750 | 0.0241205 | 0.0120603 | − | 0.999927i | \(-0.496161\pi\) | ||||
0.0120603 | + | 0.999927i | \(0.496161\pi\) | |||||||
\(884\) | −29.3709 | −0.987851 | ||||||||
\(885\) | 18.3833 | 0.617947 | ||||||||
\(886\) | −29.0734 | −0.976742 | ||||||||
\(887\) | 26.8965 | 0.903095 | 0.451548 | − | 0.892247i | \(-0.350872\pi\) | ||||
0.451548 | + | 0.892247i | \(0.350872\pi\) | |||||||
\(888\) | 193.608 | 6.49706 | ||||||||
\(889\) | 2.60874 | 0.0874942 | ||||||||
\(890\) | 5.45134 | 0.182729 | ||||||||
\(891\) | 14.5063 | 0.485978 | ||||||||
\(892\) | −3.18148 | −0.106524 | ||||||||
\(893\) | 3.12300 | 0.104507 | ||||||||
\(894\) | −145.559 | −4.86820 | ||||||||
\(895\) | 5.35765 | 0.179086 | ||||||||
\(896\) | −11.4417 | −0.382241 | ||||||||
\(897\) | 2.34457 | 0.0782828 | ||||||||
\(898\) | −23.5858 | −0.787070 | ||||||||
\(899\) | −0.261926 | −0.00873571 | ||||||||
\(900\) | −65.8222 | −2.19407 | ||||||||
\(901\) | 37.7673 | 1.25821 | ||||||||
\(902\) | 38.6869 | 1.28813 | ||||||||
\(903\) | 27.4481 | 0.913415 | ||||||||
\(904\) | 43.5882 | 1.44972 | ||||||||
\(905\) | 37.0789 | 1.23255 | ||||||||
\(906\) | −116.732 | −3.87816 | ||||||||
\(907\) | −10.5602 | −0.350645 | −0.175323 | − | 0.984511i | \(-0.556097\pi\) | ||||
−0.175323 | + | 0.984511i | \(0.556097\pi\) | |||||||
\(908\) | 44.2928 | 1.46991 | ||||||||
\(909\) | −4.55086 | −0.150942 | ||||||||
\(910\) | −9.33820 | −0.309558 | ||||||||
\(911\) | −30.8567 | −1.02233 | −0.511164 | − | 0.859483i | \(-0.670785\pi\) | ||||
−0.511164 | + | 0.859483i | \(0.670785\pi\) | |||||||
\(912\) | −22.5073 | −0.745291 | ||||||||
\(913\) | −70.3830 | −2.32934 | ||||||||
\(914\) | 68.5628 | 2.26786 | ||||||||
\(915\) | 3.26341 | 0.107885 | ||||||||
\(916\) | 4.88723 | 0.161479 | ||||||||
\(917\) | 5.72726 | 0.189131 | ||||||||
\(918\) | 55.9053 | 1.84515 | ||||||||
\(919\) | −34.7982 | −1.14789 | −0.573944 | − | 0.818895i | \(-0.694587\pi\) | ||||
−0.573944 | + | 0.818895i | \(0.694587\pi\) | |||||||
\(920\) | 4.39544 | 0.144913 | ||||||||
\(921\) | −26.1338 | −0.861139 | ||||||||
\(922\) | −16.3661 | −0.538990 | ||||||||
\(923\) | 12.1797 | 0.400901 | ||||||||
\(924\) | −103.249 | −3.39664 | ||||||||
\(925\) | 28.1304 | 0.924921 | ||||||||
\(926\) | −51.5719 | −1.69476 | ||||||||
\(927\) | 89.9720 | 2.95507 | ||||||||
\(928\) | 18.9414 | 0.621781 | ||||||||
\(929\) | 25.3258 | 0.830911 | 0.415456 | − | 0.909613i | \(-0.363622\pi\) | ||||
0.415456 | + | 0.909613i | \(0.363622\pi\) | |||||||
\(930\) | 1.04899 | 0.0343978 | ||||||||
\(931\) | 5.27235 | 0.172794 | ||||||||
\(932\) | 107.854 | 3.53286 | ||||||||
\(933\) | 43.2879 | 1.41718 | ||||||||
\(934\) | 80.6791 | 2.63990 | ||||||||
\(935\) | 30.9834 | 1.01326 | ||||||||
\(936\) | −63.8288 | −2.08631 | ||||||||
\(937\) | −1.07542 | −0.0351324 | −0.0175662 | − | 0.999846i | \(-0.505592\pi\) | ||||
−0.0175662 | + | 0.999846i | \(0.505592\pi\) | |||||||
\(938\) | −28.8151 | −0.940848 | ||||||||
\(939\) | −20.1884 | −0.658822 | ||||||||
\(940\) | 21.4309 | 0.699000 | ||||||||
\(941\) | −46.5173 | −1.51642 | −0.758210 | − | 0.652011i | \(-0.773926\pi\) | ||||
−0.758210 | + | 0.652011i | \(0.773926\pi\) | |||||||
\(942\) | −41.8066 | −1.36213 | ||||||||
\(943\) | −1.11532 | −0.0363199 | ||||||||
\(944\) | −33.7307 | −1.09784 | ||||||||
\(945\) | 12.3770 | 0.402625 | ||||||||
\(946\) | 111.970 | 3.64046 | ||||||||
\(947\) | −40.5378 | −1.31730 | −0.658651 | − | 0.752448i | \(-0.728873\pi\) | ||||
−0.658651 | + | 0.752448i | \(0.728873\pi\) | |||||||
\(948\) | 9.95464 | 0.323312 | ||||||||
\(949\) | −4.77017 | −0.154846 | ||||||||
\(950\) | −7.08603 | −0.229901 | ||||||||
\(951\) | −2.86321 | −0.0928459 | ||||||||
\(952\) | −30.1973 | −0.978702 | ||||||||
\(953\) | −1.92904 | −0.0624879 | −0.0312439 | − | 0.999512i | \(-0.509947\pi\) | ||||
−0.0312439 | + | 0.999512i | \(0.509947\pi\) | |||||||
\(954\) | 145.548 | 4.71229 | ||||||||
\(955\) | 4.97467 | 0.160977 | ||||||||
\(956\) | −50.5890 | −1.63616 | ||||||||
\(957\) | −47.0215 | −1.51999 | ||||||||
\(958\) | −24.2485 | −0.783433 | ||||||||
\(959\) | −8.48828 | −0.274101 | ||||||||
\(960\) | −8.50401 | −0.274466 | ||||||||
\(961\) | −30.9909 | −0.999706 | ||||||||
\(962\) | 48.3738 | 1.55964 | ||||||||
\(963\) | 20.0882 | 0.647333 | ||||||||
\(964\) | −68.9336 | −2.22020 | ||||||||
\(965\) | 24.1991 | 0.778997 | ||||||||
\(966\) | 4.27469 | 0.137536 | ||||||||
\(967\) | 28.4008 | 0.913308 | 0.456654 | − | 0.889644i | \(-0.349048\pi\) | ||||
0.456654 | + | 0.889644i | \(0.349048\pi\) | |||||||
\(968\) | −164.503 | −5.28733 | ||||||||
\(969\) | 9.91092 | 0.318385 | ||||||||
\(970\) | −55.6960 | −1.78829 | ||||||||
\(971\) | −35.4842 | −1.13874 | −0.569371 | − | 0.822081i | \(-0.692813\pi\) | ||||
−0.569371 | + | 0.822081i | \(0.692813\pi\) | |||||||
\(972\) | −54.7435 | −1.75590 | ||||||||
\(973\) | 9.06115 | 0.290487 | ||||||||
\(974\) | −66.9022 | −2.14368 | ||||||||
\(975\) | −14.6265 | −0.468424 | ||||||||
\(976\) | −5.98789 | −0.191668 | ||||||||
\(977\) | 32.7689 | 1.04837 | 0.524185 | − | 0.851604i | \(-0.324370\pi\) | ||||
0.524185 | + | 0.851604i | \(0.324370\pi\) | |||||||
\(978\) | 88.9429 | 2.84408 | ||||||||
\(979\) | 8.49225 | 0.271414 | ||||||||
\(980\) | 36.1804 | 1.15574 | ||||||||
\(981\) | 71.5315 | 2.28382 | ||||||||
\(982\) | 73.9552 | 2.36001 | ||||||||
\(983\) | 57.7029 | 1.84044 | 0.920218 | − | 0.391405i | \(-0.128011\pi\) | ||||
0.920218 | + | 0.391405i | \(0.128011\pi\) | |||||||
\(984\) | 47.8881 | 1.52662 | ||||||||
\(985\) | −27.9612 | −0.890917 | ||||||||
\(986\) | −24.3877 | −0.776661 | ||||||||
\(987\) | 11.7531 | 0.374106 | ||||||||
\(988\) | −8.48509 | −0.269947 | ||||||||
\(989\) | −3.22803 | −0.102645 | ||||||||
\(990\) | 119.404 | 3.79490 | ||||||||
\(991\) | 25.8703 | 0.821796 | 0.410898 | − | 0.911681i | \(-0.365215\pi\) | ||||
0.410898 | + | 0.911681i | \(0.365215\pi\) | |||||||
\(992\) | −0.658274 | −0.0209002 | ||||||||
\(993\) | −61.0384 | −1.93700 | ||||||||
\(994\) | 22.2065 | 0.704347 | ||||||||
\(995\) | 22.8370 | 0.723981 | ||||||||
\(996\) | −154.498 | −4.89545 | ||||||||
\(997\) | −62.9735 | −1.99439 | −0.997195 | − | 0.0748476i | \(-0.976153\pi\) | ||||
−0.997195 | + | 0.0748476i | \(0.976153\pi\) | |||||||
\(998\) | −75.3184 | −2.38416 | ||||||||
\(999\) | −64.1156 | −2.02853 |
(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 | 6023.2.a.b.1.6 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.6 | ✓ | 99 | 1.1 | even | 1 | trivial |