Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.10114 | 1.21309 | 0.606546 | − | 0.795049i | \(-0.292555\pi\) | ||||
0.606546 | + | 0.795049i | \(0.292555\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.16694 | 1.86351 | 0.931757 | − | 0.363084i | \(-0.118276\pi\) | ||||
0.931757 | + | 0.363084i | \(0.118276\pi\) | |||||||
\(6\) | −2.10114 | −0.857785 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.41477 | 0.471590 | ||||||||
\(10\) | −4.16694 | −1.31770 | ||||||||
\(11\) | −3.72895 | −1.12432 | −0.562160 | − | 0.827029i | \(-0.690029\pi\) | ||||
−0.562160 | + | 0.827029i | \(0.690029\pi\) | |||||||
\(12\) | 2.10114 | 0.606546 | ||||||||
\(13\) | −3.37061 | −0.934840 | −0.467420 | − | 0.884035i | \(-0.654816\pi\) | ||||
−0.467420 | + | 0.884035i | \(0.654816\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 8.75531 | 2.26061 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.77414 | 0.430293 | 0.215146 | − | 0.976582i | \(-0.430977\pi\) | ||||
0.215146 | + | 0.976582i | \(0.430977\pi\) | |||||||
\(18\) | −1.41477 | −0.333464 | ||||||||
\(19\) | 0.724455 | 0.166201 | 0.0831006 | − | 0.996541i | \(-0.473518\pi\) | ||||
0.0831006 | + | 0.996541i | \(0.473518\pi\) | |||||||
\(20\) | 4.16694 | 0.931757 | ||||||||
\(21\) | −2.10114 | −0.458505 | ||||||||
\(22\) | 3.72895 | 0.795014 | ||||||||
\(23\) | 1.41023 | 0.294054 | 0.147027 | − | 0.989132i | \(-0.453030\pi\) | ||||
0.147027 | + | 0.989132i | \(0.453030\pi\) | |||||||
\(24\) | −2.10114 | −0.428892 | ||||||||
\(25\) | 12.3634 | 2.47268 | ||||||||
\(26\) | 3.37061 | 0.661032 | ||||||||
\(27\) | −3.33078 | −0.641010 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −0.0884609 | −0.0164268 | −0.00821339 | − | 0.999966i | \(-0.502614\pi\) | ||||
−0.00821339 | + | 0.999966i | \(0.502614\pi\) | |||||||
\(30\) | −8.75531 | −1.59849 | ||||||||
\(31\) | 6.94489 | 1.24734 | 0.623669 | − | 0.781688i | \(-0.285641\pi\) | ||||
0.623669 | + | 0.781688i | \(0.285641\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.83502 | −1.36390 | ||||||||
\(34\) | −1.77414 | −0.304263 | ||||||||
\(35\) | −4.16694 | −0.704342 | ||||||||
\(36\) | 1.41477 | 0.235795 | ||||||||
\(37\) | 3.16503 | 0.520329 | 0.260164 | − | 0.965564i | \(-0.416223\pi\) | ||||
0.260164 | + | 0.965564i | \(0.416223\pi\) | |||||||
\(38\) | −0.724455 | −0.117522 | ||||||||
\(39\) | −7.08212 | −1.13405 | ||||||||
\(40\) | −4.16694 | −0.658851 | ||||||||
\(41\) | 8.67761 | 1.35521 | 0.677607 | − | 0.735424i | \(-0.263017\pi\) | ||||
0.677607 | + | 0.735424i | \(0.263017\pi\) | |||||||
\(42\) | 2.10114 | 0.324212 | ||||||||
\(43\) | 5.90642 | 0.900720 | 0.450360 | − | 0.892847i | \(-0.351296\pi\) | ||||
0.450360 | + | 0.892847i | \(0.351296\pi\) | |||||||
\(44\) | −3.72895 | −0.562160 | ||||||||
\(45\) | 5.89526 | 0.878814 | ||||||||
\(46\) | −1.41023 | −0.207928 | ||||||||
\(47\) | 9.49335 | 1.38475 | 0.692374 | − | 0.721539i | \(-0.256565\pi\) | ||||
0.692374 | + | 0.721539i | \(0.256565\pi\) | |||||||
\(48\) | 2.10114 | 0.303273 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −12.3634 | −1.74845 | ||||||||
\(51\) | 3.72771 | 0.521984 | ||||||||
\(52\) | −3.37061 | −0.467420 | ||||||||
\(53\) | −0.0494789 | −0.00679644 | −0.00339822 | − | 0.999994i | \(-0.501082\pi\) | ||||
−0.00339822 | + | 0.999994i | \(0.501082\pi\) | |||||||
\(54\) | 3.33078 | 0.453262 | ||||||||
\(55\) | −15.5383 | −2.09518 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.52218 | 0.201617 | ||||||||
\(58\) | 0.0884609 | 0.0116155 | ||||||||
\(59\) | 9.33056 | 1.21474 | 0.607368 | − | 0.794421i | \(-0.292225\pi\) | ||||
0.607368 | + | 0.794421i | \(0.292225\pi\) | |||||||
\(60\) | 8.75531 | 1.13031 | ||||||||
\(61\) | 1.98664 | 0.254364 | 0.127182 | − | 0.991879i | \(-0.459407\pi\) | ||||
0.127182 | + | 0.991879i | \(0.459407\pi\) | |||||||
\(62\) | −6.94489 | −0.882001 | ||||||||
\(63\) | −1.41477 | −0.178244 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.0452 | −1.74209 | ||||||||
\(66\) | 7.83502 | 0.964424 | ||||||||
\(67\) | 4.62317 | 0.564810 | 0.282405 | − | 0.959295i | \(-0.408868\pi\) | ||||
0.282405 | + | 0.959295i | \(0.408868\pi\) | |||||||
\(68\) | 1.77414 | 0.215146 | ||||||||
\(69\) | 2.96309 | 0.356714 | ||||||||
\(70\) | 4.16694 | 0.498045 | ||||||||
\(71\) | 2.75923 | 0.327461 | 0.163730 | − | 0.986505i | \(-0.447647\pi\) | ||||
0.163730 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(72\) | −1.41477 | −0.166732 | ||||||||
\(73\) | −10.6270 | −1.24379 | −0.621897 | − | 0.783099i | \(-0.713638\pi\) | ||||
−0.621897 | + | 0.783099i | \(0.713638\pi\) | |||||||
\(74\) | −3.16503 | −0.367928 | ||||||||
\(75\) | 25.9772 | 2.99959 | ||||||||
\(76\) | 0.724455 | 0.0831006 | ||||||||
\(77\) | 3.72895 | 0.424953 | ||||||||
\(78\) | 7.08212 | 0.801892 | ||||||||
\(79\) | −4.76465 | −0.536066 | −0.268033 | − | 0.963410i | \(-0.586374\pi\) | ||||
−0.268033 | + | 0.963410i | \(0.586374\pi\) | |||||||
\(80\) | 4.16694 | 0.465878 | ||||||||
\(81\) | −11.2427 | −1.24919 | ||||||||
\(82\) | −8.67761 | −0.958282 | ||||||||
\(83\) | −5.90454 | −0.648107 | −0.324054 | − | 0.946039i | \(-0.605046\pi\) | ||||
−0.324054 | + | 0.946039i | \(0.605046\pi\) | |||||||
\(84\) | −2.10114 | −0.229253 | ||||||||
\(85\) | 7.39275 | 0.801856 | ||||||||
\(86\) | −5.90642 | −0.636905 | ||||||||
\(87\) | −0.185868 | −0.0199272 | ||||||||
\(88\) | 3.72895 | 0.397507 | ||||||||
\(89\) | −0.395919 | −0.0419674 | −0.0209837 | − | 0.999780i | \(-0.506680\pi\) | ||||
−0.0209837 | + | 0.999780i | \(0.506680\pi\) | |||||||
\(90\) | −5.89526 | −0.621415 | ||||||||
\(91\) | 3.37061 | 0.353336 | ||||||||
\(92\) | 1.41023 | 0.147027 | ||||||||
\(93\) | 14.5921 | 1.51314 | ||||||||
\(94\) | −9.49335 | −0.979164 | ||||||||
\(95\) | 3.01876 | 0.309718 | ||||||||
\(96\) | −2.10114 | −0.214446 | ||||||||
\(97\) | 2.82779 | 0.287118 | 0.143559 | − | 0.989642i | \(-0.454145\pi\) | ||||
0.143559 | + | 0.989642i | \(0.454145\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −5.27560 | −0.530218 | ||||||||
\(100\) | 12.3634 | 1.23634 | ||||||||
\(101\) | −4.25472 | −0.423361 | −0.211680 | − | 0.977339i | \(-0.567894\pi\) | ||||
−0.211680 | + | 0.977339i | \(0.567894\pi\) | |||||||
\(102\) | −3.72771 | −0.369099 | ||||||||
\(103\) | −9.65549 | −0.951384 | −0.475692 | − | 0.879612i | \(-0.657802\pi\) | ||||
−0.475692 | + | 0.879612i | \(0.657802\pi\) | |||||||
\(104\) | 3.37061 | 0.330516 | ||||||||
\(105\) | −8.75531 | −0.854431 | ||||||||
\(106\) | 0.0494789 | 0.00480581 | ||||||||
\(107\) | −2.00663 | −0.193988 | −0.0969941 | − | 0.995285i | \(-0.530923\pi\) | ||||
−0.0969941 | + | 0.995285i | \(0.530923\pi\) | |||||||
\(108\) | −3.33078 | −0.320505 | ||||||||
\(109\) | −4.16416 | −0.398854 | −0.199427 | − | 0.979913i | \(-0.563908\pi\) | ||||
−0.199427 | + | 0.979913i | \(0.563908\pi\) | |||||||
\(110\) | 15.5383 | 1.48152 | ||||||||
\(111\) | 6.65017 | 0.631206 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −0.204182 | −0.0192078 | −0.00960391 | − | 0.999954i | \(-0.503057\pi\) | ||||
−0.00960391 | + | 0.999954i | \(0.503057\pi\) | |||||||
\(114\) | −1.52218 | −0.142565 | ||||||||
\(115\) | 5.87636 | 0.547974 | ||||||||
\(116\) | −0.0884609 | −0.00821339 | ||||||||
\(117\) | −4.76864 | −0.440861 | ||||||||
\(118\) | −9.33056 | −0.858948 | ||||||||
\(119\) | −1.77414 | −0.162635 | ||||||||
\(120\) | −8.75531 | −0.799247 | ||||||||
\(121\) | 2.90503 | 0.264094 | ||||||||
\(122\) | −1.98664 | −0.179862 | ||||||||
\(123\) | 18.2328 | 1.64400 | ||||||||
\(124\) | 6.94489 | 0.623669 | ||||||||
\(125\) | 30.6829 | 2.74436 | ||||||||
\(126\) | 1.41477 | 0.126038 | ||||||||
\(127\) | 21.8542 | 1.93924 | 0.969621 | − | 0.244611i | \(-0.0786604\pi\) | ||||
0.969621 | + | 0.244611i | \(0.0786604\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.4102 | 1.09266 | ||||||||
\(130\) | 14.0452 | 1.23184 | ||||||||
\(131\) | 19.2128 | 1.67863 | 0.839317 | − | 0.543643i | \(-0.182955\pi\) | ||||
0.839317 | + | 0.543643i | \(0.182955\pi\) | |||||||
\(132\) | −7.83502 | −0.681951 | ||||||||
\(133\) | −0.724455 | −0.0628182 | ||||||||
\(134\) | −4.62317 | −0.399381 | ||||||||
\(135\) | −13.8792 | −1.19453 | ||||||||
\(136\) | −1.77414 | −0.152132 | ||||||||
\(137\) | 10.4333 | 0.891379 | 0.445689 | − | 0.895188i | \(-0.352959\pi\) | ||||
0.445689 | + | 0.895188i | \(0.352959\pi\) | |||||||
\(138\) | −2.96309 | −0.252235 | ||||||||
\(139\) | 19.5290 | 1.65643 | 0.828214 | − | 0.560412i | \(-0.189357\pi\) | ||||
0.828214 | + | 0.560412i | \(0.189357\pi\) | |||||||
\(140\) | −4.16694 | −0.352171 | ||||||||
\(141\) | 19.9468 | 1.67982 | ||||||||
\(142\) | −2.75923 | −0.231550 | ||||||||
\(143\) | 12.5688 | 1.05106 | ||||||||
\(144\) | 1.41477 | 0.117897 | ||||||||
\(145\) | −0.368612 | −0.0306115 | ||||||||
\(146\) | 10.6270 | 0.879495 | ||||||||
\(147\) | 2.10114 | 0.173299 | ||||||||
\(148\) | 3.16503 | 0.260164 | ||||||||
\(149\) | −10.3545 | −0.848271 | −0.424136 | − | 0.905599i | \(-0.639422\pi\) | ||||
−0.424136 | + | 0.905599i | \(0.639422\pi\) | |||||||
\(150\) | −25.9772 | −2.12103 | ||||||||
\(151\) | 6.14103 | 0.499750 | 0.249875 | − | 0.968278i | \(-0.419611\pi\) | ||||
0.249875 | + | 0.968278i | \(0.419611\pi\) | |||||||
\(152\) | −0.724455 | −0.0587610 | ||||||||
\(153\) | 2.51000 | 0.202922 | ||||||||
\(154\) | −3.72895 | −0.300487 | ||||||||
\(155\) | 28.9389 | 2.32443 | ||||||||
\(156\) | −7.08212 | −0.567023 | ||||||||
\(157\) | 11.3661 | 0.907110 | 0.453555 | − | 0.891228i | \(-0.350156\pi\) | ||||
0.453555 | + | 0.891228i | \(0.350156\pi\) | |||||||
\(158\) | 4.76465 | 0.379056 | ||||||||
\(159\) | −0.103962 | −0.00824470 | ||||||||
\(160\) | −4.16694 | −0.329426 | ||||||||
\(161\) | −1.41023 | −0.111142 | ||||||||
\(162\) | 11.2427 | 0.883313 | ||||||||
\(163\) | 4.48214 | 0.351068 | 0.175534 | − | 0.984473i | \(-0.443835\pi\) | ||||
0.175534 | + | 0.984473i | \(0.443835\pi\) | |||||||
\(164\) | 8.67761 | 0.677607 | ||||||||
\(165\) | −32.6481 | −2.54165 | ||||||||
\(166\) | 5.90454 | 0.458281 | ||||||||
\(167\) | 2.78465 | 0.215483 | 0.107741 | − | 0.994179i | \(-0.465638\pi\) | ||||
0.107741 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(168\) | 2.10114 | 0.162106 | ||||||||
\(169\) | −1.63896 | −0.126074 | ||||||||
\(170\) | −7.39275 | −0.566998 | ||||||||
\(171\) | 1.02494 | 0.0783788 | ||||||||
\(172\) | 5.90642 | 0.450360 | ||||||||
\(173\) | −7.26658 | −0.552468 | −0.276234 | − | 0.961090i | \(-0.589086\pi\) | ||||
−0.276234 | + | 0.961090i | \(0.589086\pi\) | |||||||
\(174\) | 0.185868 | 0.0140906 | ||||||||
\(175\) | −12.3634 | −0.934586 | ||||||||
\(176\) | −3.72895 | −0.281080 | ||||||||
\(177\) | 19.6048 | 1.47358 | ||||||||
\(178\) | 0.395919 | 0.0296754 | ||||||||
\(179\) | −15.0451 | −1.12452 | −0.562260 | − | 0.826960i | \(-0.690068\pi\) | ||||
−0.562260 | + | 0.826960i | \(0.690068\pi\) | |||||||
\(180\) | 5.89526 | 0.439407 | ||||||||
\(181\) | 7.54085 | 0.560507 | 0.280253 | − | 0.959926i | \(-0.409581\pi\) | ||||
0.280253 | + | 0.959926i | \(0.409581\pi\) | |||||||
\(182\) | −3.37061 | −0.249847 | ||||||||
\(183\) | 4.17421 | 0.308566 | ||||||||
\(184\) | −1.41023 | −0.103964 | ||||||||
\(185\) | 13.1885 | 0.969639 | ||||||||
\(186\) | −14.5921 | −1.06995 | ||||||||
\(187\) | −6.61568 | −0.483787 | ||||||||
\(188\) | 9.49335 | 0.692374 | ||||||||
\(189\) | 3.33078 | 0.242279 | ||||||||
\(190\) | −3.01876 | −0.219004 | ||||||||
\(191\) | −11.0001 | −0.795938 | −0.397969 | − | 0.917399i | \(-0.630285\pi\) | ||||
−0.397969 | + | 0.917399i | \(0.630285\pi\) | |||||||
\(192\) | 2.10114 | 0.151636 | ||||||||
\(193\) | −12.4495 | −0.896132 | −0.448066 | − | 0.894001i | \(-0.647887\pi\) | ||||
−0.448066 | + | 0.894001i | \(0.647887\pi\) | |||||||
\(194\) | −2.82779 | −0.203023 | ||||||||
\(195\) | −29.5108 | −2.11331 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −11.5949 | −0.826105 | −0.413052 | − | 0.910707i | \(-0.635537\pi\) | ||||
−0.413052 | + | 0.910707i | \(0.635537\pi\) | |||||||
\(198\) | 5.27560 | 0.374920 | ||||||||
\(199\) | 23.5489 | 1.66934 | 0.834670 | − | 0.550751i | \(-0.185658\pi\) | ||||
0.834670 | + | 0.550751i | \(0.185658\pi\) | |||||||
\(200\) | −12.3634 | −0.874225 | ||||||||
\(201\) | 9.71391 | 0.685166 | ||||||||
\(202\) | 4.25472 | 0.299361 | ||||||||
\(203\) | 0.0884609 | 0.00620874 | ||||||||
\(204\) | 3.72771 | 0.260992 | ||||||||
\(205\) | 36.1591 | 2.52546 | ||||||||
\(206\) | 9.65549 | 0.672730 | ||||||||
\(207\) | 1.99516 | 0.138673 | ||||||||
\(208\) | −3.37061 | −0.233710 | ||||||||
\(209\) | −2.70145 | −0.186863 | ||||||||
\(210\) | 8.75531 | 0.604174 | ||||||||
\(211\) | 8.12493 | 0.559343 | 0.279672 | − | 0.960096i | \(-0.409774\pi\) | ||||
0.279672 | + | 0.960096i | \(0.409774\pi\) | |||||||
\(212\) | −0.0494789 | −0.00339822 | ||||||||
\(213\) | 5.79752 | 0.397240 | ||||||||
\(214\) | 2.00663 | 0.137170 | ||||||||
\(215\) | 24.6117 | 1.67850 | ||||||||
\(216\) | 3.33078 | 0.226631 | ||||||||
\(217\) | −6.94489 | −0.471450 | ||||||||
\(218\) | 4.16416 | 0.282033 | ||||||||
\(219\) | −22.3287 | −1.50883 | ||||||||
\(220\) | −15.5383 | −1.04759 | ||||||||
\(221\) | −5.97995 | −0.402255 | ||||||||
\(222\) | −6.65017 | −0.446330 | ||||||||
\(223\) | 0.299212 | 0.0200367 | 0.0100184 | − | 0.999950i | \(-0.496811\pi\) | ||||
0.0100184 | + | 0.999950i | \(0.496811\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 17.4914 | 1.16609 | ||||||||
\(226\) | 0.204182 | 0.0135820 | ||||||||
\(227\) | 2.38947 | 0.158595 | 0.0792973 | − | 0.996851i | \(-0.474732\pi\) | ||||
0.0792973 | + | 0.996851i | \(0.474732\pi\) | |||||||
\(228\) | 1.52218 | 0.100809 | ||||||||
\(229\) | 4.41118 | 0.291499 | 0.145749 | − | 0.989322i | \(-0.453441\pi\) | ||||
0.145749 | + | 0.989322i | \(0.453441\pi\) | |||||||
\(230\) | −5.87636 | −0.387476 | ||||||||
\(231\) | 7.83502 | 0.515506 | ||||||||
\(232\) | 0.0884609 | 0.00580774 | ||||||||
\(233\) | −23.0826 | −1.51219 | −0.756094 | − | 0.654463i | \(-0.772895\pi\) | ||||
−0.756094 | + | 0.654463i | \(0.772895\pi\) | |||||||
\(234\) | 4.76864 | 0.311736 | ||||||||
\(235\) | 39.5582 | 2.58049 | ||||||||
\(236\) | 9.33056 | 0.607368 | ||||||||
\(237\) | −10.0112 | −0.650296 | ||||||||
\(238\) | 1.77414 | 0.115001 | ||||||||
\(239\) | 6.62522 | 0.428550 | 0.214275 | − | 0.976773i | \(-0.431261\pi\) | ||||
0.214275 | + | 0.976773i | \(0.431261\pi\) | |||||||
\(240\) | 8.75531 | 0.565153 | ||||||||
\(241\) | −13.7325 | −0.884585 | −0.442292 | − | 0.896871i | \(-0.645835\pi\) | ||||
−0.442292 | + | 0.896871i | \(0.645835\pi\) | |||||||
\(242\) | −2.90503 | −0.186743 | ||||||||
\(243\) | −13.6302 | −0.874375 | ||||||||
\(244\) | 1.98664 | 0.127182 | ||||||||
\(245\) | 4.16694 | 0.266216 | ||||||||
\(246\) | −18.2328 | −1.16248 | ||||||||
\(247\) | −2.44186 | −0.155372 | ||||||||
\(248\) | −6.94489 | −0.441001 | ||||||||
\(249\) | −12.4062 | −0.786213 | ||||||||
\(250\) | −30.6829 | −1.94056 | ||||||||
\(251\) | −21.9424 | −1.38499 | −0.692496 | − | 0.721422i | \(-0.743489\pi\) | ||||
−0.692496 | + | 0.721422i | \(0.743489\pi\) | |||||||
\(252\) | −1.41477 | −0.0891221 | ||||||||
\(253\) | −5.25868 | −0.330611 | ||||||||
\(254\) | −21.8542 | −1.37125 | ||||||||
\(255\) | 15.5332 | 0.972725 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.5009 | −0.842160 | −0.421080 | − | 0.907023i | \(-0.638349\pi\) | ||||
−0.421080 | + | 0.907023i | \(0.638349\pi\) | |||||||
\(258\) | −12.4102 | −0.772624 | ||||||||
\(259\) | −3.16503 | −0.196666 | ||||||||
\(260\) | −14.0452 | −0.871044 | ||||||||
\(261\) | −0.125152 | −0.00774670 | ||||||||
\(262\) | −19.2128 | −1.18697 | ||||||||
\(263\) | −6.32792 | −0.390196 | −0.195098 | − | 0.980784i | \(-0.562503\pi\) | ||||
−0.195098 | + | 0.980784i | \(0.562503\pi\) | |||||||
\(264\) | 7.83502 | 0.482212 | ||||||||
\(265\) | −0.206176 | −0.0126653 | ||||||||
\(266\) | 0.724455 | 0.0444192 | ||||||||
\(267\) | −0.831880 | −0.0509102 | ||||||||
\(268\) | 4.62317 | 0.282405 | ||||||||
\(269\) | 27.9637 | 1.70498 | 0.852488 | − | 0.522747i | \(-0.175093\pi\) | ||||
0.852488 | + | 0.522747i | \(0.175093\pi\) | |||||||
\(270\) | 13.8792 | 0.844660 | ||||||||
\(271\) | −16.2051 | −0.984387 | −0.492194 | − | 0.870486i | \(-0.663805\pi\) | ||||
−0.492194 | + | 0.870486i | \(0.663805\pi\) | |||||||
\(272\) | 1.77414 | 0.107573 | ||||||||
\(273\) | 7.08212 | 0.428629 | ||||||||
\(274\) | −10.4333 | −0.630300 | ||||||||
\(275\) | −46.1025 | −2.78008 | ||||||||
\(276\) | 2.96309 | 0.178357 | ||||||||
\(277\) | 1.83271 | 0.110117 | 0.0550584 | − | 0.998483i | \(-0.482466\pi\) | ||||
0.0550584 | + | 0.998483i | \(0.482466\pi\) | |||||||
\(278\) | −19.5290 | −1.17127 | ||||||||
\(279\) | 9.82541 | 0.588232 | ||||||||
\(280\) | 4.16694 | 0.249022 | ||||||||
\(281\) | 24.6518 | 1.47060 | 0.735300 | − | 0.677742i | \(-0.237041\pi\) | ||||
0.735300 | + | 0.677742i | \(0.237041\pi\) | |||||||
\(282\) | −19.9468 | −1.18782 | ||||||||
\(283\) | −3.58234 | −0.212948 | −0.106474 | − | 0.994315i | \(-0.533956\pi\) | ||||
−0.106474 | + | 0.994315i | \(0.533956\pi\) | |||||||
\(284\) | 2.75923 | 0.163730 | ||||||||
\(285\) | 6.34282 | 0.375716 | ||||||||
\(286\) | −12.5688 | −0.743211 | ||||||||
\(287\) | −8.67761 | −0.512223 | ||||||||
\(288\) | −1.41477 | −0.0833661 | ||||||||
\(289\) | −13.8524 | −0.814848 | ||||||||
\(290\) | 0.368612 | 0.0216456 | ||||||||
\(291\) | 5.94156 | 0.348301 | ||||||||
\(292\) | −10.6270 | −0.621897 | ||||||||
\(293\) | −25.6236 | −1.49694 | −0.748472 | − | 0.663166i | \(-0.769212\pi\) | ||||
−0.748472 | + | 0.663166i | \(0.769212\pi\) | |||||||
\(294\) | −2.10114 | −0.122541 | ||||||||
\(295\) | 38.8799 | 2.26368 | ||||||||
\(296\) | −3.16503 | −0.183964 | ||||||||
\(297\) | 12.4203 | 0.720700 | ||||||||
\(298\) | 10.3545 | 0.599818 | ||||||||
\(299\) | −4.75336 | −0.274894 | ||||||||
\(300\) | 25.9772 | 1.49979 | ||||||||
\(301\) | −5.90642 | −0.340440 | ||||||||
\(302\) | −6.14103 | −0.353376 | ||||||||
\(303\) | −8.93975 | −0.513575 | ||||||||
\(304\) | 0.724455 | 0.0415503 | ||||||||
\(305\) | 8.27823 | 0.474010 | ||||||||
\(306\) | −2.51000 | −0.143487 | ||||||||
\(307\) | −26.0229 | −1.48520 | −0.742601 | − | 0.669734i | \(-0.766408\pi\) | ||||
−0.742601 | + | 0.669734i | \(0.766408\pi\) | |||||||
\(308\) | 3.72895 | 0.212476 | ||||||||
\(309\) | −20.2875 | −1.15412 | ||||||||
\(310\) | −28.9389 | −1.64362 | ||||||||
\(311\) | −17.4574 | −0.989918 | −0.494959 | − | 0.868916i | \(-0.664817\pi\) | ||||
−0.494959 | + | 0.868916i | \(0.664817\pi\) | |||||||
\(312\) | 7.08212 | 0.400946 | ||||||||
\(313\) | 27.7186 | 1.56675 | 0.783375 | − | 0.621550i | \(-0.213497\pi\) | ||||
0.783375 | + | 0.621550i | \(0.213497\pi\) | |||||||
\(314\) | −11.3661 | −0.641423 | ||||||||
\(315\) | −5.89526 | −0.332160 | ||||||||
\(316\) | −4.76465 | −0.268033 | ||||||||
\(317\) | −22.7307 | −1.27668 | −0.638341 | − | 0.769754i | \(-0.720379\pi\) | ||||
−0.638341 | + | 0.769754i | \(0.720379\pi\) | |||||||
\(318\) | 0.103962 | 0.00582989 | ||||||||
\(319\) | 0.329866 | 0.0184689 | ||||||||
\(320\) | 4.16694 | 0.232939 | ||||||||
\(321\) | −4.21620 | −0.235325 | ||||||||
\(322\) | 1.41023 | 0.0785893 | ||||||||
\(323\) | 1.28529 | 0.0715152 | ||||||||
\(324\) | −11.2427 | −0.624596 | ||||||||
\(325\) | −41.6723 | −2.31156 | ||||||||
\(326\) | −4.48214 | −0.248243 | ||||||||
\(327\) | −8.74946 | −0.483847 | ||||||||
\(328\) | −8.67761 | −0.479141 | ||||||||
\(329\) | −9.49335 | −0.523385 | ||||||||
\(330\) | 32.6481 | 1.79722 | ||||||||
\(331\) | −12.7200 | −0.699152 | −0.349576 | − | 0.936908i | \(-0.613674\pi\) | ||||
−0.349576 | + | 0.936908i | \(0.613674\pi\) | |||||||
\(332\) | −5.90454 | −0.324054 | ||||||||
\(333\) | 4.47779 | 0.245382 | ||||||||
\(334\) | −2.78465 | −0.152369 | ||||||||
\(335\) | 19.2645 | 1.05253 | ||||||||
\(336\) | −2.10114 | −0.114626 | ||||||||
\(337\) | −12.9452 | −0.705171 | −0.352586 | − | 0.935780i | \(-0.614697\pi\) | ||||
−0.352586 | + | 0.935780i | \(0.614697\pi\) | |||||||
\(338\) | 1.63896 | 0.0891475 | ||||||||
\(339\) | −0.429014 | −0.0233008 | ||||||||
\(340\) | 7.39275 | 0.400928 | ||||||||
\(341\) | −25.8971 | −1.40241 | ||||||||
\(342\) | −1.02494 | −0.0554222 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.90642 | −0.318453 | ||||||||
\(345\) | 12.3470 | 0.664742 | ||||||||
\(346\) | 7.26658 | 0.390654 | ||||||||
\(347\) | 22.5772 | 1.21201 | 0.606005 | − | 0.795461i | \(-0.292771\pi\) | ||||
0.606005 | + | 0.795461i | \(0.292771\pi\) | |||||||
\(348\) | −0.185868 | −0.00996359 | ||||||||
\(349\) | −21.8222 | −1.16812 | −0.584058 | − | 0.811712i | \(-0.698536\pi\) | ||||
−0.584058 | + | 0.811712i | \(0.698536\pi\) | |||||||
\(350\) | 12.3634 | 0.660852 | ||||||||
\(351\) | 11.2268 | 0.599242 | ||||||||
\(352\) | 3.72895 | 0.198753 | ||||||||
\(353\) | 17.0465 | 0.907295 | 0.453647 | − | 0.891181i | \(-0.350123\pi\) | ||||
0.453647 | + | 0.891181i | \(0.350123\pi\) | |||||||
\(354\) | −19.6048 | −1.04198 | ||||||||
\(355\) | 11.4976 | 0.610227 | ||||||||
\(356\) | −0.395919 | −0.0209837 | ||||||||
\(357\) | −3.72771 | −0.197292 | ||||||||
\(358\) | 15.0451 | 0.795156 | ||||||||
\(359\) | 6.03456 | 0.318492 | 0.159246 | − | 0.987239i | \(-0.449094\pi\) | ||||
0.159246 | + | 0.987239i | \(0.449094\pi\) | |||||||
\(360\) | −5.89526 | −0.310708 | ||||||||
\(361\) | −18.4752 | −0.972377 | ||||||||
\(362\) | −7.54085 | −0.396338 | ||||||||
\(363\) | 6.10387 | 0.320370 | ||||||||
\(364\) | 3.37061 | 0.176668 | ||||||||
\(365\) | −44.2820 | −2.31783 | ||||||||
\(366\) | −4.17421 | −0.218189 | ||||||||
\(367\) | −14.3415 | −0.748618 | −0.374309 | − | 0.927304i | \(-0.622120\pi\) | ||||
−0.374309 | + | 0.927304i | \(0.622120\pi\) | |||||||
\(368\) | 1.41023 | 0.0735135 | ||||||||
\(369\) | 12.2768 | 0.639106 | ||||||||
\(370\) | −13.1885 | −0.685638 | ||||||||
\(371\) | 0.0494789 | 0.00256881 | ||||||||
\(372\) | 14.5921 | 0.756568 | ||||||||
\(373\) | 8.07437 | 0.418075 | 0.209038 | − | 0.977908i | \(-0.432967\pi\) | ||||
0.209038 | + | 0.977908i | \(0.432967\pi\) | |||||||
\(374\) | 6.61568 | 0.342089 | ||||||||
\(375\) | 64.4689 | 3.32916 | ||||||||
\(376\) | −9.49335 | −0.489582 | ||||||||
\(377\) | 0.298168 | 0.0153564 | ||||||||
\(378\) | −3.33078 | −0.171317 | ||||||||
\(379\) | 3.16812 | 0.162735 | 0.0813677 | − | 0.996684i | \(-0.474071\pi\) | ||||
0.0813677 | + | 0.996684i | \(0.474071\pi\) | |||||||
\(380\) | 3.01876 | 0.154859 | ||||||||
\(381\) | 45.9185 | 2.35248 | ||||||||
\(382\) | 11.0001 | 0.562813 | ||||||||
\(383\) | −34.5340 | −1.76460 | −0.882301 | − | 0.470685i | \(-0.844007\pi\) | ||||
−0.882301 | + | 0.470685i | \(0.844007\pi\) | |||||||
\(384\) | −2.10114 | −0.107223 | ||||||||
\(385\) | 15.5383 | 0.791905 | ||||||||
\(386\) | 12.4495 | 0.633661 | ||||||||
\(387\) | 8.35622 | 0.424771 | ||||||||
\(388\) | 2.82779 | 0.143559 | ||||||||
\(389\) | −6.41454 | −0.325230 | −0.162615 | − | 0.986690i | \(-0.551993\pi\) | ||||
−0.162615 | + | 0.986690i | \(0.551993\pi\) | |||||||
\(390\) | 29.5108 | 1.49434 | ||||||||
\(391\) | 2.50196 | 0.126529 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 40.3688 | 2.03633 | ||||||||
\(394\) | 11.5949 | 0.584144 | ||||||||
\(395\) | −19.8540 | −0.998965 | ||||||||
\(396\) | −5.27560 | −0.265109 | ||||||||
\(397\) | −11.3409 | −0.569183 | −0.284591 | − | 0.958649i | \(-0.591858\pi\) | ||||
−0.284591 | + | 0.958649i | \(0.591858\pi\) | |||||||
\(398\) | −23.5489 | −1.18040 | ||||||||
\(399\) | −1.52218 | −0.0762042 | ||||||||
\(400\) | 12.3634 | 0.618170 | ||||||||
\(401\) | 34.5847 | 1.72708 | 0.863539 | − | 0.504282i | \(-0.168243\pi\) | ||||
0.863539 | + | 0.504282i | \(0.168243\pi\) | |||||||
\(402\) | −9.71391 | −0.484486 | ||||||||
\(403\) | −23.4085 | −1.16606 | ||||||||
\(404\) | −4.25472 | −0.211680 | ||||||||
\(405\) | −46.8478 | −2.32789 | ||||||||
\(406\) | −0.0884609 | −0.00439024 | ||||||||
\(407\) | −11.8022 | −0.585015 | ||||||||
\(408\) | −3.72771 | −0.184549 | ||||||||
\(409\) | −25.5737 | −1.26454 | −0.632268 | − | 0.774750i | \(-0.717876\pi\) | ||||
−0.632268 | + | 0.774750i | \(0.717876\pi\) | |||||||
\(410\) | −36.1591 | −1.78577 | ||||||||
\(411\) | 21.9218 | 1.08132 | ||||||||
\(412\) | −9.65549 | −0.475692 | ||||||||
\(413\) | −9.33056 | −0.459127 | ||||||||
\(414\) | −1.99516 | −0.0980566 | ||||||||
\(415\) | −24.6039 | −1.20776 | ||||||||
\(416\) | 3.37061 | 0.165258 | ||||||||
\(417\) | 41.0331 | 2.00940 | ||||||||
\(418\) | 2.70145 | 0.132132 | ||||||||
\(419\) | −8.56975 | −0.418659 | −0.209330 | − | 0.977845i | \(-0.567128\pi\) | ||||
−0.209330 | + | 0.977845i | \(0.567128\pi\) | |||||||
\(420\) | −8.75531 | −0.427215 | ||||||||
\(421\) | 7.18854 | 0.350348 | 0.175174 | − | 0.984537i | \(-0.443951\pi\) | ||||
0.175174 | + | 0.984537i | \(0.443951\pi\) | |||||||
\(422\) | −8.12493 | −0.395515 | ||||||||
\(423\) | 13.4309 | 0.653033 | ||||||||
\(424\) | 0.0494789 | 0.00240291 | ||||||||
\(425\) | 21.9344 | 1.06398 | ||||||||
\(426\) | −5.79752 | −0.280891 | ||||||||
\(427\) | −1.98664 | −0.0961405 | ||||||||
\(428\) | −2.00663 | −0.0969941 | ||||||||
\(429\) | 26.4088 | 1.27503 | ||||||||
\(430\) | −24.6117 | −1.18688 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −3.33078 | −0.160252 | ||||||||
\(433\) | 0.351305 | 0.0168826 | 0.00844131 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844131 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(434\) | 6.94489 | 0.333365 | ||||||||
\(435\) | −0.774503 | −0.0371346 | ||||||||
\(436\) | −4.16416 | −0.199427 | ||||||||
\(437\) | 1.02165 | 0.0488722 | ||||||||
\(438\) | 22.3287 | 1.06691 | ||||||||
\(439\) | 25.3258 | 1.20874 | 0.604368 | − | 0.796706i | \(-0.293426\pi\) | ||||
0.604368 | + | 0.796706i | \(0.293426\pi\) | |||||||
\(440\) | 15.5383 | 0.740759 | ||||||||
\(441\) | 1.41477 | 0.0673700 | ||||||||
\(442\) | 5.97995 | 0.284437 | ||||||||
\(443\) | 39.5951 | 1.88122 | 0.940610 | − | 0.339490i | \(-0.110254\pi\) | ||||
0.940610 | + | 0.339490i | \(0.110254\pi\) | |||||||
\(444\) | 6.65017 | 0.315603 | ||||||||
\(445\) | −1.64977 | −0.0782067 | ||||||||
\(446\) | −0.299212 | −0.0141681 | ||||||||
\(447\) | −21.7561 | −1.02903 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 10.7410 | 0.506897 | 0.253449 | − | 0.967349i | \(-0.418435\pi\) | ||||
0.253449 | + | 0.967349i | \(0.418435\pi\) | |||||||
\(450\) | −17.4914 | −0.824551 | ||||||||
\(451\) | −32.3583 | −1.52369 | ||||||||
\(452\) | −0.204182 | −0.00960391 | ||||||||
\(453\) | 12.9031 | 0.606242 | ||||||||
\(454\) | −2.38947 | −0.112143 | ||||||||
\(455\) | 14.0452 | 0.658447 | ||||||||
\(456\) | −1.52218 | −0.0712825 | ||||||||
\(457\) | 7.78725 | 0.364272 | 0.182136 | − | 0.983273i | \(-0.441699\pi\) | ||||
0.182136 | + | 0.983273i | \(0.441699\pi\) | |||||||
\(458\) | −4.41118 | −0.206121 | ||||||||
\(459\) | −5.90929 | −0.275822 | ||||||||
\(460\) | 5.87636 | 0.273987 | ||||||||
\(461\) | −35.7287 | −1.66405 | −0.832026 | − | 0.554737i | \(-0.812819\pi\) | ||||
−0.832026 | + | 0.554737i | \(0.812819\pi\) | |||||||
\(462\) | −7.83502 | −0.364518 | ||||||||
\(463\) | 28.2617 | 1.31343 | 0.656716 | − | 0.754138i | \(-0.271945\pi\) | ||||
0.656716 | + | 0.754138i | \(0.271945\pi\) | |||||||
\(464\) | −0.0884609 | −0.00410670 | ||||||||
\(465\) | 60.8046 | 2.81975 | ||||||||
\(466\) | 23.0826 | 1.06928 | ||||||||
\(467\) | −8.99206 | −0.416103 | −0.208052 | − | 0.978118i | \(-0.566712\pi\) | ||||
−0.208052 | + | 0.978118i | \(0.566712\pi\) | |||||||
\(468\) | −4.76864 | −0.220431 | ||||||||
\(469\) | −4.62317 | −0.213478 | ||||||||
\(470\) | −39.5582 | −1.82469 | ||||||||
\(471\) | 23.8816 | 1.10041 | ||||||||
\(472\) | −9.33056 | −0.429474 | ||||||||
\(473\) | −22.0247 | −1.01270 | ||||||||
\(474\) | 10.0112 | 0.459829 | ||||||||
\(475\) | 8.95673 | 0.410963 | ||||||||
\(476\) | −1.77414 | −0.0813177 | ||||||||
\(477\) | −0.0700012 | −0.00320513 | ||||||||
\(478\) | −6.62522 | −0.303031 | ||||||||
\(479\) | −4.93539 | −0.225504 | −0.112752 | − | 0.993623i | \(-0.535967\pi\) | ||||
−0.112752 | + | 0.993623i | \(0.535967\pi\) | |||||||
\(480\) | −8.75531 | −0.399623 | ||||||||
\(481\) | −10.6681 | −0.486424 | ||||||||
\(482\) | 13.7325 | 0.625496 | ||||||||
\(483\) | −2.96309 | −0.134825 | ||||||||
\(484\) | 2.90503 | 0.132047 | ||||||||
\(485\) | 11.7832 | 0.535049 | ||||||||
\(486\) | 13.6302 | 0.618276 | ||||||||
\(487\) | −14.9389 | −0.676948 | −0.338474 | − | 0.940976i | \(-0.609911\pi\) | ||||
−0.338474 | + | 0.940976i | \(0.609911\pi\) | |||||||
\(488\) | −1.98664 | −0.0899312 | ||||||||
\(489\) | 9.41758 | 0.425878 | ||||||||
\(490\) | −4.16694 | −0.188243 | ||||||||
\(491\) | −12.3283 | −0.556370 | −0.278185 | − | 0.960527i | \(-0.589733\pi\) | ||||
−0.278185 | + | 0.960527i | \(0.589733\pi\) | |||||||
\(492\) | 18.2328 | 0.822000 | ||||||||
\(493\) | −0.156942 | −0.00706833 | ||||||||
\(494\) | 2.44186 | 0.109864 | ||||||||
\(495\) | −21.9831 | −0.988067 | ||||||||
\(496\) | 6.94489 | 0.311835 | ||||||||
\(497\) | −2.75923 | −0.123769 | ||||||||
\(498\) | 12.4062 | 0.555937 | ||||||||
\(499\) | 28.4866 | 1.27523 | 0.637617 | − | 0.770353i | \(-0.279920\pi\) | ||||
0.637617 | + | 0.770353i | \(0.279920\pi\) | |||||||
\(500\) | 30.6829 | 1.37218 | ||||||||
\(501\) | 5.85092 | 0.261400 | ||||||||
\(502\) | 21.9424 | 0.979337 | ||||||||
\(503\) | 27.8364 | 1.24116 | 0.620582 | − | 0.784141i | \(-0.286896\pi\) | ||||
0.620582 | + | 0.784141i | \(0.286896\pi\) | |||||||
\(504\) | 1.41477 | 0.0630188 | ||||||||
\(505\) | −17.7292 | −0.788938 | ||||||||
\(506\) | 5.25868 | 0.233777 | ||||||||
\(507\) | −3.44367 | −0.152939 | ||||||||
\(508\) | 21.8542 | 0.969621 | ||||||||
\(509\) | −29.4632 | −1.30594 | −0.652968 | − | 0.757386i | \(-0.726476\pi\) | ||||
−0.652968 | + | 0.757386i | \(0.726476\pi\) | |||||||
\(510\) | −15.5332 | −0.687820 | ||||||||
\(511\) | 10.6270 | 0.470110 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.41300 | −0.106537 | ||||||||
\(514\) | 13.5009 | 0.595497 | ||||||||
\(515\) | −40.2339 | −1.77292 | ||||||||
\(516\) | 12.4102 | 0.546328 | ||||||||
\(517\) | −35.4002 | −1.55690 | ||||||||
\(518\) | 3.16503 | 0.139064 | ||||||||
\(519\) | −15.2681 | −0.670193 | ||||||||
\(520\) | 14.0452 | 0.615921 | ||||||||
\(521\) | −2.06603 | −0.0905145 | −0.0452573 | − | 0.998975i | \(-0.514411\pi\) | ||||
−0.0452573 | + | 0.998975i | \(0.514411\pi\) | |||||||
\(522\) | 0.125152 | 0.00547775 | ||||||||
\(523\) | 15.5160 | 0.678467 | 0.339234 | − | 0.940702i | \(-0.389832\pi\) | ||||
0.339234 | + | 0.940702i | \(0.389832\pi\) | |||||||
\(524\) | 19.2128 | 0.839317 | ||||||||
\(525\) | −25.9772 | −1.13374 | ||||||||
\(526\) | 6.32792 | 0.275910 | ||||||||
\(527\) | 12.3212 | 0.536721 | ||||||||
\(528\) | −7.83502 | −0.340975 | ||||||||
\(529\) | −21.0112 | −0.913532 | ||||||||
\(530\) | 0.206176 | 0.00895569 | ||||||||
\(531\) | 13.2006 | 0.572857 | ||||||||
\(532\) | −0.724455 | −0.0314091 | ||||||||
\(533\) | −29.2489 | −1.26691 | ||||||||
\(534\) | 0.831880 | 0.0359990 | ||||||||
\(535\) | −8.36151 | −0.361500 | ||||||||
\(536\) | −4.62317 | −0.199691 | ||||||||
\(537\) | −31.6117 | −1.36415 | ||||||||
\(538\) | −27.9637 | −1.20560 | ||||||||
\(539\) | −3.72895 | −0.160617 | ||||||||
\(540\) | −13.8792 | −0.597265 | ||||||||
\(541\) | −25.7753 | −1.10817 | −0.554083 | − | 0.832461i | \(-0.686931\pi\) | ||||
−0.554083 | + | 0.832461i | \(0.686931\pi\) | |||||||
\(542\) | 16.2051 | 0.696067 | ||||||||
\(543\) | 15.8443 | 0.679946 | ||||||||
\(544\) | −1.77414 | −0.0760658 | ||||||||
\(545\) | −17.3518 | −0.743270 | ||||||||
\(546\) | −7.08212 | −0.303087 | ||||||||
\(547\) | 14.5458 | 0.621935 | 0.310967 | − | 0.950421i | \(-0.399347\pi\) | ||||
0.310967 | + | 0.950421i | \(0.399347\pi\) | |||||||
\(548\) | 10.4333 | 0.445689 | ||||||||
\(549\) | 2.81064 | 0.119955 | ||||||||
\(550\) | 46.1025 | 1.96582 | ||||||||
\(551\) | −0.0640859 | −0.00273015 | ||||||||
\(552\) | −2.96309 | −0.126118 | ||||||||
\(553\) | 4.76465 | 0.202614 | ||||||||
\(554\) | −1.83271 | −0.0778643 | ||||||||
\(555\) | 27.7109 | 1.17626 | ||||||||
\(556\) | 19.5290 | 0.828214 | ||||||||
\(557\) | 31.9790 | 1.35500 | 0.677498 | − | 0.735525i | \(-0.263064\pi\) | ||||
0.677498 | + | 0.735525i | \(0.263064\pi\) | |||||||
\(558\) | −9.82541 | −0.415943 | ||||||||
\(559\) | −19.9083 | −0.842030 | ||||||||
\(560\) | −4.16694 | −0.176085 | ||||||||
\(561\) | −13.9004 | −0.586877 | ||||||||
\(562\) | −24.6518 | −1.03987 | ||||||||
\(563\) | −15.8799 | −0.669259 | −0.334629 | − | 0.942350i | \(-0.608611\pi\) | ||||
−0.334629 | + | 0.942350i | \(0.608611\pi\) | |||||||
\(564\) | 19.9468 | 0.839912 | ||||||||
\(565\) | −0.850814 | −0.0357940 | ||||||||
\(566\) | 3.58234 | 0.150577 | ||||||||
\(567\) | 11.2427 | 0.472151 | ||||||||
\(568\) | −2.75923 | −0.115775 | ||||||||
\(569\) | −9.83766 | −0.412416 | −0.206208 | − | 0.978508i | \(-0.566112\pi\) | ||||
−0.206208 | + | 0.978508i | \(0.566112\pi\) | |||||||
\(570\) | −6.34282 | −0.265672 | ||||||||
\(571\) | −0.577642 | −0.0241736 | −0.0120868 | − | 0.999927i | \(-0.503847\pi\) | ||||
−0.0120868 | + | 0.999927i | \(0.503847\pi\) | |||||||
\(572\) | 12.5688 | 0.525530 | ||||||||
\(573\) | −23.1127 | −0.965545 | ||||||||
\(574\) | 8.67761 | 0.362196 | ||||||||
\(575\) | 17.4353 | 0.727102 | ||||||||
\(576\) | 1.41477 | 0.0589487 | ||||||||
\(577\) | −20.8449 | −0.867783 | −0.433892 | − | 0.900965i | \(-0.642860\pi\) | ||||
−0.433892 | + | 0.900965i | \(0.642860\pi\) | |||||||
\(578\) | 13.8524 | 0.576185 | ||||||||
\(579\) | −26.1580 | −1.08709 | ||||||||
\(580\) | −0.368612 | −0.0153058 | ||||||||
\(581\) | 5.90454 | 0.244961 | ||||||||
\(582\) | −5.94156 | −0.246286 | ||||||||
\(583\) | 0.184504 | 0.00764137 | ||||||||
\(584\) | 10.6270 | 0.439747 | ||||||||
\(585\) | −19.8707 | −0.821551 | ||||||||
\(586\) | 25.6236 | 1.05850 | ||||||||
\(587\) | 15.3372 | 0.633035 | 0.316518 | − | 0.948587i | \(-0.397486\pi\) | ||||
0.316518 | + | 0.948587i | \(0.397486\pi\) | |||||||
\(588\) | 2.10114 | 0.0866494 | ||||||||
\(589\) | 5.03125 | 0.207309 | ||||||||
\(590\) | −38.8799 | −1.60066 | ||||||||
\(591\) | −24.3625 | −1.00214 | ||||||||
\(592\) | 3.16503 | 0.130082 | ||||||||
\(593\) | −2.38692 | −0.0980192 | −0.0490096 | − | 0.998798i | \(-0.515606\pi\) | ||||
−0.0490096 | + | 0.998798i | \(0.515606\pi\) | |||||||
\(594\) | −12.4203 | −0.509612 | ||||||||
\(595\) | −7.39275 | −0.303073 | ||||||||
\(596\) | −10.3545 | −0.424136 | ||||||||
\(597\) | 49.4795 | 2.02506 | ||||||||
\(598\) | 4.75336 | 0.194379 | ||||||||
\(599\) | 14.1797 | 0.579365 | 0.289682 | − | 0.957123i | \(-0.406450\pi\) | ||||
0.289682 | + | 0.957123i | \(0.406450\pi\) | |||||||
\(600\) | −25.9772 | −1.06051 | ||||||||
\(601\) | 36.7754 | 1.50010 | 0.750049 | − | 0.661382i | \(-0.230030\pi\) | ||||
0.750049 | + | 0.661382i | \(0.230030\pi\) | |||||||
\(602\) | 5.90642 | 0.240728 | ||||||||
\(603\) | 6.54072 | 0.266359 | ||||||||
\(604\) | 6.14103 | 0.249875 | ||||||||
\(605\) | 12.1051 | 0.492142 | ||||||||
\(606\) | 8.93975 | 0.363152 | ||||||||
\(607\) | 8.74541 | 0.354965 | 0.177483 | − | 0.984124i | \(-0.443205\pi\) | ||||
0.177483 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(608\) | −0.724455 | −0.0293805 | ||||||||
\(609\) | 0.185868 | 0.00753177 | ||||||||
\(610\) | −8.27823 | −0.335176 | ||||||||
\(611\) | −31.9984 | −1.29452 | ||||||||
\(612\) | 2.51000 | 0.101461 | ||||||||
\(613\) | −37.4432 | −1.51232 | −0.756158 | − | 0.654389i | \(-0.772926\pi\) | ||||
−0.756158 | + | 0.654389i | \(0.772926\pi\) | |||||||
\(614\) | 26.0229 | 1.05020 | ||||||||
\(615\) | 75.9752 | 3.06361 | ||||||||
\(616\) | −3.72895 | −0.150243 | ||||||||
\(617\) | −28.8062 | −1.15970 | −0.579848 | − | 0.814725i | \(-0.696888\pi\) | ||||
−0.579848 | + | 0.814725i | \(0.696888\pi\) | |||||||
\(618\) | 20.2875 | 0.816083 | ||||||||
\(619\) | 2.42681 | 0.0975419 | 0.0487709 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487709 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(620\) | 28.9389 | 1.16222 | ||||||||
\(621\) | −4.69718 | −0.188492 | ||||||||
\(622\) | 17.4574 | 0.699977 | ||||||||
\(623\) | 0.395919 | 0.0158622 | ||||||||
\(624\) | −7.08212 | −0.283512 | ||||||||
\(625\) | 66.0368 | 2.64147 | ||||||||
\(626\) | −27.7186 | −1.10786 | ||||||||
\(627\) | −5.67611 | −0.226682 | ||||||||
\(628\) | 11.3661 | 0.453555 | ||||||||
\(629\) | 5.61522 | 0.223894 | ||||||||
\(630\) | 5.89526 | 0.234873 | ||||||||
\(631\) | −43.8429 | −1.74536 | −0.872679 | − | 0.488293i | \(-0.837620\pi\) | ||||
−0.872679 | + | 0.488293i | \(0.837620\pi\) | |||||||
\(632\) | 4.76465 | 0.189528 | ||||||||
\(633\) | 17.0716 | 0.678534 | ||||||||
\(634\) | 22.7307 | 0.902750 | ||||||||
\(635\) | 91.0650 | 3.61380 | ||||||||
\(636\) | −0.103962 | −0.00412235 | ||||||||
\(637\) | −3.37061 | −0.133549 | ||||||||
\(638\) | −0.329866 | −0.0130595 | ||||||||
\(639\) | 3.90368 | 0.154427 | ||||||||
\(640\) | −4.16694 | −0.164713 | ||||||||
\(641\) | −18.2665 | −0.721484 | −0.360742 | − | 0.932666i | \(-0.617477\pi\) | ||||
−0.360742 | + | 0.932666i | \(0.617477\pi\) | |||||||
\(642\) | 4.21620 | 0.166400 | ||||||||
\(643\) | −15.3716 | −0.606197 | −0.303098 | − | 0.952959i | \(-0.598021\pi\) | ||||
−0.303098 | + | 0.952959i | \(0.598021\pi\) | |||||||
\(644\) | −1.41023 | −0.0555710 | ||||||||
\(645\) | 51.7125 | 2.03618 | ||||||||
\(646\) | −1.28529 | −0.0505689 | ||||||||
\(647\) | −4.70441 | −0.184949 | −0.0924747 | − | 0.995715i | \(-0.529478\pi\) | ||||
−0.0924747 | + | 0.995715i | \(0.529478\pi\) | |||||||
\(648\) | 11.2427 | 0.441656 | ||||||||
\(649\) | −34.7932 | −1.36575 | ||||||||
\(650\) | 41.6723 | 1.63452 | ||||||||
\(651\) | −14.5921 | −0.571911 | ||||||||
\(652\) | 4.48214 | 0.175534 | ||||||||
\(653\) | 4.11941 | 0.161205 | 0.0806024 | − | 0.996746i | \(-0.474316\pi\) | ||||
0.0806024 | + | 0.996746i | \(0.474316\pi\) | |||||||
\(654\) | 8.74946 | 0.342131 | ||||||||
\(655\) | 80.0588 | 3.12815 | ||||||||
\(656\) | 8.67761 | 0.338804 | ||||||||
\(657\) | −15.0347 | −0.586560 | ||||||||
\(658\) | 9.49335 | 0.370089 | ||||||||
\(659\) | 40.4232 | 1.57466 | 0.787332 | − | 0.616529i | \(-0.211462\pi\) | ||||
0.787332 | + | 0.616529i | \(0.211462\pi\) | |||||||
\(660\) | −32.6481 | −1.27082 | ||||||||
\(661\) | −9.16820 | −0.356602 | −0.178301 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178301 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(662\) | 12.7200 | 0.494375 | ||||||||
\(663\) | −12.5647 | −0.487972 | ||||||||
\(664\) | 5.90454 | 0.229140 | ||||||||
\(665\) | −3.01876 | −0.117062 | ||||||||
\(666\) | −4.47779 | −0.173511 | ||||||||
\(667\) | −0.124751 | −0.00483036 | ||||||||
\(668\) | 2.78465 | 0.107741 | ||||||||
\(669\) | 0.628685 | 0.0243063 | ||||||||
\(670\) | −19.2645 | −0.744252 | ||||||||
\(671\) | −7.40809 | −0.285986 | ||||||||
\(672\) | 2.10114 | 0.0810531 | ||||||||
\(673\) | 35.3917 | 1.36425 | 0.682126 | − | 0.731235i | \(-0.261056\pi\) | ||||
0.682126 | + | 0.731235i | \(0.261056\pi\) | |||||||
\(674\) | 12.9452 | 0.498631 | ||||||||
\(675\) | −41.1798 | −1.58501 | ||||||||
\(676\) | −1.63896 | −0.0630368 | ||||||||
\(677\) | −48.9462 | −1.88116 | −0.940578 | − | 0.339577i | \(-0.889716\pi\) | ||||
−0.940578 | + | 0.339577i | \(0.889716\pi\) | |||||||
\(678\) | 0.429014 | 0.0164762 | ||||||||
\(679\) | −2.82779 | −0.108520 | ||||||||
\(680\) | −7.39275 | −0.283499 | ||||||||
\(681\) | 5.02059 | 0.192390 | ||||||||
\(682\) | 25.8971 | 0.991651 | ||||||||
\(683\) | 24.5212 | 0.938276 | 0.469138 | − | 0.883125i | \(-0.344565\pi\) | ||||
0.469138 | + | 0.883125i | \(0.344565\pi\) | |||||||
\(684\) | 1.02494 | 0.0391894 | ||||||||
\(685\) | 43.4750 | 1.66110 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 9.26848 | 0.353615 | ||||||||
\(688\) | 5.90642 | 0.225180 | ||||||||
\(689\) | 0.166774 | 0.00635359 | ||||||||
\(690\) | −12.3470 | −0.470044 | ||||||||
\(691\) | −11.5290 | −0.438582 | −0.219291 | − | 0.975659i | \(-0.570374\pi\) | ||||
−0.219291 | + | 0.975659i | \(0.570374\pi\) | |||||||
\(692\) | −7.26658 | −0.276234 | ||||||||
\(693\) | 5.27560 | 0.200403 | ||||||||
\(694\) | −22.5772 | −0.857020 | ||||||||
\(695\) | 81.3762 | 3.08677 | ||||||||
\(696\) | 0.185868 | 0.00704532 | ||||||||
\(697\) | 15.3953 | 0.583139 | ||||||||
\(698\) | 21.8222 | 0.825983 | ||||||||
\(699\) | −48.4996 | −1.83442 | ||||||||
\(700\) | −12.3634 | −0.467293 | ||||||||
\(701\) | −29.3131 | −1.10714 | −0.553569 | − | 0.832803i | \(-0.686735\pi\) | ||||
−0.553569 | + | 0.832803i | \(0.686735\pi\) | |||||||
\(702\) | −11.2268 | −0.423728 | ||||||||
\(703\) | 2.29292 | 0.0864793 | ||||||||
\(704\) | −3.72895 | −0.140540 | ||||||||
\(705\) | 83.1172 | 3.13038 | ||||||||
\(706\) | −17.0465 | −0.641554 | ||||||||
\(707\) | 4.25472 | 0.160015 | ||||||||
\(708\) | 19.6048 | 0.736792 | ||||||||
\(709\) | 10.5540 | 0.396363 | 0.198181 | − | 0.980165i | \(-0.436496\pi\) | ||||
0.198181 | + | 0.980165i | \(0.436496\pi\) | |||||||
\(710\) | −11.4976 | −0.431496 | ||||||||
\(711\) | −6.74089 | −0.252803 | ||||||||
\(712\) | 0.395919 | 0.0148377 | ||||||||
\(713\) | 9.79391 | 0.366785 | ||||||||
\(714\) | 3.72771 | 0.139506 | ||||||||
\(715\) | 52.3736 | 1.95866 | ||||||||
\(716\) | −15.0451 | −0.562260 | ||||||||
\(717\) | 13.9205 | 0.519870 | ||||||||
\(718\) | −6.03456 | −0.225208 | ||||||||
\(719\) | 45.7652 | 1.70676 | 0.853378 | − | 0.521293i | \(-0.174550\pi\) | ||||
0.853378 | + | 0.521293i | \(0.174550\pi\) | |||||||
\(720\) | 5.89526 | 0.219703 | ||||||||
\(721\) | 9.65549 | 0.359589 | ||||||||
\(722\) | 18.4752 | 0.687574 | ||||||||
\(723\) | −28.8537 | −1.07308 | ||||||||
\(724\) | 7.54085 | 0.280253 | ||||||||
\(725\) | −1.09368 | −0.0406182 | ||||||||
\(726\) | −6.10387 | −0.226536 | ||||||||
\(727\) | −19.4640 | −0.721880 | −0.360940 | − | 0.932589i | \(-0.617544\pi\) | ||||
−0.360940 | + | 0.932589i | \(0.617544\pi\) | |||||||
\(728\) | −3.37061 | −0.124923 | ||||||||
\(729\) | 5.08940 | 0.188496 | ||||||||
\(730\) | 44.2820 | 1.63895 | ||||||||
\(731\) | 10.4788 | 0.387574 | ||||||||
\(732\) | 4.17421 | 0.154283 | ||||||||
\(733\) | −10.0824 | −0.372401 | −0.186201 | − | 0.982512i | \(-0.559617\pi\) | ||||
−0.186201 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(734\) | 14.3415 | 0.529353 | ||||||||
\(735\) | 8.75531 | 0.322944 | ||||||||
\(736\) | −1.41023 | −0.0519819 | ||||||||
\(737\) | −17.2396 | −0.635027 | ||||||||
\(738\) | −12.2768 | −0.451916 | ||||||||
\(739\) | −35.9632 | −1.32293 | −0.661464 | − | 0.749977i | \(-0.730065\pi\) | ||||
−0.661464 | + | 0.749977i | \(0.730065\pi\) | |||||||
\(740\) | 13.1885 | 0.484819 | ||||||||
\(741\) | −5.13067 | −0.188480 | ||||||||
\(742\) | −0.0494789 | −0.00181643 | ||||||||
\(743\) | 35.3905 | 1.29835 | 0.649176 | − | 0.760639i | \(-0.275114\pi\) | ||||
0.649176 | + | 0.760639i | \(0.275114\pi\) | |||||||
\(744\) | −14.5921 | −0.534974 | ||||||||
\(745\) | −43.1465 | −1.58076 | ||||||||
\(746\) | −8.07437 | −0.295624 | ||||||||
\(747\) | −8.35356 | −0.305641 | ||||||||
\(748\) | −6.61568 | −0.241893 | ||||||||
\(749\) | 2.00663 | 0.0733207 | ||||||||
\(750\) | −64.4689 | −2.35407 | ||||||||
\(751\) | 13.2709 | 0.484263 | 0.242131 | − | 0.970243i | \(-0.422153\pi\) | ||||
0.242131 | + | 0.970243i | \(0.422153\pi\) | |||||||
\(752\) | 9.49335 | 0.346187 | ||||||||
\(753\) | −46.1039 | −1.68012 | ||||||||
\(754\) | −0.298168 | −0.0108586 | ||||||||
\(755\) | 25.5893 | 0.931290 | ||||||||
\(756\) | 3.33078 | 0.121139 | ||||||||
\(757\) | −27.7626 | −1.00905 | −0.504525 | − | 0.863397i | \(-0.668332\pi\) | ||||
−0.504525 | + | 0.863397i | \(0.668332\pi\) | |||||||
\(758\) | −3.16812 | −0.115071 | ||||||||
\(759\) | −11.0492 | −0.401061 | ||||||||
\(760\) | −3.01876 | −0.109502 | ||||||||
\(761\) | 11.7325 | 0.425302 | 0.212651 | − | 0.977128i | \(-0.431790\pi\) | ||||
0.212651 | + | 0.977128i | \(0.431790\pi\) | |||||||
\(762\) | −45.9185 | −1.66345 | ||||||||
\(763\) | 4.16416 | 0.150753 | ||||||||
\(764\) | −11.0001 | −0.397969 | ||||||||
\(765\) | 10.4590 | 0.378147 | ||||||||
\(766\) | 34.5340 | 1.24776 | ||||||||
\(767\) | −31.4497 | −1.13558 | ||||||||
\(768\) | 2.10114 | 0.0758182 | ||||||||
\(769\) | −25.8694 | −0.932875 | −0.466438 | − | 0.884554i | \(-0.654463\pi\) | ||||
−0.466438 | + | 0.884554i | \(0.654463\pi\) | |||||||
\(770\) | −15.5383 | −0.559961 | ||||||||
\(771\) | −28.3671 | −1.02162 | ||||||||
\(772\) | −12.4495 | −0.448066 | ||||||||
\(773\) | 1.57045 | 0.0564853 | 0.0282426 | − | 0.999601i | \(-0.491009\pi\) | ||||
0.0282426 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(774\) | −8.35622 | −0.300358 | ||||||||
\(775\) | 85.8624 | 3.08427 | ||||||||
\(776\) | −2.82779 | −0.101512 | ||||||||
\(777\) | −6.65017 | −0.238573 | ||||||||
\(778\) | 6.41454 | 0.229972 | ||||||||
\(779\) | 6.28653 | 0.225238 | ||||||||
\(780\) | −29.5108 | −1.05666 | ||||||||
\(781\) | −10.2890 | −0.368170 | ||||||||
\(782\) | −2.50196 | −0.0894698 | ||||||||
\(783\) | 0.294644 | 0.0105297 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 47.3617 | 1.69041 | ||||||||
\(786\) | −40.3688 | −1.43991 | ||||||||
\(787\) | −38.5631 | −1.37463 | −0.687313 | − | 0.726361i | \(-0.741210\pi\) | ||||
−0.687313 | + | 0.726361i | \(0.741210\pi\) | |||||||
\(788\) | −11.5949 | −0.413052 | ||||||||
\(789\) | −13.2958 | −0.473343 | ||||||||
\(790\) | 19.8540 | 0.706375 | ||||||||
\(791\) | 0.204182 | 0.00725987 | ||||||||
\(792\) | 5.27560 | 0.187460 | ||||||||
\(793\) | −6.69621 | −0.237790 | ||||||||
\(794\) | 11.3409 | 0.402473 | ||||||||
\(795\) | −0.433203 | −0.0153641 | ||||||||
\(796\) | 23.5489 | 0.834670 | ||||||||
\(797\) | −37.4659 | −1.32711 | −0.663555 | − | 0.748127i | \(-0.730953\pi\) | ||||
−0.663555 | + | 0.748127i | \(0.730953\pi\) | |||||||
\(798\) | 1.52218 | 0.0538845 | ||||||||
\(799\) | 16.8426 | 0.595847 | ||||||||
\(800\) | −12.3634 | −0.437112 | ||||||||
\(801\) | −0.560134 | −0.0197914 | ||||||||
\(802\) | −34.5847 | −1.22123 | ||||||||
\(803\) | 39.6274 | 1.39842 | ||||||||
\(804\) | 9.71391 | 0.342583 | ||||||||
\(805\) | −5.87636 | −0.207115 | ||||||||
\(806\) | 23.4085 | 0.824531 | ||||||||
\(807\) | 58.7555 | 2.06829 | ||||||||
\(808\) | 4.25472 | 0.149681 | ||||||||
\(809\) | 52.6102 | 1.84968 | 0.924838 | − | 0.380361i | \(-0.124200\pi\) | ||||
0.924838 | + | 0.380361i | \(0.124200\pi\) | |||||||
\(810\) | 46.8478 | 1.64606 | ||||||||
\(811\) | −31.2247 | −1.09645 | −0.548224 | − | 0.836331i | \(-0.684696\pi\) | ||||
−0.548224 | + | 0.836331i | \(0.684696\pi\) | |||||||
\(812\) | 0.0884609 | 0.00310437 | ||||||||
\(813\) | −34.0490 | −1.19415 | ||||||||
\(814\) | 11.8022 | 0.413668 | ||||||||
\(815\) | 18.6768 | 0.654220 | ||||||||
\(816\) | 3.72771 | 0.130496 | ||||||||
\(817\) | 4.27893 | 0.149701 | ||||||||
\(818\) | 25.5737 | 0.894162 | ||||||||
\(819\) | 4.76864 | 0.166630 | ||||||||
\(820\) | 36.1591 | 1.26273 | ||||||||
\(821\) | 5.07279 | 0.177041 | 0.0885207 | − | 0.996074i | \(-0.471786\pi\) | ||||
0.0885207 | + | 0.996074i | \(0.471786\pi\) | |||||||
\(822\) | −21.9218 | −0.764611 | ||||||||
\(823\) | 8.66809 | 0.302151 | 0.151075 | − | 0.988522i | \(-0.451726\pi\) | ||||
0.151075 | + | 0.988522i | \(0.451726\pi\) | |||||||
\(824\) | 9.65549 | 0.336365 | ||||||||
\(825\) | −96.8675 | −3.37249 | ||||||||
\(826\) | 9.33056 | 0.324652 | ||||||||
\(827\) | −8.35328 | −0.290472 | −0.145236 | − | 0.989397i | \(-0.546394\pi\) | ||||
−0.145236 | + | 0.989397i | \(0.546394\pi\) | |||||||
\(828\) | 1.99516 | 0.0693365 | ||||||||
\(829\) | −18.2454 | −0.633688 | −0.316844 | − | 0.948478i | \(-0.602623\pi\) | ||||
−0.316844 | + | 0.948478i | \(0.602623\pi\) | |||||||
\(830\) | 24.6039 | 0.854013 | ||||||||
\(831\) | 3.85077 | 0.133582 | ||||||||
\(832\) | −3.37061 | −0.116855 | ||||||||
\(833\) | 1.77414 | 0.0614704 | ||||||||
\(834\) | −41.0331 | −1.42086 | ||||||||
\(835\) | 11.6035 | 0.401554 | ||||||||
\(836\) | −2.70145 | −0.0934317 | ||||||||
\(837\) | −23.1319 | −0.799556 | ||||||||
\(838\) | 8.56975 | 0.296037 | ||||||||
\(839\) | 28.2759 | 0.976194 | 0.488097 | − | 0.872789i | \(-0.337691\pi\) | ||||
0.488097 | + | 0.872789i | \(0.337691\pi\) | |||||||
\(840\) | 8.75531 | 0.302087 | ||||||||
\(841\) | −28.9922 | −0.999730 | ||||||||
\(842\) | −7.18854 | −0.247733 | ||||||||
\(843\) | 51.7967 | 1.78397 | ||||||||
\(844\) | 8.12493 | 0.279672 | ||||||||
\(845\) | −6.82943 | −0.234940 | ||||||||
\(846\) | −13.4309 | −0.461764 | ||||||||
\(847\) | −2.90503 | −0.0998181 | ||||||||
\(848\) | −0.0494789 | −0.00169911 | ||||||||
\(849\) | −7.52699 | −0.258326 | ||||||||
\(850\) | −21.9344 | −0.752345 | ||||||||
\(851\) | 4.46344 | 0.153005 | ||||||||
\(852\) | 5.79752 | 0.198620 | ||||||||
\(853\) | −3.60131 | −0.123306 | −0.0616532 | − | 0.998098i | \(-0.519637\pi\) | ||||
−0.0616532 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(854\) | 1.98664 | 0.0679816 | ||||||||
\(855\) | 4.27085 | 0.146060 | ||||||||
\(856\) | 2.00663 | 0.0685852 | ||||||||
\(857\) | −8.20880 | −0.280407 | −0.140204 | − | 0.990123i | \(-0.544776\pi\) | ||||
−0.140204 | + | 0.990123i | \(0.544776\pi\) | |||||||
\(858\) | −26.4088 | −0.901583 | ||||||||
\(859\) | −6.14705 | −0.209735 | −0.104867 | − | 0.994486i | \(-0.533442\pi\) | ||||
−0.104867 | + | 0.994486i | \(0.533442\pi\) | |||||||
\(860\) | 24.6117 | 0.839252 | ||||||||
\(861\) | −18.2328 | −0.621373 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 0.777033 | 0.0264505 | 0.0132253 | − | 0.999913i | \(-0.495790\pi\) | ||||
0.0132253 | + | 0.999913i | \(0.495790\pi\) | |||||||
\(864\) | 3.33078 | 0.113316 | ||||||||
\(865\) | −30.2794 | −1.02953 | ||||||||
\(866\) | −0.351305 | −0.0119378 | ||||||||
\(867\) | −29.1058 | −0.988485 | ||||||||
\(868\) | −6.94489 | −0.235725 | ||||||||
\(869\) | 17.7671 | 0.602709 | ||||||||
\(870\) | 0.774503 | 0.0262581 | ||||||||
\(871\) | −15.5829 | −0.528008 | ||||||||
\(872\) | 4.16416 | 0.141016 | ||||||||
\(873\) | 4.00067 | 0.135402 | ||||||||
\(874\) | −1.02165 | −0.0345578 | ||||||||
\(875\) | −30.6829 | −1.03727 | ||||||||
\(876\) | −22.3287 | −0.754417 | ||||||||
\(877\) | 42.9631 | 1.45076 | 0.725381 | − | 0.688348i | \(-0.241664\pi\) | ||||
0.725381 | + | 0.688348i | \(0.241664\pi\) | |||||||
\(878\) | −25.3258 | −0.854705 | ||||||||
\(879\) | −53.8386 | −1.81593 | ||||||||
\(880\) | −15.5383 | −0.523796 | ||||||||
\(881\) | 15.6798 | 0.528264 | 0.264132 | − | 0.964486i | \(-0.414914\pi\) | ||||
0.264132 | + | 0.964486i | \(0.414914\pi\) | |||||||
\(882\) | −1.41477 | −0.0476378 | ||||||||
\(883\) | −46.6948 | −1.57140 | −0.785702 | − | 0.618605i | \(-0.787698\pi\) | ||||
−0.785702 | + | 0.618605i | \(0.787698\pi\) | |||||||
\(884\) | −5.97995 | −0.201128 | ||||||||
\(885\) | 81.6919 | 2.74604 | ||||||||
\(886\) | −39.5951 | −1.33022 | ||||||||
\(887\) | −14.5601 | −0.488882 | −0.244441 | − | 0.969664i | \(-0.578604\pi\) | ||||
−0.244441 | + | 0.969664i | \(0.578604\pi\) | |||||||
\(888\) | −6.65017 | −0.223165 | ||||||||
\(889\) | −21.8542 | −0.732965 | ||||||||
\(890\) | 1.64977 | 0.0553005 | ||||||||
\(891\) | 41.9235 | 1.40449 | ||||||||
\(892\) | 0.299212 | 0.0100184 | ||||||||
\(893\) | 6.87750 | 0.230147 | ||||||||
\(894\) | 21.7561 | 0.727634 | ||||||||
\(895\) | −62.6919 | −2.09556 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −9.98744 | −0.333471 | ||||||||
\(898\) | −10.7410 | −0.358431 | ||||||||
\(899\) | −0.614351 | −0.0204898 | ||||||||
\(900\) | 17.4914 | 0.583046 | ||||||||
\(901\) | −0.0877826 | −0.00292446 | ||||||||
\(902\) | 32.3583 | 1.07741 | ||||||||
\(903\) | −12.4102 | −0.412985 | ||||||||
\(904\) | 0.204182 | 0.00679099 | ||||||||
\(905\) | 31.4223 | 1.04451 | ||||||||
\(906\) | −12.9031 | −0.428678 | ||||||||
\(907\) | −29.1050 | −0.966417 | −0.483209 | − | 0.875505i | \(-0.660529\pi\) | ||||
−0.483209 | + | 0.875505i | \(0.660529\pi\) | |||||||
\(908\) | 2.38947 | 0.0792973 | ||||||||
\(909\) | −6.01945 | −0.199653 | ||||||||
\(910\) | −14.0452 | −0.465592 | ||||||||
\(911\) | −21.3731 | −0.708121 | −0.354060 | − | 0.935223i | \(-0.615199\pi\) | ||||
−0.354060 | + | 0.935223i | \(0.615199\pi\) | |||||||
\(912\) | 1.52218 | 0.0504043 | ||||||||
\(913\) | 22.0177 | 0.728679 | ||||||||
\(914\) | −7.78725 | −0.257579 | ||||||||
\(915\) | 17.3937 | 0.575018 | ||||||||
\(916\) | 4.41118 | 0.145749 | ||||||||
\(917\) | −19.2128 | −0.634464 | ||||||||
\(918\) | 5.90929 | 0.195036 | ||||||||
\(919\) | 39.6249 | 1.30710 | 0.653552 | − | 0.756881i | \(-0.273278\pi\) | ||||
0.653552 | + | 0.756881i | \(0.273278\pi\) | |||||||
\(920\) | −5.87636 | −0.193738 | ||||||||
\(921\) | −54.6775 | −1.80169 | ||||||||
\(922\) | 35.7287 | 1.17666 | ||||||||
\(923\) | −9.30031 | −0.306124 | ||||||||
\(924\) | 7.83502 | 0.257753 | ||||||||
\(925\) | 39.1306 | 1.28661 | ||||||||
\(926\) | −28.2617 | −0.928736 | ||||||||
\(927\) | −13.6603 | −0.448663 | ||||||||
\(928\) | 0.0884609 | 0.00290387 | ||||||||
\(929\) | 49.0030 | 1.60774 | 0.803868 | − | 0.594808i | \(-0.202772\pi\) | ||||
0.803868 | + | 0.594808i | \(0.202772\pi\) | |||||||
\(930\) | −60.8046 | −1.99386 | ||||||||
\(931\) | 0.724455 | 0.0237430 | ||||||||
\(932\) | −23.0826 | −0.756094 | ||||||||
\(933\) | −36.6803 | −1.20086 | ||||||||
\(934\) | 8.99206 | 0.294229 | ||||||||
\(935\) | −27.5672 | −0.901543 | ||||||||
\(936\) | 4.76864 | 0.155868 | ||||||||
\(937\) | −34.1545 | −1.11578 | −0.557890 | − | 0.829915i | \(-0.688389\pi\) | ||||
−0.557890 | + | 0.829915i | \(0.688389\pi\) | |||||||
\(938\) | 4.62317 | 0.150952 | ||||||||
\(939\) | 58.2406 | 1.90061 | ||||||||
\(940\) | 39.5582 | 1.29025 | ||||||||
\(941\) | 32.1044 | 1.04657 | 0.523286 | − | 0.852157i | \(-0.324706\pi\) | ||||
0.523286 | + | 0.852157i | \(0.324706\pi\) | |||||||
\(942\) | −23.8816 | −0.778105 | ||||||||
\(943\) | 12.2375 | 0.398507 | ||||||||
\(944\) | 9.33056 | 0.303684 | ||||||||
\(945\) | 13.8792 | 0.451490 | ||||||||
\(946\) | 22.0247 | 0.716085 | ||||||||
\(947\) | 18.9027 | 0.614256 | 0.307128 | − | 0.951668i | \(-0.400632\pi\) | ||||
0.307128 | + | 0.951668i | \(0.400632\pi\) | |||||||
\(948\) | −10.0112 | −0.325148 | ||||||||
\(949\) | 35.8195 | 1.16275 | ||||||||
\(950\) | −8.95673 | −0.290595 | ||||||||
\(951\) | −47.7602 | −1.54873 | ||||||||
\(952\) | 1.77414 | 0.0575003 | ||||||||
\(953\) | −10.6723 | −0.345709 | −0.172855 | − | 0.984947i | \(-0.555299\pi\) | ||||
−0.172855 | + | 0.984947i | \(0.555299\pi\) | |||||||
\(954\) | 0.0700012 | 0.00226637 | ||||||||
\(955\) | −45.8367 | −1.48324 | ||||||||
\(956\) | 6.62522 | 0.214275 | ||||||||
\(957\) | 0.693093 | 0.0224045 | ||||||||
\(958\) | 4.93539 | 0.159455 | ||||||||
\(959\) | −10.4333 | −0.336910 | ||||||||
\(960\) | 8.75531 | 0.282576 | ||||||||
\(961\) | 17.2314 | 0.555853 | ||||||||
\(962\) | 10.6681 | 0.343954 | ||||||||
\(963\) | −2.83892 | −0.0914829 | ||||||||
\(964\) | −13.7325 | −0.442292 | ||||||||
\(965\) | −51.8762 | −1.66995 | ||||||||
\(966\) | 2.96309 | 0.0953359 | ||||||||
\(967\) | 8.52232 | 0.274059 | 0.137030 | − | 0.990567i | \(-0.456244\pi\) | ||||
0.137030 | + | 0.990567i | \(0.456244\pi\) | |||||||
\(968\) | −2.90503 | −0.0933713 | ||||||||
\(969\) | 2.70056 | 0.0867545 | ||||||||
\(970\) | −11.7832 | −0.378337 | ||||||||
\(971\) | −28.5639 | −0.916660 | −0.458330 | − | 0.888782i | \(-0.651552\pi\) | ||||
−0.458330 | + | 0.888782i | \(0.651552\pi\) | |||||||
\(972\) | −13.6302 | −0.437187 | ||||||||
\(973\) | −19.5290 | −0.626071 | ||||||||
\(974\) | 14.9389 | 0.478675 | ||||||||
\(975\) | −87.5591 | −2.80414 | ||||||||
\(976\) | 1.98664 | 0.0635910 | ||||||||
\(977\) | 28.1693 | 0.901217 | 0.450608 | − | 0.892722i | \(-0.351207\pi\) | ||||
0.450608 | + | 0.892722i | \(0.351207\pi\) | |||||||
\(978\) | −9.41758 | −0.301141 | ||||||||
\(979\) | 1.47636 | 0.0471847 | ||||||||
\(980\) | 4.16694 | 0.133108 | ||||||||
\(981\) | −5.89133 | −0.188096 | ||||||||
\(982\) | 12.3283 | 0.393413 | ||||||||
\(983\) | 36.4579 | 1.16283 | 0.581413 | − | 0.813609i | \(-0.302500\pi\) | ||||
0.581413 | + | 0.813609i | \(0.302500\pi\) | |||||||
\(984\) | −18.2328 | −0.581241 | ||||||||
\(985\) | −48.3154 | −1.53946 | ||||||||
\(986\) | 0.156942 | 0.00499806 | ||||||||
\(987\) | −19.9468 | −0.634914 | ||||||||
\(988\) | −2.44186 | −0.0776858 | ||||||||
\(989\) | 8.32943 | 0.264861 | ||||||||
\(990\) | 21.9831 | 0.698669 | ||||||||
\(991\) | −23.0254 | −0.731427 | −0.365714 | − | 0.930727i | \(-0.619175\pi\) | ||||
−0.365714 | + | 0.930727i | \(0.619175\pi\) | |||||||
\(992\) | −6.94489 | −0.220500 | ||||||||
\(993\) | −26.7263 | −0.848135 | ||||||||
\(994\) | 2.75923 | 0.0875176 | ||||||||
\(995\) | 98.1270 | 3.11084 | ||||||||
\(996\) | −12.4062 | −0.393106 | ||||||||
\(997\) | −11.5669 | −0.366328 | −0.183164 | − | 0.983082i | \(-0.558634\pi\) | ||||
−0.183164 | + | 0.983082i | \(0.558634\pi\) | |||||||
\(998\) | −28.4866 | −0.901727 | ||||||||
\(999\) | −10.5420 | −0.333536 |
(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 | 6034.2.a.n.1.19 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.19 | ✓ | 24 | 1.1 | even | 1 | trivial |