Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.719826 | −0.508994 | −0.254497 | − | 0.967074i | \(-0.581910\pi\) | ||||
−0.254497 | + | 0.967074i | \(0.581910\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.48185 | −0.740925 | ||||||||
\(5\) | 1.82945 | 0.818153 | 0.409076 | − | 0.912500i | \(-0.365851\pi\) | ||||
0.409076 | + | 0.912500i | \(0.365851\pi\) | |||||||
\(6\) | −0.719826 | −0.293868 | ||||||||
\(7\) | 0.414755 | 0.156762 | 0.0783812 | − | 0.996923i | \(-0.475025\pi\) | ||||
0.0783812 | + | 0.996923i | \(0.475025\pi\) | |||||||
\(8\) | 2.50633 | 0.886120 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.31688 | −0.416435 | ||||||||
\(11\) | −2.75956 | −0.832040 | −0.416020 | − | 0.909356i | \(-0.636575\pi\) | ||||
−0.416020 | + | 0.909356i | \(0.636575\pi\) | |||||||
\(12\) | −1.48185 | −0.427773 | ||||||||
\(13\) | 0.245564 | 0.0681073 | 0.0340536 | − | 0.999420i | \(-0.489158\pi\) | ||||
0.0340536 | + | 0.999420i | \(0.489158\pi\) | |||||||
\(14\) | −0.298551 | −0.0797911 | ||||||||
\(15\) | 1.82945 | 0.472361 | ||||||||
\(16\) | 1.15958 | 0.289895 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.719826 | −0.169665 | ||||||||
\(19\) | 0.386626 | 0.0886981 | 0.0443491 | − | 0.999016i | \(-0.485879\pi\) | ||||
0.0443491 | + | 0.999016i | \(0.485879\pi\) | |||||||
\(20\) | −2.71096 | −0.606190 | ||||||||
\(21\) | 0.414755 | 0.0905069 | ||||||||
\(22\) | 1.98641 | 0.423503 | ||||||||
\(23\) | 6.58248 | 1.37254 | 0.686271 | − | 0.727346i | \(-0.259246\pi\) | ||||
0.686271 | + | 0.727346i | \(0.259246\pi\) | |||||||
\(24\) | 2.50633 | 0.511602 | ||||||||
\(25\) | −1.65313 | −0.330626 | ||||||||
\(26\) | −0.176764 | −0.0346662 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.614604 | −0.116149 | ||||||||
\(29\) | −0.775585 | −0.144022 | −0.0720112 | − | 0.997404i | \(-0.522942\pi\) | ||||
−0.0720112 | + | 0.997404i | \(0.522942\pi\) | |||||||
\(30\) | −1.31688 | −0.240429 | ||||||||
\(31\) | 2.70422 | 0.485693 | 0.242846 | − | 0.970065i | \(-0.421919\pi\) | ||||
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(32\) | −5.84735 | −1.03368 | ||||||||
\(33\) | −2.75956 | −0.480378 | ||||||||
\(34\) | −0.719826 | −0.123449 | ||||||||
\(35\) | 0.758771 | 0.128256 | ||||||||
\(36\) | −1.48185 | −0.246975 | ||||||||
\(37\) | 7.95789 | 1.30827 | 0.654134 | − | 0.756379i | \(-0.273033\pi\) | ||||
0.654134 | + | 0.756379i | \(0.273033\pi\) | |||||||
\(38\) | −0.278304 | −0.0451468 | ||||||||
\(39\) | 0.245564 | 0.0393218 | ||||||||
\(40\) | 4.58519 | 0.724982 | ||||||||
\(41\) | −4.65488 | −0.726970 | −0.363485 | − | 0.931600i | \(-0.618413\pi\) | ||||
−0.363485 | + | 0.931600i | \(0.618413\pi\) | |||||||
\(42\) | −0.298551 | −0.0460674 | ||||||||
\(43\) | −1.77108 | −0.270088 | −0.135044 | − | 0.990840i | \(-0.543118\pi\) | ||||
−0.135044 | + | 0.990840i | \(0.543118\pi\) | |||||||
\(44\) | 4.08926 | 0.616479 | ||||||||
\(45\) | 1.82945 | 0.272718 | ||||||||
\(46\) | −4.73824 | −0.698615 | ||||||||
\(47\) | 1.23213 | 0.179725 | 0.0898626 | − | 0.995954i | \(-0.471357\pi\) | ||||
0.0898626 | + | 0.995954i | \(0.471357\pi\) | |||||||
\(48\) | 1.15958 | 0.167371 | ||||||||
\(49\) | −6.82798 | −0.975426 | ||||||||
\(50\) | 1.18997 | 0.168287 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.363890 | −0.0504624 | ||||||||
\(53\) | 3.82181 | 0.524966 | 0.262483 | − | 0.964937i | \(-0.415459\pi\) | ||||
0.262483 | + | 0.964937i | \(0.415459\pi\) | |||||||
\(54\) | −0.719826 | −0.0979559 | ||||||||
\(55\) | −5.04847 | −0.680736 | ||||||||
\(56\) | 1.03951 | 0.138910 | ||||||||
\(57\) | 0.386626 | 0.0512099 | ||||||||
\(58\) | 0.558286 | 0.0733066 | ||||||||
\(59\) | 2.36846 | 0.308348 | 0.154174 | − | 0.988044i | \(-0.450728\pi\) | ||||
0.154174 | + | 0.988044i | \(0.450728\pi\) | |||||||
\(60\) | −2.71096 | −0.349984 | ||||||||
\(61\) | 5.98058 | 0.765735 | 0.382867 | − | 0.923803i | \(-0.374937\pi\) | ||||
0.382867 | + | 0.923803i | \(0.374937\pi\) | |||||||
\(62\) | −1.94657 | −0.247215 | ||||||||
\(63\) | 0.414755 | 0.0522542 | ||||||||
\(64\) | 1.88991 | 0.236239 | ||||||||
\(65\) | 0.449247 | 0.0557222 | ||||||||
\(66\) | 1.98641 | 0.244510 | ||||||||
\(67\) | 9.15259 | 1.11817 | 0.559083 | − | 0.829111i | \(-0.311153\pi\) | ||||
0.559083 | + | 0.829111i | \(0.311153\pi\) | |||||||
\(68\) | −1.48185 | −0.179701 | ||||||||
\(69\) | 6.58248 | 0.792437 | ||||||||
\(70\) | −0.546183 | −0.0652813 | ||||||||
\(71\) | −3.23725 | −0.384191 | −0.192095 | − | 0.981376i | \(-0.561528\pi\) | ||||
−0.192095 | + | 0.981376i | \(0.561528\pi\) | |||||||
\(72\) | 2.50633 | 0.295373 | ||||||||
\(73\) | −3.86850 | −0.452774 | −0.226387 | − | 0.974037i | \(-0.572691\pi\) | ||||
−0.226387 | + | 0.974037i | \(0.572691\pi\) | |||||||
\(74\) | −5.72829 | −0.665901 | ||||||||
\(75\) | −1.65313 | −0.190887 | ||||||||
\(76\) | −0.572922 | −0.0657187 | ||||||||
\(77\) | −1.14454 | −0.130433 | ||||||||
\(78\) | −0.176764 | −0.0200145 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 2.12139 | 0.237179 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.35070 | 0.370023 | ||||||||
\(83\) | 15.9173 | 1.74715 | 0.873574 | − | 0.486692i | \(-0.161796\pi\) | ||||
0.873574 | + | 0.486692i | \(0.161796\pi\) | |||||||
\(84\) | −0.614604 | −0.0670588 | ||||||||
\(85\) | 1.82945 | 0.198431 | ||||||||
\(86\) | 1.27487 | 0.137473 | ||||||||
\(87\) | −0.775585 | −0.0831514 | ||||||||
\(88\) | −6.91637 | −0.737287 | ||||||||
\(89\) | −0.214602 | −0.0227478 | −0.0113739 | − | 0.999935i | \(-0.503621\pi\) | ||||
−0.0113739 | + | 0.999935i | \(0.503621\pi\) | |||||||
\(90\) | −1.31688 | −0.138812 | ||||||||
\(91\) | 0.101849 | 0.0106767 | ||||||||
\(92\) | −9.75425 | −1.01695 | ||||||||
\(93\) | 2.70422 | 0.280415 | ||||||||
\(94\) | −0.886922 | −0.0914790 | ||||||||
\(95\) | 0.707311 | 0.0725686 | ||||||||
\(96\) | −5.84735 | −0.596793 | ||||||||
\(97\) | 18.6375 | 1.89235 | 0.946174 | − | 0.323660i | \(-0.104913\pi\) | ||||
0.946174 | + | 0.323660i | \(0.104913\pi\) | |||||||
\(98\) | 4.91496 | 0.496486 | ||||||||
\(99\) | −2.75956 | −0.277347 | ||||||||
\(100\) | 2.44969 | 0.244969 | ||||||||
\(101\) | 4.52955 | 0.450707 | 0.225353 | − | 0.974277i | \(-0.427646\pi\) | ||||
0.225353 | + | 0.974277i | \(0.427646\pi\) | |||||||
\(102\) | −0.719826 | −0.0712734 | ||||||||
\(103\) | −4.82523 | −0.475444 | −0.237722 | − | 0.971333i | \(-0.576401\pi\) | ||||
−0.237722 | + | 0.971333i | \(0.576401\pi\) | |||||||
\(104\) | 0.615464 | 0.0603513 | ||||||||
\(105\) | 0.758771 | 0.0740484 | ||||||||
\(106\) | −2.75104 | −0.267204 | ||||||||
\(107\) | −17.0658 | −1.64981 | −0.824907 | − | 0.565269i | \(-0.808772\pi\) | ||||
−0.824907 | + | 0.565269i | \(0.808772\pi\) | |||||||
\(108\) | −1.48185 | −0.142591 | ||||||||
\(109\) | 16.0479 | 1.53711 | 0.768556 | − | 0.639782i | \(-0.220976\pi\) | ||||
0.768556 | + | 0.639782i | \(0.220976\pi\) | |||||||
\(110\) | 3.63402 | 0.346490 | ||||||||
\(111\) | 7.95789 | 0.755329 | ||||||||
\(112\) | 0.480942 | 0.0454447 | ||||||||
\(113\) | 2.71994 | 0.255870 | 0.127935 | − | 0.991783i | \(-0.459165\pi\) | ||||
0.127935 | + | 0.991783i | \(0.459165\pi\) | |||||||
\(114\) | −0.278304 | −0.0260655 | ||||||||
\(115\) | 12.0423 | 1.12295 | ||||||||
\(116\) | 1.14930 | 0.106710 | ||||||||
\(117\) | 0.245564 | 0.0227024 | ||||||||
\(118\) | −1.70488 | −0.156947 | ||||||||
\(119\) | 0.414755 | 0.0380205 | ||||||||
\(120\) | 4.58519 | 0.418568 | ||||||||
\(121\) | −3.38481 | −0.307710 | ||||||||
\(122\) | −4.30498 | −0.389754 | ||||||||
\(123\) | −4.65488 | −0.419717 | ||||||||
\(124\) | −4.00725 | −0.359862 | ||||||||
\(125\) | −12.1715 | −1.08866 | ||||||||
\(126\) | −0.298551 | −0.0265970 | ||||||||
\(127\) | 9.03607 | 0.801821 | 0.400911 | − | 0.916117i | \(-0.368694\pi\) | ||||
0.400911 | + | 0.916117i | \(0.368694\pi\) | |||||||
\(128\) | 10.3343 | 0.913431 | ||||||||
\(129\) | −1.77108 | −0.155935 | ||||||||
\(130\) | −0.323379 | −0.0283622 | ||||||||
\(131\) | −10.2707 | −0.897360 | −0.448680 | − | 0.893693i | \(-0.648106\pi\) | ||||
−0.448680 | + | 0.893693i | \(0.648106\pi\) | |||||||
\(132\) | 4.08926 | 0.355924 | ||||||||
\(133\) | 0.160355 | 0.0139045 | ||||||||
\(134\) | −6.58827 | −0.569140 | ||||||||
\(135\) | 1.82945 | 0.157454 | ||||||||
\(136\) | 2.50633 | 0.214916 | ||||||||
\(137\) | 4.90565 | 0.419118 | 0.209559 | − | 0.977796i | \(-0.432797\pi\) | ||||
0.209559 | + | 0.977796i | \(0.432797\pi\) | |||||||
\(138\) | −4.73824 | −0.403346 | ||||||||
\(139\) | −14.1097 | −1.19677 | −0.598386 | − | 0.801208i | \(-0.704191\pi\) | ||||
−0.598386 | + | 0.801208i | \(0.704191\pi\) | |||||||
\(140\) | −1.12438 | −0.0950279 | ||||||||
\(141\) | 1.23213 | 0.103764 | ||||||||
\(142\) | 2.33026 | 0.195551 | ||||||||
\(143\) | −0.677651 | −0.0566680 | ||||||||
\(144\) | 1.15958 | 0.0966318 | ||||||||
\(145\) | −1.41889 | −0.117832 | ||||||||
\(146\) | 2.78465 | 0.230459 | ||||||||
\(147\) | −6.82798 | −0.563162 | ||||||||
\(148\) | −11.7924 | −0.969329 | ||||||||
\(149\) | 11.9807 | 0.981499 | 0.490750 | − | 0.871301i | \(-0.336723\pi\) | ||||
0.490750 | + | 0.871301i | \(0.336723\pi\) | |||||||
\(150\) | 1.18997 | 0.0971603 | ||||||||
\(151\) | 7.94967 | 0.646935 | 0.323467 | − | 0.946239i | \(-0.395151\pi\) | ||||
0.323467 | + | 0.946239i | \(0.395151\pi\) | |||||||
\(152\) | 0.969011 | 0.0785972 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0.823871 | 0.0663894 | ||||||||
\(155\) | 4.94723 | 0.397371 | ||||||||
\(156\) | −0.363890 | −0.0291345 | ||||||||
\(157\) | −8.53506 | −0.681172 | −0.340586 | − | 0.940213i | \(-0.610625\pi\) | ||||
−0.340586 | + | 0.940213i | \(0.610625\pi\) | |||||||
\(158\) | −0.719826 | −0.0572663 | ||||||||
\(159\) | 3.82181 | 0.303089 | ||||||||
\(160\) | −10.6974 | −0.845704 | ||||||||
\(161\) | 2.73011 | 0.215163 | ||||||||
\(162\) | −0.719826 | −0.0565549 | ||||||||
\(163\) | 8.76964 | 0.686891 | 0.343446 | − | 0.939173i | \(-0.388406\pi\) | ||||
0.343446 | + | 0.939173i | \(0.388406\pi\) | |||||||
\(164\) | 6.89784 | 0.538631 | ||||||||
\(165\) | −5.04847 | −0.393023 | ||||||||
\(166\) | −11.4577 | −0.889287 | ||||||||
\(167\) | 6.48978 | 0.502194 | 0.251097 | − | 0.967962i | \(-0.419209\pi\) | ||||
0.251097 | + | 0.967962i | \(0.419209\pi\) | |||||||
\(168\) | 1.03951 | 0.0802000 | ||||||||
\(169\) | −12.9397 | −0.995361 | ||||||||
\(170\) | −1.31688 | −0.101000 | ||||||||
\(171\) | 0.386626 | 0.0295660 | ||||||||
\(172\) | 2.62448 | 0.200115 | ||||||||
\(173\) | 7.89825 | 0.600493 | 0.300246 | − | 0.953862i | \(-0.402931\pi\) | ||||
0.300246 | + | 0.953862i | \(0.402931\pi\) | |||||||
\(174\) | 0.558286 | 0.0423236 | ||||||||
\(175\) | −0.685643 | −0.0518298 | ||||||||
\(176\) | −3.19994 | −0.241205 | ||||||||
\(177\) | 2.36846 | 0.178025 | ||||||||
\(178\) | 0.154476 | 0.0115785 | ||||||||
\(179\) | 4.81548 | 0.359926 | 0.179963 | − | 0.983673i | \(-0.442402\pi\) | ||||
0.179963 | + | 0.983673i | \(0.442402\pi\) | |||||||
\(180\) | −2.71096 | −0.202063 | ||||||||
\(181\) | −13.9833 | −1.03937 | −0.519686 | − | 0.854357i | \(-0.673951\pi\) | ||||
−0.519686 | + | 0.854357i | \(0.673951\pi\) | |||||||
\(182\) | −0.0733135 | −0.00543436 | ||||||||
\(183\) | 5.98058 | 0.442097 | ||||||||
\(184\) | 16.4978 | 1.21624 | ||||||||
\(185\) | 14.5585 | 1.07036 | ||||||||
\(186\) | −1.94657 | −0.142729 | ||||||||
\(187\) | −2.75956 | −0.201799 | ||||||||
\(188\) | −1.82584 | −0.133163 | ||||||||
\(189\) | 0.414755 | 0.0301690 | ||||||||
\(190\) | −0.509141 | −0.0369370 | ||||||||
\(191\) | −12.1242 | −0.877280 | −0.438640 | − | 0.898663i | \(-0.644540\pi\) | ||||
−0.438640 | + | 0.898663i | \(0.644540\pi\) | |||||||
\(192\) | 1.88991 | 0.136393 | ||||||||
\(193\) | −2.70545 | −0.194743 | −0.0973713 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973713 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(194\) | −13.4157 | −0.963193 | ||||||||
\(195\) | 0.449247 | 0.0321712 | ||||||||
\(196\) | 10.1180 | 0.722717 | ||||||||
\(197\) | 8.78690 | 0.626041 | 0.313020 | − | 0.949746i | \(-0.398659\pi\) | ||||
0.313020 | + | 0.949746i | \(0.398659\pi\) | |||||||
\(198\) | 1.98641 | 0.141168 | ||||||||
\(199\) | 7.23231 | 0.512685 | 0.256343 | − | 0.966586i | \(-0.417482\pi\) | ||||
0.256343 | + | 0.966586i | \(0.417482\pi\) | |||||||
\(200\) | −4.14328 | −0.292974 | ||||||||
\(201\) | 9.15259 | 0.645574 | ||||||||
\(202\) | −3.26048 | −0.229407 | ||||||||
\(203\) | −0.321677 | −0.0225773 | ||||||||
\(204\) | −1.48185 | −0.103750 | ||||||||
\(205\) | −8.51585 | −0.594773 | ||||||||
\(206\) | 3.47332 | 0.241998 | ||||||||
\(207\) | 6.58248 | 0.457514 | ||||||||
\(208\) | 0.284752 | 0.0197440 | ||||||||
\(209\) | −1.06692 | −0.0738004 | ||||||||
\(210\) | −0.546183 | −0.0376902 | ||||||||
\(211\) | −25.5292 | −1.75750 | −0.878750 | − | 0.477283i | \(-0.841622\pi\) | ||||
−0.878750 | + | 0.477283i | \(0.841622\pi\) | |||||||
\(212\) | −5.66335 | −0.388961 | ||||||||
\(213\) | −3.23725 | −0.221813 | ||||||||
\(214\) | 12.2844 | 0.839745 | ||||||||
\(215\) | −3.24010 | −0.220973 | ||||||||
\(216\) | 2.50633 | 0.170534 | ||||||||
\(217\) | 1.12159 | 0.0761384 | ||||||||
\(218\) | −11.5517 | −0.782381 | ||||||||
\(219\) | −3.86850 | −0.261409 | ||||||||
\(220\) | 7.48108 | 0.504374 | ||||||||
\(221\) | 0.245564 | 0.0165184 | ||||||||
\(222\) | −5.72829 | −0.384458 | ||||||||
\(223\) | 17.2162 | 1.15288 | 0.576441 | − | 0.817139i | \(-0.304441\pi\) | ||||
0.576441 | + | 0.817139i | \(0.304441\pi\) | |||||||
\(224\) | −2.42522 | −0.162041 | ||||||||
\(225\) | −1.65313 | −0.110209 | ||||||||
\(226\) | −1.95788 | −0.130236 | ||||||||
\(227\) | 18.3239 | 1.21620 | 0.608099 | − | 0.793862i | \(-0.291933\pi\) | ||||
0.608099 | + | 0.793862i | \(0.291933\pi\) | |||||||
\(228\) | −0.572922 | −0.0379427 | ||||||||
\(229\) | −24.4035 | −1.61263 | −0.806315 | − | 0.591486i | \(-0.798542\pi\) | ||||
−0.806315 | + | 0.591486i | \(0.798542\pi\) | |||||||
\(230\) | −8.66835 | −0.571574 | ||||||||
\(231\) | −1.14454 | −0.0753053 | ||||||||
\(232\) | −1.94387 | −0.127621 | ||||||||
\(233\) | 24.0462 | 1.57532 | 0.787659 | − | 0.616112i | \(-0.211293\pi\) | ||||
0.787659 | + | 0.616112i | \(0.211293\pi\) | |||||||
\(234\) | −0.176764 | −0.0115554 | ||||||||
\(235\) | 2.25412 | 0.147043 | ||||||||
\(236\) | −3.50971 | −0.228462 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | −0.298551 | −0.0193522 | ||||||||
\(239\) | 22.5991 | 1.46181 | 0.730906 | − | 0.682478i | \(-0.239098\pi\) | ||||
0.730906 | + | 0.682478i | \(0.239098\pi\) | |||||||
\(240\) | 2.12139 | 0.136935 | ||||||||
\(241\) | 25.1640 | 1.62095 | 0.810477 | − | 0.585770i | \(-0.199208\pi\) | ||||
0.810477 | + | 0.585770i | \(0.199208\pi\) | |||||||
\(242\) | 2.43647 | 0.156622 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −8.86233 | −0.567352 | ||||||||
\(245\) | −12.4914 | −0.798047 | ||||||||
\(246\) | 3.35070 | 0.213633 | ||||||||
\(247\) | 0.0949416 | 0.00604099 | ||||||||
\(248\) | 6.77767 | 0.430382 | ||||||||
\(249\) | 15.9173 | 1.00872 | ||||||||
\(250\) | 8.76139 | 0.554119 | ||||||||
\(251\) | −19.9536 | −1.25946 | −0.629729 | − | 0.776815i | \(-0.716834\pi\) | ||||
−0.629729 | + | 0.776815i | \(0.716834\pi\) | |||||||
\(252\) | −0.614604 | −0.0387164 | ||||||||
\(253\) | −18.1648 | −1.14201 | ||||||||
\(254\) | −6.50439 | −0.408122 | ||||||||
\(255\) | 1.82945 | 0.114564 | ||||||||
\(256\) | −11.2187 | −0.701170 | ||||||||
\(257\) | 6.37818 | 0.397860 | 0.198930 | − | 0.980014i | \(-0.436253\pi\) | ||||
0.198930 | + | 0.980014i | \(0.436253\pi\) | |||||||
\(258\) | 1.27487 | 0.0793701 | ||||||||
\(259\) | 3.30057 | 0.205087 | ||||||||
\(260\) | −0.665716 | −0.0412860 | ||||||||
\(261\) | −0.775585 | −0.0480075 | ||||||||
\(262\) | 7.39315 | 0.456751 | ||||||||
\(263\) | 28.4679 | 1.75541 | 0.877704 | − | 0.479203i | \(-0.159074\pi\) | ||||
0.877704 | + | 0.479203i | \(0.159074\pi\) | |||||||
\(264\) | −6.91637 | −0.425673 | ||||||||
\(265\) | 6.99179 | 0.429502 | ||||||||
\(266\) | −0.115428 | −0.00707732 | ||||||||
\(267\) | −0.214602 | −0.0131334 | ||||||||
\(268\) | −13.5628 | −0.828478 | ||||||||
\(269\) | 16.5425 | 1.00861 | 0.504307 | − | 0.863524i | \(-0.331748\pi\) | ||||
0.504307 | + | 0.863524i | \(0.331748\pi\) | |||||||
\(270\) | −1.31688 | −0.0801429 | ||||||||
\(271\) | 24.4858 | 1.48741 | 0.743705 | − | 0.668508i | \(-0.233067\pi\) | ||||
0.743705 | + | 0.668508i | \(0.233067\pi\) | |||||||
\(272\) | 1.15958 | 0.0703100 | ||||||||
\(273\) | 0.101849 | 0.00616418 | ||||||||
\(274\) | −3.53121 | −0.213328 | ||||||||
\(275\) | 4.56192 | 0.275094 | ||||||||
\(276\) | −9.75425 | −0.587137 | ||||||||
\(277\) | 2.17957 | 0.130958 | 0.0654789 | − | 0.997854i | \(-0.479143\pi\) | ||||
0.0654789 | + | 0.997854i | \(0.479143\pi\) | |||||||
\(278\) | 10.1566 | 0.609149 | ||||||||
\(279\) | 2.70422 | 0.161898 | ||||||||
\(280\) | 1.90173 | 0.113650 | ||||||||
\(281\) | −2.91692 | −0.174009 | −0.0870043 | − | 0.996208i | \(-0.527729\pi\) | ||||
−0.0870043 | + | 0.996208i | \(0.527729\pi\) | |||||||
\(282\) | −0.886922 | −0.0528154 | ||||||||
\(283\) | −9.99042 | −0.593869 | −0.296934 | − | 0.954898i | \(-0.595964\pi\) | ||||
−0.296934 | + | 0.954898i | \(0.595964\pi\) | |||||||
\(284\) | 4.79712 | 0.284657 | ||||||||
\(285\) | 0.707311 | 0.0418975 | ||||||||
\(286\) | 0.487790 | 0.0288437 | ||||||||
\(287\) | −1.93063 | −0.113962 | ||||||||
\(288\) | −5.84735 | −0.344558 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.02135 | 0.0599760 | ||||||||
\(291\) | 18.6375 | 1.09255 | ||||||||
\(292\) | 5.73254 | 0.335471 | ||||||||
\(293\) | 5.35560 | 0.312877 | 0.156439 | − | 0.987688i | \(-0.449999\pi\) | ||||
0.156439 | + | 0.987688i | \(0.449999\pi\) | |||||||
\(294\) | 4.91496 | 0.286646 | ||||||||
\(295\) | 4.33297 | 0.252275 | ||||||||
\(296\) | 19.9451 | 1.15928 | ||||||||
\(297\) | −2.75956 | −0.160126 | ||||||||
\(298\) | −8.62404 | −0.499577 | ||||||||
\(299\) | 1.61642 | 0.0934801 | ||||||||
\(300\) | 2.44969 | 0.141433 | ||||||||
\(301\) | −0.734565 | −0.0423396 | ||||||||
\(302\) | −5.72238 | −0.329286 | ||||||||
\(303\) | 4.52955 | 0.260216 | ||||||||
\(304\) | 0.448325 | 0.0257132 | ||||||||
\(305\) | 10.9411 | 0.626488 | ||||||||
\(306\) | −0.719826 | −0.0411497 | ||||||||
\(307\) | 20.0480 | 1.14420 | 0.572099 | − | 0.820185i | \(-0.306129\pi\) | ||||
0.572099 | + | 0.820185i | \(0.306129\pi\) | |||||||
\(308\) | 1.69604 | 0.0966408 | ||||||||
\(309\) | −4.82523 | −0.274498 | ||||||||
\(310\) | −3.56114 | −0.202259 | ||||||||
\(311\) | 14.8123 | 0.839931 | 0.419965 | − | 0.907540i | \(-0.362042\pi\) | ||||
0.419965 | + | 0.907540i | \(0.362042\pi\) | |||||||
\(312\) | 0.615464 | 0.0348438 | ||||||||
\(313\) | 2.76838 | 0.156478 | 0.0782390 | − | 0.996935i | \(-0.475070\pi\) | ||||
0.0782390 | + | 0.996935i | \(0.475070\pi\) | |||||||
\(314\) | 6.14376 | 0.346712 | ||||||||
\(315\) | 0.758771 | 0.0427519 | ||||||||
\(316\) | −1.48185 | −0.0833606 | ||||||||
\(317\) | 18.8127 | 1.05662 | 0.528312 | − | 0.849050i | \(-0.322825\pi\) | ||||
0.528312 | + | 0.849050i | \(0.322825\pi\) | |||||||
\(318\) | −2.75104 | −0.154271 | ||||||||
\(319\) | 2.14028 | 0.119832 | ||||||||
\(320\) | 3.45749 | 0.193280 | ||||||||
\(321\) | −17.0658 | −0.952520 | ||||||||
\(322\) | −1.96521 | −0.109517 | ||||||||
\(323\) | 0.386626 | 0.0215125 | ||||||||
\(324\) | −1.48185 | −0.0823250 | ||||||||
\(325\) | −0.405950 | −0.0225180 | ||||||||
\(326\) | −6.31262 | −0.349623 | ||||||||
\(327\) | 16.0479 | 0.887452 | ||||||||
\(328\) | −11.6667 | −0.644183 | ||||||||
\(329\) | 0.511033 | 0.0281742 | ||||||||
\(330\) | 3.63402 | 0.200046 | ||||||||
\(331\) | −23.3912 | −1.28569 | −0.642847 | − | 0.765994i | \(-0.722247\pi\) | ||||
−0.642847 | + | 0.765994i | \(0.722247\pi\) | |||||||
\(332\) | −23.5870 | −1.29451 | ||||||||
\(333\) | 7.95789 | 0.436089 | ||||||||
\(334\) | −4.67151 | −0.255614 | ||||||||
\(335\) | 16.7442 | 0.914831 | ||||||||
\(336\) | 0.480942 | 0.0262375 | ||||||||
\(337\) | −11.9605 | −0.651529 | −0.325765 | − | 0.945451i | \(-0.605622\pi\) | ||||
−0.325765 | + | 0.945451i | \(0.605622\pi\) | |||||||
\(338\) | 9.31433 | 0.506633 | ||||||||
\(339\) | 2.71994 | 0.147727 | ||||||||
\(340\) | −2.71096 | −0.147023 | ||||||||
\(341\) | −7.46248 | −0.404116 | ||||||||
\(342\) | −0.278304 | −0.0150489 | ||||||||
\(343\) | −5.73522 | −0.309673 | ||||||||
\(344\) | −4.43892 | −0.239330 | ||||||||
\(345\) | 12.0423 | 0.648335 | ||||||||
\(346\) | −5.68537 | −0.305647 | ||||||||
\(347\) | −11.1748 | −0.599892 | −0.299946 | − | 0.953956i | \(-0.596969\pi\) | ||||
−0.299946 | + | 0.953956i | \(0.596969\pi\) | |||||||
\(348\) | 1.14930 | 0.0616090 | ||||||||
\(349\) | 34.0195 | 1.82102 | 0.910511 | − | 0.413485i | \(-0.135689\pi\) | ||||
0.910511 | + | 0.413485i | \(0.135689\pi\) | |||||||
\(350\) | 0.493544 | 0.0263810 | ||||||||
\(351\) | 0.245564 | 0.0131073 | ||||||||
\(352\) | 16.1361 | 0.860059 | ||||||||
\(353\) | −26.9914 | −1.43661 | −0.718303 | − | 0.695731i | \(-0.755081\pi\) | ||||
−0.718303 | + | 0.695731i | \(0.755081\pi\) | |||||||
\(354\) | −1.70488 | −0.0906134 | ||||||||
\(355\) | −5.92237 | −0.314327 | ||||||||
\(356\) | 0.318009 | 0.0168544 | ||||||||
\(357\) | 0.414755 | 0.0219511 | ||||||||
\(358\) | −3.46631 | −0.183200 | ||||||||
\(359\) | 28.5330 | 1.50591 | 0.752957 | − | 0.658069i | \(-0.228627\pi\) | ||||
0.752957 | + | 0.658069i | \(0.228627\pi\) | |||||||
\(360\) | 4.58519 | 0.241661 | ||||||||
\(361\) | −18.8505 | −0.992133 | ||||||||
\(362\) | 10.0656 | 0.529034 | ||||||||
\(363\) | −3.38481 | −0.177656 | ||||||||
\(364\) | −0.150925 | −0.00791061 | ||||||||
\(365\) | −7.07721 | −0.370438 | ||||||||
\(366\) | −4.30498 | −0.225025 | ||||||||
\(367\) | 34.1865 | 1.78452 | 0.892261 | − | 0.451521i | \(-0.149118\pi\) | ||||
0.892261 | + | 0.451521i | \(0.149118\pi\) | |||||||
\(368\) | 7.63292 | 0.397894 | ||||||||
\(369\) | −4.65488 | −0.242323 | ||||||||
\(370\) | −10.4796 | −0.544808 | ||||||||
\(371\) | 1.58511 | 0.0822950 | ||||||||
\(372\) | −4.00725 | −0.207766 | ||||||||
\(373\) | 32.4578 | 1.68060 | 0.840300 | − | 0.542121i | \(-0.182379\pi\) | ||||
0.840300 | + | 0.542121i | \(0.182379\pi\) | |||||||
\(374\) | 1.98641 | 0.102715 | ||||||||
\(375\) | −12.1715 | −0.628535 | ||||||||
\(376\) | 3.08813 | 0.159258 | ||||||||
\(377\) | −0.190456 | −0.00980898 | ||||||||
\(378\) | −0.298551 | −0.0153558 | ||||||||
\(379\) | −7.52217 | −0.386388 | −0.193194 | − | 0.981161i | \(-0.561885\pi\) | ||||
−0.193194 | + | 0.981161i | \(0.561885\pi\) | |||||||
\(380\) | −1.04813 | −0.0537679 | ||||||||
\(381\) | 9.03607 | 0.462932 | ||||||||
\(382\) | 8.72735 | 0.446530 | ||||||||
\(383\) | −3.83802 | −0.196113 | −0.0980567 | − | 0.995181i | \(-0.531263\pi\) | ||||
−0.0980567 | + | 0.995181i | \(0.531263\pi\) | |||||||
\(384\) | 10.3343 | 0.527370 | ||||||||
\(385\) | −2.09388 | −0.106714 | ||||||||
\(386\) | 1.94745 | 0.0991228 | ||||||||
\(387\) | −1.77108 | −0.0900293 | ||||||||
\(388\) | −27.6179 | −1.40209 | ||||||||
\(389\) | 4.16830 | 0.211341 | 0.105671 | − | 0.994401i | \(-0.466301\pi\) | ||||
0.105671 | + | 0.994401i | \(0.466301\pi\) | |||||||
\(390\) | −0.323379 | −0.0163749 | ||||||||
\(391\) | 6.58248 | 0.332890 | ||||||||
\(392\) | −17.1131 | −0.864344 | ||||||||
\(393\) | −10.2707 | −0.518091 | ||||||||
\(394\) | −6.32504 | −0.318651 | ||||||||
\(395\) | 1.82945 | 0.0920494 | ||||||||
\(396\) | 4.08926 | 0.205493 | ||||||||
\(397\) | −19.5347 | −0.980417 | −0.490209 | − | 0.871605i | \(-0.663079\pi\) | ||||
−0.490209 | + | 0.871605i | \(0.663079\pi\) | |||||||
\(398\) | −5.20601 | −0.260954 | ||||||||
\(399\) | 0.160355 | 0.00802779 | ||||||||
\(400\) | −1.91694 | −0.0958470 | ||||||||
\(401\) | −24.1661 | −1.20680 | −0.603399 | − | 0.797440i | \(-0.706187\pi\) | ||||
−0.603399 | + | 0.797440i | \(0.706187\pi\) | |||||||
\(402\) | −6.58827 | −0.328593 | ||||||||
\(403\) | 0.664061 | 0.0330792 | ||||||||
\(404\) | −6.71211 | −0.333940 | ||||||||
\(405\) | 1.82945 | 0.0909059 | ||||||||
\(406\) | 0.231552 | 0.0114917 | ||||||||
\(407\) | −21.9603 | −1.08853 | ||||||||
\(408\) | 2.50633 | 0.124082 | ||||||||
\(409\) | −20.9646 | −1.03663 | −0.518316 | − | 0.855189i | \(-0.673441\pi\) | ||||
−0.518316 | + | 0.855189i | \(0.673441\pi\) | |||||||
\(410\) | 6.12993 | 0.302736 | ||||||||
\(411\) | 4.90565 | 0.241978 | ||||||||
\(412\) | 7.15026 | 0.352268 | ||||||||
\(413\) | 0.982330 | 0.0483373 | ||||||||
\(414\) | −4.73824 | −0.232872 | ||||||||
\(415\) | 29.1198 | 1.42943 | ||||||||
\(416\) | −1.43590 | −0.0704008 | ||||||||
\(417\) | −14.1097 | −0.690956 | ||||||||
\(418\) | 0.767997 | 0.0375639 | ||||||||
\(419\) | 10.3584 | 0.506041 | 0.253021 | − | 0.967461i | \(-0.418576\pi\) | ||||
0.253021 | + | 0.967461i | \(0.418576\pi\) | |||||||
\(420\) | −1.12438 | −0.0548644 | ||||||||
\(421\) | −38.6490 | −1.88364 | −0.941819 | − | 0.336121i | \(-0.890885\pi\) | ||||
−0.941819 | + | 0.336121i | \(0.890885\pi\) | |||||||
\(422\) | 18.3766 | 0.894557 | ||||||||
\(423\) | 1.23213 | 0.0599084 | ||||||||
\(424\) | 9.57870 | 0.465183 | ||||||||
\(425\) | −1.65313 | −0.0801886 | ||||||||
\(426\) | 2.33026 | 0.112901 | ||||||||
\(427\) | 2.48047 | 0.120039 | ||||||||
\(428\) | 25.2890 | 1.22239 | ||||||||
\(429\) | −0.677651 | −0.0327173 | ||||||||
\(430\) | 2.33231 | 0.112474 | ||||||||
\(431\) | 33.6185 | 1.61934 | 0.809672 | − | 0.586882i | \(-0.199645\pi\) | ||||
0.809672 | + | 0.586882i | \(0.199645\pi\) | |||||||
\(432\) | 1.15958 | 0.0557904 | ||||||||
\(433\) | −3.19007 | −0.153305 | −0.0766525 | − | 0.997058i | \(-0.524423\pi\) | ||||
−0.0766525 | + | 0.997058i | \(0.524423\pi\) | |||||||
\(434\) | −0.807349 | −0.0387540 | ||||||||
\(435\) | −1.41889 | −0.0680306 | ||||||||
\(436\) | −23.7806 | −1.13889 | ||||||||
\(437\) | 2.54496 | 0.121742 | ||||||||
\(438\) | 2.78465 | 0.133056 | ||||||||
\(439\) | −38.7166 | −1.84784 | −0.923921 | − | 0.382582i | \(-0.875035\pi\) | ||||
−0.923921 | + | 0.382582i | \(0.875035\pi\) | |||||||
\(440\) | −12.6531 | −0.603214 | ||||||||
\(441\) | −6.82798 | −0.325142 | ||||||||
\(442\) | −0.176764 | −0.00840779 | ||||||||
\(443\) | 0.0361883 | 0.00171936 | 0.000859680 | − | 1.00000i | \(-0.499726\pi\) | ||||
0.000859680 | 1.00000i | \(0.499726\pi\) | ||||||||
\(444\) | −11.7924 | −0.559642 | ||||||||
\(445\) | −0.392603 | −0.0186112 | ||||||||
\(446\) | −12.3927 | −0.586810 | ||||||||
\(447\) | 11.9807 | 0.566669 | ||||||||
\(448\) | 0.783849 | 0.0370334 | ||||||||
\(449\) | 3.50805 | 0.165555 | 0.0827776 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827776 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(450\) | 1.18997 | 0.0560955 | ||||||||
\(451\) | 12.8454 | 0.604868 | ||||||||
\(452\) | −4.03054 | −0.189581 | ||||||||
\(453\) | 7.94967 | 0.373508 | ||||||||
\(454\) | −13.1900 | −0.619037 | ||||||||
\(455\) | 0.186327 | 0.00873515 | ||||||||
\(456\) | 0.969011 | 0.0453781 | ||||||||
\(457\) | 7.99570 | 0.374023 | 0.187011 | − | 0.982358i | \(-0.440120\pi\) | ||||
0.187011 | + | 0.982358i | \(0.440120\pi\) | |||||||
\(458\) | 17.5663 | 0.820819 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −17.8449 | −0.832021 | ||||||||
\(461\) | 18.4814 | 0.860766 | 0.430383 | − | 0.902646i | \(-0.358378\pi\) | ||||
0.430383 | + | 0.902646i | \(0.358378\pi\) | |||||||
\(462\) | 0.823871 | 0.0383299 | ||||||||
\(463\) | −26.8168 | −1.24628 | −0.623142 | − | 0.782109i | \(-0.714144\pi\) | ||||
−0.623142 | + | 0.782109i | \(0.714144\pi\) | |||||||
\(464\) | −0.899354 | −0.0417515 | ||||||||
\(465\) | 4.94723 | 0.229422 | ||||||||
\(466\) | −17.3091 | −0.801827 | ||||||||
\(467\) | 33.0861 | 1.53104 | 0.765522 | − | 0.643410i | \(-0.222481\pi\) | ||||
0.765522 | + | 0.643410i | \(0.222481\pi\) | |||||||
\(468\) | −0.363890 | −0.0168208 | ||||||||
\(469\) | 3.79608 | 0.175287 | ||||||||
\(470\) | −1.62258 | −0.0748438 | ||||||||
\(471\) | −8.53506 | −0.393275 | ||||||||
\(472\) | 5.93614 | 0.273233 | ||||||||
\(473\) | 4.88742 | 0.224724 | ||||||||
\(474\) | −0.719826 | −0.0330627 | ||||||||
\(475\) | −0.639143 | −0.0293259 | ||||||||
\(476\) | −0.614604 | −0.0281703 | ||||||||
\(477\) | 3.82181 | 0.174989 | ||||||||
\(478\) | −16.2674 | −0.744053 | ||||||||
\(479\) | 13.6621 | 0.624239 | 0.312120 | − | 0.950043i | \(-0.398961\pi\) | ||||
0.312120 | + | 0.950043i | \(0.398961\pi\) | |||||||
\(480\) | −10.6974 | −0.488268 | ||||||||
\(481\) | 1.95417 | 0.0891026 | ||||||||
\(482\) | −18.1137 | −0.825056 | ||||||||
\(483\) | 2.73011 | 0.124224 | ||||||||
\(484\) | 5.01578 | 0.227990 | ||||||||
\(485\) | 34.0962 | 1.54823 | ||||||||
\(486\) | −0.719826 | −0.0326520 | ||||||||
\(487\) | −25.0693 | −1.13600 | −0.568000 | − | 0.823029i | \(-0.692283\pi\) | ||||
−0.568000 | + | 0.823029i | \(0.692283\pi\) | |||||||
\(488\) | 14.9893 | 0.678533 | ||||||||
\(489\) | 8.76964 | 0.396577 | ||||||||
\(490\) | 8.99164 | 0.406201 | ||||||||
\(491\) | 29.1872 | 1.31720 | 0.658600 | − | 0.752493i | \(-0.271149\pi\) | ||||
0.658600 | + | 0.752493i | \(0.271149\pi\) | |||||||
\(492\) | 6.89784 | 0.310979 | ||||||||
\(493\) | −0.775585 | −0.0349306 | ||||||||
\(494\) | −0.0683414 | −0.00307483 | ||||||||
\(495\) | −5.04847 | −0.226912 | ||||||||
\(496\) | 3.13577 | 0.140800 | ||||||||
\(497\) | −1.34266 | −0.0602267 | ||||||||
\(498\) | −11.4577 | −0.513430 | ||||||||
\(499\) | 17.8077 | 0.797184 | 0.398592 | − | 0.917128i | \(-0.369499\pi\) | ||||
0.398592 | + | 0.917128i | \(0.369499\pi\) | |||||||
\(500\) | 18.0364 | 0.806612 | ||||||||
\(501\) | 6.48978 | 0.289942 | ||||||||
\(502\) | 14.3631 | 0.641056 | ||||||||
\(503\) | 3.69088 | 0.164568 | 0.0822841 | − | 0.996609i | \(-0.473779\pi\) | ||||
0.0822841 | + | 0.996609i | \(0.473779\pi\) | |||||||
\(504\) | 1.03951 | 0.0463035 | ||||||||
\(505\) | 8.28656 | 0.368747 | ||||||||
\(506\) | 13.0755 | 0.581276 | ||||||||
\(507\) | −12.9397 | −0.574672 | ||||||||
\(508\) | −13.3901 | −0.594090 | ||||||||
\(509\) | −11.4789 | −0.508792 | −0.254396 | − | 0.967100i | \(-0.581877\pi\) | ||||
−0.254396 | + | 0.967100i | \(0.581877\pi\) | |||||||
\(510\) | −1.31688 | −0.0583125 | ||||||||
\(511\) | −1.60448 | −0.0709779 | ||||||||
\(512\) | −12.5931 | −0.556540 | ||||||||
\(513\) | 0.386626 | 0.0170700 | ||||||||
\(514\) | −4.59118 | −0.202508 | ||||||||
\(515\) | −8.82749 | −0.388986 | ||||||||
\(516\) | 2.62448 | 0.115536 | ||||||||
\(517\) | −3.40015 | −0.149539 | ||||||||
\(518\) | −2.37584 | −0.104388 | ||||||||
\(519\) | 7.89825 | 0.346695 | ||||||||
\(520\) | 1.12596 | 0.0493765 | ||||||||
\(521\) | −25.6691 | −1.12458 | −0.562291 | − | 0.826939i | \(-0.690080\pi\) | ||||
−0.562291 | + | 0.826939i | \(0.690080\pi\) | |||||||
\(522\) | 0.558286 | 0.0244355 | ||||||||
\(523\) | −40.2412 | −1.75962 | −0.879812 | − | 0.475322i | \(-0.842332\pi\) | ||||
−0.879812 | + | 0.475322i | \(0.842332\pi\) | |||||||
\(524\) | 15.2197 | 0.664876 | ||||||||
\(525\) | −0.685643 | −0.0299239 | ||||||||
\(526\) | −20.4920 | −0.893492 | ||||||||
\(527\) | 2.70422 | 0.117798 | ||||||||
\(528\) | −3.19994 | −0.139260 | ||||||||
\(529\) | 20.3290 | 0.883871 | ||||||||
\(530\) | −5.03287 | −0.218614 | ||||||||
\(531\) | 2.36846 | 0.102783 | ||||||||
\(532\) | −0.237622 | −0.0103022 | ||||||||
\(533\) | −1.14307 | −0.0495120 | ||||||||
\(534\) | 0.154476 | 0.00668485 | ||||||||
\(535\) | −31.2210 | −1.34980 | ||||||||
\(536\) | 22.9394 | 0.990830 | ||||||||
\(537\) | 4.81548 | 0.207803 | ||||||||
\(538\) | −11.9077 | −0.513379 | ||||||||
\(539\) | 18.8422 | 0.811593 | ||||||||
\(540\) | −2.71096 | −0.116661 | ||||||||
\(541\) | −44.1060 | −1.89626 | −0.948132 | − | 0.317876i | \(-0.897030\pi\) | ||||
−0.948132 | + | 0.317876i | \(0.897030\pi\) | |||||||
\(542\) | −17.6255 | −0.757082 | ||||||||
\(543\) | −13.9833 | −0.600082 | ||||||||
\(544\) | −5.84735 | −0.250703 | ||||||||
\(545\) | 29.3588 | 1.25759 | ||||||||
\(546\) | −0.0733135 | −0.00313753 | ||||||||
\(547\) | −35.4235 | −1.51460 | −0.757299 | − | 0.653068i | \(-0.773481\pi\) | ||||
−0.757299 | + | 0.653068i | \(0.773481\pi\) | |||||||
\(548\) | −7.26943 | −0.310535 | ||||||||
\(549\) | 5.98058 | 0.255245 | ||||||||
\(550\) | −3.28379 | −0.140021 | ||||||||
\(551\) | −0.299861 | −0.0127745 | ||||||||
\(552\) | 16.4978 | 0.702195 | ||||||||
\(553\) | 0.414755 | 0.0176372 | ||||||||
\(554\) | −1.56891 | −0.0666567 | ||||||||
\(555\) | 14.5585 | 0.617975 | ||||||||
\(556\) | 20.9085 | 0.886718 | ||||||||
\(557\) | 21.1443 | 0.895912 | 0.447956 | − | 0.894056i | \(-0.352152\pi\) | ||||
0.447956 | + | 0.894056i | \(0.352152\pi\) | |||||||
\(558\) | −1.94657 | −0.0824049 | ||||||||
\(559\) | −0.434915 | −0.0183950 | ||||||||
\(560\) | 0.879857 | 0.0371807 | ||||||||
\(561\) | −2.75956 | −0.116509 | ||||||||
\(562\) | 2.09967 | 0.0885693 | ||||||||
\(563\) | 8.02512 | 0.338218 | 0.169109 | − | 0.985597i | \(-0.445911\pi\) | ||||
0.169109 | + | 0.985597i | \(0.445911\pi\) | |||||||
\(564\) | −1.82584 | −0.0768817 | ||||||||
\(565\) | 4.97598 | 0.209341 | ||||||||
\(566\) | 7.19136 | 0.302275 | ||||||||
\(567\) | 0.414755 | 0.0174181 | ||||||||
\(568\) | −8.11361 | −0.340439 | ||||||||
\(569\) | −36.4770 | −1.52919 | −0.764597 | − | 0.644509i | \(-0.777062\pi\) | ||||
−0.764597 | + | 0.644509i | \(0.777062\pi\) | |||||||
\(570\) | −0.509141 | −0.0213256 | ||||||||
\(571\) | −1.68511 | −0.0705195 | −0.0352597 | − | 0.999378i | \(-0.511226\pi\) | ||||
−0.0352597 | + | 0.999378i | \(0.511226\pi\) | |||||||
\(572\) | 1.00418 | 0.0419867 | ||||||||
\(573\) | −12.1242 | −0.506498 | ||||||||
\(574\) | 1.38972 | 0.0580058 | ||||||||
\(575\) | −10.8817 | −0.453798 | ||||||||
\(576\) | 1.88991 | 0.0787463 | ||||||||
\(577\) | −27.6311 | −1.15030 | −0.575149 | − | 0.818048i | \(-0.695056\pi\) | ||||
−0.575149 | + | 0.818048i | \(0.695056\pi\) | |||||||
\(578\) | −0.719826 | −0.0299408 | ||||||||
\(579\) | −2.70545 | −0.112435 | ||||||||
\(580\) | 2.10258 | 0.0873050 | ||||||||
\(581\) | 6.60176 | 0.273887 | ||||||||
\(582\) | −13.4157 | −0.556100 | ||||||||
\(583\) | −10.5465 | −0.436793 | ||||||||
\(584\) | −9.69572 | −0.401212 | ||||||||
\(585\) | 0.449247 | 0.0185741 | ||||||||
\(586\) | −3.85510 | −0.159253 | ||||||||
\(587\) | 36.6930 | 1.51448 | 0.757241 | − | 0.653136i | \(-0.226547\pi\) | ||||
0.757241 | + | 0.653136i | \(0.226547\pi\) | |||||||
\(588\) | 10.1180 | 0.417261 | ||||||||
\(589\) | 1.04552 | 0.0430800 | ||||||||
\(590\) | −3.11899 | −0.128407 | ||||||||
\(591\) | 8.78690 | 0.361445 | ||||||||
\(592\) | 9.22782 | 0.379261 | ||||||||
\(593\) | −28.8174 | −1.18339 | −0.591695 | − | 0.806162i | \(-0.701541\pi\) | ||||
−0.591695 | + | 0.806162i | \(0.701541\pi\) | |||||||
\(594\) | 1.98641 | 0.0815032 | ||||||||
\(595\) | 0.758771 | 0.0311066 | ||||||||
\(596\) | −17.7536 | −0.727217 | ||||||||
\(597\) | 7.23231 | 0.295999 | ||||||||
\(598\) | −1.16354 | −0.0475808 | ||||||||
\(599\) | −12.3914 | −0.506298 | −0.253149 | − | 0.967427i | \(-0.581466\pi\) | ||||
−0.253149 | + | 0.967427i | \(0.581466\pi\) | |||||||
\(600\) | −4.14328 | −0.169149 | ||||||||
\(601\) | −16.2368 | −0.662313 | −0.331157 | − | 0.943576i | \(-0.607439\pi\) | ||||
−0.331157 | + | 0.943576i | \(0.607439\pi\) | |||||||
\(602\) | 0.528759 | 0.0215506 | ||||||||
\(603\) | 9.15259 | 0.372722 | ||||||||
\(604\) | −11.7802 | −0.479330 | ||||||||
\(605\) | −6.19232 | −0.251754 | ||||||||
\(606\) | −3.26048 | −0.132448 | ||||||||
\(607\) | −5.80246 | −0.235514 | −0.117757 | − | 0.993042i | \(-0.537570\pi\) | ||||
−0.117757 | + | 0.993042i | \(0.537570\pi\) | |||||||
\(608\) | −2.26074 | −0.0916851 | ||||||||
\(609\) | −0.321677 | −0.0130350 | ||||||||
\(610\) | −7.87572 | −0.318879 | ||||||||
\(611\) | 0.302568 | 0.0122406 | ||||||||
\(612\) | −1.48185 | −0.0599003 | ||||||||
\(613\) | −23.3330 | −0.942411 | −0.471205 | − | 0.882024i | \(-0.656181\pi\) | ||||
−0.471205 | + | 0.882024i | \(0.656181\pi\) | |||||||
\(614\) | −14.4310 | −0.582390 | ||||||||
\(615\) | −8.51585 | −0.343392 | ||||||||
\(616\) | −2.86860 | −0.115579 | ||||||||
\(617\) | 10.9987 | 0.442793 | 0.221396 | − | 0.975184i | \(-0.428939\pi\) | ||||
0.221396 | + | 0.975184i | \(0.428939\pi\) | |||||||
\(618\) | 3.47332 | 0.139718 | ||||||||
\(619\) | 19.2753 | 0.774739 | 0.387369 | − | 0.921925i | \(-0.373384\pi\) | ||||
0.387369 | + | 0.921925i | \(0.373384\pi\) | |||||||
\(620\) | −7.33105 | −0.294422 | ||||||||
\(621\) | 6.58248 | 0.264146 | ||||||||
\(622\) | −10.6623 | −0.427520 | ||||||||
\(623\) | −0.0890073 | −0.00356600 | ||||||||
\(624\) | 0.284752 | 0.0113992 | ||||||||
\(625\) | −14.0015 | −0.560060 | ||||||||
\(626\) | −1.99275 | −0.0796463 | ||||||||
\(627\) | −1.06692 | −0.0426087 | ||||||||
\(628\) | 12.6477 | 0.504698 | ||||||||
\(629\) | 7.95789 | 0.317302 | ||||||||
\(630\) | −0.546183 | −0.0217604 | ||||||||
\(631\) | 17.4524 | 0.694768 | 0.347384 | − | 0.937723i | \(-0.387070\pi\) | ||||
0.347384 | + | 0.937723i | \(0.387070\pi\) | |||||||
\(632\) | 2.50633 | 0.0996963 | ||||||||
\(633\) | −25.5292 | −1.01469 | ||||||||
\(634\) | −13.5418 | −0.537815 | ||||||||
\(635\) | 16.5310 | 0.656012 | ||||||||
\(636\) | −5.66335 | −0.224566 | ||||||||
\(637\) | −1.67671 | −0.0664336 | ||||||||
\(638\) | −1.54063 | −0.0609940 | ||||||||
\(639\) | −3.23725 | −0.128064 | ||||||||
\(640\) | 18.9060 | 0.747326 | ||||||||
\(641\) | −42.4645 | −1.67725 | −0.838624 | − | 0.544711i | \(-0.816639\pi\) | ||||
−0.838624 | + | 0.544711i | \(0.816639\pi\) | |||||||
\(642\) | 12.2844 | 0.484827 | ||||||||
\(643\) | 10.1855 | 0.401677 | 0.200838 | − | 0.979624i | \(-0.435633\pi\) | ||||
0.200838 | + | 0.979624i | \(0.435633\pi\) | |||||||
\(644\) | −4.04562 | −0.159420 | ||||||||
\(645\) | −3.24010 | −0.127579 | ||||||||
\(646\) | −0.278304 | −0.0109497 | ||||||||
\(647\) | 47.0665 | 1.85037 | 0.925187 | − | 0.379511i | \(-0.123908\pi\) | ||||
0.925187 | + | 0.379511i | \(0.123908\pi\) | |||||||
\(648\) | 2.50633 | 0.0984578 | ||||||||
\(649\) | −6.53592 | −0.256557 | ||||||||
\(650\) | 0.292213 | 0.0114615 | ||||||||
\(651\) | 1.12159 | 0.0439585 | ||||||||
\(652\) | −12.9953 | −0.508935 | ||||||||
\(653\) | −2.16854 | −0.0848616 | −0.0424308 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424308 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(654\) | −11.5517 | −0.451708 | ||||||||
\(655\) | −18.7898 | −0.734177 | ||||||||
\(656\) | −5.39772 | −0.210745 | ||||||||
\(657\) | −3.86850 | −0.150925 | ||||||||
\(658\) | −0.367855 | −0.0143405 | ||||||||
\(659\) | −47.4420 | −1.84808 | −0.924038 | − | 0.382300i | \(-0.875132\pi\) | ||||
−0.924038 | + | 0.382300i | \(0.875132\pi\) | |||||||
\(660\) | 7.48108 | 0.291201 | ||||||||
\(661\) | −23.1248 | −0.899451 | −0.449726 | − | 0.893167i | \(-0.648478\pi\) | ||||
−0.449726 | + | 0.893167i | \(0.648478\pi\) | |||||||
\(662\) | 16.8376 | 0.654411 | ||||||||
\(663\) | 0.245564 | 0.00953693 | ||||||||
\(664\) | 39.8939 | 1.54818 | ||||||||
\(665\) | 0.293361 | 0.0113760 | ||||||||
\(666\) | −5.72829 | −0.221967 | ||||||||
\(667\) | −5.10527 | −0.197677 | ||||||||
\(668\) | −9.61688 | −0.372088 | ||||||||
\(669\) | 17.2162 | 0.665617 | ||||||||
\(670\) | −12.0529 | −0.465643 | ||||||||
\(671\) | −16.5038 | −0.637122 | ||||||||
\(672\) | −2.42522 | −0.0935547 | ||||||||
\(673\) | 36.0969 | 1.39143 | 0.695717 | − | 0.718316i | \(-0.255087\pi\) | ||||
0.695717 | + | 0.718316i | \(0.255087\pi\) | |||||||
\(674\) | 8.60947 | 0.331624 | ||||||||
\(675\) | −1.65313 | −0.0636290 | ||||||||
\(676\) | 19.1747 | 0.737488 | ||||||||
\(677\) | 20.6626 | 0.794130 | 0.397065 | − | 0.917791i | \(-0.370029\pi\) | ||||
0.397065 | + | 0.917791i | \(0.370029\pi\) | |||||||
\(678\) | −1.95788 | −0.0751920 | ||||||||
\(679\) | 7.72997 | 0.296649 | ||||||||
\(680\) | 4.58519 | 0.175834 | ||||||||
\(681\) | 18.3239 | 0.702172 | ||||||||
\(682\) | 5.37169 | 0.205692 | ||||||||
\(683\) | 35.9726 | 1.37645 | 0.688227 | − | 0.725495i | \(-0.258389\pi\) | ||||
0.688227 | + | 0.725495i | \(0.258389\pi\) | |||||||
\(684\) | −0.572922 | −0.0219062 | ||||||||
\(685\) | 8.97461 | 0.342902 | ||||||||
\(686\) | 4.12836 | 0.157621 | ||||||||
\(687\) | −24.4035 | −0.931053 | ||||||||
\(688\) | −2.05372 | −0.0782972 | ||||||||
\(689\) | 0.938500 | 0.0357540 | ||||||||
\(690\) | −8.66835 | −0.329998 | ||||||||
\(691\) | −30.6870 | −1.16739 | −0.583694 | − | 0.811973i | \(-0.698393\pi\) | ||||
−0.583694 | + | 0.811973i | \(0.698393\pi\) | |||||||
\(692\) | −11.7040 | −0.444920 | ||||||||
\(693\) | −1.14454 | −0.0434775 | ||||||||
\(694\) | 8.04388 | 0.305342 | ||||||||
\(695\) | −25.8130 | −0.979142 | ||||||||
\(696\) | −1.94387 | −0.0736822 | ||||||||
\(697\) | −4.65488 | −0.176316 | ||||||||
\(698\) | −24.4881 | −0.926889 | ||||||||
\(699\) | 24.0462 | 0.909510 | ||||||||
\(700\) | 1.01602 | 0.0384020 | ||||||||
\(701\) | −47.7345 | −1.80291 | −0.901454 | − | 0.432876i | \(-0.857499\pi\) | ||||
−0.901454 | + | 0.432876i | \(0.857499\pi\) | |||||||
\(702\) | −0.176764 | −0.00667151 | ||||||||
\(703\) | 3.07673 | 0.116041 | ||||||||
\(704\) | −5.21533 | −0.196560 | ||||||||
\(705\) | 2.25412 | 0.0848951 | ||||||||
\(706\) | 19.4291 | 0.731223 | ||||||||
\(707\) | 1.87865 | 0.0706539 | ||||||||
\(708\) | −3.50971 | −0.131903 | ||||||||
\(709\) | −0.239120 | −0.00898033 | −0.00449017 | − | 0.999990i | \(-0.501429\pi\) | ||||
−0.00449017 | + | 0.999990i | \(0.501429\pi\) | |||||||
\(710\) | 4.26308 | 0.159990 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −0.537864 | −0.0201573 | ||||||||
\(713\) | 17.8005 | 0.666634 | ||||||||
\(714\) | −0.298551 | −0.0111730 | ||||||||
\(715\) | −1.23972 | −0.0463631 | ||||||||
\(716\) | −7.13582 | −0.266678 | ||||||||
\(717\) | 22.5991 | 0.843977 | ||||||||
\(718\) | −20.5388 | −0.766501 | ||||||||
\(719\) | −30.6832 | −1.14429 | −0.572145 | − | 0.820152i | \(-0.693889\pi\) | ||||
−0.572145 | + | 0.820152i | \(0.693889\pi\) | |||||||
\(720\) | 2.12139 | 0.0790596 | ||||||||
\(721\) | −2.00128 | −0.0745317 | ||||||||
\(722\) | 13.5691 | 0.504989 | ||||||||
\(723\) | 25.1640 | 0.935859 | ||||||||
\(724\) | 20.7212 | 0.770097 | ||||||||
\(725\) | 1.28214 | 0.0476176 | ||||||||
\(726\) | 2.43647 | 0.0904260 | ||||||||
\(727\) | 26.1729 | 0.970701 | 0.485350 | − | 0.874320i | \(-0.338692\pi\) | ||||
0.485350 | + | 0.874320i | \(0.338692\pi\) | |||||||
\(728\) | 0.255267 | 0.00946081 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.09436 | 0.188551 | ||||||||
\(731\) | −1.77108 | −0.0655059 | ||||||||
\(732\) | −8.86233 | −0.327561 | ||||||||
\(733\) | 7.82983 | 0.289202 | 0.144601 | − | 0.989490i | \(-0.453810\pi\) | ||||
0.144601 | + | 0.989490i | \(0.453810\pi\) | |||||||
\(734\) | −24.6083 | −0.908310 | ||||||||
\(735\) | −12.4914 | −0.460753 | ||||||||
\(736\) | −38.4901 | −1.41876 | ||||||||
\(737\) | −25.2572 | −0.930359 | ||||||||
\(738\) | 3.35070 | 0.123341 | ||||||||
\(739\) | 31.2670 | 1.15018 | 0.575088 | − | 0.818092i | \(-0.304968\pi\) | ||||
0.575088 | + | 0.818092i | \(0.304968\pi\) | |||||||
\(740\) | −21.5735 | −0.793059 | ||||||||
\(741\) | 0.0949416 | 0.00348777 | ||||||||
\(742\) | −1.14101 | −0.0418876 | ||||||||
\(743\) | −17.3813 | −0.637658 | −0.318829 | − | 0.947812i | \(-0.603290\pi\) | ||||
−0.318829 | + | 0.947812i | \(0.603290\pi\) | |||||||
\(744\) | 6.77767 | 0.248481 | ||||||||
\(745\) | 21.9181 | 0.803016 | ||||||||
\(746\) | −23.3640 | −0.855415 | ||||||||
\(747\) | 15.9173 | 0.582383 | ||||||||
\(748\) | 4.08926 | 0.149518 | ||||||||
\(749\) | −7.07812 | −0.258629 | ||||||||
\(750\) | 8.76139 | 0.319921 | ||||||||
\(751\) | 15.6507 | 0.571103 | 0.285551 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285551 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(752\) | 1.42876 | 0.0521015 | ||||||||
\(753\) | −19.9536 | −0.727148 | ||||||||
\(754\) | 0.137095 | 0.00499271 | ||||||||
\(755\) | 14.5435 | 0.529292 | ||||||||
\(756\) | −0.614604 | −0.0223529 | ||||||||
\(757\) | 45.2503 | 1.64465 | 0.822326 | − | 0.569017i | \(-0.192676\pi\) | ||||
0.822326 | + | 0.569017i | \(0.192676\pi\) | |||||||
\(758\) | 5.41466 | 0.196669 | ||||||||
\(759\) | −18.1648 | −0.659339 | ||||||||
\(760\) | 1.77275 | 0.0643045 | ||||||||
\(761\) | 33.9249 | 1.22978 | 0.614888 | − | 0.788614i | \(-0.289201\pi\) | ||||
0.614888 | + | 0.788614i | \(0.289201\pi\) | |||||||
\(762\) | −6.50439 | −0.235629 | ||||||||
\(763\) | 6.65595 | 0.240962 | ||||||||
\(764\) | 17.9663 | 0.649999 | ||||||||
\(765\) | 1.82945 | 0.0661437 | ||||||||
\(766\) | 2.76270 | 0.0998206 | ||||||||
\(767\) | 0.581610 | 0.0210007 | ||||||||
\(768\) | −11.2187 | −0.404821 | ||||||||
\(769\) | −50.3111 | −1.81427 | −0.907133 | − | 0.420844i | \(-0.861734\pi\) | ||||
−0.907133 | + | 0.420844i | \(0.861734\pi\) | |||||||
\(770\) | 1.50723 | 0.0543167 | ||||||||
\(771\) | 6.37818 | 0.229705 | ||||||||
\(772\) | 4.00907 | 0.144290 | ||||||||
\(773\) | 11.3678 | 0.408871 | 0.204436 | − | 0.978880i | \(-0.434464\pi\) | ||||
0.204436 | + | 0.978880i | \(0.434464\pi\) | |||||||
\(774\) | 1.27487 | 0.0458244 | ||||||||
\(775\) | −4.47043 | −0.160583 | ||||||||
\(776\) | 46.7116 | 1.67685 | ||||||||
\(777\) | 3.30057 | 0.118407 | ||||||||
\(778\) | −3.00045 | −0.107571 | ||||||||
\(779\) | −1.79970 | −0.0644809 | ||||||||
\(780\) | −0.665716 | −0.0238365 | ||||||||
\(781\) | 8.93340 | 0.319662 | ||||||||
\(782\) | −4.73824 | −0.169439 | ||||||||
\(783\) | −0.775585 | −0.0277171 | ||||||||
\(784\) | −7.91760 | −0.282771 | ||||||||
\(785\) | −15.6144 | −0.557303 | ||||||||
\(786\) | 7.39315 | 0.263705 | ||||||||
\(787\) | −18.8362 | −0.671436 | −0.335718 | − | 0.941962i | \(-0.608979\pi\) | ||||
−0.335718 | + | 0.941962i | \(0.608979\pi\) | |||||||
\(788\) | −13.0209 | −0.463850 | ||||||||
\(789\) | 28.4679 | 1.01349 | ||||||||
\(790\) | −1.31688 | −0.0468526 | ||||||||
\(791\) | 1.12811 | 0.0401108 | ||||||||
\(792\) | −6.91637 | −0.245762 | ||||||||
\(793\) | 1.46862 | 0.0521521 | ||||||||
\(794\) | 14.0616 | 0.499026 | ||||||||
\(795\) | 6.99179 | 0.247973 | ||||||||
\(796\) | −10.7172 | −0.379861 | ||||||||
\(797\) | −31.2170 | −1.10576 | −0.552882 | − | 0.833259i | \(-0.686472\pi\) | ||||
−0.552882 | + | 0.833259i | \(0.686472\pi\) | |||||||
\(798\) | −0.115428 | −0.00408610 | ||||||||
\(799\) | 1.23213 | 0.0435898 | ||||||||
\(800\) | 9.66643 | 0.341760 | ||||||||
\(801\) | −0.214602 | −0.00758260 | ||||||||
\(802\) | 17.3954 | 0.614252 | ||||||||
\(803\) | 10.6754 | 0.376726 | ||||||||
\(804\) | −13.5628 | −0.478322 | ||||||||
\(805\) | 4.99459 | 0.176036 | ||||||||
\(806\) | −0.478008 | −0.0168371 | ||||||||
\(807\) | 16.5425 | 0.582324 | ||||||||
\(808\) | 11.3525 | 0.399380 | ||||||||
\(809\) | 7.91592 | 0.278309 | 0.139154 | − | 0.990271i | \(-0.455562\pi\) | ||||
0.139154 | + | 0.990271i | \(0.455562\pi\) | |||||||
\(810\) | −1.31688 | −0.0462705 | ||||||||
\(811\) | −12.3154 | −0.432453 | −0.216227 | − | 0.976343i | \(-0.569375\pi\) | ||||
−0.216227 | + | 0.976343i | \(0.569375\pi\) | |||||||
\(812\) | 0.476678 | 0.0167281 | ||||||||
\(813\) | 24.4858 | 0.858756 | ||||||||
\(814\) | 15.8076 | 0.554056 | ||||||||
\(815\) | 16.0436 | 0.561982 | ||||||||
\(816\) | 1.15958 | 0.0405935 | ||||||||
\(817\) | −0.684748 | −0.0239563 | ||||||||
\(818\) | 15.0909 | 0.527639 | ||||||||
\(819\) | 0.101849 | 0.00355889 | ||||||||
\(820\) | 12.6192 | 0.440682 | ||||||||
\(821\) | −28.6856 | −1.00113 | −0.500567 | − | 0.865698i | \(-0.666875\pi\) | ||||
−0.500567 | + | 0.865698i | \(0.666875\pi\) | |||||||
\(822\) | −3.53121 | −0.123165 | ||||||||
\(823\) | −10.0482 | −0.350259 | −0.175130 | − | 0.984545i | \(-0.556034\pi\) | ||||
−0.175130 | + | 0.984545i | \(0.556034\pi\) | |||||||
\(824\) | −12.0936 | −0.421300 | ||||||||
\(825\) | 4.56192 | 0.158826 | ||||||||
\(826\) | −0.707107 | −0.0246034 | ||||||||
\(827\) | −13.8280 | −0.480846 | −0.240423 | − | 0.970668i | \(-0.577286\pi\) | ||||
−0.240423 | + | 0.970668i | \(0.577286\pi\) | |||||||
\(828\) | −9.75425 | −0.338984 | ||||||||
\(829\) | 41.1327 | 1.42860 | 0.714300 | − | 0.699840i | \(-0.246745\pi\) | ||||
0.714300 | + | 0.699840i | \(0.246745\pi\) | |||||||
\(830\) | −20.9612 | −0.727573 | ||||||||
\(831\) | 2.17957 | 0.0756085 | ||||||||
\(832\) | 0.464095 | 0.0160896 | ||||||||
\(833\) | −6.82798 | −0.236575 | ||||||||
\(834\) | 10.1566 | 0.351693 | ||||||||
\(835\) | 11.8727 | 0.410871 | ||||||||
\(836\) | 1.58102 | 0.0546806 | ||||||||
\(837\) | 2.70422 | 0.0934716 | ||||||||
\(838\) | −7.45625 | −0.257572 | ||||||||
\(839\) | −31.3760 | −1.08322 | −0.541609 | − | 0.840630i | \(-0.682185\pi\) | ||||
−0.541609 | + | 0.840630i | \(0.682185\pi\) | |||||||
\(840\) | 1.90173 | 0.0656158 | ||||||||
\(841\) | −28.3985 | −0.979258 | ||||||||
\(842\) | 27.8206 | 0.958760 | ||||||||
\(843\) | −2.91692 | −0.100464 | ||||||||
\(844\) | 37.8304 | 1.30218 | ||||||||
\(845\) | −23.6725 | −0.814358 | ||||||||
\(846\) | −0.886922 | −0.0304930 | ||||||||
\(847\) | −1.40386 | −0.0482373 | ||||||||
\(848\) | 4.43170 | 0.152185 | ||||||||
\(849\) | −9.99042 | −0.342870 | ||||||||
\(850\) | 1.18997 | 0.0408155 | ||||||||
\(851\) | 52.3826 | 1.79565 | ||||||||
\(852\) | 4.79712 | 0.164347 | ||||||||
\(853\) | −4.24630 | −0.145390 | −0.0726952 | − | 0.997354i | \(-0.523160\pi\) | ||||
−0.0726952 | + | 0.997354i | \(0.523160\pi\) | |||||||
\(854\) | −1.78551 | −0.0610989 | ||||||||
\(855\) | 0.707311 | 0.0241895 | ||||||||
\(856\) | −42.7725 | −1.46193 | ||||||||
\(857\) | 34.1449 | 1.16637 | 0.583184 | − | 0.812340i | \(-0.301807\pi\) | ||||
0.583184 | + | 0.812340i | \(0.301807\pi\) | |||||||
\(858\) | 0.487790 | 0.0166529 | ||||||||
\(859\) | −22.5724 | −0.770160 | −0.385080 | − | 0.922883i | \(-0.625826\pi\) | ||||
−0.385080 | + | 0.922883i | \(0.625826\pi\) | |||||||
\(860\) | 4.80135 | 0.163725 | ||||||||
\(861\) | −1.93063 | −0.0657958 | ||||||||
\(862\) | −24.1994 | −0.824237 | ||||||||
\(863\) | −17.3207 | −0.589604 | −0.294802 | − | 0.955558i | \(-0.595254\pi\) | ||||
−0.294802 | + | 0.955558i | \(0.595254\pi\) | |||||||
\(864\) | −5.84735 | −0.198931 | ||||||||
\(865\) | 14.4494 | 0.491295 | ||||||||
\(866\) | 2.29630 | 0.0780313 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −1.66203 | −0.0564129 | ||||||||
\(869\) | −2.75956 | −0.0936118 | ||||||||
\(870\) | 1.02135 | 0.0346271 | ||||||||
\(871\) | 2.24755 | 0.0761553 | ||||||||
\(872\) | 40.2213 | 1.36207 | ||||||||
\(873\) | 18.6375 | 0.630782 | ||||||||
\(874\) | −1.83193 | −0.0619659 | ||||||||
\(875\) | −5.04820 | −0.170660 | ||||||||
\(876\) | 5.73254 | 0.193685 | ||||||||
\(877\) | −53.0590 | −1.79167 | −0.895837 | − | 0.444383i | \(-0.853423\pi\) | ||||
−0.895837 | + | 0.444383i | \(0.853423\pi\) | |||||||
\(878\) | 27.8692 | 0.940541 | ||||||||
\(879\) | 5.35560 | 0.180640 | ||||||||
\(880\) | −5.85412 | −0.197342 | ||||||||
\(881\) | −46.9575 | −1.58204 | −0.791019 | − | 0.611791i | \(-0.790449\pi\) | ||||
−0.791019 | + | 0.611791i | \(0.790449\pi\) | |||||||
\(882\) | 4.91496 | 0.165495 | ||||||||
\(883\) | 27.4476 | 0.923684 | 0.461842 | − | 0.886962i | \(-0.347189\pi\) | ||||
0.461842 | + | 0.886962i | \(0.347189\pi\) | |||||||
\(884\) | −0.363890 | −0.0122389 | ||||||||
\(885\) | 4.33297 | 0.145651 | ||||||||
\(886\) | −0.0260493 | −0.000875143 0 | ||||||||
\(887\) | 38.7268 | 1.30032 | 0.650160 | − | 0.759797i | \(-0.274702\pi\) | ||||
0.650160 | + | 0.759797i | \(0.274702\pi\) | |||||||
\(888\) | 19.9451 | 0.669312 | ||||||||
\(889\) | 3.74775 | 0.125695 | ||||||||
\(890\) | 0.282606 | 0.00947297 | ||||||||
\(891\) | −2.75956 | −0.0924489 | ||||||||
\(892\) | −25.5118 | −0.854199 | ||||||||
\(893\) | 0.476375 | 0.0159413 | ||||||||
\(894\) | −8.62404 | −0.288431 | ||||||||
\(895\) | 8.80965 | 0.294474 | ||||||||
\(896\) | 4.28620 | 0.143192 | ||||||||
\(897\) | 1.61642 | 0.0539708 | ||||||||
\(898\) | −2.52519 | −0.0842666 | ||||||||
\(899\) | −2.09735 | −0.0699507 | ||||||||
\(900\) | 2.44969 | 0.0816564 | ||||||||
\(901\) | 3.82181 | 0.127323 | ||||||||
\(902\) | −9.24648 | −0.307874 | ||||||||
\(903\) | −0.734565 | −0.0244448 | ||||||||
\(904\) | 6.81705 | 0.226732 | ||||||||
\(905\) | −25.5817 | −0.850365 | ||||||||
\(906\) | −5.72238 | −0.190113 | ||||||||
\(907\) | 6.62249 | 0.219896 | 0.109948 | − | 0.993937i | \(-0.464932\pi\) | ||||
0.109948 | + | 0.993937i | \(0.464932\pi\) | |||||||
\(908\) | −27.1532 | −0.901111 | ||||||||
\(909\) | 4.52955 | 0.150236 | ||||||||
\(910\) | −0.134123 | −0.00444614 | ||||||||
\(911\) | 36.4150 | 1.20648 | 0.603241 | − | 0.797559i | \(-0.293876\pi\) | ||||
0.603241 | + | 0.797559i | \(0.293876\pi\) | |||||||
\(912\) | 0.448325 | 0.0148455 | ||||||||
\(913\) | −43.9247 | −1.45370 | ||||||||
\(914\) | −5.75551 | −0.190375 | ||||||||
\(915\) | 10.9411 | 0.361703 | ||||||||
\(916\) | 36.1624 | 1.19484 | ||||||||
\(917\) | −4.25984 | −0.140672 | ||||||||
\(918\) | −0.719826 | −0.0237578 | ||||||||
\(919\) | −30.1480 | −0.994490 | −0.497245 | − | 0.867610i | \(-0.665655\pi\) | ||||
−0.497245 | + | 0.867610i | \(0.665655\pi\) | |||||||
\(920\) | 30.1819 | 0.995068 | ||||||||
\(921\) | 20.0480 | 0.660603 | ||||||||
\(922\) | −13.3034 | −0.438125 | ||||||||
\(923\) | −0.794953 | −0.0261662 | ||||||||
\(924\) | 1.69604 | 0.0557956 | ||||||||
\(925\) | −13.1554 | −0.432548 | ||||||||
\(926\) | 19.3035 | 0.634351 | ||||||||
\(927\) | −4.82523 | −0.158481 | ||||||||
\(928\) | 4.53512 | 0.148872 | ||||||||
\(929\) | −6.35944 | −0.208646 | −0.104323 | − | 0.994543i | \(-0.533268\pi\) | ||||
−0.104323 | + | 0.994543i | \(0.533268\pi\) | |||||||
\(930\) | −3.56114 | −0.116775 | ||||||||
\(931\) | −2.63988 | −0.0865184 | ||||||||
\(932\) | −35.6328 | −1.16719 | ||||||||
\(933\) | 14.8123 | 0.484934 | ||||||||
\(934\) | −23.8163 | −0.779292 | ||||||||
\(935\) | −5.04847 | −0.165103 | ||||||||
\(936\) | 0.615464 | 0.0201171 | ||||||||
\(937\) | −43.7477 | −1.42918 | −0.714588 | − | 0.699545i | \(-0.753386\pi\) | ||||
−0.714588 | + | 0.699545i | \(0.753386\pi\) | |||||||
\(938\) | −2.73252 | −0.0892198 | ||||||||
\(939\) | 2.76838 | 0.0903426 | ||||||||
\(940\) | −3.34027 | −0.108948 | ||||||||
\(941\) | −39.9043 | −1.30084 | −0.650422 | − | 0.759573i | \(-0.725408\pi\) | ||||
−0.650422 | + | 0.759573i | \(0.725408\pi\) | |||||||
\(942\) | 6.14376 | 0.200175 | ||||||||
\(943\) | −30.6407 | −0.997797 | ||||||||
\(944\) | 2.74643 | 0.0893886 | ||||||||
\(945\) | 0.758771 | 0.0246828 | ||||||||
\(946\) | −3.51809 | −0.114383 | ||||||||
\(947\) | −44.7528 | −1.45427 | −0.727136 | − | 0.686494i | \(-0.759149\pi\) | ||||
−0.727136 | + | 0.686494i | \(0.759149\pi\) | |||||||
\(948\) | −1.48185 | −0.0481283 | ||||||||
\(949\) | −0.949966 | −0.0308372 | ||||||||
\(950\) | 0.460072 | 0.0149267 | ||||||||
\(951\) | 18.8127 | 0.610042 | ||||||||
\(952\) | 1.03951 | 0.0336907 | ||||||||
\(953\) | −16.6817 | −0.540374 | −0.270187 | − | 0.962808i | \(-0.587085\pi\) | ||||
−0.270187 | + | 0.962808i | \(0.587085\pi\) | |||||||
\(954\) | −2.75104 | −0.0890681 | ||||||||
\(955\) | −22.1806 | −0.717749 | ||||||||
\(956\) | −33.4884 | −1.08309 | ||||||||
\(957\) | 2.14028 | 0.0691853 | ||||||||
\(958\) | −9.83436 | −0.317734 | ||||||||
\(959\) | 2.03464 | 0.0657019 | ||||||||
\(960\) | 3.45749 | 0.111590 | ||||||||
\(961\) | −23.6872 | −0.764102 | ||||||||
\(962\) | −1.40666 | −0.0453527 | ||||||||
\(963\) | −17.0658 | −0.549938 | ||||||||
\(964\) | −37.2893 | −1.20101 | ||||||||
\(965\) | −4.94947 | −0.159329 | ||||||||
\(966\) | −1.96521 | −0.0632295 | ||||||||
\(967\) | 22.2995 | 0.717102 | 0.358551 | − | 0.933510i | \(-0.383271\pi\) | ||||
0.358551 | + | 0.933510i | \(0.383271\pi\) | |||||||
\(968\) | −8.48343 | −0.272668 | ||||||||
\(969\) | 0.386626 | 0.0124202 | ||||||||
\(970\) | −24.5433 | −0.788039 | ||||||||
\(971\) | −7.79177 | −0.250050 | −0.125025 | − | 0.992154i | \(-0.539901\pi\) | ||||
−0.125025 | + | 0.992154i | \(0.539901\pi\) | |||||||
\(972\) | −1.48185 | −0.0475304 | ||||||||
\(973\) | −5.85207 | −0.187609 | ||||||||
\(974\) | 18.0455 | 0.578217 | ||||||||
\(975\) | −0.405950 | −0.0130008 | ||||||||
\(976\) | 6.93497 | 0.221983 | ||||||||
\(977\) | 13.9986 | 0.447856 | 0.223928 | − | 0.974606i | \(-0.428112\pi\) | ||||
0.223928 | + | 0.974606i | \(0.428112\pi\) | |||||||
\(978\) | −6.31262 | −0.201855 | ||||||||
\(979\) | 0.592209 | 0.0189271 | ||||||||
\(980\) | 18.5104 | 0.591293 | ||||||||
\(981\) | 16.0479 | 0.512371 | ||||||||
\(982\) | −21.0097 | −0.670447 | ||||||||
\(983\) | −22.6636 | −0.722858 | −0.361429 | − | 0.932400i | \(-0.617711\pi\) | ||||
−0.361429 | + | 0.932400i | \(0.617711\pi\) | |||||||
\(984\) | −11.6667 | −0.371919 | ||||||||
\(985\) | 16.0752 | 0.512197 | ||||||||
\(986\) | 0.558286 | 0.0177795 | ||||||||
\(987\) | 0.511033 | 0.0162664 | ||||||||
\(988\) | −0.140689 | −0.00447592 | ||||||||
\(989\) | −11.6581 | −0.370707 | ||||||||
\(990\) | 3.63402 | 0.115497 | ||||||||
\(991\) | 16.9148 | 0.537318 | 0.268659 | − | 0.963235i | \(-0.413420\pi\) | ||||
0.268659 | + | 0.963235i | \(0.413420\pi\) | |||||||
\(992\) | −15.8125 | −0.502049 | ||||||||
\(993\) | −23.3912 | −0.742296 | ||||||||
\(994\) | 0.966485 | 0.0306550 | ||||||||
\(995\) | 13.2311 | 0.419455 | ||||||||
\(996\) | −23.5870 | −0.747383 | ||||||||
\(997\) | −47.3564 | −1.49979 | −0.749896 | − | 0.661555i | \(-0.769897\pi\) | ||||
−0.749896 | + | 0.661555i | \(0.769897\pi\) | |||||||
\(998\) | −12.8185 | −0.405762 | ||||||||
\(999\) | 7.95789 | 0.251776 |
(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 | 4029.2.a.k.1.11 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.11 | ✓ | 31 | 1.1 | even | 1 | trivial |