Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-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 | ||||||||
\(3\) | −1.49577 | −0.863583 | −0.431791 | − | 0.901974i | \(-0.642118\pi\) | ||||
−0.431791 | + | 0.901974i | \(0.642118\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.91198 | −1.74949 | −0.874744 | − | 0.484585i | \(-0.838971\pi\) | ||||
−0.874744 | + | 0.484585i | \(0.838971\pi\) | |||||||
\(6\) | −1.49577 | −0.610645 | ||||||||
\(7\) | 2.85048 | 1.07738 | 0.538691 | − | 0.842504i | \(-0.318919\pi\) | ||||
0.538691 | + | 0.842504i | \(0.318919\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.762675 | −0.254225 | ||||||||
\(10\) | −3.91198 | −1.23708 | ||||||||
\(11\) | 5.45305 | 1.64416 | 0.822078 | − | 0.569374i | \(-0.192814\pi\) | ||||
0.822078 | + | 0.569374i | \(0.192814\pi\) | |||||||
\(12\) | −1.49577 | −0.431791 | ||||||||
\(13\) | 2.90708 | 0.806280 | 0.403140 | − | 0.915138i | \(-0.367919\pi\) | ||||
0.403140 | + | 0.915138i | \(0.367919\pi\) | |||||||
\(14\) | 2.85048 | 0.761824 | ||||||||
\(15\) | 5.85141 | 1.51083 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.18307 | −1.49961 | −0.749807 | − | 0.661656i | \(-0.769854\pi\) | ||||
−0.749807 | + | 0.661656i | \(0.769854\pi\) | |||||||
\(18\) | −0.762675 | −0.179764 | ||||||||
\(19\) | −0.516450 | −0.118482 | −0.0592409 | − | 0.998244i | \(-0.518868\pi\) | ||||
−0.0592409 | + | 0.998244i | \(0.518868\pi\) | |||||||
\(20\) | −3.91198 | −0.874744 | ||||||||
\(21\) | −4.26366 | −0.930408 | ||||||||
\(22\) | 5.45305 | 1.16259 | ||||||||
\(23\) | 2.30990 | 0.481648 | 0.240824 | − | 0.970569i | \(-0.422582\pi\) | ||||
0.240824 | + | 0.970569i | \(0.422582\pi\) | |||||||
\(24\) | −1.49577 | −0.305323 | ||||||||
\(25\) | 10.3036 | 2.06071 | ||||||||
\(26\) | 2.90708 | 0.570126 | ||||||||
\(27\) | 5.62809 | 1.08313 | ||||||||
\(28\) | 2.85048 | 0.538691 | ||||||||
\(29\) | 1.70467 | 0.316549 | 0.158274 | − | 0.987395i | \(-0.449407\pi\) | ||||
0.158274 | + | 0.987395i | \(0.449407\pi\) | |||||||
\(30\) | 5.85141 | 1.06832 | ||||||||
\(31\) | 1.93749 | 0.347983 | 0.173992 | − | 0.984747i | \(-0.444333\pi\) | ||||
0.173992 | + | 0.984747i | \(0.444333\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −8.15651 | −1.41987 | ||||||||
\(34\) | −6.18307 | −1.06039 | ||||||||
\(35\) | −11.1510 | −1.88487 | ||||||||
\(36\) | −0.762675 | −0.127112 | ||||||||
\(37\) | −5.17117 | −0.850135 | −0.425067 | − | 0.905162i | \(-0.639750\pi\) | ||||
−0.425067 | + | 0.905162i | \(0.639750\pi\) | |||||||
\(38\) | −0.516450 | −0.0837793 | ||||||||
\(39\) | −4.34832 | −0.696289 | ||||||||
\(40\) | −3.91198 | −0.618538 | ||||||||
\(41\) | 8.84244 | 1.38096 | 0.690478 | − | 0.723353i | \(-0.257400\pi\) | ||||
0.690478 | + | 0.723353i | \(0.257400\pi\) | |||||||
\(42\) | −4.26366 | −0.657898 | ||||||||
\(43\) | −12.6113 | −1.92320 | −0.961600 | − | 0.274454i | \(-0.911503\pi\) | ||||
−0.961600 | + | 0.274454i | \(0.911503\pi\) | |||||||
\(44\) | 5.45305 | 0.822078 | ||||||||
\(45\) | 2.98356 | 0.444764 | ||||||||
\(46\) | 2.30990 | 0.340577 | ||||||||
\(47\) | −6.22673 | −0.908262 | −0.454131 | − | 0.890935i | \(-0.650050\pi\) | ||||
−0.454131 | + | 0.890935i | \(0.650050\pi\) | |||||||
\(48\) | −1.49577 | −0.215896 | ||||||||
\(49\) | 1.12525 | 0.160750 | ||||||||
\(50\) | 10.3036 | 1.45714 | ||||||||
\(51\) | 9.24844 | 1.29504 | ||||||||
\(52\) | 2.90708 | 0.403140 | ||||||||
\(53\) | 1.75975 | 0.241720 | 0.120860 | − | 0.992670i | \(-0.461435\pi\) | ||||
0.120860 | + | 0.992670i | \(0.461435\pi\) | |||||||
\(54\) | 5.62809 | 0.765886 | ||||||||
\(55\) | −21.3322 | −2.87643 | ||||||||
\(56\) | 2.85048 | 0.380912 | ||||||||
\(57\) | 0.772490 | 0.102319 | ||||||||
\(58\) | 1.70467 | 0.223834 | ||||||||
\(59\) | 10.1312 | 1.31897 | 0.659487 | − | 0.751716i | \(-0.270773\pi\) | ||||
0.659487 | + | 0.751716i | \(0.270773\pi\) | |||||||
\(60\) | 5.85141 | 0.755414 | ||||||||
\(61\) | −10.6073 | −1.35812 | −0.679060 | − | 0.734083i | \(-0.737612\pi\) | ||||
−0.679060 | + | 0.734083i | \(0.737612\pi\) | |||||||
\(62\) | 1.93749 | 0.246061 | ||||||||
\(63\) | −2.17399 | −0.273897 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.3724 | −1.41058 | ||||||||
\(66\) | −8.15651 | −1.00400 | ||||||||
\(67\) | 7.97994 | 0.974905 | 0.487453 | − | 0.873149i | \(-0.337926\pi\) | ||||
0.487453 | + | 0.873149i | \(0.337926\pi\) | |||||||
\(68\) | −6.18307 | −0.749807 | ||||||||
\(69\) | −3.45508 | −0.415943 | ||||||||
\(70\) | −11.1510 | −1.33280 | ||||||||
\(71\) | 0.744429 | 0.0883475 | 0.0441737 | − | 0.999024i | \(-0.485934\pi\) | ||||
0.0441737 | + | 0.999024i | \(0.485934\pi\) | |||||||
\(72\) | −0.762675 | −0.0898821 | ||||||||
\(73\) | −10.5711 | −1.23726 | −0.618629 | − | 0.785683i | \(-0.712312\pi\) | ||||
−0.618629 | + | 0.785683i | \(0.712312\pi\) | |||||||
\(74\) | −5.17117 | −0.601136 | ||||||||
\(75\) | −15.4117 | −1.77959 | ||||||||
\(76\) | −0.516450 | −0.0592409 | ||||||||
\(77\) | 15.5438 | 1.77138 | ||||||||
\(78\) | −4.34832 | −0.492351 | ||||||||
\(79\) | 11.6973 | 1.31604 | 0.658022 | − | 0.752998i | \(-0.271393\pi\) | ||||
0.658022 | + | 0.752998i | \(0.271393\pi\) | |||||||
\(80\) | −3.91198 | −0.437372 | ||||||||
\(81\) | −6.13030 | −0.681145 | ||||||||
\(82\) | 8.84244 | 0.976484 | ||||||||
\(83\) | −9.52116 | −1.04508 | −0.522542 | − | 0.852614i | \(-0.675016\pi\) | ||||
−0.522542 | + | 0.852614i | \(0.675016\pi\) | |||||||
\(84\) | −4.26366 | −0.465204 | ||||||||
\(85\) | 24.1880 | 2.62356 | ||||||||
\(86\) | −12.6113 | −1.35991 | ||||||||
\(87\) | −2.54979 | −0.273366 | ||||||||
\(88\) | 5.45305 | 0.581297 | ||||||||
\(89\) | 18.7254 | 1.98489 | 0.992443 | − | 0.122709i | \(-0.0391583\pi\) | ||||
0.992443 | + | 0.122709i | \(0.0391583\pi\) | |||||||
\(90\) | 2.98356 | 0.314495 | ||||||||
\(91\) | 8.28659 | 0.868670 | ||||||||
\(92\) | 2.30990 | 0.240824 | ||||||||
\(93\) | −2.89804 | −0.300512 | ||||||||
\(94\) | −6.22673 | −0.642238 | ||||||||
\(95\) | 2.02034 | 0.207283 | ||||||||
\(96\) | −1.49577 | −0.152661 | ||||||||
\(97\) | −12.3870 | −1.25771 | −0.628856 | − | 0.777522i | \(-0.716477\pi\) | ||||
−0.628856 | + | 0.777522i | \(0.716477\pi\) | |||||||
\(98\) | 1.12525 | 0.113668 | ||||||||
\(99\) | −4.15890 | −0.417986 | ||||||||
\(100\) | 10.3036 | 1.03036 | ||||||||
\(101\) | 5.84555 | 0.581654 | 0.290827 | − | 0.956776i | \(-0.406070\pi\) | ||||
0.290827 | + | 0.956776i | \(0.406070\pi\) | |||||||
\(102\) | 9.24844 | 0.915732 | ||||||||
\(103\) | −10.3675 | −1.02154 | −0.510771 | − | 0.859717i | \(-0.670640\pi\) | ||||
−0.510771 | + | 0.859717i | \(0.670640\pi\) | |||||||
\(104\) | 2.90708 | 0.285063 | ||||||||
\(105\) | 16.6793 | 1.62774 | ||||||||
\(106\) | 1.75975 | 0.170922 | ||||||||
\(107\) | −14.4937 | −1.40116 | −0.700580 | − | 0.713574i | \(-0.747075\pi\) | ||||
−0.700580 | + | 0.713574i | \(0.747075\pi\) | |||||||
\(108\) | 5.62809 | 0.541563 | ||||||||
\(109\) | 16.7151 | 1.60102 | 0.800509 | − | 0.599321i | \(-0.204563\pi\) | ||||
0.800509 | + | 0.599321i | \(0.204563\pi\) | |||||||
\(110\) | −21.3322 | −2.03395 | ||||||||
\(111\) | 7.73487 | 0.734162 | ||||||||
\(112\) | 2.85048 | 0.269345 | ||||||||
\(113\) | 4.78584 | 0.450214 | 0.225107 | − | 0.974334i | \(-0.427727\pi\) | ||||
0.225107 | + | 0.974334i | \(0.427727\pi\) | |||||||
\(114\) | 0.772490 | 0.0723503 | ||||||||
\(115\) | −9.03628 | −0.842638 | ||||||||
\(116\) | 1.70467 | 0.158274 | ||||||||
\(117\) | −2.21716 | −0.204976 | ||||||||
\(118\) | 10.1312 | 0.932656 | ||||||||
\(119\) | −17.6247 | −1.61566 | ||||||||
\(120\) | 5.85141 | 0.534158 | ||||||||
\(121\) | 18.7358 | 1.70325 | ||||||||
\(122\) | −10.6073 | −0.960336 | ||||||||
\(123\) | −13.2262 | −1.19257 | ||||||||
\(124\) | 1.93749 | 0.173992 | ||||||||
\(125\) | −20.7474 | −1.85570 | ||||||||
\(126\) | −2.17399 | −0.193674 | ||||||||
\(127\) | −2.61522 | −0.232063 | −0.116032 | − | 0.993246i | \(-0.537017\pi\) | ||||
−0.116032 | + | 0.993246i | \(0.537017\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 18.8635 | 1.66084 | ||||||||
\(130\) | −11.3724 | −0.997429 | ||||||||
\(131\) | 21.6185 | 1.88882 | 0.944408 | − | 0.328777i | \(-0.106636\pi\) | ||||
0.944408 | + | 0.328777i | \(0.106636\pi\) | |||||||
\(132\) | −8.15651 | −0.709933 | ||||||||
\(133\) | −1.47213 | −0.127650 | ||||||||
\(134\) | 7.97994 | 0.689362 | ||||||||
\(135\) | −22.0170 | −1.89492 | ||||||||
\(136\) | −6.18307 | −0.530194 | ||||||||
\(137\) | 16.7400 | 1.43020 | 0.715098 | − | 0.699024i | \(-0.246382\pi\) | ||||
0.715098 | + | 0.699024i | \(0.246382\pi\) | |||||||
\(138\) | −3.45508 | −0.294116 | ||||||||
\(139\) | 17.2878 | 1.46633 | 0.733165 | − | 0.680050i | \(-0.238042\pi\) | ||||
0.733165 | + | 0.680050i | \(0.238042\pi\) | |||||||
\(140\) | −11.1510 | −0.942433 | ||||||||
\(141\) | 9.31375 | 0.784359 | ||||||||
\(142\) | 0.744429 | 0.0624711 | ||||||||
\(143\) | 15.8525 | 1.32565 | ||||||||
\(144\) | −0.762675 | −0.0635562 | ||||||||
\(145\) | −6.66862 | −0.553798 | ||||||||
\(146\) | −10.5711 | −0.874874 | ||||||||
\(147\) | −1.68312 | −0.138821 | ||||||||
\(148\) | −5.17117 | −0.425067 | ||||||||
\(149\) | 20.6188 | 1.68916 | 0.844579 | − | 0.535431i | \(-0.179851\pi\) | ||||
0.844579 | + | 0.535431i | \(0.179851\pi\) | |||||||
\(150\) | −15.4117 | −1.25836 | ||||||||
\(151\) | −1.64808 | −0.134119 | −0.0670593 | − | 0.997749i | \(-0.521362\pi\) | ||||
−0.0670593 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(152\) | −0.516450 | −0.0418896 | ||||||||
\(153\) | 4.71567 | 0.381239 | ||||||||
\(154\) | 15.5438 | 1.25256 | ||||||||
\(155\) | −7.57941 | −0.608793 | ||||||||
\(156\) | −4.34832 | −0.348145 | ||||||||
\(157\) | 21.7783 | 1.73809 | 0.869047 | − | 0.494729i | \(-0.164733\pi\) | ||||
0.869047 | + | 0.494729i | \(0.164733\pi\) | |||||||
\(158\) | 11.6973 | 0.930584 | ||||||||
\(159\) | −2.63218 | −0.208746 | ||||||||
\(160\) | −3.91198 | −0.309269 | ||||||||
\(161\) | 6.58434 | 0.518919 | ||||||||
\(162\) | −6.13030 | −0.481642 | ||||||||
\(163\) | −4.33889 | −0.339848 | −0.169924 | − | 0.985457i | \(-0.554352\pi\) | ||||
−0.169924 | + | 0.985457i | \(0.554352\pi\) | |||||||
\(164\) | 8.84244 | 0.690478 | ||||||||
\(165\) | 31.9081 | 2.48404 | ||||||||
\(166\) | −9.52116 | −0.738986 | ||||||||
\(167\) | −2.53407 | −0.196092 | −0.0980462 | − | 0.995182i | \(-0.531259\pi\) | ||||
−0.0980462 | + | 0.995182i | \(0.531259\pi\) | |||||||
\(168\) | −4.26366 | −0.328949 | ||||||||
\(169\) | −4.54887 | −0.349913 | ||||||||
\(170\) | 24.1880 | 1.85514 | ||||||||
\(171\) | 0.393883 | 0.0301210 | ||||||||
\(172\) | −12.6113 | −0.961600 | ||||||||
\(173\) | 12.2243 | 0.929396 | 0.464698 | − | 0.885469i | \(-0.346163\pi\) | ||||
0.464698 | + | 0.885469i | \(0.346163\pi\) | |||||||
\(174\) | −2.54979 | −0.193299 | ||||||||
\(175\) | 29.3701 | 2.22017 | ||||||||
\(176\) | 5.45305 | 0.411039 | ||||||||
\(177\) | −15.1540 | −1.13904 | ||||||||
\(178\) | 18.7254 | 1.40353 | ||||||||
\(179\) | 14.2787 | 1.06724 | 0.533619 | − | 0.845725i | \(-0.320832\pi\) | ||||
0.533619 | + | 0.845725i | \(0.320832\pi\) | |||||||
\(180\) | 2.98356 | 0.222382 | ||||||||
\(181\) | −19.5444 | −1.45272 | −0.726362 | − | 0.687313i | \(-0.758790\pi\) | ||||
−0.726362 | + | 0.687313i | \(0.758790\pi\) | |||||||
\(182\) | 8.28659 | 0.614243 | ||||||||
\(183\) | 15.8660 | 1.17285 | ||||||||
\(184\) | 2.30990 | 0.170288 | ||||||||
\(185\) | 20.2295 | 1.48730 | ||||||||
\(186\) | −2.89804 | −0.212494 | ||||||||
\(187\) | −33.7166 | −2.46560 | ||||||||
\(188\) | −6.22673 | −0.454131 | ||||||||
\(189\) | 16.0428 | 1.16694 | ||||||||
\(190\) | 2.02034 | 0.146571 | ||||||||
\(191\) | −0.858528 | −0.0621209 | −0.0310605 | − | 0.999518i | \(-0.509888\pi\) | ||||
−0.0310605 | + | 0.999518i | \(0.509888\pi\) | |||||||
\(192\) | −1.49577 | −0.107948 | ||||||||
\(193\) | 7.52385 | 0.541578 | 0.270789 | − | 0.962639i | \(-0.412715\pi\) | ||||
0.270789 | + | 0.962639i | \(0.412715\pi\) | |||||||
\(194\) | −12.3870 | −0.889337 | ||||||||
\(195\) | 17.0105 | 1.21815 | ||||||||
\(196\) | 1.12525 | 0.0803751 | ||||||||
\(197\) | −6.22799 | −0.443726 | −0.221863 | − | 0.975078i | \(-0.571214\pi\) | ||||
−0.221863 | + | 0.975078i | \(0.571214\pi\) | |||||||
\(198\) | −4.15890 | −0.295560 | ||||||||
\(199\) | 8.36632 | 0.593072 | 0.296536 | − | 0.955022i | \(-0.404168\pi\) | ||||
0.296536 | + | 0.955022i | \(0.404168\pi\) | |||||||
\(200\) | 10.3036 | 0.728571 | ||||||||
\(201\) | −11.9362 | −0.841911 | ||||||||
\(202\) | 5.84555 | 0.411292 | ||||||||
\(203\) | 4.85912 | 0.341044 | ||||||||
\(204\) | 9.24844 | 0.647521 | ||||||||
\(205\) | −34.5914 | −2.41597 | ||||||||
\(206\) | −10.3675 | −0.722339 | ||||||||
\(207\) | −1.76170 | −0.122447 | ||||||||
\(208\) | 2.90708 | 0.201570 | ||||||||
\(209\) | −2.81623 | −0.194803 | ||||||||
\(210\) | 16.6793 | 1.15098 | ||||||||
\(211\) | −6.91765 | −0.476231 | −0.238115 | − | 0.971237i | \(-0.576530\pi\) | ||||
−0.238115 | + | 0.971237i | \(0.576530\pi\) | |||||||
\(212\) | 1.75975 | 0.120860 | ||||||||
\(213\) | −1.11349 | −0.0762954 | ||||||||
\(214\) | −14.4937 | −0.990769 | ||||||||
\(215\) | 49.3350 | 3.36462 | ||||||||
\(216\) | 5.62809 | 0.382943 | ||||||||
\(217\) | 5.52278 | 0.374911 | ||||||||
\(218\) | 16.7151 | 1.13209 | ||||||||
\(219\) | 15.8120 | 1.06847 | ||||||||
\(220\) | −21.3322 | −1.43822 | ||||||||
\(221\) | −17.9747 | −1.20911 | ||||||||
\(222\) | 7.73487 | 0.519131 | ||||||||
\(223\) | −4.84079 | −0.324163 | −0.162082 | − | 0.986777i | \(-0.551821\pi\) | ||||
−0.162082 | + | 0.986777i | \(0.551821\pi\) | |||||||
\(224\) | 2.85048 | 0.190456 | ||||||||
\(225\) | −7.85826 | −0.523884 | ||||||||
\(226\) | 4.78584 | 0.318349 | ||||||||
\(227\) | −12.7637 | −0.847159 | −0.423580 | − | 0.905859i | \(-0.639227\pi\) | ||||
−0.423580 | + | 0.905859i | \(0.639227\pi\) | |||||||
\(228\) | 0.772490 | 0.0511594 | ||||||||
\(229\) | −15.3170 | −1.01217 | −0.506086 | − | 0.862483i | \(-0.668908\pi\) | ||||
−0.506086 | + | 0.862483i | \(0.668908\pi\) | |||||||
\(230\) | −9.03628 | −0.595835 | ||||||||
\(231\) | −23.2500 | −1.52974 | ||||||||
\(232\) | 1.70467 | 0.111917 | ||||||||
\(233\) | 0.614597 | 0.0402636 | 0.0201318 | − | 0.999797i | \(-0.493591\pi\) | ||||
0.0201318 | + | 0.999797i | \(0.493591\pi\) | |||||||
\(234\) | −2.21716 | −0.144940 | ||||||||
\(235\) | 24.3588 | 1.58899 | ||||||||
\(236\) | 10.1312 | 0.659487 | ||||||||
\(237\) | −17.4964 | −1.13651 | ||||||||
\(238\) | −17.6247 | −1.14244 | ||||||||
\(239\) | 9.56775 | 0.618886 | 0.309443 | − | 0.950918i | \(-0.399857\pi\) | ||||
0.309443 | + | 0.950918i | \(0.399857\pi\) | |||||||
\(240\) | 5.85141 | 0.377707 | ||||||||
\(241\) | −11.1574 | −0.718710 | −0.359355 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359355 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(242\) | 18.7358 | 1.20438 | ||||||||
\(243\) | −7.71476 | −0.494902 | ||||||||
\(244\) | −10.6073 | −0.679060 | ||||||||
\(245\) | −4.40195 | −0.281231 | ||||||||
\(246\) | −13.2262 | −0.843275 | ||||||||
\(247\) | −1.50136 | −0.0955295 | ||||||||
\(248\) | 1.93749 | 0.123031 | ||||||||
\(249\) | 14.2415 | 0.902516 | ||||||||
\(250\) | −20.7474 | −1.31218 | ||||||||
\(251\) | −9.61550 | −0.606925 | −0.303462 | − | 0.952843i | \(-0.598143\pi\) | ||||
−0.303462 | + | 0.952843i | \(0.598143\pi\) | |||||||
\(252\) | −2.17399 | −0.136949 | ||||||||
\(253\) | 12.5960 | 0.791905 | ||||||||
\(254\) | −2.61522 | −0.164094 | ||||||||
\(255\) | −36.1797 | −2.26566 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.0832 | 1.37751 | 0.688757 | − | 0.724992i | \(-0.258157\pi\) | ||||
0.688757 | + | 0.724992i | \(0.258157\pi\) | |||||||
\(258\) | 18.8635 | 1.17439 | ||||||||
\(259\) | −14.7403 | −0.915919 | ||||||||
\(260\) | −11.3724 | −0.705288 | ||||||||
\(261\) | −1.30011 | −0.0804746 | ||||||||
\(262\) | 21.6185 | 1.33559 | ||||||||
\(263\) | 5.60551 | 0.345651 | 0.172825 | − | 0.984952i | \(-0.444710\pi\) | ||||
0.172825 | + | 0.984952i | \(0.444710\pi\) | |||||||
\(264\) | −8.15651 | −0.501998 | ||||||||
\(265\) | −6.88410 | −0.422887 | ||||||||
\(266\) | −1.47213 | −0.0902622 | ||||||||
\(267\) | −28.0088 | −1.71411 | ||||||||
\(268\) | 7.97994 | 0.487453 | ||||||||
\(269\) | 1.51483 | 0.0923608 | 0.0461804 | − | 0.998933i | \(-0.485295\pi\) | ||||
0.0461804 | + | 0.998933i | \(0.485295\pi\) | |||||||
\(270\) | −22.0170 | −1.33991 | ||||||||
\(271\) | 9.34971 | 0.567955 | 0.283977 | − | 0.958831i | \(-0.408346\pi\) | ||||
0.283977 | + | 0.958831i | \(0.408346\pi\) | |||||||
\(272\) | −6.18307 | −0.374904 | ||||||||
\(273\) | −12.3948 | −0.750169 | ||||||||
\(274\) | 16.7400 | 1.01130 | ||||||||
\(275\) | 56.1858 | 3.38813 | ||||||||
\(276\) | −3.45508 | −0.207971 | ||||||||
\(277\) | 28.5493 | 1.71536 | 0.857679 | − | 0.514185i | \(-0.171905\pi\) | ||||
0.857679 | + | 0.514185i | \(0.171905\pi\) | |||||||
\(278\) | 17.2878 | 1.03685 | ||||||||
\(279\) | −1.47767 | −0.0884660 | ||||||||
\(280\) | −11.1510 | −0.666401 | ||||||||
\(281\) | 13.1826 | 0.786409 | 0.393205 | − | 0.919451i | \(-0.371366\pi\) | ||||
0.393205 | + | 0.919451i | \(0.371366\pi\) | |||||||
\(282\) | 9.31375 | 0.554626 | ||||||||
\(283\) | −26.9503 | −1.60203 | −0.801013 | − | 0.598647i | \(-0.795705\pi\) | ||||
−0.801013 | + | 0.598647i | \(0.795705\pi\) | |||||||
\(284\) | 0.744429 | 0.0441737 | ||||||||
\(285\) | −3.02196 | −0.179006 | ||||||||
\(286\) | 15.8525 | 0.937376 | ||||||||
\(287\) | 25.2052 | 1.48782 | ||||||||
\(288\) | −0.762675 | −0.0449410 | ||||||||
\(289\) | 21.2303 | 1.24884 | ||||||||
\(290\) | −6.66862 | −0.391595 | ||||||||
\(291\) | 18.5281 | 1.08614 | ||||||||
\(292\) | −10.5711 | −0.618629 | ||||||||
\(293\) | 23.8893 | 1.39563 | 0.697815 | − | 0.716278i | \(-0.254156\pi\) | ||||
0.697815 | + | 0.716278i | \(0.254156\pi\) | |||||||
\(294\) | −1.68312 | −0.0981613 | ||||||||
\(295\) | −39.6332 | −2.30753 | ||||||||
\(296\) | −5.17117 | −0.300568 | ||||||||
\(297\) | 30.6903 | 1.78083 | ||||||||
\(298\) | 20.6188 | 1.19442 | ||||||||
\(299\) | 6.71508 | 0.388343 | ||||||||
\(300\) | −15.4117 | −0.889797 | ||||||||
\(301\) | −35.9482 | −2.07202 | ||||||||
\(302\) | −1.64808 | −0.0948362 | ||||||||
\(303\) | −8.74360 | −0.502306 | ||||||||
\(304\) | −0.516450 | −0.0296205 | ||||||||
\(305\) | 41.4953 | 2.37602 | ||||||||
\(306\) | 4.71567 | 0.269577 | ||||||||
\(307\) | 4.79854 | 0.273867 | 0.136933 | − | 0.990580i | \(-0.456275\pi\) | ||||
0.136933 | + | 0.990580i | \(0.456275\pi\) | |||||||
\(308\) | 15.5438 | 0.885692 | ||||||||
\(309\) | 15.5074 | 0.882186 | ||||||||
\(310\) | −7.57941 | −0.430482 | ||||||||
\(311\) | −0.139042 | −0.00788433 | −0.00394217 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394217 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(312\) | −4.34832 | −0.246175 | ||||||||
\(313\) | 24.3189 | 1.37458 | 0.687292 | − | 0.726381i | \(-0.258799\pi\) | ||||
0.687292 | + | 0.726381i | \(0.258799\pi\) | |||||||
\(314\) | 21.7783 | 1.22902 | ||||||||
\(315\) | 8.50460 | 0.479180 | ||||||||
\(316\) | 11.6973 | 0.658022 | ||||||||
\(317\) | 17.7111 | 0.994753 | 0.497377 | − | 0.867535i | \(-0.334297\pi\) | ||||
0.497377 | + | 0.867535i | \(0.334297\pi\) | |||||||
\(318\) | −2.63218 | −0.147605 | ||||||||
\(319\) | 9.29564 | 0.520456 | ||||||||
\(320\) | −3.91198 | −0.218686 | ||||||||
\(321\) | 21.6792 | 1.21002 | ||||||||
\(322\) | 6.58434 | 0.366931 | ||||||||
\(323\) | 3.19325 | 0.177677 | ||||||||
\(324\) | −6.13030 | −0.340572 | ||||||||
\(325\) | 29.9533 | 1.66151 | ||||||||
\(326\) | −4.33889 | −0.240309 | ||||||||
\(327\) | −25.0019 | −1.38261 | ||||||||
\(328\) | 8.84244 | 0.488242 | ||||||||
\(329\) | −17.7492 | −0.978544 | ||||||||
\(330\) | 31.9081 | 1.75648 | ||||||||
\(331\) | 29.3181 | 1.61147 | 0.805734 | − | 0.592277i | \(-0.201771\pi\) | ||||
0.805734 | + | 0.592277i | \(0.201771\pi\) | |||||||
\(332\) | −9.52116 | −0.522542 | ||||||||
\(333\) | 3.94392 | 0.216125 | ||||||||
\(334\) | −2.53407 | −0.138658 | ||||||||
\(335\) | −31.2173 | −1.70559 | ||||||||
\(336\) | −4.26366 | −0.232602 | ||||||||
\(337\) | 15.7130 | 0.855944 | 0.427972 | − | 0.903792i | \(-0.359228\pi\) | ||||
0.427972 | + | 0.903792i | \(0.359228\pi\) | |||||||
\(338\) | −4.54887 | −0.247426 | ||||||||
\(339\) | −7.15851 | −0.388797 | ||||||||
\(340\) | 24.1880 | 1.31178 | ||||||||
\(341\) | 10.5652 | 0.572139 | ||||||||
\(342\) | 0.393883 | 0.0212988 | ||||||||
\(343\) | −16.7459 | −0.904192 | ||||||||
\(344\) | −12.6113 | −0.679954 | ||||||||
\(345\) | 13.5162 | 0.727687 | ||||||||
\(346\) | 12.2243 | 0.657183 | ||||||||
\(347\) | 22.4086 | 1.20296 | 0.601479 | − | 0.798888i | \(-0.294578\pi\) | ||||
0.601479 | + | 0.798888i | \(0.294578\pi\) | |||||||
\(348\) | −2.54979 | −0.136683 | ||||||||
\(349\) | −6.38298 | −0.341673 | −0.170837 | − | 0.985299i | \(-0.554647\pi\) | ||||
−0.170837 | + | 0.985299i | \(0.554647\pi\) | |||||||
\(350\) | 29.3701 | 1.56990 | ||||||||
\(351\) | 16.3613 | 0.873303 | ||||||||
\(352\) | 5.45305 | 0.290649 | ||||||||
\(353\) | 9.69691 | 0.516114 | 0.258057 | − | 0.966130i | \(-0.416918\pi\) | ||||
0.258057 | + | 0.966130i | \(0.416918\pi\) | |||||||
\(354\) | −15.1540 | −0.805426 | ||||||||
\(355\) | −2.91219 | −0.154563 | ||||||||
\(356\) | 18.7254 | 0.992443 | ||||||||
\(357\) | 26.3625 | 1.39525 | ||||||||
\(358\) | 14.2787 | 0.754651 | ||||||||
\(359\) | 5.84467 | 0.308470 | 0.154235 | − | 0.988034i | \(-0.450709\pi\) | ||||
0.154235 | + | 0.988034i | \(0.450709\pi\) | |||||||
\(360\) | 2.98356 | 0.157248 | ||||||||
\(361\) | −18.7333 | −0.985962 | ||||||||
\(362\) | −19.5444 | −1.02723 | ||||||||
\(363\) | −28.0244 | −1.47090 | ||||||||
\(364\) | 8.28659 | 0.434335 | ||||||||
\(365\) | 41.3540 | 2.16457 | ||||||||
\(366\) | 15.8660 | 0.829330 | ||||||||
\(367\) | −0.873000 | −0.0455702 | −0.0227851 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227851 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(368\) | 2.30990 | 0.120412 | ||||||||
\(369\) | −6.74390 | −0.351074 | ||||||||
\(370\) | 20.2295 | 1.05168 | ||||||||
\(371\) | 5.01614 | 0.260425 | ||||||||
\(372\) | −2.89804 | −0.150256 | ||||||||
\(373\) | 37.6523 | 1.94956 | 0.974780 | − | 0.223169i | \(-0.0716401\pi\) | ||||
0.974780 | + | 0.223169i | \(0.0716401\pi\) | |||||||
\(374\) | −33.7166 | −1.74344 | ||||||||
\(375\) | 31.0333 | 1.60255 | ||||||||
\(376\) | −6.22673 | −0.321119 | ||||||||
\(377\) | 4.95561 | 0.255227 | ||||||||
\(378\) | 16.0428 | 0.825152 | ||||||||
\(379\) | 1.50114 | 0.0771084 | 0.0385542 | − | 0.999257i | \(-0.487725\pi\) | ||||
0.0385542 | + | 0.999257i | \(0.487725\pi\) | |||||||
\(380\) | 2.02034 | 0.103641 | ||||||||
\(381\) | 3.91177 | 0.200406 | ||||||||
\(382\) | −0.858528 | −0.0439261 | ||||||||
\(383\) | 13.4312 | 0.686302 | 0.343151 | − | 0.939280i | \(-0.388506\pi\) | ||||
0.343151 | + | 0.939280i | \(0.388506\pi\) | |||||||
\(384\) | −1.49577 | −0.0763307 | ||||||||
\(385\) | −60.8071 | −3.09902 | ||||||||
\(386\) | 7.52385 | 0.382954 | ||||||||
\(387\) | 9.61829 | 0.488925 | ||||||||
\(388\) | −12.3870 | −0.628856 | ||||||||
\(389\) | −16.5486 | −0.839047 | −0.419523 | − | 0.907745i | \(-0.637803\pi\) | ||||
−0.419523 | + | 0.907745i | \(0.637803\pi\) | |||||||
\(390\) | 17.0105 | 0.861362 | ||||||||
\(391\) | −14.2823 | −0.722286 | ||||||||
\(392\) | 1.12525 | 0.0568338 | ||||||||
\(393\) | −32.3363 | −1.63115 | ||||||||
\(394\) | −6.22799 | −0.313762 | ||||||||
\(395\) | −45.7594 | −2.30241 | ||||||||
\(396\) | −4.15890 | −0.208993 | ||||||||
\(397\) | 28.3813 | 1.42442 | 0.712208 | − | 0.701968i | \(-0.247695\pi\) | ||||
0.712208 | + | 0.701968i | \(0.247695\pi\) | |||||||
\(398\) | 8.36632 | 0.419366 | ||||||||
\(399\) | 2.20197 | 0.110236 | ||||||||
\(400\) | 10.3036 | 0.515178 | ||||||||
\(401\) | 23.6405 | 1.18055 | 0.590275 | − | 0.807202i | \(-0.299019\pi\) | ||||
0.590275 | + | 0.807202i | \(0.299019\pi\) | |||||||
\(402\) | −11.9362 | −0.595321 | ||||||||
\(403\) | 5.63244 | 0.280572 | ||||||||
\(404\) | 5.84555 | 0.290827 | ||||||||
\(405\) | 23.9816 | 1.19166 | ||||||||
\(406\) | 4.85912 | 0.241154 | ||||||||
\(407\) | −28.1986 | −1.39775 | ||||||||
\(408\) | 9.24844 | 0.457866 | ||||||||
\(409\) | −6.01198 | −0.297273 | −0.148637 | − | 0.988892i | \(-0.547488\pi\) | ||||
−0.148637 | + | 0.988892i | \(0.547488\pi\) | |||||||
\(410\) | −34.5914 | −1.70835 | ||||||||
\(411\) | −25.0392 | −1.23509 | ||||||||
\(412\) | −10.3675 | −0.510771 | ||||||||
\(413\) | 28.8789 | 1.42104 | ||||||||
\(414\) | −1.76170 | −0.0865830 | ||||||||
\(415\) | 37.2466 | 1.82836 | ||||||||
\(416\) | 2.90708 | 0.142531 | ||||||||
\(417\) | −25.8585 | −1.26630 | ||||||||
\(418\) | −2.81623 | −0.137746 | ||||||||
\(419\) | −16.8076 | −0.821107 | −0.410554 | − | 0.911837i | \(-0.634665\pi\) | ||||
−0.410554 | + | 0.911837i | \(0.634665\pi\) | |||||||
\(420\) | 16.6793 | 0.813869 | ||||||||
\(421\) | −17.2956 | −0.842937 | −0.421468 | − | 0.906843i | \(-0.638485\pi\) | ||||
−0.421468 | + | 0.906843i | \(0.638485\pi\) | |||||||
\(422\) | −6.91765 | −0.336746 | ||||||||
\(423\) | 4.74897 | 0.230903 | ||||||||
\(424\) | 1.75975 | 0.0854611 | ||||||||
\(425\) | −63.7076 | −3.09027 | ||||||||
\(426\) | −1.11349 | −0.0539490 | ||||||||
\(427\) | −30.2358 | −1.46321 | ||||||||
\(428\) | −14.4937 | −0.700580 | ||||||||
\(429\) | −23.7116 | −1.14481 | ||||||||
\(430\) | 49.3350 | 2.37914 | ||||||||
\(431\) | 19.9251 | 0.959758 | 0.479879 | − | 0.877335i | \(-0.340681\pi\) | ||||
0.479879 | + | 0.877335i | \(0.340681\pi\) | |||||||
\(432\) | 5.62809 | 0.270782 | ||||||||
\(433\) | −33.0782 | −1.58964 | −0.794819 | − | 0.606847i | \(-0.792434\pi\) | ||||
−0.794819 | + | 0.606847i | \(0.792434\pi\) | |||||||
\(434\) | 5.52278 | 0.265102 | ||||||||
\(435\) | 9.97471 | 0.478251 | ||||||||
\(436\) | 16.7151 | 0.800509 | ||||||||
\(437\) | −1.19295 | −0.0570665 | ||||||||
\(438\) | 15.8120 | 0.755526 | ||||||||
\(439\) | −2.33731 | −0.111554 | −0.0557768 | − | 0.998443i | \(-0.517764\pi\) | ||||
−0.0557768 | + | 0.998443i | \(0.517764\pi\) | |||||||
\(440\) | −21.3322 | −1.01697 | ||||||||
\(441\) | −0.858200 | −0.0408667 | ||||||||
\(442\) | −17.9747 | −0.854969 | ||||||||
\(443\) | −38.6638 | −1.83697 | −0.918486 | − | 0.395454i | \(-0.870587\pi\) | ||||
−0.918486 | + | 0.395454i | \(0.870587\pi\) | |||||||
\(444\) | 7.73487 | 0.367081 | ||||||||
\(445\) | −73.2532 | −3.47253 | ||||||||
\(446\) | −4.84079 | −0.229218 | ||||||||
\(447\) | −30.8410 | −1.45873 | ||||||||
\(448\) | 2.85048 | 0.134673 | ||||||||
\(449\) | −27.9726 | −1.32011 | −0.660054 | − | 0.751218i | \(-0.729467\pi\) | ||||
−0.660054 | + | 0.751218i | \(0.729467\pi\) | |||||||
\(450\) | −7.85826 | −0.370442 | ||||||||
\(451\) | 48.2183 | 2.27051 | ||||||||
\(452\) | 4.78584 | 0.225107 | ||||||||
\(453\) | 2.46514 | 0.115823 | ||||||||
\(454\) | −12.7637 | −0.599032 | ||||||||
\(455\) | −32.4169 | −1.51973 | ||||||||
\(456\) | 0.772490 | 0.0361752 | ||||||||
\(457\) | 5.37327 | 0.251351 | 0.125675 | − | 0.992071i | \(-0.459890\pi\) | ||||
0.125675 | + | 0.992071i | \(0.459890\pi\) | |||||||
\(458\) | −15.3170 | −0.715714 | ||||||||
\(459\) | −34.7989 | −1.62427 | ||||||||
\(460\) | −9.03628 | −0.421319 | ||||||||
\(461\) | 15.0988 | 0.703222 | 0.351611 | − | 0.936146i | \(-0.385634\pi\) | ||||
0.351611 | + | 0.936146i | \(0.385634\pi\) | |||||||
\(462\) | −23.2500 | −1.08169 | ||||||||
\(463\) | 14.1717 | 0.658616 | 0.329308 | − | 0.944223i | \(-0.393185\pi\) | ||||
0.329308 | + | 0.944223i | \(0.393185\pi\) | |||||||
\(464\) | 1.70467 | 0.0791372 | ||||||||
\(465\) | 11.3370 | 0.525743 | ||||||||
\(466\) | 0.614597 | 0.0284707 | ||||||||
\(467\) | 31.2076 | 1.44411 | 0.722057 | − | 0.691833i | \(-0.243197\pi\) | ||||
0.722057 | + | 0.691833i | \(0.243197\pi\) | |||||||
\(468\) | −2.21716 | −0.102488 | ||||||||
\(469\) | 22.7467 | 1.05034 | ||||||||
\(470\) | 24.3588 | 1.12359 | ||||||||
\(471\) | −32.5753 | −1.50099 | ||||||||
\(472\) | 10.1312 | 0.466328 | ||||||||
\(473\) | −68.7699 | −3.16204 | ||||||||
\(474\) | −17.4964 | −0.803636 | ||||||||
\(475\) | −5.32127 | −0.244157 | ||||||||
\(476\) | −17.6247 | −0.807828 | ||||||||
\(477\) | −1.34212 | −0.0614513 | ||||||||
\(478\) | 9.56775 | 0.437619 | ||||||||
\(479\) | −24.4964 | −1.11927 | −0.559634 | − | 0.828740i | \(-0.689058\pi\) | ||||
−0.559634 | + | 0.828740i | \(0.689058\pi\) | |||||||
\(480\) | 5.85141 | 0.267079 | ||||||||
\(481\) | −15.0330 | −0.685446 | ||||||||
\(482\) | −11.1574 | −0.508205 | ||||||||
\(483\) | −9.84865 | −0.448129 | ||||||||
\(484\) | 18.7358 | 0.851626 | ||||||||
\(485\) | 48.4578 | 2.20035 | ||||||||
\(486\) | −7.71476 | −0.349949 | ||||||||
\(487\) | 7.59090 | 0.343976 | 0.171988 | − | 0.985099i | \(-0.444981\pi\) | ||||
0.171988 | + | 0.985099i | \(0.444981\pi\) | |||||||
\(488\) | −10.6073 | −0.480168 | ||||||||
\(489\) | 6.48998 | 0.293487 | ||||||||
\(490\) | −4.40195 | −0.198860 | ||||||||
\(491\) | 22.3729 | 1.00968 | 0.504838 | − | 0.863214i | \(-0.331552\pi\) | ||||
0.504838 | + | 0.863214i | \(0.331552\pi\) | |||||||
\(492\) | −13.2262 | −0.596285 | ||||||||
\(493\) | −10.5401 | −0.474701 | ||||||||
\(494\) | −1.50136 | −0.0675495 | ||||||||
\(495\) | 16.2695 | 0.731261 | ||||||||
\(496\) | 1.93749 | 0.0869958 | ||||||||
\(497\) | 2.12198 | 0.0951839 | ||||||||
\(498\) | 14.2415 | 0.638175 | ||||||||
\(499\) | 44.1792 | 1.97773 | 0.988866 | − | 0.148812i | \(-0.0475449\pi\) | ||||
0.988866 | + | 0.148812i | \(0.0475449\pi\) | |||||||
\(500\) | −20.7474 | −0.927850 | ||||||||
\(501\) | 3.79039 | 0.169342 | ||||||||
\(502\) | −9.61550 | −0.429161 | ||||||||
\(503\) | 4.78572 | 0.213385 | 0.106692 | − | 0.994292i | \(-0.465974\pi\) | ||||
0.106692 | + | 0.994292i | \(0.465974\pi\) | |||||||
\(504\) | −2.17399 | −0.0968372 | ||||||||
\(505\) | −22.8677 | −1.01760 | ||||||||
\(506\) | 12.5960 | 0.559961 | ||||||||
\(507\) | 6.80406 | 0.302179 | ||||||||
\(508\) | −2.61522 | −0.116032 | ||||||||
\(509\) | −22.4385 | −0.994569 | −0.497285 | − | 0.867587i | \(-0.665670\pi\) | ||||
−0.497285 | + | 0.867587i | \(0.665670\pi\) | |||||||
\(510\) | −36.1797 | −1.60206 | ||||||||
\(511\) | −30.1328 | −1.33300 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.90663 | −0.128331 | ||||||||
\(514\) | 22.0832 | 0.974050 | ||||||||
\(515\) | 40.5575 | 1.78718 | ||||||||
\(516\) | 18.8635 | 0.830421 | ||||||||
\(517\) | −33.9547 | −1.49332 | ||||||||
\(518\) | −14.7403 | −0.647653 | ||||||||
\(519\) | −18.2847 | −0.802611 | ||||||||
\(520\) | −11.3724 | −0.498714 | ||||||||
\(521\) | −38.5387 | −1.68841 | −0.844205 | − | 0.536020i | \(-0.819927\pi\) | ||||
−0.844205 | + | 0.536020i | \(0.819927\pi\) | |||||||
\(522\) | −1.30011 | −0.0569041 | ||||||||
\(523\) | −24.4090 | −1.06733 | −0.533665 | − | 0.845696i | \(-0.679185\pi\) | ||||
−0.533665 | + | 0.845696i | \(0.679185\pi\) | |||||||
\(524\) | 21.6185 | 0.944408 | ||||||||
\(525\) | −43.9309 | −1.91730 | ||||||||
\(526\) | 5.60551 | 0.244412 | ||||||||
\(527\) | −11.9796 | −0.521841 | ||||||||
\(528\) | −8.15651 | −0.354966 | ||||||||
\(529\) | −17.6643 | −0.768015 | ||||||||
\(530\) | −6.88410 | −0.299026 | ||||||||
\(531\) | −7.72684 | −0.335316 | ||||||||
\(532\) | −1.47213 | −0.0638250 | ||||||||
\(533\) | 25.7057 | 1.11344 | ||||||||
\(534\) | −28.0088 | −1.21206 | ||||||||
\(535\) | 56.6990 | 2.45131 | ||||||||
\(536\) | 7.97994 | 0.344681 | ||||||||
\(537\) | −21.3576 | −0.921648 | ||||||||
\(538\) | 1.51483 | 0.0653090 | ||||||||
\(539\) | 6.13605 | 0.264298 | ||||||||
\(540\) | −22.0170 | −0.947459 | ||||||||
\(541\) | 7.64893 | 0.328853 | 0.164426 | − | 0.986389i | \(-0.447423\pi\) | ||||
0.164426 | + | 0.986389i | \(0.447423\pi\) | |||||||
\(542\) | 9.34971 | 0.401605 | ||||||||
\(543\) | 29.2339 | 1.25455 | ||||||||
\(544\) | −6.18307 | −0.265097 | ||||||||
\(545\) | −65.3891 | −2.80096 | ||||||||
\(546\) | −12.3948 | −0.530449 | ||||||||
\(547\) | 11.2499 | 0.481010 | 0.240505 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240505 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(548\) | 16.7400 | 0.715098 | ||||||||
\(549\) | 8.08989 | 0.345268 | ||||||||
\(550\) | 56.1858 | 2.39577 | ||||||||
\(551\) | −0.880376 | −0.0375053 | ||||||||
\(552\) | −3.45508 | −0.147058 | ||||||||
\(553\) | 33.3428 | 1.41788 | ||||||||
\(554\) | 28.5493 | 1.21294 | ||||||||
\(555\) | −30.2586 | −1.28441 | ||||||||
\(556\) | 17.2878 | 0.733165 | ||||||||
\(557\) | −20.1901 | −0.855481 | −0.427740 | − | 0.903902i | \(-0.640690\pi\) | ||||
−0.427740 | + | 0.903902i | \(0.640690\pi\) | |||||||
\(558\) | −1.47767 | −0.0625549 | ||||||||
\(559\) | −36.6620 | −1.55064 | ||||||||
\(560\) | −11.1510 | −0.471217 | ||||||||
\(561\) | 50.4322 | 2.12925 | ||||||||
\(562\) | 13.1826 | 0.556075 | ||||||||
\(563\) | 24.1740 | 1.01881 | 0.509406 | − | 0.860526i | \(-0.329865\pi\) | ||||
0.509406 | + | 0.860526i | \(0.329865\pi\) | |||||||
\(564\) | 9.31375 | 0.392179 | ||||||||
\(565\) | −18.7221 | −0.787644 | ||||||||
\(566\) | −26.9503 | −1.13280 | ||||||||
\(567\) | −17.4743 | −0.733853 | ||||||||
\(568\) | 0.744429 | 0.0312356 | ||||||||
\(569\) | 14.4340 | 0.605106 | 0.302553 | − | 0.953133i | \(-0.402161\pi\) | ||||
0.302553 | + | 0.953133i | \(0.402161\pi\) | |||||||
\(570\) | −3.02196 | −0.126576 | ||||||||
\(571\) | 7.30129 | 0.305550 | 0.152775 | − | 0.988261i | \(-0.451179\pi\) | ||||
0.152775 | + | 0.988261i | \(0.451179\pi\) | |||||||
\(572\) | 15.8525 | 0.662825 | ||||||||
\(573\) | 1.28416 | 0.0536465 | ||||||||
\(574\) | 25.2052 | 1.05205 | ||||||||
\(575\) | 23.8002 | 0.992537 | ||||||||
\(576\) | −0.762675 | −0.0317781 | ||||||||
\(577\) | −7.34658 | −0.305842 | −0.152921 | − | 0.988238i | \(-0.548868\pi\) | ||||
−0.152921 | + | 0.988238i | \(0.548868\pi\) | |||||||
\(578\) | 21.2303 | 0.883065 | ||||||||
\(579\) | −11.2539 | −0.467698 | ||||||||
\(580\) | −6.66862 | −0.276899 | ||||||||
\(581\) | −27.1399 | −1.12595 | ||||||||
\(582\) | 18.5281 | 0.768016 | ||||||||
\(583\) | 9.59601 | 0.397426 | ||||||||
\(584\) | −10.5711 | −0.437437 | ||||||||
\(585\) | 8.67347 | 0.358604 | ||||||||
\(586\) | 23.8893 | 0.986860 | ||||||||
\(587\) | −5.64225 | −0.232881 | −0.116440 | − | 0.993198i | \(-0.537148\pi\) | ||||
−0.116440 | + | 0.993198i | \(0.537148\pi\) | |||||||
\(588\) | −1.68312 | −0.0694105 | ||||||||
\(589\) | −1.00062 | −0.0412297 | ||||||||
\(590\) | −39.6332 | −1.63167 | ||||||||
\(591\) | 9.31564 | 0.383194 | ||||||||
\(592\) | −5.17117 | −0.212534 | ||||||||
\(593\) | −26.9550 | −1.10691 | −0.553455 | − | 0.832879i | \(-0.686691\pi\) | ||||
−0.553455 | + | 0.832879i | \(0.686691\pi\) | |||||||
\(594\) | 30.6903 | 1.25924 | ||||||||
\(595\) | 68.9475 | 2.82657 | ||||||||
\(596\) | 20.6188 | 0.844579 | ||||||||
\(597\) | −12.5141 | −0.512167 | ||||||||
\(598\) | 6.71508 | 0.274600 | ||||||||
\(599\) | −28.5194 | −1.16527 | −0.582635 | − | 0.812734i | \(-0.697978\pi\) | ||||
−0.582635 | + | 0.812734i | \(0.697978\pi\) | |||||||
\(600\) | −15.4117 | −0.629181 | ||||||||
\(601\) | −14.9903 | −0.611466 | −0.305733 | − | 0.952117i | \(-0.598901\pi\) | ||||
−0.305733 | + | 0.952117i | \(0.598901\pi\) | |||||||
\(602\) | −35.9482 | −1.46514 | ||||||||
\(603\) | −6.08610 | −0.247845 | ||||||||
\(604\) | −1.64808 | −0.0670593 | ||||||||
\(605\) | −73.2939 | −2.97982 | ||||||||
\(606\) | −8.74360 | −0.355184 | ||||||||
\(607\) | −31.4329 | −1.27582 | −0.637911 | − | 0.770110i | \(-0.720201\pi\) | ||||
−0.637911 | + | 0.770110i | \(0.720201\pi\) | |||||||
\(608\) | −0.516450 | −0.0209448 | ||||||||
\(609\) | −7.26813 | −0.294519 | ||||||||
\(610\) | 41.4953 | 1.68010 | ||||||||
\(611\) | −18.1016 | −0.732313 | ||||||||
\(612\) | 4.71567 | 0.190620 | ||||||||
\(613\) | −30.9411 | −1.24970 | −0.624851 | − | 0.780744i | \(-0.714840\pi\) | ||||
−0.624851 | + | 0.780744i | \(0.714840\pi\) | |||||||
\(614\) | 4.79854 | 0.193653 | ||||||||
\(615\) | 51.7407 | 2.08639 | ||||||||
\(616\) | 15.5438 | 0.626279 | ||||||||
\(617\) | 27.2781 | 1.09817 | 0.549087 | − | 0.835765i | \(-0.314976\pi\) | ||||
0.549087 | + | 0.835765i | \(0.314976\pi\) | |||||||
\(618\) | 15.5074 | 0.623800 | ||||||||
\(619\) | 21.1983 | 0.852032 | 0.426016 | − | 0.904716i | \(-0.359917\pi\) | ||||
0.426016 | + | 0.904716i | \(0.359917\pi\) | |||||||
\(620\) | −7.57941 | −0.304396 | ||||||||
\(621\) | 13.0003 | 0.521686 | ||||||||
\(622\) | −0.139042 | −0.00557506 | ||||||||
\(623\) | 53.3763 | 2.13848 | ||||||||
\(624\) | −4.34832 | −0.174072 | ||||||||
\(625\) | 29.6454 | 1.18582 | ||||||||
\(626\) | 24.3189 | 0.971978 | ||||||||
\(627\) | 4.21243 | 0.168228 | ||||||||
\(628\) | 21.7783 | 0.869047 | ||||||||
\(629\) | 31.9737 | 1.27487 | ||||||||
\(630\) | 8.50460 | 0.338831 | ||||||||
\(631\) | −17.4526 | −0.694776 | −0.347388 | − | 0.937722i | \(-0.612931\pi\) | ||||
−0.347388 | + | 0.937722i | \(0.612931\pi\) | |||||||
\(632\) | 11.6973 | 0.465292 | ||||||||
\(633\) | 10.3472 | 0.411265 | ||||||||
\(634\) | 17.7111 | 0.703397 | ||||||||
\(635\) | 10.2307 | 0.405992 | ||||||||
\(636\) | −2.63218 | −0.104373 | ||||||||
\(637\) | 3.27120 | 0.129610 | ||||||||
\(638\) | 9.29564 | 0.368018 | ||||||||
\(639\) | −0.567757 | −0.0224601 | ||||||||
\(640\) | −3.91198 | −0.154634 | ||||||||
\(641\) | −23.0179 | −0.909153 | −0.454576 | − | 0.890708i | \(-0.650209\pi\) | ||||
−0.454576 | + | 0.890708i | \(0.650209\pi\) | |||||||
\(642\) | 21.6792 | 0.855611 | ||||||||
\(643\) | −11.7524 | −0.463469 | −0.231734 | − | 0.972779i | \(-0.574440\pi\) | ||||
−0.231734 | + | 0.972779i | \(0.574440\pi\) | |||||||
\(644\) | 6.58434 | 0.259459 | ||||||||
\(645\) | −73.7937 | −2.90563 | ||||||||
\(646\) | 3.19325 | 0.125637 | ||||||||
\(647\) | −38.4497 | −1.51162 | −0.755808 | − | 0.654794i | \(-0.772756\pi\) | ||||
−0.755808 | + | 0.654794i | \(0.772756\pi\) | |||||||
\(648\) | −6.13030 | −0.240821 | ||||||||
\(649\) | 55.2462 | 2.16860 | ||||||||
\(650\) | 29.9533 | 1.17486 | ||||||||
\(651\) | −8.26080 | −0.323766 | ||||||||
\(652\) | −4.33889 | −0.169924 | ||||||||
\(653\) | 32.6070 | 1.27601 | 0.638005 | − | 0.770032i | \(-0.279760\pi\) | ||||
0.638005 | + | 0.770032i | \(0.279760\pi\) | |||||||
\(654\) | −25.0019 | −0.977653 | ||||||||
\(655\) | −84.5710 | −3.30446 | ||||||||
\(656\) | 8.84244 | 0.345239 | ||||||||
\(657\) | 8.06234 | 0.314542 | ||||||||
\(658\) | −17.7492 | −0.691935 | ||||||||
\(659\) | 32.0876 | 1.24996 | 0.624978 | − | 0.780642i | \(-0.285108\pi\) | ||||
0.624978 | + | 0.780642i | \(0.285108\pi\) | |||||||
\(660\) | 31.9081 | 1.24202 | ||||||||
\(661\) | 3.37129 | 0.131128 | 0.0655640 | − | 0.997848i | \(-0.479115\pi\) | ||||
0.0655640 | + | 0.997848i | \(0.479115\pi\) | |||||||
\(662\) | 29.3181 | 1.13948 | ||||||||
\(663\) | 26.8860 | 1.04417 | ||||||||
\(664\) | −9.52116 | −0.369493 | ||||||||
\(665\) | 5.75895 | 0.223322 | ||||||||
\(666\) | 3.94392 | 0.152824 | ||||||||
\(667\) | 3.93762 | 0.152465 | ||||||||
\(668\) | −2.53407 | −0.0980462 | ||||||||
\(669\) | 7.24070 | 0.279942 | ||||||||
\(670\) | −31.2173 | −1.20603 | ||||||||
\(671\) | −57.8419 | −2.23296 | ||||||||
\(672\) | −4.26366 | −0.164474 | ||||||||
\(673\) | −0.769850 | −0.0296755 | −0.0148378 | − | 0.999890i | \(-0.504723\pi\) | ||||
−0.0148378 | + | 0.999890i | \(0.504723\pi\) | |||||||
\(674\) | 15.7130 | 0.605244 | ||||||||
\(675\) | 57.9893 | 2.23201 | ||||||||
\(676\) | −4.54887 | −0.174957 | ||||||||
\(677\) | −16.1994 | −0.622592 | −0.311296 | − | 0.950313i | \(-0.600763\pi\) | ||||
−0.311296 | + | 0.950313i | \(0.600763\pi\) | |||||||
\(678\) | −7.15851 | −0.274921 | ||||||||
\(679\) | −35.3090 | −1.35504 | ||||||||
\(680\) | 24.1880 | 0.927568 | ||||||||
\(681\) | 19.0916 | 0.731592 | ||||||||
\(682\) | 10.5652 | 0.404564 | ||||||||
\(683\) | 12.0081 | 0.459476 | 0.229738 | − | 0.973252i | \(-0.426213\pi\) | ||||
0.229738 | + | 0.973252i | \(0.426213\pi\) | |||||||
\(684\) | 0.393883 | 0.0150605 | ||||||||
\(685\) | −65.4865 | −2.50211 | ||||||||
\(686\) | −16.7459 | −0.639360 | ||||||||
\(687\) | 22.9106 | 0.874095 | ||||||||
\(688\) | −12.6113 | −0.480800 | ||||||||
\(689\) | 5.11574 | 0.194894 | ||||||||
\(690\) | 13.5162 | 0.514553 | ||||||||
\(691\) | 35.2406 | 1.34062 | 0.670308 | − | 0.742083i | \(-0.266162\pi\) | ||||
0.670308 | + | 0.742083i | \(0.266162\pi\) | |||||||
\(692\) | 12.2243 | 0.464698 | ||||||||
\(693\) | −11.8549 | −0.450330 | ||||||||
\(694\) | 22.4086 | 0.850620 | ||||||||
\(695\) | −67.6294 | −2.56533 | ||||||||
\(696\) | −2.54979 | −0.0966495 | ||||||||
\(697\) | −54.6734 | −2.07090 | ||||||||
\(698\) | −6.38298 | −0.241599 | ||||||||
\(699\) | −0.919296 | −0.0347710 | ||||||||
\(700\) | 29.3701 | 1.11009 | ||||||||
\(701\) | 21.5333 | 0.813300 | 0.406650 | − | 0.913584i | \(-0.366697\pi\) | ||||
0.406650 | + | 0.913584i | \(0.366697\pi\) | |||||||
\(702\) | 16.3613 | 0.617519 | ||||||||
\(703\) | 2.67065 | 0.100725 | ||||||||
\(704\) | 5.45305 | 0.205520 | ||||||||
\(705\) | −36.4352 | −1.37223 | ||||||||
\(706\) | 9.69691 | 0.364948 | ||||||||
\(707\) | 16.6626 | 0.626663 | ||||||||
\(708\) | −15.1540 | −0.569522 | ||||||||
\(709\) | −27.9947 | −1.05136 | −0.525681 | − | 0.850682i | \(-0.676190\pi\) | ||||
−0.525681 | + | 0.850682i | \(0.676190\pi\) | |||||||
\(710\) | −2.91219 | −0.109293 | ||||||||
\(711\) | −8.92121 | −0.334571 | ||||||||
\(712\) | 18.7254 | 0.701763 | ||||||||
\(713\) | 4.47541 | 0.167606 | ||||||||
\(714\) | 26.3625 | 0.986593 | ||||||||
\(715\) | −62.0145 | −2.31921 | ||||||||
\(716\) | 14.2787 | 0.533619 | ||||||||
\(717\) | −14.3111 | −0.534460 | ||||||||
\(718\) | 5.84467 | 0.218121 | ||||||||
\(719\) | −4.08740 | −0.152434 | −0.0762171 | − | 0.997091i | \(-0.524284\pi\) | ||||
−0.0762171 | + | 0.997091i | \(0.524284\pi\) | |||||||
\(720\) | 2.98356 | 0.111191 | ||||||||
\(721\) | −29.5524 | −1.10059 | ||||||||
\(722\) | −18.7333 | −0.697180 | ||||||||
\(723\) | 16.6889 | 0.620666 | ||||||||
\(724\) | −19.5444 | −0.726362 | ||||||||
\(725\) | 17.5641 | 0.652315 | ||||||||
\(726\) | −28.0244 | −1.04008 | ||||||||
\(727\) | 17.2234 | 0.638782 | 0.319391 | − | 0.947623i | \(-0.396522\pi\) | ||||
0.319391 | + | 0.947623i | \(0.396522\pi\) | |||||||
\(728\) | 8.28659 | 0.307121 | ||||||||
\(729\) | 29.9304 | 1.10853 | ||||||||
\(730\) | 41.3540 | 1.53058 | ||||||||
\(731\) | 77.9763 | 2.88406 | ||||||||
\(732\) | 15.8660 | 0.586425 | ||||||||
\(733\) | 25.1996 | 0.930769 | 0.465385 | − | 0.885109i | \(-0.345916\pi\) | ||||
0.465385 | + | 0.885109i | \(0.345916\pi\) | |||||||
\(734\) | −0.873000 | −0.0322230 | ||||||||
\(735\) | 6.58431 | 0.242866 | ||||||||
\(736\) | 2.30990 | 0.0851441 | ||||||||
\(737\) | 43.5150 | 1.60290 | ||||||||
\(738\) | −6.74390 | −0.248246 | ||||||||
\(739\) | −2.38421 | −0.0877046 | −0.0438523 | − | 0.999038i | \(-0.513963\pi\) | ||||
−0.0438523 | + | 0.999038i | \(0.513963\pi\) | |||||||
\(740\) | 20.2295 | 0.743650 | ||||||||
\(741\) | 2.24569 | 0.0824976 | ||||||||
\(742\) | 5.01614 | 0.184148 | ||||||||
\(743\) | 32.8316 | 1.20448 | 0.602238 | − | 0.798317i | \(-0.294276\pi\) | ||||
0.602238 | + | 0.798317i | \(0.294276\pi\) | |||||||
\(744\) | −2.89804 | −0.106247 | ||||||||
\(745\) | −80.6603 | −2.95516 | ||||||||
\(746\) | 37.6523 | 1.37855 | ||||||||
\(747\) | 7.26155 | 0.265686 | ||||||||
\(748\) | −33.7166 | −1.23280 | ||||||||
\(749\) | −41.3140 | −1.50958 | ||||||||
\(750\) | 31.0333 | 1.13317 | ||||||||
\(751\) | −11.0473 | −0.403121 | −0.201561 | − | 0.979476i | \(-0.564601\pi\) | ||||
−0.201561 | + | 0.979476i | \(0.564601\pi\) | |||||||
\(752\) | −6.22673 | −0.227065 | ||||||||
\(753\) | 14.3826 | 0.524130 | ||||||||
\(754\) | 4.95561 | 0.180473 | ||||||||
\(755\) | 6.44724 | 0.234639 | ||||||||
\(756\) | 16.0428 | 0.583470 | ||||||||
\(757\) | −18.6842 | −0.679087 | −0.339544 | − | 0.940590i | \(-0.610273\pi\) | ||||
−0.339544 | + | 0.940590i | \(0.610273\pi\) | |||||||
\(758\) | 1.50114 | 0.0545239 | ||||||||
\(759\) | −18.8407 | −0.683875 | ||||||||
\(760\) | 2.02034 | 0.0732855 | ||||||||
\(761\) | −7.65353 | −0.277440 | −0.138720 | − | 0.990332i | \(-0.544299\pi\) | ||||
−0.138720 | + | 0.990332i | \(0.544299\pi\) | |||||||
\(762\) | 3.91177 | 0.141708 | ||||||||
\(763\) | 47.6461 | 1.72491 | ||||||||
\(764\) | −0.858528 | −0.0310605 | ||||||||
\(765\) | −18.4476 | −0.666974 | ||||||||
\(766\) | 13.4312 | 0.485289 | ||||||||
\(767\) | 29.4523 | 1.06346 | ||||||||
\(768\) | −1.49577 | −0.0539739 | ||||||||
\(769\) | 38.4120 | 1.38517 | 0.692587 | − | 0.721334i | \(-0.256471\pi\) | ||||
0.692587 | + | 0.721334i | \(0.256471\pi\) | |||||||
\(770\) | −60.8071 | −2.19133 | ||||||||
\(771\) | −33.0314 | −1.18960 | ||||||||
\(772\) | 7.52385 | 0.270789 | ||||||||
\(773\) | −46.0469 | −1.65619 | −0.828096 | − | 0.560586i | \(-0.810576\pi\) | ||||
−0.828096 | + | 0.560586i | \(0.810576\pi\) | |||||||
\(774\) | 9.61829 | 0.345722 | ||||||||
\(775\) | 19.9630 | 0.717093 | ||||||||
\(776\) | −12.3870 | −0.444668 | ||||||||
\(777\) | 22.0481 | 0.790972 | ||||||||
\(778\) | −16.5486 | −0.593296 | ||||||||
\(779\) | −4.56668 | −0.163618 | ||||||||
\(780\) | 17.0105 | 0.609075 | ||||||||
\(781\) | 4.05941 | 0.145257 | ||||||||
\(782\) | −14.2823 | −0.510734 | ||||||||
\(783\) | 9.59402 | 0.342862 | ||||||||
\(784\) | 1.12525 | 0.0401875 | ||||||||
\(785\) | −85.1960 | −3.04078 | ||||||||
\(786\) | −32.3363 | −1.15340 | ||||||||
\(787\) | −21.7091 | −0.773845 | −0.386922 | − | 0.922112i | \(-0.626462\pi\) | ||||
−0.386922 | + | 0.922112i | \(0.626462\pi\) | |||||||
\(788\) | −6.22799 | −0.221863 | ||||||||
\(789\) | −8.38456 | −0.298498 | ||||||||
\(790\) | −45.7594 | −1.62805 | ||||||||
\(791\) | 13.6419 | 0.485052 | ||||||||
\(792\) | −4.15890 | −0.147780 | ||||||||
\(793\) | −30.8362 | −1.09502 | ||||||||
\(794\) | 28.3813 | 1.00721 | ||||||||
\(795\) | 10.2970 | 0.365198 | ||||||||
\(796\) | 8.36632 | 0.296536 | ||||||||
\(797\) | 24.6514 | 0.873197 | 0.436598 | − | 0.899657i | \(-0.356183\pi\) | ||||
0.436598 | + | 0.899657i | \(0.356183\pi\) | |||||||
\(798\) | 2.20197 | 0.0779489 | ||||||||
\(799\) | 38.5003 | 1.36204 | ||||||||
\(800\) | 10.3036 | 0.364286 | ||||||||
\(801\) | −14.2814 | −0.504607 | ||||||||
\(802\) | 23.6405 | 0.834775 | ||||||||
\(803\) | −57.6449 | −2.03425 | ||||||||
\(804\) | −11.9362 | −0.420956 | ||||||||
\(805\) | −25.7578 | −0.907842 | ||||||||
\(806\) | 5.63244 | 0.198394 | ||||||||
\(807\) | −2.26584 | −0.0797612 | ||||||||
\(808\) | 5.84555 | 0.205646 | ||||||||
\(809\) | −5.27338 | −0.185402 | −0.0927011 | − | 0.995694i | \(-0.529550\pi\) | ||||
−0.0927011 | + | 0.995694i | \(0.529550\pi\) | |||||||
\(810\) | 23.9816 | 0.842627 | ||||||||
\(811\) | −12.8916 | −0.452685 | −0.226342 | − | 0.974048i | \(-0.572677\pi\) | ||||
−0.226342 | + | 0.974048i | \(0.572677\pi\) | |||||||
\(812\) | 4.85912 | 0.170522 | ||||||||
\(813\) | −13.9850 | −0.490476 | ||||||||
\(814\) | −28.1986 | −0.988362 | ||||||||
\(815\) | 16.9736 | 0.594561 | ||||||||
\(816\) | 9.24844 | 0.323760 | ||||||||
\(817\) | 6.51309 | 0.227864 | ||||||||
\(818\) | −6.01198 | −0.210204 | ||||||||
\(819\) | −6.31997 | −0.220838 | ||||||||
\(820\) | −34.5914 | −1.20798 | ||||||||
\(821\) | −4.37698 | −0.152758 | −0.0763789 | − | 0.997079i | \(-0.524336\pi\) | ||||
−0.0763789 | + | 0.997079i | \(0.524336\pi\) | |||||||
\(822\) | −25.0392 | −0.873342 | ||||||||
\(823\) | 27.3019 | 0.951685 | 0.475843 | − | 0.879530i | \(-0.342143\pi\) | ||||
0.475843 | + | 0.879530i | \(0.342143\pi\) | |||||||
\(824\) | −10.3675 | −0.361170 | ||||||||
\(825\) | −84.0410 | −2.92593 | ||||||||
\(826\) | 28.8789 | 1.00483 | ||||||||
\(827\) | −4.45600 | −0.154950 | −0.0774751 | − | 0.996994i | \(-0.524686\pi\) | ||||
−0.0774751 | + | 0.996994i | \(0.524686\pi\) | |||||||
\(828\) | −1.76170 | −0.0612235 | ||||||||
\(829\) | 9.83165 | 0.341467 | 0.170734 | − | 0.985317i | \(-0.445386\pi\) | ||||
0.170734 | + | 0.985317i | \(0.445386\pi\) | |||||||
\(830\) | 37.2466 | 1.29285 | ||||||||
\(831\) | −42.7031 | −1.48135 | ||||||||
\(832\) | 2.90708 | 0.100785 | ||||||||
\(833\) | −6.95750 | −0.241063 | ||||||||
\(834\) | −25.8585 | −0.895408 | ||||||||
\(835\) | 9.91323 | 0.343061 | ||||||||
\(836\) | −2.81623 | −0.0974013 | ||||||||
\(837\) | 10.9044 | 0.376910 | ||||||||
\(838\) | −16.8076 | −0.580610 | ||||||||
\(839\) | −33.1175 | −1.14334 | −0.571672 | − | 0.820483i | \(-0.693705\pi\) | ||||
−0.571672 | + | 0.820483i | \(0.693705\pi\) | |||||||
\(840\) | 16.6793 | 0.575492 | ||||||||
\(841\) | −26.0941 | −0.899797 | ||||||||
\(842\) | −17.2956 | −0.596046 | ||||||||
\(843\) | −19.7182 | −0.679130 | ||||||||
\(844\) | −6.91765 | −0.238115 | ||||||||
\(845\) | 17.7951 | 0.612169 | ||||||||
\(846\) | 4.74897 | 0.163273 | ||||||||
\(847\) | 53.4060 | 1.83505 | ||||||||
\(848\) | 1.75975 | 0.0604301 | ||||||||
\(849\) | 40.3114 | 1.38348 | ||||||||
\(850\) | −63.7076 | −2.18515 | ||||||||
\(851\) | −11.9449 | −0.409466 | ||||||||
\(852\) | −1.11349 | −0.0381477 | ||||||||
\(853\) | −54.7531 | −1.87471 | −0.937354 | − | 0.348377i | \(-0.886733\pi\) | ||||
−0.937354 | + | 0.348377i | \(0.886733\pi\) | |||||||
\(854\) | −30.2358 | −1.03465 | ||||||||
\(855\) | −1.54086 | −0.0526964 | ||||||||
\(856\) | −14.4937 | −0.495385 | ||||||||
\(857\) | −26.4355 | −0.903020 | −0.451510 | − | 0.892266i | \(-0.649114\pi\) | ||||
−0.451510 | + | 0.892266i | \(0.649114\pi\) | |||||||
\(858\) | −23.7116 | −0.809502 | ||||||||
\(859\) | 22.4718 | 0.766729 | 0.383364 | − | 0.923597i | \(-0.374765\pi\) | ||||
0.383364 | + | 0.923597i | \(0.374765\pi\) | |||||||
\(860\) | 49.3350 | 1.68231 | ||||||||
\(861\) | −37.7012 | −1.28485 | ||||||||
\(862\) | 19.9251 | 0.678652 | ||||||||
\(863\) | −6.70965 | −0.228399 | −0.114200 | − | 0.993458i | \(-0.536430\pi\) | ||||
−0.114200 | + | 0.993458i | \(0.536430\pi\) | |||||||
\(864\) | 5.62809 | 0.191472 | ||||||||
\(865\) | −47.8212 | −1.62597 | ||||||||
\(866\) | −33.0782 | −1.12404 | ||||||||
\(867\) | −31.7557 | −1.07848 | ||||||||
\(868\) | 5.52278 | 0.187455 | ||||||||
\(869\) | 63.7858 | 2.16378 | ||||||||
\(870\) | 9.97471 | 0.338174 | ||||||||
\(871\) | 23.1984 | 0.786046 | ||||||||
\(872\) | 16.7151 | 0.566045 | ||||||||
\(873\) | 9.44727 | 0.319742 | ||||||||
\(874\) | −1.19295 | −0.0403521 | ||||||||
\(875\) | −59.1400 | −1.99930 | ||||||||
\(876\) | 15.8120 | 0.534237 | ||||||||
\(877\) | −41.1863 | −1.39076 | −0.695381 | − | 0.718641i | \(-0.744765\pi\) | ||||
−0.695381 | + | 0.718641i | \(0.744765\pi\) | |||||||
\(878\) | −2.33731 | −0.0788803 | ||||||||
\(879\) | −35.7329 | −1.20524 | ||||||||
\(880\) | −21.3322 | −0.719108 | ||||||||
\(881\) | −7.02626 | −0.236721 | −0.118360 | − | 0.992971i | \(-0.537764\pi\) | ||||
−0.118360 | + | 0.992971i | \(0.537764\pi\) | |||||||
\(882\) | −0.858200 | −0.0288971 | ||||||||
\(883\) | 18.3987 | 0.619166 | 0.309583 | − | 0.950872i | \(-0.399811\pi\) | ||||
0.309583 | + | 0.950872i | \(0.399811\pi\) | |||||||
\(884\) | −17.9747 | −0.604554 | ||||||||
\(885\) | 59.2821 | 1.99274 | ||||||||
\(886\) | −38.6638 | −1.29893 | ||||||||
\(887\) | −39.3363 | −1.32078 | −0.660392 | − | 0.750921i | \(-0.729610\pi\) | ||||
−0.660392 | + | 0.750921i | \(0.729610\pi\) | |||||||
\(888\) | 7.73487 | 0.259565 | ||||||||
\(889\) | −7.45465 | −0.250021 | ||||||||
\(890\) | −73.2532 | −2.45545 | ||||||||
\(891\) | −33.4289 | −1.11991 | ||||||||
\(892\) | −4.84079 | −0.162082 | ||||||||
\(893\) | 3.21579 | 0.107612 | ||||||||
\(894\) | −30.8410 | −1.03148 | ||||||||
\(895\) | −55.8578 | −1.86712 | ||||||||
\(896\) | 2.85048 | 0.0952279 | ||||||||
\(897\) | −10.0442 | −0.335366 | ||||||||
\(898\) | −27.9726 | −0.933457 | ||||||||
\(899\) | 3.30277 | 0.110154 | ||||||||
\(900\) | −7.85826 | −0.261942 | ||||||||
\(901\) | −10.8807 | −0.362487 | ||||||||
\(902\) | 48.2183 | 1.60549 | ||||||||
\(903\) | 53.7702 | 1.78936 | ||||||||
\(904\) | 4.78584 | 0.159175 | ||||||||
\(905\) | 76.4572 | 2.54152 | ||||||||
\(906\) | 2.46514 | 0.0818989 | ||||||||
\(907\) | 28.3747 | 0.942166 | 0.471083 | − | 0.882089i | \(-0.343863\pi\) | ||||
0.471083 | + | 0.882089i | \(0.343863\pi\) | |||||||
\(908\) | −12.7637 | −0.423580 | ||||||||
\(909\) | −4.45825 | −0.147871 | ||||||||
\(910\) | −32.4169 | −1.07461 | ||||||||
\(911\) | −30.6980 | −1.01707 | −0.508536 | − | 0.861041i | \(-0.669813\pi\) | ||||
−0.508536 | + | 0.861041i | \(0.669813\pi\) | |||||||
\(912\) | 0.772490 | 0.0255797 | ||||||||
\(913\) | −51.9194 | −1.71828 | ||||||||
\(914\) | 5.37327 | 0.177732 | ||||||||
\(915\) | −62.0674 | −2.05189 | ||||||||
\(916\) | −15.3170 | −0.506086 | ||||||||
\(917\) | 61.6231 | 2.03497 | ||||||||
\(918\) | −34.7989 | −1.14853 | ||||||||
\(919\) | −55.5616 | −1.83281 | −0.916404 | − | 0.400254i | \(-0.868922\pi\) | ||||
−0.916404 | + | 0.400254i | \(0.868922\pi\) | |||||||
\(920\) | −9.03628 | −0.297917 | ||||||||
\(921\) | −7.17750 | −0.236507 | ||||||||
\(922\) | 15.0988 | 0.497253 | ||||||||
\(923\) | 2.16412 | 0.0712328 | ||||||||
\(924\) | −23.2500 | −0.764868 | ||||||||
\(925\) | −53.2814 | −1.75188 | ||||||||
\(926\) | 14.1717 | 0.465711 | ||||||||
\(927\) | 7.90704 | 0.259701 | ||||||||
\(928\) | 1.70467 | 0.0559584 | ||||||||
\(929\) | 21.2688 | 0.697808 | 0.348904 | − | 0.937158i | \(-0.386554\pi\) | ||||
0.348904 | + | 0.937158i | \(0.386554\pi\) | |||||||
\(930\) | 11.3370 | 0.371756 | ||||||||
\(931\) | −0.581136 | −0.0190460 | ||||||||
\(932\) | 0.614597 | 0.0201318 | ||||||||
\(933\) | 0.207974 | 0.00680877 | ||||||||
\(934\) | 31.2076 | 1.02114 | ||||||||
\(935\) | 131.898 | 4.31354 | ||||||||
\(936\) | −2.21716 | −0.0724701 | ||||||||
\(937\) | 5.45972 | 0.178361 | 0.0891807 | − | 0.996015i | \(-0.471575\pi\) | ||||
0.0891807 | + | 0.996015i | \(0.471575\pi\) | |||||||
\(938\) | 22.7467 | 0.742706 | ||||||||
\(939\) | −36.3754 | −1.18707 | ||||||||
\(940\) | 24.3588 | 0.794497 | ||||||||
\(941\) | 53.2700 | 1.73655 | 0.868277 | − | 0.496080i | \(-0.165228\pi\) | ||||
0.868277 | + | 0.496080i | \(0.165228\pi\) | |||||||
\(942\) | −32.5753 | −1.06136 | ||||||||
\(943\) | 20.4252 | 0.665135 | ||||||||
\(944\) | 10.1312 | 0.329744 | ||||||||
\(945\) | −62.7590 | −2.04155 | ||||||||
\(946\) | −68.7699 | −2.23590 | ||||||||
\(947\) | 3.57908 | 0.116304 | 0.0581522 | − | 0.998308i | \(-0.481479\pi\) | ||||
0.0581522 | + | 0.998308i | \(0.481479\pi\) | |||||||
\(948\) | −17.4964 | −0.568257 | ||||||||
\(949\) | −30.7312 | −0.997576 | ||||||||
\(950\) | −5.32127 | −0.172645 | ||||||||
\(951\) | −26.4917 | −0.859052 | ||||||||
\(952\) | −17.6247 | −0.571221 | ||||||||
\(953\) | −23.1390 | −0.749544 | −0.374772 | − | 0.927117i | \(-0.622279\pi\) | ||||
−0.374772 | + | 0.927117i | \(0.622279\pi\) | |||||||
\(954\) | −1.34212 | −0.0434527 | ||||||||
\(955\) | 3.35854 | 0.108680 | ||||||||
\(956\) | 9.56775 | 0.309443 | ||||||||
\(957\) | −13.9041 | −0.449457 | ||||||||
\(958\) | −24.4964 | −0.791442 | ||||||||
\(959\) | 47.7171 | 1.54087 | ||||||||
\(960\) | 5.85141 | 0.188854 | ||||||||
\(961\) | −27.2461 | −0.878908 | ||||||||
\(962\) | −15.0330 | −0.484684 | ||||||||
\(963\) | 11.0540 | 0.356210 | ||||||||
\(964\) | −11.1574 | −0.359355 | ||||||||
\(965\) | −29.4331 | −0.947485 | ||||||||
\(966\) | −9.84865 | −0.316875 | ||||||||
\(967\) | 49.9955 | 1.60775 | 0.803874 | − | 0.594800i | \(-0.202769\pi\) | ||||
0.803874 | + | 0.594800i | \(0.202769\pi\) | |||||||
\(968\) | 18.7358 | 0.602190 | ||||||||
\(969\) | −4.77636 | −0.153439 | ||||||||
\(970\) | 48.4578 | 1.55588 | ||||||||
\(971\) | 2.75022 | 0.0882587 | 0.0441294 | − | 0.999026i | \(-0.485949\pi\) | ||||
0.0441294 | + | 0.999026i | \(0.485949\pi\) | |||||||
\(972\) | −7.71476 | −0.247451 | ||||||||
\(973\) | 49.2785 | 1.57980 | ||||||||
\(974\) | 7.59090 | 0.243228 | ||||||||
\(975\) | −44.8032 | −1.43485 | ||||||||
\(976\) | −10.6073 | −0.339530 | ||||||||
\(977\) | −54.1191 | −1.73142 | −0.865712 | − | 0.500543i | \(-0.833134\pi\) | ||||
−0.865712 | + | 0.500543i | \(0.833134\pi\) | |||||||
\(978\) | 6.48998 | 0.207527 | ||||||||
\(979\) | 102.110 | 3.26346 | ||||||||
\(980\) | −4.40195 | −0.140615 | ||||||||
\(981\) | −12.7482 | −0.407018 | ||||||||
\(982\) | 22.3729 | 0.713949 | ||||||||
\(983\) | 32.1045 | 1.02397 | 0.511987 | − | 0.858993i | \(-0.328910\pi\) | ||||
0.511987 | + | 0.858993i | \(0.328910\pi\) | |||||||
\(984\) | −13.2262 | −0.421637 | ||||||||
\(985\) | 24.3638 | 0.776294 | ||||||||
\(986\) | −10.5401 | −0.335664 | ||||||||
\(987\) | 26.5487 | 0.845054 | ||||||||
\(988\) | −1.50136 | −0.0477647 | ||||||||
\(989\) | −29.1308 | −0.926306 | ||||||||
\(990\) | 16.2695 | 0.517080 | ||||||||
\(991\) | 2.29004 | 0.0727455 | 0.0363728 | − | 0.999338i | \(-0.488420\pi\) | ||||
0.0363728 | + | 0.999338i | \(0.488420\pi\) | |||||||
\(992\) | 1.93749 | 0.0615153 | ||||||||
\(993\) | −43.8531 | −1.39164 | ||||||||
\(994\) | 2.12198 | 0.0673052 | ||||||||
\(995\) | −32.7288 | −1.03757 | ||||||||
\(996\) | 14.2415 | 0.451258 | ||||||||
\(997\) | −0.679662 | −0.0215251 | −0.0107626 | − | 0.999942i | \(-0.503426\pi\) | ||||
−0.0107626 | + | 0.999942i | \(0.503426\pi\) | |||||||
\(998\) | 44.1792 | 1.39847 | ||||||||
\(999\) | −29.1038 | −0.920804 |
(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 | 6046.2.a.f.1.16 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.f.1.16 | ✓ | 67 | 1.1 | even | 1 | trivial |