Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6015,2,Mod(1,6015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6015, 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("6015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6015 = 3 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6015.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: | \(48.0300168158\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.894188 | 0.632287 | 0.316143 | − | 0.948711i | \(-0.397612\pi\) | ||||
0.316143 | + | 0.948711i | \(0.397612\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.20043 | −0.600214 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.894188 | 0.365051 | ||||||||
\(7\) | −1.23837 | −0.468061 | −0.234031 | − | 0.972229i | \(-0.575192\pi\) | ||||
−0.234031 | + | 0.972229i | \(0.575192\pi\) | |||||||
\(8\) | −2.86178 | −1.01179 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.894188 | −0.282767 | ||||||||
\(11\) | −2.33822 | −0.704999 | −0.352499 | − | 0.935812i | \(-0.614668\pi\) | ||||
−0.352499 | + | 0.935812i | \(0.614668\pi\) | |||||||
\(12\) | −1.20043 | −0.346534 | ||||||||
\(13\) | 2.73582 | 0.758781 | 0.379390 | − | 0.925237i | \(-0.376134\pi\) | ||||
0.379390 | + | 0.925237i | \(0.376134\pi\) | |||||||
\(14\) | −1.10734 | −0.295949 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.158119 | −0.0395298 | ||||||||
\(17\) | 2.62798 | 0.637380 | 0.318690 | − | 0.947859i | \(-0.396757\pi\) | ||||
0.318690 | + | 0.947859i | \(0.396757\pi\) | |||||||
\(18\) | 0.894188 | 0.210762 | ||||||||
\(19\) | 6.44686 | 1.47901 | 0.739506 | − | 0.673150i | \(-0.235059\pi\) | ||||
0.739506 | + | 0.673150i | \(0.235059\pi\) | |||||||
\(20\) | 1.20043 | 0.268424 | ||||||||
\(21\) | −1.23837 | −0.270235 | ||||||||
\(22\) | −2.09081 | −0.445761 | ||||||||
\(23\) | 0.252290 | 0.0526060 | 0.0263030 | − | 0.999654i | \(-0.491627\pi\) | ||||
0.0263030 | + | 0.999654i | \(0.491627\pi\) | |||||||
\(24\) | −2.86178 | −0.584159 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.44634 | 0.479767 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.48658 | 0.280937 | ||||||||
\(29\) | −4.04780 | −0.751658 | −0.375829 | − | 0.926689i | \(-0.622642\pi\) | ||||
−0.375829 | + | 0.926689i | \(0.622642\pi\) | |||||||
\(30\) | −0.894188 | −0.163256 | ||||||||
\(31\) | −3.99704 | −0.717890 | −0.358945 | − | 0.933359i | \(-0.616863\pi\) | ||||
−0.358945 | + | 0.933359i | \(0.616863\pi\) | |||||||
\(32\) | 5.58218 | 0.986799 | ||||||||
\(33\) | −2.33822 | −0.407031 | ||||||||
\(34\) | 2.34991 | 0.403007 | ||||||||
\(35\) | 1.23837 | 0.209323 | ||||||||
\(36\) | −1.20043 | −0.200071 | ||||||||
\(37\) | −5.94314 | −0.977046 | −0.488523 | − | 0.872551i | \(-0.662464\pi\) | ||||
−0.488523 | + | 0.872551i | \(0.662464\pi\) | |||||||
\(38\) | 5.76471 | 0.935159 | ||||||||
\(39\) | 2.73582 | 0.438082 | ||||||||
\(40\) | 2.86178 | 0.452488 | ||||||||
\(41\) | −7.32162 | −1.14344 | −0.571722 | − | 0.820447i | \(-0.693725\pi\) | ||||
−0.571722 | + | 0.820447i | \(0.693725\pi\) | |||||||
\(42\) | −1.10734 | −0.170866 | ||||||||
\(43\) | −6.68308 | −1.01916 | −0.509580 | − | 0.860423i | \(-0.670199\pi\) | ||||
−0.509580 | + | 0.860423i | \(0.670199\pi\) | |||||||
\(44\) | 2.80686 | 0.423150 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0.225594 | 0.0332621 | ||||||||
\(47\) | 9.58108 | 1.39754 | 0.698772 | − | 0.715344i | \(-0.253730\pi\) | ||||
0.698772 | + | 0.715344i | \(0.253730\pi\) | |||||||
\(48\) | −0.158119 | −0.0228226 | ||||||||
\(49\) | −5.46643 | −0.780919 | ||||||||
\(50\) | 0.894188 | 0.126457 | ||||||||
\(51\) | 2.62798 | 0.367991 | ||||||||
\(52\) | −3.28416 | −0.455431 | ||||||||
\(53\) | 7.13339 | 0.979847 | 0.489924 | − | 0.871765i | \(-0.337025\pi\) | ||||
0.489924 | + | 0.871765i | \(0.337025\pi\) | |||||||
\(54\) | 0.894188 | 0.121684 | ||||||||
\(55\) | 2.33822 | 0.315285 | ||||||||
\(56\) | 3.54396 | 0.473581 | ||||||||
\(57\) | 6.44686 | 0.853907 | ||||||||
\(58\) | −3.61950 | −0.475263 | ||||||||
\(59\) | −13.0441 | −1.69820 | −0.849099 | − | 0.528233i | \(-0.822855\pi\) | ||||
−0.849099 | + | 0.528233i | \(0.822855\pi\) | |||||||
\(60\) | 1.20043 | 0.154975 | ||||||||
\(61\) | 8.58250 | 1.09888 | 0.549438 | − | 0.835534i | \(-0.314842\pi\) | ||||
0.549438 | + | 0.835534i | \(0.314842\pi\) | |||||||
\(62\) | −3.57411 | −0.453912 | ||||||||
\(63\) | −1.23837 | −0.156020 | ||||||||
\(64\) | 5.30776 | 0.663470 | ||||||||
\(65\) | −2.73582 | −0.339337 | ||||||||
\(66\) | −2.09081 | −0.257360 | ||||||||
\(67\) | 2.37402 | 0.290032 | 0.145016 | − | 0.989429i | \(-0.453677\pi\) | ||||
0.145016 | + | 0.989429i | \(0.453677\pi\) | |||||||
\(68\) | −3.15470 | −0.382564 | ||||||||
\(69\) | 0.252290 | 0.0303721 | ||||||||
\(70\) | 1.10734 | 0.132352 | ||||||||
\(71\) | −8.87660 | −1.05346 | −0.526729 | − | 0.850033i | \(-0.676582\pi\) | ||||
−0.526729 | + | 0.850033i | \(0.676582\pi\) | |||||||
\(72\) | −2.86178 | −0.337265 | ||||||||
\(73\) | −12.6997 | −1.48638 | −0.743192 | − | 0.669078i | \(-0.766689\pi\) | ||||
−0.743192 | + | 0.669078i | \(0.766689\pi\) | |||||||
\(74\) | −5.31429 | −0.617773 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −7.73899 | −0.887723 | ||||||||
\(77\) | 2.89559 | 0.329983 | ||||||||
\(78\) | 2.44634 | 0.276993 | ||||||||
\(79\) | 5.00742 | 0.563379 | 0.281690 | − | 0.959506i | \(-0.409105\pi\) | ||||
0.281690 | + | 0.959506i | \(0.409105\pi\) | |||||||
\(80\) | 0.158119 | 0.0176783 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.54691 | −0.722985 | ||||||||
\(83\) | 15.7216 | 1.72567 | 0.862836 | − | 0.505484i | \(-0.168686\pi\) | ||||
0.862836 | + | 0.505484i | \(0.168686\pi\) | |||||||
\(84\) | 1.48658 | 0.162199 | ||||||||
\(85\) | −2.62798 | −0.285045 | ||||||||
\(86\) | −5.97593 | −0.644401 | ||||||||
\(87\) | −4.04780 | −0.433970 | ||||||||
\(88\) | 6.69147 | 0.713313 | ||||||||
\(89\) | −0.511577 | −0.0542271 | −0.0271135 | − | 0.999632i | \(-0.508632\pi\) | ||||
−0.0271135 | + | 0.999632i | \(0.508632\pi\) | |||||||
\(90\) | −0.894188 | −0.0942557 | ||||||||
\(91\) | −3.38797 | −0.355156 | ||||||||
\(92\) | −0.302855 | −0.0315748 | ||||||||
\(93\) | −3.99704 | −0.414474 | ||||||||
\(94\) | 8.56729 | 0.883649 | ||||||||
\(95\) | −6.44686 | −0.661434 | ||||||||
\(96\) | 5.58218 | 0.569729 | ||||||||
\(97\) | −8.25939 | −0.838614 | −0.419307 | − | 0.907845i | \(-0.637727\pi\) | ||||
−0.419307 | + | 0.907845i | \(0.637727\pi\) | |||||||
\(98\) | −4.88802 | −0.493764 | ||||||||
\(99\) | −2.33822 | −0.235000 | ||||||||
\(100\) | −1.20043 | −0.120043 | ||||||||
\(101\) | 8.20247 | 0.816177 | 0.408088 | − | 0.912942i | \(-0.366196\pi\) | ||||
0.408088 | + | 0.912942i | \(0.366196\pi\) | |||||||
\(102\) | 2.34991 | 0.232676 | ||||||||
\(103\) | −13.5598 | −1.33609 | −0.668045 | − | 0.744121i | \(-0.732869\pi\) | ||||
−0.668045 | + | 0.744121i | \(0.732869\pi\) | |||||||
\(104\) | −7.82933 | −0.767729 | ||||||||
\(105\) | 1.23837 | 0.120853 | ||||||||
\(106\) | 6.37860 | 0.619544 | ||||||||
\(107\) | −1.07130 | −0.103567 | −0.0517833 | − | 0.998658i | \(-0.516491\pi\) | ||||
−0.0517833 | + | 0.998658i | \(0.516491\pi\) | |||||||
\(108\) | −1.20043 | −0.115511 | ||||||||
\(109\) | −6.38693 | −0.611757 | −0.305878 | − | 0.952071i | \(-0.598950\pi\) | ||||
−0.305878 | + | 0.952071i | \(0.598950\pi\) | |||||||
\(110\) | 2.09081 | 0.199351 | ||||||||
\(111\) | −5.94314 | −0.564098 | ||||||||
\(112\) | 0.195811 | 0.0185024 | ||||||||
\(113\) | 7.79616 | 0.733401 | 0.366701 | − | 0.930339i | \(-0.380487\pi\) | ||||
0.366701 | + | 0.930339i | \(0.380487\pi\) | |||||||
\(114\) | 5.76471 | 0.539914 | ||||||||
\(115\) | −0.252290 | −0.0235261 | ||||||||
\(116\) | 4.85909 | 0.451156 | ||||||||
\(117\) | 2.73582 | 0.252927 | ||||||||
\(118\) | −11.6639 | −1.07375 | ||||||||
\(119\) | −3.25443 | −0.298333 | ||||||||
\(120\) | 2.86178 | 0.261244 | ||||||||
\(121\) | −5.53274 | −0.502977 | ||||||||
\(122\) | 7.67437 | 0.694805 | ||||||||
\(123\) | −7.32162 | −0.660168 | ||||||||
\(124\) | 4.79816 | 0.430887 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.10734 | −0.0986496 | ||||||||
\(127\) | −4.50707 | −0.399938 | −0.199969 | − | 0.979802i | \(-0.564084\pi\) | ||||
−0.199969 | + | 0.979802i | \(0.564084\pi\) | |||||||
\(128\) | −6.41823 | −0.567296 | ||||||||
\(129\) | −6.68308 | −0.588412 | ||||||||
\(130\) | −2.44634 | −0.214558 | ||||||||
\(131\) | 9.83424 | 0.859222 | 0.429611 | − | 0.903014i | \(-0.358651\pi\) | ||||
0.429611 | + | 0.903014i | \(0.358651\pi\) | |||||||
\(132\) | 2.80686 | 0.244306 | ||||||||
\(133\) | −7.98362 | −0.692268 | ||||||||
\(134\) | 2.12282 | 0.183383 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −7.52073 | −0.644897 | ||||||||
\(137\) | 7.76121 | 0.663085 | 0.331543 | − | 0.943440i | \(-0.392431\pi\) | ||||
0.331543 | + | 0.943440i | \(0.392431\pi\) | |||||||
\(138\) | 0.225594 | 0.0192039 | ||||||||
\(139\) | −20.5265 | −1.74103 | −0.870517 | − | 0.492139i | \(-0.836215\pi\) | ||||
−0.870517 | + | 0.492139i | \(0.836215\pi\) | |||||||
\(140\) | −1.48658 | −0.125639 | ||||||||
\(141\) | 9.58108 | 0.806873 | ||||||||
\(142\) | −7.93735 | −0.666088 | ||||||||
\(143\) | −6.39695 | −0.534940 | ||||||||
\(144\) | −0.158119 | −0.0131766 | ||||||||
\(145\) | 4.04780 | 0.336152 | ||||||||
\(146\) | −11.3559 | −0.939821 | ||||||||
\(147\) | −5.46643 | −0.450864 | ||||||||
\(148\) | 7.13431 | 0.586437 | ||||||||
\(149\) | −7.19674 | −0.589580 | −0.294790 | − | 0.955562i | \(-0.595250\pi\) | ||||
−0.294790 | + | 0.955562i | \(0.595250\pi\) | |||||||
\(150\) | 0.894188 | 0.0730102 | ||||||||
\(151\) | −17.6348 | −1.43510 | −0.717548 | − | 0.696509i | \(-0.754736\pi\) | ||||
−0.717548 | + | 0.696509i | \(0.754736\pi\) | |||||||
\(152\) | −18.4495 | −1.49645 | ||||||||
\(153\) | 2.62798 | 0.212460 | ||||||||
\(154\) | 2.58920 | 0.208644 | ||||||||
\(155\) | 3.99704 | 0.321050 | ||||||||
\(156\) | −3.28416 | −0.262943 | ||||||||
\(157\) | −14.1066 | −1.12583 | −0.562913 | − | 0.826516i | \(-0.690319\pi\) | ||||
−0.562913 | + | 0.826516i | \(0.690319\pi\) | |||||||
\(158\) | 4.47758 | 0.356217 | ||||||||
\(159\) | 7.13339 | 0.565715 | ||||||||
\(160\) | −5.58218 | −0.441310 | ||||||||
\(161\) | −0.312429 | −0.0246228 | ||||||||
\(162\) | 0.894188 | 0.0702541 | ||||||||
\(163\) | −16.7070 | −1.30859 | −0.654296 | − | 0.756238i | \(-0.727035\pi\) | ||||
−0.654296 | + | 0.756238i | \(0.727035\pi\) | |||||||
\(164\) | 8.78907 | 0.686311 | ||||||||
\(165\) | 2.33822 | 0.182030 | ||||||||
\(166\) | 14.0581 | 1.09112 | ||||||||
\(167\) | −20.7124 | −1.60277 | −0.801386 | − | 0.598148i | \(-0.795904\pi\) | ||||
−0.801386 | + | 0.598148i | \(0.795904\pi\) | |||||||
\(168\) | 3.54396 | 0.273422 | ||||||||
\(169\) | −5.51528 | −0.424252 | ||||||||
\(170\) | −2.34991 | −0.180230 | ||||||||
\(171\) | 6.44686 | 0.493004 | ||||||||
\(172\) | 8.02255 | 0.611714 | ||||||||
\(173\) | −11.0999 | −0.843908 | −0.421954 | − | 0.906617i | \(-0.638656\pi\) | ||||
−0.421954 | + | 0.906617i | \(0.638656\pi\) | |||||||
\(174\) | −3.61950 | −0.274393 | ||||||||
\(175\) | −1.23837 | −0.0936122 | ||||||||
\(176\) | 0.369717 | 0.0278685 | ||||||||
\(177\) | −13.0441 | −0.980456 | ||||||||
\(178\) | −0.457446 | −0.0342871 | ||||||||
\(179\) | −22.6227 | −1.69090 | −0.845448 | − | 0.534057i | \(-0.820667\pi\) | ||||
−0.845448 | + | 0.534057i | \(0.820667\pi\) | |||||||
\(180\) | 1.20043 | 0.0894746 | ||||||||
\(181\) | −21.9859 | −1.63420 | −0.817099 | − | 0.576498i | \(-0.804419\pi\) | ||||
−0.817099 | + | 0.576498i | \(0.804419\pi\) | |||||||
\(182\) | −3.02948 | −0.224560 | ||||||||
\(183\) | 8.58250 | 0.634436 | ||||||||
\(184\) | −0.721998 | −0.0532264 | ||||||||
\(185\) | 5.94314 | 0.436948 | ||||||||
\(186\) | −3.57411 | −0.262066 | ||||||||
\(187\) | −6.14480 | −0.449352 | ||||||||
\(188\) | −11.5014 | −0.838825 | ||||||||
\(189\) | −1.23837 | −0.0900784 | ||||||||
\(190\) | −5.76471 | −0.418216 | ||||||||
\(191\) | −3.62710 | −0.262448 | −0.131224 | − | 0.991353i | \(-0.541891\pi\) | ||||
−0.131224 | + | 0.991353i | \(0.541891\pi\) | |||||||
\(192\) | 5.30776 | 0.383055 | ||||||||
\(193\) | 18.8754 | 1.35868 | 0.679340 | − | 0.733824i | \(-0.262266\pi\) | ||||
0.679340 | + | 0.733824i | \(0.262266\pi\) | |||||||
\(194\) | −7.38545 | −0.530244 | ||||||||
\(195\) | −2.73582 | −0.195916 | ||||||||
\(196\) | 6.56205 | 0.468718 | ||||||||
\(197\) | −10.4283 | −0.742987 | −0.371494 | − | 0.928436i | \(-0.621154\pi\) | ||||
−0.371494 | + | 0.928436i | \(0.621154\pi\) | |||||||
\(198\) | −2.09081 | −0.148587 | ||||||||
\(199\) | 24.7050 | 1.75129 | 0.875646 | − | 0.482953i | \(-0.160436\pi\) | ||||
0.875646 | + | 0.482953i | \(0.160436\pi\) | |||||||
\(200\) | −2.86178 | −0.202359 | ||||||||
\(201\) | 2.37402 | 0.167450 | ||||||||
\(202\) | 7.33455 | 0.516057 | ||||||||
\(203\) | 5.01269 | 0.351822 | ||||||||
\(204\) | −3.15470 | −0.220874 | ||||||||
\(205\) | 7.32162 | 0.511364 | ||||||||
\(206\) | −12.1250 | −0.844792 | ||||||||
\(207\) | 0.252290 | 0.0175353 | ||||||||
\(208\) | −0.432586 | −0.0299945 | ||||||||
\(209\) | −15.0742 | −1.04270 | ||||||||
\(210\) | 1.10734 | 0.0764136 | ||||||||
\(211\) | −6.11184 | −0.420756 | −0.210378 | − | 0.977620i | \(-0.567469\pi\) | ||||
−0.210378 | + | 0.977620i | \(0.567469\pi\) | |||||||
\(212\) | −8.56312 | −0.588118 | ||||||||
\(213\) | −8.87660 | −0.608215 | ||||||||
\(214\) | −0.957945 | −0.0654838 | ||||||||
\(215\) | 6.68308 | 0.455782 | ||||||||
\(216\) | −2.86178 | −0.194720 | ||||||||
\(217\) | 4.94983 | 0.336016 | ||||||||
\(218\) | −5.71112 | −0.386806 | ||||||||
\(219\) | −12.6997 | −0.858165 | ||||||||
\(220\) | −2.80686 | −0.189238 | ||||||||
\(221\) | 7.18970 | 0.483632 | ||||||||
\(222\) | −5.31429 | −0.356672 | ||||||||
\(223\) | 1.81356 | 0.121445 | 0.0607225 | − | 0.998155i | \(-0.480660\pi\) | ||||
0.0607225 | + | 0.998155i | \(0.480660\pi\) | |||||||
\(224\) | −6.91282 | −0.461882 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 6.97124 | 0.463720 | ||||||||
\(227\) | −4.82939 | −0.320538 | −0.160269 | − | 0.987073i | \(-0.551236\pi\) | ||||
−0.160269 | + | 0.987073i | \(0.551236\pi\) | |||||||
\(228\) | −7.73899 | −0.512527 | ||||||||
\(229\) | −3.75378 | −0.248057 | −0.124028 | − | 0.992279i | \(-0.539581\pi\) | ||||
−0.124028 | + | 0.992279i | \(0.539581\pi\) | |||||||
\(230\) | −0.225594 | −0.0148752 | ||||||||
\(231\) | 2.89559 | 0.190516 | ||||||||
\(232\) | 11.5839 | 0.760523 | ||||||||
\(233\) | −7.14068 | −0.467801 | −0.233901 | − | 0.972261i | \(-0.575149\pi\) | ||||
−0.233901 | + | 0.972261i | \(0.575149\pi\) | |||||||
\(234\) | 2.44634 | 0.159922 | ||||||||
\(235\) | −9.58108 | −0.625001 | ||||||||
\(236\) | 15.6585 | 1.01928 | ||||||||
\(237\) | 5.00742 | 0.325267 | ||||||||
\(238\) | −2.91007 | −0.188632 | ||||||||
\(239\) | −18.6288 | −1.20500 | −0.602499 | − | 0.798119i | \(-0.705828\pi\) | ||||
−0.602499 | + | 0.798119i | \(0.705828\pi\) | |||||||
\(240\) | 0.158119 | 0.0102066 | ||||||||
\(241\) | 22.4227 | 1.44437 | 0.722186 | − | 0.691699i | \(-0.243138\pi\) | ||||
0.722186 | + | 0.691699i | \(0.243138\pi\) | |||||||
\(242\) | −4.94731 | −0.318025 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −10.3027 | −0.659560 | ||||||||
\(245\) | 5.46643 | 0.349238 | ||||||||
\(246\) | −6.54691 | −0.417415 | ||||||||
\(247\) | 17.6375 | 1.12225 | ||||||||
\(248\) | 11.4387 | 0.726356 | ||||||||
\(249\) | 15.7216 | 0.996317 | ||||||||
\(250\) | −0.894188 | −0.0565534 | ||||||||
\(251\) | 15.6303 | 0.986576 | 0.493288 | − | 0.869866i | \(-0.335795\pi\) | ||||
0.493288 | + | 0.869866i | \(0.335795\pi\) | |||||||
\(252\) | 1.48658 | 0.0936456 | ||||||||
\(253\) | −0.589908 | −0.0370872 | ||||||||
\(254\) | −4.03017 | −0.252875 | ||||||||
\(255\) | −2.62798 | −0.164571 | ||||||||
\(256\) | −16.3546 | −1.02216 | ||||||||
\(257\) | −9.45626 | −0.589865 | −0.294933 | − | 0.955518i | \(-0.595297\pi\) | ||||
−0.294933 | + | 0.955518i | \(0.595297\pi\) | |||||||
\(258\) | −5.97593 | −0.372045 | ||||||||
\(259\) | 7.35983 | 0.457317 | ||||||||
\(260\) | 3.28416 | 0.203675 | ||||||||
\(261\) | −4.04780 | −0.250553 | ||||||||
\(262\) | 8.79366 | 0.543274 | ||||||||
\(263\) | 0.547871 | 0.0337832 | 0.0168916 | − | 0.999857i | \(-0.494623\pi\) | ||||
0.0168916 | + | 0.999857i | \(0.494623\pi\) | |||||||
\(264\) | 6.69147 | 0.411832 | ||||||||
\(265\) | −7.13339 | −0.438201 | ||||||||
\(266\) | −7.13886 | −0.437711 | ||||||||
\(267\) | −0.511577 | −0.0313080 | ||||||||
\(268\) | −2.84983 | −0.174081 | ||||||||
\(269\) | −0.925980 | −0.0564580 | −0.0282290 | − | 0.999601i | \(-0.508987\pi\) | ||||
−0.0282290 | + | 0.999601i | \(0.508987\pi\) | |||||||
\(270\) | −0.894188 | −0.0544186 | ||||||||
\(271\) | 1.09783 | 0.0666882 | 0.0333441 | − | 0.999444i | \(-0.489384\pi\) | ||||
0.0333441 | + | 0.999444i | \(0.489384\pi\) | |||||||
\(272\) | −0.415535 | −0.0251955 | ||||||||
\(273\) | −3.38797 | −0.205049 | ||||||||
\(274\) | 6.93999 | 0.419260 | ||||||||
\(275\) | −2.33822 | −0.141000 | ||||||||
\(276\) | −0.302855 | −0.0182297 | ||||||||
\(277\) | −18.3973 | −1.10539 | −0.552693 | − | 0.833385i | \(-0.686400\pi\) | ||||
−0.552693 | + | 0.833385i | \(0.686400\pi\) | |||||||
\(278\) | −18.3545 | −1.10083 | ||||||||
\(279\) | −3.99704 | −0.239297 | ||||||||
\(280\) | −3.54396 | −0.211792 | ||||||||
\(281\) | 10.9689 | 0.654348 | 0.327174 | − | 0.944964i | \(-0.393904\pi\) | ||||
0.327174 | + | 0.944964i | \(0.393904\pi\) | |||||||
\(282\) | 8.56729 | 0.510175 | ||||||||
\(283\) | 14.9113 | 0.886388 | 0.443194 | − | 0.896426i | \(-0.353845\pi\) | ||||
0.443194 | + | 0.896426i | \(0.353845\pi\) | |||||||
\(284\) | 10.6557 | 0.632300 | ||||||||
\(285\) | −6.44686 | −0.381879 | ||||||||
\(286\) | −5.72007 | −0.338235 | ||||||||
\(287\) | 9.06690 | 0.535202 | ||||||||
\(288\) | 5.58218 | 0.328933 | ||||||||
\(289\) | −10.0937 | −0.593747 | ||||||||
\(290\) | 3.61950 | 0.212544 | ||||||||
\(291\) | −8.25939 | −0.484174 | ||||||||
\(292\) | 15.2450 | 0.892149 | ||||||||
\(293\) | 21.8589 | 1.27701 | 0.638504 | − | 0.769618i | \(-0.279554\pi\) | ||||
0.638504 | + | 0.769618i | \(0.279554\pi\) | |||||||
\(294\) | −4.88802 | −0.285075 | ||||||||
\(295\) | 13.0441 | 0.759458 | ||||||||
\(296\) | 17.0080 | 0.988569 | ||||||||
\(297\) | −2.33822 | −0.135677 | ||||||||
\(298\) | −6.43524 | −0.372783 | ||||||||
\(299\) | 0.690219 | 0.0399164 | ||||||||
\(300\) | −1.20043 | −0.0693067 | ||||||||
\(301\) | 8.27614 | 0.477029 | ||||||||
\(302\) | −15.7688 | −0.907392 | ||||||||
\(303\) | 8.20247 | 0.471220 | ||||||||
\(304\) | −1.01937 | −0.0584651 | ||||||||
\(305\) | −8.58250 | −0.491432 | ||||||||
\(306\) | 2.34991 | 0.134336 | ||||||||
\(307\) | −3.59398 | −0.205119 | −0.102560 | − | 0.994727i | \(-0.532703\pi\) | ||||
−0.102560 | + | 0.994727i | \(0.532703\pi\) | |||||||
\(308\) | −3.47594 | −0.198060 | ||||||||
\(309\) | −13.5598 | −0.771392 | ||||||||
\(310\) | 3.57411 | 0.202996 | ||||||||
\(311\) | 14.1229 | 0.800839 | 0.400419 | − | 0.916332i | \(-0.368864\pi\) | ||||
0.400419 | + | 0.916332i | \(0.368864\pi\) | |||||||
\(312\) | −7.82933 | −0.443249 | ||||||||
\(313\) | 0.158146 | 0.00893895 | 0.00446947 | − | 0.999990i | \(-0.498577\pi\) | ||||
0.00446947 | + | 0.999990i | \(0.498577\pi\) | |||||||
\(314\) | −12.6139 | −0.711845 | ||||||||
\(315\) | 1.23837 | 0.0697744 | ||||||||
\(316\) | −6.01105 | −0.338148 | ||||||||
\(317\) | 1.95832 | 0.109990 | 0.0549952 | − | 0.998487i | \(-0.482486\pi\) | ||||
0.0549952 | + | 0.998487i | \(0.482486\pi\) | |||||||
\(318\) | 6.37860 | 0.357694 | ||||||||
\(319\) | 9.46464 | 0.529918 | ||||||||
\(320\) | −5.30776 | −0.296713 | ||||||||
\(321\) | −1.07130 | −0.0597942 | ||||||||
\(322\) | −0.279370 | −0.0155687 | ||||||||
\(323\) | 16.9423 | 0.942692 | ||||||||
\(324\) | −1.20043 | −0.0666904 | ||||||||
\(325\) | 2.73582 | 0.151756 | ||||||||
\(326\) | −14.9392 | −0.827405 | ||||||||
\(327\) | −6.38693 | −0.353198 | ||||||||
\(328\) | 20.9529 | 1.15693 | ||||||||
\(329\) | −11.8650 | −0.654136 | ||||||||
\(330\) | 2.09081 | 0.115095 | ||||||||
\(331\) | −3.56211 | −0.195791 | −0.0978955 | − | 0.995197i | \(-0.531211\pi\) | ||||
−0.0978955 | + | 0.995197i | \(0.531211\pi\) | |||||||
\(332\) | −18.8727 | −1.03577 | ||||||||
\(333\) | −5.94314 | −0.325682 | ||||||||
\(334\) | −18.5208 | −1.01341 | ||||||||
\(335\) | −2.37402 | −0.129706 | ||||||||
\(336\) | 0.195811 | 0.0106824 | ||||||||
\(337\) | −15.8481 | −0.863299 | −0.431649 | − | 0.902041i | \(-0.642068\pi\) | ||||
−0.431649 | + | 0.902041i | \(0.642068\pi\) | |||||||
\(338\) | −4.93169 | −0.268249 | ||||||||
\(339\) | 7.79616 | 0.423429 | ||||||||
\(340\) | 3.15470 | 0.171088 | ||||||||
\(341\) | 9.34595 | 0.506111 | ||||||||
\(342\) | 5.76471 | 0.311720 | ||||||||
\(343\) | 15.4381 | 0.833579 | ||||||||
\(344\) | 19.1255 | 1.03118 | ||||||||
\(345\) | −0.252290 | −0.0135828 | ||||||||
\(346\) | −9.92538 | −0.533592 | ||||||||
\(347\) | −13.4216 | −0.720511 | −0.360256 | − | 0.932854i | \(-0.617311\pi\) | ||||
−0.360256 | + | 0.932854i | \(0.617311\pi\) | |||||||
\(348\) | 4.85909 | 0.260475 | ||||||||
\(349\) | 4.04184 | 0.216355 | 0.108177 | − | 0.994132i | \(-0.465499\pi\) | ||||
0.108177 | + | 0.994132i | \(0.465499\pi\) | |||||||
\(350\) | −1.10734 | −0.0591897 | ||||||||
\(351\) | 2.73582 | 0.146027 | ||||||||
\(352\) | −13.0523 | −0.695693 | ||||||||
\(353\) | −6.67569 | −0.355311 | −0.177656 | − | 0.984093i | \(-0.556851\pi\) | ||||
−0.177656 | + | 0.984093i | \(0.556851\pi\) | |||||||
\(354\) | −11.6639 | −0.619929 | ||||||||
\(355\) | 8.87660 | 0.471121 | ||||||||
\(356\) | 0.614112 | 0.0325478 | ||||||||
\(357\) | −3.25443 | −0.172242 | ||||||||
\(358\) | −20.2289 | −1.06913 | ||||||||
\(359\) | 20.1867 | 1.06541 | 0.532707 | − | 0.846300i | \(-0.321175\pi\) | ||||
0.532707 | + | 0.846300i | \(0.321175\pi\) | |||||||
\(360\) | 2.86178 | 0.150829 | ||||||||
\(361\) | 22.5620 | 1.18747 | ||||||||
\(362\) | −19.6595 | −1.03328 | ||||||||
\(363\) | −5.53274 | −0.290394 | ||||||||
\(364\) | 4.06701 | 0.213169 | ||||||||
\(365\) | 12.6997 | 0.664732 | ||||||||
\(366\) | 7.67437 | 0.401146 | ||||||||
\(367\) | 9.43628 | 0.492570 | 0.246285 | − | 0.969197i | \(-0.420790\pi\) | ||||
0.246285 | + | 0.969197i | \(0.420790\pi\) | |||||||
\(368\) | −0.0398919 | −0.00207951 | ||||||||
\(369\) | −7.32162 | −0.381148 | ||||||||
\(370\) | 5.31429 | 0.276277 | ||||||||
\(371\) | −8.83380 | −0.458628 | ||||||||
\(372\) | 4.79816 | 0.248773 | ||||||||
\(373\) | 18.2109 | 0.942923 | 0.471461 | − | 0.881887i | \(-0.343727\pi\) | ||||
0.471461 | + | 0.881887i | \(0.343727\pi\) | |||||||
\(374\) | −5.49461 | −0.284119 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −27.4190 | −1.41403 | ||||||||
\(377\) | −11.0741 | −0.570344 | ||||||||
\(378\) | −1.10734 | −0.0569554 | ||||||||
\(379\) | −5.25106 | −0.269729 | −0.134864 | − | 0.990864i | \(-0.543060\pi\) | ||||
−0.134864 | + | 0.990864i | \(0.543060\pi\) | |||||||
\(380\) | 7.73899 | 0.397002 | ||||||||
\(381\) | −4.50707 | −0.230904 | ||||||||
\(382\) | −3.24331 | −0.165942 | ||||||||
\(383\) | 27.3701 | 1.39854 | 0.699272 | − | 0.714855i | \(-0.253507\pi\) | ||||
0.699272 | + | 0.714855i | \(0.253507\pi\) | |||||||
\(384\) | −6.41823 | −0.327529 | ||||||||
\(385\) | −2.89559 | −0.147573 | ||||||||
\(386\) | 16.8782 | 0.859075 | ||||||||
\(387\) | −6.68308 | −0.339720 | ||||||||
\(388\) | 9.91480 | 0.503348 | ||||||||
\(389\) | −27.0288 | −1.37041 | −0.685207 | − | 0.728349i | \(-0.740288\pi\) | ||||
−0.685207 | + | 0.728349i | \(0.740288\pi\) | |||||||
\(390\) | −2.44634 | −0.123875 | ||||||||
\(391\) | 0.663013 | 0.0335300 | ||||||||
\(392\) | 15.6438 | 0.790129 | ||||||||
\(393\) | 9.83424 | 0.496072 | ||||||||
\(394\) | −9.32488 | −0.469781 | ||||||||
\(395\) | −5.00742 | −0.251951 | ||||||||
\(396\) | 2.80686 | 0.141050 | ||||||||
\(397\) | −9.61301 | −0.482463 | −0.241232 | − | 0.970468i | \(-0.577551\pi\) | ||||
−0.241232 | + | 0.970468i | \(0.577551\pi\) | |||||||
\(398\) | 22.0909 | 1.10732 | ||||||||
\(399\) | −7.98362 | −0.399681 | ||||||||
\(400\) | −0.158119 | −0.00790597 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 2.12282 | 0.105876 | ||||||||
\(403\) | −10.9352 | −0.544721 | ||||||||
\(404\) | −9.84647 | −0.489880 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 4.48229 | 0.222452 | ||||||||
\(407\) | 13.8964 | 0.688817 | ||||||||
\(408\) | −7.52073 | −0.372331 | ||||||||
\(409\) | 36.3963 | 1.79968 | 0.899841 | − | 0.436218i | \(-0.143682\pi\) | ||||
0.899841 | + | 0.436218i | \(0.143682\pi\) | |||||||
\(410\) | 6.54691 | 0.323329 | ||||||||
\(411\) | 7.76121 | 0.382832 | ||||||||
\(412\) | 16.2776 | 0.801940 | ||||||||
\(413\) | 16.1535 | 0.794861 | ||||||||
\(414\) | 0.225594 | 0.0110874 | ||||||||
\(415\) | −15.7216 | −0.771744 | ||||||||
\(416\) | 15.2719 | 0.748764 | ||||||||
\(417\) | −20.5265 | −1.00519 | ||||||||
\(418\) | −13.4791 | −0.659286 | ||||||||
\(419\) | 17.9732 | 0.878050 | 0.439025 | − | 0.898475i | \(-0.355324\pi\) | ||||
0.439025 | + | 0.898475i | \(0.355324\pi\) | |||||||
\(420\) | −1.48658 | −0.0725375 | ||||||||
\(421\) | −7.56122 | −0.368511 | −0.184256 | − | 0.982878i | \(-0.558987\pi\) | ||||
−0.184256 | + | 0.982878i | \(0.558987\pi\) | |||||||
\(422\) | −5.46513 | −0.266038 | ||||||||
\(423\) | 9.58108 | 0.465848 | ||||||||
\(424\) | −20.4142 | −0.991403 | ||||||||
\(425\) | 2.62798 | 0.127476 | ||||||||
\(426\) | −7.93735 | −0.384566 | ||||||||
\(427\) | −10.6283 | −0.514341 | ||||||||
\(428\) | 1.28602 | 0.0621621 | ||||||||
\(429\) | −6.39695 | −0.308847 | ||||||||
\(430\) | 5.97593 | 0.288185 | ||||||||
\(431\) | 38.1848 | 1.83930 | 0.919649 | − | 0.392742i | \(-0.128474\pi\) | ||||
0.919649 | + | 0.392742i | \(0.128474\pi\) | |||||||
\(432\) | −0.158119 | −0.00760752 | ||||||||
\(433\) | 14.8475 | 0.713525 | 0.356762 | − | 0.934195i | \(-0.383881\pi\) | ||||
0.356762 | + | 0.934195i | \(0.383881\pi\) | |||||||
\(434\) | 4.42608 | 0.212459 | ||||||||
\(435\) | 4.04780 | 0.194077 | ||||||||
\(436\) | 7.66704 | 0.367185 | ||||||||
\(437\) | 1.62648 | 0.0778049 | ||||||||
\(438\) | −11.3559 | −0.542606 | ||||||||
\(439\) | 4.53100 | 0.216253 | 0.108126 | − | 0.994137i | \(-0.465515\pi\) | ||||
0.108126 | + | 0.994137i | \(0.465515\pi\) | |||||||
\(440\) | −6.69147 | −0.319003 | ||||||||
\(441\) | −5.46643 | −0.260306 | ||||||||
\(442\) | 6.42895 | 0.305794 | ||||||||
\(443\) | 4.37559 | 0.207891 | 0.103945 | − | 0.994583i | \(-0.466853\pi\) | ||||
0.103945 | + | 0.994583i | \(0.466853\pi\) | |||||||
\(444\) | 7.13431 | 0.338579 | ||||||||
\(445\) | 0.511577 | 0.0242511 | ||||||||
\(446\) | 1.62166 | 0.0767880 | ||||||||
\(447\) | −7.19674 | −0.340394 | ||||||||
\(448\) | −6.57299 | −0.310544 | ||||||||
\(449\) | −14.4095 | −0.680027 | −0.340014 | − | 0.940420i | \(-0.610432\pi\) | ||||
−0.340014 | + | 0.940420i | \(0.610432\pi\) | |||||||
\(450\) | 0.894188 | 0.0421524 | ||||||||
\(451\) | 17.1195 | 0.806127 | ||||||||
\(452\) | −9.35873 | −0.440197 | ||||||||
\(453\) | −17.6348 | −0.828553 | ||||||||
\(454\) | −4.31838 | −0.202672 | ||||||||
\(455\) | 3.38797 | 0.158830 | ||||||||
\(456\) | −18.4495 | −0.863978 | ||||||||
\(457\) | 23.8458 | 1.11546 | 0.557729 | − | 0.830023i | \(-0.311673\pi\) | ||||
0.557729 | + | 0.830023i | \(0.311673\pi\) | |||||||
\(458\) | −3.35658 | −0.156843 | ||||||||
\(459\) | 2.62798 | 0.122664 | ||||||||
\(460\) | 0.302855 | 0.0141207 | ||||||||
\(461\) | 2.05310 | 0.0956226 | 0.0478113 | − | 0.998856i | \(-0.484775\pi\) | ||||
0.0478113 | + | 0.998856i | \(0.484775\pi\) | |||||||
\(462\) | 2.58920 | 0.120460 | ||||||||
\(463\) | −4.02036 | −0.186842 | −0.0934210 | − | 0.995627i | \(-0.529780\pi\) | ||||
−0.0934210 | + | 0.995627i | \(0.529780\pi\) | |||||||
\(464\) | 0.640036 | 0.0297129 | ||||||||
\(465\) | 3.99704 | 0.185358 | ||||||||
\(466\) | −6.38511 | −0.295784 | ||||||||
\(467\) | −12.1488 | −0.562178 | −0.281089 | − | 0.959682i | \(-0.590696\pi\) | ||||
−0.281089 | + | 0.959682i | \(0.590696\pi\) | |||||||
\(468\) | −3.28416 | −0.151810 | ||||||||
\(469\) | −2.93992 | −0.135753 | ||||||||
\(470\) | −8.56729 | −0.395180 | ||||||||
\(471\) | −14.1066 | −0.649996 | ||||||||
\(472\) | 37.3294 | 1.71823 | ||||||||
\(473\) | 15.6265 | 0.718507 | ||||||||
\(474\) | 4.47758 | 0.205662 | ||||||||
\(475\) | 6.44686 | 0.295802 | ||||||||
\(476\) | 3.90670 | 0.179063 | ||||||||
\(477\) | 7.13339 | 0.326616 | ||||||||
\(478\) | −16.6577 | −0.761905 | ||||||||
\(479\) | 5.23016 | 0.238972 | 0.119486 | − | 0.992836i | \(-0.461875\pi\) | ||||
0.119486 | + | 0.992836i | \(0.461875\pi\) | |||||||
\(480\) | −5.58218 | −0.254791 | ||||||||
\(481\) | −16.2594 | −0.741364 | ||||||||
\(482\) | 20.0501 | 0.913257 | ||||||||
\(483\) | −0.312429 | −0.0142160 | ||||||||
\(484\) | 6.64165 | 0.301893 | ||||||||
\(485\) | 8.25939 | 0.375040 | ||||||||
\(486\) | 0.894188 | 0.0405612 | ||||||||
\(487\) | −19.2870 | −0.873979 | −0.436989 | − | 0.899467i | \(-0.643955\pi\) | ||||
−0.436989 | + | 0.899467i | \(0.643955\pi\) | |||||||
\(488\) | −24.5613 | −1.11184 | ||||||||
\(489\) | −16.7070 | −0.755516 | ||||||||
\(490\) | 4.88802 | 0.220818 | ||||||||
\(491\) | −9.18328 | −0.414436 | −0.207218 | − | 0.978295i | \(-0.566441\pi\) | ||||
−0.207218 | + | 0.978295i | \(0.566441\pi\) | |||||||
\(492\) | 8.78907 | 0.396242 | ||||||||
\(493\) | −10.6376 | −0.479092 | ||||||||
\(494\) | 15.7712 | 0.709580 | ||||||||
\(495\) | 2.33822 | 0.105095 | ||||||||
\(496\) | 0.632009 | 0.0283781 | ||||||||
\(497\) | 10.9925 | 0.493083 | ||||||||
\(498\) | 14.0581 | 0.629958 | ||||||||
\(499\) | −8.60218 | −0.385087 | −0.192543 | − | 0.981288i | \(-0.561674\pi\) | ||||
−0.192543 | + | 0.981288i | \(0.561674\pi\) | |||||||
\(500\) | 1.20043 | 0.0536847 | ||||||||
\(501\) | −20.7124 | −0.925361 | ||||||||
\(502\) | 13.9764 | 0.623799 | ||||||||
\(503\) | 4.71685 | 0.210314 | 0.105157 | − | 0.994456i | \(-0.466465\pi\) | ||||
0.105157 | + | 0.994456i | \(0.466465\pi\) | |||||||
\(504\) | 3.54396 | 0.157860 | ||||||||
\(505\) | −8.20247 | −0.365005 | ||||||||
\(506\) | −0.527488 | −0.0234497 | ||||||||
\(507\) | −5.51528 | −0.244942 | ||||||||
\(508\) | 5.41041 | 0.240048 | ||||||||
\(509\) | −11.6534 | −0.516527 | −0.258264 | − | 0.966074i | \(-0.583150\pi\) | ||||
−0.258264 | + | 0.966074i | \(0.583150\pi\) | |||||||
\(510\) | −2.34991 | −0.104056 | ||||||||
\(511\) | 15.7269 | 0.695719 | ||||||||
\(512\) | −1.78766 | −0.0790041 | ||||||||
\(513\) | 6.44686 | 0.284636 | ||||||||
\(514\) | −8.45567 | −0.372964 | ||||||||
\(515\) | 13.5598 | 0.597518 | ||||||||
\(516\) | 8.02255 | 0.353173 | ||||||||
\(517\) | −22.4027 | −0.985268 | ||||||||
\(518\) | 6.58107 | 0.289156 | ||||||||
\(519\) | −11.0999 | −0.487231 | ||||||||
\(520\) | 7.82933 | 0.343339 | ||||||||
\(521\) | 14.5413 | 0.637064 | 0.318532 | − | 0.947912i | \(-0.396810\pi\) | ||||
0.318532 | + | 0.947912i | \(0.396810\pi\) | |||||||
\(522\) | −3.61950 | −0.158421 | ||||||||
\(523\) | −24.4936 | −1.07103 | −0.535515 | − | 0.844526i | \(-0.679883\pi\) | ||||
−0.535515 | + | 0.844526i | \(0.679883\pi\) | |||||||
\(524\) | −11.8053 | −0.515717 | ||||||||
\(525\) | −1.23837 | −0.0540470 | ||||||||
\(526\) | 0.489899 | 0.0213606 | ||||||||
\(527\) | −10.5042 | −0.457568 | ||||||||
\(528\) | 0.369717 | 0.0160899 | ||||||||
\(529\) | −22.9363 | −0.997233 | ||||||||
\(530\) | −6.37860 | −0.277069 | ||||||||
\(531\) | −13.0441 | −0.566066 | ||||||||
\(532\) | 9.58375 | 0.415508 | ||||||||
\(533\) | −20.0307 | −0.867624 | ||||||||
\(534\) | −0.457446 | −0.0197956 | ||||||||
\(535\) | 1.07130 | 0.0463164 | ||||||||
\(536\) | −6.79392 | −0.293453 | ||||||||
\(537\) | −22.6227 | −0.976240 | ||||||||
\(538\) | −0.828000 | −0.0356976 | ||||||||
\(539\) | 12.7817 | 0.550547 | ||||||||
\(540\) | 1.20043 | 0.0516582 | ||||||||
\(541\) | −10.6550 | −0.458095 | −0.229048 | − | 0.973415i | \(-0.573561\pi\) | ||||
−0.229048 | + | 0.973415i | \(0.573561\pi\) | |||||||
\(542\) | 0.981663 | 0.0421660 | ||||||||
\(543\) | −21.9859 | −0.943504 | ||||||||
\(544\) | 14.6699 | 0.628966 | ||||||||
\(545\) | 6.38693 | 0.273586 | ||||||||
\(546\) | −3.02948 | −0.129650 | ||||||||
\(547\) | −13.5171 | −0.577947 | −0.288974 | − | 0.957337i | \(-0.593314\pi\) | ||||
−0.288974 | + | 0.957337i | \(0.593314\pi\) | |||||||
\(548\) | −9.31677 | −0.397993 | ||||||||
\(549\) | 8.58250 | 0.366292 | ||||||||
\(550\) | −2.09081 | −0.0891523 | ||||||||
\(551\) | −26.0956 | −1.11171 | ||||||||
\(552\) | −0.721998 | −0.0307303 | ||||||||
\(553\) | −6.20106 | −0.263696 | ||||||||
\(554\) | −16.4506 | −0.698921 | ||||||||
\(555\) | 5.94314 | 0.252272 | ||||||||
\(556\) | 24.6406 | 1.04499 | ||||||||
\(557\) | 15.8094 | 0.669865 | 0.334933 | − | 0.942242i | \(-0.391286\pi\) | ||||
0.334933 | + | 0.942242i | \(0.391286\pi\) | |||||||
\(558\) | −3.57411 | −0.151304 | ||||||||
\(559\) | −18.2837 | −0.773319 | ||||||||
\(560\) | −0.195811 | −0.00827451 | ||||||||
\(561\) | −6.14480 | −0.259434 | ||||||||
\(562\) | 9.80824 | 0.413736 | ||||||||
\(563\) | −9.59235 | −0.404270 | −0.202135 | − | 0.979358i | \(-0.564788\pi\) | ||||
−0.202135 | + | 0.979358i | \(0.564788\pi\) | |||||||
\(564\) | −11.5014 | −0.484296 | ||||||||
\(565\) | −7.79616 | −0.327987 | ||||||||
\(566\) | 13.3336 | 0.560451 | ||||||||
\(567\) | −1.23837 | −0.0520068 | ||||||||
\(568\) | 25.4029 | 1.06588 | ||||||||
\(569\) | −25.6094 | −1.07360 | −0.536800 | − | 0.843709i | \(-0.680367\pi\) | ||||
−0.536800 | + | 0.843709i | \(0.680367\pi\) | |||||||
\(570\) | −5.76471 | −0.241457 | ||||||||
\(571\) | 35.5587 | 1.48809 | 0.744043 | − | 0.668132i | \(-0.232906\pi\) | ||||
0.744043 | + | 0.668132i | \(0.232906\pi\) | |||||||
\(572\) | 7.67907 | 0.321078 | ||||||||
\(573\) | −3.62710 | −0.151524 | ||||||||
\(574\) | 8.10751 | 0.338401 | ||||||||
\(575\) | 0.252290 | 0.0105212 | ||||||||
\(576\) | 5.30776 | 0.221157 | ||||||||
\(577\) | −12.9952 | −0.540997 | −0.270498 | − | 0.962720i | \(-0.587188\pi\) | ||||
−0.270498 | + | 0.962720i | \(0.587188\pi\) | |||||||
\(578\) | −9.02566 | −0.375418 | ||||||||
\(579\) | 18.8754 | 0.784434 | ||||||||
\(580\) | −4.85909 | −0.201763 | ||||||||
\(581\) | −19.4692 | −0.807720 | ||||||||
\(582\) | −7.38545 | −0.306137 | ||||||||
\(583\) | −16.6794 | −0.690791 | ||||||||
\(584\) | 36.3437 | 1.50391 | ||||||||
\(585\) | −2.73582 | −0.113112 | ||||||||
\(586\) | 19.5459 | 0.807435 | ||||||||
\(587\) | 19.0102 | 0.784636 | 0.392318 | − | 0.919830i | \(-0.371673\pi\) | ||||
0.392318 | + | 0.919830i | \(0.371673\pi\) | |||||||
\(588\) | 6.56205 | 0.270615 | ||||||||
\(589\) | −25.7684 | −1.06177 | ||||||||
\(590\) | 11.6639 | 0.480195 | ||||||||
\(591\) | −10.4283 | −0.428964 | ||||||||
\(592\) | 0.939726 | 0.0386225 | ||||||||
\(593\) | 16.6492 | 0.683702 | 0.341851 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341851 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(594\) | −2.09081 | −0.0857868 | ||||||||
\(595\) | 3.25443 | 0.133418 | ||||||||
\(596\) | 8.63916 | 0.353874 | ||||||||
\(597\) | 24.7050 | 1.01111 | ||||||||
\(598\) | 0.617186 | 0.0252386 | ||||||||
\(599\) | −2.54859 | −0.104133 | −0.0520663 | − | 0.998644i | \(-0.516581\pi\) | ||||
−0.0520663 | + | 0.998644i | \(0.516581\pi\) | |||||||
\(600\) | −2.86178 | −0.116832 | ||||||||
\(601\) | −5.38650 | −0.219720 | −0.109860 | − | 0.993947i | \(-0.535040\pi\) | ||||
−0.109860 | + | 0.993947i | \(0.535040\pi\) | |||||||
\(602\) | 7.40043 | 0.301619 | ||||||||
\(603\) | 2.37402 | 0.0966774 | ||||||||
\(604\) | 21.1693 | 0.861365 | ||||||||
\(605\) | 5.53274 | 0.224938 | ||||||||
\(606\) | 7.33455 | 0.297946 | ||||||||
\(607\) | 27.2500 | 1.10604 | 0.553021 | − | 0.833167i | \(-0.313475\pi\) | ||||
0.553021 | + | 0.833167i | \(0.313475\pi\) | |||||||
\(608\) | 35.9875 | 1.45949 | ||||||||
\(609\) | 5.01269 | 0.203124 | ||||||||
\(610\) | −7.67437 | −0.310726 | ||||||||
\(611\) | 26.2121 | 1.06043 | ||||||||
\(612\) | −3.15470 | −0.127521 | ||||||||
\(613\) | 27.8673 | 1.12555 | 0.562775 | − | 0.826610i | \(-0.309734\pi\) | ||||
0.562775 | + | 0.826610i | \(0.309734\pi\) | |||||||
\(614\) | −3.21369 | −0.129694 | ||||||||
\(615\) | 7.32162 | 0.295236 | ||||||||
\(616\) | −8.28654 | −0.333874 | ||||||||
\(617\) | −3.90079 | −0.157040 | −0.0785199 | − | 0.996913i | \(-0.525019\pi\) | ||||
−0.0785199 | + | 0.996913i | \(0.525019\pi\) | |||||||
\(618\) | −12.1250 | −0.487741 | ||||||||
\(619\) | 23.0232 | 0.925379 | 0.462689 | − | 0.886520i | \(-0.346885\pi\) | ||||
0.462689 | + | 0.886520i | \(0.346885\pi\) | |||||||
\(620\) | −4.79816 | −0.192699 | ||||||||
\(621\) | 0.252290 | 0.0101240 | ||||||||
\(622\) | 12.6286 | 0.506360 | ||||||||
\(623\) | 0.633524 | 0.0253816 | ||||||||
\(624\) | −0.432586 | −0.0173173 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.141412 | 0.00565198 | ||||||||
\(627\) | −15.0742 | −0.602004 | ||||||||
\(628\) | 16.9339 | 0.675736 | ||||||||
\(629\) | −15.6185 | −0.622750 | ||||||||
\(630\) | 1.10734 | 0.0441174 | ||||||||
\(631\) | −28.5584 | −1.13689 | −0.568447 | − | 0.822720i | \(-0.692455\pi\) | ||||
−0.568447 | + | 0.822720i | \(0.692455\pi\) | |||||||
\(632\) | −14.3302 | −0.570023 | ||||||||
\(633\) | −6.11184 | −0.242924 | ||||||||
\(634\) | 1.75111 | 0.0695454 | ||||||||
\(635\) | 4.50707 | 0.178858 | ||||||||
\(636\) | −8.56312 | −0.339550 | ||||||||
\(637\) | −14.9552 | −0.592546 | ||||||||
\(638\) | 8.46317 | 0.335060 | ||||||||
\(639\) | −8.87660 | −0.351153 | ||||||||
\(640\) | 6.41823 | 0.253703 | ||||||||
\(641\) | 6.40836 | 0.253115 | 0.126558 | − | 0.991959i | \(-0.459607\pi\) | ||||
0.126558 | + | 0.991959i | \(0.459607\pi\) | |||||||
\(642\) | −0.957945 | −0.0378071 | ||||||||
\(643\) | 49.0025 | 1.93247 | 0.966234 | − | 0.257665i | \(-0.0829531\pi\) | ||||
0.966234 | + | 0.257665i | \(0.0829531\pi\) | |||||||
\(644\) | 0.375048 | 0.0147790 | ||||||||
\(645\) | 6.68308 | 0.263146 | ||||||||
\(646\) | 15.1496 | 0.596052 | ||||||||
\(647\) | −17.0173 | −0.669020 | −0.334510 | − | 0.942392i | \(-0.608571\pi\) | ||||
−0.334510 | + | 0.942392i | \(0.608571\pi\) | |||||||
\(648\) | −2.86178 | −0.112422 | ||||||||
\(649\) | 30.5000 | 1.19723 | ||||||||
\(650\) | 2.44634 | 0.0959534 | ||||||||
\(651\) | 4.94983 | 0.193999 | ||||||||
\(652\) | 20.0555 | 0.785435 | ||||||||
\(653\) | −0.168620 | −0.00659862 | −0.00329931 | − | 0.999995i | \(-0.501050\pi\) | ||||
−0.00329931 | + | 0.999995i | \(0.501050\pi\) | |||||||
\(654\) | −5.71112 | −0.223322 | ||||||||
\(655\) | −9.83424 | −0.384256 | ||||||||
\(656\) | 1.15769 | 0.0452002 | ||||||||
\(657\) | −12.6997 | −0.495462 | ||||||||
\(658\) | −10.6095 | −0.413602 | ||||||||
\(659\) | −6.27007 | −0.244247 | −0.122124 | − | 0.992515i | \(-0.538970\pi\) | ||||
−0.122124 | + | 0.992515i | \(0.538970\pi\) | |||||||
\(660\) | −2.80686 | −0.109257 | ||||||||
\(661\) | 36.3017 | 1.41197 | 0.705986 | − | 0.708225i | \(-0.250504\pi\) | ||||
0.705986 | + | 0.708225i | \(0.250504\pi\) | |||||||
\(662\) | −3.18519 | −0.123796 | ||||||||
\(663\) | 7.18970 | 0.279225 | ||||||||
\(664\) | −44.9919 | −1.74602 | ||||||||
\(665\) | 7.98362 | 0.309591 | ||||||||
\(666\) | −5.31429 | −0.205924 | ||||||||
\(667\) | −1.02122 | −0.0395417 | ||||||||
\(668\) | 24.8637 | 0.962005 | ||||||||
\(669\) | 1.81356 | 0.0701163 | ||||||||
\(670\) | −2.12282 | −0.0820116 | ||||||||
\(671\) | −20.0677 | −0.774706 | ||||||||
\(672\) | −6.91282 | −0.266668 | ||||||||
\(673\) | −36.9261 | −1.42340 | −0.711698 | − | 0.702485i | \(-0.752074\pi\) | ||||
−0.711698 | + | 0.702485i | \(0.752074\pi\) | |||||||
\(674\) | −14.1711 | −0.545852 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 6.62069 | 0.254642 | ||||||||
\(677\) | −6.02639 | −0.231613 | −0.115807 | − | 0.993272i | \(-0.536945\pi\) | ||||
−0.115807 | + | 0.993272i | \(0.536945\pi\) | |||||||
\(678\) | 6.97124 | 0.267729 | ||||||||
\(679\) | 10.2282 | 0.392523 | ||||||||
\(680\) | 7.52073 | 0.288407 | ||||||||
\(681\) | −4.82939 | −0.185062 | ||||||||
\(682\) | 8.35704 | 0.320007 | ||||||||
\(683\) | 23.9474 | 0.916323 | 0.458161 | − | 0.888869i | \(-0.348508\pi\) | ||||
0.458161 | + | 0.888869i | \(0.348508\pi\) | |||||||
\(684\) | −7.73899 | −0.295908 | ||||||||
\(685\) | −7.76121 | −0.296541 | ||||||||
\(686\) | 13.8046 | 0.527061 | ||||||||
\(687\) | −3.75378 | −0.143216 | ||||||||
\(688\) | 1.05672 | 0.0402872 | ||||||||
\(689\) | 19.5157 | 0.743489 | ||||||||
\(690\) | −0.225594 | −0.00858823 | ||||||||
\(691\) | 34.0282 | 1.29449 | 0.647247 | − | 0.762281i | \(-0.275920\pi\) | ||||
0.647247 | + | 0.762281i | \(0.275920\pi\) | |||||||
\(692\) | 13.3246 | 0.506525 | ||||||||
\(693\) | 2.89559 | 0.109994 | ||||||||
\(694\) | −12.0015 | −0.455570 | ||||||||
\(695\) | 20.5265 | 0.778614 | ||||||||
\(696\) | 11.5839 | 0.439088 | ||||||||
\(697\) | −19.2411 | −0.728809 | ||||||||
\(698\) | 3.61417 | 0.136798 | ||||||||
\(699\) | −7.14068 | −0.270085 | ||||||||
\(700\) | 1.48658 | 0.0561873 | ||||||||
\(701\) | −38.8971 | −1.46912 | −0.734561 | − | 0.678542i | \(-0.762612\pi\) | ||||
−0.734561 | + | 0.678542i | \(0.762612\pi\) | |||||||
\(702\) | 2.44634 | 0.0923312 | ||||||||
\(703\) | −38.3146 | −1.44506 | ||||||||
\(704\) | −12.4107 | −0.467746 | ||||||||
\(705\) | −9.58108 | −0.360845 | ||||||||
\(706\) | −5.96932 | −0.224658 | ||||||||
\(707\) | −10.1577 | −0.382020 | ||||||||
\(708\) | 15.6585 | 0.588483 | ||||||||
\(709\) | −24.2856 | −0.912064 | −0.456032 | − | 0.889963i | \(-0.650730\pi\) | ||||
−0.456032 | + | 0.889963i | \(0.650730\pi\) | |||||||
\(710\) | 7.93735 | 0.297884 | ||||||||
\(711\) | 5.00742 | 0.187793 | ||||||||
\(712\) | 1.46402 | 0.0548666 | ||||||||
\(713\) | −1.00841 | −0.0377653 | ||||||||
\(714\) | −2.91007 | −0.108907 | ||||||||
\(715\) | 6.39695 | 0.239232 | ||||||||
\(716\) | 27.1569 | 1.01490 | ||||||||
\(717\) | −18.6288 | −0.695706 | ||||||||
\(718\) | 18.0507 | 0.673647 | ||||||||
\(719\) | 30.3900 | 1.13336 | 0.566678 | − | 0.823939i | \(-0.308228\pi\) | ||||
0.566678 | + | 0.823939i | \(0.308228\pi\) | |||||||
\(720\) | 0.158119 | 0.00589276 | ||||||||
\(721\) | 16.7921 | 0.625372 | ||||||||
\(722\) | 20.1747 | 0.750824 | ||||||||
\(723\) | 22.4227 | 0.833908 | ||||||||
\(724\) | 26.3925 | 0.980868 | ||||||||
\(725\) | −4.04780 | −0.150332 | ||||||||
\(726\) | −4.94731 | −0.183612 | ||||||||
\(727\) | 3.98401 | 0.147759 | 0.0738793 | − | 0.997267i | \(-0.476462\pi\) | ||||
0.0738793 | + | 0.997267i | \(0.476462\pi\) | |||||||
\(728\) | 9.69564 | 0.359344 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.3559 | 0.420301 | ||||||||
\(731\) | −17.5630 | −0.649592 | ||||||||
\(732\) | −10.3027 | −0.380797 | ||||||||
\(733\) | 42.7431 | 1.57875 | 0.789376 | − | 0.613910i | \(-0.210404\pi\) | ||||
0.789376 | + | 0.613910i | \(0.210404\pi\) | |||||||
\(734\) | 8.43781 | 0.311445 | ||||||||
\(735\) | 5.46643 | 0.201632 | ||||||||
\(736\) | 1.40833 | 0.0519116 | ||||||||
\(737\) | −5.55096 | −0.204472 | ||||||||
\(738\) | −6.54691 | −0.240995 | ||||||||
\(739\) | −38.6570 | −1.42202 | −0.711010 | − | 0.703182i | \(-0.751762\pi\) | ||||
−0.711010 | + | 0.703182i | \(0.751762\pi\) | |||||||
\(740\) | −7.13431 | −0.262262 | ||||||||
\(741\) | 17.6375 | 0.647928 | ||||||||
\(742\) | −7.89908 | −0.289984 | ||||||||
\(743\) | 48.0976 | 1.76453 | 0.882265 | − | 0.470752i | \(-0.156017\pi\) | ||||
0.882265 | + | 0.470752i | \(0.156017\pi\) | |||||||
\(744\) | 11.4387 | 0.419362 | ||||||||
\(745\) | 7.19674 | 0.263668 | ||||||||
\(746\) | 16.2839 | 0.596197 | ||||||||
\(747\) | 15.7216 | 0.575224 | ||||||||
\(748\) | 7.37638 | 0.269707 | ||||||||
\(749\) | 1.32667 | 0.0484755 | ||||||||
\(750\) | −0.894188 | −0.0326511 | ||||||||
\(751\) | −46.7733 | −1.70678 | −0.853391 | − | 0.521272i | \(-0.825458\pi\) | ||||
−0.853391 | + | 0.521272i | \(0.825458\pi\) | |||||||
\(752\) | −1.51495 | −0.0552447 | ||||||||
\(753\) | 15.6303 | 0.569600 | ||||||||
\(754\) | −9.90230 | −0.360621 | ||||||||
\(755\) | 17.6348 | 0.641795 | ||||||||
\(756\) | 1.48658 | 0.0540663 | ||||||||
\(757\) | 5.76736 | 0.209618 | 0.104809 | − | 0.994492i | \(-0.466577\pi\) | ||||
0.104809 | + | 0.994492i | \(0.466577\pi\) | |||||||
\(758\) | −4.69544 | −0.170546 | ||||||||
\(759\) | −0.589908 | −0.0214123 | ||||||||
\(760\) | 18.4495 | 0.669235 | ||||||||
\(761\) | 14.9700 | 0.542662 | 0.271331 | − | 0.962486i | \(-0.412536\pi\) | ||||
0.271331 | + | 0.962486i | \(0.412536\pi\) | |||||||
\(762\) | −4.03017 | −0.145998 | ||||||||
\(763\) | 7.90940 | 0.286340 | ||||||||
\(764\) | 4.35407 | 0.157525 | ||||||||
\(765\) | −2.62798 | −0.0950150 | ||||||||
\(766\) | 24.4740 | 0.884281 | ||||||||
\(767\) | −35.6864 | −1.28856 | ||||||||
\(768\) | −16.3546 | −0.590147 | ||||||||
\(769\) | −35.5597 | −1.28232 | −0.641158 | − | 0.767409i | \(-0.721546\pi\) | ||||
−0.641158 | + | 0.767409i | \(0.721546\pi\) | |||||||
\(770\) | −2.58920 | −0.0933082 | ||||||||
\(771\) | −9.45626 | −0.340559 | ||||||||
\(772\) | −22.6585 | −0.815498 | ||||||||
\(773\) | −11.3942 | −0.409821 | −0.204911 | − | 0.978781i | \(-0.565690\pi\) | ||||
−0.204911 | + | 0.978781i | \(0.565690\pi\) | |||||||
\(774\) | −5.97593 | −0.214800 | ||||||||
\(775\) | −3.99704 | −0.143578 | ||||||||
\(776\) | 23.6366 | 0.848504 | ||||||||
\(777\) | 7.35983 | 0.264032 | ||||||||
\(778\) | −24.1688 | −0.866494 | ||||||||
\(779\) | −47.2015 | −1.69117 | ||||||||
\(780\) | 3.28416 | 0.117592 | ||||||||
\(781\) | 20.7554 | 0.742687 | ||||||||
\(782\) | 0.592858 | 0.0212006 | ||||||||
\(783\) | −4.04780 | −0.144657 | ||||||||
\(784\) | 0.864349 | 0.0308696 | ||||||||
\(785\) | 14.1066 | 0.503485 | ||||||||
\(786\) | 8.79366 | 0.313660 | ||||||||
\(787\) | 15.8265 | 0.564153 | 0.282076 | − | 0.959392i | \(-0.408977\pi\) | ||||
0.282076 | + | 0.959392i | \(0.408977\pi\) | |||||||
\(788\) | 12.5184 | 0.445951 | ||||||||
\(789\) | 0.547871 | 0.0195047 | ||||||||
\(790\) | −4.47758 | −0.159305 | ||||||||
\(791\) | −9.65456 | −0.343277 | ||||||||
\(792\) | 6.69147 | 0.237771 | ||||||||
\(793\) | 23.4802 | 0.833806 | ||||||||
\(794\) | −8.59584 | −0.305055 | ||||||||
\(795\) | −7.13339 | −0.252995 | ||||||||
\(796\) | −29.6566 | −1.05115 | ||||||||
\(797\) | 6.49567 | 0.230088 | 0.115044 | − | 0.993360i | \(-0.463299\pi\) | ||||
0.115044 | + | 0.993360i | \(0.463299\pi\) | |||||||
\(798\) | −7.13886 | −0.252713 | ||||||||
\(799\) | 25.1789 | 0.890767 | ||||||||
\(800\) | 5.58218 | 0.197360 | ||||||||
\(801\) | −0.511577 | −0.0180757 | ||||||||
\(802\) | 0.894188 | 0.0315749 | ||||||||
\(803\) | 29.6946 | 1.04790 | ||||||||
\(804\) | −2.84983 | −0.100506 | ||||||||
\(805\) | 0.312429 | 0.0110117 | ||||||||
\(806\) | −9.77812 | −0.344420 | ||||||||
\(807\) | −0.925980 | −0.0325960 | ||||||||
\(808\) | −23.4737 | −0.825802 | ||||||||
\(809\) | −11.3612 | −0.399439 | −0.199719 | − | 0.979853i | \(-0.564003\pi\) | ||||
−0.199719 | + | 0.979853i | \(0.564003\pi\) | |||||||
\(810\) | −0.894188 | −0.0314186 | ||||||||
\(811\) | −3.57942 | −0.125690 | −0.0628452 | − | 0.998023i | \(-0.520017\pi\) | ||||
−0.0628452 | + | 0.998023i | \(0.520017\pi\) | |||||||
\(812\) | −6.01737 | −0.211168 | ||||||||
\(813\) | 1.09783 | 0.0385024 | ||||||||
\(814\) | 12.4260 | 0.435530 | ||||||||
\(815\) | 16.7070 | 0.585220 | ||||||||
\(816\) | −0.415535 | −0.0145466 | ||||||||
\(817\) | −43.0849 | −1.50735 | ||||||||
\(818\) | 32.5452 | 1.13791 | ||||||||
\(819\) | −3.38797 | −0.118385 | ||||||||
\(820\) | −8.78907 | −0.306928 | ||||||||
\(821\) | 36.7564 | 1.28281 | 0.641404 | − | 0.767203i | \(-0.278352\pi\) | ||||
0.641404 | + | 0.767203i | \(0.278352\pi\) | |||||||
\(822\) | 6.93999 | 0.242060 | ||||||||
\(823\) | −43.1865 | −1.50539 | −0.752693 | − | 0.658371i | \(-0.771246\pi\) | ||||
−0.752693 | + | 0.658371i | \(0.771246\pi\) | |||||||
\(824\) | 38.8053 | 1.35185 | ||||||||
\(825\) | −2.33822 | −0.0814063 | ||||||||
\(826\) | 14.4443 | 0.502580 | ||||||||
\(827\) | −49.2282 | −1.71183 | −0.855916 | − | 0.517115i | \(-0.827006\pi\) | ||||
−0.855916 | + | 0.517115i | \(0.827006\pi\) | |||||||
\(828\) | −0.302855 | −0.0105249 | ||||||||
\(829\) | −17.3300 | −0.601895 | −0.300948 | − | 0.953641i | \(-0.597303\pi\) | ||||
−0.300948 | + | 0.953641i | \(0.597303\pi\) | |||||||
\(830\) | −14.0581 | −0.487963 | ||||||||
\(831\) | −18.3973 | −0.638195 | ||||||||
\(832\) | 14.5211 | 0.503428 | ||||||||
\(833\) | −14.3657 | −0.497742 | ||||||||
\(834\) | −18.3545 | −0.635566 | ||||||||
\(835\) | 20.7124 | 0.716781 | ||||||||
\(836\) | 18.0954 | 0.625844 | ||||||||
\(837\) | −3.99704 | −0.138158 | ||||||||
\(838\) | 16.0715 | 0.555179 | ||||||||
\(839\) | 48.5427 | 1.67588 | 0.837940 | − | 0.545762i | \(-0.183760\pi\) | ||||
0.837940 | + | 0.545762i | \(0.183760\pi\) | |||||||
\(840\) | −3.54396 | −0.122278 | ||||||||
\(841\) | −12.6153 | −0.435010 | ||||||||
\(842\) | −6.76115 | −0.233005 | ||||||||
\(843\) | 10.9689 | 0.377788 | ||||||||
\(844\) | 7.33681 | 0.252544 | ||||||||
\(845\) | 5.51528 | 0.189731 | ||||||||
\(846\) | 8.56729 | 0.294550 | ||||||||
\(847\) | 6.85160 | 0.235424 | ||||||||
\(848\) | −1.12793 | −0.0387332 | ||||||||
\(849\) | 14.9113 | 0.511756 | ||||||||
\(850\) | 2.34991 | 0.0806014 | ||||||||
\(851\) | −1.49939 | −0.0513985 | ||||||||
\(852\) | 10.6557 | 0.365059 | ||||||||
\(853\) | −37.3764 | −1.27974 | −0.639872 | − | 0.768482i | \(-0.721012\pi\) | ||||
−0.639872 | + | 0.768482i | \(0.721012\pi\) | |||||||
\(854\) | −9.50373 | −0.325211 | ||||||||
\(855\) | −6.44686 | −0.220478 | ||||||||
\(856\) | 3.06583 | 0.104788 | ||||||||
\(857\) | −10.1630 | −0.347162 | −0.173581 | − | 0.984820i | \(-0.555534\pi\) | ||||
−0.173581 | + | 0.984820i | \(0.555534\pi\) | |||||||
\(858\) | −5.72007 | −0.195280 | ||||||||
\(859\) | −45.9498 | −1.56779 | −0.783894 | − | 0.620895i | \(-0.786769\pi\) | ||||
−0.783894 | + | 0.620895i | \(0.786769\pi\) | |||||||
\(860\) | −8.02255 | −0.273567 | ||||||||
\(861\) | 9.06690 | 0.308999 | ||||||||
\(862\) | 34.1444 | 1.16296 | ||||||||
\(863\) | 36.5510 | 1.24421 | 0.622105 | − | 0.782934i | \(-0.286278\pi\) | ||||
0.622105 | + | 0.782934i | \(0.286278\pi\) | |||||||
\(864\) | 5.58218 | 0.189910 | ||||||||
\(865\) | 11.0999 | 0.377407 | ||||||||
\(866\) | 13.2764 | 0.451152 | ||||||||
\(867\) | −10.0937 | −0.342800 | ||||||||
\(868\) | −5.94191 | −0.201682 | ||||||||
\(869\) | −11.7084 | −0.397182 | ||||||||
\(870\) | 3.61950 | 0.122712 | ||||||||
\(871\) | 6.49488 | 0.220071 | ||||||||
\(872\) | 18.2780 | 0.618972 | ||||||||
\(873\) | −8.25939 | −0.279538 | ||||||||
\(874\) | 1.45438 | 0.0491950 | ||||||||
\(875\) | 1.23837 | 0.0418647 | ||||||||
\(876\) | 15.2450 | 0.515082 | ||||||||
\(877\) | 6.64708 | 0.224456 | 0.112228 | − | 0.993682i | \(-0.464201\pi\) | ||||
0.112228 | + | 0.993682i | \(0.464201\pi\) | |||||||
\(878\) | 4.05157 | 0.136734 | ||||||||
\(879\) | 21.8589 | 0.737281 | ||||||||
\(880\) | −0.369717 | −0.0124632 | ||||||||
\(881\) | −33.7476 | −1.13698 | −0.568492 | − | 0.822689i | \(-0.692473\pi\) | ||||
−0.568492 | + | 0.822689i | \(0.692473\pi\) | |||||||
\(882\) | −4.88802 | −0.164588 | ||||||||
\(883\) | −44.1013 | −1.48413 | −0.742063 | − | 0.670330i | \(-0.766153\pi\) | ||||
−0.742063 | + | 0.670330i | \(0.766153\pi\) | |||||||
\(884\) | −8.63071 | −0.290282 | ||||||||
\(885\) | 13.0441 | 0.438473 | ||||||||
\(886\) | 3.91260 | 0.131446 | ||||||||
\(887\) | 26.1653 | 0.878544 | 0.439272 | − | 0.898354i | \(-0.355237\pi\) | ||||
0.439272 | + | 0.898354i | \(0.355237\pi\) | |||||||
\(888\) | 17.0080 | 0.570751 | ||||||||
\(889\) | 5.58143 | 0.187195 | ||||||||
\(890\) | 0.457446 | 0.0153336 | ||||||||
\(891\) | −2.33822 | −0.0783332 | ||||||||
\(892\) | −2.17705 | −0.0728930 | ||||||||
\(893\) | 61.7679 | 2.06698 | ||||||||
\(894\) | −6.43524 | −0.215227 | ||||||||
\(895\) | 22.6227 | 0.756192 | ||||||||
\(896\) | 7.94816 | 0.265529 | ||||||||
\(897\) | 0.690219 | 0.0230458 | ||||||||
\(898\) | −12.8848 | −0.429972 | ||||||||
\(899\) | 16.1792 | 0.539608 | ||||||||
\(900\) | −1.20043 | −0.0400142 | ||||||||
\(901\) | 18.7465 | 0.624535 | ||||||||
\(902\) | 15.3081 | 0.509704 | ||||||||
\(903\) | 8.27614 | 0.275413 | ||||||||
\(904\) | −22.3109 | −0.742051 | ||||||||
\(905\) | 21.9859 | 0.730835 | ||||||||
\(906\) | −15.7688 | −0.523883 | ||||||||
\(907\) | 7.53650 | 0.250245 | 0.125123 | − | 0.992141i | \(-0.460068\pi\) | ||||
0.125123 | + | 0.992141i | \(0.460068\pi\) | |||||||
\(908\) | 5.79733 | 0.192391 | ||||||||
\(909\) | 8.20247 | 0.272059 | ||||||||
\(910\) | 3.02948 | 0.100426 | ||||||||
\(911\) | 21.9719 | 0.727962 | 0.363981 | − | 0.931406i | \(-0.381417\pi\) | ||||
0.363981 | + | 0.931406i | \(0.381417\pi\) | |||||||
\(912\) | −1.01937 | −0.0337548 | ||||||||
\(913\) | −36.7606 | −1.21660 | ||||||||
\(914\) | 21.3226 | 0.705289 | ||||||||
\(915\) | −8.58250 | −0.283729 | ||||||||
\(916\) | 4.50614 | 0.148887 | ||||||||
\(917\) | −12.1785 | −0.402168 | ||||||||
\(918\) | 2.34991 | 0.0775587 | ||||||||
\(919\) | 8.33852 | 0.275062 | 0.137531 | − | 0.990497i | \(-0.456083\pi\) | ||||
0.137531 | + | 0.990497i | \(0.456083\pi\) | |||||||
\(920\) | 0.721998 | 0.0238036 | ||||||||
\(921\) | −3.59398 | −0.118426 | ||||||||
\(922\) | 1.83586 | 0.0604609 | ||||||||
\(923\) | −24.2848 | −0.799344 | ||||||||
\(924\) | −3.47594 | −0.114350 | ||||||||
\(925\) | −5.94314 | −0.195409 | ||||||||
\(926\) | −3.59496 | −0.118138 | ||||||||
\(927\) | −13.5598 | −0.445364 | ||||||||
\(928\) | −22.5956 | −0.741736 | ||||||||
\(929\) | 23.3917 | 0.767457 | 0.383728 | − | 0.923446i | \(-0.374640\pi\) | ||||
0.383728 | + | 0.923446i | \(0.374640\pi\) | |||||||
\(930\) | 3.57411 | 0.117200 | ||||||||
\(931\) | −35.2413 | −1.15499 | ||||||||
\(932\) | 8.57186 | 0.280781 | ||||||||
\(933\) | 14.1229 | 0.462365 | ||||||||
\(934\) | −10.8633 | −0.355458 | ||||||||
\(935\) | 6.14480 | 0.200956 | ||||||||
\(936\) | −7.82933 | −0.255910 | ||||||||
\(937\) | −42.7989 | −1.39818 | −0.699090 | − | 0.715034i | \(-0.746411\pi\) | ||||
−0.699090 | + | 0.715034i | \(0.746411\pi\) | |||||||
\(938\) | −2.62884 | −0.0858346 | ||||||||
\(939\) | 0.158146 | 0.00516090 | ||||||||
\(940\) | 11.5014 | 0.375134 | ||||||||
\(941\) | 4.46473 | 0.145546 | 0.0727730 | − | 0.997349i | \(-0.476815\pi\) | ||||
0.0727730 | + | 0.997349i | \(0.476815\pi\) | |||||||
\(942\) | −12.6139 | −0.410984 | ||||||||
\(943\) | −1.84717 | −0.0601521 | ||||||||
\(944\) | 2.06253 | 0.0671295 | ||||||||
\(945\) | 1.23837 | 0.0402843 | ||||||||
\(946\) | 13.9730 | 0.454302 | ||||||||
\(947\) | −0.0122997 | −0.000399687 0 | −0.000199843 | − | 1.00000i | \(-0.500064\pi\) | ||||
−0.000199843 | 1.00000i | \(0.500064\pi\) | ||||||||
\(948\) | −6.01105 | −0.195230 | ||||||||
\(949\) | −34.7441 | −1.12784 | ||||||||
\(950\) | 5.76471 | 0.187032 | ||||||||
\(951\) | 1.95832 | 0.0635029 | ||||||||
\(952\) | 9.31347 | 0.301851 | ||||||||
\(953\) | −35.0610 | −1.13574 | −0.567869 | − | 0.823119i | \(-0.692232\pi\) | ||||
−0.567869 | + | 0.823119i | \(0.692232\pi\) | |||||||
\(954\) | 6.37860 | 0.206515 | ||||||||
\(955\) | 3.62710 | 0.117370 | ||||||||
\(956\) | 22.3626 | 0.723257 | ||||||||
\(957\) | 9.46464 | 0.305948 | ||||||||
\(958\) | 4.67675 | 0.151099 | ||||||||
\(959\) | −9.61128 | −0.310364 | ||||||||
\(960\) | −5.30776 | −0.171307 | ||||||||
\(961\) | −15.0237 | −0.484635 | ||||||||
\(962\) | −14.5389 | −0.468754 | ||||||||
\(963\) | −1.07130 | −0.0345222 | ||||||||
\(964\) | −26.9168 | −0.866932 | ||||||||
\(965\) | −18.8754 | −0.607620 | ||||||||
\(966\) | −0.279370 | −0.00898858 | ||||||||
\(967\) | 30.1640 | 0.970009 | 0.485004 | − | 0.874512i | \(-0.338818\pi\) | ||||
0.485004 | + | 0.874512i | \(0.338818\pi\) | |||||||
\(968\) | 15.8335 | 0.508908 | ||||||||
\(969\) | 16.9423 | 0.544263 | ||||||||
\(970\) | 7.38545 | 0.237132 | ||||||||
\(971\) | 55.5418 | 1.78242 | 0.891210 | − | 0.453590i | \(-0.149857\pi\) | ||||
0.891210 | + | 0.453590i | \(0.149857\pi\) | |||||||
\(972\) | −1.20043 | −0.0385037 | ||||||||
\(973\) | 25.4194 | 0.814910 | ||||||||
\(974\) | −17.2462 | −0.552605 | ||||||||
\(975\) | 2.73582 | 0.0876164 | ||||||||
\(976\) | −1.35706 | −0.0434384 | ||||||||
\(977\) | −55.1344 | −1.76390 | −0.881952 | − | 0.471339i | \(-0.843771\pi\) | ||||
−0.881952 | + | 0.471339i | \(0.843771\pi\) | |||||||
\(978\) | −14.9392 | −0.477703 | ||||||||
\(979\) | 1.19618 | 0.0382300 | ||||||||
\(980\) | −6.56205 | −0.209617 | ||||||||
\(981\) | −6.38693 | −0.203919 | ||||||||
\(982\) | −8.21158 | −0.262042 | ||||||||
\(983\) | −6.30521 | −0.201105 | −0.100553 | − | 0.994932i | \(-0.532061\pi\) | ||||
−0.100553 | + | 0.994932i | \(0.532061\pi\) | |||||||
\(984\) | 20.9529 | 0.667954 | ||||||||
\(985\) | 10.4283 | 0.332274 | ||||||||
\(986\) | −9.51199 | −0.302923 | ||||||||
\(987\) | −11.8650 | −0.377666 | ||||||||
\(988\) | −21.1725 | −0.673587 | ||||||||
\(989\) | −1.68607 | −0.0536139 | ||||||||
\(990\) | 2.09081 | 0.0664502 | ||||||||
\(991\) | 26.3922 | 0.838377 | 0.419189 | − | 0.907899i | \(-0.362315\pi\) | ||||
0.419189 | + | 0.907899i | \(0.362315\pi\) | |||||||
\(992\) | −22.3122 | −0.708413 | ||||||||
\(993\) | −3.56211 | −0.113040 | ||||||||
\(994\) | 9.82941 | 0.311770 | ||||||||
\(995\) | −24.7050 | −0.783202 | ||||||||
\(996\) | −18.8727 | −0.598003 | ||||||||
\(997\) | 46.1483 | 1.46153 | 0.730766 | − | 0.682628i | \(-0.239163\pi\) | ||||
0.730766 | + | 0.682628i | \(0.239163\pi\) | |||||||
\(998\) | −7.69197 | −0.243485 | ||||||||
\(999\) | −5.94314 | −0.188033 |
(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 | 6015.2.a.c.1.19 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6015.2.a.c.1.19 | ✓ | 28 | 1.1 | even | 1 | trivial |