Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32475 | −1.64385 | −0.821924 | − | 0.569597i | \(-0.807099\pi\) | ||||
−0.821924 | + | 0.569597i | \(0.807099\pi\) | |||||||
\(3\) | 2.00106 | 1.15531 | 0.577657 | − | 0.816280i | \(-0.303967\pi\) | ||||
0.577657 | + | 0.816280i | \(0.303967\pi\) | |||||||
\(4\) | 3.40448 | 1.70224 | ||||||||
\(5\) | 3.04764 | 1.36294 | 0.681472 | − | 0.731844i | \(-0.261340\pi\) | ||||
0.681472 | + | 0.731844i | \(0.261340\pi\) | |||||||
\(6\) | −4.65197 | −1.89916 | ||||||||
\(7\) | −5.08642 | −1.92249 | −0.961244 | − | 0.275700i | \(-0.911090\pi\) | ||||
−0.961244 | + | 0.275700i | \(0.911090\pi\) | |||||||
\(8\) | −3.26506 | −1.15437 | ||||||||
\(9\) | 1.00425 | 0.334749 | ||||||||
\(10\) | −7.08500 | −2.24047 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 6.81257 | 1.96662 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 11.8247 | 3.16028 | ||||||||
\(15\) | 6.09851 | 1.57463 | ||||||||
\(16\) | 0.781510 | 0.195377 | ||||||||
\(17\) | 4.98005 | 1.20784 | 0.603919 | − | 0.797046i | \(-0.293605\pi\) | ||||
0.603919 | + | 0.797046i | \(0.293605\pi\) | |||||||
\(18\) | −2.33463 | −0.550276 | ||||||||
\(19\) | −4.25776 | −0.976796 | −0.488398 | − | 0.872621i | \(-0.662419\pi\) | ||||
−0.488398 | + | 0.872621i | \(0.662419\pi\) | |||||||
\(20\) | 10.3756 | 2.32006 | ||||||||
\(21\) | −10.1782 | −2.22108 | ||||||||
\(22\) | −2.32475 | −0.495639 | ||||||||
\(23\) | 3.33940 | 0.696313 | 0.348156 | − | 0.937437i | \(-0.386808\pi\) | ||||
0.348156 | + | 0.937437i | \(0.386808\pi\) | |||||||
\(24\) | −6.53359 | −1.33366 | ||||||||
\(25\) | 4.28809 | 0.857618 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.99363 | −0.768574 | ||||||||
\(28\) | −17.3166 | −3.27253 | ||||||||
\(29\) | 0.0575180 | 0.0106808 | 0.00534041 | − | 0.999986i | \(-0.498300\pi\) | ||||
0.00534041 | + | 0.999986i | \(0.498300\pi\) | |||||||
\(30\) | −14.1775 | −2.58845 | ||||||||
\(31\) | 4.65867 | 0.836722 | 0.418361 | − | 0.908281i | \(-0.362605\pi\) | ||||
0.418361 | + | 0.908281i | \(0.362605\pi\) | |||||||
\(32\) | 4.71331 | 0.833203 | ||||||||
\(33\) | 2.00106 | 0.348340 | ||||||||
\(34\) | −11.5774 | −1.98550 | ||||||||
\(35\) | −15.5016 | −2.62024 | ||||||||
\(36\) | 3.41893 | 0.569822 | ||||||||
\(37\) | −1.03109 | −0.169510 | −0.0847549 | − | 0.996402i | \(-0.527011\pi\) | ||||
−0.0847549 | + | 0.996402i | \(0.527011\pi\) | |||||||
\(38\) | 9.89823 | 1.60571 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.95072 | −1.57335 | ||||||||
\(41\) | 12.3888 | 1.93481 | 0.967404 | − | 0.253238i | \(-0.0814954\pi\) | ||||
0.967404 | + | 0.253238i | \(0.0814954\pi\) | |||||||
\(42\) | 23.6619 | 3.65111 | ||||||||
\(43\) | 0.344029 | 0.0524639 | 0.0262320 | − | 0.999656i | \(-0.491649\pi\) | ||||
0.0262320 | + | 0.999656i | \(0.491649\pi\) | |||||||
\(44\) | 3.40448 | 0.513244 | ||||||||
\(45\) | 3.06058 | 0.456244 | ||||||||
\(46\) | −7.76328 | −1.14463 | ||||||||
\(47\) | 5.15893 | 0.752507 | 0.376253 | − | 0.926517i | \(-0.377212\pi\) | ||||
0.376253 | + | 0.926517i | \(0.377212\pi\) | |||||||
\(48\) | 1.56385 | 0.225722 | ||||||||
\(49\) | 18.8717 | 2.69596 | ||||||||
\(50\) | −9.96875 | −1.40979 | ||||||||
\(51\) | 9.96538 | 1.39543 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.27048 | 0.723956 | 0.361978 | − | 0.932187i | \(-0.382102\pi\) | ||||
0.361978 | + | 0.932187i | \(0.382102\pi\) | |||||||
\(54\) | 9.28419 | 1.26342 | ||||||||
\(55\) | 3.04764 | 0.410943 | ||||||||
\(56\) | 16.6075 | 2.21927 | ||||||||
\(57\) | −8.52003 | −1.12851 | ||||||||
\(58\) | −0.133715 | −0.0175577 | ||||||||
\(59\) | −4.35492 | −0.566962 | −0.283481 | − | 0.958978i | \(-0.591489\pi\) | ||||
−0.283481 | + | 0.958978i | \(0.591489\pi\) | |||||||
\(60\) | 20.7622 | 2.68039 | ||||||||
\(61\) | 13.7147 | 1.75599 | 0.877994 | − | 0.478671i | \(-0.158881\pi\) | ||||
0.877994 | + | 0.478671i | \(0.158881\pi\) | |||||||
\(62\) | −10.8303 | −1.37545 | ||||||||
\(63\) | −5.10802 | −0.643550 | ||||||||
\(64\) | −12.5203 | −1.56504 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.65197 | −0.572618 | ||||||||
\(67\) | −0.194220 | −0.0237277 | −0.0118639 | − | 0.999930i | \(-0.503776\pi\) | ||||
−0.0118639 | + | 0.999930i | \(0.503776\pi\) | |||||||
\(68\) | 16.9544 | 2.05603 | ||||||||
\(69\) | 6.68234 | 0.804459 | ||||||||
\(70\) | 36.0373 | 4.30728 | ||||||||
\(71\) | 13.1520 | 1.56086 | 0.780430 | − | 0.625243i | \(-0.215000\pi\) | ||||
0.780430 | + | 0.625243i | \(0.215000\pi\) | |||||||
\(72\) | −3.27893 | −0.386425 | ||||||||
\(73\) | 9.71787 | 1.13739 | 0.568695 | − | 0.822548i | \(-0.307448\pi\) | ||||
0.568695 | + | 0.822548i | \(0.307448\pi\) | |||||||
\(74\) | 2.39703 | 0.278649 | ||||||||
\(75\) | 8.58073 | 0.990817 | ||||||||
\(76\) | −14.4954 | −1.66274 | ||||||||
\(77\) | −5.08642 | −0.579652 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.22146 | −0.362442 | −0.181221 | − | 0.983442i | \(-0.558005\pi\) | ||||
−0.181221 | + | 0.983442i | \(0.558005\pi\) | |||||||
\(80\) | 2.38176 | 0.266289 | ||||||||
\(81\) | −11.0042 | −1.22269 | ||||||||
\(82\) | −28.8009 | −3.18053 | ||||||||
\(83\) | 7.54152 | 0.827789 | 0.413895 | − | 0.910325i | \(-0.364168\pi\) | ||||
0.413895 | + | 0.910325i | \(0.364168\pi\) | |||||||
\(84\) | −34.6516 | −3.78080 | ||||||||
\(85\) | 15.1774 | 1.64622 | ||||||||
\(86\) | −0.799782 | −0.0862427 | ||||||||
\(87\) | 0.115097 | 0.0123397 | ||||||||
\(88\) | −3.26506 | −0.348057 | ||||||||
\(89\) | −2.89929 | −0.307324 | −0.153662 | − | 0.988123i | \(-0.549107\pi\) | ||||
−0.153662 | + | 0.988123i | \(0.549107\pi\) | |||||||
\(90\) | −7.11509 | −0.749996 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 11.3689 | 1.18529 | ||||||||
\(93\) | 9.32229 | 0.966677 | ||||||||
\(94\) | −11.9932 | −1.23701 | ||||||||
\(95\) | −12.9761 | −1.33132 | ||||||||
\(96\) | 9.43162 | 0.962610 | ||||||||
\(97\) | −3.31003 | −0.336083 | −0.168041 | − | 0.985780i | \(-0.553744\pi\) | ||||
−0.168041 | + | 0.985780i | \(0.553744\pi\) | |||||||
\(98\) | −43.8721 | −4.43175 | ||||||||
\(99\) | 1.00425 | 0.100931 | ||||||||
\(100\) | 14.5987 | 1.45987 | ||||||||
\(101\) | −11.7377 | −1.16794 | −0.583970 | − | 0.811775i | \(-0.698501\pi\) | ||||
−0.583970 | + | 0.811775i | \(0.698501\pi\) | |||||||
\(102\) | −23.1670 | −2.29388 | ||||||||
\(103\) | 3.28198 | 0.323383 | 0.161692 | − | 0.986841i | \(-0.448305\pi\) | ||||
0.161692 | + | 0.986841i | \(0.448305\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −31.0196 | −3.02720 | ||||||||
\(106\) | −12.2526 | −1.19007 | ||||||||
\(107\) | −2.65096 | −0.256278 | −0.128139 | − | 0.991756i | \(-0.540900\pi\) | ||||
−0.128139 | + | 0.991756i | \(0.540900\pi\) | |||||||
\(108\) | −13.5962 | −1.30830 | ||||||||
\(109\) | 3.20728 | 0.307202 | 0.153601 | − | 0.988133i | \(-0.450913\pi\) | ||||
0.153601 | + | 0.988133i | \(0.450913\pi\) | |||||||
\(110\) | −7.08500 | −0.675528 | ||||||||
\(111\) | −2.06327 | −0.195837 | ||||||||
\(112\) | −3.97509 | −0.375611 | ||||||||
\(113\) | −2.96858 | −0.279260 | −0.139630 | − | 0.990204i | \(-0.544591\pi\) | ||||
−0.139630 | + | 0.990204i | \(0.544591\pi\) | |||||||
\(114\) | 19.8070 | 1.85509 | ||||||||
\(115\) | 10.1773 | 0.949035 | ||||||||
\(116\) | 0.195819 | 0.0181813 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.1241 | 0.932000 | ||||||||
\(119\) | −25.3306 | −2.32205 | ||||||||
\(120\) | −19.9120 | −1.81771 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −31.8833 | −2.88658 | ||||||||
\(123\) | 24.7908 | 2.23531 | ||||||||
\(124\) | 15.8603 | 1.42430 | ||||||||
\(125\) | −2.16965 | −0.194059 | ||||||||
\(126\) | 11.8749 | 1.05790 | ||||||||
\(127\) | −11.9699 | −1.06216 | −0.531080 | − | 0.847321i | \(-0.678214\pi\) | ||||
−0.531080 | + | 0.847321i | \(0.678214\pi\) | |||||||
\(128\) | 19.6800 | 1.73948 | ||||||||
\(129\) | 0.688423 | 0.0606122 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.94560 | 0.606840 | 0.303420 | − | 0.952857i | \(-0.401871\pi\) | ||||
0.303420 | + | 0.952857i | \(0.401871\pi\) | |||||||
\(132\) | 6.81257 | 0.592958 | ||||||||
\(133\) | 21.6568 | 1.87788 | ||||||||
\(134\) | 0.451513 | 0.0390048 | ||||||||
\(135\) | −12.1711 | −1.04752 | ||||||||
\(136\) | −16.2602 | −1.39430 | ||||||||
\(137\) | 3.71854 | 0.317697 | 0.158848 | − | 0.987303i | \(-0.449222\pi\) | ||||
0.158848 | + | 0.987303i | \(0.449222\pi\) | |||||||
\(138\) | −15.5348 | −1.32241 | ||||||||
\(139\) | −7.03252 | −0.596491 | −0.298245 | − | 0.954489i | \(-0.596401\pi\) | ||||
−0.298245 | + | 0.954489i | \(0.596401\pi\) | |||||||
\(140\) | −52.7747 | −4.46028 | ||||||||
\(141\) | 10.3233 | 0.869381 | ||||||||
\(142\) | −30.5752 | −2.56582 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.784828 | 0.0654024 | ||||||||
\(145\) | 0.175294 | 0.0145574 | ||||||||
\(146\) | −22.5917 | −1.86970 | ||||||||
\(147\) | 37.7634 | 3.11468 | ||||||||
\(148\) | −3.51032 | −0.288546 | ||||||||
\(149\) | 13.3703 | 1.09533 | 0.547667 | − | 0.836696i | \(-0.315516\pi\) | ||||
0.547667 | + | 0.836696i | \(0.315516\pi\) | |||||||
\(150\) | −19.9481 | −1.62875 | ||||||||
\(151\) | 11.3479 | 0.923483 | 0.461741 | − | 0.887015i | \(-0.347225\pi\) | ||||
0.461741 | + | 0.887015i | \(0.347225\pi\) | |||||||
\(152\) | 13.9018 | 1.12759 | ||||||||
\(153\) | 5.00119 | 0.404323 | ||||||||
\(154\) | 11.8247 | 0.952860 | ||||||||
\(155\) | 14.1979 | 1.14041 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.2941 | −1.69946 | −0.849729 | − | 0.527220i | \(-0.823234\pi\) | ||||
−0.849729 | + | 0.527220i | \(0.823234\pi\) | |||||||
\(158\) | 7.48909 | 0.595800 | ||||||||
\(159\) | 10.5465 | 0.836396 | ||||||||
\(160\) | 14.3644 | 1.13561 | ||||||||
\(161\) | −16.9856 | −1.33865 | ||||||||
\(162\) | 25.5821 | 2.00992 | ||||||||
\(163\) | −10.7358 | −0.840890 | −0.420445 | − | 0.907318i | \(-0.638126\pi\) | ||||
−0.420445 | + | 0.907318i | \(0.638126\pi\) | |||||||
\(164\) | 42.1774 | 3.29351 | ||||||||
\(165\) | 6.09851 | 0.474768 | ||||||||
\(166\) | −17.5322 | −1.36076 | ||||||||
\(167\) | −15.1963 | −1.17592 | −0.587961 | − | 0.808889i | \(-0.700069\pi\) | ||||
−0.587961 | + | 0.808889i | \(0.700069\pi\) | |||||||
\(168\) | 33.2326 | 2.56395 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −35.2836 | −2.70613 | ||||||||
\(171\) | −4.27584 | −0.326981 | ||||||||
\(172\) | 1.17124 | 0.0893061 | ||||||||
\(173\) | 1.28222 | 0.0974855 | 0.0487428 | − | 0.998811i | \(-0.484479\pi\) | ||||
0.0487428 | + | 0.998811i | \(0.484479\pi\) | |||||||
\(174\) | −0.267572 | −0.0202846 | ||||||||
\(175\) | −21.8110 | −1.64876 | ||||||||
\(176\) | 0.781510 | 0.0589085 | ||||||||
\(177\) | −8.71446 | −0.655019 | ||||||||
\(178\) | 6.74014 | 0.505195 | ||||||||
\(179\) | −10.0223 | −0.749099 | −0.374549 | − | 0.927207i | \(-0.622203\pi\) | ||||
−0.374549 | + | 0.927207i | \(0.622203\pi\) | |||||||
\(180\) | 10.4197 | 0.776636 | ||||||||
\(181\) | 21.9616 | 1.63239 | 0.816197 | − | 0.577774i | \(-0.196079\pi\) | ||||
0.816197 | + | 0.577774i | \(0.196079\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.4440 | 2.02872 | ||||||||
\(184\) | −10.9033 | −0.803805 | ||||||||
\(185\) | −3.14238 | −0.231033 | ||||||||
\(186\) | −21.6720 | −1.58907 | ||||||||
\(187\) | 4.98005 | 0.364177 | ||||||||
\(188\) | 17.5634 | 1.28095 | ||||||||
\(189\) | 20.3133 | 1.47757 | ||||||||
\(190\) | 30.1662 | 2.18849 | ||||||||
\(191\) | −0.205772 | −0.0148892 | −0.00744458 | − | 0.999972i | \(-0.502370\pi\) | ||||
−0.00744458 | + | 0.999972i | \(0.502370\pi\) | |||||||
\(192\) | −25.0539 | −1.80811 | ||||||||
\(193\) | 4.47205 | 0.321905 | 0.160952 | − | 0.986962i | \(-0.448543\pi\) | ||||
0.160952 | + | 0.986962i | \(0.448543\pi\) | |||||||
\(194\) | 7.69500 | 0.552469 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 64.2483 | 4.58916 | ||||||||
\(197\) | −9.65570 | −0.687940 | −0.343970 | − | 0.938981i | \(-0.611772\pi\) | ||||
−0.343970 | + | 0.938981i | \(0.611772\pi\) | |||||||
\(198\) | −2.33463 | −0.165915 | ||||||||
\(199\) | 0.490365 | 0.0347610 | 0.0173805 | − | 0.999849i | \(-0.494467\pi\) | ||||
0.0173805 | + | 0.999849i | \(0.494467\pi\) | |||||||
\(200\) | −14.0009 | −0.990011 | ||||||||
\(201\) | −0.388646 | −0.0274129 | ||||||||
\(202\) | 27.2871 | 1.91992 | ||||||||
\(203\) | −0.292561 | −0.0205337 | ||||||||
\(204\) | 33.9269 | 2.37536 | ||||||||
\(205\) | 37.7566 | 2.63704 | ||||||||
\(206\) | −7.62979 | −0.531593 | ||||||||
\(207\) | 3.35358 | 0.233090 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.25776 | −0.294515 | ||||||||
\(210\) | 72.1129 | 4.97626 | ||||||||
\(211\) | 24.7914 | 1.70671 | 0.853356 | − | 0.521329i | \(-0.174564\pi\) | ||||
0.853356 | + | 0.521329i | \(0.174564\pi\) | |||||||
\(212\) | 17.9432 | 1.23235 | ||||||||
\(213\) | 26.3180 | 1.80328 | ||||||||
\(214\) | 6.16282 | 0.421282 | ||||||||
\(215\) | 1.04847 | 0.0715054 | ||||||||
\(216\) | 13.0394 | 0.887221 | ||||||||
\(217\) | −23.6960 | −1.60859 | ||||||||
\(218\) | −7.45613 | −0.504993 | ||||||||
\(219\) | 19.4461 | 1.31404 | ||||||||
\(220\) | 10.3756 | 0.699523 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.79660 | 0.321926 | ||||||||
\(223\) | −20.9129 | −1.40043 | −0.700215 | − | 0.713932i | \(-0.746913\pi\) | ||||
−0.700215 | + | 0.713932i | \(0.746913\pi\) | |||||||
\(224\) | −23.9739 | −1.60182 | ||||||||
\(225\) | 4.30630 | 0.287087 | ||||||||
\(226\) | 6.90121 | 0.459062 | ||||||||
\(227\) | 9.40504 | 0.624235 | 0.312117 | − | 0.950044i | \(-0.398962\pi\) | ||||
0.312117 | + | 0.950044i | \(0.398962\pi\) | |||||||
\(228\) | −29.0063 | −1.92099 | ||||||||
\(229\) | 3.22675 | 0.213229 | 0.106615 | − | 0.994300i | \(-0.465999\pi\) | ||||
0.106615 | + | 0.994300i | \(0.465999\pi\) | |||||||
\(230\) | −23.6596 | −1.56007 | ||||||||
\(231\) | −10.1782 | −0.669679 | ||||||||
\(232\) | −0.187800 | −0.0123297 | ||||||||
\(233\) | −25.5696 | −1.67512 | −0.837562 | − | 0.546343i | \(-0.816020\pi\) | ||||
−0.837562 | + | 0.546343i | \(0.816020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.7225 | 1.02562 | ||||||||
\(236\) | −14.8262 | −0.965105 | ||||||||
\(237\) | −6.44633 | −0.418734 | ||||||||
\(238\) | 58.8874 | 3.81711 | ||||||||
\(239\) | −18.0533 | −1.16777 | −0.583885 | − | 0.811836i | \(-0.698468\pi\) | ||||
−0.583885 | + | 0.811836i | \(0.698468\pi\) | |||||||
\(240\) | 4.76604 | 0.307647 | ||||||||
\(241\) | −4.45917 | −0.287240 | −0.143620 | − | 0.989633i | \(-0.545874\pi\) | ||||
−0.143620 | + | 0.989633i | \(0.545874\pi\) | |||||||
\(242\) | −2.32475 | −0.149441 | ||||||||
\(243\) | −10.0393 | −0.644019 | ||||||||
\(244\) | 46.6914 | 2.98911 | ||||||||
\(245\) | 57.5141 | 3.67444 | ||||||||
\(246\) | −57.6325 | −3.67451 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −15.2109 | −0.965890 | ||||||||
\(249\) | 15.0910 | 0.956356 | ||||||||
\(250\) | 5.04389 | 0.319004 | ||||||||
\(251\) | 2.24448 | 0.141670 | 0.0708351 | − | 0.997488i | \(-0.477434\pi\) | ||||
0.0708351 | + | 0.997488i | \(0.477434\pi\) | |||||||
\(252\) | −17.3901 | −1.09548 | ||||||||
\(253\) | 3.33940 | 0.209946 | ||||||||
\(254\) | 27.8272 | 1.74603 | ||||||||
\(255\) | 30.3708 | 1.90190 | ||||||||
\(256\) | −20.7105 | −1.29441 | ||||||||
\(257\) | 1.79575 | 0.112016 | 0.0560081 | − | 0.998430i | \(-0.482163\pi\) | ||||
0.0560081 | + | 0.998430i | \(0.482163\pi\) | |||||||
\(258\) | −1.60041 | −0.0996374 | ||||||||
\(259\) | 5.24455 | 0.325881 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0577622 | 0.00357539 | ||||||||
\(262\) | −16.1468 | −0.997553 | ||||||||
\(263\) | 26.8199 | 1.65378 | 0.826892 | − | 0.562361i | \(-0.190107\pi\) | ||||
0.826892 | + | 0.562361i | \(0.190107\pi\) | |||||||
\(264\) | −6.53359 | −0.402115 | ||||||||
\(265\) | 16.0625 | 0.986711 | ||||||||
\(266\) | −50.3466 | −3.08695 | ||||||||
\(267\) | −5.80166 | −0.355056 | ||||||||
\(268\) | −0.661217 | −0.0403902 | ||||||||
\(269\) | 14.9673 | 0.912572 | 0.456286 | − | 0.889833i | \(-0.349179\pi\) | ||||
0.456286 | + | 0.889833i | \(0.349179\pi\) | |||||||
\(270\) | 28.2948 | 1.72197 | ||||||||
\(271\) | 4.90091 | 0.297709 | 0.148855 | − | 0.988859i | \(-0.452441\pi\) | ||||
0.148855 | + | 0.988859i | \(0.452441\pi\) | |||||||
\(272\) | 3.89195 | 0.235984 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.64470 | −0.522245 | ||||||||
\(275\) | 4.28809 | 0.258581 | ||||||||
\(276\) | 22.7499 | 1.36938 | ||||||||
\(277\) | −8.61514 | −0.517634 | −0.258817 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258817 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(278\) | 16.3489 | 0.980540 | ||||||||
\(279\) | 4.67846 | 0.280092 | ||||||||
\(280\) | 50.6136 | 3.02474 | ||||||||
\(281\) | 7.50695 | 0.447827 | 0.223913 | − | 0.974609i | \(-0.428117\pi\) | ||||
0.223913 | + | 0.974609i | \(0.428117\pi\) | |||||||
\(282\) | −23.9992 | −1.42913 | ||||||||
\(283\) | −22.5526 | −1.34061 | −0.670306 | − | 0.742084i | \(-0.733837\pi\) | ||||
−0.670306 | + | 0.742084i | \(0.733837\pi\) | |||||||
\(284\) | 44.7758 | 2.65696 | ||||||||
\(285\) | −25.9660 | −1.53809 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −63.0148 | −3.71964 | ||||||||
\(288\) | 4.73332 | 0.278914 | ||||||||
\(289\) | 7.80085 | 0.458874 | ||||||||
\(290\) | −0.407515 | −0.0239301 | ||||||||
\(291\) | −6.62357 | −0.388281 | ||||||||
\(292\) | 33.0843 | 1.93611 | ||||||||
\(293\) | −21.9190 | −1.28052 | −0.640262 | − | 0.768156i | \(-0.721174\pi\) | ||||
−0.640262 | + | 0.768156i | \(0.721174\pi\) | |||||||
\(294\) | −87.7907 | −5.12006 | ||||||||
\(295\) | −13.2722 | −0.772738 | ||||||||
\(296\) | 3.36657 | 0.195678 | ||||||||
\(297\) | −3.99363 | −0.231734 | ||||||||
\(298\) | −31.0826 | −1.80056 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 29.2129 | 1.68661 | ||||||||
\(301\) | −1.74988 | −0.100861 | ||||||||
\(302\) | −26.3812 | −1.51807 | ||||||||
\(303\) | −23.4878 | −1.34934 | ||||||||
\(304\) | −3.32748 | −0.190844 | ||||||||
\(305\) | 41.7975 | 2.39332 | ||||||||
\(306\) | −11.6265 | −0.664645 | ||||||||
\(307\) | −22.2819 | −1.27169 | −0.635846 | − | 0.771816i | \(-0.719349\pi\) | ||||
−0.635846 | + | 0.771816i | \(0.719349\pi\) | |||||||
\(308\) | −17.3166 | −0.986706 | ||||||||
\(309\) | 6.56744 | 0.373609 | ||||||||
\(310\) | −33.0067 | −1.87466 | ||||||||
\(311\) | −10.5412 | −0.597735 | −0.298867 | − | 0.954295i | \(-0.596609\pi\) | ||||
−0.298867 | + | 0.954295i | \(0.596609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1202 | 1.36335 | 0.681676 | − | 0.731654i | \(-0.261251\pi\) | ||||
0.681676 | + | 0.731654i | \(0.261251\pi\) | |||||||
\(314\) | 49.5036 | 2.79365 | ||||||||
\(315\) | −15.5674 | −0.877123 | ||||||||
\(316\) | −10.9674 | −0.616963 | ||||||||
\(317\) | 5.12796 | 0.288015 | 0.144007 | − | 0.989577i | \(-0.454001\pi\) | ||||
0.144007 | + | 0.989577i | \(0.454001\pi\) | |||||||
\(318\) | −24.5181 | −1.37491 | ||||||||
\(319\) | 0.0575180 | 0.00322039 | ||||||||
\(320\) | −38.1573 | −2.13306 | ||||||||
\(321\) | −5.30473 | −0.296081 | ||||||||
\(322\) | 39.4873 | 2.20054 | ||||||||
\(323\) | −21.2038 | −1.17981 | ||||||||
\(324\) | −37.4636 | −2.08131 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.9580 | 1.38230 | ||||||||
\(327\) | 6.41796 | 0.354914 | ||||||||
\(328\) | −40.4503 | −2.23349 | ||||||||
\(329\) | −26.2405 | −1.44668 | ||||||||
\(330\) | −14.1775 | −0.780447 | ||||||||
\(331\) | −16.2969 | −0.895759 | −0.447879 | − | 0.894094i | \(-0.647821\pi\) | ||||
−0.447879 | + | 0.894094i | \(0.647821\pi\) | |||||||
\(332\) | 25.6749 | 1.40909 | ||||||||
\(333\) | −1.03547 | −0.0567432 | ||||||||
\(334\) | 35.3276 | 1.93304 | ||||||||
\(335\) | −0.591911 | −0.0323396 | ||||||||
\(336\) | −7.95440 | −0.433948 | ||||||||
\(337\) | −12.0708 | −0.657541 | −0.328770 | − | 0.944410i | \(-0.606634\pi\) | ||||
−0.328770 | + | 0.944410i | \(0.606634\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.94031 | −0.322633 | ||||||||
\(340\) | 51.6710 | 2.80225 | ||||||||
\(341\) | 4.65867 | 0.252281 | ||||||||
\(342\) | 9.94027 | 0.537508 | ||||||||
\(343\) | −60.3845 | −3.26046 | ||||||||
\(344\) | −1.12328 | −0.0605630 | ||||||||
\(345\) | 20.3653 | 1.09643 | ||||||||
\(346\) | −2.98085 | −0.160251 | ||||||||
\(347\) | 15.4440 | 0.829079 | 0.414540 | − | 0.910031i | \(-0.363943\pi\) | ||||
0.414540 | + | 0.910031i | \(0.363943\pi\) | |||||||
\(348\) | 0.391845 | 0.0210051 | ||||||||
\(349\) | 16.3111 | 0.873116 | 0.436558 | − | 0.899676i | \(-0.356197\pi\) | ||||
0.436558 | + | 0.899676i | \(0.356197\pi\) | |||||||
\(350\) | 50.7053 | 2.71031 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.71331 | 0.251220 | ||||||||
\(353\) | −13.3191 | −0.708905 | −0.354453 | − | 0.935074i | \(-0.615333\pi\) | ||||
−0.354453 | + | 0.935074i | \(0.615333\pi\) | |||||||
\(354\) | 20.2590 | 1.07675 | ||||||||
\(355\) | 40.0826 | 2.12737 | ||||||||
\(356\) | −9.87058 | −0.523140 | ||||||||
\(357\) | −50.6881 | −2.68270 | ||||||||
\(358\) | 23.2993 | 1.23141 | ||||||||
\(359\) | 7.76716 | 0.409935 | 0.204967 | − | 0.978769i | \(-0.434291\pi\) | ||||
0.204967 | + | 0.978769i | \(0.434291\pi\) | |||||||
\(360\) | −9.99298 | −0.526676 | ||||||||
\(361\) | −0.871506 | −0.0458688 | ||||||||
\(362\) | −51.0553 | −2.68341 | ||||||||
\(363\) | 2.00106 | 0.105028 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.6165 | 1.55020 | ||||||||
\(366\) | −63.8005 | −3.33490 | ||||||||
\(367\) | 33.5692 | 1.75230 | 0.876149 | − | 0.482040i | \(-0.160104\pi\) | ||||
0.876149 | + | 0.482040i | \(0.160104\pi\) | |||||||
\(368\) | 2.60977 | 0.136044 | ||||||||
\(369\) | 12.4414 | 0.647675 | ||||||||
\(370\) | 7.30526 | 0.379783 | ||||||||
\(371\) | −26.8079 | −1.39180 | ||||||||
\(372\) | 31.7375 | 1.64551 | ||||||||
\(373\) | 15.6957 | 0.812693 | 0.406346 | − | 0.913719i | \(-0.366803\pi\) | ||||
0.406346 | + | 0.913719i | \(0.366803\pi\) | |||||||
\(374\) | −11.5774 | −0.598652 | ||||||||
\(375\) | −4.34160 | −0.224199 | ||||||||
\(376\) | −16.8442 | −0.868674 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −47.2233 | −2.42891 | ||||||||
\(379\) | −9.90362 | −0.508715 | −0.254357 | − | 0.967110i | \(-0.581864\pi\) | ||||
−0.254357 | + | 0.967110i | \(0.581864\pi\) | |||||||
\(380\) | −44.1768 | −2.26622 | ||||||||
\(381\) | −23.9526 | −1.22713 | ||||||||
\(382\) | 0.478370 | 0.0244755 | ||||||||
\(383\) | 35.1438 | 1.79577 | 0.897883 | − | 0.440233i | \(-0.145104\pi\) | ||||
0.897883 | + | 0.440233i | \(0.145104\pi\) | |||||||
\(384\) | 39.3808 | 2.00965 | ||||||||
\(385\) | −15.5016 | −0.790033 | ||||||||
\(386\) | −10.3964 | −0.529163 | ||||||||
\(387\) | 0.345490 | 0.0175622 | ||||||||
\(388\) | −11.2689 | −0.572093 | ||||||||
\(389\) | 24.8371 | 1.25929 | 0.629645 | − | 0.776883i | \(-0.283200\pi\) | ||||
0.629645 | + | 0.776883i | \(0.283200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6304 | 0.841033 | ||||||||
\(392\) | −61.6173 | −3.11214 | ||||||||
\(393\) | 13.8986 | 0.701091 | ||||||||
\(394\) | 22.4471 | 1.13087 | ||||||||
\(395\) | −9.81783 | −0.493989 | ||||||||
\(396\) | 3.41893 | 0.171808 | ||||||||
\(397\) | 18.4965 | 0.928313 | 0.464157 | − | 0.885753i | \(-0.346357\pi\) | ||||
0.464157 | + | 0.885753i | \(0.346357\pi\) | |||||||
\(398\) | −1.13998 | −0.0571419 | ||||||||
\(399\) | 43.3365 | 2.16954 | ||||||||
\(400\) | 3.35118 | 0.167559 | ||||||||
\(401\) | −5.62259 | −0.280779 | −0.140389 | − | 0.990096i | \(-0.544835\pi\) | ||||
−0.140389 | + | 0.990096i | \(0.544835\pi\) | |||||||
\(402\) | 0.903505 | 0.0450627 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −39.9606 | −1.98811 | ||||||||
\(405\) | −33.5369 | −1.66646 | ||||||||
\(406\) | 0.680132 | 0.0337544 | ||||||||
\(407\) | −1.03109 | −0.0511091 | ||||||||
\(408\) | −32.5376 | −1.61085 | ||||||||
\(409\) | 6.49631 | 0.321222 | 0.160611 | − | 0.987018i | \(-0.448654\pi\) | ||||
0.160611 | + | 0.987018i | \(0.448654\pi\) | |||||||
\(410\) | −87.7748 | −4.33489 | ||||||||
\(411\) | 7.44104 | 0.367039 | ||||||||
\(412\) | 11.1734 | 0.550475 | ||||||||
\(413\) | 22.1510 | 1.08998 | ||||||||
\(414\) | −7.79624 | −0.383164 | ||||||||
\(415\) | 22.9838 | 1.12823 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.0725 | −0.689133 | ||||||||
\(418\) | 9.89823 | 0.484138 | ||||||||
\(419\) | −36.1997 | −1.76847 | −0.884237 | − | 0.467039i | \(-0.845321\pi\) | ||||
−0.884237 | + | 0.467039i | \(0.845321\pi\) | |||||||
\(420\) | −105.605 | −5.15302 | ||||||||
\(421\) | −10.6708 | −0.520061 | −0.260030 | − | 0.965600i | \(-0.583733\pi\) | ||||
−0.260030 | + | 0.965600i | \(0.583733\pi\) | |||||||
\(422\) | −57.6339 | −2.80558 | ||||||||
\(423\) | 5.18083 | 0.251901 | ||||||||
\(424\) | −17.2084 | −0.835715 | ||||||||
\(425\) | 21.3549 | 1.03586 | ||||||||
\(426\) | −61.1829 | −2.96432 | ||||||||
\(427\) | −69.7588 | −3.37587 | ||||||||
\(428\) | −9.02512 | −0.436246 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.43745 | −0.117544 | ||||||||
\(431\) | 0.747781 | 0.0360193 | 0.0180097 | − | 0.999838i | \(-0.494267\pi\) | ||||
0.0180097 | + | 0.999838i | \(0.494267\pi\) | |||||||
\(432\) | −3.12106 | −0.150162 | ||||||||
\(433\) | −9.08995 | −0.436835 | −0.218417 | − | 0.975855i | \(-0.570089\pi\) | ||||
−0.218417 | + | 0.975855i | \(0.570089\pi\) | |||||||
\(434\) | 55.0873 | 2.64428 | ||||||||
\(435\) | 0.350774 | 0.0168183 | ||||||||
\(436\) | 10.9191 | 0.522931 | ||||||||
\(437\) | −14.2183 | −0.680156 | ||||||||
\(438\) | −45.2073 | −2.16009 | ||||||||
\(439\) | 32.2269 | 1.53810 | 0.769052 | − | 0.639186i | \(-0.220729\pi\) | ||||
0.769052 | + | 0.639186i | \(0.220729\pi\) | |||||||
\(440\) | −9.95072 | −0.474382 | ||||||||
\(441\) | 18.9518 | 0.902469 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.16298 | −0.340323 | −0.170162 | − | 0.985416i | \(-0.554429\pi\) | ||||
−0.170162 | + | 0.985416i | \(0.554429\pi\) | |||||||
\(444\) | −7.02436 | −0.333361 | ||||||||
\(445\) | −8.83599 | −0.418866 | ||||||||
\(446\) | 48.6173 | 2.30210 | ||||||||
\(447\) | 26.7547 | 1.26545 | ||||||||
\(448\) | 63.6835 | 3.00876 | ||||||||
\(449\) | 14.0670 | 0.663864 | 0.331932 | − | 0.943303i | \(-0.392300\pi\) | ||||
0.331932 | + | 0.943303i | \(0.392300\pi\) | |||||||
\(450\) | −10.0111 | −0.471927 | ||||||||
\(451\) | 12.3888 | 0.583367 | ||||||||
\(452\) | −10.1065 | −0.475368 | ||||||||
\(453\) | 22.7079 | 1.06691 | ||||||||
\(454\) | −21.8644 | −1.02615 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 27.8184 | 1.30272 | ||||||||
\(457\) | −1.76158 | −0.0824032 | −0.0412016 | − | 0.999151i | \(-0.513119\pi\) | ||||
−0.0412016 | + | 0.999151i | \(0.513119\pi\) | |||||||
\(458\) | −7.50139 | −0.350517 | ||||||||
\(459\) | −19.8884 | −0.928313 | ||||||||
\(460\) | 34.6483 | 1.61548 | ||||||||
\(461\) | 35.0354 | 1.63176 | 0.815880 | − | 0.578221i | \(-0.196253\pi\) | ||||
0.815880 | + | 0.578221i | \(0.196253\pi\) | |||||||
\(462\) | 23.6619 | 1.10085 | ||||||||
\(463\) | −18.0450 | −0.838622 | −0.419311 | − | 0.907843i | \(-0.637728\pi\) | ||||
−0.419311 | + | 0.907843i | \(0.637728\pi\) | |||||||
\(464\) | 0.0449509 | 0.00208679 | ||||||||
\(465\) | 28.4110 | 1.31753 | ||||||||
\(466\) | 59.4431 | 2.75365 | ||||||||
\(467\) | 10.2052 | 0.472242 | 0.236121 | − | 0.971724i | \(-0.424124\pi\) | ||||
0.236121 | + | 0.971724i | \(0.424124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.987884 | 0.0456162 | ||||||||
\(470\) | −36.5510 | −1.68597 | ||||||||
\(471\) | −42.6109 | −1.96341 | ||||||||
\(472\) | 14.2191 | 0.654486 | ||||||||
\(473\) | 0.344029 | 0.0158185 | ||||||||
\(474\) | 14.9861 | 0.688336 | ||||||||
\(475\) | −18.2576 | −0.837718 | ||||||||
\(476\) | −86.2375 | −3.95269 | ||||||||
\(477\) | 5.29286 | 0.242343 | ||||||||
\(478\) | 41.9694 | 1.91964 | ||||||||
\(479\) | −39.0076 | −1.78230 | −0.891151 | − | 0.453706i | \(-0.850102\pi\) | ||||
−0.891151 | + | 0.453706i | \(0.850102\pi\) | |||||||
\(480\) | 28.7441 | 1.31198 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.3665 | 0.472179 | ||||||||
\(483\) | −33.9892 | −1.54656 | ||||||||
\(484\) | 3.40448 | 0.154749 | ||||||||
\(485\) | −10.0878 | −0.458062 | ||||||||
\(486\) | 23.3388 | 1.05867 | ||||||||
\(487\) | −31.7323 | −1.43793 | −0.718963 | − | 0.695048i | \(-0.755383\pi\) | ||||
−0.718963 | + | 0.695048i | \(0.755383\pi\) | |||||||
\(488\) | −44.7794 | −2.02707 | ||||||||
\(489\) | −21.4829 | −0.971492 | ||||||||
\(490\) | −133.706 | −6.04022 | ||||||||
\(491\) | 19.6523 | 0.886898 | 0.443449 | − | 0.896300i | \(-0.353755\pi\) | ||||
0.443449 | + | 0.896300i | \(0.353755\pi\) | |||||||
\(492\) | 84.3997 | 3.80503 | ||||||||
\(493\) | 0.286442 | 0.0129007 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.06058 | 0.137563 | ||||||||
\(496\) | 3.64080 | 0.163477 | ||||||||
\(497\) | −66.8968 | −3.00073 | ||||||||
\(498\) | −35.0829 | −1.57210 | ||||||||
\(499\) | 30.1913 | 1.35155 | 0.675774 | − | 0.737109i | \(-0.263809\pi\) | ||||
0.675774 | + | 0.737109i | \(0.263809\pi\) | |||||||
\(500\) | −7.38651 | −0.330335 | ||||||||
\(501\) | −30.4087 | −1.35856 | ||||||||
\(502\) | −5.21786 | −0.232884 | ||||||||
\(503\) | −32.6853 | −1.45737 | −0.728683 | − | 0.684851i | \(-0.759867\pi\) | ||||
−0.728683 | + | 0.684851i | \(0.759867\pi\) | |||||||
\(504\) | 16.6780 | 0.742898 | ||||||||
\(505\) | −35.7721 | −1.59184 | ||||||||
\(506\) | −7.76328 | −0.345120 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −40.7514 | −1.80805 | ||||||||
\(509\) | 27.5311 | 1.22029 | 0.610147 | − | 0.792288i | \(-0.291111\pi\) | ||||
0.610147 | + | 0.792288i | \(0.291111\pi\) | |||||||
\(510\) | −70.6047 | −3.12643 | ||||||||
\(511\) | −49.4292 | −2.18662 | ||||||||
\(512\) | 8.78685 | 0.388328 | ||||||||
\(513\) | 17.0039 | 0.750740 | ||||||||
\(514\) | −4.17469 | −0.184138 | ||||||||
\(515\) | 10.0023 | 0.440753 | ||||||||
\(516\) | 2.34372 | 0.103176 | ||||||||
\(517\) | 5.15893 | 0.226889 | ||||||||
\(518\) | −12.1923 | −0.535698 | ||||||||
\(519\) | 2.56580 | 0.112626 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0836 | 0.704634 | 0.352317 | − | 0.935881i | \(-0.385394\pi\) | ||||
0.352317 | + | 0.935881i | \(0.385394\pi\) | |||||||
\(522\) | −0.134283 | −0.00587740 | ||||||||
\(523\) | −2.15081 | −0.0940485 | −0.0470243 | − | 0.998894i | \(-0.514974\pi\) | ||||
−0.0470243 | + | 0.998894i | \(0.514974\pi\) | |||||||
\(524\) | 23.6461 | 1.03299 | ||||||||
\(525\) | −43.6452 | −1.90483 | ||||||||
\(526\) | −62.3496 | −2.71857 | ||||||||
\(527\) | 23.2004 | 1.01063 | ||||||||
\(528\) | 1.56385 | 0.0680578 | ||||||||
\(529\) | −11.8484 | −0.515149 | ||||||||
\(530\) | −37.3413 | −1.62200 | ||||||||
\(531\) | −4.37341 | −0.189790 | ||||||||
\(532\) | 73.7299 | 3.19660 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 13.4874 | 0.583658 | ||||||||
\(535\) | −8.07915 | −0.349292 | ||||||||
\(536\) | 0.634139 | 0.0273907 | ||||||||
\(537\) | −20.0552 | −0.865444 | ||||||||
\(538\) | −34.7952 | −1.50013 | ||||||||
\(539\) | 18.8717 | 0.812862 | ||||||||
\(540\) | −41.4363 | −1.78313 | ||||||||
\(541\) | −14.8583 | −0.638808 | −0.319404 | − | 0.947619i | \(-0.603483\pi\) | ||||
−0.319404 | + | 0.947619i | \(0.603483\pi\) | |||||||
\(542\) | −11.3934 | −0.489389 | ||||||||
\(543\) | 43.9465 | 1.88593 | ||||||||
\(544\) | 23.4725 | 1.00637 | ||||||||
\(545\) | 9.77462 | 0.418699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1548 | −1.16105 | −0.580527 | − | 0.814241i | \(-0.697153\pi\) | ||||
−0.580527 | + | 0.814241i | \(0.697153\pi\) | |||||||
\(548\) | 12.6597 | 0.540796 | ||||||||
\(549\) | 13.7730 | 0.587815 | ||||||||
\(550\) | −9.96875 | −0.425069 | ||||||||
\(551\) | −0.244898 | −0.0104330 | ||||||||
\(552\) | −21.8183 | −0.928647 | ||||||||
\(553\) | 16.3857 | 0.696791 | ||||||||
\(554\) | 20.0281 | 0.850911 | ||||||||
\(555\) | −6.28810 | −0.266915 | ||||||||
\(556\) | −23.9421 | −1.01537 | ||||||||
\(557\) | −1.56382 | −0.0662613 | −0.0331307 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331307 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(558\) | −10.8763 | −0.460429 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −12.1146 | −0.511936 | ||||||||
\(561\) | 9.96538 | 0.420739 | ||||||||
\(562\) | −17.4518 | −0.736160 | ||||||||
\(563\) | 22.1420 | 0.933172 | 0.466586 | − | 0.884476i | \(-0.345484\pi\) | ||||
0.466586 | + | 0.884476i | \(0.345484\pi\) | |||||||
\(564\) | 35.1455 | 1.47989 | ||||||||
\(565\) | −9.04715 | −0.380616 | ||||||||
\(566\) | 52.4292 | 2.20376 | ||||||||
\(567\) | 55.9722 | 2.35061 | ||||||||
\(568\) | −42.9422 | −1.80182 | ||||||||
\(569\) | −19.4029 | −0.813412 | −0.406706 | − | 0.913559i | \(-0.633323\pi\) | ||||
−0.406706 | + | 0.913559i | \(0.633323\pi\) | |||||||
\(570\) | 60.3645 | 2.52839 | ||||||||
\(571\) | 6.21755 | 0.260196 | 0.130098 | − | 0.991501i | \(-0.458471\pi\) | ||||
0.130098 | + | 0.991501i | \(0.458471\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.411763 | −0.0172017 | ||||||||
\(574\) | 146.494 | 6.11453 | ||||||||
\(575\) | 14.3196 | 0.597170 | ||||||||
\(576\) | −12.5735 | −0.523894 | ||||||||
\(577\) | −38.5071 | −1.60307 | −0.801535 | − | 0.597948i | \(-0.795983\pi\) | ||||
−0.801535 | + | 0.597948i | \(0.795983\pi\) | |||||||
\(578\) | −18.1351 | −0.754319 | ||||||||
\(579\) | 8.94884 | 0.371901 | ||||||||
\(580\) | 0.596784 | 0.0247801 | ||||||||
\(581\) | −38.3594 | −1.59141 | ||||||||
\(582\) | 15.3982 | 0.638275 | ||||||||
\(583\) | 5.27048 | 0.218281 | ||||||||
\(584\) | −31.7295 | −1.31297 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 50.9564 | 2.10499 | ||||||||
\(587\) | −36.5181 | −1.50726 | −0.753632 | − | 0.657297i | \(-0.771700\pi\) | ||||
−0.753632 | + | 0.657297i | \(0.771700\pi\) | |||||||
\(588\) | 128.565 | 5.30192 | ||||||||
\(589\) | −19.8355 | −0.817307 | ||||||||
\(590\) | 30.8546 | 1.27026 | ||||||||
\(591\) | −19.3216 | −0.794786 | ||||||||
\(592\) | −0.805805 | −0.0331184 | ||||||||
\(593\) | −39.6301 | −1.62741 | −0.813707 | − | 0.581275i | \(-0.802554\pi\) | ||||
−0.813707 | + | 0.581275i | \(0.802554\pi\) | |||||||
\(594\) | 9.28419 | 0.380935 | ||||||||
\(595\) | −77.1985 | −3.16483 | ||||||||
\(596\) | 45.5187 | 1.86452 | ||||||||
\(597\) | 0.981250 | 0.0401599 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3326 | −0.667332 | −0.333666 | − | 0.942691i | \(-0.608286\pi\) | ||||
−0.333666 | + | 0.942691i | \(0.608286\pi\) | |||||||
\(600\) | −28.0166 | −1.14377 | ||||||||
\(601\) | −20.6168 | −0.840975 | −0.420488 | − | 0.907298i | \(-0.638141\pi\) | ||||
−0.420488 | + | 0.907298i | \(0.638141\pi\) | |||||||
\(602\) | 4.06803 | 0.165801 | ||||||||
\(603\) | −0.195044 | −0.00794282 | ||||||||
\(604\) | 38.6338 | 1.57199 | ||||||||
\(605\) | 3.04764 | 0.123904 | ||||||||
\(606\) | 54.6032 | 2.21811 | ||||||||
\(607\) | 27.2740 | 1.10702 | 0.553508 | − | 0.832844i | \(-0.313289\pi\) | ||||
0.553508 | + | 0.832844i | \(0.313289\pi\) | |||||||
\(608\) | −20.0681 | −0.813870 | ||||||||
\(609\) | −0.585432 | −0.0237229 | ||||||||
\(610\) | −97.1688 | −3.93425 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 17.0264 | 0.688253 | ||||||||
\(613\) | 22.7881 | 0.920401 | 0.460201 | − | 0.887815i | \(-0.347777\pi\) | ||||
0.460201 | + | 0.887815i | \(0.347777\pi\) | |||||||
\(614\) | 51.7998 | 2.09047 | ||||||||
\(615\) | 75.5533 | 3.04660 | ||||||||
\(616\) | 16.6075 | 0.669135 | ||||||||
\(617\) | −1.28652 | −0.0517933 | −0.0258967 | − | 0.999665i | \(-0.508244\pi\) | ||||
−0.0258967 | + | 0.999665i | \(0.508244\pi\) | |||||||
\(618\) | −15.2677 | −0.614156 | ||||||||
\(619\) | −16.7525 | −0.673339 | −0.336669 | − | 0.941623i | \(-0.609300\pi\) | ||||
−0.336669 | + | 0.941623i | \(0.609300\pi\) | |||||||
\(620\) | 48.3366 | 1.94124 | ||||||||
\(621\) | −13.3363 | −0.535167 | ||||||||
\(622\) | 24.5056 | 0.982585 | ||||||||
\(623\) | 14.7470 | 0.590827 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.0527 | −1.12211 | ||||||||
\(626\) | −56.0734 | −2.24114 | ||||||||
\(627\) | −8.52003 | −0.340257 | ||||||||
\(628\) | −72.4954 | −2.89288 | ||||||||
\(629\) | −5.13487 | −0.204741 | ||||||||
\(630\) | 36.1904 | 1.44186 | ||||||||
\(631\) | 39.1631 | 1.55906 | 0.779529 | − | 0.626366i | \(-0.215458\pi\) | ||||
0.779529 | + | 0.626366i | \(0.215458\pi\) | |||||||
\(632\) | 10.5183 | 0.418394 | ||||||||
\(633\) | 49.6091 | 1.97179 | ||||||||
\(634\) | −11.9212 | −0.473453 | ||||||||
\(635\) | −36.4800 | −1.44767 | ||||||||
\(636\) | 35.9055 | 1.42374 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.133715 | −0.00529383 | ||||||||
\(639\) | 13.2079 | 0.522496 | ||||||||
\(640\) | 59.9774 | 2.37082 | ||||||||
\(641\) | 6.31152 | 0.249290 | 0.124645 | − | 0.992201i | \(-0.460221\pi\) | ||||
0.124645 | + | 0.992201i | \(0.460221\pi\) | |||||||
\(642\) | 12.3322 | 0.486712 | ||||||||
\(643\) | 5.47875 | 0.216061 | 0.108030 | − | 0.994148i | \(-0.465546\pi\) | ||||
0.108030 | + | 0.994148i | \(0.465546\pi\) | |||||||
\(644\) | −57.8271 | −2.27871 | ||||||||
\(645\) | 2.09806 | 0.0826111 | ||||||||
\(646\) | 49.2937 | 1.93943 | ||||||||
\(647\) | 7.22980 | 0.284233 | 0.142116 | − | 0.989850i | \(-0.454609\pi\) | ||||
0.142116 | + | 0.989850i | \(0.454609\pi\) | |||||||
\(648\) | 35.9295 | 1.41144 | ||||||||
\(649\) | −4.35492 | −0.170946 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −47.4171 | −1.85842 | ||||||||
\(652\) | −36.5497 | −1.43140 | ||||||||
\(653\) | 13.2893 | 0.520050 | 0.260025 | − | 0.965602i | \(-0.416269\pi\) | ||||
0.260025 | + | 0.965602i | \(0.416269\pi\) | |||||||
\(654\) | −14.9202 | −0.583425 | ||||||||
\(655\) | 21.1677 | 0.827090 | ||||||||
\(656\) | 9.68198 | 0.378018 | ||||||||
\(657\) | 9.75914 | 0.380740 | ||||||||
\(658\) | 61.0026 | 2.37813 | ||||||||
\(659\) | −4.15593 | −0.161892 | −0.0809461 | − | 0.996718i | \(-0.525794\pi\) | ||||
−0.0809461 | + | 0.996718i | \(0.525794\pi\) | |||||||
\(660\) | 20.7622 | 0.808169 | ||||||||
\(661\) | −35.1591 | −1.36753 | −0.683765 | − | 0.729702i | \(-0.739659\pi\) | ||||
−0.683765 | + | 0.729702i | \(0.739659\pi\) | |||||||
\(662\) | 37.8863 | 1.47249 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.6235 | −0.955578 | ||||||||
\(665\) | 66.0019 | 2.55944 | ||||||||
\(666\) | 2.40720 | 0.0932773 | ||||||||
\(667\) | 0.192075 | 0.00743719 | ||||||||
\(668\) | −51.7354 | −2.00170 | ||||||||
\(669\) | −41.8480 | −1.61794 | ||||||||
\(670\) | 1.37605 | 0.0531613 | ||||||||
\(671\) | 13.7147 | 0.529451 | ||||||||
\(672\) | −47.9732 | −1.85061 | ||||||||
\(673\) | 5.17495 | 0.199479 | 0.0997397 | − | 0.995014i | \(-0.468199\pi\) | ||||
0.0997397 | + | 0.995014i | \(0.468199\pi\) | |||||||
\(674\) | 28.0617 | 1.08090 | ||||||||
\(675\) | −17.1250 | −0.659142 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.11284 | 0.311802 | 0.155901 | − | 0.987773i | \(-0.450172\pi\) | ||||
0.155901 | + | 0.987773i | \(0.450172\pi\) | |||||||
\(678\) | 13.8098 | 0.530360 | ||||||||
\(679\) | 16.8362 | 0.646115 | ||||||||
\(680\) | −49.5551 | −1.90035 | ||||||||
\(681\) | 18.8201 | 0.721187 | ||||||||
\(682\) | −10.8303 | −0.414712 | ||||||||
\(683\) | −18.6591 | −0.713969 | −0.356985 | − | 0.934110i | \(-0.616195\pi\) | ||||
−0.356985 | + | 0.934110i | \(0.616195\pi\) | |||||||
\(684\) | −14.5570 | −0.556600 | ||||||||
\(685\) | 11.3328 | 0.433003 | ||||||||
\(686\) | 140.379 | 5.35970 | ||||||||
\(687\) | 6.45692 | 0.246347 | ||||||||
\(688\) | 0.268862 | 0.0102503 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −47.3444 | −1.80237 | ||||||||
\(691\) | 29.5207 | 1.12302 | 0.561510 | − | 0.827470i | \(-0.310221\pi\) | ||||
0.561510 | + | 0.827470i | \(0.310221\pi\) | |||||||
\(692\) | 4.36529 | 0.165944 | ||||||||
\(693\) | −5.10802 | −0.194038 | ||||||||
\(694\) | −35.9036 | −1.36288 | ||||||||
\(695\) | −21.4326 | −0.812983 | ||||||||
\(696\) | −0.375799 | −0.0142446 | ||||||||
\(697\) | 61.6969 | 2.33694 | ||||||||
\(698\) | −37.9194 | −1.43527 | ||||||||
\(699\) | −51.1664 | −1.93529 | ||||||||
\(700\) | −74.2552 | −2.80658 | ||||||||
\(701\) | 32.4406 | 1.22526 | 0.612632 | − | 0.790368i | \(-0.290111\pi\) | ||||
0.612632 | + | 0.790368i | \(0.290111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.39012 | 0.165577 | ||||||||
\(704\) | −12.5203 | −0.471876 | ||||||||
\(705\) | 31.4617 | 1.18492 | ||||||||
\(706\) | 30.9637 | 1.16533 | ||||||||
\(707\) | 59.7027 | 2.24535 | ||||||||
\(708\) | −29.6682 | −1.11500 | ||||||||
\(709\) | −47.2300 | −1.77376 | −0.886880 | − | 0.462000i | \(-0.847132\pi\) | ||||
−0.886880 | + | 0.462000i | \(0.847132\pi\) | |||||||
\(710\) | −93.1822 | −3.49707 | ||||||||
\(711\) | −3.23514 | −0.121327 | ||||||||
\(712\) | 9.46637 | 0.354767 | ||||||||
\(713\) | 15.5572 | 0.582620 | ||||||||
\(714\) | 117.837 | 4.40995 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −34.1206 | −1.27515 | ||||||||
\(717\) | −36.1257 | −1.34914 | ||||||||
\(718\) | −18.0567 | −0.673871 | ||||||||
\(719\) | 39.5065 | 1.47334 | 0.736672 | − | 0.676250i | \(-0.236396\pi\) | ||||
0.736672 | + | 0.676250i | \(0.236396\pi\) | |||||||
\(720\) | 2.39187 | 0.0891398 | ||||||||
\(721\) | −16.6935 | −0.621700 | ||||||||
\(722\) | 2.02604 | 0.0754013 | ||||||||
\(723\) | −8.92307 | −0.331852 | ||||||||
\(724\) | 74.7678 | 2.77872 | ||||||||
\(725\) | 0.246642 | 0.00916006 | ||||||||
\(726\) | −4.65197 | −0.172651 | ||||||||
\(727\) | −1.94811 | −0.0722515 | −0.0361258 | − | 0.999347i | \(-0.511502\pi\) | ||||
−0.0361258 | + | 0.999347i | \(0.511502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.9235 | 0.478648 | ||||||||
\(730\) | −68.8511 | −2.54830 | ||||||||
\(731\) | 1.71328 | 0.0633679 | ||||||||
\(732\) | 93.4324 | 3.45336 | ||||||||
\(733\) | −41.7816 | −1.54324 | −0.771618 | − | 0.636086i | \(-0.780552\pi\) | ||||
−0.771618 | + | 0.636086i | \(0.780552\pi\) | |||||||
\(734\) | −78.0401 | −2.88051 | ||||||||
\(735\) | 115.089 | 4.24513 | ||||||||
\(736\) | 15.7396 | 0.580170 | ||||||||
\(737\) | −0.194220 | −0.00715417 | ||||||||
\(738\) | −28.9232 | −1.06468 | ||||||||
\(739\) | 10.6578 | 0.392054 | 0.196027 | − | 0.980598i | \(-0.437196\pi\) | ||||
0.196027 | + | 0.980598i | \(0.437196\pi\) | |||||||
\(740\) | −10.6982 | −0.393272 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 62.3217 | 2.28790 | ||||||||
\(743\) | 12.3377 | 0.452626 | 0.226313 | − | 0.974055i | \(-0.427333\pi\) | ||||
0.226313 | + | 0.974055i | \(0.427333\pi\) | |||||||
\(744\) | −30.4379 | −1.11591 | ||||||||
\(745\) | 40.7477 | 1.49288 | ||||||||
\(746\) | −36.4886 | −1.33594 | ||||||||
\(747\) | 7.57354 | 0.277101 | ||||||||
\(748\) | 16.9544 | 0.619916 | ||||||||
\(749\) | 13.4839 | 0.492691 | ||||||||
\(750\) | 10.0931 | 0.368549 | ||||||||
\(751\) | −28.8574 | −1.05302 | −0.526511 | − | 0.850168i | \(-0.676500\pi\) | ||||
−0.526511 | + | 0.850168i | \(0.676500\pi\) | |||||||
\(752\) | 4.03175 | 0.147023 | ||||||||
\(753\) | 4.49134 | 0.163674 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.5844 | 1.25866 | ||||||||
\(756\) | 69.1561 | 2.51518 | ||||||||
\(757\) | 6.38475 | 0.232058 | 0.116029 | − | 0.993246i | \(-0.462983\pi\) | ||||
0.116029 | + | 0.993246i | \(0.462983\pi\) | |||||||
\(758\) | 23.0235 | 0.836250 | ||||||||
\(759\) | 6.68234 | 0.242554 | ||||||||
\(760\) | 42.3678 | 1.53684 | ||||||||
\(761\) | 9.99134 | 0.362186 | 0.181093 | − | 0.983466i | \(-0.442037\pi\) | ||||
0.181093 | + | 0.983466i | \(0.442037\pi\) | |||||||
\(762\) | 55.6839 | 2.01721 | ||||||||
\(763\) | −16.3136 | −0.590591 | ||||||||
\(764\) | −0.700547 | −0.0253449 | ||||||||
\(765\) | 15.2418 | 0.551069 | ||||||||
\(766\) | −81.7008 | −2.95197 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −41.4430 | −1.49545 | ||||||||
\(769\) | 14.2532 | 0.513982 | 0.256991 | − | 0.966414i | \(-0.417269\pi\) | ||||
0.256991 | + | 0.966414i | \(0.417269\pi\) | |||||||
\(770\) | 36.0373 | 1.29869 | ||||||||
\(771\) | 3.59342 | 0.129414 | ||||||||
\(772\) | 15.2250 | 0.547959 | ||||||||
\(773\) | −20.1973 | −0.726445 | −0.363222 | − | 0.931702i | \(-0.618323\pi\) | ||||
−0.363222 | + | 0.931702i | \(0.618323\pi\) | |||||||
\(774\) | −0.803178 | −0.0288696 | ||||||||
\(775\) | 19.9768 | 0.717588 | ||||||||
\(776\) | 10.8075 | 0.387965 | ||||||||
\(777\) | 10.4947 | 0.376494 | ||||||||
\(778\) | −57.7401 | −2.07008 | ||||||||
\(779\) | −52.7486 | −1.88991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.1520 | 0.470617 | ||||||||
\(782\) | −38.6615 | −1.38253 | ||||||||
\(783\) | −0.229705 | −0.00820900 | ||||||||
\(784\) | 14.7484 | 0.526729 | ||||||||
\(785\) | −64.8968 | −2.31627 | ||||||||
\(786\) | −32.3108 | −1.15249 | ||||||||
\(787\) | −32.9401 | −1.17419 | −0.587093 | − | 0.809519i | \(-0.699728\pi\) | ||||
−0.587093 | + | 0.809519i | \(0.699728\pi\) | |||||||
\(788\) | −32.8726 | −1.17104 | ||||||||
\(789\) | 53.6682 | 1.91064 | ||||||||
\(790\) | 22.8240 | 0.812043 | ||||||||
\(791\) | 15.0994 | 0.536875 | ||||||||
\(792\) | −3.27893 | −0.116512 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −42.9998 | −1.52601 | ||||||||
\(795\) | 32.1420 | 1.13996 | ||||||||
\(796\) | 1.66943 | 0.0591716 | ||||||||
\(797\) | 10.2184 | 0.361953 | 0.180977 | − | 0.983487i | \(-0.442074\pi\) | ||||
0.180977 | + | 0.983487i | \(0.442074\pi\) | |||||||
\(798\) | −100.747 | −3.56639 | ||||||||
\(799\) | 25.6917 | 0.908906 | ||||||||
\(800\) | 20.2111 | 0.714570 | ||||||||
\(801\) | −2.91161 | −0.102877 | ||||||||
\(802\) | 13.0711 | 0.461558 | ||||||||
\(803\) | 9.71787 | 0.342936 | ||||||||
\(804\) | −1.32313 | −0.0466634 | ||||||||
\(805\) | −51.7659 | −1.82451 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.9505 | 1.05431 | ||||||||
\(808\) | 38.3242 | 1.34824 | ||||||||
\(809\) | −46.1097 | −1.62113 | −0.810565 | − | 0.585649i | \(-0.800840\pi\) | ||||
−0.810565 | + | 0.585649i | \(0.800840\pi\) | |||||||
\(810\) | 77.9650 | 2.73941 | ||||||||
\(811\) | 25.9692 | 0.911904 | 0.455952 | − | 0.890004i | \(-0.349299\pi\) | ||||
0.455952 | + | 0.890004i | \(0.349299\pi\) | |||||||
\(812\) | −0.996017 | −0.0349533 | ||||||||
\(813\) | 9.80702 | 0.343947 | ||||||||
\(814\) | 2.39703 | 0.0840157 | ||||||||
\(815\) | −32.7187 | −1.14609 | ||||||||
\(816\) | 7.78804 | 0.272636 | ||||||||
\(817\) | −1.46479 | −0.0512466 | ||||||||
\(818\) | −15.1023 | −0.528040 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 128.542 | 4.48886 | ||||||||
\(821\) | −37.0459 | −1.29291 | −0.646455 | − | 0.762952i | \(-0.723749\pi\) | ||||
−0.646455 | + | 0.762952i | \(0.723749\pi\) | |||||||
\(822\) | −17.2986 | −0.603357 | ||||||||
\(823\) | −20.7517 | −0.723360 | −0.361680 | − | 0.932302i | \(-0.617797\pi\) | ||||
−0.361680 | + | 0.932302i | \(0.617797\pi\) | |||||||
\(824\) | −10.7159 | −0.373305 | ||||||||
\(825\) | 8.58073 | 0.298743 | ||||||||
\(826\) | −51.4955 | −1.79176 | ||||||||
\(827\) | 16.7564 | 0.582675 | 0.291338 | − | 0.956620i | \(-0.405900\pi\) | ||||
0.291338 | + | 0.956620i | \(0.405900\pi\) | |||||||
\(828\) | 11.4172 | 0.396774 | ||||||||
\(829\) | −16.9103 | −0.587317 | −0.293659 | − | 0.955910i | \(-0.594873\pi\) | ||||
−0.293659 | + | 0.955910i | \(0.594873\pi\) | |||||||
\(830\) | −53.4317 | −1.85464 | ||||||||
\(831\) | −17.2394 | −0.598029 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 93.9819 | 3.25628 | ||||||||
\(834\) | 32.7151 | 1.13283 | ||||||||
\(835\) | −46.3127 | −1.60272 | ||||||||
\(836\) | −14.4954 | −0.501335 | ||||||||
\(837\) | −18.6050 | −0.643083 | ||||||||
\(838\) | 84.1555 | 2.90710 | ||||||||
\(839\) | −8.60829 | −0.297191 | −0.148596 | − | 0.988898i | \(-0.547475\pi\) | ||||
−0.148596 | + | 0.988898i | \(0.547475\pi\) | |||||||
\(840\) | 101.281 | 3.49452 | ||||||||
\(841\) | −28.9967 | −0.999886 | ||||||||
\(842\) | 24.8069 | 0.854901 | ||||||||
\(843\) | 15.0219 | 0.517380 | ||||||||
\(844\) | 84.4018 | 2.90523 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0442 | −0.414087 | ||||||||
\(847\) | −5.08642 | −0.174772 | ||||||||
\(848\) | 4.11893 | 0.141445 | ||||||||
\(849\) | −45.1291 | −1.54883 | ||||||||
\(850\) | −49.6448 | −1.70280 | ||||||||
\(851\) | −3.44321 | −0.118032 | ||||||||
\(852\) | 89.5992 | 3.06962 | ||||||||
\(853\) | −15.7832 | −0.540407 | −0.270204 | − | 0.962803i | \(-0.587091\pi\) | ||||
−0.270204 | + | 0.962803i | \(0.587091\pi\) | |||||||
\(854\) | 162.172 | 5.54941 | ||||||||
\(855\) | −13.0312 | −0.445658 | ||||||||
\(856\) | 8.65554 | 0.295840 | ||||||||
\(857\) | 18.2640 | 0.623887 | 0.311944 | − | 0.950101i | \(-0.399020\pi\) | ||||
0.311944 | + | 0.950101i | \(0.399020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.02303 | 0.0690248 | 0.0345124 | − | 0.999404i | \(-0.489012\pi\) | ||||
0.0345124 | + | 0.999404i | \(0.489012\pi\) | |||||||
\(860\) | 3.56951 | 0.121719 | ||||||||
\(861\) | −126.096 | −4.29735 | ||||||||
\(862\) | −1.73841 | −0.0592103 | ||||||||
\(863\) | 32.2203 | 1.09679 | 0.548395 | − | 0.836219i | \(-0.315239\pi\) | ||||
0.548395 | + | 0.836219i | \(0.315239\pi\) | |||||||
\(864\) | −18.8232 | −0.640378 | ||||||||
\(865\) | 3.90775 | 0.132867 | ||||||||
\(866\) | 21.1319 | 0.718091 | ||||||||
\(867\) | 15.6100 | 0.530143 | ||||||||
\(868\) | −80.6724 | −2.73820 | ||||||||
\(869\) | −3.22146 | −0.109280 | ||||||||
\(870\) | −0.815463 | −0.0276468 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −10.4720 | −0.354626 | ||||||||
\(873\) | −3.32409 | −0.112503 | ||||||||
\(874\) | 33.0541 | 1.11807 | ||||||||
\(875\) | 11.0357 | 0.373076 | ||||||||
\(876\) | 66.2036 | 2.23681 | ||||||||
\(877\) | 24.0953 | 0.813640 | 0.406820 | − | 0.913508i | \(-0.366638\pi\) | ||||
0.406820 | + | 0.913508i | \(0.366638\pi\) | |||||||
\(878\) | −74.9195 | −2.52841 | ||||||||
\(879\) | −43.8614 | −1.47941 | ||||||||
\(880\) | 2.38176 | 0.0802890 | ||||||||
\(881\) | −37.1187 | −1.25056 | −0.625280 | − | 0.780400i | \(-0.715015\pi\) | ||||
−0.625280 | + | 0.780400i | \(0.715015\pi\) | |||||||
\(882\) | −44.0584 | −1.48352 | ||||||||
\(883\) | 31.7603 | 1.06882 | 0.534409 | − | 0.845226i | \(-0.320534\pi\) | ||||
0.534409 | + | 0.845226i | \(0.320534\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.5585 | −0.892754 | ||||||||
\(886\) | 16.6522 | 0.559440 | ||||||||
\(887\) | 22.8376 | 0.766813 | 0.383406 | − | 0.923580i | \(-0.374751\pi\) | ||||
0.383406 | + | 0.923580i | \(0.374751\pi\) | |||||||
\(888\) | 6.73671 | 0.226069 | ||||||||
\(889\) | 60.8842 | 2.04199 | ||||||||
\(890\) | 20.5415 | 0.688553 | ||||||||
\(891\) | −11.0042 | −0.368656 | ||||||||
\(892\) | −71.1975 | −2.38387 | ||||||||
\(893\) | −21.9655 | −0.735046 | ||||||||
\(894\) | −62.1981 | −2.08022 | ||||||||
\(895\) | −30.5442 | −1.02098 | ||||||||
\(896\) | −100.101 | −3.34413 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32.7023 | −1.09129 | ||||||||
\(899\) | 0.267958 | 0.00893688 | ||||||||
\(900\) | 14.6607 | 0.488690 | ||||||||
\(901\) | 26.2472 | 0.874421 | ||||||||
\(902\) | −28.8009 | −0.958966 | ||||||||
\(903\) | −3.50161 | −0.116526 | ||||||||
\(904\) | 9.69259 | 0.322371 | ||||||||
\(905\) | 66.9310 | 2.22486 | ||||||||
\(906\) | −52.7903 | −1.75384 | ||||||||
\(907\) | 0.817669 | 0.0271502 | 0.0135751 | − | 0.999908i | \(-0.495679\pi\) | ||||
0.0135751 | + | 0.999908i | \(0.495679\pi\) | |||||||
\(908\) | 32.0193 | 1.06260 | ||||||||
\(909\) | −11.7875 | −0.390967 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.0495 | −0.896191 | −0.448095 | − | 0.893986i | \(-0.647897\pi\) | ||||
−0.448095 | + | 0.893986i | \(0.647897\pi\) | |||||||
\(912\) | −6.65849 | −0.220485 | ||||||||
\(913\) | 7.54152 | 0.249588 | ||||||||
\(914\) | 4.09524 | 0.135458 | ||||||||
\(915\) | 83.6393 | 2.76503 | ||||||||
\(916\) | 10.9854 | 0.362967 | ||||||||
\(917\) | −35.3283 | −1.16664 | ||||||||
\(918\) | 46.2357 | 1.52601 | ||||||||
\(919\) | 1.21525 | 0.0400874 | 0.0200437 | − | 0.999799i | \(-0.493619\pi\) | ||||
0.0200437 | + | 0.999799i | \(0.493619\pi\) | |||||||
\(920\) | −33.2294 | −1.09554 | ||||||||
\(921\) | −44.5874 | −1.46920 | ||||||||
\(922\) | −81.4486 | −2.68237 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −34.6516 | −1.13995 | ||||||||
\(925\) | −4.42140 | −0.145375 | ||||||||
\(926\) | 41.9502 | 1.37857 | ||||||||
\(927\) | 3.29592 | 0.108252 | ||||||||
\(928\) | 0.271100 | 0.00889929 | ||||||||
\(929\) | −6.38753 | −0.209568 | −0.104784 | − | 0.994495i | \(-0.533415\pi\) | ||||
−0.104784 | + | 0.994495i | \(0.533415\pi\) | |||||||
\(930\) | −66.0485 | −2.16581 | ||||||||
\(931\) | −80.3511 | −2.63340 | ||||||||
\(932\) | −87.0513 | −2.85146 | ||||||||
\(933\) | −21.0935 | −0.690571 | ||||||||
\(934\) | −23.7246 | −0.776294 | ||||||||
\(935\) | 15.1774 | 0.496353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.36713 | −0.0773308 | −0.0386654 | − | 0.999252i | \(-0.512311\pi\) | ||||
−0.0386654 | + | 0.999252i | \(0.512311\pi\) | |||||||
\(938\) | −2.29659 | −0.0749862 | ||||||||
\(939\) | 48.2659 | 1.57510 | ||||||||
\(940\) | 53.5270 | 1.74586 | ||||||||
\(941\) | −39.7672 | −1.29637 | −0.648187 | − | 0.761481i | \(-0.724472\pi\) | ||||
−0.648187 | + | 0.761481i | \(0.724472\pi\) | |||||||
\(942\) | 99.0598 | 3.22754 | ||||||||
\(943\) | 41.3712 | 1.34723 | ||||||||
\(944\) | −3.40341 | −0.110772 | ||||||||
\(945\) | 61.9075 | 2.01385 | ||||||||
\(946\) | −0.799782 | −0.0260032 | ||||||||
\(947\) | 20.3615 | 0.661659 | 0.330830 | − | 0.943690i | \(-0.392671\pi\) | ||||
0.330830 | + | 0.943690i | \(0.392671\pi\) | |||||||
\(948\) | −21.9464 | −0.712786 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 42.4445 | 1.37708 | ||||||||
\(951\) | 10.2614 | 0.332747 | ||||||||
\(952\) | 82.7060 | 2.68052 | ||||||||
\(953\) | −46.3605 | −1.50176 | −0.750882 | − | 0.660437i | \(-0.770371\pi\) | ||||
−0.750882 | + | 0.660437i | \(0.770371\pi\) | |||||||
\(954\) | −12.3046 | −0.398376 | ||||||||
\(955\) | −0.627119 | −0.0202931 | ||||||||
\(956\) | −61.4620 | −1.98782 | ||||||||
\(957\) | 0.115097 | 0.00372056 | ||||||||
\(958\) | 90.6830 | 2.92984 | ||||||||
\(959\) | −18.9141 | −0.610768 | ||||||||
\(960\) | −76.3551 | −2.46435 | ||||||||
\(961\) | −9.29676 | −0.299896 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.66221 | −0.0857887 | ||||||||
\(964\) | −15.1811 | −0.488951 | ||||||||
\(965\) | 13.6292 | 0.438739 | ||||||||
\(966\) | 79.0165 | 2.54231 | ||||||||
\(967\) | −25.9505 | −0.834511 | −0.417256 | − | 0.908789i | \(-0.637008\pi\) | ||||
−0.417256 | + | 0.908789i | \(0.637008\pi\) | |||||||
\(968\) | −3.26506 | −0.104943 | ||||||||
\(969\) | −42.4301 | −1.36305 | ||||||||
\(970\) | 23.4516 | 0.752985 | ||||||||
\(971\) | −33.0430 | −1.06040 | −0.530200 | − | 0.847873i | \(-0.677883\pi\) | ||||
−0.530200 | + | 0.847873i | \(0.677883\pi\) | |||||||
\(972\) | −34.1784 | −1.09627 | ||||||||
\(973\) | 35.7704 | 1.14675 | ||||||||
\(974\) | 73.7697 | 2.36373 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7182 | 0.343081 | ||||||||
\(977\) | 49.6432 | 1.58823 | 0.794113 | − | 0.607770i | \(-0.207936\pi\) | ||||
0.794113 | + | 0.607770i | \(0.207936\pi\) | |||||||
\(978\) | 49.9425 | 1.59699 | ||||||||
\(979\) | −2.89929 | −0.0926618 | ||||||||
\(980\) | 195.805 | 6.25477 | ||||||||
\(981\) | 3.22090 | 0.102835 | ||||||||
\(982\) | −45.6868 | −1.45793 | ||||||||
\(983\) | 9.33920 | 0.297874 | 0.148937 | − | 0.988847i | \(-0.452415\pi\) | ||||
0.148937 | + | 0.988847i | \(0.452415\pi\) | |||||||
\(984\) | −80.9435 | −2.58038 | ||||||||
\(985\) | −29.4271 | −0.937624 | ||||||||
\(986\) | −0.665907 | −0.0212068 | ||||||||
\(987\) | −52.5088 | −1.67137 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.14885 | 0.0365313 | ||||||||
\(990\) | −7.11509 | −0.226132 | ||||||||
\(991\) | −0.819686 | −0.0260382 | −0.0130191 | − | 0.999915i | \(-0.504144\pi\) | ||||
−0.0130191 | + | 0.999915i | \(0.504144\pi\) | |||||||
\(992\) | 21.9578 | 0.697160 | ||||||||
\(993\) | −32.6111 | −1.03488 | ||||||||
\(994\) | 155.519 | 4.93275 | ||||||||
\(995\) | 1.49445 | 0.0473773 | ||||||||
\(996\) | 51.3771 | 1.62795 | ||||||||
\(997\) | 42.0034 | 1.33026 | 0.665130 | − | 0.746728i | \(-0.268376\pi\) | ||||
0.665130 | + | 0.746728i | \(0.268376\pi\) | |||||||
\(998\) | −70.1873 | −2.22174 | ||||||||
\(999\) | 4.11778 | 0.130281 |
(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 | 1859.2.a.t.1.4 | yes | 21 | |
13.12 | even | 2 | 1859.2.a.s.1.18 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.18 | ✓ | 21 | 13.12 | even | 2 | ||
1859.2.a.t.1.4 | yes | 21 | 1.1 | even | 1 | trivial |