Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −25.4513 | −1.12480 | −0.562400 | − | 0.826865i | \(-0.690122\pi\) | ||||
−0.562400 | + | 0.826865i | \(0.690122\pi\) | |||||||
\(3\) | 80.7952 | 0.575890 | 0.287945 | − | 0.957647i | \(-0.407028\pi\) | ||||
0.287945 | + | 0.957647i | \(0.407028\pi\) | |||||||
\(4\) | 135.770 | 0.265177 | ||||||||
\(5\) | −783.444 | −0.560587 | −0.280293 | − | 0.959914i | \(-0.590432\pi\) | ||||
−0.280293 | + | 0.959914i | \(0.590432\pi\) | |||||||
\(6\) | −2056.34 | −0.647762 | ||||||||
\(7\) | −5744.00 | −0.904219 | −0.452109 | − | 0.891963i | \(-0.649328\pi\) | ||||
−0.452109 | + | 0.891963i | \(0.649328\pi\) | |||||||
\(8\) | 9575.55 | 0.826530 | ||||||||
\(9\) | −13155.1 | −0.668350 | ||||||||
\(10\) | 19939.7 | 0.630549 | ||||||||
\(11\) | 2593.14 | 0.0534022 | 0.0267011 | − | 0.999643i | \(-0.491500\pi\) | ||||
0.0267011 | + | 0.999643i | \(0.491500\pi\) | |||||||
\(12\) | 10969.6 | 0.152713 | ||||||||
\(13\) | −108940. | −1.05790 | −0.528949 | − | 0.848654i | \(-0.677414\pi\) | ||||
−0.528949 | + | 0.848654i | \(0.677414\pi\) | |||||||
\(14\) | 146193. | 1.01707 | ||||||||
\(15\) | −63298.5 | −0.322837 | ||||||||
\(16\) | −313225. | −1.19486 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 334816. | 0.751761 | ||||||||
\(19\) | 95650.6 | 0.168382 | 0.0841912 | − | 0.996450i | \(-0.473169\pi\) | ||||
0.0841912 | + | 0.996450i | \(0.473169\pi\) | |||||||
\(20\) | −106369. | −0.148655 | ||||||||
\(21\) | −464088. | −0.520731 | ||||||||
\(22\) | −65999.0 | −0.0600669 | ||||||||
\(23\) | −92928.9 | −0.0692429 | −0.0346215 | − | 0.999400i | \(-0.511023\pi\) | ||||
−0.0346215 | + | 0.999400i | \(0.511023\pi\) | |||||||
\(24\) | 773658. | 0.475990 | ||||||||
\(25\) | −1.33934e6 | −0.685742 | ||||||||
\(26\) | 2.77268e6 | 1.18992 | ||||||||
\(27\) | −2.65316e6 | −0.960787 | ||||||||
\(28\) | −779865. | −0.239778 | ||||||||
\(29\) | −2.91402e6 | −0.765071 | −0.382536 | − | 0.923941i | \(-0.624949\pi\) | ||||
−0.382536 | + | 0.923941i | \(0.624949\pi\) | |||||||
\(30\) | 1.61103e6 | 0.363127 | ||||||||
\(31\) | −2.18026e6 | −0.424014 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
−0.212007 | + | 0.977268i | \(0.568000\pi\) | |||||||
\(32\) | 3.06931e6 | 0.517447 | ||||||||
\(33\) | 209513. | 0.0307538 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.50010e6 | 0.506893 | ||||||||
\(36\) | −1.78608e6 | −0.177231 | ||||||||
\(37\) | −1.09912e7 | −0.964131 | −0.482066 | − | 0.876135i | \(-0.660113\pi\) | ||||
−0.482066 | + | 0.876135i | \(0.660113\pi\) | |||||||
\(38\) | −2.43444e6 | −0.189397 | ||||||||
\(39\) | −8.80185e6 | −0.609233 | ||||||||
\(40\) | −7.50190e6 | −0.463342 | ||||||||
\(41\) | −1.11239e7 | −0.614794 | −0.307397 | − | 0.951581i | \(-0.599458\pi\) | ||||
−0.307397 | + | 0.951581i | \(0.599458\pi\) | |||||||
\(42\) | 1.18116e7 | 0.585718 | ||||||||
\(43\) | 1.20690e7 | 0.538348 | 0.269174 | − | 0.963092i | \(-0.413249\pi\) | ||||
0.269174 | + | 0.963092i | \(0.413249\pi\) | |||||||
\(44\) | 352072. | 0.0141610 | ||||||||
\(45\) | 1.03063e7 | 0.374669 | ||||||||
\(46\) | 2.36516e6 | 0.0778845 | ||||||||
\(47\) | −5.88161e7 | −1.75815 | −0.879075 | − | 0.476684i | \(-0.841839\pi\) | ||||
−0.879075 | + | 0.476684i | \(0.841839\pi\) | |||||||
\(48\) | −2.53071e7 | −0.688107 | ||||||||
\(49\) | −7.36005e6 | −0.182389 | ||||||||
\(50\) | 3.40880e7 | 0.771323 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.47909e7 | −0.280530 | ||||||||
\(53\) | −1.85335e7 | −0.322638 | −0.161319 | − | 0.986902i | \(-0.551575\pi\) | ||||
−0.161319 | + | 0.986902i | \(0.551575\pi\) | |||||||
\(54\) | 6.75265e7 | 1.08069 | ||||||||
\(55\) | −2.03158e6 | −0.0299366 | ||||||||
\(56\) | −5.50020e7 | −0.747364 | ||||||||
\(57\) | 7.72811e6 | 0.0969697 | ||||||||
\(58\) | 7.41657e7 | 0.860553 | ||||||||
\(59\) | −9.51920e7 | −1.02274 | −0.511372 | − | 0.859360i | \(-0.670862\pi\) | ||||
−0.511372 | + | 0.859360i | \(0.670862\pi\) | |||||||
\(60\) | −8.59406e6 | −0.0856087 | ||||||||
\(61\) | 4.53894e7 | 0.419730 | 0.209865 | − | 0.977730i | \(-0.432697\pi\) | ||||
0.209865 | + | 0.977730i | \(0.432697\pi\) | |||||||
\(62\) | 5.54905e7 | 0.476932 | ||||||||
\(63\) | 7.55632e7 | 0.604335 | ||||||||
\(64\) | 8.22531e7 | 0.612833 | ||||||||
\(65\) | 8.53486e7 | 0.593043 | ||||||||
\(66\) | −5.33240e6 | −0.0345919 | ||||||||
\(67\) | 2.09338e8 | 1.26915 | 0.634574 | − | 0.772862i | \(-0.281176\pi\) | ||||
0.634574 | + | 0.772862i | \(0.281176\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.50820e6 | −0.0398763 | ||||||||
\(70\) | −1.14534e8 | −0.570154 | ||||||||
\(71\) | −2.05372e8 | −0.959132 | −0.479566 | − | 0.877506i | \(-0.659206\pi\) | ||||
−0.479566 | + | 0.877506i | \(0.659206\pi\) | |||||||
\(72\) | −1.25968e8 | −0.552412 | ||||||||
\(73\) | −1.16456e8 | −0.479966 | −0.239983 | − | 0.970777i | \(-0.577142\pi\) | ||||
−0.239983 | + | 0.970777i | \(0.577142\pi\) | |||||||
\(74\) | 2.79740e8 | 1.08446 | ||||||||
\(75\) | −1.08212e8 | −0.394912 | ||||||||
\(76\) | 1.29865e7 | 0.0446510 | ||||||||
\(77\) | −1.48950e7 | −0.0482873 | ||||||||
\(78\) | 2.24019e8 | 0.685265 | ||||||||
\(79\) | 3.90576e8 | 1.12819 | 0.564096 | − | 0.825709i | \(-0.309225\pi\) | ||||
0.564096 | + | 0.825709i | \(0.309225\pi\) | |||||||
\(80\) | 2.45394e8 | 0.669822 | ||||||||
\(81\) | 4.45700e7 | 0.115043 | ||||||||
\(82\) | 2.83118e8 | 0.691521 | ||||||||
\(83\) | −2.81235e8 | −0.650455 | −0.325227 | − | 0.945636i | \(-0.605441\pi\) | ||||
−0.325227 | + | 0.945636i | \(0.605441\pi\) | |||||||
\(84\) | −6.30093e7 | −0.138086 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.07172e8 | −0.605534 | ||||||||
\(87\) | −2.35439e8 | −0.440597 | ||||||||
\(88\) | 2.48308e7 | 0.0441385 | ||||||||
\(89\) | −9.72872e8 | −1.64362 | −0.821809 | − | 0.569763i | \(-0.807035\pi\) | ||||
−0.821809 | + | 0.569763i | \(0.807035\pi\) | |||||||
\(90\) | −2.62310e8 | −0.421427 | ||||||||
\(91\) | 6.25753e8 | 0.956570 | ||||||||
\(92\) | −1.26170e7 | −0.0183616 | ||||||||
\(93\) | −1.76154e8 | −0.244186 | ||||||||
\(94\) | 1.49695e9 | 1.97757 | ||||||||
\(95\) | −7.49369e7 | −0.0943929 | ||||||||
\(96\) | 2.47985e8 | 0.297993 | ||||||||
\(97\) | −1.27923e9 | −1.46715 | −0.733575 | − | 0.679609i | \(-0.762149\pi\) | ||||
−0.733575 | + | 0.679609i | \(0.762149\pi\) | |||||||
\(98\) | 1.87323e8 | 0.205151 | ||||||||
\(99\) | −3.41132e7 | −0.0356914 | ||||||||
\(100\) | −1.81843e8 | −0.181843 | ||||||||
\(101\) | −8.97078e7 | −0.0857796 | −0.0428898 | − | 0.999080i | \(-0.513656\pi\) | ||||
−0.0428898 | + | 0.999080i | \(0.513656\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.43613e9 | −1.25726 | −0.628630 | − | 0.777705i | \(-0.716384\pi\) | ||||
−0.628630 | + | 0.777705i | \(0.716384\pi\) | |||||||
\(104\) | −1.04316e9 | −0.874384 | ||||||||
\(105\) | 3.63587e8 | 0.291915 | ||||||||
\(106\) | 4.71701e8 | 0.362903 | ||||||||
\(107\) | −2.21353e9 | −1.63252 | −0.816259 | − | 0.577687i | \(-0.803956\pi\) | ||||
−0.816259 | + | 0.577687i | \(0.803956\pi\) | |||||||
\(108\) | −3.60221e8 | −0.254778 | ||||||||
\(109\) | −1.92348e9 | −1.30517 | −0.652587 | − | 0.757714i | \(-0.726316\pi\) | ||||
−0.652587 | + | 0.757714i | \(0.726316\pi\) | |||||||
\(110\) | 5.17065e7 | 0.0336727 | ||||||||
\(111\) | −8.88033e8 | −0.555234 | ||||||||
\(112\) | 1.79916e9 | 1.08041 | ||||||||
\(113\) | 2.87568e9 | 1.65916 | 0.829578 | − | 0.558391i | \(-0.188581\pi\) | ||||
0.829578 | + | 0.558391i | \(0.188581\pi\) | |||||||
\(114\) | −1.96691e8 | −0.109072 | ||||||||
\(115\) | 7.28046e7 | 0.0388167 | ||||||||
\(116\) | −3.95638e8 | −0.202879 | ||||||||
\(117\) | 1.43313e9 | 0.707046 | ||||||||
\(118\) | 2.42276e9 | 1.15038 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.06118e8 | −0.266834 | ||||||||
\(121\) | −2.35122e9 | −0.997148 | ||||||||
\(122\) | −1.15522e9 | −0.472113 | ||||||||
\(123\) | −8.98757e8 | −0.354054 | ||||||||
\(124\) | −2.96015e8 | −0.112439 | ||||||||
\(125\) | 2.57946e9 | 0.945005 | ||||||||
\(126\) | −1.92318e9 | −0.679756 | ||||||||
\(127\) | −4.75500e9 | −1.62193 | −0.810967 | − | 0.585091i | \(-0.801059\pi\) | ||||
−0.810967 | + | 0.585091i | \(0.801059\pi\) | |||||||
\(128\) | −3.66494e9 | −1.20676 | ||||||||
\(129\) | 9.75116e8 | 0.310029 | ||||||||
\(130\) | −2.17224e9 | −0.667056 | ||||||||
\(131\) | −3.33130e9 | −0.988310 | −0.494155 | − | 0.869374i | \(-0.664523\pi\) | ||||
−0.494155 | + | 0.869374i | \(0.664523\pi\) | |||||||
\(132\) | 2.84457e7 | 0.00815519 | ||||||||
\(133\) | −5.49417e8 | −0.152254 | ||||||||
\(134\) | −5.32794e9 | −1.42754 | ||||||||
\(135\) | 2.07860e9 | 0.538604 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.02387e8 | 0.0733366 | 0.0366683 | − | 0.999327i | \(-0.488326\pi\) | ||||
0.0366683 | + | 0.999327i | \(0.488326\pi\) | |||||||
\(138\) | 1.91094e8 | 0.0448529 | ||||||||
\(139\) | 4.37194e9 | 0.993362 | 0.496681 | − | 0.867933i | \(-0.334552\pi\) | ||||
0.496681 | + | 0.867933i | \(0.334552\pi\) | |||||||
\(140\) | 6.10981e8 | 0.134416 | ||||||||
\(141\) | −4.75206e9 | −1.01250 | ||||||||
\(142\) | 5.22699e9 | 1.07883 | ||||||||
\(143\) | −2.82498e8 | −0.0564941 | ||||||||
\(144\) | 4.12052e9 | 0.798584 | ||||||||
\(145\) | 2.28297e9 | 0.428889 | ||||||||
\(146\) | 2.96397e9 | 0.539866 | ||||||||
\(147\) | −5.94656e8 | −0.105036 | ||||||||
\(148\) | −1.49228e9 | −0.255665 | ||||||||
\(149\) | 4.14348e9 | 0.688696 | 0.344348 | − | 0.938842i | \(-0.388100\pi\) | ||||
0.344348 | + | 0.938842i | \(0.388100\pi\) | |||||||
\(150\) | 2.75415e9 | 0.444198 | ||||||||
\(151\) | −2.51094e9 | −0.393043 | −0.196521 | − | 0.980500i | \(-0.562964\pi\) | ||||
−0.196521 | + | 0.980500i | \(0.562964\pi\) | |||||||
\(152\) | 9.15907e8 | 0.139173 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.79098e8 | 0.0543136 | ||||||||
\(155\) | 1.70811e9 | 0.237697 | ||||||||
\(156\) | −1.19503e9 | −0.161554 | ||||||||
\(157\) | 1.22353e10 | 1.60719 | 0.803594 | − | 0.595177i | \(-0.202918\pi\) | ||||
0.803594 | + | 0.595177i | \(0.202918\pi\) | |||||||
\(158\) | −9.94067e9 | −1.26899 | ||||||||
\(159\) | −1.49741e9 | −0.185804 | ||||||||
\(160\) | −2.40463e9 | −0.290074 | ||||||||
\(161\) | 5.33784e8 | 0.0626107 | ||||||||
\(162\) | −1.13436e9 | −0.129400 | ||||||||
\(163\) | 1.89763e9 | 0.210556 | 0.105278 | − | 0.994443i | \(-0.466427\pi\) | ||||
0.105278 | + | 0.994443i | \(0.466427\pi\) | |||||||
\(164\) | −1.51030e9 | −0.163029 | ||||||||
\(165\) | −1.64142e8 | −0.0172402 | ||||||||
\(166\) | 7.15779e9 | 0.731632 | ||||||||
\(167\) | 9.60173e9 | 0.955268 | 0.477634 | − | 0.878559i | \(-0.341494\pi\) | ||||
0.477634 | + | 0.878559i | \(0.341494\pi\) | |||||||
\(168\) | −4.44389e9 | −0.430399 | ||||||||
\(169\) | 1.26349e9 | 0.119147 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.25830e9 | −0.112538 | ||||||||
\(172\) | 1.63861e9 | 0.142757 | ||||||||
\(173\) | −1.86000e10 | −1.57872 | −0.789359 | − | 0.613932i | \(-0.789587\pi\) | ||||
−0.789359 | + | 0.613932i | \(0.789587\pi\) | |||||||
\(174\) | 5.99223e9 | 0.495584 | ||||||||
\(175\) | 7.69317e9 | 0.620061 | ||||||||
\(176\) | −8.12237e8 | −0.0638081 | ||||||||
\(177\) | −7.69106e9 | −0.588988 | ||||||||
\(178\) | 2.47609e10 | 1.84874 | ||||||||
\(179\) | −8.64877e8 | −0.0629674 | −0.0314837 | − | 0.999504i | \(-0.510023\pi\) | ||||
−0.0314837 | + | 0.999504i | \(0.510023\pi\) | |||||||
\(180\) | 1.39929e9 | 0.0993533 | ||||||||
\(181\) | 1.36211e10 | 0.943322 | 0.471661 | − | 0.881780i | \(-0.343655\pi\) | ||||
0.471661 | + | 0.881780i | \(0.343655\pi\) | |||||||
\(182\) | −1.59263e10 | −1.07595 | ||||||||
\(183\) | 3.66725e9 | 0.241719 | ||||||||
\(184\) | −8.89845e8 | −0.0572313 | ||||||||
\(185\) | 8.61097e9 | 0.540479 | ||||||||
\(186\) | 4.48337e9 | 0.274660 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.98548e9 | −0.466220 | ||||||||
\(189\) | 1.52398e10 | 0.868761 | ||||||||
\(190\) | 1.90724e9 | 0.106173 | ||||||||
\(191\) | 1.73416e10 | 0.942844 | 0.471422 | − | 0.881908i | \(-0.343741\pi\) | ||||
0.471422 | + | 0.881908i | \(0.343741\pi\) | |||||||
\(192\) | 6.64565e9 | 0.352925 | ||||||||
\(193\) | −2.27653e10 | −1.18104 | −0.590522 | − | 0.807022i | \(-0.701078\pi\) | ||||
−0.590522 | + | 0.807022i | \(0.701078\pi\) | |||||||
\(194\) | 3.25580e10 | 1.65025 | ||||||||
\(195\) | 6.89576e9 | 0.341528 | ||||||||
\(196\) | −9.99276e8 | −0.0483652 | ||||||||
\(197\) | 1.74962e10 | 0.827646 | 0.413823 | − | 0.910357i | \(-0.364193\pi\) | ||||
0.413823 | + | 0.910357i | \(0.364193\pi\) | |||||||
\(198\) | 8.68226e8 | 0.0401457 | ||||||||
\(199\) | −2.80077e10 | −1.26602 | −0.633008 | − | 0.774146i | \(-0.718180\pi\) | ||||
−0.633008 | + | 0.774146i | \(0.718180\pi\) | |||||||
\(200\) | −1.28249e10 | −0.566787 | ||||||||
\(201\) | 1.69135e10 | 0.730890 | ||||||||
\(202\) | 2.28318e9 | 0.0964850 | ||||||||
\(203\) | 1.67381e10 | 0.691792 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.71495e9 | 0.344645 | ||||||||
\(206\) | 3.65513e10 | 1.41417 | ||||||||
\(207\) | 1.22249e9 | 0.0462785 | ||||||||
\(208\) | 3.41228e10 | 1.26404 | ||||||||
\(209\) | 2.48036e8 | 0.00899199 | ||||||||
\(210\) | −9.25377e9 | −0.328346 | ||||||||
\(211\) | 3.44587e10 | 1.19682 | 0.598409 | − | 0.801191i | \(-0.295800\pi\) | ||||
0.598409 | + | 0.801191i | \(0.295800\pi\) | |||||||
\(212\) | −2.51629e9 | −0.0855559 | ||||||||
\(213\) | −1.65931e10 | −0.552355 | ||||||||
\(214\) | 5.63372e10 | 1.83626 | ||||||||
\(215\) | −9.45538e9 | −0.301791 | ||||||||
\(216\) | −2.54055e10 | −0.794119 | ||||||||
\(217\) | 1.25234e10 | 0.383402 | ||||||||
\(218\) | 4.89551e10 | 1.46806 | ||||||||
\(219\) | −9.40911e9 | −0.276408 | ||||||||
\(220\) | −2.75829e8 | −0.00793848 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.26016e10 | 0.624527 | ||||||||
\(223\) | 5.53067e10 | 1.49764 | 0.748818 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748818 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(224\) | −1.76301e10 | −0.467885 | ||||||||
\(225\) | 1.76192e10 | 0.458316 | ||||||||
\(226\) | −7.31898e10 | −1.86622 | ||||||||
\(227\) | −5.01007e10 | −1.25235 | −0.626177 | − | 0.779681i | \(-0.715381\pi\) | ||||
−0.626177 | + | 0.779681i | \(0.715381\pi\) | |||||||
\(228\) | 1.04925e9 | 0.0257141 | ||||||||
\(229\) | 7.23759e10 | 1.73914 | 0.869569 | − | 0.493812i | \(-0.164397\pi\) | ||||
0.869569 | + | 0.493812i | \(0.164397\pi\) | |||||||
\(230\) | −1.85297e9 | −0.0436610 | ||||||||
\(231\) | −1.20345e9 | −0.0278082 | ||||||||
\(232\) | −2.79033e10 | −0.632354 | ||||||||
\(233\) | 4.45995e10 | 0.991353 | 0.495676 | − | 0.868507i | \(-0.334920\pi\) | ||||
0.495676 | + | 0.868507i | \(0.334920\pi\) | |||||||
\(234\) | −3.64749e10 | −0.795286 | ||||||||
\(235\) | 4.60791e10 | 0.985596 | ||||||||
\(236\) | −1.29243e10 | −0.271207 | ||||||||
\(237\) | 3.15566e10 | 0.649715 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.46746e10 | −1.28216 | −0.641081 | − | 0.767473i | \(-0.721514\pi\) | ||||
−0.641081 | + | 0.767473i | \(0.721514\pi\) | |||||||
\(240\) | 1.98267e10 | 0.385744 | ||||||||
\(241\) | 6.97798e9 | 0.133246 | 0.0666228 | − | 0.997778i | \(-0.478778\pi\) | ||||
0.0666228 | + | 0.997778i | \(0.478778\pi\) | |||||||
\(242\) | 5.98418e10 | 1.12159 | ||||||||
\(243\) | 5.58232e10 | 1.02704 | ||||||||
\(244\) | 6.16254e9 | 0.111303 | ||||||||
\(245\) | 5.76618e9 | 0.102245 | ||||||||
\(246\) | 2.28746e10 | 0.398240 | ||||||||
\(247\) | −1.04202e10 | −0.178131 | ||||||||
\(248\) | −2.08772e10 | −0.350461 | ||||||||
\(249\) | −2.27224e10 | −0.374591 | ||||||||
\(250\) | −6.56508e10 | −1.06294 | ||||||||
\(251\) | 4.27892e10 | 0.680460 | 0.340230 | − | 0.940342i | \(-0.389495\pi\) | ||||
0.340230 | + | 0.940342i | \(0.389495\pi\) | |||||||
\(252\) | 1.02592e10 | 0.160255 | ||||||||
\(253\) | −2.40978e8 | −0.00369773 | ||||||||
\(254\) | 1.21021e11 | 1.82435 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.11640e10 | 0.744534 | ||||||||
\(257\) | 2.86215e10 | 0.409255 | 0.204627 | − | 0.978840i | \(-0.434402\pi\) | ||||
0.204627 | + | 0.978840i | \(0.434402\pi\) | |||||||
\(258\) | −2.48180e10 | −0.348721 | ||||||||
\(259\) | 6.31333e10 | 0.871786 | ||||||||
\(260\) | 1.15878e10 | 0.157261 | ||||||||
\(261\) | 3.83344e10 | 0.511336 | ||||||||
\(262\) | 8.47861e10 | 1.11165 | ||||||||
\(263\) | 1.14839e11 | 1.48009 | 0.740043 | − | 0.672560i | \(-0.234805\pi\) | ||||
0.740043 | + | 0.672560i | \(0.234805\pi\) | |||||||
\(264\) | 2.00621e9 | 0.0254190 | ||||||||
\(265\) | 1.45199e10 | 0.180866 | ||||||||
\(266\) | 1.39834e10 | 0.171256 | ||||||||
\(267\) | −7.86034e10 | −0.946543 | ||||||||
\(268\) | 2.84219e10 | 0.336548 | ||||||||
\(269\) | 8.32291e10 | 0.969148 | 0.484574 | − | 0.874750i | \(-0.338975\pi\) | ||||
0.484574 | + | 0.874750i | \(0.338975\pi\) | |||||||
\(270\) | −5.29033e10 | −0.605823 | ||||||||
\(271\) | −2.33646e10 | −0.263146 | −0.131573 | − | 0.991307i | \(-0.542003\pi\) | ||||
−0.131573 | + | 0.991307i | \(0.542003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.05578e10 | 0.550879 | ||||||||
\(274\) | −7.69615e9 | −0.0824890 | ||||||||
\(275\) | −3.47310e9 | −0.0366202 | ||||||||
\(276\) | −1.01939e9 | −0.0105743 | ||||||||
\(277\) | −1.27545e11 | −1.30168 | −0.650839 | − | 0.759216i | \(-0.725583\pi\) | ||||
−0.650839 | + | 0.759216i | \(0.725583\pi\) | |||||||
\(278\) | −1.11272e11 | −1.11733 | ||||||||
\(279\) | 2.86816e10 | 0.283390 | ||||||||
\(280\) | 4.30910e10 | 0.418962 | ||||||||
\(281\) | 4.64733e10 | 0.444657 | 0.222329 | − | 0.974972i | \(-0.428634\pi\) | ||||
0.222329 | + | 0.974972i | \(0.428634\pi\) | |||||||
\(282\) | 1.20946e11 | 1.13886 | ||||||||
\(283\) | 4.19339e10 | 0.388621 | 0.194311 | − | 0.980940i | \(-0.437753\pi\) | ||||
0.194311 | + | 0.980940i | \(0.437753\pi\) | |||||||
\(284\) | −2.78834e10 | −0.254339 | ||||||||
\(285\) | −6.05454e9 | −0.0543600 | ||||||||
\(286\) | 7.18995e9 | 0.0635446 | ||||||||
\(287\) | 6.38957e10 | 0.555908 | ||||||||
\(288\) | −4.03772e10 | −0.345836 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −5.81047e10 | −0.482415 | ||||||||
\(291\) | −1.03355e11 | −0.844917 | ||||||||
\(292\) | −1.58113e10 | −0.127276 | ||||||||
\(293\) | 1.45256e11 | 1.15141 | 0.575705 | − | 0.817658i | \(-0.304728\pi\) | ||||
0.575705 | + | 0.817658i | \(0.304728\pi\) | |||||||
\(294\) | 1.51348e10 | 0.118144 | ||||||||
\(295\) | 7.45776e10 | 0.573336 | ||||||||
\(296\) | −1.05246e11 | −0.796883 | ||||||||
\(297\) | −6.88003e9 | −0.0513082 | ||||||||
\(298\) | −1.05457e11 | −0.774645 | ||||||||
\(299\) | 1.01237e10 | 0.0732519 | ||||||||
\(300\) | −1.46920e10 | −0.104721 | ||||||||
\(301\) | −6.93243e10 | −0.486784 | ||||||||
\(302\) | 6.39067e10 | 0.442095 | ||||||||
\(303\) | −7.24796e9 | −0.0493996 | ||||||||
\(304\) | −2.99601e10 | −0.201193 | ||||||||
\(305\) | −3.55601e10 | −0.235295 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.59150e11 | −1.02255 | −0.511275 | − | 0.859417i | \(-0.670827\pi\) | ||||
−0.511275 | + | 0.859417i | \(0.670827\pi\) | |||||||
\(308\) | −2.02230e9 | −0.0128047 | ||||||||
\(309\) | −1.16032e11 | −0.724043 | ||||||||
\(310\) | −4.34737e10 | −0.267362 | ||||||||
\(311\) | −6.44453e10 | −0.390634 | −0.195317 | − | 0.980740i | \(-0.562574\pi\) | ||||
−0.195317 | + | 0.980740i | \(0.562574\pi\) | |||||||
\(312\) | −8.42825e10 | −0.503549 | ||||||||
\(313\) | −1.46687e11 | −0.863859 | −0.431929 | − | 0.901907i | \(-0.642167\pi\) | ||||
−0.431929 | + | 0.901907i | \(0.642167\pi\) | |||||||
\(314\) | −3.11405e11 | −1.80777 | ||||||||
\(315\) | −5.91995e10 | −0.338782 | ||||||||
\(316\) | 5.30286e10 | 0.299170 | ||||||||
\(317\) | 2.69726e11 | 1.50022 | 0.750111 | − | 0.661311i | \(-0.230000\pi\) | ||||
0.750111 | + | 0.661311i | \(0.230000\pi\) | |||||||
\(318\) | 3.81112e10 | 0.208992 | ||||||||
\(319\) | −7.55648e9 | −0.0408565 | ||||||||
\(320\) | −6.44407e10 | −0.343546 | ||||||||
\(321\) | −1.78842e11 | −0.940151 | ||||||||
\(322\) | −1.35855e10 | −0.0704246 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 6.05128e9 | 0.0305067 | ||||||||
\(325\) | 1.45908e11 | 0.725445 | ||||||||
\(326\) | −4.82972e10 | −0.236833 | ||||||||
\(327\) | −1.55408e11 | −0.751637 | ||||||||
\(328\) | −1.06517e11 | −0.508146 | ||||||||
\(329\) | 3.37840e11 | 1.58975 | ||||||||
\(330\) | 4.17763e9 | 0.0193918 | ||||||||
\(331\) | −6.83090e10 | −0.312789 | −0.156395 | − | 0.987695i | \(-0.549987\pi\) | ||||
−0.156395 | + | 0.987695i | \(0.549987\pi\) | |||||||
\(332\) | −3.81833e10 | −0.172485 | ||||||||
\(333\) | 1.44590e11 | 0.644378 | ||||||||
\(334\) | −2.44377e11 | −1.07449 | ||||||||
\(335\) | −1.64005e11 | −0.711468 | ||||||||
\(336\) | 1.45364e11 | 0.622199 | ||||||||
\(337\) | −3.32556e11 | −1.40453 | −0.702263 | − | 0.711917i | \(-0.747827\pi\) | ||||
−0.702263 | + | 0.711917i | \(0.747827\pi\) | |||||||
\(338\) | −3.21575e10 | −0.134016 | ||||||||
\(339\) | 2.32341e11 | 0.955492 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.65373e9 | −0.0226433 | ||||||||
\(342\) | 3.20253e10 | 0.126583 | ||||||||
\(343\) | 2.74067e11 | 1.06914 | ||||||||
\(344\) | 1.15567e11 | 0.444960 | ||||||||
\(345\) | 5.88226e9 | 0.0223541 | ||||||||
\(346\) | 4.73394e11 | 1.77574 | ||||||||
\(347\) | −4.91489e11 | −1.81983 | −0.909916 | − | 0.414792i | \(-0.863855\pi\) | ||||
−0.909916 | + | 0.414792i | \(0.863855\pi\) | |||||||
\(348\) | −3.19656e10 | −0.116836 | ||||||||
\(349\) | 3.69150e11 | 1.33195 | 0.665976 | − | 0.745973i | \(-0.268015\pi\) | ||||
0.665976 | + | 0.745973i | \(0.268015\pi\) | |||||||
\(350\) | −1.95802e11 | −0.697445 | ||||||||
\(351\) | 2.89036e11 | 1.01641 | ||||||||
\(352\) | 7.95916e9 | 0.0276328 | ||||||||
\(353\) | 6.87046e10 | 0.235505 | 0.117752 | − | 0.993043i | \(-0.462431\pi\) | ||||
0.117752 | + | 0.993043i | \(0.462431\pi\) | |||||||
\(354\) | 1.95748e11 | 0.662494 | ||||||||
\(355\) | 1.60897e11 | 0.537677 | ||||||||
\(356\) | −1.32087e11 | −0.435849 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.20123e10 | 0.0708258 | ||||||||
\(359\) | −2.85442e11 | −0.906971 | −0.453486 | − | 0.891264i | \(-0.649820\pi\) | ||||
−0.453486 | + | 0.891264i | \(0.649820\pi\) | |||||||
\(360\) | 9.86886e10 | 0.309675 | ||||||||
\(361\) | −3.13539e11 | −0.971647 | ||||||||
\(362\) | −3.46676e11 | −1.06105 | ||||||||
\(363\) | −1.89967e11 | −0.574248 | ||||||||
\(364\) | 8.49588e10 | 0.253660 | ||||||||
\(365\) | 9.12370e10 | 0.269063 | ||||||||
\(366\) | −9.33363e10 | −0.271885 | ||||||||
\(367\) | 1.61232e11 | 0.463931 | 0.231966 | − | 0.972724i | \(-0.425484\pi\) | ||||
0.231966 | + | 0.972724i | \(0.425484\pi\) | |||||||
\(368\) | 2.91076e10 | 0.0827355 | ||||||||
\(369\) | 1.46336e11 | 0.410898 | ||||||||
\(370\) | −2.19161e11 | −0.607932 | ||||||||
\(371\) | 1.06456e11 | 0.291735 | ||||||||
\(372\) | −2.39166e10 | −0.0647523 | ||||||||
\(373\) | −1.20896e10 | −0.0323388 | −0.0161694 | − | 0.999869i | \(-0.505147\pi\) | ||||
−0.0161694 | + | 0.999869i | \(0.505147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.08408e11 | 0.544219 | ||||||||
\(376\) | −5.63196e11 | −1.45316 | ||||||||
\(377\) | 3.17454e11 | 0.809367 | ||||||||
\(378\) | −3.87873e11 | −0.977183 | ||||||||
\(379\) | 3.36624e11 | 0.838047 | 0.419023 | − | 0.907975i | \(-0.362373\pi\) | ||||
0.419023 | + | 0.907975i | \(0.362373\pi\) | |||||||
\(380\) | −1.01742e10 | −0.0250308 | ||||||||
\(381\) | −3.84181e11 | −0.934056 | ||||||||
\(382\) | −4.41368e11 | −1.06051 | ||||||||
\(383\) | −2.76830e11 | −0.657383 | −0.328692 | − | 0.944437i | \(-0.606608\pi\) | ||||
−0.328692 | + | 0.944437i | \(0.606608\pi\) | |||||||
\(384\) | −2.96109e11 | −0.694963 | ||||||||
\(385\) | 1.16694e10 | 0.0270692 | ||||||||
\(386\) | 5.79408e11 | 1.32844 | ||||||||
\(387\) | −1.58769e11 | −0.359805 | ||||||||
\(388\) | −1.73681e11 | −0.389054 | ||||||||
\(389\) | 1.58309e11 | 0.350536 | 0.175268 | − | 0.984521i | \(-0.443921\pi\) | ||||
0.175268 | + | 0.984521i | \(0.443921\pi\) | |||||||
\(390\) | −1.75506e11 | −0.384151 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7.04764e10 | −0.150750 | ||||||||
\(393\) | −2.69153e11 | −0.569158 | ||||||||
\(394\) | −4.45301e11 | −0.930937 | ||||||||
\(395\) | −3.05994e11 | −0.632450 | ||||||||
\(396\) | −4.63156e9 | −0.00946452 | ||||||||
\(397\) | −2.73210e11 | −0.552000 | −0.276000 | − | 0.961158i | \(-0.589009\pi\) | ||||
−0.276000 | + | 0.961158i | \(0.589009\pi\) | |||||||
\(398\) | 7.12834e11 | 1.42401 | ||||||||
\(399\) | −4.43903e10 | −0.0876818 | ||||||||
\(400\) | 4.19515e11 | 0.819365 | ||||||||
\(401\) | −9.21298e11 | −1.77931 | −0.889653 | − | 0.456637i | \(-0.849054\pi\) | ||||
−0.889653 | + | 0.456637i | \(0.849054\pi\) | |||||||
\(402\) | −4.30472e11 | −0.822105 | ||||||||
\(403\) | 2.37518e11 | 0.448564 | ||||||||
\(404\) | −1.21797e10 | −0.0227467 | ||||||||
\(405\) | −3.49181e10 | −0.0644915 | ||||||||
\(406\) | −4.26008e11 | −0.778128 | ||||||||
\(407\) | −2.85017e10 | −0.0514868 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.51756e11 | −1.50508 | −0.752541 | − | 0.658545i | \(-0.771172\pi\) | ||||
−0.752541 | + | 0.658545i | \(0.771172\pi\) | |||||||
\(410\) | −2.21807e11 | −0.387657 | ||||||||
\(411\) | 2.44314e10 | 0.0422338 | ||||||||
\(412\) | −1.94983e11 | −0.333396 | ||||||||
\(413\) | 5.46783e11 | 0.924783 | ||||||||
\(414\) | −3.11141e10 | −0.0520541 | ||||||||
\(415\) | 2.20332e11 | 0.364637 | ||||||||
\(416\) | −3.34372e11 | −0.547406 | ||||||||
\(417\) | 3.53232e11 | 0.572068 | ||||||||
\(418\) | −6.31284e9 | −0.0101142 | ||||||||
\(419\) | 1.81027e11 | 0.286932 | 0.143466 | − | 0.989655i | \(-0.454175\pi\) | ||||
0.143466 | + | 0.989655i | \(0.454175\pi\) | |||||||
\(420\) | 4.93643e10 | 0.0774090 | ||||||||
\(421\) | −4.26322e11 | −0.661406 | −0.330703 | − | 0.943735i | \(-0.607286\pi\) | ||||
−0.330703 | + | 0.943735i | \(0.607286\pi\) | |||||||
\(422\) | −8.77021e11 | −1.34618 | ||||||||
\(423\) | 7.73734e11 | 1.17506 | ||||||||
\(424\) | −1.77468e11 | −0.266670 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.22315e11 | 0.621289 | ||||||||
\(427\) | −2.60717e11 | −0.379528 | ||||||||
\(428\) | −3.00531e11 | −0.432905 | ||||||||
\(429\) | −2.28245e10 | −0.0325344 | ||||||||
\(430\) | 2.40652e11 | 0.339454 | ||||||||
\(431\) | −3.32704e10 | −0.0464419 | −0.0232210 | − | 0.999730i | \(-0.507392\pi\) | ||||
−0.0232210 | + | 0.999730i | \(0.507392\pi\) | |||||||
\(432\) | 8.31037e11 | 1.14800 | ||||||||
\(433\) | 8.54358e11 | 1.16800 | 0.584002 | − | 0.811752i | \(-0.301486\pi\) | ||||
0.584002 | + | 0.811752i | \(0.301486\pi\) | |||||||
\(434\) | −3.18738e11 | −0.431250 | ||||||||
\(435\) | 1.84453e11 | 0.246993 | ||||||||
\(436\) | −2.61152e11 | −0.346101 | ||||||||
\(437\) | −8.88870e9 | −0.0116593 | ||||||||
\(438\) | 2.39474e11 | 0.310903 | ||||||||
\(439\) | −3.21290e11 | −0.412864 | −0.206432 | − | 0.978461i | \(-0.566185\pi\) | ||||
−0.206432 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(440\) | −1.94535e10 | −0.0247435 | ||||||||
\(441\) | 9.68224e10 | 0.121900 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.17716e12 | 1.45218 | 0.726089 | − | 0.687601i | \(-0.241336\pi\) | ||||
0.726089 | + | 0.687601i | \(0.241336\pi\) | |||||||
\(444\) | −1.20569e11 | −0.147235 | ||||||||
\(445\) | 7.62191e11 | 0.921391 | ||||||||
\(446\) | −1.40763e12 | −1.68454 | ||||||||
\(447\) | 3.34773e11 | 0.396613 | ||||||||
\(448\) | −4.72462e11 | −0.554135 | ||||||||
\(449\) | 4.16601e10 | 0.0483740 | 0.0241870 | − | 0.999707i | \(-0.492300\pi\) | ||||
0.0241870 | + | 0.999707i | \(0.492300\pi\) | |||||||
\(450\) | −4.48432e11 | −0.515514 | ||||||||
\(451\) | −2.88459e10 | −0.0328314 | ||||||||
\(452\) | 3.90432e11 | 0.439969 | ||||||||
\(453\) | −2.02872e11 | −0.226349 | ||||||||
\(454\) | 1.27513e12 | 1.40865 | ||||||||
\(455\) | −4.90243e11 | −0.536241 | ||||||||
\(456\) | 7.40008e10 | 0.0801484 | ||||||||
\(457\) | 9.56563e11 | 1.02587 | 0.512933 | − | 0.858429i | \(-0.328559\pi\) | ||||
0.512933 | + | 0.858429i | \(0.328559\pi\) | |||||||
\(458\) | −1.84206e12 | −1.95618 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.88471e9 | 0.0102933 | ||||||||
\(461\) | 1.45395e12 | 1.49932 | 0.749661 | − | 0.661822i | \(-0.230217\pi\) | ||||
0.749661 | + | 0.661822i | \(0.230217\pi\) | |||||||
\(462\) | 3.06293e10 | 0.0312787 | ||||||||
\(463\) | 3.76717e11 | 0.380978 | 0.190489 | − | 0.981689i | \(-0.438993\pi\) | ||||
0.190489 | + | 0.981689i | \(0.438993\pi\) | |||||||
\(464\) | 9.12744e11 | 0.914151 | ||||||||
\(465\) | 1.38007e11 | 0.136887 | ||||||||
\(466\) | −1.13512e12 | −1.11507 | ||||||||
\(467\) | −8.09866e11 | −0.787929 | −0.393964 | − | 0.919126i | \(-0.628897\pi\) | ||||
−0.393964 | + | 0.919126i | \(0.628897\pi\) | |||||||
\(468\) | 1.94576e11 | 0.187492 | ||||||||
\(469\) | −1.20244e12 | −1.14759 | ||||||||
\(470\) | −1.17278e12 | −1.10860 | ||||||||
\(471\) | 9.88555e11 | 0.925564 | ||||||||
\(472\) | −9.11516e11 | −0.845328 | ||||||||
\(473\) | 3.12966e10 | 0.0287490 | ||||||||
\(474\) | −8.03158e11 | −0.730800 | ||||||||
\(475\) | −1.28109e11 | −0.115467 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.43810e11 | 0.215635 | ||||||||
\(478\) | 1.64605e12 | 1.44218 | ||||||||
\(479\) | 2.67750e11 | 0.232391 | 0.116196 | − | 0.993226i | \(-0.462930\pi\) | ||||
0.116196 | + | 0.993226i | \(0.462930\pi\) | |||||||
\(480\) | −1.94283e11 | −0.167051 | ||||||||
\(481\) | 1.19738e12 | 1.01995 | ||||||||
\(482\) | −1.77599e11 | −0.149875 | ||||||||
\(483\) | 4.31271e10 | 0.0360569 | ||||||||
\(484\) | −3.19226e11 | −0.264420 | ||||||||
\(485\) | 1.00220e12 | 0.822465 | ||||||||
\(486\) | −1.42078e12 | −1.15521 | ||||||||
\(487\) | 8.91220e11 | 0.717967 | 0.358984 | − | 0.933344i | \(-0.383123\pi\) | ||||
0.358984 | + | 0.933344i | \(0.383123\pi\) | |||||||
\(488\) | 4.34628e11 | 0.346920 | ||||||||
\(489\) | 1.53319e11 | 0.121257 | ||||||||
\(490\) | −1.46757e11 | −0.115005 | ||||||||
\(491\) | 1.52071e12 | 1.18081 | 0.590405 | − | 0.807107i | \(-0.298968\pi\) | ||||
0.590405 | + | 0.807107i | \(0.298968\pi\) | |||||||
\(492\) | −1.22025e11 | −0.0938868 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.65208e11 | 0.200362 | ||||||||
\(495\) | 2.67258e10 | 0.0200081 | ||||||||
\(496\) | 6.82912e11 | 0.506637 | ||||||||
\(497\) | 1.17966e12 | 0.867265 | ||||||||
\(498\) | 5.78315e11 | 0.421340 | ||||||||
\(499\) | −1.68185e12 | −1.21432 | −0.607162 | − | 0.794578i | \(-0.707692\pi\) | ||||
−0.607162 | + | 0.794578i | \(0.707692\pi\) | |||||||
\(500\) | 3.50215e11 | 0.250593 | ||||||||
\(501\) | 7.75773e11 | 0.550130 | ||||||||
\(502\) | −1.08904e12 | −0.765382 | ||||||||
\(503\) | −1.69051e12 | −1.17750 | −0.588752 | − | 0.808314i | \(-0.700381\pi\) | ||||
−0.588752 | + | 0.808314i | \(0.700381\pi\) | |||||||
\(504\) | 7.23559e11 | 0.499501 | ||||||||
\(505\) | 7.02811e10 | 0.0480869 | ||||||||
\(506\) | 6.13321e9 | 0.00415921 | ||||||||
\(507\) | 1.02084e11 | 0.0686154 | ||||||||
\(508\) | −6.45588e11 | −0.430099 | ||||||||
\(509\) | 5.84673e11 | 0.386085 | 0.193043 | − | 0.981190i | \(-0.438164\pi\) | ||||
0.193043 | + | 0.981190i | \(0.438164\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.68926e11 | 0.433994 | ||||||||
\(512\) | 5.74257e11 | 0.369310 | ||||||||
\(513\) | −2.53777e11 | −0.161779 | ||||||||
\(514\) | −7.28456e11 | −0.460330 | ||||||||
\(515\) | 1.12512e12 | 0.704803 | ||||||||
\(516\) | 1.32392e11 | 0.0822124 | ||||||||
\(517\) | −1.52519e11 | −0.0938891 | ||||||||
\(518\) | −1.60683e12 | −0.980585 | ||||||||
\(519\) | −1.50279e12 | −0.909168 | ||||||||
\(520\) | 8.17260e11 | 0.490168 | ||||||||
\(521\) | −1.46396e12 | −0.870483 | −0.435241 | − | 0.900314i | \(-0.643337\pi\) | ||||
−0.435241 | + | 0.900314i | \(0.643337\pi\) | |||||||
\(522\) | −9.75661e11 | −0.575151 | ||||||||
\(523\) | 1.26928e12 | 0.741822 | 0.370911 | − | 0.928668i | \(-0.379045\pi\) | ||||
0.370911 | + | 0.928668i | \(0.379045\pi\) | |||||||
\(524\) | −4.52292e11 | −0.262077 | ||||||||
\(525\) | 6.21571e11 | 0.357087 | ||||||||
\(526\) | −2.92279e12 | −1.66480 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −6.56248e10 | −0.0367465 | ||||||||
\(529\) | −1.79252e12 | −0.995205 | ||||||||
\(530\) | −3.69551e11 | −0.203439 | ||||||||
\(531\) | 1.25226e12 | 0.683551 | ||||||||
\(532\) | −7.45946e10 | −0.0403743 | ||||||||
\(533\) | 1.21184e12 | 0.650389 | ||||||||
\(534\) | 2.00056e12 | 1.06467 | ||||||||
\(535\) | 1.73417e12 | 0.915168 | ||||||||
\(536\) | 2.00453e12 | 1.04899 | ||||||||
\(537\) | −6.98779e10 | −0.0362623 | ||||||||
\(538\) | −2.11829e12 | −1.09010 | ||||||||
\(539\) | −1.90857e10 | −0.00973997 | ||||||||
\(540\) | 2.82213e11 | 0.142825 | ||||||||
\(541\) | −2.67177e12 | −1.34095 | −0.670473 | − | 0.741934i | \(-0.733909\pi\) | ||||
−0.670473 | + | 0.741934i | \(0.733909\pi\) | |||||||
\(542\) | 5.94660e11 | 0.295986 | ||||||||
\(543\) | 1.10052e12 | 0.543250 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.50694e12 | 0.731663 | ||||||||
\(546\) | −1.28676e12 | −0.619630 | ||||||||
\(547\) | −1.35773e12 | −0.648442 | −0.324221 | − | 0.945981i | \(-0.605102\pi\) | ||||
−0.324221 | + | 0.945981i | \(0.605102\pi\) | |||||||
\(548\) | 4.10552e10 | 0.0194471 | ||||||||
\(549\) | −5.97104e11 | −0.280527 | ||||||||
\(550\) | 8.83951e10 | 0.0411904 | ||||||||
\(551\) | −2.78728e11 | −0.128824 | ||||||||
\(552\) | −7.18951e10 | −0.0329590 | ||||||||
\(553\) | −2.24347e12 | −1.02013 | ||||||||
\(554\) | 3.24618e12 | 1.46413 | ||||||||
\(555\) | 6.95725e11 | 0.311257 | ||||||||
\(556\) | 5.93580e11 | 0.263416 | ||||||||
\(557\) | −2.10630e11 | −0.0927199 | −0.0463599 | − | 0.998925i | \(-0.514762\pi\) | ||||
−0.0463599 | + | 0.998925i | \(0.514762\pi\) | |||||||
\(558\) | −7.29986e11 | −0.318758 | ||||||||
\(559\) | −1.31480e12 | −0.569516 | ||||||||
\(560\) | −1.40954e12 | −0.605665 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.18281e12 | −0.500151 | ||||||||
\(563\) | −1.83542e12 | −0.769923 | −0.384961 | − | 0.922933i | \(-0.625785\pi\) | ||||
−0.384961 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(564\) | −6.45189e11 | −0.268492 | ||||||||
\(565\) | −2.25293e12 | −0.930101 | ||||||||
\(566\) | −1.06727e12 | −0.437121 | ||||||||
\(567\) | −2.56010e11 | −0.104024 | ||||||||
\(568\) | −1.96655e12 | −0.792752 | ||||||||
\(569\) | 3.55367e12 | 1.42125 | 0.710627 | − | 0.703569i | \(-0.248411\pi\) | ||||
0.710627 | + | 0.703569i | \(0.248411\pi\) | |||||||
\(570\) | 1.54096e11 | 0.0611441 | ||||||||
\(571\) | −2.88312e12 | −1.13501 | −0.567505 | − | 0.823370i | \(-0.692091\pi\) | ||||
−0.567505 | + | 0.823370i | \(0.692091\pi\) | |||||||
\(572\) | −3.83548e10 | −0.0149809 | ||||||||
\(573\) | 1.40112e12 | 0.542975 | ||||||||
\(574\) | −1.62623e12 | −0.625286 | ||||||||
\(575\) | 1.24463e11 | 0.0474828 | ||||||||
\(576\) | −1.08205e12 | −0.409587 | ||||||||
\(577\) | 1.69258e12 | 0.635710 | 0.317855 | − | 0.948139i | \(-0.397037\pi\) | ||||
0.317855 | + | 0.948139i | \(0.397037\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.83933e12 | −0.680151 | ||||||||
\(580\) | 3.09960e11 | 0.113731 | ||||||||
\(581\) | 1.61541e12 | 0.588153 | ||||||||
\(582\) | 2.63053e12 | 0.950363 | ||||||||
\(583\) | −4.80599e10 | −0.0172296 | ||||||||
\(584\) | −1.11513e12 | −0.396706 | ||||||||
\(585\) | −1.12277e12 | −0.396361 | ||||||||
\(586\) | −3.69696e12 | −1.29511 | ||||||||
\(587\) | 1.14137e12 | 0.396786 | 0.198393 | − | 0.980123i | \(-0.436428\pi\) | ||||
0.198393 | + | 0.980123i | \(0.436428\pi\) | |||||||
\(588\) | −8.07367e10 | −0.0278531 | ||||||||
\(589\) | −2.08543e11 | −0.0713965 | ||||||||
\(590\) | −1.89810e12 | −0.644889 | ||||||||
\(591\) | 1.41360e12 | 0.476633 | ||||||||
\(592\) | 3.44271e12 | 1.15200 | ||||||||
\(593\) | −2.80279e12 | −0.930775 | −0.465387 | − | 0.885107i | \(-0.654085\pi\) | ||||
−0.465387 | + | 0.885107i | \(0.654085\pi\) | |||||||
\(594\) | 1.75106e11 | 0.0577115 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.62562e11 | 0.182626 | ||||||||
\(597\) | −2.26289e12 | −0.729086 | ||||||||
\(598\) | −2.57662e11 | −0.0823938 | ||||||||
\(599\) | −1.23194e12 | −0.390993 | −0.195497 | − | 0.980704i | \(-0.562632\pi\) | ||||
−0.195497 | + | 0.980704i | \(0.562632\pi\) | |||||||
\(600\) | −1.03619e12 | −0.326407 | ||||||||
\(601\) | 1.57757e12 | 0.493233 | 0.246617 | − | 0.969113i | \(-0.420681\pi\) | ||||
0.246617 | + | 0.969113i | \(0.420681\pi\) | |||||||
\(602\) | 1.76440e12 | 0.547535 | ||||||||
\(603\) | −2.75388e12 | −0.848235 | ||||||||
\(604\) | −3.40911e11 | −0.104226 | ||||||||
\(605\) | 1.84205e12 | 0.558988 | ||||||||
\(606\) | 1.84470e11 | 0.0555648 | ||||||||
\(607\) | −6.19694e12 | −1.85280 | −0.926399 | − | 0.376544i | \(-0.877112\pi\) | ||||
−0.926399 | + | 0.376544i | \(0.877112\pi\) | |||||||
\(608\) | 2.93581e11 | 0.0871289 | ||||||||
\(609\) | 1.35236e12 | 0.398396 | ||||||||
\(610\) | 9.05051e11 | 0.264660 | ||||||||
\(611\) | 6.40744e12 | 1.85994 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.17001e12 | −1.76487 | −0.882436 | − | 0.470432i | \(-0.844098\pi\) | ||||
−0.882436 | + | 0.470432i | \(0.844098\pi\) | |||||||
\(614\) | 4.05059e12 | 1.15017 | ||||||||
\(615\) | 7.04126e11 | 0.198478 | ||||||||
\(616\) | −1.42628e11 | −0.0399109 | ||||||||
\(617\) | −5.25289e12 | −1.45920 | −0.729600 | − | 0.683874i | \(-0.760294\pi\) | ||||
−0.729600 | + | 0.683874i | \(0.760294\pi\) | |||||||
\(618\) | 2.95317e12 | 0.814404 | ||||||||
\(619\) | −3.86095e12 | −1.05703 | −0.528514 | − | 0.848925i | \(-0.677251\pi\) | ||||
−0.528514 | + | 0.848925i | \(0.677251\pi\) | |||||||
\(620\) | 2.31911e11 | 0.0630317 | ||||||||
\(621\) | 2.46555e11 | 0.0665277 | ||||||||
\(622\) | 1.64022e12 | 0.439385 | ||||||||
\(623\) | 5.58818e12 | 1.48619 | ||||||||
\(624\) | 2.75696e12 | 0.727946 | ||||||||
\(625\) | 5.95035e11 | 0.155985 | ||||||||
\(626\) | 3.73339e12 | 0.971669 | ||||||||
\(627\) | 2.00401e10 | 0.00517840 | ||||||||
\(628\) | 1.66119e12 | 0.426189 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.50671e12 | 0.381063 | ||||||||
\(631\) | −1.39505e12 | −0.350314 | −0.175157 | − | 0.984541i | \(-0.556043\pi\) | ||||
−0.175157 | + | 0.984541i | \(0.556043\pi\) | |||||||
\(632\) | 3.73998e12 | 0.932485 | ||||||||
\(633\) | 2.78410e12 | 0.689236 | ||||||||
\(634\) | −6.86488e12 | −1.68745 | ||||||||
\(635\) | 3.72527e12 | 0.909235 | ||||||||
\(636\) | −2.03304e11 | −0.0492708 | ||||||||
\(637\) | 8.01806e11 | 0.192949 | ||||||||
\(638\) | 1.92322e11 | 0.0459554 | ||||||||
\(639\) | 2.70170e12 | 0.641037 | ||||||||
\(640\) | 2.87127e12 | 0.676495 | ||||||||
\(641\) | −4.45436e11 | −0.104214 | −0.0521068 | − | 0.998642i | \(-0.516594\pi\) | ||||
−0.0521068 | + | 0.998642i | \(0.516594\pi\) | |||||||
\(642\) | 4.55177e12 | 1.05748 | ||||||||
\(643\) | 2.04454e12 | 0.471678 | 0.235839 | − | 0.971792i | \(-0.424216\pi\) | ||||
0.235839 | + | 0.971792i | \(0.424216\pi\) | |||||||
\(644\) | 7.24720e10 | 0.0166029 | ||||||||
\(645\) | −7.63949e11 | −0.173798 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.07293e12 | 1.13812 | 0.569062 | − | 0.822295i | \(-0.307307\pi\) | ||||
0.569062 | + | 0.822295i | \(0.307307\pi\) | |||||||
\(648\) | 4.26782e11 | 0.0950864 | ||||||||
\(649\) | −2.46847e11 | −0.0546168 | ||||||||
\(650\) | −3.71356e12 | −0.815981 | ||||||||
\(651\) | 1.01183e12 | 0.220797 | ||||||||
\(652\) | 2.57642e11 | 0.0558344 | ||||||||
\(653\) | −6.33100e12 | −1.36258 | −0.681292 | − | 0.732012i | \(-0.738581\pi\) | ||||
−0.681292 | + | 0.732012i | \(0.738581\pi\) | |||||||
\(654\) | 3.95534e12 | 0.845441 | ||||||||
\(655\) | 2.60989e12 | 0.554034 | ||||||||
\(656\) | 3.48428e12 | 0.734591 | ||||||||
\(657\) | 1.53200e12 | 0.320785 | ||||||||
\(658\) | −8.59847e12 | −1.78815 | ||||||||
\(659\) | −3.82450e12 | −0.789934 | −0.394967 | − | 0.918695i | \(-0.629244\pi\) | ||||
−0.394967 | + | 0.918695i | \(0.629244\pi\) | |||||||
\(660\) | −2.22856e10 | −0.00457169 | ||||||||
\(661\) | 5.35631e12 | 1.09134 | 0.545669 | − | 0.838001i | \(-0.316276\pi\) | ||||
0.545669 | + | 0.838001i | \(0.316276\pi\) | |||||||
\(662\) | 1.73855e12 | 0.351826 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.69297e12 | −0.537620 | ||||||||
\(665\) | 4.30438e11 | 0.0853518 | ||||||||
\(666\) | −3.68002e12 | −0.724796 | ||||||||
\(667\) | 2.70797e11 | 0.0529758 | ||||||||
\(668\) | 1.30363e12 | 0.253315 | ||||||||
\(669\) | 4.46851e12 | 0.862473 | ||||||||
\(670\) | 4.17414e12 | 0.800259 | ||||||||
\(671\) | 1.17701e11 | 0.0224145 | ||||||||
\(672\) | −1.42443e12 | −0.269451 | ||||||||
\(673\) | 9.69427e12 | 1.82158 | 0.910788 | − | 0.412873i | \(-0.135475\pi\) | ||||
0.910788 | + | 0.412873i | \(0.135475\pi\) | |||||||
\(674\) | 8.46399e12 | 1.57981 | ||||||||
\(675\) | 3.55349e12 | 0.658852 | ||||||||
\(676\) | 1.71545e11 | 0.0315949 | ||||||||
\(677\) | −4.82449e12 | −0.882678 | −0.441339 | − | 0.897341i | \(-0.645496\pi\) | ||||
−0.441339 | + | 0.897341i | \(0.645496\pi\) | |||||||
\(678\) | −5.91338e12 | −1.07474 | ||||||||
\(679\) | 7.34787e12 | 1.32662 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.04789e12 | −0.721219 | ||||||||
\(682\) | 1.43895e11 | 0.0254692 | ||||||||
\(683\) | −7.33823e12 | −1.29032 | −0.645161 | − | 0.764046i | \(-0.723210\pi\) | ||||
−0.645161 | + | 0.764046i | \(0.723210\pi\) | |||||||
\(684\) | −1.70840e11 | −0.0298425 | ||||||||
\(685\) | −2.36903e11 | −0.0411115 | ||||||||
\(686\) | −6.97538e12 | −1.20257 | ||||||||
\(687\) | 5.84762e12 | 1.00155 | ||||||||
\(688\) | −3.78031e12 | −0.643249 | ||||||||
\(689\) | 2.01904e12 | 0.341317 | ||||||||
\(690\) | −1.49711e11 | −0.0251440 | ||||||||
\(691\) | −7.59504e12 | −1.26730 | −0.633649 | − | 0.773621i | \(-0.718444\pi\) | ||||
−0.633649 | + | 0.773621i | \(0.718444\pi\) | |||||||
\(692\) | −2.52532e12 | −0.418639 | ||||||||
\(693\) | 1.95946e11 | 0.0322728 | ||||||||
\(694\) | 1.25091e13 | 2.04695 | ||||||||
\(695\) | −3.42517e12 | −0.556866 | ||||||||
\(696\) | −2.25446e12 | −0.364167 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −9.39536e12 | −1.49818 | ||||||||
\(699\) | 3.60342e12 | 0.570910 | ||||||||
\(700\) | 1.04451e12 | 0.164426 | ||||||||
\(701\) | 5.36973e12 | 0.839887 | 0.419944 | − | 0.907550i | \(-0.362050\pi\) | ||||
0.419944 | + | 0.907550i | \(0.362050\pi\) | |||||||
\(702\) | −7.35636e12 | −1.14326 | ||||||||
\(703\) | −1.05131e12 | −0.162343 | ||||||||
\(704\) | 2.13294e11 | 0.0327267 | ||||||||
\(705\) | 3.72297e12 | 0.567595 | ||||||||
\(706\) | −1.74862e12 | −0.264896 | ||||||||
\(707\) | 5.15282e11 | 0.0775635 | ||||||||
\(708\) | −1.04422e12 | −0.156186 | ||||||||
\(709\) | −7.02128e12 | −1.04354 | −0.521769 | − | 0.853087i | \(-0.674728\pi\) | ||||
−0.521769 | + | 0.853087i | \(0.674728\pi\) | |||||||
\(710\) | −4.09505e12 | −0.604780 | ||||||||
\(711\) | −5.13808e12 | −0.754028 | ||||||||
\(712\) | −9.31578e12 | −1.35850 | ||||||||
\(713\) | 2.02609e11 | 0.0293600 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.21321e11 | 0.0316698 | ||||||||
\(716\) | −1.17425e11 | −0.0166975 | ||||||||
\(717\) | −5.22539e12 | −0.738385 | ||||||||
\(718\) | 7.26489e12 | 1.02016 | ||||||||
\(719\) | −2.98659e12 | −0.416769 | −0.208384 | − | 0.978047i | \(-0.566821\pi\) | ||||
−0.208384 | + | 0.978047i | \(0.566821\pi\) | |||||||
\(720\) | −3.22819e12 | −0.447676 | ||||||||
\(721\) | 8.24911e12 | 1.13684 | ||||||||
\(722\) | 7.97998e12 | 1.09291 | ||||||||
\(723\) | 5.63787e11 | 0.0767349 | ||||||||
\(724\) | 1.84935e12 | 0.250147 | ||||||||
\(725\) | 3.90287e12 | 0.524642 | ||||||||
\(726\) | 4.83493e12 | 0.645914 | ||||||||
\(727\) | 1.37734e13 | 1.82868 | 0.914339 | − | 0.404950i | \(-0.132711\pi\) | ||||
0.914339 | + | 0.404950i | \(0.132711\pi\) | |||||||
\(728\) | 5.99193e12 | 0.790634 | ||||||||
\(729\) | 3.63298e12 | 0.476419 | ||||||||
\(730\) | −2.32210e12 | −0.302642 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.97903e11 | 0.0640981 | ||||||||
\(733\) | −3.47927e10 | −0.00445164 | −0.00222582 | − | 0.999998i | \(-0.500709\pi\) | ||||
−0.00222582 | + | 0.999998i | \(0.500709\pi\) | |||||||
\(734\) | −4.10357e12 | −0.521830 | ||||||||
\(735\) | 4.65880e11 | 0.0588818 | ||||||||
\(736\) | −2.85228e11 | −0.0358295 | ||||||||
\(737\) | 5.42844e11 | 0.0677753 | ||||||||
\(738\) | −3.72446e12 | −0.462178 | ||||||||
\(739\) | 3.58403e12 | 0.442051 | 0.221025 | − | 0.975268i | \(-0.429060\pi\) | ||||
0.221025 | + | 0.975268i | \(0.429060\pi\) | |||||||
\(740\) | 1.16911e12 | 0.143322 | ||||||||
\(741\) | −8.41902e11 | −0.102584 | ||||||||
\(742\) | −2.70945e12 | −0.328144 | ||||||||
\(743\) | −7.13249e12 | −0.858601 | −0.429301 | − | 0.903162i | \(-0.641240\pi\) | ||||
−0.429301 | + | 0.903162i | \(0.641240\pi\) | |||||||
\(744\) | −1.68677e12 | −0.201827 | ||||||||
\(745\) | −3.24619e12 | −0.386074 | ||||||||
\(746\) | 3.07697e11 | 0.0363747 | ||||||||
\(747\) | 3.69968e12 | 0.434732 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.27145e13 | 1.47615 | ||||||||
\(750\) | −5.30426e12 | −0.612138 | ||||||||
\(751\) | 6.98174e12 | 0.800911 | 0.400455 | − | 0.916316i | \(-0.368852\pi\) | ||||
0.400455 | + | 0.916316i | \(0.368852\pi\) | |||||||
\(752\) | 1.84227e13 | 2.10074 | ||||||||
\(753\) | 3.45716e12 | 0.391870 | ||||||||
\(754\) | −8.07964e12 | −0.910376 | ||||||||
\(755\) | 1.96718e12 | 0.220335 | ||||||||
\(756\) | 2.06911e12 | 0.230375 | ||||||||
\(757\) | −7.16189e12 | −0.792677 | −0.396338 | − | 0.918105i | \(-0.629719\pi\) | ||||
−0.396338 | + | 0.918105i | \(0.629719\pi\) | |||||||
\(758\) | −8.56752e12 | −0.942636 | ||||||||
\(759\) | −1.94698e10 | −0.00212948 | ||||||||
\(760\) | −7.17562e11 | −0.0780186 | ||||||||
\(761\) | −1.69932e12 | −0.183672 | −0.0918360 | − | 0.995774i | \(-0.529274\pi\) | ||||
−0.0918360 | + | 0.995774i | \(0.529274\pi\) | |||||||
\(762\) | 9.77791e12 | 1.05063 | ||||||||
\(763\) | 1.10485e13 | 1.18016 | ||||||||
\(764\) | 2.35448e12 | 0.250020 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.04569e12 | 0.739425 | ||||||||
\(767\) | 1.03702e13 | 1.08196 | ||||||||
\(768\) | 4.13380e12 | 0.428770 | ||||||||
\(769\) | −5.97176e12 | −0.615791 | −0.307896 | − | 0.951420i | \(-0.599625\pi\) | ||||
−0.307896 | + | 0.951420i | \(0.599625\pi\) | |||||||
\(770\) | −2.97002e11 | −0.0304475 | ||||||||
\(771\) | 2.31248e12 | 0.235686 | ||||||||
\(772\) | −3.09086e12 | −0.313185 | ||||||||
\(773\) | 3.23402e12 | 0.325788 | 0.162894 | − | 0.986644i | \(-0.447917\pi\) | ||||
0.162894 | + | 0.986644i | \(0.447917\pi\) | |||||||
\(774\) | 4.04089e12 | 0.404709 | ||||||||
\(775\) | 2.92011e12 | 0.290765 | ||||||||
\(776\) | −1.22493e13 | −1.21264 | ||||||||
\(777\) | 5.10087e12 | 0.502053 | ||||||||
\(778\) | −4.02917e12 | −0.394283 | ||||||||
\(779\) | −1.06401e12 | −0.103520 | ||||||||
\(780\) | 9.36240e11 | 0.0905652 | ||||||||
\(781\) | −5.32559e11 | −0.0512198 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.73137e12 | 0.735070 | ||||||||
\(784\) | 2.30535e12 | 0.217929 | ||||||||
\(785\) | −9.58569e12 | −0.900969 | ||||||||
\(786\) | 6.85031e12 | 0.640190 | ||||||||
\(787\) | 1.34733e13 | 1.25195 | 0.625974 | − | 0.779844i | \(-0.284702\pi\) | ||||
0.625974 | + | 0.779844i | \(0.284702\pi\) | |||||||
\(788\) | 2.37546e12 | 0.219472 | ||||||||
\(789\) | 9.27840e12 | 0.852367 | ||||||||
\(790\) | 7.78796e12 | 0.711380 | ||||||||
\(791\) | −1.65179e13 | −1.50024 | ||||||||
\(792\) | −3.26652e11 | −0.0295000 | ||||||||
\(793\) | −4.94474e12 | −0.444032 | ||||||||
\(794\) | 6.95356e12 | 0.620890 | ||||||||
\(795\) | 1.17314e12 | 0.104159 | ||||||||
\(796\) | −3.80262e12 | −0.335718 | ||||||||
\(797\) | −3.19049e12 | −0.280089 | −0.140044 | − | 0.990145i | \(-0.544724\pi\) | ||||
−0.140044 | + | 0.990145i | \(0.544724\pi\) | |||||||
\(798\) | 1.12979e12 | 0.0986246 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.11085e12 | −0.354835 | ||||||||
\(801\) | 1.27983e13 | 1.09851 | ||||||||
\(802\) | 2.34483e13 | 2.00136 | ||||||||
\(803\) | −3.01988e11 | −0.0256313 | ||||||||
\(804\) | 2.29636e12 | 0.193815 | ||||||||
\(805\) | −4.18190e11 | −0.0350988 | ||||||||
\(806\) | −6.04515e12 | −0.504545 | ||||||||
\(807\) | 6.72451e12 | 0.558123 | ||||||||
\(808\) | −8.59001e11 | −0.0708994 | ||||||||
\(809\) | 5.90985e11 | 0.0485074 | 0.0242537 | − | 0.999706i | \(-0.492279\pi\) | ||||
0.0242537 | + | 0.999706i | \(0.492279\pi\) | |||||||
\(810\) | 8.88711e11 | 0.0725401 | ||||||||
\(811\) | −1.20312e13 | −0.976595 | −0.488297 | − | 0.872677i | \(-0.662382\pi\) | ||||
−0.488297 | + | 0.872677i | \(0.662382\pi\) | |||||||
\(812\) | 2.27254e12 | 0.183447 | ||||||||
\(813\) | −1.88775e12 | −0.151543 | ||||||||
\(814\) | 7.25406e11 | 0.0579124 | ||||||||
\(815\) | −1.48669e12 | −0.118035 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.15441e12 | 0.0906482 | ||||||||
\(818\) | 2.16783e13 | 1.69292 | ||||||||
\(819\) | −8.23187e12 | −0.639324 | ||||||||
\(820\) | 1.18323e12 | 0.0913919 | ||||||||
\(821\) | 1.33649e13 | 1.02665 | 0.513325 | − | 0.858194i | \(-0.328413\pi\) | ||||
0.513325 | + | 0.858194i | \(0.328413\pi\) | |||||||
\(822\) | −6.21812e11 | −0.0475046 | ||||||||
\(823\) | −1.17056e13 | −0.889397 | −0.444698 | − | 0.895680i | \(-0.646689\pi\) | ||||
−0.444698 | + | 0.895680i | \(0.646689\pi\) | |||||||
\(824\) | −1.37517e13 | −1.03916 | ||||||||
\(825\) | −2.80610e11 | −0.0210892 | ||||||||
\(826\) | −1.39164e13 | −1.04020 | ||||||||
\(827\) | −2.08998e13 | −1.55370 | −0.776849 | − | 0.629687i | \(-0.783183\pi\) | ||||
−0.776849 | + | 0.629687i | \(0.783183\pi\) | |||||||
\(828\) | 1.65978e11 | 0.0122720 | ||||||||
\(829\) | −3.37506e12 | −0.248191 | −0.124096 | − | 0.992270i | \(-0.539603\pi\) | ||||
−0.124096 | + | 0.992270i | \(0.539603\pi\) | |||||||
\(830\) | −5.60773e12 | −0.410143 | ||||||||
\(831\) | −1.03050e13 | −0.749623 | ||||||||
\(832\) | −8.96067e12 | −0.648314 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.99022e12 | −0.643462 | ||||||||
\(835\) | −7.52242e12 | −0.535511 | ||||||||
\(836\) | 3.36759e10 | 0.00238447 | ||||||||
\(837\) | 5.78458e12 | 0.407387 | ||||||||
\(838\) | −4.60737e12 | −0.322742 | ||||||||
\(839\) | −1.34167e13 | −0.934794 | −0.467397 | − | 0.884047i | \(-0.654808\pi\) | ||||
−0.467397 | + | 0.884047i | \(0.654808\pi\) | |||||||
\(840\) | 3.48154e12 | 0.241276 | ||||||||
\(841\) | −6.01562e12 | −0.414666 | ||||||||
\(842\) | 1.08505e13 | 0.743950 | ||||||||
\(843\) | 3.75482e12 | 0.256074 | ||||||||
\(844\) | 4.67848e12 | 0.317368 | ||||||||
\(845\) | −9.89874e11 | −0.0667920 | ||||||||
\(846\) | −1.96926e13 | −1.32171 | ||||||||
\(847\) | 1.35054e13 | 0.901640 | ||||||||
\(848\) | 5.80514e12 | 0.385506 | ||||||||
\(849\) | 3.38806e12 | 0.223803 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.02140e12 | 0.0667593 | ||||||||
\(852\) | −2.25285e12 | −0.146472 | ||||||||
\(853\) | 7.18446e12 | 0.464647 | 0.232324 | − | 0.972639i | \(-0.425367\pi\) | ||||
0.232324 | + | 0.972639i | \(0.425367\pi\) | |||||||
\(854\) | 6.63559e12 | 0.426893 | ||||||||
\(855\) | 9.85806e11 | 0.0630876 | ||||||||
\(856\) | −2.11957e13 | −1.34932 | ||||||||
\(857\) | 1.77742e13 | 1.12558 | 0.562790 | − | 0.826600i | \(-0.309728\pi\) | ||||
0.562790 | + | 0.826600i | \(0.309728\pi\) | |||||||
\(858\) | 5.80913e11 | 0.0365947 | ||||||||
\(859\) | −4.33599e12 | −0.271718 | −0.135859 | − | 0.990728i | \(-0.543379\pi\) | ||||
−0.135859 | + | 0.990728i | \(0.543379\pi\) | |||||||
\(860\) | −1.28376e12 | −0.0800278 | ||||||||
\(861\) | 5.16246e12 | 0.320142 | ||||||||
\(862\) | 8.46775e11 | 0.0522379 | ||||||||
\(863\) | 2.34250e13 | 1.43758 | 0.718790 | − | 0.695228i | \(-0.244696\pi\) | ||||
0.718790 | + | 0.695228i | \(0.244696\pi\) | |||||||
\(864\) | −8.14338e12 | −0.497156 | ||||||||
\(865\) | 1.45720e13 | 0.885008 | ||||||||
\(866\) | −2.17446e13 | −1.31377 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.70031e12 | 0.101669 | ||||||||
\(869\) | 1.01282e12 | 0.0602480 | ||||||||
\(870\) | −4.69458e12 | −0.277818 | ||||||||
\(871\) | −2.28054e13 | −1.34263 | ||||||||
\(872\) | −1.84184e13 | −1.07877 | ||||||||
\(873\) | 1.68284e13 | 0.980570 | ||||||||
\(874\) | 2.26229e11 | 0.0131144 | ||||||||
\(875\) | −1.48164e13 | −0.854491 | ||||||||
\(876\) | −1.27748e12 | −0.0732968 | ||||||||
\(877\) | 9.16908e12 | 0.523393 | 0.261696 | − | 0.965150i | \(-0.415718\pi\) | ||||
0.261696 | + | 0.965150i | \(0.415718\pi\) | |||||||
\(878\) | 8.17727e12 | 0.464390 | ||||||||
\(879\) | 1.17360e13 | 0.663085 | ||||||||
\(880\) | 6.36342e11 | 0.0357700 | ||||||||
\(881\) | −3.09781e13 | −1.73246 | −0.866230 | − | 0.499645i | \(-0.833464\pi\) | ||||
−0.866230 | + | 0.499645i | \(0.833464\pi\) | |||||||
\(882\) | −2.46426e12 | −0.137113 | ||||||||
\(883\) | −3.55305e13 | −1.96688 | −0.983441 | − | 0.181231i | \(-0.941992\pi\) | ||||
−0.983441 | + | 0.181231i | \(0.941992\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.02551e12 | 0.330179 | ||||||||
\(886\) | −2.99604e13 | −1.63341 | ||||||||
\(887\) | −3.33279e13 | −1.80780 | −0.903902 | − | 0.427740i | \(-0.859310\pi\) | ||||
−0.903902 | + | 0.427740i | \(0.859310\pi\) | |||||||
\(888\) | −8.50340e12 | −0.458917 | ||||||||
\(889\) | 2.73127e13 | 1.46658 | ||||||||
\(890\) | −1.93988e13 | −1.03638 | ||||||||
\(891\) | 1.15576e11 | 0.00614355 | ||||||||
\(892\) | 7.50901e12 | 0.397138 | ||||||||
\(893\) | −5.62580e12 | −0.296041 | ||||||||
\(894\) | −8.52043e12 | −0.446111 | ||||||||
\(895\) | 6.77583e11 | 0.0352987 | ||||||||
\(896\) | 2.10514e13 | 1.09118 | ||||||||
\(897\) | 8.17946e11 | 0.0421851 | ||||||||
\(898\) | −1.06031e12 | −0.0544111 | ||||||||
\(899\) | 6.35332e12 | 0.324401 | ||||||||
\(900\) | 2.39217e12 | 0.121535 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 7.34166e11 | 0.0369287 | ||||||||
\(903\) | −5.60107e12 | −0.280334 | ||||||||
\(904\) | 2.75362e13 | 1.37134 | ||||||||
\(905\) | −1.06714e13 | −0.528814 | ||||||||
\(906\) | 5.16335e12 | 0.254598 | ||||||||
\(907\) | 3.18916e13 | 1.56475 | 0.782373 | − | 0.622810i | \(-0.214009\pi\) | ||||
0.782373 | + | 0.622810i | \(0.214009\pi\) | |||||||
\(908\) | −6.80219e12 | −0.332095 | ||||||||
\(909\) | 1.18012e12 | 0.0573309 | ||||||||
\(910\) | 1.24773e13 | 0.603164 | ||||||||
\(911\) | −7.61425e12 | −0.366264 | −0.183132 | − | 0.983088i | \(-0.558624\pi\) | ||||
−0.183132 | + | 0.983088i | \(0.558624\pi\) | |||||||
\(912\) | −2.42063e12 | −0.115865 | ||||||||
\(913\) | −7.29281e11 | −0.0347357 | ||||||||
\(914\) | −2.43458e13 | −1.15389 | ||||||||
\(915\) | −2.87308e12 | −0.135504 | ||||||||
\(916\) | 9.82650e12 | 0.461179 | ||||||||
\(917\) | 1.91350e13 | 0.893649 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.31210e13 | −1.06927 | −0.534635 | − | 0.845083i | \(-0.679551\pi\) | ||||
−0.534635 | + | 0.845083i | \(0.679551\pi\) | |||||||
\(920\) | 6.97143e11 | 0.0320831 | ||||||||
\(921\) | −1.28586e13 | −0.588877 | ||||||||
\(922\) | −3.70049e13 | −1.68644 | ||||||||
\(923\) | 2.23733e13 | 1.01466 | ||||||||
\(924\) | −1.63392e11 | −0.00737408 | ||||||||
\(925\) | 1.47209e13 | 0.661146 | ||||||||
\(926\) | −9.58794e12 | −0.428525 | ||||||||
\(927\) | 1.88924e13 | 0.840290 | ||||||||
\(928\) | −8.94404e12 | −0.395884 | ||||||||
\(929\) | 1.71091e13 | 0.753627 | 0.376813 | − | 0.926289i | \(-0.377020\pi\) | ||||
0.376813 | + | 0.926289i | \(0.377020\pi\) | |||||||
\(930\) | −3.51247e12 | −0.153971 | ||||||||
\(931\) | −7.03993e11 | −0.0307110 | ||||||||
\(932\) | 6.05529e12 | 0.262883 | ||||||||
\(933\) | −5.20687e12 | −0.224962 | ||||||||
\(934\) | 2.06122e13 | 0.886263 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.37230e13 | 0.584395 | ||||||||
\(937\) | −2.00547e13 | −0.849939 | −0.424969 | − | 0.905208i | \(-0.639715\pi\) | ||||
−0.424969 | + | 0.905208i | \(0.639715\pi\) | |||||||
\(938\) | 3.06037e13 | 1.29081 | ||||||||
\(939\) | −1.18516e13 | −0.497488 | ||||||||
\(940\) | 6.25618e12 | 0.261357 | ||||||||
\(941\) | 3.17254e13 | 1.31903 | 0.659514 | − | 0.751692i | \(-0.270762\pi\) | ||||
0.659514 | + | 0.751692i | \(0.270762\pi\) | |||||||
\(942\) | −2.51600e13 | −1.04108 | ||||||||
\(943\) | 1.03373e12 | 0.0425701 | ||||||||
\(944\) | 2.98165e13 | 1.22203 | ||||||||
\(945\) | −1.19395e13 | −0.487016 | ||||||||
\(946\) | −7.96541e11 | −0.0323369 | ||||||||
\(947\) | 3.38012e13 | 1.36571 | 0.682854 | − | 0.730555i | \(-0.260739\pi\) | ||||
0.682854 | + | 0.730555i | \(0.260739\pi\) | |||||||
\(948\) | 4.28445e12 | 0.172289 | ||||||||
\(949\) | 1.26868e13 | 0.507755 | ||||||||
\(950\) | 3.26054e12 | 0.129877 | ||||||||
\(951\) | 2.17925e13 | 0.863964 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.11972e13 | 0.439737 | 0.219868 | − | 0.975530i | \(-0.429437\pi\) | ||||
0.219868 | + | 0.975530i | \(0.429437\pi\) | |||||||
\(954\) | −6.20529e12 | −0.242546 | ||||||||
\(955\) | −1.35862e13 | −0.528546 | ||||||||
\(956\) | −8.78089e12 | −0.339999 | ||||||||
\(957\) | −6.10527e11 | −0.0235289 | ||||||||
\(958\) | −6.81459e12 | −0.261394 | ||||||||
\(959\) | −1.73691e12 | −0.0663123 | ||||||||
\(960\) | −5.20649e12 | −0.197845 | ||||||||
\(961\) | −2.16861e13 | −0.820212 | ||||||||
\(962\) | −3.04750e13 | −1.14724 | ||||||||
\(963\) | 2.91193e13 | 1.09109 | ||||||||
\(964\) | 9.47403e11 | 0.0353336 | ||||||||
\(965\) | 1.78354e13 | 0.662077 | ||||||||
\(966\) | −1.09764e12 | −0.0405568 | ||||||||
\(967\) | −8.04781e12 | −0.295977 | −0.147989 | − | 0.988989i | \(-0.547280\pi\) | ||||
−0.147989 | + | 0.988989i | \(0.547280\pi\) | |||||||
\(968\) | −2.25142e13 | −0.824173 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.55074e13 | −0.925109 | ||||||||
\(971\) | −3.30383e13 | −1.19270 | −0.596351 | − | 0.802724i | \(-0.703383\pi\) | ||||
−0.596351 | + | 0.802724i | \(0.703383\pi\) | |||||||
\(972\) | 7.57914e12 | 0.272347 | ||||||||
\(973\) | −2.51124e13 | −0.898217 | ||||||||
\(974\) | −2.26827e13 | −0.807570 | ||||||||
\(975\) | 1.17887e13 | 0.417777 | ||||||||
\(976\) | −1.42171e13 | −0.501518 | ||||||||
\(977\) | −4.36000e13 | −1.53095 | −0.765475 | − | 0.643466i | \(-0.777496\pi\) | ||||
−0.765475 | + | 0.643466i | \(0.777496\pi\) | |||||||
\(978\) | −3.90218e12 | −0.136390 | ||||||||
\(979\) | −2.52280e12 | −0.0877729 | ||||||||
\(980\) | 7.82877e11 | 0.0271129 | ||||||||
\(981\) | 2.53036e13 | 0.872313 | ||||||||
\(982\) | −3.87041e13 | −1.32818 | ||||||||
\(983\) | −5.21672e13 | −1.78200 | −0.890998 | − | 0.454008i | \(-0.849994\pi\) | ||||
−0.890998 | + | 0.454008i | \(0.849994\pi\) | |||||||
\(984\) | −8.60609e12 | −0.292636 | ||||||||
\(985\) | −1.37073e13 | −0.463968 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.72958e13 | 0.915522 | ||||||||
\(988\) | −1.41476e12 | −0.0472362 | ||||||||
\(989\) | −1.12156e12 | −0.0372768 | ||||||||
\(990\) | −6.80206e11 | −0.0225052 | ||||||||
\(991\) | −5.63343e13 | −1.85542 | −0.927709 | − | 0.373305i | \(-0.878225\pi\) | ||||
−0.927709 | + | 0.373305i | \(0.878225\pi\) | |||||||
\(992\) | −6.69189e12 | −0.219405 | ||||||||
\(993\) | −5.51904e12 | −0.180132 | ||||||||
\(994\) | −3.00238e13 | −0.975501 | ||||||||
\(995\) | 2.19425e13 | 0.709712 | ||||||||
\(996\) | −3.08503e12 | −0.0993326 | ||||||||
\(997\) | −2.50390e13 | −0.802581 | −0.401291 | − | 0.915951i | \(-0.631438\pi\) | ||||
−0.401291 | + | 0.915951i | \(0.631438\pi\) | |||||||
\(998\) | 4.28053e13 | 1.36587 | ||||||||
\(999\) | 2.91614e13 | 0.926325 |
(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 | 289.10.a.i.1.14 | 52 | ||
17.5 | odd | 16 | 17.10.d.a.8.11 | ✓ | 52 | ||
17.7 | odd | 16 | 17.10.d.a.15.11 | yes | 52 | ||
17.16 | even | 2 | inner | 289.10.a.i.1.13 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.d.a.8.11 | ✓ | 52 | 17.5 | odd | 16 | ||
17.10.d.a.15.11 | yes | 52 | 17.7 | odd | 16 | ||
289.10.a.i.1.13 | 52 | 17.16 | even | 2 | inner | ||
289.10.a.i.1.14 | 52 | 1.1 | even | 1 | trivial |