Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,10,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, 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("29.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(14.9360392488\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 2901 x^{7} - 4592 x^{6} + 2830996 x^{5} + 7409504 x^{4} - 1038861888 x^{3} - 2974719488 x^{2} + \cdots + 456378417152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(15.4003\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −15.4003 | −0.680604 | −0.340302 | − | 0.940316i | \(-0.610529\pi\) | ||||
−0.340302 | + | 0.940316i | \(0.610529\pi\) | |||||||
\(3\) | −207.293 | −1.47754 | −0.738770 | − | 0.673958i | \(-0.764593\pi\) | ||||
−0.738770 | + | 0.673958i | \(0.764593\pi\) | |||||||
\(4\) | −274.831 | −0.536779 | ||||||||
\(5\) | 1546.00 | 1.10623 | 0.553114 | − | 0.833106i | \(-0.313439\pi\) | ||||
0.553114 | + | 0.833106i | \(0.313439\pi\) | |||||||
\(6\) | 3192.38 | 1.00562 | ||||||||
\(7\) | 3958.22 | 0.623101 | 0.311550 | − | 0.950230i | \(-0.399152\pi\) | ||||
0.311550 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(8\) | 12117.4 | 1.04594 | ||||||||
\(9\) | 23287.4 | 1.18312 | ||||||||
\(10\) | −23808.9 | −0.752902 | ||||||||
\(11\) | −22657.1 | −0.466591 | −0.233296 | − | 0.972406i | \(-0.574951\pi\) | ||||
−0.233296 | + | 0.972406i | \(0.574951\pi\) | |||||||
\(12\) | 56970.5 | 0.793112 | ||||||||
\(13\) | −60218.4 | −0.584769 | −0.292384 | − | 0.956301i | \(-0.594449\pi\) | ||||
−0.292384 | + | 0.956301i | \(0.594449\pi\) | |||||||
\(14\) | −60957.7 | −0.424085 | ||||||||
\(15\) | −320475. | −1.63450 | ||||||||
\(16\) | −45898.7 | −0.175090 | ||||||||
\(17\) | 5542.42 | 0.0160946 | 0.00804729 | − | 0.999968i | \(-0.497438\pi\) | ||||
0.00804729 | + | 0.999968i | \(0.497438\pi\) | |||||||
\(18\) | −358633. | −0.805238 | ||||||||
\(19\) | 832454. | 1.46544 | 0.732721 | − | 0.680529i | \(-0.238250\pi\) | ||||
0.732721 | + | 0.680529i | \(0.238250\pi\) | |||||||
\(20\) | −424888. | −0.593799 | ||||||||
\(21\) | −820511. | −0.920656 | ||||||||
\(22\) | 348926. | 0.317564 | ||||||||
\(23\) | −1.66666e6 | −1.24185 | −0.620927 | − | 0.783868i | \(-0.713244\pi\) | ||||
−0.620927 | + | 0.783868i | \(0.713244\pi\) | |||||||
\(24\) | −2.51186e6 | −1.54541 | ||||||||
\(25\) | 436991. | 0.223739 | ||||||||
\(26\) | 927382. | 0.397996 | ||||||||
\(27\) | −747173. | −0.270573 | ||||||||
\(28\) | −1.08784e6 | −0.334467 | ||||||||
\(29\) | −707281. | −0.185695 | ||||||||
\(30\) | 4.93541e6 | 1.11244 | ||||||||
\(31\) | −7.33478e6 | −1.42646 | −0.713230 | − | 0.700930i | \(-0.752769\pi\) | ||||
−0.713230 | + | 0.700930i | \(0.752769\pi\) | |||||||
\(32\) | −5.49727e6 | −0.926770 | ||||||||
\(33\) | 4.69666e6 | 0.689407 | ||||||||
\(34\) | −85355.0 | −0.0109540 | ||||||||
\(35\) | 6.11940e6 | 0.689291 | ||||||||
\(36\) | −6.40010e6 | −0.635076 | ||||||||
\(37\) | 1.86401e7 | 1.63509 | 0.817544 | − | 0.575866i | \(-0.195335\pi\) | ||||
0.817544 | + | 0.575866i | \(0.195335\pi\) | |||||||
\(38\) | −1.28200e7 | −0.997386 | ||||||||
\(39\) | 1.24829e7 | 0.864019 | ||||||||
\(40\) | 1.87335e7 | 1.15704 | ||||||||
\(41\) | −4.20403e6 | −0.232348 | −0.116174 | − | 0.993229i | \(-0.537063\pi\) | ||||
−0.116174 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(42\) | 1.26361e7 | 0.626602 | ||||||||
\(43\) | −2.70316e7 | −1.20577 | −0.602884 | − | 0.797829i | \(-0.705982\pi\) | ||||
−0.602884 | + | 0.797829i | \(0.705982\pi\) | |||||||
\(44\) | 6.22686e6 | 0.250456 | ||||||||
\(45\) | 3.60024e7 | 1.30880 | ||||||||
\(46\) | 2.56670e7 | 0.845211 | ||||||||
\(47\) | 2.31538e6 | 0.0692122 | 0.0346061 | − | 0.999401i | \(-0.488982\pi\) | ||||
0.0346061 | + | 0.999401i | \(0.488982\pi\) | |||||||
\(48\) | 9.51448e6 | 0.258702 | ||||||||
\(49\) | −2.46861e7 | −0.611745 | ||||||||
\(50\) | −6.72979e6 | −0.152278 | ||||||||
\(51\) | −1.14891e6 | −0.0237804 | ||||||||
\(52\) | 1.65499e7 | 0.313892 | ||||||||
\(53\) | −2.48108e7 | −0.431916 | −0.215958 | − | 0.976403i | \(-0.569287\pi\) | ||||
−0.215958 | + | 0.976403i | \(0.569287\pi\) | |||||||
\(54\) | 1.15067e7 | 0.184153 | ||||||||
\(55\) | −3.50278e7 | −0.516156 | ||||||||
\(56\) | 4.79634e7 | 0.651724 | ||||||||
\(57\) | −1.72562e8 | −2.16525 | ||||||||
\(58\) | 1.08923e7 | 0.126385 | ||||||||
\(59\) | −1.25543e8 | −1.34883 | −0.674416 | − | 0.738351i | \(-0.735605\pi\) | ||||
−0.674416 | + | 0.738351i | \(0.735605\pi\) | |||||||
\(60\) | 8.80764e7 | 0.877362 | ||||||||
\(61\) | 3.97338e7 | 0.367431 | 0.183715 | − | 0.982979i | \(-0.441188\pi\) | ||||
0.183715 | + | 0.982979i | \(0.441188\pi\) | |||||||
\(62\) | 1.12958e8 | 0.970854 | ||||||||
\(63\) | 9.21767e7 | 0.737205 | ||||||||
\(64\) | 1.08160e8 | 0.805853 | ||||||||
\(65\) | −9.30977e7 | −0.646887 | ||||||||
\(66\) | −7.23299e7 | −0.469213 | ||||||||
\(67\) | −2.81728e8 | −1.70802 | −0.854011 | − | 0.520255i | \(-0.825837\pi\) | ||||
−0.854011 | + | 0.520255i | \(0.825837\pi\) | |||||||
\(68\) | −1.52323e6 | −0.00863923 | ||||||||
\(69\) | 3.45486e8 | 1.83489 | ||||||||
\(70\) | −9.42406e7 | −0.469134 | ||||||||
\(71\) | −2.53917e7 | −0.118585 | −0.0592923 | − | 0.998241i | \(-0.518884\pi\) | ||||
−0.0592923 | + | 0.998241i | \(0.518884\pi\) | |||||||
\(72\) | 2.82184e8 | 1.23747 | ||||||||
\(73\) | 1.94855e7 | 0.0803079 | 0.0401540 | − | 0.999194i | \(-0.487215\pi\) | ||||
0.0401540 | + | 0.999194i | \(0.487215\pi\) | |||||||
\(74\) | −2.87064e8 | −1.11285 | ||||||||
\(75\) | −9.05851e7 | −0.330584 | ||||||||
\(76\) | −2.28784e8 | −0.786619 | ||||||||
\(77\) | −8.96816e7 | −0.290733 | ||||||||
\(78\) | −1.92240e8 | −0.588055 | ||||||||
\(79\) | −5.92481e8 | −1.71140 | −0.855702 | − | 0.517468i | \(-0.826875\pi\) | ||||
−0.855702 | + | 0.517468i | \(0.826875\pi\) | |||||||
\(80\) | −7.09594e7 | −0.193689 | ||||||||
\(81\) | −3.03483e8 | −0.783342 | ||||||||
\(82\) | 6.47433e7 | 0.158137 | ||||||||
\(83\) | −8.55323e7 | −0.197824 | −0.0989119 | − | 0.995096i | \(-0.531536\pi\) | ||||
−0.0989119 | + | 0.995096i | \(0.531536\pi\) | |||||||
\(84\) | 2.25502e8 | 0.494189 | ||||||||
\(85\) | 8.56859e6 | 0.0178043 | ||||||||
\(86\) | 4.16295e8 | 0.820650 | ||||||||
\(87\) | 1.46614e8 | 0.274372 | ||||||||
\(88\) | −2.74546e8 | −0.488025 | ||||||||
\(89\) | 9.41706e8 | 1.59096 | 0.795482 | − | 0.605977i | \(-0.207218\pi\) | ||||
0.795482 | + | 0.605977i | \(0.207218\pi\) | |||||||
\(90\) | −5.54447e8 | −0.890777 | ||||||||
\(91\) | −2.38358e8 | −0.364370 | ||||||||
\(92\) | 4.58048e8 | 0.666601 | ||||||||
\(93\) | 1.52045e9 | 2.10765 | ||||||||
\(94\) | −3.56576e7 | −0.0471061 | ||||||||
\(95\) | 1.28697e9 | 1.62111 | ||||||||
\(96\) | 1.13955e9 | 1.36934 | ||||||||
\(97\) | 5.83360e7 | 0.0669058 | 0.0334529 | − | 0.999440i | \(-0.489350\pi\) | ||||
0.0334529 | + | 0.999440i | \(0.489350\pi\) | |||||||
\(98\) | 3.80174e8 | 0.416356 | ||||||||
\(99\) | −5.27625e8 | −0.552035 | ||||||||
\(100\) | −1.20098e8 | −0.120098 | ||||||||
\(101\) | 4.25382e8 | 0.406755 | 0.203377 | − | 0.979100i | \(-0.434808\pi\) | ||||
0.203377 | + | 0.979100i | \(0.434808\pi\) | |||||||
\(102\) | 1.76935e7 | 0.0161850 | ||||||||
\(103\) | 1.30643e8 | 0.114372 | 0.0571860 | − | 0.998364i | \(-0.481787\pi\) | ||||
0.0571860 | + | 0.998364i | \(0.481787\pi\) | |||||||
\(104\) | −7.29693e8 | −0.611632 | ||||||||
\(105\) | −1.26851e9 | −1.01846 | ||||||||
\(106\) | 3.82094e8 | 0.293964 | ||||||||
\(107\) | −1.17614e8 | −0.0867426 | −0.0433713 | − | 0.999059i | \(-0.513810\pi\) | ||||
−0.0433713 | + | 0.999059i | \(0.513810\pi\) | |||||||
\(108\) | 2.05346e8 | 0.145238 | ||||||||
\(109\) | −3.17965e8 | −0.215755 | −0.107877 | − | 0.994164i | \(-0.534405\pi\) | ||||
−0.107877 | + | 0.994164i | \(0.534405\pi\) | |||||||
\(110\) | 5.39439e8 | 0.351298 | ||||||||
\(111\) | −3.86397e9 | −2.41591 | ||||||||
\(112\) | −1.81677e8 | −0.109099 | ||||||||
\(113\) | 1.72545e9 | 0.995520 | 0.497760 | − | 0.867315i | \(-0.334156\pi\) | ||||
0.497760 | + | 0.867315i | \(0.334156\pi\) | |||||||
\(114\) | 2.65751e9 | 1.47368 | ||||||||
\(115\) | −2.57665e9 | −1.37377 | ||||||||
\(116\) | 1.94383e8 | 0.0996773 | ||||||||
\(117\) | −1.40233e9 | −0.691854 | ||||||||
\(118\) | 1.93340e9 | 0.918020 | ||||||||
\(119\) | 2.19381e7 | 0.0100285 | ||||||||
\(120\) | −3.88333e9 | −1.70958 | ||||||||
\(121\) | −1.84460e9 | −0.782292 | ||||||||
\(122\) | −6.11912e8 | −0.250075 | ||||||||
\(123\) | 8.71466e8 | 0.343303 | ||||||||
\(124\) | 2.01582e9 | 0.765694 | ||||||||
\(125\) | −2.34394e9 | −0.858721 | ||||||||
\(126\) | −1.41955e9 | −0.501745 | ||||||||
\(127\) | −3.28989e9 | −1.12218 | −0.561092 | − | 0.827754i | \(-0.689619\pi\) | ||||
−0.561092 | + | 0.827754i | \(0.689619\pi\) | |||||||
\(128\) | 1.14891e9 | 0.378304 | ||||||||
\(129\) | 5.60346e9 | 1.78157 | ||||||||
\(130\) | 1.43373e9 | 0.440274 | ||||||||
\(131\) | −5.91876e9 | −1.75594 | −0.877970 | − | 0.478715i | \(-0.841103\pi\) | ||||
−0.877970 | + | 0.478715i | \(0.841103\pi\) | |||||||
\(132\) | −1.29079e9 | −0.370059 | ||||||||
\(133\) | 3.29503e9 | 0.913119 | ||||||||
\(134\) | 4.33869e9 | 1.16249 | ||||||||
\(135\) | −1.15513e9 | −0.299315 | ||||||||
\(136\) | 6.71599e7 | 0.0168339 | ||||||||
\(137\) | 4.07090e9 | 0.987296 | 0.493648 | − | 0.869662i | \(-0.335663\pi\) | ||||
0.493648 | + | 0.869662i | \(0.335663\pi\) | |||||||
\(138\) | −5.32059e9 | −1.24883 | ||||||||
\(139\) | −1.65106e9 | −0.375142 | −0.187571 | − | 0.982251i | \(-0.560061\pi\) | ||||
−0.187571 | + | 0.982251i | \(0.560061\pi\) | |||||||
\(140\) | −1.68180e9 | −0.369997 | ||||||||
\(141\) | −4.79963e8 | −0.102264 | ||||||||
\(142\) | 3.91039e8 | 0.0807091 | ||||||||
\(143\) | 1.36437e9 | 0.272848 | ||||||||
\(144\) | −1.06886e9 | −0.207153 | ||||||||
\(145\) | −1.09346e9 | −0.205421 | ||||||||
\(146\) | −3.00082e8 | −0.0546579 | ||||||||
\(147\) | 5.11727e9 | 0.903878 | ||||||||
\(148\) | −5.12288e9 | −0.877680 | ||||||||
\(149\) | 1.09621e9 | 0.182203 | 0.0911014 | − | 0.995842i | \(-0.470961\pi\) | ||||
0.0911014 | + | 0.995842i | \(0.470961\pi\) | |||||||
\(150\) | 1.39504e9 | 0.224996 | ||||||||
\(151\) | 7.42003e9 | 1.16147 | 0.580737 | − | 0.814091i | \(-0.302764\pi\) | ||||
0.580737 | + | 0.814091i | \(0.302764\pi\) | |||||||
\(152\) | 1.00872e10 | 1.53276 | ||||||||
\(153\) | 1.29069e8 | 0.0190419 | ||||||||
\(154\) | 1.38112e9 | 0.197874 | ||||||||
\(155\) | −1.13396e10 | −1.57799 | ||||||||
\(156\) | −3.43067e9 | −0.463787 | ||||||||
\(157\) | −1.06087e10 | −1.39353 | −0.696763 | − | 0.717302i | \(-0.745377\pi\) | ||||
−0.696763 | + | 0.717302i | \(0.745377\pi\) | |||||||
\(158\) | 9.12439e9 | 1.16479 | ||||||||
\(159\) | 5.14311e9 | 0.638173 | ||||||||
\(160\) | −8.49878e9 | −1.02522 | ||||||||
\(161\) | −6.59699e9 | −0.773801 | ||||||||
\(162\) | 4.67372e9 | 0.533145 | ||||||||
\(163\) | 1.08213e10 | 1.20071 | 0.600353 | − | 0.799735i | \(-0.295027\pi\) | ||||
0.600353 | + | 0.799735i | \(0.295027\pi\) | |||||||
\(164\) | 1.15540e9 | 0.124719 | ||||||||
\(165\) | 7.26103e9 | 0.762641 | ||||||||
\(166\) | 1.31722e9 | 0.134640 | ||||||||
\(167\) | 1.93867e10 | 1.92876 | 0.964382 | − | 0.264514i | \(-0.0852117\pi\) | ||||
0.964382 | + | 0.264514i | \(0.0852117\pi\) | |||||||
\(168\) | −9.94248e9 | −0.962948 | ||||||||
\(169\) | −6.97824e9 | −0.658045 | ||||||||
\(170\) | −1.31959e8 | −0.0121176 | ||||||||
\(171\) | 1.93857e10 | 1.73380 | ||||||||
\(172\) | 7.42911e9 | 0.647231 | ||||||||
\(173\) | 5.01394e9 | 0.425570 | 0.212785 | − | 0.977099i | \(-0.431747\pi\) | ||||
0.212785 | + | 0.977099i | \(0.431747\pi\) | |||||||
\(174\) | −2.25791e9 | −0.186739 | ||||||||
\(175\) | 1.72970e9 | 0.139412 | ||||||||
\(176\) | 1.03993e9 | 0.0816953 | ||||||||
\(177\) | 2.60242e10 | 1.99295 | ||||||||
\(178\) | −1.45026e10 | −1.08282 | ||||||||
\(179\) | −1.65570e10 | −1.20543 | −0.602717 | − | 0.797955i | \(-0.705915\pi\) | ||||
−0.602717 | + | 0.797955i | \(0.705915\pi\) | |||||||
\(180\) | −9.89456e9 | −0.702538 | ||||||||
\(181\) | −2.74840e10 | −1.90338 | −0.951691 | − | 0.307058i | \(-0.900656\pi\) | ||||
−0.951691 | + | 0.307058i | \(0.900656\pi\) | |||||||
\(182\) | 3.67078e9 | 0.247991 | ||||||||
\(183\) | −8.23654e9 | −0.542894 | ||||||||
\(184\) | −2.01956e10 | −1.29890 | ||||||||
\(185\) | 2.88176e10 | 1.80878 | ||||||||
\(186\) | −2.34154e10 | −1.43448 | ||||||||
\(187\) | −1.25575e8 | −0.00750959 | ||||||||
\(188\) | −6.36338e8 | −0.0371516 | ||||||||
\(189\) | −2.95747e9 | −0.168594 | ||||||||
\(190\) | −1.98198e10 | −1.10334 | ||||||||
\(191\) | −2.99580e10 | −1.62878 | −0.814391 | − | 0.580316i | \(-0.802929\pi\) | ||||
−0.814391 | + | 0.580316i | \(0.802929\pi\) | |||||||
\(192\) | −2.24208e10 | −1.19068 | ||||||||
\(193\) | 1.12672e10 | 0.584531 | 0.292266 | − | 0.956337i | \(-0.405591\pi\) | ||||
0.292266 | + | 0.956337i | \(0.405591\pi\) | |||||||
\(194\) | −8.98392e8 | −0.0455363 | ||||||||
\(195\) | 1.92985e10 | 0.955802 | ||||||||
\(196\) | 6.78451e9 | 0.328372 | ||||||||
\(197\) | 2.69790e9 | 0.127623 | 0.0638113 | − | 0.997962i | \(-0.479674\pi\) | ||||
0.0638113 | + | 0.997962i | \(0.479674\pi\) | |||||||
\(198\) | 8.12558e9 | 0.375717 | ||||||||
\(199\) | 3.36839e10 | 1.52259 | 0.761296 | − | 0.648405i | \(-0.224564\pi\) | ||||
0.761296 | + | 0.648405i | \(0.224564\pi\) | |||||||
\(200\) | 5.29520e9 | 0.234017 | ||||||||
\(201\) | 5.84003e10 | 2.52367 | ||||||||
\(202\) | −6.55101e9 | −0.276839 | ||||||||
\(203\) | −2.79957e9 | −0.115707 | ||||||||
\(204\) | 3.15755e8 | 0.0127648 | ||||||||
\(205\) | −6.49942e9 | −0.257029 | ||||||||
\(206\) | −2.01195e9 | −0.0778421 | ||||||||
\(207\) | −3.88121e10 | −1.46927 | ||||||||
\(208\) | 2.76395e9 | 0.102387 | ||||||||
\(209\) | −1.88610e10 | −0.683763 | ||||||||
\(210\) | 1.95354e10 | 0.693164 | ||||||||
\(211\) | −3.90404e10 | −1.35595 | −0.677975 | − | 0.735085i | \(-0.737142\pi\) | ||||
−0.677975 | + | 0.735085i | \(0.737142\pi\) | |||||||
\(212\) | 6.81877e9 | 0.231843 | ||||||||
\(213\) | 5.26352e9 | 0.175214 | ||||||||
\(214\) | 1.81129e9 | 0.0590373 | ||||||||
\(215\) | −4.17908e10 | −1.33385 | ||||||||
\(216\) | −9.05381e9 | −0.283002 | ||||||||
\(217\) | −2.90327e10 | −0.888828 | ||||||||
\(218\) | 4.89676e9 | 0.146843 | ||||||||
\(219\) | −4.03921e9 | −0.118658 | ||||||||
\(220\) | 9.62673e9 | 0.277062 | ||||||||
\(221\) | −3.33756e8 | −0.00941161 | ||||||||
\(222\) | 5.95063e10 | 1.64428 | ||||||||
\(223\) | 1.18395e9 | 0.0320598 | 0.0160299 | − | 0.999872i | \(-0.494897\pi\) | ||||
0.0160299 | + | 0.999872i | \(0.494897\pi\) | |||||||
\(224\) | −2.17594e10 | −0.577471 | ||||||||
\(225\) | 1.01764e10 | 0.264711 | ||||||||
\(226\) | −2.65725e10 | −0.677554 | ||||||||
\(227\) | −2.34636e10 | −0.586514 | −0.293257 | − | 0.956034i | \(-0.594739\pi\) | ||||
−0.293257 | + | 0.956034i | \(0.594739\pi\) | |||||||
\(228\) | 4.74253e10 | 1.16226 | ||||||||
\(229\) | −3.40676e10 | −0.818619 | −0.409309 | − | 0.912396i | \(-0.634230\pi\) | ||||
−0.409309 | + | 0.912396i | \(0.634230\pi\) | |||||||
\(230\) | 3.96812e10 | 0.934995 | ||||||||
\(231\) | 1.85904e10 | 0.429570 | ||||||||
\(232\) | −8.57043e9 | −0.194226 | ||||||||
\(233\) | −6.05483e10 | −1.34586 | −0.672931 | − | 0.739705i | \(-0.734965\pi\) | ||||
−0.672931 | + | 0.739705i | \(0.734965\pi\) | |||||||
\(234\) | 2.15963e10 | 0.470878 | ||||||||
\(235\) | 3.57958e9 | 0.0765644 | ||||||||
\(236\) | 3.45030e10 | 0.724025 | ||||||||
\(237\) | 1.22817e11 | 2.52867 | ||||||||
\(238\) | −3.37854e8 | −0.00682546 | ||||||||
\(239\) | 7.37646e9 | 0.146237 | 0.0731185 | − | 0.997323i | \(-0.476705\pi\) | ||||
0.0731185 | + | 0.997323i | \(0.476705\pi\) | |||||||
\(240\) | 1.47094e10 | 0.286183 | ||||||||
\(241\) | −6.41814e10 | −1.22555 | −0.612777 | − | 0.790256i | \(-0.709948\pi\) | ||||
−0.612777 | + | 0.790256i | \(0.709948\pi\) | |||||||
\(242\) | 2.84075e10 | 0.532431 | ||||||||
\(243\) | 7.76165e10 | 1.42799 | ||||||||
\(244\) | −1.09201e10 | −0.197229 | ||||||||
\(245\) | −3.81648e10 | −0.676730 | ||||||||
\(246\) | −1.34208e10 | −0.233653 | ||||||||
\(247\) | −5.01291e10 | −0.856946 | ||||||||
\(248\) | −8.88787e10 | −1.49199 | ||||||||
\(249\) | 1.77303e10 | 0.292293 | ||||||||
\(250\) | 3.60974e10 | 0.584449 | ||||||||
\(251\) | 1.01708e11 | 1.61743 | 0.808713 | − | 0.588203i | \(-0.200165\pi\) | ||||
0.808713 | + | 0.588203i | \(0.200165\pi\) | |||||||
\(252\) | −2.53330e10 | −0.395716 | ||||||||
\(253\) | 3.77616e10 | 0.579439 | ||||||||
\(254\) | 5.06652e10 | 0.763762 | ||||||||
\(255\) | −1.77621e9 | −0.0263065 | ||||||||
\(256\) | −7.30713e10 | −1.06333 | ||||||||
\(257\) | 1.03674e11 | 1.48242 | 0.741208 | − | 0.671276i | \(-0.234253\pi\) | ||||
0.741208 | + | 0.671276i | \(0.234253\pi\) | |||||||
\(258\) | −8.62950e10 | −1.21254 | ||||||||
\(259\) | 7.37816e10 | 1.01882 | ||||||||
\(260\) | 2.55861e10 | 0.347235 | ||||||||
\(261\) | −1.64708e10 | −0.219701 | ||||||||
\(262\) | 9.11507e10 | 1.19510 | ||||||||
\(263\) | 1.21236e11 | 1.56254 | 0.781268 | − | 0.624196i | \(-0.214573\pi\) | ||||
0.781268 | + | 0.624196i | \(0.214573\pi\) | |||||||
\(264\) | 5.69114e10 | 0.721077 | ||||||||
\(265\) | −3.83575e10 | −0.477797 | ||||||||
\(266\) | −5.07445e10 | −0.621472 | ||||||||
\(267\) | −1.95209e11 | −2.35071 | ||||||||
\(268\) | 7.74275e10 | 0.916830 | ||||||||
\(269\) | −7.61186e10 | −0.886351 | −0.443175 | − | 0.896435i | \(-0.646148\pi\) | ||||
−0.443175 | + | 0.896435i | \(0.646148\pi\) | |||||||
\(270\) | 1.77893e10 | 0.203715 | ||||||||
\(271\) | −1.01182e11 | −1.13957 | −0.569787 | − | 0.821793i | \(-0.692974\pi\) | ||||
−0.569787 | + | 0.821793i | \(0.692974\pi\) | |||||||
\(272\) | −2.54390e8 | −0.00281799 | ||||||||
\(273\) | 4.94099e10 | 0.538371 | ||||||||
\(274\) | −6.26930e10 | −0.671957 | ||||||||
\(275\) | −9.90093e9 | −0.104395 | ||||||||
\(276\) | −9.49503e10 | −0.984930 | ||||||||
\(277\) | 1.08999e10 | 0.111241 | 0.0556203 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556203 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(278\) | 2.54268e10 | 0.255323 | ||||||||
\(279\) | −1.70808e11 | −1.68768 | ||||||||
\(280\) | 7.41514e10 | 0.720955 | ||||||||
\(281\) | −6.18982e10 | −0.592242 | −0.296121 | − | 0.955150i | \(-0.595693\pi\) | ||||
−0.296121 | + | 0.955150i | \(0.595693\pi\) | |||||||
\(282\) | 7.39157e9 | 0.0696011 | ||||||||
\(283\) | 1.12113e11 | 1.03900 | 0.519502 | − | 0.854469i | \(-0.326118\pi\) | ||||
0.519502 | + | 0.854469i | \(0.326118\pi\) | |||||||
\(284\) | 6.97841e9 | 0.0636537 | ||||||||
\(285\) | −2.66781e11 | −2.39526 | ||||||||
\(286\) | −2.10118e10 | −0.185701 | ||||||||
\(287\) | −1.66404e10 | −0.144776 | ||||||||
\(288\) | −1.28017e11 | −1.09648 | ||||||||
\(289\) | −1.18557e11 | −0.999741 | ||||||||
\(290\) | 1.68396e10 | 0.139810 | ||||||||
\(291\) | −1.20926e10 | −0.0988560 | ||||||||
\(292\) | −5.35521e9 | −0.0431076 | ||||||||
\(293\) | 1.76830e11 | 1.40169 | 0.700845 | − | 0.713314i | \(-0.252807\pi\) | ||||
0.700845 | + | 0.713314i | \(0.252807\pi\) | |||||||
\(294\) | −7.88074e10 | −0.615183 | ||||||||
\(295\) | −1.94089e11 | −1.49212 | ||||||||
\(296\) | 2.25870e11 | 1.71020 | ||||||||
\(297\) | 1.69288e10 | 0.126247 | ||||||||
\(298\) | −1.68819e10 | −0.124008 | ||||||||
\(299\) | 1.00363e11 | 0.726198 | ||||||||
\(300\) | 2.48956e10 | 0.177450 | ||||||||
\(301\) | −1.06997e11 | −0.751315 | ||||||||
\(302\) | −1.14271e11 | −0.790503 | ||||||||
\(303\) | −8.81787e10 | −0.600996 | ||||||||
\(304\) | −3.82086e10 | −0.256584 | ||||||||
\(305\) | 6.14284e10 | 0.406462 | ||||||||
\(306\) | −1.98770e9 | −0.0129600 | ||||||||
\(307\) | −6.54871e10 | −0.420758 | −0.210379 | − | 0.977620i | \(-0.567470\pi\) | ||||
−0.210379 | + | 0.977620i | \(0.567470\pi\) | |||||||
\(308\) | 2.46473e10 | 0.156060 | ||||||||
\(309\) | −2.70815e10 | −0.168989 | ||||||||
\(310\) | 1.74633e11 | 1.07399 | ||||||||
\(311\) | 8.21809e9 | 0.0498137 | 0.0249069 | − | 0.999690i | \(-0.492071\pi\) | ||||
0.0249069 | + | 0.999690i | \(0.492071\pi\) | |||||||
\(312\) | 1.51260e11 | 0.903710 | ||||||||
\(313\) | 3.27979e11 | 1.93151 | 0.965754 | − | 0.259458i | \(-0.0835440\pi\) | ||||
0.965754 | + | 0.259458i | \(0.0835440\pi\) | |||||||
\(314\) | 1.63378e11 | 0.948438 | ||||||||
\(315\) | 1.42505e11 | 0.815517 | ||||||||
\(316\) | 1.62832e11 | 0.918646 | ||||||||
\(317\) | −1.22951e11 | −0.683857 | −0.341929 | − | 0.939726i | \(-0.611080\pi\) | ||||
−0.341929 | + | 0.939726i | \(0.611080\pi\) | |||||||
\(318\) | −7.92054e10 | −0.434343 | ||||||||
\(319\) | 1.60249e10 | 0.0866439 | ||||||||
\(320\) | 1.67215e11 | 0.891457 | ||||||||
\(321\) | 2.43806e10 | 0.128166 | ||||||||
\(322\) | 1.01596e11 | 0.526651 | ||||||||
\(323\) | 4.61381e9 | 0.0235857 | ||||||||
\(324\) | 8.34064e10 | 0.420481 | ||||||||
\(325\) | −2.63149e10 | −0.130836 | ||||||||
\(326\) | −1.66652e11 | −0.817205 | ||||||||
\(327\) | 6.59120e10 | 0.318786 | ||||||||
\(328\) | −5.09420e10 | −0.243021 | ||||||||
\(329\) | 9.16479e9 | 0.0431262 | ||||||||
\(330\) | −1.11822e11 | −0.519056 | ||||||||
\(331\) | 3.75660e11 | 1.72016 | 0.860081 | − | 0.510158i | \(-0.170413\pi\) | ||||
0.860081 | + | 0.510158i | \(0.170413\pi\) | |||||||
\(332\) | 2.35069e10 | 0.106188 | ||||||||
\(333\) | 4.34081e11 | 1.93451 | ||||||||
\(334\) | −2.98560e11 | −1.31272 | ||||||||
\(335\) | −4.35551e11 | −1.88946 | ||||||||
\(336\) | 3.76604e10 | 0.161197 | ||||||||
\(337\) | 1.35186e11 | 0.570949 | 0.285474 | − | 0.958386i | \(-0.407849\pi\) | ||||
0.285474 | + | 0.958386i | \(0.407849\pi\) | |||||||
\(338\) | 1.07467e11 | 0.447868 | ||||||||
\(339\) | −3.57674e11 | −1.47092 | ||||||||
\(340\) | −2.35491e9 | −0.00955695 | ||||||||
\(341\) | 1.66185e11 | 0.665574 | ||||||||
\(342\) | −2.98546e11 | −1.18003 | ||||||||
\(343\) | −2.57441e11 | −1.00428 | ||||||||
\(344\) | −3.27553e11 | −1.26116 | ||||||||
\(345\) | 5.34122e11 | 2.02981 | ||||||||
\(346\) | −7.72161e10 | −0.289645 | ||||||||
\(347\) | −2.54223e11 | −0.941309 | −0.470654 | − | 0.882318i | \(-0.655982\pi\) | ||||
−0.470654 | + | 0.882318i | \(0.655982\pi\) | |||||||
\(348\) | −4.02942e10 | −0.147277 | ||||||||
\(349\) | −4.42380e10 | −0.159618 | −0.0798088 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798088 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(350\) | −2.66379e10 | −0.0948844 | ||||||||
\(351\) | 4.49936e10 | 0.158223 | ||||||||
\(352\) | 1.24552e11 | 0.432423 | ||||||||
\(353\) | −2.56826e10 | −0.0880345 | −0.0440172 | − | 0.999031i | \(-0.514016\pi\) | ||||
−0.0440172 | + | 0.999031i | \(0.514016\pi\) | |||||||
\(354\) | −4.00780e11 | −1.35641 | ||||||||
\(355\) | −3.92555e10 | −0.131182 | ||||||||
\(356\) | −2.58810e11 | −0.853996 | ||||||||
\(357\) | −4.54762e9 | −0.0148176 | ||||||||
\(358\) | 2.54983e11 | 0.820423 | ||||||||
\(359\) | −2.97776e10 | −0.0946160 | −0.0473080 | − | 0.998880i | \(-0.515064\pi\) | ||||
−0.0473080 | + | 0.998880i | \(0.515064\pi\) | |||||||
\(360\) | 4.36256e11 | 1.36893 | ||||||||
\(361\) | 3.70292e11 | 1.14752 | ||||||||
\(362\) | 4.23261e11 | 1.29545 | ||||||||
\(363\) | 3.82374e11 | 1.15587 | ||||||||
\(364\) | 6.55080e10 | 0.195586 | ||||||||
\(365\) | 3.01246e10 | 0.0888388 | ||||||||
\(366\) | 1.26845e11 | 0.369495 | ||||||||
\(367\) | −2.75687e11 | −0.793268 | −0.396634 | − | 0.917977i | \(-0.629822\pi\) | ||||
−0.396634 | + | 0.917977i | \(0.629822\pi\) | |||||||
\(368\) | 7.64974e10 | 0.217436 | ||||||||
\(369\) | −9.79010e10 | −0.274896 | ||||||||
\(370\) | −4.43800e11 | −1.23106 | ||||||||
\(371\) | −9.82065e10 | −0.269127 | ||||||||
\(372\) | −4.17866e11 | −1.13134 | ||||||||
\(373\) | −2.48124e11 | −0.663710 | −0.331855 | − | 0.943330i | \(-0.607674\pi\) | ||||
−0.331855 | + | 0.943330i | \(0.607674\pi\) | |||||||
\(374\) | 1.93389e9 | 0.00511106 | ||||||||
\(375\) | 4.85883e11 | 1.26879 | ||||||||
\(376\) | 2.80565e10 | 0.0723916 | ||||||||
\(377\) | 4.25913e10 | 0.108589 | ||||||||
\(378\) | 4.55459e10 | 0.114746 | ||||||||
\(379\) | −2.18518e11 | −0.544016 | −0.272008 | − | 0.962295i | \(-0.587688\pi\) | ||||
−0.272008 | + | 0.962295i | \(0.587688\pi\) | |||||||
\(380\) | −3.53700e11 | −0.870179 | ||||||||
\(381\) | 6.81970e11 | 1.65807 | ||||||||
\(382\) | 4.61363e11 | 1.10856 | ||||||||
\(383\) | −4.48827e11 | −1.06582 | −0.532911 | − | 0.846171i | \(-0.678902\pi\) | ||||
−0.532911 | + | 0.846171i | \(0.678902\pi\) | |||||||
\(384\) | −2.38161e11 | −0.558959 | ||||||||
\(385\) | −1.38648e11 | −0.321617 | ||||||||
\(386\) | −1.73518e11 | −0.397834 | ||||||||
\(387\) | −6.29496e11 | −1.42657 | ||||||||
\(388\) | −1.60325e10 | −0.0359136 | ||||||||
\(389\) | 7.28717e11 | 1.61356 | 0.806781 | − | 0.590850i | \(-0.201207\pi\) | ||||
0.806781 | + | 0.590850i | \(0.201207\pi\) | |||||||
\(390\) | −2.97203e11 | −0.650522 | ||||||||
\(391\) | −9.23732e9 | −0.0199871 | ||||||||
\(392\) | −2.99132e11 | −0.639847 | ||||||||
\(393\) | 1.22692e12 | 2.59447 | ||||||||
\(394\) | −4.15485e10 | −0.0868604 | ||||||||
\(395\) | −9.15976e11 | −1.89320 | ||||||||
\(396\) | 1.45008e11 | 0.296321 | ||||||||
\(397\) | −9.30288e9 | −0.0187958 | −0.00939788 | − | 0.999956i | \(-0.502991\pi\) | ||||
−0.00939788 | + | 0.999956i | \(0.502991\pi\) | |||||||
\(398\) | −5.18742e11 | −1.03628 | ||||||||
\(399\) | −6.83037e11 | −1.34917 | ||||||||
\(400\) | −2.00573e10 | −0.0391744 | ||||||||
\(401\) | 4.65633e11 | 0.899278 | 0.449639 | − | 0.893210i | \(-0.351553\pi\) | ||||
0.449639 | + | 0.893210i | \(0.351553\pi\) | |||||||
\(402\) | −8.99381e11 | −1.71762 | ||||||||
\(403\) | 4.41689e11 | 0.834150 | ||||||||
\(404\) | −1.16908e11 | −0.218337 | ||||||||
\(405\) | −4.69184e11 | −0.866554 | ||||||||
\(406\) | 4.31142e10 | 0.0787505 | ||||||||
\(407\) | −4.22331e11 | −0.762918 | ||||||||
\(408\) | −1.39218e10 | −0.0248728 | ||||||||
\(409\) | 1.38225e11 | 0.244249 | 0.122125 | − | 0.992515i | \(-0.461029\pi\) | ||||
0.122125 | + | 0.992515i | \(0.461029\pi\) | |||||||
\(410\) | 1.00093e11 | 0.174935 | ||||||||
\(411\) | −8.43869e11 | −1.45877 | ||||||||
\(412\) | −3.59048e10 | −0.0613925 | ||||||||
\(413\) | −4.96926e11 | −0.840459 | ||||||||
\(414\) | 5.97719e11 | 0.999989 | ||||||||
\(415\) | −1.32233e11 | −0.218838 | ||||||||
\(416\) | 3.31037e11 | 0.541947 | ||||||||
\(417\) | 3.42253e11 | 0.554287 | ||||||||
\(418\) | 2.90465e11 | 0.465372 | ||||||||
\(419\) | 8.14126e11 | 1.29041 | 0.645206 | − | 0.764009i | \(-0.276772\pi\) | ||||
0.645206 | + | 0.764009i | \(0.276772\pi\) | |||||||
\(420\) | 3.48625e11 | 0.546685 | ||||||||
\(421\) | 6.26961e11 | 0.972682 | 0.486341 | − | 0.873769i | \(-0.338331\pi\) | ||||
0.486341 | + | 0.873769i | \(0.338331\pi\) | |||||||
\(422\) | 6.01235e11 | 0.922864 | ||||||||
\(423\) | 5.39193e10 | 0.0818866 | ||||||||
\(424\) | −3.00643e11 | −0.451757 | ||||||||
\(425\) | 2.42199e9 | 0.00360099 | ||||||||
\(426\) | −8.10597e10 | −0.119251 | ||||||||
\(427\) | 1.57275e11 | 0.228946 | ||||||||
\(428\) | 3.23240e10 | 0.0465616 | ||||||||
\(429\) | −2.82825e11 | −0.403144 | ||||||||
\(430\) | 6.43591e11 | 0.907825 | ||||||||
\(431\) | 1.05646e11 | 0.147471 | 0.0737356 | − | 0.997278i | \(-0.476508\pi\) | ||||
0.0737356 | + | 0.997278i | \(0.476508\pi\) | |||||||
\(432\) | 3.42943e10 | 0.0473745 | ||||||||
\(433\) | 5.56220e11 | 0.760416 | 0.380208 | − | 0.924901i | \(-0.375852\pi\) | ||||
0.380208 | + | 0.924901i | \(0.375852\pi\) | |||||||
\(434\) | 4.47112e11 | 0.604940 | ||||||||
\(435\) | 2.26666e11 | 0.303518 | ||||||||
\(436\) | 8.73866e10 | 0.115813 | ||||||||
\(437\) | −1.38741e12 | −1.81987 | ||||||||
\(438\) | 6.22050e10 | 0.0807591 | ||||||||
\(439\) | 1.21419e12 | 1.56025 | 0.780127 | − | 0.625621i | \(-0.215155\pi\) | ||||
0.780127 | + | 0.625621i | \(0.215155\pi\) | |||||||
\(440\) | −4.24447e11 | −0.539867 | ||||||||
\(441\) | −5.74877e11 | −0.723771 | ||||||||
\(442\) | 5.13994e9 | 0.00640557 | ||||||||
\(443\) | −9.56779e11 | −1.18031 | −0.590154 | − | 0.807291i | \(-0.700933\pi\) | ||||
−0.590154 | + | 0.807291i | \(0.700933\pi\) | |||||||
\(444\) | 1.06194e12 | 1.29681 | ||||||||
\(445\) | 1.45588e12 | 1.75997 | ||||||||
\(446\) | −1.82331e10 | −0.0218200 | ||||||||
\(447\) | −2.27236e11 | −0.269212 | ||||||||
\(448\) | 4.28120e11 | 0.502128 | ||||||||
\(449\) | 1.05651e12 | 1.22678 | 0.613388 | − | 0.789781i | \(-0.289806\pi\) | ||||
0.613388 | + | 0.789781i | \(0.289806\pi\) | |||||||
\(450\) | −1.56719e11 | −0.180163 | ||||||||
\(451\) | 9.52509e10 | 0.108411 | ||||||||
\(452\) | −4.74207e11 | −0.534374 | ||||||||
\(453\) | −1.53812e12 | −1.71612 | ||||||||
\(454\) | 3.61346e11 | 0.399183 | ||||||||
\(455\) | −3.68501e11 | −0.403076 | ||||||||
\(456\) | −2.09101e12 | −2.26472 | ||||||||
\(457\) | −6.18622e11 | −0.663442 | −0.331721 | − | 0.943378i | \(-0.607629\pi\) | ||||
−0.331721 | + | 0.943378i | \(0.607629\pi\) | |||||||
\(458\) | 5.24651e11 | 0.557155 | ||||||||
\(459\) | −4.14115e9 | −0.00435476 | ||||||||
\(460\) | 7.08143e11 | 0.737413 | ||||||||
\(461\) | −5.66710e10 | −0.0584395 | −0.0292198 | − | 0.999573i | \(-0.509302\pi\) | ||||
−0.0292198 | + | 0.999573i | \(0.509302\pi\) | |||||||
\(462\) | −2.86297e11 | −0.292367 | ||||||||
\(463\) | 2.64517e11 | 0.267509 | 0.133755 | − | 0.991014i | \(-0.457297\pi\) | ||||
0.133755 | + | 0.991014i | \(0.457297\pi\) | |||||||
\(464\) | 3.24633e10 | 0.0325133 | ||||||||
\(465\) | 2.35062e12 | 2.33154 | ||||||||
\(466\) | 9.32462e11 | 0.915998 | ||||||||
\(467\) | −2.81110e11 | −0.273496 | −0.136748 | − | 0.990606i | \(-0.543665\pi\) | ||||
−0.136748 | + | 0.990606i | \(0.543665\pi\) | |||||||
\(468\) | 3.85404e11 | 0.371373 | ||||||||
\(469\) | −1.11514e12 | −1.06427 | ||||||||
\(470\) | −5.51266e10 | −0.0521100 | ||||||||
\(471\) | 2.19912e12 | 2.05899 | ||||||||
\(472\) | −1.52126e12 | −1.41079 | ||||||||
\(473\) | 6.12457e11 | 0.562601 | ||||||||
\(474\) | −1.89142e12 | −1.72102 | ||||||||
\(475\) | 3.63774e11 | 0.327877 | ||||||||
\(476\) | −6.02927e9 | −0.00538311 | ||||||||
\(477\) | −5.77780e11 | −0.511010 | ||||||||
\(478\) | −1.13600e11 | −0.0995294 | ||||||||
\(479\) | −1.90719e12 | −1.65533 | −0.827666 | − | 0.561221i | \(-0.810332\pi\) | ||||
−0.827666 | + | 0.561221i | \(0.810332\pi\) | |||||||
\(480\) | 1.76174e12 | 1.51480 | ||||||||
\(481\) | −1.12248e12 | −0.956149 | ||||||||
\(482\) | 9.88413e11 | 0.834116 | ||||||||
\(483\) | 1.36751e12 | 1.14332 | ||||||||
\(484\) | 5.06954e11 | 0.419918 | ||||||||
\(485\) | 9.01874e10 | 0.0740130 | ||||||||
\(486\) | −1.19532e12 | −0.971896 | ||||||||
\(487\) | 3.72536e11 | 0.300115 | 0.150058 | − | 0.988677i | \(-0.452054\pi\) | ||||
0.150058 | + | 0.988677i | \(0.452054\pi\) | |||||||
\(488\) | 4.81471e11 | 0.384310 | ||||||||
\(489\) | −2.24319e12 | −1.77409 | ||||||||
\(490\) | 5.87749e11 | 0.460585 | ||||||||
\(491\) | −1.79011e12 | −1.39000 | −0.694998 | − | 0.719012i | \(-0.744595\pi\) | ||||
−0.694998 | + | 0.719012i | \(0.744595\pi\) | |||||||
\(492\) | −2.39506e11 | −0.184278 | ||||||||
\(493\) | −3.92005e9 | −0.00298869 | ||||||||
\(494\) | 7.72002e11 | 0.583240 | ||||||||
\(495\) | −8.15708e11 | −0.610677 | ||||||||
\(496\) | 3.36657e11 | 0.249758 | ||||||||
\(497\) | −1.00506e11 | −0.0738902 | ||||||||
\(498\) | −2.73051e11 | −0.198935 | ||||||||
\(499\) | −5.78422e10 | −0.0417631 | −0.0208815 | − | 0.999782i | \(-0.506647\pi\) | ||||
−0.0208815 | + | 0.999782i | \(0.506647\pi\) | |||||||
\(500\) | 6.44188e11 | 0.460943 | ||||||||
\(501\) | −4.01872e12 | −2.84982 | ||||||||
\(502\) | −1.56634e12 | −1.10083 | ||||||||
\(503\) | 1.92887e12 | 1.34353 | 0.671763 | − | 0.740766i | \(-0.265537\pi\) | ||||
0.671763 | + | 0.740766i | \(0.265537\pi\) | |||||||
\(504\) | 1.11694e12 | 0.771071 | ||||||||
\(505\) | 6.57640e11 | 0.449963 | ||||||||
\(506\) | −5.81539e11 | −0.394368 | ||||||||
\(507\) | 1.44654e12 | 0.972288 | ||||||||
\(508\) | 9.04162e11 | 0.602364 | ||||||||
\(509\) | 1.43973e12 | 0.950716 | 0.475358 | − | 0.879792i | \(-0.342319\pi\) | ||||
0.475358 | + | 0.879792i | \(0.342319\pi\) | |||||||
\(510\) | 2.73542e10 | 0.0179043 | ||||||||
\(511\) | 7.71278e10 | 0.0500399 | ||||||||
\(512\) | 5.37079e11 | 0.345401 | ||||||||
\(513\) | −6.21987e11 | −0.396509 | ||||||||
\(514\) | −1.59661e12 | −1.00894 | ||||||||
\(515\) | 2.01975e11 | 0.126522 | ||||||||
\(516\) | −1.54000e12 | −0.956309 | ||||||||
\(517\) | −5.24598e10 | −0.0322938 | ||||||||
\(518\) | −1.13626e12 | −0.693416 | ||||||||
\(519\) | −1.03935e12 | −0.628797 | ||||||||
\(520\) | −1.12810e12 | −0.676604 | ||||||||
\(521\) | −5.70392e11 | −0.339159 | −0.169580 | − | 0.985516i | \(-0.554241\pi\) | ||||
−0.169580 | + | 0.985516i | \(0.554241\pi\) | |||||||
\(522\) | 2.53655e11 | 0.149529 | ||||||||
\(523\) | −7.74760e11 | −0.452803 | −0.226402 | − | 0.974034i | \(-0.572696\pi\) | ||||
−0.226402 | + | 0.974034i | \(0.572696\pi\) | |||||||
\(524\) | 1.62666e12 | 0.942552 | ||||||||
\(525\) | −3.58556e11 | −0.205987 | ||||||||
\(526\) | −1.86707e12 | −1.06347 | ||||||||
\(527\) | −4.06525e10 | −0.0229583 | ||||||||
\(528\) | −2.15570e11 | −0.120708 | ||||||||
\(529\) | 9.76591e11 | 0.542203 | ||||||||
\(530\) | 5.90717e11 | 0.325191 | ||||||||
\(531\) | −2.92357e12 | −1.59584 | ||||||||
\(532\) | −9.05576e11 | −0.490143 | ||||||||
\(533\) | 2.53160e11 | 0.135870 | ||||||||
\(534\) | 3.00628e12 | 1.59990 | ||||||||
\(535\) | −1.81831e11 | −0.0959570 | ||||||||
\(536\) | −3.41382e12 | −1.78648 | ||||||||
\(537\) | 3.43216e12 | 1.78108 | ||||||||
\(538\) | 1.17225e12 | 0.603253 | ||||||||
\(539\) | 5.59316e11 | 0.285435 | ||||||||
\(540\) | 3.17465e11 | 0.160666 | ||||||||
\(541\) | −2.44001e12 | −1.22463 | −0.612313 | − | 0.790615i | \(-0.709761\pi\) | ||||
−0.612313 | + | 0.790615i | \(0.709761\pi\) | |||||||
\(542\) | 1.55824e12 | 0.775597 | ||||||||
\(543\) | 5.69724e12 | 2.81232 | ||||||||
\(544\) | −3.04682e10 | −0.0149160 | ||||||||
\(545\) | −4.91574e11 | −0.238674 | ||||||||
\(546\) | −7.60927e11 | −0.366417 | ||||||||
\(547\) | 2.14873e11 | 0.102622 | 0.0513109 | − | 0.998683i | \(-0.483660\pi\) | ||||
0.0513109 | + | 0.998683i | \(0.483660\pi\) | |||||||
\(548\) | −1.11881e12 | −0.529960 | ||||||||
\(549\) | 9.25297e11 | 0.434716 | ||||||||
\(550\) | 1.52477e11 | 0.0710515 | ||||||||
\(551\) | −5.88779e11 | −0.272126 | ||||||||
\(552\) | 4.18641e12 | 1.91918 | ||||||||
\(553\) | −2.34517e12 | −1.06638 | ||||||||
\(554\) | −1.67862e11 | −0.0757108 | ||||||||
\(555\) | −5.97370e12 | −2.67254 | ||||||||
\(556\) | 4.53762e11 | 0.201368 | ||||||||
\(557\) | −5.57453e11 | −0.245392 | −0.122696 | − | 0.992444i | \(-0.539154\pi\) | ||||
−0.122696 | + | 0.992444i | \(0.539154\pi\) | |||||||
\(558\) | 2.63050e12 | 1.14864 | ||||||||
\(559\) | 1.62780e12 | 0.705095 | ||||||||
\(560\) | −2.80873e11 | −0.120688 | ||||||||
\(561\) | 2.60309e10 | 0.0110957 | ||||||||
\(562\) | 9.53250e11 | 0.403082 | ||||||||
\(563\) | 3.48512e12 | 1.46194 | 0.730971 | − | 0.682409i | \(-0.239068\pi\) | ||||
0.730971 | + | 0.682409i | \(0.239068\pi\) | |||||||
\(564\) | 1.31909e11 | 0.0548930 | ||||||||
\(565\) | 2.66755e12 | 1.10127 | ||||||||
\(566\) | −1.72657e12 | −0.707149 | ||||||||
\(567\) | −1.20125e12 | −0.488101 | ||||||||
\(568\) | −3.07682e11 | −0.124032 | ||||||||
\(569\) | 3.49069e11 | 0.139607 | 0.0698034 | − | 0.997561i | \(-0.477763\pi\) | ||||
0.0698034 | + | 0.997561i | \(0.477763\pi\) | |||||||
\(570\) | 4.10850e12 | 1.63022 | ||||||||
\(571\) | 2.03779e12 | 0.802226 | 0.401113 | − | 0.916029i | \(-0.368623\pi\) | ||||
0.401113 | + | 0.916029i | \(0.368623\pi\) | |||||||
\(572\) | −3.74972e11 | −0.146459 | ||||||||
\(573\) | 6.21009e12 | 2.40659 | ||||||||
\(574\) | 2.56268e11 | 0.0985350 | ||||||||
\(575\) | −7.28313e11 | −0.277852 | ||||||||
\(576\) | 2.51876e12 | 0.953424 | ||||||||
\(577\) | 1.32732e12 | 0.498522 | 0.249261 | − | 0.968436i | \(-0.419812\pi\) | ||||
0.249261 | + | 0.968436i | \(0.419812\pi\) | |||||||
\(578\) | 1.82582e12 | 0.680427 | ||||||||
\(579\) | −2.33561e12 | −0.863668 | ||||||||
\(580\) | 3.00515e11 | 0.110266 | ||||||||
\(581\) | −3.38555e11 | −0.123264 | ||||||||
\(582\) | 1.86230e11 | 0.0672817 | ||||||||
\(583\) | 5.62140e11 | 0.201528 | ||||||||
\(584\) | 2.36114e11 | 0.0839970 | ||||||||
\(585\) | −2.16801e12 | −0.765348 | ||||||||
\(586\) | −2.72324e12 | −0.953995 | ||||||||
\(587\) | 3.75909e12 | 1.30681 | 0.653403 | − | 0.757010i | \(-0.273341\pi\) | ||||
0.653403 | + | 0.757010i | \(0.273341\pi\) | |||||||
\(588\) | −1.40638e12 | −0.485183 | ||||||||
\(589\) | −6.10587e12 | −2.09040 | ||||||||
\(590\) | 2.98903e12 | 1.01554 | ||||||||
\(591\) | −5.59256e11 | −0.188568 | ||||||||
\(592\) | −8.55558e11 | −0.286287 | ||||||||
\(593\) | 1.34815e12 | 0.447705 | 0.223853 | − | 0.974623i | \(-0.428137\pi\) | ||||
0.223853 | + | 0.974623i | \(0.428137\pi\) | |||||||
\(594\) | −2.60708e11 | −0.0859241 | ||||||||
\(595\) | 3.39163e10 | 0.0110939 | ||||||||
\(596\) | −3.01272e11 | −0.0978026 | ||||||||
\(597\) | −6.98244e12 | −2.24969 | ||||||||
\(598\) | −1.54563e12 | −0.494253 | ||||||||
\(599\) | 6.21339e12 | 1.97200 | 0.986002 | − | 0.166735i | \(-0.0533224\pi\) | ||||
0.986002 | + | 0.166735i | \(0.0533224\pi\) | |||||||
\(600\) | −1.09766e12 | −0.345770 | ||||||||
\(601\) | −4.22268e12 | −1.32024 | −0.660121 | − | 0.751159i | \(-0.729495\pi\) | ||||
−0.660121 | + | 0.751159i | \(0.729495\pi\) | |||||||
\(602\) | 1.64778e12 | 0.511347 | ||||||||
\(603\) | −6.56072e12 | −2.02080 | ||||||||
\(604\) | −2.03925e12 | −0.623455 | ||||||||
\(605\) | −2.85176e12 | −0.865393 | ||||||||
\(606\) | 1.35798e12 | 0.409040 | ||||||||
\(607\) | −1.16200e12 | −0.347423 | −0.173712 | − | 0.984797i | \(-0.555576\pi\) | ||||
−0.173712 | + | 0.984797i | \(0.555576\pi\) | |||||||
\(608\) | −4.57622e12 | −1.35813 | ||||||||
\(609\) | 5.80332e11 | 0.170962 | ||||||||
\(610\) | −9.46016e11 | −0.276640 | ||||||||
\(611\) | −1.39429e11 | −0.0404731 | ||||||||
\(612\) | −3.54721e10 | −0.0102213 | ||||||||
\(613\) | −5.93205e12 | −1.69681 | −0.848404 | − | 0.529349i | \(-0.822436\pi\) | ||||
−0.848404 | + | 0.529349i | \(0.822436\pi\) | |||||||
\(614\) | 1.00852e12 | 0.286370 | ||||||||
\(615\) | 1.34729e12 | 0.379771 | ||||||||
\(616\) | −1.08671e12 | −0.304089 | ||||||||
\(617\) | 3.86247e12 | 1.07296 | 0.536478 | − | 0.843914i | \(-0.319754\pi\) | ||||
0.536478 | + | 0.843914i | \(0.319754\pi\) | |||||||
\(618\) | 4.17063e11 | 0.115015 | ||||||||
\(619\) | −2.89472e12 | −0.792498 | −0.396249 | − | 0.918143i | \(-0.629688\pi\) | ||||
−0.396249 | + | 0.918143i | \(0.629688\pi\) | |||||||
\(620\) | 3.11646e12 | 0.847031 | ||||||||
\(621\) | 1.24528e12 | 0.336012 | ||||||||
\(622\) | −1.26561e11 | −0.0339034 | ||||||||
\(623\) | 3.72748e12 | 0.991331 | ||||||||
\(624\) | −5.72947e11 | −0.151281 | ||||||||
\(625\) | −4.47723e12 | −1.17368 | ||||||||
\(626\) | −5.05098e12 | −1.31459 | ||||||||
\(627\) | 3.90975e12 | 1.01029 | ||||||||
\(628\) | 2.91560e12 | 0.748015 | ||||||||
\(629\) | 1.03311e11 | 0.0263160 | ||||||||
\(630\) | −2.19462e12 | −0.555044 | ||||||||
\(631\) | 4.46252e12 | 1.12059 | 0.560297 | − | 0.828292i | \(-0.310687\pi\) | ||||
0.560297 | + | 0.828292i | \(0.310687\pi\) | |||||||
\(632\) | −7.17935e12 | −1.79002 | ||||||||
\(633\) | 8.09281e12 | 2.00347 | ||||||||
\(634\) | 1.89348e12 | 0.465436 | ||||||||
\(635\) | −5.08616e12 | −1.24139 | ||||||||
\(636\) | −1.41348e12 | −0.342558 | ||||||||
\(637\) | 1.48656e12 | 0.357730 | ||||||||
\(638\) | −2.46789e11 | −0.0589701 | ||||||||
\(639\) | −5.91306e11 | −0.140300 | ||||||||
\(640\) | 1.77621e12 | 0.418490 | ||||||||
\(641\) | 2.58707e12 | 0.605268 | 0.302634 | − | 0.953107i | \(-0.402134\pi\) | ||||
0.302634 | + | 0.953107i | \(0.402134\pi\) | |||||||
\(642\) | −3.75468e11 | −0.0872300 | ||||||||
\(643\) | −3.66867e12 | −0.846368 | −0.423184 | − | 0.906044i | \(-0.639088\pi\) | ||||
−0.423184 | + | 0.906044i | \(0.639088\pi\) | |||||||
\(644\) | 1.81305e12 | 0.415360 | ||||||||
\(645\) | 8.66295e12 | 1.97082 | ||||||||
\(646\) | −7.10541e10 | −0.0160525 | ||||||||
\(647\) | −1.39863e12 | −0.313786 | −0.156893 | − | 0.987616i | \(-0.550148\pi\) | ||||
−0.156893 | + | 0.987616i | \(0.550148\pi\) | |||||||
\(648\) | −3.67743e12 | −0.819326 | ||||||||
\(649\) | 2.84443e12 | 0.629354 | ||||||||
\(650\) | 4.05257e11 | 0.0890473 | ||||||||
\(651\) | 6.01827e12 | 1.31328 | ||||||||
\(652\) | −2.97404e12 | −0.644513 | ||||||||
\(653\) | 5.69525e12 | 1.22575 | 0.612877 | − | 0.790178i | \(-0.290012\pi\) | ||||
0.612877 | + | 0.790178i | \(0.290012\pi\) | |||||||
\(654\) | −1.01506e12 | −0.216967 | ||||||||
\(655\) | −9.15040e12 | −1.94247 | ||||||||
\(656\) | 1.92959e11 | 0.0406817 | ||||||||
\(657\) | 4.53767e11 | 0.0950142 | ||||||||
\(658\) | −1.41140e11 | −0.0293518 | ||||||||
\(659\) | 6.98509e12 | 1.44274 | 0.721370 | − | 0.692550i | \(-0.243513\pi\) | ||||
0.721370 | + | 0.692550i | \(0.243513\pi\) | |||||||
\(660\) | −1.99555e12 | −0.409370 | ||||||||
\(661\) | −5.29754e12 | −1.07936 | −0.539682 | − | 0.841869i | \(-0.681455\pi\) | ||||
−0.539682 | + | 0.841869i | \(0.681455\pi\) | |||||||
\(662\) | −5.78528e12 | −1.17075 | ||||||||
\(663\) | 6.91853e10 | 0.0139060 | ||||||||
\(664\) | −1.03643e12 | −0.206911 | ||||||||
\(665\) | 5.09412e12 | 1.01012 | ||||||||
\(666\) | −6.68497e12 | −1.31664 | ||||||||
\(667\) | 1.17879e12 | 0.230607 | ||||||||
\(668\) | −5.32805e12 | −1.03532 | ||||||||
\(669\) | −2.45424e11 | −0.0473696 | ||||||||
\(670\) | 6.70762e12 | 1.28597 | ||||||||
\(671\) | −9.00251e11 | −0.171440 | ||||||||
\(672\) | 4.51057e12 | 0.853237 | ||||||||
\(673\) | 2.16032e12 | 0.405929 | 0.202965 | − | 0.979186i | \(-0.434942\pi\) | ||||
0.202965 | + | 0.979186i | \(0.434942\pi\) | |||||||
\(674\) | −2.08190e12 | −0.388590 | ||||||||
\(675\) | −3.26508e11 | −0.0605377 | ||||||||
\(676\) | 1.91784e12 | 0.353225 | ||||||||
\(677\) | −7.73764e12 | −1.41566 | −0.707831 | − | 0.706382i | \(-0.750326\pi\) | ||||
−0.707831 | + | 0.706382i | \(0.750326\pi\) | |||||||
\(678\) | 5.50829e12 | 1.00111 | ||||||||
\(679\) | 2.30906e11 | 0.0416891 | ||||||||
\(680\) | 1.03829e11 | 0.0186221 | ||||||||
\(681\) | 4.86384e12 | 0.866597 | ||||||||
\(682\) | −2.55929e12 | −0.452992 | ||||||||
\(683\) | −3.00805e12 | −0.528923 | −0.264461 | − | 0.964396i | \(-0.585194\pi\) | ||||
−0.264461 | + | 0.964396i | \(0.585194\pi\) | |||||||
\(684\) | −5.32779e12 | −0.930667 | ||||||||
\(685\) | 6.29361e12 | 1.09217 | ||||||||
\(686\) | 3.96467e12 | 0.683516 | ||||||||
\(687\) | 7.06197e12 | 1.20954 | ||||||||
\(688\) | 1.24072e12 | 0.211117 | ||||||||
\(689\) | 1.49407e12 | 0.252571 | ||||||||
\(690\) | −8.22564e12 | −1.38149 | ||||||||
\(691\) | −9.43997e12 | −1.57514 | −0.787571 | − | 0.616224i | \(-0.788662\pi\) | ||||
−0.787571 | + | 0.616224i | \(0.788662\pi\) | |||||||
\(692\) | −1.37798e12 | −0.228437 | ||||||||
\(693\) | −2.08845e12 | −0.343974 | ||||||||
\(694\) | 3.91511e12 | 0.640658 | ||||||||
\(695\) | −2.55254e12 | −0.414993 | ||||||||
\(696\) | 1.77659e12 | 0.286976 | ||||||||
\(697\) | −2.33005e10 | −0.00373954 | ||||||||
\(698\) | 6.81278e11 | 0.108636 | ||||||||
\(699\) | 1.25512e13 | 1.98856 | ||||||||
\(700\) | −4.75376e11 | −0.0748334 | ||||||||
\(701\) | −3.69624e12 | −0.578135 | −0.289067 | − | 0.957309i | \(-0.593345\pi\) | ||||
−0.289067 | + | 0.957309i | \(0.593345\pi\) | |||||||
\(702\) | −6.92915e11 | −0.107687 | ||||||||
\(703\) | 1.55170e13 | 2.39613 | ||||||||
\(704\) | −2.45058e12 | −0.376004 | ||||||||
\(705\) | −7.42023e11 | −0.113127 | ||||||||
\(706\) | 3.95520e11 | 0.0599166 | ||||||||
\(707\) | 1.68375e12 | 0.253449 | ||||||||
\(708\) | −7.15224e12 | −1.06978 | ||||||||
\(709\) | −3.08928e12 | −0.459144 | −0.229572 | − | 0.973292i | \(-0.573733\pi\) | ||||
−0.229572 | + | 0.973292i | \(0.573733\pi\) | |||||||
\(710\) | 6.04546e11 | 0.0892827 | ||||||||
\(711\) | −1.37974e13 | −2.02480 | ||||||||
\(712\) | 1.14111e13 | 1.66405 | ||||||||
\(713\) | 1.22246e13 | 1.77146 | ||||||||
\(714\) | 7.00347e10 | 0.0100849 | ||||||||
\(715\) | 2.10932e12 | 0.301832 | ||||||||
\(716\) | 4.55038e12 | 0.647051 | ||||||||
\(717\) | −1.52909e12 | −0.216071 | ||||||||
\(718\) | 4.58584e11 | 0.0643960 | ||||||||
\(719\) | −1.23477e13 | −1.72308 | −0.861539 | − | 0.507692i | \(-0.830499\pi\) | ||||
−0.861539 | + | 0.507692i | \(0.830499\pi\) | |||||||
\(720\) | −1.65246e12 | −0.229158 | ||||||||
\(721\) | 5.17115e11 | 0.0712653 | ||||||||
\(722\) | −5.70260e12 | −0.781008 | ||||||||
\(723\) | 1.33044e13 | 1.81080 | ||||||||
\(724\) | 7.55344e12 | 1.02170 | ||||||||
\(725\) | −3.09075e11 | −0.0415473 | ||||||||
\(726\) | −5.88867e12 | −0.786688 | ||||||||
\(727\) | −7.91650e12 | −1.05106 | −0.525531 | − | 0.850774i | \(-0.676133\pi\) | ||||
−0.525531 | + | 0.850774i | \(0.676133\pi\) | |||||||
\(728\) | −2.88828e12 | −0.381108 | ||||||||
\(729\) | −1.01159e13 | −1.32657 | ||||||||
\(730\) | −4.63927e11 | −0.0604640 | ||||||||
\(731\) | −1.49821e11 | −0.0194063 | ||||||||
\(732\) | 2.26365e12 | 0.291414 | ||||||||
\(733\) | −7.02524e12 | −0.898863 | −0.449431 | − | 0.893315i | \(-0.648373\pi\) | ||||
−0.449431 | + | 0.893315i | \(0.648373\pi\) | |||||||
\(734\) | 4.24567e12 | 0.539901 | ||||||||
\(735\) | 7.91129e12 | 0.999895 | ||||||||
\(736\) | 9.16206e12 | 1.15091 | ||||||||
\(737\) | 6.38313e12 | 0.796948 | ||||||||
\(738\) | 1.50770e12 | 0.187095 | ||||||||
\(739\) | −5.62787e12 | −0.694136 | −0.347068 | − | 0.937840i | \(-0.612823\pi\) | ||||
−0.347068 | + | 0.937840i | \(0.612823\pi\) | |||||||
\(740\) | −7.91997e12 | −0.970914 | ||||||||
\(741\) | 1.03914e13 | 1.26617 | ||||||||
\(742\) | 1.51241e12 | 0.183169 | ||||||||
\(743\) | −5.57889e11 | −0.0671580 | −0.0335790 | − | 0.999436i | \(-0.510691\pi\) | ||||
−0.0335790 | + | 0.999436i | \(0.510691\pi\) | |||||||
\(744\) | 1.84239e13 | 2.20447 | ||||||||
\(745\) | 1.69474e12 | 0.201558 | ||||||||
\(746\) | 3.82118e12 | 0.451723 | ||||||||
\(747\) | −1.99183e12 | −0.234050 | ||||||||
\(748\) | 3.45119e10 | 0.00403099 | ||||||||
\(749\) | −4.65542e11 | −0.0540494 | ||||||||
\(750\) | −7.48275e12 | −0.863546 | ||||||||
\(751\) | 1.10236e13 | 1.26457 | 0.632286 | − | 0.774735i | \(-0.282117\pi\) | ||||
0.632286 | + | 0.774735i | \(0.282117\pi\) | |||||||
\(752\) | −1.06273e11 | −0.0121183 | ||||||||
\(753\) | −2.10834e13 | −2.38981 | ||||||||
\(754\) | −6.55920e11 | −0.0739060 | ||||||||
\(755\) | 1.14714e13 | 1.28485 | ||||||||
\(756\) | 8.12804e11 | 0.0904978 | ||||||||
\(757\) | −7.03280e12 | −0.778389 | −0.389195 | − | 0.921156i | \(-0.627247\pi\) | ||||
−0.389195 | + | 0.921156i | \(0.627247\pi\) | |||||||
\(758\) | 3.36525e12 | 0.370259 | ||||||||
\(759\) | −7.82771e12 | −0.856144 | ||||||||
\(760\) | 1.55948e13 | 1.69558 | ||||||||
\(761\) | −1.03885e13 | −1.12285 | −0.561426 | − | 0.827527i | \(-0.689747\pi\) | ||||
−0.561426 | + | 0.827527i | \(0.689747\pi\) | |||||||
\(762\) | −1.05025e13 | −1.12849 | ||||||||
\(763\) | −1.25857e12 | −0.134437 | ||||||||
\(764\) | 8.23339e12 | 0.874296 | ||||||||
\(765\) | 1.99540e11 | 0.0210647 | ||||||||
\(766\) | 6.91208e12 | 0.725402 | ||||||||
\(767\) | 7.55999e12 | 0.788755 | ||||||||
\(768\) | 1.51472e13 | 1.57111 | ||||||||
\(769\) | −1.69193e13 | −1.74467 | −0.872335 | − | 0.488909i | \(-0.837395\pi\) | ||||
−0.872335 | + | 0.488909i | \(0.837395\pi\) | |||||||
\(770\) | 2.13522e12 | 0.218894 | ||||||||
\(771\) | −2.14909e13 | −2.19033 | ||||||||
\(772\) | −3.09657e12 | −0.313764 | ||||||||
\(773\) | −6.76726e12 | −0.681718 | −0.340859 | − | 0.940114i | \(-0.610718\pi\) | ||||
−0.340859 | + | 0.940114i | \(0.610718\pi\) | |||||||
\(774\) | 9.69443e12 | 0.970930 | ||||||||
\(775\) | −3.20523e12 | −0.319155 | ||||||||
\(776\) | 7.06882e11 | 0.0699793 | ||||||||
\(777\) | −1.52944e13 | −1.50535 | ||||||||
\(778\) | −1.12225e13 | −1.09820 | ||||||||
\(779\) | −3.49966e12 | −0.340492 | ||||||||
\(780\) | −5.30382e12 | −0.513054 | ||||||||
\(781\) | 5.75301e11 | 0.0553306 | ||||||||
\(782\) | 1.42257e11 | 0.0136033 | ||||||||
\(783\) | 5.28461e11 | 0.0502441 | ||||||||
\(784\) | 1.13306e12 | 0.107110 | ||||||||
\(785\) | −1.64011e13 | −1.54156 | ||||||||
\(786\) | −1.88949e13 | −1.76581 | ||||||||
\(787\) | −1.40500e13 | −1.30554 | −0.652768 | − | 0.757558i | \(-0.726392\pi\) | ||||
−0.652768 | + | 0.757558i | \(0.726392\pi\) | |||||||
\(788\) | −7.41466e11 | −0.0685051 | ||||||||
\(789\) | −2.51313e13 | −2.30871 | ||||||||
\(790\) | 1.41063e13 | 1.28852 | ||||||||
\(791\) | 6.82971e12 | 0.620309 | ||||||||
\(792\) | −6.39346e12 | −0.577394 | ||||||||
\(793\) | −2.39271e12 | −0.214862 | ||||||||
\(794\) | 1.43267e11 | 0.0127925 | ||||||||
\(795\) | 7.95124e12 | 0.705965 | ||||||||
\(796\) | −9.25737e12 | −0.817295 | ||||||||
\(797\) | −6.87502e11 | −0.0603547 | −0.0301774 | − | 0.999545i | \(-0.509607\pi\) | ||||
−0.0301774 | + | 0.999545i | \(0.509607\pi\) | |||||||
\(798\) | 1.05190e13 | 0.918249 | ||||||||
\(799\) | 1.28328e10 | 0.00111394 | ||||||||
\(800\) | −2.40226e12 | −0.207355 | ||||||||
\(801\) | 2.19299e13 | 1.88231 | ||||||||
\(802\) | −7.17089e12 | −0.612052 | ||||||||
\(803\) | −4.41484e11 | −0.0374710 | ||||||||
\(804\) | −1.60502e13 | −1.35465 | ||||||||
\(805\) | −1.01989e13 | −0.856000 | ||||||||
\(806\) | −6.80214e12 | −0.567725 | ||||||||
\(807\) | 1.57789e13 | 1.30962 | ||||||||
\(808\) | 5.15453e12 | 0.425440 | ||||||||
\(809\) | 2.31429e12 | 0.189954 | 0.0949772 | − | 0.995479i | \(-0.469722\pi\) | ||||
0.0949772 | + | 0.995479i | \(0.469722\pi\) | |||||||
\(810\) | 7.22558e12 | 0.589780 | ||||||||
\(811\) | 2.07750e13 | 1.68635 | 0.843175 | − | 0.537640i | \(-0.180684\pi\) | ||||
0.843175 | + | 0.537640i | \(0.180684\pi\) | |||||||
\(812\) | 7.69408e11 | 0.0621090 | ||||||||
\(813\) | 2.09744e13 | 1.68376 | ||||||||
\(814\) | 6.50402e12 | 0.519245 | ||||||||
\(815\) | 1.67298e13 | 1.32825 | ||||||||
\(816\) | 5.27333e10 | 0.00416370 | ||||||||
\(817\) | −2.25026e13 | −1.76698 | ||||||||
\(818\) | −2.12871e12 | −0.166237 | ||||||||
\(819\) | −5.55073e12 | −0.431095 | ||||||||
\(820\) | 1.78624e12 | 0.137968 | ||||||||
\(821\) | 1.17400e13 | 0.901826 | 0.450913 | − | 0.892568i | \(-0.351098\pi\) | ||||
0.450913 | + | 0.892568i | \(0.351098\pi\) | |||||||
\(822\) | 1.29958e13 | 0.992844 | ||||||||
\(823\) | 5.32682e12 | 0.404733 | 0.202367 | − | 0.979310i | \(-0.435137\pi\) | ||||
0.202367 | + | 0.979310i | \(0.435137\pi\) | |||||||
\(824\) | 1.58306e12 | 0.119626 | ||||||||
\(825\) | 2.05239e12 | 0.154247 | ||||||||
\(826\) | 7.65281e12 | 0.572019 | ||||||||
\(827\) | 1.19872e13 | 0.891137 | 0.445569 | − | 0.895248i | \(-0.353002\pi\) | ||||
0.445569 | + | 0.895248i | \(0.353002\pi\) | |||||||
\(828\) | 1.06668e13 | 0.788672 | ||||||||
\(829\) | 8.60218e12 | 0.632577 | 0.316288 | − | 0.948663i | \(-0.397563\pi\) | ||||
0.316288 | + | 0.948663i | \(0.397563\pi\) | |||||||
\(830\) | 2.03643e12 | 0.148942 | ||||||||
\(831\) | −2.25947e12 | −0.164363 | ||||||||
\(832\) | −6.51321e12 | −0.471238 | ||||||||
\(833\) | −1.36821e11 | −0.00984578 | ||||||||
\(834\) | −5.27080e12 | −0.377250 | ||||||||
\(835\) | 2.99718e13 | 2.13365 | ||||||||
\(836\) | 5.18357e12 | 0.367030 | ||||||||
\(837\) | 5.48035e12 | 0.385961 | ||||||||
\(838\) | −1.25378e13 | −0.878259 | ||||||||
\(839\) | −2.40899e13 | −1.67844 | −0.839222 | − | 0.543789i | \(-0.816989\pi\) | ||||
−0.839222 | + | 0.543789i | \(0.816989\pi\) | |||||||
\(840\) | −1.53711e13 | −1.06524 | ||||||||
\(841\) | 5.00246e11 | 0.0344828 | ||||||||
\(842\) | −9.65539e12 | −0.662011 | ||||||||
\(843\) | 1.28311e13 | 0.875061 | ||||||||
\(844\) | 1.07295e13 | 0.727845 | ||||||||
\(845\) | −1.07884e13 | −0.727948 | ||||||||
\(846\) | −8.30374e11 | −0.0557323 | ||||||||
\(847\) | −7.30134e12 | −0.487447 | ||||||||
\(848\) | 1.13878e12 | 0.0756240 | ||||||||
\(849\) | −2.32402e13 | −1.53517 | ||||||||
\(850\) | −3.72993e10 | −0.00245085 | ||||||||
\(851\) | −3.10667e13 | −2.03054 | ||||||||
\(852\) | −1.44658e12 | −0.0940509 | ||||||||
\(853\) | 1.41735e13 | 0.916659 | 0.458329 | − | 0.888782i | \(-0.348448\pi\) | ||||
0.458329 | + | 0.888782i | \(0.348448\pi\) | |||||||
\(854\) | −2.42208e12 | −0.155822 | ||||||||
\(855\) | 2.99703e13 | 1.91798 | ||||||||
\(856\) | −1.42518e12 | −0.0907273 | ||||||||
\(857\) | −5.36376e12 | −0.339669 | −0.169834 | − | 0.985473i | \(-0.554323\pi\) | ||||
−0.169834 | + | 0.985473i | \(0.554323\pi\) | |||||||
\(858\) | 4.35559e12 | 0.274381 | ||||||||
\(859\) | −1.25726e13 | −0.787870 | −0.393935 | − | 0.919138i | \(-0.628887\pi\) | ||||
−0.393935 | + | 0.919138i | \(0.628887\pi\) | |||||||
\(860\) | 1.14854e13 | 0.715984 | ||||||||
\(861\) | 3.44945e12 | 0.213912 | ||||||||
\(862\) | −1.62699e12 | −0.100369 | ||||||||
\(863\) | 7.75614e12 | 0.475989 | 0.237994 | − | 0.971267i | \(-0.423510\pi\) | ||||
0.237994 | + | 0.971267i | \(0.423510\pi\) | |||||||
\(864\) | 4.10741e12 | 0.250759 | ||||||||
\(865\) | 7.75154e12 | 0.470778 | ||||||||
\(866\) | −8.56596e12 | −0.517542 | ||||||||
\(867\) | 2.45761e13 | 1.47716 | ||||||||
\(868\) | 7.97907e12 | 0.477104 | ||||||||
\(869\) | 1.34239e13 | 0.798527 | ||||||||
\(870\) | −3.49072e12 | −0.206576 | ||||||||
\(871\) | 1.69652e13 | 0.998798 | ||||||||
\(872\) | −3.85292e12 | −0.225666 | ||||||||
\(873\) | 1.35850e12 | 0.0791579 | ||||||||
\(874\) | 2.13666e13 | 1.23861 | ||||||||
\(875\) | −9.27783e12 | −0.535070 | ||||||||
\(876\) | 1.11010e12 | 0.0636932 | ||||||||
\(877\) | −1.47870e12 | −0.0844077 | −0.0422039 | − | 0.999109i | \(-0.513438\pi\) | ||||
−0.0422039 | + | 0.999109i | \(0.513438\pi\) | |||||||
\(878\) | −1.86988e13 | −1.06191 | ||||||||
\(879\) | −3.66557e13 | −2.07105 | ||||||||
\(880\) | 1.60773e12 | 0.0903736 | ||||||||
\(881\) | 1.94808e13 | 1.08947 | 0.544736 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544736 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(882\) | 8.85327e12 | 0.492601 | ||||||||
\(883\) | 6.32492e12 | 0.350132 | 0.175066 | − | 0.984557i | \(-0.443986\pi\) | ||||
0.175066 | + | 0.984557i | \(0.443986\pi\) | |||||||
\(884\) | 9.17264e10 | 0.00505195 | ||||||||
\(885\) | 4.02334e13 | 2.20466 | ||||||||
\(886\) | 1.47347e13 | 0.803321 | ||||||||
\(887\) | −1.96859e13 | −1.06782 | −0.533912 | − | 0.845540i | \(-0.679279\pi\) | ||||
−0.533912 | + | 0.845540i | \(0.679279\pi\) | |||||||
\(888\) | −4.68214e13 | −2.52689 | ||||||||
\(889\) | −1.30221e13 | −0.699234 | ||||||||
\(890\) | −2.24210e13 | −1.19784 | ||||||||
\(891\) | 6.87603e12 | 0.365501 | ||||||||
\(892\) | −3.25385e11 | −0.0172090 | ||||||||
\(893\) | 1.92745e12 | 0.101426 | ||||||||
\(894\) | 3.49951e12 | 0.183226 | ||||||||
\(895\) | −2.55971e13 | −1.33348 | ||||||||
\(896\) | 4.54763e12 | 0.235722 | ||||||||
\(897\) | −2.08046e13 | −1.07299 | ||||||||
\(898\) | −1.62706e13 | −0.834949 | ||||||||
\(899\) | 5.18775e12 | 0.264887 | ||||||||
\(900\) | −2.79678e12 | −0.142091 | ||||||||
\(901\) | −1.37512e11 | −0.00695151 | ||||||||
\(902\) | −1.46689e12 | −0.0737852 | ||||||||
\(903\) | 2.21797e13 | 1.11010 | ||||||||
\(904\) | 2.09080e13 | 1.04125 | ||||||||
\(905\) | −4.24902e13 | −2.10557 | ||||||||
\(906\) | 2.36875e13 | 1.16800 | ||||||||
\(907\) | 1.82940e13 | 0.897583 | 0.448792 | − | 0.893636i | \(-0.351855\pi\) | ||||
0.448792 | + | 0.893636i | \(0.351855\pi\) | |||||||
\(908\) | 6.44852e12 | 0.314828 | ||||||||
\(909\) | 9.90605e12 | 0.481241 | ||||||||
\(910\) | 5.67502e12 | 0.274335 | ||||||||
\(911\) | 3.22004e13 | 1.54892 | 0.774459 | − | 0.632624i | \(-0.218022\pi\) | ||||
0.774459 | + | 0.632624i | \(0.218022\pi\) | |||||||
\(912\) | 7.92037e12 | 0.379113 | ||||||||
\(913\) | 1.93791e12 | 0.0923029 | ||||||||
\(914\) | 9.52697e12 | 0.451541 | ||||||||
\(915\) | −1.27337e13 | −0.600564 | ||||||||
\(916\) | 9.36282e12 | 0.439417 | ||||||||
\(917\) | −2.34277e13 | −1.09413 | ||||||||
\(918\) | 6.37749e10 | 0.00296386 | ||||||||
\(919\) | −1.03091e13 | −0.476760 | −0.238380 | − | 0.971172i | \(-0.576616\pi\) | ||||
−0.238380 | + | 0.971172i | \(0.576616\pi\) | |||||||
\(920\) | −3.12224e13 | −1.43688 | ||||||||
\(921\) | 1.35750e13 | 0.621687 | ||||||||
\(922\) | 8.72751e11 | 0.0397742 | ||||||||
\(923\) | 1.52905e12 | 0.0693446 | ||||||||
\(924\) | −5.10921e12 | −0.230584 | ||||||||
\(925\) | 8.14556e12 | 0.365833 | ||||||||
\(926\) | −4.07364e12 | −0.182068 | ||||||||
\(927\) | 3.04235e12 | 0.135316 | ||||||||
\(928\) | 3.88811e12 | 0.172097 | ||||||||
\(929\) | 2.21597e13 | 0.976096 | 0.488048 | − | 0.872817i | \(-0.337709\pi\) | ||||
0.488048 | + | 0.872817i | \(0.337709\pi\) | |||||||
\(930\) | −3.62002e13 | −1.58686 | ||||||||
\(931\) | −2.05501e13 | −0.896478 | ||||||||
\(932\) | 1.66405e13 | 0.722430 | ||||||||
\(933\) | −1.70355e12 | −0.0736018 | ||||||||
\(934\) | 4.32918e12 | 0.186142 | ||||||||
\(935\) | −1.94139e11 | −0.00830732 | ||||||||
\(936\) | −1.69927e13 | −0.723636 | ||||||||
\(937\) | −3.88326e13 | −1.64577 | −0.822884 | − | 0.568209i | \(-0.807636\pi\) | ||||
−0.822884 | + | 0.568209i | \(0.807636\pi\) | |||||||
\(938\) | 1.71735e13 | 0.724346 | ||||||||
\(939\) | −6.79878e13 | −2.85388 | ||||||||
\(940\) | −9.83779e11 | −0.0410982 | ||||||||
\(941\) | 1.41008e13 | 0.586262 | 0.293131 | − | 0.956072i | \(-0.405303\pi\) | ||||
0.293131 | + | 0.956072i | \(0.405303\pi\) | |||||||
\(942\) | −3.38670e13 | −1.40136 | ||||||||
\(943\) | 7.00667e12 | 0.288542 | ||||||||
\(944\) | 5.76226e12 | 0.236167 | ||||||||
\(945\) | −4.57225e12 | −0.186503 | ||||||||
\(946\) | −9.43202e12 | −0.382908 | ||||||||
\(947\) | 4.54768e12 | 0.183745 | 0.0918725 | − | 0.995771i | \(-0.470715\pi\) | ||||
0.0918725 | + | 0.995771i | \(0.470715\pi\) | |||||||
\(948\) | −3.37540e13 | −1.35734 | ||||||||
\(949\) | −1.17339e12 | −0.0469616 | ||||||||
\(950\) | −5.60224e12 | −0.223154 | ||||||||
\(951\) | 2.54869e13 | 1.01043 | ||||||||
\(952\) | 2.65834e11 | 0.0104892 | ||||||||
\(953\) | −2.19885e13 | −0.863529 | −0.431764 | − | 0.901986i | \(-0.642109\pi\) | ||||
−0.431764 | + | 0.901986i | \(0.642109\pi\) | |||||||
\(954\) | 8.89798e12 | 0.347795 | ||||||||
\(955\) | −4.63151e13 | −1.80180 | ||||||||
\(956\) | −2.02728e12 | −0.0784969 | ||||||||
\(957\) | −3.32185e12 | −0.128020 | ||||||||
\(958\) | 2.93714e13 | 1.12662 | ||||||||
\(959\) | 1.61135e13 | 0.615185 | ||||||||
\(960\) | −3.46625e13 | −1.31716 | ||||||||
\(961\) | 2.73594e13 | 1.03479 | ||||||||
\(962\) | 1.72865e13 | 0.650758 | ||||||||
\(963\) | −2.73893e12 | −0.102627 | ||||||||
\(964\) | 1.76390e13 | 0.657851 | ||||||||
\(965\) | 1.74191e13 | 0.646624 | ||||||||
\(966\) | −2.10601e13 | −0.778149 | ||||||||
\(967\) | 2.23013e13 | 0.820185 | 0.410093 | − | 0.912044i | \(-0.365496\pi\) | ||||
0.410093 | + | 0.912044i | \(0.365496\pi\) | |||||||
\(968\) | −2.23519e13 | −0.818229 | ||||||||
\(969\) | −9.56411e11 | −0.0348488 | ||||||||
\(970\) | −1.38891e12 | −0.0503735 | ||||||||
\(971\) | −2.09688e13 | −0.756986 | −0.378493 | − | 0.925604i | \(-0.623558\pi\) | ||||
−0.378493 | + | 0.925604i | \(0.623558\pi\) | |||||||
\(972\) | −2.13314e13 | −0.766516 | ||||||||
\(973\) | −6.53525e12 | −0.233751 | ||||||||
\(974\) | −5.73716e12 | −0.204259 | ||||||||
\(975\) | 5.45489e12 | 0.193315 | ||||||||
\(976\) | −1.82373e12 | −0.0643333 | ||||||||
\(977\) | 4.90198e13 | 1.72126 | 0.860629 | − | 0.509232i | \(-0.170071\pi\) | ||||
0.860629 | + | 0.509232i | \(0.170071\pi\) | |||||||
\(978\) | 3.45458e13 | 1.20745 | ||||||||
\(979\) | −2.13363e13 | −0.742330 | ||||||||
\(980\) | 1.04888e13 | 0.363254 | ||||||||
\(981\) | −7.40459e12 | −0.255265 | ||||||||
\(982\) | 2.75683e13 | 0.946036 | ||||||||
\(983\) | 1.41129e13 | 0.482086 | 0.241043 | − | 0.970514i | \(-0.422511\pi\) | ||||
0.241043 | + | 0.970514i | \(0.422511\pi\) | |||||||
\(984\) | 1.05599e13 | 0.359073 | ||||||||
\(985\) | 4.17095e12 | 0.141180 | ||||||||
\(986\) | 6.03700e10 | 0.00203411 | ||||||||
\(987\) | −1.89980e12 | −0.0637206 | ||||||||
\(988\) | 1.37770e13 | 0.459990 | ||||||||
\(989\) | 4.50524e13 | 1.49739 | ||||||||
\(990\) | 1.25622e13 | 0.415629 | ||||||||
\(991\) | 2.87585e13 | 0.947183 | 0.473592 | − | 0.880744i | \(-0.342957\pi\) | ||||
0.473592 | + | 0.880744i | \(0.342957\pi\) | |||||||
\(992\) | 4.03213e13 | 1.32200 | ||||||||
\(993\) | −7.78718e13 | −2.54161 | ||||||||
\(994\) | 1.54782e12 | 0.0502899 | ||||||||
\(995\) | 5.20753e13 | 1.68433 | ||||||||
\(996\) | −4.87282e12 | −0.156896 | ||||||||
\(997\) | 2.29667e13 | 0.736156 | 0.368078 | − | 0.929795i | \(-0.380016\pi\) | ||||
0.368078 | + | 0.929795i | \(0.380016\pi\) | |||||||
\(998\) | 8.90788e11 | 0.0284241 | ||||||||
\(999\) | −1.39274e13 | −0.442410 |
(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 | 29.10.a.a.1.4 | ✓ | 9 | |
3.2 | odd | 2 | 261.10.a.b.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.10.a.a.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial | |
261.10.a.b.1.6 | 9 | 3.2 | odd | 2 |