Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,21,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(15.2108259062\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 3396x^{4} + 2813589x^{2} + 548136050 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{31}\cdot 3^{17} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(-16.8544i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.21.b.a.5.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 724.077i | − | 0.707107i | ||||||
\(3\) | 41792.5 | − | 41715.4i | 0.707759 | − | 0.706454i | ||||
\(4\) | −524288. | −0.500000 | ||||||||
\(5\) | 805527.i | 0.0824859i | 0.999149 | + | 0.0412430i | \(0.0131318\pi\) | ||||
−0.999149 | + | 0.0412430i | \(0.986868\pi\) | |||||||
\(6\) | −3.02052e7 | − | 3.02610e7i | −0.499538 | − | 0.500461i | ||||
\(7\) | −3.63571e8 | −1.28709 | −0.643545 | − | 0.765408i | \(-0.722537\pi\) | ||||
−0.643545 | + | 0.765408i | \(0.722537\pi\) | |||||||
\(8\) | 3.79625e8i | 0.353553i | ||||||||
\(9\) | 6.43531e6 | − | 3.48678e9i | 0.00184563 | − | 0.999998i | ||||
\(10\) | 5.83264e8 | 0.0583264 | ||||||||
\(11\) | − | 7.52991e9i | − | 0.290310i | −0.989409 | − | 0.145155i | \(-0.953632\pi\) | ||
0.989409 | − | 0.145155i | \(-0.0463682\pi\) | |||||||
\(12\) | −2.19113e10 | + | 2.18709e10i | −0.353880 | + | 0.353227i | ||||
\(13\) | −1.09577e11 | −0.794849 | −0.397425 | − | 0.917635i | \(-0.630096\pi\) | ||||
−0.397425 | + | 0.917635i | \(0.630096\pi\) | |||||||
\(14\) | 2.63254e11i | 0.910110i | ||||||||
\(15\) | 3.36029e10 | + | 3.36649e10i | 0.0582725 | + | 0.0583802i | ||||
\(16\) | 2.74878e11 | 0.250000 | ||||||||
\(17\) | 2.97597e12i | 1.47618i | 0.674702 | + | 0.738090i | \(0.264272\pi\) | ||||
−0.674702 | + | 0.738090i | \(0.735728\pi\) | |||||||
\(18\) | −2.52470e12 | − | 4.65966e9i | −0.707106 | − | 0.00130506i | ||||
\(19\) | −9.19319e12 | −1.49944 | −0.749722 | − | 0.661753i | \(-0.769813\pi\) | ||||
−0.749722 | + | 0.661753i | \(0.769813\pi\) | |||||||
\(20\) | − | 4.22328e11i | − | 0.0412430i | ||||||
\(21\) | −1.51945e13 | + | 1.51665e13i | −0.910949 | + | 0.909270i | ||||
\(22\) | −5.45223e12 | −0.205281 | ||||||||
\(23\) | 8.43375e12i | 0.203583i | 0.994806 | + | 0.101792i | \(0.0324575\pi\) | ||||
−0.994806 | + | 0.101792i | \(0.967542\pi\) | |||||||
\(24\) | 1.58362e13 | + | 1.58655e13i | 0.249769 | + | 0.250231i | ||||
\(25\) | 9.47186e13 | 0.993196 | ||||||||
\(26\) | 7.93420e13i | 0.562043i | ||||||||
\(27\) | −1.45183e14 | − | 1.45990e14i | −0.705146 | − | 0.709062i | ||||
\(28\) | 1.90616e14 | 0.643545 | ||||||||
\(29\) | − | 6.14898e14i | − | 1.46158i | −0.682602 | − | 0.730790i | \(-0.739152\pi\) | ||
0.682602 | − | 0.730790i | \(-0.260848\pi\) | |||||||
\(30\) | 2.43760e13 | − | 2.43311e13i | 0.0412810 | − | 0.0412049i | ||||
\(31\) | 5.36607e14 | 0.654696 | 0.327348 | − | 0.944904i | \(-0.393845\pi\) | ||||
0.327348 | + | 0.944904i | \(0.393845\pi\) | |||||||
\(32\) | − | 1.99033e14i | − | 0.176777i | ||||||
\(33\) | −3.14113e14 | − | 3.14693e14i | −0.205091 | − | 0.205470i | ||||
\(34\) | 2.15483e15 | 1.04382 | ||||||||
\(35\) | − | 2.92866e14i | − | 0.106167i | ||||||
\(36\) | −3.37396e12 | + | 1.82808e15i | −0.000922815 | + | 0.499999i | ||||
\(37\) | −6.40512e15 | −1.33202 | −0.666009 | − | 0.745943i | \(-0.731999\pi\) | ||||
−0.666009 | + | 0.745943i | \(0.731999\pi\) | |||||||
\(38\) | 6.65658e15i | 1.06027i | ||||||||
\(39\) | −4.57948e15 | + | 4.57104e15i | −0.562562 | + | 0.561524i | ||||
\(40\) | −3.05798e14 | −0.0291632 | ||||||||
\(41\) | − | 1.51532e16i | − | 1.12893i | −0.825457 | − | 0.564465i | \(-0.809083\pi\) | ||
0.825457 | − | 0.564465i | \(-0.190917\pi\) | |||||||
\(42\) | 1.09817e16 | + | 1.10020e16i | 0.642951 | + | 0.644138i | ||||
\(43\) | −2.28528e16 | −1.05744 | −0.528719 | − | 0.848797i | \(-0.677327\pi\) | ||||
−0.528719 | + | 0.848797i | \(0.677327\pi\) | |||||||
\(44\) | 3.94784e15i | 0.145155i | ||||||||
\(45\) | 2.80869e15 | + | 5.18382e12i | 0.0824858 | + | 0.000152238i | ||||
\(46\) | 6.10668e15 | 0.143955 | ||||||||
\(47\) | − | 2.22157e16i | − | 0.422359i | −0.977447 | − | 0.211180i | \(-0.932269\pi\) | ||
0.977447 | − | 0.211180i | \(-0.0677305\pi\) | |||||||
\(48\) | 1.14878e16 | − | 1.14666e16i | 0.176940 | − | 0.176613i | ||||
\(49\) | 5.23916e16 | 0.656600 | ||||||||
\(50\) | − | 6.85836e16i | − | 0.702296i | ||||||
\(51\) | 1.24144e17 | + | 1.24373e17i | 1.04285 | + | 1.04478i | ||||
\(52\) | 5.74498e16 | 0.397425 | ||||||||
\(53\) | − | 3.38516e17i | − | 1.93562i | −0.251679 | − | 0.967811i | \(-0.580983\pi\) | ||
0.251679 | − | 0.967811i | \(-0.419017\pi\) | |||||||
\(54\) | −1.05708e17 | + | 1.05124e17i | −0.501382 | + | 0.498614i | ||||
\(55\) | 6.06554e15 | 0.0239465 | ||||||||
\(56\) | − | 1.38021e17i | − | 0.455055i | ||||||
\(57\) | −3.84206e17 | + | 3.83497e17i | −1.06124 | + | 1.05929i | ||||
\(58\) | −4.45233e17 | −1.03349 | ||||||||
\(59\) | 3.93698e17i | 0.770270i | 0.922860 | + | 0.385135i | \(0.125845\pi\) | ||||
−0.922860 | + | 0.385135i | \(0.874155\pi\) | |||||||
\(60\) | −1.76176e16 | − | 1.76501e16i | −0.0291363 | − | 0.0291901i | ||||
\(61\) | 7.29236e17 | 1.02228 | 0.511140 | − | 0.859498i | \(-0.329223\pi\) | ||||
0.511140 | + | 0.859498i | \(0.329223\pi\) | |||||||
\(62\) | − | 3.88545e17i | − | 0.462940i | ||||||
\(63\) | −2.33969e15 | + | 1.26769e18i | −0.00237549 | + | 1.28709i | ||||
\(64\) | −1.44115e17 | −0.125000 | ||||||||
\(65\) | − | 8.82670e16i | − | 0.0655639i | ||||||
\(66\) | −2.27862e17 | + | 2.27442e17i | −0.145289 | + | 0.145021i | ||||
\(67\) | −5.04483e17 | −0.276757 | −0.138378 | − | 0.990379i | \(-0.544189\pi\) | ||||
−0.138378 | + | 0.990379i | \(0.544189\pi\) | |||||||
\(68\) | − | 1.56027e18i | − | 0.738090i | ||||||
\(69\) | 3.51817e17 | + | 3.52467e17i | 0.143822 | + | 0.144088i | ||||
\(70\) | −2.12058e17 | −0.0750713 | ||||||||
\(71\) | − | 6.11896e18i | − | 1.87973i | −0.341553 | − | 0.939863i | \(-0.610953\pi\) | ||
0.341553 | − | 0.939863i | \(-0.389047\pi\) | |||||||
\(72\) | 1.32367e18 | + | 2.44301e15i | 0.353553 | + | 0.000652529i | ||||
\(73\) | 9.17001e17 | 0.213374 | 0.106687 | − | 0.994293i | \(-0.465976\pi\) | ||||
0.106687 | + | 0.994293i | \(0.465976\pi\) | |||||||
\(74\) | 4.63780e18i | 0.941879i | ||||||||
\(75\) | 3.95852e18 | − | 3.95122e18i | 0.702943 | − | 0.701647i | ||||
\(76\) | 4.81988e18 | 0.749722 | ||||||||
\(77\) | 2.73766e18i | 0.373656i | ||||||||
\(78\) | 3.30978e18 | + | 3.31590e18i | 0.397058 | + | 0.397791i | ||||
\(79\) | −7.30923e18 | −0.771970 | −0.385985 | − | 0.922505i | \(-0.626138\pi\) | ||||
−0.385985 | + | 0.922505i | \(0.626138\pi\) | |||||||
\(80\) | 2.21421e17i | 0.0206215i | ||||||||
\(81\) | −1.21576e19 | − | 4.48770e16i | −0.999993 | − | 0.00369125i | ||||
\(82\) | −1.09721e19 | −0.798274 | ||||||||
\(83\) | 1.57590e19i | 1.01566i | 0.861458 | + | 0.507829i | \(0.169552\pi\) | ||||
−0.861458 | + | 0.507829i | \(0.830448\pi\) | |||||||
\(84\) | 7.96631e18 | − | 7.95162e18i | 0.455475 | − | 0.454635i | ||||
\(85\) | −2.39722e18 | −0.121764 | ||||||||
\(86\) | 1.65472e19i | 0.747721i | ||||||||
\(87\) | −2.56507e19 | − | 2.56981e19i | −1.03254 | − | 1.03445i | ||||
\(88\) | 2.85854e18 | 0.102640 | ||||||||
\(89\) | 2.49058e19i | 0.798732i | 0.916792 | + | 0.399366i | \(0.130770\pi\) | ||||
−0.916792 | + | 0.399366i | \(0.869230\pi\) | |||||||
\(90\) | 3.75348e15 | − | 2.03371e18i | 0.000107649 | − | 0.0583263i | ||||
\(91\) | 3.98389e19 | 1.02304 | ||||||||
\(92\) | − | 4.42171e18i | − | 0.101792i | ||||||
\(93\) | 2.24261e19 | − | 2.23848e19i | 0.463367 | − | 0.462513i | ||||
\(94\) | −1.60859e19 | −0.298653 | ||||||||
\(95\) | − | 7.40536e18i | − | 0.123683i | ||||||
\(96\) | −8.30274e18 | − | 8.31807e18i | −0.124885 | − | 0.125115i | ||||
\(97\) | 8.81363e19 | 1.19519 | 0.597596 | − | 0.801798i | \(-0.296123\pi\) | ||||
0.597596 | + | 0.801798i | \(0.296123\pi\) | |||||||
\(98\) | − | 3.79356e19i | − | 0.464286i | ||||||
\(99\) | −2.62551e19 | − | 4.84573e16i | −0.290310 | − | 0.000535806i | ||||
\(100\) | −4.96598e19 | −0.496598 | ||||||||
\(101\) | 3.79360e19i | 0.343430i | 0.985147 | + | 0.171715i | \(0.0549308\pi\) | ||||
−0.985147 | + | 0.171715i | \(0.945069\pi\) | |||||||
\(102\) | 9.00557e19 | − | 8.98897e19i | 0.738771 | − | 0.737409i | ||||
\(103\) | 6.07442e19 | 0.451994 | 0.225997 | − | 0.974128i | \(-0.427436\pi\) | ||||
0.225997 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(104\) | − | 4.15981e19i | − | 0.281022i | ||||||
\(105\) | −1.22170e19 | − | 1.22396e19i | −0.0750019 | − | 0.0751405i | ||||
\(106\) | −2.45112e20 | −1.36869 | ||||||||
\(107\) | 1.68003e20i | 0.854043i | 0.904241 | + | 0.427021i | \(0.140437\pi\) | ||||
−0.904241 | + | 0.427021i | \(0.859563\pi\) | |||||||
\(108\) | 7.61179e19 | + | 7.65405e19i | 0.352573 | + | 0.354531i | ||||
\(109\) | −1.05514e20 | −0.445701 | −0.222850 | − | 0.974853i | \(-0.571536\pi\) | ||||
−0.222850 | + | 0.974853i | \(0.571536\pi\) | |||||||
\(110\) | − | 4.39192e18i | − | 0.0169328i | ||||||
\(111\) | −2.67686e20 | + | 2.67192e20i | −0.942748 | + | 0.941010i | ||||
\(112\) | −9.99376e19 | −0.321772 | ||||||||
\(113\) | − | 2.96849e20i | − | 0.874481i | −0.899345 | − | 0.437241i | \(-0.855956\pi\) | ||
0.899345 | − | 0.437241i | \(-0.144044\pi\) | |||||||
\(114\) | 2.77682e20 | + | 2.78195e20i | 0.749030 | + | 0.750413i | ||||
\(115\) | −6.79361e18 | −0.0167928 | ||||||||
\(116\) | 3.22383e20i | 0.730790i | ||||||||
\(117\) | −7.05161e17 | + | 3.82070e20i | −0.00146700 | + | 0.794848i | ||||
\(118\) | 2.85068e20 | 0.544663 | ||||||||
\(119\) | − | 1.08198e21i | − | 1.89998i | ||||||
\(120\) | −1.27801e19 | + | 1.27565e19i | −0.0206405 | + | 0.0206024i | ||||
\(121\) | 6.16051e20 | 0.915720 | ||||||||
\(122\) | − | 5.28023e20i | − | 0.722861i | ||||||
\(123\) | −6.32123e20 | − | 6.33291e20i | −0.797537 | − | 0.799010i | ||||
\(124\) | −2.81337e20 | −0.327348 | ||||||||
\(125\) | 1.53119e20i | 0.164411i | ||||||||
\(126\) | 9.17907e20 | + | 1.69412e18i | 0.910108 | + | 0.00167973i | ||||
\(127\) | −2.54380e18 | −0.00233048 | −0.00116524 | − | 0.999999i | \(-0.500371\pi\) | ||||
−0.00116524 | + | 0.999999i | \(0.500371\pi\) | |||||||
\(128\) | 1.04351e20i | 0.0883883i | ||||||||
\(129\) | −9.55075e20 | + | 9.53314e20i | −0.748411 | + | 0.747031i | ||||
\(130\) | −6.39121e19 | −0.0463607 | ||||||||
\(131\) | − | 1.41992e21i | − | 0.954005i | −0.878902 | − | 0.477003i | \(-0.841723\pi\) | ||
0.878902 | − | 0.477003i | \(-0.158277\pi\) | |||||||
\(132\) | 1.64686e20 | + | 1.64990e20i | 0.102545 | + | 0.102735i | ||||
\(133\) | 3.34238e21 | 1.92992 | ||||||||
\(134\) | 3.65285e20i | 0.195697i | ||||||||
\(135\) | 1.17598e20 | − | 1.16949e20i | 0.0584876 | − | 0.0581647i | ||||
\(136\) | −1.12975e21 | −0.521908 | ||||||||
\(137\) | 4.18638e21i | 1.79735i | 0.438613 | + | 0.898676i | \(0.355470\pi\) | ||||
−0.438613 | + | 0.898676i | \(0.644530\pi\) | |||||||
\(138\) | 2.55213e20 | − | 2.54743e20i | 0.101886 | − | 0.101698i | ||||
\(139\) | −4.37665e21 | −1.62552 | −0.812762 | − | 0.582595i | \(-0.802037\pi\) | ||||
−0.812762 | + | 0.582595i | \(0.802037\pi\) | |||||||
\(140\) | 1.53546e20i | 0.0530834i | ||||||||
\(141\) | −9.26738e20 | − | 9.28450e20i | −0.298377 | − | 0.298929i | ||||
\(142\) | −4.43060e21 | −1.32917 | ||||||||
\(143\) | 8.25103e20i | 0.230753i | ||||||||
\(144\) | 1.76893e18 | − | 9.58438e20i | 0.000461407 | − | 0.250000i | ||||
\(145\) | 4.95316e20 | 0.120560 | ||||||||
\(146\) | − | 6.63980e20i | − | 0.150878i | ||||||
\(147\) | 2.18957e21 | − | 2.18554e21i | 0.464715 | − | 0.463858i | ||||
\(148\) | 3.35813e21 | 0.666009 | ||||||||
\(149\) | 5.43464e21i | 1.00765i | 0.863807 | + | 0.503823i | \(0.168073\pi\) | ||||
−0.863807 | + | 0.503823i | \(0.831927\pi\) | |||||||
\(150\) | −2.86099e21 | − | 2.86628e21i | −0.496140 | − | 0.497056i | ||||
\(151\) | 2.46101e21 | 0.399342 | 0.199671 | − | 0.979863i | \(-0.436013\pi\) | ||||
0.199671 | + | 0.979863i | \(0.436013\pi\) | |||||||
\(152\) | − | 3.48996e21i | − | 0.530133i | ||||||
\(153\) | 1.03765e22 | + | 1.91513e19i | 1.47618 | + | 0.00272448i | ||||
\(154\) | 1.98227e21 | 0.264214 | ||||||||
\(155\) | 4.32252e20i | 0.0540032i | ||||||||
\(156\) | 2.40097e21 | − | 2.39654e21i | 0.281281 | − | 0.280762i | ||||
\(157\) | 6.22259e21 | 0.683872 | 0.341936 | − | 0.939723i | \(-0.388917\pi\) | ||||
0.341936 | + | 0.939723i | \(0.388917\pi\) | |||||||
\(158\) | 5.29245e21i | 0.545866i | ||||||||
\(159\) | −1.41213e22 | − | 1.41474e22i | −1.36743 | − | 1.36995i | ||||
\(160\) | 1.60326e20 | 0.0145816 | ||||||||
\(161\) | − | 3.06627e21i | − | 0.262030i | ||||||
\(162\) | −3.24944e19 | + | 8.80303e21i | −0.00261011 | + | 0.707102i | ||||
\(163\) | −1.11796e22 | −0.844407 | −0.422203 | − | 0.906501i | \(-0.638743\pi\) | ||||
−0.422203 | + | 0.906501i | \(0.638743\pi\) | |||||||
\(164\) | 7.94466e21i | 0.564465i | ||||||||
\(165\) | 2.53494e20 | − | 2.53026e20i | 0.0169484 | − | 0.0169171i | ||||
\(166\) | 1.14107e22 | 0.718178 | ||||||||
\(167\) | − | 1.73774e22i | − | 1.02996i | −0.857203 | − | 0.514979i | \(-0.827800\pi\) | ||
0.857203 | − | 0.514979i | \(-0.172200\pi\) | |||||||
\(168\) | −5.75759e21 | − | 5.76822e21i | −0.321475 | − | 0.322069i | ||||
\(169\) | −6.99790e21 | −0.368215 | ||||||||
\(170\) | 1.73577e21i | 0.0861002i | ||||||||
\(171\) | −5.91610e19 | + | 3.20546e22i | −0.00276742 | + | 1.49944i | ||||
\(172\) | 1.19814e22 | 0.528719 | ||||||||
\(173\) | 7.77319e21i | 0.323697i | 0.986816 | + | 0.161848i | \(0.0517455\pi\) | ||||
−0.986816 | + | 0.161848i | \(0.948254\pi\) | |||||||
\(174\) | −1.86074e22 | + | 1.85731e22i | −0.731465 | + | 0.730116i | ||||
\(175\) | −3.44369e22 | −1.27833 | ||||||||
\(176\) | − | 2.06980e21i | − | 0.0725776i | ||||||
\(177\) | 1.64233e22 | + | 1.64536e22i | 0.544160 | + | 0.545165i | ||||
\(178\) | 1.80338e22 | 0.564789 | ||||||||
\(179\) | − | 7.39680e21i | − | 0.219035i | −0.993985 | − | 0.109518i | \(-0.965069\pi\) | ||
0.993985 | − | 0.109518i | \(-0.0349306\pi\) | |||||||
\(180\) | −1.47256e21 | − | 2.71781e18i | −0.0412429 | − | 7.61192e-5i | ||||
\(181\) | −1.29288e22 | −0.342589 | −0.171295 | − | 0.985220i | \(-0.554795\pi\) | ||||
−0.171295 | + | 0.985220i | \(0.554795\pi\) | |||||||
\(182\) | − | 2.88465e22i | − | 0.723400i | ||||||
\(183\) | 3.04766e22 | − | 3.04204e22i | 0.723528 | − | 0.722193i | ||||
\(184\) | −3.20166e21 | −0.0719776 | ||||||||
\(185\) | − | 5.15950e21i | − | 0.109873i | ||||||
\(186\) | −1.62083e22 | − | 1.62383e22i | −0.327046 | − | 0.327650i | ||||
\(187\) | 2.24088e22 | 0.428551 | ||||||||
\(188\) | 1.16474e22i | 0.211180i | ||||||||
\(189\) | 5.27845e22 | + | 5.30776e22i | 0.907587 | + | 0.912626i | ||||
\(190\) | −5.36205e21 | −0.0874571 | ||||||||
\(191\) | − | 1.13683e23i | − | 1.75939i | −0.475539 | − | 0.879695i | \(-0.657747\pi\) | ||
0.475539 | − | 0.879695i | \(-0.342253\pi\) | |||||||
\(192\) | −6.02293e21 | + | 6.01182e21i | −0.0884699 | + | 0.0883067i | ||||
\(193\) | 4.54944e22 | 0.634432 | 0.317216 | − | 0.948353i | \(-0.397252\pi\) | ||||
0.317216 | + | 0.948353i | \(0.397252\pi\) | |||||||
\(194\) | − | 6.38175e22i | − | 0.845128i | ||||||
\(195\) | −3.68209e21 | − | 3.68889e21i | −0.0463179 | − | 0.0464034i | ||||
\(196\) | −2.74683e22 | −0.328300 | ||||||||
\(197\) | 4.92490e22i | 0.559416i | 0.960085 | + | 0.279708i | \(0.0902377\pi\) | ||||
−0.960085 | + | 0.279708i | \(0.909762\pi\) | |||||||
\(198\) | −3.50868e19 | + | 1.90107e22i | −0.000378872 | + | 0.205280i | ||||
\(199\) | −5.74544e22 | −0.589919 | −0.294960 | − | 0.955510i | \(-0.595306\pi\) | ||||
−0.294960 | + | 0.955510i | \(0.595306\pi\) | |||||||
\(200\) | 3.59575e22i | 0.351148i | ||||||||
\(201\) | −2.10836e22 | + | 2.10447e22i | −0.195877 | + | 0.195516i | ||||
\(202\) | 2.74686e22 | 0.242842 | ||||||||
\(203\) | 2.23559e23i | 1.88119i | ||||||||
\(204\) | −6.50871e22 | − | 6.52073e22i | −0.521427 | − | 0.522390i | ||||
\(205\) | 1.22063e22 | 0.0931208 | ||||||||
\(206\) | − | 4.39835e22i | − | 0.319608i | ||||||
\(207\) | 2.94066e22 | + | 5.42738e19i | 0.203583 | + | 0.000375739i | ||||
\(208\) | −3.01202e22 | −0.198712 | ||||||||
\(209\) | 6.92238e22i | 0.435304i | ||||||||
\(210\) | −8.86241e21 | + | 8.84607e21i | −0.0531324 | + | 0.0530344i | ||||
\(211\) | 1.23285e22 | 0.0704832 | 0.0352416 | − | 0.999379i | \(-0.488780\pi\) | ||||
0.0352416 | + | 0.999379i | \(0.488780\pi\) | |||||||
\(212\) | 1.77480e23i | 0.967811i | ||||||||
\(213\) | −2.55255e23 | − | 2.55727e23i | −1.32794 | − | 1.33039i | ||||
\(214\) | 1.21647e23 | 0.603900 | ||||||||
\(215\) | − | 1.84085e22i | − | 0.0872237i | ||||||
\(216\) | 5.54213e22 | − | 5.51153e22i | 0.250691 | − | 0.249307i | ||||
\(217\) | −1.95095e23 | −0.842653 | ||||||||
\(218\) | 7.64000e22i | 0.315158i | ||||||||
\(219\) | 3.83237e22 | − | 3.82531e22i | 0.151017 | − | 0.150739i | ||||
\(220\) | −3.18009e21 | −0.0119733 | ||||||||
\(221\) | − | 3.26097e23i | − | 1.17334i | ||||||
\(222\) | 1.93468e23 | + | 1.93825e23i | 0.665394 | + | 0.666624i | ||||
\(223\) | 2.77290e23 | 0.911771 | 0.455885 | − | 0.890039i | \(-0.349323\pi\) | ||||
0.455885 | + | 0.890039i | \(0.349323\pi\) | |||||||
\(224\) | 7.23626e22i | 0.227527i | ||||||||
\(225\) | 6.09544e20 | − | 3.30263e23i | 0.00183307 | − | 0.993194i | ||||
\(226\) | −2.14941e23 | −0.618352 | ||||||||
\(227\) | 3.44678e23i | 0.948758i | 0.880321 | + | 0.474379i | \(0.157327\pi\) | ||||
−0.880321 | + | 0.474379i | \(0.842673\pi\) | |||||||
\(228\) | 2.01435e23 | − | 2.01063e23i | 0.530622 | − | 0.529644i | ||||
\(229\) | 3.61164e23 | 0.910647 | 0.455323 | − | 0.890326i | \(-0.349524\pi\) | ||||
0.455323 | + | 0.890326i | \(0.349524\pi\) | |||||||
\(230\) | 4.91910e21i | 0.0118743i | ||||||||
\(231\) | 1.14202e23 | + | 1.14413e23i | 0.263971 | + | 0.264458i | ||||
\(232\) | 2.33431e23 | 0.516747 | ||||||||
\(233\) | − | 3.43352e23i | − | 0.728082i | −0.931383 | − | 0.364041i | \(-0.881397\pi\) | ||
0.931383 | − | 0.364041i | \(-0.118603\pi\) | |||||||
\(234\) | 2.76648e23 | + | 5.10591e20i | 0.562042 | + | 0.00103732i | ||||
\(235\) | 1.78954e22 | 0.0348387 | ||||||||
\(236\) | − | 2.06411e23i | − | 0.385135i | ||||||
\(237\) | −3.05471e23 | + | 3.04907e23i | −0.546369 | + | 0.545362i | ||||
\(238\) | −7.83435e23 | −1.34349 | ||||||||
\(239\) | 2.16021e23i | 0.355236i | 0.984100 | + | 0.177618i | \(0.0568391\pi\) | ||||
−0.984100 | + | 0.177618i | \(0.943161\pi\) | |||||||
\(240\) | 9.23669e21 | + | 9.25375e21i | 0.0145681 | + | 0.0145950i | ||||
\(241\) | −9.22135e23 | −1.39516 | −0.697580 | − | 0.716506i | \(-0.745740\pi\) | ||||
−0.697580 | + | 0.716506i | \(0.745740\pi\) | |||||||
\(242\) | − | 4.46068e23i | − | 0.647512i | ||||||
\(243\) | −5.09967e23 | + | 5.05283e23i | −0.710362 | + | 0.703837i | ||||
\(244\) | −3.82330e23 | −0.511140 | ||||||||
\(245\) | 4.22028e22i | 0.0541603i | ||||||||
\(246\) | −4.58552e23 | + | 4.57706e23i | −0.564985 | + | 0.563944i | ||||
\(247\) | 1.00736e24 | 1.19183 | ||||||||
\(248\) | 2.03710e23i | 0.231470i | ||||||||
\(249\) | 6.57392e23 | + | 6.58607e23i | 0.717515 | + | 0.718841i | ||||
\(250\) | 1.10870e23 | 0.116256 | ||||||||
\(251\) | 2.06405e23i | 0.207962i | 0.994579 | + | 0.103981i | \(0.0331580\pi\) | ||||
−0.994579 | + | 0.103981i | \(0.966842\pi\) | |||||||
\(252\) | 1.22667e21 | − | 6.64635e23i | 0.00118775 | − | 0.643544i | ||||
\(253\) | 6.35053e22 | 0.0591024 | ||||||||
\(254\) | 1.84191e21i | 0.00164790i | ||||||||
\(255\) | −1.00186e23 | + | 1.00001e23i | −0.0861796 | + | 0.0860207i | ||||
\(256\) | 7.55579e22 | 0.0625000 | ||||||||
\(257\) | − | 6.45642e23i | − | 0.513642i | −0.966459 | − | 0.256821i | \(-0.917325\pi\) | ||
0.966459 | − | 0.256821i | \(-0.0826750\pi\) | |||||||
\(258\) | 6.90273e23 | + | 6.91548e23i | 0.528231 | + | 0.529207i | ||||
\(259\) | 2.32872e24 | 1.71443 | ||||||||
\(260\) | 4.62773e22i | 0.0327819i | ||||||||
\(261\) | −2.14401e24 | − | 3.95706e21i | −1.46158 | − | 0.00269754i | ||||
\(262\) | −1.02813e24 | −0.674584 | ||||||||
\(263\) | − | 1.51145e24i | − | 0.954631i | −0.878732 | − | 0.477316i | \(-0.841610\pi\) | ||
0.878732 | − | 0.477316i | \(-0.158390\pi\) | |||||||
\(264\) | 1.19465e23 | − | 1.19245e23i | 0.0726446 | − | 0.0725106i | ||||
\(265\) | 2.72684e23 | 0.159662 | ||||||||
\(266\) | − | 2.42014e24i | − | 1.36466i | ||||||
\(267\) | 1.03896e24 | + | 1.04088e24i | 0.564268 | + | 0.565310i | ||||
\(268\) | 2.64494e23 | 0.138378 | ||||||||
\(269\) | − | 3.30874e23i | − | 0.166779i | −0.996517 | − | 0.0833893i | \(-0.973425\pi\) | ||
0.996517 | − | 0.0833893i | \(-0.0265745\pi\) | |||||||
\(270\) | −8.46802e22 | − | 8.51504e22i | −0.0411286 | − | 0.0413570i | ||||
\(271\) | −2.87491e24 | −1.34565 | −0.672824 | − | 0.739803i | \(-0.734919\pi\) | ||||
−0.672824 | + | 0.739803i | \(0.734919\pi\) | |||||||
\(272\) | 8.18028e23i | 0.369045i | ||||||||
\(273\) | 1.66497e24 | − | 1.66190e24i | 0.724068 | − | 0.722732i | ||||
\(274\) | 3.03126e24 | 1.27092 | ||||||||
\(275\) | − | 7.13222e23i | − | 0.288335i | ||||||
\(276\) | −1.84453e23 | − | 1.84794e23i | −0.0719111 | − | 0.0720440i | ||||
\(277\) | 1.28399e24 | 0.482797 | 0.241398 | − | 0.970426i | \(-0.422394\pi\) | ||||
0.241398 | + | 0.970426i | \(0.422394\pi\) | |||||||
\(278\) | 3.16903e24i | 1.14942i | ||||||||
\(279\) | 3.45324e21 | − | 1.87103e24i | 0.00120833 | − | 0.654695i | ||||
\(280\) | 1.11179e23 | 0.0375356 | ||||||||
\(281\) | 2.56237e24i | 0.834793i | 0.908724 | + | 0.417397i | \(0.137057\pi\) | ||||
−0.908724 | + | 0.417397i | \(0.862943\pi\) | |||||||
\(282\) | −6.72270e23 | + | 6.71030e23i | −0.211374 | + | 0.210985i | ||||
\(283\) | −5.83054e24 | −1.76947 | −0.884737 | − | 0.466090i | \(-0.845662\pi\) | ||||
−0.884737 | + | 0.466090i | \(0.845662\pi\) | |||||||
\(284\) | 3.20810e24i | 0.939863i | ||||||||
\(285\) | −3.08917e23 | − | 3.09488e23i | −0.0873763 | − | 0.0875377i | ||||
\(286\) | 5.97438e23 | 0.163167 | ||||||||
\(287\) | 5.50928e24i | 1.45303i | ||||||||
\(288\) | −6.93984e23 | − | 1.28084e21i | −0.176776 | − | 0.000326264i | ||||
\(289\) | −4.79216e24 | −1.17911 | ||||||||
\(290\) | − | 3.58647e23i | − | 0.0852487i | ||||||
\(291\) | 3.68343e24 | − | 3.67664e24i | 0.845907 | − | 0.844347i | ||||
\(292\) | −4.80773e23 | −0.106687 | ||||||||
\(293\) | − | 1.20765e24i | − | 0.258979i | −0.991581 | − | 0.129489i | \(-0.958666\pi\) | ||
0.991581 | − | 0.129489i | \(-0.0413338\pi\) | |||||||
\(294\) | −1.58250e24 | − | 1.58542e24i | −0.327997 | − | 0.328603i | ||||
\(295\) | −3.17134e23 | −0.0635364 | ||||||||
\(296\) | − | 2.43155e24i | − | 0.470940i | ||||||
\(297\) | −1.09929e24 | + | 1.09322e24i | −0.205848 | + | 0.204711i | ||||
\(298\) | 3.93510e24 | 0.712513 | ||||||||
\(299\) | − | 9.24142e23i | − | 0.161818i | ||||||
\(300\) | −2.07541e24 | + | 2.07158e24i | −0.351472 | + | 0.350824i | ||||
\(301\) | 8.30862e24 | 1.36102 | ||||||||
\(302\) | − | 1.78196e24i | − | 0.282377i | ||||||
\(303\) | 1.58252e24 | + | 1.58544e24i | 0.242618 | + | 0.243066i | ||||
\(304\) | −2.52700e24 | −0.374861 | ||||||||
\(305\) | 5.87419e23i | 0.0843237i | ||||||||
\(306\) | 1.38670e22 | − | 7.51342e24i | 0.00192650 | − | 1.04382i | ||||
\(307\) | −1.19854e24 | −0.161164 | −0.0805822 | − | 0.996748i | \(-0.525678\pi\) | ||||
−0.0805822 | + | 0.996748i | \(0.525678\pi\) | |||||||
\(308\) | − | 1.43532e24i | − | 0.186828i | ||||||
\(309\) | 2.53865e24 | − | 2.53397e24i | 0.319903 | − | 0.319313i | ||||
\(310\) | 3.12984e23 | 0.0381860 | ||||||||
\(311\) | 9.58705e23i | 0.113261i | 0.998395 | + | 0.0566306i | \(0.0180357\pi\) | ||||
−0.998395 | + | 0.0566306i | \(0.981964\pi\) | |||||||
\(312\) | −1.73528e24 | − | 1.73849e24i | −0.198529 | − | 0.198896i | ||||
\(313\) | 1.25498e25 | 1.39057 | 0.695284 | − | 0.718736i | \(-0.255279\pi\) | ||||
0.695284 | + | 0.718736i | \(0.255279\pi\) | |||||||
\(314\) | − | 4.50564e24i | − | 0.483570i | ||||||
\(315\) | −1.02116e24 | − | 1.88469e21i | −0.106167 | − | 0.000195945i | ||||
\(316\) | 3.83214e24 | 0.385985 | ||||||||
\(317\) | 9.84338e24i | 0.960620i | 0.877099 | + | 0.480310i | \(0.159476\pi\) | ||||
−0.877099 | + | 0.480310i | \(0.840524\pi\) | |||||||
\(318\) | −1.02438e25 | + | 1.02249e25i | −0.968703 | + | 0.966917i | ||||
\(319\) | −4.63012e24 | −0.424312 | ||||||||
\(320\) | − | 1.16089e23i | − | 0.0103107i | ||||||
\(321\) | 7.00832e24 | + | 7.02127e24i | 0.603342 | + | 0.604457i | ||||
\(322\) | −2.22021e24 | −0.185283 | ||||||||
\(323\) | − | 2.73586e25i | − | 2.21345i | ||||||
\(324\) | 6.37407e24 | + | 2.35285e22i | 0.499997 | + | 0.00184563i | ||||
\(325\) | −1.03790e25 | −0.789441 | ||||||||
\(326\) | 8.09492e24i | 0.597086i | ||||||||
\(327\) | −4.40967e24 | + | 4.40154e24i | −0.315449 | + | 0.314867i | ||||
\(328\) | 5.75255e24 | 0.399137 | ||||||||
\(329\) | 8.07700e24i | 0.543614i | ||||||||
\(330\) | −1.83211e23 | − | 1.83549e23i | −0.0119622 | − | 0.0119843i | ||||
\(331\) | −1.77602e25 | −1.12504 | −0.562520 | − | 0.826784i | \(-0.690168\pi\) | ||||
−0.562520 | + | 0.826784i | \(0.690168\pi\) | |||||||
\(332\) | − | 8.26225e24i | − | 0.507829i | ||||||
\(333\) | −4.12190e22 | + | 2.23332e25i | −0.00245841 | + | 1.33202i | ||||
\(334\) | −1.25826e25 | −0.728290 | ||||||||
\(335\) | − | 4.06374e23i | − | 0.0228285i | ||||||
\(336\) | −4.17664e24 | + | 4.16894e24i | −0.227737 | + | 0.227317i | ||||
\(337\) | −4.77958e24 | −0.252983 | −0.126491 | − | 0.991968i | \(-0.540372\pi\) | ||||
−0.126491 | + | 0.991968i | \(0.540372\pi\) | |||||||
\(338\) | 5.06702e24i | 0.260367i | ||||||||
\(339\) | −1.23832e25 | − | 1.24060e25i | −0.617781 | − | 0.618922i | ||||
\(340\) | 1.25684e24 | 0.0608820 | ||||||||
\(341\) | − | 4.04060e24i | − | 0.190065i | ||||||
\(342\) | 2.32100e25 | + | 4.28372e22i | 1.06026 | + | 0.00195686i | ||||
\(343\) | 9.96209e24 | 0.441987 | ||||||||
\(344\) | − | 8.67550e24i | − | 0.373861i | ||||||
\(345\) | −2.83922e23 | + | 2.83398e23i | −0.0118852 | + | 0.0118633i | ||||
\(346\) | 5.62839e24 | 0.228888 | ||||||||
\(347\) | − | 1.74076e25i | − | 0.687773i | −0.939011 | − | 0.343887i | \(-0.888256\pi\) | ||
0.939011 | − | 0.343887i | \(-0.111744\pi\) | |||||||
\(348\) | 1.34484e25 | + | 1.34732e25i | 0.516270 | + | 0.517224i | ||||
\(349\) | 2.19322e25 | 0.818141 | 0.409071 | − | 0.912503i | \(-0.365853\pi\) | ||||
0.409071 | + | 0.912503i | \(0.365853\pi\) | |||||||
\(350\) | 2.49350e25i | 0.903918i | ||||||||
\(351\) | 1.59087e25 | + | 1.59971e25i | 0.560485 | + | 0.563597i | ||||
\(352\) | −1.49870e24 | −0.0513201 | ||||||||
\(353\) | − | 2.59460e25i | − | 0.863621i | −0.901964 | − | 0.431811i | \(-0.857875\pi\) | ||
0.901964 | − | 0.431811i | \(-0.142125\pi\) | |||||||
\(354\) | 1.19137e25 | − | 1.18917e25i | 0.385490 | − | 0.384779i | ||||
\(355\) | 4.92899e24 | 0.155051 | ||||||||
\(356\) | − | 1.30578e25i | − | 0.399366i | ||||||
\(357\) | −4.51351e25 | − | 4.52185e25i | −1.34225 | − | 1.34473i | ||||
\(358\) | −5.35586e24 | −0.154881 | ||||||||
\(359\) | 4.81350e24i | 0.135368i | 0.997707 | + | 0.0676841i | \(0.0215610\pi\) | ||||
−0.997707 | + | 0.0676841i | \(0.978439\pi\) | |||||||
\(360\) | −1.96791e21 | + | 1.06625e24i | −5.38244e−5 | + | 0.0291631i | ||||
\(361\) | 4.69247e25 | 1.24833 | ||||||||
\(362\) | 9.36148e24i | 0.242247i | ||||||||
\(363\) | 2.57463e25 | − | 2.56988e25i | 0.648109 | − | 0.646914i | ||||
\(364\) | −2.08871e25 | −0.511521 | ||||||||
\(365\) | 7.38669e23i | 0.0176003i | ||||||||
\(366\) | −2.20267e25 | − | 2.20674e25i | −0.510668 | − | 0.511611i | ||||
\(367\) | −4.68969e25 | −1.05799 | −0.528997 | − | 0.848624i | \(-0.677432\pi\) | ||||
−0.528997 | + | 0.848624i | \(0.677432\pi\) | |||||||
\(368\) | 2.31825e24i | 0.0508958i | ||||||||
\(369\) | −5.28360e25 | − | 9.75158e22i | −1.12893 | − | 0.00208359i | ||||
\(370\) | −3.73588e24 | −0.0776918 | ||||||||
\(371\) | 1.23075e26i | 2.49132i | ||||||||
\(372\) | −1.17578e25 | + | 1.17361e25i | −0.231683 | + | 0.231256i | ||||
\(373\) | 1.87545e25 | 0.359764 | 0.179882 | − | 0.983688i | \(-0.442428\pi\) | ||||
0.179882 | + | 0.983688i | \(0.442428\pi\) | |||||||
\(374\) | − | 1.62257e25i | − | 0.303031i | ||||||
\(375\) | 6.38743e24 | + | 6.39923e24i | 0.116149 | + | 0.116363i | ||||
\(376\) | 8.43365e24 | 0.149327 | ||||||||
\(377\) | 6.73785e25i | 1.16174i | ||||||||
\(378\) | 3.84323e25 | − | 3.82200e25i | 0.645324 | − | 0.641761i | ||||
\(379\) | 7.50824e25 | 1.22785 | 0.613926 | − | 0.789363i | \(-0.289589\pi\) | ||||
0.613926 | + | 0.789363i | \(0.289589\pi\) | |||||||
\(380\) | 3.88254e24i | 0.0618415i | ||||||||
\(381\) | −1.06312e23 | + | 1.06116e23i | −0.00164942 | + | 0.00164638i | ||||
\(382\) | −8.23153e25 | −1.24408 | ||||||||
\(383\) | − | 4.04145e24i | − | 0.0595044i | −0.999557 | − | 0.0297522i | \(-0.990528\pi\) | ||
0.999557 | − | 0.0297522i | \(-0.00947182\pi\) | |||||||
\(384\) | 4.35302e24 | + | 4.36107e24i | 0.0624423 | + | 0.0625576i | ||||
\(385\) | −2.20525e24 | −0.0308213 | ||||||||
\(386\) | − | 3.29415e25i | − | 0.448611i | ||||||
\(387\) | −1.47065e23 | + | 7.96826e25i | −0.00195164 | + | 1.05744i | ||||
\(388\) | −4.62088e25 | −0.597596 | ||||||||
\(389\) | − | 4.28049e25i | − | 0.539508i | −0.962929 | − | 0.269754i | \(-0.913058\pi\) | ||
0.962929 | − | 0.269754i | \(-0.0869424\pi\) | |||||||
\(390\) | −2.67104e24 | + | 2.66612e24i | −0.0328122 | + | 0.0327517i | ||||
\(391\) | −2.50986e25 | −0.300526 | ||||||||
\(392\) | 1.98892e25i | 0.232143i | ||||||||
\(393\) | −5.92325e25 | − | 5.93419e25i | −0.673961 | − | 0.675206i | ||||
\(394\) | 3.56601e25 | 0.395567 | ||||||||
\(395\) | − | 5.88778e24i | − | 0.0636767i | ||||||
\(396\) | 1.37652e25 | + | 2.54056e22i | 0.145155 | + | 0.000267903i | ||||
\(397\) | −4.70070e25 | −0.483346 | −0.241673 | − | 0.970358i | \(-0.577696\pi\) | ||||
−0.241673 | + | 0.970358i | \(0.577696\pi\) | |||||||
\(398\) | 4.16014e25i | 0.417136i | ||||||||
\(399\) | 1.39686e26 | − | 1.39429e26i | 1.36592 | − | 1.36340i | ||||
\(400\) | 2.60360e25 | 0.248299 | ||||||||
\(401\) | − | 1.50490e26i | − | 1.39979i | −0.714246 | − | 0.699895i | \(-0.753230\pi\) | ||
0.714246 | − | 0.699895i | \(-0.246770\pi\) | |||||||
\(402\) | 1.52380e25 | + | 1.52661e25i | 0.138251 | + | 0.138506i | ||||
\(403\) | −5.87997e25 | −0.520385 | ||||||||
\(404\) | − | 1.98894e25i | − | 0.171715i | ||||||
\(405\) | 3.61496e22 | − | 9.79326e24i | 0.000304476 | − | 0.0824854i | ||||
\(406\) | 1.61874e26 | 1.33020 | ||||||||
\(407\) | 4.82300e25i | 0.386699i | ||||||||
\(408\) | −4.72151e25 | + | 4.71281e25i | −0.369385 | + | 0.368704i | ||||
\(409\) | 9.99015e25 | 0.762674 | 0.381337 | − | 0.924436i | \(-0.375464\pi\) | ||||
0.381337 | + | 0.924436i | \(0.375464\pi\) | |||||||
\(410\) | − | 8.83833e24i | − | 0.0658463i | ||||||
\(411\) | 1.74637e26 | + | 1.74959e26i | 1.26975 | + | 1.27209i | ||||
\(412\) | −3.18475e25 | −0.225997 | ||||||||
\(413\) | − | 1.43137e26i | − | 0.991406i | ||||||
\(414\) | 3.92984e22 | − | 2.12927e25i | 0.000265688 | − | 0.143955i | ||||
\(415\) | −1.26943e25 | −0.0837774 | ||||||||
\(416\) | 2.18094e25i | 0.140511i | ||||||||
\(417\) | −1.82911e26 | + | 1.82574e26i | −1.15048 | + | 1.14836i | ||||
\(418\) | 5.01234e25 | 0.307807 | ||||||||
\(419\) | − | 1.68130e26i | − | 1.00810i | −0.863673 | − | 0.504052i | \(-0.831842\pi\) | ||
0.863673 | − | 0.504052i | \(-0.168158\pi\) | |||||||
\(420\) | 6.40524e24 | + | 6.41707e24i | 0.0375010 | + | 0.0375703i | ||||
\(421\) | −2.69174e26 | −1.53891 | −0.769454 | − | 0.638702i | \(-0.779471\pi\) | ||||
−0.769454 | + | 0.638702i | \(0.779471\pi\) | |||||||
\(422\) | − | 8.92679e24i | − | 0.0498392i | ||||||
\(423\) | −7.74613e25 | − | 1.42965e23i | −0.422359 | − | 0.000779519i | ||||
\(424\) | 1.28509e26 | 0.684345 | ||||||||
\(425\) | 2.81880e26i | 1.46614i | ||||||||
\(426\) | −1.85166e26 | + | 1.84824e26i | −0.940730 | + | 0.938995i | ||||
\(427\) | −2.65129e26 | −1.31577 | ||||||||
\(428\) | − | 8.80821e25i | − | 0.427021i | ||||||
\(429\) | 3.44195e25 | + | 3.44831e25i | 0.163016 | + | 0.163318i | ||||
\(430\) | −1.33292e25 | −0.0616765 | ||||||||
\(431\) | − | 2.03349e26i | − | 0.919325i | −0.888094 | − | 0.459663i | \(-0.847970\pi\) | ||
0.888094 | − | 0.459663i | \(-0.152030\pi\) | |||||||
\(432\) | −3.99077e25 | − | 4.01293e25i | −0.176287 | − | 0.177265i | ||||
\(433\) | 2.77208e26 | 1.19654 | 0.598269 | − | 0.801296i | \(-0.295856\pi\) | ||||
0.598269 | + | 0.801296i | \(0.295856\pi\) | |||||||
\(434\) | 1.41264e26i | 0.595845i | ||||||||
\(435\) | 2.07005e25 | − | 2.06623e25i | 0.0853273 | − | 0.0851700i | ||||
\(436\) | 5.53195e25 | 0.222850 | ||||||||
\(437\) | − | 7.75330e25i | − | 0.305262i | ||||||
\(438\) | −2.76982e25 | − | 2.77493e25i | −0.106588 | − | 0.106785i | ||||
\(439\) | 1.39900e26 | 0.526227 | 0.263113 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263113 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(440\) | 2.30263e24i | 0.00846638i | ||||||||
\(441\) | 3.37156e23 | − | 1.82678e26i | 0.00121184 | − | 0.656599i | ||||
\(442\) | −2.36119e26 | −0.829677 | ||||||||
\(443\) | 3.90868e26i | 1.34274i | 0.741121 | + | 0.671372i | \(0.234295\pi\) | ||||
−0.741121 | + | 0.671372i | \(0.765705\pi\) | |||||||
\(444\) | 1.40344e26 | − | 1.40086e26i | 0.471374 | − | 0.470505i | ||||
\(445\) | −2.00623e25 | −0.0658842 | ||||||||
\(446\) | − | 2.00779e26i | − | 0.644719i | ||||||
\(447\) | 2.26708e26 | + | 2.27127e26i | 0.711855 | + | 0.713170i | ||||
\(448\) | 5.23961e25 | 0.160886 | ||||||||
\(449\) | − | 1.44307e26i | − | 0.433337i | −0.976245 | − | 0.216668i | \(-0.930481\pi\) | ||
0.976245 | − | 0.216668i | \(-0.0695190\pi\) | |||||||
\(450\) | −2.39136e26 | − | 4.41357e23i | −0.702294 | − | 0.00129618i | ||||
\(451\) | −1.14102e26 | −0.327740 | ||||||||
\(452\) | 1.55634e26i | 0.437241i | ||||||||
\(453\) | 1.02852e26 | − | 1.02662e26i | 0.282638 | − | 0.282116i | ||||
\(454\) | 2.49574e26 | 0.670873 | ||||||||
\(455\) | 3.20913e25i | 0.0843866i | ||||||||
\(456\) | −1.45585e26 | − | 1.45854e26i | −0.374515 | − | 0.375207i | ||||
\(457\) | 4.81844e26 | 1.21267 | 0.606337 | − | 0.795208i | \(-0.292638\pi\) | ||||
0.606337 | + | 0.795208i | \(0.292638\pi\) | |||||||
\(458\) | − | 2.61511e26i | − | 0.643925i | ||||||
\(459\) | 4.34460e26 | − | 4.32061e26i | 1.04670 | − | 1.04092i | ||||
\(460\) | 3.56181e24 | 0.00839638 | ||||||||
\(461\) | 2.75250e26i | 0.634918i | 0.948272 | + | 0.317459i | \(0.102830\pi\) | ||||
−0.948272 | + | 0.317459i | \(0.897170\pi\) | |||||||
\(462\) | 8.28441e25 | − | 8.26914e25i | 0.187000 | − | 0.186655i | ||||
\(463\) | −4.81179e26 | −1.06291 | −0.531456 | − | 0.847086i | \(-0.678355\pi\) | ||||
−0.531456 | + | 0.847086i | \(0.678355\pi\) | |||||||
\(464\) | − | 1.69022e26i | − | 0.365395i | ||||||
\(465\) | 1.80315e25 | + | 1.80649e25i | 0.0381508 | + | 0.0382213i | ||||
\(466\) | −2.48613e26 | −0.514832 | ||||||||
\(467\) | 3.81939e26i | 0.774150i | 0.922048 | + | 0.387075i | \(0.126515\pi\) | ||||
−0.922048 | + | 0.387075i | \(0.873485\pi\) | |||||||
\(468\) | 3.69707e23 | − | 2.00315e26i | 0.000733499 | − | 0.397424i | ||||
\(469\) | 1.83415e26 | 0.356211 | ||||||||
\(470\) | − | 1.29576e25i | − | 0.0246347i | ||||||
\(471\) | 2.60057e26 | − | 2.59578e26i | 0.484016 | − | 0.483124i | ||||
\(472\) | −1.49458e26 | −0.272331 | ||||||||
\(473\) | 1.72079e26i | 0.306985i | ||||||||
\(474\) | 2.20777e26 | + | 2.21184e26i | 0.385629 | + | 0.386341i | ||||
\(475\) | −8.70765e26 | −1.48924 | ||||||||
\(476\) | 5.67267e26i | 0.949988i | ||||||||
\(477\) | −1.18033e27 | − | 2.17846e24i | −1.93562 | − | 0.00357244i | ||||
\(478\) | 1.56416e26 | 0.251190 | ||||||||
\(479\) | − | 3.81517e25i | − | 0.0600011i | −0.999550 | − | 0.0300005i | \(-0.990449\pi\) | ||
0.999550 | − | 0.0300005i | \(-0.00955090\pi\) | |||||||
\(480\) | 6.70043e24 | − | 6.68807e24i | 0.0103203 | − | 0.0103012i | ||||
\(481\) | 7.01852e26 | 1.05875 | ||||||||
\(482\) | 6.67697e26i | 0.986528i | ||||||||
\(483\) | −1.27910e26 | − | 1.28147e26i | −0.185112 | − | 0.185454i | ||||
\(484\) | −3.22988e26 | −0.457860 | ||||||||
\(485\) | 7.09961e25i | 0.0985864i | ||||||||
\(486\) | 3.65864e26 | + | 3.69256e26i | 0.497688 | + | 0.502302i | ||||
\(487\) | −1.00915e27 | −1.34483 | −0.672413 | − | 0.740176i | \(-0.734742\pi\) | ||||
−0.672413 | + | 0.740176i | \(0.734742\pi\) | |||||||
\(488\) | 2.76836e26i | 0.361430i | ||||||||
\(489\) | −4.67225e26 | + | 4.66363e26i | −0.597637 | + | 0.596535i | ||||
\(490\) | 3.05581e25 | 0.0382971 | ||||||||
\(491\) | − | 1.48221e27i | − | 1.82009i | −0.414505 | − | 0.910047i | \(-0.636045\pi\) | ||
0.414505 | − | 0.910047i | \(-0.363955\pi\) | |||||||
\(492\) | 3.31415e26 | + | 3.32027e26i | 0.398768 | + | 0.399505i | ||||
\(493\) | 1.82992e27 | 2.15756 | ||||||||
\(494\) | − | 7.29406e26i | − | 0.842752i | ||||||
\(495\) | 3.90337e22 | − | 2.11492e25i | 4.41964e−5 | − | 0.0239465i | ||||
\(496\) | 1.47502e26 | 0.163674 | ||||||||
\(497\) | 2.22468e27i | 2.41938i | ||||||||
\(498\) | 4.76882e26 | − | 4.76003e26i | 0.508297 | − | 0.507360i | ||||
\(499\) | 3.86304e26 | 0.403575 | 0.201788 | − | 0.979429i | \(-0.435325\pi\) | ||||
0.201788 | + | 0.979429i | \(0.435325\pi\) | |||||||
\(500\) | − | 8.02786e25i | − | 0.0822053i | ||||||
\(501\) | −7.24904e26 | − | 7.26243e26i | −0.727618 | − | 0.728962i | ||||
\(502\) | 1.49453e26 | 0.147051 | ||||||||
\(503\) | − | 1.39761e27i | − | 1.34805i | −0.738708 | − | 0.674026i | \(-0.764564\pi\) | ||
0.738708 | − | 0.674026i | \(-0.235436\pi\) | |||||||
\(504\) | −4.81247e26 | − | 8.88206e23i | −0.455054 | − | 0.000839863i | ||||
\(505\) | −3.05585e25 | −0.0283281 | ||||||||
\(506\) | − | 4.59828e25i | − | 0.0417917i | ||||||
\(507\) | −2.92460e26 | + | 2.91920e26i | −0.260607 | + | 0.260127i | ||||
\(508\) | 1.33368e24 | 0.00116524 | ||||||||
\(509\) | − | 2.29175e27i | − | 1.96331i | −0.190665 | − | 0.981655i | \(-0.561064\pi\) | ||
0.190665 | − | 0.981655i | \(-0.438936\pi\) | |||||||
\(510\) | 7.24085e25 | + | 7.25423e25i | 0.0608258 | + | 0.0609382i | ||||
\(511\) | −3.33395e26 | −0.274631 | ||||||||
\(512\) | − | 5.47097e25i | − | 0.0441942i | ||||||
\(513\) | 1.33470e27 | + | 1.34211e27i | 1.05733 | + | 1.06320i | ||||
\(514\) | −4.67495e26 | −0.363200 | ||||||||
\(515\) | 4.89311e25i | 0.0372831i | ||||||||
\(516\) | 5.00734e26 | − | 4.99811e26i | 0.374206 | − | 0.373516i | ||||
\(517\) | −1.67282e26 | −0.122615 | ||||||||
\(518\) | − | 1.68617e27i | − | 1.21228i | ||||||
\(519\) | 3.24262e26 | + | 3.24861e26i | 0.228677 | + | 0.229099i | ||||
\(520\) | 3.35084e25 | 0.0231803 | ||||||||
\(521\) | − | 9.81031e26i | − | 0.665741i | −0.942973 | − | 0.332871i | \(-0.891983\pi\) | ||
0.942973 | − | 0.332871i | \(-0.108017\pi\) | |||||||
\(522\) | −2.86522e24 | + | 1.55243e27i | −0.00190745 | + | 1.03349i | ||||
\(523\) | 1.08594e27 | 0.709232 | 0.354616 | − | 0.935012i | \(-0.384612\pi\) | ||||
0.354616 | + | 0.935012i | \(0.384612\pi\) | |||||||
\(524\) | 7.44447e26i | 0.477003i | ||||||||
\(525\) | −1.43920e27 | + | 1.43655e27i | −0.904751 | + | 0.903083i | ||||
\(526\) | −1.09440e27 | −0.675026 | ||||||||
\(527\) | 1.59693e27i | 0.966449i | ||||||||
\(528\) | −8.63427e25 | − | 8.65022e25i | −0.0512727 | − | 0.0513675i | ||||
\(529\) | 1.64503e27 | 0.958554 | ||||||||
\(530\) | − | 1.97444e26i | − | 0.112898i | ||||||
\(531\) | 1.37274e27 | + | 2.53357e24i | 0.770268 | + | 0.00142163i | ||||
\(532\) | −1.75237e27 | −0.964959 | ||||||||
\(533\) | 1.66044e27i | 0.897329i | ||||||||
\(534\) | 7.53675e26 | − | 7.52285e26i | 0.399734 | − | 0.398997i | ||||
\(535\) | −1.35331e26 | −0.0704465 | ||||||||
\(536\) | − | 1.91514e26i | − | 0.0978483i | ||||||
\(537\) | −3.08560e26 | − | 3.09131e26i | −0.154738 | − | 0.155024i | ||||
\(538\) | −2.39579e26 | −0.117930 | ||||||||
\(539\) | − | 3.94504e26i | − | 0.190618i | ||||||
\(540\) | −6.16554e25 | + | 6.13150e25i | −0.0292438 | + | 0.0290823i | ||||
\(541\) | −3.41024e27 | −1.58786 | −0.793929 | − | 0.608010i | \(-0.791968\pi\) | ||||
−0.793929 | + | 0.608010i | \(0.791968\pi\) | |||||||
\(542\) | 2.08166e27i | 0.951517i | ||||||||
\(543\) | −5.40328e26 | + | 5.39332e26i | −0.242471 | + | 0.242024i | ||||
\(544\) | 5.92316e26 | 0.260954 | ||||||||
\(545\) | − | 8.49940e25i | − | 0.0367640i | ||||||
\(546\) | −1.20334e27 | − | 1.20556e27i | −0.511049 | − | 0.511993i | ||||
\(547\) | −2.62335e27 | −1.09391 | −0.546956 | − | 0.837161i | \(-0.684214\pi\) | ||||
−0.546956 | + | 0.837161i | \(0.684214\pi\) | |||||||
\(548\) | − | 2.19487e27i | − | 0.898676i | ||||||
\(549\) | 4.69286e24 | − | 2.54268e27i | 0.00188675 | − | 1.02228i | ||||
\(550\) | −5.16428e26 | −0.203884 | ||||||||
\(551\) | 5.65287e27i | 2.19156i | ||||||||
\(552\) | −1.33805e26 | + | 1.33559e26i | −0.0509428 | + | 0.0508488i | ||||
\(553\) | 2.65742e27 | 0.993595 | ||||||||
\(554\) | − | 9.29709e26i | − | 0.341389i | ||||||
\(555\) | −2.15230e26 | − | 2.15628e26i | −0.0776201 | − | 0.0777634i | ||||
\(556\) | 2.29462e27 | 0.812762 | ||||||||
\(557\) | − | 3.25407e27i | − | 1.13208i | −0.824379 | − | 0.566038i | \(-0.808476\pi\) | ||
0.824379 | − | 0.566038i | \(-0.191524\pi\) | |||||||
\(558\) | −1.35477e27 | − | 2.50041e24i | −0.462939 | − | 0.000854416i | ||||
\(559\) | 2.50414e27 | 0.840504 | ||||||||
\(560\) | − | 8.05024e25i | − | 0.0265417i | ||||||
\(561\) | 9.36518e26 | − | 9.34791e26i | 0.303310 | − | 0.302751i | ||||
\(562\) | 1.85536e27 | 0.590288 | ||||||||
\(563\) | − | 3.38094e27i | − | 1.05670i | −0.849025 | − | 0.528352i | \(-0.822810\pi\) | ||
0.849025 | − | 0.528352i | \(-0.177190\pi\) | |||||||
\(564\) | 4.85878e26 | + | 4.86775e26i | 0.149189 | + | 0.149464i | ||||
\(565\) | 2.39119e26 | 0.0721324 | ||||||||
\(566\) | 4.22176e27i | 1.25121i | ||||||||
\(567\) | 4.42014e27 | + | 1.63160e25i | 1.28708 | + | 0.00475097i | ||||
\(568\) | 2.32291e27 | 0.664583 | ||||||||
\(569\) | 1.42049e27i | 0.399316i | 0.979866 | + | 0.199658i | \(0.0639832\pi\) | ||||
−0.979866 | + | 0.199658i | \(0.936017\pi\) | |||||||
\(570\) | −2.24093e26 | + | 2.23680e26i | −0.0618985 | + | 0.0617844i | ||||
\(571\) | 1.15178e25 | 0.00312614 | 0.00156307 | − | 0.999999i | \(-0.499502\pi\) | ||||
0.00156307 | + | 0.999999i | \(0.499502\pi\) | |||||||
\(572\) | − | 4.32591e26i | − | 0.115377i | ||||||
\(573\) | −4.74233e27 | − | 4.75109e27i | −1.24293 | − | 1.24522i | ||||
\(574\) | 3.98914e27 | 1.02745 | ||||||||
\(575\) | 7.98832e26i | 0.202198i | ||||||||
\(576\) | −9.27426e23 | + | 5.02498e26i | −0.000230704 | + | 0.125000i | ||||
\(577\) | −4.17787e27 | −1.02140 | −0.510701 | − | 0.859759i | \(-0.670614\pi\) | ||||
−0.510701 | + | 0.859759i | \(0.670614\pi\) | |||||||
\(578\) | 3.46990e27i | 0.833755i | ||||||||
\(579\) | 1.90132e27 | − | 1.89782e27i | 0.449025 | − | 0.448197i | ||||
\(580\) | −2.59688e26 | −0.0602799 | ||||||||
\(581\) | − | 5.72951e27i | − | 1.30724i | ||||||
\(582\) | −2.66217e27 | − | 2.66709e27i | −0.597044 | − | 0.598147i | ||||
\(583\) | −2.54899e27 | −0.561931 | ||||||||
\(584\) | 3.48117e26i | 0.0754391i | ||||||||
\(585\) | −3.07767e26 | − | 5.68026e23i | −0.0655638 | − | 0.000121007i | ||||
\(586\) | −8.74431e26 | −0.183126 | ||||||||
\(587\) | 6.55137e27i | 1.34881i | 0.738361 | + | 0.674406i | \(0.235600\pi\) | ||||
−0.738361 | + | 0.674406i | \(0.764400\pi\) | |||||||
\(588\) | −1.14797e27 | + | 1.14585e27i | −0.232357 | + | 0.231929i | ||||
\(589\) | −4.93313e27 | −0.981680 | ||||||||
\(590\) | 2.29630e26i | 0.0449270i | ||||||||
\(591\) | 2.05444e27 | + | 2.05824e27i | 0.395202 | + | 0.395932i | ||||
\(592\) | −1.76063e27 | −0.333005 | ||||||||
\(593\) | 7.48816e27i | 1.39261i | 0.717748 | + | 0.696303i | \(0.245173\pi\) | ||||
−0.717748 | + | 0.696303i | \(0.754827\pi\) | |||||||
\(594\) | 7.91574e26 | + | 7.95969e26i | 0.144753 | + | 0.145557i | ||||
\(595\) | 8.71561e26 | 0.156721 | ||||||||
\(596\) | − | 2.84931e27i | − | 0.503823i | ||||||
\(597\) | −2.40116e27 | + | 2.39673e27i | −0.417521 | + | 0.416751i | ||||
\(598\) | −6.69150e26 | −0.114423 | ||||||||
\(599\) | − | 6.04562e27i | − | 1.01665i | −0.861165 | − | 0.508326i | \(-0.830264\pi\) | ||
0.861165 | − | 0.508326i | \(-0.169736\pi\) | |||||||
\(600\) | 1.49998e27 | + | 1.50275e27i | 0.248070 | + | 0.248528i | ||||
\(601\) | 3.88315e27 | 0.631596 | 0.315798 | − | 0.948827i | \(-0.397728\pi\) | ||||
0.315798 | + | 0.948827i | \(0.397728\pi\) | |||||||
\(602\) | − | 6.01608e27i | − | 0.962385i | ||||||
\(603\) | −3.24651e24 | + | 1.75902e27i | −0.000510791 | + | 0.276756i | ||||
\(604\) | −1.29028e27 | −0.199671 | ||||||||
\(605\) | 4.96245e26i | 0.0755340i | ||||||||
\(606\) | 1.14798e27 | − | 1.14586e27i | 0.171873 | − | 0.171556i | ||||
\(607\) | −4.08940e27 | −0.602245 | −0.301122 | − | 0.953586i | \(-0.597361\pi\) | ||||
−0.301122 | + | 0.953586i | \(0.597361\pi\) | |||||||
\(608\) | 1.82975e27i | 0.265067i | ||||||||
\(609\) | 9.32585e27 | + | 9.34308e27i | 1.32897 | + | 1.33143i | ||||
\(610\) | 4.25337e26 | 0.0596258 | ||||||||
\(611\) | 2.43433e27i | 0.335712i | ||||||||
\(612\) | −5.44030e27 | − | 1.00408e25i | −0.738089 | − | 0.00136224i | ||||
\(613\) | −3.61790e27 | −0.482895 | −0.241447 | − | 0.970414i | \(-0.577622\pi\) | ||||
−0.241447 | + | 0.970414i | \(0.577622\pi\) | |||||||
\(614\) | 8.67837e26i | 0.113960i | ||||||||
\(615\) | 5.10133e26 | − | 5.09192e26i | 0.0659071 | − | 0.0657855i | ||||
\(616\) | −1.03928e27 | −0.132107 | ||||||||
\(617\) | − | 6.19841e26i | − | 0.0775226i | −0.999248 | − | 0.0387613i | \(-0.987659\pi\) | ||
0.999248 | − | 0.0387613i | \(-0.0123412\pi\) | |||||||
\(618\) | −1.83479e27 | − | 1.83818e27i | −0.225788 | − | 0.226205i | ||||
\(619\) | 1.52572e27 | 0.184743 | 0.0923713 | − | 0.995725i | \(-0.470555\pi\) | ||||
0.0923713 | + | 0.995725i | \(0.470555\pi\) | |||||||
\(620\) | − | 2.26624e26i | − | 0.0270016i | ||||||
\(621\) | 1.23124e27 | − | 1.22444e27i | 0.144353 | − | 0.143556i | ||||
\(622\) | 6.94176e26 | 0.0800877 | ||||||||
\(623\) | − | 9.05504e27i | − | 1.02804i | ||||||
\(624\) | −1.25880e27 | + | 1.25648e27i | −0.140640 | + | 0.140381i | ||||
\(625\) | 8.90972e27 | 0.979635 | ||||||||
\(626\) | − | 9.08700e27i | − | 0.983279i | ||||||
\(627\) | 2.88770e27 | + | 2.89303e27i | 0.307522 | + | 0.308090i | ||||
\(628\) | −3.26243e27 | −0.341936 | ||||||||
\(629\) | − | 1.90615e28i | − | 1.96630i | ||||||
\(630\) | −1.36466e24 | + | 7.39398e26i | −0.000138554 | + | 0.0750711i | ||||
\(631\) | 1.61675e28 | 1.61566 | 0.807830 | − | 0.589416i | \(-0.200642\pi\) | ||||
0.807830 | + | 0.589416i | \(0.200642\pi\) | |||||||
\(632\) | − | 2.77477e27i | − | 0.272933i | ||||||
\(633\) | 5.15238e26 | − | 5.14288e26i | 0.0498851 | − | 0.0497931i | ||||
\(634\) | 7.12737e27 | 0.679261 | ||||||||
\(635\) | − | 2.04910e24i | − | 0.000192232i | ||||||
\(636\) | 7.40364e27 | + | 7.41732e27i | 0.683714 | + | 0.684977i | ||||
\(637\) | −5.74090e27 | −0.521898 | ||||||||
\(638\) | 3.35257e27i | 0.300034i | ||||||||
\(639\) | −2.13355e28 | − | 3.93775e25i | −1.87972 | − | 0.00346928i | ||||
\(640\) | −8.40571e25 | −0.00729079 | ||||||||
\(641\) | 1.31157e28i | 1.11998i | 0.828499 | + | 0.559990i | \(0.189195\pi\) | ||||
−0.828499 | + | 0.559990i | \(0.810805\pi\) | |||||||
\(642\) | 5.08394e27 | − | 5.07457e27i | 0.427415 | − | 0.426627i | ||||
\(643\) | 1.37768e27 | 0.114035 | 0.0570174 | − | 0.998373i | \(-0.481841\pi\) | ||||
0.0570174 | + | 0.998373i | \(0.481841\pi\) | |||||||
\(644\) | 1.60761e27i | 0.131015i | ||||||||
\(645\) | −7.67920e26 | − | 7.69338e26i | −0.0616196 | − | 0.0617334i | ||||
\(646\) | −1.98098e28 | −1.56514 | ||||||||
\(647\) | − | 6.44182e27i | − | 0.501148i | −0.968097 | − | 0.250574i | \(-0.919381\pi\) | ||
0.968097 | − | 0.250574i | \(-0.0806193\pi\) | |||||||
\(648\) | 1.70364e25 | − | 4.61532e27i | 0.00130506 | − | 0.353551i | ||||
\(649\) | 2.96451e27 | 0.223617 | ||||||||
\(650\) | 7.51516e27i | 0.558219i | ||||||||
\(651\) | −8.15350e27 | + | 8.13846e27i | −0.596395 | + | 0.595295i | ||||
\(652\) | 5.86135e27 | 0.422203 | ||||||||
\(653\) | 1.28868e28i | 0.914142i | 0.889430 | + | 0.457071i | \(0.151102\pi\) | ||||
−0.889430 | + | 0.457071i | \(0.848898\pi\) | |||||||
\(654\) | 3.18706e27 | + | 3.19294e27i | 0.222645 | + | 0.223056i | ||||
\(655\) | 1.14378e27 | 0.0786920 | ||||||||
\(656\) | − | 4.16529e27i | − | 0.282232i | ||||||
\(657\) | 5.90119e24 | − | 3.19738e27i | 0.000393809 | − | 0.213374i | ||||
\(658\) | 5.84837e27 | 0.384393 | ||||||||
\(659\) | 1.94022e28i | 1.25602i | 0.778206 | + | 0.628009i | \(0.216130\pi\) | ||||
−0.778206 | + | 0.628009i | \(0.783870\pi\) | |||||||
\(660\) | −1.32904e26 | + | 1.32659e26i | −0.00847419 | + | 0.00845856i | ||||
\(661\) | −2.25373e28 | −1.41543 | −0.707713 | − | 0.706500i | \(-0.750273\pi\) | ||||
−0.707713 | + | 0.706500i | \(0.750273\pi\) | |||||||
\(662\) | 1.28598e28i | 0.795523i | ||||||||
\(663\) | −1.36033e28 | − | 1.36284e28i | −0.828911 | − | 0.830442i | ||||
\(664\) | −5.98251e27 | −0.359089 | ||||||||
\(665\) | 2.69237e27i | 0.159191i | ||||||||
\(666\) | 1.61710e28 | + | 2.98457e25i | 0.941878 | + | 0.00173836i | ||||
\(667\) | 5.18589e27 | 0.297553 | ||||||||
\(668\) | 9.11075e27i | 0.514979i | ||||||||
\(669\) | 1.15886e28 | − | 1.15673e28i | 0.645314 | − | 0.644124i | ||||
\(670\) | −2.94246e26 | −0.0161422 | ||||||||
\(671\) | − | 5.49108e27i | − | 0.296778i | ||||||
\(672\) | 3.01863e27 | + | 3.02421e27i | 0.160738 | + | 0.161035i | ||||
\(673\) | 2.20415e28 | 1.15635 | 0.578176 | − | 0.815912i | \(-0.303765\pi\) | ||||
0.578176 | + | 0.815912i | \(0.303765\pi\) | |||||||
\(674\) | 3.46079e27i | 0.178886i | ||||||||
\(675\) | −1.37516e28 | − | 1.38279e28i | −0.700349 | − | 0.704237i | ||||
\(676\) | 3.66892e27 | 0.184107 | ||||||||
\(677\) | − | 2.53010e28i | − | 1.25098i | −0.780232 | − | 0.625490i | \(-0.784899\pi\) | ||
0.780232 | − | 0.625490i | \(-0.215101\pi\) | |||||||
\(678\) | −8.98293e27 | + | 8.96636e27i | −0.437644 | + | 0.436837i | ||||
\(679\) | −3.20438e28 | −1.53832 | ||||||||
\(680\) | − | 9.10046e26i | − | 0.0430501i | ||||||
\(681\) | 1.43784e28 | + | 1.44050e28i | 0.670254 | + | 0.671492i | ||||
\(682\) | −2.92571e27 | −0.134396 | ||||||||
\(683\) | − | 1.37371e28i | − | 0.621855i | −0.950434 | − | 0.310927i | \(-0.899360\pi\) | ||
0.950434 | − | 0.310927i | \(-0.100640\pi\) | |||||||
\(684\) | 3.10174e25 | − | 1.68058e28i | 0.00138371 | − | 0.749720i | ||||
\(685\) | −3.37224e27 | −0.148256 | ||||||||
\(686\) | − | 7.21332e27i | − | 0.312532i | ||||||
\(687\) | 1.50939e28 | − | 1.50661e28i | 0.644519 | − | 0.643330i | ||||
\(688\) | −6.28173e27 | −0.264359 | ||||||||
\(689\) | 3.70935e28i | 1.53853i | ||||||||
\(690\) | 2.05202e26 | + | 2.05581e26i | 0.00838863 | + | 0.00840412i | ||||
\(691\) | 5.91223e27 | 0.238216 | 0.119108 | − | 0.992881i | \(-0.461997\pi\) | ||||
0.119108 | + | 0.992881i | \(0.461997\pi\) | |||||||
\(692\) | − | 4.07539e27i | − | 0.161848i | ||||||
\(693\) | 9.54560e27 | + | 1.76177e25i | 0.373655 | + | 0.000689630i | ||||
\(694\) | −1.26045e28 | −0.486329 | ||||||||
\(695\) | − | 3.52551e27i | − | 0.134083i | ||||||
\(696\) | 9.75564e27 | − | 9.73765e27i | 0.365732 | − | 0.365058i | ||||
\(697\) | 4.50956e28 | 1.66650 | ||||||||
\(698\) | − | 1.58806e28i | − | 0.578513i | ||||||
\(699\) | −1.43231e28 | − | 1.43495e28i | −0.514356 | − | 0.515307i | ||||
\(700\) | 1.80549e28 | 0.639166 | ||||||||
\(701\) | 4.28515e28i | 1.49550i | 0.663981 | + | 0.747750i | \(0.268866\pi\) | ||||
−0.663981 | + | 0.747750i | \(0.731134\pi\) | |||||||
\(702\) | 1.15831e28 | − | 1.15191e28i | 0.398523 | − | 0.396323i | ||||
\(703\) | 5.88835e28 | 1.99729 | ||||||||
\(704\) | 1.08517e27i | 0.0362888i | ||||||||
\(705\) | 7.47891e26 | − | 7.46512e26i | 0.0246574 | − | 0.0246119i | ||||
\(706\) | −1.87869e28 | −0.610672 | ||||||||
\(707\) | − | 1.37924e28i | − | 0.442025i | ||||||
\(708\) | −8.61052e27 | − | 8.62642e27i | −0.272080 | − | 0.272583i | ||||
\(709\) | −5.69549e28 | −1.77447 | −0.887235 | − | 0.461318i | \(-0.847377\pi\) | ||||
−0.887235 | + | 0.461318i | \(0.847377\pi\) | |||||||
\(710\) | − | 3.56897e27i | − | 0.109638i | ||||||
\(711\) | −4.70372e25 | + | 2.54857e28i | −0.00142477 | + | 0.771969i | ||||
\(712\) | −9.45488e27 | −0.282394 | ||||||||
\(713\) | 4.52561e27i | 0.133285i | ||||||||
\(714\) | −3.27417e28 | + | 3.26813e28i | −0.950864 | + | 0.949111i | ||||
\(715\) | −6.64642e26 | −0.0190339 | ||||||||
\(716\) | 3.87805e27i | 0.109518i | ||||||||
\(717\) | 9.01140e27 | + | 9.02805e27i | 0.250958 | + | 0.251421i | ||||
\(718\) | 3.48535e27 | 0.0957198 | ||||||||
\(719\) | 2.55879e28i | 0.693019i | 0.938046 | + | 0.346510i | \(0.112633\pi\) | ||||
−0.938046 | + | 0.346510i | \(0.887367\pi\) | |||||||
\(720\) | 7.72048e26 | + | 1.42492e24i | 0.0206214 | + | 3.80596e-5i | ||||
\(721\) | −2.20848e28 | −0.581757 | ||||||||
\(722\) | − | 3.39771e28i | − | 0.882703i | ||||||
\(723\) | −3.85383e28 | + | 3.84672e28i | −0.987438 | + | 0.985617i | ||||
\(724\) | 6.77844e27 | 0.171295 | ||||||||
\(725\) | − | 5.82422e28i | − | 1.45164i | ||||||
\(726\) | −1.86079e28 | − | 1.86423e28i | −0.457437 | − | 0.458282i | ||||
\(727\) | −1.24111e28 | −0.300930 | −0.150465 | − | 0.988615i | \(-0.548077\pi\) | ||||
−0.150465 | + | 0.988615i | \(0.548077\pi\) | |||||||
\(728\) | 1.51239e28i | 0.361700i | ||||||||
\(729\) | −2.34714e26 | + | 4.23905e28i | −0.00553686 | + | 0.999985i | ||||
\(730\) | 5.34853e26 | 0.0124453 | ||||||||
\(731\) | − | 6.80092e28i | − | 1.56097i | ||||||
\(732\) | −1.59785e28 | + | 1.59490e28i | −0.361764 | + | 0.361097i | ||||
\(733\) | −2.22545e28 | −0.497024 | −0.248512 | − | 0.968629i | \(-0.579942\pi\) | ||||
−0.248512 | + | 0.968629i | \(0.579942\pi\) | |||||||
\(734\) | 3.39570e28i | 0.748115i | ||||||||
\(735\) | 1.76051e27 | + | 1.76376e27i | 0.0382617 | + | 0.0383324i | ||||
\(736\) | 1.67859e27 | 0.0359888 | ||||||||
\(737\) | 3.79871e27i | 0.0803454i | ||||||||
\(738\) | −7.06090e25 | + | 3.82573e28i | −0.00147332 | + | 0.798272i | ||||
\(739\) | 3.40139e27 | 0.0700183 | 0.0350091 | − | 0.999387i | \(-0.488854\pi\) | ||||
0.0350091 | + | 0.999387i | \(0.488854\pi\) | |||||||
\(740\) | 2.70506e27i | 0.0549364i | ||||||||
\(741\) | 4.21000e28 | − | 4.20224e28i | 0.843530 | − | 0.841974i | ||||
\(742\) | 8.91155e28 | 1.76163 | ||||||||
\(743\) | 6.28612e28i | 1.22601i | 0.790078 | + | 0.613006i | \(0.210040\pi\) | ||||
−0.790078 | + | 0.613006i | \(0.789960\pi\) | |||||||
\(744\) | 8.49783e27 | + | 8.51353e27i | 0.163523 | + | 0.163825i | ||||
\(745\) | −4.37774e27 | −0.0831166 | ||||||||
\(746\) | − | 1.35797e28i | − | 0.254392i | ||||||
\(747\) | 5.49481e28 | + | 1.01414e26i | 1.01566 | + | 0.00187453i | ||||
\(748\) | −1.17487e28 | −0.214275 | ||||||||
\(749\) | − | 6.10811e28i | − | 1.09923i | ||||||
\(750\) | 4.63354e27 | − | 4.62500e27i | 0.0822811 | − | 0.0821294i | ||||
\(751\) | −1.54822e28 | −0.271291 | −0.135645 | − | 0.990757i | \(-0.543311\pi\) | ||||
−0.135645 | + | 0.990757i | \(0.543311\pi\) | |||||||
\(752\) | − | 6.10661e27i | − | 0.105590i | ||||||
\(753\) | 8.61027e27 | + | 8.62617e27i | 0.146915 | + | 0.147187i | ||||
\(754\) | 4.87872e28 | 0.821472 | ||||||||
\(755\) | 1.98241e27i | 0.0329401i | ||||||||
\(756\) | −2.76743e28 | − | 2.78279e28i | −0.453793 | − | 0.456313i | ||||
\(757\) | −2.73490e28 | −0.442571 | −0.221285 | − | 0.975209i | \(-0.571025\pi\) | ||||
−0.221285 | + | 0.975209i | \(0.571025\pi\) | |||||||
\(758\) | − | 5.43655e28i | − | 0.868223i | ||||||
\(759\) | 2.65404e27 | − | 2.64915e27i | 0.0418302 | − | 0.0417531i | ||||
\(760\) | 2.81126e27 | 0.0437285 | ||||||||
\(761\) | − | 5.31431e28i | − | 0.815832i | −0.913020 | − | 0.407916i | \(-0.866256\pi\) | ||
0.913020 | − | 0.407916i | \(-0.133744\pi\) | |||||||
\(762\) | 7.68358e25 | + | 7.69778e25i | 0.00116416 | + | 0.00116631i | ||||
\(763\) | 3.83617e28 | 0.573657 | ||||||||
\(764\) | 5.96027e28i | 0.879695i | ||||||||
\(765\) | −1.54269e25 | + | 8.35858e27i | −0.000224731 | + | 0.121764i | ||||
\(766\) | −2.92632e27 | −0.0420760 | ||||||||
\(767\) | − | 4.31401e28i | − | 0.612248i | ||||||
\(768\) | 3.15775e27 | − | 3.15193e27i | 0.0442349 | − | 0.0441534i | ||||
\(769\) | −1.39897e29 | −1.93440 | −0.967200 | − | 0.254018i | \(-0.918248\pi\) | ||||
−0.967200 | + | 0.254018i | \(0.918248\pi\) | |||||||
\(770\) | 1.59677e27i | 0.0217940i | ||||||||
\(771\) | −2.69332e28 | − | 2.69830e28i | −0.362864 | − | 0.363535i | ||||
\(772\) | −2.38522e28 | −0.317216 | ||||||||
\(773\) | − | 3.22372e28i | − | 0.423216i | −0.977355 | − | 0.211608i | \(-0.932130\pi\) | ||
0.977355 | − | 0.211608i | \(-0.0678700\pi\) | |||||||
\(774\) | 5.76964e28 | + | 1.06486e26i | 0.747720 | + | 0.00138002i | ||||
\(775\) | 5.08267e28 | 0.650241 | ||||||||
\(776\) | 3.34587e28i | 0.422564i | ||||||||
\(777\) | 9.73228e28 | − | 9.71434e28i | 1.21340 | − | 1.21116i | ||||
\(778\) | −3.09941e28 | −0.381490 | ||||||||
\(779\) | 1.39307e29i | 1.69277i | ||||||||
\(780\) | 1.93048e27 | + | 1.93404e27i | 0.0231589 | + | 0.0232017i | ||||
\(781\) | −4.60752e28 | −0.545704 | ||||||||
\(782\) | 1.81733e28i | 0.212504i | ||||||||
\(783\) | −8.97686e28 | + | 8.92729e28i | −1.03635 | + | 1.03063i | ||||
\(784\) | 1.44013e28 | 0.164150 | ||||||||
\(785\) | 5.01246e27i | 0.0564098i | ||||||||
\(786\) | −4.29681e28 | + | 4.28889e28i | −0.477443 | + | 0.476562i | ||||
\(787\) | 1.46996e29 | 1.61272 | 0.806360 | − | 0.591425i | \(-0.201434\pi\) | ||||
0.806360 | + | 0.591425i | \(0.201434\pi\) | |||||||
\(788\) | − | 2.58207e28i | − | 0.279708i | ||||||
\(789\) | −6.30506e28 | − | 6.31671e28i | −0.674403 | − | 0.675649i | ||||
\(790\) | −4.26321e27 | −0.0450262 | ||||||||
\(791\) | 1.07926e29i | 1.12554i | ||||||||
\(792\) | 1.83956e25 | − | 9.96710e27i | 0.000189436 | − | 0.102640i | ||||
\(793\) | −7.99073e28 | −0.812558 | ||||||||
\(794\) | 3.40367e28i | 0.341777i | ||||||||
\(795\) | 1.13961e28 | − | 1.13751e28i | 0.113002 | − | 0.112794i | ||||
\(796\) | 3.01227e28 | 0.294960 | ||||||||
\(797\) | 1.69393e29i | 1.63799i | 0.573801 | + | 0.818995i | \(0.305468\pi\) | ||||
−0.573801 | + | 0.818995i | \(0.694532\pi\) | |||||||
\(798\) | −1.00957e29 | − | 1.01144e29i | −0.964068 | − | 0.965849i | ||||
\(799\) | 6.61133e28 | 0.623478 | ||||||||
\(800\) | − | 1.88521e28i | − | 0.175574i | ||||||
\(801\) | 8.68412e28 | + | 1.60277e26i | 0.798731 | + | 0.00147416i | ||||
\(802\) | −1.08966e29 | −0.989801 | ||||||||
\(803\) | − | 6.90493e27i | − | 0.0619447i | ||||||
\(804\) | 1.10539e28 | − | 1.10335e28i | 0.0979386 | − | 0.0977580i | ||||
\(805\) | 2.46996e27 | 0.0216138 | ||||||||
\(806\) | 4.25755e28i | 0.367968i | ||||||||
\(807\) | −1.38026e28 | − | 1.38281e28i | −0.117821 | − | 0.118039i | ||||
\(808\) | −1.44015e28 | −0.121421 | ||||||||
\(809\) | − | 1.09964e28i | − | 0.0915727i | −0.998951 | − | 0.0457864i | \(-0.985421\pi\) | ||
0.998951 | − | 0.0457864i | \(-0.0145793\pi\) | |||||||
\(810\) | −7.09108e27 | − | 2.61751e25i | −0.0583260 | − | 0.000215297i | ||||
\(811\) | −1.15750e29 | −0.940396 | −0.470198 | − | 0.882561i | \(-0.655817\pi\) | ||||
−0.470198 | + | 0.882561i | \(0.655817\pi\) | |||||||
\(812\) | − | 1.17209e29i | − | 0.940593i | ||||||
\(813\) | −1.20150e29 | + | 1.19928e29i | −0.952395 | + | 0.950638i | ||||
\(814\) | 3.49222e28 | 0.273437 | ||||||||
\(815\) | − | 9.00550e27i | − | 0.0696517i | ||||||
\(816\) | 3.41244e28 | + | 3.41874e28i | 0.260713 | + | 0.261195i | ||||
\(817\) | 2.10090e29 | 1.58557 | ||||||||
\(818\) | − | 7.23364e28i | − | 0.539292i | ||||||
\(819\) | 2.56376e26 | − | 1.38909e29i | 0.00188816 | − | 1.02304i | ||||
\(820\) | −6.39963e27 | −0.0465604 | ||||||||
\(821\) | − | 6.50646e28i | − | 0.467642i | −0.972280 | − | 0.233821i | \(-0.924877\pi\) | ||
0.972280 | − | 0.233821i | \(-0.0751230\pi\) | |||||||
\(822\) | 1.26684e29 | − | 1.26450e29i | 0.899505 | − | 0.897847i | ||||
\(823\) | 9.49304e28 | 0.665897 | 0.332949 | − | 0.942945i | \(-0.391956\pi\) | ||||
0.332949 | + | 0.942945i | \(0.391956\pi\) | |||||||
\(824\) | 2.30600e28i | 0.159804i | ||||||||
\(825\) | −2.97523e28 | − | 2.98073e28i | −0.203696 | − | 0.204072i | ||||
\(826\) | −1.03642e29 | −0.701030 | ||||||||
\(827\) | − | 7.39489e28i | − | 0.494170i | −0.968994 | − | 0.247085i | \(-0.920527\pi\) | ||
0.968994 | − | 0.247085i | \(-0.0794727\pi\) | |||||||
\(828\) | −1.54175e28 | − | 2.84551e25i | −0.101791 | − | 0.000187870i | ||||
\(829\) | 2.50384e29 | 1.63328 | 0.816640 | − | 0.577147i | \(-0.195834\pi\) | ||||
0.816640 | + | 0.577147i | \(0.195834\pi\) | |||||||
\(830\) | 9.19164e27i | 0.0592396i | ||||||||
\(831\) | 5.36611e28 | − | 5.35622e28i | 0.341704 | − | 0.341074i | ||||
\(832\) | 1.57917e28 | 0.0993562 | ||||||||
\(833\) | 1.55916e29i | 0.969260i | ||||||||
\(834\) | 1.32197e29 | + | 1.32442e29i | 0.812012 | + | 0.813512i | ||||
\(835\) | 1.39979e28 | 0.0849570 | ||||||||
\(836\) | − | 3.62932e28i | − | 0.217652i | ||||||
\(837\) | −7.79065e28 | − | 7.83390e28i | −0.461657 | − | 0.464220i | ||||
\(838\) | −1.21739e29 | −0.712838 | ||||||||
\(839\) | − | 2.79539e29i | − | 1.61742i | −0.588208 | − | 0.808710i | \(-0.700166\pi\) | ||
0.588208 | − | 0.808710i | \(-0.299834\pi\) | |||||||
\(840\) | 4.64646e27 | − | 4.63789e27i | 0.0265662 | − | 0.0265172i | ||||
\(841\) | −2.01105e29 | −1.13622 | ||||||||
\(842\) | 1.94903e29i | 1.08817i | ||||||||
\(843\) | 1.06890e29 | + | 1.07088e29i | 0.589743 | + | 0.590833i | ||||
\(844\) | −6.46368e27 | −0.0352416 | ||||||||
\(845\) | − | 5.63700e27i | − | 0.0303725i | ||||||
\(846\) | −1.03518e26 | + | 5.60880e28i | −0.000551203 | + | 0.298653i | ||||
\(847\) | −2.23978e29 | −1.17861 | ||||||||
\(848\) | − | 9.30505e28i | − | 0.483905i | ||||||
\(849\) | −2.43673e29 | + | 2.43223e29i | −1.25236 | + | 1.25005i | ||||
\(850\) | 2.04103e29 | 1.03671 | ||||||||
\(851\) | − | 5.40192e28i | − | 0.271177i | ||||||
\(852\) | 1.33827e29 | + | 1.34074e29i | 0.663970 | + | 0.665196i | ||||
\(853\) | 2.04793e29 | 1.00421 | 0.502105 | − | 0.864807i | \(-0.332559\pi\) | ||||
0.502105 | + | 0.864807i | \(0.332559\pi\) | |||||||
\(854\) | 1.91974e29i | 0.930387i | ||||||||
\(855\) | −2.58208e28 | − | 4.76558e25i | −0.123683 | − | 0.000228273i | ||||
\(856\) | −6.37782e28 | −0.301950 | ||||||||
\(857\) | − | 4.15136e29i | − | 1.94260i | −0.237864 | − | 0.971298i | \(-0.576447\pi\) | ||
0.237864 | − | 0.971298i | \(-0.423553\pi\) | |||||||
\(858\) | 2.49684e28 | − | 2.49224e28i | 0.115483 | − | 0.115270i | ||||
\(859\) | −3.68833e29 | −1.68616 | −0.843079 | − | 0.537790i | \(-0.819259\pi\) | ||||
−0.843079 | + | 0.537790i | \(0.819259\pi\) | |||||||
\(860\) | 9.65138e27i | 0.0436119i | ||||||||
\(861\) | 2.29822e29 | + | 2.30246e29i | 1.02650 | + | 1.02840i | ||||
\(862\) | −1.47240e29 | −0.650061 | ||||||||
\(863\) | 2.25722e29i | 0.985065i | 0.870294 | + | 0.492533i | \(0.163929\pi\) | ||||
−0.870294 | + | 0.492533i | \(0.836071\pi\) | |||||||
\(864\) | −2.90567e28 | + | 2.88963e28i | −0.125346 | + | 0.124653i | ||||
\(865\) | −6.26151e27 | −0.0267004 | ||||||||
\(866\) | − | 2.00720e29i | − | 0.846079i | ||||||
\(867\) | −2.00276e29 | + | 1.99907e29i | −0.834524 | + | 0.832985i | ||||
\(868\) | 1.02286e29 | 0.421326 | ||||||||
\(869\) | 5.50378e28i | 0.224111i | ||||||||
\(870\) | −1.49611e28 | − | 1.49888e28i | −0.0602243 | − | 0.0603355i | ||||
\(871\) | 5.52796e28 | 0.219980 | ||||||||
\(872\) | − | 4.00556e28i | − | 0.157579i | ||||||
\(873\) | 5.67185e26 | − | 3.07312e29i | 0.00220588 | − | 1.19519i | ||||
\(874\) | −5.61399e28 | −0.215853 | ||||||||
\(875\) | − | 5.56697e28i | − | 0.211611i | ||||||
\(876\) | −2.00927e28 | + | 2.00556e28i | −0.0755086 | + | 0.0753694i | ||||
\(877\) | −1.17025e29 | −0.434793 | −0.217396 | − | 0.976083i | \(-0.569756\pi\) | ||||
−0.217396 | + | 0.976083i | \(0.569756\pi\) | |||||||
\(878\) | − | 1.01299e29i | − | 0.372099i | ||||||
\(879\) | −5.03775e28 | − | 5.04706e28i | −0.182957 | − | 0.183295i | ||||
\(880\) | 1.66728e27 | 0.00598663 | ||||||||
\(881\) | 2.06068e29i | 0.731562i | 0.930701 | + | 0.365781i | \(0.119198\pi\) | ||||
−0.930701 | + | 0.365781i | \(0.880802\pi\) | |||||||
\(882\) | −1.32273e29 | − | 2.44127e26i | −0.464286 | − | 0.000856901i | ||||
\(883\) | 1.64553e29 | 0.571082 | 0.285541 | − | 0.958367i | \(-0.407827\pi\) | ||||
0.285541 | + | 0.958367i | \(0.407827\pi\) | |||||||
\(884\) | 1.70969e29i | 0.586670i | ||||||||
\(885\) | −1.32538e28 | + | 1.32294e28i | −0.0449685 | + | 0.0448855i | ||||
\(886\) | 2.83019e29 | 0.949463 | ||||||||
\(887\) | − | 1.17405e29i | − | 0.389449i | −0.980858 | − | 0.194724i | \(-0.937619\pi\) | ||
0.980858 | − | 0.194724i | \(-0.0623812\pi\) | |||||||
\(888\) | −1.01433e29 | − | 1.01620e29i | −0.332697 | − | 0.333312i | ||||
\(889\) | 9.24851e26 | 0.00299954 | ||||||||
\(890\) | 1.45267e28i | 0.0465871i | ||||||||
\(891\) | −3.37920e26 | + | 9.15455e28i | −0.00107161 | + | 0.290309i | ||||
\(892\) | −1.45380e29 | −0.455885 | ||||||||
\(893\) | 2.04233e29i | 0.633304i | ||||||||
\(894\) | 1.64457e29 | − | 1.64154e29i | 0.504287 | − | 0.503358i | ||||
\(895\) | 5.95832e27 | 0.0180673 | ||||||||
\(896\) | − | 3.79388e28i | − | 0.113764i | ||||||
\(897\) | −3.85510e28 | − | 3.86222e28i | −0.114317 | − | 0.114528i | ||||
\(898\) | −1.04490e29 | −0.306415 | ||||||||
\(899\) | − | 3.29959e29i | − | 0.956891i | ||||||
\(900\) | −3.19576e26 | + | 1.73153e29i | −0.000916536 | + | 0.496597i | ||||
\(901\) | 1.00741e30 | 2.85733 | ||||||||
\(902\) | 8.26190e28i | 0.231747i | ||||||||
\(903\) | 3.47237e29 | − | 3.46597e29i | 0.963272 | − | 0.961496i | ||||
\(904\) | 1.12691e29 | 0.309176 | ||||||||
\(905\) | − | 1.04145e28i | − | 0.0282588i | ||||||
\(906\) | −7.43353e28 | − | 7.44727e28i | −0.199486 | − | 0.199855i | ||||
\(907\) | 3.55363e28 | 0.0943190 | 0.0471595 | − | 0.998887i | \(-0.484983\pi\) | ||||
0.0471595 | + | 0.998887i | \(0.484983\pi\) | |||||||
\(908\) | − | 1.80711e29i | − | 0.474379i | ||||||
\(909\) | 1.32275e29 | + | 2.44130e26i | 0.343429 | + | 0.000633845i | ||||
\(910\) | 2.32366e28 | 0.0596703 | ||||||||
\(911\) | − | 1.10794e29i | − | 0.281404i | −0.990052 | − | 0.140702i | \(-0.955064\pi\) | ||
0.990052 | − | 0.140702i | \(-0.0449360\pi\) | |||||||
\(912\) | −1.05610e29 | + | 1.05415e29i | −0.265311 | + | 0.264822i | ||||
\(913\) | 1.18664e29 | 0.294856 | ||||||||
\(914\) | − | 3.48892e29i | − | 0.857491i | ||||||
\(915\) | 2.45044e28 | + | 2.45497e28i | 0.0595708 | + | 0.0596808i | ||||
\(916\) | −1.89354e29 | −0.455323 | ||||||||
\(917\) | 5.16242e29i | 1.22789i | ||||||||
\(918\) | −3.12846e29 | − | 3.14583e29i | −0.736044 | − | 0.740130i | ||||
\(919\) | −7.17188e29 | −1.66908 | −0.834541 | − | 0.550945i | \(-0.814267\pi\) | ||||
−0.834541 | + | 0.550945i | \(0.814267\pi\) | |||||||
\(920\) | − | 2.57902e27i | − | 0.00593714i | ||||||
\(921\) | −5.00900e28 | + | 4.99976e28i | −0.114066 | + | 0.113855i | ||||
\(922\) | 1.99302e29 | 0.448955 | ||||||||
\(923\) | 6.70496e29i | 1.49410i | ||||||||
\(924\) | −5.98749e28 | − | 5.99856e28i | −0.131985 | − | 0.132229i | ||||
\(925\) | −6.06684e29 | −1.32296 | ||||||||
\(926\) | 3.48411e29i | 0.751592i | ||||||||
\(927\) | 3.90908e26 | − | 2.11802e29i | 0.000834214 | − | 0.451993i | ||||
\(928\) | −1.22385e29 | −0.258373 | ||||||||
\(929\) | − | 8.87877e28i | − | 0.185437i | −0.995692 | − | 0.0927184i | \(-0.970444\pi\) | ||
0.995692 | − | 0.0927184i | \(-0.0295556\pi\) | |||||||
\(930\) | 1.30804e28 | − | 1.30562e28i | 0.0270265 | − | 0.0269767i | ||||
\(931\) | −4.81646e29 | −0.984535 | ||||||||
\(932\) | 1.80015e29i | 0.364041i | ||||||||
\(933\) | 3.99928e28 | + | 4.00666e28i | 0.0800138 | + | 0.0801616i | ||||
\(934\) | 2.76553e29 | 0.547407 | ||||||||
\(935\) | 1.80509e28i | 0.0353494i | ||||||||
\(936\) | −1.45043e29 | − | 2.67697e26i | −0.281021 | − | 0.000518662i | ||||
\(937\) | −2.44477e29 | −0.468642 | −0.234321 | − | 0.972159i | \(-0.575287\pi\) | ||||
−0.234321 | + | 0.972159i | \(0.575287\pi\) | |||||||
\(938\) | − | 1.32807e29i | − | 0.251879i | ||||||
\(939\) | 5.24485e29 | − | 5.23518e29i | 0.984186 | − | 0.982372i | ||||
\(940\) | −9.38232e27 | −0.0174193 | ||||||||
\(941\) | 4.19504e29i | 0.770619i | 0.922787 | + | 0.385310i | \(0.125905\pi\) | ||||
−0.922787 | + | 0.385310i | \(0.874095\pi\) | |||||||
\(942\) | −1.87954e29 | − | 1.88302e29i | −0.341620 | − | 0.342251i | ||||
\(943\) | 1.27799e29 | 0.229831 | ||||||||
\(944\) | 1.08219e29i | 0.192567i | ||||||||
\(945\) | −4.27554e28 | + | 4.25193e28i | −0.0752788 | + | 0.0748631i | ||||
\(946\) | 1.24599e29 | 0.217071 | ||||||||
\(947\) | 1.10768e30i | 1.90949i | 0.297433 | + | 0.954743i | \(0.403870\pi\) | ||||
−0.297433 | + | 0.954743i | \(0.596130\pi\) | |||||||
\(948\) | 1.60155e29 | − | 1.59859e29i | 0.273185 | − | 0.272681i | ||||
\(949\) | −1.00482e29 | −0.169600 | ||||||||
\(950\) | 6.30502e29i | 1.05305i | ||||||||
\(951\) | 4.10621e29 | + | 4.11379e29i | 0.678634 | + | 0.679888i | ||||
\(952\) | 4.10745e29 | 0.671743 | ||||||||
\(953\) | − | 6.95375e29i | − | 1.12536i | −0.826676 | − | 0.562679i | \(-0.809771\pi\) | ||
0.826676 | − | 0.562679i | \(-0.190229\pi\) | |||||||
\(954\) | −1.57737e27 | + | 8.54650e29i | −0.00252610 | + | 1.36869i | ||||
\(955\) | 9.15747e28 | 0.145125 | ||||||||
\(956\) | − | 1.13257e29i | − | 0.177618i | ||||||
\(957\) | −1.93504e29 | + | 1.93147e29i | −0.300311 | + | 0.299757i | ||||
\(958\) | −2.76248e28 | −0.0424272 | ||||||||
\(959\) | − | 1.52205e30i | − | 2.31335i | ||||||
\(960\) | −4.84268e27 | − | 4.85163e27i | −0.00728406 | − | 0.00729752i | ||||
\(961\) | −3.83843e29 | −0.571373 | ||||||||
\(962\) | − | 5.08195e29i | − | 0.748652i | ||||||
\(963\) | 5.85790e29 | + | 1.08115e27i | 0.854042 | + | 0.00157625i | ||||
\(964\) | 4.83465e29 | 0.697580 | ||||||||
\(965\) | 3.66470e28i | 0.0523317i | ||||||||
\(966\) | −9.27882e28 | + | 9.26171e28i | −0.131136 | + | 0.130894i | ||||
\(967\) | −9.64276e29 | −1.34877 | −0.674383 | − | 0.738382i | \(-0.735590\pi\) | ||||
−0.674383 | + | 0.738382i | \(0.735590\pi\) | |||||||
\(968\) | 2.33868e29i | 0.323756i | ||||||||
\(969\) | −1.14128e30 | − | 1.14339e30i | −1.56370 | − | 1.56659i | ||||
\(970\) | 5.14067e28 | 0.0697111 | ||||||||
\(971\) | − | 8.85040e29i | − | 1.18787i | −0.804511 | − | 0.593937i | \(-0.797573\pi\) | ||
0.804511 | − | 0.593937i | \(-0.202427\pi\) | |||||||
\(972\) | 2.67370e29 | − | 2.64914e29i | 0.355181 | − | 0.351918i | ||||
\(973\) | 1.59122e30 | 2.09220 | ||||||||
\(974\) | 7.30703e29i | 0.950936i | ||||||||
\(975\) | −4.33762e29 | + | 4.32962e29i | −0.558734 | + | 0.557704i | ||||
\(976\) | 2.00451e29 | 0.255570 | ||||||||
\(977\) | − | 7.84234e29i | − | 0.989692i | −0.868981 | − | 0.494846i | \(-0.835224\pi\) | ||
0.868981 | − | 0.494846i | \(-0.164776\pi\) | |||||||
\(978\) | 3.37683e29 | + | 3.38307e29i | 0.421814 | + | 0.422593i | ||||
\(979\) | 1.87539e29 | 0.231880 | ||||||||
\(980\) | − | 2.21264e28i | − | 0.0270801i | ||||||
\(981\) | −6.79013e26 | + | 3.67903e29i | −0.000822599 | + | 0.445700i | ||||
\(982\) | −1.07323e30 | −1.28700 | ||||||||
\(983\) | 2.58895e29i | 0.307319i | 0.988124 | + | 0.153659i | \(0.0491058\pi\) | ||||
−0.988124 | + | 0.153659i | \(0.950894\pi\) | |||||||
\(984\) | 2.40413e29 | − | 2.39970e29i | 0.282493 | − | 0.281972i | ||||
\(985\) | −3.96714e28 | −0.0461440 | ||||||||
\(986\) | − | 1.32500e30i | − | 1.52562i | ||||||
\(987\) | 3.36935e29 | + | 3.37558e29i | 0.384038 | + | 0.384748i | ||||
\(988\) | −5.28146e29 | −0.595916 | ||||||||
\(989\) | − | 1.92735e29i | − | 0.215277i | ||||||
\(990\) | −1.53137e28 | − | 2.82634e25i | −0.0169327 | − | 3.12516e-5i | ||||
\(991\) | 1.58655e30 | 1.73667 | 0.868337 | − | 0.495975i | \(-0.165189\pi\) | ||||
0.868337 | + | 0.495975i | \(0.165189\pi\) | |||||||
\(992\) | − | 1.06802e29i | − | 0.115735i | ||||||
\(993\) | −7.42243e29 | + | 7.40874e29i | −0.796257 | + | 0.794789i | ||||
\(994\) | 1.61084e30 | 1.71076 | ||||||||
\(995\) | − | 4.62811e28i | − | 0.0486600i | ||||||
\(996\) | −3.44663e29 | − | 3.45300e29i | −0.358758 | − | 0.359420i | ||||
\(997\) | −3.38521e28 | −0.0348846 | −0.0174423 | − | 0.999848i | \(-0.505552\pi\) | ||||
−0.0174423 | + | 0.999848i | \(0.505552\pi\) | |||||||
\(998\) | − | 2.79714e29i | − | 0.285371i | ||||||
\(999\) | 9.29918e29 | + | 9.35081e29i | 0.939268 | + | 0.944483i |
(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 | 6.21.b.a.5.3 | ✓ | 6 | |
3.2 | odd | 2 | inner | 6.21.b.a.5.6 | yes | 6 | |
4.3 | odd | 2 | 48.21.e.b.17.2 | 6 | |||
12.11 | even | 2 | 48.21.e.b.17.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.21.b.a.5.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6.21.b.a.5.6 | yes | 6 | 3.2 | odd | 2 | inner | |
48.21.e.b.17.1 | 6 | 12.11 | even | 2 | |||
48.21.e.b.17.2 | 6 | 4.3 | odd | 2 |